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<archimedes xmlns:xlink="http://www.w3.org/1999/xlink" >      <info>        <author>Caverni, Raffaello</author>        <title>Storia del Metodo Sperimentale in Italia</title>        <date>1891</date>        


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<p type="main">

<pb xlink:href="020/01/001.jpg"></pb><s><foreign lang="en">350478 Storia Del Metodo Sperimentale Italia </foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>THE SOURCES OF SCIENCE<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>Editor-in-Chief: Harry Woolf<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph><emph type="italics"></emph>Willis K. </foreign></s>

<s><foreign lang="en">Shepard Professor of the History of <lb></lb>Science, The Johns Hopkins University<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></foreign></s></p><pb xlink:href="020/01/002.jpg"></pb><p type="main">

<s><foreign lang="en"><emph type="center"></emph><emph type="bold"></emph><emph type="italics"></emph>Storia del Metodo <lb></lb>Sperimentale in Italia<emph.end type="italics"></emph.end><emph.end type="bold"></emph.end><emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>by RAFFAELLO CAVERNI<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>in Six Volumes<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>Volume I<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>WITH AN INTRODUCTORY NOTE BY <lb></lb>GIORGIO TABARRONI<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>THE SOURCES OF SCIENCE, NO. 134<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>NEW YORK LONDON 1972<emph.end type="center"></emph.end></foreign></s></p><pb xlink:href="020/01/003.jpg"></pb><p type="main">

<s><foreign lang="en"><emph type="center"></emph>Reproduced here is the Florence edition of 1891-1900.<emph.end type="center"></emph.end></foreign></s></p><figure id="id.020.01.003.1.jpg" xlink:href="020/01/003/1.jpg"></figure><p type="main">

<s><foreign lang="en"><emph type="center"></emph>Copyright © 1972 by Johnson Reprint Corporation All rights reserved <lb></lb>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>111 Fifth Avenue, New York, N.Y. 10003, U.S.A.<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>Shipton Group House, 24/28 Oval Road, London, NW17DD, England<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph><emph type="italics"></emph>Printed in Italy<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></foreign></s></p><pb xlink:href="020/01/004.jpg"></pb><p type="main">

<s><foreign lang="en"><emph type="center"></emph><emph type="bold"></emph><emph type="italics"></emph>Raffaello Caverni and his Work<emph.end type="italics"></emph.end><emph.end type="bold"></emph.end><emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>AN INTRODUCTORY NOTE BY GIORGIO TABARRONI<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>TRANSLATED BY BARBARA BIANCHI<emph.end type="center"></emph.end><pb xlink:href="020/01/005.jpg"></pb></foreign></s></p><pb xlink:href="020/01/006.jpg"></pb><p type="main">

<s><foreign lang="en">1. <emph type="italics"></emph>Validity of the work and scope of this edition.<emph.end type="italics"></emph.end> 2. <emph type="italics"></emph>Biographical <lb></lb>note.<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>Early writings.<emph.end type="italics"></emph.end> 4. <emph type="italics"></emph>Studies<emph.end type="italics"></emph.end> Sulla filosofia delle scienze <lb></lb>naturali <emph type="italics"></emph>(On the philosophy of natural science) and their banning by the <lb></lb>Congregation of the Holy Office.<emph.end type="italics"></emph.end> 5. <emph type="italics"></emph>Popular works.<emph.end type="italics"></emph.end> 6. <emph type="italics"></emph>The great<emph.end type="italics"></emph.end><lb></lb>Storia. </foreign></s>

<s><foreign lang="en">7. <emph type="italics"></emph>Caverni&#039;s last years.<emph.end type="italics"></emph.end> 8. <emph type="italics"></emph>Odyssey of the manuscripts.<emph.end type="italics"></emph.end><lb></lb>9. <emph type="italics"></emph>Conclusion.<emph.end type="italics"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>1. VALIDITY OF THE WORK AND SCOPE OF THIS EDITION<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en">The first edition of the work presented here in photographic reprint was of <lb></lb>modest proportions. </foreign></s>

<s><foreign lang="en">The author was a clergyman of the Florentine diocese, a <lb></lb>student of philosophy and the history of science, and when he died in early <lb></lb>1900 the work was suspended halfway through the sixth volume even though <lb></lb>a practically completed manuscript did exist. </foreign></s>

<s><foreign lang="en">Nor was it ever reprinted, <lb></lb>although our literature is anything but rich in this field, especially in that <lb></lb>turn-of-the-century period. </foreign></s>

<s><foreign lang="en">From a distance of seventy years one might well <lb></lb>ask whether Caverni&#039;s work is still valid or if it is not by now completely out­<lb></lb>dated, to be exhumed only as a document of a bygone phase of the history of <lb></lb>science. </foreign></s></p><p type="main">

<s><foreign lang="en">Recently, however, a voice of great authority has assured us that the work <lb></lb>is still of cultural importance. </foreign></s>

<s><foreign lang="en">Eugenio Garin, in a lecture on <emph type="italics"></emph>La cultura <lb></lb>fiorentina nell&#039;età di Leonardo<emph.end type="italics"></emph.end> (Florentine culture in the age of Leonardo) <lb></lb>includes a penetrating and original opinion of Caverni, referring to <emph type="italics"></emph>La storia <lb></lb>del metodo sperimentale in Italia<emph.end type="italics"></emph.end> as “a work wrongly forgotten.” <lb></lb><lb></lb>For the <lb></lb>oblivion in which it has remained for so long, almost an unjust and mistaken <lb></lb>ostracism, has encouraged the persistence of the legend that it is an essentially <lb></lb>anti-Galilean work. </foreign></s>

<s><foreign lang="en">Actually, the critical perspective and the dispassionate <lb></lb>(even if, naturally, not infallible) examination of the sources that characterize <lb></lb>this work are clearly in contrast with the emphasis and tone of the writings of <lb></lb>the Italian Galileans who, from Viviani to Favaro, have felt they had to serve<gap></gap><lb></lb>unsolicited and superfluous, as the extreme apologists or defenders of Galileo<gap></gap><lb></lb>The latest representatives of this tradition, whom we cannot hesitate to cal<gap></gap><pb xlink:href="020/01/007.jpg" pagenum="viii"></pb>scarcely brilliant from an epistemological point of view, blamed Raffaello <lb></lb>Caverni as the sole individual responsible for certain reservations and limita­<lb></lb>tions formulated at the beginning of the century, especially abroad, concerning <lb></lb>the validity and originality of Galileo&#039;s work. </foreign></s>

<s><foreign lang="en">They evidently did not realize <lb></lb>that one of the major causes of this truly anti-Galilean reaction lay, instead, <lb></lb>principally in their panegyrics and hagiographical essays. </foreign></s>

<s><foreign lang="en">The validity of <lb></lb>Caverni&#039;s writings today lies exactly in his having sensed that while in the past <lb></lb>crediting Galileo indiscriminately with everything worthwhile accomplished in <lb></lb>Italy from the end of the sixteenth century to the second half of the seventeenth <lb></lb>may have increased esteem for and diffusion of his works and thought, with <lb></lb>modern historians it could seriously compromise, as indeed has happened, his <lb></lb>authentic merits, in spite of their greatness. </foreign></s>

<s><foreign lang="en">It has been said and repeated by <lb></lb>his critics that Caverni has drastically stripped the laurels wreathing the fore­<lb></lb>head of the great Tuscan scientist. </foreign></s>

<s><foreign lang="en">They have not understood that he has only <lb></lb>tried, instead, without false piety, to free the votive monument, erected to the <lb></lb>man with the best of intentions, of all its tinsel and gingerbread, that it might <lb></lb>better show its gold and gems. </foreign></s></p><p type="main">

<s><foreign lang="en">It must surely be opportune, therefore, to exhume this work. </foreign></s>

<s><foreign lang="en">We might <lb></lb>question, instead, the photographic reproduction of the original edition, with <lb></lb>its numerous typographical errors and incomplete indexes, without notes for <lb></lb>clarification or cross-reference, without the verification and completion of the <lb></lb>bibliographical references and, above all, without the necessary indication of the <lb></lb>inevitable mistakes the author made in his exegesis of the sources, in which <lb></lb>task he was a real pioneer. </foreign></s>

<s><foreign lang="en">In addition, perhaps it would have been possible to <lb></lb>bring to light that part of the manuscript still, unfortunately, unprinted. </foreign></s>

<s><foreign lang="en"><lb></lb>However, a new edition that would satisfy such a vast and ambitious program <lb></lb>implies no small amount of labor, which besides requiring a considerable amount <lb></lb>of time would be hampered by the lack of a congruous number of copies of the <lb></lb>text. </foreign></s>

<s><foreign lang="en">The six volumes of this work have become a rarity: few libraries possess <lb></lb>any of them; very few have all of them—not even the Nazionale of Florencel <lb></lb>Let us consider this present undertaking then as the first step toward a new, <lb></lb>more dispassionate study of the work and toward a broader diffusion of it, so <lb></lb>that we may have, in the near future, that new, corrected edition which per­<lb></lb>haps Caverni himself, who died at the peak of maturity, had hoped to prepare. </foreign></s>

<s><foreign lang="en"><lb></lb>And we need not exclude in that event a more complete rendering of the sixth <lb></lb>volume left truncated at the end of an even numbered page, right in the middle <lb></lb>of a sentence. </foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>2. BIOGRAPHICAL NOTE<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en">Raffaello Caverni led a life of the greatest simplicity. </foreign></s>

<s><foreign lang="en">Aldo Mieli, presenting a <lb></lb>series of articles for and against the <emph type="italics"></emph>Storia del metodo sperimentale<emph.end type="italics"></emph.end> in one of the <pb xlink:href="020/01/008.jpg" pagenum="ix"></pb>first-year issues of his <emph type="italics"></emph>Archivio,<emph.end type="italics"></emph.end> sums up his life in less than ten lines, and says <lb></lb>practically all there is to say. <lb></lb><lb></lb>Yet, Martini <lb></lb><lb></lb>in 1902, Orlando <lb></lb><lb></lb>in 1906, and <lb></lb>Giovannozzi <lb></lb><lb></lb>in 1910, without producing any salient facts, have enriched the <lb></lb>brief, recorded data with notes on his character and with a few significant <lb></lb>episodes which serve today to render his figure lifelike and to shed further light <lb></lb>on his already clear personality. </foreign></s>

<s><foreign lang="en">The sense of the man that one gathers from <lb></lb>this information, which might be thought to be biased since it is handed down <lb></lb>to us by men who were his devoted friends, is fully confirmed by accounts one <lb></lb>can still hear from the lips of the old parishioners of Quarate in the Ema Valley, <lb></lb>or from Lamberto Caverni, the oldest of his grandnephews who was only a few <lb></lb>years old when Don Raffaello died, but who remembers clearly everything his <lb></lb>father, Egisto, had to tell about that uncle. </foreign></s>

<s><foreign lang="en">Some of these details and others <lb></lb>besides can be checked against the documents and papers, although there are <lb></lb>some, together with a great many manuscripts, which the heirs jealously keep <lb></lb>to themselves. </foreign></s></p><p type="main">

<s><foreign lang="en">Raffaello Caverni was born in San Quirico di Montelupo in a house on the <lb></lb>Via Pisana. </foreign></s>

<s><foreign lang="en">The place is now marked by a memorial plaque with an epigraph <lb></lb>by Father G. Giovannozzi, placed there in July 1902, which following the <lb></lb>unfortunate cultural customs of those times remembers him in a rather <lb></lb>infelicitous manner as “most celebrated writer ... with German erudition <lb></lb>and Italian genius.” Such rhetoric hardly suits his work which, though not <lb></lb>always polished and rigorous, is brilliant, sagacious, and often piercing—in a <lb></lb>word, truly Tuscan. </foreign></s>

<s><foreign lang="en">The Registry of baptisms in Pieve di Montelupo shows <lb></lb>that <emph type="italics"></emph>Raffaello Gregorio<emph.end type="italics"></emph.end> (the second name perhaps in honor of the reigning <lb></lb>Pope) <emph type="italics"></emph>Gaspero, son of Vincenzo son of Pietro Caverni and Assunta Mancioli<emph.end type="italics"></emph.end><lb></lb>was born in <emph type="italics"></emph>S. </foreign></s>

<s><foreign lang="en">Quirico at the Ambrogiana<emph.end type="italics"></emph.end> (the lovely Medici villa now an <lb></lb>asylum for the criminal insane) <emph type="italics"></emph>on March 12, 1837, at 8:00 p.m.<emph.end type="italics"></emph.end> He was the <pb xlink:href="020/01/009.jpg" pagenum="x"></pb>third of seven children of a modest family which owned a kiln and delivered <lb></lb>bricks and other construction material to builders, especially in Florence, with <lb></lb>their own <emph type="italics"></emph>barocci,<emph.end type="italics"></emph.end> the traditional two-wheeled carts which, horse-drawn and <lb></lb>balanced, have for centuries performed this task over the greater part of the <lb></lb>Italian countryside. </foreign></s>

<s><foreign lang="en">Less sturdy than the other children, he was sent to the town <lb></lb>school where, it seems, he distinguished himself so well that at the age of <lb></lb>thirteen, having already decided on his vocation, he went to Florence to study. </foreign></s>

<s><foreign lang="en"><lb></lb>Since there was no seminary then, he became one of the young clergy of the <lb></lb>Cathedral and enrolled in the Collegio Eugeniano, an excellent school of <lb></lb>humanistic leaning, where he completed the entire course corresponding to <lb></lb>what would later be the Gymnasium. </foreign></s>

<s><foreign lang="en">His success there seemed to point to the <lb></lb>concinuation of literary studies, but Caverni had already made another choice. </foreign></s>

<s><foreign lang="en"><lb></lb>For three years after the Collegio he attended the public Scuole Pie, run by the <lb></lb>Scolopian Fathers at S. Giovannino. </foreign></s>

<s><foreign lang="en">There he received a basis foundation in <lb></lb>what were to become his favorite subjects: philosophy, taught by the Rosminian <lb></lb>Father Zini, and physics with Father Cecchi who together with Father Antonelli <lb></lb>was to furnish the loggia dei Lanzi in 1860 with a pair of exceptional instru­<lb></lb>ments: a thermometer and a barometer with a face of more than 1.5 meters. </foreign></s>

<s><foreign lang="en"><lb></lb>Then, instead of going to the University, for a few years he attended the <lb></lb>Istituto Ximeniano, also run by the Scolopians, where he had Antonelli for <lb></lb>astronomy and higher mathematics and Father Barsanti for mechanics and <lb></lb>hydraulics. </foreign></s>

<s><foreign lang="en">And thus he became a priest with the hobby of philosophy and <lb></lb>science, following an inclination which seems traditional in the Florentine <lb></lb>clergy—the desire to reconcile what appears to be irreconcilable! </foreign></s></p><p type="main">

<s><foreign lang="en">During the school year 1859-60, at the same time that the Granducal <lb></lb>government failed, the Archbishop of Florence sent him as professor of philos­<lb></lb>ophy and mathematics to the Seminary of Firenzuola, a sort of citadel in a <lb></lb>gorge in the Apennines, exactly halfway between Florence and Bologna. </foreign></s>

<s><foreign lang="en">There <lb></lb>he was ordained on the second of June 1860 and there he spent, in great <lb></lb>serenity, a period which the young priests of the diocese considered a kind of <lb></lb>severe penance. </foreign></s>

<s><foreign lang="en">During the ten years he remained there he studied nature with <lb></lb>enthusiasm, gaining thereby a rapid and complete maturity while filling entire <lb></lb>notebooks with observations, records, and meditations. </foreign></s>

<s><foreign lang="en">But at the end of 1870, <lb></lb>shortly after Porta Pia, he was at last recalled from his exile of sorts and assigned <lb></lb>to a parish about 12 kilometers from Florence. </foreign></s>

<s><foreign lang="en">As Father Givannozzi has <lb></lb>observed, this parish was small, well supplied, and conveniently close to the <lb></lb>libraries of the city, and this made it possible for him in the course of a simple <lb></lb>life to return again with zeal to his favorite studies, but without neglecting his <lb></lb>ministry. </foreign></s>

<s><foreign lang="en">In that place, even less populous today, he is still remembered <lb></lb>with admiration, almost veneration, by the oldest inhabitants who used to <lb></lb>study catechism with him. </foreign></s>

<s><foreign lang="en">Giovannozzi observes that he was “as good a <lb></lb>priest as he was a diligent scholar.” But he found neither one nor the other <lb></lb>occupation without its thorns and difficulties. </foreign></s></p><pb xlink:href="020/01/010.jpg" pagenum="xi"></pb><p type="main">

<s><foreign lang="en"><emph type="center"></emph>3. EARLY WRITINGS<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en">In 1872 Caverni was ready with his first publications. </foreign></s>

<s><foreign lang="en">There are the curious <lb></lb>“Ricreazioni scientifiche” (scientific pastimes), a column at once instructive <lb></lb>and amusing where science is handled in a conversational and easily com­<lb></lb>prehensible manner, while the part reserved for the history of science (for <lb></lb>example, to science in Dante) is characterized by profound research and a <lb></lb>rigorous exposition that is not always easy and never elementary. </foreign></s>

<s><foreign lang="en">These articles, <lb></lb>which appeared periodically, were first printed in the magazine <emph type="italics"></emph>La Scuola<emph.end type="italics"></emph.end> that <lb></lb>had just been founded by Augusto Alfani (another Florentine who knew how <lb></lb>to reconcile faith and science and, even more daring, was among those who <lb></lb>hoped to see closer ties between Church and State). They were continued in the <lb></lb>periodical <emph type="italics"></emph>Letture di famiglia<emph.end type="italics"></emph.end> and collected under the same title in a volume <lb></lb>published in 1882 which Giovannozzi in 1910 declared was already almost im­<lb></lb>possible to find. </foreign></s>

<s><foreign lang="en">I myself have never seen it even mentioned in a catalogue. </foreign></s></p><p type="main">

<s><foreign lang="en">Another series of articles appeared in the same magazines in almost the same <lb></lb>period, but was concluded more rapidly. </foreign></s>

<s><foreign lang="en">This series was entitled “Consigli <lb></lb>sopra allo studio delle lettere a un giovanetto” (advice to a young man on the <lb></lb>study of literature) and was published in volume form in 1879 with the title <lb></lb><emph type="italics"></emph>Dell&#039;arte dello scrivere<emph.end type="italics"></emph.end> (on the art of writing). (Unfortunately, the copy at the <lb></lb>Nazionale of Florence was a victim of the flood.) Together with these, Caverni <lb></lb>also published studies of Dante&#039;s physics which were never reprinted alone. </foreign></s>

<s><foreign lang="en">In <lb></lb>1874 his first book appeared: <emph type="italics"></emph>Problemi naturali di Galileo e della sua scuola<emph.end type="italics"></emph.end><lb></lb>(natural problems of Galileo and his school), published by Sansoni and, like his <lb></lb>other works, not easily found today. </foreign></s>

<s><foreign lang="en">His <emph type="italics"></emph>Dizionarietto di voci e modi dell&#039;uso <lb></lb>popolare toscano nella Divina Commedia<emph.end type="italics"></emph.end> (little Dictionary of Tuscan words and <lb></lb>phrases in the Divine Comedy), published in 1877, was however destined to <lb></lb>enjoy a certain popularity. </foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>4. STUDIES <emph type="italics"></emph>Sulla filosofia delle scienze naturali<emph.end type="italics"></emph.end> (ON THE PHILOSOPHY OF <lb></lb>NATURAL SCIENCE) AND THEIR BANNING BY THE CONGREGATION OF THE <lb></lb>HOLY OFFICE<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en">In the meantime, the <emph type="italics"></emph>Rivista Universale<emph.end type="italics"></emph.end> (universal magazine) began to appear <lb></lb>in Florence, soon changing its letterhead to <emph type="italics"></emph>Rassegna Nazionale<emph.end type="italics"></emph.end> (national <lb></lb>review). The Treccani terms it the magazine of conservative Catholics, but <lb></lb>Giovannozzi is more detailed and precise, recalling it as the periodical that was <lb></lb>the “champion, for many years the only one, of the struggle for faith and <lb></lb>nationality indissolubly united,” when during the long papacy of Leon XIII <lb></lb>(1878-1903) such a program was considered almost nonsensical and little less <lb></lb>than heretical. </foreign></s>

<s><foreign lang="en">Caverni immediately took advantage of this arena and in 1875 <lb></lb>and 1876 published a series of epistemological studies which Giovannozzi <lb></lb>properly calls “his most beautiful work.” The original title was <emph type="italics"></emph>Sulla filosofia<emph.end type="italics"></emph.end><pb xlink:href="020/01/011.jpg" pagenum="xii"></pb><emph type="italics"></emph>delle scienze naturali<emph.end type="italics"></emph.end> (on the philosophy of natural science), changed—who <lb></lb>knows why—with publication in volume form in 1877 into the less significant <lb></lb><emph type="italics"></emph>De&#039;nuovi studi della filosofia, Discorsi di Raffaello Caverni a un giovane studente<emph.end type="italics"></emph.end><lb></lb>(on the new studies of philosophy, conversations of Raffaello Caverni with a <lb></lb>young student). Here he maintained that philosophy too is a science of observa­<lb></lb>tion, that is, basically experimental, and criticized both those philosophers who <lb></lb>want to consider man prescinding from any scientific preparation and without <lb></lb>any knowledge of physiology in particular and those scientists who see in man <lb></lb>only his material being. </foreign></s>

<s><foreign lang="en">But the central theme of this treatise is delicate and <lb></lb>controversial for his times. </foreign></s>

<s><foreign lang="en">Caverni undertook a critical examination of <lb></lb>Darwin&#039;s theory of evolution as contained in <emph type="italics"></emph>The Descent of Man,<emph.end type="italics"></emph.end> which had <lb></lb>appeared in 1871. A subtitle of the third chapter declared “That the new <lb></lb>doctrine of Darwin and natural science ought not frighten the faithful who <lb></lb>should be allowed to cultivate them in all serenity and we too, confuting them <lb></lb>where necessary, should cultivate them with love.” His program was clear but <lb></lb>hardly in harmony with the position taken by the Catholic world. </foreign></s>

<s><foreign lang="en">And thus, <lb></lb>while the articles printed in the magazine miraculously passed, not so the book <lb></lb>which was put on the Index with a decree dated July 1, 1878. Father Gio­<lb></lb>vanozzi, particularly competent in the matter, wrote, “I believe the prohibition <lb></lb>of the book was due not to its defense of the evolutionary hypothesis, but to the <lb></lb>rather sharp and caustic attacks against institutes, methods and persons of the <lb></lb>ecclesiastical world.” <lb></lb><lb></lb>In any case, this episode marked the parting of ways—a <lb></lb>break only on a cultural plane, of course, yet even so, sharp and precise—with <lb></lb>a rejection which was to be constant and unhesitating of a certain “tradition” <lb></lb>that Caverni found stale and moldy. </foreign></s>

<s><foreign lang="en">For even after the decision of the Con­<lb></lb>gregation of the Index, his ideas did not change essentially. </foreign></s>

<s><foreign lang="en">In the <emph type="italics"></emph>Rassegna <lb></lb>Nazionale<emph.end type="italics"></emph.end> he continued to publish articles on an analogous subject, <emph type="italics"></emph>Sull&#039; <lb></lb>antichità dell&#039;uomo<emph.end type="italics"></emph.end> (on the antiquity of man); in this series, which appeared in <lb></lb>volume form in 1881, he concluded, as in his preceding work, that the faithful <lb></lb>may tranquilly attend geologists&#039;debates on the matter. </foreign></s>

<s><foreign lang="en">The substance is more <lb></lb>or less the same. </foreign></s>

<s><foreign lang="en">Perhaps this time he simply refrained from those biting <lb></lb>allusions to some colleagues which, to tell the truth, he brings off so skillfully. </foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>5. POPULAR WORKS<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en">From 1884 to 1888 Raffaello Caverni dedicated himself to scientific populariza­<lb></lb>tion, without doubt a congenial genre. </foreign></s>

<s><foreign lang="en">For his task he put aside those regal and <lb></lb>curial robes he had donned to write of philosophy and the history of science and <lb></lb>treated the subjects of physics and natural science in limpid, fluent language, <lb></lb>presenting orderly ideas and familiar images. </foreign></s>

<s><foreign lang="en">For this reason the environment, <lb></lb>mentality, and customs of his times enter freely into these pages and they <pb xlink:href="020/01/012.jpg" pagenum="xiii"></pb>reflect more than others the years that have passed. </foreign></s>

<s><foreign lang="en">Nonetheless, they still <lb></lb>make pleasurable reading and, more important, they have remained in the <lb></lb>memory of those who read them as children: I have seen eyes shine at their <lb></lb>mention. </foreign></s></p><p type="main">

<s><foreign lang="en">These writings originated in 1884 when the ex-publishing company <lb></lb>Lemonnier decided to produce a “Library for young girls” (even this label <lb></lb>conveys at once the sense of bygone years) and asked Caverni for a brief book <lb></lb>on elementary physics. </foreign></s>

<s><foreign lang="en">He gave them <emph type="italics"></emph>L&#039;estate in montagna<emph.end type="italics"></emph.end> (summer in the <lb></lb>mountains), a gentle book for young people whose subject is woven into a <lb></lb>delicate and ingenuous love story. </foreign></s>

<s><foreign lang="en">A young invalid girl finds in the mountains <lb></lb>health and her young man, the author of popular notes on physics which have <lb></lb>amused and sustained her during the long months of her solitary convalescence. </foreign></s>

<s><foreign lang="en"><lb></lb>This little volume with drawings by Mazzanti, popular illustrator of Collodi&#039;s <lb></lb>books, was well received and reached a third edition, which encouraged its <lb></lb>author to continue. </foreign></s>

<s><foreign lang="en">At two-year intervals it was followed by <emph type="italics"></emph>Tra il verde e i <lb></lb>fiori<emph.end type="italics"></emph.end> (among the greens and flowers), a book on botany published in the same <lb></lb>series and <emph type="italics"></emph>Cogli occhi per terra<emph.end type="italics"></emph.end> (with eyes on the ground), dedicated to <lb></lb>mineralogy and published in Paggi&#039;s “Biblioteca Scolastica” (scholastic library). <lb></lb>Pursuit of this hobby, as we might call it, was for Caverni a singular prepara­<lb></lb>tion for his most important work and perhaps an interlude during its actual <lb></lb>creation. </foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>6. THE GREAT <emph type="italics"></emph>Storia<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en">Since in this reprint, as in the 1890 version, the <emph type="italics"></emph>Relazione della Giunta del R. </foreign></s>

<s><foreign lang="en"><lb></lb>Istituto Veneto deputata all&#039;esame dei lavori presentati al concorso della <lb></lb>Fondazione Tomasoni<emph.end type="italics"></emph.end> (report of the Committee of the Royal Venetian In­<lb></lb>stitute for the examination of the works presented for the Tomasoni Foundation <lb></lb>contest) precedes the text, readers are referred to that ample account for all <lb></lb>information regarding the genesis of the <emph type="italics"></emph>Storia del metodo sperimentale in <lb></lb>Italia<emph.end type="italics"></emph.end> (history of the experimental method in Italy) and its well-deserved <lb></lb>success in that contest whose prize was a sum roughly the equivalent of two <lb></lb>years&#039;salary of a <emph type="italics"></emph>liceo<emph.end type="italics"></emph.end> professor! The concise comment on the entire work <lb></lb>found in the second part of that <emph type="italics"></emph>Relazione<emph.end type="italics"></emph.end> is particularly interesting. </foreign></s>

<s><foreign lang="en">We know, <lb></lb>from the draft of a letter kept by the heirs, that the committee—and for it the <lb></lb><emph type="italics"></emph>relatore,<emph.end type="italics"></emph.end> Antonio Favaro—made ample use of this critical summary in pre­<lb></lb>paring the larger work for publication. </foreign></s>

<s><foreign lang="en">It seems that the author himself had <lb></lb>been requested to provide the summary when awarded the prize since it had <lb></lb>been impossible to read all the three thousand folio pages thickly covered with <lb></lb>script which he had submitted. </foreign></s>

<s><foreign lang="en">This contest, announced in 1880, had expired <lb></lb>March 31, 1889 when, after a first session in 1885, neither of the two works <lb></lb>presented had been found worthy of the prize. </foreign></s>

<s><foreign lang="en">The judges, more than a year <lb></lb>later in the solemn session of May 25, 1890, proclaimed that work the winner <pb xlink:href="020/01/013.jpg" pagenum="xiv"></pb>which had for its motto a tercet of Dante, the one (Paradise, II, 94-96) in the <lb></lb>learned canto on the lunar spots where Beatrice exalts Experimentation <lb></lb>“which is the spring for the rivers of your arts.” In the first part of the <lb></lb><emph type="italics"></emph>Relazione,<emph.end type="italics"></emph.end> which displays the unmistakable style and spirit of Favaro, there <lb></lb>is sincere praise and a warm appreciation of Caverni&#039;s monumental work. </foreign></s>

<s><foreign lang="en"><lb></lb>However, the <emph type="italics"></emph>relatore<emph.end type="italics"></emph.end> wants to make it clear (p. </foreign></s>

<s><foreign lang="en">12) that it “did not seem in <lb></lb>our eyes altogether free of error.” And thus begins that series of criticisms that <lb></lb>will with time gather impetus, increasing and thundering like an avalanche. <lb></lb></foreign></s>

<s><foreign lang="en">“As concerns the sources, it is said to be somewhat wanting in knowledge of <lb></lb>the foreign ones,” but this is the least of it; there is worse. </foreign></s>

<s><foreign lang="en">The work is found <lb></lb>to reflect “a tendency to be too easily infatuated with the novelty of the con­<lb></lb>clusions,” and there is the suggestion that “perhaps alarmed by the unjust <lb></lb>opinion of those who wished to exalt Galileo to the prejudice of all his con­<lb></lb>temporaries, he seems almost always on guard against conclusions unduly <lb></lb>favorable to the supreme philosopher.” And after some examples, for a few of <lb></lb>which such reservations can be accepted, the committee concludes ingenuously, <lb></lb>“And this we point out fully certain the author, asked to better ponder these <lb></lb>matters, shall want to change his mind.” Evidently they had not reckoned with <lb></lb>the character of Prior Caverni (although it shows in every page of his <emph type="italics"></emph>Storia<emph.end type="italics"></emph.end>): <lb></lb>he was, by general consensus, most pious, patient, and diligent in his ministry, <lb></lb>but bizarre and touchy as a man, extremely proud and intolerant of any <lb></lb>restriction of his liberty as a scholar. </foreign></s></p><p type="main">

<s><foreign lang="en">In the brief memorial which he delivered on February 25, 1900 at the Reale <lb></lb>Istituto Veneto, shortly after Caverni&#039;s death, Favaro says bitterly, “Such <lb></lb>criticism, opportunely exemplified and applied, was not graciously received by <lb></lb>the author. </foreign></s>

<s><foreign lang="en">Indeed, at the time of publication he increased the dose in the <lb></lb>passages that had been pointed out to him....” And he is careful to note that <lb></lb>“the five volumes [the sixth, uncompleted, was to appear posthumously that <lb></lb>year] of the <emph type="italics"></emph>Storia del metodo sperimentale in Italia<emph.end type="italics"></emph.end> published by Caverni have <lb></lb>very little in general and nothing in many places to do [sic] with the work <lb></lb>submitted to the Institute and by it judged worthy of the prize.” Favaro returned <lb></lb>to this subject in 1907 in his essay <emph type="italics"></emph>Antichi e moderni detrattori di Galileo<emph.end type="italics"></emph.end><lb></lb>(ancient and modern detractors of Galileo) published in the February 16th <lb></lb>issue of <emph type="italics"></emph>La Rassegna Nazionale<emph.end type="italics"></emph.end> that year and written in answer to “a tendency <lb></lb>to renew Arago&#039;s accusations in different form, but with even greater acrimony, <lb></lb>with the addition of new and numerous points (!)” Although in the conclusion, <lb></lb>alluding to Caverni, he recalls that “We had promised ourselves not to lift the <lb></lb>veil from this shabby display since it seemed to us only charitable to ignore the <lb></lb>outbursts of a most great mind who let himself be led astray by personal motives <lb></lb>[his exclusion from the committee for the National Edition of the Works of <lb></lb>Galileo] to the point of striking one of our most pure and genuine glories...,” <lb></lb>he had already aired his long repressed grievances. </foreign></s>

<s><foreign lang="en">The beginning of the seventh <lb></lb>paragraph, which ends this essay, reads: “Except that it would be hardly tactful <pb xlink:href="020/01/014.jpg" pagenum="xv"></pb>of us to lament foreigners&#039;lack of reverence towards Galileo; none of them has <lb></lb>reached the point of one Italian who seemed to have taken upon himself the <lb></lb>wretched task of stripping all he could of the laurels that embrace the im­<lb></lb>mortal brow of the restorer of the experimental method and in some ponderous <lb></lb>volumes in which he set himself to weave its history, he has spared no low <lb></lb>insult nor poisonous insinuation to damage the dead in order to spite the <lb></lb>living”! The rest is in the same tone. </foreign></s>

<s><foreign lang="en">I think I can identify in this harsh <lb></lb>accusation the echo of much of the criticism and even of the charges which <lb></lb>were brought against the incautious <emph type="italics"></emph>rapporteur<emph.end type="italics"></emph.end> of the Committee for the <lb></lb>Tomasoni Prize instituted so few years after the breach of Porta Pia and <lb></lb>destined <emph type="italics"></emph>“to whomsoever shall better tell the history of the experimental method <lb></lb>in Italy,”<emph.end type="italics"></emph.end> certainly presuming that the new atmosphere would lead to a freer, <lb></lb>more open condemnation of the old obscurantism. </foreign></s></p><p type="main">

<s><foreign lang="en">The news that the winner was a parish priest from some little hill town in <lb></lb>Tuscany must have aroused much disappointment and not a little annoyance! <lb></lb>But actually Favaro and his accusers were not altogether wrong. </foreign></s>

<s><foreign lang="en">Giovannozzi, <lb></lb>who has been the only defender of Caverni, also admits that “Strange and <lb></lb>almost incredible, there seems to linger in all this work an anti-Galilean spirit; <lb></lb>a subtle irony pervades it now and then, the intent to make use of every <lb></lb>opportunity to strip the laurels of the great old man of Arcetri, a frenzy to find <lb></lb>him at fault, to diminish his merits in order to attribute them to others, to <lb></lb>accuse him of having wanted to appropriate them all for himself.” He does <lb></lb>attempt, timidly, an explanation: “Who knows? </foreign></s>

<s><foreign lang="en">Perhaps he wanted to guard <lb></lb>against an excessive admiration or idolatry and ended up falling into the <lb></lb>opposite defect.” And he seems to abstain from an all-out defense almost as <lb></lb>though afraid of being more damaging than useful to his friend and teacher. </foreign></s>

<s><foreign lang="en"><lb></lb>The reasons justifying Caverni only in part, but which do explain his behavior <lb></lb>as that of a man of terrible, albeit resolute character rather than that of a <lb></lb>factious priest as Timpanaro would have him, <lb></lb><lb></lb>are also mentioned fleetingly <lb></lb>by Giovannozzi. </foreign></s>

<s><foreign lang="en">There are three main ones. </foreign></s>

<s><foreign lang="en">The recommendation of the <lb></lb>Committee that he mitigate his opinion of Galileo must have vexed Caverni <lb></lb>greatly; he must have felt that they had not tried to understand his labors. </foreign></s>

<s><foreign lang="en"><lb></lb>Second, he was immediately reminded that he had to publish the <emph type="italics"></emph>whole<emph.end type="italics"></emph.end> work <lb></lb>at his own expense in order to have the prize, according to the instructions of <lb></lb>the testator who certainly had not imagined that publication would have meant <lb></lb>an expense far surpassing the amount of the prize. </foreign></s>

<s><foreign lang="en">And last, he was profoundly <lb></lb>embittered and disappointed by the news that reached him shortly after he <lb></lb>learned of the prize thus conditioned, that his name had been excluded from the <lb></lb>committee for the monumental Galilean edition. </foreign></s>

<s><foreign lang="en">This certainly was not <pb xlink:href="020/01/015.jpg" pagenum="xvi"></pb>ambition in a man who, to his archbishop&#039;s displeasure, went about with his hat <lb></lb>in rags and his pants too short, like a so-called second-rate priest and who had <lb></lb>refused an offer from the university and membership in the Accademia dei <lb></lb>Lincei. </foreign></s></p><p type="main">

<s><foreign lang="en">Having dedicated most of his energy and the greater part of his life for <lb></lb>almost thirty years to the study of thousands of Galilean documents, his <lb></lb>profound knowledge of the thought and works of the great master of the <lb></lb>experimental method, his unique familiarity with the surviving instruments <lb></lb>and with the language of Galileo must certainly have led Caverni to feel that <lb></lb>it was at once his right and his duty to sit on that committee. </foreign></s>

<s><foreign lang="en">Disappointment <lb></lb>and bitterness are bad counselors and temptation does not spare even the <lb></lb>ministers of the Lord. </foreign></s>

<s><foreign lang="en">And thus, even if I do not feel I can agree (in the spirit <lb></lb>of the images and comparisons of Favaro) that Caverni intended to make <lb></lb>poisonous insinuations and basely insult the dead Galileo, there is no doubt <lb></lb>that Favaro is right when he accuses Caverni of having wanted to spite the <lb></lb>living. </foreign></s>

<s><foreign lang="en">In modifying his early manuscript (the so-called Venetian manuscript), <lb></lb>in the end he exaggerated and in some places was carried away by the spirit <lb></lb>of criticism at the expense of historic truth and calm judgment. </foreign></s>

<s><foreign lang="en">This is the <lb></lb>consequence of a deprecable exasperation, that exasperation which often over­<lb></lb>comes candid souls! </foreign></s></p><p type="main">

<s><foreign lang="en">As for publication, it was only possible thanks to the assistance, which <lb></lb>Giovannozzi characterizes as “munificent,” of commendator Antonio Civelli, <lb></lb>whose firm published the democratic newspaper <emph type="italics"></emph>Il Corriere italiano,<emph.end type="italics"></emph.end> owned the <lb></lb>comparable Milanese paper <emph type="italics"></emph>La Lombardia<emph.end type="italics"></emph.end> and the Veronese <emph type="italics"></emph>L&#039;Adige,<emph.end type="italics"></emph.end> and who <lb></lb>was known, among other things, for having published the <emph type="italics"></emph>Dizionario corografo <lb></lb>dell&#039;Italia<emph.end type="italics"></emph.end> (chorographic dictionary of Italy). The first volume appeared in 1891 <lb></lb>and the relative scarcity of reviews leads us to think that it was met with <lb></lb>suspicion by both the right and the left. </foreign></s>

<s><foreign lang="en">One voice, however, rose clear and <lb></lb>competent to review it at such length that the “Cenno bibliografico” (biblio­<lb></lb>graphical note) was in reality the main article of the April 1892 issue of the <lb></lb>magazine <emph type="italics"></emph>Il Pensiero italiano<emph.end type="italics"></emph.end> (Italian thought). <lb></lb><lb></lb>That well-balanced and <lb></lb>impartial voice was Giovanni Virginio Schiaparelli&#039;s. </foreign></s>

<s><foreign lang="en">Director of the Brera <lb></lb>Observatory, he was internationally known as an astronomer and also as a <lb></lb>profound commentator on the writings and documents of ancient astronomy. </foreign></s>

<s><foreign lang="en"><lb></lb>In judging Caverni&#039;s work he seeks no compromise or halfway measures: the <lb></lb>errors exist, rather serious ones at that, but the merits are such that the rest <lb></lb>seems of secondary importance. </foreign></s>

<s><foreign lang="en">He says in the beginning, “... no one in the <lb></lb>history of science and certainly never in the history of practical science was <lb></lb>ever granted the liberty to write without practical knowledge of his subject.” <lb></lb>But “it seems that the gifts of the great scientist and those of the judicious <lb></lb>historian, elegant and erudite, have rarely been reconciled in the same person.” <pb xlink:href="020/01/016.jpg" pagenum="xvii"></pb>And thus “we must consider it quite a rare event and receive with all the <lb></lb>more satisfaction this <emph type="italics"></emph>Storia del metodo sperimentale in Italia,<emph.end type="italics"></emph.end> whose author <lb></lb>shows himself not unequal both in scholarship and narrative art to the high <lb></lb>and difficult task he sets himself.” After masterfully condensing and com­<lb></lb>menting on the vast contents of the part already published, Schiaparelli, <lb></lb>expert of ancient and modern science that he was, comments on certain of <lb></lb>Caverni&#039;s opinions and “demonstrations”: “He feels a strong attraction to <lb></lb>some of his personages and just as pronounced an antipathy for others His <lb></lb>enthusiasm for Plato is truly excessive ... without considering that Platonic <lb></lb>speculation is the exact antithesis of the experimental method.... On the <lb></lb>contrary, according to Caverni, Aristotle is the evil star,” while “it is commonly <lb></lb>held that that great thinker was instead one of the greatest observers of <lb></lb>antiquity and not even altogether unfamiliar with the art of experimentation. <lb></lb>... Obviously Caverni has confused Aristotle with the peripatetics of low <lb></lb>extraction who were contemporaries of Galileo.” (We can readily agree with <lb></lb>Schiaparelli that Caverni, who never did things halfway, exaggerated some­<lb></lb>what in refusing to recognize any Aristotelian components in the currents of <lb></lb>thought that determined the scientific method. </foreign></s>

<s><foreign lang="en">As for Plato, however, para­<lb></lb>doxical as it may seem, we must agree with Caverni who sees him as the true, <lb></lb>great inspirer of the decisive turn of knowledge from Copernicus to Galileo. </foreign></s>

<s><foreign lang="en"><lb></lb>Plato, in fact, scorned the casual and unconditioned <emph type="italics"></emph>experience<emph.end type="italics"></emph.end> of our senses, not <lb></lb><emph type="italics"></emph>experimentation<emph.end type="italics"></emph.end> which in its artificiality is a completely different thing and is <lb></lb>intimately bound to abstractions of the Platonic type!) At this point close to <lb></lb>the end of his long review, the great astronomer of Brera, after saying “I have <lb></lb>not found another work comparable to this in our scientific literature, unless it <lb></lb>be the <emph type="italics"></emph>Storia delle Matematiche in Italia<emph.end type="italics"></emph.end> by Gugliemo Libri,” comes to the <lb></lb>burning question, that of the so-called anti-Galilean Caverni: “He is a great <lb></lb>admirer of the science of Galileo, but this does not prevent him from presenting <lb></lb>the nature of it in a paradoxical light. </foreign></s>

<s><foreign lang="en">According to Caverni, Galileo was a <lb></lb>common egoist, a scientific pirate, constantly spying for the opportunity to rob <lb></lb>his predecessors, his contemporaries, his friends, his disciples, of the merit of <lb></lb>their inventions and discoveries, to attribute everything to himself ... to be <lb></lb>the only King in the realm of the new science. </foreign></s>

<s><foreign lang="en">And with this accusation, <lb></lb>Caverni calls for a new trial of Galileo, quite different from the ones he under­<lb></lb>went during his lifetime and one which no one would have ever thought of.... <lb></lb>He takes it upon himself to strip as much as possible the laurels which circle the <lb></lb>brows of the great old man of Arcetri and this constant concern sometimes leads <lb></lb>to curious errors.... Fortunately these errors in judgment, which one en­<lb></lb>counters here and there in the <emph type="italics"></emph>Discorso preliminare,<emph.end type="italics"></emph.end> occur more rarely in the <lb></lb>specific part of the work.” (Actually, only the first volume had by then <lb></lb>appeared.) “And let all this be said not for the mania of finding fault, of looking <lb></lb>for spots on the sun, but to show that the praises of Caverni&#039;s work given here <lb></lb>are the result of an impartial and pondered study of it.” And reviewing the <pb xlink:href="020/01/017.jpg" pagenum="xviii"></pb>plan Caverni gave of the whole work, he concludes, almost as though he thought <lb></lb>the ambitious program might remain unfinished, “But whatever may come of <lb></lb>this, what he has already done gives him the right to consider his work as the <lb></lb>greatest body of scientific history Italian literature can boast.” </foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>7. CAVERNI&#039;S LAST YEARS<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en">For publication, Caverni completely rewrote the contest manuscript, adding, <lb></lb>amplifying, completing, and perhaps sometimes spoiling (Favaro <lb></lb><lb></lb>in an essay <lb></lb>of 1919 demonstrates that the most malicious and unfounded accusation <lb></lb>against Galileo, who was supposed to have had from Castelli the first news of the <lb></lb>phases of Venus, was not in the <emph type="italics"></emph>Venetian manuscript<emph.end type="italics"></emph.end> because it was “an <lb></lb>addition made to his work at the time of publication”). This labor must have <lb></lb>absorbed all the energy and attention to Caverni, who was evidently spurred on <lb></lb>and excited by the many disappointments of which we have spoken. </foreign></s>

<s><foreign lang="en">In a <lb></lb>certain sense, it must also have concerned and galvanized all the little com­<lb></lb>munity of which he was the spiritual leader. </foreign></s>

<s><foreign lang="en">I recently found a local inhabitant, <lb></lb>one Egidio Longhi of considerable age but most lucid memory, who told me, <lb></lb>“It was my grandfather Giovanni who took the manuscripts to the printer, to <lb></lb>Civelli.” And he must have made many trips and carried many papers if we <lb></lb>consider that in fewer than ten years a little under 3,500 large quarto pages, <lb></lb>dense with characters, were printed! </foreign></s></p><p type="main">

<s><foreign lang="en">Caverni was a healthy man. </foreign></s>

<s><foreign lang="en">He led the most wholesome and methodical life <lb></lb>one can imagine, with a walk every day and an excursion, always the same one, <lb></lb>in the surrounding countryside every week. </foreign></s>

<s><foreign lang="en">But that intense and hurried work, <lb></lb>that prize they did not want to give him if he did not publish everything first, <lb></lb>those comments and reviews of which only the favorable ones failed to affect <lb></lb>him, must have undermined his physical resistance. </foreign></s>

<s><foreign lang="en">It seems that in the winter <lb></lb>between 1899 and 1900 he neglected a case of nephritis; toward the end of <lb></lb>January he was found unconscious by the man who served as his housekeeper. </foreign></s>

<s><foreign lang="en"><lb></lb>He died a few days later, without either his relatives or a doctor having been <lb></lb>called. </foreign></s>

<s><foreign lang="en">His death was reported by Procacci in that <emph type="italics"></emph>Rassegna Nazionale<emph.end type="italics"></emph.end> with <lb></lb>which Caverni had so actively collaborated. <lb></lb><lb></lb>I quote from his announcement, <lb></lb>omitting a few adjectives: “He died on the 30th last at 4:25 in the morning at <lb></lb>the age of 63.... The florid health he enjoyed and his robust physical con­<lb></lb>stitution had led us to hope that ... he would reach a very advanced age.... <lb></lb>Although he dedicated all his time to study, he did not neglect his duties as <lb></lb>parish priest, to which he attended with untiring zeal and intelligent love. </foreign></s>

<s><foreign lang="en">Not <pb xlink:href="020/01/018.jpg" pagenum="xix"></pb>only his own parishioners, but vacationers from the neighboring countryside as <lb></lb>well came willingly to hear his Sunday lectures on the Gospels.... Both the <lb></lb>clergy and the population of the town of Bagno a Ripoli, among whom he lived <lb></lb>for so long and who could therefore judge his great virtues at close hand, <lb></lb>flocked in great numbers to accompany him to his grave and a colleague, Prior <lb></lb>Cini,... praised his knowledge, virtue and modesty. </foreign></s>

<s><foreign lang="en">Two musical societies <lb></lb>rendered the funeral procession more solemn.” And the long and steep walk up <lb></lb>to the cemetery which dominates the river from the other flank of the valley <lb></lb>must have reminded that little crowd, all village and country folk, of his <lb></lb>countless methodical hikes over the same splendid hills. </foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>8. ODYSSEY OF THE MANUSCRIPTS<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en">In his will which he had drawn up just three months earlier, besides giving <lb></lb>instructions for his funeral—significant for the simplicity and the poetry that <lb></lb>inspires them—he left his books and manuscripts to his older brother, Giuseppe, <lb></lb>with the obligation to transmit them to his eldest son, Egisto, who was in turn <lb></lb>to leave them to his firstborn and so on, as has been done. </foreign></s>

<s><foreign lang="en">Egisto Caverni, the <lb></lb>favorite nephew with whom his uncle often met in Florence and who had <lb></lb>taken up the trade of carpenter, went to get them at the parsonage of San <lb></lb>Bartolomeo in Quarate with one of those two-wheeled carts which once carried <lb></lb>bricks to the building yards of Florence, and in 1906 Filippo Orlando could <lb></lb>write that “the books, the manuscripts of Caverni, some unpublished and <lb></lb>important, are still kept in an orderly collection with pious veneration by his <lb></lb>family in S. </foreign></s>

<s><foreign lang="en">Quirico di Montelupo where he was born; his nephew, Egisto <lb></lb>Caverni, full of intelligence and reverent affection although he lives by the <lb></lb>work of his hands, keeps them all in order in the best room of the house....” <lb></lb>This old friend expressed the hope that these papers would be passed on to <lb></lb>the Biblioteca Nazionale of Florence. <lb></lb><lb></lb>Twelve years later, Father Giovanni <lb></lb>Giovannozzi, printing an unpublished chapter of the <emph type="italics"></emph>Storia,<emph.end type="italics"></emph.end> spoke again of that <lb></lb>precious material: “In my studies I have more than once consulted the original <lb></lb>manuscript possessed by the nephews and heirs of Abbot Caverni and made <lb></lb>extracts of it. </foreign></s>

<s><foreign lang="en">And now, in agreement with the owners, I am happy to offer <lb></lb>students of the history of science the chapter concerning the doctrine and <lb></lb>works of the ex-Scolopian Famiano Michelini....” <lb></lb><lb></lb>Since then, that is, for <lb></lb>about half a century, I do not think there was any further news of those <lb></lb>manuscripts, nor was there any trace of them in the Florentine archives. <pb xlink:href="020/01/019.jpg" pagenum="xx"></pb>At Montelupo I heard that the Caverni had moved away some time ago; <lb></lb>fortunately, a relative was able to tell me they now live in Prato. </foreign></s>

<s><foreign lang="en">Thus I <lb></lb>was able to trace Egisto&#039;s eldest son, Lamberto, and at his home I was able <lb></lb>to look the manuscripts over and hear of their vicissitudes. </foreign></s>

<s><foreign lang="en">Lamberto Caverni <lb></lb>does not remember Giovannozzi&#039;s visits; during those years he was away in <lb></lb>the war. </foreign></s>

<s><foreign lang="en">He does remember that his father&#039;s large family (Egisto raised ten <lb></lb>children) was always ready to receive and assist anyone who declared he <lb></lb>wanted to study or copy those papers. </foreign></s>

<s><foreign lang="en">But not everyone behaved as loyally <lb></lb>as Giovannozzi: someone even published some unprinted works in his own <lb></lb>name, not without taking all the postage stamps off the correspondence! In <lb></lb>the meantime, by making many sacrifices, Egisto Caverni was able to set up a <lb></lb>saw mill with a shop for making packing cases; he rented a place in the street <lb></lb>named today for Raffaello Caverni in a zone separated from the capital, <lb></lb>Montelupo, only by the Pesa river which flows into the Arno there. </foreign></s>

<s><foreign lang="en">After a <lb></lb>few years, not far from there, he began to build himself a new house on the <lb></lb>avenue that leads to the Villa Ambrogiana. </foreign></s>

<s><foreign lang="en">The manuscripts, naturally, <lb></lb>followed the family as it moved and were always allotted the most decorous <lb></lb>space possible. </foreign></s>

<s><foreign lang="en">Once the war was over and the two sons who had taken part in <lb></lb>it returned home, the little packing case factory began to prosper. </foreign></s>

<s><foreign lang="en">But on the <lb></lb>day of Epiphany in 1920, after a period of heavy rains, the rivers swelled <lb></lb>beyond measure and the Pesa overflowed with incredible violence. </foreign></s>

<s><foreign lang="en">The <lb></lb>manuscripts were on the ground floor in the “office” and were transferred to <lb></lb>the upper floor just in time. </foreign></s>

<s><foreign lang="en">The fury of the waters destroyed the stone walls <lb></lb>around the property and swept away all the lumber stored there; the house <lb></lb>itself seemed about to collapse. </foreign></s>

<s><foreign lang="en">During the months following the flood every <lb></lb>attempt was made to recover from that ruin, but a year later another flood <lb></lb>similar to the first put a definite end to the artisan activity of that large family, <lb></lb>reducing it, literally, to desperation. </foreign></s>

<s><foreign lang="en">It was then they thought of moving to <lb></lb>Prato because their best clients were there and, perhaps, to avoid the risk of <lb></lb>another useless effort. </foreign></s>

<s><foreign lang="en">But they needed at last 20,000 lire to set themselves up <lb></lb>in business again, capital which a relative was ready to offer, against, however, <lb></lb>ample guarantees. </foreign></s>

<s><foreign lang="en">For these he asked for Raffaello Caverni&#039;s manuscripts <lb></lb>which Egisto and his ten children had shown they cared for more than anything <lb></lb>else! In a few years of hard work in the favorable zone of Prato, the Caverni put <lb></lb>their old business back on its feet. </foreign></s>

<s><foreign lang="en">But Lamberto remembers that his father, by <lb></lb>then old and infirm, could find no peace until he could go to Montelupo to repay <lb></lb>that debt and regain the manuscripts. </foreign></s>

<s><foreign lang="en">Naturally, their troubles were not over. </foreign></s>

<s><foreign lang="en"><lb></lb>During the Second World War, in the air raid of January 17, 1943, the <lb></lb>Caverni house and factory were once again destroyed, but the manuscripts had <lb></lb>already been opportunely evacuated to a safe place under the church of nearby <lb></lb>Figline and could thus be returned undamaged to the family. </foreign></s>

<s><foreign lang="en">Indeed, Lamberto <lb></lb>Caverni, following the instructions of his great-uncle&#039;s will has already con-<pb xlink:href="020/01/020.jpg" pagenum="xxi"></pb>signed them to Pietro, his firstborn, who keeps them at the disposition of those <lb></lb>scholars of the history of science who at last want to remember their existence. </foreign></s></p><p type="main">

<s><foreign lang="en"><emph type="center"></emph>9. CONCLUSION<emph.end type="center"></emph.end></foreign></s></p><p type="main">

<s><foreign lang="en">To the long oblivion of the manuscripts there corresponds a silence almost as <lb></lb>continuous in the last half century regarding the volumes of the <emph type="italics"></emph>Storia.<emph.end type="italics"></emph.end> And <lb></lb>if some sporadic attention has been given them, this has been abroad rather than <lb></lb>in Italy. </foreign></s>

<s><foreign lang="en">Here, in fact, one of the last times someone concerned himself with the <lb></lb>work, naturally in deprecation of it, was at the tenth meeting of the <emph type="italics"></emph>Società <lb></lb>italiana per il progresso delle scienze<emph.end type="italics"></emph.end> (Italian society for the progress of science) <lb></lb>held in Pisa in April 1919. In conclusion of two “laborious and crowded <lb></lb>sessions” of the history of science section, an order of the day was approved <lb></lb>in which, besides voting to reprint the national edition of Galileo&#039;s works, the <lb></lb>hope was expressed that “in view of renewed anti-Galilean attempts,” prime <lb></lb>responsibility for which was imputed to the scholar of Montelupo,” a critical <lb></lb>review of Caverni&#039;s <emph type="italics"></emph>Storia<emph.end type="italics"></emph.end> would be made, to bring to light the intentions and <lb></lb>the means employed by the author in judging Galileo&#039;s work.” <lb></lb><lb></lb>A series of <lb></lb>articles in the “Archivio” follows this proposal, among which there is also one <lb></lb>which Mieli accepted in favor of Caverni, written by Giovannozzi. </foreign></s>

<s><foreign lang="en">The other <lb></lb>writers were Favaro, with the article already cited regarding the matter of the <lb></lb>phases of Venus, the only page of Caverni which should, in fact, be censured, <lb></lb>and the physicist Carlo Del Lungo who had raised the question at the meeting <lb></lb>and who gave Mieli two rather ample essays. <lb></lb><lb></lb>There is nothing new in them. </foreign></s>

<s><foreign lang="en"><lb></lb>The most valid criticism concerns the interpretation of Santorio&#039;s <emph type="italics"></emph>Cotyla,<emph.end type="italics"></emph.end> which <lb></lb>Caverni at first took to be a real pendulum clock when it is actually a small <lb></lb>pendulum whose length can be regulated and which is made to oscillate by <lb></lb>hand, like Santorio&#039;s similar <emph type="italics"></emph>pulsilogio.<emph.end type="italics"></emph.end> Schiaparelli had already noticed this <lb></lb>oversight almost twenty years before, and Caverni himself in the fourth volume <lb></lb>of his <emph type="italics"></emph>Storia<emph.end type="italics"></emph.end> had made ample amends for this error. </foreign></s>

<s><foreign lang="en">Del Lungo&#039;s insistence is <lb></lb>therefore useless; moreover, his article (the nemesis of chance) is illustrated by <lb></lb>a drawing of the <emph type="italics"></emph>Cotyla<emph.end type="italics"></emph.end> reproduced upside down! With this the “critical re­<lb></lb>view” voted at Pisa by the Italian scientists in congress ended with the classical <lb></lb>results of the mountain&#039;s travail. </foreign></s></p><p type="main">

<s><foreign lang="en">Abroad, as we have said, interest in the <emph type="italics"></emph>Storia del metodo sperimentale in <lb></lb>Italia<emph.end type="italics"></emph.end> registers further significant episodes. </foreign></s>

<s><foreign lang="en">In 1952 George Sarton, in his book <lb></lb><emph type="italics"></emph>A Guide to the History of Science,<emph.end type="italics"></emph.end> puts Caverni&#039;s <emph type="italics"></emph>Storia<emph.end type="italics"></emph.end> in the first place for <pb xlink:href="020/01/021.jpg" pagenum="xxii"></pb>Italy, followed by only two other titles (<emph type="italics"></emph>Da Leonardo a Marconi<emph.end type="italics"></emph.end> by Savorgnan <lb></lb>di Brazzà and <emph type="italics"></emph>Un secolo di progresso scientifico italiano<emph.end type="italics"></emph.end> in 7 volumes, edited by <lb></lb>L. Silla). Many years before, Leonardo Olschki, <lb></lb><lb></lb>in his history of scientific <lb></lb>works in the vulgar tongue, also left unfinished, cites Caverni repeatedly <lb></lb><lb></lb>and <lb></lb>it is obvious that he thinks highly of the man&#039;s ample exegesis of the sources of <lb></lb>common interest. </foreign></s>

<s><foreign lang="en">Even this new reprint is an initiative of American origin. </foreign></s>

<s><foreign lang="en"><lb></lb>And it was Harry Woolf, former editor of <emph type="italics"></emph>Isis,<emph.end type="italics"></emph.end> who invited me to write this <lb></lb>introductory note, for which I am truly grateful. </foreign></s>

<s><foreign lang="en">It is still not a study of this <lb></lb>work, but, I hope, a premise and a
stimulus to finally beginning one. </foreign></s></p><pb xlink:href="020/01/022.jpg"></pb><pb xlink:href="020/01/023.jpg"></pb><pb xlink:href="020/01/024.jpg"></pb><p type="main">

<s><emph type="center"></emph>RELAZIONE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DELLA<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>GIUNTA DEL R. ISTITUTO VENETO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEPUTATA ALL&#039;ESAME<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEI LAVORI PRESENTATI AL CONCORSO DELLA FONDAZIONE TOMASONI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SUL TEMA:<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>STORIA DEL METODO SPERIMENTALE IN ITALIA<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Per la seconda volta è chiamato il R. </s>

<s>Istituto a pronunziare il suo <lb></lb>giudizio intorno ai lavori, presentati al concorso della fondazione Tomasoni <lb></lb>sul tema: <emph type="italics"></emph>“ Storia del metodo sperimentale in Italia ”,<emph.end type="italics"></emph.end> e, per agevolare <lb></lb>in questo caso l&#039;adempimento di tale, che è fra le più alte missioni del­<lb></lb>l&#039;Istituto nostro, la Commissione, deputata a fornirvi gli elementi per siffatto <lb></lb>giudizio, ha stimato opportuno di cominciare dall&#039;esporvi succintamente le <lb></lb>varie fasi, attraverso le quali questo importante concorso è finora passato. </s></p><p type="main">

<s>Il defunto Giovanni Tomasoni, con suo testamento olografo del 4 di­<lb></lb>cembre 1879, disponeva a favore del nostro Istituto un legato di lire cin­<lb></lb>quemila, da darsi in premio <emph type="italics"></emph>“ a chi detterà meglio la storia del metodo <lb></lb>sperimentale in Italia ”.<emph.end type="italics"></emph.end> La medesima disposizione testamentaria recando, <lb></lb>che il programma di concorso fosse determinato dall&#039;Istituto, questo for­<lb></lb>mulava il tema nei seguenti termini: <emph type="italics"></emph>“ Esporre le vicende ed i progressi <lb></lb>del metodo sperimentale in Italia, principalmente studiato nelle sue <lb></lb>applicazioni alle scienze fisiche, con particolare riguardo a tutto ciò <lb></lb>che esso offre di notevole nei quattro secoli fra il principio del de­<lb></lb>cimoquinto e la fine del decimottavo, comprendendo la scopcrta della <lb></lb>pila voltaica. </s>

<s>A compiere la trattazione del quesito basterà aggiungere <lb></lb>un ragguaglio storico, ristretto all&#039;Italia, sul progressivo e rapido svol­<lb></lb>gimento, non solo delle scienze fisiche, ma benanco delle economiche e <lb></lb>sociali per opera del metodo sperimentale ”.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Allo scopo di meglio chiarire i suoi intendimenti, la Commissione, alla <lb></lb>quale era stato affidato l&#039;incarico di formulare il tema, aggiungeva che, <lb></lb>secondo il suo parere, opportuna introduzione al corpo principale dello <lb></lb>scritto avrebbe dovuto essere un cenno storico riassuntivo di quantò si operò <lb></lb>nell&#039;antichità in Italia con indirizzo sperimentale, studiando le cause, per <lb></lb>le quali quelle sane idee rimasero affogate sotto la marea dei peripatetici <pb xlink:href="020/01/025.jpg" pagenum="6"></pb>sedicenti seguaci di Aristotele; e che infine opportuna conchiusione del la­<lb></lb>voro avrebbe dovuto essere lo studio della influenza esercitata dalla scuola <lb></lb>Galileiana, mettendo in luce se e qual parte abbiano avuta gli stranieri nella <lb></lb>definitiva adozione del metodo sperimentale. </s>

<s>Queste ultime avvertenze, in­<lb></lb>tese, più che ad altro, a render maggiormente chiaro il concetto della Com­<lb></lb>missione presso l&#039;Istituto, che doveva giudicarne l&#039;elaborato, vennero, e forse <lb></lb>con non molta opportunità, aggiunte al programma di concorso. </s></p><p type="main">

<s>Alla scadenza del concorso fissata per il febbraio dell&#039;anno 1885 fu­<lb></lb>rono presentati due lavori, uno dei quali contraddistinto dal motto: <emph type="italics"></emph>“ Va­<lb></lb>gliami&#039;l lungo studio e&#039;l grande amore ”;<emph.end type="italics"></emph.end> e l&#039;altro colla divisa del: <emph type="italics"></emph>“ Pro­<lb></lb>vando e riprovando ”.<emph.end type="italics"></emph.end> Accogliendo le conchiusioni della Commissione, <lb></lb>l&#039;Istituto non conferi il premio ad alcuno di essi, e, dovendo, in obbedienza <lb></lb>alle tavole di fondazione, essere il tema medesimo posto a concorso, fintan­<lb></lb>tochè se ne abbia una soluzione che del premio sia degna, la Commissione <lb></lb>stessa sottopose all&#039;Istituto alcune considerazioni sulla opportunità di mo­<lb></lb>dificare alquanto i termini e le condizioni del primitivo enunciato di esso. </s>

<s><lb></lb>Riflettendo alla vastità grandissima del tema ed alle difflcoltà gravissime che <lb></lb>ne presenta una lodevole soluzione, la Commissione era venuta unanime <lb></lb>nella deliberazione di chiedere all&#039;Istituto che il concorso venisse riaperto, <lb></lb>limitandolo soltanto alle scienze fisiche, naturali e biologiche, escludendo <lb></lb>affatto le scienze morali, od almeno lasciandone la trattazione all&#039;arbitrio <lb></lb>dei concorrenti, Osservava la Commissione che, anche cosi limitato, il tema <lb></lb>nulla perdeva della sua grandissima importanza relativa, ed esigeva pur tut­<lb></lb>tavia, così gran somma di lavoro, da non riuscire ad esso sproporzionato il <lb></lb>cospicuo premio largito dalla generosità del testatore. </s>

<s>Che anzi essa Com­<lb></lb>missione si era mostrata così profondamente penetrata dell&#039;altezza del tema <lb></lb>e delle difficoltà che esso offre, da non esitare ad esprimere il desiderio <lb></lb>che venisse apertamente dichiarato come <emph type="italics"></emph>anche una monografia di grande <lb></lb>valore, la quale contemplasse soltanto l&#039;epoca più saliente nella storia <lb></lb>del metodo sperimentale, quale sarebbe quella rappresentata da uno stu­<lb></lb>dio profondo e completo intorno a Galileo ed alla sua scuola, sarebbe <lb></lb>tornata bene accetta all&#039;Istituto, ed avrebbe potuto essere giudicata me­<lb></lb>ritevole di premio.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>L&#039;Istituto accolse la prima proposta della Commissione; ma rispetto alla <lb></lb>seconda non stimò opportuno di limitare il tema da porsi al concorso, e, <lb></lb>riservandosi piena libertà di azione quanto ai lavori che fossero per essere <lb></lb>prodotti, e riconoscendo che anche quella più ristretta monografia, quando <lb></lb>fosse stata di eccezionale valore, avrebbo dovuto esser presa in considera­<lb></lb>zione, preferì di mantenere al tema la sua vastità, chiarendo anzi che, oltre <lb></lb>alle scienze fisiche, avrebbe dovuto essere studiata la storia del metodo spe­<lb></lb>rimentale anco rispetto alle naturali e biologiche. </s>

<s>In seguito a ciò, mante­<lb></lb>nuta la dizione conforme alla volontà del testatore, cioè, dichiarato che il <lb></lb>premio sarebbe stato conferito <emph type="italics"></emph>“ a chi detterà meglio la storia del metodo <lb></lb>sperimentale in Italia ”,<emph.end type="italics"></emph.end> volle specificato il tema nei termini seguenti: <pb xlink:href="020/01/026.jpg" pagenum="7"></pb><emph type="italics"></emph>“ Esporre le origini, le vicende ed i progressi del metodo sperimentale in <lb></lb>Italia, studiato nelle suc applicazioni alle scienze fisiche, naturali e bio­<lb></lb>logiche, con particolare riguardo a tutto ciò ch&#039;esso offre di notevole nei <lb></lb>quattro secoli fra il principio del decimoquinto e la fine del decimottavo, <lb></lb>compresa la scoperta della pila voltaica ”,<emph.end type="italics"></emph.end> aggiuntavi poi l&#039;avvertenza che <lb></lb>era <emph type="italics"></emph>“ lasciato all&#039;arbitrio dei concorrenti il trattare, con quell&#039;estensione <lb></lb>che crederanno, la storia del metodo sperimentale applicato alle scienze <lb></lb>morali ”.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Due furono i lavori presentati alla scadenza del concorso, fissata al 31 <lb></lb>marzo 1889. </s></p><p type="main">

<s><emph type="italics"></emph>Spes premii minuit vim laboris<emph.end type="italics"></emph.end> è il motto sotto il quale si ripresenta <lb></lb>l&#039;autore, che, nel primo concorso, s&#039;era coperto della celebre divisa: <emph type="italics"></emph>“ Pro­<lb></lb>vando e riprovando ”.<emph.end type="italics"></emph.end> È d&#039;uopo convenire che il lavoro rifatto presenta <lb></lb>minori mende del primo; ma purtroppo queste sono tuttavia in così gran <lb></lb>numero e talmente gravi, da togliere ad esso qualsiasi considerazione. </s>

<s>L&#039;au­<lb></lb>tore si è per verità sforzato di esaurire tutto intero il programma del con­<lb></lb>corso; ma il modo, col quale il lavoro è anche questa volta condotto, di­<lb></lb>mostra, in maniera troppo evidente, che all&#039;autore di esso fanno soverchio <lb></lb>difetto estensione e profondità di coltura per potersi accingere ad un tanto <lb></lb>cimento. </s></p><p type="main">

<s>Ed anzitutto ammetteremo che l&#039;esemplare, il quale ne abbiamo sot­<lb></lb>t&#039;occhio, sia l&#039;opera di un amanuense, e che all&#039;autore sia mancato anche <lb></lb>il tempo di rileggerlo, perchè, quando così non fosse, alcuni grossolani er­<lb></lb>rori ci avrebbero consigliato a chiudere senz&#039;altro il volume, per non spre­<lb></lb>care il tempo, che pure abbiamo dovuto spendervi intorno per diligente­<lb></lb>mente esaminarlo. </s>

<s>Nè questo avremmo notato se certi indizi, di grande <lb></lb>significato per un attento osservatore, non ci avessero dimostrato che, se <lb></lb>non tutti, parecchi almeno di quegli errori appariscono dovuti a quel ca­<lb></lb>pitale difetto che pur ora abbiamo avvertito. </s>

<s>Il quale si manifesta princi­<lb></lb>mente nella scelta delle fonti, che non sono mai le prime, mentre quelle <lb></lb>di seconda o di terza mano, alle quali attinse l&#039;autore, non sono le migliori, <lb></lb>imperocchè la massima parte delle citazioni (e potremmo quasi dire tutte) <lb></lb>si riferiscono a lavori di compilazione, il più delle volte dovuti a scrittori <lb></lb>che non passano per i più scrupolosi (quando non sieno di autori troppo <lb></lb>noti per la loro parzialità), e che, per l&#039;epoca alla quale appartengono, non <lb></lb>poterono approffittare dei più recenti studi condotti con quelle norme, dalle <lb></lb>quali la critica, degna di tal nome, non vuole che si prescinda. </s></p><p type="main">

<s>Anche la cronologia, la cui esattezza deve pur tenersi per tanta parte <lb></lb>in un lavoro destinato a porgere un quadro delle origini e dello sviluppo <lb></lb>del metodo sperimentale, lascia moltissimo a desiderare; nè mancano esempi <lb></lb>di fatti i quali vengono ripetuti, attribuendoli ad epoche fra loro diverse. </s></p><p type="main">

<s>Di queste mende di varia natura, ma indistintamente assai gravi, si <pb xlink:href="020/01/027.jpg" pagenum="8"></pb>risente il lavoro in tutte le sue parti, le quali non sono nemmeno ben pro­<lb></lb>porzionate fra loro, poichè quasi due terzi del cammino vengono percorsi <lb></lb>prima di incontrare l&#039;opera Galileiana; cosicchè si comprende quanto ina­<lb></lb>deguatamente rimanga trattata la scuola dell&#039;immortale filosofo, della quale <lb></lb>l&#039;autore non sospetta nemmeno i copiosi ed importanti materiali che avrebbe <lb></lb>potuto fornire al suo lavoro. </s></p><p type="main">

<s>Quando finalmente avremo ancora soggiunto, che, in generale, l&#039;autore <lb></lb>si tiene sempre ad affermare senza porgere dimostrazioni, che le questioni <lb></lb>più gravi sono trattate nel modo più superficiale che immaginar si possa, <lb></lb>e che anche i fatti più salienti, oltre ad essere assai scarsamente lumeg­<lb></lb>giati, vengono esposti, senza curare di porne in evidenza la parte essenziale, <lb></lb>cioè il nesso colla creazione, colla adozione e col progresso del metodo spe­<lb></lb>rimentale, del quale deve scriversi la storia, ci pare che non vi sia bisogno <lb></lb>di entrare in più minute analisi, per giustificare la couchiusione che in <lb></lb>nessun modo può questo lavoro aspirare al conferimento del premio. </s></p><p type="main">

<s>Un indirizzo completamente diverso, e quasi diremmo opposto, ha se­<lb></lb>guito l&#039;autore dell&#039;altro lavoro, di proporzioni veramente colossali (sono 3264 <lb></lb>pagine di grandissimo formato tutte scritte per intero), il quale vi ha posta <lb></lb>in fronte la significante terzina dantesca: </s></p><p type="main">

<s><emph type="center"></emph>“ Da questa instanzia può deliberarti <lb></lb>Esperienza, se giammai la provi <lb></lb>Ch&#039;esser suol fonte a&#039;rivi di vostr&#039;arti ”.<emph.end type="center"></emph.end></s></p><p type="main">

<s>S&#039;apre il lavoro con un magistrale discorso preliminare, nel quale, con <lb></lb>una robusta sintesi, tracciato un quadro di quella, che volentieri chiame­<lb></lb>remmo preistoria del metodo sperimentale, se ne mostrano i fondamenti, <lb></lb>porgendo in pari tempo il disegno di tutta l&#039;opera. </s></p><p type="main">

<s>E prendendo le mosse dal “ primo acquisto delle cognizioni ”, il nostro <lb></lb>autore ci addita in Platone ed in Aristotele i primi ed i principali che in­<lb></lb>vestigassero le leggi, secondo le quali si acquistano dall&#039;intelletto umano e <lb></lb>si svolgono nel pensiero le cognizioni; e, mostrato il diverso indirizzo da <lb></lb>loro seguìto e la inutilità del metodo sperimentale tanto per l&#039;uno quanto <lb></lb>per l&#039;altro, chiarisce tuttavia come, mentre la Stagirita credeva di potere <lb></lb>supplire in ogni modo, colla ragione, all&#039;esperienza, il fondatore dell&#039;Acca­<lb></lb>demia venisse efficacemente avviando gli ingegni all&#039;arte dello sperimentare, <lb></lb>preparandoveli colla geometria. </s></p><p type="main">

<s>Di Grecia mostra diffondersi le dottrine dei due maestri in Italia, con <lb></lb>varia vicenda, e con Tommaso d&#039;Aquino istituirsi la scuola peripatetica, che <lb></lb>soggiogò gli ingegni, insino a tutto il secolo XVI. </s>

<s>Nessun vantaggio egli <lb></lb>riconosce alla scienza sperimentale da parte della schiera dei cosidetti ra­<lb></lb>zionalisti, alla quale appartennero Francesco Patrizio, Bernardino Telesio, <lb></lb>Giordano Bruno, Tommaso Campanella, poichè, se pur insorsero a scuotere <pb xlink:href="020/01/028.jpg" pagenum="9"></pb>il lungo giogo, non fecero altro che sostituirè alla ragione ed alla autorità <lb></lb>di Aristotele, la ragione e l&#039;autorità loro propria. </s></p><p type="main">

<s>Primi a promuovere quella scienza egli ci addita coloro, che, indipen­<lb></lb>dentemente dagli insegnamenti ricevuti nella scuola, rivolsero gli occhi a <lb></lb>contemplar la natura, nei varì e molteplici esercizi dell&#039;arte. </s>

<s>Così, dall&#039;arte <lb></lb>del verso, ebbe origine la fisica sperimentale dell&#039;Alighieri; dell&#039;arte navi­<lb></lb>gatoria, la meteorologia e la geografia fisica di Cristoforo Colombo e l&#039;astro­<lb></lb>nomia di Amerigo Vespucci; come, dall&#039;arte del disegno, scaturì quella larga <lb></lb>vena di scienza naturale, che non si finirebbe di ammirar mai negli scritti <lb></lb>di Leonardo da Vinci. </s></p><p type="main">

<s>Non tralascia tuttavia il nostro autore di toccare di alcuni, i quali in <lb></lb>que&#039;secoli, essendo pure imbevuti dei principì peripatetici, ebbero qualche <lb></lb>sentore ed esercizio d&#039;arte sperimentale: primi fra questi il Fracastoro, il <lb></lb>Cardano ed il Cesalpino; ma i frutti di scienza naturale, che trovansi di­<lb></lb>spersi quà e là per i loro volumi, egli li riconosce non tanto dalle scuole, <lb></lb>quanto invece dal pratico esercizio dell&#039;arte medica. </s></p><p type="main">

<s>E che più efficacemente conferisse ai progressi del metodo sperimen­<lb></lb>tale la vita pratica e la conoscenza del mondo che non la scuola, ne trova <lb></lb>il nostro Autore la prova suprema nel Sarpi, del quale è caldissimo ed <lb></lb>anzi, a parer nostro, esagerato ammiratore. </s>

<s>Questo egli dipinge, circon­<lb></lb>dato dal Ghetaldi, dal Porta, dal Sagredo, dall&#039;Antonini e dal De Dominis, <lb></lb>attendere ad osservazioni, a discussioni, ad esperienze: in tal nucleo di stu­<lb></lb>diosi egli ravvisa i veri precursori e gli efficaci promotori del metodo spe­<lb></lb>rimentale, il quale aveva avuto già da un secolo una assai efficace promo­<lb></lb>zione in Toscana dall&#039;Accademia platonica instituita nella Corte dei Medici. </s>

<s><lb></lb>Allora, ad abbattare il Peripato, che conformava alla ragione e al senso le <lb></lb>leggi della natura, il nostro autore ci mostra il sorgere dell&#039;Accademia, la <lb></lb>quale, insegnando a leggere in quel libro, che ci si squaderna innanzi agli <lb></lb>occhi, e che è scritto con caratteri geometrici, invitò gli studiosi a svolgere <lb></lb>insieme coi volumi di Platone, quelli altresì di due dei più eccellenti, che <lb></lb>fiorissero in quella scuola, Archimede ed Erone. </s></p><p type="main">

<s>Cosi, dal quadro, del quale andiamo riproducendo le linee massime, <lb></lb>appariscono disposte le cose per modo che la instituzione dell&#039;arte speri­<lb></lb>mentale dovesse occorrere alla Toscana; cosi avvenne di fat<emph type="italics"></emph>t<emph.end type="italics"></emph.end>o, per il magi­<lb></lb>stero di Galileo Galilei, a cui i posteri, plaudendo e gratulando, attribuirono, <lb></lb>del pari che al maestro, dal quale prese la ispirazione, il nome di divino. </s>

<s><lb></lb>Egli, fuggendo il Peripato, da Platone succhiò i primi e veri principì della <lb></lb>scienza del moto; da Archimede, oltre alla scienza del moto; e dell&#039;equili­<lb></lb>brio de&#039;corpi solidi e liquidi, ebbe le prime rivelazioni del sistema del mondo, <lb></lb>e da Erone apprese i primi saggi di fisica sperimentale. </s></p><p type="main">

<s>Se Galileo fosse rimasto solo, come tanti suoi predecessori, non avrebbe <lb></lb>avuto certamente quella grande efficacia, che egli ebbe, nel promuovere le <lb></lb>scienze sperimentali. </s>

<s>Uno dei più gran meriti, che se gli deve attribuire, è <lb></lb>dunque quello d&#039;avere formato una scuola, in cui s&#039;ebbero i primi seggi il <pb xlink:href="020/01/029.jpg" pagenum="10"></pb>Castelli, il Torricelli, il Cavalieri. </s>

<s>E qui il nostro autore lascia a divedere <lb></lb>che questo formarsi e svolgersi della scuola Galileiana costituirà il principale <lb></lb>nucleo del suo lavoro. </s></p><p type="main">

<s>Morti, con Galileo, il Castelli ed il Cavalieri, rimase il Torricelli a rap­<lb></lb>presentare quella scuola dentro a quel recinto, dov&#039;ebbe la sua culla, cioè <lb></lb>la corte medicea. </s>

<s>Nella celebre esperienza dell&#039;argento vivo, che il Mersenne <lb></lb>attinse in Roma dalla bocca di Michelangelo Ricci, e che egli poi, il Mer­<lb></lb>senne, comunicò al Pascal, ritornato in Francia, ci addita la scintilla, che <lb></lb>secondò una gran fiamma, a cui si scaldarono e illuminarono tutti gli in­<lb></lb>gegni di Europa. </s>

<s>Nel Torricelli, che, alla corte del Granduca Ferdinando II <lb></lb>fabbricava telescopi, e inventava altri strumenti, riconosce egli l&#039;autore del <lb></lb>più grande incremento che ricevesse mai in quel tempo l&#039;istituzione Gali­<lb></lb>leiana. </s>

<s>Ed a lui, rapito così presto alla scienza, ci mostra succedere il Vi­<lb></lb>viani, il Borelli ed il Rinaldini, sui quali tre validissimi ingegni, ma sui <lb></lb>primi due principalmente, fondava Leopoldo de&#039;Medici le generose speranze <lb></lb>di istituire un&#039;Accademia, a cui si potesse, anco formalmente, attribuire un <lb></lb>tal nome. </s>

<s>Tale fu l&#039;Accademia del Cimento, nella quale, sebbene gli scien­<lb></lb>tifici consessi incominciassero infìno dal 1657, non ostante, al pubblico, non <lb></lb>se ne comunicarono le scoperte, se non che nel 1666 in quel volume, a <lb></lb>cui si volle dar giustamente il titolo di <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> perchè nient&#039;altro son vera­<lb></lb>mente se non che saggi di quella ricca e feconda miniera d&#039;oro, che si ri­<lb></lb>man tuttavia nascosta e involta nella scoria dei manoscritti. </s></p><p type="main">

<s>Conveniamo con l&#039;autore nel tenere che, fatto cardinale il Principe <lb></lb>Leopoldo, l&#039;Accademia non svanisse per essersi l&#039;institutore di essa rivolto <lb></lb>tutto agli studi ecclesiastici; ma nella risoluzione del Borelli di ritornarsene <lb></lb>in patria, nelle esercitazioni idrauliche a cui il Principe ed i privati tennero <lb></lb>continuamente rivolto il Viviani, nelle lontane peregrinazioni del Magalotti, <lb></lb>noi non ravvisiamo, come vorrebbe il nostro autore, la causa, ma bensì l&#039;ef­<lb></lb>fetto della cessazione della sperimentale Accademia, poichè si trova in più <lb></lb>luoghi affermato che la morte di essa fu posta da Roma come condizione <lb></lb>per insignire il Principe Leopoldo della porpora cardinalizia. </s></p><p type="main">

<s>Al Borelli ed al Viviani il nostro fa seguire lo Stenone ed il Redi, i <lb></lb>quali p<emph type="italics"></emph>o<emph.end type="italics"></emph.end>rtarono di preferenza la loro attenzione sulle cose di storia natu­<lb></lb>rale, e fa vedere come il Borelli, che aveva applicata la matematica alla fi­<lb></lb>siologia, il Michelini, che lo stesso metodo aveva applicato all&#039;arte medica, <lb></lb>e fu primo institutore della medicina sperimentale, fecondando gli ingegni <lb></lb>del Malpighi e del Redi, operarono sì, che, se non dentro l&#039;Accademia del <lb></lb>Cimento, poco però al di fuori, sorgessero prosperose l&#039;Anatomia micro­<lb></lb>scopica e la vera Storia Naturale, che vennero cosi a dar la massima esten­<lb></lb>sione, e a render quasi compiuta la grande instituzione di Galileo. </s></p><p type="main">

<s>Tutto questo grande avvicendarsi di studi, tutte queste piramidi di luce, <lb></lb>che muovono da Galileo stesso, come da prima luminosa sorgente, e si ri­<lb></lb><gap></gap>ettono, e si rinfrangono, e s&#039;incolorano in tanti illustri ingegni, prende <lb></lb>adunque il nostro autore a trattare, pigliando le mosse dalla storia dei prin-<pb xlink:href="020/01/030.jpg" pagenum="11"></pb>cipali strumenti che servono all&#039;arte sperimentale, alla quale prima parte <lb></lb>di storia seguono immediatamente le altre due concernenti l&#039;applicazione <lb></lb>dello stesso metodo sperimentale alle scienze fisiche ed alla storia naturale. </s>

<s><lb></lb>A questa trattazione è dedicato il primo volume diviso in due parti; ed in <lb></lb>essa è lasciata indietro la storia della meccanica e della idraulica, due scienze <lb></lb>eminentemente italiane, e delle quali i primi e principali institutori e mae­<lb></lb>stri, per unanime consenso, sono riconosciuti Galileo ed il Castelli; alla storia <lb></lb>del metodo sperimentale applicato alla scienza del moto dei gravi è dedi­<lb></lb>cato il secondo volume; il terzo ed ultimo dei presenti alla storia del me­<lb></lb>todo stesso applicato al moto dell&#039;acque. </s></p><p type="main">

<s>E qui ci sia concesso ripetere le parole colle quali il nostro autore <lb></lb>chiude il discorso preliminare. </s></p><p type="main">

<s>“ Co&#039;tre ponderosi volumi però, co&#039;quali usciamo in campo noi, che <lb></lb>ci sentiamo di così lieve armatura, non vuol farsi credere che si pretenda <lb></lb>essere stato trattato in tutta la sua estensione, e nella sua intensione il <lb></lb>sì difficile tema. </s>

<s>È tanto vasta la superficie di questo mare, e son le acque <lb></lb>di lui tanto profonde, che si richiede a correrlo altra barca della nostra, <lb></lb>e altro nocchiero. </s>

<s>L&#039;instituto stesso preso da noi, che è di non asserire <lb></lb>mai i fatti, senza produrre gli opportuni documenti, ci fa bene avvertiti <lb></lb>de&#039;ritrosi e degli scogli, da cui facilmente potremmo esser rimasti aggi­<lb></lb>rati ed offesi, perchè recando altri nuovi documenti, da noi non veduti, <lb></lb>si verrebbero necessariamente a rìformare certe nostre storiche conclu­<lb></lb>sioni. </s>

<s>Ma pure, da quello stesso instituto che noi proseguiamo, ha avuto <lb></lb>origine il volume quarto <emph type="italics"></emph>(il quale non è fra i presentati al concorso),<emph.end type="italics"></emph.end><lb></lb>che aggiungiamo all&#039;Opera nostra, qualunque essa si sia, come corredo ”.</s></p><p type="main">

<s>“ Questo ultimo volume infati si compila tutto di documenti, per la <lb></lb>massima parte inediti, che noi abbiamo scelti e ordinati da&#039;numerosissimi <lb></lb>manoscritti galileiani, e da quegli altri non men numerosi appartenenti <lb></lb>alla medicea Accademia del Cimento ... Come gemma in corona s&#039;aggiun­<lb></lb>gono i documenti di scienza sperimentale, ordinatamente disposti in forma <lb></lb>di Trattatelli, a render conte e proficue agli Italiani le solitarie specula­<lb></lb>zioni di Leonardo ... Da alcuni libri più rari, benchè stampati, abbiamo <lb></lb>pure fatta diligente raccolta di documenti, che alla massima parte de&#039;let­<lb></lb>tori giungeran come nuovi, ond&#039;è che, se noi non ci possiam lusingare <lb></lb>d&#039;aver fatto in queste lunghe e laboriose pagine, che presentiamo, opera <lb></lb>nè perfetta e nemmeno sufficiente; incoriamo però una dolce speranza <lb></lb>d&#039;aver forse aperta la via, e d&#039;aver adunati i materiali a qualche altro <lb></lb>Autore più dotto e più fortunato di noi, il quale, in modo veramente de­<lb></lb>gno della sua Nazione, torni a scriver la Storia del Metodo sperimentale <lb></lb>in Italia ”.</s></p><p type="main">

<s>Ed ora, dovremo noi con una diligente analsi seguire l&#039;autore passo a <lb></lb>passo nello svolgimento del suo disegno? </s>

<s>È facile il vedere che un simile <lb></lb>lavoro di analisi ci condurrebbe poco meno che ad aggiungere un nuovo <lb></lb>volume alla storia ch&#039;egli ha scritta, laonde stimiamo meglio consentaneo <pb xlink:href="020/01/031.jpg" pagenum="12"></pb>all&#039;ufficio nostro, ed insieme meglio appropriato allo scopo, il tentare un <lb></lb>giudizio sintetico, almeno per ciò che concerne la prima parte, dal quale <lb></lb>risultino in evidenza i criteri generali ch&#039;egli ha seguìti nello svolgimento <lb></lb>dell&#039;arduo tema; dal qual giudizio apparirà che, se molto abbiamo fortuna­<lb></lb>tamente da lodare, questo poderoso lavoro non apparve tuttavia agli occhi <lb></lb>nostri affatto scevro da mende, le quali abbiamo reputato nostro dovere di <lb></lb>non passare sotto silenzio. </s></p><p type="main">

<s>E quanto alle fonti, diciamo subito che l&#039;Autore, pur avendo pienissima <lb></lb>conoscenza delle italiane edite e inedite, di queste anzi tale e tanta da non <lb></lb>potersi desiderare maggiore, pecca alquanto di difetto nella cognizione delle <lb></lb>straniere, e nei giudizi intorno ad esse formulate; e questo carattere si ri­<lb></lb>specchia in tutto il lavoro, ed è causa talvolta di giudizi non scrupolosa­<lb></lb>mente esatti, e tal&#039;altra di lacune, le quali tuttavia a lui, meglio che ad <lb></lb>ogni altro, riuscirà agevole il colmare. </s></p><p type="main">

<s>Meno lieve ci apparve invece l&#039;altra menda, che deriva da un troppo <lb></lb>facile invaghirsi della novità delle conchiusioni, la quale, sia pur detto con <lb></lb>tutta la deferenza, che si merita uno studioso di tanta levatura, quanta ne <lb></lb>dimostra il nostro Autore, lo induce talvolta ad una interpretazione dei do­<lb></lb>cumenti, la quale a noi non parve sempre scrupolosamente conforme al ri­<lb></lb>gore storico. </s>

<s>E poichè quesa imputazione non può mantenersi campata in <lb></lb>aria; ma è pur mestieri fornirne una qualche giustificazione, è d&#039;uopo che <lb></lb>noi entriamo in alcuni particolari. </s></p><p type="main">

<s>L&#039;Autore si manifesta senza reticenze ammiratore profondo di Galileo <lb></lb>(e chi mai non lo sarebbe?); ma egli, forse posto in sull&#039;avviso dall&#039;ingiusto <lb></lb>giudizio di chi volle esaltare Galileo con pregiudizio di tutti i contemporanei, <lb></lb>e non consentendo in esso, pare quasi sempre in guardia contro conchiu­<lb></lb>sioni che al sommo filosofo riescano soverchiamente favorevoli, ed il <emph type="italics"></emph>ratio­<lb></lb>nabile obseqium,<emph.end type="italics"></emph.end> che lo storico deve prefiggersi come massima indeclina­<lb></lb>bile, è da lui spinto, ci sia lecito il dirlo, ad un eccesso che noi reputiamo <lb></lb>ingiustifistificato. </s></p><p type="main">

<s>Noi non consentiamo col nostro autore nella incondizionata ammira­<lb></lb>zione per Fra Paolo Sarpi scienziato; ma quand&#039;anche dividessimo tutto <lb></lb>intero il suo entusiamo, non sapremmo mai indurci, come egli vorrebbe, a <lb></lb>dividere fra Galileo ed il Sarpi il merito delle scoperte annunziate al mondo <lb></lb>dal <emph type="italics"></emph>Sidereus Nuncius.<emph.end type="italics"></emph.end> I giudizi del Borelli sulle cose galileiane, inspirati <lb></lb>in gran parte dal desiderio di far dispetto all&#039;odiato Viviani, da lui accettati <lb></lb>troppo facilmente, lo inducono a defraudare Galileo della parte che gli spetta <lb></lb>nella invenzione del termometro. </s>

<s>Arrischiato poi, ed in nessun modo giu­<lb></lb>stificato dagli adotti documenti, e nemmeno dalle sue stesse conchiusioni, <lb></lb>non esitiamo ad affermare il tentativo di spogliare Galileo del merito, che <lb></lb>incontrastabilmente gli spetta d&#039;aver scoperta la natura della curva descritta <lb></lb>dai proietti. </s>

<s>E questo noi notiamo colla piena certezza che l&#039;autore, richia­<lb></lb>mato a ponderar meglio questi argomenti, riformerà i suoi giudizi. </s></p><p type="main">

<s>Imperocchè, se a lui, che, forse per il primo, con intelletto d&#039;amore si <pb xlink:href="020/01/032.jpg" pagenum="13"></pb>mise per entro alla ingente mole di manoscritti che rimangono a testificare <lb></lb>della attività dei discepoli di Galileo e di quella dell&#039;Accademia del Cimento, <lb></lb>risultarono in tanta copia cose nuove, anzi nemmeno sospettate: e quei <lb></lb>sommi, la cui luce era in certo qual modo ecclissata dal risplendere del­<lb></lb>l&#039;astro maggiore, apparvero a lui in tutta la effettiva loro grandezza, do­<lb></lb>veva egli serbare anco rispetto ad essi un pò di quel <emph type="italics"></emph>rationabile obseqium<emph.end type="italics"></emph.end><lb></lb>non sempre a proposito adoperato rispetto a Galileo. </s>

<s>Ma questi documenti <lb></lb>gli mancarono per fondarvi gli entusiastici giudizi ch&#039;egli formula sul Sarpi; <lb></lb>imperocchè al nostro autore, di documenti così sottile ed acuto indagatore, <lb></lb>non può essere sfuggito che questi, nello stretto senso della parola, gli fa­<lb></lb>cevano difetto per giudicare l&#039;opera scientifica del celebre Consultore della <lb></lb>Serenissima, e che le relazioni postume d&#039;altri, anzi le stesse sue dichiara­<lb></lb>zioni, vanno accolte col benefizio dell&#039;inventario, imperocchè un ben me­<lb></lb>schino concetto del Sarpi scienziato ci faremmo noi, se, come egli afferma, <lb></lb>dovessimo credere che parlasse o scrivesse delle scoperte annunziate dal <lb></lb><emph type="italics"></emph>Sidereus Nuncius<emph.end type="italics"></emph.end> senza cùrarsi di leggerlo! Del rimanente, troppo era im­<lb></lb>merso il Sarpi negli affari di Stato, sicchè gli rimanesse il tempo neces­<lb></lb>sario a tener dietro al potentissimo impulso che allora appunto ricevevano <lb></lb>le scienze matematiche e naturali: e riconosciamo volentieri, che la mente <lb></lb>potentissima potè suggerirgli idee e concetti originali ed innovatori, i quali <lb></lb>però, essendo monchi per difficoltà di gestazione, rimasero per la maggior <lb></lb>parte infecondi. </s>

<s>Di qui, adunque, al fare del Sarpi l&#039;institutore della prima <lb></lb>accademia sperimentale che sia stata in Italia, il precursore del Gilbert, l&#039;i­<lb></lb>spiratore di Galileo, come pretenderebbe il nostro, ci corre e di molto. </s></p><p type="main">

<s>E, discendendo a cose più minute, ci pare di poter osservare che tal­<lb></lb>volta (benchè assai di rado) gli sia accaduto di non attingere proprio alle <lb></lb>fonti prime, come, per modo di esempio, nella istoria dei metodi primi di <lb></lb>osservazione delle macchie solari, ed ancora là dove con qualche inesattezza <lb></lb>accenna alle esperienze del Keplero per determinare la ragione dell&#039;angolo <lb></lb>d&#039;incidenza all&#039;angolo di rifrazione di un raggio di luce che dall&#039;aria passa <lb></lb>nel vetro; ed in genere anche in qualche altro argomento di ottica, nella <lb></lb>quale l&#039;Autore ci sembra essere meno profondo in confronto di altri argo­<lb></lb>menti. </s>

<s>E ciò che avvertiamo rispetto alle fonti, ripeteremmo volontieri per <lb></lb>certi apprezzamenti. </s>

<s>Cosl, sempre per modo di esempio, della regolare suc­<lb></lb>cessione delle fasi di Venere, come modo per determinare il periodo della <lb></lb>sua rotazione, ci sembra ch&#039;egli parli con qualche leggerezza; così ancora <lb></lb>egli vorrà concederci che, quantunqe lo neghi, possano molto più propria­<lb></lb>mente dirsi microscopi quelle palline di vetro, colle quali tutti ricordiamo <lb></lb>di esserci trastullati nella nostra adolescenza, che non sia somiglianza, la <lb></lb>quale pure egli vorrebbe vedere, tra un pozzo ed un cannocchiale. </s></p><p type="main">

<s>Queste poche, fra molte altre osservazioni di simil genere, le quali <lb></lb>pure potrebbero farsi, abbiamo voluto notare, poichè a quelle della prima <lb></lb>categoria egli potrà facilmente ovviare con una più frequente e regolare ci­<lb></lb>tazione delle fonti, e fors&#039;anche con una più accurata critica di esse, ed a <pb xlink:href="020/01/033.jpg" pagenum="14"></pb>quelle della seconda basterà certamente l&#039;avervi richiamata sopra la dì lui <lb></lb>attenzione. </s>

<s>Enumerare distintamente tutti i punti, nei quali non ci trove­<lb></lb>ressimo completamente d&#039;accordo coll&#039;autore, non è nè nostro ufficio, nè <lb></lb>nostro assunto. </s></p><p type="main">

<s>E poichè vogliamo finirla colle censure, aggiungeremo ancora, che non <lb></lb>siamo d&#039;accordo col nostro autore in certi criteri di selezione, ch&#039;egli vor­<lb></lb>rebbe adottati là dove parla della pubblicazione dei manoscritti vinciani: nè <lb></lb>avremmo notata questa, che potrà anco essere stimata una minuzia, se non <lb></lb>vi vedessimo per entro una questione generale e di altissima importanza. </s>

<s>— <lb></lb>Giusti sono gli appunti che egli fa ai primi editori del trattato di Leonardo <lb></lb>intorno al moto ed alla misura delle acque; ma quando, alla sua volta, egli <lb></lb>applica il suo principio di selezione ad un nuovo ordinamento di questa <lb></lb>magistrale scrittura, è egli proprio ben certo di essere penetrato nelle in­<lb></lb>tenzioni dell&#039;autore? </s>

<s>o piuttosto non è ragionevole il timore di aver sosti­<lb></lb>tuito, al pensiero di quello, il proprio? </s>

<s>e che altri venga poi collo stesso <lb></lb>principio, e creda di farsene più fedele interprete con l&#039;adottare criteri di­<lb></lb>versi di selezione? </s>

<s>Che mai ne verrebbe di tutte le cose vinciane, anzi <lb></lb>di quello stesso Codice Atlantico, il quale, del resto, è cosa ben diversa <lb></lb>da quello che mostra di credere il nostro autore, qualora nella pubblicazione <lb></lb>di esse prevalesse un tale indirizzo? </s>

<s>Quando dieci studiosi avessero fatto <lb></lb>sui manoscritti di Leonardo un lavoro analogo a quello che vi condusse il <lb></lb>Richter, oppure anche adottando i più perfetti criteri di selezione, rimar­<lb></lb>rebbe pur sempre il desiderio della pubblicazione integrale e diplomatica, <lb></lb>poichè ognuno vuole giudicare da sè, e quello che a taluno sfugge, perchè <lb></lb>stimato di poco momento, colpisce tal altro che, in un ordine alquanto di­<lb></lb>verso di idee, lo stima importante; nè l&#039;uomo coscienzioso di studio lascierà <lb></lb>mai in pace quelle carte preziose: e rinunzierà di risalire agli originali sol­<lb></lb>tanto allora, che ne sia stata condotta una edizione conforme a quella che <lb></lb>il Ravaisson-Mollien sta pubblicando, e che per il Codice Atlantico il non <lb></lb>mai abbastanza compianto nostro Govi preparava, facendo opera egregia, de­<lb></lb>gna della patria di Leonardo, e del Re che la promuoveva. </s></p><p type="main">

<s>Queste cose abbiamo voluto notare, perchè, con qualche altra di minor <lb></lb>conto, nell&#039;insieme bene armonizzato di questo ragguardevolissimo lavoro, <lb></lb>ci parvero vere stuonature: “ un corno, un oboè fuori di chiave ” in mezzo <lb></lb>ad un concerto che nel suo complesso appaga lo spirito, sodisfa la mente e <lb></lb>delizia le orecchie. </s>

<s>Ed è invero deliziato il lettore, oltre che dalla sostanza, <lb></lb>dalla forma data all&#039;opera poderosa. </s>

<s>L&#039;Autore, in certo punto del suo lavoro <lb></lb>si dice “ nato per fortuna sulle rive dell&#039;Arno ”: dichiarazione superflua, <lb></lb>poichè, pur non sapendolo, avremmo potuto dirgli: </s></p><p type="main">

<s><emph type="center"></emph>“ La tua loquela ti fa manifesto <lb></lb>Di quella nobil patria natìo ”.<emph.end type="center"></emph.end></s></p><p type="main">

<s>E con uno stile piano e semplice, con una lingua perfetta, con una <lb></lb>forma che incanta e seduce, e ricorda, senza ombra di esagerazione, quella <pb xlink:href="020/01/034.jpg" pagenum="15"></pb>dei grandi, i quali dal suo lavoro rimangono irradiati di novella luce, che <lb></lb>rende meno ispide le non infrequenti dimostrazioni matematiche e mecca­<lb></lb>niche, è condotto il lavoro tutto intero, poichè del vastissimo campo può <lb></lb>ben dirsi che nessun angolo rimanga inesplorato. </s></p><p type="main">

<s>Dei <emph type="italics"></emph>principali strumenti del metodo sperimentale<emph.end type="italics"></emph.end> indaga la storia del <lb></lb>termometro, dell&#039;orologio a pendolo, dei cannocchiali di Galileo, del Fon­<lb></lb>tana, del Torricelli e del telescopio a riflessione, del micrometro, del bino­<lb></lb>culo, del barometro, dell&#039;igrometro, del corno acustico, del pluviometro, del <lb></lb>microscopio, dell&#039;areometro e di altri macchinamenti ingegnosi e curiosi, <lb></lb>nei quali possono ravvisarsi i germi di altri maggiori strumenti, che diedero <lb></lb>celebrità a più recenti inventori. </s></p><p type="main">

<s>Studiando la <emph type="italics"></emph>storia del metodo sperimentale applicato alle scienze fisi­<lb></lb>che,<emph.end type="italics"></emph.end> ne indaga specificatamente le vicende rispetto all&#039;ottica, alla catottrica, <lb></lb>alla dottrica, alle diffrazioni ed alle interferenze, al suono, al calore, al ma­<lb></lb>gnetismo, alla meteorologia, alla geografia, alla cosmografia, all&#039;astronomia <lb></lb>dei pianeti ed a quella del sole, della luna e delle comete. </s></p><p type="main">

<s>La <emph type="italics"></emph>storia del metodo sperimentale applicato alla storia naturale<emph.end type="italics"></emph.end> stu­<lb></lb>dia, esaminandone gli effetti sullo svolgimento dell&#039;anatomia, dell&#039;entomo­<lb></lb>logia, e dedica speciali ricerche alla circolazione del sangue, alla meccanica <lb></lb>dei moti interni, all&#039;ematosi, alla meccanica animale dei movimenti locali, <lb></lb>agli organi dei sensi, alla medicina sperimentale, alla fisiologia delle piante <lb></lb>ed ai sistemi di loro classificazione, e per ultimo alla geologia. </s>

<s>In questa <lb></lb>così ricca rassegna potrebbero per verità notarsi alcune lacune; ma, come <lb></lb>già si è avvertito, furono dall&#039;autore lasciate ad arte, affinchè rimanessero <lb></lb>impregiudicate le questioni che hanno attinenza colla seconda e colla terza <lb></lb>parte del lavoro (alle quali, come s&#039;è detto, sono respettivamente dedicati il <lb></lb>secondo ed il terzo volume), vale a dire colla storia del metodo sperimen­<lb></lb>tale applicato alla scienza del moto dei gravi, ed alla scienza del moto delle <lb></lb>acque. </s></p><p type="main">

<s>E quanto alla seconda parte ecco, colla maggior possibile brevità, come <lb></lb>essa si appresenti al nostro autore. </s></p><p type="main">

<s>Gli studi del moto, benchè fossero da altri, sopra gli insegnamenti di <lb></lb>Archimede, in qualche modo iniziati, non presero nulladimeno ordinamento <lb></lb>di scienza, prima di Galileo, il quale, in un trattatello, che corse a principio <lb></lb>manoscritto, illustrò e completò la teoria delle macchine, e in altre scrit­<lb></lb>ture svolse e formulò i principii archimedei dei moti equabili. </s>

<s>Indagando <lb></lb>tuttavia il cammino, che, su questa via, erasi percorso dai predecessori del <lb></lb>sommo filosofo, avverte il nostro che nessuno aveva pensato di comporre <lb></lb>un trattatello compiuto di meccanica, a quel modo che si fece dell&#039;idraulica, <lb></lb>servendosi dei materiali dispersi per i manoscritti di Leonardo da Vinci; <lb></lb>questo fece l&#039;autore, tenendo conto di ciò che ormai si ha alle stampe, e <lb></lb>giova credere che pregevoli aggiunte gli saranno fornite dalle cose vinciane <lb></lb>pubblicate posteriormente alla presentazione di questo lavoro. </s>

<s>Il trattato poi <lb></lb>della <emph type="italics"></emph>Nuova Scientia<emph.end type="italics"></emph.end> del Tartaglia, conosciuto, ma non curato da Galileo, <pb xlink:href="020/01/035.jpg" pagenum="16"></pb>diligentemente analizzato, apparisce meritevolissimo di storia; e benchè il <lb></lb>matematico bresciano non riuscisse a scoprire la legge dei moti accelerati e <lb></lb>le vere curve descritte dai proietti, apparisce nulladimeno mirabile che tanto <lb></lb>assottigliasse la geometria da costringerla a rivelargli che la massima am­<lb></lb>piezza del tiro avviene quando l&#039;obice è inclinato all&#039;orizzonte di 45.° </s></p><p type="main">

<s>Or dunque i primi studi di Galileo il nostro autore ce li mostra ri­<lb></lb>volti ad assicurarsi dell&#039;errore aristotelico, che teneva le velocità dei gravi <lb></lb>cadenti esser proporzionali alla quantità di materia. </s>

<s>E, <gap></gap>yocata ad esame <lb></lb>la famosa leggenda della lampada nel Duomo di Pisa, pone m luce la sot­<lb></lb>tigliezza mirabile dell&#039;argomentazione di Galileo, il quale pronunziò sicura­<lb></lb>mente, contro Aristotile, quel che non poteva essere confermato che dal­<lb></lb>l&#039;uso della macchina pneumatica, che cioè i gravi nel vuoto scenderebbero <lb></lb>tutti in egual tempo, qualunque pure si fosse la loro mole e la loro materia. </s></p><p type="main">

<s>Nell&#039;investigare la legge sopra esposta, Galileo era stato preceduto da <lb></lb>altri matematici, come dal Moletti e dal Benedetti: nello studio dei moti <lb></lb>equabili pure era stato prevenuto da Archimede o dai numerosi seguaci di <lb></lb>lui. </s>

<s>Rimaneva a scoprir la legge dei moti accelerati, tentata prima invano <lb></lb>da tutti. </s>

<s>E Galileo vi si preparò col chiarirsi bene in mente il principio <lb></lb>d&#039;inerzia, unico fondamento della scienza del moto. </s>

<s>Vuole l&#039;autor nostro che <lb></lb>il pendolo non sia stato da principio per Galileo se non uno strumento <lb></lb>sperimentatore della legge dei gravi cadenti, e che, sperimentando, siasi av­<lb></lb>veduto dell&#039;isocrinismo delle vibrazioni di esso, del qual fatto voleva Galileo <lb></lb>stesso ritrovar la dimostrazione matematica, ma non riusciva a spuntarla; <lb></lb>nè lo spuntarla, per verità, era possibile, non potendo la matematica dimo­<lb></lb>strargli vero quel che la fisica stessa gli accennava esser falso. </s>

<s>Ma, qual ri­<lb></lb>compensa di questi suoi lunghi ed ostinati studi, ebbe la scoperta del bra­<lb></lb>chistocronismo degli archi rispetto alle corde. </s></p><p type="main">

<s>Da questo argomento, nel quale il nostro autore giunge a conchiusioni <lb></lb>importanti e, almeno in parte, nuove, passa a considerare la teoria dei <lb></lb>proietti, la quale, lasciata a mezzo dal Tartaglia, fu ripresa da Galileo nei <lb></lb>primi suoi studi giovanili. </s>

<s>Ci narra come fossero incerti que&#039;primi passi e <lb></lb>fallaci, e più tontani dal vero di quel che ne fossero gli stessi suoì prede­<lb></lb>cessori. </s>

<s>Ripigliando il soggetto de&#039;moti accelerati ci descrive l&#039;esperienza <lb></lb>galileiana che condusse il suo autore ad accertarsi come veramente gli spazi <lb></lb>sono proporzionali ai quadrati dei tempi, e ci narra in che modo Galileo <lb></lb>stesso riuscisse alla dimostrazione matematica di questa nuova legge da sè <lb></lb>scoperta, ammettendo che le velocità son sempre e costantemente in ragion <lb></lb>del tempo. </s></p><p type="main">

<s>Dopo la dimostrazione della legge dei moti accelerati, mostra occorsa a <lb></lb>Galileo una nuova scoperta sui proietti, la quale consisteva nell&#039;avere ritro­<lb></lb>vato per esperienza che il proietto stesso descrive la curva in quel mede­<lb></lb>simo tempo, che abbandonato a sè, per impulso della gravità naturale, <lb></lb>avrebbe passato il perpendicolo. </s></p><p type="main">

<s>Narrati così i particolari storici di questa scoperta, passa il nostro Au-<pb xlink:href="020/01/036.jpg" pagenum="17"></pb>tore a far la storia di altre scoperte galileiane non meno importanti, e son <lb></lb>quelle che risguardano la resistenza dei solidi allo spezzarsi. </s>

<s>Di questi nuovi <lb></lb>studi meccanici si contano qui i principì, e si risguardano come precipua <lb></lb>parte del trattato <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> rimasto, fino a questi ultimi tempi, inedito, e <lb></lb>a cui poi suplì l&#039;autore colla pubblicazione de&#039;<emph type="italics"></emph>Dialoghi delle due Nuove <lb></lb>Scienze.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Giudicasi pertanto in questa storia, la quale noi andiamo fedelmente <lb></lb>seguendo, che non piacendo a Galileo la forma latina e l&#039;ordine dato alle <lb></lb>prime scritture <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> e d&#039;altra parte le questioni astronomiche recla­<lb></lb>mando più sollecita pubblicazione delle meccaniche, ne&#039;<emph type="italics"></emph>Dialoghi dei due <lb></lb>Massimi Sistemi<emph.end type="italics"></emph.end> avrebbe pensato di inserirvi tutte le scoperte da lui fatte <lb></lb>infino a quel tempo, rispetto alle proprietà ed alle leggi dei moti, ed è <lb></lb>perciò che non trovando quivi nemmeno il più lontano sentore che la curva <lb></lb>di proiezione potesse essere una parabola, è condotto il nostro alla tratta­<lb></lb>zione erronea, della quale abbiamo già tenuto parola, rispetto alla parte che <lb></lb>in questa scoperta egli vorrebbe fare al Cavalieri. </s></p><p type="main">

<s>Segue in appresso accuratamente tracciata la storia dei dialoghi ma­<lb></lb>noscritti dello Nuove Scienze e delle vicende subìte nella loro pubblicazione, <lb></lb>narrando in particolar modo come riuscisse a Galileo di dimostrare la se­<lb></lb>conda e terza legge dei moti pendolari, e come, soltanto allora, secondo che <lb></lb>il nostro opina, pensasse di servirsene alla misura dei minimi tempi; inve­<lb></lb>stigando poi e svolgendo quel sottilissimo filo di dimostrazioni, che, dipen­<lb></lb>dendo da due o tre proposizioni fondamentali, compongono il terzo dialogo <lb></lb>di esse Nuove Scienze, chiarisce qual si fosse il primo processo dello di­<lb></lb>mostrazioni di Galileo sui numerosi teoremi dei moti accelerati, come questo <lb></lb>processo fosse emendato nella pubblicazione del terzo dialogo surriferito, e <lb></lb>come, dopo la pubblicazione, coll&#039;aiuto del Torricelli, pensasse a dare altro <lb></lb>ordine e più chiarezza alle sue dimostrazioni, quando a quella di Leida <lb></lb>avessero dovuto succedere altre edizioni. </s></p><p type="main">

<s>Il confronto fra le dimostrazioni sui proietti pubblicate, e le anteriori <lb></lb>e le posteriori alla pubblicazione di Leida, rimaste quest&#039;ultime manoscritte <lb></lb>nei codici galileiani, e la dimostrazione data dal sommo filosofo della com­<lb></lb>posizione delle forze richiamano in appresso tutta l&#039;attenzione del nostro <lb></lb>autore. </s></p><p type="main">

<s>Alla prima edizione di Leida, che si componeva di soli quattro dialoghi, <lb></lb>se ne aggiunsero dagli editori seguenti altri due: il quinto che è della <lb></lb>scienza universale delle proporzioni, e il sesto della forza della percossa. </s>

<s><lb></lb>Del ritrovamento e delle vicende subìte dal manoscritto di questo ultimo dia­<lb></lb>logo o Congresso, come chiamavalo Galileo, è fatto soggetto particolare di <lb></lb>storia, concludendo che egli lo ripudiò, e che, quando non lo avesse così <lb></lb>ripudiato, quel dialogo doveva andare in ordine il quinto e non il sesto. </s></p><p type="main">

<s>Stabilito poi, come uno dei fondamenti dell&#039;edifizio galileiano fosse il <lb></lb>principio che due gravi hanno acquistato una ugual velocità, dopo essere <lb></lb>scesi per due diverse linee, le quali però abbiano una medesima caduta, <pb xlink:href="020/01/037.jpg" pagenum="18"></pb>principio dapprima supposto per vero, si mostra, come, dopo la pubblica­<lb></lb>zione dei dialoghi, riuscisse a Galileo di trovare quella dimostrazione, e come <lb></lb>la divulgasse fra gli amici e gli scolari. </s></p><p type="main">

<s>Dopo i dialoghi delle Nuove Scienze sono presi in esame il trattato del <lb></lb>Baliani, ponendo in chiaro come da esso differisca quello del Torricelli, e <lb></lb>tutta la importanza che rivestono quelli del Borelli, e dimostrandosi come, <lb></lb>se fossero noti al mondo i manoscritti del Viviani, apparirebbe assai più <lb></lb>evidente com&#039;egli fu dei primi, dei più assidui e de&#039;più strenui propugna­<lb></lb>tori e promulgatori delle dottrine galileiane concernenti la scienza del moto. </s></p><p type="main">

<s>Infine l&#039;autore nostro ha voluto prendere in esame alcune difficoltà pro­<lb></lb>mosse contro le dottrine galileiane dagli scienziati stranieri intrattenendosi più <lb></lb>particolarmente a far rilevare le incongruenze e gli invidiosi fastidi cartesiani. </s></p><p type="main">

<s>Ed ora, con analisi altrettanto rapida, prendiamo in esame il terzo ed <lb></lb>ultimo volume. </s></p><p type="main">

<s>Come ogni parte di scienza sperimentale in Italia incomincia con Ga­<lb></lb>lileo, così il nostro autore dà principio alla storia dell&#039;applicazione di essa <lb></lb>alle dottrine intorno al moto delle acque, esponendo le speculazioni e le espe­<lb></lb>rienze, colle quali il nuovo Archimede promosse la scienza dell&#039;equilibrio <lb></lb>de&#039;liquidi, iniziata già dall&#039;Archimede antico. </s>

<s>Passa poi a narrare come e <lb></lb>quando il Castelli riuscisse a formulare ed a dimostrare geometricamente le <lb></lb>proposizioni fondamentali di questa scienza, che cioè le quantità dell&#039;acqua <lb></lb>fluente da una luce son proporzionali alla velocità moltiplicata per la se­<lb></lb>zione; narrando poi come, da questa, il Castelli stesso svolgesse una serie <lb></lb>di proposizioni o teoremi, che compongono il primo libro della <emph type="italics"></emph>misura delle <lb></lb>acque correnti.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Opportunamente avverte l&#039;autore, che il Bisenzio fu in Toscana il primo <lb></lb>fiume, a cui si applicassero le nuove leggi idrauliche già scoperte, e perciò <lb></lb>egli prende a narrare l&#039;occasione ed il modo particolare di questa applica­<lb></lb>zione; e, sottoponendo a diligente esame storico-critico le dottrine meccanico­<lb></lb>idrauliche professate da Galileo nella lettera o trattato del fiume Bisenzio, <lb></lb>discute la celebre questione insorta fra lui e Andrea Arrighetti. </s>

<s>Con altret­<lb></lb>tanta diligenza viene poi esaminata l&#039;altra delle scritture idrauliche galileiane <lb></lb>rimasteci, cioè il breve discorso contro il Bertizzolo. </s>

<s>Ritorna poi al Castelli, <lb></lb>il quale, preparandosi con speculazioni ed esperienze nuove a risolvere la <lb></lb>questione della laguna veneta, s&#039;abbattè a scoprire un fatto, nella dimo­<lb></lb>strazione del quale lo sovvenne il Cavalieri; e degli incidenti a questo ar­<lb></lb>gomento relativi è fornita una narrazione particolareggiata ed importante. </s></p><p type="main">

<s>Il regolamento delle Chiane, morto Galilei, fu uno dei primi e princi­<lb></lb>pali problemi offertisi a risolvere a&#039;discepoli di lui. </s>

<s>Il Michelini proponeva, <lb></lb>per velocitarne il corso, di abbassar lo sbocco del fiume; il Torricelli si op­<lb></lb>poneva, propugnando il principio che le velocità sono da regolarsi, non se­<lb></lb>condo il declivio dell&#039;alveo, ma della superficie dell&#039;acqua. </s>

<s>Le fasi diverse <lb></lb>di questo dibattito sono accuratamente studiate dal nostro autore nelle cause <lb></lb>e nelle conseguenze. </s></p><pb xlink:href="020/01/038.jpg" pagenum="19"></pb><p type="main">

<s>Il secondo libro del Castelli, essendo postumo, qui, coll&#039;appoggio prin­<lb></lb>cipale di inediti documenti, si fa la storia del manoscritto, si narra come, <lb></lb>e fino a qual punto, lo pubblicasse il Barattieri, e si passa poì a far la storia <lb></lb>della pubblicazione del Dozza, nella quale storia si narrano fedelmente, per <lb></lb>la prima volta, le emendazioni della proposizione seconda: emendazioni pro­<lb></lb>poste dal principe Leopoldo, da poi che si avvertì che la legge della velo­<lb></lb>cità conclusa in quella stessa proposizione, non consentiva con quell&#039;altra <lb></lb>scoperta e dimostrata dal Torricelli. </s></p><p type="main">

<s>Il nome di Gio. </s>

<s>Battista Barattieri è assai ben noto nella scienza; ma <lb></lb>ignorasi quasi affatto quello del discepolo di Galileo, Cosimo Noferi, la <emph type="italics"></emph>Tra­<lb></lb>vagliata Architettura<emph.end type="italics"></emph.end> del quale è rimasta inedita, in quattro volumi. </s>

<s>Sem­<lb></lb>brando pertanto al nostro autore che fossero meritevoli di qualche notizia, <lb></lb>egli vien rendendone conto. </s>

<s>In molti particolari entra egli in appresso ri­<lb></lb>spetto a Famiano Michelini ed alla storia del famoso trattato della <emph type="italics"></emph>Direzione <lb></lb>dei fiumi,<emph.end type="italics"></emph.end> principalmente per ciò che concerne il principio in esso profes­<lb></lb>sato e per il quale l&#039;acqua eserciterebbe tutta la sua pressione sul fondo e <lb></lb>pochissimo o nulla sulle sponde del vaso. </s>

<s>Del principio della eguaglianza <lb></lb>delle pressioni ignorato dal Michelini e da molti altri de&#039;nostri italiani, <lb></lb>viene attribuito il merito della scoperta al Pascal; ma si dimostra qui che <lb></lb>il Torricelli l&#039;aveva trovato parecchi anni prima e ne aveva fatta l&#039;applica­<lb></lb>zione al barometro. </s>

<s>Vincenzio Viviani è conosciuto solamente per i suoi di­<lb></lb>scorsi di idraulica pratica relativi al regolamento dell&#039;Arno; ma che fosse <lb></lb>uno dei più infaticabili in idrometria, confermando con nuove dimostra­<lb></lb>zioni geometriche e con nuove esperienze i principì del Torricelli, espone <lb></lb>e dimostra il nostro autore, producendone ed illustrandone gli scritti ine­<lb></lb>diti: il quale poi ci addita in Geminiano Montanari il primo che applicasse <lb></lb>la scienza all&#039;idrografia dei mari, ed in Bernardino Ramazzini lo scopritore <lb></lb>dei pozzi artesiani. </s></p><p type="main">

<s>L&#039;idrometria restava tuttavia incerta fra la legge supposta dal Castelli <lb></lb>e la dimostrata dal Torricelli: e qui il nostro autore segnala l&#039;intervento <lb></lb>del Cassini, i cui progressi idraulici sono diligentemente narrati, notandosi <lb></lb>come intorno a questo tempo entrino ad ingerirsi di tali studi anco gli stra­<lb></lb>nieri, fra i quali il Varignon, di cui si dimostrano gli errori commessi in <lb></lb>voler analiticamente confermare la legge delle velocità scoperta dal Torri­<lb></lb>celli. </s>

<s>Detto della invenzione degli idrometri, entra a discorrere del trattato <lb></lb>del Guglielmini sulla misura delle acque correnti, in cui si introducono per <lb></lb>la prima volta nell&#039;idrometria le velocità medie e si conferma con nuove e <lb></lb>solenni esperienze la legge torricelliana; nonchè delle tre celebri lettere <lb></lb>idrostatiche, nelle quali esso Guglielmini si difende contro le imputazioni del <lb></lb>Papin, sciogliendo il problema nuovo delle velocità dell&#039;acqua ne&#039;tubi pieni. </s>

<s><lb></lb>E, nel narrare questa parte di storia, nota il nostro autore come, a propo­<lb></lb>sito dell&#039;intervento della pressione dell&#039;aria in que&#039;fatti idraulici, prendesse il <lb></lb>Guglielmini occasione di illustrare magistralmente la teoria del barometro. </s></p><p type="main">

<s>Nè sono trascurate le applicazioni che all&#039;idraulica fece dei teoremi di <pb xlink:href="020/01/039.jpg" pagenum="20"></pb>meccanica il Grandi, nè le contribuzioni del Poleni allo studio delle leggi <lb></lb>d&#039;efflusso attraverso alle diverse figure di tubi addizionali, nè gli sperimenti <lb></lb>del Michelotti, e nemmeno i fiumi artificiali del Genetti. </s></p><p type="main">

<s>L&#039;origine dei fiumi, che fu già soggetto di poema, si fa or qui sog­<lb></lb>getto di storia, prima di parlar della legge degli alvei, dentro cui scorrono <lb></lb>i fiumi. </s>

<s>Notasi in appresso che prima di Galileo e del Guglielmini, gli idrau­<lb></lb>lici, rispetto agli alvei, versavano in molti errori, i quali furono tolti di <lb></lb>mezzo, ed è minutamente narrato come riuscisse al Guglielmini di asse­<lb></lb>gnare le leggi allo stabilirsi degli alvei stessi. </s></p><p type="main">

<s>Col trattato della natura dei fiumi il nostro Autore ci mostra compiuto <lb></lb>il grande edifizio iniziato nelle poche pagine del Castelli. </s>

<s>I successori del <lb></lb>Guglielmini egli ce li addita intenti a confermare e ad illustrare le dottrine <lb></lb>di lui, nella quale opera designa particolarmente il Manfredi, lo Ximenes, <lb></lb>il Lecchi, lo Zendrini, il Frisi e il Perelli, di ciascun dei quali rende bre­<lb></lb>vemente conto in quest&#039;ultimo capitolo della sua storia. </s></p><p type="main">

<s>Ora, nonostante la vastità, la quale, senza ombra di esagerazione, è da <lb></lb>dirsi imponente, di questo lavoro, che l&#039;autore vorrà certamente corredare <lb></lb>di copiosi indici per nomi e per materie, possiamo noi conchiudere che esso <lb></lb>risolva completamente il quesito, quale fu posto dall&#039;Istituto? </s>

<s>A questo <lb></lb>dobbiamo sinceramente rispondere che, mentre il quadro delle origini e <lb></lb>dello sviluppo del metodo sperimentale in Italia è magistralmente condotto <lb></lb>fino agli ultimi discepoli, anzi quasi fino agli ultimi discepoli dei discepoli <lb></lb>di Galileo, pure esso non è proseguito fino a comprendervi la scoperta della <lb></lb>pila voltaica, come tassativamente era stato dall&#039;Istituto richiesto. </s></p><p type="main">

<s>Ma altrettanto sinceramente dobbiamo dichiarare, che quella monografia, <lb></lb>per modo di dire più ristretta, alla quale la vostra Giunta aveva esplicita­<lb></lb>mente accennato nell&#039;aprire per la seconda volta il concorso, e la quale si <lb></lb>convenne sarebbe tornata bene accetta all&#039;Istituto ed avrebbe potuto essere <lb></lb>giudicata meritevole di premio, viene ad essere ad esuberanza rappresentata, <lb></lb>e in modo che, toltene alcune mende, non potrebbe, per originalità di ri­<lb></lb>cerche, profondità di vedute e coscienza di studi desiderarsi migliore, da <lb></lb>questo lavoro: e che noi stimiamo per esso pienamente soddisfatta la volontà <lb></lb>del testatore, dal quale l&#039;Istituto ebbe incarico di conferire il premio: <emph type="italics"></emph>“ a <lb></lb>chi detterà meglio la storia del metodo sperimentale in Italia ”.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Venezia, li 16 febbraio 1890. </s></p><p type="main">

<s>Dott. </s>

<s>ANGELO MINICH </s></p><p type="main">

<s>GIUSEPPE LORENZONI <lb></lb></s></p><p type="main">

<s>ANTONIO FAVARO <emph type="italics"></emph>Relatore.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/040.jpg"></pb><p type="main">

<s><emph type="center"></emph>AVVERTIMENTO<emph.end type="center"></emph.end></s></p><p type="main">

<s>Citiamo, coll&#039;abbreviatura <emph type="italics"></emph>Alb.,<emph.end type="italics"></emph.end> l&#039;opere complete di Galileo stampate in Firenze, dal <lb></lb>1842 al 1856, dalla società editrice fiorentina, in quindici tomi, con più un tomo di <emph type="italics"></emph>Sup­<lb></lb>plemento,<emph.end type="italics"></emph.end> sotto la direzione di Eugenio Albèri. </s>

<s>Il numero romano indica il tomo, l&#039;arabo <lb></lb>la pagina. </s></p><p type="main">

<s>I manoscritti galileiani, esistenti nella R. </s>

<s>Biblioteca Nazionale di Firenze, si citano <lb></lb>colla seguente abbreviatura: <emph type="italics"></emph>MSS. Gal. </s>

<s>Divis.... P.... T.... c....<emph.end type="italics"></emph.end> che vuol dire <emph type="italics"></emph>Ma­<lb></lb>noscritti galileiani, Divisione.... Parte.... Tomo .... carle ....<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Coll&#039;abbreviatura <emph type="italics"></emph>MSS. Gal. </s>

<s>Disc.<emph.end type="italics"></emph.end> s&#039;indica la Divisione IV dei medesimi Manoscritti <lb></lb>appartenenti ai varii e numerosi Discepoli di Galileo, e il numero romano indica il tomo, <lb></lb>l&#039;arabo la carta. </s></p><p type="main">

<s>Per l&#039;abbreviatura in ultimo <emph type="italics"></emph>MSS. Cim.<emph.end type="italics"></emph.end> s&#039;indica la Divisione V, che è dei Poste­<lb></lb>riori di Galileo o degli Accademici del Cimento, e, al solito, co&#039;due numeri che segui­<lb></lb>tano appresso s&#039;accenna al tomo corrispondente e alla carta. </s></p><p type="main">

<s>Perchè poi gli studiosi, che volessero riscontrare le nostre citazioni sui Manoscritti, <lb></lb>sentiranno il bisogno di rilevarne più largamente il senso da tutto il contesto, abbiamo <lb></lb>creduto inutile, citando la carta, d&#039;indicar se il passo trascritto o accennato si trovi pre­<lb></lb>cisamente nella prima fronte o nel tergo. </s></p><p type="main">

<s>Spesso, di alcuni documenti che videro la pubblica luce, per opera del Nelli, del Tar­<lb></lb>gioni, del Fabbroni e di altri, citiamo il Manoscritto, piuttosto che la stampa, e ciò si fa <lb></lb>da noi, quando i Documenti stessi non sieno stati pubblicati con quella integrità o con <lb></lb>quella fedeltà, che, a parer nostro, richiedeva l&#039;importanza del soggetto. <pb xlink:href="020/01/041.jpg"></pb></s></p><pb xlink:href="020/01/042.jpg"></pb><p type="main">

<s><emph type="center"></emph>DELL&#039;ORIGINE E DE&#039;PROGRESSI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEL<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>METODO SPERIMENTALE IN ITALIA<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DISCORSO PRELIMINARE<emph.end type="center"></emph.end><pb xlink:href="020/01/043.jpg"></pb></s></p><pb xlink:href="020/01/044.jpg"></pb><p type="main">

<s><emph type="center"></emph>PARTE PRIMA<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del primo acquisto delle cognizioni. </s>

<s>— II. </s>

<s>Platone e Aristotile. </s>

<s>— III. </s>

<s>Della Filosofia naturale de­<lb></lb>rivata dall&#039;Accademia e dal Peripato — IV. </s>

<s>Come le due Filosofie, la platonica e l&#039;aristotelica, <lb></lb>venissero a introdursi nella Società cristiana. </s>

<s>— V. De&#039;medici peripatetici: Girolamo Fracastoro, <lb></lb>Andrea Cisalpino. </s>

<s>— VI Girolamo Cardano, Giuseppe Scaligero, Niccolò Tartaglia. </s>

<s>— VII. </s>

<s>Dei <lb></lb>filosofi razionalisti: Francesco Patrizio, Bernardino Telesio, Giordano Bruno e Tommaso Cam­<lb></lb>panella — VIII. De&#039;frutti di scienza naturale raccolti nel secolo XVI dalle tre Filosofie, acca­<lb></lb>demica, peripatetica e razionalistica. </s>

<s>— IX. De&#039;cultori dell&#039;arte, veri precursori del metodo <lb></lb>sperimentale; Dante Alighieri, Leon Battista Alberti, Cristoforo Colombo e Amerigo Vespucci. </s>

<s>— <lb></lb>X. </s>

<s>Leonardo da Vinci — XI. </s>

<s>Degli anatomici padovani del secolo XVI, e segnatamente di <lb></lb>Realdo Colombo — XII. </s>

<s>Come nel secolo XVI gli esercizi sperimentali e le notizie dei fatti <lb></lb>naturali si diffondessero dai libri d&#039;uomini letterati: Giovan Battista Porta e Ferrante Impe­<lb></lb>rato. </s>

<s>— XIII. De&#039;più immediati precursori e cooperatori alla grande Instaurazione galileiana: <lb></lb>Giovan Battista Benedetti e Santorre Santorio. </s>

<s>— XIV. </s>

<s>Paolo Sarpi. </s>

<s>— XV. Dell&#039;Accademia <lb></lb>de&#039;Lincei e di Francesco Bacone </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Accingendoci alla difficile opera di narrare le recondite vie, <lb></lb>proseguendo le quali l&#039;uomo giunse all&#039;acquisto delle cognizioni <lb></lb>sperimentali, sentiamo vivo il bisogno di risalir col nostro pensiero <lb></lb>a ricercar, nel nostro intelletto, l&#039;origine prima, e, se tanto avre­<lb></lb>mo di forza, il principio delle nostre cognizioni e le fonti naturali. </s>

<s><lb></lb>Questa ultima espressione valga intanto ad assicurare i lettori che <lb></lb>non saremo per condurli attraverso agli aerei campi de&#039;metafisici, <lb></lb>nè per menarli in giro fra le combattenti schiere de&#039;filosofi spe­<lb></lb>culativi, ma, indossata oramai la divisa di storici del Metodo spe­<lb></lb>rimentale applicato all&#039;acquisto delle verità naturali, dello stesso <pb xlink:href="020/01/045.jpg" pagenum="26"></pb>metodo sperimentale ci serviremo pure a investigar l&#039;origine prima <lb></lb>e i progressi delle nostre cognizioni. </s></p><p type="main">

<s>I fantastici sistemi dei così detti Ontologi, e lo sbagliato me­<lb></lb>todo dei sensisti loro oppositori, sembrò, nel secolo scorso, che <lb></lb>fossero consigliati di posar l&#039;armi e di ridursi al silenzio da quel <lb></lb>Tommaso Reid, capo della scuola scozzese, che primo insegnò d&#039;in­<lb></lb>vestigar le leggi dell&#039;intelletto dietro la diligente osservazione dei <lb></lb>fatti. </s>

<s>I pedagogisti poi, nel presente secolo, seppero sapientemente <lb></lb>trar pro da que&#039;nuovi e fecondi ammaestramenti, e la Necker e il <lb></lb>Guillemon, nello studio amoroso della vita degl&#039;infanti, raccolsero <lb></lb>così gran numero di osservazioni, che si potè, dietro ad esse, sco­<lb></lb>prire sperimentalmente la legge, secondo la quale, in principio, <lb></lb>l&#039;uomo ama ed intende. </s>

<s>Proseguendo questo stesso metodo d&#039;in­<lb></lb>terne osservazioni Alessandro Manzoni, nel suo Romanzo, ci dipinse <lb></lb>tale qual&#039;è il cuore dell&#039;uomo, e Raffaello Lambruschini, ne&#039;suoi <lb></lb>Dialoghi, espose eloquentemente agli italiani la detta legge del­<lb></lb>l&#039;amare e dell&#039;intendere, scoperta così dietro a quelle nuove espe­<lb></lb>rienze. </s></p><p type="main">

<s>Una delle principali e delle più importanti conclusioni, che de­<lb></lb>rivarono immediatamente da così fatte esperienze, fu che le prime <lb></lb>notizie delle cose hanno origine nell&#039;intelletto da tutt&#039;altra fonte <lb></lb>che dai sensi. </s>

<s>Il Reid argomenta, dietro accurate osservazioni, che <lb></lb>il primo oggetto conosciuto dal bambino è la sua propria madre, <lb></lb>e ch&#039;ei la conosce e intende non altrimenti, che come un essere <lb></lb>intelligente ed amante. </s>

<s>Il primo linguaggio, secondo il filosofo scoz­<lb></lb>zese, con cui la donna si comunica col portato delle sue viscere, <lb></lb>è il linguaggio dell&#039;amore: importantissima scoperta, per la quale <lb></lb>si rende solubile il problema dell&#039;origine del linguaggio stesso, es­<lb></lb>sendo incongruente quel che pareva ammettersi, prima, da&#039;filosofi, <lb></lb>che cioè si possa la parola insegnare per mezzo della parola. </s></p><p type="main">

<s>Da queste nuove dottrine, e da quelle, altresì, più antiche, <lb></lb>scende un&#039;altra importantissima conclusione, ed è la necessità delle <lb></lb>tradizioni. </s>

<s>La fiaccola dell&#039;intelletto par che imiti strettamente <lb></lb>l&#039;esempio di queste nostre fiaccole artificiali, le quali non si accen­<lb></lb>dono, se non che nella luce di un altra fiaccola, che a loro si ap­<lb></lb>pressi. </s>

<s>Le osservazioni dei nuovi filosofi o psicologi sperimentali, <lb></lb>non che la storia dell&#039;umano incivilimento, dimostrano quella ne­<lb></lb>cessità degl&#039;insegnamenti tradizionali con evidentissima prova di <lb></lb>fatti. </s>

<s>È perciò la necessità delle tradizioni una legge, alla quale <lb></lb>inesorabilmente soggiace ogni svolgimento dell&#039;umano pensiero, <pb xlink:href="020/01/046.jpg" pagenum="27"></pb>cosicchè l&#039;ammettere l&#039;esistenza d&#039;ingegni veramente <emph type="italics"></emph>creatori<emph.end type="italics"></emph.end> è un <lb></lb>errore in filosofia, com&#039;è un errore in fisica l&#039;ammettere la gene­<lb></lb>razione spontanea. </s></p><p type="main">

<s>Non dissimuliamo che la legge ora annunziata viene a porre <lb></lb>in grande impaccio i neoterici, i quali ammettono che, così nel­<lb></lb>l&#039;ordine cosmico, come nell&#039;intellettuale, tutto sia giunto per sè <lb></lb>al presente grado di perfezione, per via di successivo, graduale e <lb></lb>spontaneo svolgimento. </s>

<s>Che se, non potendo conciliare i fatti con <lb></lb>la necessità che li governa, alcuni altri sapienti ammettono un prin­<lb></lb>cipio prestabilito all&#039;ordine mondano e una primitiva civiltà rive­<lb></lb>lata, hanno tuttavia diritto di credere nell&#039;esistenza di quel primo <lb></lb>Architettore del mondo e di quel primo Maestro dell&#039;uomo, che <lb></lb>essi appellano col nome di Dio, infintanto che gli scienziati novelli <lb></lb>non sieno giunti a dimostrar con più di evidenza le misteriose ori­<lb></lb>gini della civiltà e del cosmo. </s></p><p type="main">

<s>Dell&#039;ammettere l&#039;esistenza di quel primo Maestro, che per mezzo <lb></lb>della madre si comunica al bambinello, sentirono vivamente il bi­<lb></lb>sogno, così il Reid, come i pedagogisti inspiràti agl&#039;insegnamenti <lb></lb>di lui, e negando, anzi, come si disse, che le prime notizie appro­<lb></lb>dino alla mente per via dei sensi, non dubitarono d&#039;affermar che <lb></lb>l&#039;intelletto s&#039;apre alla luce di Dio, come s&#039;apre il fiore al primo <lb></lb>raggio di sole. </s>

<s>Dio che è luce, l&#039;intelletto umano, il qual è l&#039;occhio <lb></lb>che vede, gli esseri creati, che s&#039;irraggiano di quella divina luce <lb></lb>e la riflettono al veggente, formano il soggetto e compongono l&#039;en­<lb></lb>ciclopedia di tutto il nostro sapere. </s>

<s>Lasciando ad altri di trattar la <lb></lb>scienza che riguarda il primo e il secondo di que&#039;soggetti, quel che <lb></lb>importa a noi non è propriamente che il terzo, le prime notizie del <lb></lb>quale vediamo com&#039;incominci ad apprenderle il bambino. </s></p><p type="main">

<s>O rivolga egli spontanea l&#039;attenzione agli oggetti circostanti, o <lb></lb>alcuno, vezzeggiandolo, glieli presenti innanzi e lo inviti e lo alletti <lb></lb>a riguardarli, lo vediamo immobile e contemplativo tener fissi gli <lb></lb>occhi in que&#039;medesimi oggetti. </s>

<s>Dop&#039;esser rimasto alquanto in quella <lb></lb>estatica contemplazione, il bambinello, che non ha ancora incomin­<lb></lb>ciato a pigliar possesso del mondo, se l&#039;oggetto in qualche modo <lb></lb>lo alletta, colla bellezza delle forme esteriori e del colore, stende <lb></lb>innanzi il braccio e apre la mano per prendersi quell&#039;oggetto, ma <lb></lb>è notabile ch&#039;ei non si sporga punto per aggiungerlo, cosicchè se <lb></lb>gli riesce più lontano di quel che bisogni per toccarlo, mena a vuoto <lb></lb>a tresca per l&#039;aria con quel braccio teso e con quella manina aperta. </s>

<s><lb></lb>Questo è segno che egli non ha ancora imparato a misurar la di-<pb xlink:href="020/01/047.jpg" pagenum="28"></pb>stanza, e che i visibili oggetti gli si presentano come se fossero <lb></lb>dipinti sopra una tela calatagli innanzi agli occhi. </s>

<s>Di qui viene <lb></lb>ad acquistare la prima idea dello spazio superficiale, circoscritto <lb></lb>all&#039;intorno dal più semplice e regolare de&#039;perimetri, il cerchio. </s>

<s><lb></lb>L&#039;esercizio poi e l&#039;uso che egli arcanamente impara a fare degli <lb></lb>argomenti della parallasse, lo rendono accorto dell&#039;altra dimensione <lb></lb>dello spazio, della profondità, cosicchè dalla superficie passa ad <lb></lb>acquistar l&#039;idea del solido e dalla nozione del cerchio passa a quella <lb></lb>dell&#039;emisfero. </s>

<s>È la geometria dunque la prima scienza che l&#039;uomo <lb></lb>impara, e la prima arte che lo guida in acquistar le prime notizie <lb></lb>del mondo creato. </s>

<s>Quel bambinello intanto, il quale aveva poco più <lb></lb>che quaranta giorni, ha passato già dell&#039;età sua il primo anno. </s>

<s>Tor­<lb></lb>niamo ad osservarne gli atti, e a veder quali novità presentano i <lb></lb>suoi costumi. </s>

<s>Non è più, com&#039;allora, estatico e contemplativo: ei <lb></lb>si vede anzi vivameute commosso alle impressioni che fanno sopra <lb></lb>lui gli oggetti esteriori, e alcuni lo impauriscono, per cui rifugge <lb></lb>strillando da loro, e altri lo allettano, e sorridendo si sporge per <lb></lb>averli, e avutili, desiderosamente, gli stringe e se ne impossessa. </s>

<s><lb></lb>Non si contenta più di contemplare con gli occhi l&#039;esteriore appa­<lb></lb>renza di quelle cose, ma le stringe fortemente fra le sue mani, per <lb></lb>renderne più intimo e più squisito il contatto, le lacera quasi vo­<lb></lb>lesse penetrare a veder quel che v&#039;è dentro e sotto esse nascosto, <lb></lb>e tanta avidità ha di compenetrarsi con quelli oggetti, che tutto <lb></lb>vorrebbe cacciar dentro alla sua bocca. </s>

<s>L&#039;altro passo dunque che <lb></lb>fa l&#039;uomo, per pigliar pieno possesso del mondo è quello dell&#039;eser­<lb></lb>cizio de&#039;sensi e dell&#039;arte dell&#039;esperienza. </s></p><p type="main">

<s>Ma prima di giungere a questo secondo passo, proseguendo per <lb></lb>la dirittura di quella via, che conduce l&#039;uomo alle prime notizie del <lb></lb>mondo creato, percorre una via traversa, e si direbbe perciò che <lb></lb>delira. </s>

<s>Alla serena contemplazione che abbiamo ammirata dianzi, <lb></lb>prima che il bambino passi a quella sua vivacità di atti per cui il <lb></lb>mondo si assoggetta a&#039;suoi sensi; succede una specie d&#039;irrequie­<lb></lb>tezza, la quale non è poi altro se non che l&#039;effetto di un segreto <lb></lb>orgoglioso delirio. </s>

<s>Il bambino è irrequieto, perchè vorrebbe che il <lb></lb>mondo procedesse a modo suo, e prima d&#039;imparar che il mondo <lb></lb>si governa con leggi sue proprie, vorrebbe esser egli il legislatore <lb></lb>del mondo. </s></p><p type="main">

<s>La storia, che abbiamo così a chiare note letta, in quel micro­<lb></lb>cosmo intellettuale, è la storia che si verifica nella vita dell&#039;uomo <lb></lb>adulto, anzi è la storia dell&#039;origine e de&#039;progressi che conducono <pb xlink:href="020/01/048.jpg" pagenum="29"></pb>tutto un popolo incivilito all&#039;acquisto delle verità naturali. </s>

<s>Dalle <lb></lb>osservazioni fatte sopra il bambino risulta che, degli oggetti creati, <lb></lb>prima acquista notizia della forma, per mezzo della geometria, e <lb></lb>poi della materia per mezzo dei sensi e dell&#039;esperienza. </s>

<s>Così, basta <lb></lb>appena volgere un occhiata fuggitiva alla storia della scienza, per <lb></lb>vedere che, in ogni periodo d&#039;incivilimento prima sono state a fio­<lb></lb>rire le scienze matematiche e poi le fisiche. </s>

<s>Nelle stesse scienze <lb></lb>fisiche matematiche si verifica pure la medesima legge. </s>

<s>L&#039;astrono­<lb></lb>mia matematica, per esempio, precede all&#039;astronomia fisica, e alla <lb></lb>meccanica razionale precede la scienza astratta del moto. </s>

<s>La Fisica, <lb></lb>la Chimica e la Geologia, il soggetto delle quali è più remoto dalla <lb></lb>forma e più prossimo che mai alla materia, sono scienze apparite <lb></lb>via via in questi tre ultimi secoli. </s></p><p type="main">

<s>Tali semplicissime osservazioni storiche dei fatti bastano a per­<lb></lb>suader chiunque che la legge, la quale governa lo svolgimento in­<lb></lb>tellettuale dell&#039;individuo, è la legge stessa che governa gli svolgi­<lb></lb>menti intellettuali di un intero popolo incivilito. </s>

<s>Ma perchè ogni <lb></lb>popolo incivilito riconosce qualche suo insigne capo-scuola e mae­<lb></lb>stro, ne&#039;libri scritti dal quale si compendia e si ritrae quasi in <lb></lb>ispecchio tutto ciò che di vero ha quello stesso popolo imparato e <lb></lb>scoperto; noi vogliamo dimostrare ai nostri lettori come la divisata <lb></lb>legge storica si verifichi negli insegnamenti lasciati dai due più <lb></lb>insigni capo scuola e maestri dello scientifico incivilimento, Platone, <lb></lb>e Aristotile. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Che la civiltà e la cultura, nella nostra Italia approdasse dalla <lb></lb>contigua Grecia è cosa tanto nota, e così naturale, che la Geografia <lb></lb>stessa quasi serve di prova. </s>

<s>La forma peninsulare delle due terre, <lb></lb>su cui il sole con temperata letizia dolcemente sorride, e il mare, <lb></lb>che largamente le bagna e ne&#039;golfi e ne&#039;seni e negl&#039;ismi stretta­<lb></lb>mente le abbraccia, furono forse le cause principali, per cui lo spi­<lb></lb>rito delle più antiche civiltà asiatiche e affricane liberamente alitasse <lb></lb>per le loro felici contrade. </s>

<s>Uno de&#039;primi e principali uomini, che <lb></lb>la face della scienza accendesse sulle rive del Nilo, e la trasportasse <lb></lb>con la scrittura di libri eloquentissimi di Grecia in Italia, fu quel <pb xlink:href="020/01/049.jpg" pagenum="30"></pb>Platone che del nostro scientifico progresso si dee da noi riguardare <lb></lb>qual efficacissimo promotore e maestro. </s></p><p type="main">

<s>Socrate gli educò, nella patria Atene, il cuore e la mente. </s>

<s>E <lb></lb>chi era Socrate? </s>

<s>— Io son figlio, ei risponde nel Teeteto appresso <lb></lb>lo stesso Platone, di una valentissima levatrice, che si chiama Fe­<lb></lb>narete, e anch&#039;io, come lei, esercito questa medesima arte. </s>

<s>Infe­<lb></lb>condo per me stesso, ostetrico i parti altrui e gli educo alla luce. </s>

<s>— <lb></lb>Se gli avesse alcuno domandato quali precetti gli fosse bisognato <lb></lb>osservare per conseguire la moralità e la scienza, compendiosamente <lb></lb>rispondeva <emph type="italics"></emph>conosci te stesso.<emph.end type="italics"></emph.end> Platone dunque si fece imitatore fede­<lb></lb>lissimo di quell&#039;arte ostetrica, e osservatore diligentissimo di quel <lb></lb>precetto, per cui, sebbene sia sembrato che il Reid e i pedagogisti <lb></lb>moderni abbiano ora nuovamente e per i primi introdotto nella <lb></lb>psicologia il metodo dell&#039;osservazione sperimentale; quel metodo <lb></lb>nonostante è antichissimo, e quasi un eco del socratico responso. </s>

<s><lb></lb>Non riuscirà perciò cosa di meraviglia a nessuno quella, che saremo <lb></lb>ora per profferire, ed è questa: che le platoniche dottrine sono una <lb></lb>viva espressione e uno splendidissimo dramma, che rappresenta in <lb></lb>atto lo stato e le condizioni della mente dell&#039;uomo, nel primo <lb></lb>acquisto delle verità naturali, secondo ci risultava dall&#039;osservare i <lb></lb>fatti del bambinello, che di poco ha passato quaranta giorni. </s>

<s>Anche <lb></lb>egli infatti, Platone, ammette che primo maestro all&#039;uomo non è <lb></lb>che Dio, l&#039;esistenza del quale, nel libro decimo delle Leggi, è di­<lb></lb>mostrata con tutti quegli argomenti, a cui sembra che poco di più <lb></lb>nuovo e di più bello abbian saputo aggiungervi i teologi moderni. </s>

<s><lb></lb>Della necessità delle tradizioni poi è così ben persuaso il filosofo <lb></lb>greco, da doversi anzi dire che tutto il suo sistema è informato di <lb></lb>quel principio. </s>

<s>E in vero non vuol nemmeno che le notizie acqui­<lb></lb>state si appellino col nome di <emph type="italics"></emph>scienza,<emph.end type="italics"></emph.end> ma piuttosto con quello di <lb></lb><emph type="italics"></emph>reminiscenza,<emph.end type="italics"></emph.end> come se l&#039;intelletto le avesse prima possedute, attin­<lb></lb>gendole direttamente dal cielo, e poi avesse via via occasione di <lb></lb>ridursele alla memoria. </s></p><p type="main">

<s>Chi poi volesse vedere in Platone eloquentemente rappresen­<lb></lb>tate queste stesse dottrine sotto forma di apologo, legga il principio <lb></lb>del libro VII <emph type="italics"></emph>Dello Stato,<emph.end type="italics"></emph.end> dove l&#039;intelletto che apprende le cose, <lb></lb>per mezzo dei sensi, vien rassomigliato a un uomo, che vede appa­<lb></lb>rire e sparire gli oggetti per le loro ombre proiettate sul fondo di <lb></lb>una spelonca, dentro alla quale sia condannato a starsene rinchiuso <lb></lb>per tutto il tempo della sua vita. </s></p><p type="main">

<s>La filosofia insomma del grande Ateniese, fa, secondo noi, esat-<pb xlink:href="020/01/050.jpg" pagenum="31"></pb>tissimo ritratto di quella contemplazione estatica, nella quale ve­<lb></lb>diamo assorto il bambino, quando prima incomincia a pigliar notizia <lb></lb>del mondo. </s>

<s>La geometria delle forme, secondo si disse, è il primo <lb></lb>oggetto e la prima arte della sua cognizione. </s>

<s>Ed ecco infatti il Filo­<lb></lb>sofo greco proclamare l&#039;utilità grandissima e l&#039;importanza, che per <lb></lb>l&#039;acquisto delle verità naturali ha la geometria e la scienza dei nu­<lb></lb>meri in generale. </s>

<s>“ Questa scienza, dice egli nell&#039;Epinomide, mentre <lb></lb>è la sorgente di tutti i beni non è sorgente di verun male, il che <lb></lb>è facile a provare. </s>

<s>Il numero non entra per nulla in ogni specie <lb></lb>di metro, dove non regna nè regime, nè ordine, nè figura, nè mi­<lb></lb>sura, nè armonia: in una parola, in tutto ciò che partecipa a qualche <lb></lb>male. </s>

<s>” Così par si voglia insinuar dall&#039;Autore, che la Matematica <lb></lb>è tutto insieme principio di moralità, e fondamento di scienza. </s></p><p type="main">

<s>A Platone succede immediatamente nell&#039;ufficio di maestro e <lb></lb>nell&#039;autorità di capo scuola, così del greco, come dell&#039;italico incivi­<lb></lb>limento, un altr&#039;uomo, che sebben sia discepolo di lui e per di­<lb></lb>ciassett&#039;anni frequenti l&#039;Accademia, professa nulladimeno dottrine <lb></lb>tutt&#039;affatto diverse. </s>

<s>Questo è il famosissimo Aristotile, il quale, nato <lb></lb>in Stagira, benchè di sangue greco, piccola e ignobile città della <lb></lb>Tracia, risente alquanto della ruvidezza natia e della operosità del <lb></lb>montanaro. </s>

<s>Ma quella sua ruvidezza e quella operosità, che fà così <lb></lb>risentito contrasto colla placida contemplazione platonica, è la rap­<lb></lb>presentazione più viva di quella irrequietezza che vedemmo succe­<lb></lb>dere alle estatiche e serene centemplazioni del bambinello. </s>

<s>Noi giu­<lb></lb>dicammo quella addirittura una fase morbosa, per la quale passa <lb></lb>la mente nel progredire all&#039;acquisto delle verità naturali, e la qua­<lb></lb>lificammo per un delirio. </s>

<s>Nè dubitiamo ora di qualificar similmente <lb></lb>per una fase morbosa e per un delirio la filosofia aristotelica, la <lb></lb>quale rappresenta per noi quel secondo stato, in cui si trova nella <lb></lb>successiva conquista delle cognizioni, la mente dell&#039;uomo. </s></p><p type="main">

<s>Per qual motivo l&#039;irrequietezza che si osserva nel bambino, e <lb></lb>che vien rappresentata dalla operosità aristotelica, fu qualificata da <lb></lb>noi per un delirio? </s>

<s>Perchè così il bambino come Aristotile vor­<lb></lb>rebbero che la Natura si governasse a loro proprio modo, e preten­<lb></lb>derebbero d&#039;imporre piuttosto che assoggettarsi alle leggi di lei. </s>

<s><lb></lb>Tale appunto è il carattere, di che s&#039;impronta la filosofia naturale <lb></lb>del famosissimo Stagirita. </s>

<s>Mentre che Platone conclude le prime <lb></lb>e più universali notizie delle cose derivare da tutt&#039;altra fonte che <lb></lb>dai sensi, esce invece il discepolo a sentenziare nulla essere nel­<lb></lb>l&#039;intelletto che non sia prima stato nel senso, per cui se il primo <pb xlink:href="020/01/051.jpg" pagenum="32"></pb>insegna il particolare essere incluso nell&#039;universale che lo precede, <lb></lb>l&#039;altro, tutt&#039;al contrario, asserisce che il particolare precede all&#039;uni­<lb></lb>versale, il concetto di cui la mente sa formarselo da sè stessa. </s>

<s>Ecco <lb></lb>quello che si può chiamare un indiarsi della ragione, la quale, come <lb></lb>fecondamente produce i concetti universali, per opera dialettica del­<lb></lb>l&#039;astrazione; così dà leggi ai particolari via via che occorra di rico­<lb></lb>noscerli per la percezione de&#039;sensi. </s>

<s>Di qui è che il Filosofo intende <lb></lb>com&#039;ad opera principale, a dar regole e a istituir precetti intorno <lb></lb>alla dialettica e alla rettorica, ed è riconosciuto da tutti per primo <lb></lb>inventore argutissimo del sillogismo. </s>

<s>Che cos&#039;è alle mani di Ari­<lb></lb>stotile il sillogismo? </s>

<s>È un artificio lusinghiero, per cui si dà a cre­<lb></lb>dere con gran facilità che la conclusione derivi dalle premesse, non <lb></lb>per necessità logica, ma per sola opera dialettica della mente ragio­<lb></lb>natrice. </s>

<s>Perciò egli, nell&#039;investigare le cause de&#039;fatti naturali aborre <lb></lb>dalla troppa semplicità: quelle cause non son vere, per lui, se non <lb></lb>quando sieno state ritrovate da&#039;più sottili e artificiosi ragionamenti. </s>

<s><lb></lb>Com&#039;esempio di ciò può citarsi, dal libro delle Meteore, e da quello <lb></lb>dei Problemi, ciò che dice dell&#039;origine delle fontane, ripudiando <lb></lb>l&#039;opinion di coloro che riconoscevano quelle segrete origini dalli <lb></lb>stillicidii de&#039;monti imbevuti delle nevi squagliate e delle pioggie <lb></lb>invernali. </s>

<s>Attendendo poi bene, si trova non aver quel ripudio, nella <lb></lb>mente del Filosofo, altro motivo, se non per esser quella opinione <lb></lb>troppo ovvia e facile a ritrovar dagl&#039;ingegni volgari. </s>

<s>Chi svolge i <lb></lb>libri dello Stagirita s&#039;abbatte frequentemente a trovar di ciò simili <lb></lb>altri esempi. </s></p><p type="main">

<s>Platone aveva bandita aspra guerra ai sofisti, e nell&#039;Eutidemo <lb></lb>svela i più intricati laberinti dei loro errori e gli sconfigge coll&#039;arguta <lb></lb>ironia, che dardeggia dalle semichiuse labbra di Socrate. </s>

<s>Nel Pro­<lb></lb>tagora poi aveva già con pari arte eloquente, confutato il sensismo, <lb></lb>conchiudendo che, se regola del nostro conoscere sono i sensi, nulla <lb></lb>è più nel mondo d&#039;immutabile e di vero. </s>

<s>Ma Aristotele, benchè sia <lb></lb>sollecito di rimuover da sè la taccia d&#039;essere incorso negli errori <lb></lb>di Protagora e di Eutidemo, è nonostante di fatto più sensista del <lb></lb>primo e più sofista del secondo, non consistendo bene spesso la sua <lb></lb>dialettica in altro, che in appuntar la freccia ai sofismi, ed essendo <lb></lb>i suoi libri fisici una continuata apoteosi dei sensi. </s>

<s>Il discepolo in­<lb></lb>somma professa apertamente dottrine, non solo diverse, ma tutt&#039;af­<lb></lb>fatto contrarie a quelle del suo maestro, e, in ordine al proposito <lb></lb>nostro, il succedersi dell&#039;una scuola all&#039;altra, segna nella storia <lb></lb>delle scienze sperimentali, un notabilissimo regresso. </s></p><pb xlink:href="020/01/052.jpg" pagenum="33"></pb><p type="main">

<s>Dalle due antiche scuole di Grecia derivarono gli Accademici <lb></lb>e i Peripatetici, i quali, da quasi ventitrè secoli, hanno tenuto il <lb></lb>campo della scienza in Europa, essendo mirabilmente le loro arche <lb></lb>rimaste galleggianti sui flutti agitatori di tanti popoli fra sè divisi <lb></lb>per varietà di climi e di costumi, per comuni sventure e per con­<lb></lb>trarie passioni. </s>

<s>Dietro ciò, si comprenderà assai facilmente come <lb></lb>debba la Storia del metodo sperimentale incominciare dalla institu­<lb></lb>zione dell&#039;Accademia, a cui segue immediatamente quella del Pe­<lb></lb>ripato, considerando con brevità, ma colla diligenza che ci sarà pos­<lb></lb>sibile, ciò che conferissero quelle due scuole a dar gli inizii e a <lb></lb>promuovere in qualche modo quegli stessi metodi sperimentali. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Prendano dunque le mosse queste nostre considerazioni dal <lb></lb>sistema filosofico di Platone, brevemente aggirandoci, insiem coi <lb></lb>nostri lettori, per i lussureggianti orti di Academo. </s>

<s>La lussuria degli <lb></lb>alberi, che ombreggiano i viali, fa senza dubbio ritratto della esu­<lb></lb>berante facondia di colui che, avvolto nel pallio filosofale, parla alla <lb></lb>numerosa e scelta gioventù ateniese tratta ad udirlo. </s>

<s>Ma il refri­<lb></lb>gerio che vien da una tal lussuria di fronde a&#039;cocenti ardori del <lb></lb>sole e il grato odore che esala dai dolci pomi maturi, persuadono <lb></lb>facilmente ognuno che ivi l&#039;utilità va congiunta al diletto. </s></p><p type="main">

<s>La qualità principale e il carattere distintivo di quella platonica <lb></lb>scuola, già dicemmo essere la contemplazione. </s>

<s>“ La verità, va tut­<lb></lb>tavia ripetendo il gran maestro, non si può conoscere da noi quaggiù <lb></lb>in terra, se non isforzandoci a rompere i vincoli che ci tengono <lb></lb>strinti e avviluppati nel corpo. </s>

<s>” È questa del gran filosofo, senza <lb></lb>dubbio, una esagerazione, anzi diciamolo addirittura un errore, per­<lb></lb>chè se l&#039;uomo è naturalmente composto di anima e di corpo, deb­<lb></lb>bono ambedue insieme, con provvida legge concorrere a un mede­<lb></lb>simo ufficio: onde, la conseguenza che immediatamente deriva dalle <lb></lb>platoniche dottrine sarebbe che l&#039;acquisto della scienza non è per <lb></lb>noi che un inutile desiderio. </s>

<s>Dall&#039;altra parte poi, se il corpo è di im­<lb></lb>paccio continuo all&#039;anima, e se non sono i sensi altro che una fonte <lb></lb>perenne d&#039;inganni, è chiaro che non utile alla ricerca della verità, <lb></lb>ma sommamente dannosa, dovrebbe, secondo il sistema filosofico di <lb></lb>Platone, riuscir qualunque istituzione del metodo sperimentale. </s></p><pb xlink:href="020/01/053.jpg" pagenum="34"></pb><p type="main">

<s>Questa infatti è la conclusione a cui giunge il discepolo di quel <lb></lb>Socrate, che fu udito dire più volte aver nello studio della storia <lb></lb>naturale trovato piuttosto da perdere che da guadagnare. </s>

<s>Così stando <lb></lb>appunto le cose, quale speranza possiamo dunque aver noi di veder <lb></lb>la Filosofia sperimentale spuntar su dalle verdeggianti aiuole del­<lb></lb>l&#039;Accademia? </s>

<s>I nostri lettori perciò, che attendono curiosi la risposta, <lb></lb>dovrebbero rammemorarsi come noi dicemmo, ne&#039;principii del no­<lb></lb>stro Discorso, che la filosofia platonica rappresenta quel primo stato <lb></lb>della mente dell&#039;uomo, in cui, degli oggetti creati ella apprende <lb></lb>le prime notizie, piuttosto per via delle forme geometriche, che per <lb></lb>la materiale impressione del senso. </s>

<s>D&#039;onde si può comprendere, <lb></lb>che se quella Filosofia non introduce nell&#039;arte sperimentale, e anzi <lb></lb>la ripudia reputandola non solo inutile, ma, che è peggio, dannosa; <lb></lb>vi sostituisce però un&#039;altr&#039;arte che la precede e che è, o dovrebbe <lb></lb>essere il fondamento di quella, essendo certissima legge che gli og­<lb></lb>getti si conoscono prima per la forma e poi per materia. </s>

<s>Platone <lb></lb>insomma non introduce nella fisica, ma in quella che può chiamarsi <lb></lb>matematica della fisica. </s></p><p type="main">

<s>Egli è infatti, il filosofo atienese, gran maestro di Geometria. </s>

<s><lb></lb>Fiorirono nella scuola di lui Aristeo, Eudossio, Mnecmo e Dinostrato, <lb></lb>i quali riuscirono a dar la soluzione de&#039;due più difficili problemi, <lb></lb>che fossero proposti alla geometria: la duplicazione del cubo e la <lb></lb>trisezione dell&#039;angolo. </s>

<s>Alla scuola di Platone appartengono pure i <lb></lb>due più insigni maestri che abbia avuto, e in così lungo decorrere <lb></lb>di secoli, abbia tuttavia la scienza, Euclide e Archimede. </s></p><p type="main">

<s>Tratteniamoci a consïderare un poco il sublime aspetto e la <lb></lb>maestà veneranda del nostro Siracusano. </s>

<s>Egli è la prima splendida <lb></lb>apparizione, e la rappresentazione più viva di ciò che fosse l&#039;arte <lb></lb>sperimentale in Italia nel III secolo prima di Gesù Cristo. </s>

<s>Il disco­<lb></lb>pritore del furto dell&#039;oro nella corona del rè Gerone, l&#039;incendiatore <lb></lb>delle navi di Marco Marcello, il taumaturgo, che per mezzo di una <lb></lb>semplicissima leva si dà vanto di poter commuovere la terra e il cielo, <lb></lb>passa per il primo gran fisico sperimentale che abbia avuto l&#039;Italia, <lb></lb>e perciò non sembra che possa essere uscito Archimede dalla scuola <lb></lb>matematica di Platone. </s></p><p type="main">

<s>Considerando però più sottilmente, si troverà che l&#039;abito del <lb></lb>Siracusano non differisce in nulla dal pallio del filosofo atienese. </s>

<s><lb></lb>Così l&#039;uno come l&#039;altro tengon dietro alle forme dei corpi, e non <lb></lb>vogliono avvilir l&#039;ingegno dietro alla loro materia. </s>

<s>Questa nota del­<lb></lb>l&#039;ingegno archimedeo è posta in piena evidenza da ciò che ne scrive <pb xlink:href="020/01/054.jpg" pagenum="35"></pb>Plutarco nella vita di Marco Marcello, dove dice appunto che Ar­<lb></lb>chimede non faceva nessun conto delle sue fisiche e meccaniche <lb></lb>invenzioni, non essendo esse altro che <emph type="italics"></emph>giochi di geometria, ne&#039;quali <lb></lb>s&#039;era abbattuto trattenendovisi attorno per suo passatempo.<emph.end type="italics"></emph.end> Ecco il <lb></lb>carattere distintivo della fisica platonica, ecco in qual concetto si <lb></lb>tenevan dagli Accademici i fatti naturali: giochi di geometria e pas­<lb></lb>satempi. </s>

<s>Di un tal suggello è profondamente impresso il primo Trat­<lb></lb>tato di fisica tramandatoci dall&#039;antichità, gli <emph type="italics"></emph>Spiritali<emph.end type="italics"></emph.end> di Herone <lb></lb>alessandrino, discepolo di Archimede: trattato, dove l&#039;ingegno <lb></lb>scherza intorno ai moti prodotti principalmente dal dilatarsi e dal <lb></lb>condensarsi dell&#039;aria, come Ctesibio, altro discepolo dello stesso <lb></lb>Archimede, scherza intorno a simili altri moti prodotti dall&#039;acqua. </s></p><p type="main">

<s>Ma esistono del gran discepolo di Platone, onore di Siracusa <lb></lb>e d&#039;Italia, e son pervenuti infino a noi, attraverso alle vicende dei <lb></lb>secoli, due Trattati insigni, quello degli <emph type="italics"></emph>Equiponderanti<emph.end type="italics"></emph.end> e quello dei <lb></lb><emph type="italics"></emph>Galleggianti,<emph.end type="italics"></emph.end> dove si pongono così saldi fondamenti scienziali alla <lb></lb>Statica e alla Idrostatica, da non passar per la mente a nessuno che <lb></lb>possa altri qualificarli per giochi di geometria o per fisici passatempi. </s>

<s><lb></lb>Verissimo: ma essi pure, que&#039;due Trattati del matematico siracu­<lb></lb>sano, presentano il carattere proprio e distintivo della Filosofia na­<lb></lb>turale di Platone, che è quello di astrarre dalle proprietà naturali <lb></lb>dei corpi, per trattenersi a contemplare le proprietà matematiche e <lb></lb>geometriche delle loro forme. </s>

<s>La leva archimedea infatti, sul prin­<lb></lb>cipio della quale è fondata tutta la Statica, non è una verga solida, <lb></lb>ma una linea geometrica, e la potenza e la resistenza son forze che <lb></lb>sembrano esser messe in atto piuttosto da spiriti incorporei, che da <lb></lb>materie solide e ponderanti. </s>

<s>Similmente l&#039;umido delle archimedee <lb></lb>idrostatiche immersioni è un liquido che non esiste in natura, ma <lb></lb>nelle mentali astrazioni del filosofo, il qual suppone che le molecole <lb></lb>rasentino le pareti de&#039;vasi e fluiscano le une attorno alle altre senza <lb></lb>patirvi la minima resistenza, a quel modo che un punto genera una <lb></lb>linea geometrica liberamente fluendo nello spazio. </s>

<s>Quel flusso geo­<lb></lb>metrico è moto, e anzi al moto di un punto che genera una linea, <lb></lb>al moto di una linea che genera una superficie, e al moto di una <lb></lb>superficie che genera un solido, si riduce il concetto genetico della <lb></lb>Geometria, che giusto, nel risalire alle sue più sublimi alture, prende <lb></lb>per suo proprio e particolare il titolo di <emph type="italics"></emph>Flussioni.<emph.end type="italics"></emph.end> Non fa perciò <lb></lb>maraviglia che uscissero dalla scuola di Platone i due più insigni <lb></lb>maestri della scienza del moto Archimede e Galileo. </s></p><p type="main">

<s>Ma per non prevenire i tempi moderni, soffermiamoci breve-<pb xlink:href="020/01/055.jpg" pagenum="36"></pb>mente a considerare in Archimede e nella sua scuola quali sieno <lb></lb>le note proprie e distintive della Filosofia naturale derivata dall&#039;Ac­<lb></lb>cademia. </s>

<s>Fedele agli insegnamenti di Platone, essa contempla nella <lb></lb>natura le forme geometriche, e dilettandosene sublimemente, dà <lb></lb>mirabili impulsi da progredire non a sola la Geometria pura, ma <lb></lb>alla Geometria applicata al moto dei gravi, degli astri, della luce e <lb></lb>de&#039;suoni. </s>

<s>La Meccanica, l&#039;Astronomia, l&#039;Ottica, la Musica e simili <lb></lb>altre discipline e arti, in quanto si riducono a simmetria di linee <lb></lb>o ad armonia di numeri, son frutti allegati nel fiore degli orti Ac­<lb></lb>cademici. </s>

<s>L&#039;altro aspetto poi sotto cui si presenta la natura, nel <lb></lb>rivelarsi per l&#039;organo dei sensi, perciocchè questi sono ingannevoli, <lb></lb>si riguardan da quella filosofia non altrimenti che quali scherzi im­<lb></lb>meritevoli affatto della seria attenzion de&#039;filosofi. </s>

<s>Per i platonici <lb></lb>insomma la Filosofia sperimentale, o la natura che ne forma il sog­<lb></lb>getto, nient&#039;altro si è che, o una lasciva fanciulla che scherza, o una <lb></lb>paurosa maga che incanta. </s>

<s>E in fatti tutti i libri di fisica scritti <lb></lb>dagli autori di quella scuola si vedon portare scritto in fronte il <lb></lb>titolo o di <emph type="italics"></emph>Magia naturale<emph.end type="italics"></emph.end> o di <emph type="italics"></emph>Spettacoli maravigliosi della natura.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma quale Filosofia sperimentale poteva derivar mai dal Peri­<lb></lb>pato? </s>

<s>Attendiamo bene al principio che informa quella scuola. </s>

<s>Già <lb></lb>noi lo mostrammo apertamente più sopra, e dicemmo consistere <lb></lb>quel principio nel far dipendere dalla nostra ragione le leggi che <lb></lb>governano la Natura. </s>

<s>In conseguenza di ciò, l&#039;esperienza è inutile, <lb></lb>e la ragione legislatrice e signora non ha bisogno di travagliarsi <lb></lb>servilmente a osservare e a cimentare i fatti naturali. </s>

<s>A che dal­<lb></lb>l&#039;altra parte mostrarsi bisognosi d&#039;inventare e di fabbricare stru­<lb></lb>menti da rendere più squisito l&#039;uso dei sensi? </s>

<s>Alla ragione basta <lb></lb>quel poco che i sensi stessi possono porgerle, in qualunque maniera <lb></lb>sia fatto: al resto ella supplisce bene da sè medesima, senz&#039;altro <lb></lb>estrinseco aiuto. </s></p><p type="main">

<s>Quali potevano essere insomma i frutti di così fatte dottrine? </s>

<s><lb></lb>Quelli, che si possono aspettar da un albero in una opaca e neb­<lb></lb>biosa valle, senza alcuna posa combattuta dai venti. </s>

<s>Il Peripato perciò <lb></lb>dee essere necessariamente infecondo, chiuso, e quasi diremmo in­<lb></lb>crisalidato nella propria ragione, e combattuto dai venti dell&#039;orgo­<lb></lb>glio. </s>

<s>Eppure è stato scritto da alcuni che Aristotile è gran maestro <lb></lb>di fisici sperimenti, per cui egli incarna le astratte speculazioni, e <lb></lb>colorisce i disegni aerei di Platone. </s>

<s>Magnificano costoro la Storia <lb></lb>degli animali del filosofo di Stagira, e la vorrebbero proporre come <lb></lb>esempio di diligentissime osservazioni de&#039;fatti naturali. </s>

<s>Ma, se bene <pb xlink:href="020/01/056.jpg" pagenum="37"></pb>si bada, si vedrà che l&#039;osservazione di Aristotile è affatto superfi­<lb></lb>ciale: è quella stessa che non isfugge a nessuno, il quale apre gli <lb></lb>occhi a guardare le esteriori apparenze dei corpi. </s>

<s>Quando però si <lb></lb>tratta di entrare addentro alla natura delle cose, l&#039;autore incespica <lb></lb>e rimane intrigato in gravissimi errori, come per esempio nel caso <lb></lb>di determinare il modo dell&#039;incesso de&#039;quadrupedi e del risolvere <lb></lb>molte altre simili questioni di meccanica animale. </s>

<s>Del resto, anco <lb></lb>in quella Storia, il filosofo rivela il suo proprio genio, e diciamo <lb></lb>così, la sua propria ambizione, qual era quella di dar anima alla <lb></lb>natura col suo proprio discorso, lusingandosi quasi d&#039;esserne il <lb></lb>Creatore, nell&#039;atto che ne divisava le proprietà e ne annoverava le <lb></lb>specie. </s>

<s>Egli è, ricordiamocene, nò nella sola storia naturale ma, in <lb></lb>ogni scibile, il Maestro delle <emph type="italics"></emph>Categorie.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Chi volesse poi formarsi una più giusta idea di quel genio <lb></lb>aristotelico; e volesse anche meglio persuadersi della falsità dell&#039;as­<lb></lb>serto riferito di sopra, che cioè sia il Filosofo di Stagira gran maestro <lb></lb>di fisici sperimenti; non ha a far altro che svolgerne i <emph type="italics"></emph>Problemi<emph.end type="italics"></emph.end><lb></lb>per tutte quelle XXXVIII sezioni in cui l&#039;Autore gli volle distri­<lb></lb>buiti. </s>

<s>Essi comprendono tutta intera l&#039;enciclopedia della scienza <lb></lb>naturale a quei tempi, e s&#039;intende di dare a quel modo le risposte <lb></lb>più sincere alle varie domande che si posson far dai curiosi. </s></p><p type="main">

<s>Non men falso poi reputiamo l&#039;altro asserto pur di sopra no­<lb></lb>tato, che cioè Aristotile compia le dottrine del suo Maestro. </s>

<s>Fra&#039;due <lb></lb>filosofi è così aperto il dissidio, che è impossibile trovar ordine e <lb></lb>modo da ricongiungerli insieme. </s>

<s>Pur nonostante è vero che in al­<lb></lb>cuni punti si riscontrano, ma però si riscontrano a quel modo che <lb></lb>avvien delle vie tortuose che s&#039;intersecano e procedono per qualche <lb></lb>tratto con le diritte rendendo più che mai però intralciato il viaggio. </s>

<s><lb></lb>S&#039;incontrano senza dubbio ambedue i Filosofi greci in questo, in <lb></lb>recidere cioè gli stami ai progressi dell&#039;arte sperimentale, renden­<lb></lb>dola l&#039;uno impossibile e l&#039;altro inutile. </s>

<s>All&#039;impossibilità riducesi <lb></lb>evidentemente da Platone, insegnando che i sensi non rappresentano <lb></lb>all&#039;anima altro che larve fuggitive ed inganni, e si riduce ad una <lb></lb>inutilità per Aristotile, il quale professa che al difetto dei sensi può <lb></lb>supplire, per sè medesima, la ragione. </s>

<s>Così è che se, per gli Acca­<lb></lb>demici, la Filosofia naturale è un ludibrio spettacoloso, per i Peri­<lb></lb>patetici non è altro più che una sottile esercitazion<gap></gap> d&#039;ingegno. </s>

<s><lb></lb>D&#039;ond&#039;è che gli spettacoli della Natura andando bene spesso, da&#039;loro <lb></lb>autori, accompagnati dalle sottigliezze della Dialettica, non è facile <lb></lb>a discerner se uno de&#039;così fatti libri appartiene all&#039;una o all&#039;altra <pb xlink:href="020/01/057.jpg" pagenum="38"></pb>scuola, rimanendo a distinguerli questa sola infausta qualità, che è <lb></lb>del vedervi costantemente i fatti naturali accomodati a secondare <lb></lb>la fantasia. </s></p><p type="main">

<s>Alla scuola platonica però rimane incontrastabile il merito di <lb></lb>aver suggerita la prima arte di decifrare il libro della Natura, per <lb></lb>mezzo della Geometria, mentre alla Aristotelica non riman forse altro <lb></lb>vanto da quello in fuori d&#039;aver rivolti gl&#039;ingegni a facilitar le re­<lb></lb>gole del calcolo numerico, intorno a che principalmente si distin­<lb></lb>sero gli arabi. </s>

<s>L&#039;Algebra è senza dubbio un frutto del Peripato, <lb></lb>come la Geometria è un frutto dell&#039;Accademia. </s>

<s>Che se, avuto ri­<lb></lb>guardo all&#039;utilità e alla eccellenza delle due discipline, si vorrà <lb></lb>decidere che i meriti sono uguali, avuto riguardo all&#039;applicabilità <lb></lb>delle stesse due discipline all&#039;interpetrazion de&#039;fatti naturali, si vedrà <lb></lb>che, mentre la Geometria è ala da sollevar la mente sublime alla <lb></lb>contemplazione del mondo, l&#039;Algebra non è che strumento da fa­<lb></lb>cilitare alcune delle più faticose esercitazioni del nostro ingegno. </s>

<s><lb></lb>Tale forse non è l&#039;ufficio dell&#039;Algebra in sè, ma è pure l&#039;ufficio a <lb></lb>cui venne rivolta dal Peripato, al quale parve che il fare scaturire <lb></lb>una conclusione dal meccanico operar sulle cifre, fosse un nuovo e <lb></lb>lusinghiero argomento, di quella potenza dell&#039;ingegno, con che dal <lb></lb>sillogismo facevasi scaturire, quasi creazion della mente, la verità <lb></lb>e la certezza di tutte quante le cose. </s>

<s>Perciò, mentre la Geometria <lb></lb>è rimasta sempre nella sua incorruttibile dignità, l&#039;Algebra s&#039;è ve­<lb></lb>duta degenerar talvolta negli abusi e ne&#039;vizii della Dialettica. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dalle due scuole di Platone e di Aristotile, o come si voglia <lb></lb>dire altrimenti, dall&#039;Accademia e dal Peripato, derivarono le tradi­<lb></lb>zioni della scienza e dell&#039;arte, che ridussero in istato di civiltà le <lb></lb>nazioni europee e principalmente la nostra Italia. </s>

<s>L&#039;impulso che <lb></lb>venne alle menti e agli animi da quelle dottrine, fu così potente, <lb></lb>che, mirabile a dirsi, dura tuttavia dopo un sì lungo decorrere di <lb></lb>secoli. </s>

<s>Tu<gap></gap> le varietà dei sistemi, che hanno tenuto, e tengono <lb></lb>fra sè divisi gl&#039;ingegni speculativi, tutte le varietà dei gusti seguite <lb></lb>e manifestate in così varie maniere dalle opere degli artisti, si po­<lb></lb>trebbero con gran facilità ridurre a due tipi, in uno dei quali si <pb xlink:href="020/01/058.jpg" pagenum="39"></pb>vedrebbe impresso il sigillo del Peripato, e nell&#039;altro quello del­<lb></lb>l&#039;Accademia. </s></p><p type="main">

<s>Delle due influenti scuole prima a introdursi in Italia e di li <lb></lb>per tutta l&#039;Europa, fu la Platonica. </s>

<s>Le tradizioni pitagoriche dovet­<lb></lb>tero, senza dubbio, concorrere a tal preferenza, ma ben più facil­<lb></lb>mente vi concorsero l&#039;indole e il genio scientifico dei Romani <lb></lb>scolpitamente rappresentato da Cicerone. </s>

<s>Basta leggere il Trattato <lb></lb><emph type="italics"></emph>Delle Leggi<emph.end type="italics"></emph.end> e il libro dell&#039;<emph type="italics"></emph>Oratore<emph.end type="italics"></emph.end> del filosofo romano, per ricono­<lb></lb>scervi l&#039;inspirazione diretta e immediata del Trattato delle Leggi e <lb></lb>del Fedro del filosofo greco. </s>

<s>La politica e la morale erano princi­<lb></lb>palmente le due scienze, che premeva di coltivare a quel popolo, <lb></lb>il quale deve alla disciplina degli animi, da cui provennero i sa­<lb></lb>pienti ordinamenti civili, la sua propria grandezza. </s>

<s>Dedito alla vita <lb></lb>attiva, piuttosto che alla contemplativa, della Geometria non si curò <lb></lb>gran fatto. </s>

<s>Nella filosofia naturale però fece quell&#039;operoso popolo <lb></lb>romano di notabili progressi, intanto che, a qualche concetto che <lb></lb>si rivela dai versi di Lucrezio Caro, all&#039;invenzione di alcuni stru­<lb></lb>menti descritti da Vitruvio, a parecchie questioni risolute da Seneca, <lb></lb>e a certe teorie intravedute da Frontino, si riappiccano propriamente <lb></lb>le tradizioni intercise del risorto metodo sperimentale. </s>

<s>È però vero <lb></lb>che una tal messe di fisiche verità non fu e non poteva esser rac­<lb></lb>colta dagli orti dell&#039;Accademia: essa fu, come si vedrà meglio tra <lb></lb>poco in altri esempi, frutto di una sapienza che non sarebbe po­<lb></lb>tuta derivar da nessuna scuola. </s></p><p type="main">

<s>L&#039;istituzione del Cristianesimo, dopo i tempi di Augusto, rin­<lb></lb>novellò la vita del popolo romano, ma in questa profonda innova­<lb></lb>zione una cosa rimane immutabile, l&#039;impero di Roma, che dalle <lb></lb>mani della Politica passa a quelle della Religione. </s>

<s>Roma è ancora, <lb></lb>passato lo splendore dei Cesari, e forse con più vivo senso di prima, <lb></lb>capo e cuore del mondo. </s>

<s>Da essa fluisce la civiltà come sangue <lb></lb>dalla grande arteria, e ad essa, come per condotto di vene, conti­<lb></lb>nuamente ritorna. </s>

<s>A Cicerone sottentrano, nell&#039;ufficio di oratori, <lb></lb>Minuzio Felice, Basilio Magno, Agostino, i quali o sien nati sul <lb></lb>Tevere, o sui lidi dell&#039;Ellesponto, o non lungi dalle rive del Nilo, <lb></lb>son tutti pure, in una mente e in un cuore, ugualmente romani. </s>

<s><lb></lb>La nuova arte oratoria però è varia, perchè varii ne sono i fini, ma <lb></lb>non per questo manco nobili e generose ne sono le intenzioni. </s>

<s>Essi <lb></lb>vogliono persuadere agli adoratori de&#039;falsi dèi l&#039;esistenza di un Dio <lb></lb>unico, Creatore e Conservatore del mondo, e sentono che il vero <lb></lb>modo a illuminar quelle menti è di accender ne&#039;loro cuori il calor <pb xlink:href="020/01/059.jpg" pagenum="40"></pb>dell&#039;affetto. </s>

<s>Essi perciò eleggono, non argomenti sottili, ma bellezze <lb></lb>d&#039;immagini, e fanno uso, piuttosto che dell&#039;arguzie della Dialettica, <lb></lb>de&#039;fiori della Poesia. </s>

<s>Platone veniva così naturalmente a presentarsi <lb></lb>maestro e a porgersi imitabile esempio alla nuova eloquenza cri­<lb></lb>stiana, e Minuzio Felice, nell&#039;<emph type="italics"></emph>Ottavio,<emph.end type="italics"></emph.end> lo imita perfino nelle forme <lb></lb>esteriori del dialogo, e Basilio Magno nell&#039;<emph type="italics"></emph>Esaemerone<emph.end type="italics"></emph.end> risale con <lb></lb>sublime ala platonica, dalle pittoresche bellezze della Natura infino <lb></lb>al trono di Dio, mentre S. </s>

<s>Agostino nelle sue <emph type="italics"></emph>Confessioni,<emph.end type="italics"></emph.end> scrutando <lb></lb>le più profonde latebre del proprio cuore, mette in pratica il pre­<lb></lb>cetto socratico del Conosci te stesso. </s></p><p type="main">

<s>Per tali spiracoli e per tal magistero, venne a introdursi la <lb></lb>Filosofia di Platone in mezzo alla nuova civiltà cristiana. </s>

<s>Ma la <lb></lb>Filosofia di Aristotile vi s&#039;introdusse molto più tardi, e per un ma­<lb></lb>gistero tanto diverso, quanto esser può diversa, dalla toga magnifica <lb></lb>di un romano, la cappa voluttuosa di un arabo. </s>

<s>Averrois è pro­<lb></lb>priamente colui, che si dà all&#039;opera di tradurre i libri dello Sta­<lb></lb>girita, e d&#039;illustrarli col suo commento, diffondendone le dottrine <lb></lb>fra la sua gente, che, sebbene abbia invasa e siasi per nuova patria <lb></lb>usurpata la Spagna, serba nostante impresse nell&#039;ingegno le mono­<lb></lb>tone solitudini delle lande affricane, e nel cuore, gli alidori di quelle <lb></lb>arene, che gli avi avean calcate largamente col piede. </s>

<s>Quel maestro, <lb></lb>che insegnava a ridur tutto a regola di compasso, e dagli ammaestra­<lb></lb>menti del quale si concludeva così facilmente la libertà del poter <lb></lb>governare sè stesso e la natura a proprio talento, non poteva non <lb></lb>piacere a quegli uomini, tutti dediti a riconoscere freddamente e a <lb></lb>noverar gli oggetti, che più fanno impressione e più dilettano i <lb></lb>sensi. </s></p><p type="main">

<s>Sotto le larghe pieghe della bianca cappa dell&#039;arabo, veniva <lb></lb>così dunque Aristotile a introdursi in mezzo alla società cristiana. </s>

<s><lb></lb>Ma come poteva quella Filosofia accomodarsi ai precetti del Van­<lb></lb>gelo, o come poteva quell&#039;alidor di numeri scritti nel fango, andare <lb></lb>a genio a un popolo che sospirava per sua patria il cielo immen­<lb></lb>surabile eterno? </s>

<s>Più volte infatti Concilii, presieduti dagli stessi <lb></lb>Pontefici romani, dannarono la lettura de&#039;libri aristotelici, ma pur <lb></lb>poco stette che Aristotile stesso, quasi per incantesimo, si trovò <lb></lb>spogliato della cappa dell&#039;arabo e rivestito della tonaca del frate, <lb></lb>dall&#039;alhambra, mirabilmente trapassando al convento. </s></p><p type="main">

<s>Era già incominciato il tempo delle eresie, per cui, piuttosto <lb></lb>che badare a insinuare la verità, si sentiva il bisogno di confutare <lb></lb>l&#039;errore. </s>

<s>Per confutarlo conveniva servirsi delle armi medesime <pb xlink:href="020/01/060.jpg" pagenum="41"></pb>degli oppositori, le quali consistevano nella Dialettica, e nel far uso <lb></lb>degli argomenti della ragione contro i dommi inconcussi della fede. </s></p><p type="main">

<s>L&#039;eloquenza platonica perciò de&#039;primi Padri della Chiesa do­<lb></lb>vette cedere alle acute sillogistiche argomentazioni de&#039;novelli Dottori, <lb></lb>e a far l&#039;ufficio del monachismo sottentrarono gli Ordini regolari. </s>

<s><lb></lb>Alle orazioni e alle omelie meditate lungo le rive di un fiume, o <lb></lb>all&#039;ombra di un palmeto, e recitate poi dal pergamo al popolo cri­<lb></lb>stiano, succedono le aride disputazioni teologiche, scritte fra il tanfo <lb></lb>di una cella e diffuse per innumerevoli altre celle o a viva voce o <lb></lb>per copie manoscritte. </s>

<s>Il primo che pensi di raccogliere quelle <lb></lb>sparse disputazioni, e di ordinarle insieme in una <emph type="italics"></emph>Somma teologica,<emph.end type="italics"></emph.end><lb></lb>è Alessandro di Hales, a cui poco dopo tien dietro Alberto Magno, <lb></lb>maestro a quel Tommaso d&#039;Aquino, grande istitutore della Teologia <lb></lb>scolastica. </s>

<s>Narrano i biografi di lui, e si va ripetendo fra gli aned­<lb></lb>doti della sua vita, com&#039;egli, sedendo a mensa con gli altri frati, <lb></lb>rimanesse una volta senza nulla curarsi del cibo, e stato alquanto <lb></lb>così cogitabondo, uscisse poi con incomposta esultanza a dire: <emph type="italics"></emph>l&#039;ho <lb></lb>trovato, l&#039;ho trovato.<emph.end type="italics"></emph.end> E che cosa aveva egli trovato? </s>

<s>Nient&#039;altro se <lb></lb>non un argomento da risolvere una sottile questione teologica, che <lb></lb>egli era andato inutilmente cercando per lungo tempo. </s>

<s>Il fatto non <lb></lb>può non richiamare alla memoria quell&#039;altro simile e ben più fa­<lb></lb>moso aneddoto, che si racconta della vita di Archimede, per cui <lb></lb>manifesto risulta da tal confronto che il Filosofo di Aquino, in <lb></lb>investigar gli argomenti di ragione prosegue con quello stesso ar­<lb></lb>dore di metodo, che il matematico di Siracusa in investigar le verità <lb></lb>più recondite della Natura. </s>

<s>Ed ecco posto così in piena evidenza <lb></lb>il carattere proprio della filosofia scolastica. </s></p><p type="main">

<s>Non è del presente nostro proposito il dar giudizio di S. </s>

<s>Tom­<lb></lb>maso come filosofo speculativo e come metafisico: intorno a ciò, <lb></lb>egli ha senza dubbio meriti insigni, confermatigli dall&#039;ossequioso <lb></lb>consenso di cinque secoli. </s>

<s>Il giudizio nostro solamente versa circa <lb></lb>la Filosofia naturale, che il padre della Scolastica attinse tutta da <lb></lb>Aristotile, insegnando a legger piuttosto ne&#039;libri di lui, che in quelli <lb></lb>della Natura. </s>

<s>Ecco da che venerande mani furono nel secolo XIII <lb></lb>instaurati in Italia gl&#039;idoli aristotelici. </s>

<s>E qual maraviglia è che la <lb></lb>turba ossequiosa vi s&#039;inchinasse ciecamente a offerirgli incensi? </s></p><p type="main">

<s>La grande autorità di S. </s>

<s>Tommaso fu senza dubbio una delle <lb></lb>cause principali, per cui il Peripato nuovo venne a costituirsi, ma <lb></lb>non fu l&#039;unica. </s>

<s>Le molte altre che vi concorsero, e non punto meno <lb></lb>efficaci, si potrebbero ritrovar facilmente in quella comodità, che <pb xlink:href="020/01/061.jpg" pagenum="42"></pb>veniva dal supplir con la lettura di un libro, al faticoso esercizio <lb></lb>dello sperimentare. </s>

<s>Un tal metodo doveva riuscir tanto meglio ac­<lb></lb>comodato alla qualità degli abitatori del chiostro, in quanto che, <lb></lb>non avendo essi occasione di travagliarsi col mondo per provvedere <lb></lb>alle necessità e sodisfare ai piaceri della vita, si potevano lusingar <lb></lb>facilmente che le leggi naturali si potessero indurre con la stessa <lb></lb>facilità, con cui si conducevano i sillogismi. </s>

<s>Di qui è che un prin­<lb></lb>cipio di vanità e di orgoglio doveva essere il carattere proprio di <lb></lb>quella filosofia, vanità ed orgoglio che divamparono putidamente, <lb></lb>quando, per le opposizioni, il Peripato si ristrinse insieme congiu­<lb></lb>rato in una setta. </s>

<s>Chì ripensi ora che i chiostri erano i soli asili <lb></lb>in cui si rifugiava e da cui si diffondeva la scienza, comprenderà <lb></lb>quali dovessero essere le condizioni delle scienze naturali per tutto <lb></lb>il tempo che dominò quella scuola. </s>

<s>Condizioni generali però, per­<lb></lb>chè non mancò fin d&#039;allora chi si volse a filosofar, piuttosto che <lb></lb>sui libri, sull&#039;osservazione e sull&#039;esperienza de&#039;fatti, come si vedrà <lb></lb>seguitando il nostro Discorso. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Perchè sempre i primi impulsi, che rivolsero la mente del­<lb></lb>l&#039;uomo alla investigazione dei fatti naturali, derivarono dai bisogni <lb></lb>e dal desiderio di conseguire alcuni utilı fini, e perchè per primi e <lb></lb>principali fra questi utili e questi bisogni venivano a rappresentarsi <lb></lb>quelli, che concernevano il modo di conservare la sanità o di re­<lb></lb>staurarla con l&#039;arte, se in qualunque modo fosse stata perduta; si <lb></lb>comprenderà facilmente com&#039;uno de&#039;primi oggetti, a cui si rivolse <lb></lb>la Filosofia naturale, dovess&#039;essere la Medicina: Platone e Aristotile <lb></lb>non avevano trascurato di farsi maestri anco di quest&#039;arte, e come <lb></lb>nelle discipline speculative, così in questa tennero divise, nella di­<lb></lb>versità de&#039;principii informativi e delle opinioni, le loro scuole: In­<lb></lb>stauratosi il nuovo Peripato non sembra che si sapesse trovare alla <lb></lb>cultura delle scienze fisiche miglior campo di quello della stessa <lb></lb>Medicina. </s>

<s>Ruggero Bacone, Alberto Magno, Raimondo Lullo perdono <lb></lb>il loro tempo e consumano il loro inchiostro in formular ricette e <lb></lb>in trovar segreti da guarire ogni sorta di mali. </s>

<s>Più tardi, anco <lb></lb>quando l&#039;Anatomia e la Fisica presentivano così d&#039;appresso l&#039;isti-<pb xlink:href="020/01/062.jpg" pagenum="43"></pb>tuzione galileiana, il Falloppio e il Porta, per tacere di altri minori, <lb></lb>rinnovellarono l&#039;esempio di que&#039;ricettarii e lusingarono i semplici <lb></lb>con que&#039;loro segreti. </s></p><p type="main">

<s>Apriamo per curiosità i libri <emph type="italics"></emph>De secretis mulierum<emph.end type="italics"></emph.end> di Alberto <lb></lb>Magno, o quell&#039;altro di Raimondo Lullo, che messer Pietro Lauro <lb></lb>volle rendere popolare, traducendolo dal latino, e facendolo stam­<lb></lb>pare in Venezia nel 1567 dai fratelli Sessa. </s>

<s>Il libro del Lullo, a <lb></lb>cui erasi dato nel frontespizio il titolo di filosofo acutissimo e di <lb></lb>celebre medico, è rivolto a trovar nientedimeno che la <emph type="italics"></emph>quintessenza,<emph.end type="italics"></emph.end><lb></lb>e il libro di Alberto a svelare i segreti della generazione. </s>

<s>I libri <lb></lb>di quegli antichi dottori, benchè fossero conosciuti a più prove non <lb></lb>contenere che falsità, allettarono nonostante così i medici e gli <lb></lb>scrittori del secolo XVI, che il gran Falloppio non isdegna abbas­<lb></lb>sarsi a impugnar la penna, per iscrivere un libro di <emph type="italics"></emph>Secreti diversi <lb></lb>e miracolosi.<emph.end type="italics"></emph.end> Forse, per onor del grand&#039;uomo potrebbesi ragione­<lb></lb>volmente congetturare che il libro fosse compilato dai discepoli e <lb></lb>spacciato sotto il suo nome, la qual congettura verrebbe confermata <lb></lb>dal veder che la stampa eseguita in Venezia nel 1582 occorse di­<lb></lb>ciannove anni dopo la morte dell&#039;Autore. </s>

<s>In qualunque modo, non <lb></lb>cessa perciò quella Falloppiana raccolta di Segreti diversi di esser <lb></lb>documento che attesti da quali umili principii avesse origine la <lb></lb>scienza naturale, in quel secolo, che immediatamente precede a <lb></lb>quello di Galileo. </s>

<s>E perchè più efficace riesca una tale testimonianza, <lb></lb>leggansi i soggetti che si trattano ne&#039;tre libri, ne&#039;quali la Raccolta <lb></lb>stessa dal compilatore venne divisa. </s>

<s>Nel primo si tratta il modo <lb></lb>di fare diversi olii, cerotti, unguenti, unzioni, elettuarii, pillole e <lb></lb>infiniti altri medicamenti. </s>

<s>Nel secondo s&#039;insegna a fare alcune sorti <lb></lb>di vini e acque molto salutifere, e nel terzo si contengono alcuni <lb></lb>importanti segreti di Alchimia ed alcuni altri segreti dilettevoli e <lb></lb>curiosi. </s></p><p type="main">

<s>Parecchi di que&#039;segreti, che si leggono nella Raccolta, la quale <lb></lb>và sotto il nome del Falloppio, piacquero a quell&#039;altro infaticabile <lb></lb>compilatore di ricette altrui e di altrui invenzioni, che fu Giovan <lb></lb>Batista Porta, ed ei ne infarcì que&#039;suoi quattro libri <emph type="italics"></emph>De&#039;miracoli <lb></lb>e maravigliosi effetti della Natura.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma che cosa sono in sostanza questi segreti proposti, e questi <lb></lb>miracolosi effetti della Natura, spacciati dagli Autori di così fatti <lb></lb>libri? </s>

<s>Niente altro, si capirà bene, che voci di cerretani. </s>

<s>Il prin­<lb></lb>cipio peripatetico, che cioè la Natura si governa colla ragione del­<lb></lb>l&#039;uomo e si muove, nel produrre i suoi effetti, a seconda dell&#039;umano <pb xlink:href="020/01/063.jpg" pagenum="44"></pb>discorso, vedesi vivamente in que&#039;libri, meglio che altrove, incar­<lb></lb>nato, apparendo chiaro per essi come nell&#039;arte medica non ci ha <lb></lb>a che far nulla l&#039;esperienza, e tutto consiste nello stillarsi il cer­<lb></lb>vello, e nel fare a chi sa meglio comporre insieme una strana ri­<lb></lb>cetta. </s>

<s>La sottilità dialettica, o per dir meglio, la più sfrenata fantasia <lb></lb>del medico è quella che dee operar nel malato ogni efficacia. </s></p><p type="main">

<s>Che il Peripato nuovo fosse principalmente rivolto alla Medi­<lb></lb>cina, lo attestano tre de&#039;più famosi fra i cultori delle scienze na­<lb></lb>turali, nel secolo XVI, Girolamo Fracastoro, Girolamo Cardano, e <lb></lb>Andrea Cesalpino, tutti e tre medici celebratissimi di professione. </s>

<s><lb></lb>Il primo di questi, veronese di patria e vissuto dal 1483 al 1553, <lb></lb>se si vuol pareggiar nell&#039;ingegno agli altri due, non è dubbio però <lb></lb>ch&#039;egli è d&#039;assai superiore a loro nella dignità della vita. </s>

<s>Che il <lb></lb>Fracastoro appartenga alla scuola peripatetica, a noi par cosa certa <lb></lb>bench&#039;egli molte volte dimostri di saper pensare da sè, cercando <lb></lb>cose nuove e tentando d&#039;investigare alcune delle verità naturali, <lb></lb>non colla dialettica aristotelica, ma per la via diretta dell&#039;esperienza. </s></p><p type="main">

<s>Che il celebre veronese avesse veramente saputo pensare anche <lb></lb>da sè, lo dice quel libro ch&#039;egli scrisse degli <emph type="italics"></emph>Omocentrici,<emph.end type="italics"></emph.end> dedicato <lb></lb>a quello stesso Paolo III, a cui il Copernico dedicò la grande opera <lb></lb><emph type="italics"></emph>De revolutionibus.<emph.end type="italics"></emph.end> Il nostro italiano, volere o no, rinnovellatore del­<lb></lb>l&#039;opinione di Eudossio, è il più prossimo precursore dell&#039;insigne <lb></lb>astronomo prussiano, restauratore del sistema di Aristarco. </s>

<s>Egli in­<lb></lb>tende principalmente a dimostrar che i pianeti non fanno le loro <lb></lb>rivoluzioni per cerchi eccentrici, ma per omocentrici e argutamente <lb></lb>interpetra alcune anomalie de&#039;loro moti mostrando, per esempio, <lb></lb>che il moto obliquo del sole per l&#039;ecclettica risulta dalla composi­<lb></lb>zione de&#039;due moti in longitudine e in latitudine, e affermando la <lb></lb>varietà dell&#039;inclinazione dell&#039;ecclittica stessa esser costante, e dover <lb></lb>perciò un giorno tornare a confondersi con l&#039;equatore, sicchè par <lb></lb>voglia così convalidare, coi placiti della scienza, una volgare opi­<lb></lb>nione degli antichi egiziani. </s></p><p type="main">

<s>Nel libro degli <emph type="italics"></emph>Omocentrici,<emph.end type="italics"></emph.end> o consapevole o no, vi si sente <lb></lb>aliar lo spirito di Platone, ed è forse perciò che il Fracastoro mo­<lb></lb>stra di sentir dispiacere e non lascia di far qualche scusa per avere <lb></lb>a contradire talvolta al suo Aristotile. </s>

<s>Così, in sul principio del ca­<lb></lb>pitolo sesto, riferendo l&#039;opinion del Filosofo, conforme alla quale le <lb></lb>orbite dei pianeti vengono per l&#039;attrito via via sempre più indugiate <lb></lb>dal primo mobile, secondo che sono a lui sempre più vicine, ragion <lb></lb>per cui tardissima è la sfera di Saturno, e velocissima quella della <pb xlink:href="020/01/064.jpg" pagenum="45"></pb>Luna; prima di sentenziar che una tale opinione o non è vera o <lb></lb>che è in contradizione con altri detti aristotelici, premette le parole: <lb></lb><emph type="italics"></emph>si licet de tanto philosopho dicere.<emph.end type="italics"></emph.end> Ritorna però l&#039;Autore agli os­<lb></lb>sequi del suo maestro, ogni volta che, disceso dalle sublimità della <lb></lb>Geometria platonica, viene a rasentare colle ali basse la fisica pe­<lb></lb>ripatetica. </s></p><p type="main">

<s>Egli vuol, per esempio, nel Capitolo VIII della II

a Sezione dello <lb></lb>stesso libro degli <emph type="italics"></emph>Omocentrici,<emph.end type="italics"></emph.end> render la ragione della varietà del <lb></lb>diametro apparente, che presentano il Sole e la Luna, secondo che <lb></lb>son più presso all&#039;orizzonte o al zenit, o secondo che si trovano <lb></lb>nel perigeo o nell&#039;apogeo, e crede di dover riconoscere quella ra­<lb></lb>gione, come fece Galileo, negli effetti ottici prodotti dalla sfera va­<lb></lb>porosa dell&#039;aria. </s>

<s>Ma, mentre Galileo attribuisce quegli effetti alla <lb></lb>maggiore o minore convessità della detta sfera, il Fracastoro invece <lb></lb>gli attribuiva alla maggiore o minore altezza del mezzo, professando <lb></lb>il principio che un diafano soprapposto a un diafano ingrandisce <lb></lb>sempre le specie. </s>

<s>Ora è chiaro che un tal principio derivava per <lb></lb>diretta via dalle fonti peripatetiche, o in altre parole non consisteva <lb></lb>altrimenti che in una ipotesi immaginaria, imperocchè, secondo fu <lb></lb>ritrovato poi dal medesimo Galileo, per esperienza, facilmente si <lb></lb>osserva che, soprainfondendo acqua ad acqua dentro un catino, la <lb></lb>moneta posata sul suo fondo non cresce nel diametro apparente, <lb></lb>anzi sembra talvolta qualche poco diminuire. </s></p><p type="main">

<s>Ma ciò che più chiaramente dimostra non essersi il Fracastoro <lb></lb>potuto sottrarre ai perniciosi influssi della scuola peripatetica, è <lb></lb>quell&#039;altro suo libro <emph type="italics"></emph>De Sympatia et anthipatia rerum,<emph.end type="italics"></emph.end> che egli <lb></lb>scrisse come Prodromo alla trattazione sua medica dei contagi. </s>

<s>E <lb></lb>a quel modo che egli attribuisce alla simpatia e alla antipatia le <lb></lb>cause fisiologiche e patologiche ne&#039;morbi pestilenziali; così alla <lb></lb>simpatia e alla antipatia attribuisce pure le cause occulte delle at­<lb></lb>trazioni elettriche e magnetiche nei fatti naturali. </s>

<s>Egli è vero, non <lb></lb>tralascia talvolta di ricorrere all&#039;esperienza, per assicurarsi de&#039;fatti <lb></lb>più particolari di quelle attrazioni, ma com&#039;egli mal vi riesca, si <lb></lb>vede nel capitolo VIII del citato libro <emph type="italics"></emph>De Sympathia.<emph.end type="italics"></emph.end> Il nostro me­<lb></lb>dico veronese fu de&#039;primi, com&#039;avvertì nell&#039;opera sua lo stesso Gil­<lb></lb>berto, ad attribuire la direzione dell&#039;ago magnetico ad alcune <lb></lb>montagne ferruginose, esistenti nelle regioni del polo nordico. </s>

<s>Ma <lb></lb>come anco questa non fosse, nella mente dell&#039;Autore, altro che una <lb></lb>pura ipotesi peripatetica, o in altri termini, immaginaria, lo dimo­<lb></lb>stra ad evidenza nel capitolo ultimo quella risposta, che ivi fa a <pb xlink:href="020/01/065.jpg" pagenum="46"></pb>Giovan Battista Rannusio, il quale opponeva che, se avesse fonda­<lb></lb>mento di qualche verità l&#039;ipotesi del Fracastoro, si sarebbe dovuto <lb></lb>veder fare qualche notabile alterazione all&#039;ago nautico, nel passar <lb></lb>che fanno i navigli presso all&#039;isola dell&#039;Elba. </s></p><p type="main">

<s>In qualunque modo però, il Fracastoro è un ingegno serio e <lb></lb>se cade in errore non se ne compiace e non lo scansa, perchè non <lb></lb>lo conosce. </s>

<s>Non così può dirsi dell&#039;altro medico milanese Girolamo <lb></lb>Cardano, che ebbe i natali in Pavia nel 1501. La lunghissima vita <lb></lb>protratta infino al 1596 non valse a correggerlo delle sue turpitu­<lb></lb>dini, le quali sfacciatamente confessa al pubblico nella Autobiografia, <lb></lb>attribuendole a inevitabili suggestioni de&#039;suoi Demonii. </s>

<s>Qualunque <lb></lb>siasi però la moralità de&#039;suoi costumi, a noi non s&#039;appartiene di <lb></lb>parlare che della scienza, la quale, perchè forse insozzata di fango <lb></lb>e rimescolata ai più strani errori e alle fantasie più stravaganti, è <lb></lb>stata, secondo noi, fin qui mal giudicata. </s>

<s>Di che si può fra&#039;molti <lb></lb>esempi citar quello de&#039;fuochi di S. Elmo, annoverandosi fra le <lb></lb>infinite stravaganze di lui quel che ne scrive nel II Libro <emph type="italics"></emph>De subti­<lb></lb>litate;<emph.end type="italics"></emph.end> stravaganze che poi il Beccaria ridusse alle vere cause dei <lb></lb>fenomeni e degli effetti consueti d&#039;operarsi naturalmente dall&#039;im­<lb></lb>provviso fulminare delle stellette o de&#039;fuochi elettrici. (Dell&#039;Elet­<lb></lb>tric., Torino 1753, pag. </s>

<s>222). </s></p><p type="main">

<s>L&#039;altro medico di professione, che qui s&#039;interza al Fracastoro <lb></lb>e al Cardano è quell&#039;Andrea Cesalpino, in cui si gloria la sua pa­<lb></lb>tria Arezzo d&#039;aver dato un precursore al fortunassimo Harvey. </s>

<s>Quali <lb></lb>meriti veramente competano al Peripatetico aretino, rispetto alla <lb></lb>grande scoperta della circolazione del sangue, lo vedranno i lettori <lb></lb>nel seguito della nostra storia, dove anche troveranno argomenti <lb></lb>da ammirare ciò che egli osservò di fisiologia vegetabile, e ciò che <lb></lb>egli speculò per sottordinare in generi e specie la svariata famiglia <lb></lb>delle piante. </s>

<s>Ma pure appresso a quelle pagine, dove in tanto piena <lb></lb>evidenza si mette l&#039;uso e l&#039;ufficio naturale della vena arteriosa e <lb></lb>dell&#039;arteria venosa, seguono altre pagine, dove l&#039;Autore intende a <lb></lb>sostener l&#039;opinione aristotelica dell&#039;origine dei nervi dal cuore. </s>

<s>Si­<lb></lb>milmente agli impulsi fisici di capillarità, per cui la linfa ascende <lb></lb>dalle radici alle foglie attraverso ai vasi, fa concorrere efficacemente, <lb></lb>l&#039;Autor <emph type="italics"></emph>De plantis,<emph.end type="italics"></emph.end> i superni influssi celesti. </s>

<s>Ma i cinque libri delle <lb></lb><emph type="italics"></emph>Peripatetiche questioni<emph.end type="italics"></emph.end> sono una tal palestra di sottigliezza d&#039;ingegno, <lb></lb>che se la Natura veramente assecondasse per poco il cervello del Ce­<lb></lb>salpino e quello di Aristotile suo maestro, il mondo, e le leggi che <lb></lb>lo governano, sarebbero sostanzialmente trasformate dall&#039;esser loro. </s></p><pb xlink:href="020/01/066.jpg" pagenum="47"></pb><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Fra&#039;tre sopra commemorati merita particolare attenzione quel <lb></lb>Girolamo Cardano, di cui si disse già, e ora da noi si ripete, che <lb></lb>la scienza fu mal giudicata. </s>

<s>Egli, oppresso dalla turba dei peripa­<lb></lb>tetici, e tante volte da loro soggiogato e ridotto alla più abietta viltà <lb></lb>dell&#039;ossequio, si prova di tratto in tratto a levar alta la fronte e <lb></lb>declama contro l&#039;autorità del Maestro, contrapponendogli l&#039;autorità <lb></lb>del raziocino e della esperienza. </s></p><p type="main">

<s>Due sono principalmente i libri scritti da lui in soggetto di <lb></lb>scienze sperimentali: quello <emph type="italics"></emph>De subtilitate<emph.end type="italics"></emph.end> e l&#039;altro <emph type="italics"></emph>De rerum va­<lb></lb>rietate.<emph.end type="italics"></emph.end> Il primo è una storia generale de&#039;principii delle cose natu­<lb></lb>rali e artificiali; il secondo si direbbe il <emph type="italics"></emph>Cosmo scientifico<emph.end type="italics"></emph.end> di quei <lb></lb>tempi. </s>

<s>Dedicando nel 1552 a Ferdinando Gonzaga, Principe di Mol­<lb></lb>fetta, i libri XXI <emph type="italics"></emph>De subtilitate,<emph.end type="italics"></emph.end> scrive che molte delle cose ivi dette <lb></lb>e delle più importanti, le ha dovute nasconder <emph type="italics"></emph>sub cortice,<emph.end type="italics"></emph.end> in grazia <lb></lb>de&#039;suoi contradittori, i quali, son sue parole, non hanno altro ar­<lb></lb>gomento da appormi da quello in fuori, <emph type="italics"></emph>quod ab Aristotile dissen­<lb></lb>tire videar. </s>

<s>Nam adeo humanum genus sibi iam prurit, ut malint <lb></lb>a veritate a sensu ab experimento a rationeque, denique ab omnibus <lb></lb>quam ab auctoritate viri discedere.<emph.end type="italics"></emph.end> E prosegue a dir di non sapere <lb></lb>intendere come mai si lodi Galeno, che tante volte contradice ad <lb></lb>Aristotele, e si condanni lui, che se ne dilunga una o due volte, e <lb></lb>dove vi sia costretto da chiarissime ragioni e da certissimi espe­<lb></lb>rimenti. </s></p><p type="main">

<s>I XVII libri <emph type="italics"></emph>De rerum varietate<emph.end type="italics"></emph.end> furono nel 1556 dedicati a <lb></lb>Cristoforo Madruzio, e nella lettera dedicatoria inveisce l&#039;Autore <lb></lb>contro quei pervicaci, i quali presumono il pelago immenso della <lb></lb>divina Sapienza restringer a capir nell&#039;umano vasello aristotelico <lb></lb><emph type="italics"></emph>exiguo nec satis integro,<emph.end type="italics"></emph.end> ed esclama contro costoro: <emph type="italics"></emph>Nonne stultos <lb></lb>si credant, invidos si non credant eos existimare oportet?<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Nel cap. </s>

<s>XXXVIII del libro VII di questa medesima opera, a <lb></lb>proposito del celebre Trattato <emph type="italics"></emph>De piscibus<emph.end type="italics"></emph.end> del Rondelezio, il Cardano <lb></lb>scriveva le notabilissime parole seguenti: “ Laudo equidem quod <lb></lb>propter veritatem Aristotilem et Galenum relinquat: quod autem <lb></lb>veritatem relinquat ut ab Aristotile vel alio discedat, non laudo. <pb xlink:href="020/01/067.jpg" pagenum="48"></pb>Multi enim conantur nos imitari, qui ab Aristotile dissentimus <lb></lb>uno vel altero loco, sed non ita dissentimus, ut experimentum <lb></lb>et validas rationes illi opponamus. </s>

<s>Atque id non ut illum oppu­<lb></lb>gnemus, sed quoniam ars ipsa, quae innumera docet artificia, <lb></lb>aliter constitui non poterat, adeo ut si ipse reviviscat Aristotiles, <lb></lb>vel in nostram opinionem venturus sit, vel saltem non aegre la­<lb></lb>turus quod tot evidentibus rationibus, ob tantamque utilitatem <lb></lb>ab eo discesserim ” (Basilaee 1581, pag. </s>

<s>381). E chi è mai che, <lb></lb>leggendo queste parole, non ricorra col pensiero e non torni colla <lb></lb>memoria a quell&#039;altre simili scritte da Galileo: “ Avete voi forse <lb></lb>dubbio che, quando Aristotele vedesse le novità scoperte in cielo, <lb></lb>e&#039;non fosse per mutare opinione e per emendare i suoi libri? </s>

<s>” <lb></lb>(Alb. </s>

<s>I, 124). Il Cardano dunque professa principii simili a quelli <lb></lb>di Galileo, e ha sotto le zolle inculte seminati i medesimi germi <lb></lb>scienziali, da cui non è possibile che non si produca, alla sua sta­<lb></lb>gione, qualche buon frutto, e sia pure, come si vuole silvestro e <lb></lb>immaturo. </s>

<s>Aprendo gl&#039;incolti rami intricati, e scoprendo le foglie <lb></lb>lussuriose, a chi dentro ci guardi attentamente non è difficile d&#039;in­<lb></lb>contrar qua e là con l&#039;occhio in qualcuno di questi frutti. </s></p><p type="main">

<s>Apriamo nel libro II <emph type="italics"></emph>De subtilitate,<emph.end type="italics"></emph.end> dove tratta degli elementi. </s>

<s><lb></lb>S&#039;entra addentro a una questione di meccanica importantissima, dal <lb></lb>gran maestro Aristotele così mal definita: alla questione dei moti <lb></lb>violenti. </s>

<s>Dop&#039;avere annoverate le varie sentenze degli antichi filo­<lb></lb>sofi, il Cardano conclude: “ Sed nos magis indigemus prima, quae <lb></lb>est simplicissima, et etiam non tantas difficultates patitur, et cum <lb></lb>supponitur quod omne quod movetur ab aliquo movetur, veris­<lb></lb>simum est sed illud quod movet est impetus acquisitus, sicut <lb></lb>calor in aqua ” (Lugduni 1580, pag. </s>

<s>93). </s></p><p type="main">

<s>Ecco intanto confermata, contro i perniciosi errori di Aristotile, <lb></lb>la verità che il proietto non è mosso dall&#039;aria, ma dalla virtù del <lb></lb>proiciente, che gli rimane impressa come il calore nell&#039;acqua, ed <lb></lb>ecco insieme, col principio d&#039;inerzia, posti i primi fondamenti alla <lb></lb>Meccanica. </s>

<s>Il moto violento, prosegue a dir l&#039;Autore, è tanto più <lb></lb>celere quanto il proiciente si muove più celermente e per più lungo <lb></lb>spazio accompagna il proietto, e quanto è meno denso il mezzo e <lb></lb>il proietto stesso è più acuminato. </s>

<s>La via descritta per l&#039;aria in <lb></lb>principio a in fine del moto, è retta, <emph type="italics"></emph>sed media quasi linea quae <lb></lb>parabolae forma imitatur<emph.end type="italics"></emph.end> (ibi. </s>

<s>pag. </s>

<s>96). Che se a colui che ri­<lb></lb>pensa ai progressi galileiani sembrano queste antiche tradizioni della <lb></lb>scienza italiana di grande importanza, d&#039;importanza minore non <pb xlink:href="020/01/068.jpg" pagenum="49"></pb>giudicherà certo quel che seguita a specular l&#039;Autore intorno ai <lb></lb>pendoli di varia lunghezza, e alla ragion ch&#039;ei ne rende del veder <lb></lb>gravissimi corpi sospesi venir mossi quasi col soffio incantatore di <lb></lb>una parola. </s></p><p type="main">

<s>Ma il cap. </s>

<s>VI del I libro <emph type="italics"></emph>De rerum varietate,<emph.end type="italics"></emph.end> a chi ripensi che <lb></lb>fu scritto tanti anni prima di quello del Castelli, riesce un mara­<lb></lb>viglioso trattatello della misura delle acque correnti. </s>

<s>La gran legge <lb></lb>delle quantità proporzionali al prodotto della velocità per la sezione, <lb></lb>il Cardano non la dimostra, ma la tien come un supposto; tanto a <lb></lb>lui, com&#039;a tutti, par semplice e vera. “ Ut vero eam constituamus, <lb></lb>duo supponere necesse est: alterum quod iuxta foraminis ampli­<lb></lb>tudinem aqua defertur; alterum quod iuxta impetum ” (pag. </s>

<s>61). </s></p><p type="main">

<s>Nel correr che fa l&#039;acqua dentro i tubi chiusi, specialmente <lb></lb>se sieno pieni, osserva sagacemente il Cardano che la non è libera <lb></lb>nel suo moto, dovendosi tirare altr&#039;acqua dietro, per evitare la <lb></lb>discontinuità, ma giunta allo sbocco, si trova a dover ubbidire al­<lb></lb>l&#039;impeto di due forze, una violenta e l&#039;altra naturale, per cui segue <lb></lb>una via di mezzo. </s>

<s>Chi ripensi alle difficoltà incontrate in tal pro­<lb></lb>posito da Galileo, promosse da coloro che dicevano non esser pos­<lb></lb>sibile che di due forze, le quali operano nello stesso tempo con <lb></lb>varia direzione d&#039;impulsi, l&#039;una non impedisca il libero esercizio <lb></lb>dell&#039;altra, ammirerà il Cardano che per la intricata via della verità <lb></lb>procede così diritto e sicuro. </s>

<s>Nè l&#039;ammirerà meno, quando pro­<lb></lb>ponendosi di risolvere il quesito: <emph type="italics"></emph>cur aquae a lateribus etiam stan­<lb></lb>tium paludum effusae per rimas tabularum impetum secum affe­<lb></lb>rant<emph.end type="italics"></emph.end> (pag. </s>

<s>69) mostra di non aver nemmeno aombrato, non che <lb></lb>offeso nell&#039;errore del Michelini, il quale verrà, dopo i tempi di Ga­<lb></lb>lileo e del Castelli e del Torricelli, ad affermar che l&#039;acqua non <lb></lb>fa impeto alcuno sopra le sponde, ma lo rivolge tutto a premere <lb></lb>il fondo dei vasi. </s></p><p type="main">

<s>Intin da que&#039;tempi, notizia da non si dover trascurare nella <lb></lb>storia dell&#039;Idraulica, a riconoscer la varia velocità degli strati delle <lb></lb>acque correnti, si faceva uso degli <emph type="italics"></emph>Idrometri,<emph.end type="italics"></emph.end> e segnatamente di <lb></lb>quelli, dall&#039;altra parte semplicissimi, de&#039;quali il Cabeo si dice che <lb></lb>fosse il primo a far uso. </s>

<s>E giusto col <emph type="italics"></emph>baculo idrometrico<emph.end type="italics"></emph.end> s&#039;era vo­<lb></lb>luto, a tempi del Cardano, argomentar che gli strati infimi corrono <lb></lb>più velocemente de&#039;sommi, dal veder che l&#039;estremità inferiore del <lb></lb>baculo stesso veniva pinta in avanti. </s>

<s>Ma il Cardano, che negava il <lb></lb>fatto e ammetteva esser più veloci di tutti gli altri, gli strati superfi­<lb></lb>ciali, ricorre a un argomento, che ha dello strano, benchè sia però <pb xlink:href="020/01/069.jpg" pagenum="50"></pb>largamente ricompensata questa stranezza da un&#039;altra osservazione <lb></lb>idrometrica, che non fa qui, ma nell&#039;altro libro <emph type="italics"></emph>De subtilitate.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Una tale osservazione riguarda l&#039;equilibrio dell&#039;acqua ne&#039;sifoni, <lb></lb>e scopre un errore di coloro, i quali credono potersi per un con­<lb></lb>dotto far tanto risalir l&#039;acqua quanto ella è scesa. </s>

<s>Ma il vero è, dice <lb></lb>il Cardano, che la si riman l&#039;acqua stessa sempre alquanto al disotto <lb></lb>e con tanta maggior differenza quanto la via percorsa è più lunga. <lb></lb>“ Quanto enim longior via fuerit, eo maior differentia, iuxta alti­<lb></lb>tudinis mensuram esse debet. </s>

<s>Hinc errores quorundam, qui ad <lb></lb>libramentum cum conati essent aquas deducere maximas iactu­<lb></lb>ras impensarum susceperunt ” (pag. </s>

<s>25). Quando in Firenze, <lb></lb>tanti anni dopo da che furono scritte queste parole, si vollero <lb></lb>dalle sorgenti di Pratolino derivar l&#039;acque ad alimentar le fon­<lb></lb>tane di Boboli, Andrea Arrighetti teoricamente confermava gli av­<lb></lb>vertimenti pratici del Cardano, e i fatti in quel caso sperimentati <lb></lb>attestarono delle verità predicate dal fisico milanese, e dal disce­<lb></lb>polo di Galileo. </s></p><p type="main">

<s>Ma un&#039;altro discepolo di Galileo, Evangelista Torricelli, in fatto <lb></lb>della più rumorosa e più importante scoperta che sia stata fatta, <lb></lb>va a riscontrarsi colle stesse sottilità della fisica antica. </s>

<s>Il vieto au­<lb></lb>tore di queste <emph type="italics"></emph>Sottilità<emph.end type="italics"></emph.end> non vuol sentir parlare di orrore o di fuga <lb></lb>del vacuo. </s>

<s>Là dove si prova a render la ragione del moto ne&#039;sifoni <lb></lb>da travasare i liquidi, accenna all&#039;aria sopraincombente che ne aiuta <lb></lb>quel moto, benchè sarebbe senza dubbio temerità l&#039;asserire che <lb></lb>avesse riconosciuto in quel fatto idrostatico l&#039;intervento della pres­<lb></lb>sione atmosferica. </s>

<s>Altrove infatti nel render la ragione del perchè <lb></lb>in un vaso, estratta coll&#039;aspirazion della bocca l&#039;aria, si veda sot­<lb></lb>tentrare in suo luogo l&#039;acqua, dice che la poca aria rimasta, affinchè <lb></lb>non diasi il vuoto, attrae l&#039;acqua stessa di che lo Scaligero lo ri­<lb></lb>prende con queste parole: “ Nam quare sapientiorem facis aerem <lb></lb>ut moveat aquam ad subeundum, aquam negligentiorem ad adim­<lb></lb>plendum vacuum? </s>

<s>” (De subtil. </s>

<s>Francof. </s>

<s>1592, pag. </s>

<s>58). Il Car­<lb></lb>dano insomma non si appose al vero, ma non è piccola gloria per <lb></lb>lui l&#039;aver, benchè così dalla lontana, aperti i chiusi e intricati sen­<lb></lb>tieri al Torricelli, sostituendo a un nome vano un fatto. </s>

<s>Il fatto <lb></lb>fisico che egli sostituisce al peripatetico orrore del vacuo è che i <lb></lb>corpi non patiscono d&#039;essere rarefatti, se non che dentro certi li­<lb></lb>miti, oltrepassati i quali o si rompono o danno luogo per attrazione <lb></lb>a sottentrarvi altri corpi. “ Ergo in universum tres erunt motus <lb></lb>naturales. </s>

<s>Primus quidem ac validissimum a vacui fuga, sed ve-<pb xlink:href="020/01/070.jpg" pagenum="51"></pb>rius a forma elementi, cum maiorem raritatem non admittat, nec <lb></lb>materiae partes separari nunquam queant ” (pag. </s>

<s>17). </s></p><p type="main">

<s>Il nome di Giuseppe Scaligero è tanto strettamente connesso <lb></lb>con quel del Cardano, che quasi, com&#039;è avvenuto a noi stessi di <lb></lb>sopra, non si può parlare della scienza dell&#039;uno, senza che si vegga <lb></lb>intromettersi per qualche parte, e anzi irrompere con violenza in <lb></lb>mezzo la scienza anche dell&#039;altro. </s>

<s>Egli infatti scrisse un libro collo <lb></lb>stesso titolo <emph type="italics"></emph>De subtilitate,<emph.end type="italics"></emph.end> a solo fine di contrapporre a quelle del <lb></lb>Cardano le sottigliezze sue proprie. </s>

<s>Il filosofo veronese però, sia <lb></lb>scaltrezza o sia ossequio sincero, non appunta mai direttamente <lb></lb>l&#039;armi del raziocinio e della esperienza contro Aristotile, che egli <lb></lb>appella <emph type="italics"></emph>humanae sapientiae parentem,<emph.end type="italics"></emph.end> ma, là dove il testo non gli <lb></lb>par che s&#039;arrenda bene ai nuovi fatti sperimentali, ne scusa reve­<lb></lb>rentemente il Filosofo e ne incolpa i commentatori. </s></p><p type="main">

<s>Una delle sottigliezze cardaniche da farne più conto, vedemmo <lb></lb>esser quella, che l&#039;Autore esercitò a definir la natura del moto vio­<lb></lb>lento e a stabilire il principio d&#039;inerzia. </s>

<s>Lo Scaligero si mise con <lb></lb>altre sottilità a frugar dentro allo stesso soggetto, e non potendo <lb></lb>questa volta cogliere in fallo il suo nemico, lo punzecchia dicendo <lb></lb>ch&#039;egli era venuto a insegnar cose note infino ai fanciulli, i quali <lb></lb>pur sanno <emph type="italics"></emph>vim impellentis nervi relictam in sagitta.<emph.end type="italics"></emph.end> L&#039;esempio poi <lb></lb>del moto che rimane impresso nel mobile, come il calore nell&#039;acqua, <lb></lb>dice essere stato addotto già dall&#039;antico filosofo Temistio. </s>

<s>Del resto, <lb></lb>soggiunge lo Scaligero, che l&#039;aria non abbia parte nel moto violento, <lb></lb>non occorrono a persuadercelo gli argomenti del Cardano, avendone <lb></lb>noi le certissime prove nell&#039;esperienza. “ Quam vero ea ratio nulla <lb></lb>sit satis patebit demonstratione. </s>

<s>Sit levissima tabula ex qua exi­<lb></lb>matur orbis torno aut circino incidente, ita ut sine mutuo attritu <lb></lb>orbis ille intra illud cavum circumagi queat ” (ibi pag. </s>

<s>130). Fatta <lb></lb>girar la ruzzola, per via di un manubrio infisso, ella seguita a gi­<lb></lb>rare anco quando sia rimossa la mano. </s>

<s>Or dov&#039;è qui l&#039;aria, domanda <lb></lb>lo Scaligero, che mantien vivo nella stessa ruzzola il moto? </s>

<s>Quella <lb></lb>che riman dentro al sottilissimo fesso è sì poca, da non si creder <lb></lb>capace di produr quell&#039;effetto. </s></p><p type="main">

<s>Chi leggendo queste parole del peripatetico di Verona, si ri­<lb></lb>sovviene di una simile esperienza descritta, a provar lo stesso in­<lb></lb>tento, da Galileo, resterà preso da qualche maraviglia, la quale gli <lb></lb>si dovrebbe accrescere anche di più passando alla 331 Esercitazione, <lb></lb>dove l&#039;Autore tratta della forza della percossa. </s>

<s>Ivi, dop&#039;aver confu­<lb></lb>tate le puerilità del Cardano e avervi sostituito quel principio vero <pb xlink:href="020/01/071.jpg" pagenum="52"></pb>che il moto al mobile grave aggiunge sempre più peso; commemora <lb></lb>affettuosamente il suo Maestro, unico interprete de&#039;disegni archi­<lb></lb>tettonici di Bramante, il qual Maestro aveva calcolato qual propor­<lb></lb>zione avesse il pugno dell&#039;uomo in quiete col pugno che ferisce. <lb></lb>“ Sed et haec et alia tunc illa demonstrabat, quae postea fortunae <lb></lb>saevitia interiere. </s>

<s>” Che se invece fosse stata la fortuna propizia, <lb></lb>avremmo avuto in Giovanni Del Giocondo quella parte di scienza <lb></lb>Nuova quasi un secolo prima di Galileo. </s></p><p type="main">

<s>E più di un secolo prima aveva lo stesso Scaligero preannun­<lb></lb>ziata quella verità tanto contraria agli oracoli aristotelici che cioè la <lb></lb>luce, come il suono, si muove in tempo e nò in istante, verità a <lb></lb>dimostrar la quale, si faticarono inutilmente Galileo e i più insigni <lb></lb>sperimentatori della sua scuola. “ Non enim ab immaterialitate <lb></lb>ductum argumentum, egli dice, satis validum est. </s>

<s>Nam neque soni <lb></lb>species, quae aeque immaterialis est, sine tempore defertur ”<lb></lb>(pag. </s>

<s>873). </s></p><p type="main">

<s>Or chi, oltre alle cose qui sopra esposte, ripensi all&#039;importanza <lb></lb>che ebbero queste dottrine ne&#039;progressi dell&#039;ottica, e alla più grande <lb></lb>importanza che ebbe le questione del vacuo, la quale si pose dallo <lb></lb>Scaligero, pur contro alle comuni dottrine aristoteliche, per condi­<lb></lb>zione essenziale alla natura del moto; s&#039;avvedrà quanto diritto <lb></lb>s&#039;abbian questi farraginosi volumi, che abbiam nel presente para­<lb></lb>grafo squadernati innanzi ai nostri lettori, ad esser commemorati <lb></lb>in una storia del metodo sperimentale in Italia. </s></p><p type="main">

<s>Un altro nome, oltre allo Scaligero, che si collega, benchè con <lb></lb>altro vincolo e per altro richiamo al Cardano, è quello di Niccolò <lb></lb>Tartaglia, nato in Brescia intorno al 1500 e morto 57 anni dopo. </s>

<s><lb></lb>Ei si potrebbe senza dubbio annoverare tra quei cultori dell&#039;arte, <lb></lb>de&#039;quali parleremo più sotto, che non avendo avuto a maestri i <lb></lb>libri ma la stessa Natura, e non essendo perciò rimasti offesi dai <lb></lb>pregiudizi peripatetici, poterono liberamente correr la via de&#039;loro <lb></lb>progressi. </s>

<s>Quel che infatti il Papadopoli afferma esser cioè venuto <lb></lb>Niccolò con Lodovico Balbisone allo studio di Padova, non s&#039;è po­<lb></lb>tuto ancora provare con documenti, e dall&#039;altra parte è assai chiara <lb></lb>la storia che ne&#039;<emph type="italics"></emph>Quesiti e Inventioni<emph.end type="italics"></emph.end> fa l&#039;Autore di sè e de&#039;suoi <lb></lb>studii. </s></p><p type="main">

<s>Lo stile incolto, con ch&#039;è scritto quel libro e l&#039;altro della <emph type="italics"></emph>Nuova <lb></lb>Scientia<emph.end type="italics"></emph.end> dello stesso Tartaglia, ci confermano in quella opinione e <lb></lb>costituiscono uno de&#039;punti più caratteristici della somiglianza che <lb></lb>passa tra Niccolò da Brescia e Leonardo da Vinci; somiglianza <pb xlink:href="020/01/072.jpg" pagenum="53"></pb>esteriore di forma, che fa presentire una più intima somiglianza <lb></lb>della materia e del soggetto proprio de&#039;loro studi. </s>

<s>Chi volesse poi <lb></lb>scorgere quel tal punto di somiglianza un po&#039;più d&#039;appresso, non <lb></lb>dovrebbe far altro che mettersi a confrontare la prima carta de&#039;<emph type="italics"></emph>Que­<lb></lb>siti e Inventioni,<emph.end type="italics"></emph.end> dove si espongono i soggetti da trattarsi ne&#039;primi <lb></lb>sei libri, con la lettera che Leonardo scriveva a Lodovico Moro, <lb></lb>perchè, riconosciutane l&#039;abilità, si risolvesse di richiamarlo più sol­<lb></lb>lecitamente al suo servizio. </s></p><p type="main">

<s>Ma il Bresciano, che rimane inferiore a quel da Vinci nella <lb></lb>varietà e nella estensione de&#039;soggetti naturali trattati, lo supera <lb></lb>nella intensità e nel lucido ordine con che è riuscito a trattare le <lb></lb>parti. </s>

<s>La <emph type="italics"></emph>Nuova Scientia,<emph.end type="italics"></emph.end> per verità, non ha molto del nuovo. </s>

<s>La <lb></lb>legge della caduta dei gravi è quella stessa professata da Leonardo <lb></lb>da Vinci e da tutti coloro che rimasero ingannati dal creder che <lb></lb>gl&#039;impeti sieno proporzionali alle altezze d&#039;onde discendono i corpi. </s>

<s><lb></lb>Rispetto alla curva descritta dai proietti, il Tartaglia rimane indietro <lb></lb>al Cardano, che intravide nelle curve traiettorie una certa somi­<lb></lb>glianza colla parabola. </s>

<s>Nonostante è notabile che fosse dalle sotti­<lb></lb>gliezze geometriche condotto a indovinare la massima ampiezza <lb></lb>de&#039;tiri di artiglieria aversi allora, quando l&#039;obice è inclinato di 45 <lb></lb>gradi sull&#039;orizzonte. </s>

<s>Poco perciò sembra che giovasse a scoprir cose <lb></lb>nuove l&#039;ordine matematico tenuto dall&#039;Autore e la lucida esposi­<lb></lb>zione del libro. </s>

<s>Più novità forse ha nell&#039;altro delle <emph type="italics"></emph>Inventioni,<emph.end type="italics"></emph.end> scritto <lb></lb>in Dialogo, e dove si contrappongono agli errori di Aristotile i veri <lb></lb>principii della statica. </s>

<s>Dialogizzando l&#039;Autore con don Diego di Men­<lb></lb>doza, nel VII libro introduce il discorso intorno alle Questioni mec­<lb></lb>caniche di Aristotile, e segnatamente sopra la prima espressa dal <lb></lb>Filosofo in questa forma “ Perchè causa le maggior libre ovver <lb></lb>bilance sono più diligenti delle minori. </s>

<s>” Il Tartaglia esamina sot­<lb></lb>tilmente la cosa e incomincia dall&#039;osservare che il problema è di­<lb></lb>fettoso nella stessa sua enunciazione e che sarebbe convenuto prima <lb></lb>di tutto all&#039;Autore distinguere tra il fatto naturale e il fatto mate­<lb></lb>matico. </s>

<s>Riguardate matematicamente le braccia della bilancia, come <lb></lb>linee geometriche, è vero, dice il Tartaglia, l&#039;asserto di Aristotile, <lb></lb>ma è falso riguardate quelle stesse braccia fisicamente, e tali quali <lb></lb>sono in natura, perchè allora, invece di essere più diligenti le bi­<lb></lb>lancie di lunghe braccia sono invece quelle di braccia corte, come <lb></lb>l&#039;esperienza dimostra nelle bilancette o saggiatori degli orefici e <lb></lb>dei monetari. </s></p><p type="main">

<s>La questione meccanica sottilmente discussa qui dal Bresciano, <pb xlink:href="020/01/073.jpg" pagenum="54"></pb>è notabilissima, perchè forse è la prima volta che il testo aristotelico <lb></lb>si accusi di errore a viso aperto. </s>

<s>E benchè l&#039;Ambasciatore cesareo, <lb></lb>interlocutore nel Dialogo, non si conducesse così facilmente a cre­<lb></lb>dere la cosa, perchè Aristotile <emph type="italics"></emph>non era un oca,<emph.end type="italics"></emph.end> l&#039;Autore pure lo <lb></lb>persuade con buone ragioni, concludendo che il Filosofo era incorso <lb></lb>in tal grossolano errore, perchè a lui mancava la <emph type="italics"></emph>scienza dei pesi,<emph.end type="italics"></emph.end><lb></lb>ossia i principii della statica, de&#039;quali il Tartaglia poi di proposito <lb></lb>passa a trattar nel seguente VIII libro delle <emph type="italics"></emph>Inventioni.<emph.end type="italics"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Abbiamo detto che il Tartaglia fù de&#039;primi a notare gli errori <lb></lb>aristotelici a viso aperto: gli esempi infatti recati dal Fracastoro, <lb></lb>dallo Scaligero, e da molti altri hanno mostrato una certa trepida­<lb></lb>zione, ogni volta che son dovuti mettersi a contradire al loro e <lb></lb>universale Maestro. </s>

<s>Il Cardano stesso intrattien lunghi discorsi qua <lb></lb>e là per iscusarsene, e non trova altro migliore espediente a placar <lb></lb>gli animi degli scandalizzati, che di accusar le corruzioni del testo <lb></lb>e l&#039;ignoranza dei commentatori. </s>

<s>Ma il rimprovero che in uno dei <lb></lb>passi da noi sopra citati fa a coloro, che troppo audacemente vo­<lb></lb>levano imitarlo, in denunziar pubblicamente i falli dell&#039;oracolo <lb></lb>venerato, mostra che negli ingegni speculativi ferveva un segreto <lb></lb>ardore di conquistare la propria libertà, per cui poco stette che <lb></lb>que&#039;tumulti così compressi, uscirono in una guerra combattuta in <lb></lb>campo aperto, in mezzo al quale fù de&#039;primi e più animosi a com­<lb></lb>parire il Tartaglia, senza visiera. </s></p><p type="main">

<s>Il campo tenuto dal Tartaglia però era circoscritto e ristretto <lb></lb>nelle questioni della meccanica e in alcuni problemi di fisica, di <lb></lb>che non restavan contenti i filosofi che intendevano oramai di con­<lb></lb>quistare la loro piena libertà in ogni genere di scientifica cultura. </s>

<s><lb></lb>A capitanar la numerosa falange, uscita fuori a questa nuova con­<lb></lb>quista, insorsero principalmente Bernardino Telesio consentino, e <lb></lb>Francesco Petrinsevich, dalmata, conosciuto sotto il nome latiniz­<lb></lb>zato di Patricio, per noi Patrizio, ambedue i quali dettero opera a <lb></lb>speculare una nuova Filosofia della Natura, da contrapporsi a quella <lb></lb>dello Stagirita. </s>

<s>Il Patrizio, nel II tomo delle sue <emph type="italics"></emph>Discussioni,<emph.end type="italics"></emph.end> an­<lb></lb>dava liberamonte scrivendo che l&#039;ammirazione avuta da tutti per <pb xlink:href="020/01/074.jpg" pagenum="55"></pb>Aristotile era immeritata, imperocchè moltissime delle cose scritte <lb></lb>da lui son desunte da più antichi filosofi, specialmente pitagorici, <lb></lb>e altrove più ricisamente soggiunge che Aristotile stesso ne&#039;suoi <lb></lb>libri poco o nulla ha del suo. </s></p><p type="main">

<s>Da ciò è facile intravedere la risoluzione presa dal Filosofo <lb></lb>dalmata di rivolgersi ad altre scuole e con preferenza alla pitagorica <lb></lb>e alla platonica, o meglio di speculare colla sua propria ragione, <lb></lb>piuttosto che con quella del preteso maestro di coloro che sanno. </s>

<s><lb></lb>Una tal animosa risoluzione viene eloquentemente espressa dal­<lb></lb>l&#039;Autore in quella Apologia, che egli scrisse contro un tal Teodoro <lb></lb>Angeluzio, che s&#039;era accanitamente posto contro i nuovi insorti a <lb></lb>difendere il sacro regno peripatetico. </s>

<s>“ Ma regnate, egli dice in la­<lb></lb>tino eloquio, regnate, infintanto che a voi è lecito o piace. </s>

<s>Noialtri <lb></lb>omiccioli lasciateci vivere, lasciateci spirar quest&#039;aure, che sono a <lb></lb>tutti comuni, permetteteci sentimenti e idee, che non sieno aristo­<lb></lb>teliche. </s>

<s>Non ci disprezzate, non ci avventate ingiurie, non carica­<lb></lb>teci di calunnie. </s>

<s>Non vi adirate con noi, perchè non guardiamo ai <lb></lb>medesimi obietti e non accolghiamo i medesimi responsi. </s>

<s>Permet­<lb></lb>teci poter esser platonici, se vogliamo, e in Filosofia piuttosto amici <lb></lb>a Plotino a Proclo a Damascio, che a que&#039;vostri omaccioni, Averrois, <lb></lb>Duns, Janduno, Tartareto, e simili altre filosofiche quisquiglie. </s>

<s>Per <lb></lb>metteteci di pensare anche qualche cosa col nostro ingegno, tenue <lb></lb>sì ma libero. </s>

<s>Non ci siate tiranni nè vogliate implicarci nelle reti <lb></lb>delle vostre contenzioni o avvolgerci fra le tenebre de&#039;vostri dom­<lb></lb>mi ” (Ferrariae, 1584, pag. </s>

<s>4). </s></p><p type="main">

<s>Da così fatte parole del Patrizio, come da altre simili che si <lb></lb>potrebbero citar dal Telesio, si sentono spirar con impeto le aure <lb></lb>della libertà, ma quell&#039;impeto è temperato, e se fa piegar gagliar­<lb></lb>damente le fronde, pur non le schianta. </s>

<s>Non è così de&#039;due altri <lb></lb>insorti a detronizzare Aristotile poco dopo i tempi del filosofo con­<lb></lb>sentino e del dalmata. </s>

<s>Essi sono due frati, che perciò ingaggiano <lb></lb>una doppia battaglia, contro i Filosofi e contro i Teologi dei loro <lb></lb>tempi e hanno fieramente impugnato le armi contro due regni fra <lb></lb>sè confederati: quello del Peripato e quello della Scolastica. </s>

<s>L&#039;uno <lb></lb>di que&#039;due, nato a Nola, verso la metà del secolo XVI, e spento <lb></lb>nel 1600 per morte violenta, è il celebre Giordano Bruno, l&#039;altro, <lb></lb>nato in Stilo di Calabria e che passò molta parte della vita, decor­<lb></lb>sagli dal 1568 al 1639, nel fondo di una carcere, è il non men ce­<lb></lb>lebre Tommaso Campanella. </s>

<s>Son due fieri ingegni: lo spirito di li­<lb></lb>bertà soffia dal loro petto, colla furia incomposta dell&#039;uragano, per <pb xlink:href="020/01/075.jpg" pagenum="56"></pb>cui l&#039;uno incontrò la carcere e l&#039;altro il rogo. </s>

<s>Nessuno in Filosofia <lb></lb>ne sa&#039;quanto loro: Aristotile, per Giordano, è un povero ingegno <lb></lb>meschino, pel Campanella è uno stolto. </s></p><p type="main">

<s>A così fatti arditissimi ingegni si suol da&#039;moderni dare il no­<lb></lb>me di <emph type="italics"></emph>Razionalisti,<emph.end type="italics"></emph.end> e son la delizia e l&#039;ammirazione degli scrittori <lb></lb>de&#039;nostri tempi, alcuni de&#039;quali riconoscono in essi i precursori <lb></lb>del metodo sperimentale, e altri, con più ardente zelo, gli venerano <lb></lb>come confessori e martiri del libero pensiero. </s>

<s>Non è del proposito <lb></lb>nostro trattar di confessioni o di martirii, ma della scoperta de&#039;veri <lb></lb>sperimentali, in cooperare alla quale scoperta, giova, con breve e <lb></lb>diligente esame veder qual fosse veramente il merito di quegli <lb></lb>ammirati filosofi peregrini. </s></p><p type="main">

<s>Chi provasse piacere di sentirsi portato in aria sull&#039;ali di me­<lb></lb>tafisiche speculazioni, e veder dalla fantasia architettati i mondi, <lb></lb>potrebbe per prima cosa, fra gli altri libri, scegliere quel che il <lb></lb>Telesio intitolò <emph type="italics"></emph>De natura iuxta propria principia.<emph.end type="italics"></emph.end> Chi desiderasse <lb></lb>poi di scendere a cose più positive, potrebbe dello stesso Autore <lb></lb>leggere i Commentarii, che egli scrisse pur <emph type="italics"></emph>De Rerum Natura,<emph.end type="italics"></emph.end> ma <lb></lb>a chi piacesse meglio vedere in più ristretto campo condensate e <lb></lb>raccolte le virtù dello scrittore, basterebbe si rivolgesse a que&#039;tre <lb></lb>brevi opuscoli stampati separatamente in Napoli, tutti e tre nel me­<lb></lb>desimo anno 1570, e nel primo de&#039;quali si tratta de&#039;fenomeni che <lb></lb>si osservan nell&#039;aria, nel secondo, di ciò che accade nel mare, e <lb></lb>si dà nel terzo la teoria de&#039;colori. </s></p><p type="main">

<s>Nel primo di quegli opuscoli piglia ad esaminare il Telesio le <lb></lb>teorie fisiche professate da Aristotile circa all&#039;origine delle pioggie <lb></lb>e dei venti, e nega che questi, sempre, come vuole il Filosofo, si <lb></lb>generino dalle umide esalazioni della terra. </s>

<s>Egli avverte, al contrario, <lb></lb>che per lo più i venti si levano su dal mare, il quale, più che la <lb></lb>terra stessa, offre abbondante copia di umidità, che rarefatta al calor <lb></lb>del sole si trasforma in esalazione ventosa. </s>

<s>Di qui si comprende <lb></lb>intanto che il filosofo di Cosenza, censore acuto del filosofo di Sta­<lb></lb>gira, non fa poi altro che ritornar sui medesimi errori fisici di lui, <lb></lb>il quale, ingannato dagli effetti dell&#039;evaporazion dell&#039;acqua al calore, <lb></lb>si dava facilmente a credere che l&#039;acqua stessa si trasformasse nella <lb></lb>sostanza del vento. </s></p><p type="main">

<s>Nè miglior fisico dell&#039;antico si mostra il nuovo nell&#039;altro opu­<lb></lb>scolo, dove tratta della salsedine del mare e del flusso e riflusso. </s>

<s><lb></lb>Diceva Aristotile che il mare era salato perchè il sole, facendolo <lb></lb>evaporare, ne avea sottratta la parte dolce. </s>

<s>Il Telesio osserva che <pb xlink:href="020/01/076.jpg" pagenum="57"></pb>ciò non può essere, perchè i fiumi restituiscono tutto ciò che il <lb></lb>calor solare ne asciuga, per cui conclude, nel capitolo IV, che il <lb></lb>mare stesso è salato di sua natura, e che è scaturito, come si vede <lb></lb>nell&#039;acque dolci, da salse fonti di sotto terra. </s>

<s>Nel terzo opuscolo il <lb></lb>disprezzator di Aristotile non sa dir de&#039;colori nulla di meglio di <lb></lb>quel che Aristotile stesso avesse insegnato. </s>

<s>Il lettore esce da quegli <lb></lb>intricati discorsi del Cosentino persuaso che all&#039;opinione peripate­<lb></lb>tica, secondo la quale i colori si generano da un contemperato pro­<lb></lb>porzionamento d&#039;ombra mescolata alla luce, non s&#039;è saputo aggiun­<lb></lb>ger nulla di nuovo. </s></p><p type="main">

<s>Nè nulla di nuovo pure, sa, in simili fatti di fisica sperimen­<lb></lb>tale, scoprire il Patrizio, benchè nell&#039;Opera sua che egli fastosamente <lb></lb>intitola <emph type="italics"></emph>Nova de universis Philosophia<emph.end type="italics"></emph.end> si faccia architettore di quat­<lb></lb>tro nuovi mondi. </s>

<s>A più umile prosa scende il filosofo dalmata in <lb></lb>un suo libro, che egli intitola <emph type="italics"></emph>Della rettorica degli antichi,<emph.end type="italics"></emph.end> stam­<lb></lb>pato in Venezia nel 1562. Se nella Nuova Filosofia l&#039;autore imita <lb></lb>Platone nell&#039;altezza delle speculazioni, in questo libro della Retto­<lb></lb>rica lo imita in quella sua graziosa e facile maniera di presentar <lb></lb>la scienza sotto forma di apologhi, fra&#039;quali apologhi è principal­<lb></lb>mente notabile quello che il Patrizio finge essere stato da un abis­<lb></lb>sino raccontato al conte Baldassarre Castiglione. </s>

<s>In quel romanzo <lb></lb>dunque dell&#039;abissino, che non può non far tornare alla memoria <lb></lb>quell&#039;Eve armeno, il quale, nel X libro dello Stato di Platone, ri­<lb></lb>suscitato da morte, racconta ai vivi i destini da sè veduti delle anime <lb></lb>umane; in quel romanzo si dice come la Terra fu un tempo così <lb></lb>rarefatta e spugnosa, che per la grande ampiezza del suo volume <lb></lb>confinava quasi col cielo. </s>

<s>Gli uomini abitavano a principio nella <lb></lb>cavità di quella spugna, come in nidi beati, ma, essendosi poi in­<lb></lb>superbiti, e osando levar la fronte orgogliosa contro gli Dei, Giove <lb></lb>di sopra coi fulmini e Plutone di sotto coi terremoti, incomincia­<lb></lb>rono a scuotere orribilmente la Terra, la quale ricadde tutta nelle <lb></lb>proprie caverne, e rientrò in sè stessa, dando così occasione al for­<lb></lb>marsi dei monti e delle valli, de&#039;laghi di acqua dolce e dei mari. </s></p><p type="main">

<s>Si comprende bene come l&#039;ingegnoso romanzo del Patrizio, <lb></lb>tendeva a dar la soluzione di due problemi: uno teologico del pec­<lb></lb>cato originale, e l&#039;altro geologico e paleontologico della formazion <lb></lb>della terra e del ritrovamento delle reliquie marine sull&#039;alta cima <lb></lb>dei monti. </s>

<s>Quando, in sui principii del secolo XVIII, s&#039;incomincia­<lb></lb>rono dagli immaginosi scienziati stranieri ad architettare sistemi <lb></lb>geologici, Tommaso Burnet rinnovellò sul serio il <emph type="italics"></emph>Sogno galante<emph.end type="italics"></emph.end> e <pb xlink:href="020/01/077.jpg" pagenum="58"></pb>il <emph type="italics"></emph>Romanzo bizzarro<emph.end type="italics"></emph.end> dell&#039;abissino. </s>

<s>Questi titoli, che non sono stati <lb></lb>ritrovati da noi, ma da quell&#039;Antonio Vallisnieri, il quale, insieme <lb></lb>con Lazzaro Moro pose i fondamenti più saldi alla nuova Scienza <lb></lb>della Geologia, bastano a qualificare i meriti che ebbe Francesco <lb></lb>Patrizio in ispecular quella sua nuova filosofia naturale. </s></p><p type="main">

<s>Spento Giordano Bruno, quando già Galileo aveva accesa in <lb></lb>Padova la nuova lampada della Scienza, che diffondeva il suo splen­<lb></lb>dore per ogni parte d&#039;Europa, e sopravvissuto il Campanella di ben <lb></lb>sette anni alla pubblicazione de&#039;Dialoghi dei Massimi Sistemi, s&#039;aspet­<lb></lb>terebbe ognuno che questi due gran pensatori dovessero riuscir pre­<lb></lb>cursori del metodo sperimentale più prossimi e immediati di quel <lb></lb>che non fossero il Telesio e il Patrizio. </s>

<s>Ma rivolgiamo un po&#039;lo <lb></lb>sguardo sui loro libri. </s></p><p type="main">

<s>Del Campanella il libro che scende a trattar di fatti fisici, in <lb></lb>qualche modo più particolare, è forse quello dell&#039;<emph type="italics"></emph>Astrologia.<emph.end type="italics"></emph.end> Ei si <lb></lb>può ben ridere delle opinioni di Aristotile e di Seneca, secondo le <lb></lb>quali, a confricar coll&#039;aglio la calamita, si viene a toglierle la virtù <lb></lb>sua nativa d&#039;attrarre il ferro, essendo già da trent&#039;anni pubblicata <lb></lb>la Fisiologia Nuova del Gilberto, e si può ridere altresì di quel che <lb></lb>credevasi da alcuni filosofi delle palle di piombo, che esplose dalla <lb></lb>canna, al gran calore si liquefanno, perchè già da sette anni il <emph type="italics"></emph>Sag­<lb></lb>giatore<emph.end type="italics"></emph.end> era stato pubblicato da Galileo, ma là dove il gran filosofo <lb></lb>si pone a investigar le cause naturali da sè medesimo, non sa, come <lb></lb>i peripatetici, far uso d&#039;altro che della propria fantasia e del pro­<lb></lb>prio discorso, co&#039;quali due strumenti compone una Fisiologia contro <lb></lb>quella di tutte le sette, e inventa un nuovo sistema del mondo, re­<lb></lb>pudiati tutti i precedenti, non eccettuato quello dello stesso Coper­<lb></lb>nico. </s>

<s>Ma come saggio di quella Fisiologia che il Campanella vuol <lb></lb>sostituire e soprapporre alle Fisiologie di tutte le altre sette, basti <lb></lb>il commemorar le cause fisiche dalle quali, nel citato libro astro­<lb></lb>logico, riconosce gli effetti dell&#039;intumidire e del deprimersi, di sei <lb></lb>in sei ore, con vicenda continua, le acque del mare; cause che <lb></lb>non consistono in altro, secondo l&#039;Autore, che nel calor del sole, <lb></lb>il quale opera a quel modo stesso che il fuoco di un fornello sopra <lb></lb>l&#039;acqua della pentola messa ivi a bollire. </s>

<s>Del resto un sistema in­<lb></lb>tero di Meteorologia è fatto nelle sue cause dipendere dalla natura, <lb></lb>dall&#039;aspetto, dalle varie congiunzioni degli astri; e il filosofo che <lb></lb>tutto disprezza e in tutto crede d&#039;avere a ritrovare egli il primo <lb></lb>qualche cosa di nuovo, non fa bene spesso altro che ripetere le più <lb></lb>strane stranezze del Cardano. </s></p><pb xlink:href="020/01/078.jpg" pagenum="59"></pb><p type="main">

<s>Non è però, secondo pretendono i suoi adoratori, così di Gior­<lb></lb>dano Bruno: egli è per essi il riformatore della nuova Astronomia. </s>

<s><lb></lb>Che il sole è una stella, che le stelle son soli, che le comete son <lb></lb>pianeti, che i travi sono asteroidi, son dottrine espressamente in­<lb></lb>segnate dal gran filosofo nolano, e che i filosofi posteriori hanno <lb></lb>ritrovate e professate per vere, come tanti anni prima erano state <lb></lb>predicate da lui. </s></p><p type="main">

<s>Noi, a tanto fulgore di scienza, ci sentiamo inchinare maravi­<lb></lb>gliati le ciglia, e levandole poi in alto, domandiamo, con quella <lb></lb>libertà che ci è permessa da&#039;nuovi evangelizzatori del libero esame: <lb></lb>in che modo scoperse il Bruno e annunziò tante astronomiche ve­<lb></lb>rità? </s>

<s>Certo egli dee essere stato un osservatore diligentissimo dei <lb></lb>fenomeni celesti, e un abilissimo sperimentatore. </s>

<s>Ma nel fatto poi <lb></lb>quell&#039;astronomo, che osservando un trave rasentare i tetti di Nola, <lb></lb>dal vederlo sorvolare alla cima del Monte Cicala, argomenta che <lb></lb>egli è animato e che si muove con ispontaneità di moto, scansando <lb></lb>gl&#039;impedimenti come un uccello; ci riesce men che un fanciullo, <lb></lb>per non dire a dirittura che egli dee essere un gran matto. </s>

<s>E quello <lb></lb>sperimentatore, il quale argomenta all&#039;esistenza delle macchie cen­<lb></lb>trali nel sole da ciò che si osserva in una sfera di ghiaccio, la <lb></lb>quale mostra più fosca nel centro che verso la periferia del cerchio <lb></lb>massimo di proiezione, è tale da dover tornare ancora sotto la di­<lb></lb>sciplina del pedagogo, che gl&#039;infonda un buon pizzico di sale a <lb></lb>condirgli il cervello. </s></p><p type="main">

<s>Nè scusa punto l&#039;insipienza del Bruno il citar che fa Niccolò <lb></lb>da Cusa, come Autore della trovata rassomiglianza tra le macchie <lb></lb>del sole e ciò che si osserva dentro a una palla ghiacciata, non ve­<lb></lb>dendosi come si possa spiegar con quella similitudine l&#039;origine delle <lb></lb>macchie solari, secondo il concetto che se ne era formato il gran <lb></lb>filosofo nolano. </s>

<s>Questi infatti dice essere il sole una lucerna a olio, <lb></lb>per cui sembrerebbe che, tutt&#039;altro che riconoscere l&#039;apparenza <lb></lb>delle macchie solari nell&#039;analogia de&#039;raggi rifranti in una palla di <lb></lb>ghiaccio, ne avesse dovuto ritrovar l&#039;origine nella rassomiglianza <lb></lb>delle parti fosche e delle chiare, che sempre si osservano intorno <lb></lb>alle fiamme delle nostre lucerne. </s>

<s>Questo stesso concetto infatti porse <lb></lb>occasione di filosofar sottilmente intorno all&#039;origine e alla natura <lb></lb>delle macchie del sole a Benedetto Castelli, in una sua lettera a <lb></lb>Galileo (MSS. Gal. </s>

<s>Divis. </s>

<s>II, P. III, T. X, c. </s>

<s>55). Ma dal Castelli al <lb></lb>Bruno è un abisso di separazione, com&#039;è tra il Bruno stesso e il <lb></lb>Keplero, vero distruttore delle fantastiche sfere aristoteliche, e tra <pb xlink:href="020/01/079.jpg" pagenum="60"></pb>il medesimo Bruno e il Borelli, a cui si dee l&#039;aver prima di ogni <lb></lb>altro dimostrato con meccanici e fisici argomenti la teoria plane­<lb></lb>taria delle comete. </s></p><p type="main">

<s>In ogni modo, si può domandare agli esagerati ammiratori: <lb></lb>quali sono i fisici argomenti addotti dal celebrato astronomo di <lb></lb>Nola? </s>

<s>Egli asserisce, per esempio, che la Terra si muove, non per <lb></lb>motore assistente, ma per proprio intrinseco impulso, come gli altri <lb></lb>pianeti. </s>

<s>Ebbene, volevasi domandare, asserisce egli ciò per avere <lb></lb>intraveduto il principio delle forze centrali, o per esser ricorso a <lb></lb>qualche rassomiglianza colle attrazioni magnetiche, come fecero il <lb></lb>Keplero e il Borelli, o almeno per esservi condotto da quella ana­<lb></lb>logia che è tra il moto de&#039;pianeti e de&#039;nostri proietti, secondo il <lb></lb>concetto degli antichi pitagorici divulgato ne&#039;libri di Plutarco? </s>

<s><lb></lb>Niente affatto è di ciò: l&#039;impulso intrinseco, per cui si muove la <lb></lb>Terra, dice Giordano, è un principio di animalità che l&#039;avviva, come <lb></lb>avviva col sole tutti gli altri pianeti, e anzi tutti gli infiniti corpi <lb></lb>celesti. </s></p><p type="main">

<s>Una tale ipotesi è il segreto magico da cui il nostro Filosofo <lb></lb>fu condotto alle ammirate astronomiche scoperte, imperocchè, se <lb></lb>tutto è animato nel mondo, e se ogni principio di animalità vuol <lb></lb>esser congiunto a un organo corporeo acconcio, ne vien per legit­<lb></lb>tima conseguenza che il sole e la terra e le stelle e le comete, e <lb></lb>tutt&#039;altro che si muove nel libero spazio, sieno informati alle me­<lb></lb>desime leggi, non essendo tra loro altra varietà che di grandezza e <lb></lb>di moti. </s>

<s>S&#039;aggiunga poi la dottrina trascendentale professata dal <lb></lb>Bruno delle contrarietà, che s&#039;identificano nell&#039;infinito, e si vedrà <lb></lb>come questa, applicata alla natura degli astri, dovesse condurlo a <lb></lb>incontrarsi in qualcuno di quei concetti, che hanno una somiglianza <lb></lb>o un&#039;apparenza di veri. </s></p><p type="main">

<s>Ma quella di Giordano non era scienza nè di osservazioni nè <lb></lb>d&#039;esperienze: era una metafisica strana e dai filosofi di miglior <lb></lb>senno repudiata: era una ipotesi, della quale ora si ridono piace­<lb></lb>volmente gli stessi fanciulli. </s>

<s>Dove son dunque i meriti del procla­<lb></lb>mato precursore del metodo sperimentale, o quali sono i prestigi <lb></lb>che hanno affascinati tanti suoi ammiratori? </s>

<s>Di questi prestigi uno <lb></lb>è senza dubbio l&#039;aureola, come dicono, del martirio, e l&#039;altro è <lb></lb>l&#039;esempio dato dall&#039;ardente Nolano della rivolta contro ogni auto­<lb></lb>rità sacra e profana, cosa che va tanto a genio de&#039;settatori di lui, <lb></lb>ma il più affascinatore è il buio delle filosofiche speculazioni. </s>

<s>È una <lb></lb>grand&#039;arte, a sedur certi ingegni com&#039;usano sventuratamente oggidi <pb xlink:href="020/01/080.jpg" pagenum="61"></pb>fra noi, quella di saper dir cose che nessuno intende, o che cia­<lb></lb>scuno può intendere a suo modo e ritrovarci il suo; arte dalla quale <lb></lb>dipende così la fortuna incontrata da Giordano Bruno, come quella <lb></lb>incontrata da tanti sistemi di Filosofia, e da tanti libri di lettera­<lb></lb>tura, specialmente tedesca. </s></p><p type="main">

<s><emph type="center"></emph>VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il soggetto, che ci è capitato a trattar fra mano, è di tale e <lb></lb>tanta importanza, che non si vuol passar da noi senza riflettere un <lb></lb>po&#039;da senno sopra l&#039;indole e i meriti di questi tanto famigerati <lb></lb>razionalisti. </s>

<s>E quanto all&#039;indole, a noi sembra per verità che non <lb></lb>differiscano dagli stessi peripatetici, anzi egli è certo che proseguono <lb></lb>e professano i medesimi principii, che son quelli di sostituire i pla­<lb></lb>citi della ragione alla realtà de&#039;fatti naturali. </s>

<s>Non si sa perciò com­<lb></lb>prender da noi, com&#039;essendo così, intendano gli uni di contrapporre <lb></lb>i loro metodi e le loro dottrine ai metodi e alle dottrine professate <lb></lb>dagli altri. </s>

<s>Il Telesio, il Patrizio, il Bruno e il Campanella, seguono <lb></lb>precisamente gli esempii di Aristotile, accomodando la Natura ai <lb></lb>loro proprii cervelli, e se ne dilungano in questo solo, in dir cioè <lb></lb>che il Filosofo antico non aveva accomodate le cose tanto bene, e <lb></lb>che perciò credono, coi loro nuovi sistemi, di averle accomodate <lb></lb>molto meglio di lui. </s></p><p type="main">

<s>La similitudine, dall&#039;altra parte, e la parentela fra la Filosofia <lb></lb>vecchia e la nuova, è confermata dal veder che poi i frutti sono <lb></lb>stati gli stessi. </s>

<s>Se infecondi dello scoprimento di nuove cose in <lb></lb>natura sono stati i peripatetici, i razionalisti si son mostrati più <lb></lb>infecondi che mai. </s>

<s>Le idee sparse per tanti loro libri ammirati son <lb></lb>simili a nuvole agitate dai venti o dlpinte di bei colori, ma da cui <lb></lb>non si spreme una stilla a rinfrescar le arsure dell&#039;assetata cam­<lb></lb>pagna. </s>

<s>Un indizio però più sicuro che quelle due scuole apparten­<lb></lb>gono alla medesima stirpe è il vederle ambedue affette dal medesimo <lb></lb>peccato originale, peccato, che secondo s&#039;accennò altrove, consiste <lb></lb>nella vanità e nell&#039;orgoglio. </s>

<s>I dialoghi delle Due Nuove Scienze <lb></lb>contenevano bene altre novità di quelle così pomposamente annun­<lb></lb>ziate dalle due Nuove Filosofie sulla Natura del Telesìo e del Pa­<lb></lb>trizio: e Galileo stesso ebbe a cogliere Aristotile in fallo, in bene <pb xlink:href="020/01/081.jpg" pagenum="62"></pb>altri fatti più positivi di quel che non occorresse al Campanella e <lb></lb>al Bruno; e pur nonostante ei non lo disprezza come que&#039;due frati, <lb></lb>e non gli avventa incontro titoli sì inverecondi. </s>

<s>Anzi, se spesso lo <lb></lb>confuta, non di rado anco lo commenta, e talvolta altresì, genero­<lb></lb>samente lo loda. </s></p><p type="main">

<s>Negheremo noi per questo ogni merito ai razionalisti? </s>

<s>No: essi <lb></lb>hanno anzi un merito singolare e perciò unico, il merito di aver <lb></lb>riconosciuto e protestato come quel diritto, che aveva Aristotile, lo <lb></lb>avevano anch&#039;essi e tutti i loro fratelli: il diritto di far uso della <lb></lb>propria ragione. </s>

<s>Ecco da qual lato i razionalisti differiscono dai pe­<lb></lb>ripatetici, ecco in che propriamente hanno merito d&#039;esser detti <lb></lb>razionalisti. </s>

<s>I peripatetici, accettando per vero, perchè dall&#039;altra <lb></lb>parte era assai comodo, che la Natura si dovesse assettare ai cer­<lb></lb>velli degli uomini, scelsero come misura d&#039;ogni sapienza il più gran <lb></lb>cervello stimato da loro, che fu quello di Aristotile, e lo insignirono <lb></lb>di tanta autorità magistrale, che ogni questione, in fatto di cose <lb></lb>naturali, si decideva dagli oracoli e dai responsi di lui. </s>

<s>I razionalisti <lb></lb>però si levarono a dire che quello di Aristotile non era poi quel <lb></lb>gran cervello che si credeva, e che ce n&#039;erano o ce ne potevano <lb></lb>essere de&#039;più sottili di lui, per cui uno per esempio citava il cer­<lb></lb>vello di Platone, e un&#039;altro, com&#039;è più naturale, il cervello suo <lb></lb>proprio. </s>

<s>Questi secondi furono de&#039;più arditi e intesero a scuotere <lb></lb>il giogo di ogni autorità, per cui da molti sono stati encomiati e <lb></lb>benedetti. </s>

<s>Non si accorgon però costoro, che scotendosi così anche <lb></lb>il giogo della Natura, e invece di assoggettarsi essi a lei, preten­<lb></lb>dendo che ella debba assoggettarsi a loro, tornano perciò alla scienza, <lb></lb>lasciamo star la Religione e la Morale, più nocivi degli stessi pe­<lb></lb>ripatetici. </s></p><p type="main">

<s>Che sia anzi così di fatto, che cioè il razionalismo sia riuscito <lb></lb>più nocivo alle scienze sperimentali dello stesso peripaticismo, si <lb></lb>può vedere dai frutti. </s>

<s>Imperocchè essendosi quello ribellato a ogni <lb></lb>autorità magistrale, rimase come un ramo reciso dall&#039;albero di cia­<lb></lb>scuna delle due scuole, della platonica e della aristotelica, e si rese <lb></lb>perciò incapace di menar frutti proprii dell&#039;una e dell&#039;altra. </s>

<s>E quali <lb></lb>sono questi frutti? </s>

<s>Lo dicemmo già di sopra: frutti del Peripato <lb></lb>sono i calcoli numerici e algebrici; e frutti dell&#039;Accademia sono <lb></lb>la Geometria astratta e l&#039;applicata. </s>

<s>Ora è un fatto che dalla scuola <lb></lb>del razionalismo del Patrizio e del Bruno non uscì fuori nè un <lb></lb>geometra mai nè un algebrista. </s></p><p type="main">

<s>Nel decorrere del secolo XVI que&#039;due alberi della scienza del <pb xlink:href="020/01/082.jpg" pagenum="63"></pb>Peripato e dell&#039;Accademia, ciascuno nella sua specie, si mostrò lar­<lb></lb>gamente fecondo. </s>

<s>Se Luca Paciolo, aveva già nel secolo precedente <lb></lb>ritrovato il metodo da risolvere l&#039;equazioni de&#039;due primi gradi, <lb></lb>Girolamo Cardano e Niccolò Tartaglia rivaleggiano insieme a fare <lb></lb>a chi produce la più semplice formula da risolvere l&#039;equazioni del <lb></lb>terzo e del quarto grado. </s>

<s>Raffaello Bombelli, bolognese, è il primo <lb></lb>ad osservar, nella sua Algebra stampata nel 1579, che nel così detto <lb></lb><emph type="italics"></emph>caso irriducibile,<emph.end type="italics"></emph.end> le parti della formula rappresentanti una radice <lb></lb>compongono insieme una radice reale, e Francesco Maurolico for­<lb></lb>mula le prime leggi, secondo cui procedono le serie e le somme <lb></lb>delle stesse serie dei numeri naturali, quadrati, triangolari e cosi <lb></lb>via via. </s></p><p type="main">

<s>L&#039;Accademia poi dette in quel medesimo secolo il più lauto <lb></lb>frutto che si potesse imbandire al convito della scienza: il sistema <lb></lb>vero del mondo. </s>

<s>Che un tal frutto veramente allegasse nel fiore di <lb></lb>quella Filosofia, eloquentemente esposta in quel dialogo del Timeo <lb></lb>scritto dal discepolo di Pitagora, si presente dagli odori esalanti qua <lb></lb>e là per le platoniche carte di Niccolò Copernico. </s>

<s>“ Chi, egli dice <lb></lb>a persuader la verità del nuovo sistema, collocherebbe, in questo <lb></lb>bellissimo tempio questa lampada in altro miglior luogo, che in <lb></lb>quello, d&#039;onde ella potesse tutto insieme illuminarlo? </s>

<s>E in verità <lb></lb>non a torto alcuni chiamano il sole lucerna del mondo, altri Mente, <lb></lb>altri Rettore. </s>

<s>Trismegistio lo chiama visibile Dio, e Sofocle, nel­<lb></lb>l&#039;Elettra, occhio che vede tutto. </s>

<s>Così di fatto, risedendo il sole nel <lb></lb>suo regal soglio, governa la famiglia degli astri, che gli rigirano <lb></lb>intorno. </s>

<s>La terra stessa non è defraudata del lunar ministero, ma, <lb></lb>come Aristotile dice, la Luna è alla Terra cognata. </s>

<s>Ella concepisce <lb></lb>intanto per opera del sole e s&#039;impregna dell&#039;annuale suo parto. </s>

<s><lb></lb>Ritrovasi dunque in così fatto ordinamento una simmetria tanto <lb></lb>ammiranda fra le parti del mondo, un così stabile nesso fra i moti <lb></lb>e le grandezze degli orbi, che in altro modo non sarebbe possibile <lb></lb>trovare di meglio. </s>

<s>” </s></p><p type="main">

<s>Abbiamo scelto dal libro I <emph type="italics"></emph>De revolutionibus<emph.end type="italics"></emph.end> questo passo, <lb></lb>fra&#039;tanti altri, perchè sommamente espressivo del carattere geome­<lb></lb>trico di quelle prove, che ivi adduce l&#039;Autore. </s>

<s>Poi suggerirà il Gil­<lb></lb>berto i primi argomenti fisici, per quello almeno che concerne la <lb></lb>rotazion della terra dedotti dalla Nuova Fisiologia magnetica, e <lb></lb>pochi anni dopo Galileo confermerà il sistema con altri più validi <lb></lb>argomenti desunti dalla rotazione del Sole, dalla circolazione dei <lb></lb>satelliti intorno al centro di Giove e dalle osservazioni delle fasi <pb xlink:href="020/01/083.jpg" pagenum="64"></pb>rappresentate dai due pianeti inferiori. </s>

<s>Ma intanto il grande Astro­<lb></lb>nomo prussiano che non ha ancora il minimo sentore di quelle <lb></lb>fisiche prove, si assicura di aver colto nel vero, scortovi unicamente <lb></lb>dalla Geometrizzante Natura, e si compiace di esser così riuscito a <lb></lb>risolvere il celebre problema pitagorico, proposto in così fatti ter­<lb></lb>mini da Platone: “ quomodo per ordinatos circulares et æquales <lb></lb>motus salvari possunt phænomena. </s>

<s>” </s></p><p type="main">

<s>Sembrerebbe che un altro frutto allegato e maturato negli orti <lb></lb>di Academo, allato all&#039;Astronomia copernicana, dovesse esser l&#039;Ot­<lb></lb>tica. </s>

<s>Il carattere geometrico infatti di questa scienza persuase alcuni <lb></lb>autori a scrivere che ella fu coltivata principalmente dai discepoli <lb></lb>di Platone, e infatti dette opera a scriver dell&#039;Ottica lo stesso <lb></lb>Euclide. </s>

<s>Dell&#039;Ottica però scrisse anche Tolomeo, le dottrine del <lb></lb>quale furono accolte e diffuse dall&#039;arabo Alhazen, cosicchè può dirsi <lb></lb>che fosse questa scienza coltivata con egual profitto dalle due scuole. </s>

<s><lb></lb>Nè ciò fa maraviglia, perchè se la platonica s&#039;aiutava della Geome­<lb></lb>tria, l&#039;aristotelica si giovava del principio dell&#039;intromissione delle <lb></lb>specie nell&#039;occhio, mentre il principio platonico dell&#039;estramissione <lb></lb>impediva grandemente alla scienza di progredire. </s>

<s>Di qui è che <lb></lb>s&#039;intende come potesse avvantaggiarsi l&#039;Ottica in Vilellione, il quale <lb></lb>ai placiti del Filosofo ateniese oppose la proposizione V del terzo <lb></lb>libro stampato per cura di Pietro Appiano in Norimberga nel 1551. <lb></lb>“ Impossibile est visum rebus visis applicari per radios ab oculis <lb></lb>egressos. </s>

<s>” Le prove di ciò addotte dall&#039;Autore sono inoppugnabili. </s>

<s><lb></lb>Se i raggi visivi, egli dice, escon dall&#039;occhio o son corporei o sono <lb></lb>incorporei. </s>

<s>Se corporei, com&#039;è possibile che lo spirito visivo si <lb></lb>diffonda così corporalmente infino alle più lontane stelle? </s>

<s>se in­<lb></lb>corporei, come possono far impressione corporale sopra gli organi <lb></lb>de&#039;sensi? </s></p><p type="main">

<s>In così argomentare, accenna il famoso Autore pollacco a una <lb></lb>questione, che teneva incerte tutte le scuole di que&#039;tempi, ed è la <lb></lb>questione celebre della natura della luce, dalla soluzion della quale <lb></lb>dovevano dipendere le future sorti dell&#039;Ottica. </s></p><p type="main">

<s>Francesco Maurolico non riuscì a risolvere la difficile questione, <lb></lb>ma egli è nulladimeno il primo che preluda ai progressi dell&#039;ottica <lb></lb>neutoniana. </s>

<s>I <emph type="italics"></emph>Photismi de Lumine et umbra,<emph.end type="italics"></emph.end> ossia la Calottrica, e <lb></lb>i <emph type="italics"></emph>Diaphanorum partes<emph.end type="italics"></emph.end> ossia la Diottrica furono due libri scritti dal­<lb></lb>l&#039;Autore in sul finir della prima metà del secolo XVI, e nonostante <lb></lb>non videro la luce prima del 1611 in Napoli, quando i fisici si sen­<lb></lb>tivan vivamente frugati dal desiderio d&#039;intendere in che modo quei <pb xlink:href="020/01/084.jpg" pagenum="65"></pb>vetri del canocchiale avessero la misteriosa virtù d&#039;ingrandire gli <lb></lb>oggetti. </s>

<s>Il Maurolico nella Diottrica aveva data la teoria, non delle <lb></lb>lenti accoppiate ma delle semplici, e meglio di tutti quei che gli <lb></lb>successero per molti anni, dimostrò l&#039;effetto che facevano sulla vista <lb></lb>dei giovani e dei vecchi le varie rifrangenze dei raggi attraverso <lb></lb>al diafano degli occhiali. </s>

<s>Fu il nostro messinese altresì il primo a <lb></lb>dimostrar le aberrazioni di sfericità, e a divisare il modo del di­<lb></lb>pingersi le immagini reali e rovesciate attraverso alle sfere cristal­<lb></lb>line e alle lenti convesse. </s>

<s>Ei riconobbe inoltre l&#039;origine de&#039;colori <lb></lb>in una certa costipazione, che subiscono i raggi variamente rifratti <lb></lb>attraverso al diafano de&#039;prismi triangolari, e applicò una tale dot­<lb></lb>trina alle gocciole delle nubi, per cui si disegnano e si coloriscono <lb></lb>gli archi celesti. </s></p><p type="main">

<s>Mirabile è per que&#039;tempi il giudizioso modo di procedere del <lb></lb>nostro Abbate di Santa Maria in Porto. </s>

<s>Egli seppe destramente co­<lb></lb>gliere i frutti menati da ambedue le filosofie dominanti. </s>

<s>Nell&#039;Al­<lb></lb>gebra e nell&#039;Ottica non fu meno valoroso che in Geometria. </s>

<s>Da <lb></lb>quasi un secolo ei preveniva la dimostrazione delle proposizioni <lb></lb>geometriche degl&#039;inscritti e dei circoscritti, alle quali il Torricelli <lb></lb>credette di avere atteso per il primo, fintantochè non venne a farlo <lb></lb>ravveder del suo errore una lettera di Michelangiolo Ricci (MSS. <lb></lb>Gal., Dis. </s>

<s>T. XLII c. </s>

<s>145); lettera che è un importante documento <lb></lb>di storia, essendo che per essa apparisce come si fosse in Italia <lb></lb>atteso ad osservare diligentemente le forme cristalline dei sali, molti <lb></lb>anni prima che, all&#039;occasione di studiar l&#039;organo del gusto, vi at­<lb></lb>tendessero il Bellini e il Malpighi. </s></p><p type="main">

<s>Tali insomma furono i frutti che si raccolsero nel secolo XVI <lb></lb>dalle due filosofie peripatetica e accademica, frutti cospicui e glo­<lb></lb>riosi alla scienza italiana, specialmente se si ripensi a quai passi si <lb></lb>condusse a fare in que&#039;tempi l&#039;Algebra e l&#039;Astronomia. </s>

<s>Abbiamo <lb></lb>detto che furono ambedue questi frutti gloriosi alla scienza italiana, <lb></lb>perchè lasciano stare le antiche tradizioni pitagoriche, le quali si <lb></lb>posson dire in qualche modo italiane, il grande Astronomo turonese <lb></lb>ebbe più immediata preparazione in Niccolò da Cusa e nel Fraca­<lb></lb>storo; ebbe in Domenico Maria Novara maestro italiano, e s&#039;educò <lb></lb>il giovane ingegno ai due de&#039;più fiorenti nostri studii di Padova e <lb></lb>di Bologna. </s></p><p type="main">

<s>Ma quali altri frutti si raccolsero della Filosofia razionalistica? </s>

<s><lb></lb>Aerei sistemi nel Telesio e nel Patrizio: balenanti nubi gravide di <lb></lb>tempesta in Giordano Bruno e nel Campanella, dentro alle bizzarre <pb xlink:href="020/01/085.jpg" pagenum="66"></pb>e capricciose forme delle quali filosofiche nubi, i loro ammiratori <lb></lb>intravidero annunziate e scoperte verità, a quel modo che Leonardo <lb></lb>da Vinci intravedeva cavalli e cavalieri ordinati in battaglia, nei <lb></lb>muschi degli alberi, negli sputi e in altre macchie rimaste a caso <lb></lb>sull&#039;intonaco dei muri. </s></p><p type="main">

<s><emph type="center"></emph>IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Abbiamo fin qui parlato di scuole e di libri, e de&#039;frutti di <lb></lb>scienza sperimentale raccolti dai loro insegnamenti. </s>

<s>Ma que&#039;frutti, <lb></lb>a riguardarli bene, ci si trovan fra mano assai scarsi, e quei pochi <lb></lb>e de&#039;migliori si son riconosciuti uscir da tutt&#039;altra fonte che da <lb></lb>quella de&#039;libri filosofici. </s>

<s>Si diceva già, in fin dai principii del no­<lb></lb>stro Discorso, che delle due Filosofie dominanti una rendeva inutile <lb></lb>e l&#039;altra impossibile ogni arte sperimentale, per cui vedemmo il <lb></lb>Cardano principalmente e il Tartaglia entrar coi settatori della <lb></lb>scuola in isdegnoso dissidio. </s></p><p type="main">

<s>Ben però più risentitamente erano già que&#039;dissidii insorti nel­<lb></lb>l&#039;animo di un&#039;altra gente che, o dalle condizioni della nascita o dagli <lb></lb>esercizi della vita erano tenuti lontani dal partecipare ai puhblici <lb></lb>insegnamenti. </s>

<s>Amerigo Vespucci abbandona in gioventù la scuola <lb></lb>di umanità, per darsi alla mercanzia, e poi più tardi ai viaggi. </s>

<s>Egli <lb></lb>non ha perciò a che far nulla con la scuola de&#039;filosofi, e anzi si fa <lb></lb>ardito di rinfacciare i loro errori “ Parmi, Magnifico Lorenzo, che <lb></lb>la maggior parte dei filosofi in questo mio viaggio sia reprobata, <lb></lb>che dicono che dentro della torrida zona non si può abitare a causa <lb></lb>del gran calore, e io ho trovato in questo mio viaggio essere il <lb></lb>contrario ” (Bandini, Vita e lettere di A. Vespucci, Firenze 1745, <lb></lb>pag. </s>

<s>73). Egli sa di scrivere <emph type="italics"></emph>in barbaro stile e fuori di ogni ordine <lb></lb>di umanità,<emph.end type="italics"></emph.end> e dà nonostante opera a scrivere un libro, che egli in­<lb></lb>titola le <emph type="italics"></emph>Quattro Giornate<emph.end type="italics"></emph.end> “ nel quale ho relato, egli dice, la maggior <lb></lb>parte delle cose, che io vidi assai distintamente .... Quivi dunque io <lb></lb>viddi molte altre stelle i varii movimenti delle quali diligentemente <lb></lb>osservando, ne composi assegnatamente un libro ” (ivi, pag. </s>

<s>18 e <lb></lb>115). Ei si compiace delle tante nuove cose scoperte, e ripensando <lb></lb>alle sterilità, e anzi agli errori in che versavano i filosofi <emph type="italics"></emph>in libris,<emph.end type="italics"></emph.end><lb></lb>conclude essere certo che <emph type="italics"></emph>più vale la pratica che la teorica.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/086.jpg" pagenum="67"></pb><p type="main">

<s>Ben più sdegnoso, perchè più irritato, è l&#039;animo di Leonardo <lb></lb>da Vinci, che scrive così contro i filosofi <emph type="italics"></emph>schonfiati<emph.end type="italics"></emph.end> e <emph type="italics"></emph>pomposi,<emph.end type="italics"></emph.end> non <lb></lb>ritrovatori di cose nuove, ma <emph type="italics"></emph>recitatori e trombetti delle opere al­<lb></lb>trui.<emph.end type="italics"></emph.end> “ Se, bene, come loro, non sapessi allegare gli autori, molto <lb></lb>maggiore e più degna cosa allegherò allegando l&#039;esperienza maestra <lb></lb>ai loro maestri ”. (Libri Histoire et cet. </s>

<s>T. III, Paris 1840, pag. </s>

<s>238). </s></p><figure id="id.020.01.086.1.jpg" xlink:href="020/01/086/1.jpg"></figure><p type="main">

<s>Amerigo e Leonardo, che basterebbero per se stessi a provare <lb></lb>come la scienza della Natura si ricoverò ne&#039;suoi primi principii <lb></lb>altrove che per gli alloggiamenti de&#039;Filosofi, non sono soli: essi <lb></lb>rappresentano un ordine di persone, che attende all&#039;esercizio o delle <lb></lb>arti utili, o delle arti belle; ordine a cui principalmente apparten­<lb></lb>gono Dante Alighieri, Cristoforo Colombo, Leon Battista Alberti. <pb xlink:href="020/01/087.jpg" pagenum="68"></pb>Illustre stuolo egli è questo, innanzi al quale il mondo de&#039;Filosofi <lb></lb>sperimentali inchina per gran riverenza spontaneamente le ciglia. </s>

<s><lb></lb>Ebbene: di chi son discepoli tutti costoro, di Platone o di Aristo­<lb></lb>tele? </s>

<s>Non hanno maestro nessun filosofo o accademico o peripate­<lb></lb>tico, nè pretendono di farla da filosofi essi stessi come i razionalisti: <lb></lb>libro e maestro a loro è la Natura. </s>

<s>Dai faticosi esercizii dell&#039;arte <lb></lb>si persuasero facilmente che la materia, sotto alle forme della <lb></lb>quale s&#039;agita la vita dell&#039;Universo, tutt&#039;altro che essere arrendevole <lb></lb>al nostro ingegno, è sorda alle intenzioni dell&#039;artista, ond&#039;è che ap­<lb></lb>presero di qui la soggezione agli ordini naturali e impararono ad <lb></lb>osservarli con diligente riverenza amorosa, ministri e sacerdoti nel <lb></lb>sacro Tempio, e non Iddei. </s>

<s>Essi dunque rappresentano quel terzo <lb></lb>stato, in cui vedemmo passar finalmente il bambino, dopo le prime <lb></lb>platoniche illusioni e i primi aristotelici delirii; lo stato in cui l&#039;uomo <lb></lb>incomincia, per il sincero uso de&#039;sensi, a pigliare stabile possesso <lb></lb>del mondo. </s>

<s>Su questi che sono i naturali e legittimi iniziatori <lb></lb>del metodo di osservazione, giova intrattenere alquanto il nostro <lb></lb>discorso. </s></p><p type="main">

<s>Nei primi palpiti del nostro risorgimento nazionale, quando <lb></lb>l&#039;Italia si sentiva potentemente convenire in un animo solo, e in <lb></lb>un solo intendimento, si rivolse, con più desideroso amore che mai, <lb></lb>a quell&#039;uomo di carattere fiero e generoso, che più al vivo la rap­<lb></lb>presentava di ogni altro Fu allora che s&#039;incominciò a magnificare <lb></lb>e a superesaltare i meriti di lui, cosicchè non si lasciò indietro arte <lb></lb>nè scienza, di cui non si predicasse Dante per gran precursore. </s>

<s><lb></lb>Lo zelo degli animi e la leggerezza degl&#039;ingegni hanno spinto ora­<lb></lb>mai l&#039;esagerazione a tal punto, che il severo tribunale della critica <lb></lb>ha da sentenziar molte cose contro a loro, ed è rimasto a quel tri­<lb></lb>bunale il debito di ridur dentro i termini del vero ogni eccesso <lb></lb>inconsiderato. </s></p><p type="main">

<s>Gli antichi furono, nell&#039;ammirazione dell&#039;Alighieri, assai più <lb></lb>temperati, e perchè nella temperanza consiste la verità, lo amarono <lb></lb>perciò e lo intesero molto meglio di noi. </s>

<s>Una delle prime e più <lb></lb>rilevanti qualità che distinguono l&#039;ingegno dantesco è l&#039;armonia: <lb></lb>armonia di numeri, che risuona nel verso, simmetria di linee, a <lb></lb>regola delle quali è architettato il divino Poema. </s>

<s>Il Landino e il <lb></lb>Vellutello, i due più antichi e rinomati commentatori, non trascu­<lb></lb>rano di avvertire come il teatro, in cui si rappresenta l&#039;infernale <lb></lb>tragedia, sia stato prima così ben compassato dalla mente geome­<lb></lb>trica del Poeta, che tutto procede e corrisponde a una preordinata <pb xlink:href="020/01/088.jpg" pagenum="69"></pb>misura. </s>

<s>Quale però si fosse questa misura cadde in controversia <lb></lb>fra il Landino, che sosteneva l&#039;opinione di Antonio Manetti, e il Vel­<lb></lb>lutello, che seguiva un&#039;opinione alquanto diversa. </s>

<s>Baccio Valori, <lb></lb>consolo dell&#039;Accademia fiorentina, dette poi a decidere la contro­<lb></lb>versia a Galileo, ciò che egli fece in due lezioni accademiche, pub­<lb></lb>blicate nel 1855 da Ottavio Gigli, sentenziando in favor del Manetti. </s></p><p type="main">

<s>Se la Conca infernale e il Monte purgatorio dimostrano in Dante <lb></lb>una gran perizia di arte, diremo così, topografica, il gran Pano­<lb></lb>rama del Paradiso attesta che egli doveva essere esercitatissimo <lb></lb>ne&#039;calcoli dell&#039;astronomia. </s>

<s>La distanza de&#039;pianeti dalla Terra, le <lb></lb>loro grandezze relative, le paralassi del Sole e della Luna, tutto ciò <lb></lb>insomma che poteva servire a que&#039;calcoli di fondamento, è de­<lb></lb>sunto, com&#039;appar dal <emph type="italics"></emph>Convito,<emph.end type="italics"></emph.end> da Tolomeo, da Alfagrano e da si­<lb></lb>mili altri autori di opere astronomiche, delle quali dà prova il <lb></lb>Nostro di essere massimamente erudito. </s>

<s>Su tali dati poi, qualunque <lb></lb>ne sia la certezza, i calcoli astronomici danteschi son condotti con <lb></lb>tal matematico rigore, che noi più volte, per nostro giovanile eser­<lb></lb>cizio, ci siam provati a ritesserli e gli abbiamo trovati riscontrar <lb></lb>sempre, con maraviglioso diletto. </s></p><p type="main">

<s>Che l&#039;Alighieri si fosse accorto del sonno delle piante, e avesse <lb></lb>riconosciuto la causa dell&#039;ascensione della linfa su per i vasi; che <lb></lb>il velocitarsi delle acque correnti l&#039;attribuisse alla pressione degli <lb></lb>strati superiori; che ne&#039;condensamenti e nelle dilatazioni dell&#039;aria <lb></lb>prodotta dal calor del sole riconoscesse l&#039;origine dei venti; che i <lb></lb>vapori acquosi disseminati nell&#039;aria, condensati dal freddo, tornino <lb></lb>in pioggia: queste e simili altre cose che vanno a ripescare a gara <lb></lb>qua e là pel Poema sacro i dantisti, son senza dubbio esagerazioni, <lb></lb>specialmente se si vogliono intendere quelle parole nel preciso si­<lb></lb>gnificato scientifico de&#039;moderni; son conati di farfallette, che in­<lb></lb>tendono a sollevare più in alto che mai un gigante col leggiero <lb></lb>tremolare delle ali. </s></p><p type="main">

<s>Il vero si è che il Poeta riassume tutta la scienza de&#039;suoi <lb></lb>tempi, e la commenta e la condensa ne&#039;suoi splendidi versi, na­<lb></lb>scondendola talvolta così fra le loro pieghe, che occhio poco esperto <lb></lb>non se ne accorge. </s>

<s>Un esempio di quei commenti si può citare, <lb></lb>nel XV canto del Purgatorio, dalle terzine 6 e 7, nelle quali si <lb></lb>rendono compiute le leggi della Calottrica, soggiungendo che il rag­<lb></lb>gio d&#039;incidenza e quello di riflessione si ritrovano in un medesimo <lb></lb>piano perpendicolare alla superficie riflettente. </s></p><p type="main">

<s>Dell&#039;ardito modo come il grande artefice del verso toscano sa-<pb xlink:href="020/01/089.jpg" pagenum="70"></pb>pesse condensare, e quasi trafugare una proposizione di scienza di­<lb></lb>mostrata, in un semplice inciso, molti si potrebbero recare esempi, <lb></lb>de&#039;quali nonostante può bastare uno solo, che si toglie dalla t. </s>

<s>17 <lb></lb>del XII canto del Paradiso. </s>

<s>Per la <emph type="italics"></emph>lunga foga<emph.end type="italics"></emph.end> i commentatori <lb></lb>tutti intendono la distanza del sole nel parallelo di longitudine, <lb></lb>ma è chiaro che dee intendersi della lunga foga del mare, per cui, <lb></lb>a cagione della convessità della superficie delle acque, si nasconde <lb></lb>la vista delle cose lontane. </s>

<s>Ecco in due parole risoluta una que­<lb></lb>stione, che dette occasione fra&#039;dotti di que&#039;tempi a tante contro­<lb></lb>versie; Questione che Dante stesso trattò in Verona, il dì 20 di <lb></lb>Gennaio 1320, in una eruditissima dissertazione latina. </s></p><p type="main">

<s>Del resto, se il gran Vate pieno di tutta scienza, non precorse <lb></lb>i tempi di Galileo, con nessuna importante scoperta, preparò senza <lb></lb>dubbio dalla lontana quel sicuro metodo di osservare la Natura, <lb></lb>che fu poi fecondo di ogni più bella e più nuova scoperta. </s>

<s>Se nulla <lb></lb>scopri di nuovo nella fisiologia delle piante, pure attentamente ne <lb></lb>osservò i fiori e le foglie, e ne descrisse i moti prodotti dalla luce <lb></lb>e dal calore. </s>

<s>Se non pose i fondamenti all&#039;Idraulica, presentì pure <lb></lb>in qualche modo, che le acque stesse sottostavano a una legge, in <lb></lb>quel loro correre apparentemente scomposto, e se va ripetendo le <lb></lb>viete dottrine aristoteliche intorno a molti fatti di Meteorologia, <lb></lb>pur gli osserva e gli descrive, non accomodandoli alla sua propria <lb></lb>ragione, ma ricevendoli tali e quali glieli porge sotto gli occhi la <lb></lb>Natura. </s></p><p type="main">

<s>Da leggere questo gran Libro della Natura, forse troppo fu <lb></lb>distratto l&#039;Alighieri dalla lettura de&#039;libri dei filosofi. </s>

<s>Ma ecco suc­<lb></lb>cedere a lui un altro grande spirito italiano, a cui la Natura stessa <lb></lb>ampiamente si rivelò squadernandogli innanzi agli occhi il volume <lb></lb>del Mondo Universo. </s>

<s>Egli è ìl gran Cristoforo Colombo, e nessuno <lb></lb>meglio dell&#039;ardito navigator genovese potrebbe stare a lato al su­<lb></lb>blime Poeta fiorentino. </s>

<s>Ma prima di parlar di lui, che ebbe la Na­<lb></lb>tura per solo e immediato Maestro, dobbiamo trattenerci sopra un&#039;al­<lb></lb>tra grande figura d&#039;uomo, a cui fu maestra la Natura stessa per <lb></lb>mezzo dell&#039;arte. </s></p><p type="main">

<s>Leon Battista Alberti è costui, nato, come l&#039;Alighieri, d&#039;illustre <lb></lb>e antica famiglia fiorentina e vissuto nel secolo posteriore a quello <lb></lb>del Poeta, dal 1404 al 1485. Informato alle scienze dagli insegna­<lb></lb>menti delle scuole, più forse dal proprio genio che dalle consue­<lb></lb>tudini dei tempi, fu portato da giovane a secondare i placiti della <lb></lb>Filosofia platonica, la quale sodisfaceva, meglio della peripatetica, <pb xlink:href="020/01/090.jpg" pagenum="71"></pb>agl&#039;ingegni meditativi. </s>

<s>Egli perciò si dette allo studio delle mate­<lb></lb>matiche, applicando queste discipline alle arti, che posson meglio <lb></lb>servire agli usi della vita e a sodisfarne ai bisogni. </s>

<s>Ma l&#039;Alberti, <lb></lb>indulgendo al genio proprio dei giovani, tien più spesso dietro e <lb></lb>vagheggia le curiosità e gli spettacoli, informato da quello spirito <lb></lb>del platonismo, che, se scende talvolta a implicarsi ne&#039;fatti parti­<lb></lb>colari della Natura, non gli riguarda altrimenti che come scherzi. </s>

<s><lb></lb>Il titolo di <emph type="italics"></emph>Ludi matematici<emph.end type="italics"></emph.end> dato dall&#039;Autore a un&#039;operetta, nella <lb></lb>quale è la Geometria applicata all&#039;altimetria, alla topografia, alla <lb></lb>gnomonica, alla meccanica e a simili altre discipline, per sè dice <lb></lb>assai, ma più efficacemente a noi sembra che di ciò facciano prova <lb></lb>quelle così dette <emph type="italics"></emph>Dimostrazioni,<emph.end type="italics"></emph.end> le quali niente altro eran poi, se <lb></lb>non che spettacoli ottici, o come Leon Battista stesso gli chiamava <lb></lb><emph type="italics"></emph>Miracoli della Pittura.<emph.end type="italics"></emph.end> Con queste Dimostrazioni spettacolose e con <lb></lb>questi Miracoli racconta l&#039;Autore stesso d&#039;essersi ricreato più volte <lb></lb>in Roma insieme coi suoi compagni. </s>

<s>Di così fatte Dimostrazioni <lb></lb>nessuno sa dirci nulla di particolare, da quell&#039;Anonimo biografo in <lb></lb>fuori contemporaneo dell&#039;Alberti, la scrittura del quale fu raccolta <lb></lb>e pubblicata dal Muratori. </s>

<s>Da essa chiaramente si rileva in che <lb></lb>propriamente consistessero quelle Albertiane Dimostrazioni. </s>

<s>Ma per­<lb></lb>chè oramai i ciechi ammiratori del grande artista si sono fitti in <lb></lb>testa non essere quelle così fatte Dimostrazioni altro che le stesse <lb></lb>ottiche rappresentanze degli oggetti sul fondo di una camera oscura, <lb></lb>con manifesta intenzione di dare al loro Autore la precedenza su <lb></lb>Leonardo e sul Porta; si son ridotti a dire che le parole del Bio­<lb></lb>grafo anonimo non son troppo chiare. </s>

<s>Ma chiarissime sembrano a <lb></lb>noi, e siamo certi che tali pur sembreranno agli intelligenti e im­<lb></lb>parziali, che, dopo un&#039;attenta lettura, concluderanno come i giochi <lb></lb>ottici dell&#039;Alberti consistevano nel contraffare e trasformare le im­<lb></lb>magini per via di colori artificiali e di artificiali riflessioni di spec­<lb></lb>chi, mostrandole agli spettatori curiosi proiettate sulla parete di una <lb></lb>camera oscura. </s>

<s>L&#039;apparecchio ottico dunque dell&#039;Alberti era cosa <lb></lb>più artificiosa e applicata ad uso un po&#039;diverso dallo strumento <lb></lb>del Porta. </s></p><p type="main">

<s>Nel libro insomma dei Ludi, e in quello che si può chiamar <lb></lb>Magia delle Dimostrazioni, come in altre operette, a cui piace a <lb></lb>noi di dare il titolo di giovanili o minori, troppo il nostro Autore <lb></lb>si compiace di quella curiosità, che è sodisfatta, non dall&#039;esser veri <lb></lb>i fatti della Natura, ma dall&#039;apparir nuovi e maravigliosi. </s>

<s>Il libro <lb></lb>della Prospettiva, pubblicato nel IV Tomo delle opere volgari da <pb xlink:href="020/01/091.jpg" pagenum="72"></pb>Anicio Bonucci, non è più che un commentario assai magro del­<lb></lb>l&#039;Ottica di Euclide, e tra que&#039;Ludi stessi, che si leggono in fine di <lb></lb>questo Tomo, molti son quelli che si risentono de&#039;difetti notati dal <lb></lb>Sagredo ne&#039;Ludi del Porta. </s>

<s>Anco l&#039;VIII, che è del misurare la <lb></lb>profondità di qualunque mare, subodorato da Silvio Belli e pub­<lb></lb>blicato nel 1565 dai manoscritti albertiani, ha il difetto di riposar <lb></lb>sul principio dell&#039;equabilità del moto de&#039;gravi cadenti in mezzo al­<lb></lb>l&#039;acqua, senza che l&#039;Autore cerchi di assicurarsene in qualche modo, <lb></lb>per via dell&#039;esperienza. </s>

<s>È vero che l&#039;esperienze dell&#039;Oliva fatta di­<lb></lb>poi nell&#039;Accademia del Cimento parvero essere favorevoli al prin­<lb></lb>cipio, dall&#039;Alberti ammesso per vero, ma il Borelli poco dopo, nella <lb></lb>propos. </s>

<s>246. <emph type="italics"></emph>De motion. </s>

<s>natur.,<emph.end type="italics"></emph.end> dimostrò che la discesa da gravi e <lb></lb>l&#039;ascesa de&#039;galleggianti erano velocitate, confermando le teorie con <lb></lb>isperimenti ingegnosi. </s></p><p type="main">

<s>Venne tempo però che, lasciata la curiosità delle cose nuove, <lb></lb>e la leggerezza degli spettacoli, si rivolse l&#039;Alberti tutto alla Natura, <lb></lb>ed essa invocò ed elesse per sua principale Maestra. </s>

<s>La nuova vo­<lb></lb>cazione incominciò dallo studio d&#039;imitare coll&#039;arte quella simmetria <lb></lb>ed eleganza di forma, che ella è solita dare alla fabbrica di tutte <lb></lb>le cose mondane. </s>

<s>Leon Battista vien così a farsi autore di Archi­<lb></lb>tettura, non imitando servilmente, ma rinnovellando fibre e dando <lb></lb>altra forma di membra agli spiriti dell&#039;antico Vitruvio. </s>

<s>Ecco l&#039;opera <lb></lb>dove propriamente il Nostro investiga le occulte cause, scioglie <lb></lb>questioni di fatti naturali e inventa strumenti facendo uso di quel­<lb></lb>l&#039;arte, e proseguendo quello stesso metodo sperimentale, di cui il <lb></lb>regolare istituto dovea stabilirsi un secolo e mezzo dopo. </s>

<s>Lo studio <lb></lb>intorno all&#039;origine delle fonti e alle scaturigini delle acque, attri­<lb></lb>buite dal Nostro Autore all&#039;umidità delle pioggie e delle nevi pe­<lb></lb>netrate nei crepacci e imbevute dai pori della terra, lo conduce <lb></lb>impensatamente a fare una nuova esperienza, e ad applicarla alla <lb></lb>costruzione di uno strumento, che egli offre qual primizia alla Me­<lb></lb>teorologia “ Noi abbiamo provato, egli scrive, che una spugna di­<lb></lb>venta umida per la umidità dell&#039;aria e di qui caviamo una regola <lb></lb>da pesare, colla quale noi pesiamo quanto siano gravi e quanto <lb></lb>secchi i venti e l&#039;aria ”. </s></p><p type="main">

<s>Lo studio scientifico e sperimentale dei fatti meteorologici, che <lb></lb>l&#039;Alberti iniziò colla invenzione dell&#039;Igrometro, rimase così profon­<lb></lb>damente impresso d&#039;un tal qual carattere di nazionalità, che la Me­<lb></lb>teorologia durò ad essere una scienza di special cultura italiana, <lb></lb>anco quando ne incominciarono a riconoscere l&#039;importanza e a darvi <pb xlink:href="020/01/092.jpg" pagenum="73"></pb>opera efficacemente gli scienziati di Europa. </s>

<s>Ma a confermarle quel <lb></lb>carattere, con più profonda impressione che mai, conferì quel Cri­<lb></lb>stoforo Colombo, intorno a cui dianzi interrompemmo il discorso. </s></p><p type="main">

<s>Il genio di osservare con quasi religiosa venerazione i fatti <lb></lb>della Natura, che egli ora sperimentava in sè dolcemente benefici, <lb></lb>ora potentemente tremendi, si rivela da quel Giornale, di cui parla <lb></lb>Ferdinando, nel cap. </s>

<s>XVI, della Vita che scrisse di suo padre. </s>

<s>In <lb></lb>quel giornale il Discopritore del Nuovo mondo andava via via no­<lb></lb>tando tutto quel che gli occorreva ad osservare e a considerare di <lb></lb>più memorabile. </s>

<s>“ Fu diligentissimo l&#039;Ammiraglio, dice ivi il bio­<lb></lb>grafo, a scrivere di giorno in giorno minutamente tutto quello che <lb></lb>succedeva nel viaggio, specificando i venti che soffiavano, quanto <lb></lb>viaggio egli facea con ciascuno, e con quali vele e correnti, e quali <lb></lb>cose per la via egli vedeva, uccelli o pesci, od altri così fatti segni ”. </s></p><p type="main">

<s>L&#039;Humboldt, che amorosamente e da quel grande scienziato <lb></lb>che egli era, prese ad esaminare un tal giornale, restò maravigliato <lb></lb>della copia delle osservazioni, e dell&#039;acume, con cui moltissimi e <lb></lb>varii fatti naturali vi sono investigati. </s>

<s>La direzione dei venti tropi­<lb></lb>cali da occidente in oriente, per cui nello stesso verso è sospinta <lb></lb>la gran corrente marina, vi si trova per la prima volta diligente­<lb></lb>mente descritta; vi è notata l&#039;efficacia, che ha il verde fogliame delle <lb></lb>foreste di condensare i vapori acquosi dell&#039;aria, facendoli tornare <lb></lb>in pioggia. </s>

<s>Vi è assegnata l&#039;altezza dell&#039;aria, a cui sono limitati i vari <lb></lb>e più consueti fatti meteorologici che avvengono in essa, e vi son <lb></lb>riconosciuti i più notabili effetti, che il calore del sole produce sul­<lb></lb>l&#039;Oceano e sull&#039;ammosfera. </s></p><p type="main">

<s>Il medesimo Humboldt non cessa di far le meraviglie e di <lb></lb>magnificare una osservazione importantissima allo studio della nuova <lb></lb>Geologia; osservazione che il Colombo stesso lasciò fra le molte al­<lb></lb>tre registrata nel suo Giornale. </s>

<s>L&#039;osservazione fatta dal nostro in­<lb></lb>signe Navigatore, nel suo primo viaggio, è quella del vedere vege­<lb></lb>tare insieme e pacificamente convivere nell&#039;isola di Cuba, conifore <lb></lb>e palme. </s>

<s>E perchè l&#039;osservazione che pare ovvia si giudichi come <lb></lb>ella dovesse essere fatta con sottile intendimento scientifico, giova <lb></lb>notare che il nostro Botanico del secolo XV aveva tanto tempo <lb></lb>prima dell&#039;Heritier riconosciuto che i <emph type="italics"></emph>podocarpi<emph.end type="italics"></emph.end> hanno altri carat­<lb></lb>teri, per cui si distinguono dagli <emph type="italics"></emph>abietini.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Quanto poi l&#039;Alunno della Natura, sapesse, nello studiare le <lb></lb>ammirande opere di lei, congiungere alle osservazioni passive la <lb></lb>sagace attività delle esperienze, si dimostra per quel che egli os-<pb xlink:href="020/01/093.jpg" pagenum="74"></pb>servò, sperimentò e speculò intorno alle proprietà naturali e agli <lb></lb>effetti della calamita. </s>

<s>La variazione della declinazione, al variare <lb></lb>delle latitudini, fu diligentemente osservata da lui, e a lui si deve <lb></lb>il primo concetto, benchè poi in pratica riuscisse inefficace, di ser­<lb></lb>virsi dell&#039;ago magnetico a risolvere l&#039;importantissimo problema delle <lb></lb>longitudini. </s></p><p type="main">

<s>Lo spirito di Cristoforo Colombo si trasfuse poi negli altri na­<lb></lb>vigatori, che gli successero, specialmente italiani, i quali con rive­<lb></lb>rente amore, leggendo nel cielo, nel mare e nella terra le opere <lb></lb>ammirande della Natura, seppero investigarne il segreto magistero, <lb></lb>meglio di tanti filosofi non dediti a leggere altro che i libri. </s>

<s>Ame­<lb></lb>rigo Vespucci fu il primo a proporre i metodi astronomici per tro­<lb></lb>vare le longitudini; metodi che rimasero unicamente efficaci negli <lb></lb>usi dei navigatori, specialmente da poi che Giovanni da Empoli e <lb></lb>Filippo Sassetti ebbero sperimentato che i gradi della declinazione <lb></lb>magnetica non serbano alcuna regola di proporzione coi gradi dei <lb></lb>meridiani. </s></p><p type="main">

<s><emph type="center"></emph>X.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Fra coloro che a osservare diligentemente e a investigare le <lb></lb>cause degli effetti naturali vi furono rivolti dall&#039;esercizio dell&#039;arte, <lb></lb>vuol essere commemorato principale fra tutti Leonardo da Vinci. </s>

<s><lb></lb>L&#039;ingegno perciò del figliuolo di Ser Piero, e la speranza dei frutti <lb></lb>che si vedranno raccolti da lui nel campo delle scienze naturali, <lb></lb>non in altro si potranno meglio conoscere, nè da altro più sicura­<lb></lb>mente indovinare, che da quelle opere d&#039;arte condotte da lui, e <lb></lb>nelle quali ritrova la Natura, con maravigliosa rassomiglianza, effi­<lb></lb>giato il suo volto. </s>

<s>Chi contempla, nel cartone di Adamo e di Eva, <lb></lb>lumeggiato di biacca quel praticello verdeggiante di un infinita <lb></lb>sorta di erbe, fra le quali vanno pascendo varie specie di animali, <lb></lb>o vi stanno a loro diletto; chi osserva in quel fico lo scortar delle <lb></lb>foglie e la veduta dei rami, e in que&#039;palmizi le nervature che <lb></lb>s&#039;aprono a formare la rotondità delle ruote, e le sottoposte vena­<lb></lb>ture e la minuta peluria dell&#039;epidermide, dice: colui che ha fatto <lb></lb>un tal lavoro è senza dubbio o ha grande attitudine a diventare <lb></lb>un zoologo, un botanico. </s></p><pb xlink:href="020/01/094.jpg" pagenum="75"></pb><p type="main">

<s>Chi pon mente a que&#039;nudi, che nelle varie attitudini occorrono <lb></lb>a vedere per questi dipinti e per questi disegni; a quel gruppo di <lb></lb>cavalli e di cavalieri, che nella storia di Niccolò Piccinino si con­<lb></lb>tendono rabbiosamente una bandiera, e vede con qual verità sono <lb></lb>disegnate le masse muscolari, di cui si seguono con l&#039;occhio nei <lb></lb>solchi le testure delle fibre e i complicati andamenti; dice: costui <lb></lb>è certamente maestro d&#039;Anatomia descrittiva e d&#039;Anatomia compa­<lb></lb>rata. </s>

<s>Ma chi guarda nel ritratto di Mona Lisa que&#039;lustri e quegli <lb></lb>acquitrini degli occhi, quei pori della pelle nelle guance e nel <lb></lb>volto, e la peluria leggerissima e delicata che n&#039;esce, soggiunge, <lb></lb>non dover essere costui contento all&#039;anatomia superficiale, ma dover <lb></lb>esser di più penetrato addentro a indagarne l&#039;istologia. </s></p><p type="main">

<s>Chi poi non guarda solamente con gli occhi, ma considera con <lb></lb>l&#039;intelletto, avvedendosi bene che in que&#039;volti son così vivamente <lb></lb>espressi gli interiori pensieri e le passioni e gli affetti, conclude <lb></lb>che l&#039;Artefice deve essere entrato addentro a speculare le segrete <lb></lb>cause e gli organi, per cui l&#039;interiore spirito si rivela al di fuori. </s>

<s><lb></lb>Il pittore da Vinci insomma si riconosce nelle opere sue per uno <lb></lb>che ha sperimentato e ha speculato, o che almeno ha grandissima <lb></lb>attitudine a sperimentare e a speculare intorno a ogni sorta di fatti <lb></lb>naturali. </s>

<s>E così è veramente come lo attestano i documenti-che ci <lb></lb>son rimasti di lui. </s></p><p type="main">

<s>Così fatti documenti, che non potrebbero essere per verità più <lb></lb>autentici, consistono nelle stesse carte di Leonardo scritte, per uno <lb></lb>de&#039;soliti capricci degli artisti, alla rovescia. </s>

<s>I biografi ce lo dipingono <lb></lb>con un lapis e un libretto pendenti dalla cintola, ad uso dei così <lb></lb>detti taccuini moderni, dov&#039;egli andava notando tutto ciò che gli <lb></lb>occorreva di osservare, di sperimentare o di speculare via via. </s>

<s><lb></lb>Così fatti libretti, che si empivano rapidamente, vennero, in parte <lb></lb>dall&#039;Autore stesso, e in parte dagli eredi di lui, in qualche modo <lb></lb>ordinati e rilegati in volumi, le prime vicende subìte dai quali son <lb></lb>narrate in quel documento, che da pag. </s>

<s>130-33 si legge nelle <emph type="italics"></emph>Me­<lb></lb>morie storiche<emph.end type="italics"></emph.end> dell&#039;Amoretti, (Milano, 1804). Per quel che riguarda <lb></lb>poi le ultime vicende, si sa come dalla Biblioteca Ambrosiana, fos­<lb></lb>sero quelle preziose carte rapite e trasportate a Parigi, dove a nostro <lb></lb>dispetto rimangono tuttavia. </s></p><p type="main">

<s>Giorgio Vasari, del contenuto in quei volumi accennò a qual­<lb></lb>che cosa, non concernente però se non l&#039;arte. </s>

<s>Per quel che s&#039;ap­<lb></lb>partiene alla scienza, si contentò di dire che Leonardo “ fra gli <lb></lb>altri tanti suoi capricci ebbe anco quello che, filosofando delle cose <pb xlink:href="020/01/095.jpg" pagenum="76"></pb>naturali, attese a intendere le proprietà dell&#039;erbe, continuando ed <lb></lb>osservando il moto del cielo, il corso della luna e gli andamenti <lb></lb>del sole ”. </s>

<s>Anche l&#039;Oltrocchi, bibliotecario dell&#039;Ambrosiana, che <lb></lb>perciò ebbe agio di consultare i manoscritti vinciani, mentre che <lb></lb>ancora erano ivi esistenti, non si curò di trascriverne e di com­<lb></lb>mentarne, se non solo quelle parti che riguardano le arti del <lb></lb>disegno. </s></p><p type="main">

<s>Il primo che rivolgesse l&#039;attenzione alle preziose note, per leg­<lb></lb>gervi ciò che ne concerne la scienza, fu Giovan Battista Venturi, <lb></lb>in quel tempo che soggiornava a Parigi, dove scrisse e nel 1797 <lb></lb>pubblicò quel suo celebre <emph type="italics"></emph>Essai,<emph.end type="italics"></emph.end> verso cui si rivolsero e da cui <lb></lb>presero l&#039;inspirazione tutti quegli italiani, che incominciarono allora <lb></lb>e seguitano tuttavia a magnificare l&#039;ingegno scientifico di Leonardo. </s>

<s><lb></lb>Il Venturi fece senza dubbio opera pia verso la patria, per cui con­<lb></lb>viene che gliene professiamo la gratitudine dovuta. </s>

<s>Ma più grati ci <lb></lb>sentiremmo all&#039;illustre fisico modanese, se le parole almeno ce le <lb></lb>avesse trascritte nella favella che risuona dolcemente ancora sul <lb></lb>labbro de&#039;villici da Vinci, e più che mai grata gli sarebbe la sto­<lb></lb>ria, se interpretando i concetti scientifici del suo Autore, non ci <lb></lb>avesse inteso spesso una cosa per un&#039;altra, o non avesse intraveduto <lb></lb>talvolta nelle parole espresso ciò che veramente non ci era. </s></p><p type="main">

<s>Nel 1840, Guglielmo Libri apre il secondo libro della sua <emph type="italics"></emph>Hi­<lb></lb>stoire des sciences mathematiques en Italie,<emph.end type="italics"></emph.end> col trattar di Leonardo <lb></lb>da Vinci, i manoscritti del quale dice che non erano stati ancora <lb></lb>seriamente studiati. </s>

<s>Egli poi gli descrive minutamente, e prolissa­<lb></lb>mente ivi si studia di annoverarne i soggetti varii toccati, e di <lb></lb>porre in rilievo la novità de&#039;concetti e la importanza delle in­<lb></lb>venzioni. </s>

<s>Dei quali concetti più notabili e delle quali invenzioni, <lb></lb>acciochè possano i lettori averne qualche saggio, trascrive alcuni <lb></lb>passi dai vari manoscritti e gli pon sott&#039;occhio in quelle <emph type="italics"></emph>XXI Notes<emph.end type="italics"></emph.end><lb></lb>apposte in calce al III Tomo della citata <emph type="italics"></emph>Histoire.<emph.end type="italics"></emph.end> Eppure si pos­<lb></lb>sono ancora, dop&#039;aver letto le prime 58 pagine del <emph type="italics"></emph>livre second,<emph.end type="italics"></emph.end> e <lb></lb>le <emph type="italics"></emph>XXI Notes,<emph.end type="italics"></emph.end> ripetere al Libri le sue stesse parole, che egli pro­<lb></lb>nunziava dop&#039;aver dato il suo giudizio sull&#039;<emph type="italics"></emph>Essai<emph.end type="italics"></emph.end> del Venturi: “ Or <lb></lb>ces manuscrits n&#039;ont jamais été serieusement étudiés ” (Paris 1840, <lb></lb>Tome III, pag. </s>

<s>39). A studiarli seriamente poi più tardi incomin­<lb></lb>ciarono due stranieri, Carlo Ravaisson-Mollien a Parigi, e Giovan <lb></lb>Paulo Richter a Londra. </s>

<s>Gli italiani che van buccinando il nome <lb></lb>di Leonardo con tuba sì sonora, non hanno dato, fin qui, opera <lb></lb>che a&#039;illustrare alcuni disegni scelti dal Codice Atlantico, pub-<pb xlink:href="020/01/096.jpg" pagenum="77"></pb>blicati in XXIV tavole litografate, per modo di saggio, in Milano <lb></lb>nel 1872: lavoro non scientifico, ma accademico, e benissimo atto <lb></lb>a secondare il genio de&#039;convenuti a una festa. </s></p><p type="main">

<s>Toccheremo qualche cosa più qua delle pubblicazioni fatte dai <lb></lb>due benemeriti stranieri: quel che ora però più preme, è di offerir <lb></lb>qualche esempio delle osservazioni naturali e delle speculazioni di <lb></lb><figure id="id.020.01.096.1.jpg" xlink:href="020/01/096/1.jpg"></figure><lb></lb>Leonardo, che quasi promesseci nei dipinti, si trovano poi fedel­<lb></lb>mente osservate nei manoscritti. </s></p><p type="main">

<s>Dicemmo che il cartone, il quale doveva servire al dipinto di <lb></lb>quelle portiere, da eseguirsi pel re di Portogallo, rivelava nell&#039;ar­<lb></lb>tefice un botanico squisito, e soggiungemmo potersi argomentare <lb></lb>da tutto insieme che l&#039;artefice stesso non dovess&#039;essere un semplice <pb xlink:href="020/01/097.jpg" pagenum="78"></pb>osservatore, ma un filosofante delle proprietà naturali dell&#039;erbe. </s>

<s><lb></lb>Ecco infatti una nota dai Manoscritti, nella quale apparisce che ve­<lb></lb>ramente Leonardo attese a quell&#039;ordine simmetrico e vario, nelle <lb></lb>varie specie di piante, che le foglie tengono nel disporsi intorno <lb></lb>all&#039;asse del ramo, e che i moderni appellano col nome di <emph type="italics"></emph>fillotassi.<emph.end type="italics"></emph.end><lb></lb>“ Tale è il nascimento, egli dice, delle ramificazioni delle piante <lb></lb>sopra i lor rami principali, qual è quello del nascimento delle fo­<lb></lb>glie sopra i ramicoli del medesimo anno di esse foglie, le quali <lb></lb>foglie hanno quattro modi di procedere l&#039;una più alta che l&#039;altra. </s>

<s><lb></lb>Il primo più universale è che sempre la sesta di sopra nasce sopra <lb></lb>la sesta di sotto: e il secondo è che le due terze di sopra son <lb></lb>sempre le due terze di sotto; e il terzo modo è che la terza di <lb></lb>sopra è sopra la terza di sotto. </s>

<s>” (Richter, Londra, 1883, T.I, pag. </s>

<s>211). </s></p><p type="main">

<s>Che se di qui non trasparisce altro più che il semplice osser­<lb></lb>vatore, la seguente nota ci rivela il filosofo: “ Sempre la foglia <lb></lb>volge il suo diritto inverso il cielo acciò possa meglio ricevere con <lb></lb>tutta la sua superficie la rugiada che con lento moto discende dal­<lb></lb>l&#039;aria, e tali foglie sono in modo compartite sopra le loro piante, <lb></lb>che l&#039;una occupa l&#039;altra il men che sia possibile, coll&#039;interzarsi <lb></lb>l&#039;una sopra dell&#039;altra, come si vede fare all&#039;edera che copre li <lb></lb>muri; e tale intrecciamento serve a due cose: cioè al lasciare l&#039;in­<lb></lb>tervallo che l&#039;aria e il sole possa penetrare in fra loro e che le <lb></lb>goccie che caggiono dalla prima foglia possan cadere sopra la quarta <lb></lb>e la sesta degli altri alberi. </s>

<s>” (ivi, pag. </s>

<s>214). </s></p><p type="main">

<s>L&#039;osservazione, che portò Leonardo sulla realtà dei modelli, <lb></lb>per ritrarre al vivo la carne degli uomini, gli servì d&#039;occasione a <lb></lb>coltivar lo studio di quell&#039;altra fra le scienze naturali, che è l&#039;Ana­<lb></lb>tomia. </s>

<s>Quali aiuti gli venissero intorno a ciò da Marcantonio Della <lb></lb>Torre non è facile definire, ma forse la perizia del sezionare di <lb></lb>questo, era compiuta dalla sagacia delle osservazioni e delle inda­<lb></lb>gini dell&#039;altro. </s>

<s>Nel dipingere un occhio s&#039;accorge Leonardo di un <lb></lb>fatto assai curioso; di un fatto, che Galileo scommette non esser­<lb></lb>vene due fra mille che l&#039;abbiano osservato (Alb. </s>

<s>I, 394) e par che <lb></lb>voglia insinuar collo stesso silenzio che l&#039;osservazione è sua, ben­<lb></lb>chè il Porta l&#039;avesse descritta nella Diottrica e l&#039;Acquapendente <lb></lb>avesse pubblicato com&#039;occorresse al Sarpi di farla negli occhi dei <lb></lb>gatti e poi degli uomini. </s>

<s>Ma più di un secolo prima del Porta e <lb></lb>del Sarpi avea il nostro pittore da Vinci osservato il fenomeno, e <lb></lb>v&#039;avea filosofato attorno con assai retto giudizio. </s>

<s>Hanno inteso i <lb></lb>lettori che il fenomeno di cui si tratta è il dilatarsi e il restrin-<pb xlink:href="020/01/098.jpg" pagenum="79"></pb>gersi della pupilla, sotto le impressioni della varia intensità della <lb></lb>luce; fenomeno che non solo fu da Leonardo materialmente osser­<lb></lb>vato, ma altresì filosoficamente illustrato, in ordine a ciò che con­<lb></lb>cerne la teoria della visione. </s>

<s>“ Questa nostra pupilla, ci lasciò scritto, <lb></lb>cresce e diminuisce secondo la chiarità o scurità del suo obietto, <lb></lb>e perchè con qualche tempo fa esso crescere o descrescere, esso <lb></lb>non vede così presto uscendo dal lume e andando all&#039;oscuro, e <lb></lb>similmente dall&#039;oscuro al luminoso, e questa cosa già m&#039;ingannò <lb></lb>nel dipingere un occhio e di lì l&#039;imparai. </s>

<s>” (Ivi, pag. </s>

<s>23). </s></p><p type="main">

<s>Il curioso fatto imparato nel dipingere la pupilla, invogliò forse <lb></lb>Leonardo a penetrare più addentro all&#039;anatomia dell&#039;occchio, e ad <lb></lb>estrarlo dal cadavere per sezionarlo. </s>

<s>In altro modo riuscirebbe assai <lb></lb>difficile intendere com&#039;egli vi avesse potuto scoprir l&#039;inversioni delle <lb></lb>immagini, a cui accenna nella nota seguente: “ Nessuno spazio di sì <lb></lb>minimo corpo penetra nell&#039;occhio che non si volti sottosopra. </s>

<s>” No­<lb></lb>tabili son poi le parole, colle quali prosegue e in che si studia di <lb></lb>risolvere quel famoso problema, che ha tenuto gli ottici in così lungo <lb></lb>travaglio, problema che è quello del vedersi da noi le immagini <lb></lb>dirette, mentre sul fondo del nostro occhio son dipinte a rovescio. </s>

<s><lb></lb>Leonardo n&#039;esce da par suo ammettendo un&#039;ipotesi assai strana. </s>

<s><lb></lb>Professando le dottrine galeniche, secondo le quali la lente cristal­<lb></lb>lina è la sede della visione, e ingannato forse da alcuni effetti ve­<lb></lb>duti fare ai processi ciliari, credette che fosse a questi stessi com­<lb></lb>messo l&#039;ufficio di capovolgere la medesima lente cristallina, per cui <lb></lb>venissero così a raddrizzarsi le immagini degli oggetti “ e nel pe­<lb></lb>netrare, (tali son le parole soggiunte alle precedenti citate), la spera <lb></lb>cristallina ancora si rivolta sottosopra e così ritorna diritto lo spa­<lb></lb>zio dentro all&#039;occhio, com&#039;era l&#039;obietto di fuori dell&#039;occhio. </s>

<s>” (ivi, <lb></lb>pag. </s>

<s>48). Da ciò dovette seguitar senza dubbio l&#039;invenzione della <lb></lb>camera ottica e l&#039;applicazione ch&#039;ei ne fa alla teoria della visione, <lb></lb>conforme a ciò che leggesi in quell&#039;altra nota trascritta e pubbli­<lb></lb>cata già dal Venturi. </s>

<s>L&#039;invenzione della camera oscura par dunque <lb></lb>certo esser cosa appartenente a Leonardo, almeno per ciò che con­<lb></lb>cerne l&#039;applicazione di lei alla teorica del vedere: applicazione alla <lb></lb>quale non poteva pensare l&#039;Alberti, professando egli apertamente <lb></lb>le dottrine platoniche de&#039;raggi visivi che escon dagli occhi, e vanno <lb></lb>a ricongiungersi col fuoco celeste, essendo parole espresse di lui <lb></lb>che la visione si porge e distende verso la cosa visibile. (Op. </s>

<s>volg. </s>

<s><lb></lb>Firenze, 1847, T. IV, pag. </s>

<s>100) e che il raggio della veduta esce <lb></lb>dall&#039;occhio di chi riguarda. (Archit. </s>

<s>Milano, 1833, pag. </s>

<s>362). </s></p><pb xlink:href="020/01/099.jpg" pagenum="80"></pb><p type="main">

<s>Delle molte altre scoperte o speculazioni di Fisica, e osserva­<lb></lb>zioni di Storia naturale, occorrerà via via di far parola per entro <lb></lb>ai volumi che si parano innanzi agli occhi dei nostri lettori; sco­<lb></lb>perte che Leonardo faceva non consultando libri, ma direttamente <lb></lb>interrogando la stessa Natura per via dell&#039;esperienza. </s>

<s>Che tale fosse <lb></lb>l&#039;indole e il metodo seguito dall&#039;Autore, noi lo abbiamo fin qui <lb></lb>argomentato dai fatti, e sono i nostri argomenti confermati dalle <lb></lb>stesse parole di lui, che egli scrive contro l&#039;arroganza dei filosofi <lb></lb><emph type="italics"></emph>in libris.<emph.end type="italics"></emph.end> “ Molti mi crederanno ragionevolmente, egli nota, poter <lb></lb>riprendere allegando le mie prove esser contro all&#039;antorità di al­<lb></lb>quanti uomini di gran riverenza appresso de&#039;loro inesperti giudizii, <lb></lb>non considerando le mie cose essere nate sotto la semplice espe­<lb></lb>rienza, la quale è maestra vera. </s>

<s>” (Richter, ivi, pag. </s>

<s>15). </s></p><p type="main">

<s>E che veramente potesse l&#039;esperienza, assai meglio de&#039;libri, <lb></lb>condurre Leonardo alla scoperta della camera ottica, e l&#039;osserva­<lb></lb>zione rivelargli la fillotassi, come altresì que&#039;molti e varii fatti na­<lb></lb>turali, che si leggon notati qua e là ne&#039;suoi Manoscritti, è cosa <lb></lb>facilissima a comprendersi da tutti. </s>

<s>Nè difficile è pure intendere <lb></lb>come l&#039;osservazione stessa e la propria esperienza potessero con­<lb></lb>durlo a scoprir quella legge fondamentale, che governa il moto <lb></lb>dell&#039;acque, a cui, per la stessa via, eran giunti Frontino, i Pretori <lb></lb>romani, e più recentemente l&#039;Alberti; legge, dalla quale, filosofando <lb></lb>e sperimentando, non difficilmente si sarebbero svolti nell&#039;ingegno <lb></lb>di Leonardo que&#039;teoremi, che raccolti insieme e ordinati, compon­<lb></lb>gono quel Trattato idraulico, il quale va sotto il nome di lui. </s></p><p type="main">

<s>Ma non sempre le note che ricorrono per i manoscritti vin­<lb></lb>ciani versano circa a soggetti di Fisica sperimentale, o di Storia na­<lb></lb>turale, o di Meccanica pratica. </s>

<s>La miglior parte e più importante <lb></lb>di quelle note contiene dimostrazioni di Meccanica razionale, alle <lb></lb>quali non sarebbe potuto Leonardo riuscire in qualche modo, sen­<lb></lb>z&#039;esservisi prima preparato con discipline e con istudii, che non <lb></lb>si apprendono se non dalla lettura dei libri o dalla voce dei mae­<lb></lb>stri. </s>

<s>Luca Paciolo, amico suo, gli dovett&#039;essere, senza dubbio, nelle <lb></lb>Matematiche di grande aiuto, e l&#039;Amoretti a pag. </s>

<s>86 delle citate <lb></lb><emph type="italics"></emph>Memorie<emph.end type="italics"></emph.end> fa menzione di una scrittura del Nostro, nella quale ri­<lb></lb>chiede l&#039;Archimede del vescovo di Padova. </s>

<s>Per ciò a noi sembra <lb></lb>ragionevolissimo il credere che il Matematico di Siracusa colla let­<lb></lb>tera morta, e il Matematico del Borgo colla parola viva, iniziassero <lb></lb>l&#039;ingegno di Leonardo a intendere le proposizioni della Geometria <lb></lb>e al farne l&#039;applicazione ai teoremi della Meccanica. </s></p><pb xlink:href="020/01/100.jpg" pagenum="81"></pb><p type="main">

<s>Benchè si ritenga da noi una tal credenza, per cosa certissima, <lb></lb>il veder nonostante il discepolo far così gran progressi nella scuola <lb></lb>de&#039;due più insigni Maestri di scienza matematica, di che si glorii <lb></lb>l&#039;Italia, ha tanto del maraviglioso, e tanto esce fuori de&#039;consueti <lb></lb>ordini della storia, che ne rimane stupefatto il nostro povero in­<lb></lb>telletto. </s>

<s>Ciò che quell&#039;artista seppe speculare della Scienza del moto <lb></lb>e per quanto largo spazio riuscisse a conquistare le incognite pro­<lb></lb>vincie, nelle quali Galileo stabilì il suo Nuovo Regno, i lettori, a <lb></lb>cui basterà la pazienza di seguirci in questo lungo viaggio, lo ve­<lb></lb>dranno bene a suo tempo. </s>

<s>S&#039;abbatteranno, leggendo, in un Tratta­<lb></lb>tello di <emph type="italics"></emph>Meccanica razionale,<emph.end type="italics"></emph.end> da noi con diligente amore compilato <lb></lb>da quei manoscritti vinciani, che abbiamo potuto vedere alla pub­<lb></lb>blica luce, e che si son potuti da noi, con qualche comodità, con­<lb></lb>sultare. </s>

<s>Con pari amor diligente è stato pure compilato da noi quel­<lb></lb>l&#039;altro Trattatello d&#039;Idraulica, che vedranno i nostri lettori inserito <lb></lb>a suo luogo, compendiato da quello, che per la prima volta fu <lb></lb>nel 1828 pubblicato in Bologna. </s>

<s>La brevità stessa, se non il nuovo <lb></lb>ordine che noi ci siamo studiati di dare alle parti di quel Tratta­<lb></lb>tello, gioveranno a porre in più vivo rilievo la scienza di Leonardo, <lb></lb>perciocchè il compilator primo e più antico di quel Trattato in­<lb></lb>tiero, oltre ad esser trascorso in errori gravissimi materiali e for­<lb></lb>mali, non ha usato discrezione alcuna così nella scelta come nel­<lb></lb>l&#039;ordine dei teoremi. </s></p><p type="main">

<s>Un&#039;altra compilazione fatta allo stesso modo è pure il Trattato <lb></lb>della Pittura, nè sappiamo intendere come gli artisti e i letterati <lb></lb>lo abbiano potuto così confidentemente ritener per legittimo parto <lb></lb>del Vinci, tanto nella materia che nella forma. </s>

<s>Il sospetto ragio­<lb></lb>vole del Venturi sarebbe confermato dal ripensare a quel carattere <lb></lb>incontentabile, come è il grande Artista dipinto dal Vasari, il quale <lb></lb>dice di lui che il cercar nell&#039;opere eccellenza sopra eccellenza, <lb></lb>com&#039;ei sempre faceva, <emph type="italics"></emph>era cagione che nessuna ne lasciasse asso­<lb></lb>luta.<emph.end type="italics"></emph.end> Da un&#039;altra parte Leonardo si confessa da sè medesimo per <lb></lb>uomo senza lettere, e inetto a ben dire quello che voleva trattare. <lb></lb></s>

<s>“ Diranno che per non avere io lettere non poterei ben dire quello <lb></lb>che voglio trattare. </s>

<s>Or non sanno questi che le mie cose son più <lb></lb>da esser trattate dalla sperienza che d&#039;altra parola, la quale fu <lb></lb>maestra di chi bene scrisse e così per maestra la, in tutti i casi, <lb></lb>allegherò. </s>

<s>” (ivi, pag. </s>

<s>14). </s></p><p type="main">

<s>Sopra questi certissimi argomenti noi crediamo di potere af­<lb></lb>fermare che Leonardo non ebbe quella pazienza o quella costanza, <pb xlink:href="020/01/101.jpg" pagenum="82"></pb>e diciam pure quell&#039;arte letteraria, che si richiedeva a dar forma <lb></lb>di Trattato alle varie materie e a ordinarle in libri, in capitoli, in <lb></lb>proposizioni, come asseriscono molti. </s>

<s>Ond&#039;è che da noi si potrebbe <lb></lb>facilmente mostrar l&#039;inganno che fu preso dall&#039;Amoretti nel § XXXII <lb></lb>delle <emph type="italics"></emph>Memorie,<emph.end type="italics"></emph.end> dove annovera un lungo catalogo di Trattati, già <lb></lb>bell&#039;e messi all&#039;ordine da Leonardo, alcuni de&#039;quali anco scritti <lb></lb>in latino; si potrebbe far ciò diciamo assai facilmente, se l&#039;Autore <lb></lb>stesso non avesse dato a vedere d&#039;essersi già per sè medesimo ac­<lb></lb>corto di quell&#039;inganno. </s>

<s>Nè più difficile pure sarebbe il mostrar <lb></lb>qual conto si debba fare e in qual significato debbono interpetrarsi <lb></lb>le autorevoli testimonianze di Luca Pacioli. </s></p><p type="main">

<s>Concludiamo insomma come tutto quello che è proprietà let­<lb></lb>teraria del Nostro, si contiene in quelle note, in quegli appunti, <lb></lb>in quei ricordi, che ci son rimasti tuttavia manoscritti autografi <lb></lb>nella carte di lui. </s>

<s>La non breve vita decorsagli dal 1452 al 1519 <lb></lb>e la costante abitudine di nulla tralasciar d&#039;inosservato, fa ragio­<lb></lb>nevolmente presupporre che molti più de&#039;pervenuti infino a noi <lb></lb>dovessero essere i libretti vinciani, e dall&#039;altra parte non è possi­<lb></lb>bile che, in tanto tramestar di mani e traslocar di paesi, non an­<lb></lb>dassero in qualche parte smarriti. </s>

<s>Pure è tanta l&#039;eredità scientifica <lb></lb>a noi trasmessa, che ce ne dovremmo contentare e pensar piuttosto <lb></lb>al miglior modo di usufruirla. </s></p><p type="main">

<s>Si diceva dianzi che ad usufruirla pensò, de&#039;primi, in Francia, <lb></lb>il Ravaisson-Mollien, che ci dette fotografata una buona parte delle <lb></lb>carte vinciane sottovi trascritte le note conforme all&#039;ortografia mo­<lb></lb>derna, e di rincontro al testo la traduzione francese. </s>

<s>È naturalis­<lb></lb>simo ch&#039;ei dovesse incontrarsi in grandissime difficoltà, sì rispetto <lb></lb>alla materia, sì rispetto al modo d&#039;interpetrarla, ciò che troppo <lb></lb>bene apparisce dalle stesse versioni e da quegl&#039;indici posti in fine <lb></lb>ai volumi, dove l&#039;egregio uomo andò a rifugiare i commenti scien­<lb></lb>tifici, talvolta importantissimi, ch&#039;ei fa al testo vinciano. </s>

<s>Ma un&#039;oc­<lb></lb>casione insuperabile di errori è in lui, e ne&#039;pari suoi, il non aver <lb></lb>senso di quel vernacolo toscano, di che fa uso nelle solitarie sue <lb></lb>scritture Leonardo. </s>

<s>Ciò conduce il benemerito editor parigino in <lb></lb>errori gravissimi, e di ciò in fine della presente parte del nostro <lb></lb>Discorso sottoporremo al giudizio de&#039;nostri lettori, in nota, un <lb></lb>esempio. </s></p><p type="main">

<s>È ben vero però che ad apparecchiar l&#039;ordinamento de&#039;con­<lb></lb>cetti di Leonardo, e a pubblicarli in modo che se ne possano gio­<lb></lb>vare gli studiosi, non si richiedeva di meglio della laboriosissima <pb xlink:href="020/01/102.jpg" pagenum="83"></pb>opera del Parigino, che noi facciamo voto di veder presto condotta <lb></lb>alla sua mèta. </s>

<s>Con tutti quei materiali alla mano si potrà allora <lb></lb>incominciare a costruire, e il giudizioso Architetto, fra quegli stessi <lb></lb>materiali di ugual sostanza e di non differente forma, sceglierà <lb></lb>opportunamente i migliori e lascerà indietro i disutili, per qualsi­<lb></lb>voglia ragion di difetto che ritrovisi in essi. </s></p><p type="main">

<s>Chi attende con qualche studio ai Manoscritti vinciani, facil­<lb></lb>mente ritrova che ora una nota, perchè l&#039;Autore v&#039;ha ripensato <lb></lb>un po&#039;meglio, contradice a un&#039;altra; ora il concetto che qui viene <lb></lb>espresso in confuso, altrove è meglio spiegato; ora è una specula­<lb></lb>zione interrotta che poi viene ripresa e continuata, aggiungendo <lb></lb>qualche cosa al già detto, che è ripetuto sotto altra forma. </s>

<s>Qui è <lb></lb>trascorso un errore, e più qua lo troviamo o confermato o corretto. </s>

<s><lb></lb>Molte volte quel che sente d&#039;averlo espresso male, si prova a ri­<lb></lb>dirlo un po&#039;meglio. </s>

<s>Il non voler far uso in questi casi di una giu­<lb></lb>diziosa scelta, è un volere stampar volumi sopra volumi per de­<lb></lb>corarne le biblioteche, non perchè se ne giovino gli studiosi. </s></p><p type="main">

<s>Siam venuti così preparando le file a intessere il nostro giu­<lb></lb>dizio intorno all&#039;opera fatta dal Richter, il quale ha già dato <lb></lb>mano, non come il Mollien a preparare o mettere all&#039;ordine i ma­<lb></lb>teriali, ma a costruire. </s>

<s>Forse egli ha avuto in ciò far troppa fretta <lb></lb>e non avendo potuto giustamente estimare ogni più minuta par­<lb></lb>ticolarità; non è riuscito a farne convenientemente la scelta. </s>

<s>Ma <lb></lb>pure ha di una scelta riconosciuto giudiziosamente il bisogno, e <lb></lb>poniamo che la difficile impresa non sia andata, com&#039;asseriscono i <lb></lb>censori di lui, esente da gravissimi difetti; a noi par nonostante <lb></lb>che l&#039;editor londinese abbia tenuta la via conveniente a chi si <lb></lb>dava cura di pubblicar le opere di Leonardo, per benefizio degli <lb></lb>studiosi. </s></p><p type="main">

<s>Alcuno ha apposto per difetto al Richter l&#039;aver trascurati i <lb></lb>commenti, nè si sa di qual sorte commenti abbia inteso costui. </s>

<s><lb></lb>Commenti filologici, senza dubbio sarebbero stati opportuni, ma <lb></lb>non era in grado di farli un inglese, che anzi cade anch&#039;egli assai <lb></lb>spesso negli errori, notati di sopra nel Mollien, per non aver senso <lb></lb>e pratica del vernacolo toscano. </s>

<s>Commenti scientifici, più che op­<lb></lb>portuni, sembrerebbero necessari, ma per farli occorrerebbe di co­<lb></lb>noscer lo stato della scienza a&#039;tempi di Leonardo, scienza affidata <lb></lb>alla viva voce dei maestri e alle carte neglette e perciò disperse <lb></lb>nè, per umana industria forse recuperabili. </s>

<s>Se si potessero aver <lb></lb>sott&#039;occhio quei documenti, Leonardo da Vinci apparirebbe sempre <pb xlink:href="020/01/103.jpg" pagenum="84"></pb>un&#039;ingegno straordinario, ma cesserebbe di rappresentarsi al nostro <lb></lb>giudizio sotto l&#039;aspetto d&#039;ingegno miracoloso, ritrovandosi che an­<lb></lb>ch&#039;egli ha, per legge ordinaria, dovuto soggiacere alle necessità <lb></lb>delle tradizioni, a ministrar le quali gli dovevano esser soccorsi i <lb></lb>libri antichi e gl&#039;insegnamenti de&#039;suoi tempi. </s>

<s>Quella po&#039;di luce che <lb></lb>poteva venirgli da così fatti insegnamenti era sufficiente a indirizzar <lb></lb>Leonardo per i sentieri del vero, a proseguir lungo i quali lo con­<lb></lb>duceva per mano la stessa Natura, negli amati esercizi dell&#039;arte. </s></p><p type="main">

<s><emph type="center"></emph>XI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Trattenendo il pensiero meditativo, così sopra questa maravi­<lb></lb>gliosa figura dì Leonardo, come su quella degli altri cultori del­<lb></lb>l&#039;arte, sia essa l&#039;arte del verso nell&#039;Alighieri, sia l&#039;arte navigatoria <lb></lb>nel Colombo, sia l&#039;arte edilizia nell&#039;Alberti, ci persuadiam facilmente <lb></lb>che quegli uomini singolari attesero non ad assottigliar l&#039;ingegno <lb></lb>nella dialettica dei sofismi, ma a inacutire i sensi per pigliar più <lb></lb>sicuro possesso delle cose reali. </s>

<s>L&#039;arte navigatoria e quella della <lb></lb>stampa felicemente ritrovate nel medesimo tempo, eran come i due <lb></lb>remi maestri che a quel possesso conducevano la navicella, dentro <lb></lb>alla quale fa, la mente dell&#039;uomo, da nocchiero. </s>

<s>Di qui è che in <lb></lb>affidarsi al mar periglioso, vollesi a quella stessa navicella rivedere <lb></lb>ogni testura, e far esperienza di ciò che potesse incontro all&#039;in­<lb></lb>sorger tempestoso dei flutti e del vento. </s>

<s>Se ci si conceda ora che <lb></lb>si possa, per una tal navicella, rappresentare il corpo dell&#039;uomo, <lb></lb>si comprenderà come la condizione dei tempi e il progredir nelle <lb></lb>cognizioni, dovessero portare allo studio dell&#039;Anatomia, e di quegli <lb></lb>organi dei sensi in particolare, per cui l&#039;uomo entra nel pieno e <lb></lb>reale possesso del mondo. </s></p><p type="main">

<s>Fino al terminar di quel secolo, in cui fu spento Leonardo, <lb></lb>tutto ciò che si sapeva della fabbrica del corpo umano s&#039;appren­<lb></lb>deva dai libri dell&#039;antico Galeno, il quale era ai medici, come Ari­<lb></lb>stotile ai filosofi, l&#039;oracolo venerato degl&#039;infallibili responsi. </s>

<s>Ma <lb></lb>scese dal Belgio in Italia un uomo che, colle sacrileghe mani, osò <lb></lb>di atterrar dagli altari quell&#039;idolo, con audace pretensione di di­<lb></lb>mostrare che la maggior parte di que&#039;suoi responsi erano bugiardi. </s>

<s><lb></lb>Un tale uomo nativo di Bruxelles si chiamava Andrea Vesalio, il <pb xlink:href="020/01/104.jpg" pagenum="85"></pb>quale, eletto a professar Anatomia nello studio di Padova, sezionando <lb></lb>cadaveri umani e mettendo sott&#039;occhio le parti nelle loro vere forme <lb></lb>naturali, le veniva sagacemente comparando alle forme stesse de­<lb></lb>scritte da Galeno, e ad ogni passo ne scopriva un errore. </s>

<s>Additava <lb></lb>anco il Vesalio la fonte originaria di tali errori, ch&#039;ei loquacemente <lb></lb>riconosceva nell&#039;aver l&#039;anatomico greco descritta non la fabbrica <lb></lb>del corpo dell&#039;uomo, ma quella del bruto. </s></p><p type="main">

<s>Le religiose superstizioni pagane, per le quali si reputava atto <lb></lb>sacrilego lo scompaginar violentemente le membra anco ad un uomo <lb></lb>morto, e l&#039;opinione che fossero similmente configurate le membra <lb></lb>al di dentro, com&#039;appariscono al di fuori, negli uomini e nei bruti, <lb></lb>furono senza dubbio le due principali sorgenti di quegli antichi <lb></lb>errori, che il Vesalio era venuto a scoprire al troppo credulo mondo. </s>

<s><lb></lb>La scienza perciò professerà eterna gratitudine a quell&#039;uomo, e lo <lb></lb>riconoscerà per primo Istitutore dell&#039;Anatomia. </s>

<s>Ma, o fosse giova­<lb></lb>nile baldanza o natìo orgoglio, non serbò, nel geloso esercizio del <lb></lb>suo ministero, il debito modo, per cui gli si concitarono incontro <lb></lb>dai Galenisti inimicizie e persecuzioni sì fiere, che quelle esercitate <lb></lb>poi da&#039;peripatetici contro Galileo, al paragone, sembran carezze. </s></p><p type="main">

<s>Successe al Vesalio, nello studio padovano, Realdo Colombo <lb></lb>di Cremona, il quale era stato già spettatore delle sezioni e udi­<lb></lb>tore delle acerbe diatribe declamate dall&#039;ardente brussellese. </s>

<s>Nel <lb></lb>temperato animo del nostro italiano parvero, infin da giovane, quelle <lb></lb>diatribe contro l&#039;antico maestro un po&#039;troppo esagerate, e succe­<lb></lb>duto nella cattedra di lui non mancò di confessarle e di dare esempii <lb></lb>d&#039;una critica più mite e più giudiziosa. </s>

<s>Il Vesalio aveva atterrate <lb></lb>le mura del tempio galenico, il primo, con ardimento inaudito, per <lb></lb>cui, mentre da una parte perseguitavasi a morte, s&#039;esaltava, dal­<lb></lb>l&#039;altra, col titolo di <emph type="italics"></emph>divino.<emph.end type="italics"></emph.end> Il Colombo, entrato il primo per quella <lb></lb>breccia aperta, v&#039;instaurò il nuovo regno dell&#039;Anatomia descrittiva <lb></lb>e sperimentale, e operò con tant&#039;arte giudiziosa, che la violenta <lb></lb>conquista vesaliana prese aspetto di una successione legittima. </s></p><p type="main">

<s>Chi vuol giustamente apprezzare i meriti dell&#039;Anatomico cre­<lb></lb>monese, e ravvisar quella fina arte ch&#039;egli usò per diffondere la <lb></lb>nuova scienza, non distruggendo con rabbioso orgoglio l&#039;antico edi­<lb></lb>fizio, ma correggendolo con giudiziosa industria e ampliandone la <lb></lb>struttura; non dee far altro che svolgere quelle splendide pagine, <lb></lb>che egli scrisse e intitolò <emph type="italics"></emph>De re anatomica,<emph.end type="italics"></emph.end> stampate nel 1559 in <lb></lb>Venezia dalla tipografia di Niccolò Bevilacqua. </s>

<s>A noi sembra questo <lb></lb>il più bel libro, che in materia scientifica sia uscito fuori in quel <pb xlink:href="020/01/105.jpg" pagenum="86"></pb>tempo, ed è tanta la sobrietà dell&#039;erudizione, tanta l&#039;arte colla quale <lb></lb>sa nuotar fuori del gazzabuglio delle opinioni e sollevarsi alto sulla <lb></lb>nebbia uggiosa de&#039;placiti delle scuole, tanta la lucidezza delle ar­<lb></lb>gomentazioni e la oppurtunità delle esperienze, che sembra essere <lb></lb>stata scritta quell&#039;opera dopo i tempi di Galileo. </s>

<s>Se si ripensa anzi <lb></lb>a quella generosa e temperata franchezza, colla quale egli emenda <lb></lb>gli errori, in che incorsero Aristotile e Galeno e lo stesso Vesalio, <lb></lb>si crederà che l&#039;Autore non iscrivesse, come Galileo stesso, in tempi <lb></lb>di controversie, ma nella pacifica dominazione del Metodo speri­<lb></lb>mentale, tanto è serena la mente di Realdo Colombo nello stesso <lb></lb>fervoroso zelo dell&#039;eloquente parola. </s></p><p type="main">

<s>Il primo libro anatomico del Cremonese tratta delle ossa. </s>

<s>Egli <lb></lb>ivi diligentemente attende a descrivere le <emph type="italics"></emph>epifisi,<emph.end type="italics"></emph.end> dell&#039;utilità delle <lb></lb>quali, egli dice, Galeno, d&#039;altra parte solertissimo investigatore <lb></lb>della Natura, non scrisse, e ciò che più fa meraviglia, non scrisse <lb></lb>nemmeno il Vesalio, <emph type="italics"></emph>quippe qui ardiret cupiditate increbili in <lb></lb>Galenum invehendi et eius errores adnotandi.<emph.end type="italics"></emph.end> (Da re anat. </s>

<s>edit. </s>

<s><lb></lb>cit. </s>

<s>pag. </s>

<s>4). Nel divisare, delle ossa una classificazione veramente <lb></lb>scientifica, dice di non aver seguito gli esempii nè di Galeno an­<lb></lb>tico nè del Vesalio moderno, intorno a che tanto vivo sente il <lb></lb>dovere di non dilungarsi capricciosamente dall&#039;insegnamento dei <lb></lb>primi maestri, che vuol, del fatto, mostrar di averne la sua buona <lb></lb>ragione. “ Nam licet Galenum, tamquam numen veneremur, Vesa­<lb></lb>lioque in dissectionis arte plurimum tribuamus, ubi cum rei na­<lb></lb>tura consentiunt: tamen cum aliquando videamus rem aliter multo <lb></lb>se habere ac ipsi descripserint, veritas eadem, cui magis addicti <lb></lb>sumus, nos coegit ab illis interdum recedere ” (ibi, pag. </s>

<s>10). </s></p><p type="main">

<s>Memoranda sentenza sulla bocca di uno scienziato, che scrive <lb></lb>nella prima metà del secolo XVI: io seguo, nell&#039;investigare i fatti <lb></lb>della Natura, la verità, non il maestro, e sia pure un Galeno, un <lb></lb>Vesalio. </s>

<s>E conforme a una tal professione di fede, il Colombo os­<lb></lb>serva i fatti, e come gli si rappresentano agli occhi, fedelmente <lb></lb>così gli descrive, facendo tratto tratto le maraviglie che quello stesso <lb></lb>gran Vesalio, il quale non la finisce mai contro Galeno, per aver <lb></lb>descritta l&#039;anatomia non dell&#039;uomo, ma delle scimmie, egli, il cen­<lb></lb>sore ardente, l&#039;obiurgatore ingiurioso sia bene spesso caduto negli <lb></lb>errori stessi rinfacciati a Galeno. </s>

<s>Questa specie di recriminazione <lb></lb>occorre al Nostro di farla a ogni piè sospinto, ma specialmente a <lb></lb>proposito de&#039;muscoli della laringa e dell&#039;occhio. </s></p><p type="main">

<s><emph type="italics"></emph>De oculis<emph.end type="italics"></emph.end> è il soggetto proprio del X libro, intorno a che è <pb xlink:href="020/01/106.jpg" pagenum="87"></pb>per prima cosa sollecito di avvertire il lettore che, innanzi a lui, <lb></lb>nessun altro anatomico non aveva descritto veramente, se non l&#039;oc­<lb></lb>chio del bruto. </s>

<s>Ond&#039;è che egli esce con ardente zelo a rimprove­<lb></lb>rare e a muovere accuse contro gli uomini della scienza, e special­<lb></lb>mente contro Galeno e il Vesalio, <emph type="italics"></emph>qui tantam rem, tam illustrem, <lb></lb>tam optatam, tam negligenter scribendam putarent, belluinum <lb></lb>oculum pro humano dissecantes<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>216). </s></p><p type="main">

<s>Quando però il Colombo, invitato dalla nobiltà e dalla impor­<lb></lb>tanza del soggetto, entra a far l&#039;anatomia dei mezzi refringenti e <lb></lb>a speculare intorno a&#039;loro ottici effetti, par che non sappia ripeter <lb></lb>altro di meglio delle dottrine ricevute per tradizione da&#039;suoi mag­<lb></lb>giori. </s>

<s>Il principale strumento del vedere, è, secondo lui, come per <lb></lb>Galeno e per il Vesalio, l&#039;umor cristallino, il qual cristallino perciò <lb></lb><emph type="italics"></emph>idolum simulacrumque visionis non iniure appellatur<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>219). <lb></lb>Nonostante si dee al Nostro una curiosa esperienza in proposito, <lb></lb>che egli ivi accenna, ed è quella dell&#039;avere estratto il cristallino <lb></lb>dall&#039;occhio, e dell&#039;aver trovato che i caratteri di uno scritto appa­<lb></lb>riscono ingranditi a chi traguarda con esso, e questa dice esser <lb></lb>forse l&#039;occasione che portò a far la prima scoperta degli occhiali. <lb></lb>“ Huius substantia durinscula est, quam sia sua sede dimoveris, et <lb></lb>ad scriptos caracteres accedat, maiores esse videntur et facilius <lb></lb>conspiciuntur, suspicorque hinc specillorum inventionem origi­<lb></lb>nem duxisse ” (ibi). </s></p><p type="main">

<s>Fin qui il grande anatomico cremonese non ha fatto altro che <lb></lb>insistere sulle orme del Vesalio, il quale, nel descriver la fabbrica <lb></lb>del corpo umano si trattenne principalmente intorno alle parti este­<lb></lb>riori composte delle ossa, dei muscoli e dei ligamenti. </s>

<s>La Splacno­<lb></lb>logia, la parte più importante e più nuova, dal Brussellese fu ap­<lb></lb>pena sfiorata. </s>

<s>Ma Realdo ha nell&#039;Opera sua due libri insigni, il <lb></lb>VII che è <emph type="italics"></emph>De corde et arteriis,<emph.end type="italics"></emph.end> e l&#039;XI che è <emph type="italics"></emph>De visceribus,<emph.end type="italics"></emph.end> e se­<lb></lb>gnatamente <emph type="italics"></emph>De pulmone.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In generale dagli storici dell&#039;anatomia non si dà altro merito <lb></lb>al Nostro, che di aver detto il mediastino del cuore non essere <lb></lb>perforato. “ Inter hos ventriculos septum adest, per quod fere omnes <lb></lb>existimant sanguini a dextro ventriculo ad sinistrum aditum pa­<lb></lb>tefieri.... sed longa errant via, nam sanguis per arteriosam venam <lb></lb>ad pulmonem fertur, ibique attenuatur, deinde cum aere una per <lb></lb>arteriam venalem ad sinistrum cordis ventriculum defertur. </s>

<s>Quod <lb></lb>nemo hactenus aut animadvertit aut scriptum reliquit, licet maxime <lb></lb>sit ab omnibus animadvertendum ” (ibi, pag. </s>

<s>177). La piccola cir-<pb xlink:href="020/01/107.jpg" pagenum="88"></pb>colazione pulmonare si persuadono gli storici che fosse stata de­<lb></lb>scritta già da Galeno, e che fosse il Cesalpino precursore non solo, <lb></lb>ma competitor coll&#039;Harvey. </s>

<s>In quel capitolo dove da noi, dietro un <lb></lb>diligente esame dei documenti, si narra la storia della scoperta del <lb></lb>circolo sanguigno, troveranno dimostrato i lettori come le teorie <lb></lb>galeniche non consistessero in altro che in un giochetto di parole, <lb></lb>e vedranno come il Cesalpino sciogliesse quel giochetto, riducendo <lb></lb>al loro vero valore anatomico l&#039;espressioni che ricorrono nell&#039;autor <lb></lb>greco di <emph type="italics"></emph>vena arteriosa<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>arteria venosa.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma quel giochetto era stato sciolto prima da Realdo Colombo, <lb></lb>il quale, dimostrando che tra il cuore e il polmone intercede un <lb></lb>circolo continuo di sangue, disse che i dutti erano una vera arteria <lb></lb>e una vera vena, nonostante che quella movesse dal ventricolo de­<lb></lb>stro e questa dal ventricolo sinistro del cuore. </s></p><p type="main">

<s>Scrivono gli Anatomici, così con memorande parole si esprime <lb></lb>il Colombo, che ufficio proprio dell&#039;arteria venosa sia quello di por­<lb></lb>tar l&#039;aria alterata nel cuore, ai polmoni, i quali, a guisa di flabelli <lb></lb>stanno lì ordinati a fargli vento e a rinfrescarlo dai soverchi ardori. </s>

<s><lb></lb>Quegli stessi poco prudenti, prosegue a dire, si persuadono che nel <lb></lb>cuore si generino fumi, quasi fosse un focolare sopra a cui siano <lb></lb>state gittate ad ardere legna verdi. “ Ego vero oppositum prorsus <lb></lb>sentio hanc scilicet arteriam venalem factam esse ut sanguinem <lb></lb>cum aere e pulmonibus mixtum adferant ad sinistrum cordis <lb></lb>ventriculum ” (ibi, pag. </s>

<s>178). </s></p><p type="main">

<s>Ecco la grande rivelazione fatta alla scienza, ecco una grande <lb></lb>scoperta: l&#039;arteria venosa non ha nulla delle proprietà naturali delle <lb></lb>vene, ma è una vera arteria, perchè, anch&#039;essa, come la grande <lb></lb>arteria riversa il sangue nel ventricolo sinistro del cuore. </s>

<s>E che ciò <lb></lb>sia vero, verissimo, che cioè per quel dutto arterioso, che dal pol­<lb></lb>mone viene al cuore scorra sangue e non aria fuligginosa, com&#039;era <lb></lb>fin allora generalmente creduto, il nostro Autore lo prova invocando <lb></lb>l&#039;esperienza, non solo sui cadaveri, ma sopra gli stessi animali vivi, <lb></lb>nei quali <emph type="italics"></emph>hanc arteriam in omnibus sanguine refertam invenies, <lb></lb>quod nullo pacto eveniret si ob aerem dumtaxat, et vapores con­<lb></lb>structa foret. </s>

<s>Quocirca ego illos anatomicos non possum satis mi­<lb></lb>rari qui rem tam praeclaram, tantique momenti non animadverte­<lb></lb>rint<emph.end type="italics"></emph.end> (ibi). </s></p><p type="main">

<s>E questo, si può dire, il primo elettissimo frutto dell&#039;esperienza <lb></lb>applicata alla Fisiologia, la quale esperienza com&#039;ha condotto Realdo <lb></lb>a scoprire il fatto della circolazion polmonare, così lo conduce alla <pb xlink:href="020/01/108.jpg" pagenum="89"></pb>scoperta di quell&#039;altro importantissimo fatto a lui relativo, a quello <lb></lb>della respirazione. </s>

<s>I polmoni non son flabelli, come scioccamente <lb></lb>credevano gli antichi, ma loro ufficio proprio è quello di rimescolar <lb></lb>l&#039;aria col sangue rendendolo più tenue e più spiritoso. </s>

<s>Questo san­<lb></lb>gue è per l&#039;arteria venosa ricondotto al cuore e di lì, per la grande <lb></lb>arteria, a tutto quanto il corpo (ivi, pag. </s>

<s>223). A questo punto però <lb></lb>il nostro Autore sente come la novità del fatto, che nessuno ancora <lb></lb>ha sognato, sarà per commuovere gli animi degl&#039;increduli e più <lb></lb>vivamente quello degli aristotelici, i quali s&#039;aspetta che lo repute­<lb></lb>ranno un paradosso. </s>

<s>Ma egli vuol che gli sia fatta ragione, non <lb></lb>dall&#039;autorità dei maestri, ma da quella della esperienza, per cui <lb></lb>così caldamente conclude rivolgendo tali eloquenti parole al suo <lb></lb>lettore: “ Tu vero, candide lector, doctorum hominum studiose, ve­<lb></lb>ritatis autem studiosissime, experire, obsecro, in brutis animanti­<lb></lb>bus, quae viva ut seces moneo atque hortor: experire inquam an <lb></lb>id quod dixi cum re ipsa consentiat, nam in illis arteriam venalem <lb></lb>illiusmodi sanguinis plenam invenies non aere plenam aut fumis, <lb></lb>ut vocant, capinosis ” (ibi, pag. </s>

<s>224). </s></p><p type="main">

<s>Che se mirabile è un tal sicuro uso dell&#039;esperienza, in un <lb></lb>autore della prima metà del secolo XVI, non men mirabile è l&#039;uso <lb></lb>ch&#039;egli sa fare dell&#039;induzione. </s>

<s>La verità del circolo sanguigno egli <lb></lb>sagacemente la induce dall&#039;artifizio e dai manifesti ufficii, a cui <lb></lb>sono ordinate le valvole del cuore, le quali son, per maggior sicu­<lb></lb>rezza, fermate e mantenute in posto da certi filamenti, che, presi <lb></lb>da Aristotile per nervi, lo fecero andare in quella perniciosa sen­<lb></lb>tenza che i nervi stessi avessero origine dal cuore e non dal cer­<lb></lb>vello e dalla midolla spinale (ivi, pag. </s>

<s>179). Altro bell&#039;esempio di <lb></lb>un argomento d&#039;induzione ci si porge da quel ragionamento ch&#039;ei <lb></lb>fa, per dimostrar che il sangue vitale, il sangue arterioso, non può <lb></lb>in altro organo generarsi che nel polmone. </s>

<s>Quel ragionamento, a <lb></lb>cui chiede poi così caldamente il conforto dell&#039;esperienza, è rivolto <lb></lb>a persuadere gl&#039;increduli aristotelici <emph type="italics"></emph>quos oro rogoque ut pulmo­<lb></lb>nis magnitudinem contemplentur, quae absque vitali sanyuine per­<lb></lb>manere non poterat, cum nulla sit tam minima corporis particula, <lb></lb>quae illo destituatur. </s>

<s>Quod si vitalis hic sanguis in pulmonibus <lb></lb>non gignitur, a qua parte trasmitti poterat, praeter quam ab ahorti <lb></lb>arteria? </s>

<s>et ab ahorti arteria ramus nullus neque magnus neque <lb></lb>parvulus ad pulmones mittitur<emph.end type="italics"></emph.end> ” (ibi, pag. </s>

<s>223). </s></p><p type="main">

<s>Tali erano gl&#039;inizii, che Realdo Colombo, non finito mai d&#039;am­<lb></lb>mirare dai giusti estimatori, dava in Italia alla scienza sperimentale <pb xlink:href="020/01/109.jpg" pagenum="90"></pb>applicata alla fabbrica anatomica del corpo umano e alle funzioni <lb></lb>fisiologiche di lui. </s>

<s>Egli ebbe una illustre sequela ne&#039;nomi di Bar­<lb></lb>tolommeo Eustachio, di Gabriele Falloppio, di Girolamo Fabrizi <lb></lb>d&#039;Acquapendente, a&#039;quali ripensando la scienza italiana si sopra­<lb></lb>esalta. </s>

<s>Or chi non crederebbe mai che succedendo così fatti uomini <lb></lb>al Cremonese, per non interrotta catena infino alla fine del se­<lb></lb>colo XVI, non dovessero portare infino a&#039;suoi più alti fastigi l&#039;ana­<lb></lb>tomia sperimentale? </s>

<s>Chi non s&#039;aspetterebbe che la luminosa dimo­<lb></lb>strazione data da Realdo della piccola circolazione polmonare non <lb></lb>dovesse alle mani di tre tali insigni anatomici suoi successori com­<lb></lb>piersi nella scoperta del circolo universale del sangue ne&#039;suoi vasi? </s></p><p type="main">

<s>Eppure è un fatto, che desta gran maraviglia in chi vi ripensa, <lb></lb>è un fatto, dico, che così l&#039;Eustachio come il Falloppio e l&#039;Acqua­<lb></lb>pendente non fecero altro più che ripetere le viete dottrine di <lb></lb>Galeno e del Vesalio intorno alle funzioni fisiologiche del cuore e <lb></lb>del polmone. </s>

<s>Il libro <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> fu per loro come se fosse <lb></lb>stato scritto al vento. </s>

<s>Solamente il Vidio e l&#039;Aranzio, un po&#039;più <lb></lb>tardi dell&#039;Eustachio e del Falloppio, si rivolsero a confermare a il­<lb></lb>lustrare e a difendere il sistema cardiaco del grande Maestro cre­<lb></lb>monese, ma non osando negare al fegato le funzioni di secernere <lb></lb>il sangue venoso alimentatore, nè sapendo a quale altro più cospi­<lb></lb>cuo ufficio potesse essere ordinato quel viscere dalla Natura, s&#039;ar­<lb></lb>restarono a quel punto dov&#039;era, speculando e sperimentando, per­<lb></lb>venuto il Colombo. </s>

<s>Il Cesalpino pose con nuovi argomenti in piena <lb></lb>evidenza la circolazion polmonare, e non badando troppo al fegato, <lb></lb>rivolse principalmente la sua attenzione sulle funzioni del cuore. </s>

<s><lb></lb>Ma il troppo servile ossequio di lui ai placiti aristotelici gl&#039;impedì <lb></lb>di precorrere con libero piede alla gloriosa scoperta arveiana. </s></p><p type="main">

<s>Così, maestro in cattedra rimase unico Andrea Vesalio, da cui <lb></lb>s&#039;imparò a coltivare l&#039;Anatomia descrittiva, infaustamente lasciando <lb></lb>negletta quell&#039;anatomia sperimentale instituita dal successore di lui, <lb></lb>a cui più meritamente forse s&#039;apparterrebbe il titolo di divino. </s>

<s><lb></lb>Seguendo però i discepoli gli ammaestramenti dell&#039;odiato e perse­<lb></lb>guitato Brussellese, non ne imitarono gli esempi, quanto al modo <lb></lb>di porgerli o con la viva voce o con gli scritti. </s>

<s>Che se non ci s&#039;in­<lb></lb>travedesse sotto sotto uno splendor vivo di luce, apertamente poi <lb></lb>sfolgorata nelle dottrine darviniane de&#039;nostri giorni, si chiamerebbe <lb></lb>un sottile artifizio di furberia quello, col quale il Falloppio intende <lb></lb>a conciliar, nelle anatomiche dissezioni fetali, Galeno e il Vesalio. </s>

<s><lb></lb>Ma nè furberia nè arte scaltrita si direbbe quella, colla quale <pb xlink:href="020/01/110.jpg" pagenum="91"></pb>l&#039;Acquapendente è geloso di non offendere la reputazion di Galeno, <lb></lb>e di non mostrarsi apertamente mai ribelle alle dottrine aristote­<lb></lb>liche. </s>

<s>Quella è religiosa fede non finta, sebbene il medico milio­<lb></lb>nario, il latinista eloquente senta alitarsi in petto le aure della <lb></lb>nascente libertà, invocando talvolta, contro Aristotile stesso e contro <lb></lb>Galeno, la sua propria esperienza. </s></p><p type="main">

<s>Forse le splendide illustrazioni splacnologiche del Colombo si <lb></lb>neglessero dai successori di lui, e si neglessero insieme gl&#039;iniziati <lb></lb>metodi sperimentali, per secondar ciò che altamente si reclamava <lb></lb>dai tempi; tempi in cui risvegliato l&#039;uomo dai sonni contemplativi <lb></lb>di Platone e sollevatosi dai fanciulleschi trastulli aristotelici, si sen­<lb></lb>tiva trasportato a impossessarsi del mondo, mettendo in esercizio <lb></lb>e invocando aiuti agli organi de&#039;sensi, tra&#039;quali è tenuto il primo <lb></lb>luogo dalla vista e dall&#039;udito. </s>

<s>S&#039;intende perciò come dovessero esser <lb></lb>questi i primi ad essere anatomicamente investigati. </s>

<s>E infatti l&#039;Eu­<lb></lb>stachio scopre e descrive quella tuba aerea, alla quale è rimasto <lb></lb>tuttavia il nome del discopritore, e che mette in comunicazione le <lb></lb>cavità interne dell&#039;orecchio con quelle della bocca. </s>

<s>Il Falloppio ci dà <lb></lb>quella mirabile descrizione di tutte le più minute parti della rocca <lb></lb>petrosa, e l&#039;Acquapendente scrive un Trattato intero sugli organi e <lb></lb>sulle funzioni della voce, della vista e dell&#039;udito, che diletta col bello <lb></lb>stile ed erudisce colla dottrina. </s></p><p type="main">

<s><emph type="center"></emph>XII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Così con Bartolommeo Eustachio, morto nel 1574, con Gabriele <lb></lb>Falloppio morto in giovane età di 40 anni nel 1563, e con Giro­<lb></lb>lamo Fabrizi che dal 1537 protrasse la lunga e onorata vecchiezza <lb></lb>infino al 1619, si varcava di alquanti passi la soglia che s&#039;interpone <lb></lb>fra l&#039;uscir del secolo XVI e l&#039;entrar del seguente secolo alle scienze <lb></lb>sperimentali tanto altamente glorioso. </s>

<s>Pervenuti a questo punto giova <lb></lb>ritornare indietro e raccogliere in un pensiero le cose fin qui lun­<lb></lb>gamente discorse. </s>

<s>La filosofia accademica, per sè contemplativa e <lb></lb>sterile di scoperte sperimentali, veniva fecondata dai cultori del­<lb></lb>l&#039;arte, i quali mostraron di fatto non esser vero che sempre i sensi <lb></lb>sono a noi occasione inevitabile d&#039;inganni. </s>

<s>La filosofia peripatetica <lb></lb>anch&#039;essa veniva emendata dal Razionalismo, uscito a dimostrar che <pb xlink:href="020/01/111.jpg" pagenum="92"></pb>il diritto riserbato al solo Aristotile era proprio del libero ingegno <lb></lb>di ogni uomo. </s>

<s>Dall&#039;altra parte Realdo Colombo aveva dato i più <lb></lb>savii esempii di quella filosofica libertà, e ne avea raccolti squisi­<lb></lb>tissimi frutti. </s>

<s>Infin dalla seconda metà del secolo XVI, s&#039;eran dun­<lb></lb>que fatti nella via del metodo sperimentale notabili progressi, a <lb></lb>rendere i quali più spediti mancavano ancora due cose: che dai <lb></lb>cultori dell&#039;arte passassero gli esercizii sperimentali ne&#039;libri dei <lb></lb>filosofi, e che il soggetto anatomico in che erasi ristretto il Colombo <lb></lb>si estendesse a ogni sorta di fatti naturali. </s>

<s>Ad adempire a un tale <lb></lb>ufficio furono deputati, nell&#039;ordine della Storia, due napoletani, <lb></lb>Giovan Battista Porta e Ferrante Imperato, o come altri vuole Co­<lb></lb>lantonio Stalliola, su&#039;due quali conviene a noi ora intrattenere al­<lb></lb>quanto il nostro Discorso. </s></p><p type="main">

<s>Il Porta, che morì nel 1615, si trovò spettatore e parte alla <lb></lb>inaugurazione de&#039;trionfi di Galileo, e vide sboccare i rivi della sua <lb></lb>scienza a rimescolarsi con le larghe onde sonanti di questo fiume <lb></lb>reale. </s>

<s>A molti que&#039;rivi parvero scarsi, alcuni altri di più gli repu­<lb></lb>tarono impuri e limacciosi. </s>

<s>Martino Hasdale si sforza di convincere <lb></lb>con infinite tare il nostro Napoletano, dicendo ch&#039;ei <emph type="italics"></emph>non intendeva <lb></lb>molti capitoli della Magìa, nè manco la sapeva spiegare in vol­<lb></lb>gare, iscusandosi che erano tutte cose avute da altri così scritte <lb></lb>in latino, come stavano stampate nel suo libro<emph.end type="italics"></emph.end> (Alb. </s>

<s>VIII, 84). Il <lb></lb>Sagredo giudica il libro della Magìa Naturale <emph type="italics"></emph>goffissimo al possibile,<emph.end type="italics"></emph.end><lb></lb>e stima che l&#039;Autore fra&#039;dotti <emph type="italics"></emph>tenga il luogo che tengono le cam­<lb></lb>pane tra gli strumenti di musica<emph.end type="italics"></emph.end> (Alb. </s>

<s>Suppl., pag. </s>

<s>67, 68). Que­<lb></lb>sti giudizi erano pronunziati al cospetto di Galileo, che tacendo, <lb></lb>compiacente acconsentiva. </s>

<s>Il Kepler però ne giudicava più retta­<lb></lb>mente, e con animo imparziale. </s>

<s>Ringraziava da un lato il Porta che <lb></lb>gli avesse insegnato il modo come si fa la vista, e dall&#039;altro non <lb></lb>taceva che certe conclusioni ottiche di lui erano <emph type="italics"></emph>ex insufficienti et <lb></lb>non universali demonstratione profectae<emph.end type="italics"></emph.end> (Paralip. </s>

<s>ad Vitell., Fran­<lb></lb>cof. </s>

<s>1604, pag. </s>

<s>180). </s></p><p type="main">

<s>Con questo giudizio del Kepler però si concilia il giudizio dello <lb></lb>stesso Sagredo, uomo da non perdere il senno per compiacere al <lb></lb>suo Galileo. </s>

<s>Egli infatti veniva a dire che nel libro della Magìa vi <lb></lb>erano delle gofferie, ma ci aveva pur trovata anco quella gran ve­<lb></lb>rità della teorica della visione. </s>

<s>Dall&#039;altra parte l&#039;esempio delle cam­<lb></lb>pane, alle quali si fa dir quel che uno vuole, era benissimo applicato <lb></lb>a qualificar quegli enimmi, di cui il Porta tanto si compiace. </s>

<s>Il <lb></lb>sentenziar poi che il Napoletano seguiva lo stile dei filosofi piut-<pb xlink:href="020/01/112.jpg" pagenum="93"></pb>tosto che quello dei matematici (Alb. </s>

<s>Suppl., pag. </s>

<s>60) includeva un <lb></lb>giudizio acutissimo e vero. </s>

<s>Per filosofi infatti intendeva il Sagredo <lb></lb>i settatori di Aristotile, e per matematici, i seguaci del retto me­<lb></lb>todo sperimentale. </s>

<s>Ora è verissimo che, per la massima parte, nel <lb></lb>libro del Porta la Natura scaturisce al modo aristotelico, per quasi <lb></lb>magica incantazione dalla fantasia dell&#039;Autore. </s>

<s>Verissime altresì pos­<lb></lb>sono essere le tare appostegli dall&#039;Hasdale, e anche molte se si <lb></lb>vuole, non però, com&#039;egli dice, infinite. </s>

<s>Si ripensi poi che così fatte <lb></lb>tare erano inevitabili a chi si era proposto di allettare col maravi­<lb></lb>glioso, e si era dato a raccoglier per ogni parte la scienza naturale <lb></lb>dispersa, in un libro solo. </s>

<s>Nella prefazione alla Magìa Naturale in <lb></lb>XX libri, l&#039;Autore dice chiaramente di avere a compor l&#039;opera sua <lb></lb>sfiorate le carte di tutti, che ne avevano scritto prima di lui. “ Dein, <lb></lb>quum Italiani, Galliam et Hispaniam peragrassem, bibliothecas et <lb></lb>doctissimos quosque adii, artifices etiam conveni, ut si quid novi <lb></lb>curiosique nacti essent ediscerem. </s>

<s>” Poco di poi soggiunge che <lb></lb>prima di consegnare al suo libro le raccolte notizie, <emph type="italics"></emph>intensissimo <lb></lb>studio pertinacique experientia<emph.end type="italics"></emph.end> erasi dato a sceverar le vere dalle <lb></lb>false, ma pur troppo sarà talora mancato al suo proposito come <lb></lb>disse l&#039;Hasdale, e tal altra non vi sarà riuscito. </s></p><p type="main">

<s>L&#039;Opera della Magìa Naturale però, che è quella sola su cui <lb></lb>par che l&#039;Hasdale e il Sagredo e il Kepler giudicassero dei meriti <lb></lb>scientifici del Porta, non vuole esser passata da noi senza qualche <lb></lb>breve, ma pur diligente esame. </s>

<s>Comparve prima in quattro libri <lb></lb>pubblicata dall&#039;Autore, quando aveva quindici anni, poi in libri XX <lb></lb>quando, come dice l&#039;Autore stesso nella Prefazione, ne aveva cin­<lb></lb>quanta. </s>

<s>Essendo egli nato nel 4535, come s&#039;ha dal Catalogo de&#039;Lin­<lb></lb>cei, sotto la prima forma il libro dee esser dunque stato pubblicato <lb></lb>nel 1550; sotto la seconda, nel 1585. Nonostante, della Magìa in <lb></lb>IV libri, dicono i Bibliografi, la prima edizione che si conosca esser <lb></lb>quella fatta da Mattia Cancer in Napoli, nel 1558, otto anni dunque <lb></lb>posteriore a quella, che veramente, secondo attesta lo stesso Autore, <lb></lb>è la prima. </s>

<s>Qui, di ciò che più importa alla storia della Scienza, <lb></lb>non s&#039;ha che l&#039;ultimo libro, nel secondo capitolo del quale si legge <lb></lb>la descrizione della camera oscura, con l&#039;applicazione di lei alla <lb></lb>teoria della vista. </s>

<s>Nel cap. </s>

<s>XVIII, dove insegna in che modo s&#039;im­<lb></lb>piombino i vetri per uso di specchi, è notabile quel che dice del <lb></lb>fondo dell&#039;occhio rassomigliato nella forma e nell&#039;ufficio a uno spec­<lb></lb>chio concavo, in cui fa da amalgama il pimmento coroideo. </s></p><p type="main">

<s>La prima edizione della Magìa Naturale in XX libri, se quel-<pb xlink:href="020/01/113.jpg" pagenum="94"></pb>l&#039;anno della nascita è vero, e se è vero ciò che dice l&#039;Autore, do­<lb></lb>vendo esser del 1585, forse è quella in 16.°, che nelle recensioni <lb></lb>bibliografiche ha la data “ Antuerpiae ex officina Christofori Plan­<lb></lb>tini M.D.LXXXV. ” Procediamo così dubitativi, vedendo notate altre <lb></lb>tre edizioni anteriori all&#039;LXXXV, una del LXIX, e le altre due <lb></lb>del LXXVI e dell&#039;LXXXI: chè, se, non è abbaglio preso da&#039;biblio­<lb></lb>grafi non sapremmo per verità conciliare il fatto coi detti dell&#039;Autore. </s></p><p type="main">

<s>In qualunque modo, abbiamo in questa nuova Magìa moltipli­<lb></lb>cate le curiosità, e diciamolo francamente col Sagredo, le gofferie, <lb></lb>ma abbiamo anco insieme moltiplicati i contributi alla scienza. </s>

<s>Chè <lb></lb>là dove questi contributi si riducevano a un libro solo, qui si di­<lb></lb>stendono in quattro: nel VII <emph type="italics"></emph>De miraculis magnetis<emph.end type="italics"></emph.end> nel XVII <emph type="italics"></emph>De <lb></lb>catoptricis imaginibus,<emph.end type="italics"></emph.end> nel XVIII <emph type="italics"></emph>De staticis experimentis,<emph.end type="italics"></emph.end> nel XIX <lb></lb><emph type="italics"></emph>De pneumaticis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Nel VII son raccolte l&#039;esperienze sul magnete fatte da Paolo <lb></lb>Sarpi, che l&#039;Autore nella prefazioncella al libro, chiama splendor di <lb></lb>Venezia, anzi d&#039;Italia. </s>

<s>Il magnetizzamento delle verghe di ferro per <lb></lb>confricazione e per influenza, con molti altri fatti nuovamente os­<lb></lb>servati e diligentemente descritti, attestano che la scienza magne­<lb></lb>tica ebbe in Italia gl&#039;inizii quindici anni per lo meno prima che in <lb></lb>Inghilterra. </s>

<s>Nel XVII libro la camera oscura nella sua descrizione <lb></lb>vien perfezionata coll&#039;aggiunta della lente cristallina biconvessa, che <lb></lb>si applica al foro per cui s&#039;intromettono i raggi, e ciò conduce <lb></lb>l&#039;Autore, a modificar la prima teorica della visione, sostituendo le <lb></lb>refringenze del cristallino alle riflessioni speculari della coroide <lb></lb>(Cap. </s>

<s>VI). </s></p><p type="main">

<s>Il Capitolo VIII del XVIII libro è notabile per la descrizione <lb></lb>della bilancetta idrostatica a risolvere praticamente il <emph type="italics"></emph>Problema della <lb></lb>Corona,<emph.end type="italics"></emph.end> e a ritrovare il peso specifico de&#039;varii corpi duri. </s>

<s>Anco <lb></lb>quando fosse vero quel che dice il Viviani, che cioè Galileo avesse in­<lb></lb>ventato quello strumento nel 1586, tempo in cui incominciò ad atten­<lb></lb>dere agli studii intorno alle opere di Archimede, il Porta lo avrebbe <lb></lb>preceduto di un anno per lo meno, e di 18 anni avrebbe preceduto <lb></lb>il Ghetaldo. </s>

<s>Comunque siasi, il Porta nel Cap. </s>

<s>VI di questo stesso <lb></lb>libro dette in que&#039;galleggianti volgari, meglio che nella bilancetta, <lb></lb>i veri e legittimi progenitori di quegli idrostammi o densimetri o <lb></lb>pesa liquori inventati già e messi in uso in que&#039;Medicei consessi, <lb></lb>che precedettero all&#039;Accademia del Cimento. </s>

<s>La Pneumatica però <lb></lb>del libro XIX non ha nulla, a voler dire il vero, che la renda no­<lb></lb>tabile sopra quella dell&#039;antico Herone. </s></p><pb xlink:href="020/01/114.jpg" pagenum="95"></pb><p type="main">

<s>Nè si creda poi che negli altri libri della Magìa tutto sia goffag­<lb></lb>gine e stravaganze. </s>

<s>Quando, nella citata prefazioncella al VII libro, <lb></lb>l&#039;Autore indovinava che due uomini si potessero parlar di lontano <lb></lb><emph type="italics"></emph>duobus nauticis pyxidibus alphabeto circumscriptis,<emph.end type="italics"></emph.end> parve certa­<lb></lb>mente a Galileo che avesse detto una stravaganza, e nel I Dialogo <lb></lb>dei Massimi Sistemi (Alb. </s>

<s>I, 107) se ne ride e inventa su quel fatto <lb></lb>argutamente una burla. </s>

<s>Qual sarebbe rimasto se si fosse trovato a <lb></lb>veder nel telegrafo a galvanometro perfettamente avverata la tanto <lb></lb>stravagante profezia! </s></p><p type="main">

<s>Tutte le goffaggini poi e le stravaganze son dall&#039;Autore assom­<lb></lb>mate nell&#039;ultimo libro, che meritamente è intitolato <emph type="italics"></emph>Chaos.<emph.end type="italics"></emph.end> Eppure <lb></lb>anche qui, come pietre preziose rotolate fra&#039;ciottoli di un fiume, <lb></lb>s&#039;ha nel Cap. </s>

<s>V la descrizione del corno acustico, strumento che <lb></lb>serve a inacutir l&#039;udito, come a inacutir la vista servono, egli dice, <lb></lb>acconciamente disposte, due lenti. </s>

<s>Notabile quel ch&#039;egli scrive es­<lb></lb>sergli stata una tale invenzione suggerita dalle orecchie degli ani­<lb></lb>mali, e particolarmente delle lepri, e più notabile il principio ge­<lb></lb>nerale che ivi professa del doversi perscrutar la natura, e imitar <lb></lb>con l&#039;arte i macchinamenti di lei. </s></p><p type="main">

<s>Ciò che s&#039;è fin qui discorso, può servire a giustificare il Porta <lb></lb>dalle imputazioni dell&#039;Hasdale e del Sagredo, ma non si vuol tacere <lb></lb>come que&#039;severi giudizi non furon dati che sul libro della Magìa, <lb></lb>quasi non avesse l&#039;Autore pubblicati altri documenti della sua scienza. </s>

<s><lb></lb>Eppure, quando l&#039;Hasdale e il Sagredo scrissero i due sopra citati <lb></lb>giudizii in due lettere scritte a Galileo, aveva il Porta pubblicati, <lb></lb>fra gli altri, due libri, de&#039;quali sarebbe colpa tacere nella storia <lb></lb>de&#039;progressi fatti, in sul finir del secolo XVI dalla scienza speri­<lb></lb>mentale italiana. </s>

<s>Di que&#039;due libri il primo è <emph type="italics"></emph>De refractione optices<emph.end type="italics"></emph.end><lb></lb>pubblicato in Napoli nel 1593, il secondo è <emph type="italics"></emph>Pneumaticorum libri <lb></lb>tres<emph.end type="italics"></emph.end> che vide pure in Napoli la luce nel 1601. Il Sagredo non dee <lb></lb>aver veduto quel libro di Ottica, forse perchè difficile a trovarsi <lb></lb>venale. </s>

<s>Anche il Kepler infatti, che ardeva di gran desiderio di ve­<lb></lb>der quel che vi avesse scritto l&#039;Autore intorno alle rifrazioni della <lb></lb>luce attraverso le lenti, dice nei Paralipomeni a Vitellione “ a li­<lb></lb>brariis frustra hactenus requisivi ” (edit. </s>

<s>cit. </s>

<s>pag. </s>

<s>202). Non dee il <lb></lb>Sagredo, lo ripetiamo, aver veduto quel libro, perchè, sagace e giu­<lb></lb>dizioso qual&#039;era, non par possibile ch&#039;ei non si sentisse come noi <lb></lb>sorpreso di maraviglia e non restasse alla prima in dubbio se quello <lb></lb>lì era proprio l&#039;Autore goffissimo della Magìa. </s>

<s>Il Kepler senza dub­<lb></lb>bio si sarebbe dalla lettura confermato in quel suo giudizio, che il <pb xlink:href="020/01/115.jpg" pagenum="96"></pb>fisico napoletano avesse mente davvero e cognizioni diottriche tali, <lb></lb>da specular l&#039;invenzione del canocchiale. </s>

<s>Di ciò pure si persuade­<lb></lb>ranno con facilità i nostri lettori, dop&#039;avere scorso anche brevemente <lb></lb>i IX libri delle Diottriche rifrazioni, ma prima di far ciò vediamo <lb></lb>in qual modo si studiasse di raccogliere le disperse membra della <lb></lb>scienza naturale Ferrante Imperato. </s></p><p type="main">

<s>Il libro di lui s&#039;intitola giusto <emph type="italics"></emph>Historia naturale<emph.end type="italics"></emph.end> e si pubblicò <lb></lb>in Napoli la prima volta nel 1599. Antonio Nardi, discepolo di Ga­<lb></lb>lileo, in quelle sue <emph type="italics"></emph>Scene Accademiche,<emph.end type="italics"></emph.end> delle quali, essendo rimaste <lb></lb>inedite, daremo in quest&#039;altra parte del nostro Discorso, qualche <lb></lb>breve notizia ai nostri lettori, giudicò il Naturalista napoletano per <lb></lb>uno de&#039;più avveduti e giudiziosi scrittori di cose naturali che avesse <lb></lb>veduto mai (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XX, p. </s>

<s>592). I libri e le sentenze <lb></lb>dei tanti autori antichi e moderni da cui raccoglie, non le cita mai <lb></lb>senza darne, come dice lo stesso Nardi, <emph type="italics"></emph>una candida e valida cen­<lb></lb>sura.<emph.end type="italics"></emph.end> Candida sempre, valida a seconda delle cognizioni che si po­<lb></lb>tevano avere a que&#039;tempi. </s>

<s>Non fa perciò maraviglia se l&#039;Imperato <lb></lb>annoverando le bufoniti, gli entrochi, le pietre giudaiche, le frumen­<lb></lb>tarie fra le sostanze minerali, ammettesse la vegetazion delle pietre; <lb></lb>errore largamente ricompensato da quel che poi nel rimanente del <lb></lb>XXV libro si specula delle pietre stesse, aprendo così tanto dalla <lb></lb>lontana le vie ai progressi della moderna cristallografia. </s></p><p type="main">

<s>Soggiunge il Nardi, nel passo sopra citato, d&#039;aver sentito vivis­<lb></lb>simo il desiderio che l&#039;Autore v&#039;avesse trattato non di sola una <lb></lb>parte, ma di tutta la <emph type="italics"></emph>fisica,<emph.end type="italics"></emph.end> alla qual parola egli dà senza dubbio <lb></lb>il significato di Scienza della Natura. </s>

<s>Ma accettando pure quella <lb></lb>parola <emph type="italics"></emph>fisica<emph.end type="italics"></emph.end> nel significato che suole avere oggidì, sentiamo anche <lb></lb>noi il desiderio che egli avesse più largamente trattato di quei sog­<lb></lb>getti di Meteorologia, di Ottica, di Magnetismo, intorno ai quali <lb></lb>scopre e annunzia alcune di quelle recondite verità della fisica mo­<lb></lb>derna, cacciando gli ostinati errori peripatetici col raziocinio e con <lb></lb>l&#039;esperienza. </s>

<s>Di queste verità scoperte e insegnate non si vuol la­<lb></lb>sciar di dare ai lettori qualche notizia, e così, dopo avere accennato <lb></lb>alle due diverse maniere tenute in compilare la scienza ereditata <lb></lb>dai due scrittori napoletani, trapassare a veder ciò che seppero am­<lb></lb>bedue speculare coi loro proprii intelletti. </s></p><p type="main">

<s>Tornando perciò al Porta, poniamoci innanzi agli occhi i due <lb></lb>libri sopra citati e incominciamo dallo scorrer per primo quello che <lb></lb>è forse di minore importanza, e che, per la rarità dell&#039;originale, <lb></lb>leggiamo nella versione italiana fatta da Ivan Escrivano e pubblicata <pb xlink:href="020/01/116.jpg" pagenum="97"></pb>col titolo di <emph type="italics"></emph>Tre libri di Spiritali<emph.end type="italics"></emph.end> in Napoli nel 1606. Le materie <lb></lb>ivi trattate, molto meglio che il titolo, dicono che il primo impulso <lb></lb>è venuto da Herone, ma là dove il Fisico alessandrino trascura i <lb></lb>fondamenti della scienza e descrive le sue macchine, senza avvedersi <lb></lb>che a provar di metterle a gioco, non rispondono bene spesso alle <lb></lb>intenzioni; il Porta incomincia nel libro I dallo sperimentare sulla <lb></lb>elasticità dell&#039;aria, e dal confermare i principii dell&#039;Idrostatica. </s>

<s>Gli <lb></lb>effetti dell&#039;elaterio dell&#039;aria compressa da uno stantuffo dentro a <lb></lb>una canna da archibuso, son descritti nel cap. </s>

<s>VI, ma nel X nota­<lb></lb>bilissima è quella teoria delle pressioni de&#039;liquidi, che per comune <lb></lb>sentimento degli eruditi s&#039;attribuisce allo Stevino. </s>

<s>Vedremo che <lb></lb>parecchi anni prima aveva il Benedetti, nelle sue <emph type="italics"></emph>Speculazioni,<emph.end type="italics"></emph.end> di­<lb></lb>mostrato già quel principio idrostatico, ma il Porta vi procede con <lb></lb>passo più largo e più sicuro, e che è più, conferma le teorie col­<lb></lb>l&#039;esperienze. </s>

<s>Fra queste esperienze, a provar che le pressioni ope­<lb></lb>rano secondo l&#039;altezza del perpendicolo, è notabile quella del liquido <lb></lb>contenuto dentro una gran botte, che vien sollevato dal premer <lb></lb>d&#039;altro liquido infuso in un sottil cannello comunicante, come pure <lb></lb>è notabile quell&#039;altra esperienza degli zampilli, che si sollevano a <lb></lb>uguale altezza e raggiungon precisamente il livello del liquido nella <lb></lb>conserva: notabili diciamo queste esperienze del disprezzato fisico <lb></lb>napoletano, perchè ci fanno ripensare alla fama in che vennero poi, <lb></lb>per quelle stesse esperienze, il Mariotte e il Torricelli. </s></p><p type="main">

<s>Il secondo libro è applicato alla descrizione delle macchine da <lb></lb>sollevar l&#039;acqua, gareggiandosi con Herone a chi sa immaginarne <lb></lb>delle più nuovamente ingegnose. </s>

<s>Ma è qui però debito confessare <lb></lb>che il Nostro cade, e forse più spesso che mai, ne&#039;difetti stessi <lb></lb>notati da lui nel fisico antico, proponendo macchinalmenti, che o <lb></lb>per l&#039;elasticità dell&#039;aria o per la pressione dell&#039;acqua, non in altro <lb></lb>giocano che nella esaltata fantasia dell&#039;inventore. </s>

<s>Ne sia esempio <lb></lb>fra gli altri quel che nel cap. </s>

<s>I del terzo libro dice del potersi tra­<lb></lb>vasare un lago in un altro lago o nel mare, per via di un sifone <lb></lb>che cavalchi l&#039;altura di un monte: strana impresa che riuscita pa­<lb></lb>recchi anni dopo, vuota di effetto alle mani del Baliani, gli dette <lb></lb>occasione a specular sulla pressione ammosferica e a indovinar la <lb></lb>prima teoria del barometro ad acqua. </s></p><p type="main">

<s>Questo terzo libro, che incomincia con una stranezza, termina <lb></lb>coll&#039;invenzione di un utilissimo strumento, di cui da quasi tutti <lb></lb>s&#039;ignora l&#039;autore, ed è la livella ad acqna, nemmeno oggidì uscita <lb></lb>affatto fuor d&#039;uso, e che il Porta fu il primo a sostituire all&#039;antico <pb xlink:href="020/01/117.jpg" pagenum="98"></pb>corobate vitruviano. </s>

<s>De&#039;capitoli di mezzo, notabile è il IV, dove si <lb></lb>descrive l&#039;esperienza della diffusione del vino di un bicchiere at­<lb></lb>traverso al piccolo foro di una palla di vetro ripiena d&#039;acqua: espe­<lb></lb>rienza, che nel I Dialogo delle Due Nuove scienze fu amorevolmente <lb></lb>raccolta da Galileo e tenuta per sua (Alb. </s>

<s>XIII, 74), come pure per <lb></lb>sua volle rivendicar quell&#039;altra descritta qui dal Nostro, nel cap. </s>

<s>VII, <lb></lb>del materazzo o caraffella, dentro al collo della quale il calore am­<lb></lb>biente fa scender l&#039;acqua e il freddo la fa risalire, la quale espe­<lb></lb>rienza il Porta stesso aveva già 47 anni prima descritta nel cap. </s>

<s>XXII <lb></lb>del secondo fra i quattro libri della Magìa. </s></p><p type="main">

<s>Più commemorabili di questi tre degli Spiritali, son per l&#039;im­<lb></lb>portanza e la difficoltà del soggetto, i nove libri delle <emph type="italics"></emph>Ottiche rifra­<lb></lb>zioni.<emph.end type="italics"></emph.end> La scienza, infino a qui, non aveva fatto grandi progressi: <lb></lb>si ripetevano le dottrine antiche di Tolomeo e di Euclide, non molto <lb></lb>per verità promosse da Alhazen e da Vitellione. </s>

<s>Gli scritti dell&#039;Al­<lb></lb>berti, del Vinci, del Maurolico a&#039;tempi del Porta, erano sconosciuti, <lb></lb>cosicchè, questo Trattato del Fisico napoletano è il primo da cui la <lb></lb>Diottrica incomincia i suoi progressi. </s></p><p type="main">

<s>A così fatti progressi il primo valido impulso vien dalla pro­<lb></lb>posizione VIII del libro I, dove l&#039;Autore dimostra esser falso quel <lb></lb>che insegnò Vitellione, che cioè gli angoli dell&#039;incidenza e della <lb></lb>rifrazione serbino costante proporzione geometrica, variandosi l&#039;obli­<lb></lb>quità con cui cade il raggio luminoso. </s>

<s>A confermar la sua dimo­<lb></lb>strazione, contro l&#039;autorevole e inveterato magistero dell&#039;Ottico po­<lb></lb>lacco, invoca lo sperimento da farsi con un vaso ripieno d&#039;acqua. </s></p><p type="main">

<s>Contro un altro magistero non meno autorevole per que&#039;tempi, <lb></lb>ed è quello del Fracastoro settatore di più antiche dottrine, è pure <lb></lb>la proposizione XI di questo stesso libro I, nella quale si dimostra <lb></lb>che la refringenza alle superficie piane non ingrandisce le immagini, <lb></lb>ma sì le ingrandisce alle superficie curve, conforme a ciò che pure <lb></lb>accennava il giovane Galileo (Ediz. </s>

<s>naz., Firenze, 1890, Vol. </s>

<s>I, <lb></lb>pag. </s>

<s>314). E mentre che lo stesso Galileo meditava arguzie, da tor <lb></lb>fede a Ticone, che fu il primo, osservando gli astri, a tener conto <lb></lb>degli effetti prodotti sulla vista dalle rifrazioni, è notabile quel che <lb></lb>nelle proposizioni XVII e XIX avverte il Porta delle fallacie che, <lb></lb>per via de&#039;raggi refratti nell&#039;aria, si commettono osservando oggetti <lb></lb>che radono l&#039;orizzonte o livellando collo strumento, per lunghi tratti. </s></p><p type="main">

<s>Il secondo libro, che è delle immagini e dell&#039;andamento dei <lb></lb>raggi rifratti nelle sfere cristalline, ha strettissima relazione col li­<lb></lb>bro VIII, dove si espongono le teorie diottriche delle lenti. </s>

<s>È questa <pb xlink:href="020/01/118.jpg" pagenum="99"></pb>parte del Trattato che principalmente eccitava, di vederlo, i desiderii <lb></lb>al Keplero, e non sappiamo se ne fosse stato poi sodisfatto, quando <lb></lb>nel 1611 pubblicò il Trattato suo della Diottrica. </s>

<s>Facendo però il <lb></lb>confronto fra&#039;due autori, non temiam di asserire che il secondo nel <lb></lb>tempo riman secondo altresì nel merito, perchè il Porta introduce, <lb></lb>nel divisar le immagini reali e virtuali rappresentate dalle lenti, i <lb></lb><emph type="italics"></emph>cateti,<emph.end type="italics"></emph.end> ossia gli <emph type="italics"></emph>assi principali e secondari,<emph.end type="italics"></emph.end> senza che, nel Kepler <lb></lb>e negli altri autori di que&#039;tempi, le immagini stesse rimangono in­<lb></lb>determinate di grandezza e di luogo. </s>

<s>Di più, l&#039;Ottico alemanno nella <lb></lb>proposizione sua XCVI fa convergere i raggi che escon refratti dalle <lb></lb>lenti concave verso l&#039;occhio, quasi che il loro foco fosse reale e non <lb></lb>virtuale: errore gravissimo cansato assai destramente dal nostro Na­<lb></lb>poletano. </s></p><p type="main">

<s>L&#039;anatomia dell&#039;occhio professata nel III libro è conforme alla <lb></lb>descrizione che ne dette il Vesalio, nè fa maraviglia che sia ripe­<lb></lb>tuto qui l&#039;errore, sull&#039;autorità di Galeno oramai divenuto comune, <lb></lb>del far organo della rappresentazion visiva il cristallino: senza ma­<lb></lb>raviglia però non si può passar da chi legge la proposizione VI, al <lb></lb>vedervisi pubblicata quella osservazione del dilatamento e del re­<lb></lb>stringimento della pupilla annunziata sette anni dopo dall&#039;Acqua­<lb></lb>pendente come una osservazione nuova del Sarpi o sua. </s>

<s>Galileo <lb></lb>ripete quasi a parole nel III Dialogo de&#039;Massimi Sistemi (Alb. </s>

<s>I, <lb></lb>394) ciò che qui avea scritto il disprezzato fisico napoletano, e nelle <lb></lb><emph type="italics"></emph>Operazioni astronomiche<emph.end type="italics"></emph.end> procede Galileo stesso in un modo simile <lb></lb>al Porta, per determinar l&#039;ampiezza del foro pupillare, con una tal <lb></lb>sola differenza, che mentre questi attribuisce il metodo ad Archi­<lb></lb>mede, quello, e nelle citate <emph type="italics"></emph>Operazioni<emph.end type="italics"></emph.end> e nelle lettere al Renieri <lb></lb>lo dà per invenzione sua propria. </s></p><p type="main">

<s>Se il fortunato discopritore de&#039;satelliti di Giove si fosse mai <lb></lb>degnato di rivolger lo sguardo sul sesto libro di questa Diottrica, <lb></lb>non è qui luogo a ricercare. </s>

<s>Non si vuol tacere però, per la novità <lb></lb>e l&#039;importanza del tema, che, secondo il Borelli, i metodi usati da <lb></lb>Galileo per ritrovar collo strumento la media distanza de&#039;Gioviali <lb></lb>dal centro del pianeta, avrebbero avuto il loro principio dai curiosi <lb></lb>fenomeni, che, per l&#039;artificiosa e forzata direzione degli assi ottici <lb></lb>de&#039;due occhi, si producono nel guardare gli oggetti; fenomeni mi­<lb></lb>rabilmente osservati e descritti dal Nostro nelle varie proposizioni <lb></lb>di quello stesso sesto libro. </s></p><p type="main">

<s>Nel trattare all&#039;ultimo dell&#039;iride e de&#039;colori il Porta non pro­<lb></lb>muove nemmen di un passo la scienza e si rimane anzi indietro al <pb xlink:href="020/01/119.jpg" pagenum="100"></pb>Maurolico per lungo tratto di via. </s>

<s>Ma Ferrante Imperato, all&#039;<emph type="italics"></emph>Historia <lb></lb>naturale<emph.end type="italics"></emph.end> del quale ora si torna, largamente ristora il difetto del <lb></lb>suo concittadino, divisando dell&#039;iride interna e della esterna la vera <lb></lb>teoria ottica 38 anni prima che a menarne vanto uscisse fuori il <lb></lb>Cartesio. </s></p><p type="main">

<s>Ma perchè il rispondere ai vanti con altrettanti vanti esaltati <lb></lb>è triste vezzo, che ha tolto fede oramai alle osservazioni de&#039;più <lb></lb>giudiziosi, vadasi all&#039;XI libro di questa Storia, e si leggano atten­<lb></lb>tamente i capitoli VIII e IX, osservando che l&#039;Autore, quanto alla <lb></lb>vista, professa l&#039;opinion platonica della emissione. </s>

<s>Conforme a queste <lb></lb>professate dottrine egli dice perciò: <emph type="italics"></emph>li raggi visivi infratti dagli <lb></lb>corpuscoli delle gocce andar dalla vista al lummare<emph.end type="italics"></emph.end> (Venetia 1672, <lb></lb>pag. </s>

<s>288). Come poi nelle gocciole si facciano queste infrazioni e <lb></lb>dalle infrazioni congiunte a riflessioni si produca l&#039;iride colorata, <lb></lb>a quel modo che si vede <emph type="italics"></emph>negli globi et ampolle chiarissime di vetro <lb></lb>e nelle colonne (prismi) triangolari<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>294); lo aveva detto <lb></lb>con mirabile esattezza più sopra, ove scrisse: “ Occorrendo la vista <lb></lb>alla sua superficie convessa, fa semplice riflessione e penetrando, <lb></lb>il che si fa con infrazione, alla cava, ivi riflessa, ritorna ad uscir <lb></lb>con la seconda infrazione. </s>

<s>Sono dunque due infrazioni, l&#039;una men­<lb></lb>tre dal più raro entra nel denso, l&#039;altra, nella quale dal più denso <lb></lb>ritorna nel più raro, quali ambe infrazioni sono nella superficie <lb></lb>prima che occorra, et vi è la riflessione tramezzo fatta nella super­<lb></lb>ficie più lontana ” (ivi, pag. </s>

<s>288). </s></p><p type="main">

<s>Quanto all&#039;iride esterna che egli rimprovera ad Aristotile, <lb></lb>l&#039;aver promesso, ma non mantenuto di trattarne, o trattandone di <lb></lb>aver ridotto il fenomeno a cause vane; ecco quel che egli dice nel <lb></lb>cap. </s>

<s>IX: “ Essendo della goccia due semisferi, l&#039;uno dalla parte <lb></lb>dell&#039;asse (del cono che ha l&#039;iride per base) l&#039;altro dalla parte op­<lb></lb>posta, e potendo il raggio visivo nell&#039;uno e nell&#039;altro incorrere a <lb></lb>riflettersi al luminare: nel primo penetrando nell&#039;interno ed uscendo <lb></lb>per l&#039;esterno, e nel secondo penetrando per l&#039;esterno ed uscendo <lb></lb>per l&#039;interno, nel qual secondo modo il raggio che esce e va al <lb></lb>sole per la molta infrazione si taglia col raggio della vista che entra; <lb></lb>è necessario per questo che due siano gli archi celesti e che ab­<lb></lb>biano li colori a contrario ” (ivi, pag. </s>

<s>290). Conclude notando il <lb></lb>licenzioso accoppiamento che Aristotile, a spiegare il fenomeno, fa <lb></lb>di due cause contrarie, e accennando ad altre dottrine del Filosofo <lb></lb>meritevoli di maggior riprensione. </s></p><p type="main">

<s>Se qui l&#039;Imperato emenda gli errori ripetuti dal Porta nell&#039;ul-<pb xlink:href="020/01/120.jpg" pagenum="101"></pb>timo libro della Diottrica, altrove intorno all&#039;argomento del Magnete <lb></lb>ne compie le teorie divisate nel VII libro della <emph type="italics"></emph>Magia.<emph.end type="italics"></emph.end> Anche il <lb></lb>nostro autor dell&#039;<emph type="italics"></emph>Historia naturale<emph.end type="italics"></emph.end> parlando nel libro XXVI della <lb></lb>pietra calamita ne avverte il magnetismo per influenza e lo illustra <lb></lb>con luminoso concetto, rassomigliando le linee radiose, in che si <lb></lb>dispongono le particelle della limatura del ferro intorno ai poli ma­<lb></lb>gnetici, alla dirittura delle linee, in che intorno al centro della <lb></lb>Terra, insistendo l&#039;uno sull&#039;altro, si dispongono i corpi gravi (ivi, <lb></lb>pag. </s>

<s>614). Or che altro mancava se non che formular questo stesso <lb></lb>concetto a modo del Gilberto perchè riuscisse a dire che la Terra <lb></lb>è un magnete, e che il Magnete stesso è una terrella? </s></p><p type="main">

<s><emph type="center"></emph>XIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La filosofica libertà, con la quale esamina e scopre gli errori <lb></lb>di Aristotile Ferrante Imperato, in quasi tutte le parti dell&#039;opera <lb></lb>sua voluminosa, e specialmente dove tocca soggetti di Meteorologia, <lb></lb>fra&#039;quali è notabilissimo quel che nel cap. </s>

<s>III del X libro dice del <lb></lb>tuono e del baleno contro il Filosofo; basterebbe a meritargli uno <lb></lb>dei primi seggi fra coloro che più efficacemente cooperarono a re­<lb></lb>staurare le scienze sperimentali. </s>

<s>I due libri pure del Porta da noi <lb></lb>sopra brevemente discorsi, son dettati col medesimo intento di sco­<lb></lb>prir gli errori de&#039;peripatetici non solo, ma di ogni sorta di autori <lb></lb>le dottrine de&#039;quali non si conformino alla rettitudine de&#039;raziocinii <lb></lb>e alla prova degli sperimenti. </s>

<s>Ma il primo de&#039;due fisici napoletani <lb></lb>rimase dimenticato per ragioni che troppo lungo sarebbe l&#039;inve­<lb></lb>stigare, e il secondo, competitore di Galileo, rimase oscurato dai <lb></lb>trionfi di lui. </s>

<s>Non ebbero perciò le molte e importanti verità sco­<lb></lb>perte e dimostrate da&#039;due autori quell&#039;incontro che si sarebbero <lb></lb>meritato, nè recarono quegli aiuti a&#039;progressi della scienza, che <lb></lb>avrebbero veramente potuto. </s></p><p type="main">

<s>Più diffusa e più intensa, e perciò più giovevole riuscì l&#039;opera <lb></lb>di tre grandi uomini nati sulle rive di quel mare, su cui regnò <lb></lb>libera Venezia. </s>

<s>Giovan Batista Benedetti, Santorre Santorio e Paolo <lb></lb>Sarpi, hanno, dopo tanto lungo tempo e tante prove tentate dai loro <lb></lb>predecessori, aperta alla scienza la retta via, e v&#039;hanno impresse <lb></lb>oramai orme così profonde, che non è possibile più lo smarrirle. <pb xlink:href="020/01/121.jpg" pagenum="102"></pb>Rimasti tutti e tre nascosti nelle fondamenta dell&#039;edifizio galileiano, <lb></lb>non può farsi la giusta stima della loro grandezza, se non da chi <lb></lb>penetri addentro colla vista attenta ed acuta. </s>

<s>E a chi riguardi il <lb></lb>Benedetti in questo modo, se lo vede presentare innanzi in sereno <lb></lb>e dignitoso abito di libero filosofo, che vuol contemperare l&#039;osse­<lb></lb>quio all&#039;autorità delle tradizioni, con l&#039;ossequio alle verità scoperte <lb></lb>dalla ragione. “ Liberum enim est cuique scribere quod libet, nec <lb></lb>Aristotilem afficit iniuria, quicumque illi fidem suam non acco­<lb></lb>modat, etsi valde iniquus sit quisquis maiorum opiniones veras <lb></lb>et ab omnibus merito comprobatas non admittit ” (Speculationum <lb></lb>lib. </s>

<s>Venetiis 1599, pag. </s>

<s>228). </s></p><p type="main">

<s>Nella Prefazioncella alle Disputazioni <emph type="italics"></emph>De quibusdam placitis <lb></lb>Aristotelis,<emph.end type="italics"></emph.end> dove dà il Benedetti il più bell&#039;esempio di quella filo­<lb></lb>sofica libertà vendicatrice dei diritti della ragione, dop&#039;avere accen­<lb></lb>nato ai pericoli corsi da colui, che scrive cose contrarie all&#039;am­<lb></lb>mirabile sapienza dell&#039;antico Maestro “ Verumtamen, egli tosto <lb></lb>francamente soggiunge, studio veritatis impulsus, cuius ipse amore <lb></lb>in seipsum si viveret excitaretur, in medium quaedam proferre <lb></lb>non dubitavi, in quibus me inconcussa mathematicae philosophiae <lb></lb>basis, cui semper insisto, ab eo dissentire coegit ” (ibi, pag. </s>

<s>168). </s></p><p type="main">

<s>Da Parma, dove insegnava, fu chiamato a Torino, dal Duca, il <lb></lb>quale, secondo il costume de&#039;principi di allora, si compiaceva, spe­<lb></lb>cialmente in tempo di villeggiatura, d&#039;interrogare il suo Filosofo <lb></lb>e Matematico e di proporgli a risolvere questioni d&#039;Aritmetica, di <lb></lb>Geometria, di Ottica, di Musica e anco di Astrologia. </s>

<s>Gli amici pure <lb></lb>lo interrogavano, e ad essi mandava i suoi <emph type="italics"></emph>Responsi,<emph.end type="italics"></emph.end> i quali, come <lb></lb>prima, egli dice “ per ocium licuit, collegi, relegi, ac tandem de <lb></lb>manu mittere decrevi. </s>

<s>Tum, ut scientia ipsa quo magis diffun­<lb></lb>deretur, crescat, et quidquid valeo sine invidia, in communem <lb></lb>utilitatem conferam ” (ibi, pag. </s>

<s>204). </s></p><p type="main">

<s>Così fatti Responsi, sotto forma epistolare, son gran parte del <lb></lb>libro <emph type="italics"></emph>Speculationum<emph.end type="italics"></emph.end> stampato prima nel 1580 in Torino, e poi nuo­<lb></lb>vamente nel 1599 in Venezia: speculazioni, che l&#039;Autore presenta <lb></lb>al suo lettore per nuove, se non sempre nella sostanza, certo nel <lb></lb>modo di dimostrarle. </s>

<s>Ed è verissimo: è anzi per entro a quelle <lb></lb>pagine tanta novità, che, scomparso affatto il vecchio mondo ari­<lb></lb>stotelico, ti senti trasportar nell&#039;ampie e libere regioni di un Mondo <lb></lb>nuovo. </s></p><p type="main">

<s>Nelle sopra citate Disputazioni contro Aristotile, quelle parole, <lb></lb>nelle quali chiama il nuovo Sistema del Mondo “ pulcherrimam <pb xlink:href="020/01/122.jpg" pagenum="103"></pb>Aristarchi Samii opinionem, divinitus a Nicolao Copernico ex­<lb></lb>pressam, contra quam nil plane valent rationes ab Aristotile, <lb></lb>neque etiam a Ptolomeo propositae ” (ibi, pag. </s>

<s>195) dicono ab­<lb></lb>bastanza chiaro quanto fosse il Benedetti inclinato a cooperare ai <lb></lb>progressi dell&#039;Astronomia, ma perchè ei non fu in tempo a veder <lb></lb>l&#039;invenzione del canocchiale, fu nella Meccanica e nella Fisica, dove <lb></lb>principalmente esercitò le sue nuove speculazioni. </s></p><p type="main">

<s>La scienza del moto, resa impossibile dagli errori di Aristotile, <lb></lb>era si può dir rimasta stazionaria ne&#039;libri dell&#039;antico Archimede. </s>

<s><lb></lb>Il nostro Benedetti fu de&#039;più validi in promuoverla, confutando con <lb></lb>argomenti di ragione quegli aristotelici errori, in parecchi de&#039;quali <lb></lb>era incorso lo stesso Niccolò Tartaglia sì rispetto ai moti naturali <lb></lb>che ai violenti. </s>

<s>Così l&#039;antico Filosofo di Stagira come il nuovo di <lb></lb>Brescia avevano insegnato che ne&#039;gravi cadenti le velocità son pro­<lb></lb>porzionali alle moli, ma il nostro Veneziano gli avverte in proposito <lb></lb>com&#039;e&#039;non avevan posto mente “ quam magna resistentiarum sit <lb></lb>differentia, quae tam diversitate figurarum quam ex magnetudi­<lb></lb>num varietate exoriri potest ” (ibi, pag. </s>

<s>168) e svolgendo queste <lb></lb>sottili speculazioni relative alle varie resistenze opposte ai mobili, <lb></lb>dalle varie densità dei mezzi, conclude: “ quod in vacuo corpora <lb></lb>eiusdem materiae aequali velocitate moverentur ” (pag. </s>

<s>174). </s></p><p type="main">

<s>Il medesimo Aristotile aveva detto, nel cap. </s>

<s>VIII del I libro <emph type="italics"></emph>De <lb></lb>coelo,<emph.end type="italics"></emph.end> che il mobile tanto più si accelera quanto più si avvicina al <lb></lb>termine <emph type="italics"></emph>ad quem,<emph.end type="italics"></emph.end> ma il Benedetti avverte che avrebbe dovuto il <lb></lb>Filosofo dire invece che anzi il mobile si accelera tanto più, quanto <lb></lb>più si dilunga dal termine <emph type="italics"></emph>a quo,<emph.end type="italics"></emph.end> “ quia tanto maior fit semper <lb></lb>impressio quanto magis movetur naturaliter corpus, et continuo <lb></lb>novum impetum recipit, cum in se motus causam contineat, quae <lb></lb>est inclinatio ad locum suum eundi ” (ibi, pag. </s>

<s>184). </s></p><p type="main">

<s>Il Nostro insomma, un quarto di secolo prima che a queste <lb></lb>stesse speculazioni rivolgesse la mente Galileo, aveva pubblicamente <lb></lb>insegnato che ne&#039;moti accelerati le velocità son proporziali ai tempi, <lb></lb>concludendo come Galileo questo teorema fondamentale da quel <lb></lb>principio d&#039;inerzia, stabilito già dal Cardano, e confermato colle <lb></lb>bellissime esperienze dello Scaligero. </s></p><p type="main">

<s>Tanto è vero che il Benedetti accoglie quel principio come cosa <lb></lb>già certa nella scienza, e dimostrata, da non vedere il bisogno di <lb></lb>assumersi altro ufficio, che di rimuoverne le difficoltà, come giusto <lb></lb>si vede far da lui nel Trattato <emph type="italics"></emph>De Mechanicis<emph.end type="italics"></emph.end> e nell&#039;Epistola a Paolo <lb></lb>Capra <emph type="italics"></emph>De motu molae et trochi.<emph.end type="italics"></emph.end> Si propone ivi il quesito come mai <pb xlink:href="020/01/123.jpg" pagenum="104"></pb>una mola mossa non perpetua il suo moto, come dovrebbe per il <lb></lb>principio d&#039;inerzia, e risponde che ciò avviene per più ragioni: per <lb></lb>l&#039;attrito de&#039;perni, per la resistenza, dell&#039;aria e per gli effetti della <lb></lb>forza centrifuga (ivi, pag. </s>

<s>159). E qui l&#039;Autore, che fu primo di <lb></lb>tutti i meccanici a specular su questo genere di forza, stabilisce <lb></lb>quella legge verissima delle forze centrifughe, benchè poi stimata <lb></lb>falsissima da Galileo (Alb. </s>

<s>I, 233) che cioè <emph type="italics"></emph>quanto maior est aliqua <lb></lb>rota tanto maiorem quoque impetum et impressionem motus eius <lb></lb>circumferentiae partes necipiant<emph.end type="italics"></emph.end> (Speculat. </s>

<s>lib. </s>

<s>pag. </s>

<s>159). Ma nella <lb></lb>sopra citata Lettera al Capra, le speculazioni in tal proposito son <lb></lb>anco più sottili, e, dal risolversi in orizzontale, per la vertigine, <lb></lb>l&#039;impeto naturalmente diretto per la verticale, scioglie alcuni curiosi <lb></lb>problemi relativi allo star ritte sul punzone le trottole giranti, e al <lb></lb>leggerissimo gravitar sul sostegno un corpo, che vi si muova sopra <lb></lb>veloce (ivi, pag. </s>

<s>286). </s></p><p type="main">

<s>Rispetto ai moti violenti, il Benedetti conferma le verità di­<lb></lb>mostrate già dal Cardano contro Aristotile, ma perchè il Tartaglia <lb></lb>aveva al Cardano stesso negato poter muoversi un grave nel mede­<lb></lb>simo tempo con moto naturale e con moto violento, il Nostro sottil­<lb></lb>mente dimostra come veramente ogni punto della traiettoria risulti <lb></lb>dalla composizione di quei due moti (ivi, pag. </s>

<s>365) per cui ebbe <lb></lb>a concludere altrove, contro ambedue, il Cardano cioè e il Tarta­<lb></lb>glia, come per nessun suo tratto quella stessa traiettoria è retta, e <lb></lb>com&#039;ella, appena uscito il proietto dal proiciente, <emph type="italics"></emph>cito fiat curva<emph.end type="italics"></emph.end><lb></lb>(ivi, pag. </s>

<s>161). </s></p><p type="main">

<s>E pur contro lo stesso Tartaglia è quella Epistola del Benedetti <lb></lb>che s&#039;intitola <emph type="italics"></emph>De ictu bombardae,<emph.end type="italics"></emph.end> nella quale si propone a scio­<lb></lb>gliere il quesito come mai la palla faccia più gran percossa, quando <lb></lb>il cannone è elevato, che quando è livellato coll&#039;orizzonte. </s>

<s>Giudica <lb></lb>le ragioni del Matematico bresciano <emph type="italics"></emph>nullius momenti<emph.end type="italics"></emph.end> (pag. </s>

<s>258) e <lb></lb>veramente son tali, ma nè quelle del Nostro colgono pure, questa <lb></lb>volta nel segno, come non colgon nel segno quelle che Galileo (Ediz. </s>

<s><lb></lb>naz. </s>

<s>cit. </s>

<s>Vol. </s>

<s>I, pag. </s>

<s>337-40) fedelmente ripete dal matematico ve­<lb></lb>neziano. </s></p><p type="main">

<s>Se a queste che concernono i moti naturali e i violenti s&#039;ag­<lb></lb>giungano le speculazioni del Benedetti intorno alla leva angolare e <lb></lb>intorno al cuneo, s&#039;argomenterà quanto gran maestro egli fosse <lb></lb>nella scienza del moto. </s>

<s>E perchè Galileo nelle Meccaniche s&#039;apre <lb></lb>la via a trattar del piano inclinato e della vite, rimovendo l&#039;antico <lb></lb>errore di Pappo, è giusto si aggiunge qui da noi come il Benedetti <pb xlink:href="020/01/124.jpg" pagenum="105"></pb>stesso aveva, nel Trattatello suo <emph type="italics"></emph>De mechanicis,<emph.end type="italics"></emph.end> rimosso già quel­<lb></lb>l&#039;errore del Matematico alessandrino, dimostrando che una sfera <lb></lb>grave posata su un piano orizzontale può rimuoversi dalla sua <lb></lb>quiete <emph type="italics"></emph>absque ulla difficultate<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>155). </s></p><p type="main">

<s>Si dice che dopo Archimede uno de&#039;primi e principali pro­<lb></lb>motori dell&#039;Idrostatica fosse, in sull&#039;entrar del secolo XVII, Simeone <lb></lb>Stevino, e s&#039;attribuisce a lui il paradosso che, indipendentemente <lb></lb>dalla sua mole, il liquido preme secondo l&#039;altezza sua verticale, il <lb></lb>fondo del vaso. </s>

<s>Ma il nostro Benedetti aveva già da vent&#039;anni di­<lb></lb>mostrato questo stesso paradosso idrostatico, applicandolo, come i <lb></lb>fisici moderni fanno, a spiegar l&#039;equilibrio de&#039;liquidi in due vasi <lb></lb>di varia capacità, comunicanti. </s>

<s>Chi vuol persuadersene legga l&#039;Epi­<lb></lb>stola o Responso a Giovan Paolo Capra <emph type="italics"></emph>De machina quae aquam <lb></lb>impellit et sublevat<emph.end type="italics"></emph.end> a pag. </s>

<s>287-88 della citata edizione. </s></p><p type="main">

<s>Fosse stato così felice il Matematico del Duca di Savoia in in­<lb></lb>vestigar le leggi delle acque correnti! Tutt&#039;all&#039;opposto egli incorre <lb></lb>in tali errori, che non si crederebbero da chi ammira la sagacia di <lb></lb>quell&#039;ingegno, se al citato Responso non si vedesse, nel Libro Delle <lb></lb>Speculazioni, seguitar l&#039;altro col titolo <emph type="italics"></emph>Nova solutio problematis de <lb></lb>vase pleno liquoris<emph.end type="italics"></emph.end> (pag. </s>

<s>289) a risolvere il quale ammette, come <lb></lb>principio notissimo e vero, che le quantità di liquido, fluito da un <lb></lb>vaso di qualunque figura, sieno sempre proporzionali ai tempi. </s>

<s>In <lb></lb>ciò egli è tanto inferiore al Cardano, quanto in Fisica è superiore <lb></lb>a tutti. </s></p><p type="main">

<s>E per incominciar di là, dove primo s&#039;introdusse a speculare <lb></lb>il Cardano, si notò com&#039;egli volesse banditi dalla scienza que&#039;nomi <lb></lb>vani di fuga e di orrore del vacuo, e come, a spiegare il fatto del <lb></lb>vaso, dentro cui, succhiata l&#039;aria, entra l&#039;acqua, dicesse che questa <lb></lb>era attratta da quella. </s>

<s>Lo Scaligero non seppe veder dove mai rise­<lb></lb>desse questa forza di attrazione, ma, facile a negare, null&#039;altro in <lb></lb>sostanza, a supplire al difetto e a mostrare il vero, asserisce. </s>

<s>Il Tar­<lb></lb>taglia, attendendo a quell&#039;altro modo del rarefarsi l&#039;aria per opera <lb></lb>del calore, e al fatto che pur così il vaso attrae l&#039;acqua, avea pro­<lb></lb>clamato il principio che sia proprietà del calore l&#039;attrarre. </s>

<s>Ma il <lb></lb>Benedetti se ne ride, e dice esser proprietà del calore non l&#039;attrarre <lb></lb>ma il dilatare. </s>

<s>Cosa poi notabile è che, estendendo questo poter di­<lb></lb>latante a tutti i corpi, soggiunge come per via del dilatarsi e del <lb></lb>restringersi, al crescere e al diminuir del calore, i vasi si rompono <lb></lb>nelle loro parti più deboli (pag. </s>

<s>27). Nelle Disputazioni sui Placiti <lb></lb>di Aristotile (pag. </s>

<s>194) torna su questo stesso argomento, rendendo <pb xlink:href="020/01/125.jpg" pagenum="106"></pb>la ragione dell&#039;aderire così tenacemente che fanno alla carne le <lb></lb>cucurbite mediche e del salir dell&#039;acqua o del vino ne&#039;cannellini, <lb></lb>che poi servirono ad uso di termometro; ragioni che son quelle <lb></lb>stesse che rendeva Galileo tanti anni dopo, e delle quali si trovava <lb></lb>così soddisfatto e ammirato il Sagredo. </s></p><p type="main">

<s>Nè si vuol tacer qui, a proposito degli effetti calorifici, un er­<lb></lb>rore aristotelico emendato dal Benedetti, benchè ripetuto poi da <lb></lb>tutti gli addetti alla Scuola galileiana infino al Borelli. </s>

<s>Aveva detto <lb></lb>il Filosofo, nel II Libro Delle Meteore, che il calor del sole è che <lb></lb>attrae e solleva i vapori. </s>

<s>E il nostro Fisico veneziano dice, più di <lb></lb>ottant&#039;anni prima del Fisico messinese, che ciò è apertamente falso, <lb></lb><emph type="italics"></emph>quia sol nil aliud facit quam calefacere cuius caloris ratione ea <lb></lb>materia rarefit et ob rarefactionem levior facta ascendit, non quia <lb></lb>sursum a sole feratur,<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>194). </s></p><p type="main">

<s>Ma intorno agli effetti del raro e del denso seguita sottilmente <lb></lb>a disputar contro Aristotile il Nostro, e dice la ragione perchè si <lb></lb>condensi nell&#039;inverno e si renda visibile il vapor acqueo esalato <lb></lb>dalla bocca e dalle narici degli animali (pag. </s>

<s>191) e perchè sudino <lb></lb>nell&#039;estate ripieni d&#039;acqua fresca i vasi, ridendosi dei filosofi che <lb></lb>dicevano quel sudore esalare attraverso ai sottilissimi pori. </s>

<s>Soggiunge <lb></lb>poi le notabilissime parole seguenti: “ Neque silentio involvendum <lb></lb>est nec Aristotilem, neque alium ex suis fautoribus animadvertisse <lb></lb>densum et rarum esse causam ventorum ” (pag. </s>

<s>192). Non solo <lb></lb>non aveva avvertito questo nessun seguace di Aristotile, ma nessun <lb></lb>seguace di Galileo, e durò l&#039;errore infin tanto che non vennero <lb></lb>alla luce le sepolte <emph type="italics"></emph>Lezioni accademiche<emph.end type="italics"></emph.end> del Torricelli, nelle quali <lb></lb>insegnò l&#039;Autore, a quel modo stesso che aveva tanti anni prima <lb></lb>fatto il Benedetti, come dal dilatarsi dell&#039;aria al calor del sole ave­<lb></lb>vano origine tutti i venti. </s>

<s>Gentile è poi quell&#039;osservazione fatta della <lb></lb>nuvola che produce vento al di sotto, velando e rivelando al sole <lb></lb>il suo raggio, secondo che si legge a pag. </s>

<s>192 del citato Libro delle <lb></lb>Speculazioni. </s></p><p type="main">

<s>Un&#039;altra cosa ben assai più notabile delle dette fin qui è che <lb></lb>il Benedetti, in tempi così remoti abbia tanto chiaramente veduta, <lb></lb>in quegli stessi effetti di rarefazione e di condensazione la causa <lb></lb>vera de&#039;suoni. </s>

<s>La storia dell&#039;Acustica rimane in certo modo umi­<lb></lb>liata a dover narrare che un Fisico della qualità del Montanari, <lb></lb>presso al fine del secolo XVII, dicesse come il suono si produce <lb></lb>dalla collisione dell&#039;aria coi corpi duri. </s>

<s>Eppure il fisico veneziano <lb></lb>aveva un secolo avanti insegnato che l&#039;aria corre velocemente a <pb xlink:href="020/01/126.jpg" pagenum="107"></pb>riempire i luoghi rimasti vacui <emph type="italics"></emph>unde generatur sonus quod hucusque <lb></lb>a nemine animadversum fuisse comperio<emph.end type="italics"></emph.end> (pag. </s>

<s>289). E più sottil­<lb></lb>mente altrove esponendo le sue speculazioni soggiunge esser neces­<lb></lb>sario che il corpo tremi. “ Neque etiam absque aere sonus effici <lb></lb>potest, quia aer sonat ingrediendo velociter ad implendum locum <lb></lb>ut non remaneat vacuus ” (pag. </s>

<s>190). </s></p><p type="main">

<s>Se non fosse cosa certa che Giovan Batista Porta, infin dal 1558, <lb></lb>descrisse la camera oscura e applicò quello strumento alla teorica <lb></lb>della visione, diremmo che il Benedetti era ben meritevole che fosse <lb></lb>riserbata a lui questa primizia delle sue speculazioni. </s>

<s>Forse egli fu <lb></lb>il primo ad applicar la lente biconvessa al foro, per cui s&#039;introdu­<lb></lb>cono i raggi solari (pag. </s>

<s>270) e senza dubbio l&#039;applicazion ch&#039;ei ne <lb></lb>fa al modo del vedere per l&#039;organo fisiologico dell&#039;occhio (pag. </s>

<s>297), <lb></lb>è di ben altro scienzato dall&#039;Autor della <emph type="italics"></emph>Magia Naturale.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Benchè nell&#039;Ottica non abbia fatto il Benedetti que&#039;gran pro­<lb></lb>gressi che fece nell&#039;Acustica, nella Meteorologia e in altre parti della <lb></lb>Fisica o più difficili o più importanti, non è da tacer nondimeno <lb></lb>la ragion ch&#039;ei rende del color rosso negli ecclissi di Luna, desunta <lb></lb>dalle rifrazioni che subiscono i raggi solari che perciò entrano nel <lb></lb>cono ombroso (pag. </s>

<s>257) e quell&#039;altra ragion ben più nuova dello <lb></lb>scintillar che fanno le stelle fisse; ragione desunta dal vario indice <lb></lb>di refrazione degli strati aerei e vaporosi che s&#039;interpongono fra <lb></lb>que&#039;lontanissimi corpi lucidi e il proprio occhio nostro (pag. </s>

<s>186). </s></p><p type="main">

<s>Il titolo di <emph type="italics"></emph>Speculazioni<emph.end type="italics"></emph.end> dato al libro, d&#039;onde tante nuove verità <lb></lb>della scienza si diffondevano a illuminar le tenebre di quei tempi, <lb></lb>è benissimo appropriato, perchè infatti l&#039;Autore non si contenta che <lb></lb>di speculare. </s>

<s>Santorre Santorio invece, nato 31 anno dopo il Bene­<lb></lb>detti in Capo d&#039;Istria nel 1561, è l&#039;uomo d&#039;azione e l&#039;arte medica <lb></lb>professata da lui è che potentemente l&#039;inclina a mettere in esercizio <lb></lb>le solitarie speculazioni della scienza. </s>

<s>Così, mentre lo stesso Bene­<lb></lb>detti s&#039;era contentato di specular le ragioni per cui, in un cannel­<lb></lb>lino di vetro, condensata l&#039;aria, vi sottentra l&#039;acqua, e variando la <lb></lb>temperatura l&#039;acqua stessa ora s&#039;alza nel cannellino ora s&#039;abbassa; <lb></lb>il Santorio pensa di sottoporre a misura quegli alzamenti e quegli <lb></lb>abbassamenti, per servirsene come di sicuro argomento a misurare <lb></lb>il giusto grado degli accessi e dei recessi ne&#039;calori febbrili. </s>

<s>E mentre <lb></lb>dall&#039;altra parte Galileo, sperimentando coi pendoli le prime leggi <lb></lb>della caduta dei gravi, s&#039;accorge dell&#039;isocronismo delle loro vibra­<lb></lb>zioni, e accenna all&#039;uso che se ne potrebbe far nella misura dei <lb></lb>minimi tempi, il Santorio pensa d&#039;applicar quello strumento a ri-<pb xlink:href="020/01/127.jpg" pagenum="108"></pb>conoscer da un giorno a un altro negli infermi la frequenza dei <lb></lb>polsi. </s></p><p type="main">

<s>Ma di simili altri strumenti, applicabili tutti all&#039;arte sua pre­<lb></lb>diletta, il Santorio è inventore fecondo, e aveva già divisato di con­<lb></lb>sacrare a descriverli tutti insieme un libro intero. </s>

<s>Se fosse un tal <lb></lb>dìvisamento poi mandato ad effetto, non si sa, perchè il libro degli <lb></lb><emph type="italics"></emph>Istrumenti medici<emph.end type="italics"></emph.end> a noi non è noto. </s>

<s>È certo però che l&#039;inventore <lb></lb>non teneva il segreto, e secondo che egli stesso scrive, la sua casa <lb></lb>in Padova era aperta a tutti coloro, che o per curiosità o per amore <lb></lb>di scienza accorrevano a veder tutte insieme raccolte, e come in <lb></lb>un piccolo museo ordinate e messe in mostra, quelle sue nuove <lb></lb>invenzioni. </s></p><p type="main">

<s>Quali che si fossero le dottrine professate dal nostro medico <lb></lb>giustinopolitano, è un fatto che questa così feconda vena d&#039;inven­<lb></lb>tare e di costruire e di utilmente applicare strumenti, era una pro­<lb></lb>testa viva e parlante contro i principii aristotelici, i quali, procla­<lb></lb>mando la mente sovrana e legislatrice della Natura, venivano a <lb></lb>concluder che la mente stessa sovrasta ai sensi anco infermi e non <lb></lb>bisognosi perciò di aiuti. </s></p><p type="main">

<s>Che se il Santorio non sa talvolta tener monde le vesti della <lb></lb>mota peripatetica, non è però che egli strascichi, come tanti suoi <lb></lb>pari fanno, in quel lurido fango la toga. </s>

<s>Egli non sempre forse pro­<lb></lb>cederà a diritto col raziocinio, ma sentendosi vacillare s&#039;aiuta delle <lb></lb>esperienze delle quali è senza dubbio un insigne monumento quella <lb></lb><emph type="italics"></emph>Medicina Statica,<emph.end type="italics"></emph.end> ordinata a riformar l&#039;arte ippocratica Chi ripensi <lb></lb>che quel Trattatello dettato in forma aforistica e divisato con me­<lb></lb>todo quasi geometrico, fu scritto in tempi, in cui si soleva affogar <lb></lb>da tutti le idee in un mar di parole, non finirà mai di ammirare <lb></lb>il Santorio, il quale fu primo a concluder le regole dell&#039;arte me­<lb></lb>dica dal fatto fisiologico dell&#039;insensibile traspirazione dimostrata con <lb></lb>tutto il più rigoroso procedere del metodo sperimentale. </s></p><p type="main">

<s><emph type="center"></emph>XIV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>E ora che abbiamo veduto come la speculativa del Benedetti <lb></lb>e la pratica del Santorio compiendosi preparassero le fondamenta <lb></lb>alla grande Instaurazione galileana, convien passare a parlare di <pb xlink:href="020/01/128.jpg" pagenum="109"></pb>quel terzo che aggiungemmo a que&#039;due primi compagno, e che <lb></lb>dette valida mano alla stessa grande Instaurazione insieme con <lb></lb>Galileo. </s></p><p type="main">

<s>Non si può pronunziare il nome di Paolo Sarpi, senza che <lb></lb>l&#039;animo di chi ascolta non esca in ammirazioni declamatorie o in <lb></lb>disprezzi triviali. </s>

<s>Le trivialità e le declamazioni son l&#039;eccesso di <lb></lb>que&#039;giudizii, che sempre si fanno da coloro, i quali non ben cono­<lb></lb>scono l&#039;uomo giudicato. </s>

<s>E in fatti, lasciando da parte la Religione <lb></lb>e la Politica, per non curarsi d&#039;altro che della scienza, a convin­<lb></lb>cersi che il Sarpi dee essere stato mal giudicato perchè non inteso, <lb></lb>basta il modo come sono state pubblicate le Lettere di lui. </s>

<s>Quella, <lb></lb>per esempıo, del 2 Settembre 1602 diretta a Galileo, fu per questo <lb></lb>lasciata addietro dall&#039;Albèrti perchè <emph type="italics"></emph>oscura e mal dettata.<emph.end type="italics"></emph.end> Il Poli­<lb></lb>dori, nonostante, credè bene di pubblicarla insiem con l&#039;altre dili­<lb></lb>gentemente raccolte in due volumi stampati nel 1863 in Firenze. </s>

<s><lb></lb>Ma l&#039;oscurità, a voler dire il vero, non dipende già da chi scrive: <lb></lb>dipende piuttosto da chi legge e non sa di qual soggetto pro­<lb></lb>priamente si parla. </s>

<s>A chi sapesse che l&#039;Autore citato ivi è il Gil­<lb></lb>bert; che la questione è trattata nella Fisiologia nuova del Magnete, <lb></lb>che ivi trovasi disegnata la figura, alla quale il Sarpi si richiama; <lb></lb>le difficoltà spariscono e la scienza si vede a un tratto scaturir, <lb></lb>come da un arido masso, acqua viva. </s>

<s>Allo stesso modo son nella <lb></lb>Raccolta del Polidori aombrate le altre lettere del Sarpi, unico do­<lb></lb>cumento pubblico, da cui si possa giudicare della scienza naturale <lb></lb>di lui. </s>

<s>Ma benchè sieno, in materia scientifica quelle lettere poche, <lb></lb>pure apparecchiano innanzi a chi ha buono stomaco da digerirlo, <lb></lb>cibo che nutrisce assai meglio delle più squisite vivande imbandite <lb></lb>al più liberale convito. </s>

<s>Anzi quella concisione di linguaggio scien­<lb></lb>tifico, quasi ridotto a formule matematiche, per cui a chi non ha <lb></lb>acume da entrarci bene addentro pare enimmaticamente oscuro, è, <lb></lb>secondo noi, uno dei pregi più singolari del Sarpi, di che in lui e <lb></lb>nel Santorio s&#039;ha esempio unico in quei tempi </s></p><p type="main">

<s>Del resto, anco quando non s&#039;avesse nessuna scrittura scien­<lb></lb>tifica dell&#039;Autore, basterebbero a testimoniar della scienza di lui le <lb></lb>sincere ammirazioni e le lodi dei contemporanei, fra&#039;quali Galileo <lb></lb>e il Gilbert soli varrebbero per tutti gli altri. </s>

<s>Ma giacchè quelle <lb></lb>scritture ci sono e son vive e parlanti, studiamoci di leggerle, con <lb></lb>la serenità stessa di chi nulla altro ama e null&#039;altro vuole annun­<lb></lb>ziar che il vero. </s></p><p type="main">

<s>Nel 1608, immerso tutto nelle faccende politiche, scriveva il <pb xlink:href="020/01/129.jpg" pagenum="110"></pb>di 22 Luglio al Groslot, come innanzi che le occorrenze del mondo <lb></lb>lo invitassero a pensar come cose serie e non come passatempi a <lb></lb>quelle faccende, aveva tutti i suoi gusti nelle scienze naturali e <lb></lb>nelle matematiche (Polidori, ivi, vol. </s>

<s>I, pag. </s>

<s>76). Qual fosse poi il <lb></lb>metodo ch&#039;ei proseguiva, s&#039;argomenta da ciò che altrove, allo stesso <lb></lb>Groslot scrive del non doversi filosofar, conforme al precetto di So­<lb></lb>crate, sopra esperienze non vedute da sè proprio (ivi, pag. </s>

<s>181). In <lb></lb>questo modo protestava apertamente contro Aristotile, e soggiun­<lb></lb>gendo poco appresso ch&#039;ei sentiva qualche opposizione in trattar <lb></lb>cose astratte, perchè non si metteva in conto la repugnanza della <lb></lb>materia, mostrava di voler seguire altra via da coloro, che, fedeli <lb></lb>troppo a Platone, discorrevano, colle astrazioni matematiche, de&#039;fatti <lb></lb>particolari della Natura. </s></p><p type="main">

<s>Fra&#039;soggetti naturali, che più vivamente richiamassero a sè <lb></lb>l&#039;attenzione de&#039;Filosofi e la voglia de&#039;curiosi, eran que&#039;moti irre­<lb></lb>golari veduti fare alla calamita, i quali scoperti prima dal Colombo <lb></lb>furono poi confermati dalle osservazioni degli altri navigatori. </s>

<s>Così <lb></lb>il Colombo però come Giovanni da Empoli si stettero contenti a <lb></lb>osservare e a descrivere i semplici fatti: il Sassetti che si volle <lb></lb>provare a filosofarvi sopra, assai presto se ne tolse giù, atterrito <lb></lb>dalla difficoltà del soggetto. </s></p><p type="main">

<s>Il primo che ardisse d&#039;affrontare quelle difficoltà, predisponendo <lb></lb>l&#039;ingegno alle filosofiche speculazioni colle osservazioni sensate e <lb></lb>colle più sottili esperienze, fu il nostro Sarpi, di cui il Porta, nel <lb></lb>settimo libro della Magìa raccolse per avventura gli studi e le sco­<lb></lb>perte magnetiche, le quali sarebbero andate altrimenti con grave <lb></lb>danno perdute. </s></p><p type="main">

<s>Nè a quella vigorosa gioventù di mente questo fra&#039;soggetti na­<lb></lb>turali poteva esaurire le forze. </s>

<s>Si vuole anzi che nulla fosse dal <lb></lb>Sarpi lasciato addietro di ciò che allora, o in cose di fisica o in <lb></lb>cose di storia naturale potesse attrarre a sè l&#039;attenzione degli in­<lb></lb>gegni speculativi. </s>

<s>Il Grisellini, fra le altre, vorrebbe attribuirgli la <lb></lb>scoperta delle valvole delle vene e fargli di lì indurre l&#039;altra più <lb></lb>grande scoperta della circolazione del sangue. </s>

<s>E perchè l&#039;argomento <lb></lb>è di troppo alta importanza, non si vuol lasciar qui da noi senza <lb></lb>esame. </s></p><p type="main">

<s>“ Mediante dunque le sue esercitazioni anatomıche (così scrive <lb></lb>lo stesso Grisellini di fra Paolo quando aveva 26 anni) avendo sco­<lb></lb>perte le valvole delle vene onde la successione del sangue da que­<lb></lb>ste nelle arterie si rende manifesta, ne veniva quinci dimostrata <pb xlink:href="020/01/130.jpg" pagenum="111"></pb>e stabilita la circolazione del sangue, che per alcune anteriori os­<lb></lb>servazioni di Realdo Colombo, del Serveto e del Cesalpino era stata <lb></lb>accennata, egli, io dico avendo scoperte esse valvole non tacque la <lb></lb>sua scoperta al celebre Fabrizio d&#039;Acquapendente, il quale, coll&#039;oc­<lb></lb>casione di trasferirsi in Venezia.... aveva contratto seco amicizia. </s>

<s>” <lb></lb>(Mem. </s>

<s>aned. </s>

<s>Losanna 1760, pag. </s>

<s>20). </s></p><p type="main">

<s>Che il Sarpi facesse veramente soggetto di speculazioni e di <lb></lb>esperienze anco l&#039;Anatomia è cosa probabilissima, ed è certo che <lb></lb>l&#039;Acquapendente apprese dallo stesso Sarpi quel curioso fatto del <lb></lb>ristringersi e del dilatarsi delle pupille osservato già molto tempo <lb></lb>prima, senza che si sapesse, da Leonardo. </s>

<s>Ma che l&#039;Acquapendente <lb></lb>apprendesse dal Sarpi, come il Grisellini asserisce, la scoperta delle <lb></lb>valvole delle vene, non solo non s&#039;ha certa dimostrazione da nes­<lb></lb>sun documento, ma i documenti che abbiamo stanno a provar tutto <lb></lb>il contrario. </s></p><p type="main">

<s>Il Falloppio ha un passo notabilissimo, che si vedrà trascritto <lb></lb>a suo luogo, dal quale apparisce che in alcune vene l&#039;esistenza <lb></lb>delle valvole fu ritrovata già da Giovan Batista Canani. </s>

<s>La scoperta <lb></lb>fu divulgata da G. </s>

<s>Rodriguez conosciuto sotto il nome di Amato <lb></lb>Lusitano, ed è contro a lui che fieramente se la prende il Fallop­<lb></lb>pio, asserendo che l&#039;illustre Canano non poteva essere incorso in <lb></lb>un errore così madornale. </s>

<s>La scoperta, che in tal modo il grande <lb></lb>anatomico modenese lasciò scapparsi di mano, venne tutta alle mani <lb></lb>dell&#039;Acquapendente, il quale con gran diligenza racconta da sè me­<lb></lb>desimo qual fosse l&#039;anno e a quale occasione gli occorresse di far <lb></lb>quella scoperta invidiata. </s></p><p type="main">

<s>Leggesi un tal racconto scritto nel Trattatello stampato in Pa­<lb></lb>dova nel 1603 dalla tipografia di Lorenzo Pasquati. </s>

<s>Ci è nato il <lb></lb>sospetto che, o per la rarità o per altra ragione quel Trattatello <lb></lb>dell&#039;Acquapendente non fosse veduto mai da nessun di coloro che <lb></lb>lo citano, incominciando dall&#039;alterare il titolo stesso da quello che <lb></lb>dall&#039;Autore gli è imposto. <emph type="italics"></emph>De valvulis<emph.end type="italics"></emph.end> lo intitola il Magiotti, <emph type="italics"></emph>De <lb></lb>ostiolis sanguinis<emph.end type="italics"></emph.end> il Grisellini, <emph type="italics"></emph>De ostiolis venarum<emph.end type="italics"></emph.end> il Puccinotti; <lb></lb>ma è un fatto che il titolo vero è <emph type="italics"></emph>De venarum ostiolis.<emph.end type="italics"></emph.end> Non fa <lb></lb>perciò maraviglia se quegli autori, i quali o non poterono o non <lb></lb>si curarono di consultar ciò che lo scopritore delle valvole delle <lb></lb>vene ne scrisse, raccontano a uria e giudicano delle cose. </s></p><p type="main">

<s>Consultando però senz&#039;animo preoccupato quella scrittura, ci si <lb></lb>trova un tal carattere di verità, nella narrazione e nella descrizione, <lb></lb>che il voler negar fede alle parole dell&#039;Autore sarebbe un profes-<pb xlink:href="020/01/131.jpg" pagenum="112"></pb>sare addirittura il più assoluto pirronismo storico. </s>

<s>Incomincia da <lb></lb>far le meraviglie come mai l&#039;esistenza delle valvole delle vene po­<lb></lb>tesse esser rimasta agli anatomici per così lungo tempo occulta, e <lb></lb>soggiunge che nel sezionare i cadaveri s&#039;abbattè a vederle per la <lb></lb>prima volta nel 1574. (De ven. </s>

<s>ost. </s>

<s>pag. </s>

<s>1). La via della scoperta <lb></lb>gli era stata preparata già da ciò che eragli occorso d&#039;osservare <lb></lb>nelle vene allacciate o compresse (ivi, pag. </s>

<s>2) le quali inturgidendo <lb></lb>di sangue mostrano nel loro decorso certi nodi, come quei delle <lb></lb>canne, ond&#039;è che mettendosi a dissecare per veder ciò che fossero <lb></lb>veramente quei nodi, ritrovò che egli eran dovuti a un ristagno di <lb></lb>sangue, operatovi dalle valvole, a quel modo che si vede fare alle <lb></lb>cateratte attraverso al corso di un fiume. </s></p><p type="main">

<s>Ora, è egli credibile che Girolamo Fabrizi d&#039;Acquapendente, <lb></lb>nella vita sua civile e scientifica così dignitoso, avesse osato d&#039;as­<lb></lb>serire tali falsità e di scriverle sotto gli occhi di Fra Paolo? </s>

<s>E <lb></lb>dall&#039;altra parte egli invoca, a far testimonianza del vero, l&#039;inclita <lb></lb>nazione Germanica, alla quale dedica il Trattatello, e nella stessa <lb></lb>Lettera dedicatoria ringrazia Salomone Alberto, per aver nella sua <lb></lb>nazione divulgata quella scoperta. </s></p><p type="main">

<s>Ritornando ora alle osservazioni del Grisellini, diciamo che, <lb></lb>sebbene debba credersi vero autore della scoperta delle valvole delle <lb></lb>vene nò il Sarpi, ma l&#039;Acquapendente, è falso nulladimeno che i <lb></lb>due grandi uomini o di li o d&#039;altronde pigliassero argomento a di­<lb></lb>mostrar il circolo del sangue. </s>

<s>Vari passi potrebbero citarsi dalle <lb></lb>opere dell&#039;Acquapendente, e specie dal cap. </s>

<s>VIII, Parte II. <emph type="italics"></emph>De for­<lb></lb>mato foetu,<emph.end type="italics"></emph.end> da&#039;quali si proverebbe com&#039;egli, trattando degli usi <lb></lb>del polmone, ripete le antiche dottrine galeniche approvate già dal <lb></lb>Vesalio e dal Falloppio, nulla accettando nemmeno di ciò che, ri­<lb></lb>spetto alla piccola circolazione, avevano dimostrato il Colombo e il <lb></lb>Cesalpino. </s>

<s>Dall&#039;altra parte, per lo stesso Trattato <emph type="italics"></emph>De venarum ostiolis<emph.end type="italics"></emph.end><lb></lb>si par chiaro che l&#039;Autore attribuiva alle valvole un ufficio ben di­<lb></lb>verso da quello che veramente hanno in natura, il qual&#039;è di faci­<lb></lb>litare il corso del sangue verso il lago del cuore. </s>

<s>L&#039;Acquapendente <lb></lb>infatti ammettendo che il sangue venoso abbia virtù di alimentare, <lb></lb>dice che le valvole sono ordinate a distribuir quell&#039;alimonia per <lb></lb>tutto equamente. </s>

<s>Che se nelle vene più lontane dal centro del cuore, <lb></lb>come in quelle delle braccia e delle gambe, osserva le valvole ri­<lb></lb>correre ivi più spesse, non sospetta per niente che ciò sia perchè <lb></lb>il sangue abbisogna, in quelle condizioni, d&#039;aiuti maggiori, avendo <lb></lb>a fare un viaggio più lungo per tornarsene al suo principio; ma <pb xlink:href="020/01/132.jpg" pagenum="113"></pb>dice che, essendo le gambe e le braccia soggette a fare sforzi, per <lb></lb>cui il sangue correrebbevi troppo veloce, a temperarne la forza vi <lb></lb>bisogna un più frequente uso di valvole. </s>

<s>Che poi ne anco il Sarpi <lb></lb>non avesse nemmen la più lontana idea del circolo del sangue, <lb></lb>s&#039;argomenta da alcune espressioni che ricorrono negli scritti di lui <lb></lb>e segnatamente ne&#039;principii delle Lettere CXXIV e CCXX, fra le <lb></lb>pubblicate dal Polidori. </s></p><p type="main">

<s>Gli ammiratori ferventi del frate servita intesero a glorificarlo <lb></lb>altresì coll&#039;attribuirgli l&#039;invenzione di alcuni de&#039;principali strumenti <lb></lb>del metodo sperimentale, fra&#039;quali è il Telescopio. </s>

<s>Ma del Tele­<lb></lb>scopio tratta il Sarpi nelle sue Lettere a varie occasioni, e ne tratta <lb></lb>in modo da potere informare sulle sue stesse parole il più retto <lb></lb>giudizio. </s>

<s>In una Lettera al Groslot, che è la LII della Raccolta del <lb></lb>Polidori, dop&#039;essersi fatto intendere che verso la fine del Novem­<lb></lb>bre 1608 ebbe avviso <emph type="italics"></emph>delli nuovi occhiali<emph.end type="italics"></emph.end> sei mesi prima che quello <lb></lb>stesso avviso pervenisse alle orecchie di Galileo, soggiunge che, <lb></lb>quando egli era giovane, pensò ad una tal cosa e gli passò per la <lb></lb>mente che un occhial fatto di figura di parabola potesse far tale <lb></lb>effetto. </s></p><p type="main">

<s>Le lenti paraboliche poi dettero soggetto di specular lunga­<lb></lb>mente agli ottici infino ai tempi del Newton, nonostante che il Ca­<lb></lb>valieri avesse geometricamente dimostrato, nel suo <emph type="italics"></emph>Specchio Ustorio,<emph.end type="italics"></emph.end><lb></lb>esser quella una inutile squisitezza, stante che, tra un menisco sfe­<lb></lb>rico e un iperbolico, è trascurabile la differenza. </s>

<s>Ma è, in tal pro­<lb></lb>posito assai importante una lettera del 4 Ottobre 1614, nella quale <lb></lb>Bartolommeo Imperiali propone a Galileo la soluzione di quell&#039;enim­<lb></lb>ma, che il Porta scrisse nel cap. </s>

<s>XI del XVII libro della Magìa. </s>

<s><lb></lb>Quell&#039;enimma concerne uno strumento da veder le cose lontane, <lb></lb>e l&#039;Imperiali indovinerebbe che consistesse nella lente parabolica. </s>

<s><lb></lb>Dice ivi che il Porta, <emph type="italics"></emph>per quanta istanza li sia stata fatta da prin­<lb></lb>cipi b letterati s&#039;è potuto mai inchinare a dichiarar l&#039;animo suo: <lb></lb>solo disse che maestro Paolo da Venezia servita l&#039;aveva capito.<emph.end type="italics"></emph.end><lb></lb>(Mss. </s>

<s>Gal. </s>

<s>Div. </s>

<s>II, P. VI, T. IX, c. </s>

<s>206). Di qui facilmente si rac­<lb></lb>coglie d&#039;onde attingesse il Porta l&#039;idea dello strumento da veder <lb></lb>le cose lontane, e poniamo pure che rimanesse un&#039;idea, nonostante <lb></lb>non è piccola gloria di lui e del Sarpi l&#039;aver creduto possibile il <lb></lb>Telescopio, a cui il gran Kepler non ebbe fede, in fin tanto che <lb></lb>non se lo vide fra le mani, e non ne fece esperienza con gli occhi. </s></p><p type="main">

<s>Divenuta la possibilità in atto, per la fortunatissima opera di <lb></lb>Galileo, il Sarpi non rimase indietro nelle osservazioni celesti. </s>

<s>In <pb xlink:href="020/01/133.jpg" pagenum="114"></pb>una lettera del 16 marzo 1610, dopo aver fra Paolo annunziato al <lb></lb>Leschassier che più di due anni fa gli Olandesi avevano scoperto <lb></lb>uno strumento pel quale si vedevano le cose lontane. </s>

<s>“ Di questo <lb></lb>trovato, soggiunge, un nostro Matematico di Padova e altri italiani <lb></lb>intendenti della materia principiarono a valersi per l&#039;Astronomia, <lb></lb>e dalla esperienza avvalorati lo ridussero più atto e perfezionato. </s>

<s>” <lb></lb>(Polidori, vol. </s>

<s>II, pag. </s>

<s>41). Che quel matematico di Padova sia Ga­<lb></lb>lileo, è fuor di dubbio, ma giacchè lo scrittore di quelle parole ci <lb></lb>riveìa l&#039;importantissima notizia che cioè, contemporaneamente a <lb></lb>Galileo, il quale si crede da tutti il primo e il solo, ci fossero <emph type="italics"></emph>altri <lb></lb>italiani,<emph.end type="italics"></emph.end> i quali attendevano a perfezionare il canocchiale, e a far <lb></lb>con esso osservazioni celesti; chi sono, si domanda, questi italiani? </s>

<s><lb></lb>E alla domanda si risponde da noi dicendo che quegli italiani erano <lb></lb>appunto il Sarpi e gli altri che in Venezia conferivan con lui. </s></p><p type="main">

<s>Giungerà forse come cosa nuova ai lettori e per la novità parrà <lb></lb>non credibile, che il <emph type="italics"></emph>Nuncio Sidereo,<emph.end type="italics"></emph.end> e quanto alle osservazioni <lb></lb>degli occhi, e quanto alle speculazioni della mente, sia opera tutto <lb></lb>insieme, e forse per egual merito, di Galileo e del Sarpi. </s>

<s>Eppure <lb></lb>i documenti, che ai giudiziosi e agli spassionati appariranno chia­<lb></lb>rissimi, tolgon via intorno a ciò tutti i dubbi. </s></p><p type="main">

<s>In quella lettera al Leschassier, ora ultimamente citata, pro­<lb></lb>segue a dire il Sarpi, a proposito delle osservazioni celesti fatte col <lb></lb>canocchiale, come in Toscana erano state osservate nuove cose nella <lb></lb>stella di Giove, che ei leggerà nell&#039;<emph type="italics"></emph>opuscolo<emph.end type="italics"></emph.end> offertogli a nome suo <lb></lb>dal Legato. </s>

<s>Quell&#039;opuscolo era senza dubbio il Nunzio Sidereo, al­<lb></lb>quante copie del quale Galileo, appresso allo stampatore avea rila­<lb></lb>sciate a disposizione di Fra Paolo, che le dispensava agli amici. </s>

<s><lb></lb>Mentre che però era sollecito di diffondere quel libro negli altri, <lb></lb>egli ancora non lo aveva letto, e nonostante torna poco dopo a <lb></lb>scrivere una nuova lettera allo stesso Leschassier, nella quale si <lb></lb>contengono annunziate le principali fra le scoperte celesti, che ve­<lb></lb>nivano annunziate al mondo dall&#039;opuscolo di Galileo. </s>

<s>Questo è poi <lb></lb>un argomento certo della verità di quel che vedremo più sotto es­<lb></lb>sere asserito dallo stesso Sarpi, che cioè egli aveva conferito quelle <lb></lb>osservazioni celesti coll&#039;Autor dell&#039;opuscolo, per cui s&#039;intende come <lb></lb>potesse render conto di quel che trattava, senza averlo letto. </s></p><p type="main">

<s>Anco quando il Nunzio Sidereo fosse andato smarrito, questa <lb></lb>lettera CXXXVI della citata Roccolta varrebbe a ristorar la scienza <lb></lb>di quella iattura, per ciò almeno che concerne le macchie della <lb></lb>Luna. </s>

<s>L&#039;antico Plutarco ebbe la felicissima idea che la Luna fosse <pb xlink:href="020/01/134.jpg" pagenum="115"></pb>fisicamente costituita come la Terra, e aveva ad occhio distinte due <lb></lb>diverse qualità di macchie, alcune variabili che egli attribuiva al­<lb></lb>l&#039;ombra de&#039;monti insolati, e altre permanenti, che egli attribuiva <lb></lb>alla superficie dei mari. </s>

<s>Una tal novità, fu, com&#039;è naturale, rifiu­<lb></lb>tata dai Peripatetici, ma i più sagaci che vi sentiron dentro alitare <lb></lb>un soave spirito di verità, l&#039;accolsero con amore. </s>

<s>Dubitavano però <lb></lb>se più di luce si dovesse rifletter dai mari o dai continenti. </s>

<s>Il pro­<lb></lb>blema veramente era illusorio e vi rimase preso anco il Keplero, <lb></lb>che lietamente accogliendo i placiti del Cheronese <emph type="italics"></emph>hac in parte,<emph.end type="italics"></emph.end><lb></lb>soggiunge, <emph type="italics"></emph>non assentior. </s>

<s>Magis est consentaneum quae sunt in <lb></lb>Luna partes lucidae maria credi, quae maculosae terras, conti­<lb></lb>nentes et insulas.<emph.end type="italics"></emph.end> (Paralip. </s>

<s>edit. </s>

<s>cit. </s>

<s>pag. </s>

<s>201). Galileo nel <emph type="italics"></emph>Nuncio<emph.end type="italics"></emph.end><lb></lb>esce destramente dalla controversia saettando simili parole: “ La <lb></lb>terra dee apparir più chiara del mare, e intorno a ciò <emph type="italics"></emph>mihi dubuim <lb></lb>fiut unquam.<emph.end type="italics"></emph.end> ” (Alb. </s>

<s>III, pag. </s>

<s>65). </s></p><p type="main">

<s>Che il Keplero alla contraria sentenza, così laconicamente pro­<lb></lb>nunziata da Galileo, ne rimanesse persuaso, e tornasse anco per <lb></lb>questa parte al suo Plutarco, non fa maraviglia. </s>

<s>Fa però maraviglia <lb></lb>il sentirlo dire che fu condotto in quella persuasione di creder cioè <lb></lb>mari le macchie della luna, da ciò che ne disse Galileo stesso <emph type="italics"></emph>di­<lb></lb>sputatione exactissima<emph.end type="italics"></emph.end> e di più <emph type="italics"></emph>illatione argutissima et invicta.<emph.end type="italics"></emph.end><lb></lb>(Alb. </s>

<s>V, 418, 19) mentre Galileo nel <emph type="italics"></emph>Nuncio<emph.end type="italics"></emph.end> tutt&#039;altro che dispu­<lb></lb>tare e argomentare, si sta contento ad asserir semplicemente il fatto <lb></lb>che egli tiene anzi così certo, da non aver bisogno alcuno di prove. </s></p><p type="main">

<s>Chi veramente disputa su tale importante soggetto e argomenta <lb></lb>è il Sarpi, nella citata lettera al suo Leschassier e le disputazioni <lb></lb>e gli argomenti son suggellati dalla esperienza. </s>

<s>“ Se Ella porrà di <lb></lb>contro al sole ma lungi da sè una pietra rotonda e uno specchio <lb></lb>sferico della stessa grandezza, vedrà l&#039;emisfero della pietra rischia­<lb></lb>rato e tutto lo specchio oscuro, all&#039;infuori di quella minima parti­<lb></lb>cella, in cui le si offrirà alla vista un certo piccol sole. </s>

<s>Che se <lb></lb>tanto l&#039;allontanerà da essere insensibile l&#039;angolo, cioè quel piccol <lb></lb>sole, appena Ella vedrà lo specchio; il sole poi apparirà splendi­<lb></lb>dissimo. </s>

<s>L&#039;acqua e la terra sono sferiche e la Luna ha una parte <lb></lb>lucida ed una macchiata: applichi ad essa questi riflessi e toccherà <lb></lb>con mano la cosa. </s>

<s>” (Polidori, vol. </s>

<s>II, pag. </s>

<s>63). </s></p><p type="main">

<s>Galileo non argomenta nè disputa intorno alla ragion fisica <lb></lb>delle macchie permanenti della Luna, se non parecchi anni dopo <lb></lb>nel primo Dialogo dei Due Massimi Sistemi (Alb. </s>

<s>I, 15, 88) ricor­<lb></lb>rendo all&#039;esperienza dello specchio sferico e della pietra scabrosa <pb xlink:href="020/01/135.jpg" pagenum="116"></pb>o del muro, a quel modo che aveva fatto già il Sarpi nelle lettere <lb></lb>e nelle parole sopra trascritte ond&#039;è che non a torto si può quella <lb></lb>stessa lettera al Leschassier riguardar come un trattatello d&#039;Astro­<lb></lb>nomia fisica lunare, più compiuto del Nuncio Sidereo. </s></p><p type="main">

<s>A chi rifletta con giudiziosa mente a queste cose non sembrerà <lb></lb>perciò alieno dal vero quel che s&#039;asseriva di sopra, che cioè in <lb></lb>gran parte si debbano al Sarpi le novità scoperte e annunziate da <lb></lb>Galileo. </s>

<s>La nostra asserzione poi fondata sui fatti dà suggello di <lb></lb>verità alle parole con le quali fra Paolo, accennando al matematico <lb></lb>dello studio di Padova esordisce il suo compendioso Nunzio Astro­<lb></lb>nomico: “ Spesso abbiamo conferito insieme su quell&#039;argomento e <lb></lb>molte osservazioni ci scambiammo. </s>

<s>” (Polid. </s>

<s>vol. </s>

<s>II, pag. </s>

<s>61). </s></p><p type="main">

<s>Ed ecco insieme i fatti stessi confermare altri detti citati più <lb></lb>sopra a proposito di quegli italiani che attendevano in Venezia a <lb></lb>perfezionare il canocchiale e a far con esso osservazioni celesti. </s>

<s>A <lb></lb>quel numero appartenevano gli eruditi di cui il Sarpi scrive nella <lb></lb>lettera CXLI, i quali comprendendo che mal si sarebbe riusciti a <lb></lb>perfezionare il canocchiale senza prima conoscerne le teorie, dise­<lb></lb>gnavano di fare un piccolo commentorio sulla visione <emph type="italics"></emph>ove esporranno <lb></lb>la maniera e la cagione del trovato olandese<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>81). Nel­<lb></lb>l&#039;agosto 1610 quel Commentario, che senza dubbio è il Trattato <lb></lb>del De Dominis <emph type="italics"></emph>De radiis visus et lucis,<emph.end type="italics"></emph.end> non era ancora finito di <lb></lb>stampare e si attendeva a mettere all&#039;ordine le incisioni (ivi, <lb></lb>pag. </s>

<s>108). </s></p><p type="main">

<s>A chi poi si maravigliasse come mai l&#039;Autore del Nunzio Si­<lb></lb>dereo non facesse il più piccolo accenno al suo collaboratore nelle <lb></lb>osservazioni celesti, si risponderà più avanti, quando altri simili <lb></lb>fatti ci faranno meglio conoscere un&#039;indole propria di Galileo. </s>

<s>Ba­<lb></lb>sti rìsponder per ora che, nella prima lettera familiare la quale <lb></lb>gli occorresse di scrivere al Sarpi dopo la pubblicazione del Mes­<lb></lb>saggero, Galileo ne esalta le virtù e i meriti e professa di tenergli <lb></lb>obblighi infiniti (Alb. </s>

<s>VI, 141). </s></p><p type="main">

<s><emph type="center"></emph>XV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi si rivolge indietro a comprendere in una occhiata sola la <lb></lb>lunga schiora passata da noi fin qui in rassegna, da Dante Alighieri <lb></lb>a Paolo Sarpi, non può non restar sorpreso da maraviglia, e non <pb xlink:href="020/01/136.jpg" pagenum="117"></pb>confessare a sè medesimo ch&#039;ei non l&#039;avrebbe creduta mai nè sì <lb></lb>eletta, nè sì numerosa. </s>

<s>Essa rimane ancora immobile sotto lo sguardo <lb></lb>dei nostri lettori e par che voglia star lì a fronte alta per chieder <lb></lb>ragione e vendicar l&#039;accusa che fu data a loro da tanti d&#039;esser e <lb></lb>vissuti cioè in secoli di barbarie, e di non aver saputo cacciar di­<lb></lb>nanzi a sè le tenebre dell&#039;ignoranza. </s>

<s>A chi li rimproverò e gli <lb></lb>compianse, perchè avessero tenute aggiogate le loro cervici sotto <lb></lb>l&#039;autorità di Aristotile, e non avessero saputo far altro che ridire <lb></lb>in prosa gli errori declamati da lui, rispondono squadernando in­<lb></lb>nanzi agli occhi i loro volumi, e accennando colla punta del dito <lb></lb>alle nuove speculazioni e alle nuove scoperte, frutto di libera filo­<lb></lb>sofia e d&#039;ingegnosa arte sperimentale. </s></p><p type="main">

<s>Si sentiva nonostante in sul primo entrar del secolo XVII che <lb></lb>i frutti menati dall&#039;albero della scienza non rispondevano, nè in <lb></lb>qualità, nè in numero, all&#039;abbondanza dei rami, per cui fu creduto <lb></lb>si potesse utilmente provvedere alla loro ubertà col moitiplicare i <lb></lb>cultori a ciò chiamati ed eletti. </s>

<s>Un tal pensiero accolto in un animo <lb></lb>generoso e che per opera di un Principe romano d&#039;animo non <lb></lb>men generoso si potè mettere in atto, diè luogo all&#039;istituzione del­<lb></lb>l&#039;Accademia de&#039;Lincei, la seconda forse, che dopo la Platonica fio­<lb></lb>rentina, si vedesse in Italia. </s></p><p type="main">

<s>Il principio informativo della nuova Accademia è notabile che <lb></lb>si desumesse dall&#039;istituzione dei Cherici regolari, e che, come questi <lb></lb>si proponevano di diffonder la fede cristiana e i buoni costumi, così <lb></lb>gli Accademici lincei si proponessero di diffonder la scienza natu­<lb></lb>rale e i retti metodi sperimentali. </s>

<s>Il <emph type="italics"></emph>Linceografo<emph.end type="italics"></emph.end> infatti s&#039;assomi­<lb></lb>glia molto alle regole dei frati, i Collegi lincei ai conventi, e l&#039;isti­<lb></lb>tuzione delle colonie lincee alle Missioni. </s>

<s>Di qui è che avendo le <lb></lb>leggi stesse e le costituzioni risentendo molto dell&#039;aristotelico e ciò <lb></lb>vuol dire del gretto e del compassato, male erano atte a predisporre <lb></lb>quel nobile e generoso consesso al libero filosofare, e a coglier quei <lb></lb>buoni frutti, che si ripromettevano le speranze del Principe insti­<lb></lb>tutore. </s></p><p type="main">

<s>Ben assai più efficaci erano stati e duravano tuttavia ad esser <lb></lb>gli influssi dell&#039;Accademia platonica, benchè non facesse professione <lb></lb>di scienze naturali, ma di sola Filosofia speculativa. </s>

<s>Tommaso Cam­<lb></lb>panella, in una sua lettera del dì 6 Luglio 1628 al Granduca Fer­<lb></lb>dinando, dice che noi italiani “ portiamo grande obbligo ai Principi <lb></lb>medicei, che facendo comparire i libri platonici in Italia, non visti <lb></lb>da&#039;nostri antichi, fur cagione di levarci dalle spalle il giogo d&#039;Ari-<pb xlink:href="020/01/137.jpg" pagenum="118"></pb>stotile, e per conseguenza poi tutti i sofisti, e cominciò l&#039;Italia ad <lb></lb>esaminare la Filosofia delle Nazioni con ragione ed esperienza nella <lb></lb>Natura, e no nelle parole degli uomini ” (MSS. Cim. </s>

<s>T. XXVI, c. </s>

<s>13). <lb></lb>La cosa è tanto vera che ha il suo pieno riscontro nei fatti da noi <lb></lb>discorsi e più in quelli che si discorreranno fra poco. </s></p><p type="main">

<s>Ma per tornare all&#039;Accademia de&#039;Lincei, le intenzioni, per quanto <lb></lb>generose fossero, dello Stelluti e del Cesi, tornarono vane, perchè <lb></lb>principalmente non era quella l&#039;opportunità nè il bisogno richie­<lb></lb>deva di convocare un Accademia. </s>

<s>Il difetto che si ritrovava allora <lb></lb>nell&#039;albero della scienza era quello stesso, che si vede negli alberi <lb></lb>naturali, quando per lunga età son trascorsi, a rimediare ai quali, <lb></lb>invece di moltiplicare i rami alla chioma e i polloni al piede, con­<lb></lb>vien reciderli, e in un tronco solo avviar l&#039;alimento e fomentarvi <lb></lb>gli spiriti vitali. </s>

<s>Non una Repubblica in altre parole conveniva isti­<lb></lb>tuire, ma un Regno assoluto, in cui risedesse la tirannica potestà <lb></lb>nelle mani di un solo. </s>

<s>Ciò non poteva ottenersi che per via di una <lb></lb>conquista, la quale veramente fu tentata in Inghilterra da Francesco <lb></lb>Bacone, ma con poco felice riuscita, si conseguì in parte da Renato <lb></lb>Cartesio in Francia, e Galileo Galilei in Italia riportò la completa <lb></lb>vittoria. </s></p><p type="main">

<s>Francesco Bacone dette al suo nuovo Regno scientifico il nome <lb></lb>d&#039;<emph type="italics"></emph>Instauratio Magna,<emph.end type="italics"></emph.end> e si credè di dover esserne investito Monarca, <lb></lb>per avere architettata l&#039;Enciclopedia d&#039;ogni scienza e arte nel libro <lb></lb><emph type="italics"></emph>De augmentis scientiarum,<emph.end type="italics"></emph.end> e per aver nel <emph type="italics"></emph>Novum Organum<emph.end type="italics"></emph.end> minu­<lb></lb>tamente divisate le regole da seguirsi nel metodo sperimentale. </s>

<s>È <lb></lb>facile però persuadersi che quella sua Monarchia non era altro che <lb></lb>di un nome vuoto, o se si vuole, di un regno già trapassato. </s>

<s>Se, <lb></lb>infatti, scienza veramente non ci è, e non ci è stata mai, come <lb></lb>vuole Bacone, egli divisa dunque nella sua Enciclopedia i loculi <lb></lb>senza avere di che riempirli. </s>

<s>E dall&#039;altro lato le regole di un arte <lb></lb>suppongono già l&#039;istituzione dell&#039;arte stessa. </s>

<s>Così, dopo gli scrittori, <lb></lb>venne la Grammatica, dopo i pittori le regole per l&#039;arte della pit­<lb></lb>tura e dopo i gran capitani le regole dell&#039;arte della guerra. </s>

<s>Nè <lb></lb>l&#039;arte di sperimentare può perciò trascendere da questa legge uni­<lb></lb>versale: ella pure suppone sperimentatori dei fatti naturali. </s>

<s>Ma nes­<lb></lb>suno, dice il Barone di Verulamio, ha saputo fin qui sperimentare <lb></lb>e osservare, e se qualcuno vi s&#039;è provato mai, avendo sbagliato <lb></lb>via, non può assicurarsi di riuscire a trovar qualche cosa di nuovo. </s></p><p type="main">

<s>Niccolò Copernico ha contemplato da filosofo il cielo, ma a noi <lb></lb>giova meglio di contemplarlo alla maniera del volgo, senza punto <pb xlink:href="020/01/138.jpg" pagenum="119"></pb>badare a quel che se ne dicano gli astronomi, o a quel che s&#039;in­<lb></lb>segni nelle scuole, che senza ragione, bene spesso, godono di con­<lb></lb>tradire al senso con sofisticherie (Nov. </s>

<s>Org. </s>

<s>Lib. </s>

<s>II, § 36). Altrove, <lb></lb>nel IV libro <emph type="italics"></emph>De augmentis scientiarum,<emph.end type="italics"></emph.end> dice che la sentenza coper­<lb></lb>nicana, come non repugnante alle apparenze, non si può confutar <lb></lb>co&#039;principii astronomici, ma si può bene coi principii della Filosofia <lb></lb>naturale <emph type="italics"></emph>recte positis<emph.end type="italics"></emph.end> (Lugani 1763, pag. </s>

<s>235). Si capisce bene che <lb></lb>i principii della Filosofia naturale invocati qui erano quegli stessi <lb></lb>de&#039;peripatetici contradittori del Copernico e del Galilei. </s></p><p type="main">

<s>Il qual Galilei, prosegue a dire il Cancellier d&#039;Inghilterra, ha <lb></lb>inventato un nuovo maraviglioso strumento, con cui è ruscito a <lb></lb>scoprir ne&#039;cieli cose non più vedute, ma chi potrebbe con sicurezza <lb></lb>prestargli fede? </s>

<s>Il mio sospetto nasce principalmente dal veder <lb></lb>poche osservazioni, mentre se ne sarebbero potute far moltissime <lb></lb>in una innumerevole varietà di oggetti (Nov. </s>

<s>Org. </s>

<s>Lib. </s>

<s>II, § 39). <lb></lb>In questo stesso errore dice di essere incorso il connazionale suo <lb></lb>Guglielmo Gilbert, il quale, da ripetute esperienze sopra un soggetto <lb></lb>solo, volle dedurne una filosofia generale, sull&#039;esempio di Aristotile, <lb></lb>e perciò una filosofia fantastica e povera, qual è quella che deriva­<lb></lb>rono i chimici dai loro alambicchi (ivi, Lib. </s>

<s>I, § 44). Egli, il Gilbert, <lb></lb>durò tanta fatica e usò tanta diligenza per venire a capo di uno <lb></lb>sperimento particolare intorno alla calamita, come gli alchimisti <lb></lb>intorno all&#039;oro (ivi, § 70). </s></p><p type="main">

<s>Ne è solo il male che nessuno fin qui abbia seguito il retto <lb></lb>filosofare, il peggio si è che Bacone prevede e presagisce che, anco <lb></lb>quando gli uomini eccitati da&#039;suoi impulsi, si daranno seriamente <lb></lb>all&#039;esperienza, rinunziando alle sofistiche dottrine, nonostante, per <lb></lb>la fretta e ansietà del loro intelletto voglioso di volare alle gene­<lb></lb>ralità, le loro filosofie soggiaceranno inevitabilmente a grave pe­<lb></lb>ricolo (ivi, § 74). Per Bacone insomma, non solo non ci è stato mai <lb></lb>scienza e non ci è, ma prevede e presagisce che nemmen ci sarà. </s>

<s><lb></lb>Ciò che vuol dire per noi che il suo Regno non è e non è per <lb></lb>venire. </s></p><p type="main">

<s>Potrebbe esser però che egli pretendesse di costituire il regno <lb></lb>della scienza col suo proprio intelletto, e perciò giova investigarne <lb></lb>le dovizie e mostrar quali e quante elle sono. </s></p><p type="main">

<s>Nel secondo libro del Nuovo Organo al § 45 descrive per ve­<lb></lb>rità alcune poche esperienze, delle quali però nessuna ha l&#039;impronta <lb></lb>di originale, da quella infuori, forse, della incompressibilità del­<lb></lb>l&#039;acqua rinchiusa dentro una sfera di metallo, che fortemente com-<pb xlink:href="020/01/139.jpg" pagenum="120"></pb>pressa da un torchio, deformata trasuda. </s>

<s>Delle altre esperienze, come <lb></lb>di quella dell&#039;aria che estratta per succhiamento dall&#039;uovo filosofico, <lb></lb>dà luogo a sottentrarvi spontaneamente l&#039;acqua, gli esempii sono anti­<lb></lb>chi, e risalgono al Cardano, anzi più su, fino ad Herone di Alessandria. </s></p><p type="main">

<s>Rispetto alle varie forze sollecitanti la materia, non si puo la­<lb></lb>sciar di notare quelle sottili osservazioni, che ricorrono in questo <lb></lb>stesso II libro al § 25, relative alle proprietà che hanno l&#039;acqua e <lb></lb>l&#039;aria, ridotte in minime particelle, di attrarsi a vicenda; e là dove <lb></lb>al § 36 entra a parlar de&#039;proietti, non è priva certo di sottilità <lb></lb>l&#039;esperienza citata delle lamine elastiche, per provar che la forza <lb></lb>d&#039;impulso non vien dall&#039;aria. </s>

<s>Ma quelle tante distinzioni di moti <lb></lb>ridotte in numero di diciannove, qui nel § 48, sono il parto e il <lb></lb>portato di una filosofia, che non è punto varia dalla aristotelica. </s></p><p type="main">

<s>Del resto, per quanto è a noi noto, non ha il Verulamio, in <lb></lb>soggetto di scienze fisiche e sperimentali, pubblicato altro libro da <lb></lb>quello in fuori che s&#039;intitola <emph type="italics"></emph>Historia naturalis et experimentalis <lb></lb>de ventis.<emph.end type="italics"></emph.end> Giacchè dunque egli ha raccolto dentro a queste pagine <lb></lb>tutto il frutto de&#039;suoi metodi elaborati, il sapore attesterà della <lb></lb>bontà dell&#039;albero che gli ha prodotti. </s>

<s>Nè la prima vista, per verità <lb></lb>ci dà liete speranze. </s>

<s>Quelle distinzioni di distinzioni prolisse e <lb></lb>ignude, come di ramo che si divide, e suddivide poi in rami aridi <lb></lb>e brulli, con qualche ciuffo di foglie in sulle cime, ci assicurano <lb></lb>non per altro esser venuto l&#039;Autore a sconfiggere Aristotile, che per <lb></lb>indossare le stesse sue divise. </s>

<s>Che poi egli ne abbia di più imbe­<lb></lb>vuti gli spiriti si parrà dall&#039;esame delle dottrine. </s></p><p type="main">

<s>La causa generale dei venti, egli dice, è il moto del cielo, <lb></lb>che rapisce e mena seco in volta la sfera dell&#039;aria. </s>

<s>Sotto i tropici, <lb></lb>per essere i circoli maggiori, il vento generale è più manifesto, ma <lb></lb>non è però che non dia luogo ai venti particolari. “ Si quis sit talis <lb></lb>ventus generalis ex ordine motus coeli, non adeo firmus est quin <lb></lb>ventis particularibus cedat. </s>

<s>Manifestior est autem intra tropicos <lb></lb>propter circulos quos conficit maiores ” (Lugd. </s>

<s>Batav. </s>

<s>1648, pa­<lb></lb>gina 15). In fin qui però non si sente nulla di nuovo, vi si ripete <lb></lb>la Fisica antica divinamente cantata dall&#039;Alighieri, nella terzina 35 <lb></lb>e 36 del XXVIII del Purgatorio. </s></p><p type="main">

<s>Più avanti però, trattando dei venti particolari o delle <emph type="italics"></emph>brezze,<emph.end type="italics"></emph.end><lb></lb>aveva sentita la possibilità che v&#039;abbia anche parte a produrle il <lb></lb>calor del sole, <emph type="italics"></emph>quia calor omnem aerem dilatat.<emph.end type="italics"></emph.end> Proseguendo poi a <lb></lb>ragionare, questa tal possibilità gli si converte in certezza, affer­<lb></lb>mando che senza dubbio è il sole causa efficiente e primaria della <pb xlink:href="020/01/140.jpg" pagenum="121"></pb>massima parte dei venti, operando per via del calore sopra duplice <lb></lb>materia, <emph type="italics"></emph>corpus scilicet aeris et vapores sive exhalationes<emph.end type="italics"></emph.end> (ivi, pa­<lb></lb>gina 53). Che sia veramente il calore efficace a produrre il vento <lb></lb>dice di averlo sperimentato in una torricella chiusa, dentro alla <lb></lb>quale ardeva un buon fuoco, osservando che girava un molinello <lb></lb>fatto di piume sospeso a un filo, e che usciva fuori con forza il <lb></lb>fiato da uno spiraglio. </s></p><p type="main">

<s>Che poi sia varia la materia de&#039;venti, aria cioè e vapori, e che <lb></lb>da ciò si produca varietà di effetti, intende a provarlo pure col­<lb></lb>l&#039;esperienza, rinchiudendo nella medesima torricella, un vaso pieno <lb></lb>d&#039;acqua bollente, che esala vapori in copia. </s>

<s>Dice di avere osservato <lb></lb>che il molinello girava ancora mosso dal fumo, però più languida­<lb></lb>mente assai di quando ardeva il fuoco vivo, e l&#039;esalazione spiritosa <lb></lb>era secca. </s>

<s>Ond&#039;egli così conclude: “ Itaque excitationes motus in <lb></lb>ventis causa est praecipua superesoneratio aeris ex nova acces­<lb></lb>sione aeris facti ex vaporibus ” (ivi, pag. </s>

<s>65). </s></p><p type="main">

<s>Che si può ora egli giudicare di questa teoria, se non che ad <lb></lb>essa manca un principio generale che l&#039;informa, rimanendo, al <lb></lb>modo aristotelico, sminuzzata ne&#039;fatti particolari? </s>

<s>Bacone insomma <lb></lb>non seppe sollevarsi a veder quel che chiarissimamente poi vide il <lb></lb>Torricelli, che cioè dai condensamenti e dalle dilatazioni dell&#039;aria <lb></lb>prodotte dal variar dell&#039;intensità calorifica del sole, hanno, come <lb></lb>da causa generale semplice e unica, origine ogni sorta di venti. </s></p><p type="main">

<s>Il tesoro dunque del gran Cancelliere non par che sia troppo <lb></lb>dovizioso, almeno quanto a scienza sperimentale. </s>

<s>Che se si fosse <lb></lb>dovuta una tale scienza promuovere da lui solo, potremmo star si­<lb></lb>curi che la non avrebbe fatto nemmeno un passo per uscir fuori <lb></lb>de&#039;libri del Filosofo antico. </s>

<s>Molti che convengono in questo giudizio, <lb></lb>danno però il merito all&#039;Autor <emph type="italics"></emph>De augmentis<emph.end type="italics"></emph.end> d&#039;aver profondamente <lb></lb>filosofato intorno alle ragioni de&#039;progressi sperimentali. </s>

<s>Nè ciò si <lb></lb>nega da noi, si vuol dir solo che spesso, in queste stesse filosofiche <lb></lb>speculazioni, manca quel giudizioso acume e quell&#039;ampiezza di ve­<lb></lb>dute, che qualificano i veri innovatori della scienza. </s>

<s>Si veda, per <lb></lb>esempio quel che nel cap. </s>

<s>IV del III libro dice delle cause finali. </s>

<s><lb></lb>Che queste, sostituendosi alle cause fisiche e reali, abbiano vera­<lb></lb>mente indugiati i progressi della scienza, si comprende assai facil­<lb></lb>mente e si consente da tutti. </s>

<s>Non si consente però al Verulamio <lb></lb>il dir che, nella filosofia di Aristotile e di Platone, s&#039;inculcano quelle <lb></lb>cause finali allo stesso modo, contentandosi di ammetter come sola <lb></lb>differenza una reità maggiore nel discepolo che nel maestro. </s></p><pb xlink:href="020/01/141.jpg" pagenum="122"></pb><p type="main">

<s>Ma il vero si è, che le cause finali son parto legittimo ed esclu­<lb></lb>sivo della filosofia aristotelica, di quella filosofia cioè che accomoda <lb></lb>la Natura ai cervelli. </s>

<s>Perchè, secondo il Cremonino, non possono <lb></lb>esistere i satelliti di Giove? </s>

<s>Perchè non s&#039;intenderebbe altrimenti <lb></lb>quali potessero essere i loro influssi. </s>

<s>Perchè il canal toracico si <lb></lb>nega dal Riolano? </s>

<s>Perchè non s&#039;intende come mai il chilo crudo <lb></lb>e non concotto nel fegato debba, per una via lunga, risalir su fino <lb></lb>alla vena cava ascendente, mentre pel fegato e per la cava discen­<lb></lb>dente la via è tanto più facile e più spedita. </s></p><p type="main">

<s>La Filosofia di Platone, che ammetteva Dio legislatore della <lb></lb>Natura, non era punto favorevole, nè come vuol Bacone, inculcava <lb></lb>le cause finali, ma là dove le cause fisiche riuscivano ignote, s&#039;at­<lb></lb>tribuivano gli effetti immediatamente a Dio stesso Prima Causa <lb></lb>universale. </s>

<s>Ora, se ben si osserva, è conforme ai placiti di questa <lb></lb>Filosofia il processo storico <emph type="italics"></emph>De augmentis scientiarum.<emph.end type="italics"></emph.end> Così per <lb></lb>esempio in fatto di Cosmoteoria, la scienza antica attribuiva il moto <lb></lb>circolare de&#039;pianeti immediatamente alla mano di Dio, che gli so­<lb></lb>stenta e gli mantiene ne&#039;loro orbi. </s>

<s>Il Boulliaud dopo Galileo intro­<lb></lb>dusse il moto naturale de&#039;corpi cadenti, e il Borelli il principio <lb></lb>delle forze centrali, ma è sempre il dito di Dio che volge i moti <lb></lb>diretti in circolari, e determina a suo placito l&#039;eccentricità delle <lb></lb>orbite ellittiche. </s>

<s>Il Newtòn poi dimostra che quella eccentricità è <lb></lb>determinata dal grado dell&#039;intension delle forze attrattive e repul­<lb></lb>sive. </s>

<s>Così, progredendo la scienza col sostituire via via la cause fisiche <lb></lb>e particolari, non si sentì, ai tempi del Filosofo inglese, bisogno di <lb></lb>ricorrere alla Causa prima per altro, che per ispiegiar l&#039;origine <lb></lb>dell&#039;attrazione universale. </s>

<s>Par che con simile processo la scienza <lb></lb>insegua e cacci dalla Natura Iddio, ma non fa in sostanza che ri­<lb></lb>durlo sempre più su nella Maestà della sua sede. </s></p><p type="main">

<s>Grande è dunque la differenza tra le due filosofie, che il Ve­<lb></lb>rulamio accusa della medesima colpa, e il non avere avvertito questa <lb></lb>tal differenza, è uno di que&#039;difetti notabili in un filosofo, il quale <lb></lb>vuole insegnare al mondo ignorante il modo d&#039;investigar le vie, <lb></lb>che conducon la mente dell&#039;uomo o a scoprir la verità o a cader <lb></lb>nell&#039;errore. </s></p><p type="main">

<s>Dalle cose fin qui discorse perciò si conclude che il vantato <lb></lb>Instauratore inglese non promosse veramente le scienze sperimen­<lb></lb>tali, nè coll&#039;esempio nè colle dottrine. </s>

<s>Ma non per questo si po­<lb></lb>trebbe con giustizia asserire che i libri scritti da lui non avesser <lb></lb>nessuna efficacia, specie sulla mente de&#039;suoi connazionali. </s>

<s>Il Boyle, <pb xlink:href="020/01/142.jpg" pagenum="123"></pb>l&#039;Hook il Wren si sentirono venir l&#039;impulso a filosofare dalla let­<lb></lb>tura di que&#039;libri, ma niente altro è che la loro facondia, la quale <lb></lb>gli commuove: è quella voce potente di un che grida nella solitu­<lb></lb>dine: lasciate i sofismi e studiate la Natura. </s>

<s>Di questa efficacia in <lb></lb>fuori, che egli ebbe sui contemporanei e sui discendenti, Bacone è <lb></lb>un filosofo de&#039;tempi passati imbevuto di quegli spiriti aristotelici, <lb></lb>che egli, sotto le forme di un razionalismo medio fra quello del <lb></lb>Campanella e del Patrizio, largamente diffonde in tutti i suoi libri. </s>

<s><lb></lb>All&#039;albero perciò della scienza, per troppo lunga età trascorso e <lb></lb>infiacchito, non solo egli non ha saputo trovare efficace rimedio da <lb></lb>ringiovanirlo, ma ne ha di più esaurite le forze col moltiplicare le <lb></lb>sterili fronde sul ramo vecchio. </s>

<s>Sicchè non riman che l&#039;opera sola <lb></lb>fatta da Galileo e dal Cartesio, l&#039;azion de&#039;quali che ora si vuol <lb></lb>mettere in vista de&#039;nostri lettori, fa mutare scena alla rappresen­<lb></lb>tazione di questo Dramma. </s></p><pb xlink:href="020/01/143.jpg" pagenum="124"></pb><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nota I relativa a pag. </s>

<s>69 lin. </s>

<s>19.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Di questi problemi, ci piace qui di recarne uno per saggio ai nostri lettori, e ab­<lb></lb>biamo scelto il seguente, a mostrar come si possa rendere più compiuta la illustrazione <lb></lb>data nella prima delle <emph type="italics"></emph>Lettere astronomiche<emph.end type="italics"></emph.end> credute di Galileo, e pubblicate, da pa­<lb></lb>gina 135-44, negli <emph type="italics"></emph>Studii sulla Divina Commedia<emph.end type="italics"></emph.end> da Ottavio Gigli (Firenze, Le Mon­<lb></lb>nier, 1885). </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Problema di Astronomia dantesca:<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><lb></lb>Si come quando i primi raggi vibra, <lb></lb>La dove il suo Fattore il sangue sparse <lb></lb>(Cadendo Ibero sotto l&#039;alta libra). <lb></lb>E l&#039;onde in Gange, da nona riarse; <lb></lb>Si stava il Sole; onde il giorno sen gia, <lb></lb>Quando l&#039;Angel di Dio lieto ci apparse. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>(Purg.,<emph.end type="italics"></emph.end> C. XXVIII, t. </s>

<s>1, 2).<emph.end type="center"></emph.end></s></p><p type="main">

<s>Posto che, a muovere dall&#039;Isole Fortunate, ora Canarie, la longitudine della fonte <lb></lb>dell&#039;Ibero sia 12° 30′, e 16° la longitudine della sua foce; posto che sia 66° la longi­<lb></lb>tudine di Gerusalemme, e 148° 30′ quella della foce più orientale del Gange; si domanda <lb></lb><emph type="italics"></emph>come stava,<emph.end type="italics"></emph.end> secondo la descrizione fattane dal Poeta, il sole rispetto all&#039;orizzonte del <lb></lb>Purgatorio o di Gerusalemme? </s></p><p type="main">

<s>Rappresenti il gran cerchio AEDF (fig. </s>

<s>I) l&#039;Equatore celeste, e il piccolo cerchio <lb></lb><figure id="id.020.01.143.1.jpg" xlink:href="020/01/143/1.jpg"></figure></s></p><p type="caption">

<s>Fig. </s>

<s>I<lb></lb>HSGT concentrico a lui, un cerchio massimo della Terra. </s>

<s><lb></lb>Sia P il polo, PL il meridiano principale delle Isole Fortu­<lb></lb>nate, PM il meridiano, che passa sull&#039;Ibero e per la Libbra, <lb></lb>PN quello che passa sulla foce del Gange, PO il meridiano del <lb></lb>sole, nel tempo a cui si riferisce l&#039;osservazione, e AHD il <lb></lb>meridiano comune al Purgatorio e a Gerusalemme. </s>

<s>Si cerca <lb></lb>l&#039;angolo FPO=FDE—EDO=180°—EDO. </s>

<s>Ma EDO= <lb></lb>EL+LM+MO perciò, a risolvere il problema, conviene <lb></lb>cercare i tre angoli che compongono il secondo membro di <lb></lb>questa equazione: EL=90°—LD=90—66=24. LM <lb></lb>potrebbe tanto farsi uguale a 12° 30′, quanto a 16° non di­<lb></lb>cendo nulla il Poeta che accenni, dell&#039;Ibero, o alla sorgente o alla foce. </s>

<s>Ma osservando <lb></lb>anche noi con Galileo (ivi, pag. </s>

<s>135) che <emph type="italics"></emph>caggiono propriamente i fiumi dalle loro <lb></lb>fonti,<emph.end type="italics"></emph.end> crediamo di poter fare LM=12°, 30′, MO, dall&#039;altra parte, è uguale a 360°—OAM, <lb></lb>e quest&#039;angolo OAM sarebbe l&#039;ascensione retta di un punto M, o di una delle stelle, in <lb></lb>cui si configura la Libbra. </s>

<s>Qui sembra anche a noi con Galileo d&#039;avere un indizio più <lb></lb>certo, imperocchè, dando il Poeta l&#039;epiteto di <emph type="italics"></emph>alta<emph.end type="italics"></emph.end> alla Libbra, par chiaro volere accen­<lb></lb>nare alla lance di lei più settentrionale, e di questa lance più settentrionale, alla stella <lb></lb>più cospicua. </s>

<s>Nelle <emph type="italics"></emph>Tavole alfonsine,<emph.end type="italics"></emph.end> delle quali si dovette anche Dante servire, si re­<lb></lb>gistra, del bacino settentrionale della Libbra, una stella di seconda grandezza, la quale <pb xlink:href="020/01/144.jpg" pagenum="125"></pb>aveva allora 221° di longitudine e di latitudine 8° 30′. </s>

<s>A questa stella par doversi riferire <lb></lb>il meridiano, al quale accenna il Poeta. </s>

<s>Ond&#039;è che posto <foreign lang="grc">ι</foreign>=221, <foreign lang="grc">λ</foreign>=8°, 30′, <foreign lang="grc">ε</foreign>=23°, 30′, <lb></lb>si potrà colle ordinarie formule date dai <emph type="italics"></emph>Formularii<emph.end type="italics"></emph.end> di Trigonometria cos.P=cos.<foreign lang="grc">Ι</foreign>.cos.<foreign lang="grc">λ</foreign>, <lb></lb>tang <foreign lang="grc">φ</foreign>=(tang.<foreign lang="grc">λ</foreign>)/(sen <foreign lang="grc">ι</foreign>), tang.<foreign lang="grc">α</foreign>=tang.<foreign lang="grc">φ</foreign> cos (<foreign lang="grc">ε</foreign>+<foreign lang="grc">φ</foreign>), calcolare OAM=<foreign lang="grc">α</foreign>, che, eseguiti con­<lb></lb>venientemente i calcoli, si troverà uguale a 221°, 13′. </s>

<s>Perciò avremo MO=138° 47′, <lb></lb>EDO=175° 17′, FO=4° 43′. </s>

<s>Onde il sole, quando l&#039;Angel di Dio apparse ai Poeti, <lb></lb><emph type="italics"></emph>stava<emph.end type="italics"></emph.end> così: era alto cioè 4° 43′ sull&#039;orizzonte di Gerusalemme. </s></p><p type="main">

<s>Sarebbe così tutto bene aggiustato, per modo che l&#039;interpretazione astronomica, la <lb></lb>quale abbiamo data sulle orme di Galileo, risponderebbe a tutte le parti della descrizione <lb></lb>fatta nelle due sopra citate terzine dal Poeta, imperocchè PN, meridiano che passa per <lb></lb>la foce del Gange non sarebbe lontano da PO, meridiano del Sole, che di soli 2° 47′; <lb></lb>onde s&#039;accomoda, anco per questa parte, l&#039;interpretazione astronomica a quel che sog­<lb></lb>giunge alla sua descrizione il Poeta: <emph type="italics"></emph>E l&#039;onde in Gange da nona riarse.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Se non che ci si fanno qui incontro alcune difficoltà. </s>

<s>Come mai poteva dire il Poeta <lb></lb>che il sole vibrava i primi raggi sui colli di Gerusalemme, essendo già alto più di quattro <lb></lb>gradi e mezzo sull&#039;orizzonte? </s>

<s>Di più, noi abbiamo supposto con Galileo che fosse il sole <lb></lb>nel punto preciso dell&#039;Equinozio di Primavera. </s>

<s>Ma è ciò contrario all&#039;opinione di tutti <lb></lb>quanti i commentatori, i quali dicono che a tempo dell&#039;Equinozio incomincia la rappre­<lb></lb>sentazione del Dramma, e che la scena, la quale qui si dipinge, dovette seguire almeno <lb></lb>tre o quattro giorni dopo, nel qual tempo si doveva il sole esser dilungato da quel punto <lb></lb>equinoziale, in longitudine, tre o quattro gradi. </s></p><p type="main">

<s>Le difficoltà a noi sembrano giuste, ond&#039;è che proporremmo di riformare l&#039;inter­<lb></lb>pretazione galileiana al modo seguente. </s>

<s>Osservando che anche Gerusalemme è situata in <lb></lb>altura, e che è contrapposta, nella fantasia del Poeta, alla montagna altissima del Purga­<lb></lb>torio, ci sembra assai ragionevole che, com&#039;egli mise in conto una notevole depressione <lb></lb>dell&#039;orizzonte per l&#039;una, così qualche depressione dovesse pure mettere in conto per <lb></lb>l&#039;altra. </s>

<s>Immaginiamo perciò che sulla vetta delle più alte torri di Gerusalemme inco­<lb></lb>minciasse il sole a vibrare i suoi raggi, quand&#039;era ancora di 1° 17′ sotto all&#039;orizzonte <lb></lb>razionale. </s>

<s>In questa ipotesi, ritenute tutte le altre parti della dimostrazione, si potrebbe <lb></lb>dare al sole sei gradi di ascensione retta, i quali, calcolando la formula tang. </s>

<s>c=. . . <lb></lb>tang. </s>

<s>a cos. </s>

<s>B, si trovano corrispondere a 4° 9′ di longitudine. </s>

<s>Così rimarrebbero, come <lb></lb>sopra, tutte le partt aggiustate, nè sarebbe a dubitar che non si potesse, con quella posizione <lb></lb>del sole, accordar l&#039;effetto del riardere l&#039;onde del Gange, perchè l&#039;ora di nona, com­<lb></lb>prendendo le prime sei ore avanti mezzogiorno, comprende certamente anco quella, nella <lb></lb>quale si trova il sole sei gradi di distanza dal meridiano, e potea perciò ben dire il Poeta <lb></lb>che in quella posizione del sole le onde del Gange eran riarse dall&#039;ore di nona. </s></p><p type="main">

<s>Se l&#039;aver concordate così tutte quante le parti astronomiche e geografiche della de­<lb></lb>scrizione dantesca, ci potesse assicurare della verità della nostra interpetrazione, avremmo <lb></lb>di qui un dato certo a poter inferire il mese e il giorno preciso, nel quale immagina il <lb></lb>Poeta essersi rappresentata la scena. </s>

<s>Poniamo, infatti, secondo la più probabile e più co­<lb></lb>mune opinione, che fosse il 1300 l&#039;anno della visione dantesca. </s>

<s>Quando l&#039;Angel di Dio <lb></lb>apparse ai Poeti, abbiam veduto che il sole dovea avere 4° 9′ in longitudine, e dovevan <lb></lb>perciò esser trascorsi più di quattro giorni, da quello in cui entra il sole nel punto di <lb></lb>Primavera. </s>

<s>Se, come a noi, così ai tempi di Dante, fosse entrata la Primavera il dì 21 di <lb></lb>Marzo, è certo che la scena descritta nel XXVII del Purgatorio, si sarebbe rappresentata <lb></lb>la sera del dì 25 di quello stesso mese. </s>

<s>Ma per que&#039;disordini cronologici, che hanno la <lb></lb>loro origine in quella parte frammentaria de&#039;giorni, ne&#039;quali compiesi la tropica rivolu-<pb xlink:href="020/01/145.jpg" pagenum="126"></pb>zione del sole, disordini non potuti evitare dagli emendamenti giuliani; nel 1300 doveva <lb></lb>l&#039;Equinozio di Primavera precedere il dì 21 di Marzo di alquanti giorni. </s>

<s>Il numero poi <lb></lb>preciso di questi giorni si trova assai facilmente osservando che, dall&#039;anno 325 in cui <lb></lb>l&#039;Equinozio di Primavera cadde il dì 21 Marzo, al 1300, decorsero 975 giorni, ne&#039;quali <lb></lb>s&#039;aggiunsero, secondo il calendario giuliano, 243 bisestili. </s>

<s>Ma secondo la riforma nuova <lb></lb>gregoriana i bisestili da aggiungere dovevano essere non 975/4, ma (975X125)/516, ossia 236; <lb></lb>ond&#039;è che nel 1300 l&#039;Equinozio di Primavera precedeva il dì 21 di 7 giorni, e che è <lb></lb>lo stesso, avveniva quell&#039;Equinozio il dì 14 di Marzo, e perciò la scena, che Dante lì <lb></lb>rappresenta, si dovrebbe precisamente riferire alla sera del dì 18 di Marzo. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nota II relativa a pag. </s>

<s>82 lin. </s>

<s>37.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Perchè abbiano i lettori qualche saggio degli errori, in che incorse il Mollien per <lb></lb>ragion della lingua, citeremo il seguente passo, prima nell&#039;ortografia originale, poi ridetto <lb></lb>da noi all&#039;ortografia moderna, poi dallo stessio Mollien tradotto in francese. </s></p><p type="main">

<s>“ eglie . un pozo . il quale . a nel suo fondo unotro . di tal . grandezza e intal <lb></lb>modo . situato . che disotto . e dalato . non sitrova più . duno dito . di grossezza dacqua . <lb></lb>imodo chellacqua che si posa sul fondo pesa . libbre 100 . e quella chessiposa . sopra . <lb></lb>della baga . pesa libbre 10000 . se cosie la baga scopiera avendo soprasse . tanto peso . <lb></lb>esequel peso . nolla prieme . chello sostiene . esseppure esso fussi sostenuto . perche <lb></lb>arebbe appassare . l&#039;otro sopra . l&#039;acqua . esseppure lacqua charicha . sopra . il suo . <lb></lb>fondo . perche non patisce passione unomo (<emph type="italics"></emph>menomo<emph.end type="italics"></emph.end> intende il Mollien!) passione . di <lb></lb>peso . stando . sopra il suo fondo . adunque sella ba sostiene lacqua la baga . toglie il <lb></lb>peso . dessa acqua . alfondo . del pozzo ”. </s></p><p type="main">

<s>“ Egli è un pozzo, il quale ha nel suo fondo un otro di tal grandezza e in tal <lb></lb>modo situato, che di sotto e da lato non si trova più di un dito di grossezza d&#039;acqua, <lb></lb>in modo che l&#039;acqua che riposa sul fondo pesa libbre 100, e quella che si posa sopra <lb></lb>della baga pesa libbre 10,000. Se così è la baga scoppierà avendo sopra sè tanto peso. </s>

<s><lb></lb>E se quel peso non la preme, che lo sostiene? </s>

<s>E se pure esso fussi sostenuto, perchè <lb></lb>avrebbe a passare l&#039;otro sopra l&#039;acqua? </s>

<s>E se pure l&#039;acqua carica sopra il suo fondo, per­<lb></lb>chè non patisce passione un uomo, passione di peso, stando sopra il suo fondo? </s>

<s>Adunque <lb></lb>se la baga sostiene l&#039;acqua, la baga toglie il peso di essa acqua al fondo del pozzo. </s>

<s>” </s></p><p type="main">

<s>“ Il y è un puits, le qual a dans sons fonds une outre, de telle grandeur et situee <lb></lb>di telle fac<gap></gap>n, que dessous et sur les cotes, ne se trouve pas plus d&#039;un doigt d&#039;<gap></gap>paisseur <lb></lb>d&#039;eau. </s>

<s>l&#039;<emph type="italics"></emph>eau<emph.end type="italics"></emph.end> en sorte que l&#039;eau qui se pose sur le fond pèse 100 livres et celle qui pose <lb></lb>au-dessus de l&#039;outre pèse 10,000 livres; s&#039;il en est ainsi, l&#039;outre celetera. </s>

<s>en ayant sur <lb></lb>elle <emph type="italics"></emph>cette<emph.end type="italics"></emph.end> un tel poids, et si ce poids ne la presse pas qu&#039;elle soutient, et si aussi il etait <lb></lb>soutenou, parce que l&#039;outre avrait a passer au-dessus de l&#039;eau, et aussi si l&#039;eau charge <lb></lb>(pèse) sur son fond, parce qu&#039;elle ne supportarien, ne supporte qu&#039;un moindre poids, <lb></lb>ètant sur son fond. </s>

<s>Donc, si l&#039;outre soutient l&#039;eau, l&#039;outre ôte le poids de cette eau au <lb></lb>fond du puits. </s>

<s>” (Manos. </s>

<s>A fol. </s>

<s>25 verso). </s></p><pb xlink:href="020/01/146.jpg"></pb><p type="main">

<s><emph type="center"></emph>PARTE SECONDA<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Di Galileo Galilei e dell&#039;indole propria della sua nuova Instaurazione scientifica. </s>

<s>— II. </s>

<s>Si giustifi­<lb></lb>cano le cose asserite nel paragrafo precedente. </s>

<s>— III. </s>

<s>Dei benefizi che derivarono alle scienze <lb></lb>sperimentali dalla nuova Instaurazione galileiana. </s>

<s>— IV. </s>

<s>Renato Cartesio. </s>

<s>— V. De&#039;primi e <lb></lb>principali discepoli di Galileo. </s>

<s>— VI. </s>

<s>Della grande esperienza torricelliana dell&#039;argento vivo, e <lb></lb>come per lei si diffondessero, d&#039;Italia in tutta Europa, l&#039;amore e gli esercizi dell&#039;arte speri­<lb></lb>mentale. </s>

<s>— VII. </s>

<s>Di Evangelista Torricelli e di Vincenzio Viviani, e di ciò che operassero nelle <lb></lb>Instituzioni della sperimentale Accademia Medicea. </s>

<s>— VIII. </s>

<s>Del primo periodo della Fiorentina <lb></lb>Accademia del Cimento. </s>

<s>— IX. </s>

<s>Del secondo periodo della Fiorentina Accademia del Cimento. </s>

<s>— <lb></lb>X. </s>

<s>Delle principali Accademie private istituite in Italia a imitazione di quella del Cimento; del <lb></lb>felice esito dell&#039;Istituzione Medicea, nonostante le rivalità con gli stranieri, i dissensi fra i Socii, <lb></lb>le opposizioni dei Peripatetici. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Egli è verissimo che tutte le cose del mondo son soggette a <lb></lb>invecchiare, e invecchiando andare irreparabilmente alla morte. </s>

<s>Non <lb></lb>vi è perciò altro rimedio per loro, che quello di tentare di ringio­<lb></lb>vanirle e, il miglior modo a far ciò, trattandosi d&#039;istituzioni umane, <lb></lb>disse argutamente il Machiavelli che consisteva nel ritirarle verso <lb></lb>i loro principii. </s>

<s>L&#039;esempio che s&#039;adduceva dianzi degli alberi tra­<lb></lb>scorsi, i quali si ringiovaniscono recidendo i rami e talvolta lo stesso <lb></lb>tronco infino al piede, commenta le dottrine del Segretario fioren­<lb></lb>tino, secondo le quali un principato, che va a dissolversi, ringio­<lb></lb>vanisce spesso per via di una tirannide. </s></p><p type="main">

<s>Per una tirannide o per una conquista, in quella che è delle <lb></lb>nobilissime fra le istituzioni umane, si qualificò da noi sopra l&#039;opera <pb xlink:href="020/01/147.jpg" pagenum="128"></pb>di Galileo, il quale volle scrivere in una cocca del suo vessillo queste <lb></lb>parole: <emph type="italics"></emph>Molti si pregiano di aver molte autorità d&#039;uomini per con­<lb></lb>fermazione delle loro opinioni, ed io vorrei essere stato il PRIMO <lb></lb>e il SOLO a trovarle.<emph.end type="italics"></emph.end> Abbiamo detto in una cocca, perchè spie­<lb></lb>gatamente in campo non sarebbero state lette tali parole dagli occhi <lb></lb>abbagliati de&#039;riguardanti, se gli editori non le avessero accolte in <lb></lb>una nota apposta a piè di pagina (Alb. </s>

<s>I, 440). Ma che giova l&#039;espres­<lb></lb>sione delle parole, se d&#039;ogni parte si sente alitar quello spirito di <lb></lb>conquista proprio di un che ha fermo oramai di voler essere in <lb></lb>tutto il <emph type="italics"></emph>primo<emph.end type="italics"></emph.end> e il <emph type="italics"></emph>solo?<emph.end type="italics"></emph.end></s></p><p type="main">

<s>I fatti che saranno candidamente narrati, nelle varie parti di <lb></lb>questa Storia, mostrano que&#039;propositi fermi coraggiosamente man­<lb></lb>dati ad effetto, ma perchè troppo importa a noi di rappresentar fin <lb></lb>d&#039;ora al giudizio dei nostri lettori l&#039;opera galileiana sotto l&#039;aspetto <lb></lb>di una conquista, e troppo ci preme di persuader fin d&#039;ora i ritrosi <lb></lb>esser quello il vero aspetto, sotto cui s&#039;appresenta la nuova instau­<lb></lb>razione scientifica, crederemmo di dover esser notati d&#039;imprudenza, <lb></lb>asserendo cose tanto lontane dalla comune opinione, senza preva­<lb></lb>lerci di qualche discorso da servirsene come di prova. </s></p><p type="main">

<s>Bacone scrive in un luogo del suo libro <emph type="italics"></emph>De augmentis scien­<lb></lb>tiarum<emph.end type="italics"></emph.end> che non parve ad Aristotile potersi bene assicurare del <lb></lb>Regno, <emph type="italics"></emph>nisi, more Ottomannorum, fratres suos omnes contruci­<lb></lb>dasset<emph.end type="italics"></emph.end> (Lugani 1763, Part. </s>

<s>I, pag. </s>

<s>211), e son, secondo il Verulamio, <lb></lb>de&#039;più illustri fra que&#039;trucidati fratelli, Pitagora, Filolao, Xenofane, <lb></lb>Anassagora, Parmenide, Leucippo, Democrito. </s>

<s>Aveva così Galileo, <lb></lb>della Tirannide che meditava d&#039;ìnstaurare, nello stesso Aristotile, <lb></lb>un esempio di tanto felice riuscita, che in ogni modo conveniva <lb></lb>imitare. </s></p><p type="main">

<s>Platone e Archimede son tanto lontani e tanto innocui, che <lb></lb>non gli turbano i sonni. </s>

<s>Ma glieli turba bene Ticone, glieli turba <lb></lb>il Keplero, i quali ambedue, a voler regnar solo, bisogna contru­<lb></lb>cidare. </s>

<s>E benchè non si convenga, nè sia espediente tenere il modo <lb></lb>degli Ottomanni, son dirette pure a trapassare il cuore, colle loro <lb></lb>acute punte, e a trafigger Ticone quelle parole di Galileo, nelle <lb></lb>quali scrive del grande Astronomo danese, che calcolò le Tavole <lb></lb>Rodolfine, senza punto intender nè l&#039;Almagesto di Tolomeo nè le <lb></lb>Rivoluzioni del Copernico, e che non sapeva neanco i primi ele­<lb></lb>menti di Geometria (Alb. </s>

<s>VI, 329). Che se egli, e il suo seguace e <lb></lb>ammiratore Keplero, credessero di toglierli di mano lo scettro, non <lb></lb>gli fanno spavento que&#039;due <emph type="italics"></emph>Primati:<emph.end type="italics"></emph.end> egli gli assicura d&#039;aver tanto <pb xlink:href="020/01/148.jpg" pagenum="129"></pb>valore da sentirsi crescere il coraggio a seguitar contro a loro la <lb></lb>intrapresa conquista (ivi, pag. </s>

<s>310). </s></p><p type="main">

<s>Ma il Keplero, per verità, era uno di quei giganti da non ce­<lb></lb>dere al primo colpo, per cui, meglio che il ferro tagliente e nudo, <lb></lb>conobbe Galileo che avrebbe servito bene il veleno confettato con <lb></lb>arte per toglierli l&#039;amaro. </s>

<s>Una fra le tante di così fatte confezioni <lb></lb><figure id="id.020.01.148.1.jpg" xlink:href="020/01/148/1.jpg"></figure><lb></lb>è quella che ha nell&#039;ultimo Dialogo dei Due Massimi Sistemi, dove <lb></lb>l&#039;influenze della Luna sulla marea, sagacemente indovinate dal­<lb></lb>l&#039;Alemanno, <emph type="italics"></emph>ingegno libero e acuto,<emph.end type="italics"></emph.end> sono annoverate fra le altre <lb></lb><emph type="italics"></emph>fanciullezze<emph.end type="italics"></emph.end> (Alb. </s>

<s>I, 499). E perchè, anco le confezioni più avvele­<lb></lb>nate, quello era tale stomaco da digerirle, Galileo si risolvè di esi­<lb></lb>liar quell&#039;ombra paurosa da&#039;suoi confini, dichiarando di non aver <pb xlink:href="020/01/149.jpg" pagenum="130"></pb>nulla a che rivedere con lui. </s>

<s>Che se talvolta s&#039;incontra in qualche <lb></lb>concetto simile, afferma esser ciò tanto avvenuto di rado, da non <lb></lb>si verificare di uno in cento de&#039;suoi pensieri (Alb. </s>

<s>VII, 56). </s></p><p type="main">

<s>Quell&#039;esilio, dall&#039;altra parte, è decretato con editto irrevoca­<lb></lb>bile. </s>

<s>L&#039;Autore del Commentario sulla stella di Marte, dimostra co­<lb></lb>me cosa di fatto, che le orbite dei pianeti sono ellittiche. </s>

<s>Ma Ga­<lb></lb>lileo non si rimuove dalla platonica perfezione delle orbite circolari. </s>

<s><lb></lb>L&#039;Autore dei Paralipomeni a Vitellione, dimostra ad evidenza, per, <lb></lb>ciò che si sperimenta nella camera oscura, che le immagini si di­<lb></lb>pingono rovesciate sulla retina, ma Galileo persiste nelle viete gale­<lb></lb>niche dottrine, a seconda delle quali il luogo, dove si rappresentan <lb></lb>diritte le immagini, è il centro della pupilla, ossia il cristallino. </s>

<s><lb></lb>L&#039;Autore della <emph type="italics"></emph>Diottrica<emph.end type="italics"></emph.end> aveva divisate le leggi del rifrangersi i <lb></lb>raggi luminosi nelle lenti concave e nelle convesse, e s&#039;era, per <lb></lb>teoria, incontrato nella scoperta del canocchiale astronomico, ma <lb></lb>Galileo dice al Tarde che quel Trattatello è così oscuro, da non <lb></lb>restarne sodisfatto nemmeno l&#039;Autore stesso. </s></p><p type="main">

<s>Che il Kepler non tutto abbia dimostrato e concluso con chia­<lb></lb>rezza, potrebbe anco esser vero. </s>

<s>Ma vero certamente non è quel che <lb></lb>Galileo stesso soggiungeva non aver nel 1614, quand&#039;ebbe quel col­<lb></lb>loquio col Tarde, nessuno ancora scritto della teoria del canocchiale. </s>

<s><lb></lb>Ne aveva già scritto il De Dominis, il Trattato del quale gli fu spe­<lb></lb>dito a Firenze dal Sagredo (Alb. </s>

<s>Supplem. </s>

<s>pag. </s>

<s>58), e ne aveva in <lb></lb>certo modo scritto anco il Maurolico, benchè non trattasse propria­<lb></lb>mente delle lenti composte nel canocchiale, ma della diottrica delle <lb></lb>lenti separate, in quel libretto postumo che vide, nel 1611, la luce <lb></lb>insiem con quello del De Dominis e del Keplero. </s></p><p type="main">

<s>L&#039;esilio dunque, a quel che pare, è bandito contro di tutti <lb></lb>senza eccezione, e basta legger le Opere di Galileo per vederne <lb></lb>eseguito il decreto. </s>

<s>Egli non ha, e non riconosce maestro: nessuno <lb></lb>dee venirgli innanzi a dir che egli abbia scoperto qualche cosa di <lb></lb>nuovo: tutte le nuove scoperte vuole averle fatte da sè, il primo <lb></lb>e il solo. </s>

<s>Gli si cita dal Sarsi il Cardano e il Telesio: quel che <lb></lb>abbiano scritto, risponde, il Cardano e il Telesio, io non l&#039;ho veduto <lb></lb>(Alb. </s>

<s>IV, 178). Non ha veduto o fa vista di non aver veduto il Tar­<lb></lb>taglia, che fu de&#039;primi a notare gli errori meccanici di Aristotile, <lb></lb>e a porre i fondamenti alla teoria e alla pratica de&#039;proietti, non <lb></lb>ha veduto il Fracastoro, che al corso obliquo del sole applicava il <lb></lb>teorema della composizione dei moti. </s></p><p type="main">

<s>Lorenzo Crasso fra gli Elogi degli uomini letterati raccolse an-<pb xlink:href="020/01/150.jpg" pagenum="131"></pb>che quello di Galileo, e ce lo rappresenta timido in dar fuori i suoi <lb></lb>sentimenti circa la Filosofia Naturale, i quali vuol che egli cavasse <lb></lb>da Celio Calcagnini e dal Patrizio. </s>

<s>Michelangiolo Ricci, l&#039;amico e <lb></lb>il Discepolo prediletto del Torricelli, e il consultore dell&#039;Accademia <lb></lb>del Cimento, in una lettera al principe Leopoldo dei Medici, rim­<lb></lb>provera l&#039;Autore di quegli Elogi per aver taciuto di annoverare <lb></lb>fra&#039;maestri di Galileo il Benedetti, <emph type="italics"></emph>che gli aprì la strada più che <lb></lb>ogni altro e forse fu solo a lui scorta nel suo filosofare, come avrà <lb></lb>ben notato V. A. paragonando i concetti dell&#039;uno e dell&#039;altro che <lb></lb>sono tanto conformi.<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Cim. </s>

<s>XVIII, 359). </s></p><p type="main">

<s>I nostri lettori, i quali hanno passato in esame con noi, di so­<lb></lb>pra, il libro delle Speculazioni del Fisico veneziano, sentono la ve­<lb></lb>rità del giudizio del Ricci, e dall&#039;altra parte chi collaziona le parole <lb></lb>scritte da Galileo, in sul principio della sua Lettera al Mazzoni <lb></lb>(Alb. </s>

<s>II, 1), con quel che il Mazzoni stesso dice nel Cap. </s>

<s>XVIII, <lb></lb>de&#039;<emph type="italics"></emph>Preludi alla Filosofia di Platone e di Aristotile,<emph.end type="italics"></emph.end> da pag. </s>

<s>187-95 <lb></lb>dell&#039;edizion di Venezia 1597; rileva chiaramente che in Pisa i due <lb></lb>professori conferivano insieme sulle Questioni Meccaniche del Be­<lb></lb>nedetti, intorno alle quali il giovane Galileo s&#039;esercitò tanto studio­<lb></lb>samente, che ne compose quel Trattato informe <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> dato ora <lb></lb>che è poco alla luce da pag. </s>

<s>251-419 del volume primo dell&#039;edizion <lb></lb>Nazionale (Firenze 1890). Eppure, benchè Michelangiolo Ricci, e, <lb></lb>che più conta, i fatti attestino che Galileo bevve così largamente al <lb></lb>libro delle Speculazioni, non è possibile il trovare in nessuna delle <lb></lb>Scritture galileiane, o edite o inedite o pubbliche o familiari, ricor­<lb></lb>dato mai o almeno accennato al nome di Giovan Battista Benedetti. </s></p><p type="main">

<s>Solenne maestro in Idrostatica, poco prima che Galileo dasse <lb></lb>opera alle <emph type="italics"></emph>Galleggianti,<emph.end type="italics"></emph.end> era dalla lontana Bruges apparito Simeone <lb></lb>Stevino, un&#039;altra di quelle ombre paurose che, a voler regnar solo, <lb></lb>o bisognava contrucidare, o in qualche modo esiliare dai proprii <lb></lb>confini. </s>

<s>Or avvenne che codesto bandito straniero, allacciato quasi <lb></lb>alla coda di un Discorso accademico letto in Roma da Giovanni <lb></lb>Bardi, comparisse al cospetto di Galileo. </s>

<s>Quel Discorso è inti­<lb></lb>tolato <emph type="italics"></emph>Eorum quae vehuntur in aquis Experimenta<emph.end type="italics"></emph.end> (Targioni, Ag­<lb></lb>grandim. </s>

<s>T. II, P. I, pag. </s>

<s>2) e si termina dall&#039;Autore coll&#039;aggiungervi <lb></lb>quel curioso paradosso, dimostrato dallo Stevino ne&#039;suoi Elementi <lb></lb>d&#039;Idrostatica, di un vaso cilindrico pieno d&#039;acqua che, sollevato in <lb></lb>alto sotto un cilindro solido fisso nel muro, in modo che entri dentro <lb></lb>a quello di sotto, scacciandone via l&#039;acqua, da rimanerne quasi vuoto; <lb></lb>pesa nonostante sulla stadera, allo stesso modo che quando era pieno. <pb xlink:href="020/01/151.jpg" pagenum="132"></pb>— Quale sciocchezza sarebbe a lasciar questa perla così preziosa ad­<lb></lb>addosso a questo straniero? </s>

<s>Facciamola nostra, pensò Galileo, e poi <lb></lb>rimandiamolo addietro. </s>

<s>— Chi legge la Lettera a Tolomeo Nozzolini <lb></lb>(Alb. </s>

<s>XII, 112) ritrova questo appropriamento fatto con sì maravi­<lb></lb>gliosa destrezza, che la poca facondia di qualunque oratore baste­<lb></lb>rebbe a rimandare il colpevole assoluto. </s>

<s>Nè minor destrezza, per <lb></lb>non moltiplicare in esempi, usò nel III Dialogo de&#039;Due Massimi Si­<lb></lb>stemi, in appropriarsi l&#039;osservazione dei varii dilatamenti della pu­<lb></lb>pilla, al variar dell&#039;intensità luminosa. (Alb. </s>

<s>I, 394). </s></p><p type="main">

<s>In un altro Autore così fatte destrezze di mano passerebbero <lb></lb>inosservate, ma in Galileo rivelano l&#039;esecuzione di un tenace pro­<lb></lb>posito, qual era di voler essere in qualunque modo o di apparire <lb></lb>in tutto il primo e il solo. </s>

<s>Da questo stesso genio veniva frugato <lb></lb>a moltissime occasioni, quando si trattava di rivendicare scoperte, <lb></lb>che sarebbero state per giustizia appartenute agli odiati molesti <lb></lb>competitori. </s>

<s>Gli dà nuova il Sagredo di aver veduto in Padova, ap­<lb></lb>presso il Santorio, uno strumento da misurar col compasso i gradi <lb></lb>del calore e del freddo. </s>

<s>Galileo risponde che quello strumento era <lb></lb>di sua propria invenzione. </s>

<s>Ma in effetto, col pretesto di rivendicare <lb></lb>a sè l&#039;esperienza, intendeva usurparsi l&#039;applicazione della esperienza <lb></lb>stessa, nella quale sola consisteva il merito dell&#039;invenzione del ter­<lb></lb>mometro. </s>

<s>Che anzi, sebbene egli dice di aver fatto quella tale espe­<lb></lb>rienza in Padova nel 1606 (Alb. </s>

<s>VI), 313) gli si può rispondere che, <lb></lb>fin dal 1550, l&#039;aveva pubblicata il Porta nel II Libro fra&#039;quattro <lb></lb>della <emph type="italics"></emph>Magia,<emph.end type="italics"></emph.end> e nel 1601, nel III Libro degli Spiritali l&#039;aveva ar­<lb></lb>gutamente illustrata, applicandola alla soluzione di un importantis­<lb></lb>simo problema, qual&#039;è quello di trovare il volume, a cui può, per <lb></lb>la massima dilatazione, ridursi l&#039;aria. </s>

<s>La teoria poi dello strumento <lb></lb>fondata sul principio materiale degli egnicoli, di che tanto rimase <lb></lb>sodisfatto il Sagredo, a una lettera di Galileo, l&#039;avea data già il Be­<lb></lb>nedetti con più squisito giudizio. </s></p><p type="main">

<s>E intorno alla scoperta delle macchie solari, che fiera guerra <lb></lb>non muove questo ardito conquistatore! E perchè? </s>

<s>Se si riguarda <lb></lb>la materiale e occasionale osservazione del fatto, non ci è dubbio <lb></lb>che il Fabricio, e tutti coloro che, eccitati dall&#039;<emph type="italics"></emph>Avviso sidereo,<emph.end type="italics"></emph.end> eb­<lb></lb>bero il coraggio di farsi bruciare gli occhi, osservando direttamente <lb></lb>il sole, o si prevalsero dell&#039;ingegno di riguardarlo per proiezione; <lb></lb>precedettero lo Scheiner e Galileo. </s>

<s>Se si ha riguardo a chi primo <lb></lb>si rivolse all&#039;osservazione del fatto, con vero intendimento scienti­<lb></lb>fico, i documenti attestano che lo Scheiner precedè Galileo Se si <pb xlink:href="020/01/152.jpg" pagenum="133"></pb>attende poi a chi primo filosofò sulla natura del fatto, e investigò <lb></lb>la fisica costituzione del sole nelle sue macchie, nessuno può venire <lb></lb>alle prove con Galileo. </s>

<s>Ora è chiaro che tutto il merito scientifico <lb></lb>consisteva qui, e di ciò solo poteva meritamente gloriarsi e con­<lb></lb>tentarsi l&#039;Autore delle Lettere velseriane. </s>

<s>Eppure egli sputa fuoco <lb></lb>e veleno contro il Gesuita tedesco, perchè, anche nell&#039;osservazione <lb></lb>materiale del fatto, anche in averne conosciuta e apprezzata l&#039;im­<lb></lb>portanza scientifica, non vuol competitori, vuole in tutto e per tutto <lb></lb>essere il primo ed il solo. </s>

<s>E da quale altro genio era mosso, se <lb></lb>non da questo, quando s&#039;indusse a tacer della cooperazione, che <lb></lb>ebbe il Sarpi in quelle osservazioni celesti, di cui volle apparire <lb></lb>al mondo primo e unico Messaggero? </s></p><p type="main">

<s>Il canocchiale, che andava oramai per le mani di molti signori, <lb></lb>e si sapeva per fatto certo da tutti esser venuto d&#039;Olanda, non era, <lb></lb>com&#039;altri ritrovati, di così facile conquista. </s>

<s>Perciò qui procede Ga­<lb></lb>lileo con più liberalità, che nell&#039;affar delle macchie solari. </s>

<s>Renunzia <lb></lb>alla fortuita materialità dell&#039;invenzione, e si contenta di appropriarsi <lb></lb>la soluzione di un problema diottrico, già formulato; soluzione a <lb></lb>che egli dice esser riuscito per opera di solo discorso, e in che egli <lb></lb>afferma consistere tutto il vero merito di quella stessa invenzione. <lb></lb>(Alb. </s>

<s>IV, 207, 8). Altri prima di noi ha notato l&#039;incongruenza, che <lb></lb>è fra questa storia del ritrovamento del canocchiale data nel Sag­<lb></lb>giatore, e in altre varie Scritture di Galileo, e ciò sarebbe segno <lb></lb>che quelle narrazioni non avevano i fondamenti sinceri e confer­<lb></lb>mati nel vero. </s>

<s>Ma quanto vana pretensione fosse quella sua d&#039;aver <lb></lb>ritrovata la composizione dell&#039;ammirabile strumento per via di di­<lb></lb>scorso, si parrà dai fatti che a suo luogo si narreranno. </s>

<s>Giova in­<lb></lb>tanto osservare, a proposito di questi diottrici discorsi fatti nel <lb></lb>Nunzio Sidereo e nel Saggiatore, le varietà e anzi le contradizioni <lb></lb>che si rilevano apertamente collazionando l&#039;uno coll&#039;altro. </s>

<s>Là, nel <lb></lb>Nunzio, aveva riconosciuto il modo e la ragion dell&#039;operare del ca­<lb></lb>nocchiale, nel condensamento de&#039;raggi attraverso al diafano delle <lb></lb>lenti (Alb. </s>

<s>III, 62); qui, nel Saggiatore, confuta quelle medesime <lb></lb>dottrine, contradicendo a se stesso, nell&#039;atto che vuol contradire al <lb></lb>Sarsi. </s>

<s>Notabile di più che in questa strana argomentazione di Ga­<lb></lb>lileo contro il suo avversario, si trova aggirato in un altra contra­<lb></lb>dizione, la quale consiste in ammetter che i raggi <emph type="italics"></emph>entrino<emph.end type="italics"></emph.end> nelle <lb></lb>pupille, mentre sempre, e in questa stessa scrittura del Saggiatore, <lb></lb>dice che <emph type="italics"></emph>escono,<emph.end type="italics"></emph.end> professando le platoniche teorie dell&#039;estramissione. <lb></lb>(Alb. </s>

<s>IV, 203). </s></p><pb xlink:href="020/01/153.jpg" pagenum="134"></pb><p type="main">

<s>Così fatte contradizioni hanno in tutti gli Autori origine dal <lb></lb>progredir della mente, e piuttosto che contradizioni si dovrebbero <lb></lb>dire e sono ritrattazioni. </s>

<s>Ma Galileo, se si corregge, lo fa con tale <lb></lb>studioso accorgimento, da non fare apparir che egli abbia errato, <lb></lb>specialmente se da qualcuno gli è stato suggerito di corregger l&#039;er­<lb></lb>rore. </s>

<s>Di ciò pure è bene sodisfare ai nostri lettori di qualche esempio. </s></p><p type="main">

<s>Nel Nunzio Sidereo dice che il piccolo corpo globoso delle stelle, <lb></lb>per via dell&#039;irradiazione, s&#039;accresce di grandezza nell&#039;occhio, co­<lb></lb>sicchè il canocchiale radendo all&#039;astro il capellizio, è cagione di <lb></lb>rappresentarlo più terminato sì nel suo contorno, ma pur alquanto <lb></lb>rimpiccolito. </s>

<s>Dall&#039;esser soggetto però a tale accrescimento e decre­<lb></lb>mento di grandezza apparente esclude la Luna (Alb. </s>

<s>III, 74). Un <lb></lb>anno dopo, scrivendo al Grienberger, dice che <emph type="italics"></emph>la Luna s&#039;incorona <lb></lb>ella ancora come ogni altro corpo luminoso de&#039;suoi raggi<emph.end type="italics"></emph.end> (ivi, pa­<lb></lb>gina 65), ma, soggiungendo che il Telescopio <emph type="italics"></emph>toglie in gran parte <lb></lb>la detta irradiazione col portarci la specie della luna molto vicina<emph.end type="italics"></emph.end><lb></lb>(ivi, pag. </s>

<s>168), dà a diveder che egli persiste tuttavia in credere la <lb></lb>irradiazione risieder nell&#039;astro e no nell&#039;occhio. </s>

<s>Nel Saggiatore, che <lb></lb>vuol dire nel 1623, dodici anni dopo avere scritta la citata lettera <lb></lb>al Grienbergero, l&#039;Autore ha mutato opinione anco rispetto a questa <lb></lb>seconda parte della sua dottrina. </s>

<s>Afferma ivi, senz&#039;altro, che <emph type="italics"></emph>quel <lb></lb>fulgore ascitizio delle stelle non è realmente intorno alle stelle ma <lb></lb>è nel nostro occhio<emph.end type="italics"></emph.end> (Alb. </s>

<s>IV, 194) e ciò torna solennemente a con­<lb></lb>fermare nel III Dialogo dei Massimi Sistemi, dove descrivendo la <lb></lb>corda tesa ad uso di micrometro, dice che essa, <emph type="italics"></emph>nel coprire il nudo <lb></lb>corpicello della stella, leva via i capelli che non son suoi ma del <lb></lb>nostro occhio<emph.end type="italics"></emph.end> (Alb. </s>

<s>I, 393). Ora tutti questi che paion frutti germo­<lb></lb>gliati spontaneamente, sono invece il portato di un ramo nuovo ri­<lb></lb>messo in luogo del vecchio, reciso dalla forbice del Keplero, il quale <lb></lb>aveva, nella Dissertazione sul Nunzio Sidereo, richiamato sopra la <lb></lb>sua <emph type="italics"></emph>Ottica<emph.end type="italics"></emph.end> l&#039;attenzione di Galileo, e aveva concluso contro di lui <lb></lb>“ Neque perspicillum in terra adimit aliquid stellis in coelo, sed <lb></lb>adimit aliquid lucis retiformi, quantum eius redundat ” (Alb. </s>

<s>V, 425). </s></p><p type="main">

<s>Uno de&#039;più curiosi problemi, proposti all&#039;Ottica astronomica, <lb></lb>era quello del Sole ellittico sull&#039;orizzonte. </s>

<s>Ticone, il Keplero, e più <lb></lb>particolarmente lo Scheiner, che ne scrisse un libro apposito e ne <lb></lb>offerì una copia a Galileo (Campori, Carteg. </s>

<s>galil. </s>

<s>Modena 1881, <lb></lb>pag. </s>

<s>86), avevano tentato in qualche modo di risolvere il problema. </s>

<s><lb></lb>Ma l&#039;Autore del Saggiatore, che non aveva potuto ancora perdonare <lb></lb>al gesuita tedesco l&#039;avere osato d&#039;ingerirsi del suo Regno, in ri-<pb xlink:href="020/01/154.jpg" pagenum="135"></pb>compensa del dono ricevuto, deride amaramente l&#039;Autore, per avere <lb></lb>scritto del sole ellittico, come di problema astruso, un intiero trat­<lb></lb>tato, <emph type="italics"></emph>ancorchè tutto il mistero non ricerchi maggior profondità di <lb></lb>dottrina che l&#039;intender per qual ragione un cerchio veduto in <lb></lb>maestà ci paia rotondo, ma guardato in iscorcio ci apparisce ovato<emph.end type="italics"></emph.end><lb></lb>(Alb. </s>

<s>IV, 344). Ma come c&#039;entra il cerchio se si tratta del sole che <lb></lb>è una sfera? </s>

<s>La cosa dovette sembrare allo stesso Autore assai <lb></lb>strana, e tornandoci sopra a speculare, s&#039;avvide che il problema <lb></lb>non era di così facile soluzione, come l&#039;aveva prima creduto, e <lb></lb>perciò nelle <emph type="italics"></emph>Operazioni astronomiche,<emph.end type="italics"></emph.end> correggendo colle rifrazioni <lb></lb>di Ticone e del Keplero le riflessioni speculari dello Scheiner, riuscì <lb></lb>finalmente a incontrarsi nel vero, benchè seguitasse a esprimersi <lb></lb>ancora sotto forma di dubbio. </s>

<s>Se il sole si mostra bislungo, credo <lb></lb>io veramente accadere, egli scrive, <emph type="italics"></emph>perchè, mercè dei vapori bassi, <lb></lb>l&#039;inferior parte del disco solare viene più inalzata che la superiore, <lb></lb>restando l&#039;altra dimensione, cioè la lunghezza, inalterata<emph.end type="italics"></emph.end> (Alb. </s>

<s>V, <lb></lb>383, 84). Anco questo però appar sotto tutt&#039;altro aspetto che di una <lb></lb>ritrattazione, e anzi è notabile lo studio posto dall&#039;Autore in cansar <lb></lb>ogni più piccolo accenno, per cui potessero risovvenirsi i lettori e <lb></lb>accorgersi di un errore trascorso. </s></p><p type="main">

<s>La libidine del regnare non conosce ritegni: si trucidano gli <lb></lb>stranieri e i fratelli, si spogliano delle sostanze i nemici paurosi, e <lb></lb>gli amici più confidenti. </s>

<s>Fra questi più confidenti amici di Galileo <lb></lb>era Bonaventura Cavalieri, il quale aveva appresi i principii dimo­<lb></lb>strativi delle leggi del moto dalla meditazione dei Dialoghi de&#039;Due <lb></lb>Massimi Sistemi. </s>

<s>Or avendo, in un suo libro, a trattar delle sezioni <lb></lb>del cono, applicando quei meccanici principii, si trovò, quasi senz&#039;av­<lb></lb>vedersene, condotta in mano la dimostrazione che i proietti, non <lb></lb>avuto riguardo alle resistenze, descrivevano nel libero spazio vuoto <lb></lb>una parabola. </s>

<s>Nel mentre che il libro faceva i primi passi per <lb></lb>uscire alla luce, il modesto Autore dello <emph type="italics"></emph>Specchio Ustorio<emph.end type="italics"></emph.end> dà avviso <lb></lb>all&#039;amato Maestro della bella e nuova proposizione dimostrata, spe­<lb></lb>rando se ne dovesse assai compiacere. </s>

<s>Ma qual divenne l&#039;umile <lb></lb>fraticello, quando Cesare Marsili ebbe a leggergli quella lettera di <lb></lb>Galileo, piena di rimproveri sdegnosi saettati in mezzo all&#039;imper­<lb></lb>versare più tempestoso dell&#039;ira? </s>

<s>E perchè mai tanto sdegno? </s>

<s>Perchè <lb></lb>colui che in tutto voleva essere il primo e il solo, pretendeva che <lb></lb>il teorema delle traiettorie paraboliche fosse suo. </s>

<s>Il fatto e il modo <lb></lb>di una tale usurpazione, forniranno un soggetto de&#039;più nuovi e <lb></lb>importanti alla nostra storia, ma intanto, perchè in brevi tratti <pb xlink:href="020/01/155.jpg" pagenum="136"></pb>di penna si concluda, ecco l&#039;esempio di un&#039;altra usurpazione più <lb></lb>manifesta di quella e più violenta. </s></p><p type="main">

<s>Il dì 19 Dicembre 1634 il Cavalieri scriveva una lettera a Ga­<lb></lb>lileo, nella quale gli domandava il suo giudizio intorno alla <emph type="italics"></emph>Geo­<lb></lb>metria degli indivisibili,<emph.end type="italics"></emph.end> non ancora finita di stampare, poi soggiunge <lb></lb>le seguenti parole: “ Scrivo in fretta, perciò mi scusi della negli­<lb></lb>genza dello scrivere, e ciò per avere io voluto trascrivere un pen­<lb></lb>siero intorno alla definizione V. del Quinto d&#039;Euclide, quale le <lb></lb>mando per sentirne il suo parere.... Se le paresse cosa buona, <lb></lb>averei pensiero di metterla nel fine della mia Geometria ” (Campori, <lb></lb>ivi, pag. </s>

<s>423). Al sagace lettore quel Pensiero del Cavalieri parve <lb></lb>anzi tanto buono, che disegnò di farlo suo, e perciò distolse, con <lb></lb>lusinghiera persuasione, l&#039;Autore dal pubblicarlo. </s>

<s>Ciò si rileva da <lb></lb>un altra lettera dello stesso Cavalieri, il quale troppo facilmente <lb></lb>lasciatosi vincere alle lusinghe, proponeva d&#039;aspettare a pubblicar <lb></lb>ciò che intendeva di metter per appendice alla sua Geometria, <emph type="italics"></emph>più <lb></lb>opportuna occasione<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>429). Ma il fatto si è che, invece di <lb></lb>andar quell&#039;appendice a incoronar la Geometria degli indivisibili, <lb></lb>andò ad aggiungersi ai quattro Dialoghi delle Due Nuove Scienze. </s>

<s><lb></lb>Ii Pensiero trascritto e mandato da Bologna a Galileo, il giorno, il <lb></lb>mese e l&#039;anno suddetto, non è smarrito. </s>

<s>Quando noi lo sottopor­<lb></lb>remo all&#039;esame de&#039;nostri lettori, vedranno che, non la materia sola, <lb></lb>ma la mossa stessa e gli stessi andamenti del dialogo galileiano son <lb></lb>ritratti da quel <emph type="italics"></emph>Pensiero<emph.end type="italics"></emph.end> scritto dal Cavalieri. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Benchè non la fantasia o il passionato giudizio ma i fatti ci <lb></lb>abbiano rappresentato Galileo, come Aristotile si rappresentò al Ve­<lb></lb>rulamio, sotto l&#039;aspetto di un conquistatore, che stabilisca il suo <lb></lb>regno a somiglianza de&#039;più scaltri e coraggiosi tiranni; prevediamo, <lb></lb>nonostante, che molti resteranno scandalizzati alla verità, che ha <lb></lb>sapore di amaro. </s>

<s>Anzi siam di ciò più che certi, tanto vanno a ri­<lb></lb>troso della corrente opinione quelle nostre storiche conclusioni. </s>

<s>E <lb></lb>come infatti si possono conciliare insieme i titoli di tiranno e di <lb></lb>divino? </s>

<s>Se nei conquistatori politici gli conciliò spesso l&#039;adulazione <lb></lb>o il timore, non hanno simili passioni alcun effetto nel caso nostro, <pb xlink:href="020/01/156.jpg" pagenum="137"></pb>in cui nulla s&#039;ha da perdere o da sperare. </s>

<s>Non si può altro dir <lb></lb>dunque se non che questa invalsa e corrente opinione, che contra­<lb></lb>dice ai fatti storici, abbia tolta la libera serenità dei giudizî. </s></p><p type="main">

<s>Che sia veramente così, ne possiamo vedere gli esempi in due <lb></lb>dei più grandi uomini, che, tra il finire del secolo passato e il co­<lb></lb>minciare del nostro, fiorirono fra i cultori degli studi galileiani. </s>

<s>Da <lb></lb>che il Lagrangia affermò e il Venturi diffuse la sentenza, s&#039;è ripe­<lb></lb>tuto e si ripete da tutti che Galileo fu primo a introdurre nella <lb></lb>Meccanica il principio della composizione delle forze e delle velocità <lb></lb>virtuali. </s>

<s>Ora è un fatto che, fra tutte le sentenze, nessun altra è <lb></lb>più aliena dal vero di questa. </s></p><p type="main">

<s>Qual documento che attesti aver Galileo veramente professato <lb></lb>il principio, che la resultante di due forze è determinata in inten­<lb></lb>sità e in direzione dalla diagonale, si cita il teorema II della quarta <lb></lb>Giornata delle Due Nuove. </s>

<s>Scienze. </s>

<s>Ma il Cartesio, nel tempo stesso, <lb></lb>aveva applicato quel teorema alla luce, come si può veder dal § 2° <lb></lb>del secondo capitolo della <emph type="italics"></emph>Diottrica<emph.end type="italics"></emph.end> pubblicata in francese nel 1637. <lb></lb>Ed è a notar che l&#039;Autore, il quale, come altrove, anco qui insiste <lb></lb>sulle orme del Keplero, ripete i processi dimostrativi della propo­<lb></lb>sizione XIX dei <emph type="italics"></emph>Paralipomeni a Vitellione,<emph.end type="italics"></emph.end> dove il moto obliquo del <lb></lb>raggio luminoso e incidente sopra lo specchio si decompone in due, <lb></lb>uno perpendicolare e l&#039;altro parallelo alla superficie del medesimo <lb></lb>specchio (Francof. </s>

<s>1604, pag. </s>

<s>15). Anzi quell&#039;ingenuo e schietto ca­<lb></lb>rattere del grande Alemanno non tace che l&#039;applicazione del teo­<lb></lb>rema meccanico ai moti della luce risale su fino ad Alhazen e a <lb></lb>Vitellione, de&#039;quali autori scrive queste parole: “ Et addunt subtile <lb></lb>nescio quid motum lucis oblique incidentis componi ex motu per­<lb></lb>pendiculari et motu parallelo ad densi superficiem ” (ibi, pag. </s>

<s>84). </s></p><p type="main">

<s>Galileo propriamente non fece altro che tentar del teorema una <lb></lb>dimostrazione, la quale è fondata sopra l&#039;equivoco tra <emph type="italics"></emph>potenza di­<lb></lb>namica<emph.end type="italics"></emph.end> e <emph type="italics"></emph>potenza numerica.<emph.end type="italics"></emph.end> Preso a quell&#039;equivoco rimase a prin­<lb></lb>cipio anche il Mersenno, come si par dalla proposizione XXII della <lb></lb>sua <emph type="italics"></emph>Meccanica<emph.end type="italics"></emph.end> (Parisiis 1644, pag. </s>

<s>81) e se ne accorse o ne fu fatto <lb></lb>accorto appena stampato il libro. </s>

<s>Perciò, nella Prefazione innume­<lb></lb>rata, fra le altre cose di che si ricrede, ci è anche quella proposi­<lb></lb>zione, della quale, dopo aver detto che <emph type="italics"></emph>est ex mente Galilaei pag. </s>

<s>250 <lb></lb>Dialogorum,<emph.end type="italics"></emph.end> immediatamente soggiunge: “ quod tamen minime <lb></lb>verum esse videtur. </s>

<s>” Non falso il teorema, falso il principio dimo­<lb></lb>strativo, che cioè la potenza della resultante sia uguale alla somma <lb></lb>delle potenze o de&#039;quadrati delle due componenti: anzi il teorema <pb xlink:href="020/01/157.jpg" pagenum="138"></pb>stesso, secondo i principii galileiani, non sarebbe vero, se non nel <lb></lb>caso delle forze ortogonali. </s>

<s>Le perniciose conseguenze di così fatte <lb></lb>dottrine daranno alla nostra storia della Meccanica soggetto di lungo <lb></lb>e importante discorso, ma intanto passiamo a veder quel che si dice <lb></lb>di Galileo, rispetto alle velocità virtuali. </s></p><p type="main">

<s>Ch&#039;ei veramente professasse questo principio è chiaro da quel <lb></lb>che nella <emph type="italics"></emph>Scienza Meccanica<emph.end type="italics"></emph.end> si legge (Alb. </s>

<s>XI, 93), e da quel che <lb></lb>dice altrove (Alb. </s>

<s>XIII, 176) raccogliesi che, nel trattar delle Mec­<lb></lb>caniche, quello stesso principio non era nuovo agli autori. </s>

<s>Guidu­<lb></lb>baldo Del Monte infatti, benchè non sapesse formularlo e renderlo <lb></lb>generale, pur ne fece in qualche modo l&#039;applicazione nella proposi­<lb></lb>zione XIII <emph type="italics"></emph>De trochlea,<emph.end type="italics"></emph.end> e nel corollario I della prima proposizione <emph type="italics"></emph>De <lb></lb>axe in peritochio,<emph.end type="italics"></emph.end> come in altre parti del suo <emph type="italics"></emph>Machenicorum liber.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Galileo poi è verissimo che, di quel principìo delle velocità <lb></lb>virtuali, ne fece due insigni applicazioni, distanti così di tempo fra <lb></lb>loro, da segnare i due termini estremi della gloriosa scientifica sua <lb></lb>carriera: l&#039;una all&#039;equilibrio dei liquidi nei vasi comunicanti, l&#039;altra <lb></lb>alla teoria dei piani inclinati. </s>

<s>Non sapremmo dir propriamente se <lb></lb>l&#039;Autore del Discorso intorno ai galleggianti presentisse le difficoltà <lb></lb>promosse contro la sua dimostrazione, la quale in verità non con­<lb></lb>clude, se non nel caso che i due vasi comunicanti sien cilindrici <lb></lb>e verticali, e ambedue di ugual calibro. </s>

<s>Quel che possiamo però <lb></lb>asserire per cosa certa è che, non appena ebbe trattata, in quell&#039;Ag­<lb></lb>giunta da farsi alla stampa leydese del III Dialogo, la nuova teoria <lb></lb>del piano inclinato col principio delle velocità virtuali, che cominciò <lb></lb>a scrupoleggiare intorno alla verità di quello stesso principio. </s></p><p type="main">

<s>Si fonda questa nostra certezza sull&#039;esame di quelle carte in­<lb></lb>formi e disordinate, su cui la mano dell&#039;Autore e del Torricelli <lb></lb>divisarono la riforma, in gran parte radicale, da farsi al Trattato <lb></lb>delle Due Nuove Scienze. </s>

<s>Si rileva da queste carte che uno dei <lb></lb>principii da riformare era quello appunto delle velocità virtuali, <lb></lb>avendo qualche durezza nell&#039;apprendersi come mai <emph type="italics"></emph>quella mag­<lb></lb>gioranza che non è, ma ancora ha da essere, possa produrre un <lb></lb>effetto presente<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Div. </s>

<s>II. P. V. T. IV. c. </s>

<s>29). S&#039;accenna evi­<lb></lb>dentemente, con sì fatte parole, alla teoria della libbra di braccia <lb></lb>disuguali; teoria applicata da Galileo alle braccia di disugual ca­<lb></lb>pacità di un sifone pieno di liquido: ma che il dubbio si estendesse <lb></lb>altresì alla nuova teoria del piano inclinato, si par da quell&#039;altra <lb></lb>nota che dice: <emph type="italics"></emph>pensare se è vero che, per ritenere un peso, serva <lb></lb>tanta forza quanta ne fa quello per scendere<emph.end type="italics"></emph.end> (ivi). </s></p><pb xlink:href="020/01/158.jpg" pagenum="139"></pb><p type="main">

<s>Che il principio delle velocità virtuali si ritenesse poi per dubbio <lb></lb>e inconcludente, s&#039;argomenta dai modi che il Torricelli, il Borelli <lb></lb>e il Viviani, con tutta l&#039;altra scuola galileiana, tennero nei loro <lb></lb>meccanici teoremi, nei quali quello stesso principio, non solamente <lb></lb>non si vede promosso, ma vi è cansato con ogni più sollecito studio. </s></p><p type="main">

<s>Antonio Nardi, anzi, nelle <emph type="italics"></emph>Scene Accademiche,<emph.end type="italics"></emph.end> adduce quella <lb></lb>stessa di Galileo per ragione del suo repudio, dichiarandosi aper­<lb></lb>tamente “ che male si persuadono i Meccanici comunemente com­<lb></lb>pensarsi in una bilancia di disuguali braccia la velocità del moto <lb></lb>con la grandezza del momento, onde cercano di render ragione, <lb></lb>perchè questi pesi disuguali, da distanze reciprocamente disuguali, <lb></lb>pesino ugualmente, ma ciò non è in vero cagione dell&#039;equilibrio, <lb></lb>perchè così discorrendo s&#039;adduce di un effetto in atto una ragione <lb></lb>in potenza ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XX, pag. </s>

<s>862). </s></p><p type="main">

<s>Nè era, in quegli ingegni sagaci, senza un giusto motivo il re­<lb></lb>pudio di una dottrina, dall&#039;altra parte, verissima, perciocchè, man­<lb></lb>cando essi del calcolo infinitesimale, sentivano che, senza gli aiuti <lb></lb>di quello, il principio delle velocità virtuali mancava di fondamento <lb></lb>dimostrativo. </s>

<s>E infatti all&#039;aiuto degli infinitesimi ebbe in ultimo a <lb></lb>ricorrere il Grandi, per tentar di salvare il teorema galileiano del­<lb></lb>l&#039;equilibrio dei liquidi nei vasi comunicanti, benchè non riuscisse, <lb></lb>a parer nostro, a metterlo al sicuro di quelle argute censure pro­<lb></lb>mossegli incontro dallo stesso Nardi, nel seguito del discorso ora <lb></lb>citato. </s>

<s>Si vede dunque, per ridursi alla conclusione, con quanta <lb></lb>storica verità ed esattezza, nella comune opinione, si tenga che i <lb></lb>principii delle velocità virtuali e della composizione de&#039;moti s&#039;in­<lb></lb>cominciassero ad introdurre e ad applicarsi al trattato delle Mec­<lb></lb>caniche da Galileo e dalla scuola di lui. </s></p><p type="main">

<s>Si comprende, dopo ciò, assai facilmente in qual conto si possan <lb></lb>tener da noi le sentenze di uomini reputati autorevolissimi, quali <lb></lb>sono il Lagrangia e il Venturi, per tacere di altri. </s>

<s>Che se noi ve­<lb></lb>niamo a concludere altrimenti da loro, non vorranno i lettori far­<lb></lb>sene maraviglia, e anzi speriamo che si arrenderanno docili a ciò <lb></lb>che ne rappresenta la Storia, le conseguenze della quale, solo, ci <lb></lb>rendon la ragione di alcuni fatti, e ci scoprono nel tempo stesso o <lb></lb>la falsità o l&#039;insufficienza delle ragioni invocate fin qui, per ispiegarli. </s></p><p type="main">

<s>L&#039;aspetto, sotto cui si è presentato Galileo agli occhi affascinati <lb></lb>di tutti, è proprio quello ch&#039;ei divisava nelle sue intenzioni: a nessun <lb></lb>altro meglio che a lui è riuscito mai di farsi credere al mondo <lb></lb>qual&#039;ei voleva apparire, l&#039;unico sole che sorge, senz&#039;esser prece-<pb xlink:href="020/01/159.jpg" pagenum="140"></pb>duto da aurora, a illuminare le tenebre del mondo; il creatore in­<lb></lb>somma dal nulla di ogni scienza sperimentale. </s>

<s>Ma chiunque, dai <lb></lb>pregiudizi, non s&#039;è lasciato in tutto privare del senno, comprende <lb></lb>assai facilmente che una tal pretensione è contraria ai fatti, ed è <lb></lb>contraria ai consueti ordini della natura, com&#039;è giusto contrario a <lb></lb>questi stessi ordini che il sole nasca sull&#039;orizzonte, senz&#039;esser pre­<lb></lb>ceduto da aurora. </s></p><p type="main">

<s>Che sia veramente quella tal pretensione contraria ai fatti, lo <lb></lb>mostra ad evidenza, ci sembra, la prima parte del nostro Discorso. </s>

<s><lb></lb>Quale eletto e numeroso stuolo di combattenti per la verità, contro <lb></lb>gli aristotelici errori, non ci passò allora ordinata sotto i nostri occhi <lb></lb>maravigliati? </s>

<s>Or tutti costoro precedettero Galileo, nello speculare <lb></lb>e nello sperimentare intorno ai fatti della Natura, e gli furono o <lb></lb>gli potevano esser maestri. </s></p><p type="main">

<s>Che quella pretensione poi di non voler Galileo riconoscere, <lb></lb>fuor che qualche antico, nessun altro a maestro, sia contraria ai <lb></lb>consueti ordini della Natura, si dimostrò da noi infin dai primi prin­<lb></lb>cipii del nostro Discorso, quando, a investigar l&#039;origine del nostro <lb></lb>conoscere, ci incontrammo nella necessità delle tradizioni. </s>

<s>I fatti <lb></lb>naturali hanno ultimamente dimostrato che son rimasti lungamente <lb></lb>immobilì nella così detta età della pietra o in istato anco più sel­<lb></lb>vaggio i popoli, infintantochè non siano approdati a loro altri popoli <lb></lb>più inciviliti. </s>

<s>Da Platone e da Archimede voler d&#039;un salto giungere <lb></lb>a Galileo sarebbe lo stesso che, da&#039;gioghi della Falterona, voler <lb></lb>saltare alle foci dell&#039;Arno. </s>

<s>Troppi altri rivi, troppi altri fiumi sono <lb></lb>scesi per ogni parte e si sono aggiunti a far la piena a quell&#039;acqua. </s></p><p type="main">

<s>È forza dunque di confessare che son rimasti ingannati tutti <lb></lb>coloro, i quali, non ripensando a que&#039;rivi, a que&#039;fiumi e anzi ne­<lb></lb>gando la loro confluenza, hanno creduto che d&#039;un unico fonte, prin­<lb></lb>cipio di sè medesimo, sia scaturita l&#039;ubertà di quel fiume reale. </s>

<s><lb></lb>Le nostre conclusioni storiche perciò così repugnanti all&#039;opinione <lb></lb>comune svelano quell&#039;inganno, e nelle sue ragioni spiegano il fatto. </s>

<s><lb></lb>Perciocchè noi non neghiamo, contrariamente alla verità delle cose, <lb></lb>quella confluenza, ma la mettiamo anzi all&#039;aperto degli artifizii di <lb></lb>colui, che s&#039;era studiato d&#039;occultare i segreti canali, d&#039;onde gli de­<lb></lb>rivò tale abbondanza d&#039;acqua fluente. </s></p><p type="main">

<s>L&#039;albero della scienza, per tornare a quell&#039;altra nostra prima <lb></lb>immagine, era stato troncato dal ferro infino alla sua ceppaia. </s>

<s>Sorse <lb></lb>dal taglio un solitario pollone, che attrasse tutti a sè i succhi nu­<lb></lb>tritizi ricircolanti nelle barbe sottoterra. </s>

<s>Quella profonda ceppaia, <pb xlink:href="020/01/160.jpg" pagenum="141"></pb>lungo lavorìo di secoli, rimasta un po&#039;per natura un po&#039;per arte <lb></lb>nascosta, secondò le intenzioni di Galileo, in dare a credere che <lb></lb>non fosse quello veramente un pollone rigoglioso, ma un albero, <lb></lb>il quale non riconoscesse altra origine che dal suo proprio seme. </s>

<s><lb></lb>Il nostro scandolezzante discorso ha messo quella sotterranea cep­<lb></lb>paia allo scoperto, e al miracolo (giacchè l&#039;albero in che si vuole <lb></lb>impersonar Galileo, se fosse nato di seme e giunto a sì grande altezza <lb></lb>sarebbe miracoloso) ha sostituito un fatto naturale e perciò vero. </s></p><p type="main">

<s>In altro modo, per ripigliar quell&#039;altra similitudine forse meglio <lb></lb>appropriata, Galileo instituì una Tirannide in un Principato decre­<lb></lb>pito, usando l&#039;arte di tutti i conquistatori, che è quella di arric­<lb></lb>chirsi delle spoglie degli uccisi. </s>

<s>Queste spoglie volle far credere che <lb></lb>non fossero appartenute a nessuno, e il nostro Discorso ha scoperto <lb></lb>che ciò non è vero, come lo attestano i fatti e lo conferma la na­<lb></lb>tura di ogni conquista. </s>

<s>Ma un&#039;altra più efficace conferma, che ve­<lb></lb>ramente l&#039;istaurazione galileiana avesse la natura di una conquista, <lb></lb>s&#039;ha dal vederne conseguitare al conquistatore i consueti danno­<lb></lb>sissimi effetti. </s></p><p type="main">

<s>Le usurpazioni, l&#039;esilio, le stragi, che è costretto a commettere <lb></lb>colui, il quale vuol solo partecipare del Regno, sono per necessità <lb></lb>occasioni di odii e di vendette, che si suscitano più che mai feroci, <lb></lb>dal sangue e dalle ceneri stesse dei vinti. </s>

<s>Di questi odii e di queste <lb></lb>vendette il Regno di Galileo và famoso, nè par che sieno state fin <lb></lb>qui ritrovate, di tanto effetto, le giuste e proporzionate cagioni. </s>

<s>Son <lb></lb>ricorsi, per consueto refugio, all&#039;ignoranza dei tempi e alle reli­<lb></lb>giose superstizioni, quasi che le innovatrici dottrine dei nostri giorni, <lb></lb>che son giorni di libertà e di progressi, non abbiano avuto e non <lb></lb>sieno per avere sempre, fra gli uomini che adombrano ad ogni <lb></lb>novità, i medesimi sfavorevoli incontri. </s></p><p type="main">

<s>Come si concilii la condanna dei Dialoghi dei Due Massimi <lb></lb>Sistemi, e la dedica al Papa, del libro <emph type="italics"></emph>De revolutionibus,<emph.end type="italics"></emph.end> è proble­<lb></lb>ma lasciato irresoluto ancora da tanti declamatori, ai quali riman <lb></lb>pure a spiegare come mai fosse tolta libertà a Galileo di toccar delle <lb></lb>dottrine del Copernico, e fosse largamente concessa al Bullialdo, <lb></lb>mutato nome in quello di Filolao. </s>

<s>Come mai così franco il Roberval, <lb></lb>per fare una burla agli scienziati, facesse pubblicare al Mersanne <lb></lb>l&#039;<emph type="italics"></emph>Aristarco,<emph.end type="italics"></emph.end> e il Borelli nella Lettera sulla Cometa uscisse fuori in <lb></lb>abito pitagorico, tanto pauroso, adombrando dell&#039;Inquisitore, pa­<lb></lb>rendogli di vederselo innanzi sulla punta dei piedi (MSS. Gal. </s>

<s>Cim. </s>

<s><lb></lb>T. XVIII, c. </s>

<s>125). E chi volesse per curiosità seguitare a interrogare <pb xlink:href="020/01/161.jpg" pagenum="142"></pb>i muti, domanderebbe ancora come si concilîno i rigorosi divieti <lb></lb>di Roma colla pubblicazione delle <emph type="italics"></emph>Theoricae Mediceorum.<emph.end type="italics"></emph.end> Il prin­<lb></lb>cipe Leopoldo stà in gran trepidazione, perchè ha saputo che l&#039;In­<lb></lb>quisitor di Firenze fa difficoltà d&#039;approvar la stampa del libro. </s>

<s>Manda <lb></lb>il Redi, il quale torna dicendo che all&#039;Inquisitore era giunta cosa <lb></lb>totalmente nuova, asserendo che egli <emph type="italics"></emph>non aveva mai fatta minima <lb></lb>difficoltà<emph.end type="italics"></emph.end> (ivi, c. </s>

<s>132). </s></p><p type="main">

<s>Ma perchè da troppe parti tornerebbe provato che nell&#039;igno­<lb></lb>ranza dei tempi e nelle religiose superstizioni non si trova la causa <lb></lb>sufficiente degli odii suscitati contro Galileo, noi crediamo però di <lb></lb>non andare errati, attribuendo quella causa alle offese fatte ai tanti, <lb></lb>che rimasero segno alla sua conquista. </s>

<s>Michelangiolo Ricci, che <lb></lb>poteva intender quell&#039;animo grande meglio di nessun altro, attri­<lb></lb>buiva le contradizioni patite da Galileo all&#039;<emph type="italics"></emph>essersela voluta prendere <lb></lb>con questo e con quello<emph.end type="italics"></emph.end> (ivi, T. XIX, c. </s>

<s>205). Nè senza profonda <lb></lb>considerazione si può passar questo fatto: che, mentre tanti decla­<lb></lb>matori son sorti, specialmente oggidi, a rimpiangere sopra le sue <lb></lb>sventure; egli, Galileo, non ne abbia fatto mai motto, nemmeno nelle <lb></lb>lettere più segrete e più confidenti. </s>

<s>Nella schiettezza della sua co­<lb></lb>scienza, e nell&#039;altezza del suo proprio senno, troppo ben conosceva <lb></lb>il vizio di noi uomini di dar la colpa ora a una cosa ora a un altra, <lb></lb>mentre siam quasi sempre noi stessi occasione e causa della nostra <lb></lb>sventura. </s>

<s>In conformità di questi sentimenti, che non gli abbiamo <lb></lb>attribuiti a caso, nella solitudine di Arcetri, vicino a lasciar quel <lb></lb>Regno che avea con tanta contrarietà conquistato, dava al suo di­<lb></lb>letto Viviani questo documento: <emph type="italics"></emph>procurare ad ogni potere di sfug­<lb></lb>gìre ogni lite e controversie letterarie con chi si sia<emph.end type="italics"></emph.end> (ivi, T. XVII, <lb></lb>c. </s>

<s>69). Egli riportò è vero le pene delle liti e delle controversie <lb></lb>da sè in tanti modi contro sè provocate, ma gli riman la gloria <lb></lb>d&#039;avere egli solo recato inestimabili benefizi alla scienza. </s></p><p type="main">

<s>Come mai il male sia quasi una necessità, d&#039;onde tante volte <lb></lb>vedesi derivare un gran bene, è un mistero che a noi non tocca <lb></lb>d&#039;investigare. </s>

<s>Ma è forza in ogni modo riconoscere che i vizii, no­<lb></lb>tati da noi così liberamente e irreverentemente se si vuole, nella <lb></lb>vita scientifica di Galileo, furono una necessità a condur la difficile <lb></lb>impresa. </s>

<s>Perchè, o la si rappresenta la scienza sotto l&#039;immagine <lb></lb>di un albero, e ci bisognava la violenza del ferro per recidere i <lb></lb>rami vecchi e farvi sopra ripullulare un ramo nuovo: o la si rap­<lb></lb>presenta sotto l&#039;immagine di un Regno, e bisognava contrucidare <lb></lb>i fratelli, perchè il potere vacillante e disperso, si riducesse alle <pb xlink:href="020/01/162.jpg" pagenum="143"></pb>mani di un solo. </s>

<s>Contristati fin qui dai mali licenziosi e dalle pene <lb></lb>della Tirannide, passiamo a rasserenare il pensiero ne&#039;grandissimi <lb></lb>benefizi che ne son conseguiti. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il primo e principale dei benefizi che possa un conquistatore <lb></lb>arrecare al suo principato, e che sarebbe sufficiente per sè solo a <lb></lb>dover perdonargli le offese, è quello d&#039;istituirvi ordini savi, per i <lb></lb>quali possa la Repubblica prosperamente vivere e progredire. </s>

<s>Galileo <lb></lb>veramente incominciò a instituire questa saviezza di ordini, nella <lb></lb>Repubblica delle scienze, le quali ebbero perciò di qui il più valido <lb></lb>impulso ai loro progressi. </s>

<s>Fra&#039;due più grandi antichi Maestri e Le­<lb></lb>gislatori dell&#039;umana sapienza, preferì i plaeiti di Platone, in con­<lb></lb>formità dei quali sentenziava che “ il voler trattar le questioni na­<lb></lb>turali, senza Geometria, è tentar di far quello che è impossibile ad <lb></lb>esser fatto ” (Alb. </s>

<s>I, 224). La vera Filosofia, egli dice “ è scritta in <lb></lb>questo grandissimo libro che continuamente ci sta aperto innanzi <lb></lb>agli occhi (io dico l&#039;Universo) ma non si può intendere, se prima <lb></lb>non s&#039;impara a intender la lingua e conoscere i caratteri ne&#039;quali <lb></lb>è scritto. </s>

<s>Egli è scritto in lingua matematica, e i caratteri son trian­<lb></lb>goli, cerchi ed altre figure geometriche, senza i quali mezzi è im­<lb></lb>possibile intenderne umanamente parola: senza questi è un aggirarsi <lb></lb>vanamente per un oscuro laberinto ” (Alb. </s>

<s>IV, 171). </s></p><p type="main">

<s>Quell&#039;altra Filosofia più comunemente seguìta gli parve un&#039;or­<lb></lb>gogliosa vanità, una temerità estrema. </s>

<s>“ Estrema temerità mi è <lb></lb>parsa sempre quella di coloro che voglion fare la capacità umana <lb></lb>misura di quanto possa e sappia operar la Natura ” (Alb. </s>

<s>I, 114). <lb></lb>Che se Aristotile fa scaturir le cause degli effetti naturali dalla <lb></lb>dialettica de&#039;suoi sillogismi, Galileo gli si oppone così con animosa <lb></lb>franchezza: “ A me pare che la Logica insegni a conoscere se i <lb></lb>discorsi e le dimostrazioni.... procedono concludentemente, ma che <lb></lb>ella insegni a trovare i discorsi.... non credo io ” (Alb. </s>

<s>XIII, 135). <lb></lb>E se il Principe dei peripatetici va così studiosamente in cerca delle <lb></lb>argute speculazioni, e quanto son più recondite, tanto più volentieri <lb></lb>le dà per vere; Galileo, tutto al contrario sentenzia che “ la più <lb></lb>ammirabile e più da stimarsi condizione delle scienze dimostrative <lb></lb>è lo scaturire e pullulare da principii notissimi (ivi, pag. </s>

<s>90). </s></p><pb xlink:href="020/01/163.jpg" pagenum="144"></pb><p type="main">

<s>Ma a poco gioverebbe istituire ordini savi un principe, che non <lb></lb>volesse o non sapesse seguirli con gli esempi. </s>

<s>Ciò, come si vide, <lb></lb>tanto poco giovò al Verulamio, che per questo solo andò a vuoto <lb></lb>la sua così ben divisata Instaurazione. </s>

<s>Galileo invece non si con­<lb></lb>tentò di segnar la via o di ordinare il campo della battaglia, uscì <lb></lb>fuori con le armi in mano, contro l&#039;errore, e tanta gloria riportò <lb></lb>dalle sue vittorie e tanta autorità ne conseguì, che, non Tirannide <lb></lb>apparve o si disse la sua, ma legittimo principato. </s>

<s>Or questo è un <lb></lb>altro benefizio grandissimo recato alla scienza da quell&#039;uomo. </s></p><p type="main">

<s>L&#039;intrattenersi qui a noverar quelle vittorie parrebbe opera <lb></lb>vana, perchè troppo anzi bene son conosciute da tutti e da tutti <lb></lb>così magnificate, che Colui, il quale le riportò, non è solamente <lb></lb>tenuto come principe valoroso, ma è adorato come un Nume. </s>

<s>Or <lb></lb>perchè questa è una esagerazione, e ogni vizio conduce nell&#039;errore, <lb></lb>non farà maraviglia se da noi si asserisce che Galileo, da&#039;suoi stessi <lb></lb>adoratori, è così poco inteso e così poco studiato. </s>

<s>Chi fa oggidì più <lb></lb>speciale professione di studii galileiani, non entra mica addentro <lb></lb>alle speculazioni della gran mente: crede aver fatto assai a venire <lb></lb>a contarci del suo processo, delle amicizie, del numero de&#039;suoi libri <lb></lb>stampati, o dei manoscritti. </s>

<s>E ha ragione costui, perchè, se quella <lb></lb>mente divina à un sacro tempio, non debbono entrarvi dentro a <lb></lb>celebrarne i misteri piedi profani. </s></p><p type="main">

<s>Ma a noi per verità è sembrato altrimenti. </s>

<s>Persuasi che Galileo <lb></lb>è un grand&#039;uomo, ma pur un uomo come noi, soggetto a vizii e <lb></lb>ad errori, gli ci siamo avvicinati per vederlo e intenderlo meglio, <lb></lb>e abbiamo imparato da lui a non credere e sostener per vera una <lb></lb>cosa, perchè l&#039;ha detta un uomo. </s>

<s>Que&#039;fanatici, che inorridiscono <lb></lb>a sentir dire che Galileo ha sbagliato, non imitano certo i più affe­<lb></lb>zionati e valorosi discepoli, come il Sagredo l&#039;Aggiunti il Nardi, il <lb></lb>Viviani stesso, i quali notarono con libertà gli errori detti dal loro <lb></lb>venerato Maestro, e ne lasciarono scritte argute censure. </s>

<s>Non si <lb></lb>avvedono quegli stessi fanatici che, se fossero nati tre secoli addietro, <lb></lb>si sarebbero sottoscritti nella lista dei Cremonini, e non ripensano <lb></lb>che Aristotile, verso cui si commisero tante irreverenze, era vene­<lb></lb>rando a quei tempi, ben assai più di quel che non sia ora lo stesso <lb></lb>Galileo, lodato a cielo, perchè fu il più irriverente di tutti. </s></p><p type="main">

<s>Ripigliando il costrutto del discorso interrotto si voleva dunque <lb></lb>dire che giusto appunto, per essere le opere scientifiche di Galileo <lb></lb>esageratamente note, e perciò, ci si perdoni il bisticcio, ignote, ave­<lb></lb>vano bisogno di essere con più discrezione esaminate. </s>

<s>Ma perchè <pb xlink:href="020/01/164.jpg" pagenum="145"></pb>dall&#039;altra parte si può dir che questo è l&#039;intento principale di tutta <lb></lb>la nostra Storia, crediamo perciò di dovercene passare, contentan­<lb></lb>doci solo di notare una cosa: che mentre gli adoratori attribuiscono <lb></lb>a Galileo, perchè qualche uomo autorevole e male informato glie <lb></lb>l&#039;ha suggerito, meriti che non gli appartengono, non si curano poi <lb></lb>di riconoscerne e di esaltarne i meriti veri. </s></p><p type="main">

<s>Nella scienza del moto i meriti veri di Galileo incominciano <lb></lb>dalla dimostrazione delle leggi dei gravi, che cadono naturalmente <lb></lb>o scendono per gli archi di un cerchio. </s>

<s>Tutte le altre scoperte, che <lb></lb>precedono a questa, son retaggio di una scienza più antica. </s>

<s>Di qui <lb></lb>è che, se i suoi ammiratori male a ragione lo dicono creatore della <lb></lb>Dinamica, troppo debolmente, dall&#039;altra parte mettono in opera le <lb></lb>loro armi, per chiarir l&#039;efficacia, che ebbero le galileiane scoperte <lb></lb>in aprire alla Meccanica la via de&#039;suoi gloriosi progressi. </s></p><p type="main">

<s>In Idrostatica, Galileo riman forse inferiore a Simeone Stevino. </s>

<s><lb></lb>Il Discorso intorno alle Galleggianti è uno splendido commento alle <lb></lb>teorie di Archimede, ma se pure la scienza vi si illustra, non però <lb></lb>si promuove. </s>

<s>Le tavolette d&#039;ebano, o d&#039;altra materia più grave in <lb></lb>specie dell&#039;acqua, non galleggiano per la spinta idrostatica di sotto <lb></lb>in su, come si poteva concludere dai teoremi steviniani, ma si so­<lb></lb>stengono a galla, perchè, secondo Galileo, aderiscono all&#039;aria, la quale <lb></lb>per attrazione le tien sospese come il ferro la calamita. </s>

<s>Nonostante, <lb></lb>l&#039;aver dichiarate così eloquentamente quelle dottrine, rimaste nei <lb></lb>libri di Archimede, o ignorate o male intese, fu merito grande, e <lb></lb>occasione che altri, come poi presto si vide nel Castelli e nel Tor­<lb></lb>ricelli, vi facessero grandi progressi. </s></p><p type="main">

<s>Nell&#039;Idraulica, qualunque sieno le pretensioni degli idolatri, <lb></lb>Galileo è seguace del Castelli, ma il Trattato in forma di lettera <lb></lb>sul fiume Bisenzio, benchè la matematica astrattezza delle dottrine <lb></lb>non le faccia applicabili alla pratica delle acque correnti, apri no­<lb></lb>nostante largamente la via a nuove speculazioni. </s></p><p type="main">

<s>Nell&#039;Astronomia, l&#039;ingegno in Galileo concorse colla fortuna. </s>

<s><lb></lb>Il felice accorgimento che egli ebbe di badare, non alla chiarezza <lb></lb>dei vetri ma alla figura, lo fece uno de&#039;più abili fabbricatori del <lb></lb>canocchiale, che, rivoltolo alle plaghe del cielo, gli svelò quelle sue <lb></lb>gran maraviglie. </s>

<s>Ma in tutto ciò, per cui vien esaltato lo scopritore, <lb></lb>ha più merito la fortuna che non l&#039;ingegno, o per dir più giusto, <lb></lb>quello è merito di un esperto meccanico, no di uno scienziato. </s>

<s>Così, <lb></lb>nè il Fontana, nè il Campani, nè il Divini, squisitissimi artefici di <lb></lb>canocchiali, hanno giusto merito perciò di esser chiamati astronomi. </s></p><pb xlink:href="020/01/165.jpg" pagenum="146"></pb><p type="main">

<s>Astronomo è Galileo quando, posato lo strumento e chiusi gli <lb></lb>occhi della vista materiale, apre quelli dell&#039;intelletto a specular sui <lb></lb>fenomeni osservati intorno a Giove, o nella faccia della Luna e del <lb></lb>Sole. </s>

<s>Astronomo è quando inventa nuovi strumenti e divisa nuovi <lb></lb>metodi a prefinir, nei moti planetarii, gli spazii giustissimi e i tempi. </s>

<s><lb></lb>S&#039;ammira e s&#039;esalta, per avere egli il primo scoperto il mondo <lb></lb>gioviale, e se alcuno mai muove voce d&#039;averlo preceduto nella sco­<lb></lb>perta, è afferrato dal furore degli zelanti, che gli soffocano le parole <lb></lb>nella strozza. </s>

<s>Ma quando pur fosse che o Simon Mario o altri aves­<lb></lb>sero veduto le quattro lune intorno a Giove prima di Galileo, che <lb></lb>vorrebb&#039;egli dir ciò, se non che que&#039;tali avevano strumenti più <lb></lb>squisiti, e occhi più acuti di lui? </s>

<s>Or chi oserebbe dire che ciò non <lb></lb>fosse possibile? </s></p><p type="main">

<s>Il merito dunque non consiste qui, e chi ce lo fa consistere <lb></lb>mal provvede alla gloria di Galileo. </s>

<s>Il merito vero, e per cui ver­<lb></lb>rebbe giustamente esaltato quell&#039;uomo, consiste nell&#039;aver dimostrato <lb></lb>esser le stelle circungioviali veramente lune, e nell&#039;averne esatta­<lb></lb>mente misurati i tempi periodici e le medie distanze dal centro di <lb></lb>Giove. </s>

<s>Ma chi è, tra i fanatici ammiratori, che si sia curato d&#039;in­<lb></lb>vestigare per quali ingegnosissimi metodi e strumenti riuscisse con <lb></lb>tanta felicità Galileo, in quest&#039;operazione affatto nuova nell&#039;Astro­<lb></lb>nomia? </s>

<s>Parve aver fatto una grande scoperta a colui che trovò e <lb></lb>dette alla luce l&#039;Effemeridi de&#039;Satelliti di Giove, ma codeste son le <lb></lb>scompaginate e rimescolate ossa di un cadavere; per cui vera sco­<lb></lb>perta sarebbe stata piuttosto l&#039;infondere in quelle membra il primo <lb></lb>loro, e antico spirito della vita. </s></p><p type="main">

<s>In ogni modo, tanta varia novità di scoperte e di dottrine, <lb></lb>uscite fuori con quella splendida veste che ritraeva così bene in sè <lb></lb>la magnificenza del pallio filosofico di Platone, conferiva, per una­<lb></lb>nime consenso a Galileo l&#039;autorevole dignità del Principato. </s>

<s>Ecco <lb></lb>felicemente conseguito il fine della nobile e altissima impresa. </s>

<s>Tutti <lb></lb>i dotti di que&#039;tempi, non eccettuato il Keplero che primeggia fra <lb></lb>tutti, s&#039;inchinano a quella Autorità o con le voci congratulanti o <lb></lb>col silenzio. </s>

<s>Quei che possono ascoltar la viva voce del Maestro di <lb></lb>tante verità o aver con lui familiari colloqui, e corrispondenza epi­<lb></lb>stolare, se ne tengon beati. </s></p><p type="main">

<s>Son de&#039;principali fra costoro Daniele Antonini, che il vuoto <lb></lb>lasciatogli dentro dalla vita diplomatica riempiva di speculazioni e <lb></lb>di fisici sperimenti, Cesare Marsili, studioso di Astronomia e delle <lb></lb>proprietà del magnete, Paolo Aproino inventore del corno acustico, <pb xlink:href="020/01/166.jpg" pagenum="147"></pb>e Giovan Francesco Sagredo, la più amabile figura, fra le tante <lb></lb>comparse sopra questa magnifica scena. </s>

<s>Gentiluomo e patrizio ve­<lb></lb>neziano, fra le delizie della vita signorile e le gravi cure della poli­<lb></lb>tica, attende alla fabbrica dei vetri per i canocchiali e de&#039;cannellini <lb></lb>per uso dei termometri, co&#039;quali, da sè perfezionati, sperimenta <lb></lb>ne&#039;varii ambienti le varie temperature dell&#039;aria. </s>

<s>Tanti anni avanti <lb></lb>all&#039;invenzione dello strumento torricelliano e della macchina pneu­<lb></lb>matica, egli è il primo a far l&#039;esperienza del suono nel vuoto, e <lb></lb>indovina la vera teorica della visione, senza pensare al Porta o aver <lb></lb>letto ancora il Keplero. </s>

<s>Ei, con libera franchezza, sostiene in tal <lb></lb>proposito, la sua propria opinione, contro il diverso parere di Ga­<lb></lb>lileo, che a lui sembra e apertamente lo dichiara per un errore. </s></p><p type="main">

<s>Anche l&#039;arte si rivolse a riconoscere l&#039;autorità di questo prin­<lb></lb>cipato, presaga forse de&#039;nuovi benefizi e iniziatrice de&#039;nuovi connubi, <lb></lb>che sarebbe per contrar colla scienza. </s>

<s>Bell&#039;esempio di questi nuovi <lb></lb>connubi l&#039;abbiamo in due eccellenti pittori, Domenico Passignani <lb></lb>e Lodovico Cardi Cigoli, che appuntano la matita dei pittori a di­<lb></lb>segnare le macchie solari. </s>

<s>Anzi il Passignani ne fu osservatore così <lb></lb>diligente e appassionato, da venire in contesa con Galileo. </s>

<s>A lui in <lb></lb>ogni modo si dee la prima osservazione di quelle profondità vora­<lb></lb>ginose, che ammannirono al Wilson, tanti anni dopo, le sue teorie <lb></lb>(Alb. </s>

<s>VIII, 170). a lui le prime osservazioni delle montuosità nella <lb></lb>circonferenza lunare (MSS. Galil. </s>

<s>Div. </s>

<s>II. P. I. T. VII, c. </s>

<s>12). </s></p><p type="main">

<s>Il Cigoli lasciò manoscritto un libro di Prospettiva, a cui, per <lb></lb>essere stampato, non mancò nemmeno l&#039;approvazione ecclesiastica <lb></lb>sottoscritta nel dì 6 di Febbraio 1628 (MSS. Gal. </s>

<s>Div. </s>

<s>III. T. VIII, <lb></lb>c. </s>

<s>107). L&#039;Alberti e il Vinci avevano immaginato qualche ingegno, <lb></lb>per eseguire con più facilità e prestezza, che non per le solite regole <lb></lb>delle linee, i disegni di Prospettiva, ma il Cigoli riconoscendoli <lb></lb>all&#039;arte di piccolo aiuto, inventò due nuovi strumenti, nella loro <lb></lb>semplicità ingegnosissimi, che egli nel II libro del suo Trattato <lb></lb>minutamente descrive nelle parti e nell&#039;uso. </s>

<s>Benchè le regole, che <lb></lb>ivi egli espone dell&#039;arte sua, sieno puramente pratiche, senz&#039;altra <lb></lb>dimostrazione; non si può tuttavia lasciar di notare che v&#039;è trattata <lb></lb>un importante questione scientifica, ed è quella del modo e del <lb></lb>luogo dove si rappresenta la vista. </s>

<s>Che la vista non si faccia nella <lb></lb>parte anteriore dell&#039;occhio, e nemmeno del centro del cristallino, <lb></lb>come diceva Galileo, il Pittore lo dimostra con argomenti e con <lb></lb>esperienze si nuove, che se ne potrebbe onorar degnamente qua­<lb></lb>lunque filosofo. </s>

<s>“ Quando si fa qualche concorso di materia fra il <pb xlink:href="020/01/167.jpg" pagenum="148"></pb>cristallino e la cornea, egli dice, ci par veder per l&#039;aria alquanto <lb></lb>lontano qualche cosa di simile alla tela del ragno, e così di colore <lb></lb>oscuro...... il che ci fa manifesto che la sensazione è più interna <lb></lb>dell&#039;umore acqueo e non pare che possa essere il centro del cri­<lb></lb>stallino perchè come centro non è capace della diversa quantità ” <lb></lb>(ivi, c. </s>

<s>25). </s></p><p type="main">

<s>Il Cigoli però, così come il Sagredo, erano alieni dal far pro­<lb></lb>fessione di scienza: l&#039;Antonini, il Marsili, l&#039;Aproino non ne ave­<lb></lb>vano nemmeno essi la pretensione, il Passignani che pretendeva <lb></lb>qualche cosa di più, come impotente di studii e di esercizi letterari, <lb></lb>era sotto sotto da&#039;suoi amici deriso. </s>

<s>Ma bisognava pure che l&#039;au­<lb></lb>torità del nuovo principato galileiano fosse primieramente ricono­<lb></lb>sciuta da coloro che esercitavano il ministero della scienza o nel <lb></lb>pubblico insegnamento delle scuole o ne&#039;libri. </s>

<s>Nelle scuole però i <lb></lb>professori facevano assai, se approvavano col silenzio. </s>

<s>Fra coloro poi <lb></lb>che diffondevano la scienza sperimentale ne&#039;libri val per tutti l&#039;esem­<lb></lb>pio del genovese Giovan Batista Baliani. </s></p><p type="main">

<s>Chi dipinse il Baliani invidioso delle glorie di Galileo e suo <lb></lb>competitore, non lesse bene addentro nell&#039;animo, e ne&#039;libri di lui. </s>

<s><lb></lb>Il Trattato <emph type="italics"></emph>De motu naturali<emph.end type="italics"></emph.end> è, nell&#039;aperta intenzione dello stesso <lb></lb>autore, una conferma dei teoremi dimostrati ne&#039;Dialoghi delle <lb></lb>Scienze Nuove, conclusi per una via diversa e in un altro modo, <lb></lb>che, per il lucido ordine e per la brevità, riesce maraviglioso. </s>

<s>Chi <lb></lb>vuol vedere qual fosse l&#039;animo del filosofo genovese verso il Prin­<lb></lb>cipe della Nuova Filosofia, ne legga il commercio epistolare, spe­<lb></lb>cialmente là dove la libertà del giudizio concilia fede alla sincerità <lb></lb>dell&#039;ossequio. </s>

<s>Così là dove critica la teoria delle comete data nel <lb></lb>Saggiatore (Alb. </s>

<s>Supplem. </s>

<s>pag. </s>

<s>136); così là dove dice che non è <lb></lb>tolta una delle maggiori difficoltà, nel risolvere, nell&#039;ultimo Dialogo <lb></lb>dei Due Massimi Sistemi, il maraviglioso problema del flusso del <lb></lb>mare (Alb. </s>

<s>IX, 266). </s></p><p type="main">

<s>Con fiducia di discepolo ricorre il Baliani a Galileo, quando <lb></lb>vuol saper quanto vada lungo il pendolo che batte i secondi, per <lb></lb>servirsene, fra i tanti usi, a quello di trovare le longitudini; quando <lb></lb>vuol imparare il modo di ritrovare il peso specifico dell&#039;aria, quando <lb></lb>conferisce con lui i suoi pensieri intorno alla pressione atmosferica, <lb></lb>per cui si sostien l&#039;acqua dentro i sifoni, non più su che a una <lb></lb>determinata altezza. </s></p><p type="main">

<s>Ma che ci tratteniamo noi con gli ammiratori seguaci o dietro <lb></lb>a coloro che ne professarono le dottrine, con ossequio di discepoli? <pb xlink:href="020/01/168.jpg" pagenum="149"></pb>A confermar Galileo nel principato della scienza conferirono massi­<lb></lb>mamente gli stessi suoi contradittori. </s>

<s>Si venne a verificare così anche <lb></lb>da questa parte quella approvata sentenza, che i nostri più grandi <lb></lb>benefattori sono i nostri propri nemici. </s>

<s>Quanti gran benefizi infatti <lb></lb>non vennero alla scienza dalle contradizioni dei peripatetici? </s>

<s>Si dee <lb></lb>senza dubbio a costoro l&#039;aver dato occasione a Galileo di scrivere <lb></lb>più che la metà de&#039;suoi libri, e dei più belli: essi, nel fare ogni <lb></lb>sforzo di toglierla, gli confermarono in fronte la corona del Principato. </s></p><p type="main">

<s>E ora che, co&#039;savii ordini instaurati e coll&#039;esempio del suo <lb></lb>valore, è riuscito a conquistarsi quella corona, concludiamo i gran­<lb></lb>dissimi benefizi che alla Repubblica della scienza seguitarono da <lb></lb>tale conquista. </s>

<s>A far ciò non bisogna oramai a noi troppo lunghe <lb></lb>parole, ritornando indietro colla memoria ai principii del nostro <lb></lb>Discorso. </s>

<s>Dicemmo infatti che la miglior maniera da ringiovanire <lb></lb>l&#039;albero della scienza, per troppo lunga età trascorso, era quello di <lb></lb>ravviare i succhi nutritivi dispersi, e condensar gli spiriti dissipati <lb></lb>in un tronco solo. </s>

<s>Questo è ciò appunto che riuscì di fare a Galileo, <lb></lb>e per cui egli è così meritamente glorioso. </s></p><p type="main">

<s>Noi rassomigliammo col Verulamio la grande impresa a una <lb></lb>conquista politica, nella quale la forza sola non basta, se non và <lb></lb>spesso congiunta coll&#039;astuzia. </s>

<s>Di queste astuzie, da noi di sopra <lb></lb>notate nella vita scientifica di Galileo, molti saranno rimasti scan­<lb></lb>dalizzati, ma costoro se non s&#039;acquietano ai fatti si acquietino al­<lb></lb>meno in quel principio che, nella infermità delle operazioni umane, <lb></lb>suol prevalere alla retta morale, del fine che giustifica i mezzi. </s>

<s>Tru­<lb></lb>cidare i fratelli e arricchirsi delle loro spoglie, è un mezzo illecito, <lb></lb>ma pure era necessario a instituire una Monarchia nella scienza, <lb></lb>com&#039;è necessario al fine del villico il trucidare in un albero i rami. </s>

<s><lb></lb>Fossero rimaste le varie speculazioni e le varie scoperte disperse <lb></lb>nello Stevino, nel Santorio, nel Cavalieri e in tanti altri, non sareb­<lb></lb>bero riuscite ai progressi delle scienze sperimentali tanto efficaci, <lb></lb>come digeste in uno stomaco solo, d&#039;onde si dispenseranno a tante <lb></lb>membra la vita e gli alimenti. </s></p><p type="main">

<s>Ripensando quello a che fu dalla Provvidenza riserbato Galileo, <lb></lb>chi meglio lo riconosce nell&#039;esser suo, e più l&#039;ammira. </s>

<s>Egli non <lb></lb>fu, ne poteva essere il creatore della scienza sperimentale, ma ne <lb></lb>fu il rigeneratore, e tra poco vedremo la fecondità della sua prole. </s>

<s><lb></lb>Prima però convien che ci tratteniamo intorno agli ordini e agli <lb></lb>effetti di quell&#039;altra Instaurazione, a cui s&#039;accennava già in quel <lb></lb>primo nostro introdursi a discorrer di questa. </s></p><pb xlink:href="020/01/169.jpg" pagenum="150"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Non aveva ancora Galileo dato l&#039;ultima mano alla costituzione <lb></lb>del suo nuovo Regno, che si leva dalla montagnosa Bretagna un <lb></lb>vento impetuoso a ferire, abbattere e disperdere tutto ciò che egli <lb></lb>incontra per via. </s>

<s>Quel vento è l&#039;orgoglio filosofico di Renato Car­<lb></lb>tesio, il quale proclamando ad alta voce che tutto il mondo era fino <lb></lb>a quel tempo vissuto nelle tenebre e nell&#039;errore, viene ad abbat­<lb></lb>tere il tristo e buio tugurio dell&#039;ignoranza per sostituire ad esso, <lb></lb>di sua propria mano ricostruito, il nuovo edifizio della scienza. </s></p><p type="main">

<s>È questo dunque un conquistatore ben assai più ardito: Galileo <lb></lb>rispettò i placiti dell&#039;antica filosofia, e fecesi discepolo di Platone, <lb></lb>seguace di Archimede; il suo Regno è circoscritto, e non esce fuori <lb></lb>della cerchia dei fatti naturali. </s>

<s>Il Cartesio invece protesta di non <lb></lb>riconoscere tradizioni di nessuna maniera; la sua impresa è quella <lb></lb>di voler da sè solo restaurar la scienza universale. </s>

<s>Se egli avesse <lb></lb>confidato in segreto a qualche suo savio amico questa ardita inten­<lb></lb>zione, ei ne lo avrebbe senza dubbio distolto, dicendogli non poter <lb></lb>esser quella altro che una follia. </s>

<s>Ma pure è mirabile che uscito il <lb></lb>Cartesio in pubblico, a divisare gli ordini e i modi di quella sua <lb></lb>titanica impresa, tutt&#039;altro ch&#039;esser tenuto folle, ebbe plauso dalla <lb></lb>turba maravigliata e titolo di sapiente. </s></p><p type="main">

<s>Il libro, in cui si divisano quegli ordini e quei modi, uscì in <lb></lb>pubblico nel 1637 con un titolo, che si tradusse in quello di <emph type="italics"></emph>Spe­<lb></lb>cimina Fhilosophiae<emph.end type="italics"></emph.end> o altrimenti <emph type="italics"></emph>Dissertatio de methodo recte re­<lb></lb>gendae rationis.<emph.end type="italics"></emph.end> La bellezza del patrio lìnguaggio, in cui prima uscì <lb></lb>fuori alla luce il libro, fu una delle principali cagioni per cui ri­<lb></lb>masero così dolcemente allettati, e quasi si direbbe sedotti i lettori. </s>

<s><lb></lb>Altra poi di quelle cagioni fu senza dubbio un aura conciliatrice <lb></lb>di pace nella prima, e un approvato sentimento di verità nell&#039;altre <lb></lb>due regole provvisorie da seguirsi, intanto che, distrutta la vecchia, <lb></lb>non si sia rifatta dall&#039;Autore e ricostruita la nuova scienza morale. </s></p><p type="main">

<s>L&#039;efficacia poi di queste regole sull&#039;animo del lettore, e quel­<lb></lb>l&#039;aura conciliatrice di pace che si diceva, si rendono manifeste dal <lb></lb>considerar che la bellezza e la verità di quelle stesse regole son che <lb></lb>tolgono ai divisamenti dell&#039;Autore il carattere della follia. </s>

<s>Perciò <pb xlink:href="020/01/170.jpg" pagenum="151"></pb>questi son passati e quasi non sentiti in grazia di quelle, e la con­<lb></lb>tradizione, che fra loro è manifesta, finisce poi di operare la seduzion <lb></lb>dell&#039;effetto. </s></p><p type="main">

<s>Che fra le regole del metodo e i divisamenti del Cartesio passi <lb></lb>un&#039;aperta contradizione si prova con facilità in poche parole. </s>

<s>È la <lb></lb>prima di quelle regole infatti che si debbono seguir le usanze del <lb></lb>proprio paese. </s>

<s>Questa regola è senza dubbio conciliatrice di pace, <lb></lb>ma è in aperta contradizione coi principii professati dall&#039;Autore, <lb></lb>secondo i quali son quelle usanze false, perchè suggerite dalla igno­<lb></lb>ranza universale. </s></p><p type="main">

<s>La terza regola bellissima è che non si dee voler mutar l&#039;or­<lb></lb>dine al mondo, ma alle nostre cupidigie. </s>

<s>Ora se si trasporta questa <lb></lb>regola dalla Filosofia morale, alla naturale, contradice apertamente <lb></lb>ai metodi filosofici del Cartesio, conforme ai quali il mondo si muta <lb></lb>veramente a seconda delle cupidigie del nostro intelletto. </s>

<s>E di ciò <lb></lb>basti la famosa teoria dei vortici per esempio. </s></p><p type="main">

<s>Senz&#039;altro, s&#039;intravede già che se Galileo è il Platone di questo <lb></lb>nuovo periodo del risorgimento della scienza, il Cartesio è l&#039;Aristo­<lb></lb>tile. </s>

<s>E tanto è vivo e incarnato lo spirito del filosofo di Stagira nelle <lb></lb>membra del Filosofo bretone, che d&#039;ogni parte ne traspira la so­<lb></lb>miglianza. </s>

<s>Aristotile accomoda la Natura alla capacità del proprio <lb></lb>intelletto, e la ragion dei fatti la fa scaturire dall&#039;artificiosa dialet­<lb></lb>tica dei sillogismi. </s>

<s>Perciò quanto una di queste ragioni è più sottile <lb></lb>e arguta, tanto ha secondo lui più sapore di vero. </s>

<s>La facilità di <lb></lb>spiegare i fatti naturali si aborrisce da lui e dalla sua scuola, come <lb></lb>segno della impotenza della ragione a dominarli. </s></p><p type="main">

<s>Che da un simile principio sien pure informate le fisiche spe­<lb></lb>culazioni del Cartesio, due soli fra i molti esempii piace a noi di <lb></lb>sciegliere per provarlo, e son questi due esempi l&#039;uno tolto dalla <lb></lb>ragion ch&#039;ei rende dell&#039;origine dei venti, l&#039;altro dell&#039;origine delle <lb></lb>fonti. </s>

<s>La vecchia fisica ammetteva che le esalazioni di sotto terra <lb></lb>commovessero i vapori dell&#039;aria, e così avessero origine i venti. </s>

<s>Al <lb></lb>Cartesio troppo facile parve questa spiegazione, nè men semplice <lb></lb>e quasi puerile gli sembrò quell&#039;altra delle dilatazioni e dei con­<lb></lb>densamenti, che l&#039;avvicendarsi del calore e del freddo producono <lb></lb>sulla mole dell&#039;aria. </s>

<s>Perciò soccorse così a quel difetto colle arguzie <lb></lb>della sua nuova filosofia. </s>

<s>Immaginò che le dilatazioni, da cui vien <lb></lb>commossa l&#039;aria, si producessero nelle minime particelle del vapore, <lb></lb>le quali, agitate e mosse in giro dal secondo elemento, occupano <lb></lb>maggiore spazio, a somiglianza di una bandiera menata in volta <pb xlink:href="020/01/171.jpg" pagenum="152"></pb>dalle agili mani dell&#039;alfiere. </s>

<s>“ Quum vaporis formam habent, agi­<lb></lb>tatio illarum adeo est concitata ut celerrime rotentur in omnes <lb></lb>partes, quemadmodum baculo per quem funiculus traiectus est, ce­<lb></lb>lerrime rotato, videmus funiculum rectum atque extensum porrigi ” <lb></lb>(Meter. </s>

<s>Francof. </s>

<s>1692, pag. </s>

<s>131). </s></p><p type="main">

<s>La scmplicità della fisica antica ammetteva che dagli stillicidi <lb></lb>delle nevi e dalla infiltrazione delle acque piovane avessero la loro <lb></lb>origine le fonti. </s>

<s>Ma il Cartesio, come di sopra era ricorso all&#039;arguzia <lb></lb>delle banderuole, così qui ricorre all&#039;arguzia degli alambicchi. </s>

<s>Im­<lb></lb>maginò che le acque del mare s&#039;insinuassero di sottoterra e si sol­<lb></lb>levassero allo stato di vapori, i quali condensati poi dal freddo sotto <lb></lb>le cupole dei monti, giusto come nel cappello dell&#039;alambicco, tor­<lb></lb>nassero ad apparire qua e là in acque sorgenti. </s></p><p type="main">

<s>Questa nuova sorta di Filosofia naturale, che tanto al vivo si <lb></lb>rassomiglia alla vecchia filosofia di Aristotile, viziata nelle radici, <lb></lb>non poteva non riuscir, al pari di quella, sterile di buoni frutti. </s>

<s><lb></lb>Quali frutti in verità dette la Filosofia cartesiana alle scienze speri­<lb></lb>mentali? </s>

<s>È vero che il celebre Autore della Dissertazione del Me­<lb></lb>todo formulò nella Diottrica la legge delle rifrazioni, e divisò nella <lb></lb>Meteorologia il modo vero del dipingersi e del rappresentarsi ai <lb></lb>nostri occhi l&#039;iride in cielo, ma sta a vedere se questi sieno ve­<lb></lb>ramente frutti della Filosofia cartesiana. </s>

<s>Il Newton, a principio gli <lb></lb>credette tali, ma poi si ridisse, e attribuì la legge delle rifrazioni <lb></lb>allo Snellio, e al De Dominis la teoria dell&#039;arco baleno. </s></p><p type="main">

<s>Meglio che al manoscritto dello Snellio, come fu primo a in­<lb></lb>sinuare l&#039;Huyghens, il quale però, a riscontrare il fatto sulle pagine <lb></lb>dello stesso manoscritto fu secondo dopo Isacco Vossio; noi credia­<lb></lb>mo che il Cartesio attingesse piuttosto a un libro stampato, qual&#039;è <lb></lb>il Corso matematico di Pietro Herigonio. </s>

<s>Perciò, non è merito del­<lb></lb>l&#039;Autore della Diottrica nemmeno l&#039;aver formulata, come l&#039;Huyghens <lb></lb>e il Newton par che gli concedano, quella legge della proporzione <lb></lb>costante fra i seni degli angoli incidenti e dei rifratti: nè suoi pure, <lb></lb>ma del Keplero, ne sono i principii dimostrativi. </s></p><p type="main">

<s>Quanto all&#039;iride, il Newton che nelle Lezioni di Ottica s&#039;era <lb></lb>contentato di dire essere stata dal Cartesio, a spiegare il fenomeno, <lb></lb>apparecchiata la via, nel Trattato di Ottica poi dice che fu il De <lb></lb>Dominis <emph type="italics"></emph>vir celeberrimus,<emph.end type="italics"></emph.end> il quale prima insegnò che l&#039;iride inte­<lb></lb>riore si fa per due rifrazioni e una riflessione e l&#039;esteriore per due <lb></lb>rifrazioni e due riflessioni. </s>

<s>Or, per amore alla verità, convien dire <lb></lb>che questo è falso, e siam costretti a concludere che il Newton o <pb xlink:href="020/01/172.jpg" pagenum="153"></pb>non vedesse o non esaminasse bene il Trattato <emph type="italics"></emph>De radiis visus et <lb></lb>lucis<emph.end type="italics"></emph.end> del celebre spalatrese. </s>

<s>È chiaro infatti che le doppie rifrazioni <lb></lb>e le doppie riflessioni del De Dominis hanno tutt&#039;altro significato <lb></lb>che nel Cartesio, e se queste son conformi alla verità, quelle son <lb></lb>delle solite peripatetiche immaginazioni. </s>

<s>Nè affatto giusta sembra <lb></lb>a noi quell&#039;altra sentenza del Newton che cioè il Cartesio non in­<lb></lb>tendesse la natura dei colori, avendo egli rassomigliati i colori del­<lb></lb>l&#039;iride a quelli in che si disperdono i raggi del sole refratti attra­<lb></lb>verso ai prismi triangolari. </s></p><p type="main">

<s>Se qualcuno perciò precedè il Cartesio nella scientifica spie­<lb></lb>gazione del fenomeno meteorologico, questi fu, nò il De Dominis <lb></lb>ma Ferrante Imperato. </s>

<s>E perchè non è facile che il lontano e su­<lb></lb>perbo Bretone si piegasse a leggere l&#039;Historia Naturale del nostro <lb></lb>Napoletano, non resta ad ammettere se non che egli attingesse, <lb></lb>come da prima fonte, al Maurolico citato dallo stesso Cartesio con <lb></lb>orgoglioso disprezzo. </s></p><p type="main">

<s>Or il Maurolico, che fra tutti i precursori del Newton fu primo <lb></lb>a intraveder la teoria dei colori e a trattar dell&#039;iride come d&#039;un <lb></lb>fenomeno d&#039;ottica matematica, bastava solo ad aprir la via al Car­<lb></lb>tesio, a cui, prevenuto già nell&#039;esperienza delle palle piene d&#039;acqua <lb></lb>che appariscono iridescenti collocate, rispetto all&#039;occhio, in deter­<lb></lb>minata posizione e distanza; non bisognò, a risolvere il problema, <lb></lb>altro più che l&#039;uso del calcolo e della geometria. </s></p><p type="main">

<s>Qui poi, cioè nel calcolo geometrico consistono i meriti singo­<lb></lb>lari del Cartesio, il quale ci rivela anco da questa parte lo spirito <lb></lb>aristotelico informatore della sua nuova Filosofia. </s>

<s>Si vide infatti che <lb></lb>unico frutto della scuola peripatetica non fu che l&#039;algebra, come <lb></lb>l&#039;algebra applicata fu pure l&#039;unico frutto della scuola cartesiana. </s>

<s><lb></lb>Questa stessa applicazione dell&#039;Algebra alla Geometria rende la ra­<lb></lb>gione di qualcuno di quei progressi, che lo stesso Cartesio fece nella <lb></lb>Meccanica, benchè anco di qui trasudi la pece aristotelica in quelle <lb></lb>sofistiche sottigliezze, tese qua e là, per le sue Lettere, come lacci <lb></lb>insidiosi, a cogliere in fallo i teoremi di Galileo. </s></p><p type="main">

<s>Ma della sterilità d&#039;ogni buon frutto di scienza sperimentale il <lb></lb>Cartesio da sè stesso s&#039;accusa e si confessa. </s>

<s>S&#039;accusa, quando, nella <lb></lb>Prefazione alla traduzione latina dei Principii della Filosofia, dice <lb></lb>che gli resterebbe a trattar della Medicina e delle arti meccaniche, <lb></lb>per le quali si richiedono sperimenti e spese <emph type="italics"></emph>quibus privatus qualis <lb></lb>ego sum nisi a publico adiuvaretur par esse non posset.<emph.end type="italics"></emph.end> Galileo, <lb></lb>che fu tanto più povero di lui, non fece mai di queste scuse, e si <pb xlink:href="020/01/173.jpg" pagenum="154"></pb>liberò dalle spese, che occorrono a sperimentare, fabbricando gli <lb></lb>strumenti colle sue proprie mani. </s></p><p type="main">

<s>Il Cartesio altresì da se stesso si confessa, quando in sulla fine <lb></lb>della sua celebre Dissertazione del Metodo, dop&#039;avere accennato <lb></lb>alle dottrine fisiche professate ed esposte nella Diottrica e nella <lb></lb>Meteorologia, soggiunge queste parole: “ Nec me etiam primum <lb></lb>ullarum inventorem esse iacto, sed tantum me nunquam illas pro <lb></lb>meis adoptasse, vel quod ab aliis prius receptae fuissent, vel quod <lb></lb>non fuissent, verum unicam hanc ob causam quod mihi eas ratio <lb></lb>persuasisset ” (Francof. </s>

<s>1692, pag. </s>

<s>40). E così intende forse di sde­<lb></lb>bitarsi col Maurolico e col Keplero, col De Dominis e con lo Snellio. </s></p><p type="main">

<s>Ma come si conciliano così fatte confessioni colle orgogliose <lb></lb>pretese del Cartesio? </s>

<s>Una tal domanda non può mover che da co­<lb></lb>loro, i quali si persuadono che l&#039;Autore della Dissertazione del Me­<lb></lb>todo dasse qualche importanza alla spiegazione di un particolar fatto <lb></lb>di Ottica o di Meleorologia. </s>

<s>Queste non son per lui altro che miche <lb></lb>cadute giù da più lauta mensa. </s>

<s>Miche son tutte quelle raccattale <lb></lb>ne&#039;suoi libri da Galileo, e fra quelle stesse miche, dalla teoria della <lb></lb>musica in fuori, non ci è nulla di buono. </s>

<s>Che se tu vuoi sedere <lb></lb>al convito della scienza, par che egli dica al lettore, cerca il mio <lb></lb>libro che s&#039;intitola <emph type="italics"></emph>Principii della Filosofia.<emph.end type="italics"></emph.end> Vedrai come dalle co­<lb></lb>gitazioni del lilosofo, nella prima parte dello stesso libro, esca fuori <lb></lb>l&#039;esistenza di Dio e del mondo. </s>

<s>Vedrai, nella terza parte, come, per <lb></lb>mezzo di moti vertiginosi, si stabiliscan le leggi che governano <lb></lb>l&#039;Universo, e nell&#039;ultima di quelle parti assisterai da te stesso al <lb></lb>nascere e al trasformarsi il seno della tua madre Terra. </s></p><p type="main">

<s>Quando si pubblicò il Cosmoleoro dell&#039;Huyghens e il Newton <lb></lb>dimostrò della Filosofia naturale più veri Principii, disparvero quei <lb></lb>seducenti fantasmi cartesiani dagli occhi di tutti. </s>

<s>E che ci rimase <lb></lb>di realtà? </s>

<s>Ci rimase l&#039;Algebra geometrica e i due Trattati <emph type="italics"></emph>Passiones <lb></lb>animae<emph.end type="italics"></emph.end> e <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end> dove s&#039;instituisce l&#039;interiore esame della <lb></lb>coscienza, e i fatti psicologici s&#039;illustrano colle matematiche e colla <lb></lb>fisiologia. </s>

<s>Ecco quel che di scienza vera rimane al Cartesio e alla <lb></lb>Francia. </s>

<s>Tutto il resto vi approdò d&#039;Italia, come frutto di quell&#039;al­<lb></lb>bero che unico seppe metter le radici nel buon terreno, e che ri­<lb></lb>mase perciò unico a regnare in mezzo alla foresta. </s></p><p type="main">

<s>Mentre la patria insomma, lusingata dal seducente linguaggio <lb></lb>e dalle belle promesse, s&#039;aspettava di riposare all&#039;ombra, e sten­<lb></lb>dendo la mano ai rami dell&#039;amata indigena pianta, largamente <lb></lb>saziar la fame della scienza, si trovò a mendicare altri frutti ma-<pb xlink:href="020/01/174.jpg" pagenum="155"></pb>turati sotto altro sole in terra straniera. </s>

<s>Per men vergogna, e quasi <lb></lb>che alla mendicità si volesse attribuire qualche parte del merito, <lb></lb>il pietoso ufficio fu commesso a due uomini, i quali partecipavano <lb></lb>delle due patrie: Niccolò Fabrizi di Peiresc ed Elia Diodati. </s>

<s>Nati <lb></lb>ambedue di stirpe Toscana, dalla Toscana trapiantarono in Francia <lb></lb>la scienza, come i loro avi vi avevano già trapiantata la famiglia, <lb></lb>e per loro mezzo principalmente risuonò in fin là il nome di Ga­<lb></lb>lileo, e vi si diffusero le dottrine. </s>

<s>Ismaele Bullialdo ne illustrava <lb></lb>le dottrine astronomiche e Pier Gassendo le meccaniche. </s>

<s>La fisica <lb></lb>sperimentale, anch&#039;essa dal Cartesio antivacuista resa impotente, <lb></lb>fu introdotta in Francia da Marino Mersenno, l&#039;insetto volante, che <lb></lb>portò d&#039;Italia sull&#039;ali il polline fecondatore. </s></p><p type="main">

<s>Qual più piena conquista, qual più larga vittoria si poteva ri­<lb></lb>promettere il nostro grande Italiano? </s>

<s>Quell&#039;orgoglioso Bretone, che, <lb></lb>per libidine di regnar solo, intendeva non tanto di trucidare i fra­<lb></lb>telli, ma disperdere per fino ogni memoria degli avi, rimase tru­<lb></lb>cidato anch&#039;esso, non dalla punta, ma dall&#039;ombra della spada di <lb></lb>Galileo, il cui Regno unico dura, e i discendenti del quale son come <lb></lb>terribile oste ordinata in battaglia contro l&#039;errore. </s></p><p type="main">

<s>Sarebbe ora il tempo per noi di passare in rivista quei com­<lb></lb>battenti sotto un unica insegna, se non ci attraessero a sè gli sguardi <lb></lb>due ombre solitarie, che avvolte nel pallio filosofale procedono con <lb></lb>regal maestà indipendenti. </s>

<s>Come mai, in mezzo alla strage otto­<lb></lb>manna de&#039;due fieri conquistatori, essi soli son rimasti superstiti, <lb></lb>quasi fossero giudicati i soli meritevoli di compartecipare alle glorie <lb></lb>del Regno? </s>

<s>Sono essi Guglielmo Gilbert, e Guglielmo Harvey, sui <lb></lb>quali due, per conoscerli meglio, convien tener alquanto fisso lo <lb></lb>sguardo. </s></p><p type="main">

<s>Fruga senza dubbio la nostra curiosità il veder che Galileo, <lb></lb>unico fra i contemporanei, accoglie il Gilbert e l&#039;esalta quasi alla <lb></lb>dignità dei Filosofi antichi. </s>

<s>Nè con minore curiosità pure si osserva <lb></lb>che il Cartesio, nel Gilbert e nell&#039;Harvey, come nelle due sole im­<lb></lb>mobili torri, abbia fiaccato il vento desolatore della sua superbia. </s>

<s><lb></lb>Ciò vuol dire esser grandi davvero, se come tali furon sentiti e <lb></lb>temuti da quei due che volevano sovraneggiare su tutti; ond&#039;ei non <lb></lb>è fuor di proposito l&#039;investigar qui brevemente, di quella grandezza <lb></lb>che esce così fuori dell&#039;ordinario, la ragione e i meriti. </s></p><p type="main">

<s>Nè in ordine a ciò è da lasciar di notare per prima cosa che <lb></lb>i due grandi Inglesi si distinguono per due qualità diverse; l&#039;uno <lb></lb>dedito principalmente all&#039;esperienza, l&#039;altro alla speculazione. </s>

<s>Il <pb xlink:href="020/01/175.jpg" pagenum="156"></pb>libro <emph type="italics"></emph>De magnete<emph.end type="italics"></emph.end> è una sequela di fisici sperimenti, senza dubbio <lb></lb>avvedutissimi e nuovi, ma che tutti si aggirano intorno al medesimo <lb></lb>soggetto, con una certa prolìssità, non forse ingiustamente notata <lb></lb>dal Verulamio. </s>

<s>Di speculazioni veramente non ha il Gilbert altro <lb></lb>che quel concetto lodato da Galileo, e qualificato per istupendo, di <lb></lb>riguardar cioè la Terra come un magnete e il magnete stesso come <lb></lb>una terrella. </s>

<s>Del resto egli rifugge dall&#039;approvar que&#039;fluidi magne­<lb></lb>tici introdotti dal Sarpi e dal Porta, e gli piace meglio di dar, con <lb></lb>l&#039;antico Talete e con lo Scaligero, alla calamita spirito di vita e <lb></lb>senso animale. </s></p><p type="main">

<s>L&#039;esercitazione anatomica <emph type="italics"></emph>De motu cordis<emph.end type="italics"></emph.end> dell&#039;Harvey è al <lb></lb>contrario tutta una speculazione. </s>

<s>Non è egli mica che dimostri spe­<lb></lb>rimentalmente il moto del sangue nel circolo universale dei vasi. </s>

<s><lb></lb>Egli lo induce principalmente dall&#039;anatomia delle arterie e dalle <lb></lb>valvole delle vene. </s>

<s>Del resto, egli non sa se veramente il sangue <lb></lb>arterioso ritorni nelle vene per anastomosi, o perchè le vene stesse <lb></lb>lo risorbono disperso e ristagnante in mezzo alle fibre muscolari. </s>

<s><lb></lb>L&#039;esperienza stessa proposta da Galeno a lui pare impossibile d&#039;ese­<lb></lb>guirla negli animali vivi. </s>

<s>Non gli par che possa riuscire a nessuno <lb></lb>d&#039;introdurre un cannellino di materia trasparente nelle due imboc­<lb></lb>cature dell&#039;arteria recisa, e ciò per la gran violenza del sangue <lb></lb>che irrompe. </s>

<s>Eppure il nostro Tommaso Cornelio dimostrò, contro <lb></lb>l&#039;Harveio, che l&#039;esperienza di Galeno si poteva benissimo praticare, <lb></lb>e, negli animali vivi, por, sotto gli occhi de&#039;riguardanti stupiti, il <lb></lb>sangue che fugge espulso dalla sistole del cuore. </s></p><p type="main">

<s>L&#039;altro libro non men celebre dell&#039;Harvey è quello <emph type="italics"></emph>De gene­<lb></lb>ratione animalium.<emph.end type="italics"></emph.end> Si disse che per lui fù finalmente cacciato quel <lb></lb>pernicioso errore della generazione spontanea. </s>

<s>Chi vi torna sopra <lb></lb>però con più maturo giudizio, è costretto a concludere che il gran <lb></lb>Filosofo inglese niente altro fa che sostituire a un errore, un errore <lb></lb>più vieto. </s>

<s>Egli ammette infatti nella materia certi principii animali, <lb></lb>predisposti dall&#039;Artefice eterno, nella primitiva creazion delle cose: <lb></lb>principii che l&#039;Elmont chiamò col nome di <emph type="italics"></emph>archei,<emph.end type="italics"></emph.end> e l&#039;Harveio, con <lb></lb>fedel traduzione, primordii. </s>

<s>Da così fatti principii disseminati qua <lb></lb>e là per l&#039;aria e caduti per caso in parte dove trovassero favore­<lb></lb>voli condizioni al loro incubamento, avrebbero, secondo l&#039;Autore, <lb></lb>origine tutti quegl&#039;insetti, che non riconoscono un padre. </s>

<s>Ma a di­<lb></lb>mostrar che veramente ogni animale, sia pure di qualunque infimo <lb></lb>ordine, riconosce un padre e una madre della medesima specie, vi <lb></lb>bisognavano quelle attente e pazientemente ripetute esperienze, alle <pb xlink:href="020/01/176.jpg" pagenum="157"></pb>quali si credeva l&#039;Harvey di poter supplir con le ipotesi e con le <lb></lb>induzioni: esperienze che poi riuscirono così bene alle mani del <lb></lb>Redi e del Malpighi. </s></p><p type="main">

<s>In ogni modo, il Gilbert e l&#039;Harvey sono due ingegni singo­<lb></lb>lari: il primo è mirabile per l&#039;arte squisitissima di sperimentare e <lb></lb>l&#039;altro per una potentissima virtù d&#039;indurre la verità dai fatti sem­<lb></lb>plicemente osservati. </s>

<s>Se avessero avuta comune la potenza dell&#039;in­<lb></lb>gegno, com&#039;ebbero comune la patria, d&#039;ambedue loro insieme sa­<lb></lb>rebbe uscita al mondo una cosa perfetta. </s></p><p type="main">

<s>Or su quale albero mai è maturata quella tal perfezione? </s>

<s>Sul­<lb></lb>l&#039;albero vecchio, rispondasi, della scienza italiana. </s>

<s>Chi legge la Fi­<lb></lb>siologia Nuova del Magnete non ha bisogno di tanti argomenti a <lb></lb>persuadersi che il Gilbert non attinge d&#039;altronde le prime tradi­<lb></lb>zioni della scienza magnetica che dall&#039;Italia; dal Fracastoro, dal <lb></lb>Sarpi, dal Porta. </s>

<s>Chi legge l&#039;Esercitazione anatomica <emph type="italics"></emph>De motu cordis<emph.end type="italics"></emph.end><lb></lb>non ha bisogno di far tante domande: risponde da sè medesimo <lb></lb>l&#039;Autore, più coi fatti che con le parole, esser quello il frutto elet­<lb></lb>tissimo degli insegnamenti padovani. </s></p><p type="main">

<s>Consolati dall&#039;ammirar tali due frutti che insaporarono sotto i <lb></lb>soli d&#039;Italia, sopra i più sporgenti rami del vecchio albero della <lb></lb>scienza, ora è tempo di venire una volta a veder quai rigogliosi <lb></lb>rampolli, e quale ubertà di frutti si producessero nell&#039;albero nuovo. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il primo e più eletto di quei rampolli, è il bresciano don Be­<lb></lb>nedetto Castelli. </s>

<s>Come nella generazione animale il primogenito <lb></lb>suol, meglio degli altri parti, rassomigliar le virtù e le fattezze stesse <lb></lb>del padre; così nelle opere dell&#039;ingegno il Castelli ha più strette <lb></lb>le somiglianze con Galileo. </s>

<s>L&#039;Autore dei Dialoghi del moto, potè <lb></lb>con diritto intitolar quell&#039;opera <emph type="italics"></emph>Scienza Nuova,<emph.end type="italics"></emph.end> e Scienza Nuova, <lb></lb>con pari diritto, poteva intitolare i suoi libri l&#039;Autore della Misura <lb></lb>delle acque correnti. </s>

<s>Nè l&#039;esser preceduto dall&#039;Alberti e dal Cardano <lb></lb>o dal più antico Frontino gli toglie nulla a quella novità, o gli detrae <lb></lb>del suo principato, se per poco si ripensi che non consiste la scienza <lb></lb>in alcune pratiche cognizioni, ma nell&#039;ordinata sequela di teoremi <lb></lb>dimostrati e conclusi da veri e approvati principii. </s>

<s>Non gli detrae <pb xlink:href="020/01/177.jpg" pagenum="158"></pb>nulla Leonardo da Vinci, le speculazioni e l&#039;esperienze del quale <lb></lb>rimanevano tuttavia informi e sepolte nei manoscritti. </s>

<s>In ogni modo, <lb></lb>gli errori che si commettevano nelle dispense delle acque in Lom­<lb></lb>bardia, con sì grave danno ora dei compratori, ora dei venditori, <lb></lb>attestano che a quei tempi nessuno ancora gli aveva notati, e se <lb></lb>tanto zelo bisognò al Castelli per persuader quelle verità negli usi <lb></lb>inveterati, è ciò manifestissimo segno dell&#039;apparir nuove fra gli <lb></lb>uomini le verità stesse predicate da lui. </s>

<s>Nuove, non che ad altri, <lb></lb>apparvero al medesimo Galileo, come, per citare un fatto solo, po­<lb></lb>trebbesi argomentar facilmente comparando il Discorso contro il <lb></lb>Bertazzolo, con la Lettera sul fiume Bisenzio. </s></p><p type="main">

<s>Altro punto di rassomiglianza, che il Castelli ha con Lui che <lb></lb>lo aveva generato alla scienza, è l&#039;ardor di diffondere quelle astro­<lb></lb>nomiche verità, che un profondo sentimento sincero di Religione <lb></lb>gli persuadeva esser tanto meglio adattate degli antichi sistemi a <lb></lb>rivelar le glorie del Creatore. </s>

<s>Nelle fasi di Venere, prima che Ga­<lb></lb>lileo gli avesse palesati i suoi pensieri, nei moti di alcune stelle, che <lb></lb>ei dubita esser effetti della parallasse annuale, sagacemente intra­<lb></lb>vede argomenti concludenti<gap></gap>simi a confermare la verità del sistema <lb></lb>copernicano. </s>

<s>Nel piccolo mondo gioviale riconosce perfettamente <lb></lb>ritratta l&#039;immagine del più gran mondo solare, e nelle quattro lune <lb></lb>che si rivolgono intorno al centro di Giove, gli par avere il più <lb></lb>bello argomento a provar che i pianeti si rivolgono in simil modo <lb></lb>intorno al centro del sole. </s>

<s>Egli, più infaticabile forse di quel che <lb></lb>non apparisce dai pochi documenti rimasti, a calcolar l&#039;Effemeridi <lb></lb>dei quattro satelliti cooperava con Galileo, che di quando in quando <lb></lb>nota ne&#039;suoi Registri, che l&#039;osservazione fatta, per quel tal giorno <lb></lb>e per quell&#039;ora, è <emph type="italics"></emph>Patris Benedicti.<emph.end type="italics"></emph.end> E quando il Cassini attendeva <lb></lb>all&#039;Effemeridi bolognesi, il Viviani, perchè se ne potesse giovare, <lb></lb>e perchè le riscontrasse con le sue nuove osservazioni, gli mandava <lb></lb>una tavola dei moti de&#039;Medicei, incerto se essa apparteneva a Ga­<lb></lb>lileo o al Castelli. </s></p><p type="main">

<s>Nè da passare inconsiderata, a proposito delle esercitazioni <lb></lb>astronomiche del p. </s>

<s>Benedetto, è la prima osservazione di quella <lb></lb>fascia, che precinge il corpo di Giove, con quell&#039;altra, che concerne <lb></lb>la luce secondaria, di che va suffusa la Luna vicina al primo quarto. </s>

<s><lb></lb>Dice che, facendo egli riflessione a quel che Galileo ne&#039;Dialoghi del <lb></lb>Sistema accenna della medesima luce secondaria, più cospicua la <lb></lb>mattina che la sera, adducendone per ragione l&#039;essere in quel tempo <lb></lb>la Luna illuminata dal riflesso di vastissimi continenti della Terra; <pb xlink:href="020/01/178.jpg" pagenum="159"></pb>giudicò che ritrovandosi, in quel tempo che faceva le sue osserva­<lb></lb>zioni, la Luna meridionale, dovesse essere illustrata dalla Terra, e <lb></lb>perciò gli venne in mente che le terre meridionali, allora incognite, <lb></lb>dovessero essere vastissime provincie (Alb. </s>

<s>X, 244). Galileo approvò <lb></lb>la congettura (ivi, pag. </s>

<s>248), e le scoperte geografiche avverarono <lb></lb>il vaticinio. </s></p><p type="main">

<s>Educatosi alla lettura del Saggiatore, che, spiegava come testo <lb></lb>di Fisica nuova nella sua scuola, il Castelli scrisse, in soggetto di <lb></lb>fisica sperimentale, alcuni Trattatelli o Discorsi, amorosamente rac­<lb></lb>colti o fatti pubblicare nel 1669 dal principe Leopoldo dei Medici, <lb></lb>venticinque anni dopo la morte dell&#039;Autore. </s>

<s>Quello <emph type="italics"></emph>Sulla vista<emph.end type="italics"></emph.end> non <lb></lb>è per verità che un commentario delle dottrine ottiche del Keplero. </s>

<s><lb></lb>In quello che egli intitola <emph type="italics"></emph>Mattonata<emph.end type="italics"></emph.end> si descrivono le prime espe­<lb></lb>rienze e si tentano le prime teorie del calorico raggiante, e in <lb></lb>quell&#039;altro <emph type="italics"></emph>Del modo di conservare i grani<emph.end type="italics"></emph.end> si notano per la prima <lb></lb>volta i varii gradi di conducibilità del calore nelle varie costituzioni <lb></lb>dei corpi. </s>

<s>Il <emph type="italics"></emph>Discorso sulla Calamila,<emph.end type="italics"></emph.end> pubblicato in questi ultimi <lb></lb>anni, non ha, a voler esser giusti, di che la scienza del Magnete <lb></lb>s&#039;avvantaggi. </s></p><p type="main">

<s>Immediatamente dopo il Castelli, si dovrebbe collocare, in questo <lb></lb>splendido Senato della scienza italiana, Bonaventura Cavalieri, se, <lb></lb>piuttosto che alle scienze sperimentali, non avesse atteso alla Ma­<lb></lb>tematica pura e alla Geometria, nelle quali discipline fece così <lb></lb>grandi progressi, da meritarsi che Galileo lo onorasse pubblicamente <lb></lb>asserendo di lui ch&#039;ei sarebbe per riuscire uno de&#039;principali ma­<lb></lb>tematici di quei tempi (Alb. </s>

<s>XIII, 45). Dallo sperimentare il Cava­<lb></lb>lieri non è alieno, ma non ha, o non sa trovare il modo d&#039;eserci­<lb></lb>tarvisi. </s>

<s>Si prova a disegnar qualche macchina, ma nell&#039;effetto non <lb></lb>riesce. </s>

<s>Proposto dal Torricelli al Granduca per uno degli arbitri a <lb></lb>decidere le famose controversie del regolamento delle Chiane, se <lb></lb>ne scusa, rispondendo che a lui <emph type="italics"></emph>mancava quella esperienza che <lb></lb>bisogneria ancora aver fatto per poter parlar francamente in simil <lb></lb>materia<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XLI, c. </s>

<s>223). Nonostante a lui si deb­<lb></lb>bono alcuni utili avvertimenti intorno alle figure geometriche da <lb></lb>darsi ai vetri, per uso dei canocchiali, e fu il primo che pubbli­<lb></lb>casse, nel suo <emph type="italics"></emph>Specchio Ustorio,<emph.end type="italics"></emph.end> il pensiero sovvenutogli di com­<lb></lb>porre insieme, negli strumenti astronomici, le lenti cristalline e gli <lb></lb>specchi. </s>

<s>Richiestone dal Castelli, egli fu che distese la famosa Di­<lb></lb>mostrazione della proposizione II, inserita dal suo stesso Autore. </s>

<s><lb></lb>senza mutar parola, nel II Libro della Misura delle Acque correnti. <pb xlink:href="020/01/179.jpg" pagenum="160"></pb>Egli fu che di splendidi e nuovi concetti illustrò la dimostrazione <lb></lb>galileiana delle leggi dei moti naturali e dei proietti. </s></p><p type="main">

<s>Alla fama, che è certa di non essere smentita, alla fede che <lb></lb>s&#039;alimenta d&#039;affetto, alla morte che fa l&#039;uomo credulo e piamente <lb></lb>indulgente, piuttosto che alle opere scritte e stampate, va debitore <lb></lb>d&#039;essere annoverato qui in terzo luogo, Vincenzio Renieri. </s>

<s>Nel tempo <lb></lb>che il negoziato delle Longitudini con gli Stati Uniti di Olanda sol­<lb></lb>lecitava Galileo di dar compiuto ordine alle Effemeridi gioviali, il <lb></lb>Renieri pensava a stampar le sue <emph type="italics"></emph>Tabulae Secundorum mobilium,<emph.end type="italics"></emph.end><lb></lb>che il Cavalieri giudicò degne di essere dagli studiosi dell&#039;Astro­<lb></lb>nomia annoverate fra.i libri di maggiore utilità (Alb. </s>

<s>X, 398). Della <lb></lb>stampa ne trattava l&#039;Autore, nel marzo del 1637, con Galileo, pre­<lb></lb>gandolo volesse scrivere a Roma due righe al Castelli, perchè si <lb></lb>prendesse cura di muovere parola allo stampatore Guglielmo Fa­<lb></lb>ciotti (ivi, pag. </s>

<s>200). Le trattative andarono però a vuoto, e le Tavole <lb></lb>dei Secondi Mobili, intitolate Medicee, perchè dedicale al Granduca <lb></lb>Ferdinando II, si stamparono in Firenze nel 1639. Largamente poi <lb></lb>ampliate e corrette, quelle stesse Tavole, furono nuovamente im­<lb></lb>presse dal medesimo stampatore nel 1647. Pregato il Torricelli di <lb></lb>riveder le bozze di stampa, in sul punto che doveva incoglierlo la <lb></lb>morte, supplì al tedioso ufficio il Viviani (MSS. Gal.Dis. </s>

<s>T. CXLIV, c.4). </s></p><p type="main">

<s>Tornando ora indietro al 1637, Galileo, che sollecitato dal ne­<lb></lb>gozio delle Longitudini si sentiva, per la vecchiezza e per la cecità, <lb></lb>a così faticosa opera impotente, pensò di chieder l&#039;aiuto del Renieri, <lb></lb>riconosciuto per i calcoli delle Tavole Medicee, il più esperto fra i <lb></lb>suoi Discepoli. </s>

<s>Il Renieri, dall&#039;altra parte, con lettera del dì 11 Di­<lb></lb>cembre 1637, rispose che non avrebbe tralasciato cura o diligenza <lb></lb>alcuna possibile per servirlo (Alb. </s>

<s>X, 247). </s></p><p type="main">

<s>Preordinate così le cose, Galileo incominciò col padre Vincenzio <lb></lb>una specie d&#039;istituzione intorno alle operazioni astronomiche ne­<lb></lb>cessarie a perfezionare i calcoli delle Medicee, e per prima gli in­<lb></lb>segna la sua invenzione del misurare il foro della pupilla. </s>

<s>Poi torna <lb></lb>a descrivergli l&#039;uso dello strumento per misurarne più esattamente <lb></lb>le distanze dei pianeti dal centro di Giove, e gli consegna, perchè <lb></lb>gli possano servire di norma, le Effemeridi calcolate già da sè e <lb></lb>dal Castelli. </s>

<s>Nell&#039;Aprile del 1639 l&#039;Osservatore di Genova scrive a <lb></lb>Galileo poco mancargli per avere emendato in tutto il moto delle <lb></lb>Medicee, e per rendere assolute l&#039;Effemeridi di sei mesi futuri <lb></lb>(Alb. </s>

<s>X, 336). Nel maggio ammalato, tornato nel giugno al faticoso <lb></lb>lavoro, s&#039;accorse che, ad emendar que&#039;moti, all&#039;equazion tolemaica <pb xlink:href="020/01/180.jpg" pagenum="161"></pb>dei giorni naturali conveniva aggiungervene in ogni modo un&#039;altra, <lb></lb><emph type="italics"></emph>cagionata dal mancar la velocità del moto diurno nell&#039;allontanarsi <lb></lb>la Terra dal sole apogeo<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>339). </s></p><p type="main">

<s>Proseguiva il valente osservatore, con grande alacrità nell&#039;im­<lb></lb>presa, tanto più ch&#039;ei ci vedeva infervorati il Granduca e il Prin­<lb></lb>cipe Leopoldo, che lo fornivano de&#039;più eccellenti canocchiali, che <lb></lb>si sapesse essere stati fabbricati in Europa. </s>

<s>Perciò, alla corte di <lb></lb>Firenze, il Renieri mandava l&#039;Effemeridi calcolate via via, prima <lb></lb>che ad Arcetri. </s>

<s>Il principe Leopoldo però ne faceva riscontrar l&#039;esat­<lb></lb>tezza, e avute quelle per l&#039;aprile e pel maggio 1640, nelle notti del <lb></lb>due e degli otto di quel medesimo mese di Maggio, furono osservati <lb></lb>tre satelliti sempre occidentali e uno orientale. </s>

<s>“ Ora avendosi dal­<lb></lb>l&#039;Effemeridi (scrive lo stesso Principe al Renieri) che in tal notte <lb></lb>si dovevano vedere due di quelle stelle orientali e due occidentali, <lb></lb>mi fa venir dubbio che una tanta differenza, quale non può nascere, <lb></lb>nè per lo svariar degli orioli nè per negligenza dell&#039;osservatore, <lb></lb>possa venire dall&#039;errore della stampa ” (MSS. Gal. </s>

<s>Dis. </s>

<s>T. V. c. </s>

<s>248). </s></p><p type="main">

<s>Par che dunque fossero quelle Effemeridi stampate, e così forse <lb></lb>l&#039;Autore intendeva di mettere insieme a poco per volta il suo libro. </s>

<s><lb></lb>Ma in sette anni, quanti ne decorsero dalla data di questa lettera, <lb></lb>che è del 13 maggio 1640, alla morte dell&#039;Autore, la pubblicazione <lb></lb>di quelle Tavole di tanti desiderii, non solo non ebbe effetto, ma <lb></lb>nessuno sa dir se nemmeno ella avesse avuto principio. </s>

<s>Ragione di <lb></lb>una tale incertezza è il celebre fatto della dispersione delle carte <lb></lb>e degli strumenti astronomici del Renieri, immediatamente avve­<lb></lb>nuta dopo la morte di lui. </s>

<s>Celebre fatto diciamo, per le tante cose <lb></lb>che da tanti ne sono scritte. </s>

<s>A noi basta richiamar l&#039;attenzione <lb></lb>sopra una lettera, che, pochi giorni dopo la morte del fratello, scri­<lb></lb>veva a uno sconosciuto cortigiano de&#039;Medici Giovan Battista Renieri. <lb></lb></s>

<s>“ Vivo in speranza, egli dice, circa la ricuperazione delli scritti <lb></lb>della felice memoria di mio fratello: ne attendo pertanto l&#039;avviso <lb></lb>dell&#039;effetto, avendo intenzione di pubblicare alle stampe l&#039;opera che <lb></lb>egli ha composto del moto de&#039;pianeti medicei di Giove. </s>

<s>E perchè <lb></lb>forse l&#039;immatura sua morte gli ha tronco que&#039;concetti, che sperava <lb></lb>col tempo di produrre alla luce, desidererei pertanto, avendomeli <lb></lb>in sua vita partecipati, farli pubblicare sotto il suo nome ” (MSS. Gal. </s>

<s><lb></lb>Disc. </s>

<s>T. V. c. </s>

<s>232). Da chi Giovan Battista sperasse di recuperare <lb></lb>quei manoscritti, non si sa, perchè non lo dice. </s>

<s>Forse potrebb&#039;esser <lb></lb>quel Giuseppe Agostini, su cui fecero cadere un sospetto di furto <lb></lb>Cosimo Galilei e il Viviani. </s>

<s>In ogni modo però, nè Giovan Batista <pb xlink:href="020/01/181.jpg" pagenum="162"></pb>Renieri, nè Cosimo Galilei riuscirono a recuperare le carte del fra­<lb></lb>tello e dell&#039;avo. </s>

<s>Che le venissero poi da Pisa alla Biblioteca pala­<lb></lb>tina di Firenze, non si sa però come nè quando, lo afferma l&#039;Alberi; <lb></lb>e se delle Effemeridi e degli altri studii intorno al sistema di Giove <lb></lb>non si trovarono veramente, fra le carte del Monaco olivetano, altro <lb></lb>che le cose pubblicate dal medesimo Albèri, si può ripetere quel <lb></lb>che si diceva dianzi, che cioè la gloria scientifica di Vincenzio Re­<lb></lb>nieri è affidata alla fama, alla fede, a quella riverenza che inspira <lb></lb>la morte. </s></p><p type="main">

<s>Men famoso nei posteri e men fortunato, perchè nell&#039;opere <lb></lb>pubblicamente note potè la censura esercitare il suo dente, fu don <lb></lb>Famiano Michelini, una strana figura di uomo, che sognando di <lb></lb>chiappar milioni con le sue scoperte, morì nel 1666, vecchio di 73 <lb></lb>anni, nell&#039;indigenza. </s>

<s>Propugnatore della Medicina statica del Santo­<lb></lb>rio, perchè più volte il giorno, quand&#039;era ancora scolopio sotto il nome <lb></lb>di fra Francesco da S. Giuseppe, si pesava sulla stadera, per fare <lb></lb>esperienza in se dell&#039;insensibile traspirazione; i ragazzi lo additavano <lb></lb>per le vie di Firenze chiamandolo il <emph type="italics"></emph>Padre Staderone.<emph.end type="italics"></emph.end> Spacciando <lb></lb>nelle bibite limonate il migliore specifico per cacciar la febbre, i <lb></lb>fiorentini lo proverbiarono con motti arguti, e con epigrammi. </s>

<s>Il <lb></lb>Cavalieri, confondendo insieme l&#039;abilità d&#039;idraulico con quella di <lb></lb>medico, illuso prima e poi deluso dell&#039;efficacia della ricetta, scriveva <lb></lb>al Torricelli, a proposito delle Chiane, “ che la proposta del padre <lb></lb>Francesco anderà al pari con l&#039;altra di risanarmi dalla podagra ” <lb></lb>(MSS. Gal. </s>

<s>Dis. </s>

<s>T. XL. c. </s>

<s>223) e il Granduca, in ogni modo, non gli <lb></lb>poteva perdonare l&#039;apostasia dall&#039;ordine calasanziano. </s>

<s>Ciò nonostante, <lb></lb>fu eletto ad ammaestrare nelle matematiche il giovanetto principe <lb></lb>Leopoldo, in cui infuse un grande amore alle scienze sperimentali, <lb></lb>e gli raffinò il gusto a sentir quanto fosse di vero nelle nuove dot­<lb></lb>trine promulgate da Galileo. </s>

<s>Se non avesse altro merito, basterebbe <lb></lb>questo per dovere annoverare il Michelini tra i più validi coope­<lb></lb>ratori ai progressi della scienza italiana. </s>

<s>Ma egli vi cooperò, e più <lb></lb>efficacemente di quel che non si stimi, con le proprie speculazioni <lb></lb>e con le proprie esperienze, esposte in iscritti, in cui la bellezza <lb></lb>del dettato aggiunge splendore all&#039;importanza della materia. </s></p><p type="main">

<s>Il Trattato della <emph type="italics"></emph>Direzione dei fiumi,<emph.end type="italics"></emph.end> co&#039;suoi errori non lievi, <lb></lb>è pure il primo che dirige l&#039;opera da praticarsi sui fiumi, con la <lb></lb>scorta di una scienza, che quasi sempre è sicura. </s>

<s>Il Viviani, dietro <lb></lb>quegli insegnamenti, regolava l&#039;Arno con altri fiumi della Toscana, <lb></lb>e per mezzo di Ottavio Falconieri insegnava a regolar similmente <pb xlink:href="020/01/182.jpg" pagenum="163"></pb>il Tevere agli ingegneri romani. </s>

<s>Nei Discorsi medici don Famiano <lb></lb>ha senza dubbio delle stranezze, ma egli è il primo, co&#039;suoi metodi <lb></lb>matematici, a cacciar l&#039;empirismo e ad esaltar l&#039;arte medica al <lb></lb>grado e alla dignità di scienza. </s>

<s>Fu dagli insegnamenti di lui che <lb></lb>ebbe principio la tanto benemerita scuola medica sperimentale isti­<lb></lb>tuita dal Redi. </s></p><p type="main">

<s>Men noti dei quattro annoverati fin qui, sono altri illustri allievi <lb></lb>di quella prima scuola galileiana, i quali, dallo scrivere e dal pub­<lb></lb>blicar gli scritti delle loro speculazioni, o furon divietati da una <lb></lb>morte immatura, o ne furon distratti dall&#039;attendere a varii altri <lb></lb>ufficii. </s>

<s>Primo fra questi occorre a commemorare Niccolò Aggiunti <lb></lb>che, nato nel 1600, in 35 anni compì tutto insieme il corso delle <lb></lb>scienze e della vita. </s>

<s>Quel che egli sperimentò di fisica o dimostrò <lb></lb>di meccanica è rimasto negli informi manoscritti di lui, chi svolge <lb></lb>i quali, si sente stringere il cuore da pietà, che gli impedisse la <lb></lb>morte di maturare quella così feconda novità di pensieri. </s>

<s>Si direbbe, <lb></lb>a leggere quelle note e quegli appunti rimasti di lui, che Galileo <lb></lb>infuse nel giovane alunno quegli spiriti latenti, che si manifestarono <lb></lb>poi nei Dialoghi delle Due Nuove Scienze. </s>

<s>Chi non direbbe infatti <lb></lb>che quelle proposizioni dimostrate dall&#039;Aggiunti intorno alla ten­<lb></lb>sione delle corde sonore, non fossero cadute dalla penna di Galileo, <lb></lb>quando pensava di dar fondamenti matematici all&#039;Acustica? </s>

<s>Le so­<lb></lb>luzioni di parecchi problemi, che si leggono in questi manoscritti, <lb></lb>come quello delle condizioni dell&#039;equilibrio di un pezzo di legno, <lb></lb>in parte campato in aria e in parte sostenuto da un piano, somi­<lb></lb>gliante a quell&#039;altro, qui pur risoluto, della catena in parte distesa <lb></lb>su un asse e in parte pendula, rivelano che l&#039;Autore, nella scienza <lb></lb>del moto, precorreva al Maestro. </s></p><p type="main">

<s>Ma che egli lo precorresse veramente finiscono di persuaderlo <lb></lb>quei meccanici teoremi, la matematica dimostrazione dei quali non <lb></lb>par che avesse altro intento, che di supplire al difetto dei Dialoghi <lb></lb>de&#039;Due Massimi Sistemi. </s>

<s>Galileo infatti, contento ad enunciarli, lascia <lb></lb>ivi i principali teoremi del moto indimostrati, riserbandosi a farlo <lb></lb>negli altri Dialoghi, che meditava di scrivere intorno a quel proprio <lb></lb>soggetto. </s>

<s>Ma intanto l&#039;Aggiunti cerca e ritrova da sè così fatte di­<lb></lb>mostrazioni. </s>

<s>Tale è quella del pendolo, pubblicata nei Saggi di storia <lb></lb>letteraria dal Nelli (Lucca 1759, pag. </s>

<s>89, 90), tal&#039;è quella del teore­<lb></lb>ma, così formulato: “ La medesima velocità nelle maggiori o minori <lb></lb>quantità di materia, opera più o meno potentemente secondo la <lb></lb>proporzione di essa materia ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XVIII, c. </s>

<s>95), tale, <pb xlink:href="020/01/183.jpg" pagenum="164"></pb>per tacere di altre, la dimostrazione della palla perfettamente sfe­<lb></lb>rica, posata su un piano perfettamente orizzontale, che non tende <lb></lb>a muoversi più verso l&#039;una parte che l&#039;altra (ivi, c. </s>

<s>100). </s></p><p type="main">

<s>Che poi l&#039;Aggiunti procedesse, nella dimostrazione di questi <lb></lb>teoremi galileiani del moto, indipendentemente dalla guida del Mae­<lb></lb>stro, lo prova quella stessa libertà, colla quale ne censura alcune <lb></lb>dottrine. </s>

<s>Esempio ne sia quello delle forze centrifughe, delle quali <lb></lb>tratta Galileo nel II Dialogo dei Massimi Sistemi (Alb. </s>

<s>I. 213,38). <lb></lb>Ammesso dall&#039;Aggiunti il principio che “ acciocchè un mobile <lb></lb>acquisti, da virtù intrinseca, impeto di muoversi per una tal dire­<lb></lb>zione, bisogna che il motore l&#039;abbia movendo accompagnato per <lb></lb>qualche spazio in essa dirittura ” perciocchè in un cerchio non ci <lb></lb>è dirittura alcuna, conclude: “ laonde sarà falso che dalla vertigine <lb></lb>di una ruota si conferisca alle sue parti impeto di muoversi per la <lb></lb>tangente, com&#039;asserisce l&#039;eccellentissimo signor Galileo ” (ivi, c. </s>

<s>59). </s></p><p type="main">

<s>La censura se non è vera, è senza dubbio assai arguta, come <lb></lb>argute sono altre censure, che promuove contro lo stesso Galileo <lb></lb>rispetto alla teoria de&#039;galleggianti. </s>

<s>Accomodato un parallelepipedo <lb></lb>nelle condizioni di galleggiamento richieste da Galileo, l&#039;Aggiunti <lb></lb>così soggiunge: “ Tutto questo passa bene, secondo la dottrina del <lb></lb>signor Galileo, se porremo che l&#039;acqua sia solamente da una banda. </s>

<s><lb></lb>Ma qui mi nascono molte difficoltà, che fanno contro al Galileo <lb></lb>ancora, perchè non pare che basti, acciò un solido men grave in <lb></lb>specie dell&#039;acqua, sia alzato, che l&#039;acqua lo bagni da una parte sola, <lb></lb>e secondo quell&#039;altezza che vuole il Galileo, ma tal sollevamento <lb></lb>bisogna che sia a mio giudizio d&#039;ogni intorno ” (ivi, c. </s>

<s>107). Qui <lb></lb>l&#039;Autore del manoscritto, che nota come la cosa vuol esser pensata <lb></lb>meglio, ha più ragione di censurare che dianzi: quelle galileiane <lb></lb>dottrine son difettose, perchè, nello spiegar l&#039;effetto de&#039;galleggia­<lb></lb>menti, s&#039;esclude l&#039;intervento delle pressioni idrostatiche, per cui <lb></lb>con ragione, l&#039;Aggiunti che non seppe pensar da sè all&#039;efficacia di <lb></lb>quelle pressioni, si sentiva aggirar la mente da quei dubbi penosi. </s></p><p type="main">

<s>Ben più sicuro però del fatto suo è là dove, per supplire ai <lb></lb>difetti di Erone, divisa la nuova teoria del moto delle acque nei <lb></lb>sifoni ritorti. </s>

<s>Si lagnava il Castelli con Galileo, perchè l&#039;Aggiunti, <lb></lb>senza fargliene parola, andava spacciando che nel Discorso Della <lb></lb>Misura delle Acque correnti ci erano alcuni errori gravi (Campori <lb></lb>Cartag. </s>

<s>gal. </s>

<s>cit. </s>

<s>pag. </s>

<s>417). Quali fossero gli errori gravi notati dal­<lb></lb>l&#039;Aggiunti, benchè il Castelli non si spieghi davvantaggio, si può <lb></lb>arguir facilmente da queste teorie del sifone eroniano, nel dimostrar <pb xlink:href="020/01/184.jpg" pagenum="165"></pb>le quali si ammette dall&#039;Autore che le velocità nel flusso dell&#039;acqua, <lb></lb>come nella caduta di tutti gli altri corpi gravi sieno proporzionali <lb></lb>alle radici delle altezze. </s>

<s>Ora perchè il Castelli in quel suo Trattato, <lb></lb>professava il principio che le stesse velocità fossero proporzionali <lb></lb>alle semplici altezze, può esser benissimo che l&#039;Aggiunti spacciasse <lb></lb>questo per un errore. </s>

<s>Un errore poi lo credette il Torricelli, e i <lb></lb>seguaci delle teorie di lui, ond&#039;è che nel proporre quelle nuove <lb></lb>teorie, l&#039;Aggiunti prevenne di parecchi anni lo stesso Torricelli. </s></p><p type="main">

<s>Fra le molte esperienze di fisica, che si trovano descritte o <lb></lb>accennate per questi manoscritti, la più importante, a nostro giu­<lb></lb>dizio, e la più nuova è quella del dilatarsi de&#039;solidi al calore, ciò <lb></lb>che egli dimostra in un filo metallico o in un ago, e per cui spiega <lb></lb>la varietà de&#039;suoni dati dalle corde degli strumenti, al variare delle <lb></lb>stagioni. </s>

<s>Notabile è che gli effetti di quel dilatamento lineare dei <lb></lb>solidi l&#039;attribuisca all&#039;aria che s&#039;interpone fra i pori di tutti i corpi, <lb></lb>e più notabili che mai quei pensieri intorno al vacuo, e alla forza <lb></lb>necessaria a superarlo, che gli occorrono in tal proposito: pensieri <lb></lb>che fanno così perfetto riscontro con quelli che, nel primo Dialogo <lb></lb>delle Due Nuove Scienze, alquanti anni dopo la morte del Nostro, <lb></lb>rivelò Galileo. </s>

<s>Che poi l&#039;Aggiunti, dalle speculate esperienze e dalle <lb></lb>minute osservazioni, sapesse con ardito volo risalire ai principii ge­<lb></lb>nerali, lo dimostra quella sottile ipotesi del moto occulto dell&#039;acqua, <lb></lb>con cui spiega e applica gli effetti di capillarità a innumerabili e <lb></lb>inesplicati fatti della Natura. </s>

<s>Nè si può senza gran maraviglia pen­<lb></lb>sare, che egli spieghi per questo modo il moto del chilo negli ani­<lb></lb>mali, mentre parecchi anni dopo il gran Pecquet aveva bisogno di <lb></lb>ricorrere miseramente al moto vermicolare dei vasi, e alla com­<lb></lb>pressione toracica degli atti respiratorii. </s></p><p type="main">

<s>Dei danni recati all&#039;incremento della scienza dagli inesorabili <lb></lb>casi della vita, in questa così ristretta cerchia dei primi Discepoli <lb></lb>di Galileo, due altri esempi abbiamo a deplorare in Cosimo Noferi, <lb></lb>e in Antonio Nardi. </s>

<s>Per cominciare a parlar del primo, ei lasciò <lb></lb>quattro bei volumi manoscritti, di carettere nitido, e ornati, nei <lb></lb>frontespizi e altrove, di tocchi in penna così ben condotti, da esser <lb></lb>tenuti in qualche pregio artistico dagl&#039;intendenti. </s>

<s>Son que&#039;volumi <lb></lb>altrettanti libri divisi ciascuno in Discorsi, che par l&#039;Autore gli leg­<lb></lb>gesse via via in qualche Accademia fiorentina. </s>

<s>Si discorre princi­<lb></lb>cipalmente nel I libro dell&#039;ordine di fabbricare le fondamenta, in <lb></lb>qualsivoglia luogo, dell&#039;ordine delle armature e fabbriche delle volte, <lb></lb>dell&#039;ordine di diversi cavalletti per le coperte. </s>

<s>Si passa nel II libro <pb xlink:href="020/01/185.jpg" pagenum="166"></pb>a discorrere dell&#039;ordine e della fabbrica dei ponti murati, dei ponti <lb></lb>di un solo arco, dei ponti sui fiumi reali. </s></p><p type="main">

<s>Nel III libro, che è il più importante per noi, si discorre del <lb></lb>modo di regolare i fiumi; libro che, se fosse stato pubblicato a suo <lb></lb>tempo, o avrebbe risparmiato in parte o avrebbe diminuiti i meriti <lb></lb>al Trattato del Michelini. </s>

<s>Incomincia a dire che fino allora, nei la­<lb></lb>vori fatti sui fiumi, s&#039;erano commessi di grandi errori, e s&#039;era speso, <lb></lb>dal pubblico e dai privati, in false operazioni. </s>

<s>Nota poi come quegli <lb></lb>errori dipendessero principalmente da non essere conosciuti bene <lb></lb>i moti, a cui va soggetta l&#039;acqua, e distingue quei moti in tre: <lb></lb><emph type="italics"></emph>spulsivo, naturale<emph.end type="italics"></emph.end> e <emph type="italics"></emph>laterale.<emph.end type="italics"></emph.end> Ammettendo nell&#039;acqua il moto late­<lb></lb>rale, o obliquo, come l&#039;Autore stesso lo chiama, scansa il gravissimo <lb></lb>errore, in che incorse il Michelini, ma poi ci incappa al pari di lui, <lb></lb>quando distingue il moto <emph type="italics"></emph>spulsivo,<emph.end type="italics"></emph.end> ossia quello fatto nella pendenza <lb></lb>dell&#039;alveo, dal naturale fatto nella perpendicolare, essendo che lo <lb></lb>spulsivo, non è un moto diverso, ma è una delle parti dello stesso <lb></lb>moto naturale, decomposto in due. </s></p><p type="main">

<s>Il moto spulsivo poi il Noferi lo riguarda come efficiente nel <lb></lb>venir premuta l&#039;acqua dall&#039;altr&#039;acqua che lo precede, e così rende <lb></lb>la ragione dello scorrere i liquidi, anche in canali perfettamente <lb></lb>livellati. </s>

<s>Questa così importante dottrina era stata professata già, <lb></lb>contro la comune opinione degli idraulici, da Galileo, che il Noferi <lb></lb>ormeggia spesso con studio, che si direbbe servile. </s>

<s>Così occorren­<lb></lb>dogli di trattar del problema della corda tesa, ricopia a parola ciò <lb></lb>che sta scritto nel IV Dialogo delle Due Nuove Scienze, e dettando <lb></lb>i suoi Discorsi in tempi, in cui certamente doveva essere stata fatta <lb></lb>e divulgata la celebre esperienza torricelliana, discorre della teoria <lb></lb>delle trombe idrauliche allo stesso modo, che se ne discorre nel I <lb></lb>dei citati Dialoghi, da Galileo. </s>

<s>Rimasto preso di grande ammira­<lb></lb>zione alla lettura delle opere di lui, ne sceglie i più curiosi e im­<lb></lb>portanti problemi, e sotto il titolo di <emph type="italics"></emph>Ricreazioni matematiche<emph.end type="italics"></emph.end> gli <lb></lb>ordina in due libretti “ quali due libretti spero in breve farvi ve­<lb></lb>dere. </s>

<s>Ma quell&#039;opera poi che più mi ha ritardato, è l&#039;avere con­<lb></lb>dotto a fine il mio Apollonio Pergeo, per benefizio ed utile degli <lb></lb>studiosi ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XIV, c. </s>

<s>2). </s></p><p type="main">

<s>Quanto però il Noferi è ossequioso verso Galileo, tanto par ir­<lb></lb>riverente verso il Castelli. </s>

<s>La censura che egli fa della proposizione <lb></lb>fondamentale dimostrata nel Trattato delle Acque Correnti, che cioè <lb></lb>le velocità sono in ragione inversa delle sezioni, non è per verità di <lb></lb>matematico, nè si saprebbe altrimenti spiegare che in una smania <pb xlink:href="020/01/186.jpg" pagenum="167"></pb>del censore, d&#039;introdur nella scienza quella sua novità del <emph type="italics"></emph>moto <lb></lb>spulsivo.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Antonio Nardi, aretino, componeva col Magiotti e col Torricelli, <lb></lb>in Roma, quel triumvirato, che Galileo manda così spesso a salu­<lb></lb>tare nelle sue lettere familiari. </s>

<s>Più tardi, quando quel triumvirato <lb></lb>si sciolse, Michelangiolo Ricci, dando al Torricelli stesso venuto in <lb></lb>Firenze, le nuove degli amici lontani, in una sua lettera così gli <lb></lb>scriveva: “ Il signor Antonio Nardi fatica intorno l&#039;Opera sua. </s>

<s>Ha <lb></lb>dato perfezione alla parte metafisica, ora è d&#039;intorno la fisica, e <lb></lb>poi vedrà le matematiche, il che non potrà seguire prima di dieci <lb></lb>mesi ovvero in un anno. </s>

<s>E mi duole che tardi tanto ad uscire in <lb></lb>luce Opera, che si spera che debba essere doviziosa di tutte le <lb></lb>speculazioni, cioè pasto per ogni sorta di professori di scienza ” <lb></lb>(MSS. Gal. </s>

<s>Disc. </s>

<s>T. XLII, c. </s>

<s>121). Nel Giugno 1645 torna a scrivergli: <lb></lb>“ Il signor Antonio Nardi riverisce V. S. con ogni affetto, e nella <lb></lb>stampa del libro suo va un poco lento, perchè ci restano da rive­<lb></lb>dere le materie matematiche, e non ha potuto attendere per molti <lb></lb>giorni, impedito da un poco d&#039;indisposizione ” (ivi, c. </s>

<s>136). Non <lb></lb>sapremmo precisamente dire quanto quella indisposizione durasse, <lb></lb>ma sembra che l&#039;Autore fosse impedito per qualche anno, dopo il <lb></lb>qual tempo scriveva il medesimo Ricci al Torricelli: “ Il sig. </s>

<s>Nardi <lb></lb>si trattiene in Arezzo e li giorni passati mi mandò l&#039;Opera sua ori­<lb></lb>ginale, perchè la facessi rivedere al S. </s>

<s>Uffizio ” (ivi, c. </s>

<s>183). </s></p><p type="main">

<s>Il libro e l&#039;Opera originale del Nardi, di che qui si parla, porta <lb></lb>il titolo di <emph type="italics"></emph>Scene,<emph.end type="italics"></emph.end> senz&#039;altro aggiunto nella fronte, ma, nell&#039;Indice <lb></lb>finale, il titolo compiuto è di <emph type="italics"></emph>Scene Accademiche.<emph.end type="italics"></emph.end> È un volumone <lb></lb>di pagine 1392, che riman tuttavia manoscritto, copiato da più <lb></lb>mani, e non ha di autografo che alcune correzioni e postille, i <lb></lb>passi greci, e i disegni abbozzati delle figure geometriche. </s>

<s>Una certa <lb></lb>somiglianza di carattere calligrafico fece credere a qualcuno che <lb></lb>v&#039;avesse dato mano, a copiar quelle carte, anche il Torricelli, ma <lb></lb>le sopra citate lettere del Ricci par che rendano poco probabile <lb></lb>quel supposto. </s></p><p type="main">

<s>Impedita per la morte dell&#039;Autore la stampa, per la quale <lb></lb>tutto era preparato, il manoscritto, dagli eredi del Nardi passò nel <lb></lb>concittadino di lui Francesco Redi, che par avesse intenzione di <lb></lb>mandarlo alla luce (Targioni, Aggrandim. </s>

<s>T. I. P. I. pag. </s>

<s>173). Ma <lb></lb>qualunque fosse il motivo, rimasto il volume tuttavia inedito, dal <lb></lb>Granduca Cosimo III che l&#039;ebbe dal Redi, passò alla biblioteca del <lb></lb>Museo fiorentino di Fisica e di Storia Naturale, d&#039;onde finalmente <pb xlink:href="020/01/187.jpg" pagenum="168"></pb>andò a prender posto al numero XX, fra i tomi che compongono <lb></lb>la seconda Divisione dei manoscritti galileiani. </s></p><p type="main">

<s>Le scene in tutto son nove, e ciascuna è divisa in articoli, col <lb></lb>titolo di <emph type="italics"></emph>Vedute.<emph.end type="italics"></emph.end> Vi si tratta, senz&#039;ordine, d&#039;ogni soggetto scientifico, <lb></lb>cosicchè l&#039;Opera somiglia a tanti numeri messi insieme di un gior­<lb></lb>nale enciclopedico. </s>

<s>A que&#039;tempi forse era questo il miglior modo <lb></lb>a diffondere la scienza, e tale dee essere stata senza dubbio l&#039;in­<lb></lb>tenzion dell&#039;Autore. </s>

<s>Ora però, un&#039;opera scritta in quelle forme, non <lb></lb>sarebbe comportabile, per cui par che sia condannata in perpetuo <lb></lb>a rimanersene manoscritta. </s>

<s>Chi facesse, nonostante, una scelta degli <lb></lb>articoli di matematica o di fisica sperimentale, potrebbe arrecar <lb></lb>qualche giovamento alla storia della scienza, benchè il non aver <lb></lb>risentito il Nardi gli impulsi, che alle stesse scienze sperimentali <lb></lb>provennero dalla grande esperienza torricelliana, a que&#039;medesimi <lb></lb>articoli, si diminuisca notabilmente l&#039;importanza. </s></p><p type="main">

<s>La veduta 41 della Scena VII è intitolata: <emph type="italics"></emph>Censure sopra varii <lb></lb>pensieri di Galileo<emph.end type="italics"></emph.end> (pag. </s>

<s>967-74) pensieri tutti però che concernono <lb></lb>le teorie galileiane del moto. </s>

<s>Ma qua e lȧ, per le altre Scene, oc­<lb></lb>corre pure all&#039;Autore di intrattener l&#039;esame critico sopra altre dot­<lb></lb>trine del suo Maestro, le quali ora, con temperato zelo difende dalle <lb></lb>ingiuste censure altrui, e ora con filosofica libertà condanna ed <lb></lb>emenda. </s></p><p type="main">

<s>L&#039;argutissima censura, che in quella Veduta, la quale porta il <lb></lb>titolo: <emph type="italics"></emph>Sopra la definizione dell&#039;umido e sua Natura posta da Ar­<lb></lb>chimede nei principii delle cose che galleggiano<emph.end type="italics"></emph.end> (pag. </s>

<s>873), fa il <lb></lb>Nardi del principio delle velocità virtuali applicato da Galileo a di­<lb></lb>mostrar l&#039;equilibrio dei liquidi ne&#039;vasi comunicanti, ci fa sovvenire <lb></lb>di un altro Discepolo, che, pure in materie idrauliche, oppose libere <lb></lb>censure alle dottrine dello stesso Galileo, e che, per aver affidata la <lb></lb>sua scienza a lettere, per la maggior parte inedite, è rimasto nella <lb></lb>Repubblica scientifica oscuro, o quanto pur si meriterebbe non ap­<lb></lb>prezzato. </s>

<s>Costui è il fiorentino Senatore Andrea Arrighetti, di cui <lb></lb>così, in un poscritto di lettera a Galileo, scriveva il Castelli: “ Tengo <lb></lb>una lettera lunga del sig. </s>

<s>Andrea Arrighetti, sottilissima e bella, in <lb></lb>proposito di fiumi, nella quale ho avuto che imparare assai ” (Alb. </s>

<s><lb></lb>Supplem. </s>

<s>pag. </s>

<s>239). Questa, che forse è ancora inedita, dee essere <lb></lb>una di quelle fra le prime lettere, che Andrea scriveva a Niccolò <lb></lb>Arrighetti suo cugino intorno al fiume Bisenzio, professandovi dot­<lb></lb>trine vere contro a quelle, riconosciute erronee, di Galileo. </s>

<s>E l&#039;avere <lb></lb>il discepolo con sicurtà e dirittura colto nel segno meglio del suo <pb xlink:href="020/01/188.jpg" pagenum="169"></pb>Maestro, e il confessar che il Castelli fa dell&#039;aver trovato da imparare <lb></lb>assai dalla scrittura di lui, compongono il più bell&#039;elogio, che si possa <lb></lb>fare di Andrea Arrighetti. </s>

<s>Nella grande raccolta fiorentina degli <lb></lb>Autori, che trattano del moto dell&#039;acque, s&#039;inserirono, nel IV Tomo, <lb></lb>sei lettere dell&#039;Arrighetti al Castelli, nelle quali s&#039;apre il fiore di <lb></lb>alcuni pensieri, che allegarono poi in squisitissimi frutti. </s>

<s>Tale è, <lb></lb>nella II Lettera, la legge della velocità dei flussi, fior di pensiero <lb></lb>allegato nel Torricelli, e nel Newton fatto poi più maturo; tale la <lb></lb>speculazione del librarsi i liquidi che scendono e risalgono per <lb></lb>lunghi canali, qual sarebbe quello che dalle fontane di Boboli faceva <lb></lb>zampillar le acque condottevi da Pratolino: sottile speculazione e <lb></lb>fecondo fiore di novità, che se pure è allegato in frutto, non par <lb></lb>che la scienza ancora l&#039;abbia colto maturo. </s></p><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi si trattiene a meditare alquanto su questo primo e così <lb></lb>largo svolgimento delle nuove dottrine, in sì breve spazio di tempo, <lb></lb>che non oltrepassa, se non di pochissimi anni quello della morte di <lb></lb>Galileo, non può non rimanere ammirato di quella forza potente, <lb></lb>che valse a dare e a diffondere nella scienza tant&#039;onda di vita. </s>

<s>Ma <lb></lb>pure, quella scienza ancora ha poco dello sperimentale. </s>

<s>La forma <lb></lb>dura tuttavia a signoreggiare sulla materia, la matematica prevale <lb></lb>alla fisica, e la speculazione, troppo sicura di sè, non degna di <lb></lb>scendere dalle sue alture per cimentarsi colla esperienza. </s>

<s>Che sia <lb></lb>veramente così, insigni esempii ci son porti in fin da coloro, che si <lb></lb>dissero precursori, ma che son da dir forse meglio attori di questa, <lb></lb>che per la nostra scienza si appella età del Rinnovamento. </s>

<s>Tali <lb></lb>sarebbero, principali fra gli altri, il Maurolico e il Benedetti. </s>

<s>Il <lb></lb>primo di questi, nel trattar dell&#039;iride, assegna all&#039;angolo formato <lb></lb>dai raggi, che vengon da una gocciola della nube rorida all&#039;occhio, <lb></lb>45 gradi, per l&#039;iride interna, e 56 e un quarto per l&#039;iride esterna. </s>

<s><lb></lb>Le dignità matematiche son quelle, che lo conducono alla certezza <lb></lb>di così fatte conclusioni. </s>

<s>Ma pure, è vero che quegli angoli sono <lb></lb>alquanto minori, e il Maurolico lo sa, e a chi gli domanda come <lb></lb>la cosa vada <emph type="italics"></emph>nescio quid hic respondeam,<emph.end type="italics"></emph.end> ma la matematica non <lb></lb>può fallire, e potrebb&#039;esser, soggiunge, che il non rispondere il fatto <pb xlink:href="020/01/189.jpg" pagenum="170"></pb>incerto ai calcoli certissimi, dipendesse dal non esser le gocciole <lb></lb>perfettamente sferiche, ma notabilmente allungate in ovale. </s></p><p type="main">

<s>In Galileo poi gli esempi, che si potrebbero citare, del prevaler <lb></lb>nelle sue dottrine le speculazioni alle esperienze, son tanti, che, <lb></lb>anche ai più ritrosi a consentir con noi, parrebbero da vantaggio. </s>

<s><lb></lb>Egli par già che da sè stesso lo senta, e che si voglia far quasi <lb></lb>percotere il petto di rimbalzo dalla punta delle parole, che pone <lb></lb>in bocca a Simplicio: “ queste sottigliezze matematiche son vere <lb></lb>in astratto, ma applicate poi alla materia sensibile e fisica non ri­<lb></lb>spondono ” (Alb. </s>

<s>I, 224). </s></p><p type="main">

<s>Sia primo a citare fra questi notabilissimi esempi il pendolo, <lb></lb>intorno al quale il giudizio di Galileo procede in modo simile a <lb></lb>quello del Maurolico, ora citato. </s>

<s>La matematica gli ha fatto con­<lb></lb>cludere, per certissima dimostrazione, che le vibrazioni o ampie <lb></lb>per tutto il quadrante, o ristrette in piccolissimi archi sono in ogni <lb></lb>modo isocrone. </s>

<s>Nel fatto però non son tali, e Galileo lo sà: sa che <lb></lb>le più ampie sono alquanto più diuturne. </s>

<s>A chi gli domanda come <lb></lb>quel fatto vada, <emph type="italics"></emph>Nescio quid hic respondeam,<emph.end type="italics"></emph.end> ma potrebb&#039;esser, <lb></lb>soggiunge, che ciò dipenda dall&#039;esser le vibrazioni, che vanno più <lb></lb>al largo, alquanto di più indugiate dalla resistenza maggior che <lb></lb>incontran nell&#039;aria. </s>

<s>Eppure si sarebbe potuto anche da ciò facil­<lb></lb>mente deliberare, con una tale esperienza, che può sovvenire alla <lb></lb>mente di tutti, benchè l&#039;Huyghens sia stato quello che primo l&#039;ha <lb></lb>suggerita. </s>

<s>Consiste quella facilissima e concludentissima esperienza <lb></lb>in prender due pendoli di lunghezza uguale, e in dar le mosse a <lb></lb>ciascuno dalla medesima parte, in modo però che l&#039;uno scenda <lb></lb>molto da alto e l&#039;altro da basso. </s>

<s>È facile veder che presto i due <lb></lb>pendoli non passano più il perpendicolo insieme, ma quel che va <lb></lb>più ristretto è giusto quello che precede. </s></p><p type="main">

<s>E la celebre dimostrazione della legge della caduta dei gravi, <lb></lb>egli è pure un fatto che Galileo non la raccolse altrimenti, che per <lb></lb>una matematica conclusione dal principio che le velocità sono pro­<lb></lb>porzionali ai tempi. </s>

<s>Il riscontro dell&#039;esperienza, così minutamente <lb></lb>descritta nel III Dialogo delle Due Nuove Scienze (Alb. </s>

<s>XIII, 172, 73), <lb></lb>è affatto superfluo, perchè nessun crede all&#039;Autore che, dal pesar <lb></lb>dell&#039;acqua sgocciolante dalla clessidra, potesse aver la misura giusta <lb></lb>di que&#039;minimi tempi, difficilissimi a trovar con gli stessi più squisiti <lb></lb>cronometri moderni. </s></p><p type="main">

<s>Altro insigne esempio del prevaler nella mente di Galileo la <lb></lb>precisione matematica e l&#039;ordine geometrico alla osservazione dei <pb xlink:href="020/01/190.jpg" pagenum="171"></pb>fatti, è quello che concerne le orbite dei pianeti. </s>

<s>Il Keplero aveva <lb></lb>dimostrato, come cosa di fatto, che quelle orbite sono ellittiche. </s>

<s>Ma <lb></lb>ciò, secondo Galileo, repugna alla platonica perfezione degli ordi­<lb></lb>namenti celesti, per cui tenacemente si attiene alla geometria dei <lb></lb>circoli, e rifugge dalla fisica delle ellissi. </s>

<s>Quando poi più tardi ri­<lb></lb>trovò la legge dei moti ne&#039;pendoli di varie lunghezze, ritrovò anco <lb></lb>insieme un nuovo argomento per non dover consentire a un&#039;altra <lb></lb>delle leggi planetarie, scoperte pur dal Keplero. </s>

<s>Rassomigliando nei <lb></lb><emph type="italics"></emph>Massimi Sistemi<emph.end type="italics"></emph.end> i pianeti a tanti pendoli, che abbiano il loro centro <lb></lb>di sospensione nel sole, la sua matematica gli concludeva che i <lb></lb>tempi periodici debbono essere proporzionali alle radici degli assi. </s>

<s><lb></lb>Or questa sua matematica volle Galileo che prevalesse al fatto con­<lb></lb>cluso dal Keplero, secondo il quale, i quadrati dei tempi periodici <lb></lb>sarebbero come i cubi delle medie lunghezze degli assi. </s>

<s>Così venne <lb></lb>a persuadersi di più, che le tre leggi Kepleriane, in cui parevagli <lb></lb>di non ravvisar la solita Natura geometrizzante, non fossero più che <lb></lb>altrettante chimere. </s></p><p type="main">

<s>Ma che molte dottrine di Galileo sien vere in astratto e poi <lb></lb>non corrispondano ai fatti, come diceva Simplicio, abbiamo, a per­<lb></lb>suadere i più ritrosi, un argomento concludentissimo, in quei teo­<lb></lb>remi del moto applicato all&#039;acque correnti nella celebre Lettera sul <lb></lb>fiume Bisenzio. </s>

<s>Ivi si professa dall&#039;Autore il principio che l&#039;acqua, <lb></lb>fra tutti i corpi gravi, è quella, in cui si verificano più esattamente <lb></lb>le leggi della caduta dei gravi, specialmente lungo i piani inclinati, <lb></lb>e ciò perch&#039;ella non è soggetta, per sua propria natura, agli urti <lb></lb>e agli attriti, che sogliono essere le più valide cause, per cui si <lb></lb>alterano quelle stesse leggi. </s>

<s>Così, immaginandosi un piano liquido <lb></lb>tangente ne&#039;punti di sporgenza delle asperità delle rive o dell&#039;alveo, <lb></lb>l&#039;acqua, che riceve impedimento da sì fatte asperità, non è che <lb></lb>quella sola, la quale si trova rinchiusa fra quel piano immaginario <lb></lb>e le sinuosità e le sporgenze delle rive e dell&#039;alveo. </s>

<s>Il rimanente <lb></lb>scorre, per mezzo a quello stesso piano liquido, senza violenza di <lb></lb>attrito, come un corpo duro sopra un tersissimo specchio. </s>

<s>Da ciò <lb></lb>derivava per legittima conseguenza che la corrente dovesse giungere <lb></lb>al suo termine con tutta la velocità, che conviene alla caduta. </s>

<s>Or <lb></lb>non par credibile che Galileo approvasse tali teorie, tanto eviden­<lb></lb>temente contrarie all&#039;esperienza. </s>

<s>È chiaro infatti, secondo quelle <lb></lb>teorie, che, dovendo essere le fila superficiali della corrente tutte <lb></lb>ugualmente veloci, non vi si dovrebbe mai vedere nel mezzo il <lb></lb>filone. </s>

<s>Che se davvero ogni fiume, specialmente in tempo di piena, <pb xlink:href="020/01/191.jpg" pagenum="172"></pb>giunge allo sbocco con tutta la velocità conveniente alla caduta, <lb></lb>chi non vede che, arrivate a un punto, le sezioni non si potrebbero <lb></lb>ritenere più insieme, come giusto si osserva nel cader delle trosce <lb></lb>d&#039;acqua da qualche grande altezza? </s>

<s>Fu per questo che il Barattieri, <lb></lb>con giudizio diverso da quello di Galileo, stimando i fatti più con­<lb></lb>cludenti delle matematiche dimostrazioni, si rivolse a professar, per <lb></lb>l&#039;acqua e per tutti i gravi cadenti in generale, la legge dimostrata <lb></lb>dal Tartaglia delle velocità proporzionali ai semplici spazi, a pre­<lb></lb>ferenza della vera, dimostrata già dallo stesso Galileo. </s>

<s>Anzi, paren­<lb></lb>dogli dover esser la corrente, anco velocitata così, troppo più pre­<lb></lb>cipitosa di quel che non dimostrano i fatti, considera che ella vien <lb></lb>giustamente rattemperata, nel suo corso, da tanti impedimenti. </s></p><p type="main">

<s>Qual più valido argomento di questo si potrebb&#039;egli recare a <lb></lb>prova del nostro assunto, che cioè Galileo faceva prevalere le astratte <lb></lb>speculazioni ai fatti? </s>

<s>E i fatti, dall&#039;altra parte, oltre ad essere per <lb></lb>sè medesimi così manifesti, gli eran messi in considerazione da <lb></lb>quelle lunghe e dotte lettere che, a dimostrar la fallacia di que&#039;suoi <lb></lb>idraulici insegnamenti, con tanta filosofica libertà, gli scriveva Andrea <lb></lb>Arrighetti. </s></p><p type="main">

<s>Questo Arrighetti, coll&#039;Aggiunti, col Castelli e con pochi altri, <lb></lb>son senza dubbio de&#039;primi che, progredendo negli studi sperimen­<lb></lb>tali, passano dalle astratte forme geometriche a considerare le par­<lb></lb>ticolari affezioni della materia. </s>

<s>Ma gli esempi ancora, come si disse, <lb></lb>son pochi: le vie sono incerte, e da tutto apparisce che l&#039;arte di <lb></lb>sperimentare è tuttavia ne&#039;suoì principii. </s>

<s>Per vederla nel suo pieno <lb></lb>esercizio conviene ancora aspettare che la celebre Accademia del <lb></lb>Cimento sia convocata, e che ella abbia almeno pubblicati i suoi <lb></lb><emph type="italics"></emph>Saggi.<emph.end type="italics"></emph.end> Ma, in questo non breve spazio di tempo, la Francia è com­<lb></lb>mossa di maraviglia alle esperienze del Pascal, dell&#039;Auzout, del <lb></lb>Roberval, del Pacquet; l&#039;Inghilterra a quelle del Boyle; la Ger­<lb></lb>mania a quelle del Guericke, e, a restare ammirata alle nuove <lb></lb>esperienze di Valeriano Magno, non ultima di tutte è la solitaria <lb></lb>Polonia. </s>

<s>Il vantarsi perciò che la nostra Accademia del Cimento <lb></lb>sia stata la prima, fra tutte le altre instituite in Europa, si riduce <lb></lb>a una vanità, considerando che i nomi ora citati valgono, ciascuno <lb></lb>per sè, quanto un&#039;intiera Accademia, e che i <emph type="italics"></emph>Saggi di Naturali <lb></lb>Esperienze<emph.end type="italics"></emph.end> paragonati agli <emph type="italics"></emph>Esperimenti fisico meccanici,<emph.end type="italics"></emph.end> appariscon <lb></lb>non più che come una spigolatura dopo la messe. </s></p><p type="main">

<s>In ogni modo però è verissimo, a nostro conforto, che quelle <lb></lb>onde di scienza sperimentale che si diffondono così al largo per <pb xlink:href="020/01/192.jpg" pagenum="173"></pb>tutta l&#039;Europa, ebbero il loro centro d&#039;impulsione in Italia. </s>

<s>Che fa, <lb></lb>in vero, il Pascal a Roano, in mezzo a quella folla di popolo, per <lb></lb>gran curiosità concorsavi d&#039;ogni parte? </s>

<s>Verifica un&#039;esperienza ve­<lb></lb>nuta d&#039;Italia, la conferma con altre nuove stupende esperienze, e <lb></lb>si studia in ogni modo di persuadere i contradicenti. </s>

<s>Che fanno <lb></lb>l&#039;Auzout, e il Roberval a Parigi, se non che diffonder la notizia di <lb></lb>quella esperienza italiana nelle pubbliche scuole, alla presenza dei <lb></lb>giovani studiosi; e che fa il Pacquet, se non che applicare quella <lb></lb>stessa esperienza a risolvere compiutamente il problema arveiano <lb></lb>della circolazione del sangue? </s>

<s>E che altro mai fa il Guericke, in <lb></lb>mezzo ai principi, ai magnati e al popolo concorsi sulle pubbliche <lb></lb>piazze di Magdeburgo, se non che sottoporre a nuove e maravi­<lb></lb>gliose esperienze i concetti stessi di Galileo? </s>

<s>Valeriano Magno fa <lb></lb>stupire la corte del Re di Polonia con una esperienza, che tutti <lb></lb>dicono esser venuta di Firenze, ma che egli spaccia per invenzione <lb></lb>sua propria. </s>

<s>Nessuno però di questi stranieri s&#039;esercitò mai con <lb></lb>tant&#039;arte e con tanto studio intorno a quella italiana esperienza, <lb></lb>quanto Roberte Boyle, emulo al connazionale suo Guglielmo Gilbert, <lb></lb>in dare al pubblico i primi e più splendidi esempi dell&#039;arte spe­<lb></lb>rimentale. </s></p><p type="main">

<s>S&#039;indovina assai facilmente che l&#039;esperienza italiana, di cui si <lb></lb>parla, è quella celeberrima dell&#039;argento vivo, fatta dal Torricelli, <lb></lb>e da cui veramente l&#039;arte sperimentale ha principio. </s>

<s>Scriveva il <lb></lb>Pecquet, negli Esperimenti nuovi anatomici, e dava gran lode al <lb></lb>Pascal “ qui primus in Gallia nostra vix natum apud exteros, et in <lb></lb>cunabulis pene suffocatum de vacuo experimentum hydrargirio non <lb></lb>solum, sed et liquoribus suscitavit, imo tam felici provexit mirabilis <lb></lb>industriae successu, ut per totam Europam tentandi vacui studium <lb></lb>verae sapientiae cultoribus indiderit ” (Parisiis, 1654, pag. </s>

<s>55). Ora <lb></lb>si domanda: aveva egli ragione il Pecquet d&#039;affermare che l&#039;espe­<lb></lb>rienza torricelliana fosse rimasta soffocata nella cuna? </s>

<s>Si comprende <lb></lb>che la ragione del vantato nostro primato, sopra le altre nazioni <lb></lb>europee, dipende da questa risposta. </s>

<s>E noi, dandola con la solita <lb></lb>nostra imparzialità, diciamo che, a giudicar dai pubblici documenti, <lb></lb>il Pecquet aveva ragione. </s>

<s>Nel 1648 infatti si pubblicarono le prime <lb></lb>esperienze del Pascal fatte a Roano; nel 1654, il Pecquet stesso <lb></lb>pubblicava i suoi Nuovi Esperimenti anatomici; nel 1657 lo Schott <lb></lb>dava notizia al pubblico, a nome del Guericke, dei primi Esperi­<lb></lb>menti Nuovi di Magdeburgo, e il Boyle, nel 1659, pubblicava i suoi <lb></lb>Esperimenti fisico meccanici. </s>

<s>In Italia, dall&#039;epistola di Timeo Lo-<pb xlink:href="020/01/193.jpg" pagenum="174"></pb>crese in fuori, che è del 1648, nessuna esercitazione sull&#039;esperienza <lb></lb>torricelliana comparve in pubblico prima del 1666, anno in cui si <lb></lb>misero in luce i <emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> della fiorentina Accademia. </s>

<s>Se poi si va a <lb></lb>ricercare quel che rimase rinchiuso fra le splendide pareti del pa­<lb></lb>lazzo Pitti, o venne affidato a carte mutilate e neglette, il Pecquet <lb></lb>non affermò cosa che fosse mai tanto lontana dal vero. </s></p><p type="main">

<s>Non si può, in questo proposito, non meditar profondamente <lb></lb>sopra certi fatti particolari, che altri forse direbbe dipendere da un <lb></lb>Destino, ma che meglio si attribuirebbero a un indole propria della <lb></lb>gente italiana. </s>

<s>A legger la Narrazione, che il Roberval fa nella sua <lb></lb>Lettera al Noyers, o quel che scrive il Magno nella <emph type="italics"></emph>Dimostrazione <lb></lb>oculare,<emph.end type="italics"></emph.end> e lo Schott e il Guericke negli Esperimenti di Magdeburgo, <lb></lb>si resta maravigliati a sentir che francesi, alemanni, polacchi, no­<lb></lb>bili e plebe, principi e magnati concorressero a veder lo spettacolo <lb></lb>dell&#039;esperienza del vuoto in tanta folla, da non esserne capaci le <lb></lb>pubbliche piazze; mentre in Roma, Gaspero Berti, alquanti anni <lb></lb>prima che ne sapessero nulla que&#039;francesi, quegli alemanni, quei <lb></lb>pollacchi, al suo pubblico spettacolo non aveva assistenti che il Ma­<lb></lb>giotti, il Kircher, lo Zucchi, e pochi altri dotti. </s>

<s>Anche in Firenze <lb></lb>il Granduca, per compiacer talvolta qualche straniero erudito, chia­<lb></lb>mava il Torricelli a ripetere l&#039;esperienza sotto le solitarie amene <lb></lb>ombre del giardino di Boboli; compiacenza offerta raramente però, <lb></lb>e toccata a pochi altri, oltre al Moncony e al Mersenno, che primo <lb></lb>ne diè avviso al Pascal, da cui, come scintilla, divampò l&#039;incendio <lb></lb>per tutta l&#039;Europa. </s></p><p type="main">

<s>Che si dirà, a spiegar questi fatti, dell&#039;indole degli italiani? </s>

<s><lb></lb>Si dirà che non avevano amore alla scienza? </s>

<s>Ma il non trarre il <lb></lb>popolo nostro, come gli stranieri, a spettacolo sì fatto, forse niente <lb></lb>altro dice, se non ch&#039;egli era più colto, essendo sempre la curio­<lb></lb>sità figliola dell&#039;ignoranza. </s>

<s>Una tal curiosità è poi naturale che non <lb></lb>frugasse troppo a vivo una gente avvezza oramai a sentir delle tante <lb></lb>maraviglie operate da Galileo. </s></p><p type="main">

<s>Si dirà che non presentivano i Nostri le conseguenze di quei <lb></lb>fatti spettacolosi, dai quali sarebbe incominciato, e avrebbe ricevuto <lb></lb>la fisica sperimentale così valido impulso? </s>

<s>Che non avessero così <lb></lb>vivo quel presentimento forse è vero, perchè non si saprebbe spie­<lb></lb>gare altrimenti il silenzio, che si tenne da tutti intorno alla storia <lb></lb>della grande scoperta. </s>

<s>Non è cosa che tanto rechi meraviglia, quanto <lb></lb>il veder il Viviani, che v&#039;ebbe tanta parte, e molti altri che, anche <lb></lb>morto il Torricelli, potevano attinger notizia da lui; come ci lascino <pb xlink:href="020/01/194.jpg" pagenum="175"></pb>così al buio intorno a ciò che dette occasione alla esperienza del­<lb></lb>l&#039;argento vivo, contentandosi di accennare ai concetti di Galileo, <lb></lb>che saranno stati un occasione sì, ma un occasione troppo remota. </s>

<s><lb></lb>Il Mersenno, e tutti noi si vorrebbe saper qual fu l&#039;immediata <lb></lb>scintilla, da cui si accese la gran fiamma, e nessun lo sa dire, nè <lb></lb>si legge in nessuna di quelle tante carte dei manoscritti galileiani, <lb></lb>d&#039;onde pur s&#039;attinge la segreta storia di tante cose. </s>

<s>Altra gran ma­<lb></lb>raviglia è che il Torricelli non pubblicasse e nemmeno scrivesse <lb></lb>di proposito nulla intorno alla sua grande invenzione. </s>

<s>Le lettere <lb></lb>stesse a Michelangiolo Ricci, che sarebbero forse andate smarrite <lb></lb>se il Borelli, recatele da Roma, non l&#039;avesse consegnate al principe <lb></lb>Leopoldo de&#039;Medici, non si pubblicarono prima del 1663, nella Let­<lb></lb>tera di Timauro ai Filaleti. </s>

<s>Il Torricelli e il Viviani è verosimile <lb></lb>che non avrebbero operato così, se avessero presentito i benefizi <lb></lb>immensi, che sarebbero derivati alla scienza universale da quel loro <lb></lb>cannello di vetro, mezzo pieno di mercurio e mezzo vuoto. </s></p><p type="main">

<s>Il non aver però questo presentimento e il non aver dato a <lb></lb>quel loro sperimentale apparato tutta quella importanza, che gli <lb></lb>dettero gli stranieri, non vuol dir, com&#039;affermava il Pecquet, che <lb></lb>l&#039;avessero lasciato morire appena nato. </s>

<s>A rivendicar l&#039;onta, che si <lb></lb>fa all&#039;Italia con quelle parole dall&#039;anatomico francese, sovverranno <lb></lb>i fatti, pochi ma concludenti, da cui si prova come, dopo le prime <lb></lb>esperienze, proseguisse, nello studio delle proprietà del vacuo e <lb></lb>degli effetti naturali della pressione ammosferica, il Torricelli aiu­<lb></lb>tato e sollecitato all&#039;opera dall&#039;amico suo Raffaello Magiotti. </s></p><p type="main">

<s>La lettera del di 11 di Giugno 1644, dove l&#039;Autore descrive a <lb></lb>Michelangiolo Ricci l&#039;esperienza dell&#039;argomento vivo, perchè la pri­<lb></lb>ma fra le rimaste, si dà come primo documento degli studi speri­<lb></lb>mentali su quel soggetto. </s>

<s>Ma chi attende bene, rileva con facilità, <lb></lb>dalle sue proprie parole, che lo scrivente era già fatto certo, non <lb></lb>solo che l&#039;aria pesa, ma che il peso di lei varia da un giorno al­<lb></lb>l&#039;altro, per cui l&#039;assunto di quella Lettera al Ricci non è che di <lb></lb>dargli notizia de&#039;tentativi fatti per costruire un nuovo strumento, <lb></lb>da servir di misura a quelle ammosferiche variazioni. </s>

<s>Or perchè la <lb></lb>notizia di una cosa tanto nuova, qual&#039;è quella dell&#039;aria, che preme <lb></lb>con varia forza di torchio da un giorno all&#039;altro, non poteva esser <lb></lb>se non che frutto di ripetute diligentissime esperienze, si veda <lb></lb>quanto mal s&#039;appongono coloro, che riguardano l&#039;esperienza del <lb></lb>mercurio nel cannello di vetro, alle mani del Torricelli, come un <lb></lb>fatto solitario e indipendente, senza principio e senza sequele. </s>

<s>Delle <pb xlink:href="020/01/195.jpg" pagenum="176"></pb>notizie delle esperienze precedenti a quella del mercurio sodisfa­<lb></lb>remo ai lettori in luogo più opportuno: quanto alle conseguenti, <lb></lb>basti il citar la testimonianza dei nostri Accademici del Cimento, <lb></lb>i quali riconoscono il Torricelli per primo Autore, che sperimen­<lb></lb>tasse la vita degli animali nel vuoto. </s>

<s>E quando pur ci mancassero <lb></lb>altre testimonianze, chi potrebbe creder che colui, il quale aprì la <lb></lb>via a così nuove e importanti esperienze, si rimanesse dal vagar <lb></lb>per altre parti della spaziosa ubertà di quel campo? </s>

<s>Vero egli è <lb></lb>bene che mancava uno strumento adattato, perchè, diffidando forse <lb></lb>delle legature, non pensò nè ardì di aprire i fondi dei vasi, per <lb></lb>introdurvi dentro gli oggetti. </s>

<s>Ma chi oserebbe prescrivere così fatti <lb></lb>limiti a quel grandissimo ingegno? </s>

<s>Chi potrebbe decider se sia <lb></lb>vero che non avesse tempo di mettersi attorno a raffinare quelle <lb></lb>esperienze nel vuoto, o non sia avvenuto piuttosto che ne sia per­<lb></lb>duta la memoria, come di tante altre cose di lui e del Magiotti? </s></p><p type="main">

<s>Raffaello Magiotti, nato in Toscana nel paesello di Montevarchi, <lb></lb>è un elettissimo ingegno, ma sventuratamente rimasto soffocato dalla <lb></lb>polvere della Biblioteca Vaticana. </s>

<s>Quella corrispondenza di amiche­<lb></lb>voli ufficii e di studii, che passò fra lui e il Torricelli, quando gio­<lb></lb>vani in Roma s&#039;educavano l&#039;ingegno alle nuove dottrine galileiane <lb></lb>sotto la disciplina del P. Castelli; si mantenne integra e viva anco <lb></lb>dappoi, che il Torricelli stesso era venuto a Firenze, e vi s&#039;era <lb></lb>stabilito in qualità di Matematico del Granduca. </s>

<s>Le lettere fra i due <lb></lb>amici intercedevano assai frequenti, e non occorreva speculazione <lb></lb>o scoperta all&#039;ingegno e all&#039;esercizio dell&#039;uno, che non fosse co­<lb></lb>municata o conferita con l&#039;altro. </s>

<s>Pensa il Torricelli che le velocità <lb></lb>del flusso dei liquidi non siano proporzionali alle semplici altezze <lb></lb>ma alle loro radici, e il Magiotti conferma il fatto con ripetute e <lb></lb>diligenti esperienze. </s>

<s>Si è il Torricelli stesso abbattuto a nuovi fatti <lb></lb>curiosi circa il galleggiare e il sommergersi alcune palline di vetro <lb></lb>vuote e aperte in un sottilissimo foro, per dove può passare o acqua <lb></lb>o nuov&#039;aria, e avvisa di questa curiosità proponendogliela sotto forma <lb></lb>di Problemi il Magiotti, che gli risolve mirabilmente nell&#039;unica <lb></lb>scrittura, che di lui s&#039;abbia alle stampe, sotto il titolo di <emph type="italics"></emph>Renitenza <lb></lb>certissima dell&#039;acqua alla compressione.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Che le prime scoperte del variar della pressione ammosferica <lb></lb>fossero comunicate dall&#039;Autore al suo amico in Roma, più che pro­<lb></lb>babile, sembra a noi cosa certa, e se ci fossero rimaste le lettere, <lb></lb>nelle quali il Torricelli conferiva col Magiotti quelle sue stesse sco­<lb></lb>perte, non sarebbe lasciato forse altro più da desiderare alla cu-<pb xlink:href="020/01/196.jpg" pagenum="177"></pb>riosità della storia. </s>

<s>In ogni modo, anco dai pochi documenti che <lb></lb>ci son pervenuti, o da qualche accenno, che si trova fatto qua e là <lb></lb>dagli scrittori, s&#039;argomenta che il Magiotti s&#039;esercitò intorno all&#039;espe­<lb></lb>rienza del vuoto in più varii modi, e con più solerzia, di quel che <lb></lb>non facessero qualche anno dopo tanti stranieri. </s>

<s>Lo Schott l&#039;anno­<lb></lb>vera fra coloro che assisterono al pubblico esperimento del vuoto, <lb></lb>fatto con l&#039;acqua dentro un lungo tubo applicato alla parete esterna <lb></lb>della propria casa d&#039;abitazione da Gaspero Berti. </s>

<s>Il Mersenno però, <lb></lb>non come semplice spettatore ce lo rappresenta, ma come princi­<lb></lb>pale attore della nuova e importante esperienza. </s>

<s>Nel capitolo VI <lb></lb>delle sue <emph type="italics"></emph>Nuove Osservazioni,<emph.end type="italics"></emph.end> dopo avere accennato alla possibilità <lb></lb>del vacuo, e all&#039;esperienze più opportune per dimostrarlo, soggiunge: <lb></lb>“ Bombus volantis crabronis aptissimus videtur, sed et aquae, vel <lb></lb>alterius liquoris guttulas possis in illo tubo vacuo experiri, num <lb></lb>tubo concusso guttulae illae, lapidum instar parietes internos cy­<lb></lb>lindri percussurae sint ut clariss. </s>

<s>Magiottus in tubo factum esse <lb></lb>dicebat, ex quo fuerat haustus aer diabete ” (T. III. Parisiis, 1647, <lb></lb>pag. </s>

<s>104, 5). Da sì importante documento si raccoglie dunque, che <lb></lb>infin dal 1644, o in quel torno che il Mersenno trovavasi a Roma, <lb></lb>il Magiotti usava di fare il vuoto colla siringa, e per tal modo spe­<lb></lb>rimentò il colpo secco, che danno i liquidi, non impediti ne fra­<lb></lb>stagliati dall&#039;aria. </s>

<s>Questo solo fatto attesta che il nostro sperimen­<lb></lb>tatore era proceduto così avanti, da raggiungere quasi il Boyle, e <lb></lb>da emulare gli stessi Accademici fiorentini, che sarebbero venuti <lb></lb>parecchi anni dipoi. </s></p><p type="main">

<s>Anzi di questa ultima nostra asserzione abbiam certezza di <lb></lb>prove da alcune lettere del Borelli. </s>

<s>Essendo egli nell&#039;estate del 1658 <lb></lb>in Roma, ebbe ordine dal principe Leopoldo d&#039;informarsi di ciò <lb></lb>che fosse avvenuto dei manoscritti lasciati dopo la morte dal Ma­<lb></lb>giotti. </s>

<s>E raccolse dalle sue informazioni, il Borelli, come il cardinal <lb></lb>Sacchetti, alle mani del quale erano venuti que&#039;fogli, avessegli con­<lb></lb>segnati a Michelangiolo Ricci, perchè gli ordinasse in quel modo <lb></lb>che sapesse migliore. </s>

<s>“ Mi dice però il detto Signore (cioè il Ricci, <lb></lb>e son parole dello stesso Borelli) che pochissime cose buone ha <lb></lb>ritrovato fra i detti scartafacci, particolarmente di quelle belle cose <lb></lb>geometriche e filosofiche che aveva ritrovato quel grande ingegno, <lb></lb>e queste per esser notate in cartucce furono disprezzate e poi bru­<lb></lb>ciate da quella canaglia che aveva cura di spurgare le case dopo <lb></lb>la peste ” (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVI. c. </s>

<s>100). </s></p><p type="main">

<s>Non sodisfatto, il Principe insiste per aver più particolari in-<pb xlink:href="020/01/197.jpg" pagenum="178"></pb>formazioni, e dopo pochi giorni, il dì 3 d&#039;Agosto, il Borelli risponde: <lb></lb>“ Mi sono poi meglio informato di quelle poche scritture rimaste <lb></lb>del signor Magiotti.... Di più vi sono alcune poche sperienze sopra <lb></lb>il vaso d&#039;argento vivo.... e per quanto mi dice il signor Michelan­<lb></lb>giolo non vi è niente di più di quello, che si è sperimentato nel­<lb></lb>l&#039;Accademia di Vostra Altezza ” (ivi, c.103). Ora, se si ripensi che <lb></lb>tra le prime e principali cure dell&#039;Accademia del Cimento fu quella <lb></lb>di sperimentare nel vaso dell&#039;argento vivo, e che moltissime e delle <lb></lb>principali fra queste stesse esperienze ne erano state fatte già nel­<lb></lb>l&#039;estate del 58, quando appunto scriveva il Borelli; si concluderà <lb></lb>dunque dalle parole di lui che il Magiotti, se non aveva fatto di <lb></lb>più, aveva fatto almeno, intorno all&#039;esperienza torricelliana, tutto <lb></lb>quel che nel Libro dei Saggi di Naturali Esperienze, dopo più che <lb></lb>22 anni, vi fu particolarmente narrato e descritto. </s>

<s>Che se veramente <lb></lb>è così, vedasi quanto a torto asserisse il Pecquet essere l&#039;esperi­<lb></lb>mento dell&#039;idrargiro <emph type="italics"></emph>vix natum<emph.end type="italics"></emph.end> appresso noi italiani, <emph type="italics"></emph>et in cuna­<lb></lb>bulis suffocatum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma insomma, la ragione e i diritti del primato d&#039;Italia ne&#039;pro­<lb></lb>gressi delle scienze sperimentali resultano da documenti sconosciuti <lb></lb>non solo al Pecquet, e agli altri stranieri, ma non saputi nemmeno <lb></lb>da molti di noi italiani, che pure abbiamo così gran pretensioni, e <lb></lb>meniamo così gran vanto. </s>

<s>I nostri competitori perciò hanno avuto <lb></lb>fin qui ragione o di andare in collera con noi, o di deriderci, com­<lb></lb>patendo alla nostra vanità, e avranno ragione ancora di farlo, in­<lb></lb>fintanto che non si confermi quel nostro primato sopra più stabile <lb></lb>fondamento. </s>

<s>Alla patria nostra non mancherà, speriamo, chi voglia <lb></lb>e sappia degnamente farlo, ma intanto ne tratteremo qualche cosa <lb></lb>noi, quanto lo comporti la sufficienza nostra e la brevità richiesta <lb></lb>al presente Discorso. </s></p><p type="main">

<s><emph type="center"></emph>VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Perchè noi teniamo per cosa certa aver l&#039;arte sperimentale <lb></lb>avuto i suoi primi principii e i suoi primi istituti dal Torricelli, e <lb></lb>perchè i cenni già fatti, essendo troppo scarsi all&#039;importanza del <lb></lb>soggetto, richiedono d&#039;esser suppliti e confortati d&#039;altri argomenti; <lb></lb>giova, prima, intrattenere alquanto la nostra considerazione sulla <pb xlink:href="020/01/198.jpg" pagenum="179"></pb>persona di lui, che, dopo Galileo, è al parer nostro il principale <lb></lb>attore di questa Parte della nostra Storia. </s></p><p type="main">

<s>Evangelista Torricelli, a cui si dà da molti per patria Faenza, <lb></lb>si sentì consapevole della potenza del proprio ingegno alla lettura <lb></lb>dei Dialoghi delle Due Nuove Scienze, ai teoremi dimostrati ne&#039;quali <lb></lb>fece alcune aggiunte o <emph type="italics"></emph>progressi,<emph.end type="italics"></emph.end> com&#039;ei stesso si esprime (MSS. <lb></lb>Gal. </s>

<s>Disc. </s>

<s>T. XL, c. </s>

<s>78), che ordinati e trascritti, verso il Febbraio <lb></lb><figure id="id.020.01.198.1.jpg" xlink:href="020/01/198/1.jpg"></figure><lb></lb>del 1641, mandò al suo Maestro e Protettore Benedetto Castelli. </s>

<s>Il <lb></lb>Castelli fece di ciò consapevole Galileo, che se ne rallegrò molto, <lb></lb>e nel seguente aprile invitava l&#039;Autore di quei <emph type="italics"></emph>progressi<emph.end type="italics"></emph.end> a tratte­<lb></lb>nersi per qualche giorno seco in Arcetri. </s>

<s>Il principe Leopoldo poi <lb></lb>fece sì, che la semplice visita si riducesse a stabile soggiorno. </s>

<s>Tal <lb></lb>notizia raccogliesi dalla minuta autografa di una lettera, che lo <lb></lb>stesso principe indirizzava a Michelangiolo Ricci, nella quale, a <pb xlink:href="020/01/199.jpg" pagenum="180"></pb>proposito del nuovo libro che meditava il Borelli sulla forza della <lb></lb>percossa, scrive che la buona memoria di Galileo gli aveva detto <lb></lb>più volte d&#039;aver ritrovata la misura di quella forza “ ma non potè <lb></lb>per l&#039;età o per qualsivoglia altro accidente, che ne fosse cagione, <lb></lb>darla fuori, com&#039;io le feci ben cento volte istanza, ed al qual fine <lb></lb>condussi qui il Torricelli di suo consenso, perchè potesse servire <lb></lb>in mettere in carta i suoi pensieri, ma tutto fu invano ” (MSS. Gal. </s>

<s><lb></lb>Cim. </s>

<s>T. XXIII. c. </s>

<s>113). Galileo che, secondo narreremo a suo luogo, <lb></lb>aveva già nell&#039;animo repudiata quella speculazione della percossa, <lb></lb>si proponeva di conferire col Torricelli altri suoi pensieri matema­<lb></lb>tici e fisici, per poter con l&#039;aiuto di lui ripulirli e mandarli alla <lb></lb>luce (Alb. </s>

<s>VII. pag. </s>

<s>367). In effetto però non fece aiutarsi che nelle <lb></lb>aggiunte, nelle correzioni dei Dialoghi del Moto, e nel nuovo ordine <lb></lb>che meditava di dare ai teoremi dimostrati nel Dialogo terzo. </s>

<s>Nè, <lb></lb>a quel che apparisce dai manoscritti galileiani, furono scarsi intorno <lb></lb>a ciò gli aiuti prestati dal Torricelli, tanto più se si ripensi ch&#039;ei <lb></lb>non istette ospite in Arcetri che dall&#039;Ottobre al Gennaio. </s></p><p type="main">

<s>Morto Galileo, il Torricelli fu trattenuto in Firenze e onorato, <lb></lb>ad insinuazione di Andrea Arrighetti, di un duplice ufficio; di quello <lb></lb>di Filosofo e matematico del Granduca Ferdinando II, e dell&#039;altro <lb></lb>di Lettore di Matematiche nel pubblico Studio fiorentino. </s>

<s>Ai due <lb></lb>speciali ufficii corrispose con opere, diverse di natura e di successo. </s>

<s><lb></lb>Come professore di Matematiche raccolse in un volume, sotto il <lb></lb>titolo di <emph type="italics"></emph>Opere geometriche,<emph.end type="italics"></emph.end> ciò che aveva speculato così intorno <lb></lb>alle proprietà della sfera e dei solidi sferali, come intorno al moto <lb></lb>de&#039;gravi solidi e liquidi naturalmente discendenti e proietti, e con­<lb></lb>tiene quel volume, pubblicato in Firenze nel 1644, tutto ciò che <lb></lb>vide la pubblica luce vivente l&#039;Autore. </s></p><p type="main">

<s>Tutte le altre scritture rimaste inedite pervennero, alla morte <lb></lb>del Torricelli avvenuta nel 1647, dopo soli 39 anni di vita, nelle <lb></lb>mani di Lodovico Serenai, che, copiate in gran parte le consegnò <lb></lb>al Viviani, affinchè le ordinasse per dare alle stampe. </s>

<s>L&#039;accusa <lb></lb>mossagli poi dal Nelli e ripetuta da altri, di non aver adempiuto <lb></lb>per invidia al pietoso amichevole ufficio, parrà ingiustissima a tutti <lb></lb>coloro, i quali sanno come il Viviani, e per la mal ferma salute e <lb></lb>per i pubblici impieghi, fosse impedito di pubblicare le molte opere <lb></lb>sue proprie. </s></p><p type="main">

<s>Le Lezioni Accademiche del Torricelli, alcune delle quali trattan <lb></lb>soggetti di Meccanica e di Fisica, importantissimi, ignote a quel che <lb></lb>che sembra al Borelli, ma vedute già dal Viviani, furono pubbli-<pb xlink:href="020/01/200.jpg" pagenum="181"></pb>cate, per la prima volta nel 1715, da Tommaso Bonaventuri, e le <lb></lb>varie Scritture sopra le Chiane capitate, dopo varie vicende, alle <lb></lb>mani del p. </s>

<s>Guido Grandi, s&#039;inserirono, nel 1768, nella Raccolta <lb></lb>fiorentina degli Autori, che trattano del moto delle acque. </s></p><p type="main">

<s>Come Filosofo e Matematico del Granduca Ferdinando II, il <lb></lb>Torricelli, infino dal 1642, dette opera a istituire la sperimentale <lb></lb>Accademia Medicea, nella quale, quasi con mano ostetricante, si <lb></lb>estraevano dalle Opere di Galileo esperienze e invenzioni di strumenti <lb></lb>nuovi, da scoprir le più recondite cause di tanti effetti della Natura. </s>

<s><lb></lb>Dicemmo che così fatti studi ed esercizi sperimentali, com&#039;erano <lb></lb>in soggetto diverso, così ebbero diverso successo da quegli altri <lb></lb>studi, che fece lo stesso Torricelli come pubblico professore, per­<lb></lb>ciocchè questi furono principalmente di argomento geometrico, e <lb></lb>andarono sotto il nome del loro proprio Autore, mentre l&#039;espe­<lb></lb>rienze fatte e gli strumenti inventati e costruiti nel palazzo dei Pitti, <lb></lb>s&#039;attribuirono, per cortigiano ossequio, al granduca Ferdinando. </s></p><p type="main">

<s>Che sia andata veramente la cosa a questo modo, non par che <lb></lb>ci sia bisogno di troppo lunghe parole a provarlo, e perciò, ammesso <lb></lb>che le belle esperienze e gli utili strumenti attribuiti al Granduca, <lb></lb>fossero veramente opera e studio del Torricelli, vediamo quali fos­<lb></lb>sero quelle particolari esperienze e quelle invenzioni, primaticci <lb></lb>frutti della nascente Accademia sperimentale di Firenze. </s></p><p type="main">

<s>Si disse che il Torricelli ostetricò i suoi parti sperimentali dalle <lb></lb>Opere di Galileo, a conferma di che, occorre prima di tutto a notar <lb></lb>l&#039;origine di quei vari strumenti inventati. </s>

<s>Son questi principalmente <lb></lb>il Termometro a liquido, l&#039;Igrometro a condensazione, e varie sorta <lb></lb>d&#039;Idrostammi o pesa liquori, che furono poi tutti diligentemente <lb></lb>descritti nel libro dei Saggi di Naturali esperienze. </s>

<s>Ma che essi <lb></lb>appartengano veramente a questi primordii dell&#039;Accademia Medicea, <lb></lb>si argomenta da quel <emph type="italics"></emph>Registro di varie Esperienze fatte e osservate <lb></lb>dal Serenissimo Granduca Ferdinando II<emph.end type="italics"></emph.end> che redatto da Paolo Mi­<lb></lb>nucci, e copiato poi dal Viviani, fu inserito nella prima carta del <lb></lb>primo Tomo dei Manoscritti del Cimento, e pubblicato dal Targioni. </s>

<s><lb></lb>Il primo concetto di quella importantissima trasformazione del Ter­<lb></lb>mometro ad aria, nello strumento perpetuo che, secondo si legge <lb></lb>nel citato Registro, <emph type="italics"></emph>dimostra la differenza di caldo e freddo dell&#039;aria <lb></lb>e de&#039;liquidi,<emph.end type="italics"></emph.end> sovvenne senza dubbio al Torricelli da quella espe­<lb></lb>rienza della caraffa col collo assai lungo, empiuta d&#039;acqua insino <lb></lb>al collo, e messa al fuoco, che si legge nella <emph type="italics"></emph>Risposta a Lodovico <lb></lb>delle Colombe.<emph.end type="italics"></emph.end> L&#039;Igrometro a condensazione, di cui dava notizia lo <pb xlink:href="020/01/201.jpg" pagenum="182"></pb>stesso Torricelli a Michelangiolo Ricci, (tanto è vero che l&#039;inven­<lb></lb>zione è sua e non del Granduca) occorse facilmente all&#039;inventore, <lb></lb>a fin di decidere la questione che s&#039;agita, fra le tante, nella citata <lb></lb>Risposta al Colombo, se cioè quella rugiada, che si depone sulla <lb></lb>superficie dei corpi divenuti più freddi dell&#039;ambiente, sia aria tra­<lb></lb>sformata nell&#039;elemento dell&#039;acqua. </s>

<s>I densimetri poi torricelliani, di <lb></lb>che il Serenissimo si serviva per riconoscer le qualità delle varie <lb></lb>acque sorgenti, e per distinguer le varie bontà dei vini, scaturirono <lb></lb>senza dubbio dal primo Dialogo delle Due Nuove Scienze, dove <lb></lb>Galileo propone d&#039;immergere una palla di cera, per conoscer negli <lb></lb>usi medici i vari gradi della gravità o leggerezza dell&#039;acqua. </s></p><p type="main">

<s>Anzi ebbero di qui origine quelle belle e feconde esperienze <lb></lb>delle palline di vetro vuote e galleggianti dentro un bocciol pieno <lb></lb>d&#039;acquà, che il Torricelli mostrava al Moncony, primo tra&#039;francesi <lb></lb>a testimoniare nelle scienze sperimentali il primato dell&#039;Italia. </s>

<s>Co­<lb></lb>teste palline dettero occasione a scoprire altri fatti idrostatici curiosi <lb></lb>e nuovi, che si mandarono a risolvere ai varii dotti, sotto le velate <lb></lb>forme di problemi, per cui non fa maraviglia che, venuti a notizia <lb></lb>del Cartesio, o egli si appropriasse o altri spontaneamente gli attri­<lb></lb>buissero quegli idrostatici giochetti. </s>

<s>Giochetti non furon però alle <lb></lb>mani del Torricelli, che, dal veder variare il modo del galleggia­<lb></lb>mento di quelle palline, al vario premer col dito l&#039;aria alla bocca <lb></lb>del vaso, ebbe i primi indizii del variar della pressione atmosferica: <lb></lb>giochetti non furono alle mani del Magiotti, che di li prese occa­<lb></lb>sione a dimostrar la verità di quell&#039;importantissimo fatto idrostatico <lb></lb>delle pressioni dei liquidi per tutti i versi, e della instantanea dif­<lb></lb>fusione dei loro moti. </s></p><p type="main">

<s>Quel Moncony, di cui si diceva, recò d&#039;Italia in Francia, e anzi <lb></lb>trasportò seco ne&#039;suoi viaggi in Egitto, uno de&#039;più squisiti canoc­<lb></lb>chiali che fossero usciti dalle mani del Torricelli, giacchè, a questi <lb></lb>primordii o primo periodo della sperimentale Accademia fiorentina, <lb></lb>appartiene altresì il perfezionamento del Canocchiale galileiano e <lb></lb>del Microscopio. </s>

<s>Anzi, il Microscopio, così detto <emph type="italics"></emph>della perlina,<emph.end type="italics"></emph.end> che <lb></lb>trovò poi tanto facile accoglienza in Olanda, è invenzione tutta pro­<lb></lb>pria del Torricelli e noi diremo a suo luogo il modo, ch&#039;ei teneva <lb></lb>facilissimo di fabbricar questo, che par, fra gli strumenti di ottica, <lb></lb>un balocco, ma che è pure di grandissimo effetto. </s></p><p type="main">

<s>Notabile è però che il costruttore e l&#039;inventore di questi così <lb></lb>squisiti ottici strumenti non pensasse d&#039;applicarli o alle osservazioni <lb></lb>naturali o alle celesti. </s>

<s>Vero è bene che, in questi stessi tempi della <pb xlink:href="020/01/202.jpg" pagenum="183"></pb>sperimentale Accademia fiorentina, si riscontrarono i moti dei sa­<lb></lb>telliti di Giove sulle Effemeridi, che mandava il Renieri, ma forse <lb></lb>que&#039;riscontri eran fatti, per ordine del principe Leopoldo, dal Vi­<lb></lb>viani. </s>

<s>Il Torricelli pare che non fosse molto inclinato a così fatti <lb></lb>esercizi, e in ogni modo, benchè gareggiasse col Fontana e si van­<lb></lb>tasse di aver superato in perfezione i canocchiali di lui, non fece, <lb></lb>in Astronomia, nessuna scoperta. </s>

<s>Nella Primavera del 1647 racconta <lb></lb>al Renieri come gli occorresse di veder Mercurio in congiunzione <lb></lb>con Venere “ e così all&#039;improvviso, sul campanile del Duomo, di­<lb></lb>scorrendo con alcuni giovani, che erano meco, feci un certo calco­<lb></lb>laccio, per la prima volta che avevo veduto Mercurio, e conietturai <lb></lb>che egli di diametro reale fosse meno di otto miglia delle nostre ” <lb></lb>(MSS. Gal. </s>

<s>Dis. </s>

<s>T. XL, c. </s>

<s>13). </s></p><p type="main">

<s>Alla morte del Torricelli, sopravvenuta inaspettatamente nel­<lb></lb>l&#039;anno stesso in cui scriveva queste parole, non cessò nel Granduca <lb></lb>Ferdinando il prnrito, e nel principe Leopoldo quella nobile e gen­<lb></lb>tile predilezione, che egli ebbe sempre per le scienze sperimentali. </s>

<s><lb></lb>A tale servizio in corte fu sostituito quel Vincenzio Viviani, che si <lb></lb>soleva chiamar l&#039;ultimo, ma il più affezionato dei discepoli di Ga­<lb></lb>lileo. </s>

<s>Che egli fosse anzi svisceratamente affezionato, lo dimostrò <lb></lb>nello zelo dell&#039;illustrarne e diffonderne le dottrine, come, e anco <lb></lb>più, in sostener l&#039;onore e rivendicarne i diritti delle scoperte. </s>

<s>Fanno <lb></lb>al proposito le seguenti relazioni, che dava a un amico: “ Le dirò <lb></lb>ancora come tra quelle povere fatiche di matematica abbozzate da <lb></lb>me, dal 1639 fin al 1644, quando per servizio attuale del Serenis­<lb></lb>simo G. D. mio Signore convennemi abbandonare sì fatti studi, io <lb></lb>pensavo di fare scelta di quella, che ne&#039;continui impieghi e con la <lb></lb>poca salute che io mi trovavo, mi fosse stata di più facile esecu­<lb></lb>zione. </s>

<s>Questa era l&#039;illustrazione e promozione delle opere di Galileo <lb></lb>mio Maestro, da accoppiarsi con la descrizione della sua vita, la quale <lb></lb>da ogni altro assai meglio sì, ma non già sì veridica nè di notizie <lb></lb>così copiosa potesse scriversi ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLII, c. </s>

<s>130). </s></p><p type="main">

<s>Nonostante però la mal ferma salute e gli impieghi, fu il Vi­<lb></lb>viani fecondissimo nello speculare e infaticabile nell&#039;operare. </s>

<s>A <lb></lb>raccogliere tutti insieme, e ad ordinare i varii teoremi, che dimostrò <lb></lb>e i varii problemi, che risolse intorno alle dottrine del moto, si <lb></lb>comporrebbe un Trattato di <emph type="italics"></emph>aggiunte e progressi<emph.end type="italics"></emph.end> ai Dialoghi delle <lb></lb>Nuove Scienze, che se cede al Torricelli nell&#039;elegante facilità di <lb></lb>dimostrare, lo supera senza dubbio nella varietà e nell&#039;abbondanza. </s>

<s><lb></lb>In Idrometrìa, il Viviani fu instancabile, e d&#039;ogni parte traspira <pb xlink:href="020/01/203.jpg" pagenum="184"></pb>un ardentissimo zelo di diffondere le dottrine torricelliane. </s>

<s>A lui <lb></lb>il principio delle velocità proporzionali alle altezze professato dal <lb></lb>Castelli sembrava men vero di quel che non si concludeva dalle <lb></lb>teorie o si verificava nei fatti; e intorno alle controversie se l&#039;acque <lb></lb>giungono allo sbocco con tutta la velocità conveniente alla caduta, <lb></lb>oppur ricevano impedimento e patiscano indugio dagli attriti, la­<lb></lb>sciato per amor della verità da parte il suo Galileo, consentiva <lb></lb>pienamente coll&#039;Arrighetti. </s>

<s>Moltissime e importantissime son l&#039;espe­<lb></lb>rienze fatte dal Viviani, per misurar le varie quantità d&#039;acqua, che <lb></lb>in egual tempo si raccolgono dalle varie figure delle bocche di ero­<lb></lb>gazione, ora radenti, ora sporgenti in tubi addizionali, o brevi o <lb></lb>lunghi, o diritti o flessuosi. </s></p><p type="main">

<s>Il Trattato del votamento dei vasi o delle <emph type="italics"></emph>Clessidre,<emph.end type="italics"></emph.end> diviso in <lb></lb>quattro libri, col titolo un po&#039;romantico di <emph type="italics"></emph>Sogno idrometrico,<emph.end type="italics"></emph.end> sa­<lb></lb>rebbe riuscito opera insigne e da risparmiare il Trattato del Moto <lb></lb>delle Acque del Grandi, e di altri Autori, se avesse avuto il Nostro <lb></lb>il tempo e la comodità di pubblicarlo. </s>

<s>Quest&#039;opera, nella quale, <lb></lb>come si diceva dianzi, il principio torricelliano delle velocità pro­<lb></lb>porzionali alle radici delle altezze ha il suo ampio svolgimento e <lb></lb>la sua più compiuta dimostrazione, con altri teoremi speculati a <lb></lb>solo fine di promuovere il trattato <emph type="italics"></emph>De motu aquarum,<emph.end type="italics"></emph.end> finiscono di <lb></lb>persuader coloro, che dissero temerariamente aver il Viviani tenute <lb></lb>per invidia e per gelosia nascoste le scritture inedite del Torricelli. </s></p><p type="main">

<s>Col segreto dello stesso Torricelli, avuto dal Granduca che lo <lb></lb>teneva gelosamente custodito, e con altre regole proprie apprese <lb></lb>dalla teoria e dalla pratica, il Viviani dava opera alla costruzione <lb></lb>dei canocchiali, e attendeva, ora per proprio genio, ora per parti­<lb></lb>ticolare ordine del principe Leopoldo, alle osservazioni celesti. </s>

<s>Ma <lb></lb>la mal ferma salute non permettendogli le lunghe e faticose vigilie, <lb></lb>non fece, come il Torricelli, in Astronomia molti progressi. </s>

<s>Dei mol­<lb></lb>tissimi però fatti nella Fisica sperimentale diremo più qua, quando <lb></lb>c&#039;incontreremo un&#039;altra volta nel Viviani come accademico del Ci­<lb></lb>mento, ma intanto, a svolgere que&#039;cento tanti e più volumi delle <lb></lb>sue carte, non par possibile che un uomo, e sia pur che la vita gli <lb></lb>decorresse lunghissima dal 1622 al 1703 potesse attendere a tante <lb></lb>e sì difficili cose. </s>

<s>Stanco delle proprie speculazioni, si ricreava in <lb></lb>tradurre dal latino o dal francese ciò che di nuovo e di bello aves­<lb></lb>sero speculato gli altri nei loro proprii libri; ora compendiava trat­<lb></lb>tati intieri, forse per uso dei principi padroni, ora ne disegnava e <lb></lb>in parte coloriva de&#039;nuovi, in soggetto di matematiche, di cosmo-<pb xlink:href="020/01/204.jpg" pagenum="185"></pb>grafia o di qualsivoglia altro. </s>

<s>“ Se io avessi, scriveva a un amico, a <lb></lb>cucire tutte le mie speculazioni imbastite e finire di riempir tutti i <lb></lb>miei orditi con obbligo ancora di non dover pensare a niun altra cosa <lb></lb>di nuovo, non mi sarebbe tanto il vivere fino a cent&#039;anni, con sanità <lb></lb>perfetta e disoccupazione da ogni altro impiego ” (ivi, T. CXLII, c.270). </s></p><p type="main">

<s>Quando scriveva così, il Viviani contava 56 anni, e non aveva <lb></lb>altro pubblicato che <emph type="italics"></emph>De maximis et minimis,<emph.end type="italics"></emph.end> la <emph type="italics"></emph>Scienza Universale <lb></lb>delle proporzioni,<emph.end type="italics"></emph.end> il <emph type="italics"></emph>Diporto geometrico,<emph.end type="italics"></emph.end> l&#039;<emph type="italics"></emph>Enodatio problematum<emph.end type="italics"></emph.end><lb></lb>che son piccola parte, e non la più importante delle opere di lui. </s>

<s><lb></lb>Il rimanente, da poche altre cose in fuori, è tuttavia inedito, e ciò <lb></lb>vuol dire che un dovizioso tesoro della scienza italiana è rimasto da <lb></lb>tanto tempo, disutile e infruttuoso. </s>

<s>A lui vecchio di settantott&#039;anni <lb></lb>il p. </s>

<s>ab. </s>

<s>Grandi, scrivendogli di Roma, faceva questa domanda: <lb></lb>“ È fuori voce in Roma che le opere di V. S. si ristampino in <lb></lb>Londra, e che que&#039;signori della Società Regia abbiano impetrato <lb></lb>dal Serenissimo Granduca li di lei scritti, per imprimerli con altre <lb></lb>sue opere .... È egli vero tuttociò, oppure posso io seguitare ad as­<lb></lb>sicurare l&#039;Italia che le di lei fatiche saranno impresse per opera <lb></lb>del sig. </s>

<s>Panzanini? </s>

<s>” (ivi, T. CXLVII. c. </s>

<s>189). A che il buon vecchio <lb></lb>così rispondeva: “ È ben falsa quella voce che è fuori, perchè l&#039;opere <lb></lb>di quello scimunito dolcissimo, nè per mano di lui nè di altri non <lb></lb>v&#039;è apparenza che si sieno per vedere, se Dio non fa miracoli ” <lb></lb>(ivi, T. CXLVIII. c. </s>

<s>36). E i miracoli ancora non sono stati fatti. </s></p><p type="main">

<s>Ma passiamo a veder quel che operasse il Viviani in questo, <lb></lb>che da noi si distingue col nome di secondo periodo della speri­<lb></lb>mentale Accademia medicea. </s>

<s>Soggetto principale di queste espe­<lb></lb>rienze, che si direbbero, alla maniera dei nostri giorni, esperienze <lb></lb>di gabinetto, furon quelle degli agghiacciamenti dell&#039;acque, per <lb></lb>veder che varietà facessero esposti i vasi in varie situazioni all&#039;aria <lb></lb>aperta. </s>

<s>Cominciarono queste esperienze nel Dicembre 1648, e si <lb></lb>proseguirono per più altre invernate successive (MSS. Cim. </s>

<s>T. I, c. </s>

<s>5, <lb></lb>13 ecc.). Appartengono pure a questo periodo dell&#039;Accademia quelle <lb></lb>osservazioni, di non lieve importanza per la teoria della conduci­<lb></lb>bilità del calore, che concernono il vario tempo del consumarsi il <lb></lb>ghiaccio nelle varie materie, di che son formati i recipienti. </s>

<s>Di tali <lb></lb>osservazioni poi si fece qualche cenno anco nel Libro dei <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end><lb></lb>ma vi si tace di un&#039;altra esperienza, fatta pure in questo medesimo <lb></lb>tempo, ed è quella del traforare in vario tempo, pallottole di varia <lb></lb>materia e di ugual grossezza, posate sopra una larga lastra di <lb></lb>ghiaccio. (Targioni, Aggrandim. </s>

<s>T. II. P. II. pag. </s>

<s>164). </s></p><pb xlink:href="020/01/205.jpg" pagenum="186"></pb><p type="main">

<s>Oltre a queste, si fecero pure altre esperienze, che non si sa­<lb></lb>rebbero potute praticare fra le chiuse pareti di una stanza, nè <lb></lb>eseguire da un osservatore solo. </s>

<s>Ed ecco di qui l&#039;occasione e il <lb></lb>bisogno d&#039;organar la sua vita in varie membra, e pigliar la Medicea <lb></lb>sperimentale istituzione più conveniente ordine di Accademia. </s>

<s>Queste <lb></lb>esperienze furon quelle che si fecero, tra il 1656 e 57, intorno alle <lb></lb>velocità del suono e della luce, e nelle quali, ad aiutare il Viviani, <lb></lb>venivan chiamati il Borelli e il Rinaldini. </s>

<s>Dall&#039;altra parte, il bisogno <lb></lb>di avere, a sperimentar simili effetti naturali, strumenti e spazii che <lb></lb>non erano nè potevano essere di proprietà e di diritto di uomini <lb></lb>privati, fece sentir vivo il bisogno che la scienza aveva della pro­<lb></lb>tezione dei principi, e ai principi stessi fece pregustar la gloria di <lb></lb>partecipare ai meriti scientifici dei privati. </s>

<s>D&#039;ond&#039;è che i consessi <lb></lb>scientifici, nel palazzo granducale dei Medici, passarono a pigliar <lb></lb>ordinamento e instituto più proprio di Accademia, in un-terzo pe­<lb></lb>riodo, che si distinse dagli altri col titolo di <emph type="italics"></emph>Cimento.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>I principi Medicei, dai quali invocava la scienza i validi aiuti, <lb></lb>erano il granduca Ferdinando II e Leopoldo fratello di lui. </s>

<s>Che <lb></lb>fosse Ferdinando inclinato a favorire gli studi sperimentali, lo pro­<lb></lb>verebbe, senz&#039;altro, l&#039;essersi egli ingerito nell&#039;invenzione di quegli <lb></lb>strumenti, che certamente è dovuta al Torricelli. </s>

<s>Ma pur di qui <lb></lb>s&#039;argomenta che predominasse in lui all&#039;ingegno la curiosità e <lb></lb>l&#039;ambizione. </s>

<s>Dall&#039;altra parte chi aveva largamente speso per far <lb></lb>quelle esperienze, e per eseguire quegli strumenti, pareva in certo <lb></lb>modo che avesse il diritto di usarli per se, di dirli o di farli dir <lb></lb>suoi. </s>

<s>In seguito, se cedè alquanto nell&#039;animo suo l&#039;ambizione, non <lb></lb>cessò per questo la curiosità, o una certa sua particolar prurigine <lb></lb>di sapere. </s>

<s>Noi, non potremmo in altro miglior modo rappresentare <lb></lb>ai lettori o qualificare quella curiosità granducale, che per la se­<lb></lb>guente scenetta, colorita da noi su una nota, che si legge a carte 120 <lb></lb>del X Tomo dei Manoscritti del Cimento. </s></p><p type="main">

<s>La sera del di 5 Dicembre 1665, a qualche ora di notte, una <lb></lb>carrozza di corte si ferma dinanzi alla porta di casa del Viviani. </s>

<s><lb></lb>Scende uno staffiere, entra: — Sor Vincenzio, il Padron Serenissimo <lb></lb>l&#039;attende a palazzo — E il signor Vincenzio vestirsi, entrare in car­<lb></lb>rozza, scendere nel cortile, e su per lo scalone dei Pitti. </s>

<s>Francesco <lb></lb>Redi l&#039;introduce in camera: il Granduca era a letto. </s>

<s>— V&#039;ho man­<lb></lb>dato a chiamare, dice il Serenissimo, sollevandosi sulle coltri e <lb></lb>accennando alla fiamma del camminetto, per saper da voi in che <lb></lb>maniera, dagli spiragli della porta di camera e della finestra, benchè <pb xlink:href="020/01/206.jpg" pagenum="187"></pb>il tutto serrato, entri in camera vento, come si manifesta dal veder <lb></lb>muoversi indentro la fiammella di una candela: e perchè sia la <lb></lb>stessa fiammella con gran velocità rapita, accostatala agli spiragli <lb></lb>dell&#039;asse del cammino. </s>

<s>— </s></p><p type="main">

<s>Il principe Leopoldo aveva della scienza più nobili e dignitosi <lb></lb>sentimenti, e se la sua condizione non rendesse difficile il farne la <lb></lb>giusta stima, diremmo che aveva altra cultura scientifica e altra <lb></lb>forza d&#039;ingegno. </s>

<s>Difficile è il farne la giusta stima, perchè alcune <lb></lb>speculazioni e scoperte si dubita che sieno attribuite a lui dall&#039;os­<lb></lb>sequio e dalla adulazione. </s>

<s>Così, per citare un esempio, la causa del <lb></lb>così detto <emph type="italics"></emph>salto dell&#039;immersione<emph.end type="italics"></emph.end> osservato nelle caraffe a lungo collo <lb></lb>ripiene d&#039;acqua e sommerse nella neve, il Borelli, con tutti gli altri, <lb></lb>dice essere stata investigata e scoperta dal Principe, quando però <lb></lb>discorre con lui e gli scrive in lettere familiari. </s>

<s>Ma liberato poi da <lb></lb>ogni servitù cortigianesca, dice francamente, nel libro <emph type="italics"></emph>De motioni­<lb></lb>bus natural.<emph.end type="italics"></emph.end> del salto dell&#039;immersione: “ Ego animadverti et docui <lb></lb>hoc contingere a restrictione eiusdem vasis ” (Regio Julio 1670, <lb></lb>pag. </s>

<s>547). </s></p><p type="main">

<s>Ma pure, la giudiziosa critica fatta dal Principe ad alcune spe­<lb></lb>culazioni, come sarebbe giusto quella dello stesso Borelli concer­<lb></lb>nente le cause del variar la pressione ammosferica, quando il tempo <lb></lb>si dispone o si scioglie in pioggia, e come sarebbe l&#039;altra con la <lb></lb>quale il Renieri, per similitudine della varia disposizione delle lenti <lb></lb>nel canocchiale, spiegava il ricrescer l&#039;apparente figura degli astri, <lb></lb>giunti vicino a toccar l&#039;orizzonte; mentre rivelano una non ordi­<lb></lb>naria acutezza d&#039;ingegno, rendon nel medesimo tempo bella testi­<lb></lb>monianza di quel modesto riserbo, con cui il Principe stesso entrava <lb></lb>nel pericolo di quelle scientifiche discussioni. </s></p><p type="main">

<s>Quel che però abbiam per certissimo, è che in mezzo ai pia­<lb></lb>ceri e agli svaghi di una splendida corte, attese con grande amore <lb></lb>agli studii matematici, infino da giovanetto. </s>

<s>Di ventun&#039;anno faceva <lb></lb>richiedere a Galileo la dimostrazione allora allora trovata dal famoso <lb></lb>supposto meccanico, per mezzo del suo precettore don Famiano Mi­<lb></lb>chelini, il quale così scriveva al medesimo Galileo: “ Il Serenissimo <lb></lb>ha di già visti i sei libri di Euclide e di presente vede l&#039;undecimo, <lb></lb>e il detto libro del Moto (i Dial. </s>

<s>delle Due N. S.) con pensiero di <lb></lb>veder prima le Opere di V. S. </s>

<s>Molto Illustre ed Eccellentissima e <lb></lb>poi il resto dei matematici ” (MSS. Gal. </s>

<s>Div. </s>

<s>II. P. VI. T. XIII. c. </s>

<s>112). </s></p><p type="main">

<s>L&#039;anno dopo, avendo Fortunio Liceti già pubblicato il suo libro <lb></lb><emph type="italics"></emph>De Lapide bononiensi,<emph.end type="italics"></emph.end> nel capitolo L, del quale, contro le dottrine <pb xlink:href="020/01/207.jpg" pagenum="188"></pb>di Galileo, attribuiva il color cinereo della Luna a un fenomeno di <lb></lb>fosforescenza, il principe Leopoldo, nel dar relazione del nuovo libro <lb></lb>peripatetico, sollecita Galileo stesso a difender le sue dottrine, ciò <lb></lb>che egli poi fece in quella Lettera sul Candore lunare, che è una <lb></lb>delle più belle scritture astronomiche del nostro Autore. </s>

<s>Di questa <lb></lb>lettera, scrivendo il giovane principe Leopoldo da Siena, il dì 14 <lb></lb>maggio 1640, diceva a Galileo: “ Io, tra le altre cose che in essa <lb></lb>sono, ho ammirato quella di dimostrare, benchè tanto lontani dalla <lb></lb>Luna, che il lume in essa riflesso dalla Terra sia maggiore del <lb></lb>nostro lume crepuscolino, e in conseguenza di quello che la me­<lb></lb>desima Luna sopra di noi riflette. </s>

<s>E perchè io non posso godere e <lb></lb>cavar quel frutto che desidererei dalla conversazione sua, cerco di <lb></lb>trattenermi e di ammaestrarmi in qualche parte, nel leggere le sue <lb></lb>Opere. </s>

<s>E però, avendo finito di scorrere l&#039;undecimo e duodecimo <lb></lb>di Euclide, sto vedendo adesso il suo Libretto delle Galleggianti, <lb></lb>parto non meno degli altri degno del suo intelletto, soggiungendole <lb></lb>che farò ancora un poco di sessione con Mons. </s>

<s>Arcivescovo Picco­<lb></lb>lomini, tanto affezionato a V.S. e alle cose sue, dove si leggerà la <lb></lb>scrittura sopra il lume secondario della Luna. </s>

<s>Spero io d&#039;esser poi <lb></lb>da lei in questa state dove discorrerò seco di alcune cose, che mi <lb></lb>sono sovvenute in diverse materie, non lo potendo tanto bene fare <lb></lb>con la penna, quanto con la voce ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLVIII. <lb></lb>c. </s>

<s>37). E venuta l&#039;estate non mancò il giovane Principe di scender <lb></lb>dalle splendide sale dei Pitti, per salir su al tugurio di Arcetri, a <lb></lb>trattenervisi col venerando vecchio che l&#039;abitava in scientifici col­<lb></lb>loqui. </s>

<s>Frutto di quei colloqui fu la chiamata del Torricelli a Firenze, <lb></lb>da cui ebbe principio, come si vide, la sperimentale Accademia <lb></lb>Medicea, e d&#039;onde s&#039;avviarono a istituirsi quegli altri celebri con­<lb></lb>sessi accademici detti del Cimento, ai quali convien che si rivolga <lb></lb>il nostro Discorso. </s></p><p type="main">

<s><emph type="center"></emph>VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Incominciarono quei consessi nel mese di Giugno del 1657, e <lb></lb>i primi e principali collaboratori all&#039;esperienze naturali che vi si <lb></lb>fecero, furon quei tre, che vedemmo esercitarsi in Firenze e in <lb></lb>Pisa intorno al misurare la velocità della luce e del suono. </s>

<s>Pare <lb></lb>che, anche in questo nuovo ordinamento, il Viviani serbi una certa <pb xlink:href="020/01/208.jpg" pagenum="189"></pb>preminenza, che giustamente gli è attribuita, sì per essere stato col­<lb></lb>lega e successore al Torricelli in quell&#039;ufficio, e sì per lo zelo, per la <lb></lb>dottrina, e per l&#039;operosità con cui, da parecchi anni, l&#039;aveva esercitato. </s></p><p type="main">

<s>Gian Alfonso Borelli, chiamato di Messina a professare le Ma­<lb></lb>tematiche nello studio pisano, aveva fin d&#039;allora dato saggio del­<lb></lb>l&#039;acume e della novità delle sue speculazioni, non che di un&#039;arte <lb></lb>squisitissima di sottoporle al cimento. </s>

<s>Tutti gli studii sperimentali <lb></lb>di lui, anche in apparenza più disparati, convenivano in un unica <lb></lb>intenzione, che era quella di applicar la Meccanica e la Fisica al <lb></lb>moto degli animali. </s>

<s>Si preparava perciò il nostro Autore a scrivere <lb></lb>il celeberrimo Trattato con due libri, uno di Meccanica, intitolato <lb></lb><emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> pubblicato nel 1667, e l&#039;altro col titolo <emph type="italics"></emph>De mo­<lb></lb>tionibus naturalibus,<emph.end type="italics"></emph.end> pubblicato nel 1670, quasi lemmi premessi <lb></lb>alla grande Opera <emph type="italics"></emph>De motu animalium.<emph.end type="italics"></emph.end> Alle osservazioni naturali, <lb></lb>che bisognavano a condurla, attendeva già da lungo tempo, e il dì <lb></lb>16 Marzo 1663 pregava per mezzo del Michelini, che il principe <lb></lb>Leopoldo si compiacesse di farlo venire a Livorno, per <emph type="italics"></emph>far espe­<lb></lb>rienze sui pesci vivi, per capire perfettamente come si muovono e <lb></lb>nuotano i pesci<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVII. c. </s>

<s>188). Sotto il di 6 d&#039;Aprile <lb></lb>1665, scriveva direttamente al Principe che era entrato a specular <lb></lb>la natura e la proprietà della percossa, intorno alla quale il gran <lb></lb>Galileo nulla aveva lasciato in iscritto (ivi, T. XVIII. c. </s>

<s>152), prepa­<lb></lb>randosi così a distendere il primo libro da premettersi al Trattato <lb></lb>dei Moti animali. </s>

<s>Quattro anni dopo, nel Luglio, scriveva allo stesso, <lb></lb>rendendogli conto così de&#039;suoi studi: “ Ho già all&#039;ordine questo <lb></lb>secondo Tomo pur preparatorio della materia principale. </s>

<s>Tratto in <lb></lb>questo dei moti naturali dipendenti dalla gravità ” (ivi, T. XIX, <lb></lb>c. </s>

<s>263) e verso la metà d&#039;Aprile del 71: “ Spero poi questa state <lb></lb>perfezionare il terzo libro della immensa forza de&#039;muscoli con le <lb></lb>sue cause meccaniche dimostrate, cosa affatto nuova. </s>

<s>Appresso rac­<lb></lb>corrò in un altro libro tutto il resto di questa ammirabile Filosofia ” <lb></lb>(ivi, T. XX, c. </s>

<s>49). E infatti, mantenuto il proposito, torna a scri­<lb></lb>vere sotto il dì 22 Luglio “ porrò mano subito allo stampa del mio <lb></lb>libro della forza dei muscoli, il quale è ridotto quasi a perfezione ” <lb></lb>(ivi, c. </s>

<s>65). Le pubbliche e private sventure però non permisero al <lb></lb>Borelli di mandare ad effetto così questo proposito, com&#039;avea man­<lb></lb>dato quello, e la prima parte della grande Opera, dove si tratta <lb></lb>della forza immensa dei muscoli, fu pubblicata postuma in Roma <lb></lb>nel 1680: l&#039;altra parte, dove si tratta il resto di quella ammirabile <lb></lb>Filosofia, vide ivi pure la luce nell&#039;anno dopo. </s></p><pb xlink:href="020/01/209.jpg" pagenum="190"></pb><p type="main">

<s>Dicemmo che, a specular questa Filosofia, la quale fu poi ve­<lb></lb>ramente riconosciuta da tutti per ammirabile e nuova, concorrevano <lb></lb>nell&#039;intenzion dell&#039;Autore gli studi più varii della sua vita. </s>

<s>E in­<lb></lb>fatti, quando, venutagli occasione d&#039;appuntare in Giove uno squi­<lb></lb>sitissimo canocchial del Campani, si trovò senza volere implicato <lb></lb>negli studii astronomici, frutto de&#039;quali fu l&#039;Opera insigne <emph type="italics"></emph>Theo­<lb></lb>ricae Mediceorum,<emph.end type="italics"></emph.end> così nel pubblicare il libro scriveva il Borelli <lb></lb>al Lettore: “ Erit igitur huiusmodi opusculum non interruptio mei <lb></lb>prioris instituti, sed veluti parenthesis quaedam meorum studiorum, <lb></lb>nam denuo ad intermissum opus De motu anim. </s>

<s>redii ” (Floren­<lb></lb>tiae, 1665, pag. </s>

<s>VII). Figuriamoci quel che dee essere il periodo, se <lb></lb>la Teorica de&#039;pianeti medicei, che è il preludio alla nuova Astrono­<lb></lb>mia neutoniana, non è che una parentesi! Parentesi, nella quale, <lb></lb>come inciso, concludesi la teoria planetaria delle comete. </s>

<s>La for­<lb></lb>tezza di S. </s>

<s>Miniato al Monte era la specula, dove il Borelli faceva <lb></lb>le sue osservazioni, e dov&#039;egli aveva erette quelle macchine, a di­<lb></lb>mostrare il viaggio parabolico descritto da que&#039;corpi celesti creduti <lb></lb>vagabondi per lo spazio e senza leggi. </s>

<s>Gli strumenti, che adorna­<lb></lb>vano le stanze di S. </s>

<s>Miniato sopra Firenze, primo osservatorio astro­<lb></lb>nomico d&#039;Italia, eran lavorati con semplicità, ed eran pure tanto <lb></lb>precisi. </s>

<s>“ Ho fatto, con grandissimo frutto, scriveva al principe Leo­<lb></lb>poldo, fabbricare un istrumento da servir di sestante, il cui semi­<lb></lb>diametro sarà 5 braccia. </s>

<s>È composto di semplici regoli, facilissimo <lb></lb>a fabbricarsi ed adoperarsi, col quale spero di fare osservazioni così <lb></lb>squisite, come coloro che spendono centinaia di scudi in simiglianti <lb></lb>strumenti ” (ivi, T. XVIII. c. </s>

<s>154). </s></p><p type="main">

<s>Gli strumenti e l&#039;esperienze del Torricelli, nel primo periodo <lb></lb>dell&#039;Accademia Medicea, vedemmo essere un frutto allegato nel fiore <lb></lb>delle opere di Galileo: anco l&#039;esperienze intorno alle quali, nel se­<lb></lb>condo periodo, si travagliò il Viviani, per decidere se la luce si <lb></lb>muove in tempo, non avevano altra intenzione, che di mandare ad <lb></lb>effetto un pensiero proposto nel I Dialogo delle Due Nuove Scienze. </s>

<s><lb></lb>Nè il Borelli, a ricercar le tradizioni della scienza galileiana, fu <lb></lb>punto inferiore agli stessi suoi colleghi. </s>

<s>Molte delle Scritture del <lb></lb>gran Maestro, come sarebbero le Tavole de&#039;moti medii dei satelliti <lb></lb>di Giove, l&#039;Istruzione intorno al modo d&#039;usar lo strumento nelle <lb></lb>osservazioni gioviali, il Discorso dell&#039;ufficio meccanico del timone <lb></lb>nel diriger le navi, e altre scritture galileiane, delle quali s&#039;è perduta <lb></lb>la copia e l&#039;originale, rivivono nelle opere o manoscritte o stam­<lb></lb>pate dello stesso Borelli. </s></p><pb xlink:href="020/01/210.jpg" pagenum="191"></pb><p type="main">

<s>Quel che egli poi, per far progredire le dottrine sperimentali, <lb></lb>conforme ai metodi di Galileo, operasse in questo terzo periodo <lb></lb>dell&#039;Accademia Medicea, o del Cimento, l&#039;abbiamo diligentemente <lb></lb>annoverato da lui medesimo, nel libro <emph type="italics"></emph>De motionibus naturalibus,<emph.end type="italics"></emph.end><lb></lb>nello scrivere il quale, anzi, secondo che egli stesso dichiara, ebbe <lb></lb>questa particolare intenzione. </s>

<s>Accennando ivi al fatto della bilancia <lb></lb>equilibrata, che riscaldando l&#039;aria ambiente a un de&#039;piattelli tra­<lb></lb>bocca dall&#039;altra parte, soggiunge: “ Rationem huius admirabilis <lb></lb>effectus excogitavi et amico petenti reddidi, eamque communicavi <lb></lb>Societati doctissimorum virorum a Sereniss. </s>

<s>et Eminentiss. </s>

<s>Cardi­<lb></lb>nali Leopoldo Mediceo erectam, quam deinceps more italico Aca­<lb></lb>demiam experimentalem mediceam vocabo ” (Regio Julio 1670, <lb></lb>pag. </s>

<s>126). Di quel gentile esperimento del fumo, che discende nel <lb></lb>vuoto torricelliano, dice “ quod Florentiae Serenissimo Leopoldo <lb></lb>cardinali mediceo communicavi ” (ivi, pag. </s>

<s>128) e il medesimo dice <lb></lb>pure di quel barometro a sifone, di cui “ ichon habetur fig. </s>

<s>34 libri <lb></lb>Experimentorum eiusdem Academiae ” (ivi, pag. </s>

<s>209). </s></p><p type="main">

<s>De&#039;varii modi per trovare il peso specifico dell&#039;aria proposti <lb></lb>nell&#039;Accademia, ne commemora “ aliquos ex multis a me ibidem <lb></lb>propositi ” (ivi, pag. </s>

<s>247) e son quegli ingegnosi strumenti chiamati <lb></lb>da lui <emph type="italics"></emph>Termostatici,<emph.end type="italics"></emph.end> all&#039;invenzion dei quali aveva pensato infino <lb></lb>dal 1656 (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVII. c. </s>

<s>1). “ Sed praecipuus ac pul­<lb></lb>cherrimus modus experiendi aeris gravitatem hic est, quem Aca­<lb></lb>demiae medicaee experimentali anno 1660 comunicavi una cum <lb></lb>eius demonstratione ” (De mot. </s>

<s>nat. </s>

<s>pag. </s>

<s>251). Nella stessa Acca­<lb></lb>demia dice pure d&#039;aver dimostrato con innumerevoli esperimenti <lb></lb>che il ghiaccio occupa maggiore spazio dell&#039;acqua liquida; “ experi­<lb></lb>menta quae omnia legi possunt in praedicto libro Experimentorum <lb></lb>a folio 127 usque ad fol. </s>

<s>165 ” (ivi, pag. </s>

<s>546). </s></p><p type="main">

<s>Anche il Viviani non si volle defraudare della sodisfazione di <lb></lb>dire quel che egli operò nell&#039;Accademia, e ciò fece palese, non al <lb></lb>pubblico, ma in una nota autografa, che si legge a c. </s>

<s>259 del Tomo X <lb></lb>dei MSS. del Cimento, e che poi il Nelli pubblicò nel suo Saggio <lb></lb>di Storia Letteraria (Lucca 1759, pag. </s>

<s>110, 11). “ Miei sono, lasciò <lb></lb>ivi iscritto il Viviani, I. </s>

<s>Li tre strumenti, per provar la pressione <lb></lb>dell&#039;aria e che mancando quella il mercurio e l&#039;acqua discendono <lb></lb>in qualunque cannello. </s>

<s>II. </s>

<s>Miei sono li cinque strumenti per pro­<lb></lb>vare la costituzione dell&#039;aria bassa ed alta. </s>

<s>III. </s>

<s>Mio lo strumento <lb></lb>cilindrico con la canna dentro, per esaminar la gravezza in specie <lb></lb>dei fluidi. </s>

<s>IV. </s>

<s>Mia la scatola per le rifrazioni de&#039;fluidi. </s>

<s>V. </s>

<s>Miei li <pb xlink:href="020/01/211.jpg" pagenum="192"></pb>due strumenti per conoscere la gravità in specie dei fluidi e dei <lb></lb>metalli. </s>

<s>VI. </s>

<s>Mie l&#039;osservazioni circa l&#039;ondata de&#039;fluidi nei sifoni. </s>

<s><lb></lb>VII. </s>

<s>Mia l&#039;osservazione de&#039;balzi delle galleggianti. </s>

<s>VIII. </s>

<s>Mio il con­<lb></lb>cetto dell&#039;equabilità de&#039;suoni e dei loro usi. </s>

<s>IX. </s>

<s>Mio il nuovo modo <lb></lb>di misurar le distanze senza la vampa. </s>

<s>X. </s>

<s>Mie l&#039;osservazioni in­<lb></lb>torno l&#039;ambra. </s>

<s>XI. </s>

<s>Miei li due strumenti per conoscer se l&#039;alzar <lb></lb>dell&#039;acqua nei cannellini proceda dalla pressione dell&#039;aria ambiente <lb></lb>con succhiar collo schizzatoio. </s>

<s>XII. </s>

<s>Mie l&#039;esperienze due proposte <lb></lb>per invalidar la detta pressione attorno li cannellini. </s>

<s>XIII. </s>

<s>Miei li <lb></lb>due strumenti intorno la pressione dell&#039;acqua. </s>

<s>XIV. </s>

<s>Mia l&#039;osser­<lb></lb>vazione che tutti i legni vanno al fondo nell&#039;acqua (provar se nel­<lb></lb>l&#039;olio). XV. </s>

<s>Mio lo strumento per aver la lunghezza de&#039;pendoli di <lb></lb>desiderata durazione. </s>

<s>XVI. </s>

<s>Mio lo strumento a palla, per la gravità <lb></lb>in specie de&#039;fluidi col mettere i pesi dentro la palla. </s>

<s>” Quest&#039;ultimo <lb></lb>strumento, da cui si son trasformati gli Areometri moderni, come <lb></lb>quello pure annoverato qui in III luogo, sono illustrati con abbozzi <lb></lb>di figure, che suppliscono a una lunga e minuta descrizione, nel <lb></lb>seguente T. XI dei Manoscritti sopra citati a carte 101 e 105. </s></p><p type="main">

<s>Dopo essersi presa così la sua porzione ciascuno di que&#039;due <lb></lb>validi commensali, si vede bene che la tavola riman quasi sparec­<lb></lb>chiata, e che non resta, se non che poco o nulla a quegli altri, ivi <lb></lb>attorno seduti. </s>

<s>Fra questi occorre primo a riguardare Carlo Rinal­<lb></lb>dini, che, messogli innanzi, non saprebbe in coscienza a che stender <lb></lb>la mano per prenderlo e tenerlo per suo. </s>

<s>Vero è che egli afferma <lb></lb>l&#039;esperienza dell&#039;anello riscaldato, a verificar se i solidi si dilatano al <lb></lb>calore, essere stata proposta da sè nell&#039;Accademia (ivi, T. XXIV. c. </s>

<s>24) <lb></lb>ma tessendo e ritessendo le speculazioni del proprio cervello colla <lb></lb>pretensione di farle valere, eziandio contro la verità dei fatti, non <lb></lb>riuscì ad altro che a far perdere la pazienza al Borelli e al Viviani. </s></p><p type="main">

<s>Un&#039;altra volta s&#039;era messo in testa che il tuonar di un can­<lb></lb>none tanto può corresse veloce, quanto in maggior numero vi fos­<lb></lb>sero accesi dentro i granelli della polvere. </s>

<s>Il Borelli dimostrò di <lb></lb>fatto, alla presenza del Granduca sulla Piazza dei Pitti, che i tuoni <lb></lb>si propagavano colla stessa velocità da una piccola spingarda e da <lb></lb>un grosso cannone. </s>

<s>Il Rinaldini disse allora che ciò seguiva perchè <lb></lb>le bocche erano rivolte verso il Palazzo, e il Granduca subito mandò <lb></lb>due lacchè, che volgessero i pezzi da lato, e nonostante anco questa <lb></lb>volta i tuoni arrivarono alle solite distanze, in tempi misurati dalle <lb></lb>vibrazioni del pendolo sempre esattamente uguali. </s></p><p type="main">

<s>Il Magalotti che, colla sua solita vivacità, racconta in una sua <pb xlink:href="020/01/212.jpg" pagenum="193"></pb>Lettera questa storia, prosegue: “ Pure il Rinaldini, che è capo <lb></lb>sodo, ma sodo bene, volle che si rifacesse ieri sera con la culatta <lb></lb>volta al Palazzo e la bocca all&#039;insù, e senza alterazione nessuna <lb></lb>tutti i suoni arrivarono in tempi uguali. </s>

<s>Sicchè V. S. si puole im­<lb></lb>maginare che il poveraccio così cammina per Firenze che pare un <lb></lb>gatto bagnato dall&#039;acqua fredda ” (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXV, c. </s>

<s>181). <lb></lb>Capo sodo si mostrò pure, quando, a profondare il vasetto del mer­<lb></lb>curio sott&#039;acqua, disse d&#039;aver trovato che il mercurio stesso dentro <lb></lb>la canna non saliva più su che un braccio e un quarto; capo sodo, <lb></lb>quando nel livello dell&#039;argento vivo, a piè e in cima del campanile <lb></lb>di Pisa, non gli riuscì di trovarci differenza. (Ivi, T. VIII, c. </s>

<s>69). </s></p><p type="main">

<s>Benchè il Viviani scrivesse che l&#039;impressione delle Opere di <lb></lb>Galileo, fatta in Bologna, era stata promossa ed ultimata per mezzo <lb></lb>del Rinaldini (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLII, c. </s>

<s>3), sembra nonostante <lb></lb>che questi poco le avesse lette, o poco le ritenesse a memoria. </s>

<s>Co­<lb></lb>me prova di ciò si potrebbe citare il fatto, che, avendo il Rinaldini <lb></lb>stesso eseguita a Livorno l&#039;esperienza che nel medesimo tempo <lb></lb>giungono al piano dell&#039;orizzonte e la palla cadente dalla bocca del <lb></lb>cannone e quella spinta per forza di polvere; domanda poi al Vi­<lb></lb>viani dove Galileo tratti di questo (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXIV. c. </s>

<s>43), <lb></lb>quasi che il secondo Dialogo de&#039;due Massimi Sistemi non fosse <lb></lb>luogo abbastanza cospicuo. (Alb. </s>

<s>I, 172). Incerto in ogni cosa, per <lb></lb>la smania d&#039;andare in cerca, non di verità ma di novità, più che <lb></lb>galileiano, è aristotelico, e in ogni modo non ha saputo scoter dal <lb></lb>pallio filosofico la polvere appiccaticcia del Peripato. </s>

<s>A persuaderci <lb></lb>di ciò, basta leggere la Prefazione a quel ponderoso volume della <lb></lb><emph type="italics"></emph>Filosofia Razionale<emph.end type="italics"></emph.end> dove, dopo aver sottilmente discorso del me­<lb></lb>todo sperimentale, e aver confessato che delle cose trattate ivi pa­<lb></lb>recchie saranno quelle da lui attinte <emph type="italics"></emph>ex peripateticorum fonte,<emph.end type="italics"></emph.end> così <lb></lb>soggiunge: “ Dum interim intelligis aliquando me paululum ab <lb></lb>Aristotelico calle declinasse, et abiecta, quam superioribus annis <lb></lb>tuebar opinione, longe diversam suscepisse, non est cur de hoc tibi <lb></lb>admiratio incessat, neminem enim praeterit scite admodum ab an­<lb></lb>tiquis veritatem Saturni, hoc est temporis, filiam habitam fuisse ” <lb></lb>(Patavii 1681, pag. </s>

<s>XII). Che fosse veramente a principio addetto <lb></lb>alla setta peripatetica, e che poi l&#039;avesse talvolta abbandonata per <lb></lb>seguir piuttosto la retta ragione, lo dice da sè il Rinaldini, colle <lb></lb>seguenti parole, le quali però non corrispondono ai fatti della sua <lb></lb>vita scientifica: “ Quamvis a teneris annis salebrosam philosophandi <lb></lb>viam calcaverim, ac animum Peripateticae doctrinae studiis mirum <pb xlink:href="020/01/213.jpg" pagenum="194"></pb>in modum imbuerim, me tamen nunquam veritatis amor deseruit, <lb></lb>quin potius illo factus ardentior, me coegit omnem auctoritatem <lb></lb>negligere solidasque rationes inquirere ut iis denique suffultus quod <lb></lb>magis rationi consentaneum est amplecti possem ” (ibi, pag. </s>

<s>314). </s></p><p type="main">

<s>Fra gli altri chiamati a partecipare ai consessi sperimentali me­<lb></lb>dicei, s&#039;ha memoria dei tre fratelli Del Buono: Paolo che fece le <lb></lb>prime esperienze sulle soluzioni dell&#039;aria nell&#039;acqua, e Candido e <lb></lb>Anton Maria, i quali immaginarono e costruirono una macchina da <lb></lb>maneggiar facilmente i canocchiali, di lunga distanza focale; mac­<lb></lb>china che si distinse col nome proprio di <emph type="italics"></emph>Arcicanna.<emph.end type="italics"></emph.end> Carlo Roberto <lb></lb>Dati pure vi fu chiamato e ivi lesse un Discorso astronomico sul <lb></lb>sistema Saturnio in favor dell&#039;Huyghens. </s>

<s>Un&#039;altra strana e torbida <lb></lb>figura di uomo venuto di Reggio di Calabria, col nome di Antonio <lb></lb>Oliva, si vede pure trasparir di mezzo a questi gentiluomini eruditi <lb></lb>fiorentini. </s>

<s>Il Borelli, nel riferir di lui un&#039;esperienza fatta, per de­<lb></lb>terminare il peso specifico dell&#039;aria, lo chiama <emph type="italics"></emph>ingeniossimus,<emph.end type="italics"></emph.end> e al­<lb></lb>trove, uomo <emph type="italics"></emph>perspicacissimi et ignei ingenii<emph.end type="italics"></emph.end> (De mot. </s>

<s>nat. </s>

<s>pag. </s>

<s>470). <lb></lb>Se però si debba giudicare dai frutti, queste lodi e altre più ma­<lb></lb>gnifiche, con le quali si messe a esaltarlo il Redi, si riconoscono <lb></lb>per non meritate. </s></p><p type="main">

<s>A valer per tutti insieme i cinque sopra commemorati, il <lb></lb>principe Leopoldo aveva rivolte le sue mire anche su Gian Do­<lb></lb>menico Cassini, il quale intanto pensava ad alcune esperienze da <lb></lb>farsi nell&#039;Accademia sopra la calamita. (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXI, c. </s>

<s>64). <lb></lb>Ma poco dopo avvenne caso, che la Corte medicea dovesse adom­<lb></lb>brare di esso, e fu quando, trovandosi col Viviani a trattar del <lb></lb>negozio delle Chiane, faceva del sì no, di che il Viviani stesso dole­<lb></lb>vasi col principe Leopoldo, qualificando l&#039;ingegnere di Papa Ales­<lb></lb>sandro VII per uomo doppio. (Ivi, T. XVII, c. </s>

<s>236). Millantatore, a <lb></lb>proposito delle sue scoperte celesti, nelle quali troppo esagerata­<lb></lb>mente vantava l&#039;eccellenza dei canocchiali di Giuseppe Campani, <lb></lb>parve al Borelli (ivi, T. XVIII, c. </s>

<s>90), e una certa sua ruvidezza <lb></lb>nizzarda lo faceva accusar di malcreato alla cortigiana galanteria del <lb></lb>Magalotti. (Targioni, Aggrandim. </s>

<s>T. I. P. I. pag. </s>

<s>249). Per tutte queste <lb></lb>ragioni, il Principe dell&#039;Accademia fiorentina par che se lo tenesse <lb></lb>un po&#039;alla lontana, benchè dispensasse anco a lui favori, e si cu­<lb></lb>rasse di far verificare in Astronomia tutte le grandi scoperte, che <lb></lb>di Roma veniva annunziando e di Parigi. </s>

<s>Duole nulladimeno a pen­<lb></lb>sare che molte di quelle insigni scoperte cassiniane, come l&#039;ombre <lb></lb>dei satelliti proiettate sul disco di Giove, e le quattro nuove lune <pb xlink:href="020/01/214.jpg" pagenum="195"></pb>saturnie, fossero messe in dubbio dai Nostri, e con poca dignità di <lb></lb>conte e con minore acume di scienziato, lo deridesse il Magalotti <lb></lb>e gli negasse fede, perchè non gli pareva possibile che avesse ve­<lb></lb>duto lui tanti mondi lontani, che non valeva a leggere un carattere <lb></lb>chiaro e ben formato, senza gli occhiali. (Targioni, ivi, pag. </s>

<s>395). </s></p><p type="main">

<s>Il Borelli e il Viviani avevano nulladimeno supplito nell&#039;Acca­<lb></lb>demia alla mancanza del Cassini, ma le belle invenzioni e le belle <lb></lb>scoperte fatte da ingegni tanto eccellenti rimanevano tuttavia rin­<lb></lb>chiuse fra le dorate pareti del Palazzo Pitti. </s>

<s>Intanto, incominciava <lb></lb>a destarsi nell&#039;animo dei Nostri qualche sentimento di gelosia e di <lb></lb>rivalità coll&#039;Accademia sperimentale instituita in Francia, e ciò ri­<lb></lb>destò qualche proposito di far noto ai nuovi Filosofi parigini quel <lb></lb>che prima di loro era stato sperimentato già in Firenze. </s>

<s>Intorno a <lb></lb>che, da Pisa il di primo Dicembre 1658 scriveva così il Borelli al <lb></lb>principe Leopoldo: “ Il sig. </s>

<s>M. A. </s>

<s>Ricci mi replica questa settimana <lb></lb>e con molte ragioni vive ed efficaci procura mostrare quanto pre­<lb></lb>giudizio si faccia alla nostra Accademia ed all&#039;Italia tutta con il <lb></lb>nostro tacere, e non scrivere a quei signori di Francia. </s>

<s>Vorrebbe <lb></lb>egli insomma che si palesassero le conclusioni da noi ritrovate e <lb></lb>dimostrate, tacendo però ed occultando le ragioni e le dimostra­<lb></lb>zioni. </s>

<s>In questa maniera, dice egli, potremo esser sicuri che non <lb></lb>ci possa esser tolto il primo luogo dell&#039;invenzione preoccupata e <lb></lb>palesata da noi ” (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVI, c. </s>

<s>130). </s></p><p type="main">

<s>Nel di primo di Febbraio del 1663, Carlo Dati avvisa il Principe <lb></lb>dell&#039;Accademia che eran già pronte “ quattro casse di carta bonis­<lb></lb>sima per la stampa del Libro delle Esperienze ” (ivi, T. XVII, c. </s>

<s>184) <lb></lb>la quale stampa, qualunque ne fosse la ragione, non ebbe effetto <lb></lb>che nel 1666. Il titolo di <emph type="italics"></emph>Saggi di Naturali esperienze<emph.end type="italics"></emph.end> dato al libro, <lb></lb>corrisponde benissimo alla realtà dei fatti, non essendovisi dato, dei <lb></lb>varii ordini di esperienze naturali, che la descrizione di qualcune <lb></lb>fra le molte, come per saggio. </s>

<s>Solo è da notare che nulla vi fu <lb></lb>saggiato di cose astronomiche, e ce ne avevan pure i nostri Acca­<lb></lb>demici delle importanti. </s>

<s>L&#039;intenzione del Principe era veramente <lb></lb>di non lasciarle addietro, e il Magalotti aveva già, fra le descrizioni <lb></lb>degli altri strumenti, distesa anche quella dei canocchiali e delle <lb></lb>macchine da maneggiarli servite nelle ossvrvazioni di Saturno (ivi, <lb></lb>T. VII, c. </s>

<s>23) con manifesto proposito di dar, anche di queste os­<lb></lb>servazioni, un qualche saggio, fra gli altri del libro. </s>

<s>Ma la causa, <lb></lb>per cui un tal proposito del Principe e del Segretario non si man­<lb></lb>dasse ad effetto, si viene a conoscere da una Lettera del Borelli, <pb xlink:href="020/01/215.jpg" pagenum="196"></pb>in cui scriveva da Pisa il di 20 Aprile 1665, le parole seguenti: <lb></lb>“ È venuta la scrittura inviata dal sig. </s>

<s>Magalotti, nella quale veggo <lb></lb>registrato parte di quelle cose che io speculai e diedi in iscritto al­<lb></lb>l&#039;A. V. S. cinque anni sono intorno al sistema di Saturno del signor <lb></lb>Hugenio. </s>

<s>E benchè il pensiero del sig. </s>

<s>Magalotti sia di toglier <lb></lb>l&#039;occasione, con la stampa, che altri non si vada usurpando le cose <lb></lb>da noi ritrovate, tuttavia, avendoci io in questo negozio il maggior <lb></lb>interesse, perchè io proposi, predissi e dimostrai l&#039;effetto della <lb></lb>macchinetta, e poi recai molte scritture, in tutte le quali i signori <lb></lb>Accademici non ci ebbero altra parte che l&#039;onore che mi fecero <lb></lb>di vederle ed approvarle per lor gentilezza; mi par di trovarmi in <lb></lb>obbligo di supplicar umilmente V. A. che si compiaccia di darmi <lb></lb>tempo per far la scelta, ed impinguare e stabilir bene le cose per <lb></lb>esser di maggiore importanza lo stampare che scrivere una lettera <lb></lb>privata ” (ivi, T. XVIII, c. </s>

<s>164). Il Borelli però non prese mai il <lb></lb>tempo, e quelle astronomiche Scritture rimasero allora e rimangono <lb></lb>tuttavia in gran parte manoscritte. </s>

<s>Manoscritto pure, nonostante la <lb></lb>benemerita opera fattavi attorno dal Targioni, dal Gazzeri, e da <lb></lb>qualcun altro, rimase gran parte di quel ricco tesoro di esperienze, <lb></lb>da cui si tolsero i <emph type="italics"></emph>Saggi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Benchè poi s&#039;aggiunga al titolo di Naturali Esperienze, che <lb></lb>furon fatte <emph type="italics"></emph>nell&#039;Accademia del Cimento sotto là protezione del prin­<lb></lb>cipe Leopoldo di Toscana,<emph.end type="italics"></emph.end> nonostante vi si accolgono anche descri­<lb></lb>zioni di esperienze e di strumenti, che appartengono al primo e al <lb></lb>secondo periodo dell&#039;Accademia Medicea. </s>

<s>Così, l&#039;esperienza dell&#039;in­<lb></lb>compressibilità dell&#039;acqua dimostrata per mezzo della sfera ammac­<lb></lb>cata, il Borelli ci dice essere stata fatta <emph type="italics"></emph>in Aula Serenissimi M. D. He­<lb></lb>truriae. </s>

<s>Is iussit (ut mihi relatum fuit) cavam pilam argenteam <lb></lb>aqua repleri, ecc.<emph.end type="italics"></emph.end> (De moti. </s>

<s>natur. </s>

<s>ed. </s>

<s>cit. </s>

<s>pag. </s>

<s>333). Il Termo­<lb></lb>metro a liquido e l&#039;Igrometro a condensazione appartengono, come <lb></lb>si vide, al primo periodo, e al secondo appartengono l&#039;esperienze <lb></lb>per la misura della velocità della luce e dei suoni. </s></p><p type="main">

<s>Da ciò si conclude che il Libro, pubblicato nel 1666, contiene <lb></lb>i <emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> di tutta la sperimentale Accademia Medicea, che ebbe nel <lb></lb>Torricelli, infino dal 1642, i suoi primi principii. </s>

<s>Essendo così, può <lb></lb>a ragione vantar l&#039;Italia il primato nella Scienza sperimentale sopra <lb></lb>tutte le altre Nazioni, avendo ella già maturati da qualche tempo i <lb></lb>suoi frutti, quando gl&#039;ingegni del Pascal e del Roberval, dell&#039;Auzout, <lb></lb>del Pacquet, del Boyle e di simili altri celebri stranieri non erano <lb></lb>ancora appena aperti nel fiore. </s></p><pb xlink:href="020/01/216.jpg" pagenum="197"></pb><p type="main">

<s>Il disteso di quel Libro, che è pure il più insigne monumento <lb></lb>che sia stato eretto alla Scienza sperimentale italiana, fu fatto da <lb></lb>Lorenzo Magalotti succeduto ad Alessandro Segni nell&#039;ufficio di Se­<lb></lb>gretario dell&#039;Accademia. </s>

<s>I meriti del Magalotti, come scienziato, non <lb></lb>sono per verità di gran rilievo. </s>

<s>Più inclinato forse allo speculare che <lb></lb>allo sperimentare, non sappiam di lui se non ch&#039;ei lesse, ne&#039;con­<lb></lb>sessi accademici, un Discorso, in cui si proponeva di rassomigliar <lb></lb>l&#039;anello di Saturno agli aloni e alle corone. </s>

<s>Come letterato però <lb></lb>è tenuto in pregio da tutti, e s&#039;ammira l&#039;eleganza, la proprietà <lb></lb>del dire, e l&#039;efficace evidenza delle sue descrizioni. </s></p><p type="main">

<s>I distesi del Magalotti, via via che erano all&#039;ordine per la stampa, <lb></lb>si mandavano a rivedere al Borelli, che vi faceva sopra assai av­<lb></lb>vertimenti, di molti de&#039;quali si tenne conto; al Viviani, più arren­<lb></lb>devole in lasciar andar le cose a modo altrui, al Rinaldini, che, <lb></lb>seguitando a fare il capo sodo, aggiungeva a i cimenti dei fatti <lb></lb>naturali, il cimento della pazienza del Principe e del Segretario. </s>

<s><lb></lb>Poi si mandava tutto a Roma, e si sottostava, come a tribunale <lb></lb>inappellabile, a ciò che ne decidesse il giudizio di M. A. Ricci, <lb></lb>eletto, infin da principio, da Leopoldo dei Medici a consultore della <lb></lb>sua sperimentale Accademia. </s></p><p type="main">

<s>Il Ricci era geometra di gran valore e uomo di gran senno e <lb></lb>prudenza. </s>

<s>A lui il Torricelli indirizzava quelle lettere, che valgono <lb></lb>per un intiero Trattato, in cui si descrive la celebre esperienza <lb></lb>dell&#039;argento vivo, e si risponde alle difficoltà promosse contro alla <lb></lb>natura del vacuo, e agli effetti della pressione ammosferica. </s>

<s>A ri­<lb></lb>chiesta di lui chiamato <emph type="italics"></emph>ingeniosissimus iuvenis,<emph.end type="italics"></emph.end> il Torricelli stesso <lb></lb>risolse il problema della Clessidra, o del vaso che versa uguali quan­<lb></lb>tità d&#039;acqua in tempi uguali, dimostrando che la forma propria di <lb></lb>un tal vaso, è il conoide generato dalla rotazione di una semipa­<lb></lb>rabola biquadratica; problema che il Mariotte, il Grandi e lo stesso <lb></lb>Viviani credettero che l&#039;Autor del Trattato <emph type="italics"></emph>De motu aquarum<emph.end type="italics"></emph.end> si <lb></lb>contentasse di proporlo agl&#039;Idrometri, ma che poi l&#039;avesse, per la <lb></lb>difficoltà, lasciato irresoluto. </s></p><p type="main">

<s><emph type="center"></emph>IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La pubblicazione del Libro dei Saggi di Naturali Esperienze, <lb></lb>parve quasi un raccoglier le vele, e un ridursi in porto a riposo, <lb></lb>dopo una lunga navigazione. </s>

<s>Eppure il viaggio dura ancora e non <pb xlink:href="020/01/217.jpg" pagenum="198"></pb>breve, benchè avesse cambiato abito il piloto, fossero ai primi sot­<lb></lb>tentrati altri nuovi e men validi remigatori, a nuova foggia si fosse <lb></lb>ricomposta la nave, e si dirigesse ad altro segno di stella. </s></p><p type="main">

<s>Il di 4 di Aprile 1667 il Borelli scriveva da Pisa una lettera <lb></lb>al principe Leopoldo, in cui gli diceva che andava <emph type="italics"></emph>disponendo le <lb></lb>cose per la partenza che non potrà esser prima di mezzo maggio,<emph.end type="italics"></emph.end><lb></lb>e intanto gli offeriva in dono e gli lasciava come ricordo di un <lb></lb>amico, che si allontana dall&#039;amico, le <emph type="italics"></emph>macchine astronomiche<emph.end type="italics"></emph.end> da sè <lb></lb>erette e costruite nella specula di S. Miniato. (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XIX, <lb></lb>c. </s>

<s>180). Il Borelli abbandonava così l&#039;ospitale Toscana per tornar­<lb></lb>sene ìn Sicilia. </s>

<s>Il dì 10 Febbraio 1668 Leopoldo de&#039;Medici, nella <lb></lb>persona del quale s&#039;era già al civile sopraggiunto il principato eccle­<lb></lb>siastico, annunziava con accorata mestizia all&#039;Huyghens che s&#039;erano <lb></lb>partiti dal suo servizio tre dei migliori soggetti, che fossero nel­<lb></lb>l&#039;Accademia (Targioni, Aggrandim. </s>

<s>T. I, pag. </s>

<s>462) ed eran questi, <lb></lb>oltre al Borelli, il Rinaldini, e l&#039;Oliva. </s>

<s>Tutto in sollecitudine per­<lb></lb>chè, da così fatta dispersione, non ne dovesse alla sua prediletta <lb></lb>Accademia conseguitare la morte, si rallegrava il Principe e Car­<lb></lb>dinale col Magalotti, per avere intanto, a sostituire a uno dei tre <lb></lb>mancati, chiamato Niccolò Stenone, danese di patria, ma divenuto <lb></lb>italiano per elezione. </s>

<s>Il Magalotti rispondeva così alla lieta novella: <lb></lb>“ Veramente nella dispersione presente della nostra Accademia, per <lb></lb>la partenza del Borelli, dell&#039;Oliva e del Rinaldini, non poteva a mio <lb></lb>credere, succedere cosa più desiderabile, e se gli altri due luoghi si <lb></lb>riempissero a questa proporzione, mi parrebbe che avessimo qual­<lb></lb>che motivo da consolarci della perdita fatta, la quale tutta insieme <lb></lb>bisogna confessare che è considerabile, perchè solamente dando al <lb></lb>Rinaldini e all&#039;Oliva quel che và loro per giustizia di approvazione <lb></lb>e di stima, il Borelli era un uomo fastidioso, e presso che io non <lb></lb>dissi affatto intollerabile, ma in sostanza era un letterato da far ri­<lb></lb>splendere una corte, perchè aveva sodezza e giudizio. (Ivi, pag. </s>

<s>463). </s></p><p type="main">

<s>Un altro di que&#039;posti lasciato vuoto nell&#039;Accademia, fu sosti­<lb></lb>tuito e, forse meglio che dallo Stenone, da Francesco Redi, il quale, <lb></lb>sebben fosse nel periodo precedente fra gli Accademici come ini­<lb></lb>ziato, e avesse parte nelle esperienze sulla digestione degli animali, <lb></lb>su cui poi ritornò nella Lettera al Kircher (Opera, T. II. </s>

<s>Napoli 1731, <lb></lb>pag. </s>

<s>49, 50), si vede nonostante esercitare con larga autorità il suo <lb></lb>ministero in questo, che è il quarto periodo della sperimentale Ac­<lb></lb>cademia Medicea, e, che va a terminare colla morte del Cardinale <lb></lb>Leopoldo. </s></p><pb xlink:href="020/01/218.jpg" pagenum="199"></pb><p type="main">

<s>Il Viviani distratto, per le continue richieste del Principe e dei <lb></lb>privati, a sopraintendere ai tanti e spinosi negozii d&#039;ingegneria <lb></lb>idraulica, il Magalotti che aveva oramai preso diletto de&#039;lontani <lb></lb>viaggi, lasciavano a collaborar nell&#039;Accademia lo Stenone e il Redi, <lb></lb>i quali proseguendo l&#039;indirizzo dei loro studii, le fecero in parte <lb></lb>cangiare istituto, trapassando, dalle scienze fisiche, a coltivar con <lb></lb>più genio la Storia naturale. </s></p><p type="main">

<s>Lo Stenone fu anatomico espertissimo, e fece fare notabili pro­<lb></lb>gressi alla Miologia. </s>

<s>La Dissertazione <emph type="italics"></emph>De solido intra solidum na­<lb></lb>turaliter contento,<emph.end type="italics"></emph.end> nella stampa della quale tanta amorosa cura si <lb></lb>prese il Viviani, è forse dalla fama esaltata sopra i meriti proprii, <lb></lb>benchè non si possa negar che non sia un precorrere alla scienza <lb></lb>dei nostri giorni l&#039;insegnar, che ivi si fa dall&#039;Autore, a riconoscer <lb></lb>l&#039;età della formazione di uno strato terrestre, congetturandola dalla <lb></lb>natura delle sostanze fossili trascinate e deposte dalle acque. (Flo­<lb></lb>rentiae 1669, pag. </s>

<s>28). Nè si può passar senza lode d&#039;ingegno l&#039;at­<lb></lb>tribuir gli effetti del trasformarsi l&#039;arida in mare e il mare in arida, <lb></lb>al non coincidere il centro di gravità della terra col centro di figura. <lb></lb>(Ivi, pag. </s>

<s>172). Nel Tomo XXXII del Cimento son raccolti i mano­<lb></lb>scritti dello Stenone in folio, di carattere minutissimo, informi, di­<lb></lb>sordinati. </s>

<s>A ricercarvi, in tanta varietà, quel che è più confacente al <lb></lb>proposito nostro, nel breve esame che ne abbiam fatto, si nota par­<lb></lb>ticolarmente l&#039;anatomia dei muscoli locomotori dell&#039;occhio, e alcune <lb></lb>osservazioni intorno alla funzione fisiologica dell&#039;organo della vista. </s></p><p type="main">

<s>Il Redi era tutt&#039;altro ingegno, e se non sodo come quel dello <lb></lb>Stenone, più elegante e più vario. </s>

<s>Il Cardinale Leopoldo annunziava <lb></lb>con gran compiacenza al Borelli un nuovo libro scritto dallo stesso <lb></lb>Redi sopra gl&#039;insetti, e il Borelli rispondeva di Messina, nell&#039;Agosto <lb></lb>1668, che vedrà quel nuovo libro assai volentieri. (MSS. Gal. </s>

<s>Cim. </s>

<s><lb></lb>T. XIX, c. </s>

<s>202). Nè il Serenissimo Cardinale di tale annunzio si <lb></lb>compiaceva senza ragione, perchè sentiva l&#039;efficacia che avrebbero <lb></lb>avuto quelle pagine, in isgombrar largamente i sentieri ai progressi <lb></lb>della Zoologia, e anzi di tutta la Storia Naturale. </s>

<s>Il nuovo Autore <lb></lb>infatti dell&#039;Esperienze intorno alla generazione degl&#039;insetti, dimo­<lb></lb>strava con sensati argomenti, ciò che non era riuscito al grandissimo <lb></lb>Harvey, esser la generazione spontanea un gravissimo e dannosis­<lb></lb>simo errore, e che anco gli animali de&#039;più infimi ordini non hanno <lb></lb>origine dalla putredine, ma vi son deposti allo stato di uovo dalle <lb></lb>sollecite madri pregnanti. </s></p><p type="main">

<s>In un grave ostacolo però offese il libero piede del nostro Redi, <pb xlink:href="020/01/219.jpg" pagenum="200"></pb>e fu quando s&#039;incontrò a decider dell&#039;origine dei vermi, nella carne <lb></lb>de&#039;frutti maturi, e dentro alle galle cresciute sui rami o sulle foglie <lb></lb>di alcuni alberi. </s>

<s>Parve a lui non “ esser gran peccato in Filosofia <lb></lb>il credere che i vermi de&#039;frutti sieno generati da quella stessa <lb></lb>anima, e da quella stessa natural virtude, che fa nascere i frutti <lb></lb>stessi nelle piante ” (Opera, ivi. </s>

<s>T. I, pag. </s>

<s>103). Ma pure, benchè <lb></lb>così si andasse lusingando il celebre Autore, era quello di dar ani­<lb></lb>ma e senso alle piante, tal peccato in Filosofia, da viziare il merito <lb></lb>delle altre sue insigni scoperte. </s></p><p type="main">

<s>Due anni dopo, lo stesso Eminentissimo Principe dell&#039;Accade­<lb></lb>mia fiorentina, dava, pure a proposito del Redi, un&#039;altra nuova al <lb></lb>Borelli, ed era intorno all&#039;esperienze fatte sulle gocciole bataviche <lb></lb>o sopra quelle perline di vetro, a rompere le codette alle quali, si <lb></lb>sgretolano tutte riducendosi in polvere. </s>

<s>Il Borelli, rispondendo da <lb></lb>Francavilla, ricorda come quindici anni prima il Card. </s>

<s>Giovan Carlo <lb></lb>avea mandato al Granduca una cassettina di quelle stesse perle, <lb></lb>sugli effetti curiosi delle quali speculando allora, si compiace che <lb></lb>si fosse riscontrato nei pensieri medesimi del Redi. (Fabbroni, Let­<lb></lb>tere, T. I. pag. </s>

<s>139). </s></p><p type="main">

<s>Quel peccato filosofico, in che offese il Nostro, e di cui si par­<lb></lb>lava dianzi a proposito della generazione di alcuni insetti, fu emen­<lb></lb>dato da Marcello Malpighi, il quale dimostrò che anche i vermi <lb></lb>delle galle e dei frutti nascevano da un uovo deposto dalle madri. </s>

<s><lb></lb>Se gli onori si dispensassero sempre nel mondo a seconda dei me­<lb></lb>riti, il Malpighi non dovrebb&#039;esser, nei fasti della scienza, men <lb></lb>glorioso del celeberrimo Harvey. </s>

<s>Imperciocchè, se l&#039;Inglese restaurò <lb></lb>la Fisiologia animale con la scoperta della circolazione del sangue, <lb></lb>il nostro Bolognese, con la scoperta del circolo della linfa, restaurò <lb></lb>la Fisiologia vegetabile. </s>

<s>L&#039;anatomia microscopica degli organi e <lb></lb>della più intima testura delle parti componenti le varie membra <lb></lb>delle piante e degli animali, è dovuta principalmente a lui. </s>

<s>Nella <lb></lb>mente di lui balenò il primo vero intorno alla teoria chimica della <lb></lb>respirazione, e fu egli il primo a dar la dimostrazione oculare del <lb></lb>moto del sangue nel circolo universale dei vasi. </s></p><p type="main">

<s>Al nome del Malpighi, non può andar disgiunto quello di Lo­<lb></lb>renzo Bellini, con l&#039;altro di Carlo Fracassati, i quali ambedue, con­<lb></lb>corsero, ciascuno per la sua parte, a dar l&#039;anatomia e la fisiologia <lb></lb>dell&#039;organo del gusto. </s>

<s>Nessuno di questi tre insigni anatomici ap­<lb></lb>partenne, è vero, all&#039;Accademia Medicea; anzi il Malpighi, cosa <lb></lb>notabilissima in uomo di tanto merito, non solo fu tenuto lontano <pb xlink:href="020/01/220.jpg" pagenum="201"></pb>dal partecipar la sua scienza con Firenze, ma si direbbe che fu <lb></lb>tenuto lontano dall&#039;Italia, dalla quale, nò nella persona ma nelle <lb></lb>opere dell&#039;ingegno, par che esulasse in Inghilterra, dove, nella <lb></lb>R. </s>

<s>Società di Londra, le tante e mirabili scoperte di lui ebbero <lb></lb>liete accoglienze, e gli scritti, così vivente l&#039;Autore che postumi, vi <lb></lb>trovarono le sollecite e amorevoli cure della pubblica stampa. </s>

<s>Non <lb></lb>appartengono propriamente, ripigliando qui il costrutto interrotto, <lb></lb>i tre grandi anatomici all&#039;Accademia fiorentina, ma son tutt&#039;e tre <lb></lb>discepoli del Borelli, e incominciarono i loro esercizi anatomici col <lb></lb>collaborare alla grande Opera dei Moti animali, che il loro Maestro <lb></lb>preparava già in Pisa e in Livorno, dove a spese e sotto la prote­<lb></lb>zione dei principi Medicei si facevano le dissezioni. </s></p><p type="main">

<s>In ogni modo, quello stesso Borelli che, instituendo, in mezzo <lb></lb>alle scienze sperimentali, la nuova scuola iatromatematica, v&#039;aveva <lb></lb>allevati il Malpighi, il Bellini e il Fracassati, i quali applicavan sa­<lb></lb>pientemente le nuove scoperte d&#039;Anatomia e di Fisiologia all&#039;eser­<lb></lb>cizio dell&#039;arte medica; dalla lontana Sicilia tornava spesso col pen­<lb></lb>siero in Toscana. </s>

<s>E ciò seguì, con più vivo desiderio che mai, quando <lb></lb>il Cardinal Leopoldo gli annunziava di aver riscontrato nella sua <lb></lb>Accademia un&#039;esperienza bellissima venuta d&#039;Inghilterra. </s>

<s>“ Ralle­<lb></lb>gromi sommamente, così incominciava lo stesso Borelli una sua <lb></lb>lettera del 2 Luglio 1669, scritta da Messina, dell&#039;esperienza del <lb></lb>Boyle, che V. A. ha fatto confrontare la qual veramente è mirabile <lb></lb>e di gran conseguenza, ed ha risvegliato in me il desiderio di To­<lb></lb>scana ” (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XIX, c. </s>

<s>263). E sotto il dì 14 Agosto <lb></lb>tornava a scrivere così sul medesimo argomento: “ Avevo io letto <lb></lb>nella Gazzetta letteraria di Roma l&#039;esperienza del Boyle, e mi pa­<lb></lb>reva veramente mirabile e però desideravo sommamente di con­<lb></lb>frontarla, sicchè può giudicare quanta consolazione io abbia avuto <lb></lb>sentendo che l&#039;A. V. l&#039;abbi sperimentata nella sua eruditissima Ac­<lb></lb>cademia; e poi con tante belle circostanze di più di quelle che <lb></lb>aveva osservate il Boyle ” (ivi, c. </s>

<s>267). </s></p><p type="main">

<s>La Lettera missiva del Serenissimo Cardinale, in data del 25 <lb></lb>Luglio 1669, e alla quale si riferisce la sopra citata responsiva del <lb></lb>Borelli, diceva così a proposito dell&#039;esperienza del Boyle, riscon­<lb></lb>trata, variata e ampliata nell&#039;Accedemia del Cimento: “ In oltre le <lb></lb>diedi conto di un&#039;esperienza fatta in Inghilterra, e rifatta qui da <lb></lb>me, la qual è che, mettendosi un pezzetto di pesce o interiora di <lb></lb>quelle che son vicine a infradiciarsi, fanno lume da sè stesse, dato <lb></lb>il solito strumento del vacuo, e facendosi la consueta operazione <pb xlink:href="020/01/221.jpg" pagenum="202"></pb>di quello, che comunemente si dice il vacuo, il lume del pesce si <lb></lb>perde, e facendo appresso un piccolo foro per introdurvi l&#039;aria, <lb></lb>all&#039;ingresso di quella di nuovo ritorna a risplendere il pezzetto di <lb></lb>pesce. </s>

<s>Ed io ho già fatto l&#039;esperienza con un pezzetto di polpa e <lb></lb>grasso di pesce spada. </s>

<s>Mi venne poi in mente di fare l&#039;esperienza <lb></lb>stessa con le lucciole, le quali ancora nel vuoto persero il lume. <lb></lb></s>

<s>È ben vero che nell&#039;istante dell&#039;introduzione dell&#039;aria s&#039;illuminò <lb></lb>per brevissimo tempo tutto il vaso, ed io dubitando che questo <lb></lb>splendore potessi procedere che nel ricever le lucciole la consola­<lb></lb>zione del ritorno dell&#039;aria facessero moto, nel quale scoprissero la <lb></lb>parte lummosa, rifeci l&#039;esperienza, mettendo dentro nel vaso tutte <lb></lb>le lucciole morte, e nondimeno successe l&#039;istessa istantanea illu­<lb></lb>minazione del vaso, nell&#039;atto dell&#039;introdurvi l&#039;aria per il solito pic­<lb></lb>colo foro formato da uno spillo. </s>

<s>Or è da sapersi di più che, dopo <lb></lb>questa illuminazione, il lume che hanno le lucciole è rimasto, <lb></lb>(sempre che si è fatta l&#039;esperienza) meno vivace, ma con tale dif­<lb></lb>ferenza che non si è potuto mettere in dubbio che non sia così. </s>

<s><lb></lb>Questa è un&#039;esperienza facile e galante, ma tale che io credo che <lb></lb>meriti che vi si faccia riflessione ” (ivi, T. XXIII, c. </s>

<s>171, e Fabbroni, <lb></lb>Lett. </s>

<s>I, pag. </s>

<s>144). </s></p><p type="main">

<s>Nel principio di questa lettera, passata fra Leopoldo de&#039;Medici <lb></lb>e Gian Alfonso Borelli, s&#039;accennava altresi a un altro soggetto di <lb></lb>scienza alquanto diversa. </s>

<s>Il Cardinale scriveva di sentir <emph type="italics"></emph>desiderio <lb></lb>d&#039;aver qualche particolare informazione delli accidenti del fuoco <lb></lb>di Catania,<emph.end type="italics"></emph.end> e il Borelli rispondeva d&#039;aver già scritto prolissamente <lb></lb>intorno a quegli accidenti e d&#039;avervi di più accompagnata una <lb></lb>pianta e disegno grande della Montagna e città di Catania, disegno <lb></lb>e scrittura che andarono forse smarriti e a cui supplì l&#039;anno dopo <lb></lb>l&#039;Autore pubblicando l&#039;<emph type="italics"></emph>Historia et Meteorologia Incendii Actnaei.<emph.end type="italics"></emph.end><lb></lb>Nella Prefazione al libro si leggono le notabilissime parole seguenti: <lb></lb>“ At non potui petitionibus plurimorum insignium virorum non <lb></lb>obtemperare, et praecipue Serenissimi ac Reverendissimi Cardinalis <lb></lb>Medicei, qui, cum proximum Incendium Aetnae undique fama cir­<lb></lb>cumferret, primis suis humanissimis literis iussit ut scientiam Na­<lb></lb>turalem promovere pro viribus satagerem, edendo Historiam et <lb></lb>Meteorologiam huius conflagrationis, iuxta praescriptum Societatis <lb></lb>seu Academiae Experimentalis Medicaee, cuius inter socios me re­<lb></lb>censere olim dignatus fuerat. </s>

<s>” </s></p><p type="main">

<s>Di qui si raccoglie che il Borelli, benchè assente dalla Toscana, <lb></lb>seguitava ad appartenere e a collaborare ancora, sotto gli ordini <pb xlink:href="020/01/222.jpg" pagenum="203"></pb>del Principe, nell&#039;Accademia del Cimento. </s>

<s>Vi collaborava altresi, <lb></lb>quando riferiva allo stesso Principe le sue osservazioni ed esperienze <lb></lb>chimiche fatte nella grotta del lago di Agnano, qualificando l&#039;ani­<lb></lb>dride carbonica per un <emph type="italics"></emph>fluore simile in sembianza all&#039;aria ma assai <lb></lb>più denso.... che smorza i lumi e soffoca le persone<emph.end type="italics"></emph.end> (ivi, T. XIX, <lb></lb>c. </s>

<s>35); vi collaborava, quando, speculando sull&#039;origine delle reliquie <lb></lb>fossili trovate da&#039;suoi Colleghi Accademici in Toscana, e da sè stesso <lb></lb>in Sicilia, poneva, insieme con lo Stenone, i fondamenti scientifici <lb></lb>alla moderna Paleontologia. </s></p><p type="main">

<s>Anche il Viviani, tornando a quando a quando in Firenze con <lb></lb>gli stivaloni inzaccherati dal diguazzar lungo l&#039;argine e per i greti <lb></lb>de&#039;fiumi, o intorno alle gore de&#039;mulini, attendeva a collaborar <lb></lb>qualche poco nell&#039;Accademia. </s>

<s>Ne&#039;suoi Manoscritti si legge, fra le <lb></lb>altre, autografa questa nota: “ D&#039;ordine del Serenissimo Principe <lb></lb>Cardinale Leopoldo de&#039;Medici, nel giardino del Serenissimo Gran­<lb></lb>duca, la sera delli 17 Luglio 1674 in Firenze, con occhiale di braccia <lb></lb>tre e mezzo, con due lenti, l&#039;obiettiva cioè e l&#039;oculare, e con oriolo <lb></lb>col pendolo aggiustato a mezzogiorno, a ore otto e un quarto po­<lb></lb>meridiane, fu principiata da me l&#039;osservazione dell&#039;ecclisse lunare ” <lb></lb>(MSS. Gal. </s>

<s>Disc. </s>

<s>T. XXXIX, c. </s>

<s>46). </s></p><p type="main">

<s>In questo quarto periodo della Sperimentale Accademìa toscana, <lb></lb>non si vede più quella regolarità di sessioni, e quegli ordini, con <lb></lb>che si regolava nel periodo precedente, ma ciò, come si notava negli <lb></lb>esempii ora citati del Borelli, da null&#039;altro dipende che dall&#039;esser <lb></lb>la maggior parte dei collaboratori dispersi, per cui, invece di trattar <lb></lb>de&#039;soggetti sperimentali colla parola viva, al cospetto del Principe, <lb></lb>ne trattavano in iscritture, le quali avevano forma di Dissertazioni <lb></lb>o di lettere che via via s&#039;indirizzavano a Firenze. </s>

<s>Due de&#039;più in­<lb></lb>faticabili e valorosi, fra&#039;così fatti collaboratori, furono Geminiano <lb></lb>Montanari e Donato Rossetti, diversi d&#039;indole e d&#039;ingegno, e perciò <lb></lb>contenziosi. </s>

<s>Le controversie fra questi due, o incominciarono o in­<lb></lb>fierirono vie più, a proposito delle esperienze sui capillari, intorno <lb></lb>a che il Borelli ebbe a risentirsi e a muover lagnanza per lettera <lb></lb>al Cardinal Leopoldo, contro lo stesso Montanari, tacciandolo di <lb></lb>discepolo ingrato e accusandolo di plagio, perchè, mentre costui <lb></lb>dimorava in Firenze, e conversava coi fratelli Del Buono, infor­<lb></lb>mandolo di tuttociò che si faceva ne&#039;consessi dell&#039;Accademia spe­<lb></lb>rimentale, ebbe dagli stessi Del Buono la notizia dell&#039;attrarsi, per <lb></lb>effetto di capillarità, i galleggianti sull&#039;acqua, e poi divulgò la cosa <lb></lb>come per sua. </s>

<s>Di ciò il Borelli infuriava e rivendicava a sè la sco-<pb xlink:href="020/01/223.jpg" pagenum="204"></pb>perta chiamando in testimonio lo stesso Granduca, e altri signori <lb></lb>della sua corte, alla presenza de&#039;quali, infino dal 1655, aveva mo­<lb></lb>strata la curiosità di quella nuova esperienza. (MSS. Gal. </s>

<s>Cim. </s>

<s><lb></lb>T. XIX, c. </s>

<s>93). </s></p><p type="main">

<s>Comunque sia, il Montanari era ingegno più maturo e più as­<lb></lb>sennato del Rossetti, e a giudicar dall&#039;opere si direbbe che il primo <lb></lb>ritrae più al vivo quella profondità e quell&#039;ampiezza di studi spe­<lb></lb>rimentali, propria del Borelli, che egli, con lo stesso Rossetti, ebbe <lb></lb>a comune maestro. </s>

<s>Il micrometro e il canocchiale livellatore fanno <lb></lb>annoverare il Montanari fra gli inventori di strumenti più utili e <lb></lb>più necessarii ai progressi della scienza. </s>

<s>Le sue esperienze e i suoi <lb></lb>Discorsi intorno alle proprietà de&#039;liquidi, e i suoi esami sopra la <lb></lb>direzione, le sue speculazioni sopra le cause e gli effetti delle cor­<lb></lb>renti marine, lo sollevano al grado di primo e principale maestro <lb></lb>nella scienza del moto dell&#039;acque. </s></p><p type="main">

<s>Per ciò che direttamente riguarda l&#039;Accademia del Cimento <lb></lb>poi, riferisce al Principe e Cardinale l&#039;esperienza della trasfusione <lb></lb>del sangue, più particolarmente descritta in una Relazione, che <lb></lb>passò per le mani del Cassini, prima di arrivare a Firenze; discute <lb></lb>la controversia ch&#039;egli ha col Rossetti intorno alle dottrine di Ar­<lb></lb>chimede e di Galileo sui galleggianti, e intorno agli effetti mec­<lb></lb>canici della bilancia di braccia uguali; racconta la storia degli <lb></lb>effetti, e specula sulla natura delle folgori, dissipando vecchi pre­<lb></lb>giudizi e presentendo le teorie elettriche dei moderni; riferisce <lb></lb>osservazioni di ecclissi di sole e di luna, di apparizioni di comete <lb></lb>e di molti altri fenomeni celesti. </s></p><p type="main">

<s>Il Rossetti, dall&#039;altra parte, mandava all&#039;Accademia fiorentina <lb></lb>una scrittura contenente XIX osservazioni fatte sulla brinata in <lb></lb>Torino nel mese di Gennaio 1675 (ivi, T. XX, c. </s>

<s>192-95), dava parte <lb></lb>di un nuovo pesce apparito nei nostri mari (ivi, c. </s>

<s>230) e riferiva <lb></lb>altre simili curiosità scoperte in fatto di storia Naturale. </s>

<s>Rendendo <lb></lb>conto degli altri suoi studi, diceva di esser per metter mano alla <lb></lb>sua Architettura militare, trattata in Dialogo “ nella quale (son sue <lb></lb>parole) dove si discorrerà di fortificarsi vicino ai fiumi, piglierò <lb></lb>l&#039;occasione di pubblicare il mio nuovo modo di frenare i fiumi, <lb></lb>acciò non si avanzino dove noi non vogliamo, e quivi, mentre non <lb></lb>abbia sentore che possa esser discaro costà in Toscana, dimostrerò <lb></lb>le falsità di alcuni principii del Michelini. </s>

<s>E dove si discorrerà di <lb></lb>fortificare accanto al mare, insegnerò il modo di murare sott&#039;acqua ” <lb></lb>(ivi, T. XX, c. </s>

<s>166). </s></p><pb xlink:href="020/01/224.jpg" pagenum="205"></pb><p type="main">

<s>Da tutte queste cose ora discorse è facile persuadersi che l&#039;Ac­<lb></lb>cademia del Cimento, in questo secondo periodo, s&#039;allargò ad ab­<lb></lb>bracciare ogni sorta di scienza sperimentale, mentre nel periodo <lb></lb>precedente parve quasi ristringersi nel campo della Fisica. </s>

<s>Si di­<lb></lb>rebbe che Leopoldo dei Medici volle onorar la Religione, nella <lb></lb>porpora cardinalizia, col coltivar più largamente e col promuover <lb></lb>con più ardore che mai la scienza, e non la sola scienza specula­<lb></lb>tiva, ma le utili applicazioni altresì che si posson fare di lei al de­<lb></lb>coro e alle comodità della vita. </s>

<s>Basterebbe, oltre alle cose dette, <lb></lb>per conferma di ciò, commemorare, non direm l&#039;accoglienza, ma gli <lb></lb>eccitamenti che dal Cardinale Leopoldo ebbero i due fratelli Cam­<lb></lb>pani, quando, per utilità della navigazione, proponevano una nuova <lb></lb>e, secondo loro, inalterabile costruzion di orologi. </s></p><p type="main">

<s>La sera del dì 10 di November dell&#039;anno 1675, colla morte del <lb></lb>Cardinale Leopoldo de&#039;Medici, le porte dell&#039;Accademia del Cimento <lb></lb>furon chiuse per sempre. </s></p><p type="main">

<s><emph type="center"></emph>X.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le virtù che risplendono dall&#039;alto raro è che non accendan <lb></lb>gli animi di chi da più basso luogo le guarda, a imitarne gli esempi. </s>

<s><lb></lb>Molti furono i signori privati in Italia che, ad imitazione di ciò che <lb></lb>facevasi in Firenze nella corte de&#039;Medici, incominciarono a intrat­<lb></lb>tener nei loro palazzi una scelta conversazione d&#039;uomini dotti, a <lb></lb>speculare e a sperimentare di cose naturali. </s>

<s>Di queste private Ac­<lb></lb>cademie si può commemorar fra le prime quella convocata nel 1674 <lb></lb>in Roma dal Cardinal Flavio Chigi, dove secondo il Porzio (Opera <lb></lb>omnia, T. II. Neap. </s>

<s>1736, pag. </s>

<s>280) si ripeterono tutte l&#039;esperienze <lb></lb>fatte nel vuoto dall&#039;Accademia fiorentina. </s>

<s>In secondo luogo poi non <lb></lb>si può tacer di quell&#039;altra istituita in Bologna nella casa dell&#039;abate <lb></lb>Sampieri, dove il Montanari fece quelle sue così importanti espe­<lb></lb>rienze sulla viscosità dei liquidi, e dove pure ei lesser que&#039;suoi Di­<lb></lb>scorsi sull&#039;Idrostatica, da&#039;quali poi largamente attinse il Guglielmini. </s></p><p type="main">

<s>Ma sopra queste due, come sopra parecchie altre, primeggia <lb></lb>l&#039;Accademia napoletana convocata da don Andrea Conclubet, mar­<lb></lb>chese d&#039;Arena. </s>

<s>Il Borelli, nel dedicare a lui il suo libro <emph type="italics"></emph>De motio­<lb></lb>nibus naturalibus.<emph.end type="italics"></emph.end> “ Tu ipse es, gli scriveva, qui in praeclara Urbe <pb xlink:href="020/01/225.jpg" pagenum="206"></pb>Partenopaea, mea parente, societatem seu Academiam in tuo Museo <lb></lb>erexisti, in qua certis et indubitatis experimentis, non vero inanibus <lb></lb>ac rixosis disputatiunculis, philosophicas veritates ad Reipublicae <lb></lb>litterariae bonum indagarentur, idque summa cura, ac munificentia <lb></lb>praestitisti, in unum collectis clarissimis doctissimisque viris, Cara­<lb></lb>muele, Thoma Cornelio, Francisco De Andrea, Leonardo Capua, <lb></lb>Luca Antonio Portio, innumerisque aliis. </s>

<s>” Fra questi soggiunge <lb></lb>tosto il Borelli d&#039;essere stato annoverato anch&#039;egli, ond&#039;è che, per <lb></lb>non presentarsi in casa il Marchese a mani vuote, gli offerisce quel <lb></lb>suo nuovo Libro “ in quo rationes Philosophiae quam plurimum <lb></lb>experimentorum naturalium afferentur, quae Florentiae in Academia <lb></lb>experimentali Medicaea vidi, pariterque accuratissime sunt observata <lb></lb>in tua Neapolitana. </s>

<s>” </s></p><p type="main">

<s>L&#039;avere il Borelli dedicato all&#039;Istitutore un Libro, che contiene <lb></lb>la Filosofia de&#039;fatti semplicemente narrati o storicamente descritti <lb></lb>ne&#039;<emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> è grande onore e attestato de&#039;meriti dell&#039;Accademia napo­<lb></lb>letana, assai più valido di quel che non sia il citare i nomi dei primi <lb></lb>fra coloro che vi appartennero. </s>

<s>Leonardo da Capua ebbe princi­<lb></lb>palmente fama da alcune <emph type="italics"></emph>Lezioni<emph.end type="italics"></emph.end> che, in affettata lingua del trecento <lb></lb>e in stil boccaccevole, pubblicò nel 1683 intorno alla natura delle <lb></lb>mofete. </s>

<s>Quel che egli ivi discorre delle esalazioni gazose del lago <lb></lb>di Agnano, della Grotta del Cane, e di simili, è una vera mofeta <lb></lb>di parole, e tutt&#039;altro che apporsi al vero intorno all&#039;essenza del­<lb></lb>l&#039;anidride carbonica, riman di molto inferiore al Borelli in quali­<lb></lb>ficarne la chimica natura. </s>

<s>Quel che egli poi, nella II Lezione, vi <lb></lb>discorre del circolo sanguigno nell&#039;animal che respira o nel feto, <lb></lb>non ha nulla che non sia stato prima insegnato dall&#039;Harvey, dal <lb></lb>Boyle, nei Proginnasmi, dal Carnelio, e, nell&#039;epistole sparse, dal <lb></lb>Malpighi. </s></p><p type="main">

<s>Luc&#039;Antonio Porzio, che non sembra abbia da vantare altra <lb></lb>invenzione da quella in fuori delle fontane intermittenti applicate <lb></lb>a svelare il celebre mistero dei fonti plimani, e rivendicate da lui <lb></lb>sullo Chales, con tanto ardore; fu il più zelante e ardito banditore <lb></lb>della filosofia cartesiana in Italia. </s>

<s>Nel Trattatello <emph type="italics"></emph>De motu corporum<emph.end type="italics"></emph.end><lb></lb>raffina la sofistica del Cartesio contro i principii meccanici comu­<lb></lb>nemente approvati, e si compiace d&#039;aver colto in fallo Galileo e i <lb></lb>seguaci di lui, i quali riguardaron le sfere gravi discendenti lungo <lb></lb>un piano inclinato, come non aventi alcuna sensibile proporzione <lb></lb>con la grandezza della sfera terrestre. </s>

<s>Così pure, ne&#039;Discorsi IV e V, <lb></lb>in argomento d&#039;acque correnti e della loro misura, applica la me-<pb xlink:href="020/01/226.jpg" pagenum="207"></pb>desima sofistica cartesiana a cogliere in fallo il Castelli, assottigliando <lb></lb>l&#039;ingegno a dimostrare a quali false conseguenze condurrebbe in <lb></lb>qualche caso l&#039;ammettere che le velocità sieno in ragion reciproca <lb></lb>delle sezioni. </s>

<s>Lo stesso sofistico genio portò il Porzio in trattar <lb></lb>l&#039;interminabile questione del vacuo; sofistico genio diciamo, perchè <lb></lb>il Cartesio inopportunamente introdusse la teoria antivacuista degli <lb></lb>spiriti eterei penetranti il vetro, insensibili, come gli stessi effluvii <lb></lb>magnetici. </s>

<s>Una tale inopportunità poi si riconosce dal veder che <lb></lb>nè il Torricelli, nè nessun altro de&#039;seguaci di lui, pretesero mai <lb></lb>altro, come sufficiente allo scopo loro, se non che lo spazio lascia­<lb></lb>tosi dietro dall&#039;argento vivo fosse vuoto di aria, non curandosi, del <lb></lb>resto, se in luogo di lei vi sottentrasse o vi rimanesse persistente, <lb></lb>e non avvertito da alcuno de&#039;nostri sensi, quell&#039;etere, che, col <lb></lb>Cartesio, il Porzio chiama <emph type="italics"></emph>primo elemento.<emph.end type="italics"></emph.end> Il principio della cir­<lb></lb>cumpulsione invocato da Galileo contro la leggerezza positiva, e <lb></lb>confermato con varii e così concludenti esperienze nell&#039;Accademia <lb></lb>fiorentina, vuole il Porzio che sia merce cartesiana. </s>

<s>“ Sempre, egli <lb></lb>dice, ne&#039;moti dei corpi viene ad essere necessaria la circumpulsione, <lb></lb>che Tommaso Cornelio chiamò platonica, ed è la stessa che Renato <lb></lb>Des Cartes, prima di Tommaso Cornelio, riconobbe darsi in tutti <lb></lb>i moti de&#039;corpi ” (Op. </s>

<s>cit. </s>

<s>pag. </s>

<s>200). </s></p><p type="main">

<s>Ma Tommaso Cornelio di Cosenza è pure il miglior soggetto <lb></lb>fra gli Accademici napoletani annoverati di sopra dal Borelli, benchè <lb></lb>il sentirlo, nel Proemio ai Proginnasmi, esaltare il Telesio e il Bruno, <lb></lb>il Campanella e lo Stelliola, il Digby e l&#039;Hobbes al grado di gran <lb></lb>filosofi a pari del Gilberto e di Galileo, possa farlo odorar di poco <lb></lb>fino giudizio. </s>

<s>Nonostante l&#039;avere avuto in Roma a Maestro, e di­<lb></lb>rettor de&#039;suoi studii Michelangiolo Ricci, conferì a infondergli quel <lb></lb>sano gusto nelle scienze sperimentali, di che dette poi splendidi <lb></lb>saggi il Cornelio, specialmente nella Fisiologia e nell&#039;Anatomia. </s>

<s>A <lb></lb>lui, come altrove si disse, è dovuta, a dimostrar la direzion del <lb></lb>moto del sangue nelle arterie, l&#039;esecuzione della esperienza gale­<lb></lb>nica, che l&#039;Harvey reputava impossibile; a lui l&#039;anatomia delle <lb></lb>tuniche, che compaginano gli intestini; a lui la prima caccia contro <lb></lb>l&#039;error del calore nativo, con attribuirne l&#039;origine al moto del sangue. </s>

<s><lb></lb>Della circumpulsione platonica, di che facevasi cenno dal Porzio <lb></lb>nelle parole citate di sopra, ne tratta il Cornelio in una sua Lettera <lb></lb>pubblicata fin dal 1648, sotto il pseudonimo di Timeo Locrese, e <lb></lb>inserita poi in calce ai Proginnasmi. </s>

<s>In cotesta Lettera, che meritò <lb></lb>la traduzione italiana del Viviani, rimasta incompiuta fra&#039;Mano-<pb xlink:href="020/01/227.jpg" pagenum="208"></pb>scritti di lui, si confermano le teorie torricelliane con argomenti <lb></lb>nuovi, e con nuove esperienze. </s>

<s>È notabile questa scrittura del Fi­<lb></lb>losofo e Medico Consentino, perchè la prima che, sopra così famoso <lb></lb>e importante soggetto, si vedesse in Italia, ciò che seguì in quel­<lb></lb>l&#039;anno stesso, in cui il Nöel pubblicava le otto celebri esperienze <lb></lb>fatte già dal Pascal a Roano e a Parigi. </s></p><p type="main">

<s>La Filosofia cartesiana infaustamente fu introdotta dal Porzio <lb></lb>in Italia, e ciò, non perchè non fosse desiderabile tor di mezzo le <lb></lb>rivalità e le inimicizie fra nostrali e stranieri, ma perchè quel cer­<lb></lb>vello un po&#039;leggiero del Fisico napoletano non parve vagheggiar <lb></lb>del Cartesio altro che i capogiroli e i sofismi. </s>

<s>Dall&#039;altra parte <lb></lb>quelle rivalità erano antiche, incominciate già fra il Cartesio stesso <lb></lb>e Galileo, due conquistatori venuti insieme a contesa del medesimo <lb></lb>principato. </s>

<s>Nell&#039;Italiano però era altera noncuranza, ma l&#039;animo <lb></lb>del Bretone covava odio e recalcitrava con invidioso dispetto. </s>

<s>Dai <lb></lb>maestri quelle stesse rivalità si tradussero poi ne&#039;discepoli e se, <lb></lb>per non avere occasione a partecipare dei vizii, da una parte riu­<lb></lb>scirono salutari, precludendo dall&#039;altra gli aditi a partecipare delle <lb></lb>virtù, tornarono, senza dubbio, nocive ai progressi scientifici delle <lb></lb>due Nazioni. </s></p><p type="main">

<s>Segnalato esempio di tali effetti nocivi lo abbiam noi Itallani <lb></lb>nella Diottrica diffusa nella <emph type="italics"></emph>Dissertazione del Metodo<emph.end type="italics"></emph.end> e, nonostante <lb></lb>alcune valide difficoltà, resa infin dal 1637 familiare in Francia. </s>

<s>Il <lb></lb>Mersenno consigliava nelle sue Lettere il Torricelli che leggesse <lb></lb>quella <emph type="italics"></emph>Dissertazione,<emph.end type="italics"></emph.end> ma questi se ne scusava, a principio, dicendo <lb></lb>che non intendeva la lingua francese. </s>

<s>Poi, quando fu fatta la tra­<lb></lb>duzione latina, torna lo stesso Mersenno a sollecitar l&#039;amico perchè si <lb></lb>risolva a comprare il libro, che troverà venale per tutto: non ostante <lb></lb>noi, dietro quel che abbiam potuto raccogliere dalla lettura del <lb></lb>carteggio manoscritto fra&#039;due celebri uomini, non siamo in grado <lb></lb>di assicurare i nostri lettori della risoluzion del Torricelli. </s>

<s>Come <lb></lb>pur siamo incerti se questi entrasse veramente in quella corrispon­<lb></lb>denza epistolare col Cartesio, dentro alla quale lo voleva ficcare il <lb></lb>Mersenno. (MSS. Gal. </s>

<s>Dis. </s>

<s>T. XLI, c. </s>

<s>42). </s></p><p type="main">

<s>Eppure il Torricelli lavorava allora attorno a cercar la miglior <lb></lb>figura da dare alle lenti dei canocchiali, e perchè si sentiva man<gap></gap><lb></lb>la scienza delle rifrazioni, non gl&#039;importa nulla d&#039;impararla alla <lb></lb>Diottrica del Cartesio, ma ne interroga in proposito il Cavalieri. </s>

<s>Il <lb></lb>Cavalieri poi rispondeva non saperne altro, da quello in fuori che <lb></lb>aveva trovato scritto nel <emph type="italics"></emph>Corso matematico<emph.end type="italics"></emph.end> dell&#039;Herigonio; prote-<pb xlink:href="020/01/228.jpg" pagenum="209"></pb>stando però di non credergli, per non gli parer possibile d&#039;applicare <lb></lb>alla luce le leggi stesse del moto dei gravi. </s>

<s>Or perchè la Diottrica <lb></lb>del Cartesio era trattata allo stesso modo che dall&#039;Herigonio, si <lb></lb>capisce d&#039;onde mai movesse, anco indipendentemente dalle rivalità <lb></lb>della scuola, la ritrosia del Torricelli e del Cavalieri, in accettar <lb></lb>la legge delle rifrazioni direttamente conclusa dai teoremi della <lb></lb>Meccanica. </s></p><p type="main">

<s>Tal ritrosia però non fu sentita dal Viviani, in mano al quale, <lb></lb>capitata per caso, nel 1660, la Dissertazione del Metodo, ne rimase <lb></lb>maravigliato e rapito come a una nuova e inaspettata rivelazione. </s>

<s><lb></lb>Fu egli che primo introdusse nell&#039;Accademia del Cimento e per <lb></lb>essa in Italia, derivandola dal Cartesio, la scienza della luce rifratta. </s>

<s><lb></lb>La ritrosia però de&#039;Colleghi fù quella forse che gl&#039;impedì di dif­<lb></lb>fondere le nuove diottriche dottrine, ciò che fù riserbato al Gri­<lb></lb>maldi, il quale, riguardando la luce come un fluido qualunque, e <lb></lb>perciò anch&#039;essa soggetta alle leggi di tutti gli altri fludi in moto, <lb></lb>s&#039;aprì la via e riuscì alle sue insigni scoperte. </s></p><p type="main">

<s>Abbiamo accennato alla ritrosia de&#039;colleghi del Viviani, fra&#039;quali <lb></lb>il più esagerato di tutti fu il Borelli, solito di chiamar le specula­<lb></lb>zioni filosofiche del Cartesio col nome di <emph type="italics"></emph>arcolai.<emph.end type="italics"></emph.end> E non il Cartesio <lb></lb>solo aveva in dispetto il Borelli, ma adombrava, benchè senza mo­<lb></lb>tivo, di tutti gli stranieri. </s>

<s>Quando, nel 1658, essendo a Roma, fa­<lb></lb>ceva, per ordine del principe Leopoldo, ricerca de&#039;manoscritti del <lb></lb>Magiotti e del Torricelli, e si trovò in mano la Lettera di questo <lb></lb>al Ricci sopra la celebre esperienza dell&#039;argento vivo, ne dava parte <lb></lb>allo stesso Principe, così scrivendo: “ Alla mia venuta recherò la <lb></lb>copia di tutte queste lettere scientifiche del Torricelli, per farle <lb></lb>stampare, acciocchè non venga l&#039;umore a qualche francese di pre­<lb></lb>tendere anteriorità (come già mi par che ve ne sia alcuno) sopra <lb></lb>questo gran concetto della compressione dell&#039;aria cagione potissima <lb></lb>ed indubitabile del sollevamento dell&#039;argento vivo nel cannello ” <lb></lb>(MSS. Gal. </s>

<s>Cim. </s>

<s>T. XVI. c. </s>

<s>103). Ora, questo del Borelli parrà un <lb></lb>temerario sospetto per chiunque ripensi che nessuno in Europa <lb></lb>ardì attribuirsi la grande scoperta torricelliana, da Valeriano Magno <lb></lb>in fuori, di cui un francese palesava pubblicamente il furto, resti­<lb></lb>tuendo per giustizia la proprietà al Matematico del Granduca di <lb></lb>Toscana. </s>

<s>La data della Lettera del Roberval al Noyers, dove con <lb></lb>tanto zelo si fa una tale rivendicazione, ha la data di Parigi, otto­<lb></lb>bre 1647, e fu ristampata in calce alla <emph type="italics"></emph>Demonstratio ocularis<emph.end type="italics"></emph.end> dello <lb></lb>stesso Magno, data in luce a Venezia due anni dopo la Lettera del <pb xlink:href="020/01/229.jpg" pagenum="210"></pb>Francese, e nove anni prima che nell&#039;animo del Borelli entrasse <lb></lb>quel sospetto. </s></p><p type="main">

<s>E poichè non si poteva ragionevolmente sospettar da nessuno <lb></lb>de&#039;francesi un attentato di furto, colla Lettera robervelliana sott&#039;oc­<lb></lb>chio, si direbbe che quasi i Nostri non fossero troppo bene infor­<lb></lb>mati di quel che si scriveva in Francia delle cose loro. </s>

<s>Ciò che poi <lb></lb>si può ritenere per certo, è che i nostri Accademici non rivolsero <lb></lb>la debita attenzione al libro degli Esperimenti del Pecquet, ne&#039;quali <lb></lb>tant&#039;oltre si promuove dall&#039;Autore la scienza torricelliana. </s>

<s>Prova <lb></lb>di questo sarebbe per noi il vedere in un Diario manoscritto essere <lb></lb>il Segretario incerto se sia del Roberval l&#039;esperienza della vescica <lb></lb>nel vuoto, e nel Libro de&#039;<emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> (Firenze 1841, pag. </s>

<s>27) s&#039;attri­<lb></lb>buisce al Roberval stesso l&#039;esperienza del vuoto nel vuoto, mentre <lb></lb>il Pacquet chiaramente dice che fu prima felicemente tentata <emph type="italics"></emph>acu­<lb></lb>tissimi Auzotii sagacitate.<emph.end type="italics"></emph.end> Benchè, a voler dir giusto, quel bellis­<lb></lb>simo esperimento non fu primo a farlo nè il Roberval nè l&#039;Auzout, <lb></lb>ma il Pascal, in più elegante e facile modo. </s></p><p type="main">

<s>Che si vedesse poi da&#039;Nostri questo ingerirsi degli stranieri <lb></lb>nella loro scienza di mal occhio, si prova per l&#039;esempio del Boyle, <lb></lb>i Nuovi Esperimenti fisico meccanici del quale furono pubblicati <lb></lb>in inglese neì 1659, e poco dopo a benefizio di tutti tradotti in la­<lb></lb>tino. </s>

<s>Quei celebri esperimenti furono tutti fatti nel vuoto operato <lb></lb>per mezzo della macchina pneumatica, che perciò si disse <emph type="italics"></emph>vuoto <lb></lb>boileiano.<emph.end type="italics"></emph.end> Eppure i nostri Accademici tanto di mal animo s&#039;indus­<lb></lb>sero a far uso di quella macchina! Forse che essi credevano il <lb></lb>vuoto torricelliano dover riuscir più perfetto? </s>

<s>Ma pure il Boyle <lb></lb>stesso ne&#039;suoi Nuovi esperimenti <emph type="italics"></emph>circa relationem inter flammam <lb></lb>et acrem<emph.end type="italics"></emph.end> aveva discusso la questione, e aveva mostrato in quali <lb></lb>casi giovi sperimentar nel voto boileiano, e in quali nel torricel­<lb></lb>liano; cosa dall&#039;altra parte che i Nostri potevano saper benissimo <lb></lb>per loro propria esperienza. </s>

<s>Ma la ragion potissima perch&#039;essi ri­<lb></lb>fuggissero così dal vuoto boileiano, ce la dice chiara il Borelli, <lb></lb>quando, trovatasi dagli Accademici del Cimento gran difficoltà nel­<lb></lb>l&#039;agitare il bastoncino per confricar nel vuoto la pallottolina del­<lb></lb>l&#039;ambra, disperati pensarono di ricorrere alla Macchina boileiana. </s>

<s><lb></lb>Allora il Borelli immaginò un nuovo apparecchio, colla pratica del <lb></lb>quale sperava di agevolar l&#039;esperienza <emph type="italics"></emph>senza chiedere aiuto a stra­<lb></lb>nieri.<emph.end type="italics"></emph.end> (Targioni, Aggrandim. </s>

<s>T. II. P. II. pag. </s>

<s>606). Mossi pure da <lb></lb>questa intenzione il Borelli stesso e il Viviani gareggiarono insieme <lb></lb>a inventare il più sicuro e più comodo <emph type="italics"></emph>vaso del gran vacuo,<emph.end type="italics"></emph.end> dentro <pb xlink:href="020/01/230.jpg" pagenum="211"></pb>il quale però non riuscirono a far l&#039;esperienza del suono collo <lb></lb>strumento a fiato; e benchè l&#039;unica, questa volta però i nostri Ita­<lb></lb>liani s&#039;ebbero a umiliare e a chiedere aiuto allo straniero. </s></p><p type="main">

<s>Questo starsene a sè i Nostri e non voler partecipare con gli <lb></lb>stranieri, specialmente francesi, si potrebbe da qualche giudice se­<lb></lb>vero sentenziare per un proceder d&#039;animi appassionati, piuttosto <lb></lb>che d&#039;uomini prudenti. </s>

<s>È da osservar nonostante che non erano <lb></lb>così fatti sentimenti, nell&#039;animo dei nostri Accademici, senza giusti <lb></lb>motivi, essendo consapevoli, e in parte testimoni, di ciò che il Mer­<lb></lb>senno aveva fatto con Galileo e col Torricelli. </s>

<s>Il Magiotti poneva <lb></lb>in tumulto l&#039;animo del buon Vecchio di Arcetri scrivendogli che <lb></lb>a quel frate era capitato in Francia il Libro <emph type="italics"></emph>De Motu,<emph.end type="italics"></emph.end> sopra il quale <lb></lb>egli, il frate stesso francese, <emph type="italics"></emph>voleva scompuzzare ogni cosa<emph.end type="italics"></emph.end> (Alb. </s>

<s>X, <lb></lb>205). Ma peggio che mai volle scompuzzare le cose al Torricelli, <lb></lb>quando, più tardi venuto in Italia, e soggiornando in Roma, si <lb></lb>messe dietro al Magiotti e al Ricci, per saper le particolarità delle <lb></lb>speculazioni torricelliane, specie intorno al moto dell&#039;acque e dei <lb></lb>proietti; speculazioni che, tornato a Parigi, divulgò ne&#039;suoi librac­<lb></lb>cioni in gran fretta, prevenendo la pubblicazione delle <emph type="italics"></emph>Opere Geo­<lb></lb>metriche<emph.end type="italics"></emph.end> dell&#039;Autore, che lentamente in quel medesimo tempo si <lb></lb>stampavano in Firenze. </s></p><p type="main">

<s>Non credendo il Mersenno capace di commettere un atto di <lb></lb>tanta viltà, quegli scienziati Romani conversavano volentieri con <lb></lb>lui, e benchè ridessero sotto sotto del sentirlo parlar familiarmente <lb></lb>un latino, <emph type="italics"></emph>che l&#039;impatta talvolta con Merlin Coccaio, io però,<emph.end type="italics"></emph.end> scrive <lb></lb>il Ricci al Torricelli, <emph type="italics"></emph>devo sempre dirne bene, se mi fa tutto quello <lb></lb>che mi ha promesso, cioè di procurarmi manoscritti e libri a noi <lb></lb>sconosciuti.<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XLII, c. </s>

<s>71). Sembra che le promesse <lb></lb>non fossero mantenute, per cui, sciolto ogni ritegno, il Ricci qua­<lb></lb>lifica il Mersenno per quel che egli era, colafizzandolo col titolo di <lb></lb><emph type="italics"></emph>Gesuito,<emph.end type="italics"></emph.end> benchè sentisse quanto quel di <emph type="italics"></emph>Minimo<emph.end type="italics"></emph.end> fosse, per altra <lb></lb>parte, tanto meglio appropriato. </s>

<s>E per ciò di lui stesso, accennando <lb></lb>in un&#039;altra Lettera al Torricelli le difficoltà immaginate contro i <lb></lb>principii meccanici di Galileo, soggiunge: “ Con questo fondamento <lb></lb>presume il Gesuito d&#039;alzar rocca inespugnabile a&#039;danni di Galileo <lb></lb>e della sua scuola, e con mille vanti di sè medesimo e scherno del <lb></lb>Galileo, si dimostra non men leggiero ne&#039;costumi che sia nelle dot­<lb></lb>trine ” (ivi, c. </s>

<s>116). Così il Mersenno rimeritava l&#039;ospitalità degli <lb></lb>scienziati italiani colla sfacciataggine degli insulti, e con l&#039;abbiet­<lb></lb>tezza de&#039;furti. </s></p><pb xlink:href="020/01/231.jpg" pagenum="212"></pb><p type="main">

<s>Quel Ricci nonostante era uomo di così perfetto giudizio da cono­<lb></lb>scer quanto decoro sarebbe sopraggiunto all&#039;Italia, e quanto se ne <lb></lb>sarebbe avvantaggiata la scienza dal partecipare insieme gli studi con <lb></lb>gli stranieri. </s>

<s>Volle perciò che la nostra del Cimento corrispondesse <lb></lb>coll&#039;Accademia di Francia, e vi riuscì col mandare al Thevenot la <lb></lb>relazione dell&#039;esperienza del fumo nel vuoto. </s>

<s>Il Thevenot stette <lb></lb>alquanto, ma poi rispose che era stata straordinariamente adunata <lb></lb>l&#039;Accademia parigina, a fine di partecipare a que&#039;signori <emph type="italics"></emph>l&#039;esperienza <lb></lb>graziosissima venuta di Firenze.<emph.end type="italics"></emph.end> (Ivi, Cim. </s>

<s>T. XVII, c. </s>

<s>81). </s></p><p type="main">

<s>I consigli e le risoluzioni prese dal Ricci non potevano non <lb></lb>esser conformi alle intenzioni del principe Leopoldo, il quale era <lb></lb>intanto egli stesso entrato in relazione scientifica con uno de&#039;più <lb></lb>celebri e dotti uomini, che dimorassero allora in Parigi, Ismaele <lb></lb>Bullialdo. </s>

<s>Il Bullialdo poi introdusse in queste relazioni un altro <lb></lb>non men celebre e dotto uomo, che dall&#039;Aja frequentava Parigi, <lb></lb>Cristiano Hugenio, e ciò fu a proposito della celebre controversia <lb></lb>sulla priorità dell&#039;applicazione del pendolo all&#039;orologio. </s>

<s>Benchè dallo <lb></lb>zelo un po&#039;troppo ardente, con che intendeva il Vivìani d&#039;esaltar <lb></lb>Galileo, l&#039;altero Barone di Zulichemme sentisse qualche disgusto, <lb></lb>nonostante ei dovette dar pace e sentirsi anzi grato dell&#039;accoglienze <lb></lb>che, fra i nostri Accademici, ebbero le sue dottrine e le sue sco­<lb></lb>perte. </s>

<s>Il Viviani stesso, non sappiamo se per suo diporto o se per <lb></lb>servizio de&#039;Principi, dava mano a tradurre l&#039;Astroscopia, o la Nuova <lb></lb>arte di osservare le stelle (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXXXVIII, c. </s>

<s>124-47), <lb></lb>e per ordine espresso del Serenissimo Cardinale Leopoldo, faceva <lb></lb>un sunto, da leggersi nell&#039;Accademia, di una Relazione intorno ad <lb></lb>alcune osservazioni fatte dall&#039;Hugenio a Parigi, il dì 12 Maggio 1667, <lb></lb>di un alone o corona apparsa in quel giorno intorno al sole. (ivi, <lb></lb>T. CXXXIII, c. </s>

<s>135-44). Il Viviani altresì riferiva agli Accademici <lb></lb>suoi colleghi la nuova costruzione del canocchiale ugeniano, e i <lb></lb>primi tentativi e le speranze concepute dall&#039;Olandese d&#039;aver trovato <lb></lb>il modo di acromatizzare le lenti. </s>

<s>E il sistema Saturnio chi sa quante <lb></lb>contradizioni ancora avrebbe patito, se le ingegnose macchine im­<lb></lb>maginate e descritte dal Borelli, non avessero fatto quasi scender <lb></lb>dal cielo il lontano pianeta, e rappresentarsi agli Accademici e agli <lb></lb>stessi più volgari spettatori, sott&#039;occhio. </s></p><p type="main">

<s>Non si può far motto del sistema Saturnio e dell&#039;Accademia <lb></lb>fiorentina, senza fare a quel dell&#039;Hugenio seguitar dietro il nome <lb></lb>di un altro straniero, a cui non sapremmo nemmen noi dar altro <lb></lb>nome che di <emph type="italics"></emph>cervellaccio.<emph.end type="italics"></emph.end> “ A quel cervellaccio, scriveva il Borelli <pb xlink:href="020/01/232.jpg" pagenum="213"></pb>di Onorato Fabry, gli son sovvenuti concetti assai simili a&#039;miei, <lb></lb>con i quali spiegò le cagioni fisiche del moto de&#039;pianeti ” (MSS. <lb></lb>Gal. </s>

<s>Cim. </s>

<s>T. XVIII, c. </s>

<s>110). Quel cervellaccio, per sostenere il gioco <lb></lb>di que&#039;suoi globi bianchi e neri, danzanti intorno a Saturno, onde <lb></lb>così spiegare i fenomeni dell&#039;anello, avrebbe seguitato ad agitare <lb></lb>interminabilmente la questione contro l&#039;Hugenio, se il Ricci non <lb></lb>avesse consigliato e operato a troncarla. </s>

<s>Tanto era poi incaponito <lb></lb>di compor Saturno a suo modo, e tanto era persuaso non avercene <lb></lb>altro miglior di quello immaginato, che avendo ricevuto invito più <lb></lb>volte da Giuseppe e da Matteo Campani di far esperienza della <lb></lb>verità delle cose, guardando con uno de&#039;più eccellenti canocchiali <lb></lb>fabbricati da loro, non ci volle comparir mai. (MSS. Gal. </s>

<s>Disc. </s>

<s><lb></lb>T. CXLIV, c. </s>

<s>269). Dopo tanto combattere, finì per rassegnarsi sotto <lb></lb>le bandiere del suo nemico, e nella fine del II de&#039;suoi Dialoghi <lb></lb>fisici annovera, tra le nuove maraviglie scoperte nel cielo, l&#039;anello <lb></lb>di Saturno <emph type="italics"></emph>a Christiano Hugenio viro clarissimo et omnigena lite­<lb></lb>ratura probe instructo<emph.end type="italics"></emph.end> (Lugduni 1665, pag. </s>

<s>65). Così in pari modo, <lb></lb>dop&#039;essersi fatto spacciare per primo autore dell&#039;esperienza dell&#039;ar­<lb></lb>gento vivo, con facilità e docilità veramente filosofica, secondo <lb></lb>l&#039;espression del Borelli, cantò la sua palinodia scrivendo nel IV <lb></lb>de&#039;Dialoghi sopra citati: “ Primus illius inventor fuit doctissimus <lb></lb>Torricellìus, vir certe, quem inter principes huius temporis geo­<lb></lb>metras iure innumero ” (ibi, pag. </s>

<s>182). </s></p><p type="main">

<s>Il Fabry, oltre ad essere straniero, era gesuita, che vuol dire <lb></lb>peripatetico o filosofante alla maniera di Aristotele intorno ai fatti <lb></lb>della Natura. </s>

<s>Assecondando perciò docilmente le cose al suo proprio <lb></lb>cervello, non risolve problema, non conclude questione ch&#039;ei non <lb></lb>la coroni compiacente con dire: <emph type="italics"></emph>quid facilius, quid clarius?<emph.end type="italics"></emph.end> Ora <lb></lb>una tal Filosofia era tutta contraria a quella professata dai nostri <lb></lb>Accademici, i quali, trepitando in dover render la ragion fisica delle <lb></lb>cose, si contentarono quasi sempre, dopo lunghi e ripetuti esperi­<lb></lb>menti, di descrivere i fatti come s&#039;eran rappresentati ai loro sensi. </s>

<s><lb></lb>Non è maraviglia perciò se nessuno de&#039;gesuiti fu chiamato mai a <lb></lb>partecipare de&#039;Medicei sperimentali consessi. </s>

<s>E nonostante n&#039;erano <lb></lb>in quel numero due, l&#039;uno e l&#039;altro italiani, che se fossero rimasti <lb></lb>nel loro filosofare liberi dal giogo peripatetico, avrebbero fatto ri­<lb></lb>splendere, non una corte, come il Magalotti diceva del Borelli, ma <lb></lb>un&#039;intera nazione. </s></p><p type="main">

<s>Giovan Batista Riccioli voleva tutto <emph type="italics"></emph>riformare,<emph.end type="italics"></emph.end> ossia ridur le <lb></lb>cose agli ordini antichi, o a que&#039;nuovi da sè immaginati. </s>

<s>E perciò, <pb xlink:href="020/01/233.jpg" pagenum="214"></pb>tutt&#039;altro che cimentare, metteva i fatti naturali a tortura, e voleva <lb></lb>che corrispondessero in ogni modo a&#039;suoi preconcetti. </s>

<s>Nessuno che <lb></lb>si mette a svolgere i suoi ponderosi volumi non può non deplorare <lb></lb>che tanta infaticabile assiduità, e tanta pazienza di sperimentare, <lb></lb>siano state rivolte piuttosto a compiacere una setta, che a benefizio <lb></lb>della scienza universale. </s></p><p type="main">

<s>Francesco Maria Grimaldi, concittadino e collega di lui negli <lb></lb>studii, presenta il caso più strano, che si sia incontrato mai nella <lb></lb>storia letteraria. </s>

<s>Il celebre Trattato <emph type="italics"></emph>De Lumine<emph.end type="italics"></emph.end> lo divide in due <lb></lb>parti, nella seconda delle quali disdice tutto ciò che avea detto nella <lb></lb>prima. </s>

<s>Ma la stranezza maggiore consiste nel veder che l&#039;Autore <lb></lb>s&#039;adagia nel falso, dop&#039;aver così strenuamente combattuto pel vero. </s>

<s><lb></lb>Qualunque sieno le ragioni pensate a spiegare un fatto tanto sin­<lb></lb>golare, le due parti contradittorie del Trattato grimaldiano ebbero <lb></lb>una grande efficacia in promuover l&#039;ottica, perchè par che la prima <lb></lb>di quelle parti abbia il precipuo scopo di dimostrare, che supposto <lb></lb>esser la luce soggetta alle passioni degli altri fluidi, si spiegano <lb></lb>facilmente gli antichi, e si scuoprono fenomeni nuovi; mentre sup­<lb></lb>posto esser la luce una qualità, conforme ai placiti peripatetici, come <lb></lb>si fa dall&#039;Autore nella parte seconda, non s&#039;incontrano che mani­<lb></lb>feste contradizioni ed errori. </s></p><p type="main">

<s>Il Riccioli ebbe qualche raro commercio con alcuni de&#039;nostri <lb></lb>Accademici privati: del Grimaldi non ne abbiamo trovato vestigio. </s>

<s><lb></lb>Si potrebbe sospettare che il principe Leopoldo non avesse così <lb></lb>fatta gente in buona grazia, e darebbe al sospetto qualche fon­<lb></lb>damento una lettera, che il Rinaldini scriveva da Pisa al Viviani, <lb></lb>nel dì 9 Marzo 1658. “ Mi vien detto, scriveva, per cosa certissima <lb></lb>che i padri Gesuiti fanno strepito avanti il tempo, conciossiachè <lb></lb>dicono che, se nel Libro delle Osservazioni naturali fatte costì, ci <lb></lb>sarà cosa che possi toccar qualcheduno di loro, che averanno uo­<lb></lb>mini, a&#039;quali dà l&#039;animo di rispondere, e che frattanto, tutto che <lb></lb>possono sapere delle cose fatte procurano di sperimentare e di farne <lb></lb>un libro ” (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXIV, c. </s>

<s>45) e seguita a rivelare in <lb></lb>gran segretezza alcune trame, e a dire un gran male de&#039;gesuiti, <lb></lb>concludendo al Viviani, se lo credesse ben fatto, di confidare il tutto <lb></lb>al principe Leopoldo. </s></p><p type="main">

<s>Che quella setta peripatotica possa aver congiurato ai danni <lb></lb>dell&#039;Accademia del Cimento, non fa maraviglia: però, da questa <lb></lb>lettera del Rinaldini in fuori, non son noti a noi, per provare il <lb></lb>fatto, altri documenti, nè ci siamo curati di ricercarli. </s>

<s>Forse il prin-<pb xlink:href="020/01/234.jpg" pagenum="215"></pb>cipe Leopoldo, che sapeva non esser nella sua Accademia stato <lb></lb>offeso nessuno, se ne viveva tranquillo, e uomo di senno, piuttosto <lb></lb>che irritarsi, come da tanti si fa, avrà pensato ai benefizi grandis­<lb></lb>simi, che conseguitano sempre dalle contradizioni, e come, se il <lb></lb>verno non li mortifica, poco giova a fecondare il seme de&#039;campi <lb></lb>il tiepore di primavera. </s>

<s>Più assai delle contrarietà de&#039;peripatetici <lb></lb>dovevano mettere in sollecitudine il Principe le dissensioni fra&#039;suoi <lb></lb>stessi Accademici, e specialmente quelle insorte fra il Borelli e il <lb></lb>Viviani. </s>

<s>Nate all&#039;occasione della teoria dell&#039;anello riscaldato e di­<lb></lb>latato al calore, infierirono, le inimicizie fra&#039;due grandi Geometri, <lb></lb>nella concorrenza che ebbero in tradurre i rimasti, e in divinare i <lb></lb>libri smarriti di Apollonio di Perga. </s>

<s>Chi conosce il carattere del <lb></lb>Borelli ammira la potenza che ebbe il principe Leopoldo in mante­<lb></lb>nerlo collega e collaboratore, per dieci anni, all&#039;odiato Viviani, e <lb></lb>in trattenerlo fino alla morte, o vicino o lontano, a suoi servigi; <lb></lb>potenza, nella quale, più che l&#039;altezza del grado, concorse l&#039;affa­<lb></lb>bilità e la dolcezza dei modi. </s></p><p type="main">

<s>Più tardi, quello stesso fastidioso Borelli, da cui tanti dispetti <lb></lb>ebbe a patire il docile Malpighi, entrò in fiera battaglia, direttamente <lb></lb>con Stefano Angeli, discepolo del Cavalieri e uno dei deputati a <lb></lb>rivedere il Trattato del Michelini, e indirettamente col Riccioli, a <lb></lb>proposito di un argomento sperimentale che questi adduce contro <lb></lb>il moto della Terra. </s>

<s>Era quella battaglia, piuttosto che condotta dal <lb></lb>valore, menata dalla rabbia, e perciò così accoratamente il principe <lb></lb>Leopoldo ne scriveva in proposito al Ricci: “ Mi dispiace, quando, <lb></lb>in queste occasioni di differenze letterarie, s&#039;esce dai termini delle <lb></lb>dispute ” (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XXIII, c. </s>

<s>149). </s></p><p type="main">

<s>Ammirabile uomo da qualunque lato si guardi! sia qual si voglia <lb></lb>la cultura o la forza dell&#039;ingegno di Leopoldo de&#039;Medici, egli è più <lb></lb>benemerito della scienza italiana di quegli stessi che sudarono sui <lb></lb>libri, o si affaticarono intorno agli esperimenti. </s>

<s>Cessata l&#039;Accademia <lb></lb>colla morte di lui, le dottrine di Galileo parvero essere esaurite, per <lb></lb>essersi svolte in soverchiante abbondanza. </s>

<s>Or essendo legge natu­<lb></lb>rale che in ogni tralcio trascorso, a voler mantenergli la virtù di <lb></lb>fruttificare, conviene o di ritirarlo col ferro verso il suo principio, <lb></lb>o infondergli in qualche altro modo vigore novello; è perciò che <lb></lb>dopo l&#039;Accademia del Cimento, incomincia per la Storia della nostra <lb></lb>Scienza un&#039;altra età, e così apresi innanzi ai nostri proprii occhi <lb></lb>una nuova scena, a rappresentare il terzo atto di questo Dramma. <pb xlink:href="020/01/235.jpg"></pb></s></p><pb xlink:href="020/01/236.jpg"></pb><p type="main">

<s><emph type="center"></emph>PARTE TERZA<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Isacco Newton. </s>

<s>— II. De&#039;principii e de&#039;progressi delle speculazioni neutoniane, e quale efficace <lb></lb>concorso v&#039;abbiano avuto le tradizioni scientifiche de&#039;nostri italiani. </s>

<s>— III. </s>

<s>Delle Istituzioni <lb></lb>idrauliche di Domenico Guglielmini, e in che modo, i principii della Filosofia neutoniana, nel <lb></lb>secolo XVIII, concorressero a farle progredire. </s>

<s>— IV. Dell&#039;elettricismo, della Chimica, dell&#039;elettro <lb></lb>chimica, e come si svolgessero, queste nuove parti della scienza, dai principii della Filosofia <lb></lb>neutoniana. </s>

<s>— V. De&#039;progressi della Storia Naturale, nel secolo XVIII. — Delle condizioni pre­<lb></lb>senti delle scienze sperimentali: qualche parola intorno alla nostra Storia. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi ripensa ai progressi straordinari fatti dalle scienze speri­<lb></lb>mentali nel secolo XVIII, s&#039;avvede assai facilmente che non può, <lb></lb>di tale effetto, esser unica tra le cause quella consueta d&#039;operarsi <lb></lb>negli ordini trascorsi, e che è di ritirarli verso i loro principii. </s>

<s><lb></lb>Quell&#039;effetto straordinario non poteva non esser prodotto da una <lb></lb>causa straordinaria, la quale consista in infondere in quegli stessi <lb></lb>ordini trascorsi, e ritirati già verso i loro principii, un vigor nuovo <lb></lb>di vita, come spesso avviene degli alberi fruttiferi della campagna. </s>

<s><lb></lb>In questo esempio si prova che sempre s&#039;accresce o si perfeziona <lb></lb>la virtù fruttificante de&#039;rami, dall&#039;infonder nel tronco la virtù di <lb></lb>un altr&#039;albero, che sia affine di genere, ma di specie alquanto di­<lb></lb>versa. </s>

<s>Or la causa per cui, nel secolo XVIII, s&#039;avvantaggiarono le <lb></lb>scienze sperimentali, in modo tanto straordinario, a noi sembra do­<lb></lb>versi riconoscere in qualche cosa di simile a quel che si vede per <lb></lb>gli esempii degli alberi stessi; doversi cioè riconoscere in una specie <pb xlink:href="020/01/237.jpg" pagenum="218"></pb>d&#039;innesto, il quale non è altro poi che un far concorrere insieme <lb></lb>due virtù coniugate a produrre un unico effetto. </s></p><p type="main">

<s>L&#039;innesto, di che si tratta, fu quello appunto che si fece in <lb></lb>quel tempo con tanto felice riuscita fra la Fisica e la Matematica. </s>

<s><lb></lb>Non si vuol già dir per questo che fosse, nel secolo precedente, <lb></lb>sconosciuto un tale efficacissimo connubio: aveva anzi Galileo mi­<lb></lb>rabilmente promossa la scienza, insegnando a interpretar, per mezzo <lb></lb>delle Matematiche, i Misteri della Natura, e il Castellì aveva dimo­<lb></lb>strato già come si dovesse trattar del moto delle acque, con rigo­<lb></lb>roso ordine di Geometria. </s>

<s>Ciò però non vuol dir altro, se non che, <lb></lb>da&#039;due grandi Maestri della Scienza del moto de&#039;gravi e delle Acque <lb></lb>correnti, s&#039;eran felicemente coniugate insieme, nel secolo XVII, la <lb></lb>Fisica e la Geometria. </s>

<s>Non però s&#039;erano coniugate la Fisica con <lb></lb>la Matematica, per la quale non s&#039;intende solo la Geometria, ma <lb></lb>la Geometria coniugata essa stessa coll&#039;Algebra, ossia quell&#039;<emph type="italics"></emph>Analisi,<emph.end type="italics"></emph.end><lb></lb>che la Scuola galileiana non conobbe, nè volle poi riconoscere, abor­<lb></lb>rendo dal parteciparne come da contagiosa merce straniera. </s></p><p type="main">

<s>Vincenzio Viviani, in una di quelle sue prefazioni, o meglio, <lb></lb>in uno di quegli abbozzi di scritture, che dovevan poi ridursi a <lb></lb>servir di prefazione a quello e quell&#039;altro libro del suo <emph type="italics"></emph>Sogno Idro­<lb></lb>metrico,<emph.end type="italics"></emph.end> scritto in tempo che l&#039;analisi, appresso gli stranieri e <lb></lb>specialmente i Francesi, era largamente e utilmente applicata; si <lb></lb>scusa del non essersene egli servito, nel trattar le sue quistioni <lb></lb>d&#039;Idrometria, e dell&#039;aver seguitato piuttosto l&#039;antico metodo in­<lb></lb>valso nella scuola galileiana, adducendo per sua ragione che se <lb></lb>l&#039;Analisi, conferisce alla brevità, recide però i nervi, e rende anzi <lb></lb>impossibile, in trattar di soggetti fisici matematici, l&#039;uso dell&#039;elo­<lb></lb>quenza. </s>

<s>Senza dubbio, una pagina irta di segni algebrici, tutt&#039;altro <lb></lb>che incantar con quella dilettevole armonia, che risuona ne&#039;Dialoghi <lb></lb>delle Due Nuove Scienze, farebbe gittar via il libro a chi ama veder <lb></lb>il vero uscir fragrante di mezzo ai fiori del bello, e in ciò il Viviani <lb></lb>aveva ragione. </s>

<s>Ma, come a tutti i vecchi avviene, era tenace troppo <lb></lb>degli usi antichi, e male secondava la gente nuova, anco per essere <lb></lb>straniera, la quale, al bello dell&#039;eloquenza, preferiva la facilità, con <lb></lb>la quale la nuova Analisi dimostrava la stessa cosa. </s>

<s>Chè, dove le <lb></lb>proposizioni di Galileo e del Torricelli e degli altri simili, prima <lb></lb>di concludere, divagavano la mente per lungo e faticoso discorso, <lb></lb>i nuovi Analisti, con pochi simboli, conducevan diritti, e veloci, <lb></lb>come saette, a coglier nel segno. </s></p><p type="main">

<s>L&#039;istituzione dell&#039;Analisi matematica non si può negar che non <pb xlink:href="020/01/238.jpg" pagenum="219"></pb>fosse un gran benefizio, sebben l&#039;unico, recato alle scienze speri­<lb></lb>mentali dalla Filosofia cartesiana. </s>

<s>E dall&#039;essersi quell&#039;Analisi inco­<lb></lb>minciata a coniugar con la Fisica, noi riconosciamo la prima di <lb></lb>quelle valide cagioni del progredir così straordinariamente le scienze, <lb></lb>nell&#039;età, che è soggetto della presente Parte del nostro Discorso. </s>

<s><lb></lb>A infonder nel vecchio albero, naturalmente esausto per la stra­<lb></lb>boccante raccolta, rigoglio nuovo di vita, concorsero, in questa nuova <lb></lb>stagione felicemente congiunte le virtù di Galileo e del Cartesio. </s>

<s><lb></lb>Così vennesi, nella cultura intellettuale, a conseguir quello stesso <lb></lb>intento e ad operar quel medesimo miracolo, che si vede operar <lb></lb>così spesso nella cultura fisica delle piante, quando a un tronco, <lb></lb>rimasto o infecondo, o di frutto insipido, s&#039;inocula la vermena di <lb></lb>un albero, che dia frutto abbondante e squisito. </s>

<s>La Filosofia car­<lb></lb>tesiana, che nell&#039;età precedente era rimasta di frutti sperimentali <lb></lb>così infeconda, inoculatasi, per mezzo dell&#039;Analisi, alla Fisica gali­<lb></lb>leiana, fecondò di nuovi e miracolosi parti la scienza. </s>

<s>S&#039;aggiunse <lb></lb>poi di più all&#039;Analisi il Calcolo differenziale, che fu come un im­<lb></lb>pennar d&#039;ali il dorso a tentar voli più arditi e più sublimi: s&#039;ag­<lb></lb>giunse di più l&#039;uso di comporre e decomporre le forze, con la regola <lb></lb>del parallelogrammo, che fu, al dir del Frisi, come il filo d&#039;Arianna, <lb></lb>da ritrovarsi in mezzo ai più intricati laberinti della Meccanica. </s></p><p type="main">

<s>Già, fin dal primo rappresentarsi al pensiero e dalla lontana <lb></lb>questa nuova disposizione di cose, un mesto presentimento si sa­<lb></lb>rebbe affacciato all&#039;animo di un italiano, e gli avrebbe detto che, <lb></lb>al cambiarsi scena a questo terzo Atto del Dramma, si sarebbe anco <lb></lb>trasferito il luogo della rappresentazione fuori d&#039;Italia. </s>

<s>L&#039;Analisi, di <lb></lb>origine affatto straniera, il Calcolo differenziale di origine schietta­<lb></lb>mente italiano, ma andato ad elaborarsi in Germania e in Inghil­<lb></lb>terra, il principio della composizione delle forze, lasciato in dimen­<lb></lb>ticanza da&#039;Nostri com&#039;inutile e anzi fallace strumento; bastavano a <lb></lb>confermar nell&#039;animo que&#039;mesti presentimenti di ciò che sarebbe <lb></lb>avvenuto, e che avvenne di fatto. </s>

<s>Il luogo della rappresentazione si <lb></lb>trasferisce d&#039;Italia in Inghilterra, e alla persona di Galileo Galilei <lb></lb>succede quella d&#039;Isacco Newton, a far le parti di Protagonista. </s></p><p type="main">

<s>La nuova successione però non avvenne al solito modo, che <lb></lb>nell&#039;Istituzione de&#039;Principati aristotelico, galileiano, cartesiano: fu <lb></lb>insomma una pacifica e legittima successione, e non una battagliera <lb></lb>conquista. </s>

<s>Il Newton non ripudiò com&#039;Aristotile, Galileo, il Cartesio, <lb></lb>le tradizioni scientifiche de&#039;maggiori, e non pretese di farsi primo <lb></lb>e solo Maestro e Duce di coloro che sanno. </s>

<s>Riconobbe anzi il ma-<pb xlink:href="020/01/239.jpg" pagenum="220"></pb>gistero del grande nostro Italiano, ne segui fedelmente i metodi, e <lb></lb>ne accolse con amore e ne promosse gl&#039;insegnamenti. </s></p><p type="main">

<s>Il Newton, come Galileo, non se ne stà che ai fatti. </s>

<s>Anch&#039;egli <lb></lb>il tentar l&#039;essenza l&#039;ha per impresa non manco impossibile, e per <lb></lb>fatica non men vana nelle prossime sostanze elementari, che nelle <lb></lb>remotissime e celesti (Alb. </s>

<s>III, 462). Di quel che non ha potuto far <lb></lb>soggetto di sperimento ne parla come di cosa da questioni. <emph type="italics"></emph>Que­<lb></lb>stioni<emph.end type="italics"></emph.end> infatti egli chiama quell&#039;alto e sottil modo di speculare in­<lb></lb>torno alle prime e più recondite cause degli effetti naturali. </s>

<s>Così <lb></lb>fatte Questioni, trattando delle proprietà della luce, volle egli ac­<lb></lb>cogliere tutte insieme, e perchè rappresentavano piuttosto le sue <lb></lb>proprie opinioni che la dimostrata certezza del vero, volle egli te­<lb></lb>nerle separate e metterle come Appendice al suo Libro. </s></p><p type="main">

<s>Se qualcuno, per esempio, si fa a domandargli: che cos&#039;è quel­<lb></lb>l&#039;attrazione, che tu poni per fondamento alla scienza del Cosmo? </s>

<s><lb></lb>Ed ei risponde: Un fatto osservato e confermato da leggi matema­<lb></lb>tiche, il qual consiste in quel conato che fanno i corpi d&#039;avvicinarsi <lb></lb>e di congiungersi insieme, dipenda egli un tal conato o da aliti <lb></lb>emessi, che commovano e sospingano i corpi, o dall&#039;azion dell&#039;etere, <lb></lb>che diffondendosi, prema, o dagli elaterii dell&#039;aria o di altro mezzo <lb></lb>qualunque. (Principia Philos. </s>

<s>Coloniae 1760, T. I, pag. </s>

<s>464). </s></p><p type="main">

<s>Ma pure, soggiunge altrove, per dir qualche cosa della gravità <lb></lb>e di questa misteriosa attrazione “ quaestionem unam de eius causa <lb></lb>investiganda subieci, quaestionem inquam, quippe qui experimentis <lb></lb>rem istam nondum habeam exploratam ” (Optices, Avvertim. alla <lb></lb>2. a ediz. del 1717).</s><s> La questione accennata è la XXI, nella quale <lb></lb>si ammette l&#039;esistenza dell&#039;etere cosmico, com&#039;efficiente dell&#039;attra­<lb></lb>zione universale. </s></p><p type="main">

<s>E pur rispetto alla luce, com&#039;entra il Newton in mezzo ai di­<lb></lb>sputanti sull&#039;essenza di lei? </s>

<s>Dop&#039;aver, nella Sezione XIV del I Libro <lb></lb>dei <emph type="italics"></emph>Princippi,<emph.end type="italics"></emph.end> dimostrato che un minimo corpo vibrato e attratto <lb></lb>da un mezzo più denso, vi descrive, penetrandolo addentro, una pa­<lb></lb>rabola, per modo che il seno dell&#039;angolo dell&#039;incidenza serbi ragion <lb></lb>costante col seno dell&#039;angolo dell&#039;emergenza; soggiunge che sì fatte <lb></lb>attrazioni non sono molto dissimili da quelle, percui si riflette e si <lb></lb>rifrange la luce. </s>

<s>— Dunque anche la luce è un corpo? </s>

<s>— Sembre­<lb></lb>rebbe di sì, risponde il Newton, giacchè ella si vede pure moversi <lb></lb>in tempo, com&#039;è dimostrato dagli ecclissi dei satelliti di Giove, e <lb></lb>viene altresì attratta dai corpi, com&#039;io stesso osservai nel fenomeno <lb></lb>grimaldiano. </s>

<s>Ma però di questo io non voglio disputare, solo io <pb xlink:href="020/01/240.jpg" pagenum="221"></pb>dimostro matematimente correre una grande analogia fra le traiet­<lb></lb>torie de&#039;minimi corpi gettati e attratti dai mezzi diafani. </s>

<s>“ Nihil <lb></lb>omnium disputans, sed traiectorias corporum traiectoriis radiorum <lb></lb>persimiles solummodo determinans ” (Principia etc. </s>

<s>ibi, pag. </s>

<s>541). </s></p><p type="main">

<s>E quanto al modo così controverso del diffondersi la luce nello <lb></lb>spazio? </s>

<s>— Riguardando il Newton la luce come un fluido qualunque, <lb></lb>col principio della repulsione molecolare ne spiegava l&#039;elasticità, <lb></lb>della quale il grado s&#039;argomentava per lui dal vederla correre tanto <lb></lb><figure id="id.020.01.240.1.jpg" xlink:href="020/01/240/1.jpg"></figure><lb></lb>veloce (Optices, quaest. </s>

<s>XXI). Così fatta elasticità, come l&#039;attrazione <lb></lb>verso i corpi taglienti e acuminati nel fenomeno grimaldiano, e le <lb></lb>traiettorie paraboliche descritte nel mezzo refringente dal raggio, <lb></lb>includevano senza dubbio l&#039;ipotesi della <emph type="italics"></emph>emissione.<emph.end type="italics"></emph.end> L&#039;Hook intanto <lb></lb>e l&#039;Huyghens professavano un&#039;ipotesi diversa, qual&#039;era quella delle <lb></lb>ondulazioni eteree. </s>

<s>Ebbene: come si governò il Newton in questo <lb></lb>negozio che era tanta parte del suo nuovo sistema ottico? </s>

<s>Trat­<lb></lb>tandosi di cosa, da non si poter decidere con gli esperimenti, la <lb></lb>lascia a trattar nelle <emph type="italics"></emph>Questioni.<emph.end type="italics"></emph.end> Confessava ivi che il fosfeno nel-<pb xlink:href="020/01/241.jpg" pagenum="222"></pb>l&#039;occhio compresso era molto favorevole all&#039;ipotesi delle onde eteree <lb></lb>(quaest. </s>

<s>XVI), ma poi nella Questione XXVIII promuove contro <lb></lb>quella stessa ipotesi alcune difficoltà, la principale delle quali è <lb></lb>questa: Se la luce si diffondesse in onde, come il suono, dovrebbe, <lb></lb>a somiglianza di questo, insinuarsi anco dietro gli ostacoli, come si <lb></lb>pruova del suono delle campane, che si sente anco al di là di un <lb></lb>monte “ At lumen nunquam compertum est vias incurvas ingredi, <lb></lb>nec sese in umbram inflectere (quest. </s>

<s>XXVIII). Volle forse perciò <lb></lb>il Newton asserir la verità di quel moto vibrante della luce, a cui <lb></lb>applicò i teoremi dimostrati in fine del suo I Libro dei <emph type="italics"></emph>Principii?<emph.end type="italics"></emph.end><lb></lb>Ecco quel che egli si contenta di dire, nella XXIX Questione: “ An <lb></lb>non radii luminis exigua sunt corpuscula a corporibus lucentibus <lb></lb>emissa? </s>

<s>” </s></p><p type="main">

<s>Parimenti intorno all&#039;origine e a&#039;fenomeni presentati dalla coda <lb></lb>delle comete, non ha appena il Newton accennato alla sua ipotesi, <lb></lb>che cioè sia quella coda una esalazione fumosa del corpo della stessa <lb></lb>cometa, respinta per circumpulsione dal centro del Sole, come i <lb></lb>nostri fumi si vedono esser respinti dal centro della Terra; che <lb></lb>egli tosto soggiunge: “ Ceterum rerum naturalium causas reddere <lb></lb>non est huius instituti ” (Opusc. </s>

<s>Lausannae 1744. T. II, pag. </s>

<s>58). </s></p><p type="main">

<s>Che poi il Newton prosegua veramente i metodi stessi di Ga­<lb></lb>lileo non vorremmo dedurlo dal citar ch&#039;ei fa il nome di lui così <lb></lb>spesso e con amore. </s>

<s>Quelle citazioni anzi rivelano che il Filosofo <lb></lb>inglese non attinse le dottrine del Nostro, alla loro sorgente. </s>

<s>Così <lb></lb>per esempio, dop&#039;avere stabilito, per prima legge del moto, l&#039;inerzia <lb></lb>della materia e gli effetti proporzionali alle forze motrici, col pa­<lb></lb>rallelogrammo delle forze posto per corollario di quelle stesse leggi, <lb></lb>soggiunge: “ per leges duas primas et corollaria duo primo, Galileus <lb></lb>invenit descensum gravium esse in duplicata ratione temporum. <lb></lb>(Principia, ibi, pag. </s>

<s>45). Ma Galileo tenne, in dimostrare quel teo­<lb></lb>rema, altri metodi. </s>

<s>Quello accennato ivi dal Newton è il metodo <lb></lb>dell&#039;Huyghens, da cui il Newton stesso par che attingesse le dot­<lb></lb>trine galileiane. </s>

<s>Vorremmo dire piuttosto che nel Professore di <lb></lb>Cambridge si trasfuse lo spirito del Professore di Padova, il quale <lb></lb>vi trovò gli organi più acconci al suo perfezionamento, e più adulte <lb></lb>ed esercitaie le membra. </s></p><p type="main">

<s>D&#039;onde avesse i primi aliti quello spirito, i nostri Lettori lo <lb></lb>sanno, e la Filosofia neutoniana segnalò la più compiuta vittoria, <lb></lb>che, sopra Aristotile, abbia conseguita Platone, sul campo della <lb></lb>scienza. </s>

<s>La Filosofia peripatetica, nuovamente apparita a sedurre <pb xlink:href="020/01/242.jpg" pagenum="223"></pb>gl&#039;ingegni con la lusinghiera eloquenza cartesiana, ebbe nel Newton <lb></lb>la sua piena sconfitta, quando nel suo Libro immortale dimostrò che <lb></lb>la Natura geometrizza veramente a modo platonico, e non fantastica <lb></lb>a modo aristotelico. </s>

<s>Che, nel dare a quel Libro il titolo di <emph type="italics"></emph>Prin­<lb></lb>cipia mathematica Philosophiae<emph.end type="italics"></emph.end> non pensasse il Filosofo inglese di <lb></lb>contrapporre, infino dal frontespizio, l&#039;opera sua dimostrata, e quel­<lb></lb>l&#039;altra immaginata dal Filosofo Bretone, con simil titolo di <emph type="italics"></emph>Prin­<lb></lb>cipia Philosophiae;<emph.end type="italics"></emph.end> non par credibile, benchè, senza rivolgersi nè a <lb></lb>destra nè a sinistra, l&#039;Autore della Nuova filosofia matematica pro­<lb></lb>ceda a diritto per la sua via. </s>

<s>Rogero Cotes però, in quel suo bel <lb></lb>Discorso premesso alla seconda edizione dei Principii neutoniani, <lb></lb>non tace del mal animo, con cui questi stessi Principii furon veduti <lb></lb>da&#039;seguaci del Cartesio, i quali sentivan pur troppo com&#039;esalasse da <lb></lb>quelle pagine uno spirito di verità, potente a cacciar via i nuvolosi <lb></lb>errori del loro Maestro. </s></p><p type="main">

<s>Dal Cartesio il Newton apprese l&#039;analisi, e va anzi debitore a <lb></lb>lui se riuscì a instituire il calcolo differenziale, e ad applicarlo così <lb></lb>utilmente alla Fisica sperimentale galileiana. </s>

<s>Giova infatti osservare <lb></lb>che il Calcolo differenziale ebbe origine dall&#039;applicar l&#039;Analisi car­<lb></lb>tesiana alla Geometria degli indivîsibili del Cavalieri, e perciò non <lb></lb>sarebbe il Newton, o il Leibniz che ne sia l&#039;Autore, potuto riuscir <lb></lb>felicemente a quella nuova istituzione, se il Cartesio non mostrava <lb></lb>come si potesse l&#039;Algebra comporre colla Geometria. </s></p><p type="main">

<s>L&#039;inspirazione poi del proprio genio, meglio che i pochi esempii <lb></lb>dell&#039;Huyghens, fu che fece presentire al Newton la fecondità del <lb></lb>metodo di comporre e decomporre le forze colla regola del parel­<lb></lb>logrammo insegnata dall&#039;Herigonio. </s>

<s>I discepoli di Galileo, fra&#039;quali <lb></lb>il Borelli, riputarono sventuratamente quella regola fallace, e là dove <lb></lb>avrebbero potuto procedere per via diretta e spedita a risolvere <lb></lb>astrusi problemi di Meccanica, s&#039;avvolsero spesso, come si mostrerà <lb></lb>per gli esempii a suo luogo, in incredibili paralogismi. </s>

<s>Ma il Newton, <lb></lb>con libero ingegno non preoccupato da pregiudizii di scuola, nè <lb></lb>soggiogato dall&#039;autorità di Galileo, riconobbe invece che quella re­<lb></lb>gola erigoniana era verissima, e sentenziò e dimostrò di fatto nel <lb></lb>corollario II alle leggi del moto premesse ai <emph type="italics"></emph>Principii matematici,<emph.end type="italics"></emph.end><lb></lb>che la regola prescritta dall&#039;Herigonio per comporre e decomporre <lb></lb>le forze <emph type="italics"></emph>abunde confirmatur ex Mechanica.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Così alle virtù ereditate da Galileo s&#039;aggiunsero, nel Filosofo <lb></lb>britanno, le tre nuove potenze enumerate, per cui s&#039;iniziò e si co­<lb></lb>stituì questo nuovo e così splendido Principato della scienza. </s>

<s>Prin-<pb xlink:href="020/01/243.jpg" pagenum="224"></pb>cipato glorioso, che il Newton conseguì felicemente senza troppo <lb></lb>dissipar le valide forze a difendersi contro i nemici, e senza tanto <lb></lb>arrovellarsi a riconquistar le proprie scoperte dagli arditi usurpa­<lb></lb>tori. </s>

<s>Qualche sua semplice lettera basta a far tacere il Cassegrain, <lb></lb>che pretendeva un diritto di anteriorità nell&#039;invenzione del canoc­<lb></lb>chiale catadiottrico, e un inciso, con cui cominciò lo scolio della <lb></lb>quarta proposizione del libro primo de&#039;<emph type="italics"></emph>Principii,<emph.end type="italics"></emph.end> parve assai a <lb></lb>sodisfare il Wrenn, l&#039;Hook e l&#039;Halley de&#039;pretesi meriti loro con­<lb></lb>cernenti la teoria delle forze centrali. </s></p><p type="main">

<s>Chi, dalle onorificenze tributate anche in vita al Newton, passa <lb></lb>a considerare le persecuzioni che ebbe anche dopo morte a patir <lb></lb>Galileo, o maledice arrabbiatamente alla malignità e all&#039;ingiustizia <lb></lb>degli uomini, o più rassegnato invoca un destino cieco distributore <lb></lb>a chi di sventure a chi di favori. </s>

<s>Noi crediamo invece che sia l&#039;uo­<lb></lb>mo stesso, il quale operando in un modo piuttosto che in un altro, <lb></lb>ora induce gli altri uomini a favorirlo, e ora al contrario gli pro­<lb></lb>voca a perseguitarlo. </s>

<s>Se anco il Newton, come Galileo, se la fosse <lb></lb>voluta prendere con quello e con questo, non gli sarebbero, senza <lb></lb>dubbio, in Inghilterra e nel secolo XVIII, mancate persecuzioni e <lb></lb>sventure. </s>

<s>Tutto altrimenti, egli aborriva dall&#039;attaccar brighe con <lb></lb>chicchessia, e per non aver che dire con l&#039;Hook, uomo litigioso, <lb></lb>tenne per tredici anni il celebre suo Trattato dell&#039;Ottica rinchiuso <lb></lb>e avvolto nel manoscritto. </s></p><p type="main">

<s>Pur troppo è vero che non è da fare il confronto fra Galileo, <lb></lb>che ebbe a fondare il suo Regno a mano armata, contro i Peripa­<lb></lb>tetici, e il Newton, che ricevè quel Regno di già stabilito, e che <lb></lb>non aveva bisogno d&#039;altro che d&#039;essere ampliato. </s>

<s>Pur troppo si <lb></lb>potrebbero dir tante altre cose, a intrigar piuttosto che a risolvere <lb></lb>la questione, e perciò, lasciando d&#039;investigar questi, che anche noi <lb></lb>chiameremo destini della vita o civile o morale, passeremo a veder <lb></lb>del Newton i principii e i progressi della vita intellettuale, e <lb></lb>qual&#039;efficace concorso v&#039;abbiano avuto le tradizioni scientifiche dei <lb></lb>nostri italiani. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>All&#039;entrar dell&#039;anno 1666 era in Cambridge tutto intento a <lb></lb>lavorare i vetri da canocchiali, studiandosi con ogni artificio di <lb></lb>configurarli in quella nuova foggia di superficie o paraboliche o <pb xlink:href="020/01/244.jpg" pagenum="225"></pb>iperboliche, le quali un&#039;antica tradizione veniva predicando per le <lb></lb>più accomodate a produr l&#039;effetto di avvalorare la virtù visiva, <lb></lb>nonostante che il laborioso esercizio fosse stato dimostrato inutile <lb></lb>dal Cavalieri. </s>

<s>Così, trattando i cristalli, venne voglia al Newton di <lb></lb>preparare uno di quei prismi triangolari, per dilettarsi nella pia­<lb></lb>cevole contemplazione degli svariati e splendidi colori. </s>

<s>Chiuse perciò <lb></lb>la finestra di camera e aperto un foro nell&#039;imposta, riceveva per <lb></lb>esso un raggio di sole, che, rifranto nel prisma, andava a dipingere <lb></lb>lo spettro colorato sopra una carta bianca. </s>

<s>Si sarebbe aspettato di <lb></lb>veder quello spettro dipinto in figura circolare com&#039;era il foro, e <lb></lb>trova con sua gran maraviglia che si distende invece allungato in <lb></lb>figura di una striscia, la quale, misurata diligentemente, riesce lunga <lb></lb>cinque tanti, presso a poco, quant&#039;ella è larga. </s>

<s>Ne osserva le due <lb></lb>estremità, e gli sembran terminare in un arco di cerchio. </s>

<s>Il raggio, <lb></lb>dunque, conclude, ha subito, attraversando il prisma, una disper­<lb></lb>sione, e ciò senza dubbio per essere alcune parti di quello stesso <lb></lb>raggio più refrangibili di alcune altre “ Unde patet veram imaginis <lb></lb>sic exporrectae causam hanc unam esse quod scilicet lux constat <lb></lb>ex radiis, quorum alii aliis magis refrangibiles sunt ” (Op. </s>

<s>omn. </s>

<s>opt. </s>

<s><lb></lb>Patavii 1773, App. </s>

<s>pag. </s>

<s>5). </s></p><p type="main">

<s>Il primo frutto che raccolse da questa scoperta, fu quello di <lb></lb>abbandonare ogni speranza di dover giungere alla desiderata per­<lb></lb>fezione del canocchiale diottrico, avendo ben conosciuto che, anco <lb></lb>quando fosse riuscito a trovar la figura del perfetto concorso, quel <lb></lb>concorso, nonostante, non avrebbe mai avuto il suo effetto, “ quia <lb></lb>lux ipsa est mixtura quaedam heterogenea composita ex radiis di­<lb></lb>versae refrangibilitatis. </s>

<s>” Il secondo frutto che si credette di poter <lb></lb>raccoglier l&#039;Autore dalla sua scoperta, fu quello di aver finalmente <lb></lb>riconosciuta l&#039;origine e le proprietà de&#039;colori. </s>

<s>Non son dunque i <lb></lb>colori, concludeva il Newton, qualificazioni della luce nate dalle <lb></lb>riflessioni o dalle rifrazioni de&#039;corpi naturali, come volgarmente si <lb></lb>crede, “ sed primigeniae et congenitae proprietates in diversis ra­<lb></lb>diis diversae. </s>

<s>Aliqui radii tantum ad rubrum, alii solum ad flavum, <lb></lb>alii ad viridem effingendum apti sunt ” (ibi, pag. </s>

<s>6). E nella seconda <lb></lb>Parte delle Lezioni Ottiche, riserbata a trattar di proposito <emph type="italics"></emph>De co­<lb></lb>lorum origine,<emph.end type="italics"></emph.end> accenna alle due principali ipotesi peripatetica e <lb></lb>cartesiana seguitate da tutti prima di lui, e mostra quanto fosser <lb></lb>lontane dalla verità delle cose. </s></p><p type="main">

<s>Che prima del Newton si seguisse in generale dagli Ottici <lb></lb>l&#039;ipotesi di Aristotile, secondo la quale i colori si generano da una <pb xlink:href="020/01/245.jpg" pagenum="226"></pb>proporzionata mistura d&#039;ombra e di luce, è vero, e fu quell&#039;ipotesi <lb></lb>accolta anche dagli Accademici del Cimento. </s>

<s>Il Viviani ha lasciato <lb></lb>fra&#039;suoi Manoscritti una schedula autografa, nella quale, assegnati <lb></lb>i due estremi del bianco e del nero, fa nascere il rosso dalla mi­<lb></lb>stura di sei gradi di bianco con uno di nero, il ranciato da cinque <lb></lb>gradi di bianco mescolato con due di nero, e così gradatamente <lb></lb>per tutti e sette i colori dello spettro. </s>

<s>Nonostante, anche prima del <lb></lb>Newton, si trovano in alcuni Autori italiani ipotesi nuove e più giu­<lb></lb>diziose e conformi ai fatti, delle antiche peripatetiche. </s>

<s>Il Maurolico, <lb></lb>per esempio, aveva, nel Teorema XVIII del primo libro <emph type="italics"></emph>Diapha­<lb></lb>norum,<emph.end type="italics"></emph.end> dimostrato l&#039;aberrazione di sfericità delle lenti, al qual teo­<lb></lb>rema, se avesse atteso il Newton, avrebbe lasciato assai prima di <lb></lb>travagliarsi intorno a&#039;canocchiali diottrici, e più per tempo si sa­<lb></lb>rebbe rivolto ai canoccbiali per riflessione. </s>

<s>Il Maurolico stesso, ri­<lb></lb>fiutando i placiti aristotelici, fu primo a dir che i colori avevano <lb></lb>origine dalla luce, la quale rifrangendosi, si trova in varie parti dello <lb></lb>spettro più o men costipata; dottrina insegnata pure dall&#039;Imperato <lb></lb>o dallo Stelliola, dodici anni prima che fosse nota al pubblico la <lb></lb>Diottrica del celebre Abate di Santa Maria in Porto. </s>

<s>E fù l&#039;Impe­<lb></lb>rato, che più di un mezzo secolo prima del Newton, quando il <lb></lb>prisma triangolare non serviva ad altro che alle piacevoli ricrea­<lb></lb>zioni, ei lo predicò <emph type="italics"></emph>strumento di refrazione all&#039;osservazione della <lb></lb>generazion dei colori tra gli altri tutti ottimo<emph.end type="italics"></emph.end> (Hist. </s>

<s>nat. </s>

<s>Venezia <lb></lb>1672, pag. </s>

<s>294). Le dottrine ottiche dei due nostri italiani furono <lb></lb>poi dal Bullialdo divulgate nella XXIX proposizione del suo celebre <lb></lb>Trattato <emph type="italics"></emph>De natura lucis,<emph.end type="italics"></emph.end> e più solennemente poi sanzionate dal <lb></lb>Grimaldi; dottrine ottiche, le quali, convenendo colle neutoniane <lb></lb>in professar che i colori non riseggan nei corpi e in dir che non <lb></lb>sian luce in potenza, come teneva il Keplero, ma che sian la luce <lb></lb>stessa in atto; ne differivan solo in ammettere una <emph type="italics"></emph>costipazione<emph.end type="italics"></emph.end><lb></lb>de&#039;raggi rifratti, invece di una <emph type="italics"></emph>dispersione.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La scoperta della dispersion della luce ne&#039;prismi triangolari, <lb></lb>e la
nuova teoria de&#039;colori che indi ne segue, furono pubblicate <lb></lb>dall&#039;Autore in una Epistola stampata prima in Cambridge e inse­<lb></lb>rita pochi anni dopo nel n. o 80 delle <emph type="italics"></emph>Transazioni filosofiche<emph.end type="italics"></emph.end> di <lb></lb>Londra, sotto il dì 19 Febbraio 1672. </s><s>Appena furon divulgate le <lb></lb>nuove dottrine, il gesuita Ignazio Pardies si mosse incontro ad <lb></lb>oppugnarle, dicendo che l&#039;allungamento dello spettro colorato non <lb></lb>dipendeva da una dispersione per via del vario grado di refrangi­<lb></lb>bilità del raggio composto, come voleva il Newton, ma avveniva per <pb xlink:href="020/01/246.jpg" pagenum="227"></pb>un fenomeno somigliantissimo a quello osservato già e descritto nel <lb></lb>Trattato <emph type="italics"></emph>De Lumine<emph.end type="italics"></emph.end> dal Grimaldi. </s>

<s>Ecco annunziarsi il titolo di un <lb></lb>libro, ecco pronunziarsi il nome di un Italiano, a cui il Filosofo <lb></lb>inglese va debitore della sua gloria. </s>

<s>Così i voli sublimi distesi pel <lb></lb>grandissimo mondo, come le sottili penetrazioni addentro alle chiuse <lb></lb>e buie regioni del piccolissimo, ebbero occasione dal rimeditar che <lb></lb>fece il Newton le pagine di quel libro. </s></p><p type="main">

<s>Veniva insomma il Pardies, operando i soliti benefici effetti di <lb></lb>tutti gli oppositori, a far provvidamente capitare a Cambridge il <lb></lb>Trattato <emph type="italics"></emph>De Lumine<emph.end type="italics"></emph.end> stampato in Bologna, e colui che sentiva con­<lb></lb>trapporre alle sue nuove, altre nuove scoperte annunziate in quel <lb></lb>Trattato, non poteva non ricercarvele dentro avidamente. </s>

<s>Legge alla <lb></lb>prima apertura del Volume che l&#039;Autore, oltre alle riflessioni e alle <lb></lb>rifrazioni, ammette nella luce una terza passione, che egli appella <lb></lb>col nome nuovo di <emph type="italics"></emph>diffrazione.<emph.end type="italics"></emph.end> Tutto attento ha il pensiero sopra <lb></lb>i due esperimenti ivi descritti a dimostrare in che modo un raggio <lb></lb>luminoso, che rasenta gli orli di un corpo opaco, vi si diffrange. </s>

<s><lb></lb>Ripete in altra maniera l&#039;esperimento, e trova che di fatto l&#039;ombre <lb></lb>riescon sempre alquanto maggiori di quel che se il raggio proce­<lb></lb>desse a diritto. </s>

<s>Non ci è dubbio dunque: ei si diffrange. </s>

<s>Ma qual&#039;è <lb></lb>la causa di quella diffrazione? </s>

<s>Il Grimaldi, contento a descrivere <lb></lb>il fatto, non lo dice: la risposta data da altri interrogati in propo­<lb></lb>sito, che cioè risegga la causa del fenomeno nelle solite rifrazioni <lb></lb>dell&#039;aria, non sodisfa il sagace investigatore. </s>

<s>Gli balena alla mente <lb></lb>un pensiero ardito: che il raggio si diffranga perchè è attratto dagli <lb></lb>orli taglienti del corpo opaco interposto? </s>

<s>“ Annon corpora agunt <lb></lb>in lumen interiecto aliquo intervallo, suaque illa actione radios eius <lb></lb>inflectunt? </s>

<s>” (Optices, Lib. </s>

<s>III, quaest. </s>

<s>I). </s></p><p type="main">

<s>L&#039;ardita ipotesi però supponeva risoluta già la gran questione <lb></lb>della natura della luce, se cioè essa sia corporea e soggetta alle <lb></lb>passioni stesse degli altri corpi ponderosi. </s>

<s>La legge delle rifrazioni <lb></lb>conclusa dalla meccanica, specialmente in Italia, dai più si ripu­<lb></lb>diava, e, per tante prove fatte, non s&#039;era ancora riusciti ad assi­<lb></lb>curarsi se un raggio luminoso si muove in tempo o si diffonde in <lb></lb>istante. </s>

<s>Il Grimaldi però tenne per risoluta la gran questione, e <lb></lb>posto per cosa certa che fosse anche la luce un corpo come tutti <lb></lb>gli altri, ammise, anteriormente a qualunque dimostrazione speri­<lb></lb>mentale, che ella si movesse in tempo. </s>

<s>Applicando poi al moto di <lb></lb>lei la legge della velocità in ragion reciproca delle sezioni, come <lb></lb>segue nel moto di tutti i fluidi, riuscì a concludere, in modo sicuro, <pb xlink:href="020/01/247.jpg" pagenum="228"></pb>che i seni degli angoli d&#039;incidenza hanno ragion costante co&#039;seni <lb></lb>degli angoli di refrazione. </s></p><p type="main">

<s>L&#039;esempio del Grimaldi e la felice scoperta del Roemer per­<lb></lb>suasero il Newton della natura corporea della luce, il quale anzi <lb></lb>tanto oltre andò, che, ammettendo un nucleo duro in tutte le par­<lb></lb>ticelle componenti ogni sorta di corpi, non dubitò di soggiungere: <lb></lb>“ quin et ipsi etiam radii luminis corpora dura esse videntur ” (ibi, <lb></lb>quaest. </s>

<s>XXXI). E mentre i discepoli di Galileo avevano adombrato <lb></lb>e recalcitrato contro la Meccanica ottica del Cartesio e dell&#039;Heri­<lb></lb>gonio, egli incomincia i suoi studii sopra la luce, applicando alla <lb></lb>stessa, nella Sez. </s>

<s>XIV del I Libro de&#039;<emph type="italics"></emph>Principii,<emph.end type="italics"></emph.end> le proprietà delle <lb></lb>traiettorie paraboliche, che Galileo avea dimostrato venir descritte <lb></lb>da tutti i corpi gravi proietti. </s></p><p type="main">

<s>Ma sia pure la luce un corpo duro, s&#039;ammetta pur possibile <lb></lb>che la diffrazione avvenga perchè le molecole dure della luce ven­<lb></lb>gono attratte dalle molecole dure che circondan gli orli del foro <lb></lb>nel fenomeno grimaldiano: con quali argomenti si possono dimo­<lb></lb>strare o si possono almeno render credibili queste cose tanto lon­<lb></lb>tane dalla comune opinione? </s></p><p type="main">

<s>Ecco aprirsi di qui la via a nuove e peregrine speculazioni, <lb></lb>dalle quali sarebbe per esser promossa tant&#039;oltre la scienza nel <lb></lb>secolo XVIII. Galileo, nel Discorso intorno alle galleggianti, non <lb></lb>pensando alle pressioni idrostatiche, dalle quali si sostengono alla <lb></lb>superficie le tavolette di gravità specifica maggiore dell&#039;acqua, si <lb></lb>ridusse ad ammettere una specie di attrazione fra l&#039;aria e la su­<lb></lb>perficie solida del galleggiante. </s>

<s>E di li passò a specular la ragione <lb></lb>di quella copula, che tiene unite insieme le minime particelle dei <lb></lb>corpi, attribuendola a una indefinita virtù calamitica del contatto, <lb></lb><emph type="italics"></emph>senza interposizione alcuna di fluidi cedenti<emph.end type="italics"></emph.end> (Alb. </s>

<s>XII, 54). Per­<lb></lb>suaso poi, dalle opposizioni giustissime che gli furon fatte, dell&#039;in­<lb></lb>sufficienza e anzi della falsità del suo principio, negò nel Saggiatore <lb></lb>(Alb. </s>

<s>IV. 299) quella virtù dell&#039;attrazione calamitica dell&#039;aria che <lb></lb>aveva prima ammessa come causa del sostenersi le tavolette d&#039;ebano, <lb></lb>non bagnate, sulla superficie dell&#039;acqua, e finalmente, nel I Dialogo <lb></lb>dello Due Nuove Scienze, tornato a specular sul fatto dell&#039;adesione <lb></lb>di due marmi venuti fra loro a squisito contatto, e sulla virtù co­<lb></lb>pulatrice della materia, non dubitò di riconoscer nella forza del <lb></lb>vacuo la causa generalissima di questo effetto (Alb. </s>

<s>XIII. pag. </s>

<s>22, 23). </s></p><p type="main">

<s>Quando poi al vacuo si sostituì la pressione ammosferica, oc­<lb></lb>corse in tal proposito un fatto singolare nella storia delle scienze. <pb xlink:href="020/01/248.jpg" pagenum="229"></pb>Il Boyle aveva sottoposto alla campana della sua macchina pneu­<lb></lb>matica uno strumento simile al termometro ad aria, se non che <lb></lb>tutto, cannello e bulbo, era pieno di acqua sostenuta, come si sa, <lb></lb>dalla pressione dell&#039;aria sulla superficie del liquido, dentro a cui <lb></lb>il cannello stesso, con la sua bocca, era immerso. </s>

<s>Fatto perciò il <lb></lb>vuoto, se questo fosse riuscito assoluto, la caraffella piena d&#039;acqua <lb></lb>si sarebbe dovuta votare affatto. </s>

<s>Ma perchè qualche poco di liquido <lb></lb>seguitava ancora a sostenersi a mezzo il cannello, il Boyle diceva <lb></lb>avvenir ciò perchè è impossibile colla macchina estrar tutta l&#039;aria, <lb></lb>e farvi sotto la campana il vuoto perfetto. </s></p><p type="main">

<s>Venne voglia all&#039;Huyghens di ripetere l&#039;esperienza boileiana, <lb></lb>e trovò che il caso descritto dall&#039;Autore non si avverava se non che <lb></lb>quando l&#039;acqua tien dentro a sè sciolta qualche particella d&#039;aria. </s>

<s><lb></lb>Sperimentando coll&#039;acqua bollita, anco fatto il vuoto, vide con sua <lb></lb>gran maraviglia che la caraffella seguitava tuttavia a rimaner piena. </s>

<s><lb></lb>Divulgato il fatto, non gli si voleva credere, per cui l&#039;Huyghens <lb></lb>stesso nel 1663, indusse la Società Reale di Londra a ripetere so­<lb></lb>lennemente l&#039;esperienza. </s>

<s>V&#039;era fra gli altri presente lo stesso Boyle, <lb></lb>sorpreso da tanto stupore, a veder davvero la caraffella rimaner <lb></lb>piena, che quasi non credeva a&#039;suoi proprii occhi. </s>

<s>Volle che ivi, <lb></lb>prima di sciogliere l&#039;Adunanza, fosse fatta l&#039;esperienza col mercurio <lb></lb>nel consueto strumento torricelliano di cannello assai stretto, e si <lb></lb>vide il liquido, solido ridursi ai 27 e 28 pollici, rimaner sostenuto <lb></lb>a 52 e talvolta anco infino a 75. </s></p><p type="main">

<s>A spiegar questo e altri simili fatti straordinari, fra&#039;quali quello <lb></lb>di due lastre di vetro che seguitano ad aderire nel vuoto, l&#039;Huy­<lb></lb>ghens, ne&#039;suoi <emph type="italics"></emph>Esperimenti fisici,<emph.end type="italics"></emph.end> si ridusse ad ammetter che sotto <lb></lb>la campana della macchina pneumatica, estratta l&#039;aria, rimanesse <lb></lb>un corpo più ponderoso di lei, l&#039;etere, causa straordinaria di quegli <lb></lb>effetti (Opera Varia, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>769-76). </s></p><p type="main">

<s>Era dunque il Newton sopra pensiero di trovare argomenti, <lb></lb>onde render probabile, se non dimostrata la reciproca attrazione <lb></lb>fra le minime particelle de&#039;corpi, e applicarla a spiegare i fatti <lb></lb>della diffrazion della luce, da lui stesso confermati con nuovi espe­<lb></lb>rimenti; quando gli occorse di tornar sopra con maggiore atten­<lb></lb>zione all&#039;esperienza ugeniana ora narrata, e sopra l&#039;ipotesi imma­<lb></lb>ginata per ispiegarla. </s>

<s>Quell&#039;ipotesi dell&#039;etere ponderoso, che riman <lb></lb>dopo estratta l&#039;aria, era merce introdotta dal Cartesio antivacuista, <lb></lb>e l&#039;Huyghens la gabellò perchè favoriva le teorie, che insiem con <lb></lb>l&#039;Hook professava intorno alla luce. </s>

<s>Al Newton però a cui l&#039;ipotesi <pb xlink:href="020/01/249.jpg" pagenum="230"></pb>dell&#039;etere ponderante sapeva dell&#039;immaginario, venne in pensiero <lb></lb>che il sostenersi i liquidi ne&#039;cannelli stretti sopra il naturale livello <lb></lb>dipendesse piuttosto da quella attrazion molecolare, di cui andava <lb></lb>sagacemente investigando argomenti, che servissero di prova spe­<lb></lb>rimentale. </s></p><p type="main">

<s>E non questi fatti soli, ma tutta la serie percorse dei così detti <lb></lb>fenomeni capillari, che ritrovaron tutti la loro adeguata ragione <lb></lb>nell&#039;attrarsi vicendevolmente le molecole fra solidi e liquidi. </s>

<s>Lo <lb></lb>stesso agglomerarsi delle minime gocciole dell&#039;acqua, o campate <lb></lb>libere in aria o posate sopra superficie a cui il liquido non aderisce, <lb></lb>servì al Newton di valido argomento a dimostrar l&#039;effetto dell&#039;at­<lb></lb>trazione molecolare prevalente intorno al centro di figura. </s>

<s>Niccolò <lb></lb>Aggiunti aveva introdotto un <emph type="italics"></emph>moto occulto<emph.end type="italics"></emph.end> dell&#039;acqua, senza però <lb></lb>determinare la natura di questo moto. </s>

<s>Donato Rossetti era già ri­<lb></lb>corso a un <emph type="italics"></emph>istinto di appetenza,<emph.end type="italics"></emph.end> col quale felicemente spiegava <lb></lb>alcuni fatti de&#039;più singolari, ma il Filosofo inglese generalizzò la <lb></lb>teoria delle forze attrattive molecolari e la rendè compiuta colla <lb></lb>dualità contrapposta delle repulsioni “ Et sicut in algebra ubi quan­<lb></lb>titates affermativae evanescunt et desinunt, ibi negativae incipiunt; <lb></lb>ita in mechanicis ubi attractio desinit, ibi vis repellens succedere <lb></lb>debet ” (Optices, Lib. </s>

<s>III, quaest. </s>

<s>XXXI). D&#039;onde, soggiunge il <lb></lb>Newton, ne conseguitano gli effetti della emission della luce e la <lb></lb>risoluzione de&#039;corpi solidi in sostanze aerose e in vapori, impe­<lb></lb>rocchè le particelle de&#039;corpi, distratte o dalla forza del calore o <lb></lb>dalla agitazione intestina delle fermentazioni, tosto che sono uscite <lb></lb>dalla sfera dell&#039;attrazione del loro centro, se ne dilungano con <lb></lb>grand&#039;impeto, e rifuggono di tornarci di nuovo. </s>

<s>Così produconsi <lb></lb>quelle violente espansioni, che si vedono in tante volgari esperienze, <lb></lb>parendo impossibile che sia contratta in un granello di polvere <lb></lb>quell&#039;aria, che s&#039;espande in un volume centinaia e migliaia di volte <lb></lb>maggiore. </s>

<s>“ Quae tam ingens contractio et expansio animo sane <lb></lb>concipi vix potest, si particolae aeris fingantur elasticae et ramosae, <lb></lb>vel viminum lentorum intra se in circulos intortorum instar esse, <lb></lb>vel ulla alia ratione, nisi ita si vim repellentem habent, qua a se <lb></lb>mutuo fugiant ” (ibi). </s></p><p type="main">

<s>Da queste immortali pagine neutoniane si sente alitare uno <lb></lb>spirito nuovo che vivifica; si vede aprirsi un chiarore di luce che <lb></lb>rallegra l&#039;intelletto offuscato dalla nebbia cartesiana. </s>

<s>Anche nella <lb></lb>scienza del mondo dei piccolissimi, sopra Aristotile, trionfa Platone: <lb></lb>alle finzioni peripatetiche sottentra la legge matematica. </s>

<s>E perchè <pb xlink:href="020/01/250.jpg" pagenum="231"></pb>il mondo dei piccolissimi riconosce il medesimo Autore, e soggiace <lb></lb>alle medesime leggi del Mondo dei grandissimi, ecco uscire le spe­<lb></lb>culazioni del Newton dalle angustie che intercedono fra un atomo <lb></lb>e l&#039;altro, e risalir con ardito volo per gli spazii smisurati del cielo. <lb></lb></s>

<s>“ Atque haec quidem omnia si ita sint, iam Natura universa valde <lb></lb>erit simplex et consimilis sui: perficiens nimirum magnos omnes <lb></lb>corporum coelestium motus attractione gravitatis, quae est multa <lb></lb>inter corpora illa omnia, et minores fere omnes particularum sua­<lb></lb>rum motus alia aliqua vi attrahente et repellente, quae est inter <lb></lb>particulas illas mutuas ” (ibi). </s></p><p type="main">

<s>Ecco il discepolo di Platone e di Galileo, che nella semplicità <lb></lb>degli ordini matematici ritrova le leggi universali della natura, fa­<lb></lb>ticosamente cercate da Aristotile e dal Cartesio nell&#039;arguzie de&#039;loro <lb></lb>cervelli. </s>

<s>Gian Alfonso Borelli aveva impresse larghe e profonde <lb></lb>orme per quella via platonica, la quale fu anzi prima aperta da <lb></lb>lui, introducendo la matematica semplicità delle forze centrali. </s>

<s>Ma <lb></lb>poi, sedotto dall&#039;autorità del Keplero, si dette a fantasticare pue­<lb></lb>rilmente intorno ai pianeti galleggianti nell&#039;etere, e non seppe sco­<lb></lb>prire il gran paralogismo che commetteva l&#039;Astronomo alemanno, <lb></lb>quando concludeva che l&#039;intensità della luce, al diffondersi della <lb></lb>quale si rassomigliava il diffondersi delle forze impulsive del sole; <lb></lb>scemasse a proporzione che crescono le semplici distanze. </s>

<s>E tanto <lb></lb>fu sottile l&#039;inganno, che vi rimase colto anche il Newton, quando <lb></lb>la prima volta istitui il calcolo della velocità, con cui sarebbe ca­<lb></lb>duta la Luna, se fosse veramente attratta, com&#039;ei supponeva, al <lb></lb>centro della Terra. </s></p><p type="main">

<s>Il Bullialdo, procedendo conforme alle vere regole della Foto­<lb></lb>metria, s&#039;era maravigliato grandemente dell&#039;errore, in che vedeva <lb></lb>essere incorso il Keplero, e aveva concluso che la luce decresce in <lb></lb>intensità, non a proporzione che crescono le semplici distanze, ma <lb></lb>i quadrati delle distanze. </s>

<s>E ciò dette occasione all&#039;Hook e all&#039;Halley <lb></lb>d&#039;applicar la medesima legge al decrescer l&#039;intensità delle forze <lb></lb>attrattive. </s>

<s>Pervenuta quella notizia alle orecchie del Newton, gli <lb></lb>parve la nuova legge assai ragionevole, e tornato ad applicarla al <lb></lb>calcolo della velocità, con cui sarebbe verso noi caduta la Luna, <lb></lb>trovò che quello stesso calcolo rispondeva esattamente all&#039;ipotesi <lb></lb>dell&#039;attrazione. </s>

<s>Applicato poi ed esteso, dalla Luna a tutti gli altri <lb></lb>sistemi, quel principio dell&#039;attrazione divenne universale. </s>

<s>Per ultimo <lb></lb>suggello, che la semplicità e uniformità della legge scoperta era <lb></lb>conforme alla verità delle cose, il Newton applicò quel principio <pb xlink:href="020/01/251.jpg" pagenum="232"></pb>alla teoria delle comete, alla precessione degli equinozii, alla nu­<lb></lb>tazione de&#039;poli, al flusso e riflusso del mare, a spiegare insomma <lb></lb>i più astrusi e reconditi misteri. </s></p><p type="main">

<s>Porre il flusso marino nel numero de&#039;più astrusi misteri, non <lb></lb>parrà alieno dal vero a chi ripensi quanto sottilmente vi stillassero <lb></lb>attorno il cervello i filosofi, da Aristotile a Galileo, e come tutti <lb></lb>rimanessero lontani dal coglier nel segno. </s>

<s>Non sentenzierebbe però <lb></lb>in conformità del vero storico colui, che volesse ancora seguitare <lb></lb>a dire essere stato il Newton il primo a risolvere l&#039;astruso pro­<lb></lb>blema col principio universale dell&#039;attrazione. </s>

<s>Era infino dal 1624 <lb></lb>apparita in Roma alla luce una Dissertazione di poche pagine, che <lb></lb>portava in fronte il titolo di <emph type="italics"></emph>Euripus,<emph.end type="italics"></emph.end> e sottoscritto il nome di un <lb></lb>Autore, appellato dal Newton stesso ad altro proposito <emph type="italics"></emph>Vir celeber­<lb></lb>rimus.<emph.end type="italics"></emph.end> Quell&#039;Autore è Marcantonio De Dominis, Arcivescovo di Spa­<lb></lb>latro, è quel <emph type="italics"></emph>certo prelato,<emph.end type="italics"></emph.end> di cui parla Galileo nella IV Giornata <lb></lb>de&#039;Due Massimi Sistemi. </s>

<s>L&#039;aver ivi taciuto il nome dell&#039;uomo <lb></lb>celeberrimo, e l&#039;aver commesso di parlarne e di darne giudizio a <lb></lb>Simplicio, sarebbe segno di disprezzo, se non è piuttosto una scusa <lb></lb>dell&#039;esser temerariamente entrato a sentenziare di una dottrina, <lb></lb>senza aver letto colla debita attenzione il libro. </s>

<s>Che quel Simplicio <lb></lb>galileiano infatti non abbia veramente letto l&#039;<emph type="italics"></emph>Euripus<emph.end type="italics"></emph.end> dello Spala­<lb></lb>trese, par chiaro dall&#039;apporgli un errore, che non si trova a parer <lb></lb>nostro in nessuna parte di quel Trattato, ed è che, la Luna abbia <lb></lb>potere d&#039;attrar l&#039;acqua marina agli antipodi, <emph type="italics"></emph>per aver ella possanza <lb></lb>di conferire una tal facoltà a quel grado del zodiaco che gli è <lb></lb>opposto<emph.end type="italics"></emph.end> (Alb. </s>

<s>I, 458). </s></p><p type="main">

<s>Il Newton che pure, a proposito dell&#039;Iride celeste, citava il <lb></lb>Trattato <emph type="italics"></emph>De radiis visus et lucis<emph.end type="italics"></emph.end> senz&#039;averlo letto, è probabilissimo <lb></lb>che non vedesse del nostro Autore nemmen questa <emph type="italics"></emph>Sentenza<emph.end type="italics"></emph.end> sul <lb></lb>flusso marino, ma è mirabile in ogni modo, il riscontro che è fra <lb></lb>le dottrine del Filosofo inglese e quelle stesse che il nostro Dalmata <lb></lb>professava un mezzo secolo avanti. </s>

<s>L&#039;intumescenza e delumescenza <lb></lb>dell&#039;acqua marina non è per lui, come da molti si diceva, un ef­<lb></lb>fetto di condensazione o di rarefazione “ Sed vere fieri motu locali <lb></lb>aquae, eiusque a loco ad locum vera confluentia et refluentia ” <lb></lb>(Euripus, Romae, 1624, pag. </s>

<s>10). Il quale effetto non è dal calore <lb></lb>del sole, ma dalle due virtù insieme congiunte del Sole e della <lb></lb>Luna, i quali due corpi celesti attraggon con varia intensità l&#039;acqua <lb></lb>marina, a quel modo che il magnete attrae a sè il ferro, e, se non <lb></lb>gli si congiunge con immediato contatto, par che pure lo renda <pb xlink:href="020/01/252.jpg" pagenum="233"></pb>più leggero. </s>

<s>“ Si enim Magnes, hoc est terra quaedam crassa et <lb></lb>rudis, mirabili illa sua vi naturali et qualitate non occulta, sed <lb></lb>quoad effectum omnibus manifestissima, trahit ad se ferrum ex una <lb></lb>parte, ex alia vero opposita id a se propellit et amovet; cur ali­<lb></lb>quid simile esse in coelestibus illis corporibus multo nobilioribus, <lb></lb>et efficacioribus negabimus? </s>

<s>” (ibi, pag. </s>

<s>4). Da ciò ne segue che <lb></lb>concorrendo insieme il Sole e la Luna a produr l&#039;effetto, benchè <lb></lb>questa sia assai più efficace e potente di quello, l&#039;effetto stesso <lb></lb>varierà al variar gli aspetti de&#039;due astri, secondoche, cioè, la Luna <lb></lb>sarà in congiunzione col Sole o nell&#039;opposizione o nelle quadrature. <lb></lb></s>

<s>“ Cum enim non sola Luna sed etiam Sol, pro suo modulo, suum <lb></lb>culmen, licet minorem efficiat, ex diversis aspectibus, qui sunt inter <lb></lb>solem et lunam, maior et minor fieri debet fluxus et refluxus ” <lb></lb>(ibi, pag. </s>

<s>59). </s></p><p type="main">

<s>Dir che il De Dominis risolva il problema, con quella sicurtà <lb></lb>e con quella pienezza che lo risolve il Newton, sarebbe troppo pre­<lb></lb>tendere. </s>

<s>Lo Spalatrese attribuisce l&#039;intumescenza marina a una <lb></lb>forza attrattiva, simile a quella che si vede operar nel Magnete, <lb></lb>ma di una tal forza non conosce la legge, e perciò, fatto certo <lb></lb>dall&#039;esperienze che nel produr l&#039;effetto la Luna è più potente, non <lb></lb>sa veder di ciò la ragione in altro, che in una simpatia per gli <lb></lb>umidi maggior in lei che nel Sole. </s>

<s>“ Luna enim habet longe ma­<lb></lb>iorem sympathiam cum humidis quam Sol ” (ibi, pag. </s>

<s>10). Questo <lb></lb>è senza dubbio un ridursi ai peripatetici alloggiamenti, ma è del <lb></lb>resto, dal nostro Autore, il flusso e riflusso marino esaminato con <lb></lb>tanta diligenza, e i molteplici casi dispersi ridotti con tanta potenza <lb></lb>di raziocinio a trovar la loro spiegazione in una causa generale e <lb></lb>suprema; che se si fossero degnati di leggere queste cose Galileo <lb></lb>e il Newton ne dovrebbero esser rimasti ammirati, e avrebbero <lb></lb>così tramandato ai posteri la memoria di un Libro, che meritava <lb></lb>di superar la fama di suo fratello, essendo il De Dominis proceduto <lb></lb>per la più diritta via in investigar la causa del flusso del mare, <lb></lb>che non quella della vista e dell&#039;arco baleno. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;Huyghens disegnò maestrevolmente, in brevi tratti, nel II Li­<lb></lb>bro del suo <emph type="italics"></emph>Cosmoteoro<emph.end type="italics"></emph.end> i progressi storici della Meccanica celeste. </s>

<s><lb></lb>Plutarco, nel suo Libro <emph type="italics"></emph>De facie in orbe Lunae,<emph.end type="italics"></emph.end> aveva detto che <pb xlink:href="020/01/253.jpg" pagenum="234"></pb>la Luna riman sospesa nello spazio, per l&#039;equilibrio della sua forza <lb></lb>di circolazione con quello di gravità; dottrina che fu seguita poi <lb></lb>dal Borelli, e applicata al moto di tutti i satelliti, e di tutti i pia­<lb></lb>neti. </s>

<s>Il Newton dimostrò matematicamente le leggi di que&#039;moti, e <lb></lb>fece veder che i fatti osservati dal Keplero erano una conseguenza <lb></lb>immediata di quelle leggi. </s>

<s>Io poi, soggiunge l&#039;Huyghens, immaginai <lb></lb>un ipotesi, da investigar la prima causa e i primi impulsi de&#039;moti <lb></lb>planetari, per via de&#039;vortici eterei, che son tutt&#039;altra cosa da quelli <lb></lb>cartesiani. </s>

<s>Anzi, io mi maraviglio, come mai il Filosofo bretone <lb></lb>possa avere sciupato il suo tempo in dare assetto a quelle sue <lb></lb>strane finzioni “ De planetarum et mundi origine commentatio <lb></lb>apud Cartesium tam levibus rationibus contexta est, ut saepe mirer <lb></lb>tantum operae in talibus concinnandis figmentis eum impendere <lb></lb>potuisse ” (Op. </s>

<s>varia, Lugd. </s>

<s>1724, pag. </s>

<s>721). La grande Opera dei <lb></lb>Principii matematici della Filosofia Naturale dissipò quel fantastico <lb></lb>edifizio cartesiano, e posò la Nuova Astronomia sopra i suoi più <lb></lb>solidi fondamenti. </s>

<s>Tutto il mistero dei Grandissimi fu allora svelato <lb></lb>dal Filosofo inglese, e i posteri non hanno fatto altro che confer­<lb></lb>mare quelle scoperte, e ampliarle nell&#039;Astronomia fisica o nella <lb></lb>Uranografia, di cui il merito è dovuto principalmente a quella per­<lb></lb>fezione, a che l&#039;arte, meglio che la scienza, ha saputo condurre i <lb></lb>canocchiali. </s></p><p type="main">

<s>Ma il Newton, come da noi s&#039;accennava di sopra, aveva prima <lb></lb>scoperto il mondo dei Piccolissimi, intorno a che il Cartesio e il <lb></lb>Gassendo eran venuti a gara delle più sottili e stravaganti finzioni. </s>

<s><lb></lb>Così fatte finzioni son quelle stesse, che illudevano il grande in­<lb></lb>gegno del Borelli, quando, per esempio, a spiegar gli effetti di <lb></lb>capillarità, da lui stesso scoperti ne&#039;corpiccioli galleggianti, im­<lb></lb>maginava quella lanugine e que&#039;cigli flessibili, con cui, sù per le <lb></lb>asperità de&#039;corpi solidi attaccandosi, potessero risalir sul naturale <lb></lb>livello le minime particelle dell&#039;acqua. </s>

<s>Il Newton, come fece pel <lb></lb>Mondo dei Grandissimi, disperse anco quest&#039;altre filosofiche finzioni, <lb></lb>introducendo il principio delle forze molecolari. </s>

<s>A ciò fare egli <lb></lb>attese in quelle celebri Questioni, che, ridotte al numero di XXXI, <lb></lb>nella seconda edizione dell&#039;Ottica, appose in fine del suo Trattato. </s>

<s><lb></lb>Tali Questioni, benchè possano essere facilmente sfuggite, per il <lb></lb>modesto luogo che fu loro assegnato e per l&#039;umile veste, alla debita <lb></lb>estimazione dei dotti, hanno nulladimeno tutta l&#039;importanza, ch&#039;ebbe <lb></lb>la grande Opera de&#039;<emph type="italics"></emph>Principii.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>A noi piace di rassomigliare i due libri del Filosofo inglese <pb xlink:href="020/01/254.jpg" pagenum="235"></pb>a&#039;due strati estremi di una profonda acqua corrente. </s>

<s>Quello dei <lb></lb>Principii della Filosofia, in cui le leggi del Grandissimo Mondo si <lb></lb>risolvono nell&#039;unico principio delle forze centrali, rappresenta lo <lb></lb>strato più alto, e più largamente visibile della corrente; quell&#039;altro, <lb></lb>che è il libro delle <emph type="italics"></emph>Questioni,<emph.end type="italics"></emph.end> e in cui le leggi del Piccolissimo <lb></lb>Mondo si risolvono nell&#039;unico principio delle forze molecolari, rap­<lb></lb>presenta lo strato più basso, e men visibile della medesima corrente. </s>

<s><lb></lb>Questo strato, quasi soffrisse la compressione de&#039;soprastanti, con­<lb></lb>tiene in sè strettamente condensate e contratte le nuove parti di <lb></lb>scienza sperimentale, che si videro svolgere e fluire nel secolo XVIII. <lb></lb>Anzi, come gli strati intermedii delle acque correnti son rapiti e <lb></lb>accelerati per la comunicazione del moto de&#039;due strati estremi; <lb></lb>così da que&#039;due strati estremi de&#039;Principii neutoniani e delle Que­<lb></lb>stioni, in mezzo a cui corre, vien rapita e accelerata, in questo <lb></lb>nuovo tratto de&#039;suoi progressi, la larga e alto sonante fiumana della <lb></lb>Scienza. </s></p><p type="main">

<s>Gran parte della scienza sperimentale, che si volge e corre giu <lb></lb>per questa fiumana, è, per la nobiltà sua propria e per l&#039;impor­<lb></lb>tanza e l&#039;utilità delle applicazioni, l&#039;Idraulica. </s>

<s>Il potente impulso, <lb></lb>che ella ricevette nella scuola galileiana per opera del Guglielmini, <lb></lb>era per se sufficiente a promuoverla ne&#039;suoi progressi, senz&#039;altri <lb></lb>estrinseci aiuti; nonostante risentì anch&#039;essa i benefici influssi delle <lb></lb>dottrine neutoniane, influssi, che si posson rassomigliare a quel­<lb></lb>l&#039;aura di vento, che, secondando il moto della corrente, giova a <lb></lb>velocitare la piena di un fiume. </s></p><p type="main">

<s>Giovan Domenico Guglielmini, già l&#039;abbiamo accennato, ap­<lb></lb>partiene alla scuola galileiana, nella quale fu allevato dal Montanari, <lb></lb>discepolo del Borelli. </s>

<s>Egli aveva già, il Guglielmini, in sul finir del <lb></lb>secolo XVII, diffuso in Bologna il suo magistero ne&#039;varii ordini <lb></lb>delle scienze sperimentali, quand&#039;ancora il sole della nuova Filo­<lb></lb>sofia inglese non era apparito sul nostro orizzonte. </s>

<s>Il Guglielmini <lb></lb>perciò appartiene al periodo storico precedente, e in quella parte <lb></lb>del Dramma si svolge la sua azione, ond&#039;è che tutt&#039;altro che ricever <lb></lb>beneficio all&#039;ingegno dalle nuove dottrine neutoniane, è ragionevole <lb></lb>pensar che il Newton stesso s&#039;ispirasse in parte alle speculazioni di <lb></lb>lui, e se ne giovasse nelle aggiunte alle succissive impressioni dei <lb></lb>suoi libri. </s>

<s>Senz&#039;ammetter ciò, non si potrebbero attribuire ad altro <lb></lb>che al caso que&#039;mirabili riscontri, che si notano fra certe idee <lb></lb>espresse negli opuscoli minori del nostro Filosofo di Bologna, e <lb></lb>certe altre idee simili, che balenano qua e là per le Questioni del <pb xlink:href="020/01/255.jpg" pagenum="236"></pb>Filosofo di Cambridge. </s>

<s>Alcuni di que&#039;riscontri ci occorreranno a <lb></lb>notare in questo stesso Discorso, ma giova intanto intrattenerci <lb></lb>brevemente sopra quegli argomenti, da cui si conclude che, in <lb></lb>Idrometria, le speculazioni del Newton prendevano probabilmente <lb></lb>l&#039;indirizzo da quelle del Guglielmini. </s></p><p type="main">

<s>Fra i Principii matematici della Filosofia Naturale non pote­<lb></lb>vano non trovar luogo quelli concernenti le leggi del moto, con cui <lb></lb>l&#039;acque fluiscono dai fori aperti ne&#039;vasi. </s>

<s>La proposizione XXXVII <lb></lb>infatti del secondo Libro di que&#039;Principii, conforme alla prima <lb></lb>edizione che fu fatta nel 1686, ha per soggetto il problema degli <lb></lb>efflussi, che dall&#039;Autor si risolve più coi calcoli arguti, che coll&#039;ap­<lb></lb>plicarvi le leggi del moto dei gravi. </s>

<s>Nella successiva edizione, che <lb></lb>è del 1713, l&#039;Autore introduce, in questa parte del suo Libro, una <lb></lb>notabilissima riforma. </s>

<s>La proposizione de&#039;flussi, ricorre in ordine <lb></lb>al numero XXXVI, e vi si professa espressamente il principio, che <lb></lb>le velocità de&#039;liquidi nel fluire da&#039;fori de&#039;vasi, son proporzionali <lb></lb>alle radici delle altezze. </s>

<s>Così fatto principio è concluso da&#039;teoremi <lb></lb>galileiani della caduta de&#039;gravi, riscontrati di fatto ne&#039;più squisiti <lb></lb>esperimenti. </s>

<s>Da&#039;teoremi sui proietti conclude il Newton che gli <lb></lb>zampilli obliqui descrivono tutti una parabola, il parametro della <lb></lb>quale varia secondo la varia distanza che passa, tra la superficie <lb></lb>del liquido, e il centro dell&#039;apertura del vaso. </s>

<s>Misurati diligente­<lb></lb>mente questi parametri e attendendo agli effetti della resistenza <lb></lb>dell&#039;aria e della contrazion della vena, trovava che gli zampilli <lb></lb>parabolici rispondevan prossimamente alle traiettorie che sarebbero <lb></lb>state descritte da un grave gettato con quell&#039;impeto, che avrebbe <lb></lb>conceputo nel cadere da tanta altezza, quanta è quella del liquido <lb></lb>sul centro del foro, da cui fluisce. </s>

<s>Questo, che fu tentato anche dai <lb></lb>nostri Accademici del Cimento, è senza dubbio il più diretto, ma <lb></lb>il più difficile modo d&#039;eseguir l&#039;esperienza: difficoltà, che dalla sola <lb></lb>raffinatissima arte del Newton sarebbesi potuta superare. </s></p><p type="main">

<s>Insistendo sempre sull&#039;applicazione de&#039;teoremi galileiani, il <lb></lb>nostro Autore conclude teoricamente, a modo del Torricelli, e spe­<lb></lb>rimentalmente conferma che gli zampilli verticali risalgono sù con <lb></lb>l&#039;impeto stesso dovuto alla caduta, e soggiunge appresso che la <lb></lb>quantità del moto si dee misurar dal prodotto della sezione del <lb></lb>foro, per il doppio della colonna e non per la semplice colonna del <lb></lb>liquido sopraincombente. </s>

<s>Le controversie insorte in tal proposito <lb></lb>fra il Jurin e il Michelotti, son notabili nella storia, ma pure il <lb></lb>Newton, professando quel principio, non faceva altro più che appli-<pb xlink:href="020/01/256.jpg" pagenum="237"></pb>care al moto de&#039;fluidi il primo de&#039;Teoremi dimostrati, nel III Dia­<lb></lb>logo, da Galileo, dovendo l&#039;acqua, in conformità di questo teorema, <lb></lb>passar con moto equabile un doppio spazio di quello che ha pas­<lb></lb>sato in cader dalla superficie e scender fino a fluire dall&#039;apertura <lb></lb>del vaso. </s>

<s>E benchè i nostri Accademici fiorentini, come si par dai <lb></lb>loro Manoscritti, avessero già fatte osservazioni e sperimenti in pro­<lb></lb>posito, nonostante è il primo il Newton a descrivere, in quella stessa <lb></lb>Proposizione citata, il contrarsi della vena all&#039;esito, e il formarsi <lb></lb>della <emph type="italics"></emph>cateratta<emph.end type="italics"></emph.end> alla superficie del liquido. </s>

<s>In occasione di questa <lb></lb>cateratta, osserva Eustachio Manfredi, nella Annotazione alla pro­<lb></lb>posizione VI del I Libro della <emph type="italics"></emph>Natura dei fiumi,<emph.end type="italics"></emph.end> che il Guglielmini <lb></lb>l&#039;aveva già descritta e matematicamente considerata, nel IV e V Li­<lb></lb>bro della sua <emph type="italics"></emph>Misura delle acque correnti.<emph.end type="italics"></emph.end> Esamineremo a suo luogo <lb></lb>così fatta osservazione del Manfredi, ma intanto, ripensando a ciò <lb></lb>che potesse aver dato occasione al Newton di ritornare ai prin­<lb></lb>cipii idrometrici professati dagl&#039;Italiani, ci occorre alla memoria il <lb></lb>Trattato della Misura delle Acque correnti, citato ora dallo stesso <lb></lb>Manfredi. </s></p><p type="main">

<s>Il dì 19 Novembre 1690, Antonio Magliabechi, celebre biblio­<lb></lb>tecario in Firenze, annunziava al Granduca d&#039;aver da qualche giorno <lb></lb>ricevuto, dal signor Guglielmini, un libro intitolato <emph type="italics"></emph>Aquarum fluen­<lb></lb>tium mensura nova methodo inquisita<emph.end type="italics"></emph.end> stampato a Bologna (MSS. <lb></lb>Gal. </s>

<s>Cim. </s>

<s>T. XXI, c. </s>

<s>16), e il 27 Ottobre 1691, lo stesso Magliabechi <lb></lb>annunziava d&#039;aver ricevuto l&#039;altra parte del libro (ivi, c. </s>

<s>18). Ci­<lb></lb>tiamo questi documenti bibliografici, per dir che la prima parte, <lb></lb>ossia i primi tre libri della Misura delle Acque correnti furono <lb></lb>pubblicati nel 1690, e gli altri tre l&#039;anno dopo. </s>

<s>L&#039;Autore di quel­<lb></lb>l&#039;Opera si assumeva un difficile incarico, qual&#039;era quello di decider <lb></lb>se la velocità delle acque correnti seguiva la legge ammessa dal <lb></lb>Castelli e confermata dalla grande autorità del Cassini, o seguiva <lb></lb>l&#039;altra dimostrata dal Torricelli, e confermata in tanti modi poi dal <lb></lb>Viviani. </s>

<s>Il Guglielmini s&#039;affidò a quella maniera di sperimenti, che <lb></lb>sembrano men soggetti ad errori di tutti gli altri, e de&#039;quali il <lb></lb>Magiotti per il primo aveva dato gli esempii. </s>

<s>Perciò, dalla quantità <lb></lb>dell&#039;acqua raccolta, in determinati tempi, dal flusso di un vaso, <lb></lb>concludeva le sue esperienze riscontrar colla legge professata dal <lb></lb>Torricelli. </s>

<s>Il Guglielmini veniva altresì, con questo libro, a intro­<lb></lb>durre nell&#039;ldrometria le <emph type="italics"></emph>velocità medie,<emph.end type="italics"></emph.end> senza l&#039;uso delle quali ri­<lb></lb>manevano incerte tutte le proposizioni dimostrate prima di lui dal <lb></lb>Castelli. </s></p><pb xlink:href="020/01/257.jpg" pagenum="238"></pb><p type="main">

<s>Dietro ciò, par probabile anche a noi ciò che accennavasi dal <lb></lb>Manfredi, ed è che il Newton, dal 1686 al 1713, nel quale spazio <lb></lb>di tempo si divulgò l&#039;Opera del Guglielmini, potesse aver riformate <lb></lb>le sue idee, intorno alla legge della velocità delle acque correnti, <lb></lb>e potesse anche aver preso occasione di rivolgersi a considerare la <lb></lb>cateratta, da ciò che ne trovò scritto dall&#039;Autore, nell&#039;Opera stessa <lb></lb><emph type="italics"></emph>Aquarum fluentium Mensura.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Con questa, e con le <emph type="italics"></emph>Lettere idrostatiche<emph.end type="italics"></emph.end> contro il Papin, nelle <lb></lb>quali si dimostra ad evidenza in che modo, per la pressione am­<lb></lb>mosferica, s&#039;alterino le leggi del moto dell&#039;Acque, ne&#039;tubi chiusi, il <lb></lb>Guglielmini si preparava a dar mano all&#039;altra insigne opera <emph type="italics"></emph>Della <lb></lb>Natura de&#039;fiumi,<emph.end type="italics"></emph.end> in cui, riducendo a un unico principio lo stabi­<lb></lb>lirsi degli alvei, parve non meritar lode minore del Newton, che <lb></lb>a un principio unico aveva pure ridotto lo stabilirsi, nella regolare <lb></lb>perpetuità degli orbi, i moti di tutti i pianeti. </s></p><p type="main">

<s>Così, l&#039;Idraulica, indipendentemente da qualunque insegna­<lb></lb>mento straniero, si serbò schiettamente italiana, ma, promossa dai <lb></lb>discepoli e dai seguaci del Guglielmini, sentì pure, nel secolo XVIII, <lb></lb>qualche benefico influsso dai nuovi metodi e dalle nuove dottrine <lb></lb>neutoniane. </s>

<s>Uno dei principali fra questi benefizii fu quello del per­<lb></lb>suadersi che fecero gli Idraulici italiani essere una reale tegnenza <lb></lb>fra le minime particelle dell&#039;acqua; tegnenza che, con più grave <lb></lb>danno di quel che non si crederebbe, Galileo le avea negata. </s>

<s>Il <lb></lb>Guglielmini rimediò felicemente al danno, proseguendo gli inse­<lb></lb>gnamenti del maestro suo Geminiano Montanari, che avrebbe potuto <lb></lb>arricchire la scienza di un nuovo e impertantissimo Trattato sulla <lb></lb><emph type="italics"></emph>Natura dei fluidi,<emph.end type="italics"></emph.end> se non l&#039;avesse il Senato distratto in costruir <lb></lb>nuovi mulini, da arricchire il pubblico erario e i mercanti di seta <lb></lb>bolognesi (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLV, c. </s>

<s>230). Nonostante, nella pri­<lb></lb>vata Accademia dell&#039;Ab. </s>

<s>Sampieri, ei fu il primo a richiamar l&#039;at­<lb></lb>tenzione de&#039;fisici, non sulla sola viscosità dell&#039;acqua, ma sulle pro­<lb></lb>porzioni che questa ha colla viscosità degli altri liquidi. </s>

<s>Le nuove <lb></lb>ricerche sperimentali ebbero occasione dall&#039;avere osservato <emph type="italics"></emph>che li <lb></lb>corpi gravi discendono più velocemente per l&#039;acqua comune, che <lb></lb>per l&#039;acquavite e per l&#039;olio<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Cim. </s>

<s>T. XIX, c. </s>

<s>69) ciò che <lb></lb>fu sospettato dipendere dalla viscosità maggiore in questi due li­<lb></lb>quidi e in altri simili, che no nell&#039;acqua. </s></p><p type="main">

<s>A queste esperienze, fatte nel 1667, non sarà stato presente il <lb></lb>Guglielmini, che aveva allora dodici anni, ma le avrà apprese in <lb></lb>seguito dal Maestro, per applicarle, come poi fece, a spiegar la <pb xlink:href="020/01/258.jpg" pagenum="239"></pb>natura e gli effetti del filone nella corrente, non che a mostrar <lb></lb>l&#039;efficacia, che gli strati superiori di essa hanno in promuovere le <lb></lb>velocità degli strati inferiori. </s>

<s>Nonostante, il principio della viscosità <lb></lb>dell&#039;acqua ammesso dal Guglielmini, e applicato alla Natura dei <lb></lb>fiumi, non aveva altro valor che di un ipotesi, appoggiata ai fatti <lb></lb>osservati nella sperimentale Accademia bolognese; fatti, e il Mon­<lb></lb>tanari stesso non lo nega, che potevano anche dipendere da tutt&#039;altra <lb></lb>cagione. </s></p><p type="main">

<s>Come ipotesi, perciò, quella della viscosità dell&#039;acqua fu nuo­<lb></lb>vamente cacciata via dalla scienza, per la grande autorità di uno <lb></lb>scrittore, che succede in tempo e in dignità al Guglielmini, il p. </s>

<s>abate <lb></lb>Guido Grandi, il quale, troppo matematico e troppo ossequioso a <lb></lb>Galileo, ne illustra, nel suo Trattato del <emph type="italics"></emph>Movimento dell&#039;acque,<emph.end type="italics"></emph.end> le <lb></lb>dottrine, e ne commenta insieme gli errori. </s>

<s>Cacciare un errore in­<lb></lb>trodotto nella scienza da una tanta autorità, qual&#039;era quella di Ga­<lb></lb>lileo, non sembrava possibile che a un&#039;altra autorità di pari grado, <lb></lb>e tale era appunto quella del Newton, dalla nuova filosofia del quale <lb></lb>si concludeva la viscosità dell&#039;acqua e di tutti gli altri liquidi, <lb></lb>com&#039;un effetto naturalissimo dell&#039;attrazione molecolare. </s>

<s>Cosi l&#039;ipo­<lb></lb>tesi del Montanari, seguita dal Guglielmini, tornò in quasi certezza <lb></lb>di matematica conclusione e Paolo Frisi, uno de&#039;più illustri seguaci <lb></lb>dello stesso Guglielmini, fu primo a risentire questi benefici effetti <lb></lb>della Filosofia neutoniana, applicando il principio della viscosità <lb></lb>dell&#039;acqua a spiegar quel particolar fatto dell&#039;accelerarsi della cor­<lb></lb>rente, che si designò col nome di <emph type="italics"></emph>chiamata allo sbocco,<emph.end type="italics"></emph.end> e intro­<lb></lb>ducendo quello stesso principio nel general modo di regolare i <lb></lb>Fiumi e i torrenti, di che arricchì la scienza di un Trattato diviso <lb></lb>in tre libri. </s></p><p type="main">

<s>Questo, d&#039;aver per sempre sconfitto un errore, che cacciato la <lb></lb>prima volta minacciava, coll&#039;autorità di Galileo, di tornare a in­<lb></lb>vadere dannosamente la scienza, fu uno de&#039;principali, ma non il <lb></lb>solo de&#039;benefizii, che venisse all&#039;Idraulica dalla Filosofia neutoniana. </s>

<s><lb></lb>Altro rilevantissimo benefizio provenne dagli impulsi efficaci e dai <lb></lb>luminosi esempi, che dava il Newton a trattar de&#039;moti delle acque <lb></lb>correnti co&#039;metodi analitici, e col buon uso di comporre e di risolver <lb></lb>le forze. </s>

<s>Il Guglielmini, nè nel Trattato Della Misura delle acque <lb></lb>correnti, nè in quell&#039;altro Della Natura de&#039;fiumi, non s&#039;era dilun­<lb></lb>gato un passo dagli antichi metodi galileiani, e occorrendogli di <lb></lb>dover assegnar la direzione e misurar la quantità di forza risultante <lb></lb>dal comporsi insieme due correnti, una delle quali confluisce con <pb xlink:href="020/01/259.jpg" pagenum="240"></pb>l&#039;altra, incespica e s&#039;avvolge ne&#039;paralogismi stessi del Maestro suo <lb></lb>Montanari, a cui, in determinar la natura e il moto della Corrente <lb></lb>adriatica e delle correnti marine in generale, tanto nocquero quei <lb></lb>meccanici paralogismi. </s></p><p type="main">

<s>Primo a lasciar le vie vecchie, per seguitare le nuove, in trattar <lb></lb>del moto dell&#039;acque, fu Bernardino Zendrini, che in comporre il <lb></lb>suo Trattato, a cui diè il titolo di <emph type="italics"></emph>Leggi e fenomeni, regolazioni ed <lb></lb>usi delle acque correnti,<emph.end type="italics"></emph.end> dava opera nel 1739 (Firenze 1770, pag. </s>

<s>49). <lb></lb>Chi legge la Prefazione al libro, s&#039;accorge tosto che l&#039;Autore intro­<lb></lb>duceva, col metodo analitico, una novità nella scienza italiana, e <lb></lb>perciò intrattien, fin da principio, i lettori, studiandosi di persua­<lb></lb>derli ad accogliere una tal novità, e a voler fare la giusta stima <lb></lb>de&#039;vantaggi di lei. </s>

<s>Fu pure il Zendrini stesso de&#039;primi, che, fattosi <lb></lb>oramai seguace de&#039;nuovi metodi neutoniani, mostrasse il retto uso <lb></lb>che doveva farsi della composizione e risoluzion delle forze, colla <lb></lb>regola del parallelogrammo. </s>

<s>Vero è che di ciò i primi esempi erano <lb></lb>stati dati dal Grandi, ma fu il nostro Matematico della Serenissima <lb></lb>Repubblica di Venezia che, richiamandosi giusto a una proposizione <lb></lb>dimostrata dallo stesso Grandi, notò, il primo, un gravissimo errore, <lb></lb>sfuggito a tutti i censori, in che era incorso il Michelini; errore, <lb></lb>che consisteva nello scambiar con una delle componenti la resul­<lb></lb>tante di quella forza, con che le acque scavano il fondo dei fiumi. </s></p><p type="main">

<s>Noi riconosciamo anche questo per uno di quei gran benefizi <lb></lb>derivati alla scienza italiana, nel secolo XVIII, dagli esempi dei <lb></lb>metodi neutoniani, non solamente, perchè la prima edizione dei <lb></lb>Principii matematici di Natural Filosofia precedè di un anno il <lb></lb>progetto della <emph type="italics"></emph>Nouvelle mechanique<emph.end type="italics"></emph.end> del Varignon, pubblicata po­<lb></lb>stuma nel 1725, ma, perchè, com&#039;ad altro proposito si diceva più <lb></lb>sopra, a sradicar dalle menti degli Italiani l&#039;opinion che fosse falso <lb></lb>il teorema dell&#039;Herigonio, opinione invalsa e confermata da due <lb></lb>grandi autorità quali eran quelle di Galileo e del Borelli; ci voleva <lb></lb>un&#039;altra autorità, che non fosse punto minore, l&#039;autorità insomma <lb></lb>d&#039;Isacco Newton. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Che i metodi della nuova Filosofia neutoniana si riscontrino <lb></lb>con quegli stessi di Galileo, e che da un tale felicissimo incontro <lb></lb>ne sien conseguiti i progressi, che fecero le scienze sperimentali <pb xlink:href="020/01/260.jpg" pagenum="241"></pb>nel secolo XVIII, i lettori ne saranno meglio persuasi dalla verità <lb></lb>delle cose, che dai nostri discorsi. </s>

<s>Giova nonostante osservare che, <lb></lb>mentre Galileo col suo Platone instituisce la sua Filosofia naturale <lb></lb>nella regolarità geometrica delle forme, ch&#039;ei serenamente contem­<lb></lb>pla, senza troppo pensare al concorso delle cause, che le hanno <lb></lb>prodotte; il Newton soggiunge, nella sua Nuova Filosofia, l&#039;opera <lb></lb>concorrente di quelle cause, che egli riconosce nella gran dualità <lb></lb>delle forze di attrazione e di repulsione. </s>

<s>Di qui è che il metodo <lb></lb>neutoniano, benchè non differisca sostanzialmente da quello di Ga­<lb></lb>lileo, è così concluso in una formula nuova: “ In mathesi investi­<lb></lb>gandae sunt virium quantitates, et rationes illae, quae ex conditio­<lb></lb>nibus quibuscumque positis consequentur: deinde, ubi in physicam <lb></lb>descenditur, conferendae sunt hae rationes cum phaenomenis, ut <lb></lb>innotescat quaenam virium conditiones singulis corporum attracti­<lb></lb>vorum generibus competant ” (Princip. </s>

<s>Lib. </s>

<s>I. </s>

<s>Coloniae 1760, pa­<lb></lb>gina 464). </s></p><p type="main">

<s>La scienza fisica dunque si riduce, pel Newton, a conoscer la <lb></lb>natura e l&#039;intensità delle forze, non che le condizioni del loro vario <lb></lb>operare. </s>

<s>E perchè da queste forze è commossa ogni minima par­<lb></lb>ticella componente de&#039;corpi, si vede di qui aprirsi altri campi a <lb></lb>una fisica nuova, la quale fu detta molecolare, ma che si potrebbe <lb></lb>più volgarmente chiamar col nome di fisica sottile. </s>

<s>La legge da <lb></lb>noi, nella prima Parte di questo Discorso formulata, che l&#039;intelli­<lb></lb>gibilità della forma precede l&#039;intelligibilità della materia, e l&#039;in­<lb></lb>telligibilità della materia crassa precede l&#039;intelligibilità della ma­<lb></lb>teria via via più sottile; qui si vede avverarsi esattamente, essendo <lb></lb>quelle due nuove parti della Fisica sottile, che si conoscono sotto il <lb></lb>nome di Elettricismo, e sotto l&#039;altro più esteso di Chimica, non <lb></lb>prima venute alla luce, che nel secolo XVIII, come parto e portato <lb></lb>della nuova Filosofia neutoniana. </s></p><p type="main">

<s>Dappoi che Ottone di Guericke dimostrò, nel Cap. </s>

<s>XV del <lb></lb>quarto Libro de&#039;suoi Esperimenti magdeburgici, come tutte le virtù <lb></lb>della materia universale sien rappresentate da una sfera di zolfo, <lb></lb>confricata colle mani, mentre che celerissimamente è girata attorno; <lb></lb>e come quella stessa sfera dia evidenti segni della virtù calorifica <lb></lb>e della lucente; invalse l&#039;opinione che sieno le sostanze sulfuree <lb></lb>primo e principale elemento del calore e della luce. </s>

<s>Il Guglielmini <lb></lb>se ne giovò per cacciar dalla Fisiologia l&#039;errore della <emph type="italics"></emph>fiamma vi­<lb></lb>tale,<emph.end type="italics"></emph.end> asserendo esser causa del calore negli animali l&#039;agitazione <lb></lb>delle sostanze sulfuree contenute nel sangue. </s>

<s>Tutti i fenomeni elet-<pb xlink:href="020/01/261.jpg" pagenum="242"></pb>trici e fosforici, non eccettuati i baleni e le folgori, eran ridotti a <lb></lb>esalazioni sulfuree, disperse per l&#039;aria e per le sostanze dei corpi. </s>

<s><lb></lb>Nè da queste stesse idee si dilunga il Newton nell&#039;VIII delle sue <lb></lb>Questioni. </s></p><p type="main">

<s>S&#039;era intanto osservato che la virtù di attrarre i minimi cor­<lb></lb>piccioli e d&#039;investirli di luce, non era propria a soli i globi di zolfo, <lb></lb>ma conveniva altresì, e forse meglio, ai globi o ai cilindri di vetro, <lb></lb>celermente girati e confricati allo stesso modo. </s>

<s>Così, il globo me­<lb></lb>tafisico del Guericke dette occasione a costruir le prime macchine, <lb></lb>per via delle quali, dice il Newton stesso, nella citata Questione: <lb></lb>“ vapor electricus, frictione manus e vitro excitatus, et ad cartam <lb></lb>albam, linteum vel digitum allisus, ita agitabitur, ut lucem continuo <lb></lb>emittat. </s>

<s>” Questo vapore elettrico fu largo e glorioso soggetto al <lb></lb>Franklin, al Symmer al Nollet d&#039;esperienze e di teorie, ma di così <lb></lb>fatte teorie quelle che più giovassero alla scienza, e che furon più <lb></lb>tenute in onore, si debbono ai due grandi elettricisti italiani, a <lb></lb>Giovan Batista Beccaria di Mondovì, e al comasco Alessandro Volta, <lb></lb>l&#039;ingegno de&#039;quali il Newton fecondò con gli spiriti della sua Nuova <lb></lb>Filosofia. </s></p><p type="main">

<s>Che siano le speculazioni del Fisico monregalese veramente <lb></lb>avvivate da quelli spiriti, se ne avvede presto ogni lettore che svolge <lb></lb>i due Libri <emph type="italics"></emph>Dell&#039;elettricismo artificiale e naturale,<emph.end type="italics"></emph.end> avendo quelle <lb></lb>stesse speculazioni ivi esposte, trovato nell&#039;Autore conforto e scusa <lb></lb>da una sentenza ch&#039;ei cita dalla XXXI Questione neutoniana (Del­<lb></lb>l&#039;elettric. </s>

<s>Torino 1753, pag. </s>

<s>40). Nè solo il metodo attinge il Nostro <lb></lb>a quelle filosofiche fonti, ma il principio altresì, che informa le sue <lb></lb>nuove dottrine: principio ch&#039;ei sagacemente ritrova nella parola <lb></lb>stessa di <emph type="italics"></emph>vapore,<emph.end type="italics"></emph.end> con cui il Newton qualifica la natura propria della <lb></lb>sostanza elettrica “ Chiamo, egli dice, vapore elettrico, il fluido che <lb></lb>ne&#039;corpi elettrizzati seintilla, fa sentire il venticello elettrico, forma <lb></lb>il fiocco elettrico, e la stelletta elettrica, ritenendo il nome datoli <lb></lb>da Newton lib. </s>

<s>III Ottica, questione VIII ” (ivi, pag. </s>

<s>10). Dall&#039;avere <lb></lb>infatti l&#039;elettricità natura di vapore conclude il Beccaria l&#039;esistenza <lb></lb>e il modo di quell&#039;elettricismo <emph type="italics"></emph>effluente<emph.end type="italics"></emph.end> e di quell&#039;altro elettricismo <lb></lb><emph type="italics"></emph>affluente,<emph.end type="italics"></emph.end> ambedue costituiti di materie somigliantissime, che egli <lb></lb>sostituisce all&#039;elettricità vitrea e resinosa del Symmer, e all&#039;elet­<lb></lb>tricità positiva e negativa del Franklin. </s></p><p type="main">

<s>Dal riguardar la materia elettrica sotto l&#039;aspetto neutoniano, <lb></lb>conclude il Nostro una legge unica e universalissima, ciò che nes­<lb></lb>suno aveva tentato prima di lui, dalla quale dipende e si regola <pb xlink:href="020/01/262.jpg" pagenum="243"></pb>una varietà complicatissima di effetti. </s>

<s>L&#039;applicazione di quella legge <lb></lb>non fu sempre trovata sufficiente, e talvolta fu scoperta anco fal­<lb></lb>lace, ma pur conduce spesso l&#039;Autore a incontrarsi in concetti, <lb></lb>che un secolo e più dopo, ad alcuni scrittori di elettricità, parvero <lb></lb>nuovi. </s>

<s>Di tali concetti si potrebbe, per esempio, citar quello del <lb></lb>riconoscer la causa del più violento irrompere della scarica in quel <lb></lb>punto, in cui più si ristringe un cilindro conduttore, nella legge <lb></lb>di tutti i fluidi in moto applicata alla elettricità, che cioè le velocità <lb></lb>stanno in ragion reciproca delle sezioni, e perciò, dove la sezione <lb></lb>è minima, come nelle punte, ivi il vapore elettrico acquista impeto <lb></lb>da vincer la resistenza che gli fa l&#039;aria attraversata (ivi, pag. </s>

<s>57). </s></p><p type="main">

<s>Ma il Volta sente penetrarsi anco più addentro gli spiriti della <lb></lb>Filosofia neutoniana. </s>

<s>I nuovi scritti sull&#039;<emph type="italics"></emph>Elettricità vindice<emph.end type="italics"></emph.end> e sopra <lb></lb>le <emph type="italics"></emph>Ammosfere elettriche,<emph.end type="italics"></emph.end> pubblicati in seguito alla citata Opera del <lb></lb>Beccaria, fanno pensare al giovane Fisico di Como che tutto si può <lb></lb>ridurre a una legge semplicissima, qual&#039;è quella dell&#039;attrazione, <lb></lb>intorno a che scriveva un Epistola diretta allo stesso Beccaria col <lb></lb>titolo: <emph type="italics"></emph>De vi attractiva ignis electrici.<emph.end type="italics"></emph.end> Lo splendido pensiero lo <lb></lb>aveva, infin dal 1763, comunicato al Nollet, il qual gli rispose pa­<lb></lb>rergli difficilissimo il poter ridurre i fenomeni elettrici a consentir <lb></lb>colle leggi dell&#039;attrazion neutoniana. </s>

<s>Ma il Volta soggiunge ch&#039;ei <lb></lb>non intendeva insistere su quella attrazione universale “ quae est <lb></lb>massae proportionalis, et decrescit in ratione duplicata distantiarum, <lb></lb>qua nimirum et corpora adducuntur in centrum et Planetae in <lb></lb>eorum orbitis continentur ” (Opere, Firenze 1816, T. I. p. </s>

<s>6). Oltre <lb></lb>di questa, soggiunge, vi è un altro genere di attrazione, che inter­<lb></lb>cede fra le minime particelle de&#039;corpi, e da cui hanno origine <lb></lb>effetti particolari. </s>

<s>Sono indizio manifesto e argomento certo di così <lb></lb>fatto genere di attrazione, le riflessioni e le rifrazioni della luce, <lb></lb>con tutte le varie specie di fenomeni capillari “ quod quidem vel <lb></lb>in sola postrema Quaestione Opticae Newtoni abunde patet ” (ibi, <lb></lb>pag. </s>

<s>7). Cosi, viene a concluder che, non ammettendo queste forze <lb></lb>attrattive, è impossibile trovare in altro principio la ragion de&#039;più <lb></lb>ovvii e principali effetti dell&#039;elettricità sulla varia natura dei corpi. </s></p><p type="main">

<s>Il Volta stesso, nel passo ora citato, a provar l&#039;esistenza e il <lb></lb>fatto dell&#039;attrazione molecolare, adduceva fra gli altri argomenti <lb></lb>anche quello delle chimiche operazioni “ cuius nulla est pars, egli <lb></lb>dice, in qua praeter inertiam massae et specificam gravitatem, alia <lb></lb>virium mutuarum genera, non ubique se prodant et, vel invitis, <lb></lb>incurrant in oculos. </s>

<s>” Chi può negare infatti che la Chimica, quella <pb xlink:href="020/01/263.jpg" pagenum="244"></pb>che con tal proprio nome si vide nel secolo passato acquistare essere <lb></lb>e dignità di scienza, non sia venuta a un tal essere e a una tal <lb></lb>dignità, dappoichè il Newton scoperse e dimostrò le attrazioni e le <lb></lb>repulsioni molecolari? </s>

<s>Le chimiche affinità, che presiedono alla <lb></lb>composizione de&#039;corpi sono effetti di quelle attrazioni: l&#039;elasticità <lb></lb>delle materie aerose, in che si decompongono i corpi sono effetto <lb></lb>di quelle repulsioni: d&#039;onde è che, nelle scoperte neutoniane, trovan <lb></lb>loro principio e ragione, sien per sintesi o per analisi, tutte quante <lb></lb>le chimiche operazioni. </s></p><p type="main">

<s>La più gloriosa età per la Chimica, incomincia, senza dubbio, <lb></lb>dalla scoperta dell&#039;ossigeno, nella quale si dice, ed è vero, che <lb></lb>non ebbero parte i nostri Italiani, benchè se la sentisse presente <lb></lb>Gianfrancesco Cigna, quando volle prima sperimentar sul fatto del­<lb></lb>l&#039;estinguersi le fiamme e del morir gli animali nell&#039;aria chiusa. </s>

<s><lb></lb>Era nulladimeno italiano di Savoia quel Claudio Luigi Berthollet, <lb></lb>che tanta parte ebbe in istituir la nuova nomenclatura, e che di­<lb></lb>mostrò al Lavoisier e agli altri Accademici francesi come troppo <lb></lb>affrettatamente era stato imposto il nome di <emph type="italics"></emph>ossigeno<emph.end type="italics"></emph.end> all&#039;antico <lb></lb><emph type="italics"></emph>flogisto,<emph.end type="italics"></emph.end> essendo che anco l&#039;idrogeno può acidificare una base, co­<lb></lb>me fece veder per l&#039;esempio del gas acido solfidrico. </s>

<s>Fu pure il <lb></lb>Berthollet che scoperse i varii modi tenuti dall&#039;ossigeno in com­<lb></lb>binarsi a una medesima base, a compor con essa acidi di diversa <lb></lb>natura, facendo veder che l&#039;acido solforoso non è altro che lo stesso <lb></lb>acido solforico con un equivalente di ossigeno di meno. </s>

<s>Ma perchè <lb></lb>i grandi meriti del Berthollet son troppo più noti ai francesi che <lb></lb>a noi, domandiamo quali furono i principii filosofici seguiti dal <lb></lb>nostro Autore? </s>

<s>e si risponde che furon quelli dell&#039;attrazion mole­<lb></lb>colare, i quali ei contrappose alle sterili teorie del Bergmann, ond&#039;è <lb></lb>che fu, il Berthollet stesso, appellato col nome di Newton della <lb></lb>Chimica. </s></p><p type="main">

<s>Più gloriosa età di quella della scoperta dell&#039;ossigeno, ricorse <lb></lb>però alla Chimica, quand&#039;ella strinse coll&#039;Elettricità quel nuovo <lb></lb>connubio, della fecondità del quale và la scienza in tutto debitrice <lb></lb>all&#039;Italia. </s>

<s>Come poi il fatto avesse le sue prime e più remote inspi­<lb></lb>razioni dalla Filosofia neutoniana, si raccoglie dal ripensare a ciò, <lb></lb>che prima inspirò e dette occasione alla grande scoperta dell&#039;Elet­<lb></lb>tricità dinamica. </s></p><p type="main">

<s>Il Beccaria, nella sua Opera sopra citata <emph type="italics"></emph>Dell&#039;Elettricismo,<emph.end type="italics"></emph.end> ri­<lb></lb>serba il Cap. </s>

<s>VII del primo Libro a trattar dell&#039;elettricismo stesso, <lb></lb>per rispetto ai vegetabili, agli animali e ai metalli. </s>

<s>E studiandosi <pb xlink:href="020/01/264.jpg" pagenum="245"></pb>d&#039;avvalorare le sue proprie speculazioni coll&#039;autorità dei placiti <lb></lb>neutoniani, cita varii passi qua e là dalle varie <emph type="italics"></emph>Questioni,<emph.end type="italics"></emph.end> tradu­<lb></lb>cendo, dalla XXIV, fra gli altri, il passo seguente: “ Il moto ani­<lb></lb>male non farebbesi esso dalle vibrazioni del suddetto mezzo (etereo) <lb></lb>che si eccitino pella potestà del volere, e indi si propaghino affine <lb></lb>di accorciarsi e dilatarsi ne&#039;muscoli, per li solidi, pellucidi, ed uni­<lb></lb>formi capilllamenti de&#039;nervi? </s>

<s>” Dopo il qual passo il Beccaria im­<lb></lb>mediatamente soggiunge: “ Le ulteriori esperienze e scoperte fatte <lb></lb>nell&#039;elettricismo, di che Newton non ha visto che il principio, pare <lb></lb>che aggiungano forza a&#039;dubbi del gran filosofo. </s>

<s>La velocità con che <lb></lb>si muove, cambia direzione, s&#039;arresta e di nuovo si slancia l&#039;elet­<lb></lb>trico vapore, pare che possano sodisfare alla velocità e cambiamento <lb></lb>delle sensazioni e movimenti animali ” (ediz. </s>

<s>cit. </s>

<s>pag. </s>

<s>126). Queste <lb></lb>parole, scritte da chi era reputato solenne maestro nelle elettriche <lb></lb>dottrine, ebbero grande efficacia sull&#039;ingegno, specialmente de&#039;Fi­<lb></lb>siologi italiani, i quali dalle ipotesi passando ai fatti, trovarono che <lb></lb>davvero, sotto l&#039;azione dell&#039;elettricità, s&#039;eccitavano le membra agli <lb></lb>animali, è più vivamente che mai ai più sensibili, come alle rane. </s></p><p type="main">

<s>Uno de&#039;più indefessamente studiosi, tra questi Fisiologi, era il <lb></lb>bolognese Luigi Galvani, il quale fu fatto accorto, da coloro che lo <lb></lb>assistevano nelle esperienze, come le rane morte o scorticate si <lb></lb>commovevano, anche trovandosi fuori della sfera di azione della <lb></lb>macchina elettrica, a pur toccarne, con uno scalpello di ferro, i <lb></lb>nervi crurali. </s>

<s>Avendo trovato con sua gran sorpresa che il fatto <lb></lb>era vero, volle farne esperienza coll&#039;elettricità naturale, esponendo <lb></lb>all&#039;aria le rane attaccate per un uncino alla ringhiera di ferro del <lb></lb>terrazzo, su cui davan le finestre di casa. </s>

<s>Sotto il ciel tempestoso, <lb></lb>osservava le solite commozioni che sotto l&#039;azione della macchina <lb></lb>elettrica, non però così a ciel sereno, benchè fosse fatto certo, dalle <lb></lb>osservazioni dell&#039;elettometro, che l&#039;aria, anche in quello stato me­<lb></lb>teorologico, era imbevuta di elettricità come sotto il ciel nuvoloso. </s>

<s><lb></lb>Ritornato a tentar per molti giorni, e non vedendoci risoluzione, <lb></lb>portò una di quelle rane, attaccate per l&#039;uncino alla ringhiera, in <lb></lb>una stanza al coperto, e posatala sopra una lamiera di ferro, che <lb></lb>egli teneva per una mano, cominciò coll&#039;altra a stuzzicare i nervi <lb></lb>del giacente animale, servendosi di quello stesso uncino, a cui era <lb></lb>affissa. </s>

<s>Si ridestò l&#039;animo dell&#039;intento osservatore a nuovi sensi <lb></lb>di maraviglia, quando vide seguitar da quell&#039;atto le solite contra­<lb></lb>zioni nelle gambe della rana, e i soliti guizzi. </s>

<s>Ripetuta l&#039;esperienza <lb></lb>in varii altri modi, esultò, parendogli che venissero i fatti a sin-<pb xlink:href="020/01/265.jpg" pagenum="246"></pb>cerarlo dei dubbii del Newton, e delle congetture del Beccaria. </s>

<s>Il <lb></lb>fluido etereo, concluse, risiede ne&#039;musculi dell&#039;animale, i quali ve <lb></lb>lo tengono dentro condensato come l&#039;elettricità fra le due armature <lb></lb>di una bottiglia di Leyda: i nervi sono i conduttori di quel fluido <lb></lb>latente, che salta a commuover le membra all&#039;animale, scaricandosi <lb></lb>attraverso a un arco di metallico, che fa l&#039;ufficio di eccitatore. </s></p><p type="main">

<s>La storia della maravigliosa scoperta e delle esperienze, che <lb></lb>lo condussero ad essa, il Galvani ce la narrò ne&#039;suoi più minuti <lb></lb>particolari, nelle tre prime parti di un suo Commentario in latino <lb></lb>pubblicato in Bologna nel 1791. L&#039;ultima parte di quel Commen­<lb></lb>tario la riserbò l&#039;Autore a dichiarare alcune sue congetture e con­<lb></lb>seguenze di quel suo nuovo elettricismo animale. </s></p><p type="main">

<s>La lettura di quel Commentario eccitò, nell&#039;animo de&#039;Fisiologi, <lb></lb>commozioni non meno vive e inaspettate di quelle, che l&#039;elettricità <lb></lb>producesse ne&#039;muscoli delle rane. </s>

<s>Chi più di tutti poi si commosse <lb></lb>fu il Volta, il quale, trovate vere l&#039;esperienze descritte dal Galvani, <lb></lb>a principio ne approvò anco insieme le congetture. </s>

<s>Altre esperienze <lb></lb>però lo indussero poi in seguito a dubitarne, e finì per convincersi <lb></lb>che non eran le rane da rassomigliarsi a bottiglie di Leyda, ma sì <lb></lb>meglio a sensibilissimi elettroscopi, svolgendosi ed eccitandosi il <lb></lb>fluido elettrico, non da&#039;muscoli, ma dal contatto de&#039;due metalli di <lb></lb>che si componevano gli archi eccitatori. </s>

<s>A confermare i contradi­<lb></lb>centi in questa sua persuasione, dimostrò che sempre, al contatto <lb></lb>di due metalli di natura diversa, come sarebbe un disco di zinco <lb></lb>accoppiato a un altro di rame, si svolge un&#039;elettricità in tutto si­<lb></lb>mile a quella, che si produce dai cilindri o dai dischi di vetro <lb></lb>confricati nelle macchine ordinarie. </s>

<s>E perchè l&#039;elettricità svolta da <lb></lb>sola una coppia metallica è debole, mostrò come si potevano far <lb></lb>concorrere insieme le virtù di più coppie, ponendo l&#039;una in co­<lb></lb>municazione coll&#039;altra, o per mezzo dell&#039;acqua pura, o per l&#039;inter­<lb></lb>posizione di dischi porosi imbevuti di acqua. </s>

<s>Di qui ebbe origine <lb></lb>quel portentoso elettromotore a tazze, e a pila, che il Volta stesso <lb></lb>descrive in sue varie scritture, ma specialmente nelle tre Lettere <lb></lb>al Gren, e in quell&#039;altra al De-la-Metherie; lettere che si possono <lb></lb>veder raccolte nella II Parte del Tomo II delle Opere, stampate <lb></lb>nel 1816, in Firenze. </s></p><p type="main">

<s>Le applicazioni della Pila voltaia son note oramai ai dotti e <lb></lb>al volgo, com&#039;è nota la stessa sfera del sole, ma non era nostra <lb></lb>intenzione d&#039;accennar se non a sole quelle applicazioni, che più <lb></lb>specialmente concernon la chimica. </s>

<s>L&#039;elettricità dinamica, scriveva <pb xlink:href="020/01/266.jpg" pagenum="247"></pb>lo stesso Volta, apre un campo fecondo di nuove speculazioni e <lb></lb>ricerche intorno all&#039;influenza del fluido elettrico ne&#039;fenomeni chi­<lb></lb>mici, alle mutue relazioni di questi con quelle ” (Opera cit. </s>

<s>T. II, <lb></lb>P. II. pag. </s>

<s>142), e così appunto scriveva, il celebre inventor della <lb></lb>Pila, rispondendo al Landriani, il quale gli annunziava come il <lb></lb>Nicholson a Londra era felicemente riuscito a decompor l&#039;acqua <lb></lb>fredda. </s>

<s>Presto s&#039;avverarono que&#039;presentimenti del Volta, quando, <lb></lb>oltre all&#039;acqua, si decomposero i sali; di che si trovò la Pila aver <lb></lb><figure id="id.020.01.266.1.jpg" xlink:href="020/01/266/1.jpg"></figure><lb></lb>la più squisita virtù analitica. </s>

<s>Il veder gli acidi concorrere costan­<lb></lb>temente al polo positivo, e le basi al negativo, parve ai chimici <lb></lb>una sperimentale dimostrazione di ciò che avea sospettato il Newton, <lb></lb>quando scrisse, ne&#039;principii della Questione XXXI: “ et fortasse <lb></lb>attractio electrica ad huiusmodi exigua intervalla extendi potest, <lb></lb>etiamsi non excitetur frictione. </s>

<s>” Ammisero infatti i Chimici che <lb></lb>fossero le molecole circondate da ammosfere elettriche, le quali <lb></lb>perturbate, fosser cagione del portarsi ciascuna di quelle molecole, <lb></lb>per attrazione, al polo di nome contrario. </s></p><pb xlink:href="020/01/267.jpg" pagenum="248"></pb><p type="main">

<s>Così ebbe origine l&#039;elettrochimica, di che il Volta stesso, nella <lb></lb>citata risposta al Landriani, accenna ai principii e a&#039;primi fonda­<lb></lb>menti posti da lui. </s>

<s>Ma molto prima aveva concorso, il celebre pro­<lb></lb>fessor di Pavia, a promuover le chimiche scoperte con gli studii <lb></lb>sulle esalazioni delle varie arie infiammabili, da cui ebbero origine, <lb></lb>non diremo i moschetti e le prime lampade a gasse, che pure tanto <lb></lb>piacquero al Furstenberger, da farle sue; ma quel nuovo <emph type="italics"></emph>Eudio­<lb></lb>metro,<emph.end type="italics"></emph.end> che fu trovato il più squisito strumento, da servire all&#039;analisi <lb></lb>volumetrica de&#039;corpi aerosi. </s></p><p type="main">

<s>La Meteorologia elettrica ebbe pure efficacissimi impulsi, per <lb></lb>opera del Volta e del Beccaria, a cui si dee la pratica applicazione <lb></lb>de&#039;parafulmini in Italia, e gli studii sopra l&#039;elettricità a ciel sereno. </s>

<s><lb></lb>Ma benchè, sì il Franklin che lo stesso Beccaria, avessero dimo­<lb></lb>strato in tante varie maniere l&#039;esistenza dell&#039;elettricità nelle nubi, <lb></lb>non avevano conosciuto però nè il modo nè l&#039;origine di quelli <lb></lb>effluvi. </s>

<s>La scoperta di ciò occorse al Volta nel fare in Parigi, in <lb></lb>compagnia del Lavoisier e del La-Place, esperienze sull&#039;elettricità <lb></lb>che si svolge, quando l&#039;acqua si trasforma in vapore. </s>

<s>“ L&#039;esperienze <lb></lb>fatte fin qui, egli scrive nell&#039;Appendice alla II Parte della Memoria <lb></lb>sul Condensatore, benchè non sien molte, tutte però concorrono a <lb></lb>mostrarci che i vapori dell&#039;acqua, e generalmente le parti d&#039;ogni <lb></lb>corpo, che si staccan volatizzandosi, portano via seco una quantità <lb></lb>di fluido elettrico, a spese dei corpi fissi che rimangono, lasciandoli <lb></lb>perciò elettrizzati negativamente ” (Op. </s>

<s>cit. </s>

<s>T. II. P. I. pag. </s>

<s>275). <lb></lb>Così per analogia veniva a dimostrarsi l&#039;origine dell&#039;elettricità po­<lb></lb>sitiva delle nubi. </s></p><p type="main">

<s>Ma perchè il Volta, sempre nelle esperienze cercava lume alle <lb></lb>teorie, ricorreva col pensiero alle somiglianze, che passano tra questi <lb></lb>nuovi fatti elettrici e altri fatti calorifici nuovamente scoperti. </s>

<s>Il <lb></lb>Guglielmini, tre anni prima che fossero pubblicate le celebri Que­<lb></lb>stioni neutoniane, aveva già, nel suo Trattato <emph type="italics"></emph>De sanguinis natura,<emph.end type="italics"></emph.end><lb></lb>fatto distinzione fra calore e luce, attribuendone la varietà dell&#039;ef­<lb></lb>fetto al vario modo di ondulare dell&#039;etere. </s>

<s>“ Quid enim impedit <lb></lb>quominus undulationes iis similes, quae ab ignis agitatione profi­<lb></lb>ciscuntur, etiam ab aliis motibus aetheri imprimantur? </s>

<s>An excita­<lb></lb>bitur in retina igniculus, cum, presso oculo, lucis scintillae videntur <lb></lb>observari? </s>

<s>” (Venetiis, 1701, pag. </s>

<s>93). Il Newton poi più solenne­<lb></lb>mente aveva esposto, sotto la solita forma di dubbio, il pensiero <lb></lb>che l&#039;elettricità, il calore e la luce si potessero ridurre al vario <lb></lb>moto del mezzo etereo, ciò che oggidì si ritien dai fisici per la <pb xlink:href="020/01/268.jpg" pagenum="249"></pb>più probabile ipotesi, a ridurre in unità di principio la molteplice <lb></lb>varietà dei nuovi fatti osservati. </s>

<s>Così, prima che s&#039;accogliessero <lb></lb>d&#039;unanime consenso queste dottrine, aveva il Volta trovata un&#039;altra <lb></lb>analogia fra l&#039;elettricità e il calore. </s>

<s>L&#039;acquistare infatti maggior <lb></lb>capacità, rispetto al fluido elettrico, i corpi che si risolvono in va­<lb></lb>pori, l&#039;assomiglia a ciò che si osserva del calorico latente. </s>

<s>“ Chi <lb></lb>non sarà colpito, egli scrive, da così bella analogia, per cui l&#039;elet­<lb></lb>tricità porta del lume alla novella dottrina del calore e ne riceve <lb></lb>a vicenda? </s>

<s>Parlo della dottrina del calor latente o specifico, come <lb></lb>si vuol chiamare, di cui Black e Wilke colle stupende loro scoperte <lb></lb>han gittato i semi ” (ivi, pag. </s>

<s>275). </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quell&#039;Antonio Conti, che va debitore della sua fama alla va­<lb></lb>rietà dell&#039;erudizione, e alla sua faccendiera eloquenza, scriveva in <lb></lb>una lettera del dì 16 Settembre 1747 a Francesco Maria Zanotti: <lb></lb>“ Pare adesso cangiarsi tutta la Filosofia e ridursi alle forze elet­<lb></lb>triche, di cui tante sono l&#039;esperienze in tutti i paesi ” (Lett. </s>

<s>d&#039;il­<lb></lb>lustri ital. </s>

<s>Milano 1830, pag. </s>

<s>127). Eppure non erano ancora, quando <lb></lb>il Conti così scriveva, uscite alla luce le nuove Filosofie del Bec­<lb></lb>caria, del Galvani e del Volta. </s>

<s>Che non si fossero, dietro alla nuova <lb></lb>preda, i Naturalisti cacciati in troppo numero e con troppa furia, <lb></lb>non si potrebbe per verità negare nè al Conti nè a qualche altro <lb></lb>che l&#039;affermò, più giudizioso di lui. </s>

<s>Nonostante, quel creder che <lb></lb>tutti i misteri della Natura fossero rimasti fin allora occulti agli <lb></lb>occhi de&#039;Filosofi, sotto un medesimo velo intessuto di materia elet­<lb></lb>trica, giovò, non foss&#039;altro, con gli stessi arditi tentativi, a far pro­<lb></lb>gredire la scienza. </s></p><p type="main">

<s>De&#039;tanti misteri, quel che più vivamente frugasse la curiosità <lb></lb>de&#039;Fisiologi, era quello concernente il principio della vita, la quale <lb></lb>si rivela a noi principalmente, per la spontaneità de&#039;moti muscu­<lb></lb>lari. </s>

<s>Il Cartesio, giocando sempre al suo solito di fantasia, aveva <lb></lb>ammesso che gli spiriti animali, stillati dal cerebro, scendessero <lb></lb>in uno o più musculi, dalle fibre canoliculate de&#039;quali passassero <lb></lb>nelle fibre di altri muscoli opposti, in modo da riversarvi dentro <lb></lb>tutti i loro succhi spiritosi e così impinguarli, mentre essi stessi <lb></lb>perciò ne rimanevano esausti. </s>

<s>“ Qua ratione omnes spiritus antea, <pb xlink:href="020/01/269.jpg" pagenum="250"></pb>contenti in his duobus musculis confluunt celerrime in unum eo­<lb></lb>rum, et sic inflant et contrahunt eum, dum alter extenditur et re­<lb></lb>mittitur ” (Passion. </s>

<s>animae, Francof. </s>

<s>1692, pag. </s>

<s>5). Da questo passo, <lb></lb>e da tutto ciò che nel resto del Trattato ne dice, si vede ben che <lb></lb>l&#039;Autore non aveva nemmen la più lontana idea dell&#039;Anatomia mu­<lb></lb>scolare, la quale fu però posta dal Borelli per fondamento alle sue <lb></lb>nuove dottrine de&#039;moti animali. </s>

<s>Nel Cap. </s>

<s>III della Parte II di quel­<lb></lb>l&#039;Opera insigne, rifiutati gli spiriti cartesiani, ammette l&#039;esistenza <lb></lb>del succo nerveo, che, stillando in mezzo alle fibre muscolari e <lb></lb>mescendosi ivi alla linfa e al sangue, vi produce una subìta effer­<lb></lb>vescenza, com&#039;a versare olio di tartaro sullo spirito di vetriolo. <lb></lb></s>

<s>“ Igitur pariter in musculis non dissimilis mistura fieri potest, ex <lb></lb>quo fermentatio et ebullitio subitanea subsequatur, a cuius mole <lb></lb>porositates musculorum repleantur, et amplientur et consequantur <lb></lb>turgentia et inflatio ” (Romae 1681, pag. </s>

<s>57). </s></p><p type="main">

<s>Al principio vitale e troppo grossolano del Borelli il Newton <lb></lb>sostituì il mezzo etereo, il quale s&#039;incarnò nell&#039;elettricismo animale <lb></lb>del Galvani, che, nonostantè le valide opposizioni del Volta, rimase <lb></lb>il più sicuro rifugio, che avesse in sè la Fisiologia, intantochè Vin­<lb></lb>cenzio Malacarne giunse a rassomigliare il cervello a una vera pila <lb></lb>voltaia. </s>

<s>Pretender d&#039;aver con ciò svelati i misteri della vita, sarebbe <lb></lb>senza dubbio una follia, ma pure, non si può negar che non sieno <lb></lb>più sodisfacenti le ipotesi del Galvani, di quelle del Borelli, e sa­<lb></lb>rebbe una ingratitudine il non riconoscer le benemerenze del Gal­<lb></lb>vanismo nella Terapeutica. </s></p><p type="main">

<s>Molto prima che a svelare i misteri della vita animale, s&#039;era <lb></lb>applicata l&#039;elettricità a spiegar le funzioni della vita vegetativa. </s>

<s>Da <lb></lb>che il Nollet, nel Discorso IV delle sue <emph type="italics"></emph>Ricerche sulle ragioni par­<lb></lb>ticolari dell&#039;elettricità,<emph.end type="italics"></emph.end> dimostrò che il fluido elettrico aveva virtù <lb></lb>d&#039;accelerar l&#039;evaporazione dell&#039;umidità delle piante e delle frutte, <lb></lb>si pensò da&#039;Botanici che lo stesso fluido elettrico potesse efficace­<lb></lb>mente concorrere nelle funzioni della vegetazione. </s>

<s>Perciò molti fu­<lb></lb>rono coloro, che si misero dietro a questo nuovo genere di espe­<lb></lb>rienze, fra&#039;quali si distinse il Jallebert di Ginevra, a cui parve che <lb></lb>i bulbi de&#039;narcisi, delle giunchiglie e dei giacinti più rigogliosa­<lb></lb>mente vegetassero nell&#039;acqua delle caraffe elettrizzate, che no nelle <lb></lb>naturali. </s></p><p type="main">

<s>Il Beccaria, nel Cap. </s>

<s>VII del I Libro dell&#039;<emph type="italics"></emph>Elettricismo,<emph.end type="italics"></emph.end> dietro <lb></lb>la considerazione di questi fatti, esprime cosi un suo pensiero: <lb></lb>“ Ora questo vapore elettrico, che spinto dall&#039;arte entro i vegeta-<pb xlink:href="020/01/270.jpg" pagenum="251"></pb>bili, sensibilmente agevola ed accresce la loro nutritura e vegeta­<lb></lb>zione, non sarebbe esso (giacchè la Natura l&#039;ha in ogni corpo in <lb></lb>certa quantità e misura universalmente distribuito) una delle prin­<lb></lb>cipali cause efficienti delle suddette naturali funzioni ne&#039;vegetabili <lb></lb>e negli animali? </s>

<s>” (ediz. </s>

<s>cit. </s>

<s>pag. </s>

<s>125, 26). E prosegue ivi a con­<lb></lb>fortare questo suo pensiero con altri pensieri scelti dalle <emph type="italics"></emph>Questioni<emph.end type="italics"></emph.end><lb></lb>del Newton, in cui si sospetta che, per mezzo del fluido etereo, <lb></lb>s&#039;esercitino le funzioni del senso e della vita negli animali. </s>

<s>Così, la <lb></lb>Botanica sperava d&#039;usufruir bene dell&#039;elettricità, non punto meno <lb></lb>di quel che ne avesse usufruito la Fisiologia, e poniamo che da <lb></lb>ambedue queste scienze si fosse raccolto qualche buon frutto, l&#039;ab­<lb></lb>bondanza però non corrispose agli ardori delle prime concepute <lb></lb>speranze. </s></p><p type="main">

<s>Da tutt&#039;altra parte che dalla Fisica elettrica, vennero nel se­<lb></lb>colo XVIII, alla Botanica le speranze e l&#039;efficacia de&#039;suoi progressi. </s>

<s><lb></lb>Carlo Linneo aveva scoperto il mistero della fecondazione de&#039;fiori <lb></lb>e avendo riconosciuto in essi organi e funzioni somigliantissime a <lb></lb>quelle degli animali, le designò co&#039;medesimi nomi. </s>

<s>Così si distin­<lb></lb>sero anco le piante in maschi e in femmine, e s&#039;attribuì pure ad <lb></lb>esse un&#039;intelligenza di amore, e si prescrissero nuovi riti alle loro <lb></lb>nozze. </s>

<s>Alla strana novità annunziata dallo Svedese, recalcitrarono, <lb></lb>secondo il solito, molti, fra&#039;quali uno de&#039;più illustri botanici d&#039;Italia, <lb></lb>Giulio Pontedera. </s>

<s>L&#039;autorità di lui sarebbe stata di grande ostacolo <lb></lb>a introdur le nuove dottrine fra noi, se non gli fosse sorto incontro <lb></lb>uno scrittore, oggidì pochissimo conosciuto, il siciliano Filippo Arena, <lb></lb>che nel suo Trattato <emph type="italics"></emph>Della Natura e cultura de&#039;fiori,<emph.end type="italics"></emph.end> messo in luce <lb></lb>nel 1768 in Palermo, confermò con nuove osservazioni il sistema, <lb></lb>e dimostrò che le verità scoperte dal Linneo s&#039;estendevano ad ogni <lb></lb>maniera d&#039;inflorescenza. </s></p><p type="main">

<s>A leggere il Trattato del Beccaria, che noi abbiamo oramai <lb></lb>citato più volte, si vede che i Fisici avevano nell&#039;Elettricità sperato <lb></lb>di trovar non solo le recondite cause efficienti della vita delle piante <lb></lb>e degli animali, ma avevano altresì distese quelle loro ardite spe­<lb></lb>ranze a scrutar altri di que&#039;misteri, che la Natura celebra ne&#039;più <lb></lb>riposti suoi nascondigli. </s>

<s>Si trattava di riconoscer nell&#039;elettricità <lb></lb>l&#039;origine di quel fuoco sotterraneo, l&#039;esistenza del quale veniva <lb></lb>resa manifesta dalle fusioni de&#039;metalli scavati, e dalle visibili eru­<lb></lb>zioni de&#039;Vulcani. </s>

<s>Da questo fatto del fuoco centrale bene consi­<lb></lb>derato, e dagli effetti che naturalmente ne conseguitano, ebbe il <lb></lb>principio quella nuova scienza, la quale nel suo studio comprende <pb xlink:href="020/01/271.jpg" pagenum="252"></pb>tutta intera la Storia Naturale, e che ha avuto il nome proprio di <lb></lb>Geologia. </s></p><p type="main">

<s>La Geologia, che penetra addentro alle viscere della Terra, e <lb></lb>per riconoscerle nelle loro cause e ne&#039;loro effetti ne notomizza la <lb></lb>materia, appartiene alla Fisica sottile, ed è perciò nata in questi <lb></lb>ultimi tempi, e risente, quanto pure è disposta a riceverli, gl&#039;in­<lb></lb>flussi neutoniani. </s>

<s>Notabile che questi influssi stranieri fossero più <lb></lb>efficacemente sentiti da un Italiano, che non dal Burnet o dal <lb></lb>Woodward, i quali seguitaron piuttosto i metodi del rinnovato <lb></lb>aristotelismo cartesiano. </s></p><p type="main">

<s>Uno de&#039;più curiosi problemi, che si proponesse a risolvere ai <lb></lb>Naturalisti, era quello dell&#039;esistenza delle reliquie fossili di alcuni <lb></lb>animali marini, che si trovano, anche scavando a fior di terra, di­<lb></lb>spersi per le alture de&#039;monti. </s>

<s>Leonardo da Vinci si rideva di co­<lb></lb>loro, che volevan dire “ li nicchi esser prodotti dalla Natura in essi <lb></lb>monti, mediante le costellazioni ” affermando sapientemente che <lb></lb>essi eran reliquie di molluschi vissuti un tempo fa e, dopo morte, <lb></lb>ivi deposti dalle acque dei diluvii. </s></p><p type="main">

<s>Più di due secoli dopo, uno de&#039;più grandi nostri Naturalisti, <lb></lb>Antonio Vallisnieri, a risolvere il difficile problema, non sapeva in <lb></lb>sostanza dir punto nulla di più o di meglio di quel che ne avesse <lb></lb>detto già Leonardo. </s>

<s>Il Vallisnieri però, in quel suo Trattato, in cui <lb></lb>descrive i varii crostacei e le produzioni di mare, che si trovan sui <lb></lb>monti di Verona, e più particolarmente i pesci e le erbe marine, <lb></lb>che quasi imbalsamate si trovan fra una pagina schistosa e l&#039;altra <lb></lb>comprese nelle pietre del monte Bolca; faceva inconsapevolmente <lb></lb>un gran passo, trattenendosi a esaminar que&#039;fatti, che ne assicura­<lb></lb>vano del ritiramento del mare, e delle trasformazioni subìte dalla <lb></lb>faccia della Terra. </s>

<s>Altro gran passo poi fece lo stesso Vallisnieri, <lb></lb>quando, nell&#039;altro Trattatello più importante di quello che ora ab­<lb></lb>biamo citato, sull&#039;origine delle fontane, descriveva così avveduta­<lb></lb>mente le direzioni e le disposizioni degli strati petrosi, quasi nuova <lb></lb>Anatomia sottile dell&#039;ossatura de&#039;monti. </s>

<s>Fu questa nuova anatomia <lb></lb>descrittiva, che servì d&#039;uno de&#039;più validi argomenti, da risolvere il <lb></lb>problema dell&#039;origine delle produzioni marine fra terra; problema <lb></lb>che fu felicemente risoluto da Anton Lazzaro Moro, friulano, di­<lb></lb>mostrando la seguente proposizione: “ Gli animali e vegetabili ma­<lb></lb>rini, le cui spoglie in oggi o sopra o sotto certi monti si trovano, <lb></lb>nati, nutriti e cresciuti nelle marine acque, innanzi che que&#039;monti <lb></lb>sopra la superficie del mare si alzassero, allora là furono spinti <pb xlink:href="020/01/272.jpg" pagenum="253"></pb>dove ora esistono per lo più impietriti, quando que&#039;monti, uscendo <lb></lb>dal seno della terra coperta, si alzarono a quelle altezze in cui ora <lb></lb>si vedono ” (De crostacei, ecc. </s>

<s>Venezia 1740, pag. </s>

<s>231). La mecca­<lb></lb>nica di questi sollevamenti, di che s&#039;aveva a que&#039;tempi sotto gli <lb></lb>occhi l&#039;esempio nella nuova isola di Santorino, l&#039;attribuiva il Moro <lb></lb>al fuoco sotterraneo. </s>

<s>Di questo fuoco però, manifesto ne&#039;fatti, non <lb></lb>si conosceva ancora la causa, e benchè il Lemery si avvisasse di <lb></lb>ritrovarla nelle chimiche combinazioni, e ne&#039;loro effetti di effer­<lb></lb>vescenza, parve nulladimeno assai meglio di ricorrere a quel panurgo <lb></lb>dell&#039;elettricità, per cui così, nel sopra citato Libro Dell&#039;Elettricismo, <lb></lb>scriveva il Beccaria: “ Congetturo che circoli esso vapore (elettrico) <lb></lb>in particolare maniera per alcuni particolari sotterranei corpi; im­<lb></lb>perocchè la sua grande attività non ne farebbe essa pensare che <lb></lb>sia egli principio motore del fuoco centrale, che i Filosofi hanno <lb></lb>riconosciuto dentro la Terra? </s>

<s>” (pag. </s>

<s>225). </s></p><p type="main">

<s>Così, da più parti, in Italia concorrevasi a confermare quei <lb></lb>fondamenti, che aveva posti Lazzaro Moro alla nuova scienza della <lb></lb>Geologia. </s>

<s>Come poi della stessa cultura di questa scienza si sien <lb></lb>fatta esclusiva gloria gli studiosi stranieri, troppo lungo sarebbe <lb></lb>a dire, ma le usurpazioni incominciarono infino da Odoardo King, <lb></lb>che, nel 1767, espose innanzi alla R. </s>

<s>Società di Londra, come spe­<lb></lb>culazione sua propria, il sistema geologico pubblicato, trentasei anni <lb></lb>prima, dal nostro Friulano. </s>

<s>Forse intesero quegli inglesi di trar <lb></lb>larga usura delle inspirazioni, che ebbe il Moro a ricevere dall&#039;in­<lb></lb>glese Filosofia neutoniana, da lui invocata a varie occasioni, e verso <lb></lb>la quale si rivolge come a faro di sicurezza, quando teme di smar­<lb></lb>rirsi in quell&#039;alto mare, da nessun altro corso prima di lui. </s></p><p type="main">

<s>Meglio però che le ipotesi degli elettricisti, venivano prepa­<lb></lb>rando i progressi alla Geologia le nuove osservazioni e le nuove <lb></lb>esperienze di Lazzero Spallanzani. </s>

<s>Cimentando egli le produzioni <lb></lb>vulcaniche e le rocce primitive nel fuoco delle fornaci, concluse <lb></lb>che i filosofi troppo avevano esagerato nell&#039;apprezzare il grado di <lb></lb>attività e di intensità del fuoco centrale. </s>

<s>Ritrovava altresì, per queste <lb></lb>sue esperienze, che le lave al calore si risolvevano in un gasse, <lb></lb>d&#039;origine misterioso al par di quello, in che si risolve e per cui <lb></lb>rendesi bollicosa l&#039;acqua ghiacciata. </s>

<s>Alla elasticità di questi gassi <lb></lb>credette lo Spallanzani di dover attribuire la forza di deizione delle <lb></lb>lave, in fin su alla bocca de&#039;vulcani. </s>

<s>Ma perchè poi l&#039;esperienze <lb></lb>parvero dimostrargli che quelle sole forze non erano sufficienti; <lb></lb>riconobbe in ciò l&#039;opera, ch&#039;ei dimostrò con varii argomenti effi-<pb xlink:href="020/01/273.jpg" pagenum="254"></pb>cacissima, delle acque circolanti sottoterra, trasformate in vapori. </s>

<s><lb></lb>Ora i Geologi moderni, così italiani come stranieri, professano le <lb></lb>medesime dottrine, senza punto risovvenirsi di ciò che fu scritto, <lb></lb>molti anni prima, nel Cap. </s>

<s>XXI <emph type="italics"></emph>De&#039;Viaggi alle due Sicilie,<emph.end type="italics"></emph.end> dove <lb></lb>l&#039;Autore osserva di più come cosa notabile, benchè qualche mo­<lb></lb>derno siasi creduto d&#039;essere stato il primo a notarla “ che i vul­<lb></lb>cani sparsi nel globo, e che attualmente gettan fuoco, sono o cir­<lb></lb>condati dal mare, o poco da esso discosti, e che quelli che da lungo <lb></lb>hanno lasciato di bruciare, esistono ora la più parte lungi da lui ” <lb></lb>(Opere, Mìlano 1825, T. II, pag. </s>

<s>305); osservazione che soccorreva <lb></lb>opportunissima a confermare il sistema di Lazzaro Moro. </s>

<s>Le De­<lb></lb>scrizioni de&#039;Viaggi alle Due Sicilie e in alcune parti dell&#039;Appennino, <lb></lb>son del resto uno de&#039;più varii, e de&#039;più ricchi monumenti, che <lb></lb>sia stato eretto in Italia, nel secolo XVIII, alla Storia Naturale, <lb></lb>che vi si trova discorsa per quasi ogni sua parte. </s>

<s>Ora il lettore <lb></lb>è istruito dallo scienziato che scopre cose nuove, ora è dilettato <lb></lb>dall&#039;Alpinista, che descrive viaggi non più tentati, qual sarebbe <lb></lb>l&#039;ascesa e la discesa del cono dell&#039;Etna, con che incomincia il <lb></lb>Capitolo IX. </s></p><p type="main">

<s>Le insigni scoperte anatomiche fatte in questo secolo, princi­<lb></lb>palmente dal Valsalva e dal Morgagni, dal Cotugno e dallo Scarpa, <lb></lb>sembrava che dovessero ammannire ad altre scoperte nuove in <lb></lb>Fisiologia. </s>

<s>Ma que&#039;grandi uomini, a differenza degli anatomici an­<lb></lb>tichi, sapevano tutto insieme l&#039;arte di descrivere e d&#039;indurre, d&#039;os­<lb></lb>servare e di sperimentare. </s>

<s>Così, dop&#039;avere il Cotugno scoperta la <lb></lb>linfa nel labirinto, e dop&#039;aver lo Scarpa descritta la finestra rotonda <lb></lb>e il timpano secondario, risalgono alle più alte e sottili speculazioni <lb></lb>fisiologiche e filosofiche intorno al senso dell&#039;udito. </s>

<s>Lo Spallanzani, <lb></lb>non essendo anatomico, non poteva sperare di far scoperte fisiolo­<lb></lb>giche in soggetto nuovo: egli torna perciò su soggetti tentati già <lb></lb>prima di lui, e che in lui ritrovano la loro soluzione finale. </s>

<s>Egli <lb></lb>è in vero, il primo a dimostrare il fatto della circolazione del san­<lb></lb>gue, nel giro universale de&#039;vasi, divinata dall&#039;Harvey, e in soli gli <lb></lb>animali a sangue freddo mostrata dal Malpighi; egli è il primo a <lb></lb>illustrare, se non a scoprir la chimica della respirazione, e a di­<lb></lb>mostrar che la pelle, in alcuni animali degl&#039;infimi ordini, supplisce <lb></lb>largamente al difetto, e fa l&#039;ufficio stesso de&#039;polmoni. </s></p><p type="main">

<s>Occorre, in questo periodo della scienza sperimentale italiana, <lb></lb>un fatto, che a noi sembra degno di esser notato, ed è la relazione <lb></lb>intima e la corrispondenza che passa, fra gli studi de&#039;Nostri e <pb xlink:href="020/01/274.jpg" pagenum="255"></pb>quegli degli stranieri. </s>

<s>Quanta differenza tra ciò che si osserva in <lb></lb>questo, e nel secolo precedente, quando, a indurre i nostri Acca­<lb></lb>demici fiorentini a corrispondere con gli Accademici di Parigi, ci <lb></lb>bisognarono le insinuazioni di Michelangiolo Ricci, e l&#039;Autorità di <lb></lb>Leopoldo de&#039;Medici! In questo secolo il Volta sperimenta a Parigi <lb></lb>col Lavoisier e col La-Place, come co&#039;suoi più familiari amici e <lb></lb>colleghi, e lo Spallanzani dedica al Nollet le sue esperienze sugli <lb></lb>animali, e all&#039;Haller le sue fisiologiche speculazioni. </s>

<s>Sembra a noi <lb></lb>che l&#039;anello di congiunzione, meglio che il Cartesio, sia stato il <lb></lb>Newton, il quale, avendo ricevuto lume dall&#039;Italia, sull&#039;Italia stessa <lb></lb>lo rimandò potentemente riflesso. </s>

<s>Altro soggetto degno di conside­<lb></lb>razione ci si porge dal comparar, co&#039;due precedenti, il secolo XIX. </s>

<s><lb></lb>Ora son nuovamente rotte le relazioni e i commerci di studi fra <lb></lb>italiani e stranieri, con questa differenza, che, mentre i Discepoli <lb></lb>di Galileo si tenevan da parte, per non si degnare degli stranieri, <lb></lb>ora invece gli stranieri si tengon da parte, perchè non si degnan <lb></lb>di noi. </s></p><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Non infruttuoso riuscirebbe l&#039;andare investigando le cause di <lb></lb>quell&#039;altero contegno e di quello sprezzante riserbo, usato oggidi <lb></lb>dagli scienziati stranieri verso i nostri italiani. </s>

<s>Ma perchè ciò non <lb></lb>potrebbesi fare, senz&#039;entrare in confronti, i quali sempre riescono <lb></lb>odiosi, e perchè sempre si vede seguitar male a colui, che si vuol <lb></lb>mettere a dar giudizio de&#039;contemporanei, meglio è lasciar gli uo­<lb></lb>mini, e rivolgere uno sguardo fuggitivo alle cose, considerando le <lb></lb>condizioni, in cui le scienze sperimentali si trovano al presente. </s></p><p type="main">

<s>Quella legge da noi più volte ricordata, in conformità della <lb></lb>quale il soggetto propostoci a investigar dalla mente procede dal­<lb></lb>l&#039;intelligibilità della forma all&#039;intelligibilità della materia, e dalla <lb></lb>materia crassa prosegue via via alla più sottile; si vede verificarsi <lb></lb>anche in questo nostro secolo, in cui par che l&#039;intento de&#039;fisici, <lb></lb>sia tutto rivolto a trovar, ne&#039;moti e nelle altre affezioni dell&#039;etere, <lb></lb>quell&#039;unità di principio, a cui, come a causa unica, ridurre quella <lb></lb>complicata moltiplicità di effetti, che producon sui nostri sensi, <lb></lb>l&#039;elettricità, il calore e la luce. </s>

<s>Sotto questo lato perciò riguardata, <pb xlink:href="020/01/275.jpg" pagenum="256"></pb>non par che la scienza abbia nulla cambiato il suo andamento: <lb></lb>ella non ha fatto altro che accelerare, a proporzione della distanza, <lb></lb>que&#039;primi impulsi che, infin dal primo entrar del secolo scorso, <lb></lb>ricevè dalla Filosofia neutoniana. </s>

<s>Quel compiacersi, che fanno i con­<lb></lb>temporanei dello stato attuale, è forse una di quelle solite lusinghe, <lb></lb>in cui si trattien l&#039;animo di un padre, che, qualunque ella sia, si <lb></lb>compiace della sua prole. </s>

<s>Ma non si può negar che la scienza fisica <lb></lb>sperimentale, oggidì, per lo troppo lungo decorrere, non sia defa­<lb></lb>tigata, e perciò ella, o invoca il soccorso che si suole apprestare <lb></lb>agli ordini trascorsi, d&#039;esser ritirata verso i suoi principii, o ella <lb></lb>aspetta che le sia trasfuso per le vene uno spirito di gioventù no­<lb></lb>vello. </s>

<s>Ella aspetta insomma o un altro Newton o un altro Galileo. </s></p><p type="main">

<s>A molti sembra che l&#039;aspettato sia già venuto e salutano in <lb></lb>Carlo Darwin un nuovo Restauratore della scienza sperimentale. </s>

<s><lb></lb>Egli come Galileo, e come il Newton, pone a fondamento della sua <lb></lb>nuova Filosofia un principio semplicissimo, e che non può non es­<lb></lb>sere ammesso e comprovato dall&#039;esperienza di ognuno: il principio <lb></lb>che tutto quaggiù si trasforma col tempo. </s></p><p type="main">

<s>Ecco una parola, con cui si esprime il concetto più misterioso, <lb></lb>che sia nella vita e nella scienza dell&#039;uomo. </s>

<s>Noi viviamo nel tempo, <lb></lb>e perciò non è possibile il definire a noi stessi che cosa sia il tempo, <lb></lb>giusto a quel modo che non è possibile il definir la figura e la gran­<lb></lb>dezza del sole, all&#039;occhio che è tutto immerso nella sfera del sole. </s>

<s><lb></lb>Ma pure, il tempo è uno degli elementi, che entrano a compor quel­<lb></lb>l&#039;altro non meno misterioso concetto di forza. </s>

<s>Galileo e il Newton <lb></lb>avevano piuttosto rappresentato le forze, con quell&#039;altro elemento <lb></lb>loro componente, e che pare a prima vista men misterioso, lo spazio, <lb></lb>e perciò fecero uso della Geometria. </s>

<s>Il Darwin insiste sull&#039;elemento <lb></lb>del tempo, e come quell&#039;antico Archimede chiedeva che gli fosse <lb></lb>dato spazio sufficiente, e prometteva di trovar la forza necessaria <lb></lb>a commuovere l&#039;Universo; così il Darwin non chiede che tempo, <lb></lb>e promette di svelar con esso molti de misteri della Natura. </s>

<s>Il <lb></lb>tempo è una dinamia, è una forza che opera instancabile sempre, <lb></lb>ma degli effetti della quale non ci avvediamo, se non quando i <lb></lb>momenti sieno in molto numero accumulati. </s>

<s>La nuova dinamica <lb></lb>darviniana non è trattata coi processi matematici, ma è pure una <lb></lb>matematica anch&#039;essa, e l&#039;Autore non si dilunga in sostanza dai <lb></lb>metodi e dai precetti neutoniani, secondo i quali convien prima, <lb></lb>nelle matematiche, investigare le quantità delle forze e le ragioni. <lb></lb></s>

<s>“ Deinde, ubi in physicam descenditur, conferendae sunt hae ra-<pb xlink:href="020/01/276.jpg" pagenum="257"></pb>tiones cum phaenomenis ut innotescat quaenam virium conditiones <lb></lb>singulis corporum attractivorum generibus competant. </s>

<s>” Se non che <lb></lb>il Darwin, non discende a trattar la Fisica, propriamente detta, ma <lb></lb>la Storia Naturale, e perciò le forze attrattive essendo differenti, <lb></lb>vengono anche designate con un nome speciale, qual&#039;è quello di <lb></lb><emph type="italics"></emph>selezione.<emph.end type="italics"></emph.end> Nel conferir poi la ragione di quelle forze, coi fenomeni <lb></lb>particolari, il nuovo Filosofo si studia d&#039;osservare i precetti del più <lb></lb>antico Filosofo inglese, ed è per l&#039;osservanza di quegli stessi pre­<lb></lb>cetti, quando altro non gli si frapponga a rimuoverlo dalla retta via, <lb></lb>che vien condotto alle sue nuove scoperte. </s></p><p type="main">

<s>I germi di queste novità però scoppiano da radice più antica <lb></lb>e di origine schiettamente italiana, intanto che, se la moderna Fi­<lb></lb>losofia naturale fù istituita nella patria del Newton, si può dir che <lb></lb>ella niente altro fa propriamente che ripigliare un costrutto rimasto <lb></lb>per lungo tempo interrotto sulla punta della penna, e per le carte <lb></lb>de&#039;predecessori e de&#039;contemporanei di Galileo. </s>

<s>Le sottili osserva­<lb></lb>zioni che fa il Darwin intorno al feto degli animali d&#039;ordini supe­<lb></lb>riori, al qual feto ritrova le membra organizzate a quel modo, che <lb></lb>si convien meglio all&#039;organismo di animali di specie inferiori; erano <lb></lb>state fatte prima in gran parte dal Falloppio, quando, a conciliar <lb></lb>la nuova Anatomia del Vesalio con quella di Galeno, dimostrava <lb></lb>che l&#039;antico Maestro si poteva in certo modo scusar d&#039;errore, per <lb></lb>avere attribuito all&#039;uomo l&#039;anatomia de&#039;cani e delle scimmie, ri­<lb></lb>scontrandosi veramente una tal somiglianza anatomica con gli ani­<lb></lb>mali degli ordini inferiori, nel feto umano, nè essendone in tutto <lb></lb>cancellate le vestigie nel neonato. </s>

<s>Alcuni anzi de&#039;più curiosi pro­<lb></lb>blemi naturali, che si proponga a risolvere la Filosofia darviniana, <lb></lb>trovano ne&#039;principii professati dal Falloppio una soluzione più di­<lb></lb>retta, più facile e più dimostrativa. </s>

<s>Che se dalle osservazioni ana­<lb></lb>tomiche si passa a quelle, che concernono gl&#039;istinti animali, noi <lb></lb>non vediamo che nessuno de&#039;più celebri Naturalisti moderni possa <lb></lb>venire al confronto dell&#039;Acquapendente, in quel suo Libro, che egli <lb></lb>intitolò <emph type="italics"></emph>De Brutorum loquela.<emph.end type="italics"></emph.end> Egli osserva il tuono vario e il vario <lb></lb>modular de&#039;suoni negli animali, per esprimere le loro varie pas­<lb></lb>sioni. </s>

<s>La descrizione che egli fa di una gallina, co&#039;suoi pulcini in­<lb></lb>torno, insidiata da un cane; il vario modo del chiocciar di lei, <lb></lb>quando impone a&#039;suoi piccoli che si allontanino dal pericolo, quando <lb></lb>và incontro al cane per invitarlo disperatamente alla battaglia, <lb></lb>quando finalmente, rimasta vincitrice, richiama a sè i suoi pulcini, <lb></lb>perchè tornin sicuri a ricoverarsi sotto la protezione delle ali ma-<pb xlink:href="020/01/277.jpg" pagenum="258"></pb>terne (Patavii, 1603, pag. </s>

<s>23, 24); son, fra le molte, una di quelle <lb></lb>pagine, che sarebbe difficile trovar l&#039;eguale nella moderna lette­<lb></lb>ratura darviniana. </s></p><p type="main">

<s>Ma il Falloppio e l&#039;Acquapendente, professando così fatte dot­<lb></lb>trine, seppero sinceramente mantenersi credenti in Dio e nella di­<lb></lb>gnità dell&#039;anima umana, nè si vede in che i settatori della novella <lb></lb>Filosofia sappiano ritrovar giuste ragioni di non doverne imitare <lb></lb>gli esempi. </s>

<s>Perciò, se non possiam non approvare i nuovi metodi <lb></lb>e non plaudire alle scoperte fatte dai Filosofi novelli, non sappiamo <lb></lb>approvar quel loro ingerirsi a definir cose, che si spettano alla <lb></lb>Metafisica e alla Teologia. </s>

<s>E dall&#039;altra parte se mal provvedono al <lb></lb>lieto e pacifico progredir della Scienza que&#039;Naturalisti, che la vo­<lb></lb>glion fare da Metafisici e da Teologi, mal provvedono a mantenere <lb></lb>in dignità e in rispetto le loro contemplazioni que&#039;Teologi, che <lb></lb>voglion farla da Naturalisti. </s></p><p type="main">

<s>Non è uscito mai fuori nessun sistema di Filosofia Naturale a <lb></lb>insegnar cose contrarie alla corrente opinione, che non si sia ten­<lb></lb>tato di oppugnarlo con l&#039;armi teologiche. </s>

<s>Per tacere del Coperni­<lb></lb>cismo, le vicende del quale sono oramai troppo note, la vera scienza <lb></lb>sperimentale in Italia, e di li in tutta Europa, ebbe i primi prin­<lb></lb>cipii e i più validi impulsi, com&#039;altre volte si è detto, dalla cele­<lb></lb>berrima dimostrazione torricelliana del vacuo. </s>

<s>Insorsero, chi se lo <lb></lb>sarebbe aspettato mai? </s>

<s>i Teologi ad oppugnare anco questo fatto, <lb></lb>tassandolo di quell&#039;eresia, derivata dagli errori epicurei, e secondo <lb></lb>la quale si veniva, a parer de&#039;nuovi censori, a negar l&#039;unione e la <lb></lb>conservazione nell&#039;Universo. </s>

<s>Ma qual giudizio si facesse, infino dal <lb></lb>loro primo insorgere, di que&#039;teologici argomenti, vogliamo ce lo <lb></lb>dica un uomo, il quale, essendo uno de&#039;più benemeriti de&#039;pro­<lb></lb>gressi delle scienze sperimentali in Italia, ed essendo dall&#039;altra <lb></lb>parte monsignore in Roma e poi cardinale, è atto a inspirar, me­<lb></lb>glio di qualunque altro, riverenza e tacito ossequio negli animi <lb></lb>de&#039;professanti contrarie opinioni. </s>

<s>Michelangiolo Ricci, dop&#039;avere in <lb></lb>una sua lettera riferito al Torricelli la nuova maniera d&#039;argomentar <lb></lb>di que&#039;Teologi, da&#039;quali veniva l&#039;Autor dell&#039;esperienza dell&#039;argento <lb></lb>vivo ad essere annoverato fra il gregge di Epicuro, così tosto pro­<lb></lb>segue: “ Ciò sia detto con riverenza di V. S., la quale non vo&#039;tediare <lb></lb>con altro che le potrei soggiungere appresso, in questa materia, <lb></lb>perchè stimo che sarà pur troppo nauseata dalla temeraria opinione <lb></lb>de&#039;suddetti Teologi, e dal costume suo costante di mescolar subito <lb></lb>le cose di Dio ne&#039;ragionamenti naturali, dovecchè quelle dovrebbero <pb xlink:href="020/01/278.jpg" pagenum="259"></pb>con maggior rispetto e riverenza esser trattate ” (MSS. Gal. </s>

<s>Disc. </s>

<s><lb></lb>T. XLII, c. </s>

<s>32). </s></p><p type="main">

<s>Ma perchè i dissidenti, a cui manca il senno e la scienza di <lb></lb>Michelangiolo Ricci, non è da sperare che sieno per convertirsi al <lb></lb>vero, persuasi dalle parole di lui, ci sentiam lieti in pensare e in <lb></lb>dovere avvertire i nostri lettori, che la Filosofia Naturale da cui <lb></lb>son venute alla scienza le vitali riforme e i bene augurati incre­<lb></lb>menti, non entra affatto nella nostra Storia, soggetto della quale <lb></lb>non è propriamente che la Filosofia di Galileo e de&#039;seguaci di lui <lb></lb>nella fiorentina Accademia del Cimento. </s>

<s>I secoli che precedettero <lb></lb>a questo, e quello che immediatamente lo segue, in tanto son per <lb></lb>noi soggetto storico, in quanto, in quegli stessi secoli anteriori si <lb></lb>prepararono, e nel posteriore si svolsero o s&#039;infusero nuovi spiriti <lb></lb>di vita nelle dottrine insegnate e promulgate dalla scuola galileiana. </s></p><p type="main">

<s>La nostra Storia sarà ripartita in sette Tomi. </s>

<s>In questo primo, <lb></lb>al presente Discorso preliminare, seguiterà la storia dell&#039;invenzione <lb></lb>de&#039;principali strumenti, che servono al Metodo sperimentale. </s>

<s>Nel <lb></lb>secondo, si darà la storia del Metodo sperimentale applicato alle <lb></lb>scienze fisiche, e nel terzo narreremo i progressi fatti, per l&#039;appli­<lb></lb>cazione dello stesso metodo, da quella, a cui diamo nel più largo <lb></lb>significato il nome di Storia Naturale. </s></p><p type="main">

<s>Con questi primi tre Tomi sembrerebbe che si fosse sodisfatto, <lb></lb>in qualche modo, al debito che ci siamo imposti. </s>

<s>Ma se può dirsi <lb></lb>che siasi così storicamente dimostrato ai nostri lettori come la <lb></lb>scuola galileiana, applicando i metodi sperimentali abbia scoperto <lb></lb>verità nuove, in ogni parte della Natura; non saremmo però an­<lb></lb>cora penetrati addentro a scoprir da quali occulte radici attingessero, <lb></lb>quegli stessi metodi, i succhi nutritizii. </s>

<s>Que&#039;succhi dell&#039;altra parte <lb></lb>derivano sottilmente stillati, e vitalmente trasfusi nella nuova arte <lb></lb>sperimentale, dalla scienza del moto, ignorandosi la quale, vien <lb></lb>necessariamente a ignorarsi ogni altra scienza della Natura. </s>

<s>E per­<lb></lb>ciò, mentre in quei tre primi Tomi la nostra Storia pareva essere <lb></lb>di ogni parto assoluta, ora si comprende come, terminandosi qui, <lb></lb>a quell&#039;edifizio che studiosamente attendiamo a costruire manche­<lb></lb>rebbero le fondamenta, fondamenta che noi poniamo ne&#039;due Tomi <lb></lb>appresso, dove si narra la storia de&#039;processi dimostrativi matema­<lb></lb>tici e sperimentali della Meccanica. </s>

<s>Nel Tomo IV perciò, si dà <lb></lb>la storia delle dottrine meccaniche di Galileo, e nel V vedremo <lb></lb>come fossero quelle stesse dottrine svolte e confermate da&#039;seguaci <lb></lb>di lui. </s></p><pb xlink:href="020/01/279.jpg" pagenum="260"></pb><p type="main">

<s>Ma perchè apparisca anche meglio evidente la verità di quel­<lb></lb>l&#039;antica sentenza, pronunziata dal Filosofo, che cioè, <emph type="italics"></emph>ignorato motu <lb></lb>ignoratur Natura,<emph.end type="italics"></emph.end> abbiamo sentito vivo il bisogno di mostrar come <lb></lb>fosse la Meccanica immediatamente feconda di un&#039;altra scienza, al <lb></lb>pari di lei Nuova, e al pari di lei Italiana di origine e di cultura; <lb></lb>scienza che è una delle più splendide e più benefiche applicazìoni <lb></lb>delle matematiche astratte alle naturali esperienze. </s>

<s>Gli altri due <lb></lb>Tomi perciò s&#039;intratterranno intorno alla Storia dell&#039;Idraulica, nar­<lb></lb>randosi di lei nel VI Tomo l&#039;origine e i progressi fatti per opera <lb></lb>di Galileo e del Castelli, e riserbando il VII a mostrare in qual <lb></lb>grado di perfezione fosse ridotta la scienza del Moto delle acque <lb></lb>da&#039;discepoli e da&#039;seguaci de&#039;due grandi Maestri. </s>

<s>E perchè, nell&#039;ap­<lb></lb>plicazione del metodo sperimentale, oltre alle scienze fisiche, hanno <lb></lb>sperato di trovar aiuti e validi impulsi a progredire, anche le scienze <lb></lb>morali, se ci basteranno le forze dell&#039;ingegno, daremo anche di ciò <lb></lb>qualche saggio: e perchè tutto il nostro lavoro storico è condotto <lb></lb>sui documenti, per la massima parte non molto noti, se l&#039;acco­<lb></lb>glienza de&#039;lettori ci darà qualche speranza che non sieno per riuscire <lb></lb>inutili affatto le nostre fatiche, ai sette già designati faremo suc­<lb></lb>cedere via via, come Appendice alla nostra Storia, altri volumi. </s></p><p type="main">

<s>Al pararsi innanzi la macchina di questo ponderoso edifizio, <lb></lb>sentiamo gemerci sotto affaticate le nostre povere spalle, che ora <lb></lb>procedono vacillanti, ora temono il più grave pericolo di rimanere <lb></lb>oppresse. </s>

<s>Ma comunque ci avvenga di poter condurre al desiderato <lb></lb>termine l&#039;Opera nostra, non è credibile che ella non debba riuscir <lb></lb>per moltissime parti difettosa. </s>

<s>E perchè sappiano i lettori che non <lb></lb>si dice ciò per iscusa o per modestia, ma perchè siamo fermamente <lb></lb>persuasi in quella credenza, accenneremo ad una delle principali <lb></lb>occasioni, d&#039;onde inevitabilmente avranno origine i più temuti fra <lb></lb>que&#039;difetti. </s></p><p type="main">

<s>La storia della scienza ha avuto sempre una certa predilezione <lb></lb>nella cultura, qualunque ella siasi, de&#039;nostri studi. </s>

<s>Già, infin dal­<lb></lb>l&#039;anno 1878, si mandava a Roma, all&#039;egregio Principe D. </s>

<s>Baldassarre <lb></lb>Boncompagni, alcune <emph type="italics"></emph>Notizie Storiche intorno all&#039;invenzione del <lb></lb>Termometro,<emph.end type="italics"></emph.end> pubblicate, in quello stesso anno, nel <emph type="italics"></emph>Bullettino di <lb></lb>bibliografia e di storia delle scienze matematiche e fisiche,<emph.end type="italics"></emph.end> nel fa­<lb></lb>scicolo del Settembre. </s>

<s>Dal 1878 al 1885 le <emph type="italics"></emph>Letture di Famiglia<emph.end type="italics"></emph.end><lb></lb>dispensavano a sorsi, in Firenze, alcune nostre scritture in forma <lb></lb>di Lezioni, contenenti <emph type="italics"></emph>Saggi di storia della Fisica sperimentale <lb></lb>italiana,<emph.end type="italics"></emph.end> dai tempi di Dante a quelli di Galileo: scritture che si <pb xlink:href="020/01/280.jpg" pagenum="261"></pb>interpolavano, nello stesso Periodico, con altre sotto il titolo di <emph type="italics"></emph>Ri­<lb></lb>creazioni scientifiche,<emph.end type="italics"></emph.end> raccolte e pubblicate dal Direttore, pure in <lb></lb>Firenze, nel 1883, in un volumetto elegante. </s>

<s>Anche nel dare quelle <lb></lb>Nozioni di Fisica e di Botanica, sotto le dilettevoli forme di Rac­<lb></lb>conto o di domestiche scene, in que&#039;due libretti, che portano il titolo <lb></lb>di <emph type="italics"></emph>Estate in Montagna<emph.end type="italics"></emph.end> e <emph type="italics"></emph>Fra il Verde e i fiori,<emph.end type="italics"></emph.end> pubblicati nel 1884, <lb></lb>e nel 1886, con sì amorevoli cure, dai Successori Le Monnier di <lb></lb>Firenze, in quella loro elegantissima Biblioteca delle Giovanette; <lb></lb>com&#039;anche in quell&#039;altro libretto di Mineralogia, che il signor Paggi <lb></lb>pubblicò, pure in Firenze, nel 1888, e che s&#039;intitola <emph type="italics"></emph>Con gli occhi <lb></lb>per terra;<emph.end type="italics"></emph.end> abbiamo colto volentieri qua e là l&#039;occasione di trattar <lb></lb>qualche punto di storia della scienza italiana, sembrandoci che a <lb></lb>concepire stima e a ricevere impulsi d&#039;imitar ciò che hanno sco­<lb></lb>perto e speculato gli avi nostri, fossero benissimo accomodati e <lb></lb>disposti gli animi delle fanciulle italiane, e de&#039;giovanetti. </s></p><p type="main">

<s>Parecchie delle notizie storiche però, che ne&#039;citati volumetti, <lb></lb>pubblicati nel corso di dieci anni, si davano come cosa certa, si <lb></lb>sono ora dovute da noi riformare, narrando molto altrimenti i fatti, <lb></lb>e secondo che alla verità storica gli abbiano trovati meglio con­<lb></lb>formi. </s>

<s>Il più notevole esempio di ciò, vien posto dal paragonar la <lb></lb>storia dell&#039;invenzion del Termometro, com&#039;è narrata qui appresso, <lb></lb>e nel citato fascicolo del Bullettino romano di Bibliografia fisica e <lb></lb>matematica. </s>

<s>Similmente, per tacere di altro, l&#039;Igrometro descritto <lb></lb>nella Lettera del Magalotti, è tutt&#039;altro da quello, che fu disegnato <lb></lb>a pag. </s>

<s>129 dell&#039;<emph type="italics"></emph>Estate in Montagna.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>L&#039;esperienza insomma ci ha pur troppo, a più incontri, dimo­<lb></lb>strato come cosa di fatto, che, assumendo noi gli uffici di storici, <lb></lb>abbiam creduto, e che è peggio, si è dato qualche volta a credere <lb></lb>cose, che non son vere. </s>

<s>L&#039;occasione poi di cadere, e di far cadere <lb></lb>altrui in errore, si è riconosciuta provenir da due parti: prima dal <lb></lb>non aver potuto ancora vedere, e dal non aver bene esaminati i <lb></lb>documenti: seconda, dall&#039;avere anche noi creduta una cosa vera, <lb></lb>perchè tutti gli altri l&#039;hanno creduta, sull&#039;autorità di uomini re­<lb></lb>putati sapienti. </s></p><p type="main">

<s>Ora son queste per l&#039;appunto le occasioni, donde si diceva <lb></lb>dianzi che avrebbero avuto origine i più temuti difetti della nostra <lb></lb>Storia. </s>

<s>Inevitabili si credon da noi questi difetti, perchè, come si <lb></lb>può presumere d&#039;aver veduti sempre e d&#039;essersi felicemente in­<lb></lb>contrati in que&#039;documenti dimostrativi de&#039;fatti storici, o come ci <lb></lb>possiam lusingare d&#039;aver noi soli spogliato un abito, che è nelle <pb xlink:href="020/01/281.jpg" pagenum="262"></pb>consuetudini di tutti? </s>

<s>Perciò, come noi trovando nuovi documenti, <lb></lb>abbiam colto in fallo noi stessi, così in fallo ci possono cogliere <lb></lb>gli altri. </s>

<s>In qualunque modo, è stato nostro sollecito studio di scan­<lb></lb>sare il mal vezzo del creder vere e del raccontar per vere le cose, <lb></lb>perchè altri prima di noi l&#039;hanno dette. </s>

<s>Con questo studio, che pur <lb></lb>ci può tante volte esser fallito, abbiam condotta l&#039;opera nostra, che, <lb></lb>qualunque ella sia, si vuol da noi dedicare alle glorie scientifiche <lb></lb>dell&#039;Italia. </s></p><pb xlink:href="020/01/282.jpg"></pb><p type="main">

<s><emph type="center"></emph>DE&#039;PRINCIPALI STRUMENTI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEL<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>METODO SPERIMENTALE<emph.end type="center"></emph.end><pb xlink:href="020/01/283.jpg"></pb></s></p><pb xlink:href="020/01/284.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del Termometro<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. Dell&#039;invenzione e degli usi del Termometro santoriano. </s>

<s>— II. </s>

<s>Delle applicazioni dell&#039;antichissima <lb></lb>esperienza eroniana, e segnatamente di quella fatta da Daniele Antonini, e da Cornelio Dreb­<lb></lb>bellio. </s>

<s>— III. </s>

<s>Della medesima esperienza fatta da Galileo. </s>

<s>— IV. </s>

<s>Se si debba giustamente at­<lb></lb>tribuire a Galileo l&#039;invenzion del Termometro ad aria; de&#039;perfezionamenti che tentò Giovan <lb></lb>Francesco Sagredo d&#039;introdurre nello strumento. </s>

<s>— V. </s>

<s>Della prima invenzione del Termometro <lb></lb>a liquido. </s>

<s>— VI. </s>

<s>Della prima scoperta, e delle prime ragioni rese del fatto del dilatarsi i liquidi <lb></lb>al calore. </s>

<s>— VII. </s>

<s>Della scoperta della dilatazion cubica de&#039;solidi al calore, e delle applicazioni <lb></lb>di lei alla Termometria. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La storia dell&#039;invenzion del Termometro è stata fin qui una delle più <lb></lb>controverse, forse perchè non si sono esaminati, colla debita diligenza, i <lb></lb>documenti, e i giudizi non sono stati imparziali. </s></p><p type="main">

<s>Il primo e certo documento storico da potersi citar da noi in così fatto <lb></lb>proposito, è senza dubbio quello che si legge ne&#039;Commentari del Santorio <lb></lb>sull&#039;Arte medicinale di Galeno. </s>

<s>La prima pubblicazione di quest&#039;opera si sa <lb></lb>che fu fatta in Venezia, nel 1612, e in essa, alla fine della particola X del <lb></lb>Capitolo LXXXV della Parte III, si legge: “ Volo vos admonere mirabilem <lb></lb>modum quo ego, quodam instrumento vitreo, soleo demetiri temperaturam <lb></lb>frigidam et calidam aeris omnium regionum, omnium locorum et omnium <lb></lb>partium corporis, et adeo exacte, ut qualibet hora diei possimus gradus et <lb></lb>ultimas mansiones caliditatis et frigiditalis circino dimetiri: illudque est in <lb></lb>aede nostra patavina, illudque omnibus libentissime ostendimus. </s>

<s>Nos polli­<lb></lb>cemur vel brevius in lucem daturos librum <emph type="italics"></emph>De instrumentis medicis,<emph.end type="italics"></emph.end> in <pb xlink:href="020/01/285.jpg" pagenum="266"></pb>quo iconem, constructionem, et usus huius instrumenti antiquissimi propo­<lb></lb>nemus ” (Santorii Op. </s>

<s>Omnia Venetiis 1660, T. I, pag. </s>

<s>538). </s></p><p type="main">

<s>E altrove, nella particula III del Cap. </s>

<s>86 della Parte citata, “ Nos enim, <lb></lb>egli dice, habemus instrumentum, quo metimur, non solum aeris caliditatem <lb></lb>et frigiditatem, sed omnes gradus caliditatis et frigiditatis corporis partium, <lb></lb>quod Patavii ostendimus auditoribus nostris, eiusque usus docuimus ” (ibi, <lb></lb>pag. </s>

<s>568). </s></p><p type="main">

<s>Il Libro <emph type="italics"></emph>De instrumentis medicis<emph.end type="italics"></emph.end> del Santorio, come abbiamo udito, <lb></lb>promesso al pubblico, o non fu scritto altrimenti dall&#039;Autore, o non fu pub­<lb></lb>blicato, ma la descrizione dello strumento vitreo misuratore, per via di una <lb></lb>scala graduata, (circino) del calore e del freddo, non mancò di darcela l&#039;Au­<lb></lb>tore stesso in un altro suo libro intitolato Commentari sopra la prima Fen <lb></lb>del primo libro del Canone di Avicenna, che vide la prima volta la luce, <lb></lb><figure id="id.020.01.285.1.jpg" xlink:href="020/01/285/1.jpg"></figure></s></p><p type="caption">

<s>Figura 2.<lb></lb>nel 1625, in Venezia. </s>

<s>Nella VI Questione infatti, dop&#039;aver <lb></lb>descritto il Pulsilogio, illustrato dalla prima figura, passa <lb></lb>immediatamente a descrivere il Termometro illustrato dalla <lb></lb>figura seconda, scrivendo nella seguente forma. </s>

<s>“ Secunda <lb></lb>figura est vas vitreus, quo facillime possumus singulis horis <lb></lb>dimetiri temperaturam frigidam vel calidam, et perfecte scire <lb></lb>horis quantum temperatura recedat a naturali statu prius <lb></lb>mensurati. </s>

<s>Quod vas ab Herone in alium usum proponitur. </s>

<s><lb></lb>Nos vero illud accomodavimus et pro dignoscenda temperatura <lb></lb>calida et frigida aeris, et omnium partium corporis et pro di­<lb></lb>gnoscendo gradu caloris febricitantium, quod fit duobus modis: <lb></lb>alter est dum aegri manu apprehendunt partem supernam <lb></lb>vitri, quae est D (fig. </s>

<s>2); alter dum aegri ori applicant eam­<lb></lb>dem vitri partem exufflando, sicut ostenditur fol. </s>

<s>219 instru­<lb></lb>mento primo, idque fit per aliquod breve spatium, veluti per <lb></lb>decem pulsilogii pulsationes, ut possimus diei sequenti expe­<lb></lb>riri, an eodem spatio aqua idem faciendo aeque descendat; <lb></lb>ob frigus nam ascendit, sicuti ubi est in O: ob calorem vero <lb></lb>rarefacientem aerem descendit, inde enim colligemus an aeger in melius vel <lb></lb>in peius labatur, quae differentiae si exiguae sint, a medicis, sine instrumento, <lb></lb>minime percipi possunt ” (ivi, T. III, pag. </s>

<s>30, 31). </s></p><p type="main">

<s>Per adattar poi lo strumento medico al primo uso accennato, qual&#039;è <lb></lb>quello di riconoscere la temperatura del corpo dell&#039;infermo, per la imposi­<lb></lb>zione e comprensione della palla vitrea fatta colla mano, non che per esplo­<lb></lb>rare i varii gradi di temperatura, in cui rimane o per cui passa via via un <lb></lb>ambiente; il Santorio immaginò un tripode, dentro il quale, infilato il lungo <lb></lb>collo dell&#039;ampolla vitrea, potesse questa trasportarsi con facilità e mante­<lb></lb>nersi sempre in posizione verticale ed eretta. </s>

<s>“ In prima figura, quae tripodi <lb></lb>ad aedium ornatum superimponi potest, singulis horae momentis, observari <lb></lb>possunt gradus caloris, frigoris et gradus temperati ipsius aeris. </s>

<s>Aquae <lb></lb>descensus in tubulo incluso existentis indicat caloris gradus; ascensus fri-<pb xlink:href="020/01/286.jpg" pagenum="267"></pb>giditatis. </s>

<s>Si aer fiat calidior, aqua descendit, quia caliditas rarefacit aerem <lb></lb>in globulo inclusum, qui rarefactus occupat maiorem locum. </s>

<s>Inde aqua <lb></lb>descendat oportet. </s>

<s>Ut aqua vero nobis clarior appareat, viridis efficitur. </s>

<s>Si­<lb></lb>militer, manum temperatam et intemperatam, ex eodem instrumento, digno­<lb></lb>scemus, ut superius docuimus (ibi, p. </s>

<s>426). </s></p><p type="main">

<s>Ma nella questione XXXIV, insieme con questo della imposizion della <lb></lb>mano sopra la palla dello strumento sostenuto dal tripode, descrive parti­<lb></lb>colarmente gli altri modi di ritrovare il grado della temperatura negli am­<lb></lb>malati. </s>

<s>Il primo consiste nel far tener loro in bocca, per uno spazio deter­<lb></lb>minato di tempo, la palla vitrea dello strumento, il cannello del quale non <lb></lb>è diritto, ma tortuoso, o avvolto in spira, senza dubbio per renderlo più <lb></lb>sensibile alle variazioni di temperatura, o come esprimevansi gli Accademici <lb></lb>del Cimento, più geloso. </s>

<s>Il secondo modo consiste nell&#039;applicar la palla vitrea <lb></lb>a contatto della parte del corpo, di cui vuolsi esplorare la temperatura, <lb></lb>riducendola alla figura di un emisfero, terminato da una superficie piana, <lb></lb>per aver maggiore estensione degli stessi punti del contatto. </s>

<s>Il terzo modo <lb></lb>consiste nel terminare o chiudere l&#039;emisfero con una superficie concava, <lb></lb>dentro alla quale, alitando l&#039;infermo, fa risentire gli effetti o il grado del <lb></lb>suo proprio calore all&#039;aria inchiusa dentro alla cavità della palla. </s></p><p type="main">

<s>Da così fatti documenti sembra a noi che risulti chiaramente avere il <lb></lb>Santorio fatto uso medico del Termometro ad aria, il qual Termometro era <lb></lb>graduato, comunque poi fosse fatta una tale graduazione, ed aveva il liquido <lb></lb>colorito in verde, per poter meglio distinguere i gradi indicati sopra la scala <lb></lb>adiacente. </s></p><p type="main">

<s>Abbiamo udito in oltre come chiami l&#039;Autore stesso questo strumento <lb></lb><emph type="italics"></emph>antichissimo,<emph.end type="italics"></emph.end> la quale espressione vien poi chiaramente commentata da quel <lb></lb>che soggiunge altrove, aver egli accomodato, all&#039;uso proprio di riconoscere le <lb></lb>varie temperature dell&#039;aria, una esperienza dell&#039;antichissimo Erone. </s>

<s>L&#039;espe­<lb></lb>rienza del Fisico alessandrino, a cui accenna, nelle sopra citate parole, il <lb></lb>Santorio, è senza dubbio quella che, nel libro degli <emph type="italics"></emph>Spiritali,<emph.end type="italics"></emph.end> si legge sotto <lb></lb>il numero XLVII e che porta il titolo “ Della goccia che stilla percossa dal <lb></lb>sole ” Il giochetto pneumatico è fondato sopra le dilatazioni e le conden­<lb></lb>sazioni dell&#039;aria prodotte dal calore o dal freddo, la quale aria, ora dilatan­<lb></lb>dosi ora contraendosi, fa sì che il liquido sottoposto ora si veda essere spinto <lb></lb>innanzi, e ora ritirato indietro, dentro un cannello di vetro trasparente, e <lb></lb>perciò visibile all&#039;occhio dello spettatore curioso. </s></p><p type="main">

<s>Comprendesi bene esser questo il principio, su cui è fondato il Termo­<lb></lb>metro ad aria, e il Santorio perciò cita quel fatto fisico, attribuendolo al suo <lb></lb>primo osservatore antichissimo. </s>

<s>Il Santorio stesso, insomma, confessa di non <lb></lb>avere altro merito, nell&#039;invenzione di quel suo strumento medico, da quello <lb></lb>in fuori di avere applicato a un caso particolare un fatto fisico già molto <lb></lb>prima scoperto, e a quel suo tempo a tutti notissimo. </s></p><p type="main">

<s>Ma perchè intanto si sappia dai lettori della nostra Storia e si dia quella <lb></lb>giusta parte del merito che s&#039;appartiene al nostro Giustinopolitano, giova <pb xlink:href="020/01/287.jpg" pagenum="268"></pb>qui di non passar sotto silenzio com&#039;egli, oltre all&#039;uso medico, tentò di ap­<lb></lb>plicare il Termometro alla soluzion di un problema, che frugò vivamente <lb></lb>la curiosità de&#039;Fisici, la quale non parve essere pienamente sodisfatta, se <lb></lb>non dai moderni inventori di strumenti ben assai più sensibili dei santoriani. </s>

<s><lb></lb>Il problema, e la ricercata soluzione di lui, concernono il sensibile effetto <lb></lb>dei raggi calorifici della Luna. </s>

<s>Geminiano Montanari, nella sua <emph type="italics"></emph>Astrologia <lb></lb>convinta di falso,<emph.end type="italics"></emph.end> più di un secolo e mezzo prima, che il Melloni venisse <lb></lb>a confermare il fatto, per mezzo del suo <emph type="italics"></emph>Termo moltiplicatore,<emph.end type="italics"></emph.end> aveva tro­<lb></lb>vato che il raggio lunare, riflesso da uno specchio ustorio grande su un <lb></lb><figure id="id.020.01.287.1.jpg" xlink:href="020/01/287/1.jpg"></figure></s></p><p type="caption">

<s>Figura 3.<lb></lb><emph type="italics"></emph>Termometro delicato di moto,<emph.end type="italics"></emph.end> (Ve­<lb></lb>nezia 1685, pag. </s>

<s>8) si rendeva sen­<lb></lb>sibile, e benchè non faccia alcun <lb></lb>cenno dell&#039;Autore più antico, no­<lb></lb>nostante l&#039;esperienza e il fatto son <lb></lb>quegli stessi descritti nelle se­<lb></lb>guenti parole dal nostro Santorio: <lb></lb>“ Figura A (fig. </s>

<s>3) est luna plena: <lb></lb>figura B est speculum concavum <lb></lb>quod lumen Lunae recipit: figu­<lb></lb>ra C est vas ex vitro, quo dimeti­<lb></lb>mur gradus caloris et frigoris. </s>

<s>A <lb></lb>speculo concavo lumen facit cu­<lb></lb>spidatam figuram C. </s>

<s>Permittimus ut luminis Lunae cuspis <lb></lb>feriat figuram C per spatium decem, vel plurium pulsationum <lb></lb>instrumenti (un orologio a pendolo di cui parleremo a suo <lb></lb>luogo) ut inde possit observari per quot gradus rarefiat aer <lb></lb>inclusus in figura C .... Praeterea, si velimus dignoscere <lb></lb>differentiam inter calorem solis et Lunae, curamus ut specu­<lb></lb>lum radios solis recipiat hoc fine, ut turbinate cuspis radio­<lb></lb>rum solis feriat vas vitreum signatum litera C: tunc statim <lb></lb>apparet quantum calefaciet sol, et quaenam sit proportio ca­<lb></lb>loris Lunae ad Solem. </s>

<s>Observavimus per spacium decem <lb></lb>pulsationum luminis Lunae cuspidem decem caloris gradus <lb></lb>efficere. </s>

<s>Solis vero lumen in eodem instrumento cuspidatim <lb></lb>tangendo, idem vas vitreum, in unica pulsatione, 120 gradus caloris efficere. </s>

<s><lb></lb>Varii tamen gradus fiunt prout varia sunt instrumenta, et variae sunt pul­<lb></lb>sationes ” (Sanctorii, Comment. </s>

<s>in prim. </s>

<s>Fen. </s>

<s>Op. </s>

<s>Omn. </s>

<s>Venetiis 1660, T. III, <lb></lb>pag. </s>

<s>108), per cui non può rilevarsi, da questa santoriana notabilissima <lb></lb>esperienza, il grado assoluto del calor della Luna, benchè si raccolga chia­<lb></lb>ramente essersi al Santorio mostrato, quello stesso calore, assai sensibile. </s>

<s><lb></lb>Soggiunge ivi poi d&#039;avere altre volte sostituito allo specchio una palla di <lb></lb>vetro piena di acqua, o un globo di cristallo, ciò che particolarmente descrive <lb></lb>più sotto a pag. </s>

<s>486 della citata edizione di questo stesso Commentario. </s></p><p type="main">

<s>Sembrerebbe da così fatti documenti indubitabilmente potersi conclu-<pb xlink:href="020/01/288.jpg" pagenum="269"></pb>dere che al Santorio si dovesse il merito della prima invenzione del Ter­<lb></lb>mometro e a una tal conclusione di fatti vennero molti scrittori, non sola­<lb></lb>mente di quegli che si possono credere male informati o pregiudicati contro <lb></lb>Galileo, come sarebbe, per esempio il Biancani o Giovanni Nardi, ma di <lb></lb>quegli stessi, che appartennero alla scuola del gran Filosofo, o che furono <lb></lb>ammaestrati da coloro, i quali, conversando familiarmente con lui, potevano <lb></lb>far testimonianza degli oracoli raccolti dalla bocca dei loro proprii Maestri. </s>

<s><lb></lb>Tali sarebbero fra gli altri, il Borelli e il Malpighi. </s></p><p type="main">

<s>Il primo di questi, discepolo del Castelli, e uno de&#039;più diligenti racco­<lb></lb>glitori delle tradizioni scientifiche di Galileo, sempre che gli occorre, nelle <lb></lb>lettere familiari o nelle Opere minori, di commemorare il Termometro, <lb></lb>ne fa autore il Santorio: sentenza che egli poi solennemente pronunziò <lb></lb>nella CLXXV proposizione della II Parte <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> così scri­<lb></lb>vendo: “ Omnium primus Sanctorius excogitavit organum, quo mensurantur <lb></lb>aeris gradus caliditatis, quod postea Thermometrum appellarunt, cuius <lb></lb>structura talis est... ” (Romae, 1681, pag. </s>

<s>358) e seguita a descrivere lo <lb></lb>strumento, conforme alla descrizione fattane, come vedemmo di sopra, dalla <lb></lb>penna medesima del Santorio. </s></p><p type="main">

<s>L&#039;altra autorevole testimonianza del Malpighi non è certamente diretta, <lb></lb>ma pure, benchè indiretta, ha gran peso, perchè il Papadopoli, medico mes­<lb></lb>sinese, scriveva a nome di lui, che era suo Maestro, e che perciò tacitamente <lb></lb>approvava, e facevasi quasi mallevadore di tutto ciò che asseriva il discepolo, <lb></lb>per prova di che occorre osservare che la <emph type="italics"></emph>Risposta alle opposizioni de&#039;Ga­<lb></lb>lenisti<emph.end type="italics"></emph.end> fatta dal Messinese, venne accolta fra le Opere postume dello stesso <lb></lb>Malpighi. </s>

<s>Il Papadopoli dunque ha nella citata <emph type="italics"></emph>Risposta<emph.end type="italics"></emph.end> le parole seguenti: <lb></lb>“ Il Santorio, fra gli altri inventi suoi gloriosi, lasciò uno strumento chia­<lb></lb>mato il Termometro, quale se dall&#039;Oppositore o da altro curioso sarà posto <lb></lb>ne&#039;ventricoli del cuore d&#039;un bue, cervo, o altro animale vivente, e farà il <lb></lb>simile nelle carni ed intestini, troverà che il grado del calore è uguale, e <lb></lb>che il più intenso non passa la temperie dell&#039;aria riscaldata dal sole nel <lb></lb>Leone ” (Malpighi, Op. </s>

<s>posth. </s>

<s>Londini 1697, P. II, pag. </s>

<s>30). </s></p><p type="main">

<s>I sopraccitati Autori però non dovettero venire a quella tal conclusione <lb></lb>per altra via, che per la lettura delle Opere del Santorio, in che trovarono <lb></lb>il documento più giusto, e raccolsero l&#039;argomento più certo, a dover con­<lb></lb>cluderne il vero storico. </s>

<s>Ma Giovan Francesco Sagredo ebbe la notizia <lb></lb>dell&#039;invenzion santoriana da uno di quegli stessi, a cui liberalmente l&#039;Autore <lb></lb>l&#039;aveva mostrata nelle sue proprie case in Padova, e fu costui appunto <lb></lb>Agostino Mula. </s>

<s>Il Sagredo infatti, scrivendo il dì 30 Giugno 1612 a Galileo, <lb></lb>così gli diceva: “ Il signor Mula fu al Santo, e mi riferi aver veduto uno <lb></lb>strumento dal signor Santorio, col quale si misurava il freddo ed il caldo <lb></lb>col compasso, e finalmente mi comunicò questo essere una gran bolla di <lb></lb>vetro con un collo lungo, onde subito mi son dato a fabbricarne de&#039;molto <lb></lb>squisiti e belli ” (Alb. </s>

<s>XIII, 218). Il Sagredo in vero erasi dato in questo <lb></lb>tempo studiosamente a perfezionare il Termometro santoriano, e vi fece tali <pb xlink:href="020/01/289.jpg" pagenum="270"></pb>progressi, che non può tacer di loro la nostra Storia. </s>

<s>Ma prima, convien tratte­<lb></lb>nerci alquanto sulle applicazioni di quella esperienza eroniana, che per es­<lb></lb>sere stata genitrice dello strumento da misurare il calore, e per essere stata <lb></lb>soggetto di novità spettacolose, si è acquistata perciò, per noi, una parti­<lb></lb>colare importanza. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nel libro degli <emph type="italics"></emph>Spiritali<emph.end type="italics"></emph.end> tradotto, come i nostri lettori sanno, nel 1606, <lb></lb>ma scritto originalmente in latino nel 1601, il Porta descriveva così l&#039;espe­<lb></lb>rienza eroniana, con intenzione d&#039;applicarla ad uso diverso sì, ma non punto <lb></lb>meno importante di quello, a cui seppe ingegnosamente applicarla il Santorio: </s></p><p type="main">

<s>“ Sia il vaso A (fig. </s>

<s>4); questo abbi la bocca dentro <lb></lb><figure id="id.020.01.289.1.jpg" xlink:href="020/01/289/1.jpg"></figure></s></p><p type="caption">

<s>Figura 4.<lb></lb>un vaso B, piano, pieno d&#039;acqua, il quale vaso sarà pieno <lb></lb>di aria, grosso nella sua consistenza, più o meno, secondo <lb></lb>il luogo e la stagione. </s>

<s>Poi accosterete un vaso pieno di <lb></lb>fuoco al corpo del vaso in A, e l&#039;aria, subito riscaldan­<lb></lb>dosi, si anderà assottigliando, e fatta più sottile, vuole più <lb></lb>gran luogo, e cercando uscir fuori, verrà fuori dell&#039;acqua, <lb></lb>e si vedrà l&#039;acqua bollire, che è segno che l&#039;aria fugge, <lb></lb>e quanto si andrà più riscaldando, l&#039;acqua più boglierà, <lb></lb>ma, essendo ridotta tenuissima, l&#039;acqua non boglierà più. </s>

<s><lb></lb>All&#039;hora rimovete il vaso del fuoco dal ventre A, e l&#039;aria <lb></lb>rinfrescandosi, s&#039;andrà ingrossando, e vuol minor luogo, e <lb></lb>non havendo come riempir il vano del vaso, perchè ha la <lb></lb>bocca sotto l&#039;acqua, tirerà a sè l&#039;acqua del vaso, e si vedrà <lb></lb>salir l&#039;acqua su con gran furia a riempir tutto il vaso, lasciando vacua quella <lb></lb>parte, dove l&#039;aria stà ridotta già nella sua natura di prima. </s>

<s>E se di nuovo <lb></lb>accostarete il fuoco a quella poca aria, attenuandosi di nuovo, calerà giù <lb></lb>tutta l&#039;acqua, e rimovendo il fuoco tornerà a salir l&#039;acqua ” (Napoli 1606, <lb></lb>pag. </s>

<s>77). L&#039;esperienza stessa però, come semplice curiosità spettacolosa, era <lb></lb>stata descritta già dall&#039;Autore nel cap. </s>

<s>XXII del secondo fra i Quattro libri <lb></lb>della Magia, e nel cap. </s>

<s>I dell&#039;ottavo della Magia stessa in XX libri. </s></p><p type="main">

<s>La gran diffusione, che ebbero queste varie opere del Porta, rese l&#039;espe­<lb></lb>rienza eroniana quasi diremmo popolare, e alcuni destramente pensarono di <lb></lb>servirsene a dimostrarla al pubblico, qual&#039;effetto spettacoloso, e per metterla <lb></lb>a prezzo, con Re e con principi, come un segreto de&#039;più preziosamente ge­<lb></lb>losi. </s>

<s>Giuliano de&#039;Medici scriveva così da Praga a Galileo, nell&#039;Ottobre del <lb></lb>1610: “ Non voglio restar di dirle che qui ci è un Fiammingo, che viene <lb></lb>d&#039;Inghilterra, che pretende avere trovato il moto perpetuo, ed avendone <lb></lb>solo prima dato uno strumento al Re d&#039;Inghilterra, ne ha dato un altro a <pb xlink:href="020/01/290.jpg" pagenum="271"></pb>S. M. Cesarea, che dimostra di pregiarsene molto, ed ha caro che non lo <lb></lb>comunichi con altri, e consiste questo moto d&#039;acqua che in un cannello, <lb></lb>fatto quasi in forma di Luna, và ora in su ed ora in giu da una banda al­<lb></lb>l&#039;altra. </s>

<s>Il signor Gleppero (Kepler) non ci ha una fede al mondo, se non <lb></lb>vede come gli sta ” (Campori, Carteggio ecc. </s>

<s>Modena 1881, pag. </s>

<s>38). </s></p><p type="main">

<s>Due anni dopo, la notizia del curioso spettacolo era pervenuta a Bru­<lb></lb>xelles, alle orecchie di Daniele Antonini, il quale, sotto il di 4 di Febbraio 1612, <lb></lb>scriveva così al medesimo Galileo: “ Molti giorni sono io intesi che il Rè <lb></lb>d&#039;Inghilterra aveva un moto perpetuo, nel quale, entro un canale di vetro, <lb></lb>si muove certa acqua or abbassandosi a guisa (dicevasi) del flusso e riflusso <lb></lb>del mare (MSS Gal. </s>

<s>Div. </s>

<s>II. P. VI. T. VIII, c. </s>

<s>82). </s></p><p type="main">

<s>Parecchi anni ancora dopo, o fosse quello stesso che era andato in In­<lb></lb>ghilterra o in Germania, o fosse qualcun&#039;altro che avesse imparato da lui, <lb></lb>della viva rappresentazione del flusso marino dentro l&#039;ampolla vitrea, si <lb></lb>venne a farne pubblico spettacolo in Italia, e Cesare Marsili, con lettera del <lb></lb>dì 3 Aprile 1624, ne dava, al solito, avviso a Galileo, il quale rispondeva in <lb></lb>proposito: “ Quanto al flusso e riflusso di che mi accenna, ne sentirei vo­<lb></lb>lentieri l&#039;effetto, il quale, per mio parere non credo che possa dipendere da <lb></lb>altra cagione celeste, che dallo scaldarsi l&#039;aria il giorno, e rinfrescarsi la <lb></lb>notte, e l&#039;elezione dell&#039;acqua salsa credo che sia una coperta all&#039;artificio, <lb></lb>e che l&#039;istesso farebbe la dolce, e un tale scherzo feci io venti anni sono <lb></lb>in Padova ” (Alb. </s>

<s>VI, 313). Di questo stesso parere era stato già l&#039;Antonini, <lb></lb>il quale, nella lettera sopra citata, dop&#039;avere accennato allo spettacolo del <lb></lb>flusso marino, dentro l&#039;ampolla, così soggiunge: “ Sopra il che, conside­<lb></lb>rando io, caddi in pensiero che questo non fusse altrimenti flusso e reflusso, <lb></lb>ma così si dicesse per coprir la vera causa e la verità fusse che questo moto <lb></lb>fusse dalla mutazione dell&#039;aria, cioè di caldo e freddo fusse causato, cavando <lb></lb>questo dalla speculativa di quella esperienza del bellicone, che V. S. sa, e <lb></lb>perciò m&#039;ingegnai di fare anch&#039;io uno di questi moti, e fecilo, non come <lb></lb>m&#039;era stato disegnato quel d&#039;Inghilterra, che ha il canale rotondo a guisa <lb></lb>d&#039;un anello, ma con il canal retto, come V. S. potrà, dal profilo, che io le <lb></lb>mando, vedere ” e seguita a descrivere uno strumento, dove l&#039;acqua entra <lb></lb>ed esce o si alza, e si abbassa, al dilatarsi e al condensarsi dell&#039;aria, dentro <lb></lb>un tubo assai più capace di quello, in cui si fa visibile il moto della stes­<lb></lb>s&#039;acqua. </s>

<s>Pochi giorni dopo torna a descrivere un nuovo strumento più in­<lb></lb>gegnosamente costruito, e in cui si mostra il medesimo spettacoloso effetto. </s></p><p type="main">

<s>Da questi due strumenti dell&#039;Antonini non diversifica in sostanza quello, <lb></lb>che descrisse Cornelio Drebbel, a pag. </s>

<s>25 e 26 del suo libro <emph type="italics"></emph>De natura <lb></lb>elementorum,<emph.end type="italics"></emph.end> stampato a Ginevra nel 1628, colle seguenti parole, che noi <lb></lb>traduciamo, perchè sieno meno offese le orecchie de&#039;nostri lettori dalla bar­<lb></lb>barie originale del linguaggio latino: “ Se tu prendi un vaso di vetro, il <lb></lb>collo del quale, essendo assai lungo, si ripieghi incurvandosi a guisa di <lb></lb>corno, e la bocca vada a immergersi in acqua fredda, mentre tu avrai ac­<lb></lb>ceso il fuoco sotto il ventre del vaso, vedrai poco dopo gorgogliar l&#039;acqua, <pb xlink:href="020/01/291.jpg" pagenum="272"></pb>per l&#039;aria che va via; che se poi tu ritirerai il fuoco, l&#039;aria, che prima <lb></lb>riscaldata erasi espansa, si contrarrà nuovamente in sè stessa, e si farà più <lb></lb>che mai densa, e su per il vetro incomincerà a risalir l&#039;acqua che verrà a <lb></lb>occupare quello stesso spazio, dove prima il fuoco avea fatto distendere l&#039;aria. </s>

<s><lb></lb>Se, senza pericolo di romperlo, puoi fortemente riscaldare il vetro, lo ve­<lb></lb>drai, nel raffreddarsi, tanto succiar dell&#039;acqua, che quasi se n&#039;empierà tutto. </s>

<s><lb></lb>Un simil vaso di terra reggerebbe al fuoco assai meglio, ma impedirebbe <lb></lb>all&#039;occhio il poterne veder l&#039;effetto. </s>

<s>Chè, se, invece di aria tu mettessi nel <lb></lb>vaso al fuoco, acqua, la vedresti dilatarsi con tanto più di forza, quanto <lb></lb>l&#039;acqua stessa e più densa dell&#039;aria, e diecimila tanti di più ricrescerà sopra <lb></lb>quel che l&#039;aria stessa non faccia. </s>

<s>” </s></p><p type="main">

<s>Ora è notabile che sia stata attribuita al Drebbel l&#039;invenzion del Ter­<lb></lb>mometro non sopr&#039;altro argomento che sopra la descrizione di questa espe­<lb></lb>rienza, la quale, quand&#039;avesse veramente il diritto di conferire il titolo <lb></lb>d&#039;inventore a chi prima l&#039;ha fatta o l&#039;ha pubblicamente descritta, non do­<lb></lb>vrebbe, per giustizia, parteciparne il merito al Drebbel, ma al Cerretano <lb></lb>fiammingo, ma all&#039;Antonini, ma al Porta, e anzi ad Herone stesso prima che <lb></lb>ad ogni altro. </s>

<s>Questa considerazione è quella appunto che ci apre la via a <lb></lb>discorrer di Galileo, a cui pure, come al Drebbellio, fu attribuito il merito <lb></lb>dell&#039;invenzion del Termometro, per avere anch&#039;egli, fra&#039;tanti altri, atteso <lb></lb>all&#039;esperienza eroniana. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Un anno dopo avere il Sagredo dato avviso per lettera a Galileo dello <lb></lb>strumento veduto in Padova dal Mula, appresso il Santorio, torna in altra <lb></lb>sua a scrivere allo stesso in questa maniera: “ L&#039;istrumento per misurare <lb></lb>il caldo <emph type="italics"></emph>inventato da V. S. E.<emph.end type="italics"></emph.end> è stato da me ridotto in diverse forme assai <lb></lb>comode ed esquisite, intanto che la differenza di temperie da una stanza <lb></lb>all&#039;altra si vede fin cento gradi ” (Alb. </s>

<s>VIII, 218). </s></p><p type="main">

<s>Riscontrando i due passi delle due lettere citate, apparisce evidente­<lb></lb>mente una varietà di giudizi, imperocchè, nel primo, pare apertamente at­<lb></lb>tribuirsi l&#039;invenzion del Termometro al Santorio, e nel secondo più aper­<lb></lb>tamente che mai attribuiscesi a Galileo. </s>

<s>L&#039;Albèri, a render qualche ragione <lb></lb>di queste parole scritte in tempi diversi e in così diverse sentenze, disse <lb></lb>che, dopo la prima lettera, Galileo dee aver fatto sapere al Sagredo che <lb></lb>l&#039;invenzione non era altrimenti del Santorio ma sua, per cui il Gentiluomo <lb></lb>veneziano, credette, senza voler discuterla, alla franca affermazione di lui. </s></p><p type="main">

<s>Nella medesima opinion del Sagredo, dalle informazioni avute a voce <lb></lb>dallo stesso Galileo, fu condotto il Castelli, come si par da una lettera pub­<lb></lb>blicata nella sua integrità, pochi anni addietro, nel <emph type="italics"></emph>Bullettino<emph.end type="italics"></emph.end> del principe <pb xlink:href="020/01/292.jpg" pagenum="273"></pb>Boncompagni. </s>

<s>Quella lettera è indirizzata a mons. </s>

<s>Ferdinando Cesarini, ed <lb></lb>ha per soggetto la cura di un ferito, a cui le intestina erano uscite fuori <lb></lb>del ventre. </s>

<s>Il Castelli, applicando un fatto fisico a un caso patologico, in­<lb></lb>tende a dimostrar, per la dilatazione e la contrazione dell&#039;aria chiusa dentro <lb></lb>il tubo intestinale, quel rigonfiamento straordinario, che si vide fare al me­<lb></lb>desimo intestino, subito che fu uscito fuori del ventre al povero ferito, e <lb></lb>l&#039;esperienza del fatto fisico, che l&#039;Autore intende di applicare al caso pato­<lb></lb>logico, l&#039;attribuisce, per sua propria testimonianza, a Galileo. </s></p><p type="main">

<s>Dopo avere infatti narrato il caso, e aver detto del felicissimo esito che <lb></lb>ebbe la cura di quell&#039;infermo affidata al celebre Trullo, soggiunge il Ca­<lb></lb>stelli stesso le parole seguenti: “ Il caso fu bello, ed il rimedio facilissimo <lb></lb>ed intelligibile. </s>

<s>Ma io rimasi da una difficoltà sopraggiunto, la quale mi ha <lb></lb>dato che pensare assai a questo fatto: poichè alcuni giorni sono, discorrendo <lb></lb>col medesimo signor Trullo di questa cura, egli mi disse che sempre, in <lb></lb>simili ferite, coll&#039;uscita dell&#039;intestino, seguiva l&#039;istesso accidente del rigon­<lb></lb>fiarsi, e di più, che sempre il ferito veniva da crudelissimi dolori tormentato. </s>

<s><lb></lb>In questo, mi sovvenne un&#039;esperienza fattami vedere, già più di trentacinque <lb></lb>anni sono, dal nostro signor Galileo, la quale fu che, presa una caraffella di <lb></lb>vetro di grandezza di un piccolo uovo di gallina, col collo lungo due palmi <lb></lb>in circa, e sottile quanto un gambo di pianta di grano, e riscaldata bene <lb></lb>colle palme delle mani la detta caraffella, e poi rivoltando la bocca di essa <lb></lb>in un vaso sottoposto, nel quale era un poco di acqua, lasciando libera dal <lb></lb>calor delle mani la caraffella, subito l&#039;acqua cominciò a salire nel collo, e <lb></lb>sormontò sopra il livello dell&#039;acqua del vaso, più di un palmo, del quale <lb></lb>effetto poi, il medesimo signor Galileo si era servito per fabbricare un <lb></lb>istrumento da esaminare i gradi del caldo e del freddo, intorno al quale <lb></lb>strumento sarebbe che dire assai, ma, per quanto fa al proposito nostro <lb></lb>basta che, in sostanza, si osserva che l&#039;acqua, quanto più l&#039;aria circonfusa <lb></lb>intorno alla caraffella si trova più e più fredda, tanto più sale l&#039;acqua sopra <lb></lb>il livello della sotto posta, e quanto lo strumènto vien portato in aria meno <lb></lb>fredda, tanto più l&#039;acqua si va abbassando nel collo della caraffella ” (Bul­<lb></lb>lettino ecc, T. XI, pag. </s>

<s>645, 46). </s></p><p type="main">

<s>In queste parole è evidentemente descritto dal Castelli il Termometro <lb></lb>ad aria, nella precisa forma del Santoriano, ma nonostante assai più imper­<lb></lb>fetto di questo, non facendosi menzione nè della scala di graduazione, nè <lb></lb>delle molte altre raffinatezze introdottevi dal Medico di Capo d&#039;Istria. </s>

<s>Pur <lb></lb>si volle, dietro così fatto documento, inferir da&#039;critici, che Galileo aveva <lb></lb>inventato lo strumento già fin dal 1603, mentre i Commentarii santoriani <lb></lb>sull&#039;arte medica di Galeno non videro la pubblica luce che nel 1612, come <lb></lb>vedemmo. </s>

<s>L&#039;età della invenzione galileiana la desumono dalla data della <lb></lb>lettera al Cesarini, che è del 1638, per cui, dicendo ivi il Castelli essergli <lb></lb>stata mostrata da Galileo quella fisica esperienza <emph type="italics"></emph>trentacinque anni sono,<emph.end type="italics"></emph.end><lb></lb>confidentemente concludono che infino dal 1603 aveva Galileo stesso mo­<lb></lb>strato al Castelli il suo Termometro. </s></p><pb xlink:href="020/01/293.jpg" pagenum="274"></pb><p type="main">

<s>Vincenzio Viviani, nella Vita che scrisse dell&#039;amatissimo suo Maestro, <lb></lb>fa risalir la scoperta dello strumento da misurare il calore anche a piùu anni <lb></lb>avanti, cioè tra il 1593 e il 1597 (Alb. </s>

<s>XV, 337). Su quali fondamenti poi <lb></lb>posi il Viviani quella sua asserzione, a noi nè a nessuno è possibile saperlo, <lb></lb>perchè l&#039;Autore della Vita di Galileo non ne fa motto, cosicchè pochissima <lb></lb>è la fede che possiamo avere nella verità di questa, come di altre asser­<lb></lb>zioni storiche di lui. </s></p><p type="main">

<s>Nè maggior certezza di fede crediamo che si possa dar da noi alle pa­<lb></lb>role, che ne scrisse il Castelli, imperocchè, a trattenersi, per prima cosa sui <lb></lb>numeri che sono i più precisi testimoni di tutti, quell&#039;affermarsi che l&#039;espe­<lb></lb>rienza della caraffella fu fatta da Galileo nel 1603 è uno sbaglio manifesto, <lb></lb>asserendo Galileo stesso che fu fatta invece nel 1606. Ciò rilevasi dalla so­<lb></lb>pracitata lettera del Marsili, la quale fu scritta il di 25 Aprile 1626. E perciò <lb></lb>dicendo ivi che l&#039;esperienza stessa era stata fatta venti anni prima, conclu­<lb></lb>desi che dunque nel 1606 e nò nel 1603, come asseriva il Castelli, Galileo <lb></lb>dee essersi ricreato a far lo scherzo della esperienza eroniana. </s></p><p type="main">

<s>Dall&#039;altra parte poi nè il Castelli fa nè da luogo a fare una distinzione <lb></lb>importante, ed è tra la esperienza pneumatica e l&#039;applicazione di lei allo <lb></lb>strumento misuratore de&#039;gradi del calore. </s>

<s>Da una tal confusione dipende <lb></lb>appunto l&#039;incertezza, che ha la lettera al Cesarini, invocata come documento <lb></lb>storico, da cui non può concludersi come e quando occorresse a Galileo di <lb></lb>far l&#039;esperienza, e come e quando pensasse d&#039;applicarla a costruire il nuovo <lb></lb>strumento, di che la critica imparziale può negargli il merito ambito. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Ma perchè defraudare all&#039;ambizion di un tant&#039;uomo, favorita dal cre­<lb></lb>dulo ossequio di altri grandi uomini, come il Sagredo, il Castelli, il Viviani, <lb></lb>non si può far da noi senza pericolo di essere accusati di temerarii, doman­<lb></lb>diamo alla coscienza de&#039;nostri lettori se credono che, dai documenti sopra <lb></lb>citati, si possa avere una prova certa dell&#039;appartenere allo stesso Galileo un <lb></lb>qualche diritto di preferenza sopra il Santorio. </s>

<s>Noi siam sicuri che rispon­<lb></lb>deranno di no, perchè in tutti i modi ha diritto alla prima invenzione colui, <lb></lb>che prima di tutti l&#039;ha pubblicata. </s>

<s>Ora il Santorio pubblicò la invenzione <lb></lb>sua del Termometro ad aria in un&#039;opera diffusissima a que&#039;tempi, e che <lb></lb>vide la luce nel 1612. Quali sono, domandiamo, le opere di Galileo anteriori <lb></lb>al 1612, nelle quali faccia pure un cenno di questo suo nuovo strumento <lb></lb>inventato? </s>

<s>Anzi, non solo nelle opere anteriori a quell&#039;anno non fa Galileo <lb></lb>menzione alcuna dello strumento, ma nemmen nelle altre, pubblicate dopo, <lb></lb>e che son delle maggiori, come i Dialoghi dei Massimi Sistemi e delle Due <lb></lb>Nuove Scienze. </s>

<s>Nel Tomo IV della Parte V de&#039;manoscritti di Galileo, a <lb></lb>carte 33, si leggono alcune postille e note da apporsi ai Dialoghi del Moto <pb xlink:href="020/01/294.jpg" pagenum="275"></pb>della prima edizione di Leyda, di cui lo scrittore cita via via la pagina, a <lb></lb>cui si riferiscono quelle stesse postille e lo scrittore è Vincenzio Viviani, di <lb></lb>propria mano. </s>

<s>Tali postille, poche di numero, non sono per verità molto <lb></lb>importanti, e in una, che si riferisce a pag. </s>

<s>70 della citata edizione leidese, <lb></lb>il Viviani stesso scrive queste parole: “ Nel discorso del Salviati potrebbesi <lb></lb>aggiungere la fabbrica delle due palline, e con questa occasione accennare <lb></lb>come l&#039;istrumento per conoscere le mutazioni del caldo e del freddo nel­<lb></lb>l&#039;aria è invenzione del Galileo ”. </s>

<s>Ma perchè Galileo, domandiamo noi, tra­<lb></lb>scurò di far questo cenno, o come mai si mostrò così smemorato da aver <lb></lb>bisogno de&#039;suggerimenti del suo discepolo? </s>

<s>Perchè non colse una così fa­<lb></lb>vorevole occasione di rivendicar la scoperta, egli che tante altre volte, di <lb></lb>tali rivendicazioni anche meno importanti, si mostra così geloso? </s></p><p type="main">

<s>Tutti sanno che Galileo non fa menzion del Termometro, dalle Lettere <lb></lb>familiari in fuori, altro che in que&#039;frammenti, i quali, raccolti poi dal Vi­<lb></lb>viani, si pubblicarono sotto il titolo di <emph type="italics"></emph>Pensieri varii.<emph.end type="italics"></emph.end> E qui pure suppone <lb></lb>lo strumento già come noto, e piuttosto che attendere con diligente amor <lb></lb>d&#039;inventore a farne la descrizione delle parti componenti, e del modo di <lb></lb>operare e dell&#039;uso, nient&#039;altro fa che ripeter de&#039;fisici le teorie, per render <lb></lb>la ragione del moto dell&#039;acqua dentro il cannello dello strumento. </s>

<s>Il San­<lb></lb>torio invece vedemmo che applicò la sua nuova invenzione, non a soli gli <lb></lb>usi medici ma a ricerche scientifiche di non lieve importanza. </s>

<s>Galileo del <lb></lb>Termometro non si sa ch&#039;ei ne facesse alcun uso. </s>

<s>Anzi, rispondendo a un <lb></lb>problema termico propostogli dal conte Piero de&#039;Bardi (Alb. </s>

<s>XIV, pag. </s>

<s>297-99) <lb></lb>giudica della temperie dell&#039;aria e dell&#039;acqua dalle impressioni fatte sui sensi, <lb></lb>per cui Giuseppe del Papa, e tutti i savii con lui, conclusero che, quando <lb></lb>Galileo fece quella risposta non dovette aver nessuna idea, nè conosciuto nem­<lb></lb>meno dalla lontana, il possibile uso del Termometro. </s>

<s>È questa una tal conclu­<lb></lb>sione, che mette i galileiani in grande imbarazzo, perchè, dicendo ivi l&#039;Autore <lb></lb>che il problema gli fu proposto nella sua villa di Arcetri, cioè dopo il 1633, <lb></lb>come và, si domanda che Galileo mostra d&#039;ignorar quello strumento, che si <lb></lb>vorrebbe dare ad intendere essere stato 37 anni prima da lui stesso inventato? </s></p><p type="main">

<s>Molte cose ci si potrebbero qui rispondere è vero. </s>

<s>Si potrebbe dir che <lb></lb>nel problema proposto dal Bardi era implicata la teoria del calorico latente <lb></lb>sconosciuta a que&#039;tempi: si potrebbe dir che il Termometro ad aria, a quel <lb></lb>modo che solevasi costruire allora, non era atto ad immergersi ne&#039;liquidi, <lb></lb>per esplorarne la temperatura. </s>

<s>Ma tutte queste risposte non bastano a sodisfar <lb></lb>punto a coloro, i quali seguitano a credere ancora che Galileo non comprese <lb></lb>come quella proposta del Bardi era in sostanza un problema di Termome­<lb></lb>tria. </s>

<s>Ond&#039;è che agli stessi più gelosi di Galileo convien confessare come, a <lb></lb>voler attribuire a lui l&#039;invenzione del Termometro, mancano i documenti, <lb></lb>e come i documenti che in fino a questo presente giorno, son noti, stanno <lb></lb>a provar che la prima invenzion dello strumento e le prime applicazioni di <lb></lb>lui agli usi della scienza, son giustamente dovute al Santorio. </s></p><p type="main">

<s>In conferma di che e delle altre cose fin qui discorse, senza entrare <pb xlink:href="020/01/295.jpg" pagenum="276"></pb>in più minuti particolari, ci basti sottoporre alla considerazione dei nostri <lb></lb>lettori le parole seguenti, che il Sagredo scriveva a Galileo, in una lettera <lb></lb>del dì 15 marzo 1615: “ All&#039;istrumento, dice egli, per misurare li tempe­<lb></lb>ramenti, io sono andato giornalmente aggiungendo e mutando, in modo che, <lb></lb>quando avessi a bocca e di presenza a trattare con lei, potrei principiando <lb></lb>ab ovo facilmente raccontarle tutta l&#039;istoria delle mie invenzioni, o per dire, <lb></lb>miglioramenti. </s>

<s>Ma perchè, com&#039;ella mi scrisse, e io certamente credo, V. S. E. <lb></lb>n&#039;è stata il primo autore e inventore, perciò credo che gli strumenti fatti <lb></lb>da lei e dal suo esquisitissimo artefice avanzino di gran lunga i miei; onde <lb></lb>la prego con la prima occasione, scrivermi qual sorta di opere finora ella <lb></lb>abbia fatto fare, chè io le scriverò quel di più o di meno che finora s&#039;è <lb></lb>operato di quà, e toccando in ogni nostra lettera alcune cose in questo pro­<lb></lb>posito, io le scriverò alcune mie imperfette speculazioni, le quali dal per­<lb></lb>fettissimo suo giudizio ed intelligenza saranno senza studio e ancora con <lb></lb>gusto perfezionate. </s>

<s>Quello che si fa autore di questi strumenti è poco atto, <lb></lb>per non dire in tutto inetto ad istruirmi conforme al bisogno e desiderio <lb></lb>mio, siccome io veramente mi sono affaticato a dargli ad intendere la ca­<lb></lb>gione degli effetti che si vedono in alcuni de&#039;miei strumenti, dirò così, com­<lb></lb>positi e multiplicati ” (Alb. </s>

<s>VIII, 363, 64). </s></p><p type="main">

<s>Da tali parole si rilevano in proposito importanti notizie, e prima di <lb></lb>tutto siamo certificati essersi fatto Galileo, come l&#039;Albèri sospettò, e dichia­<lb></lb>rato al Sagredo, primo autore e inventor del Termometro. </s>

<s>Sappiamo, in <lb></lb>secondo luogo, che Galileo stesso aveva scritto di esercitare e di fare eser­<lb></lb>citare la mano agli artefici intorno alla costruzion de&#039;Termometri e in <lb></lb>intorno ad alcune esperienze fatte con essi. </s>

<s>Ma quale fosse la squisita com­<lb></lb>posizione de&#039;Termometri galileiani, quai le osservazioni o l&#039;esperienze ter­<lb></lb>miche fatte con essi, non è facile a saperlo, essendo sventuratamente smar­<lb></lb>rite le corrispondenze epistolari col gentiluomo veneziano. </s>

<s>In ogni modo però <lb></lb>sembra che poco potrebbero quelle lettere giovare a coloro, che intendono <lb></lb>di attribuire a Galileo l&#039;invenzion dello strumento, essendo documenti po­<lb></lb>steriori alla pubblicazione fatta già dal Santorio. </s></p><p type="main">

<s>Ma la notizia più importante, che si possa attinger dalle parole del Sa­<lb></lb>gredo sopra trascritte, è che egli speculava intensamente intorno al migliorar <lb></lb>le forme del Termometro, e intorno alle teorie fisiche degli effetti, che sopra <lb></lb>l&#039;aria inclusa vi produce il calore. </s>

<s>Circa a ciò s&#039;intrattien lungamente il <lb></lb>Gentiluomo veneto in un&#039;altra sua lettera, scritta il dì 11 aprile di quel <lb></lb>medesimo anno 1615, dalla quale apparisce che, non avendo potuto per sè <lb></lb>medesimo ritrovar la ragione dell&#039;ascendere e del discendere il liquido nel <lb></lb>cannello, al variar della temperatura, ebbe ricorso all&#039;oracolo di Galileo e <lb></lb>de&#039;responsi di lui rimase sodisfatto. </s>

<s>“ Ho intesa l&#039;opinione sua, così scrive, <lb></lb>circa la ragione dell&#039;operare di essi strumenti, la quale mi è riuscita ca­<lb></lb>rissima e molto ingegnosa ed ardirei di dire ancor vera, se non fosse che <lb></lb>questa non è per sè stessa palese al senso, nè credo che per le cose palesi <lb></lb>al medesimo senso si possa perfettamente procurare ” (Alb. </s>

<s>VIII, 371). </s></p><pb xlink:href="020/01/296.jpg" pagenum="277"></pb><p type="main">

<s>La ragione dell&#039;operare dello strumento, insegnata da Galileo al Sagredo, <lb></lb>doveva esser quella degli egnicoli, che presenti ingrossan l&#039;aria di mole, <lb></lb>e assenti la diminuiscono, per cui il calore dilata e il freddo restringe. </s>

<s>E <lb></lb>benchè il discepolo dica che quella ragione non si rende manifesta al senso, <lb></lb>il Maestro nonstante credeva di vederla con gli occhi in quelle bollicelle <lb></lb>di aria, che si sciolgono dal liquido riscaldato, e che egli teneva essere mi­<lb></lb>nime particelle di fuoco. </s>

<s>In ogni modo però, il Sagredo non sapeva rendersi <lb></lb>la ragione di un altro fatto notabilissimo, osservato nel suo strumento, e il <lb></lb>fatto era che il liquido nel cannello vedevasi risalir con più lunghi passi <lb></lb>ne&#039;gradi inferiori, che nei superiori. </s>

<s>Ciò è cosa ora nota che dipende dalla <lb></lb>varia elasticità dell&#039;aria; elasticità della quale a que&#039;tempi, come si vedrà <lb></lb>meglio a suo luogo, non si aveva chiarissima idea. </s></p><p type="main">

<s>I miglioramenti poi che dal Fisico veneziano si tentò d&#039;introdurre nello <lb></lb>strumento, consistono principalmente nel diminuire il calibro del tubo e nel <lb></lb><figure id="id.020.01.296.1.jpg" xlink:href="020/01/296/1.jpg"></figure></s></p><p type="caption">

<s>Figura 5.<lb></lb>piegarlo orizzontalmente, affin­<lb></lb>chè nell&#039;ascesa non dovesse tro­<lb></lb>var qualche impedimento nel <lb></lb>suo proprio peso. </s></p><p type="main">

<s>Il passo, che nella sopra <lb></lb>citata lettera, appella a questi <lb></lb>perfezionamenti, è dall&#039;Albèri, <lb></lb>non si sa perchè, mutilato, ond&#039;è <lb></lb>che noi crediamo opportuno di <lb></lb>ridurlo qui alla sua integrità, <lb></lb>servendosi dell&#039;autografo, che <lb></lb>si trova inserito nel Tomo IX <lb></lb>della Parte VI dei Manoscritti <lb></lb>di Galileo: “ Quanto alla dif­<lb></lb>ferenza e disugualità dell&#039;ascesa <lb></lb>dell&#039;acqua e del vino (tali sono <lb></lb>le autentiche parole che si leggono in quella scrittura) sebben da principio io <lb></lb>feci una esperienza in tutto simile alla sua, dell&#039;applicazione della cannella più <lb></lb>grossa, ma però senza vino, regolata da un&#039;altra misura equivalente; tuttavia <lb></lb>usai altra maniera, che fu col lasciare attraer nella cannella una determi­<lb></lb>nata quantità di liquore, e levato il vasetto di sotto lasciavo ascendere e <lb></lb>discendere quel liquore; maniera però, che fu da me lasciata in poco tempo, <lb></lb>siccome un&#039;altra che fu il torcere ad angoli retti il capo della cannella verso <lb></lb>la palla, e parimenti dalla parte contraria l&#039;altro capo, sicchè posto a questo <lb></lb>vasetto la cannella restasse a livello in questo modo . . . . . ” (c. </s>

<s>252) che <lb></lb>più scolpitamente si rappresenta da noi nella Fig. </s>

<s>5. </s></p><p type="main">

<s>Di qui si pare che le molte squisitezze, studiatesi d&#039;introdur nella fab­<lb></lb>brica del Termometro, furono presto riconosciute inutili dallo stesso Sagredo, <lb></lb>e ciò è manifesto indizio della sua sagacia, specialmente per aver ricono­<lb></lb>sciuto, almeno in pratica, se non in teoria, che verso la forza che ha il <pb xlink:href="020/01/297.jpg" pagenum="278"></pb>calore di dilatare un corpo, quella del suo proprio peso, riesce a nulla. </s>

<s>In <lb></lb>ogni modo egli giustamente si compiace di aver costruito Termometri <emph type="italics"></emph>mol­<lb></lb>tiplicatori,<emph.end type="italics"></emph.end> co&#039;quali sperimentando potè avvedersi che l&#039;aria nell&#039;inverno è <lb></lb>assai più fredda del ghiaccio, e che alcuni ambienti hanno molto diverso <lb></lb>grado di temperatura, da quel che se ne suol talvolta stimare dai sensi. </s></p><p type="main">

<s>Il Sagredo però non si compiace d&#039;altro che della pratica dell&#039;artefice, <lb></lb>professandosi ignorante delle teoriche dello scienziato per imparar le quali <lb></lb>si rivolge, come s&#039;è visto, a Galileo, asserendo che <emph type="italics"></emph>quello che si fa inven­<lb></lb>tore di questi strumenti non era atto a istruirlo conforme al bisogno.<emph.end type="italics"></emph.end> Se <lb></lb>non intende qui il Sagredo del Porta, morto in quel medesimo anno 1615, <lb></lb>non si può creder che la censura cada sopr&#039;altri che sul Santorio. </s>

<s>Eppur <lb></lb>potrebb&#039;essere che Galileo abbia operato ad avvilir così il suo rivale nella <lb></lb>stima del troppo credulo e ossequioso amico. </s>

<s>I giudici imparziali però non <lb></lb>crederanno mai che l&#039;Autor de&#039;Commentari sopr&#039;Avicenna non intendesse gli <lb></lb>effetti del Termometro, ch&#039;ei descrive, almeno a quel modo che pretendeva <lb></lb>Galileo d&#039;essere stato, a intenderli e a farli intendere, il primo. </s>

<s>Perchè, in <lb></lb>ogni modo, la teoria del Termometro e la ragion fisica dell&#039;antichissima <lb></lb>esperienza eroniana era già divulgata in un libro, da cui potevano facilmente <lb></lb>apprenderla il Santorio, il Sagredo e Galileo. </s>

<s>Infatti, nelle celebri Disputa­<lb></lb>zioni <emph type="italics"></emph>De quibusdam placitis Aristotelis,<emph.end type="italics"></emph.end> raccolte poi fra le altre <emph type="italics"></emph>Specula­<lb></lb>zioni<emph.end type="italics"></emph.end> del Benedetti, dop&#039;aver l&#039;Autore insegnata la ragione dell&#039;attrar che <lb></lb>fanno la cucurbite la carne dell&#039;infermo, soggiunge: “ Idem cum amphora, <lb></lb>in qua nullum aliud quam aereum sit corpus experiri possumus, si eam <lb></lb>ad ignem primo calefactam, deinde eam ore in amplo aliquo cyatho, aut <lb></lb>alio vase, vino aut aqua pleno, ubi videbimus huiusmodi liquorem statim <lb></lb>sursum ferri, quia, dum calefit amphora, rarefit quoque aer, qui in ea con­<lb></lb>tinetur. </s>

<s>Et, quia rarescit, dilatatur, et quia dilatatur eget maiore loco, et <lb></lb>ideo magna pars eius foras exit. </s>

<s>Cum vero ea aeris portio quae intus re­<lb></lb>manserit, iterum condensatur ob defectum caloris restringitur, minorique <lb></lb>indiget loco. </s>

<s>Quod cum ita se habeat, necessarium est, ne aliquis locus va­<lb></lb>cuus remaneat, ut aliud quoddam corpus ingrediatur, cum ad ingrediendum <lb></lb>aeri non patuerit aditus ” (Venetiis 1599, pag. </s>

<s>193). Ai quali insegnamenti <lb></lb>del Fisico veneziano ripensando, e a tutto l&#039;altro che s&#039;è fin qui discorso, <lb></lb>ci sembrerebbe un voler rimanere ostinati ne&#039;soliti pregiudizii a riguardarsi <lb></lb>del concluder che a Galileo non si compete alcuna anteriorità, nè quanto <lb></lb>all&#039;invenzione, nè quanto agli usi, nè quanto alla stessa teoria del Termo­<lb></lb>metro, che egli pure pretende d&#039;attribuirsi, non per alcun diritto, ma per <lb></lb>secondar quel suo genio di voler essere in tutto il primo ed il solo. </s></p><pb xlink:href="020/01/298.jpg" pagenum="279"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il Termometro ad aria, di cui faceva uso il Santorio, nonostante le <lb></lb>modificazioni e i miglioramenti ingegnosamente introdottivi dal Sagredo, se­<lb></lb>guitò per lungo tempo a serbar le medesime forme immaginate dal suo <lb></lb>primo autore, e sotto le quali oramai erasi divulgato. </s>

<s>Bacone infatti, nel <lb></lb>paragrafo 28 del secondo libro del suo <emph type="italics"></emph>Nuovo Organo,<emph.end type="italics"></emph.end> pubblicato otto anni <lb></lb>dopo i Commentarii del Santorio, descrive lo strumento, e ne insegna gli <lb></lb>usi, a quel modo per l&#039;appunto che aveva fatto il nostro Medico giustino­<lb></lb>politano, tanto è certo di qui che non compete al Filosofo inglese per nulla <lb></lb>il merito dell&#039;invenzione, che alcuni pure gli hanno attribuito. </s>

<s>Nè in altro <lb></lb>modo descrive il barone di Verulamio il Termometro stesso negli altri suoi <lb></lb>libri, succeduti al Nuovo Organo, come sarebbe l&#039;<emph type="italics"></emph>Historia naturalis ven­<lb></lb>torum,<emph.end type="italics"></emph.end> nella quale, da pag. </s>

<s>135-75 della edizione, nell&#039;originale latino <lb></lb>(Lugduni Batav. </s>

<s>1648), si traducono a parole, e s&#039;inseriscono gli aforismi <lb></lb>del citato libro secondo dello stesso Nuovo Organo, dove si descrive, ne&#039;pre­<lb></lb>cisi termini come s&#039;è detto, il Termometro santoriano. </s></p><p type="main">

<s>“ Infra tutti i corpi, che ci son noti, scrisse ivi Bacone, l&#039;aria è quella <lb></lb>che più presto acquista e perde il calore. </s>

<s>” Fu per questa proprietà, molto <lb></lb>ben conosciuta infin dai tempi dell&#039;antichissimo Herone, che primi occorsero <lb></lb>a inventarsi, a tenersi in seguito in pregio, e ad usarsi nelle ricerche scien­<lb></lb>tifiche i Termometri ad aria. </s>

<s>Il Borelli, in alcune sue Annotazioni al ma­<lb></lb>noscritto de&#039;<emph type="italics"></emph>Saggi di Naturali Esperienze,<emph.end type="italics"></emph.end> in tal proposito scriveva: “ Di <lb></lb>più ricordo che i nostri Strumenti, ne&#039;quali s&#039;adopra aria rinchiusa in <lb></lb>qualche vaso, sono tanto gelosi, che non vi è Termometro di acqua arzente <lb></lb>(alcool) per grande che egli si sia, che si alteri dal caldo e dal freddo con <lb></lb>tanta facilità: e veramente non v&#039;è fluido, nel quale il caldo e il freddo operi <lb></lb>più dilatandolo e restringendolo, e senza metodo regolato atto a misurarsi <lb></lb>di quel che sia l&#039;aria ” (Targioni, Aggrandim. </s>

<s>T. II. P. II. pag. </s>

<s>604). E il <lb></lb>Montanari, nel sopra citato passo dell&#039;<emph type="italics"></emph>Astrologia,<emph.end type="italics"></emph.end> diceva che sarebbe difficile <lb></lb>il render sensibile il calor de&#039;raggi lunari, usando Termometri <emph type="italics"></emph>pieni d&#039;altro <lb></lb>che d&#039;aria.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Nonostante, avevano que&#039;così fatti Strumenti un dıfetto notabilissimo, <lb></lb>ed era quello di risentirsi, non tanto delle variazioni della temperatura, quanto <lb></lb>di quelle della pressione ammosferica. </s>

<s>La ragione però da cui dipende un <lb></lb>tal difetto non poteva esser riconosciuta, se non che dopo la grande Espe­<lb></lb>rienza torricelliana. </s>

<s>Fu infatti quello stesso difetto notato colle seguenti <lb></lb>parole, che si leggono nel Tomo IV de&#039;Manoscritti del Cimento, dove si <lb></lb>descrivono <emph type="italics"></emph>alcune varie esperienze attenenti alla questione dell&#039;aria:<emph.end type="italics"></emph.end> “ Da <pb xlink:href="020/01/299.jpg" pagenum="280"></pb>questa varietà di pressioni e costipazioni dell&#039;aria già molto bene scoperta <lb></lb>dal variar d&#039;altezza, che fa l&#039;argento vivo ne&#039;soliti strumenti, la quale è <lb></lb>tale che da che io osservo, trovo la sua massima altezza superare la minima <lb></lb>intorno alla quattordicesima parte di sè stessa; parmi che si possa dedurre <lb></lb>un&#039;altra notizia da non sprezzarsi, ed è che i Termometri a aria non son <lb></lb>così veridichi, nè così atti a mostrare il caldo e il freddo dell&#039;ambiente, <lb></lb>come quelli a acqua serrati dell&#039;ultima invenzione del Galileo, e ciò perchè <lb></lb>in quelli l&#039;acqua nel cannello va mutando altezza, non per l&#039;ingresso ed <lb></lb>uscita del caldo solamente, come bisognerebbe (oltre al non essere eterni <lb></lb>perchè l&#039;acqua per l&#039;apertura si può asciugare) ma perchè la pressione del­<lb></lb>l&#039;istessa aria esterna si va mutando dalla pressione dell&#039;interno del vaso, e <lb></lb>nel voler queste forze equilibrarsi fra loro, l&#039;acqua del cannello ne va di <lb></lb>mezzo con alzarsi ed abbassarsi, il che non segue nei Termometri a acqua <lb></lb>serrati, dove non è contrasto di pressioni, e solo v&#039;opera il caldo che entra <lb></lb>ed esce. </s>

<s>Se però, acciò si conosca che negli umani artifizi non si può dar <lb></lb>perfezione, non si voglia dire, che pur questi ancora non son del tutto fe­<lb></lb>deli, per l&#039;alterazione ultimamente scoperta nella capacità delli stessi vasi di <lb></lb>vetro contenenti l&#039;acqua, per cagione del caldo e del freddo, benchè questa <lb></lb>eccezione saria forse tenuta scrupolosa di soverchio e di niuno sensibile <lb></lb>pregiudizio ” (c. </s>

<s>9). </s></p><p type="main">

<s>In ogni modo poi, tanto è vero esser soggetto il Termometro santoriano, <lb></lb>a risentirsi delle variazioni della pressione ammosferica, che il Boyle pensò <lb></lb>di potersene servire, e se ne servì di fatto utilmente ad uso di Barometro <lb></lb>quando volle verificar la celebre esperienza del Pascal sui monti inglesi. <lb></lb></s>

<s>“ Sed communis tubi loco (scrive egli nel Cap. </s>

<s>IV della Difesa contro Fran­<lb></lb>cesco Lini) Thermometro quodam utebamur, ut inclusus aer ad eventum <lb></lb>reddendum notabilem conferret, ob rationem paulo infra commemorandam, <lb></lb>mercuriique vice communem aquam in tubo ad Thermometrum pertinente <lb></lb>adhibebamus, ut leves mutationes in pondere seu resistentia atmosphaerae, <lb></lb>aeri incluso oppositae dignosci magis possent ” (Op. </s>

<s>Omn. </s>

<s>Venetiis 1697, <lb></lb>T. I, pag. </s>

<s>162). </s></p><p type="main">

<s>Un altro inconveniente del Termometro ad aria, a quel modo almeno <lb></lb>che solevasi costruire dietro i primi modelli offerti dal Santorio, era quello <lb></lb>di non si poter trasportare comodamente, nè di poter immergerlo ne&#039;liquidi, <lb></lb>per esplorarne la temperatura. </s>

<s>È vero che s&#039;era cercato di correggere questi <lb></lb>difetti con lo adottare una costruzione diversa dalla santoriana, facendo cioè <lb></lb>servire il vasetto tutto insieme da recipiente dell&#039;aria e dell&#039;acqua, e sal­<lb></lb>dando il cannello, che mezzo entra dentro e mezzo esce fuori, alla bocca <lb></lb>dello stesso vasetto, a quel modo per l&#039;appunto, che vedesi disegnato a pa­<lb></lb>gina 89 de&#039;Circoli Pisani del Beriguardi, stampati in Udine nel 1643 dallo <lb></lb>Schiratti. </s>

<s>A solo guardar questo nuovo disegno di Termometro ad aria, che <lb></lb>noi poniam sotto gli occhi de&#039;lettori nella Fig. </s>

<s>6, si vede che lo strumento <lb></lb>è facilmente maneggevole, potendosi prendere per la sommità del cannello <lb></lb>a quest&#039;uopo piegato a manico, e potendosi altresì immergere dentro un <pb xlink:href="020/01/300.jpg" pagenum="281"></pb>liquido per esser chiuso da ogni parte, e per avere il cannello stesso saldato <lb></lb>alla bocca del vaso. </s></p><p type="main">

<s>Ma, nonostante questa nuova e più comoda costruzione, benchè ivi lo <lb></lb>chiami il Beriguardi <emph type="italics"></emph>instrumentum vitreum satis vulgare ad caloris et <lb></lb><figure id="id.020.01.300.1.jpg" xlink:href="020/01/300/1.jpg"></figure></s></p><p type="caption">

<s>Figura 6.<lb></lb>frigoris gradus dignoscendos,<emph.end type="italics"></emph.end> non era pure così divulgato, <lb></lb>quanto poi furono divulgati quegli altri Strumenti, i quali, <lb></lb>avendo per loro corpo termometrico non l&#039;aria ma un liquido, <lb></lb>si prestavan comodamente ad esser con tutta facilità traspor­<lb></lb>tati, e ad essere immersi negli altri liquidi, per esplorarli. </s>

<s><lb></lb>Quando e come avvenisse d&#039;introdur nella costruzione dei <lb></lb>Termometri un così notabile perfezionamento, è soggetto <lb></lb>meritevole delle nostre storiche investigazioni. </s></p><p type="main">

<s>In Italia fu senza dubbio divulgato il nuovo Misuratore <lb></lb>del caldo tra il 1643 e il 1660, e ciò può argomentarsi dal <lb></lb>collazionare le due edizioni che fece, in quelle due date di­<lb></lb>verse, de&#039;suoi Circoli Pisani, il Beriguardi. </s>

<s>Nella prima di <lb></lb>quelle edizioni infatti, nel Circolo IV dedicato al principe <lb></lb>Leopoldo de&#039;Medici, descrive il Termometro ad aria, come si <lb></lb>disse di sopra. </s>

<s>Ma venendo l&#039;autore a far dell&#039;Opera sua <lb></lb>una nuova edizione, che ebbe luogo in Padova nel 1660, per opera del <lb></lb>tipografo Frambolti, e volendola condurre, come oggidì si direbbe alla al­<lb></lb>tezza de&#039;tempi, sostituisce alla descrizione e al disegno del Termometro <lb></lb>ad aria la descrizione e il disegno del Termometro a liquido, che pur se­<lb></lb>guita anche qui a chiamare <emph type="italics"></emph>instrumentum vitreum satis vulgare<emph.end type="italics"></emph.end> (ivi, <lb></lb>pag. </s>

<s>447). </s></p><p type="main">

<s>Nel 1644 in Francia non si conosceva altro Termometro che quel pneu­<lb></lb>matico, e a far fede di ciò, può bastar, fra tutti gli altri documenti, la <emph type="italics"></emph>Hy­<lb></lb>draulica pneumatica<emph.end type="italics"></emph.end> del Mersenno, il quale venuto a fiutar per tutto in <lb></lb>Italia, dove sentiva venir l&#039;odore di qualche invenzione, non sarebbe man­<lb></lb>cato di far preda, per trasportarla a Parigi, anco di questo Termometro a <lb></lb>liquido, se davvero ce lo avesse trovato. </s>

<s>Anzi nemmen dieci anni dopo, <lb></lb>sembra che fosse diffuso in Francia il nuovo strumento, imperocchè, negli <lb></lb><emph type="italics"></emph>Esperimenti nuovi anatomici,<emph.end type="italics"></emph.end> il Pecquet seguitò ancora a descrivere, come <lb></lb>avea fatto il Mersenno, la prima e più antica forma del Termometro san­<lb></lb>toriano. </s>

<s>E benchè nel 1666 i nuovi Strumenti a liquido si divulgassero <lb></lb>solennemente nelle descrizioni e negli iconismi de&#039;<emph type="italics"></emph>Saggi di Naturali Espe­<lb></lb>rienze,<emph.end type="italics"></emph.end> nonostante al lontano Giorgio Sinclaro non pervenne una tale im­<lb></lb>portante notizia che verso il 1669, come s&#039;ha dalle seguenti sue parole, che <lb></lb>si trascrivon qui dal I Dialogo del lib. </s>

<s>III della sua <emph type="italics"></emph>Ars nova et magna <lb></lb>gravitatis et levitatis:<emph.end type="italics"></emph.end> “ Aquam imbutam asse virtute rarefactiva, multum <lb></lb>mihi persuadetur ex nobili quodam experimento, quod <emph type="italics"></emph>nudiustertius<emph.end type="italics"></emph.end> solum <lb></lb>vidi. </s>

<s>Fuit enim Thermoscopium utrinque hermetice occlusum. </s>

<s>Nam inferne <lb></lb>rotundam habuit ampullam superne etiam aliam, sed altera multo minorem. </s>

<s><lb></lb>Inter has tenuem admodum fistulam. </s>

<s>Eius dimidium inferius aqua, vel po-<pb xlink:href="020/01/301.jpg" pagenum="282"></pb>tius praestantissimo vini spiritu, superius vero aere repletum ” (Roteroda­<lb></lb>mi, 1669, pag. </s>

<s>273, 74). </s></p><p type="main">

<s>Il Termoscopio descritto qui dal Sinclaro è quello stesso, che i nostri <lb></lb>Accademici del Cimento descrissero in primo luogo, fra i loro strumenti, <lb></lb>per conoscer le mutazioni del caldo e del freddo dell&#039;aria. </s>

<s>“ Egli è tutto <lb></lb>di cristallo finissimo (fig. </s>

<s>7) lavorato per opra di quegli artefici, i quali, ser­<lb></lb>vendosi delle proprie gote per mantice, tramandano il fiato per un organo <lb></lb>di cristallo alla fiamma d&#039;una lucerna; e quella o intera o in varie linguette <lb></lb>divisa, di mano in mano dove richiede il bisogno di lor lavoro spirando, <lb></lb>vengono a formar opere di cristallo delicatissime e maravigliose. </s>

<s>Noi un <lb></lb>tal artefice chiamiamo il Gonfia. </s>

<s>A lui dunque s&#039;apparterrà di formar la <lb></lb><figure id="id.020.01.301.1.jpg" xlink:href="020/01/301/1.jpg"></figure></s></p><p type="caption">

<s>Figura 7.<lb></lb>palla dello strumento d&#039;una tal capacità e grandezza, e di attac­<lb></lb>carvi un cannello di tal misura di vano, che riempiendolo fin a <lb></lb>certo segno del suo collo con acquarzente, il semplice freddo <lb></lb>della neve e del ghiaccio non basti a condensarlo sotto i 20 <lb></lb>gradi del cannellino; come per lo contrario, la massima attività <lb></lb>de&#039;raggi solari eziandio nel cuor della state non abbia forza di <lb></lb>rarefarlo sopra gli 80 gradi. </s>

<s>Il modo d&#039;empierlo sarà con arro­<lb></lb>ventar la palla, e poi subito tuffar la bocca del cannellino aperta <lb></lb>nell&#039;acquarzente, sicchè vada a poco a poco succiandola. </s>

<s>Ma <lb></lb>poichè è difficile, se non affatto impossibile, di cavar tutta l&#039;aria <lb></lb>per via di rarefazione, e per ogni poca che ve ne resti la palla <lb></lb>rimane scema, si potrà finir d&#039;empiere con un imbuto di cri­<lb></lb>stallo, ch&#039;abbia il collo ridotto ad un&#039;estrema sottigliezza. </s>

<s>Ciò <lb></lb>s&#039;otterrà, quando la pasta del cristallo è rovente, poichè allora <lb></lb>si tira in fila sottilissime dentro accanalate e vote, com&#039;è ma­<lb></lb>nifesto a chi di lavorare il cristallo ha notizia. </s>

<s>Con un simile <lb></lb>imbuto adunque si potrà finir d&#039;empiere il Termometro, intro­<lb></lb>ducendo nel cannellino il suo sottilissimo collo, e spingendovi <lb></lb>dentro, colla forza del fiato il liquore, o risucciandone se fosse <lb></lb>troppo. </s>

<s>È ancora da avvertire che i gradi sopra il cannello ven­<lb></lb>gano segnati giusti; e però bisogna scompartirlo tutto colle se­<lb></lb>ste diligentemente in dieci parti uguali, segnando le divisioni con un bot­<lb></lb>toncino di smalto bianco. </s>

<s>Poi si segneranno gli altri gradi di mezzo con <lb></lb>bottoncini di vetro o di smalto nero; e questo scompartimento si potrà fare <lb></lb>a occhio essendochè l&#039;esercizio, studio e industria dell&#039;arte insegna da per <lb></lb>sè stessa a ragguagliare gli spazi, e a ben aggiustare la divisione; e chi <lb></lb>v&#039;ha fatto la pratica suole sbagliar di poco. </s>

<s>Come queste cose son fatte, e <lb></lb>col cimento del sole e del ghiaccio s&#039;è aggiustata la dose dell&#039;acquarzente, <lb></lb>allora si serra la bocca del cannello col sigillo detto volgarmente d&#039;Ermete, <lb></lb>cioè, colla fiamma, ed è fatto il Termometro ” (Firenze 1841, pag. </s>

<s>12, 13). </s></p><p type="main">

<s>Da questa bellissima descrizione, lasciando indietro le altre, nelle quali <lb></lb>si dice il modo di render più sensibile lo strumento, allungando il cannello <lb></lb>e rigirandolo a spira, o compartendo in altro numero di divisioni la scala; <pb xlink:href="020/01/302.jpg" pagenum="283"></pb>abbiamo la più compiuta notizia di ciò che fosse il nuovo Termometro, più <lb></lb>comodamente trasformato e costruito sopra un altro fatto fisico diverso da <lb></lb>quello che dette origine all&#039;invenzione del Termometro santoriano. </s>

<s>Ma qui <lb></lb>occorrono a fare alcune domande, che troppo importano alla nostra storia, <lb></lb>e delle quali non dà alcuna sodisfazione l&#039;Autor de&#039;<emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> che primo di­<lb></lb>vulgò la notizia de&#039;nuovi strumenti. </s></p><p type="main">

<s>Si può per prima cosa domandare: Fu veramente il Termometro ad al­<lb></lb>cool, descritto nel Libro De&#039;Saggi di Naturali esperienze, un&#039;invenzione degli <lb></lb>Accademici del Cimento? </s>

<s>E a ciò è stato risposto già altrove ai nostri let­<lb></lb>tori, i quali sanno che fu quella invenzione attribuita al Granduca Ferdi­<lb></lb>nando II, nel primo periodo della Sperimentale Accademia medicea. </s>

<s>L&#039;Au­<lb></lb>tore però della descrizione sopra riferita, ossia il segretario Lorenzo Magalotti, <lb></lb>non fa nemmen di ciò il minimo accenno, cosicchè è impossibile saper da <lb></lb>quelli stessi, che furon primi a farne uso, chi fu l&#039;inventore del nuovo Ter­<lb></lb>mometro a liquido. </s>

<s>Nè pur cercando per i Manoscritti, sien essi i Diarii o <lb></lb>sieno altre carte appartenenti all&#039;Accademia Fiorentina, abbiam trovato modo <lb></lb>di sodisfare a questa nostra curiosità: solamente l&#039;Autore della Nota ora <lb></lb>ultimamente trascritta l&#039;abbiam sentito chiamare il nuovo Strumento <emph type="italics"></emph>Ter­<lb></lb>mometro dell&#039;ultima invenzione di Galileo.<emph.end type="italics"></emph.end> Una tal sentenza riduce in <lb></lb>certezza il sospetto che Autore di quella Nota fosse il Viviani, di cui è ora­<lb></lb>mai noto lo zelo esagerato di volere ogni nuovo genere d&#039;invenzioni attri­<lb></lb>buire al suo adorato Maestro. </s>

<s>Fa nulladimeno assai maraviglia che si risol­<lb></lb>vesse d&#039;attribuire a Galileo il nuovo Strumento colui, che trascrisse di <lb></lb>propria mano il <emph type="italics"></emph>Registro di varie esperienze fatte e osservate dal Serenis­<lb></lb>simo G. D. </s>

<s>Ferdinando II e raccolte da Paolo Minucci per propria cu­<lb></lb>riosità.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In un tal Registro, di cui la copia fattane dal Viviani, è inserita a c. </s>

<s>10 <lb></lb>del T. </s>

<s>I de&#039;Manoscritti del Cimento, si vedono in margine disegnati o di­<lb></lb>ciam meglio abbozzati, due strumenti, il primo de&#039;quali, distinto colla let­<lb></lb>tera A, rappresentante l&#039;antico Termometro santoriano, e l&#039;altro, distinto <lb></lb>colla lettera B, rappresenta precisamente il Termometro a liquido, qual fu <lb></lb>poi descritto nel libro dei <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> e qual noi di sopra abbiam riprodotto nella <lb></lb>Figura settima sotto gli occhi dei nostri lettori. </s>

<s>Allato ai due disegni, nel <lb></lb>citato <gap></gap>anoscritto, si legge: “ Lo strumento A è continuo e dimostra il caldo <lb></lb>e il freddo dell&#039;aria, per mezzo dell&#039;acqua..... Lo strumento B dimostra <lb></lb>la differenza di caldo e di freddo dell&#039;aria e de&#039;liquidi, ed è perpetuo ”. </s>

<s>Alla <lb></lb>carta 3 in un&#039;altra bozza di questo stesso Registro, è alla Figura A no­<lb></lb>tato: “ strumento contrario, che al freddo sale e al caldo scende ”. </s>

<s>In que­<lb></lb>ste noterelle si può dir che si contenga la storia autentica del Termometro <lb></lb>a liquido, la quale storia sarà per tornar tanto meglio conforme al vero, se <lb></lb>al nome di Ferdinando II Granduca, si sostituisce nel titolo del Registro il <lb></lb>nome del Torricelli, fisico e matematico. </s></p><p type="main">

<s>Gioverebbe ora proseguire a cercare a quale occasione venisse fatto al <lb></lb>Torricelli d&#039;inventare e di costruire il nuovo Termometro a liquido. </s>

<s>Ma viene <pb xlink:href="020/01/303.jpg" pagenum="284"></pb>ad arrestarci il passo un documento, che fa
così scrivere a Guglielmo Libri, <lb></lb>nel porgerlo fedelmente trascritto ai suoi lettori: “ Le premier qui, à ma <lb></lb>connaissance, ait fermè le thermomètre et l&#039;ait soustrait ainsi à l&#039;influence <lb></lb>de la variation de la pression atmosphèrique, a ètè un ingènieur romain <lb></lb>appelè Telioux, auteur d&#039;une <emph type="italics"></emph>Matematica maravigliosa,<emph.end type="italics"></emph.end> rèdigèe à Rome <lb></lb>en 1611, et qui se trouve maintenant à la Bibliothèque de l&#039;Arsenal (<emph type="italics"></emph>MSS <lb></lb>italiens<emph.end type="italics"></emph.end> n. o20, pag. 44). </s><s>Voici la description que Telioux donne du <lb></lb> thermo­<lb></lb>mètre: <emph type="italics"></emph>Instrumento composto da due fiale, col quale si conosce il cam­<lb></lb>biamento del tempo in caldo e in freddo, secondo gradi e minuti ”.<emph.end type="italics"></emph.end> (His­<lb></lb>toire des Sciences mathèm. T. IV, Paris 1841, pag. 471) e prosegue recando <lb></lb>la descrizione dell&#039;Ingegnere romano, illustrata da un&#039;apposita figura. </s>

<s>Lo <lb></lb>strumento del Telioux ha senza dubbio qualche cosa di singolare, parteci­<lb></lb>pando del Termometro ad aria, descritto dal Beriguardi nella prima edizione <lb></lb>dei Circoli Pisani, e del Termometro a liquido del Torricelli. </s>

<s>Attendendo <lb></lb>bene infatti si vede che l&#039;acqua al caldo sale e per impulso dell&#039;aria dila­<lb></lb>tata nell&#039;ampolla inferiore, e per la dilatazione sua propria. </s>

<s>Non si può <lb></lb>però in ogni modo negare all&#039;inventore di questo strumento che egli non <lb></lb>abbia, molto prima del Torricelli, conosciuta la proprietà che hanno i liquidi <lb></lb>di dilatarsi al calore, e ch&#039;ei non abbia saputo farne suo prò, nel costruire <lb></lb>un Termometro nuovo. </s>

<s>Ma perchè è difficile il far la giusta ragion del me­<lb></lb>rito a un Autore ignoto, e a un manoscritto rimasto per due secoli e mezzo <lb></lb>sepolto in paese straniero, riprendiamo l&#039;ordine della nostra storia, per ve­<lb></lb>nire a vedere a quale occasione il Torricelli pensasse di usar per misura <lb></lb>più comoda del calore le dilatazioni de&#039;liquidi, piuttosto che quelle dell&#039;aria. </s></p><p type="main">

<s>Ei, fedel seguace degli ammaestramenti di Galileo, non poteva non pren­<lb></lb>der parte alle controversie, e con tanto più ardore è da credere che vi si <lb></lb>mettesse, quando, a combattere gli avversari, vedeva scendere in campo a <lb></lb>viso scoperto il suo diletto Maestro Benedetto Castelli. </s>

<s>Perciò, nel leggere <lb></lb>la <emph type="italics"></emph>Risposta a Lodovico delle Colombe,<emph.end type="italics"></emph.end> il pensiero meditativo dell&#039;illustre <lb></lb>Discepolo dovè trattenersi intorno a quella esperienza, che si legge ivi de­<lb></lb>scritta colle seguenti parole: “ Presa poi per nostro maggiore avvertimento <lb></lb>una caraffa col collo assai lungo, e empiutala d&#039;acqua sino a mezzo il collo, <lb></lb>e messala al fuoco, ci mostrò come, nello scaldarsi, ella andava ricrescendo, <lb></lb>sicchè, avanti che levasse il bollore, era accresciuta più di tre dita: rimos­<lb></lb>sala poi dal fuoco, nell&#039;intepidirsi, andava decrescendo e riducendosi al pri­<lb></lb>miero stato ” (Alb. </s>

<s>XII, 419, 20). </s></p><p type="main">

<s>Di qui era facile il passaggio al Termometro a liquido, e il Torricelli <lb></lb>pensò ingegnosamente di costruire sul fondamento di questa esperienza de­<lb></lb>scritta dal Castelli e da Galileo, il suo nuovo strumento. </s>

<s>Se poi l&#039;invenzione <lb></lb>di questo fu applicata al Granduca Ferdinando II non si può attribuir ciò, <lb></lb>ripetiamo, ad altro che a un cortigianesco ossequio, e a quell&#039;ingerirsi che <lb></lb>faceva il <emph type="italics"></emph>Padrone<emph.end type="italics"></emph.end> nelle esperienze fisiche del suo Matematico pensionato. </s>

<s><lb></lb>In ogni modo, circa all&#039;anno 1644, questo nuovo Misuratore de&#039;gradi del <lb></lb>calore che, chiuso d&#039;ogni sua parte, si poteva, senza pericolo di versare il <pb xlink:href="020/01/304.jpg" pagenum="285"></pb>liquido rinchiuso, e senza il tedio di dovervene infonder del nuovo, quando, <lb></lb>come avveniva ne&#039;primi Termometri ad aria, fosse esalato dal vasetto, tra­<lb></lb>sportar comodamente e immerger ne&#039;liquidi e sommergersi nella neve, per <lb></lb>conoscerne la temperatura; questo nuovo strumento era usato nell&#039;Accade­<lb></lb>mia medica in fin da quel tempo, quando ancora gli scienziati stranieri se­<lb></lb>guitavano a travagliarsi con l&#039;incomodo e imperfetto Termometro santoriano. </s>

<s><lb></lb>Dalle mani del Torricelli o del Granduca Ferdinando ebbero questo Termo­<lb></lb>metro nuovo, come per legittima e necessaria eredità, gli Accademici del <lb></lb>Cimento, i quali ne diffusero nel loro Libro la notizia e l&#039;uso per ogni parte <lb></lb>d&#039;Europa. </s></p><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il nuovo Strumento, misuratore de&#039;gradi del calore, il quale, inventato <lb></lb>in Firenze e usato agli sperimenti, che si facevano nella Corte medicea, fu <lb></lb>perciò meritamente appellato col nome di <emph type="italics"></emph>Termometro fiorentino;<emph.end type="italics"></emph.end> se nella <lb></lb>pratica si rassomigliava ai Termometri santoriani, era però nella teorica al­<lb></lb>quanto diverso, fondandosi sulla proprietà che ha il calore di dilatare i li­<lb></lb>quidi. </s>

<s>Ora è notabile come questa proprietà s&#039;appresenti nella storia della <lb></lb>scienza sotto l&#039;aspetto di nuova, e contenga perciò in sè il pregio di una <lb></lb>vera scoperta. </s>

<s>Per primo indizio e avvedimento di ciò, giova sottoporre alla <lb></lb>considerazione dei nostri lettori il seguente passo, che il Torricelli leggeva <lb></lb>e che noi pure possiamo rileggere nella citata <emph type="italics"></emph>Risposta a Lodovico delle <lb></lb>Colombe:<emph.end type="italics"></emph.end> “ Ma poichè la sottigliezza del fuoco avanza quella del discorso <lb></lb>di molti, quindi hanno avuto origine quelle qualità calde, delle quali in que­<lb></lb>sto luogo scrivete, dicendo che si comunicano per lo contatto al vetro e poi <lb></lb>dal vetro all&#039;acqua, onde poi l&#039;acqua alterata si commuove per quella qua­<lb></lb>lità sua contraria, si rarefà, gonfia, circola in sè medesima per refrigerarsi <lb></lb>e conservarsi contro il suo distruttivo, nè potendo resistere interamente si <lb></lb>risolve in vapore aereo e calido, e finalmente, dopo tanti suoi decorsi e ma­<lb></lb>nifatture, facendo forza d&#039;evaporare all&#039;aria, solleva le dette falde (galleg­<lb></lb>gianti sull&#039;acqua)..... Io voglio anco in questo particolare, come in tanti <lb></lb>altri, vedere di arrecarvi qualche giovamento e cavarvi d&#039;errore .... Pigliate <lb></lb>una palla di vetro col collo lungo e assai sottile, simile a quelle che i no­<lb></lb>stri fanciulli chiamano gozzi: empietela d&#039;acqua sino a mezzo il collo, e se­<lb></lb>gnate diligentemente il termine sin dove arriva l&#039;acqua; tenete poi tal vaso <lb></lb>sopra alcuni carboni accesi, ed osservate che, come prima il fuoco percuo­<lb></lb>terà nel vetro, l&#039;acqua comincia a ricrescere (nè ci è bisogno aspettare che <lb></lb>ella bolla per vedere tal effetto, come forse vi eri immaginato).... Volendo <lb></lb>poi vedere sensatamente da che derivi questo ricrescimento, andate con di­<lb></lb>ligenza osservando e vedrete che, secondo che gli atomi di fuoco si vanno <pb xlink:href="020/01/305.jpg" pagenum="286"></pb>moltiplicando per l&#039;acqua, ed aggregandosene molti insieme, formano alcuni <lb></lb>piccoli globettini, li quali in gran numero vanno ascendendo per l&#039;acqua, e <lb></lb>scappando fuori della sua superficie; e secondo che per entro l&#039;acqua ne <lb></lb>sarà maggior numero, ella più si alzerà nel collo del vaso, e continuando <lb></lb>di tenergli sotto i carboni lungo tempo, vedrete molte migliaia di tali glo­<lb></lb>betti ascendere e scappar via. </s>

<s>Questi, signor Colombo, non sono come vi <lb></lb>credete, vapori generati da alcune parti d&#039;acqua, che, mediante la qualità <lb></lb>celida del fuoco si vada in quelli risolvendo e tramutando: il che è mani­<lb></lb>festo, perchè se, dopo che ne saranno andate moltissime migliaia, voi rimuo­<lb></lb>verete i carboni ed aspetterete che anco gli altri, che più sparsamente e <lb></lb>perciò invisibili, per l&#039;acqua erano disseminati, si partano loro ancora, ve­<lb></lb>drete l&#039;acqua andare pian piano abbassandosi, e finalmente ridursi al segno <lb></lb>medesimo che notaste nel collo del gozzo, senza essere scemata pure una <lb></lb>gocciola; e se voi mille volte tornerete a far tale operazione, vedrete pas­<lb></lb>sare per l&#039;acqua milioni di tale sferette di fuoco, senza che l&#039;acqua scemi <lb></lb>mai un capello ” (Alb. </s>

<s>XII, 466, 67). </s></p><p type="main">

<s>Da ciò si raccolgono due notizie importanti: l&#039;osservazione del ricre­<lb></lb>scer l&#039;acqua, anco prima di bollire, al calore, proposta dal Castelli e da Ga­<lb></lb>lileo alla considerazione dei Peripatetici come nuova, e le ragioni del fatto <lb></lb>riconosciute nell&#039;introdursi, fra le particelle del liquido, gli atomi ignei, resi <lb></lb>sensibili in quelle bollicelle, che noi siamo ora certi non essere altrimenti <lb></lb>piene di fuoco, ma d&#039;aria. </s>

<s>Quella osservazione diciamo che conteneva in sè <lb></lb>una nuova scoperta, nè fa nulla in contrario il sentire i Peripatetici andar <lb></lb>con gran solennità professando quel loro principio: <emph type="italics"></emph>caloris est rarefacere et <lb></lb>frigoris condensare.<emph.end type="italics"></emph.end> Benchè derivi un tal principio dall&#039;antica scuola, e for­<lb></lb>mulato in modo così generale sembri dover essere stato applicato ad ogni <lb></lb>qualità di corpi, nulladimeno è un fatto che i Fisici, coll&#039;attenzione tutta <lb></lb>rivolta alle esperienze pneumatiche di Herone, e alle applicazioni che se ne <lb></lb>fecero in tante varie e curiose maniere, non seppero applicarlo ad altro <lb></lb>corpo che all&#039;aria. </s>

<s>Gli atomi ignei infatti di Galileo, forse perchè troppo <lb></lb>manifestamente si tradivano sotto l&#039;aspetto visibile e riconoscibile dell&#039;aria, <lb></lb>furono abbandonati, specialmente dagli stranieri, per ritornar poi rimessi in <lb></lb>onore dal Borelli, e ritenuto il fatto prima notato nella citata <emph type="italics"></emph>Risposta al <lb></lb>Colombo,<emph.end type="italics"></emph.end> i Fisici vollero piuttosto attribuir l&#039;effetto del dilatarsi i liquidi <lb></lb>all&#039;aria insinuata dentro alle loro particelle; aria che si dilata ivi dentro al <lb></lb>calore, a quel modo che nel termometro santoriano. </s></p><p type="main">

<s>Una tal dottrina è quella che fu apertamente professata da Stefano <lb></lb>Noël o Natale, in quel libretto che intitolò <emph type="italics"></emph>Plenum experimentis novis con­<lb></lb>firmatum,<emph.end type="italics"></emph.end> e in cui, coll&#039;intenzione di dimostrar la falsità del vacuo, si dif­<lb></lb>fusero in Francia le otto celebri esperienze istituite dal Pascal in Roano e <lb></lb>a Parigi, per confermar la verità della grande Esperienza torricelliana. </s>

<s>Il <lb></lb>Capitolo VIII dunque, della prima parte, Sezione V, di quel libro, è dal­<lb></lb>l&#039;Autore intitolato: “ Unde motus aquae in Thermometro ” e così dice del <lb></lb>soggetto, che s&#039;era proposto di trattare in quel capitolo: “ Sensibiles mo-<pb xlink:href="020/01/306.jpg" pagenum="287"></pb>tus aquae in Thermometro nulla alia ratione explicari posse mihi videntur <lb></lb>quam per ingressionem motumque spirituum igneorum, qui ab aere calido <lb></lb>vel manu calefacta erumpunt. </s>

<s>Spiritus calidi qui continuo absistunt ex manu <lb></lb>calida, vel pruna accensa, quae vel contigua est vel vicina phialae Ther­<lb></lb>mometro, dilatant aerem, qui est in tubo, insinuando se in eius poros. </s>

<s>Hic <lb></lb>autem aer, cum iam ampliorem in Thermometro locum occupat, propellit <lb></lb>aquam eamque dum subit in eius poros se insinuat, extendit. </s>

<s>Hunc aquae <lb></lb>recessum ac tumorem ipsis etiam oculis intuemur ” (Parisiis 1648, pag. </s>

<s>24). </s></p><p type="main">

<s>Si vede bene che gli spiriti ignei, così ben distinti dall&#039;aria, secondo <lb></lb>il Noël, son tutt&#039;altra cosa dagli atomi ignei di Galieo, ne è da passar sotto <lb></lb>silenzio che il Gesuita francese par che fosse de&#039;primi a conoscere il Ter­<lb></lb>mometro a liquido, la notizia del quale attratta da Firenze per i soliti invi­<lb></lb>sibili aliti aspirati dal Collegio Romano, poteva di li, nel 1648, essere stata <lb></lb><figure id="id.020.01.306.1.jpg" xlink:href="020/01/306/1.jpg"></figure></s></p><p type="caption">

<s>Figura 8.<lb></lb>trasmessa ai colleghi di Parigi. </s>

<s>Ma che non fosse allora in <lb></lb>Francia quello strumento molto diffuso, si prova dal seguente <lb></lb>passo che noi trascriviamo dal celebre libro <emph type="italics"></emph>Experimenta <lb></lb>nova anatomica,<emph.end type="italics"></emph.end> dove il Pecquet, attentamente osservando <lb></lb>gli effetti prodotti dal calore nel Termometro santoriano, nota <lb></lb>di avere scoperto che non solo si dilata l&#039;aria, ma l&#039;acqua <lb></lb>altresì, ciò che egli attribuisce al dilatarsi e all&#039;insinuarsi <lb></lb>delle particelle aeree calde, o contenute nell&#039;ampolla, o pree­<lb></lb>sistenti già nell&#039;acqua stessa: “ Ita impacta superiori Ther­<lb></lb>mometro ampullae manus aut admotae prunae vicinia conten­<lb></lb>tam deprimit aquam: insigni sane argumento, dilatatum intus <lb></lb>aerem, exterioris, quem aqueo cedere descensui cogit robori <lb></lb>praecellere. </s>

<s>Nec suos duntaxat fines caloris incentivo producit <lb></lb>aer: etiam aquae moles extenditur. </s>

<s>Id expertu facile, si pen­<lb></lb>dulum medio Thermometri caule placeat aquae particulam C <lb></lb>(fig. </s>

<s>8), in infimam sustinentis aeris sedem reprimere; nam <lb></lb>admotus ignis superiori lagunculae A, non inclusam C, solum­<lb></lb>modo deorsnm adigit aquam, sed et eamdem (sive quem dilatat aerem A, in <lb></lb>descendentem C, aquam immergat, sive descendentis aquae partes aereas <lb></lb>ad rarefactionem excitet) ad certum usque, puta gradum, quae vix geminus <lb></lb>occupabat, cogit excrescere ” (Parisiis 1654, pag. </s>

<s>67, 68). </s></p><p type="main">

<s>Non dissimili dottrine da queste son quelle professate dal Sinclaro, nel <lb></lb>Dialogo fra Alessandro e Francesco sopra citato. </s>

<s>Dop&#039;avere Alessandro par­<lb></lb>ticolarmente descritti gli effetti degli accessi e de&#039;recessi del calore, nel cre­<lb></lb>scere o diminuir la lunghezza della colonnetta liquida nel cannello del Ter­<lb></lb>moscopio, Francesco dice: “ Opinor hoc phoenomenon evenire non ab ipsa <lb></lb>aqua, sed potins a nonnullis in ea latitantibus particulis aereis, quarum ma­<lb></lb>gna copia scatet ” a che Alessandro acconsente dicendo esser l&#039;espression <lb></lb>dell&#039;amico <emph type="italics"></emph>verisimile.<emph.end type="italics"></emph.end> (Ars Magna edit. </s>

<s>cit., pag. </s>

<s>274). </s></p><p type="main">

<s>Tutti insomma gli Autori sopra citati concordano in ammetter che il <lb></lb>calore non operi direttamente sul liquido in dilatarlo, ma indirettamente <pb xlink:href="020/01/307.jpg" pagenum="288"></pb>sull&#039;aria, intorno alla quale il Pecquet rimane incerto se ella introducasi <lb></lb>per accidentalità dal di fuori, o se vi si trovi in mezzo di già sciolta. </s>

<s>Il Sin­<lb></lb>claro, quindici anni dopo, parla con più sicurtà, asseverando che, d&#039;aria, <lb></lb>l&#039;acqua <emph type="italics"></emph>magna copia scatet.<emph.end type="italics"></emph.end> E infatti la dimostrazione sperimentale della <lb></lb>soluzione dell&#039;aria ne&#039;liquidi, fu data dai nostri Accademici del Cimento, <lb></lb>dopo che avea pubblicati i Nuovi esperimenti anatomici il Pecquet, e prima <lb></lb>che apparisse alla luce l&#039;Arte Magna del Sinclaro. </s></p><p type="main">

<s>In qualunque modo però, è notabile che, in aguzzar l&#039;ingegno per tro­<lb></lb>var la ragion degli effetti del calore ne&#039;liquidi termometrici, i Filosofi na­<lb></lb>turali di que&#039;tempi intravedessero, per ipotesi, l&#039;esistenza dell&#039;aria annida­<lb></lb>tasi dentro i pori de&#039;corpi anche più continui. </s>

<s>De&#039;Filosofi però pubblicamente <lb></lb>conosciuti nessuno a parer nostro è più acuto di un autore italiano, i con­<lb></lb>cetti del quale son rimasti sepolti e dimenticati ne&#039;suoi Manoscritti. </s>

<s>Niccolò <lb></lb>Aggiunti che, morto nel 1635, non fu in tempo a veder pubblicati i Dialo­<lb></lb>ghi delle Due Nuove Scienze del suo Maestro, ha, per render la ragione di <lb></lb>alcuni effetti molecolari prodotti dall&#039;azion del calore e, per ispiegar le mec­<lb></lb>caniche trazioni sui corpi, teorie singolarissime e, giacchè non son punto <lb></lb>fuori del proposito nostro, degnissime di esser sapute. </s></p><p type="main">

<s>Egli dunque, non solo aveva scoperto che il calore dilata un filo liquido, <lb></lb>ma che dilata altresi un filo solido di metallo: “ Cordas e metallo per se <lb></lb>contrahi et diduci, experimento adverteris si cordae pendenti e lacunari, <lb></lb>plumbeum alligaveris acuminatum: etenim subiecto signo, videbis acumen <lb></lb>modo proprius modo longius dimitti vel attolli, prout calor aut frigus impe­<lb></lb>ritaveris ” (MSS Gal. </s>

<s>Dis. </s>

<s>T. XVIII, c. </s>

<s>61). </s></p><p type="main">

<s>L&#039;esperimento semplicissimo è per la sua stessa novità <lb></lb><figure id="id.020.01.307.1.jpg" xlink:href="020/01/307/1.jpg"></figure></s></p><p type="caption">

<s>Figura 9.<lb></lb>stupendo, ma è bene assai più stupenda la teoria dal suo Au­<lb></lb>tore escogitata, per ispiegarlo. </s>

<s>Una tal teoria non è di quelle, <lb></lb>com&#039;usava a que&#039;tempi, ripescate con gli uncini aristotati­<lb></lb>lici nel cervello di un Penpaletico, ma essa pure è fondata <lb></lb>sopra un altro nuovo e singolarissimo esperimento: “ Hoc <lb></lb>proponimus animadvertendum. </s>

<s>Si fuerit poculus vel syphun­<lb></lb>culus AB (fig. </s>

<s>9) eiusque manubrium EC cui annexum sit <lb></lb>optimum obturamentum E, quod paullulum distet a fundo <lb></lb>CA ori fistulae probe occluso, cum voluerimus manubrium <lb></lb>attrahere, multo maiorem vim nobis obsistentem sentiemus, <lb></lb>quam si recluso fistulae osculo traheretur. </s>

<s>Hanc tamen vim <lb></lb>superabimus, neque enim infinita est. </s>

<s>Pertracto igitur vi ma­<lb></lb>nubrio EC, perveniet tandem ad partes MG. </s>

<s>Aer igitur, qui <lb></lb>antea concludebatur in spatio CB, iam ampliabitur, ac deducetur in maius <lb></lb>spatium CM. </s>

<s>Quia vero haec diductio violenta fuit, violenter, et sic didu­<lb></lb>ctus, manebit. </s>

<s>Quanta autem vis est, qua manubrium retinemus pertractum <lb></lb>ad loca MG, tanta est naturalis propensio atque impetus, quo rediret ad <lb></lb>pristina loca BE. </s>

<s>Quapropter statim atque vim removeris manubrium, illico <lb></lb>celeriter redibit ad partes BE, ut oculatim testatur experimentum ” (ibi). </s></p><pb xlink:href="020/01/308.jpg" pagenum="289"></pb><p type="main">

<s>Chi, da queste informi carte manoscritte, passa a legger quelle nitide <lb></lb>pagine 18 e 19 del primo Dialogo delle Due Nuove Scienze, nel Tomo XIII <lb></lb>dell&#039;edizione curata dall&#039;Albèri, non può non ripensar con sorpresa come i <lb></lb>fecondi concetti sulla natura del vacuo, ivi espressi alcuni anni dopo da Ga­<lb></lb>lileo, si riscontrino mirabilmente con quelli dell&#039;Aggiunti; e come l&#039;espe­<lb></lb>rimento là descritto dal Discepolo aprisse la via all&#039;altro importantissimo <lb></lb>esperimento, con cui quà il Maestro tentò di misurar la forza del vacuo <lb></lb>stesso. </s>

<s>Si può con facilità credere che que&#039;concetti gli avesse Galileo inspi­<lb></lb>rati nell&#039;Aggiunti, nel privato insegnamento, prima di pubblicarli solenne­<lb></lb>mente ne&#039;Dialoghi, ma se i concetti dello stesso Aggiunti non si vuole am­<lb></lb>mettere che fossero originali per rispetto al principio scenziale, non si potrà <lb></lb>però negare che non fossero originali per rispetto alle applicazioni, ch&#039;ei ne <lb></lb>fece ad alcuni fatti fisici; applicazioni, che avrebbero forse potuto aggiun­<lb></lb>gere splendore agli stessi Dialoghi galileiani. </s></p><p type="main">

<s>La prima e principale di quelle applicazioni è diretta dal nostro Autore <lb></lb>a spiegar gli effetti di elasticità e di trazione de&#039;corpi: “ Hinc igitur facile <lb></lb>intelligemus cur nonnulla corpora vi quadam extendamus, quae postmodum <lb></lb>extensa, si vim extendentem adimas, remittuntur. </s>

<s>Si enim animo concipia­<lb></lb>mus cellulas quasdam corpori quod extenditur esse aere aut alio dissipabili <lb></lb>corpore oppletas, atque has in ipsa protractione dilatari atque ampliari, et <lb></lb>interstitia, dum dilatantur, nullo alio subeunte corpore repleri; necessario <lb></lb>idem fiet atque eveniet quod in tractione manubrii syphonis: vis enim erit <lb></lb>adhibenda ut corpus illud extendatur, et cum de contractione remiseris, corda <lb></lb>vel corpus extensum contrahetur, et ad pristinum statum redigetur ” (ibi). </s></p><p type="main">

<s>L&#039;altra applicazione, che fa l&#039;Aggiunti dello sperimento dello stantuffo <lb></lb>dentro un corpo di tromba col fondo chiuso, è quella del calore, che dila­<lb></lb>tando l&#039;aria o altro corpo dissipabile, come quello che i moderni chiaman o <lb></lb>etere annidato dentro i pori de&#039;fili metallici, fa sì che questi si vadano allun­<lb></lb>gando, per cui le corde degli strumenti si sentono mutar suono, al variar <lb></lb>temperatura, nelle varie stagioni: “ Consimiliter, quia aer calori et frigori <lb></lb>rarior et densior, inde fit ut cordae nunc laxiores, nunc contractiores sint, <lb></lb>et musica organa .... possint amittere concentum ” (ibi). </s></p><p type="main">

<s>Ecco l&#039;Aggiunti, che prima del Noël, del Pecquet, del Sinclaro, e di <lb></lb>tutti i fisici di que&#039;tempi, professa l&#039;azion diretta esercitata dal calore sul­<lb></lb>l&#039;aria, piuttostochè sulla stessa sostanza de&#039;corpi liquidi e solidi. </s>

<s>Ma come <lb></lb>poteva la forza espansiva dell&#039;aria operar così validi effetti? </s>

<s>Il dubbio non <lb></lb>turbava allora il sereno di quelli ingegni, perchè forse non avvevano atteso <lb></lb>con la debita diligenza a quegli effetti, e l&#039;Aggiunti stesso, che fu de&#039;primi <lb></lb>a sperimentare gli effetti della dilatabilità lineare de&#039;corpi solidi, non par <lb></lb>che avesse presentito quella prepotente incommensurabile forza, con cui i <lb></lb>solidi si dilatano al calore per tutti i versi, Quel primo padre e Maestro della <lb></lb>Fisica Nuova, che fu Giovan Batista Benedetti, aveva sagacemente specu­<lb></lb>lato intorno alla forza del calore in frangere le cucurbite mediche o altri <lb></lb>simili vasi: “ Dum aliquod corpus calefit dilatatur et per consequens cir-<pb xlink:href="020/01/309.jpg" pagenum="290"></pb>cumcirca undique trudit, et partes vasis debiliores cedunt: dum vero dictum <lb></lb>corpus refrigeratur, restringitur ” (Speculat. </s>

<s>Lib. </s>

<s>Venetiis 1599, pag. </s>

<s>27), <lb></lb>ma ci è ancora nel Fisico veneziano troppa speculativa che riflette, com&#039;eco, <lb></lb>il principio aristotelico <emph type="italics"></emph>caloris est rarefacere et frigoris condensare<emph.end type="italics"></emph.end> senza <lb></lb>saper vederlo o distinguerlo applicato ne&#039;fatti particolari. </s></p><p type="main">

<s>La dilatazione cubica insomma, operata dal calore sui corpi solidi, e un <lb></lb>più probabile principio operante di quel che non sia l&#039;aria annidata ne&#039;loro <lb></lb>pori, causa insufficiente per sè di tanto effetto; era tuttavia, dopo la prima <lb></lb>metà del secolo XVII, una scoperta e una speculazione da farsi. </s>

<s>E perchè <lb></lb>la scoperta e la speculazione fu fatta veramente dai nostri Italiani, e perchè, <lb></lb>per essa, oltre all&#039;aria e a&#039;liquidi, si poterono eleggere, come corpi termo­<lb></lb>metrici, i solidi, e si potè così dar maggior varietà, e talvolta anco maggior <lb></lb>precisione agli Strumenti; noi crediamo di dover trattenere alquanto i let­<lb></lb>tori sopra quest&#039;altro punto di storia scientifica italiana. </s></p><p type="main">

<s><emph type="center"></emph>VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Che la dilatazione cubica dei solidi, per l&#039;azion del calore, fosse vera­<lb></lb>mente ignota ai Fisici, nonostante l&#039;esperienza dei Termometri a liquido, <lb></lb>e quella dell&#039;Aggiunti sulla dilatazion lineare de&#039;fili metallici; s&#039;argomenta <lb></lb>da un fatto occorso al Torricelli, nell&#039;esercitarsi a lavorare con la maggior <lb></lb>diligenza possibile i vetri dei canocchiali. </s>

<s>Il fatto, che formò il soggetto di <lb></lb>un suo segreto famoso, perchè diceva non essere ad altri noto che a lui <lb></lb>solo e a Dio, consisteva nell&#039;avere osservato che il calor della mestura, con <lb></lb>la quale si solevano, per levigarli, attaccare i vetri ai macinelli, gli faceva <lb></lb>ritirar più da una parte che dall&#039;altra, per cui così venivano a deformarsi <lb></lb>le lenti. </s>

<s>Il segreto fatto osservato lo confida il geloso Discopritore così scri­<lb></lb>vendo in una sua lettera al prediletto amico Raffaello Magiotti: “ Il segreto, <lb></lb>che più m&#039;importa e che non si sa da altri che da Dio e da me, è questo: <lb></lb>Non attaccare i vetri da lavorarsi con pece nè con altro per via di fuoco. </s>

<s><lb></lb>Perchè quelle materie nel freddarsi si ritirano più da una parte che dall&#039;al­<lb></lb>tra, ed inarcano il vetro, il quale, finchè sta attaccato sul macinello, ha la <lb></lb>figura colma, ma quando lo stacchiamo per metter nell&#039;occhiale, egli si <lb></lb>spiana come prima, e la figura si guasta. </s>

<s>Questo segreto che dico adesso a <lb></lb>V. S. è stato da me osservato evidentemente tanto che l&#039;ho toccato con <lb></lb>mano, e direi anco a V. S. il come, ma lo lascio per brevità ” (MSS Gal. </s>

<s><lb></lb>Disc. </s>

<s>T. XL, c. </s>

<s>35). </s></p><p type="main">

<s>La meraviglia, fuor che al. </s>

<s>Torricelli non nota ad altri che a Dio, con­<lb></lb>sisteva evidentemente negli effetti della dilatazion cubica prodotta sulla ma­<lb></lb>teria de&#039;vetri, dal calore. </s>

<s>Però, sebbene sia cosa certa che lo stesso Torri­<lb></lb>celli osservò il fatto, si riman, per la sopra citata lettera, tuttavia in dubbio <pb xlink:href="020/01/310.jpg" pagenum="291"></pb>se egli veramente conoscesse o si fosse dato a speculare la ragione del fatto. </s>

<s><lb></lb>Comunque sia, tanto lo stesso fatto quanto la ragion fisica di lui, non s&#039;ha <lb></lb>certezza che fossero osservati e speculati se non alquanti anni dopo, in <lb></lb>que&#039;primi esercizii sperimentali, a cui dette opera l&#039;Accademia del Cimento. </s>

<s><lb></lb>Si sa che di que&#039;primi esercizii furono prediletto tema per gli Accademici <lb></lb>le osservazioni e l&#039;esperienze intorno agli artificiali agghiacciamenti. </s>

<s>Frugati <lb></lb>da un vivissimo desiderio di scoprir dove mai si ritirasse a nascondersi la <lb></lb>Natura, in quell&#039;atto che agli occhi dell&#039;osservatore pareva di vedersela in­<lb></lb>nanzi più ovvia e più manifesta; prepararono alcuni vasi, per empirli d&#039;acqua <lb></lb>o d&#039;altri liquori, e per vedere ivi dentro la Natura stessa, con qual rito vi <lb></lb>celebrasse i suoi occulti misteri. </s>

<s>Il primo vaso, di cui si servirono da prin­<lb></lb>cipio fu una palla di cristallo o ampolla con lungo collo piena d&#039;acqua na­<lb></lb>turale, e sommersa nel ghiaccio. </s>

<s>Fatto ciò, prosegue a dire il Segretario: <lb></lb>“ cominciammo ad osservare con puntualissima attenzione tutti i movimenti <lb></lb>dell&#039;acqua, ponendo mente al suo livello. </s>

<s>Già sapevamo per innanzi, e lo sa <lb></lb>ognuno, che il freddo da principio opera in tutti i liquori restringimento e <lb></lb>diminuzione di mole, e di ciò, non solamente n&#039;avevamo la riprova ordi­<lb></lb>naria dell&#039;acquarzente de&#039;Termometri, ma n&#039;avevamo fatta esperienza nel­<lb></lb>l&#039;acqua, nell&#039;olio, nell&#039;argento vivo, ed in molti altri fluidi. </s>

<s>Dall&#039;altro canto <lb></lb>sapevamo ancora che nel passaggio che fa l&#039;acqua dall&#039;esser sem plicemente <lb></lb>fredda al rimoversi dalla sua fluidità e ricever consistenza e durezza con <lb></lb>l&#039;agghiacciamento, non solo ritorna alla mole che ell&#039;aveva prima di raf­<lb></lb>freddarsi, ma trapassa ad una maggiore, mentre se le veggon rompere vasi <lb></lb>di vetro e di metallo con tanta forza. </s>

<s>Ma qual poi si fosse il periodo di que­<lb></lb>ste varie alterazioni che in esse opera il freddo, questo non sapevamo an­<lb></lb>cora, nè era possibile d&#039;arrivarvi con agghiacciarla dentro a vasi opachi, <lb></lb>come quei d&#039;argento, d&#039;ottone e d&#039;oro, ne&#039;quali s&#039;era fin allora agghiac­<lb></lb>ciata: onde, per non mancare di quella notizia, che parea esser l&#039;anima di <lb></lb>tutte quest&#039;esperienze, ricorremmo al cristallo ed al vetro, sperando per la <lb></lb>trasparenza delle materie d&#039;aver presto ad assicurarci come la cosa andasse, <lb></lb>mentre si poteva a ciascun movimento che fosse apparso nell&#039;acqua del collo, <lb></lb>cavar subito la palla dal ghiaccio, e riconoscer in essa quali alterazioni gli <lb></lb>corrispondessero. </s>

<s>Ma la verità si è che noi stentammo assai più che non ci <lb></lb>saremmo mai dati ad intendere, prima di poter rinvenire alcuna cosa di certo <lb></lb>intorno a&#039;periodi di questi accidenti. </s>

<s>E per dirne più distintamente il suc­<lb></lb>cesso, è da sapere che nella prima immersione che facevamo della palla, <lb></lb>subito che ella toccava l&#039;acqua del ghiaccio, s&#039;osservava nell&#039;acqua del collo <lb></lb>un piccolo sollevamento, ma assai veloce, dopo il quale con moto assai or­<lb></lb>dinato e di mezzana velocità s&#039;andava ritirando verso la palla, finchè arri­<lb></lb>vata a un certo grado non proseguiva più oltre a discendere ma si fermava <lb></lb>quivi per qualche tempo, a giudizio degli occhi affatto priva di movimento. </s>

<s><lb></lb>Poi a poco a poco si vedea ricominciare a salire ” (Saggi Natur. </s>

<s>Esp. </s>

<s>Fi­<lb></lb>renze 1841, pag. </s>

<s>89, 90). </s></p><p type="main">

<s>Quel fatto del sollevamento dell&#039;acqua nel collo della palla di cristallo, <pb xlink:href="020/01/311.jpg" pagenum="292"></pb>appena immersa nell&#039;acqua ghiacciata, richiamò a sè l&#039;attenzione degli Ac­<lb></lb>cademici, i quali designarono il fatto stesso col nome di <emph type="italics"></emph>salto dell&#039;immer­<lb></lb>sione,<emph.end type="italics"></emph.end> e notarono che non dipendeva da alcuna alterazione intrinseca del­<lb></lb>l&#039;acqua, ma da cagioni estrinseche del vaso (ivi, pag. </s>

<s>93). </s></p><p type="main">

<s>Intraveduta sagacemente la causa produttrice di quell&#039;inaspettato salto, <lb></lb>vollero veder che altro effetto facesse a sommerger le palle stesse, tuttavia <lb></lb>piene di varii liquori, nell&#039;acqua calda, piuttosto che nella ghiacciata, e tro­<lb></lb>varono che avveniva tutto il contrario “ perchè i livelli de&#039;suddetti liquori <lb></lb>s&#039;abbassano sensibilmente e quasi pigliano un tempo per sollevarsi, come <lb></lb>chi vuole spiccare un salto ” (ivi, pag. </s>

<s>117). </s></p><p type="main">

<s>L&#039;una e l&#039;altra di queste due nuove e curiose osservazioni occorsero <lb></lb>ad esser fatte dall&#039;Accademia, nell&#039;autunno del 1657, e benchè la notizia <lb></lb>potesse esser trapelata al di fuori e andata attorno molto tempo innanzi, <lb></lb>non fu nulladimeno divulgata che dal libro dei <emph type="italics"></emph>Saggi.<emph.end type="italics"></emph.end> Comunque sia però, <lb></lb>Isacco Vossio, nel 1663, in un suo libro intitolato <emph type="italics"></emph>De motu maris et ven­<lb></lb>torum,<emph.end type="italics"></emph.end> divulgò le osservazioni fatte già sei anni prima dai Nostri, colle pa­<lb></lb>role seguenti: “ Porro aquam etiam modico calore aut frigore dilatari et <lb></lb>constringi manifeste patebit si quis vitrum amplioris uteri et angusti orifi­<lb></lb>cii aqua frigida plenum calidae aut tepenti tantum aquae immerserit. </s>

<s>Post <lb></lb>primam coarctationem, quae momentanea est et aquam frigidam ad subitum <lb></lb>contactum paululum facit subsidere, eadem mox adscendet, idque ad legem, <lb></lb>et proportionem calidae foras ambientis. </s>

<s>Quod si aquam vitro contentam mo­<lb></lb>dice calefeceris, ac frigidae immerseris, contrarium videre est. </s>

<s>Primo quippe <lb></lb>aliquantisper ascendit aqua propter repentinum frigidae contactum <figure id="id.020.01.311.1.jpg" xlink:href="020/01/311/1.jpg"></figure> qui, <lb></lb>dum calorem inclusum per orificium expellere conatur, una quoque inclu­<lb></lb>sam propellit aquam. </s>

<s>Peracto hoc momentaneo motu, sensim contrahitur <lb></lb>moles aquae, et ad inferiores orificii partes descendit ” (Hagae Com. </s>

<s>pag. </s>

<s>49). </s></p><p type="main">

<s>La copia del libro, da cui s&#039;è trascritto questo passo, conservasi nella <lb></lb>Biblioteca del R. </s>

<s>Arcispedale di S. M. N. di Firenze, ed appartenne a Vin­<lb></lb>cenzio Viviani, che vi fece di mano propria e v&#039;appose in calce e in mar­<lb></lb>gine osservazioni e note scritte con lapis piombino. </s>

<s>In una di queste osser­<lb></lb>vazioni, che si riferisce al passo, nel punto da noi sopra contrassegnato con <lb></lb>asterisco, il Viviani dice: “ Goffa ragione! Oh quanto vi tornerà nuovo, si­<lb></lb>gnor Vossi, l&#039;allargamento e stringimento del vaso per cagione del caldo <lb></lb>e del freddo! ” </s></p><p type="main">

<s>Benchè dunque fosse già divulgato il fatto del salto dell&#039;immersione, <lb></lb>par che ancora nel 1663, dai fisici stranieri non se ne sia indovinata la causa, <lb></lb>la quale fu subito speculata e sperimentalmente dimostrata in varii modi <lb></lb>nella stessa nostra Accademia. </s>

<s>E in verità il Segretario, dop&#039;aver descritto <lb></lb>le due osservazioni del repentino sollevarsi nel collo i liquori, quando la <lb></lb>palla di cristallo sia immersa nell&#039;acqua ghiacciata, e del repentino abbas­<lb></lb>sarsi quando invece sia immersa nell&#039;acqua calda; soggiunge essere un tal <lb></lb>pensiero venuto in mente agli Accademici per render la ragione dei nuovi <lb></lb>fatti osservati: “ Il pensiero fu che l&#039;apparenza di que&#039;subiti movimenti, <pb xlink:href="020/01/312.jpg" pagenum="293"></pb>nell&#039;acqua e negli altri fluidi, non derivi da alcuna intrinseca alterazione di <lb></lb>raro e di denso .... ma bensì vogliono piuttosto che ciò avvenga per lo fic­<lb></lb>camento de&#039;volanti corpicelli del fuoco che dall&#039;acqua svapora nell&#039;esterne <lb></lb>porosità del vetro; i quali, a guisa di tante biette sforzandolo, ne vien ne­<lb></lb>cessariamente sforzata l&#039;interna capacità del vaso, anche prima che per l&#039;oc­<lb></lb>culte vie dello stesso vetro si trasmettano nel liquor contenutovi: che il <lb></lb>freddo poi ristringendo gli stessi pori faccia divenir misero il vaso alla mole <lb></lb>dell&#039;acqua che v&#039;è dentro ” (Saggi ecc. </s>

<s>Ediz. </s>

<s>cit., pag. </s>

<s>118). </s></p><p type="main">

<s>Benchè sempre però, secondo l&#039;istituto, si attribuisca dal Segretario in <lb></lb>generale ogni scoperta a tutta intiera l&#039;Accademia, il Borelli è sollecito di <lb></lb>far sapere al mondo scientifico come la scoperta, e la ragione speculata del <lb></lb>salto dell&#039;immersione è particolarmente cosa tutta sua, per cui, nel Libro <lb></lb><emph type="italics"></emph>De motion. </s>

<s>natur.,<emph.end type="italics"></emph.end> lasciò così scritto: “ Verum est quod in principio im­<lb></lb>mersionis, vasi vitrei intra nivem sale aspersam primo aqua a gradu 142 <lb></lb>brevi saltu trium fere graduum elevatur, et hic licet videatur augeri et ra­<lb></lb>refieri moles aquae ipsius vasis, nihilominus <emph type="italics"></emph>ego animadverti et docui hoc <lb></lb>contingere a restrictione eiusdem vasis<emph.end type="italics"></emph.end> (Regio Julio, 1670, pag. </s>

<s>547). </s></p><p type="main">

<s>Che la nuova teoria del dilatamento de&#039;vasi, per l&#039;intrusion del calore <lb></lb>dentro i loro pori, fosse oppugnata dai Peripatetici, i quali si appagano, <lb></lb>dice lo stesso Borelli “ di quei sottili, sufficienti e virtuosissimi vocaboli, <lb></lb>cioè di qualità calda e fredda, perchè <emph type="italics"></emph>caloris est rarefacere et frigoris con­<lb></lb>densare ”<emph.end type="italics"></emph.end> (Fabbr. </s>

<s>Lett. </s>

<s>I, 93); non fa maraviglia: maggior maraviglia però <lb></lb>farebbe il veder muovere le opposizioni da uno degli stessi Accademici, se <lb></lb>non si sapesse oramai lo spirito che lo frugava di contradire e di mettere <lb></lb>scrupolo in tutto ciò che di nuovo s&#039;annunziava dall&#039;Accademia. </s>

<s>Carlo Ri­<lb></lb>naldini negava che si potessero quelle borelliane teorie applicare al fatto del <lb></lb>salto dell&#039;immersione, perchè, dilatandosi al calore tutta insieme la mole <lb></lb>del vetro, l&#039;interna superficie del cannello, come respinta in dentro, non si <lb></lb>dilata ma si ristringe. </s>

<s>Proponeva, a persuadere sperimentalmente questo suo <lb></lb>assunto, di prendere un maschio, che scorresse a freddo esattamente in un <lb></lb>anello di ferro, e presagiva che, riscaldandosi questo anello, per via del ri­<lb></lb>crescimento operatovi dal calore, il maschio non vi si sarebbe potuto infi­<lb></lb>lare altrimenti. </s>

<s>Su tale proposta, nell&#039;Accademia, il principe Leopoldo fece <lb></lb>far l&#039;esperienza, e fu trovato che, tutto al contrario di quel che avea pre­<lb></lb>sagito il Rinaldini, il maschio nell&#039;anello così riscaldato, v&#039;entrava e usciva <lb></lb>con molta più facilità di prima. </s>

<s>Poi l&#039;esperienza, a dimostrar lo stesso ef­<lb></lb>fetto, fu, diciamo così, ringentilita, facendo gli Accademici tornire un&#039;ar­<lb></lb>milla di bronzo che incastrasse per l&#039;appunto in un mastietto dello stesso <lb></lb>metallo (Saggi ecc., pag. </s>

<s>120). Il Principe, per mezzo del medesimo Bo­<lb></lb>relli, fece partecipare il resultato di questa esperienza al Rinaldini, il quale <lb></lb>così rispondeva da Pisa in una lettera del dì 11 Novembre 1657 diretta al <lb></lb>Viviani: “ Il signor Borelli mi ha partecipato una scrittagli dal serenissimo <lb></lb>principe Leopoldo, circa l&#039;esperienza che io gli proposi da farsi quanto al­<lb></lb>l&#039;anello riscaldato ecc. </s>

<s>e sento, come posto freddo nel mascolo, sicchè ci an-<pb xlink:href="020/01/313.jpg" pagenum="294"></pb>dasse calzante, poi il medesimo postovi riscaldato vi giocasse.... Dubito che <lb></lb>l&#039;effetto possa venir da altra cagione. </s>

<s>Pare che sia cosa certa che un chia­<lb></lb>vistello di ferro giochi meno ne&#039;suoi occhi pure di ferro, secondo che l&#039;aria <lb></lb>si ritruova di tale e tale costituzione ” (MSS Cim. </s>

<s>T. XXIV, c. </s>

<s>12). </s></p><p type="main">

<s>Ma il Viviani, ben persuaso della peripatetica caponaggine del Rinal­<lb></lb>dini, e aspettandosi che, come aveva già fatto perdere la pazienza a quello <lb></lb>stizzoso del Borelli volesse seguitar a mettere a più duro cimento la sua, <lb></lb>si studiava di persuader colle seguenti parole l&#039;amico e il collega della ve­<lb></lb>rità delle ragioni e dei fatti osservati intorno alla virtù che ha il calore di <lb></lb>dilatare i corpi: “ Il dubbio di V. S. E. fondato sull&#039;effetto del chiavistello, <lb></lb>veramente mi giunge nuovo, perchè mi credevo che, per dimostrare l&#039;al­<lb></lb>largamento e stringimento del vaso, mediante il caldo e il freddo, non si po­<lb></lb>tesse far più che trovar modo di toccarlo con mano, come ultimamente ci <lb></lb>ha fatto osservare S. A. S. per mezzo di quell&#039;anima di metallo applicata <lb></lb>dentro l&#039;anello pur di metallo ora caldo ed ora freddo. </s>

<s>Se dunque il senso <lb></lb>del tatto non gli par giusto giudice, giacchè ella attribuisce l&#039;effetto del me­<lb></lb>glio giocar del maschio nell&#039;anello riscaldato, all&#039;attenuazione dell&#039;aria in­<lb></lb>clusa tra l&#039;uno e l&#039;altro cagionata dal calor dell&#039;anello; consideri di grazia <lb></lb>V. S. se gli par di prestar più fede ad alcuno degli altri sensi.... Io ho <lb></lb>tese all&#039;unisono due corde di rame di ugual lunghezza e giustezza .... ed <lb></lb>assai distanti fra loro, sotto una delle quali ho rappresentato un caldanuzzo <lb></lb>con poco fuoco per riscaldarla, e toccata l&#039;una e l&#039;altra nel medesimo tempo, <lb></lb>ho sempre osservato, insieme con molti altri ai quali ho conferita questa <lb></lb>esperienza, che la corda riscaldata ingravisce notabilmente di suono.... <lb></lb>Quanto poi al senso della vista, ho preso un filo o corda di rame delle più <lb></lb>grosse da clavicembalo ben ricotta .... e ad una delle sue estremità ho at­<lb></lb>taccata una palla di piombo .... e, formato così un pendolo, sotto alla palla <lb></lb>ho accomodato una lastra di vetro distante la grossezza di un testone. </s>

<s>Ho <lb></lb>di poi, mentre tal pendolo stava fermo, o quando aveva poco moto, acco­<lb></lb>stata la fiamma d&#039;un moccolino al fil di rame, scorrendo in giù e in su <lb></lb>colla mano, e ho mille volte osservato e veduto patentemente che appena <lb></lb>riscaldato il filo la palla arrivava a toccare il vetro, e rimossa la fiammella <lb></lb>tornava immediatamente a discostarsene all&#039;altezza di prima.... Per la qual <lb></lb>dimostrazione (dell&#039;effetto dell&#039;introduzione de&#039;calidi) mi sarei persuaso che <lb></lb>il solo e semplice effetto di veder, nell&#039;atto dell&#039;immersione della boccia <lb></lb>nell&#039;acqua calda, abbassar giù per il collo l&#039;acqua inclusa, e per il contra­<lb></lb>rio alzar per l&#039;immersione della medesima boccia nell&#039;acqua fredda;.... <lb></lb>fosse stata prova bastante.... Ma già parmi che omai si possa concludere <lb></lb>il signor Borelli avere intorno a questo effetto ottimamente discorso ” (MSS. <lb></lb>Gal. </s>

<s>Dis. </s>

<s>T. CXLII, c. </s>

<s>31, 32). </s></p><p type="main">

<s>Le due esperienze descritte qui dal Viviani si trasformarono in quel­<lb></lb>l&#039;altre due, che si leggon nel libro de&#039;<emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> a pag. </s>

<s>122, 23 della citata <lb></lb>edizione. </s>

<s>Ma l&#039;esperienza della palla pendula, che in sostanza è quella fatta <lb></lb>parecchi anni prima dall&#039;Aggiunti, fu dal Viviani stesso resa più evidente, <pb xlink:href="020/01/314.jpg" pagenum="295"></pb>col farla oscillare, mostrando così che, allungandosi il filo al calore, la palla <lb></lb>fregando sulla lastra di vetro vi si arresta il suo moto (ivi, T. CXXXV, c. </s>

<s>14). </s></p><p type="main">

<s>Il Rinaldini però non così facile ad arrendersi rispondeva contro quelle <lb></lb>esperienze e contro quegli argomenti: “ Io non dico nè parlo del vaso con <lb></lb>l&#039;acqua posto nell&#039;acqua calda o fredda .... dico bene che l&#039;anello ingrossa <lb></lb>parimenti facendosi l&#039;accrescimento delle dimensioni per tutti i versi, che è <lb></lb>quello che io ho preteso ” (MSS. Cim. </s>

<s>T. XXIV, c. </s>

<s>16). </s></p><p type="main">

<s>Contro una tal pretensione del Rinaldini e de&#039;suoi seguaci il Borelli <lb></lb>scriveva che ancorchè gli desse l&#039;animo di poter con evidenza geometrica <lb></lb>persuadere ai dissidenti la sua teoria, nonostante <emph type="italics"></emph>non sarà se non bene ocu­<lb></lb>latamente far loro vedere, se è possibile, che per l&#039;inzuppamento di <lb></lb>qualche corpo venga l&#039;interna superficie di un vaso accresciuta.<emph.end type="italics"></emph.end> (Fabbr. </s>

<s><lb></lb>Lett. </s>

<s>I, 93). </s></p><p type="main">

<s>L&#039;esperienza del ricrescer gli anelli per inzuppamento di qualche li­<lb></lb>quido, e che fu poi veramente eseguita nell&#039;Accademia e descritta ne&#039;<emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.314.1.jpg" xlink:href="020/01/314/1.jpg"></figure></s></p><p type="caption">

<s>Figura 10.<lb></lb>a pag. </s>

<s>21 della citata edizione, era senza dub­<lb></lb>bio, meglio che per via geometrica, atta a per­<lb></lb>suadere l&#039;ingegno grosso dei Peripatetici, ma <lb></lb>benchè il Borelli si vantasse d&#039;aver animo da <lb></lb>persuaderli della verità, anche per via di geo­<lb></lb>metriche dimostrazioni, non si sa però che vi <lb></lb>si provasse. </s>

<s>Vi si provò bene, e vi riusci da pari <lb></lb>suo il Viviani, il quale dimostrò, con tutto il <lb></lb>rigore geometrico, il seguente Teorema: “ Sia <lb></lb>base d&#039;un anello di metallo o di vetro l&#039;ar­<lb></lb>milla, il di cui centro sia C (fig. </s>

<s>10) la circon­<lb></lb>ferenza esteriore AO, l&#039;interiore BM, e la cir­<lb></lb>conferenza di mezzo DI, la quale è sempre la <lb></lb>misura della lunghezza o giro delle armille. </s>

<s>Dico che, quantunque si am­<lb></lb>metta com&#039;è probabile che, per l&#039;introduzione de&#039;corpuscoli calidi nella <lb></lb>solidità dell&#039;anello, si facci la dilatazione della larghezza AB per tutti i versi, <lb></lb>cioè tanto per indentro che in fuori, dovendo nello stesso tempo crescere <lb></lb>ancora la lunghezza DI o giro dell&#039;anello, è necessario che la interna cir­<lb></lb>conferenza BM si dilati ed acquisti maggior capacità ” (MSS. Gal. </s>

<s>Disc. </s>

<s><lb></lb>T. CXLII, c. </s>

<s>38). </s></p><p type="main">

<s>Lo dimostrò in due varii modi e del primo modo mandò copia al Bo­<lb></lb>relli e del secondo al Rinaldini, come ivi notò l&#039;Autore stesso di propria <lb></lb>mano: “ Mandatone copia al signor Borelli con lettera del 17 Novembre 1657 <lb></lb>del primo modo, ed al signor Rinaldini, con lettera del 26 detto, del secondo <lb></lb>modo ”. </s>

<s>Il Rinaldini, a quel che pare da una sua risposta del dì 3 Dicem­<lb></lb>bre (MSS. Cim. </s>

<s>T. XXIV, c. </s>

<s>24) restò persuaso dalla forza di quella geo­<lb></lb>metrica dimostrazione, e il Borelli pure rispondeva all&#039;Autore che <emph type="italics"></emph>la gli era <lb></lb>sembrata bella e squisita quanto mai si può desiderare<emph.end type="italics"></emph.end> (ivi, c. </s>

<s>19) ma poi <lb></lb>soggiunge queste parole, che il Viviani stesso qualificò per <emph type="italics"></emph>artificiosissime:<emph.end type="italics"></emph.end><pb xlink:href="020/01/315.jpg" pagenum="296"></pb>“ Averei però avuto caro che ella avesse veduto a Firenze quelle molte pro­<lb></lb>posizioni, che io allora abbozzai su questo proposito, ma è bene che ella an­<lb></lb>cora abbia avuto la parte del gusto nell&#039;incontrare una delle ragioni di <lb></lb>quella conclusione che è verissima ”. </s></p><p type="main">

<s>Tali parole son testualmente trascritte dal Viviani in una lettera al Ri­<lb></lb>naldini, nella quale spassionandosi coll&#039;amico, prosegue così a dire contro <lb></lb>il Borelli: “ Risposta in vero che ha stomacato me non solo, ma ciascun <lb></lb>altro a cui l&#039;ho partecipata, riconoscendovisi manifestissimo il dolore di non <lb></lb>aver mai incontrata tal dimostrazione, e la grandissima volontà di appro­<lb></lb>priarsi questa, che per altro io averei stimato bagattella, ma che ora stimo <lb></lb>qualcosa, in vedendo che quelli, che in ricchezza si reputano superiori al <lb></lb>Re di Spagna, procurano con artifizii spogliarne altri di quella poca di sup­<lb></lb>pellettile, che è toccata per sorte a chi si riconosce o si credeva poveris­<lb></lb>simo.... Che se tal conclusione egli l&#039;aveva dimostrata, perchè non dirla <lb></lb>almeno al signor Principe, al quale egli aveva fatto il discorso prima che <lb></lb>ad altri? </s>

<s>discorso di que&#039;tanti cunei di fuoco penetranti et cet. </s>

<s>et cet.? Ba­<lb></lb>sta, non è poco arrivare a conoscere la natura degli uomini. </s>

<s>V. S. tenga <lb></lb>però in sè, perchè non intendo venire a rottura aperta, sebbene a san­<lb></lb>gue caldo non so quello che io me gli abbia risposto ” (MSS. Gal. </s>

<s>Dis. </s>

<s><lb></lb>T. CXLII, c. </s>

<s>40). </s></p><p type="main">

<s>Vennero pur troppo i due grandi nostri Fisici a rottura, e anzi a fiera <lb></lb>rottura aperta, quando si fecero insieme la concorrenza in tradurre e divi­<lb></lb>nare i Conici di Apollonio di Perga. </s>

<s>E benchè la storia sopra narrata sveli <lb></lb>i principii occulti di quella rottura, che seguì non senza recar gravi danni <lb></lb>ai progressi delle scienze sperimentali in Italia, non vuol nulladimeno diva­<lb></lb>gar l&#039;attenzione dal nostro tema, a cui ritorniam per concludere essere stati <lb></lb>i nostri Italiani che primi costruirono e usarono i Termometri ad aria e a <lb></lb>liquido, e che, scoprendo la proprietà de&#039;solidi di dilatarsi al calore, apri­<lb></lb>ron la via e dettero il modo alla costruzion de&#039;Pirometri e di simili altri <lb></lb>strumenti termici. </s></p><p type="main">

<s>Benchè sia tutto ciò chiaramente dimostrato dai fatti storici, che noi <lb></lb>abbiamo sopra narrati, non si dee però per amor del vero tacere che se i <lb></lb>Termometri, specialmente a liquido, ebbero in Italia il loro principio, ritro­<lb></lb>varono appresso gli stranieri i loro ultimi perfezionamenti. </s>

<s>Uno di questi <lb></lb>perfezionamenti, e de&#039;più importanti, fu senza dubbio quello di contrasse­<lb></lb>gnare il cannello dello strumento e distinguerlo in gradi. </s>

<s>Una graduazione, <lb></lb>come vedemmo, l&#039;aveva pure anche il primo Termometro santoriano, ma <lb></lb>non sappiamo però quali fossero i due punti fissi, intra i quali si determi­<lb></lb>navano dall&#039;inventore i limiti degli accessi e dei recessi. </s>

<s>Dai testi sopra al­<lb></lb>legati nient&#039;altro si può comprendere se non che que&#039;due punti fissi, nel <lb></lb>Termomatro del Santorio, erano affatto arbitrarii, come pure arbitrarii erano <lb></lb>quelli fissati dal Sagredo, che, per uniformarsi al circolo, ne divideva lo spa­<lb></lb>zio compreso sul cannello in 360 gradi. </s></p><p type="main">

<s>Gli Accademici del Cimento fecero nel determinare i punti estremi della <pb xlink:href="020/01/316.jpg" pagenum="297"></pb>scala termometrica, un passo importante, fissando il più basso o del minimo <lb></lb>recesso nel punto della fusione del ghiaccio. </s>

<s>Ma quello del massimo ac­<lb></lb>cesso rimase tuttavia arbitrario, fissandolo nel punto de&#039;massimi ardori del <lb></lb>sole in una delle più affannose giornate. </s></p><p type="main">

<s>Il grado termico dell&#039;acqua bollente, sotto una pressione atmosferica <lb></lb>invariabile, non fu assegnato come termine dei massimi accessi altro che <lb></lb>dai fisici moderni stranieri, che al trasformato strumento apposero i loro <lb></lb>nomi. </s>

<s>Cosicchè non si può più oramai parlar di Termometro senz&#039;aggiun­<lb></lb>gervi il nome o del Farenheit o del Rèaumur, i quali, per coloro che non <lb></lb>si curano di saperne la storia, son creduti e passano per i primi inventori <lb></lb>de&#039;Termometri ad alcool o a mercurio, usciti un secolo e mezzo avanti <lb></lb>dalle mani del Torrıcelli. </s></p><p type="main">

<s>Se però fra i perfezionamenti di questo Misuratore termico si vogliano <lb></lb>annoverare que&#039;macchinamenti, nella loro semplicità più o meno ingegnosi, <lb></lb>per i quali si ridussero a nuova forma, o a mera curiosità spettacolosa, o a <lb></lb>renderne più comode le osservazioni, riducendoli per esempio a segnare i <lb></lb>gradi del calore sopra una mostra come glì orologi; i nostri Italiani del se­<lb></lb>colo XVII non si lasciaron togliere, nemmeno rispetto a ciò, i primi posti. </s>

<s><lb></lb>Ma perchè lungo, e forse alieno dal nostro istituto, sarebbe il trattenersi a <lb></lb>descriver que&#039;macchinamente quali furono immaginati dai loro inventori, ci <lb></lb>contenteremo di por termine al presente capitolo col recar la descrizione, <lb></lb>che del suo nuovo Termometro a mostra fa Urbano Daviso. </s></p><p type="main">

<s>“ Mi venne in pensiero, dice egli nel <lb></lb><figure id="id.020.01.316.1.jpg" xlink:href="020/01/316/1.jpg"></figure></s></p><p type="caption">

<s>Figura 11.<lb></lb><emph type="italics"></emph>Trattato della Sfera,<emph.end type="italics"></emph.end> di trovare il modo <lb></lb>che questo crescimento e diminuzione di <lb></lb>caldo fosse dimostrato da un indice con­<lb></lb>forme si fa negli orologi per mostrare le <lb></lb>ore, e mi riuscì nella maniera seguente: <lb></lb>Feci fare un cannone di piombo, come nella <lb></lb>figura (11) ABCD, quale empii di acqua, <lb></lb>e nella parte DC vi posi un vasetto di <lb></lb>vetro con dentrovi migliarole di tal gravità <lb></lb>che, unite con detto vasetto, restasse a <lb></lb>galla in detta acqua, ed attaccata detta <lb></lb>ampolla con detto piombo G ad un filo <lb></lb>facevo passare questo sopra la girella E, <lb></lb>e lo rivoltavo attorno a quella, ed al capo <lb></lb>di detto filo, che pendeva dall&#039;altro lato, <lb></lb>appesi un&#039;altro pezzetto di piombo F di <lb></lb>poco minor peso di quello pesasse il piombo <lb></lb>e il vasetto del cannone. </s>

<s>Nella parte poi <lb></lb>del cannone AB ci mettei una boccia di vetro col collo lungo tre palmi, <lb></lb>ed essa era grossa tre quarti di palmo nel diametro del vuoto. </s>

<s>Questa, <lb></lb>avanti d&#039;immergere il collo nell&#039;acqua, riscaldai bene al fuoco e dopo im-<pb xlink:href="020/01/317.jpg" pagenum="298"></pb>mersi il detto collo nell&#039;acqua del cannone AB, e ciò feci per esser certo <lb></lb>che il caldo dell&#039;aria non potesse essere maggiore in detta boccia in alcun <lb></lb>tempo dell&#039;anno, e subito che l&#039;aria si raffreddò salì l&#039;acqua per il collo <lb></lb>della boccia, e l&#039;acqua che era nell&#039;altro braccio del cannone di piombo DC <lb></lb>calò, e così ancora il detto vasetto calò, e perchè era più grave del piombo F, <lb></lb>alzò questo e fece tornare la girella E, il pernio della quale, avendo in un <lb></lb>capo annesso l&#039;indice HI, questo mostrava, nella circonferenza d&#039;un gran <lb></lb>cerchio che era avanti a detta girella, li gradi maggiori o minori del caldo, <lb></lb>e questi con esattezza, mentre, ad ogni poco di moto della girella, il detto <lb></lb>indice, che era in maggior proporzione con la sua lunghezza di quello fosse <lb></lb>il diametro della girella, passava maggiore spazio e veniva a mostrare in <lb></lb>parti minime le alterazioni dell&#039;aria, la quale con il riscaldarsi e raffred­<lb></lb>darsi della palla della boccia occupava in essa maggiore o minor luogo, e <lb></lb>così veniva a fare scendere e salire l&#039;acqua per il suo collo, e conseguen­<lb></lb>temente ancora il vasetto del cannone opposto. </s>

<s>Bisogna però avvertire di <lb></lb>fare la detta girella di latta, che sarà leggerissima, e l&#039;indice similmente, e <lb></lb>farli stare in bilico, acciò il detto cilindro si possa voltare ad ogni picciol <lb></lb>moto, che farà l&#039;acqua del cannone, e questo l&#039;ho fatto alto un piede antico <lb></lb>romano e grosso quasi tre once, e la girella ha di diametro quattro once ” <lb></lb>(Roma 1682, pag. </s>

<s>240-43). </s></p><pb xlink:href="020/01/318.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dell&#039;Orologio a pendolo<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. De&#039;primi Orologi a pendolo del Santorio. </s>

<s>— II. De&#039;varii modi, proposti da Galileo, d&#039;applicare il <lb></lb>pendolo agli Orologi. </s>

<s>— III. </s>

<s>Del primo Orologio descritto da Cristiano Huyghens; della sim­<lb></lb>patia de&#039;pendoli. </s>

<s>— IV. </s>

<s>Del Cronoscopio di Giorgio Sinclaro, e dell&#039;Orologio circloidale del­<lb></lb>l&#039;Huyghens. </s>

<s>— V. </s>

<s>Del Cronometro degli Accademici del Cimento. </s>

<s>— VI. </s>

<s>Come probabilmente <lb></lb>il Cronometro degli Accademici fiorentini sia invenzion del Viviani; della ricerca de&#039;centri di <lb></lb>oscillazione, ne&#039;pendoli degli Orologi. </s>

<s>— VII. </s>

<s>Degli effetti prodotti dal calore sugli Orologi; <lb></lb>dell&#039;invenzione degli Orologi a bilanciere, o da tasca; della compensazione de&#039;pendoli. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La storia autentica dell&#039;applicazione del pendolo alla misura del tempo, <lb></lb>per chi vuol proseguire l&#039;istituto da noi intrapreso, che è quello di non ri­<lb></lb>ferire le opinioni o le sentenze altrui, ma di narrare i fatti quali risultano <lb></lb>dai documenti più certi; presenta difficoltà non punto minori di quelle, che <lb></lb>ci si paravano innanzi nel primo entrare alla storia del Termometro. </s></p><p type="main">

<s>Noi dunque attendendo ai documenti dimostrativi dei fatti, che abbiamo <lb></lb>preso a narrare, c&#039;incontriamo anche questa volta nel Santorio, il quale, <lb></lb>nel suo Libro <emph type="italics"></emph>Methodi vitandorum errorum,<emph.end type="italics"></emph.end> ci dice di avere, fra gli altri, <lb></lb>inventato un nuovo strumento da lui chiamato il <emph type="italics"></emph>Pulsilogio<emph.end type="italics"></emph.end> “ in quo mo­<lb></lb>tus et quietis arteriae quisque poterit exactissime dimetiri, observare, et <lb></lb>firma memoria tenere, et inde collationem facere cum pulsibus praeterita­<lb></lb>rum dierum ” (Sanctorii Sanctorii Op. </s>

<s>Omn. </s>

<s>Venetiis, 1660, T. II, pag. </s>

<s>223). <lb></lb>E poco appresso soggiunge che non vuol trattenersi a far qui la descrizione <lb></lb>minuta dello strumento, essendo sua intenzione di parlarne di proposito in <lb></lb>un suo libro da pubblicarsi, dove descriverà tutti gli strumenti da sè, via <lb></lb>via inventati, per servire agli usi medici. </s></p><pb xlink:href="020/01/319.jpg" pagenum="300"></pb><p type="main">

<s>Il libro, come altrove avvertimmo, non fu scritto, o per dir meglio non <lb></lb>fu pubblicato, nè è pervenuto alla nostra notizia, ma non lasciò per questo <lb></lb>l&#039;Autore, come fece del Termometro, di darci la promessa descrizione nella <lb></lb>Questione V dei Commentarii sopra i canoni di Avicenna. </s>

<s>Noi sottoporremo <lb></lb>qui all&#039;esame dei nostri lettori le parole testuali, da cui, meglio che da quel <lb></lb>che riferiscono gli scrittori, i quali van ripetendo ciò che ne dicono altri <lb></lb>storici, potranno giudicare quali fossero in proposito le speculate invenzioni <lb></lb>del nostro Fisico giustinopolitano. </s></p><p type="main">

<s>“ Primum (egli dunque scrive nella Questione citata) <lb></lb><figure id="id.020.01.319.1.jpg" xlink:href="020/01/319/1.jpg"></figure></s></p><p type="caption">

<s>Figura 12.<lb></lb>est nostrum pulsilogium, in quo per certitudinem mathe­<lb></lb>maticam et non per coniecturam, dimetiri possumus ulti­<lb></lb>mos gradus recessus pulsusque ad frequentiam et raritata­<lb></lb>tem, de quo instrumento aliquid diximus in libro V <emph type="italics"></emph>Methodi <lb></lb>nostrae.<emph.end type="italics"></emph.end> A dicto Pulsilogio desumpsimus hoc paratu facile, <lb></lb>quod explicatur per primam figuram, ut infra, quae conti­<lb></lb>net funiculum ex lino vel serico contextum, cui, ut vides, <lb></lb>appensa est pila plumbea (fig. </s>

<s>12), qua impulsa, si funi­<lb></lb>culus est longior, motus pilae fit tardior et rarior: si bre­<lb></lb>vior, fit frequentior et velocior. </s>

<s>Dum igitur volumus fre­<lb></lb>quentiam vel raritatem pulsus dimetiri digitis impellimus <lb></lb>pilam laxando, vel contrahendo funiculum usque eo, quo <lb></lb>motus pilae omnino conveniat cum frequentia vel raritate <lb></lb>pulsus ipsius arteriae: quo adinvento, illico e regione ob­<lb></lb>servamus gradus 70 ostensum a linea alba ipsius pilae ubi <lb></lb>est C. </s>

<s>Quo gradu memoriae consignato, iterum eadem vel <lb></lb>sequenti die, eodem instrumento, experimur an pulsus ar­<lb></lb>teriae factus sit aliquantulum frequentior vel tardior. </s>

<s>Di­<lb></lb>cimus aliquantulum quia usu istius instrumenti non quae­<lb></lb>rimus pulsus notabiles raritatis vel tarditatis differentias, <lb></lb>quas medici memoria tenere possunt, sed illas minimas, <lb></lb>quarum differentiae inter unum et alterum diem non sunt <lb></lb>scibiles. </s>

<s>In eumdem usum est aliud simile instrumentum <lb></lb>cuius ieonem videbis fol. </s>

<s>78. fig. </s>

<s>E. </s>

<s>At notandum quod <lb></lb>pila plumbea, per maiorem vel minorem vim impulsa, non <lb></lb>mutat raritatem seu frequentiam, quia in impellendo, quan­<lb></lb>tum amittitur de spacio tantum remittitur de violentia. </s>

<s>Per <lb></lb>tale instrumentum tempore sanitatis pulsus dimetimur, deinde tempore aegri­<lb></lb>tudinis animadvertimus recessum a naturali statu, qui in effectibus digno­<lb></lb>scendis, praedicendis, et curandis est maxime necessarius ” (ibi, T. III, <lb></lb>pag. </s>

<s>29). </s></p><p type="main">

<s>La nuova disposizione, certamente più comoda, data dal Santorio al filo <lb></lb>pendulo misuratore del polso, vedesi disegnata a pagina 110 del citato <lb></lb>Tomo III, e consiste nell&#039;accorciare o scorciare il filo, ritirandolo innanzi <lb></lb>e in dietro, per mezzo di un manubrio scorrente dentro la scanalatura di <pb xlink:href="020/01/320.jpg" pagenum="301"></pb>un regolo orizzontale graduato, come vedesi nella nostra figura 13, imita­<lb></lb>tiva di quella stessa, che disegna ivi l&#039;Autore. </s></p><p type="main">

<s>Intanto, dal sopra allegato testo si rilevano le seguenti importantissime <lb></lb><figure id="id.020.01.320.1.jpg" xlink:href="020/01/320/1.jpg"></figure></s></p><p type="caption">

<s>Figura 13.<lb></lb>notizie: Prima, che il Santorio ha ricono­<lb></lb>sciuto l&#039;isocronismo del pendolo, così per <lb></lb>le ampie che per le più ristrette sue vi­<lb></lb>brazioni, assegnando per causa di quel fatto <lb></lb>straordinario il principio meccanico delle <lb></lb>velocità proporzionali agli spazii. </s>

<s>Seconda, <lb></lb>che i tempi delle vibrazioni fatte da pendoli <lb></lb>più o meno lunghi sieno reciprocamente <lb></lb>proporzionali alle semplici lunghezze dei fili. </s></p><p type="main">

<s>Notabile è però che il nostro Santorio, <lb></lb>non parla solo del pendolo come misuratore <lb></lb>della relativa frequenza e remissione del <lb></lb>polso, ma ne parla altresì come di stru­<lb></lb>mento assolutamente misuratore del tempo. </s>

<s>Nella citata pagina 110, insieme <lb></lb>con quella nuova disposizione data al Pulsilogio, per allungare o scorciare <lb></lb>misuratamente il filo pendulo, vedesi disegnata un&#039;altra figura, a contorno <lb></lb>ellittico, nel mezzo della quale son rappresentati due indici, che van no im­<lb></lb>perniati nel centro di due archi di cerchio, l&#039;uno maggiore dell&#039;altro, ma <lb></lb>graduati ambedue in sette parti, che perciò riescono disuguali. </s>

<s>La figura <lb></lb><figure id="id.020.01.320.2.jpg" xlink:href="020/01/320/2.jpg"></figure></s></p><p type="caption">

<s>Figura 14.<lb></lb>che abbiamo qui ricopiata (fig. </s>

<s>14) il nostro Autore <lb></lb>la illustra colle parole seguenti: “ Figura D est pul­<lb></lb>silogium, quod nos adinvenimus, quo non solum <lb></lb>tempus sed etiam frequentiam et raritatem pulsus <lb></lb>dimetimur. </s>

<s>In hoc instrumento sunt septem diffe­<lb></lb>rentiae frequentioris vel rarioris motus quae per ra­<lb></lb>dium observantur: deinde quilibet gradus dividitur <lb></lb>in septem minuta quae, per radiolum distinguntur, <lb></lb>cuius instrumenti constructionem in libro <emph type="italics"></emph>De medicis instrumentis<emph.end type="italics"></emph.end> doce­<lb></lb>bimus ” (ibi, pag. </s>

<s>108). </s></p><p type="main">

<s>Lo strumento così disegnato e descritto dal Santorio non è solo appli­<lb></lb>cato all&#039;uso particolare del polso ma a quello generale della misura del <lb></lb>tempo, e infatti alla pagina, o diciam meglio alla colonna 486 di questa <lb></lb>stessa opera citata, dove descrive l&#039;apparecchio per misurare il calor sensi­<lb></lb>bile dei raggi della luna, col Termometro, sopra il bulbo del quale vanno <lb></lb>a ferire gli stessi raggi condensati nel fuoco di uno specchio ustorio; si <lb></lb>serve, per misurare il tempo dell&#039;azione de&#039;raggi lunari sul bulbo termo­<lb></lb>metrico, dello strumento sopra disegnato. </s>

<s>“ Per instrumentum vero secun­<lb></lb>dae figurae temporis spatium dimetimur quod declaravimus folio citato ” (ibi). </s></p><p type="main">

<s>Non potendosi consultare il Libro degli Strumenti medici, nel quale ci <lb></lb>promette l&#039;Autore di descriverci gli organi di questo Misuratore del tempo, <lb></lb>nè altrove dicendo nulla di più chiaro, noi non sappiam dire in che modo <pb xlink:href="020/01/321.jpg" pagenum="302"></pb>si movessero i due indici nel sopra disegnato orologio, ma non rappresen­<lb></lb>tando altro le due mostre che due archi di cerchio, si può asserir con cer­<lb></lb>tezza che non dovesse essere il moto nè continuo, nè regolato a una mi­<lb></lb><figure id="id.020.01.321.1.jpg" xlink:href="020/01/321/1.jpg"></figure></s></p><p type="caption">

<s>Figura 15.<lb></lb>sura prefinita, da non si poter variare all&#039;arbitrio e al fine <lb></lb>dell&#039;osservatore. </s>

<s>Ma pure, insiem con quello, il Santorio <lb></lb>descrive un altro strumento, che ha l&#039;esteriore figura e <lb></lb>forma di un vero orologio a pendolo. </s>

<s>La figura che si vede <lb></lb>nella colonna 307 è una mostra circolare digradata in 12 <lb></lb>parti, di sotto alla quale vedesi uscire il pendolo. </s>

<s>E per­<lb></lb>chè, fra le altre figure, disegnate insieme nel campo della <lb></lb>pagina citata, questa di cui particolarmente intendiamo è <lb></lb>in ordine la terza, “ tertium est (ivi dice l&#039;Autore per illu­<lb></lb>strarla) ad instar cotylae depressae, ex qua egreditur filum <lb></lb>cui appensa est pila plumbea ”. </s>

<s>Noi rappresentiamo sotto <lb></lb>gli occhi de&#039;nostri lettori l&#039;immagine di questa <emph type="italics"></emph>Cotyla<emph.end type="italics"></emph.end><lb></lb>fedelmente disegnata nella figura 15. </s></p><p type="main">

<s>Alla colonna 510 ricorre la medesima figura, della <emph type="italics"></emph>Cotyla<emph.end type="italics"></emph.end> sopra ac­<lb></lb>cennata, con questa sola differenza: che la mostra non è in 12, ma è di­<lb></lb>visa in 24 parti uguali, com&#039;usava agli orologi pubblici di que&#039;tempi. </s>

<s>Que­<lb></lb>sto orologio a pendolo, di cui si vede con fedeltà nella nostra figura 16 <lb></lb><figure id="id.020.01.321.2.jpg" xlink:href="020/01/321/2.jpg"></figure></s></p><p type="caption">

<s>Figura 16.<lb></lb>riprodotto il disegno, è ordinato dall&#039;Inventore a mi­<lb></lb>surare i moti della inspirazione e della espirazione <lb></lb>dell&#039;infermo, e intorno ad esso il nostro Medico au­<lb></lb>tore ivi scrive le seguenti parole: “ Modus vero di­<lb></lb>metiendi inspirationem et espirationem habetur per <lb></lb>instrumentum propositum. </s>

<s>Dimetimur enim facillime <lb></lb>expirationem prius manu ad cor admota, deinde cum <lb></lb>filo, cui alligatus sit globulus plumbeus satis longo, <lb></lb>motum et quietem respirationis observamus. </s>

<s>Dicimus <lb></lb>satis longo, quia, quo longuis est, motus tardior fit ”. </s></p><p type="main">

<s>Non sembra a noi poter esservi nessun dubbio <lb></lb>che questa così detta <emph type="italics"></emph>Cotyla,<emph.end type="italics"></emph.end> descrittaci o mostrataci <lb></lb>sotto velo dal Santorio, non sia un vero e proprio <lb></lb>orologio a pendolo. </s>

<s>La chiama <emph type="italics"></emph>Cotyla<emph.end type="italics"></emph.end> perchè, come <lb></lb>udimmo dire a lui stesso, la mostra era alquanto <lb></lb>incavata da presentar l&#039;immagine di una scodella, <lb></lb>ma dietro alla scodella doveva esservi qualche con­<lb></lb>gegno, il quale comunicasse all&#039;indice i moti vibra­<lb></lb>torii del pendolo. </s>

<s>In che propriamente consistesse un tal congegno, e come <lb></lb>fosse connesso con gli stessi moti vibratorii, non possiamo noi dirlo con cer­<lb></lb>tezza, ma è facile indovinare che consistesse tutto in ruote dentate, a somi­<lb></lb>glianza di quell&#039;altro orologio a pendolo, che per uso di trovar le longitudini <lb></lb>fu proposto da Galileo. </s></p><p type="main">

<s>Abbiamo detto di sopra esser questo il primo documento storico pub-<pb xlink:href="020/01/322.jpg" pagenum="303"></pb>blicamente conosciuto, e in che si abbatte colui, che vuol narrar le cose <lb></lb>non sull&#039;autorità degli scrittori, ma sopra la verità dimostrata dai fatti, co­<lb></lb>sicchè in conclusione parrebbe fosse stato il Santorio il primo a riconoscer <lb></lb>la proprietà dell&#039;isocronismo de&#039;pendoli, e ad applicarla sagacemente alla <lb></lb>misura dei tempi. </s>

<s>Contro una siffatta conclusione però insorgono molti, e <lb></lb>affermano, senza il minimo dubbio, che l&#039;isocronismo del pendolo e la prima <lb></lb>applicazione di lui all&#039;orologio, sono scoperte e invenzioni di Galileo. </s>

<s>Il fon­<lb></lb>damento principale di una tale affermazione non è in altro per costoro, che <lb></lb>nella autorità di Vincenzio Viviani, della quale sarà da noi lungamente di­<lb></lb>scorso a suo luogo. </s>

<s>Ma intanto vogliamo far conoscere ai nostri lettori altri <lb></lb>documenti, diversi dai già noti, per i quali ci potremo chiarire anche me­<lb></lb>glio come e quanto il soverchio zelo, nel fervente Ammiratore del suo Mae­<lb></lb>stro, facesse ombra a veder chiaro e a scrivere il vero. </s></p><p type="main">

<s>Nel Tomo CXVII dunque dei <emph type="italics"></emph>Discepoli,<emph.end type="italics"></emph.end> nella preziosa collezione dei <lb></lb>Manoscritti galileiani, dalla carta 60-63 si leggono alcuni studii dello stesso <lb></lb>Viviani sulle proprietà meccaniche de&#039;pendoli, e sulle matematiche loro di­<lb></lb>mostrazioni. </s>

<s>È una scrittura informe, ma dentro alla quale si leggono di <lb></lb>propria mano le parole stesse, che noi qui trascriviamo. </s></p><p type="main">

<s>“ Questa del pendolo (così par che il Viviani voglia dare il principio a <lb></lb>una sua Trattazione) si è una delle più antiche invenzioni e scoperte in na­<lb></lb>tura del Galileo, e fu circa l&#039;anno 1580, quando egli era studente a Pisa, <lb></lb>nel trovarsi egli un giorno in quel Duomo, dove si abbattè di vedere, la­<lb></lb>sciata in moto, una lampada pendente da una lunghissima corda. </s>

<s>E, come <lb></lb>quello che da giovanetto s&#039;era anche esercitato nella Musica, sotto la disci­<lb></lb>plina di quel gran Vincenzio suo Padre, che sì dottamente scrisse poi in Dia­<lb></lb>logo della Musica antica e moderna; perciocchè aveva impressa nell&#039;anima <lb></lb>l&#039;egualità de&#039;tempi, co&#039;quali essa si regola, riflettendo a quel moto, gli fu <lb></lb>facile il giudicarlo in mente sua equitemporaneo, sì nelle andate lunghe e <lb></lb>larghe al principio del moto, come nelle strette sul fine verso la quiete. </s>

<s>In <lb></lb>casa poi se ne chiarì in più modi con replicate esperienze esattissime, tro­<lb></lb>vando, coll&#039;aiuto de&#039;suoi compagni, che in un determinato numero di vibra­<lb></lb>zioni d&#039;un certo pendolo, lasciato andar sempre da una distanza medesima <lb></lb>del perpendicolo, quante ne faceva un altro pendolo delle larghe, altrettante <lb></lb>in ciascuno ne faceva delle strette e delle strettissime. </s>

<s>Che se il numero di <lb></lb>queste eccedeva di qualcosa il numero di quelle, il che però si fa visibile <lb></lb>solamente dopo un numero grandissimo delle une e delle altre, attribuiva <lb></lb>questa piccola maggioranza al minore ostacolo, che arreca l&#039;aria al mobile <lb></lb>più tardo, qual&#039;è quello del grave pendolo nel passar gli archi più piccoli, <lb></lb>che al mobile più veloce, qual&#039;è il medesimo nel passar gli archi grandi ”. </s></p><p type="main">

<s>La storia narrata in quest&#039;abbozzo di scrittura inedita è simile a quella <lb></lb>che pubblicò il Viviani nella Vita di Galileo, e che noi vedremo esaminata <lb></lb>diligentemente a suo luogo, dove dimostreremo la inverisimiglianza che la <lb></lb>prima occasione di scoprir l&#039;isocronismo del pendolo si porgesse a Galileo <lb></lb>stesso nell&#039;attendere a misurar la durata delle oscillazioni o più ampie o <pb xlink:href="020/01/323.jpg" pagenum="304"></pb>più ristrette della lampada nel Duomo di Pisa. </s>

<s>Ma non si può negare, in <lb></lb>ogni modo, che verso quel tempo indicato dal Viviani, o poco dopo, il gran <lb></lb>Maestro della nuova Scienza del moto non fosse veramente il primo a no­<lb></lb>tare quella insigne proprietà dei corpi oscillanti. </s></p><p type="main">

<s>Comunque sia, abbiamo documento certissimo che nel 1602 Galileo si <lb></lb>faticava intorno alla dimostrazione di quella proprietà naturale de&#039;corpi gravi <lb></lb>sospesi, già prima sperimentalmente scoperta, e il documento è una lettera <lb></lb>diretta a Guidubaldo del Monte, da Padova, dove da poco insegnava, collega <lb></lb>e amico di Santorre Santorio. </s>

<s>È probabilissimo perciò che il giovane Mate­<lb></lb>matico conferisse questa sua nuova speculazione col Medico già provetto, e <lb></lb>la probabilità vien maggiormente confermata dal veder che i principii mec­<lb></lb>canici dell&#039;uno erano quegli stessi professati dall&#039;altro. </s>

<s>Imperocchè il San­<lb></lb>torio ammette l&#039;isocronismo assoluto, come Galileo, per ogni ampiezza di <lb></lb>arco, e ritien che i tempi delle vibrazioni fatte da due pendoli di differente <lb></lb>lunghezza fossero ad esse lunghezze in semplice ragion reciproca propor­<lb></lb>zionali. </s>

<s>Benchè insomma il primo a pubblicar questa proprietà del pendolo <lb></lb>fosse il Santorio, è certo nulladimeno che dieci anni prima aveva privata­<lb></lb>mente fatta nota quella scoperta Galileo, come principale fondamento al <lb></lb>grande edifizio meccanico, a cui egli già incominciava a por mano. </s></p><p type="main">

<s>Ma seguitiamo a leggere quel che nella sopra allegata scrittura sog­<lb></lb>giunge appresso il Viviani: “ Assicuratosi allora di così bella notizia, come <lb></lb>che Egli era d&#039;ingegno che de&#039;primi acquisti di qualche vero non si con­<lb></lb>tenta, pensò subito di applicarlo ad uso giovevole della Medicina, nella quale, <lb></lb>per secondare il gusto del proprio Padre, faceva allora i suoi studii, ond&#039;ei <lb></lb>propose ai medici di quel tempo di valersi di un picciol pendolo, per esa­<lb></lb>minare, con un tal giudice, inalterabile e spassionato, senza dover, come <lb></lb>solevano, confidar nella propria fallace reminiscenza, la varietà della fre­<lb></lb>quenza de&#039;polsi de&#039;febbricitanti, e chiarirsi de&#039;tempi dell&#039;accesso, dell&#039;au­<lb></lb>gumento, dello stato e della declinazione delle febbri. </s>

<s>Di tal semplicissimo <lb></lb>strumento, benchè dai più fosse poco apprezzato, non mancarono però de&#039;più <lb></lb>docili che ne fecer conto, e di qui è che spargendosene l&#039;uso per l&#039;Italia <lb></lb>ed oltrè i monti, vi fu chi se ne appropriò l&#039;invenzione, senza neppur far <lb></lb>parola del suo primo e vero Autore, se non con pregiudizio di quell&#039;onore, <lb></lb>che sì giustamente gli era dovuto. </s>

<s>Il medesimo strumento fu di poi dal no­<lb></lb>stro Accademico, subito che si fu introdotto nelle Matematiche, il che segui <lb></lb>sui 22 anni della sua età, cioè intorno al 1885, adattato alla cognizione delle <lb></lb>minuzie dei tempi, per conseguir la precisione tanto necessaria nelle osser­<lb></lb>vazioni astronomiche, e per lo cui mezzo, che è in apparenza debolissimo, <lb></lb>comecchè ad un debolissimo filo stia appeso il grave pendulo misuratore, <lb></lb>ed egli e tutti gli osservatori che ne son proceduti, hanno avuto campo di <lb></lb>restaurare l&#039;Astronomia, la Nautica e la Geogralia. </s>

<s>Che perciò è verissimo <lb></lb>doversi in Natura far capitale non meno delle cose piccole che delle grandi, <lb></lb>essendo ella massima nelle minime, non che nelle grandissime. </s>

<s>Di qui è <lb></lb>che il nostro Accademico, bene sciente di ciò, seppe sempre delle cose <pb xlink:href="020/01/324.jpg" pagenum="305"></pb>naturali notabilmente approfittarsi d&#039;ogni minuzia, anco in apparenza vi­<lb></lb>lissima. </s>

<s>” </s></p><p type="main">

<s>Apparisce da queste parole essere una ferma persuasione del Viviani che <lb></lb>si debba attribuire a Galileo, non la sola scoperta del fatto concernente l&#039;iso­<lb></lb>cronismo del pendolo, ma l&#039;applicazione del fatto stesso altresi alla misura <lb></lb>delle minuzie del tempo in generale, e delle pulsazioni delle arterie in par­<lb></lb>ticolare. </s>

<s>Secondo lui, il Santorio sarebbe stato uno di quelli, che si attri­<lb></lb>buirono l&#039;invenzione di Galileo, a cui venne il primo pensiero d&#039;applicare <lb></lb>il pendolo all&#039;orologio per le mediche ascoltazioni del polso. </s>

<s>È notabile però <lb></lb>che l&#039;egregio Autore, così scrivendo, non fece altro che secondare le inspi­<lb></lb>razioni del suo cuore fervente di sviscerato ossequio verso il suo venerato <lb></lb>Maestro, avendo noi documenti che nel 1669 non aveva veduta ancora nes­<lb></lb>suna delle opere del Santorio. </s>

<s>Così fatti documenti consistono in due lettere <lb></lb>di Geminiano Montanari, nella prima delle quali, che è del dì 29 di Otto­<lb></lb>bre, avendo avuta commissione dal Viviani di guardar se appresso i librai <lb></lb>di Bologna si trovassero le Opere del Santorio venali, il Montanari stesso <lb></lb>così gli risponde: “ Del Santorio non ho mai trovato cosa alcuna, e questi <lb></lb>Medici qui gli asciugano tutti. </s>

<s>Solo ho trovato un&#039;Opera di questo Autore <lb></lb><emph type="italics"></emph>De vitandis erroribus<emph.end type="italics"></emph.end> ecc. <emph type="italics"></emph>in re medica,<emph.end type="italics"></emph.end> in folio, e mi fanno l&#039;ultimo prezzo <lb></lb>di lire 4. Se ella comanda ne sarà servita ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLV, <lb></lb>c. </s>

<s>120). E in altra del dì 3 Dicembre torna così a scrivere intorno al me­<lb></lb>desimo soggetto: “ Non mi ricordo se dissi a V. S. che quel Santorio <emph type="italics"></emph>De <lb></lb>vitandis erroribus<emph.end type="italics"></emph.end> non sapeva se gli uscirebbe così grato, poichè non vi si <lb></lb>contiene cosa alcuna nè circa la statica, nè circa l&#039;esperienza più curiosa <lb></lb>del Metrosfigmo ed altre osservazioni sue, lo che credo esser lo scopo pri­<lb></lb>mario della curiosità di V. S. circa di questo Autore, ma è ella tutta l&#039;opera <lb></lb>dottrinale medica intorno gli errori più comuni, nè forse diversa, quanto al <lb></lb>soggetto e materia principale, dall&#039;opuscolo del Cardano <emph type="italics"></emph>Consideratio me­<lb></lb>dica<emph.end type="italics"></emph.end> ecc. </s>

<s>” (ivi, c. </s>

<s>122). </s></p><p type="main">

<s>Si par chiaro di qui che alle orecchie del Viviani era pervenuto il ru­<lb></lb>more che fosse dal Santorio stato pubblicamente descritto il pulsilogio, e <lb></lb>senz&#039;aver letto e bene esaminato il Libro, si dette a creder con ferma per­<lb></lb>suasione che il Medico di Capo d&#039;Istria ne avesse destramente involata l&#039;in­<lb></lb>venzione a Galileo. </s>

<s>Ma non è ciò un proceder conforme al criterio storico, <lb></lb>come pure non è in conformità di questo criterio l&#039;asserir che fa il Viviani <lb></lb>avere il suo Galileo applicato il pendolo alla misura del tempo nelle osser­<lb></lb>vazioni astronomiche, infino dal 1585, essendo che resulti chiarissimamente <lb></lb>dai documenti che il pendolo non s&#039;incominciò ad usar per misuratore del <lb></lb>tempo in Astronomia, se non che verso il 1638, come da noi verrà dimo­<lb></lb>strato a suo luogo. </s></p><p type="main">

<s>Prima di quel tempo il pendolo, per Galileo, non era altro che uno <lb></lb>strumento meccanico, per cui crediamo di poter giustamente asserire che <lb></lb>il primo, il quale si servisse del pendolo come di strumento cronologico fu <lb></lb>il Santorio. </s>

<s>Nè la critica sa suggerirci nessun buon motivo di credere che <pb xlink:href="020/01/325.jpg" pagenum="306"></pb>la prima idea del Pulsilogio l&#039;avesse il celebre Medico attinta dai colloqui <lb></lb>con Galileo, ripensando che questi non attendeva in Padova all&#039;arte medica, <lb></lb>mentre l&#039;altro la professava ivi con gran celebrità, e per l&#039;invenzione di <lb></lb>altri strumenti era divenuto in gran fama. </s>

<s>Dall&#039;altra parte sappiamo per <lb></lb>cosa certa che Galileo non si servì del pendolo per misuratore del tempo, <lb></lb>nemmeno nelle sue sperimentali meccaniche esercitazioni, preferendo l&#039;an­<lb></lb>tica clessidra, col pesar l&#039;acqua in un dato tempo stillata. </s>

<s>Se non ne fece <lb></lb>dunque l&#039;applicazione in materia propria e in soggetto così geloso, qual&#039;era <lb></lb>quello di misurare i tempi della caduta de&#039;gravi rispetto agli spazii succes­<lb></lb>sivamente passati; com&#039;è credibile che facesse uso del pendolo, o pensasse <lb></lb>a suggerirlo a un&#039;arte aliena dalla sua professione? </s>

<s>E come si può con giu­<lb></lb>stizia asserire che il Santorio tanto solo avesse d&#039;ingegno, quanto gliene bi­<lb></lb>sognava a furar destramente una scoperta a Galileo? </s></p><p type="main">

<s>In conclusione, i documenti a favor del Santorio son certi, ma quali <lb></lb>altri documenti a favore di Galileo reca il Viviani? </s>

<s>Dov&#039;è fra le galileiane <lb></lb>una pagina o manoscritta o stampata, in cui si faccia il minimo accenno a <lb></lb>queste cose? </s>

<s>Nè l&#039;occasione solenne di far ciò sarebbe pure mancata al­<lb></lb>l&#039;Autore, là dove parla del pendolo ne&#039;<emph type="italics"></emph>Massimi Sistemi<emph.end type="italics"></emph.end> o più opportuna­<lb></lb>mente nel primo Dialogo delle <emph type="italics"></emph>Due Nuove Scienze.<emph.end type="italics"></emph.end> Perchè qui se ne passa <lb></lb>con tanta fretta, lasciando la legge importantissima, che governa il moto <lb></lb>de&#039;pendoli di lunghezza varia, senza il conforto di una matematica dimo­<lb></lb>strazione? </s></p><p type="main">

<s>A supplire al difetto di Galileo, soccorse, l&#039;anno dopo la pubblicazione <lb></lb>fatta dagli Elzevirii, uno straniero tedesco Giovan Marco De&#039;Marchi, il quale <lb></lb>in un suo Trattato <emph type="italics"></emph>De proportione motus<emph.end type="italics"></emph.end> dimostrò con rigoroso processo <lb></lb>matematico la proposizione seguente: “ Motus circulorum sunt in ratione <lb></lb>temporum quam habent diametri ad se duplicatam ” (Pragae, 1639, pag. </s>

<s>I, <lb></lb>4 vers). </s></p><p type="main">

<s>Il De Marchi si riserbò nell&#039;ultima parte del suo Trattato di parlar <lb></lb>del pendolo per uso di Pulsilogio, la descrizione del quale è similissima a <lb></lb>quella della seconda maniera del Santorio, ma la teoria è diversa, imperoc­<lb></lb>chè, mentre il Nostro ignora la legge del ritirarsi e del rilassarsi il filo per­<lb></lb>chè faccia il pendolo le sue vibrazioni in tempi determinati; il Tedesco ne <lb></lb>dà regola certa, applicando la legge sperimentalmente scoperta da Galileo, <lb></lb>e da sè matematicamente dimostrata che cioè i tempi delle vibrazioni stanno <lb></lb>in ragione delle radici delle lunghezze de&#039;fili. </s></p><p type="main">

<s>Lo stesso Autore termina il suo Trattato col proporsi di risolvere que­<lb></lb>sto problema: “ Horologium construere, quod suo motu tempus numeret <lb></lb>divisum in partes minores quam tertias unius secundi ” e la soluzione di­<lb></lb>pende dall&#039;applicare ai pendoli la dimostrata legge del variar de&#039;tempi al <lb></lb>variar delle lunghezze stesse a cui son sospesi. </s></p><pb xlink:href="020/01/326.jpg" pagenum="307"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Benchè sia un fatto che Galileo non si rivolse a principio, con fiducioso <lb></lb>amore e con sollecito studio, al pendolo, per far di lui il più squisito mi­<lb></lb>suratore del tempo, venne nulladimeno assai presto l&#039;occasione che gli fece <lb></lb>sentir come l&#039;importante problema era riserbato a risolversi da quel suo ne­<lb></lb>gletto strumento. </s>

<s>Venne appunto quell&#039;occasione, quando, per mezzo delle <lb></lb>osservazioni de&#039;Satelliti di Giove, gli cadde in pensiero che si potesse, me­<lb></lb>glio che in qualunque altro modo, ritrovar le longitudini dai naviganti. </s>

<s>Al­<lb></lb>lora tornò il suo pendolo oscillatorio a incorargli una fiducia che i tempi <lb></lb>necessarii per valersi di quelle gioviali osservazioni, non si sarebbero potuti <lb></lb>misurar nè più comodamente nè più esattamente, che dai moti invariabili <lb></lb>di lui. </s>

<s>“ Io ho tale misuratore del tempo (scriveva nell&#039;Agosto del 1636 <lb></lb>agli Stati Generali di Olanda) che se si fabbricassero quattro o sei di tali <lb></lb>strumenti, e si lasciassero scorrere, troveremmo, in confermazione della loro <lb></lb>giustezza, che i tempi di quelli misurati e mostrati, non solamente d&#039;ora in <lb></lb>ora, ma di giorno in giorno, e di mese in mese, non differirebbero tra di <lb></lb>loro, nè anco di un minuto secondo, tanto uniformemente camminano ” <lb></lb>(Alb. </s>

<s>VII, 86). </s></p><p type="main">

<s>In queste parole è evidentemente inteso il semplice pendolo, le vibra­<lb></lb>zioni del quale direttamente numerate esibiscono, senz&#039;altro meccanismo ag­<lb></lb>giuntovi, la misura esatta del tempo. </s>

<s>Ma quelle misurazioni, oltre ad esser <lb></lb>bene spesso fallaci, per mancanza di attenzione o per accidental divagamento <lb></lb>degli osservatori, riuscivan sommamente tediose, per cui parve al Renieri di <lb></lb>aver fatto in tal proposito qualche progresso, quando, avendo osservata una <lb></lb>nuova proprietà nel moto de&#039;pendoli, credette di poter per essa dedurre il <lb></lb>numero delle vibrazioni, senz&#039;aver bisogno di star lì pazientemente a con­<lb></lb>tarle a una a una. </s></p><p type="main">

<s>“ Voglio dar parte (così egli scrive in una lettera a Galileo del 27 Mar­<lb></lb>zo 1637) a V. S. di una osservazione fatta da me nelle vibrazioni de&#039;corpi <lb></lb>pendoli, che forse, se da lei non è stata avvertita, non le dispiacerà; ed è <lb></lb>che lasciandosi andar dall&#039;uno de&#039;lati dell&#039;arco da loro descritto e restrin­<lb></lb>gendosi sempre più, tante vibrazioni pongono la prima volta nel restringersi <lb></lb>un palmo, quanto ìa seconda e la terza ecc. </s>

<s>Coll&#039;esempio mi lascerò forse <lb></lb>meglio intendere. </s>

<s>Sia sospeso il pendolo A (fig. </s>

<s>17) dal punto E fino all&#039;al­<lb></lb>tezza dell&#039;arco LF. </s>

<s>Lasciandosi poi andar libero fino ad H, nel ritorno farà <lb></lb>la vibrazione d&#039;arco minore in B, la terza in C, ecc. </s>

<s>Ora, se, per esempio, <lb></lb>la decima vibrazione avrà slontanato il pendolo dalla perpendicolare all&#039;oriz­<lb></lb>zonte EI, per la quantità dell&#039;arco GL, ogni volta che il pendolo si tornerà <lb></lb>a lasciar cader libero dal punto F, e che avrà ristrette le sue vibrazioni al-<pb xlink:href="020/01/327.jpg" pagenum="308"></pb>l&#039;arco GD, saranno sempre dieci vibrazioni e non più il che potrà ser­<lb></lb>vire per numerare le vibrazioni senz&#039;averle a contare a una a una ” (ivi, <lb></lb>T. X, 201). <lb></lb><figure id="id.020.01.327.1.jpg" xlink:href="020/01/327/1.jpg"></figure></s></p><p type="caption">

<s>Figura 17.</s></p><p type="main">

<s>Sia che Galileo avesse notata o <lb></lb>no questa singolarità de&#039;pendoli pro­<lb></lb>postagli a considerar dal Renieri, ebbe <lb></lb>forse di qui occasione a speculare un <lb></lb>modo e a immaginare un congegno <lb></lb>per levare il tedio di contar le vibra­<lb></lb>zioni, d&#039;onde poi dedurne con facilità <lb></lb>la misura dei tempi trascorsi. </s>

<s>È perciò <lb></lb>che tornando nel Giugno del 1637, <lb></lb>tre mesi dopo la lettera scrittagli dal <lb></lb>Renieri, a trattar con Lorenzo Realio <lb></lb>del negozio delle Longitudini, gli pro­<lb></lb>pone, per la più facile ed esatta riso­<lb></lb>luzion del problema, uno strumento <lb></lb>misuratore del tempo da lui perfe­<lb></lb>zionato e reso di più comodo uso. </s>

<s><lb></lb>Dop&#039;avere infatti discorso delle pro­<lb></lb>prietà meccaniche de&#039;pendoli, così di <lb></lb>lunghezza invariabile come di differenti lunghezze di fili, “ Da questo verissimo <lb></lb>e stabile principio (egli tosto soggiunge) traggo io la struttura del mio Misura­<lb></lb>tore del tempo, servendomi non d&#039;un peso pendente da un filo, ma d&#039;un pen­<lb></lb>dolo di materia solida e grave, qual sarebbe ottone o rame; il qual pendulo <lb></lb>fo in forma di settore di cerchio di dodici o quindici gradi, il cui semidia­<lb></lb>metro sia due o tre palmi, e quanto maggiore sarà, con tanto minor tedio <lb></lb>se gli potrà assistere. </s>

<s>Questo tal settore fo più grosso nel semidiametro di <lb></lb>mezzo avendolo assottigliato verso i lati estremi, dove fo che termini in una <lb></lb>linea assai tagliente, per evitare quanto si possa l&#039;impedimento dell&#039;aria, <lb></lb>che sola lo va ritardando. </s>

<s>Questo è perforato nel centro, pel quale passa un <lb></lb>ferretto in forma di quelli sopra i quali si voltano le stadere; il qual fer­<lb></lb>retto, terminando nella parte di sotto in un angolo, e posando sopra due so­<lb></lb>stegni di bronzo, acciò meno consumino, pel lungo muovergli, il settore; <lb></lb>rimosso esso settore per molti gradi dallo stato perpendicolare quando sia <lb></lb>bene bilicato, prima che fermi, anderà reciprocando di qua e di là numero <lb></lb>grandissimo di vibrazioni, le quali, per potere andare continuando secondo <lb></lb>il bisogno, converrà che chi gli assiste, gli dia a tempo un impulso ga­<lb></lb>gliardo, riducendolo alle vibrazioni ample. </s>

<s>E fatta, per una volta tanto, con <lb></lb>pazienza, la numerazione delle vibrazioni che si fanno in un giorno naturale, <lb></lb>misurato colla rivoluzione di una stella fissa, s&#039;averà il numero delle vibra­<lb></lb>zioni d&#039;un&#039;ora, d&#039;un minuto, o d&#039;altra minima parte ” (ivi, T. VII, 169, 70). </s></p><p type="main">

<s>Squisiti son senza dubbio questi perfezionamenti introdotti da Galileo <lb></lb>nella costruzione dello strumento, e con tanta accortezza soccorre a rimuo-<pb xlink:href="020/01/328.jpg" pagenum="309"></pb>verne gl&#039;impedimenti, così per mezzo del coltello sopra cui si appoggia il <lb></lb>settore pendulo, come per mezzo degli orli taglienti dati allo stesso settore <lb></lb>oscillatorio; che son rimaste tuttavia nella fabbrica degli orologi moderni, <lb></lb>quelle ingegnose disposizioni, nella struttura delle lenti, e nella forma degli <lb></lb>appoggi, per diminuire più che sia possibile, gli attriti. </s>

<s>Ma rimaneva ancora, <lb></lb>come non evitato inconveniente, il tedio di numerare e la facilità di com­<lb></lb>mettere, così numerando, sbagli. </s>

<s>A ciò attese Galileo a provvedere, forse <lb></lb>come dicemmo per impulso e per suggerimento del p. </s>

<s>Renieri, ond&#039;è che <lb></lb>così, nel sopraccitato luogo, prosegue a dire al Realio: </s></p><p type="main">

<s>“ Per evitar poi il tedio di chi dovesse perpetuamente assistere a nu­<lb></lb>merare le vibrazioni, ci è un assai comodo provvedimento in questo modo: <lb></lb>cioè facendo che dal mezzo della circonferenza del settore sporga infuori un <lb></lb>piccolissimo e sottilissimo stiletto, il quale, nel passare, percuota in una se­<lb></lb>tola fissa in una delle sue estremità, la qual setola posi sopra i denti d&#039;una <lb></lb>ruota leggerissìma quanto una carta, la quale sia posta in piano orizzontale <lb></lb>vicina al pendolo, ed avendo intorno intorno denti a guisa di quelli d&#039;una <lb></lb>sega, cioè con uno de&#039;lati posti a squadra sopra il piano della ruota e l&#039;al­<lb></lb>tro inclinato obliquamente, presti questo ufficio: che nell&#039;urtare la setoletta <lb></lb>nel lato perpendicolare del dente lo muova, ma nel ritorno poi la medesima <lb></lb>setola nel lato obliquo del dente non lo muova altrimenti, ma lo vada stri­<lb></lb>sciando a piè del dente susseguente. </s>

<s>E così, nel passaggio del pendolo, si <lb></lb>muoverà la ruota per lo spazio d&#039;uno de&#039;suoi denti, ma nel ritorno del pen­<lb></lb>dolo, essa ruota non si muoverà punto; onde il suo moto ne riuscirà cir­<lb></lb>colare, sempre per l&#039;istesso verso. </s>

<s>Ed avendo contrassegnati con numeri i <lb></lb>denti si vedrà ad arbitramento la moltitudine dei denti passati, ed in con­<lb></lb>seguenza il numero delle vibrazioni e delle particelle del tempo decorso ” <lb></lb>(ivi, pag. </s>

<s>170, 71). </s></p><p type="main">

<s>Si dovrebbe dir senza dubbio, questo immaginato da Galileo, il primo <lb></lb>macchinamento adattabile all&#039;orologio, quando non ci si rappresentasse scol­<lb></lb>pito nella memoria il disegno di quella <emph type="italics"></emph>Cotyla<emph.end type="italics"></emph.end> santoriana; disegno impresso <lb></lb>nelle pagine di un libro che vide la pubblica luce dodici anni prima che <lb></lb>Galileo scrivesse quella prìvata lettera a Lorenzo Realio. </s>

<s>L&#039;indice, la mo­<lb></lb>stra divisa in 12 parti, la maglietta e il chiodo che lo rappresentano appeso <lb></lb>a una parete, fanno immaginar che l&#039;Orologio santoriano non differisse, al­<lb></lb>meno esteriormente, da uno di questi dell&#039;uso moderno. </s>

<s>È vero che non vi <lb></lb>è rappresentato nè accennato in disegno il macchinamento interiore, nè con <lb></lb>parole ci vien dall&#039;Autore in alcun modo descritto; ma è pure una ragio­<lb></lb>nevole congettura quella di creder che il pendolo comunicasse il moto cir­<lb></lb>colare all&#039;indice per mezzo di ruote dentate, e così venisse a rassomigliarsi <lb></lb>a un vero Orologio a pendolo meglio di quello che Galileo progettò all&#039;Am­<lb></lb>miraglio olandese. </s></p><p type="main">

<s>Comunque sia di ciò, e in qualunque modo fosse interiormente con­<lb></lb>gegnato l&#039;Oriolo a pendolo conforme al disegno esteriore, che si vede im­<lb></lb>presso nelle pagine del Commentario santoriano sopr&#039;Avicenne, è un fatto <pb xlink:href="020/01/329.jpg" pagenum="310"></pb>che il primo a descriverci quel congegno fu nel 1637 il Galileo. </s>

<s>Quel con­<lb></lb>gegno, sebbene in sè semplicissimo, pur conteneva e quasi diremmo com­<lb></lb>pendiava gli organi essenziali a ogni macchinamento d&#039;orologeria. </s></p><p type="main">

<s>Il Viviani ci narra e fa testimonianza che il medesimo Galileo, anche raf­<lb></lb>freddato il negozio delle Longitudini, non si rimase per questo di speculare, <lb></lb>negli ultimi anni della sua vita, e già divenuto cieco, intorno ai perfeziona­<lb></lb>menti dell&#039;Orologio. </s>

<s>I germi di questi ideati perfezionamenti s&#039;intravedono <lb></lb>nella stessa Lettera al Realio, in quelle speculazioni ch&#039;ei soggiunge dopo <lb></lb>aver descritto il pendolo e dopo aver detto del modo come il pendolo stesso <lb></lb>partecipava il moto alla ruota a denti di sega, per mezzo dello sfregamento <lb></lb>e dell&#039;urto di una setola. </s>

<s>“ Si può ancora, egli scrive, intorno al centro di <lb></lb>questa prima ruota adattarne un&#039;altra di piccol numero di denti, la quale <lb></lb>tocchi un&#039;altra maggior ruota dentata, dal moto della quale potremo appren­<lb></lb>dere il numero delle interne rivoluzioni della prima ruota, compartendo la <lb></lb>moltitudiee de&#039;denti in modo che per esempio, quando la seconda ruota <lb></lb>avrà dato una conversione, la prima ne abbia date 20, 30 o 40, o quante <lb></lb>più ne piacesse. </s>

<s>Ma il significar questo alle SS. Loro, che hanno uomini <lb></lb>esquisitissimi ed ingegnosissimi in fabbricare Orologi ed altre macchine am­<lb></lb>mirande, è cosa superflua, perchè essi medesimi sopra questo fondamento <lb></lb>nuovo di sapere che il pendolo, muovasi per grandi o per brevi spazii, fa <lb></lb>le sue reciprocazioni ugualissime, troveranno conseguenze più sottili di quelle, <lb></lb>che io possa immaginarmi. </s>

<s>E siccome la fallacia degli Orologi consiste prin­<lb></lb>cipalmente nel non s&#039;essere fin qui potuto fabbricare quello che noi chia­<lb></lb>miamo il <emph type="italics"></emph>tempo dell&#039;orologio,<emph.end type="italics"></emph.end> tanto aggiustatamente che faccia le sue vi­<lb></lb>brazioni uguali; così in questo mio pendolo semplicissimo e non soggetto <lb></lb>ad alterazione alcuna si contiene il modo di mantener sempre egualissima <lb></lb>la misura del tempo ” (ivi, pag. </s>

<s>171). </s></p><p type="main">

<s>Si vede chiaramente di qui che, infino dal 1637, Galileo pensava di <lb></lb>adattare il pendolo a quegli Orologi, i quali si componevano di un macchi­<lb></lb>namento di ruote dentate, la prima delle quali mossa o dalla gravità di un <lb></lb>peso o dall&#039;elasticità di una molla, partecipava il suo moto a tutte le altre <lb></lb>via via, infino a quella, nel centro della quale era appuntato l&#039;indice muo­<lb></lb>ventesi sopra la mostra. </s>

<s>L&#039;azione del peso o della molla non era equabile, <lb></lb>perchè il peso scendendo si accelerava e la molla svolgendosi si ritardava e <lb></lb>l&#039;indice perciò che movevasi a quel tenore non mostrava l&#039;ora giusta. </s>

<s>A <lb></lb>ciò attendevasi a rimediare per mezzo dei volanti, ma il rimedio però era <lb></lb>precario essendochè se il peso s&#039;attemperava a un&#039;ora, non s&#039;attemperava <lb></lb>ad un&#039;altra, se non che stando lì frequente a ritirare il peso stesso sopra <lb></lb>il volante ora innanzi ora indietro dal centro del moto. </s>

<s>Ma anche ciò non <lb></lb>poteva esser fatto altro che a caso, non essendo facile il misurar precisa­<lb></lb>mente quanto si dovesse ritirare il peso sopra il volante, affinchè contem­<lb></lb>perasse giusto il velocitarsi del contrappeso o il rilassarsi della molla, che <lb></lb>l&#039;una colla sua libera gravità e l&#039;altra col suo elaterio, davano impulso alle <lb></lb>ruote. </s>

<s>Questo giusto bilanciamento del peso sopra il volante era appunto <pb xlink:href="020/01/330.jpg" pagenum="311"></pb>quello che chiamavasi il <emph type="italics"></emph>tempo dell&#039;orologio,<emph.end type="italics"></emph.end> dall&#039;ignorar la regola del <lb></lb>quale, dice Galileo, che dipendeva ogni fallacia, a cui eran soggetti i mac­<lb></lb>chinamenti fabbricati allora per la misura del tempo. </s></p><p type="main">

<s>Egli sperava di poter trovar quella regola con l&#039;applicare, invece del <lb></lb>bilanciere gravato dal contrappeso, il pendolo alle ruote degli antichi oro­<lb></lb>logi da Torre. </s>

<s>Ma la difficoltà d&#039;adattare il nuovo organo oscillatorio gli si <lb></lb>presentò grave per modo, che pensò di trovare altrove che nei pesi e nelle <lb></lb>molle quella equabilità di forza necessaria al regolare e costante andamento <lb></lb>dell&#039;Orologio. </s>

<s>Questa forza credè Galileo che potesse esser somministrata <lb></lb>dall&#039;acqua. </s>

<s>E in fatti un liquido che esca fuori dall&#039;orifizio di un vaso man­<lb></lb>tenuto sempre allo stesso livello, conserva, in un punto determinato del suo <lb></lb>getto parabolico, una velocità e una quantità di moto sempre costante, ond&#039;è <lb></lb>che venendo a urtare contro l&#039;aletta di una ruota, questa si volgerà attorno <lb></lb>equabilmente. </s>

<s>Pongasi ora questa ruota idraulica in luogo del tempo del­<lb></lb>l&#039;orologio, e servirà per misura inalterabile dell&#039;ore. </s>

<s>Di questo pensiero, che <lb></lb>rivela non tanto la sagacia della mente, quanto l&#039;attività dell&#039;investigazione, <lb></lb>ne lasciò Galileo le tracce in una di quelle Aggiunte, che fece di propria <lb></lb>mano ai Dialoghi dei Due Massimi Sistemi, su un esemplare posseduto dalla <lb></lb>Biblioteca del Seminario di Padova. </s>

<s>Quell&#039;Aggiunta così dice: “ Il tempo <lb></lb>dell&#039;Oriolo mosso per l&#039;acqua può forse servire per misurar l&#039;ore ”. </s></p><p type="main">

<s>Ma questo in ogni modo non poteva riuscir quel Misuratore del tempo, <lb></lb>che richiedevasi per i regolati esercizii della vita domestica e civile, e tanto <lb></lb>meno era atto a corrispondere alle scrupolose esigenze della scienza. </s>

<s>Non <lb></lb>si può, pensava Galileo, uscir dal pendolo, e ci dee esser pur la maniera di <lb></lb>adattarlo alle ruote degli Orologi, che segnano l&#039;ore sulle pubbliche piazze. </s>

<s><lb></lb>Quella maniera vedeva egli consistere nell&#039;adattare opportunamente un con­<lb></lb>gegno, il quale facesse sì che il pendolo, invece di dare impulso, lo rice­<lb></lb>vesse dalle stesse ruote, e fosse ufficio di lui quello di regolare e di perpe­<lb></lb>tuare nelle macchine il moto così regolato. </s></p><p type="main">

<s>Il Viviani ci assicura che Galileo riuscì veramente a trovar quel con­<lb></lb>gegno che rispondeva all&#039;intento, e racconta come negli ultimi anni della <lb></lb>vita l&#039;avesse ideato, e a lui stesso, che ne racconta la storia, fatto noto. </s>

<s>In <lb></lb>quella storia, lasciando addietro tante altre particolarità che non fanno per <lb></lb>ora al caso nostro, così appunto si legge: “ Mentre dunque il Padre Re­<lb></lb>nieri attendeva alla composizione delle Tavole, si pose il Galileo a speculare <lb></lb>intorno al suo Misuratore del tempo, ed un giorno del 1641, quando io di­<lb></lb>morava appresso di lui nella Villa d&#039;Arcetri, sovviemmi che gli cadde in <lb></lb>concetto che si saria potuto adattare il pendolo agli oriuoli da contrappesi <lb></lb>e da molle, con valersene invece del solito tempo, sperando che il moto <lb></lb>egualissimo e naturale di esso pendolo avesse a correggere tutti i difetti <lb></lb>dell&#039;arte in essi oriuoli. </s>

<s>Ma perchè l&#039;esser privo di vista gli toglieva di poter <lb></lb>far disegni e modelli, a fine d&#039;incontrare quell&#039;artifizio, che più proporzio­<lb></lb>nato fosse all&#039;effetto concepito, venendo un giorno di Firenze in Arcetri il <lb></lb>detto signor Vincenzio suo figliuolo, gli conferi il Galileo il suo pensiero, e <pb xlink:href="020/01/331.jpg" pagenum="312"></pb>di poi più volte vi fecero sopra varii discorsi, e finalmente stabilirono il <lb></lb>modo che dimostra il qui aggiunto disegno, e di metterlo intanto in opera <lb></lb>per venire in cognizione del fatto di quelle difficoltà, che il più delle volte <lb></lb>nelle macchine con la semplice speculativa non si possono prevedere. </s>

<s>Ma <lb></lb>perchè il signor Vincenzio intendeva di fabbricar lo strumento di propria <lb></lb>mano, acciò questo, per mezzo degli Artefici non si divulgasse prima che <lb></lb>fosse presentato al Serenissimo Granduca suo Signore, ed appresso alli Si­<lb></lb>gnori Stati per uso della longitudine; andò differendo tanto l&#039;esecuzione che <lb></lb>indi a pochi mesi il Galileo, autore di tutte queste ammirabili invenzioni, cadde <lb></lb>ammalato, ed agli 8 di Gennaio 1642, stile Romano, mancò di vita, per lo <lb></lb>che si raffreddarono tanto i fervori nel signor Vincenzio, che non prima di <lb></lb>Aprile del 1649 intraprese la fabbrica del presente oriuolo, sul concetto som­<lb></lb>ministratogli già, me, presente, dal Galileo suo padre ” (Alb. </s>

<s>XIV, 352, 53). </s></p><p type="main">

<s>Prosegue a narrare ivi il Viviani che Vincenzio di Galileo si servì, per <lb></lb>la fabbrica di quel nuovo strumento dell&#039;opera di un tal Domenico Ba­<lb></lb>lestrieri, magnano, che aveva a quel tempo bottega al Ponte Vecchio. </s>

<s>Il con­<lb></lb>gegno fabbricato in parte dal Balestrieri conforme al disegno di Galileo e <lb></lb>agli ordini avuti da Vincenzio, il Viviani stesso seguita a descriverlo nel se­<lb></lb>guente modo: “ Da esso fecesi fabbricare il telaio di ferro, le ruote con i <lb></lb>loro fusti e rocchetti, senza intagliarle, ed il restante lavorò di propria mano, <lb></lb>facendo nella ruota più alta, detta delle tacche, numero 12 denti, con al­<lb></lb>trettanti pironi scompartiti in mezzo fra dente e dente, e col rocchetto nel <lb></lb>fusto di num. </s>

<s>6, ed altra ruota che muove la sopraddetta di num. </s>

<s>90. Fermò <lb></lb>poi da una parte del bracciuolo, che fa la croce al telaio, la chiave a scatto, <lb></lb>che posa sulla detta ruota superiore, e dall&#039;altra impernò il pendolo, che era <lb></lb>formato di un filo di ferro, nel quale stava infilata una palla di piombo, che <lb></lb>vi poteva scorrere a vite, a fine di allungarlo o scorciarlo secondo il biso­<lb></lb>gno di aggiustarlo col contrappeso. </s>

<s>Ciò fatto, volle il signor Vincenzio che <lb></lb>io (come quegli che era consapevole di questa invenzione e che l&#039;avevo sti­<lb></lb>molato ad effettuarla) vedessi così per prova e più d&#039;una volta la congiunta <lb></lb>operazione del contrappeso e del pendolo; il quale, stando fermo tratteneva <lb></lb>il discender di quello, ma sollevato in fuori e lasciato poi in libertà, nel <lb></lb>passare oltre al perpendicolo, con la più lunga delle due code annesse al­<lb></lb>l&#039;imperniatura del dondolo, alzava la chiave che posa ed incastra nella ruota <lb></lb>delle tacche, la quale tirata dal contrappeso, voltandosi con le parti supe­<lb></lb>riori verso il dondolo, con uno de&#039;suoi pironi calcava per di sopra l&#039;altra <lb></lb>codetta più corta, e le dava nel principio del suo ritorno un impulso tale, <lb></lb>che serviva d&#039;una certa accompagnatura al pendolo che lo faceva sollevare <lb></lb>fino all&#039;altezza d&#039;onde s&#039;era partito; il qual ricadendo naturalmente, e tra­<lb></lb>passando il perpendicolo, tornava a sollevare la chiave, e subito la ruota <lb></lb>delle tacche, in vigore del contrappeso, ripigliava il suo moto seguendo a <lb></lb>volgersi e spignere col pirone susseguente il detto pendolo; e così in un <lb></lb>certo modo si andava perpetuando l&#039;andata e tornata del pendolo, sino a che <lb></lb>il peso poteva calare a basso ” (ivi, pag. </s>

<s>253). </s></p><pb xlink:href="020/01/332.jpg" pagenum="313"></pb><p type="main">

<s>Il Viviani nel far la storia e la descrizione di questo Orologio accenna <lb></lb>di mandarlo accompagnato da un disegno illustrativo. </s>

<s>Di que&#039;disegni anzi <lb></lb>ne furono fatti due, il primo de&#039;quali in lapis piombino e che noi riprodu­<lb></lb>ciamo nella figura 18 dall&#039;originale, inserito a carte 54 del Tomo IV, Parte VI <lb></lb>de&#039;Manoscritti di Galileo; rappresenta l&#039;Orologio in maestà dalla parte della <lb></lb><figure id="id.020.01.332.1.jpg" xlink:href="020/01/332/1.jpg"></figure></s></p><p type="caption">

<s>Figura 18.<lb></lb>crociera, sul fusto della quale sono <lb></lb>imperniate le ruote, e la traversa <lb></lb>vedesi terminare i bracci in due <lb></lb>volute, infissavi in una la chiave a <lb></lb>scatto, e nell&#039;altra le due codette <lb></lb>ordinate a percuotere ora sull&#039;orlo <lb></lb>della ruota a tacche, ora sui pironi <lb></lb>menati in giro da lei. </s>

<s>Ma perchè di <lb></lb>questi, che sono gli organi essenziali <lb></lb>della macchina, cioè della ruota delle <lb></lb>tacche, della chiave a scatto e delle <lb></lb>due codette, non si poteva con quel <lb></lb>disegno mostrare il gioco, rimanendo <lb></lb>essi organi riparati dietro le volute <lb></lb>della traversa, si pensò di rappresen­<lb></lb>tar la macchina stessa con isguardo <lb></lb>un po&#039;obliquo, e in modo che, ta­<lb></lb>gliata la colonnetta o sostegno op­<lb></lb>posto e parallelo al fusto della cro­<lb></lb>ciera, la ruota più alta e il gioco <lb></lb>delle codette su lei e sullo scatto, <lb></lb>rimanesse allo scoperto. </s>

<s>Il disegno <lb></lb>che accompagnava la descrizione del <lb></lb>Viviani, mandata come vedremo tra <lb></lb>poco in Olanda, era una copia di <lb></lb>questo secondo, che vedesi con assai <lb></lb>diligenza delineato in una Tavola ripiegata, perchè eccedente in lunghezza <lb></lb>e larghezza il foglio 50 del Tomo manoscritto sopra citato. </s>

<s>L&#039;Albèri lo fece <lb></lb>incidere e imprimere nella II delle Tavole apposte al Tomo XIV della sua <lb></lb><emph type="italics"></emph>Edizione completa,<emph.end type="italics"></emph.end> e noi lo rappresentiamo ai nostri lettori nella figura 19. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi attentamente fissa lo sguardo sopra questo disegno, e si mette a <lb></lb>considerar quelle ruote e que&#039;pironi, quelle codette e quegli scatti, ci vede <lb></lb>la laboriosità dell&#039;ingegno, ma non ci sente l&#039;ispirazione del genio. </s>

<s>Il Vi­<lb></lb>viani ci fa saper, nel seguito delle parole da noi lasciate sopra interrotte, <lb></lb>che Vincenzio di Galileo conosceva troppo bene l&#039;imperfezione di quel mac-<pb xlink:href="020/01/333.jpg" pagenum="314"></pb>chinamento e le difficoltà che si presentavano nel sollecito studio di miglio­<lb></lb>rarlo. </s>

<s>Ma pure eran tutte quelle difficoltà, ch&#039;ei si riprometteva di supe­<lb></lb>rare, e ch&#039;egli avrebbe forse superato di fatto, se non gli fosse sopraggiunta <lb></lb>in questo mezzo tempo la morte. </s></p><p type="main">

<s>In qualunque modo gli Orologi di Galileo rimanevano sterili progetti e <lb></lb><figure id="id.020.01.333.1.jpg" xlink:href="020/01/333/1.jpg"></figure></s></p><p type="caption">

<s>Figura 19.<lb></lb>infecondi di ogni utilità per la vita <lb></lb>civile o domestica, e per la scienza. </s>

<s><lb></lb>Era preordinato che que&#039;progetti <lb></lb>non dovessero aver la loro esecu­<lb></lb>zione in Italia e Galileo stesso parve <lb></lb>che fosse di ciò presago quando, <lb></lb>nella sopra allegata Lettera al Rea­<lb></lb>lio, scriveva che, sul fondamento <lb></lb>del suo pendolo, qualcuno di quegli <lb></lb>Olandesi, fra&#039;quali erano uomini <lb></lb>squisitissimi e ingegnosissimi in fab­<lb></lb>bricare Oriuoli e altre macchine am­<lb></lb>mirande, avrebbe trovato conse­<lb></lb>guenze più sottili di quelle ch&#039;ei <lb></lb>non si sarebbe potuto immaginare. </s></p><p type="main">

<s>Nell&#039;anno 1658 infatti usciva al­<lb></lb>l&#039;Aja, dall&#039;officina di Adriano Ulacq, <lb></lb>un libretto di poche pagine intitolato <lb></lb><emph type="italics"></emph>Horologium,<emph.end type="italics"></emph.end> in cui l&#039;autore che era <lb></lb>Cristiano Huyghens descriveva il <lb></lb>modo di ridur con leggerissime tra­<lb></lb>sformazioni i vecchi orologi a ruote, <lb></lb>ne&#039;nuovi orologi regolati col pen­<lb></lb>dolo. </s>

<s>Ismaele Boulliaud dava di Pa­<lb></lb>rigi, il di 28 Febbraio 1659, nuova <lb></lb>della pubblicazione al principe Leo­<lb></lb>poldo de&#039;Medici, così scrivendo: <lb></lb>“ Sunt aliquot menses cum scripto <lb></lb>edito, additaque figura Horologium <lb></lb>a se inventum explicuit Christia­<lb></lb>nus Hugenius et Hagae Comitis in <lb></lb>Batavia edidit ” (MSS. Cim. </s>

<s>T. XVI, <lb></lb>c. </s>

<s>134). A un tal annunzio entrato il Principe in gran curiosità di sapere <lb></lb>qual relazione avesse questa nuova macchina con quella proposta già da Ga­<lb></lb>lileo, mandò a richieder di quel libretto lo stesso Boulliaud, e avutolo e let­<lb></lb>tolo, forse perchè era difficile averne un altro esemplare stampato, lo fece <lb></lb>trascrivere a ma<gap></gap> per Vincenzio Viviani, in un quinternetto che si trova <lb></lb>mserito da <gap></gap>arte 115-23 nel Tomo CXXXVIII de&#039;Manoscritti appartenenti, <lb></lb>fra&#039;Discepoli di Galileo, allo stesso Viviani. </s>

<s>Non è possibile che egli, testi-<pb xlink:href="020/01/334.jpg" pagenum="315"></pb>mone e compartecipe alle fatiche durate da Galileo e dal figlio di lui Vin­<lb></lb>cenzio, per adattare il pendolo agli antichi orologi a ruote, non sia rimasto <lb></lb>di quella mirabile facilità con cui l&#039;Huyghens era giunto all&#039;intento. </s>

<s>Lo <lb></lb>scappamento a serpe, che scivola ora da una parte ora dall&#039;altra, d&#039;infra <lb></lb>gli incastri della ruota a denti di sega, invece che dal vecchio bilanciere o <lb></lb>volante, veniva regolarmente governato dalle oscillazioni del pendolo. </s>

<s>Ecco <lb></lb>qui la somma di tutta l&#039;invenzione, la quale pur si conosce che sarebbesi <lb></lb>potuta avere anco con più semplicità, applicando direttamente il pendolo al­<lb></lb>l&#039;asse dello scappamento a serpe, come poi fece il Sinclaro, senza l&#039;aggiunta <lb></lb>del rocchetto portato in capo dallo stesso scappamento, e della ruota coro­<lb></lb>nata, all&#039;asse della quale si raccomanda la clavicola governatrice del metro <lb></lb>oscillatorio. </s></p><p type="main">

<s>Nonostante che l&#039;Autore non avesse dimenticato di dire esser dovuto <lb></lb>a Galileo <emph type="italics"></emph>viro sagacissimo<emph.end type="italics"></emph.end> questo primo uso del pendolo, il Viviani suggeri <lb></lb>le seguenti parole, che il principe Leopoldo scrisse al Boulliaud, dopo aver <lb></lb>letto e veduto l&#039;<emph type="italics"></emph>Horologium:<emph.end type="italics"></emph.end> “ Circa l&#039;oriolo regolato dal pendolo certo è <lb></lb>che l&#039;invenzione è quella, ma non si deve defraudar della gloria dovutagli <lb></lb>il nostro .... Galileo, che fin nel mille secento trentasei, se non erro, pro­<lb></lb>pose questa sì utile invenzione alli Signori Stati di Olanda, e io ne ho ri­<lb></lb>trovato, benchè un poco diverso circa la costituzione delle ruote, un modello <lb></lb>fatto già dal medesimo signor Galileo, e tre anni sono che qua si studia so­<lb></lb>pra l&#039;istesso soggetto. </s>

<s>Ne fu fatto uno da un virtuoso che spero riuscirà la <lb></lb>sua fabbrica ridotta al pulito di non minor facilità e resistenza del ritrovato <lb></lb>dal signor Cristiano Hugenio ” (ivi, T. XXIII, c. </s>

<s>201). </s></p><p type="main">

<s>Ricevuta questa lettera, dalla quale traspariva l&#039;accusa data all&#039;Huy­<lb></lb>ghens d&#039;aver defraudato ne&#039;suoi meriti Galileo, il Boulliaud, dopo pochi <lb></lb>giorni, il dì 2 di Maggio 1659, risponde: “ De pendulo ad regendam Horo­<lb></lb>logii rotarum conversionem a summo viro Galileo olim reperto, V. Cel. </s>

<s>Christ. </s>

<s><lb></lb>Hugenius mihi monendus est ” (ivi, T. VI, c. </s>

<s>152). Ma lo zelo venne così <lb></lb>nell&#039;ardente animo rattemperato da un&#039;altra lettera, che venti giorni dopo <lb></lb>scrisse a Parigi lo stesso Principe Leopoldo: “ Quand&#039;io le accennai che <lb></lb>l&#039;invenzione di adattare il pendolo era stata trovata molto tempo fa ancora <lb></lb>dal nostro signor Galileo, non intesi dire che il signor Cristiano Hugenio <lb></lb>non la potessi avere anch&#039;egli inventata da sè medesimo .... Si può ricor­<lb></lb>dare V. S. che io le accennai che altro Virtuoso tre anni sono ne inventò <lb></lb>uno simile, ma per sua disgrazia non fu applicato l&#039;animo al valersi della <lb></lb>sua invenzione ” (ivi, T. XXIII, c. </s>

<s>14). </s></p><p type="main">

<s>Nonostante il Boulliaud non mancò di dar parte di tutto quel che gli <lb></lb>era venuto scritto di Toscana all&#039;Hugenio, il quale rispose all&#039;amico a Pa­<lb></lb>rigi parole di accoramento, per avere il Principe conceputa così falsa opi­<lb></lb>nione di lui, nella quale parevagli di vedersi rassomigliato a un&#039;altro Simon <lb></lb>Mario. </s>

<s>“ Mais enfin que faut-il faire pour oter à ce Prince l&#039;opinion, qu&#039;il <lb></lb>semble avoir conçue de moi, comme si je m&#039;attribuois l&#039;invention d&#039;autrui, <lb></lb>et que je ressemblasse à ce Simon Marius? </s>

<s>” (Fabbroni, Lett. </s>

<s>I, 226). Nè <pb xlink:href="020/01/335.jpg" pagenum="316"></pb>questo accoramento dopo parecchi mesi gli era ancora passato, e anzi lo <lb></lb>coceva di più per non veder risposta dal principe Leopoldo, a cui aveva già <lb></lb>dedicato il suo Sistema Saturnio. </s>

<s>Di ciò faceva amichevole sfogo in Parigi <lb></lb>con Cosimo Brunetti, il quale così rappresentava per lettera al Principe <lb></lb>stesso la turbazion dell&#039;animo, i timori, benchè incoscienti di aver mancato, <lb></lb>e i propositi dell&#039;emenda fatti dal gentiluomo olandese: “ Ma l&#039;Hugens io <lb></lb>lo trovai in somma perplessità, non sapendo egli per qual ragione non re­<lb></lb>stava onorato di risposta alla Lettera del suo Sistema dedicato e mandato a <lb></lb>V. A. S. la quale ei temeva che potesse stimarsi offesa per due principali <lb></lb>cagioni, nella persona di Galileo. </s>

<s>La prima è ch&#039;ei potesse aver veduto una <lb></lb>Lettera che il Galileo scrisse del 1636 agli Stati d&#039;Olanda circa l&#039;invenzione <lb></lb>del pendolo, con che ei sperava di poter trovar le longitudini, sopra di che <lb></lb>egli esaggerò grandemente asserendomi di non aver mai veduto tal lettera. </s>

<s><lb></lb>L&#039;altra è che, per quel che riguarda i Telescopii, ei non abbia forse parlato <lb></lb>del Galileo con gli encomii dovutili, e in questo ei vorrebbe che il suo Sistema <lb></lb>non fosse ancora stampato, per poter parlar con termini che testificassero <lb></lb>davvantaggio quanto egli sia parziale di sì grand&#039;uomo ” (ivi, T. XVII, c. </s>

<s>30). </s></p><p type="main">

<s>Dietro questa lettera del Brunetti il Principe si mosse a scriver parole <lb></lb>che acquietarono l&#039;animo dell&#039;Hugenio, il quale era intanto rimasto sodi­<lb></lb>sfatto di un altro suo desiderio. </s>

<s>Quel desiderio veniva così espresso nel­<lb></lb>l&#039;<emph type="italics"></emph>Estratto<emph.end type="italics"></emph.end> di lettera francese pubblicato dal Fabbroni nel luogo sopra citato: <lb></lb>“ Si j&#039;avois l&#039;honneur d&#039;être plus connu de Son Altesse, et essez de har­<lb></lb>diesse, je la réquérerois pour en avoir une figure, pour voir en quoi elle <lb></lb>différe de la mienne ”. </s>

<s>E perchè questo Estratto di lettera dell&#039;Huyghens <lb></lb>si fece dal Boulliaud a quest&#039;unico fine d&#039;inviarlo al Principe Leopoldo, il <lb></lb>Principe, lieto di poter sodisfare al desiderio dell&#039;Hugenio, fece preparare <lb></lb>il disegno, e il dì 21 Agosto 1659 lo faceva spedire al Bullialdo, accompa­<lb></lb>gnandolo con una sua lettera, nella quale così scriveva: “ Sarà dunque an­<lb></lb>nesso a questa il disegno del principio dell&#039;oriuolo regolato dal pendolo, che <lb></lb>inventò il Nostro per sempre ammirabile signor Galileo. </s>

<s>Lo invio delineato <lb></lb>con quella rozzezza, con la quale è fabbricato il modello del medesimo, che <lb></lb>nella mia camera ora mi ritrovo. </s>

<s>Potrà pertanto V. S. mandarlo al Virtuo­<lb></lb>sissimo signor Cristiano Hugenio che desiderava di vederlo, e forse di que­<lb></lb>st&#039;altra settimana invierò a lei la Storia, dirò così del ritrovamento del pen­<lb></lb>dolo, che spero dovrà riuscir curiosa a V. S.... Farò fare ancora un disegno <lb></lb>di come si è accomodato da noi il pendolo a&#039;nostri Orioli, ed in particolare <lb></lb>ad uno assai grande che mostra le ore, e suona nella piazza del nostro Pa­<lb></lb>lazzo dove abitiamo e glielo invierò ” (ivi T. XXIII, c. </s>

<s>16). </s></p><p type="main">

<s>Il disegno accompagnato da questa Lettera diretta al Bullialdo, è quello <lb></lb>stesso che è stato da noi fedelissimamente nella figura XIX ritratto, e la <lb></lb>Storia del ritrovamento del pendolo, di che qui pure si fa parola, è senza <lb></lb>dubbio quella scritta dal Viviani in forma di Lettera indirizzata allo stesso <lb></lb>Principe Leopoldo, sottoscritta nel dì 20 Agosto 1659 e da cui estraemmo, <lb></lb>nel paragrafo precedente, i documenti alla nostra narrazione. </s></p><pb xlink:href="020/01/336.jpg" pagenum="317"></pb><p type="main">

<s>Come queste cose son certe però, altrettanto incerto a definirsi è qual <lb></lb>fosse e come fosse rappresentato l&#039;adattamento del pendolo all&#039;Orologio, che <lb></lb>mostrava l&#039;ore o suonava sulla piazza de&#039;Pitti. </s>

<s>In tale incertezza noi pre­<lb></lb>ghiamo i nostri Lettori a voler rivolger la loro attenzione sopra il disegno <lb></lb><figure id="id.020.01.336.1.jpg" xlink:href="020/01/336/1.jpg"></figure></s></p><p type="caption">

<s>Figura 20.<lb></lb>abbozzato e informe che noi sotto i <lb></lb>loro occhi fedelmente rappresentia­<lb></lb>mo nella figura 20. Un tal disegno <lb></lb>a penna, con altri informi più che <lb></lb>mai da&#039;quali è preceduto, vedesi ab­<lb></lb>bozzato a carte 57 di quel Tomo IV <lb></lb>de&#039;citati Manoscritti, in cui son di­<lb></lb>segnati gli altri adattamenti secondo <lb></lb>il concetto di Galileo. </s>

<s>Se all&#039;estre­<lb></lb>mità dell&#039;asse orizzontale, a cui è <lb></lb>raccomandato il pendolo, son da <lb></lb>mano sinistra veramente alette quel­<lb></lb>le, che noi vediamo in immaginazio­<lb></lb>ne, e se queste alette giocano, come <lb></lb>lo scappamento a serpe su quell&#039;ab­<lb></lb>bozzo di ruota, che pur la nostra <lb></lb>immaginazione ci fa credere aver le <lb></lb>tacche disposte a denti di sega; si <lb></lb>dovrebbe dire che fra tutti i modi di <lb></lb>adattare il pendolo agli orologi a <lb></lb>ruote è questo quello de&#039;nostri Fio­<lb></lb>rentini, che più si rassomigli a ciò <lb></lb>che fu ideato e mandato ad effetto <lb></lb>in Olanda. </s></p><p type="main">

<s>Se fosse vero insomma quel <lb></lb>che noi ci immaginiam di vedere in <lb></lb>questo schizzo a penna, sarebbe ciò <lb></lb>di gran conseguenza per la nostra <lb></lb>Storia. </s>

<s>Ma perchè noi non ne ab­<lb></lb>biam nessuna certezza contentiamoci di assicurare i Lettori di un altro <lb></lb>fatto, di non forse minore importanza, il qual si è che la Storia del ritrova­<lb></lb>mento del pendolo e il disegno dell&#039;Orologio del Palazzo Pitti, promessi di <lb></lb>mandar la settimana seguente per mezzo del Bullialdo all&#039;Hugenio, furono <lb></lb>veramente mandati, e d&#039;averli ricevuti e fatti recapitare dava lo stesso Bul­<lb></lb>lialdo sicurtà al Principe così scrivendo: “ Ad Christianum Hugenium Zu­<lb></lb>lichemium utriusque Horologii pendulo directi, quas a Celsitudine Tua ac­<lb></lb>cepi, picturas misi; et si mihi vacasset historiam inventi a Galilaeo penduli <lb></lb>ed adnotatas primum ab ipso acqualitatis motus. </s>

<s>transcriptam adiunxissem ” <lb></lb>(Fabbroni, ivi, pag. </s>

<s>199). </s></p><p type="main">

<s>Non si può dubitar che il Boulliaud non mantenesse le sue promesse <pb xlink:href="020/01/337.jpg" pagenum="318"></pb>e che venutogli tempo e ozio opportuno non si fosse messo veramente a <lb></lb>trascriver la storia del pendolo per inviarla, secondo il geloso ufficio affida­<lb></lb>togli, in Olanda all&#039;Hugenio. </s>

<s>Qual fosse poi il giudizio che dette di quella <lb></lb>storia e di quei disegni lo stesso Hugenio, lo vedremo quando nel 1673 tor­<lb></lb>nerà pubblicamente a trattar di questo argomento dell&#039;Orologio. </s></p><p type="main">

<s>Intanto giacchè abbiam sentito dire, ne&#039;documenti sopra citati, dal prin­<lb></lb>cipe Leopoldo che tre anni prima del 1659 in Toscana si pensava già ad ap­<lb></lb>plicare il pendolo alle misure dell&#039;ore, da un Virtuoso, che non seppe per sua <lb></lb>disgrazia valersi di un&#039;invenzione, la quale ridotta a pulito avrebbe dato la <lb></lb>fabbrica di un Orologio più facile e più consistente di quella stessa del signor <lb></lb>Cristiano Hugenio; crediamo esser di grande importanza per la nostra Sto­<lb></lb>ria l&#039;investigar chi fosse quel Virtuoso, e come fosse costruito quell&#039;Orolo­<lb></lb>gio Toscano, inventato in quello stesso anno 1656, in cui s&#039;inventò l&#039;olan­<lb></lb>dese, conforme alle parole con cui l&#039;Hugenio incominciò la sua Descrizione: <lb></lb>“ Temporis dimetiendi rationem novam quam exeunte anno 1656 escogita­<lb></lb>vimus.... ” (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>5). Ma pure a far ciò vogliamo <lb></lb>differire alquanto per dire altre cose, dalle quali forse verrà a diffondersi <lb></lb>un po&#039;di luce su quella via, che ci si para innanzi chiusa di nebbia. </s></p><p type="main">

<s>Diciamo dunque che sebben l&#039;Huyghens dal 1658 al 1673 non avesse <lb></lb>nulla d&#039;importanza pubblicato in proposito di perfezionare gli Orologi a pen­<lb></lb>dolo, pure egli aveva altissime e recondite cose speculato in questi quindici <lb></lb>anni. </s>

<s>A noi qui conviene far di quelle speculazioni soggetto alla nostra Sto­<lb></lb>ria, e vi ci vogliamo apparecchiare accennando a una curiosità, a cui pre­<lb></lb>sero parte gli Accademici nostri di Firenze. </s></p><p type="main">

<s>Occorrendo all&#039;Huyghens, sui principii dell&#039;anno 1665, di fare osser­<lb></lb>vazioni comparative fra due Orologi a pendolo, gli teneva a tal intento appesi <lb></lb>a un medesimo bastone nella sua stanza, quando scoprì in essi un effetto <lb></lb><emph type="italics"></emph>mirum et a nemine umquam vel cogitandum.<emph.end type="italics"></emph.end> L&#039;effetto consisteva in una <lb></lb>certa segreta simpatia, nata fra&#039;due pendoli per modo, che il vibrar dell&#039;uno <lb></lb>non differiva dal vibrar dell&#039;altro: che se anzi si turbava ad arte il loro <lb></lb>metro, tornavano dopo una mezz&#039;ora a corrispondersi esattamente, come <lb></lb>prima. </s>

<s>La storia diligente e minuta di così fatte nuove e curiose osserva­<lb></lb>zioni, fu divulgata dall&#039;Autore stesso con una Lettera data dall&#039;Aja il dì <lb></lb>25 di Febbraio 1665 (ivi, pag. </s>

<s>213, 14), che pervenuta a notizia del prin­<lb></lb>cipe Leopoldo, egli stesso faceva motto del contenuto ai due principali sog­<lb></lb>getti della sua Accademia, al Borelli e al Viviani. </s>

<s>Il Borelli di Pisa, il dì <lb></lb>13 Aprile 1665, rispondeva al Principe di non aver bene inteso “ perchè <lb></lb>non so, egli dice, se in quelle vibrazioni vi concorra suono unisono, oppure <lb></lb>sono muti. </s>

<s>Circa il suono già è stato avvertito dal Galileo, e resone la vera <lb></lb>ragione ne&#039;suoi ultimi Dialoghi delle cose che si spezzano. </s>

<s>Ma quando non <lb></lb>vi sia suono, non ho ancora potuto vedere che due pendoli egualmente lun­<lb></lb>ghi, discostando l&#039;uno dall&#039;altro un braccio, le vibrazioni dell&#039;uno si comu­<lb></lb>nichino all&#039;altro a segno tale, che gli facciano fare balzi uguali; tuttavia ci <lb></lb>penserò meglio ” (MSS. Cim. </s>

<s>T. XVIII, c. </s>

<s>158). Poi, dal Principe fu avvi-<pb xlink:href="020/01/338.jpg" pagenum="319"></pb>sato di una condizione particolare, in cui si trovavano i due pendoli sim­<lb></lb>patici, ed era quella di essere appesi ambedue gli orologi a un medesimo <lb></lb>bastone. </s>

<s>Allora il Borelli, due giorni dopo la precedente, tornando a scri­<lb></lb>vere, soggiunge: “ Circa i pendoli mi par molto vario il caso dell&#039;essere <lb></lb>attaccati al medesimo bastone all&#039;esser rinchiusi in due oriuoli, e faccia <lb></lb>Dio che finalmente il detto bastone non divenga una bacchetta assai fles­<lb></lb>sibile e mobile, se pur è vero che questo basta a produr quel tale effetto ” <lb></lb>(ivi, c. </s>

<s>162). </s></p><p type="main">

<s>In conclusione il Borelli non seppe nè osservare il fatto nè, suppostolo <lb></lb>vero, intravedere alcuna fisica ragione di quella strana simpatia. </s>

<s>L&#039;Huy­<lb></lb>ghens, nella Lettera sopra citata, aveva accennato alle agitazioni prodotte <lb></lb>nell&#039;aria dai moti de&#039;pendoli, ma poi, sulla fine della Prima Parte dell&#039;Oro­<lb></lb>logio Oscillatorio, <emph type="italics"></emph>instituto diligenti examine<emph.end type="italics"></emph.end> credette d&#039;affermare il vero <lb></lb>dicendo: “ a motu tigni ipsius, licet haudquaquam sensibili causam pe­<lb></lb>tendam esse ” (Op. </s>

<s>Var., pag. </s>

<s>49). </s></p><p type="main">

<s>Il Viviani per verità non sappiamo che decidesse nulla in proposito <lb></lb>standosene contento a descrivere così i fatti osservati, i quali par che ten­<lb></lb>dano a confermar che il simpatico mistero consiste tutto nelle agitazioni <lb></lb>dell&#039;aria comunicantisi da un pendolo all&#039;altro: “ Di due pendoli uguali di <lb></lb>filo dal centro delle palle, appesi ad un medesimo sostegno e posti in quiete <lb></lb>nel perpendicolo, se si rimuoverà uno di loro e si lascerà vibrare, si vedrà <lb></lb>che l&#039;altro subito comincerà a muoversi ed a poco a poco va continuando, <lb></lb>fino ad un particolar segno, a crescer li archi delle sue vibrazioni e poi <lb></lb>decrescerli, ed esser sempre concorde con l&#039;altro nell&#039;andare e tornare. </s>

<s>E <lb></lb>se quello, a cui si dà l&#039;andata, sarà il più grave, muoverà più facilmente e <lb></lb>per maggiori archi il minore, che non farebbe il minore il maggiore ” (MSS. <lb></lb>Cim. </s>

<s>T. X, c. </s>

<s>47). </s></p><p type="main">

<s>Ma è tempo che ritorniamo alla Storia dell&#039;Orologio. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Benchè l&#039;Huyghens, infino dal dì 16 Giugno 1657, avesse ottenuto dagli <lb></lb>Stati Uniti di Olanda il privilegio, o come oggidì si direbbe il brevetto d&#039;in­<lb></lb>venzione; benchè il libretto stampato da Adriano Ulacq nel 1658 fosse di­<lb></lb>vulgato per tutta l&#039;Europa, e per tutta l&#039;Europa si fossero veduti, benchè <lb></lb>rari in numero, orologi fabbricati su quel disegno; nonostante Giorgio Si­<lb></lb>nelaro, professore nell&#039;Università di Glascow, pubblicando nel 1699 in Rot­<lb></lb>terdam la sua <emph type="italics"></emph>Ars nova et Magna,<emph.end type="italics"></emph.end> vi poneva in Appendice, con altri, un <lb></lb>Dialogo intitolato <emph type="italics"></emph>De Cronoscopio;<emph.end type="italics"></emph.end> strumento, che egli dà come cosa di re­<lb></lb>cente invenzione, e da lui stesso <emph type="italics"></emph>nova methodo excogitata.<emph.end type="italics"></emph.end> Gli interlocu­<lb></lb>tori son Francesco e Alessandro, sotto la persona del quale si nasconde <lb></lb>l&#039;Autore. </s>

<s>Incomincia Alessandro a magnificare l&#039;eccellenza di questo <emph type="italics"></emph>quod<emph.end type="italics"></emph.end><pb xlink:href="020/01/339.jpg" pagenum="320"></pb><emph type="italics"></emph>infinitis parasangis, omnibus praecellit Chronoscopiis in hunc usque diem <lb></lb>excogitatis,<emph.end type="italics"></emph.end> per modo che fa venir voglia a Francesco di veder questa nuova <lb></lb>maraviglia, di che è appagato da Alessandro stesso, il quale avendo intro­<lb></lb>dotto l&#039;amico nel suo Museo, “ vides iam, mi Francisce, gli dice, duo illa <lb></lb>eadem forma Automata, quod libet tres palmos habere, quarum prima <emph type="italics"></emph>hora­<lb></lb>ria<emph.end type="italics"></emph.end> horis duodecim circumlata, tempus diurnum et nocturnum examussim <lb></lb>definit. </s>

<s>Secunda minutorum, quae horis singulis integrum circulum descri­<lb></lb>bens, minuita prima quam exactissime determinat. </s>

<s>Tertia <emph type="italics"></emph>secundum,<emph.end type="italics"></emph.end> quae <lb></lb>singulis horis sexagies, singulisque <emph type="italics"></emph>minutis<emph.end type="italics"></emph.end> semel circumlata, <emph type="italics"></emph>secunda hora­<lb></lb>ria<emph.end type="italics"></emph.end> ad amussim demonstrat. </s>

<s>Quoad pendulum attinet, scito id globulum <lb></lb>plumbeum esse acto unciarum, tenuissimo filo aeneo, triginta octo digitis <lb></lb>longo, cum parte decima, suspensum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> Mirum! pilo equino vix est crassius. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> Ob id facilius et liberius transcurrit globulus. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> Sed demiror valde quomodo huc illuc agitatur. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> Videsne <emph type="italics"></emph>claviculam centralem<emph.end type="italics"></emph.end> extremo inquieti (<emph type="italics"></emph>scappamento<emph.end type="italics"></emph.end>) <lb></lb>paulo altiorem? </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> Imo. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> Eius ope solummodo suspenditur globulus, ac super eo tam­<lb></lb>quam centro transcurrit. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> Nullatenus ergo penduli gravitate <emph type="italics"></emph>inquietum<emph.end type="italics"></emph.end> gravatur? </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> Nullatenus, sed eius extremo <emph type="italics"></emph>tibiam aeneam<emph.end type="italics"></emph.end> cum <emph type="italics"></emph>pede<emph.end type="italics"></emph.end> de­<lb></lb>scendentem vides. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ France.<emph.end type="italics"></emph.end> Clare. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> Ac pedem parvulo feraminulo perforatum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> Imo. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> Per id transit funiculus, cuius vibrationes eius agitatione perse­<lb></lb>verant. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> At pars superior videtur testudinis chorda. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> Sic est. </s>

<s>Ad haec, praeter rotulas, quibus indices circummoven­<lb></lb>tur, tres alias vides, quarum prima et secunda verticales sunt: tertia hori­<lb></lb>zontalis inaequalibus numero denticulis, quibus huc illuc <emph type="italics"></emph>inquietum<emph.end type="italics"></emph.end> agita­<lb></lb>tur. </s>

<s>Potissima iam huius Horologii perfectio est quod vibratio quaelibet sit <lb></lb><emph type="italics"></emph>secundum horarium,<emph.end type="italics"></emph.end> nam singulis horis ter millies et sexcenties transcur­<lb></lb>rit examussim Pendulum ” (Roterodami, 1669, pag. </s>

<s>600, 1). </s></p><p type="main">

<s>Si raccoglie di qui come la sostituzione dell&#039;<emph type="italics"></emph>antico tempo<emph.end type="italics"></emph.end> al nuovo pen­<lb></lb>dolo, che tanto dette a pensare a Galileo e al figliuolo di lui Vincenzio, <lb></lb>occorse con grandissima facilità al Sinclaro, a cui, per avere il vecchio Oro­<lb></lb>logio trasformato nel nuovo, bastò mantenere lo scappamento a serpe, disporlo <lb></lb>orizzontale, e appendere all&#039;estremità di lui un corpo oscillante. </s>

<s>Si direbbe <lb></lb>che l&#039;Orologio Scozzese, è più semplice di quello Olandese, ma non è che <lb></lb>anco all&#039;Huyghens non fosse sovvenuta in mente quella facilità di costru­<lb></lb>zione; è che voleva non facesse il pendolo troppo ampie le sue vibrazioni, <lb></lb>per cui non l&#039;applicò immediatamente allo scappamento, che era la più fa-<pb xlink:href="020/01/340.jpg" pagenum="321"></pb>cile via seguita dal Sinclaro, ma l&#039;applicò piuttosto all&#039;asse della ruota co­<lb></lb>ronata, mossa dal rocchetto portato in capo dallo stesso scappamento. </s></p><p type="main">

<s>Comunque sia, fin qui il solitario professor di Glascovia non ci ha an­<lb></lb>nunziato nulla di nuovo. </s>

<s>Però, aggiunta a quella sua descrizione del Cro­<lb></lb>nosccpio, ha una cosa, della quale forse è vero quel che egli dice <emph type="italics"></emph>nemini <lb></lb>adhuc in mentem venisse,<emph.end type="italics"></emph.end> ed è l&#039;applicazione del pendolo orizzontale o del <lb></lb>pendolo conico agli Orologi. </s>

<s>Abbiamo detto che forse è vero, ritrovando che <lb></lb>l&#039;Huyghens esordisce così la V Parte del suo <emph type="italics"></emph>Oscillatorio:<emph.end type="italics"></emph.end> “ Est et aliud <lb></lb>oscillatorii motus genus, praeter id quod hactenus pertractavimus. </s>

<s>Eiusmodi <lb></lb>nempe quo per circuli ambitum, pendulum pondus circumfertur. </s>

<s>Unde aliud <lb></lb>quoque Horologii commentum deduximus, eodem fere tempore, quo illud <lb></lb>prius ” (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>185). </s></p><p type="main">

<s>Non sarebbe dunque vero quel che credeva il Sinclaro che cioè così <lb></lb>fatta maniera di pendoli non fosse ancora nel 1669 venuta in mente a nes­<lb></lb>suno. </s>

<s>L&#039;Huyghens asserisce che eragli venuta anzi in mente tredici anni <lb></lb>prima. </s>

<s>Ma perchè non si trova che abbia pubblicameute palesato questo suo <lb></lb>pensiero prima del 1673, resta, per giustizia il diritto di quattro anni di <lb></lb>precedenza al Sinclaro, che per verità non sperimentò nè speculò su quel <lb></lb>pendolo conico molto più oltre di quel che v&#039;avessero esperimentato i no­<lb></lb>stri Accademici del Cimento. </s></p><p type="main">

<s>In qualunque modo, fu quel pendolo, alle mani del grande Olandese, <lb></lb>il fecondo seme che fruttificò alla Meccanica la teoria delle forze centrifu­<lb></lb>ghe, e alla Geometria quella delle Evolute. </s>

<s>A noi di tante alte e peregrine <lb></lb>speculazioni non occorre entrare in discorso, se non di quelle sole che tro­<lb></lb>varono un&#039;applicazione immediata alla fabbrica del nuovo Orologio. </s></p><p type="main">

<s>Vedemmo, infino da&#039;suoi primi principii, l&#039;Huyghens esser sollecito di <lb></lb>restringere più che fosse possibile al pendolo l&#039;arco delle vibrazioni. </s>

<s>Si ca­<lb></lb>pisce bene come una tale sollecitudine dovesse avere origine dalla ferma <lb></lb>persuasione che non fosse altrimenti vero quel perfetto isocronismo preteso <lb></lb>dal Galileo. </s>

<s>Certo non avrà avuto il remoto Olandese notizia di quelle nu­<lb></lb>merosissime esperienze fatte già nel secondo periodo della sperimentale <lb></lb>Accademia Medicea, nelle sale del Palazzo Pitti (Targ. </s>

<s>Aggrandim. </s>

<s>T. II, <lb></lb>pag. </s>

<s>142-62), ma, a persuadersi che le vibrazioni, quanto sono più ampie, <lb></lb>tanto più sono diuturne, gli bastò la seguente facile esperienza: “ Si enim <lb></lb>fila accipiantur eiusdem longitudinis duo, paribusque in parte ima ponderi­<lb></lb>bus religatis, utrumque scorsum suspendatur, tumque alterum eorum pro­<lb></lb>cul a linea perpendiculari, alterum parumper duntaxat extrahatur, simulque <lb></lb>e manu dimittantur, non diu utrumque simul in partes easdem ferri vide­<lb></lb>bitur, sed praevertet illud, cuius exiliores erunt recursus ” (Op. </s>

<s>Var. </s>

<s>ibi, <lb></lb>pag. </s>

<s>38). La differenza è così notabile, soggiunge l&#039;Autore, che non si può <lb></lb>attribuire alla resistenza dell&#039;aria. </s>

<s>Galileo insomma, era, così dalla geome­<lb></lb>tria come dall&#039;esperienza, ingannato in credere che la curva tautocrona fosse <lb></lb>il cerchio. </s>

<s>Qual&#039;è dunque questa curva? </s>

<s>si domandò l&#039;Huyghens, e la Geo­<lb></lb>metria gli rispose essere la cicloide. </s>

<s>Se si potesse dunque far vibrare il pen-<pb xlink:href="020/01/341.jpg" pagenum="322"></pb>dolo in archi di cicloide, e allora sarebbe tolta ai costruttori degli Orologi <lb></lb>ogni sollecitudine di far sì che quelle stesse vibrazioni vadano più ristrette <lb></lb>che sia possibile, e non sarebbe negli usi nautici alterata la regolarità del <lb></lb>moto da&#039;sussulti della nave, perchè, divarichi pure il pendolo quanto si <lb></lb>vuole, si manterranno in ogni modo isocrone le sue corse e ricorse. </s></p><p type="main">

<s>Come segno ultimo perciò a cui tendere, nel perfezionamento degli Oro­<lb></lb>logi, specialmente nautici, all&#039;insigne inventore paravasi innanzi la Cicloide. </s>

<s><lb></lb>Ma in che modo farne l&#039;applicazione? </s>

<s>La difficoltà era tale che a superarla <lb></lb>si ricercava l&#039;esplorazione e la scoperta di un nuovo campo geometrico. </s>

<s>E <lb></lb>l&#039;Huyghens attese veramente a questa esplorazione e fece questa scoperta, <lb></lb><figure id="id.020.01.341.1.jpg" xlink:href="020/01/341/1.jpg"></figure></s></p><p type="caption">

<s>Figura 21.<lb></lb>venendogli giusto l&#039;occasione di farla da quel pen­<lb></lb>dolo conico, di che si parlava più sopra. </s></p><p type="main">

<s>Udimmo come infino dal 1656 avesse pensato <lb></lb>d&#039;applicare all&#039;Orologio questa nuova maniera di <lb></lb>pendolo, e soggiunge anzi nel luogo citato che ne <lb></lb>furon veramente costruiti alquanti di così fatti Oro­<lb></lb>logi con felice successo. </s>

<s>Pure l&#039;applicazione del <lb></lb>pendolo conico presentava qualche difficoltà mag­<lb></lb>giore di quella del pendolo piano. </s>

<s>Il filo non si <lb></lb>poteva applicare al prolungamento dell&#039;asse della <lb></lb>ruota regolatrice, ma conveniva sospenderlo a un <lb></lb>braccio infisso in quel medesimo asse. </s>

<s>Conveniva <lb></lb>inoltre di dare allo stesso filo un&#039;appoggiatura, che <lb></lb>gli facesse insieme da falsaredine. </s>

<s>Così veramente <lb></lb>ideò ed eseguì il sagace Inventore: “ Axis DH <lb></lb>(fig. </s>

<s>21) ad horizontem erectus intelligendus est, <lb></lb>ac super polis duobus mobilis. </s>

<s>Huic ad A affixa <lb></lb>est lamina, latitudine aliqua praedita, curvamque <lb></lb>secundum lineam AB .... Pondus illi affixum F. </s>

<s><lb></lb>Dum axis DH in sese vertitur, filum BGF in rectam <lb></lb>lineam extensum, sphaerulam F una circumducit, ita ut circulos horizonti <lb></lb>parallelos percurrat qui maiores minoresve erunt, prout maiori aut minori <lb></lb>vi axis DH ab rotis Horologii in tympanidium K agentibus, incitabitur ” <lb></lb>(ibi, pag. </s>

<s>186). </s></p><p type="main">

<s>Lo studio della forza che fa descrivere alla palla tanto più ampii cer­<lb></lb>chi, quanto la vertigine dell&#039;asse è più concitata, fece sì che l&#039;Huyghens <lb></lb>riuscisse a formulare i XIII Teoremi <emph type="italics"></emph>De vi centrifuga,<emph.end type="italics"></emph.end> e dalla lamina AB, <lb></lb>sulla quale s&#039;appoggia il filo, scaturì la teoria delle Evolute. </s>

<s>È facile infatti <lb></lb>vedere che la figura del conoide, sulla superficie del quale s&#039;aggira sem­<lb></lb>pre nell&#039;alzarsi e nell&#039;abbassarsi la palla, dipende dalla curvatura di quella <lb></lb>lamina. </s>

<s>Or ecco il primo problema, che occorse di risolvere in questo pro­<lb></lb>posito al gran Geometra olandese: Perchè sempre i tempi de&#039;circuiti si <lb></lb>mantengano uguali, di che figura dee essere il conoide, sulla superficie del <lb></lb>quale, ne&#039;suoi giri or più alti or più bassi si mantiene la palla? </s>

<s>O altrimenti: <pb xlink:href="020/01/342.jpg" pagenum="323"></pb>in qual genere di curva dee inflettersi la lamina AB perchè la palla, disten­<lb></lb>dendosi il filo, descriva l&#039;apotema del conoide isocrono? </s>

<s>E trovò che quella <lb></lb>lamina dovea esser piegata in figura di parabola, che è l&#039;evoluta da cui si <lb></lb>descrive per evoluzione la curva genitrice di quello stesso conoide. </s></p><p type="main">

<s>Avviate per questa nuova luminosa via le idee, tutta la difficoltà del­<lb></lb>l&#039;applicare il pendolo cicloidale consisteva in trovare qual dovesse essere <lb></lb>l&#039;evoluta, dall&#039;evoluzione della quale si descrivesse una Cicloide. </s>

<s>Suppon­<lb></lb>gasi infatti che sia AB (fig. </s>

<s>22) questa evoluta configurata in lamina me­<lb></lb>tallica e che sia alla sommità di lei appeso il filo pendulo AC. </s>

<s>Nel salire <lb></lb>da C verso D avvolgendosi alla lamina, e nello scendere da D verso C svol­<lb></lb>gendosi dalla medesima, si descriverà dall&#039;estremità di quel filo una mezza <lb></lb><figure id="id.020.01.342.1.jpg" xlink:href="020/01/342/1.jpg"></figure></s></p><p type="caption">

<s>Figura 22.<lb></lb>Cicloide o un mezzo arco di Cicloide. </s>

<s>Che se si <lb></lb>assetti un&#039;altra lamina uguale, dall&#039;altra parte AE, <lb></lb>il filo stesso col peso, ricaduto da D, nel risalire <lb></lb>in F descriverà un altro arco di Cicloide, cosicchè <lb></lb>tutta la curva DCF descritta dal pendolo sarà ci­<lb></lb>cloidale, e perciò isocrona da qualunque punto ri­<lb></lb>salga il peso C e da qualunque altro punto di­<lb></lb>scenda. </s>

<s>Or la Geometria rivelò all&#039;Huyghens che le <lb></lb>due lamine AB, AE, perchè riuscissero a dare il <lb></lb>desiderato isocronismo, dovevano essere configu­<lb></lb>rate in semicicloide, conforme al Teorema da lui <lb></lb>dimostrato, nella proposiz. </s>

<s>VI della Parte III del­<lb></lb>l&#039;Orologio Oscillatorio, che cioè la curva descritta per evoluzione da un&#039;emi­<lb></lb>cicloide è un&#039;altra emicicloide uguale e simile all&#039;evoluta. </s></p><p type="main">

<s>Tale è il macchinamento che l&#039;Huyghens venne applicando, colla ferma <lb></lb>speranza di aver dato così la massima perfezione all&#039;Orologio. </s>

<s>Una verga <lb></lb>metallica raccomandata alla solida armatura della macchina sostiene le due <lb></lb>laminette piegate in figura di semicicloide, in mezzo alle quali pende il filo <lb></lb>flessibile, a cui è raccomandata la verghetta metallica del pendolo. </s>

<s>Questa <lb></lb>stessa verghetta passa attraverso al foro della clavicola fissata all&#039;estremità <lb></lb>dello scappamento a serpe, che gioca con le sue alette in posizione oriz­<lb></lb>zontale, fra le tacche della ruota a denti di sega, precisamente come nel <lb></lb>Cronoscopio descrittoci dal Sinclaro. </s></p><p type="main">

<s>La descrizione di questo nuovo Misuratore del tempo, insiem coi Teo­<lb></lb>remi concernenti la caduta de&#039;gravi per gli archi di Cicloide, e le Evolute, <lb></lb>e i Centri di oscillazione, e le Forze centrifughe furono pubblicati nel 1673 <lb></lb>in Parigi, in quell&#039;Opera immortale che s&#039;intitola <emph type="italics"></emph>Orologium oscillatorium.<emph.end type="italics"></emph.end><lb></lb>E ora è questa stessa pubblicazione, che ravvia la nostra Storia in Italia. </s></p><pb xlink:href="020/01/343.jpg" pagenum="324"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quando prima pubblicatosi all&#039;Aja l&#039;<emph type="italics"></emph>Horologium<emph.end type="italics"></emph.end> il principe Leopoldo <lb></lb>e il Viviani, coll&#039;intenzione di rivendicare a favor di Galileo la priorità della <lb></lb>scoperta, inviarono i due disegni e la Storia del ritrovamento del pendolo, <lb></lb>perchè, per mezzo del Boulliaud, capitassero in Olanda; l&#039;Huyghens e nel <lb></lb>commercio epistolare co&#039;Nostri e in pubblico si tacque, aspettando ad aprir <lb></lb>l&#039;animo suo a più propizia occasione. </s>

<s>E l&#039;occasione venne giusto in sul­<lb></lb>l&#039;atto di pubblicar solennemente l&#039;Orologio Oscillatorio, dedicato il dì 25 di <lb></lb>Marzo 1673 a Luigi XIV. </s></p><p type="main">

<s>Nella Prefazione infatti all&#039;Opera, dopo aver rimproverati coloro che, <lb></lb>parecchi anni decorsi dal 1658, attribuirono a sè o a&#039;loro connazionali l&#039;in­<lb></lb>venzione del pendolo automatico, avventa aguzzando più che mai la penna <lb></lb>così fatte parole: “ Qui vero Galileo primas hic deferre conantur, si ten­<lb></lb>tasse eum non vero perfecisse inventum dicant, illius magis quam meae <lb></lb>laudi detrahere videntur, quippe qui rem eamdem, meliori quam ille eventu <lb></lb>investigaverim. </s>

<s>Cum autem vel ab ipso Galileo vel a filio eius, quod nuper <lb></lb>voluit vir quidam eruditus, ad exitum perductum fuisse contendent, horo­<lb></lb>logiaque eiusmodi re ipsa exhibita, nescio quomodo sibi creditum iri spe­<lb></lb>rent, cum vix verisimile sit adeo utile inventum ignoratum manere potuisse <lb></lb>annis totis octo, donec a me in lucem ederetur ” (Op. </s>

<s>Var. </s>

<s>ibi, pag. </s>

<s>32). </s></p><p type="main">

<s>Chi sia quel <emph type="italics"></emph>vir quidam eruditus<emph.end type="italics"></emph.end> lo dice espressamente in una lettera <lb></lb>al principe Leopoldo: dice che egli era lo scrittore degli Esperimenti del­<lb></lb>l&#039;Accademia fiorentina (Fabbroni, Lett. </s>

<s>I, 223). Nel Libro de&#039;<emph type="italics"></emph>Saggi di Na­<lb></lb>turali esperienze,<emph.end type="italics"></emph.end> infatti, là dove si descrivono alcuni strumenti adoperati <lb></lb>per misuratori del tempo, si legge: “ Pertanto in quelle esperienze che ri­<lb></lb>chiedono squisitezza maggiore, e che sono di sì lunga osservazione, che le <lb></lb>minime disuguaglianze di tali vibrazioni dopo un gran numero arrivano a <lb></lb>farsi sensibili, fu stimato bene applicare il pendolo all&#039;orivolo, sull&#039;andar di <lb></lb>quello che prima di ogni altro immaginò il Galileo, e che dell&#039;anno 1649 <lb></lb>messe in pratica Vincenzio Galilei suo figliolo ” (Firenze, 1841, pag. </s>

<s>21, 22). </s></p><p type="main">

<s>Ma queste cose erano state pubblicamente scritte infino dal 1666, e <lb></lb>nonostante quello sdegno par che sia suscitato nell&#039;animo dell&#039;Hugenio da <lb></lb>causa recente, venendo a rinfocolar la fiamma accesavi già dall&#039;Autor della <lb></lb>Storia del ritrovamento del pendolo, e da 14 anni rimasta sopita. </s>

<s>Che sia <lb></lb>stato quel risentimento suscitato di fresco, lo dice abbastanza chiaro qnel <lb></lb><emph type="italics"></emph>nuper,<emph.end type="italics"></emph.end> per cui parrebbe che da poco tempo avesse l&#039;Huyghens letto nel <lb></lb>libro de&#039;<emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> della nostra Accademia. </s>

<s>E anzi questo dubbio si riduce a <lb></lb>certezza, rileggendo la sopra citata lettera fra le pubblicate dal Fabbroni, in <lb></lb>cui, il dì 22 Maggio 1673, l&#039;Huyghens stesso manda a ringraziare il Prin­<lb></lb>cipe del Libro degli Esperimenti donatogli insieme con gli opuscoli di Fran­<lb></lb>cesco Redi. </s></p><pb xlink:href="020/01/344.jpg" pagenum="325"></pb><p type="main">

<s>Qui resterebbe di due cose sodisfare ai curiosi: la prima, come mai il <lb></lb>Principe Leopoldo, che fu tanto sollecito e largo dispensatore del Libro a <lb></lb>tutti i dotti nostrali e stranieri, facesse così lungo indugio coll&#039;Huyghens <lb></lb>corrispondente dell&#039;Accademia infin quasi da&#039;primi anni, e fra quegli stessi <lb></lb>dotti il più insigne di tutti. </s>

<s>L&#039;altra, come mai l&#039;Huyghens così poca atten­<lb></lb>zione facesse nello svolgere il Libro, da non accorgersi che era stato pub­<lb></lb>blicato già da sette anni, benchè lo avesse ricevuto di fresco. </s>

<s>Ma perchè <lb></lb>così fatte questioni appartengono piuttosto all&#039;erudizione che alla Scienza, <lb></lb>lasceremo ad altre mani a risolvere il nodo. </s></p><p type="main">

<s>Quel rinfocolamento poi aveva il suo giusto motivo, perchè mentre l&#039;Au­<lb></lb>tore della Storia del ritrovamento del pendolo si contentava d&#039;attribuire a <lb></lb>Galileo il primo progetto e al figliuolo di lui il primo tentativo, lo Scrittore <lb></lb>del Libro degli Esperimenti sentenziava addirittura che Vincenzio di Galileo <lb></lb>aveva messo in pratica il pendolo all&#039;Orologio. </s>

<s>Per ciò privatamente l&#039;Huy­<lb></lb>ghens, nella lettera sopra citata al principe Leopoldo, si rammaricava di es­<lb></lb>sere stato tacitamente accusato di plagio, e al cospetto del pubblico poi, <lb></lb>nella Prefazione all&#039;<emph type="italics"></emph>Oscillatorio,<emph.end type="italics"></emph.end> faceva le sue ragioni, domandando come <lb></lb>mai fu tenuta per otto anni a tutti occulta l&#039;invenzione de&#039;Galilei. </s>

<s>Che se <lb></lb>ciò fu ad arte, sia mia gloria conclude l&#039;altero Olandese, <emph type="italics"></emph>id quod omnes <lb></lb>latebat mihi soli innotuisse.<emph.end type="italics"></emph.end> E perchè sapeva bene che a&#039;Galilei, padre e <lb></lb>figlio, di pubblicare quelle loro invenzioni ne avevano avuto il divieto ine­<lb></lb>sorabile dalla morte, le parole del Toparca di Zulichemme vanno diretta­<lb></lb>mente a ferire il Principe di Toscana, il quale forse non aveva ancora letta <lb></lb>quella Prefazione, perchè M. </s>

<s>De Gondy, a cui era stato commesso, non gli <lb></lb>aveva fatto recapitare il libro. </s>

<s>Ma insomma, in una sua lettera, il Principe <lb></lb>non fa altro che rispondere, in quegli stessi termini che nel 1659 scriveva <lb></lb>al Bullialdo, a quell&#039;altra lettera, nella quale l&#039;Hugenio, parendogli di es­<lb></lb>sere stato imputato di plagio, ripete le scuse antiche d&#039;aver pubblicato il suo <lb></lb>primo Orologio, senza nulla aver saputo di Galileo. </s></p><p type="main">

<s>Ma se il Principe Leopoldo de&#039;Medici e Vincenzio Viviani avranno poi <lb></lb>letta quella Prefazione all&#039;Orologio Oscillatorio, come la lessero certemente, <lb></lb>non potevano non sentirsi configgere nel cuore la punta acuta di quelle <lb></lb>alate parole. </s>

<s>Se era vero infatti che Vincenzio di Galileo infin dal 1649 aveva <lb></lb>messo in pratica l&#039;orologio a pendolo, com&#039;asseriva il Segretario Magalotti <lb></lb>a insinuazione senza dubbio del Viviani, e se era vero che infin da 1656 in <lb></lb>Toscana un Virtuoso aveva costruito un orologio più perfetto di quello del <lb></lb>signor Cristiano Hugenio; non pare anche a noi che sieno veramente degni <lb></lb>di riprensione il Principe dell&#039;Accademia fiorentina e il discepolo idolatra e <lb></lb>l&#039;amico intimo de&#039;Galilei per aver così lunghi anni tenuta occulta un&#039;in­<lb></lb>venzione di tanta importanza? </s>

<s>E avessero almeno alla tarda occasione che <lb></lb>presero di pubblicarla, provveduto degnamente! Quell&#039;Orologio, che fu pie­<lb></lb>tra di scandalo allo sdegnoso Olandese, è là nelle Tavole del Libro dell&#039;Ac­<lb></lb>cademia diligentemente disegnato sì, ma chiuso in sè stesso e d&#039;ogni loquela <lb></lb>muto. </s>

<s>Eppure, se egli parlasse, potrebbe rivendicare all&#039;Italia qualche me-<pb xlink:href="020/01/345.jpg" pagenum="326"></pb>rito sopra l&#039;Olanda, non solo quanto alla priorità del concetto, ma quanto <lb></lb>altresì alla precedenza dell&#039;esecuzione. </s>

<s>Studiamoci dunque, se ci riesce, di <lb></lb>farlo parlare. </s></p><p type="main">

<s>La chiavetta (fig. </s>

<s>23) che pende legata a un nastro allacciato al colon­<lb></lb>nino tornito, in capo al quale riposa la cassa chiusa dell&#039;orologio, ci dice <lb></lb>intanto che era impresso il moto alle ruote dall&#039;elaterio di una molla e non <lb></lb><figure id="id.020.01.345.1.jpg" xlink:href="020/01/345/1.jpg"></figure></s></p><p type="caption">

<s>Figura 23.<lb></lb>dal peso. </s>

<s>La figura stessa e le poche parole soggiunte a <lb></lb>illustrarla ci dicono di più che la mostra indicava il nu­<lb></lb>mero delle oscillazioni del pendolo da una infino a 15, e <lb></lb>il tempo di quelle stesse oscillazioni si variava a piacere <lb></lb>avvitandovi pendoli ora più lunghi, ora più corti. </s>

<s>D&#039;onde <lb></lb>s&#039;argomenta che la ruota alla quale è imperniato l&#039;indice <lb></lb>doveva avere 15 denti come quell&#039;altra mossa dal pen­<lb></lb>dolo. </s>

<s>In che modo poi questo giocasse par che possa con <lb></lb>non minor certezza argomentarsi da quelle parole che <lb></lb>dicono essere stato applicato il pendolo all&#039;oriuolo <emph type="italics"></emph>sul­<lb></lb>l&#039;andare di quello che prima di ogni altro immaginò <lb></lb>il Galileo.<emph.end type="italics"></emph.end> Dunque il pendolo giocava sulla ruota a denti <lb></lb>di sega, menando in qua e in là le due sue code, che, <lb></lb>ora dischiavandosi da&#039;denti, ora urtando ne&#039;pironi, fanno <lb></lb>a ogni vibrazione passare un dente alla ruota stessa. </s>

<s>Al­<lb></lb>l&#039;ultimo la ruota mossa dalla molla poteva avere qualun­<lb></lb>que numero di denti, non avendo altro ufficio che di <lb></lb>dare impulso a quella a denti di sega, la quale dovendo <lb></lb>essere collocata verticalmente, per via di una ruota coro­<lb></lb>nata faceva volgere una lanterna e con essa l&#039;indice <lb></lb>sulla mostra orizzontale. </s></p><p type="main">

<s>Se quelle acetose parole <emph type="italics"></emph>messe in pratica Vincenzio <lb></lb>Galilei<emph.end type="italics"></emph.end> non avessero così a un tratto irritate le narici del Barone olandese, <lb></lb>e piuttosto che gittar via il Libro, senza più degnarsi nemmeno di guardare <lb></lb>il frontespizio, per assicurarsi dell&#039;anno dell&#039;impressione; avesse letto con <lb></lb>calma, si sarebbe assai facilmente persuaso che, descrivendosi ivi un orolo­<lb></lb>gio diverso affatto dal suo, non ci era luogo a citare il suo nome e la sua <lb></lb>invenzione, e che citandosi invece il nome e l&#039;invenzione di Galileo non ve­<lb></lb>niva egli per niente a esser colto dall&#039;accusa di plagio. </s></p><p type="main">

<s>L&#039;Orologio ugeniano infatti era una macchina in sè per ogni parte <lb></lb>compiuta e applicabile a tutti gli usi: l&#039;orologio invece degli Accademici del <lb></lb>Cimento era una macchinetta costruita a solo uso di misurare le minime <lb></lb>frazioni del tempo ne&#039;fisici esperimenti. </s>

<s>Il modo stesso dell&#039;applicazione del <lb></lb>pendolo era nell&#039;una e nell&#039;altra costruzione molto diverso. </s>

<s>Si ricompone <lb></lb>dunque la lite dicendo competersi all&#039;Huyghens due meriti che nessuno per <lb></lb>verità gli potrebbe contendere: quello di avere inventato l&#039;orologio perfetto, <lb></lb>e l&#039;altro di essere stato il primo a pubblicarlo. </s>

<s>Resta dall&#039;altra parte a Ga­<lb></lb>lileo il merito di aver avuto di quella invenzione il primo concetto e a un <pb xlink:href="020/01/346.jpg" pagenum="327"></pb>nostro Toscano quello altresì d&#039;averlo in qualche modo eseguito o poco prima <lb></lb>o contemporaneamente all&#039;Hugenio, benchè non se ne fosse saputo preva­<lb></lb>lere per sua sventura. </s>

<s>Ma perchè tuttociò non si asserisca che sulle parole <lb></lb>di Vincenzio Viviani e di Leopoldo de&#039;Medici, negando fede alle quali si ver­<lb></lb>rebbe necessariamente a negar fede alla nostra Storia, che si potrebb&#039;egli <lb></lb>dire della veracità di que&#039;due uomini? </s></p><p type="main">

<s>E quanto al Viviani non può negarsi che quando narra i fatti della <lb></lb>prima vita scientifica di Galileo, non si mostri spesso male informato e che <lb></lb>non si lasci talvolta trasportar da uno zelo soverchio d&#039;esaltar la gloria del <lb></lb>venerato maestro. </s>

<s>Questa stessa storia del pendolo ne porgerà in seguito di <lb></lb>ciò molti esempii, ma intanto basti richiamar l&#039;attenzione de&#039;nostri lettori <lb></lb>su quel che egli dice della scoperta galileiana della lunghezza de&#039;pendoli in <lb></lb>proporzion duplicata dei tempi. </s>

<s>Dice che Galileo giunse a una tale scoperta <lb></lb>guidato dalla Geometria e dalla sua Nuova Scienza del moto (Alb. </s>

<s>XIV, 443). <lb></lb>Eppure è un fatto che Galileo scoperse quella legge senza geometria e senza <lb></lb>scienza del moto, per semplice esperienza. </s>

<s>Tanto poi era al Viviani questo <lb></lb>fatto ben noto, che nelle postille autografe all&#039;edizione di Leyda, crede d&#039;es­<lb></lb>sere egli stato il primo a dar alla legge sperimentale di Galileo fondamenti <lb></lb>stabili di Geometria e di Scienza del moto. </s>

<s>Ma quando il Viviani narra con <lb></lb>tutte le particolarità fatti de&#039;quali fu spettatore e attore nella sua convivenza <lb></lb>d&#039;Arcetri, parrebbe un negar fede all&#039;umana natura, e perciò a ogni parte <lb></lb>di Storia, il negar fede alla parola di lui. </s></p><p type="main">

<s>La dignità poi e l&#039;integrità di Leopoldo de&#039;Medici lascia anche meno <lb></lb>a dubitare de&#039;suoi asserti. </s>

<s>Poichè noi dunque, sulla fede del Principe, ac­<lb></lb>cettiamo per vero che un Toscano avesse costruito un&#039;orologio a pendolo <lb></lb>in quello stesso tempo e forse un po&#039;prima che in Olanda pensasse a co­<lb></lb>struirlo l&#039;Hugenio, rimane d&#039;investigar qual fosse il nome di lui e la ma­<lb></lb>niera di quella costruzione. </s></p><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Collazionando le lettere del Principe Leopoldo scritte il dì 20 Aprile e <lb></lb>22 Maggio 1659 al Bullialdo e da noi riferite più sopra, con la Storia del <lb></lb>ritrovamento del pendolo scritta dal Viviani pochi mesi dopo, s&#039;ha in que­<lb></lb>sta una dichiarazione importante degli studii fatti intorno alla applicazione <lb></lb>del pendolo e delle persone che v&#039;esercitarono l&#039;ingegno, di che in quelle <lb></lb>non si fa che un semplice accenno. </s>

<s>Si ha infatti che Filippo Treffler chia­<lb></lb>mato da Augusta a Firenze per servire in qualità di <emph type="italics"></emph>torniaio<emph.end type="italics"></emph.end> il Granduca, <lb></lb>fabbricò in quel tempo quella galante macchinetta nella quale s&#039;incarnava <lb></lb>il concetto rivelato nella Lettera di Galileo a Lorenzo Realio; s&#039;ha che Fran­<lb></lb>cesco Generini presentò allo stesso Granduca un modello in ferro, nel quale <lb></lb>era unito al pendolo il contrappeso, in modo simile a quello che 14 anni <pb xlink:href="020/01/347.jpg" pagenum="328"></pb>avanti immaginò Galileo, benchè con diversa e molto ingegnosa applicazione; <lb></lb>s&#039;ha che lo stesso Filippo adattò l&#039;invenzione a un oriuolo da camera per <lb></lb>S. A. e che ridusse a questa foggia di oriuoli a pendolo quello pubblico <lb></lb>sulla piazza de&#039;Pitti. </s></p><p type="main">

<s>Che sia dunque Francesco Generini quel Virtuoso di cui parla nelle due <lb></lb>lettere sopra citate il Principe Leopoldo? </s>

<s>A chi volesse dire così, non <lb></lb>avremmo per verità argomenti da mostrar la falsità del suo detto, ma par <lb></lb>nonostante assai più probabile che il Principe stesso intendesse di un altro, <lb></lb>che il Viviani ivi per modestia si tace o per altra più complicata ragione. </s>

<s><lb></lb>Potrebb&#039;essere insomma che l&#039;Automato inventato in Toscana e da Leo­<lb></lb>poldo de&#039;Medici messo a concorso con quello costruito in Olanda, fosse quello <lb></lb>che vedesi nelle Tavole de&#039;<emph type="italics"></emph>Saggi di Naturali Esperienze<emph.end type="italics"></emph.end> costruito da Fi­<lb></lb>lippo Treffler sul disegno avutone dal Viviani. </s></p><p type="main">

<s>A render questa nostra congettura in qualche modo probabile soccorre <lb></lb>prima di tutto il fatto che fra il 1656 e il 57 lo stesso Viviani, aiutato ta­<lb></lb>lora dal Borelli e dal Rinaldini, attendeva a far esperienze sopra la velocità <lb></lb>del suono e della luce (MSS. Cim. </s>

<s>T. X, c. </s>

<s>181), per le quali si richiede­<lb></lb>vano misuratori squisiti de&#039;minimi tempi. </s>

<s>Or chi non direbbe che un tal <lb></lb>Cronometro descritto o diciam meglio disegnato nel Libro de&#039;<emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> non <lb></lb>fosse proprio inventato a quest&#039;uso? </s>

<s>E chi potrebbe negare che a Vincen­<lb></lb>zio Viviani, il quale ebbe mano alla costruzione dell&#039;Orologio di Galileo in­<lb></lb>siem col figliuolo di lui, non cadesse in mente di rendere automatiche le <lb></lb>vibrazioni del pendolo, aosì difficilmente osservabili coll&#039;occhio, per via della <lb></lb>macchinetta di cui s&#039;è di sopra indagato il disegno, a costruir la quale aveva <lb></lb>l&#039;opera del Treffler artefice in orologeria così famoso? </s></p><p type="main">

<s>Tutto questo sembra a noi e sembrerà altresì probabile ai nostri let­<lb></lb>tori, ma ora annunziamo non più come probabilità, ma come cosa certa <lb></lb>l&#039;essersi applicato lo stesso Viviani a descrivere il modo per trovar grafi­<lb></lb>camente le lunghezze varie che occorre di dare ai pendoli, secondo si vuol <lb></lb>che l&#039;indice sulla mostra segni ora una, ora un&#039;altra minima misura dei <lb></lb>tempi trascorsi. </s>

<s>In una nota autografa infatti, dop&#039;aver matematicamente <lb></lb>dimostrato che le lunghezze dei pendoli hanno ragion duplicata dei tempi, <lb></lb>così per modo di corollario soggiunge il Viviani: </s></p><p type="main">

<s>“ Questa sì bella proprietà mi somministrò la fabbrica di uno stru­<lb></lb>mento assai facile, per aggiustar con esso speditamente la lunghezza di un <lb></lb>pendolo con quella di un altro (i tempi delle lor vibrazioni abbiano qua­<lb></lb>lunque proporzione) sfuggendo per tal via il tedio di far prove e riprove <lb></lb>con diverse lunghezze di fili, e di replicar le numerazioni delle loro dondo­<lb></lb>late, finchè si avrà a tentoni, a trovar quella che dia la divisione del tempo <lb></lb>cercata. </s>

<s>” </s></p><p type="main">

<s>“ Pongasi aversi nota la lunghezza del filo AB (fig. </s>

<s>24) di quel pendolo, <lb></lb>che in ciascuna sua vibrazione scempia di sola andata o ritorno, consumi il <lb></lb>tempo di un minuto secondo. </s>

<s>Dipoi, dentro l&#039;angolo retto CDL di un telaio <lb></lb>rettangolo CDLF di legno o di metallo, sostenuto dal piede E, si adatti e <pb xlink:href="020/01/348.jpg" pagenum="329"></pb>fermi una sottil lamina di rame o di ottone tagliata in figura di mezza pa­<lb></lb>rabola, colla cima in G, il di cui asse GD sia precisamente uguale a detto <lb></lb>filo AB, e la base DL si divida nel telaio in minute parti uguali, come in 60, <lb></lb>cominciando la numerazione di 5, in 5 o di 10, in 10 da D e terminando <lb></lb><figure id="id.020.01.348.1.jpg" xlink:href="020/01/348/1.jpg"></figure></s></p><p type="caption">

<s>Figura 24.<lb></lb>in L, che così lo strumento sarà fatto, av­<lb></lb>vertendo che, quanto questo telaio sarà più <lb></lb>lungo da C verso F, mantenuta la lun­<lb></lb>ghezza GD dell&#039;asse della parabola; tanto <lb></lb>la curva GHIL sarà più distesa, e più atta <lb></lb>all&#039;uso il quale è tale. </s>

<s>” </s></p><p type="main">

<s>“ Cerchisi per esempio la lunghezza <lb></lb>del filo di quel pendolo, che in ogni sua <lb></lb>vibrazione scempia metta la metà di un <lb></lb>minuto secondo, nel qual si fa la semplice <lb></lb>vibrazione col filo AB. </s>

<s>Si accomodi prima <lb></lb>lo strumento verticalmente. </s>

<s>Di poi, perchè <lb></lb>il n. o 30 notato qui colla lettera P, è la <lb></lb>metà di tutta la numerazione delle parti­<lb></lb>celle segnate sul regolo DL, si presenti <lb></lb>davanti e rasente al detto n.o 30 il pendolo quieto AB in PN, e fuor del <lb></lb>lembo GNL della parabola avanzerà la parte IN del filo, la quale sarà ap­<lb></lb>punto la cercata, perchè, con essa ogni scempia vibrazione del pendolo si <lb></lb>farà nella metà del tempo di quella del pendolo AB, cioè si farà in 30 terzi, <lb></lb>cioè in un mezzo secondo, sicchè ogni sua doppia vibrazione di andare e di <lb></lb>tornare sarà un secondo. </s>

<s>” </s></p><p type="main">

<s>“ Similmente cercando la lunghezza del pendolo, che si faccia ogni sua <lb></lb>mossa scendente nella terza parte di un minuto secondo, cioè in 20 terzi, <lb></lb>si applichi come sopra il termine del filo AB in Q, dove sta segnato il <lb></lb>n.o 20, terza parte di 60, sicchè AB penda in H, chè l&#039;avanzo HO del filo <lb></lb>sodisfarà al quesito. </s>

<s>” </s></p><p type="main">

<s>“ Talmente che se si troverà modo di fermare in L, H, sul lembo della <lb></lb>lamina parabolica i fili pendoli LM, IN, HO e questi si allontanino unita­<lb></lb>mente dal perpendicolo, si vedrà che ad ogni sola gita del primo, il secondo <lb></lb>ne fa due, il terzo tre, ecc. </s>

<s>ecc. </s>

<s>E la ragione di ciò si è perchè, avendo <lb></lb>la lunghezza LM alla IN suddupla proporzione del tempo di una vibrazione <lb></lb>di quelle al tempo di una di queste, come qui a principio s&#039;è dimostrato, ed <lb></lb>avendo anche per proprietà della parabola la LM alla IN suddupla ragione <lb></lb>della MG alla GN, ovver del n.o DL al n.o DP; essendo 60 doppio del 30, <lb></lb>anco il tempo d&#039;una vibrazione di LM sarà doppio del tempo di una vibra­<lb></lb>zione di IN, e per le stesse ragioni il tempo di una del pendolo LM sarà <lb></lb>triplo del tempo di una del pendolo HO. ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXVII, c. </s>

<s>64). </s></p><p type="main">

<s>Della descrizione, però un po&#039;meno perfetta, e della costruzione di que­<lb></lb>sto strumento lasciò nota altrove lo stesso Viviani (MSS. Cim. </s>

<s>T. X, c. </s>

<s>49) <lb></lb>e pare se ne compiacesse alquanto, annoverando anco questa fra le altre sue <pb xlink:href="020/01/349.jpg" pagenum="330"></pb>invenzioni: (Nelli, Saggio ecc., Lucca 1759, pag. </s>

<s>111). Si sarebbe forse al­<lb></lb>tresì compiaciuto in questo medesimo luogo dell&#039;invenzion del Cronometro, <lb></lb>per servigio del quale inventò lo strumento sopra descritto, so non avesse <lb></lb>voluto farne intiera oblazione al suo Galileo. </s></p><p type="main">

<s>Ma che egli attendesse per sè medesimo a così fatte speculazioni e ci <lb></lb>avesse acquistato meriti proprii da venire in qualche parte a contesa di <lb></lb>quella gloria che, per la pubblicità dell&#039;opera, s&#039;andò a cumular tutta in <lb></lb>fronte all&#039;Hugenio; si concluderà da ciò che siamo per dire della ricerca <lb></lb>de&#039;centri di oscillazione a proposito della fabbrica degli orologi. </s></p><p type="main">

<s>Nel 1635 Giovanni Pieroni attendeva con massima diligenza ad osser­<lb></lb>vare i moti di alcune stelle fisse per accertarsi se ell&#039;erano veramente sog­<lb></lb>gette, come da alcuni copernicani si sospettava, a parallasse annuale. </s>

<s>A tali <lb></lb>delicatissime ricerche gli bisognavano misuratori squisiti de&#039;minimi tempi. </s>

<s><lb></lb>Ma a supplire al bisogno riconosceva l&#039;inutilità de&#039;pendoli, così magnificati <lb></lb>da Galileo, se prima non si sapeva la loro lunghezza precisa e il più esatto <lb></lb>modo di computarla. </s>

<s>Perciò scriveva, in una sua lettera diretta allo stesso <lb></lb>Galileo, che gli sarebbe stato grandissimo vantaggio saper da lui <emph type="italics"></emph>quanto <lb></lb>vadia lungo un pendolo per misurare uno o alquanti secondi di tempo, <lb></lb>e se la lunghezza si prende insino a tutto il corpo grave pendente o in­<lb></lb>sino al centro di esso.<emph.end type="italics"></emph.end> (Alb. </s>

<s>X, 68). </s></p><p type="main">

<s>La responsiva a questa del Pieroni non si trova nell&#039;Epistolario gali­<lb></lb>leiano, ma in ogni modo siam certi che egli non era in grado di rispon­<lb></lb>dere alla prima domanda, perchè non aveva ancora scoperta la legge del <lb></lb>tempo relativamente alle varie lunghezze de&#039;pendoli: nè men certi siam pure <lb></lb>in dire che egli non era in grado di rispondere scientificamente nemmeno <lb></lb>alla seconda, la quale includeva in sè la soluzione del celebre problema dei <lb></lb>centri oscillatorii. </s>

<s>Un tal problema era senza dubbio occorso a Galileo nella <lb></lb>corda o nella catena che s&#039;incurva, oscillando il pendolo (Alb. </s>

<s>I, 254) ma <lb></lb>perchè di questo, nella misura del tempo, dica pure quel che si vuole il <lb></lb>Viviani, Galileo non ne fece mai uso, non sentì perciò nemmeno il bisogno <lb></lb>di decider se alla lunghezza del filo dovesse aggiungersi il diametro o il <lb></lb>raggio o altra parte della dimensione del peso pendolo, come voleva il Pie­<lb></lb>roni sapere dal suo Maestro. </s></p><p type="main">

<s>Quando nel primo periodo dell&#039;Accademia medicea si ripresero questi <lb></lb>studii, e si volle cominciare a mettere una volta in pratica quel che Gali­<lb></lb>leo si era contentato di progettare, si sentì allora seriamente il bisogno di <lb></lb>rispondere alla seconda domanda di Giovanni Pieroni e si rispose in modo <lb></lb>che in pratica almeno fu trovato conforme al vero. </s>

<s>Si rispose che essendo <lb></lb>il filo sottilissimo e il peso di materia omogenea e di figura sferica, la lun­<lb></lb>ghezza del pendolo si dovea computar dal punto di sospensione del filo al <lb></lb>centro di gravità dello stesso peso. </s>

<s>Una sì fatta risposta, se non si trova <lb></lb>espressa a parole, si trova però eloquentemente espressa ne&#039;fatti, sapendosi <lb></lb>che per le squisite osservazioni e sperienze i nostri Accademici si valevano <lb></lb>di palle di oro sospese a sottilissimi fili di seta. </s>

<s>Ma più eloquentemente che <pb xlink:href="020/01/350.jpg" pagenum="331"></pb>mai parla il disegno di quella macchinetta, che nella Tavola de&#039;<emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> si <lb></lb>vede impressa allato del sopra descritto Cronometro. </s>

<s>Quella macchinetta fu <lb></lb>pensata e fu pensato di appender la palla a due fili che le facessero di fal­<lb></lb>saredine, <emph type="italics"></emph>perchè l&#039;ordinario pendolo a un sol filo, in quella sua libertà <lb></lb>di vagare (qualunque ne sia la cagione) insensibilmente va traviando dalla <lb></lb>prima sua gita, e verso il fine, secondo ch&#039;ei s&#039;avvicina alla quiete, il <lb></lb>suo movimento non è più per un arco verticale, ma par fatto per una <lb></lb>spirale ovata, in cui più non posson distinguersi nè noverarsi le vibra­<lb></lb>zioni.<emph.end type="italics"></emph.end> (Firenze 1841, pag. </s>

<s>20). </s></p><p type="main">

<s>Ma che ci sarebb&#039;egli stato bisogno di quel macchinamento? </s>

<s>vien, leg­<lb></lb>gendo, in mente a ciascuno: quell&#039;effetto si poteva ottener con naturale fa­<lb></lb>cilità, sospendendo le palle non a fili flessibili, ma a rigide verghe di metallo. </s>

<s><lb></lb>Ora, quel che viene in mente a ciascuno non è credibile che non venisse <lb></lb>in mente ai nostri Accademici, e perciò, se non usarono di appendere il <lb></lb>peso a una verga metallica, dovevano averne qualche buona ragione. </s>

<s>La ra­<lb></lb>gione poi era questa: che, avendo la verga rigida qualche peso sensibile <lb></lb>rispetto al peso della palla, la regola di computar la lunghezza giusta del <lb></lb>pendolo non era più quella assegnata di sopra, per cui conveniva cercarne <lb></lb>altra con certezza di ragion matematica. </s>

<s>Nè di trovarla per verità era fa­<lb></lb>cile presentandosi alquanto complicato il problema de&#039;centri di oscillazione. </s></p><p type="main">

<s>Pure, quando il Viviani inventò e il Treffler costruì il Cronometro, biso­<lb></lb>gnava sospendere il filo a una verga metallica e non sì gracile, avendo ella a <lb></lb>resistere agli urti de&#039;pironi e ai contraccolpi delle ruote. </s>

<s>E da un&#039;altra parte, <lb></lb>se precisa bisognava mai computar la lunghezza de&#039;pendoli, qui proprio era <lb></lb>il caso, dipendendo da quella stessa precisione tutta l&#039;utilità e il peculiare <lb></lb>uso del nuovo misuratore delle più sminuzzate minuzie del tempo. </s>

<s>Condi­<lb></lb>zione inevitabile alla fabbrica di questo strumento era la ricerca del centro <lb></lb>oscillatorio, e il Viviani fece questa ricerca e riuscì e trovar la regola pra­<lb></lb>tica “ per conoscer qual punto del pendolo sia quello dal quale si regola <lb></lb>il moto ” (MSS. Cim. </s>

<s>T. X, c. </s>

<s>48). </s></p><p type="main">

<s>Nella ricerca del centro di oscillazione de&#039;pendoli l&#039;elegante ingegno del <lb></lb>Viviani, che si compiaceva di sparger di qualche fiore le aride vie della Ma­<lb></lb>tematica, s&#039;abbattè a inventare il gioco di quelle figurine che si soglion <lb></lb>rappresentare in molti Trattati di Fisica come grazioso esempio dell&#039;equili­<lb></lb>brio stabile dei pesi. </s>

<s>Correvano quelle figurine a fare spettacolo di sè per <lb></lb>tutta l&#039;Italia, e il padre Giuseppe Ferroni così da Bologna scriveva in pro­<lb></lb>posito allo stesso Viviani: “ Ho visto in casa del marchese Cospi una sta­<lb></lb>tuetta di legno di un maestro, la quale tenendo in mano un&#039;asta rigida con <lb></lb>due contrappesi, ed avendo nel piede una punta ferrata di trottola, posata <lb></lb>su un candeliere di legno, su quello si gira facendo molti ondeggiamenti, <lb></lb>come se volesse cadere, ma pur sempre si mantiene in piedi. </s>

<s>Io pensai a que­<lb></lb>sto equilibrio.... So questa invenzione esser venuta di Firenze, onde la stimo <lb></lb>parto dell&#039;ingegno di V. S. </s>

<s>Illustrissima ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLVI, c. </s>

<s>281). </s></p><p type="main">

<s>Il Ferroni s&#039;era bene apposto dell&#039;inventore, ma non aveva rettamente <pb xlink:href="020/01/351.jpg" pagenum="332"></pb>pensato intorno alle ragioni dell&#039;equilibrio, per cui il Viviani glie ne espone <lb></lb>la teoria in relazione ai centri oscillatorii concludendogli che “ il pendolo <lb></lb>composto di asta rigida, farebbe quegli ondeggiamenti che la macchina am­<lb></lb>mirata ” (ivi, c. </s>

<s>282). La teoria poi dell&#039;equilibrio stabile, nelle figure on­<lb></lb>deggianti, il Viviani stesso la lasciò scritta così in una sua nota: “ Tutto <lb></lb>il segreto dentro la figuretta ondeggiante col bilico senza mai cadere, ben­<lb></lb>chè ella non sia collegata col sostegno, ma solamente ci posi colla punta, <lb></lb>sta che il centro di gravità del composto si trova sempre sotto il punto del <lb></lb>sostegno ” (ivi, T. CXLIII, c. </s>

<s>64). </s></p><p type="main">

<s>L&#039;Huyghens non s&#039;incontrò nelle sue ricerche in così fatte eleganze, <lb></lb>ma molto più largamente e altamente del Viviani sollevò l&#039;ala del poten­<lb></lb>tissimo ingegno a quelle nuove e difficili speculazioni. </s>

<s>Il problema del <lb></lb>centro di oscillazione fu proposto dal Mersenno all&#039;Huyghens, quand&#039;era <lb></lb>giovanetto. </s>

<s>Il Cartesio e il Fabry lo risolsero ne&#039;più facili casi, e senza di­<lb></lb>mostrazione, ma quello stesso giovanetto divenuto già adulto, ne propose <lb></lb>teorie condotte su principii matematici, e le trovò riscontrare con gli spe­<lb></lb>rimenti. </s>

<s>L&#039;occasione di ciò, così a lui come al Viviani, gli fu porta dal­<lb></lb>l&#039;Orologio. </s>

<s>In quelli della prima fabbrica, a computar la lunghezza de&#039;pen­<lb></lb>doli e a variarla secondo i bisogni, seguì la regola de&#039;nostri Accademici, <lb></lb>facendo più sottile che fosse possibile la verga, e più pesante la palla, la <lb></lb>quale si poteva alzare o abbassare per mezzo di una vite. </s>

<s>Ma negli orologi <lb></lb>della seconda fabbrica, ossia ne&#039;cicloidali, cercando sempre nuove squisi­<lb></lb>tezze, alla palla sostituì la lente, la quale credè bene di mantener fissa in <lb></lb>quella posizione che la rendesse più atta a fender l&#039;aria, e a incontrar perciò <lb></lb>in lei minore la resistenza. </s>

<s>Mobile a vite e infilato nell&#039;asta lasciò un pic­<lb></lb>colo peso, che doveva servire, ora alzandolo ora abbassandolo, a regolare il <lb></lb>tempo dell&#039;Orologio. </s>

<s>Ma a saper con certezza di scienza quanto questo moto <lb></lb>di ascesa e discesa importasse nell&#039;abbreviare o allungare la misura prefi­<lb></lb>nita al moto del pendolo, occorreva la ricerca del centro d&#039;oscillazione, per <lb></lb>cui il pendolo composto si poteva ridurre alla vera lunghezza del pendolo <lb></lb>semplice, o pendolo matematico. </s>

<s>Così fatte ricerche furono dall&#039;Huyghens <lb></lb>instituite ed esposte nella IV Parte del suo <emph type="italics"></emph>Orologio Oscillatorio,<emph.end type="italics"></emph.end> dove alla <lb></lb>proposizione XXIII, insegna il modo di risolvere praticamente l&#039;importante <lb></lb>problema. </s></p><p type="main">

<s><emph type="center"></emph>VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>A questo punto si conclude la somma della Storia così controversa, che <lb></lb>concerne l&#039;applicazione del pendolo agli Orologi, nella quale tanta parte <lb></lb>ebbe, com&#039;abbiamo veduto, il nostro Viviani. </s>

<s>Egli, piuttosto che Galileo, e <lb></lb>l&#039;Huyghens si può dire che sieno i due competitori. </s>

<s>Ma pure è cosa nota­<lb></lb>bilissima che il Discepolo di Galileo dopo varie vicende passate non si fosse <pb xlink:href="020/01/352.jpg" pagenum="333"></pb>punto rimosso da quelle sue prime persuasioni, in cui la verità storica ri­<lb></lb>man così spesso sopraffatta dai pregiudizii. </s>

<s>E chi, fra&#039;tanti esempii che se <lb></lb>ne potrebbero addurre, non riconosce la passione che ha tolto oramai l&#039;equi­<lb></lb>librio e fatto prevaler dalla sua parte il giudizio, in quelle parole che gli <lb></lb>scrive Matteo Campani, a proposito della pubblicazione di un certo capitolo <lb></lb>in cui trattavasi dell&#039;Orologio a pendolo? </s>

<s>“ Mi permisi bensì che Ella, per <lb></lb>gloria di Galileo, avesse avuto a caro la pubblicazione di esso, mentre non si <lb></lb>fa menzione nessuna del signor Huyghens ” MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXLV, c. </s>

<s>150). </s></p><p type="main">

<s>Che nel 1682 poi, dopo tante private e pubbliche controversie, il Vi­<lb></lb>viani fosse rimasto in quelle stesse persuasioni in cui egli era prima che <lb></lb>desse mano a scriver la Storia del ritrovamento del pendolo, si par da ciò <lb></lb>che scrisse, e che aveva in animo di pubblicare come Prefazione alla <emph type="italics"></emph>Tavola <lb></lb>espansa perpetua, ad uso della Toscana per l&#039;osservanza delle ore ne&#039;pre­<lb></lb>cetti ecclesiastici,<emph.end type="italics"></emph.end> e che si trova inserita, da carte 67-86, nel Tomo CXXXVIII <lb></lb>manoscritto dei Discepoli di Galileo; Tavola che doveva servir di comple­<lb></lb>mento a quell&#039;altra <emph type="italics"></emph>Tavola dell&#039;ore, del levar del sole, mezzo giorno, mezza <lb></lb>notte<emph.end type="italics"></emph.end> ecc., stampata per cura dello stesso Viviani in Firenze, nella stampe­<lb></lb>ria granducale, nel 1660 e di cui, inserita nel Tomo manoscritto ora citato, <lb></lb>si trova una copia. </s>

<s>In quell&#039;abbozzo di Prefazione dunque gettato giù dalla <lb></lb>penna nel 1682 il Calcolator della <emph type="italics"></emph>Tavola espansa<emph.end type="italics"></emph.end> così scriveva: </s></p><p type="main">

<s>“ E qui in tale occasione sia permesso far noto ciò che, non essendo <lb></lb>forse così comune, sarà gradito il sapere, ed è che questo Oriuolo pubblico, <lb></lb>trovandosi venti anni sono, per la sua antichità avere scapitato molto della <lb></lb>sua perfezione, e facendo perciò col suo sregolato batter dell&#039;ore anticipare <lb></lb>o posticipare quelle operazioni, che gli abitanti si presumevano di far tutte <lb></lb>ben regolate; il medesimo Serenissimo Gran Duca Ferdinando, conoscendo <lb></lb>l&#039;importanza di rimediarvi in servizio e comodo, non tanto de&#039;secolari che <lb></lb>degli ecclesiastici, non solamente lo fece fabbricar di nuovo, senza riguardo <lb></lb>a spesa alcuna, ma perchè e&#039;fosse più esatto vi fece anche adattare, in luogo <lb></lb>dell&#039;usato <emph type="italics"></emph>tempo,<emph.end type="italics"></emph.end> quell&#039;altro nominato il pendolo, d&#039;invenzione ammiranda <lb></lb>del suo incomparabil Filosofo e Matematico Galileo Galilei, intorno al quale, <lb></lb>son già passati cento anni, perchè fu nel 1582, esso Galileo, nel trovarsi <lb></lb>studente a Pisa, con la sua veramente lincea accortezza in riflettere a tutti <lb></lb>gli effetti, benchè minimi della Natura, osservò un giorno, in una lampada <lb></lb>di quel Duomo stata poco prima lasciata in moto, un&#039;assai precisa ugualità <lb></lb>de&#039;passaggi delle sue andate e tornate tanto larghe per archi grandi, quanto <lb></lb>strette per piccolissimi, del qual Misuratore di tempo, da allora in poi, egli <lb></lb>si valse prima per conoscere la variazione delle frequenze del polso, e di <lb></lb>poi in servizio delle osservazioni astronomiche, bisognose della divisione <lb></lb>de&#039;brevi tempi in parti uguali minutissime, quali le somministra il pendolo <lb></lb>che sia d&#039;assai corto filo; e nel 1610, avendo il medesimo Galileo col suo <lb></lb>nuovo Occhiale, oltre agli innumerabili soli non più veduti da esso scoperti <lb></lb>in cielo, prima di ogni altro, ritrovato ancora le quattro Lune vaganti in­<lb></lb>torno al corpo di Giove, le quali, ad onore dell&#039;Augusta prosapia del G. D. Co-<pb xlink:href="020/01/353.jpg" pagenum="334"></pb>simo II suo signore volle si nominassero Stelle medicee, e giudicatele mezzi <lb></lb>proporzionati a dimostrar la via già per tanti secoli cercata, di navigar con <lb></lb>sicurezza per longitudine; pensò esso d&#039;accomodare esso pendolo agli oriuoli <lb></lb>a molla ed a contrappesi, per valersene in sussidio delle predette Medicee <lb></lb>ne&#039;tempi, che queste non fossero osservabili, e a tale effetto nel 1615 pro­<lb></lb>poselo, insieme con le Tavole calcolate da lui, per le future osservazioni di <lb></lb>quelle a Filippo III Re di Spagna, e di poi nel 1637 agli Stati di Olanda, <lb></lb>con farne loro libero dono, e descrivere un suo pensiero, per accomodare <lb></lb>esso pendolo agli usati orivoli a ruote, lo che per ultimo fece nel 1649 il <lb></lb>Dottor Vincenzio suo figliuolo, che fu il primo ad adattarlo ad un nuovo <lb></lb>Orivolo a contrappesi, intorno al quale lavorò anch&#039;egli ancora di propria <lb></lb>mano sul concetto che glie ne aveva somministrato già il proprio Padre, ed <lb></lb>in oggi sull&#039;esempio di questo, con tanto semplice ed ingegnoso trovato del <lb></lb>nostro ammirabile Galileo, si perfezionano tutti gli altri orivoli, poichè la <lb></lb>naturale ugualità delle vibrazioni del pendolo, necessita l&#039;artifizio a portar <lb></lb>le ore ugualissime ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXXXVIII, c. </s>

<s>101). </s></p><p type="main">

<s>Così il Viviani conclude a quel modo stesso che egli esordisce, e perciò <lb></lb>riescono inutili le pagine della nostra Storia, oggetto della quale non dee <lb></lb>esser per lui quello d&#039;investigare e di dire la verità, ma di esaltare il suo <lb></lb>Galileo. </s>

<s>Comunque sia, dicevasi dianzi che a quel punto a cui l&#039;abbiamo <lb></lb>condotta restavasi conclusa la somma della storia del pendolo applicato al­<lb></lb>l&#039;Orologio. </s>

<s>Ma qual&#039;è quello strumento, che esca dalle mani del suo primo <lb></lb>artefice perfetto? </s>

<s>L&#039;Huyghens credette, come si vide, di aver fatto un gran <lb></lb>passo nella via di questo perfezionamento, applicando il pendolo cicloidale, <lb></lb>che poi subito si vide andare in disuso. </s>

<s>Ciò fu per due ragioni: prima, <lb></lb>perchè col pendolo circolare s&#039;otteneva il medesimo intento, e poi, perchè <lb></lb>non era quello il vero modo d&#039;ovviare all&#039;inconveniente per cui si escogitò <lb></lb>quella nuova arguta invenzione. </s></p><p type="main">

<s>L&#039;inconveniente consisteva in certe ineguaglianze, che alcuni riduce­<lb></lb>vano a due: l&#039;una dipendente dal non esser quelle stesse vibrazioni iso­<lb></lb>crone, e l&#039;altra dipendente dal variar delle stagioni. </s>

<s>L&#039;Huyghens, ammet­<lb></lb>tendo la causa produttrice della prima ineguaglianza, rinnegava assolutamente <lb></lb>l&#039;altra: “ Penduli vero ipsius, quas adnotant, binas inaequalitates, alii au­<lb></lb>tem contra pernegant, earum alteram admittimus .... alteram plane nullam <lb></lb>esse adseverare non dubitamus ” (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>1724, pag. </s>

<s>12). Perciò <lb></lb>tutto il suo studio di recare all&#039;ultima perfezione l&#039;Orologio era rivolto al­<lb></lb>l&#039;isocronismo, e tanto era ben persuaso che a questa sola si riducesse la <lb></lb>causa di quelle inegualità, senza che le stagioni vi concorressere per nulla, <lb></lb>che, inventato il pendolo cicloidale, si vantava d&#039;aver così provveduto alla <lb></lb>massima perfezione dell&#039;Orologio. </s>

<s>Potrà bene, egli dice, il mio Automato <lb></lb>guastarsi o per vizio di fabbrica o per difficoltà, che al volgersi delle ruote <lb></lb>gli sia fatta dall&#039;aria, ma non è da temer mai che in lui s&#039;alteri la misura <lb></lb>del tempo, cosicchè sempre <emph type="italics"></emph>aut recte tempus metietur, aut omnino non <lb></lb>metietur<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>35). Ecco a che riduceva l&#039;Huyghens l&#039;influenza delle <pb xlink:href="020/01/354.jpg" pagenum="335"></pb>stagioni in alterare il moto degli orologi: al far più difficilmente volubili le <lb></lb>ruote attorno ai loro assi, per la maggior crassizie sopravvenuta nell&#039;aria. </s>

<s><lb></lb>Nessuno si crederebbe che tanto si fosse dovuto pensare prima d&#039;esser giunti <lb></lb>a riconoscere gli effetti del calore in alterare la giusta misura de&#039;pendoli, <lb></lb>e prima d&#039;avervi saputo trovar rimedio, per via delle compensazioni. </s>

<s>Perciò <lb></lb>non inutile nè discara crediamo dover riuscire ai Lettori la pagina, che si <lb></lb>aggiunge per ultima parte di questa storia. </s></p><p type="main">

<s>Golifredo Wendelin, diligentissimamente numerando le vibrazioni di un <lb></lb>medesimo pendolo in tutto il corso di un anno, s&#039;era accorto che nell&#039;estate <lb></lb>andava più pigro che nell&#039;inverno. </s>

<s>Maravigliato di questa strana novità, ri­<lb></lb>petè piu diligentemente che mai le sue osservazioni, e gli parve non esserci <lb></lb>dubbio: il pendolo estivo faceva in un giorno circa a 20 vibrazioni meno <lb></lb>dell&#039;iemale. </s>

<s>Reso pubblicamente noto il resultato di queste esperienze, nes­<lb></lb>suno gli volle credere. </s>

<s>Il Mersenno, nel Cap. </s>

<s>XIII delle sue Riflessioni fisico <lb></lb>matematiche, sottoponeva alle sue critiche, per verità non troppo acute, que­<lb></lb>sto fatto, e concludeva che il Wendelin in ogni modo si doveva essere in­<lb></lb>gannato. </s>

<s>Perchè ora, egli argomenta, misurava il tempo delle vibrazioni <lb></lb>de&#039;pendoli colle clessidre a sabbia, e queste danno veramente una differenza <lb></lb>notabile nel loro flusso, essendo che le sabbie nell&#039;estate son più sciolte <lb></lb>che nell&#039;inverno. </s>

<s>Ora misurava quel tempo colle classidre ad acqua, e sono <lb></lb>anche queste soggette a patir le medesime differenze, perchè l&#039;acqua, quanto <lb></lb>è più calda, e più facilmente scorre, e velocemente fluisce. </s>

<s>“ Quibus adde <lb></lb>calidam aquam frigida velocius fluere, si forte clariss. </s>

<s>Wendelinus aquae <lb></lb>fluxu, instar Galilaei, in Horologio suo usus est ” (Parisiis, 1647, T. III, <lb></lb>pag. </s>

<s>124). </s></p><p type="main">

<s>L&#039;Huyghens, descrivendo il suo primo Orologio, soggiunge di più che, <lb></lb>misurando talora il Wendelin il tempo delle vibrazioni per via degli orologi <lb></lb>scioterici, questi non dovevano essere stati con tutta la necessaria precisione <lb></lb>descritti, per cui, come ne dubitavano tutti gli altri, crede ragionevolmente <lb></lb>di doverne dubitare anch&#039;egli. </s>

<s>Ma comunque sia, conclude: “ Mihi certe <lb></lb>nihil eiusmodi licuit animadvertere ” (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>1724, pag. </s>

<s>13). Nè <lb></lb>di questo pare se ne fosse accorto nemmeno quindici anni dopo, quando <lb></lb>pubblicò l&#039;Orologio oscillatorio. </s></p><p type="main">

<s>Che al Wendelin, assicuratosi con tante lunghe e pazienti esperienze <lb></lb>venir dal calor dell&#039;estate ritardato il pendolo, dovesse il fatto riuscirgli un <lb></lb>mistero; che l&#039;Huyghens, il quale a tutt&#039;altro ne assegnava la causa per lui <lb></lb>certissima e dimostrata, confessasse che quello stesso fatto non gli era oc­<lb></lb>corso mai di avvertirlo, è cosa che non fa poi gran maraviglia. </s>

<s>Fa mara­<lb></lb>viglia però che in quelle medesime condizioni si trovasse la scienza de&#039;no­<lb></lb>stri Italiani, i quali s&#039;erano già allora, per tante esperienze, assicurati della <lb></lb>dilatazione così lineare come cubica subìta per effetto del calore da tutti <lb></lb>i corpi. </s></p><p type="main">

<s>Giuseppe Campani, per esempio, erasi veramente persuaso (nè pareva <lb></lb>possibile il non persuadersene, com&#039;ebbe a confessare l&#039;Hugenio) che il va-<pb xlink:href="020/01/355.jpg" pagenum="336"></pb>riar delle stagioni influisce in far variare il moto agli Orologi. </s>

<s>“ Ho tardato <lb></lb>(incomincia così una sua lettera scritta il dì 22 Novembre 1667 al principe <lb></lb>Leopoldo) perchè io volevo prima chiarirmi di un effetto del quale dubi­<lb></lb>tai ”. </s>

<s>Or sentiamo qual&#039;è questo effetto, e quale egli creda esserne la causa <lb></lb>di lui. </s>

<s>L&#039;effetto è che “ l&#039;orologio fosse per ricever qualche alterazione <lb></lb>dalle strane mutazioni de&#039;tempi, come sarebbe da tramontana a scirocco, a <lb></lb>cagione della maggiore o minore resistenza che gli vien fatta dall&#039;aria am­<lb></lb>biente, nella quale si muove, e la quale ora ingrossa e ora s&#039;assottiglia, ora <lb></lb>s&#039;aggrava più o meno ” (MSS. Cim. </s>

<s>T. XXIX, c. </s>

<s>92). </s></p><p type="main">

<s>Matteo Campani era pure della medesima opinione di suo fratello Giu­<lb></lb>seppe, per cui, studiando alla perfezione degli Orologi e attribuendo anche <lb></lb>egli la causa delle loro variazioni al vario condensamento dell&#039;aria ambiente, <lb></lb>non ci vide altro miglior rimedio, a preservarli dagli insulti ammosferici, da <lb></lb>quello in fuori di custodirli per ogni parte ben chiusi. </s>

<s>Tanto era poi per­<lb></lb>suaso dovere esser questo il più efficace rimedio, che se ne gloriava come <lb></lb>di una peregrina invenzione da dover tenersi gelosamente suggellata sotto <lb></lb>segreto. </s>

<s>“ Quanto a questi difetti (scriveva al princ. </s>

<s>Leopoldo) esteriormente <lb></lb>sopravvegnenti all&#039;oriuolo per l&#039;aria ambiente, V. A. sa che abbiamo pro­<lb></lb>curato di rimediarvi con la nostra invenzione di fabbricare in varia guisa <lb></lb>gli oriuoli chiusi, com&#039;andai accennando e descrivendo nel libretto, da me <lb></lb>due anni fa pubblicato sotto il nome anagrammatico d&#039;Antimo Tempera, ed <lb></lb>a V. A. dedicato.... Potendosi dare il caso che qualche altro ancora si fosse <lb></lb>riscontrato ne&#039;medesimi miei pensieri e maniera da me sin&#039;ora immagi­<lb></lb>nata,.... vengono da me contrassegnate le seguenti lettere,.... le quali, <lb></lb>combinate in lingua latina nel loro vero senso, spiegano individualmente la <lb></lb>mia invenzione ” (MSS. Cim. </s>

<s>T. XX, c. </s>

<s>14). </s></p><p type="main">

<s>Ora è da saper che Matteo, su questo soggetto degli orologi chiusi, che <lb></lb>egli principalmente proponeva per gli usi nautici; ebbe lunga corrispendenza <lb></lb>epistolare con Vincenzio Viviani, il quale secondava e approvava l&#039;opera del­<lb></lb>l&#039;artefice, persuaso anch&#039;egli della regolarità e quasi infallibilità dell&#039;Auto­<lb></lb>mato sottratto alle variazioni e all&#039;esteriori influenze dell&#039;aria. </s>

<s>Eppure era <lb></lb>quel Viviani, il quale, primo dopo l&#039;Aggiunti, aveva sperimentato che la <lb></lb>fiamma di un moccolino passata in su e in giù rasente al filo metallico, <lb></lb>faceva immediatamente allungare il pendolo: era quel Viviani che, primo in <lb></lb>Italia, aveva matematicamente dimostrato ehe i tempi delle oscillazioni stanno <lb></lb>come le radici delle lunghezze de&#039;pendoli. </s>

<s>Si diceva perciò dìanzi far gran­<lb></lb>dissima maraviglia che lo stesso Viviani non avesse riconosciuti applicabili <lb></lb>questi medesimi effetti ai pendoli adattati agli orologi, per i quali effetti s&#039;in­<lb></lb>tendeva chiarissimamente la recondita causa di quelle variazioni avvertite <lb></lb>già dal Wendelin tanti anni avanti. </s>

<s>S&#039;intendeva cioè esser veramente il ca­<lb></lb>lor dell&#039;estate che facendolo allungare ritardava il pendolo, mentre al con­<lb></lb>trario il freddo nell&#039;inverno lo faceva velocitare. </s>

<s>Dietro ciò, lo Scienziato <lb></lb>avrebbe dovuto consigliar l&#039;Artefice e persuaderlo che, a rinchiudere gli <lb></lb>orologi, non si otteneva l&#039;intento, perchè non lì consisteva la causa delle <pb xlink:href="020/01/356.jpg" pagenum="337"></pb>variazioni, ma negli effetti del calore, il quale passa attraverso alle pareti <lb></lb>più ben chiuse, e ben custodite. </s>

<s>Ond&#039;è che sarebbesi dovuto rivolgere ogni <lb></lb>studio a trovarci quel rimedio, rendendo ai pendoli le lunghezze inalterate, <lb></lb>nelle vicende inevitabili ora de&#039;caldi ora de&#039;freddi. </s>

<s>Prima però di giungere <lb></lb>a tanto, dovette l&#039;Orologeria fare altri progressi. </s></p><p type="main">

<s>Il pendolo rendeva l&#039;Orologio male atto a trasportarsi, e sempre lo te­<lb></lb>neva in pericolo sui navigli ondeggianti. </s>

<s>Il bilanciere, antico regolatore del <lb></lb>tempo negli Orologi, soccorse, benchè tardi, utilissimo a risolvere con fa­<lb></lb>cilità il nuovo e importante problema. </s>

<s>E perchè l&#039;andare e il ritornare di <lb></lb>una molla elastica si fa presso a poco in tempi uguali, come l&#039;andare e il <lb></lb>ritornar di una sfera pendula, bastò applicare al bilanciere antico una sot­<lb></lb>tile e delicata molla avvolta a spira, per ottener gli orologi portatili, o come <lb></lb>si dice, da tasca. </s></p><p type="main">

<s>L&#039;Huyghens così svela il segreto dell&#039;artificiosa macchinetta, della quale <lb></lb>s&#039;attribuisce altresì l&#039;invenzione: “ Arcanum inventionis consistit in pinna <lb></lb>quadam spirali, quae altera sui extremitate interiore affixa est hastae ani­<lb></lb>mulae seu rastri aequilibris (<emph type="italics"></emph>bilanciere<emph.end type="italics"></emph.end>) sed maioris ac ponderosioris quam <lb></lb>pro solito, ac supra suos cardines ultro citroque mobilis: altera vero extre­<lb></lb>mitate cohaeret particulae cuidam supra Horologii superius tegmen eminenti: <lb></lb>quaeque vibrato semel Horologii libramento spiras suas alternis comprimit <lb></lb>ac relaxat, ac accedente sibi parvulo adiumento ab Horologii rotis veniente, <lb></lb>rastri seu aequilibri motum conservat, ita quidem, ut licet maiores aut mi­<lb></lb>nores faciat excursus, eius reciprocationes tamen una alteri sint tempore <lb></lb>prorsus aequales ” (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>1724, pag. </s>

<s>254). </s></p><p type="main">

<s>Gl&#039;Inglesi però contendono all&#039;Olandese una sì bella e utile invenzione, <lb></lb>ma perchè non appartiene a noi il decider la controversia, basti il ricor­<lb></lb>dare come Lorenzo Magalotti, il dì primo di Marzo del 1668 si trovò pre­<lb></lb>sente all&#039;adunanza della Società Reale di Londra, invitatovi dall&#039;Oldembourg <lb></lb>segretario di essa. </s>

<s>Ivi, fra le altre cose, dice di aver veduto “ una mostra <lb></lb>da portare in tasca con una nuova invenzione di pendolo, ch&#039;io chiamerei <lb></lb>piuttosto una mostra con la falsaredine, essendo regolato il tempo da una <lb></lb>piccola minugia temperata a uso di molla, la quale da una delle sue estre­<lb></lb>mità è attaccata al tempo, e dall&#039;altra è raccomandata al tamburo dell&#039;oriolo. </s>

<s><lb></lb>Quellà dunque opera sì, che le corse e le ricorse del tempo son sempre <lb></lb>uguali, e se qualche irregolarità della ruota dentata lo trasportasse di van­<lb></lb>taggio, la minugia lo tiene in briglia, obbligandolo a far sempre la stessa <lb></lb>gita ” (Fabbroni, Lett. </s>

<s>I, 300). </s></p><p type="main">

<s>In questi Orologi fu notata anche un&#039;altra curiosità, ed era che, men­<lb></lb>tre a tenerli attaccati si movevano regolarmente, portandoli in tasca il loro <lb></lb>moto si alterava, e si dovettero accorger di più niente altro esser cagione <lb></lb>di ciò, se non che il calore proprio della persona. </s>

<s>Non essendosi però an­<lb></lb>cora indovinati i veri effetti che produceva il calore, andavasi dicendo che <lb></lb>egli alterava la tempera della molla, la quale, divenuta più dolce, lasciava <lb></lb>correre il tempo con più libertà. </s>

<s>Ecco le parole proprie del Magalotti: “ Di-<pb xlink:href="020/01/357.jpg" pagenum="338"></pb>cono che a tenerlo attaccato l&#039;invenzione operi bene il suo effetto, e che <lb></lb>corregga gli errori delle ruote, non meno del pendolo, ma che a portarlo <lb></lb>in tasca, a misura del calore ch&#039;ei sente, s&#039;alteri la tempera della molla, e <lb></lb>divenendo più dolce lasci correre il tempo con maggior libertà ” (ivi). </s></p><p type="main">

<s>Verso la fine di quel secolo, all&#039;ultimo, s&#039;intese che il calore operava <lb></lb>in alterare il moto degli Orologi, così da tasca com&#039;a pendolo, co&#039;suoi na­<lb></lb>turali e consueti effetti di dilatazione, e l&#039;Harrison e altri, applicando varii <lb></lb>e ingegnosi <emph type="italics"></emph>compensatori<emph.end type="italics"></emph.end> riuscirono a costruir finalmente que&#039;perfetti oro­<lb></lb>logi astronomici e nautici, intorno a&#039;quali s&#039;erano affaticati invano fra noi <lb></lb>Giuseppe e Matteo Campani. </s></p>
<pb xlink:href="020/01/358.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dell&#039;invenzione e della teoria del Canocchiale<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del primo inventore del Canocchiale. </s>

<s>— II. </s>

<s>Di ciò che, intorno all&#039;invenzione dello strumento, Ga­<lb></lb>lileo dicesse di sè, e di quel che di lui si diceva dagli altri. </s>

<s>— III. </s>

<s>Del primo concetto, e di ciò che <lb></lb>possa aver dato occasione al ritrovamento del Canocchiale. </s>

<s>— IV. </s>

<s>Delle prime speculazioni diot­<lb></lb>triche intorno alla teoria del Canocchiale. </s>

<s>— V. </s>

<s>Di altre vie tentate per risolvere il problema <lb></lb>diottrico del Canocchiale, e come fosse finalmente risoluto dall&#039;Huyghens; breve conclusione <lb></lb>delle cose fin qui discorse. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Notabile è quel che Galileo racconta, nella Giornata seconda dei Due <lb></lb>Massimi Sistemi, di quel dottore leggente in uno studio famoso, il quale <lb></lb>avendo sentito descrivere il Telescopio, da lui ancora non veduto, disse che <lb></lb>l&#039;invenzione era tolta da Aristotile. </s>

<s>Perciò “ fattosi portare un testo, trovò <lb></lb>certo luogo, dove si rende la ragione, onde avvenga che dal fondo d&#039;un <lb></lb>pozzo molto cupo si possano di giorno veder le stelle in cielo, e disse ai <lb></lb>circostanti: Eccovi il pozzo che dinota il cannone, eccovi i vapori grossi, <lb></lb>dai quali è tolta l&#039;invenzione dei cristalli, ed eccovi finalmente fortificata <lb></lb>la vista col passare i raggi per il diafano più denso ed oscuro ” (Alb. </s>

<s>I, <lb></lb>pag. </s>

<s>122, 23). </s></p><p type="main">

<s>La similitudine, per chi non giudica con quella leggerezza che sogliono <lb></lb>alcuni, non è poi tanto strana quanto parrebbe, potendosi dir che il pozzo <lb></lb>fa l&#039;ufficio del tubo, il quale senza dubbio rischiara, e perciò rischiarandoli <lb></lb>mostra in certo modo ingranditi gli oggetti. </s>

<s>Il fatto può esser con facile <lb></lb>esperienza osservato da tutti, imperocchè non occorre far altro che prendere <lb></lb>una strisciola di carta, avvolgerla intorno, in modo che se ne venga a com-<pb xlink:href="020/01/359.jpg" pagenum="340"></pb>porre un cannello di piccola luce, e con un occhio guardarci dentro e at­<lb></lb>traverso un oggetto. </s>

<s>Non fa perciò maraviglia se, conosciutosi dagli antichi <lb></lb>un tal fatto, si servissero o di un cannellino per osservare i piccoli oggetti, <lb></lb>come noi ci serviamo del Microscopio, o facessero uso di un tubo più lungo <lb></lb>per le osservazioni celesti, come noi ci serviam de&#039;Canocchiali. </s>

<s>Di questo <lb></lb>tubo e de&#039;macchinamenti annessi, per osservare e per misurare esatto il <lb></lb>diametro apparente del sole sull&#039;orizzonte, si trova fatta una descrizione mi­<lb></lb>nuta da Archimede nell&#039;Arenario (Opera, Parisiis 1615, pag. </s>

<s>452, 53) e di <lb></lb>uno di questi stessi tubi, per le osservazioni celesti, sembra che si servisse, <lb></lb>o fu creduto almeno che si scrvisse lo stesso tolomeo, se dee darsi fede al <lb></lb>Mabillon, il quale dice di aver veduto nella biblioteca dell&#039;abbadia di Scheir, <lb></lb>diocesi di Frisinga, una copia della Storia ecclesiastica di Pietro Comestore, <lb></lb>nel frontespizio della quale, essendovisi voluto personificare le arti liberali, <lb></lb>vi si vedeva, per l&#039;Astronomia, rappresentato Tolomeo che osservava gli astri <lb></lb>coll&#039;occhio appuntato all&#039;estremità di un lungo tubo, presso a poco a quel <lb></lb>modo, che si rappresenterebbe Galileo da un pittore moderno, in atto di ri­<lb></lb>guardare attraverso all&#039;oculare del suo Telescopio. </s></p><p type="main">

<s>Di qui ha avuto, senza dubbio, occasione l&#039;errore di alcuni, un po&#039;si­<lb></lb>mile a quel del Dottore argutamente deriso dal Salviati, i quali, trattando <lb></lb>della storia delle invenzioni hanno creduto, e voluto far credere che questi <lb></lb>tubi o quelle <emph type="italics"></emph>diottre,<emph.end type="italics"></emph.end> come le chiamavan Plutarco e Strabone, non fossero <lb></lb>propriamente altro che Canocchiali, non molto dissimili dai moderni. </s>

<s>Una <lb></lb>tale erronea opinione, è notabile che fosse accolta anche da Francesco Fon­<lb></lb>tana, celebre fabbricatore di Canocchiali, il quale scrisse: “ Antiquissimum <lb></lb>fuisse tubi optici usum in comperto est ” imperocchè, soggiunge, rimonta <lb></lb>infino a&#039;tempi di Tolomeo che visse 130 anni prima di G. Cristo. (Novae <lb></lb>Observat. </s>

<s>Neap. </s>

<s>1646, pag. </s>

<s>11). Ma che quelli di Archimede, di Tolomeo o <lb></lb>di altri antichi non fossero veramente canocchiali, ossia tubi muniti di lenti <lb></lb>cristalline o di specchi metallici, se ne persuaderà facilmente ciascuno che <lb></lb>pensi come quegli antichi cannoni aperti non prestavano altro ufficio, a quei <lb></lb>primi osservatori del cielo, da quello in fuori di riparar l&#039;occhio dalle ri­<lb></lb>flessioni irregolari, e di diriger la linea di mira, come nell&#039;Alidada, che <lb></lb>s&#039;incominciò ad usare agli strumenti geodetici, da&#039;Geometri arabi e dagli <lb></lb>egiziani. </s></p><p type="main">

<s>Non è in tal proposito da passar sotto silenzio un modo proposto da <lb></lb>Leonardo da Vinci, per veder le cose più da lontano; modo che consiste <lb></lb>giusto in far uso di uno di que&#039;tubi nudi o di quelle Diottre, di cui si ser­<lb></lb>virono gli antichi. </s>

<s>Il Venturi respigolò l&#039;invenzione da uno de&#039;celebri Ma­<lb></lb>noscritti, e fu così la nota vinciana da lui stesso tradotta e pubblicata in <lb></lb>francese: “ Il est possible de faire en sorte que l&#039;oeil voie les obiets eloi­<lb></lb>gnes sans qu&#039;ls souffrent toute la diminution de grandeur qui leur est cau­<lb></lb>sée par les loix de la vision. </s>

<s>Cette diminution provient des pyramides de <lb></lb>l&#039;image des obiets qui sont coupées a angle droit par le sphericité de l&#039;oeil. </s>

<s><lb></lb>Dans le fig. (25) on voit qui en pout couper ces pyramides d&#039;une autre ma-<pb xlink:href="020/01/360.jpg" pagenum="341"></pb>niere au-devante le prunelle. </s>

<s>Il est bien vrai que le prunelle nous décou­<lb></lb>vré tout l&#039;hemisphère à la fois: l&#039;artefice que j indique ne decouvrirà qu&#039;un <lb></lb>astre. </s>

<s>Mais cet astre serà grand: la Lune aussi deviendrà plus grande, et <lb></lb><figure id="id.020.01.360.1.jpg" xlink:href="020/01/360/1.jpg"></figure></s></p><p type="caption">

<s>Figura 25.<lb></lb>nous connoîtrons mieux la figure de sas <lb></lb>taches ” (Essai, etc., Paris 1797, pag. </s>

<s>23). </s></p><p type="main">

<s>Il Venturi vorrebbe far credere che qui <lb></lb>Leonardo avesse descritto un canocchiale, <lb></lb>ma pure è chiaro che il modo d&#039;avvalorar <lb></lb>la vista in tale vinciana invenzione è fondato <lb></lb>sopra un effetto ottico molto differente da <lb></lb>quelli soliti d&#039;operarsi o dalle lenti cristalline o dagli specchi. </s>

<s>L&#039;effetto ottico <lb></lb>ivi speculato, e l&#039;applicazione di lui a veder, secondo Leonardo, gli oggetti più <lb></lb>di lontano, son cose meritevolissime della nostra attenzione, riconoscendo­<lb></lb>visi l&#039;Autore studioso di adattare un tubo a portar lontano la luce, o, se­<lb></lb>condo lui, le specie visibili, a quel modo che si adatta così efficacemente a <lb></lb>portar più lontano i suoni. </s>

<s>Mirabile è questo inaspettato riscontro intrave­<lb></lb>duto tra il <emph type="italics"></emph>Portaluce<emph.end type="italics"></emph.end> e il <emph type="italics"></emph>Portavoce,<emph.end type="italics"></emph.end> ma è ben più mirabile che a quello <lb></lb>stesso riscontro vi fosse condotto Leonardo, non a caso, ma per via di re­<lb></lb>condita scienza della natura della luce e de&#039;suoni, e delle proprietà de&#039;raggi <lb></lb>sonori; scienza ignorata in gran parte, come si dimostrerà nel progresso <lb></lb>della nostra Storia, dagli stessi Fisici del secolo XVII. </s>

<s>Per Leonardo tanto <lb></lb>la luce che i suoni si diffondono in sfere o in raggi divergenti, ed è que­<lb></lb>sta la ragione per cui va languendo, per via delle distanze, la vivacità <lb></lb>delle immagini e la intensità delle voci. </s>

<s>Dentro i tubi i raggi lucidi e i so­<lb></lb>nori, impediti di divergere, si mantengono paralleli e portan perciò più lon­<lb></lb>tano le specie visibili e i tremori armonici. </s>

<s>Si comprende bene che la spe­<lb></lb>culazione del nuovo strumento ottico proposto nel Manoscritto vinciano è <lb></lb>fondato sopra la falsa ipotesi platonica de&#039;raggi luminosi che si muovon dal­<lb></lb>l&#039;occhio di chi guarda, come i raggi sonori si muovon dalle labbra di chi <lb></lb>parla, ma se è vero che la luce si propaghi in onde come il suono, non vi <lb></lb>è dubbio che, per lo strumento e per la teoria di Leonardo, i tubi chiusi <lb></lb>debbono operar sulla vista qualche altro più sottile e più recondito effetto, <lb></lb>oltre i consueti assegnati dagli Ottici, che son quelli di riparar l&#039;occhio dalla <lb></lb>soverchia luce diffusa, e dalle riflessioni irregolari. </s></p><p type="main">

<s>In ogni modo riman pur ancora lontana dal vero la sentenza del Ven­<lb></lb>turi, che nel <emph type="italics"></emph>Portaluce<emph.end type="italics"></emph.end> di Leonardo da Vinci vorrebbe veder descritto uno <lb></lb>de&#039;canocchiali moderni, essendo tutti gli scrittori concordi in affermare che <lb></lb>l&#039;invenzione di così utile strumento non occorse prima che al cominciar del <lb></lb>secolo XVII Cercar chi ne fosse primo Autore e come vi riuscisse, è im­<lb></lb>presa vana, perchè segue delle invenzioni quel che segue dell&#039;erbe, le quali <lb></lb>avendo i germi piccoli e sotto terra, non se ne conoscon le virtù nè se ne <lb></lb>sanno i nomi, se non dappoichè sono uscite fuori e hanno aperte le foglie <lb></lb>all&#039;aria. </s>

<s>Pure, non son mancati alcuni, i quali hanno preteso di saper la <lb></lb>prima origine e il nome dell&#039;inventore del Canocchiale e ne hanno compo-<pb xlink:href="020/01/361.jpg" pagenum="342"></pb>ste storie, che vanno attorno, ne&#039;loro libri, stampate, il contenuto delle quali <lb></lb>non è permesso al nostro ufficio di lasciar senza rammemorarlo ai nostri <lb></lb>Lettori. </s></p><p type="main">

<s>Ci si appresenta per primo Girolamo Sirturo, il quale scrivendo, in sog­<lb></lb>getto proprio del Telescopio, un Trattato, incomincia dal far la storia del­<lb></lb>l&#039;invenzione, che noi porgiamo così tradotta dal latino. </s></p><p type="main">

<s>“ Comparve nel 1609 un genio o che altro si fosse, di nazione olandese, <lb></lb>il quale capitò in Middelburgo, città della Zelanda, alla bottega di Giovanni <lb></lb>Lipperseim, unico artefice di occhiali che si ritrovasse allora in quella città. </s>

<s><lb></lb>Quell&#039;olandese ordinò all&#039;occhialaio alcuni vetri, così concavi come convessi, <lb></lb>e il dì stabilito tornò per veder se il lavoro era fatto. </s>

<s>L&#039;occhialaio allora <lb></lb>presentò i vetri bell&#039;e fatti a quell&#039;uomo, che si mise a specularli attraverso <lb></lb>alla mira dell&#039;occhio, ora avvicinandoli ora dilungandoli, o ciò egli facesse <lb></lb>per far prova della bontà del lavoro, o per trovare il giusto punto del con­<lb></lb>corso. </s>

<s>Così fatto, pagò l&#039;artefice e se ne andò. </s>

<s>Ma quell&#039;artefice stesso, che <lb></lb>era d&#039;ingegno acuto e molto curioso di novità, incominciò a imitare il giuoco <lb></lb>veduto fare a quell&#039;uomo, e così gli occorse, nello speculare attraverso a <lb></lb>que&#039;vetri concavi e convessi, di vedere gli oggetti ingranditi, per cui pensò <lb></lb>di sostenerli congiunti insieme per mezzo di un tubo. </s>

<s>Così vennegli fatto il <lb></lb>primo Telescopio che volò subito a mostrarlo al principe Maurizio. </s>

<s>Il Prin­<lb></lb>cipe, o l&#039;avesse veduto prima o no, pensò subito di servirsene agli usi della <lb></lb>milizia, per cui voleva tenere la cosa occulta, ma divulgatasi comunque si <lb></lb>fosse, si presero a fare di simili altri strumenti, benchè, come questo pre­<lb></lb>sentato al principe Maurizio, non fossero riusciti così perfetti. </s>

<s>Dicevasi che <lb></lb>in antico non fosse questa invenzione conosciuta da nessuno, e che comin­<lb></lb>ciasse allora, ma pure il Porta ne aveva fatto un cenno nel suo libro della <lb></lb><emph type="italics"></emph>Magia,<emph.end type="italics"></emph.end> ed era opinione di molti, che ne discorrevano alla mia presenza, non <lb></lb>esser molto difficile a chi avesse qualche po&#039;d&#039;ingegno, udito il fatto, imi­<lb></lb>tarlo. </s>

<s>Concorsero molti attratti dalla cupidità del guadagno, così Belgi che <lb></lb>Francesi e Italiani, e tutti se ne spacciavano inventori. </s>

<s>Nel mese di Maggio <lb></lb>capitò in Milano un Francese che presentò uno di così fatti Telescopi al <lb></lb>conte De Fuentes, dicendo esser socio d&#039;industria di un Olandese, che della <lb></lb>costruzione dello strumento era stato primo autore. </s>

<s>Avendolo il Conte dato <lb></lb>a un orefice perchè legasse quelle lenti in un tubo di argento, venne così <lb></lb>per caso a capitare alle mie mani: lo smontai, lo esaminai e mi detti a <lb></lb>fabbricarne di simili ” (Telescop. </s>

<s>P. I, Cap. </s>

<s>I, Francof. </s>

<s>1618, pag. </s>

<s>23, 24). </s></p><p type="main">

<s>Si vede che al Tarde non era ancora capitato in mano questo libro del <lb></lb>nostro Milanese quando nella <emph type="italics"></emph>Borbonia Sidera,<emph.end type="italics"></emph.end> libro stampato in Parigi <lb></lb>nel 1620, scriveva: “ Miror ego neminem adhuc quem viderim, huius tubi <lb></lb>Dioptrici inventoris nomen in publicum edidisse, nec modum quo in inve­<lb></lb>niendo usus est docuisse. </s>

<s>Meretur enim nobilitate decorari et laudibus or­<lb></lb>nari, qui sensum omnium nobilissimum docuit ita iuvari ” (ibi, pag. </s>

<s>85). </s></p><p type="main">

<s>A sodisfar poi meglio ai generosi desiderii del Tarde soccorse il Rheita, <lb></lb>il quale narra come Giovanni Lippens, occhialaio di Zelanda, s&#039;abbattesse <pb xlink:href="020/01/362.jpg" pagenum="343"></pb>per caso a trovar che due lenti, una concava e una convessa, congiunte in­<lb></lb>sieme ingrandivano gli oggetti traguardati. </s>

<s>Di qui fu condotto all&#039;invenzione <lb></lb>del primo Telescopio, il quale, essendo stato comprato dal marchese Spi­<lb></lb>nola, che allora soggiornava all&#039;Aja, fu da lui stesso poi regalato all&#039;arci­<lb></lb>duca Alberto di Brabante. (Oculus. </s>

<s>Enoch et Eliae, lib. </s>

<s>IV, Antuerpiae 1645). </s></p><p type="main">

<s>Ma a ricercare il nome di sì benemerito inventore si dette più di pro­<lb></lb>posito Pietro Borel, il quale ne scrisse un libro stampato all&#039;Aja nel 1655. <lb></lb>Egli dunque, nel capitolo XII di quello stesso libro che s&#039;intitola <emph type="italics"></emph>De vero <lb></lb>Telescopii inventore,<emph.end type="italics"></emph.end> dopo varii esami, per verità non di grande importanza, <lb></lb>conclude che il primo inventore del Telescopio fu Zaccaria Jansen di Middel­<lb></lb>burgo, il quale fece nel 1590 l&#039;esperienza de&#039;vetri concavi e de&#039;convessi, <lb></lb>non a caso, come dicono molti, ma ad arte, e applicò quella stessa espe­<lb></lb>rienza alle osservazioni del cielo, scoprendo altre nuove stelle nell&#039;Orsa mag­<lb></lb>giore. </s>

<s>Lo strumento così felicemente inventato fu dall&#039;inventore medesimo <lb></lb>offerto in dono al principe Maurizio, e un altro simile fu donato pure al­<lb></lb>l&#039;arciduca Alberto. </s>

<s>Il secondo inventore, pur esso middelburgese, soggiunge <lb></lb>ivi il Borel, essere stato Hans, ossia Giovanni Lipperehy, a cui, capitata a <lb></lb>caso quella prima invenzione di Zaccaria, si dee l&#039;averla condotta a mag­<lb></lb>gior perfezione. </s></p><p type="main">

<s>Abbiamo udito il Borel francamente affermare che la maravigliosa in­<lb></lb>venzione non fu fatta a caso, ma ad arte, ciò che verrebbe a confermare <lb></lb>storicamente l&#039;opinione del Tarde, il quale, dopo aver riprovata la sentenza <lb></lb>di coloro che fanno intervenir la fortuna come se da lei sola avesse rice­<lb></lb>vuto il mondo il benefizio del Canocchiale; così tosto soggiunge: “ Ego vero <lb></lb>qui nobiliori quodam modo hoc accidisse existimo, cum accuratius rem con­<lb></lb>sidero et diligentiori studio meditor, a viro optices peritissimo, non casu <lb></lb>sed arte, et exacta quadam ac diligenti investigatione inventum iudico. </s>

<s>Hic <lb></lb>enim cum novisset lentem convexam nimis augere visibilia, si remota sint, <lb></lb>et cavam nimis imminuere, ob contrarias radiorum fractiones, in mentem <lb></lb>revocavit Fhilosophiae decretum quo asseritur contrarìa contrariis pelli vel <lb></lb>saltem emendari; excogitavit periculum facere num quaedam lentium com­<lb></lb>positio, aut radiorum utraque lente refractorum proportio invenire posset, <lb></lb>qua diversae hae refractiones, variaeque radiorum flectiones sese invicem <lb></lb>emendarent ” (Loc. </s>

<s>cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Ma pure, anco di quest&#039;altro desiderio il Tarde era stato di già sodi­<lb></lb>sfatto, da chi facendo intervenir nel fatto di questa invenzione la scienza <lb></lb>piuttosto che il caso, aveva di quella stessa scienza additati i principii diot­<lb></lb>trici, e gli Autori che furon primi a insegnarli. </s>

<s>Giulio Cesare La Galla, pe­<lb></lb>ripatetico, ma più dotto degli altri suoi Colleghi, nella sua prima Disserta­<lb></lb>zione <emph type="italics"></emph>De phaenomenis in orbe Lunae,<emph.end type="italics"></emph.end> al cap. </s>

<s>V ha le seguenti parole che <lb></lb>noi liberamente così traduciamo dal latino: </s></p><p type="main">

<s>“ Fu di questa invenzione, per consenso di tutti, e per particolar te­<lb></lb>stimonianza di Giovanni Keplero, matematico chiarissimo, autore il napole­<lb></lb>tano Giovan Batista della Porta, gentiluomo dottissimo e solerte indagatore <pb xlink:href="020/01/363.jpg" pagenum="344"></pb>degli arcani della Natura, il quale nel XVII Libro della sua <emph type="italics"></emph>Magia Natu­<lb></lb>rale,<emph.end type="italics"></emph.end> capitolo X e XI, dette fuori da scienziato l&#039;invenzione di questo am­<lb></lb>mirabile strumento. </s>

<s>Dissi da scienziato, perchè settant&#039;anni prima Girolamo <lb></lb>Fracastoro ne aveva fatto qualche cenno confuso nel cap. </s>

<s>VIII de&#039;suoi Omo­<lb></lb>centrici, con queste parole: <emph type="italics"></emph>Qua de causa in eadem aqua, quae in summo <lb></lb>cernuntur minora apparent, quae in fundo maiora, et per duo specilla <lb></lb>ocularia, si quis perspiciat, altero alteri superposito, maiora multo et pro­<lb></lb>prinquiora vibebit omnia.<emph.end type="italics"></emph.end> Ma qui il Fracastoro non accenna distintamente <lb></lb>alla fabbrica dello strumento che ingrandisce e avvicina gli oggetti, nè pur <lb></lb>ne dice qual ne sia la ragione, ciò che fu fatto in bel modo dal Porta nel <lb></lb>descriver l&#039;uso delle lenti cristalline, le quali composte giudiziosamente in­<lb></lb>sieme e moltiplicate, possono trasportar, ciò che sembra impossibile, la virtù <lb></lb>visiva per spazio immenso e grandissimamente accrescer le specie delle cose. </s>

<s><lb></lb>Ma perchè egli non messe in pratica questa sua teoria, o se la messe, non <lb></lb>si curò di renderla pubblicamente nota, pochi auni or sono se ne vide fatta <lb></lb>l&#039;applicazione nel Belgio a uno strumento, per dir la verità assai rozzo e <lb></lb>imperfetto, a cui poi da Galileo, celebre matematico dello Studio di Padova, <lb></lb>fu data l&#039;ultima mano, e con esso, accomodato agli usi astronomici, fece <lb></lb>maravigliose scoperte nel cielo ” (Gal. </s>

<s>Op. </s>

<s>Alb. </s>

<s>T. III, pag. </s>

<s>253, 54). </s></p><p type="main">

<s>L&#039;Autorità del Kepler, invocata di sopra dal La Galla, a proposito di <lb></lb>ciò che tocca al Porta del merito dell&#039;invenzione, è di tal rilievo, che non <lb></lb>si può da noi trascurare, e perciò, dalla <emph type="italics"></emph>Dissertazione sul Nunzio Sidereo,<emph.end type="italics"></emph.end><lb></lb>trascriveremo tradotte dal latino le sue proprie parole. </s>

<s>Dop&#039;aver dunque <lb></lb>ivi il Kepler accennato alle grandi meraviglie mostrate dal canocchiale, così <lb></lb>prosegue: </s></p><p type="main">

<s>“ Sembra incredibile a molti l&#039;uso e l&#039;effetto di questo occhiale, ma <lb></lb>impossibile e nuovo non è, nè ci venne poco fa dal Belgio, ma fu tanti anni <lb></lb>prima messo fuori da Giovan Batista della Porta, nel XVII libro, cap. </s>

<s>X <lb></lb>della <emph type="italics"></emph>Magia Naturale,<emph.end type="italics"></emph.end> dove tratta degli effetti delle lenti cristalline. </s>

<s>E per­<lb></lb>chè apparisca chiaro non esser nuova nemmeno la composizione delle due <lb></lb>lenti, una delle quali concava e l&#039;altra convessa, permettimi, o Galileo, che <lb></lb>io ti rechi innanzi le parole stesse del Porta, le quali suonano a questo modo: <lb></lb><emph type="italics"></emph>Posto l&#039;occhio nel centro dietro la lente, vedrai gli oggetti lontani fartisi <lb></lb>così vicini, che ti sembrerà di toccarli, e così potrai riconoscere gli amici <lb></lb>lontani, e potrai correntemente leggere una lettera collocata a conveniente <lb></lb>distanza. </s>

<s>Se tu inclinerai la lente in modo che ti si debba il foglio rap­<lb></lb>presentare obliquo, vedrai farsi le lettere tanto maggiori, che tu potrai <lb></lb>leggerle anco alla distanza d&#039;una ventina di passi, e se tu avrai cura ed <lb></lb>arte di moltiplicar quelle lenti, non temo d&#039;affermar che tu potrai di­<lb></lb>stinguere le piccole lettere scritte anche a un cento di passi, ïmperocchè <lb></lb>i caratteri s&#039;ingrandiscono via via sempre più, passando attraverso dalla <lb></lb>prima alla seconda lente. </s>

<s>Chi ha difetto di occhi scelga secondo la qua­<lb></lb>lità della vista, e faccia variamente uso di questi occhiali: avrà scoperto <lb></lb>non piccolo segreto se giudiziosamente <gap></gap><emph.end type="italics"></emph.end><pb xlink:href="020/01/364.jpg" pagenum="345"></pb><emph type="italics"></emph>cave mostrano chiarissime le cose lontane, e le convesse chiarissime fanno <lb></lb>veder piuttosto le cose vicine, cosicchè ognuno potrà, secondo il bisogno <lb></lb>o la comodità della sua vista, servirsi ora delle une ora delle altre. </s>

<s>Con <lb></lb>una lente concava vedrai gli oggetti impiccoliti e lontani, ma distinti; <lb></lb>con una convessa invece più vicini e maggiori, ma un poco annebbiati. </s>

<s><lb></lb>Che se saprai, con discrezione, comporre insieme l&#039;una lente concava col­<lb></lb>l&#039;altra convessa, vedrai chiari e distinti tutti gli oggetti, così vicini come <lb></lb>lontani. </s>

<s>Io con tale arte ho potuto recar non poco giovamento agli amici, <lb></lb>che vedevano abbacinati gli oggetti lontani, e velati di nebbia i più vi­<lb></lb>cini, facendo in modo che discernessero poi sempre bene così questi come <lb></lb>quelli. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nel Cap. </s>

<s>XI tratta il Porta di quegli occhiali, con cui si posson ve­<lb></lb>dere le cose tanto lontane da vincere la stessa immaginativa, ma la dimo­<lb></lb>strazione, ad arte, come l&#039;Autore da sè stesso confessa, è sì involuta, che <lb></lb>non ti sai raccapezzar se egli intenda solo delle lenti di rifrangenza o delle <lb></lb>lenti combinate agli specchi. </s>

<s>Avendo io letto in questa parte del libro che <lb></lb>la ragione del vario operar delle lenti concave e delle convesse non era data <lb></lb>ancora da nessuno, mi ci volli provare, e sei anni or sono, nella parte Ot­<lb></lb>tica della mia Astronomia, divisai quel che accade nelle semplici lenti. </s>

<s>Tu <lb></lb>potresti vederlo ivi al capitolo V dove dimostro quelle cose che apparten­<lb></lb>gono al modo del vedere, e dove al foglio 202 è disegnata la figura di un <lb></lb>concavo e di un convesso, a quel modo che si soglion ne&#039;tubi congiungere <lb></lb>insieme quelle due lenti. </s>

<s>Che se non dette occasione all&#039;invenzione di que­<lb></lb>sto strumento la lettura del libro del Porta, e l&#039;istruzione che forse il Porta <lb></lb>stesso dette familiarmente conversando con qualche Belga, il quale, giovan­<lb></lb>dosi de&#039;silenzii del sepolcro, riuscì a spacciarlo per cosa sua; poteva senza <lb></lb>dubbio la figura impressa nel mio libro fare avvertito il lettore della strut­<lb></lb>tura e composizione dello strumento ” (Gal. </s>

<s>Op. </s>

<s>Alb. </s>

<s>V, 410-12). </s></p><p type="main">

<s>Ma come in sintesi raccolte e con fino criterio sceverate le varie sen­<lb></lb>tenze storiche da&#039;varii scrittori sopra esposte, si possono veder nell&#039;Huy­<lb></lb>ghens, là dove, nella <emph type="italics"></emph>Diottrica,<emph.end type="italics"></emph.end> si dispone a trattar de&#039;Telescopii. </s>

<s>“ Sunt <lb></lb>qui inventionis, egli scrive, sed ut dixi, fortuitae, primae laudem Jacobo <lb></lb>Metio Batavo Alcmariae civi tribuant. </s>

<s>Mihi vero certo compertum est ante <lb></lb>ipsum Telescopia fabricasse Artificem quendam Medioburgensem, apud Se­<lb></lb>landos, circa annum huius saeculi nonum, sive is fuerit cuius Sirturus <lb></lb>meminit Joh. </s>

<s>Lippersheim nomine, sive cui Borellus in libello <emph type="italics"></emph>De vero Te­<lb></lb>lescopii inventore,<emph.end type="italics"></emph.end> primas defert, Zacharias. </s>

<s>Hi tunc non maiores sesquipe­<lb></lb>dalibus tubos factitabant. </s>

<s>Utroque vero multo prior rudimenta artis tradi­<lb></lb>derat Joh. </s>

<s>Bapt. </s>

<s>Porta Neapolitanus, cuius extant de rebus Dioptricis et <lb></lb>Magia Naturali libri, totis 15 annis ante editi quam in Belgio nostro exo­<lb></lb>rirentur. </s>

<s>In quibus libris de Specillis, ut vocat, suis, memorat res procul <lb></lb>positas quasi proprinquae essent ostendentibus, deque coniunctione cavarum <lb></lb>et convexarum lentium. </s>

<s>Nihil tamen magnopere eum profecisse, hoc ipsum <lb></lb>probat quod tanto tempore ars iam coepta non ultra inclaruit, neque ipse <pb xlink:href="020/01/365.jpg" pagenum="346"></pb>Porta quidquam in coelo observavit eorum quae postea apparuerunt. </s>

<s>Hoc <lb></lb>inde est quod casui fortuitisque experimentis originem inventi debere constat. </s>

<s><lb></lb>Neque enim hic vir licet Mathematicarum aliquatenus gnarus reconditas ra­<lb></lb>tiones, quibus ars ea pro fundamentis utitur, comprehenderat ut medita­<lb></lb>tione eam eruere posset, multoque minus illi, quos ante memoravi, homi­<lb></lb>nes opifices ac scientiarum rudes. </s>

<s>Fortuna vero et casu eodem perventum <lb></lb>nihil mirum est, cum frequens usus esset, iam a trecentis atque amplius <lb></lb>annis utriusque generis lentium, quibus seorsim adhibitis vitia oculorum <lb></lb>emendantur. </s>

<s>Ut potius mirandum sit tamdiu rem obviam latuisse. </s>

<s>Ceterum <lb></lb>ut primum Teloscopiorum Belgicorum fama sparsa erat continuo Galileus <lb></lb>similia illis, ac brevi multo praestantiora effecit, quibus celeberrima illa coeli <lb></lb>phaenomena omnium primus intuitus est ” (Lugduni Batav. </s>

<s>1703, pag. </s>

<s>163, 64). </s></p><p type="main">

<s>Le autorità del Keplero e dell&#039;Huyghens concordi in ammetter probabi­<lb></lb>lissimo che l&#039;invenzione del Telescopio fosse stata inspirata a qualche ottico <lb></lb>dalla lettura della <emph type="italics"></emph>Magia Naturale,<emph.end type="italics"></emph.end> son di gran momento in dover aggiu­<lb></lb>dicare al Porta i primi meriti contesigli con più ardore da&#039;seguaci di Gali­<lb></lb>leo che dagli stessi stranieri. </s>

<s>È perciò che su que&#039;due soggetti particolar­<lb></lb>mente, su Galileo cioè e sul Porta, viene ora a indirizzarsi il filo del nostro <lb></lb>discorso. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>A chi conosce oramai l&#039;indole e quel passionato ardore che trasportava <lb></lb>Galileo a voler essere ed apparire il solo e il primo in tutte quante le cose, <lb></lb>non farà maraviglia che egli si studiasse, con le arguzie dell&#039;ingegno e col <lb></lb>fascino dell&#039;eloquenza, d&#039;ingerir nella comune opinione giudizi tutto affatto <lb></lb>diversi da quelli del Kepler, dell&#039;Huyghens e degli altri sopra citati, che le <lb></lb>prime parti nell&#039;invenzione del canocchiale attribuiscono al Porta. </s>

<s>Di quelle <lb></lb>arguzie incominciò a fare studio il Conquistatore ambizioso infino dal primo <lb></lb>apparire del Nunzio Sidereo, in cui, confessando di avere avuto una vaga <lb></lb>notizia dell&#039;invenzione, afferma che dietro quella ritrovò, nella sua propria <lb></lb>scienza delle rifrazioni, <emph type="italics"></emph>doctrinae de refractionibus innixus,<emph.end type="italics"></emph.end> la fabbrica dello <lb></lb>strumento. </s>

<s>Il Keplero però gli opponeva che quella dottrina delle rifrazioni, <lb></lb>la quale sarebbe sola potuta bastar così a lui come all&#039;occhialaio belga, per <lb></lb>riuscire alla composizione delle due lenti da veder le cose lontane; era stata <lb></lb>scritta prima e poteva averla ognuno pubblicamente letta nella Magia Na­<lb></lb>turale e nei Paralipomeni a Vitellione. </s></p><p type="main">

<s>Galileo non si sarebbe aspettato che le franche parole del Matematico <lb></lb>alemanno fossero venute così presto a rintuzzare le sue pretese, ma non si <lb></lb>scorò per questo, nè lasciava occasione di confermar nella stima degli amici <lb></lb>a cui scriveva, o de&#039;signori con cui trattava, che il Canocchiale inventato <lb></lb>era parto della scienza diottrica della sua mente. </s>

<s>Alla Signoria di Venezia <pb xlink:href="020/01/366.jpg" pagenum="347"></pb>scriveva dello stesso Canocchiale di averlo <emph type="italics"></emph>cavato dalle più recondite spe­<lb></lb>culazioni di Prospettiva<emph.end type="italics"></emph.end> (Venturi, Memor., Modena 1818, P. I, pag. </s>

<s>81) e <lb></lb>si difendeva appresso mons. </s>

<s>Piero Dini, contro l&#039;imputazion di coloro che <lb></lb>dicevano il Canocchiale non mostrar altro che ingannevoli apparenze, affer­<lb></lb>mando che della verità mostrata dallo strumento nessun altro poteva esser <lb></lb>miglior giudice di lui, che era intendente dell&#039;arte, da cui il modo di ope­<lb></lb>rar dello strumento stesso dipende, <emph type="italics"></emph>sapendosi che la fabbrica e la teorica <lb></lb>di questo occhiale dipende dalla cognizione delle rifrazioni, che è parte <lb></lb>delle scienze matematiche mia particolar professione<emph.end type="italics"></emph.end> (Alb. </s>

<s>VI, 164). Nè <lb></lb>in altri termini diversi da quelli con cui s&#039;era espresso nel Nunzio Sidereo, <lb></lb>prima che venisse il Kepler ad amareggiargli le compiacenze dell&#039;animo, con <lb></lb>lo squadernargli sotto gli occhi il XVII libro della Magia, e il cap. </s>

<s>V della <lb></lb>sua Ottica astronomica; scriveva Galileo il dì 29 Agosto 1609 a Benedetto <lb></lb>Landucci: “ Dovete dunque sapere che sono circa a due mesi che qua fu <lb></lb>sparsa fama, che in Fiandra era stato presentato al conte Maurizio un <lb></lb>Occhiale fabbricato con tale artifizio che le cose molto lontane le faceva ve­<lb></lb>der come vicinissime, sicchè un uomo per la distanza di due miglia si po­<lb></lb>teva distintamente vedere. </s>

<s>Questo mi parve effetto tanto maraviglioso che <lb></lb>mi dette occasione di pensarvi sopra, e parendomi che dovesse avere fon­<lb></lb>damento nella Scienza di Prospettiva, mi messi a pensare sopra la sua fab­<lb></lb>brica, la quale finalmente ritrovai così perfettamente, che uno che ne ho <lb></lb>fabbricato supera di assai la fama di quello di Fiandra ” (Alb. </s>

<s>VI, 75, 76). </s></p><p type="main">

<s>Così, mentre da una parte provvedeva Galileo, con sollecita accortezza, <lb></lb>a ingerir nell&#039;animo degli amici la stima di sè, studiavasi dall&#039;altra di av­<lb></lb>vilire il suo rivale. </s>

<s>Gli trasparisce viva sul volto la compiacenza in leggere <lb></lb>queste parole che Martino Hasdale scrivevagli da quella stessa città di Praga, <lb></lb>d&#039;onde, a ferirlo, il Kepler gli avea scoccato le saette acute: “ Però l&#039;altra <lb></lb>sera cenando io seco (col Wacker amico del Keplero) insiem con altri, avemmo <lb></lb>contesa sopra chi fosse stato il primo inventore di questo strumento, vo­<lb></lb>lendo egli sostenere che Giovanni della Porta avesse detto strumento, con <lb></lb>il quale Porta dice di avere egli parlato quattro volte e che l&#039;aveva trovato <lb></lb>uomo singolarissimo, nonostante che io dicessi tutto il contrario, sforzandomi <lb></lb>di convincerlo con infinite tare che so contro il Porta, il quale non inten­<lb></lb>deva molti capitoli della sua Magia, nè manco la sapeva spiegare in volgare, <lb></lb>scusandosi che erano tutte cose avute da altri, così scritte in latino come <lb></lb>stavano stampate nel suo libro ” (Alb. </s>

<s>VIII, 83, 84). </s></p><p type="main">

<s>Queste contese fra il Wacker e l&#039;Hasdale erano fra amici e muovevano <lb></lb>in questo, dall&#039;ammirazione che sentiva per Galileo, in quello, da più retto <lb></lb>e imparziale giudizio informato alla lettura del libro del Porta. </s>

<s>In ogni modo <lb></lb>però nè il Wacker nè il Kepler erano, in assegnar la giusta parte del me­<lb></lb>rito al Fisico napoletano, trasportati o da odio o da invidiosa rivalità o da <lb></lb>altra inimicizia, che avessero contro Galileo, il quale perciò sentiva l&#039;ama­<lb></lb>rezza de&#039;giudizi in qualche modo addolcita dalla sincerità de&#039;giudici e da <lb></lb>una certa benevolenza. </s></p><pb xlink:href="020/01/367.jpg" pagenum="348"></pb><p type="main">

<s>Ma non tutti erano a questo modo benevoli: le glorie e i trionfi della <lb></lb>scoperta che apparivano a tutti maravigliose, avevan suscitato già contro Ga­<lb></lb>lileo inimici invidiosi, i quali raccogliendo gli strali caduti di mano al Ke­<lb></lb>plero gli venivano avventando, con più insano furore, contro chi sapevano <lb></lb>di poter coglier nel vivo. </s>

<s>Uno de&#039;più ardenti fra questi saettatori fu quel <lb></lb>padre Orazio Grassi, che, mascherato sotto il nome di Lotario Sarsi, ebbe <lb></lb>questione intorno alla natura delle Comete, e ad altre cose accessorie, con <lb></lb>l&#039;Autor del <emph type="italics"></emph>Saggiatore.<emph.end type="italics"></emph.end> Il Sarsi dunque, a proposito del Canocchiale, diceva <lb></lb>che il nuovo strumento era <emph type="italics"></emph>allievo<emph.end type="italics"></emph.end> di Galileo e non <emph type="italics"></emph>figliolo.<emph.end type="italics"></emph.end> Galileo, dal­<lb></lb>l&#039;altra parte, che sentiva quelle parole uscir dalle labbra del gesuita asperse <lb></lb>di veleno, dette mano a più sottili arguzie e più gagliardo fiato alla sua elo­<lb></lb>quenza, per convincer di falso l&#039;asserto altrui, e per ammannir nuovi colori <lb></lb>da far pigliare aspetto di vero alle sue stesse finzioni. </s></p><p type="main">

<s>“ Qual parte io abbia, scriveva, nel ritrovamento di questo strumento, <lb></lb>e s&#039;io lo possa ragionevolmente nominar mio parto, l&#039;ho gran tempo fa ma­<lb></lb>nifestato nel mio Avviso Sidereo, scrivendo come in Venezia, dove allora mi <lb></lb>ritrovava, giunsero nuove come al sig. </s>

<s>conte Maurizio era stato presentato <lb></lb>da un Olandese un occhiale, col quale le cose lontane si vedevano così per­<lb></lb>fettamente come se fossero state molto vicine, nè più fu aggiunto. </s>

<s>Su que­<lb></lb>sta relazione io tornai a Padova, dove allora stanziava, e mi posi a pensar <lb></lb>sopra tal problema, e la prima notte dopo il mio ritorno lo ritrovai, ed il <lb></lb>giorno seguente fabbricai lo strumento ” (Alb. </s>

<s>IV, 26, 7). </s></p><p type="main">

<s>Una tal prontezza e facilità di esecuzione poteva ingerir qualche so­<lb></lb>spetto che la cosa fosse in sè ovvia, e che la facilità di risolvere il problema <lb></lb>consistesse nell&#039;avere avuto già prima notizia dell&#039;enunciato dello stesso pro­<lb></lb>blema, per cui Galileo, a superesaltare il merito della sua invenzione, è sol­<lb></lb>lecito di rimuover dagli animi quel sospetto, dimostrando che quella stessa <lb></lb>creduta facilità induce anzi, in eseguir l&#039;opera, una certa difficoltà maggiore. </s>

<s><lb></lb>Ripigliando perciò il costrutto lasciato più sopra interrotto, così soggiunge: </s></p><p type="main">

<s>“ Ma forse alcuno mi potrebbe dire che di non piccolo aiuto è al ri­<lb></lb>trovamento e risoluzion di alcun problema l&#039;esser prima in qualche modo <lb></lb>renduto consapevole della verità della conclusione, e sicuro di non cercar <lb></lb>l&#039;impossibile, e che perciò l&#039;avviso e la certezza che l&#039;Occhiale era di già <lb></lb>stato fatto, mi fosse d&#039;aiuto tale che per avventura senza quello non l&#039;avrei <lb></lb>ritrovato. </s>

<s>A questo io rispondo distinguendo e dico che l&#039;aiuto recatomi dal­<lb></lb>l&#039;avviso svegliò la volontà ad applicarvi il pensiero, che senza quello può <lb></lb>esser che io mai non v&#039;avessi pensato, ma che oltre a questo tale avviso <lb></lb>possa agevolar l&#039;invenzione io non lo credo, e dico di più che il ritrovar <lb></lb>la risoluzione d&#039;un problema pensato e nominato è opera di maggiore in­<lb></lb>gegno assai che il ritrovarne uno non pensato nè nominato, perchè in que­<lb></lb>sto può aver grandissima parte il caso, ma quello è tutto opera del di­<lb></lb>scorso ” (ivi, pag. </s>

<s>107, 8). </s></p><p type="main">

<s>E prosegue l&#039;Autore affermando che egli appunto, avutone il detto <lb></lb>avviso, ritrovò lo strumento per via di discorso. </s>

<s>Se non che là dove avea <pb xlink:href="020/01/368.jpg" pagenum="349"></pb>detto ai Signori di Venezia che quel discorso si fondava sopra le <emph type="italics"></emph>più recon­<lb></lb>dite speculazioni di Prospettiva<emph.end type="italics"></emph.end> qui confessa che quello stesso discorso in­<lb></lb>vece fu <emph type="italics"></emph>assai facile,<emph.end type="italics"></emph.end> e perchè facile torna a ripeterlo al Sarsi con le se­<lb></lb>guenti parole: </s></p><p type="main">

<s>“ Questo artifizio o consta d&#039;un vetro solo o di più di uno: d&#039;un <lb></lb>solo non può essere, perchè la sua figura o è convessa, cioè più grossa nel <lb></lb>mezzo che verso gli estremi, o è concava, cioè più sottile nel mezzo, o è <lb></lb>compresa tra superficie parallele. </s>

<s>Ma questa non altera punto gli oggetti vi­<lb></lb>sibili col crescergli e diminuirli: la concava gli diminuisce; la convessa gli <lb></lb>accresce bene, ma gli mostra assai indistinti ed abbagliati; adunque un ve­<lb></lb>tro solo non basta per produr l&#039;effetto. </s>

<s>Passando poi a due, e sapendo che <lb></lb>il vetro di superficie parallele non altera niente, come si è detto, conchiusi <lb></lb>che l&#039;effetto non poteva nè anco seguir dall&#039;accoppiamento di questo con <lb></lb>alcuno degli altri due, onde mi ristrinsi a volere esperimentare quello che <lb></lb>facesse la composizione degli altri due, cioè del convesso e del concavo, e <lb></lb>vidi come questa mi dava l&#039;intento, e tale fu il progresso del mio ritrova­<lb></lb>mento ” (ivi, pag. </s>

<s>208). </s></p><p type="main">

<s>Singolar cosa è davvero questo discorso, ma è più singolare che mai <lb></lb>il Filosofo da cui fu congegnato, il quale volendolo spacciar come specula­<lb></lb>zione sua propria coll&#039;intenzione di escludere ogni intervento del Porta, ri­<lb></lb>pete a parole il discorso fatto già 38 anni prima e letto da tutti nel cap. </s>

<s>X <lb></lb>del XVII libro della Magia. </s>

<s>Chi crederebbe mai che l&#039;ambizione avesse tanto <lb></lb>offuscato a Galileo l&#039;intelletto da non renderlo accorto che quel suo discorso <lb></lb>era una ripetizione esatta e una traduzion fedele delle parole stesse del suo <lb></lb>disprezzato rivale? <emph type="italics"></emph>Concavo longe parva vides, sed perspicua: convexo pro­<lb></lb>prinqua maiora, sed turbida; si utrunque recte componere noveris et lon­<lb></lb>ginqua et proxima maiora et clara videbis<emph.end type="italics"></emph.end> (Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>596). </s></p><p type="main">

<s>Non vi è perciò nessun lettore il quale non cominci intanto seriamente <lb></lb>a dubitare della sincerità dì quelle galileiane conclusioni. </s>

<s>Il dubbio si ve­<lb></lb>drà poi tornare in certezza, quando dimostreremo quale imperfetta scienza <lb></lb>avesse Galileo delle rifrazioni, per cui lo ebbe a dir meritamente il Carte­<lb></lb>sio <emph type="italics"></emph>parum in Opticis versatum.<emph.end type="italics"></emph.end> E anzi quella stessa certezza apparirà ne&#039;giu­<lb></lb>dizi più presto, quando in questo medesimo capitolo di storia tratteremo <lb></lb>della teoria del Telescopio. </s>

<s>Ma di poca sincerità e di poca fede è pure un <lb></lb>argomento certo l&#039;incoerenza che si nota ne&#039;particolari della narrazione fatta <lb></lb>da Galileo a varie occasioni. </s>

<s>Se il mendacio è sempre traditor di sè stesso, <lb></lb>si può dir che si tradisca anco l&#039;Autor del Saggiatore, rimandando a ciò <lb></lb>che, della prima invenzione del Canocchiale, n&#039;era stato scritto da lui stesso <lb></lb>nell&#039;Annunzio Sidereo. </s></p><p type="main">

<s>Qui aveva prima narrata la cosa a questo modo: “ Mensibus adhuc <lb></lb>decem fere, rumor ad aures nostras increpuit fuisse a quodam Belga Perspi­<lb></lb>cillum elaboratum cuius beneficio obiecta visibilia, licet ab oculo inspicien­<lb></lb>tis longe dissita, veluti proprinqua cernebantur.... Idem paucos post dies <lb></lb>mihi per literas a nobili Gallo Jacobo Badovere ex Lutetia confirmatum est, <pb xlink:href="020/01/369.jpg" pagenum="350"></pb>quod tandem in causa fuit ut ad rationes inquirendas, nec non media exco­<lb></lb>gitanda, per quae ad consimilis Organi inventionem devenirem, me totum <lb></lb>converterem, quam paulo post doctrinae de refractionibus innixus assequtus <lb></lb>sum ” (Alb. </s>

<s>III, 60). </s></p><p type="main">

<s>Quegli avverbi <emph type="italics"></emph>tandem<emph.end type="italics"></emph.end> e <emph type="italics"></emph>paulo post,<emph.end type="italics"></emph.end> che si leggon qui e quel <emph type="italics"></emph>final­<lb></lb>mente<emph.end type="italics"></emph.end> uscito dalla penna di chi scrisse la sopra citata Lettera a Benedetto <lb></lb>Landucci, attestano espressamente essere interceduta una certa oscitanza ed <lb></lb>esservi infra pposta qualche penosa difficoltà fra l&#039;annunzio avutone e l&#039;ese­<lb></lb>cuzione dell&#039;opera, mentre invece vuol far credere al Sarsi che venutogliene <lb></lb>il giorno in Venezia l&#039;avviso, la sera tornato a Padova, nella notte speculò <lb></lb>e il giorno dopo ebbe eseguito fra le mani lo strumento. </s></p><p type="main">

<s>A chi crede che Galìleo fosse un uomo come tutti gli altri e non un <lb></lb>taumaturgo, sembrerà impossibile una così facile e pronta esecuzione, ond&#039;è <lb></lb>che altrove, piuttosto che alla lettura del Saggiatore e del Nunzio Sidereo, <lb></lb>penserà di doversi rivolgere ognuno, il quale voglia di un punto così im­<lb></lb>portante di storia conoscere il vero. </s>

<s>Intorno a ciò appunto abbiamo docu­<lb></lb>menti in alcune lettere che scriveva Giovanni Bartoli, Residente toscano in <lb></lb>Venezia, al Segretario di stato Belisario Vinta. </s></p><p type="main">

<s>“ È capitato quà (son parole dello stesso Bartoli) un tale che vuol dare <lb></lb>in Signoria un segreto d&#039;un occhiale o cannone o altro istrumento, col quale <lb></lb>si vede lontano sino a 25 o 30 miglia tanto chiaro, che dicono che pare <lb></lb>presente, e molti l&#039;hanno visto e provato dal campanile di San Marco, <lb></lb>ma dicesi che in Francia ed altrove sia oramai volgare e che per pochi <lb></lb>soldi si compra, e molti dicono averne avuti e visti ” (MSS. Gal., P. III, <lb></lb>T. III, c. </s>

<s>6). </s></p><p type="main">

<s>E in altra sua così lo stesso Bartoli scrìve più al proposito nostro: “ Più <lb></lb>di tutti quasi ha dato da discorrere questa settimana il sig. </s>

<s>Galileo Galilei <lb></lb>matematico di Padova, con l&#039;invenzione dell&#039;occhiale o cannone da veder <lb></lb>da lontano. </s>

<s>E si racconta che quel tale forestiere che venne qua col segreto, <lb></lb>avendo inteso da non so chi (dicesi da fra Paolo Teologo servita) che non <lb></lb>farebbe qui frutto alcuno, pretendendo mille zecchini, se ne partì senza ten­<lb></lb>tare altro, sicchè essendo amici insieme fra Paolo et il Galilei, e datogli <lb></lb>conto del secreto veduto, dicono che esso Galilei con la mente e con l&#039;aiuto <lb></lb>di un altro simile strumento, ma non di tanto buona qualità venuto di <lb></lb>Francia, abbia investigato e trovato il segreto. </s>

<s>E, messolo in atto, con l&#039;aura <lb></lb>e favore di alcuni Senatori, si sia acquistato da questi Signori augumento <lb></lb>alle sue provvisioni sino a 10,000 fiorini l&#039;anno, con l&#039;obbligo però parmi <lb></lb>di servire nelle sue Letture perpetuamente ” (ivi). </s></p><p type="main">

<s>Ecco raccontarsi così storie che hanno faccia di vero. </s>

<s>Galileo, il quale, <lb></lb>mancando della scienza delle rifrazioni, non poteva aver tanto discorso da <lb></lb>esser da lui solo condotto all&#039;invenzione del Telescopio, vi giunse col ve­<lb></lb>derne ed esaminarne uno venuto di Francia e capitato in Venezia. </s>

<s>Cosicchè, <lb></lb>se avesse egli avuto la sincerità del Sirturo, avrebbe potuto ripeter le parole <lb></lb>stesse pronunziate da lui, dop&#039;aver, nella bottega dell&#039;orefice milanese, ve-<pb xlink:href="020/01/370.jpg" pagenum="351"></pb>duto il Telescopio del conte De Fuentes: <emph type="italics"></emph>incidit in manus meas, tractavi, <lb></lb>examinavi et similia confeci.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>E giacchè il Bartoli ha introdotto in questa storia Paolo Sarpi, non dob­<lb></lb>biam perderlo di vista, essendo che muove da lui il principio della maravi­<lb></lb>gliosa invenzione, come zampillo d&#039;acqua scaturito d&#039;arido masso in monte <lb></lb>solitario, che, dopo esser corso per varii anfratti, s&#039;allarga in fiume e irriga <lb></lb>i campi ubertosi, e fa sonare le valli. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nonostante che, dai sopra citati estratti di lettere di Giovanni Bartoli, <lb></lb>si rilevi che il Sarpi dette avviso dell&#039;invenzione del Canocchiale a Galileo <lb></lb>nel Giugno del 1609, all&#039;occasione che quel forestiero francese era venuto <lb></lb>a tentar la sorte in Venezia, esso fra Paolo, ne aveva avuto già avviso in <lb></lb>fin dal Novembre del 1608. “ L&#039;avviso delli nuovi occhiali, scriveva il dì <lb></lb>6 di Gennaio 1609 al Groslot, l&#039;ho avuto già più di un mese ” (Polidori, <lb></lb>Lett. </s>

<s>1863, T. I, pag. </s>

<s>181) e soggiunge di aver fede nella possibile riuscita <lb></lb>dello strumento, tanto più ch&#039;egli stesso da giovane, quando tutto era in­<lb></lb>tento allo studio delle Matematiche, aveva pensato al modo di ottener quel <lb></lb>tanto desiderato effetto, di veder le cose lontane, che ora dicevasi essere <lb></lb>stato raggiunto. </s>

<s>Ecco dunque, se non si vuol dare importanza al Portaluce <lb></lb>di Leonardo, d&#039;onde balena la prima idea dell&#039;invenzione del Canocchiale. <lb></lb></s>

<s>“ Quando io era giovane pensai ad una tal cosa e mi passò per la mente <lb></lb>che un occhial fatto di figura di parabola potesse far tal effetto e avevo ra­<lb></lb>gione da farne la dimostrazione ” (ivi). </s></p><p type="main">

<s>Al Sarpi era noto per diottrica dimostrazione ciò che pochi anni prima <lb></lb>aveva, ne&#039;solitari suoi manoscritti, diottricamente dimostrato il Maurolico, <lb></lb>che cioè le lenti convesse fanno convergere i raggi e le lenti concave gli <lb></lb>fanno divergere. </s>

<s>Ripensando perciò il giovane Ottico che per veder le cose <lb></lb>lontane ci bisognavano lenti che non facessero nè convergere nè divergere <lb></lb>i raggi luminosi, ma che gli mandassero paralleli, credè che si potesse un <lb></lb>tale effetto ottenere per mezzo degli occhiali parabolici. </s>

<s>La nuova specula­<lb></lb>zione era fondata sopra due ipotesi: sulla prima, alla quale era pure infor­<lb></lb>mato il Portaluce di Leonardo, che cioè le specie o i raggi visibili moves­<lb></lb>sero dall&#039;occhio; e sulla seconda che cioè i raggi passassero per rifrazione <lb></lb>attraverso al diafano parabolico, a quello stesso modo che si riflettono da <lb></lb>uno specchio. </s></p><p type="main">

<s>Intorno alla verità della prima ipotesi il Sarpi non dubitava, avendosi <lb></lb>per cosa certa che egli riprovava l&#039;opinion del Sagredo, da cui sostenevasi <lb></lb>che l&#039;occhio, nell&#039;atto del vedere, riceve dentro sè i raggi della luce e non <lb></lb>gli manda fuori, come Platone insegna, agli oggetti (Alb. </s>

<s>VIII, 204). Dubi­<lb></lb>tava bene della seconda ipotesi, ed esprimeva il dubbio con queste parole <pb xlink:href="020/01/371.jpg" pagenum="352"></pb>immediatamente soggiunte alle sopra citate; parole che fanno la più bella <lb></lb>testimonianza del senno pratico, e di quello squisito senso che, delle vere <lb></lb>regole dell&#039;arte sperimentale, aveva il nostro Servita: “ Ma poichè queste <lb></lb>sono cose astratte e non mettono in conto la repugnanza della materia, sen­<lb></lb>tivo qualche opposizione. </s>

<s>Per questo non son molto inchinato all&#039;opera, e <lb></lb>questa sarebbe stata faticosa; onde nè confermai nè riprovai il concetto mio <lb></lb>con l&#039;esperienza ” (Polid. </s>

<s>Lett., ivi). </s></p><p type="main">

<s>Le giovanili speculazioni, a che fra Paolo accenna in questa lettera fa­<lb></lb>miliare al Groslot, sarebbero senza dubbio andate in dimenticanza e il germe <lb></lb>da cui doveva svolgersi l&#039;invenzione del Canocchiale sarebbe rimasto ancora <lb></lb>per lungo tempo sepolto, se, conferite quelle speculazioni dallo stesso fra Paolo <lb></lb>al Porta, questi non le avesse solennemente divulgate nel XVII libro della <lb></lb>Magia. </s>

<s>Proponendosi di darne la dimostrazione matematica nel libro <emph type="italics"></emph>De re­<lb></lb>fractione,<emph.end type="italics"></emph.end> non dà l&#039;Autore, nel cap. </s>

<s>X del citato libro, intorno alle proprietà <lb></lb>diottriche delle lenti concave e delle convesse, altro che le conclusioni, e <lb></lb>non son pure altro che conclusioni quelle che dà, nel capitolo appresso, degli <lb></lb>occhiali parabolici <emph type="italics"></emph>quibus supra omne cogitatum quis inspicere longis­<lb></lb>sime queat.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Se il cap. </s>

<s>X richiamò a sè l&#039;attenzione de&#039;fabbricanti di occhiali, que­<lb></lb>sto XI che a lui segue pose, colle sue enimmatiche espressioni, a tortura <lb></lb>gli ingegni speculativi e fra questi quel del Keplero, il quale nelle parole <lb></lb>ivi scritte dal Porta notava più cose. </s>

<s>Prima di tutto che <emph type="italics"></emph>etsi de speculis <lb></lb>loquitur videtur tamen de perspicillis intelligi debere quia de industria <lb></lb>occultavit sententiam<emph.end type="italics"></emph.end> (Dioptric. </s>

<s>Aug. </s>

<s>Vindel. </s>

<s>1611, pag. </s>

<s>55). Notava altresì <lb></lb>che ivi mescolavansi <emph type="italics"></emph>incredibilia probabilibus,<emph.end type="italics"></emph.end> e che di più le espressioni <lb></lb>del titolo di quel cap. </s>

<s>XI non erano in coerenza con le dottrine professate <lb></lb>e dimostrate dall&#039;Autore intorno alla vista: “ Et titulus capitis XI verbis <lb></lb><emph type="italics"></emph>supra omnem cogitatum quam longissime prospicere<emph.end type="italics"></emph.end> videbatur absurdita­<lb></lb>tem opticam involvere, quasi visio fiat emittendo, et perspicilla acuant oculi <lb></lb>iaculos, ut ad remotiora penetrent, quam si nullo perspicillo adhiberentur: <lb></lb>aut si ut agnovit Porta, visio fit recipiendo, quasi tunc specilla rebus vi­<lb></lb>dendis lucem concilient vel augeant ” (Alb. </s>

<s>V, 412). </s></p><p type="main">

<s>Il Keplero notava queste cose giustamente, ma non sapeva che l&#039;Autor <lb></lb>della Magia Naturale riferiva ivi speculazioni, che non erano sue proprie, <lb></lb>ma del Sarpi, il quale, rispetto alla vista, riteneva l&#039;ipotesi platonica del­<lb></lb>l&#039;emissione, nè seppe il Matematico alemanno indovinar che il Porta stesso <lb></lb>dando per cosa riuscibile ciò di che il Sarpi dubitava, per non averne fatta <lb></lb>esperienza, confondeva insieme gli specchi e le lenti, per potere attribuire <lb></lb>a queste le proprietà dimostrate per quelli. </s></p><p type="main">

<s>Più ingenui però del Keplero sorsero a travagliarsi intorno a voler de­<lb></lb>cifrare gli enimmi del Porta, persuasi che tutto fosse nelle parole di lui <lb></lb>probabile e nulla d&#039;incredibile, due eletti ingegni italiani, seguaci delle dot­<lb></lb>trine di Galileo, a cui, il primo di que&#039;due Bartolommeo Imperiali, così scri­<lb></lb>veva il di 4 Ottobre 1614: “ È il mio desiderio che V. S. applichi il pen-<pb xlink:href="020/01/372.jpg" pagenum="353"></pb>siero al cap. </s>

<s>XI del libro XVII della Magia di Giov. </s>

<s>Battista della Porta. <lb></lb></s>

<s>È passo di cui confessa a V. S. il Keplero che non l&#039;intende, nè ho io sa­<lb></lb>puto giammai che matematico alcuno l&#039;abbia saputo dichiarare, come so che <lb></lb>l&#039;istesso Magini ha confessato, nè il Porta, per quante istanze li sia state <lb></lb>fatte da principi e letterati, si è potuto mai inchinare a dichiarare l&#039;animo <lb></lb>suo. </s>

<s>Solo che disse che maestro Paolo da Venezia servita, l&#039;aveva capito, e <lb></lb>quanto a me pare assai difficile il credere che questo sia un sibilo di vento <lb></lb>bugiardo, poichè si vede che, nel capitolo precedente, aveva così bene in­<lb></lb>segnato il modo di accoppiar le due lenti, il che però parve tanto strano <lb></lb>per tanto tempo. </s>

<s>Aggiungo che egli stesso protesta di volere nascondere <lb></lb>l&#039;artificio al volgo, ma che ai Prospettivi era cosa manifesta, sicchè uno di­<lb></lb>visando che in quelle parole sia qualche scambio o svario, siccome egli con­<lb></lb>fessa nella prefazione del libro, e di più che tal cosa non sia tanto difficol­<lb></lb>tosa ad un dotto; per tanto prego V. S. a considerare se preso quel testo <lb></lb>e trasportando le parole sicchè cominci <emph type="italics"></emph>Costituatur ....<emph.end type="italics"></emph.end> oppure <emph type="italics"></emph>Construi­<lb></lb>tur hoc modo speculum ....<emph.end type="italics"></emph.end> e poi tornar da capo alle parole <emph type="italics"></emph>Virtus costi­<lb></lb>tuatur ....<emph.end type="italics"></emph.end> si potesse per la prima aver la lettera ordinata. </s>

<s>Tanto più che <lb></lb>in questa parte, che è scritta innanzi, dice <emph type="italics"></emph>praedicti speculi<emph.end type="italics"></emph.end> non avendolo <lb></lb>ancora nominato. </s>

<s>Inoltre quelle parole <emph type="italics"></emph>sectionibus illis accomodetur<emph.end type="italics"></emph.end> sve­<lb></lb>gliano la memoria delle sezioni coniche, tanto celebri, sicchè par che egli <lb></lb>voglia intendere di una di quelle, perchè dalle opere sue par che si possa <lb></lb>cavare che questa sia la sezione parab olica, e questa è la ragione che egli <lb></lb>nel cap. </s>

<s>XIX, trattando della refrazione, insegna che con la lente parabolica <lb></lb>gagliardissimamente si accenda il fuoco, perchè tutti i raggi che passano si <lb></lb>uniscono in un punto. </s>

<s>E nel canocchiale, secondo la dottrina del Keplero <lb></lb>e l&#039;esperienza, non si richiede altro che quell&#039;unione, tanto più bella nella <lb></lb>parabola, quanto che toglie tutte le altre coincidenze più lunghe e più corte, <lb></lb>che caggiono da diverse parti della linea sferica. </s>

<s>Onde potrebbe il convesso <lb></lb>parabolico esser più grande di quantità della sferica, abbracciando più parti <lb></lb>in un tempo dell&#039;oggetto, e riuscirebbe chiarissimo. </s>

<s>E per quanto spetta <lb></lb>all&#039;incavato, di cui par che intenda il Porta in quelle parole <emph type="italics"></emph>ubi valentis­<lb></lb>sime universales solares radii disperguntur et coeunt minime,<emph.end type="italics"></emph.end> vorrebbe la <lb></lb>ragione che fosse anch&#039;egli incavato parabolico, il quale per forza disgre­<lb></lb>gherebbe i raggi, poichè fossero passati, per la contraria ragione del con­<lb></lb>cavo e del convesso, secondo la regola del Porta nel fine della 2a proposi­<lb></lb>zione del 2° libro <emph type="italics"></emph>De refractione.<emph.end type="italics"></emph.end> E dalla formazione, che egli insegna della <lb></lb>sezione parabolica, nel cap. </s>

<s>XV della Magia XVII, per via del triangolo ret­<lb></lb>tangolo, similmente si ha qualche luce da intendere quelle parole, nelle quali <lb></lb>fa menzione del triangolo e delle linee trasversali. </s>

<s>Or sarà fatica di V. S. giu­<lb></lb>dicar queste congetture, e quando pure stimasse che fosse molto lontano il <lb></lb>pensiero dal Porta, tornerei a pregarla che applicasse l&#039;animo a questo ne­<lb></lb>gozio, speculando se potesse riuscir migliore un Canocchiale fatto di cri­<lb></lb>stalli parabolici, per le ragioni che si son ricordate dal Porta, poichè, seb­<lb></lb>bene il Keplero ha più fede nell&#039;iperbola che nella parabola, nondimeno i <pb xlink:href="020/01/373.jpg" pagenum="354"></pb>concorsi e le unioni paiono più manifeste nelle sezioni paraboliche. </s>

<s>Poichè <lb></lb>se i raggi così passano come si riflettono, riflettendosi ad un punto negli <lb></lb>specchi da abbruciare, anderanno anche ad unirsi passando in un punto, vi­<lb></lb>cino al quale, posto un incavato parabolico, par che debba con maggior <lb></lb>forza distinguere quella confusione maggiore. </s>

<s>Il tutto però è rimesso al giu­<lb></lb>dizio di V. S. ” (MSS. Gal., P. VI, T. IX, c. </s>

<s>206). </s></p><p type="main">

<s>Ma perchè il giudizio di Galileo fu che il comporre il Canocchiale di <lb></lb>due lenti paraboliche, secondo il pensiero del Porta, non poteva riuscire a <lb></lb>buon effetto, l&#039;Imperiali in altra sua lettera conclude: “ Sono restato afflit­<lb></lb>tissimo, perchè avendo qualche opinione che potesse farsi quanto accenna <lb></lb>il Porta, l&#039;avermi ella accennato che stima non potersi arrivare, per essere <lb></lb>impossibile il farsi, mi ha posto in disperazione che tal cosa possa riuscire. </s>

<s><lb></lb>E l&#039;argomento ha gran forza: se il signor Galileo non l&#039;arriva, daddovero che <lb></lb>non è arrivabile ” (ivi, c. </s>

<s>218). </s></p><p type="main">

<s>Altro ardito pensiero del Porta fu quello di applicare ai raggi calori­<lb></lb>fici, negli specchi ustorii, ciò che, pe&#039;raggi luminosi, avea creduto possibile <lb></lb>nei Canocchiali; ond&#039;è che appresso ai citati pone, in quello stesso libro <lb></lb>della Magia, i due capitoli XVI e XVII, il primo de&#039;quali intitola: <emph type="italics"></emph>Quomodo <lb></lb>parabolica sectio describi possit quae oblique comburat et in longissimam <lb></lb>distantiam,<emph.end type="italics"></emph.end> e l&#039;altro: <emph type="italics"></emph>Parabolica sectio quae in infinitum comburat.<emph.end type="italics"></emph.end> Il <lb></lb>Keplero stimò queste due proposizioni impossibili, sia che s&#039;intendesse di <lb></lb>potere ottener l&#039;effetto di abbruciare in lunghissima e in infinita distanza, <lb></lb>per via di lenti cristalline, o per via di specchi: “ J. </s>

<s>Baptista Porta polli­<lb></lb>cetur problema in infinitum comburere per lineam ustoriam, quod ille de <lb></lb>speculo tradit: alii vero de lente convexa, verum esse opinantur. </s>

<s>Utrum <lb></lb>sequaris, impossibilia aggrederis ” (Dioptr., pag. </s>

<s>20). </s></p><p type="main">

<s>Nonostante, come l&#039;Imperiali aveva creduto più volentieri al Porta che <lb></lb>al Keplero, rispetto al Canocchiale parabolico, così il Cavalieri ebbe più fede <lb></lb>al Porta che al Keplero, per ciò che riguarda la possibilità di costruire e di <lb></lb>ottenere gli effetti dello specchio Ustorio. </s>

<s>Ammesso che la linea comburente <lb></lb>del Porta non si debba intendere per una vera linea geometrica, ma per un <lb></lb><emph type="italics"></emph>cilindro o cannoncino di lume, di che sottigliezza vogliamo indiffinita­<lb></lb>mente prolungato<emph.end type="italics"></emph.end> (Lo Specchio Ust. </s>

<s>Bologna 1650, pag. </s>

<s>61) stima il Cava­<lb></lb>lieri, secondo egli dimostra nel cap. </s>

<s>XXXII del libro citato, potersi ottener <lb></lb>l&#039;effetto di abbruciare in qualunque direzione e per lunghissima distanza, <lb></lb>applicando uno specchietto parabolico, girevole sopra un pernio a discre­<lb></lb>zione di chi vuol verso una parte o verso l&#039;altra dirigere l&#039;incendio, nel <lb></lb>fuoco di un altro specchio parabolico e più grande, in cui diano i liberi e <lb></lb>ardenti raggi del sole. </s></p><p type="main">

<s>Gli esempi dell&#039;Imperiali e del Cavalieri attestano che non tutti quegli <lb></lb>appartenenti alla scuola di Galileo concorrevano in far del Porta giudizi si­<lb></lb>mili a quelli dell&#039;Hasdale e del Sagredo. </s>

<s>Che se il libro della <emph type="italics"></emph>Magia Na­<lb></lb>turale<emph.end type="italics"></emph.end> valse a risvegliar tanto ardore di scientifiche investigazioni nel Fisico <lb></lb>genovese di sopra commemorato, e nell&#039;Autore della Geometria degl&#039;indivi-<pb xlink:href="020/01/374.jpg" pagenum="355"></pb>sibili, si pensi con quanto maggior desiderio dovesse esser cercato quel li­<lb></lb>bro, in tempi di minor cultura e da gente che teneva dietro curiosa a tutto <lb></lb>ciò che sapesse del nuovo e dello spettacoloso. </s>

<s>Le numerosissime edizioni, <lb></lb>che forse non se ne contano tante di nessun altro libro di quel genere, di­<lb></lb>cono che la <emph type="italics"></emph>Magia Naturale<emph.end type="italics"></emph.end> doveva esser diffusa e letta per ogni parte <lb></lb>d&#039;Europa, non senza frugar vivamente la curiosità ne&#039;lettori di veder sotto <lb></lb>i loro occhi incarnati i seducenti fantasmi ivi dipinti. </s>

<s>Narra il Keplero che <lb></lb>da queste curiosità fu più volte preso il suo Imperatore (Alb. </s>

<s>V, 412) e chi <lb></lb>poteva non sentirsi commuovere alla speranza ingeritagli di poter mandare <lb></lb>a infinita distanza da sè il lume da&#039;suoi occhi e il fuoco dalle sue mani? </s></p><p type="main">

<s>Queste considerazioni concorrono a render probabilissimo il fatto che <lb></lb>a qualche fabbricante di occhiali, di qualunque nazione si fosse, e comun­<lb></lb>que avesse nome, per suggerimento del Porta, venisse in pensiero di com­<lb></lb>porre insieme due paia di occhiali, uno da miopi e l&#039;altro da presbipi, e <lb></lb>che ritrovasse in effetto quell&#039;ingrandimento degli oggetti traguardati, dal <lb></lb>Porta stesso promesso. </s>

<s>In principio dovea aver quell&#039;artefice le due paia di <lb></lb>occhiali tenute congiunte insieme per via di verghette metalliche saldate, e <lb></lb>poi facilmente, per la proprietà benissimo allora sperimentata, che hanno i <lb></lb>tubi di diriger la linea di mira, e di togliere le riflessioni irregolari, dee <lb></lb>avere alle verghette sostituito il cannoncino. </s>

<s>Così il primo canocchiale sa­<lb></lb>rebbe stato un binoculo, e par che la congettura prenda qualche colore di <lb></lb>verità da ciò che Filippo Salviati aveva sentito dire, che cioè quell&#039;occhia­<lb></lb>laio, che aveva fatto l&#039;occhiale al conte Maurizio, aveva trovato anche inven­<lb></lb>zione di moltiplicare il vedere con due occhiali ordinari, da portare al naso <lb></lb>(MSS. Gal. </s>

<s>P. I, T. VII, c. </s>

<s>119). </s></p><p type="main">

<s>In qualunque modo, quel fatto che si diceva dianzi esser probabilissimo, <lb></lb>fu dal Porta, senza troppo esitare, tenuto e dato per cosa certa. </s>

<s>Appena <lb></lb>infatti ebbe dal principe Cesi nuova dell&#039;invenzione del Canocchiale, così gli <lb></lb>rispose da Napoli il dì 28 Agosto 1609: “ Del secreto dell&#039;occhiale l&#039;ho <lb></lb>visto, ed è una minchioneria, ed è preso dal mio libro IX <emph type="italics"></emph>De refractione ”<emph.end type="italics"></emph.end><lb></lb>(Venturi, Memorie ecc., Modena 1818, P. I, pag. </s>

<s>82). </s></p><p type="main">

<s>Qui è notabile che, invece della <emph type="italics"></emph>Magia Naturale,<emph.end type="italics"></emph.end> citi il trattato <emph type="italics"></emph>De re­<lb></lb>fractione<emph.end type="italics"></emph.end> e di questo il libro IX, forse per isbaglio, invece dell&#039;VIII, dove <lb></lb>appunto si tratta <emph type="italics"></emph>De specillis.<emph.end type="italics"></emph.end> Ma il citar quel libro, che fu primo nella <lb></lb>storia della Diottrica a dar la teoria delle lenti, invece di quell&#039;altro, dove <lb></lb>non si fa che accennarne le conclusioni, non era senza una particolare in­<lb></lb>tenzion dell&#039;Autore, nell&#039;atto di revocare a sè il diritto d&#039;aver, colle teorie <lb></lb>stesse che prefulgono alla mente, preparata la pratica esecuzione del Canoc­<lb></lb>chiale. </s>

<s>Galileo e i partigiani di lui contesero al Porta quel diritto, e le cose <lb></lb>narrate fin qui ci dispongono a credere che glielo contendessero ingiusta­<lb></lb>mente. </s>

<s>Ma ora che l&#039;ordine della nostra Storia ci conduce a discorrer della <lb></lb>teoria diottrica dello Strumento, dai fatti che esamineremo, forse anche me­<lb></lb>glio verrà decisa la questione. </s></p><pb xlink:href="020/01/375.jpg" pagenum="356"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Da quali principii diottrici fosse condotto Galileo in trattar della ra­<lb></lb>gione e del modo come si vengono a ingrandire gli oggetti, per opera del <lb></lb>Telescopio, si par manifesto da ciò che, in presentar per la prima volta al <lb></lb>pubblico il suo nuovo strumento, ne scrisse nel Nunzio Sidereo. </s>

<s>Preghiamo <lb></lb>i nostri lettori ad attender bene alla scienza ottica dalla quale sono infor­<lb></lb>mate le parole seguenti: “ Sit enim facilioris intelligentiae gratia, tubus ABCD <lb></lb><figure id="id.020.01.375.1.jpg" xlink:href="020/01/375/1.jpg"></figure></s></p><p type="caption">

<s>Figura 26.<lb></lb>(fig. </s>

<s>26) oculus inspicientis esto <lb></lb>E. Radii, dum nulla in tubo ades­<lb></lb>sent Perspicilla, ab obiecto FG ad <lb></lb>oculum E, secundum lineas rectas <lb></lb>FCE, GDE ferrentur: sed, apposi­<lb></lb>tis Perspicillis, ferentur secundum <lb></lb>lineas refractas HCE, IDE: coar­<lb></lb>ctantur enim, et qui prius liberi <lb></lb>ad FG obiectum dirigebantur, par­<lb></lb>tem tantummodo HI comprehendent ” (Alb. </s>

<s>III, 62). </s></p><p type="main">

<s>Che strana teoria del modo di operar del Canocchiale è mai questa? </s>

<s><lb></lb>Chi così ne discorse, tutt&#039;altro che aver cavato il suo discorso <emph type="italics"></emph>dalle più re­<lb></lb>condite speculazioni di Prospettiva,<emph.end type="italics"></emph.end> si direbbe che di Prospettiva, ossia di <lb></lb>scienza diottrica, non ne aveva nemmeno la prima idea. </s>

<s>Come mai s&#039;ingran­<lb></lb>discono gli oggetti per refrazione coartando i raggi, <emph type="italics"></emph>coarctantur enim?<emph.end type="italics"></emph.end> e <lb></lb>come posson le lenti mostrare ingranditi gli oggetti, se per l&#039;esempio del­<lb></lb>l&#039;Autore non si rappresenta dell&#039;oggetto FG all&#039;occhio altro che una por­<lb></lb>zione HI di lui? </s></p><p type="main">

<s>A svelare il mistero giova intanto sapere esser qui da Galileo profes­<lb></lb>sata l&#039;opinione che le lenti mostrino per refrangenza ingrandite le cose, <lb></lb>perchè, condensandone i raggi, le rappresentano all&#039;occhio più intensamente <lb></lb>illuminate. </s>

<s>Che poi, per opera delle rifrazioni, facendosi gli stessi raggi di­<lb></lb>vergere, si accresca l&#039;angolo visuale, non passa per la mente dell&#039;Autore. </s>

<s><lb></lb>L&#039;obiettivo per lui opera a quello stesso modo che opera l&#039;oculare, e am­<lb></lb>messo, a modo platonico, che le linee radiose muovan dall&#039;occhio per an­<lb></lb>dare a incontrar l&#039;oggetto <emph type="italics"></emph>(ad obiectum FG dirigebantur),<emph.end type="italics"></emph.end> non sospetta <lb></lb>nemmen dalla lontana che i raggi s&#039;incrocino mai in tutto quel tragitto che <lb></lb>fanno per venir dall&#039;oggetto lontano ad appuntarsi nell&#039;occhio. </s></p><p type="main">

<s>Poco dopo aver professate Galileo così fatte dottrine, seppure si meri­<lb></lb>tano il nome di dottrine, soggiunge ivi la promessa di dare alla prima oc­<lb></lb>casione al pubblico <emph type="italics"></emph>absolutam huius Organi theoriam,<emph.end type="italics"></emph.end> e par che questa <lb></lb>occasione aspettasse a venir tredici anni dopo, quando dette mano a scri­<lb></lb>vere il <emph type="italics"></emph>Saggiatore.<emph.end type="italics"></emph.end> Qui si torna a trattar della teoria del <gap></gap><pb xlink:href="020/01/376.jpg" pagenum="357"></pb>dell&#039;Autore, in mezzo a molte tenebre, son pure alquanto lumeggiate di <lb></lb>quella scienza diottrica, la quale nel Nunzio Sidereo assolutamente manca. </s></p><p type="main">

<s>Ivi infatti incominciò dal confutare il Sarsi, le dottrine del quale, in­<lb></lb>torno al modo d&#039;operare del Telescopio, le riduce ai due casi seguenti: “ Il <lb></lb>Telescopio rappresenta gli oggetti maggiori, perchè gli porta sotto maggior <lb></lb>angolo, che quando son veduti senza lo strumento: Il medesimo, restrin­<lb></lb>gendo quasi a un punto le specie de&#039;corpi luminosi ed i raggi sparsi, rende <lb></lb>il cono visivo, o vogliam dire la piramide luminosa, per la quale si vedono <lb></lb>gli oggetti, di gran lunga più lucida, e però gli oggetti splendidi di pari ci <lb></lb>si rappresentano ingranditi, e di maggior luce illustrati ” (Alb. </s>

<s>IV, 201). </s></p><p type="main">

<s>Conceduto dunque ed ammesso esser vero che il Telescopio ingrandi­<lb></lb>sce gli oggetti col portargli sotto maggior angolo, conclude Galileo, contro <lb></lb>l&#039;altra proposizione del Sarsi, dicendo esser <emph type="italics"></emph>falsissimo che gli oggetti lu­<lb></lb>minosi ci si rappresentino col Telescopio più lucidi che senza, anzi è vero <lb></lb>che li veggiamo assai più oscuri<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>202). </s></p><p type="main">

<s>Distingue inoltre l&#039;Autor del <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> il vario modo d&#039;operar delle <lb></lb>lenti concave e delle convesse, dicendo che queste accrescon bene gli og­<lb></lb>getti, ma gli mostrano <emph type="italics"></emph>assai indistinti ed abbagliati,<emph.end type="italics"></emph.end> mentre quelle gli rap­<lb></lb>presentano chiari ma impiccoliti (ivi, pag. </s>

<s>208) e nonostante attribuisce a <lb></lb>questa stessa concava nel Telescopio la parte più importante perchè è quella, <lb></lb>appresso alla quale si tien l&#039;occhio, e per la quale passano gli ultimi raggi <lb></lb>(ivi, pag. </s>

<s>202) che, dilatandosi nell&#039;uscir dalla lente stessa, formano il cono <lb></lb>inverso, come si sperimenta nel modo di disegnar le macchie solari per <lb></lb>proiezione (ivi, pag. </s>

<s>203). La dottrina platonica dell&#039;emissione che cioè <emph type="italics"></emph>la <lb></lb>luce ingagliardita mediante l&#039;unione de&#039;raggi rende l&#039;oggetto veduto più <lb></lb>luminoso<emph.end type="italics"></emph.end> è qui pure da Galileo riputata falsa, asserendo che <emph type="italics"></emph>sarebbe vero <lb></lb>questo, quando tal luce andasse a trovar l&#039;oggetto, ma ella vien verso <lb></lb>l&#039;occhio, il che produce poi contrario effetto<emph.end type="italics"></emph.end> (ivi). </s></p><p type="main">

<s>Or non può chi legge e medita queste cose non sentirsi preso da una <lb></lb>gran maraviglia, in ritrovar che Galileo confuta nel Saggiatore dottrine, che <lb></lb>egli aveva prima professate nel Nunzio Sidereo, per cui, mentre confuta il <lb></lb>Sarsi, vien nello stesso tempo a confutare e a contradire a sè stesso. </s>

<s>Avesse <lb></lb>fatto cenno a qualche ritrattazione, e la maraviglia cesserebbe, perchè in <lb></lb>tutti la verità è figliola del tempo, ma pur si vuol fare apparire da tutte le <lb></lb>parti che la mente dell&#039;Autor nostro sia sempre stata ugualmente amica alla <lb></lb>verità, e non abbia fornicato mai coll&#039;errore. </s>

<s>Anzi, sebben egli citi le dot­<lb></lb>trine dei Prospettivi, quelle antiche calottriche dottrine non hanno a che far <lb></lb>nulla colle sue nuove diottriche, le quali egli è venuto il primo a insegnare <lb></lb>al mondo, e senza le quali il mondo stesso ignorerebbe ancora col Sarsi il <lb></lb>modo vero com&#039;opera sulla nostra vista il Telescopio. </s>

<s>Che una tal pretesa <lb></lb>fosse veramente radicata nell&#039;animo di Galileo, lo dimostrano i fatti, intorno <lb></lb>ai quali dobbiamo ora divagare il discorso, dai quali fatti pur si conferma <lb></lb>quello spirito di conquista che, per esaltar sè, portava il Filosofo ad oppri­<lb></lb>mere glì altri <gap></gap></s></p><pb xlink:href="020/01/377.jpg" pagenum="358"></pb><p type="main">

<s>Infin dal 1521 Francesco Maurolico aveva dato mano ai suoi Trattati <lb></lb>di Ottica, e nel 1554 erano già compiuti. </s>

<s>La teoria diottrica delle lenti con­<lb></lb>cave e delle convesse è ivi per la prima volta matematicamente dimostrata, <lb></lb>e tanto lume si conobbe, da chi vide il Manoscritto, potersi diffondere, da <lb></lb>questa teoria delle lenti separate, sulla teoria delle lenti stesse composte nel <lb></lb>Canocchiale; che fu pensato di dar quelle sepolte carte alla luce, in quel <lb></lb>tempo che, de&#039;mirabili effetti dello strumento, sentivasi vivo desiderio da <lb></lb>tutti d&#039;intenderne la ragione. </s>

<s>Tarquinio Longhi infatti così diceva a Giovan <lb></lb>Battista Airolo, nel dedicargli la stampa del libro, eseguita in Napoli nel 1611: <lb></lb>“ Nam sapientiae studiosis non nisi gratissimi accident hi libri, qui veluti <lb></lb>fontes et capita sunt Perspectivae; hoc potissimum tempore, quo ingens <lb></lb>eius desiderium in omnium pectoribus excitavit novum illud et admirabile <lb></lb>Opticae fistulae inventum ”. </s></p><p type="main">

<s>La pubblicazione, intesa così dal Longhi a fine di preparare i fonda­<lb></lb>menti scienziali alla teoria del Canocchiale, era forse più opportuna di quel <lb></lb>che non si potesse presentire allora, imperocchè ha il Maurolico due Teo­<lb></lb>remi insigni, i quali parvero appositamente preparati per coloro, che avreb­<lb></lb>bero dato opera a costruire e a perfezionare i futuri Telescopi. </s>

<s>È il primo <lb></lb>di que&#039;Teoremi il XVIII del I Libro <emph type="italics"></emph>Diaphanorum,<emph.end type="italics"></emph.end> dove si dimostrano le <lb></lb>aberrazioni di sfericità prodotte per rifrazione nelle sfere cristalline: “ Pa­<lb></lb>rallelorum radiorum, intra perspicuum orbem, a centro inaequaliter distan­<lb></lb>tium, remotior, cum axe sibi parallelo propius sphaerae, concurret, quam <lb></lb>reliquus (ibi, pag. </s>

<s>41). Fu questo Teorema, che fece poi disperare il Newton <lb></lb>di poter aver ne&#039;canocchiali diottrici la desiderata perfezione. </s></p><p type="main">

<s>L&#039;altro maurolicano Teorema è il XXIII dove si dimostra il modo del <lb></lb>rappresentarsi per rifrazione le immagini nelle sfere cristalline e nelle lenti <lb></lb>convesse: “ Patet ergo ratio quare lux vel aliquod illuminatum, per conspi­<lb></lb>cilliorum vitrum trasparens, ad terminum quendam conversam porrigit ef­<lb></lb>figiem: quando quidem conspicilla superficiem habent utrinque convexam. </s>

<s><lb></lb>Immo in huiusmodi vitro talis conversa effigies expressior trasparet, quam <lb></lb>si vitrum ipsum sphaericum esset ” (ibi, pag. </s>

<s>48). </s></p><p type="main">

<s>Diciannove anni prima che questo Trattato del Maurolico fosse noto al <lb></lb>pubblico, il Porta aveva già dimostrate le proprietà diottriche delle lenti, e <lb></lb>molti altri effetti delle rifrazioni, con norme più sicure, e con più largo stu­<lb></lb>dio di quel che non avesse fatto l&#039;Ottico siciliano. </s>

<s>Questo infatti, nel Teo­<lb></lb>rema X del libro sopra citato, professa il principio di Vitellione, che cioè <lb></lb>gli angoli incidenti e i refratti stieno in proporzione uniformemente difforme, <lb></lb>o geometrica: <emph type="italics"></emph>Anguli inclinationum sunt fractionum angulis proportio­<lb></lb>nales<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>36). Quanto poi alle immagini il Mauralico dimostrò bene <lb></lb>il rappresentarsi delle immagini reali nelle lenti biconvesse, ma delle im­<lb></lb>magini virtuali, nelle biconvesse stesse e nelle concave, non fa parola, con­<lb></lb>tentandosi di concludere per le prime: <emph type="italics"></emph>Hinc ergo satis constat quod con­<lb></lb>vexa congregat,<emph.end type="italics"></emph.end> e per le seconde: <emph type="italics"></emph>Hinc ergo satis constat quod concava <lb></lb>disgregat<emph.end type="italics"></emph.end> (Diaph. </s>

<s>Lib. </s>

<s>III, pag. </s>

<s>73). </s></p><pb xlink:href="020/01/378.jpg" pagenum="359"></pb><p type="main">

<s>Il Porta, nella proposizione VIII del Libro I <emph type="italics"></emph>De refractione,<emph.end type="italics"></emph.end> dimostra <lb></lb>che il principio assunto da Vitellione, e seguito poi dal Maurolico, è falso, <lb></lb>e che i raggi incidenti e i refratti formano angoli, i quali stanno in pro­<lb></lb>porzioni non uniformemente, ma difformemente difformi: “ Sed Vitellio in <lb></lb>hoc falsus est, quod etsi aequaliter inter se distant in fundo iacentia colo­<lb></lb>rata, non ob id aequaliter distant in aquae summo puncta refractionum ” <lb></lb>(Neapoli 1593, pag. </s>

<s>17). </s></p><p type="main">

<s>Per quel che poi riguarda la rappresentazione delle immagini, il Porta <lb></lb>è il più compiuto di tutti gli Ottici che lo seguirono appresso fino allo stesso <lb></lb>Cartesio. </s>

<s>Notabile che egli primo introducesse, in questa nuova grafia diot­<lb></lb>trica, l&#039;uso degli <emph type="italics"></emph>assi,<emph.end type="italics"></emph.end> che egli appella col nome di <emph type="italics"></emph>cateti,<emph.end type="italics"></emph.end> da cui è con ve­<lb></lb>rità guidato a dimostrar il rappresentarsi delle immagini così reali come <lb></lb>virtuali nelle due forme di lenti. </s>

<s>Essendo la Diottrica una scienza nuova a <lb></lb>que&#039;tempi mirabile è in questo Trattato <emph type="italics"></emph>De refractione<emph.end type="italics"></emph.end> il libro VIII <emph type="italics"></emph>De <lb></lb>spicillis,<emph.end type="italics"></emph.end> del qual soggetto ha l&#039;Autore gran ragione di dire che egli era <lb></lb><emph type="italics"></emph>res ardua, mirabilis utilis iucunda nec ab aliquibus adhuc tentata<emph.end type="italics"></emph.end> (ibi, <lb></lb>pag. </s>

<s>173). La dimostrazione delle immagini, che in vario modo si rappre­<lb></lb>sentano dalle varie forme di lenti, è ivi data principalmente nelle tre pro­<lb></lb>posizioni: nella VII “ In convexis specillis oculo specillo proprinquo, magni­<lb></lb>tudine prope, ut procul posita, semper recta videbitur ” (pag. </s>

<s>179); nella VIII <lb></lb>“ In convexis specillis, magnitudine et oculo longe positis, inversa videbitur <lb></lb>magnitudo et proprinquior ” (pag. </s>

<s>180), e nella XV “ In concavis specillis <lb></lb>res semper minor videbitur ” pag. </s>

<s>185). </s></p><p type="main">

<s>In quel tempo stesso che il Porta dava opera a pubblicare il Trattato <lb></lb><emph type="italics"></emph>De Refractione,<emph.end type="italics"></emph.end> un altro Italiano aveva rivolte le sue speculazioni intorno <lb></lb>alle proprietà diottriche delle lenti, e ne avea dimostrati teoremi, che an­<lb></lb>davano attorno manoscritti. </s>

<s>Inventato il canocchiale, fu da alcuni, e segna­<lb></lb>tamente da quel Giovanni Bartoli che dell&#039;invenzione del canocchiale dava <lb></lb>particolari notizie al Vinta, pregato l&#039;Autore di quel Manoscritto, che era <lb></lb>Marc&#039;Antonio De Dominis, a voler applicare i teoremi dimostrati alla teo­<lb></lb>ria dello stesso Canocchiale, tanto desiderata. </s>

<s>Il <emph type="italics"></emph>De Dominis,<emph.end type="italics"></emph.end> nonostante la <lb></lb>dignità di Arcivescovo di Spalatro, della quale era stato insignito, condiscese, <lb></lb>preparando quel Trattato, che ebbe poi il titolo <emph type="italics"></emph>De radiis visus et lucis.<emph.end type="italics"></emph.end> Di <lb></lb>ciò appunto dava così notizia il Sarpi al Leschassier, con lettera del dì 8 Giu­<lb></lb>gno 1610: “ Quanto alle lenti oculari, per dirne alcun che, ci ha qui (in <lb></lb>Venezia) alcuni eruditi, che disegnano di fare un piccolo Commentario sulla <lb></lb>visione, ove esporranno la maniera e la cagione del ritrovato olandese, e <lb></lb>tutte le teorie a un tempo del Canocchiale ” (Polidori, Lettere ediz. </s>

<s>cit. </s>

<s><lb></lb>T. II, pag. </s>

<s>81). Due mesi dopo, torna lo stesso Sarpi a scrivere all&#039;amico, <lb></lb>dicendogli che il libricciuolo intorno agli occhiali non era ancora stampato, <lb></lb>ma che l&#039;Autore attendeva alle incisioni, delle quali aveva bisogno per <lb></lb>ispiegare i suoi sentimenti (ivi, pag. </s>

<s>108). Fu stampato poi quel libric­<lb></lb>ciuolo, a cui dev&#039;aver preso non piccola parte lo stesso Sarpi, in Venezia <lb></lb>nel 1611, col titolo<gap></gap> <emph type="italics"></emph>De radiis visus et lucis in vitris perspectivis et iride,<emph.end type="italics"></emph.end><pb xlink:href="020/01/379.jpg" pagenum="360"></pb><emph type="italics"></emph>Tractatus Marci Antonii De Dominis, per Joannem Bartolum in lucem <lb></lb>editus.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>L&#039;Autore mostra di avere avuto e di aver tuttavia una gran fiducia di <lb></lb>esser coll&#039;opera sua riuscito a sodisfar pienamente e con gran facilità al de­<lb></lb>siderio di coloro, che volevan saper la maniera e la ragione del ritrovato <lb></lb>olandese. </s>

<s>Una tal fiducia vien da lui stesso espressa per le seguenti parole: <lb></lb>“ Ex hactenus a nobis dictis et explicatis de vitreis perspicillis, facillimum <lb></lb>negotium redditur in conficiendo instrumento illo quod nuper videtur in­<lb></lb>ventum aut saltem, praesertim in Italia, publicatum. </s>

<s>Id enim, quemadmo­<lb></lb>dum maxima admiratione affecit et afficit plurimos, ita mihi certe qui in <lb></lb>perspectivis ante multos, sed per multos etiam annos delectationis causa men­<lb></lb>tem exercui, nulli prorsus fuit admirationi, sed cum primum illud vidi, erat <lb></lb>autem valde imperfectum, effectum duorum vitrorum aperte cognovi ” (ivi, <lb></lb>pag. </s>

<s>37, 38). </s></p><p type="main">

<s>Questa vantata facilità d&#039;intendere ciò che a tutti era sembrato tanto <lb></lb>difficile, il <emph type="italics"></emph>De Dominis<emph.end type="italics"></emph.end> la riconosce dunque dall&#039;essersi per tanti anni eser­<lb></lb>citato negli studi di Prospettiva, e dall&#039;aver saputo spiegare le proprietà delle <lb></lb>lenti. </s>

<s>E infatti egli aveva sufficientemente bene dimostrato l&#039;ingrandimento <lb></lb>virtuale delle immagini nelle lenti convesse, concludendo così la sua dimo­<lb></lb>strazione: “ Itaque oculus non videt quantitatem sub angulo directo et na­<lb></lb>turali, sed sub angulo, qui est angulus maior ” (pag. </s>

<s>19). Aveva pure in <lb></lb>sufficiente maniera descritto il rappresentarsi delle immagini virtuali nelle <lb></lb>lenti concave, concludendo così intorno ad esse: “ Oculus videt quantitatem <lb></lb>sub angulo qui est minor et strictior angulo naturali, et minorem vitri par­<lb></lb>tem occupat et consequenter res quidem minor apparebit, sed clarior et <lb></lb>distinctior ” (ibi). </s></p><p type="main">

<s>Tali diottriche conclusioni però, benchè vere e sufficientemente dimo­<lb></lb>strate, non eran quelle che più facevano all&#039;uopo. </s>

<s>Imperocchè, consistendo <lb></lb>la ragione del Canocchiale nell&#039;immagine reale e rovesciata dell&#039;obiettivo, <lb></lb>che viene ingrandita e raddirizzata dall&#039;oculare, il De Dominis intorno a ciò <lb></lb>mostra di non saperne niente, e perciò, riguardandosi da lui l&#039;obiettivo stesso <lb></lb>come una lente d&#039;ingrandimento virtuale, ecco come frantende l&#039;ufficio del­<lb></lb>l&#039;oculare, e come allo stesso tempo lasci gli studiosi in quella fame, a cui <lb></lb>con tanta facilità aveva fiducia di sodisfare. </s>

<s>“ Caeterum iam vidimus quae <lb></lb>valde remota sunt, per vitrum lenticulare cerni quidem cum ipsorum in­<lb></lb>cremento, remoto usque ad certum spacium ab oculo vitro praedicto, sed <lb></lb>turbate et indistincte, et confuse, propter mixtionem radiorum visualium di­<lb></lb>rectorum cum fractis. </s>

<s>Si igitur aliqua ratione tolli posset haec confusio, ita <lb></lb>ut sublatis radiis directis per solos refractos fiat visio, ex duplici capite illa <lb></lb>clara esset et distincta, tum ex sublata confusione praedicta, tum ex rerum <lb></lb>visibilium dilatatione. </s>

<s>Tollitur igitur confusio illa et extinguntur radii di­<lb></lb>recti, per appositionem vitri excavati inter oculum et vitrum lenticulare ” <lb></lb>(ibi, pag. </s>

<s>34). </s></p><p type="main">

<s>Tale e tanto in <gap></gap> era il fervor de&#039;nuovi studi dioffrici in Ita-<pb xlink:href="020/01/380.jpg" pagenum="361"></pb>lia, che si risvegliò all&#039;esempio, in Germania, quel gran Keplero, il quale <lb></lb>avendo, ne&#039;suoi Paralipomeni a Vitellione, sfiorato appena questi stessi nuovi <lb></lb>studii, volle tornarci sopra di proposito, a coltivarli col principale intento di <lb></lb>derivar luce di lì a intendere la ragione del Canocchiale. </s>

<s>Il Trattatello, che <lb></lb>vide pure nel 1611 in Augusta la luce, s&#039;intitolò <emph type="italics"></emph>Dioptrice, seu demonstra­<lb></lb>tio eorum quae visui et visibilibus, propter conspicilla non ita pridem in­<lb></lb>venta, accidunt,<emph.end type="italics"></emph.end> e nella teoria delle lenti semplici si va anche qui prepa­<lb></lb>rando la teoria per le lenti composte. </s></p><p type="main">

<s>Il rappresentarsi delle immagini reali nelle lenti convesse è dimostrato <lb></lb>nella proposizione XXC con tanta esattezza, che non potrebbe di meglio de­<lb></lb>siderare la scienza. </s>

<s>Ivi è invocato per la prima volta il principio che l&#039;oc­<lb></lb>chio riferisce la vista nella direzione del raggio rifratto, e con ciò venivasi <lb></lb><figure id="id.020.01.380.1.jpg" xlink:href="020/01/380/1.jpg"></figure></s></p><p type="caption">

<s>Figura 27.<lb></lb>a intendere in che modo il teorema di Tolomeo, che <lb></lb>cioè gli oggetti si vedon dall&#039;occhio nostro ingranditi <lb></lb>a proporzione dell&#039;angolo visuale, si potesse, dai di­<lb></lb>retti e naturali, applicare ai raggi rifratti. </s>

<s>Quella <lb></lb>citata proposizione XXC, in cui si dimostra così bene <lb></lb>la teoria del microscopio semplice, è conclusa dal­<lb></lb>l&#039;Autore nella forma seguente: “ Ut igitur totum DE <lb></lb>(fig. </s>

<s>27) apprehendatur, oportet venire ab oculo exte­<lb></lb>riores quam CI, CK, puta CA, CB. </s>

<s>Hae igitur si iusto <lb></lb>spacio distiterint a CI, CK, refractione in A, B facta, <lb></lb>apprehendent D, E ut sint visivae CAD, CBE. </s>

<s>Cum <lb></lb>autem ACB angulus sit maior quam ICK, quo spe­<lb></lb>ctatur visibile, remota lente, maius igitur putabitur visibile DE quam est. </s>

<s><lb></lb>Nam nescit oculus quid radiis CA, CB accidat in transitu A et B, putatque <lb></lb>illos continuari in rectum ac si essent CAF, CBG, ubi FG imaginata quantitas <lb></lb>est maior quam DE ” (ibi, pag. </s>

<s>36). </s></p><p type="main">

<s>Quanto però il Keplero è esatto in questa, altrettanto si mostra impro­<lb></lb>prio nell&#039;altra proposizione XCVI, dove tratta delle immagini rappresentate <lb></lb>dalle lenti concave. </s>

<s>L&#039;enunciato <emph type="italics"></emph>visibilia per cavas lentes rapraesentantur <lb></lb>minora<emph.end type="italics"></emph.end> (pag. </s>

<s>49) è vero, ma nel processo della dimostrazione si tien che i <lb></lb>raggi convergano verso l&#039;occhio quasi abbiano le lenti concave, come le con­<lb></lb>vesse, un foco reale. </s>

<s>Da questo errore principalmente dipende l&#039;insufficienza <lb></lb>del Keplero a spiegar la ragione del Canocchiale, imperocchè, sebbene egli, <lb></lb>nelle due proposizioni XLIV e LXXV, dimostri assai bene il rappresentarsi <lb></lb>delle immagini reali o rovesciate nelle lenti convesse, non seppe poi vedere <lb></lb>come, contrapposta una tale immagine reale per oggetto alla lente concava, <lb></lb>questa, collocata presso l&#039;occhio, per la divergenza e l&#039;incrociamento de&#039;raggi <lb></lb>in lei rifratti, venisse a ripresentar l&#039;oggetto stesso assai più grande e di­<lb></lb>ritto. </s>

<s>È perciò che il nostro Autore nella proposizione CVII, smarrita la sua <lb></lb>scienza diottrica, si abbandona alla fantasia, la quale gli fa tesser così fatto <lb></lb>discorso: La lente convessa fa troppo convergere i raggi; la concava gli fa <lb></lb>roppo divergere, ma composte insieme nel Canocchiale si emendano i due <pb xlink:href="020/01/381.jpg" pagenum="362"></pb>eccessi, e da ciò ne segue la visione distinta. </s>

<s>“ Cavae lentes de circulo ni­<lb></lb>mis angusto, si proxime oculum applicentur, confusa reddunt, propter ni­<lb></lb>miam radiorum divergentiam. </s>

<s>Sed radiationes unius puncti, per convexam <lb></lb>lentem solitariam oculo posito intra centrum concursus, praestant confusam <lb></lb>visionem propter convergentiam, et illa nimietas divergentiae et haec con­<lb></lb>vergentia, lentibus in tubum compositis, se mutuo tollunt; sublata ergo <lb></lb>convergentia et emendata nimia divergentia, sequitur distincta visio ” (ibi, <lb></lb>pag. </s>

<s>56). </s></p><p type="main">

<s>Che veramente l&#039;error fatto dal Keplero intorno al divisar le immagini <lb></lb>nelle lenti concave sia stato precipua causa, per cui egli riuscì tanto infe­<lb></lb>riore a sè stesso nello spiegar la ragione del canocchiale olandese, lo dimo­<lb></lb>stra l&#039;invenzion del <emph type="italics"></emph>Canocchiale astronomico,<emph.end type="italics"></emph.end> alla quale riuscì il Diottrico <lb></lb>alemanno, per avere escluse le lenti concave e per essersi attenuto alle sole <lb></lb>convesse, delle quali così bene aveva intesa e dimostrata la teoria. </s>

<s>Questo <lb></lb>è davvero il primo Canocchiale che non sia stato offerto dal caso, e di cui <lb></lb>può dir con coscienza il suo Autore che lo ritrovò <emph type="italics"></emph>doctrinae de refractio­<lb></lb>nibus innixus.<emph.end type="italics"></emph.end> Intorno alla ragione di questo nuovo strumento, annunziato <lb></lb>così per la prima volta al pubblico sotto forma di problema: <emph type="italics"></emph>duobus con­<lb></lb>vexis maiora et distincta praestare visibilia sed everso situ,<emph.end type="italics"></emph.end> il Keplero di­<lb></lb>scorre al modo seguente: “ Et quia imago rei visibilis est eversa per unam <lb></lb>lentem, lens vero propior non evertit denuo quod accipit a remotiori, sed <lb></lb>sic ut accipit ad oculum transmittit ex supposito: accipit autem respectu <lb></lb>rei visibilis imaginem eversam; eversam igitur respectu rei visibilis ad ocu­<lb></lb>lum mittit. </s>

<s>Et quia imago ipsa eversa, prope punctum concursus maior ap­<lb></lb>paret re ipsa, remotius aequalis et adhuc remotius minor; imago igitur haec <lb></lb>sic eversa, ubi fuerit ampliata per lentem propiorem, duobus primis casi­<lb></lb>bus maior omnino evadet re ipsa, ultimo casu vel maior vel aequalis vel <lb></lb>minor, prout fuerit lentium inter se proportio, quae est in arbitrio artifi­<lb></lb>cis ” (ibi, pag. </s>

<s>43). La teoria insomma di questo nuovo Telescopio, è se­<lb></lb>condo il Keplero semplicissima: L&#039;immagine reale e rovesciata dell&#039;obiettivo, <lb></lb>si rappresenta come oggetto alla vista dell&#039;oculare, ed è da lui virtualmente <lb></lb>ingrandito, come nel Microscopio. </s></p><p type="main">

<s>Benchè primo inventore di questo Canocchiale astronomico sia general­<lb></lb>mente riconosciuto l&#039;Autore della LXXVI proposizione della Diottrica, stam­<lb></lb>pata nel 1611 in Augusta, nonostante Francesco Fontana, pubblicando in <lb></lb>Napoli nel 1646 le sue <emph type="italics"></emph>Novae coelestium terrestriumque verum obser­<lb></lb>vationes,<emph.end type="italics"></emph.end> incomincia così la sua Prefazione: “ Tubi quadam Optici a me <lb></lb>anno 1608 duobus lentibus convexis compositi inventione reperta.... ” </s></p><p type="main">

<s>Ma del Canocchiale astronomico che egli afferma essere stato da sè in­<lb></lb>ventato, <emph type="italics"></emph>de optico tubo astronomico ab Auctore invento<emph.end type="italics"></emph.end> ne tratta il Fon­<lb></lb>tana di proposito nel cap. </s>

<s>VII del libro, dove fra le altre si leggono le se­<lb></lb>guenti parole: “ Insuper anno 1608 alium tubum opticum armatum scilicet <lb></lb>duplici lente convexa construxi ”. </s>

<s>Non è per questo che l&#039;Artefice napole­<lb></lb>tano voglia venire in contesa con l&#039;astronomo tedesco<gap></gap> dopo aver chiamato <pb xlink:href="020/01/382.jpg" pagenum="363"></pb>testimoni del fatto che cioè egli non vide la Diottrica del Keplero prima <lb></lb>del 1614, così conclude: “ Mirum autem non est recensitum Keplerum Ger­<lb></lb>maniae, meque Neapoli talis inventionis authores existere: enimvero omnes <lb></lb>duobus talentis, intellectu videlicet et operatione ditati sumus ” (pag. </s>

<s>20). </s></p><p type="main">

<s>Se si potesse provar con documenti più certi che il Fontana costruì per <lb></lb>pratica il canocchiale nel 1608, converrebbe dire che l&#039;occhialaio napoletano <lb></lb>s&#039;incontrò nell&#039;invenzione dello strumento nel tempo stesso con l&#039;occhialaio <lb></lb>olandese, ma perchè, ripetiamo, non abbiamo di ciò i documenti certi, e il <lb></lb>Fontana non fa autorità in causa propria, concludiamo il discorso, che ci ha <lb></lb>divagato dal primo soggetto, dicendo che nel 1611 erano stati fatti intorno <lb></lb>alla Diottrica specialmente in Italia notabili progressi. </s>

<s>Il Porta e il Mauro­<lb></lb>lico avevano applicato la Geometria ai raggi rifratti nelle lenti concave e nelle <lb></lb>convesse; il De Dominis aveva tentato di concluder la teoria del Canocchiale <lb></lb>da quegli stessi teoremi diottrici dimostrati, e il Keplero aveva di più ritro­<lb></lb>vato il nuovo Canocchiale astronomico scortovi dalla scienza delle rifrazioni. </s></p><p type="main">

<s>Tre anni dopo, nel 1614, Giovanni Tarde, passando per Firenze, fu a <lb></lb>far visita a Galileo, e dopo varii discorsi “ je l&#039;interpellay, dice lo stesso <lb></lb>Tarde, sur les réfractions et moyen de former le cristal du Telescope en <lb></lb>telle sorte que les obiets s&#039;agrandissent et s&#039;approchent à telle proportion <lb></lb>qu&#039;on vout. </s>

<s>A cela il me respondit que ceste science n&#039;estoit pas encore <lb></lb>bien cogneue; qu&#039;il ne sçavoit pas que personne l&#039;êut traicté autres que <lb></lb>ceux qui traitent la Perspective, si ce n&#039;est Joannes Keplerus, mathémati­<lb></lb>cien de l&#039;Empereur, qui en a faict un livre exprès, mais si obscur, qu&#039;il <lb></lb>semble que l&#039;autheur mesme ne s&#039;est pas entendu ” (Boncompagni, Bullet­<lb></lb>tino ecc, T. XX, Luglio 1887). </s></p><p type="main">

<s>Se nel numero di coloro <emph type="italics"></emph>qui traitent la Perspective,<emph.end type="italics"></emph.end> intendesse Ga­<lb></lb>lileo di comprendere i soli Alhazen e Vitellione con quel poco e inconclu­<lb></lb>dente che toccarono delle rifrazioni, o se intendesse aggiungervi il Porta e <lb></lb>il Maurolico, per quel tanto di più, di che avevano fatto progredire la scienza; <lb></lb>è per noi cosa dubbia, ma pur possiamo con certezza affermare che ingiu­<lb></lb>stamente escluse Galileo il De Dominis dal numero di coloro che avevano <lb></lb>trattato delle rifrazioni applicate al Canocchiale. </s>

<s>Nè si può scusare coll&#039;igno­<lb></lb>ranza del fatto, giacchè sappiamo che il Sagredo nel Giugno del 1612, aven­<lb></lb>dogli prima domandato se aveva <emph type="italics"></emph>veduto un trattato dell&#039;Arcivescovo di Spa­<lb></lb>latro circa l&#039;occhiale<emph.end type="italics"></emph.end> (Alb. </s>

<s>VIII, 213) e avendogli Galileo risposto di no, <lb></lb>il Sagredo stesso, accompagnatolo con lettera del dì 7 Luglio, gli mandò <lb></lb>poi quel Trattato (Alb. </s>

<s>Suppl., pag. </s>

<s>58). </s></p><p type="main">

<s>Quanto al Keplero non si può negar che, così nella Diottrica come in <lb></lb>tutte l&#039;altre sue opere, non sia ad esprimersi difficile e duro, nè si potrebbe <lb></lb>pure affermare che tutti con chiarezza fossero condotti e conclusi i suoi teo­<lb></lb>remi diottrici, ma in ogni modo sembrerà ingiusto a ciascuno imparziale <lb></lb>Galileo, il quale, non potendo negare il fatto, che cioè il Matematico del­<lb></lb>l&#039;Imperatore aveva scritto intorno al Canocchiale <emph type="italics"></emph>un livre exprès,<emph.end type="italics"></emph.end> soggiunge <lb></lb><emph type="italics"></emph>mais si obscur qu&#039;il semble que l&#039;autheur mesme ne s&#039;est pas entendu.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/383.jpg" pagenum="364"></pb><p type="main">

<s>Questi discorsi insomma fatti al Tarde a noi sembrano tante premesse <lb></lb>preparate da Galileo all&#039;unico fine di poter concludere, che nessun altro <lb></lb>prima di lui aveva chiaramente trattato delle rifrazioni nel canocchiale, e <lb></lb>che questa nuova scienza si doveva aspettar da quel Trattato promesso nel <lb></lb>Nunzio Sidereo: Trattato che andò a stemperarsi in poche pagine, scritte <lb></lb>per incidenza nel Saggiatore. </s>

<s>E ora è necessario che riprendiamo in mano <lb></lb>questo libro per decider se tanto vi sia veramente promossa dall&#039;Autore la <lb></lb>scienza del Canocchiale, da doversi tenere a vile ciò che vi specularono at­<lb></lb>torno il Porta, il De Dominis e il Keplero. </s>

<s>Ma prima conviene ai tre com­<lb></lb>memorati aggiungerne un quarto, nella persona stessa del Tarde, a cui pa­<lb></lb>rendo queste cose da&#039;suoi predecessori <emph type="italics"></emph>a quibusdam quidem leviter delibata <lb></lb>fuisse et ab aliis nimia quodam obscuritate,<emph.end type="italics"></emph.end> venne in pensiero di dover <lb></lb>egli entrare a trattarne più di proposito e con chiarezza maggiore. </s></p><p type="main">

<s>In appendice infatti alla <emph type="italics"></emph>Borbonia Sidera,<emph.end type="italics"></emph.end> libro stampato in Parigi <lb></lb>nel 1620, pose un trattatello intitolato <emph type="italics"></emph>Telescopium.<emph.end type="italics"></emph.end> Si prepara, come gli <lb></lb>altri che lo avevano preceduto, a concluder la ragione dello strumento dal <lb></lb>modo di operar delle lenti, e nella proposizione XLI dimostra la teoria del <lb></lb>Microscopio semplice in termini non punto differenti da quelli del Keplero. </s>

<s>Se <lb></lb>non che egli mesce alla verità quell&#039;errore, in cui cadde a principio Gali­<lb></lb>leo, del creder cioè che le lenti condensando la luce faccian sì che gli og­<lb></lb>getti appariscan più grandi: “ Dico, beneficio influentiae, plures radios oculi <lb></lb>pupillam ingredi et ob illam confluentiam obiectum videri mole auctum ” <lb></lb>(ibi, pag. </s>

<s>80). </s></p><p type="main">

<s>Nel divisar poi il modo del rappresentarsi le immagini virtuali nelle <lb></lb>lenti concave, il Tarde è il più preciso di tutti gli Autori che l&#039;hanno pre­<lb></lb>ceduto. </s>

<s>Leggasi nella proposizione XLVIII così formulata: <emph type="italics"></emph>Cava lente obiectum <lb></lb>videtur mole auctum.<emph.end type="italics"></emph.end> Ecco com&#039;ei la conduce e la conclude: “ Cava lens <lb></lb>extrorsum frangit radios, qui ad oculum accedunt diffluentes, et ad concur­<lb></lb>sum versus obiectum tendentes. </s>

<s>At res existimantur asse in loco ex quo <lb></lb>radii deferuntur, cum pupillam intrant; venientes ergo quasi ex concursu, <lb></lb>visibile repraesentatur minus quam sit ” (pag. </s>

<s>80). </s></p><p type="main">

<s>Nonostante, nel venire ad applicare la lente concava per oculare del <lb></lb>Telescopio, anch&#039;egli, come il De Dominis e il Keplero, non ne conosce l&#039;uf­<lb></lb>ficio, per cui, abbandonata la scienza diottrica, ricorre a una certa Filoso­<lb></lb>fia, che si potrebbe chiamare <emph type="italics"></emph>allopatica,<emph.end type="italics"></emph.end> assioma della quale è: <emph type="italics"></emph>contraria <lb></lb>contrariis pelli vel saltem emendari<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>86). Ecco infatti come, an­<lb></lb>ch&#039;egli ammettendo che la divergenza della concava emendi il soverchio con­<lb></lb>verger della convessa, concluda il modo d&#039;operar delle lenti nel Canocchiale: <lb></lb>“ Oculus in concursu omnia videt confusa et obliterata. </s>

<s>Post concursum <lb></lb>imminuta et eversa positione. </s>

<s>Lens cava radios dispergit, quae dispersio vi­<lb></lb>sui obest, et eadem prope oculum confusionem parit. </s>

<s>Horum ergo vitrorum <lb></lb>opus est certa et debita compositione ” (pag. </s>

<s>84). </s></p><p type="main">

<s>Il Tarde, che ce ne aveva dianzi sviato, è quello che ora ci riconduce <lb></lb>al <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> imperocchè chi non riconosce in queste ultime parole citate <pb xlink:href="020/01/384.jpg" pagenum="365"></pb>quello stesso famoso discorso riferito nel paragrafo XIII dello stesso libro <lb></lb>del Saggiatore a pag. </s>

<s>208 del IV Tomo delle Opere; discorso da cui dice <lb></lb>Galileo di essere stato condotto a incontrarsi nell&#039;invenzione del Telesco­<lb></lb>pio? </s>

<s>E per di più non ricorre anch&#039;egli, Galileo, in certo modo alla Filo­<lb></lb>sofia allopatica del Tarde, quando dice che la lente concava è come la <emph type="italics"></emph>con­<lb></lb>traffaccia<emph.end type="italics"></emph.end> della convessa, e <emph type="italics"></emph>l&#039;ultimo bilancio e saldo delle partite?<emph.end type="italics"></emph.end> ” (ivi, <lb></lb>pag. </s>

<s>202). </s></p><p type="main">

<s>Potrebb&#039;esser che il Francese ripetesse i detti stessi di Galileo, pub­<lb></lb>blicandoli tre anni prima di lui, ma in ogni modo que&#039;detti erano stati <lb></lb>pronunziati prima dal De Dominis e dal Keplero, i quali ambedue insomma <lb></lb>consuonano con quell&#039;altro celebre pronunziato, scritto tanti anni prima nel <lb></lb>cap. </s>

<s>X del XVII libro della <emph type="italics"></emph>Magia Naturale: “ Concavo longe parva vides <lb></lb>sed perspicua; convexo proprinqua maiora sed turbida: si utrumque recte <lb></lb>componere noveris, et longinqua et proxima maiora et clara videbis ”.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ripensando ora a ciò che fu ostacolo a tutti i predetti speculatori, in <lb></lb>riuscir felicemente a intendere la ragione del Telescopio, si vede come si <lb></lb>riduca tutto quell&#039;ostacolo nella lente concava, il modo d&#039;operar della quale <lb></lb>sull&#039;immagine rappresentata dalla convessa era rimasto a tutti un mistero. </s>

<s><lb></lb>Nè il De Dominis nè il Keplero, nè il Tarde nè Galileo s&#039;erano ancora ac­<lb></lb>corti che l&#039;oggettivo dipinge un&#039;immagine reale e rovesciata innanzi all&#039;ocu­<lb></lb>lare, il quale l&#039;ingrandisce virtualmente e tutt&#039;insieme la renda diretta. </s>

<s>Vero <lb></lb>è bene che Galileo parla del vetro concavo che dilata i raggi <emph type="italics"></emph>e forma il <lb></lb>cono inverso<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>202), ma, lasciamo stare che il cono inverso è for­<lb></lb>mato pure dal vetro convesso, quando si riceva l&#039;immagine al di là del foco, <lb></lb>questo anzi veniva a complicare più che mai il mistero, perchè restava an­<lb></lb>cora a intendere come mai l&#039;immagine ricevuta per proiezione si rappre­<lb></lb>sentasse al rovescio, e l&#039;occhio nonostante direttamente applicato la rendesse <lb></lb>nella posizione sua naturale. </s></p><p type="main">

<s>Eppure, prima che da&#039;quattro insigni Autori sopra citati si venisse in <lb></lb>pubblico a profferire una scienza del Canocchiale, riuscita nel suo princi­<lb></lb>pale intento fallace, eravi stato già chi molto meglio di loro aveva colto nel <lb></lb>segno. </s>

<s>Il solo Porta, infino dall&#039;Agosto del 1609 avea dato a vedere di es­<lb></lb>sersi inteso che l&#039;ufficio dell&#039;oculare era quello di render le immagini rap­<lb></lb>presentate dall&#039;obiettivo <emph type="italics"></emph>chiare e diritte. </s>

<s>“<emph.end type="italics"></emph.end> Mirando con quel solo primo (col <lb></lb>vetro convesso) si vedranno le cose lontane vicine, ma perchè la vista non <lb></lb>si fa nel cateto, paiono oscure ed indistinte. </s>

<s>Ponendovi l&#039;altro come con­<lb></lb>cavo, che fa il contrario effetto, si vedranno le cose <emph type="italics"></emph>chiare e diritte ”<emph.end type="italics"></emph.end> (Ven­<lb></lb>turi, Memor. </s>

<s>ecc. </s>

<s>ediz. </s>

<s>cit., P. I, pag. </s>

<s>83). Aveva perciò ragione di dire al <lb></lb>principe Cesi che tutti i libri che gli aveva mandato del Telescopio, primi <lb></lb>fra&#039;quali saranno stati quelli del De Dominis e del Keplero, <emph type="italics"></emph>non sanno se <lb></lb>sieno vivi e parlano allo sproposito, perchè non sanno di Prospettiva<emph.end type="italics"></emph.end> (ivi, <lb></lb>pag. </s>

<s>85). Soggiunge poi di aver dato mano egli stesso a scrivere sull&#039;im­<lb></lb>portante soggetto un libro, che se fosse stato visto prima dal mondo, <emph type="italics"></emph>non<emph.end type="italics"></emph.end><lb></lb><gap></gap></s></p><pb xlink:href="020/01/385.jpg" pagenum="366"></pb><p type="main">

<s>Ci è senza dubbio in queste parole molto di presunzione, ma pure è <lb></lb>un fatto che il Porta aveva penetrato più addentro al mistero diottrico di <lb></lb>tutti gli altri, che vi si stillarono il cervello dopo di lui; ond&#039;è che dietro <lb></lb>que&#039;teorici insegnamenti potè in Roma il principe Cesi aver canocchiali <lb></lb>avanti che là capitasse nessun esempio de&#039;galileiani. </s>

<s>In ogni modo però <lb></lb>prima di riuscire alla difficile soluzion del problema bisognava fare alla Diot­<lb></lb>trica altri e più segnalati progressi de&#039;quali dobbiamo ora passare a fare <lb></lb>brevemente la storia. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Disperando oramai, per gli esempi de&#039;predecessori, di aver a ritrovar <lb></lb>nella nuova scienza Diottrica una guida sicura da non andare smarriti per <lb></lb>quegli intricati laberinti, dentro a cui si aggirano i raggi luminosi tra&#039;due <lb></lb>vetri de&#039;Canocchiali; Cristoforo Scheiner pensò meglio di ridursi ne&#039;termini <lb></lb>più positivi dell&#039;esperienza. </s>

<s>Egli dunque così andò investigando le proprietà <lb></lb>diottriche delle lenti e giunse per questa via a conclusioni non nuove, ma <lb></lb>in vario modo dimostrate e, per quel ehe riguarda le immagini rappresen­<lb></lb>tate nelle lenti concave, dall&#039;osservazione de&#039;fatti rese più chiare: “ Deinde <lb></lb>omnibus (concavis) hoc est commune ut baseos communis stationem et pictu­<lb></lb>ram in charta amplificent, et porro a vitro convexo protrudant, ita ut di­<lb></lb>stantia eiusdem ab eodem maior evadat, quam si ipsum concavum ad con­<lb></lb>vexum non esset adhibitum ” (Oculus, Oeniponti, 1619, pag. </s>

<s>160). </s></p><p type="main">

<s>L&#039;esperienza confermatrice di questa proposizione vien così dall&#039;Autore <lb></lb>stesso descritta: “ Statue convexum sphaerae parvae segmentum ad fora­<lb></lb>men obscurae camerae, obtende chartam ut excipias certam aliquam rei <lb></lb>extra positae imaginem, picturam praecisam et accuratam. </s>

<s>Intersere omni­<lb></lb>bus immotis vitrum concavum ea vitrorum intercapedine, quam ipsa in tu­<lb></lb>bum compacta requirunt: videbis obiectum multo maius esse, quam fuerat <lb></lb>ante per solum convexum, et si speciem illam distinctam exoptas, oportet <lb></lb>ut chartam aliquanto amplius a priore statione elonges ” (ibi, pag. </s>

<s>161). </s></p><p type="main">

<s>Questa esperienza però è viziata da un&#039;ipotesi falsa, la quale consiste <lb></lb>nell&#039;ammetter che la lente concava, la quale protrude e ingrandisce l&#039;im­<lb></lb>magine, sia collocata, rispetto alla convessa, in quella positura conveniente <lb></lb>a dover produrre gli effetti del Canocchiale, imperocchè allora l&#039;immagine <lb></lb>stessa, ricevuta per proiezione, è protrusa e ingrandita si, ma pure anco è <lb></lb>rovesciata. </s>

<s>Notabile è che ciò non fosse avvertito dallo Scheiner, il quale <lb></lb>altrove si propone a risolvere il problema <emph type="italics"></emph>Cur vitrum interius, ante con­<lb></lb>cursum anterioris collocatum, species non erigit?<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>180) e lo ri­<lb></lb>solve assai bene, e in modo che applicata quella soluzione al Canocchiale, <lb></lb>gli avrebbe fatto forse, meglio che a tutti gli altri, intender l&#039;ufficio proprto <lb></lb>dell&#039;oculare, che è quello d&#039;ingrandire <emph type="italics"></emph>et post binam decussationem<emph.end type="italics"></emph.end> d&#039;ad­<lb></lb><gap></gap></s></p><pb xlink:href="020/01/386.jpg" pagenum="367"></pb><p type="main">

<s>Non ritrovando perciò, nemmen così, quella felice riuscita she s&#039;aspet­<lb></lb>tava, si rivolse lo Scheiner agli argomenti di analogia, e gli parve di ritro­<lb></lb>varli nella somiglianza che passa tra il modo come opera la natura nell&#039;oc­<lb></lb>chio, e l&#039;arte nel Telescopio. </s>

<s>Come la camera oscura aveva rivelati i misteri <lb></lb>dell&#039;occhio, così sperava il nostro Autore che l&#039;occhio stesso rivelerebbe i <lb></lb>misteri del nuovo strumento. </s>

<s>Nella <emph type="italics"></emph>Rosa Ursina<emph.end type="italics"></emph.end> infatti, stampata in Brac­<lb></lb>ciano tra il 1626 e il 1630, lo Scheiner intitola il cap. </s>

<s>XXIII del II libro: <lb></lb><emph type="italics"></emph>Oculi et Telescopii lentiumque telescopicarum comparatio: naturae et artis <lb></lb>admirabilis conspiratio<emph.end type="italics"></emph.end> (pag. </s>

<s>106) e nel capitolo appresso si propone di <lb></lb>dimostrare: <emph type="italics"></emph>Ut tubus oculum, sic oculus in multis arte sequitur tubum<emph.end type="italics"></emph.end><lb></lb>(ibi, pag. </s>

<s>112). Se veramente l&#039;Autore con quella Tavola, che rappresenta <lb></lb><emph type="italics"></emph>expressas septem diversas Tubi cum oculo et huius cum Tubo, in specie­<lb></lb>bus visibilibus recipiendis et praesentandis, rationes et comparationes<emph.end type="italics"></emph.end> (ibi, <lb></lb>pag. </s>

<s>106), riuscisse nell&#039;intento, lasceremo giudicarlo a fra Fulgenzio Mi­<lb></lb>canzio, in una sua lettera, dove si trovano le seguenti parole dirette a Ga­<lb></lb>lileo: “ Il signor Aproino è qui in Venezia ed è dietro alla Rosa Ursina <lb></lb>colle male parole. </s>

<s>L&#039;ho pregato a veder particolarmente quelle tante figure, <lb></lb>ove il Gesuita vuole dichiarar la natura del Canocchiale col confronto del­<lb></lb>l&#039;occhio, perchè, a dirla, in tal cosa dove avevo gran curiosità d&#039;intendere <lb></lb>la dimostrazione, o che io non ne sono stato capace, come credo, o li detti <lb></lb>dello Scheiner sono pure affermazioni senza prova ” (Alb. </s>

<s>X, 140). </s></p><p type="main">

<s>Pur troppo è vero che quelle dell&#039;Autor della Rosa Ursina sono affer­<lb></lb>mazioni senza prova, nè poteva essere altrimenti, perchè lo Scheiner s&#039;era <lb></lb>grandemente ingannato, credendo che tra l&#039;occhio e il Canocchiale passasse <lb></lb>quella stretta rassomiglianza che tra l&#039;occhio e la camera oscura, della quale <lb></lb>qui cade opportuno accennar brevemente alla storia. </s></p><p type="main">

<s>Leonardo da Vinci, nello studiar l&#039;anatomia dell&#039;occhio per poi poterlo <lb></lb>dipingere con più verità e con maggiore espressione, osservando le pitture <lb></lb>che si rappresentavano arrovesciate sul fondo di lui, per via de&#039;raggi colorati <lb></lb>passati attraverso al foro della pupilla, inventò la camera oscura, che de­<lb></lb>scrisse ne&#039;suoi Manoscritti, colle seguenti parole, tradotte dal Venturi in <lb></lb>francese: “ Lorsque les images des obiets éclairés penetrent par un petit <lb></lb>trou rond dans un appartement tres-obscur, recevez ces images dans l&#039;in­<lb></lb>terieur de l&#039;appartement sur un papier blanc situé a quelque distance du <lb></lb>trou, vous verrez sur le papier tous les obiets avec leurs propres formes et <lb></lb>couleurs, il seront diminués de grandeur, il se presenteront dans une situa­<lb></lb>tion renversée ” (Essai ecc., Parigi 1797, pag. </s>

<s>23). </s></p><p type="main">

<s>Il nuovo strumento non doveva servire a semplice curiosità, ma fu ap­<lb></lb>plicato agli usi del disegno, per cui ne fu trasmessa la memoria, non dai <lb></lb>Manoscritti, da nessuno veduti, ma dalla parola viva e dalle pratiche ope­<lb></lb>razioni de&#039;Discepoli di Leonardo. </s>

<s>Da qualcuno di essi ne ebbe notizia il gio­<lb></lb>vanetto Giovan Batista Porta, cbe andava pellegrinando a raccogliere di que­<lb></lb>ste novità, dovunque ne trovasse, ma specialmente appresso ai cultori dell&#039;arte. </s>

<s><lb></lb>Ei pubblicò l&#039;invenzione nel cap. </s>

<s>II dell&#039;ultimo de&#039;quattro libri della <emph type="italics"></emph>Magia<emph.end type="italics"></emph.end><pb xlink:href="020/01/387.jpg" pagenum="368"></pb><emph type="italics"></emph>Naturale,<emph.end type="italics"></emph.end> di cui la prima edizione fu fatta, come altrove dicemmo, nel 1550. <lb></lb>La descrizione del Porta consuona pienamente con quella di Leonardo, e per <lb></lb>indizio che una tal primizia fu presentata all&#039;Autore da qualcuno de&#039;pro­<lb></lb>fessori dell&#039;arte del disegno, si legga ciò che ivi ne scrive delle applicazioni <lb></lb>da farsi dello strumento agli usi della pittura: “ Hinc evenit ut quisque <lb></lb>picturae ignarus rei alicuius stylo describere possit, dummodo solum colo­<lb></lb>res assimilare discat hoc in subiectam tabulam vel soli diusculum papyrum <lb></lb>imagine repercussa. </s>

<s>Erit enim perito facillimum. </s>

<s>Si sol defecerit id alio imi­<lb></lb>taberis lumine, pleraque alia eveniunt et cognosces, quam et enarrare possi­<lb></lb>mus, praecipue si diligens inspector pertractaverit ” (Neapoli, 1558, pag. </s>

<s>144). </s></p><p type="main">

<s>Il Benedetti poi perfezionò l&#039;invenzione di Leonardo, applicando al foro <lb></lb>una lente convessa, secondo la descrizione ch&#039;ei ne fa in una delle sue Epi­<lb></lb>stole, raccolte nel libro delle Speculazioni, la prima edizione del quale si sa <lb></lb>essere stata fatta nel 1580, e nel 1599 fu fatta in Venezia la seconda, dalla <lb></lb>quale trascriviamo qui le parole dell&#039;Autore: “ Ad hoc tamen propositum <lb></lb>nolo tibi silentio involvi mirabilem quendam effectum eiusmodi rei. </s>

<s>Hoc est <lb></lb>ut fiat foramen illud rotundum, magnitudinis tamen unius specilli, quod <lb></lb>foramen obturatur mediante uno illorum specillorum, quae pro senibus (non <lb></lb>brevis visionis) conficiuntur, hoc est quorum ambae superficies convexae <lb></lb>sunt, non autem concavae. </s>

<s>Deinde apponatur folium album papiri, adeo <lb></lb>distans a foramine ut extrinseca obiecta in eo appareant. </s>

<s>Quae quidem obiecta <lb></lb>si a sole illustrata fuerint, tam clara et distincta videbuntur ut nihil pul­<lb></lb>chrius delectabiliusque videri poterit, inversa tamen. </s>

<s>Sed si ea directa vi­<lb></lb>dere voluerimus, hoc optime faciemus mediante reflexione alicuius speculi <lb></lb>plani ” (pag. </s>

<s>270). Il Porta, cinque anni dopo, tornando a pubblicar la sua <lb></lb>Magia in XX libri, nel cap. </s>

<s>VI del XVII tornò a descrivere la Camera <lb></lb>oscura, con quegli stessi perfezionamenti che v&#039;avea già introdotto il Fisico <lb></lb>veneziano. </s></p><p type="main">

<s>Dietro ciò si comprende bene come la lente cristallina, applicata dal <lb></lb>Benedetti al foro della camera oscura, presentava una somiglianza con l&#039;oc­<lb></lb>chio più parvente e più provata di quel che non facesse lo strumento di <lb></lb>Leonardo, specialmente da poi che il Maurolico era venuto a render così <lb></lb>evidenti gli uffici, che fa nell&#039;occhio l&#039;umor cristallino. </s>

<s>Ma passar dall&#039;oc­<lb></lb>chio al Canocchiale, come pretendeva lò Scheiner, era cosa più ardua, per­<lb></lb>chè la fisiologia della vista naturale implicava maggiori difficoltà di quelle, <lb></lb>che si potevano incontrar nella diottrica della vista artificiale. </s>

<s>Piuttosto che <lb></lb>servirsi dell&#039;occhio a intendere il Canocchiale sarebbe stato più conveniente <lb></lb>servirsi di questo a intender quello, come per esempio si vede nella cele­<lb></lb>bre questione delle immagini rovesciate sopra la retina, le quali si vedon <lb></lb>diritte a quel modo e per quella stessa ragione, che si vedon diritte nel <lb></lb>Canocchiale, benchè si rappresentino a rovescio ricevute sopra una carta per <lb></lb>proiezione. </s></p><p type="main">

<s>In ogni modo, la principale delle ragioni per cui così lo Scheiner come <lb></lb>tutti gli altri s&#039;incontrarono in quelle insuperabili difficoltà, dee senza dub-<pb xlink:href="020/01/388.jpg" pagenum="369"></pb>bio ripetersi dall&#039;aver tutti a un modo ignorata la legge dei raggi refratti. </s>

<s>Or <lb></lb>perchè una tal legge fu dal Cartesio così ben dimostrata, chi non s&#039;aspet­<lb></lb>terebbe mai che la teoria del Canocchiale non si dovesse aver finalmente <lb></lb>chiara e spiegata dal celebre Autore, in quel cap. </s>

<s>VII della <emph type="italics"></emph>Diottrica,<emph.end type="italics"></emph.end> or­<lb></lb>dinato giusto a trattar <emph type="italics"></emph>De modis visionem perficiendi?<emph.end type="italics"></emph.end> Eppure è un fatto <lb></lb>che la teoria cartesiana è la più goffa di quante altre mai ne avessero spe­<lb></lb>culate i suoi predecessori. </s></p><p type="main">

<s>Parte l&#039;Autore da questo principio: che tanto cioè più grandi si rap­<lb></lb>presentino all&#039;occhio gli oggetti, quanto più di lontano v&#039;entrano per la <lb></lb>pupilla i raggi luminosi incrociati. </s>

<s>“ Unicus tamen adhuc modus has ima­<lb></lb>gines augendi restat, quo nempe efficimus ut radii, ex diversis punctis missi, <lb></lb>quam longissime fieri potest ab oculi fundo decussentur ” (Francof. </s>

<s>1692, <lb></lb>pag. </s>

<s>80). Ora, pensava il Cartesio, che il Canocchiale è un tal artifizio, per <lb></lb>cui i raggi, che s&#039;incrocerebbero sulla superficie dell&#039;occhio, s&#039;incrociano <lb></lb>invece sulla superficie dell&#039;obiettivo, di guisa che il massimo e principale <lb></lb>efficiente della visione telescopica non sarebbe mica costituito dalle lenti, le <lb></lb>quali poco importa che abbiano una figura piuttosto che un&#039;altra, ma sì <lb></lb>dalla lunghezza del tubo: la qual lunghezza potendosi ridurre a qualunque <lb></lb>misura illimitata, fa sì che la potenza, che si può dar dall&#039;artefice a un Ca­<lb></lb>nocchiale, è indefinita. </s>

<s>“ Unicus utpote qui ad obiecta tam accessa quam <lb></lb>inaccessa, usum sui praebere possit, et cuius effectus nullis terminis cir­<lb></lb>cumscribitur; ita ut huius ope, imagines semper in maius augendo usque ad <lb></lb>indefinitam quantitatem expandere possimus ” (ibi). </s></p><p type="main">

<s>L&#039;Huyghens, dop&#039;aver notate queste cartesiane goffaggini, soggiunge: <lb></lb><emph type="italics"></emph>Quod vix credibile de tanto viro, tamque in his rebus versato.<emph.end type="italics"></emph.end> Noi però, <lb></lb>che conosciamo oramai il Cartesio, sappiamo che così fatte goffaggini sono <lb></lb>il frutto legittimo della sua Filosofia naturale, e siam persuasi che, se fosse <lb></lb>tornato a filosofare Aristotile nel 1637, non avrebbe discorso altrimenti dal­<lb></lb>l&#039;Autor della Diottrica intorno alle ragioni del Canocchiale. </s></p><p type="main">

<s>Le parole sopra citate le scriveva l&#039;Huyghens a pag. </s>

<s>166 di un suo <lb></lb>libro, che pur s&#039;intitola la <emph type="italics"></emph>Dioptrica,<emph.end type="italics"></emph.end> ma che tanto differisce dalla Dioptrica <lb></lb>cartesiana, quanto dalle fucate immagini differisce la realtà degli oggetti. </s>

<s><lb></lb>Benchè fosse quell&#039;opera insigne, dalla quale il Newton e la scienza della <lb></lb>luce rifratta ebbero così validi impulsi, pubblicata postuma in Leyda nel 1703, <lb></lb>nonostante erano stati già infino dal 1659 dimostrati e posti in ordine di <lb></lb>trattato i principali teoremi. </s>

<s>Nel <emph type="italics"></emph>Systema Saturnium<emph.end type="italics"></emph.end> infatti citava l&#039;Huy­<lb></lb>ghens la sua Diottrica ne&#039;termini seguenti: “ Illud enim in <emph type="italics"></emph>Dioptricis no­<lb></lb>stris<emph.end type="italics"></emph.end> demonstratum invenietur, speciei per tubum visae ad eam quae nudo <lb></lb>oculo percipitur, hanc secundum diametrum esse rationem, quae distantiae <lb></lb>foci in exteriori vitro, ad illam quae in interiori sive oculari vitro est, foci <lb></lb>distantiam ” (Oper. </s>

<s>var. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>538). </s></p><p type="main">

<s>Questo stesso teorema fu posto poi nella Diottrica per fondamento alla <lb></lb>teoria del Canocchiale, e intorno a ciò così l&#039;Huyghens stesso scrive: “ Quod <lb></lb>enim hic prae caeteris requirebatur, ut data lentium forma ac positu, ex <pb xlink:href="020/01/389.jpg" pagenum="370"></pb>his modus mensuraque amplificandae rei visivac definiretur, id hactenus <lb></lb>praestitum non est. </s>

<s>Nam neque Keplerus hoc docuit, etsi multa laude di­<lb></lb>gnus ob ea quae in Dioptricis primus explicuit. </s>

<s>Neque illo felicior fuit Car­<lb></lb>tesius, imo ut vere dicam a via potius aberravit in his quae de ratione <lb></lb>et effectu Telescopii demonstranda susceperat ” (Dioptr. </s>

<s>Lugd. </s>

<s>Bat. </s>

<s>1703, <lb></lb>pag. </s>

<s>166). </s></p><p type="main">

<s>Rispetto a Galileo però è certissimo ch&#039;ei non seppe dimostrare il teo­<lb></lb>rema diottrico ugeniano, e infatti nel Nunzio Sidereo (Alb. </s>

<s>III, 61, 62) in­<lb></lb>segna il modo di trovar la potenza amplificativa del Canocchiale, non desu­<lb></lb>mendola dall&#039;intrinseca costituzione diottrica di lui, ma dalla comparazione <lb></lb>degli effetti estrinsecamente osservati. </s>

<s>Sembra però che avesse ritrovato di <lb></lb>quello stesso diottrico teorema la conclusione pratica, e ciò s&#039;argomenta da <lb></lb>quel che ne riferisce il Tarde del citato colloquio avuto con Galileo, dal qual <lb></lb>colloquio il Francese trovò da raccoglier e far capitale di due notizie im­<lb></lb>portanti, <emph type="italics"></emph>le premier<emph.end type="italics"></emph.end> delle quali è <emph type="italics"></emph>que tant plus le cristal convexe prend <lb></lb>une portion d&#039;un plus grand cercle et le concave d&#039;un plus petit, tant <lb></lb>plus on voit loin.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma l&#039;Huyghens è veramente il primo che dimostri, nella proposi­<lb></lb>zione XLVIII, con tutto il rigor matematico, e sui fondamenti della scienza <lb></lb>diottrica il teorema che il Telescopio amplifica <emph type="italics"></emph>secundum rationem foci <lb></lb>distantiae lentis convexae ad distantiam puncti dispersus lentis cavae<emph.end type="italics"></emph.end> (ibi, <lb></lb>pag. </s>

<s>167). Come pure è il primo che, in quella stessa proposizione, intorno <lb></lb>alla teoria del Canocchiale, conduce a felice porto i Diottrici, dop&#039;esservisi <lb></lb>tante volte imbarcati, e aver fatti altrettanti naufragi. </s>

<s>Nelle altre proposi­<lb></lb>zioni poi seguita a dimostrare il modo e la ragion dell&#039;ingrandimento degli <lb></lb>astri nel canocchial Kepleriano con due lenti convesse, e ne&#039;canocchiali a tre <lb></lb>e a quattro lenti, procedendo in tutto con quell&#039;ordine e con quell&#039;acume <lb></lb>e profondità d&#039;investigazioni, che è proprio dell&#039;Autore. </s></p><p type="main">

<s>Dovrebbesi a questo punto terminare il presente capitolo della nostra <lb></lb>Storia, ma per tante vie tortuose ci siam dovuti aggirare, e tante volte ab­<lb></lb>biamo dovuto interrompere e riappiccar poi il filo al nostro discorso, che <lb></lb>per maggior chiarezza sentiamo il bisogno e il dovere di ristringerlo in una <lb></lb>breve conclusione. </s></p><p type="main">

<s>A chi ebbe il primo concetto e ne fece intraveder la possibilità, si deb­<lb></lb>bono i primi meriti di un&#039;invenzione, e se così l&#039;avesse intesa il Grisellini <lb></lb>non irragionevolmente avrebbe chiamato, a pigliar una delle prime parti <lb></lb>nell&#039;invenzione del Canocchiale, il suo Paolo Sarpi. </s>

<s>Che poi il giovane Ser­<lb></lb>vita con proporre quella sua lente parabolica avesse ingerito nelle menti il <lb></lb>fermento delle speculazioni, oltre agli esempi sopra citati, giova addur quello <lb></lb>di un uomo, che ebbe amichevoli consuetudini e ricevè ammaestramenti da <lb></lb>fra Paolo, Daniele Antonini, il quale scriveva così in una sua lettera a Ga­<lb></lb>lileo: “ Pensavo questi giorni circa l&#039;effetto di questi occhiali e dietro alle <lb></lb>mie speculazioni parevami che il solo vetro convesso dovesse fare questi ef­<lb></lb>fetti e in maggior perfezione di quello che dal convesso e concavo insieme <pb xlink:href="020/01/390.jpg" pagenum="371"></pb>far veggiamo. </s>

<s>E questo seguivami supponendo che il vetro convesso, nel <lb></lb>rifrangere i raggi, li unisse tutti in un punto, e preso un tal vetro in mano <lb></lb>vedevo che, nell&#039;allontanarlo dall&#039;occhio, mi cresceva l&#039;oggetto mirato, ma <lb></lb>sempre più me lo confondeva, sicchè ho creduto poi e credo ancora che <lb></lb>quel confondersi dell&#039;oggetto non sia per altro, che perchè i raggi fratti non <lb></lb>concorrono nell&#039;istesso punto, ma in diversi, alle quali diversità di concorsi <lb></lb>rimedii, poi in parte il concavo, talchè potendo noi fare un convesso di tal <lb></lb>natura che mandi i raggi fratti ad unirsi in un sol punto, a me pare che, <lb></lb>senz&#039;altro concavo, mettendo l&#039;occhio nel punto dell&#039;unione, vedremmo una <lb></lb>cosa infinitamente lontana, non maggior per sè stessa che il vetro, nello <lb></lb>stesso angolo che veggiamo il vetro. </s>

<s>Ora di tal natura parmi che debba es­<lb></lb>sere un vetro, che abbia la superficie parabolica, e siccome la forma para­<lb></lb>bolica concava riflette i raggi tutti in un punto, il che non fa la sferica; <lb></lb>così debba anco, l&#039;istesso che nella riflessione, serbare nella rifrazione ” <lb></lb>(Alb. </s>

<s>VIII, 139). </s></p><p type="main">

<s>Galileo rispondeva che sarebbe quell&#039;effetto stato meglio prodotto da un <lb></lb>vetro che <emph type="italics"></emph>piuttosto si accosti all&#039;iperbola che alla parabola<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>152) <lb></lb>ma non aveva altra ragione d&#039;asserir ciò dall&#039;autorità in fuori di quel Ke­<lb></lb>plero, che in mezzo a&#039;trucidati fratelli, volutisi ingerire del Canocchiale, è il <lb></lb>solo rimasto semivivo. </s>

<s>Il Kepler in fatti, nella proposizione LIX della Diottrica <lb></lb>aveva, contro il Porta e perciò contro lo stesso Sarpi, così concluso: “ Su­<lb></lb>perficies densi quae parallelos per corpus venientes, post corpus refractione <lb></lb>facta, perfecte concurrere facit, est hyperbolicae adfinis.... Parabola vero, <lb></lb>etsi idem facit, non est tamen similis quaesitae superficiei, ob hanc causam: <lb></lb>nullum enim ad certum angulum sese accomodat ” (Aug. </s>

<s>Vind. </s>

<s>1611, pag. </s>

<s>21). </s></p><p type="main">

<s>Abbiamo detto che Galileo non poteva aver del suo asserto nessuna <lb></lb>buona ragione, perchè tanto egli quanto il Kepler e il Sarpi, erano tutti <lb></lb>ugualmente in un inganno, scoperto poi così dal Cavalieri: “ Gli specchi <lb></lb>sferici e le lenti, le quali sieno poco colme, saranno quasi insieme e para­<lb></lb>boliche e iperboliche, e però accostandosegli tanto faranno ancora gli effetti <lb></lb>a quelli proprinquissimi, il che insieme potrà credo, servire per isgannare <lb></lb>alcuni, che stimano che un paro d&#039;occhiali parabolici o iperbolici fossero per <lb></lb>far l&#039;effetto del Canocchiale, perchè, se così fosse, accostandosi tanto vicino <lb></lb>le lenti sferiche e pochissimo colme alla detta curvità, ce ne dariano pur <lb></lb>qualche segno, il che non si vede, mentre non si accompagnino coì tra­<lb></lb>guardo (oculare) ” (Specchio Ust., Bologna 1650, pag. </s>

<s>130). </s></p><p type="main">

<s>Il modo dunque di mettere in pratica il primo concetto del Sarpi fu <lb></lb>così finalmente dimostrato fallace dalla Geometria del Cavalieri, ma non è <lb></lb>perciò che fra Paolo si debba, nell&#039;invenzione dello strumento da veder le <lb></lb>cose lontane, defraudare dei primi onori. </s>

<s>I secondi onori si debbono al Porta, <lb></lb>che divulgò i concetti del Sarpi nella <emph type="italics"></emph>Magia<emph.end type="italics"></emph.end> e che addirizzò, col Trattato <lb></lb>delle Rifrazioni, le prime vie a sciogliere il difficile problema della vision <lb></lb>telescopica: si debbono i terzi onori a quell&#039;artefice, che primo eseguì ciò <lb></lb>che il Porta aveva proposto, e i quarti onori convengono a Galileo. </s></p><pb xlink:href="020/01/391.jpg" pagenum="372"></pb><p type="main">

<s>Or resta a sodisfar chi legge di una curiosità: come mai Galileo, che <lb></lb>viene in quarto luogo, riuscì a legare così strettamente il suo nome al nuovo <lb></lb>strumento, da non si poter definire altrimenti che chiamandolo <emph type="italics"></emph>Canocchiale <lb></lb>galileiano?<emph.end type="italics"></emph.end> Le ragioni di ciò son varie e la prima si riduce a quell&#039;auto­<lb></lb>rità, che s&#039;era oramai conquistata il Principe della nuova Filosofia, il quale, <lb></lb>benchè non fosse nella invenzione soccorso dalla scienza delle rifrazioni, nè <lb></lb>da altro vi fosse scorto, come dalla somiglianza che in qualche modo passa <lb></lb>tra il Canocchiale e l&#039;occhio, intorno al modo del veder del quale egli così, <lb></lb>contro all&#039;opinion comune aberrava; potè nulladimeno con quella sua au­<lb></lb>torità far velo al difetto delle proprie speculazioni, e far creder sue quelle <lb></lb>mendicate dagli altri. </s>

<s>Si aggiunga lo zelo de&#039;partigiani, i quali si studiavano <lb></lb>d&#039;avvilire i concorrenti nell&#039;invenzione, e di negar loro i diritti, come il Sa­<lb></lb>gredo fece rispetto al Porta, e come, rispetto al Sarpi, poi fece il Dati, rim­<lb></lb>proverandolo di aver fatto un gran torto a Galileo, da lui ben conosciuto e <lb></lb>praticato, <emph type="italics"></emph>non lo nominando punto nè poco dove fa menzione del Canoc­<lb></lb>chiale e delli scoprimenti celesti<emph.end type="italics"></emph.end> (Lettere, Firenze 1825, pag. </s>

<s>160). Eppure <lb></lb>è il vero che il Sarpi invece avrebbe potuto rimproverar giustamente Ga­<lb></lb>lileo, rispetto agli scoprimenti celesti, e rispetto al Canocchiale i documenti <lb></lb>dimostrano che il Dati asserì il falso, forse per non aver ben lette le let­<lb></lb>tere di fra Paolo, o per non avere atteso a quel <emph type="italics"></emph>Matematico di Padova,<emph.end type="italics"></emph.end> di <lb></lb>cui ivi si parla, e che si commemora primo fra tutti coloro, che del Ca­<lb></lb>nocchiale <emph type="italics"></emph>principiarono a valersi per l&#039;Astronomia ”<emph.end type="italics"></emph.end> (Polid., Lett. </s>

<s>cit., <lb></lb>T. II, pag. </s>

<s>41). </s></p><p type="main">

<s>Un&#039;altra delle ragioni, per cui si congiunse con quello del Canocchiale <lb></lb>il nome di Galileo, fu perch&#039;egli riuscì artefice più esperto di tutti gli altri. </s>

<s><lb></lb>Si sa che egli aveva certi suoi <emph type="italics"></emph>artificii da lavorare gli occhiali, delli quali <lb></lb>artificii parte vanno murati<emph.end type="italics"></emph.end> (Alb. </s>

<s>VI, 124) ma s&#039;ignorano i modi partico­<lb></lb>lari di quegli artificii, che l&#039;inventore si studiava di tener, quanto fosse pos­<lb></lb>sibile, segreti. </s></p><p type="main">

<s>Il più efficace segreto però che condusse Galileo a perfezionar di tanto <lb></lb>il Canocchiale, sopra l&#039;opera di tutti gli altri artefici ordinarii, consisteva <lb></lb>nell&#039;aver conosciuto che il buon effetto delle lenti dipende principalmente <lb></lb>dalla loro figura. </s>

<s>Fu per lui una fortuna l&#039;aver da giovane atteso a un&#039;an­<lb></lb>tico insegnamento di Seneca, rinfrescato nel I libro <emph type="italics"></emph>De refractione<emph.end type="italics"></emph.end> dal Porta, <lb></lb>dove, nella proposizione XI, l&#039;Autore così scriveva: “ Sed cur sub vitro et <lb></lb>aquis maiora videantur aliam quoque (Seneca) habet rationem ex rotunda <lb></lb>vasis forma, quam reddemus quum de vitrea pila loquemur ” (Neapoli 1593, <lb></lb>pag. </s>

<s>20). Conforme a questi insegnamenti, occorrendo al giovane Galileo di <lb></lb>toccar la ragione perchè le frutta nel rinfrescatoio appariscano più grandi, <lb></lb>la riconosce anch&#039;egli, come il Filosofo antico, non nell&#039;acqua, ma nella <lb></lb>forma conica del vaso di vetro: “ Verum, non aqua, sed calicis figura, ta­<lb></lb>lis effectus causa ” (Opere, Ediz. </s>

<s>nazion., Firenze 1890, Vol. </s>

<s>I, pag. </s>

<s>314). </s></p><p type="main">

<s>Ma in ogni modo, la principal ragione per cui il Canocchiale a due <lb></lb>lenti, una concava e l&#039;altra convessa, si disse, e non immeritatamente si <pb xlink:href="020/01/392.jpg" pagenum="373"></pb>dura tuttavia a chiamare <emph type="italics"></emph>galileiano,<emph.end type="italics"></emph.end> consiste nell&#039;aver Galileo il primo ap­<lb></lb>plicato lo strumento e scoprir tante nuove maraviglie nel cielo, e nell&#039;averlo <lb></lb>saputo adattare a varii usi astronomici, come per esempio a misurar le <lb></lb>piccole distanze fra le stelle, e fra i satelliti gioviali. </s>

<s>Questa è vera gloria <lb></lb>di lui, e la massima gloria, alla quale egli avrebbe senza dubbio maggior­<lb></lb>mente conferito, se avesse renunziato alle pretensioni di apparir Autore del <lb></lb>Canocchiale, e se, con più sincerità, avesse al pubblico confessato niente <lb></lb>altro più spettargli che le ultime parti nella tanto ambita invenzione. </s></p><pb xlink:href="020/01/393.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>De&#039;Canocchiali del Fontana, del Torricelli e di altri; <lb></lb>del Telescopio a riflessione<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. De&#039;Canocchiali di Girolamo Sirturo e di Francesco Fontana. </s>

<s>— II. De&#039;Canocchiali di Evangelista <lb></lb>Torricelli. </s>

<s>— III. </s>

<s>Del segreto usato dal Torricelli, per lavorare i vetri da Canocchiali. </s>

<s>— IV. </s>

<s>Con­<lb></lb>siderazioni e giudizi intorno al Torricelli come costruttore di Canocchiali, specialmente da ser­<lb></lb>vire per gli usi astronomici. </s>

<s>— V. De&#039;Canocchiali di Cristiano Huyghens. </s>

<s>— VI. De&#039;Canocchiali. </s>

<s><lb></lb>di Giuseppe Campani e di Eustachio Divini. </s>

<s>— VII. De&#039;Telescopi a riflessione. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;ammirazione e la gloria, che Galileo erasi acquistata per sè, e l&#039;uti­<lb></lb>lità che era venuta ai progressi dell&#039;Astronomia, per la invenzione, o di­<lb></lb>ciam più propriamente per la nuova arte squisita, che egli ebbe di fabbri­<lb></lb>care i Canocchiali, non potevano non eccitare gl&#039;ingegni ad emularne gli <lb></lb>esempii, e a studiarsi d&#039;introdurre un qualche perfezionamento in quell&#039;arte <lb></lb>stessa, che dalle mani di un uomo solo, non poteva essere uscita perfetta. </s></p><p type="main">

<s>Fra costoro, che si misero all&#039;opera è da annoverar per primo quel <lb></lb>Girolamo Sirturo, che sul campanile di S. </s>

<s>Marco in Venezia, a cui toccò <lb></lb>la sorte di essere il primo teatro, su cui si rappresentò la nuova scena me­<lb></lb>ravigliosa, faceva spettacolosa mostra de&#039;suoi Canocchiali, rivaleggiando con <lb></lb>Galileo. </s>

<s>Egli ci si mostra quasi cavalier di ventura, che va in cerca di chi <lb></lb>gli insegni la nuova arte stupenda, e trovò, girando così il mondo, in Spa­<lb></lb>gna quell&#039;uomo che andava cercando, e che lo fece penetrare addentro alla <lb></lb>sua segreta officina. </s>

<s>Uscito di lì e tornato a Milano, si dette tutto agli eser­<lb></lb>cizii della Diottrica, ma non già di quella scientifica, sì bene di quella pra­<lb></lb>tica, che egli aveva appresa dal suo buono Spagnuolo in Gironda. </s>

<s>Il Kenlero, <pb xlink:href="020/01/394.jpg" pagenum="375"></pb>egli dice, ha scritto del Canocchiale per scienza, e ha insegnate nel suo libro <lb></lb>tante altre belle cose, le quali <emph type="italics"></emph>quid tamen nobis contulerint, aut quid fa­<lb></lb>cient ad rem nostram, peritorum iudicio relinquam. </s>

<s>Hoc scio neminem <lb></lb>hueusque praestitisse ex arte. </s>

<s>Ego non ex demonstrationibus opticis, non <lb></lb>ex scientia, sed ex innumeris experimentis hausisse fateor, sumptu, la­<lb></lb>bore, et sanitatis detrimento<emph.end type="italics"></emph.end> (pag. </s>

<s>75). </s></p><p type="main">

<s>E perchè della sua arte, così con tanti sacrifizii imparata, ne possa usu­<lb></lb>fruire il mondo, e tu, studioso lettore, possa saper <emph type="italics"></emph>me non mihi ipsi, sed <lb></lb>aliis natum, celebri omni aevo futurum adinventum non adhuc editum, <lb></lb>nec cuiquam praeter uni amico datum, tibi reseratum eo, quisquis es, vir­<lb></lb>tuti addictus libenter suscepturus, ut studii et laboris mei monumentum <lb></lb>aliquod perpetuo apud te et alios studiosos extet<emph.end type="italics"></emph.end> (ibi). </s></p><p type="main">

<s>Il memoriale, di cui qui intende il Sirturo, è il suo <emph type="italics"></emph>Telescopium, sive <lb></lb>Ars perficiendi novum illud Galilaei visorium instrumentum ad Sydera,<emph.end type="italics"></emph.end><lb></lb>libretto di 81 pagine, stampato a Francfort nel 1618, a cui si riferiscono i <lb></lb>passi e i luoghi sopra citati, e dove l&#039;Autore generosamente rivela i più ge­<lb></lb>losi segreti dell&#039;arte sua. </s></p><p type="main">

<s>E benchè questi segreti si risolvano in molti minuti particolari, è da <lb></lb>notar nonostante ciò che egli dice del torno, e del modo di attaccare al ma­<lb></lb>cinello le lenti. </s>

<s>Il Sagredo, che pur ebbe esperta la mano nel fabbricar ca­<lb></lb>nocchiali, confessa di aver <emph type="italics"></emph>fatto inutilmente prova di lavorare al torno i <lb></lb>vetri e pulirli<emph.end type="italics"></emph.end> (Campori, Cart. </s>

<s>gal., Modena 1881, pag. </s>

<s>139), ma il Sirturo <lb></lb>riconosce quello strumento, non solamente utile, ma necessario, ad arroton­<lb></lb>dare le lenti uscite fuori dalla fornace, purchè però sia costruito di ferro <lb></lb>adamantino, come son costruiti i torni, i quali <emph type="italics"></emph>Augustae venundantur.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Quanto al modo poi di attaccare le lenti, perchè stieno, nel lavorarle, <lb></lb>ben salde in sul tornio, ha il Sirturo un segreto importante, il quale con­<lb></lb>siste nel suggerir, per materia cementizia, non l&#039;uso della pece o di altro <lb></lb>caldo bitume, ma del gesso: “ Utere igitur gypso, ubi lens sive plano, sive <lb></lb>convexo adlaboretur ” (ibi, pag. </s>

<s>48). </s></p><p type="main">

<s>Con tutti i suoi segreti ingegnosi artifizii però, non giunse il Sirturo <lb></lb>a lavorar Canocchiali punto migliori di que&#039;primi, che erano usciti dalle <lb></lb>mani di Galileo, e benchè racconti che asceso in cima alla Torre di S. Marco, <lb></lb>per fare esperienza del suo strumento, <emph type="italics"></emph>inde nobilis iuventutis turba tanta <lb></lb>curiositate sursum ferebatur, ut parum abfuerit quin me obrueret<emph.end type="italics"></emph.end> (ibi, <lb></lb>pag. </s>

<s>25) fu nonostante l&#039;Ottico milanese all&#039;ultimo lasciato solo, e al Ma­<lb></lb>tematico di Padova furono dalla Signoria regalati que&#039;tanti zecchini, quanti <lb></lb>Giovanni Bartoli ne contava nella sua lettera al Vinta. </s></p><p type="main">

<s>Mentre intanto Galileo si compiaceva della sua vittoria, la quale veni­<lb></lb>vagli tutti i giorni sempre più confermata da que&#039;tanti, che d&#039;ogni parte <lb></lb>eran costretti di ricorrere a lui, se volevano aver Canocchiali di qualche ef­<lb></lb>fetto; sorse un altro più valido concorrente a tentargli l&#039;animo di gelosia, <lb></lb>e ad amareggiargli il gusto di quella compiacenza. </s>

<s>Fu costui quel France­<lb></lb>sco Fontana che, nell&#039;altro capitolo, udimmo vantarsi d&#039;aver per pratica co-<pb xlink:href="020/01/395.jpg" pagenum="376"></pb>struito il Canocchiale astronomico, tre anni prima che il Keplero lo proget­<lb></lb>tasse per teoria. </s>

<s>Com&#039;ei riuscisse a far ciò, quando ancora alle orecchie di <lb></lb>nessuno in Italia non era approdata la notizia del ritrovato olandese, sarebbe <lb></lb>cosa a sapersi molto importante, ma pur l&#039;Inventore si tace, contentandosi <lb></lb>di addur le testimonianze del padre Cysat, che fa il Canocchiale antico quanto <lb></lb>Tolomeo, e trascrivendo ciò che ne disse il Porta, nel cap. </s>

<s>X del XVII li­<lb></lb>bro della Magia. </s>

<s>“ Adscribitur etiam, egli poi soggiunge, inventio Galilaeo, <lb></lb>sed meo iudicio, vel quia theoricam Portae in praxim deduxit, vel quia per­<lb></lb>fecit ” (Novae Observ., Neap. </s>

<s>1646, pag. </s>

<s>12). Ma perchè la teorica del Porta <lb></lb>appella al Canocchiale coll&#039;oculare concavo, è difficile indovinar se di lì o <lb></lb>d&#039;altrove, deducesse il Fontana la pratica del suo primo canocchiale coll&#039;ocu­<lb></lb>lare convesso, nè men facile pure è rilevar dalle parole di lui come e quando <lb></lb>gli occorresse di dar mano a fabbricar canocchiali sull&#039;andare di quello di <lb></lb>Galileo. </s></p><p type="main">

<s>Comunque sia, di questi nuovi canocchiali venuti da Napoli le prime <lb></lb>notizie e le prime prove testimoniali della loro eccellenza sembra che giun­<lb></lb>gessero alle orecchie, e pervenissero nelle mani di Benedetto Castelli. </s>

<s>Col <lb></lb>nuovo strumento s&#039;eran fatte già nella Luna osservazioni importanti, nelle <lb></lb>sere de&#039;31 Ottobre 1629 e 20 e 24 Giugno 1630. Di ciò dava notizia fra <lb></lb>Fulgenzio Micanzio a Galileo, così scrivendo: “ È stato mandato qui un&#039;os­<lb></lb>servazione della Luna fatta nel 1629 e 1630 da un Francesco Fontana in <lb></lb>Napoli. </s>

<s>Questo, per le relazioni che ho, non è uomo di lettere, ma col con­<lb></lb>tinuo operare e fabbricar canocchiali, si dice esser caduto in una tal sin­<lb></lb>golarità che per le cose del cielo è un miracolo ” (MSS. Gal., P. VI, <lb></lb>T. XIII, c. </s>

<s>110). </s></p><p type="main">

<s>La Selenografia, di cui parla il Micanzio in questa lettera, che è del <lb></lb>31 Luglio 1638; Selenografia che fu pubblicata dall&#039;Autore nelle tre Ta­<lb></lb>vole, che si vedono a pag. </s>

<s>81, 83, 85 della <emph type="italics"></emph>Novae Observationes,<emph.end type="italics"></emph.end> era stata <lb></lb>già, parecchi mesi prima che al frate Veneziano, mandata al Castelli, e da <lb></lb>lui spedita in Genova al Renieri, il quale ne scrive in questi termini a Ga­<lb></lb>lileo: “ È giunto a Genova un ritratto della Luna inviato quà dal P. D. </s>

<s>Be­<lb></lb>nedetto Castelli, con voce d&#039;un Telescopio nuovo inventato da un tal Fon­<lb></lb>tana a Napoli, che mostra più squisitamente le cose che non fanno i consueti. </s>

<s><lb></lb>Non so se ella ne abbia notizia; tuttavia, per quel che dalla detta Seleno­<lb></lb>grafia posso comprendere, non so se sia per corrispondere al grido. </s>

<s>Se ne <lb></lb>ha intesa cosa alcuna, di grazia, me ne dia parte ” (Alb. </s>

<s>X, 285). </s></p><p type="main">

<s>Il Castelli, che della nuova invenzione aveva diffusa la notizia a Ge­<lb></lb>nova, non è credibile che non l&#039;avesse comunicata prima al suo venerato <lb></lb>maestro d&#039;Arcetri. </s>

<s>Comunque sia, è certissimo, che, nel Marzo del 1638, <lb></lb>quando il Renieri scrisse quella lettera, Galileo aveva avuto già da un anno, <lb></lb>la notizia del canocchiale napoletano, e l&#039;aveva avuta da Roma da Raffaello <lb></lb>Magiotti, il quale, il dì 21 Marzo 1637, così gli scriveva: “ Frattanto gli dò <lb></lb>nuova come da Napoli è venuto un cristallo che porta 15 palmi di cannone: <lb></lb><gap></gap> alle stelle <pb xlink:href="020/01/396.jpg" pagenum="377"></pb>Medicee, ma però non termina bene il disco di Giove, mostrandolo imban­<lb></lb>bagiato. </s>

<s>Così ne sono venuti dal medesimo maestro al padre Benedetto di <lb></lb>più corti, ma però, per mio giudizio, molto migliori, talchè tengo per si­<lb></lb>curo che questo strumento sia per avanzare più che mai, nonostante che <lb></lb>molti peripatetici di Roma affermino ostinatamente esser tutte illusioni degli <lb></lb>occhi ” (MSS. Gal., P. VI, T. XIII, c. </s>

<s>14). </s></p><p type="main">

<s>Quando dunque il Renieri faceva quella domanda suggestiva, Galileo <lb></lb>era bene informato dell&#039;eccellenza a cui era giunto, e di quella a cui pro­<lb></lb>metteva di giungere l&#039;Artefice napoletano, ma chi negherebbe che la gelo­<lb></lb>sia non gli venisse a far ombra al giudizio? </s>

<s>Galileo insomma rispondeva al <lb></lb>Renieri che i nuovi Canocchiali del Fontana non erano poi così miracolosi <lb></lb>come si diceva, d&#039;onde ne traeva il buon padre una consolazione curiosa: <lb></lb>“ Ho caro d&#039;intendere che i cristalli di Napoli non siano così miracolosi <lb></lb>com&#039;altri scriveva, perchè al gran prezzo, che di là ne veniva chiesto, mi <lb></lb>disperavo di poterne mai avere ” (Alb. </s>

<s>X, 296). </s></p><p type="main">

<s>Ma pur le acclamazioni, il vento delle quali spiratogli tutto intorno fa­<lb></lb>ceva gelar l&#039;animo a Galileo, si facevano ogni giorno maggiori. </s>

<s>Il Castelli <lb></lb>quasi volesse rintuzzar quel giudizio, di che s&#039;era consolato il Renieri, an­<lb></lb>dava predicando allo stesso Galileo quello del Fontana essere un&#039;<emph type="italics"></emph>occhiale <lb></lb>veramente maraviglioso<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>307) e il Cavalieri, nel fargli motto di un <lb></lb>Canocchiale napoletano posseduto dal Gassendo, gli soggiungeva: “ onde po­<lb></lb>trà dire al Serenissimo Granduca che li suoi canocchiali son per niente, <lb></lb>come anco saranno quelli di V. S. Ecc.ma rispetto a questo ” (MSS. Gal., <lb></lb>P. VI, T. XIII, c. </s>

<s>100). </s></p><p type="main">

<s>Sembran queste parole dette dal Cavalieri per ironia, ma pure egli si <lb></lb>ebbe poco di poi a persuadere che il Granduca aveva avuto da Napoli un <lb></lb>canocchiale da doversi, quello di Galileo davvero, tener per niente. </s>

<s>“ S&#039;in­<lb></lb>tende, così scrive al Castelli, che un tale signor Francesco Fontana in Na­<lb></lb>poli abbia talmente migliorato il Telescopio, che scopre in cielo, cose nuove <lb></lb>e massime nei pianeti, e perchè mi scrivono che V. P. R. ha corrispon­<lb></lb>denza con questo tale, e che egli le abbia mandato uno di questi suoi oc­<lb></lb>chiali, per il Serenissimo Granduca, perciò la prego a farmi tanto favore di <lb></lb>dirmi se è vero o no che quello trapassi di eccellenza quello che ha il si­<lb></lb>gnor Galileo ” (Alb. </s>

<s>X, 319). Il Castelli non poteva non rispondere al Ca­<lb></lb>valieri se non affermando, cosicchè oramai Galileo e i suoi fautori si davan <lb></lb>per vinti. </s></p><p type="main">

<s>Quell&#039;astutissimo fra Fulgenzio però seppe trovare il verso di sollevar <lb></lb>l&#039;animo dell&#039;amico nell&#039;atto stesso di metterlo a confronto coll&#039;emulo vit­<lb></lb>torioso, così scrivendo: “ Sento bene, nei discorsi di tutti li virtuosi e cu­<lb></lb>riosi, quanto sia grave il danno pubblico che V. S. non goda la sanità e <lb></lb>particolarmente quella degli occhi, perchè con li nuovi scoprimenti di que­<lb></lb>sto Occhiale napoletano, avressimo certo qualche considerazione e discorso <lb></lb>degno del signor Galileo. </s>

<s>Mi pare però cosa strana che dal padre Castelli, <lb></lb>che ha veduto e usato l&#039;occhiale, dal padre Cavalieri e dal Glorioso, non si <pb xlink:href="020/01/397.jpg" pagenum="378"></pb>abbia pur un verso sopra tale materia, e nemmeno dallo Scheiner, che vuol <lb></lb>saper tutto ed essere il ritrovatore di tutte le novità ” (ivi, pag. </s>

<s>318). </s></p><p type="main">

<s>Fra Fulgenzio o non era bene informato o non eransi troppo ancora <lb></lb>divulgate le scoperte celesti, che facevansi col nuovo Canocchiale, ma il Ba­<lb></lb>liani un anno dopo scriveva in altri termini allo stesso Galileo: “ Sento gran <lb></lb>cose di ciò che si ritrova in cielo con l&#039;aiuto de&#039;Telescopii lunghissimi di <lb></lb>Napoli, e che Marte sia corniculare, e che sian molte cose nella Luna e <lb></lb>altro. </s>

<s>Che se ciò è vero V. S. ne avrà avuto ragguaglio, e mi duole che <lb></lb>non possa osservarlo ” (ivi, pag. </s>

<s>367). Così, a turbar maggiormente l&#039;animo <lb></lb>di Galileo, veniva il rumore delle nuove scoperte astronomiche, alle quali, <lb></lb>la cecità e la vecchiezza gli toglievano miserabilmente di prender parte. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quell&#039;Artefice napoletano, che aveva mosso le gelosie nell&#039;animo di <lb></lb>Galileo, era venuto, poco di poi, a ridestar nell&#039;animo del Torricelli una <lb></lb>grande emulazione, e anzi una ferma fiducia di superarlo. </s>

<s>Era quell&#039;emu­<lb></lb>lazione fomentata dallo stesso Galileo, a cui pareva di veder sorgere nel <lb></lb>giovane allievo chi venisse a rivendicare l&#039;onore del suo nome, e perciò gli <lb></lb>apriva i suoi segreti, e gli dava que&#039;consigli, e quegli ammaestramenti ap­<lb></lb>presi dall&#039;esperienza e dal lungo e paziente esercizio di tanti anni: era <lb></lb>quella fiducia avvivata dall&#039;eloquente parola e dal valido aiuto del Granduca <lb></lb>Ferdinando, il quale mal sopportava che un illetterato occhialaio di Napoli <lb></lb>avesse così a prevalere sul suo Matematico di Firenze. </s></p><p type="main">

<s>Appena morto Galileo, e succeduto ai servigi del Granduca in suo luogo <lb></lb>il Torricelli, spinto da quella emulazione e incorato da quella fiducia, ei si <lb></lb>dette alacremente all&#039;opera di fabbricare e di dar conveniente figura ai vetri <lb></lb>da Canocchiali, cercando nelle rivelazioni della scienza qualche lume, che <lb></lb>gli fosse scorta nella pratica del suo lavoro. </s>

<s>A questo effetto così scriveva <lb></lb>da Firenze, il dì 25 Ottobre 1642, al Cavalieri: “ Intesi poi che V. P. aveva <lb></lb>qualche speculazione intorno alla figura de&#039;vetri per l&#039;occhiale. </s>

<s>La supplico <lb></lb>a conferirmi qualche cosa, però senza dimostrazione, ma la conclusione sola, <lb></lb>non per filosofarvi, ma per operare. </s>

<s>Vo lavorando conforme ad alcune con­<lb></lb>siderazioni del Galileo e mie, e fino ad ora non ho passato la mediocrità; <lb></lb>non ho però arrivato alli vetri del Fontana ” (MSS. Gal. </s>

<s>Disc., T. 40, c. </s>

<s>119). </s></p><p type="main">

<s>Le ricercate speculazioni diottriche del Cavalieri erano per verità troppo <lb></lb>scarse al bisogno, e non poteva di lì il Torricelli avere speranza di niun <lb></lb>progresso. </s>

<s>Perciò, dandosi più assiduamente che mai a speculare da sè, e a <lb></lb>fare esperienze, poco più che tre mesi dopo scriveva così tutto esultando al <lb></lb>carissimo amico suo Raffaello Magiotti: “ Finalmente, dopo mille vani di­<lb></lb>scorsi e mille castelli in aria, laudato sia Dio, l&#039;invenzione de&#039;vetri mi è <lb></lb>data nelle mani. </s>

<s>Ho gusto che quel Napoletano s&#039;accorga che il Granduca <pb xlink:href="020/01/398.jpg" pagenum="379"></pb>ha in casa sua chi fa quanto lui ed anco più di lui. </s>

<s>Da pochi giorni in qua <lb></lb>ne ho lavorati solo sei, tra i quali quattro ne sono riusciti con difetto ap­<lb></lb>parente; gli altri due sono stati a prova con quel perfettissimo del Gran­<lb></lb>duca fatto dal Fontana, e non si trova una minima differenza, se non che <lb></lb>quello è il meglio che sia stato fatto tra mille vetri, nello spazio di 20 anni, <lb></lb>dal Fontana, ed i miei sono scelti fra sei fatti nello spazio di otto giorni. </s>

<s><lb></lb>Io spero di passar anco più avanti, sebbene il Granduca mi dica di esser <lb></lb>soddisfatto così, ed ieri appunto mi donò di sua mano una collana di 300 <lb></lb>scudi, con medaglia e motto <emph type="italics"></emph>Virtutis praemia.<emph.end type="italics"></emph.end> Spero che V. S. n&#039;averà <lb></lb>gusto e gli sarà sprone di seguitare più avanti. </s>

<s>Mi dispiace bene di non <lb></lb>poter darle qualche luce, poichè il Granduca m&#039;ha imposto silenzio e se­<lb></lb>gretezza. </s>

<s>Che l&#039;invenzione sia la medesima che quella del Fontana, mi par <lb></lb>quasi impossibile: io pagherei bene qualche cosa che la sua non fosse come <lb></lb>la mia ” (ivi, c. </s>

<s>36). </s></p><p type="main">

<s>In questo stesso giorno 6 Febbraio 1643 dava sfogo il Torricelli alla <lb></lb>sua esultanza, scrivendo all&#039;altro suo carissimo amico M. A. Ricci, per dargli <lb></lb>nuova del dono della collana e dell&#039;invenzione de&#039;vetri, che non gli era oc­<lb></lb>corsa per caso, ma l&#039;avea <emph type="italics"></emph>trovata per via di speculazione geometrica, e <lb></lb>con la dottrina e cognizione di queste figurine coniche, e con la scienza <lb></lb>delle rifrazioni<emph.end type="italics"></emph.end> (ivi, c. </s>

<s>83). In che consistesse quella scienza delle rifrazioni <lb></lb>e in che quel segreto scoperto, che gli dette in mano l&#039;invenzione di lavo­<lb></lb>rar vetri più perfetti di quelli stessi di Napoli, lo vedremo tra poco. </s>

<s>Ma in­<lb></lb>tanto seguitiamo i progressi di questo ardente emulo di Francesco Fontana. </s></p><p type="main">

<s>Nel 1646 credeva di esser giunto a tal perfezione, che ai limiti dell&#039;arte <lb></lb>umana non fosse conceduto di passare più avanti. </s>

<s>Scorto dal principio pra­<lb></lb>tico galileiano, secondo il quale i Canocchiali tanto più ingrandiscono, quanto <lb></lb>la distanza focale dell&#039;obiettivo è maggior, rispetto alla distanza focale del­<lb></lb>l&#039;oculare, si dette a fabbricar convessi di segmenti di grandissima sfera, per <lb></lb>i quali convessi riuscivano scarsi, traforati nell&#039;anima per servir di tubi, i <lb></lb>più lunghi abeti delle foreste toscane. </s></p><p type="main">

<s>“ Il Serenissimo Granduca, così scriveva al Ricci, mi comandò che io <lb></lb>facessi un Occhiale di 20 braccia: lo feci, cioè lavorai un vetro d&#039;un palmo <lb></lb>di diametro, che andava lungo 24 passi andanti. </s>

<s>S. A. lo faceva tenere in <lb></lb>mano di un uomo, e poi si allontanava perchè facesse il suo ufficio, e con <lb></lb>quel vetro solo, senz&#039;altro vetro all&#039;occhio, vedeva gli oggetti e chiari giu­<lb></lb>sto come averebbe fatto l&#039;occhialone, ancorchè ciò si facesse in campagna, <lb></lb>nell&#039;aria aperta e luminosa, e che il vetro si tenesse da un uomo a caso e <lb></lb>non fermo bene. </s>

<s>Questa sperienza l&#039;ha replicata tante volte, che è stata ve­<lb></lb>duta da chi non l&#039;ha voluta vedere. </s>

<s>Ultimamente comandò che si facesse <lb></lb>il cannone, e si prese un abete di 20 braccia fiorentine, e fu incavato male <lb></lb>e commesso peggio per la fretta, poichè guardando io, dopo commesso, veddi <lb></lb>che la cavità, in cambio di esser conica circolare, faceva questa apparenza O. </s>

<s><lb></lb>La mattina, che S. A. era per partire alla volta di Pisa, lo feci tirar su per <lb></lb><gap></gap> sue camere e vi mettemmo il vetro: fu guardata una villa <pb xlink:href="020/01/399.jpg" pagenum="380"></pb>con infinita scomodità: non avevamo concavo proporzionato e trovammo che <lb></lb>il vetro voleva sette braccia più che l&#039;abete di lunghezza. </s>

<s>Così non si potè <lb></lb>aver gusto. </s>

<s>Mi lasciò ordine S. A. che io facessi un altro vetro un po&#039;mi­<lb></lb>nore, e facessi accomodar meglio il cannone. </s>

<s>Ho già fatto il vetro, ma è <lb></lb>riuscito pienissimo di tortiglioni. </s>

<s>Voglio nondimeno che, come torna, lo trovi <lb></lb>in ordine. </s>

<s>Quella mattina nondimeno, sebben con infinita scomodità, vede­<lb></lb>vamo certi coppi, con le macchie che vi erano sù, di grandezza stermi­<lb></lb>nata.... Quel signore Eustachio orologiaro (il Divini) è mio amico e per­<lb></lb>sona di molto buon gusto, discorso e giudizio, e non dubito che non sia per <lb></lb>far bene, ma però che sia per arrivare al segno, che ho arrivato io, non lo <lb></lb>credo ” (ivi, c. </s>

<s>93). </s></p><p type="main">

<s>Sien pure confidate in una lettera familiare a un intimo amico, queste <lb></lb>ultime espressioni suonano alquanto immodeste. </s>

<s>Si direbbe che i regali e <lb></lb>le compiacenze del Granduca, colle lodi e le adulazioni di tanti, avessero <lb></lb>fatto salire il fumo agli occhi del povero Torricelli. </s>

<s>Il Fontana dall&#039;altra <lb></lb>parte, benchè povero artefice, senza protezione di principi e senza scienza, <lb></lb>non poteva patire i fastidiosi orgogli di quel suo fortunato rivale. </s>

<s>“ Mi vien <lb></lb>riferito, scrivevagli il Ricci, il Fontana essersi piccato per l&#039;emulazione di <lb></lb>V. S. nel lavoro dei vetri, e ha mandato qua in Roma un suo vetro squi­<lb></lb>sitissimo, che lo teneva presso di sè, come singolare, acciò sia paragonato <lb></lb>con alcuni di quelli di V. S. e mi dicono che superi di gran lunga uno che <lb></lb>hanno di V. S. </s>

<s>Non so chi sian questi che hanno i vetri di V. S. </s>

<s>Lo dissi <lb></lb>al signor Raffaello (Magiotti) e mi consigliò ad accennarle questo, perchè <lb></lb>avverta di non mandar vetri se non in mano di persone discrete, le quali <lb></lb>abbiano discrezione in paragonare i vetri, che siano stimati pari dai loro <lb></lb>maestri ” (ivi, T. XLII, c. </s>

<s>153). </s></p><p type="main">

<s>È facile indovinar che i giudici del paragone, i quali erano tutti amici <lb></lb>e ammiratori del Torricelli, non eccettuato il Thevenot, il quale, ritrovan­<lb></lb>dosi allora a Roma, si volle <emph type="italics"></emph>far trombetta del valor<emph.end type="italics"></emph.end> del Matematico di Fi­<lb></lb>renze <emph type="italics"></emph>sì per le ragioni della Geometria sì nei paragoni fatti tra i vetri <lb></lb>di lui e del Fontana<emph.end type="italics"></emph.end> (ivi, c. </s>

<s>154) dovessero esaltare il Torricelli stesso Ma­<lb></lb>tematico del Granduca, a scapito del povero e disprezzato occhialaio na­<lb></lb>poletano. </s></p><p type="main">

<s>Solo, in mezzo alla turba plaudente, si faceva sentir la voce del Mer­<lb></lb>senno, che co&#039;suoi rotti modi frateschi rintuzzava i vanti torricelliani, e <lb></lb>prendeva le difese per il più debole fra i contendenti. </s>

<s>“ Optimus Magiot­<lb></lb>tus, egli scrive, mihi ostendit vitrum perspicilli, quod ad eum misisti, quod <lb></lb>cum Fontanae vitro, quod etiam habet collatum, minus bonum apparet. </s>

<s><lb></lb>Cumque legissem in tuo libro vitra a te parata superare quae hucusque ap­<lb></lb>paruere, nempe et vitra galileiana et Fontanae, miratus sum quod in illo <lb></lb>tuo vitro non deprehenderetur ” (ibi, T. XLI, c. </s>

<s>57). E in un&#039;altra lettera, <lb></lb>scritta da Parigi, gli dice liberamente che in Francia si fabbricavano ca­<lb></lb>nocchiali migliori de&#039;suoi, de&#039;quali uno eccellentissimo ne aveva il Gassendo, <lb></lb>e gli soggiunge che migliori di tutti sono i Telescopi binoculi del Rehita. <pb xlink:href="020/01/400.jpg" pagenum="381"></pb>“ Porro te monitum velim iam Augustae Vindelicorum fieri Telescopia longe <lb></lb>meliora quam tua vel cuiuspiam alterius communia, quae serviunt duobus <lb></lb>oculis, quaeque propterea capuccinus Rehita, qui nuper edidit Tractatum de <lb></lb>hoc Tubo, quem rocat <emph type="italics"></emph>Oculum Enoch et Eliae,<emph.end type="italics"></emph.end> vocat <emph type="italics"></emph>Binocula.<emph.end type="italics"></emph.end> Habent <lb></lb>itaque quatuor convexa, nullum concavum, duo pro quovis oculo quae, quia <lb></lb>obiectum invertunt, quod parum refert in astris, si tertium concavum abde­<lb></lb>tur, rectum est obiectum ” (ibi, T. XLI, c. </s>

<s>19). </s></p><p type="main">

<s>Ma il coro tutt&#039;intorno plaudente assordiva la voce rauca di Marino <lb></lb>Mersenno, cosicchè, in mezzo a quella nuvola profumata d&#039;incenso, non ve­<lb></lb>dendo altri che sè con quella sua collana di trecento scudi pendente dal <lb></lb>collo, salivano, più che mai vertiginosi dal petto, i fumi in quell&#039;ardente <lb></lb>spirito romagnolo. </s>

<s>Il Fontana, per far qualche ragione di sè col pubblico, e <lb></lb>non soccombere oppresso e invendicato, ebbe ricorso ai gesuiti del Collegio <lb></lb>napoletano, Giovan Batista Zuppi e Girolamo Sirsale, coll&#039;aiuto de&#039;quali riu­<lb></lb>scì a mettere insieme e a pubblicare in Napoli, nel 1646, le sue <emph type="italics"></emph>Novae <lb></lb>Coelestium terrestriumque rerum Observationes.<emph.end type="italics"></emph.end> Pel Torricelli questo è <emph type="italics"></emph>il <lb></lb>libro delle bestialità osservate o piuttosto sognate dal Fontana nel cielo<emph.end type="italics"></emph.end><lb></lb>(ivi, T. XL, c. </s>

<s>13). E prosegue a dire al Renieri: “ Se ella vuol vedere <lb></lb>pazze cose, cioè spropositi, finzioni, sfacciataggini, e mille vituperi simili, io <lb></lb>gli manderò il libro: potrà forse cavar roba da ridere per l&#039;opera sua ” (ivi). </s></p><p type="main">

<s>Mentre così fieramente menava il Torricelli i denti a lacerare quella <lb></lb>misera vittima napoletana, venne a dargli sotto l&#039;ugne un altro poveretto, <lb></lb>che s&#039;era fitto in testa di lavorare i vetri de&#039;Canocchiali, facendo a gara <lb></lb>con lui. </s>

<s>Chi, tra le Vite de&#039;Professori del Disegno scritte da Filippo Bal­<lb></lb>dinucci, s&#039;abbattesse a leggere quella di Antonio Novelli, si formerebbe, del <lb></lb>carattere del Matematico del Granduca, un&#039;idea tutt&#039;affatto diversa da quella <lb></lb>che ci siamo dovuti formar noi. </s>

<s>Il buon Baldinucci scrisse ivi, intorno al <lb></lb>Torricelli, una pagina, che vorrebbe essere scelta e collocata in primo luogo <lb></lb>fra gli esempi di generosità offerti all&#039;imitazione degli uomini. </s>

<s>Dop&#039;aver <lb></lb>detto che Antonio Novelli s&#039;esercitava, fra le altre cose, a lavorare i vetri <lb></lb>da Telescopi, lo stesso Baldinucci così soggiunge: </s></p><p type="main">

<s>“ Il Granduca Ferdinando, che molto di tale strumento si dilettava, fa­<lb></lb>cevane far molti al Torricelli, e poi con lodi e premii da suo pari il ricom­<lb></lb>pensava; ond&#039;egli, vedendosi così regalato da quel grande, e riflettendo al­<lb></lb>l&#039;incontro al sollievo che egli avrebbe potuto arrecare alla povertà del nostro <lb></lb>Artefice, con far conoscere suo gran talento in simile materia a Sua Al­<lb></lb>tezza, un giorno gli venne a dire essere in Firenze persona, che operava <lb></lb>meglio di lui, e che questi era Antonio Novelli, e ne riportò per risposta <lb></lb>di dovergli far vedere qualche cosa di suo. </s>

<s>Il Torricelli in questo, in vero <lb></lb>poco avveduto, per troppo desio di favorire l&#039;amico, prese un occhiale fatto <lb></lb>da sè stesso, che si estendeva per dodici braccia in circa, e mostrollo un <lb></lb>giorno al Granduca, il quale, credendolo del Novelli, disse: egli è un bonis­<lb></lb>simo Occhiale, ma e&#039;non ha che fare punto co&#039;vostri. </s>

<s>Dopo pochi giorni, il <lb></lb>Torricelli presone uno del Novelli de&#039;migliori e portatolo allo stesso Sere-<pb xlink:href="020/01/401.jpg" pagenum="382"></pb>nissimo, gli disse aver fatto questo vetro, nel quale, avendo molto sodisfatto <lb></lb>a sè stesso, desiderava che S. A. sel conservasse per sè in sua memoria. </s>

<s><lb></lb>Presolo il Granduca e fatto venire altri vetri di mano del Torricelli, e con <lb></lb>quello paragonatigli, disse: veramente questo è meglio di tutti gli altri vo­<lb></lb>stri. </s>

<s>Sicchè, replicò il Torricelli, il Novelli è miglior maestro di me, perchè <lb></lb>questo vetro è fatto dalle sue mani, non dalle mie. </s>

<s>Quell&#039;accortissimo Prin­<lb></lb>cipe, in primo moto, diede alcun segno, e con ragione, che poco le fosse <lb></lb>piaciuto quel modo di portar negozi di un suddito al suo Sovrano, ma vin­<lb></lb>cendo in lui il grande amore ch&#039;ei portava al Matematico, e il zelo che egli <lb></lb>conobbe in esso d&#039;aiutar l&#039;amico, rivoltò galantemente il fatto, ed al Tor­<lb></lb>ricelli ordinò che mettesse il prezzo all&#039;Occhiale. </s>

<s>Il Torricelli eseguì, e il <lb></lb>Novelli ne fu nobilmente ricompensato ” (Firenze 1773, T. XVI, pag. </s>

<s>220, 21). </s></p><p type="main">

<s>Ma questo del Baldinucci è un bel romanzetto trasportato al morale: la <lb></lb>storia vera la caveranno da sè i lettori dal seguente passo di lettera, che il <lb></lb>Torricelli stesso scriveva al Renieri: “ È verissimo che il Novelli ha volontà <lb></lb>di fare gli Occhiali come me. </s>

<s>È anco vero che ne ha fatto finalmente qual­<lb></lb>cuno, che ha avuto ardire di farlo comparire in palazzo. </s>

<s>Basta, è stato pro­<lb></lb>vato con i miei e può essere che qualcuno suo parziale l&#039;abbia lodato. </s>

<s>Ma <lb></lb>però il Serenissimo Padrone non veggo che si degni di parlarne. </s>

<s>Ma parlò <lb></lb>bene di quello romanesco, ancorchè poi non adegui altri Occhiali che i miei. </s>

<s><lb></lb>Un&#039;altra volta, già sono un anno e mezzo, questo medesimo Novelli ne mandò <lb></lb>due al Poggio a Caiano, mentre S. A. S. era in villa. </s>

<s>Si provarono e furono <lb></lb>ributtati coll&#039;<emph type="italics"></emph>oibò!<emph.end type="italics"></emph.end> Mi ci trovavo ancor io, e v&#039;era anco Tordo. </s>

<s>Quello che <lb></lb>propose gli occhiali fu un cav. </s>

<s>Rucellai. </s>

<s>È ben vero che mai volle nomi­<lb></lb>narne l&#039;Autore a noialtri, e solo per coniettura sapemmo che erano del No­<lb></lb>velli. </s>

<s>Quelli poi che scrivono chè fanno miracoli, bisogna che siano genti <lb></lb>che non hanno pratica de&#039;miei. </s>

<s>Ed io ho sempre detto che, non solo il No­<lb></lb>velli ed il Divini e Tordo e Fontana, ma mille altri faranno occhiali che <lb></lb>daranno grandissimo gusto, e parrà che non si possa far più. </s>

<s>Bisogna avere <lb></lb>il paragone presente de&#039;miei e degli altri e poi bisogna anco di più che il <lb></lb>giudice non sia novizio nel guardare, perchè molte volte non vedrà la dif­<lb></lb>ferenza, la quale vi è, sebben piccola; in ogni modo si stima assaissimo ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>13). </s></p><p type="main">

<s>L&#039;orgoglio, nell&#039;animo di tutti gli uomini o piccoli o grandi, è come <lb></lb>elaterio di molla che, quanto risale in su, altrettanto ricade in basso, infin­<lb></lb>tanto che la quiete non la riduca nel suo giusto mezzo. </s>

<s>Quel Torricelli, che <lb></lb>cosi viene magnificando al Renieri la sua merce, al di sopra di tutti gli altri <lb></lb>concorrenti, s&#039;era poco prima raccomandato allo stesso Renieri che s&#039;accor­<lb></lb>dasse con lui a secondarlo, e a procacciare a quella sua merce, con le lodi, <lb></lb>in pubblica piazza, un più facile smercio. </s>

<s>“ La prego a voler nella sua Opera <lb></lb>(Le Tavole dei Secondi Mobili) o a proposito di queste osservazioni, ovvero <lb></lb>nel trattar di Giove e suoi Pianetini, voler, dico, far qualche servigio alli <lb></lb>miei Occhiali, per interesse mio. </s>

<s>Spero che ella conosca di poter dire la ve­<lb></lb>rità. </s>

<s>Certo è che ella ha avuto occasione, per mezzo del Serenissimo Pa-<pb xlink:href="020/01/402.jpg" pagenum="383"></pb>drone in ciò curiosissimo, di vedere ed esperimentare i più famosi Occhiali, <lb></lb>che si facciano in Europa. </s>

<s>Che poi i miei non si possano superare la rendo <lb></lb>certa io ” (ivi, c. </s>

<s>15). </s></p><p type="main">

<s>Ma insomma quel che rendeva i Canocchiali del Torricelli insuperabili <lb></lb>era, secondo lui, tutt&#039;opera di quel famoso segreto, di che parlava dianzi al <lb></lb>Ricci e al Magiotti, e intorno al quale debbono i nostri lettori essere en­<lb></lb>trati in curiosità, e venuti in desiderio di vederlo svelato. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La sera del dì 8 Dicembre 1647, a ore quattro di notte, il Granduca <lb></lb>Ferdinando fa chiamare a sè, nelle sue stanze più riposte, il Viviani, come <lb></lb>avesse a confidargli qualche affare geloso e di grande importanza. </s>

<s>Sedeva <lb></lb>il Sovrano a una tavola, colle mani posate sopra una cassetta gelosamente <lb></lb>serrata a chiave, e dalle espressioni degli occhi e dai gesti faceva trasparir <lb></lb>che lì dentro ci dovess&#039;esser custodito qualche cosa di veramente prezioso. </s>

<s><lb></lb>Prende la chiave, apre la cassetta, ne trae fuori alcuni fogli manoscritti, e <lb></lb>nel mostrargli al Viviani così gli dice: Qui si contiene svelato il famoso <lb></lb>segreto, che la buona memoria del nostro Torricelli aveva per lavorare le <lb></lb>lenti dei Canocchiali, con altri documenti e avvertimenti utilissimi. </s>

<s>Poi ri­<lb></lb>pose quelle carte dentro <emph type="italics"></emph>e serrando,<emph.end type="italics"></emph.end> così racconta lo stesso Viviani, <emph type="italics"></emph>di pro­<lb></lb>pria mano il recipiente di detto strumento, siccome da sè stesso l&#039;aveva <lb></lb>aperto, mi consegnò la chiave che lo teneva serrato.<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXXXIII, c. </s>

<s>3). </s></p><p type="main">

<s>Prima però che al Viviani, era stato il segreto dall&#039;Autore stesso con­<lb></lb>fidato al Magiotti. </s>

<s>Udimmo da un passo di lettera trascritto di sopra come <lb></lb>al Torricelli fosse imposto silenzio dallo stesso Granduca, ma il Magiotti, <lb></lb>messo in gran curiosità, tanto fece appresso all&#039;amico, che questi ebbe final­<lb></lb>mentente a condiscendere, svelandogli il segreto in una lettera sotto il dì <lb></lb>4 Dicembre 1643 a lui diretta, che senza l&#039;invocativo e le solite cerimonie, <lb></lb>corrisponde quasi a parola collo strumento stesso consegnato al Viviani dal <lb></lb>Granduca. </s></p><p type="main">

<s>“ Sappia dunque che la centina è facilissima da farsi, e la natura me­<lb></lb>desima la fa perfetta, dove l&#039;arte non potrebbe mai arrivare. </s>

<s>Si piglia un <lb></lb>pezzo di vetro piano, ovvero rozzo, tondo e grande per l&#039;appunto, quanto <lb></lb>il vetro da lavorarsi, o pochissima cosa di più. </s>

<s>Si attacca sopra qualche cosa <lb></lb>grave, acciò la mano non porti la centina in giro. </s>

<s>Io adopro una rotella di <lb></lb>piombo, ovvero un mattone o altro. </s>

<s>Dopo questo comincio ad affondarla con <lb></lb>un vetro piccolo, pur piano, a smeriglio tagliente. </s>

<s>Nell&#039;affondarla, non os­<lb></lb>servo altro se non che il vetro, con che lo affondo, pratichi più spesso in­<lb></lb>torno al mezzo, che dalle bande della futura centina. </s>

<s>Insomma non passa <lb></lb><gap></gap><pb xlink:href="020/01/403.jpg" pagenum="384"></pb>per un occhiale di tre braccia e mezzo, lavorata da ambe le parti, inten­<lb></lb>dendo però che la centina non sia di diametro più che una piastra e due <lb></lb>terzi fiorentina. </s>

<s>” </s></p><p type="main">

<s>“ Non vorrei che ella avesse scrupolo nella centina, perchè basta che <lb></lb>ella sia incavata alla peggio, e poi, nel lavorare il vetro, la si fa perfetta <lb></lb>dalla natura medesima. </s>

<s>Fatto questo, si mette da parte quel vetro piccolo, <lb></lb>che ha incavata la centina, e si piglia il vetro, che si vuol lavorare, ben <lb></lb>tondato ed anco abbozzato in una centinuccia di rame o d&#039;altro, purchè sia <lb></lb>affatto piano, e neanco tanto colmo, che sia sproporzionato affatto con la <lb></lb>centina di già preparata. </s>

<s>Questo poi si incomincia a lavorare con spoltiglia <lb></lb>fine, sintanto che ella giudica che si sia adattato con la centina, il che si <lb></lb>conosce anco a vista, perchè il vetro, che era abbozza<emph type="italics"></emph>t<emph.end type="italics"></emph.end>o con lo smeriglio, <lb></lb>aveva la grana grossa, ma dopo, dove avesse trovata la spoltiglia, l&#039;averà <lb></lb>più minuta. </s>

<s>” </s></p><p type="main">

<s>“ Quando dunque il vetro sarà arrivato da per tutto, non vi si dà più <lb></lb>spoltiglia, ma si continua a lavorare con quel residuo, che sarà tra l&#039;un <lb></lb>vetro e l&#039;altro, ed anco negli orli. </s>

<s>Quest&#039;operazione si continua, fintanto <lb></lb>che quella materia sia consumata e ridotta bianca, palpabile e untuosa, come <lb></lb>burro, bagnando la centina, quando s&#039;asciugasse, con una mezza gocciolina <lb></lb>di acqua, ovvero con l&#039;alito della bocca messa lì vicino. </s>

<s>Se tali operazioni <lb></lb>saranno ben fatte, il vetro verrà senza graffi, e senza segni, ed averà una <lb></lb>pelle tale, che, obliquandolo all&#039;asse della visione, circa un mezzo angolo <lb></lb>retto, farà specchio delle cose luminose. </s>

<s>” </s></p><p type="main">

<s>“ Quanto al pulire, mai si pulisce sulla centina, che l&#039;ha lavorato, per­<lb></lb>chè pulisce dalle bande prima, e poi tardissimo nel mezzo, e non sempre <lb></lb>bene. </s>

<s>Bisogna dunque darvi centina più dolce. </s>

<s>Io adopro una rotella di la­<lb></lb>vagna, larga circa otto dita, e quasi direi piana. </s>

<s>Solo vi dò quattro bòtte di <lb></lb>pomice, fintantochè l&#039;occhio cominci a conoscere che la non è più piana. </s>

<s><lb></lb>Questa la metto in una tavola, con una rotella di panno sotto, acciò non si <lb></lb>rompa, e poi vi conficco sopra, con bullettine da impannata, un pezzo di <lb></lb>panno fine senza nodi, tarme, ecc., e tirato da tutte le bande quanto mai <lb></lb>è possibile. </s>

<s>Quest&#039;invenzione è meglio che legare il panno intorno alla cen­<lb></lb>tina, perchè si tira meglio, e poi, perchè essendo panno conficcato nella ta­<lb></lb>vola sottoposta, la centina viene a restare immobile sotto i giri della mano. </s>

<s><lb></lb>Il tripolo poi vi si dà in forma d&#039;unguento tanto scarso, che non faccia <lb></lb>massa intorno agli orli del panno e della centina aggiungendo ora una goc­<lb></lb>ciola d&#039;acqua, ed ora un poco di tripolo, conforme il panno ne averà biso­<lb></lb>gno. </s>

<s>Solo conviene avere un poco di pazienza nel pulire, perchè vada via <lb></lb>ogni minima bruttura od inegualità, che sia nella superficie del vetro. </s>

<s>” </s></p><p type="main">

<s>“ Quanto alla piccolezza della centina di vetro sopraddetta, cioè che sia <lb></lb>uguale al vetro da lavorarsi, V. S. lo stima un gran segreto. </s>

<s>Credo che ella <lb></lb>intendesse brevemente che se la centina non è sferica, nè anco il vetro può <lb></lb>essere di buona sferità. </s>

<s>E chi mi assicura che la centina si mantenga sfe­<lb></lb><gap></gap><pb xlink:href="020/01/404.jpg" pagenum="385"></pb>stra? </s>

<s>Ma quando siano uguali, e che la mano del lavorante farà moti irre­<lb></lb>golari e stravaganti, cioè spire, ghirigori, circoli, e sopratutto diametri molti <lb></lb>e per tutti i versi; allora sì che neanche un angelo potrà dare al vetro figura <lb></lb>più perfettamente sferica. </s>

<s>” </s></p><p type="main">

<s>“ Il segreto che più m&#039;importa, e che non si sà da altri che da Dio e <lb></lb>da me, è questo: Non attaccare i vetri da lavorarsi con pece, nè con altro, <lb></lb>per via di fuoco. </s>

<s>Perchè quelle materie, nel freddarsi, si ritirano più da <lb></lb>una parte che dall&#039;altra, ed inarcano il vetro, il quale, finchè sta attaccato <lb></lb>al macinello, ha la figura colma, ma quando lo stacchiamo, per metter nel­<lb></lb>l&#039;occhiale, egli si spiana come prima e la figura si guasta. </s>

<s>Questo segreto, <lb></lb>che dico adesso a V. S., è stato da me osservato evidentemente, tanto che <lb></lb>l&#039;ho toccato con mano, e direi anco a V. S. il come, ma lo lascio per <lb></lb>brevità. </s>

<s>” </s></p><p type="main">

<s>“ Ora, io attacco i vetri così: piglio un macinello di piombo di que­<lb></lb>sta proporzione: (fig. </s>

<s>28). Alla faccia A spianata metto una rotella di ra­<lb></lb><figure id="id.020.01.404.1.jpg" xlink:href="020/01/404/1.jpg"></figure></s></p><p type="caption">

<s>Figura 28.<lb></lb>scia o altro panno fino, cedente, acciò il vetro toc­<lb></lb>chi sul morbido, e dopo cingo sopra detto panno <lb></lb>il macinetto con una pelle di guanto tiratissima, <lb></lb>e la lego con lo spago CD stretta assai. </s>

<s>Dopo, <lb></lb>impiastro la faccia di detta pelle A con cera rossa, <lb></lb>calda e distesa sottilmente. </s>

<s>Così il vetro, purchè <lb></lb>non sia bagnato, si attaccherà sempre, sebben <lb></lb>freddo, e quando occorresse, si dà una strofina­<lb></lb>tina a detta pelle, con una palla della medesima cera rossa, che attaccherà <lb></lb>assai forte. </s>

<s>” </s></p><p type="main">

<s>“ Così ne seguita che il vetro non sarà sforzato, ma quella figura che <lb></lb>riceverà dalla centina, l&#039;istessa riterrà, quando sia staccato dal macinello. </s>

<s><lb></lb>Oltre di ciò, V. S. averà comodità di cominciare a provare il vetro, se fa <lb></lb>bene o male, subito che si comincia a pulire, e potrà staccarlo e attaccare <lb></lb>cento volte, senza danno alcuno, e piuttosto con giovamento. </s>

<s>Chè, quando si <lb></lb>adopra la pece, la regola è non lo staccar mai, se non quando egli è finito. </s>

<s>” </s></p><p type="main">

<s>“ Quanto all&#039;invenzìone del macinello di piombo, non è mia, ma è bo­<lb></lb>nissima, perchè nel dare la pelle, non occorre aggravare quasi niente la <lb></lb>mano, ma il piombo medesimo fa quasi da per lui. </s>

<s>Anco nel pulire aiuta <lb></lb>assai, ed acciò faccia meglio il servigio, abbiamo i macinelli, che son quasi <lb></lb>due dita più di diametro, che il vetro stesso, acciò gravitino quel di più, <lb></lb>ed osservi che il fare il macinello alto assai è male, perchè fa lieva e fa <lb></lb>traballare il vetro. </s>

<s>Quando V. S. proverà queste invenzioni, che non son se <lb></lb>non due: centina piccola e non adoprar fuoco, l&#039;assicuro che farà i vetri <lb></lb>buoni, anco quando la materia fosse cattiva, e non glie ne riuscirà mai nes­<lb></lb>suno cattivo affatto, ma sempre più che mediocri, e bisogna accordar molte <lb></lb>cose, la figura, la materia, e il pulimento. </s>

<s>L&#039;osservazione m&#039;ha insegnato <lb></lb>che nei vetri, la figura importa assaissimo, e il pulimento pochissimo. </s>

<s>La <lb></lb>ragione è questa: io ho provato molti de&#039;miei vetri che appena comincia-<pb xlink:href="020/01/405.jpg" pagenum="386"></pb>vano a trasparire, ed ho veduto che, nonostante la grana grossissima che <lb></lb>avevano, in ogni modo facevano bene, per essere la figura buona. </s>

<s>Altri poi <lb></lb>puliti, come diamanti, per un tantin di mancanza inimmaginabile che sia <lb></lb>nella figura, non fanno nulla. </s>

<s>La prego a tener segreto quanto le scrivo, in <lb></lb>particolare quello dell&#039;attaccare, perchè è cosa che nessuno ne sospetta, e <lb></lb>non vi è cosa che rovini più i vetri, quando però non si adoprino grossis­<lb></lb>simi ” (MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>34, 35). </s></p><p type="main">

<s>Nella cassetta, la chiave della quale fu dal Granduca consegnata al Vi­<lb></lb>viani, s&#039;accennava di sopra che ci erano dentro custoditi, oltre al segreto, <lb></lb>documenti e avvertimenti utilissimi per la perfetta fabbrica delle lenti da <lb></lb>Canocchiali. </s>

<s>Quegli avvertimenti erano scritti in latino col titolo <emph type="italics"></emph>Monita circa <lb></lb>usum Telescopii<emph.end type="italics"></emph.end> e il Viviani, nel ricopiarli fedelmente, nota in capo alla <lb></lb>pagina, per chi non lo sapesse, di averli avuti <emph type="italics"></emph>Ex munificentia Serenissimi <lb></lb>Ferdinandi M. D.<emph.end type="italics"></emph.end> Ecco in che consistono que&#039;Moniti: </s></p><p type="main">

<s>“ Illud praecipue non est negligendum tubi fabrica ne in ipso usu in­<lb></lb>flectatur, sitque maioris crassitiei, quam radios convergentes intercipere pos­<lb></lb>sit. </s>

<s>Detur etiam tribus aut quatuor internodiis, sive diaphragmatibus, qua­<lb></lb>lia sunt in grandioribus, sed perforatis, esse interseptos, ne lumen quoddam <lb></lb>intra os tubi oblique receptum incidens in cavam tubi superficiem, ad ocu­<lb></lb>lum ullo modo repercuti possit. </s>

<s>Curandum insuper est quam partem vitri <lb></lb>dissectam, sive apertam relinquamus, quod experientia manifestum est. </s>

<s>” </s></p><p type="main">

<s>“ Ad res vero minutas aspiciendas minori circulo utendum est. </s>

<s>Ete­<lb></lb>nim, quanquam vitra perfectissima sint, perraro bonitatem suam ostendere <lb></lb>possunt, ob aeris temperiem, vel enim nebula quaedam, sive caligo, sive <lb></lb>fumus tenuissimus in aere est, quarum rerum athomos, non secus ae reli­<lb></lb>qua obiecta auget, et visibilia reddit Telescopium. </s>

<s>Praeterea aer saepissime <lb></lb>tremit, et quodammodo scintillat, credo quidem ob vapores ascendentes, non <lb></lb>tantum aestate, et sub ardente sole, sed et hyeme etiam, et saepe flante <lb></lb>Borea, immo et de nocte, quando Lunam contemplanti patebit, tunc enim <lb></lb>ambitus eius tremit, maculaeque minutiores maligne cernuntur. </s>

<s>Malignius <lb></lb>autem tunc temporis figura Saturni conspicitur. </s>

<s>” </s></p><p type="main">

<s>“ Perfectissima visio fit, ut plurimum, matutino et vespertino tempore <lb></lb>averso semper sole nubilo etiam coelo, quod inverisimile est, et post plu­<lb></lb>viam clarissimus conspectus est, per tubum, dummodo species obiectorum <lb></lb>non ferantur supra frequentissima urbium loca. </s>

<s>Urbs enim ingenti copia <lb></lb>vaporum, quae de fumariis emittitur, species omnes visibiles perturbat. </s>

<s>” </s></p><p type="main">

<s>“ Plura monere poteram: pauca haec sufficiant, quae nonnisi longo usu <lb></lb>observari solent. </s>

<s>Multi enim perfectionem accusant vitrorum, cum iis contra­<lb></lb>rio tempore utantur, ipsique potius accusandi sunt ” (ivi, T. CXXXIII, c. </s>

<s>9). </s></p><p type="main">

<s>I documenti torricelliani, scritti in lingua volgare, si custodivano pure, <lb></lb>dentro la famosa cassetta, dal Granduca, e il Viviani ce ne tramandò copia <lb></lb>di sua propria mano col titolo: <emph type="italics"></emph>Condizioni richieste ne&#039;vetri.<emph.end type="italics"></emph.end> Quelle condi­<lb></lb>zioni si riducono alle seguenti: </s></p><p type="main">

<s>“ Che le <gap></gap><pb xlink:href="020/01/406.jpg" pagenum="387"></pb>poche e piccolissime: che i <emph type="italics"></emph>tortiglioni,<emph.end type="italics"></emph.end> cioè quell&#039;onde interne che talvolta <lb></lb>hanno i vetri, non vi siano di nessuna sorta, ma ne&#039;vetri piani è difficilis­<lb></lb>simo il vedergli ed è anzi impossibile, però questo documento sarà quasi <lb></lb>superfluo. </s>

<s>Il colore sia poco; qualunque sia o avvinato o bianco o capellino, <lb></lb>o verde giallo, si conosce facilmente col mettere il vetro sopra nn foglio di <lb></lb>carta o sulla pezzuola. </s>

<s>La condizione poi più necessaria di tutte è la limpi­<lb></lb>dezza, perchè, sendovi questa, ancorchè manchino le altre tutte, i vetri ver­<lb></lb>ranno buoni: quando manchi questa, ancorchè per le altre sieno perfetti, <lb></lb>mai faranno bene. </s>

<s>Il modo di conoscerli è il guardare i vetri per taglio, ma <lb></lb>che non sieno larghi più di quattro ovvero di sei dita. </s>

<s>Se il taglio sarà di­<lb></lb>ritto ę seguito, come fa il fuoco, si vedrà guardando verso il lume, per la <lb></lb>crassizie del vetro fino alla parte opposta, come se fosse ambra, o meglio <lb></lb>come acqua, e si vedrà la materia omogenea tutta di un colore e senza <lb></lb>strisce o righe, ovvero onde. </s>

<s>Quando sarà altrimenti, la pasta sarà cattiva. </s>

<s><lb></lb>Se poi il taglio sia smollettato colle tanaglie, sarà più difficile a conoscere <lb></lb>la sua bontà, ma nondimeno se si vedrà qualche poco di spanaturina, da <lb></lb>poter guardar dentro e da per tutto, si vede un&#039;allegria che brilla come dia­<lb></lb>mante. </s>

<s>Se poi si vede torbido e offuscato la pasta è cattiva ” (ivi, c. </s>

<s>10). </s></p><p type="main">

<s>Che il Granduca Ferdinando facesse benissimo a custodir quegli scritti, <lb></lb>che noi abbiamo tirati fuori dalla sua gelosa cassetta, per metterli sotto gli <lb></lb>occhi di tutti, non si potrebbe negare: tutti però siamo un po&#039;rimasti come <lb></lb>quel buon uomo, che, stando a veder partorire un monte, n&#039;ebbe a veder <lb></lb>finalmente uscire quel che canta, nella sua favola, Esopo. </s>

<s>È perciò che, trat­<lb></lb>tandosi di uno scienziato tanto insigne qual&#039;è il Torricelli, non ci dobbiam <lb></lb>passar senza trattenerci alquanto a considerare come davvero in lui, rispetto <lb></lb>all&#039;opera del Telescopio, le fronde e i fiori non corrispondano ai frutti. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi ripensa che il famoso segreto fu detto dal suo Autore essere stato <lb></lb>trovato per via di speculazioni geometriche e con la dottrina e cognizione <lb></lb>delle figure coniche e con la scienza delle rifrazioni; e chi ripensa, di più, <lb></lb>che colui, il quale annunziava queste cose, era un Torricelli, non può non <lb></lb>restar maravigliato al veder che poi in effetto quel gran segreto consisteva <lb></lb>in tutt&#039;altro che o nella Geometria o nella scienza delle rifrazioni. </s>

<s>Si ridu­<lb></lb>ceva in fatti quel segreto dal suo stesso discopritore a due capi, il più im­<lb></lb>portante de&#039;quali era che non si dovessero attaccar le lenti con pece o altro <lb></lb>caldo bitume, e ciò asseriva il Torricelli esser cosa non saputa da nessun <lb></lb>altro che da lui solo e da Dio. </s>

<s>Eppure a noi par provato che da 25 anni <lb></lb>avesse saputa quella stessa cosa o l&#039;avesse almeno potuta saper tutto il <lb></lb>mondo, avendola il Sirturo già pubblicata nel cap. </s>

<s>IX della II Parte del suo <lb></lb><emph type="italics"></emph>Telescopio.<emph.end type="italics"></emph.end> “ Idipsum autem nec pice nec bitumine unquam poteris, quia <pb xlink:href="020/01/407.jpg" pagenum="388"></pb>igne primo est semper opus emolliendae pici: calor autem liquatae picis, sive <lb></lb>bituminis maxime obest christallo, ac aliquam transmittit pinguedinem ” <lb></lb>(Francofurti 1618, pag. </s>

<s>48). Forse il Sirturo non vide chiaro, com&#039;avea sa­<lb></lb>gacemente riconosciuto il Torricelli, esser causa del guasto prodotto dal bi­<lb></lb>tume caldo sopra le lenti la dilatazione cubica operata dal calore, ma il se­<lb></lb>greto non consisteva qui, consisteva nella semplice osservazione del fatto <lb></lb>rispetto alla quale, ripetiamo, il Sirturo avea preceduto di 25 anni il Tor­<lb></lb>ricelli e avea rivelato il suo segreto a tutti coloro che volevano saperlo. </s></p><p type="main">

<s>Ma che il Torricelli, nell&#039;avere osservato gli effetti di dilatazion del ca­<lb></lb>lore per cui s&#039;altera la figura de&#039;vetri, e nell&#039;aver saputo mettere insieme <lb></lb>que&#039;pratici avvertimenti, potesse far consistere tutta la sua diottrica geome­<lb></lb>trica e la sua scienza delle rifrazioni, parrà cosa dura ad ammetter da tutti <lb></lb>coloro, che in Geometria e in Fisica conoscono il valor sommo di lui. </s>

<s>Si <lb></lb>direbbe che l&#039;amico intimo del Ricci, per dar più importanza alla cosa, si <lb></lb>credesse permesso in una lettera familiare di spacciar per scienza ciò che <lb></lb>scienza veramente non era, se uscito poi in pubblico colla sua operetta <emph type="italics"></emph>De <lb></lb>solido acuto Hyperbolico,<emph.end type="italics"></emph.end> non vi avesse così lasciato scritto: “ Decidit in­<lb></lb>termedio hoc tempore, ut plurium mensium studio, atque labore, inciderim <lb></lb>in solutionem optimi illius Problematis, tandiu perquisiti, cuius videlicet figu­<lb></lb>rae esse debeant, superficies vitrorum, quae ad usum Telescopii elaboran­<lb></lb>tur ” (Op. </s>

<s>Geom., Flor. </s>

<s>1644, pag. </s>

<s>149). </s></p><p type="main">

<s>Sembrerebbe (con tanta solennità è qui espresso) che il Problema della <lb></lb>figura de&#039;vetri dovesse esser tutt&#039;altro da quello risoluto nella lettera al <lb></lb>Magiotti, d&#039;onde si vede uscir fuori chi la scrisse, non in pallio filosofale, <lb></lb>ma vestito in farsetto colle maniche rimboccate. </s>

<s>Ma che insomma, nella ri­<lb></lb>soluzione di questo rumoroso Problema torricelliano non ci entrasse per <lb></lb>nulla nè la Geometria nè la scienza delle rifrazioni, basterà, a persuader­<lb></lb>sene facilmente, dimostrare che il TorriceHi reputò falsa e inconcludente la <lb></lb>legge, formulata in Francia infino dal 1637, che cioè i seni degli angoli <lb></lb>d&#039;incidenza e di refrazione serbino per qualunque obliquità una proporzione <lb></lb>costante. </s></p><p type="main">

<s>Pubblicando, nel 1632, il Cavalieri il suo <emph type="italics"></emph>Specchio Ustorio,<emph.end type="italics"></emph.end> deplorava <lb></lb>nelle rifrazioni il <emph type="italics"></emph>màncamento di regola universale qual&#039;è nelle riflessioni <lb></lb>che l&#039;angolo della incidenza sia uguale a quello della riflessione,<emph.end type="italics"></emph.end> e con­<lb></lb>cludeva non essersi potuto fin allora con modo sicuro e dimostrativamente <lb></lb>provare <emph type="italics"></emph>con che regola si vadano diminuendo gli angoli della rifrazione <lb></lb>in un diafano, ovvero accrescendo in relazione degli angoli dell&#039;incidenza.<emph.end type="italics"></emph.end><lb></lb>(Bologna 1650, pag. </s>

<s>47). </s></p><p type="main">

<s>La regola dal Cavalieri tanto desiderata, il Cartesio la divulgò nel 1637, <lb></lb>con gran solennità nella <emph type="italics"></emph>Diottrica.<emph.end type="italics"></emph.end> Il Torricelli nonostante, persuaso che il <lb></lb>Cavalieri fosse uomo da specular più sottilmente del Filosofo Francese, a lui <lb></lb>si rivolge, per aver qualche lume di scienza diottrica, che, in così fatti ter­<lb></lb>mini, rispondeva in proposito da Bologna. </s>

<s>“ Quanto poi ai vetri, non gli <lb></lb>posso dir altro se non di avere speculato alquanto sopra di essi, per ritro-<pb xlink:href="020/01/408.jpg" pagenum="389"></pb>vare ove sia il concorso di varie lenti fatto da raggi paralleli, qualunque <lb></lb>siano le loro due superficie, quali però suppongo sempre sferiche, e mi pare <lb></lb>d&#039;averlo trovato, almeno prossimamente, cioè non facendo caso d&#039;errore dal <lb></lb>vero, quanto è la grossezza della lente. </s>

<s>Ora perchè non ho mai applicato al <lb></lb>fabbricar lenti, perciò non posso distintamente sapere che servizio mi potrà <lb></lb>fare simile trovato, ma stimo, così in universale, che forse se ne potrà ca­<lb></lb>vare qualche benefizio ” (MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>32). </s></p><p type="main">

<s>Tornando poi lo stesso Cavalieri su questo tema delle rifrazioni trattava <lb></lb>col Torricelli dello speculare sopra la linea che possa per refrazione unire <lb></lb>in un punto, dicendo esser questa <emph type="italics"></emph>cosa da tanti ricercata, ma tentata in <lb></lb>vano.<emph.end type="italics"></emph.end> “ Sebbene, poi tosto soggiunge, mi pare che l&#039;Erigonio nel suo Corso <lb></lb>Matematico .... supponga d&#039;averla trovata, fondandosi sopra questo principio <lb></lb>che i seni delle inclinazioni sieno proporzionali con i seni delle rifrazioni, <lb></lb>ma perchè questo principio lo prova solo facendo un trapasso dalla Mecca­<lb></lb>nica alla Diottrica ... per questo sono stato sempre dubbioso ” (Lez. </s>

<s>Accad. </s>

<s><lb></lb>Torricelli, Milano 1823, pag. </s>

<s>25). </s></p><p type="main">

<s>Nel dubbio stesso restò pure involto più che mai il Torricelli, il quale, <lb></lb>come non volle saper dell&#039;Herigonio, così non volle veder nemmeno la Diot­<lb></lb>trica del Cartesio. </s>

<s>Il Mersenno gli faceva di ciò premura, ma il Nostro si <lb></lb>scusava dicendo che non intendeva la lingua francese. </s>

<s>Il Mersenno stesso, <lb></lb>più tardi, ha una buona notizia da dargli ed è che la diottrica cartesiana è <lb></lb>tradotta in latino <emph type="italics"></emph>quae si desiderat V. D. confestim a Lutetia missurus <lb></lb>sum<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>16) e perchè il Torricelli non rispondeva, <lb></lb>dopo dieci mesi, il frate francese torna a scrivergli da Parigi: “ Moneo prae­<lb></lb>terea Dioptricam cartesianam hic latine venalem esse, quam tibi facile possis <lb></lb>comparare, qui gallicam intelligere non potuisti ” (ibi, c. </s>

<s>19). Finalmente <lb></lb>il Mersenno intese che quello era un cantar la favola ai sordi. </s></p><p type="main">

<s>Se dunque è vero che il Torricelli non riconobbe la verità della legge <lb></lb>annunziata e meccanicamente dimostrata delle rifrazioni; se è vero che per <lb></lb>nulla ci entrano le sezioni coniche, come nello specchio Ustorio aveva già <lb></lb>dimostrato il Cavalieri, non si può altro concludere se non che il Problema <lb></lb>della figura dei vetri fu praticamente risoluto dallo stesso Torricelli a quel <lb></lb>modo che, da occhialaio e non già da geometra, rivelò nella lettera famosa <lb></lb>al Magiotti. </s></p><p type="main">

<s>Il Matematico insomma di Firenze, benchè volesse far credere di es­<lb></lb>sersi sublimato nelle alte speculazioni della Geometria, procedeva per quelle <lb></lb>basse e trite vie della pratica esperienza, da rimaner di molti passi indietro <lb></lb>allo stesso Occhialaio napoletano, che in sostanza non fu mai potuto arri­<lb></lb>vare. </s>

<s>E in fatti, se i Canocchiali del Torricelli bastavano a dar gusto al <lb></lb>Granduca nel riguardar le ville e i paesetti circostanti, o nell&#039;esaminar l&#039;aria <lb></lb>ora più trasparente e ora più caliginosa, a seconda che i fumaioli della città <lb></lb>o il suolo facevano esalar fumi e vaporí in più e in meno copia; non riu­<lb></lb>scivan però che di pochissimo profitto all&#039;Astronomia, la quale non fece con <lb></lb>essi in cielo mai nessuna importante scoperta. </s>

<s>Il Torricelli stesso confessa <pb xlink:href="020/01/409.jpg" pagenum="390"></pb>in una sua lettera del dì primo di Febbraio 1647 al Mersenno, che co&#039;suoi <lb></lb>lunghissimi tubi non s&#039;era fatta ancora altra osservazione che delle fascie di <lb></lb>Giove: “ Tubis nostris longissimis nìhil adhuc novi deteximus in coelo prae­<lb></lb>ter fascias ioviales quae ipsum Jovis globum tamquam terrestres nostrae <lb></lb>zonae ambiunt ” (MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>55). </s></p><p type="main">

<s>Ma perchè il Granduca intendeva d&#039;aver buoni Canocchiali per servir­<lb></lb>sene a suo diletto, il Torricelli che, inebriato dalle lodi e dai premi, non <lb></lb>aveva ad altro rivolti i suoi pensieri, che a compiacerlo, dell&#039;Astronomia se <lb></lb>ne curava assai poco. </s>

<s>Egli abitava allora in Firenze dietro il Duomo, nelle <lb></lb>case dell&#039;<emph type="italics"></emph>Opera,<emph.end type="italics"></emph.end> e i grandi palazzi signorili che le fiancheggiano, e l&#039;am­<lb></lb>pia e alta mole del Tempio che a lor si para di faccia, circoscrivevano al­<lb></lb>l&#039;Osservatore troppo angusto spazio di cielo, in che egli principalmente tro­<lb></lb>vava, a que&#039;suoi ozii astronomici, una scusa. </s>

<s>Nel passo di lettera al Mersenno <lb></lb>sopra citato soggiunge infatti, a proposito delle fascie di Giove: “ Ipse enim <lb></lb>fere nunquam in coelum aspicio, ob inopportunitatem aedium quas inha­<lb></lb>bito ” (ivi). </s></p><p type="main">

<s>A quella osservazione anzi di Giove, che fu l&#039;unica, pare si risolvesse <lb></lb>il Torricelli, non per amor della scienza, ma per alcune importune richie­<lb></lb>ste fattegli poco prima dal Ricci, a cui rispondeva: “ Quanto al veder le <lb></lb>fascie in Giove io non l&#039;ho mai vedute perchè non si vedono sempre, e <lb></lb>quando io ho avuto l&#039;occasione di guardarlo, il che è stato da quattro o sei <lb></lb>volte, dopo che son tornato in Firenze, non si vedevano.... Quanto al gi­<lb></lb>rarsi in sè io lo tengo per certo, senza vedervi altro contrassegno. </s>

<s>Ogni <lb></lb>corpo lassù, intorno al quale si girino altri corpi, V. S. dica pure che gira <lb></lb>anch&#039;esso, ma in tempo più breve che qualunque altro corpo che gli si <lb></lb>muova intorno, però io credo che s&#039;inganneranno coloro, che pensano che <lb></lb>Giove mette più giorni in fare una rivoluzione sola ” (ivi, c. </s>

<s>93). </s></p><p type="main">

<s>Il tener per certa il Torricelli la rivoluzione di Giove, prima che il <lb></lb>Cassini l&#039;avesse dimostrata, e l&#039;indovinar la brevità del periodo di quella <lb></lb>stessa rotazione, potrebbero esser forse argomento di molto acume che fosse <lb></lb>in lui, e di molta veggenza in cose di Astronomia, se non si sapesse ch&#039;ei <lb></lb>non faceva poi altro che ripetere quel che avea scritto il Keplero nella sua <lb></lb>Prefazione alla Diottrica. </s></p><p type="main">

<s>Pure, una volta il Torricelli trovò sul campanile del Duomo, uscito fuori <lb></lb>dalle sue umili case, la più aperta specula, che potesse mai desiderare, e <lb></lb>costì fece un&#039;osservazione e un calcolo intorno a Mercurio, di che così dava <lb></lb>parte al Renieri: “ Osservai questa settimana passata Mercurio quando era <lb></lb>in congiunzione di Venere, e così all&#039;improvviso, sul campanile del Duomo, <lb></lb>discorrendo con alcuni giovani che erano meco, feci un certo calcolaccio, per <lb></lb>la prima volta che avevo veduto Mercurio, e conietturai che egli, di diametro <lb></lb>reale, fosse meno di otto miglia delle nostre. </s>

<s>Lo paragonai a Venere, giudi­<lb></lb>cando quanto egli apparisse minore, poi colla memoria paragonai Venere a <lb></lb>qalche macchia di quelle tonde della Luna, e feci conto anco della lontananza: <lb></lb><gap></gap></s></p><pb xlink:href="020/01/410.jpg" pagenum="391"></pb><p type="main">

<s>Ora, con buona riverenza del Torricelli, tutti converranno che nel <emph type="italics"></emph>Li­<lb></lb>bro delle bestialità<emph.end type="italics"></emph.end> di Francesco Fontana, ce ne sien pure quante il suo <lb></lb>censore ce ne volle vedere, non ci può esser bestialità che sia simile a questa. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;intenzione del Granduca Ferdinando, nel consegnar che fece al Vi­<lb></lb>viani la chiave della cassetta, dentro alla quale si custodiva il segreto tor­<lb></lb>ricelliano, fu quella di veder proseguita nel successore del Torricelli l&#039;opera <lb></lb>dei Canocchiali. </s>

<s>Ma perchè il Viviani non avea tanto bene esercitata la mano <lb></lb>nel lavoro de&#039;cristalli, ebbe ordine dallo stesso Granduca di servirsi dell&#039;arte <lb></lb>di Filippo Treffler, a cui dovesse suggerir quelle regole che aveva apprese <lb></lb>per scienza e per esperienza sua propria, oltre agli insegnamenti ricavati dai <lb></lb>manoscritti del Torricelli. </s>

<s>“ Essendochè il Serenissimo Granduca (così lo <lb></lb>stesso Viviani lasciò scritto di sua propria mano) una sera di Dicembre <lb></lb>prossimo passato (1664), prima di andare a Pisa, tra le altre cose coman­<lb></lb>dasse a me Vincenzio Viviani scrittore della presente, che nel tempo di que­<lb></lb>sta sua campagna assistessi a M. </s>

<s>Filippo Treffler, suo torniaio che S. A. la­<lb></lb>sciava apposta in Firenze, con introdurlo e instruirlo in quelle proposizioni <lb></lb>che, per l&#039;arte del lavorare i vetri da occhialoni, si cavano dalla teorica e <lb></lb>dai fondamenti diottrici, ed avendo io come devotissimo suddito promesso di <lb></lb>ubbidire, conferii al suddetto Filippo le infrascritte cose, nel modo che ap­<lb></lb>presso, ma pure tutte in somma confidenza ” (MSS. Gal. </s>

<s>Disc., T. CXXXIII, <lb></lb>c. </s>

<s>20). E seguita a scrivere, sotto varii capi numerati, gl&#039;insegnamenti che <lb></lb>dette al Treffler, i quali però tutt&#039;altro che esser cavati dalla <emph type="italics"></emph>teorica e dai <lb></lb>fondamenti diottrici,<emph.end type="italics"></emph.end> consistono in regole pratiche, non molto diverse da <lb></lb>quelle insegnate dal Torricelli. </s>

<s>O sien sue o d&#039;altri, il Viviani stesso lasciò <lb></lb>scritte alcune <emph type="italics"></emph>Ricette per far lo stucco a freddo<emph.end type="italics"></emph.end> (ivi, c. </s>

<s>4) onde attaccar <lb></lb>con esso e non colla pece i vetri; però si conosce assai bene che egli at­<lb></lb>tendeva a queste cose, non per suo proprio genio, ma per compiacere al <lb></lb>Granduca. </s></p><p type="main">

<s>Tenue è pure lo studio che fece intorno all&#039;uso dei Canocchiali, ben­<lb></lb>chè vi si riveli il solito acume e la fecondità dell&#039;ingegno. </s>

<s>Descrisse un <lb></lb><emph type="italics"></emph>Modo di ritrovar con l&#039;Occhiale o senza, da un dato luogo, la distanza <lb></lb>di un oggetto di nota altezza o larghezza<emph.end type="italics"></emph.end> (ivi, T. CXXXIV, c. </s>

<s>2) e inse­<lb></lb>gnò una regola <emph type="italics"></emph>per conoscere l&#039;aggrandimento di un Occhiale<emph.end type="italics"></emph.end> (ivi, c. </s>

<s>3) <lb></lb>più precisa di quella insegnata già da Galileo, nel suo Nunzio Sidereo. </s></p><p type="main">

<s>Altre regole lasciò qua e là sparse per i suoi Manoscritti, alcune delle <lb></lb>quali, oltre ad essere utili a chi allora, senza troppa scienza diottrica, ma­<lb></lb>neggiava Canocchiali, si direbbero, nella loro stessa facilità, quasi eleganti. </s>

<s><lb></lb>Tal sarebbe, per esempio, la regola ch&#039;egli insegna <emph type="italics"></emph>per conoscere se l&#039;ocu­<lb></lb>lare di un Telescopio è distante dall&#039;obiettivo per la dovuta lunghezza.<emph.end type="italics"></emph.end><pb xlink:href="020/01/411.jpg" pagenum="392"></pb>“ Osserva, egli dice, se l&#039;oggetto luminoso apparisce rosso, che allora sarà <lb></lb>corto, e se si vede turchino, che allora sarà troppo lungo; onde da tai con­<lb></lb>trassegni averai modo d&#039;aggiustarlo a dovere ” (ivi, T. CXXXV, c. </s>

<s>8). </s></p><p type="main">

<s>Mentre che dal Treffler e dal Viviani s&#039;attendeva in Toscana a costruir <lb></lb>Canocchiali, per mantener vive le tradizioni di Galileo e del Torricelli, e <lb></lb>per compiacere al Granduca, Cristiano Huyghens, nella mente del quale ri­<lb></lb>fulgeva più che in altra mai la scienza diottrica, speculava intorno a per­<lb></lb>fezionar lo strumento, che gli dovea rivelare altre nuove meraviglie nel cielo. </s>

<s><lb></lb>Egli è veramente il primo che possa dire di aver cavati dai fondamenti diot­<lb></lb>trici i principii dell&#039;arte, a esercitar la quale veniva aiutato dal fratello suo <lb></lb>Costantino, che, morto, ei nel Cosmoteoro commemora con parole tuttavia <lb></lb>vive e fragranti di affetto. </s>

<s>“ Fortasse autem, ubi ad signa Borea Saturnus <lb></lb>revertetur, alteque supra horizontem attolletur, nam quo tempore haec scri­<lb></lb>bimus maxime deprimitur, aliquid circa haec novi observari continget, si <lb></lb>quis tuas tunc lentes, Frater optime, ad Telescopia pedum 170 et 210 para­<lb></lb>tas, sideribus applicet ” (Op. </s>

<s>Var. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>698). E dopo aver <lb></lb>commemorati gli sperimenti, <emph type="italics"></emph>in ambulacris suburbanis sub noctem,<emph.end type="italics"></emph.end> col dol­<lb></lb>cissimo fratello suo istituiti; così, con mestizia ineffabile, conclude: “ Quo­<lb></lb>rum equidem lubens reminiscor, simulque iucundi laboris nostri, quem in <lb></lb>elaborandis expoliendisque vitreis huiusmodi discis, impendere una soleba­<lb></lb>mus, excogitatis novis artificiis machinisque, semperque ulteriora agitan­<lb></lb>tes ” (ibi). </s></p><p type="main">

<s>Tanto era giunto nel 1655 l&#039;Huyghens, a perfezionare il suo nuovo <lb></lb>Canocchiale, che gli rivelò una luna, non più veduta ricircolare intorno a <lb></lb>Saturno. </s>

<s>Ma la sua attenzione era tutta rivolta al Pianeta, e fu quello stesso <lb></lb>Canocchiale che fecegli nascere un sospetto di ciò che fosse veramente ca­<lb></lb>gione di tanto strane apparenze. </s>

<s>Non si assicurava però ancora, infintantochè <lb></lb>non si fosse preparato uno strumento più che mai perfetto, e studiava in <lb></lb>che modo vi potesse riuscire. </s>

<s>Sagace com&#039;egli era, conobbe che doveva quel <lb></lb>modo principalmente consistere in toglier l&#039;iridescenza alle lenti, ardua im­<lb></lb>presa e da tutti allora reputata impossibile. </s>

<s>Ma l&#039;Huyghens aveva con sua <lb></lb>gran meraviglia osservato che, nei Canocchiali a tre o a quattro lenti, gli <lb></lb>effetti d&#039;iridescenza, che pareva dovessero moltiplicarsi, riuscivano invece <lb></lb>alquanto minori. </s>

<s>Incominciò a pensare intorno a ciò attentamente, cosicchè <lb></lb>all&#039;ultimo vide quella sua prima maraviglia risolversi tutta in una ragione, <lb></lb>la quale, secondo lui, consisteva in far sì che l&#039;una lente correggesse o to­<lb></lb>gliesse via i colori, che le si venivano a rappresentare dall&#039;altra. </s>

<s>Fu questa <lb></lb>speculazione che condusse l&#039;Huyghens a compor di due convessi, invece che <lb></lb>d&#039;un solo, l&#039;oculare del suo Canocchiale astronomico. </s></p><p type="main">

<s>La voce di una tale e tanta novità, introdotta nella fabbrica dei Tele­<lb></lb>scopi, corse tosto di Olanda alle orecchie di tutti gli Astronomi, e special­<lb></lb>mente d&#039;Italia, i quali entrarono in gran curiosità di sapere il vero di que­<lb></lb>sta cosa. </s>

<s>Il Cassini sollecitava un amico suo, perchè s&#039;informasse, per mezzo <lb></lb><gap></gap><pb xlink:href="020/01/412.jpg" pagenum="393"></pb><emph type="italics"></emph>altra combinazione di lenti per Telescopi, che tolga ogni colore agli og­<lb></lb>getti, e gli conservi inalterabili di figura<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Cim., T. XIV, c. </s>

<s>51). <lb></lb>Ma il Viviani annunzia nell&#039;Accademia del Cimento la cosa come certa, con­<lb></lb>forme alla seguente nota che di sua propria mano lasciò così scritta: “ Uge­<lb></lb>nio ha fatto occhiali anco più rari di nuova invenzione, dove i cristalli sono <lb></lb>composti di due convessi da una parte e piani dall&#039;altra, che così tolgono <lb></lb>i colori e mantengono tutti gli oggetti diritti ” (ivi, T. IV, c. </s>

<s>252). </s></p><p type="main">

<s>La curiosità fu poi sodisfatta in tutti e tutti pur s&#039;acquietarono nella <lb></lb>certezza del fatto, quando nel 1659 l&#039;Huyghens stesso uscì fuori col suo <lb></lb><emph type="italics"></emph>Systema Saturnium.<emph.end type="italics"></emph.end> “ Sed antequam, egli così avverte in principio, obser­<lb></lb>vationes exhibeamus, de Telescopiis nostris .... pauca referre expediat ” <lb></lb>(Op. </s>

<s>Var. </s>

<s>cit. </s>

<s>1724, pag. </s>

<s>537). E proseguendo a far la descriziono del suo <lb></lb>astronomico strumento, così particolarmente scrive dell&#039;oculare: “ Ab altera <lb></lb>parte, quae nimirum oculo admovetur, bina sunt vitra minora, 1 1/2 polli­<lb></lb>cum diametro aequantia iuncta invicem, quaeque hoc pacto aequipollent con­<lb></lb>vexo colligenti radios parallelos ad intervallum unciarum 3 aut paulo etiam <lb></lb>angustius ” (ibi). Che poi da una tale composizione di lenti glie ne fossero <lb></lb>risultati mirabili effetti, oltre al venir da sè naturalmente insinuato per la <lb></lb>scoperta che poi passa a descrivere dell&#039;anello Saturnio, lo prefinisce meglio <lb></lb>l&#039;Autore, asserendo di essere riuscito per quel modo ad ottenere un in­<lb></lb>grandimento centuplicato. </s>

<s>“ Centuplam itaque fere rationem hanc in perspi­<lb></lb>cillis nostris esse constat, cum Galileiana non ultra trigecuplam processe­<lb></lb>rint ” (ibi, pag. </s>

<s>538). </s></p><p type="main">

<s>Ma benchè tutti fossero oramai resi certi delle invenzioni delle due lenti <lb></lb>accoppiate, nessun sapeva però intendere, di quell&#039;efficace accoppiamento, <lb></lb>le vere ragioni. </s>

<s>Di qui ebbero origine que&#039;giudizi vaghi, che si fecero in­<lb></lb>torno ai nuovi Canocchiali ugeniani, l&#039;èccellenza de&#039;quali, non essendo stata <lb></lb>ancora diottricamente dimostrata, s&#039;ammetteva come possibile a spiegare i <lb></lb>maravigliosi fatti osservati. </s>

<s>Così, per esempio, il Borelli dovendo fare un <lb></lb>confronto tra i Canocchiali dell&#039;Huyghens e quelli del Divini, si esprime <lb></lb>nella forma seguente: “ Ma un giudice disappassionato direbbe che, senza <lb></lb>pregiudizio della non mai abbastanza lodata perfezione degli Occhiali di Eu­<lb></lb>stachio, potrebbero essere le lenti di quelli dell&#039;Ugenio formate d&#039;altra figura <lb></lb>che della sferica, conforme hanno creduto poter lavorarsi molti uomini in­<lb></lb>signi: di più quel raddoppiare le lenti vicino all&#039;occhio <emph type="italics"></emph>forse potrebbe<emph.end type="italics"></emph.end> far <lb></lb>buon effetto ” (MSS. Gal. </s>

<s>Cim., T. XII, c. </s>

<s>99). </s></p><p type="main">

<s>Non mancò nonostante chi apertamente uscisse fuori a mettere in dub­<lb></lb>bio, e anzi a negare in particolar modo che le due lenti accoppiate avessero <lb></lb>virtù di toglier via l&#039;iridescenza ne&#039;Canocchiali ugeniani. </s>

<s>Il marchese Cor­<lb></lb>nelio Malvasia, avendone interrogato in proposito M. Petit, n&#039;ebbe da lui <lb></lb>così fatta risposta: “ Cum autem de ipsius invento duorum ocularium simul <lb></lb>iunctorum, ad evitandos iridis colores spatiumque amplificandum, sermonem <lb></lb>facis, id seponam iamdudum nobis in mentem venisse, eoque usos fuisse <lb></lb><gap></gap> convenientis ad confectionem ocularium, <pb xlink:href="020/01/413.jpg" pagenum="394"></pb>ex utraque parte convexorum. </s>

<s>Is enim ad alios usus inutilis satis videtur, <lb></lb>nec interest convexitates istorum duorum ocularium contiguas esse ut <lb></lb>sic D⫏, vel oppositas ⫏D ut sic, aut hoc modo, quod aliis praefertur, dispo­<lb></lb>sitas ⫏⫏: nullis enim tollitur obsolute iris. </s>

<s>Si aliunde emanet hoc, est ab <lb></lb>incidentia nimis obliqua radiorum in superficiem refringen­<lb></lb>tem ” (MSS. Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>19). </s></p><p type="main">

<s>Ma non era ancora dell&#039;Huyghens pubblicata la Diottrica, <lb></lb><figure id="id.020.01.413.1.jpg" xlink:href="020/01/413/1.jpg"></figure></s></p><p type="caption">

<s>Figura 29.<lb></lb>nella quale si riserbava a dar quella teoria dell&#039;acromatismo, <lb></lb>di che aveva fatto già l&#039;applicazione alle lenti del suo Tele­<lb></lb>scopio. </s>

<s>Nella proposizìone LIV di quel celebre Trattato, uscito <lb></lb>postumo nel 1703 come sappiamo, dop&#039;aver l&#039;Autore descritto <lb></lb>l&#039;andamento dei raggi refratti ne&#039;Telescopi di quattro lenti, <lb></lb>così soggiunge, per sodisfare co&#039;principii diottrici a coloro, <lb></lb>i quali non intendevano il segreto effetto del suo oculare <lb></lb>composto: “ Mirum videtur in hoc Telescopio colores iridis <lb></lb>oriri plurium ocularium refractione, non magis quam cum una <lb></lb>ocularis adhibetur. </s>

<s>Sed ratio haec est quod lens QR (fig. </s>

<s>29) <lb></lb>corrigit et aufert colores quas lens KL produxit. </s>

<s>Idem enim <lb></lb>accidit radio OKRN, per superficies inclinatas ad K ac deinde <lb></lb>ad R transeunti, ac si per cuneos binos contrarie positos SS, TT (fig. </s>

<s>30) <lb></lb>transiret parallelis lateribus qui colore non inficitur non magis quam si per <lb></lb>laminam vitream incederet ” (Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>195, 96). <lb></lb><figure id="id.020.01.413.2.jpg" xlink:href="020/01/413/2.jpg"></figure></s></p><p type="caption">

<s>Figura 30.</s></p><p type="main">

<s>Aveva senza dubbio ragione il Petit a dire che a que­<lb></lb>sto modo <emph type="italics"></emph>nullis tollitur absolute iris,<emph.end type="italics"></emph.end> ma, a riuscire al <lb></lb>tanto desiderato effetto, aveva pure l&#039;Huyghens aperta così <lb></lb>e raddirizzata la via agli ottici futuri. </s>

<s>Il Newton poi dimo­<lb></lb>strò che non bastava comporre insieme due mezzi rifran­<lb></lb>genti della stessa natura, ma che bisognava fossero di na­<lb></lb>tura alquanto diversa e propose di accoppiare insieme lenti <lb></lb>cristalline con lenti ripiene d&#039;acqua. </s>

<s>“ Si perspicillorum <lb></lb>vitra obiectiva ex vitris duobus sphaerice figuratis et aquam <lb></lb>inter se claudentibus constentur, fieri potest ut a refractionibus aquae er­<lb></lb>rores refractionum quae fiunt in vitrorum superficiebus extremis satis ac­<lb></lb>curate corrigantur ” (Principia Philos. </s>

<s>T. I, Genevae 1739, pag. </s>

<s>547). L&#039;Eu­<lb></lb>lero ridusse a calcolo, di quelle lenti di varia rifrangibilità, lo spessore e la <lb></lb>forma, e il Dollond, componendo insieme i due cunei ugeniani sopra de­<lb></lb>scritti, di due cristalli di vario poter dispersivo, riuscì finalmente a risol­<lb></lb>vere il problema. </s></p><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Non senza una giusta ragione, ripensando l&#039;Huyghens alla numerosa se­<lb></lb>quela, che ebbero gli esempi galileiani, si compiaceva seco stesso di essere <lb></lb>stato il primo, nel numero de&#039;costruttori del Telescopio, a farsi, dopo Ga-<pb xlink:href="020/01/414.jpg" pagenum="395"></pb>lileo, messaggero agli uomini d&#039;altre nuove maravigliose novità celesti. </s>

<s>Quasi <lb></lb>tutti coloro che lo avevano preceduto, e specialmente il Torricelli, benchè aves­<lb></lb>sero di molto accresciute le lunghezze dei tubi, e con gli obiettivi di grande <lb></lb>sfera avessero ottenuti notabili ingrandimenti, fecero nonostante poco pro­<lb></lb>fitto nell&#039;osservazione degli astri, essendochè l&#039;iridescenza e l&#039;aberrazione <lb></lb>di sfericità non ne lasciassero con esattezza intravedere i contorni. </s>

<s>“ Nos <lb></lb>autem, soggiunge l&#039;Huyghens, magis auspicato rem eamdem aggressi, cum, <lb></lb>quae ad refractiones radiorum attinent perspecta haberemus, ipsique nobis <lb></lb>lentes effecissemus, ac telescopia pedes vigin ti et amplius longe, his Saturni <lb></lb>formas non ante visas deprehendimus, causamque earum annulum globo cir­<lb></lb>cumdatum nullo in caeteris planetis exemplo ” (Dioptr. </s>

<s>ibi, pag. </s>

<s>165). E prose­<lb></lb>guendo a dir di Saturno, poco appresso conclude: “ Nostris autem observatio­<lb></lb>nibus excitati Astronomi atque artifices maiora subinde Telescopia paraverunt <lb></lb>in quibus optima, quae a Josepho Campano Romae fabricata ” (ibi). </s></p><p type="main">

<s>Giuseppe Campani scrive di sè stesso dicendo di essere stato, per lungo <lb></lb>tempo, esortato ad applicar la mente e la mano agli studi diottrici, dal ce­<lb></lb>lebre padre Daniello Bartoli della compagnia di Gesù (Ragguaglio ecc., <lb></lb>Roma 1664, pag. </s>

<s>9). Con la scorta di lui, ei soggiunge, rivoltomi agli studii <lb></lb>della Diottrica “ applicai tutto l&#039;animo e tutto il mio studio all&#039;invenzione <lb></lb>d&#039;un Torno esattissimo da lavorare i vetri, senza altro mezzo di forma. </s>

<s>E <lb></lb>riuscitomi finalmente di conseguirlo, non senza lunghissime fatiche, ed in­<lb></lb>numerabili esperienze, riconosco, non dalla debolezza del mio ingegno, ma <lb></lb>da Dio questo dono; parendomi in vero, se non l&#039;intero compimento del­<lb></lb>l&#039;arte, l&#039;unico mezzo almeno da giungerne alla perfezione. </s>

<s>Perchè, con <lb></lb>l&#039;aiuto di questo Torno mi riescono gli Occhialoni, non dico d&#039;ultima squi­<lb></lb>sitezza, che non presumo d&#039;aver fissate le mete agli ingegni degli uomini, <lb></lb>ma tali certo, che da altri sono stati stimati migliori de&#039;veduti fin ora ” <lb></lb>(ivi, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>In che consistesse però l&#039;artifizio di questo Torno, non si potè mai <lb></lb>saper da nessuno, per cui, in Italia e fuori, si sospettò e s&#039;andò spargendo <lb></lb>voce che fosse una mera finzione dell&#039;artefice, per tener più sicuramente <lb></lb>occulto alle altrui perquisizioni qualche suo nuovo segreto. </s>

<s>In una bella e <lb></lb>importante lettera al principe Leopoldo de&#039;Medici tradotta dal latino, forse <lb></lb>dal Dati, l&#039;Huyghens, dop&#039;aver parlato d&#039;altre cose e tutte in soggetto astro­<lb></lb>nomico, soggiunge: “ M&#039;era prima capitata una Narrazione delle nuove os­<lb></lb>servazioni intorno a Saturno di Giuseppe Campani, nella quale, oltre alla <lb></lb>confermazione della mia ipotesi dell&#039;anello saturnino, trovai un bellissimo <lb></lb>ritrovamento d&#039;un Torno per far le lenti, proposto allora per la prima volta. </s>

<s><lb></lb>Ma siccome ciò, a prima vista, parve a me appena possibile, così mi accorsi <lb></lb>poi che anche altri ne dubitavano, siccome ancora di quello che importa <lb></lb>più, cioè se fossero migliori le lenti che si diceva che fossero state lavorate <lb></lb>a quel Torno, che quell&#039;altre che sono lavorate col metodo solito, senza <lb></lb>macchina alcuna, nè ancor per quel che io sappia è finita quella contro­<lb></lb><gap></gap> ” (MSS. Gal. </s>

<s>Cim., T. XVIII, c. </s>

<s>316). </s></p><pb xlink:href="020/01/415.jpg" pagenum="396"></pb><p type="main">

<s>Ma la controversia fu poi insomma definita dai fatti, avendo il Campani <lb></lb>apparecchiato al Cassini Canocchiali tanto più eccellenti di quelli stessi del­<lb></lb>l&#039;Huyghens, che potè il nostro celebre Astronomo italiano veder presto Sa­<lb></lb>turno circondato da due altri satelliti, oltre a quello ugeniano, e scoprir le <lb></lb>macchie in Giove e in Marte, da prefinire il periodo della loro rotazione. </s>

<s>Di <lb></lb>ciò, e della eccellenza de&#039;canocchiali del suo rivale romano, fu fatta gene­<lb></lb>rosa testimonianza dallo stesso Huyghens, il quale, dop&#039;essersi compiaciuto <lb></lb>che il Campani avesse ricevuto da&#039;suoi stessi esempi eccitamento a perfe­<lb></lb>zionare i suoi ottici strumenti, soggiunge: “ Quorum opera feliciter, decen­<lb></lb>nio post, duos alios praeter nostrum illum Comites apud Saturnum reperit <lb></lb>Dominus Cassinus. </s>

<s>Idemque in Jovis ac Martis sideribus maculas quosdam <lb></lb>observavit, ex quarum motu etiam globorum, quibus inerant, conversiones, <lb></lb>certis periodis definiret ” (Dioptr. </s>

<s>ibi). </s></p><p type="main">

<s>Comunque sia, se può mettersi in dubbio che il Campani avesse vera­<lb></lb>mente ritrovato un artifizio nuovo da formare e da pulire le lenti, è però <lb></lb>cosa certa ch&#039;ei pensò de&#039;primi a dare alle lenti stesse una nuova compo­<lb></lb>sizione nei Telescopi, e tale da diminuirne notabilmente la lunghezza del <lb></lb>tubo, e da ricavarne altri migliori effetti. </s>

<s>Richiesto da un signore, che era <lb></lb>entrato in gran curiosità di sapere il modo di quella nuova composizione, <lb></lb>così il Campani stesso, in una sua lettera del dì 6 di Settembre 1664, gliela <lb></lb>descrive: </s></p><p type="main">

<s>“ Il mio Canocchiale, che V. S. Ill.ma mi ha comandato che le descriva, <lb></lb>è fatto nella seguente maniera: ED è il canocchiale (fig. </s>

<s>31). In D sta il <lb></lb><figure id="id.020.01.415.1.jpg" xlink:href="020/01/415/1.jpg"></figure></s></p><p type="caption">

<s>Figura 31.<lb></lb>vetro oggettivo. </s>

<s>In C sta una lente <lb></lb>piana convessa, inclinata, secondo la <lb></lb>linea BC, nel piano verso D. </s>

<s>Nel can­<lb></lb>noncino AB vi è una lente oculare <lb></lb>convessa proporzionata all&#039;oggettivo D, <lb></lb>qual lente è collocata per piano oriz­<lb></lb>zontale in B, in distanza proporzionata alla lente C. </s>

<s>In A si mette l&#039;occhio, <lb></lb>che pure deve star tanto distante dalla lente B, quanto se ne terrebbe lon­<lb></lb>tano, se con essa si guardasse, e per il canocchiale, secondo il modo ordi­<lb></lb>nario. </s>

<s>In E vi è un coperchietto amovibile, e questo serve per poter diriz­<lb></lb>zare comodamente il canocchiale all&#039;oggetto. </s>

<s>” </s></p><p type="main">

<s>“ Questo mio Canocchiale mostra l&#039;oggetto con tutta quella terminazione, <lb></lb>ovvero distinzione e nettezza, che può desiderarsi, ed in qualunque parte <lb></lb>della lente inclinata, dove s&#039;imbattano a cadere le specie dell&#039;oggetto, e con <lb></lb>maggior campo ed ingrandimento di quello, che a mio parere possa aversi <lb></lb>dal Canocchiale, del quale V. S. mi ha parlato questa mattina, quand&#039;io <lb></lb>sono venuto ad invitarla a vedere il mio, e con occasione com&#039;ho raccon­<lb></lb>tato, che iersera il sig. </s>

<s>ab. </s>

<s>Falconieri mi accennò un non so che di cosa <lb></lb>simile avvisatagli da Firenze, a cui io subito mi esibii di farnele vedere l&#039;ar­<lb></lb>tificio, da me già molto prima praticato, ma poco stimato, per esserne riu­<lb></lb>scito vano il fine, che io ne pretendeva. </s>

<s>In questo l&#039;oggetto apparisce più <pb xlink:href="020/01/416.jpg" pagenum="397"></pb>che negli altri, ma assai men chiaro, e quindi nasce questa sì fatta net­<lb></lb>tezza, tanto che tolta da&#039;miei Canocchiali di quattro lenti la gran quantità <lb></lb>e grossezza delle puliche, le quali spesse volte s&#039;incontrano nel vetro, e <lb></lb>tolta la luce superflua, cioè ridotti ad ugual chiarezza degli altri del nuovo <lb></lb>modo, mostrano l&#039;oggetto ugualmente netto e terminato, e scoprono assai <lb></lb>più campo, e riescono molto più comodi. </s>

<s>Inoltre l&#039;occhiale del nuovo modo, <lb></lb>sebbene può avere il vetro oggettivo tutto aperto, ad ogni modo, per l&#039;uso <lb></lb>delle stelle, poco o niente serve, tanto che gli altri miei Canocchiali di quat­<lb></lb>tro lenti sono migliori, e possono con molto gusto e sodisfazione adoperarsi <lb></lb>anche per gli oggetti celesti. </s>

<s>” </s></p><p type="main">

<s>“ Io ne trovai l&#039;invenzione nel primo Canocchiale, che feci di quattro <lb></lb>lenti, mentre io ne andava cercando un&#039;altra, che poi non mi riuscì. </s>

<s>In luogo <lb></lb>del cannoncino e lente AB applicai un Microscopio, ed in luogo della lente C <lb></lb>una carta finissima e bianchissima, perchè speravo che forse forse quelle <lb></lb>specie dell&#039;oggetto, che dal vetro D venivano portate in C, venissero ricre­<lb></lb>sciute e vedute così bene e da vicino, come, col medesimo Microscopio av­<lb></lb>verrebbe di una piccola pittura fatta col pennello nell&#039;istessa carta, dove <lb></lb>questa doveva dipingersi, e meglio formarsi dalla natura, mediante il vetro D, <lb></lb>ed il cannone oscuro DE. </s>

<s>Ma essendomi tutto riuscito vano, il resto del­<lb></lb>l&#039;invenzione non mi par degna di molto applauso, non ritraendosene altro <lb></lb>che una certa soddisfazione di propria curiosità, senza utile considerabile, e <lb></lb>con qualche incomodo ” (MSS. Gal. </s>

<s>Cim., T. XXIV, c. </s>

<s>162). </s></p><p type="main">

<s>Benchè il Campani non sapesse tenere in debito pregio la sua nuova <lb></lb>invenzione, vedremo nonostante fra poco l&#039;utile partito che trassero di lì il <lb></lb>Newton e l&#039;Hudley nella costruzione de&#039;Telescopi catadiottrici, sostituendo <lb></lb>alla carta, sopra la quale si doveva dipinger dall&#039;obiettivo l&#039;immagine mi­<lb></lb>croscopica, uno specchio metallico o un prisma isoscele cristallino. </s>

<s>Ma in­<lb></lb>tanto non è possibile parlar di Giuseppe Campani, senza accoppiar necessa­<lb></lb>riamente al suo nome, il nome di un altro ottico, che teneva pure bottega <lb></lb>aperta in Roma, Eustachio Divini. </s>

<s>Egli è quell&#039;Eustachio orologiaro, di cui <lb></lb>parlava di sopra, in una sua lettera il Torricelli, onorandolo col titolo di <lb></lb>amico suo, perchè, sebben quello stesso orologiaro si fosse dato, infin da <lb></lb>quel tempo, a fabbricar Canocchiali, confessava nulladimeno di non esser <lb></lb>venuto ancora a quella eccellenza, a cui pretendeva di esser già arrivato il <lb></lb>Matematico del Granduca. </s>

<s>Ma se i primi e incerti passi fatti nell&#039;arte, e la <lb></lb>gran fama del Torricelli poterono per allora tener basso il Divini, s&#039;esaltò <lb></lb>fieramente, quando si trovò poi a dover competere con un suo pari. </s>

<s>“ E a <lb></lb>dirlo a V. A. S. (scriveva M. A. </s>

<s>Ricci al principe Leopoldo de&#039;Medici) que­<lb></lb>sti due artefici e virtuosi (il Campani e il Divini) sono in una sì forte emu­<lb></lb>lazione, che altri non può aprir la bocca a favor dell&#039;uno, senza che l&#039;al­<lb></lb>tro se ne offenda, quindi è che ognun si astiene dal dire il parer suo. </s>

<s>Il <lb></lb>signor Cassini ha gran sodisfazione di quello del Campani, e con esso va <lb></lb>tuttavia scoprendo cose nuove nel cielo ” (Targioni, Notizie Aggrandim., <lb></lb>T. II, P. II, pag. </s>

<s>748). </s></p><pb xlink:href="020/01/417.jpg" pagenum="398"></pb><p type="main">

<s>Ma come il Cassini restava sodisfatto dell&#039;opera del Campani, così il <lb></lb>Borelli sembrava fosse sodisfatto ugualmente dell&#039;opera del Divini, e delle <lb></lb>rivalità fra gli artefici venivano a farsi così strumento attizzatore le rivalità <lb></lb>fra&#039;due grandi Astronomi. </s>

<s>A decider però da qual parte fosse veramente il <lb></lb>vantaggio furono invocate le nuove apparenze di Saturno, per cui preten­<lb></lb>deva il Campani che, mostrando i suoi Canocchiali la vera figura dell&#039;anello, <lb></lb>dovessero esser più eccellenti di quelli del Divini, che avean dato occasione <lb></lb>al Fabry di frantendere il sistema del lontano Pianeta, introducendovi il <lb></lb>gioco di que&#039;globi bianchi e neri. </s>

<s>Il Campani stesso, traduceva, così pero­<lb></lb>rando in causa propria, a decider la gran questione innanzi all&#039;autorevole <lb></lb>tribunale del principe Leopoldo: </s></p><p type="main">

<s>“ Resta dunque da vedere chi de&#039;suoi cultori (della Diottrica) sia più <lb></lb>degli altri avanzato nella perfezione del lavoro. </s>

<s>Gli anni passati, a cagione <lb></lb>che Saturno apparve con volto diverso a diversi spettatori, che adoprarono <lb></lb>diversi Occhiali, suscitaronsi in tutta Europa, ma particolarmente in Roma <lb></lb>e in Firenze, due gagliarde controversie. </s>

<s>La prima fu circa il sistema di <lb></lb>esso Pianeta, e la seconda, dove poi venne a terminarsi dai disputanti la <lb></lb>prima, fu circa il valore dei Canocchiali, e V. A. S. fu dalle parti litiganti <lb></lb>deputato giudice della causa. </s>

<s>L&#039;ombra segante il disco di Saturno, che il <lb></lb>signor Cristiano Hugenio asseriva di aver veduta co&#039;suoi occhiali, siccome <lb></lb>rendeva verisimile il suo ingegnoso sistema, così poteva dare gran sospetto <lb></lb>dell&#039;imperfezione degli Occhialoni dell&#039;altra parte, che costantemente negava <lb></lb>l&#039;ombra suddetta, ed asseriva un altro pure assai diverso sistema, tutto <lb></lb>composto di globi bianchi e neri, perchè così glie ne davano indizio manife­<lb></lb>sto, diceva egli, le apparenze vedute in Saturno co&#039;suoi squisitissimi vetri. </s>

<s><lb></lb>Queste dispute, siccome distrassero molti a varii sentimenti, così trassero la <lb></lb>mia mente e la mano a procurar di far vetri tali, con i quali si fosse po­<lb></lb>tuto ocularmente mostrare la verità di uno dei due sistemi, parendomi di <lb></lb>fare non poco acquisto, quando ciò mi fosse riuscito, mentre, oltre al do­<lb></lb>vermisi in tal caso il nome di primo scopritore di quella verità, che era <lb></lb>dubbia ed incerta a tutti, averei liberati i seguaci di una delle parti liti­<lb></lb>ganti dagli errori così del falso sistema, come della supposta e non sussi­<lb></lb>stente bontà degli Occhiali da loro erroneamente tenuti per i migliori, ed <lb></lb>ultimamente averei fatto a me stesso questo servigio di rendere sopra quelli <lb></lb>avvantaggio li miei vetri, tuttavolta che con essi avessi io potuto far vedere <lb></lb>al mondo o quel cerchio o quell&#039;ombra o altra particolarità, che sotto a <lb></lb>quest&#039;istesso cielo romano non si erano ancora vedute con gli altri vetri, <lb></lb>nemmeno quando gli anni addietro erano molto più visibili, che non sono <lb></lb>al presente. </s>

<s>” </s></p><p type="main">

<s>“ Sebbene V. A. S. ha udite tutte queste cose, e ne ha vedute le mie <lb></lb>osservazioni, imprese ad ogni modo, perchè assai più efficacemente muo­<lb></lb>vansi gli animi dalla potenza visiva che dall&#039;udito; io sono a supplicare <lb></lb>che, immediatamente e subito che l&#039;A. V. averà fatte le osservazioni di Sa­<lb></lb>turno e di Giove, con gli altri canocchiali romani, voglia farmi questo onore <pb xlink:href="020/01/418.jpg" pagenum="399"></pb>di nuovamente osservare questi Pianeti col mio Canocchiale, levatene però <lb></lb>le due lenti oculari più lontane dall&#039;occhio, e dopo che si sarà servita della <lb></lb>propria lente oculare di questo Canocchiale, potrà anche, in luogo di que­<lb></lb>sta, servirsi di un&#039;altra lente più acuta, che ho mandata a questo fine, con <lb></lb>la quale venerdì sera, nel giardino del Papa a Monte Cavallo, si videro a <lb></lb>maraviglia distinti il cerchio ed il globo di Saturno, senza ombra veruna, <lb></lb>apparendovi solamente i meri contorni che seco porta la ragione di Pro­<lb></lb>spettiva. </s>

<s>” </s></p><p type="main">

<s>“ Supplico intanto l&#039;A. V. a degnarsi di fare adoperare ogni esatta di­<lb></lb>ligenza ed aggiustatezza de&#039;vetri, così del mio come degli altri Canocchiali, <lb></lb>in tutte le prove ed in tutti i paragoni che si faranno .... e se, dopo i pa­<lb></lb>ragoni, V. A. si compiacerà di farmene dare pieno ragguaglio per lettera, .... <lb></lb>lo riceverò per grazia speciale di V. A. ” (MSS. Gal. </s>

<s>Cim., T. XVIII, c. </s>

<s>198). </s></p><p type="main">

<s>Forse astennesi il principe Leopoldo di dar sentenza finale, per le ra­<lb></lb>gioni sopra dette dal Ricci, ma la storia ha pronunziato oramai il suo giu­<lb></lb>dizio a favore del Campani, concludendo che i Canocchiali di lui, giovarono <lb></lb>meglio di quelli del Divini ai progressi dell&#039;Astronomia, facendone di ciò <lb></lb>chiara testimonianza le insigni scoperte del Cassini. </s>

<s>Ma perchè, così il Cam­<lb></lb>pani come tutti gli altri artefici di vetri rifrattori, s&#039;incontrarono in una di <lb></lb>quelle difficoltà, credute allora insuperabili, nel tentar nuovi progressi, ebbe <lb></lb>a rivolgersi l&#039;arte ai Telescopi catottrici, il profittevole uso de&#039;quali, benchè <lb></lb>incominci dal Newton, ne fu speculato lungo tempo prima l&#039;artifizio dai no­<lb></lb>stri italiani. </s></p><p type="main">

<s><emph type="center"></emph>VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il dì 7 Luglio 1626 Cesare Marsili, incominciava così una sua lettera, <lb></lb>scritta da Bologna e indirizzata a Firenze a Galileo: “ Un certo messer Gio­<lb></lb>vanni, il quale pretende, dopo la morte di messer Cesare Carafaggi bolo­<lb></lb>gnese (che negli scoprimenti e segreti della natura, come nell&#039;ingegno più <lb></lb>che nello studio era eccellentissimo) di essere unico suo erede nel modo di <lb></lb>fabbricare specchi tanto di cristallo, che operano per rifrazione, quanto di <lb></lb>altre materie, che operano per riflessione, mi portò alcuni giorni sono l&#039;in­<lb></lb>cluso disegno, acciò l&#039;inviassi a V. S. E,, ov&#039;ella vede che egli pretende po­<lb></lb>ter fare uno specchio concavo, che non solo nella quarta, come dicono i <lb></lb>moderni, ma nel centro, come dicevano gli antichi, e oltre ancora, come anco <lb></lb>dentro della quarta in dati luoghi, possa accendere il fuoco, e in tutti i luo­<lb></lb>ghi in un medesimo tempo o in un solo, come a lui più piace. </s>

<s>Questi due <lb></lb>erano quelli che si vantavano, com&#039;egli anco professa di presente, sebbene <lb></lb>con gran tempo e con gran dispendio, di poter fare uno specchio, il quale <lb></lb>per riflessione possa fare, anzi faccia, l&#039;effetto del perspicillo ” (Alb. </s>

<s>IX, 156, 7). <lb></lb><gap></gap> accomodato ad uso di ca-<pb xlink:href="020/01/419.jpg" pagenum="400"></pb>nocchiale per rifrazione, veduto da alcuni cavalieri, benchè poco o nulla in­<lb></lb>tendenti delle ragioni di Prospettiva, gli avesse uditi asserire della verità del <lb></lb>fatto, che cioè, con quello specchio concavo, s&#039;ingrandivano ai riguardanti <lb></lb>gli oggetti, al modo stesso che nel Canocchiale ordinario. </s></p><p type="main">

<s>Dopo dieci giorni, rispondeva Galileo: “ Quanto all&#039;altro specchio, che <lb></lb>per riflessione faccia l&#039;effetto del Telescopio, lo stimerei per cosa maravi­<lb></lb>gliosa, e molto volentieri lo vedrei ” (ivi, VI, 316). Ma il Marsili, che non <lb></lb>poteva sodisfar la curiosità dell&#039;amico, si contenta d&#039;assicurarlo esser vera <lb></lb>la cosa stimata da lui maravigliosa: “ Ho poi inteso in confidenza da M. </s>

<s>Gio­<lb></lb>vanni il modo come il specchio concavo accenda in tanti luoghi. </s>

<s>Non ho ve­<lb></lb>duto l&#039;effetto ma lo vedrò, e, senza vederlo, lo credo. </s>

<s>Non riferisco il modo, <lb></lb>per avermelo detto in confidenza. </s>

<s>Intorno allo specchio, nel quale si vede <lb></lb>per riflessione, che io non ho mai potuto vedere, per più che mai sicuri <lb></lb>indizi, non è il specchio d&#039;acciaio solo che facci l&#039;effetto, ma al sicuro vi <lb></lb>si aggiungono lenti o traguardi di cristallo o ambedue ” (Campori, Carteg­<lb></lb>gio ecc., Modena 1881, pag. </s>

<s>247). Galileo, dall&#039;altra parte, conveniva dovere <lb></lb>esser vera quest&#039;ultima congettura del Marsili: “ Dell&#039;altro effetto concorro <lb></lb>con lei che il semplice specchio concavo non basti, ma vi bisogni l&#039;aggiunta <lb></lb>di lente o di traguardo; ma perchè non ho specchio concavo, non posso <lb></lb>tentare esperienza alcuna ” (Alb. </s>

<s>VI, 318). </s></p><p type="main">

<s>La morte di Cesare Carafaggi, e la poca stima che, forse meritamente, <lb></lb>facevasi del successore di lui, messer Giovanni, dovettero essere la potissima <lb></lb>ragione, per cui l&#039;invenzione non fu divulgata, ma in ogni modo, sulle con­<lb></lb>getture e sugli indizii, che equivalgono a una certezza morale, di Galileo e <lb></lb>del Marsili, possiamo asserire essere lo strumento carafaggiano il primo Te­<lb></lb>lescopio a riflessione. </s></p><p type="main">

<s>L&#039;artefice bolognese, ingegnosissimo al dir del Marsili, ma di poco stu­<lb></lb>dio, fu condotto alla sua nuova maravigliosa invenzione dalla pratica: il Ca­<lb></lb>valieri, amicissimo del Marsili e professore di Matematiche nella patria del <lb></lb>Carafaggi, pubblicando nel 1632 il suo <emph type="italics"></emph>Specchio Ustorio,<emph.end type="italics"></emph.end> discorreva così della <lb></lb>stessa invenzione per teoria: “ Potrei anco dire come l&#039;effetto del Canoc­<lb></lb>chiale si averebbe forse anco dalla combinazione di questi specchi o degli <lb></lb>specchi con le lenti, sebben la facilità del produrre la figura sferica farà <lb></lb>che ci prevagliamo piuttosto di questa che dell&#039;altra. </s>

<s>Conciossia cosa adun­<lb></lb>que che lo specchio concavo faccia l&#039;operazione della lente convessa, e lo <lb></lb>specchio convesso della lente cava, è manifesto che, se combineremo lo spec­<lb></lb>chio concavo con il convesso, ovvero con la lente cava, dovremo aver l&#039;ef­<lb></lb>fetto del Canocchiale, e tale forse fu lo specchio di Tolomeo. </s>

<s>Laonde, con <lb></lb>tale occasione, non mancherò di dire com&#039;avendo più volte sentito cercar da <lb></lb>alcuni il modo di fare un paro d&#039;occhiali, che facessero l&#039;effetto del Canoc­<lb></lb>chiale, io pensai che ciò in tal modo si potesse fare: cioè che si collocasse <lb></lb>un traguardo da una banda e dall&#039;altra un specchietto cavo, poichè, met­<lb></lb>tendoci noi questo paro di occhiali, con il contrapporvi uno specchio piano <lb></lb><gap></gap><pb xlink:href="020/01/420.jpg" pagenum="401"></pb>dentro lo specchietto cavo; (scorgendosi però l&#039;uno e l&#039;altro nello specchio <lb></lb>piano anteposto alla nostra faccia) si otterrà l&#039;effetto del Canocchiale. </s>

<s>Egli <lb></lb>è però vero che, dovendo stare questi allo scoperto, faranno il medesimo <lb></lb>che il vetro cavo o convesso, adoperato fuor della canna: anzi per farsi una <lb></lb>riflessione di più, cioè dallo specchio piano, verremo anco perciò a scapitar <lb></lb>più nell&#039;operazione. </s>

<s>Ciò però con questa occasione ho voluto accennare, come <lb></lb>per una bizzarria, per dar qualche sodisfazione a&#039;curiosi, che vogliono cer­<lb></lb>car miglior pane che di farina, poichè all&#039;eccellenza del Canocchiale non <lb></lb>arriveranno mai, per mio credere, nè gli specchi combinati insieme, nè ac­<lb></lb>compagnati con le lenti, come chi ne vorrà far prova, credo si potrà assi­<lb></lb>sicurare “ (Bologna 1650, pag. </s>

<s>76, 77). </s></p><p type="main">

<s>La prova, andata in dimenticanza quella fatta già dal Caravaggi, stette <lb></lb>ancora parecchi anni a farsi, ma poi all&#039;ultimo smentì, almeno in parte, le <lb></lb>previsioni del Cavalieri. </s>

<s>Il Gregory, pubblicando, nel 1663, la sua <emph type="italics"></emph>Optica <lb></lb>promota<emph.end type="italics"></emph.end> proponeva quel nuovo Telescopio a tutti notissimo, perchè descritto <lb></lb>in tutti i Trattati di Fisica, ma in quello stesso tempo si faceva uso in Fran­<lb></lb>cia di un altro Telescopio calottrico, dal Petit magnificato come utile Pole­<lb></lb>moscopio, e come Selenoscopio e Selenografo squisitissimo. </s>

<s>Non consisteva <lb></lb>il nuovo strumento in altro, che in uno de&#039;soliti Canocchiali Kepleriani a <lb></lb>due convessi, in cui l&#039;immagine rovesciata si faceva tornare all&#039;occhio di­<lb></lb>ritta, per via di uno specchio piano. </s>

<s>Il Petit stesso, in una sua lettera del <lb></lb>dì 25 Aprile 1664, così da Parigi lo descriveva al marchese Cornelio Malvasia: </s></p><p type="main">

<s>“ Quod autem spectat ad Telescopia, quae constant lente obiectiva, ocu­<lb></lb>lari convexo et speculo plano, quod corrigat visibilia secus inversa; haec est <lb></lb>constructio: Sumo lentem trium aut quatuor pedum, cui adhibeatur ocu­<lb></lb>lare A (fig. </s>

<s>32) cuius focus sit digitorum 1 1/2 aut duorum ad summum, <lb></lb><figure id="id.020.01.420.1.jpg" xlink:href="020/01/420/1.jpg"></figure></s></p><p type="caption">

<s>Figura 32.<lb></lb>inter quod et oculum adapta <lb></lb>exiguum illud speculum me­<lb></lb>tallicum B, inclinatum ad ho­<lb></lb>rizontem, seu tubos D, 30 <lb></lb>aut 35 grad, capsula simili <lb></lb>infundibulo contentum, et <lb></lb>undique obturatum, excepto foramine C, medii circiter digiti, per quod e <lb></lb>speculo reflectantur ad oculum (in distantia seu foco ipsius vitri ocularis col­<lb></lb>locatum) obiecta erecto situ, quae alioquin cernerentur inversa. </s>

<s>Et haec est <lb></lb>fabrica Telescopii catoptrici, non parum bello et integris aciebus conspicien­<lb></lb>dis utilis, sicut ad Lunam sectam, totam, et sine capitis ad coelum erectione <lb></lb>repraesentandam, ut in charta delineentur exacte ipsius maculae, montes, <lb></lb>faculae et caetera, quae Ricciolus, Hevelius, Eustachius, tu ipse et alii Sele­<lb></lb>nographi praetermiserunt, aut praepostere exhibuerunt, ad quod nos etiam <lb></lb>cum sociis accingimus ” (MSS. Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>22). </s></p><p type="main">

<s>Ma non consiste nell&#039;uso e nell&#039;applicazione degli specchi piani, i quali <lb></lb>non concorrono a ingrandire le immagini, il vero Canocchiale catottrico, la <lb></lb><gap></gap><pb xlink:href="020/01/421.jpg" pagenum="402"></pb>la inviò alla Società Reale di Londra, e fu inserita nelle Transazioni filo­<lb></lb>sofiche, colle seguenti parole scritte dallo stesso inventore: </s></p><p type="main">

<s>“ Novum hoc instrumentum constat ex duobus e metallo speculis, al­<lb></lb>tero concavo, quod vitri obiectivi munere fungitur, altero plano: habet prae­<lb></lb>terea exiguam lentem ocularem plano convexam. </s>

<s>Huius constructio facile .... <lb></lb>potest concipi, nempe quod Telescopii huius tubus apertus est ad eam extre­<lb></lb>mitatem quae ad obiecta convertitur, quod altera extremitate clausa est, ubi <lb></lb>locatum est speculum concavum, de quo supra meminimus; quod prope <lb></lb>extremitatem apertam est speculum planum ovale, quam potest exiguum, <lb></lb>quo minus impediat ingredientis lucis radios, et quod idem speculum incli­<lb></lb>natum ad superiorem Tubi partem versus, quae parvo terebrata est fora­<lb></lb>mine munito lente oculari, ita ut radii a re perspicienda prodeuntes prius <lb></lb>incidant in speculum concavum in imo Tubo positum, unde reflectuntur al­<lb></lb>teram Tubi extremitatem versus, ubi intercipiantur a plano speculo obli­<lb></lb>que collocato, a quo reflexi diriguntur ad exiguam lentem oculare plano <lb></lb>convexam atque adeo ad spectatoris oculum, qui, deorsum versus intuens, <lb></lb>ea videt ad quae Telescopium conversum est. </s>

<s>Ut haec plenius et melius in­<lb></lb>telligantur, Lector inspiciat, si libet, figuram 33 in qua AB est concavum <lb></lb><figure id="id.020.01.421.1.jpg" xlink:href="020/01/421/1.jpg"></figure></s></p><p type="caption">

<s>Figura 33.<lb></lb>speculum, cuius radius aut semidia­<lb></lb>meter est pollicum duodecim cum <lb></lb>besse vel tredecim, CD aliud specu­<lb></lb>lum metallicum, cuius superficies <lb></lb>plana est, peripheria vero ovalis, GD <lb></lb>est filum ferreum, quod solide retinet <lb></lb>amulum cupreum, et cui affixum est <lb></lb>speculum CD, F parva lens ocularis <lb></lb>plana superius et convexa inferius, cuius radius est uncialis, vel etiam minor. </s>

<s>” <lb></lb>E così prosegue a descriver gli altri organi inservienti alla montatura e al <lb></lb>maneggio dello strumento (Op. </s>

<s>omn. </s>

<s>opt., Patavii 1773, Apendix, pag. </s>

<s>11, 12). </s></p><p type="main">

<s>Ma in un&#039;Epistola precedente, data del 6 Febbraio 1672, e inserita nel <lb></lb>numero 80 delle Transazioni filosofiche, aveva il Newton fatto partecipare <lb></lb>alla Società Reale di Londra la sua scoperta <emph type="italics"></emph>De luce et coloribus,<emph.end type="italics"></emph.end> la quale <lb></lb>gli fu occasione, ed efficace consiglio di rivolgersi a ritrovare il nuovo stru­<lb></lb>mento. </s>

<s>“ Ineunte anno 1666, quo tempore operam dabam conficiendis opti­<lb></lb>cis vitris figurarum a sphaerica diversarum, mihi vitreum prisma trìangu­<lb></lb>lare paravi, eo notissima phaenomena colorum experturus ” (ibi, pag. </s>

<s>3). E <lb></lb>prosegue a dire come, per mezzo di quel prisma, gli occorresse a far la <lb></lb>scoperta de&#039;varii gradi di refrangibilità de&#039;raggi della luce, d&#039;onde egli venne <lb></lb>a persuadersi esser vana e inutile fatica il pretendere di ridurre i vetri da <lb></lb>canocchiali alla loro desiderata perfezione. </s>

<s>” Postquam haec intellexi, circa <lb></lb>vitra laborare destiti. </s>

<s>Noveram enim Telescopia perfectiora hucusque haberi <lb></lb>non potuisse, non solum quia deerant vitra reipsa praedita figuris quas optici <lb></lb>Auctores praescripserant .... sed etiam quia lux ipsa est mistura quaedam <lb></lb><gap></gap></s></p><pb xlink:href="020/01/422.jpg" pagenum="403"></pb><p type="main">

<s>Da queste considerazioni fu consigliato a lasciare addietro i vetri, per <lb></lb>rivolgersi tutto agli specchi. </s>

<s>“ Haec me duxerunt ad reflexiones conside­<lb></lb>randas, quas cum sibi constare reperissem, ita ut in omnibus radiorum ge­<lb></lb>neribus esset angulus reflexionis par angulo incidentiae, intellexi, quod ea­<lb></lb>rum ope instrumenta optica poterant ad quemlibet perfectionem extolli, <lb></lb>dummodo reperire liceret substantiam reflectentem, quae accuratam pulitu­<lb></lb>ram, aeque ac vitrum, reciperet, ut tantum lucis reflecteret, quantum trans­<lb></lb>mittit vitrum ” (ibi, pag. </s>

<s>6, 7). </s></p><p type="main">

<s>In questo, sopraggiunse la peste che lo costrinse a fuggir di Cambridge, <lb></lb>e a interrompere gli amati studii, non ripresi che solo nel 1668, dopo due <lb></lb>anni. </s>

<s>Allora riuscì a dar tal pulitura ai metalli, che potè con essi costruire <lb></lb>uno strumento a riflessione, <emph type="italics"></emph>quo videre poteram,<emph.end type="italics"></emph.end> egli dice, <emph type="italics"></emph>quatuor Iovis <lb></lb>Satellites illosque ostendi pluries duobus amicis<emph.end type="italics"></emph.end> (ibi). </s></p><p type="main">

<s>Nell&#039;Autunno del 1771 si dette a costruire un altro simile Telescopio, <lb></lb>il quale, sebben conoscesse e confessasse l&#039;Autore stesso, che non gli era <lb></lb>riuscito molto più perfetto del primo, nonostante, non dubito, egli soggiunge, <lb></lb><emph type="italics"></emph>quin instrumentum hoc multo perfectius reddi possit conatibus eorum, <lb></lb>qui, ut ex re audivi, operam illi Londini navant<emph.end type="italics"></emph.end> (ibi). </s></p><p type="main">

<s>Divulgatasi così, per l&#039;organo delle Transazioni filosofiche la descrizione <lb></lb>del nuovo Telescopio, un tal Cassegrain francese ebbe ricorso alla R. </s>

<s>So­<lb></lb>cietà di Londra, reclamando un&#039;anteriorità di tre mesi sopra la stessa in­<lb></lb>venzione neutoniana. </s>

<s>Il segretario partecipò ad esso Newton il reclamo, <lb></lb>trasmettendogli così insieme la breve descrizione e il disegno che l&#039;inventor <lb></lb><figure id="id.020.01.422.1.jpg" xlink:href="020/01/422/1.jpg"></figure></s></p><p type="caption">

<s>Figura 34.<lb></lb>francese faceva del suo nuovo stru­<lb></lb>mento: “ Est ABCD (fig. </s>

<s>34) fortis <lb></lb>tubus, in cuius infima parte est spe­<lb></lb>culum concavum CD, perforatum circa <lb></lb>medeluttium E. </s>

<s>Sed F est speculum <lb></lb>convexum, cuius convexitas ita est <lb></lb>disposita, ut reflectat imagines, quas <lb></lb>recipit a magno speculo, foramen E <lb></lb>versus, ubi locata est lens ocularis per quam dispiciuntur obiecta ” (ibi, <lb></lb>pag. </s>

<s>18). </s></p><p type="main">

<s>Il Newton allora scrisse una lettera di risposta al reclamo, confessando <lb></lb>essergli venuta l&#039;idea del suo Telescopio da quello, che il Gregory descrisse <lb></lb>e fece, a pag. </s>

<s>94 della sua <emph type="italics"></emph>Optica promota,<emph.end type="italics"></emph.end> rappresentare in disegno, che <lb></lb>secondo lui è simile al cassegreniano; ma però asseriva che fra que&#039;due <lb></lb>Telescopi e il suo ci correva quella differenza, che passa fra un concetto e <lb></lb>la sua pratica esecuzione, o fra una cosa possibile e una reale. </s>

<s>Citava, per <lb></lb>prova contro il Gregory, il Riveo, il quale, benchè fosse artefice tanto pe­<lb></lb>rito, messosi nonostante a costruire un Telescopio su quel modello, <emph type="italics"></emph>successu <lb></lb>caruit.<emph.end type="italics"></emph.end> Concludeva poi contro lo stesso Cassegrain, che avrebbe avuto molto <lb></lb>caro <emph type="italics"></emph>huius constructionis periculum fecisse antequam eam vulgaret: quod <lb></lb>si facere volet, in posterum sibimet satisfacturus arbitror futurum ut<emph.end type="italics"></emph.end><pb xlink:href="020/01/423.jpg" pagenum="404"></pb><emph type="italics"></emph>eventus eum doceat quam parvi momenti sint cogitationes huiusmodi, <lb></lb>donec actu quis illas exsequatur ”<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>19). </s></p><p type="main">

<s>Nè queste del Newton sono rapaci usurpazioni, o vane pretese, essendo <lb></lb>un fatto che l&#039;uso de&#039;Telescopi riflettori, nelle osservazioni celesti, ebbe i <lb></lb>primi principii da lui. </s>

<s>Che se poi ai meriti dell&#039;invenzione concorse il Gre­<lb></lb>gory co&#039;suoi progetti, forse più efficacemente v&#039;avrebbe potuto concorrere <lb></lb>il nostro Campani, il quale, due anni prima della peste di Cambridge, pensò <lb></lb>di far uso delle lenti microscopiche per oculari, e di applicar più comoda­<lb></lb>mente la vista in direzione perpendicolare all&#039;asse dello strumento. </s>

<s>Fu pure <lb></lb>il Campani che, nelle solitarie sue speculazioni, prefulse all&#039;Hudley, il quale, <lb></lb>al candor della carta e al nitor degli specchi, sostituendo un prisma isoscele <lb></lb>di cristallo, ottenne vivamente riflesse, e senza perdita sensibile di luce, le <lb></lb>immagini trasmesse dall&#039;obiettivo, e così ebbe effetto il Telescopio catot­<lb></lb>trico, che non fece buona prova alle mani del nostro Artefice romano, e <lb></lb>quello del Filosofo inglese conseguì perciò un notabile perfezionamento. </s></p><pb xlink:href="020/01/424.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Degli organi aggiunti <lb></lb>e de&#039;nuovi usi strumentali del Canocchiale<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del primo Micrometro e delle prime operazioni micrometriche di Galileo. </s>

<s>— II. </s>

<s>Del Micrometro <lb></lb>ugeniano e del Micrometro a reticolo. </s>

<s>— III. </s>

<s>Della Livella diottrica. </s>

<s>— IV. </s>

<s>Del Canocchiale bi­<lb></lb>noculo. </s>

<s>— V. Dell&#039;Elioscopio, dell&#039;Eliostata, de&#039;Diaframmi de&#039;Canocchiali. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il padre Francesco Lana, proponendosi di trattare, nel capitolo VIII e <lb></lb>ultimo del suo <emph type="italics"></emph>Prodromo all&#039;Arte maestra,<emph.end type="italics"></emph.end> dell&#039;uso de&#039;Canocchiali, scrive, <lb></lb>fra le altre, le parole seguenti: “ Egli è dunque (il Canocchiale) utile sì <lb></lb>nella guerra, come nella pace; e primieramente nella guerra serve per os­<lb></lb>servare tutti gli andamenti del nimico e spiare le azioni e le persone. </s>

<s>Così, <lb></lb>per mezzo del Canocchiale, essendo stato riconosciuto il Duca Francesco di <lb></lb>Modena, che si era inoltrato sotto la città di Cremona, gli fu tirato un colpo <lb></lb>con il cannone, da cui restò ucciso il marchese Villa, che gli stava a lato. </s>

<s><lb></lb>Può anche servire per leggere di notte lettere di segreto nella piazza asse­<lb></lb>diata e fuori. </s>

<s>Di più, non solo si potrà numerare quanti siano i pezzi di <lb></lb>alcuna batteria scoperta, quanti i soldati, ma anche si potranno vedere quelli <lb></lb>che di nascosto si avvicinano per riconoscere i posti, e questi, all&#039;incontro, <lb></lb>senza mettersi a pericolo, con troppo avvicinarsi, li potranno riconoscere da <lb></lb>lontano, con il Canocchiale. </s>

<s>Inoltre dico che, con il Canocchiale noi potremo <lb></lb>misurare l&#039;altezza delle mura, le distanze de&#039;baluardi, la lunghezza delle <lb></lb>loro facce, delle cortine, con tutto ciò che pratica la Trigonometria, il che <lb></lb>potrà servire anche in altre occasioni, quando vorremo sapere le altezze e <lb></lb>distanze di alcune case o siti, a&#039;quali non ci potiamo accostare. </s>

<s>Questa cosa, <pb xlink:href="020/01/425.jpg" pagenum="406"></pb><emph type="italics"></emph>che da altri ch&#039;io sappia non è stata osservata,<emph.end type="italics"></emph.end> si potrà facilmente prati­<lb></lb>care in questo modo: ” (Brescia 1670, pag. </s>

<s>240). </s></p><p type="main">

<s>Il Lana adunque promette d&#039;insegnar nuovi usi del Canocchiale, che <lb></lb>egli crede non sieno stati, prima di lui, praticati da nessuno. </s>

<s>E perchè que­<lb></lb>sti usi si distinguono in due classi, l&#039;una delle quali appartiene a ciò che <lb></lb>concerne l&#039;arte della guerra, e l&#039;altra all&#039;Altimetria, vediamo se veramente, <lb></lb>nel 1670, come il Lana pretende, fosse tutta questa, alla scienza, una rive­<lb></lb>lazione nuova. </s></p><p type="main">

<s>Già il Porta, nella sua <emph type="italics"></emph>Magia Naturale,<emph.end type="italics"></emph.end> aveva in varii modi insegnato <lb></lb>il segreto di leggere lettere dalla lontana, e Galileo nel 1617, scrivendo al <lb></lb>conte d&#039;Elci, in proposito dell&#039;uso che può farsi del Canocchiale, per rico­<lb></lb>noscere dalla lontana e scoprir le insidie delle navi nemiche, così gli dice: <lb></lb>“ Finalmente ho scoperto una maniera d&#039;Occhiale differente dall&#039;altra, col <lb></lb>quale si trovano gli oggetti coll&#039;istessa prestezza che coll&#039;occhio libero.... <lb></lb>Questa invenzione è stata tanto stimata da queste AA. SS. che per tenerla <lb></lb>segreta, sicchè non possa venire in notizia dell&#039;inimico, hanno deputato due <lb></lb>cavalieri nobilissimi all&#039;uso di questo strumento sul calcese ” (Alb. </s>

<s>VI, 270). </s></p><p type="main">

<s>E già l&#039;Hevelio, infino dal 1637, aveva inventato e messo in pratica un <lb></lb>suo Canocchiale, accomodato di lenti e di specchi, per mezzo del quale gli <lb></lb>atti e le mosse del nemico venivano ritratte in vicinanza e rappresentate <lb></lb>sotto il chiuso di qualche tenda; strumento che, giusto dagli usi speciali a <lb></lb>cui venne applicato, ebbe, dal suo proprio inventore, il nome di <emph type="italics"></emph>Polemo­<lb></lb>scopio<emph.end type="italics"></emph.end> (Selenographia, Gedani 1647, pag. </s>

<s>24-31). </s></p><p type="main">

<s>Essendo dunque cosa certissima che, per quello riguarda la prima parte <lb></lb>dell&#039;invenzione, fu il Lana lungamente prevenuto e dal Porta e dal Galileo <lb></lb>e dall&#039;Hevelio, e da tanti altri che si potrebbero citare, insieme con quel <lb></lb>Petit, di cui fu lo strumento polemoscopico da noi descritto nel capitolo pre­<lb></lb>cedente; vediamo se la novità dell&#039;invenzione possa attribuirsi al Gesuita <lb></lb>bresciano, per quello che particolarmente concerne l&#039;Altimetria. </s>

<s>La propo­<lb></lb>sizione è per la scienza ben assai più importante di quel che non sia sco­<lb></lb>prire un segreto altrui, o riconoscere un capitano in guerra, per appuntar­<lb></lb>gli un cannone e ammazzarlo. </s>

<s>Molta gloria perciò meriterebbesi il Lana, se <lb></lb>l&#039;applicazione del Canocchiale, a misurar le distanze e i diametri degli astri, <lb></lb>e gli angoli sottesi dagli oggetti apparentemente piccoli, si potesse dire un <lb></lb>suo ritrovato. </s>

<s>Ma molti concorrono insieme a contendergli quella gloria, e <lb></lb>così valorosi da soggiogar qualunque altro, che si faccia a loro incontro, <lb></lb>con la sola potenza del nome. </s></p><p type="main">

<s>Si tratta insomma, come bene intendono i nostri Lettori, del <emph type="italics"></emph>Microme­<lb></lb>tro,<emph.end type="italics"></emph.end> dell&#039;invenzione del quale, se questa non può, com&#039;abbiamo accennato, <lb></lb>credersi opera di Francesco Lana, dobbiamo ora narrar la storia. </s>

<s>E intanto, <lb></lb>per non dilungarci di troppo dalla lettera galileiana, dianzi citata, seguitando <lb></lb>a leggere ivi, troviamo che Galileo proponeva il sopra descritto Canocchiale, <lb></lb>oltre a quello di scoprire le navi nimiche, a un&#039;altr&#039;uso, qual&#039;era di misu­<lb></lb>rar la distanza delle medesime navi. </s>

<s>“ Apportaci l&#039;istesso strumento un&#039;al-<pb xlink:href="020/01/426.jpg" pagenum="407"></pb>tra utilità, stimata grande da&#039;medesimi signori periti del mare, ed è che, <lb></lb>nello scoprire vascelli, si può, senza nessuna fatica o dispendio di tempo, <lb></lb>sapere immediatamente la lontananza tra loro e noi ” (Alb. </s>

<s>VI, 270). </s></p><p type="main">

<s>Nel 1638 poi Galileo stesso dava di ciò regola al padre Renieri, il quale, <lb></lb>di Genova, il dì 5 di Marzo di quello stesso anno, gli risponde in proposito <lb></lb>così scrivendo: “ Dalla prima vista della sua lettera non ho ben compreso <lb></lb>il modo di misurar le distanze coll&#039;occhiale, ma forse, col porre in opera <lb></lb>lo strumento, l&#039;intenderò meglio ” (ivi, X, 285). </s></p><p type="main">

<s>Ma di questa applicazione del Canocchiale alla misura delle distanze, <lb></lb>Galileo ne aveva trattato già molti anni prima, infin da quando egli veniva <lb></lb>annunziando al mondo le sue scoperte celesti. </s>

<s>Nell&#039;introduzione infatti al­<lb></lb>l&#039;<emph type="italics"></emph>Astronomicus Nuncius,<emph.end type="italics"></emph.end> dop&#039;avere insegnato il modo di misurare i gradi <lb></lb>dell&#039;ingrandimento del Canocchiale, così soggiunge: “ Consimili parato instru­<lb></lb>mento, de ratione distantiarum dimetiendarum inquirendum erit. </s>

<s>Quod tali <lb></lb>artificio assequemur: Sit enim, facilioris intelligentiae gratia, tubus ABCD <lb></lb>(fig. </s>

<s>35), oculus inspicientis esto E. Radii, dum nulla in tubo adessent perspi­<lb></lb><figure id="id.020.01.426.1.jpg" xlink:href="020/01/426/1.jpg"></figure></s></p><p type="caption">

<s>Figura 35.<lb></lb>cilla, ab obiecto FG ad oculum E, <lb></lb>secundum lineas rectas FCE, GDE <lb></lb>ferrentur, sed appositis perspicillis <lb></lb>ferentur secundum lineas refractas <lb></lb>HCE, IDE; coarctantur enim, et qui <lb></lb>prius liberi ad FG obiectum diri­<lb></lb>gebantur, partem tantummodo III <lb></lb>comprehendent. </s>

<s>Accepta deinde ra­<lb></lb>tione distantiae EH ad lineam HI, <lb></lb>per Tabulam sinum reperietur quantitas anguli in oculo ex obiecto III con­<lb></lb>stituto, quem minuta quaedam tantum continere comperiemus. </s>

<s>Quod si spe­<lb></lb>cillo CD bracteas alias maioribus alias vero minoribus perforatas foramini­<lb></lb>bus aptaverimus, modo hanc, modo illam, prout opus fuerit superimponentes, <lb></lb>angulos alios atque alios pluribus pancioribusque minutis subtendentes, pro <lb></lb>libito constituimus: quorum ope stellarum intercapedines, per aliquot mi­<lb></lb>nuta, ad invicem dissitarum, citra unius aut alterius minuti peccatum, com­<lb></lb>mode dimetiri poterimus ” (Alb. </s>

<s>III, 62) </s></p><p type="main">

<s>Chi non riconosce in quelle lamine perforate con fori ora più ora meno <lb></lb>aperti e variamente adattabili all&#039;obiettivo del Canocchiale, secondo i varii <lb></lb>bisogni, chi non riconosce la prima idea e anzi il primo e vero uso di quello <lb></lb>strumento, che poi, ridotto a maggior perfezione, ebbe, dagli Astronomi e <lb></lb>dai Geodeti, il nome proprio di <emph type="italics"></emph>Micrometro?<emph.end type="italics"></emph.end> E fuor di dubbio dunque che i <lb></lb>primi meriti dell&#039;invenzione si debbono a Galileo. </s>

<s>Ma quanto, nelle sopraccitate <lb></lb>parole, è chiaramente espressa l&#039;idea e designata la natura dello strumento, <lb></lb>altrettanto è oscuro il modo come ivi se ne insegna a far uso. </s>

<s>Non par che <lb></lb>l&#039;Autore applichi la sua nuova invenzione ad altro, che a ritrovar l&#039;angolo sot­<lb></lb>teso dal diametro apparente, ma come poi di lì se ne deduca la misura giusta <lb></lb>delle distanze lo lasciò a investigare all&#039;ingegno matematico del suo Lettore. </s></p><pb xlink:href="020/01/427.jpg" pagenum="408"></pb><p type="main">

<s>Nella III Giornata però dei <emph type="italics"></emph>Massimi Sistemi<emph.end type="italics"></emph.end> si esprime con molto mag­<lb></lb>gior chiarezza, all&#039;occasion di proporre un modo per misurare il diametro <lb></lb>apparente di una stella, servendosi di un micrometro semplicissimo e da po­<lb></lb>tersi usar facilmente anche a occhio nudo. </s>

<s>“ Ho fatto pendere una cordi­<lb></lb>cella verso qualche stella, e io mi son servito della Lira che nascè tra set­<lb></lb>tentrione e greco, e poi con l&#039;appressarmi e slontanarmi da essa corda <lb></lb>traposta tra me e la stella, ho trovato il posto, dal quale la grossezza della <lb></lb>corda puntualmente mi nasconde la stella: fatto questo, ho preso la lonta­<lb></lb>nanza dall&#039;occhio alla corda, che viene ad essere un de&#039;lati che compren­<lb></lb>dono l&#039;angolo, che si forma nell&#039;occhio, e che insiste sopra la grossezza <lb></lb>della corda, e che è simile, anzi l&#039;istesso che l&#039;angolo, che nella sfera stel­<lb></lb>lata insiste sopra il diametro della stella, e dalla proporzione della gros­<lb></lb>sezza della corda alla distanza dall&#039;occhio alla corda, ho immediatamente <lb></lb>trovata le quantità dell&#039;angolo, usando però la solita cautela, che si os­<lb></lb>serva nel prendere angoli così acuti, di non formare il concorso de&#039;raggi <lb></lb>visuali nel centro dell&#039;occhio, dove non vanno se non refratti, ma oltre al­<lb></lb>l&#039;occhio, dove realmente la grandezza della pupilla gli manda a concorrere ” <lb></lb>(ivi, I, 393). </s></p><p type="main">

<s>La pratica è insegnata qui con più matematica precisione che nel Nun­<lb></lb>zio Sidereo, dove si propone a risolvere un triangolo, senza far conoscere <lb></lb>come son noti di lui i necessari elementi. </s>

<s>Nel presente caso ci son noti il <lb></lb><figure id="id.020.01.427.1.jpg" xlink:href="020/01/427/1.jpg"></figure></s></p><p type="caption">

<s>Figura 36.<lb></lb>diametro della corda e la distanza di lei <lb></lb>dall&#039;occhio, ciò che basta per risolvere un <lb></lb>triangolo rettangolo, e son note col diame­<lb></lb>tro le due visuali tangenti alla stessa corda, <lb></lb>ciò che pur basta a risolvere un triangolo <lb></lb>isoscele, di cui si conoscono i lati. </s>

<s>Sia CH <lb></lb>(fig. </s>

<s>36) infatti la grossezza della corda, che <lb></lb>copre all&#039;occhio posto in O il diametro EG <lb></lb>della stella. </s>

<s>Misurata OC o la sua uguale OH, <lb></lb>il triangolo OCH, nel quale si conoscono i tre lati, farà, risoluto che sia, <lb></lb>conoscere l&#039;angolo COH. </s>

<s>Se poi si volesse prendere OD per la più vera e <lb></lb>più precisa distanza, il triangolo rettangolo COD farà immediatamente cono­<lb></lb>scere COD semiangolo cercato. </s></p><p type="main">

<s>Qui Galileo non accenna a misura di distanze, ma il metodo proposto <lb></lb>già nel Nunzio Sidereo non poteva non ridursi se non a questo, quando però <lb></lb>fosse stata misurata prima la lunghezza del tubo, e fossero anche insieme <lb></lb>note la virtù dell&#039;ingrandimento del Telescopio, e la grandezza reale del­<lb></lb>l&#039;oggetto. </s>

<s>Suppongasi infatti che AB sia il semidiametro noto del foro della <lb></lb>lamina micrometrica apposta all&#039;oggettivo, e che EG sia la statura di un <lb></lb>uomo di cui si conosce la misura media: i triangoli simili ABO, EFO, in <lb></lb>cui son noti i lati OB, AB, EF danno immediatamente la cercata distanza, <lb></lb>senz&#039;altro bisogno di Trigonometria. </s></p><p type="main">

<s><gap></gap><pb xlink:href="020/01/428.jpg" pagenum="409"></pb>è perfezionato, sopra quello accennato nel <emph type="italics"></emph>Nunzio,<emph.end type="italics"></emph.end> di una squisitezza e raf­<lb></lb>finatezza nuova, qual&#039;è quella di tener conto e pigliar misura esatta del foro <lb></lb>della pupilla. </s>

<s>Qui per verità Galileo perde il tempo inutilmente, e anzi, peg­<lb></lb>gio che nella inutilità, versa nell&#039;errore, essendo che lo scrupolo di misu­<lb></lb>rar l&#039;ampiezza del foro pupillare, non da altro gli sia suggerito che dall&#039;er­<lb></lb>ronea dottrina professata da lui intorno al modo della visione. </s>

<s>Eppure Galileo <lb></lb>di quella raffinatezza di metodo se ne compiace e insegna a praticarla, dan­<lb></lb>dola com&#039;un&#039;invenzione sua propria. </s>

<s>Nel citato luogo de&#039;Due Massimi Si­<lb></lb>stemi si contentò di descrivere il metodo per ritrovar l&#039;ampiezza della pu­<lb></lb>pilla e con essa il concorso de&#039;raggi, quando l&#039;angolo visuale sia molto <lb></lb>piccolo, senz&#039;accennare a nessuna pretensione di novità, ma poi, quando <lb></lb>tornò, nel 1637, a mettere insieme e a riordinare le sue <emph type="italics"></emph>Operazioni astro­<lb></lb>miche,<emph.end type="italics"></emph.end> non mancò di far notare a coloro a&#039;quali comunicava quello stesso <lb></lb>metodo, com&#039;era una tal cosa non praticata ancora da altri prima di lui. </s></p><p type="main">

<s>Fra coloro infatti, a&#039;quali in quel tempo comunicò Galileo quel suo me­<lb></lb>todo di misurare il diametro apparente di un astro, tenendo conto dell&#039;am­<lb></lb>piezza del foro della pupilla, fu Vincenzio Renieri, che, con lettera del di <lb></lb>29 Gennaio 1638, così rispondeva: “ Ho poi sommamente gustato l&#039;inven­<lb></lb>zione sua della misura pupillare, ed io fo conto di servirmene in questo <lb></lb>modo: Produrre una linea lunga dieci e più braccia, tanto che sia capace <lb></lb>della divisione del seno totale di 100,000, e poi accomodarvi in cima una <lb></lb>tavoletta bianca divisa in parti proporzionali a quelle della linea, in modo <lb></lb>che, stando ad angoli retti, rappresenti la tangente dell&#039;arco che si sottende <lb></lb>dall&#039;altro punto della linea, e dalla larghezza di detta tavola. </s>

<s>Indi, nel mezzo <lb></lb>di detta linea, dispor la seconda tavoletta nera, com&#039;ella mi accenna. </s>

<s>Ma <lb></lb>perchè lo allontanare e avvicinare della pupilla alla estremità di detta linea, <lb></lb>stimo cosa assai lubrica, ho pensato di supplire a questo difetto col muover <lb></lb>non l&#039;occhio ma la tavoletta di mezzo, poichè dalla prima stazione nel mezzo <lb></lb>della linea, e dalla seconda più verso l&#039;occhio, non v&#039;ha difficoltà nel tro­<lb></lb>vare il diametro cercato della pupilla ” (Alb. </s>

<s>X, 261, 62). </s></p><p type="main">

<s>Il metodo che veniva così proponendo Galileo al Renieri è alquanto mo­<lb></lb>dificato da quello che s&#039;insegna nel III Dialogo dei Due Massimi Sistemi, <lb></lb>e nella prima delle <emph type="italics"></emph>Astronomiche operazioni<emph.end type="italics"></emph.end> (Alb. </s>

<s>V, 376-78), ma è in so­<lb></lb>stanza lo stesso, non essendovi altra differenza che là si muove l&#039;occhio e <lb></lb>qui si muovono invece le tavolette guardate dall&#039;occhio. </s></p><p type="main">

<s>Se il Renieri accogliesse con sincerità questa galileiana invenzione, la­<lb></lb>sciano le sue stesse parole qualche luogo a dubitarne, imperocchè, per non <lb></lb>dire espressamente ch&#039;ei credeva fuor di proposito quella operazione, ei ne <lb></lb>vien suggerendo un&#039;altra, che senza dubbio sarà stimata da tutti gl&#039;impar­<lb></lb>ziali più giudiziosa: “ Solo mi occorre di soggiungere (egli così ripiglia il <lb></lb>costrutto da noi sopra lasciato interrotto) che vorrei sapere se si potesse <lb></lb>fare l&#039;istessa operazione del misurare i diametri delle stelle col fare un buco <lb></lb>piccolo in una carta o lamina, del cui diametro saressimo più certi che di <lb></lb><gap></gap><pb xlink:href="020/01/429.jpg" pagenum="410"></pb>pilla, parmi che dovrebbe seguirne l&#039;istessa operazione. </s>

<s>Starò aspettando la <lb></lb>sua risposta, per far poi quello che ella stimerà meglio ” (Alb. </s>

<s>X, 262). </s></p><p type="main">

<s>Non sembra che Galileo rispondesse in proposito, giacchè, nel Marzo <lb></lb>successivo, torna il Renieri a scrivere così: “ Circa il misurare la gran­<lb></lb>dezza delle stelle, con un foro fatto in una lamina, stimo che si potrebbe <lb></lb>fare, servendosi del diametro di detto foro, nello stesso modo che ci ser­<lb></lb>viamo di quello della pupilla, mentre però detto foro si faccia più piccolo <lb></lb>di quello. </s>

<s>Mi avvisi per grazia se ci ha difficoltà ” (ivi, pag. </s>

<s>285). </s></p><p type="main">

<s>Nemmeno un mese e undici giorni dopo, le insistenti preghiere del Re­<lb></lb>nieri furono esaudite, giacchè torna così a ripetere: “ Il modo col quale io <lb></lb>stimava di misurare i diametri delle stelle, è quello stesso con cui daglì an­<lb></lb>tichi si misuravano i diametri del sole, che era di fare un piccol foro in una <lb></lb>lamina, alla quale ponendo l&#039;occhio, e poi fermandolo nel fine di una riga <lb></lb>di legno divisa in parti proporzionali al sino, con un altro pezzetto di ta­<lb></lb>vola, che ad angoli retti ora in su ora in giù potesse muoversi su tal riga, <lb></lb>notando il punto nel quale la tavoletta ricopre la stella, si poteva da detta <lb></lb>tavoletta, come tangente, venire in cognizione del diametro. </s>

<s>Starò attendendo <lb></lb>in ciò il suo parere ” (ivi, pag. </s>

<s>296). </s></p><p type="main">

<s>È intanto la terza volta che il Renieri invoca da Galileo e attende que­<lb></lb>sto parere, e il parere, com&#039;è certo che fu atteso per quasi tre mesi inu­<lb></lb>tilmente, così è probabile che non fosse pronunziato mai. </s>

<s>Saremmo da ciò <lb></lb>condotti a sospettare che lo stesso Galileo non volesse entrare a discuter <lb></lb>nell&#039;argomento, e che cercasse ogni scusa di scansarne il caso, per paura <lb></lb>di non trovarsi scopèrto in faccia al Renieri e costretto a confessar quasi <lb></lb>un attentato di furto. </s></p><p type="main">

<s>Il Matematico genovese infatti, accenna nelle sopra allegate parole che <lb></lb>il metodo inteso praticare da lui era il metodo stesso che praticavano gli <lb></lb>Astronomi antichi. </s>

<s>E in verità una simile pratica si vede descritta nell&#039;opera <lb></lb>più insigne, che dell&#039;antichità ci sia rimasta, nell&#039;<emph type="italics"></emph>Arenario<emph.end type="italics"></emph.end> vogliam dir di <lb></lb>Archimede. </s>

<s>L&#039;Astronomo siracusano, dop&#039;avere ivi accennato che Eudossio <lb></lb>e Aristarco avevano assegnato al diametro apparente del sole una misura <lb></lb>non molto conforme alla vera, propone un nuovo metodo più esatto, che, <lb></lb>da alcune leggiere variazioni in fuori, è quello stesso insegnato da Galileo: <lb></lb>“ Caeterum satis mihi est ut propositum demonstrem angulum sumere qui <lb></lb>maior sit angulo, cui sol accomodatur, habeatque verticem in visu. </s>

<s>Et rur­<lb></lb>sum alium angulum sumere, qui non minor sit angulo, cui sol accomoda­<lb></lb>tur, ut apicem in visu habeat. </s>

<s>Constituta ergo ad normam longa regula <lb></lb>super plano recto in loco iacente, unde sol oriens inspici queat, tum parvo <lb></lb>cylindro tornatili supra regula posito, confestim ab aurora et ortu solis, <lb></lb>postquam inceperit eiaculari radios in horizontem, potueritque ex opposito <lb></lb>videri, convertetur regula ad solem. </s>

<s>Deinde visus statuatur in extremo ipsius <lb></lb>regulae. </s>

<s>Cylindrus vero in medio admoveatur inter visum et solem, ita ut <lb></lb>adumbretur soli, tum separetur paulatim cylindrus ab oculo: et ubi ince­<lb></lb><gap></gap><pb xlink:href="020/01/430.jpg" pagenum="411"></pb>drus. </s>

<s>Sic enim accidit ut oculus ab uno puncto intueatur sub rectis ductis <lb></lb>ab extremo regulae in loco ubi consistit visus, tangentibus cylindrum, et <lb></lb>quidem angulo comprehenso sub istis ductis, minori eo angulo cui sol ac­<lb></lb>comodatur, habenti verticem in oculo, propterea, quod apparet aliquid solis <lb></lb>undequaque cylindri ” (Archimedis Opera, Parisiis 1615, pag. </s>

<s>452, 53). </s></p><p type="main">

<s>Nè qui lo stesso Archimede lascia indietro l&#039;attenzione di prendere esat­<lb></lb>tamente la misura del foro pupillare, considerando, come fa Galileo, che i <lb></lb>raggi non escono dall&#039;occhio movendo da un punto solo, ma da più. </s>

<s>“ Porro <lb></lb>quoniam visus non respicit ab uno puncto, sed ab aliqua quantitate, suma­<lb></lb>tur aliqua magnitudo teres non minor visu, et hoc rotundo corpore collo­<lb></lb>cato in extremitate regulae ubi oculus sistitur, recta agatur tangens et hoc <lb></lb>teres corpus et item cylindrum. </s>

<s>Etenim qui comprehenditur angulus sub <lb></lb>lineis ductis, minor est angulo in quo sol accomodatur, habente apicem in <lb></lb>visu. </s>

<s>Magnitudo autem non minor visu hoc pacto reperietur: ” (ibi, pag. </s>

<s>453). <lb></lb>E prosegue a descrivere il metodo di trovare il concorso de&#039;raggi visuali, in <lb></lb>ragion dell&#039;apertura della pupilla, al modo stesso di Galileo, colla differenza <lb></lb>che, invece di strisce di carta o di tavolette, come questi propone, Archi­<lb></lb>mede suggerisce cilindri o corpi arrotondati di diverso colore. </s></p><p type="main">

<s>L&#039;operazione insomma, che Galileo insegnava fare, dandola per una <lb></lb>speculazione sua nuova, il Renieri poteva averla appresa molto tempo prima <lb></lb>dall&#039;antico Matematico di Siracusa, e anco quando, ciò che non par credi­<lb></lb>bile, non gli fosse mai venuto a mano il volume delle Opere di Archimede, <lb></lb>illustrate già dal Rivalt e tradotte in latino, il Keplero, infino dal 1604, aveva <lb></lb>solennemente divulgate le dottrine dell&#039;antico Maestro, che erano divenute <lb></lb>oramai, ai tempi di Galileo e del Renieri, comun retaggio della scienza ot­<lb></lb><figure id="id.020.01.430.1.jpg" xlink:href="020/01/430/1.jpg"></figure></s></p><p type="caption">

<s>Figura 37.<lb></lb>tica moderna. </s>

<s>L&#039;Autore de&#039;Paralipomeni a Vitellione in­<lb></lb>fatti intitola il § V del V capitolo: <emph type="italics"></emph>Quac ex visionis modo <lb></lb>in Astronomiam redundant, seu de vitiata visione,<emph.end type="italics"></emph.end> e in <lb></lb>trattar di ciò, così scrive: “ Cum itaque stellarum distan­<lb></lb>tiae instrumentis astronomicis sunt capiendae, diligentiores <lb></lb>Astronomi, ut dictum, non fidunt oculo. </s>

<s>Sciunt enim, etsi <lb></lb>oculus ipsum instrumenti centrum attingat (quod tamen <lb></lb>difficulter obtinetur), non attingere tamen nisi superficie <lb></lb>tenus, in qua quidem linaee, ex utraque stella per supe­<lb></lb>riora pinnicidia ductae, non concurrant. </s>

<s>Sint F, G (fig. </s>

<s>37) <lb></lb>stellae. </s>

<s>BAC instrumentum, centro A, DA superficies oculi, <lb></lb>E centrum oculi. </s>

<s>Cum igitur non ex A sed ex E centro <lb></lb>oculi fingendae sint egredi rectae in F, G incidentes: Ap­<lb></lb>plicatis ergo pinnicidiis B, C, ut EBF, ECG sint in rectae, <lb></lb>angulus BAC vitiose metietur distantiam, critque iusto <lb></lb>maior, quia interior quam BEC super eadem basi. </s>

<s>Arcus itaque BC maior <lb></lb>iusto, quia oculi profunditas EA non patitur centra A, E instrumenti et oculi <lb></lb>coniungi .... Archimedes igitur in libello De Arenae numero cautionem.... ” <lb></lb>(Francof. </s>

<s>1604, pag. </s>

<s>212). E seguita a descrivere e a commentare i metodi <pb xlink:href="020/01/431.jpg" pagenum="412"></pb>archimedei, conforme a ciò che leggesi nell&#039;Arenario espresso con le parole <lb></lb>da noi citate di sopra. </s></p><p type="main">

<s>Per chi vede Galileo con altr&#039;occhio da quello che è veduto da noi re­<lb></lb>sterebbe misterioso a intendere come mai dottrine così divulgate e dalla <lb></lb>scienza antica e dalla moderna, si potessero proporre da lui come sue nuove <lb></lb>peregrine speculazioni. </s>

<s>Eppure, se non fosse stato trasportato da quel suo <lb></lb>genio di voler essere e apparire in tutto il primo ed il solo, e si fosse aste­<lb></lb>nuto dall&#039;insidiare le ricchezze altrui, avrebbe forse potuto pensare a tute­<lb></lb>lar meglio e a mettere in mostra le proprie. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Di quest&#039;ultimo asserto la prova ricorre opportuna a proposito del Mi­<lb></lb>crometro. </s>

<s>In quella intromessa, fuor del soggetto principale, che Galileo pone <lb></lb>in principio del suo <emph type="italics"></emph>Discorso intorno i Galleggianti,<emph.end type="italics"></emph.end> dopo aver riferito le <lb></lb>misure fin allora trovate delle rivoluzioni periodiche de&#039;satelliti intorno al <lb></lb>centro di Giove, non sodisfatto della loro precisione, per mancanza di osser­<lb></lb>vazioni più esatte delle passate, soggiunge: “ Per simili precisioni non mi <lb></lb>bastano le prime osservazioni, non solo per li brevi intervalli di tempo, ma <lb></lb>perchè non avendo io allora ritrovato modo di misurar con istrumento al­<lb></lb>cuno le distanze di luogo tra essi pianeti, notai tali interstizi con le sem­<lb></lb>plici relazioni al diametro del corpo di Giove, prese, come diciamo a oc­<lb></lb>chio ” (Alb. </s>

<s>X, 10). </s></p><p type="main">

<s>Lo strumento, a cui accenna in queste parole Galileo, non fu da lui <lb></lb>ritrovato prima della fine del 1611, ne l&#039;ebbe preparato prima del seguente <lb></lb>Gennaio 1612, e la notte del 31 di questo mese, nella seconda osservazione <lb></lb>che istitui intorno ai Gioviali, incominciò a fare di quello stesso strumento <lb></lb>il primo uso. </s>

<s>“ In hac secunda observatione primum usus sum instrumento <lb></lb>ad intercapedines exacte accipiendas, ac distantiam orientalioris proxime ac­<lb></lb>cepi: non enim fuit instrumentum adhuc exactissime paratum ” (ibi, V, 84). </s></p><p type="main">

<s>Ora, vien la curiosità di domandare: in che consiste questo nuovo stru­<lb></lb>mento <emph type="italics"></emph>ad intercapedines exacte accipiendas,<emph.end type="italics"></emph.end> e che non è certamente quello <lb></lb>delle lamine perforate applicate al Canocchiale, secondo la descrizione fatta <lb></lb>in principio del Nunzio Sidereo? </s>

<s>Della nuova invenzione, men semplice della <lb></lb>prima, e cavata da più reconditi principii, si sarebbe potuto compiacer Ga­<lb></lb>lileo con più ragione di quel che non facesse a proposito dell&#039;avere inse­<lb></lb>gnato il modo di trovar l&#039;angolo del concorso de&#039;raggi visuali nell&#039;occhio, <lb></lb>eppure non si curò l&#039;Autore di lasciarne nessuna descrizione, e se ne sa­<lb></lb>rebbe anzi perduta la notizia, se gli scolari e i seguaci di lui non l&#039;aves­<lb></lb>sero amorosamente raccolta e trasmessa alla nostra memoria. </s></p><p type="main">

<s>Di questo stesso ingegnoso strumento galileiano, che serve ad uso di Mi­<lb></lb>crometro, sarebbe qui luogo a trattare, se non avessimo stimato esser forse <pb xlink:href="020/01/432.jpg" pagenum="413"></pb>per riuscir più opportuno, quando avremo a entrare in discorso delle sco­<lb></lb>perte fatte intorno al pianeta di Giove. </s>

<s>Intanto è certo che Galieo, il primo <lb></lb>di ogni altro che si sappia, propose l&#039;uso di due Micrometri, senza l&#039;altro ap­<lb></lb>positamente preparato per le osservazioni gioviali: quello delle lamine per­<lb></lb>forate da applicarsi al Canocchiale, e quello della cordicella tesa traguar­<lb></lb>data dall&#039;occhio nudo. </s></p><p type="main">

<s>Questa seconda maniera di misurar le piccole distanze, parve, nella sua <lb></lb>semplicità, a Candido del Buono così bella, che pensò di accoppiarla essa <lb></lb>pure al Canocchiale e di renderla vie maggiormente squisita. </s>

<s>Invece di una <lb></lb>corda di certa grossezza, come richiedeva la pratica di Galileo, pensò di far <lb></lb>uso di un sottilissimo filo, attraversato al tubo, in luogo opportuno tra la <lb></lb>lente oculare e l&#039;obiettivo del Telescopio. </s>

<s>Comunicò il Del Buono questo <lb></lb>suo pensiero al Borelli, il quale non ne riconobbe l&#039;importanza, se non dap­<lb></lb>poi che l&#039;Huyghens ne pubblicò l&#039;invenzione applicandola a trovar le rela­<lb></lb>zioni di misura tra la grandezza dell&#039;anello e il corpo di Saturno. </s>

<s>Nel cap. </s>

<s>IV <lb></lb>infatti delle <emph type="italics"></emph>Theoricae Mediceorum,<emph.end type="italics"></emph.end> dopo avere in primo luogo insegnato <lb></lb>il modo di misurar le massime digressioni de&#039;satelliti dal centro di Giove, <lb></lb>il Borelli stesso così soggiunge: “ Idipsum praestari potest praeclaro arti­<lb></lb>ficio nuper ab ingeniosissimo Christiano Hugenio editum (licet multo prius <lb></lb>idipsum mihi Dominus Candidus Buonus florentinus comunicaverit): Adapta­<lb></lb>tur in tubo optico prope lentem ocularem, in eiusque foco, tenuissimum <lb></lb>filum aeneum.... ” (Florentiae 1665, pag. </s>

<s>145, 46). Ma giova, meglio che <lb></lb>alla descrizione che qui seguita a fare il Borelli, attendere a quella che ne <lb></lb>fa l&#039;Huyghens stesso nel suo <emph type="italics"></emph>Systema Saturnium,<emph.end type="italics"></emph.end> colle parole seguenti: </s></p><p type="main">

<s>“ Locus quidam est intra tubos, qui solis convexis vitris instructi sunt, <lb></lb>circiter altero tanto amplius quam convexum oculare ab oculo distans, quo <lb></lb>in loco si quid intra tubi cavitatem visui obiieiatur, quantumvis subtile aut <lb></lb>exiguum, id distincte prorsus ambituque exquisite terminato conspicitur, <lb></lb>atque ita pro ratione latitudinis suae partem aliquam rei lucidae, velut Lu­<lb></lb>nae per Telescopium spectatae, visui subducit. </s>

<s>Exacte loci determinatio, his <lb></lb>quibus nullo vitio visus laborat, in focum convexi ocularis cadit.... Hic igi­<lb></lb>tur si primo annulus statuatur cum foramine paulo angustiore, quam sit <lb></lb>vitrum ipsum oculo proximum, eo tota tubi apertura, sive spatium circu­<lb></lb>lare, quod uno obtutu in coelo detegitur, praecisa circumferentia descriptum <lb></lb>habetur. </s>

<s>Cuius spatii diameter, quot scrupula comprehendat, aliquo pacto <lb></lb>inquirendum est, atque optime quidem ex transitu sideris alicuius, cuius <lb></lb>tempus numeretur vibrationibus perpendiculi, vel ope Horologii nostri oscilla­<lb></lb>torii nuper inventi, Telescopio interim immoto manente. </s>

<s>Scimus enim 4 scru­<lb></lb>pulis horariis unum coeli gradum et exiguum quid amplius transire: ideoque, <lb></lb>si verbi gratia numerentur scrupula secunda 69, interea dum stella quaedam <lb></lb>fixa totam Telescopii capacitatem metitur, argumento id erit 17 1/2 scrupula <lb></lb>prima Telescopii huiusmodi apertura comprehendi, sicut nostro evenit. </s>

<s>Quo <lb></lb>invento, virgulam unam atque alteram, ex aere aliave materia, parare opor­<lb></lb>tet, decrescenti paulatim latitudine, tubumque perforare utrinque circa lo-<pb xlink:href="020/01/433.jpg" pagenum="414"></pb>cum illum paulo ante memoratum, quo possint in ipso eius puncto virgu­<lb></lb>lae transversae ante oculum obtendi. </s>

<s>Cum igitur Planetae alicuius diametrum <lb></lb>metiri cupimus, adhibita ex quo diximus loco virgula, notandum est quae­<lb></lb>nam huius latitudo totum planetam contingere possit. </s>

<s>Ea enim latitudine <lb></lb>acuto deinde circino accepta, atque ad totius amplitudinem collata, Planetae <lb></lb>diameter apparens facili ratiocinio innotescet ” (Op. </s>

<s>Omn., Lugd. </s>

<s>Batav. </s>

<s>1724, <lb></lb>pag. </s>

<s>593, 94). E per recare un esempio, applica lo strumento a misurare <lb></lb>il diametro apparente di Venere, che egli trova essere 51″ 45tʹ. </s></p><p type="main">

<s>Questo ugeniano è il primo Micrometro di che faccia menzione la Sto­<lb></lb>ria dell&#039;Astronomia, ma Eustachio Divini viene a rivendicar per sè il di­<lb></lb>ritto di dieci anni di anteriorità sul ritrovato olandese. </s>

<s>Il reticolo, di che <lb></lb>servivansi i disegnatori per ritrarre gli oggetti in prospettiva, ei l&#039;applicò a <lb></lb>descrivere le macchie della Luna, osservate con uno de&#039;suoi Canocchiali <lb></lb>vantato per il più eccellente che si fosse veduto. </s>

<s>Una tal Selenografia, con <lb></lb>altre apparenze osservate in Venere, in Giove e in Saturno, fece il Divini <lb></lb>inciderla in una Mappa, dedicata nel 1649 al granduca Ferdinando II, e le <lb></lb>poche copie tirate la resero rarissima. </s>

<s>Una di queste copie Giovanni Tar­<lb></lb>gioni Tozzetti la comprò dagli eredi di Antonio Cocchi, e la inserì fra&#039;suoi <lb></lb>farraginosi manoscritti. </s>

<s>Sotto la detta Mappa è impressa un&#039;inscrizione, colla <lb></lb>quale l&#039;Autore si fa innanzi a presentare i suoi disegni al Granduca, e vi <lb></lb>si leggon fra le altre le seguenti parole: “ Plenilunium Martii 1649 Tele­<lb></lb>scopio palmorum 24 observatum, quo minimas et minutissimas Lunae ma­<lb></lb>culas scrutatus est. </s>

<s>Et altero palmorum 16 instructo versus oculum non <lb></lb>vitro concavo, sed lente vitrea subtilissimis filis ad instar craticulae dispo­<lb></lb>sitis operta, qua ipsas Lunae maculas delineavit et suo quemque loco pro­<lb></lb>pria manu exactissime posuit ” (Targ. </s>

<s>Notiz. </s>

<s>aggrandim., Firenze 1780, T. I, <lb></lb>P. I, pag. </s>

<s>246). </s></p><p type="main">

<s>L&#039;applicazione della reticola fatta dal Divini a ritrarre in prospettiva <lb></lb>gli astri col Canocchiale, segna senza dubbio un notabile progresso nelle <lb></lb>Operazioni dell&#039;Astronomia, ma se non può negarsi al reticolo stesso, e al <lb></lb>modo come il suo Inventore l&#039;usava, la natura e l&#039;essere di vero Microme­<lb></lb>tro, è pure di necessità il confessare che un tal Micrometro non era appli­<lb></lb>cabile a tutti quegli usi, a cui si porgeva il Micrometro ugeniano. </s>

<s>Questo <lb></lb>dall&#039;altra parte era assai incomodo, e al tedio di tentar qual grossezza di <lb></lb>virgula fosse quella che s&#039;adattava all&#039;osservazione, s&#039;aggiungevano, in chi <lb></lb>non fosse stato così paziente e destro, molte occasioni di errore. </s></p><p type="main">

<s>Allora venne in mente a Geminiano Montanari di tender, sul cerchietto <lb></lb>descritto dall&#039;Huyghens, non un filo solo di variabile grossezza, ma più fili <lb></lb>sottilissimi, come sarebbero capelli, tutti equidistanti e paralleli tra loro, im­<lb></lb>immobili e invariabili, e con i quali si veniva a comporre un reticolo, di <lb></lb>cui l&#039;Inventore intese di servirsi principalmente per gli usi dell&#039;Altimetria. </s></p><p type="main">

<s>“ Pongasi, egli scrive, dentro la canna dell&#039;oculare, nel concorso de&#039;fo­<lb></lb>chi, invece del cerchietto, ove dissi si ponesse il capello per livellare, un al­<lb></lb>tro cerchietto guernito di molti capelli v. </s>

<s>g. </s>

<s>12 o 15, tutti equidistanti e <pb xlink:href="020/01/434.jpg" pagenum="415"></pb>paralleli fra di loro, e con essi in primo luogo si faccia la seguente pruova: <lb></lb>In luogo comodo a ciò si ponga una pertica o altra misura esatta, in di­<lb></lb>stanza di 100 pertiche, più o meno, come può portare il Canocchiale per <lb></lb>vedere l&#039;oggetto esattamente distinto, e s&#039;osservi quanti di quelli spazi fra <lb></lb>un capello e l&#039;altro occupa tutta detta pertica, oppur mezza, come torna co­<lb></lb>modo, e se non comprende spazi interi, s&#039;accomodi o s&#039;allontani all&#039;oggetto <lb></lb>quanto basta, perchè gli comprenda per l&#039;appunto, il che serve per comodo <lb></lb>maggiore, anzi è meglio fare in modo che ogni spazio comprenda tant&#039;on­<lb></lb>cie per appunto, e allora si misuri esattamente la distanza dell&#039;occhio alla <lb></lb>pertica suddetta, e questa si divida in tante parti, quant&#039;oncie abbiamo tro­<lb></lb>vato comprendersi dentro ad uno spazio. </s>

<s>Darò l&#039;esempio: con la Livella diot­<lb></lb>trica che ho fabbricata e donata a questo illustrissimo Senato, il di cui Ca­<lb></lb>nocchiale è come dissi 9 piedi, in distanza di 100 pertiche, io comprendeva <lb></lb>tra l&#039;un filo e l&#039;altro per appunto cinque oncie, onde divise in cinque parti <lb></lb>le 100 pertiche, ne toccano 20 pertiche per oncia, il che deve servirmi di <lb></lb>regola in avvenire. </s>

<s>Volendo adunque sapere quanto è lontano qualunque <lb></lb>luogo ch&#039;io possa vedere con detto Canocchiale, basta osservare l&#039;altezza <lb></lb>d&#039;una finestra, porta o colonna, torre o altra simil cosa, quanto spazio cioè <lb></lb>ella occuperà li fili suddetti posti nel Canocchiale, e far misurare sul luogo <lb></lb>la giusta altezza di detta finestra, o porta ecc. </s>

<s>per trovare quant&#039;once di <lb></lb>piede restavano comprese tra un filo e l&#039;altro, e dando 20 pertiche per oncia <lb></lb>o quel tanto che ho veduto per esperienza che porta quel Canocchiale, saprò <lb></lb>benissimo quante pertiche lontano è quell&#039;oggetto. </s>

<s>” </s></p><p type="main">

<s>Il passo fin qui trascritto si legge a pag. </s>

<s>17, 18 della <emph type="italics"></emph>Livella Diottrica,<emph.end type="italics"></emph.end><lb></lb>pubblicata dal Montanari in Bologna nel 1674, ma in una lettera indirizzata <lb></lb>da Padova al Magliabechi, in data del dì 11 Settembre 1682, l&#039;Autore stesso <lb></lb>dice di avere applicata la reticola al Canocchiale infin dal 1664, e di aver <lb></lb>con essa ritrovata facilmente la parallasse della Cometa apparita allora nel <lb></lb>cielo: “ Se la cometa si fosse lasciata vedere in siti assai alti, ond&#039;io avessi <lb></lb>potuto osservarla col mio Canocchiale a reticola, avrei trovata facilmente la <lb></lb>sua vera parallasse, col modo che adoprai in quella del 1664 allora da me <lb></lb>inventato e pubblicato.... ” (Padova 1682, pag. </s>

<s>6). </s></p><p type="main">

<s>La pubblicazione non fu fatta però formalmente per le stampe, altro <lb></lb>che nel 1674, come di sopra abbiamo veduto, e il padre Lana avea pubbli­<lb></lb>cato il Prodromo all&#039;Arte maestra quattro anni prima, descrivendovi il re­<lb></lb>ticolo applicato al Canocchiale e l&#039;uso che se ne poteva fare all&#039;Altimetria. </s>

<s><lb></lb>Il Montanari, che seco stesso si compiaceva di essere stato l&#039;inventore del <lb></lb>nuovo strumento, e che sperava di essere stato in tempo a pubblicare la sua <lb></lb>invenzione, benchè indugiata infino al 1674, restò colpito, quandò poco dopo <lb></lb>gli capitò alle mani e gli cadde sotto gli occhi il Cap. </s>

<s>VIII del citato <emph type="italics"></emph>Pro­<lb></lb>dromo.<emph.end type="italics"></emph.end> Allora, conoscendo bene di aver perduto ogni diritto di difendere <lb></lb>la sua ragione in pubblico, si contentò di farlo in privato colla seguente let­<lb></lb>tera del dì 13 Agosto 1675 indirizzata a Vincenzio Viviani: </s></p><p type="main">

<s>“ Post varios casus ecco finalmente a V. S. Ecc.ma la sua Livella diot-<pb xlink:href="020/01/435.jpg" pagenum="416"></pb>trica, che dal signor Vincenzio Landi .... sarà mandata in una cassetta, ove <lb></lb>l&#039;ho ben serrata e legata dentro per modo, che non patisca le scosse. </s>

<s>” </s></p><p type="main">

<s>“ Sarà nella stessa cassa, in una scatoletta, una Reticola da porre in <lb></lb>luogo dell&#039;altra, che è nella Livella, quando V. S. Ecc.ma vorrà valersi del <lb></lb>Canocchiale per misurar le distanze con una sola stazione, e vi saranno si­<lb></lb>milmente li vasettini di vetro da mettere nell&#039;acqua, per mettere in oriz­<lb></lb>zonte la Livella, ed una breve istruzione dell&#039;uso di essi e della Reticola <lb></lb>per l&#039;Altimetria, avendo ridotto tutte le misure a braccia e soldi fiorentini, <lb></lb>per maggior sua comodità. </s>

<s>Vedrà il mio modo di far la Reticola, e potrà <lb></lb>favorirmi di mostrarlo all&#039;Ecc.mo Sig. </s>

<s>Accademico Svetoni, per occasione di <lb></lb>valersene egli ancora per l&#039;ecclissi. </s>

<s>” </s></p><p type="main">

<s>“ Pochi giorni sono mi fu mostrato, nel <emph type="italics"></emph>Prodromo<emph.end type="italics"></emph.end> Della Lana, il pen­<lb></lb>siero di misurar con la Reticola le distanze, il che non poco mi ha fatto <lb></lb>senso. </s>

<s>Rimettendomi a memoria che sul principio del 1665 mi trovai in <lb></lb>Mantova, mentre si vedeva la seconda Cometa e conferii questa ed altre mie <lb></lb>coserelle col p. </s>

<s>Ferroni, con cui feci allora stretta amicizia, siccome nel <lb></lb>viaggio di ritorno di là la conferii col p. </s>

<s>Urbano Davisi allora Generale delli <lb></lb>PP. Gesuati, che tuttavia se ne ricorda, anzi spontaneamente ne scrisse al <lb></lb>p. </s>

<s>ab. </s>

<s>Pepoli, l&#039;anno passato, dicendogli che erano dieci anni che io glie­<lb></lb>l&#039;aveva conferita, ond&#039;egli ne aveva bramata la pubblicazione: Ora, che il <lb></lb>p. </s>

<s>Lana avesse da sè incontrata la medesima speculazione, non me ne ma­<lb></lb>raviglierei, se io non vedessi che la sua barca da navigare per aria ed il <lb></lb>suo Orologio, da durare 15 anni una caricatura, lo dichiarano troppo <emph type="italics"></emph>levis <lb></lb>armaturae,<emph.end type="italics"></emph.end> e perciò non sono senza sospetto che l&#039;abbia avuto dal p. </s>

<s>Fer­<lb></lb>roni suo amicissimo, e che l&#039;ha protetto per la pubblicazione del suo libro <lb></lb>altre volte rigettato da&#039;suoi superiori, e maggiormente che io vedo ivi ad­<lb></lb>dotti, benchè indigesti molti altri usi della Reticola nel Telescopio, di cui <lb></lb>aveva promesso io un Trattato nel mio opuscolo della Cometa, i capi del <lb></lb>quale, così per l&#039;Astronomia come per le cose terrestri, aveva letto al me­<lb></lb>desimo p. </s>

<s>Ferroni, uno de&#039;quali era <emph type="italics"></emph>De usu Reticolae ad distantias inac­<lb></lb>cessas una statione dimetiendas, cum Corollariis De navium distantia in <lb></lb>mari.<emph.end type="italics"></emph.end> Ma mio sia il danno perchè, sentito che Eustachio (il Divini) preten­<lb></lb>deva di esser l&#039;inventore della Reticola per descrivere la Luna, ancorchè <lb></lb>egli diversamente da me l&#039;avesse adoprata, ed io non pretendessi d&#039;essere <lb></lb>il primo a mettere i fili nel concorso de&#039;fochi; tuttavia, per timore che <lb></lb>quell&#039;uomo non la pigliasse con me, come fece coll&#039;Hugenio, ho procrasti­<lb></lb>nato tanto, che ho dato campo a costoro di farmela. </s>

<s>Non importa: ne tro­<lb></lb>verò dell&#039;altre, se Dio vuole, e tacerò meglio. </s>

<s>” </s></p><p type="main">

<s>“ Del signor Auzout, che, in una sua lettera al P. Oldemburgo, pro­<lb></lb>poneva, come suo segreto da farne baratto con Mons. </s>

<s>Hook, il modo di <lb></lb>misurare <emph type="italics"></emph>unica statione distantias inaccessas,<emph.end type="italics"></emph.end> non ho dubbio che non coin­<lb></lb>cidesse ne&#039;medesimi pensieri, ma egli è altro ingegno che il p. </s>

<s>Lana, e non <lb></lb>ha quella presunzione che ha questo e per l&#039;uso della sua setta e per altre <lb></lb><gap></gap><pb xlink:href="020/01/436.jpg" pagenum="417"></pb>passato, con farsene appresso molti l&#039;inventore in Venezia. </s>

<s>Gli turai la bocca <lb></lb>con poco suo gusto, ma pure, se nasceva da litigarne fra noi, ci era chi <lb></lb>portava via l&#039;.osso per altra parte. </s>

<s>Ma <emph type="italics"></emph>nimium hucusque ”<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXLVI, c. </s>

<s>58, 59). </s></p><p type="main">

<s>Ogni avvocato in causa propria è naturalmente, e quasi sempre ragio­<lb></lb>nevolmente sospetto, ma pur volendo fare pel Montanari in questo caso un <lb></lb>eccezione, si può concedere che egli avesse, infino dal 1664, pensato al suo <lb></lb>Reticolo e lo avesse altresì applicato all&#039;Altimetria e alla Astronomia. </s>

<s>No­<lb></lb>nostante è un fatto che il p. </s>

<s>Lana in Italia pubblicò per le stampe quella <lb></lb>invenzione quattro anni prima, e l&#039;Auzout in Francia si dice che, del Reticolo <lb></lb>per misurar le distanze <emph type="italics"></emph>unica statione,<emph.end type="italics"></emph.end> se ne fosse servito infino dal 1666. </s></p><p type="main">

<s>A precisar l&#039;anno, in cui l&#039;Astronomo francese s&#039;incontrò nel suo nuovo <lb></lb>strumento, ci mancano i documenti certi, ma pure è debito confessare che <lb></lb>se il Reticolo dell&#039;Auzout è posteriore in tempo a quello del Montanari, lo <lb></lb>supera nonostante in perfezione. </s>

<s>Nel Reticolo del nostro Italiano infatti i ca­<lb></lb>pelli tesi sul telaio rimangono immobili, e se l&#039;oggetto non è compreso <lb></lb>esattamente ne&#039;loro interstizi, s&#039;insegna a rimoverne o ad avvicinarne il Ca­<lb></lb>nocchiale. </s>

<s>Il Francese invece pensò, per mezzo di un congegno a vite mi­<lb></lb>crometrica, di rimovere e di avvicinare agli altri uno de&#039;fili, mantenendo <lb></lb>immobile lo stesso Canocchiale, e ne risultò uno strumento assai più comodo <lb></lb>e più squisito. </s>

<s>Il De La Hire poi rese mobile non un filo, ma un telaio di <lb></lb>fili sopra un altro telaio, e dette così alla Geodesia e all&#039;Astronomia il Mi­<lb></lb>crometro, che in sostanza è quello ancora dell&#039;uso moderno. </s></p><p type="main">

<s>Spettatore de&#039;progressì fatti in questa invenzione, che dovea tanti e <lb></lb>così segnalati servigi prestare alla scienza degli astri, fu quell&#039;Huyghens <lb></lb>che ne avea posti i principii. </s>

<s>Egli però non solo non ebbe la generosità di <lb></lb>confessar que&#039;progressi, ma li negò dicendo che la sua <emph type="italics"></emph>Virguia<emph.end type="italics"></emph.end> rimaneva <lb></lb>tuttavia micrometro più perfetto di quello a rete di fili, ultimamente inven­<lb></lb>tato. </s>

<s>“ Quomodo autem hae nostrae magnitudinum rationes inventae sint, <lb></lb>tum ex cognita proportione distantiarum a sole, tum ex mensura diame­<lb></lb>trorum, Telescopiis capta, eo, quem dixi libro ostendi: neque adhuc video <lb></lb>cur multum ab iis quas tunc definivi, recedam, etsi nihil eis deesse non <lb></lb>contenderim. </s>

<s>Nam quod multi existimant, in metiendis apparentibus diame­<lb></lb>tris praestare lamellis nostris usum <emph type="italics"></emph>Micrometrorum<emph.end type="italics"></emph.end> quae vocant, quibus fila <lb></lb>tenuissima in foco lentis maioris praetenduntur, nondum iis assentiri possum, <lb></lb>sed aptiores esse lamellas virgulasve tenues arbitror, quas eo loco obiicien­<lb></lb>das docueram ” (Cosmoth. </s>

<s>Lib. </s>

<s>I, Op. </s>

<s>Var., Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>652). </s></p><p type="main">

<s>Ma il Newton, sentendo questo giudizio essere nell&#039;Huyghens alterato <lb></lb>dall&#039;affetto paterno, dimostrò che ci era veramente nella <emph type="italics"></emph>Virgula<emph.end type="italics"></emph.end> di lui <lb></lb>un&#039;occasione di errore, evitata poi ne&#039;Micrometri a reticolo. </s>

<s>Quell&#039;occasione <lb></lb>fu acutamente ritrovata dal grande Ottico inglese nel fatto che la luce er­<lb></lb>ratica o ascitizia, come Galileo la chiamava, s&#039;espande più al largo, coperto <lb></lb>che sia il Pianeta, ond&#039;è che col metodo ugeniano le misure de&#039;diametri <lb></lb>apparenti degli astri si debbono per necessità e si trovan di fatto riuscire <pb xlink:href="020/01/437.jpg" pagenum="418"></pb>alquanto maggiori del giusto. </s>

<s>“ Hinc est quod Hugenius latitudine obsta­<lb></lb>culi, quod lucem omnem interciperet, maiores exhibuit planetarum diame­<lb></lb>tros quam ab aliis Micrometro definitum est, nam lux erratica, tecto Pla­<lb></lb>neta, latius cernitur, radiis fortioribus non amplius obscurata. </s>

<s>Hinc denique <lb></lb>est, quod planetae in sole tam graciles appareant luce dilatata attenuati ” <lb></lb>(Opusc. </s>

<s>T. II, Lausannae 1744, pag. </s>

<s>16). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La Livella diottrica, della quale faceva il Montanari menzione in prin­<lb></lb>cipio della lettera al Viviani di sopra trascritta, è un nuovo ritrovato per <lb></lb>cui venne il Canocchiale ad applicarsi a un altr&#039;uso geodetico importantis­<lb></lb>simo. </s>

<s>Il pensiero di servirsi del Telescopio come strumento livellatore, so­<lb></lb>spendendolo pel suo centro di gravità, era sovvenuto in mente all&#039;Huyghens, <lb></lb>che l&#039;esplicò in una sua scrittura intitolata <emph type="italics"></emph>Nova Libella Telescopio instructa <lb></lb>propriam secus ferens probationem et quae in unica statione verificatur <lb></lb>et rectificatur<emph.end type="italics"></emph.end> (Op. </s>

<s>Var., Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>254-61). Ma troppo inco­<lb></lb>modo a trasportarsi in campagna, e troppo complicato nell&#039;uso era il nuovo <lb></lb>Canocchiale livellatore così proposto. </s></p><p type="main">

<s>Il pensiero del vero Livello diottrico s&#039;incarnò con mirabile semplicità <lb></lb>nella mente del Montanari, ma prima di narrar come per lui si facesse il <lb></lb>felice connubio, giova toccar brevemente la storia dell&#039;invenzione del sem­<lb></lb>plice strumento da livellare, il quale col suo stesso nome di <emph type="italics"></emph>Corobate<emph.end type="italics"></emph.end> ri­<lb></lb>vela l&#039;origine sua antica e l&#039;uso, che ne fecero i Greci e gli Ingegneri <lb></lb>romani. </s></p><p type="main">

<s>Vitruvio, nel libro VIII della sua <emph type="italics"></emph>Architettura,<emph.end type="italics"></emph.end> trattando nel capi­<lb></lb>tolo VI <emph type="italics"></emph>De perductionibus et librationibus aquarum et instrumentis ad hunc <lb></lb>usum,<emph.end type="italics"></emph.end> ne lasciò la seguente descrizione: “ Chorobates autem est regula <lb></lb>longa circiter pedum viginti: ea habet ancones in capitibus extremis acquali <lb></lb>modo perfectos inque regulae capitibus ad normam coagmentatos, et inter <lb></lb>regulam et ancones a cardinibus compacta transversaria, quae habent lineas <lb></lb>ad perpendiculum recte descriptas, pendentiaque ex regula perpendicula in <lb></lb>singulis partibus singula, quae, cum regula fuerit collocata, eaque tanget <lb></lb>aeque ac pariter lineas descriptionis, indicabunt libratam collocationem ” <lb></lb>(Venetiis 1511, pag. </s>

<s>80, v.). </s></p><p type="main">

<s>Lo strumento insomma è fondato sul principio della linea verticale de­<lb></lb>scritta dal filo a piombo, ogni normale alla quale è la linea del cercato li­<lb></lb>vello. </s>

<s>Ma succede spesso in campagna che il filo pendulo venga agitato dal <lb></lb>vento, per cui si rende difficile il segnarne esattamente la direzione. </s>

<s>Allora <lb></lb>Vitruvio insegna di ricorrere all&#039;espediente dell&#039;acqua, la quale, versata den­<lb></lb>tro un canale lungo, si livella per tutto il tratto di lui dovunque alla me­<lb></lb>desima altezza: “ Sin autem ventus interpellaverit et motionibus linaee non <pb xlink:href="020/01/438.jpg" pagenum="419"></pb>potuerint certam significationem facere, tunc habeat in superiore parte ca­<lb></lb>nalem longum pedes quinque, latum digitum, altum sesquidigitum, eoque <lb></lb>aqua infundatur, et si aequaliter aqua canalis summa labra tanget, scietur <lb></lb>esse libratum ” (ibi, pag. </s>

<s>81, v.) </s></p><p type="main">

<s>Ma pur volle Giovan Battista Porta che la difficoltà, nemmeno intro­<lb></lb>ducendo l&#039;uso dell&#039;acqua, al modo che prescrive Vitruvio, fosse tolta di <lb></lb>mezzo: soggiunse anzi di più esser quella stessa difficoltà, che rende inu­<lb></lb>tile lo strumento vitruviano: “ Questa difficoltà l&#039;ha resa disutile, perchè, <lb></lb>avendosi sempre a por acqua in quella cava, bisognava che portassimo sem­<lb></lb>pre l&#039;acqua con noi ” (Spiritali, Napoli 1606, pag. </s>

<s>97). </s></p><p type="main">

<s>Fu perciò che il nostro Fisico napoletano si dette a speculare il modo <lb></lb>di toglier via le notate difficoltà, e di ridurre a più comodo uso e più per­<lb></lb>fetto la livella ad acqua, a che poi felicemente riuscì, sostituendo al canale <lb></lb>aperto un tubo chiuso, che sorgesse alle sue due estremità in due tubi di <lb></lb>vetro, attraverso ai quali traguardando, si veniva così la mira a disporre na­<lb></lb>turalmente nella linea del perfetto livello. </s>

<s>“ Stimo, egli scrive, aver ritro­<lb></lb>vato il vero modo che l&#039;acqua non si gonfi sopra il canale, nè i piombi che <lb></lb>pendono saranno turbati dal vento, nè bisogna che poniamo appresso noi <lb></lb>le botti con i carri con l&#039;acqua, quando avemo da livellar lunga distanza. </s>

<s><lb></lb>Sia la regola che abbiamo descritta di sopra AB (fig. </s>

<s>38) nel cui mezzo si <lb></lb><figure id="id.020.01.438.1.jpg" xlink:href="020/01/438/1.jpg"></figure></s></p><p type="caption">

<s>Figura 38.<lb></lb>cavi un canale di due diti di altezza e <lb></lb>di qua e di là s&#039;alzino duo cilindri di <lb></lb>vetro C, D di un piede di lunghezza <lb></lb>ben saldati nel basso del canale, e sia <lb></lb>il canal coverto di legno molto bene <lb></lb>impeciato intorno, che postovi l&#039;acqua <lb></lb>una volta non se ne scorra da qualche parte. </s>

<s>Ovvero, nella regola, se così <lb></lb>piace, sia un canale di piombo che non si assorba l&#039;acqua, che empiendosi <lb></lb>d&#039;acqua si riempiano i canaletti. </s>

<s>Dopo bisogna aggiustar molto bene la re­<lb></lb>gola che sia pianissima e che abbia i canaletti segnati nella superficie <lb></lb>egualmente intorno intorno o col smeriglio ovvero con alcun color fisso. </s>

<s>E <lb></lb>ripieno il canale d&#039;acqua infino al detto segno, si coprano all&#039;ultimo le boc­<lb></lb>che con cera. </s>

<s>Quando poi ci vogliamo servir dell&#039;istrumento, la regola si <lb></lb>deve drizzare fra duo scannetti, tanto alzando e calando i suoi estremi, fin­<lb></lb>chè l&#039;acqua tocchi egualmente la linea descritta ne&#039;canali, e allora lo stru­<lb></lb>mento sarà aggiustato ” (ivi, pag. </s>

<s>98). </s></p><p type="main">

<s>La Livella ad acqua così, infin dal 1601, inventata dal Porta, e ne&#039;suoi <lb></lb><emph type="italics"></emph>Libri tres Pneumaticorum<emph.end type="italics"></emph.end> resa pubblicamente nota, è quella stessa che, <lb></lb>per la sua semplicità e facilità di costruzione, non è, nemmeno oggidì, uscita <lb></lb>affatto fuor d&#039;uso, ed è quella altresì che il Montanari, come s&#039;accennava <lb></lb>di sopra, ebbe il felice pensiero di accoppiare allo strumento diottrico. </s>

<s>Gli <lb></lb>balenò quel pensiero un giorno che essendo a livellare in campagna, piut­<lb></lb>tosto che traguardar la mira, segnata con due fili tesi e una pallina, ad oc­<lb></lb>chio nudo, si mise a traguardarla con un canocchialetto Biconoscinti allora <pb xlink:href="020/01/439.jpg" pagenum="420"></pb>per esperienza i vantaggi che l&#039;uno strumento recava all&#039;altro, deliberò di <lb></lb>accoppiarli indivisibilmente insieme e di comporne uno strumento solo. </s>

<s>“ Io <lb></lb>perciò, così narra lo stesso Inventore, feci prova in certe occasioni di pub­<lb></lb>blico servigio, dop&#039;avere aggiustata una di queste livelle da acqua, ritirarmi <lb></lb>indietro da quella alquanti passi e riguardare con un canocchialetto in mano, <lb></lb>col quale, trovando ambi quei fili insieme con la pallina, distinguevo assai <lb></lb>meglio che con l&#039;occhio nudo, quando que&#039;fili mi venivano sotto un piano <lb></lb>e quando la pallina stava esattamente a suo luogo, oltre che poteva con <lb></lb>questo aiuto livellar molto più da lungi, e dove, con l&#039;occhio libero, in <lb></lb>25 stazioni che si fanno, il meno per miglio potevo errare 25 volte; coì ca­<lb></lb>nocchialetto alla mano, facevo molte meno stazioni, e per conseguenza molti <lb></lb>meno errori ” (Livella Diottr., Bologna 1674, pag. </s>

<s>8). </s></p><p type="main">

<s>Questa <emph type="italics"></emph>Livella diottrica<emph.end type="italics"></emph.end> poi, che è il più semplice e più naturale ac­<lb></lb>coppiamento della Livella ad acqua inventata dal Porta, col Canocchiale di <lb></lb><figure id="id.020.01.439.1.jpg" xlink:href="020/01/439/1.jpg"></figure></s></p><p type="caption">

<s>Figura 39.<lb></lb>Galileo; è dal Montanari stesso <lb></lb>così descritta in semplici e brevi <lb></lb>parole: “ AB (fig. </s>

<s>39) è il ca­<lb></lb>nocchiale tutto d&#039;un pezzo di lat­<lb></lb>toni però saldati insieme, con <lb></lb>solo il cannello B ove sta il tra­<lb></lb>guardo che può allungarsi e ac­<lb></lb>corciarsi conforme richiede la vi­<lb></lb>sta. </s>

<s>DE altra canna di latta saldata <lb></lb>con il Canocchiale, grossa dentro <lb></lb>più d&#039;un dito grosso, che dai capi <lb></lb>si rivolta in su per saldarvi li can­<lb></lb>nellini di vetro DC ed EF grossi anch&#039;essi più di un pollice. </s>

<s>” (ivi, pag. </s>

<s>12). </s></p><p type="main">

<s>Il semplice e comodo strumento livellatore del Porta era per 69 anni <lb></lb>pacificamente convivuto con i geodeti e con gli agrimensori, quando, a tur­<lb></lb>bar quella sua lunga pace e a metterlo in sospetto di chi in buona fede <lb></lb>l&#039;apprezzava e lo ricercava, vennero le censure di Gian Alfonso Borelli. </s>

<s><lb></lb>Egli, presa occasione dall&#039;inganno che, in segnare il giusto livello ne&#039;tubi, <lb></lb>fanno all&#039;occhio del riguardante i liquidi, per via de&#039;così detti fenomeni ca­<lb></lb>pillari; prosegue con una tal sequela di difetti scoperti a dir tanto male di <lb></lb>quella povera invenzione del Porta, da finir per consigliare coloro che ne <lb></lb>facevano uso ad abbandonarla e a tornare all&#039;antico Corobate di Vitruvio. </s></p><p type="main">

<s>“ Ex dictis colligitur quod fistula vitrea libellatoria (quam hydrostati­<lb></lb>cam libellam nonnulli vocant) nonnullis difficultatibus et fallaciis obnoxia <lb></lb>sit, primo, quia si fistulae vitraee erectae perpendiculariter ad planum hori­<lb></lb>zontis non fuerint praecise aeque amplae, procul dubio argines aqueos inter­<lb></lb>nos inaequales efficient, ideoque planum per summitates arginum aqueorum <lb></lb>extensum non erit horizonti aequidistans. </s>

<s>Idipsum continget si praedictae <lb></lb>duae fistulae erectae fuerint aequales inter se, at non sint omnino sordibus <lb></lb><gap></gap> illa prohibeat arginis aquei ele-<pb xlink:href="020/01/440.jpg" pagenum="421"></pb>vationem magis aut minus, pro copia aut defectu praedictae pinguedinis. </s>

<s><lb></lb>Praeterea, si una fistularum fuerit interne arida, reliqua vero madefacta, <lb></lb>argines quoque aquei in madida fistula elevantur, non vero in arida. </s>

<s>” </s></p><p type="main">

<s>“ Alio insuper nomine fallax est praedictum instrumentum, cum enim <lb></lb>aqua nunquam pura et sincera haberi possit, fit ut nisi bullulae aeraee, <lb></lb>quibus nunquam aqua spoliatur, aeque distributae sint in utraque fistula, <lb></lb>erunt moleculae illae aquaee inaequaliter graves specie, et ideo earum sum­<lb></lb>mitates habebunt inaequales elevationes, proindeque non ostendent exactam <lb></lb>libellam horizontalem. </s>

<s>Idipsum continget, quotiescumque fistulae praedictae <lb></lb>non fuerint ab eodem gradu caliditatis rarefactae, nempe si una a solaribus <lb></lb>radiis illustratur, reliqua vero in loco umbroso, aut magis frigido degat, non <lb></lb>secus si sordes terrae, aut sales inaequaliter distributi fuerint in utroque <lb></lb>canaliculo, nunquam praecise organum praedictum veram horizontalem li­<lb></lb>bellam indicabit. </s>

<s>At si loco aquae mercurium in praedicta fistula incluseri­<lb></lb>mus, non effugiemus omnes difficultates, nec in summa certi esse possumus <lb></lb>nunquam in operationibus errasse, quanta est fili alicuius tenuis crassities. </s>

<s><lb></lb>Proinde conducit laboriosam hanc machinam relinquere et more antiquo re­<lb></lb>gulis normalibus cum fune pendulo libellam horizontalem exquirere ” (De <lb></lb>Motion. </s>

<s>natur. </s>

<s>Regio Julio 1670, pag. </s>

<s>417, 18). </s></p><p type="main">

<s>Nonostante che il Borelli avesse contro la <emph type="italics"></emph>laboriosa macchina<emph.end type="italics"></emph.end> mosse <lb></lb>tali fiere accuse, e l&#039;avesse messa così in mala voce appresso agl&#039;ingegneri, <lb></lb>il Montanari non disperò di ridurla ad emenda, nè si rimosse per questo <lb></lb>dal proposito di esaltarla anco a maggior grado, disposandola al Telescopio. </s>

<s><lb></lb>Le verità, da che erano in gran parte avvalorate le accuse borelliane, e la <lb></lb>terribilità dell&#039;accusatore, consigliarono l&#039;Inventor della Livella diottrica a <lb></lb>soccorrere ai principali difetti, che presentava lo strumento inventato e <lb></lb>descritto negli <emph type="italics"></emph>Spiritali<emph.end type="italics"></emph.end> del Fisico napoletano. </s>

<s>E perchè la prima e princi­<lb></lb>pale fra quelle accuse fondavasi sull&#039;inganno, che, per i fenomeni di capil­<lb></lb>larità, si fa nell&#039;occhio; il Montanari pensò di ovviarvi facendo contrasse­<lb></lb>gnare il giusto livello dagl&#039;indici applicati a due galleggianti. </s>

<s>Provvide lo <lb></lb>stesso Montanari altresì a tor via alcuni altri inconvenienti, che presentava la <lb></lb>Livella ad acqua, e tutto ciò egli descrive colle seguenti parole, in una sua <lb></lb>lettera indirizzata da Bologna, il dì primo dell&#039;anno 1675, a Vincenzio Viviani: </s></p><p type="main">

<s>“ Con questa occasione voglio avvertire V. S. Ecc.ma un <lb></lb><figure id="id.020.01.440.1.jpg" xlink:href="020/01/440/1.jpg"></figure></s></p><p type="caption">

<s>Figura 40.<lb></lb>modo, che mi è sovvenuto di mettere nella Livella Diottrica <lb></lb>l&#039;acqua al suo segno, ed adattare l&#039;Instrumento con esattezza <lb></lb>al suo piano, perchè, com&#039;Ella sa, ed io anche nell&#039;Istruzione <lb></lb>di essa notai alla pag. </s>

<s>7, l&#039;acqua ne&#039;cannelli non pieni fa la <lb></lb>superficie concava, che perciò resta alquanto incerta la deter­<lb></lb>minazione del vero sito, sin dove ella deve collocarsi, il che <lb></lb>non resta di cagionare qualche svarietto, che solo poteva cor­<lb></lb>reggersi in parte col fare assai lunga la Livella. </s>

<s>Ora ho pensato far due <lb></lb>corpi galleggianti come questo A (fig. </s>

<s>40), che può esser di rame, con la <lb></lb>pallina vuota e chiusa, che abbia appeso al peduccio un sottile circoletto di <pb xlink:href="020/01/441.jpg" pagenum="422"></pb>lastra, onde, posta in acqua detta lastra, stia prossimamente orizzontale, ed <lb></lb>abbia questa una punta sottile nell&#039;estremità B, che servirà d&#039;indice. </s>

<s>Percioc­<lb></lb>chè posti a galla, ne&#039;cannelli di vetro della Livella, due tali corpi, e segnato <lb></lb>il luogo, ove la punta B deve stare, quando la Livella sarà orizzontale, con­<lb></lb>forme dissi in detta Istruzione, serviranno poscia per sempre a ritornarla nel <lb></lb>medesimo sito ed indicheranno, per la sottigliezza di dette punte, esattissima­<lb></lb>mente il piano desiderato. </s>

<s>E perchè alle volte pare noioso l&#039;aggiungere acqua <lb></lb>nella Livella, per ridurla precisamente a&#039;luoghi segnati, anzi la state scorsa <lb></lb>osservai, operando, per prova, in campagna, che riscaldata la livella dal sole <lb></lb>l&#039;acqua anch&#039;essa rarefatta cresceva e mutava luogo; perciò ho segnato <lb></lb>molti segni uno sopra l&#039;altro, co&#039;suoi numeri, in alcune, ed in una aggiunsi <lb></lb>un terzo cannello senza segni, nel mezzo del quale, con uno strumentino <lb></lb>di vetro, cavavo acqua, quella poca quantità per volta, che volevo ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXLVI, c. </s>

<s>28). </s></p><p type="main">

<s>La strana risoluzione presa dal Borelli di ritornare allo strumento li­<lb></lb>vellatore antico, e le sollecitudini che si dava il Montanari in restaurare il <lb></lb>nuovo, farebbero argomentar da chi vi ripensa, che nel 1670, quando si <lb></lb>pubblicò il libro <emph type="italics"></emph>De motionibus naturalibus,<emph.end type="italics"></emph.end> e nel 74 e nel 75, quando l&#039;In­<lb></lb>ventore pubblicò e pensò ad emendare la Livella Diottrica, non dovess&#039;es­<lb></lb>sere stata ancora inventata la <emph type="italics"></emph>Livella a bolla d&#039;aria.<emph.end type="italics"></emph.end> Non è credibile in­<lb></lb>fatti che, venendosi con questa nuova invenzione a toglier via la massima <lb></lb>parte de&#039;difetti notati nella ordinaria Livella ad acqua, il Borelli non volesse <lb></lb>preferirla al Corobate antico, nè è pur credibile che il Montanari, il quale <lb></lb>troppo ben per prova sapeva quanto fosse incomodo l&#039;operare in campa­<lb></lb>gna, volesse sopraccaricar sè e i suoi colleghi del fastidio di aggiustar quei <lb></lb>suoi galleggianti. </s></p><p type="main">

<s>In quale anno preciso la bolla d&#039;aria, rinchiusa dentro un tubo di ve­<lb></lb>tro, venisse a porgersi comodo ed esatto strumento libellatorio, non sapremmo <lb></lb>dirlo; ma si può congetturar facilmente che ciò fosse intorno al 1670. La <lb></lb>prima notizia di un sì bel ritrovato si sarebbe potuta diffondere in Italia da <lb></lb>una descrizioncella, che ne fece il Viviani, se non fosse rimasta fra le carte <lb></lb>di lui così manoscritta: </s></p><p type="main">

<s>“ Strumento per mettere un piano o un regolo ecc. </s>

<s>in livello orizzon­<lb></lb>tale. </s>

<s>— Questo è un cilindretto di cristallo serrato da ambe le parti, lungo <lb></lb>circa un palmo, grosso quanto il dito anulare, e pieno d&#039;acqua, lasciatovi <lb></lb>però un solo sonaglio d&#039;aria, la quale, avendo la natura di star sopra l&#039;acqua, <lb></lb>allora darà segno che il piano stia livellato, quando essa si ridurrà, posa­<lb></lb>tovi sopra il cilindro, a stare in mezzo di detto cilindro, in dubbio di muo­<lb></lb>versi o verso l&#039;una o verso l&#039;altra estremità del bocciolo ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXXXV, c. </s>

<s>8). </s></p><p type="main">

<s>Il legger così fatte parole in un volume, che s&#039;intitola <emph type="italics"></emph>Raccolta di espe­<lb></lb>rienze, senz&#039;ordine, e di pensieri diversi di me Vincenzio Viviani, in di­<lb></lb>versi propositi sovvenutimi intorno a materie meccaniche, fisiche, astro­<lb></lb>nomiche, filosofiche e altro,<emph.end type="italics"></emph.end> potrebbe far credere che fosse stato inventore <pb xlink:href="020/01/442.jpg" pagenum="423"></pb>dell&#039;elegante strumento l&#039;Autore stesso del Manoscritto. </s>

<s>Altri documenti <lb></lb>però attestano che il Viviani non per altro scrisse quelle parole, che per <lb></lb>serbar memoria di una invenzione, la quale, così per lettera, in cui manca <lb></lb>l&#039;anno della data, il Thèvenot, con lusinghiera eloquenza, descrivevagli da <lb></lb>Parigi: </s></p><p type="main">

<s>“ Ma e che cosa potrei io fare per meritare che V. S. allargasse un <lb></lb>poco quella confidenza, colla quale ella mi onora, coll&#039;accennarmi qualche <lb></lb>cosa delle scoperte, che ella ha fatto nei studi di Geometria? </s>

<s>Se con confi­<lb></lb>dargli i miei vaneggiamenti credessi di poterlo meritare, lo farei volentieri. </s>

<s><lb></lb>E qui, per obbligare V. S. a farmene quella parte, che me ne giudicherà <lb></lb>degno, per cavarne dell&#039;oro, le mando un poco di vetro. </s>

<s>Sia il cannoncino <lb></lb><figure id="id.020.01.442.1.jpg" xlink:href="020/01/442/1.jpg"></figure></s></p><p type="caption">

<s>Figura 41.<lb></lb>di vetro AB (fig. </s>

<s>41) con i suoi lati <lb></lb>ben paralleli, e turata una bocca di <lb></lb>esso, s&#039;empia d&#039;acqua per l&#039;altra <lb></lb>parte, sin per esempio al segno C, e <lb></lb>poi si sigilli e turi l&#039;apertura. </s>

<s>Sarà <lb></lb>fatto uno strumento di grand&#039;uso nelle arti, cioè un livello d&#039;aria esente di <lb></lb>molti difetti, che s&#039;incontrano nel livello ordinario. </s>

<s>Affinchè il moto dell&#039;aria <lb></lb>sia più libero è bene che il diametro del cannoncino sia di una linea ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXLVII, c. </s>

<s>230). </s></p><p type="main">

<s>Se però il Viviani non fu l&#039;inventore della Livella a bolla d&#039;aria, egli <lb></lb>fu il primo che tentò di diffonderne l&#039;uso in Italia. </s>

<s>E perchè i gonfiatori <lb></lb>di vetro in Firenze trovavano gran difficoltà in condurre uguali i tubetti, <lb></lb>pensò di rivolgersi in Roma a Matteo Campani, artefice espertissimo, e che <lb></lb>nella sua officina poteva avere arnesi e operai da condurre a perfezione il <lb></lb>lavoro. </s>

<s>I vetrai romani però s&#039;incontrarono nelle difficoltà medesime de&#039;fio­<lb></lb>rentini, e perciò, essendo allora in Roma l&#039;Auzout, lo stesso Campani si <lb></lb>rivolse a lui, per saper come facevano in Francia a tirare i tubetti di vetro <lb></lb>da livello, e appresono il modo lo riferisce al Viviani, consigliandolo ad af­<lb></lb>fidarne l&#039;esecuzione agli artefici di Firenze: “ Quanto al cilindretto di vetro <lb></lb>per livellare, mi dice il signor Auzout che, avendo qui provato più volte a <lb></lb>farne fabbricare, non gli è mai riuscito di poterne avere un pezzo total­<lb></lb>mente eguale. </s>

<s>Che però V. S. costì potrà farsi servir meglio, facendo dagli <lb></lb>artefici tirare le cannucce di vetro, non molto calde, sopra un&#039;asse di legno <lb></lb>diritta e bene spianata, perchè così dice che gli fanno in Francia ” (ivi, <lb></lb>T. CXLV, c. </s>

<s>195). </s></p><p type="main">

<s>Il Viviani, così affaccendato com&#039;era in operazioni livellatorie, e che <lb></lb>perciò meglio di ogni altro poteva conoscere e apprezzare la comodità e la <lb></lb>perfezione del nuovo strumento, non se ne sarà stato, e avrà sollecitamente <lb></lb>fatto eseguire il lavoro in Firenze, al modo che Matteo Campani aveva in­<lb></lb>teso operarsi a Parigi. </s>

<s>Ma convien pur dir che nè ancora fosse da fidarsi <lb></lb>della precisione di que&#039;tubi, se il Viviani stesso, nel 1675, quattro anni dopo <lb></lb>gl&#039;insegnamenti pratici ricevuti da Roma, approva e loda il Montanari, che <lb></lb>tuttavia attende a perfezionare l&#039;antica livella ad acqua. </s></p><pb xlink:href="020/01/443.jpg" pagenum="424"></pb><p type="main">

<s>L&#039;invenzione del Thèvenot, per le sopra dette difficoltà, s&#039;introdusse <lb></lb>poi più tardi fra noi, e sostituita all&#039;invenzione del Porta, in quel felice <lb></lb>connubio, che pensò il Montanari far di lei col Telescopio, prestò ai misu­<lb></lb>ratori de&#039;cieli non meno importanti servigi, che ai misuratori de&#039;campi. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Anche il <emph type="italics"></emph>Binoculo<emph.end type="italics"></emph.end> entra propriamente nell&#039;ordine degli strumenti, la <lb></lb>storia de&#039;quali forma il soggetto del presente Capitolo. </s>

<s>Il Nelli, il Frisi, il <lb></lb>Fabbroni crederono e fecer credere a molti che il pensiero di applicare ai <lb></lb>due occhi due tubi simili, come negli occhiali semplici s&#039;erano applicate <lb></lb>due lenti, fosse sovvenuto e fatto eseguire da Galileo. </s>

<s>Il primo de&#039;tre citati <lb></lb>Autori infatti così scrive: “ Il tempo, nel quale incominciò Galileo a porre <lb></lb>in uso il Binoculo, che denominava <emph type="italics"></emph>Testiera<emph.end type="italics"></emph.end> o <emph type="italics"></emph>Celatone,<emph.end type="italics"></emph.end> fu nel mese di <lb></lb>Marzo 1617, nel quale portatosi a Livorno, fece di esso esperienze con fe­<lb></lb>lice successo, sul molo ” (Vita di Gal., Losanna 1793, pag. </s>

<s>281). </s></p><p type="main">

<s>Il Frisi pure, nell&#039;Elogio che tanto dottamente distese del grande no­<lb></lb>stro Filosofo, ha opinioni conformi, espresse nel modo seguente: “ Colle <lb></lb>suddette Tavole (de&#039;satelliti di Giove) aveva anche esibito la Celata o Te­<lb></lb>stiera o Binoculo, che in varie prove fatte a Livorno nel 1617 s&#039;era speri­<lb></lb>mentata assai comoda, per seguitar colla vista gli oggetti in mare ” (Li­<lb></lb>vorno, 1775, pag. </s>

<s>91). </s></p><p type="main">

<s>Nè diversa punto da questa dei due citati Autori è l&#039;opinione del <lb></lb>Fabbroni, espressa così in nota a pag. </s>

<s>59 del I Tomo delle <emph type="italics"></emph>Lettere inedite <lb></lb>di Uomini illustri:<emph.end type="italics"></emph.end> “ L&#039;invenzione del Galileo, per usare navigando del­<lb></lb>l&#039;Occhiale, e ritrovare coll&#039;istessa prestezza gli oggetti, come con l&#039;occhio <lb></lb>libero, e trovati seguitarli senza rischio di perderli; consisteva in uno stru­<lb></lb>mento fatto a guisa di morione, che si adattava al capo dell&#039;osservatore, e <lb></lb>che era munito di due occhiali. </s>

<s>Il Galileo ebbe in uso di nominarlo <emph type="italics"></emph>Testiera<emph.end type="italics"></emph.end><lb></lb>o <emph type="italics"></emph>Celatone ”<emph.end type="italics"></emph.end> (Firenze, 1773). </s></p><p type="main">

<s>Concordano dunque pienamente tutti e tre insieme i citati scrittori, <lb></lb>nell&#039;asserire che un Canocchiale binoculo fosse da Galileo applicato a quel <lb></lb>Celatone, che egli immaginò e propose per uso de&#039;marinari, affinchè potes­<lb></lb>sero osservare con comodità gli oggetti, e avessero nel tempo stesso espe­<lb></lb>dite le mani. </s>

<s>Ma è veramente singolare l&#039;abbaglio preso in tal proposito da <lb></lb>scrittori di tanta erudizione e di tanto senno, quali sono specialmente il <lb></lb>Frisi e il Fabbroni, essendo chiarissimo a chi legge, che Galileo, parlando <lb></lb>dell&#039;occhiale commesso alla Celata, non fa parola che di un cannoncino solo <lb></lb>applicato da una parte, essendo dall&#039;altra l&#039;occhio libero. </s>

<s>De&#039;molti passi, <lb></lb>che noi potremmo sottoporre alla considerazione de&#039;nostri lettori, basti ci­<lb></lb>tarne uno dalla celebre Lettera scritta nel 1637, da Arcetri, a Lorenzo Rea-<pb xlink:href="020/01/444.jpg" pagenum="425"></pb>vatore col Telescopio non ricevesse turbamento dalle agitazioni della nave, <lb></lb>collocandolo sopra una sedia accomodata a imperniatura cardanica, così sog­<lb></lb>giunge: “ Io feci già sul principio, per l&#039;uso delle nostre Galere, certa cuf­<lb></lb>fia in forma di celata, che tenendola in capo l&#039;osservatore, ed avendo a <lb></lb>quella affisso <emph type="italics"></emph>un Telescopio,<emph.end type="italics"></emph.end> aggiustato in modo che rimirava sempre l&#039;istesso <lb></lb>punto, al quale l&#039;altro occhio libero indirizzava la vista, senza farci altro, <lb></lb>l&#039;oggetto, che egli riguardava con l&#039;occhio libero, si trovava sempre incon­<lb></lb>tro al Telescopio ” (Alb. </s>

<s>VII, 166). </s></p><p type="main">

<s>Ma nel 1617, il Binoculo vero era stato già ideato ed eseguito, alquanti <lb></lb>anni prima, da tutt&#039;altri inventori, che da Galileo. </s>

<s>Dicemmo altrove che <lb></lb>probabilmente la forma binoculare fu quella della prima invenzione, occorsa <lb></lb>per l&#039;accoppiamento di due paia di occhiali da naso. </s>

<s>Che però in sulla fine <lb></lb>del 1611 il Keplero avesse dato mano a tentar così fatta foggia di Canoc­<lb></lb>chiali, non è una probabilità ma un fatto. </s>

<s>Il motivo poi per cui il grande <lb></lb>Ottico alemanno abbandonò la speculazione e l&#039;opera intrapresa, è uno de&#039;più <lb></lb>curiosi che ne porga a legger la nostra Storia. </s></p><p type="main">

<s>Un giorno dunque chiama un legnaiolo di Linz, e gli ordina che assetti <lb></lb>un pezzo di legno, di figura parallelepipeda, con due occhiaie trapanate pro­<lb></lb>fondamente da parte a parte, e i rigoletti da incastrarvi dentro le lenti. </s>

<s>Torna <lb></lb>poco dopo l&#039;artefice col lavoro eseguito: il Keplero lo guarda, arriccia il <lb></lb>naso, poi fa: — Uhm! La mi pare una trappola da topi. </s>

<s>— Torna a guar­<lb></lb>dar, con più dispetto che mai, e rivolto al pover uomo, che stava lì tutto mor­<lb></lb>tificato, per la poca approvazione del suo lavoro, soggiunge: — Oramai tu <lb></lb>l&#039;hai fatto; ma per non mi far canzonare .... — e butta, in dir così, ogni <lb></lb>cosa fuor di finestra. </s></p><p type="main">

<s>Chi ha in visione una di queste macchinette da chiappar topi, che in <lb></lb>Toscana si chiama col nome di <emph type="italics"></emph>Boia,<emph.end type="italics"></emph.end> vede al tempo stesso il Binoculo, co­<lb></lb>m&#039;era lavorato dal legnaiolo di Linz, sul disegno avutone dal Keplero. </s>

<s>Le <lb></lb>due occhiaie profonde eran trapanate e larghe allo stesso modo: erano alla <lb></lb>stessa distanza l&#039;una dall&#039;altra, che i due fori del Boia, dove i topolini fic­<lb></lb>cano il muso, per giungere ad addentare addentro l&#039;esca insidiosa. </s>

<s>I rigo­<lb></lb>letti, da incastrar le lenti, erano allo stesso punto e allo stesso modo inca­<lb></lb>vati, che le scanalature delle due cateratte, fra le quali scatta e scorre l&#039;anello <lb></lb>di fil di ferro, destinato a strozzar gl&#039;incauti animaletti. </s></p><p type="main">

<s>La storiella curiosa la sentiremo fra poco raccontar dallo stesso Keplero <lb></lb>a Ottavio Pisani, matematico napoletano, il quale per benefizio di coloro, <lb></lb>che ricevevan nocumento all&#039;un occhio, con cui continuamente riguardavan <lb></lb>nel Telescopio, volle, a costo di qualunque difficoltà, riuscire a geminar lo <lb></lb>strumento. </s>

<s>Delle speculazioni, che dovean guidarlo all&#039;esecuzione dell&#039;opera, <lb></lb>dava così conto, da Anversa, il dì 15 Settembre 1613, a Galileo, in una let­<lb></lb>tera latina scritta coll&#039;ortografia della pronunzia napoletana: “ De pespicillo <lb></lb>autem dicam meam opinionem: ego paro librum de tota Prospectiva, et habeo <lb></lb>multa circa construxionem huius pespicilli, et symmetriam vitrorum, quanta <lb></lb><gap></gap> modus formandi. </s>

<s>Verum ego non facio hunc pespi-<pb xlink:href="020/01/445.jpg" pagenum="426"></pb>cillum uno oculo apponendum sed duobus oculis, et ambos oculos volvo in <lb></lb>unum, si placet tibi scribam pluribus omnia ” (Campori, Cart. </s>

<s>gal., Mo­<lb></lb>dena 1881, pag. </s>

<s>72). </s></p><p type="main">

<s>Ma perchè Galileo o non rispose, o rispose freddamente all&#039;invito, l&#039;im­<lb></lb>paziente Pisani pensò di rivolgersi al Keplero, a cui, il dì 5 d&#039;Ottobre di <lb></lb>quell&#039;anno 1613, scriveva trepidante da Anversa, per la prima volta, inco­<lb></lb>minciando dallo scusarsi della sua audacia. </s>

<s>“ Audax videbor tibi.... ” (Epi­<lb></lb>stolae ad Kepl., Lipsiae 1717, Epist. </s>

<s>CCCXLIX, pag. </s>

<s>565). Due giorni dopo, <lb></lb>non essendosi voluto spiegar nella prima, torna a scrivere una seconda let­<lb></lb>tera, aprendo così la sua intenzione al gran Maestro della scienza ottica in <lb></lb>Germania: “ Alio autem modo perspicillum construere molior, nempe duo­<lb></lb>bus oculis aptatum. </s>

<s>Multos enim scio qui, cum diutium uno oculo inspicere <lb></lb>commorantur, fere fere, inquam altero oculo caligant. </s>

<s>Tu vero, qui optime <lb></lb>in tua Optica perspicilli rationem doces, quaeso responde quid sentis. </s>

<s>Sym­<lb></lb>metriam enim seu praxin construendi non invenio a te traditam. </s>

<s>Quod si <lb></lb>respondes, plura tecum conferenda aperiam ” (ihi, epist. </s>

<s>CCCL, pag. </s>

<s>566). </s></p><p type="main">

<s>Il Keplero non mancò di rispondere, benchè un po&#039;tardi, da Linz il dì <lb></lb>16 di Dicembre. </s>

<s>Avvisa il Pisani di aver ricevute insieme le sue due let­<lb></lb>tere, e poi, a proposito del Binoculo, passa a raccontar la storiella della <lb></lb>Trappola, che gli fu precipuo motivo d&#039;abbandonare il pensiero di un&#039;in­<lb></lb>venzione da lui stimata ridicola e inutile. </s>

<s>“ Perspicillum optas aptum duo­<lb></lb>bus oculis, et a me fabricam. </s>

<s>Difficile puto. </s>

<s>Tentare coepi ante biennium. </s>

<s><lb></lb>Postquam enim capsulam exhibuit Arcularius, qualem praescripseram, visa <lb></lb>est muscipulae figuram nacta esse: — Fecisti igitur; ne essem deridi­<lb></lb>culo.... — Ac etsi faciemus qualem optas, non erit apta promiscue omni­<lb></lb>bus, nec semper eidem. </s>

<s>Crescunt homines in latitudinem, usque ad pro­<lb></lb>vectam aetatem: tum autem difficultas maxima, ut duos tubos eiusdem <lb></lb>effectus in colore, copia luminis et quantitate speciei comparemus. </s>

<s>Si mi­<lb></lb>nima discrepantia, quanta incommoditas in usu? </s>

<s>Credo autem, si diligentia <lb></lb>accedat, aliquo usque promoveri opus posse, usu unius convexi in arundine <lb></lb>admodum longa duorumque cavorum: nec multum nocituram obliquitatem <lb></lb>convexi tantulam ad cava ” (ibi, epist. </s>

<s>CCCLII, pag. </s>

<s>567). </s></p><p type="main">

<s>Il Pisani, sentendo che s&#039;arretrava alle difficoltà dell&#039;impresa un così <lb></lb>gran capitano, egli semplice milite ne rimase a principio scoraggiato, ma, <lb></lb>poi presto ripreso animo, volle provarsi a incarnare quel suo concetto, per­<lb></lb>suaso di far cosa utilissima agli amici, i quali si lagnavano di esser quasi <lb></lb>rimasti ciechi dal guardar pur coll&#039;uno, rimanendone offeso gravemente l&#039;al­<lb></lb>tro: “ Scripsisti, con tali parole il Pisani risponde al Keplero, quod diu <lb></lb>tentasti et tandem destitisti. </s>

<s>Si tu tantus Dux fugis, quid facient milites? </s>

<s><lb></lb>O quid audeam! Immo superaddis quod quamvis inveniretur, tamen opus <lb></lb>inutile esset. </s>

<s>Sane territus obstupui, sed non funditus eieci spem. </s>

<s>Nam mihi <lb></lb>videtur aliquanto bene succedere. </s>

<s>Ego adhuc laboro, et multa experior, et <lb></lb>si quid boni succedet, illico ad te mittam. </s>

<s>Ego vellem hadere tale perspi­<lb></lb>cillum duobus oculis <gap></gap><pb xlink:href="020/01/446.jpg" pagenum="427"></pb>vastat alterum. </s>

<s>Ego vidi duos amicos sane excaecatos, ob diuturnam unius <lb></lb>oculi inspectionem, altero clauso. </s>

<s>Quare omnino mihi videtur necessaria ta­<lb></lb>lis perspicilli inventio ” (ibi, epist. </s>

<s>CCCLIII, pag. </s>

<s>568, 69). </s></p><p type="main">

<s>Essendosi, per principal difficoltà, presentata al Pisani quella della sim­<lb></lb>metrica visione co&#039;due Telescopii gemelli, aveva, infin da quel primo tempo <lb></lb>che si confidò con Galileo, pensato ad ovviarvi, applicando due oculari di­<lb></lb>retti a un obiettivo solo: <emph type="italics"></emph>ambos oculos volvo in unum.<emph.end type="italics"></emph.end> Sentendo ora che <lb></lb>anche il Keplero si riscontrava in quel medesimo pensiero, e che veniva di <lb></lb>più ad assicurarlo <emph type="italics"></emph>nec multum nocituram obliquitatem convexi tantulam <lb></lb>ad cava,<emph.end type="italics"></emph.end> deliberò senz&#039;altro di costruire il nuovo Binoculo, su quel dise­<lb></lb>gno. </s>

<s>Alla capsula, che portava i due oculari, forse per evitar la ridicola im­<lb></lb>magine della Trappola, dette, dalla parte anteriore, una figura ovale, e in­<lb></lb>dietro prolungavasi, a guisa di coda, in un tubo, all&#039;estremità del quale era <lb></lb>applicato l&#039;obiettivo. </s>

<s>Nel Luglio del 1614 il nuovo Binoculo era costruito, <lb></lb>e il Pisani aveva fatto pensiero di mandarlo a Firenze a Galileo, e di offe­<lb></lb>rirlo, per mezzo di lui, al Granduca. </s>

<s>“ Io ho fatto uno di quelli occhiali <lb></lb>che V. S., quasi nuovo e celeste Amerigo, ave rivolto al cielo; ho fatto dico <lb></lb><emph type="italics"></emph>uno Teloscopio a due occhi,<emph.end type="italics"></emph.end> come gli altri sono ad uno. </s>

<s>Il corpo è poco e <lb></lb>di figura ovale. </s>

<s>Quando piacesse a S. A. </s>

<s>Serenissima farmi carità, io man­<lb></lb>daria queste cose, ed intitolaria al suo serenissimo nome ” (Campori, ivi, <lb></lb>pag. </s>

<s>82). </s></p><p type="main">

<s>Il Binoculo finalmente, da <emph type="italics"></emph>Telescopio a due occhi,<emph.end type="italics"></emph.end> si ridusse a due Te­<lb></lb>lescopii congiunti, per opera di Anton Maria Rheita, il quale affrontò ardi­<lb></lb>tamente le difficoltà della visione simmetrica, che avevan fatto così adom­<lb></lb>brare il Pisani e il Keplero. </s>

<s>L&#039;invenzione è descritta in un libro, che porta <lb></lb>lo strano titolo di <emph type="italics"></emph>Oculus Enoch et Eliae,<emph.end type="italics"></emph.end> stampato nel 1645 in quella stessa <lb></lb>città di Anversa, in cui soggiornava il nostro Pisani. </s>

<s>Nel cap. </s>

<s>VI di quel <lb></lb>libro l&#039;Autore scrive le seguenti parole, che noi traduciamo liberamente, <lb></lb>perchè l&#039;importanza delle notizie non ricompensano il tedio di legger nella <lb></lb>lingua latina originale: </s></p><p type="main">

<s>“ Benchè Galileo avesse costruito già Canocchiali eccellenti, quanto a <lb></lb>inacutire la vista, avevano nonostante quegli strumenti un difetto, qual era <lb></lb>quello di circoscrivere in troppo angusto spazio il campo della visione. </s>

<s>Per­<lb></lb>ciò, mettendomi io a ridurre alla pratica i principii diottrici del Keplero, <lb></lb>con due lenti convesse in debite proporzionali distanze fra loro insieme con­<lb></lb>giunte, e con felice artifizio segate, mi venne costruito un Telescopio, per <lb></lb>mezzo del quale si comprendevano in una occhiata sola e si annoveravano <lb></lb>distintamente infino a 50 stelle. </s>

<s>Ecco un Telescopio, che può dirsi propria­<lb></lb>mente astronomico, perchè apre un campo alla visione cento volte più am­<lb></lb>pio di quel che non facesse il primo e più antico occhiale di Galileo. </s>

<s>Non <lb></lb>contenti a solo questo monoculo, ne aggiungemmo ad esso un altro simile, <lb></lb>con felicissimo ardimento. </s>

<s>Così ci si videro comparire innanzi gli oggetti il <lb></lb>doppio più grandi e più distinti di quel che non apparissero col Monoculo, <lb></lb>e insomma passava fra l&#039;uno e l&#039;altro strumento quella differenza, che è <pb xlink:href="020/01/447.jpg" pagenum="428"></pb>tra il veder con due occhi e un occhio solo. </s>

<s>Avendo poi noi, per gli am­<lb></lb>maestramenti dell&#039;eruditissimo Cartesio, il modo di segare i vetri, secondo <lb></lb>la vera ragione e potenza delle loro rifrazioni; abbiamo speranza di scoprir, <lb></lb>con un tal Canocchiale Binoculo, i più occulti segreti del cielo. </s>

<s>” </s></p><p type="main">

<s>De&#039;nuovi strumenti binoculari del Rheita, dava così il Mersenno, co&#039;suoi <lb></lb>soliti modi sgarbati, conto al Torricelli, consigliandolo ad andare a scuola <lb></lb>dal frate cappuccino tedesco, se voleva imparare a fabbricar Canocchiali: <lb></lb>“ Porro te monitum velim iam Augustae Vindelicorum fieri Telescopia longa <lb></lb>meliora quam tua, vel cuiuspiam alterius communia, quae serviunt duo­<lb></lb>bus oculis, quaeque propterea capuccinus Rheita (qui nuper edidit tracta­<lb></lb>tum de hoc tubo, quem vocat <emph type="italics"></emph>Oculum Enoch et Eliae<emph.end type="italics"></emph.end>) vocat <emph type="italics"></emph>Binocula.<emph.end type="italics"></emph.end><lb></lb>Habent itaque quatuor convexa, nullum concavum, duo per quovis oculo, <lb></lb>quae, quia obiecta invertunt, quod parum refert in astris, si tertium conca­<lb></lb>vum adlabetur, rectum est obiectum. </s>

<s>Sed iam fortassis librum illum vide­<lb></lb>ris, nec dubito quin eadem Telescopia possis imitari, quin et superare ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>19). </s></p><p type="main">

<s>In ogni modo, il Rheita che raddoppiando lo strumento credeva di po­<lb></lb>ter raddoppiare anche insieme la potenza visiva, e che, dalla Diottrica del <lb></lb>Keplero e del Cartesio non aveva altro imparato che la pratica di quel Ca­<lb></lb>nocchiale astronomico, costruito fra noi dal Fontana tanti anni prima; era <lb></lb>un illuso. </s>

<s>A dimostrarlo tale basterebbe rivolgere gli occhi su quella Ta­<lb></lb>vola disegnata dalla sua stessa penna, e che fu inserita fra le carte astro­<lb></lb>nomiche di Galileo. </s>

<s>Le due note illustrative, scritte in due quadretti incor­<lb></lb>niciati, con cappuccinesca raffinatezza, appiè della stessa Tavola, servono di <lb></lb>conferma. </s>

<s>Dice l&#039;una di quelle note: “ Observatio stupenda Novem Comi­<lb></lb>tum Jovis a me habita die 29 Xbris 1642, qua et aliis vicibus, praeter qua­<lb></lb>tuor interiores Galilaei, alios quinque exteriores et multo maiores inveni, <lb></lb>tali prorsus dispositione et ordine, ut hic notantur. </s>

<s>” Dice l&#039;altra nota: <lb></lb>“ Qui postea, die 4 Januarii 1643, notabilissime et taliter de loco suo moti <lb></lb>et mutati sunt, prout 0, 0, 0, 0 denotant. </s>

<s>F et G vero ea die disparuere ver­<lb></lb>sus Apogaeos, aut in umbram Jovis forsan intrantes ” (MSS. Gal., P. III, <lb></lb>T. VII, c. </s>

<s>6). </s></p><p type="main">

<s>Tanto poi bene il fatto provò l&#039;illusione dell&#039;Astronomo cappuccino, <lb></lb>che andarono in dimenticanza i Binoculi astronomici di lui, insieme col suo <lb></lb>nuovo sistema gioviale. </s>

<s>Ben però rivissero lieta e splendida vita i Binoculi <lb></lb>terrestri, nè avrebbe senza dubbio il Keplero fatto un sì mal garbo a quella <lb></lb>sua ridicola Trappola da topi, se avesse potuto immaginar di vedersela tra­<lb></lb>sformata in quegli elegantissimi diottrici gemelli, di che si servono le signore, <lb></lb>per tòrre a sè gli attori lontani, e le decorazioni sceniche de&#039;teatri. </s></p><pb xlink:href="020/01/448.jpg" pagenum="429"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Uno degli usi più speciali, a cui si fece servire il Telescopio, fu quello <lb></lb>di rivolgerlo a guardar direttamente nella sfera del Sole. </s>

<s>Vi furon pur troppo, <lb></lb>e fra&#039;nostri e fra gli stranieri, alcuni audaci, che aprirono il loro occhio a <lb></lb>ricever quell&#039;onda condensata di luce scaturiente dal diafano dell&#039;oculare, <lb></lb>e benchè Galileo avesse notato già l&#039;efficacia de&#039;veli e de&#039;vetri coloriti <lb></lb>(Alb. </s>

<s>III, 74) in radere il capellizio alle stelle, per cui venisse l&#039;occhio a <lb></lb>riceverle con assai meno abbagliore, non par nulladimeno che gli cadesse in <lb></lb>mente d&#039;applicar quegli stessi veli e que&#039;vetri coloriti al Telescopio, per le <lb></lb>dirette osservazioni solari. </s>

<s>E da ciò fu il caso che venisse a perdere quel <lb></lb>primato nelle osservazioni delle macchie, che egli poi uscì a rivendicar sopra <lb></lb>lo Scheiner, senza giusta ragione. </s></p><p type="main">

<s>Fra gli osservatori però, eccitati dall&#039;esempio di Galileo, non mancò <lb></lb>chi pensasse a provvedere alla vista degli occhi, difendendoli, in osservare <lb></lb>il sole, con vetri e lenti tinte di verdi colori. </s>

<s>“ Le macchie del sole, scri­<lb></lb>veva a Galileo, il di 23 Marzo 1612, Lodovico Cigoli, con il vetro bianco <lb></lb>piccolo, non potevo fissar l&#039;occhio, che mi lacrimava, ma poi con un vetro <lb></lb>verde grosso, e perchè è incavato come il bianco ve ne pongo sopra un altro <lb></lb>piano similmente verde, di maniera che non mi dà fastidio niente a tutte <lb></lb>l&#039;ore il guardarlo ” (MSS. Gal., P. III, T. X, c. </s>

<s>61). </s></p><p type="main">

<s>Se questa, di fabbricar gli oculari di vetro verde, piuttosto che bianco, <lb></lb>fosse veramente invenzione del Cigoli o glie ne fosse venuta la notizia di <lb></lb>Germania, è incerto nè così facile a decider sui documenti che ci son noti. </s>

<s><lb></lb>In ogni modo, lo Scheiner pretende di essersi, un anno e più prima del <lb></lb>Cigoli, servito delle lenti colorite nelle osservazioni dirette del Sole, e pre­<lb></lb>tende altresì di essere stato egli il primo a trasformar così il Canocchiale, <lb></lb>da meritar che gli venga anche imposto il nuovo nome di <emph type="italics"></emph>Elioscopio.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nomine porro illius (Helioscopii) intelligo Tubum opticum vitris co­<lb></lb>loratis cum debito artificio ad istud elaboratis adornatum, ut colorum ipsis <lb></lb>inhaerentium beneficio vehementior solis radius fractus atque hebetatus, ad <lb></lb>visum moderatior minusque noxius penetret, atque, ob hanc prerogativam <lb></lb>merito huiusmodi instrumentum <emph type="italics"></emph>Helioscopii<emph.end type="italics"></emph.end> nomenclatura gaudet.... ” </s></p><p type="main">

<s>“ Helioscopium igitur vitris constat coloratis minimum duobus, convexo <lb></lb>et concavo, materia bene crassa, pura, solida, non bullis, non arenulis, mi­<lb></lb>nime vero venis, tractibus, seu undis insessa, elaborata in segmentum seu <lb></lb>frustum perfecte sphaericum, quorum alterum sit vel una ex parte, vel <lb></lb>utrinque convexum; alterum concavum vel utrinque vel concavo planum, <lb></lb>prout in Tubis non coloratis fieri consuevit.... Color omnium, quantum <lb></lb>fieri potest, sit unius generis, v. </s>

<s>g. </s>

<s>coeruleus, viridis, flavus, aut quicum­<lb></lb>que tandem aliis. </s>

<s>Quod si uniusmodi color haberi nequit, accipiantur mixtim <pb xlink:href="020/01/449.jpg" pagenum="430"></pb>qui possint. </s>

<s>Talem ego tubum ab initio composui e fragmentis caeruleis la­<lb></lb>minarum vitreorum, quo et maculas in <emph type="italics"></emph>Apelle<emph.end type="italics"></emph.end> meo editas observavi ” (Rosa <lb></lb>Ursina, Bracciani, 1626-30, pag. </s>

<s>70). </s></p><p type="main">

<s>L&#039;Elioscopio nonostante parve esser licenziato dai primi e importanti <lb></lb>servigi, che aveva prestati agli Osservatori del sole, quando la CV proposi­<lb></lb>zione della Diottrica del Keplero venne a suggerire al Castelli quel più co­<lb></lb>modo e riposato modo di osservarne e di disegnarne le macchie, descritto <lb></lb>da Galileo in sulla fine della seconda lettera velseriana. </s>

<s>“ Ma conviene, av­<lb></lb>verte ivi l&#039;Autore, andare destramente secondando il movimento del sole, e <lb></lb>spesso movendo il Telescopio, bisogna procurare di mantenerlo ben diritto <lb></lb>verso il Sole ” (Alb. </s>

<s>III, 420). </s></p><p type="main">

<s>Lo Scheiner pure, parecchi anni dopo, ripetendo gl&#039;insegnamenti dati <lb></lb>dal Castelli, per dipinger con un pennello sopra una carta l&#039;immagine te­<lb></lb>lescopica del sole, avverte: “ Et quia is continue movetur, evehit statim <lb></lb>imaginem sui e deputato atque occupato chartae loco, unde cadem propor­<lb></lb>tione est movendum instrumentum, qua sol promovetur in coelo: alias uno <lb></lb>codemque loco non continebis circulum solis, non signabis maculas ” (Rosa <lb></lb>Urs., ibi, pag. </s>

<s>78). </s></p><p type="main">

<s>Il tedio del dover sempre tenere in esercizio e impacciata la mano, a <lb></lb>muovere il Telescopio a seconda del moto del sole, non veniva evitato nem­<lb></lb>meno in quella così complicata macchina grienbergeriana, che lo stesso <lb></lb>Scheiner descrive, sotto lo specioso nome di <emph type="italics"></emph>Eliotropio,<emph.end type="italics"></emph.end> e che rappresenta <lb></lb>in ripetuti iconismi, da pag. </s>

<s>347-54 della citata sua <emph type="italics"></emph>Rosa Ursina.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Eppure, infin dal 1613, eravi stato fra noi chi aveva pensato già a le­<lb></lb>vare il tedio e a disegnar più perfettamente le macchie, facendo automati­<lb></lb>camente muovere il Telescopio, e la carta al moto del sole. </s>

<s>Il pensiero fu <lb></lb>così da Fabio Colonna espresso in una sua lettera a Galileo: “ Per dimo­<lb></lb>strare che abbi cominciato ad aver gusto delle osservazioni celesti, ancorchè <lb></lb>con cattivo strumento, massime di Agosto, ebbi osservato le macchie solari, <lb></lb>e con poca pratica a saperle segnare. </s>

<s>Pure, veda qualche vestigio di buona <lb></lb>intenzione, che possa con il tempo migliorare, e già ho pensato un modo <lb></lb>che, essendo solo, si possa muovere il Telescopio e carta al moto del sole <lb></lb>e tempo, acciò non abbi altro che far che segnar le macchie perfettamente, <lb></lb>ed ora abbisogna in più volte rimettere a sesto l&#039;istrumento e la carta, e <lb></lb>se ci è difetto, è causa la sopraddetta occasione e il tremar la mano nel­<lb></lb>l&#039;istesso segnare ” (MSS. Gal., P. VI, T. IX, c. </s>

<s>99). </s></p><p type="main">

<s>Ma questo stesso concetto dell&#039;<emph type="italics"></emph>Eliostata<emph.end type="italics"></emph.end> si riaccese e apparve più vi­<lb></lb>vamente colorito nella mente del Borelli, quando volle provarsi a misurar <lb></lb>la velocità della luce del sole, dal tempo che ella metterebbe a saltar da <lb></lb>uno a un altro, per una serie numerosa di specchi. </s>

<s>Gli si obiettava che l&#039;ul­<lb></lb>timo raggio riflesso non era più quello stesso primo incidente, rinnovandosi <lb></lb>a ogni istante del moto del sole, e che perciò l&#039;esperienza, seppure era riu­<lb></lb>scibile, si sarebbe dovuta fare con qualche altra immobile sorgente di luce. <lb></lb></s>

<s>“ Ma a questo proposito (così Cosimo Galilei riferisce in una lettera al Vi-<pb xlink:href="020/01/450.jpg" pagenum="431"></pb>viani) ha scritto il signor Dottore (il Borelli) cinque o sei proposizioni bel­<lb></lb>lissime, mostrando di potersi servire del sole, benchè continuamente si muova, <lb></lb>e con una macchina che si volta al piacer suo, e con un oriuolo a ruote <lb></lb>aggiustato, prova che sempre possa (movendo quella macchina dove dev&#039;es­<lb></lb>ser fermo lo specchio che ha da ricevere la prima riflessione o per dir meglio <lb></lb>il raggio solare) far andar sempre la riflessione per la medesima linea, che <lb></lb>vale a dire, sempre nel medesimo modo ” (MSS. Gal. </s>

<s>Disc., T. CXLIII, c. </s>

<s>101). </s></p><p type="main">

<s>Come, per le più comode e più perfette osservazioni del sole gli Astro­<lb></lb>nomi inventarono l&#039;Elioscopio e l&#039;Eliostata; così per le più perfette osser­<lb></lb>vazioni degli astri, apparentemente minori, sentirono il bisogno di assettare <lb></lb>intorno al Canocchiale altri organi, per cui si venissero que&#039;minutissimi punti <lb></lb>lucidi a rappresentare nel vero esser loro, senz&#039;illusione d&#039;ingrandimenti <lb></lb>ascitizii. </s>

<s>Due modi erano stati proposti già da Galileo: quello della cordi­<lb></lb>cella tesa e l&#039;altro de&#039;veli e de&#039;vetri colorati, ma non avendo avuto l&#039;ac­<lb></lb>corgimento di applicar questi organi al Canocchiale, si lasciò rapir di mano <lb></lb>all&#039;Huyghens l&#039;invenzione del Micrometro propriamente detto, e allo Schei­<lb></lb>ner quella dell&#039;Elioscopio. </s></p><p type="main">

<s>Benchè però non venisse in mente a Galileo di tender la cordicella o il <lb></lb>filo micrometrico nel foco delle lenti, e di tinger le lenti stesse in qualche <lb></lb>varietà di colori, non par nulladimeno che trascurasse l&#039;uso dei diaframmi, <lb></lb>come s&#039;argomenta dal seguente poscritto di lettera del p. </s>

<s>Clavio: “ Si sono <lb></lb>visti qui in Roma alcuni occhiali mandati da V. S., i quali hanno li vetri <lb></lb>convessi assai più grandi, ma coverti, con restarvi solamente un buco pic­<lb></lb>colo libero. </s>

<s>Desidererei di sapere che serve tanta grandezza, se ha da co­<lb></lb>prirsi in questo modo. </s>

<s>Pensano alcuni che sieno fatti grandi, acciò, sco­<lb></lb>prendosi tutti la notte, si possano meglio vedere le stelle ” (Alb. </s>

<s>VIII, 122). </s></p><p type="main">

<s>Dall&#039;altra parte i diaframmi venivano facilmente suggeriti dalla maestra <lb></lb>Natura, che fu prima a farne uso nella fabbrica dell&#039;occhio. </s>

<s>“ Quod autem <lb></lb>facit ad visum adumbrandum (aveva già lasciato scritto il Maurolico nel <lb></lb>lib. </s>

<s>III <emph type="italics"></emph>Diaphanorum)<emph.end type="italics"></emph.end> ea fuit uvea tunica opaca villositate adumbrans prae­<lb></lb>dictos humores.... Talis autem adumbratio facit rerum visibilium radios <lb></lb>expressius apparere, et efficacius ab humoribus praedictis sentire; siquidem <lb></lb>radii luminum inter opaca aedium recepti sunt evidentiores ” (Neap. </s>

<s>1611, <lb></lb>pag. </s>

<s>70). </s></p><p type="main">

<s>Ma nella CXXII proposizione della <emph type="italics"></emph>Diottrica,<emph.end type="italics"></emph.end> formulata: <emph type="italics"></emph>Angusta len­<lb></lb>tis convexae portione, caeteris paribus, distinctiora repraesentantur visi­<lb></lb>bilia, lata confusiora,<emph.end type="italics"></emph.end> il Keplero trattò de&#039;diaframmi per iscienza, e in modo <lb></lb>da sodisfar pienamente ai desiderii, e da risolvere i dubbii del p. </s>

<s>Clavio: <lb></lb>“ Nam (così passa l&#039;Autore a dimostrar quella diottrica proposizione) quae <lb></lb>per magnam portionem convexitatis in oculum radiant, illa, per CXIX, for­<lb></lb>tius radiant, qua fortitudine primum iridis colores, inde nebulae excitantur. </s>

<s><lb></lb>Oculorum cava et retiformis tunica est spiritu plena, et licet a puncto so­<lb></lb>lum tangatur, tamen si id punctum ex concursu radiorum multorum sit im­<lb></lb><gap></gap><pb xlink:href="020/01/451.jpg" pagenum="432"></pb>imbuitur contagione passionis penetrantis: vide LXI. Itaque, pro commo­<lb></lb>ditate oculi, instrumenti, et lucis diurnae vel nocturnae, ampliatur et rete­<lb></lb>gitur convexa lens, aut angustatur et tegitur, seu immediate, seu loco in­<lb></lb>termedio inter lentes, adhibito diaphragmate pertuso, aut collo instrumenti <lb></lb>introrsum flexo et angustato, aut productione tubi ultra lentem convexam, <lb></lb>ut eius cylindracaei orificium remotus, per LXVII, minori angulo cernatur, <lb></lb>valeatque tantum quantum angustius aliquid. </s>

<s>Natura praeclusit ampliatione <lb></lb>foraminis uvaee ad lucem nocturnam, contractione ad diurnam. </s>

<s>Habet Dia­<lb></lb>phragma et hunc usum, ut intus obscuritatem faciat, quorsum et color niger <lb></lb>intus obductus servit, et litui figura, progressu extrorsum flexa habent la­<lb></lb>tera, in medio introrsum, ne radii prope convexam ingressi, rursum pror­<lb></lb>sumque revibrentur et claritatem faciant. </s>

<s>Eodem servit et productio tubi <lb></lb>longe ultra lentem convexam, ne convexum irradietur a lateralibus hemi­<lb></lb>sphaerii partibus ” (Augustae, 1611, pag. </s>

<s>65). </s></p><p type="main">

<s>Fu de&#039;primi a mettere in pratica fra noi questi teorici Kepleriani in­<lb></lb>segnamenti il Sagredo, il quale, nel dì 4 Agosto 1618, scriveva in così fatti <lb></lb>termini a Galileo: “ In questo tempo nondimeno ho avvertito quello che <lb></lb>per altre scrissi a V. S. E. cioè che aggiunto alcun cannone all&#039;ultimo vetro <lb></lb>che lo copre dal lume, si vede molto più chiaro e distinto; e per tempe­<lb></lb>rare i lumi che vanno riflettendo dentro i cannoni, che generano vista nu­<lb></lb>volosa, ho trovato buon rimedio nell&#039;ultimo cannone, in conveniente distanza e <lb></lb>grandezza, porre un riparo di un arcoletto forato ” (Alb. </s>

<s>Supplem., pag. </s>

<s>123). </s></p><p type="main">

<s>Il gentiluomo veneziano però applicava così fatti organi al Canocchiale, <lb></lb>per servirsene a suo diletto. (Campori, Cart. </s>

<s>gal. </s>

<s>ediz. </s>

<s>cit., pag. </s>

<s>134). Ma <lb></lb>uno de&#039;primi e principali, che seppe prevalersi dell&#039;efficacia dei diaframmi <lb></lb>nelle osservazioni celesti, fu Giovanni Hevelio, il quale pensò di trasformare <lb></lb>il Canocchiale ordinario in Elioscopio, applicando presso all&#039;oculare due vetri <lb></lb>piani colorati, in mezzo a ciascun de&#039;quali sia collocato <emph type="italics"></emph>papyrus eiusdem <lb></lb>quantitatis, uno foramine parvo pertusa, quae cum vitris firmiter, vel filo, <lb></lb>vel .... glutino .... connectatur.<emph.end type="italics"></emph.end> (Selenographia, Gedani 1647, pag. </s>

<s>23). </s></p><p type="main">

<s>Per poi osservar particolarmente le stelle, insegnava così lo stesso He­<lb></lb>velio ad accomodare i diaframmi all&#039;obiettivo del Telescopio: “ Accipe Tu­<lb></lb>bum, qui observationibus Jovis ac Lunae accomodatus est, et angustius redde <lb></lb>foramen convexi lenti proximum, vel novam chartam impone, cuius forami­<lb></lb>nis circumferentiae magno piso sit aequalis ” (ibi, pag. </s>

<s>37). Così dice di <lb></lb>aver potuto l&#039;Autore veder perfettamente rotondo il corpo delle stelle fisse, <lb></lb>senza raggi avventizi, ciò che non era riuscito nè a Galileo nè al Keplero, <lb></lb>nè a nessun altro prima di lui. </s>

<s>L&#039;Huyghens nonostante trovò che così fatti <lb></lb>diaframmi heveliani non erano i più opportuni per le osservazioni delle stelle <lb></lb><emph type="italics"></emph>maxime splendidarum,<emph.end type="italics"></emph.end> e che meglio giovava, <emph type="italics"></emph>ad auferendos radios,<emph.end type="italics"></emph.end> servirsi <lb></lb>a vetri <emph type="italics"></emph>fuligine leviter infectis.<emph.end type="italics"></emph.end> (Syst. </s>

<s>Sat, Op. </s>

<s>Var., cit. </s>

<s>1724, pag. </s>

<s>540). </s></p><p type="main">

<s>Più tardi, lo stesso Huyghens pensò a un altro modo di Diaframma <lb></lb>oculare, di cui si giovò utilmente a distinguere i due satelliti di Saturno, <lb></lb><gap></gap><pb xlink:href="020/01/452.jpg" pagenum="433"></pb>con quel suo stesso Telescopio, e col solo diaframma heveliano applicato <lb></lb>all&#039;obiettivo: “ Cum Saturni comites illos cassinianos diligentius requirerem <lb></lb>eosque difficulter adsequerer, praesertim noctibus non admodum obscuris, <lb></lb>intellexi in causa esse lucem tenuem quendam ab aere ad oculum manan­<lb></lb>tem, non eam quae per lentem maiorem advenit, sed quae extrinsecus cir­<lb></lb>cum latam praeterlabitur. </s>

<s>Huic importunae luculae excludendae, nonnihil <lb></lb>quidem conducere sciebam, si circulum illum papyraceum, quo in Luna ob­<lb></lb>servanda utebar, etiam hic lenti maiori circumponerem. </s>

<s>Sed aliud efficacius <lb></lb>remedium circa haec occupato incidit, priori illi iungendum, ut nempe per­<lb></lb>foratae laminae oppositu, oculi pupilla arctaretur, quae alioqui per tenebras <lb></lb>late patere solet. </s>

<s>Cuius simul ac experimentum feci, iam clare tres Saturni <lb></lb>comites conspexi, cum amoto exiguo foramine media illa nostra tantum cer­<lb></lb>neretur ” (Astroscopia, Op. </s>

<s>Var., cit., pag. </s>

<s>275). </s></p><p type="main">

<s>Non vogliamo all&#039;ultimo passare in tal soggetto senza commemorare <lb></lb>que&#039;macchinamenti, che, sotto il nome di <emph type="italics"></emph>Arcicanna,<emph.end type="italics"></emph.end> proponevano agli Ac­<lb></lb>cademici del Cimento i due fratelli Candido e Anton Maria Del Buono, per <lb></lb>render maneggevoli in qualche modo i Telescopii, come solevano usarsi al­<lb></lb>lora, a lungo foco. </s>

<s>Intorno a ciò così scriveva il Magalotti, con intenzione, <lb></lb>che poi non ebbe effetto per le ragioni altrove accennate, d&#039;inserire anche <lb></lb>questa fra le descrizioni degli stumenti premesse al Libro de&#039;<emph type="italics"></emph>Saggi:<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Avvegnachè di niun uso sieno in queste presenti <emph type="italics"></emph>Esperienze<emph.end type="italics"></emph.end> i dise­<lb></lb>gni delle macchinè de&#039;nostri Occhiali, de&#039;quali principalmente ci servimmo <lb></lb>nell&#039;anno 1660 all&#039;osservazioni di Saturno, per esserci paruto che in essi <lb></lb>si ritrovi alcuna cosa di particolare e degna della curiosità altrui, ci siamo <lb></lb>risoluti di aggiungere le tre precedenti figure, acciò ritrovandovi altri, per <lb></lb>accidente, alcuna cosa di buono, possa servirsene, volendo ” (MSS. Cim., <lb></lb>T. VII, c. </s>

<s>23). E prosegue a rilevar le utilità e i comodi di così fatte mac­<lb></lb>chine telescopiche, descrivendone particolarmente gli organi rappresentati in <lb></lb>disegno nelle tre figure citate, e impresse nelle Tavole IX, X e XI che s&#039;al­<lb></lb>legarono infine al Tomo II, P. II delle <emph type="italics"></emph>Notizie degli Aggrandimenti delle <lb></lb>Scienze Fisiche in Toscana,<emph.end type="italics"></emph.end> pubblicate, nel 1780, in Firenze dal Targioni <lb></lb>Tozzetti. </s></p><pb xlink:href="020/01/453.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del Barometro<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle prime idee, che ebbero i Fisici intorno alla possibilità e all esistenza dei vacuo, e delle loro <lb></lb>prime esperienze intorno al peso e alle pressioni dell&#039;aria. </s>

<s>— II. </s>

<s>Della celebre esperienza del­<lb></lb>l&#039;argento vivo; delle esperienze del Pascal e di altri Francesi. </s>

<s>— III. </s>

<s>Come l&#039;esperienza dell ar­<lb></lb>gento vivo fosse, per unanime consenso degli stessi stranieri, attribuita al Torricelli. </s>

<s>— IV. </s>

<s>Delle <lb></lb>Lettere torricelliane sull&#039;esperienza dell&#039;argento vivo. </s>

<s>— V. </s>

<s>Come il Torricelli attendesse a co­<lb></lb>struir lo strumento da misurar le variazioni del peso dell&#039;aria, e come non gli riuscisse la sua <lb></lb>intenzione. </s>

<s>— VI. </s>

<s>Come e da chi lo strumento torricelliano dell&#039;argento vivo fosse applicato <lb></lb>ad uso di Barometro. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Cadere in pioggia dall&#039;alto, penetrare il suolo e sott&#039;esso scorrere in <lb></lb>sottilissime vene, ora inquinandosi di limo e ora chiarificandosi di nuovo; <lb></lb>risalire a un tratto in zampilli da un fesso, e di lì volgere in basso per tor­<lb></lb>nare a nascondersi in canaletti coperti; poi uscire in rivi mormoreggianti <lb></lb>ed, aggiungendosi ad altri rivi, riversarsi insieme in un fiume, che sonante <lb></lb>e ondoso, fra il verde delle sue rive, s&#039;affretta a scender nel mare; è la <lb></lb>continua vicenda con che si regola il corso dell&#039;acque, e a loro simiglianza <lb></lb>altresì il corso delle idee. </s>

<s>Il tema che prendiamo ora a trattare, e che si <lb></lb>aggira intorno alla scienza del peso dell&#039;aria e della natura del vuoto, offre, <lb></lb>di quel corso che naturalmente fanno le idee stesse, il più notabile esempio. </s></p><p type="main">

<s>Che sia l&#039;aria veramente un corpo; che ella occupi uno spazio deter­<lb></lb>minato, rimossa dal quale, o per attrazione o per esservi fugata dagli av­<lb></lb>versi ardori del fuoco, lo lasci di sè o d&#039;altri visibili corpi affatto vuoto; lo <lb></lb>aveva già con sottili speculazioni insegnato e con numerose e variate espe­<lb></lb>rienze dimostrato quel maestro antico della Fisica pneumatica, Herone Ales-<pb xlink:href="020/01/454.jpg" pagenum="435"></pb>sandrino. </s>

<s>Egli, addetto alla scuola di Platone, non dubitò di professar libe­<lb></lb>ramente dottrine opposte a quelle di Aristotile, il qual negava la possibilità <lb></lb>di ogni spazio vuoto. </s>

<s>Gli argomenti del Filosofo son celebri nella storia della <lb></lb>Meccanica, riducendosi a dire che, se il vacuo si dà veramente in natura, <lb></lb>non è possibile che nessun corpo si muova da luogo a luogo. </s>

<s>A un errore <lb></lb>così pernicioso erasi già contrapposto G. </s>

<s>Cesare Scaligero, il quale anzi provò <lb></lb>che il vacuo è condizione essenziale e principio del moto. </s>

<s>“ In natura va­<lb></lb>cuum dari necesse est. </s>

<s>Nempe, si non daretur, aut non esset motus, aut <lb></lb>subiret corpus in corpus. </s>

<s>Caeterum non sicut antiqui. </s>

<s>Illi enim ponebant <lb></lb>vacuum sine corpore. </s>

<s>At nos illud profitemur vacuum in quo corpus est. </s>

<s><lb></lb>Idemque esse vacuum et locum, neque differre nisi nomine. </s>

<s>Sane, si non <lb></lb>esset vacuum non esset locus. </s>

<s>Est enim vacuum spatium in quo est corpus, <lb></lb>cuius natura per se talis est ut, cedente corpore corpori, fiat vacuum ut <lb></lb>impleatur. </s>

<s>Est igitur vacuum principium motus ” (De Subtil., Francof. </s>

<s>1592, <lb></lb>pag. </s>

<s>15). </s></p><p type="main">

<s>Queste nuove dottrine però dello Scaligero conferirono più a sgombrare <lb></lb>i sentieri alla Meccanica, che non alla Fisica pneumatica. </s>

<s>Ma il Cardano fu <lb></lb>quegli che dette mano all&#039;opera, e se Herone nel Proemio agli <emph type="italics"></emph>Spiritali<emph.end type="italics"></emph.end> in­<lb></lb>segnava che, succhiando l&#039;aria da un vaso, le labbra son tirate indietro dal <lb></lb>vacuo per riempirne il luogo, e se i Fisici dopo l&#039;Alessandrino spiegarono <lb></lb>questo e altri simili fatti colla fuga o coll&#039;orrore del vacuo; il Cardano nega <lb></lb>l&#039;operar d&#039;una forza inerente in un subietto che non esiste, e cerca di spie­<lb></lb>gar quel medesimo fatto con un principio, che se non è, almeno ha l&#039;ap­<lb></lb>parenza di vero. </s>

<s>“ Ergo in universum tres erunt motus naturales. </s>

<s>Primus <lb></lb>quidem ac validissimus a vacui fuga, sed verius a forma elementi, cum ma­<lb></lb>iorem raritatem non admittat, nec materiae partes separari numquam que­<lb></lb>ant. </s>

<s>Cum igitur in follibus apertio maior est quam paucus ille aer ferre <lb></lb>possit, primum rarior redditur, cum materia prima separationem non admit­<lb></lb>tat: aer ille non sustinens maiorem raritatem aut aliquid ad se trahit, aut <lb></lb>folles ommino disrumpit. </s>

<s>Non igitur a vacuo motus ullus, sed a formis ipsis, <lb></lb>maxime aeris, dum amplius divelli nequit nec separari, fieri consuevit ” (De <lb></lb>Subtilitate, Lugduni 1580, pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Le idee dello Scaligero, che ammettevano l&#039;esistenza del vuoto, e quelle <lb></lb>del Cardano che avevano dalla Pneumatica bandito il falso principio della <lb></lb>fuga del vacuo, s&#039;andarono con rapido corso a congiungersi, come due soli­<lb></lb>tarie vene in un rivo, nella mente di Bernardino Telesio. </s>

<s>I pensamenti di <lb></lb>lui furono dal suo concittadino Tommaso Cornelio, nella celebre Epistola <emph type="italics"></emph>De <lb></lb>circumpulsione platonica,<emph.end type="italics"></emph.end> commentati ed esposti al modo che segue: </s></p><p type="main">

<s>“ Bernardinus Telesius, singulari vir ingenio, ratus est posse in rarum <lb></lb>natura existere spatium omnis corporaee substantiae expers, atque adeo pror­<lb></lb>sus inane: quamquam id non sine vi, conatuque aliquo fieri posse conten­<lb></lb>dit. </s>

<s>Ait enim mundi corpora mutuo contactu gaudere, atque conniti ne in­<lb></lb>vicem separentur seiunganturque, ac proinde quocumque corpus cesserit, <lb></lb>aliud illico subsequi ne scilicet contactu privetur. </s>

<s>Verum ubi vis nisusque <pb xlink:href="020/01/455.jpg" pagenum="436"></pb>validus contigua corpora separat, nec interea aliud corpus succederc datur, <lb></lb>cedere quidem, quamvis invita, spatiumque interiectum inane relinquere. </s>

<s>Ad­<lb></lb>ducit autem assertionis suae testem experientiam siquidem e clepsydrarum <lb></lb>foraminibus, a quibus aqua non defluit, mel liquoresque alii graviores de­<lb></lb>cidunt, pondere videlicet deorsum magno nisu premente ” (Neapoli, Rail­<lb></lb>lard 1688, pag. </s>

<s>312). </s></p><p type="main">

<s>Chi prosegue a leggere quel che ivi soggiunge l&#039;Autore s&#039;accorge as­<lb></lb>sai facilmente che egli vedeva nella Clessidra del Telesio una di quelle can­<lb></lb>nncce di vetro chiuse di sopra e aperte in un piccolo foro di sotto da cui, <lb></lb>secondo l&#039;esperienze fatte dagli Accademici del Cimento (Saggi di Nat. </s>

<s>esp., <lb></lb>Firenze 1841, pag. </s>

<s>37), <emph type="italics"></emph>tenute con la bocca volta allo ingiù, e appese in <lb></lb>aria a piombo,<emph.end type="italics"></emph.end> se non fluisce l&#039;acqua, fluisce però il mercurio, infintantochè <lb></lb>non sia sceso a far col suo premere equilibrio al premere esterno dell&#039;aria. </s>

<s><lb></lb>Il Cornelio insomma vedeva nell&#039;esperienza telesiana una immagine della <lb></lb>torricelliana, colla differenza del mele sostituito al mercurio. </s></p><p type="main">

<s>Comunque sia di ciò, corse ancora un mezzo secolo dai tempi del Te­<lb></lb>lesio, e quella che pur si può anche da noi chiamare immagine disegnata <lb></lb>collo stile e dipinta coi colori del Filosofo Razionalista, prese aspetto di realtà <lb></lb>e colore di Fisica in alcune speculazioni del Keplero. </s>

<s>Finge egli starsenc <lb></lb>uno sopra i confini dell&#039;aria nel puro etere o nel vuoto, e di lì versar den­<lb></lb>tro un sifone da una parte aria e dall&#039;altra acqua, e dice che un bicchiere <lb></lb>di questa farebbe equilibrio a 15 miriadi di miriadi di bicchieri di quella. <lb></lb></s>

<s>“ Nec dubium si quis in puro aethere consisteret, funderet hinc 1 cyathum <lb></lb>aquae inde quindecim myriadas myriadum cyathorum aeris, quin haec aequi­<lb></lb>ponderatura sint.... Non ignoro, ne credas, me physicorum reprehensionem <lb></lb>incursurum, qui aerem et hic et antea gravem seu ponderosum esse sta­<lb></lb>tuam. </s>

<s>At me sic docuit totius naturae contemplatio ” (Paralip. </s>

<s>ad Vitell., <lb></lb>Francof. </s>

<s>1604, pag. </s>

<s>128). </s></p><p type="main">

<s>Pochi anni dopo da che il Keplero scriveva così fatte parole, tenevasi <lb></lb>fra noi come cosa certa il peso dell&#039;aria, senza tanta paura di riprensioni. </s>

<s><lb></lb>Galileo aveva già, con molto maggior precisione dell&#039;Autore de&#039;Paralipo­<lb></lb>meni, ritrovato il peso specifico dell&#039;aria, e a ciò fare usava tre varii modi. </s>

<s><lb></lb>Uno di questi, con lettera del dì 12 Marzo 1613 pubblicata in Pisa nel 1864 <lb></lb>dalla tipografia Nistri, ei lo insegnava a Giovan Batista Baliani, in cui, a <lb></lb>conferirgli il merito d&#039;avere egli il primo accesa quella gran face di scienza, <lb></lb>che diffuse i suoi splendori per tutta l&#039;Europa, concorsero insieme il caso <lb></lb>e l&#039;ingegno come ora vedremo. </s></p><p type="main">

<s>Nell&#039;ottavo libro dell&#039;Architettura intitola Vitruvio il cap. </s>

<s>VII: <emph type="italics"></emph>Quot <lb></lb>modis ducantur aquae,<emph.end type="italics"></emph.end> e per via di condotti o metallici o murati insegna <lb></lb>come l&#039;acque si posson fare scender da un monte e risalire al monte op­<lb></lb>posto, attraversando la valle. </s>

<s>Or, non pensandosi che portasse differenza fra <lb></lb>il far salire l&#039;acqua per impulsione o per attrazione, il Porta, nel Libro III <lb></lb>degli <emph type="italics"></emph>Spiritali,<emph.end type="italics"></emph.end> vuole al cap. </s>

<s>I insegnare <emph type="italics"></emph>Come si possano condurre i fiumi <lb></lb>dalle basse ralli per le altissime cime dei monti<emph.end type="italics"></emph.end> <gap></gap><pb xlink:href="020/01/456.jpg" pagenum="437"></pb>modo consiste nel far cavalcare il monte a un sifone, una delle bocche del <lb></lb>quale attinga dal fiume, quasi dovesse operare come i sifoni ordinarii, che <lb></lb>s&#039;usan per travasare i liquidi o ne&#039;servigi domestici, o nell&#039;esercizio delle <lb></lb>arti. </s>

<s>Il Porta, non essendo stato sgannato dall&#039;esperienza, si credeva sicuro <lb></lb>del fatto e lo dava come cosa certa. </s>

<s>Ma il Baliani, riconosciutane l&#039;utilità, <lb></lb>volle vederne l&#039;esecuzione e trovò tutt&#039;altrimenti, ed ebbe a osservar cose <lb></lb>che lo riempirono di stupore. </s>

<s>Non sapendo che si pensare, rivolsesi a Ga­<lb></lb>lileo da Genova con lettera del dì 27 Luglio 1630, così esponendo il caso <lb></lb>e chiedendo consiglio: </s></p><p type="main">

<s>“ Ci conviene far che un&#039;acqua di due once di diametro in circa tra­<lb></lb>versi un monte, e per farlo conviene che l&#039;acqua salisca a piombo 85 palmi <lb></lb>di Genova, che son circa 70 piedi geometrici: e per farlo abbiamo fatto un <lb></lb>sifone di rame conforme al disegno inchiuso, ove CA (fig. </s>

<s>42) è il livello: <lb></lb>A ove si piglia l&#039;acqua, B ove ha da uscire, D l&#039;imbottatoio per dove si <lb></lb>empie il sifone, DE <lb></lb><figure id="id.020.01.456.1.jpg" xlink:href="020/01/456/1.jpg"></figure></s></p><p type="caption">

<s>Figura 42.<lb></lb>l&#039;altezza a piombo <lb></lb>che l&#039;acqua ha da <lb></lb>salire. </s>

<s>Però questo <lb></lb>sifone non fa l&#039;ef­<lb></lb>fetto desiderato, anzi <lb></lb>aperto, ancorchè <lb></lb>chiuso dal di sopra, <lb></lb>l&#039;acqua esce da tutte <lb></lb>due le parti, e se si <lb></lb>tien chiuso da una parte, in aprendo dall&#039;altra, ad ogni modo da questa esce <lb></lb>l&#039;acqua. </s>

<s>Io non mi posso dar a credere che l&#039;acqua abbia in questa occasione <lb></lb>voluto appartarsi dalle sue proprietà naturali, ond&#039;è forza che uscendo l&#039;acqua <lb></lb>vi sottentri aria dalla parte di sopra, però non si vede di dove. </s>

<s>” </s></p><p type="main">

<s>“ Avviene un&#039;altra cosa che mi fa stupire, ed è che, aprendosi la <lb></lb>bocca A, esce l&#039;acqua sin che dalla parte D sia scesa per la metà in circa <lb></lb>sino a F, e poi si ferma. </s>

<s>Io sono andato considerando se possa essere che <lb></lb>il canale o sifone abbia qualche pori, ma che l&#039;acqua non possa passarvi, e <lb></lb>nè anche l&#039;aria senza gran violenza, e perciò se il canale è pieno, l&#039;acqua A <lb></lb>sia tanto premuta che faccia forza tale, che l&#039;aria sottentri per li pori che <lb></lb>sono verso la parte di sopra, in modo che l&#039;acqua possa scendere per esso <lb></lb>sino a F, senza che vi rimanga vacuo. </s>

<s>Scesa poi in F, non restando nel ca­<lb></lb>nale altra acqua che la FA, questa non abbia forza di far violenza tale al­<lb></lb>l&#039;aria che possa sforzarla ad entrare per li pori suddetti.... Ho voluto nar­<lb></lb>rare questa cosa, a fine che V. S. possa più facilmente ritrovare in che <lb></lb>consista il mio errore, e favorire di avvertirmene ” (Alb. </s>

<s>IX, 195, 96). </s></p><p type="main">

<s>L&#039;Albèri osserva a questo punto in nota che <emph type="italics"></emph>ci manca la responsiva <lb></lb>di Galileo,<emph.end type="italics"></emph.end> ma il Venturi, dop&#039;aver nella Seconda Parte delle <emph type="italics"></emph>Memorie ine­<lb></lb>dite<emph.end type="italics"></emph.end> riferito il sunto della missiva del Baliani da noi trascritto, asserisce <lb></lb>confidentemente, quasi avesse letto nel documento galileiano: “ Il Galileo <pb xlink:href="020/01/457.jpg" pagenum="438"></pb>avea risposto alla lettera precedente che l&#039;altezza dell&#039;acqua sospesa entro <lb></lb>il tubo era la misura dell&#039;orrore che la natura ha contro il vacuo ” (Mo­<lb></lb>dena 1821, pag. </s>

<s>103). </s></p><p type="main">

<s>L&#039;asserto dell&#039;Autore si capisce bene non esser che una ripetizione <lb></lb>della favolosa risposta data da Galileo ai fontanieri di Boboli, ma l&#039;Albèri <lb></lb>più saviamente avvertiva, che la verità di quella risposta poteva argomen­<lb></lb>tarsi dall&#039;altra lettera, che sotto il dì 26 di Ottobre replicava il Baliani, la <lb></lb>quale, essendo stata veduta già e pubblicata in parte nel citato luogo dallo <lb></lb>stesso Venturi, porge un nuovo argomento fra i tanti della poco fina critica, <lb></lb>colla quale condusse il suo Lavoro. </s>

<s>Molto più torto poi fa all&#039;illustre Fisico <lb></lb>modanese quel suo temerario asserto, ripensando che poteva dal I Dialogo <lb></lb>delle Due Nuove Scienze ricavar con certezza a qual causa attribuisse Gali­<lb></lb>leo il salir l&#039;acqua attratta ne&#039;tubi non più su che a una determinata altezza. </s></p><p type="main">

<s>Comunque sia, la lettera di risposta al quesito del Baliani, ignota al Ven­<lb></lb>turi e all&#039;Albèri, venne poi alla luce in Pisa nel 1864 dalla Tipografia Ni­<lb></lb>stri. </s>

<s>In quella lettera, che è del dì 6 Agosto 1630, Galileo rispondeva così <lb></lb>in proposito al postulante: “ Mi dispiace bene che ella mi abbia domandato <lb></lb>il mio parere circa l&#039;esito del sifone, prima che la spesa fosse stata fatta, <lb></lb>perchè gliel&#039;avrei potuta risparmiare col mostrare, s&#039;io non m&#039;inganno, l&#039;im­<lb></lb>possibilità del quesito, la quale dipende da un mio problema più tempo fa <lb></lb>esaminato e che veramente ha del maraviglioso assai ” (Lettere di Galileo <lb></lb>pubblicate per la prima volta pel suo Trecentes. </s>

<s>natalizio in Pisa, XVIII Feb­<lb></lb>braio M.DCCC.LXIV, Tip. </s>

<s>Nistri, 1864, pag. </s>

<s>26). </s></p><p type="main">

<s>Il maraviglioso problema, da cui faceva Galileo dipendere la causa del <lb></lb>sostenersi l&#039;acqua nel tubo non più su che a quella altezza osservata dal <lb></lb>Baliani, era, secondo che seguita ivi a dire lo stesso Galileo, il problema mec­<lb></lb>canico della resistenza de&#039;solidi allo spezzarsi, paragonando un cilindro d&#039;acqua <lb></lb>a una corda o a una verga, la quale tirata giù dal suo soverchio peso final­<lb></lb>mente si strappa. </s></p><p type="main">

<s>Ricevuta una tal risposta, il Baliani ringrazia, riconosce di non aver <lb></lb>saputo far distinzione fra il salir dell&#039;acqua per attrazione o per impulso, <lb></lb>approva il ricorrere ingegnosamente al problema meccanico della resistenza <lb></lb>de solidi allo spezzarsi, per ispiegare il fatto maraviglioso, ma pur libera­<lb></lb>mente confessa che non valgon così fatte ragioni a toglierli via tutti i dubbi. </s>

<s><lb></lb>In quel tempo ch&#039;egli attendeva la risposta di Galileo non si rimase dallo <lb></lb>specular da sè, e sagacemente ne indovinò il vero. </s>

<s>Se l&#039;aria è pesa, ragio­<lb></lb>nava l&#039;arguto Genovese, l&#039;acqua dee esser sostenuta a quell&#039;altezza nel tubo <lb></lb>dal premere esteriormente dell&#039;aria stessa, e tale è la misura della forza che <lb></lb>si richiede a causare il vacuo. </s>

<s>Il ragionamento è così sottile, così la splen­<lb></lb>dida face del vero conduceva il Filosofo per quelle inesplorate sottigliezze, <lb></lb>che i principii della celebrata Scienza torricelliana, concludonsi nelle seguenti <lb></lb>parole, scritte il dì 26 Ottobre 1630 da Genova in una lettera a Galileo: </s></p><p type="main">

<s>“ Io non sono già della opinione volgare che non si dia vacuo; però <lb></lb>nen mi <gap></gap>otei dar a credere che si desse il vacuo in tanta <gap></gap><pb xlink:href="020/01/458.jpg" pagenum="439"></pb>facilmente. </s>

<s>E per non mancar di dirle la mia opinione intorno a ciò, io ho <lb></lb>creduto che naturalmente il vacuo si dia, da quel tempo che io ritrovai <lb></lb>che l&#039;aria ha peso sensibile, e che V. S. m&#039;insegnò in una sua lettera il <lb></lb>modo di ritrovarne il peso esatto, ancorchè non mi sia riuscito fin ora il <lb></lb>farne esperienza. </s>

<s>Io dunque allora formai questo concetto, che non sia vero <lb></lb>che repugni alla natura delle cose che si dia vacuo, ma ben che sia diffi­<lb></lb>cile ch&#039;esso si dia, e che non si possa dar senza gran violenza, e che si <lb></lb>possa ritrovar quanta debba essere questa tal violenza, che si richiede per <lb></lb>darsi vacuo. </s>

<s>E per dichiararmi meglio, essendo che se l&#039;aria pesa non sia <lb></lb>differenza fra l&#039;aria e l&#039;acqua che nel più e nel meno, è meglio parlar del­<lb></lb>l&#039;acqua, il cui peso è più sensibile, perchè poi lo stesso dovrà avvenire <lb></lb>dell&#039;aria. </s>

<s>” </s></p><p type="main">

<s>“ Io mi figuro dunque di essere nel fondo del mare, ove sta l&#039;acqua <lb></lb>profonda dieci mila piedi, e se non fosse il bisogno di rifiatare, io credo che <lb></lb>vi starei, sebbene mi sentirei più compresso e premuto da ogni parte di quel <lb></lb>ch&#039;io mi sia di presente: e perciò io credo che non potrei star nel fondo <lb></lb>di qualsivoglia profondità d&#039;acqua, la quale, crescendo in infinito, cresce­<lb></lb>rebbe per mio avviso tal compressione in modo, che le mie membra non <lb></lb>vi potrebbon resistere. </s>

<s>Ma per ritornare, dalla detta compressione in fuori, <lb></lb>io non sentirei altro travaglio, nè sentirei maggiormente il peso dell&#039;acqua <lb></lb>di quel ch&#039;io mi faccia, quando, entrando sotto acqua la state bagnandomi <lb></lb>nel mare, io ho dieci piedi d&#039;acqua sul capo, senza che io ne senta il peso. </s>

<s><lb></lb>Ma se io non fossi entro l&#039;acqua, che mi preme da ogni parte, e fussi, non <lb></lb>dico in vacuo, ma nell&#039;aria e che dalla mia testa in su vi fosse l&#039;acqua, al­<lb></lb>lora io sentirei un peso, ch&#039;io non potrei sostenere che quando avessi forza <lb></lb>a lui proporzionata; in modo che, ancorchè separando io violentemente le <lb></lb>parti superiori dell&#039;acqua dalle inferiori, non vi rimanesse vacuo, ma vi su­<lb></lb>bentrasse aria, ad ogni modo vi vorrebbe forza a seperarle, però non infi­<lb></lb>nita ma determinata, e via via maggiore secondo che la profondità dell&#039;acqua, <lb></lb>sotto la quale io fossi, fosse maggiore; la quale non vi ha dubbio che chi <lb></lb>fusse nel fondo detto di sopra di dieci mila piedi d&#039;acqua, stimerebbe impos­<lb></lb>sibile far detta separazione con qualunque forza, come che egli mai non ne <lb></lb>farebbe la prova; eppur si vede che non sarebbe vero che fosse impossibile, <lb></lb>ma che l&#039;impedimento gli verrebbe da non aver lui tanta forza da poter <lb></lb>far all&#039;acqua una tal violenza, che fusse bastante a separarla. </s>

<s>” </s></p><p type="main">

<s>“ Lo stesso mi è avviso che ci avvenga nell&#039;aria, che siamo nel fondo <lb></lb>della sua immensità, nè sentiamo nè il suo peso nè la compressione che ci <lb></lb>fa da ogni parte, perchè il nostro corpo è stato fatto da Dio di tal qualità, <lb></lb>che possa resistere benissimo a questa compressione senza sentirne offesa, <lb></lb>anzi ci è per avventura necessaria nè senza di lei si potrebbe stare; onde <lb></lb>io credo che, ancorchè non avessimo a respirare, non potremmo stare nel <lb></lb>vacuo, ma se fossimo nel vacuo allora si sentirebbe il peso dell&#039;aria che <lb></lb>avessimo sopra il capo, il quale io credo grandissimo, perchè, ancorchè io <lb></lb>stimi che quanto l&#039;aria è più alta sia sempre più leggera, io credo che sìa <pb xlink:href="020/01/459.jpg" pagenum="440"></pb>tanta la sua immensità, che, per poco che sia il suo peso, conviene che si <lb></lb>sentisse quel di tutta l&#039;aria che ci sta sopra, peso molto grande ma non <lb></lb>infinito, e perciò determinato, e che con forza a lui proporzionata si possa <lb></lb>superare, e perciò causarsi il vacuo. </s>

<s>Chi volesse ritrovar questa proporzione, <lb></lb>converrebbe che si sapesse l&#039;altezza dell&#039;aria e il suo peso in qualunque al­<lb></lb>tezza. </s>

<s>Ma comunque sia, io veramente lo giudicava tale che per causar va­<lb></lb>cuo, io credeva che vi si richiedesse maggior violenza di quello che può far <lb></lb>l&#039;acqua nel canale non più lungo di 80 piedi ” (Alb. </s>

<s>IX, 211-13). </s></p><p type="main">

<s>Il Baliani che teme di aver noiato Galileo <emph type="italics"></emph>con sì lunga diceria<emph.end type="italics"></emph.end> e se ne <lb></lb>scusa, lascia di far l&#039;applicazione di queste sue dottrine al fatto particolare <lb></lb>dell&#039;acqua sostenuta dentro il tubo o sifone di rame; applicazione che dal­<lb></lb>l&#039;altra parte risulta chiarissima, e che può concludersi in brevi parole: <lb></lb>L&#039;acqua che dalla parte F (figura precedente) termina col vuoto sente dal­<lb></lb>l&#039;opposta parte A il peso dell&#039;altezza dell&#039;aria come noi la sentiremmo sul <lb></lb>capo nostro se, dalle spalle in giù fossimo costituiti nel vuoto, e da quel <lb></lb>peso vien l&#039;acqua stessa sostenuta e proibita di scendere al basso. </s>

<s>Aprendo <lb></lb>l&#039;imbottatoio D, e di lì riempiutosi d&#039;aria lo spazio DF, la colonna acquea <lb></lb>non sente più quel peso, come noi non lo sentiamo quando l&#039;aria ci cir­<lb></lb>conda e ci preme per ogni parte, e perciò cade e fluisce liberamente dalla <lb></lb>bocca A, non per altro impulso che della sua propria gravezza. </s>

<s>Insomma, <lb></lb>la pressione fatta in A dalla colonna d&#039;acqua FA uguale alla pressione fatta <lb></lb>in H dalla colonna perpendicolare FH, era per il Baliani forza proporzionata <lb></lb>a superare il peso dell&#039;aria e perciò a causare il vuoto; forza che dice po­<lb></lb>trebbesi calcolare esattamente, quando si sapesse <emph type="italics"></emph>l&#039;altezza dell&#039;aria e il suo <lb></lb>peso in qualunque altezza.<emph.end type="italics"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="italics"></emph>Se questa dottrina è vera,<emph.end type="italics"></emph.end> soggiunge ivi il Baliani a Galileo, <emph type="italics"></emph>so che <lb></lb>l&#039;avrà speculata prima:<emph.end type="italics"></emph.end> e pur troppo la dottrina del Baliani era vera, ma <lb></lb>Galileo sventuratamente non l&#039;avea speculata. </s>

<s>Quand&#039;egli osservò nella ci­<lb></lb>terna che le pompe non attraevan l&#039;acqua più su che alle diciotto braccia, <lb></lb>aveva nella dottrina del Fisico genovese la ragione vera del fatto, onde potea <lb></lb>concluderne che il peso di una corda d&#039;acqua lunga diciotto braccia è forza <lb></lb>proporzionata a vincere il vacuo, ossia a far contrappeso al premere dell&#039;al­<lb></lb>tezza dell&#039;aria. </s></p><p type="main">

<s>Ma Galileo tutt&#039;altro che progredire così nelle sue speculazioni, misera­<lb></lb>mente invece indietreggiava. </s>

<s>Il Cardano aveva tentato di bandir dalla scienza <lb></lb>quel paralogismo della forza del vacuo, e il Baliani aveva ritrovato di quella <lb></lb>stessa forza la causa vera, mentre Galileo torna indietro ad appiccar il filo <lb></lb>delle idee agli ami insidiosi di quel paralogismo. </s>

<s>Rifiutato il felice pensiero <lb></lb>che gli balenò alla mente nelle sue prime speculazioni intorno alle forze mo-<pb xlink:href="020/01/460.jpg" pagenum="441"></pb>lecolari, il pensiero cioè di attribuire la coesione a una specie d&#039;attrazion <lb></lb>magnetica, si volse a professar il principio che la forza del vacuo sia l&#039;unico <lb></lb>glutine, e per se solo sufficiente a tenere insieme compaginati i corpi. </s>

<s>Am­<lb></lb>mette, com&#039;ammetteva il Telesio e tanti altri, che una tal forza di vacuo <lb></lb>sia superabile; che ella possa di più anco misurarsi, e che ne sian perciò <lb></lb>natural misura le corde di canapa e le verghe di metallo, quando finalmente <lb></lb>si strappano aggravate o tirate da soverchio peso. </s>

<s>Da questo effetto mecca­<lb></lb>nico faceva Galileo, nel 1630, dipender la causa del sostenersi l&#039;acqua nel <lb></lb>sifone di rame preparato dal Baliani, e da questo effetto meccanico, nono­<lb></lb>stante le belle speculazioni suggeritegli dallo stesso Baliani, nel 1638, nel <lb></lb>primo Dialogo delle Due Nuove Scienze, faceva pure dipendere il non risa­<lb></lb>lir l&#039;acqua nelle trombe più su che alle diciotto braccia. </s>

<s>“ Ed io sin ora <lb></lb>sono stato così poco accorto che intendendo che una corda, una mazza di <lb></lb>legno, o una verga di ferro si può tanto e tanto allungare che finalmente <lb></lb>il suo proprio peso la strappi tenendola attaccata in alto, non mi è sovve­<lb></lb>nuto che l&#039;istesso molto più agevolmente accaderà di una corda o verga di <lb></lb>acqua. </s>

<s>E che altro è quello che si attrae nella tromba che un cilindro di <lb></lb>acqua, il quale, avendo la sua attaccatura di sopra, allungato più e più, final­<lb></lb>mente arriva a quel termine, oltre al quale, tirato dal suo già fatto sover­<lb></lb>chio peso, non altrimenti che se fosse una corda si strappa? </s>

<s>” (Alb. </s>

<s>XIII, 21). </s></p><p type="main">

<s>Essendo la forza del vacuo proporzionale alla superficie di contatto e, <lb></lb>ne&#039;cilindri d&#039;ugual materia e di uguale altezza, essendo i pesi proporzionali <lb></lb>alle basi, spiegava così Galileo come al salir dell&#039;acqua nelle trombe fosse <lb></lb>in tutti casi prefinita la medesima misura, o sian le stesse trombe <emph type="italics"></emph>larghis­<lb></lb>sime o strette o strettissime quanto un filo di paglia<emph.end type="italics"></emph.end> (ivi). </s></p><p type="main">

<s>Dir queste cose in uno de&#039;Dialoghi galileiani Del Moto era un porre la <lb></lb>face sul candelabro; avventurata la scienza se fosse stata quella luce per <lb></lb>ogni parte sincera! Ma nonostante che fosse alquanto filigginosa giovò ri­<lb></lb>splendendo così dall&#039;alto, e giovò perchè insorsero i Peripatetici a reclamare <lb></lb>contro una dottrina, la quale, non solamente ammetteva il vacuo, ma ne in­<lb></lb>segnava il modo di misurarne la forza. </s>

<s>Reclamavano i Filosofi peripatetici <lb></lb>perchè quella nuova dottrina contradiceva agl&#039;insegnamenti di Aristotile; re­<lb></lb>clamavano i Teologi peripatetici, perchè contradire all&#039;autorità di Aristotile, <lb></lb>era quasi come un contradire all&#039;autorità stessa di Dio, in mano a cui te­<lb></lb>mevano che, dandosi il vacuo, si dovesse dissolvere l&#039;Universo. </s></p><p type="main">

<s>Bisognava dunque a que&#039;Filosofi e a que&#039;Teologi dimostrare che lo spa­<lb></lb>zio lasciatosi dietro dall&#039;acqua nelle trombe più lunghe delle diciotto brac­<lb></lb>cia, non era, com&#039;insegnava Galileo, uno spazio vuoto. </s>

<s>Si dettero mano <lb></lb>insieme a tentar l&#039;opera in Roma un solenne Filosofo e un Teologo peri­<lb></lb>patetico solenne, Gaspero Berti e Atanasio Kircher, e mostrarono in con­<lb></lb>durla, maggior acume di quel che non ci saremmo potuti aspettare. </s>

<s>Il par­<lb></lb>ticolar modo poi come l&#039;ingegnosa opera fu condotta, ci vien narrato dal <lb></lb>padre Gaspero Schott, nella sua <emph type="italics"></emph>Mechanica hydraulico-pneumatica,<emph.end type="italics"></emph.end> e a lui <lb></lb>prestiamo volentieri fede, perchè dice di avere attinta la storia del fatto <pb xlink:href="020/01/461.jpg" pagenum="442"></pb>dalla bocca dello stesso Raffaello Magiotti, che è per noi il giudice e il te­<lb></lb>stimone più autorevole che possa desiderarsi, sì per le relazioni che egli <lb></lb>ebbe poi intorno a tal soggetto col Torricelli, e sì per essere stato spettatore <lb></lb>al pubblico sperimento del Berti. </s></p><p type="main">

<s>Dop&#039;avere ivi accennato alla dottrina professata da coloro, che ammet­<lb></lb><figure id="id.020.01.461.1.jpg" xlink:href="020/01/461/1.jpg"></figure></s></p><p type="caption">

<s>Figura 43.<lb></lb>tevano l&#039;esistenza del vacuo, dottrina che è secondo lo <lb></lb>Schott <emph type="italics"></emph>non tantum in Philosophia absurda, sed et in <lb></lb>fide orthodoxa periculosa,<emph.end type="italics"></emph.end> soggiunge: “ Alii tamen me­<lb></lb>lioris notae Philosophi negant in praedicto tubi spatio esse <lb></lb>vere vacuum, idque variis probant rationibus atque expe­<lb></lb>rimentis. </s>

<s>Omnium pulcherrimum ingeniosissimumque vi­<lb></lb>detur esse istud, quod, suadente p. </s>

<s>Athanasio Kirchero, <lb></lb>exhibuit Romae Gaspar Bertus romanus, vir nobilis, et in <lb></lb>physicis mathematicisque solide doctus, singularisque in <lb></lb>experimentis capiendis solertiae.... Is cum audisset non­<lb></lb>nullos .... probare dari vacuum, saltem ad breve tempus, <lb></lb>inter corpora, quod aqua intra tubos ultra certam men­<lb></lb>suram elevata sisti non posset.... tubum in maiori multo <lb></lb>quam illi exposcerent longitudine, plumbeum erexit in <lb></lb>aedibus suis. </s>

<s>Centum is pedum erat in longitudine, et <lb></lb>digiti crassitudine ad supremum domus solarium pertin­<lb></lb>gens, ea forma, quam altera supra posita figura DKL <lb></lb>(fig. </s>

<s>43) monstrat. </s>

<s>In superiori huius tubi extremo .... <lb></lb>phialam primo aeream deinde vitream insignis crassitudinis <lb></lb>et studio in hunc finem conflatam imposuit, tali industria <lb></lb>a tubi collo coagmentatam, talique ingenio munitam, ut <lb></lb>omnis aeri esset ad eum interclusus aditus. </s>

<s>Intra vero <lb></lb>phialam, suggerente Kirchero, campanulam C, una cum <lb></lb>ferreo malleolo O lateribus phialae ea dexteritate inseruit, <lb></lb>ut malleolus ferreus magnete A ab extra attractus eleva­<lb></lb>tusque et mox a magnete retracto, liber, proprio pondere <lb></lb>campanulae illideretur ac sonum ederet. </s>

<s>Inferiorem vero <lb></lb>tubi partem epistomio seu aenea clavi volubili munivit. </s>

<s>” </s></p><p type="main">

<s>“ Comparatis omnibus ad experimentum capiendum <lb></lb>requisitis, tubi extremum orificium espistomio G munitum, <lb></lb>dolio MIKL aqua semiplenum immersit, totumque tubum <lb></lb>una cum phiala replevit aquis, facto in phialae vertice <lb></lb>foramine, quod postmodum diligentissime clausum sin­<lb></lb>gulari arte stamno solidavit. </s>

<s>Tum unco ferreo epistomium <lb></lb>G aperiut, viamque fecit aquae tubi ut libera posset ex <lb></lb>illo in subiectum vas defluere. </s>

<s>Et vero, ut assurgens in vase subiecto aqua <lb></lb>indicavit, defluxit quantum decem circiter pedes tubi ante replebat, reli­<lb></lb>quum intra tubum perstitit, patente licet ad multum tempus eadem via, <lb></lb>quae postea revoluta clavi, iterum conclusa est. </s>

<s>Tum vero admoto magnete <pb xlink:href="020/01/462.jpg" pagenum="443"></pb>ad superiorem phialam vitream e regione malleoli ferrei, malleolus allectus, <lb></lb>et remoto, dimissus est, a quo percussa campanula limpidissimum edidit so­<lb></lb>num, ab omnibus experimento spectatoribus auditum. </s>

<s>Sic tubo utrinque <lb></lb>probe clauso per noctem relicto, mane clavi aenea iterum convoluta, iterum <lb></lb>aperta est aquae via. </s>

<s>Verum non solum nihil amplius ex ea dimisit tubus, <lb></lb>sed ex pridie dimissa resorbuit. </s>

<s>Iteratum coram viris eruditis experimentum <lb></lb>fuit saepius, eodem semper successu, quos inter fuit Raphael Magiottus ma­<lb></lb>thematicus doctissimus a quo totam rei seriem oretenus intellexi ” (Herbi­<lb></lb>poli, 1657, pag. </s>

<s>307-9). </s></p><p type="main">

<s>Così l&#039;esperimento del Berti veniva a rassicurare i Peripatetici che lo <lb></lb>spazio lasciatosi indietro dall&#039;acqua ne&#039;tubi non era altrimenti vuoto, ma <lb></lb>che doveva esser ripieno di qualche mezzo, attraverso al quale si potessero <lb></lb>diffondere i tremori del suono. </s></p><p type="main">

<s>Si riposavan quieti i militanti per l&#039;onor di Aristotile e lieti della vit­<lb></lb>toria riportata in Roma su Galileo, quando da Firenze, in sull&#039;entrar del­<lb></lb>l&#039;anno 1644 si leva un rumore a commovere il mondo, come romba di ura­<lb></lb>gano che muova ad assalir le tende sotto cui in pace alloggiavasi il Peripato. </s>

<s><lb></lb>Il Mersenno ha ricevuto in Parigi da Michelangiolo Ricci alcune lettere scit­<lb></lb>tegli dal Torricelli, nelle quali descriveva allo stesso Ricci un&#039;esperienza <lb></lb>nuovamente da sè fatta, esperienza che consisteva nel prendere un lungo <lb></lb>tubo di vetro empierlo di mercurio, turarlo col dito, capovolgerlo in una ca­<lb></lb>tinella pur essa piena di mercurio e osservar lo spettacolo del pesante fluido <lb></lb>che, libero di uscir dal foro aperto, ritiratosi il dito, nonostante, per un <lb></lb>braccio e un quarto, ivi dentro restava sospeso. </s>

<s>Il Mersenno frugato da quella <lb></lb>sua natural curiosità viene a Firenze in cerca del Torricelli, <emph type="italics"></emph>qui Tubum <lb></lb>observatorium,<emph.end type="italics"></emph.end> egli stesso scrive, nel III Tomo delle Nuove osservazioni, <lb></lb><emph type="italics"></emph>mihi anno 1644 ostendit in Magni ducis Etruriae pergulis admirandis.<emph.end type="italics"></emph.end><lb></lb>(Parisiis 1647, pag. </s>

<s>216). </s></p><p type="main">

<s>Sulla fine dell&#039;anno dopo (1645) tornato in Francia divulgò ne&#039;suoi <lb></lb>connazionali ciò che aveva sentito dire e veduto co&#039;suoi proprii occhi in Ita­<lb></lb>lia. </s>

<s>“ Neque tamen (soggiunge il Roberval nella celebre lettera <emph type="italics"></emph>De vacuo<emph.end type="italics"></emph.end><lb></lb>ad D. Des-Noyers, ristampata in fine alla <emph type="italics"></emph>Demonstratio<emph.end type="italics"></emph.end> di Valeriano Ma­<lb></lb>gno) neque tamen eo anno aut sequenti tubos aptos Parisiis recuperare po­<lb></lb>tuit, tum quia ibi tales non fabricantur, tum etiam quia ipsa toto ferme eo <lb></lb>tempore per meridionales Regni gallici partes peregrinatus est. </s>

<s>Tandem ergo <lb></lb>idem scripsit Rotomagium ad amicos suos. </s>

<s>Ibi enim celeberrima habetur <lb></lb>vitri et chrystalli officina. </s>

<s>Sed antequam is inde tubos haberet vulgatum fue­<lb></lb>rat et ibidem experimentum et plurimis modis, tum privatim coram ami­<lb></lb>cos, tum publice coram omnibus eruditis multoties exhibitum a nobiliss. </s>

<s>viro <lb></lb>Domino De Paschal mense Januario et Februario huius anni (1647). Neque <lb></lb>id solum beneficio hydrargirii, tubis minoribus, puta 3 aut 4, aut 5 pedum <lb></lb>regiorum mensurae nostrae, sed, quod mirandum multis videbatur, benefi­<lb></lb>cio aquae et vini in tubis 40 pedum ex chrystallo mira arte fabricatis, atque <lb></lb><gap></gap> ad id paratis ita libratum erat, ut <pb xlink:href="020/01/463.jpg" pagenum="444"></pb>et attolli et deprimi ad usum requisitum facile posset ” (Venetiis Herz. </s>

<s>1649, <lb></lb>pag. </s>

<s>31, 32). </s></p><p type="main">

<s>Prosegue il Roberval in questa sua importantissima storia a dipinger <lb></lb>con vivi colori il Pascal tutto acceso in filosofico zelo di diffonder la verità, <lb></lb>e infaticabile in persuadere i perfidi Peripatetici coll&#039;eloquenza delle ragioni <lb></lb>e colle prove più decisive dei fatti. </s>

<s>Gli opponevano che lo spazio da lui pre­<lb></lb>dicato per vuoto era pieno d&#039;invisibili esalazioni, e di spiriti. </s>

<s>E il Pascal: <lb></lb>— Che ne dite, esalerà più di spirito dal vino o dall&#039;acqua? </s>

<s>— e rispon­<lb></lb>devano dal vino. </s>

<s>— Dunque il vino — proseguiva l&#039;Apostolo di Roano — <lb></lb>dovrebbe lasciar dietro a sè maggior vuoto? </s>

<s>— Sì. </s>

<s>— Ma eseguito l&#039;espe­<lb></lb>rimento, con tubi lunghi sospesi agli alberi delle navi, faceva veder col fatto <lb></lb>che avveniva tutto al contrario. </s></p><p type="main">

<s>Non contento alla viva voce, il Pascal si volle far banditore del vero <lb></lb>con gli scritti, pubblicando in Parigi un libretto col titolo <emph type="italics"></emph>Experiences <lb></lb>nouvelles touchant le vuide.<emph.end type="italics"></emph.end> La gran diffusione che ebbe in Francia, in <lb></lb>Svezia, in Olanda, in Polonia, in Alemagna e in Italia lo rese rarissimo, <lb></lb>per cui ne rimase più ferma la notizia appresso i dotti in un altro li­<lb></lb>bretto stampato l&#039;anno dopo, pur esso in Parigi, da Stefano Nöel col titolo <lb></lb><emph type="italics"></emph>Le plein du vuide<emph.end type="italics"></emph.end> e tradotto in quello stesso anno 1648 dall&#039;Autore in <lb></lb>latino. </s></p><p type="main">

<s>Il Nöel però era gesuita e perciò peripatetico e non pubblicava le otto <lb></lb>esperienze del Pascal per altro fine, che per impugnarne la conclusione. </s>

<s><lb></lb>Chi nonostante legge sente che le parole del Gesuita son come soffio di <lb></lb>vento ne&#039;carboni accesi, i quali levando più che mai viva la fiamma fanno <lb></lb>a quello splendore riconoscer meglio e apprezzar l&#039;ingegno del Pascal, che <lb></lb>variando i tubi di vetro in sifoni, in siringhe, in soffietti, riesce a dimo­<lb></lb>strare il medesimo vero, com&#039;abile musico che sa cavar da nobile o da rozzo <lb></lb>strumento la medesima dolce armonia. </s></p><p type="main">

<s>Tanta dovizia di scienza o diciam meglio di arte sperimentale era nel <lb></lb>Pascal inspirata da una voce che <emph type="italics"></emph>l&#039;apprit<emph.end type="italics"></emph.end> (dice l&#039;Autor della Prefazione al <lb></lb>Trattato postumo <emph type="italics"></emph>De l&#039;equilibre des liqueurs<emph.end type="italics"></emph.end> dello stesso Pascal) <emph type="italics"></emph>de monsieur <lb></lb>Petit Intendant des Fortifications, et tres habile dans ces sortes de scien­<lb></lb>ces, qui l&#039;avoit apprise du P. Mersenne,<emph.end type="italics"></emph.end> e la voce sparsa dal Mersenne era <lb></lb>che il Torricelli aveva fatta l&#039;esperienza dell&#039;argento vivo per dimostrare il <lb></lb>vuoto. </s>

<s>Se il Torricelli stesso avesse scritto nulla in proposito o quel che <lb></lb>avesse scritto, il Pascal lo ignorava, per cui, seguitando a tener dietro alle <lb></lb>voci sparse, <emph type="italics"></emph>cette mesme année 1647,<emph.end type="italics"></emph.end> dice l&#039;Autor della citata Prefazione, <lb></lb><emph type="italics"></emph>fut avertis d&#039;une pensée qu&#039;avoit eue Torricelli que l&#039;air estoit pesant, et <lb></lb>que sa pesanteur pouvoit estre le cause de tous les effets qu&#039;on avoit jus­<lb></lb>qu&#039;a lors attribuez à l&#039;horreur du vuide. </s>

<s>Il trouva cette pensée tout a fait <lb></lb>belle; mais comme ce n&#039;estoit qu&#039;une simple coniecture et dont on n&#039;avoit <lb></lb>aucune preuve, pour en connoistre ou la verité ou la fausseté, il fit plu­<lb></lb>sieurs experiences. </s>

<s>L&#039;une des plus considerables fut celle du vuide dans <lb></lb>le vuide.<emph.end type="italics"></emph.end> (Paris 1663). </s></p><pb xlink:href="020/01/464.jpg" pagenum="445"></pb><p type="main">

<s>L&#039;esperienza bellissima del vuoto nel vuoto, fatta ne&#039;primi di Novem­<lb></lb>bre del 1647 alla presenza di Monsieur Perier, leggesi descritta dallo stesso <lb></lb>Pascal in calce al citato <emph type="italics"></emph>Traitez de l&#039;equilibre des liqueurs.<emph.end type="italics"></emph.end> Essa dall&#039;altra <lb></lb>parte è così semplice che basta rivolger l&#039;attenzione alla qui apposta figura 44, <lb></lb>nella quale è trasformato il Tubo torricelliano ordinario. <lb></lb><figure id="id.020.01.464.1.jpg" xlink:href="020/01/464/1.jpg"></figure></s></p><p type="caption">

<s>Figura 44.<lb></lb>Riempito allo stesso modo e capovolto, parte del mer­<lb></lb>curio rimane nel tubo MN alla solita altezza, e parte <lb></lb>rimane nella scodella B. Rotta, coll&#039;unghie, la codetta M di <lb></lb>vetro che sigillava la parte superiore di quello stesso tubo, <lb></lb>a un tratto il mercurio MN precipita nella catinella N, e <lb></lb>quello della scodella B risale violentemente a riempire <lb></lb>il tubo AB. </s></p><p type="main">

<s>“ Mais cette experience, per ripigliar la storia in­<lb></lb>terrotta del nostro Autore, ne le satisfaisant pas encore <lb></lb>entièrement, il medita dès la fin de cette mesme an­<lb></lb>née 1647 l&#039;experience celebre qui fut faite en 1648 au <lb></lb>haut, et au bas d&#039;une montagne d&#039;Auvergne appellee le <lb></lb>Puy de Domme. </s>

<s>” </s></p><p type="main">

<s>Argomentava, con sottile e splendido concetto il Pa­<lb></lb>scal, che se l&#039;argento vivo sostentavasi nel cannello di <lb></lb>vetro per la pressione dell&#039;aria, come il Torricelli diceva, l&#039;altezza del livello <lb></lb>doveva riscontrarsi varia a piè e in cima della montagna. </s>

<s>Confidato il pen­<lb></lb>siero al Perier, ei fu che lo mandò con grande amore ad effetto, e delle <lb></lb>cose osservate ne distese una Relazione col titolo <emph type="italics"></emph>Recit de la grande Expe­<lb></lb>rience du Puy de Domme.<emph.end type="italics"></emph.end> Fu fatto così noto al pubblico, per questa Rela­<lb></lb>zione, come i fatti rispondessero puntualmente ai concetti del Pascal, e <lb></lb>confermassero le ragioni del Torricelli. </s></p><p type="main">

<s>“ Qu&#039;en l&#039;experience faite au plus bas lieu le vif argent rèstoit à la <lb></lb>hauteur de 26 poulces 3 lignes et demie. </s>

<s>En celle qui à esté faite en un <lb></lb>lieu élevé au dessus du plus bas d&#039;environ sept toises, le vif argent est resté <lb></lb>a la hauteur de 26 poulces, 3 lignes.... ” (Traites de l&#039;Equilib., Paris 1663, <lb></lb>pag. </s>

<s>185). E prosegue a riferir via via le misure sempre più basse ritrovate <lb></lb>nel livello del mercurio nel tubo, secondo che più e più s&#039;ascendeva in alto, <lb></lb>cosicchè alla massima altezza di 500 tese <emph type="italics"></emph>le vif argent s&#039;est trouve à la <lb></lb>hauter de&#039;23 poulces, deux lignes<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>186). </s></p><p type="main">

<s>Questa esperienza, che si appellò meritamente col nome di <emph type="italics"></emph>grande,<emph.end type="italics"></emph.end> fu <lb></lb>confermata dallo stesso Pascal con quell&#039;altra del manticetto che si può, con <lb></lb>non minor ragione chiamare <emph type="italics"></emph>elegante;<emph.end type="italics"></emph.end> esperienza, la quale, tanto piacque al <lb></lb>Royle, che volle ripeterla, e descriverla con le seguenti parole: “ Alterum <lb></lb>quod in hypothesis nostrae confirmationem adducam, est experimentum il­<lb></lb>lud,.... ab eodem Domino Paschalio factum, Harpastum scilicet languide <lb></lb>inflatum ab montis radice ad eius verticem portandi. </s>

<s>Id quippe magis, ma­<lb></lb>gisque turgescebat, quo altius portabatur, adeo ut penitus quasi tensum in <lb></lb><gap></gap> gradatim vero rursum flaccesceret prout deorsum <pb xlink:href="020/01/465.jpg" pagenum="446"></pb>ferebatur, essetque ad imum montis aeque flaccidum ac prius ” (Op. </s>

<s>Omn., <lb></lb>Venetiis 1697, T. I, pag. </s>

<s>163). </s></p><p type="main">

<s>A confermare il gran concetto del Torricelli coll&#039;esperienza, sorsero in <lb></lb>Francia, incitati dall&#039;esempio del Pascal, il Roberval che fece l&#039;esperienza <lb></lb>della vescica nel vuoto, e l&#039;Auzout che modificò alquanto l&#039;esperienza dello <lb></lb>stesso Pascal del vuoto nel vuoto. </s>

<s>Queste belle prove d&#039;arte sperimentale <lb></lb>furon fatte note al mondo dal Pecquet, il quale, accingendosi nel suo cele­<lb></lb>bre Trattato anatomico <emph type="italics"></emph>De circulatione sanguinis et chyli motu<emph.end type="italics"></emph.end> a farne la <lb></lb>descrizione, così avverte: “ Auctores adducam non librorum, quos hanc in <lb></lb>rem ne audivi quidem circumferri, sed eorum, saltem quae sequuntur Expe­<lb></lb>rimentorum, et quorum grandis auctoritas et nomen venerabile ” (Pari­<lb></lb>siis 1654, pag. </s>

<s>50). </s></p><p type="main">

<s>Alle due esperienze del Roberval e dell&#039;Auzout il Pecquet stesso ne ag­<lb></lb>giunge una sua, che è quella dell&#039;acqua sornotante al mercurio. </s>

<s>Ma egli è <lb></lb>per altro benemerito della scienza torricelliana, la quale fu per lui splendi­<lb></lb>damente applicata al moto del sangue nel cuore, come s&#039;era applicata ai <lb></lb>moti dell&#039;acqua nelle trombe. </s></p><p type="main">

<s>L&#039;espressione di scienza Torricelliana che ci è uscita dalla penna, non <lb></lb>sembrerà impropria a coloro i quali considerano le tante altre applicazioni <lb></lb>che se ne fecero a ogni sorta di fatti naturali, per cui ne uscirono tante <lb></lb>nuove insigni scoperte. </s>

<s>Ma a ciò conferì l&#039;uso della Macchina pneumatica <lb></lb>la quale, ritrovata verso il 1654 da Ottone di Guericke, fu col consenso del­<lb></lb>l&#039;inventore divulgata nel 1657 dal p. </s>

<s>Gaspero Schott sotto il titolo di <emph type="italics"></emph>Expe­<lb></lb>rimentum novum magdeburgicum.<emph.end type="italics"></emph.end> (Mechanica hydraul. </s>

<s>pneum., Herbi­<lb></lb>poli 1657, pag. </s>

<s>444-65). </s></p><p type="main">

<s>Questa macchina del Guericke era assai faticosa, dovendosi agitar la <lb></lb>pompa, per semplice moto di leva, e gli oggetti da sperimentare, ora era <lb></lb>difficile e ora affatto impossibile introdurgli nella campana. </s>

<s>Il Boyle, il quale, <lb></lb>dopo di aver fatto cenno degli Esperimenti di Magdeburgo, chiama in te­<lb></lb>stimonio il conte di Corke a cui dice <emph type="italics"></emph>me rebus ex eodem principio expe­<lb></lb>riendis sollicitum iam ante fuisse<emph.end type="italics"></emph.end> perfezionò la stessa Macchina facendo <lb></lb>muover la pompa pneumatica da un&#039;asta dentata, che menavasi in su e in <lb></lb>giù dai moti alternativi di una manovella, e sostituendo al pallone chiuso <lb></lb>del Guericke un pallone di vetro coll&#039;apertura da introdurvi il braccio di <lb></lb>un uomo, e poi sigillata, con turacciolo a vite. </s>

<s>Questa nuova macchina boi­<lb></lb>leiana fu descritta dal suo inventore nel Proemio ai <emph type="italics"></emph>Nuovi esperimenti fisico­<lb></lb>meccanici,<emph.end type="italics"></emph.end> pubblicati prima in inglese e dedicati dall&#039;Autore al detto conte <lb></lb>di Corke suo nipote, colla data del dì 20 Dicembre 1659. Col mezzo di que­<lb></lb>sta macchina principalmente si fecero dal Boyle que&#039;XLIII Esperimenti, <lb></lb>da&#039;quali si può dir che venisse a promuoversi e ad illustrarsi ogni parte <lb></lb>della scienza della Natura. </s></p><p type="main">

<s>Ma proseguendo i suoi fisici esercizii, che ogni giorno più gli diveni­<lb></lb>van tra mano fecondi, il Boyle stesso introdusse nella prima sua macchina <lb></lb>altre nuove perfezioni <emph type="italics"></emph>partim<emph.end type="italics"></emph.end> com&#039;egli dice <emph type="italics"></emph>ab in<gap></gap>enioso Domino Hooke<emph.end type="italics"></emph.end><pb xlink:href="020/01/466.jpg" pagenum="447"></pb><emph type="italics"></emph>aliis suggestas, partim proprio marte excogitatas<emph.end type="italics"></emph.end> (Novor. </s>

<s>Experim. </s>

<s>cont. </s>

<s>I, <lb></lb>Praemonitiones, Op. </s>

<s>cit., T. I, pag. </s>

<s>207), e di questa nuova macchina cosi <lb></lb>perfezionata si servì per condurre i Nuovi esperimenti descritti nella <emph type="italics"></emph>Con­<lb></lb>tinuazione prima e seconda.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Questa nuova Macchina pneumatica boileiana, che fu costruita nell&#039;of­<lb></lb>ficina del celebre Dionigi Papin, si può dire che non s&#039;avvantaggiasse sopra <lb></lb>la prima in altro, che nella migliore disposizione data al recipiente, il quale, <lb></lb>invece di essere un pallone avvitato al corpo di tromba, era una campana <lb></lb>di vetro posata con l&#039;orlo intasato di cemento su un piano, in mezzo al <lb></lb>quale s&#039;apriva il cannello aspiratore. </s>

<s>Il maneggio però rimaneva quel me­<lb></lb>desimo del rocchetto e dell&#039;asta dentata, e poniamo che fosse alquanto più <lb></lb>facile di quello della semplice leva guerricchiana, si rendeva nulladimeno, <lb></lb>via via che votavasi il recipiente, sempre più faticoso. </s>

<s>Ad alleviar la fatica <lb></lb>riuscì ingegnosamente l&#039;Hawksbee, che è il vero perfezionatore della mac­<lb></lb>china pneumatica, introducendo, invece dell&#039;unica boileiana, il gioco alter­<lb></lb>nativo di due trombe. </s>

<s>Da ciò avviene che, quando il recipiente diventa quasi <lb></lb>esausto, la compressione dell&#039;aria esteriore sopra la tromba attraente che di­<lb></lb>scende, è quasi tanto grande quant&#039;è la potenza che si richiede per solle­<lb></lb>var l&#039;altra tromba. </s>

<s>Cosicchè, mentre a muover le macchine del Guericke e <lb></lb>del Boyle, a misura che si avvicinano al vuoto, divengon più dure; <emph type="italics"></emph>que­<lb></lb>sta che io son per descrivere,<emph.end type="italics"></emph.end> dice lo stesso Inventore, <emph type="italics"></emph>nelle medesime circo­<lb></lb>stanze è tutto all&#039;opposto.<emph.end type="italics"></emph.end> (Esper. </s>

<s>fisico mecc., trad. </s>

<s>it., Firenze 1716, pag. </s>

<s>2). </s></p><p type="main">

<s>Migliorò altresì l&#039;Hawksbee la disposizione del recipiente o della cam­<lb></lb>pana facendole arrotare ben bene l&#039;orlo, e posandola sopra un cuoio bagnato. </s>

<s><lb></lb>Così liberava sè e gli altri sperimentatori dal tedio di dovere smurare il <lb></lb>recipiente stesso, e staccarlo dal piano, ogni volta che volevasi rinnovare <lb></lb>l&#039;esperienza. </s>

<s>Non senza grande commodità introdusse poi quel filo scorsoio <lb></lb>da mandar giù, tirare in su, tener sospesa o muovere qualunque cosa, che <lb></lb>più piacesse di sperimentare nel vuoto. </s>

<s>Munì inoltre la macchina di uno <lb></lb>squisito <emph type="italics"></emph>provino,<emph.end type="italics"></emph.end> che consisteva in un lungo tubo di vetro aperto di sopra <lb></lb>nel vano del recipiente e di sotto immerso in un bicchiere pieno di mer­<lb></lb>curio. </s>

<s>Un&#039;assicella graduata e applicata al tubo stesso, dal risalirvi dentro <lb></lb>più o meno alto il mercurio, segnava i gradi della rarefazione dell&#039;aria. </s>

<s>Si <lb></lb>vede dunque come, da leggerissime modificazioni in fuori, la Macchina pnen­<lb></lb>matica che s&#039;apparecchiò l&#039;Hawksbee per condurre i suoi <emph type="italics"></emph>Physico-mecha­<lb></lb>nical Experiments<emph.end type="italics"></emph.end> pubblicati in Londra nel 1709, è quella stessa che si <lb></lb>maneggia dai fisici moderni. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dalle esperienze francesi di Roano a quelle inglesi del Boyle e del­<lb></lb>l&#039;Hawksbee, in un breve corso di anni, la scienza ha fatto tali e tanti pro­<lb></lb>gressi, da recare stupore a chiunque vi ripensa. </s>

<s>E in tanta operosità di <pb xlink:href="020/01/467.jpg" pagenum="448"></pb>studii, e in tanto straboccante abbondanza di frutti, francesi e inglesi e ale­<lb></lb>manni riconoscono d&#039;unanime consenso, per loro primo e principale Mae­<lb></lb>stro in questa scienza, il Torricelli. </s>

<s>Il Boyle, che è senza dubbio il più va­<lb></lb>lente di tutti, stima che non si sarebbe potuto proporre altro miglior soggetto <lb></lb>a&#039;suoi studii, <emph type="italics"></emph>quam si nobile illud experimentum torricellianum exco­<lb></lb>lere et promovere studerem.<emph.end type="italics"></emph.end> (Nova, exper. </s>

<s>Proem. </s>

<s>Op. </s>

<s>Omn., Ven. </s>

<s>1697, <lb></lb>T. I, pag. </s>

<s>2). </s></p><p type="main">

<s>Ma pur, fra&#039;tanti, non mancò chi ebbe ardire di appropriarsi la nobile <lb></lb>esperienza, e fu Valeriano Magno, se non il primo, senza dubbio, il più avido <lb></lb>di tutti. </s>

<s>Egli pubblicò un libricciolo col titolo <emph type="italics"></emph>Demonstratio ocularis,<emph.end type="italics"></emph.end> in cui, <lb></lb>dopo d&#039;avere accennato alla lettura del I Dialogo delle Nuove Scienze di Ga­<lb></lb>lileo, dice come di lì gli venisse il pensiero di far l&#039;esperienza del vuoto col <lb></lb>mercurio. </s>

<s>Finita la sua breve <emph type="italics"></emph>Dimostrazione<emph.end type="italics"></emph.end> l&#039;Autore, come fanciullo che <lb></lb>tresca colle braccia in aria per cansare i colpi della ferza che il pedagogo <lb></lb>tien sotto la toga, aggiunge la seguente nota: “ Haec scribebam Varsaviae <lb></lb>die 12 Julii anni 1647, quae dum exhiberentur Serenissimis Principibus Regi <lb></lb>et Reginae spectaculo iucundissimo, inde erupit fama huiuscemodi miraculi <lb></lb>in natura, quae excitavit multorum ingenia ad contradicendum ” (Demon­<lb></lb>stratio ecc., Venetiis 1649, pag. </s>

<s>15). </s></p><p type="main">

<s>I più temuti però fra questi contradittori eran quelli, che gli avreb­<lb></lb>bero potuto rinfacciare i suoi furti, il più animoso fra i quali insorse quel <lb></lb>Roberval che, insieme col Pascal e con l&#039;Auzout, aveva tanto ferventemente <lb></lb>in Francia coltivato la scienza torricelliana. </s>

<s>Egli, sotto forma di Epistola al <lb></lb>Des-Noyers, data di Parigi nell&#039;Ottobre del 1647, scrisse una <emph type="italics"></emph>Narratio de <lb></lb>vacuo,<emph.end type="italics"></emph.end> la quale, ristampandosi in Venezia dall&#039;Herz, nel 1649, la <emph type="italics"></emph>Demon­<lb></lb>stratio<emph.end type="italics"></emph.end> del Magno, fu aggiunta al volumetto. </s>

<s>In tal Narrazione, con quella <lb></lb>dignitosa e gentile franchezza di chi è mosso dall&#039;amore del vero, il cele­<lb></lb>bre Matematico francese così scriveva: “ Ignoscat mihi R. P. capuccinus <lb></lb>Valerianus Magnus si dixero illum parum candide egisse in eo libello quem <lb></lb>de hac re in lucem nuperrime emisit mense Julio huius anni 1647, dum <lb></lb>celeberrimi huiusce experimenti ille primus author haberi voluit. </s>

<s>Quod certo <lb></lb>constat iam ab a. </s>

<s>1643 in Italia vulgatum fuisse ac ibidem, praecipue vero <lb></lb>Romae atque Florentiae, celeberrimas inter eruditos de ea re viguisse con­<lb></lb>troversias, quas non potuit ignorare Valerianus, qui circa eadem tempora <lb></lb>illis in regionibus degebat, et cum doctis illis conversabatur ” (ibi, pag. </s>

<s>31). </s></p><p type="main">

<s>Un altro non men celebre straniero insorse, dopo il Roberval a riven­<lb></lb>dicare al Torricelli quella esperienza, che volevasi poco onestamente appro­<lb></lb>priare il Magno, e fu Ottone di Guericke, il quale incomincia il cap. </s>

<s>XXXIV <lb></lb>del III Libro de&#039;suoi <emph type="italics"></emph>Experimenti magdeburgici<emph.end type="italics"></emph.end> con le parole seguenti: <lb></lb>“ Cum Ratisbonae in Comitiis Imperialibus inter alia Electoribus ac Prin­<lb></lb>cipibus quibusdam ut et Legatis, meorum quaedam Experimentorum exhi­<lb></lb>berem, et per hanc occasionem mihi cum admodum Rev. </s>

<s>Patre Capuccino <lb></lb>Domino Valeriano Magno, familiaritas intercederet; ille mihi exhibuit quod­<lb></lb>dam experimentum a se, uti dicebat, ad demonstrandum vacuum excogita-<pb xlink:href="020/01/468.jpg" pagenum="449"></pb>tum .... mihique communicabat Libellum suum cuius titulus <emph type="italics"></emph>Demonstratio <lb></lb>ocularis ecc.<emph.end type="italics"></emph.end> quamquam deinde tam ex ipso libello collegi, quam postea ex <lb></lb>aliis authoribus vidi, Experimentum hoc, primum a clarissimo viro Johanne <lb></lb>Torricello Magni Ducis Hetruriae Mathematico detectum fuisse ” (Amstelo­<lb></lb>dami, 1672, pag. </s>

<s>117, 18). </s></p><p type="main">

<s>Quel cervellaccio del padre Onorato Fabry che, sciabordando infatica­<lb></lb>bile nel fiume della scienza si credeva di aver chiappati tanti squisitissimi <lb></lb>pesci quanti tra le maglie della sua rete, rimanevan presi fuscelli infradi­<lb></lb>ciati e sterpi motosi; volle anch&#039;egli ingegnarsi di nobilitar la sua pesca <lb></lb>coll&#039;appropriarsi la nobilissima preda del Torricelli. </s>

<s>E perchè meglio gli riu­<lb></lb>scisse pensò, con sottile arte, di servirsi di un suo discepolo, Pietro Mou­<lb></lb>sner, a cui, in un&#039;Appendice <emph type="italics"></emph>De vacuo<emph.end type="italics"></emph.end> a un libro che stava per pubblicar <lb></lb>col titolo di <emph type="italics"></emph>Metaphisica Demonstrativa,<emph.end type="italics"></emph.end> fece scriver queste parole: “ Ante <lb></lb>aliquot annos luculento sane experimento, evinci omnino vacuum nonnulli <lb></lb>existimarunt. </s>

<s>De huius experimenti authore nihil dicam, cuius inventionem <lb></lb>non pauci quidem sibi vindicant Galli, Itali, Germani: unum scio iam sex <lb></lb>ab hinc annis a nostro Philosopho P. Hon. </s>

<s>Fabry propositum fuisse et expli­<lb></lb>catum nec nisi proxime sequenti anno ex Italia in Galliam, sub Torricelli <lb></lb>nomine migrasse; hoc demum praesenti anno a R. P. </s>

<s>Valeriano Magno <lb></lb>capuccino in Polonia edito super ea re parvo libello publicatum ” (Lug­<lb></lb>duni, 1648, pag. </s>

<s>570). </s></p><p type="main">

<s>A scoprire la sottil frode del padre Onorato e a rivendicar gli onori al <lb></lb>Torricelli e all&#039;Italia, sorse, chi il crederebbe, un altro padre gesuita, il te­<lb></lb>desco Gaspero Schott, il quale, dop&#039;aver riferite le sopra trascritte parole <lb></lb>del Mousnero, così nella sua <emph type="italics"></emph>Tecnica curiosa<emph.end type="italics"></emph.end> immediatamente soggiunge: <lb></lb>“ Scripsit haec Mousnerius anno 1647: ante sex annos, hoc est 1641, fuit <lb></lb>explicatum experimentum in Gallia a p. </s>

<s>Honorato Fabry: sequenti anno, hoc <lb></lb>est 1642, ex Italia migravit in Galliam. </s>

<s>Conciliet haec qui potest. </s>

<s>Si anno 1648 <lb></lb>ea scripsit citatus Mousnerius, migravit experimentum ex Italia in Galliam <lb></lb>anno 1643, adeoque anno praecedenti potuit a Torricello fuisse deprehen­<lb></lb>sum, quod consonat iis de quibus Dominus de Roberval scripsit ” (Norim­<lb></lb>bergae, 1664, pag. </s>

<s>167). </s></p><p type="main">

<s>Ma il padre Onorato stesso, trovatosi così scoperto di furto e con rara <lb></lb>generosità restituendo al padrone, vuol che restituiscano anche gli altri che <lb></lb>avevan rubato come lui. </s>

<s>Nel IV de&#039;suoi Dialoghi fisici infatti dop&#039;avere as­<lb></lb>serito per bocca di <emph type="italics"></emph>Antimo<emph.end type="italics"></emph.end> che del bellissimo e celeberrimo sperimento <emph type="italics"></emph>pri­<lb></lb>mus inventor fuit doctissimus Torricellius,<emph.end type="italics"></emph.end> fa insinuar dall&#039;interlocutore <lb></lb><emph type="italics"></emph>Crisocomo<emph.end type="italics"></emph.end> la notizia: “ Huius experimenti primum inventorem et aucto­<lb></lb>rem P. </s>

<s>Valerianum Magnum fuisse accepi ” a cui in nome dell&#039;Autore e in <lb></lb>conferma di ciò che Antimo avea detto di sopra, <emph type="italics"></emph>Agostino<emph.end type="italics"></emph.end> risponde: “ Nihil <lb></lb>profecto magis a veritate alienum: Torricellius haud dubie et citra omnem <lb></lb>controversiam primus inventor fuit ” (Lugd., 1665, pag. </s>

<s>182, 83). </s></p><p type="main">

<s>E perchè la storia degli atti e dei pensamenti umani ha sempre col <lb></lb>serio, assai più di quel che non pare o non si crede, mescolato il faceto, <pb xlink:href="020/01/469.jpg" pagenum="450"></pb>mentre francesi e gesuiti rassicurano la fama del Torricelli, ecco uno ze­<lb></lb>lantissimo italiano tornar dopo più di un secolo a trepidare al pericolo di <lb></lb>vederla spiumata da un Francese venuto di Moulinx a professare Filosofia <lb></lb>peripatetica nello Studio pisano. </s></p><p type="main">

<s>Giovanni Targioni, nel I Tomo delle sue <emph type="italics"></emph>Notizie,<emph.end type="italics"></emph.end> avendo riferito il do­<lb></lb>cumento di un&#039;osservazione barometrica fatta dal Borelli sul poggio di Ar­<lb></lb>timino, prosegue: “ L&#039;epoca di questa osservazione barometrica relativa a <lb></lb>quella del Pascal, parrebbe che, secondo il testo del Borelli, si dovesse fis­<lb></lb>sare intorno alll&#039;anno 1657: eppure ecco un indizio ch&#039;ella sia molto an­<lb></lb>teriore, e per lo meno del 1642, il che veramente mi rende perplesso, sa­<lb></lb>pendosi che il vacuo torricelliano fu messo in uso nel 1643, e che Biagio <lb></lb>Pascal solo nel 1646, ne fece uso per misurare le altezze dei monti. </s>

<s>Clau­<lb></lb>dio Berigardi (Beauregard) nella P. VI del suo Circolo Pisano pubblicato <lb></lb>colla data del 1° Gennaio 1643, cioè avanti a queste epoche dice: <emph type="italics"></emph>“ Com­<lb></lb>pertum est aquam vel aliud corpus liquidum, tanto magis premi, quanto <lb></lb>plus aeris ipsi incumbit. </s>

<s>Demonstratur in Tubo illo vitreo in cuius parte <lb></lb>superiori argentum vivum videtur relinquere spatium vacuum, ut iam <lb></lb>dictum est. </s>

<s>Nam in alta turri ubi minus est aeris incumbentis stagnanti <lb></lb>hydrargirio, in quo est tubus, plus relinquitur vaeui quam ad basim turris <lb></lb>vel montis, ubi altior aer magis premit hydrargirium eumque compellit <lb></lb>per tubum paulo altius efferri et sic relinquere minus vacui....<emph.end type="italics"></emph.end> Io non <lb></lb>pretendo qui di decidere dell&#039;anteriorità dell&#039;esperienza in pregiudizio della <lb></lb>gloria di Biagio Paschal, e lascerò giudicare ad altri se il medesimo Torri­<lb></lb>celli possa essere stato il primo a fare del Barometro l&#039;uso soprannotato, <lb></lb>appunto nei primi giorni della sua invenzione, e che subito ne avesse la <lb></lb>notizia il Berigardi, che era allora professore di Filosofia in Padova ” (Fi­<lb></lb>renze, 1780, pag. </s>

<s>207). </s></p><p type="main">

<s>Impacciato allo stesso modo si trovò l&#039;Antinori, che nelle <emph type="italics"></emph>Notizie sto­<lb></lb>riche<emph.end type="italics"></emph.end> premesse ai <emph type="italics"></emph>Saggi di Naturali esperienze<emph.end type="italics"></emph.end> (Firenze, 1841, pag. </s>

<s>29) <lb></lb>si assottiglia per veder pur di uscirne in qualche modo. </s>

<s>A ripensarvi però <lb></lb>sembra impossibile che due così valentuomini sieno affogati, come suol dirsi, <lb></lb>proprio in un bicchier d&#039;acqua. </s>

<s>Il Targioni stesso aveva già avvertito che <lb></lb>de&#039;<emph type="italics"></emph>Circoli Pisani<emph.end type="italics"></emph.end> furono fatte due edizioni: la prima in Udine dallo Schi­<lb></lb>ratti nel 1643 e la seconda in Padova dal Frambotti nel 1661. Ora, a risol­<lb></lb>vere il dubbio, che tenevalo in tanta pena, sarebbe bastato a lui e all&#039;An­<lb></lb>tinori collazionar insieme le due edizioni, per ritrovar che nella prima non <lb></lb>si fa alcuna menzione nè dell&#039;esperienza dell&#039;argento vivo, nè del variar del <lb></lb>livello di lui secondo le altezze, ma che l&#039;Autore aggiunse quelle notizie <lb></lb>nell&#039;edizione del 1661, diciotto anni dopo l&#039;esperienza del Torricelli, e tre­<lb></lb>dici anni dopo quella del Pascal, eseguita dal Perier sul Puy De-Domme. </s></p><p type="main">

<s>Se dunque così poco basta ad assicurar la fama del Torricelli, ella può <lb></lb>seguitare ancora a batter libere le ali. </s>

<s>Spettatore di così nobili trionfi, fu, <lb></lb>infino al 1666, quel Giovan Batista Baliani, a cui si dovrebbero per giusti­<lb></lb>zia i primi meriti, ma è credibile che egli voglia starsene e non uscir fuori <pb xlink:href="020/01/470.jpg" pagenum="451"></pb>a far col mondo le sue ragioni? </s>

<s>Il Mersenno è che gli dà la notizia della <lb></lb>celebre esperienza torricelliana, e il Baliani risponde a lui di Savona il dì <lb></lb>25 Novembre 1647 una lettera, nella quale così dice fra le molte altre cose <lb></lb>importanti: “ Ego iam abhinc pluribus annis, expertus aeris pondus, arbi­<lb></lb>tratus sum non repugnare dari vacuum. </s>

<s>” E perchè i gloriosi scientifici suc­<lb></lb>cessi fecero poi conoscere aì Baliani la grande importanza di quelle sue spe­<lb></lb>culazioni, fatte 36 anni avanti, volle nella Raccolta delle sue <emph type="italics"></emph>Opere diverse<emph.end type="italics"></emph.end><lb></lb>inserire anche la citata lettera al Mersenno, dopo la quale, in nota, così <lb></lb>soggiunge: “ Dictam epistolam ad Mersennum typis mandavi, cuius exem­<lb></lb>pla, dum essem Savonae Gubernator, misi pluribus amicis. </s>

<s>Et quoniam ex <lb></lb>eorum responsionibus patet me fuisse veracem ubi dixi me multis abhinc <lb></lb>annis amicis communicasse causam quod vacuum palam non esset, lubet <lb></lb>hic unam aut alteram ex dictis responsionibus apponere ” (Genova, Calen­<lb></lb>zani, 1666, pag. </s>

<s>281). E seguita a recar, come testimoniali, varie lettere di <lb></lb>amici, fra le quali una del gesuita Francesco Ghiringhello, e un&#039;altra di <lb></lb>Giacomo Filippo Durazzo. </s>

<s>Fa però gran maraviglia che egli, come testimo­<lb></lb>niali più autorevoli di tutte le altre, non rechi le lettere scritte e le rispo­<lb></lb>ste di Galileo, le quali sarebbero state bastanti a mostrar che in gran parte <lb></lb>era dovuta a lui quella gloria che tutto il mondo dispensava così largamente <lb></lb>a solo il Torricelli. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>A questo punto non possiamo non soffermare il passo, per fare alcune <lb></lb>considerazioni sopra le cose fin qui narrate. </s>

<s>Ci ha mosso a maraviglia il <lb></lb>vedere il Baliani mostrarsi così debole in difender le sue ragioni, quasi te­<lb></lb>messe di offender la gloria del Torricelli, ma che diremo a veder francesi <lb></lb>e gesuiti, i quali con invidiose rivalità si son quasi sempre studiati o di av­<lb></lb>vilire o di appropriarsi i meriti della scienza italiana, fosse pur ella affidata <lb></lb>ai più certi e pubblici documenti; che diremo ora di que&#039;francesi e di que&#039;ge­<lb></lb>suiti, a vederli con tanto zelo difender contro gli usurpatori la invenzione <lb></lb>di un italiano, la quale non s&#039;appoggia sopr&#039;altro documento, che sulla fama <lb></lb>volante, e sopra alcune inedite lettere familiari? </s></p><p type="main">

<s>Coloro che conoscon bene il Mersenno, in mano a cui pervennero quelle <lb></lb>lettere familiari, s&#039;aspetterebbero come cosa certa ch&#039;ei l&#039;avesse dovute bru­<lb></lb>ciare, e dar l&#039;esperienza dell&#039;argento vivo per cosa sua, com&#039;aveva date per <lb></lb>sue tante altre speculazioni dello stesso Torricelli: e nonostante ei, con rara <lb></lb>sincerità, confessa al pubblico che inventor della celebre esperienza è l&#039;il­<lb></lb>lustre Geometra italiano, <emph type="italics"></emph>qui Tubum observatorium mihi anno 1644 osten­<lb></lb>dit in Magni Ducis Etruriae pergulis admirandis. </s>

<s>De cuius observatione <lb></lb>nos etiam prius monuerat illius singularis amicus Michael Angelus Ric­<lb></lb>cius. </s>

<s>Romae .... cuius Epistola docebat ex tubo ....<emph.end type="italics"></emph.end> (Nov. </s>

<s>Observ., T. III, <pb xlink:href="020/01/471.jpg" pagenum="452"></pb>Parisiis 1647, pag. </s>

<s>216). E con generosità ben più rara divulgò l&#039;epistole <lb></lb>torricelliane, facendone prender copia ai principali scienziati di Francia. </s>

<s>“ Ha­<lb></lb>beo ego, scriveva il Roberval al Des Noyers, epistolam quam clariss. </s>

<s>Vir <lb></lb>Evang. </s>

<s>Torricellius Magni Ducis Hetruriae mathematicus misit Romam ad <lb></lb>amicum suum doctiss. </s>

<s>virum Angelum Ricci sub finem anni 1643 italice <lb></lb>scriptam, quae nihil aliud continet quam controversiam inter duos illos vi­<lb></lb>ros egregios, qui, quod et fere omnibus accidit, de tali experimento diverse <lb></lb>sentiebant. </s>

<s>Ea autem epistola cum quibusdam aliis ab ipso Ricci missa est <lb></lb>Parisios ad R. P. Mersennum, Ord. </s>

<s>Minim. </s>

<s>sub initium anni 1644 ” (Loc. </s>

<s><lb></lb>cit., pag. </s>

<s>31). </s></p><p type="main">

<s>Tanta sincerità e generosità del Mersenno, da qual che si voglia fonte <lb></lb>ella scaturisse nell&#039;animo di lui e nell&#039;ingegno, possiamo accettarla come <lb></lb>una riparazione dei danni e delle ingiurie che fece alla scienza italiana; ri­<lb></lb>parazione che cresce alquanto nella virtù espiatrice, se si ripensi che pel <lb></lb>ministero del Frate parigino si diffuse per la Francia, infin dal 1644, la copia <lb></lb>delle lettere torricelliane da nessuno o da pochissimi sapute in Italia. </s>

<s>Chi <lb></lb>può intender come mai il Ricci, così sollecito in divulgare i pensieri del <lb></lb>Torricelli fra gli stranieri, non si curasse poi di farli conoscere a&#039;suoi, i quali <lb></lb>forse ignorerebbero ancora quel che l&#039;Autor dell&#039;esperienza dell&#039;argento vivo <lb></lb>ne scrisse in proposito, se il Borelli, ritrovandosi a Roma, non avesse fatto <lb></lb>richiesta dell&#039;Epistola torricelliana <emph type="italics"></emph>ad Clarissimum Michaelem Angelum <lb></lb>Riccium missa, quam humanissime mihi communicavit anno 1658, eam­<lb></lb>que Florentiae postea serenissimo principi Leopoldo tradidi et inter ami­<lb></lb>cos evulgavi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Queste parole il Borelli le scriveva a pag. </s>

<s>228 del Trattato <emph type="italics"></emph>De motion. </s>

<s><lb></lb>natur.<emph.end type="italics"></emph.end> stampato, come si sa, nel 1670, ma in una Lettera familiare, diretta <lb></lb>da Roma il dì 3 d&#039;Agosto 1658 al principe Leopoldo, dop&#039;aver fatto cenno <lb></lb>di quella e di altre lettere del Torricelli al Ricci, il Borelli stesso così sog­<lb></lb>giungeva: “ Alla mia venuta recherò la copia di tutte queste lettere scien­<lb></lb>tifiche del Torricelli per farle stampare, acciocchè non venga l&#039;umore a qual­<lb></lb>che francese di pretendere anteriorità, come già mi par che ve ne sia alcuno, <lb></lb>sopra questo gran concetto della compressione dell&#039;aria, cagione potissima <lb></lb>ed indubitabile del&#039;sollevamento dell&#039;arg. </s>

<s>v. </s>

<s>nel cannello ” (MSS. Cim., <lb></lb>T. XVI, c. </s>

<s>103). </s></p><p type="main">

<s>I fatti però fin qui esposti dimostrano che le sollecitudini del Borelli <lb></lb>e i timori non eran giustificati, perchè anzi i francesi ci hanno data occa­<lb></lb>sion di ammirare la loro sincerità e generosità in riconoscere e in attribuire <lb></lb>al Torricelli il gran concetto della compression dell&#039;aria, cagione potissima <lb></lb>e indubitabile del sollevamento dell&#039;argento vivo nel cannello. </s>

<s>Fosse per que­<lb></lb>sto o per altri motivi è un fatto che tutt&#039;altro che mostrarsi solleciti e pre­<lb></lb>murosi i Fiorentini di fare stampar le Lettere torricelliane, indugiarono infino <lb></lb>al 1663, quando Carlo Dati le inserì nella pubblicazione della <emph type="italics"></emph>Lettera di <lb></lb>Timauro Anziate ai Filaleti.<emph.end type="italics"></emph.end></s></p><p type="main">

<s><gap></gap><pb xlink:href="020/01/472.jpg" pagenum="453"></pb>del dì 11, e l&#039;altra del dì 28 Giugno 1664. Questa seconda fu provocata da <lb></lb>una del Ricci, nella quale promoveva alcune difficoltà contro il concetto della <lb></lb>compressione dell&#039;aria; lettera che il Dati ivi pure pubblicò e di cui dee <lb></lb>aver preso copia il Borelli. </s>

<s>Non par però, ciò che più importa, che pren­<lb></lb>desse copia o che gli fosse mostrata dal Ricci un&#039;altra delle Lettere torri­<lb></lb>celliane, che esso Ricci deve aver mandata colle due sopra citate a Parigi. </s>

<s><lb></lb>Di questa terza Lettera, in cui, per ispiegar la compressione dell&#039;aria sulla <lb></lb>superficie del mercurio nella scodella chiusa, ricorre il Torricellì all&#039;esem­<lb></lb>pio de&#039;flussi dell&#039;acqua; il Mersenno fa menzione nel T. III delle sue <emph type="italics"></emph>Nuove <lb></lb>Osservazioni<emph.end type="italics"></emph.end> dove così dice: “ Si intelligatur cylindrus aqueus vel aereus <lb></lb>inferior pedalis a superiore ita separari atque dividi, ut sit eiusdem roboris <lb></lb>et resistentiae, quibus superiori coniunctus pollebat, peracque contranitatur <lb></lb>cylindro mercuriali, eodem modo quo cylindrus a reliquo cylindro aqueo <lb></lb>15 v. </s>

<s>g. </s>

<s>pedum, per lumen aliquod fluens, tantumdem aquae tribueret, quan­<lb></lb>tum cylindrus integer 16 pedum, si fingatur ille cylindrus pedalis in ea sem­<lb></lb>per manere pressione, quam a 15 pedibus prementibus acquisierat: quam <lb></lb>fuisse clarissimi Torricelli sententiam ex Litteris Excellentissimi Riccii anno, <lb></lb>si bene memini 1644, didici ” (Parisiis 1647, Praefatio innum). </s></p><p type="main">

<s>Noi argomentiamo che la lettera commemorata qui dal Mersenno, ap­<lb></lb>pelli a una terza dopo le due pubblicate dal Dati, e come un seguito di <lb></lb>quella del dì 28 Giugno, nella quale, a spiegare il medesimo concetto, in­<lb></lb>vece dell&#039;esempio scientifico della pressione dell&#039;acqua, il Torricelli adduce <lb></lb>quello volgare della lana compressa. </s></p><p type="main">

<s>Del resto, nemmeno aggiunta questa terza alle altre due prime Lettere <lb></lb>torricelliane, s&#039;ha compiuta la rappresentanza del Dramma, a cui manca <lb></lb>l&#039;introduzione. </s>

<s>Quella del dì 11 Giugno, nella quale entra il Torricelli in <lb></lb>argomento, scrivendo al Ricci: <emph type="italics"></emph>Le accennai già che si stava facendo non <lb></lb>so che esperienza filosofica intorno al vacuo,<emph.end type="italics"></emph.end> richiama altre lettere prece­<lb></lb>denti, le quali non pervennero in mano nè al Mersenno nè al Borelli. </s>

<s>Il <lb></lb>soggiunger poi che l&#039;esperienza filosofica intorno al vacuo non era <emph type="italics"></emph>per far <lb></lb>semplicemente il vacuo,<emph.end type="italics"></emph.end> fa argomentar che il soggetto preso a trattare dal <lb></lb>Torricelli, in quella sua prima citata lettera al Ricci, non era nuovo. </s>

<s>Così <lb></lb>infatti argomentava anche il Roberval, che al Des-Noyers, scriveva: “ Sed <lb></lb>in eadem epistola ex discursu apparet minime novum tunc fuisse illis expe­<lb></lb>rimentum cum multoties repetitum ” (Loc. </s>

<s>cit., pag. </s>

<s>31). </s></p><p type="main">

<s>Come e quando fosse stato fatto, prima di quel discorso torricelliano, <lb></lb>l&#039;esperimento, era ciò che vivamente frugava la curiosità nel Mersenno: <lb></lb>“ In cuius vero mentem prius illa vacui cogitatio venerit, et quis prior <lb></lb>animadverterit collum tubi sive lagenam in extremo habentis, sive solitarium <lb></lb>et in cylindri modum conformati, scire fortassis incundum fuerit. </s>

<s>Chymici <lb></lb>cuiusdam fortuitum inventum nonnulli dicent: alii referent ad acutissimi <lb></lb>philosophi meditationem, qualis philosophorum princeps Galilaeus et amici <lb></lb>Magiottus et Nardius, quos si nos docuerit incomparabilis Torricellius, gra­<lb></lb>tissimum erit ” (Nov. </s>

<s>ob. </s>

<s>servat., T. III, Parisiis 1647, pag. </s>

<s>217). </s></p><pb xlink:href="020/01/473.jpg" pagenum="454"></pb><p type="main">

<s>Gratissimo sarebbe stato, non a solo il Mersenno, ma alla Storia della <lb></lb>scienza italiana, che il Torricelli si fosse più chiaramente aperto intorno a <lb></lb>ciò che dette occasione alla celebre esperienza: egli avrebbe altresì provve­<lb></lb>duto meglio a glorificare il suo nome, se men sollecito della fabbrica de&#039;Ca­<lb></lb>nocchiali, avesse atteso con più costanza alla costruzion del Barometro, e a <lb></lb>coltivar la fisica sperimentale, da lui stesso così efficacemente iniziata. </s>

<s>Ma <lb></lb>egli non previde la gran fiamma, che sarebbe secondata alla sua scintilla; <lb></lb>la troppo sollecita morte gli impedì perfino di vederne gli albori, e dall&#039;al­<lb></lb>tra parte l&#039;ossequio cortigiano lo consigliava a contentarsi della Geometria, <lb></lb>per fare omaggio delle scoperte sue fisiche al Granduca. </s></p><p type="main">

<s>Avrebbero nonostante potuto supplire in dar sodisfazione alla storia gli <lb></lb>amici, che ragionevolmente si può credere dover essere informati de&#039;fatti. </s>

<s><lb></lb>Ma il Nardi, a quel che par dalle sue <emph type="italics"></emph>Scene Accademiche,<emph.end type="italics"></emph.end> non sa nemmeno <lb></lb>che il Torricelli abbia fatto la grande esperienza; il Magiotti, morto nel 1656 <lb></lb>di peste, non ne lasciò che qualche ricordo in alcune cartucce sparse, e il <lb></lb>Ricci, com&#039;abbiamo veduto, sollecito di diffonder le Lettere torricelliane in <lb></lb>Francia, le tenne chiuse, infino al 1658, agli scienziati d&#039;Italia. </s>

<s>Nonostante <lb></lb>egli, indirettamente tramandava alla storia una notizia importante, per mezzo <lb></lb>di quel Tommaso Cornelio, che ebbe lo stesso Ricci a maestro, e a cui de­<lb></lb>dicando un suo <emph type="italics"></emph>Proginnasma<emph.end type="italics"></emph.end> così scriveva: “ Tu enim unus omnium, iam <lb></lb>inde ab adolescentia, mihi amicissimus, studiorum meorum adiutor author­<lb></lb>que fuisti ” (Neapoli, 1688, pag. </s>

<s>263). </s></p><p type="main">

<s>Il Cornelio, mentre con tuba sonora si diffondeva per tutta Europa la <lb></lb>notizia dell&#039;Esperienza torricelliana, fu il primo e l&#039;unico che ne scrivesse <lb></lb>in Italia in quella sua Epistola <emph type="italics"></emph>De Circumpulsione platonica,<emph.end type="italics"></emph.end> data i primi di <lb></lb>Giugno del 1648. La notizia importante che si diceva, e ch&#039;egli ivi dà, è <lb></lb>che l&#039;esperienza del Berti fu che dette occasione a quella del Torricelli: <lb></lb>“ Gaspar Bertius mathematicarum artium in-Academia romana professor <lb></lb>plumbeum tubum longitudine viginti ulnarum erexit, apicique inseruit vi­<lb></lb>tream sphaeram, ut animadverteret aquam supra ulnas decem et octo as­<lb></lb>surgentem in subiectum vas continenter defluere. </s>

<s>Tandem vero Evangelista <lb></lb>Torricellius, ut praegrandis machinae laboriosam structuram vitaret, coepit <lb></lb>periculum in argento vivo facere ” (ibi, pag. </s>

<s>297, 98) </s></p><p type="main">

<s>Una tal notizia, se gli fosse giunta alle orecchie un anno prima, avrebbe <lb></lb>forse potuto appagar la curiosità nel Mersenno, ma pur le Lettere del Tor­<lb></lb>ricelli mettevano in desiderio di saperne qualche altra cosa di più; deside­<lb></lb>rio a soddisfare al quale, meglio de&#039;commemorati di sopra, pareva atto il <lb></lb>Viviani. </s>

<s>Eppure è cosa singolare che non se ne trovi fatto il minimo cenno <lb></lb>ne&#039;suoi manoscritti, pieni di tante altre minute notizie meno importanti. </s>

<s>Egli <lb></lb>dee, senza dubbio, aver riveduta la <emph type="italics"></emph>Lettera a&#039;Filaleti,<emph.end type="italics"></emph.end> e dee esser vero quel <lb></lb>che il Dati ivi scrive di lui, che cioè conferitogli il suo pensiero dal Tor­<lb></lb>ricelli, egli <emph type="italics"></emph>ansioso di vedere questa operazione fece di presente fabbricar <lb></lb>lo strumento, e procurando l&#039;argento vivo fu il primo a fare così nobile <lb></lb>csperienza:<emph.end type="italics"></emph.end> vero dee esser quel che il Dati appresso soggiunge, che cioè <pb xlink:href="020/01/474.jpg" pagenum="455"></pb>tosto il Viviani ragguagliò del seguìto il Torricelli, <emph type="italics"></emph>recandogli straordinario <lb></lb>contento, attesochè si confermò nell&#039;opinione conceputa che la ponderosità <lb></lb>dell&#039;aria, equilibrandosi con l&#039;acqua, e con l&#039;argento vivo, per la diver­<lb></lb>sità del peso, sostenesse quelli ad altezze diverse.<emph.end type="italics"></emph.end> (Firenze, 1663, pag. </s>

<s>20). </s></p><p type="main">

<s>Da questa notizia però in fuori il Dati non racconta nulla di nuovo, che <lb></lb>non fosse stato scritto alquanti anni prima dal Roberval, o contemporanea­<lb></lb>mente dall&#039;Autor della Prefazione al <emph type="italics"></emph>Traitez de l&#039;equilibre des liqueurs,<emph.end type="italics"></emph.end> il <lb></lb>quale, con impropria e imperfetta notizia storica, riconosce come inspiratore <lb></lb>immediato dell&#039;Esperienza torricelliana Galileo, che <emph type="italics"></emph>est celuy qui a remar­<lb></lb>qué le primier que les pompes aspirantes ne pouvioent élever l&#039;eau plus <lb></lb>haut que 32 ou 33 pièds:<emph.end type="italics"></emph.end> parole che sembrano esser una fedel traduzione <lb></lb>di quelle del Dati: “ Considerando il Torricelli quanto scrive il Galileo nel <lb></lb>primo Dialogo della Resistenza de&#039;corpi solidi che l&#039;acqua nelle trombe che <lb></lb>operano per attrazione non s&#039;alza oltre a 18 braccia in circa.... ” (ivi). </s></p><p type="main">

<s>Più copiose notizie storiche intorno all&#039;importante soggetto ne dava, <lb></lb>l&#039;anno dopo il 1663, lo Schott nella sua <emph type="italics"></emph>Tecnica curiosa,<emph.end type="italics"></emph.end> ma lo stesso ti­<lb></lb>tolo posto in fronte al § III del III Libro <emph type="italics"></emph>Experimenti in Italia exhibiti <lb></lb>historia ex P. </s>

<s>Athanasio Kirchero et p. </s>

<s>Nicolao Zucchio,<emph.end type="italics"></emph.end> pone in sospetto <lb></lb>della sincerità della sorgente, a cui furono attinte quelle notizie. </s>

<s>Lo Sturm, <lb></lb>nella III Appendice al <emph type="italics"></emph>Collegium experimentale sive curiosum,<emph.end type="italics"></emph.end> Appendice <lb></lb>che s&#039;intitola <emph type="italics"></emph>Baroscopii Auctor Torricellus et tota historia,<emph.end type="italics"></emph.end> è diligente rac­<lb></lb>coglitor di notizie, e il più compiuto storico della Esperienza torricelliana, <lb></lb>che, infino al 1676, ne abbia scritto, ma pur lascia ancora molto a deside­<lb></lb>rare. </s>

<s>Se a sodisfare a questi desiderii siam per riuscir noi, non isperiamo, <lb></lb>ma pure ci proveremo, studiandoci di prender di mira alle nostre indagini <lb></lb>i documenti, e di li e per lì condurre la nostra storia, a imitazion del Geo­<lb></lb>metra che, ricongiungendo alcuni punti dati, disegna a mano una curva, <lb></lb>quando non può andantemente descriverla o col girare del raggio o appog­<lb></lb>giato alla riga. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Benchè il fine principale, per cui il principe Leopoldo de&#039;Medici chiamò <lb></lb>a Firenze il Torricelli, fosse quello di aiutar Galileo, vecchio e infermo, a <lb></lb>distendere le sue speculazioni intorno alla forza della percossa, nonostante <lb></lb>è certo che, nel breve soggiorno di Arcetri, lo stesso Torricelli non in altro <lb></lb>fu adoperato dall&#039;illustre ospite suo, che in riordinare i Dialoghi delle Due <lb></lb>Nuove Scienze. </s>

<s>Discutevano insieme, in que&#039;solitarii colloqui, le dottrine in­<lb></lb>torno il vacuo esposte nel Dialogo I, e Galileo, perseverando nel credere che <lb></lb>la ragione per cui l&#039;acqua nelle trombe non sale più su che alle diciotto <lb></lb>braccia, fosse quella speculata da lui, rivelava al tempo stesso al giovane <lb></lb>alunno, mostrandogli le lettere scritte da Genova, le speculazioni che molto <lb></lb><gap></gap> faceva il Baliani. </s></p><pb xlink:href="020/01/475.jpg" pagenum="456"></pb><p type="main">

<s>Qualunque fosse il giudizio, che apertamente allora fece delle dottrine <lb></lb>del Fisico genovese al cospetto di Galileo, il Torricelli sentì da quelle lettere <lb></lb>venire un&#039;aura di verità a fecondargli mirabilmente l&#039;ingegno. </s>

<s>Il Baliani, <lb></lb>soggiogato dall&#039;autorità di Galileo, che era uscito in pubblico a professare <lb></lb>dottrine diverse, e travolto dalla comune opinione, secondo la quale si di­<lb></lb>ceva non potersi dare il vacuo se non con grandissima difficoltà e violenza, <lb></lb>aveva oramai abbandonate le sue speculazioni, lusingato che il peso di quel­<lb></lb>l&#039;acqua rimasta sospesa nel tubo di rame non potess&#039;esser forza sufficiente <lb></lb>a contrastare col peso di tutta l&#039;altezza dell&#039;aria. </s>

<s>Ma il Torricelli non si la­<lb></lb>scia trasportar dalla corrente delle opinioni: sente l&#039;autorità di Galileo, ma <lb></lb>più potentemente quella del vero, e ritenuto collo stesso Galileo che il peso <lb></lb>dell&#039;aria sia una quattrocentesima parte del peso dell&#039;acqua, e che l&#039;aria <lb></lb>vaporosa e visibile, come dimostrano gli Autori de&#039;crepuscoli, si alzi sopra <lb></lb>di noi intorno a cinquanta o cinquantaquattro miglia, trova calcolando, che <lb></lb>la pressione di tanta altezza d&#039;aria, se può parer alquanto soverchia, non è <lb></lb>però di troppo sproporzionata al peso contrastante di una colonna d&#039;acqua <lb></lb>alta diciotto braccia. </s>

<s>Quando perciò il Magiotti gli riferì l&#039;esperienza fatta <lb></lb>in Roma da Gaspero Berti, il Torricelli non dubitò di applicare, a spiegare <lb></lb>il fatto spettacoloso, le ragioni del Baliani, che ogni giorno più veniva tanto <lb></lb>facendo sue, da non accorgersi che erano state prima di altri. </s>

<s>Così, per <lb></lb>esempio, quando nella Lettera del dì 11 Giugno scriveva al Ricci: <emph type="italics"></emph>Noi siamo <lb></lb>sommersi nel fondo d&#039;un pelago d&#039;aria elementare, la quale per espe­<lb></lb>rienza indubitata si sa che pesa,<emph.end type="italics"></emph.end> non si sarà accorto ch&#039;ei si serviva delle <lb></lb>medesimi immagini e delle medesime espressioni, di che s&#039;era servito lo <lb></lb>scrittor delle Lettere dirette a Galileo da Genova, quattordici anni prima. </s></p><p type="main">

<s>Quelle però che nel Baliani erano vacillanti speculazioni, nel Torricelli <lb></lb>si ridussero a dottrine certe, dimostrate dall&#039;esperienza, le quali furono nel <lb></lb>sagace ingegno feconde di nuove scoperte. </s>

<s>Di tali scoperte notabilissima è <lb></lb>quella del variar l&#039;aria la sua pressione sui corpi sottoposti da un giorno <lb></lb>a un altro, e talvolta altresì da un&#039;ora a un&#039;altra. </s>

<s>Come il Torricelli riu­<lb></lb>scisse a fare un&#039;osservazione tanto nuova e tanto importante, è nostro prin­<lb></lb>cipal debito investigare, appuntandosi qui i desiderii di tutti coloro, che <lb></lb>amano di sapere i principii, rimasti fin qui occulti, dell&#039;invenzion del Ba­<lb></lb>rometro. </s></p><p type="main">

<s>Quel che Galileo scrive nel I Dialogo delle Nuove Scienze della palla <lb></lb>di cera, che ora galleggia, ora affonda nell&#039;acqua, non solamente coll&#039;ingra­<lb></lb>vir l&#039;acqua stessa colla mistione di qualche materia più grave di lei, ma <lb></lb>col riscaldarla o col raffreddarla (Alb. </s>

<s>XIII, 72), dette occasione al Torri­<lb></lb>celli d&#039;inventar quel Termometro, che fu in quinto luogo descritto dagli Ac­<lb></lb>cademici del Cimento fra gli strumenti, da conoscer le alterazioni dell&#039;aria <lb></lb>derivanti dal caldo e dal freddo. (Saggi Nat. </s>

<s>esp., Firenze 1841, pag. </s>

<s>16). <lb></lb>E perchè di tali esperienze, fatte con palline di vetro o di rame sottile in <lb></lb>parte piene d&#039;acqua e in parte di aria, che ora spontaneamente scendevano <lb></lb><gap></gap><pb xlink:href="020/01/476.jpg" pagenum="457"></pb>celli le modificò in varie guise, studiandosi di rendere agli occhi del So­<lb></lb>vrano lo spettacolo più giocondo coll&#039;invenzione dello strumento, che ne&#039;Re­<lb></lb>gistri appartenenti al primo periodo della Sperimentale Accademia medicea <lb></lb>si trova così descritto: “ Fatto un vaso di vetro cilindrico con la bocca stretta <lb></lb>e pieno d&#039;acqua fin vicino alla bocca, dentro si metta una palla di rame <lb></lb>sottile, che abbia un piccolo buco: con un dito andando turando più o meno <lb></lb>la bocca del vaso, la palla anderà salendo e scendendo ” (Targioni, Notiz. </s>

<s><lb></lb>Aggrand. </s>

<s>ed. </s>

<s>cit., T. I, pag. </s>

<s>155). La notizia di questo strumento e la de­<lb></lb>scrizione di que&#039;giochetti termostatici l&#039;apprese un de&#039;primi il Moncony, il <lb></lb>quale viaggiando per la prima volta in Italia, e passando per Firenze, andò <lb></lb>la mattina del dì 6 di Novembre 1646 a far visita al Torricelli, <emph type="italics"></emph>qui me dit,<emph.end type="italics"></emph.end><lb></lb>scrive nella <emph type="italics"></emph>Premiere Partie<emph.end type="italics"></emph.end> de&#039;suoi <emph type="italics"></emph>Voyages, que le Gran Due avoit di­<lb></lb>vers Thermometres pour connoître le chaud et le froid.... Il m&#039;en dit <lb></lb>une autre d&#039;une boule pleine d&#039;air à moitié, et la moitié d&#039;eau, avec un <lb></lb>trou en bas, et empêchée de monter en haut par une chaîne de verre: <lb></lb>quand l&#039;air se condense il y entre plus d&#039;eau, et ainsi la chaîne s&#039;accour­<lb></lb>cit, et la bouteille décend; quand au contraire l&#039;air se rarefie, l&#039;eau sort, <lb></lb>la bouteille monte et la chaîne est plus longue.<emph.end type="italics"></emph.end> (Paris, Delaulne 1695, <lb></lb>pag. </s>

<s>261). </s></p><p type="main">

<s>La ragione però del muoversi così le palline di vetro accomodate den­<lb></lb>tro i boccioli, il Torricelli o la confidò al Moncony in segretezza o si fidò <lb></lb>di lui che, essendo straniero e di passaggio, non l&#039;avrebbe divulgata in Fi­<lb></lb>renze, perchè il Granduca voleva non solamente far credere che fosse sua <lb></lb>l&#039;invenzione, ma che egli solo ne sapesse il mistero. </s></p><p type="main">

<s>Mosso da questa sua ambizione, appena morto il Torricelli il Granduca <lb></lb>stesso incominciò, in quegli scientifici consessi, che distinguono il secondo <lb></lb>periodo della sperimentale Accademia medicea, a dar lo spettacolo de&#039;suoi <lb></lb>giuochetti termostatici, proponendo ai convocati che ne indovinessero le ra­<lb></lb>gioni. </s>

<s>Il Viviani che, fra gli stessi convocati teneva le prime parti, fa men­<lb></lb>zione di ciò in una sua nota: “ Dopo scritto, mi è sovvenuto un modo di <lb></lb>risolvere un altro problema, che neì medesimo Congresso d&#039;ieri fu messo <lb></lb>in campo, ed è come si possa far due corpi, come due pescetti di vetro, <lb></lb>che stando nell&#039;istesso tempo uno di loro a galla in un&#039;acqua, e l&#039;altro in <lb></lb>fondo nella medesima, ad un&#039;istessa mutazione che si faccia nell&#039;acqua di <lb></lb>più calore, quello che è galleggiante se ne vadi in fondo, e nell&#039;istesso mo­<lb></lb>mento quello che è in fondo ne venga a galla; e tornando a raffreddar <lb></lb>l&#039;acqua, quello di fondo torni a galla e l&#039;altro ne vadi in fondo, onde la <lb></lb>medesima causa, nel medesimo tempo, partorisca contrarii modi ” (MSS. <lb></lb>Cim., T. X, c. </s>

<s>102). </s></p><p type="main">

<s>Non contento il Granduca di tentare i suoi di Firenze, volle proporre <lb></lb>il curioso problema ai principali Fisici d&#039;Italia, fra&#039;quali Bartolommeo Im­<lb></lb>periali e Raffaello Magiotti. </s>

<s>L&#039;Imperiali, con lettera di Genova del 1649 a <lb></lb>cui manca il mese e il giorno, rispondeva così all&#039;invito: “ Sono in obbligo <lb></lb><gap></gap><pb xlink:href="020/01/477.jpg" pagenum="458"></pb>sua grandezza, e complire alla mia parola di accennare qualche cosa intorno <lb></lb>agli effetti che si veggono e si osservano, non senza maraviglia, degli stru­<lb></lb>menti, de&#039;quali V. A. si degnò di farmi grazia. </s>

<s>Per quanto abbia, per così <lb></lb>dire, chiamato a consiglio le deboli forze del mio intelletto, nel rintracciar <lb></lb>le cagioni de&#039;buccioli di vetro, entro li quali sono le ballottine di cristallo; <lb></lb>non trovo che ciò possa dipendere che entro sono vacui gli stessi ballottini, <lb></lb>onde, col premersi l&#039;aria e acqua di sopra, premesi pur anco tutta l&#039;acqua ” <lb></lb>(ivi, T. XXI, c. </s>

<s>12). </s></p><p type="main">

<s>Il Magiotti aveva allo stesso modo, ma più completamente dell&#039;Impe­<lb></lb>riali, risoluto il Problema termostatico <emph type="italics"></emph>inviato da Fiorenza,<emph.end type="italics"></emph.end> di che rendeva <lb></lb>conto, non direttamente al Granduca, ma al principe Don Lorenzo, in una <lb></lb>breve Scrittura data da Roma lì 26 di Luglio 1648, col titolo di <emph type="italics"></emph>Renitenza <lb></lb>certissima dell&#039;acqua alla compressione.<emph.end type="italics"></emph.end> In essa, rispetto all&#039;esperienza che <lb></lb>più fa al proposito nostro, e alla quale pure appellavan le parole sopra tra­<lb></lb>scritte dell&#039;Imperiali, il Magiotti scriveva: “ Aggiungo che questi scherzi <lb></lb>son più sicuri in un cilindro pien d&#039;acqua, perchè quel serrarlo ed impri­<lb></lb>mervi leggermente la mano o dito grosso, basta e n&#039;avanza per forzar quel <lb></lb>poco d&#039;aria che sta dentro alle caraffine ” (Targioni, Notizie ecc. </s>

<s>ediz. </s>

<s>cit., <lb></lb>T. II, pag. </s>

<s>188). </s></p><p type="main">

<s>Or essendo un fatto che questa esperienza del danzar le palline o le <lb></lb>caraffine dentro l&#039;acqua de&#039;boccioli, premutane colla mano o col dito grosso <lb></lb>l&#039;aria sovrastante alla bocca, fu fatta già dal Torricelli, e fu proposta a spie­<lb></lb>gar dal Granduca, fra gli altri all&#039;Imperiali e al Magiotti; giova investigare <lb></lb>a quali occasioni e come il Torricelli stesso sapesse tanto trovar di serio <lb></lb>in ciò che, per il Sovrano e per chi lo secondava, non avea che l&#039;apparenza <lb></lb>di uno scherzo. </s></p><p type="main">

<s>Tenendo preparati que&#039;boccioli pieni d&#039;acqua, dentro alla quale stavano <lb></lb>immerse le palline di vetro, congiunte con que&#039;tubetti descritti al Moncony, <lb></lb>tubi che la fantasia del Magiotti seppe trasformar nel dorso traforato delle <lb></lb>sue figurine danzanti, e poi il Cartesio nelle code de&#039;suoi <emph type="italics"></emph>Diavoli;<emph.end type="italics"></emph.end> il Tor­<lb></lb>ricelli si accorse di un fatto singolare, che cioè quelle palline di vetro tal­<lb></lb>volta spontaneamente salivano o si abbassavano per l&#039;acqua, anco quando <lb></lb>il Termometro mostrava rimaner costante la temperatura. </s>

<s>— Che può esser <lb></lb>ragione di ciò? </s>

<s>— si domandava l&#039;arguto osservatore. </s>

<s>E tutto allora dietro <lb></lb>a ripensare e a calcolar gli effetti della pressione dell&#039;aria, gli venne il so­<lb></lb>spetto che il moto delle palline immerse, il quale non poteva dipendere dal <lb></lb>costiparsi e dilatarsi dell&#039;aria rinchiusa dentro alle stesse palline per variar <lb></lb>del freddo e del caldo, dipendesse invece dal variar la pressione dell&#039;aria <lb></lb>soprincombente alla superficie dell&#039;acqua. </s>

<s>Per assicurarsene, cominciò a pre­<lb></lb>mere e a rilassar colla palma della mano l&#039;aria alla bocca del bocciolo, e <lb></lb>trovò che premendo le palline affondavan di più, e rilassando tornavano <lb></lb>a galla. </s></p><p type="main">

<s>Fatto omaggio al Granduca di ciò che di dilettevole e di giocoso con­<lb></lb><gap></gap><pb xlink:href="020/01/478.jpg" pagenum="459"></pb>scoperta che ne avea ricavata, aggiungendo al fatto noto, e per altre vie <lb></lb>dimostrato, del premer che fa l&#039;aria con tutto il peso della sua altezza i <lb></lb>corpi sottoposti, l&#039;altro fatto nuovo della variabilità, a cui la forza di quel <lb></lb>torchio soggiace da un giorno all&#039;altro. </s></p><p type="main">

<s>Or erano rivolti tutti i pensieri del Torricelli a costruire uno strumento, <lb></lb>che desse indizio certo e segnasse allo stesso tempo la precisa misura di <lb></lb>quelle variazioni. </s>

<s>Poteva esser fondamento alla nuova invenzione quello stesso <lb></lb>bocciolo pien d&#039;acqua dentrovi immersa una pallina, alla quale, applicato un <lb></lb>filo metallico digradato, come in quei <emph type="italics"></emph>Termostatici<emph.end type="italics"></emph.end> descritti nelle proposi­<lb></lb>zioni CXVIII e CXIX <emph type="italics"></emph>De motionibus naturalibus<emph.end type="italics"></emph.end> dal Borelli, dal sollevarsi <lb></lb>e abbassarsi lo stesso filo sulla superficie dell&#039;acqua ne facesse argomentare <lb></lb>il premere or più grave, or più leggiero dell&#039;aria. </s>

<s>Ma il Torricelli rivolse <lb></lb>piuttosto il pensiero all&#039;esperienza del Berti, in cui il variar di livello l&#039;acqua <lb></lb>nel tubo indicherebbe il giusto variar della misura cercata. </s>

<s>Però quel tubo, <lb></lb>dovend&#039;essere più lungo delle diciotto braccia, non poteva tirarsi facilmente <lb></lb>di vetro, che ne facesse all&#039;occhio dell&#039;osservatore trasparir le variazioni di <lb></lb>livello, e dall&#039;altra parte quella era troppo gran macchina da non prestarsi <lb></lb>alle comodità di uno strumento osservatorio. </s></p><p type="main">

<s>Allora, s&#039;avvide il Torricelli che il grandioso e incomodo macchina­<lb></lb>mento dipendeva dall&#039;aver l&#039;acqua troppo piccola gravità specifica, da far <lb></lb>contrasto coll&#039;aria: che se invece si fosse adoperato un liquido più grave, <lb></lb>forse potevasi ridurre il tubo a tal lunghezza da maneggiarlo con facilità, e <lb></lb>da farlo anco di vetro. </s>

<s>Gli venne in mente il mercurio, al quale, essendo <lb></lb>egli 13 volte e mezzo in circa più grave dell&#039;acqua, poteva esser d&#039;avanzo <lb></lb>una canna di vetro lunga due braccia. </s>

<s>Una tal canna era facil cosa empirla <lb></lb>e capovolgerla nel mercurio, facendo il dito, a turarne e sturarne la bocca, <lb></lb>ciò che si faceva nel tubo del Berti col laborioso epistomio. </s>

<s>Conferito il pen­<lb></lb>siero col Viviani, come il Dati racconta, il giorno dopo la piccola macchi­<lb></lb>netta Torricelliana in Firenze mostrava l&#039;esperienza del vacuo, come l&#039;aveva <lb></lb>alquanti anni prima mostrata in Roma la grande e faticosa macchina Bertiana. </s></p><p type="main">

<s>Da questo punto dunque, dal punto cioè in cui il Torricelli pensò di co­<lb></lb>struire uno strumento che misurasse le variazioni dell&#039;aria, sostituendo nel <lb></lb>tubo e nell&#039;apparecchio del Berti il mercurio all&#039;acqua, taciuti i precedenti, <lb></lb>incomincia la storia del celebre fatto narrata dal Torricelli stesso al Ricci <lb></lb>nella sua prima Lettera del dì 11 Giugno 1644. “ Le accennai già che si <lb></lb>stava facendo non so che esperienza filosofica intorno al vacuo, non per far <lb></lb>semplicemente il vacuo, ma per fare uno strumento che mostrasse le mu­<lb></lb>tazioni dell&#039;aria ora più grave e grossa, ora più leggera e sottile. </s>

<s>Molti hanno <lb></lb>detto che non si dia, altri che si dia, ma con repugnanza della Natura e <lb></lb>con fatica: non so già che alcuno abbia detto che si dia senza fatica e senza <lb></lb>resistenza della Natura ” (Lett. </s>

<s>a&#039;Filaleti, Firenze 1663, pag. </s>

<s>20). E che <lb></lb>appunto il vuoto si dia, senza fatica e senza resistenza della Natura, passa <lb></lb>a dimostrarlo coll&#039;esperienza dell&#039;argento vivo da lui descritta in un breve <lb></lb>tratto di penna, perchè in sostanza non era al Ricci una cosa nuova. </s></p><pb xlink:href="020/01/479.jpg" pagenum="460"></pb><p type="main">

<s>Quel che di nuovo insegnava il Torricelli consisteva nel confermare con­<lb></lb>tro i Peripatetici le svanite dottrine del Baliani, secondo le quali lo spazio <lb></lb>lasciatosi indietro dall&#039;argento vivo era vuoto, e la causa del sostenersi il <lb></lb>liquido nel tubo era esterna e non interna. </s>

<s>Alcune però di quelle peripa­<lb></lb>tetiche contradizioni erano vecchie, e Galileo le impersonò in quel Simpli­<lb></lb>cio, che, per negare al Salviati il vuoto, che egli affermava esser rimasto <lb></lb>tra il fondo del corpo di tromba e l&#039;embolo dello stantuffo, ritirato a gran <lb></lb>forza indietro; diceva che poteva esser <emph type="italics"></emph>penetrata aria o esalazioni o altre <lb></lb>materie più sottili per le porosità del legno, e anche dall&#039;istesso vetro<emph.end type="italics"></emph.end><lb></lb>(Alb. </s>

<s>XIII, 20). Il Salviati rispondeva richiamando Simplicio all&#039;esperienza, <lb></lb>e, fatto nel fondo del corpo di tromba <emph type="italics"></emph>un poco di umbilico prominente,<emph.end type="italics"></emph.end><lb></lb>diceva che li si sarebbero dovute raccoglier le esalazioni, di che però, es­<lb></lb>sendo quel corpo di tromba un cilindro di vetro, nulla se ne scorgeva. </s></p><p type="main">

<s>Ma come pretendesse il Salviati che si potessero dal suo e dall&#039;occhio <lb></lb>di Simplicio scorgere quelle esalazioni spiritose, e invisibili anche attraverso <lb></lb>all&#039;acqua, non si capisce. </s>

<s>Il Torricelli dimostrò bene l&#039;esistenza del vacuo <lb></lb>in un altro modo, facendo salire, in luogo del mercurio, l&#039;acqua, la quale <lb></lb>con orribile impeto andò a riempir tutto il tubo. </s></p><p type="main">

<s>Ad altre peripatetiche, eppur vecchie contradizioni, Galileo non solo non <lb></lb>rispose, ma egli fu che le aveva promosse e avvalorate. </s>

<s>Que&#039;peripatetici <lb></lb>infatti, i quali sostenevano che la causa del rimanere così sospeso il mer­<lb></lb>curio era per forza interna di vacuo, professavano le dottrine stesse pro­<lb></lb>fessate contro il Baliani, nel I Dialogo delle Nuove Scienze, da Galileo; e <lb></lb>quegli altri, i quali dicevano che il mercurio dentro il tubo era attratto da <lb></lb><emph type="italics"></emph>quella roba sommamente rarefatta,<emph.end type="italics"></emph.end> ripetevano le dottrine galileiane del­<lb></lb>l&#039;aria che sostien, per attrazione calamitica, a galla le tavolette di ebano o <lb></lb>di metallo tanto più gravi in specie dell&#039;acqua. </s>

<s>A queste contradizioni, in­<lb></lb>torno a che i peripatetici stessi si facevan forti dell&#039;autorità di Galileo, il <lb></lb>Torricelli rispondeva coll&#039;esperienza, facendo il vuoto in un tubo terminato <lb></lb>alla sua sommità in una palla, mostrando che qui, dove si raccoglieva più <lb></lb>roba attraente, il mercurio era nulladimeno sostenuto alla medesima altezza. </s></p><p type="main">

<s>Alle vecchie contradizioni e difficoltà il Ricci ne aggiunse delle nuove, <lb></lb>e l&#039;espose in una sua Lettera indirizzata da Roma, il dì 18 Giugno 1644, <lb></lb>allo stesso Torricelli. </s>

<s>Quelle difficoltà si riducono a tre, ma più importanti <lb></lb>son la prima e la seconda. </s>

<s>Consisteva la prima nel dir che, chiusa la sco­<lb></lb>della del mercurio, non doveva il peso dell&#039;aria gravar che sul coperchio. </s>

<s><lb></lb>A che il Torricelli rispondeva coll&#039;esempio della lana premuta da un peso, <lb></lb>la quale, tagliata da un ferro presso il fondo, riman pure allo stesso modo <lb></lb>compressa. </s>

<s>La seconda difficoltà del Ricei consisteva nel dire che l&#039;aria non <lb></lb>esercita il suo peso che dall&#039;alto in basso, a che il Torricelli risponde con <lb></lb>parole, in cui compendiasi un trattato nuovo d&#039;Idrostatica, che così l&#039;aria <lb></lb>come l&#039;acqua, con ogni gas e con ogni liquido, esercitano la loro prèssione <lb></lb>ugualmente per tutti i versi. </s></p><p type="main">

<s>A illustrare così fatte idrostatiche dottrine, prima del 1658, cioè prima <pb xlink:href="020/01/480.jpg" pagenum="461"></pb>che fosse nota in Italia la prima Lettera torricelliana, aveva atteso pure il <lb></lb>Borelli, il quale anzi confessa al principe Leopoldo di aver sentito un gran <lb></lb>dispiacere in trovar che dal Torricelli stesso era stato prevenuto nelle sue <lb></lb>speculazioni. </s>

<s>“ In questo proposito dirò di un gusto dispiacevole che ho avuto, <lb></lb>vedendo una lettera della b. </s>

<s>m. </s>

<s>del Torrirelli diretta al signor M. A. Ricci, <lb></lb>nella quale accenna quella stessa ragione dimostrativa, che io trovai perchè, <lb></lb>otturando l&#039;inferior bocca del vaso dell&#039;argento vivo, ed impedendo la com­<lb></lb>pressione di tutta la regione aerea, tuttavia si mantiene l&#039;argento vivo nel <lb></lb>cannello alla altezza di un braccio e un quarto in circa, e per maggior mio <lb></lb>martello adopra il medesimo esempio della lana, conforme io esemplicavo la <lb></lb>cosa con molti materazzi ” (MSS. Cim., T. XVI, c. </s>

<s>103). Non mancò però <lb></lb>modo al Borelli di distinguersi per altre novità di speculazioni e di espe­<lb></lb>rienze, tutte ordinate a illustrare i principii torricelliani, e ciò egli fece con <lb></lb>grande ardore nel suo Trattato <emph type="italics"></emph>De motionibus naturalibus,<emph.end type="italics"></emph.end> in varie parti del <lb></lb>libro, ma segnatamente in quella sequela di proposizioni, dalla C alla CIX. </s></p><p type="main">

<s>Scriveva il Cornelio, dedicando la sua celebre Epistola <emph type="italics"></emph>De Circumpul­<lb></lb>sione<emph.end type="italics"></emph.end> a Marcello Crescenzio, del così decantato esperimento dell&#039;argento vivo: <lb></lb>“ de quo tot tantaque brevi temporis spatio scripta sunt volumina, quae in­<lb></lb>tegram bibliothecam possint explere. </s>

<s>” Non fu senza dubbio questione che <lb></lb>tanto venisse agitata quanto questa, non eccettuata la non men celebre con­<lb></lb>troversia copernicana, che tanto le si assomiglia e nelle avventure e nell&#039;im­<lb></lb>portanza. </s>

<s>Ma lasciando da parte quel turbolento e violento che veniva a <lb></lb>metter nella questione del vuoto la Teologia peripatetica, a intender come <lb></lb>un tal questionar di vuoto e non vuoto riuscisse tanto loquace, basta il pen­<lb></lb>sar che i contradittori del vero avevano una parte di ragione. </s>

<s>Non parliam <lb></lb>di Francesco Lino, e di quel suo <emph type="italics"></emph>funicolo<emph.end type="italics"></emph.end> tanto poderosamente rotto dal <lb></lb>Boyle, ma il gran Grimaldi si contrappose ai fautori del vuoto, dicendo che <lb></lb>la sommità della canna era invece piena delle invisibili esalazioni del mer­<lb></lb>curio. </s>

<s>“ Est autem substantia illa ab hydrargirio extracta magis quam vitrum <lb></lb>ipsum perspicua, ideoque ab aliquibus creditum fuit eam non adesse sed <lb></lb>remanere in fistula vitrea spatium aliquod vacuum ” (De Lumine, Bono­<lb></lb>niae 1665, pag. </s>

<s>52). E confortava il suo asserto coll&#039;esperienza, imperocchè <lb></lb>soggiunge: “ si fistulae summitati applicetur aliquod calefactivum, hydrar­<lb></lb>girium magis descendit in fistula; si vero applicetur aliquod frigefactivum <lb></lb>eidem summitati, hydrargirium in reliquo fistulae contentum ascendit ” (ibi). <lb></lb>Le premesse si appoggiavano sopra un vero sperimentale, ma la conclusione <lb></lb>era falsa, e in ogni modo giocava il grand&#039;uomo di fantasia, quando diceva <lb></lb>che le vibrazioni fatte dal mercurio, prima di equilibrarsi dentro la canna, <lb></lb>erano ordinate dalla natura a far più facilmente esalare que&#039;sottilissimi pro­<lb></lb>fluvii, onde provveder che lo spazio non rimanesse vuoto; fantasia che sva­<lb></lb>niva all&#039;esperienza e al discorso fatto da Donato Rossetti nella sua <emph type="italics"></emph>Dimo­<lb></lb>strazione fisico-matematica<emph.end type="italics"></emph.end> delle <emph type="italics"></emph>sette proposizioni<emph.end type="italics"></emph.end> (Firenze, 1668, prop. </s>

<s>III, <lb></lb>pag. </s>

<s>23). E sacrificava pure il Grimaldi il grande ingegno all&#039;idolo peripa­<lb></lb><gap></gap> in <gap></gap>uelle esalazioni mercuriali, piuttosto che nella pressione <pb xlink:href="020/01/481.jpg" pagenum="462"></pb>esterna dell&#039;aria, riconosceva la forza che teneva sospeso l&#039;argento vivo nella <lb></lb>canna torricelliana. </s>

<s>Il padre Daniello Bartoli, senza nominarlo, per amor fra­<lb></lb>terno e per riverenza, parve che volesse scrivere principalmente contro di <lb></lb>lui quel suo pregevole <emph type="italics"></emph>Discorso,<emph.end type="italics"></emph.end> che ha per titolo <emph type="italics"></emph>La tensione e la pressione <lb></lb>disputanti qual di loro sostenga l&#039;argento vivo ne&#039;cannelli dopo fattone il <lb></lb>vuoto:<emph.end type="italics"></emph.end> Discorso stampato in Bologna nel 1677, e dove, con sottili ragiona­<lb></lb>menti confortati d&#039;esperienze, che in tanta dovizia hanno pure del nuovo; si <lb></lb>conclude a favor della pressione torricelliana contro la tensione grimaldiana. </s></p><p type="main">

<s>Così il Bartoli, gesuita, parve che venisse a offerir la vittoria, anche a <lb></lb>nome de&#039;peripatetici, al Torricelli, la Lettera del quale al Ricci rimase ve­<lb></lb>nerando documento e sincero pascolo di scienza. </s>

<s>E ora, ritornando a leg­<lb></lb>ger quella celebre lettera, la quale contiene in una carta sola la sapienza <lb></lb>dispersa per innumerevoli volumi, duole a sentir l&#039;Autore così concludere <lb></lb>il suo discorso: <emph type="italics"></emph>La mia intenzion principale poi non è potuta riuscire, <lb></lb>cioè di conoscere quando l&#039;aria fosse più grossa e grave, e quando più <lb></lb>sottile e leggera collo strumento<emph.end type="italics"></emph.end> (Lett. </s>

<s>a&#039;Fil. </s>

<s>cit., pag. </s>

<s>21). Or se dunque <lb></lb>il Torricelli stesso confessa di non esser riuscito a far lo strumento da mi­<lb></lb>surar le variazioni del peso dell&#039;aria, s&#039;avvedono i nostri Lettori che la sto­<lb></lb>ria dell&#039;invenzion del Barometro incomincia qui, dove noi stessi e tutti ci <lb></lb>saremmo aspettati che dovess&#039;esser di già terminata. </s></p><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Se le nostre indagini storiche, con le quali ci siamo studiati di sodi­<lb></lb>sfare alla viva curiosità del Mersenno, abbiano conseguito l&#039;intento, lo la­<lb></lb>sceremo all&#039;imparziale giudizio de&#039;nostri lettori, ma in tanto non può non <lb></lb>muoverci a gran maraviglia il trovar come sia stata dal Mersenno stesso e <lb></lb>da tutti gli altri frantesa quella parte così chiara di storia, che si contiene <lb></lb>nella Lettera prima del Torricelli. </s>

<s>Il Torricelli incomincia ivi a dire che la <lb></lb>sua esperienza non <emph type="italics"></emph>era per far semplicemente il vacuo,<emph.end type="italics"></emph.end> e il Mersenno dà <lb></lb>fuori voce, o s&#039;intende quella sua voce come un dir che il Torricelli abbia <lb></lb>fatta l&#039;esperienza del vacuo. </s>

<s>In ogni modo il Pascal l&#039;intese così, e fu da <lb></lb>ciò mosso a speculare con tanto ingegno e ad eseguir con tant&#039;arte quelle <lb></lb>sue otto esperienze, con le quali, credendo di promuover l&#039;esperienza tor­<lb></lb>ricelliana, tornava invece in dietro a far, con que&#039;suoi lunghi tubi pieni <lb></lb>d&#039;acqua e di vino, carrucolati su per le antenne de&#039;vascelli roanesi, quel <lb></lb>che parecchi anni prima aveva fatto in Roma Gaspero Berti. </s></p><p type="main">

<s>Più tardi, quest&#039;altra voce si sparse e giunse essa pure alle orecchie <lb></lb>del Pascal: che il Torricelli rendeva ragione dello star sospesi i liquidi nei <lb></lb>tubi del vuoto, attribuendo il fatto spettacoloso alla pressione dell&#039;aria. </s>

<s>Que­<lb></lb>sto sì era vero, e conforme a ciò che leggevasi nella prima Lettera al Ricci, <lb></lb>ma però non era la principale intenzione che si proponesse, in trattar di <lb></lb><gap></gap><pb xlink:href="020/01/482.jpg" pagenum="463"></pb>chiaro in principio, e lo ripete in fine della Lettera stessa: l&#039;intenzion di <lb></lb>adattar lo strumento dell&#039;argento vivo a servir da Barometro. </s></p><p type="main">

<s>Ora è notabilissimo, e da non lasciarsi senza considerazione, che l&#039;in­<lb></lb>tenzion principale venisse ad essere sopraffatta dalla secondaria. </s>

<s>“ Questa, <lb></lb>scriveva il Dati, non è, come molte altre esperienze, che in sè stessa fini­<lb></lb>sca, ma ell&#039;è una perenne scaturigine d&#039;innumerevoli e profondi misteri <lb></lb>della Natura ” (Lett. </s>

<s>a&#039;Fil. </s>

<s>cit., pag. </s>

<s>24). L&#039;avere il Pecquet, per esempio, <lb></lb>svelati que&#039;misteri nella Fisiologia, il Guericke nella Meteorologia, il Boyle in <lb></lb>quasi tutti gli ordini della scienza sperimentale, senza dubbio, ricompensava <lb></lb>largamente l&#039;iattura dell&#039;aver trascurato l&#039;esperienza in sè stessa. </s>

<s>Ma non <lb></lb>s&#039;intende perchè mai coloro, che videro la Lettera torricelliana al Ricci, non <lb></lb>attendessero per prima cosa a ricercar la ragione per cui non riuscì al Tor­<lb></lb>ricelli stesso d&#039;applicar la sua esperienza a misurare la variabilità del peso del­<lb></lb>l&#039;aria. </s>

<s>Quella ragione, dall&#039;altra parte, egli da sè, il Torricelli, dice che ell&#039;era <lb></lb><emph type="italics"></emph>perchè il livello AB si muta per un&#039;altra causa, che io non credeva mai, <lb></lb>cioè pel caldo e freddo, e molto sensibilmente, appunto come se il vaso AE <lb></lb>fosse pieno d&#039;aria<emph.end type="italics"></emph.end> (Lett. </s>

<s>Fil., pag. </s>

<s>21). Gli effetti termometrici insomma <lb></lb>dubitava il Torricelli che venissero a complicarsi così coi barometrici, da <lb></lb>non poter discernere gli uni dagli altri. </s>

<s>Ecco la gran difficoltà, innanzi a <lb></lb>cui, con troppo frettolosa impazienza, si arretrò e che lo fece disperar di <lb></lb>ridurre il suo strumento dell&#039;argento vivo ad uso di Barometro. </s></p><p type="main">

<s>Fra&#039;tanti cultori della scienza torricelliana nulladimeno, uno ve ne fu, <lb></lb>e de&#039;più illustri di tutti, il quale incorò anzi speranza da ciò che aveva fatto <lb></lb>prima disperare il Torricelli. </s>

<s>Roberto Boyle ebbe anch&#039;egli a osservar che <lb></lb>il mercurio nel tubo torricelliano imitava, benchè con più tardo passo, i <lb></lb>moti stessi del Termometro. </s>

<s>“ Dum per aliquas hebdomadas tubus in fe­<lb></lb>nestra, quam raro aperuimus, consisteret, ansa mihi data est observandi <lb></lb>hydrargirium saepius motum liquoris in Thermometro contenti, passu de­<lb></lb>biliori tamen, imitari: calidiori enim coelo paulum subsidere, frigidiore ali­<lb></lb>quantulum ascendere solebat, quod nos maiori vel minori aeris in tubi summo <lb></lb>pressioni vertendum duximus, expansi nimirum aut condensati, per calorem <lb></lb>nempe vel per frigus, quibus successive ambiens aer afficiebatur ” (Experim. </s>

<s><lb></lb>Nova, Op. </s>

<s>Omn., T. I, Venetiis 1697, pag. </s>

<s>38). </s></p><p type="main">

<s>A questa osservazione il Torricelli adombrò, e abbandonò il suo nobile <lb></lb>intento, ma il Boyle proseguì animoso e ritrovò che se talvolta il mercurio <lb></lb>nello strumento del vacuo e il liquido del Termometro s&#039;imitavan nel moto, ben <lb></lb>più spesso però avveniva che si movesse questo mentre l&#039;altro restava fermo, <lb></lb>e che l&#039;uno facesse il passo in contraria parte dell&#039;altro. </s>

<s>“ Res autem cuius <lb></lb>observationi intentius inhaerebam, haec erat: quod mercurius saepe nunc <lb></lb>subsideret, nunc in tubo prosurgeret notabiliter, secus atque in Thermometris <lb></lb>usuvenit, quibus in tubi summitate aer continetur: imo nonnunquam modo <lb></lb>plane contrario se movere visus est. </s>

<s>Vidimus enim aliquando sub frigidissimo <lb></lb>coelo .... mercurium molto inferius quam aliis temporibus decidisse ” (ibi). </s></p><p type="main">

<s>Da ciò il Boyle ne concludeva ciò che aveva concluso il Torricelli, <pb xlink:href="020/01/483.jpg" pagenum="464"></pb>17 anni prima, per l&#039;osservazione delle palline immerse dentro l&#039;acqua dei <lb></lb>boccioli. </s>

<s>“ Experimentum quippe, quod huic dissertationi ansam praebuit, <lb></lb>satis probat verisimile esse quod ipsi etiam atmosphaerae non desint quasi <lb></lb>fluxus et refluxus plane admirabiles, aut saltem quod varias patiatur per <lb></lb>magnas et repentinas, secundum altitudinem suam aut densitatem mutatio­<lb></lb>nes, quarum tam causae quam et ipsi effectus incautos nos atque nihil <lb></lb>eiusmodi speculantes praetereunt ” (ibi, pag. </s>

<s>40). </s></p><p type="main">

<s>Sembrerebbe così, che da questo XVIII Esperimento boileiano incomin­<lb></lb>ciasse l&#039;applicazione dell&#039;esperienza torricelliana ad uso di Barometro, ma <lb></lb>pure era un&#039;applicazione barometrica l&#039;esperienza fatta nel 1648 da M. </s>

<s>Pe­<lb></lb>rier sul Puy De Domme, e anzi in quel tempo che lo stesso Perier speri­<lb></lb>mentava il variar della pressione ammosferica secondo il variar delle altezze, <lb></lb>sperimentava altresì il variar di lei ne&#039;varii giorni e nelle varie stagioni. </s>

<s><lb></lb>L&#039;editor del <emph type="italics"></emph>Traitez de l&#039;equilibre des liqueurs<emph.end type="italics"></emph.end> pubblicò un <emph type="italics"></emph>Recit des obser­<lb></lb>vations faites par Monsieur Perier continuellement jour par jour, pendant <lb></lb>les annees 1649, 1650, 1651 en la ville de Clermont en Auvergne, sur <lb></lb>la diversité des elevations ou abaissement du vif argent dans les tuyaux, <lb></lb>et de celles qui ont esté faites en mesme temps sur le mesme sujet a Paris <lb></lb>par un de ses amis, et a Stokolm, en Suede par Messieurs Chanut et <lb></lb>Descartes.<emph.end type="italics"></emph.end> E il Capitolo IV <emph type="italics"></emph>De la pesanteur de l&#039;air<emph.end type="italics"></emph.end> del Pascal, pubblicato <lb></lb>postumo dallo stesso editore, s&#039;intitola: “ Que comme la pesanteur de la <lb></lb>masse de l&#039;air augmente, quand il est plus chargé de vapeurs, et diminué <lb></lb>quand il l&#039;est moins; aussi les effets qu&#039;elle produit augmentent et dimi­<lb></lb>nuent a proportion ” (Paris, 1663, pag. </s>

<s>96). </s></p><p type="main">

<s>Ma l&#039;esser queste scritture del Pascal rimaste inedite infino al 1663, <lb></lb>dette luogo al Boyle di specular come cosa nuova intorno al suo XVIII Espe­<lb></lb>rimento, e ad Isacco Vossio d&#039;uscir fuori a descrivere <emph type="italics"></emph>constructionem Aero­<lb></lb>scopii, a nemine quod sciam, hactenus observati, unde quam latissime, ni <lb></lb>fallor, colligi possit quinam sit aeris status .... quod enim aeri, ipsum <lb></lb>quoque hoc hydrargiro fistulis incluso contingit ”<emph.end type="italics"></emph.end> (De motu marium et <lb></lb>vent. </s>

<s>Hagae Com., 1663, pag. </s>

<s>120, 21). </s></p><p type="main">

<s>Più tardi ancora, cioè nel 1669, il Sinclaro credeva di essere stato il <lb></lb>primo ad applicar lo strumento torricelliano alla misura delle variabilità del <lb></lb>peso dell&#039;aria secondo il variar delle altezze, e a imporre allo strumento <lb></lb>stesso il nome di <emph type="italics"></emph>Baroscopio.<emph.end type="italics"></emph.end> In un dialogo dell&#039;<emph type="italics"></emph>Ars Magna<emph.end type="italics"></emph.end> tra Francesco <lb></lb>e Alessandro, dop&#039;aver questi esposta la teoria del Baroscopio e dop&#039;aver <lb></lb>detto com&#039;ella venga confermata dall&#039;osservare le variazioni del livello del <lb></lb>mercurio nel salire e nel discender da un monte, Francesco soggiunge: <lb></lb>“ Rem quidem clarissime demonstrat hoc novum experimentum, sed scias <lb></lb>velim me prius de eo audivisse. <emph type="italics"></emph>Alex.<emph.end type="italics"></emph.end> Quid tu narras? <emph type="italics"></emph>Franc.<emph.end type="italics"></emph.end> Imo ad eam­<lb></lb>dem conclusionem illustrandam idemmet adductum vidi experimentum in <lb></lb>libello quodam nuper excuso cui epigraphe <emph type="italics"></emph>Philosophia experimentalis<emph.end type="italics"></emph.end> lin­<lb></lb>gua vulgari. </s>

<s>Quam vercor ne nimis trita tua feceris experimenta prius non­<lb></lb><gap></gap></s></p><pb xlink:href="020/01/484.jpg" pagenum="465"></pb><p type="main">

<s>Noi crediamo che queste cose il Sinclaro le dica in buona fede, e forse <lb></lb>nella remota Scozia non era veramente ancora approdata la notizia di quelle <lb></lb>scoperte, che il buon professor di Glascovia si lusingava di presentare egli <lb></lb>al mondo come primizia. </s>

<s>Ma l&#039;esperienza sul Puy De Domme fu dalla fama <lb></lb>tanto largamente diffusa, che par impossibile non ne penetrasse il suono <lb></lb>anco attraverso alle montagne Scozzesi, e il Boyle, ne&#039;suoi <emph type="italics"></emph>Nuovi experi­<lb></lb>menti,<emph.end type="italics"></emph.end> cioè dieci anni prima che fosse pubblicata l&#039;<emph type="italics"></emph>Ars Magna,<emph.end type="italics"></emph.end> aveva in­<lb></lb>differentemente chiamato Baroscopio e Barometro lo strumento torricelliano. </s></p><p type="main">

<s>Non volendo però disputar sui nomi, e lasciando liberamento al Vossio <lb></lb>chiamarlo Aeroscopio, al Sinelario Baroscopio, al Boyle Barometro, è un fatto <lb></lb>che il celebre strumento alle mani di tutti questi osservatori, non eccettuato <lb></lb>il Sinclaro, che lo trasportò non solamente sulle alture de&#039;monti, ma nelle <lb></lb>profondità delle miniere e de&#039;mari; si trova esser composto ancora di quella <lb></lb>canna di vetro e di quella catinella d&#039;immersione, che servì alla prima espe­<lb></lb>rienza del Torricelli. </s></p><p type="main">

<s>Ma questo apparecchio torricelliano non era con troppa facilità traspor­<lb></lb>tabile, e nè perciò riuscivano comparabili le osservazioni fatte in luoghi di­<lb></lb>versi. </s>

<s>Quanto alla comodità sarebbesi senza dubbio, assai meglio prestato <lb></lb>quel semplice tubo, senza catinella d&#039;immersione, che ci descrive il Viviani <lb></lb>ne&#039;suoi manoscritti (Gal. </s>

<s>Disc., T. CXXXII, c. </s>

<s>113) e che poi il Borelli pub­<lb></lb>blicò nel Trattato <emph type="italics"></emph>De motion. </s>

<s>naturalibus.<emph.end type="italics"></emph.end> “ Idipsum nostrae fistulae di­<lb></lb>rectae in aere constitutae adaptari potest, sitque illa AC (fig. </s>

<s>45) duorum <lb></lb><figure id="id.020.01.484.1.jpg" xlink:href="020/01/484/1.jpg"></figure></s></p><p type="caption">

<s>Figura 45.<lb></lb>cubitorum, habeatque orificium C insignis exiguitatis, re­<lb></lb>pleaturque mercurio, deorsumque invertatur in aere libero <lb></lb>(non enim necesse est ut os C intra scutellam mercurii <lb></lb>plenam infundatur, quando valde stricta est os eius C) <lb></lb>tunc ab infimo orificio C mercurius in aere profluet, quou­<lb></lb>sque altitudo CB fuerit unius cubiti, et quadrantis pro­<lb></lb>xime ” (Regio Julio, 1670, pag. </s>

<s>214). Un tale strumento <lb></lb>però non era applicabile che a sola la misura della discesa <lb></lb>del livello del mercurio, via via che l&#039;aria esterna rimette <lb></lb>della sua pressione. </s></p><p type="main">

<s>Il Borelli stesso aveva immaginato un altro Baro­<lb></lb>metro semplicissimo, comodo quanto quello ora descritto, <lb></lb>perchè composto anch&#039;esso di un solo tubo di vetro, e atto ugualmente a <lb></lb>misurar le pressioni ammosferiche ne&#039;loro accessi e ne&#039;loro recessi. </s>

<s>A mezzo <lb></lb>il tubo era insinuata una gocciola di mercurio, che serviva per indice della <lb></lb><figure id="id.020.01.484.2.jpg" xlink:href="020/01/484/2.jpg"></figure></s></p><p type="caption">

<s>Figura 46.<lb></lb>scala, e il tubo stesso tenevasi non eretto <lb></lb>verticalmente ma in posizione orizzon­<lb></lb>tale L&#039;inventore stesso, ne descrive così <lb></lb>la forma e l&#039;uso: “ Sia il cilindro sot­<lb></lb>tilissimo di cristallo serrato estremamente in B (fig. </s>

<s>46) ed aperto in A: si <lb></lb>metta in esso una minuta gocciola di argento vivo, e si spinga verso il <lb></lb>fondo B, come in C. </s>

<s>Questo si faccia al fondo di una torre dalla cima della, <pb xlink:href="020/01/485.jpg" pagenum="466"></pb>quale pendano due fili, a&#039;quali legando il cilindro, nel tirarlo poscia in su, <lb></lb>lo sollevino orizzontalmente. </s>

<s>Intanto diversi osservatori disposti a varie fine­<lb></lb><figure id="id.020.01.485.1.jpg" xlink:href="020/01/485/1.jpg"></figure></s></p><p type="caption">

<s>Figura 47.<lb></lb>stre della torre, nel passaggio che fa <lb></lb>da loro il cilindro, segnino con pal­<lb></lb>line di cera o con una pennata d&#039;in­<lb></lb>chiostro il luogo che occupa quivi la <lb></lb>gocciola dell&#039;argento, che condotto <lb></lb>finalmente sulla cima più alta, dal <lb></lb>luogo che ivi occuperà l&#039;istessa goc­<lb></lb>ciola e da&#039;segni fatti sopra il cilindro <lb></lb>(se le finestre saranno state in egual <lb></lb>distanza) si raccorrà quanto sia stata <lb></lb>dilatata l&#039;aria e con qual proporzione ” <lb></lb>(Targioni, Not. </s>

<s>aggrand., T. II, P. II, <lb></lb>pag. </s>

<s>690). </s></p><p type="main">

<s>Nonostante, la stessa sua sover­<lb></lb>chia semplicità non conferiva a un <lb></lb>tal Barometro borelliano quelle qua­<lb></lb>lità, che si ricercavano per render lo <lb></lb>strumento abile a rispondere a tutte <lb></lb>le intenzioni della scienza. </s>

<s>A ridurlo <lb></lb>tale rivolse verso il 1667 i suoi pen­<lb></lb>sieri il Boyle, introducendo nello stru­<lb></lb>mento stesso torricelliano il tubo a <lb></lb>sifone, solidamente applicato a una <lb></lb>tavoletta di legno. </s>

<s>“ Hisce stimulis <lb></lb>accito et ad Baroscopios portatiles <lb></lb>atque itinerarios (si sic loqui liceat) <lb></lb>factitandos memet accingenti, trina <lb></lb>haec moliri subiit. </s>

<s>Primo vas illud <lb></lb>qua sustentum, qua stagnantem mer­<lb></lb>curium conclusurum e vitro continuo <lb></lb>ac diametri aequalis adfiat: dein ut <lb></lb>post vasis istius impletionem tali illud <lb></lb>loculamento collocarem, quod et facile <lb></lb>transfretari posset, et moderatam sal­<lb></lb>tem vitro adversum illatam ab extra <lb></lb>vim defensionem praeberet, nulla eius <lb></lb>parte a machina prominente, quod in <lb></lb>aliis Baroscopiis fieri solet. </s>

<s>Tertio, ita <lb></lb>illius locationi incubui, ut fracturae <lb></lb>facill ob violentum inhospitantis mer­<lb></lb>curii motum non sit obnoxium ” <lb></lb>(Novor. </s>

<s>experim. </s>

<s>contin. </s>

<s>I, Experim. </s>

<s>XXII, Venetiis 1697, T. I, pag. </s>

<s>248). <pb xlink:href="020/01/486.jpg" pagenum="467"></pb>Una tal costruzione, che il Boyle stesso eseguì e fece rappresentare in un <lb></lb>iconismo da noi riprodotto qui nella figura 47, si può dire il tipo di tutti <lb></lb>i Barometri a mercurio. </s></p><p type="main">

<s>Il celebre Fisico inglese, che nel suo Nuovo esperimento XXXIV, fu <lb></lb>primo a far l&#039;esperienza del Baroscopio, così propriamente detto, nel vuoto, <lb></lb>pensò altresì di sostituire il Baroscopio stesso nell&#039;aria, per servirsene a mi­<lb></lb>surar la variabilità della pressione. </s>

<s>A questo nuovo strumento, che si di­<lb></lb>stinse col nome di <emph type="italics"></emph>Baroscopio statico,<emph.end type="italics"></emph.end> rivolse la sua attenzione il Viviani, e <lb></lb>studiandosi a perfezionarlo, proluse all&#039;invenzione di simili altri strumenti <lb></lb>delicatissimi, di che s&#039;onorarono poi alcuni stranieri. </s></p><p type="main">

<s>“ Il Boyle, così appunto di propria mano scrive il Viviani, propone di <lb></lb>fare un Baroscopio statico, pigliando un paio di bilance e ponendovi da una <lb></lb>parte una palla di vetro fatta alla lucerna, della grandezza di un&#039;arancia, e <lb></lb>dall&#039;altra un contrappeso di bronzo che stesse in equilibrio colla palla piena <lb></lb>d&#039;aria, col quale strumento, allorchè preponderava o la palla di vetro o <lb></lb>quella di bronzo, veniva in cognizione delle variazioni dell&#039;aria nella stessa <lb></lb>forma che col Barometro pieno di argento vivo. </s>

<s>Questo strumento del Boyle <lb></lb>patisce un&#039;eccezione, alla quale non pensò e questo si è che pel caldo e <lb></lb><figure id="id.020.01.486.1.jpg" xlink:href="020/01/486/1.jpg"></figure></s></p><p type="caption">

<s>Figura 48.<lb></lb>pel freddo l&#039;aria contenuta nella palla <lb></lb>si rarefà e si condensa e così viene <lb></lb>a esercitare minore o maggior forza, <lb></lb>come che la molla o vogliam dire ela­<lb></lb>sticità dell&#039;aria cresca con proporzion <lb></lb>reciproca della grandezza. </s>

<s>Per rime­<lb></lb>diare a questa difficoltà si può fare <lb></lb>il Barometro statico in questa guisa: <lb></lb>Si pigli un pezzo di acciaio, sopra il <lb></lb>quale si segnino minutamente i gradi <lb></lb>e vi si metta un romano, e alle estremità vi si attacchino due palle di vetro <lb></lb>aperte in cima, una delle quali si serri con una cartapecora ben sigillata e <lb></lb>l&#039;altra si lasci aperta, e posta in equilibrio col romano: si averà sempre la <lb></lb>differenza dell&#039;aria. </s>

<s>Sia l&#039;istrumento in questa guisa: (fig. </s>

<s>48). Oppure si <lb></lb><figure id="id.020.01.486.2.jpg" xlink:href="020/01/486/2.jpg"></figure></s></p><p type="caption">

<s>Figura 49.<lb></lb>potrebbe fare questo stesso strumento <lb></lb>in altra guisa, empiendolo d&#039;argento <lb></lb>vivo, facendo un cannello di vetro pieno <lb></lb>di mercurio, nell&#039;estremità del quale <lb></lb>fossero attaccate allo stesso cannello due <lb></lb>palle di vetro, che una di serrassi come <lb></lb>si è detto, l&#039;altra stesse aperta, e che si <lb></lb>notassero nel cannello i gradi, per vedere <lb></lb>l&#039;ascesa e la discesa del mercurio, il <lb></lb>che potrebbe farsi in talforma: (fig. </s>

<s>49). <lb></lb>Così, potendosi aprire la parte che si dice che dee star chiusa, ed in <lb></lb><gap></gap><pb xlink:href="020/01/487.jpg" pagenum="468"></pb>e condensazione, che s&#039;incontra nel Barometro statico proposto dal Boyle ” <lb></lb>(MSS. Gal., T. CXXXII, c. </s>

<s>16). </s></p><p type="main">

<s>Lasciamo ai nostri Lettori il ripensare alle somiglianze che passano fra <lb></lb>questo nuovo Barometro statico del Viviani e il <emph type="italics"></emph>Termometro differenziale<emph.end type="italics"></emph.end><lb></lb>del Leslie e il <emph type="italics"></emph>Termoscopio<emph.end type="italics"></emph.end> del Rumford, contentaudoci di richiamar la loro <lb></lb>attenzione sopra ciò che il Wolf, nel Cap. </s>

<s>IV del II Volume, Parte I, della <lb></lb>sua <emph type="italics"></emph>Fisica sperimentale,<emph.end type="italics"></emph.end> dice, per rivendicar l&#039;invenzione dello strumento <lb></lb>del Boyle a Ottone di Guericke. </s>

<s>Ottone, secondo il Fisico prussiano, è ve­<lb></lb>ramente l&#039;Autore dello strumento da misurar le variazioni di densità, che <lb></lb>subisce l&#039;aria e ch&#039;egli chiama col nome di <emph type="italics"></emph>Manometro.<emph.end type="italics"></emph.end> “ Primus Mano­<lb></lb>metri inventor fuit Otho Guerickius, qui hoc instrumentum anno 1661 in <lb></lb>Epistola ad eruditum Jesuitam Gasparem Schottum describit ” (Trad. </s>

<s>A. Bina, <lb></lb>Venetiis 1756, pag. </s>

<s>93). Ma la questione si dirime assai facilmente dallo <lb></lb>stesso Wolf, il quale confessa che altro era l&#039;uso del Barometro statico del <lb></lb>Boyle, altro l&#039;uso del Manometro del Guericke. </s></p><p type="main">

<s>Men facile forse potrebbe parere a trovar ragioni da rispondere al me­<lb></lb>desimo Autore della Fisica sperimentale prussiana, il quale, nel capitolo pre­<lb></lb>cedente al citato, vorrebbe far lo stesso Ottone, prima del Boyle, autor del <lb></lb>Barometro; se a ognun che guarda il X iconismo, impresso a pag. </s>

<s>99 degli <lb></lb><emph type="italics"></emph>Esperimenti nuovi<emph.end type="italics"></emph.end> di Magdeburgo (Amstelodami 1672), non fosse ovvio il <lb></lb>giudicare che, sebben quella figurina, la quale mostra col dito, sulla parete <lb></lb>del tubo di vetro dentro cui è inclusa, i gradi dell&#039;ascesa e della discesa, <lb></lb>può esser comoda e dilettevole a prognosticare il bel tempo e la pioggia, non <lb></lb>dà nulladimeno alcuna buona speranza di porgersi docile a prestar que&#039;de­<lb></lb>licati e scrupolosi servigi, a che il Barometro portatile del Boyle colle mo­<lb></lb>dificazioni introdottevi dai Meteorologi e dai Geodeti, sarebbe stato poi in­<lb></lb>vocato a prestare, nelle sue tanto gelose operazioni, alla scienza. </s></p><pb xlink:href="020/01/488.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della Macchina elettrica e della Pila voltaia<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del globo di zolfo del Guericke, e del globo di vetro dell&#039;Hawksbee; della Macchina elettrica di <lb></lb>Lipsia, del Winkler, del Nollet, del Ramsden. </s>

<s>— II. </s>

<s>Della Bottiglia di Leyda; dell&#039;Elettroforo <lb></lb>e del Condensatore del Volta. </s>

<s>— III. De&#039;primi Elettroscopii: dell&#039;Elettroscopio a boccetta, del­<lb></lb>l&#039;Elettrometro condensatore, e dell&#039;Elettrometro a quadrante. </s>

<s>— IV. </s>

<s>Della grande scoperta gal­<lb></lb>vanica dell&#039;Elettricità animale, e della nuova Elettricità metallica scoperta dal Volta. </s>

<s>— V. Del­<lb></lb>l&#039;Elettromotore del Volta a Colonna, e a Corona di tazze. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Passar dal Barometro, per chi, in questi nostri capitoli di storia, cer­<lb></lb>casse un nesso o un ordine evidente di successione, a parlar della Macchina <lb></lb>elettrica, potrebbe a prima vista parer quasi un saltar d&#039;Arno in Bacchi­<lb></lb>glione, come per proverbio si dice. </s>

<s>Nonostante, se è vero quel che s&#039;è da <lb></lb>noi asserito più volte, che cioè dalla celebre esperienza torricelliana dell&#039;ar­<lb></lb>gento vivo fu promosso ogni ordine di scienza sperimentale, non possono <lb></lb>altro aspettarsi i nostri Lettori se non che si mostri a loro come mai da <lb></lb>quella stessa esperienza torricelliana fosse promossa la scienza elettrica, la <lb></lb>quale non fu prima vista fiorire che un secolo dopo. </s>

<s>I fatti che siamo qui <lb></lb>per narrare saranno quelli, da cui si concluderà la desiderata dimostrazione, <lb></lb>benchè non sia, ne&#039;suoi primi principii, per apparire evidente, avendo anche <lb></lb>noi a pigliar le mosse da Ottone di Guericke. </s></p><p type="main">

<s>Ha il celebre Filosofo di Magdeburgo, ai fisici esperimenti, troppo spesso <lb></lb>e con troppo amore disposate le metafisiche speculazioni, con le quali ardi­<lb></lb>tamente risale a considerare le virtù mondane, ch&#039;egli poi vede tutte insieme <lb></lb>rappresentate, come in immagine viva, in un globo di zolfo. </s>

<s>Il piccolo Mondo <lb></lb>metafisico, a render più perfetta la rassomiglianza col grande Mondo fisico, <pb xlink:href="020/01/489.jpg" pagenum="470"></pb>è configurato in isfera velocemente girata attorno; e perchè, per la sua pic­<lb></lb>colezza, e per non essere altro che immagine di cosa vera, l&#039;attrito che ri­<lb></lb>ceve dall&#039;aria ambiente non basta, vi s&#039;aggiunge lo sfregar della palma della <lb></lb>mano. </s>

<s>Così le virtù mondane latenti nel piccolo globo sulfureo vengono vi­<lb></lb>vamente eccitate, e una leggera piuma che vi si appressi, essendovi ora <lb></lb>attratta e ora respinta, dà sicuro indizio della mondana virtù attrattiva e re­<lb></lb>pulsiva, e le tenebre rivelano all&#039;occhio di chi rimira il piccolo Mondo la <lb></lb>sua propria virtù lucente. </s>

<s>“ Nam si eum (globum sulphureum) in conclave <lb></lb>obscurum tecum conferas et palma sicca praeprimis noctu atteras, eadem <lb></lb>ratione lucet, qua saccharum si tundatur ” (Experim. </s>

<s>nova magd., Amste­<lb></lb>lodami 1672, pag. </s>

<s>149, 50). </s></p><p type="main">

<s>Da ciò si volle riconoscere Ottone come primo inventore della Macchina <lb></lb>elettrica, nè potendosi da noi negar ciò, e anzi soggiungendo che il Fisico <lb></lb>di Magdeburgo fece importantissime esperienze elettriche col macchinamento <lb></lb>di quel suo globo sulfureo; non possiamo non sentirci compresi di gran mara­<lb></lb>viglia in considerare che le scoperte, per le quali iniziava un nuovo e splen­<lb></lb>didissimo mondo della scienza, rimanessero per un mezzo secolo dimenticate. </s>

<s><lb></lb>Così, a un impulso che si riconosce per validissimo, non solo non fu visto <lb></lb>succedere, ne&#039;progressi della scienza elettrica, un proporzionato effetto, ma <lb></lb>nessuno effetto veramente ne conseguì, come se giusto si fosse quell&#039;im­<lb></lb>pulso esercitato nella cedevole aria a produrvi una passeggera commozione <lb></lb>di vento. </s></p><p type="main">

<s>Più sottilmente però considerando, si trova che un così fatto impulso, <lb></lb>riuscì per questo inefficace, perchè non venne per la diritta via. </s>

<s>La Metafi­<lb></lb>sica, più presto che la Fisica, era che lo dirigeva, e le aeree speculazioni <lb></lb>distolsero gli occhi dello stesso Ottone dal proseguire più attentamente i <lb></lb>fatti. </s>

<s>Ma quando questi fatti rientrarono nel loro ordine fisico, e allora la <lb></lb>scienza elettrica progredì, con lento, ma non interrotto passo, e d&#039;un sottile <lb></lb>zampillo d&#039;acqua si vide a poco a poco diventare un gran fiume, che poi <lb></lb>va a distendersi in un gran lago, da meritarsi, per l&#039;ampiezza e per la pro­<lb></lb>fondità, meglio il nome di mare. </s>

<s>Quel sottile zampillo scaturisce, come d&#039;arida <lb></lb>selce, dal vetro di uno di que&#039;tubi dello Strumento torricelliano, e di lì ha <lb></lb>origine il fiume, che si dilaga nella scienza di tutto quel calore, di tutta <lb></lb>quella luce, e di tutta quella vita, che commove il secolo presente. </s></p><p type="main">

<s>Nell&#039;anno 1675, una notte, occorse al celebre Picard di dover traspor­<lb></lb>tare da un luogo all&#039;altro un suo Barometro a mercurio, e qui fu sorpreso <lb></lb>da uno spettacolo nuovo: la così detta <emph type="italics"></emph>camera del vuoto<emph.end type="italics"></emph.end> gli apparì splen­<lb></lb>dente di una luce in tutto simile a quella, che si vede esalar dal fosforo <lb></lb>posto in un luogo oscuro. </s>

<s>Ripensando poi che il fenomeno non appariva in <lb></lb>tutti i Barometri, e non sempre nè allo stesso modo si riproduceva nel Ba­<lb></lb>rometro medesimo, riguardò quella fosforescenza come un&#039;apparizione straor­<lb></lb>dinaria, e da non farsene caso, piuttosto che come un fatto naturale meri­<lb></lb>tevole di essere speculato. </s></p><p type="main">

<s>Ma presto poi si conobbe che i Barometri atti a fosforeggiare erano <pb xlink:href="020/01/490.jpg" pagenum="471"></pb>assai più frequentati di quel che il Picard non pensasse, e il Cassini fece <lb></lb>così notare agli Accademici di Francia quella frequenza, da richiamarvi sopra <lb></lb>l&#039;attenzione di Giovanni Bernoulli. </s>

<s>Egli diligentemente sperimentando ritrovò <lb></lb>che il fosforo mercuriale, nel vuoto barometrico, non è un&#039;apparenza straor­<lb></lb>dinaria, propria e particolare di uno strumento o di un altro, ma dimostrò <lb></lb>che era un fatto naturalissimo, e ch&#039;egli avviene in tutti gli strumenti, pur­<lb></lb>chè però sodisfacciano alle richieste condizioni. </s>

<s>Del resultato di queste sue <lb></lb>nuove esperienze rendeva conto il Bernoulli, nel 1700, in una Memoria in­<lb></lb>serita negli Atti della R. </s>

<s>Accademia di Scienze. </s>

<s>Essendosi così divulgata <lb></lb>fra&#039;dotti la scoperta del fosforo mercuriale, il Musschenbroeck la diffuse nel <lb></lb>popolo, fabbricando alcuni tubi di vetro ripieni in parte di mercurio e vo­<lb></lb>tati d&#039;aria, i quali, agitati colla mano, apparivano al buio miracolosamente <lb></lb>splendenti. </s></p><p type="main">

<s>Così, scienziati e volgo quietavano nella persuasione che il mercurio <lb></lb>agitato nel vuoto acquistasse la virtù di esalare quella fosforica luce, quando <lb></lb>uno de&#039;tubi spettacolosi del Musschenbroeck capitò in Londra alle mani <lb></lb>dell&#039;Hawksbee. </s>

<s>Il giochetto, in che gli altri fanciullescamente si dilettavano, <lb></lb>a lui parve degno delle speculazioni del Filosofo, e avendo risaputo degli <lb></lb>studii, che vi aveva fatto attorno il Bernoulli, se ne volle informare con gran <lb></lb>diligenza. </s>

<s>Di quelle bernulliane osservazioni due principalmente rimasero <lb></lb>impresse nell&#039;Hawksbee: la prima, che la luce fosforica è solamente visi­<lb></lb>bìle quando il mercurio nel vuoto barometrico discende; e l&#039;altra, che quella <lb></lb>fosforica luce è più intensa, quando il tubo di vetro non è per tutto uguale <lb></lb>e andante, ma ora s&#039;allarga in ventri e ora si ristringe in istrozzature. </s>

<s>La <lb></lb>prima di quelle osservazioni, che egli sperimentando ritrovò verissima, gli <lb></lb>fece nascere il sospetto che la luce fosforica non esalasse, come dicevasi, dal <lb></lb>mercurio, ma scaturisse dal vetro; e la seconda osservazione gli fece con­<lb></lb>getturare che una tal luce, per questo appunto scaturisse dal vetro, perchè <lb></lb>eccitata dalla confricazion del mercurio. </s>

<s>Confermavasi in questa sua conget­<lb></lb>tura l&#039;arguto Fisico inglese, vedendo che, anche stando quieto il mercurio <lb></lb>al di dentro, potevasi eccitar la solita luce a pure stropicciar il vetro di fuori <lb></lb>colle dita: “ Si potrebbe, egli dice, con qualche probabilità congetturare che la <lb></lb>luce prodotta, proceda da qualche qualità nel vetro, per una tal confrica­<lb></lb>zione o moto datogli, e non dal mercurio per altro conto, se non solamente <lb></lb>in quanto egli è un corpo proprio, quale battendo o strofinando sopra il <lb></lb>vetro produca la luce. </s>

<s>E quello che pare che confermi tal congettura si è <lb></lb>che avendo stropicciato colle dita la parte superiore e vota d&#039;un Barometro <lb></lb>mercuriale, ne scaturì una luce, senza che l&#039;argento vivo si movesse ” (Esper. </s>

<s><lb></lb>fisico meccan., Firenze 1716, pag. </s>

<s>32). </s></p><p type="main">

<s>Per rendere il fenomeno più parvente l&#039;Hawksbee, invece della piccola <lb></lb>camera barometrica, sperimentò sopra un pallone di vetro votato d&#039;aria colla <lb></lb>Macchina pneumatica, e, invece di fregar col dito, fregava con tutta la palma <lb></lb>della mano il pallone stesso fatto girare velocemente attorno, per mezzo di <lb></lb><gap></gap> un globo di vetro, di circa nove dita di dia-<pb xlink:href="020/01/491.jpg" pagenum="472"></pb>metro, e ne cavai l&#039;aria.... Essendo in questa maniera assicurato il globo, <lb></lb>lo fermai ad una macchina che gli dava un moto veloce col suo asse per­<lb></lb>pendicolare all&#039;orizzonte, e dipoi, applicando la mia nuda mano distesa alla <lb></lb>superficie di quello, ne risultò che in brevissimo tempo si produsse una <lb></lb>considerabil luce ” (ivi, pag. </s>

<s>30). </s></p><p type="main">

<s>L&#039;artificio di votare il pallone dell&#039;aria contenutavi era per conformarsi <lb></lb>all&#039;esperienza del fenomeno nel vuoto barometrico, ma venuta poi voglia al­<lb></lb>l&#039;industre sparimentatore di riammettere dentro il pallone stesso l&#039;aria ca­<lb></lb>vata, restò sorpreso dal vederne uscir fuori, scoppiettando in scintille vive, <lb></lb>quella luce, che prima rimanevasi dentro ugualmente diffusa. </s>

<s>“ Procurai un <lb></lb>vetro, di figura più sferica che fusse possibile, di diametro e di lunghezza <lb></lb>di circa sette dita. </s>

<s>L&#039;asse di questo vetro, trovandosi parallelo all&#039;orizzonte, <lb></lb>ed essendone cavata l&#039;aria contenuta, gli fu dato moto da una macchina di <lb></lb>nuova invenzione. </s>

<s>E gli effetti di questa, rispetto alla luce, prodotta per l&#039;at­<lb></lb>trizione di essa, furono assai simili a quelli delle antecedenti sperienze. </s>

<s>Ma <lb></lb>quando fu lasciata rientrar l&#039;aria e fu dato come da principio il moto e <lb></lb>l&#039;attrizione, restai sorpreso dall&#039;apparenza d&#039;una vivace vigorosa luce, con­<lb></lb>tinuata tralla punta del mio dito ed il vetro. </s>

<s>Non era solamente chiara e <lb></lb>visibile sopra il dito, ma di più pareva, in una certa maniera, che perco­<lb></lb>tesse con qualche forza sopra di quello, essendo ciò facile a distinguersi al <lb></lb>tatto, mediante una forza di gentil compressione, benchè il movente corpo <lb></lb>non ne fosse toccato per quasi la grossezza d&#039;un mezzo dito. </s>

<s>Questa luce <lb></lb>pareva che uscisse dal vetro con rumore considerabile, non dissimile d&#039;una <lb></lb>voce roca, quantunque alquanto più forte ” (ivi, pag. </s>

<s>42, 43). </s></p><p type="main">

<s>La nuova scoperta del globo di vetro, che, confricato colla palma della <lb></lb>mano, anche nella luce del giorno, all&#039;appressarvi un dito o altro corpo di­<lb></lb>viene scintillante, fu descritta dall&#039;Hawksbee nel patrio linguaggio e inse­<lb></lb>rita fra&#039;suoi <emph type="italics"></emph>Physico-mechanical Experiments<emph.end type="italics"></emph.end> pubblicati in Londra nel 1609 <lb></lb>e tradotti, sette anni dopo, nella nostra lingua, in Firenze. </s>

<s>Presto se ne dif­<lb></lb>fuse in Inghilterra e per tutta l&#039;Europa la notizia, specialmente pel magi­<lb></lb>stero autorevole e universale del Newton, il quale, nella VIII Questione <lb></lb>commemorò il fatto elettrico nuovamente scoperto colle seguenti parole: “ Si­<lb></lb>militer globus vitreus, diametro circiter 8 aut 10 unciarum, machinae ver­<lb></lb>satili infixus, ut circa axem suum motu celerrimo circumagatur, qua sui <lb></lb>parte vola manus apposita inter volvendum confricetur, lucebit. </s>

<s>Quod si <lb></lb>eodem tempore charta alba, aut linteum album vel etiam digitus extremus ita <lb></lb>admoveatur, ut circiter quarta vel dimidia unciae parte distet a vitro, qua parte <lb></lb>motus eius est celerrimus, vapor elettricus frictione manus a vitro excitatus, <lb></lb>et ad chartam albam, linteum, vel digitum allisus, ita agitabitur, ut lucem <lb></lb>continuo emittat, efficiatque ut charta illa alba, linteum vel digitus, tanquam <lb></lb>cicindela lucescat, quin et a vitro erumpens, ea vi nonnunquam ad digitum <lb></lb>allidatur, ut etiam tactu percipi queat. </s>

<s>Quod idem quoque evenit, quando cy­<lb></lb>lindrus e vitro electrove, longus et amplus, charta manu admota eousque con­<lb></lb>fricetur donec vitrum <gap></gap></s></p><pb xlink:href="020/01/492.jpg" pagenum="473"></pb><p type="main">

<s>L&#039;uso di confricar colla carta, piuttosto che colla palma della mano <lb></lb>ignuda, di qui si vede che cominciò presto a precorrere all&#039;ufficio de&#039;guan­<lb></lb>cialetti, nella costruzione della Macchina elettrica, come pure assai presto si <lb></lb>pensò ai globì di sostituire i cilindri, e si volle, invece del vetro, veder se <lb></lb>migliore effetto si faceva dall&#039;ambra. </s>

<s>L&#039;Hawksbee stesso volle tentar lo spe­<lb></lb>rimento anche con cilindri di legno intonacati di ceralacca, di zolfo e di <lb></lb>pece mescolata con matton pesto, ma trovò che nulla agguagliava all&#039;effi­<lb></lb>cacia del vetro, specie avendosi cura di mantenerlo asciutto. </s></p><p type="main">

<s>Così aveva mostrato il celebre Inglese da che masso e con qual verga <lb></lb>miracolosa, potesse il Fisico fare scaturire la sorgente elettrica: mancava, <lb></lb>diciam così, la secchia da attingerla, mancavano i canali da condurla e da <lb></lb>dispensarla. </s>

<s>Aveva già Ottone di Guericke osservato e descritto, ne&#039;suoi Espe­<lb></lb>rimenti Nuovi di Magdeburgo, un fatto assai singolare, ed era che la virtù <lb></lb>attrattiva di quel suo globo di zolfo, poteva comunicarsi a un filo di lino, e <lb></lb>diffondersi per tutta la lunghezza di lui, in modo da attrarre a sè e da ran­<lb></lb>nodarsi al capo di un altro filo posatogli alquanto discosto. </s>

<s>“ Filum lineum <lb></lb>si acumini ligni acuminati, inque mensa vel scamno firmati inhaerescere fa­<lb></lb>cias, atque filum ulna longius demittas, ita quidem ut infra ibi aliud quid, <lb></lb>spatio pollicari remotius attingere possit (quoties scilicet globus excitatus, <lb></lb>summitati huius ligni admoveatur); inferius fili cum iuxsta apposito coniungi: <lb></lb>quo ad oculos demonstrandum hanc virtutem in filo lineo usque ad partes <lb></lb>infimae se extendisse, dum hoc, aut attrahit, aut seipsum alligat ” (Ed. </s>

<s>cit., <lb></lb>pag. </s>

<s>149). Lo sperimento fu molti anni dopo ripetuto dal Gray, il quale <lb></lb>trasmise la virtù elettrica di un cilindro di vetro confricato a una cordicella <lb></lb>di canapa assai lunga, e vide l&#039;estremità di lei attrarre assai vivamente i <lb></lb>fiocchetti del cotone. </s></p><p type="main">

<s>Sono i fili di lino e le cordicelle di canapa, senza dubbio, i primi con­<lb></lb>duttori elettrici, che siano stati scoperti; ma era riserbato a quel medesimo <lb></lb>Gray di rivelar la natura di que&#039;corpi, a&#039;quali eminentemente si compete­<lb></lb>rebbe la virtù di essere <emph type="italics"></emph>conduttori.<emph.end type="italics"></emph.end> Egli osservò che, confricando i globi <lb></lb>o i cilindri nella macchina dell&#039;Hawksbee, l&#039;elettricità del vetro si comu­<lb></lb>nicava alle viere di metallo, fossero pur lunghe quanto si volesse, che face­<lb></lb>vano da poli al volgere del torno. </s>

<s>Di qui ebbe origine la importantissima <lb></lb>scoperta de&#039;corpi <emph type="italics"></emph>anelettrici,<emph.end type="italics"></emph.end> che si elettrizzano per comunicazione, rice­<lb></lb>vendone la virtù dagli <emph type="italics"></emph>idioelettrici,<emph.end type="italics"></emph.end> e, senz&#039;altro; diffondendola per tutta la <lb></lb>loro lunghezza. </s></p><p type="main">

<s>La nuova e rilevantissima distinzione fra corpi <emph type="italics"></emph>idioelettrici<emph.end type="italics"></emph.end> o <emph type="italics"></emph>coibenti,<emph.end type="italics"></emph.end><lb></lb>e <emph type="italics"></emph>anelettrici<emph.end type="italics"></emph.end> o <emph type="italics"></emph>conduttori,<emph.end type="italics"></emph.end> fu per opera dello stesso Gray, introdotta nella <lb></lb>scienza elettrica, nel 1729, e di lì s&#039;incominciò a immaginare, e a far uso <lb></lb>di quegli organi riconosciuti per più atti e meglio disposti a condurre l&#039;elet­<lb></lb>tricità attinta ai globi di vetro confricati. </s>

<s>Così, nel 1741, i Fisici tedeschi <lb></lb>erano riusciti a comporre un assai buono e comodo strumento, che, sotto il <lb></lb>nome di <emph type="italics"></emph>Macchina elettrica di Lipsia,<emph.end type="italics"></emph.end> fu descritto da Giovan Maria Della <lb></lb><gap></gap><pb xlink:href="020/01/493.jpg" pagenum="474"></pb>A condurre il fluido elettrico s&#039;adoperava una catenella metallica tenuta so­<lb></lb>spesa da cordoncini di seta, ma ad attingere il fluido e a comunicarlo alla <lb></lb>stessa catenella, s&#039;adoperava una lastra di ferro, sopra la quale, come su <lb></lb>mensa, posavansi tre cannoncini, accostati insieme, di latta. </s>

<s>Poi, fra quat­<lb></lb>tro pioli di legno perpendicolarmente eretti all&#039;estremità di una crociera <lb></lb>portata da un piede pur di legno secco, s&#039;intesseva, d&#039;un cordoncino di seta, <lb></lb>una coltricella a rete, sopra la quale adagiavasi la lamiera di ferro, e dispo­<lb></lb>nevasi in modo, che i tre cannoncini di latta aprissero le loro bocche molto <lb></lb>presso al globo di vetro, per beverne avidamente l&#039;elettricità, che ne sca­<lb></lb>turiva. </s>

<s>Ma perchè talvolta, fra i labbri taglienti della rigida latta e il gire­<lb></lb>vole globo, succedeva qualche urto pericoloso, si pensò di far tre fascetti di <lb></lb>trucioli d&#039;orpello, i quali, uscendo fuori da&#039;tre cannoncini, si confregavano <lb></lb>con maggior superficie e cedevano nello stesso tempo agli urti del torno. <lb></lb>(Torre, Scienza della Natura, P. II, Napoli 1749, pag. </s>

<s>308-10). </s></p><p type="main">

<s>Fra que&#039;Tedeschi però uno ne fu, Enrico Winkler, il quale stimò di <lb></lb>ottenere miglior effetto, sostituendo al torno continuo della ruota, quello di <lb></lb>va e vieni di un arcoletto, che si faceva ora andare, ora tornare co&#039;moti <lb></lb>alternativi del piede. </s>

<s>Egli sostituiva altresì, allo sfregamento della palma della <lb></lb>mano, quello di un cuscinetto ricoperto di pelle aspersa di creta secca. </s></p><p type="main">

<s>La Macchina elettrica di Lipsia, colle modificazioni suggerite dal Win­<lb></lb>kler, quasi nello stesso tempo che da noi, s&#039;introdusse in Francia, dove il <lb></lb>Nollet esercitava il più autorevole magistero nella scienza. </s>

<s>Egli rifiutò il Tor­<lb></lb>nio del Winkler, parendogli <emph type="italics"></emph>che uno stropicciamento sostenuto o reiterato <lb></lb>nello stesso verso riesca meglio, che quando alternativamente si faceva in <lb></lb>un verso contrario.<emph.end type="italics"></emph.end> (Lezioni di Fisica, trad. </s>

<s>it., T. V, Venezia 1764, pag. </s>

<s>175). <lb></lb>Rifiutò altresì, preferendogli lo stropicciamento delle mani, l&#039;uso de&#039;guancia­<lb></lb>letti, intorno ai quali così scriveva: </s></p><p type="main">

<s>“ I Fisici, che si sono applicati all&#039;esperienze dell&#039;Elettricità, non sono <lb></lb>ben d&#039;accordo tra di loro circa la materia, che debbono preferire nello stro­<lb></lb>picciare il vetro, e gli altri corpi da elettrizzarsi. </s>

<s>Gli uni raccomandano di <lb></lb>strofinare colla man nuda, gli altri vogliono che tra la mano e il corpo che <lb></lb>si strofina, vi sia un foglio di carta grigia, o una pezza di lana o un tocco <lb></lb>di pelle di camoscio saleggiata di bianco di Spagna o di Tripoli. </s>

<s>Molti fanno <lb></lb>girare i loro globi di rincontro a guancialetti di pelle di bufalo, pieni di <lb></lb>crino, o di qualche altra materia animalesca, ed altri fanno i loro strofinac­<lb></lb>cioli con molti fogli di carta dorata o inargentata, posti gli uni sopra degli <lb></lb>altri, oppure con drappi nel cui tessuto sia entrato oro, argento o qualche <lb></lb>altro metallo.... Dirò solamente .... che nulla m&#039;è paruto così atto a que­<lb></lb>st&#039;uso, quanto la man nuda, purchè non sia umida per traspirazione o <lb></lb>altrimenti ” (ivi, pag. </s>

<s>176, 77). </s></p><p type="main">

<s>La Macchina elettrica insomma, che il Nollet prima introdusse in Fran­<lb></lb>cia, consisteva nello stesso globo tornatile dell&#039;Hawksbee, applicatovi con­<lb></lb>duttori molto più semplici e più efficaci. </s>

<s>Una catenella pendente sopra l&#039;equa­<lb></lb><gap></gap><pb xlink:href="020/01/494.jpg" pagenum="475"></pb>elettricità a una lunga asta metallica sospesa da cordoncini di seta, la quale <lb></lb>asta spesso mettevasi in comunicazione con altre aste similmente sospese, <lb></lb>di che tutto insieme componevasi il conduttore. </s></p><p type="main">

<s>Una tal nuova efficacissima disposizione di conduttori elettrici fu sug­<lb></lb>gerita al Nollet dall&#039;avere il Gordon e il Monnier osservato che un condut­<lb></lb>tore tanto meglio riesce quant&#039;egli è più lungo. </s>

<s>Quando poi una tal con­<lb></lb>clusione venne, colle teorie e colle esperienze così luminosamente dimostrata <lb></lb>dal Volta, mentre che il Beccaria aveva rese così evidenti le proprietà già <lb></lb>prima scoperte nelle punte; s&#039;intende come la Macchina elettrica potesse <lb></lb>allora giungere a que&#039;perfezionamenti, oramai notissimi a tutti, a ricevere <lb></lb>i quali l&#039;aveva, infin dal 1766, preparata il Ramsden a Londra. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I conduttori che s&#039;adopravano alle Macchine elettriche, prima del 1778, <lb></lb>cioè prima che il Volta dimostrasse con qual ragione se ne poteva aumen­<lb></lb>tare la capacità, non erano, colla loro scarica, atti a produrre nessuna com­<lb></lb>mozione sui muscoli degli animali, e ciò perchè il fluido non vi si accumulava <lb></lb>nella quantità necessaria. </s>

<s>Se insomma erasi ritrovata, ad attinger l&#039;elettricità, <lb></lb>la secchia, e s&#039;eran pure ritrovati i canali da condurla e da dispensarla, <lb></lb>non s&#039;aveva però ancora la cisterna da riporvela e da conservarla. </s>

<s>Il ritro­<lb></lb>vamento di così fatta cisterna occorse per un fatto assai singolare, e in che <lb></lb>modo si narrerà qui da noi brevemente. </s></p><p type="main">

<s>Nel 1746 il Winkler pubblicava a Lipsia un libro intitolato <emph type="italics"></emph>Della virtù <lb></lb>elettrica dell&#039;acqua elettrizzata in vasi di vetro.<emph.end type="italics"></emph.end> Si vollero l&#039;esperienze del <lb></lb>Fisico tedesco verificare in Leyda, dove s&#039;elettrizzava l&#039;acqua, facendo ripe­<lb></lb>tutamente scoccare la scintilla fra il conduttore della Macchina elettrica e <lb></lb>una verga metallica immersa, colla sua estremità inferiore, nell&#039;acqua stessa. </s>

<s><lb></lb>Ora avvenne allo sperimentatore, il quale con una mano teneva il vaso di <lb></lb>vetro, di appressar l&#039;altra mano alla verga di metallo, e nell&#039;atto stesso sentì <lb></lb>un&#039;improvvisa commozion dolorosa, nelle braccia, nel petto, e in altra parte <lb></lb>del corpo. </s></p><p type="main">

<s>La notizia del fatto giunse in Francia in quello stesso anno 1746, scri­<lb></lb>veva il Nollet, <emph type="italics"></emph>per via di due lettere in data di Leyden, l&#039;una del de­<lb></lb>funto sig. </s>

<s>Musschenbroeck al defunto signor di Reaumur, e l&#039;altra del <lb></lb>sig. </s>

<s>Alaman a me diretta, le quali ce l&#039;annunziarono come una scoperta <lb></lb>nuova e con termini capaci di sgomentare. </s>

<s>Non avendoci i detti signori <lb></lb>espressamente assegnato da chi, per la prima volta, fosse stata fatta, mi <lb></lb>sono appigliato al partito di chiamarla l&#039;esperienza di Leyden.<emph.end type="italics"></emph.end> (Lez. </s>

<s>di <lb></lb>Fis., ediz. </s>

<s>cit., T. V, pag. </s>

<s>301, 2). </s></p><p type="main">

<s>Prosegue ivi a dire l&#039;Autore che, per ordine della R. Accademia, si <lb></lb>dette a studiare le ragioni del fatto, ed esaminandone le condizioni, trovò <pb xlink:href="020/01/495.jpg" pagenum="476"></pb>che, essendo indifferente la figura del vaso, potevasi comodamente comporre <lb></lb>a foggia di bottiglia, dentro alla quale era lo stesso, invece di acqua, intro­<lb></lb>dur mercurio, migliarole, trucioli o limatura di qualunque metallo. </s>

<s>Così venne <lb></lb>ad aver la Fisica, dalle mani dello stesso Nollet, quella cisterna accumula­<lb></lb>trice dell&#039;elettricità via via raccolta, a cui non si sa ancora dare altro nome <lb></lb>che di <emph type="italics"></emph>Bottiglia di Leyda.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Un&#039;altra di così fatte cisterne trovaron poco dipoi il Wilke e l&#039;Epino <lb></lb>potersi avere da due larghi piani deferenti, affacciantisi a poca distanza, e <lb></lb>il Franklin trovò che un vetro da finestra incorniciato del suo telaio di le­<lb></lb>gno, e incollatavi sopra ambedue le facce una foglia metallica, era esso pure <lb></lb>una cisterna da elettricità, o, come in linguaggio scientifico si dice, un <emph type="italics"></emph>con­<lb></lb>densatore.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Gli organi dunque più necessarii non solo ad eccitare, ma a trattare il <lb></lb>fluido elettrico, erano stati tutti così trovati dall&#039;industria e dalla diligenza <lb></lb>de&#039;Fisici, fra&#039;quali, cosa nuova in questi Capitoli di Storia, non s&#039;ha da <lb></lb>commemorar nessuno de&#039;nostri Italiani. </s>

<s>Ma sorse all&#039;ultimo chi valse a ri­<lb></lb>vendicare, anche per questa parte, la gloria all&#039;Italia, no col concorrere a <lb></lb>perfezionare la Macchina elettrica dell&#039;Hawksbee, come fecero tedeschi e fran­<lb></lb>cesi, ma inventando una macchina nuova, che per l&#039;effetto e la comodità, <lb></lb>per non risentirsi dello stato igrometrico dell&#039;aria, e per mantenere quasi <lb></lb>indeficiente il fluido, una volta eccitatovi dallo stropicciamento; si rendeva <lb></lb>tanto eccellente sopra la Macchina antica. </s>

<s>S&#039;intende già che le nostre parole <lb></lb>accennano all&#039;<emph type="italics"></emph>Elettroforo<emph.end type="italics"></emph.end> del Volta, frutto non del caso ma dell&#039;esperienza, <lb></lb>e di quelle speculazioni intorno alla natura dell&#039;Elettricità, che s&#039;incomin­<lb></lb>ciarono ad istituire in Italia. </s></p><p type="main">

<s>Si proponeva da&#039;nostri Fisici a risolvere un così fatto problema: Quando <lb></lb>si stropiccia un nastro sopra un piano, e dopo lo stropicciamento gli resta <lb></lb>aderente, ritiene egli in tale stato l&#039;elettricità sua, ovvero la smarrisce in <lb></lb>esso, e non ritiene che la disposizione di ripigliarla, quando ne è disgiunto? </s>

<s><lb></lb>Giovan Batista Beccaria, che era giusto colui il quale proponeva un tal pro­<lb></lb>blema, risolveva la questione dicendo che, in quel caso, il nastro veramente <lb></lb>smarriva la sua elettricità, per <emph type="italics"></emph>rivendicarsela<emph.end type="italics"></emph.end> nell&#039;atto stesso che n&#039;è stac­<lb></lb>cato, d&#039;onde vennesi a qualificar col nome di <emph type="italics"></emph>vindice<emph.end type="italics"></emph.end> l&#039;elettricità produt­<lb></lb>trice di un tale effetto. </s></p><p type="main">

<s>Al Volta però parve una così fatta teoria del tutto immaginaria, perchè, <lb></lb>poniamo che potess&#039;esser l&#039;elettricità dal corpo smarrita, non si vedeva per <lb></lb>qual virtù poi si venisse a ricuperarla. </s>

<s>Perciò sostenne che l&#039;elettricità <emph type="italics"></emph>per­<lb></lb>maneva<emph.end type="italics"></emph.end> tuttavia, e suggerì da savio che non <emph type="italics"></emph>elettricità vindice<emph.end type="italics"></emph.end> si sarebbe <lb></lb>dovuta dir quella, ma sì invece <emph type="italics"></emph>elettricità permanente.<emph.end type="italics"></emph.end> E perchè il Becca­<lb></lb>ria studiavasi di confortar le sue teorie, discorrendo sopra i fenomeni pre­<lb></lb>sentati da un&#039;armatura metallica, della quale rivestivasi una lastra di vetro <lb></lb>elettrizzata; il Volta, per rispondere al suo contradittore, si trovò così, senza <lb></lb>volere, richiamato a studiar, sopra quelle lastre di vetro, l&#039;elettricità per­<lb></lb>manente. </s></p><pb xlink:href="020/01/496.jpg" pagenum="477"></pb><p type="main">

<s>A questo fine, osservando, s&#039;accorse che l&#039;elettricità non permaneva sul <lb></lb>vetro sempre per il medesimo spazio di tempo, ciò ch&#039;egli attribuiva al va­<lb></lb>riar dello stato igrometrico dell&#039;aria. </s>

<s>Da ciò venne condotto a sperimentar <lb></lb>sopra corpi meno igrometrici del vetro stesso, e togliendo e riponendo al­<lb></lb>ternativamente l&#039;armatura a una lastra di legno o di resina, trovò che, dopo <lb></lb>la scarica, le vicende di elettricità si protraevano per più lungo tempo, e i <lb></lb>segnali elettrici si estinguevano molto più lentamente, che sopra il vetro. </s>

<s><lb></lb>Ond&#039;è che, datosi tutto a studiar l&#039;elettricità, che per istropicciamento ec­<lb></lb>citavasi dalle resine stesse, ebbe a dirla non solo <emph type="italics"></emph>permanente,<emph.end type="italics"></emph.end> ma <emph type="italics"></emph>indeficiente,<emph.end type="italics"></emph.end><lb></lb>e sopr&#039;essa fondò le sue speranze di costruire una Macchina, la quale fosse <lb></lb>di fluido elettrico perenne e perpetua sorgente. </s></p><p type="main">

<s>Così fatte speranze di costruire un Elettriforo perpetuo si ridestarono <lb></lb>nell&#039;animo del Volta più lusinghiere e più vive, quando si diffuse la noti­<lb></lb>zia di un&#039;esperienza nuova fatta da Gian Francesco Cigna. </s>

<s>Consisteva que­<lb></lb>sta esperienza nell&#039;elettrizzare un nastro di seta applicato a una lamina di <lb></lb>piombo, e nel ritirarlo violentemente, nell&#039;atto che si toccava la lamina stessa <lb></lb>colla punta del dito. </s>

<s>Ripetendo più volte il gioco, era riuscito il Cigna, a <lb></lb>caricar, con questa nuova Macchina elettrica, una Bottiglia di Leyda. </s></p><p type="main">

<s>La bella esperienza veniva da Torino ad avvivar le speranze del Volta, <lb></lb>perchè vedeva in essa la forma propria che avrebbe preso il suo strumento; <lb></lb>veniva inoltre a lusingarle, perchè vedeva di poter fare con mirabile spedi­<lb></lb>tezza quel che al Cigna stesso non era riuscito che a stento. </s>

<s>Il vantaggio <lb></lb>sarebbe provenuto dal sostituire al nastro di seta una focaccia di resina e <lb></lb>all&#039;armatura immobile un mobile scudo di legno dorato. </s>

<s>Ed ecco di quali <lb></lb>semplicissimi organi componevasi la nuova e perpetua macchina elettrica, <lb></lb>dal suo proprio inventore descritta al Priestley colle seguenti parole: </s></p><p type="main">

<s>“ Ho dunque un piatto di stagno con l&#039;orlo che rileva poco più di una <lb></lb>mezza linea, d&#039;un piede di diametro: entro ho versato un mastice fuso com­<lb></lb>posto di trementina, ragia e cera, steso e rassodato in una superficie piana <lb></lb>e lucida. </s>

<s>Ne ho parecchi altri e più grandi e più piccoli di legno eziandio, <lb></lb>al cui fondo è incollata una laminetta di piombo, e in cui ho versato ove <lb></lb>zolfo, ove ceralacca ed ove altri mastici di varia composizione, ma l&#039;indi­<lb></lb>cato di sopra, ch&#039;io fo di tre parti di trementina, due di ragia ed una di <lb></lb>cera bollite insieme per più ore, mescendovi infine alquanto di minio, ad <lb></lb>oggetto di avvivarne il colore; l&#039;ho trovato il più comodo e il migliore. </s>

<s>Fa <lb></lb>l&#039;ufficio di armatura al di sopra un legno dorato della figura a un di presso <lb></lb>d&#039;uno scudo di dieci pollici di diametro, e alto due all&#039;incirca, piano nella <lb></lb>base, che dee combaciare col mastice, alquanto convesso nei lati ossia nel <lb></lb>contorno. </s>

<s>Dal centro della concavità sorge un manico di vetro, o meglio di <lb></lb>ceralacca ben levigato, che ha gli spigoli, e ciò rileva assai, smussati e ro­<lb></lb>tondati. </s>

<s>Chiamerò dunque quest&#039;armatura col nome di <emph type="italics"></emph>Scudo.<emph.end type="italics"></emph.end> Stimo super­<lb></lb>fluo l&#039;avvertire che mi attengo ordinariamente ad uno scudo di legno do­<lb></lb>rato, perchè meno dispendioso, e più leggero e manesco che uno di metallo <lb></lb><gap></gap> tutto cavo <pb xlink:href="020/01/497.jpg" pagenum="478"></pb>interiormente a foggia di una scatola, che serve per un altro apparato mi­<lb></lb>nore portatile in tasca, trovo che m&#039;offre in compenso non piccoli vantaggi, <lb></lb>uno rilevante, che è quello d&#039;essere più forbito, e perciò di dissipare meno <lb></lb>l&#039;elettricità; gli altri di sola appariscenza e comodo, per atto d&#039;esempio di <lb></lb>render sonore le scintille, anche meno vive; e di poter racchiudere in esso <lb></lb>varii strumenti che vengono ad uso, come caraffe, manichi per isolare, palle, <lb></lb>fili, ecc. </s>

<s>Ed eccovi, signore, tutto l&#039;apparato ” (Opere, Firenze 1816, T. I, <lb></lb>pag. </s>

<s>109, 10). </s></p><p type="main">

<s>La nuova e semplicissima Macchina italiana, così descritta, agli stra­<lb></lb>nieri che si compiacevano de&#039;perfezionamenti a cui il Ramsden aveva ri­<lb></lb>dotti i globi versatili dell&#039;Hawksbee, comparve inaspettata, e com&#039;è con­<lb></lb>sueto, alcuni l&#039;accolsero con applauso, mentre altri con invidiosa gelosia si <lb></lb>studiavano di detrarre ai meriti dell&#039;Inventore. </s>

<s>Non sapendo attaccarsi ad <lb></lb>altro, rassomigliavano l&#039;invenzione del nostro Italiano a un&#039;esperienza fatta <lb></lb>già dal Wilke insiem con l&#039;Epino, la quale esperienza consisteva nell&#039;em­<lb></lb>pir di zolfo fuso una coppa di metallo, e nel mostrar che s&#039;avevano i se­<lb></lb>gnali elettrici, così dal recipiente come dal zolfo medesimo strofinato, ogni <lb></lb>volta che l&#039;uno si disgiungeva dall&#039;altro, e ciò anche dopo qualche settimana <lb></lb>e qualche mese. </s></p><p type="main">

<s>A que&#039;suoi detrattori rispondeva il Volta con una Lettera scritta nel <lb></lb>Maggio del 1776, e diretta a Giuseppe Klinkosch (Op. </s>

<s>cit., T. I, pag. </s>

<s>144-63), <lb></lb>ma, meglio che con le parole, rispondeva co&#039;fatti, mostrando che il suo Elet­<lb></lb>troforo compendiava in sè tutte le virtù dell&#039;antica Macchina elettrica, e si <lb></lb>porgeva assai comodo a molti di que&#039;servigi, per i quali la Macchina stessa <lb></lb>del Ramsden invocava l&#039;aiuto di strumenti stranieri. </s>

<s>Così insegnava come, <lb></lb>dando alla focaccia resinosa poco spessore, avevasi nell&#039;Elettroforo uno stru­<lb></lb>mento atto a ricevere una gran carica, e a dar perciò un&#039;esplosione, e una <lb></lb>commozione ai muscoli degli animali, più violenta di quella eccitata col Qua­<lb></lb>dro magico, o colla Bottiglia di Leyda. </s></p><p type="main">

<s>Ma se le scosse elettriche erano spettacolose, non promovevan però la <lb></lb>scienza. </s>

<s>Il più eloquente argomento, con cui il Volta rispose a&#039;suoi detrat­<lb></lb>tori, fu quando egli mostrò che il suo Elettroforo si trasformava in un im­<lb></lb>portantissimo strumento per cui rendevasi cospicua quella virtù elettrica nel­<lb></lb>l&#039;aria serena, che altrimenti per la sua debolezza, alla percezione de&#039;semplici <lb></lb>sensi, sarebbe sfuggita. </s>

<s>Perciò all&#039;Elettroforo così trasformato impose il nome <lb></lb>di <emph type="italics"></emph>Condensatore,<emph.end type="italics"></emph.end> e nel seguente modo con brevi parole insegnava a far nello <lb></lb>strumento la facile e preziosissima trasformazione: </s></p><p type="main">

<s>“ Convien prendere un piatto d&#039;Elettroforo, che abbia l&#039;incrostatura di <lb></lb>resina assai sottile, e a cui o non sia stata dianzi impressa alcuna elettri­<lb></lb>cità, e se mai vi è stata, vi sia spenta affatto. </s>

<s>A questa faccia resinosa im­<lb></lb>mune da ogni elettricità si soprapponga convenientemente il suo scudo .... <lb></lb>collocandolo nel bel mezzo, in modo che non tocchi in alcun punto l&#039;orlo <lb></lb>metallico del piatto, ma rimanga isolato. </s>

<s>Così congiunti essendo, si adattino <lb></lb>al filo conduttore dell&#039;elettricit<gap></gap><pb xlink:href="020/01/498.jpg" pagenum="479"></pb>toccato dove che sia dal detto filo, esso solo lo scudo e in niun modo il <lb></lb>piatto. </s>

<s>In questa situazione si lascino le cose per un certo tempo, fin che <lb></lb>lo scudo possa aver raccolta competente dose di quell&#039;elettricità, che dal filo <lb></lb>conduttore gli viene molto lentamente instillata. </s>

<s>Da ultimo sottraggasi al <lb></lb>contatto e influsso del filo conduttore lo scudo tuttavia unito al suo piatto, <lb></lb>e combaciante la faccia resinosa; indi si disgiunga anche da questa, levan­<lb></lb>dolo in alto al consueto modo per il suo manico isolante: e allora sarà che <lb></lb>se ne otterranno gli aspettati segni cospicui di attrazione, di repulsione, e di <lb></lb>qualche scintilla eziandio, di pennoncelli, ecc., nel tempo che il conduttore <lb></lb>di per sè non giunge a mostrar nulla o appena un&#039;ombra di elettricità ” <lb></lb>(Opere, ivi, pag. </s>

<s>224, 25). </s></p><p type="main">

<s>A così fatto strumento era in dubbio il Volta se gli dava piuttosto il <lb></lb>nome di <emph type="italics"></emph>Elettroscopio,<emph.end type="italics"></emph.end> o anzi di <emph type="italics"></emph>Micro elettroscopio,<emph.end type="italics"></emph.end> imperocchè egli è ve­<lb></lb>ramente tale da far l&#039;ufficio designato da questo nome. </s>

<s>Ma i segnali inven­<lb></lb>tati a riconoscer l&#039;esistenza della virtù elettrica e a misurarne i gradi, e in <lb></lb>che il Volta stesso, oltre a quello del semplice Condensatore, ha molti altri <lb></lb>meriti singolari, son tanta parte de&#039;progressi fatti da questa scienza, da non <lb></lb>dover esser dimenticati nella nostra storia. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Gli Elettroscopi riconoscono senza dubbio la loro prima e più antica <lb></lb>origine in que&#039;corpuscoli leggerissimi, che si vedevano ora essere vivamente <lb></lb>attratti e ora respinti da&#039;cannelli di vetro, d&#039;ambra, o di zolfo confricati. </s>

<s>Il <lb></lb>primo però che attendesse a studiare il modo e le particolarità di così fatte <lb></lb>attrazioni e repulsioni fu Ottone di Guericke, ed ei le studiava in un Elet­<lb></lb>troscopio, offertogli spontaneamente dalla stessa Natura, nelle barbe di una <lb></lb>leggerissima piuma. </s>

<s>Notava, come segno della virtù elettrica partecipata dal <lb></lb>globo di zolfo alla piuma stessa, lo stendersi delle barbe di lei, e il vibrare <lb></lb>come se per incantesimo fosse tornata viva. </s>

<s>“ Circa quod praeterea notanda <lb></lb>sunt: Primo, eiusmodi plumam molliorem, cum in globo, tum in aere sese <lb></lb>extendere et vividam quodammodo praestare, atque omne quod propius exi­<lb></lb>stit, aut lubenter attrahere, aut si non valeat, ei scipsam applicare ” (Experim. </s>

<s><lb></lb>nova magdeb., edit. </s>

<s>cit., pag. </s>

<s>147). E prosegue a fare altre osservazioni elet­<lb></lb>troscopiche importantissime, risalendo dalla piuma attratta che rivolge verso <lb></lb>il globo di zolfo sempre la medesima faccia, alla Luna attratta verso il globo <lb></lb>della Terra, a cui pure, forse per una somigliante cagione, tien sempre ri­<lb></lb>volta la medesima faccia. </s></p><p type="main">

<s>È singolare che un simile volo dalle umili attrazioni elettriche alle su­<lb></lb>blimi attrazioni cosmiche, sollevasse la mente anche all&#039;Hawksbee, e che <lb></lb>ricevesse anch&#039;egli i primi impulsi da un Elettroscopio alquanto più artifi­<lb></lb>cioso di quello del Guericke, e meglio rappresentativo delle virtù mondane. <pb xlink:href="020/01/499.jpg" pagenum="480"></pb>“ Ho scoperto, scrive egli, alcune proprietà di questa materia elettrica, che <lb></lb>possono parere maravigliose a quelli che minutamente le considereranno. </s>

<s><lb></lb>Conciossiachè ci somministrano una sorta di rappresentazione de&#039;grandi fe­<lb></lb>nomeni dell&#039;Universo. </s>

<s>Poichè avendo osservato che i corpi leggeri, posti vi­<lb></lb>cini a qualche parte dello strofinato cilindro, parevano egualmente attratti, <lb></lb>inventai un semicircolo di fil di ferro da potersi fermare a una costante di­<lb></lb>stanza, facendolo circondare la semicilindrica superfice del vetro alla distanza <lb></lb>di quattro o cinque dita. </s>

<s>Questo fil di ferro aveva diversi fili di lana fer­<lb></lb>mati sopra di esso, che stavano pendenti dal medesimo a distanze fra loro <lb></lb>quasi eguali. </s>

<s>La lunghezza di essi era tale che venendo a stendersi diretta­<lb></lb>mente verso il centro di quello immaginario circolo sopra la superficie del <lb></lb>vetro, nel cui piano era posto il fil di ferro, arrivassero a meno della gros­<lb></lb>sezza di un dito alla circonferenza di quel circolo, ma se erano lasciati in <lb></lb>libertà stavano pendenti in una parallela positura reciproca. </s>

<s>Il cilindro fu <lb></lb>messo col suo asse parallelo all&#039;orizzonte e in questa positura fu girato ve­<lb></lb>locemente intorno, e allora per lo rapido moto e agitamento della circon­<lb></lb>dante aria i fili .... venivano alzati su e piegati all&#039;in su dall&#039;asse del ci­<lb></lb>lindro ” (Esper. </s>

<s>fisico-meccaniche, trad. </s>

<s>ital. </s>

<s>cit., pag. </s>

<s>44). </s></p><p type="main">

<s>Nonostante, gli Elettroscopi erano ancora lontani dall&#039;aver le loro pro­<lb></lb>prie forme distinte, non essendosi bene ancora distinto l&#039;essere e la natura <lb></lb>di quella elettricità, ch&#039;egli erano ordinati a rivelare. </s>

<s>Ma quando si distinse <lb></lb>poi l&#039;elettricità in vitrea e in resinosa e in positiva e negativa, e si formulò <lb></lb>il principio che due elettricità dello stesso nome si respingono e tanto più <lb></lb>vivamente si respingono, quanto la loro carica è più forte; fu allora che si <lb></lb>trovò modo e ragione a costruire l&#039;Elettroscopio, e se ne conobbe anche, <lb></lb>nello stesso tempo, il bisogno e la necessità dell&#039;usarlo. </s></p><p type="main">

<s>L&#039;invenzione del primo di questi nuovi Elettroscopi, rispondenti ai pro­<lb></lb>gressi e ai bisogni della scienza, è dovuta al napoletano Tiberio Cavallo. </s>

<s>Il <lb></lb>semplice e gelosissimo strumento, a cui tutti i Fisici fecero così lieta e li­<lb></lb>berale accoglienza, consisteva in due sottilissimi fili di metallo accoppiati in­<lb></lb>sieme e penduli, terminanti nelle loro estremità in due leggerissime pallot­<lb></lb>tole di midolla di sambuco. </s>

<s>S&#039;introducevano poi i due fili, tenuti insieme <lb></lb>nella loro parte superiore, in una boccetta di vetro, affinchè i moti esterni <lb></lb>dell&#039;aria non turbassero gl&#039;intestini moti elettrici. </s>

<s>Quasi contemporaneamente <lb></lb>all&#039;<emph type="italics"></emph>Elettroscopio a boccetta<emph.end type="italics"></emph.end> l&#039;Henley inventava il suo <emph type="italics"></emph>Elettrometro a qua­<lb></lb>drante,<emph.end type="italics"></emph.end> e tutt&#039;e due erano riserbati questi nuovi strumenti a ricevere il loro <lb></lb>ultimo grado di perfezione dalle mani del Volta. </s></p><p type="main">

<s>Incominciando dall&#039;Elettroscopio del Cavallo, uno de&#039;perfezionamenti, <lb></lb>che sembra una cosa da nulla, ma che è pure della massima importanza, <lb></lb>consisteva nell&#039;aver cambiato il Volta, ai pendolini, forma e materia, soppri­<lb></lb>mendo le pallottole di midolla di sambuco, e sostituendo ai fili metallici due <lb></lb>nude paglie, lunghe circa due pollici, le quali, sospese per mezzo di due mo­<lb></lb>bilissimi anelletti, pendessero contigue, o quasi contigue per tutta la loro <lb></lb>lunghezza. </s>

<s>Il vantaggio poi ottenuto dal sostituire ai fili le pagliette, e dal <pb xlink:href="020/01/500.jpg" pagenum="481"></pb>sopprimere i pendoli, secondo che si esprime lo stesso Volta, è “ che il mi­<lb></lb>nimo loro scostamento, la minima divergenza si rende più facilmente osser­<lb></lb>vabile, mercecchè tutta la linea del loro contatto, o quasi contatto, cade sot­<lb></lb>t&#039;occhio, onde scorgesi tosto se da un tale contatto o dal parallelismo escono <lb></lb>i due fili di paglia un minimo che, se vengono a formare il più piccolo an­<lb></lb>golo: laddove coi fili metallici aventi in fondo le palline, restando quelli un <lb></lb>dall&#039;altro discosti quanto porta la grossezza di coteste palline, ed essendo <lb></lb>altronde poco discernibili quei fili esilissimi, massime quando l&#039;Elettroscopio <lb></lb>tiensi a qualche distanza, o quando si sperimenta all&#039;aria alquanto oscura, <lb></lb>non si può così facilmente notare una piccola divergenza de&#039;medesimi, o un <lb></lb>angolo di pochissimi gradi che facciano, e puossi soltanto giudicare all&#039;in­<lb></lb>grosso dello scostamento delle pallottole ” (Op. </s>

<s>cit., T. II, P. II, pag. </s>

<s>8, 9). </s></p><p type="main">

<s>Questi miglioramenti sono sostanziali e intrinseci allo strumento, ma <lb></lb>un&#039;altro ve ne introdusse il Volta, che si può riguardare come accessorio, <lb></lb>e che consiste nell&#039;accoppiamento fecondo ch&#039;ei fece dell&#039;Elettroscopio a <lb></lb>boccetta col Condensatore. </s>

<s>Intorno a un tal felicissimo accoppiamento, per <lb></lb>cui venne la Fisica a possedere l&#039;esplorator più sottile della elettricità nei <lb></lb>corpi, così ne scriveva il suo stesso insigne Inventore. </s>

<s>“ Solamente un anno <lb></lb>dopo che io ebbi pubblicato nelle Transazioni anglicane cotesta mia inven­<lb></lb>zione del Condensator dell&#039;elettricità, mi suggerì di unirlo immediatamente <lb></lb>e farne un corpo solo coll&#039;Elettrometro a boccetta nel modo che or ora <lb></lb>dico.... Adatto a vite un piattello di due pollici circa di diametro, al bot­<lb></lb>tone del mio Elettrometro, ed applico ad esso piattello, allorchè voglio con­<lb></lb>densarvi l&#039;elettricità, il piano di marmo, l&#039;incerato, il taffetà o quel qualun­<lb></lb>que corpo semicoibente che trovo più a proposito. </s>

<s>Per maggior mio comodo <lb></lb>mi servo ordinariamente d&#039;una zona di taffetà cerato o verniciato che forma <lb></lb>come un mezzo guanto aperto d&#039;ambi i lati, nel quale entrano quattro diti <lb></lb>riuniti della mano. </s>

<s>Con questi diti così fasciati io copro e premo alquanto <lb></lb>quel piattello posto in cima all&#039;Elettrometro, intantochè il medesimo riceve <lb></lb>da un lato o per di sotto l&#039;elettricità, sia da una boccia di Leyden, sia da <lb></lb>un&#039;altra sorgente qualunque. </s>

<s>Infine ritirata la boccia, o qualsiasi il corpo <lb></lb>elettrizzante dal contatto del piattello, ne levo via anche la mano coperta <lb></lb>dal suo guanto con prestezza (giacchè la prestezza contribuisce molto al buon <lb></lb>successo) e allora veggio i pendolini balzare con vivacità, e prendere quelle <lb></lb>divergenze, che l&#039;elettricità condensata nel piattello, di cui sono dipendenze, <lb></lb>può loro dare ” (ivi, pag. </s>

<s>49-51). </s></p><p type="main">

<s>Era l&#039;Agosto del 1787, nel qual tempo il Volta scriveva la prima delle <lb></lb>sue Lettere meteorologiche al Lichtenberg, d&#039;onde abbiamo trascritte que­<lb></lb>ste parole, quando il Tralles di Amburgo, professore di Fisica a Berna, pas­<lb></lb>sando per Como, andò a far visita a Colui, ch&#039;era già la gloria della piccola <lb></lb>e illustre città lombarda. </s>

<s>Per intrattenere e onorare l&#039;ospite suo, il grande <lb></lb>Fisico comasco gli mise innanzi il suo Elettrometro condensatore, a vedere <lb></lb>e a sentir dire del quale il Tralles soggiunse che pensava anch&#039;egli, da <lb></lb><gap></gap> a costruire un simile delicatissimo strumento, sostituendo, <pb xlink:href="020/01/501.jpg" pagenum="482"></pb>ai fili metallici e alle stesse pagliette, due peli di qualche animale che gli <lb></lb>abbia finissimi o due capelli. </s>

<s>Tacque il Volta, per gentilezza a quella pro­<lb></lb>posta, ma pensava fra sè che l&#039;invenzione dell&#039;Amburghese non sarebbe per <lb></lb>riuscire, perchè, oltre alla difficoltà di mantenere que&#039;due capelli diritti, son <lb></lb>essi piuttosto coibenti che conduttori, ond&#039;è che a stento riceverebbero e <lb></lb>perderebbero l&#039;elettricità, massimamente trattandosi di quella così tenue, a <lb></lb>rivelar la quale sono ordinati gli Elettroscopi. </s></p><p type="main">

<s>Pure, aveva il Tralles, con quella sua proposta, fatto ravvedere il Volta <lb></lb>della poca squisitezza di quelle sue pagliette, anch&#039;esse non leggerissime, <lb></lb>nè così perfette conduttrici, per cui vide conveniente pensare a eleggere <lb></lb>qualche altro corpo elettroscopico, che rendesse anche più geloso che mai, <lb></lb>il suo geloso strumento. </s></p><p type="main">

<s>Si trovava dunque l&#039;Inventor dell&#039;Elettroscopio a pagliette, sopra pen­<lb></lb>siero di ciò, quando nel Settembre di quell&#039;anno 1787 essendo andato a Gi­<lb></lb>nevra, s&#039;incontrò col Zimmermann, il quale fu il primo a dargli la notizia <lb></lb>che il Bennet inglese aveva eletto per corpi elettroscopici due listerelle di <lb></lb>foglia d&#039;oro, e n&#039;avea così felicemente composto un Elettroscopio di tanto <lb></lb>prodigiosa sensibilità, da dar manifesti segnali elettrici, a pure alitar sul <lb></lb>cappelletto metallico di lui col fiato della bocca. </s>

<s>Finalmente nell&#039;Aprile del­<lb></lb>l&#039;anno 1788 pervenne alle mani del Volta la terza edizione dell&#039;<emph type="italics"></emph>Essay on <lb></lb>Electricity<emph.end type="italics"></emph.end> dell&#039;Adams, pubblicato sulla fine dell&#039;anno avanti, dove trovò, <lb></lb>in un supplemento al libro, la descrizione del nuovo Elettroscopio a fogliette <lb></lb>d&#039;oro, e di molte curiose osservazioni che il Bennet aveva fatte con esso. </s>

<s><lb></lb>Così il Fisico inglese venne a togliere la preoccupazione al Volta, e por­<lb></lb>gendogli in mano quel ch&#039;egli cercava, concorse efficacemente a render, <lb></lb>quanto mai si potesse desiderar, sensibile l&#039;Elettrometro condensatore. </s></p><p type="main">

<s>Tali furono i progressi fatti dal primo Elettroscopio a boccetta di Ti­<lb></lb>berio Cavallo, ma lo stesso Volta, che andava predicando l&#039;Elettrometro a <lb></lb>quadrante dell&#039;Henley <emph type="italics"></emph>per il migliore di quanti elettrometri si fossero im­<lb></lb>maginati<emph.end type="italics"></emph.end> (Op. </s>

<s>I, pag. </s>

<s>251), rivolse anche intorno a questo strumento i suoi <lb></lb>studi, lo migliorò assai, e, che più importa, lo rese comparabile con gli altri. </s></p><p type="main">

<s>L&#039;Elettrometro henleiano, è noto che consiste in un pendolo leggeris­<lb></lb>simo imperniato al centro di un quadrante affisso a un&#039;asticella metallica <lb></lb>elettrizzata per comunicazione. </s>

<s>La virtù repulsiva, che intercede fra il pen­<lb></lb>dolo e l&#039;asta, è che fa sollevare il pendolo stesso, e i vari gradi segnati sul <lb></lb>quadrante misurano la varia intensità di quella forza, e perciò della carica <lb></lb>elettrica. </s>

<s>Or qui sembrerebbe che dovesse lo strumento elettrico soggiacere <lb></lb>alle leggi meccaniche, conforme alle quali i pesi penduli, via via che si sol­<lb></lb>levano, non crescono a proporzione degli angoli di elevazione, ma sì a pro­<lb></lb>porzione de&#039;seni degli angoli, cosicchè, per esempio, se per sollevare il pen­<lb></lb>dolo all&#039;altezza di un grado, ci vuole una data forza, per sollevarlo all&#039;altezza <lb></lb>di due gradi non basta una forza precisamente doppia, ma se ne richiede <lb></lb>una alquanto maggiore. </s></p><p type="main">

<s>Applicando questa teoria al pendolo dell&#039;Henley, i numeri del quadrante <pb xlink:href="020/01/502.jpg" pagenum="483"></pb>che vanno in progressione aritmetica, non potrebbero ridursi a misurare il <lb></lb>proporzionato crescere dell&#039;intensità elettrica essendo che una intensità dop­<lb></lb>pia non possa aver virtù di sollevare il pendolo a un&#039;altezza doppìa, ma al­<lb></lb>cun poco minore. </s></p><p type="main">

<s>Studiandosi il Volta di comparare l&#039;Elettrometro a quadrante con l&#039;Elet­<lb></lb>trometro a pagliette, restò sorpreso da maraviglia, ritrovando che, almeno <lb></lb>dentro i limiti compresi fra i 10 e i 40 gradi, il pendolo elettrico, sottraen­<lb></lb>dosi alle leggi del pendolo meccanico, cresceva di peso a proporzion, non <lb></lb>de&#039;seni, ma degli angoli di elevazione, cosicchè veramente l&#039;intensità elet­<lb></lb>trica, la quale portava il pendolo a 30 gradi, era il doppio più potente di <lb></lb>quella che lo portava a 15. Al di sotto dei 10 gradi e al di sopra dei qua­<lb></lb>ranta, trovò che il pendolo elettrico si conformava più d&#039;appresso col pen­<lb></lb>dolo meccanico, e così, a rendere utile questo strumento e comparabile con <lb></lb>gli altri, ebbe a costruire alcune Tavole di correzione, delle quali così scri­<lb></lb>veva: “ Dirò .... per puro amore del vero che io mostrava già questo Qua­<lb></lb>drante elettrometro perfezionato a un buon segno fin dall&#039;anno 1781, e al <lb></lb>principio del 1784 anche la comparabilità de&#039;suoi gradi dentro i limiti as­<lb></lb>segnati (Op., T. I, P. II, pag. </s>

<s>36). </s></p><p type="main">

<s>A ripensar quali sollecite cure si dava il Volta di ridurre l&#039;Elettrosco­<lb></lb>pio a boccetta alle sue ultime perfezioni, e a render utile colle Tavole di <lb></lb>correzione l&#039;Elettrometro a quadrante, si sarebbe detto allora che quelle <lb></lb>cure forse eran superflue, e che non meritava il conto che un genio di tal <lb></lb>fatta s&#039;occupasse di tali minuzie. </s>

<s>Ma presentiva bene quel genio come così <lb></lb>fatte spregevoli minuzie, spese nell&#039;apparecchiarsi i più squisiti Elettrome­<lb></lb>tri, gli avrebbero raffinato il senso a discerner la generazione elettrica da <lb></lb>un tal concorso di cause tanto straordinario, che ne sarebbe stupito il mondo <lb></lb>intiero. </s>

<s>Stupito a veder due metalli, venuti a filosofico contatto, fremere <lb></lb>negli spiriti della vita e coruscare di luce. </s></p><p type="main">

<s>Come l&#039;umile e paziente perfezionatore degli Elettrometri meritasse di <lb></lb>venire esaltato alla gloria d&#039;essere egli il primo ad annunziare al mondo <lb></lb>un tale e tanto miracolo, è ciò che a noi resta a narrare. </s>

<s>Ma perchè ora­<lb></lb>mai l&#039;Italia, concorsa tardi a coltivare gli studi elettrici, dovea mostrare che <lb></lb>ciò non era un sonno inerte, ma un riposo ristoratore di forze; la scoperta <lb></lb>del moto elettrico generato dal contatto de&#039;metalli dovea esser preceduta e <lb></lb>occasionata dall&#039;altra grande scoperta della generazione del moto elettrico <lb></lb>dai muscoli degli animali. </s>

<s>Le garrule abitatrici delle paludi, che immolate <lb></lb>da Marcello Malpighi sull&#039;altare di Minerva in Bologna, rivelarono agli oc­<lb></lb>chi del Filosofo, per la prima volta, il circolo del sangue nel giro univer­<lb></lb>sale de&#039;vasi; le medesime, immolate pure in Bologna da Luigi Galvani, ri­<lb></lb>velarono per la prima volta agli occhi del Filosofo come circolassero per le <lb></lb>loro membra gli occulti spiriti della vita. </s>

<s>Il nuovo sagrificio immolato nel <lb></lb>Tempio della scienza, merita di esser così fedelmente descritto nelle parti­<lb></lb>colarità de&#039;suoi riti, che noi ci sentiamo accesi di sdegno contro alcuni scrit­<lb></lb><gap></gap> Quegli scrittori, per buona ventura, <pb xlink:href="020/01/503.jpg" pagenum="484"></pb>non sono italiani, ma non è già che gli stessi italiani si sien mostrati sol­<lb></lb>leciti e diligenti di saper la storia sincera di un fatto, che forma una delle <lb></lb>principali glorie scientifiche della loro nazione. </s>

<s>Per essi invano Luigi Gal­<lb></lb>vani scriveva: “ Operae itaque pretium facturum me esse existimavi, si bre­<lb></lb>vem et accuratam inventorum historiam afferrem eo ordine, et ratione, qua <lb></lb>mihi illam partim casus, et fortuna obtulit, partim industria et diligentia <lb></lb>detexit ” (De virib. </s>

<s>electr., Mutinae 1792, pag. </s>

<s>1), imperocchè, tutt&#039;altro che <lb></lb>ascoltar ciò che delle sue scoperte riferisce l&#039;Autore, alterano i fatti colle <lb></lb>loro arguzie, o li fingono coi loro cervelli. </s></p><p type="main">

<s>Noi perciò, volendo raccontar la storia genuina di que&#039;fatti, crediamo <lb></lb>per sincerità e per riverenza, di dover cedere la nostra parte al Galvani, il <lb></lb>quale non isdegnerà di tornare a dire delle sue scoperte e l&#039;ordine e la ra­<lb></lb>gione colla sua propria bocca. </s>

<s>Narrerà, per esser breve, la nuda storia, ta­<lb></lb>cendo le prolisse digressioni ch&#039;ei fa nel suo Commentario <emph type="italics"></emph>De viribus electri­<lb></lb>citatis,<emph.end type="italics"></emph.end> e, per minor tedio e fatica di chi ascolta, renderà il suo latino in <lb></lb>schietta favella italiana. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>“ Dissecai una rana e la scorticai, ponendole a nudo i muscoli e gli <lb></lb>interni nervi erurali, e la tenevo, così preparata, non molto distante dal con­<lb></lb>duttore della Macchina elettrica, mentre, a uno di coloro che mi aiutavano <lb></lb>nelle esperienze, vien per caso toccato leggermente un nervo colla punta di <lb></lb>uno scarpello: vede a un tratto contrarsi i muscoli della rana, come se fos­<lb></lb>sero presi da toniche convulsioni. </s>

<s>A un altro di coloro, che mi stavano più <lb></lb>d&#039;appresso, mentr&#039;io tentavo nuove elettriche esperienze, parve d&#039;avere os­<lb></lb>servato che le rane si contraevano nell&#039;atto stesso, che dalla Macchina si <lb></lb>faceva scoccare una scintilla. </s>

<s>Maravigliato del fatto ne fece avvertito me, che <lb></lb>a tutt&#039;altro pensavo, ond&#039;io mi rivolsi con incredibile studio a ripetere quelle <lb></lb>stesse esperienze, per veder ciò che sarebbe di lì per uscirne di nuovo. </s>

<s>Ac­<lb></lb>costai la punta dello scarpello ora all&#039;uno ora all&#039;altro de&#039;nervi crurali, <lb></lb>nell&#039;atto che un di coloro che v&#039;erano presenti provocava una scintilla, ed <lb></lb>ecco rinnovarsi i medesimi spettacoli: i muscoli si mettevano in convulsione, <lb></lb>quasi gli dibattesse il tetano. </s>

<s>” </s></p><p type="main">

<s>“ Mi nacque allora un sospetto: sarebb&#039;egli mai che, no dalla scintilla <lb></lb>nascesse lo stimolo, ma dal confricare colla punta dello scarpello? </s>

<s>provo a <lb></lb>pungere i nervi, mentre la Macchina è in quiete, ma la rana non si muove. </s>

<s><lb></lb>Di qui ebbi a concludere che due cause concorrevano insieme in quel fatto: <lb></lb>il toccamento del ferro, e lo scocco della scintilla. </s>

<s>Ripetendo però l&#039;espe­<lb></lb>rienza restai maravigliato dal veder come, concorrendo le due dette cause, <lb></lb>non perciò sempre infallibile ne seguiva l&#039;effetto. </s>

<s>Tenta e ritenta, per isco­<lb></lb>prir qual di questa novità ne fosse la cagione, finalmente trovai che tutto <pb xlink:href="020/01/504.jpg" pagenum="485"></pb>dipendeva dalle parti componenti lo scarpello, il quale aveva il manico d&#039;osso. </s>

<s><lb></lb>Se la mano lo impugnava, senza nulla toccar del ferro, lo spettacolo non si <lb></lb>vedeva, e scintillasse pure la Macchina, e se le avvicinasse meglio la rana. </s>

<s><lb></lb>Ripensando allora che l&#039;osso è un coibente, conclusi che il toccamento del <lb></lb>nervo voleva esser fatto da un corpo conduttore, in che venne a confer­<lb></lb>marmi il veder che i muscoli rimanevano immoti a toccarli con una bac­<lb></lb>chetta di vetro. </s>

<s>A quel conduttore poi, che è condizione così essenziale al <lb></lb>buon successo, mi piacque di applicargli il nome di <emph type="italics"></emph>conduttore de&#039;nervi ”<emph.end type="italics"></emph.end><lb></lb>(Comment. </s>

<s>cit., Pars I, pag. </s>

<s>2-4). </s></p><p type="main">

<s>“ Scoperte le cose, che vi ho narrate fin qui, intorno alla virtù del­<lb></lb>l&#039;elettricità artificiale sopra le contrazioni muscolari, mi rimaneva a investi­<lb></lb>gare se i medesimi spettacoli fossero offerti dall&#039;elettricità naturale ammo­<lb></lb>sferica; mi restava a veder cioè se seguiva colla folgore quel ch&#039;io avevo <lb></lb>sperimentato colla scintilla. </s>

<s>Perciò, eretto sul comignolo della mia casa un <lb></lb>palo di ferro, bene isolato, all&#039;appressarsi della tempesta ne appendevo al <lb></lb>conduttore, pe&#039;nervi, le rane preparate, o le gambe di qualche animale a <lb></lb>sangue caldo. </s>

<s>Le cose avvennero secondo i miei desiderii: il coruscar delle <lb></lb>folgori metteva i muscoli nelle solite convulsioni. </s>

<s>E non già le folgori sole <lb></lb>eccitavano così fatti moti convulsi, ma, imperversando il cielo, gli eccitavano <lb></lb>gli stessi nuvoloni non molto al di sopra della punta del conduttore ondeg­<lb></lb>gianti ” (Comment. </s>

<s>cit., Pars II, pag. </s>

<s>14, 15). </s></p><p type="main">

<s>“ Degli effetti dell&#039;elettricità, per così dir, procellosa, e de&#039;consensi di <lb></lb>lei coll&#039;artificiale, oramai m&#039;ero così assicurato per ogni parte, ma perchè <lb></lb>la sete della scienza accende nuova sete, volli fare esperienza anche del­<lb></lb>l&#039;elettricità placida a ciel sereno. </s>

<s>” </s></p><p type="main">

<s>“ Son le finestre della mia casa circondate da un terrazzo, dov&#039;io vi <lb></lb>tengo sopra posati vasi con pianticelle, che mi rallegrino col loro verde e <lb></lb>co&#039;fiori. </s>

<s>Tenendo attaccate le rane con uncini di rame, infissi nella midolla <lb></lb>spinale, alla ringhiera di ferro di quel mio o giardino pensile o terrazzo che <lb></lb>vogliate chiamarlo, le avevo qualche volta vedute contrarsi, anco a ciel se­<lb></lb>reno, e ciò fu che venne ad accendermi quella sete, che ho detto. </s>

<s>Sto per <lb></lb>parecchie ore a guardare, seguito per molti giorni, e aspetta, aspetta non <lb></lb>si vede nulla di nuovo. </s>

<s>Finalmente, per riposarmi della stanchezza del lungo <lb></lb>osservare, incomincio a pigiar que&#039;fili di rame, da cui pendevano le rane <lb></lb>attaccate, e a stropicciarli contro il ferro della ringhiera, per veder se nulla <lb></lb>ne nasceva di nuovo, e non di rado qualche guizzo ne&#039;muscoli lo vedevo, <lb></lb>ma però indipendente affatto dallo stato elettrico dell&#039;ammosfera. </s>

<s>” </s></p><p type="main">

<s>“ Siccome io non avevo veduto mai que&#039;moti convulsi, altro che all&#039;aria <lb></lb>aperta, e altrove non avevo ancora sperimentato, poco ci corse ch&#039;io non <lb></lb>dicessi esser l&#039;elettricità ammosferica, penetrata nell&#039;animale, che, al toc­<lb></lb>carsi dell&#039;uncino di rame col ferro della ringhiera, esce fuori, e in uscire <lb></lb>commove i muscoli. </s>

<s>Tanto è facile ingannarsi nelle esperienze, e immagi­<lb></lb>narsi di aver veduto e trovato ciò che s&#039;immaginava di vedere e di tro­<lb></lb>vare! Ma trasportata la rana in una camera chiusa, e collocata sopra una <pb xlink:href="020/01/505.jpg" pagenum="486"></pb>lamiera di ferro, vi pigio contro quell&#039;uncino di rame .... oh! ecco le me­<lb></lb>desime contrazioni, i medesimi moti. </s>

<s>Muto stanza, muto metalli, provo in <lb></lb>altre ore, provo in altri giorni, e vedo sempre le medesime cose, colla sola <lb></lb>differenza che alcuni metalli eccitavano le convulsioni più languide, altri più <lb></lb>veementi. </s>

<s>” </s></p><p type="main">

<s>“ Potete figurarvi che questi fatti ridestarono in me una grande am­<lb></lb>mirazione, e fu allora che incominciò a entrarmi il sospetto di un&#039;elettricità <lb></lb>inerente allo stesso animale. </s>

<s>Mi pareva di veder quella elettricità da&#039;nervi <lb></lb>ritornare ai muscoli, come, fra le armature e il conduttore della Bottiglia <lb></lb>di Leyda, si avverte. </s>

<s>Venne a confermarmi in questa persuasione l&#039;espe­<lb></lb>rienza, ch&#039;io vi dirò. </s>

<s>Tenevo una rana preparata al solito modo per l&#039;un­<lb></lb>cino, a cui l&#039;avevo infilata, e le facevo toccar colle gambe il piano di un <lb></lb>piattello d&#039;argento. </s>

<s>Poi, con una verga di metallo, tenuta nell&#039;altra mano, <lb></lb>toccavo gli orli dello stesso piattello, e vedevo, oltre alla mia speranza, quelle <lb></lb>gambe contrarsi, e sempre far lo stesso ogni volta ch&#039;io tornavo a ripetere <lb></lb>il gioco. </s>

<s>” </s></p><p type="main">

<s>“ Avendo avvertito già queste cose, mi trovavo a villeggiare appresso <lb></lb>quel nobilissimo uomo, che è il signor Giacomo Zambeccari, insiem con <lb></lb>un dottissimo spagnolo, appartenuto un tempo alla compagnia di Gesù, <lb></lb>di cognome Rialpo, il quale, poichè dilettavasi delle mie esperienze, pregai <lb></lb>che teness&#039;egli la rana per l&#039;uncino ed io avrei toccato l&#039;orlo del piattello <lb></lb>di argento. </s>

<s>Ma le contrazioni muscolari sparirono. </s>

<s>Ripeto come prima l&#039;espe­<lb></lb>rienza da me solo, e subito ritornarono. </s>

<s>Da ciò fui indotto a tener io so­<lb></lb>speso l&#039;uncino, e coll&#039;altra prendere per la destra il Rialpo, pregandolo a <lb></lb>toccar colla sinistra libera il piattello. </s>

<s>Che piacere per noi, in veder che, a <lb></lb>lasciarsi e a tenersi per la mano, si poteva ora far posar quelle gambe, e <lb></lb>ora nuovamente metterle in danza! ” </s></p><p type="main">

<s>“ Benchè mi paresse venir così dimostrato assai bene il circolo elet­<lb></lb>trico del fluido nerveo attraverso alla catena delle nostre mani, è nulladi­<lb></lb>meno la cosa tanto nuova e di tanta importanza, che non volli trascurare <lb></lb>di confermarla anche in altra maniera. </s>

<s>La catena si chiudeva, fra le mani <lb></lb>mie e quelle del Rialpo, ora interpostavi una bacchetta di vetro e ora una <lb></lb>verga di metallo, e s&#039;accrebbe in noi il piacere in veder che col metallo <lb></lb>uscivano dalle membra della rana i soliti moti, e col vetro restavano rin­<lb></lb>tuzzati ” (Comment. </s>

<s>cit., Pars III, pag. </s>

<s>16-18). </s></p><p type="main">

<s>“ Or da tutte queste esperienze mi pareva ne resultasse chiaro e di­<lb></lb>mostrato ricircolare per le membra degli animali un fluido, che sia a me, <lb></lb>come fu ad altri, lecito appellar col nome di <emph type="italics"></emph>Elettricità animale.<emph.end type="italics"></emph.end> Una tale <lb></lb>elettricità, senza dubbio, diffusa per tutte quante le membra, par che abbia <lb></lb>la sua propria sede ne&#039;muscoli e ne&#039;nervi, da quelli trapassando a questi, <lb></lb>attraverso a un arco metallico o a una catena di uomini, o di qualunque <lb></lb>altra sorta di corpi deferenti ” (Comment. </s>

<s>cit., Pars IV, pag. </s>

<s>38, 39). </s></p><p type="main">

<s>Questa storia e le particolari esperienze, che concorrevano ad illustrarla, <lb></lb>il Galvani la fece nota al pubblico, in un libretto in 4°, di 58 nagine stam-<pb xlink:href="020/01/506.jpg" pagenum="487"></pb>pato a Bologna nel 1791. Una copia fu dallo stesso Autore, mandata in dono <lb></lb>a Bassiano Carminati, professore nell&#039;Università di Pavia, dove aveva amici <lb></lb>e colleghi il Barletti, il Rezia, il Malacarne, e sovraeminenti a tutti lo Spal­<lb></lb>lanzani e il Volta. </s>

<s>A quest&#039;ultimo celebre oramai per le sue scoperte elet­<lb></lb>triche e per le sue invenzioni, dop&#039;averlo letto, mostrò il Carminati il Com­<lb></lb>mentario <emph type="italics"></emph>De viribus electricitatis<emph.end type="italics"></emph.end> inviatogli da Bologna. </s>

<s>Qual effetto producesse <lb></lb>nell&#039;animo e nell&#039;ingegno del Volta quella lettura, è bene ascoltarlo da lui <lb></lb>medesimo, il quale così ne scriveva: </s></p><p type="main">

<s>“ Una scoperta di questa fatta non poteva che eccitare grande entusia­<lb></lb>smo da per tutto, ove ne pervenne la notizia, e massime tra noi, essendo <lb></lb>di un nostro Italiano. </s>

<s>Ed ecco che molti si fecero a gara a ripetere le espe­<lb></lb>rienze. </s>

<s>Io fui il primo qui a Pavia eccitato da varii miei Colleghi, partico­<lb></lb>larmente da Carminati, che cortesemente prestommi la Dissertazione di Gal­<lb></lb>vani, e da Rezia, che mi favorì dell&#039;opera ed aiuto suo nelle preparazioni; <lb></lb>e il primo fui anche a Milano non molti giorni dopo, cioè verso il fine di <lb></lb>Quaresima. </s>

<s>Debbo però confessare che, incredulo e con non molta speranza <lb></lb>di buon successo, mi ridussi a fare le prime prove, tanto sorprendenti pa­<lb></lb>revanmi i descritti fenomeni, e se non contrarii, superiori troppo a tutto <lb></lb>quello che dell&#039;elettricità ci era noto, talchè mi avevano del prodigioso. </s>

<s>Della <lb></lb>quale incredulità mia e quasi ostinazione, non che mi vergogni, domando <lb></lb>perdono all&#039;Autore della scoperta, cui mi fo altrettanto maggior premura e <lb></lb>gloria di esaltare, ora che ho veduto e toccato con mano, quanto fui diffi­<lb></lb>cile a credere, prima di toccare e di vedere. </s>

<s>Infine eccomi convertito, dac­<lb></lb>chè cominciai ad essere testimonio oculare e operatore io stesso dei mira­<lb></lb>coli, e passato forse dall&#039;incredulità al fanatismo ” (Op. </s>

<s>cit., T. II, P. I, <lb></lb>pag. </s>

<s>35, 36). </s></p><p type="main">

<s>Verificate ch&#039;ebbe il Volta le principali esperienze galvaniche, come <lb></lb>quegli che si sentiva un grande ardore di promoverle, si dette tutto a ri­<lb></lb>cercare la qualità, la quantità e il modo di quella nuova elettricità propria <lb></lb>degli organi animali. </s>

<s>Da così fatte delicatissime ricerche, nelle quali ottima­<lb></lb>mente lo servì quel suo squisito Elettrometro condensatore, concludeva che <lb></lb>un elettricità molto debole era sufficiente ad eccitar nelle rane, per le mem­<lb></lb>bra, non solo piccoli moti, ma gagliardissime convulsioni; ond&#039;è che quegli <lb></lb>animaletti, così preparati a modo del Galvani, si presentavano all&#039;osserva­<lb></lb>tore sotto l&#039;aspetto di <emph type="italics"></emph>Elettrometri naturali,<emph.end type="italics"></emph.end> molto più sensibili degli stessi <lb></lb>Elettrometri artificiali. </s></p><p type="main">

<s>In questa rassomiglianza s&#039;includeva, tuttavia latente allo stesso Volta, <lb></lb>il principio che, di discorso in discorso, l&#039;avrebbe presto condotto a dissen­<lb></lb>tir dal Galvani. </s>

<s>Nonostante approvando per ora la scoperta dell&#039;elettricità <lb></lb>animale, e accettando la somiglianza tra la scarica muscolare e la scarica <lb></lb>della Bottiglia di Leyda, si contentava di notar che l&#039;insigne scopritore aveva <lb></lb>errato intorno a qualificar l&#039;elettricità propria a ciascuna parte dell&#039;organo <lb></lb>elettrico animale, e intorno al modo proprio della scarica. </s>

<s>Diceva infatti il <lb></lb>bolognese Autore del Commentario che, rappresentando due muscoli o due <pb xlink:href="020/01/507.jpg" pagenum="488"></pb>fibre muscolari a contatto le due armature della Bottiglia, e il nervo o le <lb></lb>fibrille nervee inserite nel loro mezzo, rappresentando il conduttore della <lb></lb>stessa Bottiglia; la scarica si faceva dal nervo al muscolo, cioè dal di den­<lb></lb>tro al di fuori. </s>

<s>Così venendosi ad ammettere che l&#039;influsso nerveo non mo­<lb></lb>vesse dal cervello, ma fosse diretto verso il cervello, riusciva difficilissimo <lb></lb>al Galvani il render la ragione dei moti volontarii. </s>

<s>Egli si trovò costretto in <lb></lb>fatti ad ammettere che l&#039;anima operi, non forse direttamente sopra il cer­<lb></lb>vello, ma “ ut proclivius est credere aut extra idem .... aut a membranis, <lb></lb>aut a contiguis aliis deferentibus partibus, per easque, ceu per arcum, ad­<lb></lb>musculum a quo discessit restituatur, ut nempe iuxta aequilibrii legem ad <lb></lb>negative muscularium fibrarum electricam partem ea copia tandem confluat, <lb></lb>qua a positive electrica earumdem parte per impulsum in nervo, ut opinari <lb></lb>placuit, antea effluxerit ” (Comment. </s>

<s>cit., pag. </s>

<s>53). </s></p><p type="main">

<s>Il Volta dunque trovò sperimentando che il fluido elettrico trascorre <lb></lb>nelle membra della rana, non già dal nervo al muscolo, come opinava il <lb></lb>Galvani, ma sì dal muscolo al nervo, ossia dal dl fuori al di dentro, o al­<lb></lb>trimenti, non dal nervo al cerebro, ma dal cerebro al nervo. </s>

<s>“ Or se, col <lb></lb>ministero del fluido elettrico, operansi anche nell&#039;animale vivo ed intiero le <lb></lb>contrazioni e moti volontarii de&#039;muscoli, come tutto ne porta a credere, e <lb></lb>se, come dee pure presumersi, operansi questi nel modo più facile, si farà <lb></lb>ciò collo spingere giù dal cerebro pe&#039;nervi il detto fluido verso i muscoli, <lb></lb>bastando allora una minima forza, anzichè col tirarlo in sù ” (Op. </s>

<s>cit., T. II, <lb></lb>P. I, pag. </s>

<s>42). E tanto sentivasi ancora alieno dal dissentire, che immediata­<lb></lb>mente soggiunge: “ sebbene possano anche in questo modo effettuarsi i me­<lb></lb>desimi moti, sol che s&#039;impieghi maggior forza, cioè determinarsi una cor­<lb></lb>rente più rapida e più copiosa di fluido elettrico ” (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Di ciò che aveva con grande esaltazione di animo approvato, e con gran <lb></lb>remissione riprovato intorno alle grandi scoperte di Fisiologia elettrica, de­<lb></lb>scritte nel Commentario suo dal Galvani; il Volta ne riferiva a Giuseppe <lb></lb>Baronio, con Lettera data da Milano il dì 3 Aprile 1792 (ivi, pag. </s>

<s>3-10). In <lb></lb>quel medesimo giorno, da Pavia, il Carminati, che fino allora aveva taciuto, <lb></lb>scriveva a Bologna ringraziando l&#039;amico del dono fattogli della <emph type="italics"></emph>Dissertazione <lb></lb>contenente l&#039;originale bellissima scoperta dell&#039;Elettricità naturale e spon­<lb></lb>tanea degli animali,<emph.end type="italics"></emph.end> adducendo, per iscusa dell&#039;indugio, il desiderio che <lb></lb>aveva vivissimo d&#039;informarlo di quel tanto, che v&#039;aveva il Volta gustato di <lb></lb>vero, e di quel pochissimo che vi aveva sospettato di falso. </s></p><p type="main">

<s>Più di un mese appresso, il dì 8 Maggio, il Galvani rispondeva com­<lb></lb>piacendosi, non solo in sentir che il Volta aveva confermate le sue scoperte, <lb></lb>ma in pensare altresì che l&#039;avere egli trovata la vera direzione del flusso <lb></lb>nerveo rendeva applicabili quelle stesse scoperte alla teoria de&#039;moti volon­<lb></lb>tarii. </s>

<s>“ Infatti gli esperimenti di lui chiaro dimostrerebbono potersi avere i <lb></lb>moti muscolari diretto il fluido elettrico non solo dal muscolo al nervo, sic­<lb></lb>come io supponeva, ma eziandio dal nervo al muscolo, ossia dal cervello al <lb></lb>muscolo, e potersi avere non solo per <gap></gap><pb xlink:href="020/01/508.jpg" pagenum="489"></pb>una sopraccarica forzata ed impetuosa della supposta boccia muscolare: lo <lb></lb>che ammesso, chi non vede quanto riesca felice la spiegazione de&#039;moti mu­<lb></lb>scolari volontarii? </s>

<s>” (Lett. </s>

<s>aggiunte al Comment. </s>

<s>cit., pag. </s>

<s>74). </s></p><p type="main">

<s>Si diceva dianzi che l&#039;avere il Volta rassomigliato a un Elettrometro <lb></lb>de&#039;più gelosi le rane preparate a modo del Galvani, lasciate cioè attaccate <lb></lb>le loro gambe per i nervi erurali diligentemente snudati, ed infisso uno <lb></lb>spillo od altro uncinetto metallico nell&#039;asse spinale; conteneva il germe delle <lb></lb>future contradizioni. </s>

<s>Presto infatti, rimesso il fervore di quelle prime esal­<lb></lb>tazioni, incominciò il Volta a riflettere maravigliato “ come mai una forza <lb></lb>elettrica inconcepibilmente piccola.... una carica così esile, che non muove <lb></lb>punto neppure il sommamente delicato Elettroscopio del Bennet, ... basta <lb></lb>a convellere le gambe della rana preparata nel modo indicato ” (Op. </s>

<s>cit., <lb></lb>T. II, P. I, pag. </s>

<s>79). Par che la Natura, egli poco appresso soggiunge, ab­<lb></lb>bia dotato di tale e tanta sensibilità i nervi, di tale e tanta irritabilità i mu­<lb></lb>scoli, che una forza elettrica impercettibile basti ad eccitare i moti musco­<lb></lb>lari (ivi, pag. </s>

<s>80). Di qui sentesi scoppiar dalla mente il dubbio, e non <lb></lb>reggendo a reprimerlo, esce nelle parole seguenti: “ Ma che? </s>

<s>sarà dunque <lb></lb>sopra i nervi e non sopra i muscoli che il fluido elettrico agisce <emph type="italics"></emph>immedia­<lb></lb>tamente,<emph.end type="italics"></emph.end> e la sua azione verrà limitata ad eccitar quella solamente, allorchè <lb></lb>movesi e trapassa per questo o quel membro dall&#039;animale con forza affatto <lb></lb>insensibile ai più squisiti Elettrometri? </s>

<s>Così appunto mi conducono a cre­<lb></lb>dere molte nuove esperienze che ho fatto, e che verrò tra poco esponendo, <lb></lb>cioè che il <emph type="italics"></emph>primario effetto<emph.end type="italics"></emph.end> del fluido elettrico così mosso consista nel met­<lb></lb>tere in gioco l&#039;<emph type="italics"></emph>azione nervosa,<emph.end type="italics"></emph.end> conseguenza della quale, anzi veri e propri <lb></lb>effetti della medesima sian poi i moti de&#039;<emph type="italics"></emph>muscoli volontari ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>81, 82). <lb></lb>Il principio della rivolta contro le teorie galvaniche oramai è proclamato: <lb></lb>Esaminate meglio le cose “ ho dovuto accorgermi alla fine, che assai più <lb></lb>limitato di quel che supponea Galvani, ed io con lui, egli è il gioco del <lb></lb>fluido elettrico negli organi animali, terminandosi la sua azione immediata <lb></lb>nei nervi ” (ivi, pag. </s>

<s>85). </s></p><p type="main">

<s>L&#039;esperienze, che condussero il Volta a riguardare i nervi, contro l&#039;opi­<lb></lb>nion del Galvani, come aventi la parte essenziale e primaria ne&#039;moti mu­<lb></lb>scolari, son varie, e rilevantissime per la novità e per l&#039;importanza. </s>

<s>Una di <lb></lb>queste consisteva nell&#039;applicare due listerelle di foglia metallica, una vicina <lb></lb>all&#039;estremità troncata, e l&#039;altra alcun poco sotto, nel nervo ischiatico di un <lb></lb>agnello, e nel mostrar che, facendo passare una debole scarica elettrica fra <lb></lb>le due listerelle, la gamba dibattevasi tutta quanta, benchè fosse chiaro che <lb></lb>la detta scarica non vi potesse giungere a un pezzo per la sua debolezza ” <lb></lb>(ivi, pag. </s>

<s>87). </s></p><p type="main">

<s>Ma da&#039;nervi motori passando ai sensorii, mostrava il Volta stesso che <lb></lb>l&#039;elettricità, irritando direttamente i nervi, produce le sensazioni, con due <lb></lb>esperienze insigni. </s>

<s>Consisteva la prima nel riprodurre il gusto dell&#039;acidità <lb></lb>coll&#039;applicar sulla punta della lingua una lamina di stagno, e nel mezzo di <pb xlink:href="020/01/509.jpg" pagenum="490"></pb>cazione, per mezzo del manico di un cucchiaio (ivi, pag. </s>

<s>94). Consisteva la <lb></lb>seconda nell&#039;eccitare la sensazion della luce, applicando al bulbo dell&#039;occhio <lb></lb>l&#039;estremità di una listerella di foglia di stagno, messa al contatto del manico <lb></lb>di un cucchiaio tenuto in bocca (ivi, pag. </s>

<s>164) </s></p><p type="main">

<s>Nel fare la sopra citata esperienza, sul nervo ischiatico di un agnello, <lb></lb>notava il Volta che, al buon successo di lei, si richiedeva che le due arma­<lb></lb>ture fossero <emph type="italics"></emph>dissimili<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>89), e avvertiva come il fatto era stato pure <lb></lb>osservato dal Galvani come <emph type="italics"></emph>peculiare atque animadversione dignum.<emph.end type="italics"></emph.end> Ma, <lb></lb>benchè sia un fatto provato con esperienza diretta, non sa ancora intendere <lb></lb>il Volta, perchè quelle armature vogliano esser dissimili, nè sa pur conce­<lb></lb>pir troppo bene come si muova il fluido elettrico “ da un luogo all&#039;altro <lb></lb>così vicino dell&#039;istesso nervo, per la sola applicazione di quelle armature e <lb></lb>comunicazione esterna delle medesime ” (ivi). </s></p><p type="main">

<s>Esponeva così fatti dubbi il Volta nella Memoria seconda <emph type="italics"></emph>Sull&#039;Elettri­<lb></lb>cità animale,<emph.end type="italics"></emph.end> scritta nella primavera del 1792. Verso la fine di quell&#039;anno <lb></lb>i dubbi erano risoluti, le idee avevano oramai preso un indirizzo proprio, e <lb></lb>a quelle del Galvani affatto opposto. </s>

<s>Ha trovato che l&#039;Elettricità non è ec­<lb></lb>citata nè dai muscoli nè da&#039;nervi dell&#039;animale, ma dalle virtù dei metalli e <lb></lb>del carbone posti a contatto. </s>

<s>“ Etiam si tandem electricitas haec animalis <lb></lb>activa in organis, quam Galvanius tuetur, iterum evanescet, stabit tamen <lb></lb>incomparabilis ac miranda fibrarum, praecipue nervearum, excitabilitas, ope <lb></lb>stimuli electrici. </s>

<s>Ex altera quoque parte remanebit novum electricitatis ar­<lb></lb>tificialis principium, a me detectum, quod maximam huic seientiae lucem <lb></lb>afferre potest, nempe vis ac virtus metallorum et carbonis concitandi atque <lb></lb>pellendi fluidum electricum, ope simplicis contactus cum corporibus qui­<lb></lb>buslibet humidis, ac per hanc ipsorum qualitatem deferentibus, id quod <lb></lb>experimentis, extra corpora animalia institutis, confirmavi ” (ibi, pag. </s>

<s>173). </s></p><p type="main">

<s>Nel mentre che il Volta faceva divulgare la novità strepitosa di così <lb></lb>fatte dottrine, nel <emph type="italics"></emph>Giornale di Lipsia,<emph.end type="italics"></emph.end> Giovanni Aldini rendeva nuovamente <lb></lb>alla luce, in Modena, il Commentario <emph type="italics"></emph>De viribus electricitatis<emph.end type="italics"></emph.end> di suo zio, <lb></lb>premessavi un&#039;assai dotta ed elegante Dissertazione latina, ed illustrando il <lb></lb>testo, qua e là, con note erudite. </s>

<s>Una Lettera del dì 22 Ottobre, scritta <lb></lb>dallo stesso Aldini, avvisava il Volta che gli sarebbe stata trasmessa in Mi­<lb></lb>lano una copia del libro, che nel dì 24 Novembre non aveva avuto ancora <lb></lb>il recapito. </s>

<s>Perciò, chi ne stava in attesa, così scriveva: “ Questo libro non <lb></lb>mi è pervenuto ancora; ma ho potuto leggerlo per bontà del mio amico e <lb></lb>collega Ab. </s>

<s>Spellanzani, che me lo ha prestato, e molto piacere ho avuto <lb></lb>nello scorrere sì quelle note, che la Dissertazione sua, erudita non solo, ma <lb></lb>elegantemente scritta ” (ivi, pag. </s>

<s>177). </s></p><p type="main">

<s>Così fatte parole non passavano dal Volta all&#039;Aldini per lettera fami­<lb></lb>liare, ma per la pubblica stampa, in una scrittura che, sotto forma di epi­<lb></lb>stola, comprendeva la Memoria terza <emph type="italics"></emph>Sull&#039;Elettricità animale.<emph.end type="italics"></emph.end> L&#039;intenzione <lb></lb>precipua, che in iscriver questa terza Memoria si proponeva l&#039;Autore, era <lb></lb><gap></gap> o fa-<pb xlink:href="020/01/510.jpg" pagenum="491"></pb>ceva le viste per ora di non aver compreso quello spirito di rivolta contro <lb></lb>le teorie galvaniche, suscitato dall&#039;Autore della seconda Memoria. </s>

<s>Nella Dis­<lb></lb>sertazione infatti al Galvani, al § XXI, rivendicando al Sulzer l&#039;esperienza <lb></lb>del sapore acido eccitato sopra la lingua dalle due laminette metalliche po­<lb></lb>satevi sopra e ridotte al contatto; non dà l&#039;Aldini altro merito al Volta, da <lb></lb>quello in fuori dell&#039;avere spiegato il fatto curioso per l&#039;applicazione della <lb></lb>teoria elettrica animale. </s>

<s>“ Nervi scilicet deferentibus iuncti corporibus electri­<lb></lb>cum vaporem effundunt, qui si musculis ad quos contendit fuerit restitu­<lb></lb>tus, aut contractionem aut impressionem excitabit aliquam ” (Comment. </s>

<s>cit. </s>

<s><lb></lb>Dissert., pag. </s>

<s>XVIII). </s></p><p type="main">

<s>Il Volta restò sorpreso all&#039;intender che l&#039;esperienza de&#039;sapori metallici <lb></lb>l&#039;aveva fatta, 25 anni prima di lui, il Sulzer, quell&#039;amabile Filosofo sviz­<lb></lb>zero, e celebre Accademico di Berlino, che egli dice di aver conosciuto, e <lb></lb>di aver con esso lui anche familiarmente conversato (Op. </s>

<s>cit., T. II, P. II, <lb></lb>pag. </s>

<s>183). Ringraziando però l&#039;Aldini di avergli dato il primo questa noti­<lb></lb>zia, protesta energicamente che il suo raziocinio intorno alla ragion del fatto <lb></lb>sulzeriano è informato a tutt&#039;altri principii, da quelli ammessi già dal Gal­<lb></lb>vani. </s>

<s>“ No, non fu questo il mio raziocinio, nè tale potea essere, dacchè <lb></lb>considerando io le armature, ogni qual volta sono di due metalli diversi, non <lb></lb>più quai semplici conduttori, ma quai veri eccitatori e motori del fluido elet­<lb></lb>trico, teneva che <emph type="italics"></emph>passivi<emph.end type="italics"></emph.end> soltanto fossero gli organi animali e le parti loro <lb></lb>contigue o vicine a quelle armature dissimili: che niuna mossa cioè dessero <lb></lb>per sè stessi nè i nervi nè i muscoli al fluido elettrico, ma bene i metalli, <lb></lb>per propria virtù e forza spingendolo o tirandolo, e sì l&#039;uno più dell&#039;al­<lb></lb>tro, per essere di specie diversa, es. </s>

<s>gr. </s>

<s>stagno e argento, ne lo venissero a <lb></lb>togliere dal naturale equilibrio e riposo e a mettere in corso ” (ivi, pag. </s>

<s>187). </s></p><p type="main">

<s>A tali chiare proteste dovette l&#039;Aldini finalmente intendere, e dovettero <lb></lb>insiem con lui intendere tutti gli altri fautori del Galvani, i quali con ar­<lb></lb>gomenti nuovi e con nuove esperienze, seguitava il Volta a persuadere, che <lb></lb>la causa per cui si mettono in convulsione i muscoli consiste in una elet­<lb></lb>tricità, da doversi dir <emph type="italics"></emph>metallica<emph.end type="italics"></emph.end> e non <emph type="italics"></emph>animale<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>229). Che se alcuno <lb></lb>dopo l&#039;Aldini, pretendesse ancora di tirar le sue dottrine a consentire con <lb></lb>quelle del Galvani, egli esce fuori nella Lettera III ad Anton Maria Vassalli, <lb></lb>dichiarandosi con tali ragionamenti da bastare, egli dice, a mostrar “ quanto <lb></lb>sia diversa dalla pretesa Elettricità animale, dalle idee del Galvani e suoi <lb></lb>seguaci, quell&#039;Elettricità che sostengo io, la quale non suppone alcuna ca­<lb></lb>rica o sbilancio, e conseguente scarica degli organi animali, e neppure carica <lb></lb>o scarica propriamente detta de&#039;conduttori applicati; ma una circolazione, <lb></lb>ossia corrente continua di fluido elettrico, cagionata e mantenuta da una <lb></lb>forza arcana, che risulta dal combaciamento di conduttori diversi fra loro, i <lb></lb>quali in simili circostanze, sono qualche cosa più che semplici <emph type="italics"></emph>deferenti,<emph.end type="italics"></emph.end> fa­<lb></lb>cendola da veri <emph type="italics"></emph>conduttori<emph.end type="italics"></emph.end> e <emph type="italics"></emph>motori ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>234, n.). </s></p><p type="main">

<s>Chi altri mai, fuor del Volta, avrebbe potuto sperare di persuadere al <lb></lb><gap></gap> una cosa tanto straordinaria, <pb xlink:href="020/01/511.jpg" pagenum="492"></pb>qual&#039;era la virtù di <emph type="italics"></emph>mettere in corso<emph.end type="italics"></emph.end> o di far <emph type="italics"></emph>motori<emph.end type="italics"></emph.end> dell&#039;Elettricità due <lb></lb>metalli diversi, non per essere confricati, o riscaldati o per aver subito altri <lb></lb>più raffinati artifici, ma solamente per esser venuti insieme a misterioso <lb></lb>contatto! L&#039;Elettricità animale parve allo stesso Volta <emph type="italics"></emph>superiore troppo a <lb></lb>tutto quello che dell&#039;elettricità era noto,<emph.end type="italics"></emph.end> eppure, a ricever l&#039;annunzio di <lb></lb>quella scoperta, gl&#039;ingegni ci eran già preparati dalle idee del Newton, pro­<lb></lb>mosse fra noi dal Beccaria. </s>

<s>Ma a chi poteva mai venire in testa che la fa­<lb></lb>ticosa e intermittente elettricità eccitata dai macchinamenti del Ramsden, <lb></lb>s&#039;avesse a veder fluire, in facile corso e ricorso perpetuo, col solo soprapporre <lb></lb>una lamina, per esempio, di stagno, a un&#039;altra lamina d&#039;argento? </s>

<s>Questo sì <lb></lb>che pareva non <emph type="italics"></emph>superiore,<emph.end type="italics"></emph.end> ma <emph type="italics"></emph>contrario<emph.end type="italics"></emph.end> a ciò che dell&#039;Elettricità era noto, <lb></lb>eppur compiacente il Volta, nell&#039;Ottobre del 1795, incominciava la sopra <lb></lb>commemorata Lettera al Vassalli, dicendo che <emph type="italics"></emph>dalla maggior parte de&#039;Fisici, <lb></lb>massime oltramontani erano state adottate le sue opinioni<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>230). </s></p><p type="main">

<s>Quel nuovo e straordinario <emph type="italics"></emph>Elettromotore<emph.end type="italics"></emph.end> però, benchè fosse dimostrato <lb></lb>in tanti modi, e <emph type="italics"></emph>saltasse agli occhi dell&#039;Inventore da tante sue esperienze<emph.end type="italics"></emph.end><lb></lb>(ivi, pag. </s>

<s>215) era tuttavia in potenza, e penerà ancora cinque anni, prima <lb></lb>di venir fuori alla luce. </s>

<s>Come riuscisse al genio sperimentatore e specula­<lb></lb>tore del Volta di salir sulla soglia che apriva il secolo XIX, e di li sollevar <lb></lb>colla mano in alto la portentosa Lucerna, a illuminare le nuove vie, che <lb></lb>sarebbe per correre il mondo; è ciò che a noi resta a dire, per compimento <lb></lb>e termine di questa parte di storia. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La somma della teoria, che il Volta contrapponeva a quella del Gal­<lb></lb>vani, riducevasi a professar che l&#039;elettricità, mossa in perpetuo circolo da un <lb></lb>metallo all&#039;altro, attraverso ai conduttori costituiti dalle parti umide degli <lb></lb>animali, eccitasse i nervi e venisse, mediante questi, a commovere i muscoli. </s>

<s><lb></lb>Uno de&#039;primi e principali studi ordinati a illustrare così fatta teoria, e a <lb></lb>confermar la natura de&#039;nuovi Elettromotori, consisteva nel determinar la di­<lb></lb>rezione del circolo elettrico; il punto cioè della sua partenza, e il luogo del <lb></lb>suo ritorno. </s>

<s>L&#039;importante e delicata ricerca non riuscì molto difficile al Volta, <lb></lb>il quale si servì di quel medesimo artifizio, e di quello stesso strumento, di <lb></lb>che erasi già servito per determinare la direzione del circolo galvanico. </s>

<s>Pren­<lb></lb>deva due piastre di diverso metallo, per esempio una di rame e l&#039;altra di <lb></lb>zinco, e tenutele per un manico isolatore le applicava insieme, e separatele <lb></lb>nell&#039;istante faceva, prima all&#039;una poi all&#039;altra, toccar la pallina dell&#039;Elettro­<lb></lb>metro. </s>

<s>Così trovava che il zinco era elettrizzato in più, il rame in meno, <lb></lb>come riscontrava, accostando allo stesso Elettrometro un cannello di cera­<lb></lb>lacca, ond&#039;è che, in un Elettromotore composto de&#039;due sopra detti metalli, <lb></lb>concludeva essere il corso elettrico diretto dal zinco al rame. (Op. </s>

<s>cit., T. II, <lb></lb>P. II. pag. </s>

<s>155). </s></p><pb xlink:href="020/01/512.jpg" pagenum="493"></pb><p type="main">

<s>Così fatti studi e importantissime ricerche, nel 1793, erano già state <lb></lb>fatte: anzi, premessa la distinzione fra conduttori metallici o di prima classe, <lb></lb>e conduttori umidi o di seconda classe, ne&#039;principii di quello stesso anno, <lb></lb>aveva, dietro molte esperienze, il Volta <emph type="italics"></emph>sbozzata,<emph.end type="italics"></emph.end> com&#039;egli si esprime, una <lb></lb>scala o <emph type="italics"></emph>Tavola de&#039;conduttori della prima classe, che posseggono un diverso <lb></lb>potere di spingere il fluido elettrico e cacciarlo avanti ne&#039;conduttori umidi, <lb></lb>ossia di seconda classe<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>236). </s></p><p type="main">

<s>Questi erano, senza dubbio, tali progressi da mettere al sicuro la sco­<lb></lb>perta dell&#039;Elettricità metallica, e da qualificar meglio la natura e l&#039;essere <lb></lb>de&#039;nuovi Elettromotori. </s>

<s>Ma, poniamo che valessero le esperienze a persua­<lb></lb>dere la ragion de&#039;Filosofi, non concorrevan o i fatti a persuadere i sensi de&#039;pìù <lb></lb>valgari, o de&#039;caparbi e degli ostinati, i quali non vedevano la nuova elettri­<lb></lb>cità rivelarsi in quelle scosse e in quelle scintille, con che rivelavasi l&#039;elet­<lb></lb>tricità negli antichi strumenti. </s>

<s>Conosceva perciò bene il Volta che gli restava <lb></lb>ancora un gran passo da fare: rendere, co&#039;segnali ordinarii della Macchina, <lb></lb>la nuova elettricità parvente, o, in altre parole, dimostrar l&#039;identità fra l&#039;an­<lb></lb>tico fluido elettrico e il nuovo fluido galvanico. </s>

<s>Ma far ciò non voleva dir <lb></lb>altro se non che moltiplicare la virtù elettrica nelle coppie metalliche, tro­<lb></lb>vata sempre fin qui, all&#039;Elettroscopio, così debole, da non incorar nessuna <lb></lb>speranza di ridur qualcuna di quelle coppie a un Elettromotore, che scota <lb></lb>e che lampeggi. </s></p><p type="main">

<s>La difficoltà si presentava grandissima, e chi, per la innumerevole va­<lb></lb>rietà de&#039;metalli, si fosse messo a cercare la coppia privilegiata, avrebbe eter­<lb></lb>namente perduto il tempo e la fatica. </s>

<s>Le speranze del Volta non par che <lb></lb>s&#039;appuntassero a questo fantasma, ma in ogni modo egli faceva come chi <lb></lb>va al buio, che pochi passi a diritto lo condurrebbero al termine, e nono­<lb></lb>stante gira e rigira non vi giunge che per lunga e penosissima via. </s>

<s>Ma già, <lb></lb>se questa è la storia di tutte le grandi scoperte, non fa maraviglia che sia <lb></lb>la storia anche di questa, che, fra tutte le scoperte e le invenzioni, è la <lb></lb>grandissima. </s></p><p type="main">

<s>Quella diretta via poi era tanto più illusoria, in quanto che l&#039;arte, spe­<lb></lb>cialmente fabbrile, persuadendosi sempre di superar la Natura, raro è che <lb></lb>si volga ad imitarla. </s>

<s>Anche il Volta fu per alcun tempo, come tanti altri, <lb></lb>così sedotto, ma pure all&#039;ultimo, preso miglior consiglio, trovò ne&#039;magisteri <lb></lb>della stessa Natura il prodigioso artificio. </s></p><p type="main">

<s>Uno de&#039;più fini, tra questi magisteri naturali, è quello, per cui può la <lb></lb>Torpedine istupidire il braccio dei pescatori. </s>

<s>Il fatto, quanto era ben noto <lb></lb>agli antichi, tanto alla loro scarsa scienza fisica riusciva misterioso. </s>

<s>Ma quando <lb></lb>si provarono gli effetti inaspettati della Bottiglia di Leyda, fu allora facile il <lb></lb>trovare, tra le scosse date dallo strumento e quelle date dal pesce, una stret­<lb></lb>tissima somiglianza. </s>

<s>Non si dubitò perciò allora più da nessuno che la Tor­<lb></lb>pedine non contenesse nelle viscere un organo, il quale operasse a quel <lb></lb>modo che l&#039;Apparato leydese, o il fulminante Quadro frankliniano. </s>

<s>Si inter­<lb></lb>rogò l&#039;Anatomia, la quale rispose che quell&#039;organo fulminante della Torpe-<pb xlink:href="020/01/513.jpg" pagenum="494"></pb>dine consisteva in molti sacchetti membranosi, ripieni di un gran numero <lb></lb>di pellicole, soprapposte in forma di tanti piccoli dischi, fra l&#039;uno e l&#039;altro <lb></lb>de&#039;quali stillava un umore acquoso. </s>

<s>Pensarono allora i fisici che cosiffatti <lb></lb>dischi fossero di una certa materia idoelettrica come il vetro, e che l&#039;ani­<lb></lb>male, stropicciandoli insieme per forza di muscoli, eccitasse in essi l&#039;eletri­<lb></lb>cità necessaria a caricarne l&#039;organo fulminante. </s>

<s>Il Nicholson più ingegnosa­<lb></lb>mente rassomigliava le pellicole o i dischi animali a tante foglie soprapposte <lb></lb>di talco, di che si componessero altrettanti Elettrofori condensatori. </s></p><p type="main">

<s>Così fatte spiegazioni furono accolte per buone, perchè si conosceva dal­<lb></lb>l&#039;altra parte che nulla di meglio sapeva per allora suggerire la scienza. </s>

<s>Ma <lb></lb>quando il Volta trovò che nessuna delle parti animali è coibente, e che tutte <lb></lb>anzi son conduttrici, specialmente gli umori acquosi, e allora svanirono le <lb></lb>belle e ingegnose ipotesi, e restò tuttavia a sapersi d&#039;onde abbia origine <lb></lb>l&#039;Elettricità, che a loro talento eccitano dentro sè le Torpedini e simili al­<lb></lb>tri pesci. </s></p><p type="main">

<s>Il Volta stesso, che aveva rovinato quel primo e seducente edifizio, non <lb></lb>aveva lì per lì saputo suggerire la costruzione di un nuovo, infintanto che <lb></lb>non occorsero altri notabilissimi fatti concernenti la gran questione dell&#039;Elet­<lb></lb>tricità animale. </s></p><p type="main">

<s>Eusebio Valli, fautore del Galvani, aveva trovato che si contraevano <lb></lb>tutti i muscoli della rana a pur ripiegare una gamba di lei e ridurla al con­<lb></lb>tatto de&#039;nervi ischiatici. </s>

<s>Altre esperienze simili a questa consistevano nel te­<lb></lb>ner sospesa per i piedi la rana con una mano, e coll&#039;altra o colla lingua <lb></lb>toccare i nervi scoperti, e lasciati penzoloni. </s>

<s>E poichè, a ridestar ne&#039;mu­<lb></lb>scoli così fatti mirabili moti, non interveniva nessun&#039;opera di metalli, si <lb></lb>persuadeva lo Sperimentatore d&#039;aver così decisa la controversia a favor del <lb></lb>Galvani. </s>

<s>Molti, che avevano disertato, erano per tornar di nuovo sotto gli <lb></lb>stendardi bolognesi, quando il Volta; non perdutosi di coraggio, confessò di <lb></lb>avere asserito non succeder mai le contrazioni senz&#039;alcuno intervento di <lb></lb>conduttori, che fossero di metallo o di carbone, perchè non eragli riuscito <lb></lb>mai di ottener così l&#039;effetto desiderato: ma giacchè l&#039;ha ora il Valli otte­<lb></lb>nuto, non dubito, egli dice, “ di riconoscere che qui pure la diversità dei <lb></lb>conduttori combaciantisi è necessaria, e che tutto il gioco dipende da que­<lb></lb>sta diversità ” (Op. </s>

<s>cit, T. II, P. I, pag. </s>

<s>251). Proseguendo il costrutto, <lb></lb>che qui abbiam lasciato interrotto, chiama il Volta questa sua <emph type="italics"></emph>una ulteriore <lb></lb>scoperta;<emph.end type="italics"></emph.end> scoperta, la quale consisteva nell&#039;aver trovato da aggiungere alla <lb></lb>composizione di due metalli e un umido e di due umidi e un metallo, per <lb></lb>avere un Elettromotore, la composizione di tre umidi contigui fra loro. </s></p><p type="main">

<s>Fu appunto questa nuova scoperta, fu questo progresso di idee, che <lb></lb>condusse il Volta a riconoscere una somiglianza fra l&#039;Òrgano elettrico della <lb></lb>Torpedine, e un Elettromotore, che opera per qualcuna delle sopra notate <lb></lb>composizioni. </s>

<s>Il porgersi così arrendevoli le nuove teorie ad una spiegazione, <lb></lb>che era la più ragionevole di tutte le altre ritrovate ne&#039;principii dell&#039;elet­<lb></lb><gap></gap><pb xlink:href="020/01/514.jpg" pagenum="495"></pb>nell&#039;arte da commentar la Natura. </s>

<s>Ma la compiacenza ineffabilmente si ac­<lb></lb>crebbe, quando, quasi per ricompensarlo, la Natura stessa gli suggerì le <lb></lb>invenzioni dell&#039;arte. </s></p><p type="main">

<s>In mezzo a quel corso e ricorso faticoso di esperienze tendenti tutte a <lb></lb>cercare il modo di moltiplicare l&#039;intensità elettrica delle coppie metalliche, <lb></lb>venne provvidamente a ingerirsi, nelle speculazioni del Volta, l&#039;organo della <lb></lb>Torpedine. </s>

<s>Quell&#039;organo scotente e fulminante era appunto ciò ch&#039;egli cer­<lb></lb>cava, e giacchè l&#039;aveva assomigliato a un Elettromotore, in cui le pellicole <lb></lb>soprapposte o i dischi riferissero una qualche immagine delle coppie de&#039;me­<lb></lb>talli, e que&#039;dischi vedeva nella Torpedine essere così numerosi; sarebbe <lb></lb>egli mai, pensò l&#039;arguto Speculatore, che la mia arte raggiungesse gli ef­<lb></lb>fetti della Natura col moltiplicar, per soprapposizione, le coppie de&#039;metalli <lb></lb>alternati? </s></p><p type="main">

<s>Prende una rotella di zinco, le soprappone un&#039;altra simile rotella di <lb></lb>rame, e così tenendole congiunte fa, ora all&#039;una ora all&#039;altra, toccare il piat­<lb></lb>tello dell&#039;Elettrometro condensatore. </s>

<s>Trova che il zinco dà due o tre gradi <lb></lb>di elettricità positiva, il rame due o tre gradi di elettricità negativa. </s>

<s>A que­<lb></lb>sta prima coppia ne soprappone un&#039;altra simile e similmente disposta, ma <lb></lb>in modo che il rame della inferiore tocchi immediatamente il zinco della su­<lb></lb>periore, s&#039;aspetta che l&#039;Elettrometro segni, se non il doppio, almeno qualche <lb></lb>grado di più: prova, e stupefatto e mortificato vede che l&#039;Elettrometro non <lb></lb>segna nulla (ivi, T. II, P. II, pag. </s>

<s>157). Fa le coppie di tre pezzi diversi, <lb></lb>soprappone due di queste coppie come dianzi, e, come dianzi, l&#039;Elettrome­<lb></lb>tro non si muove (ivi, pag. </s>

<s>189). </s></p><p type="main">

<s>Chi non avesse avuto la pazienza, o diciam meglio il genio sperimen­<lb></lb>tale del Volta, avrebbe per disperazione lasciato in abbandono ogni cosa. </s>

<s>Ma <lb></lb>il Nostro pensava che se la Torpedine aveva avuto il suo Elettromotore dalla <lb></lb>Natura, egli in ogni modo, per imitazione, lo avrebbe ritrovato nell&#039;arte. </s>

<s><lb></lb>Fermo in questa fiducia, ritorna colla mente sull&#039;anatomia dell&#039;Organo elet­<lb></lb>trico animale, e attende a un fatto, che ne&#039;fini della sapiente Natura, la <lb></lb>quale nulla fa a caso, dee esser di non lieve importanza: i dischi membra­<lb></lb>nosi non si tengono a immediato contatto, ma uno strato umido stilla e <lb></lb>s&#039;interpone fra l&#039;uno e l&#039;altro. </s></p><p type="main">

<s>Ritorna a far le prove, non trascurata questa parte dal natural magi­<lb></lb>stero. </s>

<s>La nuova coppia metallica segna all&#039;Elettroscopio a pagliette un ses­<lb></lb>santesimo di grado. </s>

<s>Taglia, della stessa grandezza e figura delle coppie me­<lb></lb>talliche, un cartone, lo inzuppa nell&#039;acqua, e, interpostovi questo strato <lb></lb>d&#039;umido, soprappone alla prima un&#039;altra simil coppia già preparata. </s>

<s>Prova, <lb></lb>e l&#039;Elettroscopio segna due sessantesimi. </s>

<s>Sopraggiunge, interpostivi i soliti <lb></lb>cartoni umidi, una terza, una quarta coppia, e l&#039;Elettroscopio solleva le pa­<lb></lb>gliette a tre, e a quattro sessantesimi di grado (ivi, pag. </s>

<s>187, § XX). </s></p><p type="main">

<s>A questo punto del lungo e fortunoso viaggio, con quella gioia, colla <lb></lb>quale il pellegrino ricorda il luogo, d&#039;ond&#039;ei prima vide fumare il tetto della <lb></lb>sua casa, anche il Nostro così scriveva: “ Questo è il gran passo da me <pb xlink:href="020/01/515.jpg" pagenum="496"></pb>fatto sulla fine dell&#039;anno 1799, passo che mi ha condotto ben tosto alla co­<lb></lb>struzione del nuovo apparato scuotente ” (ivi). </s></p><p type="main">

<s>Per costruire invero il nuovo apparato, dopo quel gran passo fatto, non <lb></lb>rimaneva altro al Volta che proseguir nella felicissima imitazione dell&#039;or­<lb></lb>gano della Torpedine, componendo una colonna di coppie numerose. </s>

<s>Trovò <lb></lb>che sessanta all&#039;incirca fatte di zinco e di rame, bastavano perchè la co­<lb></lb>lonna stessa potesse dare alcuna scossa “ quando si toccano le sue due estre­<lb></lb>mità con dita, che non siano asciutte, e assai più forte se si toccano con <lb></lb>metalli impugnati per larghe superficie colle mani ben umide, formando così <lb></lb>una comunicazione assai migliore ” (ivi, pag. </s>

<s>159, 60). </s></p><p type="main">

<s>S&#039;apriva il secolo XIX, e la gran Lampada che doveva illuminarlo era <lb></lb>già preparata proprio in quel punto. </s>

<s>L&#039;inventore del portentoso strumento <lb></lb>non dà in pazzia per l&#039;allegrezza. </s>

<s>È ben sodisfatto e contento, ma non già <lb></lb>sopraesaltato. </s>

<s>Procedendo di scoperta in scoperta, bevve a sorso a sorso la <lb></lb>gioia, e gli avvenne perciò di non inebriarsi come chi non tracanna la coppa <lb></lb>del vino, ma la centella. </s></p><p type="main">

<s>Nonostante egli sentiva vivissimo il desiderio, e anzi il dovere di diffon­<lb></lb>dere la notizia della sua invenzione. </s>

<s>Il più conducevole modo era di rivol­<lb></lb>gersi alla R. </s>

<s>Società di Londra, e perciò scrive di langhe pagine, e benchè <lb></lb>senta di scriverle malamente, le scrive in francese, <emph type="italics"></emph>per farsi intendere<emph.end type="italics"></emph.end> (ivi, <lb></lb>pag. </s>

<s>143). Fa poi di queste pagine un trasunto, e sotto forma di lettera, in <lb></lb>data del dì 20 Marzo 1800, lo spedisce a Sir Giuseppe Banks, Presidente. </s>

<s><lb></lb>Incomincia ivi a descrivere il suo <emph type="italics"></emph>appareil semblable .... à l&#039;organe électri­<lb></lb>que naturel de la torpille,<emph.end type="italics"></emph.end> per cui non sa per ora chiamarlo con altro nome <lb></lb>che di <emph type="italics"></emph>Organo elettrico artificiale,<emph.end type="italics"></emph.end> per essere, come poco dopo scriveva al <lb></lb>Brugnatelli, “ fondato sopra i medesimi principii e simile anche nella forma, <lb></lb>secondo la sua prima costruzione, all&#039;organo naturale della Torpedine ” (ivi, <lb></lb>pag. </s>

<s>135). Quell&#039;organo poi elettrico artificiale era dal Volta descritto, nella <lb></lb>sua particolar costruzione, al Banks, nel modo seguente: </s></p><p type="main">

<s>“ Je me fournis de quelques douzaines de petites plaques rondes ou <lb></lb>disques, de cuivre, de laiton, ou mieux d&#039;argent, d&#039;un pouce de diamètre, <lb></lb>plus ou moins (par exemple, de monnoyes), et d&#039;un nombre égal de plaques <lb></lb>d&#039;ètain, ou, ce qui est beacoup mieux, de zinc, de la mème figure et gran­<lb></lb>deur, à-peu-près; je dis à-peu-près, par ce qu&#039;une precision n&#039;est point re­<lb></lb>quise, et, en général, la grandeur, aussi bien que la figure, des pièces mé­<lb></lb>talliques, est arbitraire: on doit avoir égard soulement qu&#039;on puisse les <lb></lb>arranger commodément les unes sur les autres, en forme de colonne. </s>

<s>Je <lb></lb>prépare en outre, un nombre assez grand de rouelles de carton, de pean, <lb></lb>ou quelque autre matière spongieuse, capable d&#039;imbiber et de retenir beau­<lb></lb>coup de l&#039;eau, ou de l&#039;humidité dont il faudra, pour le succes des expé­<lb></lb>riences, qu&#039;elles soient bien trempées. </s>

<s>Ces tranches ou rouelles, que j&#039;ap­<lb></lb>pellerai disques movillés, je les fais un peu plus petites que les disques ou <lb></lb>plateaux métalliques, à fin qu&#039;interposées à ceux de la manière que je dirai </s></p><pb xlink:href="020/01/516.jpg" pagenum="497"></pb><p type="main">

<s>Descritte così le membra, prosegue il Volta a mostrar, del nuovo Or­<lb></lb>gano, quasi diremmo la vita, dopo di che soggiunge altri modi di disporre <lb></lb>quelle medesime membra, uno de&#039;quali, ch&#039;egli chiama <emph type="italics"></emph>appareil à gobe­<lb></lb>lets ou à couronne de tasses<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>114), consisteva in prendere venti o <lb></lb>trenta bicchieri pieni d&#039;acqua, facendo comunicare il primo al secondo, il <lb></lb>secondo al terzo, e così di seguito fino all&#039;ultimo, per mezzo di archi me­<lb></lb>tallici composti di una lamina di rame e di un&#039;altra di zinco, e disposti tutti <lb></lb>nel medesimo verso (ivi, pag. </s>

<s>160). </s></p><p type="main">

<s>Gli Accademici di Londra e gli scienziati d&#039;Inghilterra, fra&#039;quali rapi­<lb></lb>dissima si diffusse la notizia, dato opera a costruire il nuovo Organo elet­<lb></lb>trico, alla maniera stessa che veniva insegnato in Italia, restarono stupiti, <lb></lb>quasi paresse loro di vedere un animal mostruoso lavorato dalle mani di un <lb></lb>uomo, colle membra vive e colle viscere di metallo. </s></p><p type="main">

<s>Tanto romore si fece da quegli Inglesi, che il Volta ebbe a risolversi <lb></lb>di andare a darne qualche sodisfazione anco ai Padroni. </s>

<s>Stese perciò e lesse <lb></lb>all&#039;Istituto Nazionale, in due sedute, ne&#039;dì 7 e 12 del Novembre 1801, le <lb></lb>due parti della Memoria <emph type="italics"></emph>Sull&#039;identità del fluido elettrico col fluido galva­<lb></lb>nico,<emph.end type="italics"></emph.end> riscontrando i detti, dopo le sedute, coll&#039;esperienze. </s>

<s>Napoleone, primo <lb></lb>Console, che udì e vide insiem co&#039;più grandi scienziati convenuti d&#039;ogni <lb></lb>parte a Parigi, decretò che fosse coniata una medaglia d&#039;oro commemora­<lb></lb>tiva del grande avvenimento. </s></p><pb xlink:href="020/01/517.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Di varii altri strumenti<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMAPJO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Degli specilli semplici, o degli occhiali da naso, e del loro modo di operar sulìa vista. </s>

<s>— II. </s>

<s>Del <lb></lb>Microscopio semplice e del Microscopio composto. </s>

<s>— III. </s>

<s>Del corno acustico. </s>

<s>— IV. De&#039;primi Igro­<lb></lb>scopii, degl&#039;Igrometri del Santorio, dell&#039;Igrometro a condensazione del Torricelli, della <emph type="italics"></emph>Mostra <lb></lb>umidaria<emph.end type="italics"></emph.end> del Folli, della Legge igrometrico-meccanica del Viviani, e dell&#039;Igrometro elettrico del <lb></lb>Volta. </s>

<s>— V. Dell&#039;Arcometro e del Pluviometro. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La storia dell&#039;invenzione degli specilli semplici avrebbe dovuto prolu­<lb></lb>dere alla storia dell&#039;invenzione del Canocchiale: ma perchè, riguardati gli <lb></lb>stessi specilli nel loro semplice uso di corregger la vista, specialmente de&#039;vec­<lb></lb>chi, non appartengono strettamente all&#039;ordine degli strumenti del metodo <lb></lb>sperimentale; ci contenteremo d&#039;aggiunger qui le seguenti notizie per chi <lb></lb>desiderasse di averle, come complemento o supplemento di storia alle cose <lb></lb>già esposte nel Cap. </s>

<s>III. </s></p><p type="main">

<s>Pretendere d&#039;investigare il nome, la patria e il tempo di colui, che ri­<lb></lb>trovò l&#039;uso de&#039;cristalli convessi per restituire la bontà della vista affievolita <lb></lb>ne&#039;vecchi, è forse opera assai difficile, e anzi diremmo quasi impossibile, es­<lb></lb>sendo tante le circostanze e i modi, con che una persona o l&#039;altra può es­<lb></lb>sersi facilmente accorta che alcuni mezzi diafani soprapposti alla cornea del­<lb></lb>l&#039;occhio, fanno vedere ingranditi gli oggetti. </s>

<s>Lasciando andar ciò che Realdo <lb></lb>Colombo argutamente pensò della lente cristallina estratta dai cadaveri, la <lb></lb>quale facendo vedere ingranditi gli oggetti, poteva aver dato la prima oc­<lb></lb>casione a inventar gli occhiali: le lacrime possono essere state il primo sog­<lb></lb><gap></gap><pb xlink:href="020/01/518.jpg" pagenum="499"></pb>Francesco Redi, in quel suo Discorso che scrisse in forma di Lettera <emph type="italics"></emph>In­<lb></lb>torno all&#039;invenzion degli occhiali,<emph.end type="italics"></emph.end> riferisce due testi di due medici francesi, <lb></lb>i quali giusto accennano all&#039;efficacia de&#039;collirii da essi proposti per medi­<lb></lb>care l&#039;infiammazione degli occhi, dicendo essere di tale e tanta virtù da far <lb></lb>vedere ingranditi gli oggetti, anche senza gli occhiali. </s>

<s>“ Bernardo Gordoni, <lb></lb>professore in Monpellieri, nel libro intitolato <emph type="italics"></emph>Lilium medicinae,<emph.end type="italics"></emph.end> principiato <lb></lb>da lui, come confessa, l&#039;anno 1305 del mese di Luglio, nel capitolo <emph type="italics"></emph>De subti­<lb></lb>litate visus,<emph.end type="italics"></emph.end> dopo avere insegnato un certo suo collirio, soggiunge con gran <lb></lb>brio e un po&#039;troppo arditamente: <emph type="italics"></emph>Et est tantae virtutis quod decrepitum <lb></lb>faceret legere litteras minutas absque ocularibus.<emph.end type="italics"></emph.end> Guido da Caudiac, pro­<lb></lb>fessore anch&#039;esso di Monpellièri, nella sua <emph type="italics"></emph>Chirurgia grande,<emph.end type="italics"></emph.end> composta <lb></lb>l&#039;anno 1363, porta in quella alcuni medicamenti buoni alla debolezza degli <lb></lb>occhi, ed aggiunge di più, con sincerità maggiore di quella del Gordonio: <lb></lb><emph type="italics"></emph>Se queste e simili cose non giovano, bisogna ricorrere agli occhiali<emph.end type="italics"></emph.end> ” (Redi, <lb></lb>Cons. </s>

<s>e opusc., Firenze 1863, pag. </s>

<s>53, 54). </s></p><p type="main">

<s>Forse anche l&#039;osservazione fatta sopra gli effetti di rifrazione, che na­<lb></lb>turalmente presentano le gocciole della pioggia, le perline di cristallo, e le <lb></lb>boccie di forma sferoidea, per uso delle mense piene di acqua, dettero oc­<lb></lb>casione all&#039;arte d&#039;imitar la Natura, con facile persuasione che tutto il se­<lb></lb>greto consisteva nella curvità della superficie del mezzo diafano, ond&#039;è perciò <lb></lb>che prime a ritrovare furon non le lenti concave ma le convesse. </s>

<s>Giova a <lb></lb>questo proposito riferire una nota apposta dal Canovai al suo <emph type="italics"></emph>Elogio storico <lb></lb>di Alessando della Spina.<emph.end type="italics"></emph.end> “ Il p. </s>

<s>Alessandro, ivi egli dice, ebbe in vista <lb></lb>la sola infermità de&#039;presbiti, senza pensare affatto a quella de&#039;miopi. </s>

<s>Tanto <lb></lb>sembra insinuare Sandro di Pippozzo, allorchè caratterizza gli occhiali come <lb></lb><emph type="italics"></emph>trovati novellamente per comoditae delli poveri veki, quando affiebolano <lb></lb>dal vedere.<emph.end type="italics"></emph.end> Infatti i miopi non si conoscevano quasi punto a quei tempi, e <lb></lb>potrebbe dirsi che ne è cresciuto il numero, dopo che si è inventato un <lb></lb>rimedio anche per loro. </s>

<s>Son quasi tanto rari i giovani veramente bisognosi <lb></lb>degli occhiali concavi, quanto lo sono i vecchi, che veramente possan vedere <lb></lb>senza il soccorso dei convessi. </s>

<s>Del resto, le lenti concave hanno pochissime <lb></lb>utili proprietà come ben dimostrano gli Ottici, e l&#039;Astronomia, dopo Gali­<lb></lb>leo che le combinò nel suo Telescopio, non ne fa più alcun uso ” (Prose <lb></lb>varie, T. III, Firenze 1817, pag. </s>

<s>36). </s></p><p type="main">

<s>Non tutti certamente acconsentiranno al Canovai che, prima del se­<lb></lb>colo XIV, non ci fossero <emph type="italics"></emph>miopi,<emph.end type="italics"></emph.end> riman pur nonostante vero che della prima <lb></lb>invenzione furono le lenti convesse e dopo si fece quella delle concave. </s>

<s>Ciò <lb></lb>si spiega ripensando che quelle occorsero più facilmente a riscontrar negli <lb></lb>esempii della natura, mentre queste son piuttosto un frutto della specula­<lb></lb>zione e un portato dell&#039;arte. </s></p><p type="main">

<s>Fermo dunque stando e approvato che primi ad essere inventati furono <lb></lb>gli occhiali convessi <emph type="italics"></emph>per comodità delli poveri vecchi,<emph.end type="italics"></emph.end> e che molti possano <lb></lb>essere convenuti insieme e concorsi nell&#039;osservazione del fatto naturale rap­<lb></lb>presentato nelle immagini rifrante dai diafani terminati da superficie curve; <pb xlink:href="020/01/519.jpg" pagenum="500"></pb>si domanda chi fu il primo, il quale ridusse l&#039;osservazione naturale a sog­<lb></lb>getto di speculazione o ad esercizio di arte? </s></p><p type="main">

<s>Leopoldo del Migliore, erudito fiorentino del secolo passato, dice essere <lb></lb>stato costui Salvino degli Armati, come si legge in una epigrafe sepolcrale, <lb></lb>allora scoperta e ora visibile a tutti nel Chiostro del convento di S. </s>

<s>Maria <lb></lb>Maggiore di Firenze, dove la famiglia degli Armati ebbe gentilizia sepoltura. </s>

<s><lb></lb>Quella iscrizione, che soggiace scolpita in marmo bianco al busto di Salvino, <lb></lb>pure scolpito in marmo, dice così: <emph type="italics"></emph>Qui diace Salvino d&#039;Armato degli Ar­<lb></lb>mati di Fir. </s>

<s>inventor degli occhiali. </s>

<s>Dio gli perdoni le peccata. </s>

<s>A. D. 1317.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Dal passo del Gordonio però riferito dal Redi, sembra doversi argomen­<lb></lb>tare che, nel 1305, gli occhiali erano stati già inventati, e il Canovai, in un&#039;al­<lb></lb>tra Nota al sopra citato Elogio, asserisce non esser punto probabile che un <lb></lb>tale inventore fosse per patria fiorentino, principalmente, com&#039;egli stesso <lb></lb>dice, per questa ragione: “ Se un fiorentino trovò l&#039;arte di far gli occhiali, <lb></lb>è dunque affatto ridicolo il sentimento del B. Giordano, che, predicando pub­<lb></lb>blicamente in Firenze, si gloria di averlo conosciuto, e dice: <emph type="italics"></emph>Io vidi colui, <lb></lb>che prima la trovò e fece, e favellaili.<emph.end type="italics"></emph.end> La più gran parte degli ascoltanti <lb></lb>avrebbe potuto rispondergli: <emph type="italics"></emph>Padre, noi lo abbiamo visto e gli abbiam fa­<lb></lb>vellato prima di voi<emph.end type="italics"></emph.end> ” (ivi, pag. </s>

<s>35). </s></p><p type="main">

<s>Carlo Dati dunque, in una delle sue <emph type="italics"></emph>Veglie,<emph.end type="italics"></emph.end> dimostrò che l&#039;inventore <lb></lb>era pisano, ed era per l&#039;appunto quel frate Alessandro, di cui il Canovai <lb></lb>tesse l&#039;elogio. </s>

<s>Soggiunse il Dati di più che l&#039;invenzione occorse pochi anni <lb></lb>prima del 1300. Finge ivi l&#039;Autor delle <emph type="italics"></emph>Veglie fiorentine<emph.end type="italics"></emph.end> che un giovane <lb></lb>forestiero venuto apposta a Firenze per veder Galileo, e trattenutovisi al­<lb></lb>quanti giorni, si ritrovasse una sera, nel giardino del Duca Salviati, a col­<lb></lb>loquio con alcuni gentiluomini della città, fra&#039;quali Filippo Pandolfini. </s>

<s>Sa­<lb></lb>ziatosi quel giovane forestiero di rimirar le novità celesti con uno de&#039;migliori <lb></lb>canocchiali di Galileo, armato e diretto dall&#039;esperte mani di quei Signori, <lb></lb>fu fatto sì che il discorso cadesse intorno al primo inventore di quel sì mi­<lb></lb>rabile strumento, e poi risalendo più su, intorno al primo inventor degli oc­<lb></lb>chiali. </s>

<s>Essendo stato dimostrato, da quel dotto ed erudito consesso, che gli <lb></lb>antichi non conobbero veramente gli occhiali, il giovane forestiero allora così <lb></lb>prese a dire: “ Ma giacchè, secondo il parere di lor signori, gli antichi non <lb></lb>ebbero occhiali, quando furono egli inventati? </s>

<s>A questa domanda tutti si <lb></lb>ristrinsero nelle spalle, non sapendo che dirsi, ma il senator Filippo Pan­<lb></lb>dolfini, il quale fin allora aveva taciuto, dando segno di meditar qualche <lb></lb>cosa di gran rilievo, risolutamente rispose: Non grandi anni avanti al 1300, <lb></lb>che tanto afferma fra Giordano da Rivalto, eloquentissimo predicatore del­<lb></lb>l&#039;Ordine di S. Domenico, il quale fiorì e predicò in Santa Maria Novella, <lb></lb>poco dopo a tal tempo. </s>

<s>Dice egli dunque, in una delle sue Prediche citate <lb></lb>nel nostro Vocabolario da un mio manoscritto: <emph type="italics"></emph>Non è ancora 20 anni, che <lb></lb>si trovò l&#039;arte di fare occhiali, che fanno veder bene, che è una delle mi­<lb></lb>gliori arti e delle più necessarie, che il mondo abbia.<emph.end type="italics"></emph.end> — Nuova e curiosa <lb></lb>notizia è questa, disse il Forestiero, non avendo mai ascoltato particolare <pb xlink:href="020/01/520.jpg" pagenum="501"></pb>tanto preciso. </s>

<s>Ma dell&#039;inventore? </s>

<s>— Ella mi ha tolto la parola di bocca, ri­<lb></lb>spose il Pandolfini, perchè appunto io mi preparava a dir qualche cosa di <lb></lb>questo. </s>

<s>Quando io era giovane, andando a Pisa a studiar legge, più per co­<lb></lb>mandamento d&#039;altri che per mio genio, il quale era rivolto, piuttosto che <lb></lb>alla Giurisprudenza romana, a rinvenire le Memorie nostrali; io andava sem­<lb></lb>pre frugando le librerie manoscritte, dove per ordinario si trova qualche <lb></lb>erudizione non così esposta alla notizia universale, e particolarmente quella di <lb></lb>S. </s>

<s>Caterina de&#039;P. P. Predicatori, fornita di buonissimi testi a penna, e mi <lb></lb>ricordo benissimo, come se fusse ora, di aver letto attentamente e con dili­<lb></lb>genza sfogliata una Cronaca latina di detto Convento, scritta in cartapecora, <lb></lb>compilata brevemente, prima da fra Bartolommeo da S. </s>

<s>Concordio Autore <lb></lb>degli Ammaestramenti antichi, e poi più largamente continuata da frate Ugo­<lb></lb>lino di Sernovi, e tutta insieme raccolta e condotta, fino all&#039;anno 1400 in <lb></lb>circa, da fra Domenico da Peccioli, colla giunta del maestro fra Simone da <lb></lb>Cascia, figliolo del sopraddetto monastero, la quale non saprei dire fin dove <lb></lb>arrivassi per mancanza di alquante carte. </s>

<s>Fra le Memorie di questa Cro­<lb></lb>naca, all&#039;anno 1313, si legge che, in detto convento di S. Caterina, visse e <lb></lb>morì il p. </s>

<s>frate Alessandro Spina, religioso di ottimi costumi e di acutis­<lb></lb>simo ingegno, apprendendo tutto quello che udiva dire e vedeva fare, e che, <lb></lb>essendosi dato il caso che un tale fu il primo a inventare gli occhiali, nè <lb></lb>volendo comunicare ad altri l&#039;invenzione, egli, da per sè stesso, gli fabbricò, <lb></lb>e a tutti di buon cuore ne fece parte ” (Targioni, Notiz. </s>

<s>Aggrandim., ediz. </s>

<s><lb></lb>cit., T. II, P. I, pag. </s>

<s>59, 60). </s></p><p type="main">

<s>A questo frate Alessandro si dovrebbe dunque, circa all&#039;invenzion degli <lb></lb>occhiali, quel merito stesso che si vuole avere avuto Galileo circa all&#039;inven­<lb></lb>zione del Canocchiale; ma qualunque sia il valore che vuol darsi ai docu­<lb></lb>menti storici prodotti dal Pandolfini, è un fatto che così dell&#039;Occhial piccolo <lb></lb>come del grande, il ritrovamento è da attribuirsi all&#039;arte piuttosto che alla <lb></lb>scienza. </s>

<s>Della scienza diottrica degli specilli narrammo altrove gli Autori; ora <lb></lb>qui giova mostrar come e quando si riuscì a intendere il modo d&#039;operar degli <lb></lb>stessi specilli intorno al correggere e al migliorar la vista de&#039;giovani e <lb></lb>de&#039;vecchi. </s></p><p type="main">

<s>Il Keplero, nel Cap. </s>

<s>V, proposiz. </s>

<s>XXVIII de&#039;<emph type="italics"></emph>Paralipomeni a Vitellione,<emph.end type="italics"></emph.end><lb></lb>primà di entrare a trattar del nuovo e difficile soggetto, esclama: “ Quanta <lb></lb>admiratio rei tantae, tam late propagatum usum et tamen causam ignorari <lb></lb>hactenus!.... Unus Baptista Porta professus est rationem in Opticis red­<lb></lb>dere, quae a librariis frustra hactenus requisivi ” (Francof. </s>

<s>1604, pag. </s>

<s>202). <lb></lb>Il libro dell&#039;Ottica del Porta, a cui s&#039;accenna in queste parole, a quel che <lb></lb>pare non diffuso allora in Germania, è il Trattato <emph type="italics"></emph>De refractione,<emph.end type="italics"></emph.end> stampato <lb></lb>in Napoli nel 1593, dove giusto l&#039;Autore tratta, nel Libro VIII, <emph type="italics"></emph>De specillis,<emph.end type="italics"></emph.end><lb></lb>e proemia alla sua trattazione chiamando l&#039;opera, che egli ivi imprende, <emph type="italics"></emph>res <lb></lb>ardua, mirabilis, utilis, iucunda, nec ab aliquibus adhuc tentata<emph.end type="italics"></emph.end> (pag. </s>

<s>173). </s></p><p type="main">

<s>È dunque il Porta, senza dubbio il primo fra gli Ottici, il quale non <lb></lb>solo dimostra l&#039;andamento de&#039;raggi rifratti attraverso il diafano degli oc-<pb xlink:href="020/01/521.jpg" pagenum="502"></pb>chiali concavi e de&#039;convessi, ma investiga altresì la ragione, per cui da quel­<lb></lb>l&#039;artificioso andamento si viene a correggere il difetto naturale degli occhi. </s>

<s><lb></lb>Incomincia dal considerar quel che dice Aristotile <emph type="italics"></emph>senes procul videre, quia <lb></lb>procul radii non coeunt,<emph.end type="italics"></emph.end> e francamente pronunzia che una tale dottrina del <lb></lb>Filosofo è falsa, essendo falso il supposto da lui, che cioè, per vedere, vi <lb></lb>bisognino ambedue gli occhi, ed essendo di più la falsità manifesta dal fatto <lb></lb>de&#039;monoculi vecchi, i quali, guardando pur coll&#039;uno, <emph type="italics"></emph>procul<emph.end type="italics"></emph.end> anch&#039;essi <emph type="italics"></emph>vi­<lb></lb>dent,<emph.end type="italics"></emph.end> come coloro che guardano co&#039;due occhi. </s>

<s>“ Sed vera ratio est, sog­<lb></lb>giunge il Porta, quod senibus pupilla deducitur reseraturque, ut caetera quo­<lb></lb>que membra, non recte suo funguntur officio, humor quoque incrassatur, <lb></lb>unde maiori luce ad videndum indigent .... necesse enim habent ut quae <lb></lb>videre velint lucidiora sint, magisque coacta, quod utrumque crystallinis spe­<lb></lb>cillis emendatur, haec enim refractione radios uniunt et lux multiplicatur <lb></lb>in eis ” (pag. </s>

<s>138). </s></p><p type="main">

<s>La presbiopia insomma, pel nostro Ottico napoletano dipende dall&#039;aver <lb></lb>l&#039;occhio troppo dilatata la pupilla, e dall&#039;esser divenuto, per vecchiezza, ot­<lb></lb>tuso a sentir l&#039;impressione de&#039;raggi luminosi, a che le lenti convesse soc­<lb></lb>corrono utilmente condensando quegli stessi raggi, e perciò moltiplicando la <lb></lb>luce. </s>

<s>La miopia consiste invece nell&#039;esser la pupilla troppo ristretta e non <lb></lb>troppo diafano il cristallino; due difetti che s&#039;emendano, secondo il Porta, <lb></lb>dagli occhiali concavi, i quali fanno al di dietro divergere i raggi, e gli fanno <lb></lb>convergere dalla parte davanti, e così condensandovi il lume, rischiarano gli <lb></lb>oggetti. </s>

<s>“ Juvenes, qui arcta sunt pupilla, ac vitreo humore, qui in oculo <lb></lb>continetur non claro, duo requirerent, et quae simulacra dilatarent, ut re­<lb></lb>sarciatur vitium pupillae, et quodammodo unirent; et quod lucem clario­<lb></lb>rem redderent. </s>

<s>Duo haec praestat concavum specillum, nam et simulacrum <lb></lb>quodammodo unit ex refractionibus ut intra vitri soliditatem apparet, et quo­<lb></lb>dammodo aperiret ut videmus lineis in adversam partem refugientibus, et <lb></lb>lux pertransiens visum multiplicatur ” (pag. </s>

<s>188). </s></p><p type="main">

<s>Dopo il Porta, a specular la ragione dell&#039;operar gli occhiali sopra la <lb></lb>vista, venne il De Dominis, nel suo celebre Trattato <emph type="italics"></emph>De radiis visus et lu­<lb></lb>cis,<emph.end type="italics"></emph.end> in cui, proponendosi di rifiutar come false le dottrine del Fisico napo­<lb></lb>letano, altre false conseguenze deduce egli stesso in proposito, da più errati <lb></lb>principii. </s>

<s>Uno di questi, e de&#039;principali, è che la visione <emph type="italics"></emph>proprie et imme­<lb></lb>diate fit in ipsa pupilla, idest humore chistallino<emph.end type="italics"></emph.end> (Venetiis 1611, pag. </s>

<s>6). <lb></lb>Di qui conclude esser falsa l&#039;opinion di coloro, i quali <emph type="italics"></emph>defectum oculi se­<lb></lb>nilis totum reducunt ad dilationem foraminis uvaee<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>15), essendo <lb></lb>che nell&#039;occhio non avvengono rifrazioni, nè è vero che vi si rappresentin <lb></lb>l&#039;immagini a modo che nella camera oscura, <emph type="italics"></emph>quia et longe debitiores ibi <lb></lb>cernuntur rerum colores .... et omnia cernuntur inversa .... quod in <lb></lb>oculo neque contingit neque contingere potest<emph.end type="italics"></emph.end> (ibi). </s></p><p type="main">

<s>Da che dunque dipende per il De Dominis il difetto della vista ne&#039;vec­<lb></lb>chi? </s>

<s>Da ciò che <emph type="italics"></emph>ob diversos axes fiunt quaedam parallaxes visus sive di­<lb></lb>versitates aspectus<emph.end type="italics"></emph.end> (pag. </s>

<s>16). Ora, tali parallassi, prosegue a dire l&#039;Autore, <pb xlink:href="020/01/522.jpg" pagenum="503"></pb>son tolte via dai vetri convessi, i quali raccolgono tutti insieme, intorno al­<lb></lb>l&#039;asse della piramide visuale, i raggi che andavan prima disordinati e di­<lb></lb>spersi. </s>

<s>“ Visus enim senum invatur appositione vitri rotundi .... Tale enim <lb></lb>vitrum primo et principaliter aufert parallaxes illas et consequenter confu­<lb></lb>sionem.... Franguntur enim in tali vitro ad perpendicularem, et consequen­<lb></lb>ter uniuntur in ipsa perpendiculari, quae est axis verus pyramidis visua­<lb></lb>lis .... quae unio, et congregatio radiorum aufert omnes parallaxes. </s>

<s>Deinde <lb></lb>vere iuvat etiam visum, quia tale vitrum ampliat quantitates obiecti visi, et <lb></lb>facit ut maior appareat quam sit, quia dicta fractio ampliat et dilatat angu­<lb></lb>lum visivum ” (ibi, pag. </s>

<s>19). </s></p><p type="main">

<s>Quanto a&#039;miopi il De Dominis ne riconosce il difetto <emph type="italics"></emph>ex nimia humi­<lb></lb>ditate et liquiditate humoris crystallini<emph.end type="italics"></emph.end> (pag. </s>

<s>19), a togliere il quale giova, <lb></lb>dic&#039;egli, l&#039;occhiale concavo “ quia restringit obiectum per angulum strictio­<lb></lb>rem, quo, etsi res minor appareat quam sub angulo naturali directo, fortius <lb></lb>tamen agit in oculum, quia virtus unita fortior ” (pag. </s>

<s>20). </s></p><p type="main">

<s>Resta, da così fatti documenti, provato che nè il Porta nè il De Do­<lb></lb>minis sciolsero il problema degli occhiali, che abbrevian la vista troppo lunga, <lb></lb>e allungano convenientemente la corta, traendo conclusioni false da non retti <lb></lb>principii. </s>

<s>Parecchi anni prima però che uscissero a mettere in luce le loro <lb></lb>dottrine i due sopra commemorati Autori, il Maurolico aveva speculato nella <lb></lb>solitudine, e avea trovato, ne&#039;principii scienziali della Diottrica, quelle verità, <lb></lb>che invano i suoi successori andarono a cercar nella loro fantasia. </s></p><p type="main">

<s>La questione, secondo il Maurolico, dipende tutta dalla forma del cri­<lb></lb>stallino, che è per lui riguardato come l&#039;organo essenziale della visione. </s>

<s>“ In­<lb></lb>ter ea quae ad visum spectant, dignitatis orcem obtinet glacialis, sive chry­<lb></lb>stallinus humor, quem et pupillam appellare meo iudicio possumus, in quo <lb></lb>visiva virtus tanquam in sede consistit.... Ab huius forma dependet quali­<lb></lb>tas visus, sive brevis sive longi ” (Diaphan., lib. </s>

<s>III, Neapoli 1611, pag. </s>

<s>69, 70). </s></p><p type="main">

<s>Nel cristallino i raggi si rifrangono con quella legge <emph type="italics"></emph>quam diaphani <lb></lb>figura postulat.<emph.end type="italics"></emph.end> E perciò “ cum perspicui forma variata, variet quoque <lb></lb>fractionis angulus, iam hinc et visualium radiorum situm diversificari, con­<lb></lb>cursumque nunc anticipari, nunc differri necesse erit. </s>

<s>Et quoniam quo mi­<lb></lb>nor est perspicuus globus eo minus spatium coadunat radios; ideo et qui con­<lb></lb>globatiorem sortiti sunt pupillam breviore sunt visu praediti ” (ibi, pag. </s>

<s>77). <lb></lb>Questo è l&#039;occhio de&#039;miopi, e quello de&#039;vecchi <emph type="italics"></emph>siquidem in senibus humo­<lb></lb>ris remissio, remittit non nihil in pupilla tumoris<emph.end type="italics"></emph.end> (pag. </s>

<s>78). </s></p><p type="main">

<s>Da ciò direttamente conclude il Maurolico l&#039;effetto degli occhiali che, <lb></lb>essendo convessi, abbreviano il troppo lungo concorso de&#039;raggi refratti nella <lb></lb>pupilla, ed essendo concavi, estendon quello, che per natura sua era troppo <lb></lb>breve. </s>

<s>Da ciò si vengono ad emendare gli eccessi, e si fa sì che vada giu­<lb></lb>sto ad unirsi e a congregarsi <emph type="italics"></emph>ad opticum nervum speciem rei.<emph.end type="italics"></emph.end> “ Item con­<lb></lb>cavis conspicillis brevem oblutum extendi atque convexis longum breviari, <lb></lb>quoniam seilicet illis collecti dilatantur, his vero dilatati colliguntur radii, <lb></lb>contrariique defectus contrariis emendantur remediis ” (pag. </s>

<s>79). </s></p><pb xlink:href="020/01/523.jpg" pagenum="504"></pb><p type="main">

<s>Si vede chiaro di qui le dottrine del Maurolico avere assai da vicino <lb></lb>dato nella cruna del vero, se non che ei non conobbe nè l&#039;organo, nè il <lb></lb>modo proprio come si fa la vista. </s>

<s>Quando poi il Keplero dimostrò niente <lb></lb>altro essere il cristallino che una lente di rifrangenza, e che le immagini si <lb></lb>dipingono rovesciate sopra la retina, non bisognò fare altro che questa emen­<lb></lb>dazione alle teorie del Maurolico intorno agli occhiali, per intender, dell&#039;ope­<lb></lb>rar di questi, la ragion vera. </s></p><p type="main">

<s>Uno de&#039;primi a far ciò e a pubblicar le emendate dottrine nel suo <emph type="italics"></emph>Corso <lb></lb>Matematico,<emph.end type="italics"></emph.end> il quale vide nel 1633, per la prima volta la luce, fu l&#039;Heri­<lb></lb>gonio, così scrivendo: “ Qui longinqua tantum distincta vident ut senes, hu­<lb></lb>morem chrystallinum ex siccitate tenuiorem et spirituum penuria nimis <lb></lb>depressum, nec satis gibbosum habent ad radios divergentes singulorum <lb></lb>punctorum coaudunandos. </s>

<s>Itaque ii ut radiorum concursus non protendatur <lb></lb>ultra retinam, longe ab oculo tenent visibile, vel convexis conspicillis, ad <lb></lb>propius coadunandos radios utuntur. </s>

<s>Myopes contra habent humorem chry­<lb></lb>stallinum nimis globosum ideoque, nisi visibile fuerit valde proprinquum, <lb></lb>concursus radiorum fit illis inter humorem chrystallinum et retinam ac <lb></lb>proinde confusa vident omnia remota indigentque cavis conspicillis ad con­<lb></lb>cursum radiorum longius propagandum, distincteque videndum ” (Pari­<lb></lb>siis 1844, T. V, pag. </s>

<s>182). </s></p><p type="main">

<s>Fra&#039;nostri il Castelli in quel suo <emph type="italics"></emph>Discorso sopra la vista,<emph.end type="italics"></emph.end> raccolto fra <lb></lb>gli Opuscoli filosofici di lui pubblicati nel 1669, non lasciò di trattare, fra <lb></lb>molte altre cose importanti e curiose, anche della Miopia, e della Presbio­<lb></lb>pia. </s>

<s>Egli pure, emendando, come l&#039;Herigonio, le teorie del Maurolico con <lb></lb>le dottrine del Keplero, diceva dipendere il difetto de&#039;vecchi dall&#039;essersi con­<lb></lb>sumato parte degli umori degli occhi, per cui, venendo la retina a esser <lb></lb>ritirata troppo verso il cristallino, le immagini appariscono annebbiate, e si <lb></lb>rischiarano coll&#039;artificio degli occhiali convessi. </s>

<s>Ne&#039;miopi al contrario, avendo <lb></lb>il vitreo e il cristallino maggior convessità della necessaria, la retina riman <lb></lb>troppo lontana dal luogo della visione distinta, e l&#039;arte perciò con gli oc­<lb></lb>chiali concavi può facilmente correggere questo difetto della Natura. </s></p><p type="main">

<s>Di questo argomento fece pure soggetto il Baliani in quel suo tratta­<lb></lb>tello <emph type="italics"></emph>De visione<emph.end type="italics"></emph.end> raccolto fra le <emph type="italics"></emph>Opere diverse,<emph.end type="italics"></emph.end> pubblicate da Giovanni Ca­<lb></lb>lenzani in Genova nel 1666, ma non avendo accettate le teorie Kepleriane, <lb></lb>non potè perciò liberarsi da alcuni errori. </s></p><p type="main">

<s>Nè quel Viviani, che discorse per tutte le parti della Fisica, promoven­<lb></lb>dola nella solitudine col mirabile ingegno, lasciò indietro di risolvere il pro­<lb></lb>blema, che è forse, per il frequente e così comodo uso che si fa degli <lb></lb>occhiali, fra tutti gli altri, per un ottico, il più curioso. </s>

<s>A carte 85 del <lb></lb>Tomo CXXXIII, nella Raccolta de&#039;Manoscritti intitolati <emph type="italics"></emph>Discepoli di Gali­<lb></lb>leo,<emph.end type="italics"></emph.end> si vedono alcune figure, diligentemente disegnate a penna dallo stesso <lb></lb>Viviani, rappresentanti la sezione dell&#039;occhio, coll&#039;andamento de&#039;raggi re­<lb></lb>fratti, che per la pupilla vanno a terminar sulla retina. </s>

<s>Nello spazio, lasciato <lb></lb>fra la sopraddetta figura e il margine della carta, sotto quest&#039;enunciato di <pb xlink:href="020/01/524.jpg" pagenum="505"></pb>proposizione <emph type="italics"></emph>perchè gli occhi<emph.end type="italics"></emph.end> myopes, <emph type="italics"></emph>cioè di vista corta vegghino poco, e <lb></lb>perchè gli occhiali concavi gli facciano vedere più di quel che vedevano,<emph.end type="italics"></emph.end><lb></lb>si legge: “ A questi occhi segue questo quando l&#039;oggetto è lontano, perchè <lb></lb>i raggi, venendo tanto poco divergenti che la sua cornea non serve per <lb></lb>dargli quella rifrazione che basti, e perciò concorrono più presto che non <lb></lb>dovrebbero; ma essendo vicino, non hanno bisogno di occhiale, perchè quella <lb></lb>gran divergenza che hanno dall&#039;oggetto vicino serve per fargli concorrere <lb></lb>dove bisogna. </s>

<s>E così si vede in che maniera l&#039;occhiale concavo viene a far <lb></lb>vedere più di quello si vedeva, perchè gli occhi <emph type="italics"></emph>myopes<emph.end type="italics"></emph.end> hanno la cornea di <lb></lb>sfera più piccola, che non dovrebbero avere, che stante questo i raggi del­<lb></lb>l&#039;oggetto vengono a concorrere più presto nella retina, che è dove si forma <lb></lb>la vista, ma mettendovi avanti l&#039;occhiale concavo, che ha virtù di fare i <lb></lb>raggi più divergenti che prima, .... di tal maniera che poi la detta cornea <lb></lb>viene a fare la refrazione nella retina, è però dunque che l&#039;occhiale con­<lb></lb>cavo ha virtù di far vedere più di quello che vedeva prima. </s>

<s>” </s></p><p type="main">

<s>Poi seguita l&#039;altro enunciato di proposizione, <emph type="italics"></emph>gli occhi presbiti in che <lb></lb>maniera vegghino assai di lontano e perchè per vedere da vicino ci vuol <lb></lb>gli occhiali convessi,<emph.end type="italics"></emph.end> sotto la quale così si legge: “ Per questa dimostra­<lb></lb>zione dunque si vedrà che gli occhi presbiti, che son quelli che avendo la <lb></lb>cornea di più grande sfera che non dovrebbero avere, e così battendovi i <lb></lb>raggi all&#039;oggetto fa maggior rifrazione che non avrebbe a essere, e così <lb></lb>viene ad essere il punto dove si uniscono i raggi fuori della retina, che <lb></lb>mettendovi gli occhiali convessi gli toglie di quella divergenza e gli fa con­<lb></lb>correre più presto, in maniera tale che viene a stamparsi il punto dell&#039;og­<lb></lb>getto nella retina, che è dove si fa la vista. </s>

<s>E questo segue a questi occhi <lb></lb>quando l&#039;oggetto è vicino, perch&#039;essendo lontano non hanno bisogno d&#039;oc­<lb></lb>chiale, perchè i raggi vengono tanto più divergenti, che ogni poco di con­<lb></lb>vessità serve per fargli concorrere, e però gli serve quella della sua cornea. </s>

<s>” </s></p><p type="main">

<s>Così il Maurolico, il Castelli, il Viviani concorsero insieme, e de&#039;primi <lb></lb>fra&#039;nostri, a trovare il vero di quella dottrina mirabile utile e gioconda a <lb></lb>sapersi, intorno alla quale invano erasi affaticato il Porta. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;invenzione del Microscopio, riguardato nella sua prima semplicità, è <lb></lb>antica quant&#039;è antica l&#039;invenzione stessa degli occhiali da naso. </s>

<s>La lente <lb></lb>convessa da presbiti infatti rappresenta, anche all&#039;occhio normale, le im­<lb></lb>magini virtuali, ingrandite e diritte degli oggetti vicini. </s>

<s>Ma, forse per la fa­<lb></lb>cilità della costruzione, si ricorse in principio, più presto che alle lenti, alle <lb></lb>sfere di vetro o alle boccie ripiene d&#039;acqua, per servirsene ad uso micro­<lb></lb>scopico in condur miniature o altri minutissimi lavori. </s>

<s>Girolamo Fabrizi <lb></lb>d&#039;Acquapendente, nel 1600, scriveva così nel suo celebre Trattato <emph type="italics"></emph>De vi-<emph.end type="italics"></emph.end><pb xlink:href="020/01/525.jpg" pagenum="506"></pb><emph type="italics"></emph>sione:<emph.end type="italics"></emph.end> “ Quocirca ii, qui vulgo miniatores vocantur, lineas suas tenuissi­<lb></lb>mas et pene inconspicuas, nonnisi ad lucem refractam ducere possunt. </s>

<s>Unde <lb></lb>ea dumtaxat luce utuntur, quae post phialam aqua plenam apparet, quasi <lb></lb>necessitate quadam coacti intelligant eiusmodi lucem refractam caeteris cla­<lb></lb>riorem esse, robustioremque, ideoque dicebat Vitellio refractionem generare <lb></lb>lumen, quia adiuvat radios ” (Venetiis 1600, pag. </s>

<s>70). </s></p><p type="main">

<s>L&#039;effetto dell&#039;ingrandimento microscopico è qui dall&#039;Acquapendente, <lb></lb>come da Galileo nel Nunzio Sidereo, spiegato al modo di Vitellione, am­<lb></lb>mettendo cioè che i raggi costipati per rifrazione, accrescan lume alla vista, <lb></lb>ma infin dal 1611 il Keplero e il De Dominis avevan diottricamente dimo­<lb></lb>strato il modo del rappresentarsi le immagini virtuali e ingrandite nelle lenti <lb></lb>biconvesse, e il Maurolico aveva, forse con maggior precisione, divisato il <lb></lb>modo del rappresentarsi le immagini reali nelle lenti stesse e nelle sfere <lb></lb>cristalline. </s>

<s>Avendo inoltre il Maurolico stesso dimostrato, nel Teorema XVIII <lb></lb>de&#039;<emph type="italics"></emph>Diaphanorum partes,<emph.end type="italics"></emph.end> che il concorso de&#039;raggi è tanto più preciso, e che <lb></lb>perciò tanto son minori le aberrazioni di refrangibilità e di sfericità, quanto <lb></lb>le sfere son di minor raggio; veniva così a farsi luminosa guida ai futuri <lb></lb>costruttori dei Microscopi. </s></p><p type="main">

<s>Guidato più forse dalla propria pratica che non dalla teorica mauroli­<lb></lb>cana, uno de&#039;primi, fra così fatti costruttori, fu Galileo, il quale già, in fin <lb></lb>dal 1614, aveva con un segmento di piccola sfera lavorata una lente, e, in­<lb></lb>seritala dentro un piccolo tubo, per maneggiarla meglio, renderne più effi­<lb></lb>cace la visione e applicarla a osservar le cose minute come le esteriori ap­<lb></lb>parenze degli insetti; ne aveva così composto un Microscopio semplice, a cui <lb></lb>dava il nome di <emph type="italics"></emph>Occhialino.<emph.end type="italics"></emph.end> Aveva un tale occhialino fatto noto e dispen­<lb></lb>sato agli amici, e fra questi a Bartolommeo Imperiali, che da Genova gli <lb></lb>scriveva così in proposito, il dì 4 d&#039;Ottobre di quell&#039;anno 1614: “ Ho poi <lb></lb>fatte alcune osservazioni coll&#039;<emph type="italics"></emph>Occhialino,<emph.end type="italics"></emph.end> e fra le altre ho osservato che le <lb></lb>mosche femmine hanno minor quantità di peli e più corti assai di quel che <lb></lb>non abbiano i maschi ” (MSS. Gal., P. VI, T. IX, c. </s>

<s>206). </s></p><p type="main">

<s>Poi più tardi lo stesso Galileo pensò di aggiungere al tubo alcuni altri <lb></lb>organi per render più comode le osservazioni. </s>

<s>Così fatti organi, benchè sem­<lb></lb>plicissimi, conferiron pure ad esaltar l&#039;Occhialino all&#039;essere e alla dignità <lb></lb>di strumento, e consistevano in una colonnetta posata su un piede, alla <lb></lb>quale in alto era raccomandato un anello, dentro a cui potesse scorrere il <lb></lb>tubo o cannoncino, per accostare e discostar la lente dall&#039;oggetto, il quale, <lb></lb>per osservarlo tutto, posavasi sulla circonferenza di una piccola ruota fissa <lb></lb>a un asse girevole in un foro della stessa colonnetta, al di sotto del can­<lb></lb>noncino. </s></p><p type="main">

<s>Noi ci studiammo altrove (Estate in Montagna, Firenze 1884, pag. </s>

<s>230) <lb></lb>di rappresentare in disegno il nuovo strumento galileiano, pigliando lume <lb></lb>da un cenno di descrizione, che ne fa al principe Cesi l&#039;Inventore stesso, <lb></lb>in una sua lettera scritta da Firenze il dì 23 Settembre 1624: “ Invio a <lb></lb>V. E. un Occhialino per vedere da vicino le cose minime, del quale spero <pb xlink:href="020/01/526.jpg" pagenum="507"></pb>che ella sia per prendersi gusto, e trattenimento non piccolo, che così ac­<lb></lb>cade a me. </s>

<s>Ho tardato a mandarlo, perchè non l&#039;ho prima ridotto a per­<lb></lb>fezione, avendo avuto difficoltà nel ritrovare il modo di lavoràre i cristalli <lb></lb>perfettamente. </s>

<s>L&#039;oggetto si attacca sul cerchio mobile, che è nella base, e <lb></lb>si va movendo per vederlo tutto; atteso che quello che si vede in una oc­<lb></lb>chiata è piccola parte. </s>

<s>E perchè la distanza fra la lente e l&#039;oggetto vuol es­<lb></lb>sere puntualissima, nel guardare gli oggetti che hanno rilievo bisogna potere <lb></lb>accostare e discostare il vetro, secondo che si guarda questa o quella parte, <lb></lb>perciò il cannoncino è fatto mobile nel suo piede o guida che dir la vo­<lb></lb>gliamo ” (Alb. </s>

<s>VI, 297). </s></p><p type="main">

<s>In quel tempo che Galileo si compiaceva così, e dilettavasi della vista <lb></lb>del suo Occhialino, tre altri simili strumenti, ma costruiti in diverso modo <lb></lb>dai galileiani, furono d&#039;Oltre monte mandati al Granduca e ai principi della <lb></lb>corte di Firenze. </s>

<s>La notizia e la descrizione di questo Microscopio oltramon­<lb></lb>tano l&#039;abbiamo appresa da un <emph type="italics"></emph>Discorso dell&#039;occhiale detto di moltiplica­<lb></lb>zione cavato da una lettera scritta di .... dal sig. </s>

<s>Agnolo Marzi Medici.<emph.end type="italics"></emph.end><lb></lb>L&#039;estratto fu ritrovato fra le carte manoscritte della R. </s>

<s>Biblioteca nazionale <lb></lb>di Firenze, e ci fu mostrato a leggere e ad esaminare dal gentilissimo si­<lb></lb>gnor Bibliotecario, appena che ei per caso l&#039;ebbe scoperto. </s>

<s>In quel Discorso, <lb></lb>dop&#039;aver magnificata l&#039;eccellenza dello strumento applicato a veder cose na­<lb></lb>turalmente invisibili, specie negli insetti, l&#039;Autore soggiunge le parole se­<lb></lb>guenti: “ Mi sa male non gli poter mandar l&#039;occhiale, perchè non è mio, <lb></lb>e nemmeno dire come sta, e questo per essermi proibito rispetto al voler <lb></lb>che si vegga, e se al Galileo dà il cuore di ritrovarlo, il quale è un mese <lb></lb>che ci è dietro, ma non si è visto cosa alcuna. </s>

<s>È ben vero che con il suo <lb></lb>mutando i vetri fa una cosa piccola apparir grande, ma non con quella esatta <lb></lb>distinzione e chiarezza: mostra più offuscato e questo arriva a perfezion <lb></lb>tale che l&#039;invisibili fa apparir visibili. </s>

<s>” <lb></lb><figure id="id.020.01.526.1.jpg" xlink:href="020/01/526/1.jpg"></figure></s></p><p type="caption">

<s>Figura 50.</s></p><p type="main">

<s>Da ciò si apprende che i Microscopi oltramon­<lb></lb>tani debbono esser posteriori a quelli descritti da Ga­<lb></lb>lileo al Cesi, ne&#039;quali per veder dell&#039;oggetto le intere <lb></lb>parti e il rilievo, i vetri si dovevan <emph type="italics"></emph>mutare,<emph.end type="italics"></emph.end> ossia ora <lb></lb>avvicinare e ora discostar dall&#039;oggetto stesso, facendo <lb></lb>scorrere il tubo nell&#039;anello. </s></p><p type="main">

<s>S&#039;apprende di più, che l&#039;invenzione era confi­<lb></lb>data in segreto. </s>

<s>Qualunque però si fosse il segreto <lb></lb>imposto all&#039;Autor del Discorso, egli si fa già inten­<lb></lb>dere abbastanza bene, descrivendo il modo di far uso <lb></lb>dello strumento. </s>

<s>Ma come ciò fosse poco, viene in <lb></lb>calce a dar, con tre disegni che noi rappresentiamo <lb></lb>nelle tre figure 50, 51, 52, lo spaccato e la pianta <lb></lb>dello strumento stesso, e, distinte con numeri le <lb></lb>parti, le dichiara poi così con parole ordinatamente sotto i numeri corri­<lb></lb>spondenti: </s></p><pb xlink:href="020/01/527.jpg" pagenum="508"></pb><p type="main">

<s>“ Figura delle misure e vetri dell&#039;Occhiale sopradescritto, dal medesimo <lb></lb>signor Marzi mandata. </s>

<s>N.o 1 Profilo del cannone. </s>

<s>N.o 2 Profilo del can­<lb></lb><figure id="id.020.01.527.1.jpg" xlink:href="020/01/527/1.jpg"></figure></s></p><p type="caption">

<s>Figura 51.<lb></lb>none piccolo, che entra nel n.o 1. N.o 3 Pianta del can­<lb></lb>none 1 per di sopra. </s>

<s>N.o 4 Pianta del cannone 1 per <lb></lb>di sotto. </s>

<s>N.o 5 Pianta del cannone 2 in bocca. </s>

<s>N.o 6 <lb></lb>Pianta del cannone 2 in fondo. </s>

<s>N.o 7 dove si mettono <lb></lb>gli animali cavando il cannone n.o 2. Nel fondo di que­<lb></lb>sti cannoni, che viene ad essere il n.o 4 e 6, sono i due <lb></lb>vetri, uno al cannone grande e l&#039;altro al piccolo. </s>

<s>” </s></p><p type="main">

<s>La vantata eccellenza di questo Microscopio sopra <lb></lb>il galileiano dipendeva in primo luogo dal porta oggetti, <lb></lb>il quale, essendo il vetro piano del cannone n.o 1, lasciava traveder gli og­<lb></lb>getti investiti per ogni parte di luce, come se fossero liberamente campati <lb></lb><figure id="id.020.01.527.2.jpg" xlink:href="020/01/527/2.jpg"></figure></s></p><p type="caption">

<s>Figura 52.<lb></lb>in aria, mentre il porta oggetti del Microscopio galileiano, <lb></lb>essendo opaco, lasciava le parti di sotto e da&#039;lati delle piccole <lb></lb>cose da traguardarsi involte e sbattute nell&#039;ombra. </s>

<s>Dipen­<lb></lb>deva altresì, e con miglior ragione, quella eccellenza dall&#039;es­<lb></lb>ser la lente microscopica incastonatasi nell&#039;anello, in fondo <lb></lb>al cannone n.o 2, assai conglobata. </s></p><p type="main">

<s>Gli effetti poi de&#039;globuli di vetro ritrovati in pratica, <lb></lb>conforme alla teoria maurolicana, tanto più maravigliosi quanto più i globuli <lb></lb>stessi erano piccoli, consigliarono i Naturalisti a servirsi di cosiffatti sempli­<lb></lb>cissimi Microscopii, anche dappoi che furono inventati e divulgati i Micro­<lb></lb>scopii composti. </s></p><p type="main">

<s>Si chiamarono que&#039;globuli di vetro <emph type="italics"></emph>Microscopii olandesi,<emph.end type="italics"></emph.end> e l&#039;Huyghens <lb></lb>gli descriveva nel 1678 all&#039;Autor del <emph type="italics"></emph>Diario parigino<emph.end type="italics"></emph.end> in una sua lettera o <lb></lb>Discorso, a cui premetteva il titolo: <emph type="italics"></emph>De novo Microscopio ex Hollandia al­<lb></lb>lato.<emph.end type="italics"></emph.end> Di un tal Discorso ugeniano si legge nella Raccolta delle Opere varie <lb></lb>un estratto, che incomincia: “ Microscopium hoc ex unico formatur exiguo <lb></lb>globulo vitreo, simili illis, quibus in Hollandia et Anglia animaleuta fuere <lb></lb>observata in aqua putcali et pluvia.... ” (Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>764). </s></p><p type="main">

<s>Ritorna anco nella <emph type="italics"></emph>Diottrica<emph.end type="italics"></emph.end> l&#039;Huyghens sopra questo argomento, e rac­<lb></lb>conta che con uno di cosiffatti Microscopii olandesi una volta il Lewenhoeck <lb></lb>gli fece veder, nella coda di un&#039;anguilla, come il sangue, <emph type="italics"></emph>globulis subru­<lb></lb>bentibus constans, celeri motu per canaliculos arteriarum, qui venis con­<lb></lb>tinuantur, discurrit<emph.end type="italics"></emph.end> (Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>226). </s></p><p type="main">

<s>I Microscopii a globetti di vetro però, che intorno al 1678, secondo <lb></lb>l&#039;Huyghens, s&#039;incominciarono a fabbricare in Olanda, erano infin dal 1644 <lb></lb>notissimi in Italia, sotto il nome di <emph type="italics"></emph>Microscopii della perlina.<emph.end type="italics"></emph.end> Ne fu inven­<lb></lb>tore Evangelista Torricelli, il quale sembra non insegnasse ad altri che al <lb></lb>fratel suo Luca il modo di ridurre in perline i vetri, e di assettarle così, <lb></lb>da poter traguardar con esse i minutissimi oggetti. </s>

<s>Da Luca Torricelli ebbe <lb></lb>il segreto il Viviani, che ne lasciò così, di propia mano ricordo, fra le sue <lb></lb>carte: <emph type="italics"></emph>“ Modo di fare gli occhiali da vedere le cose piccole.<emph.end type="italics"></emph.end> Si piglia del <pb xlink:href="020/01/528.jpg" pagenum="509"></pb>cristallo sottilissimo in filo, e alla lucerna, dove si strugge il vetro o il cri­<lb></lb>stallo con il soffietto, si soffia in quel filo di cristallo, e così si viene a fare <lb></lb>una sfera piccola. </s>

<s>Questa si piglia e si accomoda fra due carte, con fare un <lb></lb>foro nel mezzo, tanto che vi stia la detta sfera, ed incollandole insieme per­<lb></lb>chè tenghino la detta sfera piccola, e poi per il detto foro si guarda al lume <lb></lb>di lucerna o di altro, quel che si vuol vedere, che si vede con grande ac­<lb></lb>crescimento ” (MSS. Gal. </s>

<s>Disc., T. CXXXIII, c. </s>

<s>12). </s></p><p type="main">

<s>Le perline olandesi poi si costruivano e si assettavano così, secondo <lb></lb>l&#039;Huyghens, in un modo non molto diverso da quelle del Torricelli: “ Fra­<lb></lb>gmina vitri minima ad imam lucernae flammam, qua parte caeruleus color <lb></lb>conspicitur, admoventur ut candescent atque ita filo ferreo quantum tenuis­<lb></lb>simum duci potest, excepta, ac porro dextre versata, in globulos abeunt, qui <lb></lb>satis magni si granum sinapi aequaverint. </s>

<s>Ex pluribus ita paratis aliquos <lb></lb>probos reperies, idque experieris postquam lamellae aeraee eos incluseris. </s>

<s><lb></lb>Quod ita fit. </s>

<s>Lamellam ex aere tenuissimo digiti longitudine, longitudine <lb></lb>dupla complicabis, tum medium hoc rectangulum acus cuspide perforabis; <lb></lb>foramina opposita coticula levigabis ne quid scabri circa margines adhaereat <lb></lb>et flammae fuligine inficies, ne quid fulgidum intus remaneat. </s>

<s>Inde sphae­<lb></lb>rulam adhuc fiilo ferreo haerentem intra lamellam atque ad ipsa foramina <lb></lb>inseres; pressamque continebis adactis circum aeneis tribus claviculis ex filo <lb></lb>desectis, malleoque firmatis. </s>

<s>Sic levi opera Microscopia efficies, ex quibus <lb></lb>quae optima seliges ” (Dioptr. </s>

<s>Lugd. </s>

<s>1703, pag. </s>

<s>225). </s></p><p type="main">

<s>Ma i Microscopii semplici, e questi stessi squisitissimi delle perline, <lb></lb>così torricelliani come olandesi, con i quali s&#039;erano già scoperti gli sper­<lb></lb>matozoi, e le anguillette dell&#039;aceto, e i così detti animalucci delle infusioni, <lb></lb>erano nonostante ancora assai di lungi dal prestar que&#039;così comodi e così lar­<lb></lb>ghi servigi alla scienza, che erano ordinati a prestarle i Microscopii composti. </s></p><p type="main">

<s>Nella storia dell&#039;invenzione di questo nuoyo e importantissimo stru­<lb></lb>mento hanno alcuni dato grande importanza a un fatto, che si dice essere <lb></lb>stato osservato e considerato da Galileo, ma che non potevà sfuggire agli <lb></lb>occhi di molti fra coloro, che si trovavano in mano a trattare un Canoc­<lb></lb>chiale olandese. </s>

<s>Il fatto consiste nell&#039;osservar che gli oggetti vicini, ritirando <lb></lb>indietro l&#039;oculare a una notabile distanza dall&#039;obiettivo, appariscono ingran­<lb></lb>diti. </s>

<s>In qualunque modo però, inconsideratamente si crede da costoro che <lb></lb><emph type="italics"></emph>il Telescopio accomodato per veder gli oggetti vicinissimi<emph.end type="italics"></emph.end> (Alb. </s>

<s>IV, 248), <lb></lb>come Galileo talvolta per curiosità accomodava il suo, possa qualificarsi <lb></lb>per un vero Microscopio, in cui siasi trasformato lo stesso Telescopio ga­<lb></lb>lileiano. </s></p><p type="main">

<s>Non dal galileiano, ma dal Telescopio astronomico doveva aspettarsi la <lb></lb>trasformazione, e il Keplero che aveva dimostrata la teoria diottrica del Mi­<lb></lb>croscopio semplice, e che, componendo insieme due Microscopii semplici, <lb></lb>aveva speculata l&#039;invenzione dello stesso Telescopio astronomico, si può dir <lb></lb>perciò che fosse nello stesso tempo il primo inventore del Microscopio com­<lb></lb>posto. </s>

<s>La trasformazione infatti del Telescopio kepleriano in Microscopio si <pb xlink:href="020/01/529.jpg" pagenum="510"></pb>ottiene immediata, dando contrariamente grandezza e distanza focale alle <lb></lb>lenti: ciò vuol dire che se al Telescopio s&#039;applica un obiettivo più grande <lb></lb>e d&#039;un fuoco più lungo, al Microscopio invece s&#039;applica un obiettivo più <lb></lb>piccolo e di un fuoco più corto. </s></p><p type="main">

<s>Ma il Keplero, come non eseguì il Telescopio, così non pensò a tra­<lb></lb>mutar l&#039;obiettivo nell&#039;oculare, e a suggerir la pratica del Microscopio. </s>

<s>Se <lb></lb>il Matematico alemanno però speculava, un nostro ottico italiano operava, <lb></lb>ed è quel Francesco Fontana che, essendo stato primo ad eseguire il Tele­<lb></lb>scopio astronomico, fu primo anche a inventare il Microscopio composto. </s>

<s>Il <lb></lb>Trattato VIII delle <emph type="italics"></emph>Novae coelestium terrestriumque rerum observationes<emph.end type="italics"></emph.end><lb></lb>s&#039;intitola <emph type="italics"></emph>De Microscopio,<emph.end type="italics"></emph.end> e l&#039;Autore incomincia così a dire nel capitolo I: <lb></lb>“ Inventionem hanc reperi in anno 1618. Duo assero: primo, dictum spe­<lb></lb>cillum antiqius non esse dicto anno. </s>

<s>Secundo, me fuisse inventorem in hac <lb></lb>civitate Neapolitana, in qua haec publici iuris fiunt. </s>

<s>Limito dictum quia, ut <lb></lb>etiam supra in alia mea inventione Telescopii duarum lentium convexarum <lb></lb>insinuavi, omnes intellectu et operatione praediti sumus, atque adeo Micro­<lb></lb>scopii inventio, alibi, citato anno antiquior esse potest. </s>

<s>Quoad primum pa­<lb></lb>tet, quia antea nullum extabat vestigium huiusmodi specilli, nec ullus Au­<lb></lb>thor, saltem ante recensitum annum, meminerat. </s>

<s>Dixi ante recensitum annum, <lb></lb>nam in anno 1626 Pater Scheiner e Societate Jesu, in sua Rosa Ursina, <lb></lb>Lib. </s>

<s>I, Cap. </s>

<s>XXX, asserit: <emph type="italics"></emph>Eadem arte natum est illud admirabile Mi­<lb></lb>croscopium, quo musca in elephantem et pulex in camelum amplifica­<lb></lb>tur.<emph.end type="italics"></emph.end> Certum tamen est me prius dicto anno 1626 tale specillum adinvenisse, <lb></lb>ut fidem facit admodum R. P. </s>

<s>Hieronymus Sirsalis eiusdem Societatis Jesu ” <lb></lb>(Neapoli 1646, pag. </s>

<s>145, 46). </s></p><p type="main">

<s>Ma l&#039;Huyghens ebbe qualche scrupolo di accettar per verità storiche <lb></lb>le asserzioni del Fontana, perchè <emph type="italics"></emph>testimonium Hier. </s>

<s>Sirsalis quod addu­<lb></lb>cit, non est antiqius anno 1625<emph.end type="italics"></emph.end> (Dioptr. </s>

<s>ibi, pag. </s>

<s>221), perciò soggiunge: <lb></lb>“ Anno autem 1621 apud Drebelium nostratem, conspecta fuisse Microsco­<lb></lb>pia huiusmodi Londini in Britannia, ipsi qui adfuerant saepe mihi narrave­<lb></lb>runt, ipsumque primum auctorem eorum tunc habitum ” (ibi). </s></p><p type="main">

<s>Noi però non dubitiamo della verità dell&#039;asserto del nostro Ottico na­<lb></lb>poletano, perchè è un fatto che fu egli il primo a costruire il Telescopio <lb></lb>speculato già dal Keplero, e da questo al Microscopio composto la trasfor­<lb></lb>mazione è così naturale, che ci fa anzi gran maraviglia che non gli occor­<lb></lb>resse di farla prima del 1618. Come, dall&#039;altra parte, fosse condotto il Fon­<lb></lb>tana, dalla costruzione del tubo astronomico a quello microscopico, lo espone <lb></lb>al Cap. </s>

<s>II del citato Trattato VIII con sì lucido processo, da persuader fa­<lb></lb>cilmente dover esser per quello, come da sicura e diritta scorta, guidato <lb></lb>alla sua invenzione. </s>

<s>“ Quia opposita iuxta se posita magis clarescunt, ut in­<lb></lb>quiunt Philosophi, propterea ipsius specilli melius structura dignoscetur, si <lb></lb>tubo optico astronomico contrapponetur. </s>

<s>In multis opponuntur astronomicus <lb></lb>tubus et specillum. </s>

<s>Hoc primo quoad lentem convexam exteriorem: nam tubi <lb></lb>astronomici quo maioris diametri est lens, eo perfectior est tubus; specilli <pb xlink:href="020/01/530.jpg" pagenum="511"></pb>vero, quo minoris diametri, eo magis visibile auget, perfectiusque videre <lb></lb>facit ” (Novae Observat. </s>

<s>ibi, pag. </s>

<s>146). E prosegue così a contrapporre e a <lb></lb>rilevar le differenze e le somiglianze che passano fra&#039;due strumenti. </s></p><p type="main">

<s>In far tali riscontri non lascia addietro il Fontana di accennare anche <lb></lb>all&#039;uso del Telescopio galileiano, in cui le immagini microscopiche si rap­<lb></lb>presentan diritte: “ Si autem desiderabis per parvum specillum non inversa <lb></lb>sed directa videre, adhuc in hoc varietur constructio respectu Tubi astro­<lb></lb>nomici. </s>

<s>Nam lens exterior parvi specilli eamdem servare debet ab obiecto <lb></lb>distantiam, ac per inversionem. </s>

<s>Similiter lens concava in hoc specillo qua­<lb></lb>druplicatam ab obiecto distantiam diametri exterioris lentis servare necesse <lb></lb>est. </s>

<s>Non sic vero in Tubo astronomico res se habet, ut patet ” (ibi, pag. </s>

<s>147). </s></p><p type="main">

<s>Qui però ben s&#039;intende che l&#039;Autore propone il caso per una semplice <lb></lb>curiosità, come pure lo proponeva Galileo, il quale perciò nelle sue osser­<lb></lb>vazioni naturali si servì sempre dell&#039;Occhialino. </s>

<s>E in vero, benchè sia un <lb></lb>fatto che si può il Telescopio galileiano accomodare a veder così gli oggetti <lb></lb>vicini come i lontani, nonostante l&#039;immagine reale dell&#039;obiettivo convesso, <lb></lb>formandosi a gran distanza dal centro della lente, e dovendosi perciò riti­<lb></lb>rar molto indietro l&#039;oculare concavo, veniva lo strumento per la sua ecces­<lb></lb>siva lunghezza a rendersi tanto incomodo nelle osservazioni, tanto si disper­<lb></lb>deva di luce e tanto si rappresentavano le immagini poco precise, da non <lb></lb>passar per la mente a nessuno di preferir tanto scapito al meschino gua­<lb></lb>dagno di veder gli oggetti nella loro posizion naturale. </s>

<s>Da un&#039;altra parte <lb></lb>poco fa, se nell&#039;osservar un piccolo oggetto, per esempio un animaluccio <lb></lb>infusorio, apparisce il capo dov&#039;è la coda. </s></p><p type="main">

<s>Il tutto poi vien suggellato dal fatto che i costruttori de&#039;Microscopii <lb></lb>composti non hanno poi seguita altra regola, nè hanno cercata altra com­<lb></lb>posizione di lenti, ma si son solamente studiati di ridurre a maggior per­<lb></lb>fezione l&#039;opera del nostro Ottico napoletano. </s></p><p type="main">

<s>Nella grande riforma neutoniana degli strumenti diottrici la mente del <lb></lb>Filosofo inglese non lasciò indietro di speculare anche intorno alla perfe­<lb></lb>zione dei Microscopii. </s>

<s>“ Saepius, egli scrive, cogitavi de construendo Micro­<lb></lb><figure id="id.020.01.530.1.jpg" xlink:href="020/01/530/1.jpg"></figure></s></p><p type="caption">

<s>Figura 53.<lb></lb>scopio, quod pro vitro <lb></lb>obiectivo haberet lami­<lb></lb>nam ex metallo refle­<lb></lb>ctentem. </s>

<s>Etenim haec <lb></lb>instrumenta ad maio­<lb></lb>rem perfectionem, quam <lb></lb>nunc habent adhuc pos­<lb></lb>se videntur aeque ac <lb></lb>Telescopia, et fortasse <lb></lb>magis, siquidem Micro­<lb></lb>scopia opus habent una metalli lamina reflectente ut videri potest in Dia­<lb></lb>grammate (fig. </s>

<s>53) in quo AB est Obiectivum ex metallo; CD vitrum <lb></lb><gap></gap> metallo <pb xlink:href="020/01/531.jpg" pagenum="512"></pb>conflati, ubi obiectum est locatum ” (Op. </s>

<s>Omn. </s>

<s>Optica, Patavii 1773, Ap­<lb></lb>pendice, pag. </s>

<s>6). </s></p><p type="main">

<s>I Microscopii però non s&#039;aspettarono il loro perfezionamento dagli spec­<lb></lb>chi del Newton, ma dalle lenti, che riuscirono poi a lavorare squisitissime, <lb></lb>il Dollond in Inghilterra, e l&#039;Amici in Italia. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Agli strumenti così utilmente inventati per aiutare la vista a veder me­<lb></lb>glio in chi ne avesse difetto, e per rappresentare i minimi oggetti ingran­<lb></lb>diti nelle studiose osservazioni di cose naturali, s&#039;aggiunge un&#039;altra inven­<lb></lb>zione da aiutar la sensibilità di quell&#039;organo, che è, dopo la vista, il più <lb></lb>nobile del nostro corpo, e che massimamente conferisce all&#039;educazione del <lb></lb>nostro intelletto. </s>

<s>Vogliam dire del corno acustico, strumento ordinato ad av­<lb></lb>viare dentro la concavità dell&#039;orecchio le onde sonore per modo, che più <lb></lb>intensamente colpiscano il timpano, in chi troppo debole e ottuso avesse <lb></lb>l&#039;udito. </s></p><p type="main">

<s>Il Porta, nel Libro XX della sua <emph type="italics"></emph>Magia Naturale,<emph.end type="italics"></emph.end> intitola il capitolo V: <lb></lb><emph type="italics"></emph>Quomodo instrumentum fieri possit quo longe audiamus.<emph.end type="italics"></emph.end> L&#039;invenzione e <lb></lb>la forma di questo nuovo strumento, dice l&#039;Autore, potersi desumere dalla <lb></lb>stessa Natura, della quale ha deliberato di seguire, ne&#039;precetti di magia na­<lb></lb>turale, il sapiente magistero: “ Sancitum est enim, in magiae naturalis prae­<lb></lb>ceptis, quum aliqua nova investiganda sunt, naturam perscrutandam et imi­<lb></lb>tandam censeamus ” (Lugd. </s>

<s>Batav. </s>

<s>1655, pag. </s>

<s>654). Conforme a questo <lb></lb>verissimo principio, fecondo a chi sa di tante nuove scoperte, il nostro Fi­<lb></lb>sico osserva che gli animali di udito squisitissimo sopra gli altri, hanno gli <lb></lb>orecchi sporti esternamente a guisa del padiglion di una tromba, per cui con­<lb></lb>clude: “ Forma igitur instrumenti auditus oportet sit ampla et concava et <lb></lb>aperta, et intus cochlearia duplici de causa: prima, si soni intus recte fer­<lb></lb>rentur oblaederent sensum; secunda, quia per cochleam circumferuntur, et <lb></lb>allisa vox per aurium anfractus multiplicatur, ut de echo videmus. </s>

<s>Argu­<lb></lb>mentum rei esse potest cochlea marina illa, quae auribus admota strepitum <lb></lb>quaedam leve efficitur ” (ibi, pag. </s>

<s>656). </s></p><p type="main">

<s>Simili osservazioni e simili idee si possono vedere espresse dall&#039;Acqua­<lb></lb>pendente, nel Cap. </s>

<s>II della terza Parte del suo Trattato <emph type="italics"></emph>De aure auditus <lb></lb>organo,<emph.end type="italics"></emph.end> dove discorre, a imitazion del libro <emph type="italics"></emph>De usu partium<emph.end type="italics"></emph.end> di Galeno, <lb></lb>dell&#039;utilità che prestano agli animali gli orecchi esterni. </s>

<s>“ Exterior autem <lb></lb>ita anfractuosa tortuosaque est ad bonam auditionem per tres utilitates, ut <lb></lb>scilicet facile distincteque sonus tum excipiatur, tum intendatur, tum in­<lb></lb>trorsum deferatur. </s>

<s>Supra enim dictum est sonum facillime et exactissime <lb></lb>omnium recipi in concavis, duris, et complanatis corporibus, ita ut si etiam <lb></lb>articulatus sonus veniat, similiter articulatus excipiatur, quae proinde per <lb></lb><gap></gap> 1600 pag. </s>

<s>19) </s></p><pb xlink:href="020/01/532.jpg" pagenum="513"></pb><p type="main">

<s>L&#039;Acquapendente però, in quella sua prolissa enumerazione delle uti­<lb></lb>lità, che può ricavar l&#039;animale, per la più squisita percezione de&#039;suoni, dal <lb></lb>padiglione esterno degli orecchi; non accenna all&#039;idea di fabbricare uno stru­<lb></lb>mento configurato a quel modo, per moltiplicare il suono nell&#039;orecchio del­<lb></lb>l&#039;uomo, ma quella idea è rivelata per la prima volta, da Paolo Aproino, in <lb></lb>una lettera scritta a Galileo da Treviso, il dì 26 Gennaio 1613. Non sa­<lb></lb>premmo per verità dire quali relazioni di idee e di pensieri potessero pas­<lb></lb>sar fra&#039;due Autori, ma è notabile in ogni modo che l&#039;Aproino si riscontra <lb></lb>col Porta nelle accidentali particolarità della storia dell&#039;invenzione, e nel­<lb></lb>l&#039;argomento principale di essa, desunto dal fatto della conca marina appres­<lb></lb>sata all&#039;orecchio. </s></p><p type="main">

<s>Aveva fatto intenzion l&#039;Aproino, come rilevasi dalla lettera citata, di <lb></lb>pubblicare la descrizione dello strumento, dedicandola, per l&#039;intermedio di <lb></lb>Galileo, al Granduca, ma poi, non sapremmo dire per qual motivo, non <lb></lb>mandò l&#039;Autore il suo proposito ad effetto, benchè la descrizione stessa del­<lb></lb>l&#039;invenzione e la storia si legga in un&#039;altra lettera dell&#039;Aproino al mede­<lb></lb>simo Galileo, scritta il dì 27 di Luglio di quell&#039;anno. </s>

<s>“ Ebbe dunque ori­<lb></lb>gine la speculazione da questo: che rivedendo io un giorno certe conchiglie, <lb></lb>che avevo portate meco dal viaggio di mare, che feci l&#039;altr&#039;anno, insieme <lb></lb>con l&#039;istoria intorno a ciò di Guglielmo Rondelezio, e vedendomi innanzi <lb></lb>quella, che egli chiama <emph type="italics"></emph>Aurita,<emph.end type="italics"></emph.end> mi fece saltar capriccio di forare nel fondo <lb></lb>una turbinata assai grande, ch&#039;io avevo, e metterla nell&#039;orecchio, per ten­<lb></lb>tar qualche esperimento. </s>

<s>E infatti successe che mi parve di sentir molto <lb></lb>aggrandirsi la voce, sebben ora che ho l&#039;orecchio avvezzo a cose maggiori, <lb></lb>pare a me che faccia molto poco, per non dir niente. </s>

<s>Ma per essere accom­<lb></lb>pagnato quel poco di aggrandire, con un buccinamento grande, mi apparve <lb></lb>conspicuo, sicchè ne feci qualche conto. </s>

<s>Allora io, invaghito dalla novità <lb></lb>della cosa, proposi a diversi amici ch&#039;io aveva inteso che uno voleva augu­<lb></lb>mentare il suono, per sentire com&#039;essi si moveano, ed insieme per iscoprire <lb></lb>se sapeano che altri avesse osservato questo particolare. </s>

<s>E sebbene da al­<lb></lb>cuni il problema fu reputato degno di speculazione, fu però dagli altri quasi <lb></lb>tutti deriso e stimato per impossibile. </s>

<s>Onde io mi mossi a meglio conside­<lb></lb>rare la natura del suono e delle sue differenze, e in ciò ebbi per fondamento <lb></lb>principale alcune cose, che io mi ricordo aver imparate da V. S. </s>

<s>Nel resto <lb></lb>Boezio mi fu scorta per sapere quanto finora ne sia stato detto, sveglian­<lb></lb>domi intanto in alcune cose quel galantuomo del Maurolico, e in certe altre <lb></lb>Vetruvio, in quel Capo dove parla del risonar delle scene, sebben, per dire <lb></lb>il vero, quello che finora se n&#039;è detto, è molto poco, e questo poco in gran <lb></lb>parte malinteso, e parte falso e lontano dagli esperimenti. </s>

<s>Ma chi sa che <lb></lb>questa nobil parte di Filosofia, tanto interessata con noi, abbandonata da <lb></lb>tutti e negletta, non sia un dì per essere suscitata ed accresciuta! ” (Alb. </s>

<s><lb></lb>VIII, 277). </s></p><p type="main">

<s>Sembra che in queste parole volesse divinar l&#039;Aproino le presenti sco­<lb></lb>perte maravigliose dell&#039;elettricità applicata, nel Telefono e nel Fonografo, <pb xlink:href="020/01/533.jpg" pagenum="514"></pb>alla propagazione e fissazione de&#039;suoni, ma è notabile in ogni modo che fosse <lb></lb>egli il primo a creder possibile l&#039;invenzione di uno strumento da inacutir <lb></lb>l&#039;udito, com&#039;era stata già possibile l&#039;invenzione dello strumento da inacu­<lb></lb>tir la vista; e, non contento a ciò, la possibilità ridusse all&#039;essere, fabbri­<lb></lb>cando così, com&#039;ei prosegue a descriverlo, il suo Corno acustico: “ Prima <lb></lb>dunque fabbricai un cono alto il doppio del suddetto e con sei girate spi­<lb></lb>rali, e più aperto forse otto o dieci gradi, per poter fare gli esperimenti più <lb></lb>in grande, e far riuscire più sensibili le differenze. </s>

<s>E fattone un altro eguale <lb></lb>a questo, in luogo delle spire, che erano alquanto difficili da lavorare, vi ho <lb></lb>messo dentro sei altri coni successivamente più piccoli, in modo che sta­<lb></lb>vano l&#039;un dall&#039;altro separati, il qual modo parve che mi riuscisse piuttosto <lb></lb>migliore del primo che altri modi. </s>

<s>Ne feci poi anche un semplice della stessa <lb></lb>misura, che parea a me che giovasse molto meno degli altri ” (ivi, pag. </s>

<s>278). </s></p><p type="main">

<s>Ricerando in appresso l&#039;Autore altre nuove squisitezze da introdurre <lb></lb>nello strumento, ei si credette di conseguirle, sciegliendo per materia il ve­<lb></lb>tro, e facendone eseguir la fabbrica alle Fornaci di Murano. </s></p><p type="main">

<s>Perchè sperasse ritrovar così fatti vantaggi nel vetro, non è punto dif­<lb></lb>ficile l&#039;indovinarlo a chi ripensa alle insufficienti nozioni, che s&#039;avevano a <lb></lb>que&#039;tempi, intorno alla generazione del suono, e intorno al modo e alle leggi <lb></lb>del diffondersi di lui nello spazio. </s>

<s>Si credeva che non potessero risonare altro <lb></lb>che i corpi duri, per collisione, e che l&#039;aria ne portasse tanto più facilmente <lb></lb>i tremori, quanto più libera la via ne lasciassero aperta a&#039;moti di lei le su­<lb></lb>perficie piane e levigate de&#039;corpi. </s>

<s>Non fa perciò meraviglia che il vetro pa­<lb></lb>resse all&#039;Aproino, per la sua durezza e per la sua levigatezza materia attis­<lb></lb>sima a produr di simili effetti. </s></p><p type="main">

<s>Che s&#039;ignorasse veramente, ai tempi del nostro Trevigiano e alquanto <lb></lb>dopo, il modo e la legge del diffondersi il suono in onde sferiche, per cui <lb></lb>l&#039;intensità scema a proporzione che crescono i quadrati delle distanze, può <lb></lb>vedersi da ciò che ne dice il Cavalieri, ne&#039;capitoli XXXV, XXXVI, e XXXVII <lb></lb>del suo Specchio Ustorio, ne&#039;quali si parla sempre di <emph type="italics"></emph>linee sonore,<emph.end type="italics"></emph.end> e non <lb></lb>mai di <emph type="italics"></emph>onde:<emph.end type="italics"></emph.end> per cui, a desumerne di qui le teorie, si direbbe che il Corno <lb></lb>acustico opera non altrimenti, che lo stesso Specchio Ustorio, condensando <lb></lb>cioè i raggi sonori nel fuoco, in cui, per l&#039;ascoltazione, dee trovarsi collo­<lb></lb>cato puntualmente l&#039;orecchio. </s></p><p type="main">

<s>L&#039;applicazione immediata delle teorie acustiche allo strumento del­<lb></lb>l&#039;Aproino è trascurata dal Cavalieri che solo si contenta di render ragione <lb></lb>del <emph type="italics"></emph>Portavoce,<emph.end type="italics"></emph.end> dicendo che per esso si può parlar di lontano, mantenen­<lb></lb>dovisi la voce gagliarda, <emph type="italics"></emph>per la superficie tersa del canale, e per il tremito <lb></lb>dell&#039;aria, che, senza patire turbamento per la strada, incorrotta perviene <lb></lb>all&#039;orccchio<emph.end type="italics"></emph.end> (Bologna 1650, pag. </s>

<s>81). Quell&#039;applicazione però, che sfuggì al <lb></lb>Cavalieri, a notizia di cui non era pervenuta l&#039;invenzione dell&#039;Aproino, fu <lb></lb>fatta dal Viviani, il quale, di sua propria mano, lasciò disegnato un tubo <lb></lb>in figura di conoide parabolico, nella cavità del quale, per tante linee pa­<lb></lb>rallele, si rappresentano i raggi sonori, i quali vanno tutti insieme a con-<pb xlink:href="020/01/534.jpg" pagenum="515"></pb>correre nel foco, presso all&#039;apice spuntato del conoide, che dee chi ascolta <lb></lb>introdurre nella cavità del suo orecchio. </s>

<s>Il disegno è senz&#039;altro illustrato <lb></lb>dallo stesso Viviani, sottoscrivendovi le parole: <emph type="italics"></emph>Strumento per audizione<emph.end type="italics"></emph.end><lb></lb>(MSS. Cim., T. IV, c. </s>

<s>261). È anche il Corno acustico insomma una di quelle <lb></lb>tante invenzioni, a cui furon gli Autori menati dalla pratica, senza alcuna <lb></lb>scorta di teoria. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Gli Specilli, il Microscopio, il Corno acustico, ordinati dall&#039;arte ad emen­<lb></lb>dare i difetti naturali della vista e dell&#039;udito, o a renderli più squisiti, onde <lb></lb>entrare in più intime relazioni col mondo creato, primeggiano, per nobiltà <lb></lb>ed eccellenza, sopra molti altri strumenti. </s>

<s>Ma l&#039;uomo, che ama di conser­<lb></lb>var collo stesso mondo creato quelle relazioni costanti, fu sollecito d&#039;inve­<lb></lb>stigar le cause della mutabilità e de&#039;guasti, negli oggetti che lo circondano, <lb></lb>e nella propria salute, una delle quali cause egli ebbe presto a riconoscerla <lb></lb>nell&#039;umidità dell&#039;aria. </s>

<s>È perciò che antiche sono le osservazioni igroscopi­<lb></lb>che, le quali, in sul primo nascer dell&#039;arte sperimentale, dettero occasione <lb></lb>a inventare i primi Igrometri. </s>

<s>Leon Battista Alberti, che professando l&#039;arte <lb></lb>sua, ebbe a riconoscere i guasti prodotti dall&#039;umidità dell&#039;aria sugli edifizi, <lb></lb>pensando al miglior modo di difenderli e di preservarli, volle veder quali <lb></lb>fossero i venti più umidi di tutti gli altri, e vi riuscì con l&#039;invenzione di <lb></lb>uno de&#039;primi Igrometri ad assorbimento. </s>

<s>“ Noi abbiamo provato (egli dice <lb></lb>nel Cap. </s>

<s>III del X libro dell&#039;Architettura) che una spugna diventa umida <lb></lb>per la ùmidità dell&#039;aria, e di qui caviamo una regola da pesare, con la <lb></lb>quale noi pesiamo quanto siano gravi e quanto secchi i venti e l&#039;aria ” (Mi­<lb></lb>lano 1833, pag. </s>

<s>349). </s></p><p type="main">

<s>A un Igrometro per assorbimento, servendosi egli pure di una Bilan­<lb></lb>cia ordinarià, nella quale vien turbato l&#039;equilibrio dal preponderare di un <lb></lb>corpo facile a imbeversi dell&#039;umidità dell&#039;aria, aveva pensato anche quel­<lb></lb>l&#039;altro fecondissimo ingegno di curiose ed utili invenzioni, Leonardo da Vinci. </s></p><p type="main">

<s>Ma nell&#039;Alberti e in Leonardo la scienza veniva sopraffatta dall&#039;arte, co­<lb></lb>sicchè può dirsi che i primi Igrometri fossero introdotti nel metodo speri­<lb></lb>mentale, dall&#039;ingegno e dall&#039;industria del Santorio. </s>

<s>Egli quasi prolude a <lb></lb>questo genere d&#039;invenzioni proponendo l&#039;uso di uno strumento, che è forse <lb></lb>il primo Igrometro chimico da noi conosciuto. </s>

<s>Nella III Particola infatti, <lb></lb>capitolo LXXXV del Commentario sull&#039;Arte medica di Galeno, dop&#039;avere ac­<lb></lb>cennato al Termometro, “ Insuper nos, egli tosto soggiunge, invenimus mo­<lb></lb>dum certissimum pro dignoscenda aeris humiditatem, quantam videlicet quo­<lb></lb>tidie sit, et talis est: sumimus tartarum combustum, quod a vulgo dicitur <lb></lb>alumen foecis: hoc exponitur aeri, sed antequam exponatur, exactissime <lb></lb><gap></gap> enim expositum aeri magis ponderat, nos enim pro <pb xlink:href="020/01/535.jpg" pagenum="516"></pb>varietate ponderis dicimus maius pondus maiorem humiditatem, et minus <lb></lb>minorem in aere dominari. </s>

<s>Ex his igitur ultimos gradus activarum et pas­<lb></lb>sivarum qualitatum exactissime percipere possumus ” (Op. </s>

<s>Omn, Vene­<lb></lb>tiis 1660, T. I, pag. </s>

<s>365). </s></p><p type="main">

<s>In questo Igrometro chimico non par che per altro il Santorio pro­<lb></lb>muova l&#039;invenzion dell&#039;Alberti, che per la scelta del corpo igroscopico. </s>

<s>Ma <lb></lb>ne&#039;Commentarii sopr&#039;Avicenna esce lo strumento dalla mente dell&#039;Inven­<lb></lb>tore con organi proprii, i quali saranno quelli, che in sostanza manterrà <lb></lb>poi nelle varie forme dategli da&#039;successivi perfezionatori. </s>

<s>Anche in questi <lb></lb>Commentarii, dopo aver l&#039;Autore, più diligentemente che altrove, descritto <lb></lb>il Termometro ad aria e il Pulsilogio “ deinde habemus, egli soggiunge, <lb></lb>duos modos dimetiendi siccitatem et humiditatem recedentem a naturali statu, <lb></lb>de quibus mentionem facimus aphorismo quarto sesundae setionis Staticae <lb></lb>nostrae ” (ibi, T. III, pag. </s>

<s>31). </s></p><p type="main">

<s>Consiste il primo di questi modi in una corda tesa fra due chiodi e <lb></lb>gravata dal peso di una palla, che pende lungo un regolo graduato. </s>

<s>Imbe­<lb></lb>vendosi di umidità più o meno, la corda si fa più tirata, la palla pendula <lb></lb>si solleva con essa, e indica i varii gradi segnati sopra la scala. </s>

<s>“ Primus <lb></lb>modus explicatur per figuram tertiam in qua extenditur funis aut, si ma­<lb></lb>vis, corda testudimis, crassa tamen applicetur corda parieti, vel aliis locis <lb></lb>et in medio ponatur pila plumbea ac prope signentur gradus. </s>

<s>Dum aer hu­<lb></lb><figure id="id.020.01.535.1.jpg" xlink:href="020/01/535/1.jpg"></figure></s></p><p type="caption">

<s>Figura 54.<lb></lb>mescit corda contrahitur, <lb></lb>dum vero exiccatur per <lb></lb>aerem borealem laxatur. </s>

<s><lb></lb>Aliquando nam aer au­<lb></lb>strinus ita humectat et <lb></lb>contrahit cordam, ut at­<lb></lb>tollatur usque ad litte­<lb></lb>ram A (fig. </s>

<s>54): dum <lb></lb>vero spirant venti septen­<lb></lb>trionales, ita exiccatur ut <lb></lb>pila perveniat ad ipsum <lb></lb>B; ita ut licet nulla spiret aura, quotidie gradus siccilatis vel humiditatis <lb></lb>aeris, quot sint, observari possint ” (ibi). </s></p><p type="main">

<s>L&#039;altra forma d&#039;Igrometro, che passa a descrivere il Santorio, è anche <lb></lb>più ingegnosa, e si può dir la prima Mostra umidaria. </s>

<s>Consiste in un disco <lb></lb>o di cartone o di latta, nel centro del quale è imperniato un leggerissimo <lb></lb>indice, a cui è impresso il movimento da una specie di subbio o di verricello, <lb></lb>attorno al quale è avvolta una corda di canapa o di lino che, allungandosi <lb></lb>o scorciandosi, nelle varie vicende o dell&#039;umido o del secco, dà regola allo <lb></lb>strumento. </s>

<s>“ Secundus modus explicatur per quartam figuram (corrispon­<lb></lb>dente alla nostra fig. </s>

<s>55) quae emulatur Horologium. </s>

<s>Sumitur corda ex lino <lb></lb>satis crassa et longa, quia, quo crassior et longior, eo melius inservit huic <lb></lb><gap></gap><pb xlink:href="020/01/536.jpg" pagenum="517"></pb>humidum vertit radium ad gradus propositos; dum vero per aerem siccum <lb></lb>exiccatur, laxatur, et in alios gradus declinat. </s>

<s>Quanti vero momenti sit haec <lb></lb><figure id="id.020.01.536.1.jpg" xlink:href="020/01/536/1.jpg"></figure></s></p><p type="caption">

<s>Figura 55.<lb></lb>observatio sciunt aegrotantes, qui humido et qui sicco <lb></lb>morbo fuerint oppressi, quos ope istorum instru­<lb></lb>mentorum ad sanitatem perduximus ” (ibi, pag. </s>

<s>33). </s></p><p type="main">

<s>Così aveva il Santorio, nel 1625, divulgata l&#039;in­<lb></lb>venzione di tre varie maniere d&#039;Igrometri. </s>

<s>Ma per­<lb></lb>chè erano quegli strumenti ristretti agli usi medici, <lb></lb>o per qualche altra più complicata ragione, non <lb></lb>par che se ne diffondesse la notizia fra coloro, che, <lb></lb>seguaci della scuola di Galileo, intendevano a pro­<lb></lb>movere, per l&#039;universalità de&#039;suoi soggetti, la scienza <lb></lb>sperimentale. </s>

<s>Fatto sta che in Firenze ebbe lo strumento da tutti altri prin­<lb></lb>cipii la vita, come se fossero quelle prime santoriane invenzioni rimaste ir­<lb></lb>rigidite o morte in mezzo all&#039;aria mefitica di un ospedale. </s></p><p type="main">

<s>Da una lauta mensa principesca ebbe invece origine il primo Igrome­<lb></lb>tro fiorentino. </s>

<s>In uno de&#039;più affannosi giorni estivi del 1645, là sulla fine <lb></lb>del Luglio, vien fatto al Granduca Ferdinando di rivolgere l&#039;attenzione a <lb></lb>quella sottilissima rugiada, di che vedea velarsi i tersissimi cristalli delle <lb></lb>bocce piene d&#039;acqua, posate da&#039;coppieri sulla tavola imbandita. </s>

<s>Manda a <lb></lb>chiamare il Torricelli per saper se il velo rugiadoso era, come dicevano i <lb></lb>Filosofi, aria convertita in acqua. </s>

<s>Il Torricelli rispose esser quello un er­<lb></lb>rore de&#039;peripatetici, i quali, fra alcuni altri, adducevano anche un tal fatto <lb></lb>a provar la trasformazione degli elementi. </s>

<s>Si studiava di persuadere il Gran­<lb></lb>duca, allegando alcuni passi dalla <emph type="italics"></emph>Risposta a Lodovico delle Colombe<emph.end type="italics"></emph.end> (Alb. </s>

<s><lb></lb>XII, 347, 467), dove concorrevano insieme a riprovar l&#039;errore peripatetico <lb></lb>le grandi autorità di Galileo e del Castelli. </s></p><p type="main">

<s>— Da che dunque ha origine questa rugiada? </s>

<s>— riprese a domandare <lb></lb>il Granduca, e il Torricelli: — da quel sottilissimo umido, che è per l&#039;aria, <lb></lb>rimasto a poco a poco invischiato al freddo del vetro — per conferma di <lb></lb>che, soggiungeva come una di quelle stesse bocce si sarebbe veduta sudar <lb></lb>più direttemente, a portarla dalla sala da pranzo giù in qualche cantina. </s>

<s><lb></lb>Il Granduca si mostrò allora curioso di vederne la prova, e il Torricelli pro­<lb></lb>mise che avrebbe pensato al miglior modo di farla. </s>

<s>Tornò pochi giorni dopo <lb></lb>collo strumento già preparato, il quale consisteva in un vaso di vetro, in <lb></lb>figura di cono, co&#039;lati sfuggevoli e colla punta assai acuta. </s>

<s>Infilava cotesto <lb></lb>vaso dentro un anello sorretto da un tripode, e lo faceva empire di ghiac­<lb></lb>cio. </s>

<s>Il vetro cominciò a sudare, e colando giù per la punta, mostrava nella <lb></lb>sala da pranzo di far tre gocciole al minuto: portato in una cantina, dov&#039;era <lb></lb>una fonte, delle gocciole ne dava quindici nel medesimo tempo. </s></p><p type="main">

<s>Fece poi il Granduca per suo diletto ripetere l&#039;esperienza, ora all&#039;aria <lb></lb>aperta in un prato, ora in una ghiacciaia; ora al sole ora al foco di cu­<lb></lb>cina; ora al vento di Tramontana ora a quello di Scirocco (Targioni, No­<lb></lb>tizie ecc. </s>

<s>cit., T. II, P. I, pag. </s>

<s>163, 64), e della nuova invenzione si mostrava <pb xlink:href="020/01/537.jpg" pagenum="518"></pb>assai sodisfatto. </s>

<s>Ma il Torricelli che sentiva di aver ridotto una bagattella <lb></lb>da putti a uno strumento, il quale sarebbe alla Meteorologia riuscito utilis­<lb></lb>simo, ne divulgava la notizia ne&#039;suoi amici di Roma, fra&#039;quali il Ricci così <lb></lb>in tal proposito, per lettera del dì 13 Agosto 1645, gli rispondeva: “ Di <lb></lb>cotesto strumento acqueo per l&#039;umido, è arrivata la notizia ai padri del Col­<lb></lb>legio romano, i quali se ne sono fabbricati uno e mi riferisce il sig. </s>

<s>Bonac­<lb></lb>corsi che vi faccian sopra delle maraviglie grandi. </s>

<s>Veramente non gli si può <lb></lb>negar molta lode, portando a tanta conseguenza una bagattella maneggiata <lb></lb>da putti più che da cerretani ” (MSS. Gal. </s>

<s>Disc., T. XLII, c. </s>

<s>147). </s></p><p type="main">

<s>Questo del Torricelli, che è il primo Igrometro a condensazione di che <lb></lb>abbia fatto uso la scienza, negletto per alcun tempo, tornò a rivivere fra le <lb></lb>mani degli Accademici del Cimento, a cui il Granduca, secondato dall&#039;osse­<lb></lb>quio de&#039;cortigiani, lo consegnò come cosa tutta sua. </s>

<s>Nel consegnarlo però, <lb></lb>mostrava il desiderio che aveva di ridurre lo strumento a segnare i gradi <lb></lb>dell&#039;umido e del secco, a quel modo che il Termometro segnava i gradi <lb></lb>del caldo e del freddo, ciò che dette forse occasione al Viviani di pensare <lb></lb>a raccogliere le gocciole stillate in un bicchiere alto a foggia di cilindro spar­<lb></lb>tito in gradi, piuttosto che numerarle, come faceva il Torricelli, e lo in­<lb></lb>dusse a perfezionare il primo strumento torricelliano a quel modo, che fu <lb></lb>poi descritto nel Libro de&#039;<emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> (Firenze 1841, pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Intanto era sparsa la voce fra&#039;cortigiani di questo desiderio o di que­<lb></lb>sto studio, come dicevano essi, che si dava il Granduca, per ridur l&#039;Igro­<lb></lb>metro a segnare le variazioni dell&#039;umidità con regolata misura. </s>

<s>Era fra <lb></lb>que&#039;cortigiani un tal Paolo Poltri, amico a quel Francesco Folli da Poppi, <lb></lb>celebre per aver egli il primo pensato alla trasfusione del sangue. </s>

<s>E come <lb></lb>fosse motivata da questa amicizia la desiderata invenzione, il Folli stesso <lb></lb>così lo racconta, dop&#039;avere accennato alla notizia del ritrovato olandese, che <lb></lb>motivò l&#039;invenzione del Telescopio. </s>

<s>“ Il simile occorse a me nel ritrovar lo <lb></lb>strumento da conoscere i gradi dell&#039;umido e del secco dell&#039;aria, poichè se <lb></lb>il signor Paolo Poltri, mentre eramo a caccia poco fuori di Bibbiena, non <lb></lb>mi avesse motivato che il Serenissimo Granduca andava investigando il modo <lb></lb>di fare uno strumento da conoscere i gradi dell&#039;umido e del secco, come <lb></lb>era seguìto pochi anni avanti il ritrovamento del Termometro; io certo non <lb></lb>vi avrei pensato. </s>

<s>Eppure la notte seguente lo speculai, ed il giorno dopo <lb></lb>lo feci e glielo presentai, e ciò fu l&#039;anno 1664, e quando venni a stare a <lb></lb>Firenze, che fu l&#039;anno 1665, ne presentai uno al medesimo Serenissimo Pa­<lb></lb>drone, che mostrò gradirlo, e ne fece fare alcuni, che subito mandò a varii <lb></lb>principi d&#039;Europa ” (Stadera medica, Firenze 1680, pag. </s>

<s>113, 14). </s></p><p type="main">

<s>Uno ne fu presentato anche al Papa, non dal Granduca però, nè di­<lb></lb>rettamente dal principe Leopoldo, ma per l&#039;intermedio di mons. </s>

<s>Cesare Ma­<lb></lb>galotti, a cui il conte Lorenzo, in una Lettera ne descriveva l&#039;adattamento <lb></lb>e l&#039;uso, accennando a que&#039;perfezionamenti che l&#039;arte squisita del Campani <lb></lb>avrebbe saputi introdurre nella fabbrica dello strumento (Targ., Notizie cit., <lb></lb>T. II, P. I, pag. </s>

<s>337, 38). </s></p><pb xlink:href="020/01/538.jpg" pagenum="519"></pb><p type="main">

<s>Il Granduca però, piuttosto che al Campani, aveva pensato a Filippo <lb></lb>Treffler, dell&#039;arte del quale era tanto rimasto sodisfatto, quando l&#039;ebbe a&#039;suoi <lb></lb>servigi in Firenze, e perciò comandava al Viviani scrivesse a lui diretta­<lb></lb>mente, ordinandogli che pensasse a costruire con maggior perfezione l&#039;Igro­<lb></lb>metro, per sè già sensibilissimo, del Folli. </s>

<s>Quella lettera, data da Firenze <lb></lb>il dì 21 Novembre 1665, e dallo stesso Viviani spedita ad Augusta, così <lb></lb>diceva: </s></p><p type="main">

<s>“ Per l&#039;aggiunto disegno si dimostra un semplicissimo strumento, che <lb></lb>a&#039;mesi addietro fu presentato al nostro Padron serenissimo, per mezzo del <lb></lb>quale si conoscono le piccole mutazioni dell&#039;aria dal più al meno umido <lb></lb>che vi si trovi. </s>

<s>Tutta l&#039;invenzione si riduce all&#039;avervi ingegnosamente adat­<lb></lb>tato quell&#039;ordinarissimo effetto che tutti i giorni si vede ne&#039;fogli delle fine­<lb></lb><figure id="id.020.01.538.1.jpg" xlink:href="020/01/538/1.jpg"></figure></s></p><p type="caption">

<s>Figura 56.<lb></lb>stre incartate, che è di star ben <lb></lb>tirati ne&#039;tempi asciutti e di al­<lb></lb>lentare negli umidi. </s>

<s>” </s></p><p type="main">

<s>“ S&#039;immagini pertanto ABC <lb></lb>(fig. </s>

<s>56) essere una striscia di <lb></lb>carta da impannata, a guisa <lb></lb>d&#039;un nastro, lunga circa due <lb></lb>terzi di braccio, o più o meno, <lb></lb>e larga meno di un dito. </s>

<s>Que­<lb></lb>sta è avvolta ne&#039;suoi estremi A, <lb></lb>C su due subbietti imperniati, <lb></lb>da potergli ben fermare, ma <lb></lb>anco girare bisognando, in oc­<lb></lb>casione di allungare o scor­<lb></lb>ciare il detto nastro di carta, <lb></lb>per temperare il suo benchè <lb></lb>leggerissimo peso con quello <lb></lb>di un piccolo contrappeso, che <lb></lb>deve sempre tenerla tesa, e mi credo che nel fermarvela da principio si <lb></lb>debba prima privarla interamente dell&#039;umido, con scaldarla, e in tale stato <lb></lb>immediatamente tirarvela, distendendola per linea retta da A a B. </s>

<s>In mezzo <lb></lb>di tal nastro nel punto B sta fermato il capo del filo BDE, il quale cavalca <lb></lb>sopra un piccolissimo rocchetto di ottone, o di legno che sia, col suo asse <lb></lb>che dentro i fori di due ali sta imperniato sopra i suoi poli, nell&#039;estremità <lb></lb>di uno de&#039;quali sta fissa la lancetta DF, che nel volgersi al moto del detto <lb></lb>rocchetto dimostra i gradi o minuti sulla circonferenza della sfera stabile o <lb></lb>mostra FG, avendo però riguardo che la detta lancetta e l&#039;imperniatura siano <lb></lb>agilissimi al moto. </s>

<s>All&#039;altro estremo del filo in E sta pendente un piccol <lb></lb>peso H, il quale va aggiustato con tal discrezione, che, per ogni minimo al­<lb></lb>lungamento della suddetta striscia di carta e&#039;sia appunto bastante, senza <lb></lb>sforzarla, a tenerla ben distesa per le due linee AB, BC. </s>

<s>Così temperato lo <lb></lb><gap></gap> nell&#039;operare, che per <pb xlink:href="020/01/539.jpg" pagenum="520"></pb>ogni poco di alito umido che alla carta s&#039;imprima o che, con qualche ben­<lb></lb>chè debolissimo grado di caldo asciutto le si tolga, si fa subito o all&#039;innanzi <lb></lb>o all&#039;indietro visibilissima variazione dell&#039;indice sulla mostra, ma rimosse <lb></lb>queste cagioni alteranti, riducesi quasi immediatamente sul medesimo segno, <lb></lb>dov&#039;era prima. </s>

<s>” </s></p><p type="main">

<s>“ Nonostante ciò, quell&#039;impareggiabile esquisitezza di gusto e nobile <lb></lb>curiosità, con cui V. S. sa che osserva e filosofa il Serenissimo Granduca, <lb></lb>gli fa desiderare in questo strumento qualche maggior perfezione, e però <lb></lb>mi ha comandato che io lo descriva a V. S., affinchè, fabbricandone uno, <lb></lb>ella possa pensare ai modi di migliorarlo. </s>

<s>” </s></p><p type="main">

<s>“ Vorrebbe S. A. primieramente che due di tali strumenti, tenuti in <lb></lb>un medesimo luogo, andassero, se è possibile, sempre concordi nel dimo­<lb></lb>strare i gradi sulle loro mostre; Che nel trasportarsi da un luogo all&#039;altro, <lb></lb>la lancetta non si movesse di sito come fa adesso, mediante il moto del <lb></lb>peso H e del medesimo strumento; Che si potesse tenerlo esposto all&#039;aria <lb></lb>fuori delle stanze, assicurato dalla polvere, dall&#039;acqua e dal vento, ed a que­<lb></lb>sto effetto era sovvenuto a S. A. di rinchiuderlo, fino al di sotto della mo­<lb></lb>stra, in cassetta senza coperchio, con le sponde di vetro piane, ben sigillate <lb></lb>fra di loro e sul fondo, coprendo poi tutto lo strumento con un&#039;altra simile <lb></lb>cassetta volta all&#039;ingiù, ma che lasci, rasente il fondo, tanta apertura, che <lb></lb>l&#039;aria interna possa con prontezza accomodarsi con l&#039;umido ambiente; Che <lb></lb>finalmente ella provi se vi sia altra materia più resistente, ma così pronta <lb></lb>o più della carta, a ricevere le varie impressioni dell&#039;aria. </s>

<s>” </s></p><p type="main">

<s>“ Se poi le sovvenisse altra migliore invenzione, per ottenere gli effetti <lb></lb>sopra accennati, V. S. è ormai consapevole che tutto sarà gratissimo all&#039;A. S., <lb></lb>e di quanto le riuscirà di conseguire, potrà ella subito darne parte ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXLII, c. </s>

<s>103). </s></p><p type="main">

<s>A questa lettera il Treffler, dopo pochi giorni rispose da Augusta sotto <lb></lb>il dì 4 Dicembre, dicendo al Viviani di aver ricevuto il disegno d&#039;uno stru­<lb></lb>mento che deve servir per riconoscere le minime differenze del secco e del­<lb></lb>l&#039;umido. </s>

<s>“ Ho inteso benissimo, soggiunge, la sua relazione e l&#039;invenzione <lb></lb>mi piace assai. </s>

<s>Farò tutto l&#039;istrumento d&#039;ottone che così l&#039;aria non potrà <lb></lb>muovere e tirarlo dalla sua perfezione e mi servirò di carta pecora sottile <lb></lb>ed in scambio del contrappeso cercherò di servirmi di una molletta leggera <lb></lb>per fuggire il moto del pesino ed in tal modo ancora sarà più facile di po­<lb></lb>terlo portare. </s>

<s>Poi penserò di potere ancora migliorare che per brevità del <lb></lb>tempo non ho potuto considerare tutto quello si potrà fare ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. CLXIV, c. </s>

<s>287). </s></p><p type="main">

<s>Ma intanto il Viviani, lasciando al Treffler di pensare a dar sodisfazione <lb></lb>al Granduca, introducendo nello strumento maggior comodità ed eleganza, <lb></lb>egli attendeva, colla semplicità e con la precisione, a soccorrere ai bisogni <lb></lb>della scienza. </s>

<s>La semplicità la trovò facile fissando i due capi d&#039;una lunga <lb></lb>striscia di cartapecora a un asse di legno, e facendo pender dal mezzo un <pb xlink:href="020/01/540.jpg" pagenum="521"></pb>inchiodata sull&#039;asse, la qual placca era contrassegnata di gradi, tutti di ugual <lb></lb>misura. </s>

<s>O sel sapesse il Viviani o no, costruendo questo Igrometro, di cui <lb></lb>nel R. </s>

<s>Museo di Fisica di Firenze si vede un modello, s&#039;incontrava nello <lb></lb>stesso Igrometro descritto già dal Santorio, colla sola differenza d&#039;aver so­<lb></lb>stituito la cartapecora alla corda tesa. </s>

<s>Le scale, così nello strumento del Fi­<lb></lb>sico fiorentino come in quello del Medico giustinopolitano, erano digradate <lb></lb>allo stesso modo, e ciò non conferiva a quella precisione ch&#039;era l&#039;intento <lb></lb>precipuo del Viviani, e che vale a renderlo per il merito eccellente sopra <lb></lb>tutti gli altri. </s></p><p type="main">

<s>Infino allora s&#039;erano compartiti, per le scale igrometriche, gli spazi <lb></lb>uguali, ma ripensando maturamente il Viviani sopra ciò, ebbe a entrare in <lb></lb>qualche dubbio, da lui così espresso: “ Dubito che nè gli uguali allunga­<lb></lb>menti, nè gli uguali abbassamenti sieno fatti da ugual quantità di umido ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CXXXIV, c. </s>

<s>49). A sincerarsi del qual dubbio invo­<lb></lb>cando per primo aiuto l&#039;esperienza, ebbe a trovar che “ si ricerca più umido <lb></lb>ad abbassare dal secondo al terzo grado, che dal primo al secondo, e maggiore <lb></lb>dal terzo al quarto che dal secondo al terzo, supposti i gradi uguali ” (ivi). </s></p><p type="main">

<s>Pure, non essendo ancora contento, voleva di questi abbassamenti, re­<lb></lb>lativamente agli allungamenti della striscia di carta per effetto dell&#039;umidità, <lb></lb>ritrovare una legge matematica, ed ebbe in taìe investigazione a riconoscere <lb></lb>assai facilmente che il problema igrometrico si riscontrava col problema mec­<lb></lb>canico della corda tesa e gravata nel mezzo, propostosi a risolvere da Ga­<lb></lb>lileo dopo la proposizione ultima del IV Dialogo delle Due Nuove Scienze. </s>

<s><lb></lb>Fu questa l&#039;occasione, che fece rivolgere il Viviani a considerare più attenta­<lb></lb>mente quel problema, per cui venne suo malgrado a riconoscere che la so­<lb></lb>luzione galileiana era sbagliata. </s>

<s>Di ciò avremo non lieve argomento di trat­<lb></lb>tazione nella nostra storia della Meccanica, ma intanto basti il dire che lo <lb></lb>stesso Viviani, in ordine all&#039;Igrometro, riuscì a formular questa legge: “ Gli <lb></lb>allungamenti stanno fra di loro prossimamente nella proporzione de&#039;qua­<lb></lb>drati deglli abbassamenti, e gli abbassamenti come gli angoli prossimamente, <lb></lb>ma però ne&#039;primi piccoli abbassamenti ” (ivi, c. </s>

<s>53). </s></p><p type="main">

<s>Sopra questa legge, in un altro Igrometro di forma anche più sem­<lb></lb>plice del primo, e maneggevole, perchè non consisteva in altro che in un <lb></lb>regolo di ottone, all&#039;estremità del quale due colonnette sostenevano in capo <lb></lb>i due estremi della striscia di carta gravata da un peso, radente una placca <lb></lb>saldata nel mezzo dello stesso regolo, di che due modelli similissimi si ve­<lb></lb>dono nel sopra detto Museo; sopra questa legge, per via di esperienze e di <lb></lb>meccaniche speculazioni scoperta, il Viviani compartì la scala igrometrica <lb></lb>del suo nuovo e sventuratamente negletto strumento. </s></p><p type="main">

<s>Diciamo con tanto più di ragione questo Igrometro sventuratamente ne­<lb></lb>gletto, ripensando alla sorte ch&#039;ebbe quel balocco ad avena d&#039;esser comme­<lb></lb>morato da varii Scrittori. </s>

<s>Giorgio Sinclaro, Filosofo per questa parte vera­<lb></lb>mente curioso, come in dar nel 1669 per cosa nuova l&#039;Orologio a pendolo <lb></lb><gap></gap> e il Boyle avessero frugato per <pb xlink:href="020/01/541.jpg" pagenum="522"></pb>i suoi manoscritti; così dando nel 1669 per cosa nuova l&#039;Igrometro ad avena, <lb></lb>portò sull&#039;Hook quel medesimo sospetto pazzamente geloso. </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> Creaturam hanc Hygroscopii nomine indigitare statui, eo quod <lb></lb>acutissime aeris temperiem humidam et siccam manifestet. <emph type="italics"></emph>Franc.<emph.end type="italics"></emph.end> Id no­<lb></lb>vum videtur inventum, nam non mihi prius innotuit. </s>

<s>Memini tamen me id <lb></lb>in libro quodam nuper vulgari sermone edito, cui epigraphe <emph type="italics"></emph>Micrographia<emph.end type="italics"></emph.end><lb></lb>videre. <emph type="italics"></emph>Alex.<emph.end type="italics"></emph.end> Quid? </s>

<s>an Hygroscopii nomine? <emph type="italics"></emph>Franc.<emph.end type="italics"></emph.end> Imo. <emph type="italics"></emph>Alex.<emph.end type="italics"></emph.end> Quam ve­<lb></lb>reor ne praeter nomen alia nonnulla ex nostro manuscripto mutuatus sit <lb></lb>auctor. </s>

<s>Sed primus omnium qui illius rei meminit fuit Baptista Porta, verbo <lb></lb>solum. </s>

<s>Quo ad eius fabricam et structuram attinet, sumatur <emph type="italics"></emph>grani venacei <lb></lb>arista,<emph.end type="italics"></emph.end> cuius altero extremo corpori alicui plano infixo, indicem transversa­<lb></lb>rium ex materia aliqua levissima alterum superferet, quem iuxta aeris al­<lb></lb>terationem, ex siccitate in humiditatem, et ex humiditate in siccitatem con­<lb></lb>verti videbis ” (Ars magna ecc., Roterodami 1669, pag. </s>

<s>535). </s></p><p type="main">

<s>Se avesse il Sinclaro potuto sapere che il Moncony vide uno di questi <lb></lb>Igrometri ad avena, nel 1646, in Firenze appresso il Torricelli (Premier vo­<lb></lb>yage en Italie, Paris 1695, pag. </s>

<s>229), chi sa che non avesse seguitato ne&#039;suoi <lb></lb>sospetti, com&#039;a saper che nel 1657 lo Schott aveva nella sua <emph type="italics"></emph>Mechanica <lb></lb>hydraulico-pneum.<emph.end type="italics"></emph.end> descritto il medesimo strumento come invenzione già <lb></lb>conosciuta? </s>

<s>“ Rem totam, egli dice, describit fuse Kirkerius lib. </s>

<s>III Artis <lb></lb>magnet., pars. </s>

<s>II, cap. </s>

<s>III, Progymnasma I ” (Herbipoli 1657, pag. </s>

<s>333). <lb></lb>Anzi si accenna ivi dallo Schott una cosa, per cui renderebbesi molto pro­<lb></lb>babile che così fatti Igrometri fossero stati conosciuti dal volgo, molto tempo <lb></lb>prima che venissero descritti dai Filosofi, dicendovisi che le proprietà igro­<lb></lb>scopiche dell&#039;avena son comuni a tutte le pianticelle gracili e rampicanti, <lb></lb>come i convolvoli o i così detti vilucchi. </s>

<s>“ Eamdem hanc proprietatem ha­<lb></lb>bent omnes illae herbae et plantae, quae incremento suo in spiras sese na­<lb></lb>turaliter contorquent, cuiusmodi sunt omnia convolvulorum genera ” (ibi, <lb></lb>pag. </s>

<s>234). </s></p><p type="main">

<s>Ma lasciando gli uccellini di carta affissi ad un gambo di avena dar di <lb></lb>sè giocondo spettacolo ai visitatori del Museo kirkeriano, gl&#039;Igrometri dot­<lb></lb>tamente speculati per giovare ai progressi della scienza, rimasero chiusi nel­<lb></lb>l&#039;officina di Filippo Treffler, e sepolti con le carte manoscritte di Vincenzio <lb></lb>Viviani. </s>

<s>Perciò il Folli, che nel 1680 vedeva esser già la sua invenzione nel <lb></lb>mondo quasi morta, si studiò di renderla a vita in un libro, da lui stesso <lb></lb>scritto e intitolato <emph type="italics"></emph>Stadera medica.<emph.end type="italics"></emph.end> Ivi si descrive dall&#039;Inventore, non però <lb></lb>con quella evidenza del Viviani nella Lettera Treffler, il suo nuovo stru­<lb></lb>mento, a cui “ per non far questo sfregio alla lingua toscana col dichia­<lb></lb>rarla fallita e bisognosa d&#039;andar mendicando fra&#039;greci vocaboli ” (Stad. </s>

<s>med., <lb></lb>Firenze 1680, pag. </s>

<s>115) dava il nome di <emph type="italics"></emph>Mostra umidaria.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Così, nel decorso del secolo XVII, avevano gl&#039;Italiani fornito la Meteo­<lb></lb>rologia di varia maniera d&#039;Igrometri, alcuni de&#039;quali riuscivano sensibilis­<lb></lb>simi e sufficientemente precisi. </s>

<s>Eppure, nel secolo appresso quando il Saus­<lb></lb>ssure istituì le <gap></gap><pb xlink:href="020/01/542.jpg" pagenum="523"></pb>uno strumento, che agli occhi degli scienziati apparve nuovo, e che fu giu­<lb></lb>dicato dal Volta <emph type="italics"></emph>eccellente ad ogni riguardo<emph.end type="italics"></emph.end> (Op. </s>

<s>cit., T. I, P. II, pag. </s>

<s>84). <lb></lb>Nonostante, a volere esser giusti, le strisciole di carta del Viviani non pre­<lb></lb>sentavano maggiori imperfezioni de&#039;famosi capelli, e in ogni modo, chi da <lb></lb>carte 42 a carte 60 svolge il citato Tomo CXXXIV manoscritto, e considera <lb></lb>quelle frettolose note interpolate a tanti calcoli laboriosi, è costretto a con­<lb></lb>fessar che il Discepolo di Galileo non pose minore studio e diligenza, in re­<lb></lb>golar le sue scale umidarie, di quel che vi ponesse il Gay-Lussac in costruire <lb></lb>quelle sue Tavole di correzione. </s></p><p type="main">

<s>Lo stesso Volta però che aveva fatto così lieta accoglienza all&#039;Igrome­<lb></lb>tro saussuriano, non seppe rintuzzare il desiderio che lo frugava di proporne <lb></lb>uno nuovo, adattando inaspettatamente a quell&#039;uso il Pendolo elettrometrico <lb></lb>dell&#039;Henley. </s>

<s>Egli e tutti i Fisici avevano dovuto osservare che, se l&#039;aria è <lb></lb>molto secca, il pendolo si sostien sul quadrante per parecchi minuti, e tal­<lb></lb>volta anche per qualche ora; mentre, se l&#039;aria è umida, non si sostiene il <lb></lb>pendolo che per qualche minuto secondo. </s></p><p type="main">

<s>Il progetto di stabilir sopra queste osservazioni un Igrometro, era, per <lb></lb>la novità sua, seducente, ma oltre al riuscir l&#039;apparato assai incomodo per <lb></lb>richiedervisi il concorso della Macchina elettrica o dell&#039;Elettroforo, la scala <lb></lb>igrometrica, per la sua grandissima estensione, era impraticabile, ond&#039;ebbe <lb></lb>a confessare lo stesso Volta e a dire: “ chi mai vorrebbe intraprendere una <lb></lb>serie di esperienze di questa sorta, che non sono, lo confesso io medesimo, <lb></lb>di una grandissima importanza? </s>

<s>” (ivi, pag. </s>

<s>443). </s></p><p type="main">

<s>Sicchè l&#039;Igrometro elettrico, benchè ingegnoso, non potrebbe aversi che <lb></lb>qual semplice <emph type="italics"></emph>Elettroscopio.<emph.end type="italics"></emph.end> Or che altro hanno dovuto sentenziare i Fisici <lb></lb>del celebre strumento saussuriano? </s>

<s>Bisogna rassegnarsi, essi dicono, ad usare <lb></lb>anco l&#039;Igrometro a capello, come si farebbe di qualunque altro elettroscopio <lb></lb>di quelli anticamente inventati dagli italiani. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Terminandosi da noi, in quest&#039;ultimo paragrafo, la storia de&#039;principali <lb></lb>strumenti del Metodo sperimentale, non presumiamo, nemmen dentro i ter­<lb></lb>mini che ci siamo prescritti, d&#039;aver di tutti narrato ciò che concerne il modo <lb></lb>e la ragione delle loro invenzioni. </s>

<s>Di parecchi altri ci occorrerà di parlarne <lb></lb>in sul punto, che dovremo vedere i varii ordini di scienze sperimentali, pro­<lb></lb>gredendo via via, provocarli, e reclamarli, come necessaria condizione di <lb></lb>que&#039;loro progressi. </s>

<s>Solo crediamo di dover aggiunger qui qualche parola, <lb></lb>per dir dell&#039;Arcometro e del Pluviometro, che, così semplici ambedue nella <lb></lb>costruzione, son pure altrettanto importanti negli usi. </s></p><p type="main">

<s>L&#039;Areometro o Pesaliquori, ingentilito poi dalla scienza, riconosce la <lb></lb>prima sua origine da quel rozzo strumento, con cui l&#039;antico Sozione inse-<pb xlink:href="020/01/543.jpg" pagenum="524"></pb>gnava, secondo riferisce il Porta, a conoscer se il mosto era puro, o s&#039;era <lb></lb>stato mescolato coll&#039;acqua. </s>

<s>“ Unde si in mustum mala vel pyra silvestria <lb></lb>immiseris, et mustum purissimum erit, supernatabunt mala et fluitabunt. </s>

<s>At <lb></lb>si aquam admistam habuerint, mala fundum petunt introque merguntur. </s>

<s><lb></lb>Cum enim aqua musto tenuior sit, et levior facit ut malum subsidat. </s>

<s>Quod <lb></lb>optime a Sotione descriptum est et satis curiose. </s>

<s>Inquit: ut sciamus mustum <lb></lb>an aquam habeat, pyra silvestria, hoc est crudissima, in mustum coniice, et <lb></lb>si quidem aquam habuerit ad fundum mergentur. </s>

<s>Nam si vas musto repleas, <lb></lb>dum sorbum aut pyrum immerges, supernatabit, quanto plus aquae addes, <lb></lb>plus mergetur malum ” (Magia Nat, Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>618, 19). </s></p><p type="main">

<s>Galileo, il quale non immeritamente si riconosce per primo inventore <lb></lb>dell&#039;Areometro, applicato agli usi della scienza, nella I Giornata delle Due <lb></lb>Nuove Scienze, descrive il seguente dialogo passato fra il Sagredo e il Sal­<lb></lb>viati: “ — Io con un altro artifizio ingannai alcuni amici, appresso i quali <lb></lb>m&#039;era vantato di ridurre quella palla di cera al giusto equilibrio con l&#039;acqua, <lb></lb>ed avendo messo nel fondo del vaso una parte d&#039;acqua salata e sopra quella <lb></lb>della dolce, mostrai loro la palla, che a mezz&#039;acqua si fermava, e spinta nel <lb></lb>fondo o sospinta ad alto nè in questo nè in quel sito restava, ma ritornava <lb></lb>nel mezzo. </s>

<s>— Non è cotesta esperienza priva d&#039;utilità, perchè, trattandosi <lb></lb>dai medici in particolare, delle diverse qualità di acqua e tra l&#039;altre prin­<lb></lb>cipalmente della leggerezza e gravità più di questa che di quella, con una <lb></lb>simil palla aggiustata, sicchè resti ambigua per così dire tra lo scendere e <lb></lb>il salire in un&#039;acqua, per minima che sia la differenza di peso tra due acque, <lb></lb>se in una tal palla scenderà, nell&#039;altra che sia più grave salirà ” (Alb. </s>

<s>XIII, 72). </s></p><p type="main">

<s>Dalle citate parole sembra che, rispetto alla invenzione, sieno da distin­<lb></lb>guere due tempi: il primo, in cui la palla galleggiante non serviva ad altro <lb></lb>che alla curiosità di uno spettacolo, e il secondo in cui si fece di questa <lb></lb>stessa palla galleggiante l&#039;applicazione all&#039;uso areometrico. </s>

<s>Il primo tempo <lb></lb><figure id="id.020.01.543.1.jpg" xlink:href="020/01/543/1.jpg"></figure></s></p><p type="caption">

<s>Figura 57.<lb></lb>par doversi ridurre intorno al 1604, come si rileva da una lettera <lb></lb>di Don Antonio de&#039;Medici che fa richiesta a Galieo della palla spet­<lb></lb>tacolosa. </s>

<s>“ Intendo (diceva quella lettera che è del 28 Giugno) che <lb></lb>V. S. ha una palla, che gettandola nell&#039;acqua sta fra le due acque. </s>

<s><lb></lb>Vengo con la presente a pregarla vivamente di voler favorirmene <lb></lb>e consegnarla al P. D. </s>

<s>Antonio Cerrato ” (Volinski, Lett. </s>

<s>in. </s>

<s>a <lb></lb>Gal., Firenze 1874, Lett. </s>

<s>IV, pag. </s>

<s>16). </s></p><p type="main">

<s>Quanto al secondo tempo, potrebb&#039;essere che fosse verso il 1612, <lb></lb>quando pensò di trovare il peso specifico dell&#039;aria, riducendo il <lb></lb>galleggiante in figura di quella caraffalla, che fu poi, in quasi <lb></lb>tutte le varie forme di questo strumento, adottata dai successivi <lb></lb>inventori. </s>

<s>Così infatti ce ne descrive Galileo la figura e l&#039;uso in <lb></lb>una Lettera al Nozzolini: “ Facciasi un vaso di vetro simile al­<lb></lb>l&#039;ABC (fig. </s>

<s>57) di qualsivoglia grandezza col collo AB lunghetto al­<lb></lb>quanto ma stretto, e nel fondo C se gli attacchi tanto piombo o altro peso <lb></lb><gap></gap> si sommerga, sicchè solo avanzi fuori del-<pb xlink:href="020/01/544.jpg" pagenum="525"></pb>l&#039;acqua una parte del collo AB, nel qual collo si noti con diligenza, con <lb></lb>legarvi un filo sottile, sino a qual parte e&#039;si demerga. </s>

<s>Di poi scaldisi sopra <lb></lb>la brace accesa il vaso, in guisa che il fuoco scacci tutta o la maggior parte <lb></lb>dell&#039;aria in esso contenuta, e prima che rimoverlo dal fuoco, serrisi esqui­<lb></lb>sitamente la bocca A, sicchè non vi possa rientrar aria. </s>

<s>Levisi di poi dal <lb></lb>fuoco e lascisi così stare, finchè si freddi, partendosi per la porosità del ve­<lb></lb>tro quell&#039;esalazione ignea che vi penetrò e scacciò l&#039;aria. </s>

<s>Dipoi tornisi a <lb></lb>metter nell&#039;acqua, e vedrassi galleggiare notabilmente più che prima, stando <lb></lb>del collo assai maggior parte fuori, e ciò per essergli stata rimossa o tutta <lb></lb>o parte dell&#039;aria, che prima lo riempiva, senza che in luogo di quella sia <lb></lb>succeduto altro corpo ” (Alb XII, 114, 15). </s></p><p type="main">

<s>La forma di questo strumento galileiano e l&#039;uso suggerirono facilmente <lb></lb>al Torricelli l&#039;invenzione di quegli Idrostammi, co&#039;quali s&#039;intendeva di mi­<lb></lb>surare il peso de&#039;liquidi, nel modo stesso che Galileo aveva misurato quello <lb></lb>dell&#039;aria. </s>

<s>Perciò fra gli strumenti attribuiti al Granduca Ferdinando se ne <lb></lb>trova annoverati e descritti anco alcuni ordinati <emph type="italics"></emph>a conoscere la gravezza <lb></lb>e la leggerezza di una cosa liquida<emph.end type="italics"></emph.end> (Targioni, Notizie cit., T. I, pag. </s>

<s>153). <lb></lb>“ Lo strumento B si deve mettere nel liquido che uno vuol provare, e si <lb></lb>vede quanto sta all&#039;equilibro appunto: se sopravanza, si deve accrescere di <lb></lb>peso con anelli segnati C, che sieno d&#039;un grano, mezzo grano, un dodice­<lb></lb>simo, ventiquattresimo, e quarantottesimo e più se si vuole, fino resti al­<lb></lb>l&#039;equilibrio, e torni su appunto, e poi provare agli altri, e vedere la diffe­<lb></lb>renza del peso, o aggiunto o levato, e da questo cavarne, che dove si metterà <lb></lb>più peso, sarà più grave, e dove se ne metterà meno, sarà più leggeri ” <lb></lb>(ivi, T. II, P. I, pag. </s>

<s>169). </s></p><p type="main">

<s>È facile vedere in questo strumento una grandissima somiglianza colla <lb></lb><emph type="italics"></emph>Bilancia areometrica<emph.end type="italics"></emph.end> del Nicholson, e con l&#039;Areometro del Fahrenheit, ma <lb></lb>un altro Idrostammo è pure annoverato fra gli strumenti del Granduca, il <lb></lb>quale, consistendo in una bolla di vetro dentrovi migliarole o mercurio, con <lb></lb>un lungo collo graduato, non par che differisca di nulla o d&#039;assai poco dal­<lb></lb>l&#039;Areometro, che va comunemente sotto il nome del Baumè. </s>

<s>“ Lo stru­<lb></lb>mento A messo in qualsivoglia liquido si deve osservare quanti gradi re­<lb></lb>stino fuori di quello a misura, e poi messo negli altri osservare quanti gradi <lb></lb>medesimamente restino fuori: dove resteranno più gradi fuori, sarà più <lb></lb>grave, e dove meno, sarà più leggeri ” (ivi). </s></p><p type="main">

<s>Un disegno di questo Idrostammo vedesi abbozzato di mano del Viviani <lb></lb>ne&#039;MSS Cim., T. XI, c. </s>

<s>105, e a lato si legge: <emph type="italics"></emph>Strumento per conoscere la <lb></lb>gravità de&#039;fluidi.<emph.end type="italics"></emph.end> Di qui parrebbe che fosse questa invenzione dello stesso <lb></lb>Viviani, intorno a che poi ci rende certi l&#039;Inventore scrivendo: “ Mio lo <lb></lb>strumento a palla per la gravità in specie de&#039;fluidi, col mettere i pesi den­<lb></lb>tro la palla ” (ivi, T. X, c. </s>

<s>259). </s></p><p type="main">

<s>In quella stessa carta, dove abbiamo detto vedersi l&#039;abbozzo di questo <lb></lb><emph type="italics"></emph>strumento a palla,<emph.end type="italics"></emph.end> vedesi dalla stessa mano abbozzato un altro disegno illu­<lb></lb><gap></gap> detto .... <pb xlink:href="020/01/545.jpg" pagenum="526"></pb>ovvero <emph type="italics"></emph>Stadera de&#039;liquidi.<emph.end type="italics"></emph.end> ” Rappresenta un tubo barometrico immerso <lb></lb>nella vaschetta del mercurio, sopra il quale versando un liquido o un altro, <lb></lb>ne resulta una specie di stadera, per la quale si misurano i pesi dalla virtù <lb></lb>che gli stessi varii liquidi infusi hanno di far sollevare più o meno il mer­<lb></lb>curio nel tubo barometrico. </s>

<s>Varii altri strumenti, o dallo stesso Viviani o da <lb></lb>altri Aceademici, furono inventati <emph type="italics"></emph>per pesare i liquidi nel vuoto,<emph.end type="italics"></emph.end> la descri­<lb></lb>zion de&#039;quali si legge nel Tomo VI de&#039;citati Manoscritti del Cimento. </s></p><p type="main">

<s>Così la storia dell&#039;invenzion dell&#039;Areometro, che riconosce la sua prima <lb></lb>origine in una sorba agresta o in una pera galleggiante, ci mostra come tal­<lb></lb>volta i più ıozzi naturali strumenti vengano a trasformarsi, raffinati nelle <lb></lb>mani dell&#039;arte. </s>

<s>Un altro simile esempio lo abbiamo nel Pluviometro, che fu <lb></lb>a principio uno di que&#039;vasi di vetro, a cui il Castelli, stato il primo ad usarlo <lb></lb>per misurare la quantità dell&#039;acqua piovuta in un dato tempo, dava, seguendo <lb></lb>il volgar linguaggio, il nome di orinale. </s>

<s>Narra lo stesso Castelli, in una Let­<lb></lb>tera a Galileo copiata in calce al Libro I, Della Misura delle acque correnti, <lb></lb>come ripensando agli effetti prodotti dalla siccità nel lago di Perugia, ritor­<lb></lb>nato che fu dalla visita dell&#039;emissario in città, segui una pioggia non molto <lb></lb>grossa, ma continuata assai ed uniforme, la quale durò per ispazio di otto <lb></lb>ore in circa. </s>

<s>“ Allora mi venne in pensiero di volere esaminare, stando in <lb></lb>Perugia, quanto con quella pioggia poteva essere cresciuto e rialzato il Lago, <lb></lb>supponendo, come aveva assai del probabile, che la pioggia fosse universale <lb></lb>sul lago, ed uniforme a quella che cadeva in Perugia, e così preso un vaso <lb></lb>di vetro di forma cilindrica alto un palmo in circa, e largo mezzo palmo, ed <lb></lb>avendo infusa un poco d&#039;acqua, tanto che coprisse il fondo del vaso, notai <lb></lb>diligentemente il segno dell&#039;altezza dell&#039;acqua del vaso, e poi l&#039;esposi al­<lb></lb>l&#039;aria aperta a ricevere l&#039;acqua della pioggia che ci cascava dentro, e lo la­<lb></lb>sciai stare per ispazio di un&#039;ora, ed avendo osservato che nel detto tempo <lb></lb>l&#039;acqua si era alzata nel vaso quanto la seguente linea —— considerai <lb></lb>che se io avessi esposti alla medesima pioggia altri simili ed uguali vasi, in <lb></lb>ciascuno di essi si sarebbe rialzata l&#039;acqua, secondo la medesima misura, e <lb></lb>per tanto conclusi che ancora in tutta l&#039;ampiezza del Lago era necessario <lb></lb>che l&#039;acqua si fosse rialzata nello spazio di un&#039;ora la medesima misura ” <lb></lb>(Bologna 1660, pag. </s>

<s>50). </s></p><p type="main">

<s>Di questo stesso vaso di vetro, di cui erasi già servito il Castelli per <lb></lb>misurare la quantità d&#039;acqua piovuta, si servì poi per misurare la quantità <lb></lb>d&#039;acqua evaporata, offerendo così come primizia i due nuovi strumenti alla <lb></lb>nascente Meteorologia. </s></p><pb xlink:href="020/01/546.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICI<emph.end type="center"></emph.end><pb xlink:href="020/01/547.jpg"></pb></s></p><pb xlink:href="020/01/548.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE DEI CAPITOLI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Discorso Preliminare.<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>PARTE PRIMA<emph.end type="center"></emph.end></s></p><p type="main">

<s>I Del primo acquisto delle cognizioni <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 25 </s></p><p type="main">

<s>II Platone e Aristotile ” 29 </s></p><p type="main">

<s>III Della Filosofia naturale derivata dall&#039;Accademia e dal Peripato ” 33 </s></p><p type="main">

<s>IV Come le due Filosofie, la platonica e l&#039;aristotelica, venissero a introdursi nella Società <lb></lb>cristiana ” 38 </s></p><p type="main">

<s>V De&#039;medici peripatetici; Girolamo Fracastoro; Andrea Cesalpino ” 42 </s></p><p type="main">

<s>VI Girolamo Cardano, Giuseppe Scaligero, Niccolò Tartaglia ” 47 </s></p><p type="main">

<s>VII De&#039;Filosofi razionalisti: Francesco Patrizio, Bernardino Telesio, Giordano Bruno e Toin­<lb></lb>maso Campanella ” 54 </s></p><p type="main">

<s>VIII De&#039;frutti di scienza naturale raccolti nel secolo XVI dalle tre Filosofie, accademica, peri­<lb></lb>patetica e razionalistica ” 61 </s></p><p type="main">

<s>IX De&#039;cultori dell&#039;arte, veri precursori del metodo sperimentale: Dante Alighieri, Leon Bat­<lb></lb>tista Alberti, Cristoforo Colombo e Amerigo Vespucci ” 66 </s></p><p type="main">

<s>X Leonardo da Vinci ” 74 </s></p><p type="main">

<s>XI Degli anatomici padovani del secolo XVI, e segnatamente di Realdo Colombo ” 84 </s></p><p type="main">

<s>XII Come nel secolo XVI gli esercizi sperimentali e le notizie dei fatti naturali si diffondes­<lb></lb>sero dai libri d&#039;uomini letterati: Giovan Battista Porta e Ferrante Imperato ” 91 </s></p><p type="main">

<s>XIII De&#039;più immediati precursori e cooperatori alla grande Instaurazione galileiana: Giovan <lb></lb>Battista Benedetti e Santorre Santorio ” 101 </s></p><p type="main">

<s>XIV Paolo Sarpi ” 108 </s></p><p type="main">

<s>XV Dell&#039;Accademia de&#039;Lincei, e di Francesco Bacone ” 116 </s></p><p type="main">

<s><emph type="italics"></emph>Nota I<emph.end type="italics"></emph.end> ” 124 </s></p><p type="main">

<s><emph type="italics"></emph>Nota II<emph.end type="italics"></emph.end> ” 126 </s></p><p type="main">

<s><emph type="center"></emph>PARTE SECONDA<emph.end type="center"></emph.end></s></p><p type="main">

<s>I Di Galileo Galilei e della sua nuova instaurazione scientifica <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>127 </s></p><p type="main">

<s>II Si giustificano le cose asserite nel paragrafo precedente ” 136 </s></p><p type="main">

<s>III Dei benefizi che derivarono alle scienze sperimentali dalla nuova Instaurazione galileiana ” 143 </s></p><p type="main">

<s>IV Renato Cartesio ” 150 </s></p><p type="main">

<s>V De&#039;primi e principali Discepoli di Galileo ” 157 </s></p><p type="main">

<s>VI Della grande esperienza torricelliana dell&#039;argento vivo, e come per lei si diffondessero, <lb></lb>d&#039;Italia in tutta Europa, l&#039;amore e gli esercizi dell&#039;arte sperimentale ” 169 </s></p><p type="main">

<s>VII Di Evangelista Torricelli, di Vincenzio Viviani e di ciò che operassero nelle istituzioni <lb></lb>della sperimentale Accademia medicea ” 178 </s></p><p type="main">

<s>VIII Del primo periodo della fiorentina Accademia del Cimento ” 188 </s></p><p type="main">

<s>IX Del secondo periodo della fiorentina Accademia del Cimento ” 197 </s></p><p type="main">

<s>X Delle principali Accademie private istituite in Italia a imitazione di quella del Cimento; <lb></lb>del felico esito della Istituzione medicea, nonostante le rivalità degli stranieri, i dis­<lb></lb><gap></gap> dei Perinatetici ” 205 </s></p><pb xlink:href="020/01/549.jpg" pagenum="530"></pb><p type="main">

<s><emph type="center"></emph>PARTE TERZA<emph.end type="center"></emph.end></s></p><p type="main">

<s>I Isacco Newton <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>217 </s></p><p type="main">

<s>II De&#039;principii e de&#039;progressi delle speculazioni neutoniane, e quale efficace concorso v&#039;ab­<lb></lb>biano avuto le tradizioni scientifiche da&#039;nostri Italiani ” 224 </s></p><p type="main">

<s>III Delle Istituzioni idrauliche di Domenico Guglielmini, e in che modo i principii della Fi­<lb></lb>losofia neutoniana, nel secolo XVIII, concorressero a farla progredire ” 233 </s></p><p type="main">

<s>IV Dell&#039;Elettricismo, della Chimica, dell&#039;Elettro chimica, e come si svolgessero queste nuove <lb></lb>parti delle scienze dai principii della Filosofia neutoniana ” 240 </s></p><p type="main">

<s>V Dei progressi della Storia Naturale nel secolo XVIII ” 249 </s></p><p type="main">

<s>VI Delle condizioni presenti delle scienze sperimentali: qualche parola intorno alla nostra <lb></lb>Storia ” 255 </s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>De&#039;principali strumenti del metodo sperimentale.<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del Termometro.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Dell&#039;invenzione e degli usi del Termometro santoriano <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>265 </s></p><p type="main">

<s>II Delle applicazioni dell&#039;antichissima esperienza eroniana, e segnatamente di quella fatta <lb></lb>da Daniele Antonini e da Cornelio Drebbellio ” 270 </s></p><p type="main">

<s>III Della medesima esperienza fatta da Galileo ” 272 </s></p><p type="main">

<s>IV Se si debba giustamente attribuire a Galileo l&#039;invenzion del Termometro ad aria; de&#039;per­<lb></lb>fezionamenti che tentò Giovan Francesco Sagredo d&#039;introdurre nello strumento ” 274 </s></p><p type="main">

<s>V Della prima invenzione del Termometro a liquido ” 279 </s></p><p type="main">

<s>VI Della prima scoperta e delle prime ragioni rese del fatto del dilatarsi i liquidi al calore ” 285 </s></p><p type="main">

<s>VII Della scoperta della dilatazione cubica de&#039;solidi al calore, e delle applicazioni di lei alla <lb></lb>Termometria ” 290 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dell&#039;orologio a pendolo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I De&#039;primi Orologi a pendolo del Santorio <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>299 </s></p><p type="main">

<s>II De&#039;varii modi proposti da Galileo di applicare il pendolo agli Orologi ” 307 </s></p><p type="main">

<s>III Del primo Orologio descritto da Cristiano Huyghens; della simpatia de&#039;pendoli ” 313 </s></p><p type="main">

<s>IV Del Cronoscopio di Giorgio Sinclaro e dell&#039;Orologio cicloidale dell&#039;Huyghens ” 319 </s></p><p type="main">

<s>V Del Cronometro degli Accademici del Cimento ” 324 </s></p><p type="main">

<s>VI Come probabilmente il Cronometro degli Accademici fiorentini sia invenzione del Vi­<lb></lb>viani: della ricerca del centro di oscillazione, ne&#039;pendoli degli Orologi ” 327 </s></p><p type="main">

<s>VII Degli effetti prodotti dal calore negli Orologi: dell&#039;invenzione degli Orologi a bilanciere <lb></lb>o da tasca: della compensazione de&#039;pendoli ” 332 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dell&#039;invenzione e della teoria del Canocchiale.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Del primo inventore del Canocchiale <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>339 </s></p><p type="main">

<s>II Di ciò che, intorno all&#039;invenzione dello Strumento, Galileo dicesse di sè, e di quel che <lb></lb>di lui si diceva dagli altri ” 346 </s></p><pb xlink:href="020/01/550.jpg" pagenum="531"></pb><p type="main">

<s>III Del primo concetto, e di ciò che possa aver dato occasione al ritrovamento del Canoc­<lb></lb>chiale <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>351 </s></p><p type="main">

<s>IV Delle prime speculazioni diottriche intorno alla teoria del Canocchiale ” 356 </s></p><p type="main">

<s>V Di altre vie tentate per risolvere il problema diottrico del Canocchiale, e come fosse final­<lb></lb>mente risoluto dell&#039;Huyghens: breve conclusione delle cose fin qui discorse ” 366 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>De&#039;Canocchiali del Fontana, del Torricelli e di altri; <lb></lb>del Telescopio a riflessione.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I De&#039;Canocchiali di Girolamo Sirturo e di Francesco Fontana <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 374 </s></p><p type="main">

<s>II De&#039;Canocchiali di Evangelista Torricelli ” 378 </s></p><p type="main">

<s>III Del segreto usato dal Torricelli per lavorare i vetri da Canocchiali ” 383 </s></p><p type="main">

<s>IV Considerazioni o giudizi intorno al Torricelli come costruttore di Canocchiali, special­<lb></lb>mente da servire per gli usi astronomici ” 387 </s></p><p type="main">

<s>V De&#039;Canocchiali di Cristiano Huyghens ” 391 </s></p><p type="main">

<s>VI De&#039;Canocchiali di Giuseppe Campani, e di Eustachio Divini ” 394 </s></p><p type="main">

<s>VII De&#039;Telescopii a riflessione ” 399 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Degli organi aggiunti, e de&#039;nuovi usi strumentali del Canocchiale.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Del primo Micrometro e delle prime operazioni micrometriche di Galileo <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>405 </s></p><p type="main">

<s>II Del Micrometro ugeniano e del Micrometro a reticolo ” 412 </s></p><p type="main">

<s>III Della Livella diottrica ” 418 </s></p><p type="main">

<s>IV Del Canocchiale binoculo ” 424 </s></p><p type="main">

<s>V Dell&#039;Elioscopio, dell&#039;Eliostata, de&#039;Diaframmi de&#039;Canocchiali ” 429 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del Barometro.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle prime idee, che ebbero i Fisici intorno alla possibilità e all&#039;esistenza del vacuo, e <lb></lb>delle loro prime esperienze intorno al peso e alle pressioni dell&#039;aria <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>434 </s></p><p type="main">

<s>II Della celebre esperienza dell&#039;argento vivo: delle esperienze del Pascal e di altri Francesi. </s>

<s>” 440 </s></p><p type="main">

<s>III Come l&#039;esperienza dell&#039;argento vivo fosse, per unanime consenso degli stessi stranieri, <lb></lb>attribuita al Torricelli ” 447 </s></p><p type="main">

<s>IV Della Lettera torricelliana sull&#039;esperienza dell&#039;argento vivo ” 451 </s></p><p type="main">

<s>V Come il Torricelli attendesse a costruire lo strumento da misurar le variazioni del peso <lb></lb>dell&#039;aria, e come non gli riuscisse la sua intenzione ” 455 </s></p><p type="main">

<s>VI Come e da chi lo strumento torricelliano dell&#039;argento vivo fosse applicato ad uso di <lb></lb>Barometro ” 462 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Della Macchina elettrica e della Pila voltaia.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Del globo di zolfo del Guericke, e dèl globo di vetro dell&#039;Hawksbec: della Macchina elet­<lb></lb>trica di Lipsia, del Winkler, del Nollet, del Ramsden <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>469 </s></p><p type="main">

<s>II Della Bottiglia di Leyda; dell&#039;Elettroforo e del Condensatore del Volta ” 475 </s></p><p type="main">

<s>III De&#039;primi elettroscopii; dell&#039;Elettroscopio a boccetta, dell&#039;Elettrometro condensatore, e <lb></lb>dell&#039;Elettrometro a quadrante ” 479 </s></p><p type="main">

<s>IV Della grande scoperta galvanica dell&#039;Elettricità animale, e della nuova elettricità me­<lb></lb>tallica scoperta dal Volta ” 484 </s></p><p type="main">

<s><gap></gap> ” 492 </s></p><pb xlink:href="020/01/551.jpg" pagenum="532"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Di varii altri strumenti.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Degli specilli semplici o degli occhiali da naso, e del loro modo di operar sulla vista <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>498 </s></p><p type="main">

<s>II Del Microscopio semplice e del Microscopio composto ” 505 </s></p><p type="main">

<s>III Del corno acustico ” 512 </s></p><p type="main">

<s>IV De&#039;primi Igroscopii, degl&#039;Igrometri del Santorio, dell&#039;Igrometro a condensazione del <lb></lb>Torricelli, della <emph type="italics"></emph>Mostra umidaria<emph.end type="italics"></emph.end> del Folli, della legge igrometrico meccanica del <lb></lb>Viviani e dell&#039;Igrometro elettrico del Volta ” 545 </s></p><p type="main">

<s>V Dell&#039;Areometro e del Pluviometro ” 523 </s></p><pb xlink:href="020/01/552.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE ALFABETICO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEGLI AUTORI E DELLE COSE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Co&#039;numeri s&#039;accenna alle pagine.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Accademia platonica,<emph.end type="bold"></emph.end> carattere filosofico di lei 34, Accad. </s>

<s>napoletana del Conclubet 205. </s></p><p type="main">

<s><emph type="bold"></emph>Acquapendente (d&#039;) Eabrizi Girolamo,<emph.end type="bold"></emph.end> anatomico 91. </s></p><p type="main">

<s><emph type="bold"></emph>Acromatismo<emph.end type="bold"></emph.end> delle lenti 394. </s></p><p type="main">

<s><emph type="bold"></emph>Aggiunti Niccolò,<emph.end type="bold"></emph.end> discepolo di Galileo 163, sue notabili esperienze e ragioni della dilatazione lineare <lb></lb>de&#039;solidi al calore 288. </s></p><p type="main">

<s><emph type="bold"></emph>Alberti Leon Battista,<emph.end type="bold"></emph.end> sua scienza sperimentale 72. </s></p><p type="main">

<s><emph type="bold"></emph>Alighieri Dante,<emph.end type="bold"></emph.end> sua Filosofia naturale 69. </s></p><p type="main">

<s><emph type="bold"></emph>Antonini Daniele<emph.end type="bold"></emph.end> fa l&#039;esperienza eroniana del Termometro ad aria 271, propone le lenti paraboliche <lb></lb>per uso de&#039;canocchiali 371. </s></p><p type="main">

<s><emph type="bold"></emph>Aproino Paolo<emph.end type="bold"></emph.end> pensa al modo di aumentare il suono 513, inventa e descrive il corno acustico 514. </s></p><p type="main">

<s><emph type="bold"></emph>Archimede,<emph.end type="bold"></emph.end> sua Fisica 35, suo modo di misurare l&#039;ampiezza della pupilla nelle osservazioni celesti 410. </s></p><p type="main">

<s><emph type="bold"></emph>Areometro,<emph.end type="bold"></emph.end> sua invenzione 524, sua prima forma di caraffa galleggiante datale da Galileo 525. </s></p><p type="main">

<s><emph type="bold"></emph>Aristotile,<emph.end type="bold"></emph.end> sua Filosofia 31. </s></p><p type="main">

<s><emph type="bold"></emph>Aristotelismo,<emph.end type="bold"></emph.end> come s&#039;introducesse nella società Cristiana 40. </s></p><p type="main">

<s><emph type="bold"></emph>Armati Salvino<emph.end type="bold"></emph.end> inventore degli occhiali 500. </s></p><p type="main">

<s><emph type="bold"></emph>Arrighetti Andrea,<emph.end type="bold"></emph.end> discepolo di Galileo, 168. </s></p><p type="main">

<s><emph type="bold"></emph>Bacone Francesco,<emph.end type="bold"></emph.end> tenta nella scienza una nuova e grande Instaurazione 113. </s></p><p type="main">

<s><emph type="bold"></emph>Baliani Giovan Batista,<emph.end type="bold"></emph.end> sue relazioni con Galileo 148, fa la prima esperienza dell&#039;acqua, che ne&#039;canali <lb></lb>non si sostiene più su che ad una determinata altezza 437, attribuisce il maraviglioso effetto al <lb></lb>peso dell&#039;aria esterna 439, rammemora, a&#039;tempi del Torricelli, le sue prime e antiche idee in­<lb></lb>torno al modo di superare la forza del vacuo 451. </s></p><p type="main">

<s><emph type="bold"></emph>Barometro,<emph.end type="bold"></emph.end> come dai fenomeni di fosforescenza osservati in lui avesse i principii la Scienza elet­<lb></lb>trica 470. </s></p><p type="main">

<s><emph type="bold"></emph>Bartoli Giovanni,<emph.end type="bold"></emph.end> sue relazioni intorno a ciò che dicevasi in Venezia dell&#039;inventore del canocchiale 350. </s></p><p type="main">

<s><emph type="bold"></emph>Beccaria Giovan Batista,<emph.end type="bold"></emph.end> sue teorie elettriche 242. </s></p><p type="main">

<s><emph type="bold"></emph>Benedetti Giovan Batista,<emph.end type="bold"></emph.end> suo Libro delle <emph type="italics"></emph>Speculazioni<emph.end type="italics"></emph.end> esaminato 102, maestro a Galileo 131, è il <lb></lb>primo a fare e a rendere la ragione dell&#039;esperienza eroniana applicata poi ad uso di Termome­<lb></lb>tro 278, perfeziona la Camera oscura, e il Porta la divulga 368. </s></p><p type="main">

<s><emph type="bold"></emph>Bennet,<emph.end type="bold"></emph.end> sua invenzione dell&#039;Elettroscopio a foglia di oro 482. </s></p><p type="main">

<s><emph type="bold"></emph>Beriguardi Claudio,<emph.end type="bold"></emph.end> come s&#039;ingannassero il Targioni e l&#039;Antinori in crederlo primo autore dell&#039;espe­<lb></lb>rienza torricelliana 450. </s></p><p type="main">

<s><emph type="bold"></emph>Bernoulli Giovanni,<emph.end type="bold"></emph.end> osserva e sperimenta intorno alla fosforescenza mercuriale de&#039;Barometri 471. </s></p><p type="main">

<s><emph type="bold"></emph>Binoculo,<emph.end type="bold"></emph.end> non è invenzione del Galileo 424. </s></p><p type="main">

<s><emph type="bold"></emph>Borelli Gian Alfonso,<emph.end type="bold"></emph.end> accademico del Cimento 189, seguita ad appartenere e a collaborare nell&#039;Acca­<lb></lb>demia, anco dopo tornato a Messina 202, origine dell&#039;inimicizia di lui col Viviani 296, non com­<lb></lb>prende il fatto della così detta <emph type="italics"></emph>simpatia de&#039;pendoli<emph.end type="italics"></emph.end> 319, nota sottilmente i difetti della livella ad <lb></lb>acqua 421, illustra l&#039;esperienza torricelliana 461, forma semplicissima data da lui a&#039;tubi torricel­<lb></lb>liani, per uso di Barometro 465. </s></p><p type="main">

<s><emph type="bold"></emph>Bottiglia di Leyda,<emph.end type="bold"></emph.end> come e quando fosse stata scoperta 475. </s></p><pb xlink:href="020/01/553.jpg" pagenum="534"></pb><p type="main">

<s><emph type="bold"></emph>Boyle Roberto,<emph.end type="bold"></emph.end> sua Macchina pneumatica e come facessero uso di lei gli Accademici del Cimento 210, <lb></lb>ripete l&#039;esperienza del manticetto, che si gonfia via via nel salire un monte 445, perfeziona la <lb></lb>Macchina pneumatica 446, come s&#039;accorgesse della variabilità della pressione ammosferica 464, <lb></lb>primo costruttore del Barometro portatile 466. </s></p><p type="main">

<s><emph type="bold"></emph>Boulliaud Ismaele,<emph.end type="bold"></emph.end> intermediario fra il principe Leopoldo de&#039;Medici e l&#039;Huyghens nella vertenza <lb></lb>concernente l&#039;invenzione dell&#039;Orologio a pendolo 315. </s></p><p type="main">

<s><emph type="bold"></emph>Bruno Giordano,<emph.end type="bold"></emph.end> giudizio de&#039;meriti di lui nelle scienze sperimentali 59. </s></p><p type="main">

<s><emph type="bold"></emph>Camera oscura,<emph.end type="bold"></emph.end> inventore e perfezionatore di essa 367. </s></p><p type="main">

<s><emph type="bold"></emph>Campanella Tommaso,<emph.end type="bold"></emph.end> sua Fisiologia 58. </s></p><p type="main">

<s><emph type="bold"></emph>Campani Giuseppe,<emph.end type="bold"></emph.end> suo tornio per lavorare le lenti da Canocchiali 395, suo nuovo Canocchiale de­<lb></lb>scritto 396. </s></p><p type="main">

<s><emph type="bold"></emph>Campani Matteo,<emph.end type="bold"></emph.end> da opera con suo fratello Giuseppe a perfezionare gli Orologi per gli usi nautici 336. </s></p><p type="main">

<s><emph type="bold"></emph>Canocchiale<emph.end type="bold"></emph.end> astronomico speculato dal Keplero, eseguito dal Fontana 362, a due lenti, una concava e <lb></lb>l&#039;altra convessa, perchè dicasi <emph type="italics"></emph>galileiano<emph.end type="italics"></emph.end> 372. </s></p><p type="main">

<s><emph type="bold"></emph>Capua (da) Leonardo,<emph.end type="bold"></emph.end> accademico napoletano 206. </s></p><p type="main">

<s><emph type="bold"></emph>Carafaggi Cesare,<emph.end type="bold"></emph.end> primo a tentar la costruzione de&#039;Telescopii a riflessione 400. </s></p><p type="main">

<s><emph type="bold"></emph>Cardano Girolamo,<emph.end type="bold"></emph.end> sue opposizioni contro Aristotile 47, conosce il principio d&#039;inerzia 48, ha sentore <lb></lb>delle traìettorie paraboliche, ivi, e della proprietà de&#039;pendoli 49, veri principii idraulici professati <lb></lb>da lui 50. Confuta la dottrina della fuga del vacuo 435. </s></p><p type="main">

<s><emph type="bold"></emph>Cartesio Renato,<emph.end type="bold"></emph.end> indole della sua Filosofia sperimentale 151, sua teoria del Canocchiale 369. </s></p><p type="main">

<s><emph type="bold"></emph>Cassegrain,<emph.end type="bold"></emph.end> suo Telescopio a riflessione descritto 403. </s></p><p type="main">

<s><emph type="bold"></emph>Cassini Gian Domenico<emph.end type="bold"></emph.end> non fu accademico del Cimento 194. </s></p><p type="main">

<s><emph type="bold"></emph>Castelli Benedetto,<emph.end type="bold"></emph.end> primo discepolo di Galileo 158, riferisce l&#039;esperienza eroniana del Termometro <lb></lb>ad aria fatta da Galileo 273. </s></p><p type="main">

<s><emph type="bold"></emph>Cavalieri Bonaventura,<emph.end type="bold"></emph.end> uno de&#039;primi e più illustri discepoli di Galileo 159, interpetra un passo oscuro <lb></lb>del Porta relativo allo Specchio ustorio 354, dimostra l&#039;inefficacia delle lenti paraboliche sostituite <lb></lb>alle sferiche ne&#039;tubi de&#039;Canocchiali 371, sua speculazione intorno al comporre insieme le lenti <lb></lb>con gli specchi nei Telescopi 401. </s></p><p type="main">

<s><emph type="bold"></emph>Cavallo Tiberio,<emph.end type="bold"></emph.end> suo Elettroscopio a boccetta 480. </s></p><p type="main">

<s><emph type="bold"></emph>Cesalpino Andrea,<emph.end type="bold"></emph.end> carattere della sua Filosofia sperimentale 46. </s></p><p type="main">

<s><emph type="bold"></emph>Cicloide<emph.end type="bold"></emph.end> applicata all&#039;isocronismo del pendolo negli Orologi 323. </s></p><p type="main">

<s><emph type="bold"></emph>Cigoli Lodovico,<emph.end type="bold"></emph.end> suo Trattato manoscritto di Prospettiva 147. </s></p><p type="main">

<s><emph type="bold"></emph>Cognizione<emph.end type="bold"></emph.end> della forma precede a quella della materia 29. </s></p><p type="main">

<s><emph type="bold"></emph>Cognizioni,<emph.end type="bold"></emph.end> primo loro apparire osservato ne&#039;bambini 27. </s></p><p type="main">

<s><emph type="bold"></emph>Colombo Cristoforo,<emph.end type="bold"></emph.end> sue osservazioni naturali 73. </s></p><p type="main">

<s><emph type="bold"></emph>Colombo Realdo,<emph.end type="bold"></emph.end> esame del suo libro <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> 86. </s></p><p type="main">

<s><emph type="bold"></emph>Colonna Fabio,<emph.end type="bold"></emph.end> accenna al primo <emph type="italics"></emph>Eliostata<emph.end type="italics"></emph.end> 430. </s></p><p type="main">

<s><emph type="bold"></emph>Compensazioni<emph.end type="bold"></emph.end> agli effetti prodotti dal calore ne&#039;pendoli degli orologi 337. </s></p><p type="main">

<s><emph type="bold"></emph>Condensatori elettrici<emph.end type="bold"></emph.end> da chi costruiti 476, condensatori del Volta 478. </s></p><p type="main">

<s><emph type="bold"></emph>Conduttori elettrici<emph.end type="bold"></emph.end> primi scoperti 473. </s></p><p type="main">

<s><emph type="bold"></emph>Copernico Niccolò<emph.end type="bold"></emph.end> filosofo platonico 63. </s></p><p type="main">

<s><emph type="bold"></emph>Cordicella<emph.end type="bold"></emph.end> tesa ad uso di Micrometro 408. </s></p><p type="main">

<s><emph type="bold"></emph>Cornelio Tommaso<emph.end type="bold"></emph.end> accademico napoletano 207, da un&#039;importante notizia relativa a ciò che dette oc­<lb></lb>casione allo sperimento torricelliano 454. </s></p><p type="main">

<s><emph type="bold"></emph>Corobate<emph.end type="bold"></emph.end> vitruviano descritto 416. </s></p><p type="main">

<s><emph type="bold"></emph>Cotyla,<emph.end type="bold"></emph.end> orologio a pendolo del Santorio 302. </s></p><p type="main">

<s><emph type="bold"></emph>Cronometro<emph.end type="bold"></emph.end> degli Accademici del Cimento descritto 326. </s></p><p type="main">

<s><emph type="bold"></emph>Darwin Carlo,<emph.end type="bold"></emph.end> sua nuova Filosofia naturale 256. </s></p><p type="main">

<s><emph type="bold"></emph>Daviso Urbano,<emph.end type="bold"></emph.end> descrizione del suo Termometro a mostra 297. </s></p><p type="main">

<s><emph type="bold"></emph>De Dominis Marcantonio,<emph.end type="bold"></emph.end> suo Trattato diottrico e sue teorie del Canocchiale 360, come spieghi il modo <lb></lb>dell&#039;operar gli occhiali nella vista 502. </s></p><p type="main">

<s><emph type="bold"></emph>Del Buono Candido<emph.end type="bold"></emph.end> s&#039;incontra coll&#039;Huyghens nella invenzione del Micrometro 413. </s></p><p type="main">

<s><emph type="bold"></emph>Diaframmi,<emph.end type="bold"></emph.end> loro usi ne&#039;Canocchiali 431. </s></p><p type="main">

<s><emph type="bold"></emph>Divini Eustachio<emph.end type="bold"></emph.end> rivaleggia col Campani nella fabbrica de&#039;Canocchiali 397, suo reticolo applicato ad <lb></lb>uso di Micrometro 414. </s></p><p type="main">

<s><emph type="bold"></emph>Drebbel Cornelio<emph.end type="bold"></emph.end> fa l&#039;esperienza eroniana del Termometro ad aria 272. </s></p><p type="main">

<s><emph type="bold"></emph>Elettroforo perpetuo<emph.end type="bold"></emph.end> inventato e descritto dal Volta 477. </s></p><p type="main">

<s><gap></gap></s></p><pb xlink:href="020/01/554.jpg" pagenum="535"></pb><p type="main">

<s><emph type="bold"></emph>Elioscopio<emph.end type="bold"></emph.end> inventato dallo Scheiner 429. </s></p><p type="main">

<s><emph type="bold"></emph>Eliostata<emph.end type="bold"></emph.end> immaginato e proposto dal Borelli 430. </s></p><p type="main">

<s><emph type="bold"></emph>Esperienze<emph.end type="bold"></emph.end> delle membra animali fosforescenti nel vuoto 201, del Torricelli coll&#039;argento vivo, e sua <lb></lb>grande efficacia ne&#039;progressi delle scienze sperimentali 173 seg. </s></p><p type="main">

<s><emph type="bold"></emph>Fabry Onorato,<emph.end type="bold"></emph.end> corrispondente dell&#039;Accademia del Cimento 213, tenta appropriarsi l&#039;esperimento tor­<lb></lb>ricelliano 449. </s></p><p type="main">

<s><emph type="bold"></emph>Falloppio Gabriele<emph.end type="bold"></emph.end> anatomico 90. </s></p><p type="main">

<s><emph type="bold"></emph>Filosofia scolastica,<emph.end type="bold"></emph.end> carattere distintivo di lei 41. </s></p><p type="main">

<s><emph type="bold"></emph>Folli Francesco<emph.end type="bold"></emph.end> come inventasse la sua Mostra umidaria 518. </s></p><p type="main">

<s><emph type="bold"></emph>Fontaua Francesco,<emph.end type="bold"></emph.end> suoi Canocchiali 376. </s></p><p type="main">

<s><emph type="bold"></emph>Fracastoro Girolamo,<emph.end type="bold"></emph.end> carattere della sua Filosofia sperimentale 44. </s></p><p type="main">

<s><emph type="bold"></emph>Galilei Galileo<emph.end type="bold"></emph.end> risolve un problema di Astronomia dantesca 124, si contradice in alcune sue dottrine 133, <lb></lb>come si portasse rispetto alla dimostrazione delle traiettorie paraboliche col Cavalieri 135, non fu <lb></lb>il primo a dimostrare il Teorema della composizion delle forze 137, professò a principio, e poi du­<lb></lb>bitò di ammettere le velocità virtuali 138, sue savie istituzioni di scienza 144, suoi meriti veri 145, <lb></lb>prevale in lui l&#039;astrazione matematica all&#039;esperienza de&#039;fatti 170, non e inventor del Termome­<lb></lb>tro 275, pretende all&#039;invenzione del Canocchiale 347, sua teoria del Canocchiale 357, suoi diversi <lb></lb>strumenti inventati ad uso di Micrometro 413, a qual causa attribuisse il non potersi sostener <lb></lb>l&#039;acqua nelle pompe più su che ad una determinata altezza 438, 441. </s></p><p type="main">

<s><emph type="bold"></emph>Galleggianti<emph.end type="bold"></emph.end> proposti dal Montanari per correggere gli errori della livella a acqua 422. </s></p><p type="main">

<s><emph type="bold"></emph>Galvani Luigi<emph.end type="bold"></emph.end> incomincia a narrar la storia della sua scoperta dell&#039;elettricità animale 484. </s></p><p type="main">

<s><emph type="bold"></emph>Geometria,<emph.end type="bold"></emph.end> prima scienza appresa dall&#039;uomo 28. </s></p><p type="main">

<s><emph type="bold"></emph>Gilberto Guglielmo<emph.end type="bold"></emph.end> sua arte sperimentale 156. </s></p><p type="main">

<s><emph type="bold"></emph>Giocondo Giovanni<emph.end type="bold"></emph.end> aveva, secondo riferisce lo Scaligero, dimostrata la forza della percossa 52. </s></p><p type="main">

<s><emph type="bold"></emph>Grimaldi Francesco Maria,<emph.end type="bold"></emph.end> suo Trattato <emph type="italics"></emph>De Lumine<emph.end type="italics"></emph.end> 214. </s></p><p type="main">

<s><emph type="bold"></emph>Guglielmini Domenico,<emph.end type="bold"></emph.end> relazioni fra le dottrine di lui e le neutoniane 236. </s></p><p type="main">

<s><emph type="bold"></emph>Guericke Ottone<emph.end type="bold"></emph.end> inventor della Macchina pneumatica 446. </s></p><p type="main">

<s><emph type="bold"></emph>Harvey Guglielmo<emph.end type="bold"></emph.end> sua acutezza nello speculare 1<gap></gap>6. </s></p><p type="main">

<s><emph type="bold"></emph>Hawksbee<emph.end type="bold"></emph.end> dà l&#039;ultima perfezione alla Macchina pneumatica 447, ritrova che la fosforescenza de&#039;Baro­<lb></lb>metri è dovuta alla confricazione del mercurio sopra il vetro del tubo 471, cava scintille di foco <lb></lb>elettrico da un globo di vetro girato attorno 472. </s></p><p type="main">

<s><emph type="bold"></emph>Hevelio,<emph.end type="bold"></emph.end> suoi diafranuni specialmente accomodati alle osservazioni solari 432. </s></p><p type="main">

<s><emph type="bold"></emph>Horologium,<emph.end type="bold"></emph.end> prima invenzione e descrizione dell&#039;Huyghens 314. </s></p><p type="main">

<s><emph type="bold"></emph>Huyghens Cristiano<emph.end type="bold"></emph.end> ripete l&#039;esperienza boileiana del sostenersi l&#039;acqua ne&#039;cannelli stretti sopra il pro­<lb></lb>prio naturale livello, anche nel vuoto 229, che ne dice dell&#039;Inventore del Canocchiale 345, sua teoria <lb></lb>dottrica del Canocchiale 370, suo modo di costruire gli oculari per renderli acromatici 392, suo Mi­<lb></lb>crometro descritto 413, suoi speciali Diaframmi per l&#039;osservazion delle stelle 433. </s></p><p type="main">

<s><emph type="bold"></emph>Igrometro,<emph.end type="bold"></emph.end> sue prime invenzioni 515, Igrometro e corda 516, a mostra 517, Igrometro fiorentino; d&#039;onde <lb></lb>avesse occasione 517, Igrometro ad avena 522, Igrometro elettrico 523. </s></p><p type="main">

<s><emph type="bold"></emph>Imperato Ferrante,<emph.end type="bold"></emph.end> sua Historia naturale 96, esame di essa 100. </s></p><p type="main">

<s><emph type="bold"></emph>Imperiali Bartolommeo<emph.end type="bold"></emph.end> interpetra un passo oscuro del Porta relativo al Canocchiale 353. </s></p><p type="main">

<s><emph type="bold"></emph>Keplero Giovanni,<emph.end type="bold"></emph.end> sue opinioni intorno all&#039;inventore del Canocchiale 344, suoi Teoremi relativi alle <lb></lb>immagini rappresentate dalle lenti 361; sue teorie del Canocchiale 362, come pensi, sull&#039;esempio <lb></lb>di Archimede, ad emendare la visione viziata nelle osservazioni celesti 411, storiella curiosa a pro­<lb></lb>posito del Binoccolo 425, ammette, contro l&#039;opinione comune, il peso dell&#039;aria 436. </s></p><p type="main">

<s><emph type="bold"></emph>La Galla Giulio Cesare<emph.end type="bold"></emph.end> narra come fosse inventato il Canocchiale 343. </s></p><p type="main">

<s><emph type="bold"></emph>Lettere torricelliane<emph.end type="bold"></emph.end> sull&#039;esperienza dell&#039;argento vivo 452. </s></p><p type="main">

<s><emph type="bold"></emph>Lincei<emph.end type="bold"></emph.end> (Accademia de&#039;) fini e frutti della sua istituzione 117. </s></p><p type="main">

<s><emph type="bold"></emph>Liquidi,<emph.end type="bold"></emph.end> ragioni del Noel e del Pacquet del loro dilatarsi per effetto del calore 287. </s></p><p type="main">

<s><emph type="bold"></emph>Livella ad acqua<emph.end type="bold"></emph.end> descritta 419, Livella diottrica descritta 420, Livella a bolla d&#039;aria 422. </s></p><p type="main">

<s><emph type="bold"></emph>Macchina<emph.end type="bold"></emph.end> pneumatica 446, Macchina elettrica di Lipsia descritta da G. M. </s>

<s>Della Torre 474. </s></p><p type="main">

<s><emph type="bold"></emph>Magalotti Lorenzo<emph.end type="bold"></emph.end> accademico e segretario dell&#039;Accademia del Cimento 197. </s></p><p type="main">

<s><emph type="bold"></emph>Magiotti Raffaello<emph.end type="bold"></emph.end> collaboratore al Torricelli nelle esperienze del vuoto 176. </s></p><pb xlink:href="020/01/555.jpg" pagenum="536"></pb><p type="main">

<s><emph type="bold"></emph>Magno Valeriano<emph.end type="bold"></emph.end> si fa autore dell&#039;esperienza torricelliana dell&#039;argento vivo 418. </s></p><p type="main">

<s><emph type="bold"></emph>Malpighi Marcello,<emph.end type="bold"></emph.end> 200. </s></p><p type="main">

<s><emph type="bold"></emph>Maurolico Francesco,<emph.end type="bold"></emph.end> sue opere di ottica 64, suoi Teoremi diottrici 358, come spieghi l&#039;azione degli <lb></lb>occhiali in correggere i difetti della vista 503. </s></p><p type="main">

<s><emph type="bold"></emph>Medici Ferdinando II,<emph.end type="bold"></emph.end> Granduca di Toscana, sua curiosità per gli studii sperimentali 186. </s></p><p type="main">

<s><emph type="bold"></emph>Medici Leopoldo,<emph.end type="bold"></emph.end> principe di Toscana, suo amore per gli studii sperimentali 186, sua autorità di go­<lb></lb>verno nel principato accademico 215. </s></p><p type="main">

<s><emph type="bold"></emph>Mersenno Marino,<emph.end type="bold"></emph.end> suoi mali portamenti verso gli scienziati italiani 211, diffonde in Francia la notizia <lb></lb>dello sperimento torricelliano 443. </s></p><p type="main">

<s><emph type="bold"></emph>Michelini Famiano<emph.end type="bold"></emph.end> discepolo di Galileo 162. </s></p><p type="main">

<s><emph type="bold"></emph>Micrometro<emph.end type="bold"></emph.end> primo di Galileo 407. </s></p><p type="main">

<s><emph type="bold"></emph>Microscopii<emph.end type="bold"></emph.end> olandesi 508, loro fabbrica descritta dall&#039;Huyghens 509, microscopii della perlina come <lb></lb>fossero costruiti dal Torricelli, ivi. </s></p><p type="main">

<s><emph type="bold"></emph>Microscopio<emph.end type="bold"></emph.end> composto è invenzione di Francesco Fontana 510, Microscopio catottrico 511. </s></p><p type="main">

<s><emph type="bold"></emph>Montanari Geminiano<emph.end type="bold"></emph.end> accademico del Cimento 204, suo reticolo micrometrico descritto 414, rivendicò <lb></lb>a sè sul p. </s>

<s>Lana l&#039;invenzione del Micrometro a reticolo 416, inventore della Livella diottrica 420. </s></p><p type="main">

<s><emph type="bold"></emph>Moro Lazzero,<emph.end type="bold"></emph.end> suo sistema geolo<gap></gap>co 252. </s></p><p type="main">

<s><emph type="bold"></emph>Nardi Antonio<emph.end type="bold"></emph.end> discepolo di Galileo 167. </s></p><p type="main">

<s><emph type="bold"></emph>Newton Isacco,<emph.end type="bold"></emph.end> metodo della sua Filosofia 220, influsso efficace che sulla Filosofia di lui ebbero gli <lb></lb>Italiani 224, paragonato col De Dominis nella teoria del flusso marino 232, importanza delle sue <lb></lb><emph type="italics"></emph>Questioni<emph.end type="italics"></emph.end> 234, descrive il suo Telescopio a riflessione 402, diffonde la notizia dalle scoperte elet­<lb></lb>triche dell&#039;Hawksbee 472. </s></p><p type="main">

<s><emph type="bold"></emph>Noferi Cosimo<emph.end type="bold"></emph.end> discepolo di Galileo 166. </s></p><p type="main">

<s><emph type="bold"></emph>Nollet,<emph.end type="bold"></emph.end> suoi perfezionamenti introdotti nella macchina elettrica 474. </s></p><p type="main">

<s><emph type="bold"></emph>Novelli Antonio<emph.end type="bold"></emph.end> fabbrica canocchiali 381, sua emulazione col Torricelli 382. </s></p><p type="main">

<s><emph type="bold"></emph>Occhiale<emph.end type="bold"></emph.end> così detto di moltiplicazione venuto d&#039;oltremonti, poco dopo che Galileo avea divulgato il suo <lb></lb>occhialino 508. </s></p><p type="main">

<s><emph type="bold"></emph>Occhiall,<emph.end type="bold"></emph.end> occasione del loro ritrovato, secondo Realdo Colombo 87. </s></p><p type="main">

<s><emph type="bold"></emph>Occhialino,<emph.end type="bold"></emph.end> microscopio semplice di Galileo 506. </s></p><p type="main">

<s><emph type="bold"></emph>Orologi da tasca<emph.end type="bold"></emph.end> come e da chi inventati 337. </s></p><p type="main">

<s><emph type="bold"></emph>Orologio a pendolo<emph.end type="bold"></emph.end> primo progetto di Galileo 309, orologio ad acqua dello stesso Galileo 311. </s></p><p type="main">

<s><emph type="bold"></emph>Oscillazione,<emph.end type="bold"></emph.end> suo centro ne&#039;pendoli applicati all&#039;orologio 330. </s></p><p type="main">

<s><emph type="bold"></emph>Pascal Biagio,<emph.end type="bold"></emph.end> dimestra il vuoto terricelliano 444, fa l&#039;esperienza del vuoto nel vuoto, e sul Puy de <lb></lb>Domme 445. </s></p><p type="main">

<s><emph type="bold"></emph>Patrizio Francesco<emph.end type="bold"></emph.end> insorge centro Aristotile 55, suoi sistemi filosofici 57. </s></p><p type="main">

<s><emph type="bold"></emph>Pendoli,<emph.end type="bold"></emph.end> strumento inventato dai Viviani per aggiustare la loro lunghezza ai tempi 328. </s></p><p type="main">

<s><emph type="bold"></emph>Pendolo conico<emph.end type="bold"></emph.end> applicato agli Orologi 321, leggi del pendolo circolare scoperte da Galileo 304, progetti <lb></lb>di applicarlo agli Orologi a torre 312. </s></p><p type="main">

<s><emph type="bold"></emph>Peripato,<emph.end type="bold"></emph.end> suo carattere filosofico 36. </s></p><p type="main">

<s><emph type="bold"></emph>Petit<emph.end type="bold"></emph.end> descrive il Telescopio calottrico 491. </s></p><p type="main">

<s><emph type="bold"></emph>Pisani Ottavio<emph.end type="bold"></emph.end> primo costruttor del Binoculo 426. </s></p><p type="main">

<s><emph type="bold"></emph>Platone,<emph.end type="bold"></emph.end> sua Filosofia 30. </s></p><p type="main">

<s><emph type="bold"></emph>Platonismo,<emph.end type="bold"></emph.end> come s&#039;introducesse nella Società cristiana 39. </s></p><p type="main">

<s><emph type="bold"></emph>Pluviometro<emph.end type="bold"></emph.end> sua prima origine ed uso fattone dal Castelli 526. </s></p><p type="main">

<s><emph type="bold"></emph>Polemoscopio<emph.end type="bold"></emph.end> 406. </s></p><p type="main">

<s><emph type="bold"></emph>Porta Glovan Battista,<emph.end type="bold"></emph.end> sue opere di Filosofia sperimentale 92, suo trattato delle Rifrazioni 95, esame <lb></lb>del suo libro degli Spiritali 97, esame del suo trattato delle Rifrazioni 98, fa l&#039;esperienza eroniana, <lb></lb>d&#039;ond&#039;ebbe origine il Termometro ad aria 270, suoi teoremi intorno alla proprietà delle lenti ri­<lb></lb>spetto alle immagini 359, inventore della livella ad acqua 419, primo a investigare il modo come <lb></lb>sulla vista operano gli occhiali 502, propone uno strumento da udir da lontano 512. </s></p><p type="main">

<s><emph type="bold"></emph>Portaluce<emph.end type="bold"></emph.end> di Leonardo da Vinci 341. </s></p><p type="main">

<s><emph type="bold"></emph>Porzio Lucantonio<emph.end type="bold"></emph.end> accademico napoletano 206. </s></p><p type="main">

<s><emph type="bold"></emph>Pulsilogio<emph.end type="bold"></emph.end> e suo inventore 300. </s></p><p type="main">

<s><emph type="bold"></emph>Pupilla,<emph.end type="bold"></emph.end> misura di lei nelle osservazioni celesti 409. </s></p><p type="main">

<s><emph type="bold"></emph>Ravaisson Mollien<emph.end type="bold"></emph.end> dà opera a pubblicare i manoscritti vinciani 82, di un passo vinciano da lui in­<lb></lb>terpetrato 126. </s></p><p type="main">

<s><emph type="bold"></emph>Razionalisti,<emph.end type="bold"></emph.end> loro metodi 60, loro meriti 61. </s></p><pb xlink:href="020/01/556.jpg" pagenum="537"></pb><p type="main">

<s><emph type="bold"></emph>Redi Francesco,<emph.end type="bold"></emph.end> accademico del Cimento 199. </s></p><p type="main">

<s><emph type="bold"></emph>Renieri Vincenzio<emph.end type="bold"></emph.end> discepolo di Galileo 160, sua osservazione sul moto de&#039;pendoli 308, suo metodo di <lb></lb>misurare il diametro della pupilla 409. </s></p><p type="main">

<s><emph type="bold"></emph>Rheita Anton Maria<emph.end type="bold"></emph.end> compone il Binoculo di due Canocchiali astronomici accoppiati 427. </s></p><p type="main">

<s><emph type="bold"></emph>Riccioli Giovan Batista<emph.end type="bold"></emph.end> pretende di riformare la scienza 214. </s></p><p type="main">

<s><emph type="bold"></emph>Richter Giovan Paolo<emph.end type="bold"></emph.end> pubblica i manoscritti vinciani 83. </s></p><p type="main">

<s><emph type="bold"></emph>Rinaldini Carlo<emph.end type="bold"></emph.end> accademico del Cimento 192, sue opposizioni contro la ragione di alcuni effetti ope­<lb></lb>rati dal calore nel dilatare i corpi 294. </s></p><p type="main">

<s><emph type="bold"></emph>Rossetti Donato<emph.end type="bold"></emph.end> accademico del Cimento 204. </s></p><p type="main">

<s><emph type="bold"></emph>Saggi<emph.end type="bold"></emph.end> di naturali esperienze fatte nell&#039;Accademia del Cimento, quando e come fossero pubblicati 195. </s></p><p type="main">

<s><emph type="bold"></emph>Sagredo Giovan Francesco<emph.end type="bold"></emph.end> perfeziona il Termometro 277. </s></p><p type="main">

<s><emph type="bold"></emph>Salto<emph.end type="bold"></emph.end> dell&#039;immersione ne&#039;liquidi posti a ghiacciare e sue ragioni 292. </s></p><p type="main">

<s><emph type="bold"></emph>Santorio Santorre<emph.end type="bold"></emph.end> fisico sperimentale 107, inventor del Termometro ad aria 266, primo ad applicare <lb></lb>il pendolo alla misura del tempo 305, varie maniere d&#039;Igrometri inventati da lui 516, 517. </s></p><p type="main">

<s><emph type="bold"></emph>Sarpi Paolo,<emph.end type="bold"></emph.end> sua scienza naturale 109, qual parte avesse nelle osservazioni celesti pubblicate da Ga­<lb></lb>lileo nel suo Nunzio Sidereo 114, ha il primo concetto di uno strumento da veder di lontano 351. </s></p><p type="main">

<s><emph type="bold"></emph>Scaligero Giuseppe<emph.end type="bold"></emph.end> dimostra sperimentalmente il principio d&#039;inerzia 51, ammette la luce diffondersi <lb></lb>in tempo, e il vacuo come condizione del moto 52, 435. </s></p><p type="main">

<s><emph type="bold"></emph>Scheiner Cristoforo,<emph.end type="bold"></emph.end> sua teoria del Canocchiale 367, descrive il modo di colorire le lenti, ad uso di <lb></lb>Elioscopio 429. </s></p><p type="main">

<s><emph type="bold"></emph>Schott Gaspero<emph.end type="bold"></emph.end> narra la storia dell&#039;esperienza del vuoto fatta in Roma dal Berti 442. </s></p><p type="main">

<s><emph type="bold"></emph>Sinclaro Giorgio,<emph.end type="bold"></emph.end> suo Orologio a pendolo descritto, 320, si crede essere stato il primo inventore del <lb></lb>Baroscopio 464. </s></p><p type="main">

<s><emph type="bold"></emph>Sirturo Girolamo<emph.end type="bold"></emph.end> narra come fosse inventato il Canocchiale 342, costruisee egli stesso Canocchiali 375. </s></p><p type="main">

<s><emph type="bold"></emph>Socrate,<emph.end type="bold"></emph.end> sua filosofia 30. </s></p><p type="main">

<s><emph type="bold"></emph>Spina Alessandro<emph.end type="bold"></emph.end> inventor degli occhiali 501. </s></p><p type="main">

<s><emph type="bold"></emph>Stenone Niccolò<emph.end type="bold"></emph.end> accademico del Cimento 199. </s></p><p type="main">

<s><emph type="bold"></emph>Stevino Simeone,<emph.end type="bold"></emph.end> paradosso idrostatico di lui appropriatosi da Galileo 132. </s></p><p type="main">

<s><emph type="bold"></emph>Tarde Giovanni,<emph.end type="bold"></emph.end> sua teoria del Canocchiale 364. </s></p><p type="main">

<s><emph type="bold"></emph>Tartaglia Niccolò<emph.end type="bold"></emph.end> 53. </s></p><p type="main">

<s><emph type="bold"></emph>Telegrafo<emph.end type="bold"></emph.end> a galvanometro divinato dal Porta 95. </s></p><p type="main">

<s><emph type="bold"></emph>Telesio Bernardino,<emph.end type="bold"></emph.end> sua filosofia 56, ammette che si possa dare il vacuo in natura, e che sia supe­<lb></lb>rabile da forza finita 436. </s></p><p type="main">

<s><emph type="bold"></emph>Termometro<emph.end type="bold"></emph.end> applicato a render sensibile il calore de&#039;raggi lunari 268, a liquido, quando fu inven­<lb></lb>tato 281. </s></p><p type="main">

<s><emph type="bold"></emph>Termostatici,<emph.end type="bold"></emph.end> problemi proposti dal Granduca Ferdinando II a risolvere a varii scienziati, 457. </s></p><p type="main">

<s><emph type="bold"></emph>Thevenot Melchisedec<emph.end type="bold"></emph.end> inventore della Livella a bolla d&#039;aria 423. </s></p><p type="main">

<s><emph type="bold"></emph>Torpedine,<emph.end type="bold"></emph.end> come si spiegasse il modo dell&#039;operare del suo organo elettrico 494. </s></p><p type="main">

<s><emph type="bold"></emph>Torricelli Evangelista<emph.end type="bold"></emph.end> discepolo di Galileo 179, inventore del Termometro a liquido 283, suoi Canoc­<lb></lb>chiali 379, sua emulazione col Fontana 380, suo segreto per lavorare le lenti de&#039;Canocchiali 383, <lb></lb>suoi avvertimenti per la buona fabbrica de&#039;cristalli 386, qual fosse la scienza che egli aveva delle <lb></lb>Rifrazioni 389, come fosse poco esercitato nell&#039;Astronomia 390, come si accorgesse che la pressione <lb></lb>ammosferica variava da un giorno all&#039;altro 456, risponde alle obiezioni, fattegli dal Ricci, contro <lb></lb>le ragioni del sostenersi l&#039;argento vivo nello strumento 460, in che trovasse difficoltà d&#039;applicar <lb></lb>l&#039;esperienza dell&#039;argento vivo ad uso di Barometro 463, primo inventore dell&#039;Igrometro a con­<lb></lb>densazione 517, Areometri da lui inventati 525. </s></p><p type="main">

<s><emph type="bold"></emph>Tradizioni,<emph.end type="bold"></emph.end> loro necessità 26. </s></p><p type="main">

<s><emph type="bold"></emph>Treffier Filippo<emph.end type="bold"></emph.end> pensa a costruire e a migliorare l&#039;Igrometro del Folli 520. </s></p><p type="main">

<s><emph type="bold"></emph>Vesalio Andrea<emph.end type="bold"></emph.end> anatomico 85. </s></p><p type="main">

<s><emph type="bold"></emph>Vespucci Amerigo<emph.end type="bold"></emph.end> osservatore de&#039;fatti naturali 66. </s></p><p type="main">

<s><emph type="bold"></emph>Vinci (da) Leonardo,<emph.end type="bold"></emph.end> sue osservazioni naturali 77, suo trattato d&#039;idraulica 80, suoi manoscritti 82. </s></p><p type="main">

<s><emph type="bold"></emph>Virgula<emph.end type="bold"></emph.end> ugeniana ad uso di Micrometro 413. </s></p><p type="main">

<s><emph type="bold"></emph>Visione<emph.end type="bold"></emph.end> viziata nelle osservazioni astronomiche 411. </s></p><p type="main">

<s><emph type="bold"></emph>Viviani Vincenzio<emph.end type="bold"></emph.end> discepolo di Galileo 183, accademico del Cimento 191, sue esperienze del dilatarsi <lb></lb>le corde metalliche al calore 294, origine delle inimicizie di lui col Borelli 296, studia il fatto cu­<lb></lb>rioso della simpatia de&#039;pendoli 319, qual opera dasse alla fabbrica de&#039;Canocchiali 391, spiega il <lb></lb><gap></gap> Treffler l&#039;Igrome-<pb xlink:href="020/01/557.jpg" pagenum="538"></pb>tro del Folli 519, costruisce un Igrometro semplicissimo, e studia le leggi dell&#039;allungarsi della <lb></lb>corda e dell&#039;abbassarsi del peso che la tira, per digradare la scala igrometrica 521, inventa un <lb></lb>areometro simile a quello del Baumè 525, e la stadera de&#039;liquidi 526. </s></p><p type="main">

<s><emph type="bold"></emph>Volta Alessandro,<emph.end type="bold"></emph.end> suoi principii intorno alla scienza elettrica 243, perfeziona l&#039;Elettroscopio di Tiberio <lb></lb>Cavallo, e l&#039;accoppia all&#039;Elettroforo 481, rende comparabile l&#039;Elettrometro a quadrante dell&#039;Hen­<lb></lb>ley 488, legge il Commentario del Galvani e ne rimane esaltato 487, scopre l&#039;error del Galvani, <lb></lb>dimostrando che il moto del fluido elettrico si fa dal muscolo al nervo 488, trova che l&#039;azione <lb></lb>immediata del fluido elettrico è sui nervi 489, sue insigni esperienze per provar che l&#039;elettricità <lb></lb>irritando direttamente i nervi, produce le sensaxioni, ivi, s&#039;accorge finalmente che l&#039;elettricità <lb></lb>detta animale muove dal contatto di due metalli 490, protesta in faccia all&#039;Aldini che le sue dot­<lb></lb>trine son diverse da quelle del Galvani 491, sue ulteriori scoperte intorno agli organi produttori <lb></lb>dell&#039;elettricità animale 494, sue prime prove colle coppie metalliche soprapposte, non riuscite 495, <lb></lb>riesce finalmente a costruire il suo Organo elettrico artificiale, e ne diffonde la notizia 496, pro­<lb></lb>pone un Igrometro elettrico 523. </s></p><p type="main">

<s><emph type="bold"></emph>Vo<gap></gap>sle Is<gap></gap><emph.end type="bold"></emph.end> si crede essere stato il primo inventore dell&#039;Aeroscopio 464. </s></p><p type="main">

<s><emph type="bold"></emph>Wendel<gap></gap>n<emph.end type="bold"></emph.end> è il primo a notar le differenze del numero delle vibrazioni, fatte da un medesimo pendolo <lb></lb>nell&#039;estate e nell&#039;inverno 335. </s></p><pb xlink:href="020/01/558.jpg"></pb><p type="main">

<s>Finito di stampare in Bologna presso la <lb></lb>Libreria Editrice Forni nel Gennaio 1970 </s></p><pb xlink:href="020/01/559.jpg"></pb></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Editor-in-Chief: Harry Woolf<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Willis K. </s>

<s>Shepard Professor of the History of <lb></lb>Science, The Johns Hopkins University<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/560.jpg"></pb><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph><emph type="italics"></emph>Storia del Metodo <lb></lb>Sperimentale in Italia<emph.end type="italics"></emph.end><emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>by RAFFAELLO CAVERNI <lb></lb>in Six Volumes<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Volume II<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE, NO. 134<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT CORPORATION <lb></lb>NEW YORK LONDON 1972<emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/561.jpg"></pb><p type="main">

<s>Reproduced here is the Florence edition of 1891-1900. </s></p><p type="main">

<s><emph type="center"></emph>Copyright © 1972 by Johnson Reprint Corporation All rights reserved <lb></lb>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT CORPORATION <lb></lb>111 Fifth Avenue, New York, N.Y. 10003, U.S.A. <lb></lb>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Shipton Group House, 24/28 Oval Road, London, NW1 7DD, England<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Printed in Italy<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/562.jpg"></pb><p type="main">

<s><emph type="center"></emph>DEL METODO SPERIMENTALE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>APPLICATO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>ALLE SCIENZE FISICHE<emph.end type="center"></emph.end><pb xlink:href="020/01/563.jpg"></pb></s></p><pb xlink:href="020/01/564.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della luce diretta e della luce riflessa<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. De&#039;primi e principali cultori dell&#039;Ottica. </s>

<s>— II. </s>

<s>Della legge fondamentale della luce riflessa. </s>

<s>— <lb></lb>III. De&#039;corpi diafani e degli opachi; delle ombre e delle penombre. </s>

<s>— IV. </s>

<s>Di alcune espe­<lb></lb>rienze singolari sulle ombre: del passaggio della luce attraverso piccoli fori. </s>

<s>— V. </s>

<s>Delle leggi <lb></lb>della intensitá luminosa. </s>

<s>— VI. </s>

<s>Della velocità della luce. </s>

<s>— VII. </s>

<s>Delle ipotesi delle ondula­<lb></lb>zioni eterce e dell&#039;emissione. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Un celebre letterato fiorentino del secolo XVI volendo in una Lezione <lb></lb>accademica dare a intendere ciò che si volesse da&#039;Filosofi significar per i <lb></lb>nomi di riflessione e di rifrazione, a proposito della luce, “ nè crediate, di­<lb></lb>ceva a&#039;suoi uditori, che i Latini e i Greci, cioè quegli che sanno la lingua <lb></lb>o greca o latina, le possano intendere quantunque dotti, se prima non istu­<lb></lb>diano, non solo le discipline matematiche, ma ancora la Filosofia naturale, <lb></lb>perchè la Prospettiva, avendo per soggetto il razzo visuale ovvero la linea <lb></lb>radiosa, che è il medesimo, è subalternata parte alle Matematiche rispetto <lb></lb>alle linee, e parte alla Filosofia naturale, rispetto alla radiosità ” (Lez. </s>

<s>su <lb></lb>Dante di B. Varchi, Firenze 1841, pag. </s>

<s>300). </s></p><p type="main">

<s>Benchè qui dicasi le linee e la radiosità essere una medesima cosa, fa­<lb></lb>cendole nonostante parte a discipline così varie, quali sono la Filosofia na­<lb></lb>turale o la Fisica, e la Matematica, s&#039;insinua una notabile distinzione, che <lb></lb>s&#039;ammetteva allora fra linea e ciò che chiamavasi radiosità, della qual di­<lb></lb>stinzione possiamo noi dire del Varchi quel che il Boulliaud diceva del Pa­<lb></lb>trizio, possiamo cioè dire essere stata suggerita <emph type="italics"></emph>opticae disciplinae ignoran­<lb></lb>tia<emph.end type="italics"></emph.end> (De natura lucis, Parisiis 1638, pag. </s>

<s>122), non essendo la radiosità nulla <lb></lb>di reale ma una mera affezione dell&#039;occhio. </s></p><pb xlink:href="020/01/565.jpg" pagenum="8"></pb><p type="main">

<s>Intanto però intravedonsi di qui, non le vestigia sole de&#039;progressi, ma <lb></lb>e le mosse con gli andamenti varii dell&#039;Ottica da&#039;suoi primi e più antichi <lb></lb>principii. </s>

<s>Benchè infatti quella special distinzione insinuata dal Letterato fio­<lb></lb>rentino e professata dal Filosofo dalmata, non sia che un inganno, pur è <lb></lb>vero che la luce si presenta a studiare obiettivamente o nel raggio, e su­<lb></lb>biettivamente o nell&#039;occhio. </s>

<s>Quella è subalternata parte alle Matematiche, <lb></lb>questa alla Filosofia naturale, o come più propriamente si direbbe oggidì, <lb></lb>alla Fisiologia. </s></p><p type="main">

<s>L&#039;importante soggetto non poteva non eccitar le menti di Platone e <lb></lb>di Aristotile a filosofarvi attorno, e furono, come nelle altre cose, anco in <lb></lb>ciò i due grandi Maestri discordi, per cui presero le loro scuole due varii <lb></lb>indirizzi, e, conforme alle verità istituite e professate o agli errori, riuscì <lb></lb>ciascuna a varietà di progressi. </s>

<s>L&#039;aristotelismo ammettendo che l&#039;occhio <lb></lb>vede per recezione, secondava i progressi nello studio del fenomeno subiet­<lb></lb>tivo, per cui la teorica della visione fu efficacemente promossa da&#039;settatori <lb></lb>di quella scuola. </s>

<s>Il platonismo, tutt&#039;al contrario col professare il principio <lb></lb>dell&#039;emissione delle specie, rendeva affatto impossibile lo studio del feno­<lb></lb>meno subiettivo, mentre poi da un&#039;altra parte, dando alla luce proprietà di <lb></lb>sostanza, dava efficace impulso a ciò che concerne gli studii del fenomeno <lb></lb>obiettivo, d&#039;ond&#039;è che ai platonici, meglio che a nessun&#039;altro, fu facile in­<lb></lb>trodursi a speculare intorno alle proprietà della luce. </s></p><p type="main">

<s>Primi infatti a ridurre in ordine di trattato l&#039;Ottica, o come allora di­<lb></lb>cevasi la Prospettiva, furono Euclide, principe de&#039;Geometri, ed Eliodoro di <lb></lb>Larissa, ad Herone il meccanico, e Tolomeo e Teone con parecchi alfri ri­<lb></lb>masti dimenticati, in così lungo decorrere di tempi, e tutti addetti alla scuola <lb></lb>di Platone. </s>

<s>Della Prospettiva di Euclide, e di quella di Eliodoro, avemmo <lb></lb>noi italiani, infin dal secolo XVI, una bella traduzione dottamente commen­<lb></lb>tata da Egnazio Danti, frate domenicano e Cosmografo del Granduca di To­<lb></lb>scana. </s>

<s>Il principio platonico, di che s&#039;informano e son radicalmente infette <lb></lb>le speculazioni de&#039;due greci Autori, si rivela, infin dalle prime pagine, in <lb></lb>quella Prefazione o <emph type="italics"></emph>Dichiarazione<emph.end type="italics"></emph.end> premessa al Trattato di Euclide, e che <lb></lb>fu, secondo il Danti, dettata da Teone. </s>

<s>Essendosi già dichiarato che i raggi <lb></lb>visivi escono dall&#039;occhio, soggiunge quest&#039;altre parole per sua ragione: <lb></lb>“ Onde, se i corpi che muovono la vista venissero all&#039;occhio senza che da <lb></lb>esso si partissero i raggi per trovare la cosa veduta, era mestiero nel fab­<lb></lb>bricare l&#039;occhio di farlo concavo, acciò fosse più comodo a ricevere i simu­<lb></lb>lacri delle cose vedute. </s>

<s>Ma questo veggiamo essere in verità altrimenti, per­<lb></lb>chè piuttosto la figura dell&#039;occhio è tonda e sferica ” (La Prospettiva di <lb></lb>Euclide trad. </s>

<s>da E. Danti, Firenze 1573, pag. </s>

<s>4). Similmente il Larisseo, in <lb></lb>sull&#039;ultimo del suo Trattatello, che lo stesso Danti traduce in poche pagine <lb></lb>innumerate, e apposte al Trattato di Euclide, così concludeva: “ Le quali <lb></lb>cose stando così, non credo che nessuno si vergognerà di affermare che la <lb></lb>luce esca dagli occhi nostri, vedendo così gran somiglianza e convenienza <lb></lb>che è fra il veder nostro e il sole. </s>

<s>Laonde il gran Platone disse che, fra <pb xlink:href="020/01/566.jpg" pagenum="9"></pb>tutti gli strumenti de&#039;sensi, solamente quel del vedere era similissimo al <lb></lb>sole, e che rappresentava principalmente la figura ed immagine sua. </s>

<s>” </s></p><p type="main">

<s>In conformità di questi principii i due greci Autori s&#039;intrattengono <lb></lb>molto volentieri intorno allo esaminar, con finezza mirabile d&#039;osservazione, <lb></lb>e a spiegare alcuni fatti concernenti la vista, come sarebbe per esempio che <lb></lb>nessuna cosa visibile si può tutta vedere in un tratto. </s>

<s>Lo dimostra Euclide <lb></lb>da ciò che si osserva avvenire in colui, che ha per caso perduto un ago, e <lb></lb>lo va diligentemente cercando. </s>

<s>“ Dal che chiaro si scorge, egli dice, che non <lb></lb>si vedendo quel piccolo corpo, che con tanta attenzione si cerca, non si vede <lb></lb>manco il luogo ove egli luce. </s>

<s>Onde dall&#039;occhio non sono viste in un tratto <lb></lb>tutte le parti del luogo ove egli mira, perchè se ciò fosse che fissando gli <lb></lb>occhi vedesse ogni parte del luogo, che attentamente riguarda, vedrebbe <lb></lb>anche l&#039;ago, che sì accuratamente cerca, e nondimeno non lo vede ” (ivi, <lb></lb>pag. </s>

<s>2). Aggiunge poi a conferma di ciò l&#039;altro esempio di quei che fissa­<lb></lb>mente guardano sopra un libro aperto, e non possono nemmeno essi veder <lb></lb>tutte a un tratto le lettere scritte nel libro. </s>

<s>“ E spesse volte sforzandosi di <lb></lb>trovare alcune lettere, che radamente nella detta faccia erano scritte, non <lb></lb>potevano. </s>

<s>E questo avviene perchè i raggi visuali non si gettano in un tratto <lb></lb>a ciascuna lettera del foglio, nè manco sono insieme uniti e congiunti, ma <lb></lb>distinti e divisi l&#039;uno dall&#039;altro per qualche spazio ed intervallo, dal che <lb></lb>nasce che ogni lettera del foglio non si può nel medesimo tempo vedere. </s>

<s><lb></lb>E di qui si manifesta che non si vede tutto il luogo del foglio ” (ivi, pag. </s>

<s>3). </s></p><p type="main">

<s>La matematica delle linee però e de&#039;raggi luminosi, in questi Autori, <lb></lb>è impacciata nel suo progredire dal falso principio dell&#039;emissione, ciò che <lb></lb>particolarmente si prova per l&#039;esempio di Tolomeo, il più compiuto autore <lb></lb>antico di Prospettiva. </s>

<s>Com&#039;era infatti possibile trattar, con precisione di linee <lb></lb>matematiche, i raggi che non hanno direzion prefinita e forma certa dalla <lb></lb>posizione e dalla figura immutabile degli oggetti, ma dalla mobilità subiet­<lb></lb>tiva degli occhi? </s>

<s>Com&#039;era possibile avere in considerazione di linee geome­<lb></lb>triche que&#039;raggi, che uscendo, al dir di Tolomeo, umidi dagli stessi occhi <lb></lb>si rasciugavano al contatto dell&#039;aria appena usciti fuori? </s></p><p type="main">

<s>Di qui è che sebbene i Platonici s&#039;avvantaggiassero sopra gli aristote­<lb></lb>lici in riguardar la luce com&#039;essere sostanziale, per cui l&#039;Ottica matematica <lb></lb>riusciva così fondata sopra una realtà e non sopra vaghe accidentalità senza <lb></lb>subietto; tanto nonostante giovò agli aristotelici l&#039;aver professato il princi­<lb></lb>pio della recezion de&#039;raggi visivi nell&#039;occhio, ch&#039;ebbe la Prospettiva ad <lb></lb>aspettarsi un migliore andamento da costoro, primo de&#039;quali fu l&#039;arabo <lb></lb>Alhazeno. </s>

<s>Il trattato di lui, che riuscì disordinato e verboso più forse per <lb></lb>colpa di chi ebbe in seguito a maneggiarlo, che per difetto dell&#039;Autore, fu <lb></lb>nel secolo XIII ordinato, e ridotto in parte a compendio, da un matematico <lb></lb>pollacco di cognome Ciolek, ma più volgarmente noto sotto il nome di Vi­<lb></lb>tellione. </s>

<s>Egli solennemente bandiva dall&#039;Ottica l&#039;errore platonico ripetendo <lb></lb>la sentenza: <emph type="italics"></emph>Impossibile est visum rebus visis applicari per radios ab ocu­<lb></lb>lis egressos.<emph.end type="italics"></emph.end> (Norimbergae 1535, pag. </s>

<s>55 v.). Provava egli poi la verità della <pb xlink:href="020/01/567.jpg" pagenum="10"></pb>sua sentenza con argomenti, a cui male avrebbero trovato che rispondere i <lb></lb>Platonici. </s>

<s>I raggi, che voi dite uscire dagli occhi, scriveva Vitellione contro <lb></lb>essi, o son corporei o no. </s>

<s>Se son corporei, come può dall&#039;occhio, senza pa­<lb></lb>tirne difetto, uscir tanta materia, che vada a riempire l&#039;universo? </s>

<s>come giu­<lb></lb>sto avverrebbe, quando l&#039;occhio stesso si trattiene a contemplare un bel <lb></lb>cielo stellato. </s>

<s>Se sono incorporei, “ cum sensus non sit nisi in re corporali, <lb></lb>tunc ipsi radii non sentirent rem visam, ergo nec oculus corporeus, me­<lb></lb>diante hoc incorporeo non sentiente, poterit sentire ” (ivi). </s></p><p type="main">

<s>Vitellione riuscì perciò nell&#039;Ottica quel Maestro di coloro che sanno, <lb></lb>che Aristotile era riuscito nella Filosofia universale, per cui, quando s&#039;in­<lb></lb>sorse contro il venerato idolo greco, ebbe a sentirne offesa anche il vene­<lb></lb>rato idolo pollacco. </s>

<s>“ È così grande l&#039;autorità di Vitellione (scriveva Pietro <lb></lb>Accolti) unico e principal capo della Scuola de&#039;Prospettivi, che chiunque <lb></lb>ardisca pronunziare egli aver falsamente o dimostrato o insegnato può di <lb></lb>facile essere reputato temerario o ardito molto. </s>

<s>Con tuttociò sendo la scienza <lb></lb>delle Matematiche .... fondata meramente e unicamente sopra la evidenza <lb></lb>delle dimostrazioni e matematiche proposizioni, e non punto sopra l&#039;auto­<lb></lb>rita del Maestro .... perciò si è costumato sempre dar franchezza e libertà <lb></lb>di far dimostrazione di quello che, chicchessia, diversamente stimasse ” (Lo <lb></lb>inganno degli occhi, Firenze 1625, pag. </s>

<s>116). E prosegue l&#039;Accolti a dire <lb></lb>come e perchè sia falso un teorema di Vitellione. </s>

<s>Ma più di trent&#039;anni prima <lb></lb>aveva il Porta avventato contro lo stesso Vitellione un giudizio che, se non <lb></lb>è calunnioso, non può non sembrare soverchiamente severo. </s>

<s>E quel giudizio <lb></lb>è tale: “ In universo enim opere suo quidquid ex se, supra illud Alhazen <lb></lb>est, falsum fere est ” (De refraction. </s>

<s>Neapoli 1593, pag. </s>

<s>64). </s></p><p type="main">

<s>Comunque sia, tanto tempo prima che con sì libera libertà si svelas­<lb></lb>sero in Italia gli errori dell&#039;Ottico pollacco, eravi chi in coltivar nella so­<lb></lb>litudine la scienza facevasi a sè stesso maestro. </s>

<s>Leonardo da Vinci avrà <lb></lb>senza dubbio appresi dalle tradizioni i fondamenti dell&#039;Ottica, e non è cre­<lb></lb>dibile ch&#039;e&#039;non rimanesse anch&#039;egli irretito in parecchi degli antichi errori. </s>

<s><lb></lb>Nulladimeno è mirabile il fino giudizio, con cui, riconosciuti quegli errori, <lb></lb>si studia di cansarli, e così cansati progredire senza altra scorta, e precor­<lb></lb>rere a chi tanto tempo dopo, sarebbe per riuscire in Ottica solenne mae­<lb></lb>stro al mondo. </s>

<s>Un mezzo secolo dopo Leonardo, Francesco Maurolico, conse­<lb></lb>gnava anch&#039;egli a solitari manoscritti i suoi <emph type="italics"></emph>Photismi<emph.end type="italics"></emph.end> e i suoi <emph type="italics"></emph>Diaphanorum <lb></lb>Partes,<emph.end type="italics"></emph.end> ne&#039;quali, della riflessione e della rifrazione della luce, s&#039;insegnavano <lb></lb>cose che nessuno degli antichi aveva mai più pensate. </s></p><p type="main">

<s>Tra il finire del secolo XVI o il cominciar del seguente Giovan Bati­<lb></lb>sta Porta e Giovanni Keplero iniziarono la scienza delle rifrazioni, l&#039;uno <lb></lb>mostrando a&#039;troppo creduli gli errori di Vitellione, l&#039;altro promovendo la <lb></lb>scienza dal punto, dove Vitellione stesso l&#039;aveva lasciata. </s>

<s>L&#039;invenzione poi <lb></lb>del canocchiale e la viva curiosità che frugava tutti d&#039;intendere la ragione <lb></lb>com&#039;operava il maraviglioso strumento, produssero alla luce i Fotismi e i <lb></lb>Diafani del Maurolico rimasti per più di sessant&#039;anni manoscritti: dettero <pb xlink:href="020/01/568.jpg" pagenum="11"></pb>eccitamento di scrivere la sua <emph type="italics"></emph>Dioptrica<emph.end type="italics"></emph.end> al Keplero, e al De Dominis di ri­<lb></lb>prendere in mano e condurre a termine il suo <emph type="italics"></emph>De radiis visus et lucis,<emph.end type="italics"></emph.end> cc­<lb></lb>leberrimo Trattato. </s></p><p type="main">

<s>La storia nel Tomo precedente da noi già narrata, mostra assai chiaro <lb></lb>come nessuno de&#039;sopra commemorati autori potè riuscire a dimostrar la ra­<lb></lb>gione del Canocchiale olandese, primieramente perchè ignoravano la legge <lb></lb>delle relazioni costanti che passano fra gli angoli d&#039;incidenza e quelli di ri­<lb></lb>frazione, e in secondo luogo perchè non era facile, anche conosciuta che <lb></lb>fosse quella legge, il saperla applicare alla composizione delle lenti concave <lb></lb>e delle convesse. </s>

<s>Willebrod Snellio ne&#039;suoi Manoscritti de&#039;quali s&#039;ebbe poi <lb></lb>relazione da Isacco Vossio, e Renato Cartesio concorsero insieme a investi­<lb></lb>gare, a dimostrare sperimentalmente e a divulgare quella celebre legge diot­<lb></lb>trica, la quale, benchè fosse il sospiro di tutti i Filosofi, ella fu nonostante <lb></lb>o accolta con diffidenza o apertamente ripudiata. </s></p><p type="main">

<s>Più risoluti di tutti gli altri in così fatto ripudio furono i nostri Ita­<lb></lb>liani, a&#039;quali, per i gravi errori in che incorse Galileo e per la poca cultura <lb></lb>che raccomandò alla sua scuola, sarebbe forse mancata ogni scienza ottica, <lb></lb>se dal gregge avverso al gregge galileiano non fosse col suo celebre trat­<lb></lb>tato <emph type="italics"></emph>De lumine<emph.end type="italics"></emph.end> uscito fuori Francesco Maria Grimaldi. </s>

<s>Egli discopritore di <lb></lb>una nuova proprietà nella luce, oltre alle due notissime della riflessione e <lb></lb>della rifrazione, ebbe al di fuori d&#039;Italia una gloriosa progenie nell&#039;Huy­<lb></lb>ghens e nel Newton i quali ambedue perciò parteciparono, benchè con più <lb></lb>vigoria di natural complessione e di gioventù, delle virtù paterne. </s>

<s>Il Gri­<lb></lb>maldi specula intorno alle teorie dell&#039;Ottica, con argomenti fisici e matema­<lb></lb>tici: l&#039;Huyghens nel Trattato <emph type="italics"></emph>De la lumiere<emph.end type="italics"></emph.end> è più fisico che matematico, <lb></lb>ma nella <emph type="italics"></emph>Dioptrica,<emph.end type="italics"></emph.end> la quale preparata parecchi anni prima non si vide alla <lb></lb>luce, postuma, che nel 1703, ripudiata ogni fisica ipotesi, prosegue con tutto <lb></lb>il rigore della Geometria. </s>

<s>Il Newton sa così ben contemperar la Fisica alla <lb></lb>Matematica, che le ipotesi par s&#039;illustrino d&#039;evidenza matematica anch&#039;esse. </s>

<s><lb></lb>Per lui così le nuove scoperte grimaldiane, come le altre proprietà più an­<lb></lb>ticamente conasciutesi della luce, trovarono nella Geometria quelle dimo­<lb></lb>strazioni, che i predecessori invano erano andati cercando desiderosi per <lb></lb>tante vie. </s></p><p type="main">

<s>Tali sono in brevi tratti i progressi che, per opera e studio de&#039;suoi <lb></lb>cultori, fece l&#039;Ottica da&#039;suoi principii infino al cominciar del secolo XVIII. </s>

<s><lb></lb>Ora è da narrare in che modo si facesse il progredir della scienza ne&#039;suoi <lb></lb>particolari soggetti. </s>

<s>E perchè questi tanto son di natura varii e nel com­<lb></lb>plesso loro così numerosi, non c&#039;intratterremo perciò che intorno a&#039;princi­<lb></lb>pali concernenti la luce riflessa, la rifratta e la diffratta, toccando altresì <lb></lb>quelle quistioni che più strettamente s&#039;attengono a queste tre capitali pro­<lb></lb>prietà della luce. </s></p><pb xlink:href="020/01/569.jpg" pagenum="12"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Che il primo studio de&#039;Filosofi e de&#039;Matematici dovess&#039;esser rivolto a <lb></lb>ricercar la legge secondo la quale riflettesi la luce dai corpi opachi, s&#039;in­<lb></lb>tende con assai facilità, ripensando esser questo il fenomeno, che più ov­<lb></lb>viamente occorre ad osservare. </s>

<s>Gli specchi, d&#039;uso antichissimo, e gli studiosi <lb></lb>atteggiamenti di chi trattenevasi a rimirare in essi specchiata la propria im­<lb></lb>magine, suggerirono ai Filosofi il primo strumento da dimostrar che i raggi <lb></lb>della luce cadono sullo specchio, e risaltano alla parte opposta sempre ugual­<lb></lb>mente inclinati. </s></p><p type="main">

<s>Euclide infatti pone per fondamento alla sua Calottrica, fra le altre, <lb></lb>anco questa supposizione, che in ordine per lui è la terza. </s>

<s>“ Se lo specchio <lb></lb>si collocherà in un piano sopra il quale sia a piombo qualche altezza, la <lb></lb><figure id="id.020.01.569.1.jpg" xlink:href="020/01/569/1.jpg"></figure></s></p><p type="caption">

<s>Figura 1.<lb></lb>ragione che harà la linea intrapresa fra quel che <lb></lb>mira e lo specchio alla linea che è fra lo specchio <lb></lb>e la già detta altezza, harà anco l&#039;altezza di quel <lb></lb>che mira all&#039;altezza della cosa elevata a piombo <lb></lb>sopra il piano nel quale è lo specchio ” (Traduz. </s>

<s><lb></lb>cit., pag. </s>

<s>77, 78). </s></p><p type="main">

<s>Sia il punto T (fig. </s>

<s>1) lo specchio e CZ il <lb></lb>piano su cui va collocato. </s>

<s>Sia CT <emph type="italics"></emph>la linea in­<lb></lb>trapresa fra quel che mira e lo specchio,<emph.end type="italics"></emph.end> e sia <lb></lb>TZ <emph type="italics"></emph>la linea che è fra lo specchio e la già data altezza. </s>

<s>L&#039;altezza di quel <lb></lb>che mira<emph.end type="italics"></emph.end> sia BC, e sia DZ <emph type="italics"></emph>l&#039;altezza della cosa elevata a piombo sopra il <lb></lb>piano, nel quale è lo specchio;<emph.end type="italics"></emph.end> suppone Euclide come cosa di fatto che sia <lb></lb>CT:TZ=BC:DZ. </s></p><p type="main">

<s>Da un tal supposto conclude l&#039;Autore il suo I Teorema così formulato: <lb></lb><figure id="id.020.01.569.2.jpg" xlink:href="020/01/569/2.jpg"></figure></s></p><p type="caption">

<s>Figura 2.<lb></lb>“ — I raggi visuali si riflettono ad angoli pari, <lb></lb>tanto negli specchi piani come anco ne&#039;rotondi <lb></lb>e ne&#039;concavi. </s>

<s>— Sia l&#039;occhio nel punto B (fig. </s>

<s>2), <lb></lb>lo specchio piano sia AG ed esca dall&#039;occhio il <lb></lb>raggio BC, che si riflette nel punto D: dico che <lb></lb>l&#039;angolo della riflessione Z è uguale all&#039;angolo <lb></lb>della incidenza E. </s>

<s>Imperocchè tirinsi le due linee <lb></lb>a piombo BG e DA sopra lo specchio AG: e sarà <lb></lb>la BG alla GC com&#039;è la DA alla AC, per la terza <lb></lb>supposizione. </s>

<s>Per il che il triangolo BGC sarà simile al triangolo DAC, tal <lb></lb>che l&#039;angolo E sarà uguale all&#039;angolo Z, essendo i triangoli simili di angoli <lb></lb>uguali ” (ivi, pag. </s>

<s>80). </s></p><p type="main">

<s>È manifesto di qui che la dimostrazione del Teorema euclideo non con­<lb></lb>sisteva in altro che nell&#039;applicazione del fatto sperimentale supposto, e con <pb xlink:href="020/01/570.jpg" pagenum="13"></pb>ciò si dichiarava l&#039;Autore che la legge fondamentale della Calottrica era, <lb></lb>secondo lui, per via geometrica indimostrabile. </s>

<s>Per non dimostrabile altri­<lb></lb>menti che dal fatto sperimentato l&#039;ebbe pure Tolomeo, come si par dal Teo­<lb></lb>rema XLV del I Libro Degli Specchi, e l&#039;ebbe altresì per tale Alhazeno, <lb></lb>nelle proposizioni X e XVIII del suo IV Libro. </s>

<s>Nè altra via da&#039;suoi illustri <lb></lb>predecessori seppe tener Vitellione, il quale si trattiene assai lungamente, <lb></lb>nella proposizione IX del suo V Libro di Prospettiva, a descrivere lo stru­<lb></lb>mento <emph type="italics"></emph>in quo modi omnium reflexionum a quibuscumque regularibus spe­<lb></lb>culis instrumentaliter declarantur<emph.end type="italics"></emph.end> (Edit. </s>

<s>cit., pag. </s>

<s>123). Proponendosi egli <lb></lb>infatti nel seguente Teorema X, di dimostrar l&#039;uguaglianza che passa tra <lb></lb>gli angoli dell&#039;incidenza e quelli della riflessione, non sa trovare altra mi­<lb></lb>glior via della sperimentale, applicandovi lo strumento da sè prima così mi­<lb></lb>nutamente descritto: “ In speculis planis (così viene enunciato quel X Teo­<lb></lb>rema) radii oblique incidentis, fit ad aliam partem reflexio, semperque <lb></lb>angulum incidentiae aequale esse angulo reflexionis <emph type="italics"></emph>experimentaliter<emph.end type="italics"></emph.end> com­<lb></lb>probatur ” (ibi, pag. </s>

<s>124). </s></p><p type="main">

<s>Lo strumento calottrico di Vitellione, e il modo di farne esperienza, non <lb></lb>differivano si può dir di niente dallo strumento e dal modo che, per lo stesso <lb></lb>effetto. </s>

<s>è tenuto oggidì dalla Fisica sperimentale. </s>

<s>Consisteva in un semicer­<lb></lb>chio di ottone diviso in due quadranti da una linea perpendicolare, che bat­<lb></lb>teva sul centro del semicerchio stesso, a cui soggiaceva applicato lo spec­<lb></lb>chio. </s>

<s>Uno spiraglio da una parte e un traguardo dall&#039;altra, scorrevoli per <lb></lb>la curvità degli orli sui quadranti graduati, servivano, come servono tutta­<lb></lb>via ai moderni, per isperimentar che il raggio tanti gradi segna dalla parte <lb></lb>d&#039;onde cade, quanti dall&#039;altra dove risale. </s></p><p type="main">

<s>Così dimostravansi, con una sola esperienza, le due leggi fondamentali <lb></lb>della Calottrica, imperocchè dalla disposizione stessa dello strumento veni­<lb></lb>vasi a concludere che i due raggi, l&#039;incidente e il riflesso, trovansi sempre <lb></lb>in un medesimo piano eretto a perpendicolo sulla superficie dello specchio. </s>

<s><lb></lb>L&#039;Alighieri espose le due leggi calottriche in versi, che sembrano scritti ap­<lb></lb>posta per persuadere che il bello è lo splendore del vero. </s>

<s>“ Come quando, <lb></lb>dall&#039;acqua o dallo specchio, salta lo raggio all&#039;oppo­<lb></lb>sita parte, salendo su per lo modo parecchio a quel <lb></lb><figure id="id.020.01.570.1.jpg" xlink:href="020/01/570/1.jpg"></figure></s></p><p type="caption">

<s>Figura 3.<lb></lb>che scende, e, tanto si diparte dal cader della pietra <lb></lb>in igual tratta, sì come mostra esperienza ed arte.... ” <lb></lb>(Purg. </s>

<s>XV, t. </s>

<s>6, 7). </s></p><p type="main">

<s>In quel dir che il raggio sale per lo modo pa­<lb></lb>recchio (cioè pari o nel medesimo piano) a quel che <lb></lb>scende, esprimesi l&#039;una delle due leggi: l&#039;altra vien <lb></lb>così dimostrata. </s>

<s>Sia AB (fig. </s>

<s>3) la superficie riflet­<lb></lb>tente acqua o specchio: CD il cader della pietra, ossia la perpendicolare, <lb></lb>EC il raggio incidente e CF il riflesso. </s>

<s>Dice che, presa sulla perpendicolare <lb></lb>un <emph type="italics"></emph>igual tratta,<emph.end type="italics"></emph.end> per esempio CG, tanto si diparte dal punto G il raggio che <lb></lb>scende, quanto il raggio che sale; ciò che torna a dire che le due perpen-<pb xlink:href="020/01/571.jpg" pagenum="14"></pb>dicolari GE, GF, le quali son la giusta misura del dipartirsi i due raggi, sono <lb></lb>fra loro uguali. </s>

<s>D&#039;onde, essendo i due triangoli EGC, FGC uguali è facile <lb></lb>concludere che i due angoli ECB, ACF debbon pure essere uguali. </s></p><p type="main">

<s>Le due leggi, soggiunge ivi Dante essere dimostrate dall&#039;<emph type="italics"></emph>esperienza<emph.end type="italics"></emph.end> e <lb></lb>dall&#039;<emph type="italics"></emph>arte,<emph.end type="italics"></emph.end> ossia dal ragionamento, il qual ragionamento è quello che noi ab­<lb></lb>biamo ora spiegato dai versi del Poeta. </s>

<s>Ma è facile vedere che anco qui, <lb></lb>come in Euclide a cui il Cantore de&#039;citati versi tien d&#039;occhio, tutto il fon­<lb></lb>damento è nel fatto sperimentale e poco o nulla nell&#039;arte, la quale ancora <lb></lb>doveva essere attesa assai lungamente. </s></p><p type="main">

<s>Non prima infatti del cominciar del secolo XVII si vide nel Keplero chi <lb></lb>tentasse di maneggiar quell&#039;arte, invocando la Geometria applicata al moto <lb></lb>de&#039;corpi, per dimostrar ciò che Euclide, e tutti gli altri Ottici dopo di lui, <lb></lb>avevano reputato geometricalmente indimostrabile. </s>

<s>Quel <emph type="italics"></emph>nescio quid subtile<emph.end type="italics"></emph.end><lb></lb>per cui s&#039;erano l&#039;Alhazen e Vitellione argomentati <emph type="italics"></emph>motum lucis oblique in­<lb></lb>cidentis componi ex motu perpendiculari et motu parallelo ad densi su­<lb></lb>perficiem<emph.end type="italics"></emph.end> (Paralipom. </s>

<s>ad Vitell., Francof. </s>

<s>1604, pag. </s>

<s>84), parve al Keplero <lb></lb>esser uno spiraglio aperto alle nuove speranze d&#039;ostetricare il primo parto <lb></lb>di quel connubio fra l&#039;Ottica e la Meccanica, da&#039;due commemorati Autori <lb></lb>felicemente iniziato. </s></p><p type="main">

<s>La proposizione XIX formulata ne&#039;Paralipomeni a Vitellione <emph type="italics"></emph>Repercus­<lb></lb>sus fit ad aequales angulos et eius quod oblique incidit ad latus alterum,<emph.end type="italics"></emph.end><lb></lb>è quella stessa formulata tanti secoli prima nel suo I Teorema di Prospet­<lb></lb>tiva da Euclide, ma la dimostrazione è nel Matematico alemanno, dopo tanti <lb></lb>secoli, nuova, e a chi si diffidava di riuscir nella difficile impresa, si pre­<lb></lb>senta inaspettata. </s></p><p type="main">

<s>Invocando dunque il Keplero il principio della composizion delle forze <lb></lb>applicato al moto della luce, così comincia e procede in quella sua dimo­<lb></lb>strazione: “ Cum quid oblique movetur ver­<lb></lb>sus superficiem, motus is componitur ex <lb></lb><figure id="id.020.01.571.1.jpg" xlink:href="020/01/571/1.jpg"></figure></s></p><p type="caption">

<s>Figura 4.<lb></lb>perpendiculari et parallelo superficiei. </s>

<s>Al <lb></lb>superficies tantum ei parti obiicitur, quae <lb></lb>est in se perpendicularis, non ei quae est <lb></lb>sibi parallelos. </s>

<s>Quare nec impedit partem <lb></lb>sibi parallelon, sed palitur mobile resiliendo <lb></lb>pergere ad partem alteram sicut advenerat. </s>

<s><lb></lb>Sit CDF (fig. </s>

<s>4) superficies, BD motus lu­<lb></lb>cis: continuetur BD in E, secans CDF in <lb></lb>D, et sit CDE aequalis CDA ” (ibi, pag. </s>

<s>14). </s></p><p type="main">

<s>La ragione di questa uguaglianza la dimostra il Keplero così argomen­<lb></lb>tando: Siccome il moto dalla parte D verso C non è impedito, ma è impe­<lb></lb>dito solo quello da C verso E, dunque il raggio riflesso AD deve serbar <lb></lb>quella medesima inclinazione verso la superficie riflettente CD secondo la <lb></lb>quale procederebbe il raggio BDE quando non fosse impedito. </s>

<s>In altre pa­<lb></lb>role, deve esser CDE=CDA. </s>

<s>Ma perchè CDE è uguale a BDF “ ergo (con-<pb xlink:href="020/01/572.jpg" pagenum="15"></pb>clude il Keplero) BDF incidentiae et ADC reflexionis anguli sunt aequales ” <lb></lb>(ibi, pag. </s>

<s>15). </s></p><p type="main">

<s>Questa nuova dimostrazione kepleriana piacque molto al Cartesio, che <lb></lb>l&#039;accolse nella sua Diottrica ringentilita e con più lucido ordine condotta. </s>

<s><lb></lb>Suppone A (fig. </s>

<s>5) essere una palla obliquamente <lb></lb><figure id="id.020.01.572.1.jpg" xlink:href="020/01/572/1.jpg"></figure></s></p><p type="caption">

<s>Figura 5.<lb></lb>cacciata nella direzione AB percotere in B sopra un <lb></lb>punto della superfice CE, che egli suppone <emph type="italics"></emph>exacte <lb></lb>planam duramque esse.<emph.end type="italics"></emph.end> Fa altresì astrazione dalla <lb></lb>gravezza, peso e misura della palla stessa, cose tutte <lb></lb>affatto inutili a essere considerate, per non si voler <lb></lb>d&#039;altro intendere che della luce, <emph type="italics"></emph>ad quam omnia <lb></lb>haec referri debent.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Così essendo, si domanda verso qual parte si <lb></lb>rifletterà la detta palla scagliata, e si fa via alla ri­<lb></lb>sposta decomponendo, a imitazione del Keplero, il <lb></lb>moto obliquo AB nell&#039;orizzontale AH e nel perpendicolare AC, osservando <lb></lb>che questo solo è quello, a cui fa impedimento il piano del rimbalzo. </s>

<s>Dopo <lb></lb>di che il Cartesio, così prosegue nella dimostrazione: </s></p><p type="main">

<s>“ Ut accurate igitur inquiramus ad quam partem pila illisa debeat re­<lb></lb>silire, describamus circulum ex centro B, qui transeat per punctum A, et <lb></lb>dicamus: spatio temporis eodem quo progressa est ab A ad B, necessario <lb></lb>illam a B ad aliquod punctum huius circuli circumferentiae reverti debere. </s>

<s><lb></lb>Nam omnia puncta quae eodem intervallo distant a B, quo distat A, in hac <lb></lb>circumferentia occurrunt, et pilae motum iam supra aeque velocem finxi­<lb></lb>mus. </s>

<s>Tandem ad designandum ipsum punctum, quod ex omnibus huius <lb></lb>circumferentiae tangere debet, erigamus ad normam tres rectas AC, HB et <lb></lb>FE, supra CE, hac ratione ut nec maius nec minus spatium interiaciat AC <lb></lb>et HB, quam HB et FE. </s>

<s>Deinde dicamus: idem tempus quod pilam dextror­<lb></lb>sum porrexit ab A uno punctorum linaee AC, usque ad B unum ex punctis <lb></lb>linaee HB, illam resilientem ab HB sistere debet in aliquo puncto linaee FE. </s>

<s><lb></lb>Nam singula puncta huius linaee FE eadem distantia hoc respectu ab HB <lb></lb>remota sunt, et eadem qua singula linaee AC, et ex priori dispositione tan­<lb></lb>tumdem eo inclinat quantum antea. </s>

<s>Jam eodem momento aliquod punctum <lb></lb>linaee FE et simul aliquod circumferentiae AFD contingere nequit, nisi in <lb></lb>puncto D vel F. </s>

<s>Nam extra haec duo nullibi mutuo secantur. </s>

<s>Terra autem <lb></lb>obstante ad B progredi non potest: sequitur itaque illam necessario tendere <lb></lb>debere ad F. </s>

<s>Et sic manifestum est qua ratione reflexio fiat, scilicet semper <lb></lb>ad angulum aequalem illi, quem vulgo incidentiae nominant. </s>

<s>Ut si radius <lb></lb>ex puncto A emanet in B, superficiem speculi plani CBE resilit ad F, ita <lb></lb>ut reflexionis angulus FBE, neque cedat, neque exuperet magnitudine al­<lb></lb>terum illum incidentiae ABC ” (De Methodo; Dioptrices, Francofurti 1692, <lb></lb>pag. </s>

<s>48). </s></p><p type="main">

<s>Nella dimostrazione condotta dal&#039;Keplero supponevasi implicita la con­<lb></lb>dizione che il raggio fosse ugualmente veloce al raggio incidente, ma il Car-<pb xlink:href="020/01/573.jpg" pagenum="16"></pb>tesio richiede quella stessa condizione esplicita, ben conoscendo come di lì <lb></lb>derivasse tutta la forza all&#039;argomento. </s>

<s>“ Hinc etiam planum minime cre­<lb></lb>dendum esse necessario pilam aliquo momento haerere puncto B, pruisquam <lb></lb>digrediatur ad F, iuxta quorumdam Philosophorum opinionem. </s>

<s>Nam inter­<lb></lb>rupto hoc motu exigua tantummodo mora, nulla extaret causa, qua inci­<lb></lb>tante, vires resumere posset ” (ibi, pag. </s>

<s>47). </s></p><p type="main">

<s>L&#039;applicazione del principio d&#039;inerzia alla forza della percossa, fu sog­<lb></lb>getto di grandi controversie fra&#039;cultori della scienza del moto, ma pur, fuori <lb></lb>di ogni controversia, è un errore manifesto il supposto qui dal Cartesio che <lb></lb>cioè un corpo duro e privo affatto d&#039;ogni elaterio, com&#039;ei professa ossere <lb></lb>un atomo di luce, mantenga dopo l&#039;urto la medesima velocità di prima e <lb></lb>la stessa quantità di moto. </s>

<s>È perciò impossibile, nella ipotesi cartesiana, che <lb></lb>un raggio di luce salti all&#039;opposta parte con angolo precisamente pari a <lb></lb>quel che scende. </s>

<s>Se con V si rappresenta la velocità perduta nel&#039;urto e con <lb></lb><foreign lang="grc">ν</foreign> la velocità, o istantaneamente come esigeva il Cartesio o con succesione <lb></lb>di minimo tempo com&#039;altri permettevano, riacquistata nel verso opposto <lb></lb>dopo l&#039;urto, e s&#039;intenda per <foreign lang="grc">β</foreign> l&#039;angolo di riflessione e per <foreign lang="grc">α</foreign> quello dell&#039;in­<lb></lb>cidenza, i Meccanici riescono all&#039;equazione tang. <foreign lang="grc">β</foreign>=V/<foreign lang="grc">ν</foreign> tang. <foreign lang="grc">α</foreign>, per la quale <lb></lb>si dimostra assai chiaramente non potersi verificare la legge fondamentale <lb></lb>della Calottrica, se non a patto che la luce sia dotata di una elasticità <lb></lb>perfetta. </s></p><p type="main">

<s>Il Cartesio perciò allucinato dalle splendide vie meccaniche apertegli <lb></lb>innanzi dal Keplero non s&#039;avvide che la severità matematica assai male si <lb></lb>confaceva al suo immaginario sistema, e o non pensò o non seppe salvar <lb></lb>le mendicate calottriche dottrine da un&#039;aperta contradizione. </s></p><p type="main">

<s>Esperto de&#039;pericoli che s&#039;incontravano in volere applicare alla luce le <lb></lb>proprietà meccaniche de&#039;corpi ponderosi, il Grimaldi, con miglior giudizio, <lb></lb>si rivolse a cercar nel campo della fisica la desiderata dimostrazione calot­<lb></lb>trica e la trovò semplice e tutto insieme ingegnosa. </s>

<s>Potrebbe dirsi altresì <lb></lb><figure id="id.020.01.573.1.jpg" xlink:href="020/01/573/1.jpg"></figure></s></p><p type="caption">

<s>Figura 6.<lb></lb>concludente se gli si conceda una sup­<lb></lb>posizione fondamentale, la qual consiste <lb></lb>nell&#039;ammetter che il raggio luminoso <lb></lb>abbia “ aliqua crassities, insensibilis <lb></lb>quidem sed tamen physica, ita ut in eo <lb></lb>concipi queant plures linaee tum extre­<lb></lb>mae, tum mediae, secundum longitudi­<lb></lb>nem illius extensae ” (De Lumine, Bo­<lb></lb>noniae 1665, pag. </s>

<s>166). </s></p><p type="main">

<s>Concessa questa supposizione, è ne­<lb></lb>cessità concedergli insieme ciò che ne <lb></lb>consegue ed è che, mantenendosi sem­<lb></lb>pre il raggio nel medesimo mezzo, non ci è ragione perchè debba, dopo <lb></lb>essere stato riflesso, alterarsi in più o in meno dalla sua prima crassizie. <pb xlink:href="020/01/574.jpg" pagenum="17"></pb>Supposto ciò, rappresenti CH (fig. </s>

<s>6) lo specchio e le due strisce KLDF, <lb></lb>GDFE rappresentino i due raggi. </s>

<s>Se la loro crassizie, dice il Grimaldi, dee, <lb></lb>com&#039;è ragionevole, mantenersi uguale, necessario è che l&#039;angolo dell&#039;inci­<lb></lb>denza EFH sia uguale ad LFD angolo della riflessione. </s>

<s>Si dimostra così dal­<lb></lb>l&#039;Autore in poche parole: </s></p><p type="main">

<s>Condotte le OF, DP perpendicolari alle DG, LF ne&#039;punti O, P, saranno <lb></lb>queste le misure giuste della crassizie de&#039;raggi. </s>

<s>I triangoli poi ODF, PFD <lb></lb>rettangoli, daranno le due proporzioni OF:DF=sen ODF:1, DP:DF= <lb></lb>sen PFD:1, onde OF:DP=sen ODF:sen PFD, ma OF è uguale a DP <lb></lb>per esser, secondo il supposto, le misure delle due crassizie uguali; dunque <lb></lb>ODF=PFD. “ Proinde non possunt non esse aequales anguli incidentiae <lb></lb>ac reflexionis, si eadem debet esse crassities in radio reflexo ac in directo, <lb></lb>quod erat ostendendum ” (ibi, pag. </s>

<s>167). </s></p><p type="main">

<s>Abbiam conceduto al Grimaldi questo supposto, che è tutto il fonda­<lb></lb>mento su cui posa la sua bella dimostrazione, ma poi ci soprapprende uno <lb></lb>scrupolo d&#039;essere stati forse troppo solleciti e liberali con esso. </s>

<s>Diasi pure <lb></lb>al raggio una qualche insensibile crassizie: questa però non può aver pro­<lb></lb>porzione alcuna fisicamente determinabile, con quelle eminenze e cavità, di <lb></lb>che il Microscopio ci rivela essere aspera qualunque superficie, la quale sem­<lb></lb>bri al tatto più levigata. </s>

<s>Di qui è che il raggio deve dopo l&#039;urto subire una <lb></lb>certa dispersione per cui venga ad alterarsi notabilmente quella sua prima <lb></lb>crassizie. </s></p><p type="main">

<s>A rimuovere un tale scrupolo dalle menti dètte opera il Newton, il <lb></lb>quale, esperto oramai delle contradizioni a cui furon fatte segno la dimo­<lb></lb>strazion meccanica del Keplero e la fisica del Grimaldi, si studiò di proce­<lb></lb>dere in modo da non offendere nè contro uno scoglio nè contro l&#039;altro. </s>

<s>Egli <lb></lb>chiede gli si conceda per prima cosa, ciò che per verità nessuno gli potrebbe <lb></lb>negare, esser gli atomi della luce corpi duri, soggetti alle leggi dell&#039;attra­<lb></lb>zione, e ch&#039;essendo così attratti da&#039;mezzi attraversati sieno perciò deviati <lb></lb>dalla dirittura de&#039;loro moti. </s>

<s>Vuole altresì gli si conceda, in secondo luogo, <lb></lb>ch&#039;esali dalle superficie riflettenti, acqua o vetro o cristallo, una sottilissima <lb></lb>aura eterea, la quale vada soprapponendosi in strati via via più densi come <lb></lb>più si dilungano dalle dette superficie. </s>

<s>“ Annon medium hoc aethereum pro <lb></lb>eo ut ex aqua, vitro, crystallo, aliisque crassis densisque corporibus in spa­<lb></lb>tia vacua eatur, densius evadit paulatim, eoque pacto radios luminis refrin­<lb></lb>git, non simul et semel in uno puncto, sed gradatim eos in curvas lineas <lb></lb>flectendo? </s>

<s>Et annon medii huius condensatio, quae ita gradatim ad usque <lb></lb>intervalla aliqua a corporibus porrigitur, eoque pacto in causa est quamo­<lb></lb>brem radii luminis, qui prope corporum densorum extrema interiecto aliquo <lb></lb>intervallo transeunt, inflectantur? </s>

<s>” (Optices, Lib. </s>

<s>III, Patavii 1773, pag. </s>

<s>143). </s></p><p type="main">

<s>Come poi que&#039;raggi, così, senza toccar la superficie dello specchio s&#039;in­<lb></lb>flettano, in modo che il secondo angolo riesca al primo ugualmente incli­<lb></lb>nato, lo dimostra il Newton, dietro que&#039;supposti, procedendo così per le vie <lb></lb>della Meccanica, a passo franco e sicuro: </s></p><pb xlink:href="020/01/575.jpg" pagenum="18"></pb><p type="main">

<s>Sieno Aa, Bb (fig. </s>

<s>7) le due linee conterminanti il mezzo diafano at­<lb></lb>traversato dall&#039;atomo di luce G nel punto H: se sia quel mezzo meno denso <lb></lb>dell&#039;altro d&#039;onde il raggio GH è venuto “ et si attractio vel impulsus po­<lb></lb><figure id="id.020.01.575.1.jpg" xlink:href="020/01/575/1.jpg"></figure></s></p><p type="caption">

<s>Figura 7<lb></lb>natur uniformis, erit ex demon­<lb></lb>stratis Galilaei curva HP parabola <lb></lb>“ (Principia mathem., Genevae <lb></lb>1739, T. I, pag. </s>

<s>534). Soggiaccia <lb></lb>allo strato etereo Ab, un altro si­<lb></lb>mile strato etereo Bc, ma alquanto <lb></lb>meno denso del primo, nel quale <lb></lb>entri, emergendo dal punto P il <lb></lb>raggio <expan abbr="Pq.">Pque</expan> Si dimostra con gran <lb></lb>facilità dal Newton che la velocità <lb></lb>del raggio avanti l&#039;incidenza è alla <lb></lb>velocità dello stesso raggio dopo <lb></lb>l&#039;emergenza, come il seno del­<lb></lb>l&#039;emergenza al seno dell&#039;incidenza <lb></lb>(Propositio XCV, ibi, pag. </s>

<s>536), <lb></lb>e il detto raggio PQ procederà <lb></lb>per le stesse ragioni in arco pa­<lb></lb>rabolico; cosicchè, avendo in Q raggiunto l&#039;angolo limite, subirà in R la <lb></lb>riflessione interna, e come i gravi proiettili attratti al centro della Terra si <lb></lb>troverà aver descritta la traiettoria HPQR semiparabolica. </s></p><p type="main">

<s>“ Perveniat corpus (giacchè l&#039;atomo luminoso è pel Newton un corpo <lb></lb>qualunque) ad hoc planum in puncto R et quoniam linea emergentiae coin­<lb></lb>cidit cum eodem plano, perspicuum est quod corpus non potest ultra per­<lb></lb>gere versus planum Ee. </s>

<s>Sed nec potest idem pergere in linea emergentiae <lb></lb>Rd, propterea quod perpetuo attrahitur vel impellitur versus medium inci­<lb></lb>dentiae. </s>

<s>Revertetur itaque inter plana Cc, Dd, describendo arcum parabolae <lb></lb>QRq cuius vertex principalis, iuxta demonstrata Galilaei, est in R; secabit <lb></lb>planum Cc in eodem angulo in q ac prius in <expan abbr="q;">que</expan> dein pergendo in arcubus <lb></lb>parabolicis qp, ph etc. </s>

<s>arcubus prioribus QP, PH, similibus et aequalibus, <lb></lb>secabit reliqua plana in iisdem angulis in p, h etc. </s>

<s>ac prius in P, H etc. </s>

<s><lb></lb>emergetque tandem eadem obliquitate in h, qua incidit in H ” (ibi, pag. </s>

<s>538). </s></p><p type="main">

<s>Il Newton, che nelle speculazioni sue era originale, procede per le vie <lb></lb>della Meccanica con passo più sicuro di quel che non facesse il Cartesio <lb></lb>imitator del Keplero. </s>

<s>Ma il forte si è che non è questione di Meccanica pura. </s>

<s><lb></lb>Nessuno può revocare in dubbio i Teoremi XLVIII, XLIX e L del Tomo I <lb></lb>de&#039;<emph type="italics"></emph>Principii,<emph.end type="italics"></emph.end> ne&#039;quali nulla osta a supporre un proiettile qualunque che at­<lb></lb>traversi mezzi via via meno densi. </s>

<s>Si può dubitar però se l&#039;etere neuto­<lb></lb>niano si trovi in così fatte condizioni. </s>

<s>Chi non direbbe piuttosto che le den­<lb></lb>sità di lui crescono via via perchè più fortemente attratto verso la superficie <lb></lb>del riflettente? </s></p><p type="main">

<s>Ma lasciamo un po&#039;da parte questo mezzo etereo, il quale non esiste <pb xlink:href="020/01/576.jpg" pagenum="19"></pb>forse che nella immaginazione de&#039;Filosofi: consideriamo l&#039;aria, per la quale <lb></lb>siam certificati dai fatti che ella è più fortemente attratta presso alla super­<lb></lb>ficie de&#039;corpi, i quali perciò tutto intorno circonda di un&#039;ammosfera via via <lb></lb>sempre più densa. </s>

<s>E poichè, nelle ottiche neutoniane speculazioni, concorre <lb></lb>anco l&#039;aria a incurvare i raggi dicendosi dal Filosofo matematico che così <lb></lb>le rifrazioni come le riflessioni non avvengono nel punto dell&#039;incidenza sul <lb></lb>vetro, <emph type="italics"></emph>sed paulatim per continuam incurvationem radiorum factam par­<lb></lb>tim in aere antequam attingunt vitrum<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>540, 4) si vede che se <lb></lb>la densità di essa aria, piuttosto che scemare ella cresce, è del tutto impos­<lb></lb>sibile che avvenga la riflessione. </s>

<s>Sia infatti nella precedente figura 7 lo <lb></lb>strato Bc più denso dell&#039;Ab e sia questo, anche più denso dell&#039;altro da cui <lb></lb>viene il raggio, e allora HP, PQ ecc. </s>

<s>invece di rifrangersi dalla perpendi­<lb></lb>colare, si rifrangeranno alla perpendicolare, e tutto insieme il raggio HPQ <lb></lb>non s&#039;avvierà per riflettersi alla parte opposta, ma si ritorcerà verso la me­<lb></lb>desima parte. </s></p><p type="main">

<s>Le speculazioni però del Newton si verificano in alcuni fatti naturali, <lb></lb>quando una superficie è fortemente riscaldata. </s>

<s>Allora gli strati dell&#039;aria di­<lb></lb>minuiscono veramente in densità secondo l&#039;ipotesi neutoniana dell&#039;etere, <lb></lb>ch&#039;esala dai corpi, ed è veramente allora la riflessione indipendente dalla <lb></lb>levigatezza della superficie. </s>

<s>Qualunque piano più scabro, e meno atto a ri­<lb></lb>fletter la luce nelle condizioni ordinarie, come sarebbe per esempio una <lb></lb>landa arenosa, può, sotto i raggi ardenti del sole, far di sè specchio agli <lb></lb>oggetti circostanti, come un lago di chiara acqua tranquilla. </s></p><p type="main">

<s>Così, tornando alla nostra figura 7, se rappresenta Ee quesla landa are­<lb></lb>nosa infocata, l&#039;occhio che fosse in g vedrebbe in G&#039;il punto G dell&#039;og­<lb></lb>getto GM, e tutto l&#039;oggetto stesso dipingersi in un&#039;immagine rovesciata nel <lb></lb>concorso de&#039;raggi visuali col cateto, precisamente come in uno specchio or­<lb></lb>dinario. </s>

<s>Fu per l&#039;applicazione diretta di questo Teorema neutoniano che An­<lb></lb>tonio Minasi e Jacopo Pignattari, verso il 1750, usi ad osservar lo spettacolo <lb></lb>sulle patrie rive marine di Reggio di Calabria, intesero il magico artifizio <lb></lb>della <emph type="italics"></emph>Fata Morgana<emph.end type="italics"></emph.end> e il Monge toglieva così d&#039;illusione gli assetati com­<lb></lb>pagni di viaggio in Egitto, dando loro a intender, come, secondo il Newton, <lb></lb>riflettan la luce allo stesso modo le fresche acque e le aride sabbie. </s></p><p type="main">

<s>Ma ritornando al principale argomento, e ripensando come per nessuna <lb></lb>delle varie vie tentate e percorse dagli Ottici si riesce a dimostrar la legge <lb></lb>delle riflessioni, senza contrarietà, e in modo che ne sien d&#039;ogni parte so­<lb></lb>disfatti gl&#039;ingegni speculativi; chi non direbbe che da Euclide in poi la Spe­<lb></lb>cularia non ha fatto progressi, o chi non reputerebbe savi gli antichi, i quali, <lb></lb>senza travagliarsi in sottili ipotesi o in calcoli faticosi, ritennero quella legge <lb></lb>come un fatto, non bisognoso, e nè suscettibile di alcuna dimostrazione? </s></p><p type="main">

<s>Se nè la Fisica dunque nè la Geometria sodisfano pienamente, è forse <lb></lb>da sperar qualche cosa nella Morale? </s>

<s>Benchè per verità non s&#039;intenda come <lb></lb>un fatto fisico possa derivare la sua ragion naturale dalla moralità delle cose, <lb></lb>nonostante il Fermat e l&#039;Huyghens invocarono nella Diottrica il principio <pb xlink:href="020/01/577.jpg" pagenum="20"></pb>delle cause finali. </s>

<s>Il Leibniz estese, con più zelo che mai, quello stesso prin­<lb></lb>cipio all&#039;Ottica, alla Catottrica e alla Diottrica, e in una sua scrittura inse­<lb></lb>rita, nel 1682, negli Atti degli Eruditi di Lipsia, e raccolta poi da pag. </s>

<s>145-50 <lb></lb>del Tomo III di tutte le opere stampate nel 1768 a Ginevra, incomincia così <lb></lb>dal dimostrar la legge delle riflessioni sul fondamento dell&#039;unica ipotesi da <lb></lb>lui costituito: <emph type="italics"></emph>Lumen a puncto radiante ad punctum illustrandum per­<lb></lb>venit via omnium facillima.<emph.end type="italics"></emph.end> La dimostrazione è semplicissima e non s&#039;aiuta <lb></lb>che della Geometria più elementare. </s></p><p type="main">

<s>“ Sit enim punctum radians C (fig. </s>

<s>8) illustrandum D, speculum pla­<lb></lb>num AB. </s>

<s>Quaeritur punctum speculi E radium ad D reflectens. </s>

<s>Dico id esse <lb></lb><figure id="id.020.01.577.1.jpg" xlink:href="020/01/577/1.jpg"></figure></s></p><p type="caption">

<s>Figura 8.<lb></lb>tale ut tota via CE+ED fiat omnium <lb></lb>minima, seu minor quam CF+FD, si <lb></lb>nimirum aliud quodcumque speculi pun­<lb></lb>ctum F fuisset assumptum. </s>

<s>Hoc obtinet <lb></lb>si E sumatur tale ut anguli CEA et DEB <lb></lb>sint aequales ut ex Geometria constat ” <lb></lb>(pag. </s>

<s>145). </s></p><p type="main">

<s>I Cartesiani, giustamente avversi al <lb></lb>principio delle cause finali, si ridevano <lb></lb>del Leibniz, quasi avesse dato al raggio uno spirito di consultazione da eleg­<lb></lb>ger, fra le infinite che gli si parano innanzi, la più facile via e la più breve. </s>

<s><lb></lb>A costoro il Leibniz stesso così rispondeva: “ Neque enim radius a C egre­<lb></lb>diens consultat quomodo ad punctum E vel D, vel G pervenire quam facil­<lb></lb>lime possit.... sed ipse Creator rerum ita creavit lucem ut ex eius natura <lb></lb>pulcherrimus ille eventus nasceretur. </s>

<s>Itaque errant, valde, ne quid gravius <lb></lb>dicam, qui causas finales cum Cartesio in physica reiiciunt ” (ibi, pag. </s>

<s>146). </s></p><p type="main">

<s>Questa arringheria però non ha virtù di rimuovere la sentenza di co­<lb></lb>loro, i quali affermano che la Speculeria, anche senza alcuna dimostrazione <lb></lb>fisica, o matematica o morale della legge della riflessione, progredì, come si <lb></lb>dimostra per l&#039;esempio di tutti gli Autori fioriti da Euclide infino al Ke­<lb></lb>plero, i quali Autori certificati per l&#039;esperienza essere, il raggio che va, <lb></lb>ugualmente inclinato a quello che viene, disegnarono con precisione le im­<lb></lb>magini in ogni configurazione di specchi e dettero ragioni certe di tutti <lb></lb>questi varii ordini di apparenze. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Conosciute così le leggi del riflettersi la luce negli specchi artificiali, <lb></lb>risalirono i Filosofi colla contemplazione ad applicarle alle apparenze cele­<lb></lb>sti, specialmente in quello specchio naturale che, riflettendo a noi i raggi <lb></lb>del sole, illumina le tenebre delle nostre notti. </s>

<s>Plutarco aveva felicemente <lb></lb>diffusa l&#039;opinione di coloro, che rassomigliando la Luna alla Terra dicevano <pb xlink:href="020/01/578.jpg" pagenum="21"></pb>le macchie di lei essere in parte dovute all&#039;ombre proiettate da&#039;monti, e in <lb></lb>parte dal riflesso de&#039;mari. </s>

<s>Ciò dette occasione a dispute fra gli stessi se­<lb></lb>guaci di questa opinione, alcuni de&#039;quali, come il Keplero, ingannati dalla <lb></lb>natural chiarezza dell&#039;acqua, attribuivano le ombre non mutabili della Luna <lb></lb>piuttosto ai continenti. </s>

<s>Galileo che, nel Nunzio Sidereo, aveva sentenziato <lb></lb>senza prove ed avea affermato come cosa da non mettersi in dubbio dover <lb></lb>l&#039;acqua, a&#039;riflessi del sole, apparir più buia della terra, nel I Dialogo de&#039;Mas­<lb></lb>simi Sistemi si studia di persuaderne Simplicio con facili ragionamenti con­<lb></lb>fortati dall&#039;esperienza. </s></p><p type="main">

<s>“ Pigliate (così dice allo stesso Simplicio il Salviati) in cortesia quello <lb></lb>specchio, che è attaccato a quel muro, e usciamo qua nella corte.... At­<lb></lb>taccate lo specchio là a quel muro, dove batte il sole: discostiamoci e riti­<lb></lb>riamoci qua all&#039;ombra. </s>

<s>Ecco là due superficie percosse dal sole, cioè il muro <lb></lb>e lo specchio. </s>

<s>Ditemi ora qual vi si presenta più chiara quella del muro o <lb></lb>quella dello specchio? </s>

<s>Voi non rispondete?.... (Alb. </s>

<s>I, pag. </s>

<s>81). Voi ve­<lb></lb>dete la differenza che cade tra le due reflessioni fatte dalle due superficie <lb></lb>del muro e dello specchio, percosse nell&#039;istesso modo per l&#039;appunto dai raggi <lb></lb>solari, e vedete come la reflession che vien dal muro si diffonda verso tutte <lb></lb>le parti opposteli, ma quella dello specchio va verso una parte sola, non <lb></lb>punto maggiore dello specchio medesimo; vedete parimente come la super­<lb></lb>ficie del muro riguardata da qualsivoglia luogo, si mostra chiara sempre <lb></lb>ugualmente a sè stessa; e per tutto assai più chiara che quella dello spec­<lb></lb>chio, eccettuatone quel piccolo luogo solamente, dove batte il riflesso dello <lb></lb>specchio, che di lì apparisce lo specchio molto più chiaro del muro ” (ivi, <lb></lb>pag. </s>

<s>83). </s></p><p type="main">

<s>Qui prosegue il Salviati ad applicar l&#039;esperienza alle riflessioni della <lb></lb>Luna, ma a persuader meglio Simplicio non trascura di rendere appresso <lb></lb>la ragione perchè, conforme alla detta esperienza, il muro apparisce al sole <lb></lb>più luminoso dello specchio. </s>

<s>“ E se voi desiderate intendere l&#039;intero di que­<lb></lb>sto negozio, considerate come l&#039;esser la superficie di quel muro aspra, è <lb></lb>l&#039;istesso che l&#039;esser composta d&#039;innumerabili superficie piccolissime, dispo­<lb></lb>ste secondo innumerabili diversità d&#039;inclinazioni, tra le quali di necessità <lb></lb>accade, che ne sieno molte disposte a mandare i raggi reflessi da loro in <lb></lb>un tal luogo, molte altre in altro, e insomma non è luogo alcuno al quale <lb></lb>non arrivino moltissimi raggi reflessi da moltissime superficiette sparse per <lb></lb>tutta l&#039;intera superficie del corpo scabroso, sopra il quale cascano i raggi <lb></lb>luminosi. </s>

<s>Dal che segue di necessità che sopra qualsivoglia parte di qua­<lb></lb>lunque superficie opposta a quella che riceve i raggi primarii incidenti, per­<lb></lb>vengano raggi reflessi, e in conseguenza l&#039;illuminazione. </s>

<s>Segueno ancora, <lb></lb>che il medesimo corpo, sul quale vengono i raggi illuminanti, rimirato da <lb></lb>qualsivoglia luogo, si mostri tutto illuminato e chiaro ” (ivi, pag. </s>

<s>87, 88). </s></p><p type="main">

<s>Se però questa dottrina galileiana, intorno alla maggior riflessione delle <lb></lb>superficie aspre rispetto alle levigate, sia veramente originale o se sia stata <lb></lb>insegnata prima da altri, darebbe a noi luogo di dubitare, attendendo a ciò <pb xlink:href="020/01/579.jpg" pagenum="22"></pb>che il Baliani scrive in una sua lettera indirizzata al medesimo Galileo, sotto <lb></lb>il di 31 Gennaio 1614. In essa, fra le altre cose, confessa di essersi ricre­<lb></lb>duto, per le argomentazioni di Filippo Salviati, di una falsa opinione ch&#039;egli <lb></lb>aveva intorno alla natura del ghiaccio, stimando ch&#039;egli fosse acqua non ra­<lb></lb>refatta ma condensata, e che dovesse perciò, per la sua maggior gravità spe­<lb></lb>cifica, andare a fondo. </s></p><p type="main">

<s>“ Del quale errore (son parole dello stesso Baliani) mi ha tolto il si­<lb></lb>gnor Filippo, dicendomi che il ghiaccio occupa maggior luogo dell&#039;acqua, <lb></lb>il che poi anche provai per esperienza, e gli dissi la mia opinione come possa <lb></lb>essere che il ghiaccio si faccia dal freddo che condensi l&#039;acqua, e che ad <lb></lb>ogni modo egli occupi maggior luogo, perchè si condensa non uniforme­<lb></lb>mente, ma piuttosto in diverse parti, fra le quali restano delle parti più <lb></lb>rare, ond&#039;egli tutto insieme viene ad essere più raro dell&#039;acqua. </s>

<s>La qual <lb></lb>difformità di parti è cagione che il ghiaccio perda in gran parte la diafa­<lb></lb>neità, e io credo avere abbastanza provato al detto signor Filippo che tutti <lb></lb>i corpi son diafani, la cui natura è totalmente conforme, cioè non più rara <lb></lb>da una parte che dall&#039;altra ” (Alb. </s>

<s>VIII, 300, 1). </s></p><p type="main">

<s>Le prove che il Baliani aveva per confermare questa sua teorica de&#039;corpi <lb></lb>opachi e de&#039;diafani, si riducono a quelle stesse, che adducevansi dianzi da <lb></lb>Galileo, per provar come il muro aspro ed opaco apparisca più luminoso <lb></lb>dello specchio di cristallo diafano e levigato. </s>

<s>Di ciò abbiamo il documento <lb></lb>certo in alcuni passi del <emph type="italics"></emph>Trattato della Pestilenza,<emph.end type="italics"></emph.end> dove rendesi la ragione <lb></lb>dell&#039;opacità, che presentano alcuni corpi diafani nel raffreddarsi, qual sa­<lb></lb>rebbe per esempio la cera o lo stesso ghiaccio. </s>

<s>“ Nè in altra guisa, egli <lb></lb>dice, credo io che induri, non solo la cera o la pece e tuttociò che è strutto <lb></lb>a forza di calore, ma l&#039;acqua eziandio, qualora divien ghiaccio, e la pioggia <lb></lb>e la grandine e l&#039;olio ed altri liquori, quando si congelano. </s>

<s>Quindi è che <lb></lb>ognuno di loro ovvero diviene opaco, ovvero perde o tanto o quanto di tra­<lb></lb>sparenza, perciocchè le parti, che nel liquido erano uniformi, si variano in <lb></lb>figura e densità, onde il lume, nel penetrarvi, costretto a far più riflessioni <lb></lb>e rifrazioni, non può trapassar dirittamente ” (Savona 1647, pag. </s>

<s>52). </s></p><p type="main">

<s>Conforme a tali principii rende il Baliani la ragione perchè l&#039;acqua si <lb></lb>mostri cerulea e diafana, e la spuma invece bianchissima e opaca. </s>

<s>“ Bianca <lb></lb>per riflettersi da ognuna di loro bollicelle il lume verso di noi, onde tanto <lb></lb>lume vediamo quante sono le bollette esterne della spuma, che quasi tanti <lb></lb>specchi tante volte ci rappresentano il lume quante elle sono. </s>

<s>Non ha tra­<lb></lb>sparenza (la spuma) come quella che dipende non dalla rarità, ma dalla uni­<lb></lb>formità del mezzo, onde entrativi i raggi nè trovando chi gli sforzi a pie­<lb></lb>garsi, e perciò camminando diritti verso gli occhi, rappresentano loro l&#039;oggetto <lb></lb>onde sono partiti. </s>

<s>Dovecchè nella spuma, le cui parti sono si diverse in den­<lb></lb>sità e figura, son costretti più volte a riflettersi, e perciò spesso a non pe­<lb></lb>netrarla, ed a rifrangersi, e per questo a non rappresentar l&#039;oggetto se non <lb></lb>se molto confuso ” (ivi, pag. </s>

<s>24, 25). </s></p><p type="main">

<s>Quasi nel medesimo tempo dottrine ottiche similissime a queste erano <pb xlink:href="020/01/580.jpg" pagenum="23"></pb>professate dall&#039;Hodierna, il quale, in uno de&#039;suoi opuscoli intitolato <emph type="italics"></emph>La Nu­<lb></lb>vola pendente,<emph.end type="italics"></emph.end> così scriveva: “ Causa della cui diafaneità (cioè dell&#039;aria) è <lb></lb>la conservazione di quei atomi nella loro minimeità, e l&#039;esser quasi conti­<lb></lb>nuati con l&#039;aria, nella guisa che il vetro ridotto in sottilissima polvere e <lb></lb>quella immersa nell&#039;acqua, si rende transpicua e insensibile ” (Palermo 1644, <lb></lb>pag. </s>

<s>12). E più sotto, per ispiegar come l&#039;acqua apparisca bianca sotto <lb></lb>l&#039;aspetto di neve, così dice: “ La causa della bianchezza della neve è la <lb></lb>massa scontinuata o congregata di moltissime goccioline; l&#039;efficiente la luce <lb></lb>che illumina tutte e ciascheduna gocciola, che li sta nel cospetto; la causa <lb></lb>formale è la specie della luce moltiplicata dalle parti innumerabili e confu­<lb></lb>samente all&#039;occhio rappresentate ” (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>Così, in Italia, nella fisica delle riflessioni, si cercava ingegnosamente <lb></lb>di render la ragione dell&#039;essere e della natura de&#039;corpi diafani e degli opa­<lb></lb>chi, mentre i Cartesiani si pascevano d&#039;immaginazioni, e comprendendo i <lb></lb>Nostri in un&#039;unica speculazione il cielo e la terra, le minime e le grandis­<lb></lb>sime cose, a una causa unica, a quella cioè de&#039;moltiplicati riflessi, riducevasi <lb></lb>il candor della spuma e della neve e il candor della Luna. </s>

<s>Ma se questa <lb></lb>sovente ne&#039;suoi mensili ritorni, alla luce del sole fa specchio e ci illumina <lb></lb>le notti, fa anche talvolta da riparo e ci ottenebra i giorni. </s>

<s>L&#039;ecclissi tro­<lb></lb>varono una facile spiegazione nelle proprietà che hanno i corpi opachi d&#039;im­<lb></lb>pedire il libero passaggio alla luce, e di gettar dietro a sè l&#039;ombre. </s>

<s>Nè fu <lb></lb>difficile intendere come dipendendo esse ombre dalla figura del corpo opaco <lb></lb>e dalle relative distanze di questo al corpo illuminante, se ne poteva trat­<lb></lb>tare applicandovi le regole geometriche. </s>

<s>Ma in progresso dovè accorgersi la <lb></lb>scienza che le tenebre erano anch&#039;esse misteriose quanto forse la stessa <lb></lb>luce, e rimase maravigliata in veder che tanto capricciosamente alle leggi <lb></lb>della Geometria recalcitravano i fatti osservati. </s></p><p type="main">

<s>Benchè fosse però lo studio dell&#039;ombre posteriore allo studio della luce, <lb></lb>e penasse alquanto la scienza ad accorgersi che non troppo bene si corri­<lb></lb>spondevano la Fisica e la Geometria, come dagli Ottici s&#039;era creduto, senza <lb></lb>troppo travagliarsi d&#039;investigare, in tal proposito, il vero; s&#039;ingannò nono­<lb></lb>stante Isacco Vossio quando, uscendo fuori nel 1662 col suo libro <emph type="italics"></emph>De na­<lb></lb>tura lucis et proprietate<emph.end type="italics"></emph.end> si lusingava d&#039;essere stato egli il primo a inse­<lb></lb>gnare la teoria dell&#039;ombre. </s>

<s>“ Sed vero qui sic existimant, graviter errant, <lb></lb>nec satis intelligunt umbrarum rationem. </s>

<s>Nullum quippe corpus est quam­<lb></lb>tumvis magnum, sive etiam quamtumvis exiguum, quod non infinitas spar­<lb></lb>gat umbras. </s>

<s>Verum quidem est ex circumferentia solis progredi radios, qui <lb></lb>umbram faciant desinentem in conum, sed, cum ex omni solis puncto ad <lb></lb>omne punctum ferantur radii, necessarium quoque est ut ab codem extremo <lb></lb>solis ambitu exeant radii ” (Hagae Comitis, pag. </s>

<s>80, 81). D&#039;onde egli con­<lb></lb>clude esser due le parti da considerarsi, una dov&#039;è l&#039;ombra assoluta, l&#039;al­<lb></lb>tra dove <emph type="italics"></emph>est umbra dubia sive umbra cum luce permixta.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Fatta una tal considerazione, che l&#039;Autore ci dà come cosa nuova, così <lb></lb>immediatamente soggiunge: “ Quamvis vero nesciam an alii, qui de luce <pb xlink:href="020/01/581.jpg" pagenum="24"></pb>scripsere, duplicis huius umbrae fecerint mentionem, non ideo tamen minus <lb></lb>vera esse quae scribimus libenter, ut puto fatebitur si quis vel digiti vel <lb></lb>cuiuscumque alius corpusculi umbram ad solem vel lucernam examinave­<lb></lb>rit. </s>

<s>Discrepantes quidem fient umbrae pro ratione intervalli et magnitudine <lb></lb>corporis lucentis et interpositi opaci.... una interior et ubique sibi simi­<lb></lb>lis, altera mixta et paulatim imbecillior ” (ibi, pag. </s>

<s>82). </s></p><p type="main">

<s>Sarà stato forse vero che nel 1662 s&#039;incominciasse in Olanda a notar <lb></lb>la differenza fra l&#039;ombra e la penombra, facendo la filosofica esperienza del <lb></lb>dito suggerita dal Vossio, ma in Italia quell&#039;osservazione è ben assai più <lb></lb>antica, e l&#039;avevan fatta i Pittori, e Leonardo ne aveva dato regola desunta <lb></lb>dalla pratica e dalla Geometria. </s>

<s>Nel 1625 Pietro Accolti dedicò la sua III Parte <lb></lb>della Prospettiva a trattar <emph type="italics"></emph>De&#039;lumi et ombre<emph.end type="italics"></emph.end> e incomincia il Capitolo XII col <lb></lb>notar che “ non solamente le ombre propagandosi fanno mutazione quanto <lb></lb>alle naturali loro intensioni, ma anche, siccome diversamente si contermi­<lb></lb>nano col lume ne&#039;progressi loro, così ancora variamente e diversamente de­<lb></lb>vono rappresentarsi ” (Firenze, pag. </s>

<s>108). Ma perchè intorno al modo del <lb></lb>conterminarsi dell&#039;ombre ne&#039;progressi loro sentiva l&#039;Accolti il bisogno di <lb></lb>spiegarsi co&#039;Pittori, che al loro pratico esercizio attendevano dalla scienza i <lb></lb>precetti; così appresso scrivava in forma di proposizione: </s></p><p type="main">

<s>“ Dico dunque che l&#039;ombre, siccome vanno costipate da&#039;lumi, che suc­<lb></lb>cessivamente le accompagnano fino ne&#039;loro posamenti, ove vanno finalmente <lb></lb>a terminare; così in tal loro concorde progresso quanto più sempre dal corpo <lb></lb>opaco si allontanano, tanto più ancora l&#039;ombra col lume ed il lume con <lb></lb>l&#039;ombra si concilia, e pare che gli estremi loro facciano passaggio dentro i <lb></lb>confini, e termini l&#039;uno dell&#039;altro per qualche poco di spazio, la qual co­<lb></lb>mune loro mistione i Pittori chiamano unione e sfumamento. </s>

<s>Ciò apparisce <lb></lb>in ogni ombra, ma notabilmente in quella, che è fatta derivante dal diurno <lb></lb>luminare del sole. </s>

<s>La causa di tale apparenza ed effetto deriva, non dal­<lb></lb>l&#039;aere ambiente il corpo luminoso, come alcuni credono, ma onninamente <lb></lb>dalla ampiezza diametrale di esso corpo luminoso, qualunque egli si sia, il <lb></lb>che meglio apparirà dalla seguente figura ” (ivi). E passa di qui l&#039;Accolti <lb></lb>a dare alla sua proposizione evidenza di prova geometrica, la quale noi lta­<lb></lb>liani avemmo dall&#039;altra parte, un secolo prima che scrivesse il Vossio il suo <lb></lb>libro, ne&#039;Fotismi del Maurolico. </s>

<s>Il teorema XVIII infatti del nostro Siciliano <lb></lb>è così formulato: “ Quo maius fuerit lucidum, quoque magis illuminatum <lb></lb>a plano in quod umbra proiicitur, distiterit, eo maiores atque intensiores <lb></lb>umbrae termini videntur ” (Neapoli 1611, pag. </s>

<s>13). </s></p><p type="main">

<s>Supposto che sia AB (fig. </s>

<s>9) il lucido, e CD l&#039;illuminato, condotte le <lb></lb>linee AK, BL e AF, BE, prosegue l&#039;Autore la sua dimostrazione, che egli <lb></lb>poi conclude nel corollario seguente: “ Aut igitur umbra est spatium in <lb></lb>quod nullum lucidi signum radiat aut id spatium, in quo nullum signum <lb></lb>est, quod ab unoquoque lucidi signo illuminatur. </s>

<s>Secundum ergo primam <lb></lb>differentiam ipsius CD umbra est spatium KL: secundum vero reliquam <lb></lb>ipsius CD umbra est totum EF spatium. </s>

<s>Nam spatium KL, a nullo lucidi <pb xlink:href="020/01/582.jpg" pagenum="25"></pb>AB signo illuminatur. </s>

<s>Spatium vero EF nullum habet punctum quod ab <lb></lb>unoquoque lucidi AB puncto illuminetur ” (ibi, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Che il libro del nostro Maurolico fosse ignorato dal Vossio è un fatto <lb></lb><figure id="id.020.01.582.1.jpg" xlink:href="020/01/582/1.jpg"></figure></s></p><p type="caption">

<s>Figura 9.<lb></lb>notabile sì, perch&#039;ebbe da quel celebre Au­<lb></lb>tore i primi ed efficaci impulsi a risorgere <lb></lb>l&#039;Ottica matematica in Europa, ma è ben <lb></lb>più notabile che l&#039;Olandese ignorasse i <emph type="italics"></emph>Pa­<lb></lb>ralipomeni<emph.end type="italics"></emph.end> di quel Keplero, che egli, in <lb></lb>proposito dell&#039;ombre negli ecclissi, prende <lb></lb>occasione di confutare. </s>

<s>Nel 1666 arricchiva <lb></lb>lo stesso Vossio la letteratura scientifica con <lb></lb>un altro libro intitolato <emph type="italics"></emph>De Nili origine,<emph.end type="italics"></emph.end> in <lb></lb>appendice al quale torna a trattare della <lb></lb>penombra negli ecclissi di Luna, e al tro­<lb></lb>varsi immersa in essa penombra attribui­<lb></lb>sce, contro l&#039;opinion del Keplero, i rossori, <lb></lb>che rendon fra le tenebre parvente la stessa <lb></lb>Luna ecclissata. </s>

<s>“ Intempestiva est enim ratio Kepleri, eorumque qui illum <lb></lb>secuti sunt, qui putant ruborem seu dilutiorem umbram quae in Lunae ap­<lb></lb>paret deliquiis, effici a radiis in hoc nostro aere refractis. </s>

<s>Fieri enim mi­<lb></lb>nime posse ut illi Solis radii hunc nostrum aerem ingrediantur, et vicissim <lb></lb>exeant.... Cum enim omnis refractio fiat a rariori ad densius, et aer ter­<lb></lb>ris vicinus densior sit illo superiore, necesse est ut quotquot radii aerem <lb></lb>ingrediuntur, in terram impingentes deficiant ” (Hagae Comitis, pag. </s>

<s>143). </s></p><p type="main">

<s>Intorno a ciò aveva senza dubbio ragione il Vossio, come si notava da <lb></lb>noi di sopra a proposito della teoria neutoniana dell&#039;etere esalato dalle su­<lb></lb>perficie riflettenti, il qual etere, se diminuisse in densità, come diminuisce <lb></lb>l&#039;aria intorno alla Terra, un raggio di luce che vi s&#039;immergesse non po­<lb></lb>trebbe risaltare al di fuori. </s>

<s>Non aveva però ragione di tornar colla sua <emph type="italics"></emph>Ap­<lb></lb>pendice<emph.end type="italics"></emph.end> a dubitar che prima di lui nessuno avesse atteso alla penombra, la <lb></lb>quale negli ecclissi accompagna l&#039;ombra proiettata dalla Terra: vi aveva at­<lb></lb>teso sessantadue anni prima quel Keplero, censurato dal Vossio, il qual Vos­<lb></lb>sio, entrando a trattare di un tal soggetto avrebbe dovuto leggere nel ca­<lb></lb>pitolo VI il § 7 che s&#039;intitola <emph type="italics"></emph>De penumbra Terrae.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Comunque sia, non si può negar che l&#039;Ottico olandese non fosse de&#039;primi <lb></lb>a risolvere alcuni capitali problemi dell&#039;ombre negli ecclissi. </s>

<s>Se non che <lb></lb>troppo si confidava che le sue linee condotte sulla carta a prefinire i limiti <lb></lb>della luce assoluta e della luce incerta, dietro i corpi opachi illuminati, aves­<lb></lb>sero a rispondere puntualmente ai fatti. </s>

<s>Egli desiderava che gli Astronomi <lb></lb>“ accuratius annotassent terminos tam interioris quam exterioris umbrae, <lb></lb>nam sane si haec differentia nota esset, utique etiam notum fieret interval­<lb></lb>lum Solis, nec quaeremus utrum Sol 700 an vero 15000 terrae semidiame­<lb></lb>tris a nobis absit ” (ibi, pag. </s>

<s>144). </s></p><p type="main">

<s>Il desiderio del Vossio, generoso certamente in sè, avrebbe per quelle <pb xlink:href="020/01/583.jpg" pagenum="26"></pb>vie potuto condurre gli Astronomi all&#039;intento, quando fosse stato facile no­<lb></lb>tare i termini tanto interiori quanto esteriori dell&#039;ombra. </s>

<s>Ma non s&#039;era an­<lb></lb>cora incontrata la scienza a doversi arretrare incerta innanzi a nessuno di <lb></lb>que&#039;misteri, che dicemmo le tenebre presentare allo studio de&#039;Filosofi; mi­<lb></lb>steri non meno impenetrabili forse di quelli della luce. </s>

<s>Come e quando oc­<lb></lb>corresse il primo, e perchè inaspettato, rumoroso fatto di que&#039;misteri pre­<lb></lb>sentati dall&#039;ombre, sarà non ignobile parte del seguente paragrafo di storia. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il celebre Filosofo francese Pietro Gassendi, facendo alcune esperienze <lb></lb>intorno all&#039;ombre proiettate da una palla opaca esposta al sole, e tornando <lb></lb>a osservare a varie ore del giorno, credè di aver trovato, con sua gran ma­<lb></lb>raviglia che, in sul mattino e in sul tramonto, quelle ombre riuscissero più <lb></lb>larghe e più lunghe, che quando il sole era presso al meridiano. </s>

<s>Frugato <lb></lb>dalla novità della cosa, ripetè, con più diligenza che mai, quelle esperienze e <lb></lb>confermatosi le novità osservate esser vere, divulgò la notizia del fatto, che <lb></lb>levò gran rumore specialmente in Italia. </s>

<s>Il Gassendi però, come dava per <lb></lb>certo quel fatto, così confessava di esser dubbioso delle ragioni, laonde Fi­<lb></lb>losofi e dilettanti, discepoli e amici si rivolgevano a Galileo che, nella pro­<lb></lb>fondità della sua scienza, ripescasse la chiave di quel mistero. </s>

<s>Fra&#039;Filosofi <lb></lb>e i discepoli s&#039;annovera il Cavalieri, e fra&#039;dilettanti e gli amici Girolamo <lb></lb>Bardi, le lettere de&#039;quali son rimaste fra&#039;manoscritti galileiani. </s></p><p type="main">

<s>“ Discorressimo lungamente (dice il Cavalieri in una lettera scritta da <lb></lb>Bologna il dì 8 Giugno 1638) sopra una osservazione fatta da un Francese <lb></lb>amico suo (di Fortunio Liceti), circa le ombre del sole poste in due siti, <lb></lb>cioè alto sopra l&#039;orizzonte e basso intorno al detto orizzonte, al quale, se si <lb></lb>supponerà un corpo ombroso, come per esempio una palia che mandi la sua <lb></lb>ombra in un piano, dal quale ella sia ugualmente lontana nel sito basso e <lb></lb>alto del sole; dice che l&#039;ombra causata dal sole vicino all&#039;orizzonte è mag­<lb></lb>giore dell&#039;ombra cagionata da esso nel sito alto, cioè che osserva che la <lb></lb>lunghezza delle ombre fatte dal sole nato di poco, e che poco dopo tra­<lb></lb>monta, nel qual sito appare maggiore per vapori ecc. </s>

<s>sono maggiori della <lb></lb>lunghezza delle ombre causate dal sole nel sito alto, stante l&#039;istesso corpo <lb></lb>ombroso e l&#039;istessa distanza dal piano, nel quale la sbatte; cosa che par <lb></lb>che debba essere al contrario, poichè, facendosi il sole apparentemente mag­<lb></lb>giore, pare che venga a tosare l&#039;ombra attorno attorno che sarìa fatta da <lb></lb>esso apparentemente minore, e che perciò quella dovrà essere minore nel <lb></lb>sito più basso. </s>

<s>Ho bene considerato che se non si parla dell&#039;ombra totale, <lb></lb>ma dell&#039;ombra con la chioma, dirò, o con quella parte, che credo i pittori <lb></lb>chiamino <emph type="italics"></emph>sbattimento,<emph.end type="italics"></emph.end> nella quale si va digradando continuamente dall&#039;om­<lb></lb>bra totale della luce totale: che l&#039;aggregato dell&#039;ombra totale e della chioma <pb xlink:href="020/01/584.jpg" pagenum="27"></pb>fatta dal sole basso cioè maggiore in apparenza, deva esser maggiore del­<lb></lb>l&#039;aggregato dell&#039;ombra totale e della chioma fatta dal sole alto, cioè minore, <lb></lb>come anco V. S. Ecc.ma facilmente intenderà esser vero, ma che la sola om­<lb></lb>bra totale del sole maggiore deva esser maggiore dell&#039;ombra del sole mi­<lb></lb>nore, il che afferma ancora della Luna alta e bassa, credo che ciò sia im­<lb></lb>possibile, s&#039;io non m&#039;inganno. </s>

<s>Tuttavia mi rimetto alla sottigliezza sua, che <lb></lb>subito intenderà qual sia la verità in questo fatto. </s>

<s>” </s></p><p type="main">

<s>“ Ho voluto formare un poco d&#039;esperienza con una riga parallela ad <lb></lb>una tavoletta, nella quale ricevendo l&#039;ombra dal sole nel mezzodì e vicino <lb></lb>al tramontare non ci ho conosciuto differenza di ombra. </s>

<s>Vero è che la riga, <lb></lb>che è lunga poco più d&#039;un palmo e mezzo, e lontana solo un palmo dalla <lb></lb>tavoletta, non faceva forse distinguere bene essa ombra, onde la voglio <lb></lb>fare con metterla assai lontana dalla tavoletta, per vedere pure se può es­<lb></lb>sere questo che dice avere osservato detto Francese ” (MSS. Gal., P. VI, <lb></lb>T. XIII, c. </s>

<s>100). </s></p><p type="main">

<s>Quasi un anno dopo, non sapendosi altro dell&#039;esperienza che aveva in <lb></lb>animo di ripetere il Cavalieri, la curiosità seguitava a frugare gl&#039;ingegni, e <lb></lb>Girolamo Bardi, così, nel di 24 Agosto 1639, scriveva a Galileo, sperando <lb></lb>d&#039;esserne sodisfatto. </s>

<s>“ Vien proposto dal signor Gassendi un problema che <lb></lb>l&#039;ombra da un corpo opaco resta maggiore dal sole orizzontale che dal me­<lb></lb>desimo verticale. </s>

<s>Vorrei che V. S. me ne desse la cagione, perchè la lon­<lb></lb>tananza del semidiametro dovrà di ragione fare insensibile mutazione ed egli <lb></lb>apparisce essere grandissima ” (ivi, c. </s>

<s>161). </s></p><p type="main">

<s>Qual risposta però avessero il Cavalieri e il Bardi alle loro desiderose <lb></lb>richieste, noi non siamo in grado di dirlo ai nostri lettori, non essendoci <lb></lb>note le responsive, le quali forse non furono scritte, o se furono scritte par <lb></lb>che del problema gassendistico Galileo confessasse di non saper che se ne <lb></lb>dire. </s>

<s>Così per noi s&#039;argomenta da quel che leggesi nella <emph type="italics"></emph>Lettera sul Can­<lb></lb>dore lunare,<emph.end type="italics"></emph.end> verso la fine, in risposta a Fortunio Liceti, il quale, amico al <lb></lb>Gassendi, fu da questi, per mezzo del Naudeo, richiesto della spiegazione <lb></lb>del fatto dell&#039;ombre, non saputa trovar da sè tale, che se ne potesse sodi­<lb></lb>sfare un filosofo. </s>

<s>Il Liceti però, il quale apparteneva a quella sètta di Fi­<lb></lb>losofi, che sanno con gran facilità trovar nel loro cervello una ragion cal­<lb></lb>zante a qualunque fatto più strano, ebbe anche una risposta pronta da dare <lb></lb>al Gassendi, e gliela fece in una lettera, a cui il Gassendi stesso rispose con <lb></lb>un&#039;altra <emph type="italics"></emph>lunghissima lettera di sedici fogli interi<emph.end type="italics"></emph.end> (Alb. </s>

<s>VII, 346). E per­<lb></lb>chè tanto il Peripatetico si compiaceva d&#039;essersi fatto maestro all&#039;inclito <lb></lb>Gassendi, dette solennità alla risposta fatta al problema dell&#039;ombre nel fa­<lb></lb>moso capitolo L del <emph type="italics"></emph>Liteosforo.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sed et partes aetheris (egli ivi scrisse) contermini solaribus affectae <lb></lb>radiis in lunare corpus opacum et obscurum natura sua repercutere pos­<lb></lb>sunt exiguum lumen quod et in deliquiis et prope coniunctiones languere <lb></lb>conspicitur, ac utcumque minuere nativam lunaris corporis obscuritatem. </s>

<s><lb></lb>Quemadmodum et apud nos aer umbrae conterminus radiis solaribus in me-<pb xlink:href="020/01/585.jpg" pagenum="28"></pb>ridie laterales umbrae partes abrodit, in eas vividiori lumine repercusso, <lb></lb>proindeque reddit umbram angustioris latitudinis, quod efficere non potest <lb></lb>aer matutinus, nec vespertinus, mitioribus radiis, imbecilliorique solis tum <lb></lb>orientis, tum occidentis lumine perfusus, ut non ita pridem scripsimus ad <lb></lb>Cl. </s>

<s>Naudaeum, qui nos inclyti Gassendi nomine rogavit causam, ob quam <lb></lb>opaci corporis umbra latior appareat sole prope finitorem humili, strictior <lb></lb>e contra editiore sole procul ab horizonte verticalem regionem perambu­<lb></lb>lante, cuius rei certas observationes, ac indubitata prorsus experimenta se <lb></lb>dicit habere Cl. </s>

<s>Mathematicus: verum hac de re late perscripsimus ad exi­<lb></lb>mium virum ” (Alb. </s>

<s>III, 188). </s></p><p type="main">

<s>Di questa soluzione, data dal Liceti al problema delle ombre, scriveva <lb></lb>così Galileo nella sopra citata Lettera sul Candore lunare: “ Circa a quello <lb></lb>che in ultimo soggiugne del farsi l&#039;ombre maggiori dal sole basso che dal­<lb></lb>l&#039;alto, non ho che dirci altro, se non che mi pare, che egli altra volta ne­<lb></lb>gasse cotal effetto ” (ivi, pag. </s>

<s>236), d&#039;onde s&#039;argomentava da noi di sopra <lb></lb>che Galileo si fosse astenuto dal dir la sua opinione al Cavalieri e al Bardi, <lb></lb>e a parecchi altri forse che se ne mostravano desiderosi. </s></p><p type="main">

<s>Le speculazioni del Cavalieri, le quali per verità si posson tener nello <lb></lb>stesso pregio di quelle del Liceti, attribuendo il grand&#039;uomo un effetto reale <lb></lb>al variare il diametro del sole, secondo le altezze sue varie sull&#039;orizzonte, <lb></lb>ciò che non è realtà, ma un inganno dell&#039;occhio; non che il tacersi di Ga­<lb></lb>lileo parrebbero una confessione delle difficoltà che incontravansi nel risol­<lb></lb>vere il problema venuto di Francia, la qual confessione toglievasi forse, come <lb></lb>peso importuno dalla coscienza, col negare, secondo accennava lo stesso Ca­<lb></lb>valieri, la verità del fatto osservato dal Gassendi. </s>

<s>Da ciò forse provenne che, <lb></lb>quietato quel subitaneo rumore, non se ne parlò più per quasi un secolo, <lb></lb>infintantochè non si sentì il bisogno di ricorrere allo studio più diligente <lb></lb>dell&#039;ombre fatte dai nostri piccoli oggetti, per interpetrare i misteri dell&#039;om­<lb></lb>bre proiettate negli spazii celesti. </s></p><p type="main">

<s>Quel misterioso apparir tuttavia rubiconda la Luna, anche immersa nel­<lb></lb>l&#039;ombra della Terra, avea tenuto e tuttavia teneva in gran travaglio l&#039;in­<lb></lb>gegno degli Astronomi, fra&#039;quali, prima del risorgere della scienza per la <lb></lb>fortunata invenzione del Canocchiale, è notabile, quel che così ne speculava <lb></lb>in proposito il Benedetti: </s></p><p type="main">

<s>“ Quod vero Luna nullum ex se habeat lumen, sufficiens inditium est <lb></lb>nos ipsam tanto magis obscuram videre, quanto magis in cono umbrae Ter­<lb></lb>rae immergitur, et si eo tempore ipsam videmus rubeo colore affectam, hoc <lb></lb>enim accidit quia radii solares undequaque refranguntur a vaporibus ipsam <lb></lb>terram circumdantibus, quae quidem refractio fit versus axem coni umbrae <lb></lb>Terrae, et propterea umbra dicti coni non est aequaliter obscura sed tene­<lb></lb>brosa. </s>

<s>Circa vero axem ipsius coni magis quam circa eius circumferentiam <lb></lb>obscuratur, et quia corpus lunare tale est ut facillime recipiat qualecumque <lb></lb>lumen, quod etiam manifeste videtur dum ipsa Luna reperitur secundum <lb></lb>longitudinem inter solem et Venerem, quod pars Lunae lumine solis desti-<pb xlink:href="020/01/586.jpg" pagenum="29"></pb>tuta, a lumine Veneris aliquantulum illustratur, quod ego saepe vidi et mul­<lb></lb>tis ostendi; propterea dum ipsa Luna in cono umbrae Terrae reperitur adhuc <lb></lb>videtur ” (Liber speculationum, Venetiis 1599, pag. </s>

<s>257). </s></p><p type="main">

<s>Ebbero, da queste speculazioni del celebre Veneziano, origine e l&#039;ipo­<lb></lb>tesi delle rifrazioni professata dal Keplero e quella della fosforescenza in­<lb></lb>nata nella Luna, a somiglianza della Pietra bolognese immaginata dal Liceti, <lb></lb>e le altre seguite da varii della illuminazion partecipata da Venere e riflessa <lb></lb>a noi dal disco lunare, non che quella dell&#039;etere ambiente professata da Ga­<lb></lb>lileo (Alb. </s>

<s>VII, 276). E benchè si mantenga in onore appresso i più degli <lb></lb>Astronomi l&#039;ipotesi kepleriana, furono tutte le altre dimostrate apertamente <lb></lb>false: anzi la stessa ipotesi del Keplero fu come vedemmo contraddetta, non <lb></lb>forse senza ragione, dal Vossio, il quale non alle rifrazioni attribuiva il fe­<lb></lb>nomeno, ma sì all&#039;esser la Luna immersa nella penombra della Terra. </s></p><p type="main">

<s>Anche questa ipotesi però, che sembra esser più naturale e accettabile <lb></lb>delle altre, fu trovata andare incontro a gravissime difficoltà. </s>

<s>L&#039;ombra as­<lb></lb>soluta della Terra dovrebbe, secondo i calcoli, distendersi per 110 de&#039;suoi <lb></lb>diametri, e perchè la Luna non ne è distante che 60 semidiametri in circa, <lb></lb>dovrebbe negli ecclissi trovarsi immersa o totalmente o parzialmente nel­<lb></lb>l&#039;ombra, e perciò o disparire del tutto, o mostrarsi falcata, fenomeno che <lb></lb>nessuno ha mai osservato. </s>

<s>Di qui se n&#039;ebbe a concludere non potersi il <lb></lb>trasparir fra le tenebre la Luna attribuirsi all&#039;essere immersa nella pe­<lb></lb>nombra. </s></p><p type="main">

<s>Il Maraldi però saviamente considerando che la Natura opera spesso al­<lb></lb>trimenti da quel che le vorrebbero prescrivere i nostri calcoli artificiosi, <lb></lb>pensò di ricorrere alla esperienza, e fu a questa occasione che tornò in <lb></lb>campo il problema del Gassendi. </s>

<s>Il valoroso nepote di Gian Domenico Cas­<lb></lb>sini (e di ciò lasciò Memoria negli Atti della R. </s>

<s>Accademia parigina del 1721) <lb></lb>trovò esser vero che le ombre proiettate da una sfera opaca o da un cilin­<lb></lb>dro son più lunghe, quando in sul mattino il sole o in sul tramonto è <lb></lb>alquanto men luminoso. </s>

<s>Trovò altresì che una sfera, la quale avrebbe do­<lb></lb>vuto gittar secondo il calcolo l&#039;ombra a 110 de&#039;suoi diametri, non raggiun­<lb></lb>geva appena i 41. Il Maraldi sperimentò in questa occasione altri fatti sul­<lb></lb>l&#039;ombre, con intenzione di illustrar l&#039;Astronomia delle ecclissi, tenendo anche <lb></lb>conto delle diffrazioni, essendo che il sole può rassomigliarsi al foro e la <lb></lb>Terra al capello o altro corpicciolo attraversato al raggio lucido nel celebre <lb></lb>esperimento grimaldiano. </s>

<s>Ma con tuttociò le ombre osservate nelle sue pic­<lb></lb>cole sfere dal Gassendi, e quelle osservate dagli astronomi nelle grandissime <lb></lb>sfere celesti, rimasero tuttavia se non ombre, certamente penombre nelle <lb></lb>menti de&#039;Filosofi. </s></p><p type="main">

<s>Dietro questi fatti la storia c&#039;insegna che i Filosofi hanno bene spesso <lb></lb>trovate difficoltà dove meno se l&#039;aspettavano. </s>

<s>Ma come si sarebbe aspettato <lb></lb>Aristotile di dovere arrestarsi dubitoso innanzi a un forellino, per cui passa <lb></lb>un raggio di sole? </s>

<s>Eppure è così: nella Sezione XV de&#039;Problemi la Que­<lb></lb>stione V è dal Filosofo posta in tal forma: “ Cur sol per quadrilatera pro-<pb xlink:href="020/01/587.jpg" pagenum="30"></pb>fluens non rectis lineis figuram decribit, sed circulum format, ut in crati­<lb></lb>bus patet? </s>

<s>” e la risposta che dà il gran Maestro di coloro che sanno, si <lb></lb>riduce a dire: “ An quod aspectuum procidentia turbine agitur, turbinis au­<lb></lb>tem basis in orbem se colligit, quamobrem quocumque radii Solis incurre­<lb></lb>rint nimirum circulares appareant? </s>

<s>An quod Solis quoque figuram rectis <lb></lb>lineis contineri necesse est, siquidem radii recti proveniunt? </s>

<s>” (Aristotelis. </s>

<s><lb></lb>Colliget, Venetiis 1610, T. IX, c. </s>

<s>298). </s></p><p type="main">

<s>Quel solenne maestro d&#039;Ottica, Vitellione che ebbe tanta autorità di <lb></lb>magistero nel mondo, quanta forse ne potè avere lo stesso Aristotile, per <lb></lb>provar la proposizione XXXIX del libro II <emph type="italics"></emph>Omne lumen per foramina an­<lb></lb>gularia incidens rotundatur<emph.end type="italics"></emph.end> (Perspectiva, edit. </s>

<s>cit., c. </s>

<s>47) introduce il prin­<lb></lb>cipio che i raggi quanto più si dilungano dal luminoso e tanto più si avvi­<lb></lb>cinano alla equidistanza (propos. </s>

<s>XXXV, c. </s>

<s>46) ond&#039;è che il lume cadendo <lb></lb>sulla superficie del foro s&#039;incomincia a rotondare. </s></p><p type="main">

<s>Ma il Cantuariense ne&#039;<emph type="italics"></emph>Tre Libri della Perspettiva<emph.end type="italics"></emph.end> tradotti dal Gallucci <lb></lb>fa almeno intendere qual sia la sua spiegazione, la quale si fonda principal­<lb></lb>mente sopra un&#039;ipotesi metafisica, ed è che gli atomi della luce dovendo <lb></lb>essere di natura perfettissima non possono essere altrimenti configurati che <lb></lb>in sfera. </s>

<s>“ Ora perchè la figura sferica è vicina alla luce ed accomodata a <lb></lb>tutti i corpi del mondo, come perfettissima e molto conservativa della na­<lb></lb>tura, e che congiunge tutte le parti compitissimamente nel suo intimo; la <lb></lb>luce dunque si muove naturalmente a questi, ed acquista quella alla di­<lb></lb>stanza terminata. </s>

<s>Si vede dunque manifestamente da queste due cause che <lb></lb>il lume che passa per un forame si fa rotondo a poco a poco ” (Vene­<lb></lb>zia 1593, c. </s>

<s>3, B). </s></p><p type="main">

<s>Contro così fatti errori del principe de&#039;Filosofi, e di coloro che gli fanno <lb></lb>intorno corona, insorgeva il Keplero a dimostrar che il fatto era a tutt&#039;al­<lb></lb>tro da attribuirsi che alla rotondità de&#039;raggi o alla perfetta figura sferica <lb></lb>degli atomi luminosi. </s>

<s>” Patuit itaque concurrere ad problema demonstran­<lb></lb>dum non radii visorii, sed ipsius solis, non quia haec perfectissima sit figura, <lb></lb>sed quia haec lucentis corporis figura sit in genere ” (Paralip. </s>

<s>ad Vitell, <lb></lb>Francofurti 1604, pag. </s>

<s>39). E la proposizione III di questo stesso cap. </s>

<s>II, <lb></lb>ordinata dall&#039;Autore a dimostrar la ragione che ha la figura dello spettro alla <lb></lb>figura del foro aperto nell&#039;imposta chiusa di una finestra, va seguita da que­<lb></lb>sto corollario: “ Sequitur hinc per singulas fenestrae alicuius puncta quo­<lb></lb>rum infinita sunt singulas adeoque infinitas transmitti in superficiem illu­<lb></lb>stratam imagines lucentis inversas, eodem ordine se mutuo consequentes, <lb></lb>quem tenent ipsa puncta fenestrae ” (ibi, pag. </s>

<s>44). </s></p><p type="main">

<s>Ma, prima che il Keplero sarebbe stato bello contrapporre al principe <lb></lb>de&#039;Filosofi e a&#039;veneratori di lui un uomo tutto alieno dal far professione <lb></lb>di Filosofia, e che seppe imparar da sè quel che, dopo faticosi studii, non <lb></lb>avevan saputo insegnare i Maestri. </s>

<s>Leonardo da Vinci, nella sua Ottica di­<lb></lb>spersa per le note manoscritte, non lasciò indietro di risolvere il problema <lb></lb>proposto da Aristotile nella sopra citata sezione, e sicuro di sè, e non come <pb xlink:href="020/01/588.jpg" pagenum="31"></pb>Aristotile stesso, dubbioso, frettolosamente scriveva: “ Nessuno spiracolo <lb></lb>può trasmutare il concorso de&#039;razzi luminosi in modo che per la lunga di­<lb></lb>stanzia non porghino all&#039;obietto la similitudine della sua cagione. </s>

<s>— Impos­<lb></lb>sibile è che i razzi luminosi passati per parallelo, dimostrino nell&#039;obbietto <lb></lb>la forma della loro cagione, poichè tutti gli effetti de&#039;corpi luminosi sono <lb></lb>dimostrativi delle loro cagioni. </s>

<s>La Luna di forma naviculare passata dallo <lb></lb>spiracolo figurerà nell&#039;obietto un corpo naviculare ” (Ravaisson-Mollien, Ma­<lb></lb>nus. </s>

<s>de Leonard. </s>

<s>A fol. </s>

<s>64, v.). </s></p><p type="main">

<s>Il concetto di Leonardo è in bel modo illustrato dall&#039;Accolti, il quale, <lb></lb>imbevuto dell&#039;Ottica kepleriana, proponendosi di risolvere il problema dello <lb></lb>spettro rotondo attraverso allo spiraglio di tutt&#039;altra figura “ stimo, egli <lb></lb>scrive, la intrinseca causa di tale effetto essere la circolarità dell&#039;istesso corpo <lb></lb>sferico luminoso del sole, e congiuntamente la distanza dell&#039;opposto piano <lb></lb>del foro, per il quale fanno passaggio sì bene tutti i raggi enascenti da cia­<lb></lb>scun punto del corpo solare, ma non già tutti unitamente, e senza disgre­<lb></lb>garsi, in detto illuminato piano pervengano ” (Prospett. </s>

<s>prat. </s>

<s>cit., pag. </s>

<s>113). </s></p><p type="main">

<s>L&#039;asserto, che contien concetti sottili quanto la luce, si studia l&#039;Autore <lb></lb>di render chiaro per la seguente dottrina: “ Sia per esempio il sferico corpo <lb></lb>luminoso del sole, di cui tanta parte di azione illuminante faccia passaggio <lb></lb>ad illustrare il piano sottopostoli, quanta capisce un dato aperto e quadrato <lb></lb>foro. </s>

<s>E perchè da ciascun punto di esso luminoso si spicca piramidalmente <lb></lb>la suddetta sferale azione del lume, ne seguirà che quanti punti si pigliano <lb></lb>a considerare in detto sferico, tante ancora in numero eguali, punte pira­<lb></lb>midali si costituischino; adunque altrettante loro basi di splendore simili <lb></lb>tutte di figura al foro, dal quale passando sono formate, ma in tanto diverse <lb></lb>fra loro di sito, quanto da diversi punti del corpo sferico.... sono dette <lb></lb>basi qua e là costituite. </s>

<s>Onde, perchè da ciascun punto del luminoso corpo <lb></lb>si fa passaggio per il dato qual si sia foro, e per ciascuna parte di esso, <lb></lb>molto bene intendiamo non solo il termine e confino di ciascuno splendore <lb></lb>dover esser causato sul piano del termine e confino del corpo luminoso.... <lb></lb>ma che la suddetta figura di splendore sul detto piano esistente, sarà com­<lb></lb>posta e resterà dintornata da tante multiplici base quadrate, in giro dispo­<lb></lb>ste, da quanti punti dell&#039;estremità circolare del raggiante corpo luminoso <lb></lb>del sole possono formarsi, i quali, perchè sono infiniti, così da infinite basi <lb></lb>resterà composta l&#039;apparenza dello splendore suddetto. </s>

<s>Adunque se il con­<lb></lb>fino o dintorno del luminoso sia circolare, com&#039;è quello del sole, così cir­<lb></lb>colarmente ed in giro si andranno buttando sul piano e disponendo dette <lb></lb>infinite basi e giuntamente con loro quella infinita multiplicità de&#039;respettivi <lb></lb>angoli di ciascheduna base, li quali unicamente lasciano dintornata sul piano <lb></lb>la figura d&#039;illuminazione, come parti più remote e le più estreme che pos­<lb></lb>sono considerarsi ne&#039;dintorni delle suddette basi piramidali. </s>

<s>Onde per sè <lb></lb>stessa si rende molto ben nota all&#039;intelligenza la cagione, per la quale cia­<lb></lb>scuna apparente illuminazione passante per foro di qualsivoglia figura, sem­<lb></lb>pre circoleggi ” (ivi, pag. </s>

<s>113, 14) </s></p><pb xlink:href="020/01/589.jpg" pagenum="32"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;Ottica non è una di quelle scienze che finisca in sè stessa, non si <lb></lb>limita cioè a studiare le proprietà della luce in quegli effetti, che più d&#039;ap­<lb></lb>presso operano sui nostri sensi, ma essendo ella quasi lo spirito animatore <lb></lb>dell&#039;Universo invita a investigarne i misteri, nel lontano e splendido cielo, <lb></lb>l&#039;affetto e l&#039;intelligenza dell&#039;uomo. </s>

<s>Le ombre osservate nelle sfere di legno <lb></lb>o di altra materia opaca fecero intender meglio con qual legge, diversa da <lb></lb>quella prescritta da&#039;calcoli, si proiettino le ombre dalla Terra, dalla Luna <lb></lb>e dagli altri pianeti. </s>

<s>Le osservazioni attente e le argute speculazioni intorno <lb></lb>ai raggi di sole passati attraverso un piccolo foro, che avevan aria di mera <lb></lb>filosofica curiosità, s&#039;accomodarono anch&#039;esse, testimone il Keplero, a più <lb></lb>nobile astronomico uso. </s>

<s>“ Caeterum et Aristotiles et is quem dixi Pisanus <lb></lb>ad emendationem argumenti pulcherrimum experimentum afferens de Solis <lb></lb>deficientis radio similiter deficiente, cum is per angustum foramen recipi­<lb></lb>tur, occasionem Reinholdo, Gemmae et Maestlino praeceptori meo submi­<lb></lb>nistravit accomodandi theorema ad usum non minus nobilem ” (Paralip. </s>

<s><lb></lb>cit., pag. </s>

<s>39). </s></p><p type="main">

<s>Di nessuna proprietà però speculata intorno alla luce si fece più no­<lb></lb>bile applicazione all&#039;Astronomia, di quella che concerne la legge dell&#039;intensità <lb></lb>del suo splendore. </s>

<s>Per essa legge, come vedremo, ebbe principio l&#039;Astro­<lb></lb>nomia matematica, e s&#039;intesero per essa le altre leggi, che governano i moti <lb></lb>dell&#039;Universo. </s>

<s>Per quali vie tortuose e lunghe si giungesse a dimostrare il <lb></lb>modo come si diffonde la luce, e come e quando la scienza ottica, dubbiosa <lb></lb>e diffidente, s&#039;acquietasse all&#039;ultimo in quelle verità, che per la Geometria <lb></lb>e per l&#039;esperienza s&#039;erano da lungo tempo già dimostrate, è ciò che noi <lb></lb>passiamo ora a narrare. </s></p><p type="main">

<s>Primo fra gli Autori d&#039;Ottica più conosciuti a speculare intorno all&#039;in­<lb></lb>tensità della luce fu il Maurolico, il quale dimostra ne&#039;suoi Fotismi i due <lb></lb>Teoremi seguenti: <emph type="italics"></emph>“ Theorema II.<emph.end type="italics"></emph.end> Aequaliter inclinati radii, aequaliter, ere­<lb></lb>ctiores autem magis, perpendiculares vero maxime illuminant ” (Neapoli 1611, <lb></lb>pag. </s>

<s>2). <emph type="italics"></emph>“ Theorema III.<emph.end type="italics"></emph.end> Aeque remota signa aequaliter; propriora vero <lb></lb>magis illuminant ” (ibi, pag. </s>

<s>3). </s></p><p type="main">

<s>I due Teoremi fotometrici limitati così a ciò che ne porgeva di più <lb></lb>certo ogni ovvia esperienza, son con facilità dimostrati, essendo evidente­<lb></lb>mente veri, ma provandosi poi il Maurolico ad allargarsi nel periglioso <lb></lb>mare inesplorato, smarrisce assai presto la diritta via, come si par dal pros­<lb></lb>simo V Teorema: “ Possibile est signa ad inaequales distantias, spacium ali­<lb></lb>quod aequaliter illustrare ” (ibi, pag. </s>

<s>4). </s></p><p type="main">

<s>Nel circolo ABD (fig. </s>

<s>10) suppone che A e B sieno due lucenti (signa) <lb></lb>che illuminino l&#039;oggetto CD: crede che, sebbene i due segni sieno diver­<lb></lb>samente lontani, possan nulladimeno illuminar con intensità uguale l&#039;oggetto. <pb xlink:href="020/01/590.jpg" pagenum="33"></pb>Crede egli così, perchè gli angoli CAD, CBD essendo uguali, comprendono <lb></lb>quantità uguale di raggi luminosi, e avendo supposto <emph type="italics"></emph>plures radios inten­<lb></lb><figure id="id.020.01.590.1.jpg" xlink:href="020/01/590/1.jpg"></figure></s></p><p type="caption">

<s>Figura 10.<lb></lb>sius, aequales vero aequaliter illuminare<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>1) <lb></lb>ne conclude perciò che debba esser l&#039;oggetto illumi­<lb></lb>nato da ugual quantità di luce o sia vicino il lucido <lb></lb>o sia piuù lontano. </s></p><p type="main">

<s>Il paralogismo era atto a sedurre qualunque più <lb></lb>acuto ingegno, e anche Galileo, come fra poco ve­<lb></lb>dremo, ne fu sedotto. </s>

<s>La radice occulta poi dell&#039;er­<lb></lb>ror seducente stava in ciò che si considerava la luce <lb></lb>diffondersi non per la solidità sferica ma per la su­<lb></lb>perficialità circolare. </s>

<s>Questo errore nel Maurolico <lb></lb>non apparisce espresso, ma il Keplero che rifuggiva <lb></lb>dall&#039;ammetter la diffusione sferica della luce, perchè essendo la trina dimen­<lb></lb>sione propria de&#039;solidi non faceva possibile intendere come potesse la stessa <lb></lb>luce penetrare altri corpi e diffondersi in istante; apertamente professò nelle <lb></lb>proposizioni VI e VII del cap. </s>

<s>I de&#039;Paralipomeni a Vitellione la diffusione <lb></lb>superficiale. </s></p><p type="main">

<s><emph type="italics"></emph>“ Prop. </s>

<s>VI.<emph.end type="italics"></emph.end> Luci cum discessu a centro accidit aliqua attenuatio in <lb></lb>latum. <emph type="italics"></emph>Prop. </s>

<s>VII.<emph.end type="italics"></emph.end> Lucis radio cum discessu a centro nulla accidit attenua­<lb></lb>tio in longum: hoc est non quo longior radius hoc rarior seu sparsior, pro­<lb></lb>pter quidem hanc ipsam longitudinem ” (edit. </s>

<s>cit., pag. </s>

<s>9). Di qui è, se­<lb></lb>condo il Keplero, che, considerato un raggio solo, egli è ugualmente vigoroso <lb></lb>a principio e a termine della sua diffusione: considerati più raggi insieme, <lb></lb>perciocchè essi non si attenuano che <emph type="italics"></emph>in latum,<emph.end type="italics"></emph.end> deve dunque la loro inten­<lb></lb>sità scemare a proposizione che crescono le semplici distanze. </s></p><p type="main">

<s>L&#039;Aguilonio, benchè tenesse anch&#039;egli la diffusione istantanea della luce <lb></lb>e le attribuisse proprietà di spirituale sostanza, non ebbe nulladimeno il co­<lb></lb>raggio di negare una cosa tanto patente al senso, qual&#039;è che i raggi lumi­<lb></lb>nosi diffondonsi d&#039;ogni parte per la solidità della sfera. </s>

<s>Egli perciò nell&#039;<emph type="italics"></emph>Ot­<lb></lb>tica,<emph.end type="italics"></emph.end> trattando al Libro V <emph type="italics"></emph>De luminis profusione,<emph.end type="italics"></emph.end> non dubita di asserire e <lb></lb>di provare “ Lumen effusum circumquaque in spherae modum distenditur ” <lb></lb>(Antuerpiae 1613, pag. </s>

<s>373). </s></p><p type="main">

<s>Dietro un tal verissimo principio l&#039;Aguilonio, primo fra gli Ottici, s&#039;av­<lb></lb>via a risolvere con buon indirizzo il problema dell&#039;intensità della luce. </s>

<s>“ Fors <lb></lb>quisquam hanc idoneam esse causam arbitrabitur, cur lumen progressione <lb></lb>languescat, quod lumen in spherae modum diffundat sese, ut prop. </s>

<s>III osten­<lb></lb>sum est. </s>

<s>Erit itaque corpus lucidum velut centrum eius sphaerae, quam <lb></lb>activitatis vocant, cuius circumferentia erit illa superficies ad quam actio <lb></lb>corporis lucentis terminatur. </s>

<s>Ab hoc ergo centro, sive corpore lucido, si re­<lb></lb>ctos undique radios ad circumferentiam protensos animo concipias, ani­<lb></lb>madvertes eos quo longuis a medio progrediuntur, eo semper ampliori in­<lb></lb>tervallo ab invicem divaricari. </s>

<s>E converso autem eo semper arctius stringi, <lb></lb>quo propius ad centrum accesserint, quoad tandem in unum simul omnes <pb xlink:href="020/01/591.jpg" pagenum="34"></pb>conveniant, seque mutuo amplectantur. </s>

<s>At coniunctum lumen efficacius ex­<lb></lb>cellentiusque est disperso, per communem notionem, igitur, iuxta sphaerae <lb></lb>centrum, intensissimum est lumen, inde vero, quo longius provehitur, eo <lb></lb>semper rarius segniusque evadit ” (ibi, pag. </s>

<s>375). </s></p><p type="main">

<s>Chi si trova nel leggere condotto a questo punto, s&#039;aspetta che l&#039;Au­<lb></lb>tore abbia presto a concluderne, proseguendo la diritta via presa, che l&#039;in­<lb></lb>tensità della luce non è in ragion reciproca delle semplici distanze, come <lb></lb>conseguiva dai falsi principii del Keplero, ma sì veramente ch&#039;ella è in re­<lb></lb>ciproca ragione de&#039;quadrati delle distanze. </s>

<s>Con sorpresa dolorosa però chi <lb></lb>legge, come chi vedesse uno tornare indietro, quando pochi passi più oltre <lb></lb>era per vincere il palio, sente così tosto soggiungere: “ Haec ratio, licet ex <lb></lb>necessariis concludere videatur, facile tamen convelli potest ” (ibi). E perchè <lb></lb>si dee così svegliere la radice a un vero tanto felicemente germogliato? </s>

<s>Per <lb></lb>più ragioni, risponde l&#039;Aguilonio. </s>

<s>Prima, perchè la virtù del magnete non si <lb></lb>diffonde in sfera ma in linea retta; poi, perchè sebben la luce si diffonda <lb></lb>in lungo e in largo, non ha luogo ciò nel raggio solitario, in cui pure l&#039;in­<lb></lb>tensità diminuisce colla distanza. </s>

<s>“ Deinde, si ea esset decrementi causa, se­<lb></lb>queretur aequalibus spatiis aequalia fieri luminis decrementa ” (ibi). </s></p><p type="main">

<s>L&#039;allucinazione dell&#039;Autore è qui veramente singolare Se l&#039;intensità <lb></lb>luminosa diminuisse in ragione della diffusione superficiale della sfera, non <lb></lb>ne seguirebbe che in spazii uguali i decrementi fossero uguali, ma sareb­<lb></lb>bero que&#039;decrementi come i quadrati degli spazii uguali. </s>

<s>Tutto l&#039;inganno <lb></lb>consiste nel considerar quegli stessi decrementi farsi a proporzion che cre­<lb></lb>scono le circonferenze de&#039;cerchi e non le superficie delle sfere. </s>

<s>“ Esto (così <lb></lb>prosegue l&#039;Autore a concludere una verità, per farla poi ministra a un pa­<lb></lb>ralogismo) corpus luminosum A (fig. </s>

<s>11), radiique ab A profusi AB et AC, <lb></lb><figure id="id.020.01.591.1.jpg" xlink:href="020/01/591/1.jpg"></figure></s></p><p type="caption">

<s>Figura 11.<lb></lb>a quibus aequales par­<lb></lb>tes obscindantur per <lb></lb>arcus BC, DE, FG et <lb></lb>HK, ex eodem centro <lb></lb>A descriptos. </s>

<s>His vero <lb></lb>arcubus subtendantur <lb></lb>chordae, quas dico pa­<lb></lb>rallelas esse.... Tanto <lb></lb>enim remissus est lu­<lb></lb>men in loco BC, quanto <lb></lb>BC maior est ipsa DE, <lb></lb>aut quanto DE ipsa BC est minor. </s>

<s>Sequitur igitur, si eam ob causam lu­<lb></lb>men protensum languescit, quod radii a corpore luminoso evibrati magis <lb></lb>ac magis divaricantur, lumina aequalibus spatiis aequalia pati decrementa ” <lb></lb>(ibi, pag. </s>

<s>376). Ma ciò non può essere, conclude l&#039;Aguilonio, dunque è falso <lb></lb>che diminuisca il lume per la sua sferica diffusione. </s></p><p type="main">

<s>Che non possa esser che il lume diminuisca in proporzion che crescono <lb></lb>le semplici distanze, l&#039;Aguilonio lo dimostra così con un ingegnoso ragio-<pb xlink:href="020/01/592.jpg" pagenum="35"></pb>namento fondato sull&#039;esperienza. </s>

<s>Sia A (fig. </s>

<s>12) un luminare splendente con <lb></lb>4 gradi d&#039;intensità, che diffonda nel prossimo spazio il suo lume, diventando <lb></lb>in spazii uguali 3, 2, 1, e finalmente riducendosi a zero. </s>

<s>Sia B un altro si­<lb></lb><figure id="id.020.01.592.1.jpg" xlink:href="020/01/592/1.jpg"></figure></s></p><p type="caption">

<s>Figura 12.<lb></lb>mile luminare, che si diffonda <lb></lb>con la medesima legge. </s>

<s>Se ve­<lb></lb>ramente i decrementi de&#039;lumi <lb></lb>in uguali spazii si facessero <lb></lb>uguali, ne verrebbe che lo spa­<lb></lb>zio interposto fra&#039;due luminari <lb></lb>dovess&#039;essere ugualmente lu­<lb></lb>minoso, avendosi quattro gradi <lb></lb>di lume per tutto. </s>

<s>“ Quis enim <lb></lb>adeo luminibus destitutus est, qui non videat inter duas lucernas centum <lb></lb>stadiis ab invecem disiunctas, minus luminis circa medium esse quam circa <lb></lb>extrema? </s>

<s>Esset autem aequale si aequalibus spatiis aequalia fierent decre­<lb></lb>menta, ut ex apposito schemate conspici potest ” (ibi, pag. </s>

<s>377). </s></p><p type="main">

<s>Lasciatosi miseramente aggirar l&#039;Aguilonio, dopo aver corso un buon <lb></lb>tratto per la diretta via, non ebbe la felicità di toccar la meta, ma come <lb></lb>segno dell&#039;esservisi molto avvicinato, lasciò nel citato libro V dell&#039;Ottica di­<lb></lb>mostrate le seguenti proposizioni: <emph type="italics"></emph>“ Prop. </s>

<s>V.<emph.end type="italics"></emph.end> Lumen longius proiectum <lb></lb>sensim languescit (pag. </s>

<s>375). <emph type="italics"></emph>Prop. </s>

<s>VI.<emph.end type="italics"></emph.end> Aequalibus spatiis inaequalia fiunt <lb></lb>luminis decrementa (pag. </s>

<s>376). <emph type="italics"></emph>Prop. </s>

<s>VII.<emph.end type="italics"></emph.end> Aequalium spatiorum quae longius <lb></lb>absunt, minora efficiunt defectionum momenta (pag. </s>

<s>377). <emph type="italics"></emph>Prop. </s>

<s>VIII.<emph.end type="italics"></emph.end> Lu­<lb></lb>men aequalibus spatiis proportionalibus decrementis languescit (pag. </s>

<s>379). <lb></lb><emph type="italics"></emph>Prop. </s>

<s>IX.<emph.end type="italics"></emph.end> Lumen uniformi difformitati decrescit ” (pag. </s>

<s>379). </s></p><p type="main">

<s>Otto anni dopo che l&#039;Aguilonio aveva dimostrate queste sue proposizioni, <lb></lb>il Keplero pubblicava di nuovo il Misterio Cosmografico <emph type="italics"></emph>De admirabili pro­<lb></lb>portione orbium coeìestium,<emph.end type="italics"></emph.end> dove il perpetuarsi de&#039;pianeti nel loro moto <lb></lb>s&#039;attribuiva agl&#039;impulsi radiosi del sole. </s>

<s>“ Ponamus igitur id quod valde <lb></lb>verisimile est, eadem ratione motum a Sole dispensari qua lucem. </s>

<s>Lucis <lb></lb>autem ex centro prorogatae debilitatio qua proportione fiat docent Optici ” <lb></lb>(Francofurti 1621, pag. </s>

<s>76). </s></p><p type="main">

<s>Fra gli Ottici era da annoverarsi, a quel tempo, anche l&#039;Aguilonio, il <lb></lb>quale anzi era divenuto il più autorevole di tutti. </s>

<s>Ora, perchè questo Au­<lb></lb>tore aveva dimostrato che il lume decresce con difformità uniforme, forse <lb></lb>il Keplero si crederebbe che avesse corrette quelle sue opinioni, e che la <lb></lb>bella dimostrazione sperimentale dell&#039;Ottico belga lo avesse persuaso non <lb></lb>patir il lume decrementi uniformemente uniformi. </s>

<s>Tutt&#039;altrimenti però l&#039;Au­<lb></lb>tore de&#039;Paralipomeni a Vitellione non s&#039;è niente rimosso da&#039;suoi instituti e <lb></lb>gli Ottici che egli dianzi citava son quegli che si uniformano a così fatti <lb></lb>istituti, secondo i quali la luce s&#039;attenua nel circolo o nò nella sfera, e per­<lb></lb>ciò il decrescere dell&#039;intensità luminosa è da misurarsi non dal crescere delle <lb></lb>superficie sferali, ma delle circonferenze de&#039;cerchi. </s>

<s>“ Nam quantum lucis <lb></lb>est in parvo circulo, tantundem etiam lucis sive radiorum solarium est in <pb xlink:href="020/01/593.jpg" pagenum="36"></pb>magno. </s>

<s>Hinc cum sit in parvo stipatior, in magno tenuior mensura huius <lb></lb>attenuationis ex ipsa circulorum proportione petenda erit, idque tam in luce, <lb></lb>quam in motrice virtute ” (ibi). </s></p><p type="main">

<s>L&#039;errore preso qui dal Keplero, fu infausto, come vedremo ai pro­<lb></lb>gressi dell&#039;Astronomia matematica, ma perchè non dovesse un simil danno <lb></lb>ricevere l&#039;arte del disegno, l&#039;Accolti fu sollecito di avvertire gli artisti del­<lb></lb>l&#039;errore in ch&#039;erano incorsi alcuni Pittori del maggior grido “ i quali hanno <lb></lb>stimato poter conoscere matematicamente e proferire la quantità dell&#039;inten­<lb></lb>sione del lume, dovuto a ciascun oggetto in pittura, rappresentati da loro <lb></lb>in diverse parti e siti dei loro piani degradati, con misurare e partire in più <lb></lb>parti perspettivamente eguali il raggio luminoso o spazio, che si frappone <lb></lb>tra l&#039;oggetto illuminato ed il corpo luminoso ” (Prospettiva cit., pag. </s>

<s>98). <lb></lb>E affine che il Pittore, nella rappresentazione di diversi oggetti da illumi­<lb></lb>narsi in diverse lontananze sappia come contenersi nel lumeggiare, dimo­<lb></lb>stra, traducendo quasi a parola l&#039;Aguilonio, com&#039;è contrario all&#039;esperienza <lb></lb>il digradar la diminuzione de&#039;lumi in prospettiva a proporzione che cre­<lb></lb>scono le semplici distanze (ivi, pag. </s>

<s>98, 99). </s></p><p type="main">

<s>Nel 1632 Galileo pubblicava i Dialoghi De&#039;due Massimi Sistemi, e in <lb></lb>quell&#039;Opera così celebre, dove tanto promovevasi la Filosofia naturale, l&#039;Ot­<lb></lb>tica non fa nemmeno un passo più avanti. </s>

<s>Nel I di que&#039;Dialoghi ha l&#039;Au­<lb></lb>tore occasione di toccare un soggetto di Fotometria, ma pronunziando che <lb></lb>“ le medesime superficie vengono dal medesimo lume più o meno illumi­<lb></lb>nate, secondo che i raggi illuminanti vi cascano sopra più o meno obliqua­<lb></lb>mente, sicchè la massima illuminazione è dove i raggi sono perpendicolari ” <lb></lb>(Alb. </s>

<s>I, 91); non faceva altro che tradurre il Teorema II del Maurolico <lb></lb>ne&#039;citati Fotismi. </s>

<s>La prima dimostrazione sperimentale, che Galileo dà è <lb></lb>ovvia al senso di tutti; la seconda dimostrazione geometrica è quella stessa, <lb></lb>che il Benedetti dava, come vedremo, per dimostrare il vario grado d&#039;in­<lb></lb>tensità calorifica ricevuta dalla superficie o tenuta obbliqua o perpendico­<lb></lb>larmente opposta all&#039;irradiazione della sorgente. </s></p><p type="main">

<s>La dimostrazione galileiana però è molto meno elaborata. </s>

<s>Fate conto <lb></lb>che tutte le linee parallele, che voi vedete partirsi dai termini A, B (fig. </s>

<s>13) <lb></lb><figure id="id.020.01.593.1.jpg" xlink:href="020/01/593/1.jpg"></figure></s></p><p type="caption">

<s>Figura 13.<lb></lb>siano i raggi, che sopra la linea CD ven­<lb></lb>gono ad angoli retti: inclinate ora la me­<lb></lb>desima CD, sicchè penda come DO, non <lb></lb>vedete voi che buona parte di quei raggi <lb></lb>che ferivano la CD, passano senza toccare <lb></lb>la DO? Adunque, se la DO è illuminata <lb></lb>da manco raggi, è ben ragionevole che il <lb></lb>lume ricevuto da lei sia più debole ” (ivi, <lb></lb>pag. </s>

<s>92). </s></p><p type="main">

<s>Nè il Benedetti nulladimeno nè Galileo dimostrarono che la intensità <lb></lb>della luce o del calore, ricevuti obliquamente sopra una superficie, è pro­<lb></lb>porzionale al seno dell&#039;angolo dell&#039;incidenza; Teorema che in generale, di <pb xlink:href="020/01/594.jpg" pagenum="37"></pb>qualunque natura sia il corpo che percote, non fu da nessuno, come vedremo <lb></lb>in altra parte di questa storia, dimostrato prima che dal Torricelli. </s></p><p type="main">

<s>Intanto, anche dopo quel fervore di studii di cose naturali eccitato dalla <lb></lb>pubblicazione de&#039;<emph type="italics"></emph>Massimi Sistemi,<emph.end type="italics"></emph.end> gli Ottici, della profusione del lume, non <lb></lb>avevan saputo ancora nulla di più di quel che aveva loro insegnato l&#039;Agui­<lb></lb>lonio. </s>

<s>Sapevan che in quella profusione l&#039;intensità diminuisce con più rapide <lb></lb>proporzioni di quelle delle semplici distanze, ma non sapevan però definire <lb></lb>quali fossero quelle proporzioni. </s></p><p type="main">

<s>Una sera di estate del 1634 il Castelli a Roma conversava con alcuni <lb></lb>amici suoi letterati, mentre la Luna nuova appariva pel sereno del cielo <lb></lb>nella sua sottilissima falce, e il resto si mostrava di una luce cinerea leg­<lb></lb>germente incandito. </s>

<s>Sollevando que&#039;letterati gli occhi alla Luna, e persuasi, <lb></lb>dagli argomenti del padre don Benedetto, che quel candore era dovuto a&#039;ri­<lb></lb>flessi della Terra, facevan nulladimeno difficoltà come potesse la Terra illu­<lb></lb>minare più la Luna di quello che fa la Luna la Terra. </s>

<s>Si proponeva così <lb></lb>un problema di Fotometria, e il Castelli, per sodisfare a que&#039;suoi amici, <lb></lb>tornò poche sere dopo, applicando a risolvere le difficoltà il Teorema così <lb></lb>da lui formulato: </s></p><p type="main">

<s>“ Se saranno due lumi, ineguali in specie ed in grandezza, illuminanti <lb></lb>la medesima sorta di oggetti in distanze ineguali, l&#039;illuminazione assoluta <lb></lb>del primo all&#039;illuminazione assoluta del secondo avrà la proporzione com­<lb></lb>posta del lume in specie del primo al lume in specie del secondo, della <lb></lb>grandezza della superficie del primo alla grandezza della superficie del se­<lb></lb>condo, e della proporzion duplicata della lontananza del secondo dall&#039;og­<lb></lb>getto illuminato alla lontananza del primo dall&#039;oggetto da lui illuminato ” <lb></lb>(Alb. </s>

<s>X, 50). </s></p><p type="main">

<s>Ecco finalmente la vera legge fotometrica scoperta: l&#039;intensità del lume <lb></lb>scema a proporzione che crescono i quadrati delle distanze. </s>

<s>Come proce­<lb></lb>desse il Castelli nella dimostrazione del suo fotometrico Teorema sarebbe <lb></lb>bello a sapere, ma perchè non è rimasto di ciò, almeno che sia noto a noi, <lb></lb>altra memoria da quella lettera a Galileo scritta il dì 12 Agosto 1634, in <lb></lb>essa, dopo aver formulato il sopraddetto Teorema, dice solo così in gene­<lb></lb>rale: “ Tutto dimostro premesse alcune definizioni e supposizioni manifeste, <lb></lb>dal che si può discorrere di quella tanto varia riflessione di lumi de&#039;Pia­<lb></lb>neti alla Terra. </s>

<s>Però lascio stare il tutto in riposo per poterlo rivedere senza <lb></lb>passione ” (ivi). </s></p><p type="main">

<s>Forse disanimato dalla poca accoglienza fatta da Galileo, il quale non <lb></lb>seppe riconoscere nè perciò debitamente pregiare la verità feconda che si <lb></lb>ascondeva nel Teorema fotometrico del suo discepolo, il Castelli non tornò <lb></lb>a rivedere la sua dimostrazione, che rimase in perpetuo riposo. </s>

<s>Così lasciava <lb></lb>il merito di pubblicarla, a benefizio universale della scienza e a gloria della <lb></lb>patria, a un Francese. </s></p><p type="main">

<s>Quattro anni dopo che il Castelli aveva annunziato il suo Teorema a <lb></lb>Galileo, Ismaele Boulliaud pubblicava in Parigi, nel 1638, un suo Trattato <pb xlink:href="020/01/595.jpg" pagenum="38"></pb><emph type="italics"></emph>De natura lucis.<emph.end type="italics"></emph.end> Avendo egli troppo ben riconosciuto quanto errasse il <lb></lb>Keplero a negare la diffusione sferica alla luce, e quanto infelicemente si <lb></lb>fosse ritirato indietro l&#039;Aguilonio dalla diritta via, per la quale s&#039;era così <lb></lb>bene incamminato, liberamente in questa forma scriveva nella sua IV pro­<lb></lb>posizione: “ Ut sphaerae incrementum dimensionum suscipiunt a digressu <lb></lb>linearum infinitarum aequalium a centro ad unam aliquam superficiem, <lb></lb>ubique a centro aequaliter distantem; ita lux incrementum dimensionum <lb></lb>suscipit a digressu radiorum infinitorum a corpore lucido ad aliquam su­<lb></lb>perficiem sphaericam ubivis terminatam.... Superficies sunt ad invicem ut <lb></lb>ratio diametrorum ad invicem dupla: crescit ergo sphaera iuxta modum <lb></lb>incrementi dimetientis suae. </s>

<s>Lux vero sphaericam figuram in effluxu obser­<lb></lb>vat; ergo lucis dimensiones crescunt porrecto radio, idest quo longius a lu­<lb></lb>cido radii defluent, eo ampliores erunt lucis dimensiones ut in sphaera ” <lb></lb>(pag. </s>

<s>9). </s></p><p type="main">

<s>Di qui veniva l&#039;Autore per diritta via condotto a formulare e a dimo­<lb></lb>strare la sua XXVII proposizione: “ Densitate superficierum luminis sunt <lb></lb>ad invicem ut rationes duplae distantiarum superficierum a corpore lucido ” <lb></lb>(pag. </s>

<s>42). </s></p><p type="main">

<s>Il libro <emph type="italics"></emph>De natura lucis<emph.end type="italics"></emph.end> fu da Parigi, accompagnato con lettera del dì <lb></lb>30 Ottobre 1637, spedito dal Boulliaud a Galileo, a cui scriveva l&#039;Autore <lb></lb>spero <emph type="italics"></emph>de illo opusculo iudicium tuum intelligam<emph.end type="italics"></emph.end> (Alb. </s>

<s>X, 242). Galileo ri­<lb></lb>spondeva il dì 1° Gennaio dell&#039;anno seguente dicendo che la cecità, sven­<lb></lb>turatamente sopravvenutagli, gl&#039;impediva di capir bene quelle dimostrazioni <lb></lb>“ quae ex figurarum dependent usu .... ea tamen quae capere auribus po­<lb></lb>tui, summa cum delectatione audivi ” (Alb. </s>

<s>VII, 206). </s></p><p type="main">

<s>Per la dimostrazione fotometrica però non c&#039;era bisogno delle figure e <lb></lb>bastava persuadersi della diffusione sferica della luce perchè del resto, con­<lb></lb>tentandosi di citarli, il Boulliaud rimanda ai notissimi teoremi geometrici <lb></lb>di Euclide Ma Galileo non pare che avesse quella persuasione, per cui di­<lb></lb>cevasi da noi più sopra che non fece buona accoglienza a quel Teorema del <lb></lb>Castelli, il quale fa perfettissimo riscontro con la proposizione XXVII del­<lb></lb>l&#039;Astronomo di Parigi. </s></p><p type="main">

<s>Che Galileo non approvasse i Teoremi dimostrati successivamente da&#039;due <lb></lb>Autori, e che non sentisse la verità feconda che s&#039;annunziava con essi, non <lb></lb>è poi una nostra congettura ma un fatto. </s>

<s>Nel 1640, sei anni cioè dopo l&#039;enun­<lb></lb>ciato dal Castelli, e due anni dopo la pubblicazione del Boulliaud, occorse <lb></lb>a Galileo di risolvere un problema di Fotometria simile a quello proposto <lb></lb>al p. </s>

<s>d. </s>

<s>Benedetto da&#039;suoi amici di Roma. </s>

<s>L&#039;occasione fu a proposito della <lb></lb>controversia con Fortunio Liceti, il quale, per negar che il candore lunare <lb></lb>era un riflesso della Terra simile al riflesso della Luna, notava che fra le <lb></lb>due riflessioni era in intensità tanta differenza da non si poter l&#039;una ras­<lb></lb>somigliare con l&#039;altra. </s>

<s>Qui Galileo poteva applicare il Teorema fotometrico <lb></lb>del Castelli o la proposizione XXVII <emph type="italics"></emph>De Natura lucis,<emph.end type="italics"></emph.end> e il problema veniva <lb></lb>con verità scientifica risoluto. </s>

<s>Ma egli è ancora col Maurolico: l&#039;intensità <pb xlink:href="020/01/596.jpg" pagenum="39"></pb>luminosa ei col Maurolico la misura dalla quantità de&#039;raggi luminosi com­<lb></lb>presi dentro l&#039;angolo che s&#039;appunta nell&#039;occhio. </s></p><p type="main">

<s>“ Di due oggetti visibili, ma in grandezza disuguali il minore ingom­<lb></lb>bra l&#039;occhio più di luce che il maggiore, ancorchè ambedue fossero del­<lb></lb>l&#039;istesso splendore in spezie. </s>

<s>Ora notisi che il disco lunare vien compreso <lb></lb>sotto un angolo acutissimo, avvengachè la sua base non sottenda più che <lb></lb>mezzo grado; ma l&#039;angolo, che dalla massima divaricazione de&#039;raggi visivi <lb></lb>si costituisce nell&#039;occhio, essendo più grande che retto, sottende a più di <lb></lb>90 gradi interi, e questo viene tutto ingombrato dall&#039;aria e piazza luminosa <lb></lb>della Terra, mentre che da vicino la rimiriamo. </s>

<s>Essendo dunque l&#039;ampiezza <lb></lb>di questo grande angolo 200 volte maggiore dell&#039;altro acuto che comprende <lb></lb>il disco lunare, maraviglia non dobbiamo prendere dell&#039;apparente maggio­<lb></lb>ranza di luce nel rimirar la Terra che la Luna incandita ” (Alb. </s>

<s>VII, <lb></lb>pag. </s>

<s>279, 80). </s></p><p type="main">

<s>Essendo così, non fa maraviglia che il Borelli nel 1665 stia ancor col <lb></lb>Keplero e desumendo la proporzione degl&#039;impulsi radiosi del sole sui pia­<lb></lb>neti più o meno lontani, dalla proporzione come nell&#039;intensità diminuisce <lb></lb>la luce, conclude con più tardo moto sospingere il Sole stesso i globi che <lb></lb>lo circondano <emph type="italics"></emph>ea proportione quam reciproce habent resistentiae seu distan­<lb></lb>tiae<emph.end type="italics"></emph.end> (Theor. </s>

<s>medic., Florentiae 1665, pag. </s>

<s>65). </s></p><p type="main">

<s>Nel 1673 era ancora questa kepleriana la legge dell&#039;intensità della luce <lb></lb>professata dal Newton, quando istituì il primo calcolo della velocità con cui <lb></lb>sarebbe sulla Terra caduta la Luna. </s>

<s>Le celebri leggi neutoniane dell&#039;attra­<lb></lb>zione universale furono finalmente quelle che persuasero esser senza ecce­<lb></lb>zione vero il Teorema fotometrico tanti anni prima dimostrato dal Castelli <lb></lb>e dal Boulliaud pubblicato, ma in Italia v&#039;era pure chi, anche senza le sco­<lb></lb>perte del grande Inglese, erasi assai per tempo assicurato, coll&#039;esperienza, <lb></lb>della vera legge della Fotometria. </s></p><p type="main">

<s>Nel 1672 Geminiano Montanari così scriveva in una sua operetta inti­<lb></lb>tolata <emph type="italics"></emph>La Fiamma volante:<emph.end type="italics"></emph.end> “ Ho più volte sperimentato nella nostra Ac­<lb></lb>cademia della Traccia che se con un lume di candela ordinaria io vedo con <lb></lb>una determinata chiarezza a leggere un dato carattere, per esempio alla di­<lb></lb>stanza di un piede e mezzo dal medesimo lume; con quattro tali lumi ve­<lb></lb>drò con pari chiarezza alla distanza di tre piedi; con nove candele alla di­<lb></lb>stanza di quattro piedi e mezzo; con sedici candele, a quella di sei piedi, e <lb></lb>così con quest&#039;ordine, che vuol dire che il numero delle candele sia sem­<lb></lb>pre il quadrato delle distanze ” (Bologna, pag. </s>

<s>42). </s></p><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I moderni, che sanno con qual certezza ritengano oggidi gli Ottici e <lb></lb>con quanta facilità di geometrica precisione dimostrino diffondersi il lume <lb></lb>sulle superficie di sfere concentriche, le quali crescono in ragione de&#039;qua-<pb xlink:href="020/01/597.jpg" pagenum="40"></pb>drati de&#039;raggi, conforme ai più antichi documenti di Euclide; non possono <lb></lb>non far le maraviglie delle tante difficoltà, che trovarono gli antichi in in­<lb></lb>vestigar quella legge, e non sanno persuadersi come, per così poco, si la­<lb></lb>sciassero indur nell&#039;errore. </s>

<s>Come mai, domanderanno, il gran Keplero perfidiò <lb></lb>nel negare alla luce una proprietà così patente qual&#039;è quella del diffondersi <lb></lb>di lei per ogni verso? </s>

<s>E benchè alla domanda si sia già risposto, ripetiamo <lb></lb>che ciò fu per salvare i principii comunemente professati allora intorno al­<lb></lb>l&#039;essere e alla natura della luce, secondo i quali principii reputavasi che <lb></lb>l&#039;agente così impercettibile alla crassizie de&#039;sensi, non dovesse soggiacere <lb></lb>alle passioni degli altri corpi. </s>

<s>Si vede bene insomma che l&#039;origine di quello <lb></lb>e di parecchi altri simili errori vien dal non essersi ancora ben definito il <lb></lb>concetto della natura di quel misterioso intangibile elemento, per cui noi <lb></lb>vediamo. </s></p><p type="main">

<s>Il bisogno di ben definir quel concetto fu sentito dal Boulliaud, il quale <lb></lb>a tale intento dette opera a scrivere il suo trattato <emph type="italics"></emph>De natura lucis.<emph.end type="italics"></emph.end> Egli <lb></lb>osserva ivi che gli antichi Euclide, Alhazeno, Vitellione non pensarono per <lb></lb>niente a definir la natura della luce: e soggiunge che il Keplero, benchè <lb></lb>abbia il gran merito di aver coniugato il primo l&#039;Ottica alla Fisica, <emph type="italics"></emph>saepius <lb></lb>tamen pungere videtur quam perforare<emph.end type="italics"></emph.end> (Editio cit. </s>

<s>pag. </s>

<s>121). </s></p><p type="main">

<s>Primo, secondo il Boulliaud, a tentare la difficile questione fu il nostro <lb></lb>Dalmata Francesco Patrizio, nel I dei dieci libri della sua <emph type="italics"></emph>Panurgia,<emph.end type="italics"></emph.end> dov&#039;egli <lb></lb>asserisce la luce essere un che di mezzo tra il corporeo e l&#039;incorporeo nel <lb></lb>sole e negli astri. </s>

<s>“ Corpus est quia in his habet molem et trinam dimen­<lb></lb>sionem, incorporea est, quia est forma solis ” (ibi) e soggiunge in oltre la <lb></lb>luce stessa <emph type="italics"></emph>in instanti moveri.<emph.end type="italics"></emph.end> L&#039;Astronomo francese rifiutata solo la di­<lb></lb>stinzione fra lume e raggi, i quali non son realtà ma affezioni dell&#039;occhio, <lb></lb>segue in tutto i placiti del Filosofo nostro razionalista. </s></p><p type="main">

<s>Indipendentemente però dalle sottili speculazioni del Patrizio, nel I libro <lb></lb>dell&#039;Ottica, sentenziava così l&#039;Aguilonio nella proposizione XXXIII “ Male <lb></lb>Empedocles lumen corpus esse dixit.... Lumen igitur non est corpus, cum <lb></lb>illud videamus ocissime et velut momento temporis longissima spatia eme­<lb></lb>tiri ” (Edit. </s>

<s>cit., pag. </s>

<s>33), e più espresso nella proposizione seguente: “ Sed <lb></lb>neque lumen corporea est qualitas: recte autem intentionalis vocari po­<lb></lb>test.... Modus existendi luminis intentionalis est, quo extra proprium su­<lb></lb>biectum, instar spiritualis substantiae totum existit simul ut in aere, aliove <lb></lb>corpore impune pervio, in quo sese plura lumina penetrant, et momento <lb></lb>temporis immensa spatia transcurrunt, more spirituum ” (ibi, pag. </s>

<s>34). </s></p><p type="main">

<s>Isacco Vossio che, dopo essersi istituita la scienza delle rifrazioni, stimò <lb></lb>doversi compiere quello del Boulliaud con un altro trattato <emph type="italics"></emph>De natura lu­<lb></lb>cis et proprietate,<emph.end type="italics"></emph.end> dimostrava la sua proposizione “ Radios lucis non esse <lb></lb>corporeos ” dal fatto che infinite particelle diffuse ne&#039;raggi lucidi possono <lb></lb>capire in un punto matematico, qual&#039;è il foco di uno specchio parabolico. </s>

<s><lb></lb>Incorona poi così dicendo quella sua proposizione: “ Ipsum hoc confirmat <lb></lb>motus lucis. </s>

<s>Cum enim omnia corpora moveantur in tempore, lucis vero <pb xlink:href="020/01/598.jpg" pagenum="41"></pb>motus sit istantaneus, et hinc quoque patet lucem non esse corporeum ” <lb></lb>(Amstelodami 1662, pag. </s>

<s>16). </s></p><p type="main">

<s>È manifesto da ciò che la natura incorporea della luce s&#039;argomentava <lb></lb>dal diffondersi di lei, come gli spiriti, nell&#039;istante. </s>

<s>Anche tutti i falsi con­<lb></lb>cetti del Keplero movevano dal supposto che la luce fosse istantanea, d&#039;onde <lb></lb>egli ne concludeva ch&#039;ella dovess&#039;essere assolutamente imponderabile e perciò <lb></lb>incorporea, e perciò non diffusibile per quelle tre dimensioni, in che si dif­<lb></lb>fonde la crassizie de&#039;corpi. </s>

<s>Quel supposto da un&#039;altra parte, con circolo ine­<lb></lb>vitabile, il Keplero stesso lo dimostra col suppor che la luce sia imponde­<lb></lb>rante, imperocchè se l&#039;impeto sta in ragione composta della celerità e del <lb></lb>peso, e se questo è zero, la velocità necessariamente ne risulta infinita. </s>

<s>“ Sed <lb></lb>hic, vis movens ad lucem movendam infinitam habet proportionem, quia luci <lb></lb>nulla materia, quare neque pondus. </s>

<s>Ita medium luci nihil resistit, quia lux <lb></lb>materia caret, per quam fiat resistentia. </s>

<s>Ergo lucis infinita celeritas est ” <lb></lb>(Paralip. </s>

<s>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Quanto a Galileo, essendo egli solito chiamar la luce <emph type="italics"></emph>l&#039;ultimo spolve­<lb></lb>ramento de&#039;corpi,<emph.end type="italics"></emph.end> par che non dubitasse della natura corporea di lei, ma <lb></lb>convien pure che potrebb&#039;esser vera la sentenza di chi credeva altrimenti. <lb></lb></s>

<s>“ Che la luce sia incorporea ed istantanea si potrebbe dire .... poichè, <lb></lb>avendo un pugnello di polvere e dandogli fuoco, ella si spande in immenso, <lb></lb>e si può vedere com&#039;è che ella sia ridotta a&#039;suoi indivisibili componenti e <lb></lb>fatta senza introduzione di corpi o di posizione di vacui quanti, ma bene <lb></lb>d&#039;infiniti indivisibili vacui, e così non occupa luogo e non ricerca tempo di <lb></lb>andare da un luogo a un altro ” (MSS. Gal., P. V, T. IV, c. </s>

<s>28), sentenza <lb></lb>conforme a quella che leggesi nel <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> (Alb. </s>

<s>IV, 338). </s></p><p type="main">

<s>Conoscendo però Galileo la grande importanza che ha il moto in defi­<lb></lb>nir la così dubbia e così controversa natura della luce, egli è il primo che, <lb></lb>a decidere se quel moto è in tempo o in istante, e se perciò la luce è spi­<lb></lb>rito o corpo, abbia pensato di ricorrere alle esperienze. </s></p><p type="main">

<s>“ La poca concludenza di queste e di altre simili osservazioni mi fece <lb></lb>una volta pensare a qualche modo di poterci senza errore accertare se l&#039;il­<lb></lb>luminazione, cioè se la espansion del lume fosse veramente instantanea; <lb></lb>poichè il moto assai veloce del suono ci assicura quello della luce non po­<lb></lb>ter esser se non velocissimo. </s>

<s>E l&#039;esperienza che mi sovvenne fu tale. </s>

<s>Voglio <lb></lb>che due piglino un lume per uno, il quale, tenendolo dentro la lanterna o <lb></lb>altro ricetto, possino andar coprendo e scoprendo con l&#039;interposizion della <lb></lb>mano alla vista del compagno, e che ponendosi l&#039;uno incontro all&#039;altro in <lb></lb>distanza di poche braccia, vadano addestrandosi nello scoprire ed occultare <lb></lb>il lor lume alla vista del compagno, sicchè, quando l&#039;uno vede il lume del­<lb></lb>l&#039;altro, immediatamente scopra il suo, la qual corrispondenza, dopo alcune <lb></lb>risposte fattesi scambievolmente, verrà loro talmente aggiustata, che senza <lb></lb>sensibile svario, alla scoperta dell&#039;uno risponderà immediatamente la sco­<lb></lb>perta dell&#039;altro, sì che quando l&#039;uno scopre il suo lume vedrà nell&#039;istesso <lb></lb>tempo comparire alla sua vista il lume dell&#039;altro. </s>

<s>” </s></p><pb xlink:href="020/01/599.jpg" pagenum="42"></pb><p type="main">

<s>“ Aggiustata cotal pratica in questa piccolissima distanza, pongansi i <lb></lb>due medesimi compagni con due simili lumi in lontananza di due o tre <lb></lb>miglia, e tornando di notte a far l&#039;istessa esperienza, vadano osservando at­<lb></lb>tentamente se le risposte delle loro scoperte e occultazioni seguono secondo <lb></lb>l&#039;istesso tenore che facevano da vicino; che seguendo, si potrà assai sicu­<lb></lb>ramente concludere l&#039;espansion del lume essere instantanea; che quando <lb></lb>ella ricercasse tempo, in una lontananza di tre miglia, che importano sei, <lb></lb>per l&#039;andata di un lume e venuta dall&#039;altro, la dimora dovrebb&#039;essere assai <lb></lb>osservabile ” (Alb. </s>

<s>XIII, 46, 47). </s></p><p type="main">

<s>Queste parole son nel Dialogo poste in bocca al Salviati, a cui doman­<lb></lb>dando il Sagredo ciò che nel praticare un&#039;invenzione non men sicura che <lb></lb>ingegnosa avesse concluso, il Salviati stesso risponde: “ Veramente non l&#039;ho <lb></lb>sperimentata, salvo che in lontananza piccola, cioè manco d&#039;un miglio, dal <lb></lb>che non ho potuto assicurarmi se veramente la comparsa del lume opposto <lb></lb>sia instantanea ” (ivi, pag. </s>

<s>47). </s></p><p type="main">

<s>L&#039;esperienza fu poi ripetuta dagli Accademici fiorentini, i quali, per la <lb></lb>lontananza di un miglio, che per l&#039;andar di un lume e la venuta dell&#039;altro <lb></lb>vuol dir due, non vi seppero trovar differenza. </s>

<s>“ Se poi, si soggiunge nei <lb></lb><emph type="italics"></emph>Saggi di Naturali esperienze,<emph.end type="italics"></emph.end> in distanza maggiore sia possibile l&#039;arrivare <lb></lb>a scorgervi qualche sensibile indugio, questo non c&#039;è per anche riuscito di <lb></lb>sperimentare ” (Firenze 1841, pag. </s>

<s>173). </s></p><p type="main">

<s>Con tali brevi parole se ne spedisce il Segretario Magalotti, ma tanta <lb></lb>fu la sollecitudine, l&#039;ingegno e l&#039;industriosa varietà de&#039;modi, con che que&#039;tre <lb></lb>primi concorsi felicemente insieme nel secondo periodo della sperimentale <lb></lb>Accademia medica si studiarono di riuscir, benchè invano, nel difficile in­<lb></lb>tento, che per l&#039;onore della scienza italiana non vogliono esser taciuti nella <lb></lb>nostra Storia. </s></p><p type="main">

<s>Principale fra que&#039;tre sappiamo oramai essere stato il Viviani, il quale <lb></lb>ritessendo, come Galileo, fra l&#039;Ottica e la Meccanica le sue speculazioni, così <lb></lb>lasciò in una nota scritto della luce: “ Un corpo mobile per un mezzo cor­<lb></lb>poreo vuol tempo a muoversi, perchè occupandovi luogo e dovendogli ce­<lb></lb>dere il mezzo ne lo trattiene, ed il medesimo corpo mobile per un mezzo <lb></lb>incorporeo, come per vacuo, non ricerca tempo, anzi vi si muove in istante, <lb></lb>e tutto questo dice Aristotile. </s>

<s>Ma io soggiungo che tanto è muoversi un <lb></lb>corpo per un mezzo incorporeo, che un mobile incorporeo per un mezzo <lb></lb>corporeo, sendochè l&#039;uno per il mezzo non si tratterrebbe, nè l&#039;altro sa­<lb></lb>rebbe trattenuto dal mezzo. </s>

<s>Adunque la luce, che per Aristotile è incorpo­<lb></lb>rea, per un mezzo corporeo qual&#039;è l&#039;aria passerebbe in istante, ma se si <lb></lb>provasse questa muoversi in tempo, ne seguirebbe che ella fosse corporea. <lb></lb>(MSS. Gal. </s>

<s>Disc, T. CXXXV, c. </s>

<s>27). </s></p><p type="main">

<s>Tanto conosceva il Viviani essere ai progressi dell&#039;Ottica importante la <lb></lb>conclusione, che per provarne il principio gli balenò in mente un concetto <lb></lb>singolare, di che troviamo fatto ricordo in un&#039;altra delle sue note: “ Sit <lb></lb>filum ferreum clavis A, B (fig. </s>

<s>14) longe dissitas religatum. </s>

<s>Constat quod <pb xlink:href="020/01/600.jpg" pagenum="43"></pb>si percutiatur in B resonabit A in eodem instanti, et sonus ex B in A in <lb></lb>non tempore tunc ferretur, ex quo patet si quo tempore fit ictus in B de­<lb></lb>tegatur lumen dignosci ex A num illuminatio fiat in instanti ” (ibi, c. </s>

<s>14). <lb></lb><figure id="id.020.01.600.1.jpg" xlink:href="020/01/600/1.jpg"></figure></s></p><p type="caption">

<s>Figura 14.</s></p><p type="main">

<s>Ma perchè per troppo breve di­<lb></lb>stanza pativa d&#039;esser teso fra&#039;due <lb></lb>anelli quel fil di ferro sonoro, per <lb></lb>avere spazii più ampii si rivolse il <lb></lb>Viviani a praticare i metodi già proposti da Galileo, e sotto il dì 14 Aprile 1657 <lb></lb>si trova di sua propria mano scritto questo ricordo: “ Feci giorni sono l&#039;espe­<lb></lb>rienza della luce nel modo insegnato da Galileo ” (MSS. Cim., T. X, c. </s>

<s>181) <lb></lb>e si scelsero per le due stazioni il monte della Verrucola e il campanile di <lb></lb>Pisa (Targioni, Notiz. </s>

<s>cit., T. II, P. II, pag 585, 86). </s></p><p type="main">

<s>Fu a questa occasione che avendo risaputo il Borelli, professore di Ma­<lb></lb>tematiche in quello studio, de&#039;preparativi che si facevano per l&#039;esperienza, <lb></lb>si sentì eccitato a speculare un più facile e più squisito modo di praticarla. </s>

<s><lb></lb>Di ciò Cosimo Galilei, giovane, e che per ragione di studii soggiornava al­<lb></lb>lora in Pisa, dava conto, con lettera del dì 4 Aprile 1657, al Viviani. </s></p><p type="main">

<s>“ Qui in Pisa vo godendo la conversazione dell&#039;Ecc.mo sig. </s>

<s>Borelli e <lb></lb>dell&#039;Illustriss. </s>

<s>signor Visconte D. </s>

<s>Giacomo Ruffo, suo camerata ... In pro­<lb></lb>posito del moto della luce ha escogitato il sig. </s>

<s>Dottore una bellissima espe­<lb></lb>rienza, per conoscere se questa cammina istantaneamente. </s>

<s>Pensa egli di ac­<lb></lb>comodare molti specchi disposti con quest&#039;ordine, come vede V. S., A, B, <lb></lb><figure id="id.020.01.600.2.jpg" xlink:href="020/01/600/2.jpg"></figure></s></p><p type="caption">

<s>Figura 15<lb></lb>C, D.... (fig. </s>

<s>15) in maniera tale che il raggio del sole <lb></lb>da A si rifletta in E, e da E in B ecc. </s>

<s>ed alla fine da Q <lb></lb>di nuovo se ne ritorni in E. </s>

<s>Certa cosa sarà, se gli spazii <lb></lb>da uno specchio all&#039;altro saranno grandi, che potrà asso­<lb></lb>lutamente, se la luce non cammina instantaneamente, l&#039;os­<lb></lb>servatore posto in E conoscer qualche differenza dall&#039;ap­<lb></lb>parire il riflesso di A da quello di <expan abbr="q.">que</expan> Sopra della qual <lb></lb>cosa vi ha egli ritrovate alcune belle proposizioni, che io <lb></lb>adesso a V. S. significare non posso per la scarsità del <lb></lb>tempo. </s>

<s>Pensa ancora di servirsi di questa esperienza per <lb></lb>vedere se veramente sia quella rifrazione nella region va­<lb></lb>porosa addotta per causa dagli Astronomi di tante e tante <lb></lb>novità contro ogni aspettazione seguite ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXLIV, c. </s>

<s>32). </s></p><p type="main">

<s>Dieci giorni dopo, lo stesso Borelli rendendo conto <lb></lb>de&#039;suoi studii al principe Leopoldo, gli descriveva il nuovo <lb></lb>modo escogitato per esperimentare la velocità della luce, <lb></lb>così concludendo: “ Questa sperienza, come vede V. A. S., <lb></lb>se nel praticarla non s&#039;incontra qualche nuova difficoltà, oltre a quelle che <lb></lb>io ho preveduto, è la più squisita che si possa immaginare in questo pro­<lb></lb>posito, se io non m&#039;inganno, e però spero questa state, coll&#039;aiuto e favore <lb></lb>di V. A. S., poterla mettere in opra, per assicurarmi d&#039;un problema tanto <pb xlink:href="020/01/601.jpg" pagenum="44"></pb>importante e desiderato da tutti i Filosofi ” (Fabbroni, Lett. </s>

<s>ecc., T. II, <lb></lb>pag. </s>

<s>61, 62). </s></p><p type="main">

<s>Non par però che nell&#039;estate s&#039;operasse nulla in proposito, come può <lb></lb>congetturarsi da ciò che Cosimo Galilei tornava a scrivere al Viviani, quasi <lb></lb>a mezzo Novembre. </s>

<s>“ Devo in nome ancora del sig. </s>

<s>Dottore avvisargli <lb></lb>com&#039;esso ha proposto al sig. </s>

<s>Principe Leopoldo il modo di chiarirsi se la <lb></lb>luce proceda in istante, come feci palese a V. S. nell&#039;ultima mia. </s>

<s>Ora non <lb></lb>può essere che in corte non se ne discorra, perciò è pregata avvisarci quello <lb></lb>che se ne dica. </s>

<s>Inoltre si è trovato chi ha opposto a questa esperienza con <lb></lb>dire che, movendosi il sole, vengono ancora a mutarsi gli angoli della ri­<lb></lb>flessione ” (MSS. Gal. </s>

<s>Disc., T. CXLIV, c. </s>

<s>101), e prosegue a dir come il <lb></lb>Borelli ovviasse alla difficoltà, applicando l&#039;<emph type="italics"></emph>Eliostata.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il Rinaldini, per non rimanere indietro a&#039;suoi Colleghi, usciva anch&#039;egli, <lb></lb>nel Novembre di quell&#039;anno 1657, a proporre un nuovo modo d&#039;esperimen­<lb></lb>tare il moto della luce, e se si potesse intendere in che maniera egli voleva <lb></lb>praticare quel suo mulinello, si direbbe che forse egli era men lontano degli <lb></lb>altri dal conseguire l&#039;intento desiderato, prevenendo il metodo delle ecclissi <lb></lb>attraverso ai fusi di una lanterna velocissimamente girata attorno, e ritro­<lb></lb>vata efficace da alcuni fisici moderni: “ Finirò, scriveva di Pisa al principe <lb></lb>Leopoldo, quell&#039;esperienza della velocità del vento incominciata, così subito <lb></lb>che il tempo lo permetta, e che sia venuto il bindolo somigliante a quello <lb></lb>del Sereniss. </s>

<s>Granduca, del quale mi vorrei parimente servire nell&#039;esperi­<lb></lb>mentare se il lume si diffonda in tempo oppure in istante ” (Fabbroni, <lb></lb>Lett. </s>

<s>ecc., T. I, pag. </s>

<s>186). </s></p><p type="main">

<s>O sia stata o no messa ad effetto, non poteva nemmen questa espe­<lb></lb>rienza del Rinaldini decider nulla in proposito, persuasi com&#039;erano tutti al­<lb></lb>lora che la velocità della luce non dovesse tanto sproporzionatamente ecce­<lb></lb>dere quella del suono. </s>

<s>Ma il Viviani non poteva darsi pace che fossero gli altri <lb></lb>metodi, per quanto ingegnosi, migliori di quel primo proposto da Galileo, e <lb></lb>ne attribuiva l&#039;inefficacia alle troppo brevi distanze, tra le quali s&#039;era fino al­<lb></lb>lora sperimentato. </s>

<s>Perciò, nell&#039;occasione ch&#039;egli ebbe d&#039;andare a Pistoia, per <lb></lb>servigio del Granduca “ la mattina de&#039;14 Luglio 1663 si pensò di valersi <lb></lb>di quella congiuntura per fare una prova se, nella distanza di 20 miglia <lb></lb>qual&#039;è da Firenze a Pistoia, di notte si scoprisse un fuoco, di qual grandezza <lb></lb>e qual sorta di fuoco più chiaramente si distinguesse, tutto affine di servirsi <lb></lb>di quei luoghi che in quella lontananza si fossero potuti vedere, per far <lb></lb>l&#039;esperienza del movimento della luce ” (Targioni, cit., T. II, P. II, pag. </s>

<s>587). </s></p><p type="main">

<s>Fatta questa prova, la sera di quel medesimo giorno, il Viviani sul Ma­<lb></lb>schio della fortezza di Pistoia, e il Magalotti sul campanile del Duomo di <lb></lb>Firenze, aiutati, per la più chiara vista de&#039;lumi, da Canocchiali, eseguirono <lb></lb>l&#039;esperienza di Galileo, e com&#039;era da aspettarsi non fu possibile nemmen <lb></lb>di qui decider nulla di certo, così per essere la distanza creduta dagli spe­<lb></lb>rimentatori notabile, invece minima, e per le difficoltà trovate nella puntua­<lb></lb>lità delle osservazioni. </s></p><pb xlink:href="020/01/602.jpg" pagenum="45"></pb><p type="main">

<s>Così, dopo tanto laborioso cimento, rimaneva l&#039;Ottica tuttavia incerta <lb></lb>della velocità della luce. </s>

<s>Nulladimeno i vecchi e i nuovi Aristotelici, vogliam <lb></lb>dire i Peripatetici e i Cartesiani con molti altri sedotti dalle astratte specu­<lb></lb>lazioni di alcuni Filosofi, come da quelle del Patrizio, attribuendo alla luce <lb></lb>o una accidentalità senza sostanza o una natura partecipante di qualità spi­<lb></lb>rituali, non dubitaron di credere che fosse quel della luce un moto in istante. </s>

<s><lb></lb>Alcuni altri però più savi ben persuasi dover ciò che agisce sui sensi esser <lb></lb>sostanza, e sostanza corporea, ne inferivano per legittima conclusione che <lb></lb>movendosi la luce da luogo a luogo non può non muoversi con qualche, <lb></lb>e sia pure insensibile, misura di tempo. </s>

<s>“ Lumen, ragionava il Grimaldi, <lb></lb>utpote sensibile, non est quid spirituale, sed est aliquid corporeum: ergo <lb></lb>iuxta leges omnium corporum vel corporeorum, non potest per vires natu­<lb></lb>rae esse de novo ubi non producitur, nisi illuc transferatur per motum lo­<lb></lb>calem, relinquendo seilicet unum locum et transeundo in alium ” (De lu­<lb></lb>mine ecc., Bononiae 1665, pag. </s>

<s>153). </s></p><p type="main">

<s>Da simili principii era stato condotto qualche anno prima ad affermare <lb></lb>la medesima conclusione il Fermat, il quale, nella controversia coi Carte­<lb></lb>siani, diceva che potevan bene negare il moto successivo nella luce, ma es­<lb></lb>sendo costretti in ogni modo ad ammettere <emph type="italics"></emph>aut facilitas aut fuga aut re­<lb></lb>sistentia maior aut minor, prout media variant,<emph.end type="italics"></emph.end> venivano a conceder di <lb></lb>fatto alla stessa luce quel che apparentemente le negavano colle parole. <lb></lb>(Descartes, Epistolae, P. III, Francof. </s>

<s>1692, pag. </s>

<s>132). </s></p><p type="main">

<s>Notabile che il Grimaldi chiamava <emph type="italics"></emph>intrepida<emph.end type="italics"></emph.end> quella sua asserzione. <lb></lb></s>

<s>“ Ergo intrepide asseri potest lumen spargi cum tempore, quod multi vel <lb></lb>non audent prae nimium meticulosa cautione, vel non examinant securitate <lb></lb>nimia confisi quod supponi potius id debeat, quam in dubium ab ullo unquam <lb></lb>revocari ” (Op. </s>

<s>cit., pag. </s>

<s>158). Se però volevaci intrepidezza per un gesuita <lb></lb>a professare quella opinione, non minore intrepidezza richiedevasi a un Pe­<lb></lb>ripatetico, il quale erasi già francato da quella meticolosa cauzione quasi un <lb></lb>secolo avanti, quando a professar che la luce muovesi in tempo era lo stesso <lb></lb>che rovesciare all&#039;edifizio aristotelico una delle più solide parti del suo fon­<lb></lb>damento. </s>

<s>Lo Scaligero dunque, disputando nell&#039;articolo II della CCXCVIII <lb></lb>Esercitazione <emph type="italics"></emph>De Subtilitate<emph.end type="italics"></emph.end> “ An lucis motus sit in tempore ” così scriveva: </s></p><p type="main">

<s>“ Memini praeceptores meos in Secundo <emph type="italics"></emph>De Anima<emph.end type="italics"></emph.end> ex vetustis recen­<lb></lb>tioribusque philosophis, ad probandum repentinam lucis celeritatem identi­<lb></lb>dem id iactare: Lux in instanti fertur ab oriente in occidentem. </s>

<s>Quod ego <lb></lb>cum me neutiquam intelligere conquererer, nunquam eos adducere potui ut <lb></lb>me docerent. </s>

<s>Id namque nonnisi Solis motu percipi potest. </s>

<s>Solus enim autor <lb></lb>eiusmodi lucis est, quae ab oriente in occidentem ferri videtur. </s>

<s>At illius <lb></lb>fulgor quaenam spatia repente occupat? </s>

<s>Profecto nulla. </s>

<s>Nonne semper illu­<lb></lb>minari aiunt orbis huius semissem? </s>

<s>Quam illustrationem adeo sensim re­<lb></lb>pere atque procedere videmus, ut nihil ad hanc persuasionem. </s>

<s>Haud enim <lb></lb>aliter sibi succedit radius, atque id loci, quae ante se est subit ac capit, <lb></lb>quam si baculus esset circumactus. </s>

<s>An vero id ita fit ut idem radius qui <pb xlink:href="020/01/603.jpg" pagenum="46"></pb>est supra Romam, idem sit cum eo qui est, exempli gratia, supra Hispa­<lb></lb>lim, ut a Roma Hispalim motus sit? </s>

<s>Non est, sed perpetua successio alia <lb></lb>atque alia pars illius speciei progeneretur. </s>

<s>Quamobrem rectius quaesissent <lb></lb>illi: an sine tempore a corpore illo lucido demittatur in terras lumen. </s>

<s>Vi­<lb></lb>detur enim hoc argumento non illo, momentaneam illam deprehendi posse <lb></lb>motionem. </s>

<s>Et fortasse verum non est. </s>

<s>Non enim ab immaterialitate ductum <lb></lb>argumentum satis validum est. </s>

<s>Nam neque soni species, quae aeque imma­<lb></lb>terialis est, sine tempore defertur. </s>

<s>Dicent esse in moto aere tamquam in <lb></lb>subiecto. </s>

<s>Quid tum? </s>

<s>Etiam lux in aere est. </s>

<s>Quem tametsi non oporteat mo­<lb></lb>veri propter illius specici delationem, tamen quantitatem habet in dimen­<lb></lb>sionibus. </s>

<s>Omnino sane valde ambigua res est ” (Francof. </s>

<s>1592, pag. </s>

<s>873). </s></p><p type="main">

<s>Ma l&#039;ambiguità, dopo tante trepidazioni e dopo tanti affanni, fu tolta, <lb></lb>quando, a misurare i suoi rapidissimi passi, ebbe la luce a distendersi per <lb></lb>spazii sufficienti. </s>

<s>Verso il 1678, per opera specialmente del Cassini, erano <lb></lb>state ridotte quasi alla desiderata perfezione le tavole de&#039;moti delle Medicee <lb></lb>per uso della navigazione. </s>

<s>Il Roemer dava opera diligentissima in riscontrar <lb></lb>quelle Tavole con le osservazioni, e trovò che, quando la Terra restava op­<lb></lb>posta a Giove al di là del Sole, le ecclissi de&#039;circumgioviali avvenivano qual­<lb></lb>che minuto più tardi, che quando la Terra stessa rimanevasi apposta a Giove, <lb></lb>al di qua del Sole. </s>

<s>Gli balenò la felice idea che ciò provenisse dal dover nel <lb></lb>primo caso la luce percorrere tanto più lungo spazio, per rivelarsi all&#039;oc­<lb></lb>chio dell&#039;osservatore, quant&#039;era il diametrò dell&#039;orbe terrestre, e benchè il <lb></lb>gran Cassini e il Maraldi fossero entrati in qualche dubbio, se dovesse in­<lb></lb>vece attribuirsi il fatto alle ineguaglianze de&#039;moti, nonostante altri osserva­<lb></lb>tori confermarono la scoperta del Roemer, e il Bradley la incoronò dell&#039;altra <lb></lb>non meno insigne scoperta dell&#039;<emph type="italics"></emph>aberrazion della luce<emph.end type="italics"></emph.end> nelle stelle fisse. </s>

<s>Così <lb></lb>l&#039;Ottica potè, fra le sue più certe proposizioni, scrivere anche questa: “ Lu­<lb></lb>men propagatur spatio temporis, a corporibus lucidis, impenditque in tran­<lb></lb>situ suo de Sole in Terram ad septem circiter vel octo minuta ” (Newton <lb></lb>Optices, Lib. </s>

<s>II, P. III, prop. </s>

<s>XI, Patavii 1772, pag. </s>

<s>109). </s></p><p type="main">

<s><emph type="center"></emph>VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La grande scoperta roemeriana veniva a dar solidi fondamenti all&#039;Ot­<lb></lb>tica del Grimaldi e preparava a quella del Newton le vie de&#039;lieti e lunghi <lb></lb>progressi. </s>

<s>Ma intanto ella dava occasione d&#039;investigare in che modo si dif­<lb></lb>fondesse la luce. </s>

<s>L&#039;Aguilonio se n&#039;era spedito colla sua IV proposizione <lb></lb>“ Lumen temporis momento totam virtutis sphaeram complet ” (Optica cit., <lb></lb>pag. </s>

<s>374). Ma il Cartesio, e i cartesiani che con sì amorosa laboriosità ne <lb></lb>illustrarono le dottrine, fecero anche le teorie della diffusion della luce rien­<lb></lb>trare nell&#039;ordine generale del loro sistema. </s>

<s>La luce per essi è un moto pro­<lb></lb>pagatosi dal pulsare in metro di sistole e di diastole del corpo luminoso <pb xlink:href="020/01/604.jpg" pagenum="47"></pb>contro gli atomi del secondo elemento, i quali, essendo perfettissimamente <lb></lb>duri, fanno che quel moto si propaghi dal lucido all&#039;occhio senza alcun <lb></lb>tempo. </s>

<s>“ Lumen, dice il Cartesio, hoc est actionem qua sol aut aliud cor­<lb></lb>pus luminosum materiam quandam subtilissimam, quae in omnibus pellu­<lb></lb>cidis corporibus reperitur, propellit ” (Dioptr. </s>

<s>cit., pag. </s>

<s>61). </s></p><p type="main">

<s>Il Mersenno che fu il più operoso commentatore e banditore delle dot­<lb></lb>trine cartesiane, “ Omne lucidum, scriveva, dilatat se, tumescitque in molem <lb></lb>maiorem iterumque contrahit se, perpetuam habens systolem et diastolem ” <lb></lb>(Opticae, Lib. </s>

<s>VII, Parisiis 1644, pag. </s>

<s>568). </s></p><p type="main">

<s>Più particolarmente poi come si diffonda questo moto di sistole e di <lb></lb>diastole in che consiste il lume, lo descrive lo stesso Mersenno al modo se­<lb></lb>guente: “ Sit propositum lucidum corpus solare cuius centrum A (fig. </s>

<s>16) <lb></lb>semidiameter AB, cui circum scribatur orbis concentricus cuius crassities <lb></lb>BC.... Rursus orbi BC circumponatur orbis alius concentricus CD, et huic <lb></lb><figure id="id.020.01.604.1.jpg" xlink:href="020/01/604/1.jpg"></figure></s></p><p type="caption">

<s>Figura 16.<lb></lb>alter DE, et eodem modo quotcumque <lb></lb>alii, quilibet cuilibet aequalis Quoniam <lb></lb>ergo exteriores circumferentiae semper <lb></lb>maiores sunt interioribus, erunt reciproce <lb></lb>crassities interiorum orbium maiores <lb></lb>quam exteriorum, quare maior est BC, <lb></lb>quam CD, et CD quam DE. Quoniam, <lb></lb>iam, per primam, Sol dilatat se et tu­<lb></lb>mescit in molem maiorem, supponamus <lb></lb>solem in diastole, sive tumescentia, ae­<lb></lb>quare totam sphaeram cuius semidiame­<lb></lb>ter est AC: necesse ergo est ut medii <lb></lb>pars quae erat in orbe BC exeat in lo­<lb></lb>cum sibi aequalem proximum, nempe in <lb></lb>orbem CD, idque eodem tempore, nam <lb></lb>quo instante incipit motus a B versus C necesse est ut incipiat motus a C <lb></lb>versus D, et a D versus E, et ab E prorsum, quare si statuatur oculus in <lb></lb>qualibet distantia a sole puta in E, quo instante incipit Sol dilatare se in B, <lb></lb>eodem ferietur oculus in E unde propagabitur motus ad retinam et inde <lb></lb>per connatum retinae nervum opticum usque ad cerebrum ” (ibi, pag. </s>

<s>569). </s></p><p type="main">

<s>Da così fatte dottrine seguiva che il lume si cagionasse dall&#039;urto pro­<lb></lb>dotto sopra la retina e sopra il nervo ottico per l&#039;instancabile pulsare del <lb></lb>lucido, e con ciò venivasi a spiegar benissimo come nelle percussioni e ne­<lb></lb>gli urti violenti si produce il fosfeno. </s>

<s>“ Confirmatur autem etiam experien­<lb></lb>tia, eo quod in omni concussione cerebri, quo fit motus aliquis per nervum <lb></lb>opticum extrorsum, ut quando oculus percutitur, apparet lumen quoddam <lb></lb>ante oculos ” (pag. </s>

<s>570). </s></p><p type="main">

<s>Il fatto del fosfeno difficilmente spiegabile in altro modo, e l&#039;esistenza <lb></lb>di un etere più ponderoso dell&#039;aria, di che sentiva l&#039;Huyghens il bisogno <lb></lb>per ispiegar come mai due marmi rimangano adesi e l&#039;acqua si sostenga al <pb xlink:href="020/01/605.jpg" pagenum="48"></pb>di sopra del natural livello ne&#039;tubi collocati nel vuoto; disposero l&#039;ingegno <lb></lb>del grande Olandese ad accomodarsi all&#039;ipotesi del lucido che vibra ne&#039;moti <lb></lb>di sistole e di diastole, i quali moti si comunicano al circostante etere, che <lb></lb>diffondesi in onde sferiche, e percote la retina come si percote il timpano <lb></lb>dalle onde sonore. </s>

<s>L&#039;ipotesi, che in sostanza è la cartesiana, ridotta a mag­<lb></lb>gior proprietà matematica, e ripurgata dall&#039;errore della diffusione istanta­<lb></lb>nea, fu dall&#039;Huyghens pubblicata nel 1678 nel suo Trattato <emph type="italics"></emph>De la lumiere.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Qualunque si fosse l&#039;accoglienza che si fece a questa ipotesi, la quale, <lb></lb>per essersi originata da quella del loro maestro, allettava i Cartesiani, il <lb></lb>Newton v&#039;ebbe qualche difficoltà, e si mostrò inclinato a seguire un&#039;altra <lb></lb>ipotesi più semplice e più naturale. </s>

<s>Chi fa del grande Ottico inglese l&#039;Au­<lb></lb>tore di un sistema nuovo, in opposizione a quello delle onde eteree, non co­<lb></lb>nosce bene l&#039;indole di quell&#039;ingegno severo, il quale non posava le sue per­<lb></lb>suasioni altro che sopra la fermezza di fatti matematicamente dimostrati. </s>

<s>Egli <lb></lb>non rifiuta l&#039;ipotesi delle ondulazioni per preferire la sua della emissione, <lb></lb>ma questiona così dell&#039;una come dell&#039;altra e mostra che se a spiegare molti <lb></lb>fenomeni si porge docile quella, questa non si porge men docile a spiegarli <lb></lb>tutti con molto minori difficoltà, e con più naturalezza. </s>

<s>Tale, a chi medita <lb></lb>le XXXI Questioni apposte al III Libro dell&#039;Ottica, si rivela l&#039;indole del­<lb></lb>l&#039;Autore. </s></p><p type="main">

<s>Solo una cosa è risoluto il Newton di negare all&#039;Huyghens, ed è la <lb></lb>ponderosità dell&#039;etere, il quale indugerebbe e impedirebbe i liberi moti ai <lb></lb>pianeti e metterebbe il languore in ogni ordine naturale. </s>

<s>“ Quo itaque lo­<lb></lb>cus sit diuturnis et regularibus planetarum cometarumque motibus, omnino <lb></lb>necesse est ut spatia coelestia omni materia sint vacua.... Fluidum densum, <lb></lb>nullo modo utile esse potest ad explicanda phaenomena naturae.... Nihil <lb></lb>facere posset istuismodi fluidum nisi ut magnorum illorum corporum mo­<lb></lb>tus interturbaret, et retardaret efficeretque ut naturae ordo languesceret ” <lb></lb>(Quaestio XXVIII, ed. </s>

<s>cit., pag. </s>

<s>150). </s></p><p type="main">

<s>Se gli Ugeniani persistono in ammettere questa ponderosa densità del <lb></lb>fluido etereo, il Newton protesta di esser contro a loro, e rigettato questo <lb></lb>“ reiicientur simul hypotheses eae quibus lumen in pressu vel motu per <lb></lb>istiusmodi medium propagato consistere fingitur ” (ibi). Ma se si ammette <lb></lb>un etere constare “ ex particulis a se invicem recedere conantibus .... et eius <lb></lb>particulas longe tenuiores esse quam aeris, vel etiam luminis ” (Quaest. </s>

<s>XXI, <lb></lb>pag. </s>

<s>144) e allora dice il Newton potrebbero anche forse spiegarsi alcuni <lb></lb>fenomeni e fatti per via del vibrar di questo mezzo etereo. </s></p><p type="main">

<s>Si potrebbe dalle varie grandezze di queste vibrazioni, spiegar la va­<lb></lb>rietà de&#039;colori (quaest. </s>

<s>XIII) si potrebbe spiegare, come mai al buio com­<lb></lb>primendo il nostro occhio si veda quel cerchietto “ coloribus variegatum <lb></lb>eorum similibus qui in pluma caudae pavonis conspiciuntur ” (quaest. </s>

<s>XVI), <lb></lb>s&#039;intenderebbe come per le vibrazioni di questo sottilissimo mezzo etereo <lb></lb>si potesse il calore trasmettere e rendersi sensibile a un Termometro col­<lb></lb>locato nel vuoto (quest. </s>

<s>XVIII); si potrebbe altresì ammettere che questo <pb xlink:href="020/01/606.jpg" pagenum="49"></pb>mezzo etereo sia più raro intra i corpi densi del sole, delle stelle, de&#039;pia­<lb></lb>neti e delle comete, e che da questi corpi infino a&#039;più grandi intervalli, vada <lb></lb>a farsi via via sempre più denso, e così spiegare come mai que&#039;corpi cele­<lb></lb>sti gravitino l&#039;uno sopra l&#039;altro (quaestio XXI). </s></p><p type="main">

<s>Ma dopo avere ammesse tutte queste possibilità esce a dire in princi­<lb></lb>pio della Questione XXVIII: “ Annon errantes sunt, hypotheses illae omnes <lb></lb>quibus lumen in pressu quodam seu motu per medium fluidum propagato <lb></lb>consistere fingitur? </s>

<s>Nam in his omnibus hypothesibus phaenomena luminis <lb></lb>usque adhuc ita explicarunt Philosophi, ut ea ex novis quibusdam radiorum <lb></lb>modificationibus oriri posuerint. </s>

<s>Quae est opinio errans ” (pag. </s>

<s>148) di che <lb></lb>reca per principale esempio la spiegazione data dall&#039;Huyghens alla doppia <lb></lb>rifrangenza dello spato islandico, scoperta da Erasmo Bartholin, e per que­<lb></lb>sto giudica essere l&#039;opinione ugeniana, de&#039;due varii mezzi vibranti nel mede­<lb></lb>simo cristallo, erronea, perchè la rifrazione straordinaria nello stesso cristallo, <lb></lb>non dipende “ ex novis modificationibus, sed ex congenitis et immutabilibus <lb></lb>radiorum proprietatibus ” (ibi). </s></p><p type="main">

<s>Perciò, dimostrata l&#039;insufficienza delle pulsazioni eteree a spiegare il <lb></lb>fenomeno bartoliniano, apre la seguente Questione XXIX, così, benchè sotto <lb></lb>le solite modeste forme del dubbio: “ Annon radii luminis exigua sunt cor­<lb></lb>puscula a corporibus lucentibus emissa? </s>

<s>” (ibi, pag. </s>

<s>151). E con questa <lb></lb>ipotesi così naturale prosegue il Newton a dire potersi facilmente spiegare <lb></lb>le principali proprietà e i fenomeni della luce, imperocchè per la teoria de&#039;co­<lb></lb>lori, per esempio, niente altro più si richiede “ quam ut radii luminis sint <lb></lb>corpuscula diversis magnitudinibus, quorum quidem ea, quae sint minima, <lb></lb>colorem constituant violaceum, utique tenebrosissimum, et languidissimum <lb></lb>colorum .... reliqua autem, ut eorum quodque in magnitudinem excedit, <lb></lb>ita colores exhibeant fortiores et clariores ” (pag. </s>

<s>152). Per ispiegar le vi­<lb></lb>cende alternative della più facile riflessione e della più facile trasmissione <lb></lb>“ nihil aliud opus est, quam ut ii exigua sint corpuscula, quae vel attractione <lb></lb>sua, vel alia aliqua vi, vibrationes quasdam in medio, in quod agunt, exci­<lb></lb>tent, quae quidem vibrationes radiis celeriores existentes, praevertant eos <lb></lb>successive, et ita agitent, ut velocitatem ipsorum augeant, imminuantque al­<lb></lb>ternis, adeoque vices illas in ipsis generent ” (ibi). </s></p><p type="main">

<s>Quanto poi all&#039;inusitata rifrazione dello spato d&#039;Islanda, è verosimile, <lb></lb>dice il Newton, che ciò avvenga per qualche virtù attrattiva fra certi lati <lb></lb>de&#039;raggi e delle particelle del cristallo di rifrangenza; virtù da potersi in <lb></lb>qualche modo rassomigliare alla polarità magnetica. </s>

<s>“ Et quoniam crystal­<lb></lb>lus, ista vi sua, non agit in radios, nisi tum cum et radiorum latera inusi­<lb></lb>tatae refractionis altera, ad plagam istam crystalli sint conversa; apparet in <lb></lb>radiorum quoque lateribus illis inesse vim sive virtutem aliquam, quae cor­<lb></lb>respondeat vi isti quae est in crystallo, eo fere modo quo binorum magne­<lb></lb>tum poli sibi invicem respondent ” (ibi). </s></p><p type="main">

<s>L&#039;ipotesi della emissione venne per la sua naturalezza e per la grande <lb></lb>autorità, fatta più potente dalla modestia di Colui che la preferiva all&#039;altra <pb xlink:href="020/01/607.jpg" pagenum="50"></pb>ugeniana, seguìta da molti, ai quali sembrava di più che le scoperte del <lb></lb>Roemer e del Bradley fossero di quella ipotesi neutoniana la più eloquente <lb></lb>conferma. </s>

<s>Così, tra l&#039;opinione delle pulsazioni eteree e delle eiaculazioni della <lb></lb>sostanza luminosa, tergiversò e seguita tuttavia a tergiversare l&#039;Ottica: e ora <lb></lb>è bene vedere che cosa, in tal proposito di così grande importanza, se ne <lb></lb>pensasse particolarmente in Italia. </s></p><p type="main">

<s>Tommaso Cornelio, sulla fine del suo Proginnasma IV <emph type="italics"></emph>De sole<emph.end type="italics"></emph.end> dedicato <lb></lb>a Daniele Spinola, con lettera che ha la data del 1661, accingendosi a spie­<lb></lb>gar la natura della luce, scriveva: “ Longe autem falluntur qui censent lu­<lb></lb>men extra oculos existere, et quicquam tale esse, quale visu percipitur. </s>

<s><lb></lb>Enimvero nusquam alibi lumen est, quam in ipsomet videntis oculo. </s>

<s>Nam <lb></lb>gignitur illud ex motu appulsuque aetheris ad eam oculi partem, quae re­<lb></lb>ticulatam tunicam format, ubi spiritus externo et adventitio pulsu agitatus <lb></lb>luminis ideam menti percipiendam indipiscit ” (Neapoli 1688, pag. </s>

<s>150). </s></p><p type="main">

<s>E dopo aver confermata questa sua dottrina col fatto del fosfeno nel­<lb></lb>l&#039;occhio vellicato, o compresso. </s>

<s>“ Fit igitur, conclude, lumen ex motu aethe­<lb></lb>ris, seu subtilis materiae a lucido corpore per spatìa diaphana oculis com­<lb></lb>municato. </s>

<s>Ea enim est lucis natura ut perenni pulsu, et veluti systole quadam <lb></lb>atque diastole circumiectum aethera propellat ” (ibi, pag. </s>

<s>149). </s></p><p type="main">

<s>Si sente bene che non è in queste dottrine, professate dal Medico na­<lb></lb>poletano, nulla di originale, e sembrano anzi troppo fedelmente ritrarre il <lb></lb>senso e comporsi al suono delle sopra citate parole del Mersenno. </s>

<s>Il Cor­<lb></lb>nelio, insieme con gli altri suoi colleghi nell&#039;Accademia del Conclubet, con­<lb></lb>tro le più lodevoli intenzioni del Borelli e degli altri addetti all&#039;Accademia <lb></lb>dei Medici, cooperarono a introdurre il cartesianismo in Italia. </s></p><p type="main">

<s>Ben più italiano è nell&#039;ingegno il gesuita Grimaldi, che alcuni hanno <lb></lb>annoverato fra coloro, i quali professarono l&#039;ipotesi delle ondulazioni. </s>

<s>Ma le <lb></lb>ondulazioni grimaldiane, nel significato proprio in che le intese l&#039;Autore, <lb></lb>differiscono notabilmente da quelle dell&#039;Huyghens. </s>

<s>Il Nostro, riguardando la <lb></lb>luce diffondersi al modo comune de&#039;fluidi, come sarebbe l&#039;acqua, oltre al <lb></lb>moto locale vi considera un moto ondoso e d&#039;increspamento che l&#039;accom­<lb></lb>pagna nel suo viaggio, come quando per esempio si getta una pietra in un <lb></lb>fiume; in ciò differente, nella luce, dal moto ondoso nell&#039;acqua, in quanto <lb></lb>che questo affetta la figura circolare, e quello si estende solamente in lato <lb></lb>e si spiega per lo lungo. </s></p><p type="main">

<s>“ Sicut aqua in quam violenter immersus fuerit lapis, statim formatur <lb></lb>in tenues fluctus circulares, qui successive unus post alium magis ac ma­<lb></lb>gis dilatantur, nec cessant sic dilatari sibique succedere, quamvis aqua tota <lb></lb>cum illis deorsum fluat per alveum fluminis; ita in lumine agnoscenda est <lb></lb>similis agitatio undosa .... cum hoc tamen discrimine quod dilatatio illa <lb></lb>circulorum in aqua est motus aliquo modo sensibilis ob tarditatem suam, in <lb></lb>lumine autem fluitatio iam explicata de novo resultans est citissima, et per <lb></lb>motum insensibilem facta. </s>

<s>Praeterea motus ille in aqua fit per spatium valde <lb></lb>magnum et circulariter, si aqua fuerit stagnans, vel saltem in latum cum <pb xlink:href="020/01/608.jpg" pagenum="51"></pb>affectatione figurae circularis, si aqua fluat. </s>

<s>At in lumine agitatio praedicta <lb></lb>modicum se extendit in latum, et tota fere in longum se explicat ” (De <lb></lb>Lumine cit., pag. </s>

<s>197, 98). </s></p><p type="main">

<s>Ma l&#039;ipotesi delle ondulazioni al modo stesso che la speculava l&#039;Huy­<lb></lb>ghens, era stata insegnata e divulgata, in una delle modeste ma fiorenti <lb></lb>scuole italiane, qualche anno prima che l&#039;avesse fatta pubblicamente nota <lb></lb>il grande Ottico olandese. </s>

<s>Quella scuola erasi instituita in Bologna, sotto il <lb></lb>magistero di quel Geminiano Montanari, che vedemmo essere stato il primo <lb></lb>a dimostrare sperimentalmente la legge del decrescere, al successivo pro­<lb></lb>gredire delle distanze, l&#039;intensità luminosa. </s>

<s>Aveva appena l&#039;Accademico della <lb></lb>Traccia conclusa quella legge, che immediatamente così soggiunge: </s></p><p type="main">

<s>“ Tralascio di rifletter qui a un argomento ch&#039;io credo non sia stato <lb></lb>avvertito sinora da altri, contro quelli che vogliono che il lume sia una so­<lb></lb>stanza, la quale dal corpo luminoso, quasi in un istante si diffonda pel <lb></lb>mezzo, e con la sua presenza lo illumini, con l&#039;assenza lo lasci tenebroso, <lb></lb>perciocchè se ciò fosse, sarebbe d&#039;uopo che l&#039;intensioni dell&#039;illuminazione <lb></lb>seguitassero la proporzione de&#039;cubi delle distanze, non quella de&#039;quadrati <lb></lb>come fanno. </s>

<s>Conciossiachè, se una quantità di luce, quella per esempio che <lb></lb>esce da una fiamma di candela, basta per illuminare a una tale intensione <lb></lb>una sfera d&#039;un braccio di semidiametro, per una sfera di due braccia, che <lb></lb>è 8 volte più capace, vi vorrebbero 8 lumi, eppure bastano 4; per una di <lb></lb>tre braccia 27 lumi, per una di quattro braccia 64 lumi, e no nove e se­<lb></lb>dici come pure vediamo che bastano, cioè tanti di più, quanto è più grande <lb></lb>la superficie non già il corpo. </s>

<s>” </s></p><p type="main">

<s>L&#039;argomento del Montanari che è forse uno de&#039;più validi contro l&#039;ipo­<lb></lb>tesi dell&#039;emissione, conducendolo a concludere che la materia luminosa pro­<lb></lb>cede nel suo moto in superficie e non in corpo, così come si vede procedere <lb></lb>anche il suono, veniva a suggerirgli spontanea l&#039;ipotesi delle ondulazioni. </s>

<s><lb></lb>Soggiunge l&#039;Autore in fine delle parole sopra citate che di ciò avrebbe avuto <lb></lb>campo di discorrerne in altra occasione, e non avrà certo mancato quel­<lb></lb>l&#039;uomo così attivo e zelante in promuovere la scienza, di mantenere le sue <lb></lb>promesse, benchè, fra le disperse e numerose scritture di lui, non siamo <lb></lb>noi in grado di dire a&#039;nostri lettori in quali di quelle ci ciò particolarmente <lb></lb>facesse. </s>

<s>Ma che non mancasse il Montanari di diffondere nella sua scuola la <lb></lb>nuova ipotesi speculata, n&#039;abbiamo argomento, si potrebbe dir certo, in colui <lb></lb>che fu il più valoroso de&#039;discepoli usciti di lì, e che ritrae più al vivo, nel­<lb></lb>l&#039;ingegno e nelle dottrine, le qualità del suo insigne maestro. </s></p><p type="main">

<s>Domenico Guglielmini, nel suo libro <emph type="italics"></emph>De sanguinis natura,<emph.end type="italics"></emph.end> per confu­<lb></lb>tar l&#039;errore dell&#039;innata fiamma vitale, e per provar che il calore del sangue <lb></lb>può esser prodotto da tutt&#039;altre cause da quelle consuete d&#039;operare nelle <lb></lb>cucine, così scriveva: “ Quid enim impedit quominus undulationes iis si­<lb></lb>miles quae ab ignis agitatione proficiscuntur etiam ab aliis motibus aetheri <lb></lb>imprimantur? </s>

<s>An excitabitur in retina igniculus, cum presso exterius oculo <lb></lb>lucis scintillae videntur observari? </s>

<s>” (Venetiis 1701, pag. </s>

<s>92). </s></p><pb xlink:href="020/01/609.jpg" pagenum="52"></pb><p type="main">

<s>E nella Dissertazione <emph type="italics"></emph>De salibus,<emph.end type="italics"></emph.end> dop&#039;aver co&#039;principii idrostatici di­<lb></lb>mostrato che le particelle saline sciolte ne&#039;liquidi son così equilibrate, che <lb></lb>qualunque minima forza è capace di turbarle da quel loro riposo; assegna <lb></lb>fra queste minime forze anche l&#039;urto, che può una delle così fatte parti­<lb></lb>celle ricevere dall&#039;ondata eterea o dalla pulsazion della luce. </s>

<s>“ Cumque tales <lb></lb>potentiae motrices plures adsint, aether praeter fluens, <emph type="italics"></emph>lucis pressio<emph.end type="italics"></emph.end> et <lb></lb>praecipue calor .... ” (Venetiis 1705, pag. </s>

<s>98): e con ciò veniva alla scienza <lb></lb>la prima idea e il primo esempio di un <emph type="italics"></emph>Radiometro,<emph.end type="italics"></emph.end> misterioso strumento, <lb></lb>per cui fu creduto di render sensibile il moto, e il meccanico operar della <lb></lb>luce su gli altri corpi. </s></p><p type="main">

<s>Or perchè le recenti scoperte di nuove proprietà nella luce, le quali si <lb></lb>dice non potersi spiegare altrimenti che nell&#039;ipotesi delle ondulazioni, hanno <lb></lb>a quella ipotesi gli Ottici fatto grande onore, e così gran lode hanno dato <lb></lb>all&#039;Huyghens, che la speculò e la diffuse; sarebbe di non lieve importanza <lb></lb>l&#039;addurre altri documenti a confermare il fatto che quella ipotesi era pro­<lb></lb>fessata in Italia qualche anno prima, e indipendentemente dall&#039;insegnamento <lb></lb>di maestri stranieri. </s>

<s>Ma di troppo oramai abbiam trapassati i limiti, che dal­<lb></lb>l&#039;ampiezza de&#039;soggetti di questa storia ci sono prescritti. </s></p><pb xlink:href="020/01/610.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della luce rifratta<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle prime teorie speculate intorno alla natura delle rifrazioni, e de&#039;primi tentativi fatti per isco­<lb></lb>prirne le leggi. </s>

<s>— II. </s>

<s>Del Teorema dello Snellio e della legge diottrica indi formulatane dal Car­<lb></lb>tesio. </s>

<s>— III. </s>

<s>Della legge diottrica dimostrata dall&#039;Herigonio; del principio delle cause finali <lb></lb>introdotto in quella dimostrazione, e come il Newton ritornasse ai principii meccanici. </s>

<s>— <lb></lb>IV. </s>

<s>Della scienza delle rifrazioni in Italia. </s>

<s>— V. </s>

<s>Delle rifrazioni astronomiche. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La proprietà che ha la luce di rompere la dirittura del suo primo cam­<lb></lb>mino, quando entri da uno in un altro mezzo di varia densità, fu conosciuta <lb></lb>infino da&#039;più antichi Ottici, e non poteva non esser ciò facilmente avvertito <lb></lb>per la così frequente occorrenza de&#039;fatti naturali. </s>

<s>Euclide fu il primo a con­<lb></lb>fermare quella proprietà per mezzo dell&#039;esperienza, ch&#039;egli così descriveva <lb></lb>nel IV de&#039;<emph type="italics"></emph>Fenomeni<emph.end type="italics"></emph.end> premessi alla sua Prospettiva: “ Se si porrà qualsivo­<lb></lb>glia cosa nel fondo d&#039;un vaso, e poi si discosti tanto dall&#039;occhio che la cosa <lb></lb>già detta non si veda più, dico che tal cosa si potrà vedere in questo luogo <lb></lb>se il vaso si empierà d&#039;acqua.... Si vedrà per i raggi rotti che si rom­<lb></lb>pono nella superficie dell&#039;acqua, che prima per i raggi retti non si potea <lb></lb>vedere ” (Traduz. </s>

<s>di E. Danti, Fiorenza 1573, pag. </s>

<s>80). </s></p><p type="main">

<s>Tolomeo, Alhazeno e Vitellione, troppo ben conoscendo che il fatto del <lb></lb>rifrangersi la luce ne&#039;mezzi di varia densità <emph type="italics"></emph>plus experientiae instrumen­<lb></lb>torum innititur quam alteri demonstrationum<emph.end type="italics"></emph.end> (Persp. </s>

<s>Vitell. </s>

<s>cit., pag. </s>

<s>47 v.), <lb></lb>attesero a perfezionare quel semplice strumento euclideo, applicandovi un <lb></lb>cerchio graduato e discriminando il raggio così incidente come rifratto con <lb></lb>farlo passare attraverso a sottilissimi fori, i quali per sottilissime linee en-<pb xlink:href="020/01/611.jpg" pagenum="54"></pb>trando e procedendo dentro il mezzo refringente o acqua o vetro o altro <lb></lb>diafano, segnassero i gradi precisi degli angoli dell&#039;incidenza e della ri­<lb></lb>frazione. </s></p><p type="main">

<s>Così poteronsi strumentalmente dimostrare alcune diottriche proposi­<lb></lb>zioni, di cui le principali sono in Vitellione per tal modo formulate: “ Per <lb></lb>medium secundi diafoni densioris primo radius perpendicularis ductus a cen­<lb></lb>tro corporis luminosi super superficiem obiecti corporis, semper penetrat ir­<lb></lb>refractus ” (Lib. </s>

<s>II, prop. </s>

<s>XLII). — “ Radio perpendiculari omne corpus <lb></lb>diafonum penetrante, radius oblique incidens in medio secundi diafoni den­<lb></lb>sioris refringitur ad perpendicularem ductam a puncto incidentiae super se­<lb></lb>cundi diaphoni superficiem, et in medio secundi diafoni rarioris refringitur <lb></lb>ab eadem ” (Lib II, prop. </s>

<s>XLVII). </s></p><p type="main">

<s>Ma perchè il fatto per sè stesso non costituisce la scienza, ufficio della <lb></lb>quale è rendere la ragione del fatto, si domandava a Vitellione: perchè mai <lb></lb>il raggio perpendicolare procede irrefratto, e perchè mai il raggio obliquo, <lb></lb>avendo a penetrare un mezzo più denso, si accosta più d&#039;appresso alla per­<lb></lb>pendicolare? </s>

<s>E il gran Maestro della Prospettiva rispondeva che le linee <lb></lb>perpendicolari son le più forti di tutte <emph type="italics"></emph>quoniam coadunantur virtute uni­<lb></lb>versali coelesti secundum lineam rectam brevissimam, omni subiecto cor­<lb></lb>pori influente<emph.end type="italics"></emph.end> (Editio cit., pag. </s>

<s>31 v.). Di più si osserva, soggiunge Vitel­<lb></lb>lione, che in tutti i moti, tanto son le percussioni oblique più forti quanto <lb></lb>più si avvicinano alla perpendicolare, la quale è la fortissima di tutte. </s>

<s>Ora <lb></lb>la luce è un corpo in velocissimo moto a cui resiste più o meno la crassi­<lb></lb>zie del diafano, e perciò, a rifarsi del danno ricevuto si studia la luce di <lb></lb>deviare dalla sua obliquità, accostandosi alla fortezza della perpendicolare. </s></p><p type="main">

<s>Si vede bene come qui la ragione, piuttosto che dalla scienza è sug­<lb></lb>gerita dalla poesia, la quale è così, dal nostro Varchi fiorentino, molto più <lb></lb>gentilmente infiorata che non dal ruvido ottico di Polonia. </s>

<s>“ Tutti i razzi <lb></lb>che sono intorno a quella linea forte e perpendicolare che si chiama lo asse, <lb></lb>i quali erano prima diffusi e disgregati, essendo in un mezzo rado, si con­<lb></lb>gregano ed uniscono insieme d&#039;intorno allo asse per essere più forti e più <lb></lb>possenti, dovendo passare e penetrare un mezzo più denso, e questo si chiama <lb></lb>perfrangersi alla perpendicolare, e di qui è detto cotal razzo, non altrimenti <lb></lb>quasi che uno esercito, il quale lontano dal nemico e per paese sicuro va <lb></lb>sparso e vagabondo, ma vicino al nemico e per paese sospetto si restringe <lb></lb>ed unisce insieme d&#039;intorno al suo asse, cioè, al capitano ” (Lezioni cit., <lb></lb>pag. </s>

<s>301). </s></p><p type="main">

<s>Nè men fragranti fiori di poesia sa spargere sopra questo sentiero di <lb></lb>luce nel Trattato suo <emph type="italics"></emph>De visione<emph.end type="italics"></emph.end> il Fabrizi d&#039;Acquapendente. </s>

<s>“ Optima vero <lb></lb>ratione accidit in prima refractione quae apparet luce per secundum me­<lb></lb>dium crassius pertranseunte omnes obliquos radios ad perpendicularem frangi <lb></lb>et ad eam accedere. </s>

<s>Quoniam cum crassius diaphanum lucis liberum tran­<lb></lb>situm haberet, propter suam opacitatem, evenit ut lux libere recteque ut <lb></lb>prius non amplius possit permeare, sed mutationem aliquam subeat, quae <pb xlink:href="020/01/612.jpg" pagenum="55"></pb>sane mutatio nulla alia est, quam inclinatio seu accesio seu refugium lucis <lb></lb>veluti ad arcem, et ad id quod potest ipsam roborare ac proinde tueri et <lb></lb>conservare. </s>

<s>Haec autem arx est radius seu linea perpendicularis, quae uti <lb></lb>dictum est quocumque progrediatur robustissima et irrefracta progreditur. </s>

<s><lb></lb>Contra accidit cum lux e denso in rarius diaphanum permeat. </s>

<s>Siquidem, <lb></lb>cum inveniat minorem diaphani resistentiam merito a perpendiculari rece­<lb></lb>dit, tamquam eius auxilio non amplius pro sui conservatione indigens ” (Ve­<lb></lb>netiis 1600, pag. </s>

<s>70). </s></p><p type="main">

<s>A rimproverar la scienza scesa a fanciulleggiare così tra i fiori della <lb></lb>poesia insorse con gran severità il Keplero “ quasi lucis species mente prae­<lb></lb>dita esset, qua et densitatem medii et suum damnum aextimaret et proprio <lb></lb>arbitratu non extranea vi agendo, non patiendo sese ipsam infringeret ” <lb></lb>(Paralip. </s>

<s>cit., pag. </s>

<s>84). Ma egli aveva notato però fra le leggerezze di Vi­<lb></lb>tellione <emph type="italics"></emph>nescio quid subtile,<emph.end type="italics"></emph.end> una sottigliezza di grande importanza ai pro­<lb></lb>gressi dell&#039;Ottica, la quale consiste nell&#039;applicare al moto della luce il prin­<lb></lb>cipio meccanico della composizione delle forze. </s></p><p type="main">

<s>Sia AC (fig. </s>

<s>17) un raggio, che obliquamente discende, e nel punto C <lb></lb><figure id="id.020.01.612.1.jpg" xlink:href="020/01/612/1.jpg"></figure></s></p><p type="caption">

<s>Figura 17.<lb></lb>incontra la superfice BE di un dia­<lb></lb>fano di varia densità da quello per <lb></lb>cui egli è venuto, fuori del qual caso <lb></lb>procederebbe per la linea CQ a di­<lb></lb>ritto. </s>

<s>Conducasi nel punto C la GH <lb></lb>perpendicolare a BE. “ Motus radii <lb></lb>incidentis oblique secundum lineam <lb></lb>AC, dice Vitellione, componitur ex <lb></lb>motu in partem perpendicularis CG <lb></lb>et ex motu facto super lineam quae <lb></lb>est perpendicularis super lineam CG ” <lb></lb>(Perspectiva cit., pag. </s>

<s>52). O altri­<lb></lb>menti essendo l&#039;atomo lucido C spinto <lb></lb>per la direzione CE e per la direzione <lb></lb>CG, nè potendo ubbidire nello stesso <lb></lb>tempo all&#039;uno impulso e all&#039;altro, prenderà una via di mezzo, e secondo il <lb></lb>bisogno o si accosterà di più a CG o si accosterà di più a CE. </s>

<s>Il bisogno poi <lb></lb>sarà dichiarato dalla natura del diafano, il quale se è più denso di quello da <lb></lb>cui il raggio è venuto, e allora avendo bisogno di maggior fortezza, per su­<lb></lb>perare l&#039;impedimento, il raggio stesso si accosterà alla linea CG perpendi­<lb></lb>colare: cessando poi questo bisogno, per essere il diafano più raro, si farà <lb></lb>invece l&#039;accostamento alla linea CE, e insomma il raggio rifratto ne&#039;due casi <lb></lb>diversi o sarà CI, o sarà CK. </s></p><p type="main">

<s>Ma pur nemmeno procedendo per questa via non s&#039;evitava quel fan­<lb></lb>tastico supposto che attribuiva alla luce un senso d&#039;andare a cercar presso <lb></lb>alla perpendicolare il rifugio e il conforto alla sua debolezza. </s>

<s>Perciò il Ke­<lb></lb>plero si studiava, così ragionando altrimenti, di giungere alla medesima con-<pb xlink:href="020/01/613.jpg" pagenum="56"></pb>clusione. </s>

<s>Il moto è causa della dispersion della luce: argomento poi di tal <lb></lb>dispersione è l&#039;incidenza obliqua, ond&#039;è che tra il moto retto e lo stesso <lb></lb>obliquo intercede sempre l&#039;angolo, dentro cui si contermina la luce dispersa. </s>

<s><lb></lb>Suppongasi ora esser quel raggio obliquo AB (fig. </s>

<s>18) il moto retto AC, e <lb></lb>BAC l&#039;angolo ora detto. </s>

<s>Incontri il moto della dispersione la superficie BC <lb></lb>del mezzo diafano più denso. </s>

<s>Se non facesse questo mezzo nessuno impedi­<lb></lb>mento alla dispersione, proseguendo in D e in E, occuperebbe tutto lo spa­<lb></lb><figure id="id.020.01.613.1.jpg" xlink:href="020/01/613/1.jpg"></figure></s></p><p type="caption">

<s>Figura 18.<lb></lb>zio DE: se poi impedisse affatto quella stessa disper­<lb></lb>sione lo spazio occupato sarebbe FE uguale a BC. </s>

<s>Ma <lb></lb>non essendo nè libera nè assolutamente quella disper­<lb></lb>sione impedita, sarà lo spazio occupato qualche cosa <lb></lb>di mezzo fra DE ed FE, per esempio EG. “ Lux igitur <lb></lb>sine ulla dispersione usque ad ED veniens, occuparet <lb></lb>spatium EF; eadem, sine ulla perturbatione eousque <lb></lb>descendens, occuparet spatium ED, spargens et exte­<lb></lb>nuans se eadem proportione. </s>

<s>Ergo cum intervenit me­<lb></lb>dium BC densius id dispersionem impediens facit ut <lb></lb>lux medium spatium occupet inter EF et ED. </s>

<s>Sit illud <lb></lb>EG. </s>

<s>Radius ergo AB refringitur in B et infra super­<lb></lb>ficiem densioris medii fiet BG accedens ad perpendicularem BF ” (Paralip. </s>

<s><lb></lb>ad Vitell., Francof. </s>

<s>1604, pag. </s>

<s>16). </s></p><p type="main">

<s>Benchè questa nuova argomentazione cessasse in qualche modo i difetti, <lb></lb>in ch&#039;erano incorsi gli Ottici suoi predecessori, conosceva nonostante bene <lb></lb>il Keplero com&#039;ella fosse tuttavia lontana da quella severità matematica, che <lb></lb>si sarebbe desiderata. </s>

<s>Quel <emph type="italics"></emph>nescio quid subtile<emph.end type="italics"></emph.end> della composizione del moto <lb></lb>si rappresentava dall&#039;altra parte per l&#039;unica via geometrica da potersi se­<lb></lb>guire con sicurezza, ma bisognava maneggiar l&#039;argomento in altro modo da <lb></lb>quel che avean fatto Alhazeno e Vitellione, senza mescolarvi cioè il princi­<lb></lb>pio delle cause intenzionali. </s>

<s>Giacchè dunque conveniva non deviar dalle leggi <lb></lb>della Meccanica, il Keplero rassomiglia la luce a un proiettile, per esempio <lb></lb>a un globo gettato nell&#039;acqua. </s>

<s>Avviene perciò, egli dice, nel lume quel che <lb></lb>ne&#039;mobili fisici, “ quoties globus in aquam torquetur, dummodo subeat <lb></lb>aquam. </s>

<s>Patet sic; liceat enim hic mihi verba Opticorum contra mentem <lb></lb>ipsorum usurpare et in meliorem sensum adducere: Sit BC (nella figura <lb></lb>preced.) aqua. </s>

<s>AB motus sphaerulae. </s>

<s>Continuetur BC in H et FB in I. </s>

<s>Cum <lb></lb>ergo motus sphaerulae AB sit quodammodo compositus ex IB in BH, acci­<lb></lb>det etiam, ut resistat illi tam profunditas BF, quam BH crassities lateralis. </s>

<s><lb></lb>Prius impedimentum tardiorem efficit eius descensum et retundit, dummodo <lb></lb>descendat. </s>

<s>Posterius vero repellit ipsam a sua linea, ut quia motus erat BD <lb></lb>futurus repellatur a BH et fiat BG ” (ibi). Supposto che la luce non pati­<lb></lb>sca altra attenuazione che <emph type="italics"></emph>in latum<emph.end type="italics"></emph.end> e non dalla parte della rettitudine ma <lb></lb>dell&#039;obliquità, il simile che ne&#039;proietti dice il Keplero avvenir nella luce, <lb></lb>ond&#039;è che il moto di lei non riceve impedimento dalla parte BC, ma dalla <lb></lb>parte BH. “ Ergo superficies ex parte BH resistit hinc motui existitque <pb xlink:href="020/01/614.jpg" pagenum="57"></pb>hinc quasi quaedam reflexio AB in BG plane similis illis quae fiunt in cor­<lb></lb>poribus naturalibus proiectis ” (ibi, pag. </s>

<s>17). </s></p><p type="main">

<s>Chiunque però sìa più largo di concessioni al Keplero non gli potrà mai <lb></lb>concedere che avvenga nella luce quel che nel globo gettato nell&#039;acqua, es­<lb></lb>sendo che questo si allontana dalla perpendicolare e quella invece se le av­<lb></lb>vicina. </s>

<s>Sia stato l&#039;Autore condotto ad ammetter quella similitudine per di­<lb></lb>fetto di osservazione, o per aver supposto che l&#039;impedimento al moto, così <lb></lb>nella luce come nel proietto, non sia fatto altro che dalla superficie del <lb></lb>mezzo; è notabile che prima del Matematico alemanno l&#039;Acquapendente ras­<lb></lb>somigliasse le ottiche rifrazioni alle meccaniche, asserendo anch&#039;egli che si <lb></lb>facevano ambedue nel medesimo verso. </s>

<s>“ Nam globulus in aere cum sit et <lb></lb>extra aquam et in aquam intret, ad perpendiculum refrangetur et accedet ” <lb></lb>(De Vis. </s>

<s>cit., pag. </s>

<s>71). </s></p><p type="main">

<s>Nel Keplero però s&#039;intende com&#039;egli ammette che il globo pieghi alla <lb></lb>perpendicolare, concessagli l&#039;ipotesi che l&#039;urto si faccia in un punto solo <lb></lb>della superficie qual sarebbe per esempio B, nella precedente figura, e che <lb></lb>perciò non sia la rifrazione, com&#039;egli professa, altro che un caso particolare <lb></lb>di riflessione. </s>

<s>Ciò dall&#039;altra parte è conforme all&#039;esperienza, perchè, se il <lb></lb>diafano non impedisce il moto altro che nella superficie, si può BC riguardar <lb></lb>come un piano resistente, e B come un punto del suo orlo, contro il quale <lb></lb>urtando una palla nella direzione AB, nel punto B veramente si piega verso <lb></lb>la perpendicolare. </s>

<s>Ma non s&#039;intende in ogni modo come si concilii questa <lb></lb>ipotesi del Keplero con quell&#039;altra da lui medesimo espressa, la quale è che <lb></lb>il globo <emph type="italics"></emph>subeat aquam,<emph.end type="italics"></emph.end> nel qual caso il supposto stesso è manifestamento <lb></lb>contrario a ciò che si vede avvenire di fatto. </s></p><p type="main">

<s>Comunque sia, eran tali quali le abbiamo esposte fin qui, le ragioni <lb></lb>che specularono gli Ottici da Vitellione al Keplero intorno ai raggi rifratti. </s>

<s><lb></lb>In quelle ragioni, se fossero state vere, ci si doveva trovare compresa la <lb></lb>legge delle relazioni che passano fra gli angoli dell&#039;incidenza e quelli della <lb></lb>rifrazione, ma perchè oramai era l&#039;Ottica esperta, per l&#039;esempio delle rifles­<lb></lb>sioni non potersi in ciò far altro fondamento che dell&#039;esperienza, all&#039;espe­<lb></lb>rienza si rivolsero Alhazeno e Vitellione. </s>

<s>Trovarono che crescendo o sce­<lb></lb>mando gli angoli dell&#039;inclinazione, gli angoli rifratti non rispondevano in <lb></lb>esatta ragione geometrica, e si assicurarono che il poter rifrangente variava <lb></lb>dall&#039;acqua al vetro. </s>

<s>Costrussero di questi loro resultati sperimentali alcune <lb></lb>Tavole che Vitellione impresse nel libro X Della Prospettiva al Teorema VIII, <lb></lb>in cui “ Anguli omnium refractionum per Tabulas declarantur ” (Edit. </s>

<s>cit., <lb></lb>pag. </s>

<s>257). </s></p><p type="main">

<s>Qualunque sia l&#039;esattezza di queste Tavole, il Maurolico ebbe torto a <lb></lb>non farne nessun conto, formulando il suo X Teorema <emph type="italics"></emph>Diaphanorum:<emph.end type="italics"></emph.end> “ An­<lb></lb>guli inclinationum sunt fractionum angulis proportionales ” (Neapoli 1611, <lb></lb>pag. </s>

<s>35). L&#039;indice di rifrazione per le sfere cristalline lo ritrovò otto terzi, <lb></lb>e tale egli stimava esser l&#039;indice, senza differenza, di tutti gli altri mezzi <lb></lb>refringenti. </s>

<s>“ Ergo et angulus inclinationis ad angulum suae fractionis sem-<pb xlink:href="020/01/615.jpg" pagenum="58"></pb>per unam servat rationem estque dupla et duas tertias superpatiens, sicut <lb></lb>experimento in crystallina sphaera probabimus ” (ibi, pag. </s>

<s>36). </s></p><p type="main">

<s>Però il nostro Ottico siciliano fu nelle applicazioni diottriche molto più <lb></lb>esatto dell&#039;Arabo e del Pollacco, come si par comparando i Teoremi XVIII <lb></lb>e XXIII dei <emph type="italics"></emph>Diaphanorum Partes<emph.end type="italics"></emph.end> colla proposizione XIV del libro X di <lb></lb>Prospettiva. </s>

<s>In questa proponevasi Vitellione di dimostrare che quanto il <lb></lb>raggio è più obliquo tanto più crescono gli effetti delle rifrazioni. </s>

<s>“ Omnium <lb></lb>formarum punctorum rei visae plus distantium a linea perpendiculari, ducta <lb></lb>a centro visus super superficiem corporis diafoni a qua fit refractio, maior <lb></lb>est refractio quam punctorum minus distantium ab illa ” (Edit. </s>

<s>cit., pag. </s>

<s>259). </s></p><p type="main">

<s>Il Teorema propostosi a dimostrar qui da Vitellione si capisce bene <lb></lb>com&#039;è il capitale della Diottrica, ma il Porta fu il primo a notar che l&#039;Au­<lb></lb>tore in dimostrar quel suo assunto dava nel falso. </s>

<s>La proposizione VIII del <lb></lb>Lib. </s>

<s>I <emph type="italics"></emph>De refractione<emph.end type="italics"></emph.end> è dal nostro Ottico napoletano formulata così in modo <lb></lb>simile all&#039;Ottico pollacco. </s>

<s>“ Res sub aquis refracta visa, quo magis ab oculo <lb></lb>distat, eo sublimior videtur ” (Neapoli 1593, pag. </s>

<s>16). Sia FBEK (fig. </s>

<s>19) <lb></lb><figure id="id.020.01.615.1.jpg" xlink:href="020/01/615/1.jpg"></figure></s></p><p type="caption">

<s>Figura 19.<lb></lb>un vaso pien d&#039;acqua sul <lb></lb>fondo del quale giacciano <lb></lb>ad ugual distanza gli og­<lb></lb>getti C, D, E: dopo aver <lb></lb>dimostrato che maggior <lb></lb>rifrazione subisce il punto <lb></lb>E del punto D, e il punto <lb></lb>D maggiore del punto C, <lb></lb>il Porta soggiunge: “ Sed <lb></lb>Vitellio in hoc falsus est <lb></lb>quod etsi aequaliter inter <lb></lb>se distent in fundo iacentia colorata C, D, E, non ob id aequaliter distant <lb></lb>in aquae summo puncta refractionum G, T, I ” (ibi, pag. </s>

<s>17). </s></p><p type="main">

<s>L&#039;osservazione è notabile, perchè di qui ebbero principio i progressi <lb></lb>alla scienza delle rifrazioni. </s>

<s>Venne poi il Keplero, il quale confermando la <lb></lb><figure id="id.020.01.615.2.jpg" xlink:href="020/01/615/2.jpg"></figure></s></p><p type="caption">

<s>Figura 20.<lb></lb>XIV del X di Vitellione esser <emph type="italics"></emph>vitiose et <lb></lb>obscure demonstrata,<emph.end type="italics"></emph.end> pensò che fosse <lb></lb>da tentare altra via. </s>

<s>Considerava che <lb></lb>tutto il fatto dipende dall&#039;obliquità del­<lb></lb>l&#039;incidenza, e che sempre l&#039;angolo della <lb></lb>dispersione cresce in ragion di quella <lb></lb>obliquità. </s>

<s>“ Hinc corollarium: si medium <lb></lb>ipsum causa suae densitatis considera­<lb></lb>tur solitarie, anguli refractionum pro­<lb></lb>portionales fierent angulis incidentiae ” <lb></lb>(Paralip. </s>

<s>ad Vitell. </s>

<s>cit., pag. </s>

<s>110). </s></p><p type="main">

<s>Ma è inoltre da considerare, proseguiva nel suo ragionamento il Ke­<lb></lb>plero, anche il raggio in sè stesso, il quale patisce, nel mezzo ch&#039;egli in-<pb xlink:href="020/01/616.jpg" pagenum="59"></pb>contra, tanto maggior resistenza, quanto vi scende sopra più obliquo. </s>

<s>Ciò <lb></lb>si dimostra dall&#039;Autore nel modo seguente: “ Sit A (fig. </s>

<s>20) lux, BC me­<lb></lb>dium densius, AB, KM paralleli vel quasi ex sole: distantia eorum in per­<lb></lb>pendiculari ML. </s>

<s>Cum igitur BLM rectus sit, et LBM ponatur obliquus, acutus <lb></lb>erit, igitur LBM minor quam BLM et LM latus minori angulo B oppositum, <lb></lb>minus erit BM latere, quod maiori angulo L opponitur. </s>

<s>Sed LM metitur la­<lb></lb>titudinem medii occurrentis luci recte illapsae, quia BLM est rectus, BM vero <lb></lb>latitudinem occurrentis luci ex obliquo; plus igitur densitatis est in BM, quam <lb></lb>in LM. </s>

<s>Maior igitur resistentia hoc respectu ” (ibi, pag. </s>

<s>111). </s></p><p type="main">

<s>Di qui ne concludeva il Keplero che la resistenza, opposta dalla densità <lb></lb>del mezzo all&#039;obliquità via via crescente del raggio, è proporzionale alla se­<lb></lb>cante BM. Ond&#039;è che, parte dell&#039;angolo di refrazione, cresce colla semplice <lb></lb>incidenza, parte cresce in proporzion maggiore della semplice incidenza; dun­<lb></lb>que anche tutto l&#039;angolo crescerà con maggiori incrementi della semplice <lb></lb>obliquità dell&#039;incidenza. </s>

<s>“ Ergo pars anguli refractionum proportionatur in­<lb></lb>cidentiis, pars maioribus rationis incrementis crescit. </s>

<s>Totus igitur angulus <lb></lb>maioribus incrementis crescit ” (ibi, pag. </s>

<s>111). </s></p><p type="main">

<s>Così veniva la Diottrica a ripigliare il vantaggio su quei regressi, verso <lb></lb>cui era stata sospinta pel Teorema X del Maurolico sopra citato. </s>

<s>Ma pur <lb></lb>conveniva determinare secondo qual precisa proporzione si facessero quegli <lb></lb>incrementi maggiori dagli angoli di refrazione, sopra quelli dell&#039;incidenza. <lb></lb></s>

<s>“ Non intentatum nec hoc, dice il Keplero, reliqui utrum semel constituta <lb></lb>horizontali refractione ex densitate medii, caeterae sinubus distantiarum a <lb></lb>vertice responderent. </s>

<s>Sed nec calculus id approbavit, nec sane opus erat <lb></lb>inquirere, nam eadem forma crescerent refractiones in omnibus mediis quod <lb></lb>repugnat experientiae (ibi, pag. </s>

<s>84). Rursum quaesivi .... an ascendant <lb></lb>imagines in proportione sinuum inclinationum: minime; nam eadem ratio <lb></lb>esset ascensus in omnibus mediis ” (ibi, pag. </s>

<s>89). </s></p><p type="main">

<s>In quello stesso anno 1611 il De Dominis pubblicava il suo celebre <lb></lb>Trattato <emph type="italics"></emph>De radiis visus et lucis,<emph.end type="italics"></emph.end> dove ritornavasi indietro a professar col <lb></lb>Maurolico la proporzionalità fra gli angoli d&#039;incidenza e quelli di rifrazione. </s>

<s><lb></lb>Vi si professano poi dall&#039;Autore idee che, per non chiamarle strane, si di­<lb></lb>ranno da noi singolari, come sarebbe per esempio che la luce non si ri­<lb></lb>frange, se il mezzo è in piccola quantità o di uniforme crassizie. </s>

<s>“ Fractio <lb></lb>haec seu refractio radiorum non fit ubi interponitur corpus diaphanum den­<lb></lb>sius aut rarius reliquo medio, si sit in pauca quantitate et aequalis crassi­<lb></lb>tiei, ut in exigua aqua altitudinis unius digiti uniformis exiguae crassitiei, <lb></lb>omnes radii tam luminosi quam visuales penetrant recta et irrefracta absque <lb></lb>ulla alteratione visus aut luminis ” (Venetiis, pag. </s>

<s>5). </s></p><p type="main">

<s>Si potrebbe credere che ciò fosse per opporsi all&#039;error del Keplero, il <lb></lb>quale ammetteva non refrangersi il raggio altro che nella superficie. </s>

<s>Ma <lb></lb>intenzion dell&#039;Autore era di apparecchiarsi la via a trattar della rifrazion <lb></lb>nelle lenti, affermando che elle non per altro rompono i raggi che per la <lb></lb>loro difforme crassizie, e che sempre si fa la frattura non verso la più sot-<pb xlink:href="020/01/617.jpg" pagenum="60"></pb>tile ma verso la parte più crassa del vetro. </s>

<s>“ Tunc fractiones semper fient <lb></lb>versus partem crassiorem, ut si vitrum rotundum sit in medio crassius et <lb></lb>convexum ac versus extrema et circumferentiam semper tenuius et graci­<lb></lb>lius, fractiones fient ad perpendicularem, idest versus axem per centrum vi­<lb></lb>tri transeuntem: contrarium continget si vitrum sit in medio gracilius et <lb></lb>versus circumferentiam crassius: perpendicularis tamen penetrat recta absque <lb></lb>sui refractione ” (ibi). </s></p><p type="main">

<s>Con sì lieve armatura non era da sperar di venire a quella conquista, <lb></lb>dalla quale erasi arretrato lo stesso Keplero. </s>

<s>Altre coti sì richiedevano ad <lb></lb>affilare quelle armi, altre avventure, le quali ora noi passeremo a narrare. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;Autore de&#039;Paralipomeni a Vitellione, lasciando a mezzo quelle sue <lb></lb>sollecite investigazioni intorno alla legge degli angoli dell&#039;incidenza rispetto <lb></lb>agli angoli formati dai raggi refratti, mentre da una parte disanimava gli <lb></lb>Ottici, che vedevano essere la difficoltà rimasta inespugnata da tanto ardore <lb></lb>e da tanta possa, additava dall&#039;altra la via, proseguendo la quale si sarebbe <lb></lb>riusciti alla vittoria. </s>

<s>Egli parve insinuare, nel § II del Cap. </s>

<s>IV, che si do­<lb></lb>vesse ritrovare ne&#039;calcoli uno de&#039;più validi argomenti per quella riuscita, <lb></lb>e in ogni modo accennava chiaro che la legge diottrica sarebbe espressa o <lb></lb>per le secanti degli angoli o per i seni o in somma per qualche funzione <lb></lb>trigonometrica. </s></p><p type="main">

<s>Come ad opera di calcolo dunque si rivolse a investigar quella legge <lb></lb>il Cartesio, che si sentiva esser divenuto più valoroso degli altri, per la fe­<lb></lb>lice applicazione dell&#039;Algebra alla Geometria. </s>

<s>Ma i calcoli, in argomento <lb></lb>fisico qual era quello di che si trattava, volevano avere il lor fondamento <lb></lb>sull&#039;esperienza, dalla quale nient&#039;altro ancora s&#039;era imparato, se non che gli <lb></lb>angoli delle rifrazioni crescono con maggior ragion d&#039;incrementi che l&#039;obli­<lb></lb>quità dell&#039;incidenza. </s>

<s>I calcoli cartesiani perciò si ritrovarono inefficaci, e sa­<lb></lb>rebbe per l&#039;Autore rimasta l&#039;impresa al punto dove l&#039;aveva lasciata il Ke­<lb></lb>plero, se per fortuna non avesse trovato a quegli stessi suoi calcoli laboriosi <lb></lb>il Cartesio, nell&#039;esperienza, sicurtà di guida e saldezza di fondamento. </s></p><p type="main">

<s>Quando la maravigliosa invenzione del Canocchiale frugava così viva­<lb></lb>mente gli Ottici per trovar nella scienza delle rifrazioni la ragion di que&#039;mi­<lb></lb>rabili effetti, e il Maurolico e il Porta, il De Dominis e il Keplero, il Tarde <lb></lb>e lo Scheiner tanto v&#039;assottigliaron dietro l&#039;ingegno, che riuscirono a pun­<lb></lb>gere, ma no a perforare, Willebrod Snellio, con miglior giudizio di tutti gli <lb></lb>altri, s&#039;avvide che non era da confidar nella Geometria o nelle astratte spe­<lb></lb>culazioni, ma principalmente nell&#039;esperienza. </s>

<s>Perciò rivolse attentamente gli <lb></lb>studii sulla XIV proposizione del libro X di Vitellione, e giacchè il Porta <lb></lb>l&#039;aveva trovata falsa e il Keplero l&#039;avea dichiarata viziosa ed oscura, nè il <pb xlink:href="020/01/618.jpg" pagenum="61"></pb>difetto da&#039;due Autori scoperto gli pareva che fosse lodevolmente emendato, <lb></lb>egli misuratore insigne del grado del meridiano terrestre, volle sottoporre <lb></lb>alle più esatte misure il sollevarsi delle immagini giacenti sul fondo del <lb></lb>vaso, nella figura e nell&#039;esempio proposto da Vitellione al luogo ora citato. </s></p><p type="main">

<s>Sia per esempio quel vaso pien d&#039;acqua AEYD (fig. </s>

<s>21) e gli oggetti <lb></lb><figure id="id.020.01.618.1.jpg" xlink:href="020/01/618/1.jpg"></figure></s></p><p type="caption">

<s>Figura 21.<lb></lb>posati sul suo fondo a di­<lb></lb>stanze uguali fra loro R, <lb></lb>P, Y. </s>

<s>Il raggio refratto RSO <lb></lb>mostra all&#039;occhio O solle­<lb></lb>vato l&#039;oggetto R in L, e <lb></lb>gli altri in Q e in D. </s>

<s>Chia­<lb></lb>ma lo Snellio OSR, ONP, <lb></lb>OFY raggi veri dell&#039;inci­<lb></lb>denza, OSL, ONQ, OFD <lb></lb>raggi apparenti e dalle mi­<lb></lb>sure collazionate in mol­<lb></lb>tissimi casi riuscì a for­<lb></lb>mulare la legge seguente: <lb></lb>“ Radius incidentiae verus ad adparentem, in eiusdem generis medio, ratio­<lb></lb>nem semper habet eamdem. </s>

<s>” </s></p><p type="main">

<s>Questo Teorema, coi calcoli delle misure e con la descrizione degli stru­<lb></lb>menti squisitissimi da ritrovarle più giuste, il celebre Matematico olandese <lb></lb>avevale esposte in un suo compitissimo trattato di Ottica diviso in tre Libri, <lb></lb>che alla sua morte avvenuta nel 1626 lasciò manoscritto. </s>

<s>Il figlio, non com­<lb></lb>portando forse la spesa della stampa, era liberale co&#039;dotti che ne lo aves­<lb></lb>sero richiesto, e uno de&#039;primi fra questi fu il Cartesio, il quale in quel <lb></lb>Teorema al modo detto di sopra formulato, vedeva d&#039;ogni parte risplendere <lb></lb>la certezza del fatto. </s>

<s>Ma egli voleva in quello stesso Teorema aver espressa la <lb></lb><figure id="id.020.01.618.2.jpg" xlink:href="020/01/618/2.jpg"></figure></s></p><p type="caption">

<s>Figura 22.<lb></lb>legge diottrica per qual­<lb></lb>che funzione trigonome­<lb></lb>trica degli angoli, e così <lb></lb>veder qual corrisponden­<lb></lb>za avesse il fatto speri­<lb></lb>mentale dello Snellio, e <lb></lb>come dovess&#039;essere for­<lb></lb>mulato conforme al cal­<lb></lb>colo kepleriano. </s>

<s>La cosa <lb></lb>era per sè facilissima e <lb></lb>il Cartesio vi fu condotto <lb></lb>per una via che presso <lb></lb>a poco era questa. </s></p><p type="main">

<s>Rivolgendo lo sguar­<lb></lb>do sopra la figura 22 dove RM rappresenta la superficie del diafano, FQ, <lb></lb>GD, IP, KO le perpendicolari ad essa superficie, ABD, HLO i raggi del-<pb xlink:href="020/01/619.jpg" pagenum="62"></pb>l&#039;incidenza vera, ABC, HLN i raggi apparenti, dal Teorema dello Snellio si ha <lb></lb>BD:BC=LO:LN, e dalla Trigonometria BD:BC=sen BCD:sen BDC; <lb></lb>LO:LN=sen LNO:sen LON. </s>

<s>Ma sen BCD=sen (180—BCE)=sen (90 <lb></lb>—CBE)=sen (90—ABR)=sen ABF; e nello stesso modo avremo pure <lb></lb>sen LNO=sen HLI, sen BDC=sen DBQ, sen LON=sen OLP. </s>

<s>Sarà <lb></lb>perciò sen ABF:sen DBQ=sen HLI:sen OLP, che vuol dire <emph type="italics"></emph>i seni degli <lb></lb>angoli dell&#039;incidenza son proporzionali ai seni degli angoli delle rifra­<lb></lb>zioni.<emph.end type="italics"></emph.end> Ed ecco così trovato come doveva essere espresso, conforme alla <lb></lb>mente del Keplero, il fatto delle relazioni fra l&#039;immagine vera e l&#039;apparente, <lb></lb>scoperto dallo Snellio. </s></p><p type="main">

<s>Era venuta così inaspettatamente alle mani del Cartesio quella scoperta <lb></lb>con tanto vivo desiderio cercata da tutti, e che nessuno ancora si confidava <lb></lb>d&#039;aver trovata. </s>

<s>Ei n&#039;esultò apparecchiandosi a pubblicarla, e lasciandosi tra­<lb></lb>sportare all&#039;aura dell&#039;ambizione, piuttostochè all&#039;amore del vero, l&#039;orgoglioso <lb></lb>Filosofo, che pretendeva far tutta la scienza scaturire dal proprio cervello, <lb></lb>disprezzata ogni tradizione de&#039;suoi maggiori, tacque d&#039;aver veduto lo Snel­<lb></lb>lio, e d&#039;essere stato inspirato alle speculazioni diottriche del Keplero. </s>

<s>Come <lb></lb>poi fosse dal suo stesso orgoglio tradito e come venisse insieme a esser tra­<lb></lb>dita la scienza, ci verrà tra poco mostrato dalla storia, ma intanto è da ve­<lb></lb>der con quale studio il Cartesio, nel capitolo II della sua Diottrica, pubbli­<lb></lb>cata in francese nel 1637, cercasse di persuadere al mondo che la legge <lb></lb>delle relazioni costanti fra i seni degli angoli d&#039;incidenza e i seni degli an­<lb></lb>goli di rifrazione fosse un legittimo parto e uno spontaneo portato della sua <lb></lb>nuova Filosofia. </s></p><p type="main">

<s>Dop&#039;avere ne&#039;primi tre paragrafi applicato il principio della composi­<lb></lb>zione del moto a dimostrar la legge delle riflessioni, come si narrò nel Ca­<lb></lb>pitolo precedente, <emph type="italics"></emph>Hinc progrediamur,<emph.end type="italics"></emph.end> incomincia così il § IV, <emph type="italics"></emph>ad refractio­<lb></lb>nem.<emph.end type="italics"></emph.end> Sia A (fig. </s>

<s>23) la solita palla gettata nella <lb></lb><figure id="id.020.01.619.1.jpg" xlink:href="020/01/619/1.jpg"></figure></s></p><p type="caption">

<s>Figura 23.<lb></lb>direzione obliqua AB, non come dianzi sopra la <lb></lb>terra dura CE, ma sopra un panno, ch&#039;ella possa <lb></lb>facilmente squarciare e passar di sotto, benchè con <lb></lb>perdita notabile della prima velocità, la quale sia <lb></lb>per esempio ridotta a mezzo. </s>

<s>Decomposto anche <lb></lb>questo secondo moto nell&#039;orizzontale e nel verti­<lb></lb>cale, quello per non ricevere offesa dal panno teso <lb></lb>rimarrà inalterato, cosicchè per quel verso passerà <lb></lb>nello stesso tempo uno spazio doppio. </s></p><p type="main">

<s>Ciò supposto e considerato “ ducto circulo AFD <lb></lb>ex centro B, et impositis C, B, E ad perpendiculum tribus lineis rectis AC, <lb></lb>HB, FE, hac ratione ut spatium interiacens FE et HB duplum illius sit quod <lb></lb>est inter HB et AC, videbimus hanc pilam ituram ad punctum I. </s>

<s>Cum enim <lb></lb>perrumpendo linteum CBE dimidiam suae velocitatis partem amittat, duplum <lb></lb>temporis ei impendendum est ut infra ex B ad aliquod punctum circumferen­<lb></lb>tiae AFD pertingat, eius quod insunsit superne ut accederet ab A ad B. </s>

<s>Et cum <pb xlink:href="020/01/620.jpg" pagenum="63"></pb>nihil ex dispositione, qua dextrorsum ferebatur intereat, in duplo illius tem­<lb></lb>poris, quo a linea AC devenit ad HB, duplum eiusdem itineris in eamdem <lb></lb>partem conficere debet, et consequenter accedere ad aliquod punctum rectae <lb></lb>FE, eodem momento quo accedit ad aliquod circumferentiae circuli AFD, <lb></lb>quod factu impossibile foret, nisi progrediatur ad I. </s>

<s>Nam in unico illo puncto <lb></lb>recta FE et circulus AFD sub linteo sese invicem secant ” (Francofurti 1692, <lb></lb>pag. </s>

<s>49). </s></p><p type="main">

<s>Il medesimo fatto prosegue a dimostrare il Cartesio che avverrebbe nella <lb></lb>palla, se CE, non un panno teso, ma fosse la superfice d&#039;un&#039;acqua. </s>

<s>Passa <lb></lb>poi nel § VI a fare un&#039;altra supposizione ed è che, giunta la palla nel <lb></lb>punto B, invece di ricevere impedimento le sopravvenga nuovo impeto al <lb></lb><figure id="id.020.01.620.1.jpg" xlink:href="020/01/620/1.jpg"></figure></s></p><p type="caption">

<s>Figura 24.<lb></lb>moto, cosicchè questo divenga per esempio un terzo <lb></lb>più veloce del primo. </s>

<s>Dalle cose nel § IV dimostrate, <lb></lb>segue manifestamente, dice l&#039;Autore, che descritto <lb></lb>il cerchio AFD (fig. </s>

<s>24) e condotte le perpendico­<lb></lb>lari AC, HB, FE, con tal ragione che la distanza tra <lb></lb>FE ed HB sia una terza parte di quella che è fra <lb></lb>HB ed AC, il punto I, comune al cerchio e alla <lb></lb>perpendicolare FI, designerà il luogo dove s&#039;addi­<lb></lb>rizza la palla, e la forza che erompe prima della <lb></lb>incidenza starà alla forza che erompe dopo la rifra­<lb></lb>zione come CB:BE, o come AH:GI. </s></p><p type="main">

<s>“ Tandem vero, prosegue a ragionare il Cartesio nel § VII, quoniam <lb></lb>lucis actio sequitur hac in re easdem leges, quas pilae motus, dicendum quo­<lb></lb>ties radii illius obliquo motu ex pellucido corpore in aliud transferuntur, <lb></lb>quod magis aut minus facile illos admittit, quamprimum ibi ita detorqueri, <lb></lb>ut semper minus inclinent in superficie quae his corporibus est communis, <lb></lb>ea parte in qua est illud corpus quod eas facilius recipit, quam ea in qua <lb></lb>alterum positum est, idque exacte ea proportione qua facilius prius quam <lb></lb>posterius illos recipit.... Ut ex. </s>

<s>gr. </s>

<s>si radius aerem permeans ab A (fig. </s>

<s>25) <lb></lb><figure id="id.020.01.620.2.jpg" xlink:href="020/01/620/2.jpg"></figure></s></p><p type="caption">

<s>Figura 25.<lb></lb>ad B, tacta in punto B superficie vitri CBR, <lb></lb>digrediatur ab I in hoc vitro: veniat deinde alius <lb></lb>a K ad B qui decedat ad L .... eadem ratio li­<lb></lb>nearum KM et LN esse debet ad invicem quae <lb></lb>est linearum AH et IG ” (ibi, pag. </s>

<s>51). </s></p><p type="main">

<s>Pubblicata la Diottrica nella celebre Dis­<lb></lb>sertazione <emph type="italics"></emph>Del Metodo<emph.end type="italics"></emph.end> i Cartesiani si può cre­<lb></lb>dere se l&#039;accolsero a grande onore, ma negli <lb></lb>altri che non erano stati sedotti dal Bretone <lb></lb>eloquente o insorsero vive le contradizioni o <lb></lb>si ritrassero da parte dubitosi delle novità e <lb></lb>diffidenti. </s>

<s>Quella diffidenza poi era inevitabile, e benchè possa apparir come <lb></lb>indizio di ritrosa caparbie negli animi, era invece argomento di senno ne­<lb></lb>gl&#039;ingegni, che ragionavano non potersi la Fisica e specialmente l&#039;Ottica <pb xlink:href="020/01/621.jpg" pagenum="64"></pb>investigare a priori, per via delle sottili speculazioni. </s>

<s>Se fosse stato il Car­<lb></lb>tesio più sincero, e avesse dato la legge diottrica, qual ei l&#039;ebbe dallo Snellio, <lb></lb>come un fatto sperimentato, la diffidenza era tolta, e perciò si diceva dianzi <lb></lb>che l&#039;orgoglio cartesiano, ponendo ostacolo al libero accoglimento del vero, <lb></lb>avea tradita la scienza nei suoi progressi. </s></p><p type="main">

<s>Ma è pure un fatto che il Filosofo, il quale volle orgogliosamente sol­<lb></lb>levarsi sopra le conculcate cervici de&#039;suoi maggiori fratelli, tradì anche in­<lb></lb>sieme la sua propria reputazione, quando giudici imparzialmente severi si <lb></lb>misero dietro a esaminare il processo delle seducenti speculazioni. </s>

<s>Il Fer­<lb></lb>mat richiesto del suo giudizio, intorno alla nuova Diottrica, dal Marsenno, <lb></lb>si maravigliava come mai l&#039;Autore, tra gl&#039;infiniti modi di decomporre in <lb></lb>due un moto solo avesse precisamente scelto quello, ch&#039;era meglio accomo­<lb></lb>dato alla sua conclusione, la quale perciò non dubita di averla come cosa <lb></lb>immaginaria. </s>

<s>La scienza ne sa ora quanto prima, soggiunge l&#039;arguto Mate­<lb></lb>matico francese, e per Bacco, nessuno mi darà mai ad intendere che da una <lb></lb>fantasia possa, come da causa vera, esser derivato un effetto reale. </s>

<s>“ Patet <lb></lb>itaque quod ex omnibus divisionibus determinationis ad motum, quae infi­<lb></lb>nitae sunt multitudinis, author non nisi eam delegit quae ad conclusionem <lb></lb>suam firmandam conducebat, atque ideo medium suum ad conclusionem <lb></lb>suam accommodavit, nobisque de eo aeque parum constat ac antea. </s>

<s>Et hercle <lb></lb>non videtur immaginaria divisio, quae in infinitis formis diversificari potest, <lb></lb>effectus cuiusdam realis causa esse posse ” (Des. </s>

<s>Cartes. </s>

<s>Epistolae, P. III, <lb></lb>Francof. </s>

<s>ad M. 1692, pag. </s>

<s>78). </s></p><p type="main">

<s>Notandosi ivi dal Fermat che il Cartesio andava accomodando la dimo­<lb></lb>strazione alle sue conclusioni, veniva così tacitamente insinuando nell&#039;animo <lb></lb>del Mersenno e di coloro i quali sarebbero poi tornati a meditare sul fatto, <lb></lb>che non fu la speculativa che condusse a ritrovare la legge delle rifrazioni, <lb></lb>ma che, conosciutasi questa legge, la speculazione si accomodò le vie da <lb></lb>scendere addirittura verso quel termine già prima designato. </s>

<s>Così il Filo­<lb></lb>sofo, che pretendeva d&#039;aver fatto conseguire l&#039;Ottica dalla speculata Geo­<lb></lb>metria, veniva a tradire il suo ingannevole intanto e a porger motivo ragio­<lb></lb>nevole ai critici sospettosi di pronunziar per sentenza finale l&#039;accusa d&#039;aver <lb></lb>furato lo Snellio. </s></p><p type="main">

<s>Altre contradizioni ebbe poi a patire il Cartesio per essersi fatto imi­<lb></lb>tatore al Keplero troppo inconsiderato. </s>

<s>Si sa che l&#039;Autore de&#039;Paralipomeni <lb></lb>a Vitellione, professando la diffusion luminosa in superficie, ammetteva che <lb></lb>sulla sola superficie del mezzo si facesse la rifrazione, e su questa ipotesi <lb></lb>son condotte le dimostrazioni di quegli Ottici Teoremi, che il Cartesio si <lb></lb>dette a imitare, non curandosi di sceverar giudiziosamente il vero dal falso. </s>

<s><lb></lb>Da questa parte vennero all&#039;Autor della nuova Diottrica i rimproveri e le <lb></lb>redarguizioni per opera d&#039;Isacco Vossio, a cui dee la scienza delle rifrazioni <lb></lb>l&#039;essere stato tolto di mezzo il pernicioso error kepleriano. </s></p><p type="main">

<s>“ Altera similitudo, scriveva lo stesso Vossio, qua lucis naturam expli­<lb></lb>care conatur, desumta est ex motu pilae: prout enim huius inclinatio re-<pb xlink:href="020/01/622.jpg" pagenum="65"></pb>gitur ad modum superficiei quam vel attingit vel penetrat, eodem modo putat <lb></lb>vel reflecti vel refringi lumen. </s>

<s>Hac comparatione, quamvis ante Cartesium <lb></lb>usus quoque sit Keplerus, multis tamen nominibus peccat, nulloque pror­<lb></lb>sus modo potest defendi. </s>

<s>Licet enim supponamus pilae motum semper ae­<lb></lb>qualem, hoc est infinitum, nihil tamen habebit simile cum radiis lucis non <lb></lb>successive sed in instanti promanantibus. </s>

<s>Modum praeterea et rationem re­<lb></lb>fractionis adsecutus non est, cum in sola superficie refractionem fieri exi­<lb></lb>stimat, ac linteo supra aquam vel aerem extenso comparat. </s>

<s>Scio quidem <lb></lb>communem omnium opticorum esse opinionem lucem in superficie tantum <lb></lb>frangi, quia nempe radii refracti a radiis veris quoad oculum separari vi­<lb></lb>dentur simul ac densius diaphanum ingrediuntur, tantum tamen abest ut <lb></lb>hoc ita sese habeat ut potius contrarium verum sit nihilque omnino in su­<lb></lb>perficie corporis diaphani patiantur radii ” (De Nat. </s>

<s>lucis., Amstelodami 1662, <lb></lb>pag. </s>

<s>33), e seguita a dimostrar che i raggi non si refrangono alla superfi­<lb></lb>cie ma dentro il mezzo con argomenti, a cui non si potrebbe nulla apporre <lb></lb>in contrario. </s></p><p type="main">

<s>Il Vossio fu forse il primo a far pubblicamente accorti gli Ottici che <lb></lb>il processo dimostrativo del Cartesio era stato prima tenuto dal Keplero: <lb></lb>ma dello Snellio tutti per ora stanno in silenzio, anche il Fermat, benchè <lb></lb>faccia trasparir qua e là nelle sue Lettere d&#039;essere entrato in qualche so­<lb></lb>spetto. </s>

<s>Il rumore incominciò dopo il 1703 e fu il Newton il più sollecito a <lb></lb>secondarlo. </s>

<s>Nelle Lezioni d&#039;Ottica, dop&#039;avere accennato all&#039;incertezza degli <lb></lb>antichi intorno alla regola delle rifrazioni, soggiunge: “ at Cartesius aliam <lb></lb>regulam primus excogitavit qua illud exactius determinaretur, ponendo dicto­<lb></lb>rum angulorum sinus esse in ratione data ” (Patavii 1773, pag. </s>

<s>13, 14). Ma <lb></lb>nello Scolio alla propos. </s>

<s>XCVI del Lib. </s>

<s>I de&#039;<emph type="italics"></emph>Principii,<emph.end type="italics"></emph.end> nella seconda edi­<lb></lb>zione, così tornava a scrivere in diversa sentenza: “ Harum attractionum <lb></lb>haud multum dissimiles sunt lucis reflexiones et refractiones, factae secun­<lb></lb>dum datam secantium rationem ut invenit Snellius, et per consequens se­<lb></lb>cundum datam sinuum rationem, ut exposuit Cartesius ” (Genevae 1739, <lb></lb>pag. </s>

<s>539). </s></p><p type="main">

<s>La ragione dell&#039;aver così il Newton cambiata sentenza dal 1670, anno <lb></lb>in cui dettava le ultime Lezioni di Ottica, al 1713, anno in cui comparì la <lb></lb>seconda edizione de&#039;<emph type="italics"></emph>Principii,<emph.end type="italics"></emph.end> è da attribuirsi alla lettura della Diottrica <lb></lb>dell&#039;Huyghens pubblicata postuma nel 1703 in Leyda, nell&#039;introduzione alla <lb></lb>quale il celebre Autore scriveva: “ Haec autem refractionum mensura non <lb></lb>sinuum, sed angulorum ipsorum proportione ab Alhaseno arabe et Vitel­<lb></lb>lione olim definita fuerat, et experimentis quibusdam utcumque confirmata. </s>

<s><lb></lb>Sed cum in maioribus radiorum inclinationibus a vero discrepare propor­<lb></lb>tio illa reperiretur, diligentius sibi Recentiores investigandam existimarunt, <lb></lb>in quibus Keplerus, plurimis frustra tentatis, ipsam quidem rei veritatem <lb></lb>non est assecutus, coniecturis tamen suis, variisque molitionibus non parum <lb></lb>sequentium studia adiuvit. </s>

<s>Post eum vero Willebrordus Snellius, cum iam <lb></lb>maius operae pretium appareret, quippe exorto Telescopii invento, multo la-<pb xlink:href="020/01/623.jpg" pagenum="66"></pb>bore, mullisque experimentis eo pervenit ut veras quidem refractionum men­<lb></lb>suras teneret ” (pag. </s>

<s>2). </s></p><p type="main">

<s>L&#039;Huyghens era mosso a rivelar questi fatti e a pronunziare questi <lb></lb>giudizii dall&#039;amor della verità e della patria, essendo lo Snellio suo conna­<lb></lb>zionale. </s>

<s>Ma un altro Olandese lo aveva in ciò preceduto ed era quell&#039;Isacco <lb></lb>Vossio, il quale parve avere avuto per principale intenzione in pubblicare <lb></lb>il suo Trattato <emph type="italics"></emph>De lucis Natura et proprietate<emph.end type="italics"></emph.end> quella di divulgare le diot­<lb></lb>triche dottrine snelliane rimaste immeritamente sconosciute in un libro che <lb></lb>egli ebbe per grazia di veder manoscritto. </s>

<s>“ Porro priusquam ad alia re­<lb></lb>fractionis pergam phaenomena, praeterire non possum insignem Willebrordi <lb></lb>Snellii observationem, quae unice sententiam nostram confirmat. </s>

<s>Quantus vir <lb></lb>ille fuerit in universa Mathesi, quamvis ex iis quae palam prostant scriptis <lb></lb>satis colligi possit, multo tamen idipsum clarius constaret, si fata permisis­<lb></lb>sent illa quoque perficere, quae utique perfecisset, si vel paulo diuturnio­<lb></lb>rem Deus vitam indulsisset. </s>

<s>Inter alia vero praeclara quae reliquit monu­<lb></lb>menta supersunt quoque tres Libri optici quorum usuram superiori hyeme <lb></lb>concessit mihi filius eius. </s>

<s>Quia illi necdum prodierunt in lucem, dignissimi <lb></lb>tamen qui prodeant, adponam hic Theorema, quo nullum in tota optica no­<lb></lb>bilius et utilius extat. </s>

<s>Sic vero se habet: Radius incidentiae verus ad adpa­<lb></lb>rentem, in eiusdem generis medio, rationem semper habet eamdem ” (Amste­<lb></lb>lodami 1662, pag. </s>

<s>36). </s></p><p type="main">

<s>È cosa assai singolare però che il Vossio, così arguto censor del Cartesio <lb></lb>e che non lascia mai l&#039;occasion di notare i molti errori di lui, per contrap­<lb></lb>porgli alle verità dimostrate dallo Snellio, non faccia una parola intorno alla <lb></lb>legge delle rifrazioni, per dir quanto fosse l&#039;Autore della Dissertazione del <lb></lb>Metodo debitor verso l&#039;Autore dell&#039;Ottica manoscritta. </s>

<s>La singolarità però <lb></lb>si spiega avvertendo a un&#039;altra singolarità, ed è che il Vossio non s&#039;accorse <lb></lb>che il Teorema snelliano e il cartesiano erano in sostanza la medesima cosa. </s>

<s><lb></lb>Il facilissimo calcolo che dal supporre il raggio vero dell&#039;incidenza propor­<lb></lb>zionale al raggio apparente conduceva a trovar la costante proporzionalità <lb></lb>fra il seno dell&#039;angolo dell&#039;incidenza e il seno dell&#039;angolo di refrazione, fu <lb></lb>trascurato affatto dal Vossio, il quale perciò rimase nella persuasione che <lb></lb>tutt&#039;altra fosse la legge dello Snellio da quella del Cartesio. </s>

<s>Di qui è che <lb></lb>l&#039;Huyghens, dop&#039;aver detto che lo stesso Snellio aveva ritrovata la vera legge <lb></lb>diottrica, <emph type="italics"></emph>nec tamen,<emph.end type="italics"></emph.end> soggiunge, <emph type="italics"></emph>quod invenerat intelligeret.<emph.end type="italics"></emph.end> È un fatto, <lb></lb>prosegue più avanti a dire il medesimo Huyghens, che “ ad hanc sinuum <lb></lb>proportionem nequaquam attendit Snellius, et usque adeo ab apparente ima­<lb></lb>gine rem omnem pendere existimavit, ut etiam in radio perpendiculari, ef­<lb></lb>fectum refractionis, seu ut falso opinatur, decurtationem radii visorii agno­<lb></lb>scat, deceptus eo, quod etiam recta desuper in vas aqua plenum inspicienti <lb></lb>fundus omni parte attolli videtur ” (Dioptr. </s>

<s>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Dal medesimo inganno si lasciò pur sedurre il Vossio seguace in tutto <lb></lb>fedelissimo dello Snellio, ond&#039;è che tutta l&#039;utilità della insigne scoperta non <lb></lb>seppero ambedue questi autori in altro riconoscerla che nell&#039;aver finalmente <pb xlink:href="020/01/624.jpg" pagenum="67"></pb>ritrovata la linea del perfetto concorso, la quale non è parabolica nè iper­<lb></lb>bolica, ma è una concoide <emph type="italics"></emph>non quidem nicomedeam, aut antinicomedeam, <lb></lb>sed aliam sui generis.<emph.end type="italics"></emph.end> (I. Voss. </s>

<s>De nat. </s>

<s>lucis cit., pag. </s>

<s>38). </s></p><p type="main">

<s>Fu insomma l&#039;Huyghens il primo ad avvertir che il Cartesio aveva con­<lb></lb>clusa la legge de&#039;seni dalla misura che lo Snellio aveva ritrovata fra i raggi <lb></lb>veri e i raggi apparenti, intorno a che giova attendere a quel che l&#039;Huy­<lb></lb>ghens stesso scriveva in questo particolare. </s>

<s>“ Haec autem omnia quae de <lb></lb>refractionis inquisitione volumine integro Snellius exposuerat, inedita man­<lb></lb>sere, quae et nos vidimus aliquando, et Cartesium quoque vidisse accepi­<lb></lb>mus ut hinc fortasse mensuram illam, quae in sinibus consistit, elicuerit ” <lb></lb>(Dioptr. </s>

<s>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Cosicchè l&#039;argomento del celebre furto del Cartesio dal manoscritto dello <lb></lb>Snellio si riduce a non più che a un <emph type="italics"></emph>si dice,<emph.end type="italics"></emph.end> e dietro ciò dette il Newton <lb></lb>il caso per fatto certo, e per fatto certo moltissimi l&#039;hanno ripetuto sull&#039;au­<lb></lb>torevole testimonianza di lui. </s>

<s>Che se quel perfetto giudizio volse il dubbio <lb></lb>dell&#039;Huyghens a certezza, non è da creder che ciò fosse senza la sua ra­<lb></lb>gione. </s>

<s>Così la legge diottrica de&#039;seni come la calottrica degli angoli son fatti <lb></lb>de&#039;quali è impossibile il dar la dimostrazione. </s>

<s>Ora, è egli mai da credere <lb></lb>che la dimostrazione sia stata quella che guidò il Filosofo alla scoperta del <lb></lb>fatto? </s>

<s>Quella credibilità da un&#039;altra parte vien naturalissima ammettendo <lb></lb>che al fatto sperimentale scoperto dallo Snellio si venisse accomodando la <lb></lb>speculata dimostrazion del Cartesio. </s>

<s>Che questi poi potesse avere per le <lb></lb>esperienze sue proprie fatta quella scoperta, non saprà persuadersene nes­<lb></lb>suno che conosce l&#039;indole di quell&#039;ingegno, e attende a quel gloriarsi che <lb></lb>e&#039;fa bene spesso d&#039;avere indovinati i fatti stessi dietro la speculativa. </s>

<s>Un <lb></lb>esempio calzante di ciò lo abbiamo in que&#039;due strumenti ch&#039;egli ammaginò <lb></lb>per la misura delle rifrazioni e de&#039;quali parla nella Lettera LXX della <lb></lb>Parte II. Dop&#039;aver detto che così fatti strumenti riescono, di quello di Vi­<lb></lb>tellione, più comodi e più precisi “ Nihilominus fieri potest, soggiunge, ut <lb></lb>decipiant, neutro enim sum usus neque aliud unquam in hac materie expe­<lb></lb>rimentum feci, nisi quod quinquennio aut sexennio abhinc curaverim effor­<lb></lb>mandum vitrum cuius figuram Dom. </s>

<s>Mygdorgius delineaverat, quo perfecte <lb></lb>radii solis omnes in punctum unum conveniebant exacte quam praedixeram <lb></lb>distantiam ” (Francof. </s>

<s>ad M. 1692, pag. </s>

<s>209). </s></p><p type="main">

<s>Ed ecco a confermare il vizio della radice venire l&#039;insipidezza de&#039;frutti, <lb></lb>qual si dimostra in quelli che seppe dalle sue scoperte raccogliere il Carte­<lb></lb>sio. </s>

<s>Egli è ancora dietro con coloro che sono affaccendati a cercar la linea <lb></lb>del perfetto concorso nelle lenti, la figura prestabilita alle quali è, giudice <lb></lb>il Fermat, una lepidezza (ivi, P. III, pag. </s>

<s>78). Dietro tutto ciò noi teniam <lb></lb>per certo col Newton quel che il prudentissimo Huyghens si contentò di <lb></lb>mettere in dubbio, e abbiamo posto questa certezza per fondamento alla <lb></lb>presente parte di storia. </s></p><pb xlink:href="020/01/625.jpg" pagenum="68"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il merito di un Filosofo non consiste solamente nell&#039;avere scoperto il <lb></lb>vero, ma nella virtù e nell&#039;efficacia del diffonderlo. </s>

<s>La vera regola delle ri­<lb></lb>frazioni era stata bene dimostrata dal Cartesio, ma da&#039;suoi ciechi ammira­<lb></lb>tori in fuori, fu difficile persuaderla a chi in un fatto fisico non aveva fede <lb></lb>alle speculazioni. </s>

<s>Abbiamo nel paragrafo precedente accennato a queste dif­<lb></lb>ficoltà, ma ora è tempo di considerarle più attentamente, e di mostrar come <lb></lb>alla fine si giunse a superarle. </s></p><p type="main">

<s>L&#039;anno dopo che fu venuta alla luce in Parigi la Diottrica cartesiana, <lb></lb>il Boulliaud pubblicava il suo Trattato <emph type="italics"></emph>De natura lucis.<emph.end type="italics"></emph.end> Forse l&#039;Autore spe­<lb></lb>culava intorno al difficile soggetto, senza nulla aver sentito delle nuove dot­<lb></lb>trine del Cartesio, e il libro dell&#039;Astronomo era tuttavia sotto i torchi, quando <lb></lb>quello del Filosofo n&#039;era uscito di poco. </s>

<s>Comunque sia, nel Boulliaud non <lb></lb>si trova fatto il minimo accenno alle novità diottriche, che gli erano nel me­<lb></lb>desimo tempo pullulate fra&#039;piedi. </s>

<s>Egli non riconosce altro predecessore a&#039;suoi <lb></lb>studii più prossimo del Keplero, di cui non approva le dottrine, nè l&#039;ana­<lb></lb>logia del moto della palla gettata, che si piega alla perpendicolare. </s>

<s>La rifra­<lb></lb>zione per lui “ nihil aliud est quam repercussio, seu ut vulgus Opticorum <lb></lb>loquitur, reflexio interna ” (Parisiis 1638, pag. </s>

<s>37), e la più giusta e rego­<lb></lb>lata misura degli angoli non sa in altro meglio trovarla che nella propor­<lb></lb>zionalità de&#039;segmenti iperbolici, come glie lo ha insegnato la stessa espe­<lb></lb>rienza. </s>

<s>“ Hiperbolis mensurari docuit experientia ” (ibi, pag. </s>

<s>38). </s></p><p type="main">

<s>Primo ad accogliere la legge cartesiana de&#039;seni fu l&#039;Herigonio, benemerito <lb></lb>della Matematica e della Fisica matematica per aver, tuttociò ch&#039;era stato <lb></lb>speculato e scoperto in que&#039;soggetti, raccolto con gran criterio e in bell&#039;or­<lb></lb>dine disposto nel suo <emph type="italics"></emph>Corso.<emph.end type="italics"></emph.end> E qui l&#039;amore della verità e il dovere della <lb></lb>coscienza ci costringono a ritrattare una nostra opinione, che i Lettori hanno <lb></lb>oramai notata nel primo Tomo di questa Storia, dove, persuasi che l&#039;edi­<lb></lb>zione del <emph type="italics"></emph>Cursus mathematicus<emph.end type="italics"></emph.end> fatta nel 1633 fosse in tutto identica a quella <lb></lb>del 1644, facemmo l&#039;Herigonio precedere al Cartesio. </s>

<s>Fummo tratti in in­<lb></lb>ganno dal veder ripetuta anche in questa edizione seconda la dedica al Mar­<lb></lb>chese Bassompierre data <emph type="italics"></emph>Lutetiae parisiorum ineunte anno a salutifero <lb></lb>partu M.DC.XXXIV,<emph.end type="italics"></emph.end> e dal vedervi riportato il Privileglo reale <emph type="italics"></emph>donné a <lb></lb>Paris le 29 iour de Decembre l&#039;an de Grace mil six cens trente-trois,<emph.end type="italics"></emph.end><lb></lb>senza dall&#039;altra parte, per esser la prima divenuta sì rara, aver potuto porre <lb></lb>a riscontro le due varie edizioni. </s>

<s>Ma poi ci siamo assicurati che nel 1633 <lb></lb>fu veramente pubblicato il Corso matematico in cinque Tomi, i primi quat­<lb></lb>tro de&#039;quali furono prestati da Galileo al Cavalieri (Alb. </s>

<s>X, 211, 28) e nel 1644 <lb></lb>fu nuovamente impresso quel <emph type="italics"></emph>Corso<emph.end type="italics"></emph.end> con molte aggiunte e con più un sesto <lb></lb>Tomo per appendice. </s></p><pb xlink:href="020/01/626.jpg" pagenum="69"></pb><p type="main">

<s>Fra quelle aggiunte notabilissima è la proposizione II della Diottrica <lb></lb>così formulata: “ Sinus inclinationum radiorum oblique incidentium eam­<lb></lb>dem inter se habent proportionem quam sinus inclinationum radiorum re­<lb></lb>fractorum ” (Cursus mathem., T. V, Parisiis 1644, pag. </s>

<s>132). L&#039;Autore tiene <lb></lb>un&#039;ipotesi più conforme all&#039;esperienza di quella tenuta dal Cartesio, la quale <lb></lb>ipotesi è che i raggi non sieno velocitati ma impediti dalla maggiore den­<lb></lb>sità del mezzo. </s>

<s>Ad evitare poi le contrarietà che sentiva avere di già incon­<lb></lb>trate lo stesso Cartesio, al principio della composizione del moto pensò di <lb></lb>sostituire quello degli equiponderanti. </s>

<s>Premessi quattro altri assiomi appro­<lb></lb>vati dagli Ottici suoi predecessori, nel V in particolare s&#039;ammette che le <lb></lb>virtù che hanno i raggi luminosi di penetrare attraverso a varii mezzi dia­<lb></lb>fani s&#039;accrescono o diminuiscono secondo la mutazione de&#039;mezzi. </s>

<s>Fra que­<lb></lb>ste virtù poi che hanno i diversi raggi di penetrare attraverso ai vari mezzi <lb></lb>diafani, intercede la proporzione medesima che è fra i momenti di un grave <lb></lb>sopra piani variamente inclinati. </s></p><p type="main">

<s>Sia per esempio O (fig. </s>

<s>26) un atomo di luce appartenente al raggio <lb></lb>AC, che scende obliquo sul diafano BC e sia pure I un altro simile atomo <lb></lb>appartenente al raggio AD, che per vie più oblique va a cadere sul mede­<lb></lb>simo diafano refringente. </s>

<s>Si domanda con qual diverso impeto i due atomi, <lb></lb><figure id="id.020.01.626.1.jpg" xlink:href="020/01/626/1.jpg"></figure></s></p><p type="caption">

<s>Figura 26<lb></lb>per la diversa loro obliquità, an­<lb></lb>deranno a penetrare sotto la su­<lb></lb>perficie BD. L&#039;Herigonio non <lb></lb>esita punto a rispondere, appli­<lb></lb>cando all&#039;Ottica i principii della <lb></lb>Meccanica, riguardando cioè i <lb></lb>due atomi quali precisamente due <lb></lb>gravi, ambedue di ugual peso, e <lb></lb>l&#039;uno scendente per il piano in­<lb></lb>clinato AC e l&#039;altro per il più <lb></lb>obliquo AD. </s>

<s>Supposto dunque <lb></lb>che sia X il peso assoluto dei due <lb></lb>atomi di luce, il peso cioè col <lb></lb>momento del quale scenderebbero nel perpendicolo, i relativi momenti O, I, <lb></lb>co&#039;quali scendono lungo i due piani inclinati, si hanno, per la Meccanica, <lb></lb>dalle due seguenti equazioni: X:O=AC:BC e X:I=AD:BD. </s></p><p type="main">

<s>Si considerino ora, prosegue a ragionar l&#039;Herigonio, i raggi AC, AD <lb></lb>che venendo dall&#039;aria s&#039;abbattono in C e in D a dover penetrare attraverso <lb></lb>a un diafano più denso, per esempio acqua o cristallo. </s>

<s>Secondo le leggi <lb></lb>della Meccanica è naturale che gli atomi O, I, in mezzo all&#039;acqua o al cri­<lb></lb>stallo, diventino più leggeri. </s>

<s>Ma per questo appunto verrebbero a perdere <lb></lb>del loro impeto e di quella prima virtù che avevano di penetrare il mezzo, <lb></lb>ond&#039;è che ben s&#039;intende come sia necessario che la natura soccorra al di­<lb></lb>fetto, perchè i raggi di luce, che non possono arrestarsi nel loro viaggio, <lb></lb>hanno bisogno di serbar sempre impeto uguale proporzionato alle resistenze <pb xlink:href="020/01/627.jpg" pagenum="70"></pb>e agl&#039;impedimenti incontrati nel mezzo. </s>

<s>I rimedii della natura son sempre <lb></lb>i più facili e i più pronti, e nel medesimo tempo i più efficaci. </s>

<s>Or qual <lb></lb>più pronto e più facile rimedio, a ristorare gl&#039;impeti perduti dagli atomi <lb></lb>O, I, per l&#039;impedimento del mezzo, di quello che rendere a proporzione più <lb></lb>inclinato il loro viaggio? </s>

<s>Supponiamo infatti che giunti i due atomi in C e <lb></lb>in D non seguitino a scendere per le due prime obliquità AC, AD, ma per <lb></lb>le altre due CF, DH, le quali sieno tanto maggiori delle prime, quanto il <lb></lb>cristallo e l&#039;acqua son più densi dell&#039;aria: è chiaro allora che i due atomi, <lb></lb>lungo i due nuovi piani inclinati CF, DH, in mezzo all&#039;acqua o al cristallo, <lb></lb>si moveranno con quell&#039;impeto stesso che si movevano scendendo per i piani <lb></lb>meno inclinati AC, AD, nel mezzo dell&#039;aria. </s>

<s>Così infatti opera la Natura. </s>

<s><lb></lb>Giunti in C e in D i raggi d&#039;incidenza non seguitano a dirittura il loro <lb></lb>viaggio, ma s&#039;inflettono o si frangono più o meno, secondo la varia densità <lb></lb>del mezzo. </s></p><p type="main">

<s>Da queste premesse concludesi facilmente dall&#039;Herigonio la proporzio­<lb></lb>nalità che passa fra i seni degli angoli d&#039;incidenza e quelli degli angoli di <lb></lb>rifrazione. </s>

<s>Si conducano infatti le perpendicolari MCE, NDZ. </s>

<s>Avremo per gli <lb></lb>atomi scendenti lungo i piani CF, DH la proporzionalità stessa che per i <lb></lb>primi, avremo cioè X:T=CF:EF; X:V=DH:HZ. </s>

<s>Queste quattro pro­<lb></lb>porzioni si trasformano facilmente nelle altre quattro seguenti: X:O= <lb></lb>1:sen ACM; X:I=1:sen ADN; X:T=1:sen ECF; X:V=1:sen ZDH, <lb></lb>d&#039;onde se ne deduce sen ACM:sen ADN=sen ECF:ZDH, che è ciò ap­<lb></lb>punto che l&#039;Autore proponevasi di dimostrare. </s></p><p type="main">

<s>Altri Cartesiani, procedendo per vie alquanto diverse, elaborarono altre <lb></lb>dimostrazioni delle quali tutte, compresavi quella stessa del Cartesio, il Fer­<lb></lb>mat dava il seguente giudizio: “ Hoc saltem addam quod viderim illud <lb></lb>ipsum D. </s>

<s>Cartesii principium in pluribus authoribus qui post ipsum scripse­<lb></lb>runt. </s>

<s>Eorum tamen demonstrationes haud magis quam ipsius D. </s>

<s>Cartesii <lb></lb>recipiendae, aut nomen istud mereri videntur. </s>

<s>Herigonius utitur ad illum <lb></lb>demonstrandum aequiponderantibus, et ratione ponderum super planis in­<lb></lb>clinatis; P. </s>

<s>Maignan alia via eo pervenire conatur, sed visu facile est eos <lb></lb>neutrum demonstrare, et lectis examinatisque studiose eorum demonstratio­<lb></lb>nibus, nos aeque incertos esse de veritate principii ac lectis iis quae scripsit <lb></lb>D. </s>

<s>Cartesius ” (Des Cartes Epist., P. III, Francof. </s>

<s>ad M. 1692, pag. </s>

<s>128). </s></p><p type="main">

<s>Così i Francesi stessi più giudiziosi confessavano di saper di Diottrica, <lb></lb>dopo gl&#039;insegnamenti cartesiani, quanto ne sapevano prima, e perchè, se­<lb></lb>condo il Fermat, tutta l&#039;incertezza dipendeva dal veder che il Cartesio aveva <lb></lb>accomodati i mezzi alla conclusione, la quale come si fosse rivelata alla mente <lb></lb>del Filosofo era un mistero, il Fermat stesso pensò di ricorrere a un argo­<lb></lb>mento tutto diverso, per veder dove fosse portato ad approdare spiegate <lb></lb>all&#039;aria incerta le vele </s></p><p type="main">

<s>Quel nuovo argomento eletto dal Matematico di Tolosa era il principio <lb></lb>delle cause finali, conforme al quale s&#039;ammetteva <emph type="italics"></emph>Naturam semper agere <lb></lb>per vias quam maxime compendiosas.<emph.end type="italics"></emph.end> Il carattere morale di questo stesso <pb xlink:href="020/01/628.jpg" pagenum="71"></pb>principio veniva ad esser diciamo così matematicato nella teoria de&#039;Massimi <lb></lb>e de&#039;Minimi, intorno alla quale il Fermat aveva metodi suoi proprii. </s>

<s>Era <lb></lb>tutto ardore per dar mano all&#039;impresa, quando a distrarnelo gli si fecero <lb></lb>incontro due ostacoli. </s>

<s>Il Petit, uomo di grande autorità, lo aveva avvertito <lb></lb>che l&#039;esperienze confermavano la legge de&#039;seni prescritta dal Cartesio, ond&#039;io <lb></lb>temo, pensava il Fermat, “ ne frustra coner introducere proportionem pro­<lb></lb>portioni eius contrariam, quodque experimenta post publicationem inventi <lb></lb>mei facienda, ipsam a vestigio destruere possent ” (ibi, pag. </s>

<s>130). Il se­<lb></lb>condo ostacolo era il tedio e la difficoltà del calcolo, in cui bisognava im­<lb></lb>barcarsi per correre il nuovo pelago periglioso. </s>

<s>Poi rimosse il primo osta­<lb></lb>colo ripensando che, anche un esattissimo e industrioso osservatore, può <lb></lb>esser tratto in inganno, e vinse il secondo con invocare, invece dell&#039;ispido <lb></lb>calcolo, l&#039;amabile Geometria. </s>

<s>Così ripreso il primo ardore, si dette all&#039;opera <lb></lb>che fu coronata di un esito felice e inaspettato. </s>

<s>“ Pretium autem laboris <lb></lb>mei fuit maxime insolitum, inopinatum atque omnium felicissimum. </s>

<s>Post­<lb></lb>quam enim omnes aequationes, multiplicationes, antitheses et alias opera­<lb></lb>tiones methodi meae percurrissem, tandemque conclusissem Problema quod <lb></lb>in schedula separata accipies, deprehendi principium meum plane et prae­<lb></lb>cise eandem refractionibus dare proportionem quam D. </s>

<s>Cartesius stabilive­<lb></lb>rat. </s>

<s>Tam insperato successu magnopere commotus et admiratione perculsus <lb></lb>fui. </s>

<s>Reiteravi saepius algebraicas meas operationes eodem semper successu, <lb></lb>quamvis demonstratio mea supponat transitum luminis per corpora densa <lb></lb>difficiliorem esse quam per rara; quod verissimum esse credo et contradi­<lb></lb>tionem non pati. </s>

<s>D. </s>

<s>Cartesius vero contrarium asseruit. </s>

<s>Quidnam ex omni­<lb></lb>bus istis nobis concludendum est? </s>

<s>Numquid id amici D. </s>

<s>Cartesii non satis <lb></lb>habebunt quod ipsi possessionem sui Theorematis liberam relinquam? </s>

<s>An­<lb></lb>non magnae ipsi gloriae erit cognovisse processum Naturae primo intuitu, <lb></lb>et absque ulla demonstratione? </s>

<s>Itaque palmam ipsi relinquo, sufficit mihi <lb></lb>quod D. </s>

<s>Clerselier admittat me in societatem probationis tanti ponderis ve­<lb></lb>ritatis, quae tam mirabiles consequentias producere debet ” (ibi, pag. </s>

<s>131). </s></p><p type="main">

<s>Tutta la gran maraviglia che dovette soprapprendere il Fermat dipen­<lb></lb>deva dall&#039;ignorare la storia gelosamente tenuta occulta dal Cartesio, il quale <lb></lb>non prescrisse la legge de&#039;seni <emph type="italics"></emph>primo intuitu et absque ulla demonstra­<lb></lb>tione,<emph.end type="italics"></emph.end> ma dietro i fatti che lo Snellio aveva sperimentalmente già dimostrati. </s>

<s><lb></lb>Comunque sia, in sul primo entrar dell&#039;anno 1662, che tale è la data della <lb></lb>Lettera al De-la-Chambre, dove il Fermat scrive i fatti da noi sopra nar­<lb></lb>rati, cessò in Francia quella diffidenza che aveva tenuti gli animi incerti <lb></lb>intorno alla Diottrica cartesiana. </s></p><p type="main">

<s>Si potrebbe creder forse che, in stabilir la scienza delle rifrazioni, la <lb></lb>Matematica dello stesso Fermat avesse avuto grande efficacia, ma poi viene <lb></lb>a rendere vacillante questo giudizio una considerazione ed è che il Carte­<lb></lb>sio e il Fermat riuscirono a concludere lo stesso dietro ipotesi fra loro con­<lb></lb>trarie, l&#039;uno ammettendo che il mezzo più denso impedisce, l&#039;altro invece <lb></lb>dicendo che facilita il moto della luce. </s>

<s>Essendo questa seconda ipolesi tanto <pb xlink:href="020/01/629.jpg" pagenum="72"></pb>contraria al modo consueto d&#039;operare della Natura, ebbe intorno a ciò il <lb></lb>Cartesio a patire una delle più forti opposizioni, dalle quali troppo debol­<lb></lb>mente per verità si difendeva col dir ch&#039;ei non faceva distinzione fra corpi <lb></lb>densi e rari, ma fra duri e molli, ne&#039;primi de&#039;quali il moto della luce è <lb></lb>facilitato, perchè non si comunica, nè perciò si disperde attraverso alle ce­<lb></lb>devoli pareti de&#039;pori. </s>

<s>“ Non enim dico lumen facilius propagari in denso <lb></lb>quam in raro, sed in duro, in quo scilicet materia substilis non communi­<lb></lb>cat motum suum parietibus meatuum quibus inest, quam in molli, sive hoc <lb></lb>sit rarius, sive densius ” (Epistolae, Pars. </s>

<s>III, edit. </s>

<s>cit., pag. </s>

<s>61). </s></p><p type="main">

<s>In qualunque modo però il veder che per due vie diverse e anzi op­<lb></lb>poste si giungeva al medesimo intento ingerì ne&#039;Filosofi poca fiducià delle <lb></lb>dimostrazioni, e se fu stabilita la nuova scienza diottrica ciò si dee alle espe­<lb></lb>rienze del Petit e degli altri investigatori de&#039;fatti, piuttosto che alle specu­<lb></lb>lazioni del Matematico di Tolosa. </s>

<s>Quando poi l&#039;Huyghens, interpetrando il <lb></lb>Vossio, svelò al mondo il mistero, e s&#039;intese che quella del Cartesio non <lb></lb>era una sua intuizione, ma un fatto dimostrato dallo Snellio, e allora la Diot­<lb></lb>trica si confermò per sempre sulla stabilità del suo fondamento. </s></p><p type="main">

<s>Ma pur se i fatti son la materia, le speculazioni son la forma della <lb></lb>scienza, ond&#039;è che, dovendosi in ogni modo speculare, e avendo gli Ottici <lb></lb>innanzi i due diversi esempii del Cartesio e del Fermat, si credè più sicuro <lb></lb>il proceder dietro le orme di questo che non di quello. </s>

<s>Perciò, sopra le di­<lb></lb>mostrazioni derivate dai principii meccanici rimasero in onore quelle fon­<lb></lb>date sul principio delle cause finali, di che son l&#039;Huyghens e il Leibniz i <lb></lb>primi e principali Autori. </s></p><p type="main">

<s>Il grande Ottico olandese inserì quella sua dimostrazione diottrica nel <lb></lb>Trattato <emph type="italics"></emph>De la lumiere<emph.end type="italics"></emph.end> e perchè l&#039;abbiamo inoculata sull&#039;albero della scienza <lb></lb>italiana, da questo pensiamo di cogliere i saggi del frutto. </s>

<s>Guido Grandi, <lb></lb>che volle applicare al moto delle acque il principio delle cause finali, si trovò <lb></lb>alle mani il Teorema ugeniano delle stesse cause finali applicato al moto <lb></lb>della luce, e lo rese compiuto e con forse maggior facilità dimostrato. </s>

<s>“ Con­<lb></lb>vien premettere, scrive il Nostro, a modo di lemma la soluzione del seguente <lb></lb>problema, il quale in parte fu già dimostrato dal signor Cristiano Ugenio <lb></lb>nel suo Trattato <emph type="italics"></emph>Del Lume,<emph.end type="italics"></emph.end> servendosene a dimostrare la ragione delle re­<lb></lb>frazioni della luce, qualora passa da un mezzo in un altro di densità di­<lb></lb>versa, come sarebbe dall&#039;aria nel cristallo, o dal vetro nell&#039;acqua, ma qui <lb></lb>da me viene steso questo problema all&#039;attraversamento di più e diversi <lb></lb>mezzi ” (Alb. </s>

<s>XIV, 135). </s></p><p type="main">

<s>Questa maggiore estensione fu data dal Grandi al Teorema ugeniano <lb></lb>per mezzo della seguente proposizione da lui stesso così formulata: “ Debba <lb></lb>un mobile portarsi da A in B (fig. </s>

<s>27) più speditamente che sia possibile, <lb></lb>andando dal punto A verso la linea CG, colla velocità FC, e nello spazio <lb></lb>interposto fra le due parallele CG, DH colla velocità Z, e nello spazio in­<lb></lb>tercetto fra le parallele DH, EX colla velocità Y, e quindi fino in B colla <lb></lb>velocità BX: si cerca per quale strada doverà andare. </s>

<s>Si dispongano le rette <pb xlink:href="020/01/630.jpg" pagenum="73"></pb>AC, CD, DE, EB, talmente che i seni de&#039;loro angoli colle perpendicolari <lb></lb>tirate sopra le date parallele, quali sono ACF, CDG, DEH, EBX, siano per <lb></lb><figure id="id.020.01.630.1.jpg" xlink:href="020/01/630/1.jpg"></figure></s></p><p type="caption">

<s>Figura 27.<lb></lb>ordine come le velocità FC, Z, Y, BX; dico che <lb></lb>per la strada ACDEB verrà il mobile da A in B <lb></lb>in minor tempo, che per qualsivoglia altra <lb></lb>strada, ritenute ne&#039;siti suddetti le stesse velo­<lb></lb>cità ” (ivi, pag. </s>

<s>135, 36). </s></p><p type="main">

<s>La dimostrazione geometrica assai facile e <lb></lb>chiara è applicata fisicamente al caso della ri­<lb></lb>frazion della luce, nel seguente corollario, che <lb></lb>il Grandi fa in primo luogo seguitare alla sua <lb></lb>proposizione: “ Quindi è manifesto che la via <lb></lb>da spedirsi in più breve tempo, andando da un <lb></lb>punto a un altro, non è la retta, se non quando <lb></lb>si ha da mantenere in tutto il viaggio la mede­<lb></lb>sima velocità; onde, se si hanno da attraversare diversi mezzi, che diver­<lb></lb>samente resistano al moto, come dovendo attraversare varii campi, altri <lb></lb>nudi, altri vestiti d&#039;erbe, altri imbarazzati da spighe, e passare varie strade <lb></lb>ingombrate da un flusso e reflusso di popolo, non sarebbe buon consiglio <lb></lb>l&#039;andare verso il termine destinato in via retta, ma sarà meglio fare tali <lb></lb>gomiti e svolte, che i seni degli angoli delle loro inclinazioni siano come le <lb></lb>facilità che si hanno ad attraversare que&#039;varii mezzi, come pratica ancora <lb></lb>la Natura nelle rifrazioni. </s>

<s>Come se un oggetto posto in A doverà mandare <lb></lb>un raggio che lo renda visibile all&#039;occhio posto in B, per varii mezzi AG, <lb></lb>CH, DX, EB, tutti diafani, ma di varia rarità, sicchè abbia in essi più fa­<lb></lb>cile il passaggio di mano in mano nella stessa misura in cui crescono i seni <lb></lb>degli angoli ACF, CDG, DEH, EBX; di fatto la via del raggio trasmesso <lb></lb>sarà il flessilineo ACDEB, e non una retta immediatamente tirata dal punto A <lb></lb>al punto B ” (ivi, pag. </s>

<s>136, 37). </s></p><p type="main">

<s>L&#039;Huyghens però, di cui la dimostrazione è stata così bene illustrata <lb></lb>e compiuta dal Grandi, è più originale del Leibniz, che imita più d&#039;appresso <lb></lb>il Fermat e lo compendia. </s>

<s>Professando anch&#039;egli il principio che la Natura <lb></lb><figure id="id.020.01.630.2.jpg" xlink:href="020/01/630/2.jpg"></figure></s></p><p type="caption">

<s>Figura 28.<lb></lb>procede sempre per le vie più facili, a proposito <lb></lb>de&#039;raggi di luce ammette che le difficoltà opposte <lb></lb>al loro viaggio sieno in ragion composta della lun­<lb></lb>ghezza e della resistenza de&#039;mezzi. </s>

<s>“ Sint rectae M, <lb></lb>et N repraesentantes resistentiam repectu luminis, <lb></lb>illa aeris, haec aquae: erit difficultas viae a C ad E <lb></lb>(fig. </s>

<s>28) ut rectangulum CE.M; ab E ad G ut re­<lb></lb>ctangulum EG.N. </s>

<s>Ergo ut difficultas viae CEG <lb></lb>sit omnium minima debet summa rectangulorum <lb></lb>CE.M+EG.N esse omnium possibilium minima, <lb></lb>seu minor quam CF.M+FG.N ” (Op. </s>

<s>Omn., Genevae 1768, T. III, <lb></lb>pag. </s>

<s>145, 46). </s></p><pb xlink:href="020/01/631.jpg" pagenum="74"></pb><p type="main">

<s>Applicando poi il Leibniz la sua teoria de&#039;Massimi e de&#039;Minimi alla <lb></lb>presente ricerca, prova CE.N:EG.M=EN:EL. “ Ergo, positis CE et EG <lb></lb>aequalibus, erit N resistentia aquae respectu luminis ad M resistentiam ae­<lb></lb>ris, ut EH sinus complementi anguli incidentiae in aere ad EL sinum com­<lb></lb>plementi anguli refractionis in aqua; seu sinus complementorum erunt in <lb></lb>reciproca resistentiae mediorum ratione ” (ibi, pag. </s>

<s>146). </s></p><p type="main">

<s>Per quanto sieno queste dimostrazioni ingegnose e, così confortate di <lb></lb>calcolo e di Geometria, facciano quasi violenza alla persuasione di chi le <lb></lb>medita e intende, nonostante si promuovono contro l&#039;Huyghens e il Leibniz <lb></lb>quelle medesime opposizioni che il Clerselier promoveva contro il Fermat, <lb></lb>quando prima introdusse nella Diottrica il principio delle cause finali. </s>

<s>“ Prin­<lb></lb>cipium quod statuis pro fundamento tuae demonstrationis, nimirum Natu­<lb></lb>ram semper agere via aut modo quam maxime brevi et simplici, non phy­<lb></lb>sicum sed morale saltem principium est, quod nunquam est aut esse potest <lb></lb>causa ullius effectus naturae.... Non potest esse causa: hoc enim posito <lb></lb>praesupponeremus cognitionem in Natura, hic autem per Naturam nihil aliud <lb></lb>intelligimus quam ordinem istum et sedem istam in mundo stabilitam talem <lb></lb>qualis est, quae non agit ex praeviso, aut cum electione, aut determinatione <lb></lb>aliqua necessaria ” (Des Cartes. </s>

<s>Epist., Pars. </s>

<s>III cit., pag. </s>

<s>138). </s></p><p type="main">

<s>L&#039;opposizione fatta dal Clerselier e dagli altri cartesiani contro chi nelle <lb></lb>fisiche dimostrazioni introduceva un principio morale, era tanto ragionevole <lb></lb>e giusta che si dovè abbandonare anco questa via, la quale erasi pure mo­<lb></lb>strata a principio tanto lusinghiera, cosicchè può dirsi che, nonostante l&#039;opera <lb></lb>di sì valorosi ingegni, la legge fondamentale della Diottrica, verso la fine del <lb></lb>secolo XVII mancava ancora della sua dimostrazione. </s>

<s>I più savi avranno <lb></lb>pensato d&#039;applicare anche qui il caso della Calottrica di Euclide, il quale <lb></lb>confessò essere la legge di lei indimostrabile, com&#039;è stato confermato da <lb></lb>tanti secoli di progressi. </s>

<s>Ma in ogni modo, come dianzi da noi si diceva, <lb></lb>non potendo consister la scienza ne&#039;semplici fatti e non potendosi dall&#039;al­<lb></lb>tra parte aver perfette le speculazioni, si riduceva ogni studio de&#039;Filosofi a <lb></lb>scansarne quanto fosse possibile i difetti. </s></p><p type="main">

<s>A ciò dette opera e riusci da par suo il Newton, che tornò ad appli­<lb></lb>care alla luce le leggi del moto de&#039;gravi. </s>

<s>L&#039;applicazion neutoniana però era <lb></lb>molto più ragionevole di quella fattane già dal Keplero e dal Cartesio, i quali <lb></lb>non si comprende come potessero sottoporre alle leggi della Meccanica e as­<lb></lb>segnare una maggiore o minore velocità a un moto, che per essi era istan­<lb></lb>taneo e senza tempo. </s>

<s>Inoltre, anco concessa quella maggiore o minore ve­<lb></lb>locità, nessuno degli ottici ne sapeva assegnare una causa fisica, e da tutti, <lb></lb>in cosa di sì grande importanza, si giocava di fantasia. </s></p><p type="main">

<s>Il Newton riguardando la luce come composta di atomi duri proiettati <lb></lb>con grande impeto dal corpo luminoso, e considerando la densità de&#039;mezzi <lb></lb>avere una virtù attrattiva su quegli stessi atomi, procedeva con tutta ragione <lb></lb>ad applicare all&#039;Ottica le leggi meccaniche benissimo allora note de&#039;corpi <lb></lb>gravi proietti. </s>

<s>Nè in quel suo modo di procedere era nulla che non fosse o <pb xlink:href="020/01/632.jpg" pagenum="75"></pb>dimostrato direttamente o per induzione. </s>

<s>Dimostrato direttamente era che la <lb></lb>luce si muove in tempo come tutti gli altri corpi: dimostrato per induzione <lb></lb>dal fenomeno grimaldiano, era che gli atomi luminosi vengono attratti, come <lb></lb>si attraggono a vicenda le minime particelle materiali in tutti i composti. </s></p><p type="main">

<s>Nell&#039;ultima Sezione perciò del I Libro de&#039;<emph type="italics"></emph>Principii<emph.end type="italics"></emph.end> applica alla luce <lb></lb>le leggi del moto de&#039;minimi corpi <emph type="italics"></emph>quae viribus centripetis ad singulas ma­<lb></lb>gni alicuius corporis partes tendentibus agitantur,<emph.end type="italics"></emph.end> e dimostrato nel Teo­<lb></lb>rema XLVIII che questi minimi corpicelli attratti da un mezzo, sempre con <lb></lb>la medesima forza, vi descrivono una linea parabolica, come i gravi proietti <lb></lb>attratti dal centro della Terra; dalle proprietà della stessa parabola ne con­<lb></lb>clude che il seno dell&#039;incidenza ha una determinata proporzione col seno <lb></lb>dell&#039;emergenza. </s>

<s>Passa poi, nel seguente Teorema, a dimostrar che la velo­<lb></lb>cità del proietto avanti l&#039;incidenza è alla velocità di lui dopo l&#039;emergenza, <lb></lb>come il seno dell&#039;emergenza è al seno dell&#039;incidenza. </s></p><p type="main">

<s>I Teoremi neutoniani, come son certissimi nella Meccanica, sarebbero <lb></lb>così certissimi nell&#039;Ottica, quando si potesse ritener come cosa certa che gli <lb></lb>atomi impalpabili della luce non differiscono sostanzialmente dalle molecole <lb></lb>componenti gli altri trattabili corpi. </s>

<s>Ma perchè questo certo non è, perciò <lb></lb>il Newton non pretende che i suoi Teoremi, i quali applicati alla luce da­<lb></lb>rebbero una dimostrazione matematicamente certa delle rifrazioni, sieno come <lb></lb>cose matematicamente dimostrate accolte dagli Ottici. </s>

<s>Solamente egli intende <lb></lb>di determinare la somiglianza che passa fra le traiettorie descritte da&#039;mi­<lb></lb>nimi proietti attraverso un mezzo attraente, e le traiettorie descritte dagli <lb></lb>atomi della luce attraverso ai diafani. </s>

<s>“ Visum est propositiones sequentes <lb></lb>in usus opticos subiungere, interea de natura radiorum utrum sint corpora <lb></lb>necne, nihil omnino disputans, sed traiectorias corporum traiectoriis radio­<lb></lb>rum persimiles solummodo determinans “ (Genevae 1739, pag. </s>

<s>541). </s></p><p type="main">

<s>Così il grande Filosofo e Matematico dava a que&#039;sapienti, che troppo <lb></lb>si confidavan di sè, un bel documento, il quale riducevasi a dire che, in­<lb></lb>fino a tanto che si sarà incerti della natura della luce, la legge delle rifra­<lb></lb>zioni, che pure è certa come un fatto fisico, non sarà mai matematicamente <lb></lb>dimostrabile. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Abbiamo percorso nel paragrafo precedente due buone terze parti del <lb></lb>secolo XVII, dal Cartesio al Newton, e fra coloro che attesero allo studio <lb></lb>delle rifrazioni, non abbiamo avuto da commemorare nessuno dei nostri Ita­<lb></lb>liani. </s>

<s>Chi volesse argomentare da ciò che poca parte dovettero i Nostri aver <lb></lb>presa in que&#039;diottrici studii, forse non in tutto s&#039;ingannerebbe, ma ab­<lb></lb>biamo in ogni modo là taciuto, per narrar qui tutti insieme i fatti, che più <pb xlink:href="020/01/633.jpg" pagenum="76"></pb>importano alla nostra Storia rimasta sopra, nel Maurolico, nel Porta e nel <lb></lb>De Dominis, interrotta. </s></p><p type="main">

<s>Il filo si riappicca alla scienza di Galileo, la quale, da chi ha letto il <lb></lb>Cap. </s>

<s>III del Tomo precedente, si sa troppo bene oramai, quant&#039;ella fosse <lb></lb>scarsa. </s>

<s>Quel ch&#039;egli poi sa in tal soggetto è appreso dagli Ottici, de&#039;quali <lb></lb>pure, insiem con le poche verità, si ripetono i molti errori. </s>

<s>Può servir <lb></lb>d&#039;esempio il concetto che avevasi dell&#039;essenza e della natura delle rifrazioni. </s>

<s><lb></lb>Il Keplero, come notammo, le riduceva a una riflessione <emph type="italics"></emph>plane similis illis <lb></lb>quae fiunt in corporibus naturalibus proiectis,<emph.end type="italics"></emph.end> e il Boulliaud, che pur non <lb></lb>consente con l&#039;error kepleriano della diffusione superficiale, d&#039;ond&#039;ebbe oc­<lb></lb>casione quella similitudine; non altrimenti qualifica la rifrazione che per una <lb></lb>riflessione interna. </s></p><p type="main">

<s>Tale è pure il concetto di Galileo, il quale, se parla di refrazioni, cause <lb></lb>de&#039;crepuscoli, delle aurore boreali, e degli effetti osservati da Ticone nelle <lb></lb>apparenze degli astri, non intende quelle stesse rifrazioni per altro modo, <lb></lb>che per riflessioni fatte da&#039;raggi luminosi, mentre incontran per la loro via <lb></lb>le vescicole del vapore acquoso, o le tenuissime particelle delle terrestri esa­<lb></lb>lazioni. </s>

<s>Perciò l&#039;aria purissima e l&#039;etere e qualunque materia, che non sia <lb></lb>atta a riflettere, non è, secondo Galileo, nemmeno atta a rifrangere i raggi <lb></lb>della luce. </s>

<s>Non volendo il Sarsi e il suo Maestro, così scrive nel <emph type="italics"></emph>Saggia­<lb></lb>tore<emph.end type="italics"></emph.end> “ che la Cometa sia un incendio ma inclinando a credere, s&#039;io non <lb></lb>erro, che almeno la sua coda sia una refrazione dei raggi solari, io gli do­<lb></lb>manderò se ei credono che la materia, nella quale si fa tal refrazione, sia <lb></lb>tagliata appunto alla misura di essa chioma, o pur che di qua e di là e di <lb></lb>ogni intorno ve ne avanzi, e se ve ne avanza, come credo che sarà rispo­<lb></lb>sto, perchè non si vede, essendo tocca dal Sole? </s>

<s>Qui non si può dire che <lb></lb>la refrazione si faccia nella sostanza dell&#039;etere, la quale come diafanissima <lb></lb>non è potente a ciò fare, nè meno in altra materia, la quale, quando fosse <lb></lb>atta a rifrangere, sarebbe ancora atta a riflettere i raggi solari ” (Alb IV, 247). </s></p><p type="main">

<s>Chi vuole, può svolgendo anche il solo <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> notare moltissimi <lb></lb>altri passi, da&#039;quali si rivela il medesimo concetto, e perciò, intesa intorno <lb></lb>a questo punto la mente di Galileo, ci spinge la curiosità a saper quel ch&#039;ei <lb></lb>ne pensasse della legge relativa alle proporzioni che passano tra gli angoli <lb></lb>incidenti e i refratti. </s></p><p type="main">

<s>Sappiamo per cosa certa che in sulla fine dell&#039;anno 1637 egli ebbe, <lb></lb>per cura del Cartesio, la Diottrica, a leggere o a farsi leggere il qual libro, <lb></lb>in quella parte specialmente dove si tratta del Telescopio, Galileo s&#039;ebbe <lb></lb>molto a male di non trovarvisi nominato. </s>

<s>Con chi facesse direttamente que­<lb></lb>sti rammarichi non sappiamo di certo, ma forse con Elia Diodati, per mezzo <lb></lb>del quale il Mersenno, che ne aveva avuta commission dal Cartesio, inviò <lb></lb>il volume da Parigi ad Arcetri. </s>

<s>Fatto si è che di que&#039;rammarichi il Mer­<lb></lb>senno stesso faceva, per lettera scritta il di 8 Gennaio 1638, consapevole il <lb></lb>Cartesio, il quale così rispondeva: “ Quantum ad illum quam me culpare <lb></lb>dicis, quod Galilaeum non nominaverim, apparet eum quaerere quod re-<pb xlink:href="020/01/634.jpg" pagenum="77"></pb>prehendat, nec tamen eius invenire causam. </s>

<s>Neque enim ipse Galilaeus sibi <lb></lb>perspicillorum inventionem attribuit, mihi autem non nisi de eorum inven­<lb></lb>tore dicendum fuit ” (Epist. </s>

<s>cit., pag. </s>

<s>88). </s></p><p type="main">

<s>Passa poi a dir perchè non nominasse nemmeno gli Autori d&#039;Ottica, <lb></lb>che lo avevano preceduto. </s>

<s>Noi sappiam bene qual si fosse di ciò la segreta <lb></lb>ragione, ma il Cartesio trova certe scuse, ripensando alle quali ci confer­<lb></lb>miam sempre più nell&#039;opinione che fossero in lui maggiori della scienza, <lb></lb>l&#039;astuzia e l&#039;orgoglio. </s>

<s>“ Neque etiam nominandi mihi fuerunt, qui ante me <lb></lb>de Optica scripserunt. </s>

<s>Neque enim scribere historiam animus erat, satisque <lb></lb>habui in genere asseruisse etiamnum fuisse qui plurima invenerint, nec pos­<lb></lb>sem argui me aliorum inventionem mihi attribuere voluisse, in quo plus <lb></lb>mihi metipsi iniuriae feci, quam illis quorum nomina omisi. </s>

<s>Cogitari quippe <lb></lb>potest eos multo plura fecisse, quam fortasse eos fecisse deprehenderetur, <lb></lb>si dixissem quinam illi essent ” (ibi). </s></p><p type="main">

<s>Il di 2 di Gennaio di quello stesso anno 1638, Elia Diodati riceve da <lb></lb>Arcetri una lettera, nella quale si diceva: “ Signor mio, il Galileo vostro <lb></lb>caro amico e servitore, da un mese in qua è fatto irreparabilmente del tutto <lb></lb>cieco ” (Alb. </s>

<s>VII, 207). La triste nuova fu dal Diodati partecipata al Mer­<lb></lb>senno, e questi, con lettera del dì 12 di Febbraio, l&#039;annunziò al Cartesio, <lb></lb>il quale dispiacente gli rispondeva: “ Doleo Galilaeum usum oculorum ami­<lb></lb>sisse, quamquam enim eum non nominatum exprimam, persuasum habeo <lb></lb>ipsum Dioptricam meam non habiturum fuisse contemtui ” (ibi, pag. </s>

<s>90). </s></p><p type="main">

<s>Noi possiamo però con tutta la probabilità asseverare che le persuasioni <lb></lb>del Cartesio riusciron fallaci. </s>

<s>Se in ogni modo Galileo non disprezzò la Diot­<lb></lb>trica, è certo ch&#039;ei non se ne curò, nè si rimosse, per le novità cartesiane, <lb></lb>dalle sue opinioni antiche. </s>

<s>Più che la non curanza però si direbbe che fu <lb></lb>dal Torricelli ereditato il disprezzo, secondo lo proverebbe il modo, com&#039;ei <lb></lb>rispose al Mersenno, che lo sollecitava a leggere la Diottrica in francese, e <lb></lb>poco di poi, per levargli ogni scusa, nella diffusissima traduzione latina. </s></p><p type="main">

<s>Anche il Cavalieri se sa nulla della legge ritrovata fra i seni delle in­<lb></lb>clinazioni e i seni delle rifrazioni, non l&#039;ha avuto dal Cartesio ma indiret­<lb></lb>tamente dall&#039;Herigonio. </s>

<s>L&#039;amico e il maestro del Torricelli però non voltò <lb></lb>con dispetto le spalle a colui, che formulò quella legge nè la rifiuta per <lb></lb>falsa: ne riman soltanto dubitoso e diffidente, perchè questo principio, egli <lb></lb>dice, lo prova l&#039;Herigonio “ solo facendo un trapasso dalla Meccanica alla <lb></lb>Diottrica, con dire che l&#039;impulso del raggio cadente per un piano eretto o <lb></lb>inclinato sopra l&#039;orizzonte, ha la medesima inclinazione che ha il raggio sopra <lb></lb>la superficie del diafano, e di questo non porta altra ragione, e per questo <lb></lb>sono stato sempre dubitoso ” (Pref. </s>

<s>alle Lez. </s>

<s>del Torricelli, Milano 1823, <lb></lb>pag. </s>

<s>25). </s></p><p type="main">

<s>Si può dire che in questa e in poche altre Lettere del Cavalieri, scritte <lb></lb>nel 1644, sia dal 1637 al 1660, concluso tuttociò che fu pensato e scritto <lb></lb>intorno alla legge delle rifrazioni in Italia, la quale perciò ne rimase in una <lb></lb>piena ignoranza In Francia invece si discuteva, con grande ardore: i Fi-<pb xlink:href="020/01/635.jpg" pagenum="78"></pb>sici più esperti e i Matematici più valorosi insorgevano contro il Cartesio, <lb></lb>il quale stizzito appellava que&#039;rivoltosi calunniatori malevoli, che non discu­<lb></lb>tono, ma fanno baccano, gente da esser guardate col ghigno della compas­<lb></lb>sione, perchè hanno perduto il bene dell&#039;intelletto. </s>

<s>“ Tibi ultro declaraverim, <lb></lb>scriveva al Mersenno, tantum abesse ut calumniis, quae de me sparguntur, <lb></lb>excandescam, ut etiam ultro gaudeam, existimando eas quo magis enormes <lb></lb>et extravagantes sunt, quippe tanto minus me feriunt, eo magis mihi hono­<lb></lb>rifices fore, atque ob ideo gratiores. </s>

<s>Et persuasum habeo malevolos non <lb></lb>tanta sollicitudine in me debacchaturos, nisi simul essent, qui de me hono­<lb></lb>rifice loquerentur sentirentque, praeterquam quod veritas interdum contra­<lb></lb>dictione opus babeat, quo magis elucescat. </s>

<s>Verum cachinno excipiendi sunt <lb></lb>illi, qui ratione et fundamentis destituti loquuntur ” (Epist. </s>

<s>cit., pag. </s>

<s>87). </s></p><p type="main">

<s>Morto il Cartesio, non cessarono le controversie nè l&#039;ardore delle in­<lb></lb>vestigazioni, le quali si fecero saviamente passare, dalle Matematiche astratte <lb></lb>e dalle aeree speculazioni, al severo giudizio delle esperienze. </s>

<s>Il Petit pro­<lb></lb>nunziò che la legge prescritta dal Cartesio riscontrava co&#039;fatti; l&#039;Autore della <lb></lb>Dottrica ritornò in onore, e in Francia erasi oramai stabilita la scienza delle <lb></lb>rifrazioni. </s>

<s>Ciò fu verso il 1660, quando ancora in Italia nessuno aveva ve­<lb></lb>duto o ripensato a quel che della Diottrica era stato scritto nella famosa <lb></lb>Dissertazione <emph type="italics"></emph>Del Metodo.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La prima copia del libro capitata in Firenze venne alle mani del priore <lb></lb>Orazio Ricasoli Rucellai, il quale, ne&#039;primi giorni di Aprile dell&#039;anno 1660, <lb></lb>si mette una mattina il libro sotto il braccio, e va a trovare l&#039;amico suo <lb></lb>Vincenzio Viviani. </s>

<s>Lo trovò nel suo studio seduto al banco, sopra il quale <lb></lb>gli pose innanzi il libro della Diottrica aperto al paragrafo IV del capitolo II. </s>

<s><lb></lb>Incomincia a leggere il Viviani: “ Hinc progrediamur ad refractionem et <lb></lb>primo fingamus pilam ab A ad B expulsam offendere non terram sed lin­<lb></lb>teum CBE.... ” E finito di leggere il paragrafo, il Rucellai gli chiude sotto <lb></lb>gli occhi per riprendersi il libro. </s>

<s>Il meditativo lettore rimase dubbioso. </s>

<s>— Ma <lb></lb>le rifrazioni della luce, diceva verso l&#039;amico, si fanno in modo contrario a <lb></lb>quello della palla; or come mai .... — nè l&#039;amico sapeva che si rispon­<lb></lb>dere. </s>

<s>Lo prega gli renda il libro, glielo lasci; il Rucellai ha fretta, vuol ri­<lb></lb>portare il libro con sè, gli stringe amichevolmente la mano, e addio. </s></p><p type="main">

<s>Il Viviani rimasto in quel dubbio penoso che lo tormentava, parendogli <lb></lb>esser certo che quello della palla grave, la quale incontra il velo o è get­<lb></lb>tata nell&#039;acqua, non era il modo delle ottiche rifrazioni, e non potendo cre­<lb></lb>dere che l&#039;Autore avesse potuto dimostrare un effetto contrario a quello che <lb></lb>si osserva in natura; non ebbe pace in fin tanto che non tornò a rileggere, <lb></lb>per veder meglio come stavan le cose. </s>

<s>Un altro suo amico, eccitato dall&#039;esem­<lb></lb>pio del Rucellai, s&#039;era fatto venire il libro, e da lui il Viviani, con più libe­<lb></lb>ralità l&#039;ebbe in prestito. </s>

<s>Lesse tutto per ordine e ne rimase così sodisfatto, <lb></lb>che subito, la mattina del dì 12 Aprile, prese la penna in mano per scri­<lb></lb>vere al Rucellai il seguente biglietto: </s></p><p type="main">

<s>“ In questo punto ho ricevuto in presto da un amico .... la Diottrica <pb xlink:href="020/01/636.jpg" pagenum="79"></pb>del Cartesio .... ed ho trovato che non senza cagione intoppai al numero IV <lb></lb>del II capitolo, dove V. S. Ill.ma mi fece leggere, perchè era necessario che <lb></lb>io vedessi innanzi le supposizioni e progressi dell&#039;Autore. </s>

<s>Ora letto il tutto, <lb></lb>è forza confessare che il modo di salvare gli effetti della riflessione e delle <lb></lb>rifrazioni è bellissimo, ingegnosissimo, e maravigliosissimo. </s>

<s>Ricordo bene a <lb></lb>V. S. che, quanto alle rifrazioni, il negozio procede sicuramente nel modo <lb></lb>che io le accennai l&#039;altro giorno, cioè che i raggi, passando da un corpo <lb></lb>raro per uno men raro, si refrangono verso la perpendicolare e non verso <lb></lb>la superficie, come segue del moto della palla dopo l&#039;incontro nel panno o <lb></lb>velo, essendo questo un esempio dato dal Cartesio di un effetto contrario <lb></lb>per contrarie cagioni ” (MSS. Gal. </s>

<s>Disc, T. CXLII, c. </s>

<s>61). </s></p><p type="main">

<s>Quel Viviani dunque succeduto a Galileo e al Torricelli a rappresentare <lb></lb>la scienza sperimentale in Italia, non ha, come il Fermat e altri insigni <lb></lb>Francesi, che ridir nulla contro i processi dimostrativi del Cartesio: tutto è <lb></lb>in lui <emph type="italics"></emph>bellissimo, ingegnosissimo, maravigliosissimo.<emph.end type="italics"></emph.end> Dietro la lettura delle <lb></lb>seducenti pagine cartesiane ritiene come per cosa certa la costante propor­<lb></lb>zione, non fra gli angoli, come professavano col Maurolico gli Italiani, ma <lb></lb>fra i seni degli angoli fatti colla perpendicolare dai raggi incidenti e dai re­<lb></lb>fratti. </s>

<s>Così la scienza diottrica veniva fra noi, dopo lungo indugio accolta <lb></lb>senza contradizioni, ciò che, se in quel primo fervore si dee alle attrattive <lb></lb>che presentava il lucido orpello cartesiano, il finale motivo per cui si per­<lb></lb>suase il Viviani della verità delle nuove dottrine fu tutto frutto delle espe­<lb></lb>rienze. </s></p><p type="main">

<s>A lui infatti è dovuta l&#039;invenzione di quella <emph type="italics"></emph>Scatola delle rifrazioni,<emph.end type="italics"></emph.end><lb></lb>che si trova descrittta dai Fisici in quasi tutti i loro Trattati, nei quali però <lb></lb>si tace l&#039;Autore, che da alcuni erroneamente si crede essere stato il Carte­<lb></lb>sio. </s>

<s>Il Viviani ha di quella Scatola varii disegni abbozzati, il più finito de&#039;quali <lb></lb>può vedersi a carte 261 del IV Tomo de&#039;MSS. del Cimento. </s>

<s>Di ciò poi s&#039;ha <lb></lb>la conferma in quella Nota d&#039;invenzioni, altra volta citata, nella quale si <lb></lb>legge di mano propria dello stesso Viviani: <emph type="italics"></emph>Mia la scatola per le rifrazioni <lb></lb>de&#039;fluidi<emph.end type="italics"></emph.end> (MSS. Cim., T. X, c. </s>

<s>259). </s></p><p type="main">

<s>Quando il Newton ebbe scoperta la varia refrangibilità de&#039;raggi com­<lb></lb>ponenti la luce, venne a metter negli Ottici uno scrupolo intorno al modo <lb></lb>di misurar, colla scatola del Viviani, le rifrazioni. </s>

<s>“ Credo enim illos qui <lb></lb>refractiones antehac mensuravere, sive id factum sit, ut iam dicta hypothe­<lb></lb>sis Cartesii probaretur, sive aliis de causis, credo illos inquam mensuram <lb></lb>instituisse ad medietatem refractae lucis, hoc est si spatium a coloribus oc­<lb></lb>cupatum spectemus ad confinium viridis et coerulei.... Porro cum forte <lb></lb>desideretur accuratius examen dictae regulae cartesianae, quam antehac insti­<lb></lb>tuebatur, dum varia radiorum refrangibilitas experientes latuit, primo dicam <lb></lb>quo pacto id non incommode fiat ” (Lectiones opt., Patavii 1773, pag. </s>

<s>15). <lb></lb>E segue appresso a descrivere un macchinamento di scrupolosa precisione, <lb></lb>ma da non venire a confronto, per la comoda facilità, colla Scatola del Vi­<lb></lb>viani, la quale perciò serve ancora a sperimentar nelle Scuole. </s></p><pb xlink:href="020/01/637.jpg" pagenum="80"></pb><p type="main">

<s>Sedotto dall&#039;esempio della palla che incontra l&#039;acqua, esempio che a <lb></lb>lui parve maravigliosissimo, il Viviani non lo lasciò sterile ricevendolo dal <lb></lb>Cartesio, come sterile l&#039;avea lasciato il Cartesio ricevendolo dal Keplero, ma <lb></lb>pensò di fecondarlo in modo, che s&#039;accostasse più strettamente il fatto mec­<lb></lb>canico a fiancheggiare il diottrico. </s>

<s>Consisteva quel pensiero nel volere spe­<lb></lb><figure id="id.020.01.637.1.jpg" xlink:href="020/01/637/1.jpg"></figure></s></p><p type="caption">

<s>Figura 29.<lb></lb>rimentare quali mutazioni, per le varie obliquità, <lb></lb>faceva la direzione della palla entrata nell&#039;acqua, <lb></lb>forse per veder se avveravasi anco in questo caso, <lb></lb>come per la luce, la legge de&#039;seni. </s>

<s>Abbiamo di <lb></lb>questo pensiero le vestigie nella seguente nota au­<lb></lb>tografa: “ Diverse prove da farsi, tra le quali que­<lb></lb>sta: se nel vaso AB (fig. </s>

<s>29) pien d&#039;acqua, la­<lb></lb>sciando scorrere giù per un&#039;assicella DF una pallina <lb></lb>per aria, che poi entri nell&#039;acqua; se, nell&#039;entrare <lb></lb>nell&#039;acqua, muti direzione di moto con alzarsi del­<lb></lb>l&#039;assicella, come io credo ” (MSS. Cim., T. IV, <lb></lb>c. </s>

<s>244). </s></p><p type="main">

<s>Non contento il Viviani di starsene ai modi di sperimentare da sè in­<lb></lb>ventati, faceva saggio de&#039;modi proposti anche dagli altri, e a carte 101 del <lb></lb>Tomo XI de&#039;citati MSS. del Cimento, si vede di sua propria mano abboz­<lb></lb>zato un disegno, allato al quale si legge: “ Strumento del Keplero per os­<lb></lb>servare gli angoli delle refrazioni. </s>

<s>” Questo strumento kepleriano è quello <lb></lb>che vedesi disegnato a principio della Diottrica, e per mezzo del quale pro­<lb></lb>ponevasi l&#039;Autore di sciogliere il seguente problema: “ Pellucidi corporis <lb></lb>duri refractiones artificiose metiri in omni radiorum inclinatione ” (Aug. </s>

<s><lb></lb>Vindel. </s>

<s>1611, pag. </s>

<s>1). </s></p><p type="main">

<s>Così, mentre il Viviani con la sua Scatola sperimentava le rifrazioni <lb></lb>ne&#039;liquidi, collo strumenlo kepleriano le sperimentava ne&#039;cristalli, non la­<lb></lb>sciando per nessuna parte il nuovo campo diottrico inesplorato. </s>

<s>Queste no­<lb></lb>stre investigazioni riuscite non affatto infelici accesero in noi il desiderio di <lb></lb>procedere a investigare se il Viviani avesse tertato nessuna applicazione di <lb></lb>que&#039;suoi studii alla diottrica delle lenti. </s>

<s>Com&#039;a splendido segno fra le te­<lb></lb>nebre si teneva da noi collo sguardo dietro alle relazioni che passarono tra <lb></lb>l&#039;Huyghens e l&#039;Accademia fiorentina, a proposito della Diottrica. </s></p><p type="main">

<s>Nella <emph type="italics"></emph>Brevis assertio Systematis sui<emph.end type="italics"></emph.end> prometteva l&#039;Autore della scoperta <lb></lb>dell&#039;Anello saturnio “ quae ad theoriam Dioptrices spectant propediem in <lb></lb>lucem mittere ” (Op. </s>

<s>varia, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>627), promessa che, <lb></lb>ripetuta per lettera privata al principe Leopoldo, moveva questi a stringere <lb></lb>il promittente a mantenere, scrivendogli il dì 19 Novembre 1660: “ Intanto <lb></lb>starò attendendo l&#039;invenzione del suo nuovo modo di Canocchiali, e dopo <lb></lb>il suo ritorno in Olanda quell&#039;Opera che ella ne promette ” (MSS. Cim., <lb></lb>T. XXIII, c. </s>

<s>44). </s></p><p type="main">

<s>Sei anni dopo, nel Giugno, tornava l&#039;Huyghens a concluder così un&#039;al­<lb></lb>tra sua Lettera indirizzata al medesimo principe Leopoldo: “ Certo che per <pb xlink:href="020/01/638.jpg" pagenum="81"></pb>la mia parte, siccome da più anni in qua ho fortemente amato questo stu­<lb></lb>dio (della Diottrica), così ho pensiero di non tralasciarlo per l&#039;avvenire, e <lb></lb>spero che un giorno si stamperà quello che in questo genere ho speculato, <lb></lb>e che anche la pratica stessa di quest&#039;arte riceverà qualche aiuto dalle mie <lb></lb>nuove speculazioni ed esperienze ” (ivi, T. XVIII, c. </s>

<s>316). Le speranze si <lb></lb>sarebbero colorite assai presto, giacchè l&#039;anno appresso mandava a dire a <lb></lb>Firenze che le figure erano già intagliate, cosicchè in breve la Diottrica de­<lb></lb>siderata si pubblicherebbe. </s></p><p type="main">

<s>“ Cristiano Ugenio nella sua de&#039;18 Novembre 1667, dopo aver rese <lb></lb>all&#039;A. V. le dovute grazie, per una mano d&#039;opere nuove matematiche sta­<lb></lb>tegli inviate da V. A. di tempo in tempo, passa a sodisfare alla richiesta di <lb></lb>lei col darle contezza de&#039;proprii studii, e in particolare del Trattato della <lb></lb>Diottrica, il quale stava in breve per pubblicare, essendo già intagliate tutte <lb></lb>le figure ” (ivi, T. XXI, c. </s>

<s>99). </s></p><p type="main">

<s>Questa scrittura che leggesi ripetuta a carte 135 del T. CXXXIII de&#039;Di­<lb></lb>scepoli di Galileo, indirizzata al principe Leopoldo, è autografa del Viviani, <lb></lb>ma la pubblicazione che par così prossima del Libro tante volte promesso <lb></lb>e con tanto desiderio aspettato, benchè il Cassini abbia sentito dire ch&#039;era <lb></lb>già stata fatta (MSS. Cim., T. XIV, c. </s>

<s>51), indugiò ancora, non sappiamo <lb></lb>dire il perchè, 36 anni intieri, e avvenne in Leyda nel 1703, quando il Vi­<lb></lb>viani moriva, e quando già di alquanti anni il principe Leopoldo e l&#039;Huy­<lb></lb>ghens lo avevano preceduto nel sepolcro. </s></p><p type="main">

<s>Le notizie di queste relazioni passate fra il celebre Autore olandese <lb></lb>della Diottrica e la nostra Accademia, non son certamente prive d&#039;impor­<lb></lb>tanza storica, ma tornaron prive di effetto per la nostra intenzione, perchè <lb></lb>non s&#039;è trovato che l&#039;Huyghens comunicasse o proponesse a speculare nes­<lb></lb>suno di que&#039;diottrici teoremi da pubblicarsi, al Viviani. </s>

<s>Nè ci è riuscito di <lb></lb>trovare altri documenti o di esperienze fatte o di teorie speculate nella fio­<lb></lb>rentina Accademia intorno alla ragione e al modo delle ottiche rifrazioni. </s>

<s><lb></lb>Solo ha il Rinaldini una Lettera indirizzata ad Anonimo, nella quale riprova <lb></lb>il processo del Maurolico di ricorrere all&#039;esperienza per prender le propor­<lb></lb>zioni fra gli angoli: egli vuol aver motivo piuttosto da filosofare, e perciò <lb></lb>dice di essersi rivolto a cercare i principii dottrinali. </s>

<s>Ma quali fossero que­<lb></lb>sti principii si può argomentar dalla leggerezza che si trova in quella stessa <lb></lb>sua Lettera, tutta la scienza contenuta nella quale si riduce a dar grande <lb></lb>importanza, e a discutere intorno a ciò che il semplice sguardo decide, ri­<lb></lb>volgendolo sulla figura che, ne&#039;<emph type="italics"></emph>Diafani<emph.end type="italics"></emph.end> del Maurolico, è impressa a illu­<lb></lb>strare il X Teorema. </s></p><p type="main">

<s>“ Mi convien dirle che, quando in quella mia lettera, che ella dice ritro­<lb></lb>varsi presso il sig. </s>

<s>Cassini, io dico che il Maurolico asserisce la proporzione <lb></lb>tra l&#039;aria ed il cristallo esser come 8 a 3, si deve intendere, com&#039;io intendo <lb></lb>con esso lui, tra l&#039;angolo dell&#039;inclinazione e non dell&#039;incidenza con quello <lb></lb>della rifrazione. </s>

<s>Ma perchè, o facciasi comparazione tra l&#039;angolo dell&#039;incli­<lb></lb>nazione con quello della rifrazione, o tra l&#039;angolo dell&#039;incidenza col mede-<pb xlink:href="020/01/639.jpg" pagenum="82"></pb>simo angolo della rifrazione, prender la proporzione dall&#039;esperienza non mi <lb></lb>pare il dovere, conciossiachè da quella può ben cavarsi motivo da filosofare, <lb></lb>ma non già da stabilire una precisa proporzione; perciò dovendo dimostrar <lb></lb>quel Teorema che in quella lettera accenno mi è parso gittarmi ad altro <lb></lb>principio. </s>

<s>Il che ho voluto significare a V. S. perchè lo conferisca anche al <lb></lb>sig. </s>

<s>Cassini, ad effetto che non credino da me essere stato detto che il Mau­<lb></lb>rolico parli della proporzione tra l&#039;angolo dell&#039;incidenza e della rifrazione, <lb></lb>perciocchè, come dissi, deve intendersi tra l&#039;angolo dell&#039;inclinazione e della <lb></lb>sua rifrazione. </s>

<s>Gli angoli poi d&#039;inclinazione vengono dal suddetto presi per <lb></lb>quelli che son formati da&#039;raggi retti con la linea perpendicolare, come in <lb></lb>quel luogo viene avvertito dal Clavio nelle sue Annotazioni ” (MSS. Cim., <lb></lb>T. XXV, c. </s>

<s>4). </s></p><p type="main">

<s>I principii diottrici insomma professati dai nostri Accademici del Ci­<lb></lb>mento rimangono ancora que&#039;<emph type="italics"></emph>bellissimi, ingegnosissimi, maravigliosissimi<emph.end type="italics"></emph.end><lb></lb>del Cartesio. </s>

<s>Pare impossibile che il Viviani rimeditando poi più riposata­<lb></lb>mente sopra quegli stessi principii non v&#039;avesse incontrata qualche difficoltà <lb></lb>in seguitare a passare per maravigliosissima quella ipotesi cartesiana, tanto <lb></lb>contraria all&#039;esperienza, de&#039;mezzi più densi che, invece d&#039;impedire, facili­<lb></lb>tano il moto alla luce. </s>

<s>L&#039;errore meccanico, così caratteristico della scuola <lb></lb>galileiana, che cioè un moto obliquo non si possa altrimenti decomporre che <lb></lb>in due ortogonali, non fece veder chiari al Viviani que&#039;difetti, nella dimo­<lb></lb>strazion cartesiana, dal Fermat, così sottilmente notati; ma non par vero <lb></lb>che il gran Fisico fiorentino non s&#039;avesse una volta a persuadere, per quelle <lb></lb>sue diottriche esperienze, che Galileo e il Cartesio si conformavano piuttosto <lb></lb>a una capricciosa ipotesi kepleriana che all&#039;evidenza de&#039;fatti naturali, quando <lb></lb>supponevano che le refrazioni non si facessero equabilmente per entro il <lb></lb>mezzo, ma nella sola superficie. </s></p><p type="main">

<s>A restaurar l&#039;onore della scienza italiana, che s&#039;era così servilmente <lb></lb>infrancesata, sorse da tutt&#039;altro gregge che da quello adunato nelle sale me­<lb></lb>dicee, nel 1665, il Grimaldi col suo celebre trattato <emph type="italics"></emph>De lumine, coloribus et <lb></lb>iride.<emph.end type="italics"></emph.end> Egli prende a esaminar sottilmente nella proposizione XIX l&#039;opinion <lb></lb>del Cartesio, nella quale s&#039;ammette che maggior resistenza faccia al moto <lb></lb>della luce un mezzo raro che un denso. </s>

<s>“ Quin immo in contrarium ma­<lb></lb>nifeste reclamat experientia, qua videmus corpora proiecta facilius moveri <lb></lb>per aerem, quam per aquam, et universaliter ea ferri velocius per medium <lb></lb>rarius, caeteris paribus, quoad impetum et conatum quo impelluntur ” (Bo­<lb></lb>noniae, pag. </s>

<s>176). </s></p><p type="main">

<s>Soggiunge poi il Grimaldi un&#039;acutissima osservazione, sfuggita forse agli <lb></lb>stessi acuti censori francesi, ed è che al Cartesio conveniva provare e non <lb></lb>gratuitamente asserire che il raggio, dop&#039;aver penetrato il diafano resistente, <lb></lb>patisce difficoltà secondo una sola delle due direzioni, in che s&#039;immagina <lb></lb>esser decomposto il suo moto. </s>

<s>“ Dato enim quod superficies talis corporis <lb></lb>resistat motui luminis quoad solum ingressum, reliquum tamen corporis infra <lb></lb>superficiem si resistit, utique aequaliter resistit secundum omnes sui partes: <pb xlink:href="020/01/640.jpg" pagenum="83"></pb>ac proinde tam quoad descensum quam quoad progressum ipsi superficiei <lb></lb>coextensum debet intelligi retardatum lumen infra superficiem illam decur­<lb></lb>rens, neque est potior ratio quod ad unam potius quam ad aliam partem <lb></lb>deflectat ” (ibi). Ma il Grimaldi s&#039;è presto infastidito dell&#039;esame di questa <lb></lb>opinion cartesiana, che crolla tentata per tutti i versi. </s>

<s>“ Alia multa possent <lb></lb>obiici contra hanc opinionem, sed satius est eam et illa dimittere ” (ibi). <lb></lb>Così lascia la ipotesi del Cartesio per venire a dire la sua. </s></p><p type="main">

<s>Della costante uniformità fra i seni degli angoli dell&#039;incidenza e i seni <lb></lb>degli angoli di rifrazione dice il Grimaldi “ posse reddi congruentem ratio­<lb></lb>nem si attendamus refractionem moderari et distribui dependenter a radii <lb></lb>dilatatione vel restrictione ” (ibi, pag. </s>

<s>184). Egli professa che la luce si re­<lb></lb>frange dalla perpendicolare mentre passa obliquamente da un più denso <lb></lb>mezzo a un più raro, <emph type="italics"></emph>quia cogitur diffundi pressius.<emph.end type="italics"></emph.end> Ma da un&#039;altra parte <lb></lb>il moto dee sempre serbarsi equabile, perchè altrimenti <emph type="italics"></emph>fluxus acceleratio <lb></lb>inferret periculum discontinuationis inter velociores partes luminis et tar­<lb></lb>diores.<emph.end type="italics"></emph.end> E in che modo si può mantenere questa equabilità? </s>

<s>Col rattempe­<lb></lb>rare il moto troppo veloce, risponde l&#039;Autore, e col velocitare il troppo tardo. </s>

<s><lb></lb>Or l&#039;artificio della Natura consiste in ciò che nel passar, per esempio, il <lb></lb>raggio dell&#039;aria nel cristallo, incontrandovi una maggior resistenza, acquista <lb></lb>nuovo impulso al suo moto, ingrossando. </s>

<s>Nè ciò può avvenire, dice il Gri­<lb></lb>maldi, se non che rifrangendosi alla perpendicolare, e lo dimostra al modo <lb></lb>che segue: </s></p><p type="main">

<s>“ Incidat superficici planae AB (fig. </s>

<s>30) radius CDE subtilissimus, et <lb></lb>crassitiei ad sensum nostrum indivisibilis, quae tamen aliqua sit, et geome­<lb></lb>trice divisibilis in partes quam plurimas. </s>

<s>Immo etiam tanta, ut non tam <lb></lb>radius ille dicendus sit quam radiatio, seu radiorum aggregatum, qui cum <lb></lb><figure id="id.020.01.640.1.jpg" xlink:href="020/01/640/1.jpg"></figure></s></p><p type="caption">

<s>Figura 30<lb></lb>veniant ab uno eodemque puncto <lb></lb>C remotissimo, poterunt conside­<lb></lb>rari tanquam paralleli saltem ad <lb></lb>sensum. </s>

<s>Ex illis autem conside­<lb></lb>rentur nunc duo tantum extremi <lb></lb>CD, et CE, qui cum oblique in­<lb></lb>currant in superficiem AB medii <lb></lb>densioris refringuntur versus per­<lb></lb>pendicularem ductam per punctum <lb></lb>incidentiae nempe CD versus DF <lb></lb>et CE versus EG, ita ut radii di­<lb></lb>recti CD refractus sit DH, et radii <lb></lb>CE refractus sit EI. </s>

<s>Totum ergo <lb></lb>lumen, quod intra duos radios CD, CE continebatur, dum per aerem exempli <lb></lb>gratia decurrebat, continetur deinde post refractionem intra duos DH, et EI <lb></lb>dum procedit per corpus aere densius, puta, per crystallum cuius plana <lb></lb>superficies est AB. ” </s></p><p type="main">

<s>“ Dico igitur lumen quod continetur in radio CDE, si velit dilatari de-<pb xlink:href="020/01/641.jpg" pagenum="84"></pb>bere flecti versus praedictas perpendiculares et per hanc solam refractionem <lb></lb>haberi intentum. </s>

<s>Si enim recta procedunt in L dubium non est quod non <lb></lb>mutaret latitudinem seu crassitiem, sed conservaret eam prorsus quam ha­<lb></lb>bebat in aere. </s>

<s>Et si diverteret versus AD recedendo a perpendiculari, mi­<lb></lb>nueret antiquam crassitiem.... At si per refractionem modo dicto flectatur <lb></lb>versus perpendicularem, ut de facto flectitur, latitudo radii, quae prius erat <lb></lb>ME, evadit DO, scilicet mensurata per transversalem lineam utrique lateri <lb></lb>radii orthogonam. </s>

<s>Est autem DO maior quam ME quia sumpto eodem ra­<lb></lb>dio seu sinu toto DE, recta DO est sinus anguli DEO, et recta ME est si­<lb></lb>nus anguli MDE; sed angulus DEO maior est angulo MDE, quia hic per <lb></lb>XXIX primi Euclidis aequatur alterno DEL (non MDL come per errore tra­<lb></lb>scorso si legge nella stampa) qui est pars totius anguli DEO. </s>

<s>Ergo et sinus <lb></lb>anguli DEO nempe DO, maior est quam sinus anguli MDE nempe ME, <lb></lb><figure id="id.020.01.641.1.jpg" xlink:href="020/01/641/1.jpg"></figure></s></p><p type="caption">

<s>Figura 31.<lb></lb>quod erat ostendendum ” <lb></lb>(ibi, pag. </s>

<s>180, 81). </s></p><p type="main">

<s>In un modo simile a <lb></lb>questo prova il Grimaldi <lb></lb>che se il raggio passa da <lb></lb>un mezzo più denso in un <lb></lb>più raro, come per esem­<lb></lb>pio dal cristallo nell&#039;aria, <lb></lb>il troppo veloce moto del <lb></lb>raggio si rattempera as­<lb></lb>sottigliandosi nella sezione <lb></lb>e perciò rifrangendosi dal­<lb></lb>la perpendicolare. </s></p><p type="main">

<s>Da così fatti principii, o diciam meglio ipotesi, fa conseguir l&#039;Autor <lb></lb><emph type="italics"></emph>De Lumine<emph.end type="italics"></emph.end> la dimostrazione della legge diottrica de&#039;seni, dimostrazione la <lb></lb>quale si può compendiare e ridurre alla forma seguente: </s></p><p type="main">

<s>Sia LE (fig. </s>

<s>31) la superficie che termina il mezzo più denso, per esem­<lb></lb>pio il cristallo, attraversato dal cilindro radioso ABCD, il quale uscendo nel­<lb></lb>l&#039;aria si rifrange dalla perpendicolare assottigliando la sua sezione come si <lb></lb>disse, e riducendosi perciò nel cilindro radioso BHIC. </s>

<s>Dai punti C e B, con­<lb></lb>dotte le FC, BG perpendicolari, queste misureranno la base o l&#039;ampiezza <lb></lb>de&#039;due cilindri radiosi, e i due triangoli rettangoli BFC, BCG daranno BC2= <lb></lb>BF2+FC2=BG2+CG2; e anche BC2—FC2=BF2, e BC2—BG2=GC2, <lb></lb>e perciò BF:CG=√BC2—FC2:√BC2—BG2. </s>

<s>Dall&#039;altra parte que&#039;due <lb></lb>medesimi triangoli danno le relazioni trigonometriche BC:BF=1:sen BCF, <lb></lb>e anche BC:CG=1:sen CBG, per cui BF:CG=sen BCF:sen CBG. </s>

<s>Ma <lb></lb>la relazione fra BF e CG ritrovata di sopra è costante per qualunque in­<lb></lb>clinazione del raggio e BCF è uguale all&#039;angolo dell&#039;incidenza, CBG è uguale <lb></lb>all&#039;angolo della rifrazione, dunque la relazione trovata fra&#039;loro seni, per <lb></lb>qualunque obliquità di raggi, è costante, come volevasi dimostrare. </s></p><p type="main">

<s>“ Poterit ergo a quadrato longitudinis baseos BC singillatim subtraih, <pb xlink:href="020/01/642.jpg" pagenum="85"></pb>tum quadratum diametri FC radii incidentis, tum quadratum diametri BG <lb></lb>radii refracti. </s>

<s>Subtrahantur iam et differentiarum, seu residuorum radices <lb></lb>quadratae, si simul comparentur, invenientur semper habere eamdem pro­<lb></lb>portionem quaecumque fuerit inclinatio radii ABCD incidentis in subiectam <lb></lb>eamdem superficiem LE, ex eodem superiori medio. </s>

<s>Siquidem huiusmodi <lb></lb>radices sunt reliqua latera BF et CG praedictis triangulis rectangulis, ut pa­<lb></lb>tet per XLVII primi Euclidis, et praeterea haec ipsa latera sunt sinus illi <lb></lb>qui praedictam eamdem proportionem conservant. </s>

<s>Sumpto enim BC pro sinu <lb></lb>toto, evadit BF sinus anguli BCF et CG sinus anguli CBG. </s>

<s>At angulus BCF <lb></lb>aequatur angulo inclinationis radii ABCD, uterque enim complet rectum cum <lb></lb>incidentiae angulo DCE, et angulus CBG aequatur angulo refracto, cum uterque <lb></lb>compleat rectum cum angulo LBH.... Itaque mirum non est, quod in iisdem <lb></lb>mediis ad quamcumque radii inclinationem refractio ita administretur ut ea­<lb></lb>dem sit semper proportio inter sinum anguli inclinationis et sinum anguli re­<lb></lb>fracti, si huiusmodi sinus ipsis diametris et crassitiebus radiorum directi ac re­<lb></lb>fracti ita alligantur, ut compleant cum ipsis eamdem potentiam ” (ibi, pag. </s>

<s>185). </s></p><p type="main">

<s>Questa dimostrazion del Grimaldi ha un carattere tutto suo originale, <lb></lb>non vedendovici nessun vestigio di que&#039;principii meccanici derivati dagli an­<lb></lb>tichi Ottici nel Keplero, e da questo trasfusi nella numerosa sequela succe­<lb></lb>dutasi dal Cartesio al Newton. </s>

<s>Si direbbe che il Nostro, riguardando il moto <lb></lb>della luce come un flusso, si fosse piuttosto aiutato da&#039;principii dell&#039;Idrau­<lb></lb>lica, se non si trovassero con essi principii le sue ipotesi apertamente di­<lb></lb>scordi. </s>

<s>Imperocchè parrebbe che attraversando la luce un mezzo più denso <lb></lb>ed entrando per le angustie de&#039;pori di lui, dovesse far come l&#039;acqua che <lb></lb>velocita il corso restringendo la sua sezione. </s>

<s>Ma allora ne verrebbe che il <lb></lb>raggio si dovesse rifrangere non alla perpendicolare, com&#039;è di fatto, ma dalla <lb></lb>perpendicolare, secondo i placiti del Grimaldi. </s>

<s>Da un&#039;altra parte poi non <lb></lb>s&#039;intende come possa serbare un fluido, conforme al supposto grimaldiano, <lb></lb>sempre la medesima quantità di moto sia che restringasi, o sia che s&#039;allar­<lb></lb>ghi indifferentemente la sezione. </s></p><p type="main">

<s>Nè quel che dice l&#039;Autore al numero 7 della proposizione XX, per pre­<lb></lb>venire una tale difficoltà, sodisfa punto a coloro che desidererebbero, nella <lb></lb>dimostrazion diottrica una maggior precisione, imperocchè sembra un ritor­<lb></lb>nare a coloro che ammettevano nella luce un senso e quasi una discrezione <lb></lb>da sapere gl&#039;impedimenti e da trovar la più facile via di scansarli, quando <lb></lb>il Grimaldi dice che i raggi fan come noi, che per durar meno fatica ci <lb></lb>pieghiamo nel nostro cammino piuttosto che affrettare il passo. </s>

<s>“ Quemad­<lb></lb>modum et nos ipsi minorem conatum experimur in flectendo nostro cursu, <lb></lb>quam in accelerando ” (ibi, pag. </s>

<s>180). Il Grimaldi, se si vuole, avrebbe po­<lb></lb>tuto suggerire un bello strattagemma al Cartesio per levarsi d&#039;impaccio da <lb></lb>chi gli opponeva, con lo stesso Grimaldi, esser contrario a quel che s&#039;espe­<lb></lb>rimenta di fatto, che cioè la luce si velociti ne&#039;mezzi più densi, imperocchè <lb></lb>poteva rispondere che ella nelle angustie de&#039;pori si velocita come l&#039;acqua <lb></lb>al restringersi delle sezioni. </s></p><pb xlink:href="020/01/643.jpg" pagenum="86"></pb><p type="main">

<s>Da ciò si conferma quel che s&#039;è da noi altre volte asserito, che cioè <lb></lb>la legge diottrica, per qualunque via si tenti, è a tutto rigore <expan abbr="iñdimostra-bile">inndimostra­<lb></lb>bile</expan>. </s>

<s>E si può da un&#039;altra parte soggiungere che, sebben tardi, ebbero gli <lb></lb>Italiani nel Grimaldi una qualche dimostrazione di quella legge che, per <lb></lb>quanto non vada esente da gravissime difficoltà, pur può stare a con­<lb></lb>fronto e anzi da qualche parte sopraeccellere a quelle stesse speculate dagli <lb></lb>stranieri. </s></p><p type="main">

<s>Parrebbe fosse insomma da concludersi che fu pel pubblico magistero <lb></lb>del Grimaldi che s&#039;introdusse finalmente in Italia la scienza delle rifrazioni. </s>

<s><lb></lb>Ma forse è una tal conclusione troppo affrettata, perchè l&#039;eccellenza del trat­<lb></lb>tato <emph type="italics"></emph>De Lumine<emph.end type="italics"></emph.end> non fu veramente riconosciuta, e in Italia e altrove, se <lb></lb>non dappoi che se ne videro derivare le insigni scoperte neutoniane. </s>

<s>La ra­<lb></lb>gion di ciò, specialmente per quel che riguarda noi Italiani, è da attribuirsi <lb></lb>al non essere appartenuto il Grimaldi alla scuola galileiana, la quale, quanto <lb></lb>fosse rimasta inferiore a sè stessa nella cultura dell&#039;Ottica, se vien mostrato <lb></lb>dai fatti narrati, si conferma altresì da quel poco, che, negli angusti termini <lb></lb>a noi prescritti, ci rimane a dire intorno all&#039;importantissimo soggetto delle <lb></lb>astronomiche rifrazioni. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La storia, da&#039;più antichi principii, ce l&#039;ha lasciata scritta il Keplero, <lb></lb>nel paragrafo primo del Cap. </s>

<s>IV de&#039;Paralipomeni a Vitellione, in modo che <lb></lb>si può andar dietro a lui sicuri, narrando egli il processo di quelle specula­<lb></lb>zioni che, per la massima parte, udi dalla bocca del suo maestro, e poi lesse <lb></lb>e meditò ne&#039;libri pubblicati da lui stesso e da&#039;suoi contradittori. </s></p><p type="main">

<s>“ Iamdudum Alhazen arabs, et ex eo Vitellio refractionum materiam <lb></lb>diligentius quam consuevere Veteres, explicare sunt aggressi. </s>

<s>Ac, cum omnis <lb></lb>nostra cognitio primum ab experientia proficiscatur, primum eorum angu­<lb></lb>lorum quantitates instrumentis explorarunt, quibus radii ex aere in aquam <lb></lb>ingressi refringuntur; tum et eorum qui ex aere in vitrum et qui ex aqua <lb></lb>in vitrum. </s>

<s>Cumque coelorum materia de veterum sententia pene vitrea, hoc <lb></lb>est, crystallina crederetur, aer vero aquae esset affinis, audacia subvecti au­<lb></lb>thores, adminiculo refractionum in coelorum arcana inquirere coeperunt. </s>

<s><lb></lb>Favit ipsorum conatibus experientia: deprehensa est aliqua etiam in stellis <lb></lb>refractionis ratio, eaque talis, ex qua per ea experimenta, quae in aqua et <lb></lb>vitro iam comprebata fuerant, aether non densior aere, sed hoc multo te­<lb></lb>nuior pronunciari posse videretur. </s>

<s>Diu neglecta haec cura, post aliquot se­<lb></lb>cula Tychonem Brahe incessit, qui subtilissimis instrumentis angulos refrac­<lb></lb>tionum in aere, quod Vitellio neglexerat, metiri est aggressus. </s>

<s>Certarunt <lb></lb>cum hoc tum plurimis aliis inventis is, quem dixi Tycho et Rothmannus <lb></lb>Hassiae Landgravii mathematicus. </s>

<s>Controversia de refractionibus multa est <pb xlink:href="020/01/644.jpg" pagenum="87"></pb>in tomo I Epistol. </s>

<s>astronomic. </s>

<s>quas anno 97 Tycho edidit: hanc qui volet <lb></lb>inde petat. </s>

<s>In praesentia summa ascribam ” (Francof. </s>

<s>1604, pag. </s>

<s>77). </s></p><p type="main">

<s>La somma è questa: Ticone s&#039;accorse degli effetti delle rifrazioni in <lb></lb>misurar le altezze del sole e ne attribuì la causa, come in Vitellione avea <lb></lb>letto, alla differenza che passa fra l&#039;etere diffuso negli spazii celesti e que­<lb></lb>sta nostra aria più bassa. </s>

<s>Insorse contro lui il Rothmann, il quale avendo <lb></lb>osservato che gli effetti delle rifrazioni cessano a una data altezza da lui <lb></lb>stesso, dietro l&#039;osservazion de&#039;crepuscoli, ridotta intorno a venti gradi, as­<lb></lb>serì che il fenomeno era prodotto dalla più bassa ammosfera vaporosa. </s></p><p type="main">

<s>Ticone allora si ridusse ad ammettere due ammosfere concentriche, una <lb></lb>aerea e l&#039;altra vaporosa, alla quale principalmente egli attribuiva quel pre­<lb></lb>cipitoso variar delle refrazioni presso all&#039;orizzonte. </s>

<s>Il Rothmann però non <lb></lb>si mostrò contento di questa ticoniana condiscendenza, e sostenne che l&#039;am­<lb></lb>mosfera vaporosa opera tutt&#039;altrimenti da quel che avea prescritto Ticone. </s>

<s><lb></lb>Se i raggi degli astri, ei ragionava, entrando obliquamente e per più lungo <lb></lb>cammino dentro la sfera de&#039;vapori grossi si refrangono, e poi abbreviando <lb></lb>quella via col diminuir l&#039;obliquità non si refrangono altrimenti, ciò vuol <lb></lb>dire che a quegli stessi raggi è stabilito un termine, oltre il quale, sosten­<lb></lb>gono la dirittura del loro viaggio imperturbati. </s></p><p type="main">

<s>“ Qua in sententia post hanc cum Rothmanno dissertationem, Tycho <lb></lb>manserit, habes in Progymn., tomo I, folio 92. Caeterum, quod inter prin­<lb></lb>cipia rerum constituendarum fieri solet, utrique aquae haesit. </s>

<s>Nam si ge­<lb></lb>nuinam refractionum mensuram adhibuissent, neque Tychoni opus fuisset <lb></lb>allegare genuinam refractionum causam geminata inquam corpora, alterum <lb></lb>aeris, alterum vaporum, neque Rothmannus negasset insensibile quippiam <lb></lb>refringi lucem etiam versus verticem. </s>

<s>Denique apparuisset superficiem quae <lb></lb>frangit radios neque vaporum esse temere oberrantium, neque corporis ali­<lb></lb>cuius sublimis ad Lunae confinia sed plane aeris eius in quo nos homines <lb></lb>spiritum eum in modum trahimus quo pisces trahunt aquam. </s>

<s>Statuisset ita­<lb></lb>que Tycho non successivam attenuationem aeris in aetherem, et obliteratio­<lb></lb>nem densitatis aeriae, sed manifestum et evidens discrimen, quod si quis <lb></lb>supra consisteret non minus ipsi in oculos esset incursum ac iam superfi­<lb></lb>cies quae aerem ab aqua separat in oculos incurrit. </s>

<s>Rothmannus contra non <lb></lb>impegisset in principio optico feriri a luce superficiem densioris medii, nec <lb></lb>tamen mutuum quicquam pati nec refringi, quodque non est in singulis <lb></lb>partibus, in conduplicatis inesse et profunditate mediorum refringit radios <lb></lb>non superficiebus quae omnia absurda sunt ” (ibi, pag. </s>

<s>79). </s></p><p type="main">

<s>Il Keplero dunque, entrando così di mezzo nella controversia insorta fra <lb></lb>Ticone e il Rothmann, intorno alla causa delle rifrazioni astronomiche, dopo <lb></lb>aver liberamente scoperte le fallacie ch&#039;erano nell&#039;una e nell&#039;altra opinione, <lb></lb>benchè non siasi egli stesso francato da tutti gli errori, pronunzia nulladi­<lb></lb>meno alcune verità tanto importanti, che, se fossero state accolte da&#039;succes­<lb></lb>sori, avrebbero potuto far progredire la scienza a gran passi. </s>

<s>Egli prima di <lb></lb>tutto asserisce che qualche rifrazione, benchè non tanto sensibile, si fa an-<pb xlink:href="020/01/645.jpg" pagenum="88"></pb>che verso il vertice: nega in secondo luogo che causa unica ed efficiente <lb></lb>del fenomeno sia l&#039;ammosfera, e fra l&#039;etere e l&#039;aria pone un deciso tra­<lb></lb>passo e una distinzione, come fra l&#039;aria stessa e l&#039;acqua. </s>

<s>Vedremo tra poco <lb></lb>come quest&#039;ultima verità specialmente conferisse a stabilire la scienza, quando <lb></lb>il concetto vago e incerto del Keplero intorno ai limiti dell&#039;ammosfera e al <lb></lb>peso dell&#039;aria, fu reso evidente dall&#039;uso del Barometro e della Macchina pneu­<lb></lb>matica, ma intanto altri fatti, benchè non così dimostrativi, aprono il terreno <lb></lb>a ricevere le radicelle di quegli stessi kepleriani concetti da&#039;quali, coltivan­<lb></lb>doli poi gli Ottici e gli Astronomi, se ne sarebbero colti i frutti desiderati. </s></p><p type="main">

<s>Que&#039;fatti, de&#039;quali intendiamo parlare, consistono in alcune astronomi­<lb></lb>che osservazioni, che fecero rimanere attonito lo Scheiner, a cui toccò d&#039;es­<lb></lb>sere il primo a veder lo spettacolo. </s>

<s>Tornato da Monaco in Ingolstad, un <lb></lb>giorno dell&#039;anno 1612, gli vien riferito che alcuni suoi scolari avevan no­<lb></lb>tate alcune macchie del sole ad occhio nudo. </s>

<s>Và di buon mattino in cam­<lb></lb>pagna, per sincerarsi del fatto, ed egli e il suo compagno avvertono che il <lb></lb>sole è ovale e non rotondo. </s>

<s>Dubita a principio che ciò sia qualche inganno <lb></lb>dell&#039;occhio, osserva col Canocchiale e il sole si mostra più distintamente che <lb></lb>mai contratto, nè per mutar posizione nell&#039;osservare quella figura si muta. </s></p><p type="main">

<s>“ Quapropter, anno 1612, die Novembris decimo hora pomeridiana ve­<lb></lb>luti quarta, cum obverterem soli Tubum modo nominatum ut in chartam <lb></lb>illius traducerem maculas solares, conspexi ipsum protinus solem luculenta <lb></lb>affectum systasi secundum attitudinem ita ut deficeret ea a longitudine nona <lb></lb>minimum diametri solaris visualis parte. </s>

<s>Haesi attonitus inopinato rei specta­<lb></lb>culo, etenim contractionis illo tempore immemor solas indagabam maculas, <lb></lb>quas ut ellipsi non circulo inclusas animadverti ” (Sol ellipticus, Augustae <lb></lb>Vindelic. </s>

<s>1615, pag. </s>

<s>3). </s></p><p type="main">

<s>E prosegue a dire che, acceso <emph type="italics"></emph>incredibili studio rei ulterius inquiren­<lb></lb>dae,<emph.end type="italics"></emph.end> spese tutto quel rimanente Novembre e una buona parte del Dicembre <lb></lb>appresso in misurar mattina e sera l&#039;ellitticità del sole. </s>

<s>Concluse dalle sue <lb></lb>osservazioni i fatti seguenti: che l&#039;ellitticità della mattina non è sempre <lb></lb>uguale a quella della sera; che la variabilità è notabile da un giorno all&#039;al­<lb></lb>tro, e anche da un luogo altro. </s></p><p type="main">

<s>Osservati così diligentemente i fatti lo Scheiner passa a investigarne le <lb></lb>ragioni, le quali egli brevemente conclude nelle parole seguenti: “ Con­<lb></lb>tractio haec solis est defectus, quo diametrus altitudinis, latitudinis diame­<lb></lb>trum relinquit, defectus autem iste generatur a duabus refractionibus, in <lb></lb>solis summa et una abside fieri solitis, quae absides diametro solari a se <lb></lb>distant: est igitur haec contractio quasi differentia duarum eiusmodi re­<lb></lb>fractionum ” (ibi, pag. </s>

<s>13). </s></p><p type="main">

<s>Che poi veramente il fenomeno sia dovuto alle rifrazioni, l&#039;argomenta <lb></lb>saggiamente lo Scheiner dal veder che l&#039;ellitticità varia a tenor che variano <lb></lb>le stesse rifrazioni, secondo l&#039;altezza. </s>

<s>“ Unde cum pateat ipsa quotidiana <lb></lb>experientia, hanc solis contractionem paulatim augeri cum eiusdem descensu, <lb></lb>imminui ascensu, quemadmodum et refractio solet, insuper cum certum sit <pb xlink:href="020/01/646.jpg" pagenum="89"></pb>ipsam circa horizontem brevissimo tempore, minimo spatio incrementa maxima <lb></lb>sumere, uti in refractione accidit, plus quam probabile, imo fere certum <lb></lb>mihi est esse proportionem inter refractiones et hasce contractiones ” (ibi). </s></p><p type="main">

<s>Cosi, mentre trovava lo Scheiner nelle rifrazioni la ragion certissima <lb></lb>del sole ellittico, proponeva l&#039;osservazione del sole ellittico come la più <lb></lb>certa prova delle rifrazioni messe in dubbio e ripudiate da tanti. </s>

<s>Egli am­<lb></lb>mira perciò Ticone, ammira il Keplero, i quali ebbero fede nella verità, an­<lb></lb>che prima di averne veduta qualche prova sperimentale. </s>

<s>Che poi non va­<lb></lb>lessero gl&#039;ingegni comunali a penetrare le sottili ragioni s&#039;intende, dice lo <lb></lb>Scheiner, ma orà come potranno negare un fatto così visibile? </s></p><p type="main">

<s>Si lusingava insomma l&#039;Autore del Sole ellittico d&#039;aver cacciato ogni <lb></lb>ombra di dubbio dalle menti. </s>

<s>Ma vediamo quali fossero di questo nuovo fer­<lb></lb>vente magistero i frutti, e vediamolo nella persona che a noi più importa, <lb></lb>e che più muove la nostra curiosità, nella persona di Galileo. </s>

<s>Egli è senza <lb></lb>dubbio nel numero di quei molti che negaron fede alle nuove dottrine pro­<lb></lb>fessate ne&#039;suoi Proginnasmi da Ticone. </s>

<s>Ciò era ben da aspettarsi, pensando <lb></lb>che Galileo, il quale aveva così scarse e così false idee delle rifrazioni ordi­<lb></lb>narie, non sarebbe penetrato a conoscere il vero di quelle stesse refrazioni <lb></lb>ne&#039;fatti astronomici. </s>

<s>Se ne persuase egli forse, quando lo Scheiner pubblicò <lb></lb>nel 1615 il suo <emph type="italics"></emph>Sol ellipticus,<emph.end type="italics"></emph.end> e due anni dopo tornò, in Ingolstad, a trat­<lb></lb>tare del medesimo soggetto nell&#039;altro libro <emph type="italics"></emph>Refractiones coelestes?<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In generale dobbiam dire che il Gesuita tedesco non aveva l&#039;amabile <lb></lb>virtù d&#039;insinuarsi negli animi, per andare a illuminare le menti. </s>

<s>Quel gi­<lb></lb>rare e rigirare sempre intorno al medesimo soggetto, e il mostrar della cosa <lb></lb>sempre la medesima faccia, dopo averla così lungamente maneggiata, riesce <lb></lb>tedioso: quel dar tanta importanza alla sua scoperta, quasi ella dovess&#039;es­<lb></lb>sere la nuova luce venuta a illuminare il mondo, rende l&#039;Autore esoso. </s>

<s>Dal­<lb></lb>l&#039;altra parte l&#039;osservazione del sole ovale è ovvia a tutti coloro, che rivol­<lb></lb>gon sulla sera lo sguardo al sole, quando egli traspare attraverso a un velo <lb></lb>di rubicondi e spessi vapori. </s>

<s>Nè pure la ragion del fatto è merito dello Schei­<lb></lb>ner, confessando egli stesso di averla letta già nel Keplero: “ E quo rursus <lb></lb>suam meretur laudem Kepleri perspicacia, qui, licet novae huius phaseos <lb></lb>sensum plane nullum experientiamve habuerit, solem tamen a sola data re­<lb></lb>fractione in ellipticam speciem conformari, contra Vitellionem et antiquos <lb></lb>astruere non est veritus, quod ego his omnibus iam habitis experientiis in <lb></lb>ipso libenter legi ” (Sol ellipticus cit., pag. </s>

<s>22). </s></p><p type="main">

<s>Lo spiegar poi il sole ellittico per mezzo delle rifrazioni, e il far del <lb></lb>sole ellittico un argomento a provare quelle stesse rifrazioni è una specie <lb></lb>di circolo vizioso, nè si sa dove consista la forza di questo argomento, a cui <lb></lb>dà lo Scheiner un valore sperimentale. </s>

<s>A ragion di esperienza si può dire <lb></lb>che lo ridusse il Vossio, il quale immaginando di avere un vaso rappresen­<lb></lb>tato dalla figura 32 mostrava che, se nella parete VA è dipinto un cerchio, <lb></lb>infusa acqua nello stesso vaso, l&#039;occhio costituito in O vedrebbe quello stesso <lb></lb>cerchio contratto in ellisse. </s>

<s>Ma tutto l&#039;argomento sperimentale del Gesuita <pb xlink:href="020/01/647.jpg" pagenum="90"></pb>consisteva nell&#039;aver preparato il Telescopio a mostrare il disco del sole proiet­<lb></lb>tato sopra una carta, com&#039;usa farsi per descriver le macchie. <lb></lb><figure id="id.020.01.647.1.jpg" xlink:href="020/01/647/1.jpg"></figure></s></p><p type="caption">

<s>Figura 32.</s></p><p type="main">

<s>Non vogliam però lasciar di notare che il Vossio <lb></lb>non giudicò rettamente dello Scheiner, nè par che <lb></lb>avesse letti i due Trattati di lui, quando, dopo aver <lb></lb>descritta la sopra citata esperienza, soggiunge: “ Et <lb></lb>hinc petenda est ratio quamobrem sol oriens et oc­<lb></lb>cidens sub ellipsis figura spectandum se praebeat, <lb></lb>quam non satis assecutus est Scheinerus, dum a <lb></lb>speculis cavis huius rei causam adstruere conatur, <lb></lb>in quibus refractio locum non habet ” (De Nili orig. </s>

<s><lb></lb>appendix. </s>

<s>Hagae Comitis 1666, pag. </s>

<s>112). </s></p><p type="main">

<s>Ripigliando il filo del nostro discorso, se queste considerazioni intorno <lb></lb>allo Scheiner valgono in generale, a più forte ragione valevano per Galileo, <lb></lb>che aveva tanta avversione contro il gesuita travestito in <emph type="italics"></emph>Apelle.<emph.end type="italics"></emph.end> Perciò se <lb></lb>tutti avevano scuse di negar l&#039;argomento delle rifrazioni, attribuendo il Sole <lb></lb>ellittico ad altre cause, fu tra questi principale Galileo, come si vede che <lb></lb>fece alla prima occasione presentatasi, e fu quella di pubblicare il suo <emph type="italics"></emph>Sag­<lb></lb>giatore.<emph.end type="italics"></emph.end> Qui un altro Gesuita sosteneva che il Sole e la Luna appariscono <lb></lb>più grandi all&#039;orizzonte, perchè, mediante la sfera vaporosa, vengono ad es­<lb></lb>sere maggiormente illuminati. </s>

<s>Ma Galileo dice a quel Gesuita che egli era <lb></lb>in inganno “ imperocchè non pel lume de&#039;vapori, ma per la figura sferica <lb></lb>dell&#039;esterna loro superficie, e per la lontananza maggiore di quella dall&#039;oc­<lb></lb>chio nostro, quando gli oggetti son più verso l&#039;orizzonte, appariscono essi <lb></lb>oggetti maggiori della lor comune apparente grandezza, e non i luminosi <lb></lb>solamente, ma qualunque altro posto fuor di tal regione. </s>

<s>Traponete tra l&#039;oc­<lb></lb>chio vostro e qualsivoglia oggetto una lente convessa cristallina in varie lon­<lb></lb>tananze; vedrete che, quando essa lente sarà vicina all&#039;occhio, poco si accre­<lb></lb>scerà la specie dell&#039;oggetto veduto, ma discostandola, vedrete successivamente <lb></lb>andar quella ingrandendosi. </s>

<s>E perchè la region vaporosa termina in una <lb></lb>superficie sferica, non molto elevata sopra il convesso della Terra, le linee <lb></lb>rette, che tirate dall&#039;occhio nostro arrivano alla detta superficie, sono disu­<lb></lb>guali, e minima di tutte la perpendicolare verso il vertice, e delle altre di <lb></lb>mano in mano maggiori sono le più inchinate verso l&#039;orizzonte che verso <lb></lb>il zenit ” (Alb. </s>

<s>IV, 344). </s></p><p type="main">

<s>Questa speculazione fu poi, senz&#039;ombra di dubbio, accolta dal Renieri, <lb></lb>il quale la proponeva, per servire al medesimo intento di Galileo, al prin­<lb></lb>cipe Leopoldo. </s>

<s>È notabile che il Principe, sinceramente confessando di aver <lb></lb><emph type="italics"></emph>poca cognizione di simili materie<emph.end type="italics"></emph.end> (Targioni, Notizie ecc., ediz. </s>

<s>cit., T. II, <lb></lb>P. II, pag. </s>

<s>751), pur sentisse quanto quelle speculazioni di Galileo e del <lb></lb>Renieri avessero dello strano, e fossero contradette dalle più volgari espe­<lb></lb>rienze. </s>

<s>Ed è a notare altresì che il Principe fosse da tanto tempo prevenuto <lb></lb>da Leonardo da Vinci, il quale risolse da maestro il problema così infelice­<lb></lb>mente tentato da Galileo e dal Renieri, professando principii ottici, che emen-<pb xlink:href="020/01/648.jpg" pagenum="91"></pb>dano gli errori del Maurolico, del Fracastoro e di tanti altri, i quali dicevano <lb></lb>le superficie piane de&#039;diafani ingrandir per rifrazione gli oggetti. </s></p><p type="main">

<s>“ Prova dell&#039;accrescimento del Sole nell&#039;occidente. </s>

<s>— Alcuni matema­<lb></lb>tici dimostrano il Sole crescere nel ponente, perchè l&#039;occhio sempre lo vede <lb></lb>per aria di maggior grossezza, allegando che le cose viste nella nebbia e <lb></lb>nell&#039;acqua paron maggiori. </s>

<s>Io rispondo di no, imperocchè le cose viste in <lb></lb>fra la nebbia son simili per colore alle lontane, e non essendo simili per <lb></lb>diminuzione appariscono di maggior grandezza. </s>

<s>Ancora nessuna cosa cresce <lb></lb>in acqua piana e la prova ne farai a lucidare un&#039;asse mezza (ma dee dir <lb></lb><emph type="italics"></emph>messa<emph.end type="italics"></emph.end>) nell&#039;acqua. </s>

<s>Ma la ragione che il Sol cresce si è che ogni corpo lu­<lb></lb>minoso quanto più s&#039;allontana, più pare grande ” (Rav. </s>

<s>Mollien Manus. </s>

<s>de <lb></lb>Leonard, MSS. A, fol. </s>

<s>64 v.). </s></p><p type="main">

<s>Quel che poi, ritornando alla speculazione sopra esposta da Galileo, è <lb></lb>anco più strano, si è che e&#039;vuole applicarla a spiegare il Sole ellittico. <lb></lb></s>

<s>“ Quindi anco, e sia detto per transito, si può facilmente raccorre la causa <lb></lb>dell&#039;apparente figura ovata del Sole e della Luna presso all&#039;orizzonte, con­<lb></lb>siderando la gran lontananza dell&#039;occhio nostro dal centro della Terra, che è <lb></lb>lo stesso che quello della sfera vaporosa, della quale apparenza, come credo <lb></lb>che sappiate, ne sono stati scritti, come di problema molto astruso, interi <lb></lb>trattati, ancorchè tutto il misterio non ricerchi maggior profondità di dot­<lb></lb>trina che l&#039;intender per qual ragione un cerchio veduto in maestà ci paia <lb></lb>rotondo, ma guardato in iscorcio ci apparisca ovato ” (Alb. </s>

<s>IV, 344). </s></p><p type="main">

<s>Chi rimedita sopra questo dottrine galileiane, specialmente se fosse stato <lb></lb>sedotto da coloro, i quali insegnano a venerar in tutto Galileo come un ora­<lb></lb>colo; rimane stupefatto ritrovandolo qui tanto inferiore a sè stesso. </s>

<s>Atten­<lb></lb>diamo bene: la ragione dell&#039;apparir maggiori gli astri all&#039;orizzonte, quale <lb></lb>l&#039;abbiamo ora letta nel <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> è strana, ma pure è derivata dalle an­<lb></lb>tiche tradizioni della scienza. </s>

<s>Il Fracastoro nel Cap. </s>

<s>VIII della Sezione II <lb></lb>degli <emph type="italics"></emph>Omocentrici<emph.end type="italics"></emph.end> aveva professato il principio che, moltiplican dosi il mezzo, <lb></lb>s&#039;ingrandiscono a proporzione le specie, e l&#039;avea applicato a risolvere il pro­<lb></lb>blema dell&#039;apparente variabile grandezza degli astri. </s>

<s>“ Sicut autem si cras­<lb></lb>sum medium sit, maiora et proprinquiora videri facit, ita et si idem multum <lb></lb>fuerit idem facit. </s>

<s>Quae nam per plus densi medii veniunt species, illa maiora <lb></lb>omnia repraesentant. </s>

<s>Qua de causa in eadem aqua quae in summo cernun­<lb></lb>tur minora apparent, quae in fundo maiora, et per duo specilla ocularia si <lb></lb>quis perspiciat altero alteri superposito, maiora multo et proprinquiora vi­<lb></lb>debit omnia. </s>

<s>Hac de causa quaecumque stellarum prope horizontem sunt <lb></lb>maiores et propinquiores videntur. </s>

<s>In medio coeli minores et remotiores. </s>

<s><lb></lb>Species nam prope horizontem per medium crassum venit, et per aerem <lb></lb>vaporibus multis plenum, qui circa terram semper sunt. </s>

<s>Sed hoc non suf­<lb></lb>ficit, nam et e medio coeli species tandem per eosdem vapores venit, cum <lb></lb>iuxta terram est, verum illud interest, quod prope horizontem per plus il­<lb></lb>lius aeris defertur species, e medio coeli per minus ” (Opera omnia, Ve­<lb></lb>netiis 1584, c. </s>

<s>13 v.). Il Maurolico dall&#039;altra parte aveva nel I Libro <emph type="italics"></emph>De&#039;dia-<emph.end type="italics"></emph.end><pb xlink:href="020/01/649.jpg" pagenum="92"></pb><emph type="italics"></emph>fani<emph.end type="italics"></emph.end> formulato il Teorema I. “ Quod per diaphanum planum transparet <lb></lb>maius quam sit ac propinqius videtur, eo magis, quo propius plano dia­<lb></lb>phani ” (Neapoli 1611, pag. </s>

<s>31). </s></p><p type="main">

<s>Leonardo da Vinci aveva antiveduto e confutato già questo errore mau­<lb></lb>rolicano, rinnovato dallo Snellio e dal Vossio, i quali ne conclusero le ri­<lb></lb>frazioni anche nel raggio perpendicolare. </s>

<s>Galileo pure cansò quell&#039;errore, e <lb></lb>richiedendo per condizione essenziale non la planizie, ma la curvità del <lb></lb>mezzo accettò del resto a spiegare il fatto della maggior grandezza appa­<lb></lb>rente degli astri all&#039;orizzonte le dottrine del Fracastoro. </s>

<s>Il principe Leopoldo <lb></lb>però faceva notare, nella persona del Renieri, alla venerata memoria del suo <lb></lb><figure id="id.020.01.649.1.jpg" xlink:href="020/01/649/1.jpg"></figure></s></p><p type="caption">

<s>Figura 33.<lb></lb>Galileo, com&#039;anche ammessa la curvità del mezzo le <lb></lb>rinnovate dottrine fracastoriane venivano dimostrate <lb></lb>false dall&#039;esperienza. </s>

<s>“ Piglisi un vaso di vetro con­<lb></lb>cavo di figura più rotonda che sia possibile, quale <lb></lb>sarebbe appunto la metà d&#039;un fiasco tagliato, ed em­<lb></lb>piendolo d&#039;acqua sino a un determinato segno e sia <lb></lb>v. </s>

<s>g. </s>

<s>AB (fig. </s>

<s>33) e sotto ponendovi l&#039;oggetto C, se si <lb></lb>guarderà coll&#039;occhio dal punto D, ancorchè io accre­<lb></lb>sca la quantità dell&#039;acqua al livello EF, non però <lb></lb>mi cresce punto l&#039;oggetto C ” (Targioni, loc. </s>

<s>cit.). </s></p><p type="main">

<s>Quelle dottrine insomma son dimostrate false nel <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> non meno <lb></lb>di quel che sieno negli <emph type="italics"></emph>Omocentrici,<emph.end type="italics"></emph.end> e s&#039;intende come e d&#039;onde abbia avuto <lb></lb>origine l&#039;inganno. </s>

<s>Ma passando all&#039;applicazione, che Galileo stesso ne fa a <lb></lb>render la ragione del Sole ellittico, chi può comprendere come c&#039;entrino i <lb></lb>cerchi o veduti in maestà o in iscorcio, se si tratta del Sole e della Luna <lb></lb>che sono sfere? </s>

<s>Lo Scheiner ne&#039;suoi due trattati ha senza dubbio difetti, <lb></lb>ma non errori così grossolani, e mentre le parole del <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> si vorreb­<lb></lb>bero, per onor di Galileo, sopprimere dal suo Libro, si ripete anche oggidi <lb></lb>da tutti gli Astronomi, come verità provata, la sentenza espressa in princi­<lb></lb>pio del Cap. </s>

<s>XXIII delle <emph type="italics"></emph>Refractiones coelestes:<emph.end type="italics"></emph.end> “ Contractio solis enascitur <lb></lb>ex inaequali partium ipsius supremarum mediarum et infimarum supra <lb></lb>horizontem elevatione: haec autem ex eo dimanat quod eae inaequaliter ad <lb></lb>perpendiculares suas refringantur ” (Ingolstadii 1617, pag. </s>

<s>34). </s></p><p type="main">

<s>Ma il fatto più singolare in questa Storia è che a quelle medesime ve­<lb></lb>rità disprezzate dovette poco dipoi convertirsi anche Galileo, benchè voglia <lb></lb>fare apparire che ciò sia stato per sua spontanea deliberazione, e di sua <lb></lb>propria scienza, nò persuaso dagl&#039;insegnamenti dell&#039;odiato Gesuita. </s>

<s>A lui in <lb></lb>ogni modo pienamente si conformava, ravvedutosi delle stranezze lasciate <lb></lb>trascorrer nel <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> quando nel 1637 (Alb. </s>

<s>VII, 193) dettando le <emph type="italics"></emph>Ope­<lb></lb>razioni Astronomiche,<emph.end type="italics"></emph.end> recava il Sole ellittico per argomento dimostrativo <lb></lb>delle rifrazioni celesti. </s>

<s>“ Posto che sia vero, che mercè della Rifrazione l&#039;og­<lb></lb>getto lucido e non molto remoto dall&#039;orizzonte, venga sollevato, che tal sol­<lb></lb>levamento sia in diversi tempi molto disuguale, ce lo mostra il solar disco, <lb></lb>il quale alcune fiate trovandosi circa un grado elevato dall&#039;orizzonte, si mo-<pb xlink:href="020/01/650.jpg" pagenum="93"></pb>stra non in figura circolare, ma bislunga, cioè d&#039;altezza notabilmente minore <lb></lb>della lunghezza, il che credo io veramente accadere, perchè mercè dei vapori <lb></lb>bassi l&#039;inferior parte del disco solare viene più inalzata che la superiore, <lb></lb>restando l&#039;altra dimensione, cioè la lunghezza, inalterata ” (Alb. </s>

<s>V, 383, 84). </s></p><p type="main">

<s>Dal 1622 dunque, anno in cui fu disteso e preparato per le stampe il <lb></lb><emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> Galileo s&#039;è alquanto addimesticato colle dottrine diottriche di <lb></lb>Ticone, del Keplero e dello Scheiner, per conferma di che può citarsi una <lb></lb>nota, la quale essendo autografa e portando i segni che lo scrivente aveva <lb></lb>il libero esercizio della vista, dee essere anteriore al 1637, anno in cui co­<lb></lb>minciò a sentire la necessità di fare scrivere perpetuamente, non solo per <lb></lb>rispondere alle lettere numerose, ma per <emph type="italics"></emph>deporre varii suoi pensieri e con­<lb></lb>cetti<emph.end type="italics"></emph.end> (Alb. </s>

<s>VII, 193). Quella nota galileiana dunque dice così: “ Incertum <lb></lb>esse numquid coeli medietas appareat supra horizontem nec ne, ex pluri­<lb></lb>bus causis contingit, maxime autem ex refractionibus stellas efferentibus, <lb></lb>praeter quam quod ipsaemet stellae circa orizontem inconspicuae sunt ” <lb></lb>(MSS. Gal., P. III, T. III, c. </s>

<s>36). </s></p><p type="main">

<s>Non è da creder per quèsto che Galileo fosse in quella ferma persua­<lb></lb>sione, ch&#039;erano il Brahe, il Kepler, lo Scheiner: anzi ei non potè mai li­<lb></lb>berarsi in tutto da un dubbio, che apertamente confessa nel principio di <lb></lb>quella V Operazione astronomica, nella quale si legge il passo da noi sopra <lb></lb>allegato. </s>

<s>“ Il negozio delle refrazioni resta per ancora appresso di me assai <lb></lb>ambiguo, nè ci so discernere precisione alcuna fondata sopra stabili e certe <lb></lb>osservazioni. </s>

<s>E veramente confesso di non esser capace come la struttura <lb></lb>delle Tavole di esse refrazioni, portata come assai risoluta in particolare da <lb></lb>Ticone, sia veramente tanto sicura, che di essa si possa fare assoluto capi­<lb></lb>tale nel calcolare le elevazioni delle stelle, in particolare ne&#039;luoghi non molto <lb></lb>alti sopra l&#039;orizzonte ” (Alb. </s>

<s>V, 383). </s></p><p type="main">

<s>La poca precisione però delle Tavole ticoniane poteva attribuirsi piut­<lb></lb>tosto alla difficoltà delle osservazioni, e alla imperfezione degli strumenti, e <lb></lb>se Galileo avesse ripensato a ciò, si sarebbe potuto almeno in parte delibe­<lb></lb>rare dalle pene del dubbio. </s>

<s>Ma egli non sapeva persuadersi che gli astri <lb></lb>avessero a mutar vista per la ragione che, secondo l&#039;antichissima esperienza <lb></lb>euclidea, invocata in proposito dal Brahe, muta vista, infusa l&#039;acqua nel <lb></lb>vaso, la moneta posata sul suo fondo. </s>

<s>Il negozio delle astronomiche refra­<lb></lb>zioni, così esprimesi lo stesso Galileo, “ mi pare differentissimo da quello <lb></lb>del vaso e dell&#039;acqua, essendo che in questo l&#039;occhio è in un diafano di­<lb></lb>versissimo da quello, nel quale si trova la moneta. </s>

<s>Ma nel nostro caso l&#039;oc­<lb></lb>chio è immerso nei medesimi vapori per li quali ha da passare la spazie. </s>

<s><lb></lb>Che se l&#039;occhio, il catino e la moneta fossero tutti nell&#039;acqua, la refra­<lb></lb>zione non vi sarebbe ” (ivi, pag. </s>

<s>385). </s></p><p type="main">

<s>Galileo non giunse a comprendere che, se l&#039;occhio fosse stato nel luogo <lb></lb>della moneta e la moneta nel luogo dell&#039;occhio, si sarebbe nulladimeno rap­<lb></lb>presentata una simile illusione, e non valse a comprender ciò perchè non <lb></lb>seppe convenientemente apprezzare il Keplero il quale, ammettendo un de-<pb xlink:href="020/01/651.jpg" pagenum="94"></pb>ciso passaggio dall&#039;etere all&#039;aria, e una diversa densità fra&#039;due elementi, <lb></lb>come fra l&#039;aria stessa e l&#039;acqua, veniva a costituir l&#039;esempio ne&#039;precisi ter­<lb></lb>mini dell&#039;occhio collocato nell&#039;acqua, che vedesse la moneta sospesa fuori <lb></lb>nell&#039;aria. </s>

<s>Nel caso particolare delle refrazioni astronomiche, l&#039;occhio è som­<lb></lb>merso nell&#039;aria, che è un mezzo più denso dell&#039;etere, da cui gli astri gli <lb></lb>mandan la luce. </s></p><p type="main">

<s>Il Barometro, presentito dal Keplero, venne a precisare alquanto le idee <lb></lb>intorno ai confini dell&#039;ammosfera, ma perchè mancavano ancora esperienze <lb></lb>dirette, che dimostrassero rifrangersi di fatto i raggi nel passar dall&#039;etere <lb></lb>nell&#039;aria, e non s&#039;era bene inteso in che propriamente consistessero le ri­<lb></lb>frazioni ordinarie, le quali si riducevano a un caso particolare di riflessione; <lb></lb>e perciò le rifrazioni astronomiche s&#039;ammettevano come un nome dato alla <lb></lb>causa, qualunque ella poi si fosse, produttrice di effetti realmente osser­<lb></lb>vati, e de&#039;quali perciò non si poteva oramai più dubitare. </s>

<s>Il Cassini, verso <lb></lb>l&#039;anno 1655, dava opera a costruire Tavole delle Rifrazioni astronomiche <lb></lb>assai più precise delle antiche, e tutti gli Astronomi, primi fra&#039;quali i nostri <lb></lb>Accademici del Cimento, erano in faccenda di misurare con la più squisita <lb></lb>esattezza le rifrazioni orizzontali del Sole e della Luna, per riscontrarle con <lb></lb>quelle stesse ritrovate già da Ticone. (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>755). </s></p><p type="main">

<s>Tutte queste insomma erano pratiche osservazioni, senz&#039;aver fonda­<lb></lb>mento di scienza, la quale tutta si riduceva a verificare i concetti keple­<lb></lb>riani, ciò ch&#039;era riserbato a farsi dalle sole esperienze. </s>

<s>A queste appunto <lb></lb>aveva pensato il Borelli, il quale, secondo riferiva Cosimo Galilei al Viviani, <lb></lb>in una sua Lettera trascritta in parte nel capitolo precedente; voleva ser­<lb></lb>virsi di quelli specchi ordinati a sperimentar la velocità della luce “ per ve­<lb></lb>dere se veramente sia quella refrazione, nella region vaporosa, addotta per <lb></lb>causa dagli Astronomi di tante e tante novità contro ogni aspettazione se­<lb></lb>guite ” (MSS. Galil. </s>

<s>Disc., T. CXLIV, c. </s>

<s>32). </s></p><p type="main">

<s>Ma come potesse accomodarsi l&#039;esperienza borelliana a riuscir nell&#039;in­<lb></lb>tento, si capisce difficilmente. </s>

<s>In ogni modo, la prova diretta per verificare <lb></lb>il conceito del Keplero era quella di veder se la luce si refrange, trapas­<lb></lb>sando, dall&#039;aria nell&#039;etere o nel vuoto torricelliano. </s>

<s>L&#039;importantissimo e <lb></lb>nuovo esperimento fu fatto, o diciam meglio, fu tentato nell&#039;Accademia fio­<lb></lb>rentina dal Viviani, di mano del quale si vede abbozzato in disegno uno <lb></lb>de&#039;soliti tubi di vetro terminati in un pallone, da fare il vuoto col mercu­<lb></lb>rio, allato al qual disegno in penna il Viviani stesso lasciò scritto di pro­<lb></lb>pria mano, così senz&#039;altro: “ Strumento per conoscer se il raggio del Sole, <lb></lb>passando per il luogo privo di aria, farà differenza dal passar per l&#039;aria ” <lb></lb>(MSS. Cim., T. XI, c. </s>

<s>195). </s></p><p type="main">

<s>Noi non siamo in grado di render conto ai nostri Lettori, che ne sa­<lb></lb>ranno desiderosissimi, del resultato della esperienza, dalla quale forse non <lb></lb>si decise nulla in proposito, per non esser riuscita così scrupolosa. </s>

<s>Dopo pa­<lb></lb>recchi anni, il bel pensiero del Viviani ebbe esito fortunatissimo per opera <lb></lb>dell&#039;inglese Giovanni Lowthorp, ma perchè i Francesi diffusero la notizia <pb xlink:href="020/01/652.jpg" pagenum="95"></pb>che l&#039;esperienza invece non era riuscita, la R. </s>

<s>Società di Londra ordinò <lb></lb>all&#039;Hawksbee che ripetesse la stessa esperienza, operando il vuoto per mezzo <lb></lb>della sua perfettissima Macchina pneumatica. </s>

<s>L&#039;Hawksbee eseguì, e divulgò <lb></lb>del fatto in questa forma la storia: </s></p><p type="main">

<s>“ Giovanni Lowthorp inventò un apparato per dimostrar la refrazione <lb></lb>dell&#039;aria.... Egli fece un vuoto tra due piani di vetro inclinati, coll&#039;aiuto <lb></lb>dell&#039;argento vivo, per entro il quale si poteva vedere che un oggetto guar­<lb></lb>dato col Canocchiale mutava sensibilmente luogo, quando s&#039;introduceva <lb></lb>l&#039;aria.... Il signor Cassini figliolo, essendo stato presente quando il Low­<lb></lb>thorp fece la sua esperienza, .... ne fece un rapporto alla R. </s>

<s>Accademia <lb></lb>di Francia nella storia della quale dell&#039;anno 1700 lasciarono scritto che <lb></lb>l&#039;esperienza inglese non riuscì.... La Società regia di Londra mi ordinò <lb></lb>che io facessi uno strumento a proposito colla direzione del signor Halley.... <lb></lb>Consisteva questo in un gagliardo prisma di ottone due lati del quale ave­<lb></lb>vano delle padellette da ricever vetri piani ed esattamente lisci, e il terzo <lb></lb>lato aveva un condotto con una chiave da serrare e aprire, a cui si potesse <lb></lb>applicar la macchina tanto da cavare. </s>

<s>quanto da condensare l&#039;aria.... Que­<lb></lb>sto strumento così preparato si accomodò a un Canocchiale lungo circa <lb></lb>10 piedi geometrici, in maniera che l&#039;asse del Canocchiale potesse passare <lb></lb>per entro il mezzo del prisma, e nel foco del Canocchiale fu adattato un ca­<lb></lb>pello sottilissimo, per dirigere la vista. </s>

<s>Avendo scelto un oggetto assai pro­<lb></lb>prio distintissimo ed eretto .... noi prima cavammo l&#039;aria dal prisma, e poi <lb></lb>applicandolo al Canocchiale, il capello orizzontale nel foco copriva un segno <lb></lb>sopra il nostro oggetto, che si vedeva distintamente per entro il vuoto, i due <lb></lb>vetri essendo ugualmente piegati verso il raggio visivo, poi, lasciando en­<lb></lb>trar l&#039;aria nel prisma si scorgeva l&#039;oggetto salire gradualmente sopra il ca­<lb></lb>pello a misura che entrava l&#039;aria, e in fine fu trovato che il capello nascon­<lb></lb>deva un segno dita dieci e un quarto sotto l&#039;antecedente segno ” (Esper. </s>

<s><lb></lb>fisico meccan., trad. </s>

<s>ital., Firenze 1716, pag. </s>

<s>143-45). </s></p><p type="main">

<s>Cosi, dopo un secolo, l&#039;esperienza dimostrava quella refrazione dall&#039;etere <lb></lb>nell&#039;aria predicata già dal Keplero, come causa efficiente del mutar vista <lb></lb>che si vede fare agli astri, nell&#039;attraversar l&#039;aria in direzione ora più ora <lb></lb>meno obliqua. </s>

<s>Quasi in quel medesimo tempo il Newton, sottoponendo alle <lb></lb>leggi universali dell&#039;attrazione anche la luce, aveva dimostrato che il raggio <lb></lb>non si refrange per una meccanica riflessione effettuata dall&#039;urto contro le <lb></lb>particelle resistenti alla superficie del mezzo più denso, ma che la virtù di <lb></lb>quello stesso mezzo, operando uniformemente per tutta la lunghezza del raggio <lb></lb>entrovi immerso, era quella che lo faceva inflettere dalla sua prima direzione. </s>

<s><lb></lb>Cosi finalmente s&#039;intese che c&#039;era una causa fisica operatrice del fenomeno <lb></lb>delle rifrazioni distinta da quella da cui si fanno le riflessioni, e s&#039;ebbe cosi <lb></lb>più chiara idea di ciò che rappresenta la luce, ossia che passi dall&#039;aria ne&#039;dia­<lb></lb>fani più densi sparsi sulla superficie terrestre, ossia che per gli spazii eterei <lb></lb>giunga attraverso all&#039;aria, dagli astri più lontani, ad approdare a&#039;nostri occhi. </s></p><pb xlink:href="020/01/653.jpg" pagenum="96"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della luce diffratta e de&#039;colori<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. Dell&#039;esperienze, da cui fu condotto il Grimaldi a professar che la luce, come i liquidi, si diffrange. <lb></lb></s>

<s>— II. </s>

<s>Come il Newton confermasse le verità de&#039;fenomeni grimaldiani, e come v&#039;applicasse a <lb></lb>spiegarli il principio dell&#039;attrazione. </s>

<s>— III. </s>

<s>Delle teorie de&#039;colori. </s>

<s>— IV. De&#039;colori e delle varie <lb></lb>apparenze dell&#039;Iride celeste. </s>

<s>— V. </s>

<s>Delle Corone e de&#039;Parelii. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La Storia, ne&#039;due precedenti Capitoli narrata, ci dimostra coi fatti che <lb></lb>la ragione, per cui l&#039;Ottica, da&#039;suoi principii infino alla prima metà del se­<lb></lb>colo XVI, ebbe così impacciati e lenti i suoi incerti progressi, dipendeva <lb></lb>principalmente dal non essersi saputo ben definire la natura e l&#039;essere della <lb></lb>luce. </s>

<s>E se l&#039;essenze delle cose son per sè tutte impenetrabili, si può a più <lb></lb>forte ragione asserir ciò della luce, che sfugge, per la sua sottigliezza, alla <lb></lb>percezion di que&#039;sensi, da cui ci si rivelano le qualità della materia. </s>

<s>Imma­<lb></lb>teriale perciò reputarono la luce gli Ottici antichi, e solo alcuni pochi altri <lb></lb>condiscesero ad ammetter ch&#039;ella fosse qualche cosa di mezzo tra gli spi­<lb></lb>riti e i corpi, tra la forma e la materia. </s>

<s>Professando così fatti principii s&#039;in­<lb></lb>tende bene come fosse impossibile salvar le riflessioni e le rifrazioni, le quali <lb></lb>perciò, non si ammettevano, se non perchè venivano dimostrate dai fatti. </s></p><p type="main">

<s>Benchè dunque non fosse da sperar per nessuno di penetrare addentro <lb></lb>all&#039;essenza della luce, pur si fece un gran passo, quando si pronunziò che <lb></lb>ell&#039;era sostanza puramente corporea, e perciò soggetta alle passioni stesse <lb></lb>di tutta l&#039;altra materia. </s>

<s>Anco il Keplero e il Cartesio è vero avevano da <lb></lb>qualche parte riguardata la luce come tale, ma si faceva da essi con ma­<lb></lb>nifesta violenza ai principii già professati. </s>

<s>Così per non ripetere l&#039;osserva-<pb xlink:href="020/01/654.jpg" pagenum="97"></pb>zione, che da que&#039;Filosofi un moto infinito si decompone in due e gli si <lb></lb>prefiniscono, per lunghezza di linee, i limiti nello spazio; non s&#039;intende, <lb></lb>nella proposizione II del Cap. </s>

<s>IV de&#039;Paralipomeni a Vitellione, come il dif­<lb></lb>fondersi istantaneo e superficiale si possa conciliar coll&#039;ipotesi che riguarda <lb></lb>i raggi terminati in grossezza fra due linee parallele, in modo che il cre­<lb></lb><figure id="id.020.01.654.1.jpg" xlink:href="020/01/654/1.jpg"></figure></s></p><p type="caption">

<s>Figura 34.<lb></lb>scer della sezione alla striscia luminosa proporzionato al crescere <lb></lb>dell&#039;obliquità incidente, sia sensibile al resister che fa in contro <lb></lb>al moto di lei la densità maggiore del mezzo in che offende. </s>

<s>Mag­<lb></lb>gior contradizione poi si nota nel Mersenno, ch&#039;è il più affac­<lb></lb>cendato seguace del Cartesio, il qual Mersenno riguarda il raggio <lb></lb>perpendicolare come una linea matematica, e il raggio obliquo <lb></lb>come avente sensibile larghezza, quasi fosse l&#039;accidentale inci­<lb></lb>denza quella che fa al raggio luminoso cangiar natura. </s>

<s>“ Possumus ergo <lb></lb>considerare radium ABCD (fig. </s>

<s>34) sine latitudine, hoc est ut linea mathe­<lb></lb>matica. </s>

<s>Sed in incidentia obliqua, ubi operatio ab F (fig. </s>

<s>35) ad planum <lb></lb><figure id="id.020.01.654.2.jpg" xlink:href="020/01/654/2.jpg"></figure></s></p><p type="caption">

<s>Figura 35.<lb></lb>in H, in maiori est distantia quam ab E in G, non <lb></lb>potest considerari EFGH ut linea mathematica, <lb></lb>quia sic consideraretur EF ut punctum mathe­<lb></lb>maticum, quod tamen consideratur uno termino <lb></lb>operari longius quam altero, hoc est consideratur <lb></lb>ut habens terminos, hoc est non ut punctum ” <lb></lb>(Univ. </s>

<s>geom. </s>

<s>Synopsis, Parisiis 1644, pag. </s>

<s>573). </s></p><p type="main">

<s>Dietro queste considerazioni s&#039;intenderà bene quanto dovesse giovare <lb></lb>ai progressi dell&#039;Ottica il tor via quel mostruoso contrasto, che nasce dal <lb></lb>plasmar, diciamo così, la luce di spirito e di materia. </s>

<s>L&#039;arrischiata impresa <lb></lb>se l&#039;assunse il Grimaldi, il quale confessa essergli bisognato a ciò animo <lb></lb>intrepido. </s>

<s>L&#039;intrepidezza poi in un Gesuita, che contradiceva non solo alla <lb></lb>corrente opinion de&#039;Filosofi, ma che toglieva di più a&#039;Mistici la consolazione <lb></lb>di riguardar la luce quale ala e veste degli spiriti celesti, era tanto più ne­<lb></lb>cessaria, in quanto che egli sentenziava la luce esser corporea sull&#039;ipotesi, <lb></lb>non potutasi mai dopo tante prove verificare, ch&#039;ella si muova in tempo <lb></lb>come si vedon muovere tutti i corpi. </s>

<s>Forse, delle due facce contrarie del <lb></lb>libro del Grimaldi si sarebbe comunemente creduto essere stato il vero scritto <lb></lb>nella seconda, se l&#039;ipotesi del moto della luce in tempo non fosse stata so­<lb></lb>lennemente confermata dai fatti, e se non ne fosse legittimamente conse­<lb></lb>guito da ciò l&#039;argomento, con cui il Grimaldi provava la materialità della <lb></lb>luce stessa. </s></p><p type="main">

<s>Così, dal fortunato riscontro ritrovato fra le speculazioni del nostro Fi­<lb></lb>losofo italiano e le osservazioni dell&#039;Astronomo danese, essendosi dimostrato <lb></lb>dover esser gli atomi componenti la luce sostanze materiali; come il Gri­<lb></lb>maldi stesso aveva mirabilmente promossa la scienza, applicando alla luce <lb></lb>la proprietà de&#039;corpi fluidi in moto, così il Newton non la promosse poi <lb></lb>meno efficacemente applicando ad essa luce le proprietà generali del moto <lb></lb>de&#039;gravi. </s>

<s>L&#039;Autore inglese è più matematico, l&#039;Italiano è più fisico, ma alla <pb xlink:href="020/01/655.jpg" pagenum="98"></pb>concorde opera loro và debitrice l&#039;Ottica d&#039;aver posato il piè sopra più sta­<lb></lb>bili fondamenti, e d&#039;essersi arricchita di nuove insigni scoperte, delle quali <lb></lb>si fa principal soggetto storico al capitolo presente. </s>

<s>E perchè per tempo e <lb></lb>per dignità vengono prima le scoperte del Grimaldi, che dettero occasione <lb></lb>e aprirono le vie filosofiche al Newton, ragion vuole che la nostra Storia in­<lb></lb>cominci da quelle. </s></p><p type="main">

<s>Noi siam tornati più volte a leggere e ripensare su quella nota XVIII, <lb></lb>che il Libri trascrive da&#039;Manoscritti di Leonardo da Vinci, nella pagina 234 <lb></lb>del III Tomo della sua <emph type="italics"></emph>Histoire des Sciences mathematiques<emph.end type="italics"></emph.end> “ Lo spira­<lb></lb>colo luminoso, dice quella Nota, veduto di loco ombroso, ancora ch&#039;esso sia <lb></lb>d&#039;uniforme larghezza, e&#039;parrà forte restringersi vicino qualunque obbietto <lb></lb>fia interposto infra l&#039;occhio e tale spiracolo. </s>

<s>” L&#039;osservazione ottica ha per <lb></lb>noi qualche cosa di singolare, e i lettori giudicheranno se ell&#039;abbia davvero <lb></lb>qualche somiglianza con quest&#039;altra che il Grimaldi descrive nel suo primo <lb></lb>Esperimento. </s></p><p type="main">

<s>“ Aperto in fenestra foraminulo per quam parvo AB (fig. </s>

<s>36) introdu­<lb></lb>catur per illud in cubiculum, alioqui valde obscurum, lumen solis coelo se­<lb></lb>renissimo, cuius diffusio erit per conum, vel quasi conum ACDB visibilem, <lb></lb>si aer fuerit refertus atomis pulvureis, vel si in eo excitetur aliquis fumus. <lb></lb><figure id="id.020.01.655.1.jpg" xlink:href="020/01/655/1.jpg"></figure></s></p><p type="caption">

<s>Figura 36.<lb></lb>Huic cono inseratur aliquod <lb></lb>corpus opacum EF, in magna <lb></lb>distantia a foramine AB, et <lb></lb>ita ut saltem unum extremum <lb></lb>corporis opaci illuminetur. </s>

<s><lb></lb>Excipiatur deinde in tabella <lb></lb>candida, vel in folio chartae <lb></lb>albae super pavimento exten­<lb></lb>sae, conus praedictus, seu ba­<lb></lb>sis eius lucida CD cum umbra <lb></lb>GH, quam proiicit opacum <lb></lb>EF insertum cono, et illumi­<lb></lb>natum in utroque sui extremo <lb></lb>E et F: quae tamen umbra <lb></lb>secundum leges opticas non erit exactissima praecisa et terminata in uno <lb></lb>puncto G versus unam partem, et in uno alio puncto H versus aliam; sed <lb></lb>ratione foraminis AB, aliquam tandem latitudinem habentis simulque ratione <lb></lb>solis in latum extensi, aliave de causa, erit confinium umbrae aliquo modo <lb></lb>incertum propter penumbram quandam, et cum sensibili decremento, seu ut <lb></lb>vocant exsumatione luminis per spatium IG inter certam umbram et nitidum <lb></lb>lumen ad unam partem praedictae basis, et per spatium HL ad aliam partem ” <lb></lb>(De lumine, Bononiae 1665, pag. </s>

<s>2). </s></p><p type="main">

<s>Due cose, prosegue a dire il Grimaldi, son notabili nell&#039;osservazione di <lb></lb>questo fatto, la prima delle quali è che calcolati i limiti dell&#039;ombra e della <lb></lb>penombra, dietro le misure date del foro AB e della grossezza del corpo opaco <pb xlink:href="020/01/656.jpg" pagenum="99"></pb>EF, non che delle distanze BF, FI, si trovan quegli stessi limiti di fatto ec­<lb></lb>cedere notabilmente le misure date dal calcolo. </s>

<s>In altre parole, mentre la <lb></lb>legge geometrica prefinirebbe all&#039;ombra lo spazio IL, si osserva che in realtà <lb></lb>si allarga più oltre fino in MN. </s></p><p type="main">

<s>“ Praeterea observetur super lucidae basis parte CM et ND, nitide ac <lb></lb>fortiter illustrata spargi et distingui tractus aliquos, seu series luminis co­<lb></lb>lorati, ita ut in qualibet serie sit in medio quidem lux valde pura et sin­<lb></lb>cera, in extremis autem sit color aliquis, nempe caeruleus in extremo ipsi <lb></lb>umbrae MN proprinquiore, et rubeus in extremo remotiore: quae series lu­<lb></lb>cidae, licet dependeant a quantitate foraminis AB, quia non apparent si il­<lb></lb>lud esset maiusculum, non sunt tamen ab eo determinatae, sicut nec deter­<lb></lb>minantur a quantitate diametri solaris. </s>

<s>Ulterius observatur tractus praedictos <lb></lb>seu series luminis colorati ita se extendere ab M versus C, et idem dic de <lb></lb>aliis ab N versus D, ut prima latior sit quam secunda, et haec latior quam <lb></lb>tertia, neque vero contigit unquam videre plus quam tres, decrescente etiam <lb></lb>in illis intensione luminis et colorum eodem ordine quo illae recedunt ab <lb></lb>umbra ” (ibi, pag. </s>

<s>3). </s></p><p type="main">

<s>Il Grimaldi, esaminato così diligentemente il fatto, ne andava cercando <lb></lb>la spiegazione, ma volle prima rappresentarsi quello stesso fatto sotto un <lb></lb>aspetto alquanto diverso, variando così e rendendo tutt&#039;insieme più efficace <lb></lb>il singolarissimo esperimento: </s></p><p type="main">

<s>“ Aperto in fenestra lignea cubiculi bene obscurati foramine fere digi­<lb></lb>talis crassitiei, applicetur ei lamina opaca subtilis AB (fig. </s>

<s>37) per cuius <lb></lb><figure id="id.020.01.656.1.jpg" xlink:href="020/01/656/1.jpg"></figure></s></p><p type="caption">

<s>Figura 37.<lb></lb>foraminulum arctissimum CD solis lumen ad­<lb></lb>missum formabit se in conum. </s>

<s>Hic vero in ma­<lb></lb>gna distantia post laminam AB ad rectos an­<lb></lb>gulos secetur ab alia lamella EF, habente pariter <lb></lb>foramen parvum GH, per quod excipiatur ali­<lb></lb>quid de praedicto luminoso cono secto a la­<lb></lb>mina EF, utique in loco ubi eius basis valde <lb></lb>superat amplitudinem foraminis GH, ut ita fo­<lb></lb>ramen hoc totum illustretur, seu lumine com­<lb></lb>pleatur. </s>

<s>Rursus ergo hoc ipsum luminis quod <lb></lb>ingreditur secundum foramen GH, formabitur <lb></lb>seu procedet formatum in conum, vel quasi co­<lb></lb>num, qui sectus orthogonaliter ac terminatus ab <lb></lb>aliquo plano mundo et candido, exhibebit in illo <lb></lb>suam basem lucidam IL notabiliter maiorem, <lb></lb>quam ferant radii per utrumque foramen recta transmissi et non solum tran­<lb></lb>seuntes per extrema foraminum ad easdem partes spectantia, ut sunt radii <lb></lb>CGL et DHM, sed etiam ad partes contrarias ut sunt radii DGN et CHO ” <lb></lb>(ibi, pag. </s>

<s>9). </s></p><p type="main">

<s>Anco qui si nota un fatto simile a quello che osservasi nell&#039;esperienza <lb></lb>precedente: il cono radioso GIKH è realmente più grande del cono geome-<pb xlink:href="020/01/657.jpg" pagenum="100"></pb>trico GNOH: si osserva inoltre che la base di esso cono è circumcinta di <lb></lb>un lume, dice il Grimaldi, in parte di color rosso e in parte di ceruleo. </s></p><p type="main">

<s>Così stando le cose, l&#039;intento osservatore domandava a sè stesso come <lb></lb>mai l&#039;ombra nel primo esperimento e il cono radioso del secondo avessero <lb></lb>in ogni caso a tornare notabilmente più grandi del dovere. </s>

<s>I sottili lati del <lb></lb>corpo opaco interposto e gli orli taglienti del secondo foro, inetti così a ri­<lb></lb>flettere com&#039;a rifrangere la luce, non davano speranza di riuscire a trovar <lb></lb>la ragione del fenomeno nelle proprietà ottiche più comunemente note, e <lb></lb>dall&#039;altra parte era chiaro che il deviar del raggio rasente gli orli del corpo <lb></lb>opaco osservava tutt&#039;altre leggi da quelle diottriche e calottriche ordinarie. </s>

<s><lb></lb>Pareva al Grimaldi che piuttosto la luce imitasse, in quel fatto singolare, <lb></lb>un filo di fluido, che si sparpaglia fatto passar rasente al sottile orlo di un <lb></lb>corpo, come si vede gettando l&#039;acqua con forza dal cannello forato di uno <lb></lb>schizzetto. </s>

<s>“ Quod si fluidum per quam valido impetu diffundatur, fieri po­<lb></lb>test ut pars illa quae uni extremo obstaculi allabitur, ac deinde ulterius <lb></lb>procedit, multipliciter frangatur, et huc illuc divisim dispergatur. </s>

<s>Videmus <lb></lb>hoc reipsa clarissime, dum aquae per fistulam violenter emissae, applicamus <lb></lb>aut etiam modice immergimus cuspidem alicuius solidi corporis, observando <lb></lb>quomodo aqua illa sic fracta disiiciatur ” (ibi, pag. </s>

<s>13, n.o 4). </s></p><p type="main">

<s>Persuaso perciò il Grimaldi che dovendo essere la luce sostanza corpo­<lb></lb>rea in moto non poteva meglio paragonarsi che al flusso di un liquido, non <lb></lb>esitò a spiegare i fenomeni presentati da&#039;suoi due esperimenti, ammettendo <lb></lb>che il raggio nel rasentar l&#039;orlo del corpo intercettante il suo cammino si <lb></lb>sparpagli, o com&#039;egli diceva si <emph type="italics"></emph>diffranga,<emph.end type="italics"></emph.end> e perciò l&#039;ombra apparisca più <lb></lb>larga di quel che non dovrebbe, se il raggio stesso andasse unito e in linea <lb></lb>retta. </s>

<s>Così ai tre modi ordinarii del propagarsi la luce, per via diretta, o per <lb></lb>riflessione o per rifrazione, ne aggiunse, il nostro Autore, un quarto, a cui <lb></lb>dà il nome proprio di <emph type="italics"></emph>Diffrazione.<emph.end type="italics"></emph.end> “ Hactenus quidem putaverunt Optici lu­<lb></lb>minis propagationem his tribus dumtaxat modis perfici directe, refracte ac <lb></lb>riflexe .... nobis alius quartus modus illuxit, quem nunc proponimus, voca­<lb></lb>musque <emph type="italics"></emph>Diffractionem ”<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>2, n.o 5). </s></p><p type="main">

<s>In quella stessa rassomiglianza intraveduta fra la luce e un fluido in <lb></lb>moto, trovava altresì il Grimaldi la ragione delle frange colorite, che ter­<lb></lb>minano l&#039;ombra nel primo esperimento, e che nel secondo precingono la <lb></lb>base al cono radioso. </s>

<s>Imperocchè egli ammetteva che que&#039;colori nascessero <lb></lb>dall&#039;increspamento ondoso del raggio, in conseguenza dell&#039;urto ricevuto dal­<lb></lb>l&#039;incontro nel corpo duro, come si vede avvenir di fatto in qualunque fluido <lb></lb>anche in moto, percosso per esempio dal cadere di un sasso. </s>

<s>“ At longe <lb></lb>maior inaequalitas motus contingit in fluido, si undose agitetur, estque in <lb></lb>hoc genere motus tam multiplex et adeo mira varietas, ut eam persequi sit <lb></lb>labyrintum desperationis intrare. </s>

<s>Unum tamen prae aliis facillimum hoc <lb></lb>adverto, videlicet posse dari undas seu fluctus in fluido, sive illud actu to­<lb></lb>tum fluat, sive in modum stagni quiescat. </s>

<s>Experire proiecto similiter lapide <lb></lb>in aquam stagnantem et in defluentem, videbis enim similes circulos unda-<pb xlink:href="020/01/658.jpg" pagenum="101"></pb>rum in utroque casu elevari ac dilatari aliis post alios succedentibus ” (ibi, <lb></lb>pag. </s>

<s>12, 13). </s></p><p type="main">

<s>A questo modo fluttuando il raggio luminoso per l&#039;urto ricevuto, nel <lb></lb>rasentare o il corpo opaco intraversato o gli orli del foro, si vengono a pro­<lb></lb>durre secondo il Grimaldi le frange alterne e colorate che si osservano <lb></lb>ne&#039;due sopra citati esperimenti. </s>

<s>“ Quid enim aliud est multiplex illa con­<lb></lb>geries luminis per series lucidas multiformiter collecti, nisi effectus agita­<lb></lb>tionis qua lumen undose glomeratum amittit uniformem illam sui diffusio­<lb></lb>nem, qua solet aequabiliter spargi, ideoque dum terminatur super tabella <lb></lb>candida non exhibet amplius illustrationem uniformiter expansam, immo vero <lb></lb>illam reddit tractibus dissimilibus intercisam et diversis gradibus lucis di­<lb></lb>scriminatam? </s>

<s>” (ibi, pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Così veniva il Grimaldi ad adempiere tutt&#039;insieme l&#039;ufficio di osserva­<lb></lb>tore attentissimo e di Filosofo, non contentandosi di descrivere solamente <lb></lb>il fatto, ma studiandosi di più di rendere qualunque ella si fosse, una ra­<lb></lb>gione del fatto. </s>

<s>Ripensando che la camera oscura era forse lo strumento ot­<lb></lb>tico più maneggiato e del più semplice artificio di tutti gli altri, e che no­<lb></lb>nostante a nessuno era riuscito di assottigliar così il senso e di aguzzare <lb></lb>l&#039;ingegno a vedervi quel che il Grimaldi ci vide, nò nelle immagini spet­<lb></lb>tacolose, ma nel semplice raggio, si riconoscerà nel nostro Autor bolognese <lb></lb>l&#039;iniziatore di quella nuova arte di finissimi ottici esperimenti, che dovevan <lb></lb>di tanta gloria circondare il Newton e poi più tardi l&#039;Young, il Malus, il <lb></lb>Fresnel. </s>

<s>Ma a dover riguardare il Grimaldi come tale e a confermargli il <lb></lb>merito insigne d&#039;avere aperto all&#039;Ottica nuovi larghi campi, ne&#039;quali si sa­<lb></lb>rebbero tanto gloriosamente esercitati i sopra detti stranieri, s&#039;aggiunge alle <lb></lb>descritte un&#039;altra scoperta, simile nella natura, e di pari novità ma supe­<lb></lb>riore nella maraviglia. </s></p><p type="main">

<s>“ Aperiantur in fenestra cubiculi obscurati duo parva foraminula tanto <lb></lb>intervallo disiuncta ut duo luminosi coni a Sole per ipsa illabentes in ma­<lb></lb>gna distantia post fenestram concurrant solum ex parte, ideoque in candida <lb></lb>tabella illos ibi orthogonaliter secante appareant circulares bases conorum <lb></lb>invicem ex parte permixtae, ut sunt in adiecta figura 38 circuli duo ABCD, <lb></lb><figure id="id.020.01.658.1.jpg" xlink:href="020/01/658/1.jpg"></figure></s></p><p type="caption">

<s>Figura 38.<lb></lb>et AECF se intersecantes, ha­<lb></lb>bentesque commune segmen­<lb></lb>tum ADCF. </s>

<s>Claudatur deinde <lb></lb>unum ex foraminibus et obser­<lb></lb>vetur conus per alterum intro­<lb></lb>missus, quomodo scilicet basis <lb></lb>illius terminetur. </s>

<s>Apparebit <lb></lb>enim in eius circulo ambitus <lb></lb>ABCD obscurus in comparatio­<lb></lb>ne luminis cadentis super me­<lb></lb>dias partes eiusdem circuli, ita ut circa ipsum manifeste videatur velut armilla <lb></lb>obscura minus ac minus habens luminis in sui partibus magis accedenti-<pb xlink:href="020/01/659.jpg" pagenum="102"></pb>bus ad extremam peripheriam; quae tamen armilla seu circellus obscurus <lb></lb>nihil aliud esse potest quam lumen debile ut revera cognoscitur si compa­<lb></lb>retur ad partes tabellae extra totum circulum ABC adiacentes et omnino <lb></lb>obscuras. </s>

<s>Idem plane observabitur in base AECF, aperto altero foramine et <lb></lb>clauso priore, ita ut non appareat basis ABCD sed sola spectetur AECF. </s>

<s>At <lb></lb>si aperto utroque foramine observetur utraque simul basis in loco ubi se <lb></lb>intersecant .... et si commune segmentum ADCF fuerit parvum eo quod <lb></lb>tabella candida illud excipiens secet utrumque conum valde prope foramina, <lb></lb>arcus uterque ADC et AFC videbitur rubescere. </s>

<s>At si tabella excipiens lu­<lb></lb>cidas bases magis distiterit a foraminibus, fueritque propterea maius com­<lb></lb>mune illud segmentum, erit circellus uterque ADC, AFC magis notabiliter <lb></lb>obscurus ” (ibi, pag. </s>

<s>187). </s></p><p type="main">

<s>Da ciò ne concludeva il Grimaldi un effetto, il quale, piuttostochè nuovo <lb></lb>e maraviglioso, direbbesi addirittura paradossastico, ed è che luce aggiunta <lb></lb>a luce non rischiara maggiormente l&#039;oggetto, ma talvolta l&#039;oscura. </s>

<s>“ Ex his <lb></lb>quae indubitanter apparent et quae facile quivis poterit experiri, probatur <lb></lb>propositio: lumen aliquando per sui communicationem reddit obscuriorem <lb></lb>superficiem corporis aliunde et prius illustratam ” (ibi). </s></p><p type="main">

<s>Ma come si può ridurre a termini di ragionevolezza il fatto, che ha così <lb></lb>tanto dello strano? </s>

<s>E il Grimaldi risponde che l&#039;oscurità prodotta dall&#039;ag­<lb></lb>giunta del lume si salva osservando che ogni colorazione è un principio di <lb></lb>oscuramento, e la colorazione non da altro dipende se non dal fluitar che <lb></lb>sopravvien nella luce, per effetto della diffrazione. </s>

<s>Così i cerchietti proiettati <lb></lb>sulla tavoletta candida, secondo il descritto esperimento, si vedono tutt&#039;in­<lb></lb>torno rosseggiare negli orli per la luce che entrando nella camera oscura <lb></lb>si diffrange in passare attraverso alle angustie de&#039;fori, “ sed haec interim <lb></lb>vix indicasse sufficiat ut constet luculentius posse aliquid habere circa se <lb></lb>plus luminis, et tamen reddi obscurius, quatenus lumen alteri lumini im­<lb></lb>perfecte admixtum minus aptum est illustrare corpus in quod incidit, ob <lb></lb>suam diffractionem et agitatam diffusionem, per quam positive etiam reprae­<lb></lb>sentat illud tanquam obscurius ” (ibi, pag. </s>

<s>189). </s></p><p type="main">

<s>Le ragioni che il Grimaldi rendeva de&#039;fenomeni così nuovi da lui stesso <lb></lb>prima osservati, e com&#039;abbiamo inteso così diligentemente descritti, erano <lb></lb>quelle che si potevano avere a que&#039;tempi, e che venivano suggerite dal pa­<lb></lb>ragonare il moto della luce al flusso di un liquido, che percosso ondeggia <lb></lb>e, percotendo, in minuti e larghi spruzzoli si diffrange. </s>

<s>In cose tanto remote <lb></lb>dai sensi com&#039;è impossibile a penetrare il vero, così anche è difficilissimo in­<lb></lb>contrarsi in quel probabile che sodisfaccia agl&#039;ingegni, liberi di pensare al­<lb></lb>trimenti, e facili a cavar dal loro proprio cervello altre diverse opinioni. </s>

<s>Ma <lb></lb>lasciando questi così fatti da parte dobbiam dir di que&#039;pochi, i quali cre­<lb></lb>deron di non dover conformar le loro alle speculazioni ottiche del Grimaldi, <lb></lb>non pervertiti da pregiudizii di scuola o dai proprii capricci, ma mossi dal <lb></lb>più attento esame dei fatti, e dalla più ingegnosa varietà data agli espe­<lb></lb>rimenti. </s></p><pb xlink:href="020/01/660.jpg" pagenum="103"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Primo e principale fra questi ci occorre a commemorare il Newton, il <lb></lb>quale iniziava allora i suoi studii ottici, quando comparve alla luce il libro <lb></lb><emph type="italics"></emph>De lumine coloribus et iride<emph.end type="italics"></emph.end> del Grimaldi. </s>

<s>Ma non era facile che questo <lb></lb>Libro, così freddamente accolto nella stessa Italia, e a quel che pare po­<lb></lb>chissimo letto e compreso, avesse potuto varcar mari e monti per giungere <lb></lb>infino a Londra, se l&#039;occasione non avesse procacciato alla scienza questa <lb></lb>buona ventura. </s>

<s>Qual fosse poi l&#039;occasione, per cui il Newton rivolse sopra <lb></lb>i nuovi fenomeni grimaldiani i suoi studii, è ciò che noi dobbiamo per prima <lb></lb>cosa narrare, e anzi è il Newton stesso che così ne esordisce la Storia. </s></p><p type="main">

<s>“ Ineunte anno 1666, quo tempore operam dabam conficiendis opticis <lb></lb>vitris figurarum a sphaerica diversarum, mihi vitreum Prisma triangulare <lb></lb>paravi, eo notissima phaenomena colorum experturus. </s>

<s>Cum idcirco cubicu­<lb></lb>lum meum obscurum raddidissem, parvoque foramine ligneam fenestram <lb></lb>pertusissem, quo satis lucis a sole venientis intrare posset, illam ingredien­<lb></lb>tem Prismate excepi, quo refracta fuit in parietem oppositum. </s>

<s>Et primo <lb></lb>quidem me non parva voluptate affecerunt vividi et intensi colores ita pro­<lb></lb>deuntes. </s>

<s>Paulo post vero, cum eos maiori cura et attentione considerarem, <lb></lb>in oblongam figuram diductos miratus sum, siquidem putabam fore, ut iuxta <lb></lb>receptas refractionum leges in circularem sese contraherent. </s>

<s>Utrinque rectis <lb></lb>lineis terminabantur, sed difficile fuisset, ob lucem gradatim evanescentem, <lb></lb>extremitatum figuram accurate definire quae tamen visa est semicircularis ” <lb></lb>(Op. </s>

<s>opt. </s>

<s>omnia, Patavii 1773, Appendix, pag. </s>

<s>3). </s></p><p type="main">

<s>Misura la lunghezza dello spettro relativamente alla larghezza, e trova <lb></lb>quella presso a poco cinque volte maggiore di questa “ quae tanta inae­<lb></lb>qualitas maximam mihi cupiditatem iniecit requirendi unde nam orire­<lb></lb>tur ” (ibi). Dubita che ciò dipenda dalla varia grossezza del prisma, il quale <lb></lb>va dal suo massiccio a terminare in tre spigoli acuti, o che sia in qualche <lb></lb>parte difettoso il prisma stesso usato per l&#039;esperienza. </s>

<s>Pensa in ogni modo <lb></lb>che i difetti del primo sarebbero emendati da un altro simile vetro che ri­<lb></lb>franga i raggi in verso contrario. </s>

<s>Ripete l&#039;esperienza e trova che i due cri­<lb></lb>stalli prismatici accoppiati non danno più il solito spettro oblungo e colo­<lb></lb>rato, ma dipingono un&#039;immagine bianca e circolare, come se fossero i raggi <lb></lb>liberamente passati attraverso all&#039;aria. </s>

<s>“ Tunc suspicatus sum colores ita di­<lb></lb>latari, quod vitrum esset inaequale, aut quavis alia ratione fortuito vitiosum. </s>

<s><lb></lb>Experturus an id verum esset, sumpsi aliud Prisma primo simile, quod ita <lb></lb>statui ut lux per utrumque transiens refringi posset ad contrarias partes, <lb></lb>et hoc pacto a secundo redigi in viam, a qua primum illum detorserat. </s>

<s>Sic <lb></lb>enim futurum existimabam, ut quae primum Prisma secundum naturae le­<lb></lb>ges effecerat, a secundo Prismate destruerentur, augescerent autem ob plu-<pb xlink:href="020/01/661.jpg" pagenum="104"></pb>res refractiones, quae contra has leges accidissent. </s>

<s>Exitus vero fuit quod lux <lb></lb>quae a primo Prismate in oblongum spatium diffusa fuerat, a secundo in <lb></lb>orbiculare coercita fuit accuratius, quam si per neutrum transmeasset. </s>

<s>Igi­<lb></lb>tur, quaecumque demum sit huius longitudinis causa, ea certe non est for­<lb></lb>tuita quaedam anomalia ” (ibi, pag. </s>

<s>3, 4). </s></p><p type="main">

<s>Se non è dunque l&#039;allungamento dello spettro un&#039;anomalia, nè una illu­<lb></lb>sione, si domandava pensosamente il Newton, qual&#039;è di questo effetto reale <lb></lb>la causa vera? </s>

<s>e dopo lunghe e accuratissime esperienze ebbe a rispondere: <lb></lb>“ Unde patet veram imaginis sic exporrectae causam hanc unam esse quod <lb></lb>scilicet <emph type="italics"></emph>Lux constat ex radiis quorum alii aliis magis refrangibiles sunt,<emph.end type="italics"></emph.end><lb></lb>qui nulla incidentiae ratione habita pro <emph type="italics"></emph>peculiaribus refrangibilitatis gra­<lb></lb>dibus,<emph.end type="italics"></emph.end> ad diversas oppositi parietis partes transmittuntur ” (ibi, pag. </s>

<s>5). </s></p><p type="main">

<s>Questa storia della scoperta de&#039;varii gradi di refrangibilità della luce <lb></lb>eterogenea attraverso il Prisma la partecipava solennemente il Newton alla <lb></lb>R. </s>

<s>Società di Londra, con lettera data da Cambridge il di 6 Febbraio 1672, <lb></lb>e la R. </s>

<s>Società ne diffondeva la notizia nel num. </s>

<s>80 delle Transazioni filo­<lb></lb>sofiche, sotto il di 19 di quel medesimo mese. </s>

<s>Non mancarono, com&#039;era da <lb></lb>aspettarsi, contradittori, fra&#039;quali il gesuita Ignazio Gastone Pardies, profes­<lb></lb>sor nel Collegio di Parigi, a cui, parendo che la nuova scoperta neutoniana <lb></lb>sovvertisse la Diottrica dalle fondamenta, soccorse in pensiero di ovviarvi <lb></lb>con dire che per questo si refrangono attraverso il prisma variamente i raggi <lb></lb>solari, e lo spettro ne apparisce bislungo, perchè le parti estese del disco <lb></lb>solare cadono sulla superficie del cristallo variamente inclinate (ivi, pag. </s>

<s>22). <lb></lb>Al Pardies che, per mezzo delle Transazioni filosofiche, faceva note al pub­<lb></lb>blico nel Giugno di quel medesimo anno 1672 le sue opposizioni, rispondeva <lb></lb>il Newton nell&#039;Aprile dell&#039;anno seguente, dicendo che il reverendo Padre <lb></lb>era allucinato, per non avere atteso che, così nel far l&#039;esperienza come nel­<lb></lb>l&#039;istituire il calcolo della varia refrangibilità de&#039;raggi, s&#039;erano anzi adoperate <lb></lb>le uguali inclinazioni. </s>

<s>“ Sed hallucinatus est Rever. </s>

<s>Pater, nam refractiones <lb></lb>a diversa parte Prismatis, quantum potest inaequales statuit R. P. Pardies, <lb></lb>cum tamen ergo tum in experimentis, tum in calculo de experimentis illis <lb></lb>inito, aequales adhibuerim ” (ibi, pag. </s>

<s>24). </s></p><p type="main">

<s>Confessando il reverendo Padre che la risposta fattagli era ingegnosis­<lb></lb>sima non per questo si assoggetta a consentir che, per le varie refrangibi­<lb></lb>lità de&#039;raggi, l&#039;immagine del Sole attraverso al prisma, debba riuscire così <lb></lb>allungata. </s>

<s>Pensa che ciò possa essere per qualche somiglianza che abbia <lb></lb>questo coll&#039;altro fenomeno grimaldiano. </s>

<s>“ Etenim in ea hypothesi, quam fuse <lb></lb>explicat noster Grimaldus, in qua supponitur lumen ease substantia quae­<lb></lb>dam rapidissime mota, posset fieri aliqua diffusio luminis post transitum fo­<lb></lb>raminis et decussationem radiorum. </s>

<s>Item in ea hypothesi, qua lumen poni­<lb></lb>tur progredi per certas quasdam materiae subtilis undulatione, ut explicat <lb></lb>subtilissimus Hookius, possunt explicari colores per certam quandam diffu­<lb></lb>sionem atque expansionem undulationuum, quae fiat ad latera radiorum <lb></lb>ultra foramen, ipso contagio ipsaque materiae continuatione ” (ibi, pag. </s>

<s>28). </s></p><pb xlink:href="020/01/662.jpg" pagenum="105"></pb><p type="main">

<s>Ecco la prima volta che risuona all&#039;orecchio del Newton il nome del <lb></lb>Grimaldi. </s>

<s>Della scoperta di lui non par ne sappia più avanti di quel che ne <lb></lb>accenna ivi il Pardies, e risponde che quella dell&#039;Hook niente altro è che <lb></lb>un&#039;ipotesi, la quale non ha nulla che rivedere coi fatti. </s>

<s>Io, dice il Newton, <lb></lb>professo i varii gradi di refrangibilità della luce come un fatto da me sco­<lb></lb>perto, e in varii e diligentissimi modi sperimentato, non come un&#039;ipotesi, <lb></lb>ch&#039;io mi sia cavata dal mio proprio cervello: e non è buona regola di filo­<lb></lb>sofare il concluder che una cosa è, dal supporre che potrebb&#039;essere. </s>

<s>“ Opti­<lb></lb>mus enim et tutissimus philosophandi modus videtur, ut in primis verum <lb></lb>proprietates diligenter inquiramus et per experimenta stabiliamus, ac dein <lb></lb>tardius contendamus ad hypotheses per earum explicatione. </s>

<s>Nam hypotheses <lb></lb>ad explicandas rerum proprietates tantum accommodari debent et non ad <lb></lb>determinandas usurpari ” (ibi, pag. </s>

<s>29). E prosegue a dir che non nega po­<lb></lb>tersi lo spettro allungato e i suoi colori spiegare per mezzo della teoria delle <lb></lb>ondulazioni dell&#039;Hook e anche per via del moto rotatorio de&#039;globuli del Car­<lb></lb>tesio, ma comunque vogliasi dar ragione del fatto a lui basta si ammetta la <lb></lb>verità del fatto, la quale consiste ne&#039;varii gradi di refrangibilità della luce. </s></p><p type="main">

<s>Qui termina la controversia col Pardies, il quale confessò di essere pie­<lb></lb>namente sodisfatto delle ragioni del Newton, ma questi ripensava tuttavia a <lb></lb>quel <emph type="italics"></emph>Grimaldus noster<emph.end type="italics"></emph.end> e a quella diffusione del lume dop&#039;avere attraver­<lb></lb>sato il foro della camera oscura, di che gli parlava dianzi quel suo opposi­<lb></lb>tore. </s>

<s>Ed ecco di qui l&#039;occasione e il motivo ch&#039;ebbe il Filosofo inglese d&#039;in­<lb></lb>formarsi meglio degli sperimenti, e di rivolger la sua mente alle speculazioni <lb></lb>del nostro Ottico di Bologna. </s></p><p type="main">

<s>Quanto al fatto, ritrovò che, adoprando per corpo opaco attraversato al <lb></lb>raggio, un capello, l&#039;ombra era veramente maggiore, e si vedevano le tre <lb></lb>frange colorite precisamente a quel modo che le aveva descritte l&#039;Autore <lb></lb><emph type="italics"></emph>De Lumine.<emph.end type="italics"></emph.end> Quanto alla teoria, trovò che l&#039;ipotesi della diffrazione non era <lb></lb>comunemente accettata: i più sostenevano che il raggio si piega rasente il <lb></lb>sottilissimo corpo opaco, per la ragione delle rifrazioni ordinarie nell&#039;aria. </s>

<s><lb></lb>Ma il Newton dimostrò che la rifrazione ordinaria non aveva alcuna parte <lb></lb>nel fenomeno, e ciò fece stringendo il capello fra due lamine di tersissimo <lb></lb>vetro, fra le quali si distendeva ugualmente, per effetto di capillarità, un <lb></lb>velo sottilissimo di acqua. </s>

<s>Misurata la larghezza dell&#039;ombra del capello in <lb></lb>aria e in acqua, trovò che sempre si manteneva la stessa: “ Cum laminam <lb></lb>vitream perpolitam madefecissem, capillumque in aqua super id vitrum po­<lb></lb>suissem, aliamque deinde laminam vitream perpolitam superimposuissem, ut <lb></lb>adeo aqua repleret id omne spatii quod inter vitra interiaceret, tenui lami­<lb></lb>nas hasce in radio luminis antedicto, ita ut lumen per vitra ad perpendicu­<lb></lb>lum transiret, iamque umbra capilli, iisdem iterum interiectis intervallis, <lb></lb>eandem, ac ante, magnitudinem habebat. </s>

<s>Porro rasurae, quae forte in poli­<lb></lb>tis vitri laminis inessent, umbras itidem proiiciebant, multo utique quam <lb></lb>fieri debuit latiores: itemque venae in eiusmodi politis vitri laminis, um­<lb></lb>beas latiores similiter proiiciebant. </s>

<s>Quare nimia harum umbrarum latitudo, <pb xlink:href="020/01/663.jpg" pagenum="106"></pb>non ex aeris scilicet refractione, sed omnino ex alia aliqua causa oriatur ne­<lb></lb>cesse est ” (Optices, Lib. </s>

<s>III, Observ. </s>

<s>I, Paduae 1773, pag. </s>

<s>127). </s></p><p type="main">

<s>È ella dunque la diffrazion grimaldiana la causa del fenomeno? </s>

<s>Il Newton <lb></lb>non risponde ancora, ma seguita a sperimentare con più esattezza che mai, <lb></lb>variando ingegnosamente modi e osservando con più grande attenzione. </s>

<s><lb></lb>Prende un pezzetto di cartone, lo tinge da tutt&#039;e due le parti di nero, vi <lb></lb>fa nel mezzo un forellino quadrato, e v&#039;incolla una lama sottilissima e acu­<lb></lb>tissima in modo, che esca fuori dell&#039;orlo del quadretto, e ne intercetti qual­<lb></lb>che poco la luce. </s>

<s>Attraversa il cartone così preparato al raggio del sole ri­<lb></lb>cevuto dentro la camera oscura, osserva il solito piegarsi di quel raggio nel <lb></lb>rasentar la punta metallica, e gli par che sia quel piegarsi quasi come se <lb></lb>fosse il raggio misteriosamente attratto verso la stessa punta per una nuova <lb></lb>magnetica simpatia. </s>

<s>Nota inoltre che i raggi sembrano essere attratti più o <lb></lb>men fortemente secondo che passano dalla punta della lamina o dal sotti­<lb></lb>lissimo coltro più o meno lontani. </s></p><p type="main">

<s>La questione dall&#039;Ottica era fatta passare così ad esser parte de&#039;prin­<lb></lb>cipii filosofici, che rendono le ragioni matematiche delle proprietà universali <lb></lb>della materia, e l&#039;Autore ridusse perciò queste speculazioni nel Libro immor­<lb></lb>tale dove scrisse quegli stessi <emph type="italics"></emph>Principii.<emph.end type="italics"></emph.end> “ Radii autem in aere existentes, <lb></lb>uti dudum Grimaldus, luce per foramen in tenebrosum cubiculum admissa, <lb></lb>invenit et ipse quoque expertus sum, in transitu suo prope corporum vel <lb></lb>opacorum vet perspicuorum angulos, quales sunt nummorum ex auro, ar­<lb></lb>gento et aere cusorum termini rectanguli circulares, et cultrorum, lapidum, <lb></lb>aut fractorum vitrorum acies, incurvantur circum corpora quasi attracti in <lb></lb>eadem; et ex his radiis qui in transitu illo propius accedunt ad corpora in­<lb></lb>curvantur magis quasi magis attracti ut ipse etiam diligenter observavi. </s>

<s>Et <lb></lb>qui transeunt ad maiores distantias adhuc maiores incurvantur aliquantulum <lb></lb>ad partes contrarias, et tres colorum fascias efformant ” (Lib. </s>

<s>I, Genevae 1739, <lb></lb>pag. </s>

<s>539, 40). </s></p><p type="main">

<s>Il modo particolare poi come il Newton immaginava che si formassero <lb></lb>le tre fasce de&#039;colori nel fenomeno grimaldiano lo aveva scritto già nella <lb></lb>Questione II e III del III Libro dell&#039;Ottica, così dicendo: “ Annon radii qui <lb></lb>differunt inter se refrangibilitate, iidem flexibilitate quoque inter se diffe­<lb></lb>runt? </s>

<s>Et diversis suis singolurum inflexionibus ita porro a se invicem se­<lb></lb>parantur, ut ordinatim exinde in ternas illas finibrias coloratas digerantur? <lb></lb></s>

<s>— Annon radii luminis inter transeundum prope corporum extremitates <lb></lb>inflectuntur ultro citroque, motu quodam undante ac sinuoso instar anguil­<lb></lb>lae? </s>

<s>Ternaeque luminis colorati fimbriae supra memoratae ex ternis istius­<lb></lb>modi inflexionibus oriuntur? (ediz. </s>

<s>cit., pag. </s>

<s>138). </s></p><p type="main">

<s>Queste fantasie, nelle quali veramente non si riconosce più il Newton, <lb></lb>che pare essersi rifugiato per un momento sotto le tende del Cartesio o del <lb></lb>Gassendo, porsero occasione e dettero poi motivo di far sentenziare agli Ot­<lb></lb>tici, che le frange grimaldiane non erano altrimenti possibili a essere spie­<lb></lb>gate che nell&#039;ipotesi delle ondulazioni. </s>

<s>Il Pardies fu de&#039;primi fra costoro e <pb xlink:href="020/01/664.jpg" pagenum="107"></pb>de&#039;più antichi, nè è da passare a questo proposito sotto silenzio che il Ge­<lb></lb>suita parigino citi l&#039;Hook e non il confratello suo Bolognese, di cui piut­<lb></lb>tosto egli segue con fedeltà le dottrine. </s>

<s>Imperocchè mentre il famoso con­<lb></lb>cittadino del Newton professa l&#039;ipotesi della diffusione delle onde eteree <lb></lb>eccitate per ogni verso dal vibrare del corpo luminoso, il Pardies ammet­<lb></lb>teva quegli increspamenti superficiali e quelle ondose diffrazioni, che si co­<lb></lb>municano lateralmente all&#039;altra parte del lume diffuso, conforme a ciò che <lb></lb>leggemmo nel Trattato <emph type="italics"></emph>De lumine.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ciò sarebbe argomento che l&#039;Ottica del Grimaldi non fosse tenuta al­<lb></lb>lora in grande onore, nemmeno appresso i suoi stessi confratelli, a riconci­<lb></lb>liarsi co&#039;più cocciuti de&#039;quali par che non bastasse all&#039;Autore l&#039;essersi con <lb></lb>strana risoluzione disdetto nelle sei proposizioni peripatetiche, contenute nel <lb></lb>Libro II. </s>

<s>Stanno in ogni modo queste cose a confermare quel che altrove <lb></lb>dicemmo che cioè nè in Italia nè fuori, non prima si apprezzarono le sco­<lb></lb>perte grimaldiane che il Newton venisse a confermarle, dimostrando altresì <lb></lb>che i fatti nuovi come dipendevano da cause non ancora ben conosciute, <lb></lb>così volevano a spiegarli anche nuove ragioni. </s></p><p type="main">

<s>Queste nuove ragioni che secondo gli Ottici, specialmente moderni, non <lb></lb>s&#039;hanno da&#039;principii matematici neutoniani, da&#039;più si crede che vengan som­<lb></lb>ministrate da quell&#039;ipotesi dell&#039;onde eteree, che l&#039;Hook, nella patria del <lb></lb>Newton speculava, e che l&#039;Huyghens poco dopo ridusse a maggior preci­<lb></lb>sione geometrica. </s>

<s>Tanto hanno anzi cotesti ottici neoterici ferma fede nella <lb></lb>dottrina delle onde eteree diffusive del lume, che la professano, non come <lb></lb>probabile ipotesi, ma come certo e dimostrato sistema. </s>

<s>Su da que&#039;calcoli, <lb></lb>che tanto ben rispondono alle speculazioni, si vede bollicare lo spirito car­<lb></lb>tesiano, il quale, dopo quasi tre secoli, non ha smentita la sua natura, ch&#039;è <lb></lb>di allettare anzi di affascinare le menti. </s>

<s>Ma non si vede come, seguendo col <lb></lb>Newton idee più semplici e più naturali, non s&#039;abbia a dar quella sodisfa­<lb></lb>zione agli intelletti, che si vuole esser data a loro da&#039;soli eteristi. </s>

<s>Così, am­<lb></lb>mettendo che gli atomi eterogenei del raggio sieno con varia forza attratti <lb></lb>verso il capello, e verso la punta acuta del coltro, si spiega come debba av­<lb></lb>venire nel raggio stesso composto una dispersione, dalla quale hanno ori­<lb></lb>gine gli iridescenti colori delle frange. </s>

<s>E se i raggi son tanto men forte­<lb></lb>mente attratti quanto più son lontani, s&#039;intende come la seconda frangia si <lb></lb>mostri men vivamente accesa della prima, ma però anche meno sbiadita <lb></lb>della terza. </s>

<s>E se all&#039;ultimo quella virtù attrattiva, dopo l&#039;intervallo occupato <lb></lb>da tre raggi l&#039;uno dietro l&#039;altro, è per riuscire insensibile, s&#039;intende come <lb></lb>tre sole e non più sieno le frange colorate. </s></p><p type="main">

<s>Anche l&#039;altro così singolare fenomeno che fece dire al Grimaldi luce <lb></lb>sopraggiunta a luce produrre oscurità, non si vede come sia impossibile spie­<lb></lb>garlo senza ricorrere all&#039;ipotesi delle <emph type="italics"></emph>Interferenze.<emph.end type="italics"></emph.end> Disposto pure l&#039;esperi­<lb></lb>mento a modo del Fresnel, gli atomi dell&#039;un raggio, che obliquamente in­<lb></lb>contrano gli atomi dell&#039;altro, urtandosi con vario impeto, secondo la varietà <lb></lb>della loro natura, possono esser sufficienti a produr quella dispersione, per <pb xlink:href="020/01/665.jpg" pagenum="108"></pb>cui si veggano apparire i colori colà dove si credeva che ci dovesse brillar <lb></lb>più che mai vivo e schietto il candor della luce. </s></p><p type="main">

<s>Queste son senza dubbio ipotesi soggette a molte difficoltà, ma son pure <lb></lb>ipotesi anche quelle degli eteristi, che non vanno esenti da difficoltà forse <lb></lb>maggiori. </s>

<s>Ma perchè ufficio nostro è non di giudicar direttamente, ma dai <lb></lb>fatti narrati far resultare spontanei i giudizii, potranno questi stessi giudizii <lb></lb>intorno alla più probabile ipotesi della natura e del modo di diffondersi la <lb></lb>luce, nella mente di coloro a cui gli lasciamo, resultare più retti, dal nar­<lb></lb>rar ciò che fu immaginato e pensato dai Filosofi per intendere la natura e <lb></lb>l&#039;origine de&#039;colori. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I Peripatetici, i quali dicevano la luce non essere sostanza, ma qualità <lb></lb>accidentale, interrogati intorno alla natura de&#039;colori rispondevano essere una <lb></lb>qualità della luce, cosicchè venivano a definirli un&#039;accidentalità di una ac­<lb></lb>cidentalità, ossia una vana apparenza e un puro nome. </s>

<s>Coloro però, che più <lb></lb>particolarmente si dettero allo studio dell&#039;Ottica, definirono in qualche modo <lb></lb>le idee, e comunque venisse lor fatto le confortarono dell&#039;esperienza. </s>

<s>Se­<lb></lb>condo Alhazeno e Vitellione i colori permanenti son proprietà de&#039;corpi e la <lb></lb>luce che gli tocca o gli attraversa si riveste delle loro forme, ciò che dice­<lb></lb>vano esser patente da quel che di fatto si osserva, quando passa un raggio <lb></lb>di sole attraverso ai vetri di una finestra. </s>

<s>“ Item lucem res coloratas per­<lb></lb>transeuntem illarum coloribus colorari, ut patet de luce transeunte vitrias <lb></lb>fenestras, quae illorum vitrorum coloribus informatur, secum formas illorum <lb></lb>colorum super obiecta corpora deferendo ” (Vitellionis Perspectiva, Norim­<lb></lb>bergae 1535, pag. </s>

<s>38, v.). </s></p><p type="main">

<s>Ben assai più difficile rimaneva l&#039;investigar l&#039;origine de&#039;colori evane­<lb></lb>scenti, che si producono per rifrazione o attraverso alle gocciole dell&#039;acqua, <lb></lb>come nell&#039;iride o attraverso ai prismi cristallini esposti al sole, a che Vi­<lb></lb>tellione confessa di non esser giunto se non che <emph type="italics"></emph>post multos cogitatus et <lb></lb>experientias<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>287, v.). Frutto di quelle speculazioni e di quelle <lb></lb>esperienze fu la conclusione che i colori iridescenti sono generati dal mi­<lb></lb>schiarsi che fa il bianco della luce colla negrezza propria dell&#039;acqua e del <lb></lb>cristallo. </s>

<s>Dov&#039;è men ombra ivi il colore è rosso, dove l&#039;ombra è massima, <lb></lb>azzurro; il verde si genera nel mezzo dove si contempera l&#039;ombra alla luce. <lb></lb></s>

<s>“ Apparent autem colores in istis luminibus sic reflexis vel refractis propter <lb></lb>mixtionem nigredinis coloris cristallini cum lumine penetrante, et propter <lb></lb>ammixtiones umbrarum partium ipsius cristalli praeminentium secundum <lb></lb>acumen suorum angulorum ” (ibi, pag. </s>

<s>296). </s></p><p type="main">

<s>Queste dottrine di Vitellione si ripeterono poi per lungo tempo quasi <lb></lb>da tutti i Filosofi, e non si dubitava di professarle in quell&#039;età, in cui già <pb xlink:href="020/01/666.jpg" pagenum="109"></pb>l&#039;Ottica prometteva di progredire a pari delle altre scienze sperimentali. </s>

<s>Ecco <lb></lb>quel che il De Dominis, spiegando meglio i concetti dell&#039;antico Maestro, <lb></lb>scriveva in sul finir del secolo XVI intorno alla natura e all&#039;origine de&#039;co­<lb></lb>lori: “ Praeter colores proprios corporum in ipsis corporibus permanentes, <lb></lb>ex quacumque tandem causa illi resultent et oriantur, dantur in natura co­<lb></lb>lores aliqui mutabiles et variabiles, qui dicuntur emphatici et apparentes, <lb></lb>quos ego colores splendidos soleo vocare. </s>

<s>Hos colores ex luce oriri mihi non <lb></lb>est dubium, imo nihil aliud sunt quam ipsamet lux, nam si in aliquo cor­<lb></lb>pore pura sit lux, ut in astris et igne, et ex aliqua causa scintillationem <lb></lb>amittat, tale corpus fit nobis album. </s>

<s>Quod si luci admisceatur opacitas ali­<lb></lb>qua, quae tamen lucem totam non impediat aut extinguat, intermedii colo­<lb></lb>res oriuntur. </s>

<s>Idcirco enim ignis noster rubescit quoniam admistos habet <lb></lb>fumos qui ipsum opacant. </s>

<s>Idcirco etiam sol et astra rubescunt prope hori­<lb></lb>zontem, quia vapores interpositi illa opacant. </s>

<s>Atque hos intermedios colores <lb></lb>tres proprie possumus enumerare: prima enim opacitatis admistio, quae albe­<lb></lb>dinis candorem aliquantum offuscat, facit ipsam lucem puniceam seu ru­<lb></lb>beam; puniceus enim, seu rubeus color, est maxime lucidus ex intermediis; <lb></lb>inter extremos, album et nigrum, ut patet manifeste in vitro oblongo trian­<lb></lb>gulari. </s>

<s>Radius enim solis qui penetrat vitrum prope angulos, ubi minima <lb></lb>est crassities, et consequenter minima opacitas, puniceus egreditur. </s>

<s>Proxime <lb></lb>sequitur viridis ex maiori crassitie, ultimus purpureus, quem pavonaceum <lb></lb>vocamus ex maiori adhuc crassitie, nam pro quantitate crassitiei opacitas <lb></lb>intenditur et remittitur. </s>

<s>Paulo maior itaque opacitas facit colorem viridem, <lb></lb>quod si adsit adhuc maior opacitas color erit coeruleus seu purpureus, qui <lb></lb>ex intermediis est maxime obscurus. </s>

<s>Si demum adhuc magis opacitas inten­<lb></lb>datur, extinguit totam lucem, et remanet nigredo; quamvis nigredo sit po­<lb></lb>tius privatio lucis quam color positivus, unde et sensus eodem modo indicat <lb></lb>meras tenebras atque corpora maxime nigra. </s>

<s>Reliqui vero colores sunt ex <lb></lb>his misti ” (De radiis visus et lucis, Venetiis 1611, pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Il De Dominis fece senza dubbio un gran passo, quando, tolte di mezzo <lb></lb>le forme e le qualità accidentali, sentenziò che i colori enfatici <emph type="italics"></emph>nihil aliud <lb></lb>sunt quam ipsamet lux,<emph.end type="italics"></emph.end> ma soggiogato del resto dall&#039;autorità di Vitellione <lb></lb>non seppe veder che la causa efficiente del fenomeno non consisteva nella <lb></lb>crassizie del mezzo, ma nelle rifrazioni. </s>

<s>Uno de&#039;primi a riconoscere questa <lb></lb>verità e a professarla contro l&#039;errore antico, fu quel Ferrante Imperato, che <lb></lb>quasi in quello stesso tempo, in cui il celebre Spalatrese meditava i suoi <lb></lb>diottrici teoremi, dava opera a descrivere la <emph type="italics"></emph>Historia naturale.<emph.end type="italics"></emph.end> L&#039;Autore di <lb></lb>questa ben si avvide che lo spettro nel prisma era un effetto della rifra­<lb></lb>zione, e, presentendo la scoperta neutoniana della luce composta, disse che <lb></lb>l&#039;oscurità, pel mescolamento della quale si generano i colori, non era nel <lb></lb>mezzo, ma ne&#039;raggi della luce stessa. </s>

<s>“ Veggiamo e con l&#039;uso e con la ra­<lb></lb>gione tutte le differenze de&#039;colori distintissimamente esser rappresentate da <lb></lb>corpi di sostanza ugualissima, purchè vi sia rifrangimento de&#039;raggi tale, che <lb></lb>gli lucidi ed opachi si meschino, come si vede ne&#039;globi ed ampolle chiaris-<pb xlink:href="020/01/667.jpg" pagenum="110"></pb>sime di vetro, e nelle colonne triangolari, istrumento di rifrazione all&#039;os­<lb></lb>servazione della generazion de&#039;colori tra gli altri tutti ottimo ” (Cap. </s>

<s>XVI, <lb></lb>Venezia 1672, pag. </s>

<s>294). </s></p><p type="main">

<s>Ma perchè le idee dell&#039;Imperato non ebbero grande efficacia ne&#039;pro­<lb></lb>gressi dell&#039;Ottica, e il gran Padre della scienza risorta, Giov. </s>

<s>Keplero, si <lb></lb>mostrò per questa parte inferiore a sè stesso, dicendo che i colori eran luce <lb></lb>in potenza e nella materia de&#039;diafani consepolta; l&#039;efficienza delle rifrazioni, <lb></lb>in produrre i colori enfatici, non fu riconosciuta nè professata dagli Ottici, <lb></lb>prima che si divulgassero gl&#039;insegnamenti del Maurolico. </s></p><p type="main">

<s>Nel Teorema XXIX del II, in cui proponesi di dimostrar che i colori <lb></lb>principali dell&#039;iride son quattro, cioè rosso, verde, azzurro e violetto, l&#039;Autor <lb></lb>de&#039;libri <emph type="italics"></emph>Diaphanorum partes<emph.end type="italics"></emph.end> procede a questo modo: Nella sfera ED (fig. </s>

<s>39) <lb></lb>che rappresenta il Sole, prende quattro piccoli cerchi uguali EO, ON, NM, <lb></lb>MD, e da ciascun punto delle divisioni fa muovere i raggi EF, OF, NF, <lb></lb><figure id="id.020.01.667.1.jpg" xlink:href="020/01/667/1.jpg"></figure></s></p><p type="caption">

<s>Figura 39.<lb></lb>MF, DF, i quali nel pun­<lb></lb>to F di una gocciola di <lb></lb>acqua FBC si refran­<lb></lb>gono in FC, FL, FK, FH, <lb></lb>FB. </s>

<s>Così fatto, a provar <lb></lb>che in BH deve essere il <lb></lb>rosso e in HK il verde, <lb></lb>il Maurolico dice: “ A <lb></lb>maiori solis superficie il­<lb></lb>luminatur BH quam HK, et ideo necesse est ut color qui in BH, cui plus lucis <lb></lb>admiscetur, ipsi luci conformior sit: color vero qui in HK, cui plus aquae <lb></lb>inest quam lucis, sit aquae similior, atque ideo color qui in BH flammeus <lb></lb>sive croceus, qui vero in HK, viridis videtur ” (Neapoli 1611, pag. </s>

<s>54, 55). A <lb></lb>provar poi che in LK dee essere il colore azzurro e in LC il violetto, il no­<lb></lb>stro Autore così prosegue: “ Et quamvis LC a superficie EO, quae ipsi DM <lb></lb>ipsam BH illuminanti, aequalis est, illuminetur, et ideo color qui in LC, si­<lb></lb>milis ei qui in BH videri oporteat, tamen, quia gyrus Iridis in LC minor <lb></lb>est quam in BH, ideo radii in LC densiores sunt quam in BH, quare color, <lb></lb>qui in LC fortior ac coloratior eo qui in BH, croceus videtur, in LC rufus, <lb></lb>sive purpureus generabitur. </s>

<s>Similiter, quamvis LK a superficie NO .... illu­<lb></lb>minetur, ideoque, qui in LK, ei qui in KH similem videri oporteret; tamen, <lb></lb>quia gyrus Iridis in LK minor est quam in KH, ideo radii in LK densiores <lb></lb>sunt quam in KH, quare color, qui in LK, fortior ac coloratior eo, qui in <lb></lb>KH videtur. </s>

<s>Sed cum in KH viridis, qui levis ac sobrius est, videatur, in KL <lb></lb>ceruleus, qui fortior ac saturior est, videbitur ” (ibi, pag. </s>

<s>55). </s></p><p type="main">

<s>Qualunque sia però il giudizio che si vuol dare di queste maurolicane <lb></lb>speculazioni, non si può negar che non sia strano ammetter che, là dove è <lb></lb>più condensata la luce, ivi il colore debba apparir più fosco. </s>

<s>Il Maurolico <lb></lb>fu condotto a dir ciò sull&#039;esempio del color della fiamma e de&#039;carboni ac­<lb></lb>cesi. </s>

<s>“ Et notandum quod, sicut ignis levis ac rarus flammeum ac croceum <pb xlink:href="020/01/668.jpg" pagenum="111"></pb>efficit colorem, velut flamma lenem fumum comburens, densus vero ac for­<lb></lb>tis ebrium ac rufum gignit colorem, velut in carbonibus ” (ibi). Ma non <lb></lb>per questo fu poi l&#039;Autore seguito dagli Ottici, i quali più ragionevolmente <lb></lb>ritennero che, là dove la luce è più condensata, ivi debbano i colori esser <lb></lb>più risplendenti. </s></p><p type="main">

<s>Il Boulliaud, nella proposizione XXIX del suo Trattato <emph type="italics"></emph>De natura lu­<lb></lb>cis,<emph.end type="italics"></emph.end> così scriveva della luce, che refratta nelle lenti cristalline o ne&#039;prismi, <lb></lb>genera la varietà de&#039;colori: “ Fortis lux et condensata coloribus splenden­<lb></lb>tibus tinguit. </s>

<s>Si enim lentem vitream soli opponas et radios post traiectio­<lb></lb>nem in alba charta excipias, in medio illuminationis color maxime vividus <lb></lb>coruscat, in confinio umbrae colores paulatim infuscantur. </s>

<s>Hic vero colores <lb></lb>papyro albae aut chartae non insunt, neque in vitrea lente, sed a lumine <lb></lb>deferuntur, cui insunt, et pro luminis fortitudinem et extenuationem mu­<lb></lb>tantur ” (Parisiis 1638, pag. </s>

<s>43). </s></p><p type="main">

<s>Il Grimaldi nonostante, il quale ben riconobbe l&#039;importanza del sog­<lb></lb>getto, e presenti che dal diligente esame dello spettro solare sarebbe uscita <lb></lb>la vera teoria de&#039;colori, fu colui che dimostrò come i più risplendenti erano <lb></lb>quelli davvero, dove i raggi, nella ineguale dispersione spettrale attraverso <lb></lb>all&#039;acqua o àl cristallo, riuscivano più costipati. </s>

<s>Sia RBCD (fig. </s>

<s>40) un vaso <lb></lb><figure id="id.020.01.668.1.jpg" xlink:href="020/01/668/1.jpg"></figure></s></p><p type="caption">

<s>Figura 40.<lb></lb>di porcellana, il candido fondo del quale sia rico­<lb></lb>perto d&#039;acqua infino al livello EP. Sia, nel punto A <lb></lb>della sponda di esso vaso, un&#039;apertura, attraverso <lb></lb>alla quale, decussati i raggi che vengon dal sole, <lb></lb>cadano a illuminare ugualmente la superficie MN <lb></lb>dell&#039;acqua, ma variamente il fondo OPQ del vaso, <lb></lb>che brilla di tre più distinti colori. </s>

<s>Dice il Grimaldi <lb></lb>che questi colori son dovuti alla varia costipazione <lb></lb>de&#039;raggi, dopo aver subite nell&#039;acqua le rifrazioni. </s>

<s><lb></lb>Verso NQ quegli stessi raggi son più costipati, e <lb></lb>il colore ivi perciò è il più vivamente splendido <lb></lb>o il rosso: verso MO i raggi son più dissipati, <lb></lb>e perciò il colore è ivi il più fosco o il violetto. </s>

<s>Che poi verso NQ i raggi <lb></lb>sien più costipati, si prova dall&#039;Autore in questo facile modo: Divide il fa­<lb></lb>scio incidente AMN in due parti uguali, colla bissettrice AI, la quale si ri­<lb></lb>frange in IP, cosicchè, nello spazio occupato dalla luce refratta IQ, debbasi <lb></lb>ritrovar la medesima copia di raggi che nell&#039;altro spazio MP. </s>

<s>Ma questo, per <lb></lb>la legge delle rifrazioni, risulta di maggior misura e capacità di quello, dun­<lb></lb>que in IQ i raggi convien che veramente vi stieno più condensati. </s>

<s>“ Siqui­<lb></lb>dem tantumdem radiorum debet intelligi inter duos refractos IP et NQ quan­<lb></lb>tum intelligitur inter duos IP et MO item refractos, quemadmodum aequalis <lb></lb>portio luminis ac radiorum continatur inter duos directos GI, LN, ac inter <lb></lb>duos directos GI, HM, quia nimirum aequalis portio solis radiat per fora­<lb></lb>men A ad aquae superficiei partem IN, atque ad partem IM. </s>

<s>Cum ergo an­<lb></lb>gustius sit spatium inter refractos NQ et IP contentum, quam contentum <pb xlink:href="020/01/669.jpg" pagenum="112"></pb>inter duos IP et MO, ob maiora incrementa refractionum in radiis magis <lb></lb>inclinatis, ut supra advertebamus ex Optica, sequitur necessario constipari <lb></lb>magis radios in spatio IPQN, quam in spatio IPOM, quia aequales numero <lb></lb>radii non possunt non esse magis conferti in spatio angustiore quam in la­<lb></lb>xiore. </s>

<s>Praeterea in huiusmodi radiatione terminata super candido vasis fundo <lb></lb>BC videmus colorem subrubeum aut flavum ad partes Q, ubi lumen magis <lb></lb>densatur, ad partes autem O, ubi lumen laxius diffusum est, observamus co­<lb></lb>lorem caeruleum, qui sane obscurior est praedictis duobus in parte oppo­<lb></lb>sita observatis ” (De lum., Bononiae 1665, pag. </s>

<s>256). </s></p><p type="main">

<s>In tutte queste speculazioni però i colori non son riguardati se non che <lb></lb>obiettivamente, come una modificazione sopravvenuta nel suo refrangersi alla <lb></lb>luce. </s>

<s>Ma pure è un fatto che dee l&#039;occhio subiettivamente percepire le va­<lb></lb>rietà di così fatte modificazioni, e per esse aver senso e discrezione delle <lb></lb>varietà degli stessi colori. </s>

<s>Il Cartesio attese a risolvere, per ciò che princi­<lb></lb>palmente riguarda il lato subiettivo, il difficile e curioso problema, e ben­<lb></lb>chè, per le sue troppo capricciose e incongruenti ipotesi, non riuscisse a dar <lb></lb>sodisfazione a&#039;più giudiziosi, aprì nulladimeno nuove splendide vie di filo­<lb></lb>sofare agl&#039;ingegni. </s></p><p type="main">

<s>Riducendo il senso della vista a una impressione tattile prodotta sulla <lb></lb>retina dai corpuscoli duri messi in moto dalla sistole e dalla diastole del <lb></lb>corpo luminoso, il Cartesio immaginò che quegli stessi corpuscoli duri, nel <lb></lb>penetrar per la porosità de&#039;corpi diafani, urtati più o men fortemente e ora <lb></lb>da una parte ora dall&#039;altra, venissero a ricevere e a far sentire alla retina <lb></lb>l&#039;impressione di un moto rotatorio più o meno veloce, cosicchè, da questa <lb></lb>maggiore o minore velocità, ne risultasse il senso del colore o più splendido <lb></lb>e vivace o più fosco e abbacinato. </s>

<s>“ Et mea quidem sententia manifeste ex <lb></lb>his omnibus liquet naturam colorum tantum in eo consistere quod particu­<lb></lb>lae materiae subtilis, actionem luminis transmittentes, maiori impetu et vi <lb></lb>rotari nitantur quam secundum lineam rectam moveri, ita ut, qui multo va­<lb></lb>lidius rotari nituntur, rubicundum colorem efficiant, et qui non nisi paulo <lb></lb>validius flavum ” e prosegue ad applicare agli altri colori dello spettro le <lb></lb>medesime dottrine. (Metereor., Cap. </s>

<s>VIII, Francof. </s>

<s>ad M. 1692, pag. </s>

<s>178). </s></p><p type="main">

<s>Questa dottrina del Cartesio parve al Grimaldi ingegnosa, e perciò si <lb></lb>volse a professarla, sostituendo, all&#039;ipotesi del moto o dell&#039;inclinazione al <lb></lb>moto de&#039;corpuscoli duri, quella delle fluitazioni ondose del lume. </s>

<s>“ Itaque <lb></lb>dicimus tot notabiliter diversos colores ideo nobis apparere quia lumen tot <lb></lb>pariter diversas fluitationes recipit ac per eas diverso et proportionato illis <lb></lb>modo afficit sensorium visionis ” (De Lum. </s>

<s>cit., pag. </s>

<s>347). Così veniva a ri­<lb></lb>trovare una nuova e splendida analogia fra la retina, che percossa dall&#039;onda <lb></lb>luminosa dà il senso della vista, e il timpano che, percosso dall&#039;onda so­<lb></lb>nora, dà il senso dell&#039;udito, intorno a che l&#039;Autore si diffonde prolissamente <lb></lb>nella XLIV sua proposizione, benchè la miglior sostanza di lei si concluda <lb></lb>in queste parole: “ Cum ergo pro auditu admittenda sit in aere agitatio <lb></lb>adeo minute crispata, ut eius tremor omnem tactus sensationem subtilitate <pb xlink:href="020/01/670.jpg" pagenum="113"></pb>sua fugiat, cumque huiusmodi tremor debeat praeterea dici adeo varius ac <lb></lb>multiplex ut omnibus vocium et sonorum differentiis satisfaciat; multo ma­<lb></lb>gis in luminis diffusione poterit concipi subtilissima illa et per quam varia <lb></lb>fluitatio, quae omnibus colorum speciebus in visione determinandis inser­<lb></lb>vire debet, absque confusione radiorum a diversis obiectis vel obiectorum <lb></lb>particulis reflexorum ” (ibi, pag. </s>

<s>392). </s></p><p type="main">

<s>L&#039;Hook e l&#039;Huyghens poi ridussero a maggior precisione queste ipo­<lb></lb>tesi, sostituendo ai globuli duri del Cartesio, il mobilissimo etere, e agli in­<lb></lb>crespamenti superficiali del Grimaldi le onde sferiche mosse nell&#039;etere stesso <lb></lb>dal vibrar del corpo luminoso, in quel modo che si muovono le onde aeree <lb></lb>eccitate dal tremor del corpo sonoro. </s></p><p type="main">

<s>Son tali i principii e i progressi delle dottrine tanto applaudite dagli <lb></lb>Ottici moderni, il germe delle quali si trova nulladimeno latente nelle spe­<lb></lb>culazioni del primo discepolo di Galileo. </s>

<s>Benedetto Castelli professava in­<lb></lb>torno alla luce la più semplice e più naturale delle ipotesi, che è quella <lb></lb>dell&#039;emissione. </s>

<s>Ei non dubita perciò di asserire che gli atomi lucidi, come <lb></lb>tutti i corpi proietti, acquistano velocità col tempo, e non producono la sen­<lb></lb>sazione della luce bianca, se non che quando hanno raggiunto la massima <lb></lb>velocità del loro moto: gli atomi men veloci danno l&#039;apparenza dell&#039;oscurità <lb></lb>e dei colori. </s>

<s>Queste speculazioni l&#039;applicava il Castelli a dimostrar non solo <lb></lb>la possibilità, ma la necessità delle macchie nel sole, e così in una lettera, <lb></lb>indirizzata a Galileo il dì 8 Maggio 1612, esprimeva quelle sue idee: </s></p><p type="main">

<s>“ Mosso poi da sì bella occasione di filosofare, dico prima che, se mi <lb></lb>fosse lecito filosofare del corpo lucido solare dai corpi luminosi nostri, direi <lb></lb>che non solo è necessario che queste macchie sieno nel corpo solare, ma <lb></lb>che io non posso pensare altrimenti. </s>

<s>Per dichiararmi meglio, piglio il lume <lb></lb>che si fa dalla carta bianca accesa dal fuoco. </s>

<s>Chiaro è che quella lucidezza <lb></lb>precede una negrezza o dirò oscurezza del pabulo di quella luce, quale a <lb></lb>poco a poco passando per l&#039;azzurro e poi al rosso, finalmente diventa luce, <lb></lb>e quest&#039;accidente è comunissimo a tutti que&#039;corpi che spandono per sè stessi <lb></lb>luce. </s>

<s>Se dunque dal sole si spande luce, non è maraviglia se si ha il pas­<lb></lb>saggio dal nero ed oscuro, ed appariscano quelle macchie. </s>

<s>Aggiungo, a con­<lb></lb>ferma delle mie supposizioni della luce, che non essendo altro corpo lucido <lb></lb>che un corpo che vibra di continuo e scaglia corpuscoli velocissimi, ed es­<lb></lb>sendo il sole lucido e conseguentemente saettando di continuo corpuscoli <lb></lb>velocissimamente, e non potendo i corpi principiare a partirsi con somma <lb></lb>velocità, non mi faranno al sicuro quella apparenza che io chiamo luce, men­<lb></lb>tre con tardità si muovono. </s>

<s>Saranno dunque di necessità le macchie nel sole, <lb></lb>che è quello che noi vediamo ” (MSS. Gal., T. III, P. X, c. </s>

<s>55). </s></p><p type="main">

<s>Le belle e sottili speculazioni però, fatte intorno ai colori dal Castelli <lb></lb>al Cartesio, e dal Grimaldi all&#039;Huyghens, accolte con tanto plauso dagli Ot­<lb></lb>tici moderni, furono dal Newton messe a pari con quelle di Vitellione e del <lb></lb>De Dominis, e da lui tutte rifiutate ugualmente, <emph type="italics"></emph>cum omnes in communi <lb></lb>quodam errore consentiant, scilicet quod modificatio lucis qua singulos<emph.end type="italics"></emph.end><pb xlink:href="020/01/671.jpg" pagenum="114"></pb><emph type="italics"></emph>colores exhibet, ei non sit insita ab origine sua, sed inter reflectendum <lb></lb>vel refringendum acquiratur.<emph.end type="italics"></emph.end> (Lectiones opt., Paduae 1773, pag. </s>

<s>62). </s></p><p type="main">

<s>Scoperta ch&#039;ebbe il Newton la varia refrangibilità de&#039;raggi, di che la <lb></lb>luce del sole gli resultò composta, ne concluse indi immediatamente la sua <lb></lb>teoria de&#039;colori. </s>

<s>“ Ut radii lucis inter se refrangibilitate discrepant, ita dif­<lb></lb>ferunt insita quadam aptitudine ad exhibendum hunc vel illum certum co­<lb></lb>lorem. </s>

<s>Colores non sunt lucis qualificationes ortae ex naturalium corporum <lb></lb>refractionibus, aut reflexionibus, ut vulgo creditur, sed primigeniae et con­<lb></lb>genitae proprietates in diversis radiis diversae. </s>

<s>Aliqui radii tantum ad ru­<lb></lb>brum, alii solum ad flavum, alii dumtaxat ad viridem colorem effingendum <lb></lb>apti sunt ” (Epistola De luce et color., Paduae 1773, pag. </s>

<s>6). </s></p><p type="main">

<s>Due, soggiunge il Newton, sono i generi dei colori, alcuni semplici e <lb></lb>primigenii, altri composti. </s>

<s>“ Colores primigenii sunt <emph type="italics"></emph>Ruber, Flavus, Viri­<lb></lb>dis, Coeruleus<emph.end type="italics"></emph.end> et <emph type="italics"></emph>Violaceo-purpureus,<emph.end type="italics"></emph.end> una cum <emph type="italics"></emph>Aureo<emph.end type="italics"></emph.end> et <emph type="italics"></emph>Indico.<emph.end type="italics"></emph.end> Il bianco <lb></lb>è colore sempre composto e ci bisognano per comporlo tutt&#039;e sette i colori <lb></lb>primigenii mescolati insieme con certa proporzione. </s>

<s>“ Saepius admirabun­<lb></lb>dus observavi quod colores omnes a Prismate detecti, cum convergentes <lb></lb>redduntur, et hoc pacto rursus miscentur ita ut erant in luce, antequam in <lb></lb>Prisma incideret, iterum exhibent lucem prorsus et perfecte candidam et <lb></lb>nihil omnino, sensu indice, diversam a directa luce solari ” (ibi, pag. </s>

<s>8). </s></p><p type="main">

<s>I colori poi naturali, che s&#039;appresentano alla superficie di tutti i corpi, <lb></lb>da null&#039;altro, secondo il Newton, dipendono, se non da ciò che quelle stesse <lb></lb>superficie son costituite e disposte a rifletter più copiosamente uno, che un&#039;al­<lb></lb>tro genere di raggi. </s>

<s>“ Cuius rei periculum feci in obscuro cubiculo super <lb></lb>haec corpora coniiciens radios simplices, at coloribus diversos. </s>

<s>Etenim hoc <lb></lb>pacto quodvis corpus quovis colore donari potest. </s>

<s>Tunc non habent colorem <lb></lb>proprium, sed semper illum adoptant, quo lux superiniecta praedita est ” <lb></lb>(ibi, pag. </s>

<s>9). </s></p><p type="main">

<s>Queste neutoniane dottrine erano così semplici e naturali e, indipen­<lb></lb>dentemente da qualunque fantasticata ipotesi, così bene dimostrate dai fatti, <lb></lb>che quasi tutti gli Ottici si rivolsero a professarle, parendo ad essi che, in <lb></lb>cosa tanto lungamente desiderata, si fosse all&#039;ultimo scoperta la faccia del <lb></lb>vero. </s>

<s>In Londra l&#039;Epistola <emph type="italics"></emph>De luce et coloribus<emph.end type="italics"></emph.end> fu divulgata nel 1672; fra <lb></lb>noi è difficile il precisare quando s&#039;introdussero quelle nuove ottiche dot­<lb></lb>trine neutoniane, ma si può con gran probabilità asserire che ciò non av­<lb></lb>venisse prima del cominciar del secolo XVIII. </s></p><p type="main">

<s>Non sarà perciò senza una qualche importanza il chiudere questo pa­<lb></lb>ragrafo di storia citando alcuni pensieri di Geminiano Montanari, a cui si <lb></lb>può credere che le novità inglesi non fossero ancora approdate alle orec­<lb></lb>chie; pensieri, che si leggono in una lettera di lui pubblicata da France­<lb></lb>sco Bianchini nell&#039;Introduzione al Dialogo postumo intitolato <emph type="italics"></emph>Le forze di <lb></lb>Eolo.<emph.end type="italics"></emph.end> Ivi il Montanari, dop&#039;aver dimostrato che il minimo angolo visibile è <lb></lb>comunemente quello di un minuto, soggiunge: “ Quindi avviene perciò che, <lb></lb>mescolando insieme due o più polveri di colore diverso, se ne produce un <pb xlink:href="020/01/672.jpg" pagenum="115"></pb>terzo color misto, non perchè ciascuna polvere partecipi intrinsecamente al­<lb></lb>l&#039;altra le sue qualità come dissero alcuni, ma perchè le parti minute di <lb></lb>esse polveri sono così piccole, che non sottendendo un minuto ciascuna da <lb></lb>sè all&#039;occhio, ne vanno a ciascun filamento i raggi di più granella, e per­<lb></lb>ciò le specie miste di più colori, e producono nell&#039;occhio la sensazione d&#039;un <lb></lb>terzo colore da ciascun d&#039;essi distinto. </s>

<s>Quindi è ancora che veduta in molta <lb></lb>distanza una fabbrica dipinta, ci si rappresenta d&#039;un sol colore, ma misto <lb></lb>di tutti quelli che da vicino poi dipinti si scorgono ” (Parma 1694). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I cenni storici che resultano dai documenti, da noi raccolti nel para­<lb></lb>grafo precedente, mostrano che la prima e principale occasione, che mosse <lb></lb>e fece rivolgere gli Ottici a speculare intorno all&#039;essere e alla generazion <lb></lb>de&#039;colori, fu quel magnifico arco che il sole oriente od occidente così spesso <lb></lb>dipinge ai nostri occhi maravigliati sulla bassa volta di un ciel nuvoloso. </s>

<s>I <lb></lb>Filosofi antichi non lasciarono di esercitarvi attorno l&#039;ingegno, e da quel <lb></lb>che si legge nel III Libro <emph type="italics"></emph>De placitis philosophorum<emph.end type="italics"></emph.end> di Plutarco par che <lb></lb>alcuni di essi fossero imboccati per quella diretta via, proseguendo per la <lb></lb>quale all&#039;ultimo si sarebbe riusciti a intendere la ragione del fenomeno stu­<lb></lb>pendo. </s>

<s>C&#039;intravidero sagacemente l&#039;opera delle rifrazioni de&#039;raggi solari av­<lb></lb>versi nelle stile roride della nube. </s>

<s>“ Siquidem animadvertere oportet umidam <lb></lb>exalationem in nubem verti subindeque in exiguas sensim stillas rorantes: <lb></lb>proinde in occiduales vergente sole partes necesse est arcum totum ex ad­<lb></lb>verso soli visitari, quandoquidem visus stillis offensis refringitur, ox quo fit <lb></lb>arcus ” (Romae 1510, fol. </s>

<s>XXI). </s></p><p type="main">

<s>Che poi fosse veramente così lo confermarono que&#039;Filosofi coll&#039;espe­<lb></lb>rienza: “ Hoc reipsa sic probare licet: si quis enim soli adversus aquam <lb></lb>ore sumat et ita insputet ut stillicidia repercussum in solem habeant, actu­<lb></lb>tum comperit arcus imaginem factam ” (ibi). </s></p><p type="main">

<s>Anche l&#039;Alighieri, seguendo i placiti di così fatti Filosofi, perchè l&#039;aere <lb></lb>si mostri adorno di diversi colori, ammette come condizion necessaria che <lb></lb>egli sia <emph type="italics"></emph>ben piorno<emph.end type="italics"></emph.end> (Purg., XXV, v. </s>

<s>91) e per via delle riflessioni della luce, <lb></lb>simili a quelle del suono da cui nasce l&#039;Eco, intende che nasca da quella <lb></lb>di dentro l&#039;iride di fuori, quando vedonsi talvolta volgere per <emph type="italics"></emph>tenera<emph.end type="italics"></emph.end> nube <lb></lb>due archi paralleli e concolori (Par., XII, t. </s>

<s>4, 5). </s></p><p type="main">

<s>I placiti filosofici però riferitici da Plutarco e cantati divinamente dal­<lb></lb>l&#039;Alighieri non sodisfacevano punto all&#039;orgoglio peripatetico, a cui pareva <lb></lb>proprio una meschinità ricorrere all&#039;esperienza dell&#039;acqua spruzzagliata dallo <lb></lb>sputo delle labbra per aria. </s>

<s>Ricorsero perciò a qualche cosa di più pelle­<lb></lb>grino, e immaginarono le nubi configurate in speechi o concavi o convessi, <lb></lb>secondo bisognava accomodarli meglio a produrre in cielo per riflessione le <lb></lb>mirabili apparenze dell&#039;Arco. </s></p><pb xlink:href="020/01/673.jpg" pagenum="116"></pb><p type="main">

<s>Di così fatta forfora peripatetica aspersi uscirono fuori Alhazeno e Vi­<lb></lb>tellione, in que&#039;loro Trattati, da&#039;quali si attingevano comunemente i responsi <lb></lb>a ogni sorta di ottiche dottrine, come da oracoli. </s>

<s>Così l&#039;arabo Autore come <lb></lb>il pollacco riconoscono la primaria efficienza dell&#039;Iride dalle riflessioni dei <lb></lb>raggi solari sulle stille roride, che compongon la nube, i quali raggi, se­<lb></lb>condo che vengono riflessi da maggiore o minor profondità della nube stessa, <lb></lb>uscendone fuori mescolati con più o meno ombra, producono perciò la splen­<lb></lb>dida varietà de&#039;colori. </s>

<s>“ Item, quoniam a remotiori videtur, tale lumen ideo <lb></lb>debilius videtur: remotio enim sive protensio visibilis a visu est causa de­<lb></lb>bìlitatis visus. </s>

<s>Item quia vapor remotior a corpore luminoso grossior est et <lb></lb>nigrior, et magis aqueus, unde nigredo, vaporis lumini incorporatum plus <lb></lb>denigrat et magis ipsum visui obscuratum penetrat, et hoc quidem in co­<lb></lb>loribus iridis aliquam causalitatem habent. </s>

<s>Totalis vero causa omnibus huius <lb></lb>coloribus universalis immixtio umbrarum ipsi fulgori luminis, quoniam enim, <lb></lb>ut patet per premissam, vapor roridus est materia iridis a cuius corpuscu­<lb></lb>lis fit reflexio luminis ad visum, omnia corpora densa in parte luminoso cor­<lb></lb>pori adversam umbram proiiciunt, patet quod radii reflexi a remotiorum <lb></lb>corpusculorum superficiebus, umbrarum anteriorum corpusculorum nigre­<lb></lb>dini se immiscent, et sic permixti colore nigro umbrarum perveniunt re­<lb></lb>flexi ad visum, et secundum quod plus vel minus umbrarum nigredine per­<lb></lb>miscentur, secundum hoc diversificant actum suae luminositatis in varios <lb></lb>colores. </s>

<s>” Alle quali sue teorie cerca l&#039;Autore il conforto dell&#039;esperienza in <lb></lb>un fenomeno di diffrazione in cui veramente l&#039;iridescenza trasparisce di <lb></lb>mezzo alle ombre. </s>

<s>” Et huius rei signum est in coloribus similibus iridi, <lb></lb>qui obducto visu ipsa manu vel alio umbroso de sub manu in fenestrarum <lb></lb>periferiis videntur ” (Vitellionis Perspectiva, edit. </s>

<s>cit., pag. </s>

<s>288). </s></p><p type="main">

<s>L&#039;Iride secondaria, ne&#039;placiti di alcuni di que&#039;Filosofi citati da Plu­<lb></lb>tarco, come abbiamo veduto in Dante, si faceva nascere per riflessione dalla <lb></lb>primaria, e benchè ciò non fosse punto conforme alla verità delle cose, so­<lb></lb>disfaceva nulladimeno agl&#039;ingegni per l&#039;esempio di ciò che vedesi negli spec­<lb></lb>chi, ne&#039;quali le immagini si rappresentano contrapposte, come contrapposti <lb></lb>si dipingono nella stessa Iride secondaria i colori. </s>

<s>A Vitellione però questo <lb></lb>modo di salvar l&#039;iride esterna, come troppo semplice, non piacque: crede <lb></lb>piuttosto ch&#039;ella si faccia in una superficie gibbosa <emph type="italics"></emph>(Sic ergo in vapore ir­<lb></lb>radiato fit quaedam gibbositas)<emph.end type="italics"></emph.end> più lontana dall&#039;occhio, e che perciò e per <lb></lb>esser maggiori gli angoli dell&#039;incidenza, oltre al venir contrapposti i colori, <lb></lb>appariscano più dilavati. </s>

<s>“ Omnes autem colores secundae iridis sunt debi­<lb></lb>liores necessario coloribus primae Iridis, quoniam fiunt a radiis magis di­<lb></lb>stantibus a perpendiculari, et secundum maiores angulos ad visum reflexis, <lb></lb>propter quod isti radii cum radiis incidentibus minus aggregantur, unde mi­<lb></lb>nus efficiunt luminis et coloris ” (ibi, pag. </s>

<s>291). </s></p><p type="main">

<s>Tali erano le dottrine divulgate intorno all&#039;Iride dal Maestro universale <lb></lb>della Scienza ottica, e sull&#039;autorità di lui da tutti approvate per vere, quando <lb></lb>gl&#039;ingegni, riconosciuto all&#039;ultimo essere una grande temerità professare una <pb xlink:href="020/01/674.jpg" pagenum="117"></pb>cosa per vera, perchè un uomo reputato da tutti sapiente l&#039;aveva insegnata, <lb></lb>si persuasero che maestra unica di verità dev&#039;esser piuttosto la Natura. </s>

<s>Fra <lb></lb>que&#039;savi, che così la pensarono, fu quel Ferrante Imperato, che i nostri Let­<lb></lb>tori oramai ben conoscono come uno de&#039;più valorosi fisici, che precorsero <lb></lb>all&#039;istituzione del Metodo sperimentale. </s>

<s>Egli che pubblicava la sua <emph type="italics"></emph>Historia <lb></lb>naturale<emph.end type="italics"></emph.end> nell&#039;ultimo anno del secolo XVI non leggendo i libri di Aristotile <lb></lb>e di Vitellione per altro, che per riconoscervi gli errori, ma osservando i <lb></lb>fatti naturali e sopr&#039;essi speculando, ritrovò le vere ragioni del dipingersi <lb></lb>l&#039;iride primaria e la secondaria, quasi quarant&#039;anni prima che fosse pub­<lb></lb>blicato il libro delle Meteore del Cartesio. </s>

<s>“ Venendo dunque all&#039;area e <lb></lb>l&#039;iride, diciamo l&#039;una e l&#039;altra farsi con raggi infratti, ma nell&#039;Iride spe­<lb></lb>zialmente intervenirvi la riflessione.... Nell&#039;Iride la riflessione è dalla nube <lb></lb>opposta. </s>

<s>Già ho detto che con detta riflessione sia aggiunta <emph type="italics"></emph>l&#039;infrazione <lb></lb>doppia, dico e nell&#039;introito e nell&#039;esito del raggio ”<emph.end type="italics"></emph.end> (Hist. </s>

<s>nat., Venetia 1672, <lb></lb>pag. </s>

<s>288). </s></p><p type="main">

<s>Nel prescriver l&#039;Iride secondaria l&#039;Imperato non è così preciso, ma pro­<lb></lb>fessando la dottrina platonica dell&#039;emissione de&#039;raggi dall&#039;occhio non è lon­<lb></lb>tano dal vero, quando riconosce la ragion del fenomeno dalla molta infra­<lb></lb>zione, per la quale <emph type="italics"></emph>il raggio che esce e va al sole si taglia col raggio della <lb></lb>vista che entra<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>290). Così compiacesi il Nostro di aver <emph type="italics"></emph>la gene­<lb></lb>razione de&#039;colori nell&#039;una e nell&#039;altra Iride dedutta dagli proprii prin­<lb></lb>cipii,<emph.end type="italics"></emph.end> e non dall&#039;autorità di Aristotile, il quale, quantunque prometta di farlo, <lb></lb>nondimeno ciò da lui o <emph type="italics"></emph>non è trattato o è ridotto a cause vane<emph.end type="italics"></emph.end> (ivi). </s></p><p type="main">

<s>Ma così queste come altre simili dottrine dell&#039;Imperato non ebbero <lb></lb>ne&#039;progressi dell&#039;Ottica nessuna efficacia, e le speculazioni dello Speziale <lb></lb>napoletano intorno all&#039;Iride passarono inosservate. </s>

<s>Il Keplero aveva pensato <lb></lb>di scrivere un Trattatello “ quod supplementum esset aristotelicae super <lb></lb>Iride disquisitionis.... itaque in presens hoc negocium deserui ” (Dioptrice, <lb></lb>Augustae Vindelic 1611, pag. </s>

<s>10, 11). Mentre però il grande Restauratore <lb></lb>dell&#039;Ottica scriveva così fatte parole in Germania, l&#039;Italia vedeva apparire <lb></lb>i due Trattati del Maurolico e del De Dominis. </s>

<s>Il maraviglioso fenomeno ve­<lb></lb>niva dall&#039;uno de&#039;due insigni Autori illustrato co&#039;principii matematici, e dal­<lb></lb>l&#039;altro coll&#039;esperienza. </s></p><p type="main">

<s>Il secondo libro <emph type="italics"></emph>Diaphanorum<emph.end type="italics"></emph.end> del nostro Ottico messinese, intitolasi <lb></lb><emph type="italics"></emph>De iride,<emph.end type="italics"></emph.end> e procedendo in esso con ordine tutto geometrico incomincia a <lb></lb>determinare la posizione e la forma della portentosa apparenza celeste, di­<lb></lb>cendo che i centri del sole e dell&#039;occhio e dell&#039;iride sono costituiti in una <lb></lb>medesima linea retta, e che l&#039;iride stessa viene a rappresentarsi sotto figura <lb></lb>di un cono retto, il vertice del quale s&#039;appunta nell&#039;occhio di chi osserva <lb></lb>(Theor. </s>

<s>XXV). I colori dell&#039;iride primaria generati dai raggi solari nella nube <lb></lb>rorida vengono refratti all&#039;occhio sotto un angolo di 45 gradi (additio ad <lb></lb>Theor. </s>

<s>cit.), cosicchè, essendo il sole sull&#039;orizzonte, l&#039;iride disegnerebbe in <lb></lb>cielo un semicerchio completo, ed essendo il sole stesso elevato per mezzo <lb></lb>angolo retto, dell&#039;Iride nulla ne apparirebbe (Theor. </s>

<s>XXVI). La larghezza <pb xlink:href="020/01/675.jpg" pagenum="118"></pb>de&#039;colori dell&#039;Iride sottende nell&#039;occhio un angolo uguale a quello, sotto cui <lb></lb>si vedrebbe il diametro apparente del sole (Theor. </s>

<s>XXVII). I colori princi­<lb></lb>pali dell&#039;Iride son quattro: rosso, verde, ceruleo e violetto, ma dall&#039;uno al­<lb></lb>tro si fa passaggio per un colore intermedio, cosicchè in tutti i colori son <lb></lb>sette “ quambrem Iris septicolor iure dici potest. </s>

<s>” Lo spettro colorato di­<lb></lb>pende dalla dispersione che i raggi solari subiscono dentro la gocciola del­<lb></lb>l&#039;acqua, e, dove i raggi stessi sono più condensati, il colore è più cupo. </s>

<s>Di <lb></lb>qui s&#039;intende perchè l&#039;azzurro sia nell&#039;interno dell&#039;arco e il rosso all&#039;esterno <lb></lb>(Theor. </s>

<s>XXIX). L&#039;iride esterna non nasce per riflessione dall&#039;iride interna <lb></lb>come dai più s&#039;è creduto, ma per effetto de&#039;raggi che vengono rifratti al­<lb></lb>l&#039;occhio sotto un angolo di un mezzo con più l&#039;ottava parte di un angolo <lb></lb>retto, ossia di 56 gradi e un quarto (Additio I ad Theor. </s>

<s>XXX). </s></p><p type="main">

<s>Tali sono i Teoremi ordinatamente dimostrati dal Maurolico intorno al­<lb></lb>l&#039;Iride, e poniamo che, verso quel che ne lasciò scritto Vitellione o qual­<lb></lb>cun altro degli antichi, segnino in questa parte di scienza ottica un nota­<lb></lb>bile progresso, l&#039;insigne Autor s&#039;ingannava credendo di dover ritrovare il <lb></lb>vero per la sola via matematica. </s>

<s>Egli par che voglia, co&#039;suoi numeri pre­<lb></lb>scriver le leggi alla Natura, come fa per esempio quando contro le osser­<lb></lb>vazioni de&#039;fatti conclude <emph type="italics"></emph>a priori,<emph.end type="italics"></emph.end> dalle dignità matematiche, che l&#039;altezza <lb></lb>dell&#039;Iride primaria dev&#039;esser per l&#039;appunto di 45 gradi, e quella della se­<lb></lb>condaria di 56 e un quarto. </s></p><p type="main">

<s>“ Itaque ut omnia paucis concludam, cum reflexio solaris radii a ro­<lb></lb>rida nube ad oculum sub dimidio recti anguli facta, per dictam octogoni <lb></lb>radiationem per octo puncta repetitam in singulis globulis generat prima­<lb></lb>riam atque coloratissimam Iridem. </s>

<s>Iam nulla alia reflexio, nisi quae ad dic­<lb></lb>tam anguli quantitatem accedens octogoni divisionem suscipiat, aliqualem <lb></lb>Iridem facere potest, sed talis reflexio non est nisi quae suscipit quinque <lb></lb>tantum octonas recti, hoc est angulum 56 1/4 graduum. </s>

<s>Igitur ipsa faciet <lb></lb>secundariam Iridem, nam si talis angulus habet 5/8 recti unius, oportebit <lb></lb>quatuor rectos singulos in 8 partes et ideo totum ambitum in 32 partes di­<lb></lb>stingi, in qua distinctione includitur octogoni divisio, nam 32 in octonas par­<lb></lb>tes secatur. </s>

<s>Hanc autem dignitatem non habet angulus 60 graduum, quia <lb></lb>postulat ambitum secari in senas partes, et proinde octagonum non susci­<lb></lb>pit. </s>

<s>Non angulus 50 graduum, quippe qui habet quinque nonas unius recti <lb></lb>et requirit divisionem totius ambitus in 36 partes, a qua excluditur octogo­<lb></lb>nus. </s>

<s>Non angulus 40 graduum habens quatuor nonas unius recti, hoc est <lb></lb>nonam partem totius ambitus, et ob id octogonum non admittit. </s>

<s>Non ceteri <lb></lb>anguli neque maiores neque minores praedictis, quoniam maiores quidem, <lb></lb>propter nimiam expansionem, minores vero propter vicinitatem radii primarii <lb></lb>debilitant omnem reflexionem. </s>

<s>Superest igitur angulus praedictus 56 1/4 gra­<lb></lb>duum ” (Neapoli 1611, pag. </s>

<s>60, 61). </s></p><p type="main">

<s>Ma che in queste sottili e astratte speculazioni la Matematica sia in op­<lb></lb>posizione co&#039;fatti, si comprende assai facilmente ripensando che le molteplici <lb></lb>riflessioni dentro la gocciola, tutt&#039;altro che rinforzare i raggi, secondo che <pb xlink:href="020/01/676.jpg" pagenum="119"></pb>dal Maurolico si suppone, gli debilitano anzi, come è dall&#039;altra parte chiaris­<lb></lb>simo per la ragione e per l&#039;esperienza. </s>

<s>Che se veramente son le molteplici <lb></lb>riflessioni che accendono i colori, essendo nell&#039;Iride primaria quelle rifles­<lb></lb>sioni 8, e nella secondaria 32, questa dovrebbe splendere in più vivaci co­<lb></lb>lori di quella. </s>

<s>Or perchè si vede esser tutto il contrario, avrebbe dovuto ser­<lb></lb>vire ciò al Maurolico d&#039;argomento, a persuadersi che quella presa a trattare <lb></lb>da lui non era questione di sola matematìca. </s></p><p type="main">

<s>Con miglior consiglio il De Dominis ebbe ricorso all&#039;esperienza, e os­<lb></lb>servando i colori in sfere piene di acqua o in globi di vetro, opportuna­<lb></lb>mente contrapposti ai raggi del sole, si studiò per questa via d&#039;investigare <lb></lb>il mistero. </s>

<s>La via diritta, senza dubbio, e più sicura era quella, ma troppo <lb></lb>imperfette idee aveva delle rifrazioni lo Spalatrese, e intorno alla generazion <lb></lb>de&#039;colori troppo cieca fede ebbe agl&#039;insegnamenti di Vitellione. </s>

<s>In ogni modo, <lb></lb>lasciata da parte ogni matematica dimostrazione, ecco ciò che il De Domi­<lb></lb>nis dice di avere scoperto dalle sue osservazioni sperimentali: </s></p><p type="main">

<s>“ Quam varietatem nunc explicare demonstrationibus non est operae <lb></lb>praetium. </s>

<s>Satis est me experimentis clarissimis comperisse in phiala aqua <lb></lb>plena et globulis vitreis aqua similiter plenis, a me ad hunc tantum effectum <lb></lb>perfici curatis, ex fundo G (fig. </s>

<s>41) opposito soli directe, praeter refractio­<lb></lb><figure id="id.020.01.676.1.jpg" xlink:href="020/01/676/1.jpg"></figure></s></p><p type="caption">

<s>Figura 41.<lb></lb>nem quae fit in V, duplices fieri reflexiones, alias statim per latera versus <lb></lb>F et E circulariter, alias vero versus solem prope perpendiculorem BA ad <lb></lb>partem anteriorem versus H et I similiter circulariter, et non per unam so­<lb></lb>lam lineam indivisibilem, sed per plures utrobique, cum aliqua latitudine, <lb></lb>ut sunt in priori reflexione GF, GN, GM; in altera vero GI, GK, GL, quae <lb></lb>latitudo oritur partim ex refractionibus, quae intra globum fiunt cum ag­<lb></lb>gregatione plurium radiorum, partim ex magna latitudine corporis lumi­<lb></lb>nosi PQT ” (De radiis ecc., Venetiis 1611, pag. </s>

<s>14). </s></p><p type="main">

<s>Ciò che sperimentalmente rappresentasi nel globo di vetro pien d&#039;acqua, <lb></lb>rappresentasi naturalmente, secondo il De Dominis, nel vapore <emph type="italics"></emph>roridus<emph.end type="italics"></emph.end> et <lb></lb><emph type="italics"></emph>stillans,<emph.end type="italics"></emph.end> di ch&#039;è composta la nube. </s>

<s>Da&#039;fascetti MF si produce l&#039;iride pri­<lb></lb>maria; dai fascetti IL la secondaria. </s>

<s>I colori sono via via sempre più oscuri, <lb></lb>secondo che maggiore opacità si aggiunge alla chiarezza. </s>

<s>Così GM, dovendo <lb></lb>attraversar maggior parte corporea della palla vitrea, esce mescolato con <pb xlink:href="020/01/677.jpg" pagenum="120"></pb>maggior ombra degli altri, e perciò sarà di colore più oscuro di tutti gli al­<lb></lb>tri, ossia violetto. </s>

<s>Per la stessa ragione GF, sarà il più lucido di tutti gli <lb></lb>altri, ossia rosso. </s>

<s>“ Dicimus radium GF esse omnium lucidissimum, quia <lb></lb>pertransit minimam crassitiem corpusculi A, radium vero sequentem GN esse <lb></lb>paulo obscuriorem, quia paulo maior ei est globuli A penetranda crassities, <lb></lb>ac demum radium GM esse obscurissimum quia adhuc maiorem penetrat cras­<lb></lb>sitiem. </s>

<s>Itaque radius GF erit puniceus, GN viridis, GM purpureus ” (ibi, <lb></lb>pag. </s>

<s>56). </s></p><p type="main">

<s>Secondo un tal principio però i colori I, K, L dovrebbero rappresen­<lb></lb>tarsi nel medesimo ordine de&#039;colori F, N, M essendo chiaro che GL attra­<lb></lb>versando minor parte corporea della gocciola, ed uscendo fuori perciò me­<lb></lb>scolato con minor parte d&#039;ombra, dee essere il più lucido di tutti gli altri, <lb></lb>cioè il rosso, mentre al contrario egli è il più oscuro, cioè il violetto. </s>

<s>Ond&#039;è <lb></lb>che, per salvare il fenomeno, dovette l&#039;Autore ricorrere ad altro principio, <lb></lb>ed è che i raggi sien tanto più lucidi, quanto a penetrare il mezzo si sen­<lb></lb>ton più forti. </s>

<s>Ma perchè tanto si senton più forti, quanto più si accostano <lb></lb>alla perpendicolare, e perciò s&#039;intende come GI debba esser, non come prima, <lb></lb>il violetto ma il rosso, che è il più lucido di tutti gli altri colori. </s>

<s>“ A luce <lb></lb>igitur fortiori radius fortior et lucidior reflectetur prope perpendicularem, <lb></lb>cuiusmodi est radius GI, a qua luce iam deflectunt radii, non ex ipso cen­<lb></lb>tro lucidissimo G prodeuntes per reflexionem, sed paulo remotiores, ut sunt <lb></lb>radii GK, GL. </s>

<s>Propterea radius GI erit lucidissimus, hoc est puniceus, GK <lb></lb>erit viridis, GL erit purpureus ” (ibi, pag. </s>

<s>63). </s></p><p type="main">

<s>La via sperimentale presa dal De Dominis era la retta, ma, per man­<lb></lb>canza di cognizioni diottriche, hanno veduto i lettori quanto infelice ne sia <lb></lb>stata la riuscita. </s>

<s>I due insigni Ottici italiani insomma, il Dalmata e il Sici­<lb></lb>liano, con tutta la loro esperienza e la loro matematica non riuscirono a dar <lb></lb>nella cruna del vero, come pure vi dette l&#039;Imperato, i concetti del quale <lb></lb>ebbero la più splendida illustrazione dal Capitolo VIII delle <emph type="italics"></emph>Meteore<emph.end type="italics"></emph.end> del <lb></lb>Cartesio. </s></p><p type="main">

<s>Tornato l&#039;Autore ad osservar la palla vitrea preparata a modo del De <lb></lb>Dominis, e costituita di contro al sole in modo che i raggi di lui si riflet­<lb></lb>tessero dalla palla stessa alla vista sotto un angolo presso a poco di 42 gradi, <lb></lb>ne&#039;punti D e K (fig. </s>

<s>42) vedeva apparire un vivace color rubicondo, e va­<lb></lb>riando alquanto posizione, vedeva, dietro a que&#039;due punti rossi, succedersi <lb></lb>e contrapporsi via via gli altri colori, se non che verso K erano alquanto più <lb></lb>sbiaditi. </s>

<s>Riconosciuta in questa esperienza, come lo stesso De Dominis l&#039;aveva <lb></lb>già riconosciuta, la viva rappresentazione delle due Iridi celesti, il Cartesio <lb></lb>passa così a descrivere l&#039;andamento de&#039;raggi dentro la palla vitrea, imma­<lb></lb>gine della gocciola della pioggia, da&#039;quali raggi variamente refratti hanno <lb></lb>origine le varie apparenze de&#039;colori: </s></p><p type="main">

<s>“ Postea cum accuratius examinarem in pila BCD unde rubeus color <lb></lb>in eius parte D conspicuus oriretur, notavi illum pendere a radiis Solis, qui <lb></lb>venientes ex A ad B aquam ingrediendo frangebantur in puncto B, et ibant <pb xlink:href="020/01/678.jpg" pagenum="121"></pb>ad C, unde reflexi ad D et ibi aquam egrediendo iterum fracti tendebant <lb></lb>ad E. </s>

<s>Nam simul ac corpus aliquod opacum et obscurum alicui linearum <lb></lb>AB, BC, CD, vel DE opponebam, rubicundus color evanescebat, et licet to­<lb></lb>tam pilam, exceptis duobus punctis B et D obnuberem, et corpora obscura <lb></lb>ubivis circumponerem, dummodo nihil actionem radiorum ABCD impediret, <lb></lb>lucide tamen ille refulgebat. </s>

<s>Postea eodem modo investigata causa rubri il­<lb></lb>lius coloris, qui apparebat in K inveni illum esse a radiis solis, qui venien­<lb></lb>tes ab F ad G, ibi refringebantur versus H, et in H reflexi ad I, rursusque <lb></lb>ab I reflexi ad K, tandemque iterum fracti in puncto K, tendebant ad E. </s>

<s><lb></lb>Atque ita primaria Iris fit a radiis post duas refractiones et unam reflexio­<lb></lb><figure id="id.020.01.678.1.jpg" xlink:href="020/01/678/1.jpg"></figure></s></p><p type="caption">

<s>Figura 42.<lb></lb>nem ad oculum venientibus; secundaria vero a radiis qui nonnisi post duas <lb></lb>refractiones et duas reflexiones eodem pertingunt. </s>

<s>Ideoque haec semper al­<lb></lb>tera minus est conspicua ” (Ibi, Francofurti ad M. 1692, pag. </s>

<s>175). </s></p><p type="main">

<s>Il problema che aveva per sì lungo tempo frugata la curiosità degli Ot­<lb></lb>tici e de&#039;Meteorologi veniva così finalmente risoluto, almeno nella parte sua <lb></lb>più sostanziale. </s>

<s>Il Grimaldi poi nelle ultime XV proposizioni del 1 Libro <emph type="italics"></emph>De <lb></lb>lumine<emph.end type="italics"></emph.end> trattò largamente e sottilmente dello stesso soggetto, apparecchian­<lb></lb>dovisi coll&#039;insegnare un modo di rappresentare artificialmente l&#039;Iride in una <lb></lb>camera oscura, spruzzandovi dentro l&#039;acqua scossa da una spazzola di scopa. <lb></lb>(Propos. </s>

<s>XLVII, n.° 4). </s></p><p type="main">

<s>Condotta infino a questo punto trovava dunque il Newton questa no-<pb xlink:href="020/01/679.jpg" pagenum="122"></pb>bile parte di scienza, quando, nel 1671, dettava l&#039;ultima delle sue <emph type="italics"></emph>Lezioni <lb></lb>di Ottica<emph.end type="italics"></emph.end> dalla cattedra leucasiana. </s>

<s>Termina l&#039;Autore quella sua Lezione <emph type="italics"></emph>De <lb></lb>variis colorum phaenomenis<emph.end type="italics"></emph.end> così scrivendo: “ Superest iam mirum illud <lb></lb>caelestis arcus spectaculum, ad cuius explicationem Cartesius viam stravit. </s>

<s><lb></lb>Huic enim debetur quod in guttis aquae pluvialis decidentibus efformari co­<lb></lb>gnoscimus. </s>

<s>Quemadmodum ex eo constat quod nunquam videtur nisi coelo <lb></lb>pluente; quod, sole pluviam decidentem illustrante, in vicis nonnunquam <lb></lb>apparuit, quasi non in coelo collocatus, sed in aere vicino, super opposita­<lb></lb>rum domuum parietibus affixus vel potius interiectus; quod aqua per arti­<lb></lb>ficium aliquod sparsim eiaculata iridem ostendit, et quod gramen rore ma­<lb></lb>tutino, quasi guttulis minutissimis conspersum colores etiam Iridis exhibet. </s>

<s><lb></lb>Huic etiam debetur ingeniosissima de refractionibus guttae et eorum limi­<lb></lb>tibus inventio, sed causam physicam minus feliciter aggressus est ” (Edit. </s>

<s><lb></lb>cit., pag. </s>

<s>127, 28). </s></p><p type="main">

<s>In questi brevi cenni storici i nostri lettori, che si rammentano del­<lb></lb>l&#039;esperienza antichissima proposta da Plutarco, riconoscono parecchie impro­<lb></lb>prietà storiche, e mentre da una parte par poco il dir del Cartesio che <emph type="italics"></emph>viam <lb></lb>stravit,<emph.end type="italics"></emph.end> sembrerà dall&#039;altra un&#039;esagerazione il fargli merito di un artificio <lb></lb>ovvio a&#039;pescatori che battono i remi in acqua, o a&#039;contemplanti, illuminato <lb></lb>dal sole, lo spettacolo di una cascata. </s></p><p type="main">

<s>Un altro difetto storico reputato più notabile è accennato qui a piè di <lb></lb>pagina dall&#039;Editore: “ Neutonus postea <emph type="italics"></emph>intellexit<emph.end type="italics"></emph.end> alios ante Cartesium huius <lb></lb>phaenomeni causam invenisse ut verba eius sequentia testantur: <emph type="italics"></emph>Hodie con­<lb></lb>venit inter omnes arcum istum refractione luminis solaris in guttulis plu­<lb></lb>viae cadentis effici. </s>

<s>Intellexerunt hoc etiam antiquorum nonnulli: inter <lb></lb>recentiores autem plenius id invenit uberiusque explicavit celeberrimus <lb></lb>Antonius De Dominis Archiepiscopus spalatensis, in libro suo<emph.end type="italics"></emph.end> De radiis vi­<lb></lb>sus et lucis, <emph type="italics"></emph>quem ante annos amplius viginti scriptum in lucem tandem <lb></lb>edidit amicus suus Bartolus, Venetiis anno 1611. In eo enim libro osten­<lb></lb>dit vir celeberrimus quemadmodum arcus interior, binis refractionibus ra­<lb></lb>diorum solis, singulisque reflexionibus inter binas istas refractiones inter­<lb></lb>venientibus, in rotundis pluviae guttis effingatur, exterior autem arcus <lb></lb>binis refractionibus binisque itidem reflexionibus interiectis, in similibus <lb></lb>aquae guttis efficiatur. </s>

<s>Suamque is explicandi rationem experimentis com­<lb></lb>probavit in phiala aquae plena et globis vitreis aquae plenis in sole col­<lb></lb>locatis, quo duorum arcuum istorum colores in illis se exhiberent contem­<lb></lb>plandos. </s>

<s>Porro eandem explicandi rationem persecutus est Cartesius in <lb></lb>Meteoris suis, eamque quae est de arcu exteriori insuper emendavit ”<emph.end type="italics"></emph.end><lb></lb>(Optic., Lib. </s>

<s>I, P. II, prop. </s>

<s>IX). </s></p><p type="main">

<s>Dev&#039;esser proprio vero che queste cose del De Dominis il Newton le <lb></lb><emph type="italics"></emph>sentì dire,<emph.end type="italics"></emph.end> perchè se avesse consultato il libro <emph type="italics"></emph>De radiis visus et lucis<emph.end type="italics"></emph.end> non <lb></lb>era possibile che non si fosse accorto come le <emph type="italics"></emph>bine rifrazioni<emph.end type="italics"></emph.end> e le <emph type="italics"></emph>bine ri­<lb></lb>flessioni,<emph.end type="italics"></emph.end> nell&#039;intenzion dello Spalatrese, non erano altro che un nome ri­<lb></lb>spondente per caso a quello scelto poi a significare le verità diottriche. </s>

<s>Nè <pb xlink:href="020/01/680.jpg" pagenum="123"></pb>pure è secondo giustizia l&#039;attribuire al Cartesio il merito di aver solamente <lb></lb>emendato le dottrine del De Dominis, per ciò che riguardi l&#039;arco esteriore: <lb></lb>egli non emendò, ma dimostrò da&#039;principii, non ad altri prima noti che a <lb></lb>Ferrante Imperato, gli andamenti de&#039;raggi atti a produrre per riflessione e <lb></lb>per rifrazione i due Archi paralleli e concolori. </s>

<s>Cosicchè, secondo il giudi­<lb></lb>zio imparziale della Storia, rimane al Nostro un merito unico ma pur as­<lb></lb>sai notabile, ed è quello di avere apparecchiate al Francese le vie del­<lb></lb>l&#039;esperienza. </s></p><p type="main">

<s>Il Newton soggiungeva al passo ora ultimamente citato che il De Dominis <lb></lb>e il Cartesio lasciarono imperfetta la teoria dell&#039;Iride, perchè ignoravano la <lb></lb>vera generazion de&#039;colori, e perciò si compiace che il dar l&#039;ultima mano a <lb></lb>così nobile opera sia stato riserbato a lui. </s>

<s>La scoperta de&#039;varii gradi di re­<lb></lb>frangibilità non solo dette al grande Ottico inglese modo a divisar le ragioni <lb></lb>de&#039;colori nell&#039;Arco, ma a precisarne altresì le misure concluse a priori dal <lb></lb>Maurolico, e stabilite così all&#039;incirca dal Cartesio e dal Grimaldi. </s>

<s>“ Itaque (ri­<lb></lb>trovava il Newton per l&#039;Iride interna) maxima eius semidiameter est 43°, 6′. </s>

<s><lb></lb>A qua, si auferatur minima semidiameter 41°, 0′, emergit Iridis crassities 2°, 0′ <lb></lb>circiter, vel potius 2°, 37′ addita diametro Solis ” (Letiones Optic. </s>

<s>cit., pag. </s>

<s>109). <lb></lb>Per l&#039;Iride esterna trovò il massimo semidiametro 52°, 51′, dalla quale “ si <lb></lb>auferatur minima 49°, 2′ et residuo addatur diameter Solis 31′, emerget huius <lb></lb>Iridis crassities 4°, 20′. </s>

<s>Sed propter maiorem huius, quam interioris Iridis <lb></lb>obscuritatem, colores vix ultra crassitiem trium graduum vel trium et se­<lb></lb>missis, videri posse coniicio ” (ibi). </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le Corone e i Parelii, con altri simili fenomeni spettacolosi che, seb­<lb></lb>bene non sì frequentemente, si osservano intorno al Sole e alla Luna, fu­<lb></lb>rono creduti dagli antichi avere così strette relazioni coll&#039;Iride, che non <lb></lb>dubitarono di riguardar quelle apparenze come un effetto di somiglianti, se <lb></lb>non affatto uguali, cagioni. </s>

<s>Vitellione si provò a sfiorar qualche cosa del dif­<lb></lb>ficile campo inesplorato nelle proposizioni LXXXI e LXXXII del suo X Li­<lb></lb>bro di Prospettiva, e anche quando, specialmente in Italia, s&#039;incominciò a <lb></lb>specular della scienza della Natura con libertà di pensiero, non si seppe, per <lb></lb>la spiegazione di quelle recondite apparenze celesti, aggiunger nulla di me­<lb></lb>glio e di nuovo ai detti dell&#039;Ottico pollacco. </s></p><p type="main">

<s>Ferrante Imperato, che così bene indovinò gli andamenti de&#039;raggi re­<lb></lb>fratti e riflessi nella nube rorida, a produr le due Iridi, trovava la ragione <lb></lb>delle Corone o delle Aree, com&#039;ei le chiama, che talvolta come l&#039;Iride stessa <lb></lb>appariscono colorate, nelle refrazioni fatte dai raggi solari in mezzo ai cor­<lb></lb>picciuoli, che compongono la consistenza della nube vaporosa o della cali­<lb></lb>gine: “ Venendo dunque all&#039;Area e l&#039;Iride, diciamo l&#039;una e l&#039;altra farsi <pb xlink:href="020/01/681.jpg" pagenum="124"></pb>con raggi infratti, ma nell&#039;Iride spezialmente intervenirvi la riflessione. </s>

<s>Di­<lb></lb>ciamo inoltre le dette infrazioni e riflessioni farsi da&#039;corpiccioli, che com­<lb></lb>pongono la consistenza della nube e della caligine. </s>

<s>Intenderemo dunque una <lb></lb>linea dal corpo lucido al punto, principio visivo come asse, e nel soggetto <lb></lb>dell&#039;area intenderemo intorno detto asse li raggi visivi infratti dagli corpu­<lb></lb>scoli delle gocce andar dalla vista al luminare. </s>

<s>Se dunque da corpi simili <lb></lb>posti similmente dobbiamo avere effetti simili, saranno le infrazioni fatte in <lb></lb>egual distanza dall&#039;asse, e per conseguenza in circolo d&#039;intorno detto asse. </s>

<s><lb></lb>Quivi dunque la infrazione è dalla nube tramezza, ma nell&#039;Iride la ri­<lb></lb>flessione è dalla nube opposta ” (Historia Natur., Lib. </s>

<s>XI, Venezia 1672, <lb></lb>pag. </s>

<s>288). </s></p><p type="main">

<s>De&#039;tre Autori poi, che tanto efficacemente concorsero a promuover l&#039;Ot­<lb></lb>tica nel primo risorgere del Metodo sperimentale, il Maurolico e il De Do­<lb></lb>minis lasciarono intatto il tema delle Corone e dei Parelii, o arretrati dalla <lb></lb>difficoltà di divisarne i più minuti particolari, o forse persuasi che ritornas­<lb></lb>sero le ragioni di quegli stessi particolari nelle generali ragioni diottriche <lb></lb>date da loro delle apparenze dell&#039;Iride. </s>

<s>Il Keplero fu tentato dalla voglia di <lb></lb>applicare le Ottiche discipline a spiegar quegli spettacoli celesti, che fruga­<lb></lb>vano le menti de&#039;Filosofi e gli animi de&#039;curiosi, ma poi abbandonò l&#039;im­<lb></lb>presa, e fece bene, perchè colle false idee che aveva dell&#039;essere e della na­<lb></lb>tura de&#039;colori, si rendeva il meno atto, non solo a condurre in porto, ma <lb></lb>pure a sospingere innanzi la barca. </s>

<s>“ Explicationem Halonis, Iridis, Pare­<lb></lb>liorum, Paraselenarumque ex Optica disciplina petendam iam olim vidit <lb></lb>Aristoteles, neque ea quae adhuc desiderantur in Meteorologicis Aristotelis <lb></lb>aliunde suppleri possunt. </s>

<s>Cogitaveram et ego hic libellum de Iride subiun­<lb></lb>gere, quod supplementum esset aristotelicae super Iride disquisitionis, sed <lb></lb>desiderantur adhuc Pareliorum genuinae causae, quae sunt causis portento­<lb></lb>sarum Iridum implexae: itaque in praesens hoc negocium deserui ” (Diop­<lb></lb>trice, Augustae Vindelic. </s>

<s>1611, pag. </s>

<s>10, 11). </s></p><p type="main">

<s>Non mancarono nonostante, poco appresso i tre celebri Ottici comme­<lb></lb>morati, alcuni i quali, benchè fossero persuasi che a produr le Corone talvolta <lb></lb>iridescenti e i Parelii dovessero necessariamente intervenire quelle rifles­<lb></lb>sioni, e quelle rifrazioni, alle quali erano già ricorsi Vitellione e i seguaci <lb></lb>di lui; s&#039;avvidero nulladimeno che simili riflessioni e rifrazioni non era pos­<lb></lb>sibile che si facessero in mezzo alle stille della nube rorida, come nell&#039;Iride <lb></lb>celeste. </s>

<s>Nè dall&#039;altra parte era difficile avvedersi di ciò, avendo osservato <lb></lb>che, mentre essa Iride non si fa mai che sotto il cielo piovoso, gli Aloni e <lb></lb>i Parelii invece si vedono sempre apparire quando non piove. </s>

<s>Dove in altro <lb></lb>dunque se no nelle gocciole piovose ritrovare il soggetto di quelle riflessioni <lb></lb>e di quelle refrazioni, riconosciute indispensabili a salvare così fatta ap­<lb></lb>parenza? </s></p><p type="main">

<s>Lo Scheiner, che senti vivo il bisogno di rispondere alla domanda, av­<lb></lb>ventò certe sue idee che riconosciute da lui stesso per enimmatiche, lasciò <lb></lb>a decifrare ai Filosofi in faccia a&#039;quali pronunziava il motto: <emph type="italics"></emph>sapientibus<emph.end type="italics"></emph.end><pb xlink:href="020/01/682.jpg" pagenum="125"></pb><emph type="italics"></emph>pauca.<emph.end type="italics"></emph.end> Ecco quali sono quelle idee, che vedonsi lampeggiar dal contesto <lb></lb>delle seguenti parole: “ Transferunt autem haec vitra (utrinque convexa et <lb></lb>utrinque concava) visas res a veris locis mirum in modum, sursum, deor­<lb></lb>sum dextrorsum sinistrorsum ecc. </s>

<s>Quod etiam in sole experiri potes per vi­<lb></lb>trum simile coloribus tinetum, aut in Luna plena vitro liquido. </s>

<s>Videbis enim <lb></lb>utrumlibet sidus in ellipsim configurari et loco transferri, pro situ et statu <lb></lb>vitri. </s>

<s>Et si eiusmodi duo aut plura vitra diversis locis inter visum et sidera <lb></lb>dicta statueris, multiplicabis eadem sidera. </s>

<s>E quibus rationem Pareliorum <lb></lb>Paraselenarumque eruere addisces. </s>

<s>Quod idem specilla polyedra edocebunt. </s>

<s><lb></lb>Sed et homocentrice convexo concava vitra eadem praestant. </s>

<s>Unde si ex <lb></lb>hisce humilibus in alia ascendere, tanquam gradibus quibusdam non pige­<lb></lb>bit, dicemus obiectu vel nobis vel vaporis, aut similis meteori diaphani re­<lb></lb>fractui et uno istorum modorum multipliciter figurati ecc. </s>

<s>solem saepuiscule <lb></lb>videri et Parelia ita gigni. </s>

<s>Sed haec ex occasione stringo non instituto enu­<lb></lb>cleo. </s>

<s>Sapientibus pauca ” (Refractiones coelestes, Ingolstadii 1617, pag. </s>

<s>40). </s></p><p type="main">

<s>Questo sfolgorar del pensiero at­<lb></lb><figure id="id.020.01.682.1.jpg" xlink:href="020/01/682/1.jpg"></figure></s></p><p type="caption">

<s>Figura 43.<lb></lb>traverso alle parole, così in fretta <lb></lb>dallo Scheiner pronunziate, era senza <lb></lb>dubbio assai seducente, ma dove tro­<lb></lb>vare in cielo que&#039;vetri cristallini e <lb></lb>que&#039;prismi atti a rifrangere in modo <lb></lb>i raggi del sole da rappresentare i <lb></lb>Parelii e le Corone? </s>

<s>Fra i Sapienti <lb></lb>che ripensavano a queste cose si trovò <lb></lb>per avventura il Cartesio, il quale, <lb></lb>nell&#039;inverno del 1635, trovandosi in <lb></lb>Amsterdam, si dette ad osservare di­<lb></lb>ligentissimamente le varie figure cri­<lb></lb>stalline della neve, in che, sotto l&#039;aria <lb></lb>freddissima, si trasformavano le goc­<lb></lb>ciole della pioggia. </s>

<s>Uscito da quella <lb></lb>contemplazione, che a lui sembrò nuo­<lb></lb>va, e ripensando che simili cristallini <lb></lb>di ghiaccio, più presto che in terra, <lb></lb>si formano in aria, dove per qualche <lb></lb>tempo vi possono rimaner sostenuti <lb></lb>dai venti; ecco, disse, i vetri lenti­<lb></lb>colari e i prismi, atti per rifrazione <lb></lb>a dipingere all&#039;occhio di noi riguar­<lb></lb>danti in Terra le Corone e gli Aloni. </s></p><p type="main">

<s>“ Sit ABC (fig. </s>

<s>43) ex. </s>

<s>gr. </s>

<s>Sol, <lb></lb>D oculus, EFG plurimae glaciei par­<lb></lb>ticulae pellucidae aliae iuxta alias iacientes, plane quemadmodum esse de­<lb></lb>bent ut in stellulas formentur, et quarum convexitas talis est ut radius <pb xlink:href="020/01/683.jpg" pagenum="126"></pb>ex. </s>

<s>gr. </s>

<s>ex puncto A ad extremitatem stellulae G perveniens, et radius ex <lb></lb>puncto C ad extremitatem stellulae F refringantur vesus D et ut etiam alii <lb></lb>plures radii perveniant ad D, ex iis qui in illas incidunt quae sunt extra <lb></lb>circulum GG. </s>

<s>Manifestum est praeter radios AD, CD et similes qui recta <lb></lb>linea tendentes solem naturali magnitudine repraesentant, alios refractos in <lb></lb>FE aerem comprehensum hoc circulo FF, satis lucidum reddituros, et cir­<lb></lb>cumferentiam illius inter circulos FF, et GG, specie coronae Iridis colori­<lb></lb>bus variegatae exhibituros. </s>

<s>Ipsum etiam rubrum intrinsecus ad F et caeru­<lb></lb>leum extrinsecus ad G visum iri plane quemadmodum observatur. </s>

<s>Et si <lb></lb>duo aut plures ordines particularum glaciei congesti sint, dummodo radios <lb></lb>solares non ideo plane excludant, illi radiorum qui per duos ordines in <lb></lb>stellarum extremitatibus penetrant bis fere tantumdem incurvati, quan­<lb></lb>tum alii qui per unum tantum, alium circulum coloratum producent ambitu <lb></lb>quidem priori longe maiorem sed minus lucidum ita ut tum duae coronae <lb></lb>quarum una alteram cingat, et quarum exterior interiori minus picta sit, <lb></lb>appareant, ut etiam interdum fuit observatum ” (Cap. </s>

<s>IX, Metereorum cit., <lb></lb>pag. </s>

<s>188, 89). </s></p><p type="main">

<s>Quanto a&#039;Parelli parve al Cartesio non gli poter salvare col ricorso alle <lb></lb>rifrazioni fatte nelle stelline ghiacciate, e non vedendosi, come dianzi, da <lb></lb>nessuna parte aperta la via dell&#039;esperienza, ritorna al gioco delle sue solite <lb></lb><figure id="id.020.01.683.1.jpg" xlink:href="020/01/683/1.jpg"></figure></s></p><p type="caption">

<s>Figura 44.<lb></lb>fantasie. </s>

<s>Come tipo generale e rappresentativo del <lb></lb>fenomeno, prese in mancanza di osservazioni proprie <lb></lb>la descrizione de&#039;Parelii osservati in Roma, il di <lb></lb>20 Marzo 1629, nella quale descrizione si diceva che <lb></lb>cinque soli apparvero, incastonati come gemme in <lb></lb>anello, in un gran circolo di color bianco. </s>

<s>L&#039;ap­<lb></lb>parenza di quel circolo, secondo il Cartesio, era do­<lb></lb>vuta alle riflessioni del sole in un anello di ghiaccio, <lb></lb>il quale, nella fantasia del Filosofo, aveva avuto ori­<lb></lb>gine a questo modo: </s></p><p type="main">

<s>“ Sit ex. </s>

<s>gr. </s>

<s>A (fig. </s>

<s>44) meridies ubi Sol con­<lb></lb>sistit comitatus vento calido tendente ad B et C Sep­<lb></lb>tentrio, unde ventus frigidus etiam ad B nititur, et <lb></lb>ibi suppono hos duos ventos vel invenire, vel cogere <lb></lb>nubem, ex glaciei particulis compositam, quae tam <lb></lb>lata est et profunda ut non possint unus super, alius <lb></lb>subter, vel per eius medium labi, quemadmodum <lb></lb>alias solent, sed cursum suum circumcirca tenere <lb></lb>cogantur, qua opera non tantum illam circumdant, <lb></lb>sed etiam qui a Meridie calidus spirat, nivem eius <lb></lb>ambitus paululum liquefacit, quae statim iterum gelata, tam frigore venti <lb></lb>borealis, quam vicinia nivis interioris nondum liquefactae, magnum quen­<lb></lb>dam velut annulum, ex glacie continua et pellucida, componit ” (ibi, <lb></lb>pag. </s>

<s>191). </s></p><pb xlink:href="020/01/684.jpg" pagenum="127"></pb><p type="main">

<s>E perciocchè dicevasi che il re di Polonia avesse, nel 1625, veduto infino <lb></lb>a sei soli incastonati nel grande anello, e i due più prossimi al sole vero <lb></lb>nell&#039;apparenza romana si diceva che rappresentassero certe frange iride­<lb></lb>scenti negli orli, e non mostrassero così bene rotondi da far supporre che <lb></lb>non fossero come gli altri, generati per riflessione, ma per rifrazione; ac­<lb></lb>comodando il Cartesio le sue speculazioni a questi fatti osservati, disegnò <lb></lb>nell&#039;iconismo ora citato i raggi venienti dal Sole all&#039;occhio dello spettatore <lb></lb>in modo, che rappresentassero le immagini di sei soli, quattro per rifles­<lb></lb>sione e due per refrazione. </s>

<s>“ Possunt etiam apparere stantibus in Terra <lb></lb>circa punctum K (fig. </s>

<s>preced.) usque ad sex Soles, qui circulo albo, tan­<lb></lb>quam annulo totidem adamantes inserti sint. </s>

<s>Primus scilicet in E, ob ra­<lb></lb>dios directe fluentes a Sole quem suppono in A: duo sequentes in D et F, <lb></lb>per refractionem radiorum qui glaciem iis in locis permeant, ubi crassitie <lb></lb>illius paulatim decrescente, introrsum ab utraque parte incurvantur, que­<lb></lb>madmodum ii qui prisma crystallinum perlabuntur. </s>

<s>Et propterea hi duo So­<lb></lb>les in oris rubrum colorem ostentant, ea parte qua E respiciunt, ubi gla­<lb></lb>cies crassior est, et coeruleum in altera ubi tenuior. </s>

<s>Quartus in H per <lb></lb>reflexionem apparet, duo itidem postremi per reflexionem in G et I ” (ibi, <lb></lb>pag. </s>

<s>192). </s></p><p type="main">

<s>Queste cartesiane ipotesi intorno all&#039;origine de&#039;Parelii era facile che si <lb></lb>mettessero in dubbio da tutti coloro, i quali non credevano che potessero <lb></lb>avere i venti tant&#039;arte da girare a tornio così puntualmente le nubi, ma a <lb></lb>sostituirne delle migliori mancavano le osservazioni dirette, non presentan­<lb></lb>dosi que&#039;fenomeni così frequenti. </s></p><p type="main">

<s>Dopo trent&#039;anni interi, da che fu pubblicata la Meteorologia del Car­<lb></lb>tesio, volle la buona ventura che uno di costoro, a cui toccò di osservar lo <lb></lb>spettacolo, fosse l&#039;Ugenio. </s>

<s>il di 12 maggio 1668, sulle ore nove della mat­<lb></lb>tina, apparve agli abitanti di Parigi un Alone o corona intorno al Sole, e <lb></lb>l&#039;Huyghens l&#039;osservava attentissimamente dalle finestre della Libreria del <lb></lb>Re. </s>

<s>Un così strenuo cultore e promotore della Diottrica non lasciò di spe­<lb></lb>culare intorno alle nuove cose osservate, e intanto che faceva esperienze e <lb></lb>instaurava calcoli per comporre la Dissertazione <emph type="italics"></emph>De Coronis<emph.end type="italics"></emph.end> et <emph type="italics"></emph>Pareliis,<emph.end type="italics"></emph.end> di­<lb></lb>stese una breve scrittura in francese, nella quale, nascondendosi come Au­<lb></lb>tore e prendendo l&#039;ufficio di semplice Relatore, descriveva il fenomeno e <lb></lb>proponeva la ipotesi per ispiegarlo. </s>

<s>Quella Relazione fu stampata, dentro il <lb></lb>medesimo anno 1667, da Giovanni Cusson a Parigi, ed ha qualche impor­<lb></lb>tanza il saper com&#039;ella venisse di Francia a farsi nota fra noi. </s></p><p type="main">

<s>Le relazioni passate fra l&#039;Huyghens e la nostra Accademia fiorentina <lb></lb>son ben note oramai ai lettori di questa Storia, e dopo lo screzio avvenuto <lb></lb>a cagion dell&#039;Orologio a pendolo, ricomposti gli animi in quiete, il prin­<lb></lb>cipe Leopoldo regalava l&#039;illustre Olandese de&#039;libri migliori che uscivano di <lb></lb>mano in mano da&#039;suoi Accademici, e lo pregava a volerne dare particolare <lb></lb>informazione de&#039;suoi studii e specialmente di quelli concernenti la Diot­<lb></lb>trica. </s>

<s>L&#039;Huyghens rispondeva in proposito con lettera del di 18 Novem-<pb xlink:href="020/01/685.jpg" pagenum="128"></pb>bre 1667, accompagnando al Principe la detta Relazione dell&#039;Alone osservato <lb></lb>a Parigi. </s></p><p type="main">

<s>Leopoldo de&#039;Medici non richiedeva quelle scientifiche informazioni per <lb></lb>sua privata curiosità, ma per diffonderle nella sua Accademia, alla quale, <lb></lb>così Cardinale com&#039;era diventato, attendeva con maggiore operosità e con <lb></lb>affetto più vivo. </s>

<s>E perchè non era allora la lingua francese d&#039;intelligenza <lb></lb>comune, ordinò al Viviani che traducesse la <emph type="italics"></emph>Relazione<emph.end type="italics"></emph.end> in lingua italiana, e <lb></lb>gli ordinò altresì ne facesse un sunto, da diffonderne con più facilità la no­<lb></lb>tizia, e da conservarsi fra&#039;documenti dell&#039;Accademia. </s>

<s>Il Viviani esegui pun­<lb></lb>tualmente i due comandi, e quanto al primo lasciò notato alla fine del ma­<lb></lb>noscritto inserito da c. </s>

<s>137-44 nel Tomo CXXXIII de&#039;Discepoli di Galileo: <lb></lb>“ Mal tradotta da me dal francese, a&#039;di 21 Dicembre 1667, e correttami dal <lb></lb>signor Francesco Pandolfini. </s>

<s>” Quanto al secondo, ivi a c. </s>

<s>135: “ Datone <lb></lb>copia al Serenissimo Cardinale Leopoldo, che mi aveva richiesto del sunto. </s>

<s>” <lb></lb>Nonostante però che il Viviani dica di aver mal tradotto, noi preferiremo la <lb></lb>versione di lui a quella latina fatta dal Dausmenil, e inserita da pag. </s>

<s>348-58 <lb></lb>(Lugd. </s>

<s>Batav. </s>

<s>1703) degli Opuscoli postumi di Cristiano Huyghens, per le <lb></lb>citazioni che occorreranno nel passar a dar brevemente conto della ipotesi <lb></lb>proposta dal celebre Autore, per salvar le Corone e i Parelii. </s></p><p type="main">

<s>L&#039;osservazione sensata gli avea dimostrato un error capitale, in ch&#039;era <lb></lb>incorso il Cartesio, e che consisteva nel dire che lo spazio rinchiuso dentro <lb></lb>la Corona fosse più chiaro dell&#039;aria all&#039;intorno. </s>

<s>L&#039;Huyghens osservò che <lb></lb>invece era più oscuro, e indi ne trasse una conclusione importante, che cioè <lb></lb>i ghiaccioli, a cui era stato commesso il gioco di rischiarar quello spazio, <lb></lb>non fossero altrimenti diafani ma opachi. </s>

<s>E perchè dall&#039;altra parte una certa <lb></lb>tal qual trasparenza superficiale era necessaria a produrre le rifrazioni, si <lb></lb>ridusse l&#039;Huyghens a trasformar le stelline cartesiane in cilindretti di ghiac­<lb></lb>cio, trasparenti alla superficie e col nocciolo opaco. </s>

<s>Per mezzo di così fatti <lb></lb>cilindretti trasportati e sostenuti per l&#039;aria, non ritti nè a diacere, ma in­<lb></lb>clinati al piano dell&#039;orizzonte per un angolo vicino al mezzo retto, pensò <lb></lb>che si potessero salvare altresi le apparenze de&#039;Parelii, e tuttociò si studiò <lb></lb>di confermare per l&#039;esperienza, costruendo alcuni di così fatti cilindretti ar­<lb></lb>tificiali, e mostrando che collocati opportunamente innanzi all&#039;occhio ripro­<lb></lb>ducevano le sembianze de&#039;fenomeni celesti. </s></p><p type="main">

<s>“ Per far vedere all&#039;occhio tutti questi differenti effetti de&#039;ci­<lb></lb>lindri, leggesi in fine alla citata <emph type="italics"></emph>Relazione<emph.end type="italics"></emph.end> tradotta dal Viviani, <lb></lb>egli ne ha portato uno di vetro lungo un piede, della forma della <lb></lb><figure id="id.020.01.685.1.jpg" xlink:href="020/01/685/1.jpg"></figure></s></p><p type="caption">

<s>Fig. </s>

<s>45.<lb></lb>45a figura, con un cilindro di legno nel mezzo, invece di nocciolo <lb></lb>opaco, e con lo spazio fra esso ripieno d&#039;acqua, in luogo di ghiaccio <lb></lb>trasparente. </s>

<s>Tal cilindro, stando esposto al sole e situato l&#039;occhio in <lb></lb>luogo a proposito, si vedevano successivamente tutte quelle rifles­<lb></lb>sioni e rifrazioni, delle quali si è parlato. </s>

<s>Dal che si poteva con­<lb></lb>cludere che, dandosi una grande quantità di simili cilindri, ma piccolissimi <lb></lb>in comparazione di questo, occupando l&#039;aria e con quelle diverse positure <pb xlink:href="020/01/686.jpg" pagenum="129"></pb>che si sono supposte, ne dovrebbero seguire precisamente tutte le apparenze <lb></lb>de&#039;Parelii e de&#039;cerchi loro. </s>

<s>Si desiderò, per maggior confermazione delle <lb></lb>verità del supposto, di poter osservare di questi piccoli cilindri caduti in <lb></lb>terra, nel tempo de&#039;Parelii, il che egli mostrò non potersi fare facilmente, <lb></lb>perchè i vapori che allora ascendono da terra e che son cagione delle loro <lb></lb>figure cilindriche, gli tengon così in aria sospesi, ed aggiunse non dover pa­<lb></lb>rere strano che dei piccolissimi grani di gragnuola fossero in tal guisa so­<lb></lb>stenuti dai vapori, i quali, nel rarefarsi ed estendersi per all&#039;insu, potevano <lb></lb>aver gran movimento per questo effetto. </s>

<s>Che questo era ben molto più fa­<lb></lb>cile a concepirsi che l&#039;immaginarsi come questi medesimi vapori potrebbero <lb></lb>tener sospeso un grandissimo e pesantissimo cerchio di ghiaccio, e tale quale <lb></lb>l&#039;ha supposto Renato Des Cartes, per dichiarare la cagion de&#039;Parelii e del <lb></lb>gran cerchio bianco dell&#039;apparenza di Roma. </s>

<s>In questo supposto erano an­<lb></lb>cora da notarsi le seguenti difficoltà, cioè che non vi si trova ragione per­<lb></lb>chè il cerchio bianco debba passar per il sole, come sempre si osserva, e <lb></lb>lo seguiti secondo che muta altezza, benchè l&#039;apparenza duri qualche volta <lb></lb>tre o quattr&#039;ore. </s>

<s>Che questo medesimo cerchio bianco fatto di ghiaccio, es­<lb></lb>sendo veduto da spettatori lontanissimi tra di loro, non potrebbe mai parere <lb></lb>tondo a tutti, com&#039;ei fa, e attraversare il sole. </s>

<s>Che quando si osservano i <lb></lb>Parelii non si vede per modo alcuno questa nuvola tonda circondata da un <lb></lb>cerchio di ghiaccio, la quale per la sua densità dovrebbe ascondere una <lb></lb>parte del cielo, ma che il tempo par quasi tutto sereno, non avendovi che <lb></lb>piccole nuvole, le quali si vedono mutar luogo, mentre che il gran cerchio <lb></lb>ed i Parelii stanno fermi. </s>

<s>Che in questo supposto non viene se non per for­<lb></lb>tuna che i Parelii, che sono accanto al Sole, apparischino nel segamento <lb></lb>d&#039;una Corona e del gran cerchio bianco, come quasi sempre si osserva, <lb></lb>così facendo ben vedere che le cause de&#039;Parelii e delle Corone son molto <lb></lb>poco differenti, contro l&#039;opinione di Monsu Des Cartes ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXXXIII, c. </s>

<s>144). </s></p><p type="main">

<s>Quello che il Viviani rimesse al principe Leopoldo, piuttosto che un <lb></lb>sunto di questa Relazione, si direbbe un assennatissimo giudizio delle ipo­<lb></lb>tesi ivi proposte a dichiarar la ragione di apparenze prodotte in luoghi e da <lb></lb>cause tanto remote e inaccessibili a noi. </s>

<s>E perchè il giudizio di un tanto <lb></lb>uomo, in cosa di tanta curiosità ed importanza, vuol tenersi in gran pregio, <lb></lb>da noi si crede esser ben fatto il riferirlo: </s></p><p type="main">

<s>“ In essa Relazione promuove e tocca leggermente sistemi oltre a modo <lb></lb>ingegnosi per salvar quelle (le Corone apparse in Parigi) ed altre simili ap­<lb></lb>parenze meteorologiche. </s>

<s>Da questo saporitissimo saggio, benchè senza dimo­<lb></lb>strazioni matematiche, si può risolutamente affermare che se tali fenomeni <lb></lb>realmente non seguono nei modi immaginati dall&#039;Ugenio (che pur non hanno <lb></lb>in sè dell&#039;impossibile, anzi assaissimo del verisimile) questo almeno (con­<lb></lb>ceduti sospesi e vaganti per l&#039;aria que&#039;piccoli grani di diaccio o tondi o <lb></lb>bislunghi, o tutti trasparenti o mezzi opachi o in uno o in altro modo si­<lb></lb>tuati) sono valevoli per sè soli a salvare quelle apparenze esplicate dall&#039;Uge-<pb xlink:href="020/01/687.jpg" pagenum="130"></pb>nio, poichè tanto necessitano a confessare le leggi infallibili della Geometria. </s>

<s><lb></lb>Se poi la Natura opera in ciò diversamente, ha nondimeno questo Autore <lb></lb>adempiuta la parte di ottimo fisico e di matematico senza pari. </s>

<s>E di vero <lb></lb>questi ed altri maravigliosi effetti intorno a materia si vasta e cotanto astrusa, <lb></lb>quanto è questa delle riflessioni e delle rifrazioni della luce, non si poteva <lb></lb>pretendere che venissero penetrati giammai da alcun Filosofo, che insieme <lb></lb>non fosse e Filosofo e Geometra sottilissimo; e siccome i passati secoli son <lb></lb>rimasti privi di notizie tanto sublimi, così il presente può gloriarsi di es­<lb></lb>ser giunto ad intender, per mezzo prima del Galileo ed ora di si alto inge­<lb></lb>gno, che nell&#039;oscurità della Fisica non si vedrà mai lume o certezza di co­<lb></lb>gnizione, senza la chiara scorta della purissima Geometria, che è quella che <lb></lb><emph type="italics"></emph>puote disnebbiar nostro intelletto ”<emph.end type="italics"></emph.end> (MSS. Cim., T. XXI, c. </s>

<s>100). </s></p><p type="main">

<s>Invitato a riferire al principe dell&#039;Accademia fiorentina intorno all&#039;ipo­<lb></lb>tesi ugeniana, che cosa il Viviani avrebbe potuto dire di più giudizioso? </s>

<s><lb></lb>Nessuno può decidere se la Natura operi veramente a quel modo, ma poi­<lb></lb>chè ella in tutte le operazioni sue geometrizza, è conforme agl&#039;istituti e al <lb></lb>magistero di lei il modo che vien proposto dall&#039;ingegnosissimo Ugenio. </s></p><p type="main">

<s>Speculò poco dopo anche il Newton sulle ragioni delle spettacolose <lb></lb>apparenze celesti, ma a che poteva egli risolversi un uomo di quell&#039;indole, <lb></lb>che professava il principio non doversi filosofar della Natura, se non che <lb></lb>sui fatti prima bene osservati? </s>

<s>Egli stesso risponde nell&#039;Avvertimento alla <lb></lb>prima edizione dell&#039;Ottica: “ Coronas colorum, quae circum solem et <lb></lb>lunam nonnumquam videntur, conatus sum quadatenus explicare; verum, <lb></lb>inopia plurium observationum, materiam illam aliis penitius explorandam <lb></lb>relinquo. </s>

<s>” </s></p><p type="main">

<s>Perciò nel libro I, parte II, dell&#039;opera che segue, accennando il Newton <lb></lb>agli Aloni, commenta le ipotesi dell&#039;Huyghens, concludendo come aveva già <lb></lb>concluso il Viviani che, sebbene non possa dimostrarsi come cosa di fatto, <lb></lb>pur è possibile che la Natura operi a quel modo. </s>

<s>“ Quae porro Halos, quo­<lb></lb>ties grando apta sit figura, colorata esse poterit: tumque intra rubra erit <lb></lb>facta, radiis minime refrangibilibus, et caerulea extra radiis maxime refran­<lb></lb>gibilibus, praesertim si grandinis particulae habeant forte in centris suis <lb></lb>opacos nivis globulos, qui lumen intra Halo intercipientes, quomodo Huge­<lb></lb>nius observavit, efficere possint ut interior ipsius pars distinctius, quam alio­<lb></lb>qui futurum esset, definita sit. </s>

<s>Etenim huiusmodi grandinis particulae, quam­<lb></lb>vis globosae, tamen terminando lumen inclusa sua nive exhibere poterunt <lb></lb>Halo rubram intra, et coloris expertem extra, atque etiam obscuriorem in­<lb></lb>tra rubram sui partem, quam extra, uti plerumque fieri solet. </s>

<s>Etenim ex <lb></lb>radiis qui proxime nivem praeterferuntur rubri refringentur minime, adeo­<lb></lb>que ad oculum in lineis directissimis pervenient. </s>

<s>Lumen quod a pluviae <lb></lb>gutta post duas refractiones et tres pluresve reflexiones egreditur, vix satis <lb></lb>forte est ad arcum efficiendum qui sub sensum cadat, at in glaciei parti­<lb></lb>culis illis cylindraceis, quarum ope Hugenius rationem Parheliorum expli­<lb></lb>cal, poterit fortasse sensu percipi ” (Edit. </s>

<s>cit., pag. </s>

<s>65). </s></p><pb xlink:href="020/01/688.jpg" pagenum="131"></pb><p type="main">

<s>Cosi il Newton gran Maestro dell&#039;Ottica, dando un bell&#039;esempio ad al­<lb></lb>cuni orgogliosi sapienti, confessava che delle Corone e de&#039;Parelii la Diottrica <lb></lb>e la Meteorologia non avrebbero saputo dire nulla di meglio, di quel che <lb></lb>l&#039;Huyghens ne scrisse, fra gli Opuscoli postumi, nella sua <emph type="italics"></emph>Dissertazione,<emph.end type="italics"></emph.end> e <lb></lb>la stessa scienza moderna, benchè abbia trovato modo di salvar qualche ap­<lb></lb>parenza, ricorrendo alle diffrazioni, per le grandi Corone e i Parelii invoca <lb></lb>ancora l&#039;efficacia de&#039;cilindretti ugeniani. </s></p><pb xlink:href="020/01/689.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del calore<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. Dell&#039;antica teoria degl&#039;ignicoli rinnovata da Galileo: della questione del freddo positive o priva­<lb></lb>tivo. </s>

<s>— II. </s>

<s>Di alcune speculazioni e sperienze meno note fatte intorno al calore dagli Accade­<lb></lb>mici del Cimento. </s>

<s>— III. </s>

<s>Del calore di comunicazione, e del calorico raggiante. </s>

<s>— IV. </s>

<s>Degli <lb></lb>effetti del calore negli agghiacciamenti. </s>

<s>— V. </s>

<s>Degli effetti del calore nelle evaporazioni. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La lampada ardente del Sole e le nostre fiamme artificiali conferma­<lb></lb>rono così nelle menti degli uomini l&#039;opinione della concomitanza della luce <lb></lb>col calore, che furono per lungo tempo credute inseparabili, cosicchè sola­<lb></lb>mente sopite, per causa estrinseca e violenta, si credeva esser rimasta la <lb></lb>luce stessa, quando in un corpo incalorito non si mostra parvente. </s>

<s>Comun­<lb></lb>que sia quella concomitanza de&#039;due elementi, ministri principali della Na­<lb></lb>tura, è così frequente, e per la comune consuetudine hanno proprietà tal­<lb></lb>mente comuni, che non si può alla storia della scienza della luce non far <lb></lb>immediatamente succedere la storia della scienza del calore. </s></p><p type="main">

<s>Resa quella scienza impossibile da&#039;Peripatetici, che reputarono essere <lb></lb>il calore stesso qualità e non sostanza, Leucippo, Democrito ed Epicuro, con <lb></lb>altri antichi Filosofi seguaci di Platone, dissero, avviando le loro specula­<lb></lb>zioni per miglior sentiero, il caldo essere una mera affezione de&#039;nostri sensi, <lb></lb>la quale non d&#039;altronde derivi che dall&#039;insinuarsi ne&#039;pori delle nostre carni, <lb></lb>uscendo con moto velocissimo, da&#039;corpi detti calidi, alcuni atomi sottilissimi <lb></lb>e perciò atti a penetrare dovunque. </s>

<s>Il veder poi che il calore era bene spesso <lb></lb>eccitato dal moto, e ch&#039;era effetto naturale di lui il rarefare i corpi, serviva <lb></lb>di conferma a quelle dottrine, che perciò, in sul primo risorgere della scienza <pb xlink:href="020/01/690.jpg" pagenum="133"></pb>fisica fra noi, si seguitarono anche da alcuni volutisi serbare dall&#039;altra parte <lb></lb>ad Aristotile sempre devoti. </s>

<s>Scriveva Andrea Cesalpino, nel libro V delle <lb></lb>sue Questioni peripatetiche: “ Caliditas igitur raritatem sequitur, quia affi­<lb></lb>nis quaedam naturae sunt: idcirco ubi una in materia oritur et altera se­<lb></lb>quitur. </s>

<s>Simul enim quid incalescit rarius etiam fit, locum ampliorem quae­<lb></lb>rens, et e converso, quod enim unum efficit alterum quoque. </s>

<s>Motus igitur <lb></lb>disgregando simul rarefacit, et caliditatem in materia educit. </s>

<s>Quies autem <lb></lb>contraria praestat, condensationem scilicet et frigiditatem, quae omnia pri­<lb></lb>vationes quaedam sunt ” (Venetiis 1571, pag. </s>

<s>70). E nel Trattato <emph type="italics"></emph>De plan­<lb></lb>tis:<emph.end type="italics"></emph.end> “ Quamvis autem sensui manifestus sit calor, non ob id negandum est: <lb></lb>quae enim minus calida sunt quam tactus nostri, frigida indicantur ” (Flo­<lb></lb>rentiae 1583, pag. </s>

<s>4). </s></p><p type="main">

<s>Dal raro e dal denso, come da effetti essenzialmente indicativi, argo­<lb></lb>mentava la natura e le proprietà del calore anche quel Giovan Batista Bene­<lb></lb>detti, primo Maestro della scienza fisica in Italia, e di cui dovremo nel <lb></lb>presente soggetto ammirar le dottrine così dalla lontana splendenti nella lieta <lb></lb>luce del vero, in mezzo alla profonda caligine peripatetica. </s>

<s>Se avesse Gali­<lb></lb>leo prese le Speculazioni di lui ad esempio del suo filosofare, avrebbe po­<lb></lb>tuto senza scapito, ed anzi con qualche avvantaggio della verità raffinare le <lb></lb>proprie, ringentilendole della grossolana materialità delle dottrine democri­<lb></lb>tiche ed epicuree, ch&#039;egli mette nuovamente in corso come monete cavate <lb></lb>dall&#039;erario dell&#039;antica Filosofia, senz&#039;essere state rifuse. </s>

<s>E se nel maneg­<lb></lb>giarle par che perdano alquanto di quella ruggine, ciò non fa veramente <lb></lb>altro effetto che di mostrar più chiara e più scolpita la poco fina arte che <lb></lb>ebbe il monetario in coniarle. </s></p><p type="main">

<s>Nel <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> trattiensi lungamente a dare al Sarsi una lezione pla­<lb></lb>tonica intorno alle qualità secondarie della materia, che non riseggono real­<lb></lb>mente in essa, ma ne&#039;nostri sensi, fuor de&#039;quali non sono altro che nomi. </s>

<s><lb></lb>Com&#039;avean fatto già Democrito ed Epicuro, applicando quelle antiche e ve­<lb></lb>rissime dottrine platoniche al calore, Galileo così scrive: “ E tornando al <lb></lb>primo mio proposito in questo luogo, avendo già veduto come molte affe­<lb></lb>zioni, che sono riputate qualità risedenti ne&#039;soggetti esterni, non hanno ve­<lb></lb>ramente altra esistenza che in noi, e fuor di noi, non sono altro che nomi; <lb></lb>dico che inchino assai a credere che il calore sia di questo genere, e che <lb></lb>quelle materie che in noi producono o fanno sentire il caldo, le quali noi <lb></lb>chiamiamo col nome generale fuoco, siano una moltitudine di corpiccioli mi­<lb></lb>nimi in tal e tal modo figurati, mossi con tanta e tanta velocità, li quali <lb></lb>incontrando il nostro corpo lo penetrino colla lor somma sottilità, e che il <lb></lb>lor toccamento, fatto nel lor passaggio per la nostra sostanza e sentito da <lb></lb>noi, sia l&#039;affezione che noi chiamiamo caldo ” (Alb. </s>

<s>IV, 333). </s></p><p type="main">

<s>Que&#039;corpiccioli ignei riputati da tutti così minimi da rendersi anco agli <lb></lb>occhi più acuti invisibili, Galileo fu il primo a vederli penetrare attraverso <lb></lb>il vetro di una caraffa posta a fuoco lento, e mescendosi all&#039;acqua ivi den­<lb></lb>tro rinchiusa, farla notabilmente crescere di volume, come dimostrava ve-<pb xlink:href="020/01/691.jpg" pagenum="134"></pb>dersi per esperienza a Lodovico delle Colombe. </s>

<s>“ Volendo poi vedere sensa­<lb></lb>tamente da che derivi questo ricrescimento, andate con diligenza osservando <lb></lb>e vedrete che, secondo che gli atomi di fuoco si vanno moltiplicando per <lb></lb>l&#039;acqua, ed aggregandosi molti insieme, formano alcuni piccoli globettini, <lb></lb>li quali in gran numero vanno ascendendo per l&#039;acqua e scappando fuori <lb></lb>della sua superficie ” (Alb. </s>

<s>XII, 466, 67). </s></p><p type="main">

<s>Come poi que&#039;globetti o quelle <emph type="italics"></emph>sferette di fuoco<emph.end type="italics"></emph.end> notassero salvi e si­<lb></lb>curi in mezzo all&#039;acqua, senza affogarvi dentro, era un mistero che il Co­<lb></lb>lombo non sapeva intendere, e che a Galileo non riuscì di spiegare. </s>

<s>Nono­<lb></lb>stante, dietro questa fede che aveva agli atomi ignei di Democrito resi agli <lb></lb>occhi suoi così visibili, scioglie alcuni problemi termici de&#039;più curiosi, uno <lb></lb>de&#039;quali è questo che si legge nella raccolta de&#039;<emph type="italics"></emph>Pensieri varii:<emph.end type="italics"></emph.end> “ Che una <lb></lb>mano che tenuta in aria ti par calda, poi posta nell&#039;acqua si raffredda; que­<lb></lb>sta ne è la cagione considerandosi il caldo esterno e l&#039;interno, che mentre <lb></lb>resta in aria, gli atomi ignei suoi proprii hanno luogo di uscire, che son <lb></lb>quelli che cagionano il caldo, ma posta in acqua, le particole d&#039;essa tornano <lb></lb>e serrano gli aditi onde escono i detti atomi, essendo le parti dell&#039;acqua <lb></lb>maggiori delle porosità, per le quali scappano fuori: il che non avviene del­<lb></lb>l&#039;aria trovando il campo libero, come quelli che non son tenuti dalle parti <lb></lb>dell&#039;aria per esser minori de&#039;pori onde <emph type="italics"></emph>erumpunt,<emph.end type="italics"></emph.end> essendo che il caldo non <lb></lb>sia altro che il contatto e solleticamento di quegli atomi calidi, i quali nello <lb></lb>scappar fuora trovano le membra del corpo ” (Alb. </s>

<s>XIV. 334). </s></p><p type="main">

<s>Un altro problema di simil genere fu proposto a risolvere a Galileo dal <lb></lb>conte Pietro de&#039;Bardi, il quale era venuto in gran curiosità di sapere come <lb></lb>mai coloro che vanno a bagnarsi la state in Arno, al primo entrar nel­<lb></lb>l&#039;acqua, provino un senso molesto di freddo: poi usciti fuori alla riva e <lb></lb>tornati a tuffarsi di nuovo, quella stessa acqua dia invece un senso di te­<lb></lb>pore giocondo. </s>

<s>Quanto alla prima parte Galileo, nella soluzione del problema <lb></lb>precedente aveva la risposta pronta, ma però non si sodisfaceva con essa <lb></lb>alla seconda parte di questo nuovo quesito, che è come mai l&#039;acqua sentita <lb></lb>dianzi così fredda, ora invece si trovi calda. </s>

<s>Ebbe a ricorrer perciò ad am­<lb></lb>metter per fondamento del suo discorso il principio che l&#039;acqua d&#039;Arno sotto <lb></lb>i raggi del sole sia realmente più fredda dell&#039;aria. </s>

<s>Avrebbe potuto assicu­<lb></lb>rarsi della verità o della falsità di un tal principio assunto, per l&#039;esperienza <lb></lb>del Termometro, ma o non seppe o non volle, o tanto poca pratica aveva <lb></lb>dello strumento, che non gli sovvenne di farlo. </s></p><p type="main">

<s>La soluzione del problema termico proposto dal conte Bardi si legge <lb></lb>stampa ta fra le opere di Galileo e, nell&#039;edizione dell&#039;Alberi segnatamente, <lb></lb>al T. XIV da pag. </s>

<s>297-99. Noi la porgeremo a leggere sotto forma men <lb></lb>conosciuta, ed è quella che le dava il Viviani dietro la dettatura dello stesso <lb></lb>Galileo, il quale voleva anche questa raccogliere fra le soluzioni degli altri <lb></lb><emph type="italics"></emph>Problemi Naturali.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Problema II. — Uno va per bagnarsi in Arno, si spoglia e si mette <lb></lb>a sedere all&#039;ombra. </s>

<s>Stando così, sente un fresco comportabile e temperato: <pb xlink:href="020/01/692.jpg" pagenum="135"></pb>entra poi nell&#039;acqua, e gli par di sentirla assai fredda. </s>

<s>Statoci un pezzo, ne <lb></lb>esce, torna all&#039;ombra e sente un freddo estremo: di nuovo si tuffa nel­<lb></lb>l&#039;acqua, e dove la prima volta gli parve molto fredda, la seconda gli appa­<lb></lb>risce piuttosto temperata e calda. </s>

<s>Si domanda adesso la cagione di tal di­<lb></lb>versità. </s>

<s>” </s></p><p type="main">

<s>“ Il Problema si risolve così: Noi abbiamo in una stanza una tinozza <lb></lb>piena d&#039;acqua e ci è stata v. </s>

<s>g. </s>

<s>15 di freddezza. </s>

<s>Vien uno, si spoglia e en­<lb></lb>tra nella tinozza. </s>

<s>Chiara cosa è ch&#039;ei sentirà assai più freddo in quell&#039;acqua, <lb></lb>ch&#039;ei non sentiva innanzi ch&#039;ei vi entrassse, dal che si può concludere che, <lb></lb>stando l&#039;aria e l&#039;acqua in un medesimo luogo, cioè ad un istesso caldo o <lb></lb>ad un istesso freddo, sempre l&#039;acqua apparirà assai più fredda dell&#039;aria. </s>

<s>Di­<lb></lb>ciamo adunque che dei gradi di freddezza, de&#039;quali l&#039;aria ne ha per es. </s>

<s>2, <lb></lb>l&#039;acqua ne abbia 10. Adunque un&#039;altr&#039;acqua, che ne abbia 6 soli, apparirà <lb></lb>fredda, in comparazione dell&#039;aria che ne ha 2, ma ben calda in relazione <lb></lb>dell&#039;acqua che ne ha 10. Ora, stante questo, colui che si va a bagnare in <lb></lb>Arno, mentre sta ignudo all&#039;ombra, gode il fresco temperato dell&#039;aria, che <lb></lb>ha 2 soli gradi di freddezza. </s>

<s>Ma quando entra nell&#039;acqua d&#039;Arno, sente la <lb></lb>freddezza sua che è di 6 gradi; di 6 gradi dico e non di 10, perchè il sole <lb></lb>ardente, che l&#039;ha percossa per lo spazio di molte miglia, glie ne viene aver <lb></lb>levati 4, e però, in rispetto dell&#039;aria che ne ha 2 soli, gli pare assai fredda. </s>

<s><lb></lb>Esce poi costui d&#039;Arno, e torna all&#039;ombra bagnato e coperto da un sotti­<lb></lb>lissimo velo d&#039;acqua, la quale, per esser pochissima, non sì tosto è condotta <lb></lb>sotto l&#039;albero all&#039;ombra, che viene ad acquistare i 4 gradi di freddezza tol­<lb></lb>tigli dal sole; onde, di 6 che ella ne aveva innanzi, si riduce ad un tratto <lb></lb>ad averne 10. Sicchè colui che si bagna non sente più 6 gradi di freddezza <lb></lb>ma 10, e perciò, mentre sta sotto l&#039;albero bagnato, sente freddo estremo, <lb></lb>ma se si torna poì a tuffarsi entra nell&#039;acqua che ha 6 gradi soli di fred­<lb></lb>dezza, onde, perdendo 4 gradi di freddo, gli pare di essere entrato in un <lb></lb>bagno temperato ” (MSS. Gal., P. VI, T. III, c. </s>

<s>29). </s></p><p type="main">

<s>Essendo falso il principio da cui muove, è naturale che fosse falso que­<lb></lb>sto discorso di Galileo, nel suo processo e nella sua conclusione. </s>

<s>Ad accor­<lb></lb>gersi della qual falsità e a palesarla al mondo par che fosse primo Tom­<lb></lb>maso Cornelio, il quale così in un suo Proginnasma dice del principio <lb></lb>galileiano, che ammette l&#039;acqua insolata ritener maggior freddezza dell&#039;aria <lb></lb>circunfusa: “ Atqui de hoc fortasse quis ambiget qui observaverit aquam <lb></lb>immobilem aestivo soli diutius expositam maiori calore tangendi sensum ef­<lb></lb>ficere quam circumpositum aerem. </s>

<s>At vero in aqua, cuius natura crassior <lb></lb>est, calor a sole excitatus magis intenditur quam in aere, qui est natura <lb></lb>tenuior, et perpetua mobilitate rarius suique dissimilis ” (Oper. </s>

<s>posth., <lb></lb>Neap. </s>

<s>1688, pag. </s>

<s>38). </s></p><p type="main">

<s>Perciò, mettendosi il Cornelio a risolvere quello stesso problema, e stu­<lb></lb>diandosi di cansar le false vie tenute da Galileo, assume per fondamento <lb></lb>del suo discorso un fatto sperimentale, ch&#039;è pure anch&#039;esso manifestamente <lb></lb>falso. </s>

<s>Il fatto è che l&#039;acqua nell&#039;aria rarefatta si riscalda, e nella compressa <pb xlink:href="020/01/693.jpg" pagenum="136"></pb>e condensata si raffredda, <emph type="italics"></emph>quod nos,<emph.end type="italics"></emph.end> afferma l&#039;Autore, <emph type="italics"></emph>comparata ad id <lb></lb>opus peculiari machina quotidie experimur<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>36). </s></p><p type="main">

<s>Quella Macchina dee esser senza dubbio la Pneumatica, e il Cornelio <lb></lb>dee esser rimasto certamente ingannato da quell&#039;effetto maraviglioso descritto <lb></lb>già dal Boyle, dell&#039;acqua tiepida che, nel vuoto o nell&#039;aria molto rarefatta, <lb></lb>si leva a bollore. </s>

<s>I nostri Accademici del Cimento però s&#039;erano sgannati <lb></lb>aprendo la palla del vuoto torricelliano, e cavandone fuori il vasetto del­<lb></lb>l&#039;acqua, alla quale <emph type="italics"></emph>non parve che da tal bollimento se le fosse accresciuto <lb></lb>calore<emph.end type="italics"></emph.end> (Saggi ecc., Firenze 1841, pag. </s>

<s>64). Che se anzi avessero con più di­<lb></lb>ligenza osservato si sarebbe in essi accresciuta la maraviglia, ritrovando che <lb></lb>in que&#039;casi la temperatura invece diminuisce, come pure si sarebbe il Cor­<lb></lb>nelio persuaso con facilissima esperienza che in ogni compressione e nella <lb></lb>percossa, di che offrono così ovvii esempi i martelli, i corpi tutt&#039;altro che <lb></lb>raffreddarsi acquistan calore. </s>

<s>Comunque sia, l&#039;Autor de&#039;Proginnasmi profes­<lb></lb>sando dottrine in aperta contradizione de&#039;fatti, asserisce che il freddo sen­<lb></lb>tito da chi si espone colla pelle umida al vento dipende da ciò, che il vento <lb></lb>stesso percotendo e comprimendo rintuzza il moto agl&#039;ignicoli che, rimasti <lb></lb>li inerti, vi producono perciò il senso della freddezza. </s></p><p type="main">

<s>“ Ex his ut arbitror perspicuum videri potest cur aestatis tempore la­<lb></lb>vaturi ut primum nudati corpore in maris aut fluminis aquas quamquam <lb></lb>calore solis quodammodo tepefactas merguntur, statim molesto frigoris sensu <lb></lb>afficiantur: mox autem brevi mora interposita suaviter degant. </s>

<s>At interea <lb></lb>si humentia membra supra aquas exerant, vel in litus ripamve exiliant, rur­<lb></lb>sus novo ingratoque frigore corripiuntur. </s>

<s>Verum ad easdem subinde aquas <lb></lb>reversi, iucundo quodam teporis sensu recreari videantur. </s>

<s>Nimirum quo­<lb></lb>tiescumque aestuantes aquas minus calidas subeunt, frigoris sensum perci­<lb></lb>piunt, donec infracto caloris excessu eorumdem corpora cum contiguis aquis <lb></lb>aequaliter temperentur: tum vero cessat frigoris sensus. </s>

<s>Sed ubi primum <lb></lb>ex aquis madentes fuerint egressi, quoniam circumfusus corpori humor a <lb></lb>quovis vento aurave protinus frigescit, subiti frigoris molestiam perpetiun­<lb></lb>tur. </s>

<s>Neque vero id unquam solet contingere nisi ubi madens corpus ventus <lb></lb>aliquis perflaverit ” (ibi, pag. </s>

<s>37). </s></p><p type="main">

<s>Così il Problema del conte Bardi non riusciva ancora ben risoluto, spe­<lb></lb>cie per quel che riguarda la seconda parte, essendo chiaro che sempre si <lb></lb>sente freddo alle membra umide esposte anco all&#039;aria quietissima, come sa­<lb></lb>rebbe nel chiuso di una stanza. </s></p><p type="main">

<s>Giuseppe Del Papa saviamente avendo riconosciuto quello essere un pro­<lb></lb>blema di Termometria, ricorse all&#039;uso degli strumenti, e benchè anche il <lb></lb>Cornelio avesse giudicato dall&#039;impressione subiettiva del senso non esser al­<lb></lb>trimenti vero l&#039;assunto di Galileo, che cioè l&#039;acqua sia più fredda dell&#039;aria <lb></lb>circunfusa; ei fu nonostante il primo a farne esperienze nell&#039;Arno co&#039;ter­<lb></lb>mometri fiorentini. </s>

<s>“ Ella supponga dunque (così scriveva al Redi nella Let­<lb></lb>tera dell&#039;Umido e del Secco) per cosa infallibile e da me più e più volte <lb></lb>ed in varie guise esperimentata, che ogni sorta d&#039;acqua tenuta al sole per <pb xlink:href="020/01/694.jpg" pagenum="137"></pb>una considerabile lunghezza di tempo, si riscalda assai più ed in sè stessa <lb></lb>ritiene maggior caldezza di quella che si ritenga dall&#039;aria, la quale sia stata <lb></lb>per altrettanto e più tempo esposta ai medesimi raggi solari ” (Firenze 1681, <lb></lb>pag. </s>

<s>89). </s></p><p type="main">

<s>Dietro questo infallibile supposto e dietro la considerazione dell&#039;aria, <lb></lb>che è a contatto della pelle ignuda attemperata al calor naturale esalato da <lb></lb>lei, rimossa la quale aria ne sottentra altra in suo luogo, che sottraendo <lb></lb>nuovo calor al contatto è causa del refrigerio prodotto dal vento; il Del Papa <lb></lb>scioglie così concludendo la prima parte del proposto problema: “ Insomma <lb></lb>evidente cosa è che l&#039;acqua d&#039;Arno, benchè in realtà sia notabilmente più <lb></lb>calda dell&#039;aere, ci apparisce fredda nel primo ingresso, perchè toglie da noi <lb></lb>quel nostro proprio vapore ed in questo caso l&#039;acqua fa l&#039;opra istessa che <lb></lb>ci fa in aria il vento, il quale parimente, perchè lungi da noi sospinge l&#039;aria <lb></lb>dalla nostra esalazione riscaldata, e in luogo di quella ci porta attorno altra <lb></lb>ed altra aria; perciò viene a privarci di una parte di caldo, ed in tal guisa <lb></lb>apportarci refrigerio e freddezza ” (ivi, pag. </s>

<s>91). </s></p><p type="main">

<s>Quanto al secondo effetto poi preso a spiegare dal Galileo, cioè che <lb></lb>dopo esserci noi trattenuti nell&#039;acqua, se ritorniamo nell&#039;aria sentiamo un <lb></lb>freddo molto notabile, dimodochè allora l&#039;acqua ci sembra assai più calda <lb></lb>dell&#039;aria; “ di tutto ciò, soggiunge il Del Papa, evidentissima cagione si è <lb></lb>l&#039;eccesso della caldezza con cui in realtà l&#039;acqua supera e vince l&#039;aere, onde <lb></lb>uscendo d&#039;un mezzo più caldo di quello nel quale entriamo novellamente, <lb></lb>dobbiamo bene per necessità sentir freddo, non essendo altro il freddo che <lb></lb>mancanza o scemamento di caldo ” (ivi, pag. </s>

<s>92). </s></p><p type="main">

<s>Nemmen questa, benchè fosse la miglior soluzione che si potesse a <lb></lb>que&#039;tempi dare al Problema, sodisfece poi pienamente agl&#039;ingegni, i quali <lb></lb>trovarono più opportuno d&#039;applicarvi la teoria del calorico latente, oggidì <lb></lb>levata anch&#039;essa di seggio da nuove altre teorie. </s>

<s>Perciò bastando allo scopo <lb></lb>nostro di aver mostrato a quali gradi fosse giunto il processo di questo ge­<lb></lb>nere di speculazioni termiche, in sulla fine del secolo XVII, le ultime pa­<lb></lb>role sopra citate da Giuseppe Del Papa ci aprono la via alla storia di una <lb></lb>questione, che se non è per sè di grande importanza serve pure a dichia­<lb></lb>rar meglio il soggetto che abbiamo preso a trattare. </s></p><p type="main">

<s>Diceva dianzi l&#039;Autor della Lettera al Redi nient&#039;altro essere il freddo <lb></lb>che <emph type="italics"></emph>mancanza<emph.end type="italics"></emph.end> o <emph type="italics"></emph>scemamento di caldo:<emph.end type="italics"></emph.end> sentenza che sebbene sia oggidì <lb></lb>da tutti senza controversia tenuta per vera, fu nonostante a&#039;tempi del Del <lb></lb>Papa, specialmente in Firenze, assai disputata. </s>

<s>La disputa ebbe origine dal <lb></lb>Gassendo, il quale, nelle sue <emph type="italics"></emph>Animadversiones in Decimum Librum Dio­<lb></lb>genis Laertii,<emph.end type="italics"></emph.end> rinnovando gli antichi placiti filosofici di Epicuro, professava <lb></lb>che come il caldo è prodotto dagli atomi ignei, così il freddo è prodotto da <lb></lb>altri atomi di natura opposta, e ch&#039;egli perciò appella frigorifici. </s>

<s>Quegli atomi <lb></lb>son di necessità in continua lotta fra loro e ora vincono gli uni, ora vin­<lb></lb>cono gli altri, per cui si vede un corpo, con ripetuta incessante vicenda, <lb></lb>passare dal freddo al caldo e dal caldo al freddo. </s></p><pb xlink:href="020/01/695.jpg" pagenum="138"></pb><p type="main">

<s>“ Atque ex his demum (scrive il Gassendo nel vol. </s>

<s>I dell&#039;opera citata) <lb></lb>intelligitur dum quaerunt vulgo an frigus sit qualitas vera et positiva, an <lb></lb>mera caloris privatio. </s>

<s>Videri omnino esse frigus veram et positivam quali­<lb></lb>tatem eo modo quo calor et caeterae sunt. </s>

<s>Tametsi enim multa videantur <lb></lb>ex sola caloris absentia frigescere, nihilominus, nisi frigus extrinsecus intro­<lb></lb>ducatur, non tam profecto frigescere quam decalescere sunt censenda. </s>

<s>Esto <lb></lb>enim lapis, lignum aut aliquid aliud, quod nec calidum nec frigidum sit: id <lb></lb>ubi fuerit admotum igni calefiat sane at cum deinceps calor excedet, neque <lb></lb>frigidum ullum circumstabit, non erit cur dicas ipsum frigefieri, potius quam <lb></lb>minus calidum fieri redireve in suum statum. </s>

<s>Profecto ii sunt frigoris ef­<lb></lb>fectus qualeis habere privatio, quae actionis est incapax, non potest. </s>

<s>Siqui­<lb></lb>dem cum per hyemem immittimus manum in labentem fluminis aquam, quod <lb></lb>frigus in ea sentitur non potest dici mera privatio, aliudque prorsus esse ap­<lb></lb>paret sentiri aquam frigidam et sentiri non calidam ” (Lugduni 1675, pag. </s>

<s>176). </s></p><p type="main">

<s>Il Gassendo fu filosofo a&#039;suoi tempi di gran reputazione, per cui le rin­<lb></lb>novate dottrine di lui si diffusero nell&#039;universale degli scienziati, come lo <lb></lb>prova il fatto che dal 1646 al 1675 furon fatte, delle <emph type="italics"></emph>Animadversiones in <lb></lb>X Laertii,<emph.end type="italics"></emph.end> tre edizioni, e si diffusero particolarmente fra&#039;nostri Accademici <lb></lb>del Cimento, come si vede qua e là dalle citazioni de&#039;<emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> e più frequen­<lb></lb>temente da quelle de&#039;Manoscritti. </s></p><p type="main">

<s>Professando così i Nostri dottrine introdotte da uno straniero non so­<lb></lb>spettavano di contrapporsi agli insegnamenti di Galileo, i quali intorno a <lb></lb>questo proposito, oltre ad essere scarsi, apparivano alquanto dubbiosi. </s>

<s>Seb­<lb></lb>bene infatti così concluda la ragion dell&#039;operare del Termometro ad aria: <lb></lb><emph type="italics"></emph>onde ne segue che il freddo non sia altro che privazione di caldo<emph.end type="italics"></emph.end> (Alb. </s>

<s><lb></lb>XIV, 334), nel risolver poi il Problema del conte Bardi par che ammetta il <lb></lb>freddo positivo, e come il caldo stesso misurabile in gradi. </s>

<s>Questi dubbii <lb></lb>però veniva a toglierli di mezzo il priore Orazio Ricasoli-Rucellai, il quale <lb></lb>gloriandosene affermava di avere <emph type="italics"></emph>visitato nella sua villa d&#039;Arcetri e udito <lb></lb>più e più volte discorrere Galileo Galilei<emph.end type="italics"></emph.end> di questo soggetto, e di avergli <lb></lb>sentito dire: “ che il freddo non sia veramente cosa positiva nella natura, <lb></lb>ma solamente privazione del caldo e che però non abbia per sè moto ed <lb></lb>azione ” (Prose e rime, Firenze 1822, pag. </s>

<s>60, 62). </s></p><p type="main">

<s>Perciò il Rucellai acceso di patrio zelo pretendeva che i suoi Fiorentini <lb></lb>disertassero dalle bandiere francesi del Gassendo, per tornare a ricoverarsi <lb></lb>sotto quelle di Galileo. </s>

<s>S&#039;incontra una mattina con Carlo Dati nel cortile <lb></lb>del palazzo Pitti, e gli entra all&#039;improvviso di questo freddo epicureo gas­<lb></lb>sendistico, giurandogli sulla fede di Galileo ch&#039;egli era una mera privazione, <lb></lb>e perciò un nulla. </s>

<s>Il Dati per l&#039;appunto aveva allora l&#039;appalto del Ghiac­<lb></lb>cio, e a sentir ch&#039;e&#039;pagava per nulla e ch&#039;e&#039;vendeva il nulla, sbalordito <lb></lb>prega il Priore che ci pensi un po&#039;meglio, perchè quella era una tal Filo­<lb></lb>sofia da rovinarlo. </s>

<s>La storia ha del comico, ma è pur così come il Dati la <lb></lb>scrisse di sua propria mano: </s></p><p type="main">

<s>“ Se io devo parlare alla libera, o signor Priore, l&#039;altra mattina io re-<pb xlink:href="020/01/696.jpg" pagenum="139"></pb>stai sbalordito, quand&#039;ella mi affrontò nel cortile del Palazzo, e mi domandò <lb></lb>all&#039;improvviso quel ch&#039;io sentivo di que&#039;cosi che V. S. chiama <emph type="italics"></emph>atomi frigo­<lb></lb>rifici<emph.end type="italics"></emph.end> e del freddo positivo, perchè non solamente non intesi lisca quant&#039;ella <lb></lb>mi diceva, ma mi messi nel capo di non poterla mai intendere, onde la prego <lb></lb>a perdonarmi se non le risposi nè bene nè male, e mi fuggii come se io <lb></lb>avessi avuto i birri dietro. </s>

<s>Ma poi avendovi dormito sopra, conobbi che que­<lb></lb>sta sua Filosofia non è tanto strana cosa quant&#039;io mi credevo, e quanto certi <lb></lb>la fanno per tenerla in reputazione, e però mi sono ardito di scriverle il <lb></lb>mio parere così alla buona. </s>

<s>” </s></p><p type="main">

<s>“ In conclusione e&#039;mi pare che V. S. voglia sapere da me se vera­<lb></lb>mente il freddo è qualche cosa effettiva oppure un nulla, cioè uno sperpe­<lb></lb>ramento, un totale scacciamento del caldo, e dico che, secondo il mio poco <lb></lb>sapere il freddo è qualche cosa, e certo s&#039;e&#039;non fosse qualche cosa, non mi <lb></lb>toccherebbe a pagare parecchi centi di scudi per avere l&#039;appalto del nulla, <lb></lb>nè la gente verrebbe a comperare da me una cosa che non è, nè del niente <lb></lb>farebbero tanto schiamazzo queste putte scodate de&#039;cortigiani quando non <lb></lb>l&#039;hanno. </s>

<s>Però, signor Priore, di grazia V. S. studii bene questo punto prima <lb></lb>di risolvere che il freddo non sia cosa alcuna, perch&#039;ella sarebbe la mia ro­<lb></lb>vina, e si compiaccia di ascoltare queste mie ragioni quali elle sono ” (MSS. <lb></lb>Cim., T. XXXIV, c. </s>

<s>32). </s></p><p type="main">

<s>Le ragioni che prosegue a esporre qui il Dati son quelle stesse in suc­<lb></lb>cinto che si leggono nell&#039;Opuscolo di Plutarco <emph type="italics"></emph>De primo frigido:<emph.end type="italics"></emph.end> e anzi, <lb></lb>non essendo a quel tempo nota la bella traduzione che ne aveva fatta Mar­<lb></lb>cello Adriani, inserita poi da pag. </s>

<s>379-403 del Tomo V insieme con gli altri <lb></lb>Opuscoli del Filosofo greco, pubblicati in Milano, dopo il primo ventennio <lb></lb>di questo presente secolo da Francesco Ambrosoli; il Dati stesso aveva fatto <lb></lb>pensiero di pigliare occasione dal tradurre il detto Opuscolo <emph type="italics"></emph>Del freddo <lb></lb>principale,<emph.end type="italics"></emph.end> per aggiungervi le speculazioni sue proprie. </s>

<s>Ciò rilevasi da que­<lb></lb>sta nota autografa, che segue alla sopra citata Lettera indirizzata al prior <lb></lb>Rucellai: “ Del Freddo positivo e privativo vedi l&#039;Opuscolo di Plutarco <emph type="italics"></emph>De <lb></lb>primo frigido,<emph.end type="italics"></emph.end> che altro non è che una prova del freddo positivo o priva­<lb></lb>tivo: questo mi parrebbe bene tradurre in toscano, e con occasione di esso <lb></lb>soggiungere quanto è da dirsi in questa materia ” (ivi, c. </s>

<s>35). </s></p><p type="main">

<s>L&#039;argomento principale addotto da Plutarco a provare l&#039;assunto di quei <lb></lb>Filosofi di cui riferisce l&#039;opinione, si riduceva a dire ch&#039;essendo il freddo un <lb></lb>agente operativo di tali e tali altri effetti, come il caldo, non poteva essere <lb></lb>perciò una semplice privazione. </s>

<s>“ Ma se nella guisa che il caldo per la te­<lb></lb>pidezza e rarità del corpo si sente, così parimente il freddo per lo stringi­<lb></lb>mento e la condensazione dell&#039;istesso si fa sentire; già si vede che siccome <lb></lb>il caldo così il freddo ha il suo proprio principio e il suo fonte ” (Opusc. </s>

<s><lb></lb>cit., T. V, Milano 1829, pag. </s>

<s>382). Passando poi a considerar la natura delle <lb></lb>vere privazioni, come per esempio del silenzio, ch&#039;è privazione della voce o <lb></lb>de&#039;suoni, il Filosofo cheronese conclude: “ Par dunque che il freddo sia <lb></lb>simile a tali privazioni e che non disponga altrimenti? </s>

<s>Anzi per lo contra-<pb xlink:href="020/01/697.jpg" pagenum="140"></pb>rio molti i gran piaceri sono dal freddo cagionati al corpo, e molti danni, <lb></lb>dolori e gravezze ” (ivi). </s></p><p type="main">

<s>Quel che poi intendeva di aggiungere il Dati a così fatti argomenti di <lb></lb>ragione, consisteva in esperienze da farsi, dell&#039;opportunità delle quali e della <lb></lb>loro concludenza giudicheranno, dalla seguente nota autografa, i nostri Let­<lb></lb>tori: “ Osservisi se lo Strumentino del caldo e del freddo nel massimo freddo <lb></lb>sale o no, e questo non solo nell&#039;inverno, ma con diaccio e salnitro e sale <lb></lb>e freddo veemente. </s>

<s>Notisi se posto in tal freddo lo Strumento scoppia come <lb></lb>fa col gran caldo. </s>

<s>Pongasi la palla di rame o di oro per la esperienza della <lb></lb>compressione anche nell&#039;acqua bollentissima per molto tempo, e veggasi <lb></lb>quello fa, e se l&#039;acqua scemi per trasudazione, che si conoscerà nell&#039;agi­<lb></lb>tarla. </s>

<s>La medesima si ponga a diacciare nel diaccio, salnitro, ecc., e se ne <lb></lb>osservi l&#039;effetto ” (MSS. Cim., T. XXXIV, c. </s>

<s>36). </s></p><p type="main">

<s>Mentre che il Dati meditava così fra sè queste cose, il prior di Firenze <lb></lb>che aveva bene ripensato al fatto suo, attendeva a scrivere un <emph type="italics"></emph>Discorso con­<lb></lb>tro il freddo positivo,<emph.end type="italics"></emph.end> che ne&#039;primi giorni dell&#039;Aprile 1666 lesse in Firenze, <lb></lb>in una solenne adunanza accademica, alla presenza del cardinal Delfino e <lb></lb>del principe Leopoldo. </s>

<s>Il moto, secondo l&#039;Autore, è l&#039;effetto del fuoco e <lb></lb>l&#039;inerzia è la natura del freddo (Prose e rime cit., pag. </s>

<s>64, 65). La nostra <lb></lb>sensazione è quella, la quale piglia le sue misure dal caldo e dal freddo, <lb></lb>non da un freddo assoluto da sè, ma dalla comparazione per rispetto al più <lb></lb>caldo (pag. </s>

<s>69). L&#039;argomento di Plutarco che cioè la privazione non operi <lb></lb>cosa che sia non vale, essendochè un nulla è solamente il vuoto, e il buio <lb></lb>per esempio contiene corpiccioli ch&#039;empiono quegli spazi, senza mescola­<lb></lb>mento di corpi lucidi (pag. </s>

<s>71). Nè è poi vero che il freddo e il caldo sieno <lb></lb>contrarii assoluti, come pure così contrarii non sono, come dicono gli av­<lb></lb>versarii, l&#039;acqua e il fuoco, conciossiachè e&#039;non potrebbero mai accozzarsi <lb></lb>insieme (pag. </s>

<s>78). Conclude all&#039;ultimo il verboso Discorso: “ Che il moto <lb></lb>anzi sia effetto che cagione del caldo, e che siccome questo non si trova <lb></lb>salvo che nelle nostre sensazioni per lo sfregamento con esso le parti sen­<lb></lb>sibili; così quello fuori del fuoco non avere veruna agitazione per sè, e che <lb></lb>per l&#039;opposito infingardo e senza movimento sia il freddo, il quale in qua­<lb></lb>lunque altra cosa risegga che non abbia mischianza col fuoco. </s>

<s>Con tal sup­<lb></lb>posto dunque io reputo più agevole di credere che anche tutte le azioni e <lb></lb>movimenti, che ci paion nel freddo o dal freddo, da impulsi invisibili deri­<lb></lb>varsi del caldo, e dove faville o corpuscoli di fuoco non sono, tutto esser <lb></lb>freddo, senza che di questo ci sia veruna sostanza speciale da se nè atomi <lb></lb>frigorifici fatti apposta dalla Natura per ciò, come i calorifici ci sono, e però <lb></lb>conchiudo altro non essere il freddo che privazione del caldo ” (pag. </s>

<s>94). </s></p><p type="main">

<s>Dall&#039;eloquenza però del gran prior di Firenze non par che il Dati re­<lb></lb>stasse persuaso, ma perchè forse comprendeva bene che alle due parti man­<lb></lb>cava a que&#039;tempi la scienza necessaria a risolvere la questione, che sareb­<lb></lb>besi, come tant&#039;altre, noiosamente prolungata in parole; a volger la cosa in <lb></lb>scherzo s&#039;aggiunse a lui il Magalotti. </s>

<s>Chi vuole, vada a carte 38 del citato <pb xlink:href="020/01/698.jpg" pagenum="141"></pb>Manoscritto e vi leggerà autografa una Lettera del Dati firmato <emph type="italics"></emph>Rovaio.<emph.end type="italics"></emph.end> “ Al <lb></lb>freddissimo, rigidissimo, grandinevoso e tre volte agghiacciato Lorenzo Ma­<lb></lb>galotti, scitico, caucaseo, islandico, Re degl&#039;Iperborei, Monarca de&#039;Rifei, Si­<lb></lb>gnor delli Appennini, Principe del Mar gelato, Imperator dell&#039;inverno, difen­<lb></lb>sore, inventor della gelatina, restauratore, mantenitore degli atomi frigorifici. </s>

<s>” <lb></lb>E ivi pure da c. </s>

<s>39-41, troverà la risposta, pur essa autografa di “ Lorenzo <lb></lb>Magalotti, per la Dio grazia, Imperator dell&#039;Inverno, Monarca della Gelatina, <lb></lb>restauratore, mantenitore, difensore degli atomi frigorifici ” data “ Nella no­<lb></lb>stra regal Ghiacciaia dal punto polare, la Notte della gran freddura. </s>

<s>” </s></p><p type="main">

<s>Noi, lasciando lo scherzare a chi piace e tornando alle cose serie, di­<lb></lb>ciamo che sotto quella nota a c. </s>

<s>35, nella quale il Dati scriveva di voler <lb></lb>tradurre l&#039;Opuscolo di Plutarco <emph type="italics"></emph>De primo frigido,<emph.end type="italics"></emph.end> e di li cogliere l&#039;occa­<lb></lb>sione a svolgere più ampiamente la materia, d&#039;altra mano a noi ignota è <lb></lb>soggiunto: “ Quello che voleva fare C. D. (Carlo Dati) l&#039;adempì quasi ne&#039;me­<lb></lb>desimi tempi il signor Giuseppe Del Papa. </s>

<s>È ben vero che tiene l&#039;opìnione <lb></lb>contraria e la prova con saldissimi argomenti e con esperienze irrefragabili; <lb></lb>è ben vero che ci sarebbe molto da poter aggiungere.... ” </s></p><p type="main">

<s>Giuseppe Del Papa pubblicava nel 1674 in Firenze una lettera <emph type="italics"></emph>Intorno <lb></lb>alla natura del caldo e del freddo,<emph.end type="italics"></emph.end> scritta a Francesco Redi, nella quale <lb></lb>compensavasi largamente la dimenticanza, in che giaceva oramai il Discorso <lb></lb>manoscritto d&#039;Orazio Ricasoli-Rucellai, edito nel 1822 dall&#039;erudito Moreni. </s>

<s><lb></lb>La principale intenzione de&#039;due Autori è la stessa, ed è quella di dimostrar <lb></lb>la verità delle dottrine professate da Galileo. </s>

<s>Ma pur troppo anche il Del <lb></lb>Papa affoga in un mar d&#039;artificiose parole i concetti, e le argute esperienze <lb></lb>non concludono, perch&#039;erano anco a lui ignoti i fatti da cui poi la Termo­<lb></lb>metria piglierebbe i principii. </s></p><p type="main">

<s>Fra l&#039;esperienze però del Del Papa e di tutti coloro che si propone­<lb></lb>vano di dimostrare esser falsa la dottrina del freddo positivo, non ve ne ha <lb></lb>una che per la novità e per la raffinatezza si possa assomigliare a quella <lb></lb>immaginata e praticata da Carlo Rinaldini. </s>

<s>Un corpo caldo, ragionava egli, <lb></lb>collocato di faccia a uno specchio concavo, rende più intensa la sua azione <lb></lb>sullo spirito di vino (passum) chiuso nel Termometro: così pure un pezzo <lb></lb>di ghiaccio dovrebbe dimostrare maggiore intensità del suo freddo, ma fatta <lb></lb>l&#039;esperienza, dice il Rinaldini, non se ne vide l&#039;effetto. </s>

<s>“ Inditium porro in <lb></lb>eo positum quod per speculum concavum reflexis radiis calor in Passo ap­<lb></lb>posite applicato potest iutendi, ut constat cum illud solaribus radiis expo­<lb></lb>nitur, eousque calor enim intenditur, ut ignis etiam procreetur. </s>

<s>At eiusdem <lb></lb>speculi expositione facta ad frigidissimum corpus, cuiusmodi est glacies, in <lb></lb>Passo quantumvis, ut par est, applicato, frigiditatis nunquam incrementum <lb></lb>experti sumus ” (Philos. </s>

<s>ration., Paravii 1681, pag. </s>

<s>320). </s></p><p type="main">

<s>Se fosse stato il Rinaldini in sperimentare più destro, o se avesse avuto <lb></lb>il Termometro più geloso, avrebbe dovuto avvertire, con sua gran sorpresa, <lb></lb>che anzi il ghiaccio dava manifesto indizio di calore piuttosto che di freddo. </s>

<s><lb></lb>Sarebbe di qui uscita più concludente la sua dimostrazione, e l&#039;effetto straor-<pb xlink:href="020/01/699.jpg" pagenum="142"></pb>dinario, ch&#039;egli sarebbe stato il primo ad osservare, lo avrebbe anche reso <lb></lb>il primo abile a risolver la controversia che, ne&#039;termini in ch&#039;erasi posta in <lb></lb>campo, riusciva interminabile. </s>

<s>Considerando bene, infatti, tutto il nodo s&#039;an­<lb></lb>dava ad aggroppar nel ghiaccio, in cui i seguaci dell&#039;opinione di Galileo cre­<lb></lb>devano che gl&#039;ignicoli fossero spenti del tutto, e che fosse il ghiaccio stesso, <lb></lb>come direbbero i Fisici odierni, della scala termometrica lo zero assoluto. </s>

<s><lb></lb>Così riducevansi nell&#039;impossibilità di spiegare alcuni fatti da loro stessi os­<lb></lb>servati, come sarebbe che <emph type="italics"></emph>l&#039;aria freddissima per tramontana è più fredda <lb></lb>del ghiaccio e della neve,<emph.end type="italics"></emph.end> fatto sperimentato da Galileo (Alb. </s>

<s>XIV, 334) col <lb></lb>Termometro alla mano. </s>

<s>Il Viviani pure argomentava che <emph type="italics"></emph>l&#039;aria può venire <lb></lb>in stato d&#039;assai maggior freddezza del medesimo ghiaccio,<emph.end type="italics"></emph.end> dal veder che <lb></lb><emph type="italics"></emph>ne&#039;freddi dell&#039;inverno l&#039;acqua ghiaccia nell&#039;aria e non ghiaccia nel ghiac­<lb></lb>cio<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>5). Di questi fatti sperimentati nè Ga­<lb></lb>lileo nè il Viviani potevano ritrovar la ragione nei loro principii, mentre ve <lb></lb>la trovavano chiarissima i Gassendisti, dicendo che l&#039;aria fredda per tramon­<lb></lb>tana è invasa da più gran numero di atomi frigorifici, dì quel che non sia <lb></lb>lo stesso ghiaccio. </s></p><p type="main">

<s>E che cosa poteva ragionevolmente rispondere il Rinaldini al Gassendo, <lb></lb>il quale diceva che le privazioni non son capaci d&#039;effetti reali? </s>

<s>Se fosse riu­<lb></lb>scito a veder nel ghiaccio gli effetti del calore la risposta l&#039;avrebbe avuta <lb></lb>pronta e verissima, dicendo che anche il freddo stesso prodotto da&#039;miscu­<lb></lb>gli frigorifici è operativo de&#039;suoi effetti, dipendenti dal calore che pur in essi <lb></lb>risiede, benchè ridotto a così minimi gradi. </s>

<s>Ma non poteva il Rinaldini altro <lb></lb>concludere da quella sua esperienza ingegnosissima sì, ma rimasta sventu­<lb></lb>ratamente imperfetta, se non che il freddo rimasto nel ghiaccio è un&#039;asso­<lb></lb>luta privazion del calore e in altri termini un nulla. </s></p><p type="main">

<s>La questione insomma agitata in Firenze a proposito del freddo o po­<lb></lb>sitivo o privativo fecero bene il Magalotti e il Dati a volgerla in scherzo e <lb></lb>finirla, perchè non si poteva risolvere co&#039;principii della Termometria pro­<lb></lb>fessati a que&#039;tempi. </s>

<s>I moderni insegnano il freddo non essere positivo ma <lb></lb>una privazione o diminuzione del calore come dicevano il Rucellai e il Del <lb></lb>Papa, ma pigliano il fondamento alle loro dottrine da un principio che nel <lb></lb>secolo XVII sarebbe sembrato strano. </s>

<s>Quel principio è che nessun corpo, <lb></lb>qualunque sia il senso o l&#039;apparente effetto della sua freddezza, è privo af­<lb></lb>fatto di calore. </s>

<s>Un tal principio poi ch&#039;è verissimo non si salva altrimenti <lb></lb>che per la teoria dinamica perchè un atomo di materia senza calore sarebbe <lb></lb>un atomo senza moto, e perciò senz&#039;essere e senza vita. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La questione del freddo positivo o privativo, forse perchè vi presero <lb></lb>gran parte il Magalotti e il Dati, fu creduto che s&#039;agitasse nell&#039;Accademia <lb></lb>del Cimento, e poniamo che qualche poco pure vi se ne discorresse e spe-<pb xlink:href="020/01/700.jpg" pagenum="143"></pb>rimentasse (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>578), è certo però che <lb></lb>il Rucellai lesse il suo <emph type="italics"></emph>Discorso<emph.end type="italics"></emph.end> in un&#039;altra Accademia, i socii della quale <lb></lb>attendevano, non a discutere intorno alla verità delle cose naturali, ma in­<lb></lb>torno alla proprietà delle parole toscane. </s>

<s>Quel che del calore fu trattato nella <lb></lb>fiorentina Accademia Sperimentale non è pubblicamente noto, se non da quel <lb></lb>che se ne legge nel libro de&#039;<emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> d&#039;onde s&#039;inferirebbe che ivi, lasciate <lb></lb>addietro le ipotesi argute e le sottili speculazioni, non si badasse ad altro <lb></lb>che a sincerarsi de&#039;fatti. </s>

<s>Ma benchè evitassero da savi, per le ragioni già <lb></lb>dette, d&#039;entrar nella questione in che voleva tirarli il Rucellai, non è per <lb></lb>questo che, tutti intenti i nostri Accademici a sperimentare, trascurassero o <lb></lb>reputassero inutile e spregevole cosa lo speculare. </s>

<s>Vero è bene che così fatte <lb></lb>speculazioni, dovute principalmente al Viviani e al Borelli, rimasero per la <lb></lb>massima parte sconosciute, ond&#039;è che non riuscirà forse discaro ai lettori il <lb></lb>proposito nostro di far qui di quelle stesse speculazioni particolare soggetto <lb></lb>storico. </s></p><p type="main">

<s>A saper solamente che si tratta dell&#039;Accademia del Cimento e del Vi­<lb></lb>viani, si giurerebbe che le opinioni ivi seguitate intorno all&#039;essere e alla na­<lb></lb>tura del calore son quelle stesse pure e prette già professate da Galileo. </s>

<s>A <lb></lb>confermar che giurerebbesi il vero, ecco infatti rappresentarsi a&#039;nostri oc­<lb></lb>chi una scrittura dello stesso Viviani, che ha per titolo: <emph type="italics"></emph>Opinione di De­<lb></lb>mocrito circa il modo che tiene il fuoco nello scaldare.<emph.end type="italics"></emph.end> In essa non ha <lb></lb>l&#039;Autore altra intenzione che di esplicare i concetti galileiani espressi nella <lb></lb><emph type="italics"></emph>Risposta a Lodovico delle Colombe,<emph.end type="italics"></emph.end> e di salvar quegli stessi concetti da ogni <lb></lb>attentato di straniere aggressioni, come ognuno vedrà che qui appresso <lb></lb>legge: </s></p><p type="main">

<s>“ Tra gli effetti maravigliosissimi della Natura, la quale in tutte le cose <lb></lb>ci si mostra sempre miracolosa, uno per certo ve ne ha non men utile che <lb></lb>curioso, e questo è come il fuoco introdur possa così violentemente e facil­<lb></lb>mente in un corpo, anco da lui per qualche spazio di braccio distante, il <lb></lb>calore, ed anco, se sarà in gran quantità, l&#039;abbruciamento. </s>

<s>Sopra cotal ef­<lb></lb>fetto, come all&#039;umano intendimento molto recondito, filosofarono non pochi <lb></lb>desiderosi d&#039;intendere, in questo gran Libro del Mondo tutto ripieno di ma­<lb></lb>raviglie, qualche piccola particolarità per capacitarne l&#039;intelletto. </s>

<s>Fra&#039;quali <lb></lb>lasciò scritto Democrito che il fuoco, facendo una vastissima e numerosis­<lb></lb>sima espansione de&#039;corpuscoli ignei, i quali, penetrando in un corpo, se­<lb></lb>condo l&#039;attività o quantità, lo riscaldano o l&#039;abbruciano. </s>

<s>Per lo che, giun­<lb></lb>gendo questi tali corpuscoli alla testura della nostra pelle, essendo di tal <lb></lb>figura atta facilmente alla penetrazione, penetrano a poco a poco nel nostro <lb></lb>corpo, facendoci nel primo moto sentire quello che noi chiamiamo calore: <lb></lb>accrescendosi poi e la velocità e la quantità delle medesime particelle o cor­<lb></lb>puscoli, si va crescendo la sensazione o calore generando prima lo scotta­<lb></lb>mento, e poi l&#039;arsione. </s>

<s>” </s></p><p type="main">

<s>“ In confermazione di che può addursi una esperienza molto esatta. </s>

<s><lb></lb>Piglisi una boccia o caraffa con il collo molto lungo e stretto, la quale v. </s>

<s>g. <pb xlink:href="020/01/701.jpg" pagenum="144"></pb>sia piena d&#039;acqua, fino al giro H (fig. </s>

<s>46). Poi sotto questa caraffa, nel <lb></lb>luogo EF, pongasi del fuoco molto lento: si vedrà a poco a poco crescer <lb></lb>l&#039;acqua fino in G, e nel fondo della caraffa si vedranno alcuni campanelletti, <lb></lb>li quali di quando in quando partendosi dal fondo ascenderanno per l&#039;acqua <lb></lb>fino alla sommità del suo livello in G, dove rompendosi si risolveranno. <lb></lb><figure id="id.020.01.701.1.jpg" xlink:href="020/01/701/1.jpg"></figure></s></p><p type="caption">

<s>Figura 46.<lb></lb>Fredda che sarà la medesima acqua, si vedrà tornare al suo primo <lb></lb>livello in H, e non esser punto scemata, ma noi per l&#039;addotta <lb></lb>esperienza ricerchiamo fuoco lento come s&#039;è detto. </s>

<s>” </s></p><p type="main">

<s>“ Si potrà dunque adesso domandare che cosa sia stato <lb></lb>ch&#039;abbia dato causa al crescer di quell&#039;acqua. </s>

<s>So che mi po­<lb></lb>trebb&#039;esser risposto che, avendo il fuoco virtù di rarefare, abbia <lb></lb>rarefatto quell&#039;acqua. </s>

<s>Ma io domando che cosa fosse in que&#039;cam­<lb></lb>panelli che, spinti di quando in quando all&#039;in su, svaporano. </s>

<s>Io <lb></lb>veramente non so qual risposta mi potrebbe esser data, ma sento <lb></lb>bene astringermi a confessare esser quelli diversi aggregati di <lb></lb>corpuscoli ignei, che sormontando per l&#039;acqua, come leggeris­<lb></lb>simi, svaporassero. </s>

<s>Quindi è ch&#039;essendone ancora gran quantità <lb></lb>mescolata nell&#039;acqua, la fanno crescere in mole; onde partendosi essi torna <lb></lb>essa allo stato di prima, il che parmi che apertamente dimostri questo che <lb></lb>noi chiamiamo calore prodursi per mezzo di questi tali corpuscoli ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXXXIV, c. </s>

<s>22). </s></p><p type="main">

<s>Benchè così fatte dottrine che si derivarono dagli Antichi fossero, come <lb></lb>vedemmo, sanzionate dall&#039;autorità di Galileo, così potente sull&#039;animo e sul­<lb></lb>l&#039;ingegno de&#039;nostri Accademici, sorse, per amor del vero, alcuno in mezzo <lb></lb>di essi che, se non ebbe la perspicacia di riconoscervi il falso, ebbe nono­<lb></lb>stante la franchezza di mettervi il dubbio. </s></p><p type="main">

<s>“ Fu addotta però, soggiunge il Viviani, in confutazione di simil parere <lb></lb>un&#039;altra esattissima prova dal signor dottor Rinaldini, la quale è che, se <lb></lb>noi piglieremo due palle di egual grandezza, l&#039;una d&#039;ebano legno durissimo, <lb></lb>l&#039;altra di sughero, e poste tutt&#039;e due in egual distanza dal fuoco e tenute <lb></lb>per qualche tempo, levate che saranno le dette palle si troverà molto più <lb></lb>calda quella di ebano che quella di sughero. </s>

<s>Di qui pareva di potersi pro­<lb></lb>durre il calore non altrimenti potersi generare per via di questi corpuscoli, <lb></lb>poichè, essendo il legno del sughero molto poroso, e per conseguenza più <lb></lb>atto a ricevere i medesimi corpuscoli, doveva trovarsi più caldo dell&#039;ebano <lb></lb>assai più nelle sue parti costipato. </s>

<s>Eppure per l&#039;esperienza tutto il contra­<lb></lb>rio succede: adunque par forza confessare il calore non prodursi in tal ma­<lb></lb>niera ” (ivi). </s></p><p type="main">

<s>Avrebbe potuto rispondere il Viviani che la superficie nera dell&#039;ebano <lb></lb>tiene, come il Castelli s&#039;immaginava, così disposti i suoi pori da introdurvi <lb></lb>più gran numero d&#039;ignicoli di quel che la superficie del sughero non fac­<lb></lb>cia, ma egli così cerca più sottili argomenti alla sua risposta, ricorrendo alla <lb></lb>varia capacità del calore, secondo la varia costituzione de&#039;corpi. </s></p><p type="main">

<s>“ L&#039;esperienza veramente, prima per essere stata addotta da eccellen-<pb xlink:href="020/01/702.jpg" pagenum="145"></pb>tissimo uomo e versatissimo in queste filosofiche scienze, secondo per l&#039;uti­<lb></lb>lità che da questa medesima può aversi circa la speculazione di effetto così <lb></lb>recondito; si deve diligentemente esaminare, e dedurre, se non quella ne­<lb></lb>cessaria condizione, almeno qualche apparente congruenza, che in qualche <lb></lb>parte il nostro annebbiato intelletto capaciti e illumini. </s>

<s>E prima è necessa­<lb></lb>rio fermare un principio dal qual, come da particolar fondamento, dipenda <lb></lb>l&#039;intelligenza di tutto il resto. </s>

<s>Vedo dunque, e di questo mio vedere è ca­<lb></lb>gione l&#039;esperienza, che quel corpo, che si rende molto facile per ricevere <lb></lb>il calore, sia ancora molto facile a perderlo, per lo che veggo io che l&#039;aria <lb></lb>facilissima a ricevere in sè il calore è anco facilissima a perderlo, onde fu <lb></lb>opinione ancora del Galileo che non si scaldasse punto. </s>

<s>L&#039;acqua men facile <lb></lb>dell&#039;aria a scaldarsi è men facile a perdere il calore e il sasso e il ferro, <lb></lb>che via più sempre hanno più difficoltà a scaldarsi, hanno ancora la mede­<lb></lb>sima maggior difficoltà a freddarsi. </s>

<s>” </s></p><p type="main">

<s>“ Quanto poi all&#039;esperienza che prima si scaldi, oppure maggiormente <lb></lb>riceva il calore la palla d&#039;ebano che quella di sughero, io certamente lo <lb></lb>credo, poichè del calore che riceve l&#039;ebano in que&#039;corpuscoli punto o po­<lb></lb>chissimo ne tramanda fuori, poichè, imprigionandosi quelli tra le di lui parti <lb></lb>molto ben costipate, non hanno così facile l&#039;esito come in un legno poroso, <lb></lb>qual&#039;è il sughero, il quale è vero che facilmente riceve il calore, ma è anco <lb></lb>verissimo, per quel che di sopra s&#039;è detto, che facilmente lo perde. </s>

<s>Onde <lb></lb>in uno spazio d&#039;un tal tempo, nel quale ambe le palle sono state al fuoco, <lb></lb>essendo esse d&#039;ugual mole, e in distanza da esso fuoco uguale, la medesima <lb></lb>quantità di corpuscoli saranno rappresentati all&#039;ebano che al sughero. </s>

<s>L&#039;ebano <lb></lb>però de&#039;corpuscoli ignei che ha in sè ricevuto, una particella molto minore <lb></lb>n&#039;ha tramandata di quella del sughero; onde se da cose eguali, cioè da cor­<lb></lb>puscoli in quantità uguali ricevuti da ambe le palle, se ne levano diseguali <lb></lb>quantità, non v&#039;è dubbio alcuno che, di dove ne saranno levati meno, più <lb></lb>ne rimarranno. </s>

<s>Onde l&#039;ebano, che assai meno ne ha mandati fuora del su­<lb></lb>ghero, più in sè ne averà ritenuti, e perciò dovrà esser più caldo del me­<lb></lb>desimo sughero. </s>

<s>” </s></p><p type="main">

<s>“ Il soggiunger poi che, mediante l&#039;espansione si fa e si genera il ca­<lb></lb>lore asserito per sentenza di Democrito, e però il sughero, conforme si dice, <lb></lb>avendo maggiore espansione doverà avere maggior calore; a questo io ve­<lb></lb>ramente direi prima non aver letto l&#039;opinione di Democrito, ma che dubito <lb></lb>grandemente che simile espansione deva piuttosto ritrovarsi nell&#039;agente, cioè <lb></lb>nel corpo che ha da scaldare, non in quello che ha da essere scaldato, poi­<lb></lb>chè giudicherei io che l&#039;espansione de&#039;corpuscoli sia piuttosto un deperdi­<lb></lb>mento di calore che accrescimento, e ciò mi vien persuaso, poichè molto più <lb></lb>facilmente si scalderà un liquore appresentato al fuoco, e posto dentro ad un <lb></lb>vaso coperto, che ad uno senza coperchio, il quale altro alla fine non fa che <lb></lb>impedire l&#039;espansione de&#039;corpuscoli, che è forza confessar causa del riscal­<lb></lb>damento ” (ivi, c. </s>

<s>24, 25). </s></p><p type="main">

<s>Le illustrazioni, che alle dottrine professate da Galileo intorno al calore <pb xlink:href="020/01/703.jpg" pagenum="146"></pb>derivarono dal Discorso del Viviani da noi riferito, benchè abbiano per noi <lb></lb>non lieve importanza storica, pur è un fatto che, versando intorno a una <lb></lb>fallace osservazione, in cui scambiavansi le gallozzole dell&#039;aria in globetti di <lb></lb>fuoco, riuscirono a&#039;progressi della scienza d&#039;assai poco profitto. </s>

<s>Con ciò pa­<lb></lb>gavasi senza dubbio il consueto tributo alla debolezza umana, ma perchè i <lb></lb>forti non hanno appena piegate per cader le ginocchia che risorgono più <lb></lb>diritti, ecco da queste stesse carte manoscritte che svolgiamo porgercisi di <lb></lb>un tal risorgimento i più belli esempi. </s></p><p type="main">

<s>Nel primo Dialogo delle Due nuove scienze ha Galileo l&#039;esperienza di <lb></lb>quella palla di cera immersa nell&#039;acqua, dalla quale il Torricelli, e poi i se­<lb></lb>guaci di lui nella sperimentale Accademia medicea, trassero così largo par­<lb></lb>tito per l&#039;invenzione de&#039;loro Idrostammi e di alcuni Termostammi di nuovo <lb></lb>genere, i quali ebbero particolarmente origine da ciò che ivi osserva Gali­<lb></lb>leo potersi far variar l&#039;equilibrio alla palla di cera col riscaldare un poco <lb></lb>o raffireddar l&#039;acqua, cosicchè “ l&#039;infonder quattro gocciole d&#039;altra acqua un <lb></lb>poco più calda o un poco più fredda .... farà che la palla vi scenda o vi <lb></lb>sormonti: vi scenderà infondendovi la calda, e monterà per l&#039;infusione della <lb></lb>fredda ” (Alb. </s>

<s>XIII, 72). </s></p><p type="main">

<s>Intorno a tal proposito il Salviati, in bocca al quale son poste queste <lb></lb>parole, non ne dice più avanti, e perciò, poniamo che non lasciasse nulla a <lb></lb>dubitare della verità e della precisione dell&#039;esperienza, rimaneva pure agli <lb></lb>altri un certo tal qual dovere filosofico di ripeterla variandone la maniera <lb></lb>e, ch&#039;era più importante, di trovar, de&#039;nuovi fatti sperimentati, la ragion <lb></lb>fisica e i modi. </s>

<s>Fu questo appunto l&#039;ufficio che si assunse il Viviani, quasi <lb></lb>pigliando il sopraccitato passo galileiano per testo de&#039;suoi studii, i quali per <lb></lb>la storia della Termologia, più che per quella dell&#039;Accademia del Cimento, <lb></lb>saranno da chi appresso legge reputati importanti. </s></p><p type="main">

<s>“ Se una migliarola di piombo si circonderà di cera bianca, in modo <lb></lb>che se ne formi una pallina, che immersa in una tal acqua comune o altro <lb></lb>liquido vadia lentissimamente al fondo; ho provato che non solo collo scal­<lb></lb>darla alquanto al lume o al fuoco, ma col solo stropicciarsela tra le palme <lb></lb>delle mani calde naturalmente, si riduce galleggiante, perchè, spingendola <lb></lb>con alquanto impeto sotto la superficie dell&#039;acqua del bicchiere, se ne va al <lb></lb>basso per quello spazio che importa l&#039;impeto impresso, ma con moto ritar­<lb></lb>dato, come non naturale, e quando si fa l&#039;equilibrio tra detto impeto e il <lb></lb>momento interno di salire, apparisce fermarsi, benchè non si trattenga per <lb></lb>minimo momento, e comincia il suo moto all&#039;insu fino alla superficie, dove <lb></lb>si ferma per tanto tempo che si parta da detta pallina tanto del calore in­<lb></lb>trodottovi, che si faccia grave in specie quanto l&#039;acqua, e di poi diventi più <lb></lb>grave tornando a immergersi e a scendere pian piano sino al fondo come <lb></lb>prima, il che si conosce col bagnare d&#039;acqua quella minima cuspide che <lb></lb>avanza sopra la superficie, mentre la palla galleggia, perchè replicando più <lb></lb>volte e spingendola leggermente sott&#039;acqua, finalmente se ne va in fondo, <lb></lb>e spesse volte si osserva che il detto equilibrio ed equipondio in specie con <pb xlink:href="020/01/704.jpg" pagenum="147"></pb>l&#039;acqua, mentre il detto calore si parte, si fa nel salire della detta pallina <lb></lb>avanti arrivi alla superficie, nel qual caso si osserva con gusto mirabile che <lb></lb>per tempo notabile si vede la pallina star ferma, e poi si vede risolvere a <lb></lb>scendere ” (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>6). </s></p><p type="main">

<s>Fatte queste diligentissime osservazioni il Viviani pensa a ciò che possa <lb></lb>essere ragione esplicitiva di esse, e non assicurandosi bene ancora, per man­<lb></lb>canza di altre esperienze, si esprime così sotto forma di dubbio: </s></p><p type="main">

<s>“ La ragione di ciò credo che sia o perchè per l&#039;introduzione de&#039;mi­<lb></lb>nimi ignei la cera si rarefaccia e così cresca di mole, stando ferma la me­<lb></lb>desima materia, e per conseguenza si faccia men grave in specie di prima, <lb></lb>e questo per doppia ragione: Prima, perchè, com&#039;ho detto, cresce la mole <lb></lb>e non la materia; seconda, perchè s&#039;introduce ne&#039;pori della cera e del <lb></lb>piombo una materia incomparabilmente più leggera in specie non solo del <lb></lb>piombo, ma dell&#039;acqua e della cera qual&#039;è il calore, oppure, perchè stando <lb></lb>ferma la mole senza rarefarsi la cera, diventi nondimeno men grave in spe­<lb></lb>cie di prima, mediante l&#039;esservisi introdotto il detto calore composto di atomi <lb></lb>tanto più leggeri di qualunque di detta materia. </s>

<s>” </s></p><p type="main">

<s>La risoluzione del dubbio, in che ondeggiava così la mente del Viviani, <lb></lb>era importantissima a decidere dagli effetti la propria natura del calore, il <lb></lb>quale se avesse veramente resa più leggera in specie la pallina aggiungen­<lb></lb>dosi a lei, come fanno i sonagli dell&#039;aria che tornano e tengono a galla an­<lb></lb>che i corpi più gravi dell&#039;acqua; non era dubbio che ciò valeva a confer­<lb></lb>mar l&#039;opinione che fossero veramente sferette di fuoco quelle che si vedevano <lb></lb>ascender e gallozzolare su pel collo sottile della caraffa. </s>

<s>Bisognava dunque <lb></lb>risolvere in ogni modo quel dubbio, ma intanto che l&#039;Autore del Mano­<lb></lb>scritto va rimeditandovi sopra, prosegue a illustrare il testo galileiano per ciò <lb></lb>che riguarda il variar dell&#039;equilibrio idrostatico della migliarola incerata, al <lb></lb>variar la densità dell&#039;acqua o mescolandovi il sale o infondendovi spirito di <lb></lb>zolfo o di vetriolo. </s></p><p type="main">

<s>Venne però il tempo in cui l&#039;esperienze decisero al Viviani che non <lb></lb>rendeva il calore più leggere in specie le palline incerate con aggiungersi <lb></lb>ad esse come i sonagli dell&#039;aria a&#039;galleggianti più gravi dell&#039;acqua, ma col <lb></lb>rarefarle rimanendo ad esse palline la medesima quantità di materia. </s></p><p type="main">

<s>“ Mi son finalmente accertato che la cera si rarefà e si condensa se­<lb></lb>condo che cresce il calore nell&#039;ambiente, poichè, prese più palline aggiustate <lb></lb>e temperate con piombo e cera, come si è detto, in modo che alcune di loro <lb></lb>in una tale costituzione o temperie di calore di una tale acqua con gran <lb></lb>difficoltà vi galleggino, ed altre con difficoltà stiano in fondo; ho veduto con <lb></lb>replicate esperienze che nel riscaldar l&#039;ambiente dell&#039;aria si riscalda l&#039;acqua <lb></lb>ancora del vaso, perciò si rarefà e diventa men grave in specie di prima, <lb></lb>onde per conseguenza pareva che le palline di fondo, in mezzo più leggeri, <lb></lb>dovessero acquistar maggior gravità e starsene in fondo più facilmente e con <lb></lb>più momento, ed all&#039;incontro che le palline galleggianti dovessero, almeno <lb></lb>alcune di loro, discendere per l&#039;acqua già fatta più rara, ma segue tutto <pb xlink:href="020/01/705.jpg" pagenum="148"></pb>l&#039;opposito, perchè non solo non discende alcuna delle galleggianti, ma ne <lb></lb>sormonta dal fondo alla superficie dove si fermano, e crescendo il calore <lb></lb>ambiente se ne vedono salire altre e altre di mano in mano, e prima quelle <lb></lb>che prima si fanno di egual gravità in specie con l&#039;acqua, e poi di minore, <lb></lb>ma tutte con moto tardissimo ed impercettibile dalla vista, che alcune volte <lb></lb>appariscono starsene ferme in mezzo l&#039;acqua per lunghissimo tempo. </s>

<s>” </s></p><p type="main">

<s>“ Tornando poi a raffreddarsi l&#039;aria e insieme l&#039;acqua del vaso, si <lb></lb>vede non solo discendere quelle palline che prima per il calore sormonta­<lb></lb>vano, e queste con ordine prepostero, perchè quelle che furono le ultime a <lb></lb>salire son le prime a calare a basso, e di mano in mano descendono quelle <lb></lb>che anticipavano le altre nel salire, ma ancora di quelle che nel primo stato <lb></lb>dell&#039;acqua stavano a galla, e che crescendo il freddo, cioè scemando sem­<lb></lb>pre più il calore dell&#039;acqua, si riducono tutte le palline galleggianti a toc­<lb></lb>care il fondo del vaso, effetto di cui altra non può essere la cagione se non <lb></lb>che il calore che s&#039;introdusse nell&#039;acqua per mezzo dell&#039;aria ambiente più <lb></lb>e con maggior proporzione rarefà la cera che l&#039;acqua, cioè con maggior <lb></lb>proporzione si scema la gravità in specie della cera che dell&#039;acqua, e per <lb></lb>il contrario, partendosi il calore, cioè raffreddandosi l&#039;acqua, più e con <lb></lb>maggior proporzione si condensa e si fa più grave in specie la cera che <lb></lb>l&#039;acqua. </s>

<s>” </s></p><p type="main">

<s>“ Che l&#039;acqua in questa esperienza si riscaldasse o si raffreddasse me <lb></lb>ne sono accertato per mezzo de&#039;gradi del Termometro, che ho tenuto im­<lb></lb>merso nella medesima acqua, quale mi mostrava che, quando cresceva il <lb></lb>numero de&#039;gradi sopra il primo stato dell&#039;aggiustamento delle palline, al­<lb></lb>cune di quelle che erano in fondo salivano a galla, e che quando il numero <lb></lb>de&#039;gradi si faccia minore del primo stato alcune di quelle che prima gal­<lb></lb>leggiavano se ne andranno in fondo ” (ivi, c. </s>

<s>7). </s></p><p type="main">

<s>Tra le prime osservazioni e queste esperienze, colle quali il Viviani <lb></lb>s&#039;accertò che la cera vien rarefatta dal calore, passò qualche spazio di tempo, <lb></lb>che quell&#039;avverbio <emph type="italics"></emph>finalmente<emph.end type="italics"></emph.end> dice dover essere stato non breve e anzi al­<lb></lb>quanto penoso. </s>

<s>Il definir con misura certa lo spazio di quel tempo non sa­<lb></lb>rebbe possibile, ma non si erra dal vero dicendo che quelle prime osserva­<lb></lb>zioni appartengono al secondo periodo della sperimentale Accademia medicea <lb></lb>e che queste esperienze appartengono a&#039;primi anni del terzo periodo. </s></p><p type="main">

<s>Il Viviani succeduto al Torricelli in rappresentar quella seconda età di <lb></lb>essa Accademia, conferiva le sue osservazioni termostatiche con i colleghi <lb></lb>Borelli e Rinaldini, al primo de&#039;quali venne in pensiero di poter adattar <lb></lb>simili palline fatte di vetro temperate con migliarole a <emph type="italics"></emph>pesar,<emph.end type="italics"></emph.end> com&#039;ei diceva, <lb></lb>il caldo e il freddo, desumendo quel peso dal grado dell&#039;immersione indi­<lb></lb>cato da un&#039;asticella divisa in parti e congiunta al vetro che affiori il liquido <lb></lb>ora più alto ora basso, secondo che cresce o scema all&#039;ambiente la tempe­<lb></lb>ratura. </s>

<s>Di ciò faceva motto il Borelli stesso al principe Leopoldo in una let­<lb></lb>tera scrittagli il di 17 Gennaio 1660 da Pisa. </s>

<s>“ Non veggo far menzione di <lb></lb>alcune scritture che inviai a V. A. li giorni passati di non so che capricci <pb xlink:href="020/01/706.jpg" pagenum="149"></pb>sovvenutimi intorno al peso dell&#039;aria ed il modo di pesare il caldo e il freddo, <lb></lb>per mezzo di quello stesso strumento, che io lasciai in nota quattro anni <lb></lb>sono all&#039;A. V., che è una palla di vetro con un filo sottilissimo di rame <lb></lb>distinto in gradi ” (MSS. Cim., T. XVII, c. </s>

<s>1). </s></p><p type="main">

<s>Il disegno di questo <emph type="italics"></emph>Termostatico<emph.end type="italics"></emph.end> ingegnosamente applicato dal suo <lb></lb>stesso inventore a ritrovare la differenza della gravità dell&#039;aria, in diversi <lb></lb>luoghi e in diversi paesi, può vedersi a pag. </s>

<s>250 del Libro <emph type="italics"></emph>De motionibus <lb></lb>naturalibus,<emph.end type="italics"></emph.end> dov&#039;è posto a illustrare la propos. </s>

<s>CXIX così formulata: “ Po­<lb></lb>stea, omissis quamplurimis Termostaticis a me inventis, afferam instrumen­<lb></lb>tum quo pondus absolutum aeris in diversis locis elevatis ac depressis et <lb></lb>varie temperatis reperiri potest. </s>

<s>” </s></p><p type="main">

<s>Il Borelli chiama questi suoi Termostatici <emph type="italics"></emph>pesatori del caldo,<emph.end type="italics"></emph.end> a quel <lb></lb>modo e per quelle stesse ragioni che gli Areometri si chiamano pesatori <lb></lb>de&#039;liquidi, ma al Viviani sovvenne un concetto anche più nuovo, e fu quello <lb></lb>di pesare addirittura il caldo per mezzo di una stadera. </s></p><p type="main">

<s>“ Si faccia una libbra di braccia disuguali che sia bilicata esquisitissi­<lb></lb>mamente sopra un pezzo di legno duro o di altra materia di figura di prisma <lb></lb>triangolare.... Attorno al braccio più lungo si avvolti una sottilissima corda <lb></lb>da cetera, come di rame o di ottone, nel modo che insegna il Galileo nella <lb></lb>sua Bilancia per conoscere i misti, sicchè tutto il braccio venga diviso per <lb></lb>esempio in 200 particelle. </s>

<s>Nell&#039;estremità del braccio più corto si appenda <lb></lb>un vaso di vetro sottile, con il collo sottilissimo volto all&#039;ingiù, e sia tale <lb></lb>che stia in equilibrio con il peso del braccio più lungo. </s>

<s>Di poi si empia il <lb></lb>vaso, e perchè si guasterà l&#039;equilibrio per l&#039;aggiunta dell&#039;acqua nel vaso, <lb></lb>si trovi un peso che posto nell&#039;estremità appunto del maggior braccio equi­<lb></lb>pondii con detto vaso con l&#039;acqua. </s>

<s>Qui non è dubbio che, rarefacendosi poi <lb></lb>per maggior caldo dallo stato primiero l&#039;aria del vaso, tanto scemerà l&#039;acqua <lb></lb>cioè il peso quanto crescerà la mole dell&#039;aria, e diminuendosi il peso del­<lb></lb>l&#039;acqua bisognerà accostare il contrappeso al sostegno, acciò si mantenga <lb></lb>l&#039;equilibrio. </s>

<s>Si accosti dunque e torni v. </s>

<s>g. </s>

<s>più vicino di prima 15 parti: <lb></lb>dico che il calore del primo stato al calore di adesso sta come la distanza <lb></lb>del primo contrappeso alla distanza del secondo ” (MSS. Cim., T. X, c. </s>

<s>103). </s></p><p type="main">

<s>La dimostrazione la fa il Viviani dipendere da proposizioni anteceden­<lb></lb>temente dimostrate e importantissime per la storia della Termometria, im­<lb></lb>perocchè di li ebbe il suo principio la razionale digradazione dello Stru­<lb></lb>mento. </s>

<s>Vedemmo a suo luogo come una scala fosse anche applicata ai <lb></lb>Termometri del Santorio e del Sagredo, ma era una pura pratica senza al­<lb></lb>cuna scorta di teoria. </s>

<s>Il Viviani è il primo che ponga per fondamento alla <lb></lb>digradazione del Termometro ad aria il principio che i ricrescimenti di vo­<lb></lb>lume dell&#039;aria stessa son proporzionali all&#039;intensità del calore, e che dimo­<lb></lb>stri come quella proporzionalità si può esprimere in numeri. </s>

<s>Non è per <lb></lb>questo che riuscisse a dare Misuratori assoluti del calore e comparabili, per­<lb></lb>chè anch&#039;egli seguiva l&#039;opinion di que&#039;tempi, che cioè fosse il ghiaccio la <lb></lb>privazione totale degl&#039;ignicoli, ma non è per questo che il documento da <pb xlink:href="020/01/707.jpg" pagenum="150"></pb>noi posto qui appresso non abbia il pregio di dimostrare d&#039;onde avesse la <lb></lb>scienza termometrica il suo primo principio. </s></p><p type="main">

<s>“ Circa il trovar modo di misurare con che proporzione vadi crescendo <lb></lb>e decrescendo il calore della medesima aria, e far sì che tal proporzione sia <lb></lb>effabile e si possa esplicare in numeri, parmi ciò esser facile a conseguire, <lb></lb>supposto questo principio: cioè che il calore d&#039;una mole d&#039;aria ridotta alla <lb></lb>minima condensazione, che per mezzo del maggior freddo ridur si possa, <lb></lb>sia nulla, cioè come zero; onde si possa dire: il calore di una quantità <lb></lb>d&#039;aria è tanto quanto l&#039;eccesso della mole di detta aria in quello stato di <lb></lb>caldezza che si trova, sopra la mole della medesima aria priva totalmente di <lb></lb>calore, cioè ridotta alla massima condensazione con la massima freddezza, o <lb></lb>per meglio dire con la total privazione di calore, a cui ridur si possa per <lb></lb>mezzo del ghiaccio. </s>

<s>” </s></p><p type="main">

<s>“ Per esempio sia un vaso di vetro come si vede (fig. </s>

<s>47) con il collo <lb></lb>assai lungo, dentro il quale si metta tant&#039;acqua, che volto poi con il collo <lb></lb><figure id="id.020.01.707.1.jpg" xlink:href="020/01/707/1.jpg"></figure></s></p><p type="caption">

<s>Figura 47.<lb></lb>all&#039;ingiù arrivi all&#039;altezza A, ed il rimanente AB sia pieno d&#039;aria: <lb></lb>dico che se si esporrà al maggior rigor d&#039;aria dell&#039;inverno nel <lb></lb>nostro clima la parte AB, e che la bocca del collo sia immersa <lb></lb>nell&#039;acqua, l&#039;aria del vaso si condenserà, potendovi succedere per <lb></lb>di sotto dell&#039;acqua. </s>

<s>Nel condensarsi l&#039;aria ed alzarsi l&#039;acqua su il <lb></lb>collo, alla fine arriverà quella alla massima condensazione, che per <lb></lb>tal mezzo conseguire si possa, e questa alla massima altezza, e sia <lb></lb>v. </s>

<s>g. </s>

<s>arrivata all&#039;altezza C. </s>

<s>Supposto dunque il calore della den­<lb></lb>sissima aria BC esser zero, avendonela privata con la maggior <lb></lb>freddezza dell&#039;ambiente e scacciati fuori i minimi del calore, ma <lb></lb>il calore della mole BA della medesima aria men densa esser quanto CA, <lb></lb>che è l&#039;eccesso della mole dell&#039;aria BA della prima costituzione sopra la <lb></lb><figure id="id.020.01.707.2.jpg" xlink:href="020/01/707/2.jpg"></figure></s></p><p type="caption">

<s>Figura 48.<lb></lb>mole BC di detta aria della massima densità; supposto questo, <lb></lb>averemo l&#039;intento con ciascuno de&#039;due soliti Termoscopii del <lb></lb>Galileo ma preparati in questo modo. </s>

<s>” </s></p><p type="main">

<s>“ Sia un vaso di vetro come AB (fig. </s>

<s>48) dentro al quale sia <lb></lb>tant&#039;acqua che non sia meno della capacità del lunghissimo can­<lb></lb>nello CD, qual bisogna che nel vano sia d&#039;uniforme grossezza <lb></lb>per tutto, e sia diviso e contrassegnato in minutissime particelle <lb></lb>eguali, facendo ad ogni cinque posti o ad ogni dieci un segno <lb></lb>differente dagli altri. </s>

<s>Questo cannello s&#039;immerga nel vaso, fin­<lb></lb>chè la bocca tocchi il fondo, e poi si sigilli benissimo attorno <lb></lb>la bocca A, e per la bocca del cannello C s&#039;infonda piano piano <lb></lb>dell&#039;acqua fino all&#039;altezza E. </s>

<s>Dopo mettasi il vaso nell&#039;acqua con <lb></lb>molto ghiaccio, o nel solo ghiaccio spezzato in piccole particelle, <lb></lb>e si lasci tanto, finchè l&#039;aria del vaso condensata al possibile, <lb></lb>abbi perso tutto il calore, come si disse nel supposto. </s>

<s>È chiaro <lb></lb>che nel luogo dov&#039;era il calore vi subentrerà dell&#039;acqua del cannello e sarà <lb></lb>calata v. </s>

<s>g. </s>

<s>fino al segno F, oltre al quale il ghiaccio non abbi facoltà di <pb xlink:href="020/01/708.jpg" pagenum="151"></pb>farla abbassare di più, e fatto qui un segno differente da tutti gli altri, e <lb></lb>levato il ghiaccio, l&#039;aria di dentro tornerà a riscaldarsi, e tanto quanto calore <lb></lb>vi entrerà (per ridursi allo stato dell&#039;aria ambiente il vaso) tant&#039;acqua ap­<lb></lb>punto s&#039;alza nel cannello sopra il segno F. </s>

<s>Sia per esempio tornata al se­<lb></lb>gno E, che il numero delle particelle che saranno tra F ed E ci danno i <lb></lb>gradi del calore dell&#039;aria del vaso, per conseguenza dell&#039;ambiente, e segui­<lb></lb>tando a riscaldarsi, cioè ad occupar più luogo, per altrettanto luogo si alzerà <lb></lb>l&#039;acqua sopra F, come sino in C, sicchè, se tra F ed E saranno 20, e tra F <lb></lb>e C 35, diremo il calor dell&#039;aria del primo stato naturale, al calor della me­<lb></lb>desima aria nel secondo stato, esser come 20 a 35 secondo il supposto. </s>

<s>Ma <lb></lb>gli stati dell&#039;aria dentro il vaso sono i medesimi dell&#039;aria ambiente, adun­<lb></lb>que con tale Strumento potrò sapere in numeri il caldo dell&#039;aria in diversi <lb></lb>tempi ed in diversi luoghi, perchè se alli 25 di Marzo per esempio il nu­<lb></lb>mero de&#039;posti sopra F sarà 12, e sia 12 ancora alli 22 di Settembre, dirò <lb></lb>che in questi giorni è stato il medesimo caldo, ancora potrò sapere di tutto <lb></lb>l&#039;anno il massimo caldo ed il minimo, che noi chiamiamo il maggior freddo, <lb></lb>e quanto sia il calor d&#039;una stanza rispetto a quello d&#039;un&#039;altra ” (ivi, c. </s>

<s>100). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Se potessimo sperare che fossero queste pagine lette da qualche Fisico <lb></lb>de&#039;nostri giorni, il quale va riguardando com&#039;un&#039;anticaglia oramai insop­<lb></lb>portabile l&#039;opinion di coloro che ammettono essere il calore un agente im­<lb></lb>ponderoso, tutto compiacendosi nelle moderne teorie del moto vibratorio e <lb></lb>dell&#039;unità delle forze; a sentire il Borelli e il Viviani proporre strumenti da <lb></lb>pesare il caldo e il freddo, e a vedere i seguaci di Galileo additare gl&#039;igni­<lb></lb>coli ch&#039;entrano ed escono dal vetro di un&#039;ampolla piena d&#039;acqua posata sul <lb></lb>fuoco, direbbero senza dubbio ch&#039;era impossibile riuscisse quella gente a <lb></lb>intender nulla delle proprietà del calore. </s>

<s>Eppure è un fatto che se ne in­<lb></lb>tesero tanto da trasmettere agli sconoscenti nepoti un&#039;eredità di scienza ter­<lb></lb>mica da giudicarsi non troppo scarsa, riguardata in sè, ma che riguardata <lb></lb>in comparazione della boriosa scienza moderna, dovrebbesi dire una dovi­<lb></lb>zia. </s>

<s>Per quel che infatti concerne il così detto calorico di stato o di comu­<lb></lb>nicazione le vecchie ipotesi degl&#039;ignicoli erano, nella loro semplicità e na­<lb></lb>turalezza, atte a spiegare i fatti forse meglio delle teorie presenti, e quanto <lb></lb>al calorico raggiante riguardandolo nel maggior numero de&#039;casi inseparabile <lb></lb>dalla luce v&#039;applicarono le stesse leggi di lei nel diffondersi e nel riflettersi <lb></lb>dalla superficie de&#039;corpi, ond&#039;è che si possono dagli stessi trattati di Ot­<lb></lb>tica argomentare, di questa parte della scienza termica degli antichi, le ve­<lb></lb>rità e gli errori. </s></p><p type="main">

<s>Una delle prime e principali proprietà conosciute da&#039;discepoli di Galileo <lb></lb>fu la varia capacità che hanno i corpi di condurre il calore, secondo la loro <pb xlink:href="020/01/709.jpg" pagenum="152"></pb>varia natura. </s>

<s>Benedetto Castelli fu il primo che pensasse d&#039;applicare util­<lb></lb>mente quella proprietà alla buona conservazione de&#039;grani, intorno a che <lb></lb>scrisse un breve ma notabile <emph type="italics"></emph>Discorso<emph.end type="italics"></emph.end> raccolto insiem con gli altri <emph type="italics"></emph>Opuscoli <lb></lb>filosofici<emph.end type="italics"></emph.end> di lui postumi stampati dal Dozza di Bologna nel 1669. “ Avendo <lb></lb>osservato (egli ivi scrisse) che diversi corpi di diverse materie ricevono molto <lb></lb>diversamente le impressioni esterne dell&#039;ambiente, cioè chi più e chi meno, <lb></lb>imperocchè esponendo noi al sole diversi corpi come sarebbero marmi, le­<lb></lb>gni, bronzi, terra, ecc., e lasciandogli stare eguale spazio di tempo, il me­<lb></lb>tallo si riscalda assai più che la pietra, e la pietra più della terra, e questa <lb></lb>più del legno; stimai che dovendo noi conservare il grano con difenderlo <lb></lb>dall&#039;umido e dalle mutazioni ed alterazioni esterne, tutto ci sarebbe riuscito <lb></lb>con rinserrarlo in vasi fatti di quella materia, la quale mantenendosi asciutta <lb></lb>fosse ancora meno capace di freddo e di altre impressioni ” (ivi, pag. </s>

<s>42). <lb></lb>Questa materia, secondo il Castelli sarebbe il sughero, la virtù coibente del <lb></lb>quale è mostrata, seguita egli a dire “ nel conservare la neve lungo tempo <lb></lb>per rinfrescare il vino e l&#039;acqua nel tempo dell&#039;estate, ed io ho sperimen­<lb></lb>tato che la neve si mantiene nei gran caldi in simili vasi di sughero più <lb></lb>che in altri di altra materia. </s>

<s>E le scarpe stesse nostre solettate di sughero <lb></lb>ci difendono i piedi nel tempo dell&#039;estate dal caldo, e nell&#039;inverno dal freddo <lb></lb>e dall&#039;umido ” (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Queste esperienze che, sebben tardi fossero venute a notizia del pub­<lb></lb>blico, nonostante il Castelli avevale già divulgate nell&#039;insegnamento orale <lb></lb>della sua scuola, accesero in desiderio il Torricelli di veder con che ordine <lb></lb>si succedessero i varii corpi, specialmente i metalli, nella virtù di conservar <lb></lb>più a lungo il ghiaccio, e perciò nel Registro delle esperienze che oramai <lb></lb>ben sappiamo esser dovute a lui, al num. </s>

<s>III si legge: “ Si fecero più vasi <lb></lb>di varie sorti di metallo e di legno, e si empirono di diaccio pesto, e si os­<lb></lb>servò come il diaccio si consumasse e si vedde che li vasi consumavano dif­<lb></lb>ferentemente, secondo la qualità. </s>

<s>” E segue una Tavola in cui per migliori <lb></lb>conduttori figurano l&#039;oro e l&#039;argento, e per maggiori coibenti di tutti gli <lb></lb>altri metalli messi alla prova, lo stagno e il ferro. (Targioni, Notizie ecc., <lb></lb>Firenze 1780, T. II, P. II, pag. </s>

<s>164). </s></p><p type="main">

<s>Seguita in quel Registro d&#039;esperienze torricelliane un&#039;altra che ha l&#039;in­<lb></lb>tento medesimo di questa, ma disposta e accomodata in nuovo elegantissimo <lb></lb>modo: “ Si fece piana una lastra di diaccio d&#039;egual grossezza e si messero <lb></lb>sopra palle fatte delli soprascritti metalli, e detto diaccio si era messo egual­<lb></lb>mente lontano dal piano, dove era posato sopra, e si trovò che le palle sfon­<lb></lb>davano secondo avevano fatto i vasi nel consumare ” (ivi). Si vollero poi <lb></lb>l&#039;esperienze della varia conducibilità calorifica de&#039;corpi desunta dal consu­<lb></lb>marsi più o meno presto il ghiaccio, ripetere dagli Accademici del Cimento, i <lb></lb>quali confessarono che <emph type="italics"></emph>nulla ne avevano cavato di certo<emph.end type="italics"></emph.end> (Saggi, Firenze 1841, <lb></lb>pag. </s>

<s>112), ben riconoscendo che quella della fusione col ghiaccio non era la <lb></lb>via da tenersi per la più sicura. </s></p><p type="main">

<s>Maggior varietà di effetti e perciò più largo campo a filosofare ne of-<pb xlink:href="020/01/710.jpg" pagenum="153"></pb>feriva il calorico raggiante, la riflession del quale sopra gli specchi concavi, <lb></lb>per condensarne i raggi dispersi, ebbe tanta efficacia in promuovere la Geo­<lb></lb>metria delle sezioni coniche appresso gli antichi. </s>

<s>Narra Plutarco nella vita <lb></lb>di Numa come il foco gelosamente custodito dalle Vestali, se per caso si <lb></lb>fosse spento, non in altro modo era ordinato si dovesse riaccendere, che de­<lb></lb>rivandolo direttamente dal cielo, e ciò con esporre al sole uno specchio in­<lb></lb>cavato in figura di parabola. </s>

<s>Così pure lasciò scritto Oronzio nella prefazione <lb></lb>al trattato <emph type="italics"></emph>De speculo ustorio,<emph.end type="italics"></emph.end> e tra&#039;meno antichi ch&#039;esercitarono nella scienza <lb></lb>più autorevole il magistero, abbiam Vitellione, che formulava così il Teo­<lb></lb>rema XLIII del IX libro della sua Prospettiva: “ Speculo concavo conca­<lb></lb>vitatis sectionis parabolae soli opposito, ita ut axis ipsius sit in directo cor­<lb></lb>poris solaris, omnes radii incidentes speculo aeque distanter axi reflectuntur <lb></lb>ad punctum unum axis distantem a superficie speculi, secundum quartam <lb></lb>lateris recti ipsius sectionis parabolae speculi superficiem causantis, ex quo <lb></lb>patet quod a superficie talium speculorum ignem est possibile accendi ” <lb></lb>(Norimbergae 1535, pag. </s>

<s>250). </s></p><p type="main">

<s>Dalla lettura di questi Autori, dice Marino Ghetaldo, essersi sentito ac­<lb></lb>cendere il desiderio di fare esperienza di quegli spettacoli “ qua in re cum <lb></lb>a me ea opera esset navata, ut tandem aliquando anno superiori (1602) pro­<lb></lb>positum sim assecutus, illud praeterea commodi accidit, ut ex accurata con­<lb></lb>sideratione repererim id non solum ei accidere speculo quod in formam pa­<lb></lb>rabolae recti atque rectanguli coni est excavatum, sed praeterea his, quae <lb></lb>a parabola coni acutanguli, obtusiangoli et scaleni etiam fuerint descripta ” <lb></lb>(De Parabola, Romae 1603, praef.), ond&#039;egli potè così formulare, estendendo <lb></lb>le proprietà ustorie a ogni genere di parabola, il suo Teorema: “ Omnes <lb></lb>radii solares in speculum concavum a quacumque parabola circa manentem <lb></lb>axem circumducta descriptum incidentes, ita ut axi aequidistent, reflectun­<lb></lb>tur ad unum idemque axis punctum quod scilicet a vertice speculi distat <lb></lb>intervallo quartae partis lateris recti parabolae ipsum speculum describen­<lb></lb>tis ” (ibi, pag. </s>

<s>17). </s></p><p type="main">

<s>Il Maurolico dop&#039;aver dimostrato, nel Teorema XXIV del libro I <emph type="italics"></emph>Dia­<lb></lb>phanorum,<emph.end type="italics"></emph.end> come si può accendere il fuoco per la refrazione de&#039;raggi solari <lb></lb>attraverso a una sfera di vetro, torna col pensiero allo Specchio ustorio pa­<lb></lb>rabolico, che si dice da alcuni essere stato fabbricato da Tolomeo, e crede <lb></lb>possibile che s&#039;otterrebbe il medesimo effetto per rifrazione da una lente <lb></lb>parabolica di cristallo. </s>

<s>“ Ita fortasse liceret fabricare ex vitro, chrystallo, <lb></lb>aliove perspicuo lapide, convexum talis figurae diaphanum, per quod fracti <lb></lb>radii in unum punctum congressi, efficacissimi essent ad ignis generatio­<lb></lb>nem. </s>

<s>Sed hoc, quoniam plus curiositatis habet, perspicacioribus ingeniis <lb></lb>perscrutandum relinquo ” (Neap. </s>

<s>1611, pag. </s>

<s>80). Quando poi le speculazioni <lb></lb>del Sarpi e del Porta si videro confermate da queste del Maurolico, dagli <lb></lb>insegnamenti del quale si sperava di attingere la scienza del Telescopio, la <lb></lb>curiosità per gli Ottici divenne un&#039;occupazione seria, di che vedemmo al­<lb></lb>trove l&#039;Antonini e l&#039;Imperiali darci il più notabile esempio. </s></p><pb xlink:href="020/01/711.jpg" pagenum="154"></pb><p type="main">

<s>In queste esperienze degli specchi e delle lenti ustorie i raggi calorifici <lb></lb>si mostrano così strettamente congiunti co&#039;luminosi, che le questioni di Ter­<lb></lb>mologia si riducono a pure questioni di Ottica. </s>

<s>Chi volesse perciò sapere <lb></lb>che cosa conoscessero gli antichi delle leggi della diffusione del calore nello <lb></lb>spazio, può rammemorarsi la storia della diffusion della luce. </s>

<s>Se non che <lb></lb>sembra che debba in questo particolare farsi un&#039;eccezione per rispetto a <lb></lb>Leonardo da Vinci, nelle note manoscritte del quale noi vediamo chiara­<lb></lb>mente dimostrata la legge dell&#039;intensità del riscaldamento in ragion reci­<lb></lb>proca de&#039;quadrati delle distanze. </s>

<s>“ Il caldo del sole, che si ritroverà sulla <lb></lb>superficie dello specchio concavo, il quale calore si partirà per li razzi pi­<lb></lb>ramidali concorrenti a uno solo punto, il qual punto quanto entrerà nella <lb></lb><figure id="id.020.01.711.1.jpg" xlink:href="020/01/711/1.jpg"></figure></s></p><p type="caption">

<s>Figura 40.<lb></lb>superficie tante volte fia più caldo del <lb></lb>caldo, che si trova sopra lo specchio, <lb></lb>e così quanto AB (fig. </s>

<s>49) o vuoi CD <lb></lb>entra nello specchio, tante volte il <lb></lb>suo calore è più potente che quello <lb></lb>dello specchio ” (Manuscr. </s>

<s>A, Mollien, <lb></lb>fol. </s>

<s>20 r.). E più compendiosamente <lb></lb>altrove si legge: “ Tanto quanto la <lb></lb>punta della piramide solare tagliata in <lb></lb>qualunque parte entra nella sua base, <lb></lb>tante volte fia più calda che essa base ” (ivi, fol. </s>

<s>54 r.). </s></p><p type="main">

<s>I Maestri della scienza però non solo ignorarono questa legge della dif­<lb></lb>fusion del calore, com&#039;avevano ignorato quella della diffusion della luce, ma <lb></lb>sopra più rimasero in dubbio se il calore stesso uniformemente si diffon­<lb></lb>desse in sfera. </s>

<s>Anzi che i raggi calorifici non si diffondessero così, come si <lb></lb>diffondono i luminosi, Galileo si credè che servisse a dimostrarlo questa espe­<lb></lb>rienza: “ Accosti chi si voglia il dito così per fianco alla fiammella di una <lb></lb>candela accesa: certo non sentirà offendersi dal caldo, sinchè per un bre­<lb></lb>vissimo spazio non se le accosta, e che poco meno che non la tocchi. </s>

<s>Ma <lb></lb>per l&#039;opposito esponga la mano sopra la medesima fiammella, sentirà l&#039;of­<lb></lb>fesa del caldo per distanza ben mille volte maggiore di quell&#039;altra per fianco, <lb></lb>mentre l&#039;illuminazione, che dalla medesima fiammella deriva, per tutti i <lb></lb>versi si diffonde, in cioè sù, in giù, lateralmente, ed in somma per tutto, <lb></lb>ed in gran lontananza sfericamente si distende ” (Alb. </s>

<s>VII, 304). </s></p><p type="main">

<s>Non parve agli Accademici del Cimento che questa volgare esperienza <lb></lb>addotta da Galileo fosse decisiva, e perciò ne fecero soggetto de&#039;loro primi <lb></lb>studii come s&#039;ha da uno de&#039;Diarii in cui sotto il dì 10 di Settembre 1657, <lb></lb>è registrata l&#039;esperienza C “ per riconoscere se l&#039;espansione del caldo e del <lb></lb>freddo fosse sfericamente uniforme ” (MSS. Cim, T. II, c. </s>

<s>263). I modi <lb></lb>d&#039;eseguirla furono varii, uno de&#039;quali, proposto dal Rinaldini, consisteva nel­<lb></lb>l&#039;applicar due Termometri simili, nel medesimo momento di tempo e in di­<lb></lb>stanze uguali, uno sotto e uno sopra una palla di ferro molto ben riscaldata. </s>

<s><lb></lb>Era naturale che il Termometro superiore mostrasse d&#039;aver ricevuta mag-<pb xlink:href="020/01/712.jpg" pagenum="155"></pb>giore impressione e “ di qui parve che si potesse raccorre che il calore <lb></lb>non si diffonda egualmente per ogni parte, ma più all&#039;in sù che all&#039;in giù ” <lb></lb>(Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>703). </s></p><p type="main">

<s>Non mancarono di avvertire alcuni fra quegli Accademici che, così in <lb></lb>questa esperienza come e nell&#039;altra di Galileo, la differente diffusion calo­<lb></lb>rifica dipendeva dal vario riscaldamento dell&#039;aria ambiente, per cui fu de­<lb></lb>liberato all&#039;ultimo di sperimentare nel vuoto. </s>

<s>Chi però legge nel libro dei <lb></lb><emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> fra l&#039;<emph type="italics"></emph>Esperienze fatte nel vuoto<emph.end type="italics"></emph.end> questa de&#039;due Termometri così de­<lb></lb>stramente introdotti nel chiuso della camera barometrica, e ne attende il <lb></lb>resultato, riman sorpreso da maraviglia in trovar ancora gli sperimentatori <lb></lb>indecisi se la differenza de&#039;gradi segnati dallo strumentino di sotto e da <lb></lb>quello di sopra dipendesse o dalla irregolare diffusion del calore o dal vario <lb></lb>riscaldamento degli strati dell&#039;aria. </s>

<s>La maraviglia cessa in ogni modo per <lb></lb>coloro, i quali considerano come professando i nostri Accademici tutti in­<lb></lb>sieme concordi l&#039;opinion degl&#039;ignicoli materiali, che a Galileo e al Viviani <lb></lb>si rendevano visibili nell&#039;acqua posta al fuoco, e si rappresentavano ai sensi <lb></lb>del Borelli in que&#039;cunei che inzeppandosi dentro i pori de&#039;corpi ne dila­<lb></lb>tano così evidentemente i volumi; non era possibile riuscissero a persua­<lb></lb>dersi che soggiacendo quegli stessi ignicoli alla circumpulsione degli altri <lb></lb>corpi gravi, non fossero meglio disposti a salire che a moversi indifferen­<lb></lb>temente per tutti i versi. </s></p><p type="main">

<s>Quando queste idee, derivate dall&#039;antica Filosofia greca nell&#039;insegna­<lb></lb>mento galileiano, si abbandonarono, per seguitar più ragionevolmente i nuovi <lb></lb>placiti degli atomi calorifici imponderabili, e allora fu che s&#039;intese come do­<lb></lb>vesse anche il calore diffondersi uniformemente in isfera, imitando la luce. </s></p><p type="main">

<s>Ma pur la stessa diffusione termica per emissione implicava i fisici in <lb></lb>quelle medesime difficoltà che l&#039;emission luminosa, e perciò il Montanari <lb></lb>discorrendo così del calore come del lume, per salvare la legge sperimen­<lb></lb>tale della ragion reciproca de&#039;quadrati delle distanze e non de&#039;cubi, si volse <lb></lb>a professar l&#039;ipotesi dell&#039;onde eteree messe in vibrazione dalle molecole del <lb></lb>corpo calescente. </s>

<s>Questa ipotesi, di che si fa gran merito ad alcuni Fisici <lb></lb>stranieri assai più recenti, era già diffusa in sul finir del secolo XVII nella <lb></lb>Scuola sperimentale bolognese istituita dal medesimo Montanari, e il Gu­<lb></lb>glielmini, uno de&#039;più celebri usciti di quella Scuola, la professava nel suo <lb></lb>trattato <emph type="italics"></emph>De sanguinis natura et proprietate,<emph.end type="italics"></emph.end> ricavandone uno de&#039;più validi <lb></lb>argomenti per confutar l&#039;errore della fiamma vitale. </s>

<s>“ Non minus pariter <lb></lb>falluntur vitalis flammae assertores, cum eius existentiam a luce, quae in <lb></lb>piscibus putrescentibus, ovis lacertorum, noctilucis ecc. </s>

<s>observatur, dedu­<lb></lb>cunt. </s>

<s>Quamvis enim lux inter ignis proprietates et effectus recenseatur, non <lb></lb>ea tamen est, ut absque igne esse nequeat. </s>

<s>Quid enim impedit quominus <lb></lb><emph type="italics"></emph>undulationes iis similes, quae ab ignis agitatione proficiscuntur etiam ab <lb></lb>aliis motibus aetheri imprimantur?<emph.end type="italics"></emph.end> An excitabitur in retina igniculus, cum <lb></lb>presso exterius oculo lucis scintillae videntur observari? </s>

<s>” (Venetiis 1701, <lb></lb>pag. </s>

<s>93). </s></p><pb xlink:href="020/01/713.jpg" pagenum="156"></pb><p type="main">

<s>Pochi anni appresso riscontravasi in questi medesimi pensieri anche il <lb></lb>Newton, mosso dalla considerazione del vedersi diffondere il calore anche <lb></lb>nel vuoto. </s>

<s>“ Si in duobus amplis altisque vitris cylindraceis inversis duo <lb></lb>parva Thermometra ita sint suspensa, ut vitrum non contingant: aerque ex <lb></lb>horum vitrorum altero sit exhaustus, vitraque hoc modo comparata e loco <lb></lb>frigido in calidum deferantur, utique Thermometrorum id quod erit in va­<lb></lb>cuo incalescet nihilo minus, neque fere tardius quam id quod non sit in <lb></lb>vacuo. </s>

<s>Annon iam calor ille exterior trans vacuum defertur, vibrationibus <lb></lb>medii cuiusdam longe quam est aer subtilioris, quod quidem medium, exhau­<lb></lb>sto aere, tamen adhuc in vacuo supersit?... Huiusque medii vibrationes <lb></lb>annon in corporibus calidis, ut eorum calor intensior sit et durabilior effi­<lb></lb>ciunt? </s>

<s>Et corpera calida annon calorem suum in frigida contigua transfe­<lb></lb>runt, vibrationibus huiusce medii e calidis in frigida propagatis? </s>

<s>” (Optices, <lb></lb>Lib. </s>

<s>III, <expan abbr="q.">que</expan> XVIII, Patavii 1773, pag. </s>

<s>142). </s></p><p type="main">

<s>La legge della varia intensità calorifica al variare della distanza, che <lb></lb>ritrovò più facile la sua dimostrazione dappoichè s&#039;introdussero nella scienza <lb></lb>le ipotesi prima professate da&#039;nostri Bolognesi e poi dal Newton, era una <lb></lb>delle principali che concernessero il calorico raggiante, ma ve n&#039;erano altre <lb></lb>pure che avevano richiamato a sè lo studio de&#039;Filosofi con maggiore atten­<lb></lb>zione. </s>

<s>Fra questi è da annoverarsi la legge del vario riscaldamento de&#039;corpi <lb></lb>dipendente dalle varie inclinazioni de&#039;raggi calorifici emessi. </s>

<s>Al problema <lb></lb>proposto a risolvere da lungo tempo alla scienza perchè l&#039;estate sia più <lb></lb>calda dell&#039;inverno, non era difficile rispondere attribuendo l&#039;effetto naturale <lb></lb>al Sole, che si volge intorno alla Terra con guardo ora più ora meno obli­<lb></lb>quo. </s>

<s>Ma restava a dimostrar come mai e con qual proporzione l&#039;intensità <lb></lb>calorifica sopra una data superficie scemi, crescendo l&#039;obliquità del raggio <lb></lb>incidente. </s></p><p type="main">

<s>La dimostrazione del Teorema fu de&#039;primi a tentarla Giovan Batista <lb></lb>Benedetti, studiandosi d&#039;esplicare un concetto espresso così nella LVII del <lb></lb>X libro di Vitellione: “ Radios corporis luminosi per reflexionem vel re­<lb></lb>fractionem aggregari palam est ” (Perspectiva cit., pag. </s>

<s>281). Sieno QP, BD <lb></lb>(fig. </s>

<s>50, 51), dice il Benedetti, due superficie uguali, e sopra la prima cada <lb></lb><figure id="id.020.01.713.1.jpg" xlink:href="020/01/713/1.jpg"></figure></s></p><p type="caption">

<s>Figura 50.<lb></lb><figure id="id.020.01.713.2.jpg" xlink:href="020/01/713/2.jpg"></figure></s></p><p type="caption">

<s>Figura 51.<lb></lb>il raggio AP, con l&#039;obliquità AQP, sopra la seconda cada UB con l&#039;obli­<lb></lb>quità UBD minore della prima. </s>

<s>Riflettendosi i raggi in ambedue i casi in <lb></lb>modo da far gli angoli d&#039;incidenza uguali agli angoli di riflessione, gli ag-<pb xlink:href="020/01/714.jpg" pagenum="157"></pb>gregati de&#039;raggi nelle riflessioni sopra le superficie QP e BD saranno pro­<lb></lb>porzionali ai triangoli OQP, IBD “ quorum duorum triangulorum nullus <lb></lb>unquam erit qui dubitari possit QOP non esse minorem BID, cum anguli <lb></lb>Q e P trianguli QOP acutiores sint angulis B et D trianguli BID, ex sup­<lb></lb>posito ” (Speculat. </s>

<s>lib., Venetiis 1599, pag. </s>

<s>188). E perciò la superficie QP <lb></lb>sarà meno riscaldata della superficie BD. </s></p><p type="main">

<s>Il Boulliaud poi seguì queste stesse norme nella proposizione XXXVI <lb></lb>del suo trattato <emph type="italics"></emph>De natura lucis,<emph.end type="italics"></emph.end> che è così formulata ed è un eco di quella <lb></lb>di Vitellione: “ Lux primaria cum secundaria idest, incidens cum repercussa <lb></lb>coniuncta plus calescunt ” (Parisiis 1638, pag. </s>

<s>55). D&#039;onde ne conclude che <lb></lb>nell&#039;estate il lume secondario si unisce col primario come nella figura 51, <lb></lb>e nell&#039;inverno si separano a vicenda come si vede nel figura 50. “ Ae­<lb></lb>state enim lumen secundarium cum primario unitur.... hieme separantur <lb></lb>ad invicem ” (ibi). </s></p><p type="main">

<s>Ma il Benedetti procede più oltre nella sua dimostrazione, ed è qui dove <lb></lb>incomincia a specular da sè stesso lasciandosi lungamente indietro il pol­<lb></lb>lacco Autore della Prospettiva più antico. </s>

<s>“ Quod vero attinet ad maiorem <lb></lb>quantitatem luminis super Terrae superficiem imaginemur radium AQ (fig. </s>

<s>52) <lb></lb><figure id="id.020.01.714.1.jpg" xlink:href="020/01/714/1.jpg"></figure></s></p><p type="caption">

<s>Figura 52.<lb></lb>cuius respectu etiam imaginemur duos super­<lb></lb>ficiei Terrae situs, quorum unus sit QO, cui <lb></lb>dictus radius sit perpendicularis, et alter QP <lb></lb>cui radius AQ ex obliquo incidat. </s>

<s>Imaginemur <lb></lb>ergo triangulum QOP, cuius angulus O rectus <lb></lb>est ex supposito, unde QO minor erit QP, <lb></lb>ex XVIII primi Euclidis. </s>

<s>Hinc fit ut super QO <lb></lb>cadat universum lumen quod super QP diffun­<lb></lb>ditur. </s>

<s>Sit QU aequalis QO et sit imaginatione <lb></lb>protracta UN aequidistans POA, unde QU il­<lb></lb>luminata erit a radio NQ minore radio <expan abbr="Aq;">Aque</expan> <lb></lb>ergo minus calida erit superficies QU ipsius <lb></lb>terrae, quam QO, quia maius lumen in se maiorem calorem includit quod <lb></lb>manifeste apparet in radiorum unione mediante reflexione aut refractione ” <lb></lb>(Speculat. </s>

<s>lib. </s>

<s>cit., pag. </s>

<s>188). </s></p><p type="main">

<s>Galileo poi compendiò e ridusse all&#039;intelligenza di Simplicio questa dimo­<lb></lb>strazione del Benedetti, nella Giornata I de&#039;<emph type="italics"></emph>Due Massimi Sistemi<emph.end type="italics"></emph.end> (Alb. </s>

<s>I, 91) <lb></lb>ma nessuno de&#039;due grandi Maestri riuscì a formulare la legge dell&#039;inten­<lb></lb>sità proporzionale al seno dell&#039;angolo dell&#039;incidenza. </s>

<s>Questo teorema, così <lb></lb>l&#039;Ottica che la Termologia, lo derivarono dalla legge meccanica della per­<lb></lb>cossa, non dimostrata prima del 1644. </s></p><p type="main">

<s>Il considerar che s&#039;ebbe a fare allora come un raggio incidente o di <lb></lb>luce o di calore serba nell&#039;illuminare e nel riscaldare le medesime leggi di <lb></lb>un grave che percotesse con quella stessa incidenza una superficie, conferì <lb></lb>moltissimo a confermare i discepoli di Galileo, a&#039;quali si deve la dimostra­<lb></lb>zione di quel Teorema della percossa, nell&#039;opinione degli ignicoli materiali, <pb xlink:href="020/01/715.jpg" pagenum="158"></pb>tanto più che per essi ignicoli insinuantisi più o men facilmente dentro i <lb></lb>pori de&#039;corpi, erasi ritrovato da sodisfar convenientemente a una curiosità <lb></lb>singolare qual&#039;era quella della varia quantità di calore assorbito dalle su­<lb></lb>perficie bianche e dalle nere esposte per lo stesso spazio di tempo all&#039;irrag­<lb></lb>giamento del medesimo corpo calescente. </s></p><p type="main">

<s>Quella curiosità non era sfuggita alla considerazion del Keplero, il quale <lb></lb>nella proposizione XXXVIII del I libro de&#039;Paralipomeni a Vitellione si pro­<lb></lb>poneva di spiegare in che modo <emph type="italics"></emph>Lux nigra facilius inflammet quam alba,<emph.end type="italics"></emph.end><lb></lb>e ritrovava quella spiegazione in ciò, ch&#039;essendo della natura della luce il <lb></lb>distruggere e il consumare, i corpi neri, che minor quantità di luce riflet­<lb></lb>tono de&#039;bianchi, vengon perciò più facilmente impregnati di calorè e più <lb></lb>pronti a infiammarsi. </s>

<s>“ Hinc orta est opinio, conclude il Keplero, nigris cogi <lb></lb>radios, albis dissipari ” (Francof. </s>

<s>1604, pag. </s>

<s>28). </s></p><p type="main">

<s>Il Castelli però ne fece particolar soggetto di esperienze e di specula­<lb></lb>zioni, ch&#039;egli espose in una sua scrittura sotto forma di lettera indirizzata <lb></lb>a Galileo, e alla quale si dava il nome di <emph type="italics"></emph>Mattonata.<emph.end type="italics"></emph.end> Venne un tal nome <lb></lb>alla detta scrittura dall&#039;essersi fatta l&#039;esperienza sopra un mattone mezzo <lb></lb>tinto di bianco e mezzo di nero, che esposto al sole di estate e poi appres­<lb></lb>sata ora all&#039;una parte ora all&#039;altra una mano, nella parte nera sentivasi <lb></lb>molto più bruciante. </s>

<s>Narra il Castelli stesso com&#039;avesse dato ad intendere <lb></lb>un tal effetto naturale a un signorino di casa Martinenghi, supposto che i <lb></lb>corpi bianchi riflettano la luce in maggior copia de&#039;neri, e immaginandosi <lb></lb>che gl&#039;ignicoli scendessero dal sole a percotere nel mattone, come tante <lb></lb>palle infocate esplose da una pistola. </s>

<s>“ Se noi sparassimo venticinque colpi <lb></lb>di pistola con palle infocate nella parte nera, e venticinque nella parte <lb></lb>bianca, senza esporre il mattone al lume del sole, e di quelle sparate dalla <lb></lb>nera ritornassero indietro venti, ma di quelle che fossero sparate nella bianca <lb></lb>ne ritornassero indietro solamente cinque; in qual parte sarebbero restate <lb></lb>più palle infocate, nella nera ovvero nella bianca? </s>

<s>pensateci bene. </s>

<s>Ed egli <lb></lb>senza molto pensarci francamente rispose: nella bianca. </s>

<s>Mi piacque fuor di <lb></lb>modo quella prontezza e vivacità di spirito, e soggiunsi: Ma la verità è, si­<lb></lb>gnor marchese, che V. S. mi ha detto poco fa che, spargendosi egualmente <lb></lb>il lume del sole sopra il nero e sopra il bianco, ritorna indietro agli occhi <lb></lb>nostri più lume dal bianco che dal nero, non è così? </s>

<s>— Padre sì — ri­<lb></lb>spose. </s>

<s>— E di più V. S. ha confessato che il lume del sole è caldo, non è <lb></lb>vero? </s>

<s>— È verissimo — disse. </s>

<s>— Adunque, soggiunsi io, non è da far ma­<lb></lb>raviglia nessuna che essendo vero che nella parte nera sono restate molto <lb></lb>maggiori moltitudini di palline calde, che nella parte bianca, quando noi ci <lb></lb>applichiamo le mani si senta maggior caldo nella parte nera che nella bianca, <lb></lb>ed ecco che il signor marchese ha saputo rispondere esquisitamente ” (Opusc. </s>

<s><lb></lb>Filos., Bologna 1669, pag. </s>

<s>60). </s></p><p type="main">

<s>In che modo fossero nella parte nera rimasti presi più ignicoli che nella <lb></lb>bianca lo dava il Castelli a intendere a quel signorino rappresentandogli al­<lb></lb>l&#039;immaginazione un certo artificio usato dalla Natura nel costruire i pori <pb xlink:href="020/01/716.jpg" pagenum="159"></pb>alle superficie nere de&#039;corpi. </s>

<s>Il Magalotti che applaudì a quel bene imma­<lb></lb>ginato artificio, e l&#039;applicò a spiegar come i raggi del sole entrino dentro <lb></lb>i chicchi dell&#039;uva a fin di dimostrar quanto fosse vero il detto galileiano <lb></lb>non esser cioè altro il vino che un composto di umore e di luce; rendeva <lb></lb>in questa forma evidenti le cose immaginate dallo stesso Castelli: “ Figu­<lb></lb>ratevi che sieno i pori di que&#039;corpi, che si chiamano neri sepolchri artifi­<lb></lb>ziosissimi della luce, talmente disposti che i raggi che gli feriscono abbian <lb></lb>sempre le loro fughe verso le parti più interne, e tutte le novelle direzioni <lb></lb>che acquistano dagli scontri di quelle facce, gl&#039;impegnino sempre più ad­<lb></lb>dentro, e in così fatto modo vi rimangan sepolti. </s>

<s>Dove per lo contrario delle <lb></lb>superficie di que&#039;corpi che si chiaman bianchi diremo ch&#039;elle sieno d&#039;un <lb></lb>così fatto lavoro, che tutti o la maggior parte de&#039;lumi che le feriscono si <lb></lb>rifondano agli occhi nostri ” (Lettere scientifiche, Firenze 1721, pag. </s>

<s>49). </s></p><p type="main">

<s>Queste però, convien confessarlo, piuttosto che speculazioni scientifiche, <lb></lb>si direbbero giochi di fantasia, conformi dall&#039;altra parte alle opinioni di quel <lb></lb>Castelli, che mostrava insieme con Galileo, e rendeva visibili a Lodovico <lb></lb>delle Colombe gli atomi del foco dentro l&#039;acqua delle ampolle di vetro ri­<lb></lb>scaldate. </s>

<s>E benchè il Magalotti non solo ma il Borelli e il Viviani si com­<lb></lb>piacessero di quelle fantasie, il Grimaldi però scioglieva questi stessi pro­<lb></lb>blemi termici in modo assai più conveniente alla natura del calore, che <lb></lb>nessuno oramai più crede di veder con gli occhi e di pesare sulle stadere. <lb></lb></s>

<s>“ Sufficiat observare ideo corpora quae dicuntur alba reflectere multum <expan abbr="lu-minīs">lu­<lb></lb>minins</expan>, quia illud quam minime debilitant per novam aliquam fluitationem <lb></lb>in eo inductam, et ex opposito nigra corpora parum luminis reflectere, quia <lb></lb>illud maxime enervant, ac fere extinguunt, obtundentes eius celeritatem ac <lb></lb>vim impetus in profusione certis ondulationibus turbata. </s>

<s>Hinc etiam pote­<lb></lb>rit reddi ratio cur alba difficilius calefiant a lumine, nigra vero facilius cae­<lb></lb>teris paribus, quia nimirum lumen ab abis expedite reflexum vix habet in <lb></lb>eorum poris luctam ullam et agitationem radiorum. </s>

<s>At dum lumen etiamsi <lb></lb>eiusdem intensionis seu densitatis incurrit in corpus nigrum, seque inter <lb></lb>poros illius insinuat, non ita expedite potest ab illis egredi, ideoque non nisi <lb></lb>cum multa lucta et post multas agitationes revertitur, quidus necessario <lb></lb>debuit impetum facere intra poros illos, simulque calorem excitare ” (De <lb></lb>Lum. </s>

<s>cit., pag. </s>

<s>361). </s></p><p type="main">

<s>Parve approvare questa ipotesi del Grimaldi anche il Newton, quando <lb></lb>così scriveva nella VI Questione: “ Annon corpora nigra calorem de lumine <lb></lb>ideo facilius quam corpora colorata concipiunt quia luminis id quod in illa <lb></lb>incidit non reflectitur extra, sed ingreditur ìn ipsa corpora, intraque ea re­<lb></lb>flectitur ac refringitur saepius atque iterum usque eo donec restinguatur <lb></lb>penitus et intercidat? </s>

<s>” (Optic, lib. </s>

<s>III cit., pag. </s>

<s>138). </s></p><p type="main">

<s>Considerando ora da qual parte la soluzione del Grimaldi e del Newton <lb></lb>s&#039;avvantaggi sopra quella del Castelli, si vede che un tal vantaggio in ciò <lb></lb>principalmente consiste, che il Castelli attribuisce il maggior riscaldamento <lb></lb>alla maggior quantità degl&#039;ignicoli rimasti presi alla trappola de&#039;pori neri, <pb xlink:href="020/01/717.jpg" pagenum="160"></pb>mentre il Grimaldi e il Newton l&#039;attribuiscono all&#039;agitamento e al moto <lb></lb>degli atomi luminosi, i quali mettono poi in moto vibratorio le molecole <lb></lb>de&#039;corpi <emph type="italics"></emph>in quo calor consistit<emph.end type="italics"></emph.end> (Optic. </s>

<s>lib. </s>

<s>III, <expan abbr="q.">que</expan> V). In sostanza però non <lb></lb>era questa dottrina nuova. </s>

<s>Galileo fu dall&#039;esperienza condotto a dire che <emph type="italics"></emph>ad <lb></lb>eccitare il caldo non basta la presenza degli ignicoli ma ci vuole il loro <lb></lb>movimento ancora<emph.end type="italics"></emph.end> (Alb. </s>

<s>IV, 337) e insegnava che due corpi confricati in­<lb></lb>sieme per questo si riscaldano perchè lo stripicciamento <emph type="italics"></emph>coll&#039;aprir l&#039;uscita <lb></lb>agl&#039;ignicoli contenuti gli riduce finalmente in moto<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>338). </s></p><p type="main">

<s>Ma il Grimaldi e il Newton, rivolgendosi più attentamente a considerar <lb></lb>le relazioni che passano fra il moto e il calore, dettero apparecchiamento <lb></lb>più prossimo a quelle teorie, che formano la compiacenza e la gloria della <lb></lb>Fisica moderna. </s>

<s>Dissero gli antichi: il moto eccita il calore. </s>

<s>Poi quando si <lb></lb>videro le macchine esser mosse dal foco, si notò che il calore produceva il <lb></lb>moto, e si finì col dire essere una medesima cosa, sotto forma e apparenza <lb></lb>diversa, il moto e il calore. </s>

<s>Così credono d&#039;aver menato finalmente trionfo <lb></lb>sopra la crassa ignoranza di chi ammetteva gl&#039;ignicoli materiali o gli atomi <lb></lb>imponderabili, e si lusingano dolcemente questi beati sapienti d&#039;avere sco­<lb></lb>perta la natura del calore, dicendo ch&#039;egli è una forza. </s>

<s>Ma che cosa è la <lb></lb>forza, che cosa è il moto? </s>

<s>Quando i Fisici sapranno rispondere, ci sapranno <lb></lb>anche insegnare che cosa è il calore, ma per ora i vantati progressi della <lb></lb>scienza non par che in altro sien fatti consistere da molti che in calcoli <lb></lb>facilissimi a far colla penna, e inspirati a quel sentimento peripatetico car­<lb></lb>tesiano, col quale si presume il Filosofo di farsi legislatore e non alunno <lb></lb>della Natura. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>In qualunque modo, poichè sempre riuscirà misteriosa al nostro debole <lb></lb>intelletto la cognizione di quella causa operatrice degli effetti, che da noi <lb></lb>s&#039;attribuiscono al calore, per non seguitare a provocarci lo sdegno di coloro <lb></lb>che si compiacciono d&#039;aver finalmente scoperta quella recondita causa, te­<lb></lb>niam dietro a que&#039;più modesti che si contentarono di considerarne gli effetti. </s></p><p type="main">

<s>Tra gli effetti del calore, ch&#039;essendo così comuni, furono perciò de&#039;primi <lb></lb>a richiamare a sè l&#039;attenzione e lo studio de&#039;Filosofi, son da annoverar gli <lb></lb>agghiacciamenti e l&#039;evaporazioni. </s>

<s>Ne&#039;primi anni del secolo XVII applican­<lb></lb>dosi da Peripatetici quel general principio approvato dalla loro Filosofia che <lb></lb>sia proprietà del freddo il condensare, si diceva senza timor di dubbio che <lb></lb>anche il ghiaccio era acqua condensata. </s>

<s>Galileo fu il primo che si oppose a <lb></lb>così fatta sentenza pronunziando ch&#039;egli avrebbe creduto “ piuttosto il ghiac­<lb></lb>cio esser acqua rarefatta che condensata, poichè la condensazione partorisce <lb></lb>diminuzione di mole e augumento di gravità, e la rarefazione maggior leg-<pb xlink:href="020/01/718.jpg" pagenum="161"></pb>gerezza e augumento di mole; e l&#039;acqua nel ghiacciarsi cresce di mole e il <lb></lb>ghiaccio già fatto è più legger dell&#039;acqua standovi a galla ” (Alb. </s>

<s>XII, 12). </s></p><p type="main">

<s>Rispondevano i Peripatetici che il ghiaccio galleggia per ragion della <lb></lb>figura sua larga e piana, nò per esser più leggero dell&#039;acqua, ond&#039;è che <lb></lb>pigliando Galileo di qui occasione a trattar delle galleggianti, lasciò il ca­<lb></lb>rico ad altri di dimostrar come l&#039;acqua sola non partecipi agli effetti di <lb></lb>condensazione consueti operarsi dal freddo in tutti gli altri corpi. </s></p><p type="main">

<s>I seguaci del Gassendo dicevano essere gli atomi frigorifici che insi­<lb></lb>nuandosi dentro l&#039;acqua ne fanno ricrescere la mole e la induriscono ce­<lb></lb>mentandone insieme le particelle. </s>

<s>Ma a costoro era facile rispondere che <lb></lb>sottentrando gli atomi frigorifici in luogo de&#039;calorifici sarebbero dovute così <lb></lb>la mole come la gravità rimaner le medesime, non vedendosi ragione perchè <lb></lb>debban gli atomi del freddo riuscir più leggeri e più voluminosi di quelli <lb></lb>del caldo. </s></p><p type="main">

<s>I seguaci di Galileo ammettendo che i vacui dell&#039;acqua liquida sien <lb></lb>pieni di un vapore igneo, fatto esalar questo dal freddo, l&#039;acqua stessa per <lb></lb>dir così si secca, e diventa più leggera. </s>

<s>“ Mirabile quidem, lasciò scritto di <lb></lb>propria mano il Viviani, est magni Galilaei praeceptoris mei amatissimi ef­<lb></lb>fatum.... Soliditatem nempe et consistentiam metallorum non ex alia forsan <lb></lb>pendere causa quam ex vacuo .... Aqua vero semper fluit cum ipsius athomi <lb></lb>semper sint admistae vapore, qui vacuum replet, qui tamen vapor interdum <lb></lb>ob nimium frigus expellitur et aqua, ut ita dicam, siccatur et fit glacies, <lb></lb>cum inter ipsius athomos remaneant vacua ac propterea glacies aquae su­<lb></lb>pernatat ” (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>17). </s></p><p type="main">

<s>Così però non rendevasi ragione del ricrescimento di mole, per cui il <lb></lb>Dati ebbe a dire che un tal fatto, il quale sempre si osserva negli agghiac­<lb></lb>ciamenti dell&#039;acqua, faceva cadere tutta quella speculazione. </s>

<s>“ E&#039;fu un tempo <lb></lb>che io credetti che partendosi le minime particelle del foco totalmente dal­<lb></lb>l&#039;acqua ne seguisse che restando l&#039;acqua in tutto priva di calore cioè di <lb></lb>foco diventasse freddissima. </s>

<s>E perchè in quegli ultimi spazii ripieni dal fuoco <lb></lb>non potesse entrare altro (perciocchè piccolissimi fossero ed impermeabili ad <lb></lb>ogni altro corpo) detti spazii restassero voti e per così dire pieni di vacui, <lb></lb>i quali vacui disseminati fossero cagione sì dell&#039;agghiacciamento .... sì della <lb></lb>leggerezza del ghiaccio sopra l&#039;acqua, essendone partito il foco ponderoso e <lb></lb>rimastovi il vacuo senza pro niuno. </s>

<s>Ma veggendosi che l&#039;acqua agghiac­<lb></lb>ciando cresce di mole, cade a terra tutta questa speculazione, ed è neces­<lb></lb>sario vedere che cosa sia quella che entra nell&#039;acqua a farla coagulare e <lb></lb>crescere insieme, vedendosi chiaro non potersi dare agghiacciamento senza <lb></lb>augumento, onde quello che fa crescere certo è che è anche la necessaria <lb></lb>cagione dell&#039;agghiacciamento ” (MSS. Cim., T. XXXIV, c. </s>

<s>37). </s></p><p type="main">

<s>Nessuno aveva ancora badato a quelle bolle disseminate per la mole <lb></lb>del ghiaccio rimaste ivi dentro prese, per così dire, alle reti del freddo. </s>

<s>Il <lb></lb>Gassendo è vero ne aveva fatto qualche cenno, ma non essendosi troppo <lb></lb>chiaramente espresso, sfuggì per qualche tempo all&#039;accortezza degli stessi <pb xlink:href="020/01/719.jpg" pagenum="162"></pb>gassendisti quel così comodo refugio. </s>

<s>“ Cum verum sit aquam calefactam <lb></lb>refrigescendo citius fortiusque conglaciare quam frigidam, ecquam aliam pu­<lb></lb>temus causam quam quia facta maiore quodam partium aquae laxitate ipsae <lb></lb>aer facilius subingreditur et vehementius stringit particulas aquae quibus <lb></lb>commiscetur? </s>

<s>” (Animadversiones in X Laertii, Lugduni 1675, T. I, pag. </s>

<s>573). </s></p><p type="main">

<s>Poi dopo si avvidero i seguaci del Gassendo del buon partito che avreb­<lb></lb>bero potuto trarne esplicando quegl&#039;involuti concetti del loro Maestro, e ap­<lb></lb>plicandoli particolarmente al fatto in questione dissero esser causa del ri­<lb></lb>crescimento del ghiaccio l&#039;aria, la quale introducendosi dal di fuori vi riman <lb></lb>presa e come agghiacciata. </s>

<s>L&#039;esperienza però degli agghiacciamenti dentro <lb></lb>i vasi di metallo pieni d&#039;acqua e benissimo chiusi, faceva cader d&#039;un tratto <lb></lb>così nuova e assai bella speculazione. </s>

<s>Si sarebbe essa potuta facilmente sal­<lb></lb>vare supponendo che l&#039;aria, invece di sopravvenir dal di fuori, preesistesse <lb></lb>già in mezzo all&#039;acqua, ma erano molto alieni dal suppor ciò come possi­<lb></lb>bile, specie i Fisici della scuola galileiana. </s></p><p type="main">

<s>L&#039;esperienza delle bollicelle che per effetto del calore si sciolgon dal <lb></lb>liquido, esperienza che avrebbe potuto ridurre quella possibilità a una prova <lb></lb>di fatto, si sa bene come fosse intesa da Galileo e dal Castelli, e come fos­<lb></lb>sero dal Viviani nel <emph type="italics"></emph>Discorso sopra Democrito<emph.end type="italics"></emph.end> confermate le illusioni de&#039;due <lb></lb>grandi Maestri. </s></p><p type="main">

<s>Abbiamo detto che alieni da quella supposizione erano particolarmente <lb></lb>i discepoli di Galileo, perchè per aria e non per globetti di fuoco erano stati <lb></lb>riconosciuti, que&#039;sonagli che si vedono salir su per l&#039;acqua riscaldata, dal <lb></lb>Noel, dal Pecquet e da tutti coloro che alla dilatazione immediata di quella <lb></lb>stessa aria annidatavi dentro attribuivano la dilatazione termometrica del­<lb></lb>l&#039;acqua. </s>

<s>Non si potrebbe affermare perciò che avessero conosciuta la pro­<lb></lb>prietà de&#039;liquidi di sciogliere i corpi gassosi: forse essi credevano che il <lb></lb>calore facesse convertire il liquido in gasse, e che perciò avvenisse di ritro­<lb></lb>var così sempre l&#039;aria in mezzo all&#039;acqua riscaldata. </s></p><p type="main">

<s>Questo anzi è certo per quel che riguarda un nostro Italiano, a cui <lb></lb>giovò l&#039;aver bevuto alle fonti cartesiane per non farsi cieco ammiratore di <lb></lb>ogni dottrina di Galileo. </s>

<s>Tommaso Cornelio osservando il gallozzolar del­<lb></lb>l&#039;acqua di un&#039;ampolla esposta ai raggi del sole, non dubitò di asserir che <lb></lb>quella era aura vaporosa in che trasformavasi l&#039;acqua stessa per opera del <lb></lb>calore. </s>

<s>“ Si vitream ampullam aquae plenam solaribus radiis exponemus, <lb></lb>videbimus infra ipsam aquam passim gigni plurimas aeris bullas margari­<lb></lb>tularum speciem gerentes.... Id autem aestate frequentius contingit, propte­<lb></lb>rea quod calor aquam in vapores facile solvit atque idcirco complures ae­<lb></lb>raee bullae progignuntur ” (Progymnasmata phisica, Neapoli 1688, pag. </s>

<s>398). </s></p><p type="main">

<s>La particolare scrittura fra&#039;Proginnasmi citati, dalla quale abbiamo tra­<lb></lb>scritte queste parole, è un&#039;Epistola intitolata <emph type="italics"></emph>De cognatione aeris et aquae<emph.end type="italics"></emph.end><lb></lb>diretta a M. </s>

<s>Aurelio Severino da Roma nel 1649. Ivi soggiornava allora <lb></lb>l&#039;Autore familiarmente conversando con Michelangiolo Ricci, dalla bocca del <lb></lb>quale ebbe la notizia dell&#039;esperienze fatte dal Torricelli e dal Magiotti in-<pb xlink:href="020/01/720.jpg" pagenum="163"></pb>torno alla renitenza certissima dell&#039;acqua alla compressione. </s>

<s>La prima espe­<lb></lb>rienza fu fatta dal Verulamio e da lui stesso descritta nel § XLV del secondo <lb></lb>libro del <emph type="italics"></emph>Nuovo Organo.<emph.end type="italics"></emph.end> Venne al Torricelli voglia di ripeterla nelle sale <lb></lb>de&#039;Pitti, per confermare l&#039;importantissima verità del fatto, e per dar gusto <lb></lb>al Granduca, il quale fece con regia liberalità tornire esquisitamente sfere <lb></lb>gettate di argento, di rame e di ottone, per servire a quest&#039;unico intento. </s>

<s><lb></lb>Chi volesse aver di ciò più particolar notizia e più compiuta, legga, invece <lb></lb>della descrizione fatta nel libro de&#039;<emph type="italics"></emph>Saggi di naturali esperienze<emph.end type="italics"></emph.end> (Firenze 1841, <lb></lb>pag. </s>

<s>130), la seguente nota scritta di propria mano da Vincenzio Viviani: </s></p><p type="main">

<s>“ Che l&#039;acqua come acqua non si possa nemmeno con qualsivoglia vio­<lb></lb>lenza condensare per minima parte, l&#039;ha sperimentato il Serenissimo Gran­<lb></lb>duca. </s>

<s>Ha fatto gettare d&#039;ogni metallo com&#039;argento, rame, ottone ecc. </s>

<s>più <lb></lb>palle vuote per di dentro e di grossezza di orlo intorno a quella di una pia­<lb></lb>stra d&#039;argento, quali poi per un foro fattovi a vite ha fatto empir d&#039;acqua <lb></lb>e serrato con vite di simili metalli strettissimamente il foro di dette palle <lb></lb>le ha poi fatte posare sopra un&#039;incudine e fattegli dare colpi gagliardi con <lb></lb>un martello d&#039;acciaio e ha osservato S. A. che l&#039;acqua inclusa per non pa­<lb></lb>tire condensazione alla violenza de&#039;colpi trasudava fuori della palla per i pori <lb></lb>del metallo ” (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>5). </s></p><p type="main">

<s>Il resultato di queste esperienze, come di tutte le altre fatte nella Corte <lb></lb>medicea, le partecipava il Torricelli a Raffaello Magiotti, il quale nel risol­<lb></lb>vere poi que&#039;problemi idrostatici mandati da Firenze e descritti a Don Lo­<lb></lb>renzo de&#039;Medici, confermò quella renitenza dell&#039;acqua alla impressione con <lb></lb>altre nuove spettacolose esperienze. </s>

<s>Il Cornelio dunque informato di tutto <lb></lb>ciò come abbiamo detto dal Ricci, ne ricavava di qui un valido argomento <lb></lb>a provar che l&#039;aria non può in nessun modo ospitare nell&#039;acqua, perchè <lb></lb>essendo questa fortemente compressa, dovrebbe almeno cedere per la cede­<lb></lb>volezza dell&#039;aria, se facesse veramente parte della sua mole. </s></p><p type="main">

<s>L&#039;argomento del Cornelio era ragionevole che potesse altresì sulle menti <lb></lb>de&#039;nostri Fiorentini in non farle andar così facilmente a supporre che l&#039;aria <lb></lb>si rannidasse naturalmente nell&#039;acqua. </s>

<s>Non avevano pensato mai però di <lb></lb>farne particolare e diligente esperienza, quando Paolo Del Buono, con let­<lb></lb>tera del dì 6 Ottobre 1657 scritta da Vienna, annunziava a Leopoldo de&#039;Me­<lb></lb>dici che s&#039;era da pochi mesi dichiarato principe dell&#039;Accademia del Cimento, <lb></lb>uno de&#039;più fantastici effetti che gli fosse a suo credere occorso di trovare <lb></lb>nella Natura. </s>

<s>Consisteva un tal effetto nel veder che dall&#039;acqua rinchiusa in <lb></lb>ampollette di vetro con sottilissimo collo, sempre si generava aria, benchè <lb></lb>in più o meno copia secondo che maggiore o minore era il caldo della sta­<lb></lb>gione. </s>

<s>Diceva in proporre quelle sue esperienze che, sebben non fosse riu­<lb></lb>scito a investigar le cause di effetti tanto stravaganti, sperava nulladimeno <lb></lb>che sarebbero “ ai signori Accademici occasioni di assai curiose speculazioni <lb></lb>non solo, ma di trarne la certezza di qualche occulta fin&#039;ora verità nelle <lb></lb>cose naturali ” (Targionì, Notizie cit., T. II, P. I, pag. </s>

<s>312). </s></p><p type="main">

<s>Proposte l&#039;esperienze del Del Buono nell&#039;Accademia e riscontratesi ve-<pb xlink:href="020/01/721.jpg" pagenum="164"></pb>rissime, il Borelli forse compiacente di non andare in tutto ai versi del Vi­<lb></lb>viani tenace di quel vapore igneo circondante gli atomi dell&#039;acqua, se­<lb></lb>condo l&#039;opinione del suo amatissimo Galileo; non dubitò di affermare che <lb></lb>l&#039;aria generatasi dall&#039;acqua nel collo delle ampolle preesistesse nell&#039;acqua <lb></lb>stessa sceveratavi dal calore. </s>

<s>Non decideva se ciò avvenisse per insinuazione <lb></lb>delle particelle aereose esterne o per sotterranee esalazioni, ma supposto in <lb></lb>ogni modo questo fatto per vero, spiegava il Borelli in una sua scrittura <lb></lb>indirizzata al principe dell&#039;Accademia da Roma il dì 21 di Settembre 1658, <lb></lb>il ricrescimento della mole del ghiaccio. </s>

<s>Supposto ciò, e accettando da Ga­<lb></lb>lileo quel che con filosofica libertà credeva di accettare, supposto di più che <lb></lb>esalato il vapor igneo d&#039;intorno agli atomi dell&#039;acqua, questi venissero più <lb></lb>prontamente a esercitare la reciproca attrazion magnetica, o molecolare come <lb></lb>si direbbe oggidì, e fossero perciò la causa dell&#039;indurirsi la mole; così l&#039;in­<lb></lb>gegnoso Fisico dimostrava il suo assunto: </s></p><p type="main">

<s>“ Supponendo il freddo esser privazione di calore, allorchè l&#039;acqua si <lb></lb>raffredda, è necessario che traspiri dalla detta acqua moltitudine grande di <lb></lb>atomi ignei. </s>

<s>Ma all&#039;assenza di detti atomi ignei segue l&#039;unione e contatto <lb></lb>delle parti acquee e libertà di esercitare la virtù magnetica, e quel moto che <lb></lb>è necessario per unirsi e scappar fuori dai buchetti degli atomi aerei, i quali <lb></lb>impedivano l&#039;unione di detti atomi, e dentro dei quali gli atomi acquei per <lb></lb>la necessità del sito stavano pravamente collocati, e fuor del loro sito na­<lb></lb>turale. </s>

<s>Adunque è necessario che tutti quegli atomi aerei, i quali son di­<lb></lb>spersi dentro la sostanza dell&#039;acqua rimangano voti d&#039;acqua.... E perchè <lb></lb>gli spazietti occupati dal foco allorchè l&#039;acqua era fluida sono incompara­<lb></lb>bilmente minori di quelli spazii vacui della concavità degli atomi aerei, per <lb></lb>esser gli atomi ignei assai più piccoli che non sono gli atomi aerei, adun­<lb></lb>que necessariamente nell&#039;atto dell&#039;addiacciamento dee ampliarsi la mole del­<lb></lb>l&#039;acqua ” (Fabbroni, Lett. </s>

<s>in., Firenze 1773, T. I, pag. </s>

<s>105, 6). </s></p><p type="main">

<s>Il Viviani però che voleva in tutto e per tutto salvar le dottrine di Ga­<lb></lb>lileo non approvava l&#039;ipotesi dell&#039;aria ospitante in mezzo all&#039;acqua, sopra <lb></lb>la quale principalmente il Borelli fondava la sua dimostrazione. </s>

<s>E tanto era <lb></lb>persuaso di ciò che, non avendo potuto liberarsi da quel bollimento che fa­<lb></lb>ceva sempre il mercurio nel tubo torricelliano, propose “ di fare un can­<lb></lb>none di stagno lungo sedici braccia e supplire sino in venti con canne di <lb></lb>vetro per aver campo di fare il vuoto con l&#039;acqua e per osservare se ve­<lb></lb>ramente queste bollicine ascendenti dall&#039;argento vivo sian particelle di aria ” <lb></lb>(Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>439). </s></p><p type="main">

<s>Questa esperienza, eseguita nel dì 18 Agosto 1660, è la prima colla <lb></lb>quale i nostri Fiorentini operarono il vuoto con tubi pieni di acqua, come <lb></lb>avevano fatto già il Berti a Roma e il Pascal a Roano ritornando così a fare <lb></lb>quel ch&#039;erasi fatto tanti anni indietro, per questo fine singolare; per aver <lb></lb>cioè uno spazio perfettamente vuoto di quelle esalazioni, che sempre si <lb></lb>vedevano uscir dal mercurio. </s>

<s>Ma come sarà rimasto il Viviani a veder nel­<lb></lb>l&#039;acqua un tal fervore di effluvii, che il mercurio al confronto era un nulla! <pb xlink:href="020/01/722.jpg" pagenum="165"></pb>Non si volle però dar vinto: fece scrivere nel Diario che l&#039;esperienza del <lb></lb>vuoto con l&#039;acqua non era riuscita, <emph type="italics"></emph>per difetto dell&#039;istrumento<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>442); <lb></lb>immaginò un apparecchio nuovo, e per dimostrar che gli effluvii dell&#039;acqua <lb></lb>non erano bolle aeree secondo voleva il Borelli, ma ignee come insegnava <lb></lb>Galileo, applicò al vaso dell&#039;immersione alquanti carboni accesi, che faces­<lb></lb>sero indizio certo del crescer per essi le ignee esalazioni nel vuoto. </s>

<s>“ Fu <lb></lb>collocato poi il vaso tutto in un luogo a parte, per vedere se in progresso <lb></lb>di tempo l&#039;acqua col sollevarsi a riempier tutta la palla dia a vedere la ma­<lb></lb>teria delle gallozzole non essere altrimenti aria, ma o fuoco o altra sostanza <lb></lb>tenuissima ” (ivi, pag. </s>

<s>443). </s></p><p type="main">

<s>Che cosa risolvesse il Viviani da queste esperienze non abbiam docu­<lb></lb>menti da informarne i lettori. </s>

<s>Ma quanto egli è certo che riconobbe l&#039;aria <lb></lb>in mezzo al mercurio, altrettanto è incerto se s&#039;inducesse poi ad ammet­<lb></lb>terla in mezzo all&#039;acqua. </s>

<s>In ogni modo, d&#039;onde avesse origine l&#039;aria nel <lb></lb>mercurio rimase al Viviani stesso un mistero. </s>

<s>Geminiano Montanari scrive­<lb></lb>vagli così nel Settembre del 1671 da Bologna: “ Adesso mi va incontrando <lb></lb>una burla bellissima col Baroscopio che non ne trovo nè regola nè cagione. </s>

<s><lb></lb>Ho tenuto tutto il verno passato il Baroscopio ed osservatone in più mesi <lb></lb>il moto giornale, nè mai ha fatte stravaganze come da mezzo Luglio in qua. </s>

<s><lb></lb>Cominciò di questo tempo a ribollire così forte il mercurio, generando ogni <lb></lb>dì nuova aria che nel corso di una settimana era scemato ben sei once, e <lb></lb>scotendolo un poco lo vedevo come ribollire e vomitar verso il vuoto gal­<lb></lb>lozzolette d&#039;aria. </s>

<s>Dubitai si fosse fesso il vetro, onde estrattone il mercurio <lb></lb>lo riconobbi e feci riconoscere da occhi migliori ben bene nè vi fu trovato <lb></lb>difetto ” (MSS. Gal. </s>

<s>Disc., T. CXXXXV, c. </s>

<s>185). </s></p><p type="main">

<s>Pochi mesi dopo tornava nel Dicembre su questo fatto il Montanari, <lb></lb>che confessava di avergli fatto perdere la pazienza. </s>

<s>Tutti i giorni era a vo­<lb></lb>tar d&#039;aria il tubo del suo Barometro e sempre ce ne rimaneva dell&#039;altra <lb></lb>senza saper d&#039;ond&#039;ella ci fosse entrata, o dove diamine mai si fosse nasco­<lb></lb>sta, e rivolto al Viviani a cui raccontava queste cose, all&#039;ultimo conclude: <lb></lb>“ Perchè dunque oramai non è finita di uscire e perchè anzi alcuna volta <lb></lb>ve ne trovo maggior quantità di prima, che certo quella che sinora n&#039;ho <lb></lb>estratta è molto più che non bisognerebbe per empir d&#039;aria sola tutta la <lb></lb>canna; V. S. Ecc.ma mi aiuti col sottilissimo suo intelletto a capir questo <lb></lb>imbroglio che per me sono intrigato ” (ivi, c. </s>

<s>210). </s></p><p type="main">

<s>E poichè siam certi che non venne dal Viviani nessuno aiuto, e che <lb></lb>rimasero anzi ambedue in quell&#039;imbroglio, ritorniamo al Borelli che nel­<lb></lb>l&#039;esperienza del vuoto operato coll&#039;acqua, in che il Viviani aveva fatto nau­<lb></lb>fragio, egli ritrovava alla sua ipotesi dell&#039;aria rimasta dentro il ghiaccio la <lb></lb>più bella conferma. </s>

<s>Così infatti scriveva nel libro <emph type="italics"></emph>De motionibus naturali­<lb></lb>bus,<emph.end type="italics"></emph.end> dove inserì quelle sue tre proposizioni dimostrate con gli stessi prin­<lb></lb>cipii e dietro le medesime cose supposte già nella sopra citata scrittura al <lb></lb>principe Leopoldo, dodici anni avanti: “ Quod confirmari potest pulcher­<lb></lb>rimo instrumento torricelliano, in quo vacuum mediante aqua efficitur. </s>

<s>Nam <pb xlink:href="020/01/723.jpg" pagenum="166"></pb>dum aqua descendit ad solitam depressionem 17 cubitorum proxime, tunc <lb></lb>videmus ab aqua tantam copiam ampullarum aerearum egredi, ut reprae­<lb></lb>sentet ebullitionem quam efficere solet fervor ignis in eadem aqua ” (Regio <lb></lb>Julio 1670, pag. </s>

<s>552). </s></p><p type="main">

<s>E perchè, in quel che fu quivi speculato dal Borelli, si conclude quella <lb></lb>parte di storia che narra come si travagliassero i Fisici per intendere il fatto <lb></lb>de&#039;naturali agghiacciamenti nella mole liquida, ci rimane a narrar breve­<lb></lb>mente di altri loro travagli durati per ritrovar la ragione di quella squisita <lb></lb>regolarità di forme geometriche, in che si dispongono le minute gocciole <lb></lb>dell&#039;acqua stessa ghiacciata sotto le apparenze di neve o di brina. </s></p><p type="main">

<s>Passeggiava tutto solo e pensoso per le vie della città Giovanni Keplero, <lb></lb>serrandosi bene addosso il mantello per ripararsi da un vento freddissimo <lb></lb>che spirava dalla parte di Tramontana, quando incominciarono a cader dal <lb></lb>cielo rannuvolato alcune squamette biancheggianti di ghiaccio. </s>

<s>Cadevano <lb></lb>quelle squamette sul panno di color nero, di cui il Matematico dell&#039;Impe­<lb></lb>ratore era coperto, ed egli, rimanendovi attaccate sopra e distese, le osser­<lb></lb>vava attentissimamente. </s>

<s>Avevano tutte la figura di una piccola stella a sei <lb></lb>punte. </s>

<s>Scuote il mantello per ricevervene sopra altre che seguitavano a ca­<lb></lb>dere, e tutte si rassomigliano puntualmente nella figura sessangolare. </s>

<s>“ Cum <lb></lb>perpetuum hoc sit, egli allora fra sè conclude, quoties ningere incipit, ut <lb></lb>prima illa nivis elementa figuram praeseferant asterisci sexanguli, causam <lb></lb>certam esse necesse est ” (De nive sexangula, Francof. </s>

<s>ad M. 1611, pag. </s>

<s>5). </s></p><p type="main">

<s>Ripensa che pur anch&#039;essi sessangolari sono i favi dell&#039;api e ne rico­<lb></lb>nosce l&#039;origine da un provvido istinto ingerito in quegl&#039;industriosi insetti <lb></lb>dalla Natura, perchè, dentro il minimo circuito, le celle costruite a riporvi <lb></lb>il miele, più che sia possibile, riescan capaci. </s>

<s>“ Vulgare est apud Physicos, <lb></lb>qui ad solam quidem sexangularem structuram respiciunt, ut illa cum hia­<lb></lb>tibus extrinsecus sese repraesentet. </s>

<s>Cum enim locum planum impleant ex­<lb></lb>cluso vacuo, tantum hae figurae triangulum, quadrangulum, sexangulum, <lb></lb>ex iis sexangulum capacissima est figura. </s>

<s>Capacitatem autem sibi parant <lb></lb>apes ad mella condenda ” (ibi, pag. </s>

<s>11). </s></p><p type="main">

<s>Ripensa inoltre tal&#039;esser pure la figura de&#039;chicchi de&#039;meli granati, e <lb></lb>ne riconosce l&#039;origine dalle pressioni per le quali, crescendo la mela, così <lb></lb>provvede la Natura a far sì che di que&#039;chicchi sia massimamente capace <lb></lb>l&#039;interna cavità del frutto, senza accrescerne soverchiamente la mole. </s>

<s>Un <lb></lb>simile effetto di pressione per ristringimento dee esser, seguita a ragionare <lb></lb>il Keplero, operato dal freddo, proprietà del quale è il ristringere e il con­<lb></lb>densare, ond&#039;è che, fra le cause estrinseche della neve sessangolare, una <lb></lb>senza dubbio potrebb&#039;essere anche questa. </s>

<s>“ Cum enim proposuissemus <lb></lb>inquirere originem figurae huius in nive inter causas extrinsecas et intrin­<lb></lb>secas, inter externas primum sese offerebat frigus. </s>

<s>Condensatio sane est a <lb></lb>frigore: per condensationem vero vapor erit in figuram stellae: videbatur <lb></lb>igitur frigus illi figuram praestare stellae ” (ibi, pag. </s>

<s>12). </s></p><p type="main">

<s>Ma non vedeva l&#039;arguto speculatore come questa causa puramente <pb xlink:href="020/01/724.jpg" pagenum="167"></pb>estrinseca potesse produrre effetti così costanti, e così regolari, per cui si <lb></lb>rivolge a pensar sopra qualche altra cosa, da cui intrinsecamente dipenda <lb></lb>quell&#039;ammirabile opera della geometrizzante Natura. </s>

<s>E dopo varii pensieri <lb></lb>passatigli per la mente “ An denique, conclude, ipsa huius formatricis na­<lb></lb>tura in intimo sinu suae essentiae particeps est sexanguli? </s>

<s>” (ibi, pag. </s>

<s>22). <lb></lb>Confermerebbe questa mia congettura, prosegue a dire il Keplero, “ opera <lb></lb>huius formatricis facultatis alia ut chrystalli omnes sexangulae, cum ada­<lb></lb>mantes octaedrici sint rarissimi. </s>

<s>Sed formatrix telluris facultas non unam <lb></lb>amplectitur figuram, gnara totius Geometricae et in ea exercita. </s>

<s>Vidi enim <lb></lb>Dresdae in aede regia cui Stabulo nomen, exornatum abacum aere argen­<lb></lb>toso, ex quo quasi efflorescebat dodecaedron avellanae parvae magnitudine, <lb></lb>dimidia parte extans. </s>

<s>Extat et in descriptione Thermarum bollensium ico­<lb></lb>saedri pars anterior inter fossilia. </s>

<s>Itaque verisimile est hanc facultatem for­<lb></lb>matricem pro diverso humore diversam fieri. </s>

<s>In vitriolo crebra est figura <lb></lb>cubica, rhombica in nitro sua est figura. </s>

<s>Dicant igitur Chymici an in nive <lb></lb>sit aliquid salis, et quodnam salis genus, et quam illud alias induat figu­<lb></lb>ram. </s>

<s>Ego namque, pulsatis Chymiae foribus, cum videam quantum restet <lb></lb>dicendum ut causa rei habeatur, malo abs te. </s>

<s>Vir solertissime, quid sentias <lb></lb>audire quam disserendo amplius fatigari ” (ibi, pag. </s>

<s>23, 24). </s></p><p type="main">

<s>Così termina la Dissertazione <emph type="italics"></emph>De nive sexangula,<emph.end type="italics"></emph.end> che l&#039;Autore indi­<lb></lb>rizza per <emph type="italics"></emph>Strenna<emph.end type="italics"></emph.end> all&#039;amico suo Giovan Matteo Wackero, e così terminando <lb></lb>lasciava a&#039;suoi successori a correre un breve tratto di via, per giungere alla <lb></lb>finale soluzion del problema. </s>

<s>Quella via però, benchè breve, fu trovata così <lb></lb>difficile e penosa, che ci vollero ancora quasi due secoli prima che si rico­<lb></lb>noscesse nell&#039;acqua quella intrinseca virtù formatrice, che il Keplero non <lb></lb>vedeva risedere in altro, che nelle soluzioni de&#039;sali. </s>

<s>In tutto quel frattempo <lb></lb>o si folleggiò o non si seppe delle ragioni pensate dal Keplero accettar che <lb></lb>quelle riguardanti le azioni estrinseche operatrici della sessangolar forma­<lb></lb>zione, invocando in proposito la Geometria de&#039;massimi e de&#039;minimi, e l&#039;esem­<lb></lb>pio de&#039;favi melliferi e de&#039;meli granati. </s></p><p type="main">

<s>Il Cartesio, come se fosse stato il primo a entrare in questa specula­<lb></lb>zione, narra nel cap. </s>

<s>VI delle <emph type="italics"></emph>Meteore<emph.end type="italics"></emph.end> come gli occorresse d&#039;osservar la <lb></lb>figura sessangolare, in che si conformano ghiacciando le gocciole della piog­<lb></lb>gia. </s>

<s>“ Referam ea quae proxima hyeme anni 1635 Amstelodami, ubi tunc <lb></lb>eram, circa hanc rem observavi. </s>

<s>Quarto februarii, quum dies admodum fri­<lb></lb>gida praecessisset, vesperi paululum pluviae decidit, quae in glaciem verte­<lb></lb>batur simul ac terram contingebat.... Sed omnium maxime admirabar quae­<lb></lb>dam ex his granis, quae postrema deciderunt parvos sex dentes circa se <lb></lb>habere, similes iis qui in horologiorum rotis ” (Francof. </s>

<s>ad M. 1692, pag. </s>

<s>158). </s></p><p type="main">

<s>O fosse per secondar quel suo genio che lo portava a disprezzare ogni <lb></lb>scientifica tradizione, o fosse veramente perchè non fosse capitata in man <lb></lb>del Cartesio la Strenna kepleriana, fatto è che, in contemplar la novità di <lb></lb>quelle squisite figure sessangolari, rimase il Filosofo sorpreso di maraviglia, <lb></lb>e badava a pensare fra sè e sè come si potessero que&#039;granelli di ghiaccio <pb xlink:href="020/01/725.jpg" pagenum="168"></pb>ridurre a pigliar forme cotanto regolari, in mezzo al disordinato imperver­<lb></lb>sare de&#039;venti. </s>

<s>“ Aegre tantummodo poteram coniicere quidnam in aere li­<lb></lb>bero, turbantibus ventis, adeo accurate hos sex dentes formare, et circa sin­<lb></lb>gula grana disponere potuisset, donec tandem in mentem venit facillime fieri <lb></lb>potuisse ut ventos nonnulla ex his granis versus alquam nubem expulerit, <lb></lb>eaque infra illam vel ultra suspensa aliquamdiu detinuerit, satis enim exi­<lb></lb>gua erant. </s>

<s>Atque ibi procul dubio ita disponi debuisse, ut singula sex aliis <lb></lb>in eodem plano sitis cingerentur, quia talis est ordo naturae ” (ibi, pag. </s>

<s>159). </s></p><p type="main">

<s>Nonostante però che il Cartesio pretendesse così di farsi primo mae­<lb></lb>stro a coloro, che desideravano d&#039;aver la ragione della neve sessangolare, <lb></lb>si riconosceva da&#039;più e si seguiva come più autorevole il magisterio di co­<lb></lb>lui, che 26 anni avanti aveva speculato di quelle cose. </s>

<s>Il Baliani fra&#039;Nostri <lb></lb>irraggiando di luce propria i concetti del Keplero, così scriveva: “ Forse <lb></lb>può essere che le bollette delle nuvole, in luogo ove sono abbandonate dal <lb></lb>calore, cominciando a congelarsi acquistino una certa tenacità e spessezza, e <lb></lb>perciò maggior gravità, onde aggravatene e compresse le inferiori e perciò <lb></lb>schiacciatesi, di sfere divengan circoli, e premute poi ognuna di loro dalle <lb></lb>collaterali si riducano in figure esagone, come avviene al favo del mele, al <lb></lb>vespaio, a&#039;granelli della mela grana, a&#039;cristalli, a tuttè quelle cose che hanno <lb></lb>figura circolare, qualora si premano e calchino fra loro per l&#039;uguaglianza <lb></lb>ch&#039;è fra il semidiametro e il lato dell&#039;esagono ” (Tratt. </s>

<s>della pestil., Sa­<lb></lb>vona 1647, pag. </s>

<s>44). </s></p><p type="main">

<s>Il Borelli però, mentre sembra che a prima vista si riscontri col Car­<lb></lb>tesio, si scopre poi aver concetti suoi originali, e anche al vero in certo modo <lb></lb>conformi, quando congettura che la figura sessangola sia originaria all&#039;ele­<lb></lb>mento dell&#039;acqua. </s>

<s>“ Si può supporre, egli dice, che gli atomi acquei sieno <lb></lb>corpi composti di altri minutissimi corpi primi e semplici.... È tal supposi­<lb></lb>zione assai conforme all&#039;ordine della natura, poichè intorno a ciaschedun <lb></lb>corpo rotondo non possono in una superficie piana collocarsi più che sei <lb></lb>altri corpi rotondi della medesima grandezza, in maniera però che tutti vi­<lb></lb>cendevolmente si tocchino, come facilmente si può dimostrare. </s>

<s>Di più l&#039;espe­<lb></lb>rienza mostra che i minutissimi granellini della neve banno la detta figura <lb></lb>di stella esagonale con le punte crinite, e perchè la neve è un aggregato <lb></lb>di certa determinata moltitudine di atomi acquei uniti insieme, assai pro­<lb></lb>babilmente dalla figura di detta neve possiamo congetturare esser tale <lb></lb>ancora la figura originaria di detta acqua ” (Fabbroni, Lett. </s>

<s>cit., T. I, <lb></lb>pag. </s>

<s>110). </s></p><p type="main">

<s>Queste non sono altro che supposizioni e probabilità, ben lo riconosce <lb></lb>il Borelli da sè, e lo confessa, ma pur è cosa da non lasciarsi senza consi­<lb></lb>derazione che così speculavasi in Italia, mentre i più insigni fisici stranieri, <lb></lb>fra&#039;quali il Willis, seguitati da alcuni de&#039;Nostri imbevuti de&#039;principii pe­<lb></lb>ripatetici, ritenevan per cosa certa “ che il sale volatile delle piante nelle <lb></lb>fredde notti del verno fa una foglia di ghiaccio su&#039;vetri delle finestre col­<lb></lb>l&#039;umido accidentale, che seco esce da&#039;rami verdi che si ardono, e in esso <pb xlink:href="020/01/726.jpg" pagenum="169"></pb>stampa e figura l&#039;immagine dell&#039;albero onde è tratto ” (Bartoli, Del ghiac­<lb></lb>cio, Roma 1681, pag. </s>

<s>118). </s></p><p type="main">

<s>Anzi in quel medesimo che da costoro si professavano simili puerilità <lb></lb>come fatti certissimi e dimostrati, un discepolo del Borelli attendeva ad os­<lb></lb>servar diligentissimamente col Microscopio i cristallini del ghiaccio, e rasso­<lb></lb>migliandoli ai cristalli precipitati dalla soluzione de&#039;sali, attribuiva il loro <lb></lb>formarsi a una virtù di attrazione magnetica, che facesse, nel riordinamento <lb></lb>delle particelle saline già prima dissolute, da necessaria guida ideale. </s></p><p type="main">

<s>Essendo il dì 19 Dicembre del 1674 caduta a Torino, dove allora di­<lb></lb>morava Donato Rossetti, gran copia di neve, e ne&#039;seguenti giorni essendosi <lb></lb>il cielo tutto rasserenato “ sopra detta neve, scrive lo stesso Rossetti, in <lb></lb>andando a spasso l&#039;ultimo dì dell&#039;anno per il nuovo accrescimento della <lb></lb>città, mi venne osservato che la brinata caduta nelle quattro notti antece­<lb></lb>denti vi s&#039;era da per tutto distribuita in alcune masserelle simili. </s>

<s>Il che <lb></lb>messemi in dubbio quello che fermamente credeva, cioè che la brinata nel <lb></lb>cadere non obbedisse se non al moto di propensione al centro della Terra, <lb></lb>e a&#039;moti che le imprimono gl&#039;incontri e gli urti che si avesse nella discesa, <lb></lb>e mossemi il dubbio che da per tutto si ammassasse nella stessa figura, per <lb></lb>quelle cagioni, per le quali io mi dò ad intendere che nella stessa figura <lb></lb>sempre si vedano, dopo giorni, rimessi insieme i sali che pesti e triti si di­<lb></lb>spergono nell&#039;acqua. </s>

<s>Movemi il dubbio, voglio dir io, che la brinata si am­<lb></lb>massasse da per tutto nella stessa figura, perchè le di lei particelle, nel ca­<lb></lb>dere una vicina all&#039;altra, fossero guidate a congiungersi per una qualche <lb></lb>virtù magnetica od appetenza e a congiungersi in certi punti come per una <lb></lb>qualche necessità ideale. </s>

<s>E questo dubbio mi ridusse a fare le seguenti os­<lb></lb>servazioni. </s>

<s>” </s></p><p type="main">

<s>“ Misi sopra una tavola neve, diaccio d&#039;acqua ordinaria, diaccio di neve <lb></lb>distrutta, diaccio di brinata strutta, pietra lavagna, ebano, panno nero di <lb></lb>lana, tela bianca di lino, carta da scrivere, mattone cotto, ed altre coserelle, <lb></lb>ed il tutto esposi al sereno sopra il tetto di casa la notte seguente il dì <lb></lb>primo di Gennaio. </s>

<s>La mattina de&#039;2 l&#039;ebano, la lavagna, e tutte le altre cose <lb></lb>non bianche, se ne eccettuiamo il mattone cotto, sopra il quale non trovai <lb></lb>mai segno di brinata, si vedevano col nudo occhio ricoperte di brinata in <lb></lb>modo, che parevano punteggiate di bianco.... Ma guardando con un Micro­<lb></lb>scopio di tre lenti molto buono, riscontrai che i punti erano ciascuno una <lb></lb>rosetta di tre, quattro e fino in sette fogliucce.... Ogni fogliuccia era come <lb></lb>sottilissima scaglietta da giudicarsi piana, nel mezzo trasparente come un <lb></lb>diaccio il più cristallino, ma terminato da una listarella bianca e opaca come <lb></lb>di neve, e tal listarella la stimai larga la terza parte de&#039;semidiametri di <lb></lb>quelle fogliucce, che poi si accostavano nella figura al cerchio ” (MSS. Cim., <lb></lb>T. XX, c. </s>

<s>192). </s></p><p type="main">

<s>Prosegue il nostro Autore a fare e a descrivere ivi altre diligentissime <lb></lb>osservazioni, <emph type="italics"></emph>per venire,<emph.end type="italics"></emph.end> com&#039;egli stesso si esprime, <emph type="italics"></emph>in chiaro di alcuni <lb></lb>particolari senza la cognizione de&#039;quali stimo non potervisi intorno di-<emph.end type="italics"></emph.end><pb xlink:href="020/01/727.jpg" pagenum="170"></pb><emph type="italics"></emph>scorrere fisico matematicamente<emph.end type="italics"></emph.end> (ivi, c. </s>

<s>194). Se poi in questi discorsi non <lb></lb>vide il vero con quella chiarezza che lo videro poi tutti quelli, a cui furono <lb></lb>aperti gli occhi dalla <emph type="italics"></emph>Cristallografia,<emph.end type="italics"></emph.end> non si può però negar che il Rossetti <lb></lb>non fosse uno de&#039;primi ad aprir le vie, per le quali, incamminandosi la <lb></lb>nuova scienza, avrebbe un secolo dopo fatti così grandi e così veloci pro­<lb></lb>gressi. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Gli effetti del calore negli agghiacciamenti, come hanno dimostrato i <lb></lb>fatti precedentemente narrati, non furono intesi nè perciò bene spiegati da <lb></lb>coloro che vi studiarono attorno nel secolo XVII, nè si può dire che molto <lb></lb>di più ne sapessero i fisici succeduti a loro infino a&#039;tempi moderni, trat­<lb></lb>tandosi di un problema a risolver completamente il quale converrebbe pe­<lb></lb>netrare addentro a veder la più intima composizione de&#039;corpi. </s>

<s>Gli altri effetti <lb></lb>prodotti dal calore stesso nelle evaporazioni sembravano implicare minori <lb></lb>difficoltà, ma pure anche qui le difficoltà non mancarono e gravi, anzi come <lb></lb>suole spesso avvenire queste nascevano in gran parte dal presentarsi sotto <lb></lb>troppo facile aspetto il problema, alla soluzion del quale in mancanza di <lb></lb>ragioni soccorreva pronta la fantasia. </s></p><p type="main">

<s>Un chiaro esempio di ciò si trova nella Filosofia peripatetica, alle fan­<lb></lb>tasie della quale un nostro insigne Italiano, a cui si dee l&#039;avere apparec­<lb></lb>chiate, benchè così dalla lontana le vie alla Fisica come scienza, sostituiva <lb></lb>tali ragioni che furon dopo varie vicende all&#039;ultimo riconosciute, in gran parte <lb></lb>almeno, per vere. </s></p><p type="main">

<s>Una di queste dispute peripatetiche in soggetto di vapori s&#039;aggirava in­<lb></lb>torno al render la ragione del perchè nell&#039;inverno si vede esalare una nu­<lb></lb>vola di fumo dalla bocca e dalle narici degli animali. </s>

<s>Giovan Batista Bene­<lb></lb>detti riconosciuto quanto stoltamente si disputasse, entrò in mezzo per il <lb></lb>primo a render così la ragion fisica del fatto. </s>

<s>“ Antiqui peripatetici de vi­<lb></lb>dendo in hyeme animalium halitu, id quod in aestate non evenit, male di­<lb></lb>sputaverunt quia hoc nascitur a condensatione halitus quae ab ambiente fri­<lb></lb>gore fit, quia halitus is ab ore aut naso animalis exiens non est purus aer <lb></lb>attractus primo, sed mixtus est cum quodam vapore excrementitio et subtili, <lb></lb>quo semper ab ea parte evacuatur corpus, qui statim ab aere frigido cir­<lb></lb>cumdatur et densatur, quam ob causam ab ipso ea luminis pars reflectìtur <lb></lb>quae eum penetrare non potest ” (Speculat. </s>

<s>Lib., Venetiis 1599, pag. </s>

<s>191). <lb></lb>E prosegue, applicando questi principii a render la ragione di un altro fatto <lb></lb>simile, ch&#039;è del vedersi fumar l&#039;acqua l&#039;inverno appena attinta dal pozzo. </s></p><p type="main">

<s>Così avviatosi il nostro Autore a insegnare a&#039;Peripatetici da quali vere <lb></lb>cause abbiano effetto le condensazioni de&#039;vapori, passa a dir della rugiada <lb></lb>che si vede velar l&#039;estate i tersi cristalli delle bocce piene d&#039;acqua ghiac-<pb xlink:href="020/01/728.jpg" pagenum="171"></pb>ciata; rugiada che i peripatetici dicevano essere umor trasudato da&#039;pori dello <lb></lb>stesso cristallo. </s>

<s>“ Neque etiam iidem noverunt causam unde fiat ut in ae­<lb></lb>state, impleto vaso vitreo aut argenteo, aut ex materia non porosa constante <lb></lb>aqua frigida, vas sudet, quod tempore hyemis, nonnisi in calidis locis eve­<lb></lb>nit, quem sudorem dicebant ipsi esse eamdem aquam, quae per poros vasis <lb></lb>exiret, quod falsissimum est, quia si per poros aqua frigida exiret, multo <lb></lb>magis exiret calida, cum subtilior sit et ad penetrandum aptior. </s>

<s>Sed hoc non <lb></lb>aliunde oritur quam a condensatione aeris vas circumdantis causata a fri­<lb></lb>giditate vasis refrigerati ab aqua, quemadmodum tempore hyberno clare vi­<lb></lb>demus mane superficies interioris vitri fenestrarum sudare, quia extrinse­<lb></lb>cum frigus refrigerando vitrum intrinsecum aerem sibi contiguum congelat ” <lb></lb>(ibi, pag. </s>

<s>192). </s></p><p type="main">

<s>Ma nel lasciar che si fa dall&#039;Autore, di discorrere sopra questo soggetto, <lb></lb>fra tutti gli errori scoperti e la sostituzione di altrettante verità per la prima <lb></lb>volta annunziate, notabile in tal proposito è la seguente, che ha più imme­<lb></lb>diato riguardo all&#039;evaporazione. </s>

<s>“ Nec proprie locutus est Aristoteles (sog­<lb></lb>giunge il Benedetti) cum dixerit calorem solis eum esse qui sursum humo­<lb></lb>res vaporesque evehat, quia sol nil aliud facit, quam calefacere, cuius caloris <lb></lb>ratione ea materia rarefit, et ob rarefationem levior facta ascendit, non quia <lb></lb>sursum a sole feratur ” (ibi, pag. </s>

<s>194). </s></p><p type="main">

<s>Così veniva il Benedetti molto per tempo a dimostrare la insufficienza <lb></lb>e anzi la falsità delle dottrine aristoteliche, mentre Galileo parecchi anni <lb></lb>dopo tornava a ricacciar la fisica dell&#039;evaporazioni nel buio di quegli anti­<lb></lb>chi peripatetici errori. </s>

<s>“ Se noi volessimo ancora, si legge nella <emph type="italics"></emph>Risposta a <lb></lb>Lodovico delle Colombe<emph.end type="italics"></emph.end> strumenti più sottili e operazione più esquisita, direi <lb></lb>che guardassimo i raggi del sole osservando con quanta diligenza vanno se­<lb></lb>parando le supreme e minime particelle dell&#039;acqua, le quali dall&#039;esalazione <lb></lb>ascendente vengono sublimate, ed essendo ridotte forse ne&#039;primi corpicelli <lb></lb>componenti sono a noi invisibili a una a una e solo ci si manifestano mol­<lb></lb>tissime insieme sotto specie di quello che noi chiamiamo vapore o nebbia o <lb></lb>nuvola o fumi o cose tali ” (Alb. </s>

<s>XII, 328) </s></p><p type="main">

<s>Così, insieme con Galileo, si seguitò da&#039;Fisici e nostrali e stranieri a <lb></lb>fornicare coll&#039;errore antico, e il Roberval, secondo riferisce l&#039;Huyghens, dopo <lb></lb>la prima metà del secolo XVII, ripetendo le dottrine stesse e le espressioni <lb></lb>usate da Aristotile nel IX e X capitolo del I e II libro delle Meteore, am­<lb></lb>metteva che il sole sollevasse vapori tutt&#039;intorno al globo di Saturno, ec­<lb></lb>cettuato che verso i poli “ ubi fortassis intensum frigus eos <emph type="italics"></emph>a sole attrahi<emph.end type="italics"></emph.end><lb></lb>prohibeat (Syst. </s>

<s>Saturnium, Op. </s>

<s>varie, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>561). L&#039;Huy­<lb></lb>ghens stesso argomentando dal variabile aspetto della fascia di Giove l&#039;esi­<lb></lb>stenza di vapori ora più ora men condensati, e perciò la generazione sulla <lb></lb>superficie di quel pianeta, come sulla nostra Terra, di piogge e di venti <lb></lb>“ erunt ergo, si esprime, et imbres et venti quia <emph type="italics"></emph>attractum a sole<emph.end type="italics"></emph.end> humo­<lb></lb>rem incidere in terram necesse est, et calore soluti vapores ventorum causa <lb></lb>sunt ” (Cosmot. </s>

<s>Lib. </s>

<s>I, Op. </s>

<s>v. </s>

<s>cit., pag. </s>

<s>681). </s></p><pb xlink:href="020/01/729.jpg" pagenum="172"></pb><p type="main">

<s>Ma per tornare al nostro Galileo, benchè avesse il Benedetti, nelle ra­<lb></lb>refazioni operate dal calore, riconosciuta la ragione del separarsi dalla ri­<lb></lb>manente mole liquida e del sollevarsi in alto i vapori; pur riducendosi noi <lb></lb>alla memoria le parole dianzi trascritte dalla Risposta a Lodovico delle Co­<lb></lb>lombe, si trova essere dall&#039;Autore invocate l&#039;<emph type="italics"></emph>esalazioni ascendenti<emph.end type="italics"></emph.end> com&#039;ef­<lb></lb>ficacissima causa dell&#039;evaporazioni. </s>

<s>Che cosa intendesse poi per quelle esa­<lb></lb>lazioni ascendenti è dichiarato meglio da ciò che altrove si legge nella detta <lb></lb><emph type="italics"></emph>Risposta.<emph.end type="italics"></emph.end> “ E in cotal guisa (cioè congiunte le bollicelle dell&#039;aria nell&#039;acqua) <lb></lb>resterebbero lungo tempo, se l&#039;esalazioni ignee e molto più sottili dell&#039;aria, <lb></lb>ascendendo continuamente non passassero pel velo di esse bolle e le dissol­<lb></lb>vessero, sublimando e portando via parte dei corpicelli dell&#039;acqua, perchè <lb></lb>mostrandoci la continua esperienza che l&#039;acqua de&#039;vasi scoperti e più sen­<lb></lb>sibilmente de&#039;panni bagnati, se ne va ascendendo, non credo che per dire <lb></lb>conforme al vero si possa dir altro se non che ella viene portata via dai <lb></lb>detti corpuscoli caldi, come la polvere dal vento ” (Alb. </s>

<s>XII, 345). </s></p><p type="main">

<s>L&#039;efficacia poi di queste esalazioni ignee in sollevar l&#039;acqua e le bol­<lb></lb>licelle di lei è resa più manifesta secondo Galileo, ne&#039;vasi larghi ed aperti <lb></lb>posti in sul fuoco a bollire. </s>

<s>“ Ma se poi voi piglierete vasi larghi ed aperti, <lb></lb>e scalderete l&#039;acqua assai, allora la grandissima copia del fuoco, ìl quale <lb></lb>dal fondo del vaso voi vedrete salire, s&#039;aggregherà in globi molto grandi, li <lb></lb>quali con impeto maggiore ascenderanno e cagioneranno quell&#039;effetto che <lb></lb>noi chiamiamo bollore, e nello scappare fuori solleveranno e porteranno seco <lb></lb>molti atomi d&#039;acqua nel modo che aliti gagliardi sollevano la polvere e seco <lb></lb>ne portano le parti più sottili ” (ivi, pag. </s>

<s>467). </s></p><p type="main">

<s>Sembrerebbe da una parte che queste di Galileo e del Castelli fossero <lb></lb>più perfette ragioni di quelle date dal Benedetti, il quale attribuendo il fatto <lb></lb>alla semplice rarefazione non sodisfaceva a coloro, che non sapevano inten­<lb></lb>dere come l&#039;acqua più grave in specie potesse così lievemente ascender per <lb></lb>l&#039;aria. </s>

<s>Di questo diremo altrove, ma per ora ci contenterem di notare che <lb></lb>le dottrine professate da Galileo erano difettose da due lati: dal creder cioè <lb></lb>che le bollicelle d&#039;aria fossero ignee esalazioni, e dall&#039;attribuire ad esse bol­<lb></lb>licelle la causa, mentre in verità non son altro che l&#039;effetto di ciò che è <lb></lb>causa vera dell&#039;ebullizione. </s></p><p type="main">

<s>Questa vera causa non fu prima riconosciuta che il Boyle facesse quella <lb></lb>sua bellissima esperienza dell&#039;acqua tiepida che bolle nel vuoto, esperienza <lb></lb>nella quale, prima che fossero fra noi divulgati i <emph type="italics"></emph>Nuovi esperimenti fisico­<lb></lb>meccanici,<emph.end type="italics"></emph.end> s&#039;erano incontrati i nostri Accademici fiorentini, quando osser­<lb></lb>varono il bollir dell&#039;acqua nello strumento torricelliano, di che nell&#039;altro <lb></lb>paragrafo da noi fu narrato. </s>

<s>Alìora si comprese che il bollimento de&#039;liquidi <lb></lb>dipende men dal calore che dall&#039;ammosfera sopraincombente alla superficie <lb></lb>del liquido, alla pression della quale anzi attempera i suoi gradi lo stesso <lb></lb>conceputo calore. </s>

<s>Sopra questo principio il Papin, che i fecondi concetti <lb></lb>boileiani incarnava in macchine esquisitissime, costruì quel suo <emph type="italics"></emph>Digestore,<emph.end type="italics"></emph.end><lb></lb>del quale il Newton nella Questione XI del III Libro dell&#039;Ottica divulgava <pb xlink:href="020/01/730.jpg" pagenum="173"></pb>così la teoria: “ Etenim si aqua in vase aliquo pellucido tepescat, et aer <lb></lb>deinde e vase exhauriatur, aqua illa in vacuo ebulliet nihilo minus vehe­<lb></lb>menter, quam si in vase igni imposito calorem multo maiorem in aperto aere <lb></lb>concepisset. </s>

<s>Nam atmosphaerae incumbentis pondus vapores deprimit impe­<lb></lb>ditque quominus aqua ebulliat, donec calorem contraxerit multo maiorem, <lb></lb>quam quo ad eiusdem in vacuo ebullitionem excitandam opus sit ” (Pata­<lb></lb>vii 1773, pag. </s>

<s>140). </s></p><p type="main">

<s>Il Papin col suo Digestore e con altre macchine ingegnosamente co­<lb></lb>struite, nelle quali il vapore acqueo veniva applicato come forza motrice, <lb></lb>tornò a sollevare la fronte dall&#039;oblio, quando gli eruditi si misero dietro a <lb></lb>ricercare i nomi e le opere di tutti coloro che, come stille d&#039;acqua concorse <lb></lb>a una fonte, scaturirono dall&#039;ingegno del Watt nel portentoso macchina­<lb></lb>mento. </s>

<s>Scavate dagli stili acuti di quegli infaticabili eruditi esultaron le ossa <lb></lb>del Porta e di Giovanni Branca, con parecchi altri venuti fuori a progettar <lb></lb>macchine da sedurre i semplici con gli strani effetti promessi, e da accen­<lb></lb>der contro sì sfacciate imposture l&#039;ira degli intelligenti. </s>

<s>Chi volesse per sua <lb></lb>ricreazione aver di ciò qualche esempio, converrebbe che cercasse nella R. </s>

<s>Bi­<lb></lb>blioteca Marucelliana di Firenze <emph type="italics"></emph>Le Machine, volume nuovo e di molto ar­<lb></lb>tifizio, da fare effetti maravigliosi tanto spiritali che animali di Giovanni <lb></lb>Branca,<emph.end type="italics"></emph.end> libro stampato in Roma nel 1629, e leggesse quelle postille, che <lb></lb>condite di sale, misto a un po&#039;di aceto e di pepe, scrisse in margine un <lb></lb>certo fiorentino. </s>

<s>Nell&#039;ultima a c. </s>

<s>17 e che appella alla XVII fra le XXV <lb></lb><emph type="italics"></emph>figure di Machine fondate sugli effetti del vuoto,<emph.end type="italics"></emph.end> così scrive il postillatore: <lb></lb>“ Ti rispondo che è falso e peggio non si può dire: addio pazzo. </s>

<s>” </s></p><p type="main">

<s>E in verità non ha nulla il Branca che non si possa dire una pazzia, <lb></lb>da quella testa vuota in fuori, la quale sputando per un cannello il vapore <lb></lb>dalla bocca sopra le alette di una ruota orizzontale, la fa volgere in giro a <lb></lb>produr qualche debole effetto di moto. </s>

<s>Di bene altra importanza è per la <lb></lb>storia italiana delle Macchine a vapore quella, che vedesi disegnata in alcune <lb></lb>carte manoscritte ritrovate nella R. </s>

<s>Biblioteca nazionale di Firenze, secondo <lb></lb>l&#039;invenzione di Alessandro Galilei architetto fiorentino, che nel 1716 l&#039;aveva <lb></lb>messa in pratica a Londra per sollevar l&#039;acqua, con gran vantaggio sopra <lb></lb>le trombe ordinarie. </s>

<s>Noi per sodisfare ai curiosi citeremo la descrizione del­<lb></lb>l&#039;ingegnoso macchinamento, come la lasciò distesa nelle dette carte il pro­<lb></lb>prio inventore, ma convien prima soggiungere qualche altra notizia alla sto­<lb></lb>ria dell&#039;evaporazione, che c&#039;è rimasta sopra interrotta. </s></p><p type="main">

<s>Era facile accorgersi, per le quotidiane esperienze, che il vento concorre <lb></lb>a far evaporar l&#039;acqua più sollecitamente talvolta di quel che non faccia lo <lb></lb>stesso calore, come vedesi per esempio l&#039;inverno venir più presto rasciugate <lb></lb>le strade dal vento di tramontana che non da&#039;raggi del sole. </s>

<s>Galileo rasso­<lb></lb>migliava l&#039;effetto al rapir che lo stesso vento fa la polvere delle strade, sol­<lb></lb>levandola in aria come le vescicole del vapore. </s>

<s>“ Siccome (leggesi nella so­<lb></lb>pracitata Risposta a Lodovico delle Colombe) in un monte di sottilissima <lb></lb>polvere si vede un leggero venticello andarne superficialmente levando molte <pb xlink:href="020/01/731.jpg" pagenum="174"></pb>particelle, lasciando l&#039;altre immote; così crederò io che i medesimi venti <lb></lb>vadano portando via con li loro sottilissimi aliti le supreme particelle del­<lb></lb>l&#039;acqua da un panno o da una pietra bagnata o dall&#039;acqua contenuta in un <lb></lb>vaso, non movendo altre parti che le sole che si separano da quelle che re­<lb></lb>stano ” (Alb. </s>

<s>XII, 327, 28). </s></p><p type="main">

<s>Così presso a poco la pensava anco il Borelli, il quale, come fu de&#039;primi <lb></lb>a riconoscer l&#039;aria ospitante in mezzo all&#039;acqua, fu così de&#039;primi a trovar <lb></lb>la ragione meccanìca dell&#039;insinuarsi fra le liquide, le particelle aerose cac­<lb></lb>ciate ivi dentro e quasi confittevi dal vento. </s>

<s>“ Et summopere advertendum <lb></lb>quod minor copia aeris reperitur intra aquam glaciatam in vase clauso, quam <lb></lb>includatur in aqua stagni, quae aeri contigua est, dum gelat. </s>

<s>In illa enim <lb></lb>paucissimae bullae aeraee reperiuntur, in hac copiosissimae et grandiores. </s>

<s><lb></lb>Ratio huius discriminis est quia aer sicut facile abradit aqueas particulas ab <lb></lb>eius superficie, sic aeraee spirulae insinuantur intra aquam. </s>

<s>Hoc suadetur <lb></lb>quia videmus linteum madidum in loco umbroso expansum etiam hyeme <lb></lb>exiccari, et spirante vento citissime arefieri. </s>

<s>Hoc certe contingit quia aeris <lb></lb>particulae a vento agitatae abradunt aquea granula et eadem violentia pluri­<lb></lb>mae aeris particulae insinuari debent intra aquam, a qua vinciuntur, ut inde <lb></lb>effugere non possint ” (De motu anim., Pars. </s>

<s>II, Romae 1681, pag. </s>

<s>218). </s></p><p type="main">

<s>Le spire aeree secondo immaginava il Borelli rimangon prese al visco <lb></lb>dell&#039;acqua, al qual visco giusto il Del Papa attribuiva una grande efficacia <lb></lb>negli effetti dell&#039;evaporazione sollecitata dal vento. </s>

<s>“ Perocchè sebbene anco <lb></lb>il vento sferzando e radendo la superficie dell&#039;acqua è potente egli stesso <lb></lb>a sospingere in alto l&#039;acqua medesima, egli è però ragionevole che in que­<lb></lb>sto effetto ancora gran parte abbia l&#039;acquea viscosità, cioè a dire quelle te­<lb></lb>nui membrane nell&#039;acqua istessa disseminate, nelle quali il vento urtando <lb></lb>e intrigandosi possa in tal modo con agevol rapina seco portare l&#039;acquee <lb></lb>sostanze ” (Della natura dell&#039;umido e del secco, Firenze 1681, pag. </s>

<s>133). </s></p><p type="main">

<s>Così fatte dottrine hanno per verità troppo del meccanico e del mate­<lb></lb>riale, e non si tien conto alcuno del grado di saturità dell&#039;aria soprastante <lb></lb>al liquido, la quale rinnovata via via è principalissima causa dell&#039;efficacia <lb></lb>del vento nelle evaporazioni. </s>

<s>Il Montanari è forse l&#039;unico che prima dello <lb></lb>stesso Borelli scrivesse intorno a ciò cose, che hanno più sembianza di vere. <lb></lb></s>

<s>“ Si vede che il vento, egli dice, ha così gran parte nell&#039;essiccare le cose <lb></lb>bagnate .... posciachè quelle particole dell&#039;umido, a causa della pressione <lb></lb>dell&#039;aria, come già dissi, si sollevano fra le particole dell&#039;aria medesima lor <lb></lb>vicina, portate via d&#039;un subito dal vento danno luogo ad altre di sollevarsi, <lb></lb>e di così successivamente svaporare ” (Lett. </s>

<s>al Sampieri, Bologna 1667, <lb></lb>pag. </s>

<s>83). </s></p><p type="main">

<s>E dalle teorie fisiche ch&#039;ebbero così nel Montanari quella maggior per­<lb></lb>fezione desiderabile a que&#039;tempi, passando alle applicazioni meccaniche da <lb></lb>noi sopra promesse, ecco la descrizione della macchina di Alessandro Ga­<lb></lb>lilei, nella quale il vapore per elasticità preme e per condensazione aspira <lb></lb>l&#039;acqua, operando con facilità quel che operano gli stantuffi mossi su e giu <pb xlink:href="020/01/732.jpg" pagenum="175"></pb>per i corpi delle trombe ordinarie, con gran pena e fatica. </s>

<s>“ Infondasi nel <lb></lb>vaso A (fig. </s>

<s>53) l&#039;acqua per il foro B fino a tre quarti della sua altezza, e <lb></lb>facendo fuoco sotto il vaso la medesima bollendo si rarefà in vapori, i quali <lb></lb>quando si gira il regolatore C verso D se ne passano per la canna E den­<lb></lb>tro il recipiente F, e chiudono una valvola che è dentro la canna in G, e <lb></lb>forzano l&#039;aria a sortire per una valvola che è in H fuori della canna I. </s>

<s><lb></lb>Quando il recipiente F è del tutto pieno di vapori, allora si torna a rigi­<lb></lb>rare il regolatore C verso E ed i medesimi vapori se ne passano per la <lb></lb><figure id="id.020.01.732.1.jpg" xlink:href="020/01/732/1.jpg"></figure></s></p><p type="caption">

<s>Figura 53.<lb></lb>canna D dentro il recipiente K, il quale è simile ed uguale all&#039;altro F, e <lb></lb>costruito nell&#039;istesso modo, e con l&#039;istesse valvole dentro la canna in G <lb></lb>ed H. </s>

<s>Subito che i vapori sono fermi in F, mentre che se ne passano per D <lb></lb>ad empire il recipiente K, si deve girar la chiave L e lasciare cadere un <lb></lb>poco d&#039;acqua fredda dentro il recipiente F, la quale subito condensa que&#039;va­<lb></lb>pori, di maniera che il suddetto recipiente rimane del tutto esausto onde <lb></lb>l&#039;ammosfera, premendo sopra l&#039;acqua M la forza ad ascendere per la canna <lb></lb>G ed a riempire il recipiente F. </s>

<s>Allora fermando i vapori in D, essendo che <pb xlink:href="020/01/733.jpg" pagenum="176"></pb>il recipiente K sarà già pieno, si lasceranno di nuovo entrare in F, i quali <lb></lb>immediatamente forzeranno tutta l&#039;acqua ad uscire per la canna I, come <lb></lb>fece prima l&#039;aria, e di nuovo il recipiente F sarà ripieno di vapori, e gi­<lb></lb>rando la chiave N, si condenseranno i vapori che sono in K e l&#039;acqua M <lb></lb>ascenderà per la canna G, come fece nell&#039;altro recipiente, onde fermati i <lb></lb>vapori in E si lasceranno entrare dentro il recipiente K e similmente l&#039;acqua <lb></lb>se ne sortirà fuori dalla canna I, ed il recipiente rimarrà pieno di vapori, e <lb></lb>così successivamente tornando a condensare e lasciare entrare i vapori den­<lb></lb>tro i recipienti, si potrà continuare ad alzar l&#039;acqua a piacere. </s>

<s>Il presente <lb></lb>modello alza in circa cinquanta barili d&#039;acqua in un&#039;ora. </s>

<s>Londra 20 Feb­<lb></lb>braio 17 15/16. Alessandro Galilei archit. </s>

<s>fiorentino. (Lavori per servire alla <lb></lb>vita di Galileo raccolti dal Viviani e dal Nelli, Filza IX, c. </s>

<s>311). </s></p><pb xlink:href="020/01/734.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del suono<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della diffusione del suono per l&#039;aria. </s>

<s>— II. </s>

<s>Delle varie esperienze ordinate a dimostrar la diffu­<lb></lb>sione, e a misurar la velocità del suono per l&#039;aria. </s>

<s>— III. </s>

<s>Delle prime fisiche ragioni date delle <lb></lb>consonanze. </s>

<s>— IV. </s>

<s>Di ciò che intorno al risonar delle corde fu dimostrato da Galileo. </s>

<s>— V. </s>

<s>Di <lb></lb>un Trattato fisico matematico, che preparava Niccolò Aggiunti sui tremori armonici nelle corde. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Alla luce e al calore aggiunsero i Pitagorici l&#039;armonia a intreare quei <lb></lb>vivifici influssi, che piovon su noi dall&#039;alto delle sfere celesti. </s>

<s>Ma perchè <lb></lb>quell&#039;armonia, insensibile all&#039;ottusità del nostro udito, non si faceva consi­<lb></lb>stere in altro che in un bell&#039;ordine di numeri, si vede qui pure verificarsi <lb></lb>la legge storica altre volte da noi avvertita, ed è che la matematica precedè <lb></lb>la fisica anche nel filosofare intorno alla natura e alla proprietà de&#039;suoni. </s>

<s><lb></lb>Le dottrine pitagoriche però e le platoniche son come fior di bellezza, che <lb></lb>aprendo leggero all&#039;aria il suo seno, col progredir del tempo allegando in <lb></lb>frutto, convien che anch&#039;egli si pieghi a terra trattovi dal proprio peso. </s>

<s>Quel <lb></lb>tornar così a soggiacere alle passioni comuni a tutti gli altri corpi, signifi­<lb></lb>cava, traducendo il simbolo a senso proprio, il passar dalle matematiche con­<lb></lb>templazioni alle fisiche realtà, che facevano le antiche dottrine; passaggio che <lb></lb>avvenne per opera della Filosofia stoica succeduta, propriamente come frutto <lb></lb>maturato, al fiore della Filosofia pitagorica. </s></p><p type="main">

<s>Agli Stoici si deve l&#039;avere avvertita quella somiglianza che passa fra <lb></lb>gl&#039;increspamenti dell&#039;aria alle vibrazioni del corpo risonante, e i cerchi che <lb></lb>si diffondono intorno a un sasso gittato sulla superficie di un&#039;acqua tran-<pb xlink:href="020/01/735.jpg" pagenum="178"></pb>quilla; somiglianza che si ripete anche oggidì nelle scuole propagatasi di <lb></lb>bocca in bocca, quasi come i cerchi stessi di quell&#039;acqua, i quali avendo il <lb></lb>loro centro nella Stoa si son tanto diffusi al largo, da giungere in fin presso <lb></lb>a toccare la nostra riva. </s>

<s>“ Dicono questi (così nel bel linguaggio del loro <lb></lb>Segretario commemorano le dottrine degli Stoici i nostri Accademici fioren­<lb></lb>tini) che, siccome veggiamo l&#039;acqua stagnante incresparsi in giro per una <lb></lb>pietruzza che in lei si getti, e tali increspamenti andarsi via via propagando <lb></lb>in cerchi successivamente maggiori, tanto ch&#039;e&#039;giungano stracchi alla riva <lb></lb>e vi muoiono, e che percotendola con impeto, da essa per all&#039;in là si ri­<lb></lb>flettono; così per appunto asseriscono la sottilissima aria dintorno al corpo <lb></lb>sonoro andarsi minutamente increspando per immenso tratto, onde incon­<lb></lb>trandosi con tali ondeggiamenti nell&#039;organo del nostro udito, e quello tro­<lb></lb>vando molle e arrendevole, gl&#039;imprime un certo tremore che noi suono ap­<lb></lb>pelliamo ” (Saggi di natur. </s>

<s>esper., Firenze 1841, pag. </s>

<s>156). </s></p><p type="main">

<s>Il modo di rappresentar così all&#039;occhio nell&#039;acqua ciò che è affatto <lb></lb>invisibile nell&#039;aria, e la semplice facilità e naturalezza della dimostrazione <lb></lb>sedussero tanto gl&#039;ingegni, che fu creduto di aver fatto un gran progresso <lb></lb>nell&#039;Ottica, quando introdotte le ondulazioni eteree si poteron ridurre a <lb></lb>quella stessa facilità e naturalezza i modi dell&#039;operar sull&#039;occhio la luce. </s>

<s>Che <lb></lb>fosse veramente quella una seduzione lo prova l&#039;esser rimasti tuttavia mi­<lb></lb>steriosi molti fatti ottici ritrosi a secondare i moti ondulatori dell&#039;etere, ma <lb></lb>ben più seduttrice fu quella facilità in coloro, che, nel primo risorgere della <lb></lb>scienza sperimentale, dall&#039;esempio stoico de&#039;circoli nell&#039;acqua passarono a <lb></lb>filosofare intorno al modo del diffondersi il suono nell&#039;aria, attribuendo a <lb></lb>questa le qualità proprie a solo il liquido elemento. </s></p><p type="main">

<s>Galileo, che tanta parte ebbe al risorgimento di quella scienza speri­<lb></lb>mentale, com&#039;aveva accolti i placiti dell&#039;antica Filosofia stoica rispetto al ca­<lb></lb>lore e alle altre qualità secondarie de&#039;corpi, così ripetè le stesse stoiche <lb></lb>dottrine relative ai suoni. </s>

<s>“ Resta poi (scrive nel <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end>) l&#039;elemento <lb></lb>dell&#039;aria per li suoni, i quali indifferentemente vengono a noi dalle parti <lb></lb>basse e dall&#039;alte e dalle laterali, essendo noi costituiti nell&#039;aria, il cui mo­<lb></lb>vimento in sè stessa, cioè nella propria regione, è ugualmente disposto per <lb></lb>tutti i versi, e la situazion dell&#039;orecchio è accomodata, il più che sia pos­<lb></lb>sibile, a tutte le positure di luogo, ed i suoni allora son fatti e sentiti da <lb></lb>noi, quando (senz&#039;altre qualità sonore e transonore) un frequente tremor <lb></lb>dell&#039;aria, in minutissime onde increspata, muove una certa cartilagine di <lb></lb>certo timpano che è nel nostro orecchio. </s>

<s>Le maniere poi esterne potenti a <lb></lb>far questo increspamento nell&#039;aria sono moltissime, le quali forse si ridu­<lb></lb>cono in gran parte al tremore di qualche corpo, che urtando nell&#039;aria l&#039;in­<lb></lb>crespa, e per essa con gran velocità si distendono l&#039;onde dalla frequenza <lb></lb>delle quali nasce l&#039;acutezza del suono e la gravità dalla rarità ” (Alb. </s>

<s>IV, 336). </s></p><p type="main">

<s>Benchè a ritrar più perfettamente le dottrine stoiche manchi in queste <lb></lb>parole di Galileo la similitudine espressa degli ondeggiamenti dell&#039;acqua, è <lb></lb>certo nulladimeno, da quel che altrove e segnatamente nel I Dialogo delle <pb xlink:href="020/01/736.jpg" pagenum="179"></pb>Due Nuove Scienze scrive del suono, e meglio dalle teorie acustiche da lui <lb></lb>stesso professate, che riguardò le onde sonore diffondersi meccanicamente a <lb></lb>quel modo che si diffondono gl&#039;increspamenti sulla superficie di un&#039;acqua <lb></lb>tranquilla intorno al centro della percossa. </s>

<s>La somiglianza però (e da que­<lb></lb>sto principalmente nacque l&#039;inganno di Galileo e de&#039;suoi discendenti) non <lb></lb>è che apparente, perchè mentre nell&#039;acqua l&#039;impulso al moto consiste nel <lb></lb>peso, nell&#039;aria invece consiste tutto nell&#039;elaterio. </s></p><p type="main">

<s>Il Frisi, ch&#039;è pure il più assennato fra quanti scrissero l&#039;Elogio di Ga­<lb></lb>lileo, fu primo a notare che nel I Dialogo delle Nuove Scienze l&#039;Autore, <lb></lb>come non aveva ben conosciuto nè la pressione nè il peso dell&#039;aria, <emph type="italics"></emph>così <lb></lb>non parve che si fosse formata una giusta idea neppure dell&#039;elasticità.<emph.end type="italics"></emph.end><lb></lb>(Elog. </s>

<s>del Gal., Livorno 1775, pag. </s>

<s>76). Non par credibile che così fatti giu­<lb></lb>dizi sieno usciti dalla penna di chi, citando quel I Dialogo galileiano, doveva <lb></lb>aver letta l&#039;esperienza del fiasco di vetro, dentro al quale condensata l&#039;aria <lb></lb>con uno schizzatoio, diceva il Salviati di aver trovato lo stesso fiasco sulla <lb></lb>bilancia esser notabilmente cresciuto di peso (Alb. </s>

<s>XIII, 81). Quanto è falso <lb></lb>però quel che asserisce il Frisi rispetto alla pressione e al peso dell&#039;aria, <lb></lb>altrettanto è giusto per quel che riguarda l&#039;elasticità, la quale non par che <lb></lb>fosse veramente conosciuta, e in ogni modo è certo che non fu applicata, <lb></lb>nè da Galileo nè da&#039;Discepoli di lui più prossimi, al moto e alla diffusione <lb></lb>ondosa del suono. </s></p><p type="main">

<s>Il Porta, nel suo libro I degli Spiritali, descrive fra le altre esperienze <lb></lb>pneumatiche quella dell&#039;archibugio di ferro, dentro il quale “ se alcuno <lb></lb>metterà la verga nel suo cavo di mezzo, la cui punta sia bagnata d&#039;olio .... <lb></lb>e col suo dito si otturi lo spiraglio per dove si dà foco che non fugga l&#039;aria, <lb></lb>di là vedremo per esperienza che con molta forza ci ficcaremo la verga den­<lb></lb>tro, perchè l&#039;aria si viene a condensare e a restringere in sè medesima, e <lb></lb>quando per forza non vi potrà più entrar dentro lascieremo libera la verga, <lb></lb>allora verrà fuori con grande strepito e violenza e balzerà di molto di lon­<lb></lb>tano ” (Napoli 1606, pag. </s>

<s>17). Il Castelli poi, nel corollario XI al I Trat­<lb></lb>tato della <emph type="italics"></emph>Misura <gap></gap>elle acque correnti,<emph.end type="italics"></emph.end> dop&#039;aver detto che l&#039;acqua non si <lb></lb>comprime nè ha molla da ritornare come la bambagia o la lana o come <lb></lb>l&#039;aria, cita l&#039;<emph type="italics"></emph>Archibugio a vento inventato a&#039;nostri tempi da M. </s>

<s>Vincenzo <lb></lb>Vincenti urbinate<emph.end type="italics"></emph.end> (Bologna 1660, pag. </s>

<s>19) che è l&#039;applicazione immediata <lb></lb>dell&#039;esperienza descritta dal Porta. </s></p><p type="main">

<s>Nonostante tutto questo, quando il Pecquet pubblicò insiem con le sue <lb></lb>l&#039;esperienze fatte dall&#039;Auzout e dal Robervall nel vuoto torricelliano, si com­<lb></lb>piacque di aver egli e i suoi illustri colleghi dimostrato per i primi riseder <lb></lb>nell&#039;aria un&#039;innata e spontanea tendenza d&#039;espander la sua mole, diminuita <lb></lb>la pressione esterna; tendenza e sforzo da essi chiamato <emph type="italics"></emph>forza elastica.<emph.end type="italics"></emph.end> Re­<lb></lb>clamò contro i vanti del Pecquet il nostro Tommaso Cornelio rivendicando <lb></lb>a sè l&#039;anteriorità di quella scoperta, nè concedendo altro merito ai fisici pa­<lb></lb>rigini da quello in fuori di aver trovato il nome da significare quella innata <lb></lb>proprietà dell&#039;aria. </s>

<s>“ Memini me olim (scriveva lo stesso Cornelio nel 1682) <pb xlink:href="020/01/737.jpg" pagenum="180"></pb>ante annos ferme quatuor supra triginta in hanc considerationem incidisse, <lb></lb>eiusque rude aliquod specimen exhibuisse in Epistola <emph type="italics"></emph>De platonica circum­<lb></lb>pulsione,<emph.end type="italics"></emph.end> quam sub idem tempus nimium festinanter scripseram. </s>

<s>Sed ecce <lb></lb>post exactos ab edita Dissertatione nostra tres annos prodit Libellus Johan­<lb></lb>nis Pecqueti, ex quo palam factum est ingeniosissimum Robervallium ad <lb></lb>exquirendam hanc spontaneam aeris distractionem dilatationemque sedulo <lb></lb>incubuisse, eamque pluribus argumentis ab experientia deductis evidentis­<lb></lb>sime demonstrasse. </s>

<s>Tum vero primum, ni fallor, in usu fuere verba illa <lb></lb><emph type="italics"></emph>elater<emph.end type="italics"></emph.end> seu <emph type="italics"></emph>vis elastica,<emph.end type="italics"></emph.end> quae respondere iis videntur, quibus usus est Lu­<lb></lb>cretius, qui saepe memoravit a circumfuso aere res agitari et verberari ” <lb></lb>(Progymnasm. </s>

<s>post., Neapoli 1688, pag. </s>

<s>11). </s></p><p type="main">

<s>Comunque sia è un fatto che, poco dopo la metà del secolo XVII, si <lb></lb>riteneva che l&#039;elaterio fosse una proprietà recentemente scoperta o dimo­<lb></lb>strata nell&#039;aria. </s>

<s>Lo Schott, per esempio, pubblicando nel 1664 la sua <emph type="italics"></emph>Tecnica <lb></lb>curiosa,<emph.end type="italics"></emph.end> discute nel cap. </s>

<s>X del lib. </s>

<s>IV la questione di questa elasticità come <lb></lb>controversa, e incomincia: “ Recentiores pneumaticorum experimentorum <lb></lb>scriptores aeri non tantum pondus sed elaterem quoque, seu vim ac pote­<lb></lb>statem elasticam attribuunt, hoc est innatum ac spontaneum nisum ad sese <lb></lb>rarefaciendum ac dilatandum, quo prementibus circum se corporibus resistat, <lb></lb>et ubi liber ab eorum pressione est spontanea dilatatione sese ad statum sibi <lb></lb>naturaliter debitum reducat ” (Norimbergae, pag. </s>

<s>292). E proseguendo ivi <lb></lb>nel § I a esporre in che modo que&#039;recenti Pneumatici dimostrassero la pro­<lb></lb>prietà innata che ha l&#039;aria di restituirsi al suo primo volume, cita gli Espe­<lb></lb>rimenti nuovi del Boyle, che ricorre agli esempi della spugna “ quae com­<lb></lb>pressa constringitur et a pressione libera sponte se se iterum dilatat, et ad <lb></lb>pristinam suam molem reducit ” (ibi, pag. </s>

<s>293) come già il Castelli era pa­<lb></lb>recchi anni prima ricorso all&#039;esempio della lana e della bambagia. </s></p><p type="main">

<s>Rimeditando sopra questi fatti occorre a distinguere fra l&#039;elasticità del­<lb></lb>l&#039;aria dimostrata dalla pressione di pesi esterni e dalla pressione in sè stessa. </s>

<s><lb></lb>Quanto al primo caso non ci è dubbio che l&#039;esperienza del Porta e l&#039;appli­<lb></lb>cazione che ne fece il Vincenti al Fucile pneumatico, non che l&#039;esperienza <lb></lb>di Galileo sulla compressione dell&#039;aria, non dimostrassero sufficientemente <lb></lb>l&#039;elaterio di lei. </s>

<s>Quanto al secondo caso occorreva sperimentare nel vuoto <lb></lb>torricelliano, come fece il Robervall, o come il Boyle sotto la campana della <lb></lb>Macchina pneumatica. </s>

<s>Così a parer nostro si spiega come potessero appresso <lb></lb>gli stranieri apparir nuove le cose che avevano i Nostri molto prima spe­<lb></lb>rimentate. </s></p><p type="main">

<s>Ne avremo di ciò una conferma confrontando insieme l&#039;illustrazione data <lb></lb>da Galileo (Alb. </s>

<s>VI, pag. </s>

<s>10, 11) e dallo Schott (Mechanica hydraulico-pneu­<lb></lb>matica, Herbipoli 1657, pag. </s>

<s>50-52) intorno al modo di operare della <emph type="italics"></emph>Lu­<lb></lb>cerna eroniana.<emph.end type="italics"></emph.end> Il Fisico tedesco avvertendo che il tubo, il quale attraversa <lb></lb>il diaframma e scende nella cavità inferiore che fa da piede alla Lucerna, <lb></lb>deve essere munito di chiavetta, determina la lunghezza di esso tubo rispetto <lb></lb>alla lunghezza dell&#039;altro tubo, che dalla coppa sale a portar l&#039;olio su al boc-<pb xlink:href="020/01/738.jpg" pagenum="181"></pb>ciolo del lucignolo, quasi che il volume dell&#039;aria dovess&#039;essere uguale al vo­<lb></lb>lume dell&#039;aria espulsa, e l&#039;aria stessa non operasse che per solo effetto di <lb></lb>impenetrabilità, e nulla per forza elastica. </s>

<s>Galileo invece contentandosi di <lb></lb>ammetter, qualunque sia la lunghezza del tubo, una comunicazione fra il <lb></lb>recipiente superiore e l&#039;inferiore della Lucerna, mostra al contrario dello <lb></lb>Schott di credere che l&#039;aria nella coppa dell&#039;olio prema per forza elastica <lb></lb>sull&#039;olio stesso, da farlo risalir per tale impulsione infino al bocciolo del lu­<lb></lb>cignolo a farlo ardere in fiamma. </s></p><p type="main">

<s>Se però dall&#039;esperienza descritta negli Spiritali dal Porta, Galileo allora <lb></lb>giovane fu persuaso dell&#039;elasticità dell&#039;aria, e l&#039;applicò a spiegare ad Alvise <lb></lb>Mocenigo che n&#039;era curioso il modo della Lucerna eroniana, non seppe ap­<lb></lb>plicarla, ciò che sarebbe stato assai più importante, alle onde sonore, le quali <lb></lb>non si diffondono per pressione idrostatica come quelle dell&#039;acqua, ma per <lb></lb>condensazione e per rarefazione. </s>

<s>Da questo ostacolo rimase chiusa per lungo <lb></lb>tempo la via da conoscere la verità, come vedesi confermato dall&#039;esame delle <lb></lb>dottrine acustiche professate da tutti i Fisici infino al Newton, i quali ben­<lb></lb>chè fossero oramai fatti certi per tante ripetute prove dell&#039;elasticità dell&#039;aria, <lb></lb>pur sedotti dalle dottrine stoiche non seppero, come Galileo non seppe, ap­<lb></lb>plicarla alla generazione del suono. </s></p><p type="main">

<s>Dall&#039;ammettere la diffusione delle onde aeree farsi a quel modo stesso <lb></lb>delle acquee veniva per prima conseguenza che non si potessero i suoni pro­<lb></lb>dur che dall&#039;urto e dalla collisione de&#039;corpi, in modo che ne venisse l&#039;aria <lb></lb>percossa e flagellata. </s>

<s>Di qui è che il Grimaldi, per citar uno de&#039;più autore­<lb></lb>voli esempi, asseriva esser da tutti i fatti universalmente provato <emph type="italics"></emph>omnia so­<lb></lb>nora debere tremere et observamus ipsam percussionem vel collisionem <lb></lb>corporum ad sonum necessariam.<emph.end type="italics"></emph.end> (De Lum., Bononiae 1665, pag. </s>

<s>374). </s></p><p type="main">

<s>Un altro esempio di Fisico non meno autorevole lo abbiamo nel Mon­<lb></lb>tanari, il quale nel suo Dialogo intitolato <emph type="italics"></emph>Le forze d&#039;Eolo,<emph.end type="italics"></emph.end> volendo dare ad <lb></lb>intendere in che modo si faccia il chiocco della frusta, dop&#039;aver sottilmente <lb></lb>dimostrato, per l&#039;applicazione delle leggi meccaniche, che tutto dipende dalla <lb></lb>velocità con che il cordone ficca nell&#039;aria la punta, e dalla sollecitudine con <lb></lb>che dal braccio la punta stessa è ritirata, conclude la ragion dell&#039;effetto col <lb></lb>dire che si fa il chiocco perchè la punta della frusta “ percote l&#039;aria con <lb></lb>strepito, e si va stracciando nell&#039;istessa più debole estremità ” (Parma 1694, <lb></lb>pag. </s>

<s>151). Or è chiaro che il chiocco si produce dal violento irrompere del­<lb></lb>l&#039;aria circostante dentro il vuoto lasciato nel repentino ritirar della punta <lb></lb>della frusta; chiocco simile a quello che si ode stappando, per esempio, la <lb></lb>bocca a una bottiglia. </s>

<s>Qui e in tanti altri esempii che ci porgono gli stru­<lb></lb>menti a fiato non ci è collisione di corpi, nè l&#039;aria è flagellata o percossa, <lb></lb>ma entrando a riempire il vuoto per elasticità, per elasticità si commuove <lb></lb>in sè stessa e suona. </s></p><p type="main">

<s>A questo punto non possiamo non trattenerci a considerare che, men­<lb></lb>tre da tali insigni Autori s&#039;ignoravano le ragioni di simili fatti acustici, il <lb></lb>Benedetti, morto quasi un secolo avanti, avesse intravedute, e, condensate <pb xlink:href="020/01/739.jpg" pagenum="182"></pb>in poche parole, avesse annunziate le verità di quelle dottrine, alle quali il <lb></lb>Newton un secolo dopo dette la più solenne e splendida esplicazione. </s>

<s>L&#039;Au­<lb></lb>tor del libro delle <emph type="italics"></emph>Speculazioni,<emph.end type="italics"></emph.end> dietro esperienze simili a quelle ora da noi <lb></lb>citate, concluse come cosa nuova e da nessun altro prima avvertita, che il <lb></lb>suono è generato dall&#039;aria mossa velocemente a riempire il vuoto. </s>

<s>E benchè <lb></lb>riconosca ne&#039;casi più ordinarii la necessità di avere un corpo che tremi, <lb></lb>que&#039;tremori nonostante mettono secondo il Benedetti l&#039;aria in moto, per­<lb></lb>ch&#039;ella velocemente sottentra a riempir il vacuo lasciato dietro a sè via via <lb></lb>dal vibrare del corpo sonoro. </s></p><p type="main">

<s>“ Posse sonum corpus aliquod quod sensu sit destitutum, ut Aristoti­<lb></lb>les IX cap. </s>

<s>lib. </s>

<s>I <emph type="italics"></emph>De coelo<emph.end type="italics"></emph.end> putavit, ostendere est falsum. </s>

<s>Corpus enim non <lb></lb>nisi a corpore potest laedi, non ergo a sono, cum sonus corpus non sit. </s>

<s>Sed <lb></lb>aer et ignis cum e contra sint corpora hoc facile praestare possunt implendo <lb></lb>aliquem locum velociter ad excludendum vacuum, unde generatur sonus, <lb></lb>quod hucusque a nemine animadversum fuisse comperio ” (Venetiis 1599, <lb></lb>pag. </s>

<s>289). E altrove: “ Necessarium quoque est ut tremat sive trepidet cor­<lb></lb>pus quod sonum edere debet. </s>

<s>Neque etiam absque aere sonus effici potest <lb></lb>quia aer sonat ingrediendo velociter ad implendum locum ut non remaneat <lb></lb>vacuus ” (ibi, pag. </s>

<s>190). </s></p><p type="main">

<s>Così fatte dottrine però non furono comprese per essere ancora troppo <lb></lb>precoci, e seguitando a insistere i Fisici sull&#039;esempio delle onde nell&#039;acqua, <lb></lb>un&#039;altra delle perniciose conseguenze derivatene si fu quella di non aver <lb></lb>riconosciuto che, per effetto dell&#039;elasticità, dovevano diffondersi le onde in­<lb></lb>torno al corpo risonante regolarmente in sfera. </s>

<s>L&#039;aver notato che i suoni <lb></lb>ci vengono indifferentemente da tutte le parti, essendo noi costituiti nell&#039;aria <lb></lb>il cui movimento in sè stessa è ugualmente disposto per tutti i versi, e <lb></lb>l&#039;aver considerato che la situazion dell&#039;orecchio è accomodata il più che sia <lb></lb>possibile a tutte le positure del luogo, non furono sufficiente avviso di quella <lb></lb>sferica diffusione de&#039;suoni a Galileo. </s>

<s>Se n&#039;ebbe poi qualche sentore dagli <lb></lb>Accademici del Cimento, ma l&#039;esperienza proposta dal Rinaldini ed eseguita <lb></lb>il dì 30 Agosto 1662 (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>564) lasciò i <lb></lb>desiderosi d&#039;intendere il vero in quella loro prima incertezza. </s></p><p type="main">

<s>E fu appunto questa stessa incertezza che portò a dubitar della legge <lb></lb>secondo la quale diminuisce l&#039;intensità del suono col crescere delle distanze. </s>

<s><lb></lb>Vedemmo che la dimostrazione certa di ciò, rispetto alla luce, non s&#039;ebbe <lb></lb>prima che si pensasse all&#039;ipotesi delle onde eteree o della diffusione sferica <lb></lb>di essa luce, ond&#039;è chiaro che, se tale ipotesi fosse stata ammessa anche per <lb></lb>la diffusione del suono, non restava nulla a dubitare che, siccome le super­<lb></lb>ficie delle sfere concentriche crescono a proporzione de&#039;quadrati de&#039;raggi, <lb></lb>così con la medesima proporzione avrebbe pur dovuto diminuire l&#039;attività <lb></lb>dell&#039;onda sonora. </s>

<s>Eppure noi leggiamo negli Autori di Acustica di que&#039;tempi <lb></lb>esser detto del suono “ che egli procede con Iddio sa qual misura di pro­<lb></lb>porzione fra il distendersi nello spazio e il diminuirsi nel grado ” (Bartoli, <lb></lb>Del suono, Roma 1679, pag. </s>

<s>44). </s></p><pb xlink:href="020/01/740.jpg" pagenum="183"></pb><p type="main">

<s>Dal non aver riconosciuta la diffusione sferica delle onde sonore dipen­<lb></lb>deva inoltre la difficoltà d&#039;intendere come mai, per esempio, una voce si <lb></lb>ascolti anco dopo un muro o s&#039;oda anche dietro un monte lo squillo delle <lb></lb>campane, per cui furono indotti i Fisici a credere e a dire che il suono, a <lb></lb>differenza della luce, proceda indifferentemente così per linee rette come per <lb></lb>linee flessuose. </s>

<s>“ Il suono, scriveva il Cavalieri, non soggiace così a queste <lb></lb>leggi come il lume, propagandosi quello anco per linee flessuose, cagionan­<lb></lb>dosi egli dalla pulsazione nell&#039;organo dell&#039;udito fatta dall&#039;aria tremante di <lb></lb>più o men veloci tremori, che fanno l&#039;alto e il basso, il grave e l&#039;acuto nel <lb></lb>suono, il qual tremore comincia col corpo sonoro e ad ogni posizione si va <lb></lb>continuamente diffondendo per diritta linea, quando non trovi ostacoli, ma <lb></lb>per diritta linea e per flessuosa, quando ritrovi impedimenti ” (Specchio <lb></lb>Ustorio, Bologna 1650, pag. </s>

<s>79). </s></p><p type="main">

<s>E giacchè il Cavalieri, fra gli Autori che si possono citare al presente <lb></lb>proposito, è uno de&#039;principali, si noti inoltre come l&#039;aver egli ignorata la <lb></lb>diffusione sferica delle onde sonore l&#039;avesse condotto a dare una spiegazione <lb></lb>falsa de&#039;tubi parlanti e del Portavoce. </s>

<s>“ Per canali rinchiusi so molto bene <lb></lb>potersi parlar di lontano, ma in questi non vi è artificio per conto di rifles­<lb></lb>sione, ma semplicemente mantengono la voce gagliarda per la superficie <lb></lb>tersa del canale, e per il tremito dell&#039;aria che, senza patir turbamento per <lb></lb>la strada, incorrotto perviene all&#039;orecchio ” (ivi, pag. </s>

<s>80). </s></p><p type="main">

<s>La ragion fisica del diffondersi i suoni per l&#039;aria dipendente dall&#039;altra <lb></lb>ragione del loro procedere in onde rarefatte e condensate, come sagacemente <lb></lb>aveva avvertito già il Benedetti, l&#039;ebbe finalmente l&#039;Acustica ordinata in pro­<lb></lb>posizioni dimostrate con rigore geometrico nel II libro de&#039;Principii di Filo­<lb></lb>sofia neutoniana. </s>

<s>La XLIII di quelle proposizioni fu che cacciò dall&#039;Acustica <lb></lb>il dannoso errore stoico delle onde sonore propagate nell&#039;aria dalla percus­<lb></lb>sione de&#039;corpi, a quel modo che si propagano le onde circolari nell&#039;acqua <lb></lb>percossa, per esempio, dal cader di una pietra. </s>

<s>“ Nam partes corporis tre­<lb></lb>muli, dice ivi il Newton spiegando il concetto antico del Benedetti, vicibus <lb></lb>alternis eundo et redeundo, itu suo urgebunt et propollent partes medii sibi <lb></lb>proximas, et urgendo compriment easdem et condensabunt: dein reditu suo <lb></lb>sinent partes compressas recedere et sese expandere. </s>

<s>Igitur partes medii <lb></lb>corpori tremulo proximae ibunt et redibunt per vices, ad instar partium <lb></lb>corporis illius tremuli, et qua ratione partes corporis huius agitabant hasce <lb></lb>medii partes, hae similibus tremoribus agitatae agitabunt partes sibi proxi­<lb></lb>mas, eaeque similiter agitatae agitabunt ulteriores, et sic deinceps in infi­<lb></lb>nitum ” (Genevae 1740, pag. </s>

<s>353). </s></p><p type="main">

<s>Avendo così spiegato in questa come nella precedente proposizione il <lb></lb>moto progressivo dell&#039;onda aerea, che riceve i suoi impulsi dal continuo di­<lb></lb>latarsi delle parti addensate verso i precedenti e successivi intervalli rima­<lb></lb>sti rarefatti; dimostra il Newton in che modo, supposto che in A (fig. </s>

<s>54) <lb></lb>sia un corpo sonoro, ed RS un ostacolo, in mezzo al quale sia aperto un <lb></lb>piccolo foro BC, s&#039;oda il suono non solo dentro il cono APQ, com&#039;avver-<pb xlink:href="020/01/741.jpg" pagenum="184"></pb>rebbe se A fosse un corpo luminoso, ma per ogni parte anche più riposta, <lb></lb>come sarebbe in NO, KL. “ Et quoniam pulsuum progressivus motus ori­<lb></lb><figure id="id.020.01.741.1.jpg" xlink:href="020/01/741/1.jpg"></figure></s></p><p type="caption">

<s>Figura 54.<lb></lb>tur a perpetua re­<lb></lb>laxatione partium <lb></lb>densiorum versus <lb></lb>antecedentia inter­<lb></lb>valla rariora, et pul­<lb></lb>sus eadem fere ce­<lb></lb>leritate sese in me­<lb></lb>dii partes quietas <lb></lb>KL, NO, hinc inde <lb></lb>relaxare debent; <lb></lb>pulsus illi eadem <lb></lb>fere celeritate sese <lb></lb>dilatabunt undique <lb></lb>in spatia immota <lb></lb>KL, NO, qua pro­<lb></lb>pagantur directe a <lb></lb>centro A, ideoque <lb></lb>spatium totum KLNO occupabunt. </s>

<s>Hoc experimur in sonis, qui vel monte <lb></lb>interposito audiuntur, vel in cubiculum per fenestram admissi sese in omnes <lb></lb>cubiculi partes dilatant, inque angulis omnibus audiuntur, non tam reflexi <lb></lb>a parietibus oppositis, quam a fenestra directe propagati, quantum ex sensu <lb></lb>iudicare licet ” (ibi, pag. </s>

<s>345, 46). </s></p><p type="main">

<s>Qui cadrebbe opportuno osservare che fu dalla dimostrazione di questo <lb></lb>Teorema condotto il Newton a negar l&#039;ipotesi delle onde eteree nella dif­<lb></lb>fusione del lume, perch&#039;egli ragionava che siccome, costituito in A, per <lb></lb>esempio, un campanello, si sente per la diffusione dell&#039;onda aerea in ogni <lb></lb>verso il suono anche nelle parti più riparate quali sarebbero KL, NO; così <lb></lb>per una simile diffusione dell&#039;onda eterea, si dovrebbero veder dietro l&#039;osta­<lb></lb>colo quelle stesse parti KL, NO, illuminate se fosse in A collocata la fiamma <lb></lb>di una candela. </s></p><p type="main">

<s>Ma perchè non è tempo oramai di tornare indietro sopra le cose già <lb></lb>prima discorse, ecco, procedendo a diritto per la nostra via, com&#039;applicando <lb></lb>il principio della diffusione sferica delle onde sonore spieghi il Newton il <lb></lb>vero modo come procedono esse onde a rinforzare il suono nel Portavoce: <lb></lb>“ Sed et cur soni in Tubis stentorophonicis valde augentur ex allatis prin­<lb></lb>cipiis manifestum est. </s>

<s>Motus enim omnis reciprocus singulis recursibus a <lb></lb>causa generante augeri solet. </s>

<s>Motus autem in tubis dilatationem sonorum <lb></lb>impedientibus, tardius amittitur et fortius recurrit et propterea a motu novo <lb></lb>singulis recursibus impresso magis augetur. </s>

<s>Et haec sunt praecipua phae­<lb></lb>nomena sonorum ” (ibi, pag. </s>

<s>396). </s></p><p type="main">

<s>Fra questi fenomeni però n&#039;è uno che se non è de&#039;precipui, è certo <lb></lb>de&#039;più curiosi. </s>

<s>Il Newton spiegò bene il modo come il suono si diffonde per <pb xlink:href="020/01/742.jpg" pagenum="185"></pb>tutto in una stanza, benchè non v&#039;abbia adito che per una piccola finestra <lb></lb>aperta, perchè comunicandosi insieme l&#039;aria le onde interne ricevono i primi <lb></lb>impulsi al moto da quelle che v&#039;entrano dal di fuori. </s>

<s>Ma se la finestra è <lb></lb>chiusa? </s>

<s>se anzi è murata? </s>

<s>il suono, benchè sia interclusa ogni comunica­<lb></lb>zione fra l&#039;aria interna e l&#039;esterna, passa ancora attraverso il muro, nè si <lb></lb>trova detta di ciò la ragione in nessun de&#039;Teoremi neutoniani. </s>

<s>Eppure si <lb></lb>mostrarono curiosi di saperla anche gli antichi, e Seneca fra gli altri, con­<lb></lb>siderando che il muro è poroso e che l&#039;aria, sottilissimo spirito, vi s&#039;insi­<lb></lb>nua assai facilmente, trovò nell&#039;aria stessa ivi dentro insinuata la continuità <lb></lb>necessaria al libero trapassare del suono. </s>

<s>“ Vox, qua ratione per parietum <lb></lb>munimenta transmittitur? </s>

<s>nisi quod solido quoque aer inest, qui sonum <lb></lb>extrinsecus missum et accipit et remittit ” (Naturalium quaestionum li­<lb></lb>bri VII, Aldus Venetiis 1522, c. </s>

<s>13). </s></p><p type="main">

<s>Era facile però avvedersi che non poteva esser questa addotta da Se­<lb></lb>neca la ragion vera del fatto, perchè il suono dovrebbe tanto più facilmente <lb></lb>avere il transito, quanto l&#039;ostacolo fosse più poroso, o contenesse maggior <lb></lb>copia d&#039;aria rinchiusa, ciò che l&#039;esperienze dimostrano esser falso. </s>

<s>Persuaso <lb></lb>di ciò il Grimaldi ebbe a concluderne che non era possibile spiegare il fatto <lb></lb>altrimenti, che ammettendo nella voce di un che parla dentro una stanza <lb></lb>la virtù di far vibrare il muro e di trasmettere all&#039;aria dell&#039;altra stanza at­<lb></lb>tigua le vibrazioni sincrone a quelle ricevute e produttrici perciò de&#039;mede­<lb></lb>simi suoni. </s>

<s>“ Si non admittatur aliquis motus in muris praedictis, vel in <lb></lb>substantia per eos diffusa, non video quomodo concipiendus sit fieri alius <lb></lb>motus in aere post murum consequente. </s>

<s>Motus enim non communicatur <lb></lb>mobili nisi per motum medii si hoc intercedat ” (De lum. </s>

<s>cit., pag. </s>

<s>391). </s></p><p type="main">

<s>Queste dottrine, che non fa maraviglia se parvero strane ai tempi del­<lb></lb>l&#039;Autore, avrebbero trovato ora la più bella dimostrazione e la più valida <lb></lb>conferma ne&#039;modi d&#039;operar del Telefono e del Fonografo, se come una sot­<lb></lb>tile laminetta metallica fosse così gelosa in sentire i tremori leggerissimi del­<lb></lb>l&#039;aria la mole solidissima di un muro. </s>

<s>È perciò che il Grimaldi raccoglie <lb></lb>insieme le forze a difender le sue dottrine, le quali prevedeva che sareb­<lb></lb>bero assalite da questa parte, facendo opportunamente osservare che basta <lb></lb>una minima forza ad eccitare e a diffondere i tremori armonici nel più pon­<lb></lb>deroso corpo, e nel più duro che sia. </s>

<s>Così a solo strisciar la punta di uno <lb></lb>spillo s&#039;ode fremer nel suono il bronzo di una campana, e le barbe di una <lb></lb>penna fregate in capo a una lunghissima trave fan sentire il fruscio a chi <lb></lb>tiene applicato l&#039;orecchio all&#039;estremità opposta. </s></p><p type="main">

<s>Altro esempio di questa maravigliosa facilità di trasmettere i suoni, da <lb></lb>una forza debolissima, lo ritrova il Grimaldi in un fatto, di che dice esser <lb></lb>soliti di pigliare esperienza i soldati, i quali argomentano dal vibrar di un <lb></lb>pendolo posato sopra la pelle di un tamburo, il calpestar de&#039;cavalli dell&#039;eser­<lb></lb>cito nemico, che s&#039;avanzano talvolta parecchie miglia di lontano. </s>

<s>“ Plura in <lb></lb>rem praesentem experimenta afferre censeo.... Unum tamen prae caeteris <lb></lb>non possum non indicare. </s>

<s>Fertur consuetum esse militibus ut, si quando <pb xlink:href="020/01/743.jpg" pagenum="186"></pb>explorare voluerint adventum hostilis equitatus, tympanum in plano terrestri <lb></lb>erectum observant, animadvertentes utrum talus aut aliud quid impositum <lb></lb>pelli tympani subsultet ob tremorem scilicet ipsius pellis in tympano bene <lb></lb>tensae, quia nimirum id eis signum est terram equorum advenentium pedi­<lb></lb>bus pulsatam et tremere ipsam et tremorem consequenter impertiri tym­<lb></lb>pano ipsi terrae imposito ” (ibi, pag. </s>

<s>387). </s></p><p type="main">

<s>Questo tamburo da militari dette poi occasione al Grimaldi d&#039;inventare <lb></lb>il primo <emph type="italics"></emph>Sismometro<emph.end type="italics"></emph.end> o <emph type="italics"></emph>Sismoscopio<emph.end type="italics"></emph.end> che si debba chiamare e di applicarlo <lb></lb>a riconoscere i minimi tremori comunicati a ogni parte di qualche vastis­<lb></lb>simo edifizio benchè prodotti da non più validi colpi di quelli dati da un <lb></lb>maglio di legno. </s>

<s>“ Solum adverto posse subtilius agnosci tremorem prae­<lb></lb>dictae pellis in tympano, si illi imponatur aliquod speculum, a quo lumen <lb></lb>aliquod reflectatur ad magnam distantiam, huiusmodi enim lumen reflexum <lb></lb>et super aliquo corpore distante praesertim candido terminatum, suo tre­<lb></lb>more notabilius indicabit tremorem speculi, et consequenter etiam tympani. </s>

<s><lb></lb>Hoc artificio usus agnovi totum aliquod ingens aedificium tremere eo ipso <lb></lb>quod tellus in aliqua notabili ab eo distantia percutiebatur gravi quodam <lb></lb>malleo ex ligno, qualis adhiberi solet dum ligna scinduntur cuneis ferreis <lb></lb>per vim intrusis ” (ibi, pag. </s>

<s>387, 88). </s></p><p type="main">

<s>Ma nè così belle e argute prove sperimentali valsero a persuadere i ri­<lb></lb>trosi, i quali andavano dicendo che sarebbero allora state concludenti, quando <lb></lb>la voce avesse virtù di mettere in tremore un edifizio o di far vibrare una <lb></lb>campana o fremere una lunga trave. </s>

<s>Contrapponevano anzi cotesti opposi­<lb></lb>tori, come vedremo, all&#039;esperienze del Grimaldi altre esperienze dimostra­<lb></lb>tive dell&#039;insufficienza delle onde aeree a muovere co&#039;loro impulsi, nonchè <lb></lb>un solido muro, una sottilissima corda tesa. </s>

<s>E per verità non par che così <lb></lb>fatte opposizioni trovassero pronta la risposta, ma perchè in ogni modo il <lb></lb>trapassar del suono attraverso ai corpi non si può spiegare altrimenti che <lb></lb>con le ipotesi del Grimaldi, si potrebbe dir per salvarle che l&#039;aria mette in <lb></lb>vibrazione non immediatamente il muro, ma gli oggetti più leggeri o che <lb></lb>siano a vibrare meglio disposti, i quali, benchè con tenui impulsi, bastano, <lb></lb>come l&#039;esperienza dimostra, a comunicare il moto anche alle più solide <lb></lb>pareti. </s></p><p type="main">

<s>Comunque sia, essendo nostro unico fine quello di narrar la Storia, <lb></lb>abbiam veduto come e quanto penasse la scienza a intendere le ragioni del <lb></lb>moto ondoso e diffusivo del suono. </s>

<s>Eppure ella v&#039;era bene arrivata dalla Fi­<lb></lb>losofia stoica, alla quale fra gli altri benefizi dobbiamo l&#039;aver sostituito al­<lb></lb>l&#039;errore peripatetico delle specie intenzionali un real moto ondulatorio nel­<lb></lb>l&#039;aria, la quale perciò supponevasi allora mezzo necessario a mettere in <lb></lb>comunicazione il corpo risonante con l&#039;organo dell&#039;udito. </s>

<s>E benchè fosse <lb></lb>una tal supposizione così ragionevole, da non trovar contradittori, pur per <lb></lb>non fondar la miglior parte dell&#039;Acustica sopra un supposto, conveniva as­<lb></lb>sicurarsene in qualche modo, e di qui ebbero occasione quelle varie espe­<lb></lb>rienze, delle quali ora passiamo a narrar brevemente il successo. </s></p><pb xlink:href="020/01/744.jpg" pagenum="187"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Sembrava che così fatte nuove e curiose esperienze non fosse possibile <lb></lb>d&#039;eseguirle, senza l&#039;uso della Macchina pneumatica, o almeno dello stru­<lb></lb>mento torricelliano: eppure, in quel tempo che disputavasi ancora con tanto <lb></lb>ardore se si dava o no il vuoto in Natura, e che si credeva da&#039;Filosofi do­<lb></lb>ver senza il mezzo dell&#039;aria tutto il mondo creato rimanersi fra le tenebre <lb></lb>e immoto; un gentiluomo veneziano che dilettavasi di questi studii, traspor­<lb></lb>tatovi dal proprio genio e dall&#039;amicizia che teneva con Galileo, riusci a di­<lb></lb>mostrare sperimentalmente e senz&#039;uso degli strumenti inventati poi per <lb></lb>fare il vuoto, che senz&#039;aria nella Natura veramente regnerebbe il più alto <lb></lb>silenzio. </s></p><p type="main">

<s>L&#039;inaspettato esperimento non veniva suggerito dal caso, ma da una <lb></lb>speculazione condotta a fil di severa logica, benchè avesse per fondamento <lb></lb>la immaginata teoria degl&#039;ignicoli, i quali in uno spazio riscaldato sotten­<lb></lb>trano d&#039;ogni parte a riempirlo in luogo dell&#039;aria. </s>

<s>Giovan Francesco Sagredo, <lb></lb>così dunque scriveva il dì 11 Aprile 1615 a Galileo, in proposito della co­<lb></lb>struzione e del modo d&#039;operar de&#039;tubi termometrici: “ Alle fornaci di Mu­<lb></lb>rano ho fatto fare un vaso di vetro con un palmo di collo, ed essendo ben <lb></lb>caldo, l&#039;ho fatto richiudere, sicchè tutto l&#039;aere, che v&#039;era dentro rinchiuso <lb></lb>pieno di calore, non potesse più uscire dopo raffreddato. </s>

<s>E per conseguenza, <lb></lb>uscito lo spirito igneo e restatoci dentro l&#039;aere di ugual temperamento al­<lb></lb>l&#039;ambiente, persuasi chi erano presenti che dentro vi fosse pochissima aria <lb></lb>siccome al senso era manifesto che non vi fosse spirito igneo. </s>

<s>Le prove fu­<lb></lb>rono due: la prima che avendovi fatto rinchiudere dentro un sonaglio da <lb></lb>sparviero, questo mosso non faceva un suono esterno se non quanto per­<lb></lb>coteva nel vetro, e per conseguenza faceva un suono esterno, il che fu as­<lb></lb>sai facilmente creduto che non avvenisse per altro, che per lo mancamento <lb></lb>dell&#039;aere nel vaso suddetto, e tanto più ch&#039;essendosi rotto detto vaso si <lb></lb>trovò il sonaglio sonoro, secondo l&#039;ordinario. </s>

<s>La seconda perchè, avendo io <lb></lb>posto esso vaso col collo in una mastella d&#039;acqua, con un ferro gentilmente <lb></lb>apersi la bocca, per la quale salendo entrò tant&#039;acqua che pareva che vo­<lb></lb>lesse riempire tutto il detto vaso ” (Alb. </s>

<s>VIII, 372). </s></p><p type="main">

<s>La bella esperienza, così ben riuscita al Sagredo con tanto semplice <lb></lb>artificio, è notabile ripensando alle incertezze e ai tanti dubbii penosi, in che <lb></lb>lo Strumento torricelliano e la stessa Macchina pneumatica lasciarono poi i <lb></lb>Fisici, che si dettero così industriosamente a investigar que&#039;medesimi ef­<lb></lb>fetti. </s>

<s>È celebre nella storia da noi già narrata la prima di così fatte inve­<lb></lb>stigazioni tentata nel vuoto torricelliano da Gaspero Berti in Roma, investi­<lb></lb>gazione che riuscì, come sappiamo, priva di effetto, perchè, ritirata la calamita <lb></lb>e cadendo perciò il martellino di ferro sul campanello, questo <emph type="italics"></emph>limpidissi-<emph.end type="italics"></emph.end><pb xlink:href="020/01/745.jpg" pagenum="188"></pb><emph type="italics"></emph>mum edidit sonum ab omnibus experimento spectatoribus auditum.<emph.end type="italics"></emph.end> Non <lb></lb>si può credere che il Magiotti, il quale era uno di quegli spettatori non ri­<lb></lb>conoscesse, com&#039;aveva già riconosciuto il Sagredo, che il suono era esterno, <lb></lb>essendo la codetta del campanello così saldata col tubo di piombo, da co­<lb></lb>municargli assai facilmente i conceputi suoi tremori sonori, ma non si ve­<lb></lb>deva dall&#039;altra parte come si potesse interrompere quella inevitabile comu­<lb></lb>nicazione. </s></p><p type="main">

<s>Furono da questa difficoltà sopraffatti gli Accademici del Cimento, i quali <lb></lb>ripeterono l&#039;esperienza del sonaglio (Saggi ecc., Firenze 1841, pag. </s>

<s>57, 58) <lb></lb>così bene riuscita al Sagredo, e credendo che si potesse quella difficoltà no­<lb></lb>tabilmente diminuire, si dettero con incredibile industria a sperimentar con <lb></lb>uno strumento a fiato, conforme a ciò che aveva progettato il Boyle nel <lb></lb>XXVII de&#039;suoi nuovi esperimenti (Op. </s>

<s>Omnia, Venetiis 1697, T. I, pag. </s>

<s>62-64). <lb></lb>Con tale occasione furono i nostri Accademici i primi a far l&#039;esperienza del <lb></lb>suono anche nell&#039;aria compressa, ma tutti questi così laboriosi tentativi eb­<lb></lb>bero un infelice successo, e fu quel che se n&#039;ebbe a concludere uno scherzo <lb></lb>espresso in tali parole: “ O l&#039;aria non ha che far col suono, o ella vale <lb></lb>in qualunque stato (o rarefatta o compressa) ad ugualmente produrlo ” <lb></lb>(Saggi cit., pag. </s>

<s>59). </s></p><p type="main">

<s>Questo era come il sorriso amaro di chi dispera di conseguire un in­<lb></lb>tento vivamente desiderato; disperazione alla quale s&#039;abbandonarono total­<lb></lb>mente gli Accademici fiorentini, quando persuasi già che il buon successo <lb></lb>dell&#039;esperienza dipendeva tutto dal far sì che il corpo sonoro non comuni­<lb></lb>chi col vaso di vetro, essendo a loro sovvenuto il pensiero di una sospen­<lb></lb>sione magnetica, riconobbero che non era effettuabile il lusinghiero progetto. <lb></lb></s>

<s>“ Si tratta di disporre il corpo sonoro (leggesi in uno de&#039;Diari dell&#039;Ac­<lb></lb>cademia) in modo che non comunichi col vaso di vetro, come per esempio <lb></lb>tenendolo sospeso senza contatto per sola virtù magnetica ” (MSS. Cim., <lb></lb>T. IV, c. </s>

<s>107). </s></p><p type="main">

<s>Anche questa storia però ne porge un altro de&#039;tanti esempi che s&#039;hanno <lb></lb>di difficoltà credute insuperabili, e di faticosi tentativi tornati sempre inu­<lb></lb>tili, che si son veduti poi riuscire con massima facilità, facendo rimanere <lb></lb>quei che s&#039;erano ritirati indietro maravigliati. </s>

<s>Per far sì che il corpo sonoro <lb></lb>non comunichi le sue vibrazioni al recipiente del vuoto fu trovato che ba­<lb></lb>stava posare una sveglia sopra una coltricetta di lana o di ovatta. </s>

<s>L&#039;espe­<lb></lb>rienza del suono nel vuoto divenne allora così facile e tanto comune, da non <lb></lb>parer credibili le difficoltà incontrate dal Boyle e da&#039;nostri Accademici di <lb></lb>Firenze, ond&#039;è che il Musschenbroek non ripensando forse a queste cose, <lb></lb>ebbe ad accusare gli stessi nostri Accademici di poco accurati nell&#039;eseguire <lb></lb>le delicate esperienze. </s>

<s>“ Experimenta quae hic a florentinis Philosophis tra­<lb></lb>duntur .... non videntur tanta accuratione capta ac desiderare posset. </s>

<s>Ma­<lb></lb>gnus compositusque instrumentorum apparatus plerumque vitiis obnoxius <lb></lb>hos perspicacissimos caeteroquin viros illusisse et in errorem coniecisse ve­<lb></lb>risimile est ” (Tentamina Experim. </s>

<s>natur., Viennae 1756, Pars I, pag. </s>

<s>88). <pb xlink:href="020/01/746.jpg" pagenum="189"></pb>Ma è falso che gli Accademici si fossero mai lusingati, come l&#039;Olandese as­<lb></lb>serisce, avendo anzi sinceramente confessato l&#039;infelice successo de&#039;loro stu­<lb></lb>dii, la quale infelicità di successo non fu occasionata dal grande e compli­<lb></lb>cato apparecchio degli strumenti, ma dal creder che si dovesse o si potesse <lb></lb>tener assolutamente separato il corpo sonoro dal recipiente del vuoto, e dal <lb></lb>non aver pensato che bastava frapporvi un corpo anelastico, il quale impe­<lb></lb>disse al tremore di comunicarsi e tradursi dal di dentro al di fuori. </s></p><p type="main">

<s>Così insomma con maravigliosa facilità riuscita la bella esperienza, che <lb></lb>erasi in principio rappresentata come non superabile ad ogni argomento del­<lb></lb>l&#039;arte, venivasi con essa a dimostrar che l&#039;etere, sottilissimo mezzo propor­<lb></lb>zionato ad operar sensibilmente sopra l&#039;organo della vista, sfuggiva per quella <lb></lb>sua sottigliezza alle percezioni dell&#039;organo dell&#039;udito accomodato a non rice­<lb></lb>ver che le impressioni dell&#039;aria o di qualche altro corpo più crasso. </s>

<s>Que­<lb></lb>sto principalmente tendeva a dimostrar l&#039;esperienza del timpano o del cam­<lb></lb>panellino nel vuoto diffusa oramai, in sul cominciar del secolo XVIII, in <lb></lb>tutte le scuole, ma il Nollet notava ch&#039;era la gentile esperienza tirata ge­<lb></lb>neralmente a diversa intenzione, a servir d&#039;argomento cioè a concludere <emph type="italics"></emph>che <lb></lb>l&#039;aria è il solo mezzo idoneo alla propagazione del suono<emph.end type="italics"></emph.end> (Lezioni di Fi­<lb></lb>sica, trad. </s>

<s>ital., T. III, Venezia 1762, pag. </s>

<s>273). Aveva inoltre il francese <lb></lb>Autore delle Lezioni di Fisica precedentemente notato che da nessuno si <lb></lb>pensava a que&#039;tempi potersi altresi diffondere il suono ne&#039;solidi e ne&#039;li­<lb></lb>quidi, ond&#039;è ch&#039;e&#039;crede essere stato egli il primo a far l&#039;esperienza della <lb></lb>diffusion del suono per l&#039;acqua, sommergendo una sveglia chiusa dentro una <lb></lb>cassetta in un gran vaso cilindrico pieno d&#039;acqua ripurgata dall&#039;aria (ivi, <lb></lb>pag. </s>

<s>272). </s></p><p type="main">

<s>Benchè sia questa veramente l&#039;opinion comune che avevano i Fisici <lb></lb>a&#039;tempi del Nollet in Francia, non è da tacer che in Italia, un secolo prima, <lb></lb>Niccolò Aggiunti, rigoglioso e ubertoso ramo che troppo presto la morte re­<lb></lb>cise dall&#039;albero della scienza, aveva avvertito come talora il suono si diffonde <lb></lb>con più intensità ne&#039;solidi che nell&#039;aria, e l&#039;argomentò da due varie espe­<lb></lb>rienze tolte dal ricco armario de&#039;fanciulleschi trastulli e da lui stesso scelte <lb></lb>e applicate al proposito con filosofico acume. </s>

<s>Fu pure il medesimo Aggiunti <lb></lb>il primo a dimostrar con facili esperienze che il suono si diffonde anco per <lb></lb>l&#039;acqua, e a congetturar che diffonderebbesi pure, benchè con tenor vario <lb></lb>anco nell&#039;olio, di che e di molte altre dottrine acustiche ben più importanti, <lb></lb>recheremo in fine del presente capitolo i documenti. </s></p><p type="main">

<s>Non si vuol tacere altresì che nell&#039;esperienza della diffusion del suono <lb></lb>per l&#039;acqua il Nollet, il quale credette essere stato il primo a farla, fu pre­<lb></lb>venuto dagli Accademici del Cimento, benchè la loro intenzion principale <lb></lb>fosse alquanto diversa, e benchè solamente parecchi anni dopo, il Targioni, <lb></lb>togliendola da&#039;Diarii ne divulgasse la notizia nel suo T. II, P. II, dove ap­<lb></lb>punto si legge: “ A&#039;dì 5 Luglio 1657. Per usare ogni possibil diligenza nel <lb></lb>riconoscere se potessero scorgersi quei cerchi nell&#039;acqua, per suono che esce <lb></lb>di sotto di essa, come si presuppone che si facciano nell&#039;aria, si pose in un <pb xlink:href="020/01/747.jpg" pagenum="190"></pb>vaso di vetro un Orivolo carico con la sveglia, ed essendosi ben chiuso si <lb></lb>seppellì in un altro vaso pieno d&#039;acqua, ma cominciando a sonare l&#039;Oriolo <lb></lb>non si poteva riconoscere increspamento alcuno nell&#039;acqua circonfusa al vaso <lb></lb>contenente detto suono: solo fu casualmente osservato che, accostandosi un <lb></lb>par di cisoie all&#039;ultimo vaso, queste erano fatte tremare, forse dall&#039;impulso <lb></lb>dell&#039;istesso suono che usciva ” (pag. </s>

<s>562, 63). </s></p><p type="main">

<s>L&#039;osservazione fatta dal Nollet a proposito del suono nell&#039;acqua, che <lb></lb>non è vera, secondo abbiamo veduto, rispetto alla diffusione, è verissima ri­<lb></lb>spetto alla velocità del suono, l&#039;esperienze della quale velocità furono prima <lb></lb>tentate nell&#039;aria riguardata come il più natural mezzo ordinato a trasmet­<lb></lb>tere i tremori armonici d&#039;ogni parte al timpano dell&#039;orecchio. </s>

<s>Perciocchè i <lb></lb>suoni non si trasmettono al nostro organo per mezzo dell&#039;acqua, se non che <lb></lb>in qualche costituzione straordinaria, come sarebbe in chi per qualche mo­<lb></lb>mento vi rimanga sommerso bagnandosi in un fiume o nel mare, e perchè <lb></lb>non si trasmettono per gli altri liquidi, se non in una costituzione ben più <lb></lb>artificiosa e diremmo quasi violenta; non fu prima pensato a sperimentar <lb></lb>la velocità del suono in mezzo a quegli stessi liquidi, se non che quando la <lb></lb>scienza si senti frugata dalla curiosità di saper tutto, ed ebbe il modo a vin­<lb></lb>cere le difficoltà dall&#039;arte più raffinata e dalla squisitezza degli strumenti. </s>

<s>Di <lb></lb>qui è che l&#039;esperienze della velocità del suono in mezzo ai liquidi si può dir <lb></lb>che sieno opera de&#039;nostri giorni, mentre l&#039;esperienze della velocità del suono <lb></lb>nell&#039;aria, la quale per ogni parte circonda il nostro corpo, e lasciandoci liberi <lb></lb>ne&#039;nostri proprii moti ci mette in comunicazione diretta con gli altri corpi, <lb></lb>incominciarono fin quasi da&#039;primi anni che l&#039;Acustica iniziò i suoi progressi. </s></p><p type="main">

<s>Nel 1644 usciva in Parigi dall&#039;officina di Antonio Bertier la <emph type="italics"></emph>Ballistica<emph.end type="italics"></emph.end><lb></lb>di Marino Mersenno, nella quale si leggeva per la prima volta una propo­<lb></lb>sizione, che è la XXXV del libro, e che veniva dall&#039;Autore annunziata sotto <lb></lb>questa forma: “ Soni velocitas maior est globorum explosorum velocitate, <lb></lb>et 230 sexpedas, spatio unius secundi minuti, conficit ” (pag. </s>

<s>138). La di­<lb></lb>mostrazione, com&#039;è facile prevedere, è tutta sperimentale e il Mersenno pro­<lb></lb>mette a chiunque voglia tornare a far esperienza della velocità di qualunque <lb></lb>suono che “ noctu diuque, sive in vallibus, sylvis, aut montibus, sive <lb></lb>adverso, sive favente vento, sive aeris facie pluvia vel serena .... semper <lb></lb>eamdem soni velocitatem inveniet ” (ibi). </s></p><p type="main">

<s>Trovò lo stesso Mersenno anche un&#039;altra proprietà singolare nel movi­<lb></lb>mento del suono, ed è che la velocità di lui non diminuisce con l&#039;intensità, <lb></lb>ma sempre si serba equabile, cosicchè in un tempo doppio o quintuplo, per <lb></lb>esempio, percorre imperturbatamente un doppio o un quintuplo spazio. <lb></lb></s>

<s>“ Postquam vero per 230 sexpedas secundum exploraveris, qui minus tor­<lb></lb>mentum explodit, iterum per alias 230 sexpedas recedat, ut abs te 460 sex­<lb></lb>pedas recesserit, idem vel aequalis sonus duo secunda in illo itinere percur­<lb></lb>rendo consumet; quod cum quinquies a nobis fuerit multiplicatum, ut ex 1150 <lb></lb>hexapedis fragorem audiremus, ignis ex ore tormenti noctu erumpere sem­<lb></lb>per quinque secundis minutis fragorem praevertit ” (ibi). </s></p><pb xlink:href="020/01/748.jpg" pagenum="191"></pb><p type="main">

<s>Da questa bella proprietà scoperta ne deduce il Mersenno una conse­<lb></lb>guenza nuova, ed è che si possono per via del suono misurare esattamente <lb></lb>le distanze, quanto per esempio “ tormenta in obsessos aut obsidentes <lb></lb>explosa distent .... ex tonitrui fragore audito visoque fulgore praecedente <lb></lb>sciri quantum illud absit ” (ibi, pag. </s>

<s>139). S&#039;erano anche gli antichi, per <lb></lb>volgari ed ovvie esperienze, accorti ch&#039;essendo l&#039;apparir della luce istanta­<lb></lb>neo il suono la seconda con tempo; ond&#039;è che Galileo, dal piccolo intervallo <lb></lb>che resta tra il veder noi il baleno e il sentire il tuono, argomentava che le <lb></lb>folgori non si fanno alte da terra neanco un miglio (Alb. </s>

<s>IV, 333). In que­<lb></lb>sta argomentazione si trova applicata la velocità del suono alla misura della <lb></lb>distanza, presa però così all&#039;ingrosso, ignorandosi da Galileo e da&#039;predeces­<lb></lb>sori di lui di quella stessa velocità il grado. </s></p><p type="main">

<s>La Ballistica del Mersenno, il quale fu de&#039;primi ad annunziare al pub­<lb></lb>blico la sperimentata misura di quel grado di velocità, non s&#039;introdusse nè <lb></lb>così facile nè così pronta in Italia, dove non facevasi dell&#039;Autor di lei troppo <lb></lb>grande stima. </s>

<s>E chi sa quanto ancora avrebbero indugiato i Nostri ad aver <lb></lb>notizia dell&#039;esperienze e delle scoperte francesi, se non fossero approdate qua <lb></lb>nel libro delle Considerazioni sopra Diogene Laerzio di Pietro Gassendi. </s>

<s>Il <lb></lb>Gassendi, sincero estimatore, promotore e difensore in Francia delle dottrine <lb></lb>di Galileo era dagli Italiani amato più forse di tutti gli altri stranieri, e la <lb></lb>teoria atomistica rinnovellata da lui piacque principalmente al Borelli. </s>

<s>Fu <lb></lb>primo infatti il Borelli ad annunziar ne&#039;medicei consessi quel che aveva spe­<lb></lb>rimentato e dimostrato il Gassendo, e fu che si diffondono con eguale ve­<lb></lb>locità i tuoni o grandi come quello di un cannone o piccoli come quel d&#039;un <lb></lb>moschetto. </s>

<s>Non era questa la più difficile tra l&#039;esperienze fatte già dal Mar­<lb></lb>senno, e il Grimaldi citava il fatto ovvio delle campane che mantengono <lb></lb>sempre la medesima armonia fra le piccole e le grandi, per qualunque va­<lb></lb>riar di distanze (De lum. </s>

<s>cit., pag. </s>

<s>377), ma pur parve al Roberval, e lo <lb></lb>riferì allo stesso Mersenno, di aver trovato qualche differenza tra il diffon­<lb></lb>dersi de&#039;grandi e de&#039;piccoli rumori; diversità che senza dubbio dipendeva <lb></lb>dalla poca esattezza dell&#039;esperienza e di che venne ad assicurarne il Gassendo. </s></p><p type="main">

<s>Il Borelli pure, non contento al dire ma pronto all&#039;operare, confermò <lb></lb>il fatto asserito nelle Considerazioni sopra Laerzio, e lo riguardò sotto un <lb></lb>aspetto nuovo sfuggito alla considerazione de&#039;Fisici francesi. </s>

<s>Proponeva la <lb></lb>questione alla presenza del Granduca e del Rinaldini se la velocità del tuono <lb></lb>d&#039;un cannone crescesse a proporzion della quantità della polvere o rima­<lb></lb>nesse sempre la medesima. </s>

<s>Il Rinaldini asseriva che sarebbe cresciuta, il <lb></lb>Borelli negava; ond&#039;è che a decidere s&#039;invocarono l&#039;esperienze, la curiosa <lb></lb>storia delle quali è così narrata dal Magalotti: “ Ho trovato grandissima di­<lb></lb>scordia tra il Borelli e il Rinaldini sopra la velocità del suono. </s>

<s>Diceva que­<lb></lb>sti che la prestezza dell&#039;arrivare il rumore d&#039;un&#039;artiglieria sarebbe cresciuta <lb></lb>a proporzione della maggior quantità della polvere.... Il Borelli diceva che <lb></lb>tutti sarebbero arrivati in tempi eguali, benchè la polvere dell&#039;uno fosse <lb></lb>stata millionecupla a quella dell&#039;altro. </s>

<s>Ciascuno portò i suoi pensieri al Gran-<pb xlink:href="020/01/749.jpg" pagenum="192"></pb>duca, il quale comandò che mercoledì sera dopo l&#039;unora di notte si facesse <lb></lb>l&#039;esperienza.... Per conoscere i tempi avevano aggiustato un funependolo <lb></lb>al suo libramento ed ei, quando si vedeva il lampo che era segno di già <lb></lb>essere sparato il pezzo, lasciavano cadere, e tanto allo sparo dello smeriglio, <lb></lb>quanto della spingarda e del mezzo cannone si contarono l&#039;istesse vibrazioni <lb></lb>a capello ” (MSS. Cim., T. XXV, c. </s>

<s>181). </s></p><p type="main">

<s>In quel capitolo del Gassendo, in che il Borelli aveva letta l&#039;esperienza <lb></lb>della ugual velocità de&#039;suoni o piccoli o grandi, trovò citate anche le osser­<lb></lb>vazioni rese note al pubblico dal Mersenno due anni avanti. </s>

<s>Fu questa ci­<lb></lb>tazione che inviò il Nostro a ricercar la <emph type="italics"></emph>Ballistica<emph.end type="italics"></emph.end> dell&#039;Autore francese, e <lb></lb>trovatevi quella nuove esperienze sulla velocità del suono, e quelle applica­<lb></lb>zioni alla misura delle distanze delle quali dianzi dicemmo, conferì il tutto <lb></lb>privatamente col Granduca, il quale volle per sua curiosità gli scrivesse di <lb></lb>quelle cose un sunto, o gliene distendesse una nota. </s></p><p type="main">

<s>In quella Nota rimessa dal Borelli al Granduca l&#039;esperienze del Mer­<lb></lb>senno si assommavano ne&#039;quattro capi seguenti: I. </s>

<s>I suoni o piccoli o grandi <lb></lb>arrivano tutti all&#039;orecchio nel medesimo tempo. </s>

<s>II. </s>

<s>Il vento anche avverso <lb></lb>non impedisce nulla il moto del suono. </s>

<s>III. All&#039;orecchio di chi sta ad os­<lb></lb>servare (è questa l&#039;espression propria dello stesso Mersenno) <emph type="italics"></emph>sive distantia <lb></lb>fuerit verticalis, sive lateralis sive obliqua, nil interest.<emph.end type="italics"></emph.end> IV. </s>

<s>I tempi di due <lb></lb>suoni qualunque sono direttamente proporzionali alle distanze. </s></p><p type="main">

<s>Sapeva bene il Granduca ch&#039;erano tutte queste particolarità ignote al <lb></lb>Viviani, non intervenuto alle esperienze fatte alla Petraia, e di ciò veniva <lb></lb>anche meglio rassicurato dal Borelli, il quale discorrendo col suo Collega <lb></lb>s&#039;era bene avveduto che in questo negozio non aveva altro sentito dire, se <lb></lb>non che il Gassendi asseriva farsi in tempi uguali tanto il colpo di un mo­<lb></lb>schetto quanto il tuono di una bombarda. </s>

<s>Perciò indulgendo a quel suo ge­<lb></lb>nio di comparire in cose fisiche a&#039;suoi sudditi primo maestro, avuto un <lb></lb>giorno il Granduca a sè il Viviani lo incominciò a tentare di quel che sa­<lb></lb>pesse rispondere intorno a quei quattro quesiti risoluti dall&#039;esperienze mer­<lb></lb>senniane, conforme alla nota trasmessagli dal Borelli. </s>

<s>Il curioso esame è così <lb></lb>candidamente descritto dallo stesso Viviani, il quale racconta come, trovan­<lb></lb>dosi un giorno a&#039;Pitti nelle stanze de&#039;Paggi, fosse mandato a chiamar dal <lb></lb>Serenissimo Granduca per fargli queste domande: </s></p><p type="main">

<s>“ Prima quale de&#039;due suoni, il grande o il piccolo arrivasse in meno <lb></lb>tempo all&#039;orecchio, al che risposi che in tempi eguali l&#039;uno e l&#039;altro. </s>

<s>Se­<lb></lb>conda, quale impedimento potesse apportare il vento al moto del suono. </s>

<s>Ri­<lb></lb>sposi: nessuno; e fin qui risposi guidato non solo dal discorso e dalle ra­<lb></lb>gioni che ne avevo, ma ancora avvalorato da ciò che ne dice il Gassendi, e <lb></lb>mi confermò il sig. </s>

<s>Borelli. </s>

<s>Passò poi più oltre con le domande e dissemi <lb></lb>qual differenza di tempo io credevo che si intermettessi nel moto del suono <lb></lb>dallo sparare una volta il pezzo con la bocca verso l&#039;orecchio di chi sta ad <lb></lb>osservare o volta all&#039;insù perpendicolarmente o volta per il contrario, al che <lb></lb>risposi subito, con tutto che mi giungesse nuovo il quesito, che averei cre-<pb xlink:href="020/01/750.jpg" pagenum="193"></pb>duto questi tempi ugualissimi tra di loro. </s>

<s>S. A. allora non mi disse se io <lb></lb>avevo risposto a&#039;quesiti bene o male, ma la sera poi .... mi accertò che <lb></lb>nelle esperienze fatte e replicate due sere avanti con un pezzo a spingarda, <lb></lb>dalla Petraia, si era trovato seguire puntualmente che i tempi del piccolo <lb></lb>suono erano uguali a quelli del grande; che il vento che la seconda sera <lb></lb>tirava per scirocco non impediva o alterava di niente, e che gli spari fatti <lb></lb>per qualunque verso non facevano variazione nel tempo del moto di detti <lb></lb>suoni. </s>

<s>” </s></p><p type="main">

<s>“ Non finirono qui l&#039;instanze fattemi da S. A. che avanti io mi par­<lb></lb>tissi .... mi domandò in ultimo quello che io avrei creduto che fossero per <lb></lb>riuscire i tempi di due suoni, cioè d&#039;uno fatto in distanza di due miglia, e <lb></lb>di un altro fatto in doppia distanza. </s>

<s>Risposi a questo che io ancora avevo <lb></lb>un tempo curiosità di chiarirmi se il moto del suono era in sè stesso di <lb></lb>velocità continuamente ritardata oppure equabile, perchè se si trovasse tale <lb></lb>mi pareva di cavarne conseguenze assai curiose e grandissime utilità. </s>

<s>Su <lb></lb>questo mi astrinse a dirne quel ch&#039;io ne credevo, perchè poi voleva farne <lb></lb>la prova. </s>

<s>Risposi, veramente con troppo ardire, che in doppia distanza si <lb></lb>ricercherebbe doppio tempo per appunto, tenendo che il moto del suono in <lb></lb>sè stesso sia uniforme, cioè che, in quali si siano tempi uguali, passi spazii <lb></lb>uguali. </s>

<s>Ma perchè sopra questo particolare ci avevo di nuovo speculato il <lb></lb>giorno avanti, e mi pareva d&#039;aver più ragioni che mi persuadessero questo <lb></lb>che il contrario; però non messi in dubbio la risposta, e qui per allora finì <lb></lb>il discorso. </s>

<s>” (Antinori, Notizie Stor. </s>

<s>relative all&#039;Accad. </s>

<s>del Cimento, Fi­<lb></lb>renze 1841, pag. </s>

<s>51, 52). </s></p><p type="main">

<s>Proseguendo il racconto importante di questa storia soggiunge ivi il <lb></lb>Viviani che supposta l&#039;equabilità del suono se ne caverebbero conseguenze <lb></lb>curiosissime e utilissime, delle quali fece per sua memoria una nota, ch&#039;ei <lb></lb>lesse al principe Leopoldo e al Granduca. </s>

<s>Questa nota autografa fu pure <lb></lb>pubblicata dall&#039;Antinori a pag. </s>

<s>53 del Discorso citato, e porta scritta la data <lb></lb>del dì 10 Ottobre 1656. Ciò vuol dir che il Viviani suppone ancora quel che <lb></lb>dodici anni prima aveva dimostrato il Mersenno, e dà come invenzione re­<lb></lb>pentinamente cadutagli in pensiero la soluzione di que&#039;problemi relativi alla <lb></lb>misura delle distanze, ch&#039;eran pur dodici anni prima, non solamente caduti <lb></lb>in pensiero, ma divulgati dallo stesso Mersenno. </s>

<s>Questo sol si può dire che <lb></lb>a&#039;tre problemi proposti come risolubili per via della velocità de&#039;suoni a <lb></lb>pag. </s>

<s>139 della Ballistica mersenniana, il Viviani in quella sua Nota aveva <lb></lb>pensato di aggiungervene alcuni altri utili particolarmente alla Geografia. </s></p><p type="main">

<s>Chi conosce l&#039;indole di quell&#039;uomo è ben persuaso ch&#039;ei doveva es­<lb></lb>sersi veramente incontrato ne&#039;medesimi pensieri del Mersenno, senz&#039;aver <lb></lb>letto il suo libro. </s>

<s>In questa tranquilla persuasione d&#039;essere stato il primo <lb></lb>ad applicare i suoni alla misura delle distanze, rimase il Viviani anche dieci <lb></lb>e più anni dopo avere scritta la sopra detta Nota, e ciò risulta non solo da <lb></lb>quel ch&#039;egli affermò <emph type="italics"></emph>suo essere il concetto dell&#039;equabilità de&#039;suoni e de&#039;loro <lb></lb>usi; suo il nuovo modo di misurare le distanze senza la vampa<emph.end type="italics"></emph.end> (MSS. <pb xlink:href="020/01/751.jpg" pagenum="194"></pb>Cim., T. X, c. </s>

<s>259), ma da quel che fece scrivere al Segretario degli Ac­<lb></lb>cademici del Cimento, i quali accolsero l&#039;esperienze del suono fatte nel se­<lb></lb>condo periodo dell&#039;Accademia medicea fra quelle particolarmente eseguite da <lb></lb>loro e descritte insiem colle altre nel loro Libro. </s>

<s>È probabile però che quelle <lb></lb>stesse esperienze fossero ripetute, e anzi abbiamo argomenti da dar ciò per <lb></lb>cosa certa, nella qual certezza occorre a notare che gli Accademici fioren­<lb></lb>tini non fanno alcuna menzion del Mersenno, unicamente proponendosi, quasi <lb></lb>come programma a&#039;loro studii, di verificar ciò che de&#039;suoni aveva nelle Con­<lb></lb>siderazioni sopra Diogene Laerzio scritto il Gassendi; programma che tro­<lb></lb>vasi inserito nel T. XXIV, de&#039;MSS. del Cimento, dove a carte 293, copiati <lb></lb>dalla detta Opera stampata la prima volta a Parigi nel 1646, si leggono i <lb></lb>passi seguenti: </s></p><p type="main">

<s><emph type="italics"></emph>“ Gassendus pag. </s>

<s>279 in Philosophia epicurea.<emph.end type="italics"></emph.end> Quod spectat ad mo­<lb></lb>tum aeris ipsius a corpore usque sonante versus aurem tendentes, id per­<lb></lb>mirum est: quaecumque sit tandem sive vehementia, sive remissio impetus, <lb></lb>quo a sonante exagitatur, translationem eius per spatium esse semper ae­<lb></lb>quivelocem. </s>

<s>Siquidem constat experientia quoslibet sonos seu parvos, seu <lb></lb>magnos, in eodem loco excitatos aequali ferri tempore in eumdem locum e <lb></lb>quo exaudiuntur. </s>

<s>Id facile nempe observatur in sonis bellicorum tormento­<lb></lb>rum uno, alterove, aut tribus passuum millibus dissitorum, dum adnotato <lb></lb>momento, quo creata simul cum sono flammula oculis apparet, numerantur <lb></lb>pulsus arteriae, aut itus reditusque chordulae pondere appenso, quousque <lb></lb>sonus ad aurem perveniat. </s>

<s>Deprehenduntur enim huiusmodi pulsus sive itus <lb></lb>ac reditus, qui aliunde sunt aequitemporanei, aequales esse numero, sive <lb></lb>sonus sit machinae ingentis, ut puta dicti <emph type="italics"></emph>Canonis,<emph.end type="italics"></emph.end> sive parvae ut vocati <lb></lb><emph type="italics"></emph>Mosqueti.<emph.end type="italics"></emph.end> Qua ratione porro id fiat insinuatur a Stoicis quatenus docent, ut <lb></lb>Plutarchus et Laertius memorant, aerem percussum quod continuus sit pe­<lb></lb>rinde formari in orbeis ac placida aqua, lapide iniecto, formatur in circu­<lb></lb>los. </s>

<s>Quippe haec in aqua circulorum formatio nihilo segnius aut velocius <lb></lb>fit, sed ad ripam usque pari tenore continuatur, seu lapis magnus seu par­<lb></lb>vus sit, et seu magna vi seu parva incidat in aquam. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Ibidem subiungit pag. </s>

<s>280:<emph.end type="italics"></emph.end> Quo loco tacenda non est Mersenni no­<lb></lb>stri observatio, qui velocitatem soni studiose emensus deprehendit ipsum <lb></lb>uno horae secundo pervadere ducentas triginta parisinas orgyas, seu hexa­<lb></lb>podas, ac uno proinde minuto horae primo, seu sexagesima horae parte su­<lb></lb>pra orgyarum quatordecim millia. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Idem ibidem:<emph.end type="italics"></emph.end> Mirabile aliud circa motum soni illud est quod nec <lb></lb>secundo flante vento acceleretur, neque adverso reflante retardetur, sed fe­<lb></lb>ratur semper aequabiliter, sive aequali tempore ex eodem loco, in eumdem <lb></lb>perveniat. </s>

<s>Sed nempe et secundus ventus est incomparabiliter segnior sono <lb></lb>(ut vel ex nubibus segetumque vel ramorum in sylvis succedentibus moti­<lb></lb>bus undulationibusque apparet) adeo ut promovere illum sensibiliter admo­<lb></lb>dum non possit. </s>

<s>” </s></p><p type="main">

<s>Tenendo a riscontro questi tre passi così trascritti con le descrizioni <pb xlink:href="020/01/752.jpg" pagenum="195"></pb>della prima e della seconda dell&#039;esperienze fatte dagli Accademici del Ci­<lb></lb>mento intorno ai movimenti del suono (Saggi ecc., Firenze 1841, pag. </s>

<s>156, 57) <lb></lb>si vede come, verificati in ogni altra parte i detti del Gassendi, lo trovarono <lb></lb>solamente falso in ciò ch&#039;egli dice di avere osservato essere gl&#039;increspa­<lb></lb>menti equiveloci o cada naturalmente il sasso nell&#039;acqua, o vengavi scagliato <lb></lb>con grandissima forza. </s>

<s>Ma nella Esperienza terza, sotto la quale si descri­<lb></lb>vono le applicazioni della ugual velocità del suono alla misura delle distanze, <lb></lb>si dice che il potersi far ciò <emph type="italics"></emph>cadde in animo a un nostro Accademico,<emph.end type="italics"></emph.end> in <lb></lb>occasione del verificarsi le sopraddette esperienze. </s>

<s>Ond&#039;è chiaro di qui che <lb></lb>non solo il Viviani ma tutta l&#039;Accademia era persuasa che quello del mi­<lb></lb>surar le distanze per via de&#039;suoni fosse un concetto nuovo, benchè a voler <lb></lb>esser giusti la novità non consistesse in altro che nell&#039;aver pensato a con­<lb></lb>seguir quelle stesse misure anco quando, per l&#039;interposizione di menti o di <lb></lb>altri ostacoli, non si potesse vedere la vampa, servendo a ciò di scala “ il <lb></lb>tempo che il suono pena a correre una distanza nota di un miglio trovato <lb></lb>da noi essere cinque minuti secondi ” (ivi, pag. </s>

<s>159). </s></p><p type="main">

<s>Gli Accademici fiorentini, così come il Mersenno prima di loro, avevano <lb></lb>ritrovate quelle misure più o meno esatte per via di esperienze dirette, e <lb></lb>ciò fu come se avessero ricevuto un dono dalle braccia sporte della Natura. </s>

<s><lb></lb>Ma il Newton, con mirabile novità d&#039;esempio, conseguì quel medesimo dono <lb></lb>come parto ostetricato con le sue proprie mani dal più intimo e fecondo <lb></lb>seno delle verità naturali. </s></p><p type="main">

<s>Il principal fondamento di questa nuova e pellegrina speculazione è po­<lb></lb>sto nel Teorema XXXVII del II Libro de&#039;Principii matematici di Filosofia <lb></lb>naturale, così formulato: “ Pulsibus per fluidum progagatis, singulae fluidi <lb></lb>particulae, motu reciproco brevissimo euntes et redeuntes, accelerantur sem­<lb></lb>per et retardantur pro lege oscillantis penduli ” (Genevae 1740, pag. </s>

<s>360). </s></p><p type="main">

<s>Cercar dunque il tempo di una pulsazione aerea e sonora si riduce pel <lb></lb>Newton a cercare il tempo dell&#039;oscillazione di un pendolo di lunghezza <lb></lb>uguale all&#039;altezza di un mezzo omogeneo, il peso di cui adegui il peso so­<lb></lb>praincombente, e la densità sia per tutto uguale a quella del mezzo stesso, <lb></lb>in che si fa la pulsazione. </s>

<s>“ Fingamus medium ab incumbente pondere pro <lb></lb>more aeris nostri comprimi, sitque A altitudo medii homogenei, cuius pon­<lb></lb>dus adaequet pondus incumbens et cuius densitas eadem sit cum densitate <lb></lb>medii compressi, in quo pulsus propagantur. </s>

<s>Constitui autem intelligatur <lb></lb>pendulum cuius longitudo inter punctum suspensionis et centrum oscillatio­<lb></lb>nis sit A.... ” (ibi, pag. </s>

<s>387). Supposto ciò e invocando il Teorema uge­<lb></lb>niano relativo alle proprietà meccaniche della Cicloide, che cioè il tempo <lb></lb>della caduta per la perpendicolare è al tempo dell&#039;oscillazione come il rag­<lb></lb>gio del circolo alla circonferenza di lui, dimostra il Newton che “ quo tem­<lb></lb>pore pendulum illud oscillationem integram ex itu et reditu compositam <lb></lb>peragit, eodem pulsus eundo conficiet spatium circumferentiae circuli radio A <lb></lb>descripti aequale ” (ibi) </s></p><p type="main">

<s>Per far poi l&#039;applicazione di questi principii matematici al caso parti-<pb xlink:href="020/01/753.jpg" pagenum="196"></pb>colare dell&#039;aria, in mezzo alla quale si diffondono i suoni, conveniva per <lb></lb>prima cosa trovar la lunghezza A del pendolo, ossia l&#039;altezza di quell&#039;aria <lb></lb>di uniforme densità capace di comprimere quell&#039;altra a sè sottoposta, che <lb></lb>supponesi dover esser messa in vibrazione sonora. </s>

<s>Essendo il peso specifico <lb></lb>dell&#039;aria a quello del mercurio come 1:11,890 prossimamente, e l&#039;altezza <lb></lb>media del mercurio nel tubo barometrico 30 digiti inglesi, la lunghezza del <lb></lb>pendolo che si cerca, o il raggio del cerchio si trova essere 356,700 di <lb></lb>que&#039;digiti, ossia di piedi 29,725, e perciò la circonferenza da esso raggio de­<lb></lb>scritta, piedi 186,768. “ Et cum pendulum digitos 39 1/5 longum oscillatio­<lb></lb>nem ex itu et reditu compositam tempore minutorum duorum, uti notum <lb></lb>est, absolvat, pendulum pedes 29,725 seu digitos 356,700 longum oscillatio­<lb></lb>nem consimilem tempore minutorum secundorum 190 1/4 absolvere debebit ” <lb></lb>(ibi, pag. </s>

<s>392). Dunque per il citato Teorema ugeniano: ” eo tempore so­<lb></lb>nus progrediendo conficiet pedes 186,768, ideoque tempore minuti unius <lb></lb>secundi pedes 979 ” (ibi). </s></p><p type="main">

<s>Tale si è la velocità del suono, supposto che sia l&#039;aria sgombra d&#039;estra­<lb></lb>nee materie come di particelle solide o di vapori, e che rispetto all&#039;elasticità <lb></lb>rimanga sempre nella medesima costituzione. </s>

<s>Ma perchè un tal supposto, <lb></lb>dice il Newton, non si verifica mai, essendo volitanti per l&#039;aria particelle <lb></lb>saline attraverso alle quali il suono si diffonderebbe in istante, calcola per­<lb></lb>ciò un aumento di velocità di 109 piedi all&#039;incirca “ ob crassitudinem par­<lb></lb>ticularum aeris, et sic sonus tempore minuti unius secundi conficiet pe­<lb></lb>des 1088 circiter ” (ibi, pag. </s>

<s>393). Ci sono inoltre nell&#039;aria disciolti i vapori <lb></lb>acquosi attraverso ai quali il suono propagasi più veloce, e una tal maggiore <lb></lb>velocità vien dal Newton calcolata in modo che la misura ultimamente de­<lb></lb>finita vien ridotta a piedi 1142. </s></p><p type="main">

<s>A queste due nuove considerazioni, trascurate già dal Mersenno e dai <lb></lb>nostri Accademici fiorentini, i quali misurarono la velocità de&#039;suoni, non so­<lb></lb>spettando che per variar delle condizioni ammosferiche si potessero in qual­<lb></lb>che modo alterare, ne soggiunge il Newton una terza, ben assai più impor­<lb></lb>tante ed espressa da lui in questa forma: “ Haec ita se habere debent tem­<lb></lb>pore verno et autumnali ubi aer per calorem temperatum rarescit et eius <lb></lb>vis clastica nonnihil intenditur. </s>

<s>At hyberno tempore, ubi aer per frigus con­<lb></lb>densatur et eius vis elastica remittitur, motus sonorum tardior esse debet <lb></lb>in subduplicata ratione densitatis et vicissim aestivo tempore debet esse ve­<lb></lb>locior ” (ibi, pag. </s>

<s>394). </s></p><p type="main">

<s>Dell&#039;aumento di velocità del suono prodotto dal trovarsi sollevati per <lb></lb>l&#039;aria gli umidi vapori, e dal trovarvisi sempre in mezzo particelle solide <lb></lb>volitanti, non par che ne facessero troppo gran conto i Fisici, giudicando <lb></lb>così fatte avvertenze quasi come sottigliezze di matematica neutoniana. </s>

<s>Ma <lb></lb>quel che argutamente il Newton stesso avvertiva dover esser cioè la velo­<lb></lb>cità del suono maggiore nell&#039;estate che nell&#039;inverno persuadeva, per la buona <lb></lb>ragione del variabile elaterio dell&#039;aria col variare della temperatura. </s>

<s>Lasciava <lb></lb>perciò l&#039;Autore de&#039;Principii di Filosofia naturale a verificar le sue dimo-<pb xlink:href="020/01/754.jpg" pagenum="197"></pb>strate proposizioni matematiche coll&#039;esperienza, e non mancarono i Fisici di <lb></lb>ricorrere ai fatti per decider se veramente questi confermavano le ragioni. </s></p><p type="main">

<s>Più solleciti di tutti fra coloro che dettero mano all&#039;opera è naturale <lb></lb>che fossero gl&#039;Inglesi, e il Flamsteed e l&#039;Halley instituirono le loro espe­<lb></lb>rienze in una campagna vicino a Londra. </s>

<s>Dietro a loro, dopo trent&#039;anni, <lb></lb>mossi dal medesimo desiderio vi si provarono i Francesi, che scelsero a far <lb></lb>le opportune esperienze il La Caille, il Cassini giovane, e il Maraldi dal seno <lb></lb>della loro Accademia. </s>

<s>Notabile cosa è che Inglesi e Francesi non trovassero <lb></lb>differenza nella velocità del suono o si diffondesse per l&#039;aria caldissima del­<lb></lb>l&#039;estate o per la freddissima dell&#039;inverno. </s></p><p type="main">

<s>Esperienze così solenni eseguite da tanto celebri sperimentatori erano <lb></lb>per far concludere che alle ragioni del Newton belle e buone in sè non ri­<lb></lb>spondevano i fatti, quando un nostro Italiano ripensando sopra ciò conclu­<lb></lb>deva non poter cause vere e reali essere inefficaci in produrre i loro effetti. </s>

<s><lb></lb>Persuaso perciò Lodovico Bianconi che l&#039;esperienze degl&#039;Inglesi e de&#039;Fran­<lb></lb>cesi dovevano essere in ogni modo o da qualsivoglia parte riuscite difettose, <lb></lb>volle egli stesso, aiutato da due suoi valentissimi amici, ripeterle con gran <lb></lb>diligenza ed ebbe il merito d&#039;aver dimostrato per il primo che i fatti fisici <lb></lb>confermavano le verità de&#039;principii matematici neutoniani. </s></p><p type="main">

<s>L&#039;esperienze furono dall&#039;Autore stesso descritte in una lettera indiriz­<lb></lb>zata a Scipione Maffei e che s&#039;intitola <emph type="italics"></emph>Della diversa velocità del suono.<emph.end type="italics"></emph.end> In­<lb></lb>comincia in essa a far la storia delle tentate prove in proposito, incomin­<lb></lb>ciando da quelle degli Accademici di Firenze, infino a quelle eseguitesi <lb></lb>presso Londra dal Flamsteed e dall&#039;Halley, nel 1708, e alle altre nel 1738 <lb></lb>eseguitesi dal Cassini e dal Maraldi presso Parigi. </s></p><p type="main">

<s>“ Prima che a noi in Italia, soggiunge poi il nostro Bianconi, giun­<lb></lb>gesse questa notizia che solo giunseci dopo la stampa degli Atti di quell&#039;Ac­<lb></lb>cademia, avendo io lette le Transazioni anglicane, vennemi voglia l&#039;anno 1740 <lb></lb>di provare in Bologna alcune delle osservazioni che fecero a Londra, e spe­<lb></lb>cialmente quella per cui dicono non aver essi trovato divario alcuno tra la <lb></lb>celerità del suono nell&#039;inverno e nell&#039;estate. </s>

<s>Parevami strano che essendo <lb></lb>nel rigido freddo l&#039;aria condensatissima, rispetto alla rarefazione che aver <lb></lb>dee nel caldo dell&#039;estate; parevami strano, dico, che nessuna differenza do­<lb></lb>vesse poi trovarsi nel suono, che dai di lei tremori è propagato. </s>

<s>” </s></p><p type="main">

<s>“ La stagione caldissima che già incominciava a farsi sentire, parve in­<lb></lb>vitarmi a mettere all&#039;opera il già divisato pensiero, cioè a provare quale <lb></lb>celerità avesse il suono nell&#039;estate per paragonarlo poi con quello che avrei <lb></lb>trovato nell&#039;inverno venturo. </s>

<s>Eccole i luoghi che determinai per fare le os­<lb></lb>servazioni: la fortezza urbana posta sulle frontiere del modanese fu l&#039;uno, <lb></lb>l&#039;altro fu il Convento dei Padri zoccolanti dell&#039;Osservanza.... Pregati il si­<lb></lb>gnor Eustachio Zanotti e il signor abate Petronio Matteucci, ambo astronomi <lb></lb>dell&#039;Osservatorio nostro dell&#039;Istituto ed amici miei ornatissimi, a venir meco <lb></lb>verso la sera al Convento stabilito, vi portammo un orologio astronomico a <lb></lb>cicloide che batteva esattissimamente i secondi.... Aspettavamo l&#039;ora del <pb xlink:href="020/01/755.jpg" pagenum="198"></pb>primo strepito del cannone, giunto il quale .... incominciaronsi allora a con­<lb></lb>tare i secondi, nè arrivò a noi il suono, prima che, contando, al sessante­<lb></lb>simosesto non fossimo giunti. </s>

<s>Replicossi per quattro volte in quella sera l&#039;os­<lb></lb>servazione e in tutte vedemmo esser costante la celerità del suono, ed <lb></lb>impiegare un minuto e sedici secondi esattissimi per venire dalla fortezza <lb></lb>urbana al Convento.... ” </s></p><p type="main">

<s>“ Altro più non restavaci a fare che aspettar l&#039;inverno, per replicare <lb></lb>in quella stagione le nostre osservazioni.... La notte precedente i sette di <lb></lb>Febbraio dell&#039;anno 1741 fu la determinata da noi per le nostre esperienze.... <lb></lb>Tenendo tutti noi gli occhi immobili all&#039;Occidente vedemmo, all&#039;ora accor­<lb></lb>data, il lampo del fuoco alla fortezza, nel qual momento cominciammo a nu­<lb></lb>merare i secondi dell&#039;orologio. </s>

<s>Questi non furono già sessantasei come l&#039;anno <lb></lb>avanti, ma furono settanta otto e mezzo costantemente, per tutte quattro le <lb></lb>volte che replicossi l&#039;esperienza.... Queste due osservazioni adunque, che <lb></lb>io le do per esattissime, dovrebbero farci credere esservi qualche divario tra <lb></lb>la velocità del suono nell&#039;estate e nell&#039;inverno. </s>

<s>” (Venezia 1746, pag. </s>

<s>82-90). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Come mai dalla sublime contemplazione delle armonie pitagoriche, d&#039;onde <lb></lb>mosse il presente capitolo, siam, procedendo di discorso in discorso, caduti <lb></lb>ne&#039;freddi calcoli matematici del Newton e nelle aride esperienze di Lodovico <lb></lb>Bianconi, potrebbe in chi a considerar ciò soffermasse il passo recare al­<lb></lb>quanto di maraviglia, se non gli occorresse poi facilmente in pensiero che <lb></lb>anzi i numeri calcolati dal Matematico di Cambridge e sperimentati dal Fi­<lb></lb>sico di Bologna mirabilmente confermano quelle speculazioni intorno ai nu­<lb></lb>meri, nella ragion de&#039;quali riconosceva il Filosofo antico le misteriose ori­<lb></lb>gini dell&#039;armonia. </s></p><p type="main">

<s>Ma in ogni modo il rimbombo de&#039;cannoni e il fragor de&#039;moschetti, in <lb></lb>mezzo ai quali s&#039;è aggirata fin qui la nostra storia, sembrerebbe meglio che <lb></lb>suoni si dovessero dir dissonanze, e che avessero perciò quella relazione alle <lb></lb>vere armonie che le ombre hanno alla luce. </s>

<s>È da risalir dunque su alla <lb></lb>storia di que&#039;pitagorici musicali concenti, d&#039;onde troppo affrettatamente siamo <lb></lb>discesi, quasi trasportati dietro a quell&#039;onda che commoveva l&#039;aria ne&#039;disor­<lb></lb>dinati fragori. </s></p><p type="main">

<s>Racconta Giamblico che passando un giorno Pitagora presso all&#039;officina <lb></lb>di un fabbro ferraio, in sul punto che il maestro e i garzoni battevano il <lb></lb>ferro sull&#039;incudine co&#039;martelli menati con vicenda misurata di tempi, sof­<lb></lb>fermasse ivi il piede e vi si trattenesse ad ascoltar quel semplice eppure ar­<lb></lb>monioso concerto. </s>

<s>Pensò che la differenza de&#039;suoni gravi ed acuti era fatta <lb></lb>dal differente peso degli stessi martelli, e gli cadde allora in animo di poter <lb></lb>per via di que&#039;pesi ritrovar le leggi delle relazioni che passano tra le varie <pb xlink:href="020/01/756.jpg" pagenum="199"></pb>intensità degl&#039;impulsi sonori. </s>

<s>Ritrovò che il peso, il quale dava la nota di <lb></lb>chiave a quelli che davano la quarta, la quinta, e l&#039;ottava era come 1 a 4/3, <lb></lb>a 3/2, a 2. Seguitando così a speculare pensò che la medesima legge doveva <lb></lb>pure verificarsi nelle corde, e pizzicatane una, che tirata da un certo peso <lb></lb>dava la chiave, trovò che riducendo quel peso a 4/3 a 3/2, al doppio si otte­<lb></lb>nevano via via per ordine le varie altre note. </s></p><p type="main">

<s>La storia di Giamblico non ha punto aria di alcuna verosomiglianza, e <lb></lb>parrebbe anzi strano che da un principio falso, qual&#039;è che tra&#039;pesi de&#039;mar­<lb></lb>telli passino le riferite proporzioni colle note sonate dalle incudini, potess&#039;es­<lb></lb>ser condotto il Filosofo a una conclusione vera concernente le corde. </s>

<s>È a <lb></lb>notar però che la conclusione, alla quale fu condotto propriamente Pitagora, <lb></lb>non è quella che riferisce Giamblico, essendochè le sopra riferite propor­<lb></lb>zioni non passano fra i pesi tendenti le corde ma fra le lunghezze di esse <lb></lb>corde sonore. </s></p><p type="main">

<s>Apparisce in ogni modo di qui essere state antichissime le prime spe­<lb></lb>culazioni intorno alla ragione degl&#039;intervalli armonici, benchè poco più oltre <lb></lb>si progredisse dagl&#039;insegnamenti pitagorici e dalle prime scoperte nel lungo <lb></lb>decorrere di duemila anni. </s>

<s>Scriveva perciò il Keplero, poco dopo il comin­<lb></lb>ciar del secolo XVII: “ Utcumque tamen antiqua sit cantus humani forma, <lb></lb>ex intervallis consonis vel concinnis composita, causae tamen intervallorum <lb></lb>latuerunt homines adeo ut ante Pythagoram ne quaererentur quidem, et <lb></lb>quaesitas per duo millia annorum, primus ego, nisi fallor, exactissime pro­<lb></lb>feram ” (Harmonices mundi lib III, Lincii Austriae 1619, pag. </s>

<s>3). </s></p><p type="main">

<s>È egli vero quel che il Kepler si lusingava così d&#039;essere stato il primo <lb></lb>a trattar della teoria della Musica? </s>

<s>Convien per risponder con fondamento <lb></lb>alla domanda che si distingua una duplice teoria, essendo che la Musica si <lb></lb>può riguardare o in quanto è sentita nell&#039;anima o in quanto è un effetto <lb></lb>del vibrar de&#039;corpi secondo una legge determinata. </s>

<s>Trattar delle ragioni del­<lb></lb>l&#039;armonia musicale nel suggetto senziente è opera de&#039;Filosofi speculativi, i <lb></lb>quali benchè sollevino i voli della mente sublimi, e largamente spaziino per <lb></lb>le aeree regioni, profitterebbero forse meglio contentandosi di dire che l&#039;ar­<lb></lb>monia nell&#039;anima è una misteriosa estasi dell&#039;intelletto dell&#039;uomo e del­<lb></lb>l&#039;amore. </s>

<s>Ma non è troppo comune ai Filosofi la virtù del tacere innanzi ai <lb></lb>misteri, nè ebbe questa virtù nemmeno il Keplero, il quale avrebbe avuto <lb></lb>senza dubbio miglior ragion di credersi primo Autore di questa nuova Fi­<lb></lb>losofia musicale, se avesse usato la Matematica e l&#039;avesse fatta servire a il­<lb></lb>lustrar le attente osservazioni de&#039;fatti. </s>

<s>Ma la Matematica per lui, tutt&#039;altro <lb></lb>ch&#039;essere ancella dell&#039;Armonia, è sorella di Lei nata dalla Divina Mente <lb></lb>Creatrice a un medesimo parto. </s></p><p type="main">

<s>Pubblicando nel 1596 per la prima volta il <emph type="italics"></emph>Mysterium Cosmographi­<lb></lb>cum<emph.end type="italics"></emph.end> aveva asserito esser cinque le consonanze musiche, perchè cinque son <lb></lb>le consonanze geometriche rappresentate dalle cinque forme regolari de&#039;corpi <lb></lb>solidi. </s>

<s>Vent&#039;anni dopo, ne&#039;V libri <emph type="italics"></emph>Armonices mundi<emph.end type="italics"></emph.end> annunziava di aver ri­<lb></lb>dotte quelle consonanze a sette, essendo veramente sette e non più le se-<pb xlink:href="020/01/757.jpg" pagenum="200"></pb>zioni armoniche di una corda armonica. </s>

<s>Una mente libera dall&#039;amor de&#039;si­<lb></lb>stemi avrebbe incominciato a dubitar se la supposta corrispondenza fra le <lb></lb>note musicali e le figure geometriche era vera, ma il Keplero, tutt&#039;altro che <lb></lb>mettere ombra di dubbio ne&#039;principii, attribuisce a una allucinazione della <lb></lb>sua propria mente la varietà delle conclusioni, alle quali era venuto in quella <lb></lb>differenza di tempi. </s>

<s>Io ricercai da principio, egli dice, le consonanze nella <lb></lb>regolarità delle figure solide, mentre invece conveniva cercarle nella rego­<lb></lb>larità geometrica delle figure piane. </s>

<s>“ Legat curiosus lector quae de his <lb></lb>sectionibus ante annos XXII scripsi in Mysterio Cosmographico, capite XII, <lb></lb>et perpendat quomodo fuerim illo loco hallucinatus super causis sectionum <lb></lb>et harmoniarum: perperam nisus eorum numerum et rationes deducere ex <lb></lb>numero quinque corporum regularium solidorum, cum verum sit hoc potius <lb></lb>tam quinque figuras solidas, quam harmonias musicas et chordae sectiones <lb></lb>communem habere originem ex figuris regularibus planis ” (ibi, pag. </s>

<s>27). </s></p><p type="main">

<s>Questo indirizzo puramente geometrico, preso in investigar le ragioni <lb></lb>dell&#039;armonia, riuscì provvidamente benefico alla scienza, perchè condusse il <lb></lb>Keplero alla scoperta delle celebri leggi cosmografiche conosciute sotto il nome <lb></lb>di lui. </s>

<s>L&#039;Acustica però non ebbe uguale fortuna, anzi ella par come sementa <lb></lb>nata in ben disposto terreno, che poi intristisce aduggiata dalle fronde e sof­<lb></lb>focata dalle spine. </s>

<s>Ma pur perchè udimmo dianzi il Keplero stesso asserir <lb></lb>che nessun altro prima di lui aveva investigata la causa de&#039;musici intervalli, <lb></lb>ed egli promette di profferirla <emph type="italics"></emph>exactissime<emph.end type="italics"></emph.end> giova veder in che modo egli poi <lb></lb>riuscisse a mantenere le sue promesse. </s></p><p type="main">

<s>La questione intorno all&#039;origine dell&#039;Armonia propostasi a risolvere dal <lb></lb>Keplero è da lui stesso formulata al modo seguente: “ Unde existat illa <lb></lb>suavitas, quae auribus allabitur ex proportione vocum, qua suavitate conso­<lb></lb>nantias definimus ” (ibi, pag. </s>

<s>14). E perchè dice che la questione non era <lb></lb>nuova, ma che anzi ella fu tra&#039;Filosofi lungamente disputata, incomincia ad <lb></lb>esaminar le loro varie opinioni. </s>

<s>“ Qui ad materiam et motum elemontorum <lb></lb>inclinant, exemplum afferunt hoc per se quidem sane quam mirabile, quod <lb></lb>chorda pulsata chordam aliam non pulsatam secum in sonitum trahit, si <lb></lb>tensa fuerit sibi consone, dissone tensam immotam relinquit ” (ibi). </s></p><p type="main">

<s>Riconosce dunque il Keplero che la teoria de&#039;suoni armonici ebbe i <lb></lb>suoi primi principi dalle osservazioni e dalle speculazioni di quel fatto sin­<lb></lb>golare che cioè una corda immota spontaneamente si commove all&#039;unisono <lb></lb>di un&#039;altra corda fatta a lei vibrare da presso. </s>

<s>Gli Autori perciò che pre­<lb></lb>corsero in questa nuova Filosofia all&#039;Alemanno essendo que&#039;che osservarono <lb></lb>e specularono intorno alla singolarità di questo fatto, giova prima di tutto <lb></lb>che si ricerchi da noi chi fossero e che ne pensassero. </s></p><p type="main">

<s>I Musici e i Lituai chi sa quante volte avranno osservato che a sonar <lb></lb>la corda di uno strumento risonava all&#039;unisono quella di un altro simile <lb></lb>strumento immoto, ma del diligente esame sperimentale del fatto uno de&#039;più <lb></lb>antichi documenti è quello forse che lasciò scritto nelle sue carte solitarie <lb></lb>Leonardo da Vinci. </s>

<s>“ Il colpo dato nella campana risponderà e moverà al-<pb xlink:href="020/01/758.jpg" pagenum="201"></pb>quanto una campana simile a sè, e la corda sonata di un liuto risponderà <lb></lb>e moverà un&#039;altra simile corda di simile boce in un altro liuto, e questo <lb></lb>vedrai con porre una paglia sopra una corda simile alla sonata ” (Mollien <lb></lb>MSS. </s>

<s>A fol. </s>

<s>22 v.). </s></p><p type="main">

<s>Nè Leonardo però nè altri prima di lui si sa che speculassero la ra­<lb></lb>gione del fatto, così bene sperimentato, e i Filosofi <emph type="italics"></emph>in libris<emph.end type="italics"></emph.end> se ne spaccia­<lb></lb>vano assai facilmente attribuendolo a un&#039;occulta e misteriosa virtù di sim­<lb></lb>patia. </s>

<s>Primo a toglier la bella esperienza da questo tenebroso regno e a <lb></lb>renderla alla luce filosofica fu il Fracastoro, il quale giusto nel trattar <emph type="italics"></emph>De <lb></lb>sympathia et antipathia rerum<emph.end type="italics"></emph.end> così scriveva: “ Unisonum aliud unisonum <lb></lb>commotat, quoniam quae similiter tensae sunt chordae consimiles aeris un­<lb></lb>dationes, et facere et recipere natae sunt: quae vero dissimiliter sunt ten­<lb></lb>sae non eisdem circulationibus natae sunt moveri, sed una circulatio aliam <lb></lb>impedit. </s>

<s>Ictus enim chordae est motus compositus ex duobus motibus, uno <lb></lb>quidem quo chorda pellitur ante, hoc est versus aeris circulationes, alio vero <lb></lb>qui retro fit, chorda redeunte sese ad situm proprium. </s>

<s>Si igitur mota una <lb></lb>chorda debet et alia moveri oportet ut in secunda talis proportio sit ut <lb></lb>undationes et circulationes aeris, quae impellunt et faciunt motum ante, non <lb></lb>impediant motum qui retro fit a chorda. </s>

<s>Quam proportionem solum eae <lb></lb>chordae habent quae etiam consimilem tensionem habent. </s>

<s>Quae vero dissi­<lb></lb>milem sortitae sunt tensionem non sese commotant, quoniam dum secun­<lb></lb>dus fit motus idest reditus chordae circulatio secunda illi obviat et se se <lb></lb>impediunt, unde nec motus fit ullus praeter primam impulsationem quae <lb></lb>insensibilis est ” (Opera omnia, Venetiis 1584, c. </s>

<s>66). </s></p><p type="main">

<s>O avesse o no veduto il Trattato del Fracastoro, si riscontrò molto da <lb></lb>presso nelle speculazioni di lui un altro eletto ingegno Italiano, consegnando <lb></lb>quelle sue solitarie speculazioni a carte manoscritte, che da non molti anni <lb></lb>in qua furon date alla luce. </s>

<s>Il titolo di quel Manoscritto, pubblicato dal Li­<lb></lb>bri nel III Tomo della sua <emph type="italics"></emph>Histoire des Sciences mathématiques,<emph.end type="italics"></emph.end> è <emph type="italics"></emph>Medi­<lb></lb>tatiunculae Guidi Ubaldi e Marchionibus Montis Sanctae Mariae de rebus <lb></lb>mathematicis.<emph.end type="italics"></emph.end> Fra quelle Meditaziuncule, parte scritte in latino e parte in <lb></lb>italiano, ve n&#039;ha alcune che riguardano le proprietà delle corde sonore, dalle <lb></lb>quali proprietà così concludesi la soluzion del problema acustico data prima <lb></lb>dal Fracastoro: </s></p><p type="main">

<s>“ Di qui ancora si pò render ragione perchè causa se saranno due istru­<lb></lb>menti vicini et habbino più corde e posta una paglia sopra le corde di uno <lb></lb>e con l&#039;altro si tocchi una corda si senta che quella corda dell&#039;altro instru­<lb></lb>mento che sarà unisono ad quella che si tocca suona ancor lei e le altre <lb></lb>non suonano, e questo potrebbe nascer da questo che l&#039;aere della corda <lb></lb>ch&#039;è sonata per la sua agitazione muove tutte le altre corde, ma perchè <lb></lb>quelle che non sono in unisono non possono ricevere il medesimo moto di <lb></lb>quella ch&#039;è sonata, e quella ch&#039;è in unisono lo pò ricevere, però ancor ella <lb></lb>suona e le altre non suonano. </s>

<s>La paglia poi che se gli mette sopra fa che <lb></lb>movendosi la corda urta nella paglia spesso e si sente al suono. </s>

<s>Favorisce <pb xlink:href="020/01/759.jpg" pagenum="202"></pb>questa ragione che bisogna che gl&#039;instrumenti siano fra loro vicini, che come <lb></lb>sono lontani non segue l&#039;effetto ” (A Paris 1841, pag. </s>

<s>396). </s></p><p type="main">

<s>La spiegazione del Fracastoro è più sottilmente condotta di questa di <lb></lb>Guidubaldo, il quale però s&#039;avvantaggia sopra l&#039;altro per aver suggerita <lb></lb>l&#039;esperienza che prova come i corsi e i ricorsi delle due corde sono isocroni <lb></lb>e non s&#039;impediscono perciò, ma si secondano i moti. </s>

<s>“ Di qui è che due <lb></lb>corde in unisono vanno bene insieme e non si percotono fra loro, mentre <lb></lb>sonano, che nasce perchè hanno il medesimo moto nell&#039;andare e tornare: <lb></lb>che se se ne scorda et muove una non sonano bene insieme, ma si perco­<lb></lb>tono et urtano insieme l&#039;una ed l&#039;altra, perchè il moto dell&#039;una non è come <lb></lb>il moto dell&#039;altra, che per essere un moto più veloce dell&#039;altro è causa che <lb></lb>si urtano, come si sente per esperienza con due corde di leuto vicine ” (ivi, <lb></lb>pag. </s>

<s>395, 96). </s></p><p type="main">

<s>Non è presumibile che il Keplero avesse inteso di queste speculazioni <lb></lb>di Guidubaldo rimaste sconosciute al pubblico e non note forse che al solo <lb></lb>Galileo, il quale ebbe da giovane così intimo privato commercio d&#039;idee col <lb></lb>Marchese del Monte. </s>

<s>Quando però si pubblicarono i V libri <emph type="italics"></emph>Harmonices <lb></lb>mundi<emph.end type="italics"></emph.end> il libro unico <emph type="italics"></emph>De sympathia et antipathia rerum<emph.end type="italics"></emph.end> era da un mezzo <lb></lb>secolo di già pubblicato, e per la celebrità dell&#039;Autore è probabile che se <lb></lb>ne fosse diffusa la notizia anche in Germania. </s>

<s>In qualunque modo, propo­<lb></lb>nendosi il Keplero di risolvere il problema <emph type="italics"></emph>quod chorda pulsata chordam <lb></lb>aliam non pulsatam secum in sonitum trahit si tensa fuerit sibi consone,<emph.end type="italics"></emph.end><lb></lb>così scrive come speculazione sua nuova, benchè di nuovo propriamente non <lb></lb>abbia che il rinnovato errore peripatetico delle specie immateriate, che si <lb></lb>diffondono dal corpo della corda: </s></p><p type="main">

<s>“ Cum igitur duarum chordarum fuerit eadem tensio, sic ut unisonum <lb></lb>reddere possint tunc sonus unius idest species immateriata corporis chor­<lb></lb>dae constitutae in vibratione, delapsa a sua chorda ferit chordam alteram, <lb></lb>sicut si quis boatum edat versus Chelyn aut aliquod cavum eo boatu per­<lb></lb>cutit id cavum facitque resonare chordas eius omnes. </s>

<s>Ferit autem illa vi­<lb></lb>brationis species chordam alteram eodem rhytmo celeritatis quo movetur et <lb></lb>haec, quia aeque tensa; ut ita singuli ictus, in quos vibratio divisa esse in­<lb></lb>telligitur, in singulas percussae alterius chordae cessiunculas perpetuo inci­<lb></lb>dant. </s>

<s>Ita fit ut omnium maxime moveatur illa chorda quae ad unisonum <lb></lb>est tensa cum prima ” (Harmonices mundi lib. </s>

<s>cit., pag. </s>

<s>14). </s></p><p type="main">

<s>Conclude poi il Keplero questa sua speculazione dicendo: “ Haec mihi <lb></lb>videtur causa mirabilis huius experimenti: qui me foelicior est indagine <lb></lb>mentis ei palmam dabo ” (ibi, pag. </s>

<s>15). Ma la palma era già stata data un <lb></lb>mezzo secolo prima al Fracastoro, e all&#039;Autore dell&#039;Armonia del mondo com­<lb></lb>peterebbe solo il merito di avere estesa la teoria fracastoriana anche alle <lb></lb>altre consonanze, se alcuni fatti di cui tra poco diremo non dimostrassero <lb></lb>essere stato più giudizioso il Nostro in restringere, che l&#039;Alemanno in al­<lb></lb>largare così il campo alla speculazione. </s></p><p type="main">

<s>“ Movetur vero et illa chorda quae duplae est aut subduplae celerita-<pb xlink:href="020/01/760.jpg" pagenum="203"></pb>tis, quia duo vibrationis ictus in una chordae cessiuncula absolvuntur, et <lb></lb>sic semper ictus a priori tertius quisque congruit in unius cessiunculae <lb></lb>extremum. </s>

<s>Movetur denique et illa chorda nonnihil quae est sesquialterae <lb></lb>celeritatis, quia tres ictiunculae fiunt in duabus huius cessiunculis. </s>

<s>Sed iam <lb></lb>incipiunt invicem obviare crebrius illi ictus et hae cessiunculae seque mu­<lb></lb>tuo impedire dum duo illius ictus a fine cessiunculae huius aberrant, unus <lb></lb>solus incidit congrue. </s>

<s>Quo occursu motus chordarum caeterarum sistitur non <lb></lb>secus ac si quis digitum vibratae admovisset ” (ibi, pag. </s>

<s>15). </s></p><p type="main">

<s>Le cose fin qui discorse somministrano gli argomenti da rispondere a <lb></lb>chi voleva sapere se avesse con ragione affermato il Keplero a proposito <lb></lb>della teoria fisica della Musica: <emph type="italics"></emph>primus ego ni fallor exactissime proferam.<emph.end type="italics"></emph.end><lb></lb>Giova nonostante, affinchè la risposta sia piena, tornare ancora sopra quella <lb></lb>distinzione che si faceva tra l&#039;armonia nel sentimento o nel subietto, e l&#039;ar­<lb></lb>monia nelle cause naturali o nell&#039;obietto: distinzione che poi corrisponde <lb></lb>all&#039;altra fatta dallo stesso Keplero tra l&#039;armonia <emph type="italics"></emph>quae est mentis opus,<emph.end type="italics"></emph.end> e <lb></lb>l&#039;armonia <emph type="italics"></emph>quae Naturae elementorum materiaeque necessitate fiat.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma sia pure che fatta questa distinzione il Fracastoro e il Del Monte <lb></lb>abbian, risolvendo il problema delle consonanze a quel modo, colte le prime <lb></lb>palme: non è questo, dice il Keplero, il fondamento a ragionar delle cause <lb></lb>degl&#039;intervalli musici e de&#039;principii dell&#039;Armonia. </s>

<s>“ Quid igitur? </s>

<s>Si celeri­<lb></lb>tas chordae unius valet ad motum chordae alterius proportionatae quae, <lb></lb>quoad visum manet intacta, an non eaedem celeritates duarum chordarum <lb></lb>inter se valebunt ad titillationem auditus suavem, propterea quod is quo­<lb></lb>dammodo uniformiter ab utraque chorda movetur, duoque ictus a duobus <lb></lb>sonis seu vibrationibus in idem momentum competunt? </s>

<s>Nequaquam vero, <lb></lb>inquam ego ” (ibi) perchè queste non son ragioni da sodisfare un profon­<lb></lb>dissimo Filosofo. </s></p><p type="main">

<s>In ben più recondite cause, prosegue a dire il Keplero, che nella soave <lb></lb>titillazion degli orecchi, consiste l&#039;armonia. </s>

<s>Ella non risiede nel semplice <lb></lb>senso ma principalmente nell&#039;intelletto, il quale allora percepisce e gusta le <lb></lb>melodie, quando le specie de&#039;suoni immateriate si conformano alla regola­<lb></lb>rità di quelle geometriche figure sulle quali è condotta l&#039;architettura del <lb></lb>Mondo. </s>

<s>I concerti musicali insomma son pel Keplero una soave espressione <lb></lb>e una sentita corrispondenza colla generale Armonia dell&#039;Universo. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Erano a questo punto pervenute le speculazioni de&#039;Filosofi alquanti <lb></lb>anni prima che Galileo rivolgesse intorno al medesimo soggetto i suoi stu­<lb></lb>dii. </s>

<s>Il <emph type="italics"></emph>nequaquam vero<emph.end type="italics"></emph.end> del Keplero fu per lui come se non fosse pronun­<lb></lb>ziato, e tenendo per profondissimi solamente coloro, che filosofano sopra i <lb></lb>fatti senza voler trascendere a ricercar le altissime ragioni, stabilisce i prin-<pb xlink:href="020/01/761.jpg" pagenum="204"></pb>cipii dell&#039;armonia nelle teorie fisiche del Fracastoro. </s>

<s>Egli nelle appassite <lb></lb>membra del Medico veronese infonde così nuovo e lieto vigore di vita: </s></p><p type="main">

<s>“ Dico che non è la ragion prossima ed immediata della forma degl&#039;in­<lb></lb>tervalli musici la lunghezza delle corde, non la tensione, non la grossezza o <lb></lb>per meglio dire non il peso, ma sì ben la proporzione dei numeri delle vi­<lb></lb>brazioni e percosse dell&#039;onde dell&#039;aria che vanno a ferire il timpano del <lb></lb>nostro orecchio, il quale esso ancora sotto le medesime misure di tempi vien <lb></lb>fatto tremare. </s>

<s>Fermato questo punto, potremo per avventura assegnare assai <lb></lb>congrua ragione onde avvenga che di essi suoni differenti di tuono alcune <lb></lb>coppie siano con gran diletto ricevute dal nostro sensorio, altre con minore, <lb></lb>ed altre ci feriscano con grandissima molestia; che è il cercare la ragione <lb></lb>delle consonanze più o men perfette, e delle dissonanze. </s>

<s>” </s></p><p type="main">

<s>“ La molestia di queste nascerà, credo io, dalle discordi pulsazioni di <lb></lb>due diversi tuoni, che sproporzionatamente colpeggiano sopra il nostro tim­<lb></lb>pano, e crudissime saranno le dissonanze, quando i tempi delle vibrazioni <lb></lb>fossero incommensurabili.... Consonanti e con diletto ricevute saranno quelle <lb></lb>coppie di suoni, che verranno a percuotere con qualche ordine sopra il tim­<lb></lb>pano, il quale ordine ricerca prima che le percosse fatte dentro all&#039;istesso <lb></lb>tempo siano commensurabili di numero, acciocchè la cartilagine del timpano <lb></lb>non abbia a stare in un perpetuo tormento d&#039;inflettersi in due diverse ma­<lb></lb>niere per acconsentire e ubbidire alle sempre discordi battiture. </s>

<s>” </s></p><p type="main">

<s>“ Sarà dunque la prima e più grata consonanza l&#039;ottava, essendo che <lb></lb>per ogni percossa, che dia la corda grave su il timpano, l&#039;acuta ne dà due, <lb></lb>talchè amendue vanno a ferire unitamente in una si e nell&#039;altra no delle <lb></lb>vibrazioni della corda acuta, sicchè di tutto il numero delle percosse la metà <lb></lb>si accordano a battere unitamente, ma i colpi delle corde unisone giungono <lb></lb>sempre tutti insieme, e però son come di una corda sola, nè fanno conso­<lb></lb>nanza. </s>

<s>La quinta diletta ancora, attesochè per ogni due pulsazioni della corda <lb></lb>grave l&#039;acuta ne dà tre, dal che ne seguita che, numerando le vibrazioni <lb></lb>della corda acuta, la terza parte di tutte si accordano a battere insieme, cioè <lb></lb>due solitarie s&#039;interpongono tra ogni coppia delle concordi, e nella Diates­<lb></lb>saron se n&#039;interpongon tre. </s>

<s>Nella seconda, cioè nel tuono sesquiottavo, per <lb></lb>ogni nove pulsazioni una sola arriva concordemente a percotere con l&#039;altra <lb></lb>della corda più grave; tutte l&#039;altre sono discordi e con molestia ricevute <lb></lb>su il timpano e giudicate dissonanti dall&#039;udito ” (Alb. </s>

<s>XIII, 106, 7). </s></p><p type="main">

<s>E perciocchè le speculazioni di Galileo intorno al vibrar delle corde so­<lb></lb>nore ebbero occasione dallo studio delle proprietà de&#039;pendoli, s&#039;incontrò fa­<lb></lb>cilmente in quell&#039;elegantissimo pensiero di render visibile e dilettevole al­<lb></lb>l&#039;occhio quel che dilettevolmente percepisce l&#039;udito, sospendendo palle di <lb></lb>piombo o altri simili gravi da tre fili di lunghezze diverse, ma tali che, nel <lb></lb>tempo che il più lungo fa due vibrazioni, il più corto ne faccia quattro e il <lb></lb>mezzano tre. </s>

<s>Rimossi tutti insieme i tre pendoli dal perpendicolo, e poi la­<lb></lb>sciatigli andare, si vedrà un intrecciamento vago di essi fili con incontri <lb></lb>vari, ma tali che ad ogni quarta vibrazione del più lungo tutti e tre arri-<pb xlink:href="020/01/762.jpg" pagenum="205"></pb>veranho al medesimo tempo unitamente, e da quello poi si partiranno rei­<lb></lb>terando di nuovo lo stesso periodo. </s>

<s>La mistione di tali vibrazioni rappresen­<lb></lb>tata così all&#039;occhio è quella che fatta dalla corda rende all&#039;udito l&#039;ottava <lb></lb>con la quinta in mezzo (ivi, pag. </s>

<s>109, 10). </s></p><p type="main">

<s>Si diceva dianzi che questa teoria galileiana delle consonanze musiche <lb></lb>era quella derivata dalle dottrine del Fracastoro, le quali negavasi dal Ke­<lb></lb>plero che potessero servir di fondamento a specular le ragioni altissime del­<lb></lb>l&#039;armonia. </s>

<s>Galileo, come abbiamo veduto, la pensava assai diversamente, e <lb></lb>anzi a noi sembra questo uno de&#039;punti più notabili che rivelano la varia <lb></lb>indole de&#039;due grandissimi ingegni. </s>

<s>È ragionevole dunque che quel fonda­<lb></lb>mento non fosse trascurato dall&#039;Autor de&#039;Dialoghi intorno alle Due Scienze <lb></lb>Nuove, il quale perciò, prende le mosse a trattar della Musica fisica col ren­<lb></lb>der ragione del maraviglioso problema della corda della cetera o del cim­<lb></lb>balo, che nuove e fa realmente sonare quella non solo che all&#039;unisono gli <lb></lb>è concorde, ma anco all&#039;ottava e alla quinta. </s></p><p type="main">

<s>Udiamo come, dopo il Fracastoro, il Del Monte e il Keplero, torni Gali­<lb></lb>leo a render la ragione di quel problema così maraviglioso. </s>

<s>“ Toccata la <lb></lb>corda, egli dice, comincia e continua le sue vibrazioni per tutto il tempo al­<lb></lb>meno che da&#039;nostri orecchi si sente durar la sua risonanza. </s>

<s>Queste vibra­<lb></lb>zioni fanno vibrare e tremare l&#039;aria che gli è appresso, i cui tremori e in­<lb></lb>crespamenti si distendono per grande spazio e vanno a urtare in tutte le <lb></lb>corde del medesimo strumento, ed anco di altri vicini. </s>

<s>La corda, che è tesa <lb></lb>all&#039;unisono con la tocca, essendo disposta a far le sue vibrazioni sotto il <lb></lb>medesimo tempo, comincia al primo impulso a muoversi un poco, e soprag­<lb></lb>giungendogli il secondo, il terzo, il ventesimo e più altri, e tutti negli ag­<lb></lb>giustati e periodici tempi, riceve finalmente il medesimo tremore che la prima <lb></lb>tocca, e si vede chiarissimamente andar dilatando le sue vibrazioni giusto <lb></lb>allo spazio della sua motrice ” (ivi, pag. </s>

<s>101). </s></p><p type="main">

<s>I nostri lettori, in mente ai quali risuonano ancora le parole riferite di <lb></lb>sopra dal libro <emph type="italics"></emph>De sympathia et antipathia rerum,<emph.end type="italics"></emph.end> sentono che questa ga­<lb></lb>lileiana teoria è una ripetizion fedelissima di quella del Fracastoro, benchè <lb></lb>in qualche parte notabilmente illustrata. </s>

<s>In quella fracastoriana spiegazione <lb></lb>infatti recava qualche difficoltà l&#039;intendere come mai i così deboli impulsi <lb></lb>dell&#039;onda aerea potessero aver virtù di muovere una corda tesa con forza. </s>

<s><lb></lb>L&#039;Autore aveva in qualche modo ovviato alla difficoltà col dire <emph type="italics"></emph>unde nec <lb></lb>motus fit ullus praeter primam impulsationem, quae insensibilis est;<emph.end type="italics"></emph.end> ma <lb></lb>queste parole avevano bisogno di spiegazione, che poi fu data da Galileo, il <lb></lb>quale ricorse a&#039;principii della Meccanica, e all&#039;esperienza de&#039;pendoli per di­<lb></lb>mostrar come debolissimi impulsi ripetuti possono accumular tanta forza da <lb></lb>mover qualunque peso. </s>

<s>“ Ad un pendolo, fa dire al Salviati, ancorchè grave <lb></lb>e posto in quiete, col solo soffiarvi dentro conferiremo noi moto a moto assai <lb></lb>grande col reiterare i soffi, ma sotto il tempo che è proprio quel delle sue <lb></lb>vibrazioni. </s>

<s>Che se al primo soffio l&#039;avremo rimosso dal perpendicolo mezzo <lb></lb>dito, aggiungendogli il secondo dopo che, sendo ritornato verso noi, comin-<pb xlink:href="020/01/763.jpg" pagenum="206"></pb>cerebbe la seconda vibrazione, gli conferiremo nuovo moto, e così successi­<lb></lb>vamente con altri soffi, ma dati a tempo e non quando il pendolo ci viene <lb></lb>incontro, che così gl&#039;impediremo e non aiuteremo il moto, e seguendo con <lb></lb>molti impulsi gli conferiremo impeto tale, che maggior forza assai che quella <lb></lb>d&#039;un soffio ci bisognerà a cessarlo ” (ivi, pag. </s>

<s>100, 1). </s></p><p type="main">

<s>Così Galileo si godeva il merito di aver posta in sicuro da tutte le dif­<lb></lb>ficoltà la dottrina del Fracastoro, e di aver perciò più compiutamente di <lb></lb>tutti risoluto il maraviglioso problema del risonar delle corde non tocche, <lb></lb>quando rigidi censori lo colsero in contradizione con sè medesimo e lo ac­<lb></lb>cusarono d&#039;incauto nell&#039;aver seguìto gli esempi del Keplero, il quale volle <lb></lb>estendere la spiegazione fracastoriana non all&#039;unisono solo, ma a tutte le <lb></lb>altre consonanze. </s></p><p type="main">

<s>“ ABC, dice uno di questi censori, sia lo spazio che corre la vibra­<lb></lb>zione della corda grave d&#039;un&#039;ottava mossa da A (fig. </s>

<s>55) e B ne sia il punto <lb></lb><figure id="id.020.01.763.1.jpg" xlink:href="020/01/763/1.jpg"></figure></s></p><p type="caption">

<s>Figura 55.<lb></lb>di mezzo, cioè quello che la parte in <lb></lb>due metà. </s>

<s>Similmente DE sia lo spa­<lb></lb>zio che corre la vibrazione della corda <lb></lb>acuta della medesima ottava, e D sia <lb></lb>il punto di mezzo ond&#039;ella è mossa. </s>

<s>Facciamo ora che nel medesimo istante <lb></lb>si muovano a far le loro vibrazioni i punti A, D e discorriamo così: Men­<lb></lb>tre A va in B, D viene in E e riceve a seconda la sospinta e l&#039;impulso fa­<lb></lb>vorevole d&#039;A. </s>

<s>Ma mentre B prosegue il suo andare in C non torna E in D? <lb></lb>e nello scontrarsi che fanno in que&#039;lor due moti contrarii non si cozzano? </s>

<s><lb></lb>non si urtano insieme l&#039;aria BC con la corda ED? ” (Bartoli, Del suono, <lb></lb>Roma 1679, pag. </s>

<s>161). </s></p><p type="main">

<s>Se fosse stata fatta una simile interrogazione a Galileo in persona avrebbe <lb></lb>dovuto confessare che così dee nè più nè meno avvenire in due corde, una <lb></lb>delìe quali fosse tesa all&#039;ottava, essendo questo proprio il caso de&#039;soffi dati <lb></lb>ad un pendolo non a tempo, ma quando il pendolo stesso ci viene incon­<lb></lb>tro, <emph type="italics"></emph>che così gl&#039;impediremo e non aiuteremo il moto.<emph.end type="italics"></emph.end> E perchè lo stesso <lb></lb>ragionamento di quel censore, può applicarsi a tutte le altre consonanze, è <lb></lb>perciò che Galileo medesimo da sè confessa non potersi applicare il princi­<lb></lb>pio de&#039;piccoli urti accumulati a muover le corde tese, non verificandosi il <lb></lb>caso di così fatti accumulamenti altro che nell&#039;unisono. </s>

<s>Di qui si prese oc­<lb></lb>casion d&#039;ammirare l&#039;accortezza del Fracastoro, che giusto al solo unisono <lb></lb>ristrinse la sua spiegazione, e s&#039;ebbe giusto motivo di tacciar d&#039;inconsiderati <lb></lb>il Keplero e Galileo, i quali estendendo quella spiegazione all&#039;Ottava e alla <lb></lb>Quinta non si avvidero come ciò non poteva farsi, perchè contradiceva a quel <lb></lb>verissimo principio e a quella sicura norma posta già dal medesimo Fracastoro, <lb></lb>e ne&#039;Dialoghi galileiani sperimentalmente confermata: <emph type="italics"></emph>oportet ut quae im­<lb></lb>pellunt et faciunt motum ante non impediant motum qui retro fit a chorda.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sopra il Keplero e il Galileo rimaneva così salvo&#039;dalle censure il solo <lb></lb>Fracastoro, quando avventati i colpi anche contro a lui cadde travolgendo <lb></lb>più abbasso nella sua propria ruina anche gli altri due grandi, che gli gia-<pb xlink:href="020/01/764.jpg" pagenum="207"></pb>cevan di sotto. </s>

<s>I colpi venivano avventati da que&#039;medesimi contradittori del <lb></lb>Grimaldi, i quali come dicemmo reputando che i leggerissimi increspamenti <lb></lb>di un&#039;onda sonora non potessero aver momento alcuno di forza in un corpo <lb></lb>solido, negavano perciò che la causa del risonar una corda non tocca, ri­<lb></lb>siedesse negli urti dell&#039;aria messa in moto da una simile altra corda so­<lb></lb>nata. </s>

<s>Cotesti contradittori nel proporsi a risolvere il maraviglioso problema, <lb></lb>risoluto con sì gran compiacenza dal Keplero e da Galileo, piuttosto che alle <lb></lb>speculazioni ebbero fede nelle esperienze, le quali rivelarono tosto a loro <lb></lb>questo fatto importante: che cioè una corda vibrata non fa risonar l&#039;altra <lb></lb>corda non tocca se non che in certe particolari condizioni, in che par che <lb></lb>vogliano trovarsi collocati i due strumenti. </s></p><p type="main">

<s>“ Temperate dunque all&#039;unisono due eccellenti chitarre spagnuole (dice <lb></lb>quel solito contradittore citato poco avanti) e posate con quel loro fondo <lb></lb>piano sopra una tavola in competente distanza, seguiva indubitatamente il <lb></lb>tremar delle corde dell&#039;una in toccando quelle dell&#039;altra. </s>

<s>Ciò fatto le por­<lb></lb>tai a posare, con la medesima distanza fra loro, sopra non mi ricordo se <lb></lb>una coltre o che che altro si fosse, solamente che cosa soffice e morbidis­<lb></lb>sima, e quivi rifatta la sperienza del toccare le corde dell&#039;una trovai che <lb></lb>quelle dell&#039;altra, che giacendo sopra la tavola eran sì vive al muoversi e <lb></lb>sì spiritose al guizzare, ora si stavano insensibili e immobili come morte, nè <lb></lb>mai seguì altramente se non solo al far che le chitarre si toccassero l&#039;una <lb></lb>l&#039;altra ” (ivi, pag. </s>

<s>165). </s></p><p type="main">

<s>Se ne volle inferir da questa, e da simili altre esperienze tutte istituite <lb></lb>a tal proposito, che il pulsar di una corda non si comunica all&#039;altra per <lb></lb>l&#039;intermedio dell&#039;aria, ma de&#039;corpi solidi interposti, i quali intanto trasmet­<lb></lb>tono il moto, in quanto son atti a vibrare a tenor del corpo risonante a cui <lb></lb>sono congiunti. </s>

<s>La conclusione par che non si possa negare se l&#039;esperienze <lb></lb>son vere. </s>

<s>Or chi può mettere in dubbio che il fatto delle due chitarre non <lb></lb>avvenga propriamente a quel modo che l&#039;Autor lo descrive? </s>

<s>Riscontra dal­<lb></lb>l&#039;altra parte con questa l&#039;esperienza degli Accademici fiorentini, benchè <lb></lb>instituita ad intento alquanto diverso. </s>

<s>“ Si messero due Viole in ugual di­<lb></lb>stanza da una di mezzo e tutte collocate orizzontalmente. </s>

<s>Indi accordate tutte <lb></lb>all&#039;unisono, data un&#039;arcata a quella di mezzo, si osservò in qual distanza <lb></lb>risonassero l&#039;altre due, per via del tremolio di un ballerino di paglia acca­<lb></lb>vallato ad una delle loro corde. </s>

<s>Si fece questa esperienza la prima volta in <lb></lb>una stanza terrena in volta, e si trovò che toccatane una ne rispondeva <lb></lb>un&#039;altra in distanza di braccia sette. </s>

<s>Trasportate poi in un giardino all&#039;aria <lb></lb>aperta, lontane poco più di un braccio non si movevano ” (Targioni, Noti­<lb></lb>zie cit., T. II, P. II, pag. </s>

<s>564). </s></p><p type="main">

<s>Or è chiaro di qui che se fosse veramente l&#039;aria il mezzo della tra­<lb></lb>smissione de&#039;moti avrebbero dovuto le due viole risonar meglio all&#039;eperto <lb></lb>che non nel chiuso di una stanza, dove seguì l&#039;effetto perchè furono i due <lb></lb>strumenti posati sopra una medesima tavola, mentre nel giardino si tenevan <lb></lb>sospesi a&#039;rami degli alberi o alle stecche di qualche pergolato. </s></p><pb xlink:href="020/01/765.jpg" pagenum="208"></pb><p type="main">

<s>Aveva anche Galileo avvertito che quell&#039;ondeggiamento che si va di­<lb></lb>stendendo per l&#039;aria muove e fa vibrare non solamente le corde, ma qual­<lb></lb>sivoglia altro corpo disposto a tremare e vibrarsi sotto quel tempo della tre­<lb></lb>mante corda, ma l&#039;esperienza ch&#039;egli adduce per provar ciò o è mal descritta <lb></lb>o è un inganno. </s>

<s>“ Se si ficcheranno, egli dice, nelle sponde dello strumento <lb></lb>diversi pezzetti di setole o di altre materie flessibili, si vedrà nel suonare il <lb></lb>cimbalo tremare or questo or quel corpuscolo, secondo che verrà toccata <lb></lb>quella corda, le cui vibrazioni van sotto il medesimo tempo: gli altri non <lb></lb>si muoveranno al suono di questa corda, nè quella tremerà al suono d&#039;altra <lb></lb>corda ” (Alb. </s>

<s>XIII, 102). </s></p><p type="main">

<s>Or com&#039;è a credere che un corpo flessibile e lasso, nè perciò disposto <lb></lb>a risentirsi in que&#039;leggeri e velocissimi tremori, in ch&#039;entran le corde so­<lb></lb>nore, possa mettersi in misurata danza con queste? </s>

<s>Se una setola si vedeva <lb></lb>vibrare sonando una corda, ciò doveva essere, senza dubbio, per aver qual­<lb></lb>che comunicazione diretta colla corda stessa, cosicchè quello che a Galileo <lb></lb>sembrava un effetto acustico di risonanza non era altro in verità che un <lb></lb>gioco meccanico. </s>

<s>In qualunque modo non solo il Bartoli (Del suonc cit., <lb></lb>pag. </s>

<s>135) ma altri forse più valenti di lui provatisi a ripetere l&#039;esperienza <lb></lb>galileiana, trovarono che non seguiva come non era possibile che ne seguisse <lb></lb>l&#039;effetto. </s></p><p type="main">

<s>E perchè il risonar di una corda non tocca e tesa all&#039;unisono di un&#039;al­<lb></lb>tra corda sonata fu esperienza spontaneamente in fin dai tempi più antichi <lb></lb>offerta dal caso, si può dir che questa della setola infilata nelle sponde del <lb></lb>cimbalo è la prima fra l&#039;esperienze che siano state fatte a studio, e in che <lb></lb>s&#039;incontri la storia dell&#039;Acustica. </s>

<s>La poca precisione di lei sarebbe non lieto <lb></lb>augurio ai progressi della scienza, se non pensassimo che a que&#039;tempi, e <lb></lb>particolarmente negli istituti galileiani, l&#039;arte sperimentale era in que&#039;suoi <lb></lb>primi principii così ancora inesperta, da non valere a scoprir nuove verità <lb></lb>ma da servir di qualche riscontro piuttosto che di conferma a quelle che <lb></lb>s&#039;erano speculate già per ragion matematica. </s></p><p type="main">

<s>Tornan perciò quegli infausti auguri scongiurati dal ripenśar che l&#039;Acu­<lb></lb>stica è fondata meglio nelle matematiche ragioni che nell&#039;esperienze de&#039;fatti, <lb></lb>ond&#039;avvenne che Galileo riuscì a promuoverla indipendentemente da quelle <lb></lb>più difficili e più gelose esperienze, le quali se talvolta sono a studio invo­<lb></lb>cate per conferma o riscontro delle matematiche conclusioni, riescono in Ga­<lb></lb>lileo stesso, come, oltre al citato, dimostreranno altri esempii, immaginarie <lb></lb>e tutt&#039;affatto ideali. </s></p><p type="main">

<s>A mostrar d&#039;onde Galileo incominciasse a promovere questa importan­<lb></lb>tissima parte della scienza de&#039;suoni giova prima vedere fino a che punto <lb></lb>l&#039;avessero lasciata i suoi predecessori da&#039;più antichi infino al Keplero. </s>

<s>Che <lb></lb>i suoni acuti dipendessero dal più veloce vibrar delle corde, e che dal loro <lb></lb>più lento moto si producessero i suoni gravi, fu dottrina universalmente <lb></lb>conosciuta perchè trasmessa dagl&#039;insegnamenti concordi di Aristotile e di <lb></lb>Platone, dal Timeo del quale quasi come aforismo citavasi la sentenza: <emph type="italics"></emph>Mo-<emph.end type="italics"></emph.end><pb xlink:href="020/01/766.jpg" pagenum="209"></pb><emph type="italics"></emph>tio quidem velox acuta provenit, tarda gravis.<emph.end type="italics"></emph.end> Il facile uso poi del Mono­<lb></lb>cordo, nel quale si poteva a piacere far vibrare una parte sola di tutta la <lb></lb>corda, e da un musico orecchio apprezzarsene il vario suono ch&#039;ella ren­<lb></lb>deva, fece riconoscere che dimezzata la corda stessa rendeva l&#039;ottava, e dette <lb></lb>modo a congetturare che la ragione di ciò consistesse nella velocità raddop­<lb></lb>piata. </s>

<s>Di qui è che ripetevasi come altro aforismo quel di Boezio nel libro IV <lb></lb><emph type="italics"></emph>De harmonia: Dimidia in quantitate duplex est in acumine,<emph.end type="italics"></emph.end> e sotto altra <lb></lb>forma dicevasi <emph type="italics"></emph>l&#039;ottava esser contenuta dalla dupla.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma le varietà del suono fatte dalle corde, secondo il variar del peso che <lb></lb>le tende e della loro propria gravezza, rimasero appresso tutti prima di Ga­<lb></lb>lileo inconsiderate. </s>

<s>Solo Guidubaldo del Monte avvertiva, nelle citate sue <lb></lb><emph type="italics"></emph>Meditaziuncule,<emph.end type="italics"></emph.end> che di due corde ugualmente lunghe e ugualmente tese <lb></lb>quella che dà il suono più acuto è la più leggera, ma egli non sa con qual <lb></lb>legge voglia quella leggerezza esser variamente dispensata. </s>

<s>“ Le corde ti­<lb></lb>rate ugualmente, quella ch&#039;è più leggera fa il suono più acuto essendo lun­<lb></lb>ghe ugualmente, come per esperienza si prova una corda di ottone o ac­<lb></lb>ciaro ed una di leuto, alle quali se gli può attaccar due pesi eguali, essendo <lb></lb>gl&#039;intervalli eguali, se quella di leuto sarà più leggera ancorchè più grossa <lb></lb>dell&#039;altra, farà il suono più acuto. </s>

<s>La ragione è che percotendole tutte due <lb></lb>quella più leggera riceve il moto più veloce nell&#039;andare e tornar che fa la <lb></lb>corda e però fa il suono più acuto ” (Libri, <emph type="italics"></emph>Histoire<emph.end type="italics"></emph.end> ecc. </s>

<s>loc. </s>

<s>cit., pag. </s>

<s>395). </s></p><p type="main">

<s>Il Keplero appositamente riserba il cap. </s>

<s>II del libro III <emph type="italics"></emph>Harmonices <lb></lb>mundi<emph.end type="italics"></emph.end> a trattar <emph type="italics"></emph>De sectione harmonica chordae,<emph.end type="italics"></emph.end> ma contento solo a ma­<lb></lb>tematicar le dottrine di Boezio sull&#039;armonia non tocca poi nulla che con­<lb></lb>cerna il vario vibrar delle corde stesse al variar loro il peso o la tensione. </s></p><p type="main">

<s>Galileo fu dunque il primo ad avvertir che la formula di Boezio, <emph type="italics"></emph>dimi­<lb></lb>dia in quantitate duplex est in acumine,<emph.end type="italics"></emph.end> se non addirittura falsa era in <lb></lb>ogni modo in sè difettosa, perchè l&#039;acume non varia solamente al variare <lb></lb>della lunghezza, ma e del peso e della trazione, e varia altresì con legge <lb></lb>diversa, la quale non è del doppio ma del quadruplo, cosicchè, a voler che <lb></lb>una corda tesa renda l&#039;ottava più acuta, convien tirarla non con un peso <lb></lb>doppio ma quadruplo, come del quadruplo e non del semplice doppio è pur <lb></lb>necessario l&#039;alleggerirla. </s>

<s>E per usare il linguaggio de&#039;Fisici moderni Gali­<lb></lb>leo fu il primo a dimostrar che le tensioni variavano direttamente e i pesi <lb></lb>inversamente come i quadrati. </s>

<s>Ma giova udire in qual forma propria espo­<lb></lb>nesse Galileo stesso le leggi da sè prima scoperte intorno al vario risonar <lb></lb>delle corde. </s></p><p type="main">

<s>“ Stetti lungo tempo perplesso, egli dice per bocca del suo caro Sa­<lb></lb>gredo, intorno a queste forme delle consonanze, non mi parendo che la ra­<lb></lb>gione che comunemente se ne adduce dagli Autori, che sin qui hanno scritto <lb></lb>dottamente della Musica, fosse concludente abbastanza. </s>

<s>Dicono essi la Dia­<lb></lb>pason, cioè l&#039;ottava, esser contenuta dalla doppia, la Diapente, che noi di­<lb></lb>ciamo la quinta, dalla sesquialtera, perchè distesa sopra il Monocordo una <lb></lb>corda, sonandola tutta e poi sonandone la metà, col mettere un ponticello <pb xlink:href="020/01/767.jpg" pagenum="210"></pb>in mezzo, si sente l&#039;ottava, e se il ponticello si metterà al terzo di tutta la <lb></lb>corda, toccando l&#039;intera e poi li due terzi, ci rende la quinta; per lo che <lb></lb>l&#039;ottava dicono esser contenuta tra il due e l&#039;uno, e la quinta tra il tre <lb></lb>e il due. </s>

<s>” </s></p><p type="main">

<s>“ Questa ragione, dico, non mi pareva concludente per poter assegnare <lb></lb>iuridicamente la dupla e la sesquialtera per forme naturali della Diapason <lb></lb>e della Diapente; e il mio motivo era tale: Tre sono le maniere colle quali <lb></lb>noi possiamo inacutire il tuono a una corda; l&#039;una è lo scorciarla, l&#039;altra <lb></lb>il tenderla più, o vogliam dir tirarla, il terzo è l&#039;assottigliarla. </s>

<s>Ritenendo la <lb></lb>medesima tiratezza e grossezza della corda, se vorremo sentir l&#039;ottava, bi­<lb></lb>sogna scorciarla la metà, cioè toccarla tutta e poi mezza. </s>

<s>Ma se ritenendo <lb></lb>la medesima lunghezza e grossezza vorremo farla montare all&#039;ottava col ti­<lb></lb>rarla più, non basta tirarla il doppio più ma ci bisogna il quadruplo, sic­<lb></lb>chè se prima era tirata dal peso d&#039;una libbra converrà attaccarvene quattro <lb></lb>per inacutirla all&#039;ottava. </s>

<s>E finalmente, se stante la medesima lunghezza e <lb></lb>tiratezza vorremo una corda che per esser più sottile renda l&#039;ottava, sarà <lb></lb>necessario che ritenga solo la quarta parte della grossezza dell&#039;altra più <lb></lb>grave. </s>

<s>E questo che dico dell&#039;ottava, cioè che la sua forma presa dalla ten­<lb></lb>sione o dalla grossezza della corda è in duplicata proporzione di quella che <lb></lb>si ha dalla lunghezza, intendasi di tutti gli altri intervalli musici ” (Alb. </s>

<s><lb></lb>XIII, 102, 3). </s></p><p type="main">

<s>Com̀e riuscisse Galileo a scoprir questa legge ei lo tace, perch&#039;era fa­<lb></lb>cile argomentare non poter essergli aperta altra via da quella in fuori del­<lb></lb>l&#039;esperienza: e lo tace anche forse perchè il comune uso che facevasi del <lb></lb>Monocordo rendeva non difficile a chi avesse saputo usarvi qualche diligenza <lb></lb>quelle stesse esperienze. </s>

<s>Ben più difficile era il dimostrar quel principio fon­<lb></lb>damentale, che s&#039;ammetteva da tutti per congettura e che consisteva in ciò <lb></lb>che nell&#039;ottava più acuta sia raddoppiato il numero delle vibrazioni che fa <lb></lb>la corda. </s>

<s>In che modo infatti sarebb&#039;egli stato possibile riscontrar quel nu­<lb></lb>mero a que&#039;tempi, quando la <emph type="italics"></emph>Ruota<emph.end type="italics"></emph.end> del Savart, e la <emph type="italics"></emph>Sirena<emph.end type="italics"></emph.end> del Cagnard­<lb></lb>Latour erano ancora lontane quasi due secoli? </s>

<s>Eppure Galileo credè d&#039;es­<lb></lb>ser riuscito il primo a dimostrare ciò per l&#039;esperienza volgarissima del <lb></lb>bicchier pieno d&#039;acqua, fregati gli orli col polpastrello del dito, facendo os­<lb></lb>servar com&#039;accadendo talvolta che il tuono salti all&#039;ottava si vedon nel­<lb></lb>l&#039;istante le onde dell&#039;acqua dividersi in due. </s>

<s>“ Ma perchè il numerare le <lb></lb>vibrazioni d&#039;una corda, che nel render la voce le fa frequentissime, è del <lb></lb>tutto impossibile, sarei, dice Galileo, restato sempre ambiguo se vero fosse <lb></lb>che la corda dell&#039;ottava più acuta facesse nel medesimo tempo doppio nu­<lb></lb>mero di vibrazioni di quelle della più grave, se le onde permanenti per <lb></lb>quanto tempo ei piace nel far sonare e vibrare il bicchiere non m&#039;avessero <lb></lb>sensatamente mostrato come, nell&#039;istesso momento che alcuna volta si sente <lb></lb>il tuono saltare all&#039;ottava, si vedono nascere altre onde più minute, le quali <lb></lb>con infinita pulitezza tagliano in mezzo ciascuna di quelle prime ” (ivi, <lb></lb>pag. </s>

<s>104). </s></p><pb xlink:href="020/01/768.jpg" pagenum="211"></pb><p type="main">

<s>Fu provato da alcuni a ripetere questa esperienza di Galileo e seguì a <lb></lb>loro quel ch&#039;era seguìto al Bartoli; seguì cioè che alla descrizione galileiana <lb></lb>non si videro punto corrispondere i fatti osservati. </s>

<s>Intorno al circuito inte­<lb></lb>rior del bicchiere non si osserva altro che una fascia o ghirlanda di crespe <lb></lb>da non si saper a chi altro meglio rassomigliarle che ai processi ciliari che <lb></lb>stanno intorno al cristallino dell&#039;occhio ” (De&#039;suoni cit., pag. </s>

<s>140). </s></p><p type="main">

<s>Forse meno ideale e immaginaria di questa è l&#039;altra esperienza che ivi <lb></lb>appresso soggiungesi delle virgolette rimaste incise sopra una lamina metal­<lb></lb>lica raschiata collo strisciarvi sopra velocemente la punta di uno scarpello. <lb></lb></s>

<s>“ L&#039;invenzione fu del caso e mia, fa dire Galileo al Salviati, fu solamente <lb></lb>l&#039;osservazione e il far di essa capitale e stima come di riprova di nobil con­<lb></lb>templazione ancorchè fattura in sè stessa assai vile. </s>

<s>Raschiando con uno <lb></lb>scarpello di ferro tagliente una piastra di ottone per levarle alcune macchie, <lb></lb>nel muovervi sopra lo scarpello con velocità, sentii una volta e due tra molte <lb></lb>strisciate fischiarne e uscirne un sibilo molto gagliardo e chiaro, e guar­<lb></lb>dando sopra la piastra vidi un lungo ordine di virgolette sottili tra di loro <lb></lb>parallele e per egualissimi intervalli l&#039;una dall&#039;altra distanti. </s>

<s>Tornando a <lb></lb>raschiar di nuovo più e più volte, mi accorsi che solamente nelle raschiate <lb></lb>che fischiavano lasciava lo scarpello le intaccature sopra la piastra, ma <lb></lb>quando la strisciata passava senza sibilo, non restava pur minima ombra di <lb></lb>tali virgolette. </s>

<s>” </s></p><p type="main">

<s>“ Replicando poi altre volte lo scherzo, strisciando ora con maggiore <lb></lb>ed ora con minore velocità, il sibilo riusciva di tuono or più acuto ed or <lb></lb>più grave, ed osservai i segni fatti nel suono più acuto esser più spessi, e <lb></lb>quelli del più grave più radi, e talora ancora, secondo che la strisciata me­<lb></lb>desima era fatta verso il fine con maggiore velocità che nel principio, si <lb></lb>sentiva il suono andarsi inacutendo, e le virgolette si vedeva essere andate <lb></lb>inspessendosi, ma sempre con estrema lindura e con assoluta equidistanza <lb></lb>segnate.... Ho anco talvolta tra le corde del cimbalo notatone due unisone <lb></lb>alli due sibili fatti strisciando al modo detto e di più differenti di tuono, dei <lb></lb>quali due precisamente distavano per una quinta perfetta, e misurando poi <lb></lb>gl&#039;intervalli delle virgolette dell&#039;una e dell&#039;altra strisciata si vedeva la di­<lb></lb>stanza che conteneva quarantacinque spazii dell&#039;una contenere trenta del­<lb></lb>l&#039;altra quale veramente è la forma che si attribuisce alla Diapente ” (Alb. </s>

<s><lb></lb>XIII, 104, 5). </s></p><p type="main">

<s>Chiunque avesse però più ferma fede nella sincerità di Galileo, direbbe <lb></lb>che il riconoscer que&#039;segni così assolutamente equidistanti e il saperne in­<lb></lb>ferir di lì la frequenza e il numero delle vibrazioni corrispondenti all&#039;acu­<lb></lb>tezza de&#039;sibili della piastra strisciata; il misurar così precisamente gli spazii <lb></lb>compresi da una serie di virgolette e il trovar che tornavano a proporzione <lb></lb>degl&#039;intervalli musici delle due corde del cembalo; non doveva esser cosa <lb></lb>tanto facile e piana come voleva farla credere lo stesso Galileo, il quale ve­<lb></lb>deva la proporzione di quegli spazii perchè prestabilita già nella sua mente <lb></lb>a quel modo che le matematiche ragioni, gli persuadevano, anche contro <pb xlink:href="020/01/769.jpg" pagenum="212"></pb>l&#039;esperienza de&#039;fatti, l&#039;isocronismo ne&#039;pendoli oscillanti. </s>

<s>Chi credesse altri­<lb></lb>menti e volesse salvar la reputazione di Galileo rendendola anche da que­<lb></lb>sta parte immacolata, si studii e veda se il noverar quelle galileiane virgo­<lb></lb>lette così ben compassate, lo dispensi dall&#039;uso e dalla spesa della Ruota <lb></lb>dentata o della Sirena. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Un certo tal qual sussulto, che dee necessariamente toccare il cuore <lb></lb>de&#039;ciechi ammiratori di Galileo, e che gli moverà forse ad ira contro di noi, <lb></lb>come contro Galileo stesso che notava gli errori di Aristotile si commove­<lb></lb>vano d&#039;ira furiosa i Peripatetici, ne porge opportuna occasione di tratte­<lb></lb>nerci a ripensar sopra queste esperienze descritte, secondo abbiamo veduto, <lb></lb>dall&#039;Autore del I Dialogo delle Due nuove Scienze. </s>

<s>C&#039;intravedono anche i <lb></lb>meno sagaci una certa compiacenza e una ostentazione di novità spettaco­<lb></lb>lose, d&#039;onde viene a spiegarsi come Galileo taccia di quelle facili esperienze <lb></lb>sul Monocordo dalle quali fu condotto a scoprir le leggi della proporziona­<lb></lb>lità delle forze traenti e de&#039;pesi delle corde, in variare il tuono de&#039;loro tre­<lb></lb>mori, e s&#039;intrattenga così minuziosamente a descriver le setole infilate nella <lb></lb>sponda del cimbalo e le onde sdoppiate nel fregar col polpastrello del dito <lb></lb>l&#039;orlo del bicchiere, e l&#039;ordine delle virgolette sulla piastra strisciata colla <lb></lb>punta dello scarpello; esperienze tutte che non riuscendo alle prove noi ab­<lb></lb>biam qualificate addirittura per cose immaginarie. </s></p><p type="main">

<s>Ma noi siamo stati forse i primi a sentenziar così con tale franchezza, <lb></lb>che ci viene imputata ad audacia: nessuno avrebbe osato di mettere in dub­<lb></lb>bio quelle acustiche esperienze, e bastava per crederle vere, il saper ch&#039;erano <lb></lb>state fatte da Galileo. </s>

<s>Il Bartoli stesso, dop&#039;aver trascritta l&#039;esperienza delle <lb></lb>setole infilate nella sponda del cimbalo, e aver detto dolergli il non poter <lb></lb>allegare in confermazione del fatto la testimonianza ancor de&#039;suoi occhi, con­<lb></lb>clude: <emph type="italics"></emph>ciò nonostante io lo prendo per indubitato.<emph.end type="italics"></emph.end> (Del suono cit., pag. </s>

<s>135). <lb></lb>E dop&#039;aver citata l&#039;esperienza dello sdoppiamento delle onde nel bicchiere <lb></lb>fregato, lo stesso Bartoli soggiunge: “ E senza bisognarmi altra pruova il <lb></lb>credo fatto non altrimenti che se io stesso l&#039;avessi veduto con gli occhi del <lb></lb>Salviati; e ciò nulla ostante il non aver risposto a me in tutto l&#039;esperienza, <lb></lb>come io mi prometteva ” (ivi, pag. </s>

<s>140). </s></p><p type="main">

<s>Che se tanto pesava l&#039;autorità di Galileo sull&#039;animo di un gesuita, pen­<lb></lb>siamo ciò che dovess&#039;essere sopra que&#039;suoi discepoli, i quali attingevan da <lb></lb>lui come ad unica sorgente, in che, raccolti d&#039;ogni parte di sotto terra e <lb></lb>purificati, si mescevano i rivi della scienza. </s>

<s>In ciò noi principalmente rico­<lb></lb>noscemmo la maravigliosa efficacia della grande Instaurazione galileiana, per <lb></lb>conferma di che ci occorre ora opportuno a citar l&#039;esempio di Niccolò Ag­<lb></lb>giunti, a cui andrebbe debitrice l&#039;Acustica del primo Trattato matematico <pb xlink:href="020/01/770.jpg" pagenum="213"></pb>sulle corde sonore, se non gli fosse stato tolto il condur l&#039;opera egregia <lb></lb>dalla troppo sollecita morte. </s></p><p type="main">

<s>L&#039;Aggiunti non va a imparar che cosa è il suono nè da Platone nè <lb></lb>da&#039;Filosofi pitagorici o dagli stoici: egli lo apprende da Galileo, il quale fa <lb></lb>sulla sua propria bocca rivivere e quasi germogliar sul nuovo albero della <lb></lb>scienza quelle antiche e verissime dottrine. </s>

<s>“ Galilaeum sequar auctorem qui <lb></lb>primus a condita Philosophia in soni contemplatione veritatis sonum emisit. </s>

<s>” </s></p><p type="main">

<s>E che cosa nel 1633 o 34, in che dee aver l&#039;Aggiunti scritte queste <lb></lb>parole, che cosa aveva filosofato e contemplato Galileo circa i suoni? </s>

<s>Quel <lb></lb>che leggesi nel <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> e che noi abbiam riferito ne&#039;principii del pre­<lb></lb>sente capitolo, dove si ripetono dall&#039;Autore gl&#039;insegnamenti platonici del­<lb></lb>l&#039;ondeggiar dell&#039;aria che percotendo la cartilagine dell&#039;orecchio v&#039;eccita la <lb></lb>sensazion dell&#039;udito, e dove, pur ripetendo antiche dottrine e dalla corrente <lb></lb>Filosofia approvate, si dice che dalla frequenza delle onde sonore nasce l&#039;acu­<lb></lb>tezza del suono e la gravità dalla rarità (Alb. </s>

<s>IV, 336). </s></p><p type="main">

<s>Singolar cosa è che avendo l&#039;Aggiunti per concluder, come vedremo, <lb></lb>una sua Proposizione, bisogno d&#039;invocar questo principio che cioè <emph type="italics"></emph>cordae <lb></lb>quae tardius suas expediunt vibrationes graviorem sonum edunt,<emph.end type="italics"></emph.end> imme­<lb></lb>diatamente soggiunge: <emph type="italics"></emph>ut Galileus probat.<emph.end type="italics"></emph.end> Ma nel <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> non ha nem­<lb></lb>meno un cenno Galileo di queste prove, e l&#039;esperienza delle virgolette ri­<lb></lb>maste impresse sulla piastra d&#039;ottone raschiata collo scarpello non ricorre <lb></lb>altrove che nel I Dialogo delle Due Nuove Scienze, pubblicate quasi tre anni <lb></lb>dopo che l&#039;Aggiunti era morto. </s>

<s>Potrebbesi pensare che il Maestro avesse al <lb></lb>suo giovane e diletto discepolo comunicato a voce e in privata conversa­<lb></lb>zione quelle esperienze, prima di pubblicarle, se le Proposizioni acustiche, <lb></lb>che lasciò manoscritte lo stesso Aggiunti, e delle quali fra poco diremo, non <lb></lb>facessero certo argomento che l&#039;Autore di quelle proposizioni ignorava quel <lb></lb>che di nuovo aveva scoperto sul risonar delle corde il Galileo, o che que­<lb></lb>sti non avesse fatto ancora, quando l&#039;Aggiunti scriveva, quelle scoperte, o <lb></lb>che volesse riserbarsele in petto, affinchè ne&#039;Dialoghi comparissero a tutti <lb></lb>nuove. </s>

<s>In ogni modo non si può intender quell&#039;<emph type="italics"></emph>ut Galileus probat<emph.end type="italics"></emph.end> se non che <lb></lb>l&#039;aver professate Galileo quelle dottrine serviva all&#039;Aggiunti come di prova. </s></p><p type="main">

<s>Se così spesso è dato a Galileo il titolo di divino per questa parte sola <lb></lb>si riconosce come non immeritato, per aversi cioè acquistata tanta virtù da <lb></lb>farsi rassomigliare a Dio, a cui si crede una cosa esser vera perch&#039;Egli l&#039;ha <lb></lb>detta. </s>

<s>S&#039;era molti secoli prima acquistata quella medesima virtù anche Ari­<lb></lb>stotile, ma egli ne abusò torcendo i suoi seguaci nella Filosofia naturale per <lb></lb>le vie dell&#039;errore, mentre invece altra ragione d&#039;appellar Galileo uomo divino <lb></lb>è quella dell&#039;avere egli addirizzato e additato il metodo delle verità natu­<lb></lb>rali, a cui rivolti que&#039;discepoli che avevano il piè valido per sè medesimi, <lb></lb>per sè medesimi pure correndo la gloriosa palestra riuscirono a precorrere <lb></lb>e talvolta a superare lo stesso Maestro. </s>

<s>Anche di ciò ne porge opportunis­<lb></lb>simo esempio il medesimo Aggiunti delle Proposizioni meccanico acustiche <lb></lb>del quale è tempo che rendiam conto ai Lettori, incominciando dal narrar <pb xlink:href="020/01/771.jpg" pagenum="214"></pb>come avessero nella mente di lui l&#039;occasione dagl&#039;insegnamenti e dalle fa­<lb></lb>miliari consuetudini ch&#039;egli ebbe con Galileo. </s></p><p type="main">

<s>Quando ricoverato a Siena, come chi uscito fuor del pelago alla riva si <lb></lb>rivolge indietro a guardar l&#039;onda pericolosa, Galileo deliberò di abbandonare <lb></lb>le contemplazioni del cielo per tornar tutto a specular quel che accade sopra <lb></lb>la terra, specialmente ne&#039;gravi che son tirati al centro di essa; quasi si <lb></lb>sentisse trascinar la mente da quella forza e seguirla docile il desiderio di <lb></lb>nascondersi agli occhi degli uomini, rivolse i suoi studii a penetrare adden­<lb></lb>tro alla più intima compagine de&#039;corpi. </s>

<s>Ricercando la natura di quel glu­<lb></lb>tine, che ne tiene unite le particelle componenti, le ridusse alla forza del <lb></lb>vacuo, e pensò allora a quello strumento, ch&#039;e descrisse poi nel I Dialogo <lb></lb>delle Nuove Scienze (Alb. </s>

<s>XIII, 18, 19) per misurar quella forza, e per con­<lb></lb>cluderne di lì le ragioni della resistenza che fanno le verghe solide allo spez­<lb></lb>zarsi. </s>

<s>Tanto si compiacque di questo primo principio dato al secondo di <lb></lb>que&#039;Trattati nuovi, di che proponevasi già di arricchire la scienza, che par­<lb></lb>tecipò la notizia delle nuove meditazioni agli amici e agli scolari, fra quali <lb></lb>era de&#039;primi Niccolò Aggiunti. </s>

<s>Questi, il dì 10 Settembre 1633, dopo su­<lb></lb>bito aver avuto quella bella notizia rispondeva così al venerato suo Maestro <lb></lb>a Siena: </s></p><p type="main">

<s>“ Io non potevo ricevere da V. S. </s>

<s>Eccellentissima maggior onore che <lb></lb>esser fatto partecipe dell&#039;ambrosia degli Dei, che tale a mio giudizio e gu­<lb></lb>sto deve chiamarsi ogni speculazione del suo sovrano ingegno. </s>

<s>Quest&#039;ultima <lb></lb>sua meditazione mi ha arrecato gusto grandissimo non solo perchè ho ve­<lb></lb>duto in essa risoluto con tanta facilità ed evidenza un quesito così bello e <lb></lb>curioso, ma ancora per l&#039;importante considerazione, che appresso ella ne fa, <lb></lb>deducendone quella mirabile necessità che nella struttura delle fabbriche <lb></lb>tanto artificiali quanto naturali si ritrova, di esserci una limitata grandezza, <lb></lb>oltre la quale l&#039;arte e la natura, tentando di fabbricare, piuttosto demoli­<lb></lb>rebbero e distruggerebbero ” (Alb. </s>

<s>IX, 393). </s></p><p type="main">

<s>Ma l&#039;Aggiunti era rimasto preso di maraviglia a considerar quel ci­<lb></lb>lindro di vetro, con quello zaffo scorrevole dentro, che tirato indietro con <lb></lb>forza dava la misura del vacuo, e nello stesso tempo della resistenza de&#039;so­<lb></lb>lidi allo spezzarsi, e gli pareva avere in mano in quello strumento la chiave <lb></lb>da aprire infiniti segreti della Natura, ond&#039;è che, una settimana dopo la <lb></lb>precedente, tornava così a scrivere a Galileo da Firenze: “ Ho voluto ve­<lb></lb>dere se mi riusciva d&#039;adoperare la chiave, che a questi giorni V. S. ci ha <lb></lb>data attissima ad aprire infiniti segreti di spezzamenti ecc., e perciò ho ten­<lb></lb>tato di risolvere il problema da lei accennatomi: glielo mando acciò veda se <lb></lb>io ho preso un granchio. </s>

<s>Sto poi attendendo con desiderio grande la sua di­<lb></lb>mostrazione ” (Targioni, Notizie cit., T. II, P. I, pag. </s>

<s>130). </s></p><p type="main">

<s>Saper qual sia questa particolar dimostrazione e questo particolar pro­<lb></lb>blema non occorre per ora: basta che fra&#039;Manoscritti dell&#039;Aggiunti si trovan <lb></lb>distese varie proposizioni, nelle quali tutte gioca per fondamento della spe­<lb></lb>culazione lo strumento proposto da Galileo per misurare la forza del vacuo. <pb xlink:href="020/01/772.jpg" pagenum="215"></pb>L&#039;uso fatto di un tale strumento dal valoroso Discepolo non dee tornar <lb></lb>nuovo ai Lettori di questa Storia, a&#039;quali descrivemmo nel cap. </s>

<s>I del Tomo I <lb></lb>quel <emph type="italics"></emph>poculus vel syphunculus, eiusque manubrium, cui annexum sit opti­<lb></lb>mum obturamentum<emph.end type="italics"></emph.end> applicato dall&#039;Autore a dimostrar come le corde me­<lb></lb>talliche, quali sarebbero quelle degli strumenti musici, si allunghino o si <lb></lb>accorcino al variar dell&#039;ambiente temperatura. </s>

<s>Cotesto <emph type="italics"></emph>poculus<emph.end type="italics"></emph.end> galileiano è <lb></lb>quello appunto che si diceva servir di fondamento, o come l&#039;Aggiunti stesso <lb></lb>esprimevasi, di chiave da aprir la via a dimostrar fra le altre queste sue <lb></lb>nuove meccaniche proposizioni. </s></p><p type="main">

<s><emph type="italics"></emph>“ Propositio V.<emph.end type="italics"></emph.end> Si fuerint duae cordae extensae, et illarum duas so­<lb></lb>lummodo partes norimus tum remissas tum extensas inter se aequales esse, <lb></lb>erunt totae inter se aequaliter extensae ” (MSS. Gal. </s>

<s>Disc., T. XVIII, c. </s>

<s>65 v.). </s></p><p type="main">

<s><emph type="italics"></emph>“ Prop. </s>

<s>VI.<emph.end type="italics"></emph.end> Partes quaecumque aequales cuiusvis cordae extensae, vi­<lb></lb>ribus aequalibus extensae sunt ” (ibi, c. </s>

<s>66). </s></p><p type="main">

<s><emph type="italics"></emph>“ Prop. </s>

<s>VIII.<emph.end type="italics"></emph.end> Si fuerint cordae similes inter se aequaliter extensae, <lb></lb>vires quibus extenduntur eamdem habent rationem quam longitudines ex­<lb></lb>tensarum ” (ibi, c. </s>

<s>66 v.). </s></p><p type="main">

<s><emph type="italics"></emph>“ Prop. </s>

<s>IX.<emph.end type="italics"></emph.end> Si corda brevissima, quanta maxima potest extensione <lb></lb>extensa fuerit nec abrupta, corda quaevis similis, quamquam longissima, <lb></lb>aequaliter et eodem quo illa modo extensa, non abrumpetur ” (ibi, c. </s>

<s>67 v.). </s></p><p type="main">

<s>Apparisce da questi enunciati di proposizione come si vedesse l&#039;Ag­<lb></lb>giunti aperto a speculare un più largo campo di quello, che non gli era <lb></lb>accennato dallo stesso Galileo, e come, oltre alla ragion dello strapparsi le <lb></lb>corde, si fosse messo dietro a investigarne altre nuove concernenti le pro­<lb></lb>prietà meccaniche delle loro tensioni. </s>

<s>Si domandava per esempio se una <lb></lb>corda sia tesa ugualmente nelle sue estremità e nel mezzo; se un mede­<lb></lb>simo peso tenda con ugual forza una corda lunga e una corta: domande <lb></lb>tutte alle quali, anche un mezzo secolo dopo, variamente si rispondeva e to­<lb></lb>glievasi l&#039;argomento alla risposta dalla sola esperienza. </s>

<s>L&#039;Aggiunti aveva <lb></lb>tanto tempo prima invocate le ragioni matematiche, delle quali fece uso prin­<lb></lb>cipalmente nelle Proposizioni sopra citate. </s>

<s>Non è questo il luogo da tratte­<lb></lb>nersi in un soggetto di Meccanica, ma perchè fu da ciò condotto il Nostro <lb></lb>a trattar de&#039;tremori armonici nelle corde, e perchè abbiano intanto i Lettori <lb></lb>un saggio del modo come il Discepolo di Galileo fece uso dello <emph type="italics"></emph>Strumento<emph.end type="italics"></emph.end><lb></lb>galileiano, abbiam creduto opportuno trascriver qui la prima dimostrata parte <lb></lb>della seguente proposizione: </s></p><p type="main">

<s>“ Si duae quaevis cordae similes eadem vel aequali vi extendantur, in­<lb></lb>ter se aequaliter extendentur, etiamsi illarum altera brevissima, altera vero <lb></lb>longissima fuerit. </s>

<s>— Proponamus nobis ob oculos <emph type="italics"></emph>Instrumentum,<emph.end type="italics"></emph.end> cuius paulo <lb></lb>ante meminimus, et quod, ut descripsimus, e cylindricis vasculis et opercu­<lb></lb>lis aequalibus et se mutuo congrue excipientibus coagmentatur. </s>

<s>Ac primo <lb></lb>quidem manu vel quovis alio modo ita retineatur, ut totum Instrumentum <lb></lb>suis urgentibus nutibus ad perpendiculum turris impendeat. </s>

<s>Deinde sit pon­<lb></lb>dus aliquod E (fig. </s>

<s>56) appensum uncinato claviculo, qui fundo tubuli AB <pb xlink:href="020/01/773.jpg" pagenum="216"></pb>fuerit applumbatus. </s>

<s>In Intrumentum autem aequalia spatia RQ, NM, HG, CB, <lb></lb>imis operculi et fundi basibus interiecta eiusdem generis materiam conti­<lb></lb>neant, quae tractioni obsequens rarior fiat. </s>

<s>Quoniam igitur gravitate ponde­<lb></lb><figure id="id.020.01.773.1.jpg" xlink:href="020/01/773/1.jpg"></figure></s></p><p type="caption">

<s>Fig. </s>

<s>56.<lb></lb>ris E tubulus AB deorsum trahitur, materies inclusa <lb></lb>spatio CB rarescat necesse est. </s>

<s>Interea, dum tubulus <lb></lb>AB deorsum fertur, et intervallum CB amplificatur. </s>

<s><lb></lb>Quia vero eadem materies quanto maiorem ad rarita­<lb></lb>tem distrahi debet, tanto maiori vi trahenda est, sit <lb></lb>ponderis E eiusmodi gravitas ut eius vi materies CB <lb></lb>rarior facta non impleat universam cavitatem tubuli <lb></lb>AB, sed dilatetur in grandiusculum spatium CB quale <lb></lb>ostendit altera figura 57. ” <lb></lb><figure id="id.020.01.773.2.jpg" xlink:href="020/01/773/2.jpg"></figure></s></p><p type="caption">

<s>Fig. </s>

<s>57.</s></p><p type="main">

<s>“ His ita se habentibus, postquam desierit rare­<lb></lb>scere materies CB, manus vel quicquid retinet tubulum <lb></lb>FG sentiet vim ponderis E, et quicquid sustinet In­<lb></lb>strumentum FB sustinebit etiam pondus E, quod qui­<lb></lb>dem conatur pessum trahere cylindrum FG, sed frustra, <lb></lb>quia manu vel alio retinaculo retinetur. </s>

<s>Quamobrem <lb></lb>si, omisso tubulo FG manu, comprehenderemus cylin­<lb></lb>drum LM, tum pondus trahens FG ipsum etiam per­<lb></lb>trahet, quia non amplius praepeditur aut retinetur. </s>

<s>Et <lb></lb>quoniam pondus E ita tubulo FG grave est, ut si ex <lb></lb>T penderet; quo igitur modo, cum pondus E depende­<lb></lb>bat ex Z et vasculum FG retinebatur, eius ponderis vi <lb></lb>distrahebatur materies CB; ita nunc retento LM idem <lb></lb>pondus velut appensum ad T distrahet materiem HG <lb></lb>et subsidenti vasculo FG laxabitur spatium HG, ut per­<lb></lb>spicuum est in altera figura. </s>

<s>” </s></p><p type="main">

<s>“ Porro autem, si detento PQ missum facias LM, pondus E cum one­<lb></lb>ret LM, qui a nullo detinetur, deferet illum deorsum, et spatium NM tam <lb></lb>late patescet quam HG et CB, et postremo manubrii S apprehensa estre­<lb></lb>mitate K et relicto PQ, pondus E, perinde quasi in X appensum, vim affe­<lb></lb>ret cylindro PQ, qui cum iam non ut antea inhibeatur descendet et spatium <lb></lb>RQ pari laxitate hiabit ut reliqua NM, HG, CB. </s>

<s>Etsi enim spatia quae su­<lb></lb>binde altiora sunt, subinde etiam ampliora fieri deberent ob maiorem acces­<lb></lb>sionem ponderis ipsius Instrumenti supra pondus appensum E, nos tamen <lb></lb>in praesens Instrumenti pondus non advertimus sed solum inquirimus id <lb></lb>quod provenit ab eppensi ponderis vi. </s>

<s>” </s></p><p type="main">

<s>“ Hactenus vidimus quomodo ab eodem pondere infime appenso aequa­<lb></lb>liter distrahantur aequales quotcumque materiae dissipabilis portiunculae, <lb></lb>sive plurimae sive paucissimae in Instrumento reperiantur. </s>

<s>Modo ponamus <lb></lb>duo Instrumenta consimili modo constructa hoc est aequalibus vasculis, ma­<lb></lb>nubriis et spatiis eadem materia refertis, quae sint.... ” (ibi, c. </s>

<s>74). </s></p><p type="main">

<s>Abbiamo detto di sopra che così fatte proposizioni meccaniche condus-<pb xlink:href="020/01/774.jpg" pagenum="217"></pb>sero l&#039;Aggiunti a trattar delle corde musicali, facilmente trapassando dai <lb></lb>semplici moti a speculare in esse corde il tenore armonico de&#039;loro tremori. </s>

<s><lb></lb>Come corollario infatti di queste e delle altre sopra enunciate deduceva un <lb></lb>argomento da confutar l&#039;errore di alcuni, i quali dicevano che perciò le <lb></lb>corde più lunghe rendono i suoni più gravi, perchè son più fortemente ri­<lb></lb>tese fra&#039;loro sostegni. </s></p><p type="main">

<s>“ Sed vel inde perspicuum fiet longiores cordas graviorem sonum edere, <lb></lb>quia retensiores sint quam breviores, nam corda AB (fig. </s>

<s>58) si duobus cla­<lb></lb><figure id="id.020.01.774.1.jpg" xlink:href="020/01/774/1.jpg"></figure></s></p><p type="caption">

<s>Figura 58.<lb></lb>viculis A, B utroquo extremo religata <lb></lb>atque extensa fuerit sub plano FG, dein­<lb></lb>de autem asserculo LM, ita introacto ut <lb></lb>nulla vi adhibita probe congruat spatio <lb></lb>interiecto intra planum et cordam, si <lb></lb>dirimatur in partes AC, CB, quarum <lb></lb>utravis percussa altera sileat; ex Pro­<lb></lb>positione.... planum est cordas BA, <lb></lb>CA aequaliter esse extensas. </s>

<s>Sed pulsata corda breviori CA acutior exit sonus <lb></lb>quam pulsata longiori BA, ut auritum docet experimentum, non ergo ab <lb></lb>extensionis inaequalitate soni discrimen proficiscitur ” (ibi, c. </s>

<s>68). </s></p><p type="main">

<s>Di qui coglie l&#039;occasione l&#039;Aggiunti di passare addirittura a trattar <lb></lb>de&#039;suoni, pigliando per fondamento quel po&#039;di principio, che ne aveva letto <lb></lb>nel <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> e ch&#039;ei fecondava con singolari osservazioni sue proprie. </s></p><p type="main">

<s>“ Ut ergo id vera ex causa cognoscamur (così ripiglia il costrutto la­<lb></lb>sciato da noi interrotto nelle sopra citate parole) peropportunum fuerit et <lb></lb>generatim quid sonum efficiat et speciatim quid gravem, quid acutum so­<lb></lb>num producat pervidere, quo loco Galilaeum sequar auctorem, qui primus <lb></lb>a condita Philosophia in soni contemplatione veritatis sonum emisit, et su­<lb></lb>per hac re suam aperuit sententiam in auri libratrice <emph type="italics"></emph>Simbella,<emph.end type="italics"></emph.end> seu veri­<lb></lb>tatis staterula, delibatione vel pensitatione.... pag..... Haec autem est il­<lb></lb>lius sententia: <emph type="italics"></emph>Cum nostri timpani auricularis cartilago quaedam tremore <lb></lb>succussu vibratur, id quod sentimus et quo afficimur in eiusmodi tremore <lb></lb>sonum vocitamus, cuius intrinsecus effectus est tremor ille cartilagineus, <lb></lb>sensus autem qui efficitur et quo sonum percipimus appellamus auditum. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Quia vero cartilago illa, quae tremula inhorruit, non ipsa seipsam <lb></lb>commovet, sed potius commota paulatim se quieti componit, adeo ut tre­<lb></lb>mula fiat, extimo aliquo pulsu eget. </s>

<s>Cum ergo externum aliquod corpus <lb></lb>erebra succussatione agitatum cogit ipsam quoque tremescere aurium car­<lb></lb>tilaginem, tunc sonus gignitur. </s>

<s>” </s></p><p type="main">

<s>“ Plerumque autem fit ut trementis corporis concussu conterminus aer, <lb></lb>crispatim et consimili modo illa concussione fluitans, nostrarum aurium <lb></lb>tympanum pulset, et cartilaginem illam sua vi tremulam faciat sonumque <lb></lb>progignat. </s>

<s>” </s></p><p type="main">

<s>“ Hoc tamen semper, ut ego ostendam, undatim crispati tremuleque <lb></lb>contorti aeris appulsu ad aures fit sonus, sed caput ipsum, tremore concus-<pb xlink:href="020/01/775.jpg" pagenum="218"></pb>sum a vi aliqua, concutit ac tremere cogit aurium cartilaginem sonumque <lb></lb>efficit, nam si ori mordicus detineris cordae caput alterum, alterum vero <lb></lb>dextrae digitis cordam hanc percusseris, maiorem hauries sonum quam si <lb></lb>eadem distenta corda inter os et digitum alterius sonuerit, ac tu ad idem <lb></lb>intervallum aures admoveris; quod iccirco accidit quia cordae tremor, prae­<lb></lb>ter aurem, caput ipsum concutit, a quo rursus aurium cartilago in tremo­<lb></lb>rem compellitur et maiorem fert sonum, qua si solo aeris tremore ageretur. </s>

<s>” </s></p><p type="main">

<s>“ Sic etiam, si virga ferrea vinclo quodam lineo adstricta levae dex­<lb></lb>traeque manus digitum bina staminis capita illigent, et geminos digitos sta­<lb></lb>mine religatos in geminas aures tuas inseras, si obseratis hoc modo auribus <lb></lb>virgam ferream in lapidem aut tale quippiam impingas ut resonet, vehe­<lb></lb>mentiorem, occlusis auribus sonitum percipies, quam si reseratis auribus ac­<lb></lb>cipias, quippe virga ferrea cum ictu percussa intremit stamen et iunctos <lb></lb>stamini digitos pari tremore concutit, et vicissim digiti concussi caput et <lb></lb>cartilaginem vehementius tremere cogunt quam si aeris solo tremore illa <lb></lb>adigerentur. </s>

<s>” </s></p><p type="main">

<s>“ Interdum etiam non aeris, sed cuiuscumque fluidi caput ambientis <lb></lb>tremore, fit sonus. </s>

<s>Itaque si caput aquis merseris et lapides manu subter <lb></lb>aquas mutuo affligas, ingentem percipies sonitum: in oleo gravior fortasse <lb></lb>sonitus foret ob eius liquoris lentum gluten et viscidum crassamentum. </s>

<s>” </s></p><p type="main">

<s>“ Plerumque tamen sonus fit ea qua diximus ratione, cum scilicet cor­<lb></lb>pus aliquod durum ac rigens concussum tremit et eius succussatione aer <lb></lb>circumfusus in tenues undulas crispatus, eaque rugosa crispatione orbicu­<lb></lb>latim fusus, ad aures pertingit et cartilaginem illam tremebundo pulsu con­<lb></lb>cutit ac sonum facit. </s>

<s>Hac de causa..... ” (ibi, c. </s>

<s>68, 69). </s></p><p type="main">

<s>A questo punto la scrittura autografa del nostro Autore si rimane in­<lb></lb>terrotta, nè abbiam trovato che ei la riprenda altrove in nessuna parte del <lb></lb>Manoscritto disordinato e confuso. </s>

<s>Con quelle considerazioni in ogni modo <lb></lb>sopra la natura, la generazione e la diffusion del suono ne&#039;varii mezzi so­<lb></lb>disfaceva al primo de&#039;propositi espressi: rimaneva l&#039;altro che si riduceva <lb></lb>per lui a vedere <emph type="italics"></emph>quid gravem quid acutum sonum producat,<emph.end type="italics"></emph.end> e lo fa di­<lb></lb>mostrando una serie di proposizioni, la prima delle quali è in ordine la XII, <lb></lb>dopo quelle meccaniche di cui parlammo di sopra, e che servivano a que­<lb></lb>ste acustiche quasi come di Lemma. </s>

<s>L&#039;enunciato di ciascuna di quelle acu­<lb></lb>stiche Proposizioni dimostrate dall&#039;Aggiunti è il seguente: </s></p><p type="main">

<s><emph type="italics"></emph>“ Propositio XII.<emph.end type="italics"></emph.end> Cordae similes, sed inaequales et inter se aequaliter <lb></lb>extensae, inaequale sonum reddunt, et longior graviorem brevior acutio­<lb></lb>rem ” (ibi, c. </s>

<s>78). </s></p><p type="main">

<s><emph type="italics"></emph>“ Prop. </s>

<s>XIII.<emph.end type="italics"></emph.end> Ex duabus cordis similibus et aequalibus, sed inter se <lb></lb>inaequaliter tensis, remissior gravior, tensior acutius sonat ” (ibi, c. </s>

<s>80). </s></p><p type="main">

<s><emph type="italics"></emph>“ Prop. </s>

<s>XIV.<emph.end type="italics"></emph.end> Si cordae similes, sed crassitudine inaequales, a qui­<lb></lb>busdam ponderibus sint inter se aequaliter extensae, pondera inter se eam­<lb></lb>dem habebunt rationem ac crassitudines vel bases cordarum: nihil autem <lb></lb>refert an aequales vel inaequales longitudine cordae fuerint ” (ibi, c. </s>

<s>81). </s></p><pb xlink:href="020/01/776.jpg" pagenum="219"></pb><p type="main">

<s><emph type="italics"></emph>“ Prop. </s>

<s>XV.<emph.end type="italics"></emph.end> Cordae similes, aequales et aequaliter tensae, quamquam <lb></lb>crassitudine inaequales, sonum efficiunt aeque acutum ” (ibi, c. </s>

<s>82). </s></p><p type="main">

<s><emph type="italics"></emph>“ Prop. </s>

<s>XVI.<emph.end type="italics"></emph.end> Corda crassior, aequalibus viribus extensa ac altera te­<lb></lb>nuior illi similis et aequalis longitudine, graviorem sonum edit ” (ibi, c. </s>

<s>83). </s></p><p type="main">

<s><emph type="italics"></emph>“ Prop. </s>

<s>XVII.<emph.end type="italics"></emph.end> Si cordae fuerint eiusdem longitudinis, crassitudinis, ac <lb></lb>tenacitatis, sed diversi ponderis, hae viribus aequalibus aequaliter extensae <lb></lb>inaequaliter resonabunt, et pondere gravior graviorem etiam sonum reddet ” <lb></lb>(ibi, c. </s>

<s>83 v.). </s></p><p type="main">

<s>Diceva l&#039;Aggiunti, come udimmo nell&#039;introdursi in questa sua tratta­<lb></lb>zione, che e&#039;seguiva Galileo per suo autore, il qual Galileo non aveva an­<lb></lb>cora per verità in Acustica scoperto nulla di nuovo. </s>

<s>Le nuove dottrine, pub­<lb></lb>blicate nel I Dialogo delle Scienze Nuove, l&#039;Aggiunti non fu sventuratamente <lb></lb>a tempo a vederle, e di quì nacque che alcune delle sopra enunciate pro­<lb></lb>posizioni di lui son difettose, e altre peggio son false. </s>

<s>Ei non sa veder quanto <lb></lb>diversamente operi, nell&#039;acutire il suono alle corde, la crassizie dal peso, e <lb></lb>la fallacia, che perciò si asconde nelle due prop. </s>

<s>XV e XVI, lo fa così con­<lb></lb>cludere nel corollario II alla XVII seguente: “ Hinc etiam manifestum est <lb></lb>maius pondus non esse caussam maioris gravitatis soni, quandoquidem vi­<lb></lb>dimus cordam, maioris ponderis quam altera corda aequaliter tensa et aeque <lb></lb>longa, nihilominus modo graviorem modo non graviorem illius sono sonum <lb></lb>excitare ” (ibi, c. </s>

<s>84 v.). </s></p><p type="main">

<s>La proposizione XIII è consenziente alle dottrine professate da&#039;Filosofi <lb></lb>antichi, e confermate da facilissime esperienze, ma non sa definire l&#039;Ag­<lb></lb>giunti con qual proporzione, e secondo qual legge, vogliano esser propria­<lb></lb>mente cresciute le tensioni. </s>

<s>Ingannato anch&#039;egli dal comune errore che <lb></lb>la forma dell&#039;Ottava sia quella desunta dalla lunghezza, ossia della dupla, <lb></lb>crede che uno strumento incordato, per esempio, di ottone dia il diapa­<lb></lb>son di un altro incordato d&#039;oro, perchè questo metallo è il doppio più <lb></lb>peso di quello, mentre è il vero, secondo Galileo dimostra e confermano i <lb></lb>fatti, che l&#039;incordatura d&#039;oro dà suono non di un&#039;ottava più grave, ma di <lb></lb>circa una quinta. </s>

<s>“ Hinc colligere licet (scrive l&#039;Aggiunti per coroll. </s>

<s>I alla <lb></lb>XVII proposizione) cur aereae et aureae cordae similes et aequales et ae­<lb></lb>qualibus viribus extensae propemodum diapason consonantiam efficiunt. </s>

<s>Cum <lb></lb>enim utraque aequali vi aequaliter propemodum extendatur, et aureum pon­<lb></lb>dus aerei ponderis sit fere duplum, necesse est ut aurea corda duplo tardius <lb></lb>quam aerea se vicissim corrigat et inflectat, seu duplo tardiores tremulae <lb></lb>concussionis peragat vices, ex quo oritur consonantia Diapason ” (ibi, c. </s>

<s>84). </s></p><p type="main">

<s>Gli errori insomma, di che riuscivano infelicemente viziate le proposi­<lb></lb>zioni del nostro Aggiunti, venivano così tutti emendati dalle dottrine gali­<lb></lb>leiane: “ Ma qui, prima di passare più avanti, voglio avvertirvi che delle <lb></lb>tre maniere d&#039;inacutire il suono quella che voi riferite alla sottigliezza della <lb></lb>corda con più verità deve attribuirsi al peso. </s>

<s>Imperocchè l&#039;alterazione presa <lb></lb>dalla grossezza risponde solo quando le corde siano della medesima materia, <lb></lb>e così una minugia, per far l&#039;ottava, deve esser più grossa quattro volte <pb xlink:href="020/01/777.jpg" pagenum="220"></pb>dell&#039;altra pur di minugia, che sia egualmente lunga ed egualmente tirata, <lb></lb>ed una di ottone più grossa quattro volte di un&#039;altra di ottone. </s>

<s>Ma se io <lb></lb>vorrò far l&#039;ottava, con una di ottone ed una di minugia di egual lunghezza <lb></lb>e tensione, non si ha da ingrossar quattro volte ma sì ben farla quattro <lb></lb>volte più grave, sicchè, quanto alla grossezza, questa di metallo non sarà <lb></lb>altrimenti quattro volte più grossa, ma ben quadrupla in gravità, che tal­<lb></lb>volta sarà più sottile che la sua rispondente all&#039;ottava più acuta, che sia di <lb></lb>minugia. </s>

<s>Onde accade che, incordandosi un cimbalo di corde di oro ed un <lb></lb>altro di ottone, se saranno della medesima lunghezza, grossezza e tensione, <lb></lb>per esser l&#039;oro quasi il doppio più grave riuscirà l&#039;accordatura circa una <lb></lb>quinta più grave ” (Alb. </s>

<s>XIII, 105, 6). </s></p><p type="main">

<s>Fu veramente una sventura l&#039;aver trovato l&#039;Aggiunti l&#039;Acustica non <lb></lb>isnebbiata ancora dal sole galileiano, e fu un&#039;altra sventura il non posse­<lb></lb>der Galileo l&#039;acume matematico del suo Discepolo. </s>

<s>Da quelle due virtù con­<lb></lb>giunte sarebbe così per tempo uscita di mezzo a noi la scienza matematica <lb></lb>de&#039;suoni. </s></p><p type="main">

<s>Le proposizioni dell&#039;Aggiunti non hanno certo nè la profondità nè la <lb></lb>finezza di quelle del Taylor, del Newton, o di Daniele Bernoulli, ma un se­<lb></lb>colo prima che fiorissero questi, quando l&#039;analisi era affatto sconosciusta e <lb></lb>così rari erano della matematica applicata alla Fisica gli esempi, chi avrebbe <lb></lb>pensato mai che si potesse matematicamente dimostrar che di due corde la <lb></lb>più lunga rende il suono più grave? </s>

<s>Ciò si teneva da tutti per esperienza, <lb></lb>e nè anco a Galileo passò per la mente che si potesse dimostrare per altra <lb></lb>via. </s>

<s>Eppure vi riuscì l&#039;Aggiunti nella sua XII proposizione, il processo di­<lb></lb>mostrativo della quale, non vogliam terminare il presente capitolo senza tra­<lb></lb>scriverlo ai nostri Lettori, lieti di veder allegati così primaticci in Italia <lb></lb>que&#039;frutti, che si videro poi maturare in terra straniera. </s></p><p type="main">

<s>“ Sint cordae, ut dictum est, longior AB (fig. </s>

<s>59) CD brevior (fig. </s>

<s>60), <lb></lb><figure id="id.020.01.777.1.jpg" xlink:href="020/01/777/1.jpg"></figure></s></p><p type="caption">

<s>Figura 59.<lb></lb>quarum media puncta E,F, ae­<lb></lb>qualibus percussa vel impulsa <lb></lb>viribus, deducta sint ad G, H. </s>

<s><lb></lb>Iam ex superioribus constat li­<lb></lb>neas AGB, CHD et sibi ipsis <lb></lb>et mutuo inter sese esse ae­<lb></lb>qualiter extensas. </s>

<s>Quoniam vero <lb></lb>punctum E pertractum est in G, simulac dempta vi cordam AGB libere <lb></lb>abire sinas, corriget illa sese et recta AEB rursus evadet, et quanta fuit vis <lb></lb><figure id="id.020.01.777.2.jpg" xlink:href="020/01/777/2.jpg"></figure></s></p><p type="caption">

<s>Figura 60.<lb></lb>illam extendens in AGB, tantus erit impetus quo se <lb></lb>contrahet in AEB. </s>

<s>Et quia cordae GB singulae par­<lb></lb>tes sunt inter se aequaliter et per consequens ae­<lb></lb>qualibus viribus extensae, iccirco aequalibus singu­<lb></lb>lae viribus contrahentur, et ob id inter contrahendum <lb></lb>aequaliter etiam inter se contrahentur. </s>

<s>” </s></p><p type="main">

<s>“ Praeterea cum GB contrahi nequeat in EB, nisi transmoveatur a po-<pb xlink:href="020/01/778.jpg" pagenum="221"></pb>sitione GB in positionem EB, atque insuper cum GB, dum contrahitur, par­<lb></lb>tes omnes inter sese aequaliter contractas habere debeat; necesse est ut, <lb></lb>dum contrahitur GB in EB, pars cordae G deferatur per perpendiculare GE, <lb></lb>et caeterae omnes partes I, K, L, R, T decurrant lineas quae ab eisdem <lb></lb>punctis ducuntur aequidistantes ipsi GE. </s>

<s>Hac enim sola ratione linea AGB, <lb></lb>partes omnes dum remiserit, habebit aequaliter remissas vel aequaliter <lb></lb>tensas. </s>

<s>” </s></p><p type="main">

<s>“ Rursusque, quoniam cum GB fit contractior et simulac G est in E, <lb></lb>partes omnes inter GB in arctius coactae sunt inter EB, ut igitur GB con­<lb></lb>trahatur in EB, quo tempore pars G delata est in E, per totam GE, eodem <lb></lb>simul pars I deferri debuit per IN ipsi EG parallelam. </s>

<s>Quare, cum sint par­<lb></lb>tes G, I similes et aequales et eodem tempore deferri debeant per spatia inae­<lb></lb>qualia GE, IN, vis deferens partem G ad vim deducentem partem I, ita se <lb></lb>haberi debet ut GE ad IN, et si a quotcumque aliis partibus cordae GB <lb></lb>ductae concipiantur parallelae ipsi EG, huiusmodi parallelae repraesentabunt <lb></lb>vires, quibus eae partes transferuntur in EB. Quamobrem, si ab omnibus <lb></lb>partibus cordae GB ductae intelligantur omnes parallelae lineae ipsi EG, eae <lb></lb>simul acceptae ostendent omnes vires quibus tota GB traducitur in EB. </s>

<s>Quod <lb></lb>si, ex GB dematur pars LB aequalis cordae HD, parallelae omnes, quae ab <lb></lb>omnibus partibus ipsius LB ductae intelligentur, denotarent vires omnes, <lb></lb>quibus tota BL in MB transponeretur. </s>

<s>Quamobrem vires deducentes BG <lb></lb>in BE, ad vires quae tempore eodem transferunt BL in MB, eam habent <lb></lb>rationem quam lineae omnes ductae a punctis omnibus lineae GB, paral­<lb></lb>lelae ipsi GE, ad lineas omnes ductas a punctis omnibus lineae BL aequi­<lb></lb>distantes lineae LM, vel GE. </s>

<s>Sed lineae omnes, quae duci possunt in trian­<lb></lb>gulo GBE parallelae ipsi GE, explent ipsum triangulum GBE, universae <lb></lb>autem parallelae ipsi LM ductae in triangulo LBM conficiunt triangulum <lb></lb>ipsum LBM; ergo vires, quibus eodem tempore GB in BE, ad vires omnes <lb></lb>quibus BL in BM, hoc est HD in DF deducitur, eam habent rationem quam <lb></lb>triangulus GBE ad triangulum LBM, sive triangulum HDF. </s>

<s>Ut ergo eodem <lb></lb>tempore orda BG transferatur in EB, et DH in FD, oportet vim deducen­<lb></lb>tem GB, ad vim quae impellit HD, ita esse, ut triangulus GBE ad trian­<lb></lb>gulum HDF. </s>

<s>Sed cum dimittimus partem G, vis deducens ipsam GB in EB <lb></lb>nihil aliud est quam vis contrahens ipsam GB, quae aequalis est vi exten­<lb></lb>denti eamdem, et amissa parte H vis quae contrahit HD illam transferri co­<lb></lb>git in FD. </s>

<s>Vires igitur deducentes sunt eiusdem momenti ac vires con­<lb></lb>trahentes. </s>

<s>Hae vero sunt aequales viribus extendentibus cordas, quare et <lb></lb>deducentes erunt eisdem aequales. </s>

<s>Sed momentum vis extendentis BG, ad <lb></lb>momentum vis extendentis HD, eam habet rationem quam longitudo EB ad <lb></lb>longitudinem FD, quae subduplicata proportio est eius, quam habet trian­<lb></lb>gulus GBE ad triangulum HDF; ergo vis deducens GB, ad vim deducen­<lb></lb>tem HD, minorem habet rationem quam ut eodem tempore esse posset GB <lb></lb>in EB, et HD in DF translata. </s>

<s>Serius ergo deveniet BG in EB, et quia tam <lb></lb>corda AB quam CD, ad quodvis aliud punctum extensa et inde dimissa, <pb xlink:href="020/01/779.jpg" pagenum="222"></pb>utraque tamen aequalibus intervallis temporum suas obit reciprocationes, <lb></lb>(cuius rei argumentum habemus quod eadem corda quomodocumque pul­<lb></lb>sata eumdem vocis gradum obtinet sibique ipsi unisona semper est) iccirco <lb></lb>corda AB suos excursus ac recursus semper tardius absolvet quam CD, et <lb></lb>ob id eodem tempore minus frequentior ibit ac redibit quam CD. </s>

<s>Sed cor­<lb></lb>dae quae tardius suas expediunt vibrationes graviorem sonum edunt, ut Ga­<lb></lb>lilaeus probat, ergo corda longior AB, licet aequaliter tensa ac CD, nihilo­<lb></lb>minus gravius sonat quam CD, quod probare voluimus ” (ibi, c. </s>

<s>78-80). </s></p><pb xlink:href="020/01/780.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del Magnete<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle più antiche osservazioni e delle prime esperienze fatte intorno al Magnete. </s>

<s>— II. </s>

<s>Di ciò che <lb></lb>a promovere la Filosofia magnetica si cooperò dal Gilberto, dal Sarpi e da Galileo. </s>

<s>— III. </s>

<s>Delle <lb></lb>teorie magnetiche, e di ciò che particolarmente ne pensarono i Filosofi inglesi. </s>

<s>— IV. Dell&#039;ipo­<lb></lb>tesi dei due fiuidi essenziali, e del loro modo di operar sul Magnete, secondo A. </s>

<s>Nardi e se­<lb></lb>condo F. M. Grimaldi. </s>

<s>— V. </s>

<s>Delle variazioni della declinazione magnetica. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Benchè le ragioni altissime dell&#039;armonia musicale rimanessero appresso <lb></lb>i Filosofi antichi, e rimangano tuttavia involte nel mistero ai moderni, lo <lb></lb>studio nonostante possibile a farsene sul soggetto fisico e particolare delle <lb></lb>corde vibranti porgeva qualche pascolo da quietare almeno, se non da sa­<lb></lb>ziare le menti. </s>

<s>Dall&#039;altra parte il più ordinario e consueto modo del diffon­<lb></lb>dersi il suono per l&#039;aria, e l&#039;aver quasi rese visibili le onde aeree nella so­<lb></lb>miglianza coll&#039;onde, che si diffondono circolarmente al largo nell&#039;acqua, <lb></lb>lusingava e lusinga ancora l&#039;intelletto per modo, da non accorgersi o da <lb></lb>passar facilmente sopra a que&#039;tanti misteri, che s&#039;ascondono sotto l&#039;incre­<lb></lb>spato velo di un&#039;onda sonora. </s></p><p type="main">

<s>Ma che sodisfazione rendeva la Scienza alle curiosità de&#039;Filosofi, quando <lb></lb>si mostrarono tanto desiderosi d&#039;intendere la ragione perchè il Magnete ap­<lb></lb>petisca di ricongiungersi al ferro con tanto ardore, e con tanta costanza, <lb></lb>allungato in ago, s&#039;appunti al segno della sua stella? </s>

<s>Migliaia di anni son <lb></lb>già passati dalla scoperta di quel primo fatto, centinaia son passati dall&#039;os-<pb xlink:href="020/01/781.jpg" pagenum="224"></pb>servazione, che del secondo ne fecero i naviganti, e i Filosofi non hanno <lb></lb>saputo far altro che immaginare un alito, il quale esali dalle occulte vene <lb></lb>della pietra misteriosa, alito invisibile in sè e da non avere a rassomigliarlo <lb></lb>a nessun fatto visibile, o a nessun sensibile respiro della silenziosa Natura. </s></p><p type="main">

<s>È perciò che della scienza magnetica pochi si hanno da contare i pro­<lb></lb>gressi dalla Storia, alla quale non molto più resta a dire dopo quelle spe­<lb></lb>culazioni, in che s&#039;assottigliarono i Filosofi intorno alle ragioni degli anti­<lb></lb>chissimi fatti osservati o di qualcun altro de&#039;nuovi scoperti. </s>

<s>Comunque sia, <lb></lb>è riserbato da noi il presente Capitolo a dar breve conto ai lettori di quei <lb></lb>fatti naturali e di quelle filosofiche speculazioni. </s></p><p type="main">

<s>Volere andare a ricercar chi fosse quel così esperto piloto, che si ab­<lb></lb>battè a riconoscere la direzione costante verso cui si volge un ago calami­<lb></lb>tato, oltre che sarebbe un trascorrere troppo fuor de&#039;termini assegnati alla <lb></lb>nostra Storia, non si potrebbe far con sodisfazione de&#039;nostri Lettori, a&#039;quali <lb></lb>non abbiamo da mettere innanzi in tal proposito nessuna certezza di docu­<lb></lb>menti. </s>

<s>Concedendo perciò di buon grado che la verticità dell&#039;ago magne­<lb></lb>tico sia stata osservata infino dagli antichi Cinesi, proseguiamo la più con­<lb></lb>corde opinione, che cioè quell&#039;utilissimo ritrovato fossero i primi in Italia, <lb></lb>e forse in Europa, a metterlo in pratica i naviganti amalfitani. </s>

<s>Quasi tutti <lb></lb>gli scrittori, così antichi come moderni, s&#039;accordano, da qualche particolare <lb></lb>in fuori di non molto rilievo, ad approvare quel che ne lasciò scritto il Porta <lb></lb>nel cap. </s>

<s>XXXII del Libro VII della <emph type="italics"></emph>Magia naturale<emph.end type="italics"></emph.end> dove, dopo aver ma­<lb></lb>gnificati i vantaggi che arrecò l&#039;uso della pisside magnetica all&#039;arte naviga­<lb></lb>toria, così soggiungeva: “ Cuius inventio Itali fuit Amalphi oriundi nostra <lb></lb>Campania, ut a Flavio traditur. </s>

<s>Qui nauticam totam ignorans acum paleae <lb></lb>vel ligno infigebat per transversum, et in lance aqua pleno mergebat acus, <lb></lb>ut natarent libere. </s>

<s>Dein magnetem circum ducendo acus eum sequebantur <lb></lb>quo subtracto, quasi quodam naturali motu, cuspides acu&#039;<gap></gap>m polo arctico ver­<lb></lb>tebantur, eoque invento quiescebant. </s>

<s>Praecognito igitur loco ad sua vota iter <lb></lb>dirigebat ” (Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>316). </s></p><p type="main">

<s>Più completa è la Storia, che in brevi parole ci tratteggia, al cap. </s>

<s>I <lb></lb>del I Libro del suo celebre Trattato, Guglielmo Gilberto: “ In Regno nea­<lb></lb>politano Melphitani omnium primi, ut ferunt, pyxidem instruebant nauticam, <lb></lb>utque Flavius Blondus melphitanus haud perperam gloriari prodit, edocti a <lb></lb>cive quodam Johanne Goia, anno post natum Christum millesimo trecen­<lb></lb>tesimo. </s>

<s>Oppidum illud in Regno neapolitano, non procul a Salerno, iuxta <lb></lb>promontorium Minervae situm, cuius principatu Carolus V Andream Doriam <lb></lb>magnum illum classicum Ducem, propter egregiam navatem operam, dona­<lb></lb>vit. </s>

<s>Atque illa quidem pyxide nihil umquam humanis excogitatum artibus <lb></lb>humano generi profuisse magis constat. </s>

<s>Inventam tamen ante ab aliis, et <lb></lb>in marinis artibus admissam, ex veteribus scriptis, et quibusdam argumen­<lb></lb>tis et coniecturis existimant nonnulli. </s>

<s>Scientia nauticae pyxidulae traducta <lb></lb>videtur in Italiam per Paulum Venetum, qui circa annum MCCLX apud <lb></lb>Chinas artem pyxidis didicit. </s>

<s>Nolim temen Melphitanos tanto honore privari, <pb xlink:href="020/01/782.jpg" pagenum="225"></pb>quod ab iis in mari Mediterraneo primum vulgariter fabricata fuerit ” (De <lb></lb>Magnete, Londini 1600, pag. </s>

<s>4). </s></p><p type="main">

<s>Nelle ristrette navigazioni del nostro Mediterraneo però era difficile, per <lb></lb>non dire affatto impossibile, accorgersi delle variazioni che fa l&#039;ago magne­<lb></lb>tico sotto diversi meridiani e per distanze notabili fra sè divisi. </s>

<s>Ma quando <lb></lb>si prese più alla larga il cammino, quel primo animoso che affidò la nave <lb></lb>allo sconfinato Oceano fu altresì il primo ad accorgersi di quella variazione <lb></lb>e a tenerne conto per dirigere più cautamente il suo viaggio. </s>

<s>Fa testimo­<lb></lb>nianza di ciò Ferdinando Colombo nel cap. </s>

<s>XVII della Vita che scrisse di <lb></lb>suo padre: “ Ma essendo poi corsi oltre cinquanta leghe verso ponente, ai <lb></lb>13 di Settembre (1482) trovò che da prima notte norvestavano le calamite <lb></lb>ne&#039;bussoli per mezza quarta, e l&#039;alba norvestava poco più d&#039;altra mezza, <lb></lb>da che conobbe che l&#039;agucchia non andava a ferire la stella che chiamano <lb></lb>Tramontana, ma un altro punto fisso e invisibile. </s>

<s>La qual varietà fino al­<lb></lb>lora mai non aveva conosciuto alcuno, e però ebbe giusta causa di maravi­<lb></lb>gliarsi di ciò ” (Traduzione di A. Ulloa, Londra 1867, pag. </s>

<s>52). </s></p><p type="main">

<s>Dalla stessa maraviglia fu preso anche l&#039;altro illustre navigatore Gio­<lb></lb>vanni da Empoli, il quale forse ignorava le osservazioni fatte già sul vario <lb></lb>declinar dell&#039;ago al variare de&#039;meridiani, da Cristoforo Colombo. </s>

<s>“ Maravi­<lb></lb>glia mi fu assai, egli scrive, il variar delle Bussole, non solo della nostra <lb></lb>ma di tutte le altre dell&#039;armata, che la fiamma della Tramontana, passando <lb></lb>noi di Ghinea cominciò ad inclinare, secondo è il parere di tutti noi e mas­<lb></lb>sime de&#039;Piloti, una quarta verso Libeccio, et alsì (altresì) passando al Capo <lb></lb>di Buona Speranza per alla Ghinea, a Scirocco. </s>

<s>Io confesso non aver tanto <lb></lb>discorso o di scienza, che io sappia ritrattare se dalla calamita o dal Sole <lb></lb>o dalla regione proceda tal cosa, ma se Iddio, la salute e la tornata mi con­<lb></lb>cede, vedrò se tanto porterà mio ingegno a sapere e tirerollo più al netto <lb></lb>potrò ” (Vieusseux, Archivio Stor. </s>

<s>Append., T. III, pag. </s>

<s>91). </s></p><p type="main">

<s>Ecco il primo Navigatore filosofo, il quale aspetta quiete e tranquillità <lb></lb>per speculare intorno ad un fatto, che il Colombo si stette solamente con­<lb></lb>tento ad osservare. </s>

<s>Se veramente Giovanni attese, tornato in patria, a sodi­<lb></lb>sfare a quel suo scientifico desiderio sarà senza dubbio dovuto tornar di­<lb></lb>giuno e disperato di conseguire il suo intento, come avvenne a un altro <lb></lb>Navigatore filosofo nostro italiano. </s>

<s>Filippo Sassetti, prima d&#039;intraprendere il <lb></lb>suo viaggio per l&#039;Indie, così scriveva il dì 18 di Dicembre 1581 da Lisbona <lb></lb>al fiorentino amico suo Baccio Valori: “ Vedrò nel viaggio la declinazione, <lb></lb>che e&#039;dicono della calamita, come ora sta sopra la linea meridiana, ora se <lb></lb>ne allontana e va discostandosi fino ad un certo che, e poi si viene a rap­<lb></lb>pressare e torna sopra mezzogiorno un&#039;altra volta; cosa che i Portoghesi la <lb></lb>sanno, ma confusamente, sicchè non si può fermare con effetto certo per <lb></lb>andare discorrendo intorno alla cagione ” (Lettere, Milano 1874, pag. </s>

<s>162). </s></p><p type="main">

<s>Voleva dunque il Sassetti far più diligenti osservazioni di quelle che <lb></lb>non avessero fatto i Portoghesi, dietro gli ammaestramenti e gli esempi di <lb></lb>Cristoforo Colombo, e da vero Filosofo, che presente le rette regole del me-<pb xlink:href="020/01/783.jpg" pagenum="226"></pb>todo sperimentale, sopra quelle osservazioni de&#039;fatti specularne le ragioni. </s>

<s><lb></lb>Tali erano le generose speranze concepute dal Sassetti, ma tornando nel <lb></lb>Settembre dell&#039;anno dopo (1582) a scrivere allo stesso Valori, così gli con­<lb></lb>clude: “ La calamita è uno strano strumento per la sua varietà, della quale <lb></lb>è difficil cosa trovare la causa. </s>

<s>Nè anche la minima parte degli accidenti si <lb></lb>conoscono, volgendosi in certi luoghi a Tramontana direttamente, in altri <lb></lb>va da Tramontana a Greco fino a 14 gradi di tutta la circonferenza del­<lb></lb>l&#039;Orizzonte. </s>

<s>Altre volte va verso Maestro e fa tutte queste differenze a grado <lb></lb>a grado, càmminando da Levante a Ponente ed anche da Mezzogiorno a Tra­<lb></lb>montana ” (ivi, pag. </s>

<s>182). </s></p><p type="main">

<s>Sei anni dopo di aver per ripetute esperienze osservato ne&#039;suoi viaggi <lb></lb>orientali il vario declinare dell&#039;ago, scrive il Sassetti da Coccino a Lorenzo <lb></lb>Giacomini a Firenze, discutendo sopra una spiegazione che, del misterioso <lb></lb>fatto del così variamente declinare la Calamita, proponeva un tal Lupicino. <lb></lb></s>

<s>“ Ho bene inteso, scrive il nostro Fiorentino viaggiatore, con molto contento <lb></lb>l&#039;effetto che fa la Calamita avvicinandosi i navili all&#039;Elba. </s>

<s>Vorrei sapere io <lb></lb>che effetti ella faccia a coloro che si avvicinano al Polo, cioè che vanno in <lb></lb>que&#039;paesi freddissimi, perchè l&#039;avvertimento del Lupicino dà per ragione <lb></lb>del volgersi in alcuna parte più che in un&#039;altra, la posizione della medesima <lb></lb>pietra in.... parte del Globo terrestre, cosa che noi possiamo credere, <lb></lb>perchè se si va dintorno ad alcuno oriolo con un pezzo di Calamita, ella <lb></lb>inebria l&#039;ago in maniera che la punta della lancetta si volge ora a Levante, <lb></lb>per calamitato ch&#039;e&#039;sia, ora a Ponente, ed ora a Mezzogiorno conforme alla <lb></lb>posizione della calamita che gli sta presso. </s>

<s>Ma in tanta distanza di paese <lb></lb>quanta può essere da questi monti non saputi fino al Capo di Buona Spe­<lb></lb>ranza, che sono per lo meno cento gradi di latitudine, variato il mezzo che <lb></lb>ha ad essere il veicolo di questa virtù da tante piagge e tanti venti e tante <lb></lb>e sì diverse costituzioni di aria, io non posso inclinare a far causa efficiente <lb></lb>di questo moto questa simpatia che è tra que&#039;monti e l&#039;ago calamitato. </s>

<s>Ag­<lb></lb>giugnete che ogni pezzo di calamita ha il suo sito di mezzogiorno e tra­<lb></lb>montana, e ciascuna parte tira la parte dell&#039;ago che è calamitato con esso, <lb></lb>cioè la parte di Tramontana della Calamita tira l&#039;ago per la lancetta della <lb></lb>freccia, e la parte di Mezzogiorno tira l&#039;ago dalla parte opposta alla lancetta. </s>

<s><lb></lb>Ora questi monti, che si suppongono sotto e presso alla Tramontana risguar­<lb></lb>dano la nostra Bussola con la parte di Mezzogiorno, in maniera che ella <lb></lb>avrebbe a tirare quella parte dell&#039;ago, che è opposta alla lancetta, e non la <lb></lb>lancetta che è calamitata con la parte opposta di Tramontana; argomento <lb></lb>che mi pare insolubile, e quanto a me inclinerei a mescolarci qualche virtù <lb></lb>celeste, quale ella si fosse ” (ivi, pag. </s>

<s>337, 38). </s></p><p type="main">

<s>Attendendo al significato di queste parole del Sassetti si rileva come, <lb></lb>speculando sopra le ragioni addotte dal Lupicino, egli avesse fatto ricerca <lb></lb>di riscontrare la nuova teoria proposta col fatto di ciò che avviene all&#039;ago, <lb></lb>avvicinandosi i vascelli all&#039;isola ferrifera dell&#039;Elba, e sembrerebbe che le <lb></lb>osservazioni fatte da&#039;marinari in proposito, e riferite al Sassetti, confermas-<pb xlink:href="020/01/784.jpg" pagenum="227"></pb>sero l&#039;opinione del Lupicino, che cioè avvicinandosi a quell&#039;Isola fosse tro­<lb></lb>vato l&#039;ago deviare notabilmente dalla direzione sua prima. </s>

<s>Questo era anzi <lb></lb>senza dubbio tale argomento da favorire il pensier di coloro i quali ricono­<lb></lb>scevano le ragioni di quella deviazione da&#039;ferriferi monti incogniti collocati <lb></lb>verso il polo Boreale. </s></p><p type="main">

<s>L&#039;avvertimento che il Sassetti dice essere stato dato dal Lupicino, au­<lb></lb>tore oscuro, era stato ridotto a teoria dal Fracastoro, teoria che il Gilberto <lb></lb>rifiuta, come il Sassetti stesso l&#039;aveva già rifiutata, dicendo esser ciò con­<lb></lb>trario a quel che si osserva di fatto. </s>

<s>“ Reiicienda est vulgaris illa recentio­<lb></lb>rum opinio de montibus magneticis, aut rupe aliqua magnetica aut polo <lb></lb>phantastico a polo mundi distante, quibus motus pyxidis aut versorii com­<lb></lb>poneretur. </s>

<s>Quam opinionem Fracastorius, ab aliis ante inventam ipse coluit <lb></lb>et auxit, omnino tamen cum experimentis non consentit. </s>

<s>Nam ad propor­<lb></lb>tionem et aequalitatem geometricam in variis locis per mare, per terras va­<lb></lb>riationis punctum mutaretur in Eurum aut occidentem semperque polum <lb></lb>magneticum versorium observaret, sed experientia docet nullum certum <lb></lb>esse polum aut terminum Tellure pro variatione fixum ” (De Magnete cit., <lb></lb>pag. </s>

<s>152) </s></p><p type="main">

<s>Cita anche il Gilberto il fatto dell&#039;isola dell&#039;Elba, ma le osservazioni sem­<lb></lb>brano aver risposto al Filosofo inglese tutto al contrario di quel che fu ri­<lb></lb>ferito al Navigator fiorentino, imperocchè servesi l&#039;Autor <emph type="italics"></emph>De Magnete<emph.end type="italics"></emph.end> di <lb></lb>quelle stesse osservazioni a dimostrare e a confermare il suo asserto: <emph type="italics"></emph>Insula <lb></lb>in Oceano variationem non mutat.<emph.end type="italics"></emph.end> Ecco le parole proprie del Gilberto, che <lb></lb>fanno a questo proposito: “ Quod de Ilva insula mirantur nonnulli, quae <lb></lb>licet magnetum ferax sit, tamen versorium sive nautica pyxidula nullam fa­<lb></lb>cit in illam peculiarem inclinationem cum prope navigia in Thyrreno pelago <lb></lb>feruntur, ut iam ostensa causa, sufficere posset, ita etiam hae causae pu­<lb></lb>tandae sunt quod virtus magneticorum minorum ex se parum aut nihil extra <lb></lb>sua metalla extendatur ” (ibi, pag. </s>

<s>161). </s></p><p type="main">

<s>Quest&#039;ultimo argomento del Gilberto si riduceva infine a quello del no­<lb></lb>stro Sassetti, il quale però non ebbe il coraggio di filosofare più oltre, e <lb></lb>atterrito dalle tante difficoltà, che gli si paravano innanzi, finì per risolvere <lb></lb>l&#039;astruso problema, come il Cardano, il Ficino, lo Scaligero, ricorrendo ai <lb></lb>superni influssi celesti. </s></p><p type="main">

<s>Fra&#039;viaggiatori filosofi, che rivolsero l&#039;occhio e la mente al misterioso <lb></lb>fatto della declinazione magnetica, non è a tacer di Giovan Francesco Sa­<lb></lb>gredo, il quale così scriveva da Aleppo in una sua lettera diretta a Galileo: <lb></lb>“ Ho fatto l&#039;osservazione della Calamita, la quale certissimamente qui de­<lb></lb>clina sette gradi e mezzo verso maestro, tanto che da Venezia a qui la dif­<lb></lb>ferenza sarebbe di quindici: ne vada V. S. investigando la ragione ” (Alb. </s>

<s><lb></lb>VIII, 50) persuaso che dovesse riuscir d&#039;intendere a Galileo quel che non <lb></lb>era potuto riuscire a nessun altro, non eccettuato lo stesso grande Gilberto. </s></p><p type="main">

<s>E anche prima di averne avuto l&#039;invito dal gentiluomo veneziano avrà, <lb></lb>per sua propria curiosità, Galileo investigata la ragione dì quel vario decli-<pb xlink:href="020/01/785.jpg" pagenum="228"></pb>nar del Versorio magnetico, ma per acuto e forte che si sentisse l&#039;ingegno <lb></lb>troppo sproporzionata ritrovava quella sua virtù alla durezza adamantina di <lb></lb>ciò che avevasi a penetrare. </s>

<s>Nè di penetrarvi è a nessuno riuscito ancora <lb></lb>dopo tanti conati, cosicchè la scienza magnetica da questa parte è rimasta <lb></lb>alle prime osservazioni di Cristoforo Colombo, senz&#039;aver fatto progressi. </s></p><p type="main">

<s>Restavano però nella misteriosa pietra d&#039;Ercole altre proprietà da sco­<lb></lb>prire e, trovata chiusa l&#039;una delle vie, si tentò di progredire per le altre, <lb></lb>tanto che della sua propria Filosofia non mancasse il Magnete. </s>

<s>Dettero mano <lb></lb>a coltivar la nuova scienza, fra noi, il Cardano e lo Scaligero, e con più <lb></lb>senno d&#039;ambedue il Fracastoro, ma primo ad abbandonare i giochi della <lb></lb>fantasia e a seguir le regole del Metodo sperimentale par che sia stato il <lb></lb>Sarpi, le speculazioni del quale e l&#039;esperienze, che lo condussero a non po­<lb></lb>che e assai notabili scoperte, furono ridotte come in ordine di Trattato dal <lb></lb>Porta e inserite a comporre il VII Libro della Magia Naturale. </s></p><p type="main">

<s>Premesse a quello stesso libro l&#039;Autore una prefazioncella, nella quale <lb></lb>fra le altre si leggono le seguenti parole: “ Venetiis eidem studio invigi­<lb></lb>lantem cognovimus R. M. </s>

<s>Paulum venetum Ordinis Servorum tunc provin­<lb></lb>cialem, nunc dignissimum procuratorem, a quo aliqua didicisse non solum <lb></lb>fateri non erubescimus, sed gloriamur, quum eo doctiorem subtilioremque <lb></lb>quotquot adhuc videre contigerit neminem cognoverimus, natum ad Enci­<lb></lb>clopediam, non tantum Venetae urbis et Italiae sed orbis splendor et or­<lb></lb>namentum ” (Editio cit., pag. </s>

<s>287). </s></p><p type="main">

<s>Il Gilberto perciò, apparecchiandosi a scrivere il suo celebre Trattato, <lb></lb>trovò nel Porta il solo e unico precursore, di cui fa il seguente giudizio: <lb></lb>“ Novissime Baptista Porta, philosophus non vulgaris, in sua Magia natu­<lb></lb>rali Librum septimum fecit condum et promum mirabilium Magnetis, sed <lb></lb>pauca illa de magneticis novit motionibus aut vidit unquam, et nonnulla de <lb></lb>manifestis viribus quae, vel ipse a R. M. </s>

<s>Paulo veneto didicit, vel suis vi­<lb></lb>giliis deprompsit, non ita bene inventa et observata sunt, sed falsissimis <lb></lb>experimentis scatent ” (De Magnete cit., pag. </s>

<s>6) </s></p><p type="main">

<s>Il giudizio, che fa qui del Porta il Gilberto, a noi sembra per verità <lb></lb>troppo severo, perchè, se non c&#039;inganniamo, ha quel VII Libro qualità pro­<lb></lb>prie, che lo distinguono sopra gli altri, e tali in ogni modo da non meri­<lb></lb>tarsi di essere accolto in fascio con essi sotto il titolo di Magia, divenuto <lb></lb>oramai meritamente obbrobrioso. </s>

<s>Non si vuol disputare qual parte abbia <lb></lb>avuto l&#039;Autore in compor quel primo Trattato di Filosofia magnetica, e quale <lb></lb>il Sarpi; noi crediamo però che da que&#039;giochetti in fuori, immaginati spesso <lb></lb>scapestratamente per dar pascolo agli sfaccendati e a&#039;curiosi, tutto quel che <lb></lb>v&#039;ha di Fisica sperimentale propriamente appartenga al Sarpi. </s></p><p type="main">

<s>Quel fatto osservato già infin dagli antichi, e di cui fa tra gli altri men­<lb></lb>zione anche S. </s>

<s>Agostino nella <emph type="italics"></emph>Città di Dio,<emph.end type="italics"></emph.end> il fatto cioè che il Magnete at­<lb></lb>trae il ferro o altro simile Magnete, anche attraverso a una tavola di legno, <lb></lb>a una carta, a una tela, a una lamina di qualunque altro metallo che non <lb></lb>sia ferro o mescolato con ferro, dà occasione al Porta di pensare alla danza <pb xlink:href="020/01/786.jpg" pagenum="229"></pb>degli aghi, o, per accrescer lo spettacolo, di figurine di cartone infilate in <lb></lb>quegli aghi; danza magicamente governata dall&#039;invisibile Magnete, che si <lb></lb>muove nascosto sotto una tavola. </s>

<s>Ma il Sarpi dà in persona dello Scrittore <lb></lb>le prime descrizioni di due esperienze, che dimostrano il magnetizzamento <lb></lb>per influenza e quello che può chiamarsi irraggiamento magnetico. </s></p><p type="main">

<s>L&#039;esperienza del magnetizzamento per influenza ecco in che modo ci <lb></lb>vien descritta: “ Alia enim dote lapis idem apud nos commendandus venit, <lb></lb>nam cum alium lapidem apprehendit, non solum eum pertinaciter complecti­<lb></lb>tur, sed in eius corpus suarum virium effluvium eructat expuitque, sed is <lb></lb>ubi uberiores vires sibi vindicavit, alium perinde manibus comprehendens, <lb></lb>facultatem eamdem expuit et diffundit; hic tertius eadem ut illa effectus, <lb></lb>undecumque ex proximo, vel longinquo alios rapit, eamdemque virtutem <lb></lb>iaculatur et vibrat, et hic alios, ut reciproco iaculatu, eadem qua tenetur <lb></lb>alios teneat, et ex unoquoque quasi iacula virtutis delibuta in alterum pro­<lb></lb>ruant, et in altum elevati quasi concatenati pendere videntur ” (Magia natur. </s>

<s><lb></lb>cit., pag. </s>

<s>301). </s></p><p type="main">

<s>Col principio del Magnetismo per influenza passa nel capitolo appresso <lb></lb>il Porta a spiegare il fatto curioso di que&#039;capillamenti in che si dirizza la <lb></lb>limatura del ferro, di che sia aspersa una verga o un globo magnetico; espe­<lb></lb>rienza affatto nuova, la quale probabilmente si deve al Sarpi, com&#039;a lui senza <lb></lb>dubbio si deve la teoria di questo, per così dire, irraggiamento magnetico. </s></p><p type="main">

<s>Un&#039;altra notabilissima esperienza è quella che il nostro Autore ci de­<lb></lb>scrive al cap. </s>

<s>XLVII del citato settimo Libro della <emph type="italics"></emph>Magia<emph.end type="italics"></emph.end> con queste pa­<lb></lb>role: “ Ferream scobem si in papyrum convolutam posuerimus, quomodo <lb></lb>seplassarii efformari solent in conum, Magnetem ei propius admoverimus, <lb></lb>tota simul universa scobs eamdem vim recipit ac longum trahit ferrum ei­<lb></lb>que vim conciliat, ut integro ferro. </s>

<s>At si scobem agitabis et iterum papyro <lb></lb>impones, vis illa confunditur et disperditur et nil operatur ” (ibi, pag. </s>

<s>324). <lb></lb>Questa stessa esperienza la troviamo citata, senza che nessuno faccia men­<lb></lb>zione di chi prima la istituì e la descrisse, da&#039;due più insigni Autori della <lb></lb>Filosofia magnetica, il Gilberto e il Grimaldi, per servirsene ambedue a con­<lb></lb>fermare le loro speculate magnetiche teorie. </s>

<s>Il primo infatti la cita nel ca­<lb></lb>pitolo XXIII, libro II, del suo Trattato per dimostrare in che modo, am­<lb></lb>messo che tutto insieme il Globo terrestre sia un gran Magnete, <emph type="italics"></emph>terrarum <lb></lb>fundamenta connectuntur, coniunguntur, ferruminantur<emph.end type="italics"></emph.end> (De Magn. </s>

<s>cit, <lb></lb>pag. </s>

<s>91). Il secondo se ne serve per dimostrare, come tra poco si vedrà <lb></lb>meglio, che la virtù magnetica dipende da un certo orientamento moleco­<lb></lb>lare che, turbato, guasta e dissolve la virtù stessa. </s></p><p type="main">

<s>Questi fatti, e altri simili che si potrebbero aggiungere, sembrano a noi <lb></lb>sufficienti a giustificare il nostro asserto parerci cioè troppo severo il giu­<lb></lb>dizio, che il Gilberto faceva del suo predecessore nella Scienza magnetica, <lb></lb>Giovan Batista Porta. </s>

<s>Che non tutti gli sperimenti descritti dal nostro Fi­<lb></lb>sico napoletano siano esatti, questo lo concediamo facilmente, comprendendo <lb></lb>assai bene che non poteva non esser così per qualche fretta, che nello spe-<pb xlink:href="020/01/787.jpg" pagenum="230"></pb>rimentare ebbe il Sarpi, e per non aver sempre il Porta appresa la verità <lb></lb>de&#039;veduti o riferiti esperimenti. </s>

<s>Ma se si bada bene allo spirito, che in dar <lb></lb>quel giudizio informava l&#039;animo del Filosofo inglese, non sarà difficile il ri­<lb></lb>trovar che, secondo lui, il gran difetto del Porta consisteva in non aver sa­<lb></lb>puto investigar l&#039;universal ragione de&#039;moti magnetici, e nell&#039;avere ammesso <lb></lb>un fluido invisibile come causa di quegli stessi occulti moti. </s></p><p type="main">

<s>Per quel che riguarda la prima parte di così fatti principii dottrinali <lb></lb>sopra cui, quasi come sopra fondamento si posa la Filosofia magnetica, po­<lb></lb>teva senza dubbio il Gilberto vantarsi di aver superato il Porta, o il Sarpi <lb></lb>che voglia dirsi, ma, quanto all&#039;altra parte, il Gilberto riman di gran lunga <lb></lb>inferiore ai due nostri Italiani, essendo stati essi i primi che, proscrivendo <lb></lb>quelle insignificanti parole di simpatia e di antipatia, introdussero i fluidi <lb></lb>magnetici per ispiegarne gli occulti e maravigliosi effetti della natura. </s></p><p type="main">

<s>Il Gilberto è nemico de&#039;fluidi corporei: la virtù magnetica egli vorrebbe <lb></lb>quasi ridurla a una proprietà metafisica, per cui vagheggiò le idee di Ta­<lb></lb>lete Milesio e dello Scaligero, che alla pietra magnetica concessero un&#039;anima. <lb></lb></s>

<s>“ Non est igitur corporeum quod defluit a Magnete, aut quod ferrum in­<lb></lb>greditur .... sed ille est, ne mundus rueret, concentus, partium nempe glo­<lb></lb>borum mundi perfectarum et homogenearum ad totum analogia.... Quare <lb></lb>in tam admirabili effectu et stupendo, ab aliis naturis diverso, vigore insito, <lb></lb>Thaletis Milesii non absurda admodum opinio, nec vehemens delirium Sca­<lb></lb>ligeri censura, quia animam Magneti concessit ” (ibi, pag. </s>

<s>67, 68). Ma la <lb></lb>Filosofia moderna ha condannato oramai l&#039;opinion del Gìlberto per assurda <lb></lb>o almeno per immaginaria, ed ha accolta l&#039;ipotesi de&#039;fluidi introdotta già <lb></lb>dal Sarpi e dal Porta, e sopra questa ipotesi ha posato anzi il fondamento <lb></lb>al grande edifizio della nuova scienza magnetico-elettrica. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;aver ridotto il Gilberto i varii e così apparentemente discordi moti <lb></lb>magnetici a una causa unica universale, è senza dubbio il precipuo e mas­<lb></lb>simo merito della sua <emph type="italics"></emph>Fisiologia nuova del Magnete.<emph.end type="italics"></emph.end> “ Io sommamente <lb></lb>laudo, scriveva Galileo, ammiro e invidio questo Autore per essergli caduto <lb></lb>in mente concetto tanto stupendo circa a cosa maneggiata da infiniti inge­<lb></lb>gni sublimi, nè da alcuno avvertita. </s>

<s>Parmi anco degno di grandissima laude <lb></lb>per le molte nuove e vere osservazioni fatte da lui, in vergogna di tanti <lb></lb>autori mendaci e vani ” (Alb. </s>

<s>I, 439). </s></p><p type="main">

<s>Il concetto tanto stupendo, che Galileo ammira e invidia al Gilberto, è <lb></lb>che il Globo terrestre sia una gran calamita e che un globo di calamita sia <lb></lb>una piccola Terra. </s>

<s>Mario Guiducci, in una sua Lezione accademica, com­<lb></lb>pendia in così belle ed eleganti parole lo svolgimento che fa di quel con­<lb></lb>cetto l&#039;Autore nel celeberrimo libro <emph type="italics"></emph>De Magnete,<emph.end type="italics"></emph.end> che i nostri Lettori con-<pb xlink:href="020/01/788.jpg" pagenum="231"></pb>sentiranno volentieri si lasci libertà di parlare intorno a così importante <lb></lb>soggetto storico all&#039;eloquentissimo discepolo di Galileo. </s></p><p type="main">

<s>“ Ma perchè lungo sarebbe, dice egli a&#039;suoi Uditori, e per avventura <lb></lb>noioso l&#039;addurre tutte le ragioni e i discorsi, onde a così affermare si mosse <lb></lb>questo grand&#039;uomo, però al suo Libro rimettendo chiunque più chiara e <lb></lb>squisita contezza bramasse in tal materia, mi basterà solo, per non passarmi <lb></lb>affatto digiuno in conclusione così nobile e cotanto lontana dai pareri popo­<lb></lb>lari e comuni, rappresentarvi in generale la maniera, colla quale procede e <lb></lb>discorre questo Filosofo, e secondariamente, di secento e più esperienze ma­<lb></lb>ravigliose, colle quali e&#039;và confermando il suo intento, addurne due o tre <lb></lb>delle più notabili. </s>

<s>Il modo dunque con cui procede il Gilberto è questo. </s>

<s><lb></lb>Dopo d&#039;aver diligentemente e minutamente osservato varie e diverse pro­<lb></lb>prietà d&#039;un piccol Globo di calamita; dopo d&#039;avere esattamente considerato <lb></lb>con quali forze e con quali ordinate e determinate regole vada movendo e <lb></lb>disponendo il ferro posato sopra il suo convesso; dopo d&#039;avere scoperta ed <lb></lb>esaminata la maravigliosa disposizione della sua virtù variamente per le varie <lb></lb>sue parti disposta, e finalmente notata la perpetua inclinazione che ha di <lb></lb>conformarsi con infallibile regola alla posizione e sito dell&#039;Universo; passa <lb></lb>alla considerazione del gran Globo terrestre. </s>

<s>E non avendo perdonato nè a <lb></lb>fatica nè a diligenza nè a spesa niuna, va rincontrando minutamente tutte <lb></lb>le medesime proprietà, inclinazione, disposizione e virtù ed il tutto così ag­<lb></lb>giustatamente e a capello rispondere, che con molta ragione chiama egli <lb></lb><emph type="italics"></emph>Terrella<emph.end type="italics"></emph.end> il piccol globo di calamita, siccome <emph type="italics"></emph>Gran calamita<emph.end type="italics"></emph.end> il globo terre­<lb></lb>stre, non riconoscendo in effetto tra essi altra differenza che di grandezza. </s>

<s>” </s></p><p type="main">

<s>“ Quanto al secondo, fra le molte e sensate prove, per confermazione <lb></lb>di tal verità, osserva il Gilberto in qualsivoglia piccola palla di calamita due <lb></lb>principali punti, diametralmente tra loro opposti, e segnalati di propria virtù, <lb></lb>i quali dispongono e indirizzano il globo conforme alla situazione e posi­<lb></lb>zione dell&#039;Universo; uno de&#039;quali perpetuamente si rivolge a settentrione, <lb></lb>l&#039;altro a mezzogiorno. </s>

<s>E questi, per la loro conformità co&#039;poli del mondo, <lb></lb>chiama egli poli della calamita. </s>

<s>E siccome ugualmente remoto dall&#039;uno e <lb></lb>dall&#039;altro polo della Terra è da Cosmografi assegnato il circolo equinoziale; <lb></lb>così ancora tra questi due poli magnetici dimostra il Gilberto ritrovarsi il <lb></lb>suo equatore di sito e d&#039;operazione altresì corrispondente all&#039;equinoziale della <lb></lb>gran Terra. </s>

<s>” </s></p><p type="main">

<s>“ Ma per venire a maggior particolarità, l&#039;esperienza ci mostra che, se <lb></lb>si toccherà colla punta d&#039;uno stile di ferro la palla di Calamita in alcun <lb></lb>de&#039;detti poli, v. </s>

<s>g. </s>

<s>nel settentrionale, si conferisce a tal ferro una virtù, me­<lb></lb>diante la quale, o sospeso da un sottil filo o posato sull&#039;acqua, sopra una <lb></lb>tavoletta di suvero o in altra guisa lasciato in libertà e indifferenza a rivol­<lb></lb>gersi verso qualunque parte, rivolge subito a settentrione la cuspide che è <lb></lb>stata toccata. </s>

<s>E la medesima, presentata al polo australe della calamita, tosto <lb></lb>ne vien respinta e indietro scacciata. </s>

<s>Il medesimo effetto si vede per l&#039;ap­<lb></lb>punto accader nei ferri, che hanno avuto per lungo tempo una continuata <pb xlink:href="020/01/789.jpg" pagenum="232"></pb>postura di riguardare con alcuno de&#039;loro termini o verso Borea o verso Au­<lb></lb>stro, i quali acquistano l&#039;istessa virtù dal Gilberto chiamata <emph type="italics"></emph>verticità<emph.end type="italics"></emph.end> d&#039;in­<lb></lb>dirizzarsi a quella medesima plaga, ove han rimirato per lungo tempo, siccome <lb></lb>parimente di rivolgersi addietro e d&#039;esser ributtati dalla contraria ed opposta. </s>

<s>” </s></p><p type="main">

<s>“ Nè paia ad alcuno incredibile che il globo terrestre abbia facoltà di <lb></lb>calamitare i ferri e di conferire ad essi questa medesima verticità, poichè <lb></lb>la Calamita stessa non altronde trae questa proprietà d&#039;indirizzarsi determi­<lb></lb>natamente con una sua parte all&#039;uno con l&#039;altra all&#039;opposto polo, che dalla <lb></lb>situazione o postura, che per gran tempo ebbe nella sua miniera, imperoc­<lb></lb>chè la lunga assuefazione a un determinato sito si converte in natura ” (Lez. </s>

<s><lb></lb>accad. </s>

<s>premesse alle Rime di M. Bonarroti, Firenze 1863, pag. </s>

<s>CXXV, VI). </s></p><p type="main">

<s>Questa nuova e stupenda teoria della verticità per assuefazione vien <lb></lb>confermata da un fatto che il Gilberto dice di avere appreso dalla lettura <lb></lb>di un libro scritto da maestro Filippo Costa da Mantova, il qual fatto è che <lb></lb>una staffa di ferro, la quale da lungo tempo serviva a sostenere le pietre <lb></lb>del campanile alla Chiesa di S. Agostino, essendosi torta e portatasi al fab­<lb></lb>bro ferraio per raddirizzarla, fu dall&#039;artefice trovato così per caso che at­<lb></lb>traeva il ferro come la Calamita. </s>

<s>Ma la prova diretta di questa verticità la <lb></lb>desume l&#039;Autor <emph type="italics"></emph>De Magnete<emph.end type="italics"></emph.end> dal fatto che, messo un ferro nella fucina e <lb></lb>poi battutolo sull&#039;incudine, avendo cura di tenerlo rivolto in direzione co­<lb></lb>stante da Borea ad Ostro, nel raffreddarsi, acquista la virtù, come la Cala­<lb></lb>mita stessa, di dirigersi al Polo (Lib. </s>

<s>III, cap. </s>

<s>XII, pag. </s>

<s>139-42). </s></p><p type="main">

<s>Gli encomii dati all&#039;opera del Gilberto, da Galileo e dai discepoli di lui <lb></lb>rappresentati in Mario Guiducci, sono informati dalla coscienza del vero e <lb></lb>come usciti da gente, che ha meditato sulle dottrine della Fisiologia del Ma­<lb></lb>gnete, e ne ha saputo trarre profitto all&#039;ingegno. </s>

<s>Non così può dirsi de&#039;giu­<lb></lb>dizi enfatici di alcuni moderni, i quali, quando si metton dietro ad Autori <lb></lb>antichi, ne parlano quasi sempre senz&#039;averli mai letti. </s>

<s>Ci serva per esem­<lb></lb>pio di ciò l&#039;Humboldt, il quale, nel Tomo II del suo celebre <emph type="italics"></emph>Cosmo,<emph.end type="italics"></emph.end> encomia <lb></lb>la Fisiologia nuova del Magnete come l&#039;opera più ingegnosa e importante <lb></lb>che sia stata mai scritta intorno alle teorie magnetoelettriche, soggiugendo <lb></lb>essere stata opinion del Gilberto che il Magnetismo e l&#039;Elettricità sieno due <lb></lb>diverse emanazioni di una medesima forza della materia, ond&#039;è ch&#039;ei fa sog­<lb></lb>getto d&#039;ambedue insieme alla sua trattazione (Traduz. </s>

<s>di V. Uberti, Na­<lb></lb>poli 1850, pag. </s>

<s>438). Ora basta leggere solamente il principio del Cap. </s>

<s>II <lb></lb>del secondo libro <emph type="italics"></emph>De Magnete<emph.end type="italics"></emph.end> per sentir come il Gilberto ridasi di coloro <lb></lb>che l&#039;attrazion dell&#039;ambra rassomigliavano a quella del Magnete, mostrando <lb></lb>com&#039;ei sien rimasti ingannati dall&#039;apparenza. </s>

<s>“ Nam in aliis corporibus, <lb></lb>egli così propriamente si esprime, aliter quam in Magnete attrahendi etiam <lb></lb>vis conspicua videtur, quaemadmodum in Succino, de quo nonnulla prius <lb></lb>dicenda sunt, ut qualis illa corporum applicatio, et quam diversa a magne­<lb></lb>ticis actionibus et aliena sit, insciis adhuc mortalibus, qui illam inclinatio­<lb></lb>nem attractionem esse putant et cum magneticis coitionibus conferunt, ap­<lb></lb>pareat ” (ibi, pag. </s>

<s>47). </s></p><pb xlink:href="020/01/790.jpg" pagenum="233"></pb><p type="main">

<s>L&#039;ammirazione sincera, che Galileo prese delle nuove speculazioni ma­<lb></lb>gnetiche del Gilberto, non poteva non accendere in lui il desiderio di rivolger <lb></lb>la mente a coltivar quegli studii, a&#039;quali aveva l&#039;arguto Britanno aperto un <lb></lb>così largo campo, e che prometteva d&#039;esser di ritrovati nuovi tanto fecondo. </s>

<s><lb></lb>E chi sa quali sensi ridestasse quel libro nell&#039;animo del Sarpi, che solen­<lb></lb>nemente sentivasi proclamare ivi per primo istitutore de&#039;magnetici esperi­<lb></lb>menti e si trovava in persona del Porta accusato per quelle pagine con ra­<lb></lb>gioni, che non apparivano vere al giudizio degli imparziali. </s></p><p type="main">

<s>È naturale perciò che critici acuti e saggiatori finissimi della bontà degli <lb></lb>argomenti sperimentali promossi dal Filosofo inglese, fossero i due sommi <lb></lb>nostri Italiani Galileo e il Sarpi, ed è cosa naturalissima che soggetto a&#039;loro <lb></lb>commerci scientifici dovessero fare anco queste nuove magnetiche questioni. </s>

<s><lb></lb>Era infatti da non bene ancora interamente due anni stata pubblicata in <lb></lb>Londra la Fisiologia magnetica del Gilberto, e il Sarpi, sotto il dì 2 Settem­<lb></lb>bre 1602, così incomincia una sua lettera da Venezia indirizzata a Padova <lb></lb>a Galileo: “ Poichè li 25 miglia, per quanto siamo distanti m&#039;impedisce il <lb></lb>discorrere con V. S., cosa che desidero sopra tutte le altre, voglio tentare <lb></lb>di farlo con intermedio delle lettere, e al presente, nel proposito ch&#039;inco­<lb></lb>minciai trattare con esso lei, quando l&#039;altro giorno fummo insieme, della <lb></lb>inclinazione della calamita con l&#039;orizzonte ” (Lettere, Firenze 1863, Vol. </s>

<s>I, <lb></lb>pag. </s>

<s>7, 8). L&#039;inclinazione dell&#039;ago, che faceva il soggetto del colloquio e del <lb></lb>carteggio passato fra due grandi uomini, è uno de&#039;movimenti della Cala­<lb></lb>mita, che Galileo, verso la fine della III Giornata de&#039;Massimi Sistemi, dice <lb></lb>essere stato <emph type="italics"></emph>nuovamente scoperto dal Gilberto<emph.end type="italics"></emph.end> (Alb. </s>

<s>I, 445). È il vero però <lb></lb>che non si fa il Gilberto nuovo scopritore della <emph type="italics"></emph>inclinazione<emph.end type="italics"></emph.end> dell&#039;ago, chia­<lb></lb>mata da lui col comun nome di <emph type="italics"></emph>Declinazione,<emph.end type="italics"></emph.end> ma ne fa autore Roberto <lb></lb>Normann, di cui così scrive sulla fine del cap. </s>

<s>I del primo libro, dopo averlo <lb></lb>annoverato fra gl&#039;inventori di nuovi strumenti nautici: “ Atque hic est ille <lb></lb>Robertus Normannus, navita peritus et ingeniosus artifex, qui primum de­<lb></lb>clinationem magnetici ferri invenit ” (De Magn. </s>

<s>cit., pag. </s>

<s>7, 8). </s></p><p type="main">

<s>Ai moti dell&#039;inclinazione dell&#039;ago consacra il Gilberto tutto il suo li­<lb></lb>bro V, che perciò egli intitola <emph type="italics"></emph>De declinatione.<emph.end type="italics"></emph.end> Sull&#039;argomento stesso, di <lb></lb>che tratta l&#039;Autore in questo suo V libro, s&#039;intrattiene il soggetto della ci­<lb></lb>tata lettera del Sarpi a Galileo, la qual lettera parve prima all&#039;Alberi e poi <lb></lb>al Polidori tanto oscura. </s>

<s>Ed è veramente tale, ma l&#039;oscurità dipende in gran <lb></lb>parte dal non essersi curati i due egregi uomini di commentarla col testo <lb></lb>gilbertiano, a cui forse non sospettaron nemmeno che avesse relazione, e <lb></lb>ad ambedue in ogni modo troppo faceva difetto la scienza necessaria a ca­<lb></lb>pir ciò che in quella oscura pagina si trattava. </s></p><p type="main">

<s>Incomincia dunque il Filosofo inglese nel cap. </s>

<s>I a descrivere lo stru­<lb></lb>mento inclinatorio, e dopo avere insegnato il modo di costruirlo così sog­<lb></lb>giunge: “ Cum in aliis magneticis motionibus telluris et lapidis iusta <lb></lb>convenientia sit et manifeste sensibus nostris apparens consensus per de­<lb></lb>monstrationes nostras; ita in hac declinatione globi terrestris cum Magnete, <pb xlink:href="020/01/791.jpg" pagenum="234"></pb>certa et perspicua est concordantia. </s>

<s>Huius tanti et tamdiu omnibus morta­<lb></lb>libus incogniti effectus talis causa certa et verissima existit ” (ibi, pag. </s>

<s>187). </s></p><p type="main">

<s>Al Sarpi però sembrava di vederci tutt&#039;altro che certezza, per cui scri­<lb></lb>veva: “ Non veggo come e a che fine, nè quali parti o quale vogli situare. </s>

<s><lb></lb>Ma egli come ha trovato il suo modo? </s>

<s>Per esperienza o per ragione? </s>

<s>Non <lb></lb>per esperienza, perchè, o con la terra, e questo ricercherebbe viaggio re­<lb></lb>golato per una quarta. </s>

<s>Non con la terrella, perchè si ricerca che il Versorio <lb></lb>non abbia sensibile proporzione con la terrella, acciò nell&#039;istesso luoco sii <lb></lb>il centro e la cuspide: altrimenti non ha fatto niente. </s>

<s>Non mi par manco <lb></lb>che per ragione, imperocchè bisogna render causa della descrizione di quei <lb></lb>cerchi, che lui chiama <emph type="italics"></emph>conversionis,<emph.end type="italics"></emph.end> che nella piccola designazione (non <emph type="italics"></emph>di­<lb></lb>chiarazione,<emph.end type="italics"></emph.end> come interpetra il Polidori, perchè <emph type="italics"></emph>disegnazione<emph.end type="italics"></emph.end> o <emph type="italics"></emph>designa­<lb></lb>zione<emph.end type="italics"></emph.end> è la traduzione della parola <emph type="italics"></emph>diagramma<emph.end type="italics"></emph.end> usata dal Gilberto) ne de­<lb></lb>scrive tre ” (Lett. </s>

<s>cit., pag. </s>

<s>8, 9). </s></p><p type="main">

<s>Le parole che seguono appresso a queste nella tanto oscura Lettera del <lb></lb>Sarpi possono essere facilmente illustrate dalla <emph type="italics"></emph>piccola designazione,<emph.end type="italics"></emph.end> come <lb></lb>il Sarpi stesso la chiamava, o diagramma, come la chiamava il Gilberto, o <lb></lb>figura, come comunemente si chiama da noi, intercalata nel testo a pag. </s>

<s>198 <lb></lb>della citata edizion del Gilberto, e anche insieme dall&#039;altra più grande de­<lb></lb>signazione, o diagramma o figura interfogliata ivi tra pag. </s>

<s>200 e pag. </s>

<s>201. <lb></lb>Ma molto meglio delle figure gioveranno a interpetrar le parole del Sarpi <lb></lb>le parole proprie con che il Gilberto stesso incomincia il capitolo VIII. “ In <lb></lb>superiore diagrammate ad corpus telluris vel terrellae circulus conversionum <lb></lb>et circulus declinationum coaptantur, cum primo, ultimo, et medio arcu con­<lb></lb>versionum et declinationum. </s>

<s>Nunc a quinta quoque parte arcus illius qui <lb></lb>conversionis arcus omnes terminat, quique in 99 partes aequales dividi <lb></lb>subintelligitur, arcus ducuntur ad polum, et a quinto quolibet gradu arcus <lb></lb>terminantis quadrantis declinationum, quadrantes ducuntur ad centrum, et <lb></lb>simul ducit linea spiralis declinationem in omni latitudine, quadrantis mo­<lb></lb>bilis adminiculo, indicans ” (De Magnete cit., pag. </s>

<s>200). </s></p><p type="main">

<s>Delle quali parole del Gilberto, ripigliando il Sarpi il costrutto, così se­<lb></lb>guita nella sopra citata lettera a scrivere a Galileo: “ Della spirale non ho <lb></lb>difficoltà alcuna, ma è un bel genere di elica, generandosi di due moti cir­<lb></lb>colari. </s>

<s>Prego V. S. che abbia un poco di considerazione sopra le mie diffi­<lb></lb>coltà, e supplisca al mancamento del mio Autore, il quale ha lasciate le <lb></lb>cause delle più oscure cose che siano. </s>

<s>Almeno avesse detto come ne è ve­<lb></lb>nuto in cognizione! Appresso, perchè desidero far isperienza di questa in­<lb></lb>clinazione, per levarmi la fatica, prego V. S. scrivermi il modo tenuto in <lb></lb>fare il Versorio, con che li applica li perni, se con fuoco o con colla, e come <lb></lb>e di che materia li fa, e sopra che li appoggia, e insomma ogni particolare, <lb></lb>perchè non vorrei consumar tempo in sperimentar molte cose, poichè ella <lb></lb>ha fatto la fatica ” (Lettere cit., pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Galileo non rispose per lettera al Sarpi, nè direttamente mandò la Bus­<lb></lb>sola di declinazione, ch&#039;egli aveva già costruita, interpetrando la descrizione <pb xlink:href="020/01/792.jpg" pagenum="235"></pb>alquanto monca ed oscura, che ne aveva fatta il Gilberto, e forse miglio­<lb></lb>randone la costruzione, ma glie la spedì per mezzo del Sagredo, a cui com­<lb></lb>mise anche insieme di rispondere alle domande fatte dal padre Maestro <lb></lb>intorno ai dubbii incontrati nel rimeditare il libro V <emph type="italics"></emph>De Magnete.<emph.end type="italics"></emph.end> Il dì <lb></lb>18 Ottobre infatti di quello stesso anno 1602 così il Sagredo incominciava <lb></lb>una sua lettera, che doveva da Venezia recapitare in Padova a Galileo: <lb></lb>“ Ringrazio V. S. Ecc.ma de&#039;ferri. </s>

<s>Darò al P. M. </s>

<s>Paolo il Declinatorio, e <lb></lb>farò l&#039;ambasciata com&#039;ella mi comanda. </s>

<s>Ho provato il Declinatorio al modo <lb></lb>com&#039;ella mi mostrò costì. </s>

<s>L&#039;effetto di star perpendicolare, posto il suo as­<lb></lb>setto sotto la meridiana, m&#039;è riuscito molto bene, e situato sotto il paral­<lb></lb>lelo ho veduto la declinazione, ma sopra il più e meno a me pare che sia <lb></lb>materia da filosofare ” (Campori, Carteggio gal. </s>

<s>ined., Modena 1881, pag. </s>

<s>6). </s></p><p type="main">

<s>Ecco che il Sagredo pure sente come il Sarpi, il bisogno di portare in <lb></lb>queste dottrine un po&#039;di Filosofia, di che pareva essere il lettore lasciato <lb></lb>in difetto dal Gilberto, e tale è pure il sentimento di Galileo, il quale, dopo <lb></lb>d&#039;aver tanto esaltati i meriti del Filosofo inglese e averne ammirato e in­<lb></lb>vidiato lo stupendo concetto, di che è informato il suo libro, così soggiunge: <lb></lb>Quello che avrei desiderato nel Gilberti è che fosse stato un poco maggior <lb></lb>matematico e in particolare ben fondato nella Geometria, la pratica della <lb></lb>quale l&#039;avrebbe reso men risoluto nell&#039;accettare per concludenti dimostra­<lb></lb>zioni quelle ragioni, ch&#039;ei produce per vere cause delle vere conclusioni <lb></lb>da sè osservate. </s>

<s>Le quali ragioni, liberamente parlando, non annodano e <lb></lb>stringono con quelle forze che indubitabilmente debbon fare quelle, che di <lb></lb>conclusioni naturali necessarie ed eterne, si possono addurre ” (Alb. </s>

<s>I, <lb></lb>439, 40). </s></p><p type="main">

<s>Prosegue ivi a dir Galileo di avere speranza che col progresso del tempo <lb></lb>si avesse a perfezionare quella nuova scienza magnetica, per via di altre <lb></lb>nuove osservazioni, e intanto egli stesso avrà cercato, co&#039;suoi proprii stu­<lb></lb>dii e con le sue proprie esperienze, che quella generosa speranza avesse il <lb></lb>desiderato suo effetto. </s>

<s>L&#039;occasione gli si offerse propizia a proposito che, <lb></lb>desiderando il Granduca di fare acquisto di un buon pezzo di calamita ga­<lb></lb>gliarda, egli ne propose il contratto con Giovan Francesco Sagredo che la <lb></lb>possedeva, e il contratto stesso per la sua mediazione ne fu stipulato. </s>

<s>Data <lb></lb>dalla munificenza del Sovrano facoltà a Galileo di poter far uso di questa <lb></lb>pietra calamitica a suo piacere, volle sperimentarne la magnificata virtù, e <lb></lb>tanto seppe aiutare la Natura con l&#039;arte, che giunse a farle sostenere una <lb></lb>libbra di peso sopra quello che sosteneva, essendo in mano del suo primo <lb></lb>padrone. </s>

<s>L&#039;arte usata attorno alla Calamita da Galileo consisteva nella scelta <lb></lb>del ferro del contatto e nella più opportuna disposizione delle parti di lui. </s></p><p type="main">

<s>“ Nè si maravigli V. S. </s>

<s>Illustrissima (scriveva il dì 8 di Febbraio 1608 <lb></lb>a Belisario Vinta) che ci sia bisogno di esperienze e investigazioni per sco­<lb></lb>prir la sua forza, perchè, prima i punti nella pietra, dove la virtù è robu­<lb></lb>stissima, sono due soli poli e questi bisogna con diligenza ritrovare. </s>

<s>Inoltre <lb></lb>la virtù del sostenere non è meno del ferro che della calamita, sicchè non <pb xlink:href="020/01/793.jpg" pagenum="236"></pb>ogni ferro nè di ogni grandezza e figura è ugualmente sostenuto, ma l&#039;ac­<lb></lb>ciaio elaboratissimo e di una particolare figura e grandezza più gagliarda­<lb></lb>mente si attacca. </s>

<s>Inoltre, le armature dei poli, attaccate un poco più qua o <lb></lb>là, possono far gran variazione: e io in questi quattro giorni che l&#039;ho te­<lb></lb>nuta nelle mani, e che mi ci sono occupato intorno, l&#039;ho fatta reggere quasi <lb></lb>una libbra di più di quello, che il padrone della pietra abbia mai veduto <lb></lb>sostenergli, e sono in speranza, facendo io fabbricare alcuni pezzi d&#039;acciaio <lb></lb>finissimo, di ridurla a sostenere ancora molto più ” (Alb. </s>

<s>VI, 46). </s></p><p type="main">

<s>Il dì 4 d&#039;Aprile infatti, tornando a scrivere allo stesso Vinta, gli dice <lb></lb>di aver ridotto la Calamita a sostenere il doppio del suo proprio peso, e <lb></lb>scrivendogli il di 3 Maggio di nuovo annunzia di esser progredito di qual­<lb></lb>che altro poco, riducendo la stessa calamita a sostener qualche cosa più del <lb></lb>doppio. </s>

<s>In questa lettera dice Galileo di aver fatto fabbricare i ferri in forma <lb></lb>di <emph type="italics"></emph>ancorette,<emph.end type="italics"></emph.end> e di qui derivò il nome di <emph type="italics"></emph>ancora,<emph.end type="italics"></emph.end> che si dà tuttavia al ferro <lb></lb>che combacia co&#039;poli dell&#039;armatura. </s>

<s>“ Ho fatto fabbricare questi due ferri <lb></lb>in forma di due ancorette, sì per dar loro qualche forma, come per allu­<lb></lb>dere a quello che forse favolosamente si scrive essersi trovato un pezzo di <lb></lb>calamita sì vasto e robusto, che sosteneva un&#039;ancòra di nave, e sì ancora <lb></lb>per la comodità di queste branche, alle quali si possono andare attaccando <lb></lb>altri diversi pezzetti fino all&#039;ultimo tentativo della sua gagliardezza ” (ivi, <lb></lb>pag. </s>

<s>54, 52). </s></p><p type="main">

<s>In questa stessa lettera Galileo manifesta una sua opinione, ed è che il <lb></lb>medesimo pezzo non sostenga con egual forza in qualunque luogo della <lb></lb>terra, ma che varii d&#039;intensità secondo la latitudine, e ciò desidererebbe egli <lb></lb>che fosse osservato con diligenza. </s>

<s>Arguta ipotesi è questa, la quale se fosse <lb></lb>stata vera avrebbe aggiunto ai tanti servigii prestati dalla Bussola, quello <lb></lb>di ritrovar con grandissima facilità le latitudini geografiche, senz&#039;altro bi­<lb></lb>sogno di ricorrere alle osservazioni celesti. </s></p><p type="main">

<s>Distratto dalle maravigliose scoperte fatte col Canocchiale e tutto im­<lb></lb>merso nelle astronomiche contemplazioni, Galileo non tornò sulla Calamita <lb></lb>se non che dopo diciott&#039;anni, dando effetto alle già concepute speranze di <lb></lb>moltiplicarne la virtù perfezionandone l&#039;armatura. </s>

<s>Scriveva in fatti così il <lb></lb>dì 27 di Giugno 1626, in una sua lettera indirizzata a Cesare Marsigli: “ Io <lb></lb>sono da tre mesi in qua sopra un maneggio ammirabile, che è di moltipli­<lb></lb>plicar con artificio estremamente la virtù della Calamita in sostenere il ferro. </s>

<s><lb></lb>Già sono arrivato a fare che un pezzetto di sei once, che per sua forza na­<lb></lb>turale non sostiene più di un&#039;oncia di ferro, ne sostiene con arte once 150, <lb></lb>e spero di avere a passare ancora a maggior quantità, e ne darò conto a <lb></lb>V. S. come a persona speculativa, e che gusta di simili accidenti, dei quali <lb></lb>io non posso abbastanza stupirmi, mentre veggo farsi tanto arrabbiatamente <lb></lb>una congiunzione con una semplice virtù immateriale, e tanto più mi pre­<lb></lb>gio in questo affare quanto che io veggo che il Gilberto, che tanto si pro­<lb></lb>fondò in questa speculazione e tanto sperimentò, e con tanta diligenza scrisse, <lb></lb>non passò a far che un simil pezzo di calamita, che per sè stesso reggesse <pb xlink:href="020/01/794.jpg" pagenum="237"></pb>non più di un&#039;oncia, con l&#039;artificio poi potesse regger più di once tre, come <lb></lb>si legge nel secondo libro suo <emph type="italics"></emph>De Magnete<emph.end type="italics"></emph.end> al capo 17 ” (ivi, pag. </s>

<s>314). </s></p><p type="main">

<s>A questa lettera risponde il Marsigli ringraziando Galileo dell&#039;onore fat­<lb></lb>togli nell&#039;avergli dato parte delle sue glorie in proposito dello straordinario <lb></lb>augumento della virtù della Calamita “ e tanto più, soggiunge, quanto sen­<lb></lb>tivo predicare per ammirabile l&#039;invenzione di Bartolommeo Sovero svizzero, <lb></lb>il quale si vantava con un cappelletto d&#039;acciaio finissimo sopra una sferetta <lb></lb>di Calamita farle moltiplicare la virtù sessanta volte più dell&#039;innata ” (Cam­<lb></lb>pori, Carteggio cit., pag. </s>

<s>246). </s></p><p type="main">

<s>Quella del Sovero non era dunque un&#039;invenzione sua propria, essen­<lb></lb>dochè i cappelletti di acciaio o i <emph type="italics"></emph>nasi<emph.end type="italics"></emph.end> ferrei, com&#039;ei gli chiama, furono prima <lb></lb>usati per armature dal Gilberto, che così gli descrive: “ Concava lamella <lb></lb>rotunda latitudinis digiti applicatur convexae Magnetis superficiei polari et <lb></lb>artificiose connectitur. </s>

<s>Aut glans ferrea basi in conum obtusum assurgens <lb></lb>excavata paululum et lapidis superficiei coaptata alligatur magneti. </s>

<s>Ferrum <lb></lb>sit optimum acciarum levigatum splendens et aequali. </s>

<s>Tali instrumento Ma­<lb></lb>gnes qui antea tantum uncias 4 ferri sustulit, nunc uncias 12 attollit ” (De <lb></lb>Magn. </s>

<s>cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Ora che il Sovero, usando lo stesso metodo, potesse aver moltiplicata <lb></lb>sessanta volte quella virtù del Magnete che al Gilberto era riuscito appena <lb></lb>di ridurre al triplo, non par credibile. </s>

<s>Galileo perciò trovando difettoso il <lb></lb>metodo delle armature usato dal Gilberto, e pedantescamente imitato dal <lb></lb>Sovero, lo corresse e lo perfezionò coll&#039;aumentar la superficie del contatto, <lb></lb>e così venne giustamente ad acquistarsi il merito di aver egli trovato il modo <lb></lb>d&#039;armar validamente la Calamita. </s>

<s>“ Questa osservazione, egli dice, di spia­<lb></lb>nar la superficie de&#039;ferri che si hanno a toccare, non fu avvertita dal Gil­<lb></lb>berto, anzi egli fa i ferri colmi, sicchè piccolo è il loro contatto, onde av­<lb></lb>viene che minore assai sia la tenacità con la quale essi ferri si attaccano ” <lb></lb>(Alb. </s>

<s>I, 443). </s></p><p type="main">

<s>A una tal pratica di armare la Calamita giunse Galileo, non già per <lb></lb>caso, ma guidatovi dal ragionamento fondato sull&#039;esperienza. </s>

<s>Assicuratosi di <lb></lb>fatto essere le particelle magnetiche nella pietra più rare assai di quelle del <lb></lb>ferro, da ciò ne concludeva che, facendosi toccar ferro con ferro, gl&#039;infiniti <lb></lb>punti dell&#039;uno s&#039;incontrano con gl&#039;infiniti punti dell&#039;altro, sicchè i filamenti <lb></lb>che collegano insieme i due ferri son molti più di quelli che collegano la <lb></lb>calamita col ferro, per essere la sostanza della calamita stessa assai più po­<lb></lb>rosa, e molto meno sincera. </s>

<s>Ond&#039;è ch&#039;ei conclude con sì fatte parole: “ Ap­<lb></lb>plicando la superficie del ferro alla superficie della calamita, le minime par­<lb></lb>ticelle del ferro, benchè continuatissime forse più di quelle di qualsivoglia <lb></lb>altro corpo (siccome ci mostra il lustrarsi egli più di qualsivoglia altra ma­<lb></lb>teria) non tutte, anzi poche, incontrano sincera calamita, ed essendo pochi <lb></lb>i contatti debile è l&#039;attraimento. </s>

<s>Ma perchè l&#039;armatura della Calamita, oltre <lb></lb>al toccar gran parte della sua superficie, si veste anco della virtù delle parti <lb></lb>vicine, ancorchè non tocche, essendo esattamente spianata quella sua faccia <pb xlink:href="020/01/795.jpg" pagenum="238"></pb>alla quale s&#039;applica l&#039;altra pur similmente bene spianata del ferro da esser <lb></lb>sostenuto; il toccamento si fa d&#039;innumerabili minime particelle, se non forse <lb></lb>degl&#039;infiniti punti di amendue le superficie, per lo che l&#039;attaccamento ne <lb></lb>riesce gagliardissimo ” (ivi, pag. </s>

<s>443). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Era nelle generose speranze di Galileo, come fu già accennato di sopra, <lb></lb>che la nuova Scienza magnetica dovesse progredire, non tanto per la sco­<lb></lb>perta di nuovi fatti, quanto per venir confermata con vere e necessarie di­<lb></lb>mostrazicni. </s>

<s>Ecco il punto della gran difficoltà, e dove Galileo sentiva riseder <lb></lb>davvero la vita di quella scienza: dimostrarne le proposizioni concludendole <lb></lb>da veri e necessarii principii. </s>

<s>Benchè fosse ciò, in soggetto fisico, un pre­<lb></lb>tender l&#039;impossibile, il Castelli nondimeno vi si volle provare, e lo fece in <lb></lb>un suo Discorso rimasto inedito e sconosciuto infino a questi ultimi giorni. </s>

<s><lb></lb>Qualche frammento che noi scegliemmo a infiorar la raccolta di <emph type="italics"></emph>Problemi <lb></lb>naturali<emph.end type="italics"></emph.end> stampata in Firenze nel 1874 da Giulio Cesare Sansoni, invogliò <lb></lb>altri a pubblicarlo nella sua integrità, inserendolo nel Tomo XVI del Bul­<lb></lb>lettino di scienze fisiche e matematiche di Roma, fascicolo dell&#039;Ottobre 1883. <lb></lb>Che debba un tal Discorso essere stato scritto dal Castelli nel 1639, s&#039;ar­<lb></lb>gomenta da una lettera di Galileo del 18 Dicembre di quello stesso anno, <lb></lb>nella quale gli dice che stava aspettando con ansietà sue scritture promesse <lb></lb>della Calamita, del terremoto, e dell&#039;origine de&#039;fiumi (Alb. </s>

<s>VII, 242). </s></p><p type="main">

<s>Il Discorso procede ordinatamente con rigoroso metodo geometrico, di­<lb></lb>stinto in proposizioni coll&#039;aggiunta di scolii e di corollarii e colla premessa <lb></lb>di definizioni e di supposti. </s>

<s>Ma a chi domandasse se veramente il Castelli <lb></lb>fosse con questa sua operetta riuscito a colorire le generose speranze di Ga­<lb></lb>lileo, risponderebbe candidamente il Castelli stesso colle seguenti parole: <lb></lb>“ Voglio però, avanti di passare più oltre, significarle qualmente facendo ri­<lb></lb>flessione a questo mio Discorso, ero precipitato in qualche mestizia, poichè, <lb></lb>a dire il vero schiettamente, con questi progressi di sopra spiegati non tro­<lb></lb>vavo d&#039;aver fatto altro che, dopo avermi accomodate alcune cosucce e sup­<lb></lb>posizioni per vere, ero poi trapassato avanti, ma mostrando sempre le me­<lb></lb>desime cose, solamente per modo di dire sotto diverse vedute, le quali poi <lb></lb>in realtà sono le medesime che quelle prime debolezze, come facilmente si <lb></lb>può comprendere ” (Bullettino cit., pag. </s>

<s>17). Nè il giudizio è inspirato dalla <lb></lb>modestia: quella lucida coscienza erasi, caso raro, severamente giudicata da <lb></lb>sè medesima. </s>

<s>Alcuni vorrebbero riconoscer qui come nuova l&#039;esperienza della <lb></lb>limatura del ferro o della calamita pestata, che si dispone in filamenti e <lb></lb>quasi imbarba i due poli della stessa calamita intera; esperienza che si legge <lb></lb>descritta, come vedemmo, tanti anni prima nella Magia Naturale del Porta. </s></p><p type="main">

<s>Aveva il nostro Autore però nel citato Discorso proposta la soluzione <pb xlink:href="020/01/796.jpg" pagenum="239"></pb>di un problema importantissimo e principalissimo in questa scienza nuova, <lb></lb>il qual problema era: come la Calamita potesse operare in distanza e at­<lb></lb>traverso a corpi amagnetici, che vi fossero in mezzo frapposti. </s>

<s>A tale in­<lb></lb>tento egli presupponeva che tutti i corpi, di qualunque natura si fossero, <lb></lb>tenessero nella loro sostanza disseminate particelle di calamita, le quali mo­<lb></lb>bilissime per la loro piccolezza fossero disposte a rivolgersi facilmente per <lb></lb>quel verso, a cui fossero dirette dalla forza del Magnete. </s>

<s>Così fatti corpu­<lb></lb>scoli, disordinatamente disseminati, costituiscono secondo il Castelli i corpi <lb></lb>magnetici, ch&#039;ei chiama di <emph type="italics"></emph>second&#039;ordine.<emph.end type="italics"></emph.end> Presupposte le quali cose “ si <lb></lb>apre, segue a dire l&#039;Autore, spaziosa strada di render la ragione come pare <lb></lb>che la virtù della Calamita penetri in certo modo quasi in istante ogni sorta <lb></lb>di corpo, e che si faccia la sua operazione come in un momento con le altre <lb></lb>calamite e con i ferri senza toccarli, in distanza molto notabile, imperocchè <lb></lb>quando si vedrà v. </s>

<s>g. </s>

<s>che la Calamita operi trapassando il vetro, il legno, <lb></lb>l&#039;argento, ecc., noi possiam dire che i corpuscoli di second&#039;ordine sparsi per <lb></lb>la sostanza de&#039;suddetti corpi, con la presenza della Calamita, subito vengono <lb></lb>ordinati calamiticamente, e però essi, senza introdurre altra penetrazione di <lb></lb>virtù, sono quelli che operano con i loro ordinati toccamenti, e rimossa la <lb></lb>Calamita, ritornando nella loro primiera costituzione, mancano di quella <lb></lb>forza ” (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>Il Grimaldi riprese poi il filo delle idee del Castelli e intessè forse la <lb></lb>più compiuta teoria che si potesse desiderare a que&#039;tempi. </s>

<s>A render conto <lb></lb>di quelle grimaldiane teorie ci porterebbe ora l&#039;ordine del nostro discorso, <lb></lb>ma tanta è l&#039;importanza della presente parte di Storia che giova, invece di <lb></lb>seguir dietro a quell&#039;ordine, risalir su a&#039;primi principii, riferendo ciò che <lb></lb>specularono i Filosofi per ritrovar qualche ragione a&#039;magnetici misteri. </s>

<s>E <lb></lb>perchè non vogliam divagarci in cercar notizie, le quali ci farebbero uscir <lb></lb>de&#039;limiti che ci siamo prescritti, e abbiamo dall&#039;altra parte quelle erudite <lb></lb>notizie compendiate e raccolte dal Gassendo, terrem dietro a ciò ch&#039;egli <lb></lb>scrive nel X libro delle sue Considerazioni su Diogene Laerzio. </s></p><p type="main">

<s>Dop&#039;aver ivi distinto una duplice virtù magnetica, quella di attrarre il <lb></lb>ferro e l&#039;altra di dirigersi al polo “ cum ab antiquis, egli tosto soggiunge, <lb></lb>disquisita causa prioris.... nihil extat tamen de posterioris, sive directricis <lb></lb>causa disputatum.... Recentiores dumtaxat fuere qui hanc edisseruerint, ut <lb></lb>idem Peregrinus opinatus ipsam a coeli polis pendere, et Ficinus nomina­<lb></lb>tim ab Austro, dum Cardanus a cauda Ursae.... Fracastorus a montibus <lb></lb>quibustam magneticis.... et Maurolicus a quadam magnetica insula.... <lb></lb>dum Gulielmus Gilbertus demum et qui illum imitati sunt, ab ipsamet Terra, <lb></lb>quae et ingens Magnes, Magnetem quasi parvam Terram et ferrum ut ipsius <lb></lb>prolem in nativum situm hoc est in Boream Austrumque conformat. </s>

<s>” </s></p><p type="main">

<s>“ Ad quod attinet ad priorem,... Cardanus innuit appetitum quemdam <lb></lb>nutritionis esse quo Magnes ferrum corripiat.... Democritus ad effluxiones <lb></lb>atomorum.... Cohaeret cum istis ex parte Platonis sententia: temetsi enim <lb></lb>ille videatur non satis perspicue se se explicare, ex Plutarchi tamen inter-<pb xlink:href="020/01/797.jpg" pagenum="240"></pb>petratione admisit quoque effluxiones quasdam, a quibus aer Magneti vici­<lb></lb>nus in orbem propulsus, dum redit ad implendum vacuum secum una cor­<lb></lb>ripiat ferrum.... Fracastorus autem cum effluvium quoque atomorum non <lb></lb>abnuat, censet tamen ferri motionem versus Magnetem fieri, non ut vacuum <lb></lb>impediatur, sed ut amotae loculis suis particulae connaturalem obtineant si­<lb></lb>tum, quod dum nituntur, sua quoque subiecta continentia moveunt. </s>

<s>” E <lb></lb>prosegue a dir del Gilberto, e com&#039;egli negasse al Magnete ogni sorta di <lb></lb>effluvi corporei e sostanziali (Lugduni 1675, T. I, pag. </s>

<s>193, 94). </s></p><p type="main">

<s>Venne dopo il Gilberto, tra&#039;Filosofi che fecero più romore, il Cartesio, <lb></lb>il quale, avendo ridotte a XXXIV le Questioni, che si possono fare intorno <lb></lb>al Magnete, prese tutte a risolverle con un&#039;ipotesi sola, dedotta come per <lb></lb>corollario dal suo fantastico sistema. </s>

<s>Egli non solo ammette, contro l&#039;opi­<lb></lb>nion del Gilberto, i magnetici efflussi corporei, ma alle particelle compo­<lb></lb>nenti que&#039;magnetici efflussi assegna la particolar figura cocleare, colle spire, <lb></lb>in quelle che vengon da Borea, in altro verso intorte da quelle che vengono <lb></lb>d&#039;Ostro. </s>

<s>E perchè così fatte particelle, chiamate dal Cartesio <emph type="italics"></emph>Striate,<emph.end type="italics"></emph.end> ve­<lb></lb>nendo dalle regioni celesti attraversan la Terra e n&#039;escon da per tutte le <lb></lb>parti, non c&#039;è pericolo che scambino mai direzione, perchè da Borea, per <lb></lb>esempio, non possono entrar ne&#039;pori aperti se non le particelle, che hanno <lb></lb>le avvitature disposte secondo la madrevite, in che si rigirano da quella <lb></lb>parte gl&#039;interni canaletti, dentro cui fanno quelle stesse particelle striate, <lb></lb>attraverso alla Terra, i loro continui corsi e ricorsi. </s>

<s>“ Ad quarum proprie­<lb></lb>tatum causas intelligendas, proponamus nobis ob oculos Terram.... note­<lb></lb>musque particulas striatas ab australi coeli parte venientes, alio plane modo <lb></lb>intortas esse quam venientes a Boreali, quo fit ut unae aliarum meatus in­<lb></lb>gredi plane non possint. </s>

<s>Notemus etiam australes quidem recta pergere.... <lb></lb>per mediam Terram.... quia meatus, per quos ab una parte ad aliam ve­<lb></lb>nerant, sunt tales ut per ipsos regredi non possint ” (Principia Philosophiae, <lb></lb>Amstelodami 1650, pag. </s>

<s>265). </s></p><p type="main">

<s>Di sì fatte goffaggini si potevano contentare i semplici, ma non sodisfar­<lb></lb>sene i Filosofi, i quali nò nelle finzioni della mente cercav<gap></gap> le cause na­<lb></lb>turali, ma ne&#039;principii matematici e negli sperimenti. </s>

<s>Necessariamente av­<lb></lb>versa alla Filosofia cartesiana era quella che il Newton aveva istituita nella <lb></lb>sua patria, dove dalle teorie sull&#039;attrazione universale si concepì la speranza <lb></lb>di derivar lume a intendere i misteri dell&#039;attrazion del Magnete. </s>

<s>Ma tor­<lb></lb>narono così belle speranze deluse, essendo l&#039;intima causa, per cui le par­<lb></lb>ticelle della materia s&#039;attraggono e si respingono a vicenda, rimasta allo <lb></lb>stesso Newton occulta. </s></p><p type="main">

<s>Non mancò nonostante la nuova Filosofia matematica di rifletter qual­<lb></lb>cuno de&#039;suoi splendidi raggi sulla Filosofia magnetica, la quale parve allora <lb></lb>che ripigliasse in Inghilterra il vigore infusole dal Gilberto, quando più ac­<lb></lb>curate osservazioni confermarono una scoperta fatta parecchi anni prima dal <lb></lb>Gillibrando. </s>

<s>Concorrevano a coltivar quegli studii, insiem col Newton, due <lb></lb>altri valorosi ingegni, l&#039;Hook e l&#039;Halley, che sorgevano in splendida Pleiade <pb xlink:href="020/01/798.jpg" pagenum="241"></pb>sull&#039;orizzonte di Londra, quando in Firenze eran già, dietro il sole di Ga­<lb></lb>lileo, tramontati i numerosi pianeti che gli facevan corona. </s>

<s>Uno solo rima­<lb></lb>neva ancora a consolar della sua luce il vedovo cielo d&#039;Italia, l&#039;astro di <lb></lb>Vincenzio Viviani. </s></p><p type="main">

<s>Vecchio di più che sett&#039;anni si trovava il Viviani a rappresentar la per­<lb></lb>sona dell&#039;ultimo Principe rimasto d&#039;una dinastia già trapassata, e che si <lb></lb>vede sorgere a petto una nuova dominazione straniera. </s>

<s>Altri forse si sarebbe <lb></lb>ritirato in sè stesso a compiacersi delle glorie antiche, non superabili dalle <lb></lb>nuove, e ad ostentare il fasto delle antiquate divise, ma il Discepolo di Ga­<lb></lb>lileo, messo da parte l&#039;orgoglio impotente e dispettoso, compiacevasi mesta­<lb></lb>mente di veder che il buon seme delle dottrine sparso dal suo Maestro, <lb></lb>sfruttato oramai il proprio campo, andasse rigogliose a crescere e a frutti­<lb></lb>ficare in campi vergini, e per piagge remote. </s>

<s>A que&#039;nuovi cultori inglesi <lb></lb>si rivolse con desiderio il vecchio Italiano, chiedendo a loro notizia de&#039;loro <lb></lb>studii, ed essi da Londra corrispondevano ossequiosi con Firenze, quasi <lb></lb>com&#039;aura che ritorna profumata da quel pomario, ch&#039;ella andò a fecondare. </s></p><p type="main">

<s>Il dì 27 Dicembre dell&#039;anno 1695 il Viviani, che aveva sentito dire di <lb></lb>quel fervore di studii con che l&#039;Hook e l&#039;Halley s&#039;erano dati a sperimentare <lb></lb>e a speculare intorno al Magnete, scriveva una lettera a Roberto Southvell, <lb></lb>allora presidente della R. Accademia, per esser particolarmente informato <lb></lb>delle scoperte, delle ipotesi, delle teorie, di tutto insomma che s&#039;era scritto <lb></lb>intorno alla natura e alle proprietà della Calamita. </s>

<s>La mal ferma salute e <lb></lb>l&#039;ufficio non permisero al Southvell di rispondere con sollecitudine, e dopo <lb></lb>otto mesi il Viviani disperava oramai di esser degnato delle desiderate no­<lb></lb>tizie, quando un giorno dell&#039;Agosto del 1696 gli agenti in Firenze di Giu­<lb></lb>seppe Cagnoni, ch&#039;esercitava la mercatura a Londra, portano a casa dello <lb></lb>stesso Viviani e gli consegnano una cassetta approdata pochi giorni prima <lb></lb>a Livorno colla nave <emph type="italics"></emph>Regina coeli<emph.end type="italics"></emph.end> capitanata da Alessandro Polino. </s>

<s>Apre <lb></lb>con cuor trepidante quella cassetta, e vi trova dentro varie carte manoscritte, <lb></lb>due fascicoli e due grossi volumi stampati. </s>

<s>Gli bastò un semplice sguardo <lb></lb>per saper che si contenevano tutte insieme raccolte in que&#039;due gran volumi <lb></lb>le opere matematiche del Wallis, e un&#039;altro semplice sguardo bastò per <lb></lb>capir che que&#039;due fascicoli contenevano due Dissertazioni magnetiche del­<lb></lb>l&#039;Halley. </s></p><p type="main">

<s>Maggior curiosità lo frugava di veder ciò che riferissero quelle carte <lb></lb>manoscritte, per prima delle quali gli venne a mano il Diploma, che lo di­<lb></lb>chiarava socio nuovamente eletto della R. </s>

<s>Accademia di Londra. </s>

<s>Erano in <lb></lb>quella stessa cassetta, insiem col Diploma, accluse due lettere, una di Ric­<lb></lb>cardo Waller, segretario, e un&#039;altra di Giovanni Wallis, sopra la quale il <lb></lb>Viviani, quietato a un tratto l&#039;animo fra quel tumulto di pensieri e di af­<lb></lb>fetti, si tratteneva a leggere ciò che, dopo essersi scusato il celebre Mate­<lb></lb>matico inglese per non ricordarsi di quel che aveva scritto allo stesso Vi­<lb></lb>viani in una lettera andata smarrita, così soggiungeva: “ Quod autem iam <lb></lb>expetis, ut earum exemplar ad te mittam praestare non valeo, quoniam <pb xlink:href="020/01/799.jpg" pagenum="242"></pb>carum exemplar vel apud me non retinui, vel nunc non possum invenire. </s>

<s><lb></lb>Sed neque satis memini quid inibi contineretur praeter officiosam saluta­<lb></lb>tionem meique in te amoris et observantiae testificationem, iustaeque de te <lb></lb>conceptae aestimationis et de Galilaeo tuo, quem ego semper magni aesti­<lb></lb>mavi, et etiam nunc veneror et cui debemus, non modo Cavalierium, Tor­<lb></lb>ricellium, Vivianum aliosque magnos viros, sed et totam quam dicimus no­<lb></lb>vam Philosophiam, quo praelucente, caeteri suas accenderunt faces ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXLVIII, c. </s>

<s>87). </s></p><p type="main">

<s>Restò commosso il buon vecchio alla lettura di queste parole, compia­<lb></lb>cendosi che quegli Inglesi inchinassero così innanzi al suo Galileo la fronte <lb></lb>baldanzosa, e gli pareva che in quel Diploma avessero gli Accademici di <lb></lb>Londra mandato a Firenze a riconoscere i diritti del principato antico della <lb></lb>scienza italiana. </s></p><p type="main">

<s>Ricomposto poi l&#039;animo, seguitò il Viviani a svolgere quelle altre carte <lb></lb>rimaste e lesse in fronte alla prima scritta di propria mano del Southvell: <lb></lb>“ Londini 20 Martii 169 5/6. Sententia excerpta ex authographo Domini Hal­<lb></lb>ley circa Magnetem, pro Domino Viviano conscripta. </s>

<s>” Lesse poi in fronte <lb></lb>a una seconda carta aggiunta e ripiegata con quella prima: “ De Gresham <lb></lb>Colledge a Londres le 9 Mar. </s>

<s>169 5/6. Opinion de Mons.r le D.r Hook tou­<lb></lb>chant le pierre d&#039;Aimant pour Mons.r Viviani. </s>

<s>” </s></p><p type="main">

<s>Le due scritture son, secondo noi, documento così importante di storia, <lb></lb>da non defraudarne della notizia i Lettori, alla maggior parte de&#039;quali non <lb></lb>sarà forse noto questo scientifico commercio ch&#039;ebbero i Colleghi del Newton <lb></lb>coll&#039;ultimo rimasto fra i Discepoli di Galileo. </s></p><p type="main">

<s>“ Authores Philosophiae magneticae quod spectat, scriveva il Southvell, <lb></lb>post Cartesium, non est quod sciam qui rem adeo difficilem aggredi ausus <lb></lb>sit novamve aliquam hypothesim comminisci, etiamsi a multis iam annis <lb></lb>apud eruditos cartesianae illae particulae striatae pro ingenioso figmento po­<lb></lb>tius quam pro vera et adaequata attractionis ac directionis magneticae causa <lb></lb>efficiente merito censeatur. </s>

<s>Latet igitur horum causa inter ardua Philoso­<lb></lb>phiae, qualia sunt causae gravitatis ac particularum materialium cohaesionis <lb></lb>ac mutui coalitus, quae, cum ipsius materiae intimam cognitionem requi­<lb></lb>rere videantur, fortasse prae tenuitate humani ingenii captum nostrum ef­<lb></lb>fugiunt. </s>

<s>” </s></p><p type="main">

<s>“ Gravitatis autem phaenomena explicuit celeberrimus noster Newtonus <lb></lb>ex sola hypothesi quod unaquaeque materiae particula gravis, sit in aliam <lb></lb>gravius particulam pro ratione distantiae ac quantitatis suae, inde demonstra­<lb></lb>vit vires attractionis vel, ut vocat centripetas corporum coelestium a summa <lb></lb>sive mole omnium particularum in illis corporibus collectarum oriri, eique <lb></lb>semper proportionatas esse; cuius quidem inventi veritas per totum mundi <lb></lb>systema elucescit. </s>

<s>Causam autem huius vis congregativae ne coniectura qui­<lb></lb>dem probabili assequi valemus. </s>

<s>Periter si lapis supponamus ex atomis ma­<lb></lb>gneticis similiter positis conflari, quarum qualibet sit axe suo ac polis prae­<lb></lb>dita, totum compositum foret etiam Magnes, qui iunctis viribus traheret <pb xlink:href="020/01/800.jpg" pagenum="243"></pb>secundum axem communem per earum medium tendentem, quo supposito, <lb></lb>plurima solvuntur Magnetis phaenomena alias satis difficilia explicatu. </s>

<s>” </s></p><p type="main">

<s>“ Acus autem magnetica, a quovis Magnete impregnata, in eodem loco <lb></lb>tandem semper acquirit positionem, nisi quod longo temporis intervallo <lb></lb>omnes ubique deviant, gradatim quidem ac regulariter apud nos in Occi­<lb></lb>dentem fertur per unum circiter gradum spatio sexennii, ac in eamdem <lb></lb>semper plagam deflexit per CXV annos, ex quo primum Londini observa­<lb></lb>tum est, quo temporis spatio plus quam XVII gradus continuo motu pro­<lb></lb>cessit. </s>

<s>Olim enim in Ortum XI gradus declinavit, hodie vero prope VII gra­<lb></lb>dus in Occasum, uti assiduis observationibus experimur. </s>

<s>Ac procul dubio <lb></lb>multo ulterius progressura est, antequam stationaria facta, iterum in Ortum <lb></lb>pedem referre incipiat. </s>

<s>Multorum enim saeculorum est periodus, nec nisi <lb></lb>longa et accurata observationum serie enucleanda uti recte observat Vir cla­<lb></lb>rissimus. </s>

<s>” </s></p><p type="main">

<s>“ A centrali vero causa per totum Terrarum orbem operanti, acumque <lb></lb>magneticam ubique locorum simul agitante, hae deflectiones oriuntur, quod <lb></lb>quidem summo studio explicare conatus est Halleus noster duabus Disser­<lb></lb>tationibus in Actis nostris philosophicis ea de re editis. </s>

<s>In priore quatuor <lb></lb>esse polos magneticos contendit, iisque loca in globi superficie designat, ex <lb></lb>quorum viribus varie compositis directionem Acus per totum Orbem gu­<lb></lb>bernari credit. </s>

<s>In posteriori causas varietatis deflectionis inquirit, globum­<lb></lb>que hunc terraqueum concavum supponit incluso vel uno vel forzam pluribus <lb></lb>minoribus globis eodem communi gravitatis centro innixis. </s>

<s>Quemadmodum <lb></lb>videmus Saturnum intra circulum sibi concentricum collocari, atque una <lb></lb>moveri. </s>

<s>Cumque globus interior possit vim Magnetis habere, simulque len­<lb></lb>tissimo motu situs eius respectu interioris possit immutari, hoc modo putat <lb></lb>omnibus totius sistematis magnetici phaenomenis satisfactum iri. </s>

<s>Quo rectius <lb></lb>possis de his hypothesibus iudicium ferre, utramque Dissertationem tibi tra­<lb></lb>smittendam curavi ” (MSS. Gal. </s>

<s>Disc., T. CXXXIV, c. </s>

<s>28). </s></p><p type="main">

<s>L&#039;altra scrittura dell&#039;Hook, come dal titolo riferito di sopra si saranno <lb></lb>accorti i lettori, era dettata in francese, e trovasi inserita a c. </s>

<s>32 del citato <lb></lb>Tomo CXXXIV. </s>

<s>Il nitido carattere e l&#039;accurata ortografia ci fanno presup­<lb></lb>porre che non sia autografa. </s>

<s>Forse il Southvell ne fece, dall&#039;autografo stesso <lb></lb>dell&#039;Hook, far quella copia, perchè riuscisse più comodamente leggibile e <lb></lb>con minor difficoltà ne potess&#039;essere intesa la lingua. </s>

<s>Benchè confessi a più <lb></lb>occasioni il Viviani di non aver gran pratica in tradur dal francese, tradusse <lb></lb>nonostante, a nostro giudizio, assai bene quella scrittura dell&#039;Hook, ond&#039;è <lb></lb>che noi, lasciato l&#039;originale, trascriveremo qui la traduzione italiana fatta <lb></lb>forse per divulgarne fra i discepoli e gli amici la notizia. </s></p><p type="main">

<s>“ Per rispondere alle questioni e domande del saggio signor Viviani in­<lb></lb>torno agli Autori, che hanno scritto sopra la Calamita, loro osservazioni, sco­<lb></lb>perte, ipotesi, teoriche, ecc., non posso al presente dir molto, poichè, per <lb></lb>quanto ho veduto finora nelle scritture e libri trattare della Calamita, io non <lb></lb>trovo cosa alcuna di considerabile per quel che riguarda a nuove scoperte <pb xlink:href="020/01/801.jpg" pagenum="244"></pb>o teoriche appartenenti a questa maravigliosa operazione della Natura, dopo <lb></lb>il Gilberti, se ciò non è nel libro del sig. </s>

<s>Gillibrand, già professore in que­<lb></lb>sto Collegio, il quale nell&#039;anno 1634 scoperse e provò il primo la variazione <lb></lb>della variazione della direzione dell&#039;ago magnetico. </s>

<s>Egli trovò allora in <lb></lb>un luogo poco lontano da Londra la variazione esser circa quattro gradi <lb></lb>verso Oriente, nonostante che un tal sig. </s>

<s>Burrocus, nell&#039;anno 1580, l&#039;avesse <lb></lb>trovata nel medesimo luogo esser tredici gradi e venti minuti verso Oriente, <lb></lb>e che un tal sig. </s>

<s>Gunter, altro professore in questo Collegio, l&#039;anno 1622, <lb></lb>ve l&#039;avesse trovata di sei gradi e tredici minuti, senz&#039;allora immaginarsi che <lb></lb>vi fosse alcuna variazione di variazione, ma attribuendo ciò piuttosto a qual­<lb></lb>che mancamento nelle osservazioni del sig. </s>

<s>Burrocus. </s>

<s>E per questa ragione <lb></lb>il sig. </s>

<s>Gillibrand, facendo comparazione di queste osservazioni con le sue <lb></lb>proprie, suppose il primo e sostenne la variazione della variazione, e pub­<lb></lb>blicò un piccol Trattato, in cui dà ragguaglio delle dette sue osservazioni e <lb></lb>delle sopraddette sue opinioni. </s>

<s>” </s></p><p type="main">

<s>“ L&#039;anno 1657 un tal chiamato il sig. </s>

<s>Bond fece nuove osservazioni, <lb></lb>ch&#039;ei parimente pubblicò in un Trattato di maggior considerazione, e trovò <lb></lb>solamente che l&#039;ago segnava la vera meridiana, senza variar nè verso Oriente <lb></lb>nè verso Occidente. </s>

<s>E dopo il suddetto tempo è stato spesse volte osser­<lb></lb>vato, e da me e da altri signori della Società Reale, che l&#039;ago continua a <lb></lb>variar sempre più verso Occidente, di modo che al presente ell&#039;è qui circa <lb></lb>sette gradi verso Occidente. </s>

<s>” </s></p><p type="main">

<s>“ Si son viste proporre differenti ipotesi per la soluzione di tali appa­<lb></lb>renze, ma io confesso di non aver ancora veduto chi ne abbia dato la so­<lb></lb>disfazione ricercata. </s>

<s>Certo si è che quelle non convengono punto con una <lb></lb>teorica, che io ne feci gran tempo fa, e che io pretendo fra poco di pub­<lb></lb>blicarla, quando le altre occupazioni mi permetteranno il tempo e la libertà <lb></lb>di porla in ordine per farla stampare, e allora io spero di provar con la <lb></lb>sperienza, nell&#039;istesso modo che con le regole della Geometria, tutte le ap­<lb></lb>parenze riguardanti la Calamita state comunemente conosciute fin ad ora, <lb></lb>con le cause probabili, almeno se non vere, e le ragioni che ne possono <lb></lb>essere assegnate. </s>

<s>Questa teoria sarà differente da quante io ne ho vedute, <lb></lb>e sarà una parte di una nuova Teorica della Fisica in generale, di cui ho <lb></lb>anche fatto il concetto differente da tutti gli altri che ho visto, ed il quale, <lb></lb>per quanto io spero, spiegherà la maggior parte delle apparenze e più chia­<lb></lb>ramente di quanti se ne son veduti fin ora. </s>

<s>E per questa ragione io mi ri­<lb></lb>guarderò di fare abortire i miei proprii parti con lo stroppiargli prima di <lb></lb>fargli nascere ” (ivi). </s></p><p type="main">

<s>Se i parti, a&#039;quali accennano queste ultime parole profferite dall&#039;Hook, <lb></lb>veramente sian nati, ce lo dirà qualche erudito Inglese, che meglio di noi <lb></lb>conosca la vita letteraria del suo celebre connazionale: noi crediamo che <lb></lb>fossero anche questi abortiti insiem con tanti altri concepiti da quell&#039;inge­<lb></lb>gno mirabilmente fecondo. </s>

<s>Che cosa insomma aveva il Viviani, circa alla Fi­<lb></lb>losofia magnetica, imparato da quegli Inglesi di nuovo? </s>

<s>Nulla di più di quel <pb xlink:href="020/01/802.jpg" pagenum="245"></pb>che ne aveva scritto il Cartesio alle strane ipotesi del quale potevansi in <lb></lb>certo modo rassomigliare le ipotesi dell&#039;Halley. </s></p><p type="main">

<s>Se qualche cosa di nuovo ci era, e di meglio di quel che fosse uscito <lb></lb>dalla fantasia del Cartesio, era stato consegnato a manoscritti o divulgato in <lb></lb>libri nostrali, a&#039;quali ricorrendo il Viviani avrebbe trovato da sodisfar, quan­<lb></lb>t&#039;era possibile, i suoi desiderii. </s>

<s>È perciò dover nostro render conto ai Let­<lb></lb>tori di quelle ipotesi e di quelle teorie magnetiche ignorate dal Discepolo <lb></lb>di Galileo, benchè fossero state professate in Italia tanti anni prima, che il <lb></lb>Southvell scrivesse essersi innanzi alle grandi difficoltà arretrati gli Accade­<lb></lb>mici suoi Londinesi. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>In quel tempo, presso a poco, che il Cartesio pubblicava i Principii <lb></lb>della Filosofia, il Castelli meditava nel suo Discorso sopra la Calamita. </s>

<s>I di­<lb></lb>fetti del Francese si qualificano in breve dicendo ch&#039;egli è un romanziere <lb></lb>e no un filosofo; i difetti del Nostro si compendiano pure in breve dicendo <lb></lb>che egli trattò del Magnete non da fisico, ma da matematico. </s>

<s>Le teorie fisi­<lb></lb>che del Magnete a noi par che cominciasse a specularle Antonio Nardi in <lb></lb>quelle <emph type="italics"></emph>Scene Accademiche<emph.end type="italics"></emph.end> dove s&#039;ha, con mirabile varietà, tutta insieme e <lb></lb>in un ampio teatro rappresentata l&#039;erudizione e la scienza italiana ai tempi <lb></lb>di Galileo. </s></p><p type="main">

<s>I flussi magnetici, secondo il Nardi, son due: differenti non tanto di <lb></lb>sito e di direzione, ma di qualità, e con essi in gioco spiega, a quel modo <lb></lb>presso a poco che i fisici moderni, la scambievole azione fra due Calamite, <lb></lb>e gli effetti loro naturali. </s>

<s>Principale fra questi effetti è che si attraggono i <lb></lb>poli di nome contrario, ciò che dal Nardi si spiega dicendo che nelle estre­<lb></lb>mità prevalgono i flussi, i quali si diffondono dal centro della Pietra, e per­<lb></lb>ciò a Borea per esempio sograggiungono quelli spirati dalla parte contraria <lb></lb>di Ostro. </s></p><p type="main">

<s>“ Ora il punto sta (dice l&#039;Autore nella Veduta XVIII della Scena IV) <lb></lb>nel cercar l&#039;origine onde avvenga che l&#039;ago verso il suo principio tirato sia <lb></lb>e si raddrizzi sempre più, quanto più al magnetico polo si accosti. </s>

<s>Stima il <lb></lb>Gilberto che dal centro della Calamita si diffonda principalmente la virtù, <lb></lb>e che termini il suo maggiore ne&#039;poli, e quindi procedendo cominci a lan­<lb></lb>guire. </s>

<s>Repugna alcuno e vuole che dai poli diffondasi: quindi cerca render <lb></lb>ragione perchè nell&#039;Equinoziale valido sia il dirigersi e nullo sia l&#039;erigersi. </s>

<s><lb></lb>Per il contrario, nel polo questo si trovi e non quello, e finalmente nelle <lb></lb>altre parti si trovi l&#039;uno e l&#039;altro composto delle proposizioni delle distanze <lb></lb>dai poli; ed altre cose che lungo il riferirle saria. </s>

<s>” </s></p><p type="main">

<s>“ Pensomi che se sia la Calamita ACB (fig. </s>

<s>61) di cui A il polo Bo­<lb></lb>reale, B l&#039;Australe, C il mezzo, non poter essere A principio di guardar <pb xlink:href="020/01/803.jpg" pagenum="246"></pb>Ostro ai ferri che quello tocchino, e niuna forza ivi risiedere, perchè inco­<lb></lb>minciando un empito reale, o eminenziale come nel caso nostro, da un punto, <lb></lb><figure id="id.020.01.803.1.jpg" xlink:href="020/01/803/1.jpg"></figure></s></p><p type="caption">

<s>Figura 61.<lb></lb>è necessario che per arrivare <lb></lb>all&#039;altro termine, nel quale si <lb></lb>finisse di comunicar l&#039;impeto, <lb></lb>si passi per mezzi infiniti e così <lb></lb>il punto A nulla forza otterrà <lb></lb>verso CB. ” </s></p><p type="main">

<s>“ Se dunque ad A s&#039;applichi la punta d&#039;un ago, riceverà la diffusione <lb></lb>valida dal punto C, di maniera che per la comune forma diventeranno un <lb></lb>sol corpo l&#039;ago e la pietra. </s>

<s>E però, supponiamo che in ogni punto dentro <lb></lb>alla Calamita si faccia simile diffusione in retto ed a tale che empia tutta <lb></lb>la sfera della sua attività, con tal ragione che, non come la luce abbia re­<lb></lb>lazione ad un solo principio, ma a due estremi ove concorrono dal centro <lb></lb>due principali linee; quindi nasce che nei punti boreali magnetici preval­<lb></lb>ghino flussi dalla parte opposta. </s>

<s>E però, se spezzeremo la Calamita, vedremo <lb></lb>cambiarsi il modo di comunicar la virtù, ma non già avverrà che la parte, <lb></lb>quale nella Calamita congiunta guardava Ostro, guardi disgiunta Borea, poi­<lb></lb>chè rimane come prima il flusso della virtù sua congiunto col flusso per­<lb></lb>petuo del Magnete universale. </s>

<s>Qui dunque alcuni forse s&#039;ingannano, i quali <lb></lb>vedendo come dal boreale toccamento acquisti l&#039;ago la direzione australe, <lb></lb>non considerano che la virtù si comunica nel punto del toccamento, ma però <lb></lb>non indi procedeva. </s>

<s>” </s></p><p type="main">

<s>“ Ora, non è maraviglia, se avendo l&#039;ago la virtù concepita in una <lb></lb>parte della Pietra dove prevale la opposta diffusione, venga poi a congiun­<lb></lb>gersi allo stesso e simil principio, perchè altrimenti non lo potrebbero in­<lb></lb>sieme unire le contrarie flussioni magnetiche, delle quali il comun termine <lb></lb>è la punta dell&#039;ago, e perchè mescolate sono nel mezzo della Pietra le flus­<lb></lb>sioni, e sincere assai negli estremi; quindi ancora si apre la strada al filo­<lb></lb>sofare intorno alla cagione, perchè negli angoli sia più efficace la calamita <lb></lb>che nel mezzo ” (MSS. Gal. </s>

<s>Disc., T. XX, c. </s>

<s>603). </s></p><p type="main">

<s>Benchè a parole non se ne trovi fatto alcun cenno, si vede nulladimeno <lb></lb>che qui il Nardi tien d&#039;occhio al Gilberto nel Cap. </s>

<s>IV del Libro III <emph type="italics"></emph>De <lb></lb>Magnete,<emph.end type="italics"></emph.end> dove proponesi di risolvere la questione: <emph type="italics"></emph>Cur ferrum tactum <lb></lb>acquirit contrariam verticitatem<emph.end type="italics"></emph.end> (Edit. </s>

<s>cit., pag. </s>

<s>125). E tanto è vero che <lb></lb>intende il nostro a infondere un qualche spirito di Filosofia nelle aride dot­<lb></lb>trine dell&#039;Inglese, che usa il linguaggio medesimo di luì nel trattar della <lb></lb>Calamita, ora segata secondo il parallelo, ossia da un piano perpendicolare <lb></lb>all&#039;asse, ora segata invece secondo il meridiano, ossia da un piano parallelo <lb></lb>allo stesso asse. </s></p><p type="main">

<s>“ Sia la Calamita, prosegue il Nardi, ACB (fig. </s>

<s>prec.) come sopra, e <lb></lb>s&#039;intenda diviso il suo asse in due parti ADE, BED: dico che ADE si riu­<lb></lb>nirà con BED, quando insieme s&#039;accostino, perch&#039;essendo la sezione DE co­<lb></lb>mune all&#039;uno ed all&#039;altro pezzo, la stessa virtù corre e ricorre da B verso A <pb xlink:href="020/01/804.jpg" pagenum="247"></pb>e da A verso B, onde anco A e B si possono congiungere per esser ter­<lb></lb>mini e principii scambievolmente di virtù, che riunirsi tenta per la somi­<lb></lb>glianza del corso. </s>

<s>E sebbene DE, rispetto ad A, riguardi Ostro, rispetto poi <lb></lb>a B riguarda B́orea, e se disgiunto è in ADE australe o in BED boreale, <lb></lb>congiunto poi è comune. </s>

<s>” </s></p><p type="main">

<s>“ Ora se la medesima Pietra si tagli, non secondo il parallelo, ma se­<lb></lb>condo il meridiano, avverrà che soprapposto il pezzo C (fig. </s>

<s>62) al pezzo D <lb></lb><figure id="id.020.01.804.1.jpg" xlink:href="020/01/804/1.jpg"></figure></s></p><p type="caption">

<s>Figura 62.<lb></lb>non si ricongiungeranno nel modo <lb></lb>che stavano prima, ma la parte che <lb></lb>guarderà Borea si volgerà in Ostro, <lb></lb>perchè noi detto abbiamo che l&#039;ago <lb></lb>si volta ad Ostro con la lancetta, <lb></lb>mentre sia posto sopra la Calamita, <lb></lb>per ricongiungersi al suo principio, e lo stesso avvenir forse bisogna nel <lb></lb>caso nostro, perchè, se nel pezzo ACB il punto A prese la virtù congiunto <lb></lb>dal toccamento nel pezzo ADB, dovrebbe ancora disgiunto aspirare allo stesso <lb></lb>toccamento, ed averà forse per tal causa il punto A nella Pietra la propria <lb></lb>sua virtù congiunta a quella dell&#039;opposto polo B, e con ogni punto australe, <lb></lb>d&#039;onde ha il principio ed a cui separata riunir circolarmente si vuole, perchè <lb></lb>la pietra è contenuta da un solo abito che in sè circolarmente ricorre ” (ivi). </s></p><p type="main">

<s>Le teorie magnetiche del Nardi, di cui abbiamo accennato alle princi­<lb></lb>pali, non son certamente compiute, e non sempre derivano da principii o <lb></lb>espressi con chiarezza o definiti con precisione filosofica. </s>

<s>Ciò non compor­<lb></lb>tavasi dall&#039;altra parte, nè era conforme all&#039;indole del suo Libro, il quale <lb></lb>non era un libro di Filosofia, ma una specie di Giornale enciclopedico, come <lb></lb>altra volta dicemmo, e che doveva servir non da face posata sul candelabro <lb></lb>a illuminare le menti, ma da cote percossa in fretta a dare scintille infiam­<lb></lb>matrici dell&#039;esca che ritrovan meglio disposta. </s>

<s>L&#039;esser rimaste quelle pa­<lb></lb>gine occulte, e però il fuoco nella cote stessa latente, impedì che si produ­<lb></lb>cessero que&#039;benefici effetti nelle menti dei lettori, di che sarebbe anche <lb></lb>maggiormente a dolersi, se a supplire al difetto delle Scene del Nardi non <lb></lb>fosse uscito in Italia il Libro <emph type="italics"></emph>De Lumine<emph.end type="italics"></emph.end> del Grimaldi. </s></p><p type="main">

<s>Come c&#039;entri il trattar del Magnete, dove il proposito era di trattar <lb></lb>della luce, potrebbe frugare alcuno di una certa curiosità, la quale poi così <lb></lb>si acquieta in poche parole. </s>

<s>Tanto la luce quanto gli effluvii magnetici erano <lb></lb>da&#039;Filosofi riguardati come qualità accidentali. </s>

<s>Proponendosi perciò il Gri­<lb></lb>maldi di dimostrar che la luce era un essere sostanziale, piglia occasione di <lb></lb>confermare il suo assunto col dimostrar l&#039;essere sostanziale del magnetico <lb></lb>effluvio. </s>

<s>Il pernicioso errore dell&#039;immaterialità di questo effluvio era stato, <lb></lb>come vedemmo, introdotto nella Filosofia magnetica dallo stesso Gilberto, <lb></lb>dall&#039;autorità del quale rimase soggiogato il Castelli, che s&#039;indusse a negare <lb></lb>il principio corporeo alla virtù magnetica dal veder ch&#039;ella, anche attraverso <lb></lb>a qualunque ostacolo che non fosse di ferro, operava in distanza. </s>

<s>Il Gri­<lb></lb>maldi dunque, contro quelle false e ai progressi della Scienza così dannose <pb xlink:href="020/01/805.jpg" pagenum="248"></pb>dottrine, dimostrava la seguente proposizione: “ Si dicatur virtutem a Ma­<lb></lb>gnete diffusam esse aliquid substantiale, per modum tenuissimae expiratio­<lb></lb>nis, multo melius intelliguntur et explicantur experimenta, quibus aliquid <lb></lb>cognoscimus de proprietatibus Magnetis ” (De Lumine, Bononiae 1665, pag. </s>

<s>65). </s></p><p type="main">

<s>Ammesso un tal sostanziale effluvio risolveva il Grimaldi il problema che <lb></lb>restò irresoluto alle mani del Castelli, dicendo che la Calamita opera sul ferro <lb></lb>a distanza attraverso a un&#039;asse di legno, a una lamina di metallo o di ve­<lb></lb>tro, perchè tutti i corpi son porosi e si lascian perciò attraversare ai ma­<lb></lb>gnetici effluvii. </s>

<s>Secondo il nostro Fisico dunque, non consiste la virtù cala­<lb></lb>mitica in qualche forza inconsapevole e immaginaria, come il Castelli stesso <lb></lb>ammetteva, e tanto meno in un principio animale, come stranamente opi­<lb></lb>nava il Gilberto, ma risiede in un fluido essenziale che riempie i pori della <lb></lb>Calamita e scorre con certa direzione segnata dai punti de&#039;poli, cosicchè i <lb></lb>profluvii son due apparentemente diversi, per quella loro direzione diversa, <lb></lb>ma sostanzialmente son della stessa natura. </s>

<s>Il ferro dolce che si calamita <lb></lb>contiene in sè questo fluido magnetico, ma disordinato, e acquista la virtù <lb></lb>calamitica per via di un&#039;orientazione dello stesso fluido che già conteneva, <lb></lb>orientazione indotta dagl&#039;influssi attivi e naturali della Pietra. </s></p><p type="main">

<s>Queste sue teorie le illustrava il Grimaldi e le confermava con le se­<lb></lb>guenti esperienze: Un ferro infocato o battuto perde la sua verticità e la <lb></lb>perde pure un ferro torto, che sia violentemente addirizzato o che venga in <lb></lb>qualunque modo ridotto a una forma diversa da quella sua prima. </s>

<s>“ Ex his <lb></lb>omnibus, prosegue a dire il Grimaldi, duo certissima inferuntur: Primo, <lb></lb>destructionem illam virtutis magneticae in ferro ignito, sive tunso, sive vio­<lb></lb>lenter ut supra inflexo et fricato, tribuendum esse non calori immediate, sed <lb></lb>mutuae dispositioni locali particularum in ferro et alicui pororum perturba­<lb></lb>tioni, hoc est diductioni simul et constrictioni. </s>

<s>Secundo, consequenter virtu­<lb></lb>tem magneticam pendere in sui diffusione, vel permanentia a porositate et <lb></lb>certa cohordinatione particularum in ferro, ac proinde esse corporeum ali­<lb></lb>quod et substantiale effluvium a Magnete trasmissum, aptumque recipi in <lb></lb>ferro et a ferro item expelli, per quamdam partium impressionem ” (ibi, <lb></lb>pag. </s>

<s>66, § 45). </s></p><p type="main">

<s>Che la verticità poi dipenda dall&#039;orientamento delle sferette magnetiche, <lb></lb>il Grimaldi lo prova con questa bella esperienza, fatta già come dicemmo <lb></lb>dal Sarpi e divulgata dal Porta nel cap. </s>

<s>XLVII del suo VII libro della Ma­<lb></lb>gia, e della quale si servì pure il Gilberto a provar nel cap. </s>

<s>XXIII del Li­<lb></lb>bro II la proposizione: “ Magnetica vis motum facit ad unitatem et unita <lb></lb>firmiter connectit ” (pag. </s>

<s>90); esperienza la quale consiste nel mostrar che <lb></lb>un cartoccio di foglio o un tubo di argento ripieni di limatura di ferro ma­<lb></lb>gnetizzata, subito perdon la loro verticità, che le particelle ferree vengano <lb></lb>disordinate col votarli e poi riempirli di nuovo. </s>

<s>“ Et ratio est, soggiunge il <lb></lb>Grimaldi, quia singula ramenta ferri habent quidem adhuc suam longitudi­<lb></lb>nem, secundum quam in illis disposita fuerat virtus magnetica, sed non or­<lb></lb>dinantur similiter omnia ut prius, immo temere huc illuc conversa, vel non <pb xlink:href="020/01/806.jpg" pagenum="249"></pb>possunt simul et per modum unius magnetici exercere virtutem quae in <lb></lb>illis remanet, vel tandem inter se conflictando mutua contrarietate illam vi­<lb></lb>cissim extingunt ” (ibi, pag. </s>

<s>68, § 47). </s></p><p type="main">

<s>In che modo si dispensi questo sostanziale magnetico effluvio, è vera­<lb></lb>mente cosa mirabile e non potendosene avere esperienza per mezzo dei sensi <lb></lb>è da confessare ingenuamente, dice il Grimaldi, che non se ne può dare <lb></lb>certezza di scienza. </s>

<s>Nè per questo, egli prosegue ivi a dire, è da ricorrere <lb></lb>alle qualità occulte che non son poi altro che un nome, ma è da ripensar <lb></lb>tra le fisiche, qual possa essere la più probabile ragione. </s>

<s>“ Itaque dicimus <lb></lb>valde probabile esse quod ab utroque polo terrestri versus alterum et ver­<lb></lb>sus totam superficiem telluris continue fluxus accurrat aliquid substantiale <lb></lb>valde tenuis, ob eam potissimum rationem qua Sol perpetuo attenuat ma­<lb></lb>gis medias partes ipsius Telluris positas intra Zonam torridam, quarum sci­<lb></lb>licet resolutio melius compensari non potest, quam per continuum affluxum <lb></lb>vicinarum. </s>

<s>Coepto autem praedicto affluxu vicinarum, facile est subinde aliae <lb></lb>atque aliac etiam remotiores occurrant ” (ibi, pag. </s>

<s>73, § 61). </s></p><p type="main">

<s>Coll&#039;ipotesi di questi due fluidi sostanziali, che corrono e ricorrono dai <lb></lb>due poli, spiega mirabilmente il Grimaldi i fatti osservati nel Magnete prima <lb></lb>di lui e quelli altresì ch&#039;egli stesso scoprì come nuovi. </s>

<s>Fra questi è nota­<lb></lb>bile il fatto della polarità magnetica, che spontaneamente s&#039;induce in una <lb></lb>sottile e lunga verga di ferro tenuta un istante in direzione perpendicolare <lb></lb>al piano dell&#039;orizzonte; fatto che fu poi osservato dal Boyle e da altri, e <lb></lb>del quale all&#039;ultimo il Musschenbroek, nella Dissertazion <emph type="italics"></emph>De Magnete,<emph.end type="italics"></emph.end> fece <lb></lb>soggetto a&#039;suoi diligentissimi esperimenti. </s>

<s>“ Observandum est, dice il no­<lb></lb>stro Grimaldi, virgam ferream uniformis crassitici et rectitudinis, et quae <lb></lb>nunquam a Magnete fuerit excitata, si sursum erecta vel parum omnino in­<lb></lb>clinata a situ perpendiculari applicetur Versorio parte sui infima, ita allicere <lb></lb>Versorium nostris hisce regionibus borealibus, ut ad eam accurrat extre­<lb></lb>mum illud Versorii quod solet converti ad Austrum. </s>

<s>At si virga eadem ap­<lb></lb>plicetur Versorio, parte sui suprema, accurrere extremum, quod de se con­<lb></lb>vertitur ad Boream, quaecumque sit ea pars virgae, quae modo ponitur in <lb></lb>imo, modo in summo ” (ibi, pag. </s>

<s>69, § 51). </s></p><p type="main">

<s>Chi in conclusione medita attentamente sopra que&#039;LXVI paragrafi, che <lb></lb>il Grimaldi aggiunse come appendice alla proposizione sua VI <emph type="italics"></emph>De lumine,<emph.end type="italics"></emph.end><lb></lb>si persuade con facilità che ivi, delle esperienze del Gilberto si trova per la <lb></lb>prima volta suggerita una qualche probabile ragione. </s>

<s>Se l&#039;Inglese dette la <lb></lb>Fisiologia del Magnete, si può dir che il Nostro ne abbia data la Filosofia, <lb></lb>che è quella in sostanza professata universalmente nelle scuole infino a que­<lb></lb>sti ultimi tempi. </s>

<s>L&#039;ipotesi de&#039;due fluidi essenziali infatti, immaginata prima <lb></lb>dal Nardi, e illustrata poi dal Grimaldi con tanta varietà di sottili argomenti, <lb></lb>è quella ch&#039;è tuttavia rimasta a spiegare in qualche modo le attrazioni, le <lb></lb>direzioni e tutti gli altri magnetici misteri. </s></p><p type="main">

<s>Quella ipotesi del flusso che si dirige da un polo verso il polo opposto <lb></lb>per ritornarvi con circolo perpetuo, d&#039;onde sono, secondo il Nardi e il Gri-<pb xlink:href="020/01/807.jpg" pagenum="250"></pb>maldi, rapiti e volti i corpi magnetici, come i galleggianti nell&#039;acqua son <lb></lb>rapiti e volti nella direzione della corrente, si potrebbe credere a prima vi­<lb></lb>sta che fosse suggerita ai Nostri dall&#039;ipotesi cartesiana. </s>

<s>Ma le particelle <lb></lb>striate operanti come le punte de&#039;succhielli, e che discese dalle regioni ete­<lb></lb>ree ronzano intorno al nostro globo e v&#039;entrano ed escono, come da&#039;loro <lb></lb>nidi le vespe, presentano delle virtù magnetiche altra immagine da quel­<lb></lb>l&#039;aura invisibile e spiritosa, che secondo il Nardi circola nella Pietra e che <lb></lb>ha origine, secondo il Grimaldi, dall&#039;azione del Sole sopra la Terra. </s>

<s>Sublime <lb></lb>concetto è questo con cui il nostro Filosofo bolognese aprì, a veder le cor­<lb></lb>renti elettro-magnetiche sulla superficie terrestre, gli occhi ad alcuni cele­<lb></lb>brati fisici de&#039;nostri giorni. </s></p><p type="main">

<s>Chi ritorni ora col pensiero sopra le cose narrate non può non mara­<lb></lb>vigliarsi come il Viviani, che aveva in Italia ciò che s&#039;era meglio speculato <lb></lb>intorno al Magnete, fosse nonostante ricorso a interpellarne gli Accademici di <lb></lb>Londra, nè s&#039;intende come potesse quietarsi alla loro risposta, che cioè nes­<lb></lb>suno dopo il Cartesio aveva osato di suggerire, in mezzo a tante difficoltà, <lb></lb>qualche ipotesi nuova. </s>

<s>Può esser che fosse al Viviani ignoto ciò che lasciò <lb></lb>Antonio Nardi manoscritto in quel Volume, conosciuto da molti in Toscana, <lb></lb>benchè letto da pochi, ma come si può scusare del non aver tenuto in nes­<lb></lb>sun conto le speculazioni magnetiche divulgate nel libro del Grimaldi? </s></p><p type="main">

<s>Il fatto ch&#039;è pur degno di qualche considerazione conferma quel che <lb></lb>fu osservato da noi ad altro proposito, ed è che il Grimaldi rimase solita­<lb></lb>rio e come fuori di strada a chi, senza rivolgersi nè da una parte nè da <lb></lb>un&#039;altra, teneva dietro sicuro alla Filosofia galileiana. </s>

<s>Quel che il Gesuita <lb></lb>bolognese scoprì intorno alle proprietà della luce si diffuse pel magisterio, <lb></lb>e si pregiò per l&#039;autorità del Newton, il quale, perchè non ebbe occasione <lb></lb>di considerare le magnetiche speculazioni grimaldiane, queste rimasero in <lb></lb>dimenticanza così appresso gl&#039;Inglesi come appresso i nostri Italiani. </s></p><p type="main">

<s>Ma se il discepolo prediletto e gli altri sviscerati ammiratori di Galileo <lb></lb>avessero pensato che la verità poteva essere stata rivelata anche a chi non <lb></lb>fosse andato allo studio di Padova, o fosse intervenuto a&#039;coloqui di Arcetri, <lb></lb>avrebbero potuto promuover più oltre la Filosofia magnetica da quel segn o <lb></lb>a che la condussero nella loro fiorentina Accademia. </s>

<s>Quel segno dall&#039;altra <lb></lb>parte è poco più qua remosso dal punto dove lo fissarono il Gilberto, il <lb></lb>Gassendo o qualcun altro, e gli Accademici lo conobbero bene e lo confes­<lb></lb>sarono, facendo dire al loro Segretario esser quelle notizie date ne&#039;Saggi di <lb></lb>Naturali esperienze <emph type="italics"></emph>assai ordinarie, e per avventura non del tutto nuove.<emph.end type="italics"></emph.end><lb></lb>(Firenze 1841, pag. </s>

<s>137). </s></p><p type="main">

<s>Ma pur, per la verità, convien dire che qualche cosa tentassero di nuovo, <lb></lb>di che non tennero conto nel sopra detto Libro de&#039;Saggi, forse per non <lb></lb>averne potuto ricavare nulla di certo. </s>

<s>Lasciamo per ora da parte l&#039;espe­<lb></lb>rienza istituita per determinare secondo qual legge diminuisca la forza del­<lb></lb>l&#039;attrazion magnetica al crescere della distanza, di che diremo altrove, ma <lb></lb>furono essi i nostri Accademici de&#039;primi a sperimentare le operazioni della <pb xlink:href="020/01/808.jpg" pagenum="251"></pb>Calamita nel vuoto. </s>

<s>Si sa come rimanessero intorno a ciò ingannati l&#039;Hart­<lb></lb>foeker, lo Sturm e lo stesso Boyle, non facendo considerazione sopra la re­<lb></lb>sistenza che variamente oppone al Versorio l&#039;aria più e meno densa, nè <lb></lb>sopra le alterazioni della gravità, che i corpi subiscon nel vuoto, per le quali <lb></lb>considerazioni s&#039;intende come, sotto la campana della Macchina pneumatica, <lb></lb>più facilmente volubile debba esser l&#039;ago, e una calamita ivi dentro non <lb></lb>sostenti tutto quel peso, che sosteneva nell&#039;aria, dove il Banoscopio dimo­<lb></lb>stra essere alquanto più leggero. </s></p><p type="main">

<s>Forse sfuggirono così fatte considerazioni anche ai nostri Accademici, <lb></lb>come s&#039;argomenta dall&#039;incertezza in che gli lasciarono due conclusioni spe­<lb></lb>rimentali fra sè discordi. </s>

<s>Nel libro de&#039;<emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> per esempio, trovarono che <lb></lb>nel vuoto la Calamita tira l&#039;ago alla distanza medesima che nell&#039;aria (pag. </s>

<s>60) <lb></lb>ma in una <emph type="italics"></emph>Nota d&#039;osservazioni e sperienze da farsi nel gran vacuo,<emph.end type="italics"></emph.end> di <lb></lb>contro all&#039;articolo che dice: <emph type="italics"></emph>Attrazioni magnetiche, se venghin tolte, im­<lb></lb>pedite o facilitate,<emph.end type="italics"></emph.end> il Viviani accennò in margine il resultato avutone, scri­<lb></lb>vendo di sua propria mano: <emph type="italics"></emph>Facilitate.<emph.end type="italics"></emph.end> (MSS. Cim., T. X, c. </s>

<s>253). </s></p><p type="main">

<s>Ma comunque sia, non perciò si può dir, come da sè medesimi con­<lb></lb>fessarono i nostri Accademici, che avessero <emph type="italics"></emph>arrecato qualche gran lume <lb></lb>nella Filosofia magnetica<emph.end type="italics"></emph.end> (Saggi cit., pag. </s>

<s>137); merito che unicamente <lb></lb>rimane al Grimaldi e in Italia e fuori, dove, piuttosto che alle generali pro­<lb></lb>prietà del Magnete, s&#039;attese a un fatto particolare, di che dobbiamo ora pas­<lb></lb>sare a narrar la storia. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il fatto particolare, che rivolse a sè l&#039;attenzione de&#039;cultori della Filo­<lb></lb>sofia magnetica, specialmente in Inghilterra e in Francia, fu quello della <lb></lb>variabile declinazione della Calamita. </s>

<s>Udimmo l&#039;Hook di sopra narrare al <lb></lb>Viviani come al Gillibrand occorresse di fare l&#039;inaspettata scoperta, e come <lb></lb>nel 1634 si studiasse l&#039;Autore, per mezzo di un Trattato scritto in tal pro­<lb></lb>posito, di divulgarla. </s>

<s>Ma come sempre avviene alle cose nuove e che hanno <lb></lb>dello straordinario, non trovò quella opinione del professor di Gresham troppo <lb></lb>facile accoglienza. </s>

<s>Molti anche fra gl&#039;Inglesi recalcitrarono, allegando l&#039;Ora­<lb></lb>colo del Gilberto, il quale aveva sentenziato <emph type="italics"></emph>Variatio unius cuiusque loci <lb></lb>constans est.<emph.end type="italics"></emph.end> (De Magn., Lib. </s>

<s>IV, cap. </s>

<s>IV, pag. </s>

<s>159). Altri fra&#039;più giudi­<lb></lb>ziosi se ne spacciavano con un <emph type="italics"></emph>può cssere,<emph.end type="italics"></emph.end> cosicchè, dopo qualche anno, <lb></lb>nessuno più ci pensava. </s></p><p type="main">

<s>Il Cartesio, alle orecchie del quale era pervenuto qualche romore, pose <lb></lb>nel IV libro de&#039;<emph type="italics"></emph>Principii della Filosofia,<emph.end type="italics"></emph.end> fra i problemi da risolversi intorno <lb></lb>al Magnete, anche il XX. <emph type="italics"></emph>Quod ista declinatio cum tempore mutari pos­<lb></lb>sit<emph.end type="italics"></emph.end> (pag. </s>

<s>264). Ma perchè i seguaci del retto metodo sperimentale, anche in <lb></lb>Francia, non tenevano in nessun conto quelle strane particelle striate, passò <pb xlink:href="020/01/809.jpg" pagenum="252"></pb>insiem con esse inosservato anche ciò che il Cartesio aveva detto della pos­<lb></lb>sibile variabilità della declinazione magnetica, cosicchè nel 1654 giunse al <lb></lb>Petit e agli altri Fisici parigini la notizia di questa scoperta come cosa del <lb></lb>tutto nuova. </s>

<s>In che modo poi occorresse una tal notizia a quel Petit, che <lb></lb>doveva promoverla con tanto studio e diffonderla con tanto zelo, ci è nar­<lb></lb>rato da lui stesso nella Dissertazione <emph type="italics"></emph>De latitudine parisiensi<emph.end type="italics"></emph.end> aggiunta, in­<lb></lb>siem con altre Dissertazioni astronomiche, all&#039;Astronomia fisica del Du-Hamel. </s></p><p type="main">

<s>Studiosissimo il Petit, sopra quanti altri mai, della Filosofia magnetica, <lb></lb>s&#039;era proposto di sperimentare se le Calamite facessero differente declina­<lb></lb>zione secondo che, nella loro nativa miniera, giacevano più o meno vicino <lb></lb>al punto del Polo. </s>

<s>Con tre pietre, avute da varie parti della Terra, calamitò <lb></lb>tre aghi di varia lunghezza, e per esplorare il grado della loro declinazione <lb></lb>costruì colla massima accuratezza tre linee meridiane in varii luoghi della <lb></lb>città di Parigi, e trovò che dovunque gli aghi soprapposti declinavano di <lb></lb>quattro gradi in Oriente. </s>

<s>Rimase il Petit sorpreso di gran maraviglia, aspet­<lb></lb>tandosi che, non facendo i tre aghi varietà fra loro, dovessero in quella im­<lb></lb>perturbata concordia declinare fra i nove o i dieci gradi, come si teneva <lb></lb>allora da tutti in Parigi, dietro le accuratissime osservazioni dell&#039;Oronzio e <lb></lb>del Castelfranco. </s></p><p type="main">

<s>Divulgatasi la notizia che la Declinazione magnetica in Parigi non era <lb></lb>altrimenti di dieci gradi, ma di soli quattro, i Fisici e gli Astronomi fran­<lb></lb>cesi si riscossero, e premurosi concorsero da varie parti a confermare colle <lb></lb>loro particolari osservazioni la verità del fatto scoperto. </s>

<s>Tanto rimasero a <lb></lb>quella inaspettata novità commossi, che ne giunse il rumore in Inghilterra, <lb></lb>e allora si sovvennero quegli Inglesi del loro Gillibrando, e riconobbero nei <lb></lb>fatti osservati a Parigi la più bella conferma di ciò che vent&#039;anni prima era <lb></lb>stato scoperto nella loro città di Londra. </s>

<s>Dettero subito di ciò avviso al Pe­<lb></lb>tit, in quel ch&#039;egli stava per sentenziar che senz&#039;altro le osservazioni del­<lb></lb>l&#039;Oronzio dovevano essere sbagliate, come il Gunter aveva creduto che fos­<lb></lb>sero sbagliate le osservazioni del Burrosio. </s></p><p type="main">

<s>“ Tum fuimus (così il Petit colle sue proprie parole prosegue la nar­<lb></lb>razione) omnes in ea sententia ut putaremus ab antiquis peccatum hic fuisse, <lb></lb>nec alias declinationis magneticae aliam extitisse positionem, cum ecce nobis <lb></lb>ab Anglia allatae sunt literae, quibus accepimus hanc dubio procul haud <lb></lb>esse constantem, quando quidem olim, anno scilicet 1580, Burrosius in ma­<lb></lb>thematicis eximius, ex observationibus Solis azimuthorum accuratissimis, <lb></lb>mense Octobri prope Londinum, acum Magnete illitam a Meridie in Ortum <lb></lb>11 grad. </s>

<s>15 min. </s>

<s>deflectere compererit: anno vero 1622, mense Junio, Gon­<lb></lb>therus metheseos professor in eodem loco declinationem multum imminu­<lb></lb>tam nempe 6 gr. </s>

<s>tantum invenerit. </s>

<s>Postremo, annis 1633 et 1634, Geli­<lb></lb>brandus Gontheri successor eamdem observationem, eodem in loco, atque <lb></lb>eadem prorsus methodo instituens, cum acus 12 digitis longas adhibuisset, <lb></lb>4 dumtaxat gradus a Meridie deflectere cognovit. </s>

<s>Quae omnia, cum in lu­<lb></lb>cem is dederit, nullus dubitandi locus relinquitur Mugnetis declinationem <pb xlink:href="020/01/810.jpg" pagenum="253"></pb>variasse, quod et nos experti sumus et quivis alius experiri facile potest ” <lb></lb>(Parisiis 1660, pag. </s>

<s>30). </s></p><p type="main">

<s>La scoperta dunque del Gillibrando veniva così confermata, secondo il <lb></lb>Petit, dai fatti per modo, che nessuno aveva oramai più ragione di metterla <lb></lb>in dubbio. </s>

<s>Ma dover de&#039;Filosofi era quello d&#039;investigarne le cause, la pro­<lb></lb>babilità delle quali, se non la verità, avrebbe giovato a persuader meglio la <lb></lb>mente dei ritrosi. </s>

<s>Or dove si sarebbero potute rinvenir queste cause, che <lb></lb>avessero almeno apparenza d&#039;esser produttrici di effetti tanto straordinari? </s>

<s><lb></lb>Il Problema però non era del tutto nuovo: ei dipendeva da un altro primo <lb></lb>problema, che tenevasi per risoluto già dal Gilberto, quando nel cap. </s>

<s>I del <lb></lb>Libro IV, rifiutate le opinioni del Ficino, del Cardano, del Maurolico, dello <lb></lb>Scaligero e di altri, attribuì all&#039;inegualità della superficie terrestre il variar <lb></lb>della Declinazione sotto i varii meridiani. </s></p><p type="main">

<s>“ Cum vero globus telluris in superficie sua mancus sit et inaequalis, <lb></lb>varia natura deformatus, summasque habeat et convexas partes, ad aliquot <lb></lb>milliariorum profunditatem, nec natura nec corpore uniformes, sed contra­<lb></lb>rias et dissimiles; fit ut vis illa tota telluris divertat in eius peripheria ma­<lb></lb>gnetica corpora versus robustiores et eminentiores continentes magneticas <lb></lb>partes. </s>

<s>Quare in superna telluris superficie a vero meridiano magnetica pau­<lb></lb>lulum perventuntur. </s>

<s>Etiam, cum globi superficies distincta sit in terrestres <lb></lb>et aqueas eminentias, in magnas terras continentes, in oceanum et maria <lb></lb>vastissima, vis vero omnium motuum magneticorum a terrestri sit natura <lb></lb>constante et magnetica, quae in maiore continente magis praevalet, non in <lb></lb>aquosa, fluida, et incerta; sequitur quod versus terram magnam, sive con­<lb></lb>tinentem magis eminentem, a quovis meridiano, sive per maria sive per <lb></lb>insulas transeunte, orientem versus aut occidentem, a vero polo inclinatio <lb></lb>magnetica partibus quibusdam fiat, ad fortiorem nempe, sive altiorem et <lb></lb>eminentiorem globi terrestris magneticam partem ” (De Magn. </s>

<s>cit., pag. </s>

<s>153). </s></p><p type="main">

<s>Se questa è dunque la causa della variazione, ammettendo che col tempo, <lb></lb>o per opera dell&#039;arte o della Natura, si trasformi in qualche modo l&#039;abito <lb></lb>della Terra, s&#039;intenderà d&#039;onde abbia origine la variazione della variazione <lb></lb>che l&#039;esperienza ci ha dimostrata. </s>

<s>Di qui infatti s&#039;attinse quella prima ra­<lb></lb>gione, che il Cartesio suggerì ai Filosofi nella forma seguente: “ Sunt qui <lb></lb>dicunt istam declinationem non semper in iisdem terrae locis eandem ma­<lb></lb>nere, sed cum tempore mutari, quod minime mirum videri debet. </s>

<s>Non modo <lb></lb>quia ferrum quotidie ex unis terrae partibus in alias ab hominibus transfer­<lb></lb>tur, sed etiam quia eius glebae quae sunt in hac terra exteriore, quibusdam <lb></lb>in locis cum tempore corrumpi possunt, et aliae in aliis generari, sive ab <lb></lb>interiore terra submitti ” (Principi Philos. </s>

<s>cit., pag. </s>

<s>278). </s></p><p type="main">

<s>Ma questa ragion del Cartesio, benchè legittimamente derivata dalle <lb></lb>dottrine del Gilberto, fu non curata da chi seguiva altri più sani principii <lb></lb>di Filosofia naturale, e i Cartesiani stessi par che pretendessero qualche cosa <lb></lb>di meglio. </s>

<s>Il Mersenno infatti, appena che per le lettere venute al Petit <lb></lb>d&#039;Inghilterra, si diffuse in Parigi la notizia della scoperta del Gillibrando, <pb xlink:href="020/01/811.jpg" pagenum="254"></pb>fu sollecito di avvertire il Kircher che dava in quel tempo opera in Roma <lb></lb>a scrivere il suo libro <emph type="italics"></emph>De arte magnetica,<emph.end type="italics"></emph.end> aspettandosi da lui in tal con­<lb></lb>giuntura qualche bella e ingegnosa spiegazione del fatto maraviglioso. </s>

<s>“ Gau­<lb></lb>deo vehementer, mi Pater, te nondum postremam manum operi magneti­<lb></lb>cae adhibuisse, cuius titulo plurimum me recreasti. </s>

<s>Enimvero iam ad te <lb></lb>quaedam admodum stupenda scripturus sum quorum, si vel probabiles ra­<lb></lb>tiones afferas, viros magneticos tibi solide obstrinxeris ” (Kircheri Magnes, <lb></lb>Romae 1654, pag. </s>

<s>340). </s></p><p type="main">

<s>Nè in mezzo a tale e a tanta commozione, di ch&#039;eran presi gli scien­<lb></lb>ziati parigini, non era credibile che se ne stesse il Gassendo, il quale, per­<lb></lb>chè non ritrovava nelle dottrine del Copernico, nè in quelle del Keplero e <lb></lb>del Gilberto, una ragione sodisfacente del fatto, aveva anch&#039;egli fiducia nella <lb></lb>solerzia ingegnosa del padre Kircher, a cui scriveva: “ De causa nihil adhuc <lb></lb>potui quod satisfaciat comminisci, tametsi varie versaverim et copernicanam <lb></lb>anticipationem, et gilbertinam verticitatem, et Keplericos nucleos, et demo­<lb></lb>criticos tramites catenulasque, et alia id genus oppido quam multa. </s>

<s>Expecto <lb></lb>quid censueris ipse qui praeter insignem solertiam perfecisti haud dubia expe­<lb></lb>rimenta longe plura ” (ibi, pag. </s>

<s>345). </s></p><p type="main">

<s>Punto da questi stimoli acuti, non rispondendo ai quali ne andava della <lb></lb>sua riputazione, il Kircher assottigliò l&#039;ingegno, ma non seppe far altro che <lb></lb>sminuzzare e stemperare, con un&#039;arte ch&#039;era tutta sua propria, l&#039;argomento <lb></lb>pensato già dal Cartesio. </s>

<s>“ Altera ratio dependet ab immutatione terrestrum <lb></lb>partium ” (ibi, pag. </s>

<s>346) della qual mutazione riconosce i più validi effi­<lb></lb>cienti ne&#039;fochi sotterranei e nei terremoti. </s></p><p type="main">

<s>Il Petit fu il primo a uscir fuori con un&#039;ipotesi, la quale tanto si mo­<lb></lb>strò più nuova, quanto parve più ardita. </s>

<s>O non sempre, egli ragionava, l&#039;ago <lb></lb>riguarda lo stesso punto del polo terrestre, o il polo terrestre non riguarda <lb></lb>sempre lo stesso punto del cielo. </s>

<s>“ Cum vero longe probabilius videatur hanc <lb></lb>varietatem prodire potius ex telluris axe, qui situm mutet, neque semper ad <lb></lb>eadem coeli puncta dirigatur, quam ex axe magnetis qui velut sub iure ac <lb></lb>dominio globi terrestris, extra controversiam positus est ” (Dissert. </s>

<s>cit., <lb></lb>pag. </s>

<s>30). A creder così fu condotto l&#039;Autore dal veder che variava col tempo <lb></lb>la latitudine de&#039;paesi, com&#039;egli stesso riscontrava di fatto, confrontando la <lb></lb>latitudine di Parigi, da sè trovata, con quella posta dall&#039;Oronzio, dal Fer­<lb></lb>nelio e dal Vieta. </s></p><p type="main">

<s>Persuaso perciò che la più probabile causa della variabilità della decli­<lb></lb>nazione magnetica consistesse nel variar che fa la linea meridiana, era il <lb></lb>Petit vivamente desideroso d&#039;osservare il fatto in meridiane diligentemente <lb></lb>descritte, e da assai lungo tempo. </s>

<s>Ma in Parigi e nelle sue vicinanze non <lb></lb>si trovava altro che Orologi scioterici, ordinati a segnar l&#039;ore, tanto da ser­<lb></lb>vire agli usi domestici o civili. </s>

<s>In questo tempo venne a saper che in Bo­<lb></lb>logna, sul pavimento della Chiesa di S. Petronio, era stata disegnata una <lb></lb>meridiana da servire agli usi proprii della scienza, e credette il Petit che, <lb></lb>diffusasi anche in Italia la notizia di ciò ch&#039;era stato osservato prima a Lon-<pb xlink:href="020/01/812.jpg" pagenum="255"></pb>dra e poi a Parigi, fosse la principale intenzione dell&#039;opera egregia quella <lb></lb>di verificare la variabilità della declinazione magnetica. </s>

<s>Il nome di Gian Do­<lb></lb>menico Cassini non par che fosse allora conosciuto in Francia, nè si sapeva <lb></lb>che la vera intenzione di lui, nel dar opera a descriver la Meridiana di <lb></lb>S. Petronio, era quella, non di giovar particolarmente alla scienza del Ma­<lb></lb>gnete, ma di erigere un monumento solenne ai progressi dell&#039;Astronomia. </s></p><p type="main">

<s>Più tardi s&#039;intese troppo chiaro anche a Parigi quale uomo fosse il <lb></lb>Cassini, ma intanto il Petit sperava di ritrovar nelle diligenti osservazioni di <lb></lb>lui la più valida conferma alla sua ipotesi. </s>

<s>Preparato perciò un esemplare <lb></lb>della dissertazione <emph type="italics"></emph>De latitudine parisiensi,<emph.end type="italics"></emph.end> la spediva a Bologna accompa­<lb></lb>gnata con una lettera, nella quale pregava il Cassini a verificar la declina­<lb></lb>zione magnetica sopra la sua esattissima Meridiana, e lo richiedeva nello <lb></lb>stesso tempo del suo giudizio intorno al decider se la ragione del variar del <lb></lb>declinatorio da un tempo a un altro dipendesse dal variar postura il Cielo o <lb></lb>la Terra. </s>

<s>Le risposte, qualunque fosse di ciò la ragione, indugiavano, ond&#039;è <lb></lb>che ritrovandosi a viaggiare fra noi quel Sauval, autore del libro sull&#039;anti­<lb></lb>chità di Parigi, e a richiesta del quale il Petit aveva misurata la precisa la­<lb></lb>titudine di quella città, e ne avea scritta la sopra citata Dissertazione; a lui <lb></lb>si rivolse come ad amico suo e a suo concittadino, per lagnarsi della poca <lb></lb>corrispondenza e della poca sincerità trovata in certi scienziati, a cui s&#039;era <lb></lb>rivolto in Italia, e per commettergli alcuni ufficii e negozi da trattarsi col <lb></lb>principe Leopoldo di Toscana. </s>

<s>Abbiamo di tutto ciò il documento in una <lb></lb>lettera, che il Petit stesso da Parigi indirizzava al Sauval a Firenze; lettera, <lb></lb>della quale il Viviani fece così la traduzione, e ne conservò l&#039;estratto di sua <lb></lb>propria mano. </s></p><p type="main">

<s>“ ....... di S. A. alla quale io pregavo di mandare i miei Discorsi, <lb></lb>che ultimamente il signor Du-Hamel ha fatto stampare con la sua Astro­<lb></lb>nomia fisica, de&#039;quali voi sapete che ve n&#039;è uno appartenente alla latitu­<lb></lb>dine di Parigi e la declinazione della Calamita fatta per voi e nell&#039;occasione <lb></lb>della vostra bell&#039;Opera <emph type="italics"></emph>Dell&#039;antichità di Parigi.<emph.end type="italics"></emph.end> Io averò ben dispiacere <lb></lb>se, per la negligenza del nostro amico Thevenot, S. A. non avesse ancora <lb></lb>ricevuto le attestazioni della mia reverenza, e li detti Discorsi, de&#039;quali vi <lb></lb>prego d&#039;informarvene e di giustificarmene. </s>

<s>Io ne mandai ancora qualche <lb></lb>esemplare al sig. </s>

<s>Settala a Milano, ed al sig. </s>

<s>Cassini a Bologna, da&#039;quali <lb></lb>non ho avuto risposta sodisfacevole, in che io gli pregavo di verificare la <lb></lb>declinazione della Calamita sopra di qualche merìdiana esattamente descritta, <lb></lb>perchè, avendola fatta quest&#039;anno a Parigi in casa di Mons. </s>

<s>Thevenot, in <lb></lb>campagna, noi aviamo trovato che non vi era alcuna declinazione, e che la <lb></lb>lancetta è propriamente sulla linea meridiana, e per quel ch&#039;è mio parere, <lb></lb>è che questa può procedere da un moto della propensione della Terra nel <lb></lb>suo centro, che fa cambiare la meridiana e non la virtù magnetica, che se­<lb></lb>guita sempre il polo della Terra. </s>

<s>Io lo avevo pregato di provarlo e di ve­<lb></lb>rificarlo sopra qualche linea antica meridiana, descritta da cinquanta o ses­<lb></lb>sant&#039;anni in qua da qualche persona diligente, se ci fosse mutazione al <pb xlink:href="020/01/813.jpg" pagenum="256"></pb>presente, e se quella che si descrivesse adesso convenisse coll&#039;antica e gli <lb></lb>fusse parallela o facesse il medesimo angolo, che la declinazione della lan­<lb></lb>cetta di que&#039;tempi fa in questi tempi. </s>

<s>Ma di tutto questo non ho avuto ri­<lb></lb>sposta alcuna da veruna parte dove ho scritto, perchè forse può essere che <lb></lb>non abbiano potuto trovare nessuna linea meridiana antica assai giusta, e <lb></lb>della quale possano esser ben certi per compararla con queste che si fanno <lb></lb>di presente, e questo è quello di ch noi doviamo dolerci, che nessuno abbia <lb></lb>pensato, da cent&#039;anni in qua, a la<gap></gap>ciarci questa linea descritta in qualche <lb></lb>luogo invariabile ed immobile, come s&#039;è fatto da poco in qua in S. </s>

<s>Petro­<lb></lb>nio di Bologna, che servirà tra qualche tempo a rettificare molte cose pel <lb></lb>cielo e per la Terra. </s>

<s>” </s></p><p type="main">

<s>“ Ma poichè sono sopra la Calamita, e tratto con voi dell&#039;isola del­<lb></lb>l&#039;Elba attenente a S. A., io vi prego d&#039;assicurarvi se è vero che la lancetta <lb></lb>declina diversamente in quell&#039;Isola, e se vi è qualche parte, dove ella de­<lb></lb>clina fino a venti gradi, cosa che io non credo, come nemmeno credo quel <lb></lb>che mi ha scritto altre volte il Settala, che aveva due o tre Pietre, che non <lb></lb>pesavano due once, che alzavano, coperte di ferro, cinquanta o sessanta lib­<lb></lb>bre. </s>

<s>Ma quand&#039;io l&#039;ho stimolato e fatto stimolare da persone di qualità di <lb></lb>trovarmene, vendermene, o prestar qualcuna sotto buona sicurezza, non ci <lb></lb>ha fatto veruna risposta. </s>

<s>Vedete quel che se ne può credere, e se voi pas­<lb></lb>sate a Milano, assicuratevene, ed attestateli che non siamo burlati a l&#039;arigi. </s>

<s><lb></lb>E se nel vostro viaggio ed in Fiorenza, dove ne deve esser molte, voi ne <lb></lb>trovassi qualcheduna buona, disarmata, e dalla quale si possa cavarne un <lb></lb>globo di due, tre o quattro dita grosso, voi mi obbligheresti infinitamente <lb></lb>a comprarla per me. </s>

<s>” </s></p><p type="main">

<s>“ Io ho qualche bell&#039;esperienza da fare, che io non finisco per man­<lb></lb>canza di quella, ancorchè voi sapete che ne ho molte altre, e per questo la <lb></lb>mia opera contro di Monsu Des Cartes resta imperfetta. </s>

<s>Me ne fanno spe­<lb></lb>rare di Norvegia, cavate secondo la mia maniera, dalla scoria o dalla mi­<lb></lb>niera, e segnate da quattro parti del mondo che le occupavano, essendovi <lb></lb>attaccate, ma se io potessi avere la medesima cosa dall&#039;Isola dell&#039;Elba, che <lb></lb>è più vicina a noi, quanto sarei obbligato a chi me ne facesse questa gra­<lb></lb>zia, ed acciocchè me le procurasse per l&#039;avanzamento di questa Filosofia <lb></lb>magnetica!.... ” (MSS. Cim., T. XXV, c. </s>

<s>154, 55). </s></p><p type="main">

<s>Ritornando ora addietro a considerar parte per parte questo, come lo <lb></lb>chiamava il Viviani, <emph type="italics"></emph>capitolo di lettera,<emph.end type="italics"></emph.end> non par che avesse il Petit ragione <lb></lb>di rammaricarsi del Thevenot, avendo egli adempiuto, sebben forse con qual­<lb></lb>che indugio, di far l&#039;ufficio col principe Leopoldo, il quale, dopo aver ri­<lb></lb>cevuto il Discorso Della Latitudine di Parigi, rispose in proposito all&#039;Autore <lb></lb>con lettera del di 2 Novembre 1665: “ Curiosa non meno che utile è stata <lb></lb>l&#039;esperienza, che V. S. ha fatto intorno alla Calamita, tanto più che nel farla <lb></lb>esattamente, ciascheduno che intende, sa ancora le difficoltà, che V. S. potrà <lb></lb>avere incontrate ” (ivi, T. XXIII, c. </s>

<s>127). </s></p><p type="main">

<s>Quanto agli incaricati di verificare la declinazione dell&#039;ago sopra meri-<pb xlink:href="020/01/814.jpg" pagenum="257"></pb>diane, che fossero state disegnate in Italia almeno da un mezzo secolo, aveva <lb></lb>ragione il Petit di scusarli, col pensar che non si saranno fidati della pre­<lb></lb>cisione di quelle linee descritte o da artefici inesperti, o con poco esatti <lb></lb>strumenti. </s>

<s>Ma non indovinava forse l&#039;Astronomo parigino che s&#039;aveva in <lb></lb>Italia un&#039;idea, che fosse difficilissimo, anzi quasi impossibile, tracciar la di­<lb></lb>rittura del meridiano, qualunque fosse la precisione degli strumenti o la <lb></lb>perizia dell&#039;arte. </s>

<s>Era stata una tale idea ingerita nelle menti da quel Nic­<lb></lb>colò Cabeo, che fu tenuto per diligentissimo e pazientissimo sperimentatore <lb></lb>dal Castelli e dal Baliani. </s></p><p type="main">

<s>Narra esso Cabeo, nel cap. </s>

<s>XV del III Libro della <emph type="italics"></emph>Filosofia magnetica,<emph.end type="italics"></emph.end><lb></lb>com&#039;essendosi tante volte provato a descriver, con una Bussola squisitissima, <lb></lb>due linee meridiane, l&#039;una poco distante dall&#039;altra, sulla soglia di una fine­<lb></lb>stra, non ci fu caso che gli volessero mai riuscir parallele, come sarebbe <lb></lb>dovuto avvenire se l&#039;ago, nelle due stazioni, avesse segnato sempre la me­<lb></lb>desima declinazione. </s>

<s>Maravigliato di questo fatto e datosi a investigarne la <lb></lb>causa, ritrovò che dipendeva dai mattoni troppo cotti, o come fra noi si dice <lb></lb><emph type="italics"></emph>inferrettati,<emph.end type="italics"></emph.end> di ch&#039;era costruito il muro della finestra, dall&#039;azione magnetica <lb></lb>de&#039;quali mattoni la direzion generale del Magnete era notabilmente alterata. <lb></lb></s>

<s>“ Causa igitur cur Versorium in parietibus sic incostanter meridianum re­<lb></lb>spiciat, sunt lateres nimium excocti, qui in tali pariete saepe delitescunt. </s>

<s><lb></lb>Ex longa enim commoratione in tali situ, virtute telluris, magneticam con­<lb></lb>trahunt naturam, ac proinde cogunt sibi etiam aliqua saltem ratione Verso­<lb></lb>rum obtemperare ” (Coloniae 1629, pag. </s>

<s>234). </s></p><p type="main">

<s>La curiosa esperienza fu confermata poi dal Cassini, per la mente del <lb></lb>quale, nell&#039;atto che apparecchiavasi a rispondere al Petit, passavano queste <lb></lb>parole, con che il Cabeo stesso concludeva quel suo capitolo sopra citato: <lb></lb>“ Hinc vides quam incerto effectu solaria horologia, si magnetico dirigan­<lb></lb>tur cuspide, collocentur supra parietes aut fenestras ” (ibi). </s></p><p type="main">

<s>Par che dunque troppo si mostrasse impaziente il Petit, lagnandosi che <lb></lb>dal Cassini non aveva avuto risposta. </s>

<s>Voleva il Cassini tempo a pensarci, <lb></lb>essendo cosa tanto nuova e di tanta importanza, e dopo averci lungamente <lb></lb>pensato rispose dubitando se i fatti osservati a Londra e a Parigi potessero <lb></lb>essere argomento sicuro, e prova dimostrativa della mobilità del cielo o della <lb></lb>terra. </s>

<s>La scrittura ci fu diligentemente conservata dal Viviani, che la copiò <lb></lb>di seguito al capitolo di Lettera del Petit, alla quale, in questa del Cassini, <lb></lb>si fa così la risposta. </s></p><p type="main">

<s>“ L&#039;esatta descrizione della meridiana richiede tante circospezioni, che, <lb></lb>non essendo di volgar perspicacia l&#039;osservarle, malamente potiam fidarci che <lb></lb>quelle che troviam descritte da altri, senza sapere il modo e la diligenza in <lb></lb>esse adoprata, non svarino alquanti minuti dal vero sito. </s>

<s>” </s></p><p type="main">

<s>“ Quelle che si descrivono per mezzo dell&#039;ombre di uno stile, che è il <lb></lb>modo più usitato, ancorchè si faccia elezione del tempo solstiziale, per la <lb></lb>perplessità nell&#039;esatta terminazione dell&#039;ombra, e per la brevità dello stile, <lb></lb>per qualsisia inegualità o scabrosità o inclinazione del piano, soggiacciono a <pb xlink:href="020/01/815.jpg" pagenum="258"></pb>svarii di gradi interi. </s>

<s>Quelle, che si descrivono per mezzo di un&#039;altezza del <lb></lb>sole presa con istrumenti ancorchè esatti, restano con molta ambiguità, <lb></lb>quando il sole, con poca mutazione d&#039;altezza, fa notabile mutazione di sito <lb></lb>orizzontale, com&#039;avviene qualche ora innanzi e dopo mezzogiorno, e presup­<lb></lb>pongono sempre molti elementi, cioè l&#039;altezza del polo, il vero luogo del <lb></lb>sole, l&#039;obliquità del Zodiaco, oltre alle rifrazioni e parallassi, e perciò, come <lb></lb>descritte con metodo troppo composto, non sogliono riuscire esatte. </s>

<s>” </s></p><p type="main">

<s>“ Con due altezze delle stelle uguali, una innanzi l&#039;altra dopo mezzo­<lb></lb>giorno, in notabil distanza dal meridiano e dal sole, ne&#039;giorni solstiziali, rie­<lb></lb>scono più accertate, siccome anco ha evidenza la descrizione della via della <lb></lb>specie del sole introdotta per un buco rotondo orizzontale molto alto in un <lb></lb>piano esattamente orizzontale, nel giorno solstiziale, per trovare, per mezzo <lb></lb>di esso e del punto verticale esattamente stabilito, la meridiana, come s&#039;è <lb></lb>fatto in S. </s>

<s>Petronio di Bologna, ed evidentissima è quella, che si cava dalle <lb></lb>due massime declinazioni diurne della Stella polare, che pigliano per mezzo <lb></lb>la meridiana, massime con istrumenti molto grandi. </s>

<s>” </s></p><p type="main">

<s>“ Ma perchè simili diligenze non si fanno che da peritissimi Astronomi, <lb></lb>per valersene di fondamento nelle osservazioni celesti, non è così in pronto <lb></lb>avere meridiane antiche di questa sorta, nè devonsi le altre meridiane, fatte <lb></lb>in alcuno de&#039;primi modi, mettere ad altro capitale che ad uso di Orologi <lb></lb>solari, ne&#039;quali si trascurano simili esattezze. </s>

<s>Nè è cosa da maravigliarsi se <lb></lb>nello stesso piano, in diversi tempi, venga la meridiana un poco diversa­<lb></lb>mente descritta, mentre ogni tal descrizione è per natura soggetta a qual­<lb></lb>che svario, e chi ne farà l&#039;esperienza troverà non poca difficoltà in descri­<lb></lb>vere, nel giorno stesso non che in diversi tempi, due lunghe meridiane <lb></lb>nello stesso piano, senza sensibile declinazione di una all&#039;altra. </s>

<s>” </s></p><p type="main">

<s>“ Non par dunque che un poco di svario, trovato fra due meridiane <lb></lb>descritte in diversi tempi, debba esser sufficiente fondamento di sospicare <lb></lb>che, da un tempo all&#039;altro, sia seguìta reale mutazione della meridiana per <lb></lb>moto del Cielo e della Terra, essendo più pronto attribuirlo alla somma dif­<lb></lb>ficoltà di descrivere con esattissimo confronto due meridiane. </s>

<s>” </s></p><p type="main">

<s>“ Quando da un tempo all&#039;altro si trovasse differenza notabilmente mag­<lb></lb>giore di quella, che possa portare la difficoltà dell&#039;esatta descrizione, e que­<lb></lb>sta si trovasse, in luoghi diversi e in diversi tempi, con certe proporzioni <lb></lb>corrispondenti a&#039;luoghi e tempi; allora potrebbesi cominciare a dubitare di <lb></lb>tal reale mutazione. </s>

<s>Ma sinora le differenze, che si presuppongono per fon­<lb></lb>damento, son così piccole, che quando tutto quello svario si attribuisse alle <lb></lb>difficoltà delle descrizioni, ancor rimane alle descrizioni stesse la lode di più <lb></lb>che mediocremente diligenti, essendo difficile a non commettere svarii mag­<lb></lb>giori con somiglianti metodi in due meridiane, nell&#039;istesso giorno e nel­<lb></lb>l&#039;istesso luogo descritte. </s>

<s>Onde tanto è lontano che le osservazioni esposte <lb></lb>debbano dar motivo d&#039;entrare in questo dubbio e di farne perquisizione, che <lb></lb>piuttosto, quando altronde vi fosse dubbio, basterebbero queste a farlo de­<lb></lb>porre, mentre le differenze sono dentro i termini di quelle, a&#039;quali soggiac-<pb xlink:href="020/01/816.jpg" pagenum="259"></pb>ciono per sè stesse le osservazioni. </s>

<s>Onde almeno potiam concludere non es­<lb></lb>servi mutazione evidentemente sensibile, ciò che siasi d&#039;una insensibile <lb></lb>mutazione, di cui non è sicuro il far prova con antiche meridiane, delle <lb></lb>quali non sappiamo che siano con straordinaria diligenza e circospezione de­<lb></lb>scritte. </s>

<s>” </s></p><p type="main">

<s>“ È difficile il trovar altre antiche meridiane che degli Orologi solari, <lb></lb>ne&#039;quali non si presuppone tanta squisitezza. </s>

<s>Tra queste, la meridiana del­<lb></lb>l&#039;Orologio della piazza di Bologna, nella faccia meridionale della Torre del <lb></lb>palazzo del Potestà, che si suppone molto antica, concorre con la gran me­<lb></lb>ridiana di S. </s>

<s>Petronio descritta con ogni diligenza nel solstizio estivo del 1656. <lb></lb>Chi avesse certezza della retta descrizione di quella, come abbiamo di que­<lb></lb>sta, potrebbe concludere non apparire per gran lunghezza di tempo sensi­<lb></lb>bile mutazione di meridiana. </s>

<s>Resta però per mezzo di questa molto maggior <lb></lb>probabilità dell&#039;immutabilità sensibile, e dalla meridiana di S. Petronio, per <lb></lb>essere molto grande ed esatta, esaminata dopo qualche lunghezza di tempo, <lb></lb>si averà maggiore evidenza della verità di questo fatto. </s>

<s>” </s></p><p type="main">

<s>“ Una insensibile mutazione del centro dell&#039;asse e de&#039;poli della Terra <lb></lb>par che si potesse presupporre dalla variazione a noi sensibile della super­<lb></lb>ficie della Terra, che si fa continuamente con abbassarsi e dimagrirsi i <lb></lb>monti e riempiersi le valli: ma siccome l&#039;inegualità della superficie della <lb></lb>Terra è molto poca, in proporzione di tutta la di lei grandezza; così questa <lb></lb>sola, nel ridursi ad ugualità non farà giammai mutazione che possa discer­<lb></lb>nersi nella meridiana, che si mutasse in diversi luoghi diversamente con la <lb></lb>mutazione de&#039;poli. </s>

<s>” </s></p><p type="main">

<s>“ Quanto alla mutazione della direzione magnetica, che in progresso di <lb></lb>tempo si vada facendo, nemmeno di questa pare sufficiente motivo di so­<lb></lb>spettare l&#039;avere in diversi tempi a diverse meridiane osservato alquanti mi­<lb></lb>nuti di diversità di declinazione, sì perchè, per le ragioni predette, non ab­<lb></lb>biamo certezza dell&#039;esatta descrizione di quelle meridiane, nel termine di <lb></lb>quei pochi minuti, sì perchè riesce sommamente difficile, anco ad una me­<lb></lb>ridiana giustissima, determinar la declinazione stessa così sottilmente, che <lb></lb>non segua svario di pochi minuti, poichè, richiedendosi in un circolo che <lb></lb>possa distinguere tutti i minuti, il diametro di lunghezza almeno di quattro <lb></lb>piedi, la lunghezza della lancetta di quattro o cinqu&#039;once, fatta diametro <lb></lb>d&#039;un circolo, appena potrà dare in esso nemmeno le diecine di minuti di­<lb></lb>stintamente. </s>

<s>Nè questa difficoltà è superabile col prolungar la linea a segno, <lb></lb>che diventi diametro d&#039;un circolo, in cui si possano distinguere i minuti, <lb></lb>perchè simili prolungazioni di linee brevi in pratica non si fanno con evi­<lb></lb>dente esattezza, e massime quelle di queste lancette, che non sono senza <lb></lb>grossezza sensibile, nè è facile sottilizzare in esse sino a questo segno con <lb></lb>l&#039;occhio l&#039;aerea linea immaginaria indivisibile della direzione. </s>

<s>” </s></p><p type="main">

<s>“ Chi farà prova di prolungare in diverse parti dello stesso piano si­<lb></lb>mili linee di quattro o cinque piedi, s&#039;accorgerà facilmente quanto sia dif­<lb></lb>ficile descriverle esattamente parallele. </s>

<s>Ond&#039;è che alcuni, avendo trovato de-<pb xlink:href="020/01/817.jpg" pagenum="260"></pb>clinar l&#039;una dall&#039;altra simili linee con diversi aghi descritte, non riflettendo <lb></lb>quanto facilmente ciò possa procedere dalla difficoltà d&#039;operare con tale esat­<lb></lb>tezza, l&#039;hanno attribuito a diversa inclinazione, che abbiano diverse calamite, <lb></lb>la quale forse non è improbabile, ma non però con simile esame a suffi­<lb></lb>cienza provata. </s>

<s>” </s></p><p type="main">

<s>“ Tralascio la circospezione, con cui bisogna in simili osservazioni guar­<lb></lb>darsi, non solo dal ferro, ma anco da certi altri corpi vicini, avendo speri­<lb></lb>mentato più d&#039;una volta che la vicinanza a mattoni più o meno cotti la <lb></lb>fanno più o meno declinare. </s>

<s>E siccome conosciam questi, così niuna cer­<lb></lb>tezza abbiamo che altri non ce ne sieno di simili facultà a noi ignote, che <lb></lb>nelle operazioni ponno per accidente incontrarsi. </s>

<s>Onde, dato ancora che fosse <lb></lb>oltre ogni speranza esattissimo il modo d&#039;operare, a tante altre cause par­<lb></lb>ziali si può attribuire simile diversità che s&#039;osservasse, che parrebbe dover <lb></lb>esser sempre l&#039;ultima la mutazione universale della direzione magnetica. </s>

<s>” </s></p><p type="main">

<s>“ Ma simili diversità, che da pochi minuti procedono, mentre stanno <lb></lb>ne&#039;termini della perplessità a cui di natura sua è soggetta l&#039;osservazione, <lb></lb>non par che debban servire di fondamento d&#039;investigar altra causa. </s>

<s>” </s></p><p type="main">

<s>“ Gli anni passati, nella campagna di Bologna e di Ferrara, fu tirata una <lb></lb>linea secondo la direzione magnetica per alquante miglia, e dopo due anni <lb></lb>tiratane un&#039;altra dall&#039;istesso principio, fu trovato nel fine discostarsi dalla <lb></lb>precedente alquanti passi, ma non perciò tale accidente fu attribuito a mu­<lb></lb>tazione della linea magnetica, ma all&#039;estrema difficoltà di prolungar giusta­<lb></lb>mente a tanta distanza una linea sì corta, quanto è quella di una lancetta. </s>

<s>” </s></p><p type="main">

<s>“ Insomma, se maggior fondamento non abbiamo della mutazione della <lb></lb>meridiana o della direzione magnetica, che la differenza di pochi minuti ve­<lb></lb>nuta nelle osservazioni, pare piuttosto che venga stabilita l&#039;immutabilità del­<lb></lb>l&#039;una e dell&#039;altra, che posta alcuna di esse in sospetto. </s>

<s>” </s></p><p type="main">

<s>“ In Bologna la Calamita non declina sensibilmente dalla meridiana, <lb></lb>ancorchè alcuni abbian pubblicato che declini tre gradi, e sebbene si può <lb></lb>attribuire questa differenza al modo di osservare, non per questo vien reso <lb></lb>probabile il perpetuo concorso della meridiana con la linea della direzione <lb></lb>magnetica, ancorchè in alcuni altri luoghi sia stato con diligente metodo os­<lb></lb>servato, poichè, pubblicandosi in molti luoghi simili declinazioni di molti <lb></lb>gradi, sarebbe un tacciare di troppo grossolane tali osservazioni, e quali sono <lb></lb>state stabilite, se allo svario di esse si attribuisse tanta differenza. </s>

<s>E si pas­<lb></lb>serebbe da un estremo all&#039;altro nel fondare su pochi minuti di differenza <lb></lb>una reale mutazione, e poi non far caso della differenza di molti gradi, per <lb></lb>istabilire l&#039;uniformità delle declinazioni. </s>

<s>Nè però deve defraudarsi della do­<lb></lb>vuta lode chi dell&#039;uno e dell&#039;altro su tali fondamenti ha dubitato, mentre <lb></lb>porge occasione e stimolo di rintracciare con maggior diligenza ed accura­<lb></lb>tezza la verità del fatto ” (ivi, c. </s>

<s>156-59). </s></p><p type="main">

<s>I lettori vedono in questo Discorso del Cassini lucidamente riflessa l&#039;in­<lb></lb>dole dell&#039;ingegno italiano, alieno dalle arrischiate ipotesi e dai facili archi­<lb></lb>tettati sistemi, e che se non è sicuro non fa progressi. </s>

<s>Quella maggior <pb xlink:href="020/01/818.jpg" pagenum="261"></pb>diligenza e accuratezza, aspettata dal Cassini, poi venne e fu confermata la <lb></lb>verità non del fatto solo osservato dal Gillibrando, ma di altri simili a quello. </s>

<s><lb></lb>Fu osservato cioè e confermato per vero che la declinazione dell&#039;ago varia, <lb></lb>non solamente di anno in anno, ma di mese in mese, e anche di giorno in <lb></lb>giorno. </s>

<s>“ Monui autem superius (dice il Musschenbroek nella Dissertazione <lb></lb>sua <emph type="italics"></emph>De Magnete<emph.end type="italics"></emph.end>) non modo singulo anno sed singulo mense et die decli­<lb></lb>nationem esse diversam, quod constat ex observationibus a patre Guy Ta­<lb></lb>chart factis anno 1682.... Nescio an ante hunc patrem aliquis hanc quo­<lb></lb>tidianam mutationem observaverit: eamdem confirmare possum propria <lb></lb>experentia ” (Viennae 1756, pag. </s>

<s>156). </s></p><pb xlink:href="020/01/819.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dell&#039;Elettro<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle prime esperienze elettriche e delle ipotesi del Gilberto e del Cabeo; delle esperienze del Gue­<lb></lb>ricke e degli Accademici del Cimento. </s>

<s>— II. De&#039;fuochi elettrici dell&#039;Hawksbee; dell&#039;elettricità <lb></lb>per comunicazione; dell&#039;elettricità vitrea e resinosa, e dell&#039;elettricità positiva e negativa. </s>

<s>— <lb></lb>III. </s>

<s>Di ciò che a promuovere la scienza elettrica, fu cooperato in Italia, principalmente dal Bec­<lb></lb>caria e dal Volta. </s>

<s>— IV. Dell&#039;elettricità e degli effetti di lei nell&#039;ammosfera. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il Magnete e l&#039;Elettro, nella loro vita avventurosa, non andarono mai <lb></lb>fra sè disgiunti. </s>

<s>Celebre fu sempre la loro fama, dice il Gilberto, nelle com­<lb></lb>memorazioni dei dotti. </s>

<s>Il Magnete e l&#039;Elettro sono invocati da alcuni Filo­<lb></lb>sofi, quando, a investigar molti effetti della Natura, riescono infermi i sensi, <lb></lb>e la ragione dietro a loro ha corte le ali. </s>

<s>Anche i Teologi curiosi, per mezzo <lb></lb>del Magnete e dell&#039;Elettro, illustrano i divini misteri e la boria de&#039;Metafi­<lb></lb>sici se ne serve come della spada di Delfo, nelle sue fantasticate battaglie, <lb></lb>a penetrare le armature più forti. </s>

<s>E che? </s>

<s>i medici stessi, sull&#039;autorevole <lb></lb>esempio di Galeno, per confermare il fatto dell&#039;attrazion de&#039;succhi nell&#039;opera <lb></lb>de&#039;purganti o nell&#039;uso degli altri medicamenti, invocano per testimonianza <lb></lb>il Magnete <emph type="italics"></emph>magnae authoritatis et efficentiae conspicuae naturam, corpus­<lb></lb>que inclytum!<emph.end type="italics"></emph.end> (De Magn. </s>

<s>cit., pag. </s>

<s>47). Dovunque insomma si tratta di <lb></lb>qualche causa, della quale non si sa far la ragione, si rimanda i clienti, <lb></lb><emph type="italics"></emph>tamquam personatos advocatos,<emph.end type="italics"></emph.end> all&#039;Elettro e al Magnete. </s></p><p type="main">

<s>Consorti nelle avventure le due materiali sostanze, nel far caro a&#039;Filo­<lb></lb>sofi de&#039;loro gelosi misteri si trovarono pure insieme consorti. </s>

<s>Com&#039;aveva <lb></lb>Plutarco ostetricata dalla divina mente platonica l&#039;ipotesi che il Magnete at-<pb xlink:href="020/01/820.jpg" pagenum="263"></pb>traesse il ferro, perchè sospintogli incontro dal vortice dell&#039;aria, così fu cre­<lb></lb>duto che venissero dall&#039;Elettro nel medesimo modo attratti i tritumi della <lb></lb>paglia. </s>

<s>I Filosofi, specialmente italiani del secolo XVI, avendo osservato che <lb></lb>l&#039;Ambra e il Gagate, per attrarre i minuzzoli de&#039;corpi, volevano esser prima <lb></lb>ben confricati, e credendo che fosse quella confricazione a questo sol ne­<lb></lb>cessaria per promuover in essi il calore, al calore stesso, e non all&#039;Ambra <lb></lb>o <gap></gap> Gagate, attribuivano la virtù di attrarre. </s>

<s>Gli esempi delle cucurbite me­<lb></lb>di<gap></gap> de&#039;tanti altri giochetti pneumatici descritti da Herone servivano a <lb></lb>que&#039;Filosofi per prova degli effetti da essi riconosciuti come naturale pro­<lb></lb>prietà del calore. </s>

<s>E benchè a rimovere dalla Fisica un tal dannosissimo er­<lb></lb>rore uscisse, come altrove dicemmo, il Benedetti a dimostrar contro il Car­<lb></lb>dano e il Tartaglia che proprietà del calore è il condensar non l&#039;attrarre, <lb></lb>pur fu così quell&#039;errore tenace, che Fisici insigni durarono per tutto il se­<lb></lb>colo XVII a credere e a dire che i vapori erano dalla superficie terrestre <lb></lb>attirati in alto dalla forza de&#039;raggi del Sole. </s></p><p type="main">

<s>Così essendo, aveva ragione il Gilberto a rimproverar tutti i Filosofi <lb></lb>suoi predecessori che si fossero messi a ragionar delle proprietà elettriche <lb></lb><emph type="italics"></emph>nullis rationibus ab experimentis et demonstrationibus inventis.<emph.end type="italics"></emph.end> “ Tantum, <lb></lb>prosegue a dire, agunt verbis, rebus ipsis maiorem culiginem inducenti­<lb></lb>bus ” (ibi, pag. </s>

<s>48). Tanto poi queste cose son vere, che nessuno ha potuto <lb></lb>ancora negare al Filosofo inglese il merito di aver egli il primo dato ini­<lb></lb>zio alla scienza elettrica, fugando le tenebrose parole de&#039;suoi predecessori, <lb></lb>colla luce de&#039;suoi nuovi esperimenti. </s></p><p type="main">

<s>Apre il Gilberto il campo alla nuova Filosofia e n&#039;estende ampiamente <lb></lb>la provincia, incominciando dal dimostrar che la virtù di attrarre non è pro­<lb></lb>pria di sola l&#039;Ambra o il Gagate, com&#039;era stato creduto fin&#039;allora, ma di <lb></lb>moltissimi altri corpi, così naturali, come artefatti. </s>

<s>“ Non solum succinum <lb></lb>et Gagates, ut illi putant allectant corpuscula, sed Adamas, Sapphirus, Car­<lb></lb>bunculus, Iris gemma, Opalus, Amethystus, Vincentina et Bristolla, Beril­<lb></lb>lus et Crystallus idem faciunt. </s>

<s>Similes etiam attrahendi vires habere videntur <lb></lb>vitrum, praesertim clarum et lucidum, tum ex vitro aut crystallo adultera­<lb></lb>tae gemmae, vitrum antimonii, et fluores plurimi ex fodinis et Belemnites. </s>

<s><lb></lb>Allicit etiam sulphur, mastix, et cera dura sigillaris ex lacca variis colori­<lb></lb>bus tincta et composita. </s>

<s>Allicit resina durior, ut Arsenicum, sed imbecillius; <lb></lb>aegre etiam et obscure in convenienti coelo sicco Sal gemma, Lapis specu­<lb></lb>laris, et Alumen rupeum ” (ibi). </s></p><p type="main">

<s>E come aveva il Gilberto esteso il numero de&#039;corpi attraenti, così, sopra <lb></lb>quel che tenevasi prima di lui, estese il numero de&#039;corpi attratti, i quali <lb></lb>dalle uniche festuche ridusse ai metalli, alle pietre, ai legni e anzi ad ogni <lb></lb>sorta di cose, <emph type="italics"></emph>quae sensibus nostris subiiciuntur.<emph.end type="italics"></emph.end> Provocava chiunque vo­<lb></lb>lesse a pigliare esperienza di ciò, insegnando a farla con un Versorio, che <lb></lb>portasse nella sua punta qualunque specie di metallo, con che intanto do­<lb></lb>tava la scienza elettrica del suo primo e semplicissimo strumento, che è una <lb></lb>specie di Elettroscopio. </s></p><pb xlink:href="020/01/821.jpg" pagenum="264"></pb><p type="main">

<s>Ma perchè la scienza non consiste solo nello sperimentare i fatti, si <lb></lb>principalmente nello specularne le recondite ragioni, il Gilberto vuol da vero <lb></lb>filosofo investigar le ragioni di quegli elettrici misteri. </s>

<s>Dicemmo che si ri­<lb></lb>ducevano quelle ragioni ai vortici dell&#039;aria e al calore, ma il nuovo Filosofo <lb></lb>crede falsa l&#039;una e l&#039;altra di queste ipotesi professate da&#039;Filosofi suoi pre­<lb></lb>decessori. </s>

<s>E quanto al dir che l&#039;Ambra attrae per effetto del calore eccitato <lb></lb>colle frizioni, il Gilberto ne mostrava la falsità con questa semplice e con­<lb></lb>cludentissima osservazione: “ Si a calore fit attractio, cur alia etiam plu­<lb></lb>rima corpora, sive igne, sole aut attritu excalefacta non attraherent? </s>

<s>” (ibi, <lb></lb>pag. </s>

<s>49). </s></p><p type="main">

<s>L&#039;altra ipotesi de&#039;vortici dell&#039;aria, come più radicata nelle menti, per <lb></lb>la lunghezza del tempo e per la grande autorità di Platone, e come più se­<lb></lb>ducente per la facilità del modo, con cui si dava per essa a intendere il <lb></lb>fatto elettrico; voleva esser confutata con più diretti argomenti, che piglias­<lb></lb>sero valore dall&#039;esperienza. </s>

<s>Due furono gli argomenti sperimentali pensati <lb></lb>in proposito dal Gilberto: il primo desunto dalla figura conica, in che si <lb></lb>assottiglia e s&#039;appunta verso l&#039;ambra una gocciola d&#039;acqua attirata: il se­<lb></lb>condo concluso dal veder che l&#039;ambra stessa non può far sì che con l&#039;aria <lb></lb>si pieghi, verso il centro dell&#039;attrazione, la fiamma di una candela. </s>

<s>“ Cor­<lb></lb>pus vero ducit ipsum manifesto in aquae globosa gutta posita supra siccum, <lb></lb>nam succinum appositum in convenienti distantia, proximas convellit par­<lb></lb>tes, et educit in conum: alioquin si ab aerè ruente adduceretur, gutta <lb></lb>tota inclinaret. </s>

<s>Quod vero aerem non trahit, sic demonstratur: Sit tenuis­<lb></lb>sima candela cerea, quae flammam minimam et claram concipiat: appone <lb></lb>huic succinum vel gagatem planum, latum, bene praeparatum, et fricatum <lb></lb>secundum artem, intra duos digitos, vel quamvis distantiam convenientem; <lb></lb>succinum tale quod longe lateque alliceret corpora, flammam tamen non <lb></lb>commovet, quod fieri, si commoveretur aer, necessum esset, flamma enim <lb></lb>fluentem aerem sequeretur ” (ibi, pag. </s>

<s>55). </s></p><p type="main">

<s>Ma l&#039;argomento più sottile e più concludente lo ritrae il Gilberto in <lb></lb>fare osservar che, per mezzo de&#039;vortici dell&#039;aria, si potrebbero bene spie­<lb></lb>gar l&#039;impeto e la veemenza, con cui le festuche son trascinate verso l&#039;am­<lb></lb>bra, ma non s&#039;intenderebbe come vi potessero essere altresì trattenute. </s>

<s>Or <lb></lb>perchè è un fatto che trattenute vi sono, dopo esservi state sospinte, la virtù <lb></lb>dunque dell&#039;ambra consiste in una vera e propria attrazione, similissima a <lb></lb>quella del Magnete e che, come quella del Magnete, s&#039;attenua essa pure col <lb></lb>crescere delle distanze. </s></p><p type="main">

<s>Qual&#039;esser può dunque, secondo il Gilberto, la causa efficiente e il prin­<lb></lb>cipio di così misteriosa attrazione? </s>

<s>“ Verisimile est, egli risponde, succinum <lb></lb>expirare aliquid peculiare quod corpora ipsa alliciat ” (ibi). Quest&#039;alito è <lb></lb>sottilissimo ne&#039;corpi elettrici; rapido e crasso ne&#039;non elettrici: in quegli si <lb></lb>ridesta per via di affrizioni leggere e sottilissime; “ ita enim tenuissima <lb></lb>evocantur effluvia ” (ibi, pag. </s>

<s>56). </s></p><p type="main">

<s>Ma come possono i corpi elettrici, per via di queste tenuissime esala-<pb xlink:href="020/01/822.jpg" pagenum="265"></pb>zioni, copulare a sè gli altri corpi? </s>

<s>“ Effluvia, risponde il Gilberto, ex subtili <lb></lb>fusione humoris existunt ” (ibi) e tutti quanti i corpi <emph type="italics"></emph>uniuntur,<emph.end type="italics"></emph.end> secondo <lb></lb>lui, <emph type="italics"></emph>et quasi ferruminantur quodammodo humore.<emph.end type="italics"></emph.end> Invoca a provar questo <lb></lb>suo assunto le attrazioni de&#039;corpuscoli galleggianti sull&#039;acqua. </s>

<s>Non ch&#039;egli <lb></lb>attribuisca il fenomeno di capillarità ad un fatto elettrico, ma lo adduce così <lb></lb>come per via di esempio, e per concluder l&#039;argomento dall&#039;analogia. </s>

<s>Pur <lb></lb>però confessando essere gli effluvii elettrici molto più sottili di quelli del­<lb></lb>l&#039;acqua, non si rimane il Gilberto dal generalizzare così la teoria dell&#039;umido <lb></lb>copulatore: “ Omnis attractio electrica fit mediante humido, ita propter hu­<lb></lb>morem omnia mutuo conveniunt ” (ibi, pag. </s>

<s>58). </s></p><p type="main">

<s>In queste speculazioni e in queste esperienze si conclude in sostanza <lb></lb>ciò che dal Gilberto, primo Autore, si trattò dell&#039;Elettro. </s>

<s>Fa maraviglia che, <lb></lb>tanto ritroso in consentire un fluido nel Magnete, a cui s&#039;attribuisce per lui <lb></lb>una virtù incorporea e immateriale, scenda a materiar poi gli effluvii elet­<lb></lb>trici da rassomigliarli alle umide esalazioni. </s>

<s>Ma la maraviglia cessa in pen­<lb></lb>sare a quali varii ufficii sieno ordinate, secondo il Filosofo, ne&#039;magisteri della <lb></lb>Natura le due diverse virtù operanti, e quale ne resulti da essa varietà di <lb></lb>moti. </s>

<s>“ Motus electricus est motus coacervationis materiae, magneticus est <lb></lb>dispositionis et conformationis. </s>

<s>Globus telluris per se electrice congregatur <lb></lb>et cohaeret, globus Telluris magnetice dirigitur et convertitur ” (ibi, pag. </s>

<s>60). </s></p><p type="main">

<s>Or è da vedere quale efficacia avessero le nuove elettriche dottrine sulla <lb></lb>mente de&#039;Filosofi curiosi d&#039;intendere la ragione di sì occulti misteri. </s>

<s>E spac­<lb></lb>ciandosene in breve, diciamo che l&#039;ipotesi gilbertina del fluido copulatore a <lb></lb>sè, per l&#039;intermedio dell&#039;umido, non sodisfece a nessuno, ond&#039;è che, non <lb></lb>vedendosi esser detto nulla di meglio, si stette all&#039;antica ipotesi di Platone. </s>

<s><lb></lb>Ne abbiamo di ciò un esempio insigne in Galileo, al quale occorrendo di do­<lb></lb>ver rendere qualche ragione delle attrazioni elettriche, le attribuì senz&#039;altro <lb></lb>all&#039;aria, che trascina nel suo vortice i corpiccioli, mostrando così di non far <lb></lb>nessun conto dell&#039;esperienze e degli argomenti che ci fondò sopra il Gilberto. <lb></lb></s>

<s>“ L&#039;ambra, egli dice, il diamante, l&#039;altre gioie e materie molto dense, ri­<lb></lb>scaldate attraggono i corpuscoli leggeri, e ciò perchè attraggono l&#039;aria nel <lb></lb>raffreddarsi, e l&#039;aria fa vento ai corpuscoli ” (Alb. </s>

<s>III, 365). </s></p><p type="main">

<s>Non avendo avuto occasion Galileo o non essendo voluto entrare in una <lb></lb>così oscura materia, all&#039;intelligenza della quale non preluceva l&#039;amabile Geo­<lb></lb>metria, non sappiamo da quali ragioni egli fosse mosso ad abbandonar nella <lb></lb>Filosofia elettrica quel Gilberto, che nella Magnetica aveva, unico fra&#039;con­<lb></lb>temporanei, così con grande ammirazion proseguito. </s>

<s>Il primo a esporre so­<lb></lb>lennemente quelle ragioni contro il gran Filosofo inglese fu Niccolò Cabeo. </s>

<s><lb></lb>Ei comincia con gran sottigliezza a discutere l&#039;ipotesi dell&#039;umido copulatore <lb></lb>in que&#039;fenomeni di capillarità, che male a nostro giudizio egli dice essere <lb></lb>stati dal Gilberto attribuiti a fenomeni elettrici. </s>

<s>Le ragioni però che ebbe <lb></lb>il nostro Ferrarese di contradire alle dottrine del Medico di Londra, pog­<lb></lb>giavano sopra più saldi fondamenti, che non sul negare l&#039;identità che passa <lb></lb>fra la causa delle attrazioni elettriche e quella dell&#039;andarsi a incontrare e a <pb xlink:href="020/01/823.jpg" pagenum="266"></pb>copularsi le festuche galleggianti sull&#039;acqua. </s>

<s>Il Cabeo, sottilissimo osserva­<lb></lb>tore, aveva a citare altri fatti che non era possibile al Gilberto spiegarli. </s></p><p type="main">

<s>Preso un pezzo d&#039;ambra e strofinatolo ben bene l&#039;applicava ad attrarre <lb></lb>la segatura del legno. </s>

<s>Osservava l&#039;attentissimo Cabeo que&#039;corpiccioli, e gli <lb></lb>vedeva dirizzarsi sulla superficie dell&#039;ambra come tanti rigidissimi peli. </s>

<s>Non <lb></lb>piegando, non cadendo, gli vedeva titubare, e dopo essere stati così alquanto <lb></lb>quasi dubbiosi, risolversi e spiccare un agilissimo salto. </s>

<s>“ Observavi autem <lb></lb>semper fere extremitates illorum pilorum fluctuare, nutare, et subinde non <lb></lb>tam decidebant extremitates illorum pilorum quam proiiciebantur procul, ut <lb></lb>manifesto observavi aliis etiam spectantibus. </s>

<s>Post aliqualem enim nutatio­<lb></lb>nem videbamus aliquas ligni particulas proiici ” (Philos. </s>

<s>magnetica, Colo­<lb></lb>niae 1629, pag. </s>

<s>194). </s></p><p type="main">

<s>Il Cabeo dunque aveva fatta una scoperta nuova e rilevantissima: aveva <lb></lb>scoperto, cioè, che non è sola proprietà dell&#039;Ambra, com&#039;aveva creduto il <lb></lb>Gilberto, quella di attrarre e di copulare, ma quella altresì di respingere e <lb></lb>separare. </s>

<s>Il fatto era per sè medesimo sufficiente a dimostrar che l&#039;ipotesi <lb></lb>gilbertina era per lo men difettosa. </s>

<s>E come potevasi dall&#039;altra parte pen­<lb></lb>sare che avesse un medesimo fluido, nello stesso tempo, due virtù così tra <lb></lb>loro contrarie, quella di attrarre e l&#039;altra di respingere? </s>

<s>Fu da ciò condotto <lb></lb>il Cabeo a negar che le due contrarie virtù fossero inerenti all&#039;ambra, ond&#039;è <lb></lb>ch&#039;ei rassomigliava quelle osservate repulsioni al rimbalzar di un corpo ela­<lb></lb>stico proiettato da qualche estrinseca forza contro un corpo duro. </s>

<s>Or dove <lb></lb>può riseder mai questa forza proiiciente? </s>

<s>E rispondeva il Cabeo: nell&#039;aria. <lb></lb></s>

<s>“ Dico igitur ex electro, seu ex quolibet corpore attrahente electrice, quando <lb></lb>sic attrahit, effluere effluvium tenuissimum, quod aerem attenuat, et disiicit, <lb></lb>imo et incitatissime impellit sed tenuiter. </s>

<s>Tum vero attenuatus et impulsus <lb></lb>aer vevertitur ad corpus electricum, secumque una rapit paleas et quae­<lb></lb>cumque obvia corpuscula ” (ibi, pag. </s>

<s>192). Così, mentre si scoprivano fatti <lb></lb>nuovi, le teorie si riducevano a quelle professate già da&#039;Filosofi antichi. </s>

<s>Un <lb></lb>secolo ancora dovrà decorrere prima che si veda la scienza uscir fuori ad <lb></lb>immaginar qualche più probabile ipotesi, a preparar la quale concorrevano <lb></lb>intanto altri nuovi e importantissimi fatti scoperti. </s></p><p type="main">

<s>La scoperta di questi nuovi fatti, che tanto poi dovevano conferire ai <lb></lb>progressi della scienza elettrica, è dovuta ad Ottone di Guericke. </s>

<s>Egli non <lb></lb>è come il Cabeo ritroso ad accettare i documenti di Filosofia magnetica del <lb></lb>Gilberto, ma gli accoglie anzi con grande amore e se ne trova mirabilmente <lb></lb>fecondato l&#039;ingegno. </s>

<s>Rimeditando su quelle parole che aveva lette: <emph type="italics"></emph>Globus <lb></lb>telluris per se electrice congregatur et cohaeret; globus telluris magnetice <lb></lb>dirigitur et convertitur,<emph.end type="italics"></emph.end> ne concludeva il Filosofo di Magdeburgo, che come <lb></lb>v&#039;è una Terrella, la quale rappresenta e imita la virtù direttrice della gran <lb></lb>Terra; così dee esservi un&#039;altra simile Terrella, che ne rappresenti e imiti <lb></lb>la virtù conservatrice, la quale principalmente dipende dalla virtù attrattiva <lb></lb>e dalla repulsiva. </s>

<s>Come il Gilberto insomma aveva ritrovata la <emph type="italics"></emph>Terrella ma­<lb></lb>gnetica,<emph.end type="italics"></emph.end> il Guericke si studiava con grande ardore di ritrovar la <emph type="italics"></emph>Terrella<emph.end type="italics"></emph.end><pb xlink:href="020/01/824.jpg" pagenum="267"></pb><emph type="italics"></emph>elettrica,<emph.end type="italics"></emph.end> la quale gli si offerse felicemente nel Zolzo, come la Terra confi­<lb></lb>gurato in globo, fatto come la Terra stessa girare attorno. </s>

<s>“ Hic globus gut­<lb></lb>tis aquarum propius admotus illas tumescentes, et turgescentes facit, pariter <lb></lb>aerem et fumum attrahit. </s>

<s>Ex quibus perspiciendum eiusmodi virtutem in <lb></lb>Tellure ad sui conservationem existere, quae etiam per attritum in singulari <lb></lb>corpore habili, videlicet hoc globulo, excitari possit ” (Experim. </s>

<s>Magdeburg. </s>

<s><lb></lb>Amstelodami 1672, pag. </s>

<s>147). </s></p><p type="main">

<s>L&#039;attrito esercitato colla mano in questo globo di zolfo fu cagione che <lb></lb>si rappresentassero agli occhi dell&#039;attento sperimentatore i fatti spettacolosi <lb></lb>da nessuno innanzi avvertiti. </s>

<s>E prima di tutto, tenne dietro a quelle repul­<lb></lb>sioni, che dal Cabeo erano state credute un puro gioco meccanico. </s>

<s>Che v&#039;in­<lb></lb>tervenisse però, non l&#039;azione esterna dell&#039;aria, ma l&#039;intrinseca virtù propria <lb></lb>del corpo elettrizzato, lo argomentò il sagace Filosofo dal fatto notabilissimo <lb></lb>che i corpuscoli attratti, e poi respinti, non tornavano ad essere attratti dal <lb></lb>globo, se non avevano prima toccato qualche altro corpo straniero. </s>

<s>S&#039;ac­<lb></lb>corse di ciò il Guericke osservando le attrazioni e le ripulsioni ne&#039;corpi <lb></lb>leggerissimi, che rimangon facilmente sospesi nell&#039;aria, fra&#039;quali corpi trovò <lb></lb>attissime alle sue esperienze le piume lanuginose e molli. </s>

<s>” Haec virtus au­<lb></lb>tem in plumis mollioribus et levioribus, omnium optime cognoscenda est, <lb></lb>quia in terram non eo citius cadunt quam alia frustula, exinde illae sur­<lb></lb>sum propulsae, in orbe virtutis huius globi pendulae, diutius sustineri, et sic <lb></lb>cum globo, eo quo velis, in toto conclavi circumagi possunt ” (ibi, pag. </s>

<s>147). </s></p><p type="main">

<s>E qui la Terrella elettrica non è in rappresentar nuovi cospicui fatti al <lb></lb>Guericke, men feconda di quel che si fosse la Terrella magnetica al Gil­<lb></lb>berto. </s>

<s>“ Circa quod praeterea notanda sunt: I. </s>

<s>Che la piuma, tanto sul globo <lb></lb>quanto per aria, distende la sua molle lanugine, come se fosse viva, e, ri­<lb></lb>manendo così sospesa, ora i corpiccioli notanti si muovono ad essa, ora è <lb></lb>proprio lei che va a cercare i corpi stabili, posandosi sopra le loro punte <lb></lb>più volentieri. </s>

<s>Appressandole una fiamma, per esempio quella di una can­<lb></lb>dela, subito rifugge al Globo, <emph type="italics"></emph>atque penes illum quasi praesidium quaerit.<emph.end type="italics"></emph.end><lb></lb>II. </s>

<s>La piuma si volge al Globo sempre dalla medesima parte, a quel modo <lb></lb>che tien sempre rivolta verso la Terra la medesima faccia la Luna. </s>

<s>III. </s>

<s>Se <lb></lb>mentre che la piuma è attaccata al Globo le si presenta la punta di un dito, <lb></lb>vi corre subito desiderosa, e poi ritorna al Globo stesso, ripetendo così lun­<lb></lb>gamente il medesimo gioco. </s>

<s>IV. </s>

<s>Se un filo di lino sospeso in alto scende a <lb></lb>toccare il Globo, rifugge indietro appuntandogli un dito. </s>

<s>V. </s>

<s>La virtù del <lb></lb>Globo si comunica a un fil di lino lungo circa un braccio in modo, che può <lb></lb>tirare il capo di un altro filo che se gli accosti, e quasi rannodarsi con esso. </s>

<s><lb></lb>VI. </s>

<s>Sottoposta la piuma al Globo confricato, sul piano della Macchina, viene <lb></lb>attratta e respinta con lunga vicenda. </s>

<s>VII. </s>

<s>Posto il medesimo Globo in una <lb></lb>stanza al buio, si mostra splendere in quella luce, che suole il zucchero <lb></lb>stritolato col pestello ” (ivi). </s></p><p type="main">

<s>Il concetto, che s&#039;era il Guericke formato della Terrella elettrica, la <lb></lb>quale rappresenta tutte insieme unite le virtù della gran Terra, serviva al <pb xlink:href="020/01/825.jpg" pagenum="268"></pb>Filosofo di fondamento a una teoria generale, che pareva dispensarlo dal­<lb></lb>l&#039;investigare altre teorie particolari. </s>

<s>Ma benchè di queste particolari teorie, <lb></lb>il valoroso Magdeburgese, non si travagli, non lascia però di confutare il <lb></lb>Cabeo, l&#039;ipotesi del quale ei giudica che sia forse men ragionevole di quella <lb></lb>del Gilberto. </s>

<s>“ Non possumus concedere hanc attractionem mediante aere <lb></lb>fieri, quia experimenta oculariter monstrant hunc sulphureum Globum, at­<lb></lb>tritione antea excitatum, suam quoque virtutem per filum lineum, ulnam <lb></lb>et ultra longum, posse exercere, et ibi aliquid attrahere ” (ibi). </s></p><p type="main">

<s>Così veniva la nuova Scienza ad arricchirsi di fatti, de&#039;quali però non <lb></lb>si penetravano le ragioni, essendo manifestamente le ipotesi del Gilberto e <lb></lb>del Cabeo insufficienti a spiegarli. </s>

<s>Nonostante, non s&#039;era ancora di quelle <lb></lb>ipotesi trovata una confutazione diretta, per la quale sarebbe stato conclu­<lb></lb>dentissimo il provar che l&#039;ambra e lo zolfo attraggono anche senza l&#039;inter­<lb></lb>vento dell&#039;aria in uno spazio vuoto. </s>

<s>Lo zelo de&#039;nostri Accademici fiorentini <lb></lb>gli indusse a tentar, con mirabile industria, la prova nel vuoto torricelliano, <lb></lb>ma le pretese ch&#039;ebbero di esercitar la confricazione in esso vuoto, riusci­<lb></lb>rono per far confessare al loro Segretario che l&#039;esperienza <emph type="italics"></emph>fu tentata per <lb></lb>tante vie inutilmente<emph.end type="italics"></emph.end> (Saggi ecc., Firenze 1841, pag. </s>

<s>54). </s></p><p type="main">

<s>Disanimati così in sulle prime, poco frutto per verità raccolsero nel <lb></lb>campo delle esperienze elettriche i Nostri. </s>

<s>Con facile trasformazione del Ver­<lb></lb>sorio gilbertino dimostrarono che la virtù dell&#039;Ambra di tirare a sè i corpi <lb></lb>“ è un&#039;azione scambievole e niente più propria dell&#039;Ambra che de&#039;mede­<lb></lb>simi corpi, da&#039;quali anch&#039;essa è tirata ” (ivi, pag. </s>

<s>146). Avvertirono altresi <lb></lb>che <emph type="italics"></emph>la seta sfilaccicata corre alla mano,<emph.end type="italics"></emph.end> e s&#039;erano proposto anco questo <lb></lb>fra alcuni altri <emph type="italics"></emph>curiosi problemi da esplorare<emph.end type="italics"></emph.end> (MSS. Cim., T. II, P. I, c. </s>

<s>178), <lb></lb>ma sventuratamente abbandonarono il proposito, che gli avrebbe potuti con­<lb></lb>durre alla scoperta fatta poi dal Symmer e da altri Fisici inglesi. </s></p><p type="main">

<s>Del resto, gli Accademici del Cimento non fecero altro che confermare, <lb></lb>e in qualche parte illustrare, l&#039;esperienze del Gilberto. </s>

<s>“ Ruunt ad electria, <lb></lb>aveva egli lasciato scritto, omnia praeter flammam et inflammata, et aerem <lb></lb>tenuissimum, sicut flammam non ducunt .... manifestum enim est quod <lb></lb>effluvia destruuntur a flamma et calore igneo, quare nec flammam nec cor­<lb></lb>pora flammae propinquiora provocant.... Fumum tamen excitatum extincto <lb></lb>lumine allectant, et quanto magis fumus ille superiora petens extenuatur, <lb></lb>tanto infirmius inclinat, nimis enim rara non deducuntur, tandemque, cum <lb></lb>iam fere evanuit, nihil inclinat, quod versus lucem facile cernitur ” (De Ma­<lb></lb>gnete cit., pag. </s>

<s>59). </s></p><p type="main">

<s>I nostri Accademici pure sperimentarono che la fiamma non solo non <lb></lb>si lascia tirar per sè “ ma se l&#039;Ambra dopo strofinata le rigira punto dat­<lb></lb>torno, spegne la virtù sua, onde vi bisogna nuovo strofinamento per farla <lb></lb>tirare ” (Saggi cit., pag. </s>

<s>145). Quanto al fumo, sperimentarono ch&#039;esso pure <lb></lb>viene attratto “ anzi assai curioso, soggiungono, è il vedere come accostan­<lb></lb>dosi l&#039;Ambra già strofinata e calda a quel fumo, che sorge da una candela <lb></lb>allora spenta, questo piega subito alla volta dell&#039;Ambra. </s>

<s>Quivi dunque parte <pb xlink:href="020/01/826.jpg" pagenum="269"></pb>ne riman preso e parte come riflesso da specchio si leva in alto, mentre <lb></lb>quello che vi rimane si raguna in sembianza di una piccola nuvoletta, la <lb></lb>quale, secondo che l&#039;Ambra va raffreddandosi, si discioglie novamente in <lb></lb>fumo e si parte ” (ivi, pag. </s>

<s>144). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dopo l&#039;esperienze del Guericke e de&#039;nostri Accademici del Cimento, <lb></lb>parve avvenisse alla Scienza elettrica quel che suole avvenire a una sementa, <lb></lb>che germogliata lietamente in Autunno arresta i suoi progressi, e quasi as­<lb></lb>siderata, intristisce sotto il cielo invernale, infin tanto che non le soprav­<lb></lb>vengano i dolci tepori e le roride piogge di Primavera. </s>

<s>Incominciò la lieta <lb></lb>stagione novella coll&#039;entrar del secolo XVIII, quando la fosforescenza osser­<lb></lb>vata nella camera barometrica, facendo risovvenir l&#039;Hawksbee della fosfo­<lb></lb>rescenza nel Globo sulfureo di Magdeburgo, lo condusse a derivare il foco <lb></lb>elettrico dai globi tornatili di vetro. </s></p><p type="main">

<s>Furono principalmente rivolte le attenzioni del Fisico inglese alla diffe­<lb></lb>rente emanazione di luce osservata, o quando il globo vitreo era vuoto, o <lb></lb>quando gli veniva riammessa la prim&#039;aria. </s>

<s>“ In questo caso è da notarsi, <lb></lb>scrive l&#039;Autore, che riscaldatosi il vetro, la mano veniva continuamente se­<lb></lb>guitata nel suo moto da una luce o lume, che andava innanzi e indietro. </s>

<s>E <lb></lb>nello stesso tempo, se un&#039;altra mano era tenuta vicino al tubo, spuntava <lb></lb>una luce evidente da quello, e questa accompagnata da uno strepito simile <lb></lb>a quello dello scoppiettare nel fuoco d&#039;una foglia verde, ma non così forte.... <lb></lb>Ma quando fu cavata l&#039;aria dal tubo, vi comparve una differenza notabile, <lb></lb>tanto in riguardo alla luce che a&#039;suoi effetti. </s>

<s>Conciossiachè alla prima con­<lb></lb>fricazione del vetro ne insorse in vero una maggior luce, ma pareva bensi <lb></lb>del tutto perduta la qualità di dar luce ad un corpo, che gli fosse tenuto <lb></lb>vicino. </s>

<s>E la luce (che è un&#039;altra non meno notabile differenza, prodotta dalla <lb></lb>confricazione dell&#039;esausto tubo) appariva totalmente per entro di quello. </s>

<s>Dove <lb></lb>che quella discoperta, quando il tubo era pieno d&#039;aria, pareva che fosse to­<lb></lb>talmente al di fuori ” (Esperienze fisico-meccaniche, traduz. </s>

<s>ital., Firenze 1716, <lb></lb>pag. </s>

<s>40). </s></p><p type="main">

<s>La differenza de&#039;fenomeni osservati però non distolse l&#039;Hawksbee dalla <lb></lb>persuasione che non fosse quella luce effluita dal vetro, e anzi riconobbe la <lb></lb>ragione di una tal differenza da&#039;varii impedimenti opposti dall&#039;aria al libero <lb></lb>passaggio di quegli effluvii. </s>

<s>Ma di qual natura è quel fuoco elettrico esa­<lb></lb>lato dal vetro, o qual relazione ha col foco ordinario? </s>

<s>La prima esperienza <lb></lb>istituita non a risponder direttamente ma a preparar le vie da rispondere <lb></lb>alla domanda, fu quella della pietra focaia, che si trovò non scintillare nel <lb></lb>vuoto, d&#039;onde se ne trasse la conclusione importante “ che la presenza del­<lb></lb>l&#039;aria sia assolutamente necessaria per quel vigoroso moto espansivo delle <lb></lb>parti de&#039;corpi, i quali costano della natura stessa del foco di cucina ” (ivi, <pb xlink:href="020/01/827.jpg" pagenum="270"></pb>pag. </s>

<s>19). Ora poichè producesi il foco elettrico anco nel vuoto, pareva se ne <lb></lb>potesse concluder di qui la differente natura di lui dal foco ordinario. </s></p><p type="main">

<s>Una dimostrazione diretta però della differente natura di questi due <lb></lb>fochi veniva dal veder che l&#039;elettrico si produceva anche nell&#039;acqua, con­<lb></lb>fricando sott&#039;essa insieme due vetri. </s>

<s>“ Vediamo dunque che la luce è pro­<lb></lb>ducibile dalla confricazione di vetro sopra vetro, non solamente in voto e in <lb></lb>aria aperta, ma nell&#039;acqua ancora. </s>

<s>Quinci evidente si è di più che i vetri <lb></lb>non sono infocati dalla confricazione qualunque si sia la somiglianza che ne <lb></lb>porta seco il colore ” (ivi, pag. </s>

<s>29). </s></p><p type="main">

<s>Venendo chiaramente dimostrato di qui che il foco elettrico è di diversa <lb></lb>natura da quello, che si produce dal calore ordinario, sarebb&#039;egli mai piut­<lb></lb>tosto identico a quello che induce la fosforescenza ne&#039;legni umidi o in altri <lb></lb>simili corpi? </s>

<s>Per rispondere a ciò “ presi, dice l&#039;Autore, un pezzo di legno, <lb></lb>il quale mi suppongo che fosse stato lungo tempo sotto terra, molto umido <lb></lb>ma non infracidito. </s>

<s>Al buio appariva vivacissimamente di color di foco, ma <lb></lb>avendolo rinchiuso in un recipiente sopra la Tromba, trovai che, a misura <lb></lb>che se ne traeva l&#039;aria, smontava a proporzione l&#039;apparenza di somiglianza <lb></lb>di foco, e da ultimo nel voto diveniva affatto privo di luce ” (ivi, pag. </s>

<s>34). <lb></lb>Agli effetti dunque non appariva nessuna corrispondenza fra i fenomeni elet­<lb></lb>trici e i fosforescenti. </s></p><p type="main">

<s>Così lasciava l&#039;Hawksbee indecisa la questione della natura del foco <lb></lb>elettrico, come il gran Newton poco di poi lasciava indecisa la questione <lb></lb>della natura e dell&#039;origine di qualunque altra sorta di foco. </s>

<s>“ Annon cor­<lb></lb>pora omnia fixa, quum sint ultra certum gradum calafacta, emittunt lumen <lb></lb>et splendent? </s>

<s>Eaque luminis emissio per motus vibrantes partium suarum <lb></lb>efficitur? </s>

<s>Et annon corpora omnia, quae partibus abundant terrestribus et <lb></lb>praesertim sulphorosis, lumen emittunt, quotiescumque partes illae satis sint <lb></lb>agitatae, sive id calore fiat, sive attritu, sive percussu, sive putrescendo, sive <lb></lb>motu aliquo vitali, sive alia quavis de causa? </s>

<s>ut aqua marina saeviente pro­<lb></lb>cella, argentum vivum in vacuo agitatum, felis dorsum vel equi collum manu <lb></lb>oblique in loco tenebricoso affrictum; ligna, carnes et pisces dum putre­<lb></lb>scunt vapores ex aquis putridis, qui ignes fatui vulgo appellantur, metae <lb></lb>foeni segetisve subhumidae fermentescentes, cicindulae, et animalium quo­<lb></lb>rundam oculi, motu quodam vitali; phosphorus bononiensis, radiis luminis <lb></lb>agitatus; phosphorus vulgaris, corporis cuiusvis attritu, vel acidis aeris par­<lb></lb>ticulis agitatus; electrum, et adamantes aliqui, feriendo, premendo vel fri­<lb></lb>cando; chalybis strigmenta, silice decussa; ferrum ictibus malleorum cale­<lb></lb>factum, donec sulphur sibi iniectum accendat; axes curruum, motu rotarum <lb></lb>rapidiore incensi; et certi liquores inter se permixti, quorum particulae cum <lb></lb>impetu concurrunt, ut oleum vitrioli a nitro pari pondere distillatum, dein <lb></lb>dupla portione mixtum cum oleo caryophillorum, sive anisi. </s>

<s>Similiter glo­<lb></lb>bus vitreus .... machinae versatili infixus .... qua sui parte vola manus <lb></lb>apposita, inter volvendum confricatur, lucebit ” (Optices lib. </s>

<s>III, quaestio VIII, <lb></lb>Patavii 1773, pag. </s>

<s>138, 39). </s></p><pb xlink:href="020/01/828.jpg" pagenum="271"></pb><p type="main">

<s>Troppo più gran progressi doveva fare la scienza, prima di assegnare <lb></lb>a ciascuna specie di fochi, nel lungo ordine dal Newton annoverati, la causa <lb></lb>distinta e l&#039;origine propria, e perciò tornando all&#039;Hawksbee è da veder quel <lb></lb>ch&#039;egli pensasse intorno alle ragioni di molti altri fatti da sè diligentissi­<lb></lb>mamente sperimentati. </s>

<s>La più bella riuscita di queste sue esperienze si potè <lb></lb>facilmente conseguirla, sostituendo al primo globo un cilindro concavo di <lb></lb>vetro, e benchè avesse così col nuovo strumento ottenuto tanto maggiore <lb></lb>energia elettrica, e tanto più cospicui gli effetti, ebbe nonostante a notare <lb></lb>una gran differenza, che non era possibile non attribuire al variar delle <lb></lb>stagioni. </s></p><p type="main">

<s>Già, infin dal Gilberto, era stato notato che il Sal gemma, la Pietra <lb></lb>speculare e l&#039;Allume di rocca non tirano, se non <emph type="italics"></emph>cum aer media hyeme <lb></lb>rigidus fuerit et clarus tenuisque<emph.end type="italics"></emph.end> (De Magn. </s>

<s>cit., pag. </s>

<s>48). Il Cabeo pure <lb></lb>aveva avvertito che l&#039;esperienze delle attrazioni elettriche volevano esser fatte <lb></lb><emph type="italics"></emph>coelo sereno et puro, non humido aut nebuloso<emph.end type="italics"></emph.end> (Phil. </s>

<s>magn. </s>

<s>cit., pag. </s>

<s>193). <lb></lb>E in conformità de&#039;due più antichi Autori veniva ripetendo l&#039;Hawksbee di <lb></lb>aver sempre osservato <emph type="italics"></emph>che l&#039;umido è gran nemico di tutte l&#039;esperienze di <lb></lb>questa sorta<emph.end type="italics"></emph.end> (Esper. </s>

<s>cit., pag, 37). </s></p><p type="main">

<s>E perchè facile parve a tutt&#039;e tre gli Autori il rinvenir la causa di un <lb></lb>effetto così costante, il Gilberto l&#039;attribuì a ciò che nell&#039;inverno <emph type="italics"></emph>effluvia <lb></lb>telluris electrica minus impediunt et electrica firmius indurescunt<emph.end type="italics"></emph.end> (De <lb></lb>Magn. </s>

<s>cit., pag. </s>

<s>48). Il Cabeo poi riconobbe l&#039;umido riuscire a&#039;corpi elet­<lb></lb>trici così nocivo, perchè <emph type="italics"></emph>aere statim obnubilatur corpus quod debet esse <lb></lb>nitidissimum, et impeditur transpiratio effluvii. </s>

<s>Imo ex hac praecipue <lb></lb>causa oritur ut electrum non trahat, nisi praeparatum fricatione<emph.end type="italics"></emph.end> (Phil. </s>

<s><lb></lb>magn. </s>

<s>cit., pag. </s>

<s>193). </s></p><p type="main">

<s>Nè dopo un mezzo secolo e alquanti anni di più, fra tante squisitezze <lb></lb>di macchine, e fra tanta dovizia di sperimenti, sa dir l&#039;Hawksbee nulla di <lb></lb>meglio de&#039;due suoi predecessori. </s>

<s>“ Quando l&#039;aria è densa o da umide ed <lb></lb>acquee o da altre più grosse e solide parti, sollevate dal vasto fondo della <lb></lb>terrestre materia, quaggiù ingombrata; non vi è dubbio che la resistenza, <lb></lb>che allora incontrano questi belli effluvii nel loro viaggio, bisogna che sia <lb></lb>molto più grande che quando l&#039;aria è schietta e libera, e che non accadono <lb></lb>tali impedimenti da opporsi nel suo passaggio. </s>

<s>Poichè gli effluvii, per quanto <lb></lb>mai sottili che si possano immaginare, sono tuttavia corpo e materia, e però <lb></lb>debbono esser soggetti alla comune legge dei corpi, quale si è di dover <lb></lb>trovare resistenza in qualche proporzione alla forza e densità del mezzo ” <lb></lb>(Esper. </s>

<s>cit., pag. </s>

<s>36). Crede anzi l&#039;Hawksbee d&#039;aver di ciò una dimostra­<lb></lb>zione oculare nell&#039;esperienza di una mussolina, che interposta e tesa fra il <lb></lb>cilindro confricato e alcuni frammenti di orpello, impedisce a questi di es­<lb></lb>sere attratti (ivi, pag. </s>

<s>37). </s></p><p type="main">

<s>Ma poniamo che queste ragioni, intorno alle quali i tre primi e prin­<lb></lb>cipali Autori della Filosofia elettrica si trovarono concordi, quietassero i cu­<lb></lb>riosi, per avere qualche apparenza d&#039;esser probabili, restavano però tuttavia <pb xlink:href="020/01/829.jpg" pagenum="272"></pb>misteriosi que&#039;molti altri fatti elettrici sperimentati in Magdeburgo. </s>

<s>La chiave <lb></lb>del mistero era capitata alle mani dello stesso Ottone di Guericke quand&#039;egli <lb></lb>ebbe trovato che la virtù del suo Globo di zolfo si <emph type="italics"></emph>comunicava,<emph.end type="italics"></emph.end> e si dif­<lb></lb>fondeva per quel braccio e più, quant&#039;era lungo il filo di lino. </s>

<s>Ma non seppe <lb></lb>indovinar di quali conseguenze sarebbe stata quella sua esperienza feconda, <lb></lb>ciò che un mezzo secolo e più dopo fu riserbato al fortunatissimo Gray. </s>

<s>Egli <lb></lb>primo accortosi che l&#039;elettricità del globo tornatile si comunicava all&#039;asse di <lb></lb>metallo, e a&#039;perni della macchina, si condusse di prova in prova a comu­<lb></lb>nicare e a diffondere l&#039;elettricità, no ne&#039;soli fili di lino, benchè tanto più <lb></lb>lunghi di quelli del Guericke, ma nelle verghe di qualunque sorta di me­<lb></lb>tallo, e anzi in tutti i corpi, eccettuati il vetro, la seta, la resina e tutti quelli <lb></lb>insomma annoverati di sopra dal Gilberto, i quali avendo la virtù di ride­<lb></lb>starla in sè stessi, non patiscono che sia l&#039;elettricità comunicata a loro dagli <lb></lb>altri corpi. </s>

<s>Anzi mettendovisi di mezzo, ne impediscono il libero corso, per <lb></lb>cui, dal contener la nativa elettricità, furono detti <emph type="italics"></emph>idioelettrici,<emph.end type="italics"></emph.end> e dall&#039;im­<lb></lb>pedirne il corso, <emph type="italics"></emph>coibenti.<emph.end type="italics"></emph.end> Per aver poi virtù a questi contrarie, tutti gli altri <lb></lb>corpi si chiamarono <emph type="italics"></emph>anelettici<emph.end type="italics"></emph.end> e <emph type="italics"></emph>deferenti.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Questa del Gray confermata dal Dufay fu un&#039;insigne scoperta, per la <lb></lb>quale venne tanto valido impulso al progredir della scienza. </s>

<s>S&#039;intese infatti <lb></lb>allora che l&#039;umidità rintuzza la forza elettrica, perch&#039;essendo l&#039;acqua un <lb></lb>corpo deferente dissipa il fluido via via ch&#039;esce dall&#039;ambra e dal vetro. </s>

<s>S&#039;in­<lb></lb>tesero allora i miracoli operati dalla piuma intorno al Globo sulfureo di <lb></lb>Magdeburgo, e com&#039;essa piuma, elettrizzata già per comunicazione, avendo <lb></lb>perduta l&#039;elettricità sua propria, per averla comunicata al corpo che la toc­<lb></lb>cava, tornasse nuovamente al Globo per riacquistarla. </s></p><p type="main">

<s>S&#039;intesero gli altri fatti ancora ordinatamente descritti dal Guericke, <lb></lb>ma pur alcuni rimanevano tuttavia irresoluti, e fra questi quello principal­<lb></lb>mente della piuma che ritorna al globo dalla fiamma della candela. </s>

<s>La dif­<lb></lb>ficoltà pareva venisse tolta dall&#039;osservazion del Gilberto confermata poi dai <lb></lb>nostri Accademici fiorentini, che cioè la fiamma spenge la virtù elettrica, ma <lb></lb>ciò non poteva entrare nell&#039;ordine delle nuove idee, se non ammettendo che <lb></lb>fosse anche la fiamma un corpo deferente. </s>

<s>Ora nè il Gray nè il Dufay ave­<lb></lb>vano osato di asserir tanto, anzi ebbero a concludere, dalle loro incerte espe­<lb></lb>rienze, che la materia elettrica o non veniva direttamente comunicata alla <lb></lb>fiamma, o che non si vedevano operarsi in lei gli effetti consueti. </s></p><p type="main">

<s>Più tardi il Krugers e il Winkler riuscirono a condur l&#039;elettricità at­<lb></lb>traverso alla fiamma di una candela, e alla vampa dello spirito di vino, ma <lb></lb>nessun seppe maneggiar la difficile sperienza con più elegante semplicità di <lb></lb>un nostro Italiano. </s>

<s>Egli è per noi senza dubbio il Gray degl&#039;Inglesi, e il <lb></lb>Dufay de&#039;Francesi, e ci duole perciò il non poterne onorare il nome, avendo <lb></lb>egli, non si sa perchè, mandato fuori, prima in Venezia nel 1746 poi l&#039;anno <lb></lb>dopo in Napoli il suo Libro <emph type="italics"></emph>Dell&#039;elettricismo,<emph.end type="italics"></emph.end> innominato. </s>

<s>Così dunque de­<lb></lb>scrive l&#039;elegante esperienza quel nostro Innominato: </s></p><p type="main">

<s>“ Io misi sopra una verga di ferro, sospesa da corde di seta orizzon-<pb xlink:href="020/01/830.jpg" pagenum="273"></pb>talmente, due piccoli cerini accesi, l&#039;uno assai vicino all&#039;altro, così però che <lb></lb>le loro fiamme si stessero lontane l&#039;una dall&#039;altra per un pollice. </s>

<s>Subito <lb></lb>che comunicai l&#039;elettricità alla verga di ferro le due fiamme, che prima sta­<lb></lb>vano ritte, si fuggirono l&#039;una dall&#039;altra. </s>

<s>Toccavo con un dito le verghe, ed <lb></lb>elleno si rimettevano nel luogo; rimovevo il dito, ed elleno ritornavano a <lb></lb>fuggirsi ” (Napoli 1647, pag. </s>

<s>144). </s></p><p type="main">

<s>Ma nè da queste sì ingegnose esperienze si vedeva ancora uscire un <lb></lb>raggio di luce all&#039;intelligenza di un altro, ch&#039;è pur tra i fatti osservati dal <lb></lb>Guericke, ed è che la piuma, più volentieri che altrove, s&#039;andava a posar <lb></lb>sulle punte dei corpi circostanti. </s>

<s>Ha questo stesso fatto una invisibile rela­<lb></lb>zione con un assai singolare effetto osservato dagli Accademici fiorentini nei <lb></lb>diamanti, ed è che, fra questi, i gruppiti son ricchi di potenza elettrica, men­<lb></lb>tre riescon, segati in tavole, così deboli e fiacchi (Saggi cit., pag. </s>

<s>147). Ma <lb></lb>per l&#039;intelligenza di simili effetti si richiedevano nella Filosofia elettrica nuovi <lb></lb>progressi, prima di venire a&#039;quali giova trattenersi sopra un&#039;altra singolar <lb></lb>differenza che fu notata, nel modo di attrarre, fra i così detti corpi idioe­<lb></lb>lettrici. </s></p><p type="main">

<s>Essendo passato l&#039;Hawksbee dalle esperienze elettriche fatte col vetro a <lb></lb>quelle fatte colla ceralacca, della miglior qualità che avesse potuto trovare, <lb></lb>parvegli aver riscontrato tanta somiglianza in que&#039;loro effetti, da conclu­<lb></lb>derne che “ l&#039;elettriche qualità di quei due corpi sono le medesime, quanto <lb></lb>a tutte le più generali proprietà: sono solamente discrepanti ne&#039;gradi, gli <lb></lb>effluvii del vetro producendo effetti più potenti di quelli della ceralacca ” <lb></lb>(Esperienze cit., pag. </s>

<s>95). </s></p><p type="main">

<s>Poco dopo s&#039;osservarono però alcuni fatti, da&#039;quali se ne volle conclu­<lb></lb>dere che questa sentenza dell&#039;Hawksbee non era vera. </s>

<s>Si osservò che il ve­<lb></lb>tro elettrizzato o non tirava a sè, o debolmente tirava certi minuzzoli di <lb></lb>vetro, che se gli ponevano appresso: si osservò pure che la ceralacca o l&#039;am­<lb></lb>bra facevano lo stesso verso bricioli della medesima sostanza resinosa, ma <lb></lb>che al contrario il vetro tirava con avidità i minimi corpiccioli della cera­<lb></lb>lacca, e la ceralacca i minimi corpiccioli del vetro. </s>

<s>Da questi fatti dunque <lb></lb>il Dufay volle concluderne che, tra la virtù elettrica del vetro e quella della <lb></lb>ceralacca, non passava, come l&#039;Hawksbee aveva asserito, una semplice di­<lb></lb>screpanza di gradi, ma di natura, e introdusse, egli stesso il Dufay, per de­<lb></lb>signare una tale essenzial discrepanza, i nomi di elettricità <emph type="italics"></emph>vitrea,<emph.end type="italics"></emph.end> e di elet­<lb></lb>tricità <emph type="italics"></emph>resinosa.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Fu questa distinzione accolta con docilità in Francia e per qualche <lb></lb>tempo anche in Inghilterra, ma il nostro Italiano innominato protestò con­<lb></lb>tro una tal distinzione, qualificandola per <emph type="italics"></emph>un&#039;ipotesi poco o niente verisi­<lb></lb>mile,<emph.end type="italics"></emph.end> e che introdurrebbe <emph type="italics"></emph>una moltiplicità nociva alle semplici maniere, <lb></lb>colle quali operar suol la Natura.<emph.end type="italics"></emph.end> (Dell&#039;Elettric. </s>

<s>cit., pag. </s>

<s>177). </s></p><p type="main">

<s>L&#039;Elettricità vitrea non è, secondo il nostro illustre Italiano, di qualità <lb></lb>e di natura diversa dalla resinosa, ma sono ambedue il medesimo fluido, che <lb></lb>quà opera in un modo, secondo il grado della sua intensità, e là si vede <pb xlink:href="020/01/831.jpg" pagenum="274"></pb>invece operare in un altro. </s>

<s>La diversità de&#039;modi com&#039;egli crede che l&#039;elet­<lb></lb>tricità operi nelle resine e ne&#039;vetri, è da lui stesso, dal nostro Autore del <lb></lb>libro <emph type="italics"></emph>Dell&#039;elettricismo,<emph.end type="italics"></emph.end> descritta colle seguenti parole, nelle quali si con­<lb></lb>tiene espressa la prima fra le teorie elettriche razionali ch&#039;abbia avuto la <lb></lb>scienza. </s></p><p type="main">

<s>“ La ragione del fenomeno qui motivato, riguardo all&#039;elettricità <emph type="italics"></emph>vitrea<emph.end type="italics"></emph.end><lb></lb>e <emph type="italics"></emph>resinosa,<emph.end type="italics"></emph.end> ci apre la strada alla risoluzione ancora di molti altri effetti, che <lb></lb>sembrano incomprensibili. </s>

<s>Cotesta ragione è fondata sulla direzione recurva <lb></lb>che prende la materia elettrica ne&#039;corpi originalmente o per comunicazione <lb></lb>elettrizzati. </s>

<s>Egli è certo che i corpi resinosi, per quanto si elettrizzino, non <lb></lb>diventano mai capaci di render fuori, toccati che siano, luce alcuna fulmi­<lb></lb>nante, come a suo luogo diremo, ond&#039;è che il loro vortice anche originario <lb></lb>tiene un vigore molto inferiore a quello de&#039;corpi vitrei, de quali il vortice <lb></lb>elettrico gode d&#039;un insigne energia. </s>

<s>” </s></p><p type="main">

<s>“ Colui che intende la dottrina de&#039;vortici sa bene che due vortici di <lb></lb>ugual vigore, e che si premono con ugual forza l&#039;uno l&#039;altro, non si pos­<lb></lb>sono alternativamente distruggere, ma ciò fanno di leggeri allora sì, quando <lb></lb>l&#039;uno si trova più debole dell&#039;altro. </s>

<s>Ora essendo proprio de&#039;corpi facilmente <lb></lb>elettrizzabili per comunicazione di ricevere e di assorbire in sè stessi la ma­<lb></lb>teria elettrica vestendosi d&#039;un vortice, subito che entrano in alcun altro <lb></lb>vortice mandato e formato da qualche corpo elettrizzato; così una foglia <lb></lb>d&#039;oro che cadendo dall&#039;alto s&#039;avvia verso la canna di vetro elettrizzata, ap­<lb></lb>pena entra nell&#039;atmosfera elettrica di essa, ossia nel di lei vortice, ch&#039;ella <lb></lb>pure si veste di un piccol vortice avente l&#039;energia stessa de&#039;strati del vor­<lb></lb>tice della canna pe&#039;quali passa, sicchè per l&#039;uguaglianza delle azioni d&#039;am­<lb></lb>bedue questi vortici, l&#039;uno maggiore e l&#039;altro minore, la foglietta d&#039;oro è <lb></lb>obbligata a star sospesa nell&#039;aria, senz&#039;ardir punto d&#039;avanzarsi più oltre <lb></lb>verso la canna stessa. </s>

<s>Ma all&#039;incontro, essendovi due vortici inuguali di <lb></lb>forze, il più forte è quello che superchia il più debole, ond&#039;è che avendo <lb></lb>la stessa foglietta d&#039;oro il suo vortice più gagliardo del vortice d&#039;un pezzo <lb></lb>d&#039;ambra o di resina, conviene ch&#039;ella s&#039;avvicini alla resina stessa giacchè <lb></lb>la resina, come un pezzo più grave e grande, non può moversi verso di lei <lb></lb>ch&#039;è un corpetto leggerissimo e sciolto. </s>

<s>” </s></p><p type="main">

<s>“ Se tal foglietta d&#039;oro corredata del suo piccolo vortice è toccata da <lb></lb>un dito, il dito assorbe in sè esso vortice, e così la foglietta resta in istato <lb></lb>d&#039;essere attirata da&#039;vortici vicini se ve ne sono. </s>

<s>Peraltro bisogna badare che <lb></lb>un vortice, quantunque più grande d&#039;un altro, egli però potrà esser più de­<lb></lb>bole di questo, quando la materia del più grande sia meno densa e veloce. </s>

<s>” </s></p><p type="main">

<s>“ Ogni vortice è composto come di tanti strati concentrici, de&#039;quali li <lb></lb>più vicini al centro sono i più densi e più forti. </s>

<s>Li vortici di materia <emph type="italics"></emph>vitrea<emph.end type="italics"></emph.end><lb></lb>sono in tutti i loro strati più forti di tutti i strati de&#039;vortici della materia <lb></lb><emph type="italics"></emph>resinosa.<emph.end type="italics"></emph.end> Ed ecco che non sono queste due specie di elettricità, ma solo due <lb></lb>diversi gradi d&#039;intensione e di vigore. </s>

<s>Immaginatevi, ciò che punto non si <lb></lb>discosta dal vero, che il vortice dell&#039;elettricità <emph type="italics"></emph>vitrea<emph.end type="italics"></emph.end> sia più denso di quello <pb xlink:href="020/01/832.jpg" pagenum="275"></pb>dell&#039;etettricità <emph type="italics"></emph>resinosa,<emph.end type="italics"></emph.end> e vi sarà facile di sciorre ogni difficoltà, che vi po­<lb></lb>tesse cadere su questo proposito ” (ivi, pag. </s>

<s>182-84). </s></p><p type="main">

<s>La teoria del nostro Italiano fu in così bel modo illustrata da Benia­<lb></lb>mino Frankliń, che s&#039;introdusse nella scienza universale dell&#039;Elettricismo <lb></lb>sotto il venerato e autorevole nome di lui. </s>

<s>Ripensava l&#039;Inglese di Pensil­<lb></lb>vania a quella piuma del Guericke, che s&#039;andava a posar sulle punte più <lb></lb>volentieri che sulle parti arrotondate de&#039;corpi, e negli insegnamenti della <lb></lb>scienza elettrica di allora non trovava tali da sodisfarsene le ragioni. </s>

<s>Era in­<lb></lb>torno a questa meditazione, in quel tempo che il Krugers e il Pons avevano <lb></lb>avvertito che l&#039;elettricità, tutt&#039;altro che indebolire, pareva anzi crescer d&#039;in­<lb></lb>tensità nelle parti estreme de&#039;lunghi fili da lei percorsi, d&#039;onde appunto <lb></lb>argomentò il sagace Filosofo americano che la virtù elettrica affluiva con più <lb></lb>libero e spontaneo moto verso le punte. </s>

<s>Non era nemmeno questo fatto <lb></lb>nuovo sfuggito alle osservazioni di quel nostro italiano Innominato, il quale <lb></lb>trovò che la luce elettrica era solita <emph type="italics"></emph>di sortir fuori dalle punte, dagli an­<lb></lb>goli e dalle pretuberanze de&#039;corpi facilmente elettrizzabili per comunica­<lb></lb>zione, massime dal ferro<emph.end type="italics"></emph.end> (Dell&#039;Elettric. </s>

<s>cit., pag. </s>

<s>262), ma il Franklin os­<lb></lb>servò di più <emph type="italics"></emph>l&#039;étonnant effet des corps pointus, tant pour tirer que pour <lb></lb>pouffer le feu électrique<emph.end type="italics"></emph.end> (Oeuvres, Paris 1773, T. I, pag. </s>

<s>3). </s></p><p type="main">

<s>L&#039;esalazione da una parte gli faceva necessariamente arguire una ri­<lb></lb>dondanza, e dall&#039;altra l&#039;attrazione gli faceva arguire un difetto nel fluido <lb></lb>elettrico, e vedeva in quel moto una tendenza del fluido stesso a ristabilirsi <lb></lb>nel suo primo e naturale equilibrio. </s>

<s>L&#039;ipotesi così dell&#039;ammosfere più dense <lb></lb>e meno dense introdotta dal nostro Innominato veniva pel Franklin ad es­<lb></lb>ser ridotta a un principio generale, ond&#039;è ch&#039;egli insegnava tutti i corpi <lb></lb>non elettrizzarsi, e non potersi artificiosamente elettrizzare che in <emph type="italics"></emph>più<emph.end type="italics"></emph.end> o in <lb></lb><emph type="italics"></emph>meno.<emph.end type="italics"></emph.end> “ De-là quelques termes nouveux se sont introduits parmi nous. </s>

<s>Nous <lb></lb>disons que B (ou tout autre corps dans les mêmes circonstances) est électrisé <lb></lb><emph type="italics"></emph>posuivement,<emph.end type="italics"></emph.end> et A <emph type="italics"></emph>négativement,<emph.end type="italics"></emph.end> ou plutòt B est électrisé <emph type="italics"></emph>plus<emph.end type="italics"></emph.end> et A l&#039;est <lb></lb><emph type="italics"></emph>moins,<emph.end type="italics"></emph.end> et tous les jours dans nos expériences nous électrisons les corps en <lb></lb><emph type="italics"></emph>plus<emph.end type="italics"></emph.end> ou en <emph type="italics"></emph>moins,<emph.end type="italics"></emph.end> suivant que nous le jugeons à propos. </s>

<s>— Pour électri­<lb></lb>ser en plus ou en moins, il faut seulement savoir que les parties du tube <lb></lb>ou du globe qui sont frottées, attirent dans l&#039;instant du frottement le feu <lb></lb>électrique, et l&#039;enlevent par conséquent à la chose frottante. </s>

<s>Les mêmes par­<lb></lb>ties, aussitòt que le frottement cesse, sont disposées à donner le feu qu&#039;elles <lb></lb>ont reçu à tout corps qui en a moins ” (là, page 8). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>In questa teoria elettrica del Franklin espressa così in semplici parole, <lb></lb>si conteneva una novità di grande importanza, la quale consisteva nell&#039;in­<lb></lb>segnar che la perenne sorgente elettrica non è nel vetro tornatile della Mac-<pb xlink:href="020/01/833.jpg" pagenum="276"></pb>china, come da tutti i Fisici allora si credeva, ma sì nel suolo, da cui ac­<lb></lb>corre allo stesso vetro, nell&#039;atto e per via dello strofinamento. </s>

<s>Non avrebbe <lb></lb>ricevuto forse appresso i Fisici la nuova ipotesi frankliniana così favorevole <lb></lb>accoglienza, se non avesse dato, quasi come primo saggio del suo valore, la <lb></lb>spiegazione di un fatto, innanzi al quale il mondo de&#039;Fisici non s&#039;era an­<lb></lb>cora riavuto dello stupore di che fu colto. </s></p><p type="main">

<s>Riferivasi quel fatto alla virtù fulminante, che risedeva in agguato <lb></lb>dentro la bottiglia di Leyda, il mistero della quale accresceva negli uomini <lb></lb>la paura. </s>

<s>Parve anche al Franklin quello uno strumento miracoloso e con­<lb></lb>fessò che trapassava la sua intelligenza, ma nonostante si studiò di farne <lb></lb>intendere l&#039;occulto modo di operare per mezzo del fluido positivo e conden­<lb></lb>sato sull&#039;una armatura, che nell&#039;andare a ristabilirsi in equilibrio, diffon­<lb></lb>dendosi sull&#039;altra armatura negativa, irrompe con quella sperimentata già e <lb></lb>così paurosa violenza. </s></p><p type="main">

<s>“ La bouteille étant électrisée (così il Franklin descrive al Collinson <lb></lb>la teoria e l&#039;uso della Bottiglia di Leyda) le feu électrique est accumulé à <lb></lb>sa surface extérieure et forme librement à l&#039;entour une atmosphère électri­<lb></lb>que d&#039;une étendue considérable, au lieu qu&#039;il est resserré de toutes parts <lb></lb>dans l&#039;intérieur. </s>

<s>En même temps que le fil d&#039;archal et le sommet de la bou­<lb></lb>teille sont électrisés <emph type="italics"></emph>positivement,<emph.end type="italics"></emph.end> ou <emph type="italics"></emph>plus,<emph.end type="italics"></emph.end> le fond de la bouteille est électrisé <lb></lb><emph type="italics"></emph>négativement,<emph.end type="italics"></emph.end> ou <emph type="italics"></emph>moins,<emph.end type="italics"></emph.end> dans une exacte proportion.... L&#039;equilibre ne sau­<lb></lb>roit ètre rétabli par la communication intérieure, ou par le contact des par­<lb></lb>ties, mais seulement par une communication formee au-dehors de la bou­<lb></lb>teille entre le haut et le bas, par le moyen de quelque corps non électri­<lb></lb>que qui les touche ” (là, pag. </s>

<s>12, 13). </s></p><p type="main">

<s>Una tale ipotesi del fluido positivo e del fluido negativo applicata a spie­<lb></lb>gare i misteriosi effetti della Bottiglia, dicemmo che sodisfece allora i Fi­<lb></lb>sici, i quali non sapevan trovare nella loro scienza elettrica altro migliore <lb></lb>argomento di questo. </s>

<s>Ma il Franklin non aveva di quella deficienza e so­<lb></lb>prabbondanza di fluido elettrico avuto altro indizio, da quello in fuori dimo­<lb></lb>stratogli dalle punte. </s>

<s>Or perchè questi infine non erano altro che fatti, non <lb></lb>pareva dicevole che si fondasse sopr&#039;essi una teoria senza renderne qual­<lb></lb>che ragione. </s></p><p type="main">

<s>L&#039;importante ufficio di supplire in ciò al difetto della scienza frankli­<lb></lb>niana se lo assunse un nostro Italiano, il quale ebbe a rivolgere la sua at­<lb></lb>tenzione sopra certe particolari esperienze eseguite dal Monnier in Parigi. </s>

<s><lb></lb>Risultava da così fatte esperienze che una lamina di piombo riquadrata, es­<lb></lb>sendo resa elettrica, scintillava men vivamente di quando, tagliata essa lamina <lb></lb>in sottili strisce, queste si disponevano per lo lungo l&#039;una dopo l&#039;altra, come <lb></lb>in ordine di catena. </s>

<s>Aveva inoltre osservato lo stesso Monnier che un lun­<lb></lb>ghissimo filo di ottone dava alla sua estremità scintille più penetranti di <lb></lb>quel che non paresse convenire all&#039;intensità della carica. </s></p><p type="main">

<s>Come simili fatti osservati già dal Krugers e dal Pons avevano ecci­<lb></lb>tato a speculare il Franklin, così questi nuovi eccitarono Giovan Batista Bec-<pb xlink:href="020/01/834.jpg" pagenum="277"></pb>caria, il quale ebbe per prima cosa a concluderne che “ il vapore con al­<lb></lb>cuna maggiore forza iscorra secondo la lunghezza, ovvero massima dimensione <lb></lb>di un corpo, e che scorra con forza maggiore per una lunghezza maggiore ” <lb></lb>(Dell&#039;Elettricismo, Torino 1753, pag. </s>

<s>55). </s></p><p type="main">

<s>A questa prima conclusione la feconda mente del nostro Autore ne fa <lb></lb>conseguire un&#039;altra, ch&#039;egli appresso soggiunge ed esprime in così fatta <lb></lb>forma: “ Questo impeto maggiore, secondo la lunghezza, produce un&#039;altra <lb></lb>proprietà nello scorrimento dell&#039;elettrico vapore, la quale non so che da altri <lb></lb>sia stata avvertita. </s>

<s>Essa è che il vapore elettrico, scorrendo dentro ad una <lb></lb>sostanza elettrizzabile per comunicazione, dove si restringe lo spessore di <lb></lb>questa sostanza, ivi a proporzione si condensa e cresce di forza e di atti­<lb></lb>vità ” (ivi, pag. </s>

<s>57). </s></p><p type="main">

<s>Il nostro Fisico torinese insomma riscontra nel fluido elettrico la legge <lb></lb>idraulica stessa che governa il moto di tutti gli altri fluidi, ed è che cor­<lb></lb>rendo per canali si velocitano reciprocamente alle sezioni. </s>

<s>“ E in queste pro­<lb></lb>prietà discerno tutta l&#039;analogia colla meccanica proprietà de&#039;fluidi elastici, <lb></lb>che movendosi da&#039;più ampi ne&#039;più ristretti spazii hanno un certo prodotto <lb></lb>di densità e velocità reciproco a&#039;spazii medesimi ” (ivi). </s></p><p type="main">

<s>Veniva così l&#039;Elettro, che non aveva fatto altra mostra di sè che di <lb></lb>fatti, e non era stato soggetto altro che d&#039;ipotesi senza dimostrazioni; a pi­<lb></lb>gliar qualche buon fondamento di scienza, e a confortarsi in quelle leggi, <lb></lb>di che si sapeva esser più certamente governato il moto della fluida mate­<lb></lb>ria. </s>

<s>Nello stesso tempo, quella ridondanza di fluido ammessa già dal Franklin <lb></lb>in conseguenza degli effetti osservati da lui nelle punte ritrovava nell&#039;espe­<lb></lb>rienze diligentissime del Beccaria una piena conferma, e nelle speculazioni <lb></lb>di lui una meccanica dimostrazione, che derivata da fonti sicure e non avendo <lb></lb>altro da sostituirle, si poteva allora tenere per certa. </s></p><p type="main">

<s>Ma questa stessa dimostrazione così ingegnosamente desunta dalla legge <lb></lb>idraulica, conosciuta sotto il nome del Castelli, non valeva se non pel caso <lb></lb>delle punte metalliche, dalle quali il vapore elettrico si disperde. </s>

<s>Era un fatto <lb></lb>però con certezza sperimentato dal Franklin che se quelle stesse punte esa­<lb></lb>lano il fluido quando ne soprabbondano, son dall&#039;altra parte avidissime di <lb></lb>assorbirlo, quando per le particolari condizioni, in che si trovano talvolta <lb></lb>rispetto agli altri corpi elettrizzati, se ne sentano qualche difetto. </s>

<s>A dar com­<lb></lb>piute perciò le sue dottrine, e a render d&#039;ogni parte sicura l&#039;ipotesi fran­<lb></lb>kliniana, conveniva al nostro Beccaria dimostrare in che modo le punte be­<lb></lb>vano così più avidamente il fluido elettrico, di quel che non si veda fare <lb></lb>alle superficie convesse o comunque sia allargate ed espanse. </s></p><p type="main">

<s>Egli dunque da savio si apparecchiò ia via per mezzo delle esperienze. </s>

<s><lb></lb>Trovò per prima cosa che un corpo più acuto tira a sè il fluido elettrico <lb></lb>da distanze maggiori, ma in minor quantità e densità, che uno meno acuto. </s>

<s><lb></lb>Trovò inoltre che un corpo acuto attira a sè il fluido elettrico da distanze <lb></lb>maggiori, ma però in minor quantità e densità che un simile altro corpo, <lb></lb>che invece di aver la sua sommità appuntata, l&#039;abbia rotonda. </s>

<s>Trovò in ul-<pb xlink:href="020/01/835.jpg" pagenum="278"></pb>timo che un corpo, il quale termina in maggior convessità, di bel nuovo tira <lb></lb>a sè il fluido da distanza maggiore, ma però in minor copia e densità di <lb></lb>un altro simile corpo, l&#039;estrema convessità del quale sia invece minore (ivi, <lb></lb>pag. </s>

<s>64). </s></p><p type="main">

<s>Osservate così diligentemente queste cose, e supposto che l&#039;aria resi­<lb></lb>sta alla libera diffusione del fluido elettrico, e che questo trapassando per <lb></lb>un tal mezzo aereo vi si faccia attraverso la via dilatandolo, come poi prova <lb></lb>con certissime esperienze, ritrova il nostro Autore la ragion facilissima per­<lb></lb>chè lo stesso fluido elettrico abbia più spedito il suo passaggio in una punta, <lb></lb>che in una superficie arrotondata ed espansa. </s>

<s>Rendeva per dir così visibile <lb></lb>la sua spiegazione, osservando nel buio a qual distanza incominciasse a ri­<lb></lb>splendere la punta di uno spillo avvicinata al conduttore di una Macchina <lb></lb>elettrica. </s>

<s>Aggiunti insieme due spilli vedeva che, perchè incominciassero come <lb></lb>dianzi a risplendere, le loro punte conveniva accostarle al conduttore di più, <lb></lb>e di più ancora se tre erano quelle stesse punte aggiunte insieme. </s>

<s>Da ciò <lb></lb>rendevasi, secondo il Beccaria, visibile ciò ch&#039;egli ragionava intorno alla sin­<lb></lb>golare proprietà delle punte, ed era che “ il vapore più rado della esteriore <lb></lb>parte dell&#039;elettrica atmosfera che unitamente correndo ad una punta sola <lb></lb>può vincere la resistenza d&#039;un filo d&#039;aria, dividendosi e dirigendosi a due <lb></lb>diverse punte non è sufficiente a vincere la doppia resistenza de&#039;due fili <lb></lb>d&#039;aria, onde le due punte si dovranno immergere più profondamente nella <lb></lb>più densa elettrica atmosfera ” (ivi, pag. </s>

<s>67). </s></p><p type="main">

<s>Così persuadevasi l&#039;illustre Fisico di Torino che, l&#039;esalar con più fa­<lb></lb>cilità la ridondanza del fluido elettrico e il ristorarne più prontamente il di­<lb></lb>fetto, non si potesse altrimenti salvar nelle punte, che per l&#039;applicazione <lb></lb>de&#039;suoi nuovi principii. </s>

<s>“ Insomma, egli dice, non m&#039;è accaduto di riflet­<lb></lb>tere ad alcuno o che sia stato da altri conosciuto o che abbia io ritrovato <lb></lb>o semplice o quanto si voglia composto sperimento, che alle punte comun­<lb></lb>que rilucenti appartenesse, di cui non mi sia paruto di scorgerne la ragione, <lb></lb>o nella particolare forza che secondo la lunghezza delle punte si propaga, <lb></lb>ed in esse si condensa, se si tratti di corpi che disperdano il loro vapore; <lb></lb>o nella maggiore unione che si fa verso una punta che verso più parti, se <lb></lb>si tratta di corpi, ne&#039;quali esso si diffonde ” (ivi). </s></p><p type="main">

<s>Per questi effetti osservati e dimostrati intorno alle punte veniva il Bec­<lb></lb>caria a porre in salvo la distinzion frankliniana del fluido positivo e del <lb></lb>fluido negativo, essendo per sè manifesto che le punte esalanti dovevan es­<lb></lb>sere elettrizzate in più, e le assorbenti in meno. </s>

<s>Perciò aveva nelle spran­<lb></lb>ghe appuntate uno strumento da riconoscer con certezza se un dato corpo <lb></lb>era elettrizzato in più o in meno. </s>

<s>Dall&#039;altra parte il diverso modo d&#039;operar <lb></lb>di esse spranghe appuntate, secondo che nella ridondanza esalano il foco <lb></lb>elettrico o lo riassorbono nel difetto, rendevasi patente per la semplice vista <lb></lb>di quello stesso foco, il quale appariva in forma di un largo fiocco nel primo <lb></lb>caso, e di una tenue stelletta nel secondo. </s></p><p type="main">

<s>Il Franklin aveva detto che il vetro della Macchina assorbisce il fluido <pb xlink:href="020/01/836.jpg" pagenum="279"></pb>elettrico dal corpo strofinatore, cosicchè questo da quello riceve. </s>

<s>Il Beccaria <lb></lb>quel ch&#039;era stato un semplice detto lo ridusse così alla dimostrazione di un <lb></lb>fatto: “ Presentate ad una qualunque parte di lei (della Macchina elettrica) <lb></lb>la punta di una spranghetta metallica alla distanza di un pollice o più, e <lb></lb>vedrete uscire da questa punta, ed indirizzarsi alla parte più vicina della <lb></lb>Macchina un fascetto d&#039;innumerabili, minutissimi, tra loro divergenti raggi <lb></lb>elettrici, che successivamente si suddividono e scompaiono a proporzione che <lb></lb>più si allontanano da essa punta ” (ivi, pag. </s>

<s>9). </s></p><p type="main">

<s>Così la punta nell&#039;apparenza del fiocco elettrico rendeva manifesto in­<lb></lb>dizio ch&#039;essa dava alla Macchina e non riceveva. </s>

<s>“ All&#039;incontrario, soggiunge <lb></lb>l&#039;Autore, se apparecchiate la spranghetta medesima ad una qualunque parte <lb></lb>della Macchina comunque elettrica, e ne presenterete alla punta di lei o la <lb></lb>palma della mano o qualunque corpo elettrizzabile per comunicazione, ve­<lb></lb>drete splendere alcuni punti del corpo, che presentate alla spranghetta e <lb></lb>vedrete adunarsi una tenue luce sulla punta della spranghetta medesima <lb></lb>incomparabilmente più piccola del fiocco elettrico ” (ivi). Questa tenue stel­<lb></lb>letta perciò dava indizio sicuro che la Macchina riceveva dalla palma della <lb></lb>mano del fluido elettrico anzi che darle nulla del suo. </s></p><p type="main">

<s>Così l&#039;ipotesi frankliniana, per opera dell&#039;Autore <emph type="italics"></emph>Dell&#039;Elettricismo ar­<lb></lb>tificiale e naturale,<emph.end type="italics"></emph.end> si veniva a trasformare in una teoria dimostrata, la <lb></lb>quale fu sentito subito quanto fosse per giovare ai progressi, verso cui si <lb></lb>vedeva lietamente incamminare la scienza. </s>

<s>Il Franklin perciò se ne com­<lb></lb>piacque grandemente, e al Dalibard che lo avea richiesto del suo autore­<lb></lb>vole giudizio intorno al libro del nostro Italiano, così rispondeva il dì 29 Giu­<lb></lb>gno del 1755 dalla sua Filadelfia: “ Vous me demandez mon sentiment sur <lb></lb>le livre italien du P. Beccaria. </s>

<s>Je l&#039;ai lu avec beaucoup de plaisir, et je le <lb></lb>regarde comme un des meilleurs ouvrages que j&#039;aye vûs, dans aucune lan­<lb></lb>gue, sur cette matière ” (Oeuvres cit., pag. </s>

<s>149). </s></p><p type="main">

<s>Il grande Filosofo americano non vedeva dunque in questo libro del <lb></lb>Beccaria solamente colui, che illustrata prima coll&#039;esperienze e colle ragioni <lb></lb>aveva data tutta la possibile estensione alla sua teoria, ma riconosceva di <lb></lb>più quella essere la miglior opera che fosse stata scritta in materia elet­<lb></lb>trica. </s>

<s>Il soggetto infatti trattato dal nostro Autore s&#039;estende a tutte quante <lb></lb>le parti della scienza elettrica d&#039;allora, e tutte le irraggia mirabilmente di <lb></lb>nuova luce. </s>

<s>Una delle più importanti fra queste parti era senza dubbio quella <lb></lb>che riguardava la causa delle attrazioni, rimasta tuttavia incerta, e dopo tante <lb></lb>fatiche di manifestarsi sempre ritrosa. </s></p><p type="main">

<s>Da che il Symmer aveva proposta l&#039;ipotesi de&#039;due fluidi distinti fra <lb></lb>loro di natura, com&#039;avevano distinto il loro modo di operare, venne in mente <lb></lb>al Nollet di salvar le attrazioni e le repulsioni ammettendo che un&#039;aura <lb></lb><emph type="italics"></emph>effluisca<emph.end type="italics"></emph.end> dal corpo elettrico, e un&#039;altra simile aura v&#039;<emph type="italics"></emph>affluisca<emph.end type="italics"></emph.end> dai corpi cir­<lb></lb>costanti. </s>

<s>Così per mezzo di queste due contrarie correnti studiavasi di spie­<lb></lb>gare ogni accostamento e discostamento, che si vede per causa dell&#039;elettri­<lb></lb>cità avvenire ne&#039;piccoli corpi: lo scostamento per l&#039;urto della materia che <pb xlink:href="020/01/837.jpg" pagenum="280"></pb>esce dal corpo elettrizzato, l&#039;accostamento per l&#039;urto di quella che viene allo <lb></lb>stesso corpo dovunque dai corpi stranieri. </s></p><p type="main">

<s>A chi poi metteva in dubbio quell&#039;aura affluente rispondeva il Nollet <lb></lb>mostrandogliela visibile nell&#039;acqua, la quale, essendo elettrizzata, affluisce in <lb></lb>vapore. </s>

<s>Ma faceva il Beccaria argutamente osservare che causa unica del­<lb></lb>l&#039;evaporazione dell&#039;acqua è l&#039;aura effluente, ossia il fluido elettrico esalato dal <lb></lb>corpo che lo contiene, perchè operando questo sopra qualsivoglia altro corpo <lb></lb>vi si diffonde a esercitarvi la sua attività naturale. </s>

<s>“ Che però, soggiunge <lb></lb>lo stesso Beccaria, alla materia effluente si può attribuire essa evaporazione, <lb></lb>senza che uopo sia fingerne la affluente, che, come si è visto qui di passag­<lb></lb>gio, ed altrove si proverà più ampiamente, affatto non esiste ” (ivi, pag. </s>

<s>33). </s></p><p type="main">

<s>A tutti quelli perciò a&#039;quali, anche senza le prove del Beccaria, pareva <lb></lb>quella materia affluente introdotta dal Nollet una cosa del tutto immagina­<lb></lb>ria; non rimaneva in salvo altra ipotesi che quella dell&#039;azione e della rea­<lb></lb>zione dell&#039;aria. </s>

<s>Così, dopo un intero secolo e un terzo, dopo tanta dovizia <lb></lb>di fatti nuovi scoperti, non sapevano i Fisici spiegare il fatto delle elettri­<lb></lb>che attrazioni punto meglio del Cabeo, anzi di quegli antichissimi Filosofi <lb></lb>riferitici da Plutarco. </s>

<s>L&#039;esperienze da&#039;nostri Accademici fiorentini tentate <lb></lb>nel vuoto torricelliano avrebbero potuto risolvere la questione da lungo <lb></lb>tempo, ma ebbero, come vedemmo, esito sfortunato. </s>

<s>Quelle eseguite poi dal <lb></lb>Dufay, introducendo corpi elettrici già prima ben confricati sotto la campana <lb></lb>della Macchina pneumatica, non parvero essere tanto dimostrative quanto ri­<lb></lb>chiedeva il bisogno. </s></p><p type="main">

<s>Il primo insomma che riuscisse a chiarire la falsità di quella ipotesi, la <lb></lb>quale attribuiva le attrazioni elettriche all&#039;azione dell&#039;aria, dimostrando che <lb></lb>avvenivano le stesse attrazioni anche nel vuoto il più squisito che sia pos­<lb></lb>sibile all&#039;arte; fu il nostro Beccaria. </s>

<s>Essendosi egli primieramente applicato <lb></lb>ad osservare i cambiamenti che soffre il fiocco elettrico eccitato dentro una <lb></lb>campana, dalla quale andavasi via via estrando l&#039;aria, restò convinto che <lb></lb>questa resiste al fluido elettrico, sicchè divide e rompe e fa divergere quei <lb></lb>raggi luminosi, che vanno liberamente nel vuoto a diritto ed uniti. </s>

<s>Avrebbe <lb></lb>incominciato di qui a sospettare che veramente conferisse qualche cosa la <lb></lb>reazione dell&#039;aria alle attrazioni de&#039;corpuscoli elettrizzati, “ ma ben presto, <lb></lb>soggiunge il Nostro, mi disingannai.... Appesi all&#039;estremità della verga (di <lb></lb>ottone introdotta attraverso a&#039;dischi di coio, di ch&#039;era otturata la bocca della <lb></lb>campana della Macchina pneumatica) un filo di refe lungo sei pollici, che <lb></lb>restava distante un pollice e mezzo dalla superficie interiore della campana, <lb></lb>e due pollici dal piano della Macchina pneumatica. </s>

<s>Sul piano medesimo al­<lb></lb>l&#039;altro lato del filo collocai un piccolo piede di ottone con sopra un dado <lb></lb>similmente di ottone, sicchè il filo pendeva di mezzo alla cavità della cam­<lb></lb>pana e di questo dado in distanza uguale dall&#039;uno e dall&#039;altro. </s>

<s>Poi fattto <lb></lb>un esattissimo vuoto ed eccitato l&#039;Elettricismo mi fu giocondissima cosa ve­<lb></lb>dere il filo, che velocissimamente si vibrava tra il dado e la campana, que­<lb></lb>sto e quella alternativamente percotendo colla sua estremità ” (ivi, pag. </s>

<s>35). </s></p><pb xlink:href="020/01/838.jpg" pagenum="281"></pb><p type="main">

<s>Non contento a ciò proseguì di sperimentare in altra maniera, introdu­<lb></lb>cendo alcune fogliette di oro nel vuoto della campana pneumatica dove os­<lb></lb>servò che, nell&#039;atto del diffondersi il fluido elettrico, alcune di quelle foglie <lb></lb>sollevavano la loro punta verso la verga, rimanendo coll&#039;altra estremità ade­<lb></lb>renti al piano del piatto. </s>

<s>Osservò inoltre con gran compiacenza che, toc­<lb></lb>cando con un dito il vetro della Campana, quelle stesse fogliette risaltavano <lb></lb>per accorrere desiderose al punto del contatto. </s>

<s>“ Questo sensibilissimo mo­<lb></lb>vimento delle foglie che accorrevano al dito, conclude ivi il Beccaria, mi <lb></lb>convinse sempre più che realmente gli elettrici movimenti si facciano indi­<lb></lb>pendentemente dall&#039;azione dell&#039;aria ” (pag. </s>

<s>36). </s></p><p type="main">

<s>Così dunque restava dimostrata falsa l&#039;ipotesi degli antichi Filosofi rin­<lb></lb>novellata dal Cabeo e proseguita dal più gran numero de&#039;fisici in fino a <lb></lb>mezzo il secolo XVIII, e poniamo che gli sperimenti del Beccaria avessero <lb></lb>ben persuaso tutti di quella falsità, rimaneva ancora vivissimo il desiderio <lb></lb>di saper quale altra si potess&#039;essere la causa di quegli elettrici moti. </s>

<s>Il Bec­<lb></lb>caria stesso sentiva in sè la necessità e il dovere di sodisfare all&#039;universale <lb></lb>desiderio, e confessava, dopo le sue invitte confutazioni, richiedersi al com­<lb></lb>pimento dell&#039;opera “ che si potesse assegnare la individua meccanica ma­<lb></lb>niera onde ..... debbano necessariamente avvenire i finora descritti mo­<lb></lb>vimenti ” (ivi, pag. </s>

<s>40). Ma sentendone la grave difficoltà se ne spaccia <lb></lb>appagandosi “ di avere ridotti ad un solo principio o, se così piaccia, ad una <lb></lb>sola universalissima legge tutti i movimenti che si eccitano pell&#039;elettricismo, <lb></lb>cioè avvenire tutti pella forza dell&#039;elettrico vapore che dal corpo in cui ve <lb></lb>ne ha più nel corpo in cui ve ne ha meno ad eguaglianza si espande ” (ivi). </s></p><p type="main">

<s>Soggiungeva il Beccaria, appena scritte queste parole, che avrebbe la­<lb></lb>sciato a&#039;più acuti e meno occupati di lui il piacere di comporre su quel <lb></lb>principio ch&#039;ei professava nuovi sistemi. </s>

<s>Ma perchè in verità non appariva <lb></lb>chiaro come si potesse derivar la causa delle attrazioni elettriche da quegli <lb></lb>stessi principii, s&#039;ebbero perciò i Fisici a rivolgere ad altri espedienti. </s>

<s>Quel­<lb></lb>l&#039;Autore Innominato che commemorammo di sopra erasi saviamente studiato <lb></lb>di ritrovar la occulta causa de&#039;movimenti elettrici ne&#039;principii neutoniani, <lb></lb>e persuaso che dovesser essere identici nella natura il fluido elettrico e il <lb></lb>fluido luminoso, così recisamente volle risolvere l&#039;astruso problema. </s>

<s>“ Circa <lb></lb>l&#039;attrazione e la ripulsione d&#039;alcuni corpi sopra la materia elettrica, quando <lb></lb>questa è la stessa materia che quella della luce, m&#039;appello all&#039;Ottica del <lb></lb>sig. </s>

<s>Newton ” (Dell&#039;Elettricismo cit., pag. </s>

<s>257). </s></p><p type="main">

<s>Una tal soluzione sarebbe senza dubbio stata la migliore che potevasi <lb></lb>desiderare, se si fosse liberamente concesso al nostro Autore quella mede­<lb></lb>simezza di natura da lui professata fra l&#039;elettrico e la luce. </s>

<s>Ma l&#039;esperienze <lb></lb>dell&#039;Hawksbee avevano già dimostrato ad evidenza che al foco elettrico non <lb></lb>competono punto le proprietà del foco ordinario, e lo stesso Beccaria, nel <lb></lb>§ III del cap. </s>

<s>VIII dell&#039;<emph type="italics"></emph>Elettricismo artificiale,<emph.end type="italics"></emph.end> proponevasi di scoprire <emph type="italics"></emph>al­<lb></lb>cune proprietà che indicano essere differente la natura del vapore elet­<lb></lb>trico dalla natura della luce e fuoco.<emph.end type="italics"></emph.end> (Ediz. </s>

<s>cit., pag. </s>

<s>137). </s></p><pb xlink:href="020/01/839.jpg" pagenum="282"></pb><p type="main">

<s>Così rimaneva soffocato il buon seme della dottrina, che il nostro In­<lb></lb>nominato avea sparso nel campo della scienza, quando a coltivarla fra noi <lb></lb>sorse un tale, a cui nessun altro sarebbe stato simile nella squisitezza dei <lb></lb>frutti e nell&#039;abbondanza della raccolta. </s>

<s>Fece, nel 1769, in Como sua patria, <lb></lb>la prima comparsa dirigendosi al Beccaria con una Dissertazione epistolare, <lb></lb>che avea il titolo <emph type="italics"></emph>De vi attractiva ignis electrici.<emph.end type="italics"></emph.end> L&#039;Autore non decide e <lb></lb>non gl&#039;importa se l&#039;elettricità sia una cosa diversa dalla luce: gli basta si <lb></lb>conceda esser ella un fluido materiale e perciò soggetto a que&#039;moti che com­<lb></lb>petono universalmente alla materia. </s>

<s>Quanto poi all&#039;esistenza di così fatti moti <lb></lb>molecolari se ne richiama anch&#039;egli al Newton, il quale aveva dimostrate <lb></lb>le attrazioni e le repulsioni, non della luce sola, ma di qualunque altra sorta <lb></lb>di corpi, quando vengano le loro minime particelle a&#039;più intimi contatti. </s></p><p type="main">

<s>“ Et vero harum virium existentiam vel sola luminis refractio erincit, <lb></lb>ubi illud, caeteris omissis, notatur radios jam tunc prope corporum super­<lb></lb>ficiem deflecti, antequam eam attingant. </s>

<s>Sed et alia quamplurima suppetunt <lb></lb>exempla harum virium, ut in corporibus perfecte laevibus, quae mutuo ad­<lb></lb>haerent vi pondus atmosphaerae longe excedente, et in duabus aquae gut­<lb></lb>tis, quae ad minimam distantiam sitae, primo apicem extendunt invicem, <lb></lb>quo se contingant, tum in unum coeunt, et in suspensione fluidorum in tu­<lb></lb>bis capillaribus, sive quod adhuc melius visitur in ascensu accelerato gut­<lb></lb>tae olei inter duas luminas vitreas, ne quid dicam de operationibus Che­<lb></lb>miae, cuius nulla est pars, in qua praeter inertiam massae et specificam <lb></lb>gravitatem, alia virium mutuarum genera non ubique se prodant, et vel <lb></lb>invitis incurrant in oculos, quod quidem vel in sola postrema quaestione <lb></lb>Opticae Newtoni abunde patet, ubi tam multa virium mutuarum indicia atque <lb></lb>argumenta proferuntur ” (A. Volta, Opere, Firenze 1816, T. I, P. I, pag. </s>

<s>7). </s></p><p type="main">

<s>Benchè la principale intenzione del Volta sia, com&#039;apparisce dal titolo <lb></lb>stesso di questa Epistola, quella di trattare delle attrazioni elettriche, v&#039;in­<lb></lb>trattien nonostante buona parte del suo discorso sopra un nuovo genere di <lb></lb>esperimenti relativi a un&#039;Elettricità comparsa sotto altro aspetto dell&#039;ordi­<lb></lb>naria, e alla quale perciò si dava il nome proprio e particolare di <emph type="italics"></emph>Elettri­<lb></lb>cità vindice.<emph.end type="italics"></emph.end> Giova accennar brevemente a ciò che dette occasione alla nuova <lb></lb>scoperta e all&#039;origine di questo nome. </s></p><p type="main">

<s>La bella esperienza, suggerita all&#039;Epino dall&#039;osservazione fatta da&#039;Ge­<lb></lb>suiti missionari, del vetro elettrizzato posto sul vetro di una Bussola nau­<lb></lb>tica; il fatto curiosissimo occorso al Symmer delle proprietà elettriche delle <lb></lb>calze di seta, avean condotto il nostro Gian Francesco Cigna a inventare una <lb></lb>Macchina che, sebbene assai scarsa, era pure una nuova sorgente di elet­<lb></lb>tricità diversa d&#039;origine da quella solita attingersi alla Macchina ordinaria. </s>

<s><lb></lb>Egli prendeva un nastro di seta fortemente elettrizzato e lo applicava a una <lb></lb>lamina di piombo isolata, la quale toccata col dito, nell&#039;atto stesso che ri­<lb></lb>tiravasi il nastro con destrezza, rimaneva essa pure elettrizzata in modo da <lb></lb>dare una scintilla. </s></p><p type="main">

<s>Il Beccaria, il quale era felicemente riuscito a dar la teorica dell&#039;elet-<pb xlink:href="020/01/840.jpg" pagenum="283"></pb>tricismo eccitato ne&#039;globi di vetro tornatili e comunicato ai conduttori me­<lb></lb>tallici, volle illustrare anche questa nuova Macchina del Cigna, derivandone <lb></lb>la ragione da&#039;più semplici fatti e più comuni. </s>

<s>Stropicciando fortemente un <lb></lb>nastro di seta sopra un piano vi resta aderente; intorno a che si doman­<lb></lb>dava: ritiene in questo caso il nastro l&#039;elettricità sua propria, ovvero la <lb></lb>smarrisce nel piano ch&#039;e&#039;tocca, per non riprendersela o <emph type="italics"></emph>rivendicarsela<emph.end type="italics"></emph.end> se <lb></lb>no nell&#039;atto che ne venga staccato? </s>

<s>Il Beccaria sosteneva il caso dell&#039;elet­<lb></lb>tricità <emph type="italics"></emph>vindice,<emph.end type="italics"></emph.end> ch&#039;egli applicava alla Macchina del Cigna, e il Cigna stesso <lb></lb>lo secondava, infintanto che non sorse a contradire all&#039;uno e all&#039;altro con <lb></lb>validi argomenti il Volta. </s></p><p type="main">

<s>La disputa fra così grandi uomini, de&#039;quali si studiava ciascuno di so­<lb></lb>stener la sua parte, escogitando nuovi argomenti, che equivalevano ad al­<lb></lb>trettante scoperte; fruttò bene alla scienza. </s>

<s>Il Beccaria, che infino da&#039;suoi <lb></lb>primi esperimenti sull&#039;Elettricismo artificiale posti per fondamento alla teo­<lb></lb>ria della Bottiglia di Leyda, aveva riconosciuta la virtù che ha il vetro di <lb></lb>accumulare così gran quantità di fluido elettrico, il quale viene ampiamente <lb></lb>distribuito su tutta la sua superficie per mezzo delle armature; richiamava <lb></lb>l&#039;attenzione del Volta sopra quel soloo di luce che trasparisce in quell&#039;atto, <lb></lb>che una lastra di vetro si snuda della sua veste. </s></p><p type="main">

<s>Ma il Volta rispondeva che anzi era quella una prova dell&#039;elettricità <lb></lb><emph type="italics"></emph>permanente<emph.end type="italics"></emph.end> nel vetro, e non ripresa da lui dalla veste che lo abbandona, <lb></lb>per rivendicarsi di ciò che la veste stessa gli avea rapito in quel primo con­<lb></lb>tatto. </s>

<s>“ Osservai, dice egli, che caricata una lastra di vetro e scaricatala, <lb></lb>nell&#039;atto indi di alzar con fili di seta la laminetta metallica, che vestiva la <lb></lb>faccia <emph type="italics"></emph>ridondante,<emph.end type="italics"></emph.end> i piccoli getti di luce non avevano più la figura di <emph type="italics"></emph>fioc­<lb></lb>chi<emph.end type="italics"></emph.end> spandentisi dalla lamina di vetro, come esser dovrebbono nella suppo­<lb></lb>sizione del P. Beccaria, ma quella anzi di luce affluente alla stessa veste con <lb></lb>apparire più che altrove distintissime le <emph type="italics"></emph>stellette<emph.end type="italics"></emph.end> agli orli e sugli angoli di <lb></lb>esse. </s>

<s>Il contrario accadeva snudando l&#039;altra faccia <emph type="italics"></emph>deficiente<emph.end type="italics"></emph.end> del vetro: la <lb></lb>foglietta metallica divenuta nella scarica, secondo i miei principii, elettrica <lb></lb>in <emph type="italics"></emph>più,<emph.end type="italics"></emph.end> tostochè alzavasi, spandeva d&#039;attorno bellissimi <emph type="italics"></emph>fiocchi.<emph.end type="italics"></emph.end> Fui dunque <lb></lb>sicuro, non per conseguenza solo de&#039;meditati principii, ma per dirette os­<lb></lb>servazioni e prove di fatto, che la faccia della lastra, all&#039;atto dello snuda­<lb></lb>mento, non ripigliava il suo primo fuoco ridondante a spese, dirò così, della <lb></lb>veste, che anzi questa ne tirava a sè per rifarsi d&#039;un già sofferto spoglia­<lb></lb>mento .... che dunque la luce trallo disgiungimento mirava non già ad in­<lb></lb>durre elettricità in ambedue, bensì a dissipar la esistente, segnatamente quella <lb></lb>della veste ” (Opere e Tomo cit., pag. </s>

<s>152, 53). </s></p><p type="main">

<s>Come fosse il frutto di così nobile e dignitosa controversia l&#039;invenzione <lb></lb>dell&#039;Elettroforo perpetuo, d&#039;onde ne conseguì il Condensatore con altri pre­<lb></lb>ziosissimi strumenti, che la scienza elettrica ebbe dalle mani del Volta; fu <lb></lb>da noi narrato altrove, ond&#039;è che dovendoci arrestar qui, per non oltrepas­<lb></lb>sare i limiti che ci sono prescritti, diciamo a coloro i quali ammirano gli <lb></lb>straordinari progressi fatti dalla Fisica sull&#039;Elettricismo in questi ultimi tempi, <pb xlink:href="020/01/841.jpg" pagenum="284"></pb>e intorno alla storia de&#039;quali si son dovuti scrivere ampli volumi; che ri­<lb></lb>pensino come nient&#039;altro sono quegli ammirati progressi che l&#039;incremento <lb></lb>sopravvenuto, per la favorevole stagione, in quel grande albero coltivato, <lb></lb>dopo il Franklin, massimamente in Italia dal Beccaria e dal Volta. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quando, per opera de&#039;tre grandi ora commemorati, s&#039;imparò a cono­<lb></lb>scer meglio quel fuoco che, con quasi nuov&#039;arte magica, facevasi scaturire <lb></lb>dalla confricazione de&#039;globi o de&#039;cilindri di vetro; come disegno svanito, che <lb></lb>rifiorisce ai raggi del Sole, ritornò alla mente de&#039;Fisici la Terrella elettrica <lb></lb>del Guericke dimostrativa tutta insieme delle virtù possedute dal globo della <lb></lb>gran Terra. </s>

<s>Non vi fu allora nessun fatto naturale rappresentatosi o nel­<lb></lb>l&#039;interiore del globo, o in mezzo all&#039;aria che lo involge, sotto le apparenze <lb></lb>della luce, che non si credesse vedervi le sembianze della luce elettrica, <lb></lb>ond&#039;è che i varii misteri o si tenevano così come per rivelati, o si riduce­<lb></lb>vano almeno sotto l&#039;ombra di un solo. </s></p><p type="main">

<s>Quante vane cose, da Filosofi solennissimi, non erano state insegnate <lb></lb>intorno alle folgori! E come potevano dall&#039;altra parte giungere quegli in­<lb></lb>gegni a capir la generazione del fuoco in mezzo alle umide nubi? </s>

<s>Ma quando <lb></lb>il Guericke mostrò generarsi un simile fuoco da un globo di zolfo freddo, <lb></lb>e in sè stesso, dall&#039;ordinaria combustione non alterato, e allora soccorse fa­<lb></lb>cilmente al pensiero di attribuire i lampi e le folgori alle sulfuree esalazioni <lb></lb>terrestri. </s></p><p type="main">

<s>Il di primo di Maggio del 1669 una saetta aveva colpito due fanciulli <lb></lb>nelle campagne circostanti a Bologna. </s>

<s>Ebbe occasione di esaminare il fatto <lb></lb>disgraziatamente occorso Geminiano Montanari, e di renderne conto all&#039;Ac­<lb></lb>cademia fiorentina, dirigendosi al cardinale Leopoldo che, in quella disper­<lb></lb>sione de&#039;socii, la rappresentava tutta insieme unita in Firenze, nella sua <lb></lb>propria persona. </s>

<s>Ne concludeva il Montanari, da ciò che v&#039;aveva diligente­<lb></lb>mente osservato, che la materia delle saette dev&#039;essere di natura fluida e <lb></lb>tale che ardendo si consumi, benchè confessasse rimanergli oscuro come po­<lb></lb>tesse una materia fluida rompere le muraglie (Fabbroni, Lett., T. I, Fi­<lb></lb>renze 1773, pag. </s>

<s>163). A che rispondeva così il Principe dell&#039;Accademia, <lb></lb>con lettera del di 7 di Maggio: “ Gratissimo mi è stato l&#039;udire l&#039;accidente <lb></lb>occorso de&#039;duoi fanciulli percossi dal fulmine, e per l&#039;opinione che io tengo <lb></lb>delle operazioni de&#039;fulmini non mi giungon nuovi gli effetti, ch&#039;ella mi a­<lb></lb>cenna, mentre io tengo per cosa molto probabile che i fulmini si gene­<lb></lb>rino dalle esalazioni della Terra ed in gran parte sulfuree ” (MSS. Cim., <lb></lb>T. XXIII, c. </s>

<s>169). </s></p><p type="main">

<s>Quando queste esalazioni sulfuree presero il nome più particolare di <lb></lb>effluvii elettrici, non mancarono il Gray e il nostro Innominato di dir che <pb xlink:href="020/01/842.jpg" pagenum="285"></pb>il baleno era un fenomeno elettrico, prodotto cioè da quella stessa materia <lb></lb>che s&#039;eccita da&#039;macchinamenti artificiali. </s>

<s>Il Nollet insistè sulla somiglianza <lb></lb>che passa tra la folgore e la scintilla scoccata dalla Machina, di che poi <lb></lb>si compiacque, quando vide quella ipotesi così spendidamente confermata <lb></lb>dai fatti. </s></p><p type="main">

<s>Ma d&#039;onde hanno origine quegli elettrici effluvii nelle nuvole, e quel <lb></lb>fuoco che dentro vi balena? </s>

<s>si domandò quando i fatti venivano ogni giorno <lb></lb>più confermando quella prima analogia intraveduta fra l&#039;elettricità naturale <lb></lb>e l&#039;artificiale. </s>

<s>La macchina esercitata dalla Natura per lo svolgimento del­<lb></lb>l&#039;elettricità da comunicarsi all&#039;aria, si pensò da principio che risedesse nel <lb></lb>mare. </s>

<s>La fosforescenza delle acque di lui, prima e anche qualche tempo <lb></lb>dopo che il Vianelli dimostrasse esser dovuta ad alcune specie d&#039;insetti, si <lb></lb>ridusse anch&#039;essa a uno de&#039;soliti fenomeni elettrici, che s&#039;attribuiva parti­<lb></lb>colarmente ai sali, non essendosi mai veduti fosforeggiare i laghi o simili <lb></lb>altre acque dolci. </s>

<s>“ Il bitume e i sali che si trovano nelle acque del mare <lb></lb>sono, scrive il nostro Innominato, quelli che più conservar possono la luce <lb></lb>dell&#039;acqua stessa, perchè ne&#039;fiumi dove l&#039;acqua è dolce ciò non succede. </s>

<s><lb></lb>Questa luce si sviluppa fuori con maggior empito, quanto più fredda e umida <lb></lb>è l&#039;aria, perchè in tal modo l&#039;aria stessa fa la funzione di un corpo manco <lb></lb>originalmente elettrizzato, e con ciò più facile ad elettrizzarsi per comuni­<lb></lb>cazione, cioè più pronto a ricevere in sè la materia elettrica che scappa <lb></lb>fuori ” (Dell&#039;Elettric. </s>

<s>cit., pag. </s>

<s>226, 27). </s></p><p type="main">

<s>Nel 1747 seguitava questa opinione del nostro Italiano anche il Fran­<lb></lb>klin, il quale riguardava “ la mer comme la grande source des éclairs, ima­<lb></lb>ginant que la lumiere qu&#039;on y apperçoit venoit du feu électrique produit <lb></lb>par le frottement des particules de l&#039;eau avec celles du sel ” (Oeuvres cit., <lb></lb>pag. </s>

<s>116). Ma nel 1750, avendo avuto occasione di far più particolari e più <lb></lb>diligenti esperienze sopra l&#039;acqua di mare raccolta e chiusa dentro una bot­<lb></lb>tiglia “ sur cette observation, egli scrive, e sur ce qu&#039;en agitant une solu­<lb></lb>tion de sel marin dans de l&#039;eau, je ne pouvois produire aucune lumiere, je <lb></lb>commençai d&#039;abord à douter de ma premiere hypothese et à soupçonner que <lb></lb>cette lumiere dans l&#039;eau de la mer devoit ètre attribuée à quelques autres <lb></lb>principes ” (là). </s></p><p type="main">

<s>Questo diverso principio, da cui sarebbe stata eccitata e comunicata l&#039;elet­<lb></lb>tricità alla gran mole dell&#039;aria, lo riconobbe il Franklin nell&#039;aria stessa, la <lb></lb>quale “ étant électriques par elles-mêmes, tirassent du feu électrique de la <lb></lb>terre dans les grands coups de vent par leur frottement contre les arbres, <lb></lb>les montagnes, les bâtiments, etc., comme autant de petits globes élettri­<lb></lb>ques frottants contre des coussins non électriques, et que les vapeurs en <lb></lb>s&#039;élevant reçùssent de l&#039;air ce feu, et que par ces moyens les nuages de­<lb></lb>vinssent électrisés ” (là, pag. </s>

<s>117). </s></p><p type="main">

<s>Persuaso in ogni modo, qualunque poi ne fosse l&#039;origine vera, dell&#039;elet­<lb></lb>tricismo esistente nell&#039;aria, e comunicato per mezzo di lei alle nuvole, oc­<lb></lb>corse al Franklin, nel proseguire i suoi prediletti esperimenti sopra la facoltà <pb xlink:href="020/01/843.jpg" pagenum="286"></pb>delle punte, di prender due bacini di rame pendenti per cordicelle di seta <lb></lb>dall&#039;estremità di un flagello da bilancia, intorno al quale potevano muoversi <lb></lb>in giro orizzontale, e anche insieme d&#039;alto in basso. </s>

<s>Elettrizzando uno di <lb></lb>cotesti bacini e facendolo poi, nel girarlo, passar sopra una punta metallica <lb></lb>opportunamente collocata sull&#039;estremità di una verga infissa sul pavimento, <lb></lb>vedeva lo stesso bacino scaricare <emph type="italics"></emph>son feu en silence sur la pointe.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In questo gli balenò alla mente un pensiero stupendo: “ Maintenant <lb></lb>si le feu de l&#039;électricité et celui de la foudre sont une seule et même chose, <lb></lb>comme j&#039;ai taché de le prouver assez amplement, ce tube de carton et ces <lb></lb>bassins peuvent représenter les nuages électrisés.... Le mouvement hori­<lb></lb>sontal des bassins sur le plancher peut représenter le mouvement des nua­<lb></lb>ges sur la terre et le poinçon élevé nous represente les montagnes et les <lb></lb>plus hauts édifices, et cela nous fait voir comment les nuages électrisés pas­<lb></lb>sant sur le montagnes et sur les bâtiments à une trop grande hauteur pour <lb></lb>les frapper, peuvent ètre attirés en bas jusqu&#039;à la proximité qui leur est <lb></lb>necessaire pour cet effet.... </s></p><p type="main">

<s>Dopo ciò, ecco lo stupendo concetto che si diceva, e ch&#039;essendo poi <lb></lb>riuscito nella pratica basterebbe egli solo a far tacere i declamatori contro <lb></lb>le oziose vanità della scienza: “ Les choses étant ainsi, je demande, si la <lb></lb>connoissance du pouvoir des pointes ne pourroit pas être de quelque avan­<lb></lb>tage aux homines pour préserver les maisons, les eglises, les vaisseaux etc., <lb></lb>des coups de la foudre, en nous engageant à fixer perpendiculairement sur <lb></lb>les parties les plus élevées des verges de fer aiguissées par la pointe comme <lb></lb>des aiguilles, et dorées pour prévenir la rouille, et à attacher au pied de <lb></lb>ces verges un fil d&#039;archal descendant le long du bâtiment dans la terre, ou <lb></lb>le long d&#039;un des aubans d&#039;un vaisseau et de son bordage jusqu&#039;à fleur d&#039;eau? </s>

<s><lb></lb>N&#039;est-il pas probable que ces verges de fer tireroient sans bruit le feu <lb></lb>électrique du nuage avant qu&#039;il vint assez près pour frapper, et que par ce <lb></lb>moyen nous serions préservés de tant de désastres soudains et terribles? </s>

<s>” <lb></lb>(là, pag. </s>

<s>61, 62). </s></p><p type="main">

<s>Tutto il fondamento però di così bella e generosa proposta consisteva <lb></lb>nell&#039;assicurarsi se veramente i nuvoli davano segnali elettrici, di che il Fran­<lb></lb>klin stesso suggeriva ivi appresso il modo servendosi di un lungo palo di <lb></lb>ferro appuntato, eretto sulla sommità di qualche alta torre, dove, dentro una <lb></lb>specie di casotto da sentinella, invigilasse un uomo co&#039;piè posati sopra uno <lb></lb>sgabello isolatore, per esplorare i segnali elettrici in tempo che le nubi pro­<lb></lb>cellose gli passavano sopra la testa. </s></p><p type="main">

<s>Il Collinson diffuse con grande ardore in Inghilterra e in Francia il <lb></lb>progetto frankliniano di riparar da&#039;fulmini i così spesso minacciati edifizi, <lb></lb>e a una tale inaspettata notizia si commosse tutta Parigi. </s>

<s>Nell&#039;animo del Re <lb></lb>era entrata così grande curiosità, che non gli dette pace infin tanto che non <lb></lb>ne ebbe veduta la prova, per eseguir la quale il duca d&#039;Ayen offerse a Sua <lb></lb>Maestà la suburbana villa di S. Germano. </s>

<s>Ma il Dalibard scelse un giardino <lb></lb>di Marly-la-ville, a una distanza di sei leghe da Parigi, dove “ le 10 Mai <pb xlink:href="020/01/844.jpg" pagenum="287"></pb>dernier, à 2 heures 20 minutes après midi, une nuée orageuse ayant passé <lb></lb>au-dessus du lieu où la barre étoit élevée, ceux que l&#039;on avoit appostés <lb></lb>pour y veiller, s&#039;approcherent et en tirerent des étincelles de feu, éprou­<lb></lb>vant les mêmes especes de commotions que dans les experiences électriques <lb></lb>ordinaires ” (Franklin, Oeuvres cit., T. I, pag. </s>

<s>104). </s></p><p type="main">

<s>Lo stesso Dalibard, tre giorni dopo, rendeva solennemente conto alla <lb></lb>R. </s>

<s>Accademia del fortunato avvenimento del dì 10 di Maggio 1752, e con <lb></lb>l&#039;animo esaltato, com&#039;è facile immaginare, terminava così la sua Relazione: <lb></lb>“ L&#039;idée qu&#039;en a eu M. </s>

<s>Franklin cesse d&#039;être d&#039;une coniecture; la voilá de­<lb></lb>venue une réalité et j&#039;ose croire que plus on approfondira tout ce qu&#039;il a <lb></lb>publié sur l&#039;électricité, plus on reconnoîtra combien la Physique lui est re­<lb></lb>devable pour cette partie ” (là, pag. </s>

<s>109, 10). </s></p><p type="main">

<s>Si può facilmente ognuno immaginare quanto si dovesse il Franklin <lb></lb>compiacere della corrispondenza che le sue idee felicemente trovarono nel­<lb></lb>l&#039;esperienze eseguite dai Fisici parigini, e fu forse una tal compiacenza, nella <lb></lb>quale egli così dolcemente riposava, che lo fece indugiare infino al Settem­<lb></lb>bre a darne sodisfazione a&#039;suoi occhi proprii. </s>

<s>“ En Septembre 1752 j&#039;éle­<lb></lb>vai sur ma maison une verge de fer pour tirer le feu du tonnerre, afin de <lb></lb>faire quelques expériences sur cela, ayant disposé deux petits timbres pour <lb></lb>m&#039;avertir quand la verge seroit électrisée, ce qui est une pratique familiere <lb></lb>a tout électricien ” (là, pag. </s>

<s>117). </s></p><p type="main">

<s>Abbiamo messo in forse questo indugio di quattro mesi, perchè una <lb></lb>volgar tradizione avvalorata da gravissimi Autori tien per cosa certa che il <lb></lb>Franklin, prima di esperimentare l&#039;elettricità delle nubi co&#039;pali di ferro, <lb></lb>com&#039;avevano fatto il Dalibard e il Lor, l&#039;avesse esplorata con maggior fa­<lb></lb>cilità, e con più semplice e pronto apparecchio, per mezzo del così detto <lb></lb><emph type="italics"></emph>Cervo volante.<emph.end type="italics"></emph.end> Carlo Barletti, il quale riserbò il V Articolo de&#039;suoi Saggi <lb></lb>di Fisica (<emph type="italics"></emph>Fhysica specimina<emph.end type="italics"></emph.end>) a trattar del modo di costruire e di far uso, <lb></lb>per esplorar l&#039;elettricità ammosferica, di quella stessa Macchina volante, si <lb></lb>credè di poter uscire in così fatta sentenza: “ Certe Franklinus ipse atmo­<lb></lb>sphaericam electricitatem anno 1572 Cervo prius volante, quam virga explo­<lb></lb>ravit ” (Mediolani 1772, pag. </s>

<s>129), ma non reca di tal certezza alcun do­<lb></lb>cumento, e cercandolo noi per le dissertazioni e per le lettere frankliniane <lb></lb>non ce lo abbiamo saputo trovare. </s></p><p type="main">

<s>Comunque sia, fa maraviglia che l&#039;infaticabile Sperimentatore ameri­<lb></lb>cano si lasciasse prevenire in sodisfare a così nobile curiosità non sol dai <lb></lb>Francesi, ma dagli stessi Italiani, appresso i quali la notizia del progetto <lb></lb>de&#039;parafulmini e della felice riuscita avutane nel Maggio a Parigi, non giunse <lb></lb>che sulla fine del prossimo Giugno. </s>

<s>“ Avuta notizia, scrive il Beccaria, sulla <lb></lb>fine di Giugno della oramai notissima esperienza inventata dal valoroso In­<lb></lb>glese Beniamino Franklin, abitante in Filadelfia, città della Pensilvania in <lb></lb>America, ed avverata in Parigi da&#039;signori De Lor, e Dalibard, m&#039;applicai <lb></lb>immantinente ad effettuarla anch&#039;io qui in Torino. </s>

<s>I. </s>

<s>Feci empire di mastice <lb></lb>all&#039;altezza di sei pollici una cassa triangolare e la feci sospendere sotto il <pb xlink:href="020/01/845.jpg" pagenum="288"></pb>tetto in contatto delle tegole. </s>

<s>II. </s>

<s>Tolte alcune tegole, feci collocare sul ma­<lb></lb>stice della cassa un trepiede che reggeva una spranga di ferro, la quale <lb></lb>s&#039;alzava da dodici piedi sopra del tetto. </s>

<s>III. </s>

<s>Al basso della spranga avea <lb></lb>fatto conficcare una spranghetta, che orizzontalmente sporgeva fuora della <lb></lb>cassa tra essa ed il tetto. </s>

<s>IV. All&#039;estremità di questa spranghetta appiccai <lb></lb>una catena, che per un buco fatto nel solaio calava in una larga stanza e <lb></lb>reggeva una palla di metallo di due pollici di diametro, in distanza di un <lb></lb>piede da un tavolato. </s>

<s>V. </s>

<s>Conficcai in questo tavolato due stili, uno con al­<lb></lb>l&#039;estremità un campanello distante tre pollici dalla palla, un altro più alto <lb></lb>con all&#039;estremità un filo di seta, che reggeva una palletta di metallo tralla <lb></lb>suddetta palla e il campanello. </s>

<s>VI. </s>

<s>E finalmente adattai in giro della spranga, <lb></lb>un po&#039;sopra del tetto, una specie d&#039;ombrello, che riparasse il mastice dalla <lb></lb>pioggia. </s>

<s>” </s></p><p type="main">

<s>“ Disposte così le cose, addi 2 Luglio, alle due ore e mezzo dopo mez­<lb></lb>zogiorno, nello spandersi verticalmente sulla spranga una nuvola assai bassa, <lb></lb>spinta da libeccio verso greco, la palla di metallo cominciò a dare scintille <lb></lb>assai vive alla distanza di dieci linee in circa e seguitò a scintillare per <lb></lb>25 minuti, cioè finchè passò la nuvola. </s>

<s>In tempo di questo elettrizzamento <lb></lb>non vi furono nè lampi nè tuoni. </s>

<s>Poco prima che esso cominciasse un&#039;al­<lb></lb>tra nuvola avea dato un poco di pioggia e s&#039;era visto a libeccio alcun lampo <lb></lb>accompagnato da tuono assai leggero ” (Dell&#039;Elettric. </s>

<s>natur., Torino 1753, <lb></lb>pag. </s>

<s>159, 60). </s></p><p type="main">

<s>Prosegue il Beccaria a descrivere colla sua solita diligenza altre simili <lb></lb>osservazioni fatte ne&#039;susseguenti mesi di Agosto e di Settembre, non tanto <lb></lb>per verificare l&#039;ipotesi frankliniana, ciò che oramai non più bisognava, quanto <lb></lb>per apparecchiarsi i fondamenti a dimostrar, nel capitolo secondo (ciò che fu <lb></lb>trascurato da&#039;Fisici parigini) <emph type="italics"></emph>la medesimezza de&#039;segni elettrici nell&#039;elettri­<lb></lb>cismo delle nuvole con i segni elettrici nell&#039;elettricismo artificiale.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Dopo questi diligentissimi studi del nostro Fisico torinese poteva con <lb></lb>più ragione che mai asserire il Dalibard che la congettura era felicemente <lb></lb>tornata nella realtà de&#039;fatti, e il Franklin aveva così nuovo motivo di com­<lb></lb>piacersi. </s>

<s>Non era però nell&#039;animo di lui quella compiacenza perfetta: egli <lb></lb>trovato falso il suo primo supposto dell&#039;origine dell&#039;elettricità ammosferica <lb></lb>dalle acque del mare, ebbe, come vedemmo, ricorso agli sfregamenti che su­<lb></lb>bisce l&#039;aria contro le asprezze superficiali della terra, nelle ventose agita­<lb></lb>zioni, e l&#039;ipotesi aveva aspetto di probabilità, <emph type="italics"></emph>mais l&#039;experience,<emph.end type="italics"></emph.end> ingenua­<lb></lb>mente confessa il Franklin, <emph type="italics"></emph>que je tentai dans cette vue ne me réussit <lb></lb>pas<emph.end type="italics"></emph.end> (Oeuvres cit., pag. </s>

<s>117). A render più che mai vacillante l&#039;ipotesi, non <lb></lb>potutasi confermare dai fatti, s&#039;aggiunse poi la scoperta del Monnier del­<lb></lb>l&#039;elettricità dell&#039;aria anche a ciel sereno, e la difficoltà veniva a complicarsi <lb></lb>anche di più per le osservazioni elettroscopiche, le quali davano ora una <lb></lb>elettricità positiva, ora una elettricità negativa, e ora un passaggio inaspet­<lb></lb>tato dell&#039;una nell&#039;altra. </s></p><p type="main">

<s>Rassicurare la scienza per questa parte così principale e, lasciate ad-<pb xlink:href="020/01/846.jpg" pagenum="289"></pb>dietro le congetture, dimostrar l&#039;origine dell&#039;elettricità ammosferica per via <lb></lb>di fatti sperimentati, e in che ritrovasse la causa sua unica e vera la sva­<lb></lb>riata moltiplicità degli effetti; era riserbato al genio di Alessandro Volta. </s></p><p type="main">

<s>Persuasi oramai i Fisici che non dovesse mancare uno svolgimento di <lb></lb>elettricità, dovunque fosse confricamento e collisione fra le particelle de&#039;corpi, <lb></lb>s&#039;erano dati con sollecito studio a ricercar di quell&#039;occulto elettricismo i <lb></lb>segnali nell&#039;evaporar che fanno i liquidi, segnatamente, e nelle fermenta­<lb></lb>zioni. </s>

<s>Il Franklin, il De Saussure, il Wenly, il Cavallo erano de&#039;principali <lb></lb>fra coloro ch&#039;eransi rivolti a così fatte ricerche, le quali poi presto ebbero ad <lb></lb>abbandonare, per non aver corrisposto i fatti alle concepute speranze. </s></p><p type="main">

<s>Ma le persuasioni del Volta in tal proposito erano assai più tenaci: egli <lb></lb>che ammaestrato dal Newton vedeva in quelle effervescenze de&#039;corpi un <lb></lb>gioco delle intestine forze molecolari; egli che giovane s&#039;introduceva alla <lb></lb>Filosofia elettrica dimostrando come le attrazioni de&#039;corpi elettrizzati eran <lb></lb>dovute a forze di uguale e di simil natura a quelle che attraggono e re­<lb></lb>spingono le minime particelle, eccitando ne&#039;corpi dissolubili le evaporazioni <lb></lb>e i fermenti; non si poteva dar pace che l&#039;elettricità non si manifestasse <lb></lb>per alcuno di tali processi, e del non essersene potuti ancora vedere i se­<lb></lb>gni, ne accagionava l&#039;imperfezione degli strumenti. </s></p><p type="main">

<s>Riuscito perciò a costruire il suo squisitissimo Elettrometro condensa­<lb></lb>tore incorò buona speranza di veder ciò, che non era a nessuno riuscito di <lb></lb>vedere prima di lui. </s>

<s>Nella primavera dell&#039;anno 1782 egli era a Parigi, e il <lb></lb>di 13 d&#039;Aprile, mostrò, per mezzo del suo eccellentissimo strumento, al La­<lb></lb>voisier e al La-Place ivi presenti, i segni chiarissimi dell&#039;elettricità dall&#039;eva­<lb></lb>porazione dell&#039;acqua. </s>

<s>L&#039;esperienze però gli riuscirono assai meglio a Lon­<lb></lb>dra alla presenza del Magellan, del Kirwan, del Walker, gli occhi de&#039;quali <lb></lb>furono testimonii de&#039;segni dell&#039;elettricità negativa che, gettate alquante goc­<lb></lb>ciole d&#039;acqua sui carboni accesi, eran dati da un braciere di rame. </s></p><p type="main">

<s>La scoperta dell&#039;elettricità svoltasi così dall&#039;acqua che si trasforma in <lb></lb>vapori, aprì la via a scoprire l&#039;elettricità, che si svolge nelle multiformi tra­<lb></lb>sformazioni de&#039;corpi, d&#039;onde tanto largo campo d&#039;aperse ai progressi della <lb></lb>nuova Scienza chimica, ma intanto il Volta applicava quella sua stessa sco­<lb></lb>perta a risolvere il problema dell&#039;origine dell&#039;elettricità ammosferica, con­<lb></lb>cludendo così l&#039;<emph type="italics"></emph>Appendice alla II Parte del Condensatore,<emph.end type="italics"></emph.end> dop&#039;aver par­<lb></lb>ticolarmente descritte l&#039;esperienze in proposito fatte a Parigi e a Londra. </s></p><p type="main">

<s>“ Le esperienze fatte fin qui e che abbiamo riferite, benchè non sian <lb></lb>molte, tutte però concorrono a mostrarci che i vapori dell&#039;acqua e general­<lb></lb>mente le parti d&#039;ogni corpo, che si staccano volatizzandosi, portano via seco <lb></lb>una quantità di fluido elettrico a spese dei corpi fissi che rimangono, la­<lb></lb>sciandoli perciò elettrizzati <emph type="italics"></emph>negativamente,<emph.end type="italics"></emph.end> non altrimenti che ne portan via <lb></lb>una quantità di fuoco elementare con ciò raffreddandoli. </s>

<s>Quindi vuolsi in­<lb></lb>ferire che i corpi, risolvendosi in vapori, o prendendo l&#039;abito aereo, acqui­<lb></lb>stino una maggior capacità rispetto al fluido elettrico, giusto come l&#039;acqui­<lb></lb>stano maggiore rispetto al fuoco comune o fluido calorifico. </s>

<s>” </s></p><pb xlink:href="020/01/847.jpg" pagenum="290"></pb><p type="main">

<s>“ Chi non sarà colpito da così bella analogia, per cui l&#039;elettricità porta <lb></lb>del lume alla novella dottrina del calore e ne riceve a vicenda? </s>

<s>Parlo della <lb></lb>dottrina del calor <emph type="italics"></emph>latente<emph.end type="italics"></emph.end> o <emph type="italics"></emph>specifico,<emph.end type="italics"></emph.end> come si vuol chiamare, di cui Black e <lb></lb>Wilke, colle stupende loro scoperte, han gettato i semi e che è stata ultima­<lb></lb>mente tanto promossa dal D. Crawford, dietro le esperienze del D. Irwine. </s>

<s>” </s></p><p type="main">

<s>“ Seguendo questa analogia, siccome i vapori, allorchè si condensano, <lb></lb>e ritornano in acqua e conseguentemente alla primiera più angusta capacità, <lb></lb>perdono il loro calore <emph type="italics"></emph>latente,<emph.end type="italics"></emph.end> ossia depongono il di più di fuoco che si <lb></lb>avevano appropriato volatizzandosi; così pure manderan fuori il fluido elet­<lb></lb>trico divenuto ora ridondante. </s>

<s>Ed ecco come nasce l&#039;<emph type="italics"></emph>elettricità di eccesso,<emph.end type="italics"></emph.end><lb></lb>che domina sempre più o meno nell&#039;aria anche serena, a quell&#039;altezza in <lb></lb>cui i vapori cominciano a condensarsi, la quale è più sensibile nelle neb­<lb></lb>bie, ove quelli si condensano maggiormente, e infine fortissima là dove le <lb></lb>folte nebbie si agglomerano in nubi, e già si figurano in gocce. </s>

<s>” </s></p><p type="main">

<s>“ Fin qui l&#039;elettricità dell&#039;ammosfera sarà sempre <emph type="italics"></emph>positiva.<emph.end type="italics"></emph.end> Ma formata <lb></lb>che sia una nube potentemente elettrica <emph type="italics"></emph>in più<emph.end type="italics"></emph.end> ella avrà una sfera di at­<lb></lb>tività intorno ad essa, nella quale, se avviene ch&#039;entri un&#039;altra nube, al­<lb></lb>lora, giusta le note leggi delle <emph type="italics"></emph>Ammosfere,<emph.end type="italics"></emph.end> gran parte del fluido elettrico <lb></lb>di questa seconda nube si ritirerà verso l&#039;estremità più lontana dalla prima, <lb></lb>e potrà anche uscirne ove incontri o altra nube o vapori o prominenze ter­<lb></lb>restri che lo possan ricevere, ed ecco una nube elettrizzata <emph type="italics"></emph>negativamente,<emph.end type="italics"></emph.end><lb></lb>la quale potrà a sua posta occasionare, coll&#039;influsso della propria ammosfera, <lb></lb>l&#039;elettricità positiva in una terza ecc. </s>

<s>In questa maniera s&#039;intende benissimo <lb></lb>come si possano avere sovente ne&#039;conduttori ammosferici segni di elettri­<lb></lb>cità <emph type="italics"></emph>negativa<emph.end type="italics"></emph.end> a cielo più che coperto, e come ne&#039;temporali specialmente, <lb></lb>ove molte nubi si veggono pensili, e staccate vergere al basso e or ondeg­<lb></lb>giare per qualche tempo, ora scorrere le une sotto le altre, or trasportarsi <lb></lb>rapidamente, l&#039;elettricità cambi più volte e spesso a un tratto da <emph type="italics"></emph>positiva<emph.end type="italics"></emph.end> in <lb></lb><emph type="italics"></emph>negativa<emph.end type="italics"></emph.end> c viceversa. </s>

<s>” (Opere cit., T. I, P. I, pag. </s>

<s>275-77). </s></p><p type="main">

<s>L&#039;analogia così felicemente dimostrata fra il fuoco delle folgori e il fuoco <lb></lb>elettrico allettò i Fisici ad ammettere una somigliante analogia tra la luce <lb></lb>emessa dai globi artificialmente confricati, e la luce naturalmente diffusa per <lb></lb>le altissime regioni dell&#039;aria nelle Aurore Boreali. </s>

<s>Prima che vedesse il Gue­<lb></lb>ricke fosforeggiare, come suole talvolta il cielo, la sua Terrella, si credeva, <lb></lb>da&#039;più savi Filosofi, che l&#039;apparenza delle Aurore Boreali nascesse dalla luce <lb></lb>del Sole riflessa ne&#039;vapori esalati su dalla Terra. </s></p><p type="main">

<s>“ Quod circa terram eleventur vapores, scriveva Galileo, qui ascenden­<lb></lb>tis solis lumen reflectant, saepissime apparet cum media interdum nocte coe­<lb></lb>lum adeo illustret, ut lumen in terram crepusculinum maius effundat. </s>

<s>Id <lb></lb>autem a me saepius observatum est et semper talis lux boream versus ap­<lb></lb>paret et ratio est manifesta, quia ex meridie vel ab ortu vel ab occasu in­<lb></lb>tra conum umbrae tales complectuntur vapores, quoniam Boream versus, ob <lb></lb>nostrum in eam partem situm, conspici possunt ut diligentius consideranti <lb></lb>patet. </s>

<s>Vidi Venetiis circa horam noctis secundam aerem ad Boream adeo <pb xlink:href="020/01/848.jpg" pagenum="291"></pb>clarum, ut adversus parietes ultra Lunae rotundae lumen illustraret, aversi <lb></lb>autem tenebrosissimi erant. </s>

<s>Novam autem admirationem afferebat quod viae <lb></lb>quae proximae ad Septentrionem dirigebantur, utrimque a splendore illu­<lb></lb>minabantuŕ, nec tecta umbram in terram demittebant, ut ex illuminatione <lb></lb>Solis et Lunae contingit, quia in his tamquam ab uno puncto provenit il­<lb></lb>luminatio tunc vero ex quarta fere anguli parte magna lux emanabat ” (MSS. <lb></lb>Gal., P. III, T. II, c. </s>

<s>13. Alb. </s>

<s>V, 393). </s></p><p type="main">

<s>Questa ipotesi galileiana dell&#039;origine delle Aurore boreali cadde insieme, <lb></lb>e per quelle stesse ragioni che caddero le altre ipotesi professate pure da <lb></lb>Galileo intorno all&#039;origine delle stelle nuove e delle Comete, essendo per­<lb></lb>suaso ognuno assai facilmente che così fatte apparenze celesti hanno sede <lb></lb>in regioni tanto più alte di quelle, alle quali si possono sublimare i vapori <lb></lb>o le altre esalazioni terrestri. </s>

<s>A chi prima, osservando la fosforescenza che <lb></lb>appariva diffondersi sulla superficie del globo sulfureo del Guericke, o me­<lb></lb>glio nell&#039;interna cavità de&#039;vetri tornatili dell&#039;Hawksbee, venisse in mente di <lb></lb>paragonare quel lume elettrico colle luminose apparenze delle Aurore, non <lb></lb>è forse facile a definire, ma dovette senza dubbio aver grande efficacia, in <lb></lb>confermar gl&#039;ingegni in così fatta opinione, ciò che ne fu scritto e divul­<lb></lb>gato per le Lettere frankliniane. </s></p><p type="main">

<s>In una di queste diretta al Collinson immagina il celebre Autore che <lb></lb>l&#039;aria, fortemente riscaldata e rarefatta dal sole sotto i tropici, si distenda <lb></lb>verso i poli, dove le due elettricità de&#039;vapori equatoriali e polari, comuni­<lb></lb>candosi insieme, si rendono all&#039;occhio dello spettatore parventi. </s>

<s>Così, ben­<lb></lb>chè paia slanciarsi la luce da settentrione a mezzodì, il progresso nulladi­<lb></lb>meno è realmente in verso contrario, e avviene in ciò quel che suole avvenire <lb></lb>de&#039;tubi pieni d&#039;acqua, nell&#039;atto che si votano, ne&#039;quali, benchè il flusso ap­<lb></lb>parisca dalla parte di sotto, il principio del moto in realtà è dalla parte di <lb></lb>sopra. </s>

<s>“ Comme lorsqu&#039;on ouvre à l&#039;une de ses extrèmités un long canal <lb></lb>repli d&#039;eau, pour le vuider, le mouvement de l&#039;eau commence d&#039;abord au­<lb></lb>près de l&#039;extrèmité ouverte, et continue vers l&#039;extrèmité fermée, quoique <lb></lb>l&#039;eau elle-même avance de l&#039;extrèmité fermée vers l&#039;extrèmité ouverte: ainsi <lb></lb>le feu électrique déchargé dans les régions polaires, peut être sur une lon­<lb></lb>gueur de mille lieves d&#039;air en vapeurs, paroît d&#039;abord là où il est en mou­<lb></lb>vement; c&#039;est-à-dire, dans les parties le plus septentrionales, et l&#039;apparition <lb></lb>s&#039;élance du còté du midi, quoi que le feu avance réellement du còté du <lb></lb>septentrion ” (Oeuvres cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Non si persuadeva per questo il Franklin d&#039;aver data la soluzione del <lb></lb>difficile problema, in modo che se n&#039;avessero tutti a sodisfare: era un&#039;ab­<lb></lb>bozzo, ch&#039;egli stesso rimetteva all&#039;opera di qualche altra mano. <emph type="italics"></emph>Ceci,<emph.end type="italics"></emph.end> con­<lb></lb>cludevano le sopra riferite parole, <emph type="italics"></emph>pourroit passer pour une explication de <lb></lb>l&#039;Aurore Borèale.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La mano che riprese poi quell&#039;opera era una delle più esperte, che si <lb></lb>potesse trovare allora; quella, vogliam dire, del nostro Beccaria. </s>

<s>Egli, nel <lb></lb>§ 657 del suo Trattato <emph type="italics"></emph>Dell&#039;Elettricismo<emph.end type="italics"></emph.end> pone con lungo ordine sotto di-<pb xlink:href="020/01/849.jpg" pagenum="292"></pb>stinti capi le analogie, che passano fra ciò che si osserva nelle Aurore bo­<lb></lb>reali e ne&#039;fenomeni elettrici, e più che in altro insiste sulla somiglianza della <lb></lb>diffusione della luce nell&#039;opera dell&#039;arte e della Natura. </s>

<s>“ Della luce appena <lb></lb>accade parlare: non v&#039;ha chi abbia osservata la luce elettrica nel voto, che <lb></lb>non vi scorga una somiglianza colle colonne lucenti dell&#039;Aurora boreale, che <lb></lb>accadono attraverso all&#039;ammosfera più alta ne&#039;luoghi dell&#039;aria meno densa ” <lb></lb>(Ediz. </s>

<s>cit., pag. </s>

<s>220, 21). </s></p><p type="main">

<s>Questa somiglianza era senza dubbio la più seducente di tutte, ma come <lb></lb>si dimostrava, dall&#039;analogia degli effetti, l&#039;identità delle cause? </s>

<s>E nel prin­<lb></lb>cipal fondamento dell&#039;ipotesi frankliniana come poteva provarsi che i vapori <lb></lb>equatoriali abbiano elettricità contraria a quella de&#039;vapori che si sollevan <lb></lb>dalla parte di Borea? </s></p><p type="main">

<s>Il prof. </s>

<s>Pierantonio Bondioli si lusingò di essersi potuto sottrarre a così <lb></lb>gravi difficoltà, dicendo che nelle regioni boreali i vapori si sollevano in più <lb></lb>gran copia, e sprigionando nel condensarsi l&#039;elettricità latente, secondo le nuove <lb></lb>dottrine insegnate dal Volta, davano origine perciò così facilmente alle Aurore. </s></p><p type="main">

<s>La Dissertazione, in che si dimostrava la ragionevolezza di questa ipo­<lb></lb>tesi, fu inviata dall&#039;Autore allo stesso Volta, il quale rispose che com&#039;egli si <lb></lb>rideva di coloro, che ogni meteora attribuiscono al fluido elettrico senza crite­<lb></lb>rio; così dubitava, per mancar la prova opportuna, dell&#039;origine elettrica delle <lb></lb>Aurore, benchè fosse inclinato a crederlo principalmente “ per la non piccola <lb></lb>somiglianza che ravvisiamo nelle fulgurazioni delle celesti Aurore, coi bei <lb></lb>getti e lampi e trascorrimenti di fuoco elettrico da noi eccitati artificialmente <lb></lb>ne&#039;recipienti d&#039;aria molto diradata ” (Opere cit., T. I, P. II, pag. </s>

<s>431, 32). </s></p><p type="main">

<s>Quanto poi al particolare della dottrina dell&#039;elettricità latente espressa <lb></lb>dal subitaneo condensamento de&#039;vapori straordinariamente affollati verso il <lb></lb>polo, dubitava il Volta se potesse quella stessa dottrina essere opportuna­<lb></lb>mente applicata a spiegare il fenomeno delle Aurore boreali, per la ragione <lb></lb>principalmente che queste si formano in regioni molto più alte di quelle, <lb></lb>alle quali possono sollevarsi i vapori terrestri. </s>

<s>“ Questa pressura però di <lb></lb>vapori, a così spiegarmi, che accader deve, se bene si esaminano le cagioni <lb></lb>fisiche (e accade infatti se ci riportiamo all&#039;osservazione medesima nella bassa <lb></lb>e nella mezzana regione dell&#039;ammosfera) veggo bene come debba produrre <lb></lb>le nebbie foltissime e i nuvoloni, i temporali e le grandi burrasche, che <lb></lb>sono sì frequenti e sì terribili in quelle parti del mondo; ma non com­<lb></lb>prendo ancora come abbiano ad esser causa delle Aurore boreali, le quali <lb></lb>tengono la loro sede nell&#039;altissima regione, negli ultimi strati e quasi fuora <lb></lb>dell&#039;ammosfera terrestre, ove, non che affollarsi, non è credibile che nep­<lb></lb>pur giungano gli acquei vapori, e seppur ve ne giungono dispersi e a così <lb></lb>dire raminghi, debbono esser ben pochi ” (ivi, pag. </s>

<s>433, 34). </s></p><p type="main">

<s>Così veniva il Volta a mettere la diffidenza anche in questa novella ipo­<lb></lb>tesi germogliata dalle sue stesse scoperte, ma egli, che pur ridevasi di co­<lb></lb>loro i quali volevan ridurre all&#039;elettricità ogni Meteora, non potè liberarsi <lb></lb>da questa scabbia pruriginosa. </s></p><pb xlink:href="020/01/850.jpg" pagenum="293"></pb><p type="main">

<s>Nelle sue Lettere di Meteorologia elettrica, e più di proposito in una <lb></lb><emph type="italics"></emph>Memoria divisa in tre parti,<emph.end type="italics"></emph.end> si propone l&#039;Autore di risolvere alcune gravi <lb></lb>difficoltà sul soggetto della formazione della grandine <emph type="italics"></emph>che è uno de&#039;più in­<lb></lb>tralciati e difficili della Meteorologia<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>304). Il De-Luc era ricorso <lb></lb>al supposto de&#039;vapori saliti alle altissime regioni, ed ivi congelati in forma <lb></lb>di fiocchi di neve più freddi assai della neve ordinaria, sicchè, cadendo ed <lb></lb>aggiungendosi ad altri vapori incontrati per via, venissero così a rivestirsi <lb></lb>di quella loro dura e grossa crosta di ghiaccio. </s>

<s>Ma poi ebbe egli stesso a <lb></lb>riconoscer falsa questa sua ipotesi, e a congetturar piuttosto che i fiocchetti <lb></lb>nevosi, i quali diverranno poi i nuclei della grandine, si formino verso l&#039;alto <lb></lb>della nuvola medesima, mercè un subitaneo raffreddamento. </s></p><p type="main">

<s>Questa nuova congettura del De-Luc parve ragionevolissima al Volta, <lb></lb>che la illustrò, nella prima parte della <emph type="italics"></emph>Memoria<emph.end type="italics"></emph.end> suddetta, coll&#039;esempio del­<lb></lb>l&#039;agghiacciamento dell&#039;acqua prodotto dall&#039;evaporazione dell&#039;etere solforico, <lb></lb>e coll&#039;analogia di ciò che avviene nella macchina idraulica dell&#039;Hell, nella <lb></lb>quale per subitanea evaporazione un getto di acqua incrosta un fazzoletto, <lb></lb>o che altro a cui si diriga (ivi, pag. </s>

<s>339). </s></p><p type="main">

<s>Non sembrava al Volta però sufficiente, a potere ingrossarsi nella cro­<lb></lb>sta di ghiaggio il nucleo nevoso, quel sì breve tempo del suo frettoloso pas­<lb></lb>saggio attribuitogli dal De-Luc attraverso allo spessor della nube, e giudi­<lb></lb>cava dall&#039;altra parte gratuita l&#039;opinion di que&#039;Fisici, che fanno cader la <lb></lb>grandine da tanta altezza quanto è necessario perchè si riduca sì grossa, <lb></lb>avendo egli anzi osservato che son le nuvole grandinose delle più basse. </s>

<s>In­<lb></lb>voca il Volta perciò i giochi dell&#039;elettricità a render la ragione di un fatto, <lb></lb>ch&#039;è in questo genere il più difficile a intendersi di tutti gli altri. </s></p><p type="main">

<s>“ Immagino io, egli dice, e tengo oramai per certo, che gli embrioni <lb></lb>della grandine, i quali soglion essere fiocchetti di neve, indi i grani stessi <lb></lb>già formati e solidi rimangano per lo più sospesi e saltellanti fra due strati <lb></lb>di nuvole collocati un sopra l&#039;altro a conveniente distanza, e contrariamente <lb></lb>elettrici, e ciò, se accade, per delle ore: durante la qual danza elettrica va­<lb></lb>dano essi grani rivestendosi di nuove lamine di ghiaccio, e s&#039;ingrossi così <lb></lb>mano mano la loro crosta. </s>

<s>Questo bel gioco è assai curioso dei grani di <lb></lb>grandine che vanno su e giù frequenti e tumultuosi tra due quasi tavole <lb></lb>di nubi; gioco da me immaginato per render ragione del più difficile a in­<lb></lb>tendersi dei suoi fenomeni, che è la tanta grossezza a cui pervengono non <lb></lb>di rado tali grani ” (ivi, pag. </s>

<s>429). </s></p><p type="main">

<s>Se fosse stato questo bel gioco della danza elettrica fra le nubi una <lb></lb>realtà, si sarebbe reso il Volta, co&#039;paragrandini, non men benemerito del <lb></lb>genere umano, di quel che non si fosse reso benemerito il Franklin co&#039;suoi <lb></lb>parafulmini; ma essendosi quel gioco ritrovato una immaginazione, riman <lb></lb>tuttavia a cercar l&#039;origine della grandine, e dove tenda, la nostra crudel <lb></lb>nemica, e com&#039;ella esca fuori da&#039;suoi freddi agguati. </s></p><pb xlink:href="020/01/851.jpg" pagenum="294"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle Meteore<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle sublimazioni de&#039;vapori vescicolari e de&#039;loro condensamenti in pioggia. </s>

<s>— II. Dell&#039;origine <lb></lb>de&#039;venti in generale, e in particolare de&#039;venti tropicali. </s>

<s>— III. </s>

<s>Delle variazioni, che subisce il <lb></lb>Barometro al vario stato del cielo. </s>

<s>— IV. </s>

<s>Delle Effemeridi meteorologiche del Ramazzini; delle <lb></lb>variazioni barometriche prodotte dallo spirare dei venti, e dall&#039;appressarsi delle procelle. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le folgori, le Aurore boreali, i nembi grandinosi, intorno a che eser­<lb></lb>citarono i loro studi gli elettricisti, appartengono a quell&#039;ordine di fatti na­<lb></lb>turali, a cui fu dato il nome di Meteore infino da&#039;Filosofi più antichi. </s>

<s>La <lb></lb>Meteorologia però, benchè possa vantarsi dell&#039;antichità del nome, fu da quegli <lb></lb>stessi antichi Maestri men coltivata delle altre scienze sorelle, le quali non <lb></lb>progredirono, per non si saper l&#039;arte, e per non avere strumenti da osser­<lb></lb>vare i fatti naturall, mentre alla Meteorologia restava, di più, difficile anche <lb></lb>l&#039;osservare quegli stessi fatti, i quali avvengono in regioni troppo lontane <lb></lb>dalla corta apprensiva de&#039;nostri sensi. </s></p><p type="main">

<s>Ma perchè questa è una tal difficoltà, che riman tuttavia e rimarrà in­<lb></lb>fintantochè l&#039;uomo non impennerà l&#039;ali per salire a sedersi sul dorso delle <lb></lb>nubi, non ha perciò la scienza delle Meteore, a progredire, altro modo che <lb></lb>quello d&#039;imitar con l&#039;arte, in questi bassi fondi, ciò che s&#039;opera dalla Na­<lb></lb>tura ne&#039;suoi sublimi teatri, e d&#039;argomentare all&#039;identità della causa dalle <lb></lb>somiglianze riscontratesi negli effetti. </s>

<s>Tale in vero è la ragione di tutte le <lb></lb>meteorologiche scoperte che si son fatte, e tale è stato sempre il processo <lb></lb>che tennero i Fisici per farle. </s>

<s>Così i colori prodotti dalle rifrazioni de&#039;raggi <pb xlink:href="020/01/852.jpg" pagenum="295"></pb>solari, ne&#039;globi di vetro pieni di acqua, dettero facile modo a intender la <lb></lb>generazione dell&#039;Iride, e i cilindretti di vetro, co&#039;loro nuclei opachi, se non <lb></lb>valsero a sodisfarla, acquietarono la curiosità di coloro, che ardevano di sa­<lb></lb>pere in che si facessero specchio il Sole e la Luna per incoronarsi di luce <lb></lb>avventizia, e moltiplicare all&#039;intorno la loro sembianza. </s>

<s>Allo stesso modo, <lb></lb>nel crepitar della scintilla elettrica, si intravide la ragione de&#039;tuoni e de&#039;ba­<lb></lb>leni, e l&#039;effusion del lume dentro i globi di vetro, vuoti d&#039;aria ed elettriz­<lb></lb>zati, passò, in mancanza d&#039;altro, per una spiegazione delle misteriose Au­<lb></lb>rore boreali. </s></p><p type="main">

<s>Di tutte queste, che appartengono alle Meteore elettriche luminose, <lb></lb>narrammo a parte a parte ne&#039;capitoli precedenti la storia, dalla quale si <lb></lb>mostra che la difficoltà d&#039;intendere la ragion di que&#039;fatti dipendeva in parte, <lb></lb>come dicemmo, dal non se ne poter far soggetto di osservazioni dirette. </s>

<s>Ma <lb></lb>il forte della difficoltà, a ripensarla meglio, si riduceva a due capi: a saper <lb></lb>trovar l&#039;artificio che imiti la Natura, e ad assicurarsi che quel tale artificio <lb></lb>è veramente imitativo della Natura. </s>

<s>Che qui principalmente, e nò nell&#039;im­<lb></lb>possibilità di osservare i fatti in sè stessi, riseggano le difficoltà che s&#039;in­<lb></lb>contrano nel risolvere i problemi di Meteorologia, si mostrerà da ciò che <lb></lb>occorse a pensare e a dire intorno all&#039;origine delle piogge e de&#039;venti. </s>

<s>Que­<lb></lb>ste che sono delle Meteore più comuni, benchè abbiano in alto i loro prin­<lb></lb>cipii, hanno pure in terra e presso a noi i loro termini e i loro effetti, e <lb></lb>nonostante, tanto si penò a intenderne le ragioni, perchè non si seppe tro­<lb></lb>var nell&#039;arte il modo d&#039;imitar la natura, o trovato, non si seppe almeno in <lb></lb>tutto riscontrarvene la somiglianza. </s></p><p type="main">

<s>La ragione della produzion delle pioggie dipende e si conclude per più <lb></lb>altre ragioni, le quali si riducono a saper come mai si sollevino i vapori <lb></lb>acquosi dalla terra, e come sollevati si condensino, s&#039;accrescano notabilmente <lb></lb>di mole, e così poi tornino in pioggia. </s>

<s>Il fatto di tali sublimazioni, che de­<lb></lb>ducevasi con certezza dal vedersi i vapori scender giù d&#039;onde e&#039;non pos­<lb></lb>sono aver le loro sedi naturali, Galileo lo dimostrava rendendolo visibile at­<lb></lb>traverso i vetri del Canocchiale, e nella maniera seguente pensava che, giunti <lb></lb>i vapori stessi a un&#039;altezza ch&#039;è il termine del purissimo nostro etere am­<lb></lb>biente, potessero per la loro accresciuta mole cadere in gocciole piovose. <lb></lb></s>

<s>“ Essendo che dalla terra si sollevano continuamente esalazioni sottili, tenui, <lb></lb>ascendenti, e intanto si portano seco vapori più grossi ed acquei, ed arri­<lb></lb>vati a un&#039;altezza, che è il termine dell&#039;etere nostro ambiente e l&#039;aria pu­<lb></lb>rissima, si dilatano, si distendono e si trattengono o calano abbasso, dopo <lb></lb>essersi fatta una costipazione o spessitudine di questi vapori, e così si fanno <lb></lb>le piogge. </s>

<s>Ma non so in che maniera, quando è un tempo serenissimo, <lb></lb>chiaro, e&#039;s&#039;abbia subitamente a rannuvolare ogni cosa, farsi grande oscurità <lb></lb>e venir milioni di botti d&#039;acqua a basso. </s>

<s>— Che continuamente si sollevino <lb></lb>vapori si fa manifesto in più maniere, poichè gittando in terra un po&#039;d&#039;acqua, <lb></lb>e guardando con l&#039;Occhiale, si vede salir con prestezza un fumo, un vapore, <lb></lb>e si fa manifesto nella fiamma che continuamente, e con gran velocità, si <pb xlink:href="020/01/853.jpg" pagenum="296"></pb>vede salire ad alto, e così nei carboni accesi quel vapore va ad alto ” (MSS. <lb></lb>Gal., P. V, T. IV, c. </s>

<s>28). </s></p><p type="main">

<s>Così presumevasi Galileo di render visibili quelle esalazioni umide e <lb></lb>secche sollevate su dall&#039;acqua e dal fuoco, ch&#039;egli accolse con troppa doci­<lb></lb>lità dalla Filosofia peripatetica, introducendo così nel suo proprio insegna­<lb></lb>mento dottrine contradittorie. </s>

<s>Egli infatti negava ad Aristotile il principio <lb></lb>della leggerezza positiva, affermando che tutti i corpi son gravi, e che se <lb></lb>talvolta, invece di cadere, salgono, ciò da nient&#039;altro dipende che dalla cir­<lb></lb>cumpulsione del mezzo. </s>

<s>Ma o Galileo non credeva l&#039;ignee esalazioni appar­<lb></lb>tenessero alla materia, o faceva per esse esalazioni una particolare eccezione <lb></lb>dalle proprietà comuni de&#039;corpi, professando ch&#039;elle son naturalmente di­<lb></lb>sposte a salire, e che sono anzi esse stesse che sublimano la materia vapo­<lb></lb>rosa, quasi portandola sulla leggerezza delle ali. </s></p><p type="main">

<s>Si potrebbero forse salvar le dottrine galileiane dicendo che si teneva <lb></lb>da esso le ignee esalazioni esser di così tenue materia, da riuscire incom­<lb></lb>parabilmente men gravi in specie dell&#039;etere purissimo o di qual si voglia <lb></lb>altra sostanza più sottile, ma non è possibile, in ogni modo, salvare intorno <lb></lb>a ciò Galileo dall&#039;imputazione di avere strascicato per la trita polvere peri­<lb></lb>patetica il suo dignitoso pallio filosofale. </s>

<s>Più grave danno si fu che si tra­<lb></lb>dussero così fatte immaginate dottrine delle esalazioni umide e secche, <lb></lb>dall&#039;autorità di un tanto maestro, nella docilità de&#039;discepoli, i quali sul fon­<lb></lb>damento degl&#039;insegnamenti galileiani elaborarono, intorno alla generazione <lb></lb>e alla produzion delle piogge, un sistema, che ha molto del singolare. </s></p><p type="main">

<s>S&#039;immaginava dunque il Borelli che le esalazioni ignee, moventisi dalle <lb></lb>parti centrali del Globo, sollevassero in alto i vapori, e così sotto terra des­<lb></lb>sero origine alle fonti, e usciti sopra terra producessero le piogge. </s>

<s>Suppo­<lb></lb>neva inoltre che tali sublimazioni procedessero reciprocamente veloci alla <lb></lb>densità de&#039;mezzi via via attraversati, cosicchè velocissime fossero colà, dove <lb></lb>l&#039;etere è sottilissimo, e anzi tanto veloci, che, non reggendo dietro a loro <lb></lb>la gravezza de&#039;vapori, rimanessero ivi abbandonati e perciò costretti a ca­<lb></lb>dere, come corpo a cui vien mancando chi lo sostenti. </s>

<s>Più singolare è poi, in <lb></lb>questo filosofico romanzetto, il modo come s&#039;immaginava che le tenui vesci­<lb></lb>cole vaporose venissero a ingrossarsi in gocciole d&#039;acqua. </s>

<s>Si ricorreva niente <lb></lb>di meno che al convergere che fanno le fila piovose verso il centro della Terra, <lb></lb>a cui si studiano di giunger cadendo, andandovi sempre più fra sè ristrette <lb></lb>e condensate. </s>

<s>Ma perchè tanto hanno così fatte cose dello strano, che difficil­<lb></lb>mente si crederebbe essere state pensate dal Borelli e accolte dal Viviani e <lb></lb>dagli altri Accademici fiorentini, trascriveremo qui, nella forma propria in cui <lb></lb>venne disteso, quello che si qualificava da noi per un filosofico romanzetto: </s></p><p type="main">

<s>“ Dalla controversia, d&#039;onde l&#039;origine avessero le fonti, passò l&#039;Ecc.mo<lb></lb>signor Borelli a dar la sua opinione circa l&#039;origine delle piogge, e non altra <lb></lb>essere alla fine concluse che la medesima, la quale dello scaturire le fonti <lb></lb>è cagione. </s>

<s>La ragione che egli medesimo, s&#039;io ben mi ricordo, n&#039;adduce è <lb></lb>la presente: che cioè gli artefici, nello scavar che fanno sotto terra per <pb xlink:href="020/01/854.jpg" pagenum="297"></pb>molte canne per ritrovar la miniera, sanno precisamente quando di sopra <lb></lb>vuol piovere, ed asseriscono ciò devenire nel veder loro passare fumi e sen­<lb></lb>tire caldo non ordinario. </s>

<s>Bisogna dunque dire che quelle esalazioni congiunte <lb></lb>con particelle acquee sormontino al cielo, e dieno a vedere quel fumo e a <lb></lb>sentire quel caldo. </s>

<s>Contrariano però alcuni Filosofi alla già detta opinione, <lb></lb>non volendo che l&#039;origine delle piogge sia questa, ma un&#039;altra ne asseri­<lb></lb>scono ed adducono essi, la quale non sarà discaro l&#039;esaminarla. </s>

<s>” </s></p><p type="main">

<s>“ Dicono dunque che il sole, con i suoi raggi, come con una tromba, <lb></lb>attinge dal mare l&#039;acqua, la quale condotta ad una tal regione dell&#039;aria, co­<lb></lb>lassù in nuvole si riduce, e abbandonata poi dal medesimo sole, cadendo a <lb></lb>basso, cagiona le piogge. </s>

<s>” </s></p><p type="main">

<s>“ Quante e quali difficoltà patisca questa opinione ciascuno, anco d&#039;in­<lb></lb>gegno ordinario, potrà conoscere, e prima, già di sopra si è detto che il <lb></lb>sole è inabile da per sè stesso a tirare all&#039;insù particelle acquee, poichè se <lb></lb>noi, di state tempo, nel quale il sole ha più ardenti i suoi raggi, scaveremo <lb></lb>sotto terra quattro o sei braccia, troveremo la terra di sotto molto più umida <lb></lb>che sopra abbondantemente; segno chiaro che il sole con i suoi raggi non <lb></lb>ci penetra, come nelle cantine e nelle ghiacciaie, dove si conserva la neve <lb></lb>e il diaccio nel medesimo tempo di state. </s>

<s>” </s></p><p type="main">

<s>“ Ma dicono essi che non altrimenti dalla terra, ma dal mare, vien con­<lb></lb>tribuito al sole l&#039;umido. </s>

<s>Io perciò non resto consapevole come, ne&#039;paesi lon­<lb></lb>tanissimi dal mare, s&#039;abbino a veder continuamente le piogge condotte sopra <lb></lb>le spalle dai raggi del sole quattro o cinquecento miglia, e ne&#039;paesi vicinis­<lb></lb>simi al mare, e dove il calor del sole è veementissimo, come nell&#039;Egitto, <lb></lb>non abbia a piover mai: come di estate non piova molto più che nell&#039;in­<lb></lb>verno, nel tempo della quale i raggi sono molto più cocenti che in verun <lb></lb>altro tempo, ed insomma per molte e molte altre difficoltà, che per non per­<lb></lb>dere tanto male il tempo tralascio, si dovrebbe vedere il contrario di quello <lb></lb>che alla giornata ne segue. </s>

<s>” </s></p><p type="main">

<s>“ Tornando dunque al nostro proposito tale esser l&#039;origine delle fonti <lb></lb>io stimo, quale dal signor dott. </s>

<s>Giov. </s>

<s>Alfonso dimostrata ne viene, ma vedo <lb></lb>già contro di me inalzarsi un Peripatetico, non volendo partirsi invendicato <lb></lb>con addurre difficoltà indissolubili contro l&#039;apportata opinione. </s>

<s>Dice egli che <lb></lb>se è la medesima la causa delle piogge, che quella delle fonti, si dovrebbe <lb></lb>vedere, avanti che cominci la pioggia, sgorgare in maggior profluvio la fonte, <lb></lb>poichè le particelle acquee trasportate dalle esalazioni ignee molto più presto <lb></lb>arrivano alla fonte che alle supreme regioni dell&#039;aria, d&#039;onde devono poi <lb></lb>partirsi e cadere in terra, sicchè, dovendo esse far molto più lungo viaggio <lb></lb>in un luogo che in un altro, dovrebbero prima sgorgar più copiosamente le <lb></lb>fonti, e poi cagionarsi le piogge. </s>

<s>Difficoltà invero degna di considerazione e <lb></lb>adattata, se però fosse in campo apportata da chi non avesse veduto ciò che, <lb></lb>circa all&#039;origine delle fonti, di sopra si è detto; cioè che esse hanno neces­<lb></lb>sità di qualche preminenza che gli sovrasti, non potendo esse nascere in un <lb></lb>piano lontanissimo da&#039;monti o sopra la cima d&#039;un monte. </s>

<s>” </s></p><pb xlink:href="020/01/855.jpg" pagenum="298"></pb><p type="main">

<s>“ Avvertasi dunque ch&#039;essendo molto spessi gli anfratti del monte, dove <lb></lb>si generano le fontane, possono le particelle acquee molto veloci nell&#039;aria <lb></lb>camminare assai più presto per quel mezzo, che non fanno le particelle <lb></lb>acquee, per il mezzo della terra, poichè, se si pone un vaso pieno d&#039;acqua <lb></lb>e il fondo turato con terra, l&#039;acqua di dentro tardissimamente andrà pas­<lb></lb>sando, e quasi incomprensibilmente per la terra, sicchè, per i molti anfratti <lb></lb>che si trovano per la terra, queste particelle acquee son ritardate, e ciò aper­<lb></lb>tamente si vede, poichè, nell&#039;istesso tempo che segue la pioggia, si vedono <lb></lb>crescere le fonti, argomento certissimo essere la medesima la cagione. </s>

<s>Nè <lb></lb>dicasi che il crescere delle fonti venga dall&#039;acqua che piove, poichè ciò ne <lb></lb>dimostra falso l&#039;esperienza certa. </s>

<s>Imperocchè se, dopo che sarà seguita la <lb></lb>pioggia, in maniera tale che sien cresciute le fonti, cominci a scalzarsi e a <lb></lb>scortecciarsi la terra per due o tre braccia, si troverà la terra non essere di <lb></lb>sotto quasi bagnata. </s>

<s>Adunque, se sotto tre braccia di terra non è passata <lb></lb>l&#039;acqua, come può essere che sia passata all&#039;origine delle fonti, la quale <lb></lb>è molto più sotterranea? </s>

<s>Sarà dunque certissimo argomento questo la me­<lb></lb>desima esser l&#039;origine delle fonti e delle piogge. </s>

<s>” </s></p><p type="main">

<s>“ — In qual maniera poi queste moli composte d&#039;esalazioni ignee e <lb></lb>particelle acquee sormontano invisibilmente a noi, e poi tornano a basso in <lb></lb>sì gran copia, che ne formino le piogge? </s>

<s>— Per dunque meglio intendere <lb></lb>questa naturale operazione, intendasi per la superficie della Terra la linea <lb></lb>ACDB (fig. </s>

<s>63), dalla quale si partano le moltissime linee CD verso EF. <lb></lb><figure id="id.020.01.855.1.jpg" xlink:href="020/01/855/1.jpg"></figure></s></p><p type="caption">

<s>Figura 63.<lb></lb>Giunte che saranno queste particelle in EF, spazio <lb></lb>lontano per qualche miglio dalla superficie della Terra; <lb></lb>onde molto maggiore sarà la circonferenza della linea EF <lb></lb>rappresentante le altissime regioni dell&#039;aria, che la su­<lb></lb>perficie CD. </s>

<s>Per lo che le particelle arrivate alla su­<lb></lb>perficie EF, nel tornar che faranno, s&#039;andranno restrin­<lb></lb>gendo, e per conseguenza accrescendosi in mole con <lb></lb>moltiplicarsi l&#039;una sopra l&#039;altra, talchè poi, arrivate alla <lb></lb>superficie terrestre, si saranno fatte a quella mole che <lb></lb>si vede. </s>

<s>Inoltre, quello che maggiormente convince è <lb></lb>che, quando le particelle si partirono dalla superficie <lb></lb>terrestre, erano piccolissime, e per conseguenza invi­<lb></lb>sibili, ma nel tornar che fanno, avendone seco dietro <lb></lb>tirate dell&#039;altre, che si vanno incontrando con quelle, conseguentemente si <lb></lb>accrescono, e possono accrescersi non solo mille, ma duemila volte e più an­<lb></lb>cora, come la linea è maggior d&#039;un suo punto. </s>

<s>” </s></p><p type="main">

<s>“ Resta solo dunque da investigarsi in qual maniera si faccia la sepa­<lb></lb>razione delle particelle acquee dalle esalazioni ignee, la quale, acciò meglio <lb></lb>da noi esser possa conosciuta, necessario è fermare due principii: l&#039;uno dei <lb></lb>quali ancora dagli avversarii è conceduto, cioè che, allontanandosi vie più <lb></lb>dalla Terra, un elere più puro si vada incontrando; l&#039;altro che i corpi più <lb></lb>duri mantenghino più lungamente il caldo, come chiaro ne mostra l&#039;espe-<pb xlink:href="020/01/856.jpg" pagenum="299"></pb>rienza. </s>

<s>Imperocchè, se noi piglieremo un sasso ed un vaso d&#039;acqua, e ambi <lb></lb>gli faremo ugualmente caldi, l&#039;acqua durerà per brevissimo tempo a con­<lb></lb>servare il suo calore, ma il sasso per un&#039;ora o due l&#039;andrà conservando. </s>

<s>E <lb></lb>similmente si dice dell&#039;aria e dell&#039;acqua, e la ragione è che più facilmente <lb></lb>passano gli spiriti ignei, parti minime del fuoco, per un mezzo men duro, <lb></lb>che per un mezzo più duro, onde nell&#039;aria velocissimamente traspirano. </s>

<s>” </s></p><p type="main">

<s>“ Supposte dunque queste cose, chiaramente si conosce la cagione per­<lb></lb>chè e in qual maniera si faccia la separazione delle particelle acquee dalle <lb></lb>esalazioni ignee, essendochè l&#039;aria vicinissima alla terra, come molto vapo­<lb></lb>rosa e quasi densa, fa che molto lentamente per il di lei mezzo passino <lb></lb>l&#039;esalazioni ignee, e per conseguenza, movendosi esse tardamente, seco ne <lb></lb>conducono le particelle acquee, ma arrivando ove l&#039;aria è più pura, l&#039;esa­<lb></lb>lazioni, movendosi più velocemente, sono abbandonate dalle particelle acquee, <lb></lb>le quali non possono seguitarle con la medesima velocità ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXXXVI, c. </s>

<s>6-8). </s></p><p type="main">

<s>Son tali quali gli abbiamo veduti, per queste pagine manoscritte rac­<lb></lb>colti, i frutti degl&#039;insegnamenti galileiani, nè quegli altri derivati dalla scuola <lb></lb>cartesiana son per verità punto migliori. </s>

<s>Il cap. </s>

<s>V delle Meteore è riserbato <lb></lb>dal Cartesio a trattar <emph type="italics"></emph>De nubibus,<emph.end type="italics"></emph.end> le quali son generate dai vapori coatti e <lb></lb>condensati. </s>

<s>Si sublimano, secondo il Filosofo, questi vapori, perchè si dila­<lb></lb>tano, e la <emph type="italics"></emph>materia sottile,<emph.end type="italics"></emph.end> che gl&#039;involge tutt&#039;intorno e gli preme ugual­<lb></lb>mente per ogni parte, è che gli riduce in quella figura di squisitissime sfe­<lb></lb>rette rotonde. </s>

<s>Sollevate che si sono così fatte sferule vaporose, a farle ricadere <lb></lb>in terra vi conferisce l&#039;aria, la quale, dilatandosi al di sotto, fa passare at­<lb></lb>traverso a sè la pioggia crivellata in minutissime gocciole; gocciole che al <lb></lb>contrario scendono assai più grosse, quando l&#039;aria preme solamente al di <lb></lb>sopra della nube. </s></p><p type="main">

<s>“ Nunc autem, ex iis quae diximus, facile intelligitur qua ratione nubes <lb></lb>solis aquae guttis constantes depluant, nempe vel pondere proprio, cum gut­<lb></lb>tae satis crassae sunt; vel cum aer inferior recessu vel superior incursu illas <lb></lb>ad descensum invitat, vel etiam quando plures ex his causis simul concur­<lb></lb>runt. </s>

<s>Atque inferiori aere se contrahente pluvia maxime minuta, et veluti <lb></lb>rorans generatur; imo aliquando adeo minuta est, ut saepissime delabentem <lb></lb>non pluviam sed nebulam potius dicamus; magna contra, seu grandibus <lb></lb>guttis colligitur, quoties nubes solo aere superiori pressa descendit; subli­<lb></lb>mes enim illius guttarum primo delapsae, alias in via inveniunt quibus <lb></lb>crassescunt ” (Francofurti ad M. 1692, pag. </s>

<s>164). </s></p><p type="main">

<s>Mentre però la maggior parte de&#039;Fisici seguitava la meteorologia peripa­<lb></lb>tetica galileiana delle esalazioni umide e secche, e altri, anche in Italia, si <lb></lb>lasciavano affascinare alle eloquenti fantasie del Cartesio, rimanevano, per <lb></lb>onor della scienza, alcuni pochi eletti ingegni fra noi che, a&#039;sistemi de&#039;nuovi <lb></lb>celeberrimi Maestri, preferivano le verità dimostrate nelle solitarie Specula­<lb></lb>zioni del Benedetti. </s>

<s>In conformità di queste così pensava il Baliani intorno <lb></lb>a ciò che dà origine e che produce la pioggia: “ L&#039;acqua è più densa, più <pb xlink:href="020/01/857.jpg" pagenum="300"></pb>grave, ma è liquida, cioè a dire ha le porzioni minime disgiunte fra loro, <lb></lb>onde il calore, per poco che sia, penetrandola agevolmente la muove, ed in <lb></lb>piccole vescichette una parte successivamente ne converte, che per farsi <lb></lb>perciò più rara di gran lunga che il rimanente, e perciò divenuta leggera, <lb></lb>s&#039;inalza e sale in aria ed è detta vapore, che non è altro che una massa di <lb></lb>bollicine acquee, le quali per esser formate di materia si liquida, agevol­<lb></lb>mente si spezzano, ondc picciol tempo durano, e di nuovo in acqua, ossia <lb></lb>in pioggia, si risolvono ” (Della Pestilenza, Savona 1647, pag. </s>

<s>37). </s></p><p type="main">

<s>L&#039;illustre Genovese, che della Fisica sperimentale e segnatamente della <lb></lb>Meteorologia è molto più benemerito del gran Galileo, conosceva bene che, <lb></lb>a voler trattar per scienza della pioggia, conveniva dimostrare due cose: <lb></lb>prima, come mai i vapori acquosi, più gravi in specie, si sollevino per l&#039;aria, <lb></lb>e poi in che modo questi stessi vapori si condensino, condensandosi ingros­<lb></lb>sino, e così ingrossati in gocciole, tornino, per la loro natural gravezza, a <lb></lb>cadere sotto forma di pioggia. </s>

<s>Ardue al Baliani parvero ambedue queste di­<lb></lb>mostrazioni, e non osando pur di provarsi intorno alla seconda, tanto lon­<lb></lb>tano dall&#039;immaginare che si potesse un giorno ridurre a soggetto di espe­<lb></lb>rienza, così lasciava scritto in che modo egli avrebbe pensato che si potessero <lb></lb>diminuire le difficoltà della prima: </s></p><p type="main">

<s>“ Ma di qual mezzo si vaglia la Natura e qual maniera ella usi, ac­<lb></lb>ciocchè la bolla si riduca a tanta leggerezza che possa salir da sè, non mi <lb></lb>riesce così facile a comprendere, cioè a dire com&#039;esser possa più grave l&#039;aria <lb></lb>semplice, che un composto d&#039;aria e d&#039;acqua, per quanto ella si assottigli, e <lb></lb>come possa racchiudersi nell&#039;acqua una sostanza tanto più dell&#039;aria leggera, <lb></lb>che la massa d&#039;ambedue, stando non pur nell&#039;acqua ma nell&#039;aria, in su se <lb></lb>ne vola. </s>

<s>Mi è caduto nel pensiero cosa, che a prima giunta parrà strana, <lb></lb>che tal sostanza sia fuoco o lume che dir vogliamo ” (ivi, pag. </s>

<s>27). </s></p><p type="main">

<s>Persuaso perciò il Montanari questa del Fisico genovese essere vera­<lb></lb>mente un&#039;idea strana, ricorse all&#039;aiuto delle agitazioni dell&#039;aria, per le quali, <lb></lb>come si vede rimaner sospeso il pulviscolo delle materie terree e degli <lb></lb>stessi metalli, così argomentava che potessero per ugual ragione rimanervi <lb></lb>in mezzo sospesi i vapori. </s>

<s>Più efficace poi, soggiungeva, dover riuscire in <lb></lb>produrre il misterioso effetto la causa da sè escogitata, aggiungendo ai tur­<lb></lb>binamenti intestini la continua irrequieta agitazione dei venti. </s></p><p type="main">

<s>“ Io mi avveggo di proporre a V. S. </s>

<s>Illustrissima (scriveva al Sampieri <lb></lb>in una Lettera aggiunta ai <emph type="italics"></emph>Pensieri fisico-matematici<emph.end type="italics"></emph.end>) un paradosso, poichè <lb></lb>tale ella lo crederà facilmente, se per l&#039;avanti ella s&#039;era sodisfatta del modo, <lb></lb>con che altri spiegano questo sollevarsi delle particelle dell&#039;acqua, come sa­<lb></lb>rebbe l&#039;acutissimo Cartesio, che le fa aggirare dai globuli di quel suo se­<lb></lb>condo elemento, oppure il Bagliani, che a guisa d&#039;ampollette le fa gonfiare <lb></lb>dall&#039;interno calore, o altri che congiungendole con particole di fuoco le fanno <lb></lb>ascender per l&#039;aria in quel modo, che piombo congiunto al sughero sormon­<lb></lb>terebbe per l&#039;acqua.... Io non contradico a si grandi uomini; ... dico per <lb></lb>tanto che, avendo veduto che l&#039;acqua, in fondo della quale sia alcuna sot-<pb xlink:href="020/01/858.jpg" pagenum="301"></pb>tilissima polvere,.... facilmente la intorbida,.... che le minime particelle <lb></lb>di quella polvere non hanno di bisogno nè di gonfiarsi, nè d&#039;attaccarsi ad <lb></lb>altre particole dell&#039;acqua più leggeri,.... e quindi essendomi caduto in <lb></lb>mente potere in qualche modo simile sollevarsi nell&#039;aria non solo le parti­<lb></lb>celle dell&#039;acqua, ma le terrestri ancora più sottili,.... il sollevarsi delle <lb></lb>quali fu anche osservato doversi al moto dell&#039;aria dal nobilissimo e dottis­<lb></lb>simo Bagliani, ne&#039;dottissimi opuscoli ultimamente da lui stampati;.... final­<lb></lb>mente mi posi a speculare alle ragioni perchè possino cioè tali minime par­<lb></lb>ticelle sollevarsi in aria, e quivi dipoi.... trattenersi senza piombare a basso, <lb></lb>tuttochè siano di essa aria più gravi in specie.... ” </s></p><p type="main">

<s>“ Molte considerazioni mi persuadono verisimile che eziandio, senz&#039;al­<lb></lb>tr&#039;opera del calore, fuor di quella che agita l&#039;acqua in diverse maniere, pos­<lb></lb>sano le particole de&#039;fluidi andarsi separando lentamente, giusta la viscosità <lb></lb>loro, dalle loro superficie, attaccandosi alle particelle dell&#039;aria che li preme, <lb></lb>e mediante l&#039;agitazione dell&#039;aria medesima, che vediamo infatti continua­<lb></lb>mente turbinarsi in mille modi in sè stessa, sollevarsi con essa lei, ìn quel <lb></lb>modo appunto che con l&#039;acqua si sollevano i torbidumi, qualora ella viene <lb></lb>agitata, e sollevati trattenervisi senza potere per la piccolezza loro scendere <lb></lb>a basso. </s>

<s>E quando pure mi negasse alcuno che fossero questi minimi del­<lb></lb>l&#039;acqua così piccoli, che non potessero superare la viscosità che ha in sè <lb></lb>l&#039;aria, io sebbene potrei mostrar loro quegli atomi terrei, che, come dissi, <lb></lb>si veggono ne&#039;raggi solari, e che pure sono maggiori e più pesanti degl&#039;in­<lb></lb>visibili minimi dell&#039;acqua; nulladimeno aggiungerei che, quando pur fosse <lb></lb>vero ciò che dicono, a me basterebbe che fossero tali che di poco la supe­<lb></lb>rassero, posciachè, aggiuntavi all&#039;incontro la continua agitazione dell&#039;aria <lb></lb>medesima, l&#039;intenderessimo ascendere non meno che si facciano le vesciche <lb></lb>dell&#039;acqua saponata..... ” </s></p><p type="main">

<s>“ Che se per sorte alla forza che ha l&#039;aria col suo peso ed al moto <lb></lb>naturale, che tale chiameremo quello con che ella, anco quando è rinchiusa, <lb></lb>va in sè stessa volutandosi, s&#039;aggiungono l&#039;esterne cause, che ponno con­<lb></lb>correre a questo sollevarsi de&#039;vapori; non ha dubbio che più facilmente e <lb></lb>in maggior copia s&#039;alzeranno, onde si vede che il vento ha così gran parte <lb></lb>nell&#039;essiccare le cose bagnate ” (Bologna 1667, pag. </s>

<s>67-83). </s></p><p type="main">

<s>Il Guglielmini, secondando gl&#039;insegnamenti del suo illustre Maestro, <lb></lb>soggiungeva alla ragion fisica addotta da lui l&#039;altra derivata dalla Geometria, <lb></lb>conforme alla quale attenuandosi le particelle vaporose in modo, che il loro <lb></lb>peso assoluto scemi con assai minor proporzione di quel che non scemi la <lb></lb>superficie, vengon per il contatto, così sproporzionatamente divenuto mag­<lb></lb>giore, a trovar maggiore la resistenza dell&#039;aria che debbon fendere, e così <lb></lb>con facilità vi rimangon sospese. </s>

<s>Condensandosi in gocciole, minore è, per <lb></lb>la ragion contraria alla sopra detta, la resistenza che quelle stesse gocciole <lb></lb>hanno da superare, e perciò cadono a terra più facilmente. </s>

<s>“ Unendosi in­<lb></lb>sieme più particelle d&#039;acqua viene il composto a crescere di peso assoluto <lb></lb>più di quello s&#039;accresca la di lui superficie, e conseguentemente viene a sce-<pb xlink:href="020/01/859.jpg" pagenum="302"></pb>marsi in proporzione la resistenza; quindi è che successivamente accresciuta <lb></lb>la potenza operante, e scemata maggiormente in proporzione la resistente, <lb></lb>è necessario che finalmente la prima superi la seconda, e perciò che l&#039;acqua <lb></lb>discenda per l&#039;aria. </s>

<s>Questi effetti della separazione ed unione delle particelle <lb></lb>dell&#039;acqua sono da noi cotidianamente osservati nell&#039;ascendere che fanno i <lb></lb>vapori e nel cadere delle piogge ” (Della Natura de&#039;fiumi, T. I, Milano 1821, <lb></lb>pag. </s>

<s>146). </s></p><p type="main">

<s>Fu questa, dopo Galileo, la ragione che principalmente s&#039;adduceva dal <lb></lb>Guglielmini e dagli altri, non solo dell&#039;intorbidamento delle acque de&#039;fiumi <lb></lb>e del loro chiarificarsi, ma delle soluzioni e delle precipitazioni delle sostanze <lb></lb>saline e metalliche ne&#039;mestrui liquidi specificamente più leggeri. </s>

<s>Venne però <lb></lb>presto l&#039;Hawksbee a ingerire un molesto sospetto in quella pace di fede, in <lb></lb>che tranquillamente riposava la Scienza. </s>

<s>Se il galleggiamento delle parti­<lb></lb>celle dell&#039;oro, nell&#039;acqua regia, discorreva il grande Fisico inglese, dipende <lb></lb>da quel grande accrescimento delle superficie ne&#039;piccoli corpi, a propor­<lb></lb>zione della loro mole “ avrebbe dovuto necessariamente apparire qualche <lb></lb>parte di questa grandissima differenza dal pesare quantità eguali di mate­<lb></lb>ria, e perciò egualmente gravi, ma di superficie molto diseguali, nell&#039;acqua <lb></lb>o in qualche altro liquido, e allora vedere colà quanto l&#039;una eccedesse l&#039;altra <lb></lb>di peso ” (Esper. </s>

<s>fisico-meccan., Traduz. </s>

<s>ital., Firenze 1716, pag. </s>

<s>148). </s></p><p type="main">

<s>Venuto alle esperienze trovò che quella differenza stimata da tutti gran­<lb></lb>dissima era invece così piccola, che non meritava d&#039;esser messa nemmeno <lb></lb>in conto, ond&#039;egli ebbe a concluderne altra dover esser la causa del gal­<lb></lb>leggiamento de&#039;corpi gravi ne&#039;mezzi più leggeri. </s>

<s>Pensò l&#039;Hawksbee che <lb></lb>potesse una tal causa risedere nell&#039;attrazione molecolare, saviamente ragio­<lb></lb>nando che la superficie cresciuta in maggior proporzione nella piccola mole, <lb></lb>ne rendesse più esteso il contatto colle particelle del mezzo ambiente, e così <lb></lb>per l&#039;aumentata intensità delle forze attrattive più difficile si rendesse la se­<lb></lb>parazione del corpicciolo dissoluto dal suo mezzo solvente. </s></p><p type="main">

<s>Terminava l&#039;Autore il racconto di questa sua Esperienza fisico-mecca­<lb></lb>nica con le seguenti notabilissime parole: “ Ma verrà forse il tempo che <lb></lb>questa maravigliosa legge dell&#039;attrazione, a misura che prevale nelle più <lb></lb>piccole porzioni della materia sarà più ampiamente e chiaramente intesa, e <lb></lb>qualche nuovo effetto di essa si scoprirà che ora non vien creduto proce­<lb></lb>dere da quella causa ” (ivi, pag. </s>

<s>151). Il vaticinio s&#039;avverò puntualmente <lb></lb>nel particolar soggetto di questa sloria, imperocchè trascuratasi l&#039;applica­<lb></lb>zione delle attrazioni molecolari a spiegar la prevalente leggerezza de&#039;corpi <lb></lb>gravi sospesi, si tornò indietro a vagheggiar le idee passate già per la mente <lb></lb>al Baliani. </s>

<s>Queste avevano avuto intanto un illustratore in Giuseppe Del <lb></lb>Papa, il quale seppe far apparir meno strana quella mistione del fuoco col­<lb></lb>l&#039;acqua delle vescicole vaporose, mettendo in gioco il glutine dell&#039;acqua <lb></lb>stessa, dal quale vien colta e tenuta sotto il suo duttile velo avvinta ia luce <lb></lb>ardente del sole. </s>

<s>“ Stariasi l&#039;acqua, egli dice, tutta perpetuamente ferma e <lb></lb>raccolta nelle più basse cavità della Terra, s&#039;egli non fosse che colta quivi <pb xlink:href="020/01/860.jpg" pagenum="303"></pb>e ferita dai fervidi raggi solari, ella col proprio glutine parte di essi in sè <lb></lb>ritenendo, e divenendo per tale mistione della luce più rarefatta e men pe­<lb></lb>sante dell&#039;aria, potesse in tal guisa nelle aeree regioni sormontare e tra­<lb></lb>scorrere ” (Dell&#039;Umido ecc., Firenze 1681, pag. </s>

<s>133). </s></p><p type="main">

<s>Se non che potevano queste del Del Papa parere stranezze nuove ag­<lb></lb>giunte a più antiche stranezze, quando quell&#039;elettricità, che s&#039;incominciò a <lb></lb>vedere in tutto e per tutto presente come la nuova vita e l&#039;anima del <lb></lb>Mondo, parve dispensar dal ricorrere in alto ad attingere la luce e il fuoco <lb></lb>dal Sole. </s></p><p type="main">

<s>Il De Saussure, dato mano al Microscopio, fece maravigliose osserva­<lb></lb>zioni intorno alla fisica costituzione de&#039;vapori vescicolari. </s>

<s>Notò fra le altre <lb></lb>cose che due tali vescicole non vengono mai a stringersi insieme in intimo <lb></lb>contatto, e che rimbalzano e rotolano sulla superficie di un&#039;acqua senza toc­<lb></lb>carla, e pronte anzi a volarsene via come v&#039;eran venute, scosse da un leg­<lb></lb>gerissimo soffio. </s>

<s>Sorpreso da una tal novità, il celebre Autore degli <emph type="italics"></emph>Essais <lb></lb>sur l&#039;Hygrometrie<emph.end type="italics"></emph.end> sospettò che il tutto dipendesse dall&#039;esser ciascuna di <lb></lb>quelle vescicole involte nell&#039;ammosfera di qualche aura sottilissima, da non <lb></lb>sapere a che altro meglio rassomigliarla che al vapore elettrico. </s>

<s>Ed ecco così <lb></lb>segnato il progresso che fecero le idee dal Baliani al Saussure: l&#039;elemento <lb></lb>della leggerezza, che s&#039;aggiunge all&#039;acqua per tenerla sollevata in vapori, è <lb></lb>pura elettricità terrestre, e non luce o foco di Sole. </s></p><p type="main">

<s>Divulgatesi queste idee nel 1783, quand&#039;era stata già scoperta e con­<lb></lb>fermata da tante esperienze l&#039;elettricità ammosferica, anche a ciel sereno, <lb></lb>non bisognava andar a cercar d&#039;onde avesse origine l&#039;elettricità nelle ammo­<lb></lb>sfere involgenti le vescicole vaporose sospese nel mezzo dell&#039;aria: potevasi <lb></lb>però domandare com&#039;andasse il vapore elettrico a distribuirsi intorno a cia­<lb></lb>scuna di esse vescicole, e come potesse rimanervi aderente sotto apparenze <lb></lb>così tanto trasformate dalle ordinarie. </s></p><p type="main">

<s>La risposta, che non avrebbe saputo darla il Saussure, fu suggerita <lb></lb>prontamente dal Volta, quand&#039;ebbe scoperta l&#039;elettricità latente espressa <lb></lb>come il calor de&#039;vapori, mentre si trasformano dallo stato elastico allo stato <lb></lb>vescicolare. </s>

<s>“ Or chi sa, dice egli, che la ridondanza del fluido elettrico, che <lb></lb>risulta dalla trasmutazione dei vapori elastici in vescicolari, non sia una <lb></lb>delle principali cagioni di cotal conformazione singolare? </s>

<s>E non potrebbe <lb></lb>questo fluido sovrabbondante concorrere ad accrescere la leggerezza specifica <lb></lb>delle vescichette, gonfiandole, estendendone la pellicola? </s>

<s>Non potrebbe il <lb></lb>medesimo costituire in gran parte, se non in tutto, quel fluido sottile, di <lb></lb>cui son piene tali vescichette, o quell&#039;ammosfera onde ciascuna va involta <lb></lb>come da un velo? (Opere, T. I, P. II, Firenze 1816, pag. </s>

<s>235). </s></p><p type="main">

<s>Così il Saussure e il Volta videro in que&#039;veli vescicolari, e quasi si sa­<lb></lb>rebbero provati di toccar colle mani le sfere elettriche, come Galileo in si­<lb></lb>miglianti vescicolette vedeva e avrebbe giurato di toccare gli atomi del fuoco, <lb></lb>i quali non erano poi altro che aria, come altro che aria non è quel velo <lb></lb>involgente le vescicole de&#039;vapori. </s>

<s>La forte aderenza di un tal velo è per <pb xlink:href="020/01/861.jpg" pagenum="304"></pb>effetto di attrazione molecolare, la quale è, secondo le speculazioni neuto­<lb></lb>niane, confermate dalle belle esperienze dell&#039;Hawksbee, tanto più forte, <lb></lb>quanto per la minima divisione a cui si riducono i corpi operano a minori <lb></lb>distanze. </s>

<s>Che del resto un tal velo sferico d&#039;aria circondante la vescicola, <lb></lb>come se facesse un corpo solo con lei, conferisca alla leggerezza, nessun <lb></lb>fisico e nessun geometra avrebbe ragione di dubitarne. </s></p><p type="main">

<s>Dell&#039;avere scambiata l&#039;aria coll&#039;elettricità non è che quel sagace Volta <lb></lb>non avesse sentito il lubrico, ad assicurarsi dal quale ebbe ricorso alle forze <lb></lb>molecolari, o <emph type="italics"></emph>forze mutue,<emph.end type="italics"></emph.end> com&#039;ei le chiama. </s>

<s>Queste come operano diver­<lb></lb>samente su tutti gli altri corpi ridotti in minime parti, ccsi operano diver­<lb></lb>samente sull&#039;elettricità ridotta a minime moli. </s>

<s>In sì fatto modo davasi a <lb></lb>intendere e si studiava di persuadere come l&#039;elettrico mobilissimo per sua <lb></lb>natura ed attivo, quasi avesse perduta la propria effigie, si vedesse lì stare <lb></lb>inerte attorno alle vescicole vaporose. </s></p><p type="main">

<s>Non avrebbe il Baliani creduto mai che, dopo tanto progredir della <lb></lb>scienza, quel concetto suo strano del lume del sole rimasto preso nelle ve­<lb></lb>scichette dell&#039;acqua si dovesse trasformare in un altro concetto non meno <lb></lb>strano, per opera di un Saussure e di un Volta. </s>

<s>Eppure questa, del pro­<lb></lb>blema che il Fisico genovese erasi proposto a risolvere, era la parte men <lb></lb>difficile. </s>

<s>Più difficile s&#039;appresentava e doveva naturalmente appresentarsi <lb></lb>l&#039;altra parte di quello stesso problema concernente il modo come i vapori <lb></lb>ascesi già in aria tornino in pioggia, perciocchè se là bastavano le specu­<lb></lb>lazioni, qui bisognavano l&#039;esperienze, le quali tanto ancora ai tempi del Ba­<lb></lb>liani eran lontane, quant&#039;era lontana l&#039;invenzione della Macchina pneu­<lb></lb>matica. </s></p><p type="main">

<s>E a Ottone di Guericke appunto occorse a dimostrar per la prima volta <lb></lb>come faccia il cielo a rannuvolarsi, a piovere, e a tornar poi nuovamente <lb></lb>sereno. </s>

<s>Prendeva un pallone di vetro munito di chiavetta, e dal quale aveva <lb></lb>estratto già l&#039;aria: un altro simile pallone, benchè un po&#039;più piccolo, era <lb></lb>pieno d&#039;aria o naturalmente umida o artificialmente inumidita, e congiun­<lb></lb>geva poi insieme i due palloni avvolgendo l&#039;un sopra l&#039;altro a vite. </s>

<s>Aperte <lb></lb>le due chiavi in modo che l&#039;aria dal pallone di sopra potesse irrompere vio­<lb></lb>lente nel pallone vuoto e posto al di sotto “ ex hac subitanea aeris in su­<lb></lb>periori vitro dilatione et descensu in inferius, aer residuus valde alteratur <lb></lb>et minuitur: multum autem aeris plus humiditatis continere potest quam <lb></lb>parum, ideoque relinquit inibi aer superfluam suam humiditatem, quae ocu­<lb></lb>lariter videri potest in guttulis minimis, quae pedetentim ad fundum de­<lb></lb>scendunt.... Ex quibus evidenter constat propter aeris contractionem vel <lb></lb>diminutionem, aquam quae est in aere se separare ab aere et in nubes con­<lb></lb>gregare. </s>

<s>Unde si epistomium omnino relaxatur et aer plene intromittitur, <lb></lb>illico nubes vel nebulae evanescunt, quia ab intrante aere absorbentur ” <lb></lb>(Experim. </s>

<s>nova magdeb., Amstelodami 1672, pag. </s>

<s>88, 89). </s></p><p type="main">

<s>Questa esperienza, nella quale si vedeva sotto un piccolo cielo artifi­<lb></lb>ciale l&#039;aria rannuvolarsi, piovere, e poi rifarsi serena, pareva che dovess&#039;es-<pb xlink:href="020/01/862.jpg" pagenum="305"></pb>sere ricevuta non con minore applauso di quel che fosse poi ricevuta l&#039;altra <lb></lb>del Franklin, che in un simile piccolo cielo artificiale rappresentava gli ef­<lb></lb>fetti del tuono e del baleno. </s>

<s>Eppure la bellissima e importantissima espe­<lb></lb>rienza guericchiana giacque negletta, e fu per questa negligenza che tanto <lb></lb>e così penosamente rimase incerta la Meteorologia barometrica, come si nar­<lb></lb>rerà appresso dop aver detto dell&#039;origine del vento. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Tutti quanti i Filosofi ripetevano da secoli e secoli i detti di Aristotile <lb></lb>intorno all&#039;origine de&#039;venti, quando, verso la fine del secolo XVI, un nostro <lb></lb>insigne italiano soggiungeva dopo di aver ridotti molti fatti fisici, che s&#039;at­<lb></lb>tribuivano all&#039;antiperistasi, alla ragione del denso e del raro, queste libere <lb></lb>e franche parole: “ Neque silentio involvendum est nec Aristotilem neque <lb></lb>alium ex suis fautoribus animadvertisse densum et rarum esse causam <lb></lb>ventorum ” (Joannis Bapt. </s>

<s>Benedicti, Speculationum liber., Venetiis 1599, <lb></lb>pag. </s>

<s>192). </s></p><p type="main">

<s>Come poi dal rarefarsi e dal condensarsi l&#039;aria, sotto le continue vi­<lb></lb>cende del caldo e del freddo, si produca quel moto nell&#039;aria che s&#039;appella <lb></lb>comunemente col nome di vento, così il Benedetti seguita a esporlo, dopo <lb></lb>aver pronunziate le sopra riferite parole: “ Rarum autem et densum me­<lb></lb>diante calore et frigore fit, et si a partibus in omogeneis licet argumentari <lb></lb>de toto deducat consequentiam qui velit, observans in calidis aestatis die­<lb></lb>bus, dum aliqua nubecula ad solem cooperiendum incedit, ibi statim agita­<lb></lb>tionem aeris sentiri: ea vero nubecula praetergressa cum fuerit, et in ea <lb></lb>parte aer ad pristinam raritatem causatam a calore solis redierit, quiescit. </s>

<s><lb></lb>Huiusmodi autem aeris agitatio a nulla certe exhalatione proficiscitur, sed a <lb></lb>motu solum locali, quem dam condensatur facit ” (ibi). </s></p><p type="main">

<s>Dopo un&#039;esperienza così semplice e un argomento così concludente, <lb></lb>pareva che dal primo e grande Maestro della Fisica sperimentale in Italia <lb></lb>fossero cacciate via per sempre le peripatetiche esalazioni, e che si fosse <lb></lb>stabilita la verace dottrina dell&#039;origine de&#039;venti. </s>

<s>Eppure è un fatto che reca <lb></lb>gran maraviglia, ma che ce lo mostrerà vero la storia, è un fatto che quella <lb></lb>dottrina era stata dimenticata da&#039;seguaci di Galileo, i quali o confessavano <lb></lb>la loro propria ignoranza in tal subietto, o tenevan dietro all&#039;errore un se­<lb></lb>colo dopo il Benedetti. </s></p><p type="main">

<s>Ebbe intorno a ciò non piccola colpa lo stesso Galileo, il quale, benchè <lb></lb>si lasciasse una volta uscir dalla bocca che “ dalle regioni scaldate, nel raf­<lb></lb>freddarsi, si eccitano i venti nelle circonvicine provincie ” (Alb. </s>

<s>III, 365) <lb></lb>mette nonostante la cosa in forse, e tanto poi si dilungò da questi savii in­<lb></lb>segnamenti del Benedetti, che si volse tutto a professar, co&#039;seguaci di Ari­<lb></lb>stotile, la falsa ipotesi delle esalazioni ventose, da buon peripatetico invo­<lb></lb>cando l&#039;antiperistasi, come presto vedremo. </s></p><pb xlink:href="020/01/863.jpg" pagenum="306"></pb><p type="main">

<s>S&#039;aggiunsero ai danni della Meteorologia le false dottrine cartesiane <lb></lb>accolte e professate con grande amore dai numerosissimi settatori di quella <lb></lb>scuola. </s>

<s>Illuso dall&#039;esempio dell&#039;Eolipila, addotto già da Vitruvio, pensava il <lb></lb>Cartesio che fosse il vento eccitato dal moto de&#039;vapori che si espandono con <lb></lb>tanta forza all&#039;intorno, essendo riscaldati. </s>

<s>“ Atque ita aer ex folle elisus vel <lb></lb>flabello impulsus ventus nominatur, licet venti latius diffusi terrasque et <lb></lb>maria perflantes nihil sint nisi vapores moti, qui dilatati ex loco arctiori in <lb></lb>quo erant, in alium ubi facilius expandantur, transeunt ” (Metereor, Cap. </s>

<s>IV, <lb></lb>Francof. </s>

<s>1692, pag. </s>

<s>141). </s></p><p type="main">

<s>Dall&#039;esperienza del vento freddo, che sogliono mandar fuori le mesco­<lb></lb>lanze frigorifere, fu similmente sedotto un altro caposcuola, ch&#039;ebbe in Fran­<lb></lb>cia e in Italia non forse minore autorità dello stesso Cartesio. </s>

<s>Il Gassendo <lb></lb>insegnava che le commozioni ventose dell&#039;ammosfera venivano suscitate dal­<lb></lb>l&#039;esalazioni de&#039;sali nitrosi terrestri sollevatisi in aria, e ivi mescolati co&#039;va­<lb></lb>pori dell&#039;acqua. </s>

<s>Così venivano da Galileo, dal Cartesio e dal Gassendo, so­<lb></lb>lenni maestri della scienza, dissipati e resi torbidi que&#039;sereni aliti di verità <lb></lb>usciti dalla bocca del Benedetti. </s></p><p type="main">

<s>Primo a rimetter la Meteorologia sopra il retto sentiero, ritornando al <lb></lb>principio del raro e del denso professato dal Fisico veneziano, fu Francesco <lb></lb>Bacone, in quel suo libro ch&#039;egli intitolò <emph type="italics"></emph>Historia naturalis et experimen­<lb></lb>talis de&#039;ventis.<emph.end type="italics"></emph.end> L&#039;esperienza del vento cagionato dall&#039;ardor de&#039;raggi del <lb></lb>sole, che vengono riparati per caso da qualche fitta nuvola interposta, la ri­<lb></lb>dusse Bacone a rappresentarsi a piacere sotto gli occhi di ognuno, imitando <lb></lb>coll&#039;arte gli effetti della Natura. </s>

<s>“ Experimentum fecimus, egli scrive, in <lb></lb>turri rotunda undique clausa, huius generis venti. </s>

<s>Nam foculum in medio <lb></lb>eius locavimus, cum prunis penitus ignitis ut minus esset fumi, et a latere <lb></lb>foculi in distantia nonnulla filum suspendimus, cum cruce ex plumis ut fa­<lb></lb>cile moveretur. </s>

<s>Itaque post parvam moram, aucto calore et dilatato aere, <lb></lb>agitabatur crux plumea cum filo suo, hinc inde motu vario, quin etiam facto <lb></lb>foramine in fenestra turris, exibat flatus calidus, neque ille continuus, sed <lb></lb>per vices et undulatus. </s>

<s>Etiam receptio aeris per frigus a dilatatione creat eius­<lb></lb>modi ventum sed debiliorem ob minores vires frigoris ” (Lugd. </s>

<s>Batav. </s>

<s>1648, <lb></lb>pag. </s>

<s>54). </s></p><p type="main">

<s>Questa stessa esperienza fu poi illustrata con più lucido concetto, e <lb></lb>con maggior finezza descritta dal nostro Borelli, benchè la principale inten­<lb></lb>zione fosse alquanto diversa. </s>

<s>“ Videmus enim maiores et ampliores flam­<lb></lb>mas in caminis accensas non vigere nec diutius perseverare, nisi adsit aditus <lb></lb>aeri de foris advenienti, per quem ingrediatur ventus perpetuus, qui inter <lb></lb>crura et foemora circumstantium excurrit versus flammam estque evidenter <lb></lb>sensibilis, nam, si cubiculi ostium claudatur extenso panno vel cortina, ut <lb></lb>fieri solet, haec inflatur versus ignem camini, ut velum navis, imo in cubi­<lb></lb>culis undique diligenter clausis, in quibus aer externus subingredi nequeat, <lb></lb>non poterit flamma sursum impelli ab aere quin cubiculum inane remaneat, <lb></lb>et tunc ignis camini nullo pacto accendi potest, nec in flammam verti, aut <pb xlink:href="020/01/864.jpg" pagenum="307"></pb>perdurare nisi ostiolum vel foramen aliquod in ipso camino aperiatur, et <lb></lb>tunc facile flamma accenditur et perseverat. </s>

<s>Ratio huius effectus pendet ne­<lb></lb>dum ab impulsu flammae sursum, sed etiam a rarefatione aeris prope ignem <lb></lb>existentis eumque ambientis per totam camini longitudinem, quia nempe <lb></lb>aer praedictus ab igne calefactus minus gravis specie redditur quam aer cu­<lb></lb>biculi et externus qui a camino distat. </s>

<s>Hoc autem necessario advenit in le­<lb></lb>gibus mechanicis et ex Archimedis demonstrationibus. </s>

<s>Necesse est enim ut <lb></lb>aer rarior et minus gravitans sursum expellatur exprimaturque a graviore <lb></lb>aere circumambiente. </s>

<s>Hinc fit ut, post ascensum illius aeris rarefacti per <lb></lb>caminum, diminuatur moles aeris ipsius cubiculi prope et circa caminum. </s>

<s><lb></lb>Non ergo mirum est novum aerem profluere ad replendum cubiculi spatium, <lb></lb>et haec est causa quare percipitur ventus ille et effluvium perpetuum dum <lb></lb>flamma camini viget ” (De motion. </s>

<s>natur., Regio Julio 1670, pag. </s>

<s>124, 25). </s></p><p type="main">

<s>Nessun altra esperienza poteva esser meglio di questa accomodata a <lb></lb>esplicare il concetto del Benedetti, e a dimostrar per la similitudine del <lb></lb>vento artificiale, che il vento naturale è veramente prodotto dall&#039;avvicen­<lb></lb>darsi del denso e del raro nell&#039;aria, per gli effetti del calore del sole. </s>

<s>Ma <lb></lb>al Borelli non sovvenne un così fatto concetto, e l&#039;intenzione per cui si <lb></lb>trattenne così a descrivere i moti dell&#039;aria nel cammino ardente, si fu quella <lb></lb>di provar contro i Peripatetici che la fiamma non sale alto per suo natu­<lb></lb>rale istinto, ma per circumpulsione del mezzo ambiente, come qualunque <lb></lb>altro corpo leggero. </s></p><p type="main">

<s>Bacone stesso non proseguì quel concetto, come pareva dal suo prin­<lb></lb>cipio, perchè il mal vezzo ch&#039;egli ebbe di cincischiare la scienza, riducen­<lb></lb>dola a categorie, lo portò a distinguere varie specie di venti, a ciascun <lb></lb>de&#039;quali assegnò le sue cause particolari. </s>

<s>Fra queste cause particolari, oltre <lb></lb>quella del raro e del denso, eravi eziandio l&#039;altra del vapor dilatato ed <lb></lb>espanso, conforme all&#039;ipotesi del Cartesio, e anco questa causa riduceva il <lb></lb>Verulamio a soggetto di esperienza, dimostrando che il molinello di piume <lb></lb>era fatto volgere attorno anche dal vapore esalato dall&#039;acqua di una pen­<lb></lb>tola che bolla. </s>

<s>“ Itaque excitationis motus in ventis, di qui ne concludeva, <lb></lb>causa est praecipua superoneratio aeris ex nova accessione aeris facti ex va­<lb></lb>poribus ” (Historie natur. </s>

<s>de ventis cit., pag. </s>

<s>65). </s></p><p type="main">

<s>Così, per non aver saputo Bacone ridur l&#039;origine de&#039;venti a una causa <lb></lb>unica e generale, rese inefficaci anche quelle vie sperimentali, ch&#039;egli <lb></lb>avea prese dietro la scorta del Benedetti, e insomma tutti quanti filosofa­<lb></lb>rono dopo di lui, infin verso il termine del secolo XVII, o seguitarono la <lb></lb>ipotesi del Cartesio o quella del Gassendo. </s>

<s>L&#039;Huyghens, che può servire per <lb></lb>esempio di tutti gli altri, così scriveva nel I libro del Cosmoteoro: “ Erunt <lb></lb>ergo et imbres et venti, quia attractum a sole humorem recidere in ter­<lb></lb>ram necesse est, et calore soluti vapores ventorum causa sunt ” (Lugd. </s>

<s><lb></lb>Batav. </s>

<s>1724, pag. </s>

<s>681). </s></p><p type="main">

<s>In Italia, dove quel <gap></gap>roso Borelli aveva saputo sostituire all&#039;autorità <lb></lb>del Cartesio l&#039;autorità s<gap></gap>a propria, si vagheggiava da molti quella proposi-<pb xlink:href="020/01/865.jpg" pagenum="308"></pb>zione L, che noi di sopra citammo dal Trattato <emph type="italics"></emph>De motionibus naturali­<lb></lb>bus,<emph.end type="italics"></emph.end> e benchè non si osasse di estenderla alla causa generale de&#039;venti, si <lb></lb>confessava nulladimeno che se la Natura non imita l&#039;arte a quel modo, l&#039;ori­<lb></lb>gine de&#039;venti rimane ancora riposta ne&#039;tesori della Divina Sapienza. </s>

<s>“ Io <lb></lb>non so, scriveva in una sua Lettera il Redi, come nel mondo grande si fac­<lb></lb>cia il vento, e mi accorgo che le cagioni sue stanno nascoste ne&#039;segreti te­<lb></lb>sori della Divina Sapienza, ma, se io fo alcuni piccoli modelli del vento ar­<lb></lb>tificiale, veggo che la cagione di quel vento è sempre il fuoco ” (Opere, <lb></lb>T. V, Napoli 1741, pag. </s>

<s>50). </s></p><p type="main">

<s>Quella renitenza, che si provava in applicar lo sperimento borelliano <lb></lb>de&#039;venti artificiali ai venti naturali, veniva ingerita dall&#039;esempio autorevole <lb></lb>dello stesso Borelli, il quale inclinatissimo alla Filosofia atomica e dando <lb></lb>grande efficacia ai sali nitrosi sollevati e sospesi per l&#039;aria, insinuava taci­<lb></lb>tamente ne&#039;Nostri l&#039;ipotesi del Gassendo a preferenza di quella del Be­<lb></lb>nedetti, benchè così ben confermata dalla somiglianza di quel vento, che <lb></lb>artificialmente si produce dal rarefarsi dell&#039;aria intorno alla fiamma dei <lb></lb>cammini. </s></p><p type="main">

<s>Giuseppe Del Papa, valente fisico della scuola del Redi, lasciò scritto <lb></lb>in proposito le parole seguenti: “ Nè voglio tacere che per avventura tal­<lb></lb>volta, ne&#039;tempi d&#039;inverno, non poca freddezza all&#039;aria vien conferita da una <lb></lb>gran quantità di sali, ond&#039;ella è ripiena, i quali, per essere della stessa na­<lb></lb>tura e forse anche della medesima sorte del salnitro e del sale armoniaco, <lb></lb>non avrei gran ripugnanza a dire poter eglino lo stesso effetto nell&#039;aria pro­<lb></lb>durre circa il raffreddarla, che essi producono nell&#039;acqua.... e quindi na­<lb></lb>sce che alcune sorti di venti, ed in particolare la Tramontana e general­<lb></lb>mente tutti quelli, i quali dalla dissoluzione delle nevi e delle grandini hanno <lb></lb>origine, tanto sensibilmente raffreddino.... E chi sa che queste sorti di <lb></lb>venti, i quali siccome ho detto hanno origine dalla grandine e dalle nevi, <lb></lb>non siano il solo sprigionamento de&#039;sali sopraddetti, i quali, all&#039;aria giun­<lb></lb>gendo, l&#039;urtino e la sospingano al moto? </s>

<s>Ma oh Dio che inavvertentemente <lb></lb>io entrerei in un pelago immenso, senza speranza di poter così tosto ricon­<lb></lb>durmi al porto, quando della generazione de&#039;venti a favellare io mi ponessi, <lb></lb>la quale chiaramente conosco ed ingenuamente confesso che è da altri omeri <lb></lb>che da&#039;miei “ (Del freddo e del caldo, Firenze 1674, pag. </s>

<s>225, 26). </s></p><p type="main">

<s>Nè la difficoltà di sciogliere il problema si fece sentir minore a un altro <lb></lb>de&#039;più valorosi fisici, che avesse l&#039;Italia, il quale, come fu franco e risoluto <lb></lb>in repudiare l&#039;ipotesi del Cartesio, parve non avversare al gioco di quelle <lb></lb>fermentazioni salino nitrose descritto dal Del Papa, e introdotto nella pre­<lb></lb>sente questione meteorologica dalla fantasia del Gassendo. </s>

<s>“ Il Cartesio ed <lb></lb>i suoi seguaci, scrive il Montanari nella sua <emph type="italics"></emph>Astrologia convinta di falso,<emph.end type="italics"></emph.end><lb></lb>vengono alquanto più alle strette, mentre, supposto quel loro secondo ele­<lb></lb>mento sottilissimo, che di continuo con velocissima agitazione si muove, as­<lb></lb>seriscono che il moto di questo vada staccando e dall&#039;acqua e dalla Terra <lb></lb>e da altri corpi sottilissime particole, le quali agitate in giro da esso ele-<pb xlink:href="020/01/866.jpg" pagenum="309"></pb>mento, occupino perciò spazio maggiore, nel modo che una bandiera, che <lb></lb>prima ripiegata poco luogo teneva, se da braccio di destro e pratico alfiere <lb></lb>vien maneggiata in giro, si fa intorno ben larga piazza, onde in tal forma <lb></lb>spiegano poscia il vento che dalle palle di Eolo, riferite e spiegate anche <lb></lb>copiosamente da Vitruvio, e da&#039;pomi al fuoco scaldati, ed altri simili corpi, <lb></lb>con sì grand&#039;empito, e in tanta copia da poca umidità scaturisce, mercecchè <lb></lb>quelle particelle d&#039;umido, che per la veemenza del fuoco si staccano dalle <lb></lb>altre, e sono in giro portate, occupano spazio di gran lunga maggiore che <lb></lb>prima non facevano, onde a furia prorompono da quel foro, da cui vien <lb></lb>loro permesso d&#039;uscire, ed in questo modo spiegano eziandio i venti, che <lb></lb>nell&#039;aria, dal moto e calore del sole, son generati, mentre quelle particelle <lb></lb>de&#039;vapori così da quell&#039;elemento agitate, occupando spazio maggiore di <lb></lb>prima, spingono l&#039;aria all&#039;intorno per ogni verso e noi il moto di questo <lb></lb>vento chiamiamo. </s>

<s>” </s></p><p type="main">

<s>“ Ma oltre tante difficoltà, ch&#039;io sento nell&#039;ammettere tutta intiera l&#039;ipo­<lb></lb>tesi cartesiana,.... io non trovo nemmen contento l&#039;intelletto mio in questa <lb></lb>particolare dottrina, mentre quell&#039;azione del secondo suo elemento suppone <lb></lb>quel moto stesso ch&#039;egli chiama calore: eppure dalla parte di Tramontana <lb></lb>spirano anche l&#039;inverno e talora per lungo tempo venti freddissimi.... Al­<lb></lb>l&#039;incontro il Gassendo ed altri con lui hanno riferite le cause de&#039;venti alla <lb></lb>varia mistione de&#039;sali o nitrosi o armoniaci o simili, che con altre esalazioni <lb></lb>dalla terra si levano, e mescolati con i vapori acquei eccitano in tutto quel <lb></lb>misto d&#039;aria d&#039;esalazioni, vapori e sali una mozione, che altri fermentazione <lb></lb>direbbero, alla qual serve necessaria rarefazione, e dalla rarefazione il moto ” <lb></lb>(Venezia 1685, pag. </s>

<s>18, 19). </s></p><p type="main">

<s>La scoperta della verità si riman tante volte lontani dal conseguirla, <lb></lb>perchè si presuppone ch&#039;ella debba esser difficile e faticosa, e non si crede <lb></lb>a colui che dice d&#039;esservi giunto per una via speditissima e piana. </s>

<s>Un sin­<lb></lb>golare esempio di ciò lo abbiamo nel soggetto di questa storia, dalla quale <lb></lb>apparisce che la ragion de&#039;venti data dal Benedetti non fu approvata, per­<lb></lb>chè parve troppo semplice, e perchè dall&#039;altra parte non si vedeva come <lb></lb>riducesse la varietà de&#039;fatti a una causa generale. </s>

<s>Ma mentre in Italia e fuori, <lb></lb>in fin presso a terminare il secolo XVII, s&#039;erano i fisici lasciati illudere da <lb></lb>simili pregiudizii, cinquanta o sessant&#039;anni prima, il Torricelli risolveva il <lb></lb>problema generale de&#039;venti, mirabilmente esplicando quel semplicissimo con­<lb></lb>cetto del Benedetti. </s>

<s>La Lezione accademica, in cui s&#039;annunziava e si dimo­<lb></lb>strava quel vero, dietro al quale i Fisici s&#039;erano così lungamente affaticati <lb></lb>invano, non vide la luce prima del 1715, ma non fa per questo che non <lb></lb>debbasi al Nostro il merito d&#039;avere alle fantasie cartesiane e gassendistiche <lb></lb>sostituite le fisiche ragioni, tanti anni prima dell&#039;Halley o di chi altri, a cui <lb></lb>s&#039;attribuisce l&#039;aver, nelle condensazioni e nelle rarefazioni dell&#039;aria, ricono­<lb></lb>sciuta la causa generale de&#039;venti. </s></p><p type="main">

<s>“ Non sarebb&#039;egli, dice il Torricelli a suoi uditori, manifesto segno <lb></lb>d&#039;avere incontrato la vera cagione dell&#039;origine dei venti, se col medesimo <pb xlink:href="020/01/867.jpg" pagenum="310"></pb>principio la causa e la necessità di tutti ugualmente si dimostrasse? </s>

<s>Questo <lb></lb>principio altro non è che quel notissimo e volgarissimo della condensazione <lb></lb>e rarefazione dell&#039;aria. </s>

<s>Con questo, preso opportunamente, e non a rovescio, <lb></lb>come da alcuno è stato fatto, procureremo di sodisfare alla produzione di <lb></lb>qualsivoglia sorta di vento. </s>

<s>” </s></p><p type="main">

<s>“ Se un grandissimo tempio fosse pieno tutto d&#039;acqua fino alla sua <lb></lb>più alta sommità, che farebbe? </s>

<s>la risposta è pronta. </s>

<s>Se le porte fossero <lb></lb>aperte l&#039;acqua per esse se n&#039;uscirebbe con grandissimo impeto, e per le <lb></lb>finestre più sublimi succederebbe nel tempio altrettant&#039;aria per l&#039;appunto, <lb></lb>quanta acqua per le porte se ne partisse, e se il tempio avesse un&#039;occulta <lb></lb>virtù di convertire subito in acqua quell&#039;aria succeduta, il profluvio delle <lb></lb>porte sarebbe continuo e non finirebbe mai, fintantochè durasse la suppo­<lb></lb>sta metamorfosi dell&#039;aria in acqua. </s>

<s>” </s></p><p type="main">

<s>“ Quello che abbiamo esemplificato in due elementi diversi si consi­<lb></lb>deri ora in un elemento solo, non tramutato di spezie ma alterato nelle <lb></lb>qualità. </s>

<s>L&#039;augustissimo tempio di Santa Maria del Fiore, qualche volta, ma <lb></lb>molto più spesso la maggior basilica di Roma hanno questa proprietà di <lb></lb>esalare, ne&#039;giorni più caldi della state, un vento assai fresco fuor delle pro­<lb></lb>prie porte, in tempo per l&#039;appunto, quando l&#039;aria si trova tranquillissima <lb></lb>e senza vento alcuno. </s>

<s>La ragione è questa: perchè l&#039;aria, dentro la vasta <lb></lb>fabbrica racchiusa, qualunque sia la ragione, si trova più fresca dell&#039;esterna <lb></lb>infiammata da tanti raggi e reflessi del sole: però, se più fresca, è anco più <lb></lb>densa; adunque sarà anco più grave. </s>

<s>E se questo è vero, dovrà dalle porte <lb></lb>uscir quel profluvio d&#039;aria, che nell&#039;acqua abbiamo esemplificato. </s>

<s>Nel tem­<lb></lb>pio di Roma il fresco sull&#039;ore meridiane di questi tempi non solo diletta, <lb></lb>ma anche offende: però il vento sulle porte di esso è tanto impetuoso che <lb></lb>apporta maraviglia. </s>

<s>” </s></p><p type="main">

<s>“ Applichiamo ora la contemplazione e passiamo dalle cavità riserrate <lb></lb>all&#039;ampiezza aperta de&#039;campi spaziosissimi dell&#039;aria. </s>

<s>Io domando: se la To­<lb></lb>scana tutta avesse sopra di sè in cambio d&#039;aria una mole egualmente alta <lb></lb>d&#039;acqua, che seguirebbe? </s>

<s>Si risponde che questa mole non potrebbe reg­<lb></lb>gersi, ma con profluvio rapidissimo si spargerebbe, dilatandosi in giro per <lb></lb>tutte le campagne degli stati circonvicini, spianando col corso impetuoso non <lb></lb>solamente le piante e gli edifizi, ma forse gli scogli e le muraglie stesse, e <lb></lb>per di sopra, per riempir la cavità che lasciasse l&#039;acqua, succederebbe al­<lb></lb>trettant&#039;aria. </s>

<s>Ecco dunque la generazione del vento per via di condensa­<lb></lb>zione. </s>

<s>” </s></p><p type="main">

<s>“ Suppongasi tutto l&#039;emisferio boreale quieto ed in istato di calma <lb></lb>tranquilla, senza un soffio di vento, senza un alito d&#039;aura. </s>

<s>Venga poi una <lb></lb>pioggia repentina o qualsivoglia altro accidente, il quale, senza alterar punto <lb></lb>il rimanente dell&#039;emisfero, accresca più del dovere il freddo solamente alla <lb></lb>Germania. </s>

<s>Certo è che subito l&#039;aria raffreddata di quel vasto regno si con­<lb></lb>denserà. </s>

<s>Condensandosi è necessario che nell&#039;alta regione dell&#039;aria si faccia <lb></lb>sopra la Germania una cavità cagionata dalla predetta condensazione: l&#039;aria <pb xlink:href="020/01/868.jpg" pagenum="311"></pb>di sopra i regni circonvicini, come fluida e lubrica, scorre a riempier quella <lb></lb>cavità improvvisamente nata, onde, nelle parti sublimi dell&#039;aria, il corso del <lb></lb>vento sarà verso la parte raffreddata, ma nell&#039;infima regione, cioè nell&#039;aria <lb></lb>conterminante colla terra, il corso andrà al contrario: avvegnachè la Ger­<lb></lb>mania ritrovandosi coperta d&#039;aria condensata e anco accresciuta, e però più <lb></lb>grave della circonvicina, manderà per tutti i versi un profluvio di vento, <lb></lb>nel medesimo modo per appunto come abbiamo esemplificato nella Toscana, <lb></lb>quando fosse tutta in cambio d&#039;aria ricoperta d&#039;acqua. </s>

<s>” </s></p><p type="main">

<s>“ In questo modo il vento sarebbe una circolazione, la quale non iscor­<lb></lb>rerebbe sopra più che ad una parte terminata della terra, e tanto durerebbe <lb></lb>l&#039;effetto della circolazione predetta, quanto durasse la causa, cioè quel freddo <lb></lb>d&#039;una provincia, maggior che non dovrebb&#039;essere in paragone di quello <lb></lb>de&#039;luoghi circonvicini. </s>

<s>Circolazione la chiamo, poichè nella parte superiore <lb></lb>tutto il moto dell&#039;aria concorre verso il centro della provincia più del do­<lb></lb>vere raffreddata. </s>

<s>Quivi poi sentendo quel medesimo freddo accidentale, si <lb></lb>condensa, si aggrava e discende a terra, ove non reggendosi scorre da tutte <lb></lb>le parti e cagiona sulla superficie del terreno un vento contrario a quello <lb></lb>delle regioni sublimi ” (Lez. </s>

<s>accad., Milano 1823, pag. </s>

<s>158-61). </s></p><p type="main">

<s>Dopo tante strane ipotesi immaginate, quando in sui principii del se­<lb></lb>colo XVIII si riconobbe la vera causa, che dà origine ai venti, i Fisici non <lb></lb>seppero dir nulla di meglio di quel che avesse così tanti anni prima inse­<lb></lb>gnato il Torricelli, sul fondamento di quel principio notissimo e volgatissimo <lb></lb>della condensazione e della rarefazione dell&#039;aria. </s>

<s>Ma, infin da quando invalse <lb></lb>tra&#039;Filosofi l&#039;opinione che la Terra si rivolgesse intorno al suo proprio asse, <lb></lb>occorse alle loro menti il pensiero che dovesse quel così rapido rivolgimento <lb></lb>cooperare a commover l&#039;aria, ond&#039;è che, mentre si fantasticava così strane <lb></lb>cose intorno all&#039;origine dei venti ordinarii, si riconobbe almeno in parte la <lb></lb>vera causa di quelli, che spirano sotto i tropici in direzioni costanti. </s></p><p type="main">

<s>Il di 17 Dicembre 1630 il Cavalieri scriveva una lettera a Galileo, nella <lb></lb>quale gli significava certi suoi concetti di non lieve importanza in questa <lb></lb>storia. </s>

<s>“ Desidererei sapere, gli dice, se ha mai pensato alla generazione dei <lb></lb>venti, e se in qualche modo, nell&#039;ipotesi copernicana, vi potessero aver che <lb></lb>fare i moti, che egli attribuisce alla Terra, cioè che nel rivolgersi con quella <lb></lb>velocità che le viene ascritta, mentre qualche materia più densa dell&#039;etere, <lb></lb>che riempie questi immensi spazii, si ritrovasse attraversare l&#039;orbe annuo <lb></lb>con altro moto, oppure in quello stesse quiescente; cioè dico che soprag­<lb></lb>giungendo la Terra col suo orbe vaporoso circonfuso sino a quella altezza, <lb></lb>che si stima costituita in somma velocità, che in caso d&#039;urtare in quella <lb></lb>materia, per dir così, cometaria, si facesse un gagliardissimo contrasto, per <lb></lb>non ubbidire ella così presto al moto della Terra, e questo fosse causa di <lb></lb>sentir vento, quale poi, dalla Terra domato, non più contumace camminasse <lb></lb>del pari con l&#039;orbe vaporoso, e questo fosse poi il passare del vento; sicchè <lb></lb>si potesse formare questo paradosso: che il vento è una materia talvolta <lb></lb>quiescente, e che quando si muove non è più vento. </s>

<s>So che si possono fare <pb xlink:href="020/01/869.jpg" pagenum="312"></pb>molte instanze, e tra le altre questa principalissima dell&#039;esser loro così tu­<lb></lb>multuari e sregolati, che nell&#039;istesso tempo spirano da parti contrarie: ma <lb></lb>credo che dall&#039;implicamento de&#039;moti di essa Terra, e de&#039;moti, che possono <lb></lb>avere tali materie, come vaganti per l&#039;etere, si potrà forse scusare il tutto ” <lb></lb>(MSS. Galileo, P. VI, T. XI, c. </s>

<s>152). </s></p><p type="main">

<s>Al desiderio del Cavalieri, anche senza saper la risposta fatta a questa <lb></lb>sua lettera, possiamo sodisfar noi, dicendo che Galileo doveva aver già pen­<lb></lb>sato a quel tempo alle relazioni che passano tra certi particolari moti ven­<lb></lb>tosi dell&#039;aria, e i moti della Terra. </s>

<s>Quando infatti ricevè quella lettera da <lb></lb>Bologna i Dialoghi manoscritti de&#039;Due Massimi Sistemi erano pronti già per <lb></lb>la stampa, e nel IV di que&#039;Dialoghi, com&#039;ora vi si legge, così si leggeva: <lb></lb>“ Dicevamo pur ora, e con qualche aggiunta replico, che l&#039;aria, come corpo <lb></lb>tenue e fluido e non saldamente congiunto alla Terra, pareva che non avesse <lb></lb>necessità d&#039;ubbidire al suo moto, se non in quanto l&#039;asprezza della super­<lb></lb>ficie terrestre ne rapisce e seco porta una parte a sè contigua, che di non <lb></lb>molto intervallo sopravanza le maggiori altezze delle montagne, la qual por­<lb></lb>zione d&#039;aria tanto meno dovrà essere renitente alla conversion terrestre, <lb></lb>quanto che ella è ripiena di vapori, fumi ed esalazioni, materie tutte par­<lb></lb>tecipanti delle qualità terrene, e per conseguenza atte nate per loro natura <lb></lb>ai medesimi movimenti. </s>

<s>Ma dove mancassero le cause del moto, cioè, dove <lb></lb>la superficie del globo avesse grandi spazii piani e meno vi fosse della mì­<lb></lb>stione dei vapori terreni, quivi cesserebbe in parte la causa, per la quale <lb></lb>l&#039;aria ambiente dovesse totalmente obbedire al rapimento della conversion <lb></lb>terrestre; sicchè in tali luoghi, mentre che la Terra si volge verso oriente, <lb></lb>si dovrebbe sentir continuamente un vento, che ci ferisse spirando da le­<lb></lb>vante verso ponente, e tale spiramento dovrebbe farsi più sensibile dove la <lb></lb>vertigine del globo fosse più veloce, il che sarebbe nei luoghi più remoti <lb></lb>dai poli e vicini al cerchio massimo della diurna conversione. </s>

<s>Ma già <emph type="italics"></emph>de <lb></lb>facto<emph.end type="italics"></emph.end> l&#039;esperienza applaude molto a questo filosofico discorso, poichè, negli <lb></lb>ampii mari e nelle lor parti lontane da terra e sottoposte alla zona torrida, <lb></lb>cioè comprese dai tropici, dove ancora l&#039;evaporazioni terrestri mancano, si <lb></lb>sente una perpetua aura muovere da oriente con tenor tanto costante, che <lb></lb>le navi, mercè di quella, prosperamente se ne vanno all&#039;Indie occidentali ” <lb></lb>(Alb. </s>

<s>I, 475, 76). </s></p><p type="main">

<s>Questo filosofico discorso è tessuto dentro all&#039;altro filosofico discorso <lb></lb>del flusso marino, in ambedue i quali non è la Filosofia per verità così <lb></lb>schietta e sincera, come presumeva di darcela Galileo. </s>

<s>All&#039;aria, non si sa <lb></lb>perchè, ei non concede le qualità terrene e la mantien disgiunta, indipen­<lb></lb>dente e immobile intorno alla Terra contro l&#039;opinione di tutti i Coper­<lb></lb>nicani, fra&#039;quali udimmo ora che è poco il Cavalieri. </s>

<s>E il Gilberto prima di <lb></lb>lui aveva scritto: “ aer omnis, terrae et aquarum spiramenta, nubes et pen­<lb></lb>dentia meteora simul cum globo circulariter concitantur ” (De Magnete, <lb></lb>Londini 1600, pag. </s>

<s>219). E dall&#039;altra parte non potevano approvar l&#039;opi­<lb></lb>nione di Galileo se non che i Peripatetici, i quali non tenevan conto del <pb xlink:href="020/01/870.jpg" pagenum="313"></pb>peso e ammettevan nell&#039;aria una leggerezza innata. </s>

<s>Comunque sia, bevve <lb></lb>quell&#039;opinione Galileo infino dai primi anni della sua vita scientifica, e la <lb></lb>mantenne lungamente salda in mezzo alle più aperte contradizioni. </s>

<s>Il passo <lb></lb>infatti che noi trascrivemmo di sopra dal IV Dialogo de&#039;Massimi Sistemi, è <lb></lb>in sentenza conforme a quello dei <emph type="italics"></emph>Sermones de&#039;motu gravium,<emph.end type="italics"></emph.end> a proposito <lb></lb>della palla di marmo girevole su&#039;suoi cardini, alla quale, dato il primo im­<lb></lb>pulso, “ tunc certo sphaera per longum temporis spatium girabit, et tamen <lb></lb>nec aer a motore fuerit commotus ” (Alb. </s>

<s>XI, 16). </s></p><p type="main">

<s>Ma pure quella falsa opinione dell&#039;immobilità dell&#039;aria intorno alla Terra <lb></lb>ebbe origine da questa meccanica esperienza, nella quale era necessario am­<lb></lb>mettere l&#039;immobilità dell&#039;aria stessa intorno alla palla marmorea, perchè <lb></lb>fosse l&#039;argomento contro i Peripatetici concludente. </s>

<s>E tutto ebbe origine in <lb></lb>Galileo dal desiderio di trasformar l&#039;esperienza dello Scaligero per farla sua <lb></lb>propria. </s>

<s>Lo Scaligero infatti concludeva, contro gli aristotelici, il principio <lb></lb>intrinseco dell&#039;inerzia della materia, e ne escludeva l&#039;intervento esterno del­<lb></lb>l&#039;aria, dimostrando che la ruzzola segata nel pezzo dell&#039;assicella di legno se­<lb></lb>guitava a girar sopra i suoi perni, ricevuto il primo impulso, e che non si <lb></lb>poteva ciò attribuire a quella minima quantità d&#039;aria rimasta in un solco <lb></lb>così sottile, quant&#039;esser può sottile la lama di una sega. </s>

<s>Galileo, che aveva <lb></lb>trasformata l&#039;esperienza nella palla di marmo, girevole in mezzo all&#039;aria <lb></lb>libera, non poteva concluder l&#039;argomento dello Scaligero, com&#039;era la sua <lb></lb>intenzione, senz&#039;ammetter che l&#039;aria ambiente, rivolgendosi la palla attorno, <lb></lb>vi rimanesse immota. </s></p><p type="main">

<s>Gratuita ipotesi in ogni modo era questa, e dubitando delle ragioni, che <lb></lb>persuadevano del contrario i copernicani, come per esempio il Gilberto e il <lb></lb>Cavalieri, giovava d&#039;invocare in proposito l&#039;esperienza. </s>

<s>Ma il vento che si <lb></lb>rende sensibile ed è menato da un solido ridotto sul torno, Galileo lo at­<lb></lb>tribuiva <emph type="italics"></emph>agli urti della sua scabrosità e porosità che si fanno nel mezzo <lb></lb>ambiente<emph.end type="italics"></emph.end> (Alb. </s>

<s>II, 320), essendo impossibile il togliere affatto simili scabro­<lb></lb>sità, per rotondar quel solido quanto più perfettamente si possa. </s></p><p type="main">

<s>Nelle controversie col Sarsi, che ammetteva esser l&#039;ammosfera menata <lb></lb>in volta dal concavo lunare intorno alla Terra immota, Galileo richiamava <lb></lb>il suo avversario all&#039;esperienza dell&#039;aria ne&#039;vasi giranti, dentro ai quali so­<lb></lb>steneva l&#039;immobilità dell&#039;aria rivelata dal rimanervi quieta la fiammella di <lb></lb>una candela. </s>

<s>“ Pigli due candelette accese, ed una ne attacchi dentro al­<lb></lb>l&#039;istesso vaso, un dito o due lontana dalla superficie, e l&#039;altra ritenga in <lb></lb>mano, pur dentro al vaso, in simil lontananza dalla medesima superficie. </s>

<s><lb></lb>Faccia poi con velocità girare il vaso, che se in alcun tempo l&#039;aria andrà <lb></lb>parimente con quello in volta, senza alcun dubbio, movendosi il vaso, l&#039;aria <lb></lb>contenuta e la candeletta attaccata, tutto colla medesima velocità, la fiam­<lb></lb>mella di essa candela non si piegherà punto, ma resterà come se il tutto <lb></lb>fosse fermo.... ma l&#039;altra candeletta ferma darà segno della circolazion del­<lb></lb>l&#039;aria, che ferendo in lei la farà piegare. </s>

<s>Ma se l&#039;evento sarà al contrario, <lb></lb>cioè se l&#039;aria non seguiterà il moto del vaso, la candela ferma manterrà la <pb xlink:href="020/01/871.jpg" pagenum="314"></pb>sua fiammella diritta e quieta, e l&#039;altra portata dall&#039;impeto del vaso, ur­<lb></lb>tando nell&#039;aria quieta, si piegherà. </s>

<s>Ora nelle esperienze vedute da me è ac­<lb></lb>caduto sempre che la fiammella ferma è restata accesa e diritta, ma l&#039;altra <lb></lb>attaccata al vaso si è sempre grandissimamente piegata e molte volte spenta ” <lb></lb>(Alb. </s>

<s>IV, 307). </s></p><p type="main">

<s>Il Venturi (Memorie di Gal., P. II, pag. </s>

<s>50) mostrò quanto fossero poco <lb></lb>accurate queste esperienze descritte nel <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> per cui Galileo, invece <lb></lb>di deliberarsene come pareva, si confermò nel suo errore di mantenere im­<lb></lb>mobile l&#039;aria intorno alla Terra, a quel modo ch&#039;ei credette di averla os­<lb></lb>servata intorno al vaso girante. </s></p><p type="main">

<s>La radice prima di questo errore la riconoscemmo in ciò che Galileo <lb></lb>negava all&#039;aria le qualità proprie alle materie terracquee, e che perciò ne <lb></lb>partecipasse agli effetti, ond&#039;è ch&#039;ei credeva intanto solo moversi es̀sa aria <lb></lb>intorno alla Terra, in quanto ella è mescolata alle esalazioni terrestri, fra <lb></lb>le quali si comprendevano anche i vapori acquosi. </s>

<s>Avendo sotto i tropici <lb></lb>perciò bisogno di costituire l&#039;ammosfera immobile, e non turbata da nes­<lb></lb>sun&#039;altra causa accidentale, poneva per condizion necessaria, oltre alla levi­<lb></lb>gatezza della superficie del mare, la scarsità delle evaporazioni di lui. </s></p><p type="main">

<s>Questa seconda condizione però, che dai mari, e specialmente da quelli <lb></lb>che soggiacciono all&#039;Equatore, non esalino vapori in più gran copia sotto la <lb></lb>gran ferza de&#039;raggi solari, ha tanto dell&#039;incredibile che non si capisce come <lb></lb>potess&#039;essere ammessa da Galileo. </s>

<s>Si direbbe anzi, e alcuni ne sospettarono <lb></lb>davvero (Humboldt Cosmo, traduz. </s>

<s>ital., T. II, Napoli 1850, pag. </s>

<s>447 n.) che <lb></lb>fosse quel passo di sopra addotto dai <emph type="italics"></emph>Massimi Sistemi<emph.end type="italics"></emph.end> adulterato, se non ci <lb></lb>fossero i documenti a provare come Galileo, non solo opinava che non eva­<lb></lb>porassero i mari, altro che poco, ma sapeva di più trovar la ragione da sal­<lb></lb>var questo, che per senso comune è un paradosso. </s></p><p type="main">

<s>Di quella ragione però e di altre simili dubitava argutamente il Vi­<lb></lb>viani, il quale non doveva ancora certamente sapere ch&#039;ell&#039;erano uscite <lb></lb>dalla divina mente del suo Galileo. </s>

<s>In una <emph type="italics"></emph>Raccolta di esperienze e di pen­<lb></lb>sieri diversi,<emph.end type="italics"></emph.end> per la massima parte originali, ma alcuni trascritti dalle carte <lb></lb>disperse di altri Autori, il Viviani stesso scrisse di sua propria mano anche <lb></lb>questo: “ Cercasi la cagione onde avvenga che i luoghi montuosi o vicini <lb></lb>alle gran montagne siano più delli altri sottoposti alle tempeste, fulmini, <lb></lb>tuoni, baleni, ecc. </s>

<s>Forse la cagione è tale, oppure è una coglio ... ria, la <lb></lb>quale il Galileo contrassegnerebbe così.... Levansi dalla terra vapori ed esa­<lb></lb>lazioni ecc. (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>21). </s></p><p type="main">

<s>Che dovessero questi pensieri meteorologici parere al Viviani cosa inde­<lb></lb>gna di Galileo, e dettatura piuttosto di qualche peripatetico, era naturale, <lb></lb>vedendovisi messo in gioco il principio delle contrarietà, e all&#039;<emph type="italics"></emph>antiperistasi<emph.end type="italics"></emph.end><lb></lb>delle esalazioni attribuita l&#039;origine delle grandini e delle tempeste. </s>

<s>Ma che <lb></lb>veramente quelle meteorologiche speculazioni appartengano a Galileo, oltre <lb></lb>all&#039;esservene l&#039;autografo (MSS. Gal., P. VI, T. II, c. </s>

<s>5), per cui gli editori <lb></lb>accolsero anche questa fra le scritture di lui, si conferma dal ritrovarsi qui <pb xlink:href="020/01/872.jpg" pagenum="315"></pb>il più chiaro commento alle idee professate ne&#039;Dialoghi de&#039;Due Massimi <lb></lb>Sistemi. </s></p><p type="main">

<s>A chi legge infatti nel IV di que&#039;Dialoghi il passo da noi sopra citato, <lb></lb>e domanda com&#039;esser possa che ivi dicasi da Galileo una cosa tanto contra­<lb></lb>ria al senso comune, qual&#039;è che negli ampii mari intertropicali <emph type="italics"></emph>manchino <lb></lb>l&#039;evaporazioni,<emph.end type="italics"></emph.end> risponde così l&#039;Autore di quel <emph type="italics"></emph>Pensiero,<emph.end type="italics"></emph.end> in margine al quale <lb></lb>dubitava il Viviani che si potesse imprimere quel bizzarro algoritmo, col <lb></lb>quale era solito lo stesso Galileo di notar, leggendo, le altrui corbellerie: <lb></lb>“ Dico inoltre maggior copia di vapori elevarsi dalla terra umida, che dal­<lb></lb>l&#039;acqua, perchè l&#039;acqua come diafana trasmette i raggi del sole e meno si <lb></lb>riscalda che la terra opaca.... Poco dunque di vapori e meno di esalazioni <lb></lb>si eleva dal mare ” (Alb. </s>

<s>XIV, 337, 38). </s></p><p type="main">

<s>Così veniva Galileo a guastarsi, diciamo così, fra le mani quel così bello <lb></lb>argomento, che porgevano a conferma del sistema copernicano i venti equa­<lb></lb>toriali, argomento di cui poi si valse il valoroso sperimentatore di Magde­<lb></lb>burgo. </s>

<s>Dal ponderar dell&#039;aria ne deduceva sicuramente il Guericke che “ si <lb></lb>Terra, secundum Copernici sententiam, motum illum vertiginis habeat, to­<lb></lb>tum quoque aereum systema simul inconcussum procedat cum Terra ” <lb></lb>(Experim. </s>

<s>magd. </s>

<s>cit., pag. </s>

<s>167). Ma benchè sia uniforme quel moto rota­<lb></lb>torio della sfera dell&#039;aria “ tamen in locis, nimirum sub Aequatore et Tro­<lb></lb>picis ubi circumvolutio Terrae, ob maiorem circumferentiam celerior est <lb></lb>quam alibi, remissio quaedam parva sentitur, ita ut aer raptui conversionis <lb></lb>terrestris totaliter non obediat ” (ibi, pag. </s>

<s>168). Hanno di qui origine quei <lb></lb>venti regolari, che spirano sotto i Tropici, e ciò, conclude il Guericke, non <lb></lb>leggero argomento <emph type="italics"></emph>ad struendum copernicanum systema adfert<emph.end type="italics"></emph.end> (ibi). </s></p><p type="main">

<s>L&#039;argomento di Ottone di Guericke però non è assoluto, perchè i venti <lb></lb>equatoriali dipendono tutto insieme dalla Terra, che si rivolge in sè stessa, <lb></lb>e sotto il Sole che ne dilata l&#039;aria più o meno, secondo che più o men di­<lb></lb>rettamente ne riceve il calore. </s>

<s>Avrebbe del sì importante problema dato il <lb></lb>Verulamio la soluzione completa, se, avverso com&#039;era all&#039;ipotesi copernicana, <lb></lb>non si fosse, co&#039;più antichi Filosofi e col nostro Alighieri, immaginato che <lb></lb><emph type="italics"></emph>in circuito tutto quanto l&#039;aer si volge con la prima volta<emph.end type="italics"></emph.end> (Purg., C. XXVIII, <lb></lb>t. </s>

<s>35), ond&#039;è che si fa vento dovunque <emph type="italics"></emph>tal moto percuote.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Quod <emph type="italics"></emph>Briza<emph.end type="italics"></emph.end> illa, si legge nella citata <emph type="italics"></emph>Historia naturalis et experi­<lb></lb>mentalis de ventis,<emph.end type="italics"></emph.end> inter tropicos luculenter spiret, res certa, causa ambigua. </s>

<s><lb></lb>Posset ea esse quia aer more coeli movetur. </s>

<s>Sed extra tropicos, quasi imper­<lb></lb>ceptibile propter circulos minores, intra, manifeste, propter circulos maiores <lb></lb>quos conficit. </s>

<s>Posset alia esse quia calor omnem aerem dilatat, nec se priori <lb></lb>loco contineri patitur. </s>

<s>Ex dilatatione autem aeris necessario fit impulsio aeris <lb></lb>contigui, quo brizam istam pariat prout progreditur sol. </s>

<s>Sed illa intra tro­<lb></lb>picos, ubi sol est ardentior, insignior est, extra, fere latet ” (pag. </s>

<s>16, 17). </s></p><p type="main">

<s>Così venivano anche i <emph type="italics"></emph>Monsoni<emph.end type="italics"></emph.end> a ridursi alla causa generale di tutti i <lb></lb>venti assegnata dal Torricelli, e alla quale dettero poi il più pieno svolgi­<lb></lb>mento l&#039;Hook e l&#039;Halley. </s></p><pb xlink:href="020/01/873.jpg" pagenum="316"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Si disse, nel chiuder la prima parte del presente Capitolo, che la Me­<lb></lb>teorologia barometrica rimase, nel render la ragione delle sue congetture, <lb></lb>così lungamente incerta, per non aver debitamente atteso a quel bellissimo <lb></lb>esperimento, per cui rappresentavasi con ingegnoso artifizio dal Guericke, <lb></lb>ora il cielo piovoso, ora il sereno. </s>

<s>Suppongasi infatti di avere introdotto <lb></lb>nella cucurbita guericchiana un Barometro: quando l&#039;aria rarefatta si ran­<lb></lb>nuvola, e il vapor condensato incomincia a cadere in pioggia, la colonna ba­<lb></lb>rometrica necessariamente si abbassa; quando, riammessa l&#039;aria, questa, <lb></lb>restituitasi alla sua primiera densità, si rasserena, la colonna barometrica non <lb></lb>men necessariamente si alza. </s></p><p type="main">

<s>Così venivano le vicende del Barometro, per quel che può dipendere <lb></lb>dall&#039;avvicendarsi delle stagioni, dimostrate, ne&#039;casi più ordinarii, per modo, <lb></lb>che sarebbero bastati i fatti sperimentali a rassicurar di ogni dubbio, e a <lb></lb>togliere alle controversie ogni mendicata occasione. </s>

<s>Tutt&#039;al contrario ha in­<lb></lb>torno a ciò la Storia tanta faccenda, che non si può così ridurre negli an­<lb></lb>gusti termini di questo paragrafo, senza timor che s&#039;abbia, per qualche parte, <lb></lb>a lasciar da noi difettosa. </s></p><p type="main">

<s>Quel Pascal, che fu il primo a sperimentare le variazioni ipsometriche <lb></lb>del Barometro, fu il primo altresì a notare con gran diligenza le variazioni <lb></lb>che subiva lo strumento al variare delle stagioni. </s>

<s>L&#039;editore del <emph type="italics"></emph>Traitez de <lb></lb>l&#039;equilibre des liqueurs<emph.end type="italics"></emph.end> pubblicò nell&#039;Appendice al particolar Trattato <emph type="italics"></emph>De la <lb></lb>pesanteur de l&#039;air<emph.end type="italics"></emph.end> alcuni frammenti di una lunga opera, o lasciata dallo <lb></lb>stesso Pascal incompiuta, o andata sventuratamente per la maggior parte <lb></lb>smarrita. </s>

<s>Fra cotesti frammenti è un capitolo che s&#039;intitola “ De la regle <lb></lb>des variations qui arrivent a ces effects, par la variété des temps. </s>

<s>” </s></p><p type="main">

<s>“ Ces vicissitudes, scrive l&#039;Autore, sont sans regles dans les chauge­<lb></lb>mens du mercure aussi bien que dans l&#039;air: de sorte que quelquefois d&#039;un <lb></lb>quart d&#039;heure a l&#039;autre il y a grande difference et quelquefois durant qua­<lb></lb>tre ou cinq&#039;jours il y en a tres peu. </s>

<s>La faison ou le mercure est le plus <lb></lb>haut pour l&#039;ordinaire est l&#039;Hyver. </s>

<s>Celle ou d&#039;ordinaire il est le plus bas est <lb></lb>l&#039;Esté. </s>

<s>Ou il est le moins variable est aux solstices; et ou il est le plus va­<lb></lb>riable est aux Equinoxes. </s>

<s>Ce n&#039;est pas que le mercure ne foit quelquefois <lb></lb>haut en Esté, bas en Hyver, incostant aux solstices, constant aux Equino­<lb></lb>xes; eat il n&#039;ya point de regle certaine; mais pour l&#039;ordinaire la chose est <lb></lb>comme nous l&#039;avons dite; parce qu&#039;aussi pour l&#039;ordinaire quoy que non pas <lb></lb>toujours, l&#039;air est le plus charge en Hyver, le moins en Esté, le plus in­<lb></lb>costant en Mars et en Septembre, et le plus constant aux Equinoxes ” (Pa­<lb></lb>ris, pag. </s>

<s>153, 54). </s></p><p type="main">

<s>In mezzo a queste osservazioni delle variazioni annuali vedute fare al <lb></lb>Barometro, occorse al Pascal di notare altre variazioni giornaliere nello stru-<pb xlink:href="020/01/874.jpg" pagenum="317"></pb>mento, le quali si accorse che dipendevano dall&#039;esser l&#039;aria ora più, ora <lb></lb>meno carica di vapori. </s>

<s>Dietro a ciò, si credeva di poterne concludere che <lb></lb>“ la pesanteur de la masse de l&#039;air augmente quand il est plus chargé de <lb></lb>vapeur, et diminué quand il l&#039;es moins ” (ivi, pag. </s>

<s>96). </s></p><p type="main">

<s>Altre simili variazioni ebbe a notare il Pascal in ordine al tempo, che, <lb></lb>s&#039;era bello, l&#039;argento vivo nella canna barometrica rimaneva più basso, ben­<lb></lb>chè fossesi accorto che non riusciva questa regola sempre infallibile, avendo <lb></lb>notato che lo stesso argento vivo talvolta si solleva, facendosi il cielo sereno. <lb></lb></s>

<s>“ Il arrive aussi peur l&#039;ordinaire que le mercure baisse quand il fait beau <lb></lb>temps, qu&#039;il hausse quand le temps devient froid ou chargé; mais cela n&#039;est <lb></lb>pas infallible; car il hausse quelquefois quand le temps s&#039;embellit, et il baisse <lb></lb>quelquefois quand le temps se couvre ” (ivi, pag. </s>

<s>154). </s></p><p type="main">

<s>Queste osservazioni fatte dal Pascal a Parigi, e altre simili fatte a Cler­<lb></lb>mont dal Perier, negli anni 1649, 50 e 51, rimasero ignote al pubblico in­<lb></lb>fino al 1663, cosicchè nulla se ne sapeva ancora in Italia, quando il Gran­<lb></lb>duca di Firenze ordinava quelle stazioni meteorologiche a notar diligentemente, <lb></lb>giorno per giorno, lo stato dell&#039;aria, la temperatura, l&#039;intensità e la direzione <lb></lb>de&#039;venti. </s></p><p type="main">

<s>Le osservazioni barometriche furono particolarmente affidate dal Gran­<lb></lb>duca al Borelli, professore allora nello studio di Pisa, il quale con gran di­<lb></lb>ligenza le proseguì per tutti i giorni dell&#039;anno 1657 e dell&#039;anno appresso. </s>

<s><lb></lb>Egli ebbe, come il Pascal, a concludere da quelle sue Effemeridi che il Ba­<lb></lb>rometro si solleva sotto il cielo nuvoloso e si abbassa quando torna sereno. </s>

<s><lb></lb>Mettendosi dietro a investigar la ragione di ciò, da nessuno, e nemmeno <lb></lb>dallo stesso Pascal per lo innanzi tentata, parvegli di riconoscerla negli stessi <lb></lb>vapori, che aggravano col loro peso il peso dell&#039;aria, e pensò di riscontrare <lb></lb>il fatto e di renderlo visibile coll&#039;esperienza. </s></p><p type="main">

<s>Preso un largo vaso cilindrico di cristallo e calato nel suo fondo un <lb></lb>Barometro, ne riempiva lo stesso vaso d&#039;olio o di altro liquido più leggero, <lb></lb>notando il livello a cui il mercurio, per l&#039;infusione del liquido, era salito. </s>

<s><lb></lb>Poi faceva sull&#039;olio gravare una scodella piena di minutissimi granelli di <lb></lb>arena, che, aggiungendo nuova pressione alla pressione dell&#039;olio, faceva ri­<lb></lb>salire alquanto il mercurio. </s>

<s>Riversati i granellini dell&#039;arena dalla scodella <lb></lb>osservava il Borelli che, nell&#039;atto della discesa, il livello barometrico non si <lb></lb>moveva, ma scesi i granellini in fondo, quel livello si restituiva a poco a poco <lb></lb>a quell&#039;altezza precisa, alla quale era giunto per la sola pressione dell&#039;olio <lb></lb>soprapposto. </s>

<s>I granellini dell&#039;arena contenuti nella scodella rappresentavano, <lb></lb>secondo il Borelli, i granellini o le vescichette dell&#039;umido, di che si com­<lb></lb>pone la nuvola; la discesa di que&#039;granellini arenosi rappresentava il cader <lb></lb>delle gocciole della pioggia, e l&#039;olio rimasto libero da que&#039;corpicelli stra­<lb></lb>nieri rendeva immagine dell&#039;aria divenuta serena, per esser caduti a terra <lb></lb>i vapori. </s></p><p type="main">

<s>Nel Novembre dell&#039;anno 1657 riferiva da Pisa queste sue speculazioni, <lb></lb>e descriveva queste esperienze al principe Leopoldo, il quale rispondeva al <pb xlink:href="020/01/875.jpg" pagenum="318"></pb>Borelli per lettera, che il Fabbroni pubblicò senza data, ma che nella copia <lb></lb>manoscritta è del dì 15 di Dicembre dell&#039;anno suddetto (MSS. Cim., T. XXIII, <lb></lb>c. </s>

<s>2). Incomincia ivi il principe a dire che gratissimo gli era riuscito il pro­<lb></lb>blema delle variazioni dell&#039;argento vivo, in relazione collo stato del cielo, e <lb></lb>che ingegnosissima gli era parsa la soluzione: dubitava però, per non averne <lb></lb>fatta esperienza, se fosse vero che, soprastando i nuvoli in alto e non toc­<lb></lb>cando terra, dovessero <emph type="italics"></emph>aggravare maggiormente sopra l&#039;argento vivo, e <lb></lb>conseguentemente alzarlo più di quando fosse compresso dall&#039;aria am­<lb></lb>biente purissima.<emph.end type="italics"></emph.end> (Fabbroni, Lett. </s>

<s>ecc., T. I, pag. </s>

<s>112). </s></p><p type="main">

<s>Il dubbio era ragionevolissimo e degno di maggior Filosofo, che non <lb></lb>potess&#039;essere il principe Leopoldo. </s>

<s>Ma le considerazioni di lui dovevano aver <lb></lb>gran fondamento in altre considerazioni suggeritegli dal Viviani, alla saga­<lb></lb>cia del quale non potevano essere sfuggiti i difetti dell&#039;esperienza e la fal­<lb></lb>lacia dell&#039;argomento del Borelli. </s>

<s>E in verità, improprio e anzi falso era il <lb></lb>dire che la scodella piena di granellini di arena, premendo sull&#039;olio, ne au­<lb></lb>menta la pressione sul fondo del vaso, perchè la pressione idrostatica non <lb></lb>può variarsi per altre ragioni, che per variar l&#039;altezza perpendicolare del li­<lb></lb>vello. </s>

<s>Nè i galleggianti aumentan nulla di peso, equilibrandosi esattamente <lb></lb>col mezzo: solo può dubitarsi, e l&#039;esperienza dovrebbe decidere, se niuna <lb></lb>alterazion sopravvenga per la discesa o l&#039;ascesa, che dentro il mezzo si fac­<lb></lb>cia da qualche corpo straniero. </s></p><p type="main">

<s>“ Se la nuvola o l&#039;umidità sta ferma o sospesa in aria (tali sono le <lb></lb>parole del Viviani) non si altera la gravità in specie dell&#039;aria premente nè <lb></lb>l&#039;altezza, in quel modo che non si altera la gravità in specie nè l&#039;altezza <lb></lb>dell&#039;acqua di un vaso pieno nell&#039;immersione di corpi galleggiantivi o di <lb></lb>corpi, se più gravi in specie, tenutivi sospesi da potenza esteriore. </s>

<s>Se le nu­<lb></lb>vole son discendenti par che deva crescere la pressione, se ascendenti che <lb></lb>deva scemare. (Esperimentar questo nell&#039;acqua con corpi discendenti ed <lb></lb>ascendenti). Se toccano terra in modo che sieno tutto un corpo continuato <lb></lb>come solido, dovrebbe mancar la pressione, perchè l&#039;aria che è sopra pose­<lb></lb>rebbe e graviterebbe sopra detto umido. </s>

<s>Ma se questo umido, che tocca <lb></lb>terra, è cedente e condensabile, la pressione dell&#039;aria opererà sopra esso, e <lb></lb>per conseguenza sopra l&#039;argento vivo, come opera l&#039;aria sopra l&#039;acqua che <lb></lb>sia sopra il mercurio ” (MSS. Cim., T. X, c. </s>

<s>156). </s></p><p type="main">

<s>Persuaso il Viviani, dictro tali considerazioni, che non era la soluzion <lb></lb>del difficile problema a ricercarla nel galleggiare e nel premere delle nubi, <lb></lb>un fatto che gli occorse di sperimentare fu quello da cui venne a essere <lb></lb>indirizzato per una via diversa, che a lui parve, ed era veramente la più <lb></lb>sicura. </s>

<s>Il fatto che si diceva è così dal Viviani stesso notato: “ Lo stru­<lb></lb>mento del mercurio portato in stanza, dove si faccia fuoco, abbassa giù per <lb></lb>il cannello, e più e più, secondo che più s&#039;avvicina al fuoco, eppure per <lb></lb>due ragioni doverebbe alzare: Prima, per l&#039;ingresso del calore nel mercurio <lb></lb>che dovrebbe far l&#039;effetto che fa ne&#039;Termometri; seconda, perchè il mer­<lb></lb>curio riscaldato si fa più leggeri in specie, ed i liquidi occupano sempre nel <pb xlink:href="020/01/876.jpg" pagenum="319"></pb>cannello maggiore altezza, secondo che sono più leggeri. </s>

<s>Se dunque que­<lb></lb>ste due cagioni non dimostrano i loro effetti, è segno che prevale la cagione <lb></lb>della minor pressione dell&#039;aria ambiente lo strumento, che per esser riscal­<lb></lb>data pesa meno ” (ivi, c. </s>

<s>53). </s></p><p type="main">

<s>Di qui fu condotto il Viviani a dar tutta l&#039;importanza e tutta l&#039;effica­<lb></lb>cia alle rarefazioni e alle condensazioni dell&#039;aria, dalle quali dipendono, e lo <lb></lb>stato del cielo e le variazioni del Barometro. </s>

<s>“ L&#039;aria umida dell&#039;inverno, <lb></lb>pensava, è più calda dell&#039;aria asciutta della medesima stagione, e perciò è <lb></lb>più rara e più leggera e meno premente. </s>

<s>L&#039;aria umida dell&#039;estate è più <lb></lb>fresca dell&#039;aria asciutta dell&#039;estate, ond&#039;è più densa e più grave e più pre­<lb></lb>mente ” (ivi, c. </s>

<s>156). Di qui ne concludeva, benchè non sicuro di questi <lb></lb>suoi argomenti, in ordine alle variazioni barometriche: “ Forse l&#039;argento <lb></lb>vivo sarà più alto nel cannello in tempo asciutto che umido, e nell&#039;estate <lb></lb>più alto in tempo umido che in tempo asciutto, ma ben nell&#039;asciutto del­<lb></lb>l&#039;estate sarà forse più basso che nell&#039;asciutto dell&#039;inverno, e nell&#039;umido <lb></lb>dell&#039;estate più basso che nell&#039;umido dell&#039;inverno ” (ivi). </s></p><p type="main">

<s>Le varietà degli effetti così saviamente dal Viviani considerati come di­<lb></lb>pendenti da quella complicanza di cause, in mezzo alle quali si smarrisce il <lb></lb>Meteorologo, che non arriva colla mente a determinare delle infinite inco­<lb></lb>gnite del problema altro che poche; mettevano il soggetto intorno a che si <lb></lb>discuteva, sotto altre forme da quelle che lo presentava il Borelli, a giudi­<lb></lb>zio del quale il fatto semplice in modo e costante, da potersene dare una <lb></lb>dimostrazione sperimentale, era questo: l&#039;aria nuvolosa è sempre più pe­<lb></lb>sante della serena. </s></p><p type="main">

<s>Che il principe Leopoldo per levar quella sua confidenza al Borelli gli <lb></lb>abbia conferiti, oltre a&#039;suoi, anche i dubbi del Viviani, e gli abbia fatto no­<lb></lb>tar quella incostanza di effetti dipendenti dalle rarefazioni e dai condensa­<lb></lb>menti dell&#039;aria, che soli hanno efficacia in alterar lo stato del cielo, e in far <lb></lb>variare il livello al Barometro; è cosa molto prababile, mentre è certo dal­<lb></lb>l&#039;altra parte, perchè dimostrato dai documenti, che lo stesso Principe, il <lb></lb>quale era intorno a ciò inspirato dal senno del Viviani, faceva avvertito il <lb></lb>Borelli che, a render variabile il livello barometrico, oltre a quello dell&#039;umido <lb></lb>e del sereno, potevano concorrere altri innumerevoli accidenti. </s>

<s>Di alcuni <lb></lb>sovvenutigli, e ridotti a otto capi principali, se ne trova nota nel T. XXIII <lb></lb>de&#039;Manoscritti del Cimento, col titolo: “ Diversità di accidenti che adesso <lb></lb>sono sovvenuti poter seguire nell&#039;aria sopra l&#039;argento vivo nello strumento <lb></lb>denominato..... ” (c. </s>

<s>205). </s></p><p type="main">

<s>Non per questo però il Borelli si rimosse dalle sue persuasioni. </s>

<s>Dodici <lb></lb>anni e più dopo, quando sotto il titolo <emph type="italics"></emph>De motionibus naturalibus a gra­<lb></lb>vitate pendentibus<emph.end type="italics"></emph.end> raccolse tutte insieme, e in ordine di Trattato, le sue <lb></lb>fisiche esperienze, non lasciò indietro quelle di Meteorologia barometrica, <lb></lb>presentandole solennemente in pubblico come le avea conferite in privato, <lb></lb>e senza nulla dubitar della verità de&#039;primi fatti osservati, e delle prime spe­<lb></lb>culate ragioni. </s>

<s>Permettendoci, per levar tedio a chi legge, di ridurre al co-<pb xlink:href="020/01/877.jpg" pagenum="320"></pb>mun linguaggio l&#039;originale dettato in latino, così narra il Borelli la storia della <lb></lb>sua scoperta e della esperienza immaginata per confermarla. </s></p><p type="main">

<s>“ Fu da noi osservato che, pur rimanendo lo Strumento stazionario, il <lb></lb>livello del mercurio non sempre si mantiene alla medesima altezza. </s>

<s>Ciò può <lb></lb>in parte dipendere dalla varia temperatura dell&#039;aria ora calda, ora fredda, <lb></lb>ma le variazioni prodotte da questa causa per verità son piccolissime, spe­<lb></lb>cialmente se vada aggiunta alla cima della canna di vetro una palla alquanto <lb></lb>grossa. </s>

<s>Le variazioni però, delle quali io intendo parlare, sono notabilissime, <lb></lb>e che non dipendano propriamente dal caldo e dal freddo me ne persuade <lb></lb>il vedersi fare simili variazioni tanto nell&#039;estate quanto nell&#039;inverno, così in <lb></lb>luogo aperto, come in una stanza chiusa riscaldata dal fuoco. </s>

<s>” </s></p><p type="main">

<s>“ Ho delle sopraddette variazioni appresso di me le Effemeridi per gli <lb></lb>anni 1657 e 58, nelle quali andavo tutti i giorni notando i gradi del Ter­<lb></lb>mometro e lo stato del cielo, se cioè era nuvolo o sereno, e da qual parte <lb></lb>e in quale ora spirasse il vento; osservazioni ch&#039;io feci ai conforti e ai co­<lb></lb>mandi del Serenissimo Ferdinando granduca di Toscana, sagacissimo esplo­<lb></lb>ratore dei segreti della Natura. </s>

<s>” </s></p><p type="main">

<s>“ Sembra ora, da tutte queste mie osservazioni comparate insieme, po­<lb></lb>tersi dedurre che molte volte, essendo imminente qualche lunga e ostinata <lb></lb>pioggia, il mercurio si solleva di alquanti gradi nella canna al di sopra del­<lb></lb>l&#039;altezza ordinaria, e al contrario si suole abbassare nell&#039;atto stesso che cade <lb></lb>la pioggia. </s>

<s>Nè è da credere che una tal differenza sia piccola, avend&#039;io più <lb></lb>volte osservato in Pisa che, in certi temporali di lunga durata, giungevano <lb></lb>queste variazioni infino a dodici gradi. </s>

<s>E perchè serbo ancora appresso di <lb></lb>me l&#039;esemplare di una lettera, che scrissi nel 1657 al serenissimo principe <lb></lb>Leopoldo, ora cardinale, in tal subietto, vo&#039;riferire qui brevemente quello <lb></lb><figure id="id.020.01.877.1.jpg" xlink:href="020/01/877/1.jpg"></figure></s></p><p type="caption">

<s>Figura 64.<lb></lb>ch&#039;io avevo già speculato per rendere la ragione di <lb></lb>questo fatto: onde avvenga cioè che l&#039;aria prema più <lb></lb>fortemente il mercurio innanzi, e meno nell&#039;atto del <lb></lb>cadere e dopo esser caduta la pioggia. </s>

<s>” </s></p><p type="main">

<s>“ Prendasi una canna barometrica AIC (fig. </s>

<s>64) e, <lb></lb>fatto il vuoto al solito modo, sia F il punto dove ascende <lb></lb>e si ferma il livello del mercurio. </s>

<s>Poi si cali questa <lb></lb>stessa canna nel più cupo fondo del vaso DK di vetro, <lb></lb>che si empie di olio o di altro liquido più leggero. </s>

<s>Il <lb></lb>livello, per la pressione del liquido sopra infuso, ascen­<lb></lb>derà da F in H. </s>

<s>Imperniata poi ne&#039;punti D e G si so­<lb></lb>prapponga all&#039;olio una scodella N, il fondo della quale <lb></lb>sia pieno di granelli minutissimi di arena o di acqua <lb></lb>o di qualche altro liquido più grave in specie dell&#039;olio. </s>

<s><lb></lb>Il livello nella canna, per la nuova pressione del corpo grave soprastante, <lb></lb>si solleverà ancora alquanto di più, passando da H per esempio in M. ” </s></p><p type="main">

<s>“ Così tutto preparato, rovescisi la scodella N, girevole intorno all&#039;asse <lb></lb>DG, in modo che i granelli dell&#039;arena o le gocciole dell&#039;acqua, di che ell&#039;era <pb xlink:href="020/01/878.jpg" pagenum="321"></pb>piena, vengano a cader giù in mezzo all&#039;olio, per similitudine di ciò che av­<lb></lb>vien nella pioggia. </s>

<s>Si vedrà che, mentre durano que&#039;granellini o quelle goc­<lb></lb>ciole a cadere, il mercurio non si rimuove dal punto M, ma cessata la ca­<lb></lb>duta, il livello nella canna si abbassa via via, per ritornare al punto H, <lb></lb>dove l&#039;aveva ridotto il premente peso dell&#039;olio. </s>

<s>” </s></p><p type="main">

<s>“ Da questi evidentissimi esperimenti io penso che si possa facilmente <lb></lb>risolvere il proposto problema. </s>

<s>E in verità che altro sono le nuvole piovose <lb></lb>se non che un aggregato d&#039;innumerevoli minutissimi granellini di acqua? </s>

<s>E <lb></lb>perciò, quando alcuna di queste nuvole nuoterà per le alte regioni dell&#039;aria, <lb></lb>o quando quelle particelle acquose scenderanno con lentissimo moto, ver­<lb></lb>ranno a comprimere con maggior forza la superficie terrestre, di quel che <lb></lb>non facciasi l&#039;aria pura. </s>

<s>Di qui è che il mercurio nella vaschetta barome­<lb></lb>trica, essendo costituito nelle più basse regioni dell&#039;ammosfera, dee neces­<lb></lb>sariamente esser premuto, non da solo il peso di tutta la soprastante mole <lb></lb>dell&#039;aria, ma dal peso altresi delle particelle acquee, di che si compone, <lb></lb>tutte raccolte insieme, la nuvola suprema. </s>

<s>Può perciò benissimo avvenire, <lb></lb>alquanto prima che la pioggia discenda, che il livello del mercurio dentro <lb></lb>la canna aggiunga alla sua massima altezza, e ivi immobilmente rimanga. </s>

<s><lb></lb>Ciò può da un&#039;altra parte avvenire, non per sola ragion delle nuvole, ma <lb></lb>di qualunque altra simile cosa gravitante, perchè se qualche poco della pol­<lb></lb>vere terrestre venga sollevata per caso e largamente dispersa dai venti per <lb></lb>l&#039;aria, non è a dubitar che ciò non sia nuova cagione di far gravitar più <lb></lb>ponderosamente l&#039;aria stessa sopra la superficie terrestre. </s>

<s>” </s></p><p type="main">

<s>“ Se poi per qualunque causa la nuvola vada dispersa, cadendo in goc­<lb></lb>ciole che bagnino il terreno, e allora è chiaro che quelle gocciole stesse po­<lb></lb>santi in terra, e non aggravantisi perciò più nel mezzo dell&#039;aria, non ag­<lb></lb>giungono ad essa la loro forza di compressione, e il mercurio perciò più <lb></lb>leggermente premuto torna ad abbassarsi o a ridursi al suo più infimo li­<lb></lb>vello ” (Regio Julio 1670, pag. </s>

<s>238-44). </s></p><p type="main">

<s>Nel 1670, quando si pubblicarono così fatte dottrine in Italia, era da <lb></lb>sette anni pubblicato in Francia il Trattato del Pascal, cosicchè si avevano <lb></lb>le due più grandi autorità in fisica meteorologica concordi in asserire che <lb></lb>l&#039;aria nuvolosa è men leggera della serena. </s>

<s>Tanta fu poi quella autorità che <lb></lb>si prestò piena fede alle asserzioni di così esperti osservatori, pochi essendo <lb></lb>in Francia coloro che sospettavano essersi ingannato un Pascal, pochissimi <lb></lb>essendo in Italia quegli altri, che sospettavano essersi ingannato un Borelli. </s>

<s><lb></lb>Fu questa fede che fece passare inosservato lo sperimento guericchiano, ma <lb></lb>pur non mancarono alcuni, i quali, osservando per sè medesimi i fatti, tro­<lb></lb>varono che corrispondevano realmente coll&#039;esperienza del Guericke e non <lb></lb>con quella del Borelli. </s></p><p type="main">

<s>È di questi da annoverar fra principali il Du-Hamel, il quale, dopo aver <lb></lb>francamente negato <emph type="italics"></emph>graviorem esse aera pluvio coelo quam sereno, cum <lb></lb>ipsa experientia contrarium demonstret,<emph.end type="italics"></emph.end> e dop&#039;aver messo in dubbio quel <lb></lb>che alcuni adducevano per ragione di questo fatto, riconoscendola negli aliti <pb xlink:href="020/01/879.jpg" pagenum="322"></pb>terrestri che tengono sollevati i vapori, quasi sopra la leggerezza delle loro <lb></lb>ali. </s>

<s>“ An potius, soggiunge tosto, idem accidit in aere quod cernimus in <lb></lb>Machina dum exhauritur. </s>

<s>Tum enim saepe vitrum velut nebula obfuscatur <lb></lb>et rore madidum apparet. </s>

<s>Sic pluvio coelo et nubibus obducto superior aer <lb></lb>multum dilatatur et permistas aquae seu vaporum partes post se relinquit, <lb></lb>ex quibus coalescentibus tum nubes tum imbres oriuntur. </s>

<s>Aer enim debi­<lb></lb>litatus tot aquae velut atomos non potest exsolvere, ac velut aqua fortis <lb></lb>simplicis aquae affusione fracti metalli pulverem, sic aquae globulos aer <lb></lb>dimittit et praecipitat ” (Philosophia vetus et nova, T. IV, Parisiis 1682, <lb></lb>pag. </s>

<s>377). </s></p><p type="main">

<s>Non ci voleva altro che il fascino dell&#039;autorità del Borelli e del Pascal <lb></lb>a non lasciarsi persuadere che tale essendo la causa, e tale l&#039;origine della <lb></lb>pioggia, l&#039;aria nuvolosa più rarefatta deve necessariamente ponderar sul Ba­<lb></lb>rometro meno della serena. </s>

<s>Ma il Du-Hamel stesso abbiam veduto com&#039;an­<lb></lb>dasse dubitoso intorno a cosa per sè tanto evidente, cosicchè, non sapendosi <lb></lb>e non osandosi fare una precisa e netta distinzione del vero dal falso, si <lb></lb>teneva l&#039;opinion di coloro, che asserivano al contrario del Pascal e del Bo­<lb></lb>relli, come solamente probabile, e da potersi seguitar con buone ragioni, a <lb></lb>pari di quelle professate da&#039;due celebratissimi Autori. </s>

<s>Giova in tal proposito <lb></lb>addur le parole, che scriveva il padre Giuseppe Ferroni, professore di Fi­<lb></lb>sica nel Collegio di Siena, al suo amico e maestro Vincenzio Viviani. </s></p><p type="main">

<s>“ ..... Nel dettar l&#039;esperienze degli Elementi, sono in quella dell&#039;aria, <lb></lb>e dopo varii e nuovi Termometri del caldo e del freddo, del secco ed umido <lb></lb>dell&#039;aria, sono in quella più bella di tutte per conoscere se il tempo si pre­<lb></lb>pari alla pioggia, o si disponga al sereno. </s>

<s>Questo è il famoso barometro del <lb></lb>Torricelli, in cui il mercurio ora alzandosi, ora abbassandosi, dà indizio della <lb></lb>mutazione del tempo, quanto al disporsi in piovoso o sereno. </s>

<s>Ma io trovo <lb></lb>gli autori sperimentali molto discordi, perchè Monsù di Amontons, accade­<lb></lb>mico di Parigi, Alfonso Borelli, Giovan Cristoforo Sturmio dicono che, di­<lb></lb>sponendosi il tempo al piovoso, per esser l&#039;aria più grave cresce e più si <lb></lb>alza nel collo del Barometro il mercurio, ma disponendosi al sereno, per la <lb></lb>minor pressione dell&#039;aria più purgata e più leggera, meno si sostenta. </s>

<s>” </s></p><p type="main">

<s>“ All&#039;incontro Giovan Batista Du-Hamel, nella sua Filosofia burgun­<lb></lb>dica, ed il nostro padre Francesco Lana ed il nostro medico ed eruditissimo <lb></lb>dottor Gabrielli sentono che l&#039;aria torbida e nugolosa, quando il tempo si <lb></lb>dispone alla pioggia o neve, sia più leggera e l&#039;aria serena sia più grave; <lb></lb>onde vogliono che, quando meno si sostenta il mercurio, sia segno di piog­<lb></lb>gia; quando più si sostenta sia per disporsi al sereno. </s>

<s>E che così sia, il no­<lb></lb>stro Medico si offerisce di farlo vedere nel suo Barometro a chi nol cre­<lb></lb>desse. </s>

<s>” </s></p><p type="main">

<s>“ Io oggi insegno l&#039;opinione di questi ultimi, ma non mi piace la <lb></lb>ragione che l&#039;aria torbida e nugolosa disponentesi a pioggia sia più leggera <lb></lb>di quello che sia l&#039;aria serena purgata come un cristallo. </s>

<s>Io assegnerò <lb></lb>un&#039;altra ragione sovvenutami ed è questa: La causa sostentativa, non sol <pb xlink:href="020/01/880.jpg" pagenum="323"></pb>del mercurio ma di altri fluidi sopra il loro livello, è senza dubbio la pres­<lb></lb>sione dell&#039;aria, ma questa non è la causa più prossima ed immediata quale <lb></lb>io stimo essere la forza elastica, forza di susta, forza di molla, che ha l&#039;aria. </s>

<s><lb></lb>Dico dunque che, quando l&#039;aria torbida e nugolosa si dispone alla pioggia <lb></lb>per i vapori acquei che salgono, resta molto inumidita, e questa umidità <lb></lb>snerva la forza elastica dell&#039;aria. </s>

<s>S&#039;io stringo in pugno la lana secca ed <lb></lb>asciutta, vedo che ella si dilata, quando apro il pugno, ma s&#039;io stringo la <lb></lb>lana bagnata, vedo che ha debilitato il suo elaterio, e poco dilatasi, aperto <lb></lb>il pugno. </s>

<s>Or così l&#039;aria serena, benchè più leggera, più sostenta nel Baro­<lb></lb>metro il mercurio, perchè dà maggior forza d&#039;arco, forza di molla. </s>

<s>Ma l&#039;aria <lb></lb>torbida disponentesi alla pioggia, benchè più pesante, sostenta meno il mer­<lb></lb>curio, perchè, inumidita dai vapori acquei che salgono, resta la sua forza <lb></lb>elastica debilitata ” (MSS. Gal. </s>

<s>Disc., T. CXLVII, c. </s>

<s>126). </s></p><p type="main">

<s>Questo suo pensiero lo scriveva il Ferroni nell&#039;Aprile del 1693, pre­<lb></lb>gando il Viviani a rispondergli se giudicava che si potesse approvare. </s>

<s>Qual <lb></lb>fosse precisamente la risposta non siamo ora noi in grado di dirlo, non es­<lb></lb>sendoci capitato sotto gli occhi il documento, ma, da quelle note che tra­<lb></lb>scrivemmo di sopra, si può facilmente argomentare che l&#039;opinion del Vi­<lb></lb>viani era molto diversa e assai più conforme alla verità di quella, ch&#039;erasi <lb></lb>composta il Ferroni nella sua fantasia. </s>

<s>Fu nonostante a quella occasione che <lb></lb>si risvegliò nello stesso Viviani il desiderio di fare esperienza di un concetto <lb></lb>sovvenutogli, dal qual concetto, quand&#039;avesse avuto corrispondenza nei fatti, <lb></lb>ne sarebbero derivate, in ordine alla causa delle variazioni barometriche, <lb></lb>conseguenze molto importanti. </s></p><p type="main">

<s>Quel desiderio si legge espresso sotto questa forma: “ Esperimentare <lb></lb>se gli archi dell&#039;aria vengano allentati con lo star lungamente compressi, e <lb></lb>se il vaso, dove si fa la compressione, si dilati e poi ritorni, ovvero anch&#039;egli <lb></lb>rimanga in progresso di tempo dilatato ” (MSS. Cim., T. X, c. </s>

<s>11). </s></p><p type="main">

<s>Forse il Ferroni dette con quel suo pensiero al Viviani l&#039;impulso di <lb></lb>mettere in esecuzione il proposito fatto da qualche tempo, ma non se ne <lb></lb>ha certezza, e non sappiam dire perciò ai nostri lettori quali si fossero i <lb></lb>resultati dell&#039;esperienza. </s>

<s>Questo solo sappiamo che fu di ciò, pochi anni <lb></lb>dipoi, pienamente sodisfatta la scienza dal valorosissimo Hawksbee, il quale, <lb></lb>mandando ad effetto quel che il Viviani si era proposto, raccolse da un suo <lb></lb>accuratissimo esperimento “ che le molle dell&#039;aria possono essere in tal modo <lb></lb>disturbate da violenti impulsi o da gagliarde compressioni, che si richieda <lb></lb>un tempo considerabile, perchè elleno ricuperino di nuovo la naturale loro <lb></lb>tensione o temporamento ” (Esper. </s>

<s>fisico-meccan. </s>

<s>cit., pag. </s>

<s>71). </s></p><p type="main">

<s>Raccolse di più che il tempo e la forza della restituzione son proporzio­<lb></lb>zionali al tempo e alla forza della compressione, e applicò queste conclu­<lb></lb>sioni a render più compiuta la notizia della causa di alcuni effetti naturali. </s>

<s><lb></lb>Passando dal senso figurato al reale, si comprende quanto il concetto del <lb></lb>Viviani, illustrato dalle esperienze dell&#039;Hawksbee, dovesse conferire a sta­<lb></lb>bilir le leggi dell&#039;attrazione molecolare, relative al diminuir dell&#039;intensità di <pb xlink:href="020/01/881.jpg" pagenum="324"></pb>lei col crescere delle distanze, e come venisse da ciò ingerito ne&#039;fisici il <lb></lb>sospetto di un&#039;occulta efficacia dell&#039;elaterio dell&#039;aria, più o meno compressa, <lb></lb>in produr tante misteriose variazioni che così spesso occorre d&#039;osservar nel <lb></lb>livello del Barometro. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Benchè fosse sottile il concetto sovvenuto in mente al Viviani di spe­<lb></lb>rimentar se l&#039;elaterio dell&#039;aria si smorza, dopo una compressione diuturna; <lb></lb>benchè i resultati sperimentali raccolti dall&#039;Hawksbee riuscissero utilissimi <lb></lb>a investigar le recondite cause di molti effetti della Natura, che special­<lb></lb>mente concernono la statica vegetabile e animale, e quella che si può per <lb></lb>similitudine chiamare statica barometrica; erano tutte queste cose però fuor <lb></lb>di proposito a decider la questione se l&#039;aria, quando è ingombra di vapori <lb></lb>nuvolosi preme sul mercurio del Barometro più o meno, che quando è lim­<lb></lb>pida e serena. </s>

<s>La decisione dall&#039;altra parte era riserbata ai fatti, i quali, <lb></lb>quando fossero stati bene accertati, avrebbero avuto virtù d&#039;infirmare le <lb></lb>autorità, benchè grandissime, del Pascal e del Borelli. </s>

<s>E benchè paresse che <lb></lb>non dovesse la cosa presentar poi troppo grandi difficoltà, vedemmo come in <lb></lb>sul finir del secolo XVII andassero cauti e quasi non sicuri di sè tutti co­<lb></lb>loro, che trovarono le variazioni barometriche andar tutto al contrario di <lb></lb>quel che furono osservate a Parigi e a Pisa. </s></p><p type="main">

<s>L&#039;incertezza fu finalmente tolta fra noi dal Ramazzini, il quale confessò <lb></lb>liberamente essere stati, a persuaderlo del vero, più eloquenti i fatti, che <lb></lb>non la grande autorità del Borelli, amatissimo suo precettore. </s>

<s>Le osserva­<lb></lb>zioni ramazziniane furono fatte nel 1694, e pubblicate l&#039;anno appresso in <lb></lb>Modena, col titolo di <emph type="italics"></emph>Ephemerides barometricae mutinenses.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Incomincia l&#039;Autore il suo Discorso facendo osservar che a principio <lb></lb>aveva creduto piuttosto alle parole altrui, che ai fatti, d&#039;ond&#039;ebbe a trovarsi <lb></lb>incautamente aggirato ne&#039;medesimi errori. </s>

<s>“ Iisdem erroribus aliorum scripta <lb></lb>me quoque per aliquot tempus transversum egisse fateri non pudet, ratio­<lb></lb>cinio enim celeberrimi viri I. </s>

<s>Alphonsi Borelli, in opere tam commendato <lb></lb><emph type="italics"></emph>De motionibus naturalibus a gravitate pendentibus,<emph.end type="italics"></emph.end> nimis fidens putabam. </s>

<s><lb></lb>Imo cum tanto praeceptore iurassem quod nebuloso coelo et impendente <lb></lb>pluvia ob auctam, saltem probabiliter, aeris gravitatem, altius in fistula de­<lb></lb>buisset elevari mercurius, sicuti post pluviam aere repurgato et redeunte <lb></lb>serenitate deprimi. </s>

<s>Verum ex observationibus singulis diebus in hac urbe, <lb></lb>per integrum annum, accurate mihi habitis, deprehendi me non leviter de­<lb></lb>ceptum ac toto coelo errasse: constanter enim, post diuturnam serenitatem, <lb></lb>coelo nubibus obducto, ac imminenti pluvia, cum aerem quilibet graviorem <lb></lb>crederet, mercurium in fistula descendere observavi, attolli autem post plu­<lb></lb>viarum descensum, aere serenato. </s>

<s>Validissima equidem sunt rationum mo-<pb xlink:href="020/01/882.jpg" pagenum="325"></pb>menta, quibus Vir clarissimus statuminare satagit propositionem suam CXV <lb></lb>quae sic habet: <emph type="italics"></emph>Mercurius in fistula torricelliana altius elevatur, dum aer <lb></lb>nebulis pluviosis impregnata, et postquam pluvia delapsa est, denuo mer­<lb></lb>curius in fistula deprimitur.<emph.end type="italics"></emph.end> Ast in contrarium ipsa reclamat experentia, <lb></lb>quae ratiociniis nostris persaepe illudit et ingeniosa conficta, sed falsis fun­<lb></lb>damentis superstructa, facillime diruit ” (Mutinae 1695, pag. </s>

<s>II, III). </s></p><p type="main">

<s>Nel qualificar così indirettamente il Ramazzini le dottrine borelliane per <lb></lb>ingegnose finzioni, si sentiva da un&#039;altra parte inclinare alla riverenza verso <lb></lb>un tanto precettore, e non sapendo far meglio si studiava di dar nuova forma <lb></lb>a quelle stesse ingegnose finzioni, per accomodarle, quanto fosse possibile, <lb></lb>alla realtà de&#039;fatti osservati. </s>

<s>Vedemmo quanto docilmente secondasse il Bo­<lb></lb>relli i placiti filosofici del Gassendo, il quale affidava al gioco delle parti­<lb></lb>celle sulfuree e nitrose sollevate dalla terra e disperse per l&#039;aria alcuni par­<lb></lb>ticolari effetti di Meteorologia. </s>

<s>Anche il Ramazzini dunque, vedendola così <lb></lb>favorita dal suo Borelli, ebbe ricorso a quella ipotesi. </s>

<s>“ Suppono itaque e <lb></lb>globo terraqueo non solum vapores, qui sunt pluviarum materia, sed mul­<lb></lb>tas exhalationes diversae indolis continuo plus et minus protrudi et aeri com­<lb></lb>misceri, ut particulas sulphureas, aluminosas, vitriolicas, mercuriales, etc. </s>

<s>” <lb></lb>(ibi, pag. </s>

<s>XLVII). </s></p><p type="main">

<s>Fatta questa supposizione, congettura il Nostro che la maggior gra­<lb></lb>vezza, che si sperimenta aver l&#039;aria quando il cielo è sereno, sia dovuta <lb></lb>principalmente a quelle invisibili particelle saline terrestri, dalle quali poi <lb></lb>venendo rilavata l&#039;aria stessa, quando i vapori si condensano e cadono in <lb></lb>pioggia, non è maraviglia se men leggermente prema sulla superficie della <lb></lb>Terra. </s>

<s>“ Et hoc pacto, ob harum partium mineralium et alterius generis <lb></lb>praecipitationem et exclusionem ab aeris poris, aer ipse redditur levius ” <lb></lb>(ibi, pag. </s>

<s>LIV). </s></p><p type="main">

<s>Le osservazioni barometriche del Ramazzini, dalle quali risultava avve­<lb></lb>nir di fatto tutto al contrario di quel che credevasi di avere osservato e di­<lb></lb>mostrato il Borelli, trovarono com&#039;è facile a supporre, contradittori, fra&#039;quali <lb></lb>un Francesco Torti, che usci fuori con una sua prima Dissertazione, alla <lb></lb>quale poi soggiunse <emph type="italics"></emph>Dissertatio epistolaris altera triceps circa mercurii <lb></lb>motiones in Barometro,<emph.end type="italics"></emph.end> stampata da Bartolommeo Soliani in Modena, nel­<lb></lb>l&#039;anno 1698. Gli argomenti del Torti però non son di molta importanza, ri­<lb></lb>ducendo la loro forza in considerar la grande autorità del Borelli, quasi fosse <lb></lb>incredibile in tant&#039;uomo un così grave errore. </s></p><p type="main">

<s>Altro più valido oppositore ebbe l&#039;Autor delle Effemeridi Modanesi nello <lb></lb>Schelhamer, il quale ben persuaso dell&#039;errore preso dal Borelli, e conve­<lb></lb>nendo che i fatti passavan pure a quel modo che gli aveva osservati il Ra­<lb></lb>mazzini, negava però l&#039;ipotesi ramazziniana, giudicandola inverisimile, e ne <lb></lb>proponeva una sua propria. </s>

<s>Fece di ciò il soggetto a un&#039;Epistola stampata <lb></lb>in Modena nel 1698, e indirizzata a Luca Schroek col titolo seguente: “ So­<lb></lb>lutio problematis cur mercurius in tubo torricelliano, seu Barometro, plu­<lb></lb>vioso tempore descendat cum deberet ascendere. </s>

<s>” </s></p><pb xlink:href="020/01/883.jpg" pagenum="326"></pb><p type="main">

<s>Le ragioni per cui lo Schelhamer crede l&#039;ipotesi del Ramazzini inve­<lb></lb>rosimile, son queste: prima, che non si vede e non s&#039;intende come e d&#039;onde <lb></lb>abbiano origine le particelle nitrose nell&#039;aria, non trovandosene altro che in <lb></lb>alcuni luoghi eccezionali assai leggeri vestigi; poi è da notar che, mentre <lb></lb>s&#039;intende a levar via con quella ipotesi un paradosso, s&#039;incappa in un altro <lb></lb>paradosso maggiore, qual sarebbe che un corpo galleggi in un mezzo tanto <lb></lb>più leggero in specie. </s>

<s>“ Admissa ratione cl. </s>

<s>Ramazzini consequens aliud <lb></lb>absurdum colligeretur. </s>

<s>Hoc enim posito, particulas salinas, nitrosas, terreas <lb></lb>in aere innatantes plus millies superare necessum foret ipsius aeris pondus <lb></lb>in quo natant, adeoque graviora corpora in leviori innatare, seu aerem ma­<lb></lb>ius pondus substinere quam ipse constituat. </s>

<s>Quod facile est ostendere. </s>

<s>Nam <lb></lb>si aqua eas deprimere et praecipitare ex aere debet, oportet eam replere <lb></lb>omnes aeris poros illosque totos, nam alias possent utraque in iisdem poris <lb></lb>simul haerere. </s>

<s>At aqua millies aequat pondus aeris: fit autem ille levior ex <lb></lb>hypothesi, si aquosae deturbant salinas. </s>

<s>Ergo necessum est eas aqua omni <lb></lb>in aere contenta fuisse graviores, adeoque plus millies aeris pondus supe­<lb></lb>rasse ” Epistola ecc., Mutinae 1698, pag. </s>

<s>4, 5). </s></p><p type="main">

<s>La soluzione, dall&#039;altro canto, che il Medico tedesco proponeva contro <lb></lb>quella del nostro Italiano, era semplicissima, e ragionevolissima, perchè così <lb></lb>ragionava: Se i nuvoli stanno sospesi per l&#039;aria, dunque son più leggeri <lb></lb>dell&#039;aria: dunque a ciel nuvoloso il mercurio nel Barometro è premuto in <lb></lb>parte dall&#039;aria soprastante, e in parte da una cosa ch&#039;è più leggera del­<lb></lb>l&#039;aria; dunque dev&#039;esser premuto men fortemente che quando la colonna <lb></lb>è tutta composta d&#039;aria schietta, ossia, quando il cielo è tutto sereno. </s></p><p type="main">

<s>Questa spiegazione, che dicemmo essere semplicissima e atta a persua­<lb></lb>der facilmente, non riusciva però compiuta, essendo che il mercurio nello <lb></lb>strumento seguita a mantenersi basso, anco quando i vapori condensati in <lb></lb>gocciole divengono talmente più gravi in specie dell&#039;aria, che sono spinti a <lb></lb>cader giù in mezzo ad essa. </s>

<s>Dall&#039;altra parte veniva dallo Schelhamer, col­<lb></lb>l&#039;argomento riferito di sopra, così ben dimostrata l&#039;inverosimiglianza delle <lb></lb>particelle saline notanti per l&#039;aria, e la loro inefficacia in produr le varia­<lb></lb>zioni barometriche, da doversene persuadere anche lo stesso Ramazzini, il <lb></lb>quale, arretratosi innanzi alle grandi difficoltà che presentava il problema, <lb></lb>si rivolse al celebre amico suo Gotifredo Leibniz per averne la soluzione. </s></p><p type="main">

<s>Il Leibniz invocò l&#039;aiuto della Meccanica, e rappresentò gli effetti me­<lb></lb>teorologici per mezzo di uno strumento, che ha grandissima somiglianza con <lb></lb>quella Bilancia immaginata e descritta da Galileo (Alb. </s>

<s>XIII, 309) per espe­<lb></lb>rimentare la forza della percossa. </s>

<s>“ Esto tubus AB (fig. </s>

<s>65) infra clausus <lb></lb>in B, aqua plenus, erectus, ex librae extremo suspensus, ac cum pondere <lb></lb>opposito in aequilibrio constitutus. </s>

<s>Ibi in aquae superficie natet cavum ali­<lb></lb>quod corpus D, ex materia gravi, casurum si aqua intraret. </s>

<s>Ponamus obtu­<lb></lb>ratum esse eius foramen, sed ita ut paulatim aquae pervium fiat; ergo, ubi <lb></lb>ea intraverit, descendet corpus D versus fundum B. </s>

<s>His positis, durante de­<lb></lb>scensu corporis D, cessaturum esse aequilibrium aio, descensurumque pon-<pb xlink:href="020/01/884.jpg" pagenum="327"></pb>dus C ac totum tubum AB elevatum iri. </s>

<s>Cuius rei ratio est manifesta quod, <lb></lb>quantum descendit D, in tantum ab aqua tubi libra non sustinetur, et ea­<lb></lb>tenus non resistit ponderi opposito. </s>

<s>Compara iam pondus C cum hydrar­<lb></lb><figure id="id.020.01.884.1.jpg" xlink:href="020/01/884/1.jpg"></figure></s></p><p type="caption">

<s>Figura 65.<lb></lb>gyro, aquam tubi cum aeris co­<lb></lb>lumna, corpus natans D guttis plu­<lb></lb>viae. </s>

<s>Nempe, cum guttae tam gran­<lb></lb>des fiunt ut amplius ab aere non <lb></lb>sustineantur, descendereque inci­<lb></lb>piunt, tota columna aeris levior <lb></lb>est quam ante, mercuriumque in <lb></lb>tubo suspensum ad priorem altitu­<lb></lb>dinem non sustinebit, itaque de­<lb></lb>scendit nonnihil mercurius. </s>

<s>Con­<lb></lb>tra, sereno aere, guttae aquae ita <lb></lb>imminuuntur, et per aerem di­<lb></lb>sperguntur, ut per se descendere <lb></lb>non possint ” (Gotifredi G. </s>

<s>Leib­<lb></lb>nitii Op. </s>

<s>Omn., T. II, P. II, Ge­<lb></lb>nevae 1768, pag. </s>

<s>75). </s></p><p type="main">

<s>Ma, anche quando il vapore elastico diffuso nel ciel sereno si condensa <lb></lb>in nuvola, il Barometro si abbassa, eppur la nuvola non discende, e riman <lb></lb>tuttavia ad aggiunger peso a quell&#039;aria, sulla quale galleggia; cosicchè, per <lb></lb>questa parte, lo sperimento leibniziano riusciva difettoso, e insufficiente a <lb></lb>rappresentar tutta intiera la verità del fatto meteorologico. </s>

<s>Piacque nono­<lb></lb>stante al Ramazzini quella meccanica dimostrazione, e ne facilitò la pratica <lb></lb>sperimentale, tenendo sospeso per un filo al giogo della bilancia un corpo <lb></lb>grave immerso nell&#039;acqua del tubo; corpo che, reciso il filo, cadeva natu­<lb></lb>ralmente in fondo trattovi dal proprio peso. </s></p><p type="main">

<s>Il Desaguliers però messe in mala fama, nelle Transazioni anglicane <lb></lb>del 1717, quel che tanti altri avevano applaudito e, o fosse per malizia, o <lb></lb>fosse per non aver bene atteso ai particolari della descrizione leibniziana, <lb></lb>supponeva che il peso, invece di gravar sulla bilancia, come il Leibniz di­<lb></lb>ceva, fosse, prima di cader per l&#039;acqua, sostenuto da qualche forza stra­<lb></lb>niera. </s>

<s>Quella scrittura del Desaguliers parve una diffamazione al nostro Pie­<lb></lb>ranton Michelotti, il quale prese perciò a far del celeberrimo amico suo le <lb></lb>difese concludendole in queste parole: </s></p><p type="main">

<s>“ Quare phaenomenon Barometri a celeberrimo Leibnitio optime.... <lb></lb>explicatur per guttas aqueas primo minores suspensas haerentes in aere, <lb></lb>quae et atmosphaeram graviorem reddunt, et columnam mercurialem in tubo <lb></lb>altius elevant; postea vero in grandiores massulas coalescentes, atque iccirco <lb></lb>superficiebus minoribus quam earum moles exigere videntur, comprehen­<lb></lb>sas, gravitate sua vim fricationis superantes: quae itaque, quum descendere <lb></lb>incipiunt, seseque a nexu villorum aereorum, quibus implicabantur, expe<gap></gap><lb></lb>diunt, statim ipsa atmosphaera levior redditur, ac proinde mercurius minu<gap></gap><pb xlink:href="020/01/885.jpg" pagenum="328"></pb>quam antea pressus protinus in tubo descendit ” (De separatione liquid., <lb></lb>Venetiis 1721, pag. </s>

<s>47, 48). </s></p><p type="main">

<s>Che il fenomeno del Barometro però fosse dal Leibniz ottimamente spie­<lb></lb>gato, si sarebbe potuto credere al Michelotti, quando fosse stato vero che il <lb></lb>livello del mercurio si abbassa dentro la canna, solamente nell&#039;atto che le <lb></lb>gocciole piovose cadono a terra; ma se l&#039;osservazione dimostra farsi quel­<lb></lb>l&#039;abbassamento anche nel tempo che le vescicole vaporose stanno sospese e <lb></lb>galleggianti per l&#039;aria, non si vede con qual ragione si potesse salvare quel­<lb></lb>l&#039;ingegnoso leibniziano esperimento. </s></p><p type="main">

<s>Chi rimedita intorno ai fatti fin qui narrati, non può non sentirsi preso <lb></lb>di gran maraviglia vedendo così grandi uomini, e nostrali e forestieri, aver <lb></lb>tanta fiducia nella soluzion di un problema, che seduceva coll&#039;artifizio dei <lb></lb>mezzi usati a risolverlo, senz&#039;essere però veramente risoluto: e dall&#039;altra <lb></lb>parte non facevasi nessun conto della vera soluzione sperimentale, che, sul <lb></lb>principio del raro e del denso, ne aveva data tanti anni prima il Guericke. </s></p><p type="main">

<s>Altro motivo del non s&#039;intender come mai Fisici così illustri non si <lb></lb>curassero d&#039;invocare il principio delle rarefazioni e de&#039;condensamenti del­<lb></lb>l&#039;aria, è che, per questo stesso principio, rendevasi anche di più la ragione <lb></lb>del variar che fa di livello il Barometro, nel così volubile moto del vento. <lb></lb></s>

<s>“ Mirum, ebbe a esclamare il Ramazzini, tornando a considerare le sue Effe­<lb></lb>meridi, mirum est autem quomodo australes venti mercurium deprimant, <lb></lb>boreales vero attollant ” (Ephaemerides cit., pag. </s>

<s>XXII). </s></p><p type="main">

<s>Pareva che tutta la maraviglia dovesse esser tolta, ripensando che l&#039;aria <lb></lb>tiepida spirata d&#039;Austro è più rarefatta, e quella fredda spirata da Borea è <lb></lb>più condensata. </s>

<s>Era un tal pensiero per verità passato in mente al Du-Ha­<lb></lb>mel, ma e&#039;fece poi più volentieri accoglienza a un altro pensiero, che lu­<lb></lb>singhiero gli ragionava essere i venti boreali sul mercurio più ponderosi, <lb></lb>perchè spirano di sopra in giù, e gli australi invece men ponderosi, perchè <lb></lb>spirano di traverso. </s>

<s>“ An potius flante aquilone aer fit densior? </s>

<s>Hinc tubo <lb></lb>optico velut undis asperior videtur, ac minus pellucet. </s>

<s>Hinc Pyrenaea iuga <lb></lb>nivibus cana et idem dicendum est de aliis montibus coelo sereno non tam <lb></lb>distincte eminus cernuntur ac coelo nubibus obducto. </s>

<s>Fieri etiam potest ut <lb></lb>Aquilo deorsum ruat, et multum materiae secum vehat, cum auster ex <lb></lb>transverso spiret ” (Philosophia cit., pag. </s>

<s>378). </s></p><p type="main">

<s>Essendosi così fatte difficoltà, prosegue ivi a dire il Du-Hamel, poco fa <lb></lb>proposte nella R. </s>

<s>Accademia parigina, <emph type="italics"></emph>hanc rationem satis idoneam red­<lb></lb>didit doctissimus Borellus,<emph.end type="italics"></emph.end> ed è la ragion che l&#039;Autore <emph type="italics"></emph>De motion. </s>

<s>natur.<emph.end type="italics"></emph.end><lb></lb>rendeva dalle variazioni barometriche, secondo il vario stato del cielo. </s>

<s>In <lb></lb>proposito di che, lasciando che altri ripensi a quel singolar favore ch&#039;ebbe <lb></lb>appresso i fisici di Parigi l&#039;ipotesi del Nostro, non è a tacer di un fatto <lb></lb>straordinario occorso a osservare in Pisa allo stesso Borelli, nè di quei che <lb></lb>faceva, dietro ciò, stravaganti presagi. </s></p><p type="main">

<s>“ Questa mattina (così scriveva il dì 5 marzo 1660 al principe Leo­<lb></lb>poldo) a caso mi sono accorto che, nel cannello ordinario dell&#039;argento vivo, <pb xlink:href="020/01/886.jpg" pagenum="329"></pb>si trova il mercurio sollevato intorno a 20 gradi sopra la massima altezza <lb></lb>osservata da me, quasi per lo spazio di tre anni.... Or questa gran stra­<lb></lb>vaganza, se è vero quello che io fin qui fermamente ho creduto, che la gra­<lb></lb>vezza maggi ore o minore dell&#039;aria sia cagione di tal disuguale sollevamento <lb></lb>dell&#039;argento vivo n el cannello, mostra che l&#039;aria, che sovrasta all&#039;orizzonte <lb></lb>di Pisa, sia eccessivamente e straordinariamente più aggravata di quel che <lb></lb>sia stato per altri tempi dalla mistura d&#039;altre materie vaporose acquee o ter­<lb></lb>restri. </s>

<s>A tale inaspettata stravaganza vedremo se ne segue qualche straor­<lb></lb>dinario effetto di eccessiva ed abbondante pioggia, oppure, quando le ma­<lb></lb>terie non sieno acquee e non venghino dissipate dai venti, vedremo se per <lb></lb>avventura ne succedesse qualche apparenza di quelle che sogliono prece­<lb></lb>dere alle comete ” (MSS. Cim., T. X, c. </s>

<s>10). </s></p><p type="main">

<s>Al principe Leopoldo non parve poi il fatto tanto straordinario, nè che <lb></lb>ne dovessero perciò seguire gli accennati pronostici, ma credeva che una <lb></lb>continuazione di venti gagliardi potesse accumulare gran quantità d&#039;aria so­<lb></lb>pra l&#039;orizzonte di Pisa e suoi contorni, dalla qual mole venisse ad accre­<lb></lb>scersi il peso dell&#039;aria, ed in conseguenza il sollevamento dell&#039;argento vivo <lb></lb>nel cannello (ivi, c. </s>

<s>12). </s></p><p type="main">

<s>Rispondeva il Borelli parergli difficil cosa che perseverassero i venti per <lb></lb>tanti giorni, e che potessero i cavalloni dell&#039;aria sostenersi così lungamente, <lb></lb>senza spianarsi. </s>

<s>Men difficile stimava a intendere “ che l&#039;aria, senza punto <lb></lb>alterar la sua sfericità, nè alzarsi sopra il livello estremo dell&#039;oceano aereo, <lb></lb>possa rendersi più grave di prima, in virtù dell&#039;aggiunta di nuove esalazioni <lb></lb>terree o acquee più gravi in spezie della stess&#039;aria ” (ivi, c. </s>

<s>14). </s></p><p type="main">

<s>Mentre che così in Toscana si disputava delle ragioni, il Guericke in <lb></lb>Magdeburgo osservava i fatti, e sopr&#039;essi fondava i suoi pronostici. </s>

<s>Aveva <lb></lb>egli notato tale costanza tra l&#039;abbassarsi del livello barometrico e il segui­<lb></lb>tarne qualche procella, che si confidò di presagirla, quasi come necessario <lb></lb>effetto di una causa già conosciuta. </s>

<s>“ Ego certe, cum praeterito anno (1660) <lb></lb>quo ingens ille ventus ac tempestas fuit, ex paulo ante memorato Experi­<lb></lb>mento singularem et extraordinariam aeris alterationem deprehendi, qui adeo <lb></lb>levis praeter consuetum alias modum fuit redditus, ut virunculi digitus (che <lb></lb>segnava il livello nel Barometro) infra infimum etiam in vitreo tubo nota­<lb></lb>tum punctum descenderit. </s>

<s>Quo viso praesentibus palam dixi magnam sine <lb></lb>dubio tempestatem alicubi extitisse. </s>

<s>Vix duae clapsae erant horae, cum ven­<lb></lb>tus ille procellosus in nostram etiam regionem, minus tamen violentus, quam <lb></lb>in Oceano fuerat, irruit ” (Esperim. </s>

<s>magdeburg. </s>

<s>cit., pag. </s>

<s>100). </s></p><p type="main">

<s>Questo modo però di presagir le procelle, per mezzo del Barometro, <lb></lb>non fu divulgato che nel 1672, quando pubblicò il Guericke i suoi Esperi­<lb></lb>menti nuovi di Magdeburgo. </s>

<s>Ebbe perciò ragione il Vossio, dando nel 1663 <lb></lb>alla luce il suo libro <emph type="italics"></emph>De motu marium et ventorum,<emph.end type="italics"></emph.end> di trattar dell&#039;Aero­<lb></lb>scopio <emph type="italics"></emph>ad praecognoscendas tempestates,<emph.end type="italics"></emph.end> e ch&#039;egli ivi nel cap. </s>

<s>XIX descrive, <lb></lb>come di uno strumento <emph type="italics"></emph>a nemine quod sciam hactenus observati.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il fondamento certo di que&#039;nuovi presagi posava tutto sul fatto che <pb xlink:href="020/01/887.jpg" pagenum="330"></pb>“ quandocumque ventus aut procella aliqua a mari oritur, sensim et mani­<lb></lb>feste deprimitur altitudinem hydrargiri, idque exacte ad legem et mensuram <lb></lb>ingruentis tempestatis. </s>

<s>Quando vero illa remittit et malacia redit, iterum <lb></lb>adscendit hydrargyrus.... Porro tantae utilitatis esse existimo hoc experi­<lb></lb>mentum ut nesciam an ullum aliud aeque tutum et idoneum ad praeviden­<lb></lb>das tempestates possit excogitari ” (Hagae Comitis, pag. </s>

<s>122). </s></p><p type="main">

<s>I presagi del Guericke e del Vossio però eran fondati sopra osserva­<lb></lb>zioni, che rendevano probabilissimo esser causa delle variazioni barometriche <lb></lb>il violento soffiar tempestoso de&#039;venti, ma non se ne aveva ancora una cer­<lb></lb>tezza sperimentale, che fu quasi un mezzo secolo dopo data dal valorosis­<lb></lb>simo Hawksbee. </s>

<s>Condensata l&#039;aria in un vaso, da cui facevala uscire in <lb></lb>soffi, che passassero sopra il mercurio della scodella, nella quale era im­<lb></lb>mersa la canna barometrica, osservava che a ogni soffio si abbassava nota­<lb></lb>bilmente nella stessa canna il livello. </s>

<s>Da un tale esperimento, ne conclu­<lb></lb>deva l&#039;Autore, “ abbiamo una chiara e naturale riprova della discesa e delle <lb></lb>vibrazioni del mercurio nelle violenti burrasche e tempeste. </s>

<s>Conciossiachè <lb></lb>l&#039;estrema forza di quelle folate di vento indeboliscono la pressione delle so­<lb></lb>prastanti ammosferiche colonne, da cui dee necessariamente seguire la di­<lb></lb>scesa del mercurio. </s>

<s>E quell&#039;interrotta ineguale azione di quelle folate, ov­<lb></lb>vero il presto e subito loro ritorno sono capaci di produrre e continuare i <lb></lb>moti vibratorii, cioè le spedite salite e discese di quello ” (Esperienze cit., <lb></lb>pag. </s>

<s>74). </s></p><p type="main">

<s>Così, in mezzo e dopo tante vicende, per le quali s&#039;è dovuta aggirare <lb></lb>la nostra storia, il Guericke e l&#039;Hawksbee fondavano quegli sperimenti, per <lb></lb>i quali finalmente s&#039;intese la vera causa delle variazioni barometriche, e si <lb></lb>ridusse alle giuste ragioni il Barometro in presagir la pioggia o il sereno <lb></lb>la tranquillità dell&#039;aria, e l&#039;imperversar dei venti. </s></p><pb xlink:href="020/01/888.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del sistema del Mondo<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del sistema del Mondo immaginato dagli antichi Peripatetici: Della Sintassi platonica e della co­<lb></lb>pernicana, e quali fossero i primi loro incontri appresso gli stranieri. </s>

<s>— II. </s>

<s>Del Sistema coper­<lb></lb>nicano in Italia, e segnatamente di Galileo Galilei. </s>

<s>— III. </s>

<s>Del Dialogo galileiano sopra i due <lb></lb>Massimi sistemi del Mondo. </s>

<s>— IV. </s>

<s>Delle avventure del Copernicismo dai tempi di Galileo alla <lb></lb>fine del secolo XVII. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I mezzi suggeriti dall&#039;arte sperimentale per lo studio delle Meteore si <lb></lb>riducono sostanzialmente a quelli, che suggerì l&#039;arte stessa ai Fisici per lo <lb></lb>studio degli astri, i quali pure, essendo costituiti in regioni così remote da <lb></lb>noi, non possono esser soggetto immediato e diretto ai nostri artificiosi espe­<lb></lb>rimenti. </s>

<s>Come perciò la storia delle cose passate ci mostrava la Meteorolo­<lb></lb>gia aiutarsi d&#039;imitare con l&#039;arte la Natura, e così riuscire ad intendere, per <lb></lb>la similitudine degli effetti osservati, la similitudine delle cause operanti; <lb></lb>s&#039;aiutò in pari modo l&#039;Astronomia rappresentando graficamente in mappe o <lb></lb>con macchine artificiali il moto e le varie apparenze dei pianeti. </s>

<s>I Globi e <lb></lb>le Sfere armillari son d&#039;uso tanto antico quanto sono antichi i principii della <lb></lb>scienza astronomica, ma chi volesse avere un esempio dell&#039;efficacia di così <lb></lb>fatti artificii, i quaii imitando gli effetti ne fanno argomentar sicuramente alle <lb></lb>cause naturali, ripensi a quella Macchinetta inventata dai nostri Accademici <lb></lb>del Cimento, per la quale, rappresentandosi tutti i fenomeni dell&#039;anello di <lb></lb>Saturno, si potè dare una fisica dimostrazione del sistema ugeniano. </s></p><p type="main">

<s>Simili in certo modo alle Meteore son, per la studiosa osservazione, gli <lb></lb>oggetti, i quali, benchè non si trovino costituiti in aria ma sopra la super-<pb xlink:href="020/01/889.jpg" pagenum="332"></pb>ficie terrestre, hanno nulladimeno rispetto a noi, o per gl&#039;impedimenti in­<lb></lb>terposti o per la lontananza, le loro vie inaccessibili. </s>

<s>Dette un sì fatto stu­<lb></lb>dio occasione a inventar le diottre e i tubi aperti a diriger la linea di mira, <lb></lb>e a togliere le irradiazioni avventizie, supplendo opportunamente e secondo <lb></lb>la loro possibilità al difetto de&#039;Canocchiali. </s>

<s>Nè perciò i Canocchiali stessi <lb></lb>dispensarono nelle osservazioni celesti dall&#039;arte imitativa delle apparenze na­<lb></lb>turali, ma dimostrando più secondo il vero quelle tali apparenze, riuscirono <lb></lb>efficacissimi a conformar meglio alle imitabili opere della Natura gli artifi­<lb></lb>ciosi nostri macchinamenti. </s></p><p type="main">

<s>Tutti questi apparati strumentali però appartengono all&#039;Astronomia fisica, <lb></lb>intorno alla quale solamente dovrebbe intrattenersi la nostra storia, ma per­<lb></lb>chè la fisica, senza la matematica, essendo materia senza forma, riuscirebbe <lb></lb>inintelligibile, non si può lasciar addietro da noi di far qualche cenno del­<lb></lb>l&#039;Astronomia matematica, la quale precede alla fisica, come sempre per legge <lb></lb>universale la sintesi precede all&#039;analisi, o come la forma precede alla materia. </s></p><p type="main">

<s>Grande Sintassi perciò soleva chiamarsi il sistema del mondo dai Filo­<lb></lb>sofi antichi. </s>

<s>Il luogo da giudicar l&#039;ordine e la particolare disposizione di <lb></lb>quella Sintassi è per noi naturalmente la Terra, dalla quale, osservandosi il <lb></lb>Cielo, in due modi ugualmente bene si salvavano le apparenze di lui: o col <lb></lb>supporre ch&#039;egli si volga attorno alla terra immota o che la Terra stessa <lb></lb>ruoti intorno al suo asse. </s>

<s>Era quel primo supposto, senza dubbio, più con­<lb></lb>forme alle esteriori apparenze e meglio accomodato all&#039;intelligenza del volgo, <lb></lb>ma que&#039;più sottili Filosofi, così esperti dell&#039;inganno che spesso ci fanno i <lb></lb>sensi, non dubitarono di attenersi al secondo, come più conforme a una <lb></lb>meglio ordinata architettura dell&#039;Universo. </s></p><p type="main">

<s>S&#039;annoverano tra così fatti Filosofi quegli antichi italiani discepoli di <lb></lb>Pitagora, i quali ebbero poi nel gran Platone la più splendida rappresen­<lb></lb>tanza. </s>

<s>Si sa essere le dottrine di lui informate da quel principio che non <lb></lb>si dee credere ai sensi, i quali si limitano alla materia, ma alla mente, nella <lb></lb>quale irraggia la divina intelligibilità della forma. </s>

<s>Platone perciò, più che <lb></lb>con gli occhi del corpo, contempla il cielo con le vedute dell&#039;intelletto, e <lb></lb>conclude che l&#039;apparir la immensa sfera stellata aggirarsi tutta intorno alla <lb></lb>nostra piccola Terra è un inganno degli occhi, e che non può la Sapienza <lb></lb>del Creatore aver disposte le cose così fuor d&#039;ordine, come si giudicherebbe <lb></lb>dai primi aspetti. </s></p><p type="main">

<s>La lampada, che d&#039;ogni parte rischiara il mondo, è il Sole, e il sa­<lb></lb>pientissimo Ordinatore dev&#039;aver collocata quella lampada ardente nel mezzo <lb></lb>del bellissimo Tempio. </s>

<s>Intorno al Sole immoto perciò, e costituito nel cen­<lb></lb>tro della immota sfera stellata, si rivolgono in orbite circolari Saturno, Giove, <lb></lb>Marte e la Terra con la sua Luna. </s>

<s>La collocazione così ordinata di questi <lb></lb>pianeti era per Platone certissima, perchè venivano a dimostrarla tale i loro <lb></lb>osservati aspetti: in gran dubbio rimaneva ancora però il luogo dove oppor­<lb></lb>tunamente collocarsi Venere e Mercurio. </s>

<s>Le loro elongazioni tanto più ri­<lb></lb>strette di quelle che si fan da Saturno, da Giove, e dallo stesso Marte, e il <pb xlink:href="020/01/890.jpg" pagenum="333"></pb>non essersi veduti mai Venere e Mercurio nell&#039;opposizione, avrebbero con­<lb></lb>sigliato il Filosofo a collocarli tra la Terra e il Sole, ma a lui, che teneva <lb></lb>tutti i pianeti essere per sè oscuri, se non in quanto gli allumina il Sole, <lb></lb>si faceva, ad ammettere quell&#039;ordinamento, una grandissima difficoltà, ed <lb></lb>era che, costituiti Venere e Mercurio inferiori, avrebbero dovuto mostrar, <lb></lb>come la Luna, la varietà delle fasi, le quali, perchè non furono osservate <lb></lb>mai, fecero deliberar finalmente Platone a costituir superiori anche quelli, <lb></lb>che parevano essere i due più prossimi Pianeti. </s></p><p type="main">

<s>Nel Timeo dunque, dove si leggono queste cose, troviamo così descritta, <lb></lb>o diciam meglio accennata, la prima gran Sintassi dell&#039;Universo. </s>

<s>Successe <lb></lb>poco dopo Aristotile, di principii tutt&#039;affatto diversi, come sappiamo. </s>

<s>Egli <lb></lb>nel II Libro <emph type="italics"></emph>De coelo<emph.end type="italics"></emph.end> discusse la question pitagorica, alla quale, dop&#039;aver <lb></lb>riferita l&#039;opinion di coloro che stabiliscon la Terra nel mezzo, accenna <lb></lb>con sì fatte parole: “ Pythagorici autem habitantes Italiam contradicunt illis <lb></lb>et dicunt.... quod Terra est stellarum una et revolvitur circulariter et ex <lb></lb>motu eius circulari fit nox et dies ” (Tomus V, Operum, Venetiis 1560, <lb></lb>c. </s>

<s>151 v.). </s></p><p type="main">

<s>Il Filosofo però rifiuta una così fatta ipotesi per più ragioni: Prima, <lb></lb>perchè il moto circolare è violento e non può perciò essere eterno; poi, <lb></lb>perchè se si movesse la Terra si dovrebbe veder qualche mutazione farsi <lb></lb>nelle stelle fisse “ hoc autem non videtur fieri, sed semper eadem apud <lb></lb>eadem loca ipsius et oriuntur et occidunt ” (ibi, c. </s>

<s>167 v.). Soggiunge inol­<lb></lb>tre che, movendosi la Terra, i proietti in gran distanza non tornerebbero <lb></lb>al luogo preciso d&#039;onde furon partiti, ond&#039;è che da tutto questo conclude: <lb></lb>“ Manifestum est igitur quod necesse est in medio Terram esse et immo­<lb></lb>bilem ” (ibi, c. </s>

<s>169). </s></p><p type="main">

<s>Notabile è quel che dice Aristotile contro i Pitagorici nell&#039;accingersi a <lb></lb>confutarli, accusandogli di avere sbagliato metodo in filosofar delle cause na­<lb></lb>turali, imperocchè non ragionan costoro, secondo lui, sui fatti, come si con­<lb></lb>verrebbe, ma i fatti accomodano alle loro intenzioni: “ Et opinantur hanc <lb></lb>opinionem, quia non quaerunt cognitionem causarum rerum et sermonum <lb></lb>in eis ex visu, sed mutant visum secundum suam voluntatem, donec labo­<lb></lb>rant in confirmando illam voluntatem ” (ibi, c. </s>

<s>151 v.). </s></p><p type="main">

<s>Dicemmo essere quell&#039;accusa notabile, perchè ci porge motivo d&#039;argo­<lb></lb>mentare che la questione del moto e della quiete della Terra si risolvesse <lb></lb>ne&#039;metodi filosofali variamente seguiti da Aristotile e da&#039;Pitagorici precur­<lb></lb>sori a Platone. </s>

<s>Del resto si può quell&#039;accusa ritorcere contro chi la mosse, <lb></lb>imperocchè, non i Pitagorici, ma gli Aristotelici piuttosto accomodavano i <lb></lb>fatti alle loro intenzioni. </s>

<s>La Terra posta immobile nel mezzo e corteggiata <lb></lb>tutto intorno dal Cielo configurava il mondo fisico sull&#039;esempio del mondo <lb></lb>intellettuale, in mezzo a cui, secondo Aristotile, risiede e regna la Ragione <lb></lb>legislatrice e dea. </s>

<s>Nel sistema pitagorico, al contrario, non è lo scettro del <lb></lb>regno posto in mano alla Ragione dell&#039;uomo rappresentata nella Terra, ma <lb></lb>nelle mani della Sapienza e Onnipotenza di Dio rappresentato nel Sole. </s>

<s>Tanto <pb xlink:href="020/01/891.jpg" pagenum="334"></pb>è poi propria questa differenza ai due differenti sistemi filosofici che, in <lb></lb>mezzo alla lunga e ostinata tirannide aristotelica, sempre si tornò a cono­<lb></lb>scere il moto della Terra intorno al Sole, che insorsero gl&#039;intelletti a ricon­<lb></lb>quistare la loro filosofica libertà con Platone. </s></p><p type="main">

<s>Nell&#039;ecclettismo enciclopedico della scuola alessandrina Aristarco di <lb></lb>Samo professa il moto della Terra, e Archimede, nel porre il fondamento a <lb></lb>quel suo celebre calcolo dell&#039;arena, lo segue, e di lui e della sua ipotesi <lb></lb>così scrive: “ Ea vero quae habentur ab astronomis scripta discutiens Ari­<lb></lb>starchus Samius hypotheses quasdam scriptis prodidit, ex quibus suppositis <lb></lb>consequitur mundum multiplicem esse eius qui mox praescriptus est. </s>

<s>Sup­<lb></lb>ponit enim inerrantia sidera et solem non moveri. </s>

<s>Terram vero ferri in gy­<lb></lb>rum circa solem qui in medio stadio iacet ” (Opera, Parisiis 1615, pag. </s>

<s>449). </s></p><p type="main">

<s>Tolomeo però si volse a professare altre dottrine. </s>

<s>Si potrebbe credere <lb></lb>che fosse rimasto impaurito delle contradizioni e delle persecuzioni, le quali <lb></lb>ebbe a sopportare Aristarco, ma forse correvano allora tempi in cui, affie­<lb></lb>volitasi l&#039;autorità di Platone, la tirannide aristotelica soggiogava più prepo­<lb></lb>tente gl&#039;ingegni. </s>

<s>In qualunque modo la Grande sintassi tolemaica era la <lb></lb>più viva incarnazione di quello spirito, che Aristotile infuse nella sua Fi­<lb></lb>losofia. </s></p><p type="main">

<s>Chi ben considera infatti è in quella Sintassi il Filosofo che assetta il <lb></lb>mondo a suo piacere, e gli prescrive le leggi. </s>

<s>I pianeti sono ora più vicini <lb></lb>ora più lontani alla Terra, perchè si volgono in orbite eccentriche intorno <lb></lb>ad essa; e ora si mostran retrogradi, ora stazionarii, perchè le orbite son <lb></lb>deferenti ciascuna di bene proporzionati epicicli. </s>

<s>Qui l&#039;orgoglio filosofico <lb></lb>riman sodisfatto, perchè può sottilizzare a suo modo intorno all&#039;Architettura <lb></lb>del mondo, ma no nella Sintassi platonica, la quale esclude ogni sottigliezza, <lb></lb>non richiedendo altro che la semplice regolarità delle forme geometriche, e <lb></lb>si accora e diffida di sè il Filosofo, dovunque una tanto desiderata sempli­<lb></lb>cità non gli sia dato di conseguirla. </s></p><p type="main">

<s>Come il vento di quell&#039;orgoglio filosofico spirasse d&#039;Egitto sopra le no­<lb></lb>stre contrade e vi mantenesse così lungamente il bel sereno del cielo pita­<lb></lb>gorico rannuvolato, non è qui luogo a narrare. </s>

<s>Soffi di vento contrario, a <lb></lb>dissipar quelle nubi, spiravano nel secolo XV da que&#039;libri illustrati e ri­<lb></lb>messi in onore dai cultori delle lettere umane, come per esempio dalle <emph type="italics"></emph>Que­<lb></lb>stioni accademiche<emph.end type="italics"></emph.end> di Cicerone, nelle quali rinfrescavasi eloquentemente la <lb></lb>memoria di Niceta da Siracusa, e dalle <emph type="italics"></emph>Questioni naturali<emph.end type="italics"></emph.end> di Seneca, dove <lb></lb>proemiando l&#039;Autore rintuzza l&#039;orgoglio degli uomini, considerando essere <lb></lb>un misero punto quello su cui fieramente combattono, per dividersi i regni, <lb></lb>e poi nel Cap. </s>

<s>II del VII Libro eccita gagliardamente i Filosofi a rivolgersi <lb></lb>alle contemplazioni celesti “ ut sciamus in quo rerum statu simus, piger­<lb></lb>rimam sortiti an velocissimam sedem; circa nos Deus omnia an nos agat ” <lb></lb>(Venetiis 1522, c. </s>

<s>38 v.). </s></p><p type="main">

<s>Ma non era questa una voce, che potessero intenderla i così detti <emph type="italics"></emph>uma­<lb></lb>nisti.<emph.end type="italics"></emph.end> Cosimo de&#039;Medici e Lorenzo il Magnifico avevano, col loro senno e <pb xlink:href="020/01/892.jpg" pagenum="335"></pb>co&#039;loro favori, cooperato alla diffusione de&#039;libri e alla illustrazione degl&#039;in­<lb></lb>segnamenti platonici in Toscana, e di li per tutta l&#039;Italia, e quella che isti­<lb></lb>tuirono sotto il titolo di <emph type="italics"></emph>Accademia<emph.end type="italics"></emph.end> era una poderosa oste ordinata a insor­<lb></lb>gere contro la tirannide aristotelica. </s>

<s>Platone allora risorse a rammemorare <lb></lb>a&#039;Filosofi le sue dottrine cosmografiche negli scritti di Niccolò da Cusa, e <lb></lb>negli insegnamenti di Domenico Maria da Novara. </s></p><p type="main">

<s>Scendeva fra noi avventurosamente in quel tempo, di Prussia, Niccolò <lb></lb>Copernico, a cui la voce di Seneca si fece più che ad altri mai sentire po­<lb></lb>tente. </s>

<s>E giacchè i rinascenti studi letterarii in Italia gli avevano messi nelle <lb></lb>mani i libri di Cicerone, dove lesse l&#039;ipotesi di Niceta e i Placiti di Plu­<lb></lb>tarco gli riferivano essere una simile ipotesi approvata da Filolao; e dal­<lb></lb>l&#039;altra parte i Filosofi maestri di lui e i dotti italiani suoi familiari lo con­<lb></lb>sigliavano a veder quella pitagorica ipotesi rivestita della divina eloquenza <lb></lb>del loro Platone; sulla diritta scorta del Timeo si avvio il Copernico alle <lb></lb>sue contemplazioni celesti. </s></p><p type="main">

<s>Non esitò a rispondere dicendo col suo Autore che no <emph type="italics"></emph>circa nos Deus <lb></lb>omnia,<emph.end type="italics"></emph.end> ma che <emph type="italics"></emph>nos agit,<emph.end type="italics"></emph.end> giudicando di nessun peso gli argomenti, che ad­<lb></lb>ducevano contro questa sentenza Aristotile e Tolomeo. </s>

<s>Diceva questi che la <lb></lb>Terra si scompaginerebbe nel suo moto vertiginoso. </s>

<s>“ Sed cur non illud, <lb></lb>rispondeva il Copernico, etiam magis de mundo suspicatur, cuius tanto ve­<lb></lb>lociorem esse motum oportet quanto maius est coelum Terra? </s>

<s>” (De revo­<lb></lb>lutionibus ecc., Norimbergae 1543, c. </s>

<s>5 v.). Soggiungeva l&#039;altro che il moto <lb></lb>semplice, ossia il retto compete agli elementi semplici, ma no il circolare: <lb></lb>a cui rispondeva ancora il Copernico che anzi il moto circolare è più sem­<lb></lb>plice del retto, essendo che per la sua causa indeficiente <emph type="italics"></emph>aequaliter sem­<lb></lb>per volvitur<emph.end type="italics"></emph.end> (ibi, c. </s>

<s>6, v.). </s></p><p type="main">

<s>La Sintassi platonica però vide accortamente il Copernico che voleva <lb></lb>essere riformata, per quel che particolarmente concerne la collocazione di <lb></lb>Venere e di Mercurio. </s>

<s>Oltre al gran valore che avevano per lui gli argo­<lb></lb>menti delle elongazioni e del modo costante, che nelle loro congiunzioni <lb></lb>tengono i due Pianeti, v&#039;erano altre ragioni molto più concludenti, e ch&#039;ei <lb></lb>derivava direttamente dagli stessi principii platonici della simmetrica collo­<lb></lb>cazione delle sfere celesti. </s>

<s>Costituiti Venere e Mercurio superiori, un troppo <lb></lb>grande intervallo restava vuoto fra la Luna e il Sole, e dall&#039;altra parte irre­<lb></lb>golarità incompatibile col sapiente ordinamento degli altri Pianeti sarebbe <lb></lb>stata quella di far descrivere a&#039;due suddetti, in tanto minor tempo, orbite <lb></lb>maggiori di quella della Terra. </s></p><p type="main">

<s>Sentì il Copernico che tanti e così validi argomenti non potevano es­<lb></lb>sere nè distrutti nè infirmati da quell&#039;unico del non essersi veduti mai Ve­<lb></lb>nere e Mercurio nè dicotomi, nè falcati, perchè pensava non esser certa­<lb></lb>mente dimostrato che i pianeti siano per sè stessi oscuri, ond&#039;eravi luogo <lb></lb>a congetturare o che anch&#039;essi, i pianeti, abbiano lume proprio, o che per <lb></lb>tutta la loro mole, qualunque ne sia il riguardo, s&#039;imbevano de&#039;raggi solari. </s></p><p type="main">

<s>Tali erano i sentimenti e i pensieri dell&#039;Autore <emph type="italics"></emph>Delle rivoluzioni,<emph.end type="italics"></emph.end> ben-<pb xlink:href="020/01/893.jpg" pagenum="336"></pb>che cos<gap></gap> gn esponga come sovvenuti in mente ad altri. </s>

<s>“ De Venere vero <lb></lb>atque Mercurio diversae reperiuntur sententiae, eo quod non omnifariam <lb></lb>elongantur a Sole ut illi. </s>

<s>Quamobrem alii supra Solem eos collocant, ut <lb></lb>Patonis Timaeus.... Igitur qui Platonem sequuntur, cum existiment omne s <lb></lb>stellas, obscura alioqui corpora, lumine solari concepto resplendere, si sub <lb></lb>Sole essent, ob non multam ab eo divulsionem, dimidia aut certe a rotun­<lb></lb>ditate deficientes cernerentur. </s>

<s>Nam lumen sursum ferme, hoc est versus So­<lb></lb>lem, referrent acceptum ut in nova Luna vel desinente videmus.... Contra <lb></lb>vero qui sub Sole Venerem et Mercurium ponunt, ex amplitudine spatii <lb></lb>quod inter Solem et Lunam comperiunt, vendicant rationem.... Non ergo <lb></lb>fatentur in stellis opacitatem esse aliquam lunari similem, sed vel proprio <lb></lb>lumine, vel solari totis imbutas corporibus fulgere ” (ibi, c. </s>

<s>7 v.). </s></p><p type="main">

<s>Questa persuasione che dovessero in ogni modo, per le sopra dette ra­<lb></lb>gioni, essere Venere e Mercurio costituiti inferiori, veniva confermata nel <lb></lb>Copernico da Marziano Capella “ qui Encyclopediam scripsit, et quidem alii <lb></lb>Latinorum percalluerunt. </s>

<s>Existimant enim quod Venus et Mercurius cir­<lb></lb>cumcurrant Solem in medio existentem et eam ob causam ab illo non ul­<lb></lb>terius digredi putant, quam suorum convexitas orbium patiatur, quoniam <lb></lb>Terram non ambiunt ut caeteri sed absidas conversas habent ” (ibi, c. </s>

<s>8 v.). </s></p><p type="main">

<s>Nè è a tacere in tal proposito che fu questo sistema, derivato da&#039;più <lb></lb>antichi Egiziani nell&#039;Enciclopedia latina del Capella, subodorato per vero, <lb></lb>tanti anni prima che dal Copernico, dal nostro Alighieri, il quale sgonfiava <lb></lb>i tumori orgogliosi de&#039;Filosofi peripatetici divinamente traducendo l&#039;espres­<lb></lb>sione di Seneca “ Punctum est illud in quo navigatis, in quo bellatis, in <lb></lb>quo regna disponitis ” nell&#039;<emph type="italics"></emph>aiola che ci fa tanto feroci<emph.end type="italics"></emph.end> (Par., C. XXII, <lb></lb>v. </s>

<s>151). Il divino Cantore dunque, rivolgendosi indietro a contemplar le <lb></lb>sfere, che via via avea trasvolate, dice di aver di lì sostenuto l&#039;aspetto di <lb></lb>Iperione e di aver pur di lì veduto <emph type="italics"></emph>come si muove circa e vicino a lui <lb></lb>Maia e Dione<emph.end type="italics"></emph.end> (ivi, v. </s>

<s>143, 44). </s></p><p type="main">

<s>Così riformata la Sintassi platonica si riduceva alla seguente descri­<lb></lb>zione copernicana: “ Prima et suprema omnium est stellarum fixarum <lb></lb>sphaera seipsam et omnia continens, ideoque immobilis.... Sequitur erran­<lb></lb>tium primus Saturnus, qui XXX anno suum complet circuitum. </s>

<s>Post hunc <lb></lb>Jupiter duodecennali revolutione mobilis. </s>

<s>Deinde Mars, qui biennio circuit. </s>

<s><lb></lb>Quartum in ordine annua revolutio locum obtinet, in quo Terram cum orbe <lb></lb>lunari, tanquam Epicyclo, contineri diximus. </s>

<s>Quinto loco Venus nono mense <lb></lb>reducitur. </s>

<s>Sextum denique locum Mercurius tenet octuaginta dierum spacio <lb></lb>circumcurrens. </s>

<s>In medio vero omnium residet Sol ” (De revolut. </s>

<s>cit., c. </s>

<s>9). </s></p><p type="main">

<s>E qui il Copernico, col viso ritornando, come l&#039;Alighieri, per tutte <lb></lb>quante le sette sfere illuminate dal Ministro maggior della Natura “ quis <lb></lb>enim, esclama con enfasi platonica, in hoc pulcherrimo templo lampadem <lb></lb>hanc in alio vel meliori loco poneret quam unde totum simul possit illu­<lb></lb>minare? </s>

<s>Siquidem non inepte quidam lucernam mundi, alii mentem, alii <lb></lb>rectorem vocant ” (ibi pag. </s>

<s>9. v.). </s></p><pb xlink:href="020/01/894.jpg" pagenum="337"></pb><p type="main">

<s>Mal si giudicherebbe però il merito del Copernico se si volesse tutto <lb></lb>ridurre all&#039;aver rinnovellata l&#039;ipotesi pitagorica, e all&#039;aver riformata la Sin­<lb></lb>tassi platonica: ma egli restaurò le fondamenta all&#039;Astronomia, costituendo <lb></lb>il Sole per centro da misurare indi la più giusta distanza de&#039;pianeti da lui, <lb></lb>e i periodi delle loro circumvoluzioni. </s>

<s>A far ciò, con tutto il rigore mate­<lb></lb>matico, e dietro quelle osservazioni possibili allora, per il difetto e per la <lb></lb>imperfezione degli strumenti astronomici, dedicò l&#039;Autore gli altri cinque <lb></lb>libri dell&#039;immortale Opera sua. </s></p><p type="main">

<s>I calcoli laboriosi disposti in Tavole e conclusi in canoni, per adattarli <lb></lb>all&#039;uso, erano stati da lungo tempo condotti, ed erano già in ordine di <lb></lb>uscir fuori alle stampe i capitoli e i libri, dove di que&#039;calcoli si espone­<lb></lb>vano dal Copernico le ragioni, ma non si risolveva ancora l&#039;Autore di pub­<lb></lb>blicarli. </s>

<s>Sentiva che troppo gagliardo tuttavia durava il vento peripatetico, <lb></lb>che avrebbe contrastato col suo malefico soffio alla diffusion dell&#039;aura de&#039;suoi <lb></lb>nuovi concetti. </s>

<s>L&#039;insurrezion de&#039;Platonici, perduti in oziose contemplazioni <lb></lb>sotto l&#039;ombre deliziose de&#039;platani di Careggi, vedeva esser riuscita ineffi­<lb></lb>cace, nè sperava che gli ammiratori di Pico della Mirandola, impugnatore <lb></lb>dell&#039;Astronomia, avrebbero fatta a lui migliore accoglienza che non a Luca <lb></lb>Paciolo, a Leonardo da Vinci e ad Amerigo Vespucci. </s></p><p type="main">

<s>Que&#039;calcoli copernicani nonostante, potendosi applicare alla riforma del <lb></lb>Calendario tanto desiderata, promettevano di aver virtù, mostrando l&#039;utilità <lb></lb>de&#039;frutti, di salvare il fiore delle dottrine, ond&#039;è che Niccolò Schonberg, <lb></lb>cardinale di Capua, richiese l&#039;Autore gli rimettesse le carte dottissime e la­<lb></lb>boriose per farle stampare a sue spese. </s>

<s>“ Dedi autem negotium Theodorico <lb></lb>a Reden ut istic, meis sumptibus, omnia describantur atque ad me transfe­<lb></lb>rantur. </s>

<s>” </s></p><p type="main">

<s>L&#039;edizione fu fatta in Norimberga nel 1543 e dedicata a Papa Paolo III <lb></lb>principe di quella Repubblica ecclesiastica, alla quale sperava il Copernico <lb></lb>non sarebbero per riuscire inutili le sue fatiche. </s>

<s>“ Nam non iam multo ante <lb></lb>sub Leone X cum in Concilio lateranensi vertebatur quaestio de emendando <lb></lb>Calendario ecclesiastico, quae tum indecisa hanc solummodo ob causam man­<lb></lb>sit, quod annorum et mensuum magnitudines, atque Solis et Lunae motus <lb></lb>nondum satis dimensi haberentur. </s>

<s>Ex quo equidem tempore his accuratius <lb></lb>observandis animum intendi, admonitus a praeclarissimo viro D. </s>

<s>Paulo epi­<lb></lb>scopo Semprionensi, qui tum isti negotio praeerat. </s>

<s>” </s></p><p type="main">

<s>Conforme a queste copernicane osservazioni fu poi veramente, sotto <lb></lb>Gregorio XIII, regolato il Calendario, e fu tale il frutto che ne raccolse la <lb></lb>Repubblica ecclesiastica e la civile: ma per salvare i principii, che si ri­<lb></lb>guardaron da noi come il fiore in che allegarono que&#039;desideratissimi frutti, <lb></lb>s&#039;ebbero a ingaggiar fierissime battaglie, che tennero per più di un secolo <lb></lb>fra sè divisa la Repubblica letteraria. </s></p><p type="main">

<s>Che i Peripatetici predominanti vedessero di mal occhio il Libro <emph type="italics"></emph>De re­<lb></lb>volutionibus orbium,<emph.end type="italics"></emph.end> appena uscito fuori, è cosa naturalissima, e benchè <lb></lb>tentassero qua e là d&#039;insorgere ad oppugnarlo, si sentivano ancora deboli e <pb xlink:href="020/01/895.jpg" pagenum="338"></pb>dispersi per la mancanza di qualche valoroso capitano, che finalmente uscì <lb></lb>fuori nella persona di Ticon Brahe. </s>

<s>La Sintassi, ch&#039;egli contrappose alla <lb></lb>copernicana, è notissima a tutti, e le ragioni, per le quali si condusse a ri­<lb></lb>pudiar la posizione del Copernico per seguitare la sua, si posson veder com­<lb></lb>pendiosamente esposte in una Lettera, ch&#039;egli scriveva dall&#039;Uraniburg il <lb></lb>dì 24 Novembre 1589 a Cristoforo Rothmann. </s>

<s>A lui, al quale vedeva arri­<lb></lb>dere il triplice moto dal Copernico attribuito alla Terra, proponeva Ticone, <lb></lb>contro ciascuno di que&#039;tre moti, qualcun fra&#039;molti <emph type="italics"></emph>non adeo operosum <lb></lb>dubium.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Quanto al moto diurno “ dic mihi, scriveva l&#039;Astronomo danese, qui <lb></lb>fieri possit ut globulus plumbeus, ex altissima turre iusto modo demissus, <lb></lb>punctum Terrae infra se positum perpendiculariter ad amussim contingat; <lb></lb>id enim circumducta interea Terra, cum cursus eius sit velocissimus, fieri <lb></lb>nequaquam posse te supputatio docebit geometrica. </s>

<s>Siquidem, in uno scru­<lb></lb>pulo secundo temporis, Terra revolvi debeat, etiam in his borealibus pla­<lb></lb>gis, sesquicentum passus maiores proxime. </s>

<s>Hinc caetera ratiocinare: neque <lb></lb>enim casus plumbi aerem concomitatur, sed violenter illum transit ” (Epistol. </s>

<s><lb></lb>astromic. </s>

<s>libri, Uraniburgi 1596, pag. </s>

<s>167). </s></p><p type="main">

<s>Quanto al moto annuo, soggiungeva Ticone, quando questo fosse vero, <lb></lb>e fosse vera la sentenza copernicana che cioè l&#039;orbe terrestre è un punto <lb></lb>rispetto all&#039;ampiezza della sfera stellata, rimarrebbe un immenso spazio vuoto <lb></lb>affatto di stelle fra Saturno e questa stessa immobile sfera. </s>

<s>“ Imo tunc quo­<lb></lb>que stellae fixae tertiae magnitudinis, quae unum minutum in diametro <lb></lb>habent, necessario erunt aequales toti huic orbi annuo, idest comprehendent <lb></lb>in diametro 2284 semidiametros Terrae: distabunt enim 7,850,000 iisdem <lb></lb>semidiametris proxime. </s>

<s>Quid dicemus de stellis primae magnitudinis, qua­<lb></lb>rum aliquae bina, quaedam fere terna minuta in diametro visibili occupant? </s>

<s><lb></lb>Et quid si adhuc altior removeatur octava sphaera, ut motus Terrae annuus <lb></lb>illic prorsus evanescat? </s>

<s>Deduc si lubet haec geometrice, et videbis quanta <lb></lb>absurda, vel sic inferendo, ut de aliis non dicam, assuntionem hanc conco­<lb></lb>mitentur. </s>

<s>Tertius, sublato annuo, per se ruit ” (ibi). </s></p><p type="main">

<s>Nè per questo il Rothmann si lasciò persuadere. </s>

<s>Diceva che l&#039;argo­<lb></lb>mento del cader del piombo era stato già enodato dallo stesso Copernico, il <lb></lb>quale, dal principio verissimo che alle parti convengono le proprietà del <lb></lb>tutto ne concludeva, che movendosi attorno la Terra dovevano seguirla di <lb></lb>pari passo anche i corpi, che son parte di lei. </s>

<s>Che se ciò non fosse, instava <lb></lb>il Rothmann, non il piombo solo, ma e la Torre stessa, e anzi tutti quanti <lb></lb>gli edifizii dovrebbero rovinare, movendosi dal suo luogo la Terra. </s>

<s>“ Sed <lb></lb>quid de casu rerum gravium solicitus es, cum omnia quae in superficie ter­<lb></lb>rae libera et a toto separata iacent, quinimo ipsa Turris, ex qua globus <lb></lb>plumbeus demittetur, ipsaque aedificia ruerent atque a Terrae motu relin­<lb></lb>querentur necesse esset, si partes non retinerent motum totius, quod quam <lb></lb>sit contra Naturae sapientiam nemo non videt ” (ibi, pag. </s>

<s>185). </s></p><p type="main">

<s>Quanto a quel che poi riguarda gli assurdi che ne conseguirebbero, <pb xlink:href="020/01/896.jpg" pagenum="339"></pb>secondo Ticone, dall&#039;ammettere il moto annuale, il Rothmann confessava di <lb></lb>non saper veder quale assurdo implicasse l&#039;ammetter che una stella possa <lb></lb>essere di diametro tanto grande, quant&#039;è grande il diametro dell&#039;orbita ter­<lb></lb>restre. </s>

<s>“ An id, aut cum voluntate divina pugnat, aut divinae Naturae im­<lb></lb>possibile est, aut infinitae naturae non competit? </s>

<s>Haec demonstranda omnino <lb></lb>tibi sunt, si absurdi quid hinc colligere volueris ” (ibi, pag. </s>

<s>186). </s></p><p type="main">

<s>Gli argomenti però del Rothmann, benchè savissimi, erano nonostante <lb></lb>negativi, ond&#039;è che a conforto del sistema copernicano non restavano altri <lb></lb>argomenti positivi da quelli in fuori che la Matematica aveva suggerito al­<lb></lb>l&#039;Autor del Libro Delle revoluzioni. </s>

<s>Non stette però molto a uscir fuori quel <lb></lb>Giovanni Keplero, che doveva colla valida mano non solo sostenere, ma dar <lb></lb>l&#039;ultima perfezione al combattuto edifizio. </s></p><p type="main">

<s>Nel 1590 frequentava in Tubinga la Scuola di Michele Maestlin, dove, <lb></lb>avendo udito esporre con sì gran plauso l&#039;opinione copernicana, dice di es­<lb></lb>sersene dilettato per modo “ ut non tantum crebro eius placita in physicis <lb></lb>disputationibus candidatorum defenderem, sed etiam accuratam disputatio­<lb></lb>nem de motu primo quod Terrae volutione accidat conscriberem. </s>

<s>Tamque <lb></lb>in eo eram ut eidem etiam Telluri motum solarem, ut Copernicus mathe­<lb></lb>maticis, sic ego physicis, seu mavis metaphisicis rationibus adscriberem ” <lb></lb>(Mysterium cosmogr., Francofurti 1621, pag. </s>

<s>7). </s></p><p type="main">

<s>Lasciamo da parte la Metafisica, la quale poco o nulla giovò al Keplero, <lb></lb>ma le ragioni fisiche di lui si ridussero al moto rotatorio del Sole e alla <lb></lb>scoperta delle orbite ellittiche, per cui le varietà de&#039;moti planetarii, credute <lb></lb>dagli Astronomi e dallo stesso Copernico apparenti, furono dimostrate reali. </s>

<s><lb></lb>Più che fisiche però queste si potevano dir prove dell&#039;ordine matematico, <lb></lb>ond&#039;è che affatto nuovi appariscono nella storia que&#039;veri argomenti fisici <lb></lb>del moto della Terra dati fuori da Guglielmo Gilberto. </s></p><p type="main">

<s>A Tolomeo, che dubitava pel moto suo vertiginoso dover dissolversi la <lb></lb>Terra, aveva dato buona sicurtà il Copernico, nel Cap. </s>

<s>VIII del Libro I, e <lb></lb>una medesima sicurtà aveva dato a Ticone, come vedemmo, il Rothmann, <lb></lb>ma erano que&#039;loro argomenti dedotti da principii metafisici e da ragioni di <lb></lb>congruenza, che intanto avevano peso, in quanto ancora la Fisica si taceva. </s>

<s><lb></lb>Fu il Gilberto il primo a parlare in nome di lei, e a dire che le parti com­<lb></lb>ponenti il Globo terrestre non si dissolvono, perchè alle forze della vertigine <lb></lb>prevalgono le forze dell&#039;attrazion magnetica, e perciò rimangono quelle stesse <lb></lb>parti componenti insieme conglutinate. </s>

<s>“ Ita etiam magnetice terrarum fun­<lb></lb>damenta connectuntur, coniunguntur, ferruminantur. </s>

<s>Quo minus Ptolomeus <lb></lb>Alexandrinus, eiusque sectatores et philosophi nostri, si Terra circulariter <lb></lb>moveretur, dissolutionem eius urgeant aut inhorroscant ” (De Magnete, Lon­<lb></lb>dini 1600, pag. </s>

<s>91). </s></p><p type="main">

<s>Aveva anche francamente il Copernico asserito co&#039;Pitagorici che la Terra <lb></lb>si rivolge intorno al suo asse, ma chi la tiene così in sito per modo, che <lb></lb>non divaghi a talento nel libero spazio, o in che risiede la fermezza del suo <lb></lb>polo? </s>

<s>Nè il Copernico nè altri, prima e dopo di lui, avevano saputo rispon-<pb xlink:href="020/01/897.jpg" pagenum="340"></pb>dere infino al Gilberto, il quale riconobbe, nella verticità magnetica, la co­<lb></lb>stante direzione e la fermezza dell&#039;asse terrestre. </s>

<s>“ Volvitur igitur Terra, <lb></lb>quae magna quadam necessitate, virtute etiam insita manifesta et conspicua <lb></lb>convertitur ad Solem circulariter, quo motu solaribus virtutibus et influen­<lb></lb>tiis gaudet, firmaturque certa sua verticitate, ne vage in omnem coeli re­<lb></lb>gionem volveretur ” (ibi, pag. </s>

<s>224). </s></p><p type="main">

<s>All&#039;obiezione aristotelica antica de&#039;proietti, che non ritornerebbero al <lb></lb>luogo d&#039;onde furon gittati, e alla più recente ticoniana de&#039;corpi cadenti dal­<lb></lb>l&#039;alto, che non batterebbero al giusto perpendicolo, movendosi la Terra in <lb></lb>velocissimo giro, avevano il Copernico e il Rothmann in qualche modo ri­<lb></lb>sposto, ma fu il Gilberto, che alle attrazioni magnetiche ridusse tutta la <lb></lb>virtù di quel fisico argomento. </s>

<s>Ei precorrendo il. </s>

<s>Newton considerava tutti <lb></lb>i corpi rimaner congiunti alla Terra sempre che non uscivano fuori di quella, <lb></lb>ch&#039;ei chiamava orbita degli effluvii terrestri, o sfera attiva dell&#039;attrazione, <lb></lb>come diremmo noi. </s>

<s>“ Dubitant nonnulli qui fieri possit ut globus ferreus <lb></lb>aut plumbeus, ex altissima turri demissus, in punctum Terrae infra se per­<lb></lb>pendiculariter positum ad amussim incidat, Terra circa suum axem mota. </s>

<s><lb></lb>Quomodo etiam sphaerulae bombardicae maioris colubrini simili pulveris <lb></lb>tormentitii quantitate et vigore pari etiam per aerem eumdem directione et <lb></lb>altitudine eiaculatae, pari intervallo ab uno certo loco et versus Eurum et <lb></lb>versus Occasum eiacularentur, mota Tellure versus Eurum. </s>

<s>Sed decipiun­<lb></lb>tur, qui huiusmodi argumenta proferunt, non animadvertentes naturam glo­<lb></lb>borum primariorum et combinationem partium cum suis globis, etiamsi so­<lb></lb>lidis partibus non adiungantur. </s>

<s>Terra vero diurna revolutione non movetur <lb></lb>separatione solidioris circumferentiae eius a circumfusis corporibus, sed cir­<lb></lb>cumfusa effluvia omnia et in illis gravia quovis modo vi pulsa simul cum <lb></lb>Tellure generali cohaerentia uniformiter procedunt. </s>

<s>Quod etiam fit in omni­<lb></lb>bus primariis corporibus, Sole, Luna, Tellure, partibus ad sua principia et <lb></lb>fontes sese conferentibus, quibus eadem appetentia annectuntur, ut terrena <lb></lb>Telluri, quae gravia nos nominamus. </s>

<s>Sic lunaria appellunt Lunam, solaria <lb></lb>Solem, intra effluviorum suorum orbes. </s>

<s>Cohaerent effluvia continuatione <lb></lb>substantiae, et gravia etiam gravitate sua uniuntur Telluri, et simul cum <lb></lb>generali motu procedunt, praesertim cum nulla corporum obstet renitentia. </s>

<s><lb></lb>Ob eamque causam, propter diurnam Telluris revolutionem, nec incitantur <lb></lb>corpora, nec retardantur, non praeveniunt non subsequuntur versus ortum <lb></lb>vel occasum emissa violenter.... Minime igitur ab illustri Tychone Brahe <lb></lb>diurnus motus Telluris talibus argumentis refellitur ” (ibi, pag 228, 29). </s></p><p type="main">

<s>In questi nuovi concetti del Gilberto sente ognuno alitar le prime aure <lb></lb>di quel gran vero, che sarebbe stato messo, un secolo dopo, in così chiara <lb></lb>luce da un altro celebre Filosofo inglese. </s>

<s>Ma intanto avrebbe il nostro Ga­<lb></lb>lileo fra non molti anni ripresi in mano e largamente svolti, a rimuovere <lb></lb>ogni difficoltà contro il moto diurno della Terra, que&#039;fisici e meccanici ar­<lb></lb>gomenti, de&#039;quali non aveva l&#039;Autor <emph type="italics"></emph>De Magnete<emph.end type="italics"></emph.end> fatto nel suo VI libro <lb></lb>altro che un cenno. </s>

<s>Ond&#039;è che siamo da ciò, dop&#039;aver detto delle vicende, <pb xlink:href="020/01/898.jpg" pagenum="341"></pb>che subì ne&#039;suoi primi tempi il Sistema Pitagorico descritto dal Copernico, <lb></lb>specialmente appresso gli stranieri; messi in via di narrar, con la solita bre­<lb></lb>vità, ciò che particolarmente se ne pensasse o se ne disputasse in Italia. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Crediamo anche noi che uno di quegli Italiani, co&#039;quali il Copernico <lb></lb>familiarmente conversava, e ch&#039;ebbero qualche efficacia in ispirargli i pla­<lb></lb>tonici concetti, fosse Girolamo Fracastoro. </s>

<s>Vanno però i momenti, per dir <lb></lb>così, di quella efficacia ben ponderati, essendo un fatto che l&#039;Autor <emph type="italics"></emph>De re­<lb></lb>volutionibus,<emph.end type="italics"></emph.end> infin dalla dedica a papa Paolo III, confessa l&#039;insufficienza del <lb></lb>sistema omocentrico a comporre ordinatamente i moti celesti. </s></p><p type="main">

<s>È a tutti noto che la ragione, per cui Tolomeo ricorse ad ammettere <lb></lb>il sistema eccentrico, era il veder variar di grandezza gli astri, e special­<lb></lb>mente la Luna, in due punti diametralmente opposti della loro orbita, che <lb></lb>perciò si dissero il perigeo e l&#039;apogeo. </s>

<s>Il Fracastoro sosteneva quella va­<lb></lb>rietà essere una semplice apparenza, come quella che da non altro, secondo <lb></lb>lui, dipende, se non dal passar le specie visibili per mezzi ora più ora meno <lb></lb>alti, ora più e ora meno densi. </s>

<s>“ Nos autem utramque dictarum causarum <lb></lb>prorsus auferimus et planetas nunquam altiores, numquam depressiores <lb></lb>reipsa fieri asseveramus: videri autem propter alias causas, quarum una a <lb></lb>medio pendet ” (Homocentricorum liber, Op. </s>

<s>omnia, Venetiis 1584, c. </s>

<s>13). </s></p><p type="main">

<s>Questa singolare ipotesi del Fracastoro (fatto notabilissimo) trovò più <lb></lb>di un secolo dopo un propugnatore zelante in Ottone di Guericke, a cui <lb></lb>parve di render, delle varie apparenti grandezze del Sole in Cancro e in <lb></lb>Capricorno, la seguente ragione: “ Porro quoque reddit diversas Solis et <lb></lb>Lunae apparentias maior vel minor aeris profunditas. </s>

<s>Nam quando Sol aut <lb></lb>Luna sunt in signis australibus adeoque humiliores, tunc aspiciuntur a no­<lb></lb>bis per maiorem aeris profunditatem, consequenter apparent maiores. </s>

<s>Unde, <lb></lb>tempore hyberno, quando Sol est in Capricorno apparet maior propter ma­<lb></lb>iorem aeris copiam, quae intermediat inter visum nostrum et corpus Solis <lb></lb>obiectum. </s>

<s>Quando autem est in Cancro, adeoque versus nostrum zenith <lb></lb>altior, per minorem aeris copiam adspicitur minor ” (Experim. </s>

<s>magd. </s>

<s>cit., <lb></lb>pag. </s>

<s>166). </s></p><p type="main">

<s>Il Copernico però, ben persuaso che le varie grandezze del Sole e della <lb></lb>Luna non sono illusioni ottiche, ma fatti reali, vide come fosse impossibile <lb></lb>salvar questi stessi fatti nel sistema assolutamente omocentrico, ma che o <lb></lb>bisognava ammettere gli eccentrici o gli omocentrici con gli epicicli. </s>

<s>“ Eius <lb></lb>autem inaeqnalitas demonstratur quod motus centri ac annuae revolutionis <lb></lb>Terrae non sit omnino circa Solis centrum. </s>

<s>Quod sane duobus modis in­<lb></lb>telligi potest, vel per eccentrum circulum, idest cuius centrum non sit Solis, <lb></lb>vel per epicyclum in homocentro ” (De revolut. </s>

<s>cit., pag. </s>

<s>85). Se l&#039;uno o <pb xlink:href="020/01/899.jpg" pagenum="342"></pb>l&#039;altro, l&#039;eccentrico cioè, o l&#039;omocentrico coll&#039;epiciclo, esista nel Cielo, sog­<lb></lb>giunge il Copernico, <emph type="italics"></emph>non est facile discernere,<emph.end type="italics"></emph.end> ma egli è in ogni modo af­<lb></lb>fatto alieno dal partecipare colle idee professate dal Fracastoro, al quale in­<lb></lb>somma non rimane altro merito, da quello in fuori di aver presentito dalla <lb></lb>lontana che il sistema vero del mondo sarebbe stato più conforme alla sem­<lb></lb>plicità platonica, che non alla complicata architettura tolemaica; sentimento <lb></lb>ch&#039;egli infuse nel grande astronomo prussiano, a cui siamo certi che fu <lb></lb>amico, e si crede che fosse anche maestro. </s></p><p type="main">

<s>Fra&#039;precursori del Copernico sarebbe da annoverar piuttosto Niccolò <lb></lb>da Cusa, a cui in questo particolar proposito compete il merito di avere, in <lb></lb>mezzo a tanta incredulità, avuto fede a quel che di Niceta gli riferiva Ci­<lb></lb>cerone, o a quel che di Filolao raccontava Plutarco. </s>

<s>In ogni modo, giacchè <lb></lb>la preparazione e gl&#039;impulsi, ch&#039;ebbe il libro <emph type="italics"></emph>De revolutionibus<emph.end type="italics"></emph.end> dagl&#039;Ita­<lb></lb>liani, son noti per i fatti sopra narrati, e ciò basta alla nostra gloria; senza <lb></lb>più perderci dietro ai precursori del Copernico passiamo a dir de&#039;seguaci. </s></p><p type="main">

<s>Non ci dà il cuore di annoverar fra questi Giordano Bruno, come al­<lb></lb>cuni, specie in questi ultimi tempi, scapestratamente hanno fatto, essendo <lb></lb>per avventura il Sistema copernicano assunto fra gli strani e sconvolti me­<lb></lb>tafisicumi del frate da Nola, come suol talvolta una pagliuzza d&#039;oro venir <lb></lb>rapita in mezzo al ciarpame, e sostenuta in aria da un vento turbinoso. </s></p><p type="main">

<s>La matematica copernicana voleva essere confortata, non da vane me­<lb></lb>tafisiche speculazioni, ma da fisiche esperienze, delle quali vide la nostra <lb></lb>Italia le primizie in un argomento sovvenuto già a Seleuco filosofo antico, <lb></lb>e a cui dette vigor nuovo di vita, nelle <emph type="italics"></emph>Questioni peripatetiche,<emph.end type="italics"></emph.end> il Cesal­<lb></lb>pino. </s>

<s>Egli dunque, non saputosi in tutto espedire dai lacci peripatetici, non <lb></lb>sa prestar fede al suo divino Aristotile, che nega il moto diurno della Terra, <lb></lb>perchè vede questo perpetuo moto nel flusso e riflusso marino dimostrato <lb></lb>con evidenza. </s>

<s>“ Quoniam autem perpetua est huiusmodi Terrae circumvo­<lb></lb>lutio, perpetua quoque redditur maris libratìo. </s>

<s>Quatenus igitur motus iste <lb></lb>est continentis, per accidens in aqua est, nec secundum eius naturam ne­<lb></lb>que praeternaturam: quaerit enim semper locum magis declivem, quia non <lb></lb>pari passu prosequitur Terrae mo­<lb></lb>tum. </s>

<s>Quod autem in maxima aqua­<lb></lb>rum congregatione hic motus contin­<lb></lb>gat, non autem in parvis ut lacubus <lb></lb>et fluminibus, iustissime evenit. </s>

<s>Cum <lb></lb>enim Terrae motus minimus sit, non <lb></lb>potest, nisi in magna aquarum mole <lb></lb>apparere. </s>

<s>Sit enim AA (fig. </s>

<s>66) su­<lb></lb><figure id="id.020.01.899.1.jpg" xlink:href="020/01/899/1.jpg"></figure></s></p><p type="caption">

<s>Figura 66.<lb></lb>perficies aquae supra perpendicu­<lb></lb>lum CD; BB autem altera superfi­<lb></lb>cies dimota super alterum perpendiculum GC: quanto magis protrahitur <lb></lb>AA, BB, tanto magis apparet seiunctio a se invicem ” (Venetiis 1571, c. </s>

<s>60 v.). </s></p><p type="main">

<s>Il Cesalpino però non seppe tanto riconquistare la propria libertà, da <pb xlink:href="020/01/900.jpg" pagenum="343"></pb>professare apertamente il sistema vero del mondo: egli è un semicoperni­<lb></lb>cano, che non sa risolversi a far posare il Sole nella sua sede, per man­<lb></lb>dargli attorno la Terra in perpetuo giro annuale. </s>

<s>Dall&#039;altra parte tanto ri­<lb></lb>mane ancora il Filosofo aretino devoto al suo Aristotile, che delle poche <lb></lb>verità spicciolate di lui non si fa conto da coloro, i quali seguitano tutt&#039;al­<lb></lb>tro metodo in filosofare. </s>

<s>Ciò poi più distintamente avvenne, quando quel <lb></lb>metodo ebbe un primo ordinatore in Giovan Batista Benedetti, dalle parole <lb></lb>del quale, che riferivano l&#039;opinion di Aristarco Samio <emph type="italics"></emph>divinitus a Nicolao <lb></lb>Copernico expressam contra quam nil plane valent rationes ab Aristotile <lb></lb>neque etiam a Ptolomeo propositae,<emph.end type="italics"></emph.end> si riconobbe autorevolmente decisa la <lb></lb>gran sentenza. </s>

<s>È perchè, segnatamente in Italia, i seguaci del retto metodo <lb></lb>sperimentale riconoscevano il Benedetti solo per primo istitutore e Maestro, <lb></lb>i Filosofi usciti di quella scuola erano tutti perciò schiettamente coper­<lb></lb>nicani. </s></p><p type="main">

<s>Fu il più insigne di meriti, e il più famoso tra costoro Galileo Galilei, <lb></lb>il quale, giovane professore nello studio pisano, ci si rivela di già per fautor <lb></lb>del Copernico in alcune dispute familiari, ch&#039;egli ebbe con l&#039;amico e col­<lb></lb>lega suo Jacopo Mazzoni. </s>

<s>Meditavano con pari amore lo <emph type="italics"></emph>Speculationum liber,<emph.end type="italics"></emph.end><lb></lb>e conferivano insieme i loro pensieri. </s>

<s>Il Mazzoni era ben persuaso di ciò <lb></lb>che il Benedetti ivi dimostrava contro Aristotile, riguardo al dir che le velo­<lb></lb>cità nel vacuo sarebbero infinite, e riguardo a tanti altri errori detti dal <lb></lb>Filosofo intorno alla natura e alle proprietà del moto. </s>

<s>Si studiava però di <lb></lb>scusare in qualche modo Aristotile, facendo per esempio osservare all&#039;amico <lb></lb>che non essendo ancora noto il Teorema archimedeo, non era da far le ma­<lb></lb>raviglie se l&#039;Autor nel <emph type="italics"></emph>VII Physicorum<emph.end type="italics"></emph.end> aveva asserito non potersi dare una <lb></lb>linea retta uguale alla circolare. </s>

<s>“ Sed tamen in isto lapsu venia dignus vi­<lb></lb>detur Aristotiles, nam, ut ait Simplicius, illius tempore nondum inventa fue­<lb></lb>rant ab Archimede elaborata Theoremata ad hoc attinentia. </s>

<s>Addamus et <lb></lb>illud quod adhuc proportio circuli et diametri non sit nobis omnino explo­<lb></lb>rata et cognita ” (In universam Plat. </s>

<s>et Arist. </s>

<s>philos. </s>

<s>praeludia. </s>

<s>Vene­<lb></lb>tiis 1597, pag. </s>

<s>194). Ma Galileo più rigido censore non voleva conoscere <lb></lb>scuse: “ Neque dicas hoc latuit Aristotilem quia Archimedes Aristotele est <lb></lb>multo recentior. </s>

<s>Nam si Aristotelem latuit demonstratio inveniendae rectae <lb></lb>curvae aequalis, latuit etiam demonstratio probans non dari rectam curvae <lb></lb>aequalem, quare non debebat temere asserere non dari talem rectam ” <lb></lb>(Alb. </s>

<s>XI, 64). </s></p><p type="main">

<s>Dalle questioni meccaniche passavano i due amici alle astronomiche, <lb></lb>intorno alle quali i dissensi erano più risoluti. </s>

<s>Galileo sosteneva aver sen­<lb></lb>tenziato verissimo il Benedetti a dir che non valgono contro il divino Co­<lb></lb>pernico le obiezioni promosse da Aristotile e da Tolomeo. </s>

<s>Contradiceva il <lb></lb>Mazzoni, asseverando che se l&#039;altezza del monte Caucaso fa così deprimere <lb></lb>l&#039;orizzonte, la distanza della Terra dal Sole, quando fosse vera l&#039;ipotesi co­<lb></lb>pernicana, altererebbe così la posizion dello stesso orizzonte, da non si poter <lb></lb>mai veder divisa per giusta metà la sfera stellata. </s></p><pb xlink:href="020/01/901.jpg" pagenum="344"></pb><p type="main">

<s>Tanto parve al Mazzoni potersi con questa difficoltà infirmare la sen­<lb></lb>tenza del Benedetti, che produsse in pubblico, dai familiari colloqui, quella <lb></lb>stessa difficoltà nella Sezione III dei sopra citati <emph type="italics"></emph>Preludi,<emph.end type="italics"></emph.end> dove così s&#039;inti­<lb></lb>tola il cap. </s>

<s>V. “ Quod Terra sit centrum mundi et quod non moveatur: <lb></lb>reiicitur commentum Pythagoreorum, Aristarchi Sami et Nicolai Copernici ” <lb></lb>(pag. </s>

<s>129). </s></p><p type="main">

<s>Una copia del libro fu dall&#039;Autore inviata immediatamente a Padova a <lb></lb>Galileo, che l&#039;ebbe appena uscite fuori le stampe, verso la metà del Mag­<lb></lb>gio. </s>

<s>Galileo rispose una lettera, in data del dì 30 di quello stesso mese e <lb></lb>di quell&#039;anno 1597, dove commemorando i primi dolci anni della loro ami­<lb></lb>cizia, quando con tanta giocondità disputavano insieme, torna a far ora quelle <lb></lb>risposte in scritto, che aveva allora pronunziate a voce. </s>

<s>Dimostra che l&#039;ar­<lb></lb>gomento si fonda sopra un inganno ottico, il quale poi facilmente si dis­<lb></lb>solve, avvertendo la gran differenza che passa, tra il far discostare l&#039;occhio <lb></lb>posto nella superficie della Terra con tutta la Terra dal centro del Cielo, e <lb></lb>tra il fare alzare l&#039;occhio sopra la superficie della Terra. </s>

<s>Dalla quale av­<lb></lb>vertenza conclude: “ forse minor diversità, circa la disegualità delle più <lb></lb>volte dette divisioni orizzontali, potria cagionare la grandissima lontananza <lb></lb>ch&#039;è tra il Sole e la Terra, che la piccola altezza del monte Caucaso ” <lb></lb>(Alb. </s>

<s>II, 4). </s></p><p type="main">

<s>Pochi mesi dopo, la fama del Matematico nello studio di Padova era <lb></lb>giunta in Germania alle orecchie del Keplero, il quale, avendo l&#039;anno <lb></lb>avanti (1596) pubblicata la prima edizione del suo <emph type="italics"></emph>Prodromus Dissertatio­<lb></lb>num cosmographicarum,<emph.end type="italics"></emph.end> inviò da Gratz una copia del libro a Galileo. </s>

<s>Que­<lb></lb>sti rispondeva da Padova, il dì 4 Agosto 1597, una lettera, nella quale, <lb></lb>dop&#039;aver ringraziato l&#039;Autore del dono, ed essersi compiaciuto di vedersi <lb></lb>onorare dell&#039;amicizia di chi aveva confermato le combattute verità con tante <lb></lb>belle invenzioni, delle quali si congratulava, “ Id autem, soggiunge, eo li­<lb></lb>bentius faciam quod in Copernici sententiam multis abhinc annis venerim, <lb></lb>et ex tali positione multorum etiam naturalium effectuum causae sint a me <lb></lb>adinventae; quae dubio procul per comunem hypothesim inexplicabiles sunt. </s>

<s><lb></lb>Multas conscripsi et rationes et argumentorum in contrarium eversiones, <lb></lb>quas tamen in lucem hucusque proferre non sum ausus, fortuna ipsius Co­<lb></lb>pernici praeceptoris nostri perterritus, qui licet sibi apud aliquos immorta­<lb></lb>lem famam paraverit, apud infinitos tamen, tantus enim est stultorum nu­<lb></lb>merus, ridendus et explodendus prodiit ” (Alb. </s>

<s>VI, 12). </s></p><p type="main">

<s>Chi ripensa sopra queste parole, e non sa che della lettera scritta al <lb></lb>Mazzoni, domanderà curioso quali sono que&#039;tanti altri scritti, ne&#039;quali Ga­<lb></lb>lileo si vanta di aver molte nuove ragioni in favor del Copernico, e molte <lb></lb>eversioni degli argomenti in contrario. </s>

<s>Risponderanno gli adoratori al solito <lb></lb>lamentando l&#039;iattura, ma noi che conosciamo l&#039;indole di quell&#039;uomo, sem­<lb></lb>pre magnificator di sè stesso, possiamo rassicurare gli animi col persuaderli <lb></lb>che tutte l&#039;eversioni degli argomenti contro il Copernico, fino a quel tempo, <lb></lb>si compendiano nella lettera al Mazzoni, e che le cause degli effetti naturali <pb xlink:href="020/01/902.jpg" pagenum="345"></pb>non esplicabili altrimenti che nella posizione copernicana, e le ragioni che <lb></lb>escogitò Galileo per confermarla, si riducono a quella falsa speculazione del <lb></lb>flusso del mare suggeritagli dalla lettura del Cesalpino. </s></p><p type="main">

<s>Così Seleuco antico, come il più recente Autore delle Questioni peri­<lb></lb>patetiche, erano semicopernicani; non attribuivano cioè alla Terra altro che <lb></lb>la conversione diurna, e facevano dipendere il flusso marino da quest&#039;unico <lb></lb>moto. </s>

<s>Voleva Galileo farne argomentò anco del moto annuo, e così pensando <lb></lb>finì per concludere che anzi era necessario questo secondo moto s&#039;aggiun­<lb></lb>gesse al primo, senza che non s&#039;intenderebbe come un semplice andamento <lb></lb>uniforme potesse esser causa di quel perpetuo e regolare avvicendarsi del <lb></lb>flusso. </s>

<s>Ci voleva una difformità nella uniformità, la quale Galileo sottilmente <lb></lb>rinvenne in quel che, supposta vera la posizione copernicana, avviene al moto <lb></lb>vertiginoso della Terra, che ora aggiunge ora detrae al moto annuale nel­<lb></lb>l&#039;orbita. </s>

<s>Tanto si compiacque poi, l&#039;inventore, di questa sottigliezza, che <lb></lb>secondo lui non ci bisognava altro per istabilire il Copernicismo nella scienza <lb></lb>astronomica, ma pur bisognava ancora mostrar che i fatti rispondevano alle <lb></lb>speculazioni. </s></p><p type="main">

<s>Mentre intanto, e per le osservazioni sue proprie e per le relazioni al­<lb></lb>trui attendeva a raccogliere e a sottordinare all&#039;immaginato sistema que&#039;fatti, <lb></lb>l&#039;apparizione di una stella nuova veniva eccitando un insolito fervore in tutti <lb></lb>gli Astronomi. </s>

<s>Galileo è nello Studio padovano de&#039;più affaccendati, e inter­<lb></lb>rotto il corso ordinario fa di quella nuova apparizione celeste particolar sog­<lb></lb>getto alle sue lezioni. </s>

<s>Quali fossero i suoi pensieri lo sappiamo oramai certo <lb></lb>da quelle note che lasciò manoscritte, e che son tutte ora venute alla pub­<lb></lb>blica luce; quali ne fossero i calcoli laboriosi può vedersi nella Giornata III <lb></lb>de&#039;due Massimi Sistemi. </s></p><p type="main">

<s>Ma fra que&#039;pensieri e que&#039;calcoli della stella nuova Seneca, intorno a <lb></lb>ciò consultato, mette in grande ardore il Professor di Padova di darsi a <lb></lb>contemplare il cielo, per decidere finalmente del sistema del mondo. </s>

<s>E per­<lb></lb>chè gli rimangano le parole del Filosofo morale più impresse, le trascrive <lb></lb>di suo proprio pugno a carte 15 del Tomo VI, Parte IV de&#039;manoscritti <lb></lb>astronomici, fra i pensieri sovvenutigli intorno all&#039;origine della stella nuova. <lb></lb></s>

<s>“ Seneca lib. </s>

<s>VII Natur. </s>

<s>quaest. </s>

<s>cap. </s>

<s>II. </s>

<s>Illo quoque pertinebit hoc exau­<lb></lb>sisse ut sciamus utrum mundus Terra stante circumeat, an mundo stante <lb></lb>Terra vertatur. </s>

<s>Fuerunt nam qui dicerent nos esse quorum rerum natura <lb></lb>nescientes ferat, nec coeli motu fieri ortus et occasus, sed ipsos oriri et oc­<lb></lb>cidere. </s>

<s>Digna res est contemplatione ut sciamus in quo rerum statu si­<lb></lb>mus, pigerrimam sortiti an velocissimam sedem; circa nos Deus omnia an <lb></lb>nos agat. </s>

<s>” </s></p><p type="main">

<s>E che veramente Galileo si fosse volto con più ardore che mai a così <lb></lb>degna contemplazione, s&#039;argomenta da certi pensieri inseriti qua e là fra <lb></lb>que&#039;calcoli disordinati, e relativi alla stella nuova, come per esempio da <lb></lb>quello che si legge a carte 22 del T. II, P. III. “ Aggiugni al volar degli <lb></lb>uccelli che il maggior deviar dalla vertigine della Terra sarebbe il volar con-<pb xlink:href="020/01/903.jpg" pagenum="346"></pb>tinuamente verso occidente, e così l&#039;uccello doventa come una freccia tirata <lb></lb>per quel verso, che non fa altro che detrarre alquanto al moto diurno. </s>

<s>” </s></p><p type="main">

<s>Avvennero queste cose dopo il 1604, anno in cui comparve quella stella <lb></lb>nuova. </s>

<s>Dieci anni dopo s&#039;avevano nella vita astronomica di Galileo da con­<lb></lb>tare ben più nuovi e più rumorosi avvenimenti. </s>

<s>Era stato inventato il Te­<lb></lb>lescopio, e s&#039;erano pubblicate, dopo il Nunzio Sidereo, le lettere velseriane. </s>

<s><lb></lb>Con tant&#039;arte seppe maneggiarsi quell&#039;uomo intorno a questi negozii, che <lb></lb>riuscì veramente, com&#039;era la sua intenzione, a comparire al mondo primo <lb></lb>e solo Messaggero del cielo, ma vi riuscì da conquistatore colle solite pre­<lb></lb>potenze e colle solite stragi, che gli suscitarono contro, in alcuni ire impo­<lb></lb>tenti, in altri odii vendicativi. </s></p><p type="main">

<s>Primo e solo voleva essere Galileo, primo e solo voleva essere il Col­<lb></lb>legio de&#039;Gesuiti. </s>

<s>Le spavalde millanterie dell&#039;uno soffiavano, col mantice <lb></lb>della gelosia, ad accendere le ire negli altri. <emph type="italics"></emph>Magna longeque admirabilia <lb></lb>apud me habeo<emph.end type="italics"></emph.end> va ricantando a Belisario Vinta, e a quanti altri gli capi­<lb></lb>tano d&#039;intorno. </s>

<s>Ha a trattare un concetto immenso e pieno di Filosofia, <lb></lb>Astronomia, Geometria; ha una scienza interamente nuova, non avendo al­<lb></lb>cun altro scoperto alcuno de&#039;sintomi ammirandi ch&#039;egli dimostra; ha da in­<lb></lb>segnar cose non più sapute intorno al suono e alla voce, alla vista e a&#039;co­<lb></lb>lori, al flusso e riflusso del mare, al moto degli animali.... (Alb. </s>

<s>VI, 97, 98). </s></p><p type="main">

<s>Questo era il linguaggio del Conquistator fortunato, a cui volevasi in <lb></lb>ogni modo rintuzzare l&#039;orgoglio. </s>

<s>Al Collegio de&#039;Gesuiti, per risorgere nel <lb></lb>regno della scienza, conveniva opprimere il baldanzoso rivale, e lo fece con <lb></lb>armi invitte perchè fatte scendere a ferire dall&#039;alto del Cielo. </s></p><p type="main">

<s>S&#039;erano quelle armi, come un acuto strale, appresentate alla fantasia <lb></lb>del Copernico, ma a non temerne le offese gli bastò il pensare che male era <lb></lb>quello strale <emph type="italics"></emph>ad suum propositum detortum.<emph.end type="italics"></emph.end> Ei non s&#039;era arretrato punto <lb></lb>per paura de&#039;Teologi, ma de&#039;Peripatetici e del volgo, il quale non si sa­<lb></lb>rebbe indotto a creder falsa un&#039;opinione confermata <emph type="italics"></emph>multorum seculorum <lb></lb>indiciis.<emph.end type="italics"></emph.end> Quando poi incominciarono fra gli Astronomi le discussioni, parve <lb></lb>anche al Rothmann che ci entrassero gli argomenti biblici come i calzari <lb></lb>degli attori in iscena; similitudine, che Ticone giudicò irriverente, soggiun­<lb></lb>gendo rifuggirgli l&#039;animo dal pensare che si potessero nelle Sante Scrit­<lb></lb>ture propor cose non vere, e avvertendo che, sebbene Mosè si accomodi <lb></lb>all&#039;intelligenza del volgo, non però dice cose da non si approvar dagli Astro­<lb></lb>nomi. </s>

<s>“ Maior enim, scriveva dall&#039;Uraniburgo allo stesso Rothmann, et est <lb></lb>et esse debet divinarum Literarum autoritas ac reverentia, quam ut sic in <lb></lb>modum cothurni eas trahi deceat. </s>

<s>Licet enim ipsae in rebus physicis et aliis <lb></lb>quibusdam, ut plurimum, ad captum vulgi sese attemperent, absit tamen <lb></lb>ut ob id statuamus eas ita vulgariter loqui quin etiam vera proponere cre­<lb></lb>damus. </s>

<s>Sic Moses, etsi in primo cap. </s>

<s>Geneseos de Mundi creatione agens <lb></lb>Astronomiae penetralia non reseret, utpote rudi populo scribens, nihil ta­<lb></lb>men in medium profert quod non etiam ab ipsis Astronomis concedi queat ” <lb></lb>(Epist. </s>

<s>astronomic., libri cit., pag. </s>

<s>147). In ogni modo il Keplero, uomo re-<pb xlink:href="020/01/904.jpg" pagenum="347"></pb>ligiosissimo e di viva fede alle verità rivelate, incomincia il suo <emph type="italics"></emph>Mysterium <lb></lb>cosmographicum<emph.end type="italics"></emph.end> col dimostrar la ragionevolezza dell&#039;ipotesi copernicana, <lb></lb>persuaso di non esser per dir nulla <emph type="italics"></emph>quod in Sacras Literas iniurium sit, <lb></lb>et si cuius Copernicus mecum convincatur,<emph.end type="italics"></emph.end> protesta liberamente, <emph type="italics"></emph>pro nullo <lb></lb>habiturum.<emph.end type="italics"></emph.end> (Editio cit., pag. </s>

<s>13). </s></p><p type="main">

<s>Tali erano pure questi sentimenti in Italia, quando a un tratto escono <lb></lb>con gran furia i frati a dire e a predicare che l&#039;ipotesi copernicana è ere­<lb></lb>tica, come quella che contradice alla Santa Scrittura. </s>

<s>Dopo settant&#039;anni, <lb></lb>ch&#039;era uscito un libro scritto da Niccolò Copernico canonico, pubblicato ad <lb></lb>istanza di Tidemanno Gisio vescovo, e di Niccolò Schonberg cardinale, e de­<lb></lb>dicato a Paolo III Pontefice sommo, insorgere i frati a dichiararlo eretico, <lb></lb>era un fatto che non sapevasi spiegare nemmen da quello stesso Galileo, <lb></lb>contro al quale, piuttosto che contro al Copernico, si moveva così aspra <lb></lb>guerra. </s>

<s>“ Ora questi buoni frati solo per un sinistro affetto contro di me, <lb></lb>sapendo ch&#039;io stimo quest&#039;Autore, si vantano di dargli il premio delle sue <lb></lb>fatiche col farlo dichiarare eretico ” (ivi, pag. </s>

<s>16). </s></p><p type="main">

<s>Quel che reca poi più gran maraviglia è che Galileo, per far le sue <lb></lb>ragioni, pensa di <emph type="italics"></emph>battere a&#039;padri Gesuiti<emph.end type="italics"></emph.end> (Alb. </s>

<s>II, 17) non comprendendo <lb></lb>che erano essi che gli facevan nascostamente la guerra, servendosi dello <lb></lb>strumento degli altri frati. </s>

<s>Essendo chiaro infatti che si combatteva no una <lb></lb>dottrina ma una persona, qual occasione o qual motivo aveva dato Galileo <lb></lb>ai frati d&#039;insorgere contro lui? </s>

<s>Ma l&#039;occasione e il motivo l&#039;aveva ben dato <lb></lb>ai Gesuiti, i quali contendevano non della verità del sistema del mondo, ma <lb></lb>del primato della scienza che si vedevano tolto di mano. </s></p><p type="main">

<s>Si sarà cominciato Galileo ad avvedere di qualche cosa, quando quel <lb></lb>Grembergiero <emph type="italics"></emph>matematico insigne e suo grandissimo amico e padrone<emph.end type="italics"></emph.end> (ivi), <lb></lb>lo trovò invece suo contradittore, e quando vide Paolo Anton Foscarini, frate <lb></lb>carmelitano, entrare in quella fatica di accordare e appaciare i luoghi della <lb></lb>Santà Scrittura coll&#039;opinione copernicana, pensando di far <emph type="italics"></emph>cosa grata agli <lb></lb>studiosi di queste dottrine ed in particolare alli dottissimi signori Galileo <lb></lb>Galilei e Giovanni Keplero<emph.end type="italics"></emph.end> (Alb. </s>

<s>V, 461). Si sarà tanto meglio poi lo stesso <lb></lb>Galileo confermato in questa opinione, quando avrà risaputo che fu la Let­<lb></lb>tera del Frate carmelitano pretesto nelle mani de&#039;Gesuiti di fare emanare <lb></lb>dalla Sacra congregazione de&#039;Cardinali il Decreto del dì 5 Marzo 1616, così <lb></lb>dal Riccioli trascritto a pag. </s>

<s>495 della I Parte del suo <emph type="italics"></emph>Almagesto Nuovo<emph.end type="italics"></emph.end><lb></lb>(Bologna 1651): </s></p><p type="main">

<s>“ Et quia etiam ad notitiam praefatae Congregationis pervenit falsam <lb></lb>illam doctrinam pythagoricam divinaeque Scripturae omnino adversantem de <lb></lb>mobilitate Terrae et immobilitate Soiis, quam Nicolaus Copernicus <emph type="italics"></emph>De re­<lb></lb>volutionibus orbium coelestium<emph.end type="italics"></emph.end> et Didacus a Stunica <emph type="italics"></emph>in Job<emph.end type="italics"></emph.end> etiam docent, <lb></lb>iam divulgari et a multis recipi, sicut videri est ex Epistola quadam im­<lb></lb>pressa cuiusdam patris carmelitae, cui titulus <emph type="italics"></emph>Lettera del R. P. maestro <lb></lb>Paolo Antonio Foscarini carmelitano sopra l&#039;opinione dei Pitagorici e del <lb></lb>Copernico della mobilità della Terra e stabilità del Sole ed il nuovo Pi-<emph.end type="italics"></emph.end><pb xlink:href="020/01/905.jpg" pagenum="348"></pb><emph type="italics"></emph>tagorico sistema del mondo; in Napoli, per Lazzero Scorriggio, 1615,<emph.end type="italics"></emph.end> in <lb></lb>qua dictus Pater ostendere conatur praefatam doctrinam de immobilitate <lb></lb>Solis in centro mundi et mobilitate Terrae consonam esse veritati et non <lb></lb>adversari Sacrae Scripturae; ideo ne ulterius huiusmodi opinio in perniciem <lb></lb>catholicae veritatis serpat, censuit dictos Nicolaum Copernicum <emph type="italics"></emph>De revolu­<lb></lb>tiodibus orbium,<emph.end type="italics"></emph.end> et Didacum a Stunica <emph type="italics"></emph>in Job<emph.end type="italics"></emph.end> suspendendos esse donec cor­<lb></lb>rigantur; librum vero P. </s>

<s>Pauli Antonii Foscarini carmelitae omnino prohi­<lb></lb>bendum atque dannandum, aliosque omnes libros pariter idem docentes <lb></lb>prohibendos, prout praesenti decreto omnes respective prohibet, damnat <lb></lb>atque suspendit. </s>

<s>” </s></p><p type="main">

<s>In questo Decreto non ci è, come si vede, nulla che tocchi diretta­<lb></lb>mente Galileo, nè ci era per verità ragione di toccarlo, non avendo negli <lb></lb>scritti fin allora da lui pubblicati dato altro indizio d&#039;essere copernicano, <lb></lb>che verso la fine del Nunzio Sidereo, dove dice che non dovrebbe fare dif­<lb></lb>ficoltà al moversi della Terra il portarsi dietro la Luna, mentre Giove stesso <lb></lb>si muove e porta seco, non una sola, ma quattro Lune (Alb. </s>

<s>III, 98). </s></p><p type="main">

<s>Eppure è certo che fu quel Decreto fatto emanare apposta contro Ga­<lb></lb>lileo, il quale assordava il mondo colle sue parole, ch&#039;erano agli amici dolci <lb></lb>promesse, e a&#039;rivali odiose minacce. </s>

<s>Tutte queste promesse poi e queste <lb></lb>minacce si concludevano in quel vero capriccio del flusso e riflusso, che, <lb></lb>occorsogli al pensiero parecchi anni avanti, come dicemmo, ora era venuto <lb></lb>confortandolo di osservazioni procuratesi qua e là da&#039;praticanti ne&#039;mari. </s>

<s>In <lb></lb>quel tempo che i cardinali in Roma meditavano il famoso Decreto, in quel <lb></lb>tempo dice Galileo (Ald. </s>

<s>VI. 279) di aver dato mano in Roma a distendere <lb></lb>il Discorso del flusso, avutone comandameuto dal cardinale Orsino. </s>

<s>Fatto sta <lb></lb>che venne quella scrittura veramente distesa in forma di Lettera indirizzata <lb></lb>a detto cardinale sotto il di 8 Gennaio 1616. </s></p><p type="main">

<s>Fra&#039;primi ad averne copia, dalle mani del medesimo Autore, fu l&#039;ami­<lb></lb>cissimo suo Gian Francesco Sagredo, il quale per lettera del dì 19 Novem­<lb></lb>bre di quell&#039;anno gli rispondeva così fatte assennate parole: “ Circa il suo <lb></lb>Discorso del flusso e riflusso del mare, scorso da me, posso dire, a volo, <lb></lb>non posso dirle altro, se non che il principio trovato da lei è sottilissimo, <lb></lb>verissimo e necessario, con tutte le conseguenze considerate da lei, stante <lb></lb>l&#039;ipotesi della Terra e sua revoluzione, e stante la natura de&#039;progetti e <lb></lb>fluidi, per la quale, non pure si verificherebbe il flusso e riflusso sensibile <lb></lb>de&#039;mari, ma ancora l&#039;insensibile dell&#039;acque, che sono rinchiuse in minime <lb></lb>caraffine, le quali proporzionatamente alla loro grandezza necessariamente <lb></lb>devono sentire l&#039;acceleramento e ritardamento del moto della Terra, e per <lb></lb>conseguenza patire i loro minimi e insensibili flussi e riflussi. </s>

<s>Ma se questa <lb></lb>dottrina avesse a divulgare, so che l&#039;umana ignoranza di tanti infiniti uo­<lb></lb>mini incapaci della sottilità del vero e della ragione farebbe una bestiale re­<lb></lb>sistenza. </s>

<s>Con comodità di tempo rileggerò esso Discorso, e l&#039;avviserò ” (MSS. <lb></lb>Gal., P. I, T. VII, c. </s>

<s>265). </s></p><p type="main">

<s>Quando il Sagredo tornò a dare l&#039;avviso, la notizia del Decreto della <pb xlink:href="020/01/906.jpg" pagenum="349"></pb>proibizione e della condanna s&#039;era largamente e con gran rumore diffusa, e <lb></lb>Galileo perciò, bene intese che conveniva, o volere o no, piegare a quel <lb></lb>vento le vele. </s>

<s>Ond&#039;è che accompagnando una copia del Discorso del flusso <lb></lb>all&#039;arciduca Leopoldo d&#039;Austria, con lettera del dì 23 Maggio 1618, dopo <lb></lb>avergli accennato alla sentenza de&#039;Teologi romani contro il moto della Terra <lb></lb>come repugnante alla Santa Scrittura, così soggiunge: “ Ora, perchè io so <lb></lb>quanto convenga ubbidire e credere alle determinazioni dei superiori, come <lb></lb>quelli che sono scorti da più alte cognizioni, alle quali la bassezza del mio <lb></lb>ingegno per sè stesso non arriva, reputo questa presente scrittura, che gli <lb></lb>mando, come quella che è fondata sopra la mobilità della Terra, ovvero che <lb></lb>è uno degli argomenti che io produceva in confermazione di essa mobilità, <lb></lb>la reputo, dico, come una poesia, ovvero un sogno, e per tale la riceva <lb></lb>l&#039;A. V. ” (Alb. </s>

<s>VI, 280). </s></p><p type="main">

<s>Era in principio di questa scrittura, che Galileo così manoscritta man­<lb></lb>dava all&#039;Arciduca, accennato che più diffusamente parlerebbe l&#039;Autore di sì <lb></lb>fatta materia nel suo Sistema del mondo (Alb. </s>

<s>II, 388), e perciò, nella Let­<lb></lb>tera che l&#039;accompagnava, dop&#039;avere umiliata la fronte innanzi al Decreto <lb></lb>de&#039;Teologi romani, conclude allo stesso Arciduca, dicendogli che il pensiero <lb></lb>di ampliarsi sopra quell&#039;argomento, apportandone altri riscontri e riordinan­<lb></lb>dolo e distinguendolo in altra miglior forma e disposizione, com&#039;avrebbe <lb></lb>fatto ne&#039;Dialoghi del Sistema del mondo, s&#039;era risoluto in nebbia insiem <lb></lb>con tutti i suoi confusi e avviluppati fantasmi (Alb. </s>

<s>VI, 280). </s></p><p type="main">

<s>Stette però poco che quella nebbia parve alquanto dileguarsi. </s>

<s>Giovanni <lb></lb>Ciampoli, Ferdinando Cesarini monsignori, Maffeo Barberini e quell&#039;Orsino, <lb></lb>a cui fu dedicato il Discorso del flusso, cardinali, insiem con altri prelati, <lb></lb>che inclinavano a favorire i progressi della scienza, sentivano gl&#039;impedi­<lb></lb>menti che veniva frapponendo il Decreto del dì 5 Marzo, e come sarebbe <lb></lb>rimproverata la Repubblica ecclesiastica d&#039;irriverenza e d&#039;ingratitudine, per <lb></lb>aver condannato un libro scritto da un religiosissimo canonico, pubblicato <lb></lb>ad istanza di un vescovo e di un cardinale, e dedicato a un Papa, e a cui <lb></lb>si doveva l&#039;utilissima riforma del Calendario. </s>

<s>Consigliati perciò dallo zelo <lb></lb>per l&#039;utilità scientifica, e dalla prudenza, promossero nel 1620 l&#039;emanazione <lb></lb>di quell&#039;altro Decreto, in cui, sebben si riconoscesse giusta dai Cardinali <lb></lb>la condanna dei libri del Copernico “ nihilominus, quia in iis multa sunt <lb></lb>Reipublicae utilissima, unanimi censensu in eam fuerunt sententiam ut Co­<lb></lb>pernici opera, ad hanc usque diem impressa, permittenda essent, prout per­<lb></lb>miserunt, iis tamen correctis, iuxta subiectam emendationem, locis in qui­<lb></lb>bus non ex hypothesi sed asserendo de situ et motu Terrae disputat ” <lb></lb>(Riccioli, Almag. </s>

<s>novum, Pars post., T. I, Bononiae 1651, pag. </s>

<s>496). </s></p><p type="main">

<s>Il Cesarini e il Ciampoli particolarmente, nel dargli la notizia di questo <lb></lb>nuovo Decreto e di quel che i fatti promettevano sopra le parole, solleva­<lb></lb>rono l&#039;animo di Galileo, il quale, ripreso in mano il Discorso del flusso, <lb></lb>insinuava all&#039;Aggiunti, per maggior pubblicità, che lo rendesse in latino. </s>

<s><lb></lb>L&#039;ossequioso discepolo teneva nel 1622 preparata per le stampe quella ver-<pb xlink:href="020/01/907.jpg" pagenum="350"></pb>sione, alla quale aveva premesso un avvertimento ai lettori, dove fra le altre <lb></lb>leggevansi queste parole: “ Hanc ego Epistolam per hos dies ex Etruria in <lb></lb>Latium transtuli, quod a me duplici de causa factum fuit; primum, quia <lb></lb>Transalpinis nationibus, harum rerum maxime studiosis et Galilaei gloriae <lb></lb>vehementer deditis, id egregie carum fore existimavi; deinde ut si pluribus <lb></lb>ille linguis legeretur, qui omnibus linguis omni aevo perpetua celebratione <lb></lb>luculentissime depraedicari debet; an non debeat qui tot inauditis ac miri­<lb></lb>ficis inventis haec nostra tempora illnstrat? </s>

<s>” (MSS. Gal., P. IV, T. IV, c 68). </s></p><p type="main">

<s>Mentre che si meditava di dar così solenne pubblicità a questa versione <lb></lb>latina, l&#039;animo di Galileo rinverdì di più liete e rigogliose speranze. </s>

<s>Quel <lb></lb>Maffeo Barberini, ch&#039;ebbe tanta parte nell&#039;emanazion del Decreto del 1620, <lb></lb>in cui si temperava il rigore di quell&#039;altro emesso quattro anni avanti dalla <lb></lb>Sacra Congregazione de&#039;Cardinali, era stato assunto al soglio pontificio sotto <lb></lb>il nome di Urbano VIII. </s>

<s>Parve che si potesse sotto un tanto protettore, non <lb></lb>solo avventurar la pubblicazione del Discorso sul flusso, ma e del Libro da <lb></lb>sì lungo tempo meditato del Sistema del mondo, e perciò il dì 9 Otto­<lb></lb>bre 1623 scrive Galileo al principe Cesi che sarebbe voluto venire a Roma <lb></lb>in tempo opportuno per baciare il piede a Sua Santità. </s>

<s>“ Io raggiro, ivi <lb></lb>soggiunge, nella mente cose di qualche momento per la Repubblica lette­<lb></lb>raria, le quali, se non si effettuano in questa mirabil congiuntura, non oc­<lb></lb>corre, almeno per quel che si aspetta per la parte mia, sperar d&#039;incon­<lb></lb>trarne mai più una simile ” (Alb. </s>

<s>VI, 289, 90). </s></p><p type="main">

<s>La congiuntura fu colta e le speranze ebbero buon effetto. </s>

<s>Eccolo tutto <lb></lb>in fervore di tessere que&#039;suoi Dialoghi, dai quali tanta luce si diffonderebbe <lb></lb>sul mondo della materia e sul mondo degl&#039;intelletti. </s>

<s>Ne&#039;principii dell&#039;anno 1625 <lb></lb>quel fervore gli si rallenta un poco, ma pur procede avanti e l&#039;assiduità fa <lb></lb>crescere il lavoro (Campori, Carteggio galil., Modena 1881, pag. </s>

<s>224): a mezzo <lb></lb>Febbraio nonostante torna a scrivere alla gagliarda (ivi, pag. </s>

<s>225). </s></p><p type="main">

<s>La notizia che Galileo attende a scrivere in Dialogo del flusso e del Si­<lb></lb>stema del mondo è diffusa per tutto, e il p. </s>

<s>Scheiner esprime il desiderio <lb></lb>vivissimo di veder quello scritto, confessando di essersi convertito al Coper­<lb></lb>nicanismo (ivi, pag. </s>

<s>233). È quella stessa notizia giunta pure in Germania, <lb></lb>e il Pieroni da Praga scrive il dì 26 Luglio 1626 a Galileo, pregando lo <lb></lb>certificasse se era vero ch&#039;egli avesse messo mano a scrivere quell&#039;opera <lb></lb>della sua mirabile invenzione, che gli aveva detto volere intitolare <emph type="italics"></emph>Fluxus <lb></lb>atque refluxus maris<emph.end type="italics"></emph.end> (MSS. Gal., P. I, T. IX, c. </s>

<s>43). </s></p><p type="main">

<s>Nel Luglio del 1627 gli amici impazienti sono intorno al Ciampoli, che <lb></lb>solleciti Galileo a sodisfar più presto che sia possibile ai loro ardentissimi <lb></lb>desiderii: “ Arrivano qua avvisi che il corso de&#039;suoi Dialoghi si muova con <lb></lb>lentezza, e noi sentendo ciò sospiriamo la perdita di sì rari tesori. </s>

<s>Non ve­<lb></lb>diamo l&#039;ora di leggerne almeno qualche partìcella, sì che nel medesimo tempo <lb></lb>molti suoi amici, e fra questi come capo il p. </s>

<s>d. </s>

<s>Benedetto, uniamo le no­<lb></lb>stre preghiere e le chiediamo instantemente due grazie: una che ci lasci <lb></lb>gustare qualche cosa del fatto fin qui; l&#039;altra ch&#039;ella voglia vincere i con-<pb xlink:href="020/01/908.jpg" pagenum="351"></pb>sigli della quiete con gli stimoli della gloria e con le esortazioni degli amici ” <lb></lb>(Campori, Carteggio cit., pag. </s>

<s>258). Un anno e mezzo dopo le grazie furono <lb></lb>esaudite: in casa del signor canonico Cini si leggono i Dialoghi galileiani <lb></lb><emph type="italics"></emph>con stupore ed infinito applauso di chiunque li ode<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>278). </s></p><p type="main">

<s>Mancavano però ancora a que&#039;Dialoghi la cerimoniale Introduzione e le <lb></lb>attaccature de&#039;principii con le materie seguenti, che sebben sieno, dice lo <lb></lb>stesso Galileo, cose piuttosto oratorie e poetiche che scientifiche, non vuol <lb></lb>tuttavia trascurarle perchè l&#039;opera abbia spirito e vaghezza (Alb. </s>

<s>VI, 333). <lb></lb>Pare nonostante che fosse questo il lavoro di pochi giorni, avendo già il <lb></lb>dì 5 di Gennaio 1630 dato avviso al Ciampoli che i Dialoghi erano felice­<lb></lb>mente terminati (Campori cit., pag. </s>

<s>289). </s></p><p type="main">

<s>Tutto il forte stava in dar quel manoscritto di tanti desiderii e di tante <lb></lb>trepidazioni alle stampe, per le quali conveniva entrar ne&#039;gelosi trattati della <lb></lb>licenza ecclesiastica. </s>

<s>Era Maestro del sacro Palazzo allora un tal padre Nic­<lb></lb>colò Riccardi, soprannominato il Mostro, assai inclinato a favorir Galileo <lb></lb>(ivi, pag. </s>

<s>290), il qual Padre aveva nel Novembre di quell&#039;anno 1630 pro­<lb></lb>messo più volte al Castelli di <emph type="italics"></emph>spedir la licenza per i Dialoghi<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>302). <lb></lb>Il dì 20 Marzo del seguente anno 1631 n&#039;erano stati stampati sei fogli <lb></lb>(Alb. </s>

<s>VI, 378) e tutto il lavoro compìto alla metà di Dicembre (Campori, <lb></lb>pag. </s>

<s>319). Si pubblicò ne&#039;primi giorni dell&#039;anno appresso 1632, in Firenze, <lb></lb>dall&#039;Officina di Giovan Batista Landini, col titolo: <emph type="italics"></emph>Dialogo di Galileo Gali­<lb></lb>lei Linceo.... dove nei congressi di quattro giornate si discorre sopra i <lb></lb>due massimi Sistemi del mondo tolemaico e copernicano.<emph.end type="italics"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>È questo finalmente quel libro con tanta solennità promesso da ven­<lb></lb>tidue anni nell&#039;Avviso sidereo (Alb. </s>

<s>III, 73) e a innumerevoli occasioni dal­<lb></lb>l&#039;Autore stesso magnificato come quello che darebbe la dimostrazione più <lb></lb>certa del Sistema copernicano. </s>

<s>Confidava l&#039;Autore che sarebbe questa nuova <lb></lb>certezza principalmente derivata dal flusso marino, che nel moto della Terra <lb></lb>e non in altro riconosceva la sua ragione, ond&#039;è che, sebben nella prima <lb></lb>pagina non si conservi altrimenti il titolo di <emph type="italics"></emph>Fluxus et Refluxus,<emph.end type="italics"></emph.end> sotto il <lb></lb>quale era stato annunziato, occupa nonostante la trattazione di quel soggetto <lb></lb>la quarta parte di tutto il Libro. </s></p><p type="main">

<s>Che vana fosse quella confidenza, di che tanto s&#039;enfiava l&#039;animo di Ga­<lb></lb>lileo, si è subodorato già dal Discorso al cardinale Orsino, ma pur era de­<lb></lb>gno l&#039;Autore allora di qualche compatimento, ripensando alle puerili ipotesi <lb></lb>che ricorrevano per i libri filosofici di que&#039;tempi. </s>

<s>Si possono così fatte ipo­<lb></lb>tesi, senza bisogno di squadernare altri libri, veder raccolte e discusse in un <lb></lb>Trattato, che Galileo ebbe ad esaminar sotto gli occhi e a confutar ne&#039;suoi <lb></lb>Dialoghi. </s></p><pb xlink:href="020/01/909.jpg" pagenum="352"></pb><p type="main">

<s>Girolamo Borro aretino, verso il 1560, aveva scritto alcuni Dialoghi in <lb></lb>volgare sul flusso e riflusso marino, mandandoli attorno fra gli amici, cosi <lb></lb>manoscritti. </s>

<s>Girolamo Ghirlanda pensò a pubblicarli, e gli fece stampare in <lb></lb>Lucca nel 1561 per il Busdrago, sotto il nome di <emph type="italics"></emph>Talascopio Alseroforo,<emph.end type="italics"></emph.end> in­<lb></lb>dirizzandoli, per mezzo di una Lettera impressa nelle prime pagine, al me­<lb></lb>desimo Autore, il quale parve se ne adirasse così un poco, ma poi compia­<lb></lb>ciutosi del favore incontrato da questa sua opera letteraria, l&#039;ampliò, la <lb></lb>corresse in qualche parte, e la stampò in Firenze nel 1577 appresso Gior­<lb></lb>gio Mariscotti col titolo: <emph type="italics"></emph>Girolamo Borro aretino, Del flusso e riflusso del <lb></lb>mare ecc.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il Talascopio Alseroforo dimostra nel suo Trattato questa proposizione <lb></lb>fondamentale: “ Come la Luna abbia possanza col suo temperato calore di <lb></lb>rarefar l&#039;acqua, la quale rarefatta viene a sollevarsi ” (pag. </s>

<s>35) e cosi con­<lb></lb>clude la ragione del sollevarsi e deprimersi il mare di sei in sei ore, in or­<lb></lb>dine al moto circolare della Luna intorno alla Terra. </s></p><p type="main">

<s>Girolamo Borro poi conferma questa sua ipotesi mostrando quant&#039;ella <lb></lb>sia più ragionevole di quell&#039;altre professate dai Peripatetici, i quali consi­<lb></lb>derando che ne&#039;fondi del mare son come sulla Terra asciutta, monti e valli, <lb></lb>dicevano che “ l&#039;acque che sono sopra i monti da fondo del mare vi stanno <lb></lb>per forza e naturalmente cercano di scendere nelle basse valli, dove tro­<lb></lb>vando le altre acque, nè con esse potendosi fermare in quel piccolo luogo, <lb></lb>le cacciano. </s>

<s>Queste cacciate per forza salgono sopra i monti del mare, d&#039;onde <lb></lb>le prime si partirono.... Il salir delle acque fa il flusso e lo scendere delle <lb></lb>medesime fa il riflusso, il quale sempre dura perchè elle sempre salgono e <lb></lb>sempre scendono ” (pag. </s>

<s>43). </s></p><p type="main">

<s>Appetto a queste ipotesi doveva a buon diritto sembrare a Galileo una <lb></lb>peregrina speculazione quella dell&#039;antico Seleuco rinnovellata dal Cesalpino, <lb></lb>e aveva qualche giusto motivo di compiacersi per averla così sottilmente ri­<lb></lb>dotta ad essere dimostrativa, non tanto del diurno, quanto del moto annuale <lb></lb>della Terra. </s>

<s>Ma chi può scusare la vanità di colui, che dentro un&#039;arca ri­<lb></lb>dotta a forma latina dall&#039;Aggiunti voleva riposti i suoi preziosi tesori, per <lb></lb>ispedirli di là dai monti e dai mari, anche dopo che il De Dominis aveva <lb></lb>pubblicato il suo <emph type="italics"></emph>Euripus?<emph.end type="italics"></emph.end> o chi può sopportare il disprezzo con che l&#039;Au­<lb></lb>tore de&#039;Due Massimi sistemi deride l&#039;opinione di quel <emph type="italics"></emph>certo prelato?<emph.end type="italics"></emph.end><lb></lb>(Alb. </s>

<s>I, 455). </s></p><p type="main">

<s>Che fosse quell&#039;opinione conforme alla verità, come fu poi dal gran <lb></lb>Newton dimostrato, non occorre ora a noi ripeterlo: basti dir come, sup­<lb></lb>posto che il flusso e riflusso marino dipenda dalle attrazioni ora concordi <lb></lb>ora discordi del Sole e della Luna, risolve il De Dominis tutte le più astruse <lb></lb>questioni, che si possono fare intorno a quel cosi complicato soggetto, delle <lb></lb>quali questioni così magistralmente risolute dall&#039;Autor dell&#039;<emph type="italics"></emph>Euripus<emph.end type="italics"></emph.end> giova <lb></lb>a noi riferire le principali: </s></p><p type="main">

<s><emph type="italics"></emph>“ Quaesitum I.<emph.end type="italics"></emph.end> Cur aliqua maria multo plus quam aliqua alia, et cur <lb></lb>aliqua etiam aut nihil, aut parum admodum intumescunt et detumescunt? <pb xlink:href="020/01/910.jpg" pagenum="353"></pb>Respondeo .... quoniam igitur aliqua maria sunt ampliora, alia angustiora, <lb></lb>et alia profundioria, alia minus profunda, ideo alia plus habent aquae trahen­<lb></lb>dae quam alia ” (Romae 1624, pag. </s>

<s>47). <lb></lb>… </s></p><p type="main">

<s><emph type="italics"></emph>“ Quaesitum III.<emph.end type="italics"></emph.end> Cur ordinarie bis in die naturali aquae intumescunt, <lb></lb>et bis detumescunt per quasi sena horarum spatia, alicubi vero saepius in <lb></lb>die?... Respondeo .... sic igitur unus ex dictis semicirculis duodecim hora­<lb></lb>rum spatio percurrit unum hemisphaerium, ascendendo nimirum per sex <lb></lb>horas quousque vertex cumuli sit in meridiano dicti hemisphaerii, et per <lb></lb>sex alias descendendo cui alter similiter semicirculus priori diametraliter <lb></lb>oppositus, per alias 12 horas succedit et sic deinceps.... Quod vero alicubi <lb></lb>saepius in die id contingit, ego fateor me non posse in mari veram causam <lb></lb>assignare ” (ibi, pag. </s>

<s>57). <lb></lb>… </s></p><p type="main">

<s><emph type="italics"></emph>“ Quaesitum V.<emph.end type="italics"></emph.end> Cur in eodem etiam loco diversis temporibus intume­<lb></lb>scentia et detumescentia maris est inaequalis? </s>

<s>Respondeo totum id contin­<lb></lb>gere ordinarie ex ipsis luminaribus ipsorumque circulis mare attrahentibus <lb></lb>vel allicientibus. </s>

<s>Cum enim non sola Luna sed etiam Sol pro suo modulo <lb></lb>suum cumulum, licet minorem, efficiat, ex diversis aspectibus qui sunt in­<lb></lb>ter Solem et Lunam, maior vel minor fieri debet fluxus et refluxus. </s>

<s>Si lu­<lb></lb>minaria sint in coniunctione vel oppositione, quia uterque cumulus utriusque <lb></lb>luminaris simul concurrunt, profecto plus aquae accumulabitur utroque cu­<lb></lb>mulo simul iuncto, ubi uterque circulus transpolaris aquas trahens, in uni­<lb></lb>cum circulum conveniunt, quod fit in coniunctione et oppositione lumina­<lb></lb>rium, quam si in alio aspectu a se invicem circuli illi disiiungantur, et se <lb></lb>invicem in sua actione impediant ” (ibi, pag. </s>

<s>59, 60). </s></p><p type="main">

<s><emph type="italics"></emph>“ Quaesitum VI.<emph.end type="italics"></emph.end> Cur non eadem diei hora aqua fit ubique et altis­<lb></lb>sima et depressissima sed magna fit in hac horarum diversitas, tum eodem <lb></lb>loco tum etiam diversis, quoad initium tum fluxus quam refluxus compara­<lb></lb>tis? </s>

<s>Respondeo ex mea positione sequi finem fluxus, hoc est maximum <lb></lb>uniuscuiusque diei tumorem aquae, ubique .... deberi contingere quando <lb></lb>Luna existit circa loci meridianum; hoc est ad horam astronomicam duo­<lb></lb>decimam solarem tam diurnam quam nocturnam; finem vero refluxus et <lb></lb>initium fluxus, quando eadem Luna existit circa horam solarem utramque <lb></lb>sextam.... Et quoniam non eadem hora solari quotidie Luna est aut in me­<lb></lb>ridiano aut in circulo horae sextae, sed variat plurimum, ideo quotidianus <lb></lb>hic effectus, finis nimirum et initium fluxus et refluxus, quotidie per totum <lb></lb>mensem variat horas solares ” (ibi, pag. </s>

<s>64, 65). </s></p><p type="main">

<s>Se Galileo avesse solamente atteso a questo notissimo fatto risoluto dal <lb></lb>De Dominis in questo suo ultimo quesito, si sarebbe facilmente persuaso <lb></lb>della falsità della sua ipotesi; cosa che gli fu poi fatta notar dal Baliani, il <lb></lb>quale giudicando tutto il quarto Dialogo maraviglioso, confessava nonostante <lb></lb>esservi una gravissima difficoltà, alla quale non si rispondeva, perchè do­<lb></lb>vrebbe, nell&#039;ipotesi galileiana, essere il flusso “ ogni di alla stess&#039;ora; ep-<pb xlink:href="020/01/911.jpg" pagenum="354"></pb>pur l&#039;opinione comune è contraria, cioè che si anticipi ogni giorno circa quat­<lb></lb>tro quinti di ora per andar esso seguendo il moto della Luna ” (Alb. </s>

<s>IX, 266). </s></p><p type="main">

<s>Ma era Galileo tanto pieno di sè, che non ci ammetteva nessun altro, <lb></lb>e lo cacciava con orgoglioso dispetto, come fece non solo con Girolamo <lb></lb>Borro, il quale diceva “ che la Luna ha possanza col suo temperato calore <lb></lb>di rarefar l&#039;acqua, la quale rarefatta viene a sollevarsi ” (Alb. </s>

<s>I 455) ma <lb></lb>con quel <emph type="italics"></emph>certo prelato<emph.end type="italics"></emph.end> autore di un trattatello dove si legge “ che la Luna <lb></lb>vagando per il cielo attrae e solleva verso di sè un cumulo d&#039;acqua, il quale <lb></lb>la va continuamente seguitando, sicchè il mare alto è sempre in quella parte <lb></lb>che soggiace alla Luna ” (ivi). </s></p><p type="main">

<s>Perchè poi è un fatto evidentissimo che il flusso ha una certa costante <lb></lb>relazione con la Luna, ecco in che Galileo fa consistere l&#039;efficienza di lei <lb></lb>sulla marea. </s>

<s>Considera ch&#039;essendo la stessa Luna ora nella congiunzione ora <lb></lb>nell&#039;opposizione fa le veci del <emph type="italics"></emph>tempo,<emph.end type="italics"></emph.end> che accomodavano gli artèfici per re­<lb></lb>golare il moto agli antichi orologi, e da ciò ne segue che la Terra intorno <lb></lb>al Sole ora si muove più, ora meno veloce con periodi e restituzioni me­<lb></lb>strue, che son la causa vera efficiente delle alterazioni periodiche mestrue <lb></lb>e annue de&#039;flussi e refiussi. </s>

<s>“ Ora vedete, conclude Galileo, come la causa <lb></lb>del periodo mestruo risiede nel moto annuo, e insieme vedete ciò che ha <lb></lb>che far la Luna in questo negozio, e come ella ci entra a parte, senza aver <lb></lb>che fare niente nè con mari nè con acqua ” (Alb. </s>

<s>I, 491). </s></p><p type="main">

<s>Il concetto galileiano del riguardar la Luna come il contrappeso, che <lb></lb>ritirato ora più ora meno dal centro, indugia o velocita il moto alla Terra, <lb></lb>benchè sia male appropriato al fatto della marea, avrebbe nonostante il me­<lb></lb>rito di esser chiamato arguto, se fosse stato originale, ma non fece altro in <lb></lb>verità Galileo che tirare alla sua ipotesi le dottrine, con le quali spiegavano, <lb></lb>secondo il Copernico, gli Astronomi antichi come mai si muova nell&#039;apogeo <lb></lb>la Luna più tarda e nel perigeo più veloce. </s>

<s>“ Sub hoc igitur orbe et ipsius <lb></lb>plano Luna semper in consequentia moveri cernitur, sed aliquando mini­<lb></lb>mum, aliquando plurimum. </s>

<s>Tanto enim tardior quanto sublimior, velocior <lb></lb>autem quo Terrae proprinquior. </s>

<s>Quod in ea facilius quam in alio quovis <lb></lb>sidere ob eius vicinitatem discerni potuit. </s>

<s>Intellexerunt igitur per epicyclum <lb></lb>fieri quum Luna illum circumcurrens in superna circumferentia detraheret <lb></lb>aequalitati, in inferna autem promoveret eamdem ” (De revolut. </s>

<s>cit., c. </s>

<s>98 v.). </s></p><p type="main">

<s>Coloro che affascinati da quell&#039;insolito splendore tutto ammiravano in <lb></lb>Galileo, dissero maravigliosa anche questa dimostrazione del flusso marino. </s>

<s><lb></lb>Ma perchè per le quotidiane osservazioni troppo si rendeva evidente la re­<lb></lb>golarità de&#039;moti del mare e la loro conformità ai moti della Luna, smar­<lb></lb>rita quella diritta via aperta già dal Gilberto e dal De Dominis, molti se­<lb></lb>guitarono le fantasie del Cartesio, che attribuiva il flusso alla maggiore o <lb></lb>minor pressione della sostanza eterea interposta fra la Terra e la Luna. </s>

<s>Il <lb></lb>Fabry, ne&#039;suoi <emph type="italics"></emph>Dialogi physici De motu Terrae,<emph.end type="italics"></emph.end> attribuì l&#039;effetto non al­<lb></lb>l&#039;etere cartesiano ma all&#039;aria, la pression della quale prevalendo ora più da <lb></lb>una parte che dall&#039;altra, fa sì che l&#039;umida superficie marina si rigonfi più <pb xlink:href="020/01/912.jpg" pagenum="355"></pb>là, dove si sente esser meno premuta. </s>

<s>Così senza soggiacerne agl&#039;influssi <lb></lb>emula il mare il moto della Luna. </s>

<s>“ Atque ita praedictus aquae tumor mo­<lb></lb>tum Lunae omnino aemulatur ” (Lugduni 1665, pag. </s>

<s>108). </s></p><p type="main">

<s>Venne curiosità al Wrenn di far della verità di queste ipotesi qualche <lb></lb>esperienza, e perciò consigliava il Boyle a prendere un lungo tubo barome­<lb></lb>trico per osservar più facilmente se, in conformità del flusso e riflusso ma­<lb></lb>rino, vi si fosse potuta notare qualche varietà di livello. </s>

<s>Quel che rispon­<lb></lb>desse il celebre Autore degli Sperimenti fisico-meccanici si può vederlo dallo <lb></lb>Sperimento XVIII, in cui, dopo aver significati i desiderii del Wrenn così <lb></lb>prosegue a dire a suo nipote: “ Cum autem comperimus hydrargyrum in <lb></lb>tubo contentum, prae accidentali, ut videtur aeris mutatione tam incertis <lb></lb>motibus sursum et deorsum ferri, in ancipiti haereo dubitans altitudinem <lb></lb>nec ne inveniemus mercurii tam regulariter variari, quam quaestionem in­<lb></lb>geniose propositam invenimus. </s>

<s>Postquam autem, Deo favente, rem repertus <lb></lb>fuero, curabo ne te lateat successus ” (Opera omnia, T. I, Venetiis 1697, <lb></lb>pag. </s>

<s>39). </s></p><p type="main">

<s>Parecchi anni prima però che al gran Fisico inglese, parve quel suc­<lb></lb>cesso essere stato rivelato a un nostro Italiano. </s>

<s>Così infatti si legge a carte 182 <lb></lb>del T. IX de&#039;Manoscritti del Cimento: <emph type="italics"></emph>“ L&#039;esperimento nuovo osservato da <lb></lb>don Francesco Tarvigia in Venezia, cavato da una Lettera indirizzata al <lb></lb>p. </s>

<s>Atanasio Kircher.<emph.end type="italics"></emph.end> — Ho osservato nella fistola o canna di vetro, con la <lb></lb>quale il Torricelli, Robervallio, Valeriano Magno e Mersenno mostrarono il <lb></lb>vacuo, che disceso il mercurio fino a quel segno che è salito di due piedi <lb></lb>più o meno, secondo la diversità de&#039;paesi, al calar dell&#039;acqua marina il mer­<lb></lb>curio s&#039;inalza un mezzo dito: nel crescer della medesima acqua si abbassa <lb></lb>e persevera con questa reciprocazione costantemente con un moto contrario <lb></lb>al moto del mare. </s>

<s>La mutazione dell&#039;aria altera talvolta l&#039;esperimento, ma <lb></lb>con la replicata operazione mi sono certificato esservi una invariabile con­<lb></lb>nessione fra il moto dell&#039;acqua marina e quello che si vede nel vetro. </s>

<s>Di <lb></lb>questa connessione supplico V. P. rendermi capace della causa fisica ” </s></p><p type="main">

<s>Ciò che si rispondesse da quel Kircher, il quale a qualunque più dif­<lb></lb>ficile problema proposto aveva pronta la soluzione, non sapremmo noi dire, <lb></lb>ma è da creder che facesse tutt&#039;altra risposta dalla vera, la quale sarebbe <lb></lb>stata che facilmente il Tarvigia s&#039;era ingannato. </s>

<s>L&#039;inganno fu poi in ogni <lb></lb>modo tolto via dalle diligentissime osservazioni del Ramazzini, dalle quali fu <lb></lb>concluso essere indipendenti le variazioni barometriche così dalle vicende <lb></lb>de&#039;pleniluni e de&#039;noviluni, come de&#039;flussi del mare e de&#039;riflussi. </s></p><p type="main">

<s>Ma è da tornare a Galileo, riguardo al quale ha la storia da notare un <lb></lb>fatto, per cui si darà sempre meglio a conoscere l&#039;indole di quell&#039;uomo. </s>

<s><lb></lb>Dop&#039;aver tanto accarezzata quella sua dimostrazione del flusso, dop&#039;averle <lb></lb>dato così precipua e splendida parte ne&#039;Dialoghi de&#039;Massimi Sistemi, dopo <lb></lb>aver negato fede al gran Gilberto, nel quale aveva letto: <emph type="italics"></emph>Videmus namque <lb></lb>quomodo oceanus sub certis quibusdam Lunae positionibus intumescat et <lb></lb>aestuet<emph.end type="italics"></emph.end> (De Magn. </s>

<s>cit., pag. </s>

<s>224), e tutto ciò per sola virtù magnetica; <pb xlink:href="020/01/913.jpg" pagenum="356"></pb>dop&#039;aver conculcato il De Dominis mettendolo alla pari di Girolamo Borro <lb></lb>e degli altri Filosofi più volgari, eccolo, all&#039;occasion di avere osservato la <lb></lb>titubazione lunare, dar abito tutt&#039;affatto diverso a&#039;suoi pensieri, approvando <lb></lb>in sostanza ciò che aveva prima confutato e deriso. </s>

<s>“ Aggiungesi (scriveva <lb></lb>al Castelli, dop&#039;avergli significate le tre nuove mutazioni osservate nella fac­<lb></lb>cia della Luna) di più una seconda maraviglia, ed è che queste tre diverse <lb></lb>mutazioni hanno tre diversi periodi, imperocchè l&#039;una si muta di giorno in <lb></lb>giorno e così viene ad avere il suo periodo diurno; la seconda si va mu­<lb></lb>tando di mese in mese, ed ha il suo periodo mestruo; la terza ha il suo <lb></lb>periodo aunuo, secondo il quale finisce la sua variazione. </s>

<s>Or che dirà la <lb></lb>P. V. R. nel confrontare questi tre periodi lunari co&#039;tre periodi diurno, <lb></lb>mestruo ed annuo de&#039;movimenti del mare, de&#039;quali per comune consenso <lb></lb>di tutti la Luna è arbitra e soprantendente? </s>

<s>” (Alb. </s>

<s>VII, 196). A che il Ca­<lb></lb>stelli non seppe dir altro, se non ch&#039;egli era curioso d&#039;intendere “ come que­<lb></lb>ste osservazioni si accordano con le dottrine de&#039;Dialoghi ” (Alb. </s>

<s>X, 246). </s></p><p type="main">

<s>Così veniva suo malgrado confessato dallo stesso Autore che la quarta <lb></lb>parte dell&#039;opera de&#039;Massimi Sistemi vacillava sul falso, in cui poi cadde irre­<lb></lb>parabilmente quando il Newton, svolgendo il germe di que&#039;concetti infusi <lb></lb>nel lib. </s>

<s>VI <emph type="italics"></emph>De Magnete<emph.end type="italics"></emph.end> confermò le dottrine colle quali il De Dominis aveva, <lb></lb>due terzi di secolo prima, sciolto il problema del flusso e del riflusso del <lb></lb>mare. </s>

<s>Quella tanto vantata dimostrazione galileiana non era dunque riuscita <lb></lb>che ad una vanità, e non ebbe di qui il sistema copernicano, per opera di <lb></lb>Galileo, nessun conforto, come non l&#039;ebbe da lui nell&#039;argomento de&#039;venti <lb></lb>tropicali. </s></p><p type="main">

<s>Passando ora ad esaminare gli altri argomenti, uno de&#039;principali che <lb></lb>si trovi svolto ne&#039;<emph type="italics"></emph>Massimi Sistemi<emph.end type="italics"></emph.end> è quello che riguarda la discesa de&#039;gravi <lb></lb>e il moto de&#039;proietti in relazione col moto vertiginoso della Terra. </s>

<s>Vedemmo <lb></lb>come alle difficoltà promosse prima da Aristotile e ripetute poi da Ticone <lb></lb>avesse risposto il Gilberto nella Fisiologia sua nuova <emph type="italics"></emph>De Magnete,<emph.end type="italics"></emph.end> segnata­<lb></lb>mente al cap. </s>

<s>V del VI libro, desumendo le prove dal principio delle ma­<lb></lb>gnetiche forze attrattive, gli effluvii delle quali o la sfera di attività come <lb></lb>si dice, si estende, secondo il Gilberto, alquanto al di là de&#039;limiti superfi­<lb></lb>ciali del Globo. </s>

<s>Dietro questo luminoso principio le conclusioni del Filosofo <lb></lb>inglese riescono invitte, e la nuova scienza neutoniana nient&#039;altro in sostanza <lb></lb>ha fatto più che stabilir meglio quello stesso principio del Gilberto e svol­<lb></lb>gerne la conclusione. </s></p><p type="main">

<s>Galileo non seppe riconoscere quanto fosse di vero in quelle forze at­<lb></lb>trattive, e ammettendo che vengano i proietti trasportati seco nella sua ver­<lb></lb>tigine dalla Terra, come vien trasportata la Luna, affermò un fatto senza <lb></lb>però dir qual ne fosse la causa misteriosa. </s>

<s>Di qui è che facendosi Galileo <lb></lb>stesso commentatore al Gilberto, svolge prolissamente nel secondo Dialogo <lb></lb>gli argomenti di lui in modo, che i Simplicii stessi ne vadan capaci, ma <lb></lb>non v&#039;infonde que&#039;principii scienziali, che si sarebbero desiderati dai Sa­<lb></lb>gredi. </s></p><pb xlink:href="020/01/914.jpg" pagenum="357"></pb><p type="main">

<s>Della perspicuità però delle galileiane dimostrazioni n&#039;abbiamo l&#039;esem­<lb></lb>pio in queste note, nelle quali condensa l&#039;Autore ciò che sciolse poi in quel <lb></lb>profluvio di parole, che si leggono nel sopra citato Dialogo secondo: “ Cor­<lb></lb>rendo una nave velocissimamente, la <lb></lb>freccia, o palla che sarà meglio, sca­<lb></lb>ricata con l&#039;arco a perpendicolo, ve­<lb></lb>ramente non riceve l&#039;impeto a per­<lb></lb>pendicolo, ma inclinato verso la parte <lb></lb>dove cammina la nave, perchè, mo­<lb></lb>vendosi per esempio la nave dalla <lb></lb>sinistra verso la destra, nello scattare <lb></lb>dell&#039;arco, la palla si trova in A (fig. </s>

<s>67) <lb></lb><figure id="id.020.01.914.1.jpg" xlink:href="020/01/914/1.jpg"></figure></s></p><p type="caption">

<s>Figura 67.<lb></lb>e nel separarsi dalla corda si trova <lb></lb>in B: adunque l&#039;impeto ricevuto è <lb></lb>secondo la linea inclinata AB, e non <lb></lb>secondo il perpendicolo. </s>

<s>” </s></p><p type="main">

<s>“ Parimente, se la Terra stesse ferma, l&#039;artiglieria A (fig. </s>

<s>68) al segno B <lb></lb>darà giusto, movendosi la palla secondo la linea ABF. </s>

<s>Ma se la Terra gi­<lb></lb><figure id="id.020.01.914.2.jpg" xlink:href="020/01/914/2.jpg"></figure></s></p><p type="caption">

<s>Figura 68.<lb></lb>rasse dovria da­<lb></lb>re alto girando <lb></lb>verso la destra, <lb></lb>e così appare a <lb></lb>chi considera <lb></lb>poco, ma a chi <lb></lb>considererà che, <lb></lb>mentre che la <lb></lb>palla cammina <lb></lb>dentro il pezzo, <lb></lb>l&#039;artiglieria vie­<lb></lb>ne da A in C, <lb></lb>onde la palla ri­<lb></lb>ceve l&#039;impeto <lb></lb>più inclinato, <lb></lb>cioè secondo la linea AD; intenderà benissimo come la botta non dovrà dar <lb></lb>alto, ma nell&#039;istesso segno B trasportato dal moto della Terra in D, men­<lb></lb>tre la palla va per aria da C in D. </s>

<s>E quanto più il moto sarà veloce, tanto <lb></lb>più grande sarà la distanza BD, ma anco tanto sarà maggiore il progresso <lb></lb>AC e l&#039;inclinazione del CD sotto al tiro primo ABF ” (MSS. Gal., P. VI, <lb></lb>T. II, c. </s>

<s>20). </s></p><p type="main">

<s>Nemmeno dunque per questa parte Galileo ha gran merito in confer­<lb></lb>mare il sistema copernicano, non avendo fatto altro che ridurre all&#039;intelli­<lb></lb>genza comune, trascurati i principii scientifici, gli argomenti del Gilberto. </s>

<s><lb></lb>Chi legge nella Giornata III le meraviglie fatte di Aristarco e del Copernico, <lb></lb>i quali, non essendo riusciti a risolvere le difficoltà delle fasi di Venere, pur <pb xlink:href="020/01/915.jpg" pagenum="358"></pb>confidentemente affermarono non poter, da quella ch&#039;essi stessi avevano di­<lb></lb>segnata, esser altra la struttura dell&#039;universo, e poi legge come il canoc­<lb></lb>chiale a lui proprio, a Galileo, mostrasse prima che ad ogni altro Venere e <lb></lb>Marte disuguali a sè stessi, secondo le proporzioni assegnate già dal Coper­<lb></lb>nico, e Venere sotto il Sole apparir falcata e mutar le sue forme nello stesso <lb></lb>modo che fa la Luna (Alb. </s>

<s>I, 365); ecco, dice, l&#039;Autore de&#039;Massimi Sistemi <lb></lb>essere il primo a dar la più splendida conferma al sistema copernicano. </s>

<s>E <lb></lb>di tal gloria veramente si compiacque Galileo, ma la critica crudele svela <lb></lb>così le occulte fraudi, che l&#039;usurpata gloria si converte finalmente in meri­<lb></lb>tata ignominia. </s></p><p type="main">

<s>Il dì 13 di Novembre 1610 il fortunato Autore del Messaggero celeste <lb></lb>scriveva a Praga a don Giuliano de&#039;Medici che, trovata la corte a Giove e <lb></lb>due servi al vecchio Saturno che non staccandosegli mai dal fianco lo aiu­<lb></lb>tino a camminare, <emph type="italics"></emph>intorno agli altri pianeti non ci è novità alcuna.<emph.end type="italics"></emph.end><lb></lb>(Alb. </s>

<s>VI, 127). </s></p><p type="main">

<s>Aveva appena Galilco spedito questa, senza speranza oramai di più re­<lb></lb>cuperarla, quando gli recapita una lettera scritta dal Castelli otto giorni <lb></lb>prima da Brescia, nella quale, come uno che si risvegli dal sonno, atten­<lb></lb>deva a leggere queste parole: “ Essendo, come credo, vera la proposizione <lb></lb>di Copernico che Venere giri intorno al Sole, è chiaro che sarebbe neces­<lb></lb>sario che fosse vista da noi alle volte cornuta, alle volte no, stando pure il <lb></lb>detto Pianeta in pari remozione dal Sole, ogni volta però che la piccolezza <lb></lb>de&#039;corni e la effusione de&#039;raggi non c&#039;impedissero l&#039;osservazione di questa <lb></lb>differenza. </s>

<s>Ora desidero saper da V. S. se lei, con l&#039;aiuto de&#039;suoi meravi­<lb></lb>gliosi occhiali, ha notata simile apparenza, quale senza dubbio saria mezzo <lb></lb>sicuro di convincer qualsivoglia ostinato ingegno. </s>

<s>Simil cosa vo sospettando <lb></lb>ancora di Marte circa il quadrato con il Sole, non dico già di apparenza <lb></lb>cornuta o non cornuta, ma almeno di semicircolare o più piana. </s>

<s>” E con­<lb></lb>clude supplicandolo di due righe in risposta (Alb. </s>

<s>VIII, 118, 19). </s></p><p type="main">

<s>E che cosa poteva rispondere? </s>

<s>Volendo esser sincero conveniva ripe­<lb></lb>tesse al Castelli quel che poche ore prima aveva scritto a don Giuliano <lb></lb>de&#039;Medici, che cioè non aveva ancora osservato alcuna di quelle novità ce­<lb></lb>lesti. </s>

<s>Ma colla sincerità non veniva a secondare que&#039;suoi fermi propositi di <lb></lb>voler essere in tutto o apparire il primo ed il solo. </s>

<s>Conveniva dunque usare <lb></lb>ogni arte, e fosse pure anche illecita, per mostrar ch&#039;era a lui sovvenuto <lb></lb>prima che al Castelli quel così importante concetto, e ch&#039;egli era stato pro­<lb></lb>priamente il primo a metterlo in atto. </s></p><p type="main">

<s>Mentre pensa ai modi più scaltri di esercitare quell&#039;arte, gli viene <lb></lb>scritto allo stesso don Giuliano, il dì 11 Dicembre, di un altro particolare <lb></lb>da sè <emph type="italics"></emph>nuovamente<emph.end type="italics"></emph.end> osservato (Alb. </s>

<s>VI, 128), che è quello delle fasi di Ve­<lb></lb>nere dichiarate in cifra per serbare il segreto geloso. </s>

<s>Così insomma resul­<lb></lb>tava da questa lettera scritta a Praga all&#039;Ambasciatore toscano, che occorse <lb></lb>l&#039;osservazion del fenomeno tra il dì 13 di Novembre e l&#039;undici del seguente <lb></lb>Dicembre 1610. Ma la lettera del Castelli precedeva col suo avviso questi <pb xlink:href="020/01/916.jpg" pagenum="359"></pb>documenti di otto giorni, ond&#039;è che il primo partito suggerito dall&#039;astuzia <lb></lb>a Galileo fu quello di soprapporre un X al 9 precedente al <emph type="italics"></emph>bre<emph.end type="italics"></emph.end> dell&#039;abbre­<lb></lb>viatura, con la quale il Castelli aveva scritto il mese di Novembre. </s>

<s>Ma l&#039;in­<lb></lb>chiostro, con cui la mano dello stesso Galileo tirò quell&#039;X, essendo molto <lb></lb>più chiaro, fa trasparir di sotto le forme distintissime del 9 scritto dal Ca­<lb></lb>stelli con inchiostro più nero, cosicchè l&#039;Alberi, come qualunque altro che <lb></lb>posasse gli occhi in fondo al tergo della c. </s>

<s>164 del T. VII, P. VI de&#039;ma­<lb></lb>noscritti galileiani, non dubiterebbe di leggervi chiara la data originalmente <lb></lb>scrittavi del Novembre. </s></p><p type="main">

<s>Riguardando dunque Galileo come un fatto vero quello ch&#039;era una sua <lb></lb>sottilissima frode, aspettò, per colorirla meglio, il 30 di Dicembre, giorno in <lb></lb>cui scrisse così al padre don Benedetto: “ Alla gratissima di V. S. molto <lb></lb>rever. <emph type="italics"></emph>delli 5 Dicembre<emph.end type="italics"></emph.end> darò breve risposta.... Sappia dunque che io, circa <lb></lb>tre mesi fa, cominciai ad osservar Venere collo strumento e la vidi di figura <lb></lb>rotonda ed assai piccola; andò di giorno in giorno crescendo in mole e man­<lb></lb>tenendo pure la medesima rotondità, finchè finalmente, venendo in assai <lb></lb>gran lontananza dal Sole, cominciò a scemare della rotondità dalla parte <lb></lb>orientale, ed in pochi giorni si ridusse al mezzo cerchio.... Quanto a Marte <lb></lb>non ardirei di affermare niente di certo, ma osservandolo da quattro mesi <lb></lb>in qua, parmi che in questi ultimi giorni, sendo in mole appena il terzo di <lb></lb>quello ch&#039;era il Settembre passato, si mostri da oriente alquanto scemo, se <lb></lb>già l&#039;effetto non m&#039;inganna, il che non credo.... Oh quante e quali con­<lb></lb>seguenze ho io dedotto, don Benedetto mio, da questa e da altre osserva­<lb></lb>zioni! ” (Alb. </s>

<s>VI, 134, 35). </s></p><p type="main">

<s>Le lettere a don Giuliano, dalle quali manifestamente apparisce che le <lb></lb>fasi di Venere incominciò Galileo ad osservarle dopo il dì 11 di Novembre, <lb></lb>e dopo l&#039;avviso avutone dal Castelli, tradiscono di menzogna la sopra rife­<lb></lb>rita asserzione che, dicendo essere incominciate invece <emph type="italics"></emph>circa tre mesi fa,<emph.end type="italics"></emph.end><lb></lb>le ridurrebbe presso alla fine di Agosto. </s>

<s>Delle contestazioni di don Giuliano <lb></lb>però Galileo non teme, e non ci pensa, nè teme pure di quel buon uomo <lb></lb>di don Benedetto, ma pensa ai posteri, appresso ai quali vuole assicurar la <lb></lb>sua gloria. </s>

<s>Da così fatti pensieri e timori fu più fortemente che mai so­<lb></lb>prappreso negli ultimi anni della sua vita, e un giorno, nella sua oscura so­<lb></lb>litudine di Arcetri, gli tornò alla memoria quella-lettera ricevuta il dì 5 del <lb></lb>Novembre 1610 da Brescia, e sentì che, con averle alterata la data, non <lb></lb>veniva in ogni modo ad assicurarsi d&#039;apparire al mondo il primo ed il solo. </s></p><p type="main">

<s>Lacerare quella lettera del Castelli era inutile, rimanendo essa comme­<lb></lb>morata e viva nella risposta del di 30 Dicembre. </s>

<s>Non ci era altra via che <lb></lb>riformarla sostituendogliene un&#039;altra, dalla quale apparisse che il concetto <lb></lb>delle fasi di Venere e delle alterazioni di figura in Marte, per trionfale con­<lb></lb>ferma del sistema copernicano, sovvenne in mente al Castelli dietro una <lb></lb>finta lettera scrittagli il di 22 d&#039;Agosto da lui stesso, che meditava questi <lb></lb>tradimenti, da Galileo. </s></p><p type="main">

<s>E secondo aveva il vecchio Tiranno di Arcetri meditato fra le cupe ge-<pb xlink:href="020/01/917.jpg" pagenum="360"></pb>losie del suo regno, mandò ad effetto. </s>

<s>Dette ad intendere al giovane Vi­<lb></lb>viani, ospite suo, ch&#039;essendosi smarrita la lettera del Castelli, alla quale <lb></lb>aveva fatto la risposta il dì 30 Dicembre 1610, voleva perciò dettargliela, <lb></lb>affinchè in luogo dell&#039;originale ne rimanesse almeno la copia. </s>

<s>Lo stesso Vi­<lb></lb>viani scrisse appunto così con le forme proprie di quel suo carattere cal­<lb></lb>ligrafico giovanile: </s></p><p type="main">

<s>“ Da che io ebbi la lettera di V. S. Ecc.ma delli 22 d&#039;Agosto, nella <lb></lb>quale mi accenna di avere osservato in cielo un&#039;altra novità inopinabile, <lb></lb>quel desiderio che ho sempre avuto di trasferirmi un&#039;altra volta dove Ella <lb></lb>si ritrovava, per poter con il suo aiuto dare qualche gagliardo principio a <lb></lb>quello studio di Geometria e Filosofia, al quale, mentre dimoravo in Pa­<lb></lb>dova, m&#039;incitò, hora in tal guisa mi s&#039;è accresciuto, che ho fatto ferma ri­<lb></lb>soluzione di venire, con buona grazia de&#039;miei Superiori, a stanziare in Fi­<lb></lb>renze, e credo che dopo Pasqua sarò consolato. </s>

<s>Dall&#039;istesso avviso che V. S. <lb></lb>mi dà, dopo varii pensieri che mi sono passati per il capo, finalmente son <lb></lb>cascato in questo: che essendo vera, come tengo verissima, la copernicana <lb></lb>costituzione del mondo, Venere abbia da fare, in pari digressioni dal Sole, <lb></lb>talvolta apparenza cornuta, talvolta non cornuta, secondo che si ritroverà o <lb></lb>di qua o di là dal Sole, ma che ne&#039;secoli passati sia stata impossibile simile <lb></lb>osservazione, per la piccolezza del globo di Venere e lo svanimento della sua <lb></lb>figura. </s>

<s>Or che V. S. con le sue immortali invenzioni ha osservato tante altre <lb></lb>maraviglie nelle cose celesti, invisibili alle forze ordinarie, desiderei sapere <lb></lb>se in questo particolare ha fatto osservazione alcuna, e se è vero quanto ho <lb></lb>sospettato. </s>

<s>Nel medesimo desiderio stanno il p. </s>

<s>d. </s>

<s>Serafino di Quinzano, e <lb></lb>gli signori Ferrante Lana e Francesco Albano affezionatissimi alle dottrine <lb></lb>di V. S. e filosofi non dozzinali. </s>

<s>Per tanto la supplico a darmene avviso, <lb></lb>perchè, oltre che la conclusione, sarà per sè stessa di gran conto, e noi <lb></lb>tutti gliene resteremo obbligatissimi: servirà parimente per convincere qual­<lb></lb>sivoglia ostinato ingegno contro Copernico. </s>

<s>Vado sospettando ancora simile <lb></lb>apparenza in Marte, ma perchè a questa terminazione si ricercherebbe più <lb></lb>esatta cognizione della remozion sua dal Sole, della quale me ne confesso <lb></lb>ancora ignorante, non dirò altro, solo che, ricordandomegli obbligatissimo <lb></lb>servitore e discepolo, li fo riverenza pregandogli da Dio benedetto ogni con­<lb></lb>tento. </s>

<s>Li soprannominati signori li bacian le mani. </s>

<s>Di Brescia 5 di Xbre 1610. <lb></lb>Devotiss. </s>

<s>servo e discepolo D. </s>

<s>Benedetto Castelli. </s>

<s>” (MSS. Gal., P. VI, <lb></lb>T. TII, c. </s>

<s>167), </s></p><p type="main">

<s>Questa dunque sarebbe stata la Lettera, che si voleva far comparire <lb></lb>nell&#039;Epistolario galileiano, ma all&#039;astuto vecchio di Arcetri mancò un punto <lb></lb>che l&#039;ha tradito. </s>

<s>Ei non si seppe risolvere a distrugger l&#039;autografo del Ca­<lb></lb>stelli, il quale venuto alle mani dell&#039;Alberi fu da lui ingenuamente pubbli­<lb></lb>cato, invece della copia rifatta. </s>

<s>Abbiam detto ingenuamente, perchè il buon <lb></lb>uomo editore era mille miglia lontano dal sospettar della tresca, e fu que­<lb></lb>sta stessa ingenuità che non gli fece ricercar come mai dica Galileo a <lb></lb>pag. </s>

<s>134 del T. VI di far la risposta <emph type="italics"></emph>alla gratissima delli 5 Dicembre,<emph.end type="italics"></emph.end><pb xlink:href="020/01/918.jpg" pagenum="361"></pb>che poi a pag. </s>

<s>117 del T. VIII lo stesso Alberi pubblicò colla vera data <lb></lb><emph type="italics"></emph>delli 5 Novembre.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La dura necessità costrinse Galileo, rispetto alle apparenze di Marte, ad <lb></lb>essere più sincero. </s>

<s>Troppo era in verità debole a scorgere così fatte sotti­<lb></lb>gliezze quel suo strumento. </s>

<s>Quando poi il Fontana ebbe costruiti que&#039;suoi <lb></lb>eccellenti canocchiali, e allora fu possibile osservare le variazioni di figura <lb></lb>anche in Marte, e fu giusto il Castelli, il quale vide prima di ogni altro, con <lb></lb>gli occhi corporei, ciò che aveva divinato già con la sagacia della mente. </s>

<s>Il <lb></lb>dì 17 Luglio 1638 così infatti scriveva a Galileo: “ Ho visto Marte, il quale, <lb></lb>ora che è intorno al quadrato del Sole, scema chiaramente dalla parte orien­<lb></lb>tale, come una Luna di dodici o tredici giorni, e si vede chiaramente che <lb></lb>la parte di esso Marte occidentale è vivissima di splendore, dove che la orien­<lb></lb>tale apparisce a poco a poco sfumata; segno manifesto che in Marte si ri­<lb></lb>trovano sparse più ombre nella detta parte orientale, che nella occidentale, <lb></lb>come parimente si osserva nella Luna ” (Alb. </s>

<s>X, 307). </s></p><p type="main">

<s>Galileo, avuta una tale notizia, risponde l&#039;osservazione di Marte esser <lb></lb>bellissima e di gran conseguenza (Alb. </s>

<s>VII, 212) e scrivendo ad Anonimo, <lb></lb>nel Gennaio dell&#039;anno dopo, così gli dice, studiandosi di tirare a sè quanto <lb></lb>fosse possibile i meriti del Castelli: “ Quanto al pianeta di Marte si è os­<lb></lb>servato che, essendo al quadrato col Sole, ei non si vede perfettamente ro­<lb></lb>tondo, ma alquanto sguanciato, simile alla Luna quando ha dodici o tredici <lb></lb>giorni: che dalla parte opposta a quella del Sole che è tocca dai raggi so­<lb></lb>lari resta non illuminato e per conseguenza non veduto; cosa che io già di­<lb></lb>cevo dovere apparire, quando Marte fusse poco superiore al Sole. </s>

<s>Ma i no­<lb></lb>stri Telescopi, come quelli che non ingrandiscono tanto, non ci mostravano <lb></lb>al senso la rotondità non perfetta di esso Marte ” (Alb. </s>

<s>VII, 227). </s></p><p type="main">

<s>Si possono raccogliere da questi fatti narrati i giusti meriti che, in con­<lb></lb>fermare il Sistema copernicano, competono all&#039;Autore dei <emph type="italics"></emph>Massimi Sistemi.<emph.end type="italics"></emph.end><lb></lb>Udimmo Ticone muovere un&#039;altra difficoltà contro il Copernico, il quale <lb></lb>aveva asserito essere la Terra rispetto al cielo <emph type="italics"></emph>ut punctum ad corpus, et <lb></lb>finitum ad infinitum magnitudine<emph.end type="italics"></emph.end> (De Revolut. </s>

<s>cit., c. </s>

<s>4 v.) e nel V ca­<lb></lb>pitolo appresso, dop&#039;aver descritte le varietà di aspetto che presentano i Pia­<lb></lb>neti “ quod autem, avea soggiunto, nihil eorum apparet in fixis, immensam <lb></lb>illorum arguit celsitudinem, quae faciat etiam annui motus orbem sive eius <lb></lb>imaginem ab oculis evanescere ” (ibi, c. </s>

<s>10). </s></p><p type="main">

<s>“ Qui si levano su, entra a dire in proposito Galileo, gli avversarii di <lb></lb>questa opinione, e posta quella nominata insensibilità del Copernico come <lb></lb>presa da lui per cosa che realmente e assolutamente sia nulla, e soggiu­<lb></lb>gnendo che una stella fissa, anco delle minori, è pur sensibile, poichè ella <lb></lb>cade sotto il senso della vista; vengono calcolando, con l&#039;intervento di altri <lb></lb>falsi assunti, e concludendo bisognare in dottrina del Copernico ammettere <lb></lb>che una stella fissa sia maggiore assai che tutto l&#039;Orbe magno. </s>

<s>Ora io, per <lb></lb>discoprir la vanità di tutto questo progresso, mostrerò che dal porre che una <lb></lb>stella fissa della sesta grandezza non sia maggior del Sole, si conclude con <pb xlink:href="020/01/919.jpg" pagenum="362"></pb>dimostrazion verace che la distanza di esse stelle fisse da noi viene ad esser <lb></lb>tanta, che basta per far che in esse non apparisca notabile il movimento <lb></lb>annuo della Terra, e che nei Pianeti cagiona sì grandi e osservabili varia­<lb></lb>zioni, e insieme particolarmente mostrerò la gran fallacia negli assunti degli <lb></lb>avversarii del Copernico ” (Alb. </s>

<s>I, 390). </s></p><p type="main">

<s>Chi prosegue oltre nella lettura, trova la dimostrazione e la conclusione <lb></lb>per prima cosa promessa da Galileo in queste parole, ma chi volesse con <lb></lb>men lungo discorso vedere più sminuzzata quella stessa dimostrazione, legga <lb></lb>la nota autografa che qui da noi si trascrive: “ La corda di un minuto è 291; <lb></lb>d&#039;un secondo è poco meno di 5. Una stella fissa della terza grandezza è 4″, <lb></lb>e la sua sottesa sarà 20. Il 20 in 100,000 entra 5000 volte. </s>

<s>La circonferenza <lb></lb>al semidiametro è come 44 a 7; la corda di un grado, che è insensibilmente <lb></lb>minore del suo arco, sarà contenuta nel semidiametro volte 57 prossima­<lb></lb>mente. </s>

<s>La corda di un minuto primo entra nel semidiametro 3436 volte; <lb></lb>la corda di un minuto secondo entra nel semidiametro 208,454; adunque, <lb></lb>posto il diametro visuale del Sole 30, entrerà nella sua distanza dalla Terra <lb></lb>114 volte, ed il diametro intero dell&#039;Orbe magno conterrà 228 diametri del <lb></lb>Sole. </s>

<s>E posto che il diametro visuale del Sole contenga 360 diametri vi­<lb></lb>suali d&#039;una stella della seconda grandezza (che sarà quando il diametro <lb></lb>visuale della stella fissa sarà cinque minuti secondi) adunque, quando si po­<lb></lb>nesse che le stelle della seconda grandezza fossero grandi quanto il Sole, la <lb></lb>distanza di tali stelle dalla Terra conterrebbe 82,080 diametri del Sole o di <lb></lb>esse stelle.... Sarà dunque la distanza delle stelle fisse 360 diametri del­<lb></lb>l&#039;Orbe magno ” (MSS. Gal., P. IV, T. VI, c. </s>

<s>19). </s></p><p type="main">

<s>Le gran fallacie poi, negli assunti degli avversarii del Copernico, che <lb></lb>prometteva dianzi di scoprir Galileo, consistono nel non avere gli Astronomi <lb></lb>suoi predecessori avvertito che le stelle fisse e i pianeti s&#039;irraggiano di crini <lb></lb>lucidi ascitizi in modo, da apparir cento e più volte maggiori del vero esser <lb></lb>loro. </s>

<s>Come, anche senza il Telescopio, si possan radere d&#039;attorno agli astri <lb></lb>que&#039;crini, per determinar la più giusta misura de&#039;loro diametri apparenti, <lb></lb>è ciò che insegna di far Galileo, concludendo che da simili fallacie ebbero <lb></lb>occasione le difficoltà promosse dagli oppositori del Sistema copernicano; <lb></lb>difficoltà che, tolte così di mezzo, lasciano mirabilmente confermata la ve­<lb></lb>rità di quello stesso sistema. </s></p><p type="main">

<s>A voler dunque esser giusti, nell&#039;avere scoperte queste fallacie degli <lb></lb>astronomi antichi consistono tutte le benemerenze che s&#039;acquistò, verso il <lb></lb>Copernicanismo, l&#039;Autore de&#039;Massimi Sistemi. </s>

<s>All&#039;aver poi raccolte insieme, <lb></lb>illustrate e con popolare eloquenza diffuse quelle dottrine; all&#039;esser riuscito <lb></lb>a comparir di esse unico Maestro al mondo; all&#039;aver saputo apparire inno­<lb></lb>cente e ingiustamente oppresso nella sventura; và debitore Galileo de&#039;me­<lb></lb>riti insigni che s&#039;acquistò nella scienza, della gloria del suo nome, della <lb></lb>fama immortale di questo Dialogo copernicano. </s></p><pb xlink:href="020/01/920.jpg" pagenum="363"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le declamazioni contro l&#039;ignoranza degli ecclesiastici hanno da due se­<lb></lb>coli e mezzo assordato il mondo, e poniamo che sempre abbian fatto stre­<lb></lb>pito nel volgo, non son però mai riuscite a persuadere i savi, i quali sanno <lb></lb>che fu il Copernicismo introdotto nella scienza per opera e virtù di soli ec­<lb></lb>clesiastici, e hanno appreso dalla storia che Galileo ricevè a larga usura di <lb></lb>quel che aveva dato al Castelli, al Cavalieri, al Renieri, tutt&#039;e tre monaci e <lb></lb>insigni astronomi copernicani. </s>

<s>Son le nuove dottrine diffuse da Parigi per <lb></lb>tutta la Francia da tre zelantissimi uomini addetti agli istituti religiosi, che <lb></lb>si chiamano Pietro Gassendo, Ismaele Bullialdo e Marino Mersenno. </s></p><p type="main">

<s>Il Gassendo, appena ricevuti in dono i Dialoghi dei Massimi Sistemi, <lb></lb>risponde lieto all&#039;Autore approvando insiem col Mersenno e congratulando <lb></lb>ammirato insiem col Morin, di cui particolarmente così gli scrive: “ Mori­<lb></lb>nus inter caeteros librum tuum avide legit, teque suspicit ut par est; non <lb></lb>fatetur tamen se victum, existimatque rationes suas in manuscriptum Pro­<lb></lb>dromum perseverare illibatas. </s>

<s>Ipse, cum multa alia in tui gratiam, edisse­<lb></lb>rui, tum praesertim exaggeravi causam abs te redditam de geminata intra <lb></lb>diem naturalem maris reciprocatione et commendatione dignissimam esse, <lb></lb>et inconcussam persistere ” (Alb. </s>

<s>IX, 310). </s></p><p type="main">

<s>Il Bullialdo aveva scritto un&#039;opera astronomica in quattro libri intito­<lb></lb>lata <emph type="italics"></emph>Philolai seu Dissertationes de vero systemate mundi,<emph.end type="italics"></emph.end> e ch&#039;era sotto i <lb></lb>torchi in Amsterdam verso la fine dell&#039;anno 1637 (Alb. </s>

<s>X, 242). Tutt&#039;altro <lb></lb>che patir molestia ebbe lode universale talmente, che tornò ad ampliare la <lb></lb>prima opera sua e la pubblicò in Parigi nel 1645 col titolo di <emph type="italics"></emph>Astronomia <lb></lb>philolaica.<emph.end type="italics"></emph.end> Per render poi ragione ai lettori di questo titolo, così scrisse <lb></lb>nella sua Introduzione: “ Ante quinquennium libros IV de vero systemate <lb></lb>mundi vulgaveram sub nomine <emph type="italics"></emph>Philolai,<emph.end type="italics"></emph.end> in quibus, Geometrae et Astronomi <lb></lb>partes agens, per principia cognoscendi Solem in medio mobilium stare, <lb></lb>Terram inter Martem et Venerem circa Solem ferri, ostenderam. </s>

<s>Philolai <lb></lb>nomen libello imposueram, quoniam, quod olim dogma Terrae mobilitatis <lb></lb>Philolaus pythagoricus docuerat, rationibus e Geometria, Optica et Astrono­<lb></lb>mia petitis, confirmabam et demontrabam ” (pag. </s>

<s>7). </s></p><p type="main">

<s>Il Mersenno conferì alla diffusione del Copernicanismo, diffondendo un <lb></lb>libro sotto il nome di Aristarco di Samo. </s>

<s>Il nome però dell&#039;Astronomo an­<lb></lb>tico non ci entrava, come quello di Filolao nell&#039;opera del Bullialdo, ma ci <lb></lb>entrava come vero e proprio Autore di quello stesso libro, il manoscritto <lb></lb>del quale finse il Roberval di averlo avuto da Pietro Brulart, consigliere <lb></lb>regio, con ordine d&#039;interpetrarlo, di annotarlo, di farne l&#039;apologia e di darne <lb></lb>il giudizio. </s></p><p type="main">

<s>Il Roberval, nell&#039;accompagnare la finta opera al Brulart, gli dice di <pb xlink:href="020/01/921.jpg" pagenum="364"></pb>avere eseguiti i comandamenti impostigli di curare il testo e d&#039;illustrarlo <lb></lb>con note: in questo però non l&#039;ha ubbidito, in far cioè l&#039;apologia, che non <lb></lb>bisogna, avendola fatta già Archimede nell&#039;Arenario, e in dare al pubblico <lb></lb>il suo giudizio per le ragioni che dice appresso: “ Sensum tamdem nostrum <lb></lb>quaeris? </s>

<s>et an valere iussis Ptolomaeo atque Tychone, soli Aristarcho pe­<lb></lb>nitus adhaereamus? </s>

<s>Absit: neque enim recte sentientem mathematicum de­<lb></lb>cet opiniones sequi aut huic adhaerere, illas vero reiiciere, donec evidens <lb></lb>prodierit vel huius demonstratio vel illarum confutatio. </s>

<s>Sed nec illud con­<lb></lb>stat quidem an ex tribus authorum ipsorum celeberrimorum diversi syste­<lb></lb>matis, aliquod verum sit ac genuinum Mundi systema. </s>

<s>Forsan etiam omnia <lb></lb>tria falsa sunt et verum ignoratur. </s>

<s>Quidquid sit ex tribus illis praedictis <lb></lb>simplicissimum et naturae legibus apprime conveniens visum est systema <lb></lb>Aristarchi, ita ut, si non certa scientia in illud abducamur, at graviori longe <lb></lb>opinione in idem quam in duo reliqua propendamus. </s>

<s>Vale. </s>

<s>Parisiis pridie <lb></lb>non. </s>

<s>Julii an. </s>

<s>1643. Ae. </s>

<s>P. Roberval. </s>

<s>” </s></p><p type="main">

<s>Quest&#039;artificiosa scrittura del Matematico francese, che si voleva far <lb></lb>passare per originale dell&#039;Astronomo greco, fu divulgata dal Mersenno nel <lb></lb>T. III delle sue <emph type="italics"></emph>Novarum Observationum<emph.end type="italics"></emph.end> stampate nel 1647 a Parigi, col <lb></lb>titolo <emph type="italics"></emph>Aristarchi Samii De mundi systemate.<emph.end type="italics"></emph.end> La burla fu creduta univer­<lb></lb>salmente in Francia, e il Roberval col Mersenno e col Brulart ridevano tutti <lb></lb>insieme contenti, e solamente stizziti, perchè non era fra gl&#039;Italiani voluto <lb></lb>entrare in quella rete il Torricelli. </s>

<s>Il Mersenno lo andava zimbellando con <lb></lb>sue lettere da Roma, e voleva ad ogni costo sapere ciò che nell&#039;Aristarco <lb></lb>gli avesse dato disgusto, non trovandoci il Roberval nulla, che non gli sia <lb></lb>per ogni parte piaciuto. </s>

<s>“ Porro quum non omnia tibi satisfacerint quae <lb></lb>penes Aristarchum legisti, gratum facies si quod minus placens moneas, ac <lb></lb>aliquam tuae displicentiae rationem innuas, quum nihil in eo fuerit quod <lb></lb>nostro Robervallio non placuerit ” (MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>52). </s></p><p type="main">

<s>S&#039;aggiunse poi a far da zimbellatore anche il Carcavy, a cui, perduta <lb></lb>finalmente la pazienza, il Torricelli rispose: “ Sed quid est cur tantopere <lb></lb>petatis iudicium meum de Aristarchi libello? </s>

<s>Idem postulavit cl. </s>

<s>Mersen­<lb></lb>nus dum esset Romae. </s>

<s>Amici mei existimant libellum plane divinum et ab <lb></lb>Auctore divino compositum. </s>

<s>Ego censeo libellum sub Aristarchi nomine edi­<lb></lb>tum conscriptum fuisse nostra hac aetate. </s>

<s>Quod attinet ad doctrinam, omnia <lb></lb>quidem optima credo cum a doctissimis viris probentur, attamen et mihi et <lb></lb>quibusdam amicis quam plurima non placent, ob ingenii nostri imbecillitate. </s>

<s><lb></lb>Sed queso ne et rationes postuletis, quemadmodum fecit ipse cl. </s>

<s>Mersen­<lb></lb>nus, cur ego libellum nuper conscriptum censeam, sive cur in eo multa <lb></lb>displiceant. </s>

<s>Ridiculum,.... circa negotium quod ad me minime attinet, <lb></lb>excruciari ” (ibi, T. XL, c. </s>

<s>38). </s></p><p type="main">

<s>La burla fu poi svelata, e que&#039;francesi ebbero a maravigliarsi del sot­<lb></lb>til fiuto del Torricelli. </s>

<s>Ma perchè il fatto è d&#039;assai maggiore importanza <lb></lb>che di una semplice curiosità letteraria, si domanda: fu veramente l&#039;inten­<lb></lb>zione del Roberval quella di fare agli Astronomi una burla? </s>

<s>Ma perchè al-<pb xlink:href="020/01/922.jpg" pagenum="365"></pb>lora usar tanto riserbo in sentenziare quale de&#039;tre sistemi del mondo pro­<lb></lb>posti da Aristarco, da Tolomeo e da Ticone fosse da seguitarsi per vero? </s>

<s><lb></lb>Perchè il Torricelli scansò d&#039;entrare e si ritirò da quella questione come se <lb></lb>fosse una fiamma che lo scottasse? </s></p><p type="main">

<s>Giova, per rispondere a così fatte domande, considerare che i Decreti <lb></lb>della Chiesa romana erano a poco a poco entrati a turbar la pace e il se­<lb></lb>reno delle coscenze. </s>

<s>Il Gassendo, dop&#039;aver mostrato tanto fervore in difen­<lb></lb>dere i principii di Galileo e in magnificarne la virtù degli argomenti, nella <lb></lb>Epistola II, <emph type="italics"></emph>Dc motu impresso a motore translato,<emph.end type="italics"></emph.end> finì per acquietarsi nella <lb></lb>immobilità della Terra, dicendo che, sebben non sia questo un articolo di <lb></lb>fede, <emph type="italics"></emph>apud universam Ecclesiam promulgatum atque receptum,<emph.end type="italics"></emph.end> non po­<lb></lb>teva nonostante un tal giudizio emanato da Lei <emph type="italics"></emph>apud Fideles non maximi <lb></lb>esse momenti<emph.end type="italics"></emph.end> (Op. </s>

<s>omn., T. III, Lugduni 1658, pag. </s>

<s>519). </s></p><p type="main">

<s>Il Mersenno poi, fra l&#039;instabilità della sua scienza combattuto dal dub­<lb></lb>bio, si consolò col dire che non era l&#039;opera del Copernico condannata come <lb></lb>eretica. </s>

<s>Così il banditore dell&#039;Aristarco Samio s&#039;opponeva insieme col Gas­<lb></lb>sendo alla intolleranza di Giusto Lipsio, di Melchior Inchofer e di Giorgio <lb></lb>Pollacco, i quali dicevano dover tenersi la stabilità della Terra come dot­<lb></lb>trina di fede. </s></p><p type="main">

<s>Il Riccioli allora con duplice autorità di Teologo e di Astronomo venne <lb></lb>ad assicurare le menti dal dubbio e a prescriver le giuste norme alle scru­<lb></lb>polose coscenze. </s>

<s>Galileo, con forze impari all&#039;arduo soggetto, come faremo <lb></lb>vedere a suo tempo, s&#039;era messo a investigare le leggi della caduta de&#039;gravi <lb></lb>in relazione col moto vertiginoso della Terra, e ne aveva concluso l&#039;acce­<lb></lb>lerazione di essi gravi essere apparente e non reale. </s>

<s>Il Riccioli si oppose <lb></lb>con dire ch&#039;essendo reale l&#039;incremento della percossa, reale doveva esser <lb></lb>pure l&#039;accelerazione del corpo cadente, e così ritorcendo l&#039;argomento nelle <lb></lb>mani stesse di Galileo veniva a concluderne, per la medesima via di lui, <lb></lb>l&#039;immobilità della Terra. </s>

<s>Quest&#039;argomento fisico-matematico del p. </s>

<s>Riccioli <lb></lb>era <emph type="italics"></emph>ad hominem<emph.end type="italics"></emph.end> contro l&#039;Autore de&#039;<emph type="italics"></emph>Massimi Sistemi,<emph.end type="italics"></emph.end> e benchè il p. </s>

<s>Ste­<lb></lb>fano Angeli e il Borelli rispondessero assai lunghe parole, la stessa inurba­<lb></lb>nità de&#039;modi venne a mettere in sospetto la validità delle ragioni. </s></p><p type="main">

<s>Di qui si sceverarono gli Astronomi in due ordini distinti. </s>

<s>I convertiti <lb></lb>dall&#039;eloquenza di Galileo, sentendogli contrapporre un argomento che pa­<lb></lb>reva non si potesse oppugnare, pensarono nel dubbio di seguire la parte <lb></lb>più sicura, avendo come Teologo il Riccioli stesso insegnato che non facendo <lb></lb>la Sacra Congregazione de&#039;Cardinali, di per sè senza il Pontefice, proposi­<lb></lb>zioni <emph type="italics"></emph>de fide,<emph.end type="italics"></emph.end> tutti i buoni Cattolici però erano obbligati ad assoggettarsi ai <lb></lb>Decreti di lei <emph type="italics"></emph>ex virtute tum Prudentiae tum Obedientiae.<emph.end type="italics"></emph.end> Quegli altri poi <lb></lb>che, nonostante gli argomenti del Riccioli, erano certi della mobilità della <lb></lb>Terra, la professavano con libertà nella loro coscienza, che veniva francata <lb></lb>dall&#039;imputazione di eresia, e in pubblico riducevano le virtù della Prudenza <lb></lb>e dell&#039;Obbedienza a tener d&#039;occhio all&#039;Inquisitore. </s></p><p type="main">

<s>Un esempio assai notabile di que&#039;primi lo abbiamo in Giorgio Sinclaro, <pb xlink:href="020/01/923.jpg" pagenum="366"></pb>il quale all&#039;argomento <emph type="italics"></emph>ad hominem<emph.end type="italics"></emph.end> contro Galileo, che il Riccioli avea de­<lb></lb>sunto dagl&#039;incrementi della percossa, ne aggiunse un altro dedotto dalle <lb></lb>leggi del pendolo. </s>

<s>Argomentava ch&#039;essendo i moti del pendolo orizzontale e <lb></lb>del verticale una sola e medesima cosa, se gl&#039;incrementi della velocità del <lb></lb>primo giusta i seni son reali, reali pure debbon essere gl&#039;incrementi della <lb></lb>velocità del secondo giusta i numeri quadrati. </s>

<s>E qui tra Alessandro, in cui <lb></lb>s&#039;impersona l&#039;Autore, e Francesco intercede un dialogo, ch&#039;è al presente <lb></lb>proposito assai importante. </s></p><p type="main">

<s>Dice Alessandro del suo argomento anticopernicano dedotto dalle leggi <lb></lb>del pendolo: “ Pungit nonnihil, at non vereor quin possit solvi, imo non <lb></lb>modo hoc, sed quodlibet, seposita S. </s>

<s>Scripturae auctoritate. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> — Quid? </s>

<s>An sententiae tam vertiginosi cerebri patrocinaris? </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> — Licet eo persuasionis nondum pervenerim, censeo tamen <lb></lb>Copernici atque Galilaei hypotheses de mundi fabrica viam esse expeditis­<lb></lb>simam ad pleraque phaenomena coelestia solvenda et explicanda. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> — Sed tutum non est vel tam haereticam sententiam nomi­<lb></lb>nare, nedum propugnare, quum aperte tam Sacris repugnet Literis, quam <lb></lb>Ecclesiae auctoritate. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> — Qui opinionem de Telluris motu sub mera hypothesi pro­<lb></lb>movere studet, erroris contra fidem vel contumaciae contra Ecclesiae aucto­<lb></lb>ritatem infirmandus non est. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> — Quam itaque ob causam tot passus est mala vir elle in­<lb></lb>comparabilis ingenii Galilaeus de Galilaeo ab Ecclesia romana? </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> — Quod monitus a cardinali Bellarmino sacris Ecclesiae cen­<lb></lb>soribus non paruerit. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> — At coactus est tamen sententiam suam publice eiurare. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> — Fateor: at crede mihi crassam Ecclesiae Doctorum ignoran­<lb></lb>tiam redolevit. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Franc.<emph.end type="italics"></emph.end> — Nil mirum, quum in studia altiora multo continuo in­<lb></lb>cumbant. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Alex.<emph.end type="italics"></emph.end> — At pudet viros doctos parum vel nihil in Astronomia sa­<lb></lb>pere ” (Ars nova et magna, Roterodami 1669, pag. </s>

<s>581, 82). </s></p><p type="main">

<s>Son fra que&#039;secondi, che si diceva aver preso la risoluzion dal Riccioli, <lb></lb>da annoverare tutti i Discepoli di Galileo, tra&#039;quali come in tutto così anche <lb></lb>in questo primeggiano il Borelli e il Viviani. </s>

<s>La Lettera <emph type="italics"></emph>Del moto della <lb></lb>Cometa<emph.end type="italics"></emph.end> scritta sotto il finto nome di Pier Maria Mutoli, e le <emph type="italics"></emph>Theoricae Me­<lb></lb>diceorum planetarum<emph.end type="italics"></emph.end> bastano a qualificare la profession copernicana del <lb></lb>primo: il secondo pochissimo si fece conoscere in pubblico, dal quale fu <lb></lb>perciò accusato di troppo meticuloso. </s></p><p type="main">

<s>Con quale intendimento incominciasse il Viviani la traduzione dell&#039;Ari­<lb></lb>starco Samio del Robervallio, che si legge da carte 86-97 del T. CXXXIX <lb></lb>de&#039;MSS. appartenenti ai Discepoli di Galileo, non sapremmo dire precisa­<lb></lb>mente, ma forse voleva, ad imitazion de&#039;Francesi, diffondere anche in Ita­<lb></lb>lia sotto quell&#039;abito le dottrine del suo Maestro, ch&#039;egli teneva per certis-<pb xlink:href="020/01/924.jpg" pagenum="367"></pb>sime, e le professava in segreto senza timor di offendere la sua propria <lb></lb>coscienza, per assicurar meglio la quale un giorno prende un foglio, che fu <lb></lb>inserito a c. </s>

<s>56 del T. IV, P. IV de&#039;manoscritti di Galileo, e ci scrive con <lb></lb>carattere scolpito così di sua propria mano: “ In parte prima Tomi primi <lb></lb>Almagesti Novi Joannis Baptistae Riccioli ferrariensis, e Soc. </s>

<s>Jesu, Philoso­<lb></lb>phiae, Theologiae et Astronomiae professoris, ad pag. </s>

<s>52 editionis bononien­<lb></lb>sis anni 1651, Scholio II, haec leguntur: — Sacra congregatio Cardinalium, <lb></lb>seorsim sumpta a Summo Pontifice, non facit propositiones de fide, etiamsi <lb></lb>eas definiat esse de fide vel oppositas esse haereticas. </s>

<s>Quare, cum nondum <lb></lb>de hac re prodierit definitio Summi Pontificis aut Concilii ab eo directi vel <lb></lb>approbati, nondum est de fide Solem moveri et Terram stare vi Decreti pre­<lb></lb>cise illius Congregationis, sed ad summum et solum vi Sacrae Scripturae, <lb></lb>apud eos quibus est evidens moraliter Deum ita revelasse. </s>

<s>Omnes tamen <lb></lb>catholici, ex virtute tum Prudentiae tum Obedientiae, obligantur ad tenen­<lb></lb>dum quod illa Congregatio decrevit, et saltem ad non docendum absolute <lb></lb>oppositum. </s>

<s>Sed de hac subtilitate theologica egi ex professo in Tractatu <emph type="italics"></emph>De <lb></lb>fide,<emph.end type="italics"></emph.end> ubi De regulis fidei. </s>

<s>” </s></p><p type="main">

<s>Era naturalissimo che il Viviani fosse copernicano al modo di Galileo, <lb></lb>e perciò dava una grande importanza all&#039;argomento del flusso e riflusso del <lb></lb>mare. </s>

<s>Rimeditava un giorno sopra questa conclusione, che aveva letta nel <lb></lb>Discorso al cardinale Orsino: <emph type="italics"></emph>sicchè delle acque che saranno contenute in <lb></lb>ricetti di uguali lunghezze, ma di disuguali profondità, quella che sarà <lb></lb>più profonda farà le sue librazioni sotto tempi più brevi, e men frequenti <lb></lb>saranno le reciprocazioni dell&#039;acque meno profonde<emph.end type="italics"></emph.end> (Alb. </s>

<s>II, 394, 95), e <lb></lb>considerando che il moto ondoso avviene alla superficie, la quale in ogni <lb></lb>mare è sempre ad ugual distanza dal centro terrestre, così credette che si <lb></lb>potesse emendare il concetto galileiano e renderlo, per altra via e con più <lb></lb>saldo fondamento di scienza, argomento dimostrativo del moto della Terra: <lb></lb>“ Cum pendentia gravia seu pendula habeant statuta tempora suarum reci­<lb></lb>procationum pro ratione distantiae a puncto suspensionis cui innituntur, exa­<lb></lb>minandum est num pendula, ex distantia semidiametro Terrae æquali, suas <lb></lb>faciant vibrationes h. </s>

<s>6 vel circiter. </s>

<s>Quod si sic esset, non incongrua erit <lb></lb>causa aestus maris, quam et revolutionis diurnae Telluris, et forsan habe­<lb></lb>bitur orbium planetarum magnitudo ex ratione temporum revolutionum ” <lb></lb>(MSS. Gal. </s>

<s>Dis., T. CXXXV, c. </s>

<s>11). </s></p><p type="main">

<s>Questo arguto pensiero, benchè sia viziato dai falsi insegnamenti ga­<lb></lb>lileiani, è nonostante notabile per l&#039;applicazione che voleva farsi delle <lb></lb>proprietà de&#039;pendoli oscillanti a dimostrare il moto della Terra. </s>

<s>Secondo <lb></lb>questo rispetto si può dire in certo modo che il Viviani precorresse il <lb></lb>Foucault, ma non come l&#039;intesero e l&#039;intendono tuttavia parecchi scrittori <lb></lb>moderni. </s></p><p type="main">

<s>Ai visitatori del R. </s>

<s>Museo di Fisica e di Storia naturale in Firenze è <lb></lb>richiamata particolarmente l&#039;attenzione verso una tavola rotonda, al centro <lb></lb>della quale sovrasta una pesante sfera di metallo pendula da un filo, non <pb xlink:href="020/01/925.jpg" pagenum="368"></pb>più lungo di cinque o sei metri. </s>

<s>Sta su quella medesima tavola posata una <lb></lb>cartella scritta, la quale così sommessamente parla ai curiosi, risparmiando <lb></lb>per un momento la voce all&#039;erudito dimostratore: </s></p><p type="main">

<s>“ La chiara dimostrazione della rotazione della Terra, che Foucault offri <lb></lb>nel 1851 per mezzo dalla deviazione del pendolo dal piano di oscillazione, <lb></lb>fu subito in questo R. </s>

<s>Museo ripetuta e lungamente osservata, adattando <lb></lb>all&#039;uopo questa Tavola, la quale aveva servito alla grande esperienza degli <lb></lb>Accademici del Cimento, ai quali, ne&#039;loro molteplici studii sul pendolo, non <lb></lb>era neppure sfuggito il fatto dello spostamento apparente del piano di oscil­<lb></lb>lazione, come rilevasi dalla Nota e dal disegno autografo del Viviani che qui <lb></lb>trascriviamo: <emph type="italics"></emph>Osservammo che tutti i pendoli da un filo deviano dal piano <lb></lb>verticale, e sempre per il medesimo verso, cioè secondo le linee AB, CD, <lb></lb>EF, da destra verso sinistra, nelle parti anteriori. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sempre il mistero nell&#039;animo degli uomini ha generato la fede, e fu <lb></lb>perciò la misteriosa maniera dell&#039;apparizione di questo documento che illuse <lb></lb>i troppo facili a credere ai miracoli dell&#039;ingegno. </s></p><p type="main">

<s>A carte 47 del Tomo X de&#039;Manoscritti del Cimento il Viviani tirò giù, <lb></lb>come gli eran venute al pensiero, alcune note <emph type="italics"></emph>De&#039;pendoli,<emph.end type="italics"></emph.end> e dopo aver de­<lb></lb>scritto il fatto delle loro <emph type="italics"></emph>simpatie,<emph.end type="italics"></emph.end> in quel modo che si riferì da noi nel <lb></lb>cap. </s>

<s>II, § III dell&#039;altro Tomo di questa Storia, così prosegue a dire in quel <lb></lb>medesimo soggetto sperimentale: </s></p><p type="main">

<s><emph type="italics"></emph>“ Osserveremo<emph.end type="italics"></emph.end> che tutti i pendoli da un <emph type="italics"></emph>sol<emph.end type="italics"></emph.end> filo deviano dal piano ver­<lb></lb>ticale, e sempre per il medesimo verso, cioè secondo le linee AB, CD, EF, <lb></lb>(fig. </s>

<s>69) da destra verso sinistra, nelle parti an­<lb></lb><figure id="id.020.01.925.1.jpg" xlink:href="020/01/925/1.jpg"></figure></s></p><p type="caption">

<s>Figura 69.<lb></lb>teriori. </s>

<s>— Ogni pendolo appeso con due fili ac­<lb></lb>coppiati insieme devia pochissimo dal verticale, <lb></lb>e assai meno che con un sol filo. </s>

<s>— Date le me­<lb></lb>desime lunghezze di pendoli, più presto deviano <lb></lb>dal piano verticale i più leggeri, che i più gravi; <lb></lb>e dati i medesimi pesi e diverse lunghezze, più <lb></lb>presto i più corti che i più lunghi. </s>

<s>” </s></p><p type="main">

<s>Il mistero così facilmente svelato rende chiaro <lb></lb>e manifesto a ciascuno che il moto della Terra <lb></lb>non entra, nemmen per sogno, in queste espe­<lb></lb>rienze, soggetto delle quali era proprio di osservar <lb></lb>quel traviamento insensibile dalle prime gite, che fa il pendolo verso la fine, <lb></lb>e di che poi fu reso conto a pag. </s>

<s>20 de&#039;<emph type="italics"></emph>Saggi di Naturali esperienze<emph.end type="italics"></emph.end> (Fi­<lb></lb>renze 1844); traviamento di cui non vogliono ivi gli Accademici fiorentini <lb></lb>dir la causa, che probabilmente è dovuta alla torsione del filo. </s></p><p type="main">

<s>Ma per tornare al primo nostro proposito, ch&#039;era quello di mostrar gli <lb></lb>effetti della proibizione ecclesiastica nell&#039;esercizio della professione coperni­<lb></lb>cana, diciamo che sulla fine del secolo XVII non avevano ancora i Peripate­<lb></lb>tici cessato di prevalersi delle armi della coscienza, per arrestar fra i Cat­<lb></lb>tolici que&#039;così rapidi progressi, che si vedevan fare alla scienza. </s>

<s>Basti per <pb xlink:href="020/01/926.jpg" pagenum="369"></pb>esser brevi citar, come prova di ciò, questo, che noi scegliamo fra molti <lb></lb>esempi. </s></p><p type="main">

<s>Era Antonio Leeuwenhoek, nella propria casa in Leyda, tutto intento <lb></lb>alle naturali esperienze, quando un giorno dell&#039;anno 1695 gli capita a visi­<lb></lb>tarlo un Professore italiano. </s>

<s>Si lamentava questi, entrato in discorso, che <lb></lb>per avere scritta e pubblicata una Tesi a dimostrare il moto della Terra, <lb></lb>gli si fossero concitati contro gli animi de&#039;suoi paesani, e particolarmente <lb></lb>di coloro, che avevano autorità di condannarlo. </s>

<s>“ Quum vero, esclama qui <lb></lb>con gioia il Leeuwenhoek, nos liberiorem hauriamus in his regionibus ae­<lb></lb>rem, ubi sententiam suam de Telluris motu libere proponere liceat, saepe <lb></lb>postea de Professoris eius querelis cogitavi, ac tandem in animum induxi <lb></lb>hasce meas theses, quibus ante aliquot annos mihi satisfacere conatus fui, <lb></lb>chartae mandare ” (Arcana Naturae continuatio, Lugd. </s>

<s>Batav. </s>

<s>1722, pag. </s>

<s>121). </s></p><p type="main">

<s>Il soggetto di queste tesi consisteva nel proporre una nuova esperienza <lb></lb>appositamente ordinata a dimostrare il moto della Terra, e lo strumento ac­<lb></lb>comodato a ciò vien dall&#039;Autore stesso così descritto: “ Conflari ego mihi <lb></lb>curavi sphaeras aliquot vitreas. </s>

<s>Has aqua replevi, ac tum sumsi ceram hispa­<lb></lb>nicam rubram antea malleo frustillatim contritam. </s>

<s>Particulis his sphaerae <lb></lb>inditis, sumsi globulum plumbeum, cui vitri apertura erat pervia. </s>

<s>Huic glo­<lb></lb>bulo plumbeo ante indideram foramen exiguum, transmittendo longo ac te­<lb></lb>nui funiculo ei infixo. </s>

<s>Postea sumsi particulam suberis sphaerae aperturae <lb></lb>aptatam, atque in ea angustam terebravi aperturam, quam funiculus, cui <lb></lb>globulus plumbeus erat affixus, aegre transibat ” (ibi, pag. </s>

<s>122). </s></p><p type="main">

<s>Faceva girare velocemente questa palla di vetro, per la torsion di una <lb></lb>fune sostenuta all&#039;estremità con una mano, e osservava, attentamente guar­<lb></lb>dando, i fatti seguenti: “ Dum sphaera illa vitrea ita in gyrum circumage­<lb></lb>batur, globulus plumbeus lente tantummodo in orbem latus quasi in aequi­<lb></lb>librio haerebat. </s>

<s>At cerae particulae, quae, dum vitrum quiesceret, circum <lb></lb>globum plumbeum iacuerant, iam, ubi sphaera ita in orbem circumfereba­<lb></lb>tur undique sese vitro interiori applicabant, atque ita, quantum per vitri <lb></lb>angustiam licebat, ab globulo dilatabantur ” (ibi, pag. </s>

<s>123). </s></p><p type="main">

<s>Fatto poi arrestare il moto alla stessa palla, posandola sopra un guan­<lb></lb>ciale di piuma “ videre licet partes cerae hispanicae admodum confuse ac <lb></lb>irregulariter moveri, cumque eae partes, dum sphaera in orbem ferebatur <lb></lb>a globulo plumbeo dilatarentur, iam e contrario eae versus globulum fere­<lb></lb>bantur, imo usque adeo ut globulus iis partibus plane fere tegebatur ” (ibi). </s></p><p type="main">

<s>Dalla diligente osservazione di questi fatti ecco, applicandoli al caso del <lb></lb>moto vertiginoso della Terra, ciò che l&#039;Autor ne conclude: “ Quemadmo­<lb></lb>dum autem iam per vitri motum partes cerae hispanicae, quae primo glo­<lb></lb>bulum plumbeum cingebant, ab eo separantur; ita etiam mihi persuadeo <lb></lb>nubes per diurnum Telluris nostrae motum sive gyrationem in aere suspen­<lb></lb>sas retineri. </s>

<s>Ac porro, sicuti ubi vitrum quiescere incipit, partes cerae sese <lb></lb>circum globum plumbeum locant, atque eum tegunt, idem ut opinor futu­<lb></lb>rum esset si Tellus quiesceret, et totum hoc Universum circum Tellurem <pb xlink:href="020/01/927.jpg" pagenum="370"></pb>in orbem ferretur, sic nempe omnes nubes ac partes aquae ceteraeque ma­<lb></lb>teriae graves inter quas vivimus in aere suspensae manere non possent, sed <lb></lb>in Tellurem ruerent atque illic quiescerent ” (ibi, pag. </s>

<s>124). </s></p><p type="main">

<s>Racconta in principio della sua Tesi lo stesso Leeuwenhoeck com&#039;es­<lb></lb>sendo andato un giorno a fargli visita Cristiano Huyghens, ed essendo en­<lb></lb>trato seco in discorso del moto della Terra, gli facesse veder quel suo globo <lb></lb>di vetro, e gli effetti ch&#039;ei dimostrava, di che prese l&#039;Huyghens tanto di­<lb></lb>letto, che chiese ed ebbe in dono dall&#039;Autore il bello strumento. </s></p><p type="main">

<s>Qual efficacia possa avere avuto questo stesso strumento leuvenoecchio <lb></lb>sui celeberrimi Teoremi ugeniani <emph type="italics"></emph>De vi centrifuga,<emph.end type="italics"></emph.end> siam costretti a passar­<lb></lb>cene per la fretta, contentandoci di dire come accomodasse lo stesso Huy­<lb></lb>ghens l&#039;esperienza del Professore di Leyda a dimostrare secondo qual ra­<lb></lb>gione, volgendosi la Terra in giro i corpi sulla superficie di lei sien da dir <lb></lb>gravi e leggeri. </s>

<s>Il documento lo abbiamo nella <emph type="italics"></emph>Cosmografia<emph.end type="italics"></emph.end> di Monsù Du <lb></lb>Rhò, le parole del quale siamo lieti di riferirle nella traduzione, che del­<lb></lb>l&#039;Opera francese lasciò manoscritta il Viviani. </s></p><p type="main">

<s>Il cap. </s>

<s>XXVIII s&#039;intitola <emph type="italics"></emph>Della gravità e della leggerezza,<emph.end type="italics"></emph.end> la causa <lb></lb>fisica de&#039;quali effetti della Natura è così, dice l&#039;Autore, sperimentalmente <lb></lb>dimostrata dal signor Hugenio: “ Egli prende un vaso di maiolica di co­<lb></lb>lor bianco, di figura tonda, che ha sette o otto pollici di diametro, del quale <lb></lb>il fondo è piano e gli argini alti circa tre pollici, ed empie d&#039;acqua questo <lb></lb>vaso, dopo averci messo un poco di cera di Spagna in polvere, che la sua <lb></lb>gravità la fa andare al fondo, ed il color rosso la rende molto visibile su <lb></lb>quel fondo bianco. </s>

<s>Egli lo copre con un vetro molto trasparente e lo sug­<lb></lb>gella, acciò niente possa scappar fuori, ed attaccando questo vaso sur un <lb></lb>pernio o sur una macchina, che egli lo possa far girare o fermare quando <lb></lb>gli piace, e&#039;lo muove in giro. </s>

<s>” </s></p><p type="main">

<s>“ Poichè questa polvere che tocca il fondo del vaso non sguizza per di <lb></lb>sopra sì felicemente come l&#039;acqua, e che per questo ancora ella è più fa­<lb></lb>cilmente strascinata; da ciò avviene che essa acquista più moto in giro che <lb></lb>non fa l&#039;acqua, e questo l&#039;obbliga a discostarsi dal centro in giro del quale <lb></lb>essa era sparsa, e ad ordinarsi per gli orli del vaso. </s>

<s>Allora facendo arre­<lb></lb>stare in un subito il moto di quella Macchina, e per conseguenza il vaso <lb></lb>che ne è imperniato, la cera di Spagna che gliscia il fondo (della quale le <lb></lb>particelle sono scabrose) non si muove più veloce dell&#039;acqua, il moto della <lb></lb>quale non si rallenta tanto, a cagione della facilità che essa ha di glisciare <lb></lb>sul fondo liscio del vaso. </s>

<s>” </s></p><p type="main">

<s>“ In questo tempo Egli fa vedere che l&#039;acqua rassembra la materia <lb></lb>fluida che circonda la Terra, e che questa polvere di cera di Spagna ras­<lb></lb>somiglia alle parti della Terra, ch&#039;è solito vedersi discendere per aria, per­<lb></lb>chè questa polvere è sforzata di avvicinarsi al centro del suo moto, verso <lb></lb>il quale essa è spinta dalle parti dell&#039;acqua, che tendono a discostarsi con <lb></lb>maggior forza, e quel centro s&#039;assomiglia ad una piccola massa tonda che <lb></lb>assomiglia alla Terra ” (MSS. Gal. </s>

<s>Disc., T. CXLI, c. </s>

<s>114). </s></p><pb xlink:href="020/01/928.jpg" pagenum="371"></pb><p type="main">

<s>Così gli effetti delle forze centrifughe, messi in considerazione dall&#039;Huy­<lb></lb>ghens, predisposero l&#039;ingegno del Newton a considerar gli effetti contrarii <lb></lb>delle forze centripete, e ingeritasi finalmente, per queste matematiche di­<lb></lb>mostrazioni, la persuasione che il Verbo creato e il Verbo scritto non po­<lb></lb>tevano contradirsi, quella libera gioia, che il Leeuwenhoek si compiaceva <lb></lb>esser solamente riserbata alla sua patria, si diffuse nella scienza universale. </s></p><pb xlink:href="020/01/929.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO X.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del Sole e della Luna<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle prime osservazioni intorno alle Macchie solari fatte in Italia, e descritte da Galileo.— <lb></lb>II. </s>

<s>Delle controversie insorte fra lo Scheiner e Galileo: dell&#039;essere e della natura delle Mac­<lb></lb>chie solari.—III. </s>

<s>Delle macchie, e di varie altre apparenze nel cerchio della Luna.—IV. </s>

<s>Del <lb></lb>Candore lunare, e particolarmente della Lettera di Galileo sopra questo argomento.—V. </s>

<s>Del color <lb></lb>rosso nelle Ecclissi di Luna. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La Matematica del Newton l&#039;aveva dunque vinta sopra la Metafisica dei <lb></lb>Peripatetici, i quali da lungo tempo s&#039;erano compiaciuti d&#039;aver dato fatica <lb></lb>al Sole d&#039;aggirarsi attorno a illuminare, e a riscaldare co&#039;suoi raggi la loro <lb></lb>Terra, e avevan trionfato in veder l&#039;immensa sfera stellata andar perpetua­<lb></lb>mente in volta a farle ricca e splendida corona. </s>

<s>E perchè fosse sodisfatto <lb></lb>più a pieno quel loro orgoglio, pretendevano di aver così fatti onorevoli ser­<lb></lb>vigi dal cielo, incorruttibile, eterno. </s>

<s>Di qui è che venne a que&#039;Filosofi altra <lb></lb>occasione a insorgere contro i progressi dell&#039;Astronomia, quando prima l&#039;ap­<lb></lb>parizione di una nuova stella pareva accusar l&#039;essere alterabile del puris­<lb></lb>simo etere, e poi il Canocchiale spiò ch&#039;era mista a fumi caliginosi la splen­<lb></lb>dentissima Lampada del mondo, e ch&#039;era anch&#039;essa, l&#039;eterna Margherita, <lb></lb>composta di vilissimo peltro. </s>

<s>Le macchie scoperte nel Sole perciò e le om­<lb></lb>bre vedute in faccia alla Luna succedono, per ordine e per importanza, nel <lb></lb>soggetto di questa Storia. </s></p><p type="main">

<s>Quando Galileo annunziava pubblicamente e solennemente al mondo le <lb></lb>sue nuove scoperte fatte col canocchiale nel Cielo in quelle memorabili pa­<lb></lb>gine, dove si passano in rivista la Luna, le Stelle, le Costellazioni, i Pia­<lb></lb>neti, non fa nessun cenno del Sole. </s>

<s>La cosa dall&#039;altra parte sembrava na-<pb xlink:href="020/01/930.jpg" pagenum="373"></pb>turalissima: com&#039;era possibile infatti, senza rimanere accecato, fissare gli <lb></lb>occhi in quella fulgidissima sfera? </s>

<s>Ciò bastava per allora a tener lontano <lb></lb>il nuovo Messaggero dalle osservazioni dirette, e il poco pregio in ch&#039;egli <lb></lb>aveva la camera oscura, e il professar tutt&#039;altre teorie ottiche da quelle che <lb></lb>si venivano sperimentalmente a dimostrare per mezzo di essa, non gli la­<lb></lb>sciavano a pensare che si potessero quelle osservazioni far sopra l&#039;imma­<lb></lb>gine ricevuta dentro una qualche candida superficie opposta ai raggi proiet­<lb></lb>tati dal Sole. </s></p><p type="main">

<s>Ma l&#039;adito a quel pensiero dovette venir presto aperto e fecondato da <lb></lb>simili altri pensieri, che nella sua Dissertazione sul Nuncio Sidereo, gli ve­<lb></lb>niva significando il Keplero. </s>

<s>Egli, senza Canocchiale, diceva di aver pure <lb></lb>ossservato il Sole guardando non <emph type="italics"></emph>converso in coelum vultu, sed averso,<emph.end type="italics"></emph.end> e <lb></lb>in questo modo aver veduto Mercurio proiettar l&#039;ombra come una macchia <lb></lb>nera sulla faccia stessa del Sole. </s>

<s>“ Stet igitur Galilaeus iuxta Keplerum. </s>

<s><lb></lb>Ille Lunam observans converso in coelum vultu, hic Solem aversus in Ta­<lb></lb>bellam (ne oculum urat specillum) suo utroque artificio .... quin etiam prae­<lb></lb>ter Lunam Mercurium ipsum in disco solis meo artificio vidi ” (Alb. </s>

<s>V, 416). </s></p><p type="main">

<s>Poco più sotto poi dichiara il pensiero di migliorare questo nuovo me­<lb></lb>todo di osservazione, trasformando l&#039;apparecchio in quell&#039;altro più compiuto <lb></lb>strumento della Camera oscura già descritto dal Porta. </s>

<s>“ Ex eo subit ani­<lb></lb>mum certare tecum in pervidendis illis minutis maculis a te primum in parte <lb></lb>lucidiori animadversis. </s>

<s>Id autem hoc pacto me spero perfecturum mea obser­<lb></lb>vandi ratione vultu a Luna averso; si Lunae lumen per foramen in tabel­<lb></lb>lam pertica circulatam intromisero, sic tamen ut foramen obvallet lens cry­<lb></lb>stallina, sphaerico maximi circuli gibbo et tabella ad locum collectionis <lb></lb>radiorum accomodetur. </s>

<s>Sic in pertica 12 pedes longa, Lunae corpus per­<lb></lb>fectissime depingetur quantitate monetae argentaee maioris. </s>

<s>Artificium de­<lb></lb>monstravi prop. </s>

<s>XXIII, fol. </s>

<s>196 et 211 Libri mei; simplicior tamen fuit <lb></lb>propositum a Porta primo titulo cap. </s>

<s>VI de lente cum ego de integro globo <lb></lb>demonstraverim ” (ibi, pag. </s>

<s>416, 17). </s></p><p type="main">

<s>Veniva così suggerito a Galileo il modo di osservare il Sole, <emph type="italics"></emph>ne ocu­<lb></lb>lum urat specillum,<emph.end type="italics"></emph.end> e varie testimonianze abbiamo che veramente l&#039;osservò <lb></lb>a questo modo, dopo la metà dell&#039;Aprile 1610, quando fu data fuori questa <lb></lb>Dissertazione kepleriana. </s></p><p type="main">

<s>Possiamo, per prima di così fatte testimonianze, recar quella del Mi­<lb></lb>canzio, il quale, dopo insorte le controversie con lo Scheiner, così, per giu­<lb></lb>stificare la priorità della scoperta e assecondare le pertinaci pretese di Ga­<lb></lb>lileo, gli scriveva: “ Io ho memoria distintissima che, quando V. S. ebbe <lb></lb>fabbricato quà (in Venezia) il primo occhiale, una delle cose che osservò fu <lb></lb>le macchie del Sole, e saprei dire il luogo ed il punto, ov&#039;ella coll&#039;Oc­<lb></lb>chiale, su una carta bianca, le mostrò al Padre (Paolo Sarpi) di gloriosa me­<lb></lb>moria, e mi ricordo delli discorsi che si facevano: prima se fosse inganno <lb></lb>dell&#039;Occhiale, se vapori del mezzo, e poi replicate l&#039;esperienze si concludeva <lb></lb>il fatto apparir tale e doversi filosofarvi sopra ” (Alb. </s>

<s>IX, 257). </s></p><pb xlink:href="020/01/931.jpg" pagenum="374"></pb><p type="main">

<s>Si raccoglie dunque da un tal documento che Galileo nel 1610, in Pa­<lb></lb>dova e in Venezia, osservò e fece osservare le macchie <emph type="italics"></emph>averso vultu,<emph.end type="italics"></emph.end> se­<lb></lb>condo il metodo kepleriano, sostituendo al foro della camera oscura il Ca­<lb></lb>nocchiale, invece della semplice lente biconvessa, e si rileva di più come <lb></lb>non si facesse altro in quel tempo che osservare il puro fatto, senza specu­<lb></lb>larne o saperne ancora specular la ragione. </s></p><p type="main">

<s>Conformi a questa del Micanzio si posson dire le testimonianze, che fa <lb></lb>in più luoghi e a diverse occasioni di sè medesimo Galileo. </s>

<s>Primo di questi <lb></lb>luoghi occorre a citare una lettera, scritta da Firenze il dì 23 Giugno 1612 <lb></lb>a don Giuliano de&#039;Medici, nella quale così gli dice: “ Sappia di più V. S. </s>

<s><lb></lb>Illustrissima come gli scoprimenti celesti non hanno ancora finito, ma sono <lb></lb>ancora <emph type="italics"></emph>quindici<emph.end type="italics"></emph.end> mesi e più che cominciai a vedere nel Sole alcune macchie <lb></lb>oscure e pur l&#039;anno passato, nel mese d&#039;Aprile, essendo in Roma, le feci <lb></lb>vedere a diversi prelati e altri signori ” (Alb. </s>

<s>VI, 188). Cosicchè parrebbe <lb></lb>di qui che occorresse a Galileo il primo scoprimento di quelle macchie oscure <lb></lb>nel Sole verso il mese di Luglio 1610. </s></p><p type="main">

<s>Da un&#039;altra testimonianza però dello stesso discopritore si conclude che <lb></lb>l&#039;osservazione gli occorse invece tre mesi dopo. </s>

<s>Nella prima Lettera al Vel­<lb></lb>sero infatti dice di avere osservate le macchie <emph type="italics"></emph>da diciotto mesi in qua<emph.end type="italics"></emph.end><lb></lb>(Alb. </s>

<s>III, 382). Ond&#039;è che avendo quella Lettera la data del dì 4 Mag­<lb></lb>gio 1612, sarebbe stato il principio, che dette Galileo alle osservazioni so­<lb></lb>lari, no del Luglio ma del Novembre 1610. </s></p><p type="main">

<s>Sarebbe una così fatta incoerenza indizio di poca sincerità, di che Ga­<lb></lb>lileo tanti esempi ne porge nella storia della sua vita scientifica, ma pur si <lb></lb>può dire che, trattandosi di cose passate e delle quali ancora non se ne <lb></lb>prevedeva l&#039;importanza, non dovesse far maraviglia se qualche poco, in de­<lb></lb>terminar la data precisa di quella scoperta, fallisse, in chi intendeva di ri­<lb></lb>vendicarsela, la memoria, per cui ne&#039;<emph type="italics"></emph>Massimi Sistemi,<emph.end type="italics"></emph.end> senza pretendere di <lb></lb>precisare il giorno nè il mese, afferma in ogni modo l&#039;Autore che il fatto <lb></lb>occorse nel 1610. “ Fu il primo scopritore e osservatore delle macchie so­<lb></lb>lari, siccome di tutte le altre novità celesti, il nostro Accademico Linceo, e <lb></lb>queste scoperse egli nel 1610, trovandosi ancora alla lettura delle Matema­<lb></lb>tiche nello studio di Padova, e quivi e in Venezia ne parlò con diversi ” <lb></lb>(Alb. </s>

<s>I, 375). </s></p><p type="main">

<s>Si conceda dunque a chi in ogni modo, o a ragione o a torto, voleva <lb></lb>in tutto essere il primo e il solo, ch&#039;egli osservasse le macchie solari dopo <lb></lb>l&#039;Aprile del 1610. Egli non presentiva però nulla ancora dell&#039;importanza di <lb></lb>quel fatto: per lui era una curiosità non punto dissimile da quella di co­<lb></lb>loro, i quali vedevano le macchie solari nello spettro proiettato dagli spira­<lb></lb>gli di una finestra sul pavimento di qualche altissimo edifizio; curiosità resa <lb></lb>per mezzo del canocchiale assai meglio sodisfatta, ma ch&#039;era tanto ancora <lb></lb>lontana dall&#039;aver merito e ragione di una vera scoperta astronomica. </s>

<s>Gali­<lb></lb>leo stesso non la stimò per lungo tempo che quale una mera curiosità, non <lb></lb>dandole nessuna importanza in mezzo alle altre sue scoperte celesti, fra le <pb xlink:href="020/01/932.jpg" pagenum="375"></pb>quali, a tante studiate occasioni, egli eloquente magnificator d&#039;ogni cosa sua, <lb></lb>non annoverò mai le macchie solari: e facendole egli vedere in Roma e al­<lb></lb>trove, non si propone altro fine, che <emph type="italics"></emph>di sodisfar la curiosità di que&#039;pre­<lb></lb>lati e di que&#039;signori<emph.end type="italics"></emph.end> (Alb. </s>

<s>III, 183). Nè poteva dall&#039;altra parte pensare al­<lb></lb>lora seriamente, Galileo, al Sole, essendo infaticabilmente dietro a ritrovare <lb></lb>i periodi de&#039;satelliti di Giove, e a dar principio a calcolar le Tavole dei loro <lb></lb>moti (Alb. </s>

<s>XII, 9; VI, 57). </s></p><p type="main">

<s>Sarebbero state forse per rimanere ancora, chi sa quanto tempo, una <lb></lb>semplice curiosità le macchie del Sole nella mente di Galileo, quando non <lb></lb>fosse provvidamente venuta a risvegliarla una lettera scritta nel dì 8 Gen­<lb></lb>naio 1612 da Augusta. </s>

<s>Marco Velseri che la scriveva, dopo altre parole sog­<lb></lb>giunge le seguenti: “ Veda ciò che si è arrischiato questo mio amico; e se <lb></lb>a Lei non riuscirà cosa totalmente nuova, come credo, spero però che le <lb></lb>sarà di gusto vedendo che ancora da questa banda de&#039;monti non manca chi <lb></lb>vada dietro alle sue pedate. </s>

<s>Ella faccia, in proposito di queste macchie so­<lb></lb>lari, di dirmene liberamente il suo parere, se giudica tali materie stelle o <lb></lb>altro, dove crede sieno situate, e qual sia il lor moto ” (Alb. </s>

<s>III, 371). </s></p><p type="main">

<s>La Lettera veniva accompagnata da tre epistole latine <emph type="italics"></emph>De maculis so­<lb></lb>laribus<emph.end type="italics"></emph.end> d&#039;incognito Autore, <emph type="italics"></emph>post tabulam latentis.<emph.end type="italics"></emph.end> Incomincia la prima epi­<lb></lb>stola col narrare in che modo occorresse all&#039;Autore, che si dà il nome di <lb></lb>Apelle, di far le prime osservazioni di quelle macchie. </s>

<s>“ Phaenomena quae <lb></lb>circa Solem observavi petenti affero, mi Velsere, nova et pene incredibilia. </s>

<s><lb></lb>Ea ingentem non solum mihi sed et amicis, primum admirationem, deinde <lb></lb>etiam animi voluptatem pepererunt; quod eorum ope, plurima, hactenus <lb></lb>astronomis aut dubitata aut ignorata aut etiam fortassis pernegata, in cla­<lb></lb>rissimam veritatis lucem, per fontem luminis et astrorum ductorem Solem, <lb></lb>protrahi posse plane persuasum habeamus. </s>

<s>Ante menses septem, octo cir­<lb></lb>citer, ego, unaque mecum amicus quidam meus Tubum opticum, quo et <lb></lb>nunc utor, quique obiectum sexcenties aut etiam octingenties in superficie <lb></lb>amplificat, in Solem direximus, dimensuri illius ad Lunam magnitudinem <lb></lb>opticam, invenimusque utriusque fere aequalem. </s>

<s>Et cum huic rei intende­<lb></lb>remus, notavimus quasdam in Sole nigricantes quodammodo maculas, instar <lb></lb>guttarum subnigrarum. </s>

<s>Quia vero tum id ex instituto non investigavimus <lb></lb>parvi rem istam pensitantes distulimus in aliud tempus. </s>

<s>Redivimus ergo ad <lb></lb>hoc negotium mense praeterito octobri, reperimusque in Sole apparentes <lb></lb>maculas eo modo fere quo descriptas vides ” (Alb. </s>

<s>III, 372, 73). Essendo <lb></lb>questa Lettera di Apelle in data del di 12 Novembre 1611, si risale dunque <lb></lb>al Febbraio o al Marzo di quello stesso anno a porre i principii delle nuove <lb></lb>spettacolose osservazioni. </s></p><p type="main">

<s>Prosegue ivi l&#039;Autore a dire in che modo abbia potuto, senz&#039;alcuna <lb></lb>offesa, tener fissi gli occhi nel Telescopio diretto al Sole: “ Primo, Sol ma­<lb></lb>tutinus et vespertinus, vicinus horizonti, per quartam horae partem nudo <lb></lb>Tubo, bono tamen, apertus et serenus utcumque impune aspicitur. </s>

<s>Secundo, <lb></lb>Sol ubicumque opertus nebula vel nube debite perspicua, nudo Tubo, sal-<pb xlink:href="020/01/933.jpg" pagenum="376"></pb>vis oculis videtur. </s>

<s>Tertio, Sol ubicumque apertus per Tubum praeter con­<lb></lb>vexum et concavum vitrum vitro insuper utrinque plano coeruleo aut viridi <lb></lb>debite crasso munitum, ea parte qua admovetur oculus, indennes adversus <lb></lb>servat oculos vel in ipso meridie, et hoc amplius, si ad ipsum coeruleum <lb></lb>vitrum non satis attemperatum accesserit in aere tenuis vel vapor vel nu­<lb></lb>becula Solem veli instar subohumbrans. </s>

<s>Quarto, Solis intuitus inchoandus <lb></lb>a perimetro et paulatim in medium est tendendum, ibique paulisper immo­<lb></lb>randum; lux enim circum stans umbras non statim admittit ” (ibi, pag. </s>

<s>375). </s></p><p type="main">

<s>Nella terza Lettera passa l&#039;Autore a dir la sua propria opinione intorno <lb></lb>all&#039;essere e alla natura di queste Macchie: “ Sed quid eae tandem sunt? </s>

<s><lb></lb>Non nubes .... sed neque Cometae.... Reliquum ergo ut sint vel partes <lb></lb>alicuius Coeli densiores, et sic erunt, secumdum Philosophos, stellae, aut <lb></lb>sint corpora per se existentia solida et opaca, et hoc ipso erunt stellae non <lb></lb>minus atque Luna et Venus, quae ex aversa a Sole parte nigrae apparent ” <lb></lb>(ibi, pag. </s>

<s>378). </s></p><p type="main">

<s>Entriamo ora addentro a scrutare da quali sentimenti dovess&#039;esser com­<lb></lb>mosso alla lettura di queste Epistole l&#039;animo di Galileo. </s>

<s>Non nuovo il fatto <lb></lb>dell&#039;osservazione, prima di tutto, nè nuovo dovette apparirgli il modo. </s>

<s>Egli <lb></lb>non s&#039;era attentato ancora mai di fissar gli occhi direttamente nel Sole, ma <lb></lb>quasi due mesi prima che il Gualdo gli scrivesse esser venuto al Pignoria <lb></lb>avviso che c&#039;erano in Germania alcuni, che <emph type="italics"></emph>cominciavano a mirare anco <lb></lb>nel Sole<emph.end type="italics"></emph.end> (Alb. </s>

<s>VIII, 178), il Cigoli, sotto il dì 16 Settembre di quell&#039;anno 1611, <lb></lb>gli aveva scritto così da Roma: “ Volevo scriverli, sino per la passata, come <lb></lb>il Passignano, avendo avuto da un amico suo in Venezia un Occhiale simile <lb></lb>a quello di V. S., con il quale dice aver osservato già molte volte il Sole <lb></lb>la mattina, al mezzogiorno e la sera, e il figliolo e il genero dice che la vista <lb></lb>non li resiste, nè io mi sono ardito, oltre al non avere avuto occasione nè <lb></lb>tempo, di tentare se la vista mi resiste, dove dice il Passignano che guarda <lb></lb>e leva l&#039;occhio e per un pezzetto non vede, ma poi tornando vede benis­<lb></lb>simo e con molta comodità ” (MSS. Gal., P. VI, T. VIII, c. </s>

<s>41). La stessa <lb></lb>cosa ripete il Cigoli in un altra del dì 23 di quel mese di Settembre pub­<lb></lb>blicata da pag. </s>

<s>169-71 nel T. VIII dall&#039;Albèri. </s></p><p type="main">

<s>Nuova non doveva pure tornare a Galileo l&#039;invenzione del vetro colo­<lb></lb>rato, imperocchè il Passignano, pochi giorni prima che avesse lo stesso Ga­<lb></lb>lileo ricevuta la lettera del Velsero con le tre Epistole di Apelle, cosi gli <lb></lb>mandava a dire da Roma: “ Credo che il signor Lodovico (Cigoli) li averà <lb></lb>scritto come con un mio Occhiale ho fatto alcune osservazioni di nubi nel <lb></lb>Sole, delle quali in questa ne mando copia a V. S., dove la vedrà il giorno e <lb></lb>l&#039;ora che si sono viste. </s>

<s>Ora io li ho mostri alli Padri Grembergero e Mal­<lb></lb>colfo, li quali dicono che si vedono e mi hanno detto come posso soffrire la <lb></lb>vista del Sole? </s>

<s>Li ho detto che avanti il vetro piccolo ci metto un vetro <lb></lb>oscuro, che modifica il calore del Sole ” (MSS. Gal., P. VI, T. VIII, c. </s>

<s>75). </s></p><p type="main">

<s>Forse nuova sarà riuscita a Galileo la osservazione di Apelle delle mac­<lb></lb>chie vedute andare più celeri nel mezzo, che verso i lembi della sfera so-<pb xlink:href="020/01/934.jpg" pagenum="377"></pb>lare, d&#039;onde ne argomentava un moto di circolazione di esse macchie o del <lb></lb>Globo centrale. </s>

<s>È certo in ogni modo che a&#039;quesiti proposti dal Velsero, <lb></lb>l&#039;Autor del Nunzio Sidereo non ci aveva punto pensato, e ne dovette rima­<lb></lb>nere sorpreso. </s>

<s>Confessare ingenuamente il fatto non era della sua indole, e <lb></lb>perciò, sollecito di cogliere la prima occasione che gli si porgesse, al Di­<lb></lb>scorso che aveva allora fra mano intorno alle cose che stanno in sull&#039;acqua, <lb></lb>appiccica, ripetendo le varie opinioni di Apelle e approvando indifferente­<lb></lb>mente le une e le altre, queste parole: “ Aggiungo a queste cose, egli dice, <lb></lb>l&#039;osservazione di alcune macchiette oscure che si scorgono nel corpo solare, <lb></lb>le quali mutando positura in quello porgono grande argomento o che il Sole <lb></lb>si rivolga in sè stesso, o che forse altre stelle, nella guisa di Venere e di <lb></lb>Mercurio, se gli volgano intorno invisibili in altri tempi, per le piccole di­<lb></lb>gressioni, minori di quelle di Mercurio, e solo visibili, quando s&#039;interpon­<lb></lb>gono tra il Sole e l&#039;occhio nostro, oppur danno segno che sia vero e que­<lb></lb>sto e quello ” (Alb. </s>

<s>XII, 11). </s></p><p type="main">

<s>Una tale aggiunta dev&#039;essere stata fatta dall&#039;Autore dopo ch&#039;egli ebbe <lb></lb>ricevuta la Lettera del Velsero, e prima del di 17 Febbraio, per le ragioni <lb></lb>che si vedranno, quando il Manoscritto già consegnato alla Revisione, non <lb></lb>dava luogo e tempo da riporvi sopra la mano. </s></p><p type="main">

<s>Intanto il dì 4 Maggio 1612 uscì in pubblico la prima Lettera Solare, <lb></lb>in risposta alla scritta, non tre mesi, come dice in principio l&#039;Autore, ma <lb></lb>quattro mesi prima, dal Velsero, se si deve stare alla data. </s>

<s>In questa Let­<lb></lb>tera Galileo professa circa alla costituzion delle macchie, idee in tutto di­<lb></lb>verse da quelle già significate nel Discorso delle Galleggianti pubblicato nel <lb></lb>precedente mese di Marzo. </s>

<s>Mentre infatti qui, nel Discorso, ammette che le <lb></lb>macchie possano anch&#039;essere stelle, là, nella Lettera, dimostra come cosa <lb></lb>certa non aver nulla che alle stelle, veramente e propriamente dette, le ras­<lb></lb>somigli. </s>

<s>Ma se a qualche cosa pure si volessero rassomigliare, dice che sa­<lb></lb>rebbero le nuvole, le quali adombrano la superficie della nostra Terra. </s></p><p type="main">

<s>Nella seconda di queste Lettere velseriane, che porta la data del dì <lb></lb>11 Agosto 1612, si diffonde più lungamente Galileo a descrivere i fenomeni <lb></lb>osservati nelle macchie, dalle quali osservazioni è condotto a congetturar <lb></lb>l&#039;esistenza di una sfera vaporosa circondante e menata in volta dal Sole, <lb></lb>che rapidamente convertesi intorno al suo proprio asse. </s></p><p type="main">

<s>Nella sopra citata Lettera a Giuliano de&#039;Medici sono così, con brevità <lb></lb>da preferirsi alla loquacità delle Lettere velseriane, descritte quelle appa­<lb></lb>renze: “ Tali macchie sono non pur vicine al Sole, ma contigue alla su­<lb></lb>perficie di quello, dove continuamente altre se ne producono e altre se ne <lb></lb>dissolvono, essendo altre di breve e altre di lunga durazione: cioè alcune <lb></lb>si disfanno in due, tre o quattro giorni, e altre duran quindici, venti, trenta <lb></lb>e ancor più. </s>

<s>Vannosi mutando di figura, le quali figure sono per lo più irre­<lb></lb>golarissime, si condensano e si distraggono, sendo talora alcune oscurissime, <lb></lb>e altre non così negre; spesso una si divide in tre o quattro ed altre volte <lb></lb>due o tre o più si aggregano in una sola. </s>

<s>Hanno poi un movimento rego-<pb xlink:href="020/01/935.jpg" pagenum="378"></pb>lato, secondo il quale uniformemente vengono tutte portate in giro dall&#039;istesso <lb></lb>corpo solare, il quale si muove in sè stesso in un mese lunare in circa ” <lb></lb>(Alb. </s>

<s>VI, 189). </s></p><p type="main">

<s>Come poi le non possano essere stelle, Galileo lo dimòstra nella III Vel­<lb></lb>seriana con matematici argomenti e con fisiche ragioni. </s>

<s>Può chi vuole leg­<lb></lb>ger quegli argomenti nel Tomo III dell&#039;Albèri, ma quanto alle ragioni fisi­<lb></lb>che concluse nelle parole che leggonsi a pag. </s>

<s>499, 500, invece delle stampate, <lb></lb>le trascriveremo ai nostri Lettori quali uscirono di primo getto dalla penna <lb></lb>stessa di Galileo, meno ordinate sì, ma più concise e più efficaci: </s></p><p type="main">

<s>“ Io poi metto tanta poca difficoltà sopra i nomi, anzi pur so che è in <lb></lb>arbitrio di ciascheduno d&#039;imporgli a modo loro, che non farei caso a chia­<lb></lb>marle stelle, e massime chiamandosi con tal nome anco le Comete, li due <lb></lb>fulgori del 1572 e del 1604, l&#039;esalazioni cadenti e discorrenti per l&#039;aria, ed <lb></lb>essendo infin conceduto agli amanti e a&#039;poeti chiamare stelle gli occhi delle <lb></lb>loro donne: <emph type="italics"></emph>Quando si vidde il successor d&#039;Astolfo sopra apparir quelle <lb></lb>ridenti stelle.<emph.end type="italics"></emph.end> E di più dire, di un alterato dal vino o stordito da una per­<lb></lb>cossa, <emph type="italics"></emph>Vidde mirando in terra alcuna stella. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ma saranno queste stelle solari differenti dalle altre in alcune con­<lb></lb>dizioni, pur di qualche considerazione, attesochè quelle ci si mostrano sem­<lb></lb>pre di una sola figura, e quella è la regolarissima fra tutte, e queste d&#039;infiniti <lb></lb>ed irregolarissimi tratti. </s>

<s>Quelle consistenti nè mai mutatesi di grandezza e <lb></lb>di forma, e queste instabili sempre e mutabili. </s>

<s>Quelle l&#039;istesse sempre e di <lb></lb>permanenza, che supera la memoria di tutti i secoli decorsi, queste gene­<lb></lb>rabili e dissolubili dall&#039;uno all&#039;altro giorno. </s>

<s>Quelle non mai visibili se non <lb></lb>piene di luce, queste oscure sempre, e splendide non mai. </s>

<s>Quelle mobili <lb></lb>ognuna per sè di moti proprii e regolari e tra di loro differentissimi, que­<lb></lb>ste mobili di un moto solo comune a tutte, regolare solo in universale, ma <lb></lb>da infinite particolari disagguaglianze alterato. </s>

<s>Quelle costituite tutte in par­<lb></lb>ticolari e diverse lontananze dal Sole, e queste tutte contigue e insensibil­<lb></lb>mente remote dalla sua superficie. </s>

<s>Quelle non mai visibili, se non quando <lb></lb>sono separate dal Sole, queste non mai vedute se non congiuntegli. </s>

<s>Quelle <lb></lb>di materia probabilissimamente densa ed opacissima, queste, a guisa di neb­<lb></lb>bia o fumo, rare. </s>

<s>E chi sarà quello che le vogli stimar cosa, con la quale <lb></lb>non hanno pur una minima particolar convenienza, che non l&#039;abbiano con <lb></lb>cent&#039;altre cose, più presto che cosa con la quale in ogni particolare con­<lb></lb>vengono? </s>

<s>” </s></p><p type="main">

<s>“ Io le ho agguagliate alle nostre nuvole o ai fumi, e certo chi le vo­<lb></lb>lesse con alcuna delle nostre materie imitare, non credo che si trovasse più <lb></lb>aggiustata imitazione che lo spruzzare sopra un ferro rovente, in piccole <lb></lb>stille, qualche bitume di difficile combustione, il quale sul ferro imprime­<lb></lb>rebbe una macchia negra, dalla quale, come da sua radice, si eleverebbe un <lb></lb>fumo oscuro, che in figure stravaganti e mutabili si andrebbe spargendo. </s>

<s>” <lb></lb>… </s></p><p type="main">

<s>“ Se le fossero stelle, o congerie o drappelli di stelle, che per l&#039;ine-<pb xlink:href="020/01/936.jpg" pagenum="379"></pb>gualità dei lor movimenti si accozzassero insieme, come tali accozzamenti si <lb></lb>farebbero sempre numerosissimi, e massimi solamente verso il mezzo del <lb></lb>Sole, ed i medesimi verso la circonferenza sempre si andrebbero dimi­<lb></lb>nuendo? </s>

<s>e com&#039;essendo alcuna macchia talvolta ben cinquanta volte mag­<lb></lb>giore in superficie di Venere, non si fa veder luminosa fuori del disco so­<lb></lb>lare? </s>

<s>” (MSS. Gal., P. III, T. X, c. </s>

<s>74). </s></p><p type="main">

<s>In pochi mesi insomma, ripigliando il filo del nostro discorso, Galileo <lb></lb>aveva fatto, nello studio delle macchie solari, grandissimi progressi. </s>

<s>Il prin­<lb></lb>cipio dell&#039;anno 1612 lo aveva trovato nuovo di quello studio: nel Giugno <lb></lb>è già penetrato addentro ai più reconditi misteri della fisica costituzione del <lb></lb>Sole. </s>

<s>Ne ha minutamente osservate e diligentemente descritte le fasi della <lb></lb>sua superficie, e ha misurato con sufficiente precisione il periodo della con­<lb></lb>versione in sè stesso. </s></p><p type="main">

<s>Per giunger però con tanta sicurezza a conclusioni così importanti, con­<lb></lb>veniva aver fatto qualche osservazione diretta sulla faccia del Sole, perchè <lb></lb>il metodo delle proiezioni, se non era troppo bene accomodato a rappresen­<lb></lb>tar con evidenza il fenomeno, tanto era meno sufficiente a ricavar con pre­<lb></lb>cisione la verità di que&#039;si svariati accidenti. </s>

<s>Galileo, il quale, come sappiamo, <lb></lb>non ammetteva nel Canocchiale l&#039;inversione de&#039;raggi, non si sarebbe facil­<lb></lb>mente per sè medesimo accorto nemmen che i punti proiettati dalla parte <lb></lb>orientale sopra la carta rispondevano alla parte occidentale della sfera so­<lb></lb>lare; per cui si può comprendere quanto dovess&#039;essere, per sua propria <lb></lb>scienza ed arte, atto a ritrovare, con quella precisione con cui lo ritrovò e <lb></lb>così presto, il periodo della rivoluzione del Sole intorno al suo proprio asse. </s>

<s><lb></lb>Di qual dunque altra scienza ed arte si giovò Galileo per risolvere i nuovi <lb></lb>problemi di Astronomia solare? </s>

<s>E risponderanno alla domanda le seguenti <lb></lb>notizie. </s></p><p type="main">

<s>Mentre in Roma, nell&#039;Aprile del 1611, faceva esso Galileo, per curio­<lb></lb>sità spettacolosa, osservar le macchie del Sole, fra&#039;curiosi concorsi vi furon <lb></lb>due celebri artisti venuti di Toscana, Lodovico Cigoli e Domenico Passi­<lb></lb>gnani. </s>

<s>Già vedemmo come fosse questo Passignani uno de&#039;primi fra noi, <lb></lb>che senza nulla ancora saper di ciò che s&#039;era incominciato a fare in Ger­<lb></lb>mania, osasse di fissare il Sole col Canocchiale scoperto, e poi v&#039;applicasse <lb></lb>i vetri neri. </s>

<s>Per qualche tempo non si curò che delle semplici osservazioni, <lb></lb>ritraendo in disegno la faccia del Sole, quasi come un nuovo esercizio del­<lb></lb>l&#039;arte sua, ma venuto a notizia delle Epistole di Aprile, che il Velsero avea <lb></lb>diffuse in Italia, dall&#039;ufficio di pittore arditamente passando a quello di astro­<lb></lb>nomo, incominciò a filosofare intorno alla natura di quelle macchie, e as­<lb></lb>serì, contro l&#039;opinion dello stesso Apelle, che le non erano ombre proiet­<lb></lb>tate da corpi opachi stellari, che s&#039;aggirassero separati dal Sole, ma che <lb></lb>ell&#039;erano dentro lo stesso Sole, come oscure voragini approfondatesi nella <lb></lb>sostanza di lui. </s>

<s>Questa sua opinione, tanto nuova e tanto contraria alle idee <lb></lb>comunemente invalse della incorruttibile integrità del Sole, il Passignani la <lb></lb>significava così a Galileo, per lettera scritta il dì 17 Febbraio 1612: </s></p><pb xlink:href="020/01/937.jpg" pagenum="380"></pb><p type="main">

<s>“ Avendo visto un Discorso venuto d&#039;Alemagna sopra le macchie, che <lb></lb>si vedono nel Sole, ed ancora una dimostrazione di alcune osservazioni, ed <lb></lb>avendone parlato con il p. </s>

<s>Griembergero, il quale è dell&#039;istesso parere di <lb></lb>questo che scrive, che è questo: Dice che le macchie che si vede sieno <lb></lb>stelle, come quelle che si vedono attorno a Giove. </s>

<s>Io sono di contraria opi­<lb></lb>nione, perchè, avendone fatto per cinque mesi osservazione, non ho potuto <lb></lb>comprendere che sieno fuori del corpo del Sole, perchè in detto tempo non <lb></lb>è possibile che non avessi visto qualcheduna, che non occupassi il dintorno <lb></lb>del Sole, siccome farebbe se le fossero fuori del corpo del Sole. </s>

<s>Ma non ne <lb></lb>ho mai viste vicine a detto dintorno, anzi cominciano un poco lontano, e si <lb></lb>vedono poco, e di mano in mano, quando si avvicinano al mezzo, si vedono <lb></lb>più, ed ancora ne ho viste da un giorno all&#039;altro venire appresso al mezzo <lb></lb>in un tratto, e poi fare il suo corso in più giorni e svanire, ed ancora ne <lb></lb>ho viste che, quando sono a mezzo venute, in pochi giorni svanire e non <lb></lb>si vedere più, e con queste dimostrazioni non so capire che le sieno stac­<lb></lb>cate dal Sole. </s>

<s>Se quando in un tratto le si vedono appresso il mezzo e poi <lb></lb>fare il corso in più giorni, già avverrebbe che in un tratto venissero e <lb></lb>poi mutassero corso e se ne andassero adagio, e per contrario ne ho viste <lb></lb>venire adagio e poi, quando sono vicine al mezzo, sparire. </s>

<s>Di qui avverrebbe <lb></lb>che avessero corso veloce ed adagio e non seguente, la qual cosa io non <lb></lb>credo che possa stare, che tengo che tutti i corpi celesti abbino il loro corso <lb></lb>seguente e che non si muti. </s>

<s>Io tengo che sieno dentro il corpo del Sole, <lb></lb>non solo in superficie, ma che s&#039;incentrino dentro, e venghino in superfi­<lb></lb>cie, ed al Rev. </s>

<s>Griembergero ho detto quello che ho veduto, che ha detto <lb></lb>che si è risoluto di far le osservazioni, che troverà tutte queste cose che ho <lb></lb>detto, e così da lei vorrei sapere se, nelle osservazioni che ha fatte, la ci <lb></lb>ha trovato queste cose che dico: la mi farà grazia di dirmi in questo quello <lb></lb>la ne pensa ” (MSS. Gal., P. VI, T. VIII, c. </s>

<s>88). </s></p><p type="main">

<s>Galileo però non rispose, ciò che il Passignano se l&#039;ebbe molto a male, <lb></lb>e <emph type="italics"></emph>andò in valigia,<emph.end type="italics"></emph.end> come il Cigoli fiorentinescamente si esprime (ivi, c. </s>

<s>128). <lb></lb>Ma se non rispose colle parole, rispose coi fatti, approvando così l&#039;opinione <lb></lb>del Passignano da farla sua, e riprovando quell&#039;altra di Apelle che aveva <lb></lb>dianzi pubblicamente approvata. </s>

<s>E perchè non rimanesse di ciò la memo­<lb></lb>ria, sempre fermo in un proposito di non confessar mai di avere errato, fa <lb></lb>ristampare il Discorso delle Galleggianti, per l&#039;unico fine di sostituire alle <lb></lb>parole scritte: <emph type="italics"></emph>essere argomento le macchie o che il Sole si rivolga in sè <lb></lb>stesso, o che forse altre stelle nella guisa di Venere e di Mercurio se gli <lb></lb>volgano intorno,<emph.end type="italics"></emph.end> il periodo seguente: “ Hannomi finalmente le continuate <lb></lb>osservazioni accertato tali macchie esser materie contigue alla superficie del <lb></lb>corpo solare, e quivi continuamente prodursene molte e poi dissolversi: <lb></lb>altre in più brevi, altre in più lunghi tempi, ed esser dalla conversione del <lb></lb>Sole in sè stesso, che in un mese lunare in circa finisce il suo periodo, <lb></lb>portate in giro: accidente per sè grandissimo e maggiore per le sue con­<lb></lb>guenze ” (Firenze, Giunti, 1612, pag. </s>

<s>2, 3). </s></p><pb xlink:href="020/01/938.jpg" pagenum="381"></pb><p type="main">

<s>La definizione di questo periodo richiedeva osservazioni diligenti, le <lb></lb>quali dubitiamo se potessero esser fatte da Galileo, tutto intento allora ai <lb></lb>satelliti gioviali. </s>

<s>Ci dee probabilmente avere avuto gran parte il Castelli, a <lb></lb>cui l&#039;Autore della II Lettera velseriana non par voglia dare altro merito <lb></lb>che di avere insegnato il modo di descriver le macchie per proiezione <lb></lb>(Alb. </s>

<s>III, 419); merito che si doveva piuttosto attribuire al Keplero, il quale <lb></lb>aveva qualche tempo prima insegnato nella proposizione XXIII dell&#039;Ottica <lb></lb>e nella CV della Diottrica “ Visibilia lente cava et convexa pingere super <lb></lb>papyro maiori quantitate, quam per solam convexam, sed eversa ” (Augustae <lb></lb>Vindelic. </s>

<s>1611, pag. </s>

<s>54). </s></p><p type="main">

<s>È poi notabile che potesse il Castelli persuadere a Galileo questa ever­<lb></lb>sione, la quale doveva stare nella mente di lui a dispetto e fare ai cozzi con <lb></lb>le altre opinioni a cui non volle mai rinunziare, benchè il Castelli non solo, <lb></lb>ma l&#039;Antonini, il Sagredo e altri di più sano giudizio, facessero notare allo <lb></lb>stesso loro riverito maestro, la irragionevole, e anzi mostruosa incongruenza. </s></p><p type="main">

<s>L&#039;Antonini, che aveva ricevute in Bruxelles le due prime Lettere vel­<lb></lb>seriane, maravigliato della scoperta e delle osservazioni delle macchie, a lui <lb></lb>giunte come cosa nuova, scriveva a Galileo ne&#039;termini seguenti: “ In quanto <lb></lb>alla speculazione, che V. S. mi dà della figura, che sopra la carta s&#039;inverte <lb></lb>e non sopra l&#039;occhio, a me non pare che perciò ne segua che siano diversi <lb></lb>que&#039;raggi, che apportan le immagini, da quelli co&#039;quali si fa la vista, e <lb></lb>prima io nego che quelle immagini, che s&#039;invertono sopra la carta, non <lb></lb>s&#039;invertano ancora sopra l&#039;occhio ” (MSS. Gal., P. VI, T. VII, c. </s>

<s>132). </s></p><p type="main">

<s>Similmente il Sagredo, quasi in quegli stessi giorni in che tali parole <lb></lb>scriveva l&#039;Antonini, cioè nel dì 7 Luglio 1612, con filosofica libertà si op­<lb></lb>poneva così alle false opinioni di Galileo: “ Circa a quello che mi scrive <lb></lb>della inversione delle macchie del Sole, che si vedono nella carta, io non <lb></lb>metto dubbio che l&#039;istesso non occorra nell&#039;occhio, il quale, per essere avvezzo <lb></lb>ad apprendere tutte le spezie a rovescio, le guarda diritte ” (Alb. </s>

<s>XVI, 59). </s></p><p type="main">

<s>Dalle quali notabilissime incongruenze delle dottrine galileiane, e dalle <lb></lb>altre cose fin qui discorse, ritornando indietro per concludere quel nostro <lb></lb>ragionamento, non sarà difficile persuadersi che la Filosofia e la Matematica <lb></lb>delle Macchie solari, sottentrate in così breve tempo ai primi errori, e così <lb></lb>largamente trasfuse nelle Lettere velseriane; le attinse, senza troppa fatica, <lb></lb>Galileo dalle osservazioni del Passignano principalmente, e dalle speculazioni <lb></lb>del Castelli. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi legge attentamente queste Lettere velseriane, fonti di scienza astro­<lb></lb>nomica e d&#039;italiana eloquenza, ci sente dentro un&#039;amarezza, e anzi un odio <lb></lb>cupo contro Apelle, quasi fossero quelle sue Epistole una usurpazione della <pb xlink:href="020/01/939.jpg" pagenum="382"></pb>prima scoperta. </s>

<s>A rispondere alle accuse Cristoforo Scheiner, che tale è il <lb></lb>nome vero del finto Apelle, scrisse un libraccione in folio di 784 pagine a <lb></lb>due colonne, col titolo di <emph type="italics"></emph>Rosa Ursina,<emph.end type="italics"></emph.end> perchè dedicato a Paolo Gior­<lb></lb>dano II Orsino, duca di Bracciano, nella qual città il libro, nel 1630, venne <lb></lb>alla luce. </s>

<s>Tutto, in quel libro, incominciando dal frontespizio, spira antipa­<lb></lb>tia, ma se si può con ragione ridere dell&#039;impresa delle tre Orse nella ca­<lb></lb>verna, a noi per verità non sembra nè ragionevole nè onesto il trattar che <lb></lb>fa Galileo l&#039;Autore di <emph type="italics"></emph>porco,<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>maligno asinaccio<emph.end type="italics"></emph.end> (Alb. </s>

<s>VII, 59). Vero <lb></lb>è che vomitava questi titoli in una lettera familiare al Micanzio, ma pure <lb></lb>anche in fine al Discorso astronomico Delle montuosità della Luna a don <lb></lb>Giacomo Muti, non lascia di appioppare allo Scheiner i titoli di arrogante, <lb></lb>d&#039;ignorantissimo, d&#039;insensato (Alb. </s>

<s>III, 182, 83). </s></p><p type="main">

<s>L&#039;Autore della <emph type="italics"></emph>Rosa Urbina<emph.end type="italics"></emph.end> non esce mai così fuori de&#039;termini della <lb></lb>civiltà, come il velenoso carcerato di Arcetri. </s>

<s>Ma a che tant&#039;ira eruttata <lb></lb>in parole così ingiuriose e plebee? </s>

<s>Non perchè l&#039;odiato rivale gli avesse <lb></lb>usurpata la teorica delle macchie, o si fosse appropriato il ritrovamento del <lb></lb>loro periodo, cose anzi che lo Scheiner generosamente concede a Galileo, e <lb></lb>con le quali riduce a consentire la prima sua dissenziente opinione, ma <lb></lb>tutta la fiera contesa versava intorno al primato della osservazione semplice <lb></lb>e materiale, che Galileo, senza pro e senza diritto, voleva ad ogni costo ri­<lb></lb>vendicare a sè stesso. </s></p><p type="main">

<s>Diciamo senza pro, perchè il merito doveva essere propriamente di colui <lb></lb>che osservò prima le Macchie proiettale attraverso a qualche alto spiraglio <lb></lb>sul pavimento di un tempio, merito che poteva essere offerto a qualunque <lb></lb>più volgare e curioso osservatore o dalla fortuna o dal caso. </s>

<s>Senza diritto, <lb></lb>perchè se la prima Lettera di Apelle ha la data del dì 12 Novembre 1611, <lb></lb>e il Discorso delle Galleggianti ha la data del dì 3 Marzo 1612, e la Storia <lb></lb>non giudica se non da ciò che è pubblicamente noto, lo Scheiner precedè <lb></lb>Galileo nell&#039;annunziare al mondo la sua scoperta di quasi quattro mesi. </s>

<s>Che <lb></lb>se lo stesso Galileo, avendo già fatta quella medesima scoperta nel 1610, <lb></lb>com&#039;ei pretese di dimostrare, non la fece pubblicamente nota, sua colpa, <lb></lb>ciò non potendo essere che o per negligenza o perchè egli non dava al fe­<lb></lb>nomeno nessuna scientifica importanza. </s>

<s>Noi affermammo che dovett&#039;essere <lb></lb>per questa ultima ragione, e mentre il Nostro si rimase così indifferente, e <lb></lb>non riguardò il fatto se non come una nuova curiosità spettacolosa, il Ge­<lb></lb>suita tedesco se ne sentì talmente commosso da levare a romore tutta l&#039;Ale­<lb></lb>magna, nella quale s&#039;incominciò a riguardar da molti nel Sole, e s&#039;ingerì <lb></lb>nell&#039;animo del Velsero e di altri Filosofi di là dai monti il desiderio di sa­<lb></lb>per l&#039;origine di que&#039;nuovi misteri. </s></p><p type="main">

<s>Quel fervore di osservazioni e di studi ebbe senza dubbio origine dal <lb></lb>Nunzio Sidereo di Galileo, dentro il quale rileggendo ammirati, e trovan­<lb></lb>dovi, contro ciò che si sarebbero aspettato o che paresse a lor conveniente, <lb></lb>dimenticato il Sole, si sentiron naturalmente frugati dalla curiosità di ri­<lb></lb>cercar se, anche in esso, il Canocchiale svelasse qualche cosa di nuovo a <pb xlink:href="020/01/940.jpg" pagenum="383"></pb>un più diligente Messaggero celeste. </s>

<s>Fa di ciò principalmente fede il Ke­<lb></lb>plero, il quale così scriveva da Linz il dì 18 Luglio 1613 a Oddone Mal­<lb></lb>cozio: </s></p><p type="main">

<s>“ Primum atque Galilaeus, inventis novis sideribus, plura arcana coe­<lb></lb>lestia iactavit, de Solis maculis cogitare coepi, si forsan earum indicio motum <lb></lb>aliquem Telluris circa Solem comprobare possimus, tunc nimirum si Sol <lb></lb>ipse non fuisset rotatus. </s>

<s>Igitur, lente convexa Telescopii optimi, quod habe­<lb></lb>bam ex concessu Electoris coloniensis, post meridiem radium Solis excepi, <lb></lb>et papyrum in puncto concursus radiorum applicavi, remoto concavo vitro. </s>

<s><lb></lb>Sed fulgor immensus radiorum collectorum, et speciei exilitas mihi obstite­<lb></lb>runt ut maculas nullas cernerem. </s>

<s>Quare curam inquirendi maculas depo­<lb></lb>sui. </s>

<s>Assumpsit autem eas quidam Fabricius Witembergae, libellumque su­<lb></lb>per hac re vulgavit, mense Junii anni 1611, quem sequtus est Augustanus <lb></lb>quidam anonymus, seu ficto nomine Apellis; quam ad famam ego ad Te­<lb></lb>lescopium redii, ususque utroque vitro, maculas tamdem et ipse detexi ” <lb></lb>(Epistolae, Lipsiae 1718, pag. </s>

<s>555). </s></p><p type="main">

<s>La naturale ingenuità di Giovanni Keplero e la serenità d&#039;animo, con <lb></lb>la quale scriveva queste parole, ci assicurano della veracità della Storia, <lb></lb>dalla quale apparisce essere stato esso Keplero il primo a pensare alle Mac­<lb></lb>chie del Sole, anche innanzi di averle vedute attraverso il Canocchiale, o in <lb></lb>quel modo ch&#039;ei suggeriva, come dicemmo, a Galileo. </s>

<s>Apparisce inoltre che <lb></lb>prima dello stesso Apelle ne aveva scritto con intendimento astronomico <lb></lb>Giovanni Fabricio, il quale, nella sua Narrazione <emph type="italics"></emph>De maculis in Sole obser­<lb></lb>vatis et apparente corum cum Sole conversione,<emph.end type="italics"></emph.end> incomincia a dire come, <lb></lb>all&#039;annunzio delle nuove scoperte celesti di Galileo, fosse mosso dalla cu­<lb></lb>riosità di vedere quel che di nuovo avesse a rivelarci la faccia del Sole. </s>

<s><lb></lb>Racconta come a principio riuscisse la cosa un po&#039;difficile, per la offesa <lb></lb>degli occhi, ma che poi la difficoltà fu vinta, approdando a principio la vista <lb></lb>nel lembo del disco solare, e poi introducendosi a poco a poco a guardare <lb></lb>nel mezzo. </s>

<s>Più tardi gli occorse al pensiero di osservar l&#039;immagine del Sole <lb></lb>proiettata sul diaframma di una camera oscura. </s>

<s>“ Cogitavimus igitur de ra­<lb></lb>diis Solis per angustum foramen intromittendis et in obscura clausis fene­<lb></lb>stris camera observandis. </s>

<s>Notum enim est Opticis, quae foris sunt et agun­<lb></lb>tur in tenebroso cubiculo possint repraesentari, aperto solum angusto quodam <lb></lb>foramine, per quod species rerum ipso foramini obiectarum illabantur, et <lb></lb>pingant parietem in cubiculo oppositum sed omnia inverso situ. </s>

<s>” </s></p><p type="main">

<s>Nè a sodisfar oziosamente la pura curiosità stette contento il Fabricio, <lb></lb>ma speculò altresì, benchè ne confessasse la difficoltà, e non sperasse di sa­<lb></lb>per nulla di certo, intorno alla natura delle Macchie osservate; e avendone <lb></lb>avvertito il loro moto, ne fece argomento a dimostrar quella vera conver­<lb></lb>sione del Sole intorno a sè stesso, <emph type="italics"></emph>quam Jordanus Bruno asseruit, et nu­<lb></lb>per admodum defendit in suis, quos de Martis motibus edidit, Commen­<lb></lb>tariis, Keplerus.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La Dissertazion kepleriana sul Nunzio Sidereo dunque e questa Narra-<pb xlink:href="020/01/941.jpg" pagenum="384"></pb>zion del Fabricio, ambedue pubblici documenti anteriori al Discorso delle <lb></lb>cose che stanno sull&#039;acqua, e alle Lettere velseriane, bastano a dimostrar <lb></lb>che Galileo non poteva pretendere il primato dell&#039;osservazione strumentale <lb></lb>delle Macchie dovuto al Keplero, nè il primato delle speculazioni intorno alla <lb></lb>natura e al moto delle stesse Macchie dovuto al Keplero medesimo e al Fa­<lb></lb>bricio. </s>

<s>E nonostante, lasciati in pace que&#039;due trionfanti competitori, non <lb></lb>muove guerra che contro il solo Apelle. </s>

<s>Son due ambiziosi conquistatori del <lb></lb>Regno della Scienza, e di una provincia che a loro men si compete si con­<lb></lb>tendono furiosamente il principato. </s>

<s>In ogni modo è lo Scheiner quello, che <lb></lb>ha la ragione, se si ha da lasciar le passioni e giudicare dai fatti, per il più <lb></lb>imparziale esame de&#039;quali convien tornare a svolgere le prolisse colonne <lb></lb>della <emph type="italics"></emph>Rosa Ursina.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>L&#039;Autore dà le prime testimonianze di sè così narrando come fosse <lb></lb>condotto all&#039;osservazione del singolar fenomeno, dietro le sue proprie espe­<lb></lb>rienze sulla camera oscura. </s>

<s>“ Cum ea tempestate species rerum visibilium <lb></lb>in loca tenebrosa immittendarum, iam diu tractatas, satisque perspectas in <lb></lb>manibus quotidie haberem, .... statim itaque ad Maculas a Sole captandas <lb></lb>idem artificium transtuli, sicque eumdem, per exile atque rotundum fora­<lb></lb>men intrare, atque arcana sua patefacere coegi, quae ego in mundissimam <lb></lb>chartam foramini, seu penicillo solis radioso orthogonos in longissima di­<lb></lb>stantia oppositam excepi, et quam potui fidelissime depinxi ” (Bracciani 1630, <lb></lb>pag. </s>

<s>10). </s></p><p type="main">

<s>Lo Scheiner dunque non manca di render pieno conto di sè innanzi al <lb></lb>tribunal della Storia. </s>

<s>Volete sapere a quale occasione gli occorresse di ri­<lb></lb>volgere il Canocchiale nella spera del Sole? </s>

<s>ed ei ve lo narra. </s>

<s>Volete sa­<lb></lb>pere come facesse a non ricevere offesa agli occhi? </s>

<s>ed ei vi risponde. </s>

<s>Vo­<lb></lb>lete sapere a qual proposito gli accadesse di osservare l&#039;immagine del Sole? </s>

<s><lb></lb>ed ei ve lo descrive e vi rammenta l&#039;esperienze preparatorie della camera <lb></lb>oscura. </s>

<s>Volete finalmente sapere in compendio tutta la storia di questo ne­<lb></lb>gozio? </s>

<s>ed ei così, con tutta l&#039;ingenuità, ve la racconta: </s></p><p type="main">

<s>“ Anno Domini millesimo sexcentesimo undecimo, cum in celeberrima <lb></lb>Universitate Ingolstadiana Scientias mathematicas publice profiterer, et ex <lb></lb>assidua diuturnaque investigatione praevia maculas in Sole, ope Telescopii, <lb></lb>primum mense Martio, Sole per nebulam inspecto cuius tunc magnitudinem <lb></lb>inquirebam, deinde mense Octobri iterum Telescopio per nebulam et sine <lb></lb>hac Helioscopii, quod ex vitris ad hunc finem coloratis convexis et cavis <lb></lb>ipsemet elaboraveram, beneficio, animadvertissem earumque tam inter se <lb></lb>quam ad Solem situm in dies, numerum, figurarum et magnitudinem quam <lb></lb>potui diligentissime observassem, idque tam immissione naturali per nudum <lb></lb>exile foramen quam directo intuitu per dictum Helioscopium, et factas obser­<lb></lb>vationes ex die in diem et ex horis pene in horas circulis observationis <lb></lb>comprehensas in chartas coniecissem, indeque observationum inter se com­<lb></lb>paratione facta apparentem macularum motum, multasque in figuris atque <lb></lb>magnitudinibus nec non sitibus mutationes quotidianas sensim accidere vi-<pb xlink:href="020/01/942.jpg" pagenum="385"></pb>dissem, alias exire alias de novo Solem subintrare, multas in medio cursu <lb></lb>deficere et vicissim novas ex ipso Sole exoriri; attonitus tanta rerum no­<lb></lb>vitate et vicissitudine patefeci ea primum discipulis meis ” (ibi, pag. </s>

<s>6). </s></p><p type="main">

<s>Poi prosegue a dire com&#039;ei ne desse qualche sentore al Velsero “ qui <lb></lb>continuis me literis fatigavit, donec a me phaenomeni inventi novitatem <lb></lb>extorsit, quo aliqnot epistolis accepto, statim animum ad illius editionem <lb></lb>adiecit, ne quid de gratiae novitatis, ut ipse aiebat, longa mora deperiret <lb></lb>aut proinde inventionis laurea aliunde decerperetur. </s>

<s>” Ma perchè poteva una <lb></lb>tale e tanta novità partorire nell&#039;animo de&#039;Filosofi qualche grave dissidio <lb></lb>“ censuerunt superiores mei procedendum caute et pedetentim, donec et <lb></lb>phaenomenon ipsa aliorum quoque experientia accedente corroboraretur, ne­<lb></lb>que a tritis Philosophorum semitis sine evidentia contraria facile receden­<lb></lb>dum, neque observata mea in Epistolis ad Velserum destinatis meo nomine <lb></lb>edendo..... Hisce cautelis factum est ut Epistolae, multo pauciores quam <lb></lb>ad Velserum exaravissem, in vulgis emanarent ut sub alieno Apellis no­<lb></lb>mine prodirent ” (ibi, pag. </s>

<s>7). </s></p><p type="main">

<s>La narrazione, esaminata in sè stessa e posta a riscontro con l&#039;Epistole <lb></lb>dello stesso Apelle, non ha nulla che dia qualche sospetto di menzogna, per <lb></lb>cui nessuno che abbia animo retto e imparziale giudizio non può non chia­<lb></lb>marsi, del conto che dà di sè lo Scheiner, sufficientemente sodisfatto. </s>

<s>Ma <lb></lb>qual conto rendesi alla Storia da Galileo? </s>

<s>Domandiamo a quale occasione <lb></lb>rivolgesse il Canocchiale in faccia al Sole e non sa dirlo. </s>

<s>Domandiamogli di <lb></lb>grazia come fece a vincere le difficoltà dell&#039;osservazione, o che fu che gli <lb></lb>suggerì il partito di guardare il Sole <emph type="italics"></emph>averso vultu?<emph.end type="italics"></emph.end> Noi lo abbiamo con­<lb></lb>getturato, ma nè da lui nè da&#039;suoi amici se ne ricava nulla di certo. </s>

<s>Si <lb></lb>prova, come vedemmo, a dire quando gli occorresse di far l&#039;ambita sco­<lb></lb>perta, e ora ne assegna un tempo ora ne assegna un altro, ingerendo così <lb></lb>il sospetto che sia quello un aggirarsi come di chi vuol dar colore di vero <lb></lb>alla menzogna. </s></p><p type="main">

<s>Da queste consi.lerazioni e da que&#039;fatti vien decisa fra lo Scheiner e <lb></lb>Galileo l&#039;antica celebre controversia, soggetto della quale era, come dicemmo, <lb></lb>il primato delle osservazioni del Sole. </s>

<s>Ma perchè in ogni modo il merito <lb></lb>della causa non consisteva qui, ma nel filosofare intorno all&#039;essere di ciò <lb></lb>che stranamente vedevasi apparire nella purissima faccia del Sole, è da av­<lb></lb>vertir meglio ad alcuni fatti particolari, dai quali verrà definita la giusta <lb></lb>parte di quel merito, che intorno a ciò competesi a Galileo. </s></p><p type="main">

<s>In quel tempo ch&#039;era per uscire alle stampe la prima edizione del Di­<lb></lb>scorso delle Galleggianti, in cui l&#039;Autore si mostrava così incerto dell&#039;es­<lb></lb>sere di quell&#039;ombre nell&#039;astro creato a dispensare al mondo la luce, il Ke­<lb></lb>plero che, come udimmo dianzi dir da sè stesso, commosso dalla fama della <lb></lb>Narrazion del Fabricio e delle Lettere di Apelle, era tornato al Telescopio, <lb></lb>fu il primo che osasse dir la sua opinione intorno all&#039;essere e alla natura <lb></lb>di quelle strane apparenze nella faccia del Sole. </s>

<s>Esprimeva così un anno <lb></lb>dopo questa sua opinione, in una Lettera del dì 10 Novembre 1612, a Simon <pb xlink:href="020/01/943.jpg" pagenum="386"></pb>Mario: “ Existimo esse analogon quippiam nubium terrestrium quod Solis <lb></lb>globus, suopte aestu coctus, excernat materiam forte cometarum qui fere a <lb></lb>Sole prodeunt ” (Epistolae, Lipsiae 1718, pag. </s>

<s>552). </s></p><p type="main">

<s>E dopo anche un altr&#039;anno, sempre più confermatosi in quella sua <lb></lb>prima opinione, la veniva così più particolarmente esplicando al Malcozio: <lb></lb>“ Scripsi sub finem anni 1611 quid de substantia macularum harum sen­<lb></lb>tirem, et parum quid mutem ex posterioribus observationibus invenio. </s>

<s>Ni­<lb></lb>mirum non sunt omnes eiusdem omnino celeritatis, nec viam Ecclipticae <lb></lb>parallelam incedunt. </s>

<s>Itaque non haerent in superficie corporis solaris, neque <lb></lb>tamen absunt ab ea visibili intervallo. </s>

<s>Ex his argumentis, et quia in ipsa <lb></lb>facie Solis oriuntur nonnullae, evanescunt aliac, densantur, rarefiunturque, <lb></lb>passim schematismos permutant sensibiliter, dum una alia celerior est; fa­<lb></lb>cile colligitur tale quid esse materiam horum macularum quale sunt in huius <lb></lb>terrestris Globi superficie nubes et nebulae, motum nonnullum obtinentes <lb></lb>in aere, qui nullis partibus a rapida gyratione Telluris superatur ” (ibi, <lb></lb>pag. </s>

<s>555). </s></p><p type="main">

<s>Ripensando poi all&#039;origine di queste fuliggini credeva che le potessero <lb></lb>essere esalate <emph type="italics"></emph>ex ignitissimo illo solaris corporis titione,<emph.end type="italics"></emph.end> e giacchè nel­<lb></lb>l&#039;Astronomia ottica aveva, alquanti anni prima, approvata l&#039;ipotesi di Dio­<lb></lb>gene Laerzio, <emph type="italics"></emph>Solem statuens esse candentem lapidem<emph.end type="italics"></emph.end> (Francof. </s>

<s>1604, <lb></lb>pag. </s>

<s>222), non era alieno dal professar quelle sozze fuliggini <emph type="italics"></emph>efflorescere, <lb></lb>ut in candenti ferro, quibus partibus ab umido aere aspiratur<emph.end type="italics"></emph.end> (Epist. </s>

<s>cit., <lb></lb>pag. </s>

<s>558). </s></p><p type="main">

<s>Queste Kepleriane opinioni intorno all&#039;essere e all&#039;origine delle mac­<lb></lb>chie solari, divulgatesi in Italia, approdarono alle orecchie di Galileo, in quel <lb></lb>medesimo tempo che il Cigoli gli riferiva da Roma le osservazioni sue pro­<lb></lb>prie, e il Passignano gli significava il suo pensiero intorno alla natura di <lb></lb>esse Macchie, dicendo che ell&#039;erano voragini aperte nella sostanza del Sole, <lb></lb>e che e&#039;le vedeva, secondo l&#039;espression del Cigoli, “ più apparenti e più <lb></lb>nere ne&#039;lembi che se siano nella superficie di verso noi, e poi girando ora <lb></lb>verso il mezzo ora verso la circonferenza per linee spirali, s&#039;immergono nel <lb></lb>corpo luminoso ” (Alb. </s>

<s>VIII, 170). </s></p><p type="main">

<s>Tutte queste opinioni e quel che lo stesso Cigoli gli riferiva de&#039;suoi <lb></lb>proprii pensieri, così espressi: “ non credo siano un cumulo di stelle se <lb></lb>però fra di loro facendo un cerchio non lasciassero uno spazio di spiracolo <lb></lb>di foro nel corpo solare, ma mi dà noia quell&#039;esser sempre la parte più ca­<lb></lb>rica di scuro verso il centro del corpo solare ” (MSS. Gal., P. III, T. X, <lb></lb>c. </s>

<s>61); persuasero intanto Galileo non poter esser, com&#039;aveva prima cre­<lb></lb>duto, le macchie solari ombre di stelle circondanti il Sole, ciò che si af­<lb></lb>frettò dl pronunziare in pubblico nella seconda edizione delle Galleggianti. </s></p><p type="main">

<s>Venuto poi a pubblicar le Lettere velseriane, e dovendo dir ciò ch&#039;ei <lb></lb>pensava dell&#039;essere e dell&#039;origine delle macchie solari, preferì all&#039;ipotesi del <lb></lb>Passignano quella del Keplero, ch&#039;ei ripetè in tutti i particolari, non eccet­<lb></lb>tuato l&#039;esempio del fumo esalato, o delle macchie rimaste sopra il ferro ro-<pb xlink:href="020/01/944.jpg" pagenum="387"></pb>vente. </s>

<s>Di qui è che lo stesso Keplero, il quale ricevè il di 18 Luglio 1613 <lb></lb>le Lettere velseriane (Epist. </s>

<s>cit., pag. </s>

<s>555), chiama quelle un <emph type="italics"></emph>accurata di­<lb></lb>scussio,<emph.end type="italics"></emph.end> e poi scrivendo al Maestlin gli diceva come, discutendo l&#039;Autor del <lb></lb>libro italiano intorno alle macchie, <emph type="italics"></emph>omne tulerit punctum<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>45). </s></p><p type="main">

<s>Il Passignani invece s&#039;ebbe molto per male in veder che Galileo non <lb></lb>si fosse degnato, nemmen privatamente, di rispondere alla sua del 17 Feb­<lb></lb>braio da noi riferita di sopra, e che scrivendo per il pubblico la Prima sua <lb></lb>velseriana, non si fosse curato di nominarlo, professando in parte altra opinion <lb></lb>dalla sua. </s>

<s>Veniva ciò significato allo stesso Galileo dal Cigoli, che così gli scri­<lb></lb>veva da Roma: “ Il signor Domenico Passignani è in valigia, sì perchè la <lb></lb>non gli ha dato risposta alla sua, come anco della diversità della sua riso­<lb></lb>luzione delle Macchie del Sole, attesochè egli è uomo molto amico di sua <lb></lb>opinione ” (MSS. Gal., P. VI, T. VIII, c. </s>

<s>128). </s></p><p type="main">

<s>Nel Pittore filosofo aveva dunque Galileo ritrovato inaspettatamente un <lb></lb>competitore, e conveniva perciò, al modo che tutti gli altri competitori nella <lb></lb>scoperta, trattarlo col solito disprezzo. </s>

<s>“ Il Passignano, gli scriveva lo <lb></lb>stesso Cigoli, fa gran cose e gran rumori e millantamenti, appropriandosi <lb></lb>del guardare e dell&#039;avere scoperto nel Sole le Macchie e le osservazioni, ed <lb></lb>inoltre mi disse iersera che ha gran cose per le mani e cor una sua inven­<lb></lb>zione, qual non mi volse dire, neanco al sig. </s>

<s>Luca (Valerio), che saperrà <lb></lb>dire cose minutissime, e che Giove lo vede montuoso ” (MSS. Gal., P. I, <lb></lb>T. VII, c. </s>

<s>12). </s></p><p type="main">

<s>Il Cigoli, com&#039;anche trasparisce da queste parole, secondava in disprez­<lb></lb>zar l&#039;amico suo e collega, il Galileo, a cui scriveva di averne sentite dire <lb></lb>al Passignano <emph type="italics"></emph>alle volte di quelle che mi fa ridere solennemente<emph.end type="italics"></emph.end> (MSS. <lb></lb>Gal., P. VI, T. VIII, c. </s>

<s>128), e ch&#039;egli non faceva altro che <emph type="italics"></emph>lucidare e ri­<lb></lb>dicolmente storpiare<emph.end type="italics"></emph.end> cose sentite già dire a Luca Valerio, e al padre Griem­<lb></lb>bergero (ivi, c. </s>

<s>117). </s></p><p type="main">

<s>Ma pure era il Cigoli stesso, il quale in altra lettera a Galileo aveva <lb></lb>fatto notar la differenza grande, che passa fra l&#039;opinion del Griemberger a <lb></lb>cui parve d&#039;acconsentir che le macchie sien ombre di stelle, e l&#039;opinion del <lb></lb>Passignano, che attribuiva le stesse macchie a voragini aperte nella corpu­<lb></lb>lenza del Sole; era il Cigoli stesso che dall&#039;apparirgli sempre <emph type="italics"></emph>la parte om­<lb></lb>brosa verso il centro del corpo solare<emph.end type="italics"></emph.end> (MSS. Gal., P. III, T. X, c. </s>

<s>61) pi­<lb></lb>gliava risoluzione di creder meno ai discorsi del Gesuita tedesco, che non <lb></lb>a quelli del Pittore toscano; era il Cigoli stesso, il quale aveva avuto prove <lb></lb>non dubbie che il Canocchiale usato dal Passignani era molto più eccellente <lb></lb>di quello che aveva Galileo per le sue osservazioni celesti. </s>

<s>Vedremo di que­<lb></lb>sta superiorità fra poco una prova di fatto, ma non sarà piccola prova in­<lb></lb>tanto il dire che i resultati delle osservazioni, a null&#039;altro fanno meglio rasso­<lb></lb>migliar lo strumento e la veggenza del nostro Passignani, che allo strumento <lb></lb>e alla veggenza dell&#039;Herschel stesso. </s>

<s>A persuadersi di che basta percorrer <lb></lb>d&#039;un volo la storia delle ipotesi varie intorno alle Macchie solari, fondate <lb></lb>sulle più o meno esatte osservazioni. </s></p><pb xlink:href="020/01/945.jpg" pagenum="388"></pb><p type="main">

<s>Le prime supposizioni kepleriane delle nuvole o de&#039;fumi fuligginosi esa­<lb></lb>lati dal tizzone infocato del Sole; supposizioni approvate da Galileo, non eb­<lb></lb>bero grande accoglienza in Germania, dove il Moestlin, persuaso che il Sole <lb></lb>s&#039;assomigliasse, come la Luna, alla Terra, per avervi scorte alcune montuo­<lb></lb>sità, andava a queste montuosità e alle valli attribuendo l&#039;origine delle mac­<lb></lb>chie solari, ond&#039;è che così in proposito scriveva allo stesso Keplero: “ Mihi, <lb></lb>ut pace tua dicam, non quales in Terra sunt nubes, sed perpetua corpora <lb></lb>videntur.... Vidimus enim pariter magnas eminentias et notabiles hiatus, <lb></lb>quales in Terra sunt montes et valles. </s>

<s>Num ergo et Solis corpus rudis ve­<lb></lb>lut Terra globus est? </s>

<s>Certe Lunam Terrae esse simillimam, prout in Di­<lb></lb>sputatione probavi, hae novae observationes, non ad credendum invitant, sed <lb></lb>ut certo asseram, cogunt ” (Ad Keplerum Epist. </s>

<s>cit., pag. </s>

<s>41). Ma quando <lb></lb>poi il Keplero fece notare al suo Maestro che la permanenza era contrariata <lb></lb>dal vedersi così spesso più Macchie confondersi un una sola, e allora ebbe <lb></lb>a dire il Moestlin: “ De maculis in Sole magis magnisque turbor ” (ivi, <lb></lb>pag. </s>

<s>44). </s></p><p type="main">

<s>Quella ipotesi moestliniana rifiorì poi in Francia, nel secolo XVIII, dalla <lb></lb>fantasia del Fontenelle, il quale immaginò, per salvarle dalle opposizioni del <lb></lb>Keplero, che le montuosità del Sole uscissero fuori da un gran mare di <lb></lb>fuoco, da cui fossero lasciate ora più ora meno allo scoperto, per un tal <lb></lb>perpetuo avvicendarsi del suo flusso e riflusso. </s>

<s>Ma all&#039;Herschel Telescopii <lb></lb>assai più squisiti rivelarono esser piuttosto voragini che montuosità sul­<lb></lb>l&#039;ignita faccia del Sole: voragini che parve poi necessario ammettere, per <lb></lb>salvare alcune delle principali apparenze presentate dalle Macchie solari. </s>

<s><lb></lb>Ond&#039;è che, se può dubitarsi della verità della posizione Herscelliana, la quale <lb></lb>ammetteva una fotosfera involgente il nucleo opaco e solido del Sole; se <lb></lb>può dubitarsi della Wilsoniana, nella quale s&#039;aggiungeva un&#039;ammosfera ne­<lb></lb>bulosa interposta tra la fotosfera stessa e l&#039;opaco globo centrale; non par <lb></lb>che possa dubitarsi di quelle voragini vedute in Roma, più di un secolo <lb></lb>prima che in Londra, da&#039;due nostri Pittori toscani. </s></p><p type="main">

<s>Aveva dunque, concludendo il nostro discorso, giusta ragione il Passi­<lb></lb>gnani appropriandosi del guardare e dell&#039;avere scoperto nel Sole l&#039;origine <lb></lb>delle Macchie, ed ebbe il torto Galileo a disprezzar questa scoperta, che fu <lb></lb>prima a farlo accorto dell&#039;errore di Apelle, e a posporla alle ipotesi del <lb></lb>Keplero. </s>

<s>Cosi, non resta all&#039;Autore delle Lettere velseriane nemmeno il me­<lb></lb>rito della scelta, la quale sebben versasse, non tra il vero e il falso, ma tra <lb></lb>il più e il meno probabile, pareva che maggior probabilità porgessero le sen­<lb></lb>sate osservazioni del Pittor nostro da Passignano, che non le ardite fanta­<lb></lb>sie dell&#039;Astronomo alemanno. </s></p><pb xlink:href="020/01/946.jpg" pagenum="389"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La faccia del Sole, per la soverchia sua visibilità, rimasta invisibile per <lb></lb>lungo tempo ai Filosofi, non fu potuta con sicura pace guardare, per osser­<lb></lb>varne le Macchie, infintanto che gli artificii della Camera oscura non inse­<lb></lb>gnarono a dipingere con precisione l&#039;immagine radiosa, e i Canocchiali, dis­<lb></lb>sipando la luce e temperando attraverso ai vetri neri gli accecanti fulgori, <lb></lb>non dettero il modo di avvalorar tutt&#039;insieme la vista, e di difendere gli <lb></lb>occhi. </s>

<s>Non fu così della Luna, i segni bui della quale fecero, infin dalla più <lb></lb>remota antichità, favoleggiar di Caino e delle spine. </s>

<s>Che se non rimase a <lb></lb>quello spettacolo il volgo indifferente, non è a creder che non volesse fru­<lb></lb>gare la curiosità de&#039;Filosofi antichi, de&#039;quali, se alcuni dissero pazze cose, <lb></lb>altri indovinarono così il vero, da recare stupore ai moderni. </s></p><p type="main">

<s>Fra gli altri suoi Opuscoli Plutarco ne ha uno, che giusto s&#039;intitola <lb></lb><emph type="italics"></emph>Della faccia, che si vede nel cerchio della Luna,<emph.end type="italics"></emph.end> dove, a proposito delle <lb></lb>Macchie, entra a trattar delle principali questioni fisiche intorno a quella, <lb></lb>ch&#039;egli elegantemente chiama <emph type="italics"></emph>nostra nutrice e fedel custode e fattrice del <lb></lb>Giorno e della Notte<emph.end type="italics"></emph.end> (Opuscoli volgarizzati, Milano 1829, T. V, pag. </s>

<s>358). <lb></lb>Dal veder, prima di tutto, ch&#039;ell&#039;è la più bassa di tutte le stelle, a propor­<lb></lb>zion delle quali si dilunga così di poco dalle regioni della nostra Terra, il <lb></lb>Filosofo di Cheronea ne conclude che non è la Luna altrimenti cosa cele­<lb></lb>ste, ma terrena. </s>

<s>Nè per esser grave è da temer ch&#039;ella cada “ essendo aiu­<lb></lb>tata dal moto e dall&#039;impeto suo, nel modo che i sassi posti dentro la fionda ” <lb></lb>(ivi, pag. </s>

<s>325). </s></p><p type="main">

<s>Essendo dunque terrena, non è tersa e pulita come uno specchio, ma <lb></lb>distinta d&#039;inegualità e di asprezze, come di monti e di valli. </s>

<s>Lo prova di­<lb></lb>cendo che non potrebbe altrimenti mostrarsi tutta illuminata, essendo che <lb></lb>uno specchio non riflette la luce che da un punto solo, là dove le innume­<lb></lb>revoli asperità della superficie “ possono scambievolmente risplendere, ed <lb></lb>in ogni modo reflettersi, invilupparsi e continuar fra sè lo splendore, come <lb></lb>se a noi venisse da molti specchi ” (ivi, pag. </s>

<s>342). </s></p><p type="main">

<s>Da questo vero modo d&#039;illuminarsi conclude inoltre il Filosofo che la <lb></lb>Luna è un corpo solido, “ perchè le riflessioni non si fanno in alcuna cosa <lb></lb>rara e composta di parti tenui, nè è facil cosa l&#039;immaginarsi reverbero del <lb></lb>fuoco nel fuoco, o del lume nel lume, ma fa di mestieri che solida e densa <lb></lb>sia quella cosa, dalla quale un&#039;altra deve essere reverberata e reflessa ” <lb></lb>(ivi, pag. </s>

<s>343). </s></p><p type="main">

<s>Che poi veramente s&#039;illumini la Luna solida e aspra per riflessione, e <lb></lb>che non sia per sè luminosa, lo prova dal fatto delle ecclissi, le quali allora <lb></lb>succedono “ quando questi tre corpi, la Terra, il Sole e la Luna si diriz­<lb></lb>zano ad una retta linea, perchè la Terra priva la Luna del Sole, o all&#039;in-<pb xlink:href="020/01/947.jpg" pagenum="390"></pb>contro la Luna ne spoglia la Terra, essendo che s&#039;oscura il Sole, quando <lb></lb>vi si frammette la Luna, e questa s&#039;ecclissa, quando v&#039;è di mezzo la Terra: <lb></lb>l&#039;una di queste ecclissi segue per la congiunzione de&#039;due luminari, l&#039;altra <lb></lb>per l&#039;opposizione ” (ivi, pag. </s>

<s>347). Se dunque per queste ecclissi si mostra <lb></lb>che la Luna nell&#039;ombra perde il suo lume, e lo ricupera quando è uscita <lb></lb>dall&#039;ombra, segno certo è che non ha lume proprio, ma che lo riceve dal <lb></lb>Sole (ivi, pag. </s>

<s>349). </s></p><p type="main">

<s>Nè fa nulla in contrario il veder la stessa Luna nell&#039;ombra delle ec­<lb></lb>clissi rosseggiar d&#039;un colore simile a quel della bragia, “ il quale si può <lb></lb>dire essere lontanissimo dalla Luna, e chiamarsi piuttosto mistura di lume <lb></lb>che manchi, e che splenda fra l&#039;ombra, ed affermare che il proprio e na­<lb></lb>tivo sia il nero e il terrestre ” (ivi, pag. </s>

<s>351). Una tal mistura, secondo Plu­<lb></lb>tarco, vien dalle innumerevoli stelle che circondano il Sole e in difetto ne <lb></lb>suppliscono al lume. </s></p><p type="main">

<s>Premessa così questa vera teoria lunare, e venendo al soggetto proprio <lb></lb>delle macchie, il grande Astronomo di Cheronea dice che le variabili son <lb></lb>dovute all&#039;ombre, ora più ora meno lunghe proiettate da&#039;monti, secondo che <lb></lb>il Sole ora più ora men lontano gl&#039;irraggia. </s>

<s>“ Ma perchè le distanze dei <lb></lb>lumi allungano l&#039;ombre de&#039;corpi, considera dunque che il Sole s&#039;ollontana <lb></lb>dalla Luna per grandissimo spazio, quando ella è piena, ed esprime chia­<lb></lb>ramente l&#039;effigie della faccia con l&#039;altezza dell&#039;ombra, perchè la distanza <lb></lb>stessa del lume fa l&#039;ombra grande, e non la grandezza delle inegualità che <lb></lb>nella Luna si trovano ” (ivi, pag. </s>

<s>355). </s></p><p type="main">

<s>Quanto poi alle altre macchie più permanenti, confutata l&#039;opinion di <lb></lb>Clearco, che le attribuiva allo specchiarsi del grand&#039;Oceano terrestre nella <lb></lb>Luna, stima Plutarco che sien piuttosto dovute a grandi cavità piene d&#039;acqua <lb></lb>o d&#039;aria caliginosa. </s>

<s>“ Siccome la nostra Terra, egli dice, ha alcuni gran seni, <lb></lb>così stimiamo che la Luna sia aperta da vaste profondità e rotture piene <lb></lb>d&#039;acqua, o d&#039;aria caliginosa, nelle quali il Sole col suo lume non penetri, <lb></lb>ma lassandole, faccia la reflessione dissipata ” (ivi, pag. </s>

<s>353). </s></p><p type="main">

<s>Queste pitagoriche dottrine di Plutarco furono contradette a&#039;suoi giorni, <lb></lb>come furono per le medesime ragioni contradette ai giorni di Galileo, e per­<lb></lb>ciò, rimaste per un tempo dimenticate, e poi rifiutate, dovettero soggiacer <lb></lb>lungamente alla tirannia dell&#039;errore. </s>

<s>L&#039;Alighieri, con argomenti che hanno <lb></lb>per quel secolo del singolare, confuta l&#039;opinion di coloro, che dicevano nella <lb></lb>Luna il raro esser cagione di quel bruno (Paradiso, C. II, t. </s>

<s>25-35) e non <lb></lb>sodisfatto, a quel che pare, di nessuna fisica ragione, và sublimandosi a ri­<lb></lb>trovarla nella Metafisica e nella Teologia. </s></p><p type="main">

<s>Quando poi l&#039;umanismo letterario fece rivivere fra&#039;libri antichi anche <lb></lb>quelli di Plutarco, e gli diffuse, curandone con diligenza il testo o facen­<lb></lb>done eleganti versioni latine; mentre alcuni privilegiati ingegni vi sentirono <lb></lb>il gusto del vero, altri, col palato guasto da&#039;simposii peripatetici, ne prova­<lb></lb>ron fastidio. </s>

<s>Nel fatto particolare delle apparenze lunari noi possiam di ciò <lb></lb>addurre alcuni pochi esempii, che valgano per i tanti altri. </s></p><pb xlink:href="020/01/948.jpg" pagenum="391"></pb><p type="main">

<s>Al peripatetico nostro Cesalpino, ostinato in mantenere alla Luna la su­<lb></lb>perficie tersa, arrise, meglio della pitagorica, l&#039;opinion di Clearco. </s>

<s>Se non <lb></lb>che, invece d&#039;esser le macchie la rappresentanza scolpita de&#039;soli mari ter­<lb></lb>restri, diceva esser l&#039;immagine specchiata di essi insieme a dei continenti. <lb></lb></s>

<s>“ Aliam cogimur.... maculae Lunae rationem excogitare. </s>

<s>An refractio fue­<lb></lb>rit nostri visus ad Terram? </s>

<s>ut Luna sit speculum quoddam in quo tota Ter­<lb></lb>rae facies cum latitudine marium appareat? </s>

<s>ut alterum maculae crus occa­<lb></lb>sum spectans Terrae illam partem repraesentet, quam nostris temporibus <lb></lb>Hispani, vastum Oceani pelagum transmeantes, invenerunt: alterum vero <lb></lb>triangulum Africae formam ostendat. </s>

<s>Reliqua autem maculae agglomeratio <lb></lb>Asiam cum Europa et mari mediterraneo exprimat, non satis distinguente <lb></lb>visu ob multas eius maris angustias ” (Peripat. </s>

<s>Quaest., Venetiis 1571, <lb></lb>pag. </s>

<s>52). </s></p><p type="main">

<s>Quell&#039;altro filosofo poi, Girolamo Borro, che scrisse del flusso e riflusso <lb></lb>marino, ripudiata con ugual nausea e l&#039;opinion di Clearco e quella di Plu­<lb></lb>tarco, non sente venir buono odore che dalla peripatetica del denso e del <lb></lb>raro, confutata dall&#039;Alighieri. </s>

<s>“ La faccia della Luna, scrive il nostro Are­<lb></lb>tino, è meno densa che non è quella del Sole e delle altre stelle, però <lb></lb>manco riluce. </s>

<s>E nella stessa faccia della Luna sono alcune parti più rare, <lb></lb>le quali fanno la macchia che in essa si vede, la quale non è nè l&#039;ombra <lb></lb>de&#039;monti nè la riverberazione del mare, nè altra somigliante cosa, ma è sola <lb></lb>una parte meno densa, però meno rilucente ” (Lucca 1561, pag. </s>

<s>52). </s></p><p type="main">

<s>Que&#039;semi del vero, che conteneva l&#039;opuscolo di Plutarco, non furono <lb></lb>riconosciuti, perchè vi stavano dentro come nella polpa di un frutto colti­<lb></lb>vato fra&#039;lazzi sorbi dagli avi, e custodito nel chiuso di un vaso, che final­<lb></lb>mente aprendosi, venne a spander le sue fragranze, e a dar gusto de&#039;suoi <lb></lb>sapori incorrotti sulla scelta mensa imbandita ai più tardi nepoti. </s>

<s>Primo a <lb></lb>sedere a quella mensa era stato il Copernico, poi il Moestlin, che ne fece, <lb></lb>venutogli a sedere al fianco, gustar soavemente al Keplero. </s>

<s>Leggiam così <lb></lb>come questi si levasse ebro di una nuova dolcezza da quel filosofico convito: </s></p><p type="main">

<s>“ Elegantissimum est illud Plutarchi Opusculum et festivissimum, di­<lb></lb>gnumque quo se Philosophus, depositis aliquando studiis gravioribus, oblectet. </s>

<s><lb></lb>Quae adeo causa est ut non invitus cum ipso tandem authore in hanc sen­<lb></lb>tentiam concedam, cuius mihi quidem iam pridem et Moestlinus praeceptor <lb></lb>meus author fuit, dicamque Lunae tale esse corpus quale haec nostra Terra <lb></lb>est, ex aquae et continentibus unum globum efficiens. </s>

<s>Id quidem pertendit <lb></lb>Plutarchius: multis rationibus, et oratorie et argute, communit contra va­<lb></lb>rias obiectiones, ut merito mirari possit Peripateticus aliquis tam multa et <lb></lb>solida contra suae sectae placita disserri posse ” (Paralip. </s>

<s>ad Vitell., Fran­<lb></lb>cofurti 1604, pag. </s>

<s>248). E prosegue a dire essergli confermata questa opi­<lb></lb>nione dalle sinuosità della Luna bissetta, le quali non possono essere effetto <lb></lb>d&#039;altro, che di qualche montuosa disuguaglianza. </s>

<s>In una cosa però dissente <lb></lb>dal suo Plutarco, parendogli più consentaneo “ quae sunt in Luna partes luci­<lb></lb>dae maria credi, quae maculosae terras, continentes et insulas ” (ibi, pag. </s>

<s>251). </s></p><pb xlink:href="020/01/949.jpg" pagenum="392"></pb><p type="main">

<s>Tanto amore poi prese il Keplero a questa opinion di Plutarco, che ve­<lb></lb>dendolo per grande antichità guasto e corrotto, vi si pose attorno ad emen­<lb></lb>darlo, a supplirne alquante lacune, a tradurlo in latino, e poi più tardi a <lb></lb>illustrarlo con note. </s>

<s>Questo studio, ch&#039;egli intraprese per .sollevarsi <emph type="italics"></emph>deposi­<lb></lb>tis aliquando studiis gravioribus,<emph.end type="italics"></emph.end> fu pubblicato postumo, insiem col <emph type="italics"></emph>Sogno <lb></lb>astronomico,<emph.end type="italics"></emph.end> dal figliolo di lui Lodovico in Francfort, nel 1634. </s></p><p type="main">

<s>Ma intanto anche tutti quegli altri dell&#039;antico Plutarco, che parevano <lb></lb>a molti astronomici sogni, Galileo venne ad annunziare al mondo che si <lb></lb>erano pienamente avverati. </s>

<s>Guardando col Canocchiale quella linea sinuosa, <lb></lb>che divide in due parti la Luna, la vide molto più frastagliata di quel che <lb></lb>non apparisse naturalmente al Keplero, per cui veniva così quasi di fatto con­<lb></lb>fermata la congettura, anzi l&#039;argomento dell&#039;Astronomo alemanno. </s>

<s>“ Quarta <lb></lb>aut quinta post coniunctionem die, cum splendida Luna sese nobis corni­<lb></lb>bus offert, iam terminus partem obscuram a luminosa dividens, non aequa­<lb></lb>liter secundum ovalem lineam extenditur, veluti in solido perfecte sphaerico <lb></lb>accideret, sed inaequali aspera et admodum sinuosa linea designatur ” <lb></lb>(Alb III, 63). D&#039;onde l&#039;Autor del Nunzio Sidereo ne conclude: “ Lunae <lb></lb>superficiem non perpolitam, aequabilem, exactissimaeque sphaericitatis exi­<lb></lb>stere, ut magna Philosophorum cohors de ipsa deque reliquis corporibus <lb></lb>coelestibus opinata est, sed contra inaequalem, asperam, cavitatibus tumo­<lb></lb>ribusque confertam, non secus ac ipsamet Telluris facies, quae montium iu­<lb></lb>gis, valliumque profunditatibus hinc inde distinguitur ” (ibi). </s></p><p type="main">

<s>Chi può immaginare la compiacenza, che dovette provare questo no­<lb></lb>stro primo Messaggero celeste? </s>

<s>Se il Keplero sentì venirsi tanto diletto dalla <lb></lb>lettura degli Opuscoli di Plutarco, che doveva esser l&#039;animo di Galileo, il <lb></lb>quale veniva ad annunziar come le congetture eran confermate dal vero? </s>

<s><lb></lb>Or chi, tutt&#039;al contrario, crederebbe mai, che fra le cupe gelosie del regno <lb></lb>dovesse l&#039;ombra del sospetto cadere anche su quel buono e amabile vec­<lb></lb>chio di Cheronea? </s>

<s>Colui che voleva in tutto essere il primo e il solo, avrebbe <lb></lb>dato chi sa che, se avesse potuto cancellar dalle menti la memoria di Plu­<lb></lb>tarco. </s>

<s>Il Copernico lo commemora nella prefazione al suo libro; gli fa cosi <lb></lb>lieta e lunga accoglienza, nell&#039;Astronomia ottica, il Keplero, ma Galileo, ch&#039;è <lb></lb>solo maestro a sè stesso e al mondo, fa vista di non lo conoscere nemmeno <lb></lb>per nome. </s>

<s>Eppure si sa che da giovane s&#039;esercitò anch&#039;egli a tradurre gli <lb></lb>Opuscoli del Filosofo greco (MSS. Gal., Nelli filza VI, c. </s>

<s>52), e di lì apprese <lb></lb>i primi pitagorici principii d&#039;astronomia lunare. </s></p><p type="main">

<s>Abbiamo una prova di ciò dalla sicurezza, con la quale seppe Galileo <lb></lb>evitare una fallacia, nella quale era incorso il Keplero. </s>

<s>Vedemmo come a <lb></lb>questi paresse più conveniente ammettere che le parti più luminose nel cer­<lb></lb>chio della Luna fossero mari, ma Galileo non si dilungò da Plutarco, l&#039;opi­<lb></lb>nion del quale, anzi la vera sentenza, scrisse così in alcune note di propria <lb></lb>mano, verso il 1604, quando forse dal latino traduceva gli Opuscoli greci, <lb></lb>e leggeva Seneca, da&#039;quali Autori senti venirsi i più forti impulsi all&#039;aperta <lb></lb>professione copernicana. </s>

<s>“ Consideretur duplicem esse reflexionem: unam a <pb xlink:href="020/01/950.jpg" pagenum="393"></pb>tota superficie rudi, alteram a parte superficiei perpolitae sphaerice. </s>

<s>A Luna <lb></lb>fit, non tamquam a Speculo, quia ab exigua eius parte fieret, cum sit con­<lb></lb>vexa et esset longe validior ” (MSS. Gal., P. IV, T. IV, c. </s>

<s>15). Questo pen­<lb></lb>siero fu poi largamente svolto nella I Giornata dei <emph type="italics"></emph>Massimi Sistemi,<emph.end type="italics"></emph.end> dove, <lb></lb>chi volesse farne il confronto, troverebbe il più splendido commento all&#039;Opu­<lb></lb>scolo di Plutarco. </s></p><p type="main">

<s>Intanto manifestava nel Nunzio Sidereo quella sua sicurtà di pensiero, <lb></lb>asserendo coll&#039;Autor antico che se son nella Luna veramente laghi o mari, <lb></lb>questi dovrebbero apparire più oscuri dei continenti, com&#039;apparirebbero <lb></lb>senza dubbio a chi guardasse di molt&#039;alto la nostra Terra: “ Mihi autem, <lb></lb>dubium fuit nunquam terrestris globi, a longe conspecti atque a radiis so­<lb></lb>laribus perfusi, terream superficiem clariorem, obscuriorem vero aqueam <lb></lb>sese in conspectum daturam ” (Alb. </s>

<s>III, 65). </s></p><p type="main">

<s>Nella Dissertazione sul Nunzio Sidereo confessò il Keplero che Galileo <lb></lb>l&#039;avea convinto del suo primo errore e confermatolo nella vera sentenza di <lb></lb>Plutarco, ma poi, nella nota 154 al <emph type="italics"></emph>Sogno Astronomico,<emph.end type="italics"></emph.end> soggiunse più par­<lb></lb>ticolarmente le ragioni di ciò suggeritegli dal ragionamento suo proprio e <lb></lb>dalla esperienza. </s>

<s>“ Hunc paragraphum allegavi in Dissertatione cum Nuncio <lb></lb>Galilaei Sidereo, quam edidi Pragae anno 1610, simulque et censuram ad­<lb></lb>didi necessariam. </s>

<s>Docuit me Galilaeus edita Lunae et aspera non maculas <lb></lb>esse sed claritatem, fusa vero in depressas partes aequora nigricare, macu­<lb></lb>larumque speciem induere..... Quod prius in contrariam iveram senten­<lb></lb>tiam causa haec fuit, quia terrae superficies varios induit colores, aquae co­<lb></lb>lore vacare censebantur ” (pag. </s>

<s>62). L&#039;esperienza che lo persuase l&#039;acqua <lb></lb>invece aver color fosco, gli occorse di farla così, com&#039;egli stesso racconta, <lb></lb>in Praga, guardando di sul Ponte, insiem con un amico oppositore di Ga­<lb></lb>lileo, gli edifizi specchiati nell&#039;acque della Moldava: “ Cum Pragae me <lb></lb>prope staret Literatus quisquam in Ponte, splendorem mihi aquarum in­<lb></lb>culcans, ut Galilaei assertionem convelleret, iussi ut imagines domorum in <lb></lb>undis respiceret, easque cum recto aspectu domuum ipsarum compararet: <lb></lb>manifestum enim claritatis discrimen est, et imagines in undis obscuriores ” <lb></lb>(ibi, pag. </s>

<s>63). </s></p><p type="main">

<s>Tornando ora alle asperità montuose riscontrate da Galileo nella Luna, <lb></lb>è da creder che i Peripatetici, i quali avevano derisi i sogni di Plutarco, ne <lb></lb>giudicassero altresi impossibili gli avveramenti. </s>

<s>I Gesuiti del Collegio ro­<lb></lb>mano al card. </s>

<s>Bellarmino, che domandava s&#039;era vero che la Luna fosse di <lb></lb>superficie aspra ed ineguale (Alb. </s>

<s>VIII, 160), rispondevano negando, man­<lb></lb>tenendosi fedeli all&#039;antica opinione peripatetica del denso e del raro (ivi, <lb></lb>pag. </s>

<s>161). </s></p><p type="main">

<s>I Gesuiti però di un altro Collegio negavano esser aspra e montuosa <lb></lb>la Luna, perchè guardandola col Canocchiale non si vedevano uscir fuori <lb></lb>prominenze dal giro luminoso intorno intorno. </s>

<s>“ Che poi veramente non vi <lb></lb>sieno monti in quel giro, scriveva il padre Biancani, lo dimostra l&#039;osser­<lb></lb>vazione, massime quando la Luna è sì vicina al plenilunio, che pare tonda, <pb xlink:href="020/01/951.jpg" pagenum="394"></pb>perchè allora non si vedono adombrazioni verune, se non poche nella parte <lb></lb>però opposta al Sole, le quali poi poco dopo spariscono, e resta in giro della <lb></lb>Luna tutto lucido senza alcuna ombra o segno d&#039;inegualità ” (Alb. </s>

<s>III, 147). </s></p><p type="main">

<s>La difficoltà era stata già presentita dallo stesso Galileo, che nel Nun­<lb></lb>zio Sidereo così soggiungeva, dop&#039;aver descritte le varie apparenze de&#039;monti <lb></lb>lunari: “ Verum magna hic dubitatione complures affici sentio, adeoque <lb></lb>gravi difficultate occupari ut iam explicatam, et tot apparentiis confirmatam <lb></lb>conclusionem in dubium revocare cogentur. </s>

<s>Si enim pars illa lunaris su­<lb></lb>perficiei, quae splendidius solares radios retorquet, anfractibus, tumoribus <lb></lb>scilicet et lacunis innumeris est repleta; cur in crescenti Luna extrema cir­<lb></lb>cumferentia, quae occasum versus spectat, in decrescenti vero altera circum­<lb></lb>ferentia orientalis, se ac in plenilunio tota peripheria non inaequalis, aspera <lb></lb>et sinuosa, verum exacte rotunda et circinata, nullisque tumoribus aut ca­<lb></lb>vitatibus corrosa conspicitur? </s>

<s>” (ibi, pag. </s>

<s>67). </s></p><p type="main">

<s>Galileo si studiò di risolvere il dubbio, riducendo il fatto a un caso di <lb></lb>prospettiva, e ad una illusione ottica occasionata dalle riflessioni de&#039;raggi <lb></lb>solari dentro l&#039;orbe vaporoso, di che supponeva esser circondato il globo <lb></lb>della Luna, ma non indovinò che tutto dipendeva dal Canocchiale inabile, <lb></lb>per il così piccolo ingrandimento, a tor via l&#039;irradiazione. </s>

<s>Il Passignani in­<lb></lb>fatti, con Strumento assai più perfetto, fu il primo ad osservare alcuni ri­<lb></lb>lievi in figura di merletti nell&#039;orlo della Luna piena, e a fargli vedere in <lb></lb>Roma agli amici, fra&#039;quali il Cigoli, che ne scrisse così a Galileo, pungen­<lb></lb>dolo di gelosia con dargli prove di fatto che venivan di fuori, a chi ne avesse <lb></lb>voluti, Canocchiali più eccellenti de&#039;suoi. </s>

<s>“ Vidi bene con il suo Canoc­<lb></lb>chiale (del Passignani) nel dintorno della Luna due merlature assai evidenti, <lb></lb>e questo fu l&#039;altra notte (sulla fin del Gennaio 1612) quando ell&#039;era quasi <lb></lb>piena. </s>

<s>Imperò me ne ha fatto venir voglia d&#039;uno, e ci è qui uno che ne <lb></lb>fa venire, e gli ho dato ordine, ed i padri Gesuiti me lo scerranno ” (MSS. <lb></lb>Gal., P. I, T. VII, c. </s>

<s>12). </s></p><p type="main">

<s>Quasi un anno dopo, anche il Keplero scriveva così a Simon Mario: <lb></lb>“ Vidi duos colliculos in interiori speciei solaris circulo, quem formabat <lb></lb>Luna corpore. </s>

<s>Sunt igitur, etiam in circumferentia Lunae, montes quibus <lb></lb>aegre carere se Galilaeus haud obscure significaverat ” (Epist. </s>

<s>cit., pag. </s>

<s>552). </s></p><p type="main">

<s>Ma il Canocchiale del Passignani e quel del Keplero non tosavano così <lb></lb>il cerchio alla Luna, che non apparissero quelle prominenze vedute in giro <lb></lb>in giro alquanto imbambagiate. </s>

<s>Primo a mostrarle così ben terminate e di­<lb></lb>stinte, da poterle riportare in disegno, fu un Canocchial del Campani, col <lb></lb>quale, afferma esso Campani, nel suo <emph type="italics"></emph>Ragguaglio di due nuove osserva­<lb></lb>zioni,<emph.end type="italics"></emph.end> che il Cassini vide la circonferenza lunare “ scabrosa e anfrattuosa <lb></lb>nella forma che, mirato da luogo eminente, apparisce il nostro orizzonte ter­<lb></lb>minato da monti spessi e lontani ” (Roma 1664, pag. </s>

<s>40). </s></p><p type="main">

<s>Un&#039;altra difficoltà, prima che fosse divulgata questa nuova osservazione <lb></lb>del Cassini, si promoveva contro l&#039;esistenza dei monti della Luna, dietro i <lb></lb>calcoli galileiani, dai quali risultando essere quegli stessi monti quasi cento <pb xlink:href="020/01/952.jpg" pagenum="395"></pb>volte più grandi dei terrestri, non parevano aver possibile proporzione a un <lb></lb>corpo così esile. </s>

<s>“ Tantum pondus, scriveva il Vossio nel Trattato <emph type="italics"></emph>De lucis <lb></lb>natura,<emph.end type="italics"></emph.end> in tam exili corpore, si Telluris vastitatem respiciamus, cum nul­<lb></lb>lam prorsus rationem habere videatur, non immerito multos promovit ut <lb></lb>dubitarent de hoc phaenomeno ” (Amstelodami 1662, pag. </s>

<s>46). </s></p><p type="main">

<s>Lo stesso Vossio fu che risolse una siffatta difficoltà, dimostrando che <lb></lb>le misure prese da Galileo venivano esagerate dalle refrazioni, dagli effetti <lb></lb>delle quali liberando quelle stesse misure, credè di averle avute così giuste <lb></lb>e così bene proporzionate, da doverne concludere: “ Quanta igitur differen­<lb></lb>tia est totius Telluris ad totam Lunam, tanta quoque est differentia inter <lb></lb>montes terrestres et lunares ” (ibi, pag. </s>

<s>48). </s></p><p type="main">

<s>Lasciando addietro quel che di meno approvato è nelle persuasioni del <lb></lb>Vossio, non può Galileo, che ammetteva allora l&#039;esistenza di un&#039;ammosfera <lb></lb>densa intorno alla Luna, andare in tutto scusato dalla censura dell&#039;Ottico <lb></lb>olandese. </s>

<s>L&#039;esistenza di quella ammosfera era stata dimostrata dal Moestlin <lb></lb>nella Disputazione <emph type="italics"></emph>De passionibus Planetarum,<emph.end type="italics"></emph.end> edita in Tubinga nel 1605, <lb></lb>sul principale argomento delle rifrazioni subite dalle Stelle presso a toccare <lb></lb>il lembo del disco lunare, e attribuiva pure a un effetto di rifrazione attra­<lb></lb>verso a una tale sfera vaporosa, il vedersi la Luna nuova chiusa in un cer­<lb></lb>chio notabilmente minore della circonferenza della sua splendida falce. </s>

<s>Que­<lb></lb>ste medesime dottrine, apprese dal Moestlin, le professava Galileo nel Nunzio <lb></lb>Sidereo, dove dice che dell&#039;essere veramente il globo lunare circondato da <lb></lb>vapori, “ signum est quod pars Lunae lumine perfusa amplioris circumfe­<lb></lb>rentiae apparet quam reliquum orbis tenebrosi ” (Alb. </s>

<s>III, 69). </s></p><p type="main">

<s>Il Keplero però, in questa parte men ossequioso al proprio maestro di <lb></lb>quel che non si fosse mostrato Galileo, accennando, nell&#039;Astronomia ottica, <lb></lb>al fatto che “ in prima vel ultima phasi Lunae cornu lucidum longe am­<lb></lb>pliori circulo claudi videtur quam reliquum corpus lumine Telluris illustra­<lb></lb>tum et clarissime conspicuum ” (edit. </s>

<s>cit., pag. </s>

<s>217) aveva detto che questo <lb></lb>e simili altri fenomeni “ ex retina tunica trahunt originem “ perchè in essa <lb></lb>non solamente si ampliano, ma quasi si moltiplicano le specie del rilucente <lb></lb>“ et id videtur esse vel propter rugas uveae, quae noctu, cum Lunam in­<lb></lb>tuemur, dilatatur et in se, inque rugas suas coit, vel propter hiatus cilia­<lb></lb>rium processuum ” (ibi, pag. </s>

<s>217). </s></p><p type="main">

<s>Vedendo poi come Galileo, invece che all&#039;irradiazione avventizia pro­<lb></lb>dotta sulla retina, avesse col Moestlin attribuito il fenomeno alle rifrazioni <lb></lb>nell&#039;orbe vaporoso della Luna, lo stesso Keplero, nella Dissertazione sul <lb></lb>Nuncio Sidereo, così conferma contro ambedue la verità della sua prima <lb></lb>sentenza: “ Verum pace vestra mihi liceat ego, etsi aerem Lunae concedo, <lb></lb>tamen super hoc experimento maneo in sententia: lumen hinc Lunae inde <lb></lb>Stellae de die etiam se se in oculo ampliare, locumque partis tenebrosae <lb></lb>carpere, et ea minuita lucida magna putatur ” (Alb. </s>

<s>V, 423). </s></p><p type="main">

<s>Rimasto a queste ragioni persuaso Galileo, ripudiò l&#039;opinion moestli­<lb></lb>niana professata nel <emph type="italics"></emph>Nuncio,<emph.end type="italics"></emph.end> per rivolgersi a questa kepleriana, intorno alla <pb xlink:href="020/01/953.jpg" pagenum="396"></pb>quale e a&#039;generali effetti delle irradiazioni ascitizie, filosofando al Griember­<lb></lb>ger, così gli scriveva nel 1611 il dì primo di Settembre: “ Ora applicando <lb></lb>queste considerazioni al nostro proposito, dico che la Luna illuminata dal <lb></lb>Sole s&#039;irraggia ed incapella di fulgori ella ancora, ma non tanto quanto <lb></lb>Venere, per esser più di quella remota dal Sole, e perchè la sua capella­<lb></lb>tura non solamente è più corta di quella di Venere, ma è aggiunta ed at­<lb></lb>taccata intorno a un grandissimo globo, che tale, per la sua vicinanza, ci si <lb></lb>rappresenta il Corpo lunare, e quindi è che la figura di essa Luna, non <lb></lb>solo tra la sua irradiazione non si smarrisce, ma pochissimo e quasi insen­<lb></lb>sibilmente si altera, e solamente si vede che la circonferenza della parte <lb></lb>illuminata alquanto si eleva sopra la circonferenza della parte oscura, sicchè <lb></lb>questa pare termine di un cerchio minore e quella di uno alquanto mag­<lb></lb>giore, e questo apparente ricrescimento della parte lucida sopra la oscura <lb></lb>non è altro che la irradiazione ascitizia ” (Alb. </s>

<s>III, 167). </s></p><p type="main">

<s>Ne&#039;<emph type="italics"></emph>Dialoghi<emph.end type="italics"></emph.end> però, dove Galileo torna a svolgere ampiamente il sog­<lb></lb>getto della Luna, non tocca di questo fenomeno, forse per non aver solen­<lb></lb>nemente a ritrattare ciò che prima aveva detto nel <emph type="italics"></emph>Nunzio,<emph.end type="italics"></emph.end> ond&#039;è che il <lb></lb>Castelli, il quale era allora tutto intorno a meditar su que&#039;Dialoghi. </s>

<s>“ Mi <lb></lb>pare d&#039;avere osservato (scriveva allo stesso Autore, quasi per supplire al <lb></lb>difetto) che la Luna intorno alle congiunzioni si mostri assai maggiore di <lb></lb>diametro, considerata la grandezza del suo disco in riguardo alla parte illu­<lb></lb>minata.... e questo eccesso mi pare tanto grande, che senza scrupolo si <lb></lb>può affermare che ancora la Luna illustrata dal Sole mostra la irradiazione <lb></lb>avventizia non meno degli altri pianeti ” (Alb. </s>

<s>IX, 273). </s></p><p type="main">

<s>Nel <emph type="italics"></emph>Discorso<emph.end type="italics"></emph.end> poi <emph type="italics"></emph>sopra la vista,<emph.end type="italics"></emph.end> riscontrandosi colle medesime dottrine <lb></lb>insegnate già dal Keplero, il Castelli ripete ch&#039;entrando i raggi della luce <lb></lb>nell&#039;occhio “ non solo conturbano la tunica retina, ma le parti della me­<lb></lb>desima retina a loro contigue, adiacenti e circonfuse, e così ci fanno appa­<lb></lb>rire l&#039;oggetto maggiore di quello che apparire dovrebbe ” (Bologna 1669, <lb></lb>pag. </s>

<s>18). Dietro questo principio spiega, insiem con parecchi altri fenomeni <lb></lb>curiosi e dipendenti dall&#039;irradiazione, in che modo la Luna “ ci apparisce <lb></lb>terminata da una circonferenza di cerchio maggiore notabilmente che quella <lb></lb>rimanente che non è ancora tocca dai raggi del Sole, la qual rimanente <lb></lb>mostra di esser terminata da circonferenza di cerchio notabilmente minore <lb></lb>della circonferenza delle corna risplendenti ” (ivi, pag. </s>

<s>18). </s></p><p type="main">

<s>Fra le apparenze lunari descritte nel Nunzio Sidereo, oltre a quelle <lb></lb>delle quali s&#039;è detto, n&#039;è una, che fece più lungamente dell&#039;altre dubitare <lb></lb>i Saggi, e che concerne quella luce di color cinereo, della quale, presso alle <lb></lb>congiunzioni, si vede essere leggermente aspersa la faccia tenebrosa della <lb></lb>luna. </s>

<s>Di quel dubbio converrebbe ora narrar la storia, ma perchè, per una <lb></lb>certa sua particolare importanza, siam consigliati di trasferire la narrazione <lb></lb>al paragrafo seguente, termineremo questo dicendo in qual vario modo ri­<lb></lb>spondessero gli Astronomi al quesito dell&#039;apparente maggior grandezza della <lb></lb>Luna all&#039;orizzonte. </s></p><pb xlink:href="020/01/954.jpg" pagenum="397"></pb><p type="main">

<s>Vedemmo altrove ciò che ne pensasse in tal proposito il Fracastoro, e <lb></lb>in modo simile a quel di luì, Galileo. </s>

<s>Il Cartesio diceva ch&#039;essendo per la <lb></lb>più gran mole de&#039;vapori interposti, la Luna e il Sole e gli astri all&#039;oriz­<lb></lb>zonte di raggio men vivi, son ricevute le loro immagini dentro a maggior <lb></lb>ampiezza di pupilla, e perciò mostran più grandi. </s>

<s>Questa si fu pure l&#039;opi­<lb></lb>nion del Gassendo, il quale, nella celebre lettera delle ombre, così scriveva <lb></lb>a Gabriele Naudeo: “ Heinc dici posse videtur primo Solem humilem oculo <lb></lb>spectatum ideo apparere maiorem, quam dum altius egreditur, quia, dum <lb></lb>vicinus est horizonti, prolixa est series vaporum, atque adeo corpusculorum <lb></lb>quae Solis radios ita retundunt, ut oculus minus conniveat, et pupilla quasi <lb></lb>umbrefacta longe magis amplificatur quam dum Sole multum elato rari va­<lb></lb>pores intercipiuntur, Solque ipse ita splendescit ut pupilla in ipsum spectans <lb></lb>contractissima efficiatur. </s>

<s>Nempe ex hoc esse videtur cur visibilis species, ex <lb></lb>Sole procedens et per pupillam amplificatam intromissa in retinam, amplio­<lb></lb>rem in illa sedem occupet, maioremque proinde creet Solis apparentiam, <lb></lb>quam dum per contractam pupillam eadem intromissa contendit ” (Opera, <lb></lb>T. III, Opuscula, Lugduni 1658, pag. </s>

<s>421). </s></p><p type="main">

<s>Il Vossio però fu de&#039;più liberi e de&#039;più solleciti a notar contro i Car­<lb></lb>tesiani come il creder che la grandezza delle immagini vada a proporzion <lb></lb>della grandezza della pupilla, era un errore dimostrato dal fatto della Ca­<lb></lb>mera oscura. </s>

<s>“ Sive enim patulum, sive angustum fuerit cubiculi foramen, <lb></lb>aequali tamen magnitudine obiecta quaevis in opposito linteo, seu pariete <lb></lb>depinguntur ” (De nat. </s>

<s>lucis. </s>

<s>cit., pag. </s>

<s>75). </s></p><p type="main">

<s>Il curioso fenomeno richiamò a sè lo studio non de&#039;soli Astronomi, ma <lb></lb>e degli Antropologi, i più giudiziosi de&#039;quali concorsero insomma in ciò che, <lb></lb>nel sopra citato Discorso, a scoprire altri simili inganni della vista, aveva <lb></lb>detto il Castelli. </s>

<s>Fermato il principio che sempre nel giudicar della gran­<lb></lb>dezza di un oggetto ci riferiamo alla grandezza di un altro oggetto a noi <lb></lb>noto, ne fece una leggiadra applicazione una sera in Roma, essendo lungo <lb></lb>il Tevere a spasso con alcuni signori e letterati amici suoi, mentre che dal­<lb></lb>l&#039;Aventino spuntava la Luna piena. </s>

<s>Domandato ad uno di costoro quanto la <lb></lb>gli paresse grande, veduta sull&#039;orlo del monte, gli parò innanzi agli occhi <lb></lb>il suo cappello per modo, che venisse il disco lunare quasi a toccare la <lb></lb>tesa, sulla quale disse maravigliato comparirgli assai men grande di prima. </s>

<s><lb></lb>Dietro questa esperienza, ripetuta anche dagli altri via via “ tutti confes­<lb></lb>sarono che, mentre noi paragoniamo la Luna col monte, ed apparendoci oc­<lb></lb>cupare un tratto di esso stimato da noi quattro o cinque braccia, ancora la <lb></lb>Luna veniva stimata di quella grandezza. </s>

<s>Ma quando, coperta la veduta del <lb></lb>colle, la medesima Luna era paragonata e riferita all&#039;ala del cappello, che <lb></lb>corrispondeva alla Luna, veniva stimata tanto minore, ed in ogni modo, con­<lb></lb>siderando quello che operava la Luna nel nostro occhio sopra la retina, im­<lb></lb>pressionandola con la sua immagine, sempre ci doveva fare sopra di essa le <lb></lb>immagini eguali per l&#039;appunto ” (pag. </s>

<s>31). </s></p><pb xlink:href="020/01/955.jpg" pagenum="398"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Fu il Venturi il primo a richiamar l&#039;attenzione di chi sarebbe per <lb></lb>scriver la storia dell&#039;Astronomia sopra una nota lasciata da Leonardo da <lb></lb>Vinci in un suo Manoscritto contrassegnato F: nota che così dice: “ La <lb></lb>Terra non è punto situata nel mezzo dell&#039;orbita del Sole, nè nel mezzo del <lb></lb>mondo: ella è nel mezzo de&#039;suoi elementi che sono a lei associati e ade­<lb></lb>renti. </s>

<s>Per un uomo che fosse nella Luna, quando nella notte ella è col Sole <lb></lb>al di sotto del nostro orizzonte, la Terra e l&#039;oceano produrrebbero sulla <lb></lb>Luna, a somiglianza del Sole, il medesimo effetto che ella produce sulla <lb></lb>Terra. </s>

<s>” </s></p><p type="main">

<s>Un tale pensiero però balenato fra le tante altre mirabili speculazioni <lb></lb>del Nostro, e rimasto per così lungo tempo nascosto, era in Germania rifio­<lb></lb>rito nella mente del Moestlin, e come un giovane arbusto dal natio vasello <lb></lb>l&#039;avea il Keplero trasposto nel campo della scienza ad assodarvi le sue ra­<lb></lb>dici e a distendere al largo l&#039;ubertosa sua chioma. </s>

<s>Il decimo paragrafo del <lb></lb>Cap. </s>

<s>VI dell&#039;Astronoma Ottica s&#039;intitola <emph type="italics"></emph>De illustratione mutua Lunae et <lb></lb>Terrae,<emph.end type="italics"></emph.end> dove, dopo di aver dimostrato che quell&#039;albor cinereo di che si vede <lb></lb>aspersa ne&#039;primi e negli ultimi giorni la faccia tenebrosa della Luna, non <lb></lb>può attribuirsi nè all&#039;essere ella diafana, come dicevano alcuni, nè al venir <lb></lb>illuminata da&#039;riflessi di Venere, come volevano altri. </s>

<s>“ Caeterum veram <lb></lb>causam, soggiunge, Moestlinus praeceptor meus primus quod sciam invenit, <lb></lb>meque et totum suum auditorium ante 12 annos docuit, et anno 1596 <lb></lb>in <emph type="italics"></emph>Disputatione de ecclipsibus,<emph.end type="italics"></emph.end> thesibus 21, 22, 23, pubblice explicavit ” <lb></lb>(Edit. </s>

<s>cit., pag. </s>

<s>254). E soggiunge appresso le testuali parole del Moestlin <lb></lb>usate a dimostrare il suo assunto, la conclusion del quale è la seguente: <lb></lb>“ Dicimus ergo Terram corusco suo, a Sole sibi immisso lumine, opacitatem <lb></lb>sive noctem in lunari corpore non minus irradiare, quam vicissim, prorsus <lb></lb>simili modo, Luna plena suis a Sole acceptis radiis nostras in Terra noctes <lb></lb>illustrat ” (ibi, pag. </s>

<s>255). </s></p><p type="main">

<s>Nonostante che il problema astronomico avesse avuto così dal Moestlin <lb></lb>la sua risoluzione completa, e che il Keplero l&#039;avesse così solennemente dif­<lb></lb>fuso e dottamente illustrato, Galileo nel suo Nunzio Sidereo lo propone come <lb></lb>cosa che fosse allora apparita nel mondo nuova, e da nessun altro, prima <lb></lb>di lui, insegnata. </s>

<s>“ Hic mirabilis fulgor non modicam Philosophantibus in­<lb></lb>tulit admirationem, pro cuius causa afferenda alii alia in medium protule­<lb></lb>runt ” (Alb. </s>

<s>III. 71). Fra queste diverse cause non annovera altro che le <lb></lb>false per confutarle, tacendo che tra-que&#039;filosofanti, da&#039;quali era stato pre­<lb></lb>ce<gap></gap>uto, avevano alcuni prima di lui dimostrata la causa, ch&#039;egli pure ap­<lb></lb>prova per vera, e parecchi anni prima con autorevole magisterio l&#039;avevano <lb></lb>già divulgata. </s></p><pb xlink:href="020/01/956.jpg" pagenum="399"></pb><p type="main">

<s>Di qui è che il Keplero non potè tenersi nella Dissertazione sul Nuncio <lb></lb>Sidereo di rivendicare al Moestlin e a sè, su Galileo, il merito d&#039;aver, fra <lb></lb>tanti errori, dimostrato per i primi la vera origine del candor della Luna, e <lb></lb>da quel sincero uomo ch&#039;egli era pronunziava in faccia a Galileo queste <lb></lb>libere parole: “ Quod vero demonstrationem attinet, quae ostendit hoc lu­<lb></lb>men ex nostra Tellure effundi, ea iam a viginti annis eoque amplius fuit <lb></lb>pene Moestlinum, ex cuius doctrina illam transtuli in meam Astronomiae <lb></lb>partem opticam, cap. </s>

<s>VI, num. </s>

<s>10, fol. </s>

<s>252, plenissimo tractatu: ubi easdem <lb></lb>etiam opiniones, quod lumen hoc sit a Sole vel a Venere tecum eodem modo <lb></lb>refuto, nisi quod hanc ultimam merito suo, paulo quam tu mollius excipio ” <lb></lb>(Alb. </s>

<s>V, 423). </s></p><p type="main">

<s>Se fosse stato Galileo trattato a quel modo, ch&#039;egli trattò il Moestlin e <lb></lb>il Keplero, avrebbe, come sempre fece anche per più leggere cagioni, messo <lb></lb>a romore il mondo: eppure il buono e generoso Alemanno si contentò di <lb></lb>rinfacciargli quelle parole, per amore e per giustizia del vero, lasciando del <lb></lb>resto libero Galileo d&#039;esercitar sue arti per consolidarsi nell&#039;usurpato pos­<lb></lb>sesso. </s>

<s>Lo consolidò poi nel Dialogo del Mondo, e tanto ben quell&#039;arti se­<lb></lb>condarono le sue intenzioni d&#039;apparir primo a dir la causa vera della luce <lb></lb>cinerea, che lui solo fecero oggetto di plauso gli amici, lui solo fecero segno <lb></lb>di contradizione i nemici. </s></p><p type="main">

<s>Ne porge una singolar prova di questo fatto il peripatetico Fortunio <lb></lb>Liceti, il quale, cogliendo l&#039;occasione di trattar nel cap. </s>

<s>L del suo Liteo­<lb></lb>sforo, <emph type="italics"></emph>De Lunae suboscura luce prope coniunctiones,<emph.end type="italics"></emph.end> pensò di dover asse­<lb></lb>gnarne altra più ragionevole causa da quella ch&#039;ei giudicò essere stata fal­<lb></lb>samente proferita da Galileo. </s>

<s>“ Primum existimo lumen illud obscurum non <lb></lb>esse Solare tunc a Terra revibratum in lunarem superficiem, sed, si qui­<lb></lb>dem Luna lucem aliquam habet in se congenitam, coniunctum quid ex im­<lb></lb>becilla Lunae luce nativa et lumine Solis in ipsam repercusso, reflexoque <lb></lb>ab aetheris alti partibus, lunare corpus ambientibus ” (Alb. </s>

<s>III, 184). </s></p><p type="main">

<s>Avuta Galileo notizia di questo suo nuovo contradittore, domandò con­<lb></lb>siglio al Renieri se fosse bene rispondergli, ed ebbe da Genova, in una let­<lb></lb>tera del dì 17 Febbraio 1640, queste parole: “ Giudico dunque bene che <lb></lb>V. S. E., mentre non venghino in campo argomenti più saldi, possa lasciar <lb></lb>la briga di rispondere; che se pur la non vuole lasciar così trascorrer tal <lb></lb>opra senza replica, mi offerisco di farlo io a capo per capo coll&#039;ordinario <lb></lb>seguente e mandarne a V. S. E. la lettera acciocchè, se giudicherà che io <lb></lb>abbia interamente sodisfatto a questo Signore, gli mandi la mia risposta ” <lb></lb>(MSS. Gal., P. III, T. VII, c. </s>

<s>180). </s></p><p type="main">

<s>Poco più di un mese dopo venne a togliere Galileo d&#039;ogni incertezza <lb></lb>una lettera scrittagli da Pisa dal principe Leopoldo, dove dicendo di aver <lb></lb>veduto il libro <emph type="italics"></emph>De lapide bononiensi<emph.end type="italics"></emph.end> e di avervi letti alcuni argomenti contro <lb></lb>quel che del candor lunare avea detto ne&#039;<emph type="italics"></emph>Massimi Sistemi,<emph.end type="italics"></emph.end> desiderava, per <lb></lb>dar causa al suo ingegno d&#039;insegnar qualche cosa di nuovo “ che gli avesse <lb></lb>scritto il suo pensiero intorno a queste nuove opposizioni ” (Alb. </s>

<s>VII, 254). </s></p><pb xlink:href="020/01/957.jpg" pagenum="400"></pb><p type="main">

<s>Non potendo mancare di ubbidire al cenno di S. A. S., come scrisse a <lb></lb>Daniele Spinola, trovandosi cieco e per vecchiezza debole di forze, con l&#039;aiuto <lb></lb>degli occhi e della mano di Vincenzio Viviani, allora giovanotto ospite e di­<lb></lb>scepolo suo, ma a cui Galileo dà il titolo di <emph type="italics"></emph>suo caro amico<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>257) <lb></lb>messe in carta quello, che pochi giorni dopo fu mandato al Principe in <lb></lb>forma di una Lettera a lui stesso diretta, dentro il mese di Aprile 1640. </s></p><p type="main">

<s>Varie copie manoscritte furono mandate agli amici, dal numero de&#039;quali <lb></lb>non fu escluso il Liceti, ed egli, tutt&#039;altro che offendersene, espresse a Ga­<lb></lb>lileo il desiderio di stampar quella Lettera al principe Leopoldo insiem con <lb></lb>le sue risposte. </s>

<s>Galileo si mostrò docile in assecondar que&#039;desiderii, ma <lb></lb>perchè la scrittura era fatta per metterla sotto gli occhi di quattro o sei, <lb></lb>ora che si trattava di metterla invece sotto milioni di occhi, voleva gli fosse <lb></lb>conceduto di rivederla e bisognando ripulirla, e senza punto alterare le cose <lb></lb>scritte distenderla in altra forma. </s>

<s>Soggiungeva allo stesso Liceti un&#039;altra in­<lb></lb>tenzione, in mandare ad effetto questa, ed era d&#039;indirizzare a lui medesimo <lb></lb>la scrittura, se così gli piaceva, aggiungendo qualche altra considerazione <lb></lb>per ampliargli il campo a risolver ciò che gli sarebbe opposto (Alb. </s>

<s>VII, 333). <lb></lb>Accettò volentieri il Liceti e Galileo, consigliatovi anche dagli amici, strinse <lb></lb>il patto scrivendo: “ Piacemi grandemente che ella applauda al mio pen­<lb></lb>siero di ridurre in altra Lettera le mie risposte, inviandole a lei medesima ” <lb></lb>(ivi, pag. </s>

<s>343). </s></p><p type="main">

<s>Dato dunque mano a ridur quella prima Lettera, così dettava al Viviani <lb></lb>il nuovo invocativo e l&#039;introduzione, sotto quest&#039;altra forma: </s></p><p type="main">

<s>“ All&#039;Illustriss. </s>

<s>ed Eccell.mo signor Fortunio Liceti, Filosofo eminen­<lb></lb>tissimo, Galileo Galilei vero e cordiale amico, salute. </s>

<s>— Appena aveva <lb></lb>V. S. Ecc.ma finito di mandare alla luce il suo Trattato della Pietra luci­<lb></lb>fera di Bologna, che ella me ne mandò una copia, accompagnandola con una <lb></lb>sua lettera piena di affetti di cortesia, nella quale, in segno della stima che <lb></lb>ella fa del mio giudizio, in poter librare con giusta lance i momenti della <lb></lb>dottrina che nel suo Trattato si contiene, mi pregò che io, con quella filo­<lb></lb>sofica libertà che tra gl&#039;indagatori del vero si ricerca, sinceramente gli sco­<lb></lb>prissi e significassi i miei sensi. </s>

<s>Io, per sodisfare a due debiti, nei quali mi <lb></lb>sentivo obbligato, risposi immediatamente al primo, che era di renderle le <lb></lb>debite grazie del regalo fattomi in mandarmi il libro, registrandomi nel nu­<lb></lb>mero dei primi e suoi più cari amici. </s>

<s>Quanto all&#039;altro obbligo, che è di <lb></lb>eseguire il suo cenno circa il liberamente manifestarle il giudizio, che fo <lb></lb>sopra la dottrina e i concetti in esso libro racchiusi; mi è stato forza, ri­<lb></lb>spetto all&#039;infelicità della perduta vista, che al servirmi nel leggere e nello <lb></lb>scrivere degli occhi e della penna di altri mi necessita; differir fino al pre­<lb></lb>sente di deporre in carta tutto quello, che ho stimato poter dare sodisfa­<lb></lb>zione alla domanda ” (MSS. Gal., P. III, T. VII, c. </s>

<s>110). </s></p><p type="main">

<s>Da questo punto prosegue il Manoscritto per alquante pagine, come <lb></lb>nella stampa, con la differenza che viene il discorso, invece che all&#039;<emph type="italics"></emph>Altezza <lb></lb>Serenissima<emph.end type="italics"></emph.end> del principe, rivolto alla <emph type="italics"></emph>Signoria Eccellentissima<emph.end type="italics"></emph.end> del dottore. <pb xlink:href="020/01/958.jpg" pagenum="401"></pb>La dettatura, con parecchie cancellature e con spessi richiami, veniva da <lb></lb>Arcetri inviata a Firenze a Vincenzio Galilei, che la riduceva a pulito, così <lb></lb>raccomandandogli lo stesso Viviani per scritto in fronte a c. </s>

<s>119: “ Signor <lb></lb>Vincenzio, V. S. abbia cura ad alcuni richiami e segni, che sono qui nel­<lb></lb>l&#039;ultimo. </s>

<s>” </s></p><p type="main">

<s>La copia a pulito di Vincenzio Galilei non va oltre le due carte 110, 111 <lb></lb>del citato Volume, e nella dettatura originale si prosegue a ridur la prima <lb></lb>Lettera, tornando a dirigere il discorso al medesimo principe Leopoldo. </s>

<s>A <lb></lb>render la ragione di un tal cambiamento soccorre opportuna la seguente let­<lb></lb>tera, che Mario Guiducci scriveva il di 17 Settembre di quell&#039;anno 1640 <lb></lb>allo stesso Galileo: </s></p><p type="main">

<s>“ ...... Io dissi alcuni giorni sono al signor Jacopo Soldani il pen­<lb></lb>siero di V. S. circa allo scrivere a dirittura al signor Liceti, quanto Ella <lb></lb>aveva scritto al Serenissimo sig. </s>

<s>principe Leopoldo, di che avendone esso <lb></lb>dato conto a S. A., ha avuto risposta che le piace il pensiero, ma che avrebbe <lb></lb>desiderato che V. S. avesse levato dal discorso alcune parole, che appari­<lb></lb>vano pungenti e piccanti, per non irritare un uomo tanto maledico, come <lb></lb>in altre occasioni si è scorto il Liceti. </s>

<s>Risposi che V. S. si sarebbe attenuto <lb></lb>al pensiero di S. A. quando le fosse stato mostrato le punture, le quali non <lb></lb>aveva avuto intenzione di mettervi come tali. </s>

<s>E perchè esso signor Jacopo <lb></lb>si esibi di notarle, insieme col signor Francesco Nerli, non ho ancora ria­<lb></lb>vuto la scrittura nè il libro. </s>

<s>Procurerò bene di riaverli quanto prima, e ver­<lb></lb>remo il sig. </s>

<s>Jacopo e io a restituirglieli ” (ivi, c. </s>

<s>176). </s></p><p type="main">

<s>Quella però del principe Leopoldo era una scusa, attraverso alla quale <lb></lb>voleva far trasparire la sua vera intenzione essere che il Discorso, in qua­<lb></lb>lunque modo fosse stato ridotto, seguitasse ad esser rivolto, non ad altri <lb></lb>che a lui. </s>

<s>Poco di poi significò più chiaramente quel suo desiderio, ond&#039;è <lb></lb>che Galileo mutò concetto, scusandosi così col Liceti: “ Pensavo a quest&#039;ora <lb></lb>di poter inviar le mie risposte sopra il candore della Luna distese in forma <lb></lb>di lettera a lei medesimo, e già le avevo quasi ridotte al netto, quando mi <lb></lb>è venuto avviso che il Serenissimo principe Leopoldo, alla cui Altezza avevo <lb></lb>in prima scritto, si maraviglia che io avessi mutato concetto..... Onde io <lb></lb>reputando a mia somma gloria che il mondo senta una testimonianza del­<lb></lb>l&#039;essere io in buon grado in grazia di tanto principe, e stimando che il <lb></lb>medesimo possa accadere a V. S., ho risoluto di ritornare in sulla prima <lb></lb>maniera di scrivere all&#039;A. S. ma con tessitura alquanto più ampla, per la <lb></lb>interposizione di varie mie considerazioncelle ” (Alb. </s>

<s>VII, 345). </s></p><p type="main">

<s>Queste considerazioncelle furono dettate da Galileo al Viviani a parte, <lb></lb>con segni di richiamo e colla nota: <emph type="italics"></emph>per inserirli in luogo opportuno.<emph.end type="italics"></emph.end> Ma <lb></lb>non essendo poi inserite altrimenti, rimasero allora e rimangono tuttavia <lb></lb>da c. </s>

<s>135-41 nel Manoscritto. </s>

<s>I più importanti fra que&#039;varii pensieri non <lb></lb>son forse che due: il primo, nel quale dimostra contro il Liceti essere per <lb></lb>sè tenebrosi anche i tre pianeti superiori, come si riferirà nel seguente no­<lb></lb>stro capitolo, e l&#039;altro, dove svolge ampiamente un suo concetto accennato <pb xlink:href="020/01/959.jpg" pagenum="402"></pb>già nel Sistema del Mondo. </s>

<s>Aveva nella Giornata I scritto che la luce se­<lb></lb>condaria si mostra notabilmente più viva, quando noi vediam la Luna sul­<lb></lb>l&#039;alba, che quando si vede in sulla sera, attribuendo la differenza all&#039;esser <lb></lb>la Luna orientale opposta all&#039;Asia, che ha poco mare e assaissima terra <lb></lb>“ dovecchè, quand&#039;ella è in occidente, riguarda grandissimi mari, cioè tutto <lb></lb>l&#039;Oceano atlantico sino alle Americhe ” (Alb. </s>

<s>I, 111). </s></p><p type="main">

<s>Rimeditando sopra queste parole il Castelli, a cui era occorso di veder <lb></lb>la luce secondaria assai cospicua nella Luna vicina al primo quarto, benchè <lb></lb>avesse letto nel Nunzio Sidereo che <emph type="italics"></emph>debilis admodum, et incerta conspici­<lb></lb>tur,<emph.end type="italics"></emph.end> giudicò che, ritrovandosi la Luna meridionale, dovesse essere illustrata <lb></lb>da qualche esteso tratto di Terra. </s>

<s>“ E però, scrive queste precise parole a <lb></lb>Galileo, mi venne in mente che le terre meridionali a noi incognite deb­<lb></lb>bono essere vastissime province, e che però riflettino gagliardo lume nella <lb></lb>Luna. </s>

<s>Se ho detto qualche sproposito me lo perdoni, perchè confesso di non <lb></lb>averci pensato abbastanza ” (Alb. </s>

<s>X, 244). </s></p><p type="main">

<s>Queste parole scritte il dì 14 Novembre 1637, richiamarono forse più <lb></lb>attentamente il pensiero di Galileo nell&#039;occasion ch&#039;egli ebbe a scrivere in­<lb></lb>torno al Candore lunare, e fu in ogni modo allora che, riconosciutane l&#039;im­<lb></lb>portanza, si dette a svolgere quel concetto accennato già nel I Dialogo dei <lb></lb>Due Massimi Sistemi, dettandolo al Viviani, <emph type="italics"></emph>per metterlo in luogo oppor­<lb></lb>tuno,<emph.end type="italics"></emph.end> in questa forma: </s></p><p type="main">

<s>“ Non voglio tacere in questo luogo a V. A. S. certa mia particolare <lb></lb>osservazione fatta nel candore della Luna, dalla quale resulta una nuova <lb></lb>molto probabil coniettura a favore del riflesso terrestre, per produrre il can­<lb></lb>dore, la quale non ha luogo nell&#039;etere ambiente, per il medesimo effetto, e <lb></lb>l&#039;osservazione è tale: Avendo io, due o tre giorni avanti il Novilunio, po­<lb></lb>sta diligente cura quale si rappresenti la chiarezza del candor lunare, men­<lb></lb>tr&#039;ella surgendo dall&#039;oriente fa di sè mostra nell&#039;Aurora, e dipoi altro e <lb></lb>tanto tempo dopo il Novilunio attentamente rimirandola in occidente nel cre­<lb></lb>puscolo vespertino, parmi aver ritrovato non piccola diminuzione nel suo <lb></lb>medesimo candore, il quale men vivo si dimostra, ed avendo pregato alcuni <lb></lb>amici che facciano la medesima osservazione, trovo che concordemente af­<lb></lb>fermano agli occhi loro dimostrarsi quella medesima differenza, che a&#039;miei <lb></lb>più volte dimostrata si era. </s>

<s>” </s></p><p type="main">

<s>“ Ora se in questo effetto si trova una tal mutazione, bene è necessa­<lb></lb>rio che, nella causa di tale effetto produttrice, mutazione si trovi quanto al <lb></lb>potere or più vivamente or meno illuminare. </s>

<s>E se la causa, com&#039;io ho sti­<lb></lb>mato, è il riflesso dei raggi solari nella terrestre superficie, converrà che <lb></lb>ella or più or meno risplendente si mostri all&#039;emisferio lunare. </s>

<s>Ed essendo <lb></lb>che, posta la Luna in oriente, a lei si espone delli due emisferi terrestri <lb></lb>separati dal nostro meridiano lo orientale, ed all&#039;incontro vede ella posta <lb></lb>in occidente l&#039;emisfero occidentale; bisognerebbe per mantenimento della <lb></lb>mia opinione, che il terrestre emisfero orientale più splendidamente riflet­<lb></lb>tesse i raggi solari che l&#039;altro emisfero occidentale. </s>

<s>” </s></p><pb xlink:href="020/01/960.jpg" pagenum="403"></pb><p type="main">

<s>“ Questa necessità m&#039;indusse a pensare se differenza alcuna potesse <lb></lb>cadere tra i detti due emisferi, per la quale, con qualche disegualità, pro­<lb></lb>cedesse il loro riflesso. </s>

<s>E veramente assai probabile mi pare che ella por <lb></lb>vi si possa, regolandoci con quella apparenza che nella Luna si scorge, cioè <lb></lb>che la sua superficie non è per tutto egualmente lucida, ma sono in quella <lb></lb>sparse molte macchie meno del restante lucide. </s>

<s>” </s></p><p type="main">

<s>“ La superficie del nostro Globo terrestre è composta di due parti mas­<lb></lb>sime, dico dei mari e dei continenti. </s>

<s>Queste percosse dai raggi del Sole non <lb></lb>egualmente illustrano, ma notabilmente più illuminano le parti terrene, che <lb></lb>quelle dell&#039;acqua, per lo che più potenti saranno i raggi reflessi dalla Terra <lb></lb>che i reflessi dal mare. </s>

<s>Ora, se noi considereremo qual proporzione abbiano <lb></lb>in grandezza le parti marittime con le terrestri nell&#039;emisferio orientale; se <lb></lb>parimenti andremo esaminando quello che accaggia tra i mari e continenti <lb></lb>dell&#039;emisferio occidentale, troveremo senza dubbio, dell&#039;emisferio orientale <lb></lb>vastissime essere le campagne terrestri, e minori assai quelle dei mari, e <lb></lb>nell&#039;altro emisferio troveremo accader tutto l&#039;opposto. </s>

<s>” </s></p><p type="main">

<s>“ Tutta l&#039;Asia, parte vastissima sopra le altre, è a noi orientale, con <lb></lb>gran parte dell&#039;Europa e dell&#039;Affrica ancora. </s>

<s>In occidente aviamo sola l&#039;Ame­<lb></lb>rica, con parte dell&#039;Affrica, e qui sono i mari vastissimi, Atlantico e Paci­<lb></lb>fico, sommamente più ampli di quelli che restano verso l&#039;Oriente. </s>

<s>Quan­<lb></lb>dunque sia vero che il riflesso della Terra superi quello del mare, molto <lb></lb>probabile coniettura averemo per render ragione del candore più lucido in <lb></lb>oriente, che in occidente, della qual differenza non si può referir la causa <lb></lb>all&#039;etere ambiente la Luna, trovandosi egli in ambedue questi casi egual­<lb></lb>mente lontano dal Sole ” (MSS. Gal., P. III, T. VII, c. </s>

<s>141). </s></p><p type="main">

<s>È questa senza dubbio una delle più argute ragioni escogitate da Ga­<lb></lb>lileo a dimostrar, contro il Liceti, che non può la luce secondaria attribuirsi <lb></lb>alle rifrazioni de&#039;raggi solari nella sfera vaporosa che circonda la Luna, <lb></lb>come si producono per un simile effetto i crepuscoli qui sulla Terra, e sa­<lb></lb>rebbe stato degno anche questo argomento d&#039;esser veramente inserito nella <lb></lb>Lettera riformata. </s>

<s>Non s&#039;intende perciò il motivo che consigliò l&#039;Autore a <lb></lb>lasciarlo indietro, come non s&#039;intende perchè, avendo Galileo dettato al Vi­<lb></lb>viani un altro bel tratto di eloquenza <emph type="italics"></emph>da inserirsi nel fine dell&#039;opera<emph.end type="italics"></emph.end> (ivi, <lb></lb>c. </s>

<s>136), fosse, come membro disutile, lasciato esso pure indietro fra le bozze <lb></lb>della scrittura. </s></p><p type="main">

<s>Forse, non essendo questo altro che un riepilogo, pensò Galileo esser <lb></lb>l&#039;Opera così breve da non averne il Lettore altrimenti bisogno. </s>

<s>Ma se pro­<lb></lb>priamente non bisogna a chi tutto per disteso ha letto il Discorso sul can­<lb></lb>dore lunare, non sarà disutile il trascriver qui le parole, che lasciò indietro <lb></lb>l&#039;Autore, e nelle quali, chi non ha tutta presente alla memoria la Let­<lb></lb>tera al principe Leopoldo, trova conclusi i principali argomenti galileiani <lb></lb>contro il Liceti: </s></p><p type="main">

<s>“ Ora, eccellentissimo mio Signore, facciami grazia di considerare con <lb></lb>quanta bella analogia si rispondano nella Luna e nella Terra le tre diverse <pb xlink:href="020/01/961.jpg" pagenum="404"></pb>illuminazioni, le quali tutte, come da un istesso fonte, scaturiscono dal ful­<lb></lb>gore immenso del lucidissimo Sole, senza il quale nè queste illuminazioni e <lb></lb>splendori, nè quello di qualsivoglia dei pianeti erranti resterebbero al mondo. </s>

<s>” </s></p><p type="main">

<s>“ E prima, essendo perpetuamente uno emisferio della Luna esposto <lb></lb>alla vista del Sole, viene in ogni sua parte egualmente da quello illustrato. </s>

<s><lb></lb>L&#039;istesso accade dell&#039;emisferio terrestre: dico di essere illuminato tutto. </s>

<s>” </s></p><p type="main">

<s>“ Oltre a questa massima illuminazione, ce n&#039;è una parziale e secon­<lb></lb>daria prodotta nella Terra, e pur dai raggi solari riflessa dalla sfera vapo­<lb></lb>rosa, la quale essa Terra circonda, e secondo che il Sole si abbassa sotto <lb></lb>l&#039;orizzonte, quella parte di essi vapori illustrati, che sopra l&#039;orizzonte ri­<lb></lb>mane, riflette i raggi solari sopra la proprinqua parte della superficie ter­<lb></lb>restre, ma questa illuminazione non molto addentro si distende, per essere <lb></lb>l&#039;altezza dei vapori non molta, e la superficie della Terra non piana ma <lb></lb>sfericamente tuberosa. </s>

<s>” </s></p><p type="main">

<s>“ A questo risponde una simile illaminazione fatta da quella parte del­<lb></lb>l&#039;etere ambiente la Luna, che per essere alquanto più denso del resto, che <lb></lb>per gl&#039;immensi spazi del cielo si diffondè; è potente a riflettere i raggi so­<lb></lb>lari intorno a quella parte dello emisferio tenebroso della Luna, la quale <lb></lb>con l&#039;altro suo emisferio illuminato dai raggi primarii del Sole è conter­<lb></lb>mina. </s>

<s>Ma tale illuminazione è assai debole, per esser la parte dell&#039;etere am­<lb></lb>biente assai meno atta a far la riflessione gagliarda sopra la Luna, che non <lb></lb>è la parte molto più densa dei vapori sopra la Terra, e questa parimente <lb></lb>non candisce tutto l&#039;emisfero tenebroso, ma solo una parte, che confina <lb></lb>l&#039;emisfero illustrato dal Sole, e di questo ne aviamo la sensata esperienza <lb></lb>nelle Ecclissi, mentre che, dopo essersi immersa la Luna nel cono dell&#039;om­<lb></lb>bra terrestre, e persa la primaria illuminazione de&#039;raggi solari, si vede im­<lb></lb>mediatamente per qualche tempo biancheggiare alquanto quella parte della <lb></lb>periferia della Luna, che fu l&#039;ultima a entrar nell&#039;ombra. </s>

<s>Ma tal bianchezza <lb></lb>tosto si perde nel profondarsi la Luna verso il mezzo del cono tenebroso. </s>

<s>” </s></p><p type="main">

<s>“ Ci è la terza e pure ampla illuminazione, prodotta in Terra pur <lb></lb>da&#039;medesimi raggi solari reflessi nella Luna, ed inviati allo intero emisfero <lb></lb>terrestre, il quale non tocco dai raggi solari è esposto alla vista della splen­<lb></lb>dida Luna. </s>

<s>A questa ultima totale illuminazione risponde il candore della <lb></lb>Luna, il quale si vede egualmente diffuso nello emisfero della Luna non <lb></lb>tocco dai raggi solari, e tal candore amplo e massimo si scorge presso alla <lb></lb>congiunzione di essa Luna col Sole, nel qual tempo viene opposto alla Luna <lb></lb>il grande emisfero terrestre illuminato dai raggi solari. </s>

<s>” </s></p><p type="main">

<s>“ Ora, Eccellentissimo Signore, qual ragione può indurla a volere di <lb></lb>questo gran candore porne la causa nel medesimo etere ambiente, il quale <lb></lb>aviamo veduto che pochissima parte della Luna tigne di un debole colore, <lb></lb>piuttosto plumbeo che argenteo, dovecchè, quando l&#039;etere ambiente fosse <lb></lb>potente a produrre l&#039;amplo e assai vivo candore, molto più vivo ci si rap­<lb></lb>presenterebbe egli nel campo oscuro della notte, che nello assai ben lucido <lb></lb>del crepuscolo e dell&#039;aurora? </s>

<s>” </s></p><pb xlink:href="020/01/962.jpg" pagenum="405"></pb><p type="main">

<s>“ Io non mi posso persuadere che, facendo V. S. col suo perspicacis­<lb></lb>simo ingegno riflessione sopra questa così bella analogia, non sia per pre­<lb></lb>stargli l&#039;assenso, e massime che io ho grande opinione che tra i fenomeni, <lb></lb>che indussero grandissimi Filosofi, e Aristotile stesso sommo tra tutti, a <lb></lb>concedere gran simpatia e corrispondenza tra la Luna e la Terra, non solo <lb></lb>la similitudine di figura e della faccia maculosa, quale in essa Luna veg­<lb></lb>giamo e nella Terra si scorgerebbe, cagionata dai mari e dai continenti, <lb></lb>quando da luogo tenebroso e molto lontano potessimo vedere la faccia ter­<lb></lb>restre illuminata, gli avesse indotti; ma molto più la corrispondenza di que­<lb></lb>sta triplice illuminazione, che non è credibile che da Aristotile, tanto sagace <lb></lb>contemplatore degli effetti di Natura, questo sì bello e nobile restasse inos­<lb></lb>servato. </s>

<s>E se io avessi quella pratica in tutti i libri fisiologici di Aristotile, <lb></lb>e che la memoria mi servisse, come di altri sagaci contemplatori accade, <lb></lb>non diffiderei di poter, con andar sottilmente rintracciando e conferendo <lb></lb>questa particola con quella, e quella con quell&#039;altra, accozzar tanti luoghi <lb></lb>insieme, che io mi ritrovassi scritta questa verità, che bene è ragionevole <lb></lb>che là tutte le verità si ritrovino, dove le proposizioni che scaturiscono son <lb></lb>tutte vere ” (ivi, c. </s>

<s>136, 37). </s></p><p type="main">

<s><emph type="center"></emph>.V<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nella Digressione fisico-matematica, fatta nel capitolo L del Liteosforo, <lb></lb>ebbe intenzione il Liceti di trattar della luce suboscura della Luna, non solo <lb></lb>presso alle congiunzioni, ma <emph type="italics"></emph>et in deliquis observata.<emph.end type="italics"></emph.end> Il singolare fenomeno, <lb></lb>che tanto frugò la curiosità degli Astronomi, e tanto ne mise in travaglio <lb></lb>la scienza, vedemmo come non isfuggì alle argute speculazioni dell&#039;antico <lb></lb>Plutarco, il quale attribuì la luce, che rende ancora visibile nelle ecclissi il <lb></lb>disco lunare, allo splendor delle Stelle che circondano il Sole. </s>

<s>Ma, che più <lb></lb>importa alla nostra Storia, non isfuggi quella stessa speculazione al primo <lb></lb>e vero padre della risorgente Scienza sperimentale in Italia, il quale disse <lb></lb>esser causa della luce rossiccia, di che si vede aspersa nelle ecclissi la fac­<lb></lb>cia della Luna, le rifrazioni fatte in mezzo alla nostra ammosfera, che ri­<lb></lb>torcono i raggi del Sole verso l&#039;asse del cono ombroso, dove vanno talvolta <lb></lb>a riflettersi anco i vivi splendori di Venere. </s></p><p type="main">

<s>“ Quod vero Luna nullum ex se habeat lumen, sufficiens inditium est <lb></lb>nos ipsam tanto magis obscuram videre, quanto magis in cono umbrae Ter­<lb></lb>rae immergitur, et si eo tempore ipsam videmus rubeo colore affectam, hoc <lb></lb>enim accidit quia radii Solares undequaque refranguntur a vaporibus ipsam <lb></lb>Terram circumdantibus, quae quidem refractio fit versus axem coni um­<lb></lb>brae Terrae, et propterea umbra dicti coni non est aequaliter obscura sed <lb></lb>tenebrosa. </s>

<s>Circa vero axem ipsius coni, magis quam circa eius circumferen­<lb></lb>tiam obscuratur, et quia Corpus lunare tale est ut facillime recipiat qua-<pb xlink:href="020/01/963.jpg" pagenum="406"></pb>lecumque lumen, quod etiam manifeste videtur dum ipse Luna reperitur <lb></lb>secundum longitudinem inter Solem et Venerem, quod pars Lunae lumine <lb></lb>Solis destituta a lumine Veneris aliquantulum illustratur, quod ego ipse vidi <lb></lb>et multis ostendi; propterea, dum ipsa Luna in cono umbrae Terrae repe­<lb></lb>ritur, adhuc videtur ” (Speculationum Liber, Venetiis 1599, pag. </s>

<s>257). </s></p><p type="main">

<s>Dopo quasi vent&#039;anni, tornò a parlar <emph type="italics"></emph>De rubore Lunae deficientis,<emph.end type="italics"></emph.end> in <lb></lb>Germania, l&#039;altro primo e vero Padre dell&#039;Ottica astronomica, e confutata, <lb></lb>fra le altre, l&#039;ipotesi di Plutarco, che fosse cioè quel color rosso dovuto a&#039;ri­<lb></lb>flessi delle stelle e di Venere “ nam si sidera Solem circumstantia Lu­<lb></lb>nam ita pinxinssent, totum eius discum aequaliter sibi obiectum pinxissent <lb></lb>aequaliter ” (Kepleri Astron. </s>

<s>pars Optica cit., pag, 276); conclude poi così, <lb></lb>quasi ripetendo a parole quello, che aveva già scritto il nostro Benedetti: <lb></lb>“ Causa vero plane est in refractionibus, ut sit nihil aliud rubor iste quam <lb></lb>illustratio Lunae a Solis radiis, per aeris densitatem transmissis, et intro <lb></lb>versus axem umbrae refractis, ut ex sequentibus experimentis clarum eva­<lb></lb>det ” (ibi, pag. </s>

<s>274). Quelli esperimenti poi si riducono ai fatti diligente­<lb></lb>mente osservati in varie ecclissi lunari, e qui dal Keplero stesso descritti. </s></p><p type="main">

<s>Il Liceti però, o non conoscesse quelle Speculazioni del Benedetti e <lb></lb>queste astronomiche osservazioni del Keplero, o conoscendole, non credesse <lb></lb>di dover approvarle per vere, attribuì la luce, che fa cospicua la Luna nel­<lb></lb>l&#039;ombra della Terra, a tutt&#039;altra cagione. </s>

<s>“ Si tamen ex sese Luna penitus <lb></lb>est obscura et opaca, perinde ac Terra, uti censet Vir clariss, (Galilaeus), <lb></lb>eam cum Lapide bononiensi magnam et nobilem analogiam habere censeo, <lb></lb>ut absente Sole ac in umbra, seu Terrae dum deficit, seu sua, dum Soli <lb></lb>coniungitur in parte lumine Solari non tacta; conservet aliquamdiu lucem, <lb></lb>quam prius a Sole susceperat ” (Alb. </s>

<s>III, 188). </s></p><p type="main">

<s>Fu a questa occasione che Galileo, per confutare il Liceti, si dette di <lb></lb>proposito a rivolgere il pensiero sopra la causa di quel rosso ne&#039;deliqui di <lb></lb>Luna; causa, intorno alla quale interpellato vent&#039;anni prima dal Cavalieri <lb></lb>(Alb. </s>

<s>IX, 10), avea col tacere confessato di non saperla. </s>

<s>Di quelle specula­<lb></lb>zioni poi, che non ebbero nulla nè di peregrino nè di nuovo, si compiacque <lb></lb>al solito Galileo magnificandole al Renieri, il quale rispondeva così in un <lb></lb>poscritto di lettera: “ Se V. S. E. mi avviserà di qualche bel problema in­<lb></lb>torno a&#039;lumi diretti e riflessi, ecclissi lunari e solari, come mi scrive di <lb></lb>avere avvertito, mi farà sommo favore ” (MSS. Gal., P. III, T. VII, c. </s>

<s>180). </s></p><p type="main">

<s>L&#039;avviso però non fu dato allora, perchè voleva Galileo tutto insieme <lb></lb>e perfetto far apparire al mondo il suo parto, ma intanto il Renieri stesso <lb></lb>lo preveniva nelle recondite speculazioni, scrivendogli, a provar che il can­<lb></lb>dor della Luna era dovuto ai riflessi della Terra, un concetto, che poi Ga­<lb></lb>lileo benignamente fece suo (Alb. </s>

<s>III, 224), e ricordandogli, rispetto al <lb></lb>rosso lunare, ciò che nell&#039;Ottica astronomica aveva insegnato il Keplero. <lb></lb></s>

<s>“ Se debbo dire, un tal mio pensiero, scriveva da Genova il dì 29 Feb­<lb></lb>braio 1640, mentre mi ricordo che alcuni hanno stimato la Luna corpo <lb></lb>diafano, perchè nella solare ecclissi notarono il disco di essa sparso di <pb xlink:href="020/01/964.jpg" pagenum="407"></pb>qualche luce, vò dubitando che tal luce fosse per appunto quella, che <lb></lb>dalle parti della Terra non ecclissata colà venia ripercossa. </s>

<s>Non è dunque <lb></lb>la luce secondaria del disco lunare altro che il riflesso de&#039;raggi del Sole, <lb></lb>colà dalla Terra ripercossi: nè perchè nell&#039;ecclisse della Luna ella resti <lb></lb>sparsa di qualche luce, può paragonarsi con la pietra di Bologna, perchè <lb></lb>tal lume, come bene avvertì il Keplero, vien cagionato da&#039;raggi del Sole, <lb></lb>che battendo nell&#039;aria contermina alla Terra si ripiegano e riflettono verso <lb></lb>la Luna, e di tal luce la spargono, come nella seguente figura può vedersi. </s>

<s>” <lb></lb>E qui, a tergo della carta 179 del citato Manoscritto, vedesi, con fedel co­<lb></lb>pia, disegnato l&#039;iconismo impresso a pag. </s>

<s>279 dell&#039;Ottica astronomica ne&#039;Pa­<lb></lb>ralipomeni a Vitellione. </s></p><p type="main">

<s>Questo, suggerito così a Galileo dal Renieri, sarebbe stato insomma il <lb></lb>modo, che le tradizioni scientifiche porgevano, a confutar l&#039;error del Liceti. </s>

<s><lb></lb>Ma Galileo non conosce maestri: la confutazione al Liteosfore è un <emph type="italics"></emph>pensiero <lb></lb>suo nuovo<emph.end type="italics"></emph.end> (Alb. </s>

<s>VII, 25). </s></p><p type="main">

<s>Giacchè dunque è aperto il cervel di Minerva, da cui è uscita fuori <lb></lb>questa bella novità di pensiero, ascoltiamo: Venere, Giove e la Canicola <lb></lb>concorrono insieme, spento il Sole, a illuminare la Luna (Alb. </s>

<s>III, 213, 14). <lb></lb>Questa novità però era tanto vecchia, che risaliva a Plutarco, la ipotesi del <lb></lb>quale si disse come fosse, con invitte ragioni, convinta di falsità dal Keplero. </s></p><p type="main">

<s>Or perchè troppo importa a noi conoscer, meglio di quel che non si <lb></lb>sia fatto fin qui, un uomo, ch&#039;è il principale attore di questa Storia, non <lb></lb>si può senza considerazione passar sopra a certi fatti, che hanno dello straor­<lb></lb>dinario, anzi del maraviglioso. </s>

<s>Chi altri, dopo la Disputazione del Moestlin <lb></lb>così solennemente bandita ne&#039;Paralipomeni a Vitellione, e dopo le calme si, <lb></lb>ma forti rivendicazioni fatte a sè e al suo proprio maestro dall&#039;Autor della <lb></lb>Dissertazione sul Nuncio Sidereo, avrebbe osato mai di rinfacciare pubbli­<lb></lb>camente a que&#039;filosofi, de&#039;quali si ripetevano le dottrine, che <emph type="italics"></emph>per tanti secoli <lb></lb>prima di lui erano rimaste occulte agl&#039;ingegni speculativi?<emph.end type="italics"></emph.end> (Alb. </s>

<s>III, 203). <lb></lb>Eppure Galileo lo fece, e principi e privati gli fecero plauso. </s></p><p type="main">

<s>Chi altri mai si sarebbe potuto così compiacentemente gloriare delle <lb></lb>falsità fotometriche, scritte nella Lettera sul Candore lunare, rifiutando, come <lb></lb>vedemmo altrove, quella vera legge di Fotometria dimostrata dal Castelli? </s>

<s><lb></lb>o chi altri sarebbesi potuto lusingar di destare ammirazione in chi legge, <lb></lb>per venire a ripetere, dopo Plutarco e il Benedetti, un errore così facil­<lb></lb>mente confutato dall&#039;osservazione de&#039;fatti? </s>

<s>Eppure quelle compiacenze e <lb></lb>queste lusinghe albergarono nel petto di Galileo, come lo attesta il sopra <lb></lb>citato poscritto di lettera del Renieri. </s></p><p type="main">

<s>Che si vorrà dunque dire? </s>

<s>che gli occhi, riguardando in quel che a <lb></lb>loro pareva un Sole, rimanessero abbarbagliati per modo, da non vedere <lb></lb>altro all&#039;intorno? </s>

<s>Ma s&#039;è cosa veramente maravigliosa la virtù ch&#039;ebbe Ga­<lb></lb>lileo di apparire unico sole a illuminare il mondo, non fa minor maraviglia <lb></lb>a vedere occhi sì acuti pigliare un comun fosforo di terra per un divino <lb></lb>raggio celeste. </s></p><pb xlink:href="020/01/965.jpg" pagenum="408"></pb><p type="main">

<s>Comunque sia, non erano un Baliani, un Cavalieri, un Renieri, per esem­<lb></lb>pio, così abbarbagliati e ritenuti da non conoscer, benchè attraverso a un <lb></lb>velo teso, gli errori di Galileo, e da non insorgere, benchè attraverso a <lb></lb>un vallo opposto, contro ciò che indebitamente pretendeva il loro ammirato <lb></lb>amico e venerato maestro, da cui, quando non dimostrava il vero, diserta­<lb></lb>vano in punta di piedi. </s></p><p type="main">

<s>Abbiam nominato il Baliani, il Cavalieri e il Renieri, perchè furono <lb></lb>questi de&#039;primi a ricevere la Lettera sul Candore lunare, facendo Galileo <lb></lb>gran conto della loro approvazione. </s>

<s>Il Baliani, così libero e arguto in dire <lb></lb>il suo parere all&#039;Autor del Saggiatore, de&#039;Massimi Sistemi e delle Due Nuove <lb></lb>Scienze, quand&#039;è richiesto della sua opinione su quella Lettera al principe <lb></lb>Leopoldo, và per le generali, contento di plaudire al vero, da Galileo dimo­<lb></lb>strato contro l&#039;error del Licetì. </s></p><p type="main">

<s>Non è a passare inosservato, quel che dice della soluzione data dallo <lb></lb>stesso Liceti al famoso problema delle ombre. </s>

<s>Quella soluzione del Peripa­<lb></lb>tetico di Bologna si riduce insomma all&#039;altra del Gassendo, il quale, sul <lb></lb>fondamento che gli astri all&#039;orizzonte hanno, per la maggior mole de&#039;va­<lb></lb>pori interposti, difetto di luce, ossia soverchianza d&#039;ombra; ne conclude <lb></lb>perciò non dover far maraviglia se le ombre, in quel caso, ci appariscon <lb></lb>maggiori. </s>

<s>Al Baliani parve vana questa risposta “ perchè io (in tal modo <lb></lb>si esprime con Galileo) non so discerner nell&#039;aria del mezzodì vivezza di <lb></lb>luce, che faccia cotal effetto: è falso il quesito, perchè l&#039;ombra mandata <lb></lb>dal medesimo corpo nella medesima lontananza, io stimo che sia la stessa <lb></lb>ad ogni ora, così dettandomi la ragione ” (MSS. Gal., P. III, T. VII, c. </s>

<s>171). </s></p><p type="main">

<s>Il Cavalieri ingenuamente rispondeva che s&#039;era vero la Luna talvolta <lb></lb>nell&#039;ecclissi scomparir tutta, non vedeva come poter altrimenti salvare il <lb></lb>fatto, che ammettendo l&#039;ipotesi di Galileo. </s>

<s>“ Mi è ben giunta nuova la ra­<lb></lb>gione del vedersi, ne&#039;totali ecclissi lunari, essa Luna talvolta e talvolta no, <lb></lb>perchè io credeva prima che sempre si vedesse, come più volte ho speri­<lb></lb>mentato, e che quel lume fosse cagionato dai raggi del Sole refratti nel­<lb></lb>l&#039;ammosfera terrestre. </s>

<s>Ma essendo vero che talvolta resti invisibile la Luna, <lb></lb>conosco che di tale effetto non può esser cagione tale refrazione, che sem­<lb></lb>pre è, o almeno tale lume deve restare insensibile, e perciò resta che sieno <lb></lb>veramente cagioni di tal lume Venere, Giove e il Cane principalmente, tro­<lb></lb>vandosi dalla banda del Sole ” (Alb. </s>

<s>X, 388). </s></p><p type="main">

<s>Avrebbe volentieri applaudito anche il Renieri a un tal concetto, se l&#039;ar­<lb></lb>gomento fattogli dal Keplero avverso, e le sue proprie osservazioni non fossero <lb></lb>venute a metterglielo in dubbio. </s>

<s>“ Ho notato (scriveva il dì 13 Aprile 1640 <lb></lb>allo stesso Galileo) il suo pensiero circa di quel rossore che ha la Luna nelli <lb></lb>Ecclissi, e sommamente mi piace. </s>

<s>Perchè in vero, se Venere a noi comu­<lb></lb>nica talvolta tanta luce, che è atta a cagionar l&#039;ombra; perchè non lo dovrà <lb></lb>fare, nello stesso modo, nella Luna? </s>

<s>Una sola cosa mi dà un poco di fa­<lb></lb>stidio, ed è la variazione di colori stravagantissimi, ed io ho osservato nel­<lb></lb>l&#039;Ecclisse dell&#039;anno 1635, a&#039;27 di Agosto, dove appariva la Luna tinta di <pb xlink:href="020/01/966.jpg" pagenum="409"></pb>macchie pallide, pavonazze e rosse in modo, che mi faceva sovvenire ciò <lb></lb>che scrive Cornelio Gemma, <emph type="italics"></emph>Cosmocritices Lib. </s>

<s>II, Anno 1569, Martii die <lb></lb>tertia, mane hora tertia, Phoebin vidi ecclipsim horrendam passam diris <lb></lb>coloribus insignitam. </s>

<s>Primo enim fuscus, inde sanguineus fulsit, mox pu­<lb></lb>niceus et virens et lividus, ac tandem incredibili varietate difformis,<emph.end type="italics"></emph.end> cosa <lb></lb>degna invero d&#039;ammirazione, e che io difficilissimamente averei creduta, se <lb></lb>non l&#039;avessi appuntino veduta con questi occhi, in tempo che l&#039;Ecclisse fu <lb></lb>centrale. </s>

<s>Facciasi per grazia V. S. E. leggere ciò che in questo proposito <lb></lb>scrive il Keplero, a carte 271 della sua <emph type="italics"></emph>Astronomia optica,<emph.end type="italics"></emph.end> dove tratta <emph type="italics"></emph>De <lb></lb>umbra<emph.end type="italics"></emph.end> (ma dice <emph type="italics"></emph>De rubore<emph.end type="italics"></emph.end>) <emph type="italics"></emph>Lunae deficientis,<emph.end type="italics"></emph.end> e dove arreca la cagione <lb></lb>perchè non crede in tutto a Ticone, che fu di questo stesso pensiero che <lb></lb>Venere comunicasse il lume alla Luna, benchè non nel tempo degli Ecclissi <lb></lb>ma circa i Plenilunii, e mi faccia grazia di dirmene il suo parere ” (MSS. <lb></lb>Gal., P. III, T. VII, c. </s>

<s>184). </s></p><p type="main">

<s>E giacchè non era punto conforme al genio di Galileo, per dire un suo <lb></lb>parere, andare alla scuola, alla quale lo consigliava il Renieri, ed è inutile per­<lb></lb>ciò attenderne la risposta; giova qui, delle involte e sparse idee, soffermarci <lb></lb>a enodare e compilare le fila. </s>

<s>Il Benedetti, a colorir la Luna ecclissata, aveva <lb></lb>fatto concorrere insieme due cause: i raggi del Sole rifratti nell&#039;ammosfera <lb></lb>terrestre, e gli splendori di Venere, i quali mancando (per non esser sem­<lb></lb>pre il Pianeta collocato in luogo opportuno, e per non aver le rifrazioni <lb></lb>tanta virtù da sè sole) facevan sì che invisibile si rendesse talvolta nell&#039;om­<lb></lb>bra lo stesso rubicondo cerchio lunare. </s></p><p type="main">

<s>Il Keplero, dall&#039;altra parte, considerando essere il lume di Venere e <lb></lb>delle stelle circostanti al Sole sempre eguale, e che perciò, contrariamente <lb></lb>alle osservazioni, avrebbe dovuto tinger la faccia della Luna sempre ugual­<lb></lb>mente, ridusse tutta l&#039;efficienza alla causa unica delle rifrazioni. </s>

<s>Ma perchè <lb></lb>queste, che sempre operano, non davan facile modo a spiegar come talvolta <lb></lb>la Luna sparisca affatto nell&#039;ombra, Galileo le escluse, chiamando, invece di <lb></lb>esse, a soccorrer la virtù di Venere, Giove e altre stelle, fra le quali il Cane <lb></lb>maggiore. </s>

<s>Implicava però questa ipotesi maggiormente nella difficoltà, che <lb></lb>cioè si sarebbe dovuta sempre d&#039;ugual colore veder tinta la faccia alla Luna; <lb></lb>difficoltà sentita dal Renieri sì forte, che lo fece tacitamente confessar la <lb></lb>cosa rimaner tuttavia involta in un gran mistero. </s></p><p type="main">

<s>I più sinceri non dubitarono di far questa medesima confessione, ma <lb></lb>perchè non è della dignità del Filosofo il dir di non sapere, per dir dun­<lb></lb>que qualche cosa, attribuivasi alle rifrazioni il color rosso nella Luna adom­<lb></lb>brata. </s>

<s>Dall&#039;altra parte il totale sperimento di lei era stato osservato da pochi, <lb></lb>e que&#039;pochi non avevano grande autorità nella scienza, potendosi dubitare <lb></lb>che avessero occhi infermi o strumenti imperfetti. </s>

<s>Così rimaneva, a tolle­<lb></lb>rato e precario servigio dell&#039;Astronomia, l&#039;ipotesi kepleriana, quando l&#039;ac­<lb></lb>cusa di falsa e d&#039;inetta venutale dall&#039;autorità concorde della scienza specu­<lb></lb>lativa e della pratica, fece sì che fosse con più severo decreto licenziata. </s></p><p type="main">

<s>L&#039;accusa di falsa si derivò dai principii dell&#039;Ottica, conforme ai quali, <pb xlink:href="020/01/967.jpg" pagenum="410"></pb>e secondo quel che si contò addietro nel cap. </s>

<s>I, un raggio di luce non si <lb></lb>ritorce, per descriver la parabola neutoniana nel mezzo rifrangente, se non <lb></lb>che quando gli strati di quello stesso mezzo scemino in densità dall&#039;alto al <lb></lb>basso. </s>

<s>“ Intempestiva est enim (disse il Vossio che fu primo a promuovere <lb></lb>quell&#039;accusa) ratio Kepleri, eorumque qui illum secuti sunt, qui putant ru­<lb></lb>borem seu dilutiorem umbram, quae in Lunae apparet deliquis, effici a ra­<lb></lb>diis in hoc nostro aere refractis. </s>

<s>Fieri enim minime posse ut ulli Solis radii <lb></lb>hunc nostrum aerem ingrediantur, et vicissim exeant, iam ante complures <lb></lb>annos, monuimus. </s>

<s>Cum enim omnis refractio fiat a rariori ad densius, et <lb></lb>aer terris vicinus densior sit illo superiore, necesse est, ut quotquot radii <lb></lb>aerem ingrediuntur, in terram impingentes deficiant ” (De Nili orig. </s>

<s>Ap­<lb></lb>pendix, Hagae Com. </s>

<s>1666, pag. </s>

<s>143). </s></p><p type="main">

<s>L&#039;accusa d&#039;insufficiente a spiegare il fatto venne all&#039;ipotesi kepleriana, <lb></lb>non da osservazioni incerte o da osservatori inesperti, ma da uno de&#039;più <lb></lb>valorosi, e perciò de&#039;più autorevoli Astronomi italiani del secolo XVII. </s>

<s>Gian <lb></lb>Alfonso Borelli, avendo osservato il dì 11 Gennaio 1675 l&#039;ecclisse di tutta <lb></lb>la Luna, il mezzo della quale avvenne in Roma a ore 8, 2′, 56″, e aven­<lb></lb>done minutamente descritte le fasi, per rimetterle al cardinale Leopoldo <lb></lb>de&#039;Medici, principe della sperimentale Accademia fiorentina, nelle Memorie <lb></lb>della quale furono inserite a carte 61 e 62 del Tomo XXV; ebbe a notare <lb></lb>due circostanze non osservate altra volta da lui. </s>

<s>“ Dopo quella rara nebbia, <lb></lb>egli dice, in faccia della Luna, la qual suol precedere l&#039;Ecclissi, comparve <lb></lb>il confine dell&#039;ombra terrena nella faccia lunare, non sfumato e tanto con­<lb></lb>fuso com&#039;è solito, ma così terminato, che distintamente si discernevano i <lb></lb>contatti di tal cerchio terminatore dell&#039;ombra, e delle circoferenze delle mac­<lb></lb>chie lunari, tanto che si potè notare il contatto della Macchia Gassendo, <lb></lb>presso il Riccioli, occorso, essendo alto il destro umero di Orione dal ver­<lb></lb>tice 58°, 46′, 25″, e così altre Macchie. </s>

<s>” </s></p><p type="main">

<s>“ Di più osservai che la parte intorno al mezzo dell&#039;ombra terrestre <lb></lb>era così oscura e tenebrosa, che dopo la totale immersione il termine orien­<lb></lb>tale della Luna non si discerneva, anzi pareva scantonato, e così anche si <lb></lb>vide prima di uscire dall&#039;ombra dalla parte occidentale, e quando fu nel <lb></lb>mezzo dell&#039;ombra, comparve intorno al centro del disco lunare una vasta <lb></lb>macchia più oscura del resto, e questo occorse essendo l&#039;aria pura ed af­<lb></lb>fatto serena spazzata dalla Tramontana. </s>

<s>E perchè tal cosa repugna alle os­<lb></lb>servazioni passate ed alla ricevuta dottrina del Keplero, mi pare che meriti <lb></lb>particolar riflessione per intenderne la causa ” (MSS. Cim., T. XXV, c. </s>

<s>60). </s></p><p type="main">

<s>La causa non fu intesa però se non che quando il Maraldi, facendo partico­<lb></lb>lari esperienze sull&#039;ombre, delle quali si rese conto addietro nel § IV del cap. </s>

<s>I, <lb></lb>non dimostrò che la Luna si rende visibile perchè si trova per lo più im­<lb></lb>a mers nella penombra, e talvolta anche sparisce o tutta o parte, perchè <lb></lb>s&#039;immerge nell&#039;ombra assoluta, la quale mostrò che di fatto non risponde <lb></lb>punto, in larghezza e in lunghezza, alle precise regole della nostra Geometria. </s></p><pb xlink:href="020/01/968.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO XI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Di Giove<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della scoperta de&#039;quattro Pianeti medicei; de&#039;metodi usati da Galileo per definirne i tempi pe­<lb></lb>riodici e le massimo digressioni. </s>

<s>— II. </s>

<s>Degli studii intorno al Sistema gioviale proseguiti dal <lb></lb>Castelli, dal Renieri e dall&#039;Hodierna. </s>

<s>— III. </s>

<s>Di ciò che a perfezionare le osservazioni, e a di­<lb></lb>mostrare le teoriche de&#039;Medicei, cooperarono il Montanari e il Borelli, il Viviani e il Cassini. <lb></lb></s>

<s>— IV. Dell&#039;aspetto di Giove, e della fisica costituzione di lui. </s>

<s>— V. </s>

<s>Del problema delle Longi­<lb></lb>tudini e della particolar soluzione di lui per mezzo delle Effemeridi gioviali. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Sceso in terra ad annunziare ai mortali ciò che, sollevato dal suo ma­<lb></lb>raviglioso strumento, giunse Galileo a veder di stupendo nella visita delle <lb></lb>varie corti celesti, dop&#039;aver narrato quel che di nuovo ritrovò nella Luna, <lb></lb>sotto l&#039;aperto candido padiglione, e in Galassia, che distende in mezzo al <lb></lb>firmamento la sua argentea benda trapunta d&#039;innumerevoli stelle; e dopo <lb></lb>aver data una descrizione più precisa e più compiuta di varie Costellazioni, <lb></lb>rivelò “ quod maximum in praesenti negotio existimandum videtur ” quat­<lb></lb>tro lucide scorte, che s&#039;eran prima tenute ad ogni vista occulte e che sta­<lb></lb>vano in assidua faccenda intorno al trono di Giove. </s></p><p type="main">

<s>Il principio della memoranda osservazione occorse a Galileo nella prima <lb></lb>ora della notte seguente al di 7 Gennaio 1610, nel qual tempo vide tre più <lb></lb>piccole stelle stare intorno al disco di Giove, due dalla parte orientale, e <lb></lb>una ad occidente. </s>

<s>La notte consecutiva al di 8, tornando ad osservare, trovò <lb></lb>che tutt&#039;e tre le stelle rimanevano dalla parte occidentale del Pianeta, e due <lb></lb>notti dopo eran passate all&#039;occidente, ma la terza, che più non si vedeva, <lb></lb>pensò che dòvess&#039;esser rimasta occulta dietro il disco gioviale. </s>

<s>“ Die decima <pb xlink:href="020/01/969.jpg" pagenum="412"></pb>apparuerunt stellae in eiusmodi ad Jovem positu: duae enim, et orientales <lb></lb>ambae aderant: tertia, ut opinatus fui, sub Jove latitante ” (Alb. </s>

<s>III, 78). </s></p><p type="main">

<s>Credette a principio Galileo che tali variazioni di posizione dipendes­<lb></lb>sero da Giove, ma poi si accorse esser le stesse stelle che si movevano <lb></lb>intorno a lui; ond&#039;è che, sentendosi più vivamente che mai frugato dalla <lb></lb>curiosità di osservare, trovò che invece di tre erano quattro stelle “ vagan­<lb></lb>tes circa Jovem instar Veneris atque Mercurii circa Solem ” (ibi). </s></p><p type="main">

<s>Le varie costituzioni di esse stelle, rispetto al centro di Giove, furono <lb></lb>da Galileo diligentemente osservate per molte notti consecutive, e infino al <lb></lb>18 Aprile descritte nel Nunzio Sidereo. </s>

<s>Quella descrizione però fu elabo­<lb></lb>rata, per dare alle stampe, sopra gli appunti presi a mente fresca sera per <lb></lb>sera, i quali, essendo rimasti ne&#039;Manoscritti galileiani, giovano molto a ri­<lb></lb>velarci in quella loro semplice e negletta veste le prime e più vive e vere <lb></lb>impressioni dell&#039;Osservatore. </s>

<s>Oltre a ciò si trovano alcuni minuti partico­<lb></lb>lari trascurati nel <emph type="italics"></emph>Nunzio,<emph.end type="italics"></emph.end> e gl&#039;iconismi originali rispondono, molto meglio <lb></lb>degli artefatti da una e altra mano, alla verità delle cose rappresentandole <lb></lb>tali quali furono osservate. </s></p><p type="main">

<s>Pare una minuzia, ma è pure di qualche importanza la nota, che si <lb></lb>legge inserita fra queste Effemeridi manoscritte, e con la quale prescriveva <lb></lb>Galileo all&#039;artista il modo di riportare fedelmente in disegno quel che avea <lb></lb>veduto con gli occhi. </s>

<s>“ Farannosi, dice delle figure quella Nota, intagliare <lb></lb>in legno tutto d&#039;un pezzo, e le stelle bianche e il resto nero: poi si seghe­<lb></lb>ranno i pezzi ” (MSS. Gal., P. III, T. III, c. </s>

<s>30, a tergo). Noi ossequiosi a <lb></lb>una tal prescrizione diamo di quelle galileiane Effemeridi manoscritte, e che <lb></lb>si potrebbero utilmente collazionare con <lb></lb>le stampate nel <emph type="italics"></emph>Nunzio Sidereo,<emph.end type="italics"></emph.end> que­<lb></lb>sto poco di Saggio ai nostri Lettori: </s></p><p type="main">

<s>“ A&#039;dì 7 di Gennaio 1610 Giove <lb></lb>si vedeva col Cannone con tre stèlle <lb></lb>fisse così: <lb></lb><figure id="id.020.01.969.1.jpg" xlink:href="020/01/969/1.jpg"></figure><lb></lb>delle quali senza il Cannone niuna si vedeva (fig. </s>

<s>70). ” </s></p><p type="main">

<s>“ A&#039;dì 8 appariva così: <lb></lb><figure id="id.020.01.969.2.jpg" xlink:href="020/01/969/2.jpg"></figure><lb></lb>Era dunque diritto e <lb></lb>non retrogrado, co­<lb></lb>me pongono i cal­<lb></lb>colatori (fig. </s>

<s>71). ” </s></p><p type="main">

<s>“ A&#039;dì 9 fu nuvolo. </s>

<s>” </s></p><p type="main">

<s>“ A&#039;dì 10 <lb></lb>si vedeva così: <lb></lb><figure id="id.020.01.969.3.jpg" xlink:href="020/01/969/3.jpg"></figure><lb></lb>cioè congiunto con la più occi­<lb></lb>dentale, sicchè si occultava per <lb></lb>quanto si può credere (fig. </s>

<s>72). ” </s></p><pb xlink:href="020/01/970.jpg" pagenum="413"></pb><p type="main">

<s>“ A&#039;dì 11 era <lb></lb>in questa guisa: <lb></lb><figure id="id.020.01.970.1.jpg" xlink:href="020/01/970/1.jpg"></figure><lb></lb>(fig. </s>

<s>73) e la stella più vicina <lb></lb>a Giove era la metà minore <lb></lb>dell&#039;altra e vicinissima all&#039;al­<lb></lb>tra, dovecchè le altre sere erano <lb></lb>le dette stelle apparite tutt&#039;e <lb></lb>tre di ugual grandezza, e tre <lb></lb>di loro ugualmente lontane. </s>

<s>Dal che appare intorno a Giove esser tre altre <lb></lb>stelle erranti invisibili ad ognune sino a questo tempo. </s>

<s>” </s></p><p type="main">

<s>“ A&#039;dì 12 si <lb></lb>vedde in tale co­<lb></lb>stituzione: <lb></lb><figure id="id.020.01.970.2.jpg" xlink:href="020/01/970/2.jpg"></figure><lb></lb>Era la stella occidentale poco <lb></lb>minore della orientale e Giove <lb></lb>era in mezzo lontano dall&#039;una <lb></lb>e dall&#039;altra quanto il suo dia­<lb></lb>metro in circa, e forse era una <lb></lb>terza piccolissima e vicinissima <lb></lb>a Giove verso oriente (fig. </s>

<s>74). Anzi pur v&#039;era veramente, avendo io con <lb></lb>più diligenza osservato, ed essendo più imbrunita la notte. </s>

<s>” </s></p><p type="main">

<s>“ A&#039;dì 13, avendo benissimo fermato lo strumento, si veddono vicinis­<lb></lb>sime a Giove quattro stelle in questa costituzione: <lb></lb><figure id="id.020.01.970.3.jpg" xlink:href="020/01/970/3.jpg"></figure><lb></lb>(fig. </s>

<s>75) o meglio così: <lb></lb><figure id="id.020.01.970.4.jpg" xlink:href="020/01/970/4.jpg"></figure><lb></lb>(fig. </s>

<s>76) e tutte apparivano della medesima grandezza. </s>

<s>Lo spazio delle tre <lb></lb>occidentali non era maggiore del diametro di Giove, ed erano fra di loro <lb></lb>notabilmente più vicine che le altre sere, nè erano in linea retta esquisita­<lb></lb>mente come per l&#039;avanti, ma la media delle tre occidentali era un poco ele­<lb></lb>vata, ovvero la più occidentale alquanto depressa. </s>

<s>Sono queste stelle tutte <lb></lb>molto lucide, benchè piccolissime, ed altre fisse che appariscono della me­<lb></lb>desima grandezza non sono così splendenti. </s>

<s>” </s></p><p type="main">

<s>“ Aì di 14 fu nugolo. </s>

<s>” </s></p><p type="main">

<s>“ A&#039;dì 15 <lb></lb>era così: <lb></lb><figure id="id.020.01.970.5.jpg" xlink:href="020/01/970/5.jpg"></figure><lb></lb>La prossima a Giove era <lb></lb>la minore e le altre di <lb></lb>mano in mano maggiori <lb></lb>(fig. </s>

<s>77). Gl&#039;interstizi tra <lb></lb>Giove e le tre seguenti <lb></lb>erano ciascheduno quan­<lb></lb>to il diametro di Giove, ma la quarta era distante dalla terza il doppio in <lb></lb>circa. </s>

<s>Non facevano interamente linea retta, ma come mostra l&#039;esempio. </s>

<s><lb></lb>Erano al solito lucidissime benchè piccole e niente scintillavano com&#039;anco <lb></lb>per l&#039;innanzi ” (ivi). </s></p><p type="main">

<s>A questo punto l&#039;avventurato Osservatore sentì che l&#039;importanza della <lb></lb>sua scoperta avrebbe di grande ammirazione commosso il mondo, a cui do-<pb xlink:href="020/01/971.jpg" pagenum="414"></pb>vendo annunziarla conveniva usare altro linguaggio. </s>

<s>Perciò incomincia a <lb></lb>stendere così le sue note in latino: “ Fuit praecedens constitutio hora noc­<lb></lb>tis tertia. </s>

<s>Sed­<lb></lb>hora septima <lb></lb>tres tantum a­<lb></lb>derant stellu­<lb></lb>lae cum Jove, <lb></lb>in taliadspectu <lb></lb><figure id="id.020.01.971.1.jpg" xlink:href="020/01/971/1.jpg"></figure><lb></lb>Minima erat Jovi vici­<lb></lb>nior, parva, reliquae 2 <lb></lb>maiores duplo et inter <lb></lb>se aequales. </s>

<s>Distantia <lb></lb>a Jove ad proximam <lb></lb>aucta erat: ipsa vicinior <lb></lb>erat secundae, nempe per dimidium diametri Jovis. </s>

<s>Tertia distabat a se­<lb></lb>cunda, paulo plus quam ipsa secunda a Jove. </s>

<s>Post vero aliam horam 2 me­<lb></lb>diae stellulae erant adhuc viciniores, (fig. </s>

<s>78) adeo ut inter ipsas spacium <lb></lb>mediaret ipsa minima stella minus, scilicet circa minuta secunda 40. ” </s></p><p type="main">

<s>“ Die 16, hora <lb></lb>prima noctis talis <lb></lb>fuit constitutio, <lb></lb><figure id="id.020.01.971.2.jpg" xlink:href="020/01/971/2.jpg"></figure><lb></lb>tres enim tantum cernebantur <lb></lb>stellulae: duae Jovi proximae <lb></lb>per quartam nempe diametri <lb></lb>ipsius partem ab eo utrimque <lb></lb>distantes scrup. </s>

<s>1. Tertia vero <lb></lb>occidentalis per quadruplum <lb></lb>diametri ipsius ab illo aberat (fig. </s>

<s>79). Proximae Jovi non maiores appa­<lb></lb>rebant remotiori sed lucidiores ” (ivi, a tergo). </s></p><p type="main">

<s>Così procede questa prima forma di Effemeride latina infino a tutto il <lb></lb>18 Aprile, come nel Nunzio Sidereo, dove dalle molteplici osservazioni ne <lb></lb>conclude Galileo le seguenti importantissime notizie: “ Ac primo cum Jo­<lb></lb>vem consimilibus interstitiis modo consequantur, modo praeeant, ab eoque <lb></lb>tum versus ortum, tum in occasum angustissimis tantum divaricationibus <lb></lb>elongentur, cundemque retrogradum pariter atque directum concomitentur; <lb></lb>quin circa illum suas conficiant conversiones, interea dum circa Mundi cen­<lb></lb>trum omnes una duodecennales periodos absolvunt, nemini dubium esse po­<lb></lb>test. </s>

<s>Convertuntur insuper in circulis inaequalibus, quod manifeste colligi­<lb></lb>tur ex eo, quia in maioribus a Jove digressionibus nunquam binos Planetas <lb></lb>iunctos videre licuit, cum tamen prope Jovem duo, tres et inerdum omnes <lb></lb>simul constipati reperti sunt. </s>

<s>Deprehenditur insuper velociores esse conver­<lb></lb>siones Planetarum angustiores circa Jovem circulos describentium; propin­<lb></lb>quiores enim Jovi stellae saepius spectantur orientales, cum pridie ex occasu <lb></lb>apparuerint, et e contra ” (Alb. </s>

<s>III, 97, 98). </s></p><p type="main">

<s>Aveva insomma Galileo raccolto da quelle sue prime osservazioni che <lb></lb>le nuove stelle scoperte si volgevano intorno a Giove in orbite di varie gran­<lb></lb>dezze, e che sopra le maggiori andavano via via meno veloci. </s>

<s>A coronare <lb></lb>perciò il merito della scoperta, e a ridurla a opera di vera scienza astrono­<lb></lb>mica, ben comprese che conveniva definir di ciascuna stella i tempi perio­<lb></lb>dici, e ritrovar le giuste misure delle loro massime digressioni. </s>

<s>Di qui è che <lb></lb>in render pubblicamente note, nell&#039;Avviso Sidereo, le sue Effemeridi, faceva <lb></lb>appello agli Astronomi “ ut ad illorum periodos inquirendas, atque definien­<lb></lb>das se conferant, quod nobis in hanc usque diem, ob temporis angustiam, <pb xlink:href="020/01/972.jpg" pagenum="415"></pb>assequi minime licuit ” (ivi, pag. </s>

<s>77). Nonostante avendo accuratamente no­<lb></lb>tato, in mezzo a queste prime osservazioni, in quanto tempo il Pianetino più <lb></lb>esterno ritornava a un medesimo punto dell&#039;orbita, gli parve che fosse in <lb></lb>circa a quattordici giorni. </s>

<s>“ At Planeta maximum permeans orbem, accurate <lb></lb>praeadnotatas reversiones perpendenti, restitutiones semimenstruas habere <lb></lb>videtur ” (ivi, pag. </s>

<s>98). </s></p><p type="main">

<s>Dal di 18 di Aprile in poi non proseguì Galileo le sue osservazioni gio­<lb></lb>viali con quella prima regolarità, ma attendeva di gran proposito a ciò che <lb></lb>era più d&#039;ogni altra cosa importante, a investigar cioè i periodi più precisi <lb></lb>dei quattro nuovi Pianeti “ materia, scriveva il dì 7 Maggio 1610 a Belisario <lb></lb>Vinta, quanto più vi penso, tanto più laboriosa, per il non si dissipar mai <lb></lb>se non per brevi intervalli l&#039;uno dall&#039;altro, e per esser questi, e di colore <lb></lb>e di grandezza, molto simili ” (Alb. </s>

<s>VI, 98). Il più esterno però, essendo il <lb></lb>più tardo, dava il modo più facile degli altri, e perciò ne ritrovò poco dopo <lb></lb>il periodo alquanto più preciso di quello primo assegnato scrivendo che “ fa <lb></lb>il suo cerchio in quindici giorni circa ” (ivi, 102). </s></p><p type="main">

<s>A mezzo Settembre, avendo <emph type="italics"></emph>perfezionato un poco più il suo strumento<emph.end type="italics"></emph.end><lb></lb>(ivi, 121) vedeva Giove e la sua corte assai più lucidi e distintì, ciò che <lb></lb>venne a incorargli una più ferma speranza “ di definire i periodi dei quat­<lb></lb>tro Pianeti medicei, stimati con gran ragione quasi inesplicabili al signor <lb></lb>Keplero ” (ivi, 128) tanto più ch&#039;essendosi allora volto a cercare un me­<lb></lb>todo, scriveva ivi a don Giuliano de&#039;Medici che sperava di averlo trovato. </s>

<s><lb></lb>Ond&#039;è che alla fine di questo anno 1610 concludeva al Castelli che il de­<lb></lb>finir i periodi di tutti quattro i Satelliti di Giove, se glielo avesse concesso <lb></lb>la salute, sarebbe stato tra breve (ivi, 136). </s></p><p type="main">

<s>Nel Febbraio però dell&#039;anno seguente (ivi, 145) e anche a&#039;principii di <lb></lb>Aprile, i periodi de&#039;quattro gioviali si trovavano tuttavia chiusi dentro i fiori <lb></lb>della speranza “ confidando in Dio Benedetto (così Galileo da Roma scriveva al <lb></lb>Vinta) che siccome mi ha fatto grazia di essere stato solo a scoprire tante <lb></lb>nuove maraviglie della sua mano; così sia per concedermi che io abbia a <lb></lb>ritrovare l&#039;ordine assoluto dei loro rivolgimenti, e forse al mio ritorno avrò <lb></lb>ridotto questa mia fatica veramente atlantica a segno di poter predire i siti <lb></lb>e le disposizioni che essi nuovi Pianeti siano per avere in ogni tempo fu­<lb></lb>turo, e abbiano anche avuto in ciascun tempo passato ” (ivi, 156, 57). </s></p><p type="main">

<s>Da queste parole siamo fatti accorti che il metodo, di che dianzi par­<lb></lb>lavasi da Galileo, consisteva nel dividere i gradi di più conversioni fatte nel <lb></lb>tempo di due delle più certe osservazioni per il numero dell&#039;ore impiegato, <lb></lb>d&#039;onde veniva a resultarne il moto medio orario, e da ciò il particolar pe­<lb></lb>riodo più assoluto di quel che non si potesse ottenere, misurando il tempo <lb></lb>passato in una conversione tra il muovere e il ritornare al medesimo punto <lb></lb>dell&#039;orbita. </s></p><p type="main">

<s>Con questo metodo, i processi del quale si posson veder pubblicati dal­<lb></lb>l&#039;Albèri (V, 10, 11), le speranze che al principiar dell&#039;Aprile erano in sul <lb></lb>fiorire, avevano verso la fine del mese allegato in frutto. </s>

<s>I primi indugi che <pb xlink:href="020/01/973.jpg" pagenum="416"></pb>si potevano attribuire alla sola difficoltà della cosa, Galileo gli attribuisce <lb></lb>invece all&#039;avere atteso allo scoprimento di Saturno tricorporeo, e di Venere <lb></lb>mutabile come la Luna, e ciò solo fu che lo distrasse dall&#039;investigazion dei <lb></lb>tempi delle conversioni di ciaschedun de&#039;quattro Pianeti medicei intorno a <lb></lb>Giove, “ la quale investigazione (dice lo stesso Galileo in principio del Di­<lb></lb>scorso intorno alle cose che stanno in sull&#039;acqua) mi succedette l&#039;Aprile <lb></lb>dell&#039;anno passato 1611, mentre ero in Roma, dove finalmente m&#039;accertai <lb></lb>che il primo e più vicino a Giove passa del suo cerchio gradi 8 e m. </s>

<s>29 in <lb></lb>circa per ora, facendo la intera conversione in giorni naturali 1 e ore 18 e <lb></lb>quasi mezza. </s>

<s>Il secondo fa nell&#039;orbe suo gr. </s>

<s>4, m. </s>

<s>13 prossimamente per <lb></lb>ora, e l&#039;intera revoluzione in giorni 3, ore 13 e un terzo in circa. </s>

<s>Il terzo <lb></lb>passa in un&#039;ora gr. </s>

<s>2, m. </s>

<s>6, in circa, del suo cerchio e lo misura tutto in <lb></lb>giorni 7 e ore quattro prossimamente. </s>

<s>Il quarto, e più lontano degli altri, <lb></lb>passa in ciaschedun&#039;ora gr. </s>

<s>0, m. </s>

<s>54 e quasi mezzo del suo cerchio, e lo <lb></lb>finisce tutto in giorni 16 e ore 18 prossimamente ” (Alb. </s>

<s>XII, 9, 10). </s></p><p type="main">

<s>In quel medesimo mese di Aprile 1611 il Keplero, che aveva prima <lb></lb>stimato la cosa tanto difficile, anzi quasi impossibile, messosi, dietro l&#039;esem­<lb></lb>pio di Galileo, all&#039;opera, riuscì con gran fatica a ritrovare il periodo di quella <lb></lb>seconda Luna gioviale, ch&#039;è prossima alla tardissima “ sed maxime omnium <lb></lb>conspicua ” la quale egli trovò avere le sue restituzioni “ spacio dierum <lb></lb>octo ” (Dioptrice, Augustae Vindelic 1611, pag. </s>

<s>14). Quanto alle rimanenti <lb></lb>due non sa dir altro, se non ch&#039;elle debbono percorrere le loro orbite in <lb></lb>tempi anche più brevi, e ciò in conseguenza e in conformità delle leggi dei <lb></lb>moti rotatorii. </s></p><p type="main">

<s>Fatta tutta intera la scoperta, la quale non era al Keplero riuscita che <lb></lb>a mezzo, Galileo ne diffuse tra gli amici compiacentissimo la notizia, e l&#039;An­<lb></lb>tonini rispondendogli da Bruxelles se ne congratulava e stupiva sopra la <lb></lb>grandezza dell&#039;invenzione “ tanto più, egli dice, ch&#039;ero anch&#039;io di quelli che <lb></lb>ciò stimavano cosa impossibile ” (Alb. </s>

<s>VIII, 151). </s></p><p type="main">

<s>Un altro di cotesti amici, a cui aveva in Roma partecipato ne&#039;familiari <lb></lb>colloqui la bella notizia, fu Giovan Batista Agucchia, il quale essendo stato <lb></lb>pregato, alquanti mesi dopo, da un Signore di fargli un&#039;<emph type="italics"></emph>Impresa<emph.end type="italics"></emph.end> di cose <lb></lb>celesti, com&#039;aveva pensato di pigliare da un Autore gravissimo il <emph type="italics"></emph>motto,<emph.end type="italics"></emph.end> così <lb></lb>aveva, dalla scoperta di Galileo, pensato di pigliare il <emph type="italics"></emph>corpo.<emph.end type="italics"></emph.end> Voleva inoltre <lb></lb>quel Signore che fosse l&#039;Impresa illustrata da un Discorso, il quale “ poi­<lb></lb>chè, scriveva a Galileo lo stesso Agucchia, si dee presentare ad un&#039;Accade­<lb></lb>mia fuori di Roma, io vorrei, con più sicurezza di quel che la memoria mi <lb></lb>dà, poterne formare la figura, ed esprimere la grandezza degli orbi che (i sa­<lb></lb>telliti) girano. </s>

<s>Perciocchè mi mostrò ben V. S. cortesemente la figura di <lb></lb>quelli e dissemi ancora i minuti del loro diametro, ma come che io possa <lb></lb>da vicino figurare gli orbi, non mi sovviene però quasi punto della misura <lb></lb>di essi. </s>

<s>Pertanto io la prego a favorirmi di significarlami più particolar­<lb></lb>mente, ed aggiungervi oltre a ciò in quanto spazio di tempo ciascuna stella <lb></lb>compia suo orbe ” (ivi, 168). </s></p><pb xlink:href="020/01/974.jpg" pagenum="417"></pb><p type="main">

<s>Galileo, per quel suo solito timore di non avere a scorbiare i suoi parti <lb></lb>prima di averli dati alla luce, non rispose con gran chiarezza, per cui l&#039;Aguc­<lb></lb>chia pensò di andarci col suo proprio ingegno. </s>

<s>Dai colloqui tenuti in Roma <lb></lb>aveva appreso il metodo de&#039;moti medii, i quali egli concluse dall&#039;Effemeridi <lb></lb>che trovò scritte nel Nunzio Sidereo, e così, dietro a qualche altro barlume, <lb></lb>riusci a definir da sè i tempi de&#039;moti periodici di tutt&#039;e quattro le Medi­<lb></lb>cee con pochissima differenza da&#039;tempi stessi trovati da Galileo. </s></p><p type="main">

<s>“ Perciò avendole io riconosciute e distinte tutte quante ad una ad una, <lb></lb>ho raccolto che la Prima della sfera più piccola, la quale non pare che si <lb></lb>allontani mai più di m. </s>

<s>2, sec. </s>

<s>40 da Giove, fa suo giro in spazio di un <lb></lb>giorno, e ore diciotto e un terzo o poco più, parendomi che, in giorni sette <lb></lb>e ore una e mezza, ella il compia quattro volte con piccola differenza dal <lb></lb>più al meno. </s>

<s>E la Seconda mi mostra che il faccia in giorni tre e ore quin­<lb></lb>dici, due volte girandolo in giorni sette e un quarto o poco manco. </s>

<s>Della <lb></lb>Terza poi, la quale in quel tempo non diede segno di discostarsi più di mi­<lb></lb>nuti otto da Giove, ho stimato che sia il periodo giorni sette e ore quattro <lb></lb>in circa, sicchè ella vi spenda quasi il doppio del tempo, che v&#039;impiega la <lb></lb>Seconda, e però, ad ogni sette giorni ed ore quattro o poco più, si con­<lb></lb>giungano particolarmente insieme. </s>

<s>L&#039;Ultima finalmente mi sembra che si <lb></lb>rivolga intorno all&#039;Orbe in giorni sedici e ore venti ” (ivi, 174, 75). </s></p><p type="main">

<s>Sopra questi elementi del Sistema gioviale disegnò l&#039;Agucchia l&#039;<emph type="italics"></emph>Im­<lb></lb>presa,<emph.end type="italics"></emph.end> ch&#039;egli illustrò veramente, come n&#039;era stato richiesto, con un Di­<lb></lb>scorso accademico intitolato <emph type="italics"></emph>Del mezzo,<emph.end type="italics"></emph.end> che incomincia con la terzina dan­<lb></lb>tesca <emph type="italics"></emph>Nel mezzo del cammin di nostra vita<emph.end type="italics"></emph.end> ecc., e termina col disegno di <lb></lb>Giove collocato in mezzo alle orbite delle sue quattro Lune, scrittovi in giro <lb></lb>il motto <emph type="italics"></emph>Medii cupidine victae.<emph.end type="italics"></emph.end> Una copia di questo Discorso fu dall&#039;Au­<lb></lb>tore mandata a Galileo e doveva esser perciò raccolta fra le carte mano­<lb></lb>scritte di lui, ma i collettori, forse per inavvertenza, inserirono la scrittura <lb></lb>del monsignor di Roma fra le carte manoscritte dei <emph type="italics"></emph>Discepoli,<emph.end type="italics"></emph.end> dove ancora <lb></lb>si trova da c. </s>

<s>95-110 del Tomo CXXXVI. </s></p><p type="main">

<s>Aveva l&#039;Agucchia in quelle sue notabili osservazioni trovato, oltre ai <lb></lb>periodi, le massime distanze angolari dal centro di Giove per i tre più pros­<lb></lb>simi Pianeti, distanze ch&#039;egli certamente misurò col metodo insegnato da <lb></lb>Galileo nelle prime pagine del Nunzio Sidereo. </s>

<s>Questo era allora l&#039;unico <lb></lb>modo micrometrico conosciuto, e Galileo stesso, per mezzo de&#039;fori più o men <lb></lb>largamente aperti in una lamina sottile, accomodata alla lente obiettiva del <lb></lb>Telescopio, misurava gl&#039;interstizii fra una luna gioviale e un&#039;altra. </s>

<s>“ Inter­<lb></lb>stitia quoque inter ipsa, per Perspicillum, superius explicata ratione, dime­<lb></lb>titus sum ” (Alb. </s>

<s>III, 78). </s></p><p type="main">

<s>Quelle misure angolari però non riuscivano assolute, se non che nella <lb></lb>grandezza definita del raggio, ch&#039;è naturalmente la distanza da noi a Giove. </s>

<s><lb></lb>Così tornava possibile il determinar l&#039;apparente grandezza del Pianeta a cui, <lb></lb>come a unità, riferire i varii interstizii fra stellina e stellina, e le misure <lb></lb>delle loro massime digressioni. </s></p><pb xlink:href="020/01/975.jpg" pagenum="418"></pb><p type="main">

<s>Nelle ricerche laboriose di così fatti elementi fu questo propriamente il <lb></lb>processo tenuto da Galileo, del qual processo abbiam l&#039;esempio in una Nota <lb></lb>pubblicata dall&#039;Albèri, dove le misure del diametro di Giove si desumono <lb></lb>così variamente da due varie osservazioni: Supposto che AB (fig. </s>

<s>80) rap­<lb></lb>presenti il diametro di Giove, e CL il diametro del foro della lamina adat­<lb></lb>tata per l&#039;una delle osservazioni, ch&#039;è del 21 Gennaio 1612, Galileo trovava <lb></lb><figure id="id.020.01.975.1.jpg" xlink:href="020/01/975/1.jpg"></figure></s></p><p type="caption">

<s>Figura 80.<lb></lb>che tra il diametro del Foro e la lun­<lb></lb>ghezza dell&#039;asse del Canocchiale pas­<lb></lb>sava la relazione di 1 a 275: trovava, <lb></lb>per l&#039;altra osservazione del dì 9 Giu­<lb></lb>gno, essere quella proporzione invece <lb></lb>di 1 a 291. Queste stesse proporzioni <lb></lb>poi, per la similitudine de&#039;triangoli, <lb></lb>esiston pure tra AB, diametro di Giove, <lb></lb>e GE o AE o BE, che tutt&#039;e tre si possono senza errore tener per eguali <lb></lb>e misuratrici della distanza del Pianeta da noi. </s>

<s>Perciò l&#039;angolo AEB s&#039;ha <lb></lb>dalla risoluzione del triangolo AEB, in cui son noti gli elementi a ciò ne­<lb></lb>cessarii. </s>

<s>“ Quia vero (inteso ciò, dice Galileo) Telescopium lineas multipli­<lb></lb>cat in rationem 18:1, fuit in prima observatione ratio distantiae a Terra <lb></lb>ad diametrum Stellae ut 4950:1; in altera vero ut 3238 ad 1. Reperitur ergo <lb></lb>per Tabulas sinium Jovis diametrum in prima observatione angul. </s>

<s>gr. </s>

<s>0°, 0′, <lb></lb>41″, 37tʹ in secunda vero subtendisse gr. </s>

<s>0°, 0′, 39″, 24tʹ (Alb. </s>

<s>V. 176). </s></p><p type="main">

<s>Trovato così il diametro di Giove, riduceva Galileo facilmente le distanze <lb></lb>angolari delle massime digressioni, misurate per mezzo della lamina micro­<lb></lb>metrica applicata al Canocchiale, in distanze lineari riferite allo stesso diame­<lb></lb>tro gioviale. </s>

<s>Così ad esempio, per il Pianeta più esterno, dice, nella III Let­<lb></lb>tera velseriana, di aver trovato quella distanza angolare 15 minuti (Alb. </s>

<s><lb></lb>III, 497, 98), ossia 900″ che divisi per 41 o per 39 davano due varie misure <lb></lb>delle massime digressioni di quel Satellite in diametri apparenti di Giove. </s></p><p type="main">

<s>Or vediamo come, giunto a tale importantissimo passo, procedesse oltre <lb></lb>Galileo nelle sue investigazioni. </s>

<s>E per prima cosa è da osservar che i moti <lb></lb>de&#039;Medicei non era possibile osservarli altrimenti, che per qualche artificio <lb></lb>simile a quello con cui gli Astronomi osservano i moti di Venere e di Mer­<lb></lb>curio, le orbite de&#039;quali sono esterne alla Terra in quel modo che sono <lb></lb>esterne, perchè non la comprendono, le orbite de&#039;Pianeti gioviali. </s>

<s>Perciò, <lb></lb>come in Venere e in Mercurio non si osservano gli archi delle orbite de­<lb></lb>scritte ne&#039;loro moti, ma le proiezioni di essi archi o i seni; così misura­<lb></lb>bili, ne&#039;Medicei, non sono altrimenti gli archi, ma i seni. </s></p><p type="main">

<s>L&#039;artificio dunque suggerito a Galileo dalla pratica degli Astronomi <lb></lb>precedenti consisteva in ciò: Posto per esempio 40″ il diametro apparente <lb></lb>di Giove, quale resultava dalla media delle due sopra riferite osservazioni, <lb></lb>e posto che la distanza angolare dal centro del Pianeta, nelle massime di­<lb></lb>gressioni del Satellite più esterno, fosse di 15′, come s&#039;ha dalla citata Let­<lb></lb>tera solare, misurata quella massima digressione in diametri gioviali, trovava <pb xlink:href="020/01/976.jpg" pagenum="419"></pb>che di que&#039;diametri una tal distanza del Satellite da Giove, ne conteneva 22 <lb></lb>prossimamente, trascurandosi la frazione. </s></p><p type="main">

<s>Perciò descritto col centro in C (fig. </s>

<s>81) un piccolo cerchio di diame­<lb></lb><figure id="id.020.01.976.1.jpg" xlink:href="020/01/976/1.jpg"></figure></s></p><p type="caption">

<s>Figura 81.<lb></lb>tro ED a rappresentare il disco di Giove, gli <lb></lb>circoscriveva un altro più gran cerchio con un <lb></lb>raggio che contenesse 22 volte il detto dia­<lb></lb>metro. </s>

<s>Così con quel cerchio si rappresentava <lb></lb>sott&#039;occhio l&#039;orbita del Satellite, la quale, poi­<lb></lb>chè Galileo supponeva essere squisitamente <lb></lb>disposta in un piano parallelo all&#039;Ecclittica, <lb></lb>veniva, per chi l&#039;avesse riguardata dalla Terra, <lb></lb>a proiettarsi sul suo proprio diametro in esqui­<lb></lb>sitissima linea retta. </s></p><p type="main">

<s>Dopo ciò, procedendo in questa pratica, <lb></lb>da ciascun punto delle 22 divisioni inalzava il <lb></lb>nostro Astronomo altrettante linee perpendi­<lb></lb>colari, cosicchè se, per esempio, il Satellite incomincia in F una sua con­<lb></lb>versione, giunto in S rappresenterà in FG proiettato l&#039;arco FS della sua <lb></lb>orbita e GC ne misurerà dal disco di Giove la relativa distanza. </s></p><p type="main">

<s>Simili altri di questi <emph type="italics"></emph>Schematismi<emph.end type="italics"></emph.end> disegnava Galileo per gli altri Sa­<lb></lb>telliti descrivendone le orbite con i raggi misurati dal contener quelle tante <lb></lb>volte il diametro gioviale. </s>

<s>L&#039;uso poi di così fatti Schematismi era questo: <lb></lb>Ad ogni osservazione giudicava così ad occhio a qual punto della linea CF <lb></lb>immaginaria potesse corrispondere la distanza reale del Satellite. </s>

<s>Giudicava <lb></lb>per esempio che corrispondesse al punto G, da cui contato il numero delle <lb></lb>segnate divisioni, scriveva senz&#039;altro nelle sue Effemeridi che il Satellite <lb></lb>stesso si trovava, in quel giorno e in quell&#039;ora, a tanti diametri di distanza <lb></lb>da Giove. </s></p><p type="main">

<s>Che fosse veramente questo l&#039;uso fatto di tali Schematismi da Galileo, <lb></lb>nel proseguire quelle sue prime Effemeridi gioviali descritte nel Nunzio Si­<lb></lb>dereo, ce lo dice da sè stesso in principio del Discorso intorno alle Galleg­<lb></lb>leggianti, dove, dopo aver riferiti i tempi periodici de&#039;quattro Medicei, così <lb></lb>soggiunge: “ Per simili precisioni non mi bastano le prime osservazioni, <lb></lb>non solo per li brevi intervalli di tempo, ma perchè non avendo io allora <lb></lb>ritrovato modo di misurar con istrumento alcuno le distanze di luogo tra <lb></lb>essi pianeti, notai tali interstizii con le semplici relazioni al diametro del <lb></lb>corpo di Giove prese, come diciamo a occhio, le quali, benchè non ammet­<lb></lb>tano errore di un minuto primo, non bastano però per la determinazione <lb></lb>delle esquisite grandezze delle sfere di esse stelle. </s>

<s>Ma ora che ho trovato <lb></lb>modo di prender tali misure, senza errore anche di pochissimi secondi, con­<lb></lb>tinuerò l&#039;osservazioni sino all&#039;occultazion di Giove, le quali dovranno essere <lb></lb>abbastanza per l&#039;intera cognizione de&#039;movimenti e delle grandezze degli orbi <lb></lb>di essi pianeti, e di alcune altre conseguenze insieme ” (Alb. </s>

<s>XII, 10). </s></p><p type="main">

<s>Dello strumento, di che qui si tratta, incominciò Galileo a fare le prime <pb xlink:href="020/01/977.jpg" pagenum="420"></pb>prove nella seconda osservazione del 31 Gennaio 1612, come si rileva dalla <lb></lb>seguente Nota interpolata all&#039;Effemeridi: “ In hac secunda observatione <lb></lb>primum usus sum Instrumento ad intercapedines exacte accipiendas, ac di­<lb></lb>stantiam Orientalioris proxime accepi, non enim fuit Instrumentum exactis­<lb></lb>sime paratum ” (Alb. </s>

<s>V, 84). </s></p><p type="main">

<s>E qui non possiamo non sentirci frugare da una gran curiosità di sapere <lb></lb>in che consistesse quello Strumento <emph type="italics"></emph>ad intercapedines exacte accipiendas,<emph.end type="italics"></emph.end><lb></lb>che non può essere il Telescopio colle brattee perforate “ quorum ope Stel­<lb></lb>larum intercapedines per aliquot minuta ad invicem dissitarum, citra unius <lb></lb>aut alterius minuti peccatum commode dimetiri poterimus ” (Alb. </s>

<s>III, 62). <lb></lb>Infatti queste brattee micrometriche, delle quali fece uso nelle prime osser­<lb></lb>vazioni descritte nel Nunzio Sidereo, erano state dallo stesso Galileo trovate <lb></lb>incomodissime, e non rispondevano oramai più ai bisogni richiesti da quel <lb></lb>nuovo ordine intrapreso di osservazioni gioviali. </s></p><p type="main">

<s>Qual&#039;è insomma quello Strumento, che non era bene ancora all&#039;ordine <lb></lb>nel 1612 la sera del dì 31 Gennaio? </s>

<s>Galileo non lo dice, e fu forse il Bo­<lb></lb>relli il primo a divulgarne la notizia, ch&#039;egli apprese o dal Castelli o dal <lb></lb>Renieri, a cui, come vedremo, Galileo stesso lo descriveva in una sua let­<lb></lb>tera, che non è a noi pervenuta, e nella quale insegnava il modo partico­<lb></lb>lare di farne uso. </s></p><p type="main">

<s>Nel capitolo IV dunque del II Libro <emph type="italics"></emph>Theoricae Medicaeorum<emph.end type="italics"></emph.end> il Borelli <lb></lb>presuppone un principio ottico, sopra il quale era fondato il nuovo Stru­<lb></lb>mento micrometrico di Galileo. </s>

<s>Quel principio così bene illustrato dal Porta, <lb></lb>nel Libro VI <emph type="italics"></emph>De refractione,<emph.end type="italics"></emph.end> dove scioglie altri curiosi problemi relativi a <lb></lb>quello <emph type="italics"></emph>Cur binis oculis rem unam cernamus,<emph.end type="italics"></emph.end> consiste nel fatto che, nella <lb></lb>visione binoculare, gli oggetti si vedon distinti solamente nel piano dove <lb></lb><figure id="id.020.01.977.1.jpg" xlink:href="020/01/977/1.jpg"></figure></s></p><p type="caption">

<s>Figura 82.<lb></lb>vanno a concorrere i <lb></lb>punti de&#039;due assi ottici, <lb></lb>oltre il qual piano, decus­<lb></lb>sandosi gli assi, le imma­<lb></lb>gini non si confondono <lb></lb>in una sola chiara e di­<lb></lb>stinta, ma si dividono <lb></lb>in due, che per un&#039;abi­<lb></lb>tudine contratta da noi <lb></lb>infin dall&#039;infanzia si giu­<lb></lb>dicano esse pure collo­<lb></lb>cate sulla medesima su­<lb></lb>perficie che termina la <lb></lb>visione. </s></p><p type="main">

<s>“ His suppositis, pro­<lb></lb>segue a dire il Borelli, <lb></lb>conspiciatur iam destro <lb></lb>oculo A (fig. </s>

<s>82) Jovis <pb xlink:href="020/01/978.jpg" pagenum="421"></pb>stella J, Telescopio CD: postea, aperto oculo sinistro B, dirigatur axis vi­<lb></lb>sualis BE ut intersecet reliquum axim AE per Telescopium traductum in <lb></lb>puncto E, atque per punctum E extendatur Reticulum vel Rastellum ali­<lb></lb>quod FG perpendiculare ad communem axim oculorum EM. </s>

<s>Patet ex dictis <lb></lb>in plano FG terminari visionem, et ideo omnia obiecta, quae duobus oculis <lb></lb>conspiciuntur, visu iudice, collocantur in dicto plano FG. </s>

<s>Et quia dexter <lb></lb>oculus A videt Stellam Telescopio aucta in E, atque sinister oculus B Re­<lb></lb>ticulum aut Rastellum FG conspicit, existimabit discum Jovis auctum occu­<lb></lb>pare interstitium Reticuli aut Rastelli, et ideo mensurari poterit diameter <lb></lb>Disci iovialis E respective ad amplitudinem Reticuli aut Rastelli FG. </s>

<s>Qua­<lb></lb>propter si integrum intervallum FG subdivisum fuerit in viginti aequalia <lb></lb>spatia, sive interstitia, apparebit diameter Jovis Telescopio aucta vigesima <lb></lb>parte Reticuli. </s>

<s>Postea, quia Telescopio nedum discus Jovis E sed Medicei <lb></lb>H, O, L, N, una cum suis distantiis a Disco ioviali E eadem proportione <lb></lb>augentur, et repraesentantur in plano FG, ubi visus terminatur; et auxilio <lb></lb>alterius oculi mensurari possunt distantiae eorumdem Mediceorum in eodem <lb></lb>Rastello a limbo vel centro Jovis et ulterius situs et inclinationes eorum­<lb></lb>dem Mediceorum praecise reperiri et delineari possunt ” (Florentiae 1665, <lb></lb>pag. </s>

<s>143, 44). </s></p><p type="main">

<s>Di questo artificio però di Galileo, che pure è <emph type="italics"></emph>pulcherrimum, dignum <lb></lb>sane sagacitate et ingenio tanti viri<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>142), confessa il Borelli stesso <lb></lb>che <emph type="italics"></emph>nullam fere utilitatem<emph.end type="italics"></emph.end> quel grand&#039;Uomo <emph type="italics"></emph>consequi potuit.<emph.end type="italics"></emph.end> Le ragioni <lb></lb>di ciò son diverse e due son dal Borelli annoverate fra le principali. </s>

<s>La <lb></lb>prima: che la troppo debole virtù del Telescopio non toglieva in tutto l&#039;ir­<lb></lb>radiazione avventizia; la seconda, che l&#039;illuminazione, necessaria a render <lb></lb>visibile il Rastrello o la Righetta micrometrica, impediva la vista de&#039;Me­<lb></lb>dicei e ingrossava allo stesso Rastrello i fili o alla Righetta i segni delle <lb></lb>divisioni. </s></p><p type="main">

<s>Tanto è vero essersi, per queste difficoltà e per que&#039;difetti, reso inu­<lb></lb>tile a Galileo quel suo ingegnoso Strumento, che l&#039;usò per sole ventuna <lb></lb>notti, dal 31 Gennaio al 20 del Febbraio seguente. </s>

<s>Nell&#039;osservazione del <lb></lb>21 appresso, <emph type="italics"></emph>sine Instrumento captae sunt distantiae<emph.end type="italics"></emph.end> (Alb. </s>

<s>V, 86). Che poi <lb></lb>veramente il nostro Osservatore tornasse a misurar quelle distanze a oc­<lb></lb>chio nello <emph type="italics"></emph>Schematismo de&#039;seni,<emph.end type="italics"></emph.end> ne abbiamo un argomento dal veder nel <lb></lb>Marzo 1612 costruito lo stesso Schematismo co&#039;nuovi moduli trovati per <lb></lb>mezzo dello Strumento, che sono per il Satellite più esterno 24 semidiame­<lb></lb>tri di Giove, e per gli altri tre interni infino al più centrale 14, 9, 5, 30 <lb></lb>(ivi, pag. </s>

<s>176). </s></p><p type="main">

<s>Di que&#039;moduli così nuovamente trovati si giovò altresì Galileo, con <lb></lb>grande industria, per riscontrare la misura del diametro apparente di Giove, <lb></lb>servendosi del Canocchiale accomodato a quel modo che si disse di sopra, <lb></lb>quando fu tolta quella stessa misura direttamente dagli angoli sottesi. </s></p><p type="main">

<s>Sia, come nella precedente figura 80, G il centro di Giove e A, B i <lb></lb>punti delle massime digressioni del più remoto Satellite, cosicchè AB rap-<pb xlink:href="020/01/979.jpg" pagenum="422"></pb>presenti il diametro dell&#039;orbita. </s>

<s>Sia CL il diametro del foro della lamina <lb></lb>applicata all&#039;obiettivo del Telescopio, della giusta misura che si ricerca per <lb></lb>questa osservazione. </s>

<s>La similitudine de&#039;triangoli dà DE:CL=GE:AB. </s>

<s>La <lb></lb>prima delle due ragioni che è dell&#039;asse del Canocchiale al diametro della <lb></lb>lamina perforata trovò Galileo essere di 100,000 a 10,968, dunque anche la <lb></lb>seconda ragione che è della distanza di Giove dalla Terra al diametro del­<lb></lb>l&#039;orbita del Satellite più esterno, sarà la stessa. </s>

<s>“ Quia vero Telescopium <lb></lb>longitudines multiplicat in rationem 19 ad 1, si numeri 10,968 undevige­<lb></lb>sima pars accipiatur, habemus rationem 100,000 ad 577 ” (ibi, pag. </s>

<s>176 n.). <lb></lb>Ond&#039;è che dal triangolo isoscele AEB, con questi dati numerici risoluto, <lb></lb>s&#039;avrà l&#039;angolo AEB=0° 2′. </s>

<s>Di qui, supposto che AB sia 24 diametri gio­<lb></lb>viali, secondo le misure già ritrovate come si avverti per mezzo dello Stru­<lb></lb>mento, Galileo ne concluse così la misura del diametro apparente di Giove: <lb></lb>“ Quod si Jovis diameter est pars 24 ciusdem diametri, ergo diameter Jovis <lb></lb>subtendit gradus 0°, 0′, 50″ et hoc accidet cum Jovis est Terrae proxi­<lb></lb>mus ” (ibi). </s></p><p type="main">

<s>Tali sono insomma i frutti delle vigilie di Galileo intorno al Mondo gio­<lb></lb>viale, e può, dietro i fatti narrati, un giusto giudice estimarne i meriti e i <lb></lb>pregi. </s>

<s>Che poi quell&#039;Uomo, magnificator d&#039;ogni cosa sua, magnificasse anche <lb></lb>questa, non fa maraviglia, come non fa maraviglia che vantandosi della prio­<lb></lb>rità della scoperta si risentisse fieramente contro chi gliel&#039;avesse contesa. </s>

<s><lb></lb>Sarebbero fra tali contenditori da annoverare quegl&#039;Italiani commemorati <lb></lb>dal Sarpi, i quali, avuto notizia del Canocchiale olandese, lo ridussero più <lb></lb>adatto e perfezionato e <emph type="italics"></emph>principiarono a valersene per l&#039;Astronomia<emph.end type="italics"></emph.end> (Let­<lb></lb>tere, Vol. </s>

<s>II, Firenze 1863, pag. </s>

<s>41) scoprendo in cielo quel che veniva, <lb></lb>nello stesso tempo, scoprendo Galileo. </s>

<s>A lui però non vollero turbare la com­<lb></lb>piacenza del primato per certe ragioni, che non valsero a legare la lingua <lb></lb>in bocca a Simon Mario nè poi a trattenergli in mano la penna. </s>

<s>Egli ebbe <lb></lb>perciò a toccarsi quella lavata di capo, che gli fu fatta senza pietà nelle <lb></lb>prime pagine del <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> dove l&#039;Autore vuol, con argomenti cronolo­<lb></lb>gici e astronomici provare ch&#039;esso Mario o non vide mai i Satelliti di Giove <lb></lb>o che gli vide solo due anni dopo la pubblicazione del Nunzio Sidereo. </s></p><p type="main">

<s>L&#039;Astronomo di Brandeburgo asseriva che il piano delle orbite de&#039;Gio­<lb></lb>viali è costantemente inclinato al piano dell&#039;Ecclittica, e che perciò sempre <lb></lb>si osservano que&#039;piccoli Pianeti avere una qualche latitudine, la quale ne&#039;se­<lb></lb>micerchi superiori è dalla parte di Austro e negl&#039;inferiori da quella di Bo­<lb></lb>rea. </s>

<s>L&#039;Astronomo di Firenze persisteva nell&#039;opinione dell&#039;esatto paralleli­<lb></lb>smo tra il piano dell&#039;Ecclittica e il piano dove giacciono le orbite de&#039;quattro <lb></lb>Medicei, attribuendo le loro latitudini apparenti alla inclinazione dell&#039;orbita <lb></lb>di Giove, e da queste stesse apparenze argomentando i tempi delle osser­<lb></lb>vazioni fatte dal suo odiato rivale. </s></p><p type="main">

<s>L&#039;Hodierna si studiò di comporre la controversia con dire che avendo <lb></lb>egli scoperto la latitudine de&#039;Medicei esser variabile, Galileo osservò quando <lb></lb>quella latitudine era nulla e Simon Mario quand&#039;era già all&#039;occhio dell&#039;Os-<pb xlink:href="020/01/980.jpg" pagenum="423"></pb>servatore parvente. </s>

<s>Non perciò vien l&#039;Hodierna a decider nulla dell&#039;altra <lb></lb>più agitata controversia intorno alla priorità della scoperta; causa che 44 anni <lb></lb>prima era stata pregiudicata da un più competente e imparzial tribunale in <lb></lb>Germania. </s></p><p type="main">

<s>Noi richiamiamo perciò la considerazione de&#039;nostri Lettori sopra le se­<lb></lb>guenti parole, che il Keplero da Praga scriveva il dì 10 Novembre 1612 allo <lb></lb>stesso Simon Mario, non a proposito di solo Giove, ma di un&#039;altra delle più <lb></lb>rumorose scoperte occorse felicemente all&#039;Astronomia in quei primi tempi: </s></p><p type="main">

<s>“ Galilaeus rerum suarum sategit; bene sibi consuluit, inquam, quippe <lb></lb>qui rerum suarum satagebat. </s>

<s>Bene fecit quod mature nos certiores reddidit <lb></lb>de inventis suis, per gryphos tamen. </s>

<s>Nam, si non mature, tu praevenisses: <lb></lb>ita Galilaeo laus primae inventionis periisset. </s>

<s>Si non per gryphos, statim <lb></lb>nos, ad quos ille scripsit, dicere potuissemus nos eodem tempore eadem vi­<lb></lb>disse vel etiam antea. </s>

<s>Tibi quoque, Mari, bene cessit gryphus, seu anagram­<lb></lb>matismus iste. </s>

<s>Nam si Galilaeus clare scripsisset tanto antea, nemo facile <lb></lb>credisset tuam esse secundam huius observationis palmam. </s>

<s>” </s></p><p type="main">

<s>“ Nunc eodem tempore et Galilaeus Florentiae sua nobis aenigmata <lb></lb>scripto detexit, et tu in Franconia observare eadem coepisti, ut impossibile <lb></lb>sit te tua ex Galilaei laboribus habere. </s>

<s>Agnoscis, ni fallor, sensum postremi <lb></lb>marginis. </s>

<s>Desine igitur te furti insimulatione queri ab eo loco, qui te furti <lb></lb>manifestissime absolvit. </s>

<s>Nam quae haec consequentia esset: quo tempore <lb></lb>Galilaeus Florentiae futuras Veneris apparentias praedixit, eodem Marius <lb></lb>illas eodem ordine observare coepit, ergo Marius ex Galilaei monitis habuit? </s>

<s><lb></lb>Numquid enim Alpes intersunt et longum iter et viginti dierum mora priu­<lb></lb>squam literae Florentia digressae Pragam appellant, quando nondum ta­<lb></lb>men in Franconiam comunicatae sunt Praga a nobis? </s>

<s>” (Epistolae mutuae, <lb></lb>Lipsiae 1718, pag. </s>

<s>551). </s></p><p type="main">

<s>Queste parole collazionate con le ultime scritte nella Prefazione alla <lb></lb>Diottrica, dove a proposito della controversia insorta fra un Alemanno e un <lb></lb>Italiano, un Alemanno, di tale e tanta autorità qual&#039;è il Keplero, decide a <lb></lb>favore del Nostro, bastano a provar che la gloria delle prime scoperte ce­<lb></lb>lesti, fra le quali è massima quella de&#039;Satelliti di Giove, è meritamente do­<lb></lb>vuta all&#039;Italia. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>E all&#039;Italia è pure dovuto il merito di aver fatti i primi validi sforzi <lb></lb>per investigar l&#039;ordine di que&#039;moti, che governano il piccolo Mondo gio­<lb></lb>viale, in cui par che, come in immagine viva, si specchi il Mondo universo. </s>

<s><lb></lb>Il Castelli come concorse a prevenire, a promuovere e a perfezionare ognuna <lb></lb>delle scoperte celesti fatte dal suo Maestro, così dette insiem con lui opera <lb></lb>assidua ad osservare il moto de&#039;Satelliti intorno a Giove. </s>

<s>Chi raccogliesse <pb xlink:href="020/01/981.jpg" pagenum="424"></pb>tra queste osservazioni quelle sole, ch&#039;ei comunicava a Galileo nelle sue let­<lb></lb>tere, per la più parte rimaste inedite, ne comporrebbe una copiosa Effeme­<lb></lb>ride. </s>

<s>Se poi fosse una tale Effemeride scritta ordinatamente dal suo Autore <lb></lb>e disposta in Tavole, da servire a&#039;comodi usi dell&#039;Astronomia è incerto, ma <lb></lb>è certissimo ch&#039;egli compose con gran diligenza una Tavola delle Epoche <lb></lb>dei moti medii, o come allora si chiamavano delle <emph type="italics"></emph>Radici,<emph.end type="italics"></emph.end> per la massima <lb></lb>parte da sè stabilite, ma alcune delle quali, ricevute da Galileo, le inserì fra <lb></lb>le sue. </s>

<s>Questa Tavola andava attorno manoscritta fra gli scolari dello stesso <lb></lb>p. </s>

<s>d. </s>

<s>Benedetto, e una copia vedremo a quale occasione e per che mezzo <lb></lb>fosse dal Borelli trasmessa al Cassini. </s></p><p type="main">

<s>Per diligenti però che fossero le osservazioni del Castelli non potevano <lb></lb>andar salve da alcuni errori inevitabili a un&#039;arte, allora del tutto nuova, e <lb></lb>nella quale perciò s&#039;aggiungeva all&#039;imperizia dell&#039;osservare l&#039;imperfezione <lb></lb>de&#039;primi fabbricati strumenti. </s>

<s>Nel corso intanto di una trentina d&#039;anni si <lb></lb>erano quelli strumenti ridotti a tale eccellenza, che non si sarebbe aspet­<lb></lb>tata mai dalla febbrile arte vetraria, ed essendosi d&#039;ogni parte moltiplicati <lb></lb>i curiosi delle novità celesti, l&#039;assiduo esercizio aveva resi più esperti gli <lb></lb>osservatori. </s>

<s>Si segnalò fra questi Vincenzio Renieri che, nel 1639 pubblicava <lb></lb>le sue <emph type="italics"></emph>Tavole medicee<emph.end type="italics"></emph.end> dei Secondi mobili “ qui comprennent, scriveva il <lb></lb>Cassini, les Tables les plus célébres faites depuis 400 ans réduites à une <lb></lb>mesme forme ” (Hypotheses des Satell. </s>

<s>de Iuppiter, Amsterdam 1736, <lb></lb>pag. </s>

<s>368). </s></p><p type="main">

<s>Abbandonate nel 1619 da Galileo le osservazioni, atterrito dalle diffi­<lb></lb>coltà, riprese nel 1620 animo quando le propose per uso delle longitudini <lb></lb>terrestri; proposta che parve essere dagli Olandesi accolta con più favore <lb></lb>nel 1636, quando il proponente si sentiva inabile all&#039;opera per la cecità so­<lb></lb>pravvenutagli e per la vecchiezza. </s>

<s>Rivoltosi perciò al valoroso calcolatore <lb></lb>delle Tavole medicee lo trovò in un giovanile ardore di darsi tutto a un&#039;im­<lb></lb>presa, che prometteva tanta utilità e tanta gloria. </s></p><p type="main">

<s>A lui consegnò Galileo i suoi lunghi calcoli laboriosi, a lui finalmente <lb></lb>aprì il segreto de&#039;suoi metodi, a lui insegnò l&#039;uso di misurar le distanze <lb></lb>con lo Strumento, sperando che sarebbe riuscito utile, applicato a Telesco­<lb></lb>pii di tanto maggiore ingrandimento de&#039;suoi. </s>

<s>Sulla fine dell&#039;anno 1637 gli <lb></lb>scriveva a Genova una lettera, dove gli raccomandava attendesse al concorso <lb></lb>de&#039;raggi visuali dietro l&#039;occhio, per avere nelle operazioni micrometriche le <lb></lb>misure angolari più giuste. </s>

<s>A che rispondeva il Renieri, verso la fin di Gen­<lb></lb>naio, proponendo di ricevere i raggi attraverso un foro invariabile aperto in <lb></lb>una carta o in una lamina, piuttosto che aftraverso al foro della pupilla, <lb></lb>tacitamente insinuando la inutilità e anzi la fallacia di una tale operazione <lb></lb>astronomica, perchè se gli angoli e le immagini non crescono nè diminui­<lb></lb>scono a proporzion del foro nella Camera oscura, non par che dovessero o <lb></lb>crescere o diminuire nell&#039;occhio, a proporzion del diametro della pupilla. </s>

<s><lb></lb>Terminava con queste parole il Renieri la sua risposta: “ Non mancherei <lb></lb>di tirar avanti le osservazioni delle Medicee, ma per non avere il suo Nun-<pb xlink:href="020/01/982.jpg" pagenum="425"></pb>zio Sidereo non mi ricordo del modo di misurare le distanze loro: di gra­<lb></lb>zia V. S. me ne avvisi la forma ” (Alb. </s>

<s>X, 262). </s></p><p type="main">

<s>Galileo allora, non solo dichiarò meglio al Renieri il modo di applicar <lb></lb>le Brattee perforate ad uso micrometrico, e già descritte nel Messaggero, <lb></lb>ma soggiunse una particolar descrizione dello strumento da misurar le di­<lb></lb>stanze, osservando con un occhio libero e con l&#039;altro applicato al Telesco­<lb></lb>pio. </s>

<s>Sempre nella speranza di mandare in breve alla luce “ tutto il resto <lb></lb>delle considerazioni fatte intorno alle altre celesti novità ” (Alb. </s>

<s>III, 506) <lb></lb>dopo quelle descritte nel Nunzio Sidereo, Galileo aveva tenuto occulto quello <lb></lb>strumento a tutti, infino a&#039;più intimi amici, fra&#039;quali il Cavalieri, che avendo <lb></lb>letto nel Discorso delle Galleggianti il modo di assicurarsi “ a discrizione <lb></lb>della distanza de&#039;Pianeti medicei fra loro e Giove ” (Campori, Carteggio <lb></lb>gal., Modena 1881, pag. </s>

<s>186) era entrato in gran desiderio d&#039;intenderlo. </s></p><p type="main">

<s>Fallite oramai le speranze di scrivere il libro delle <emph type="italics"></emph>Novità celesti,<emph.end type="italics"></emph.end> Ga­<lb></lb>lileo dunque descriveva quello strumento da misurar la distanza fra&#039;Medi­<lb></lb>cei, a quel modo presso a poco che leggemmo di sopra nel Borelli. </s>

<s>Il Re­<lb></lb>nieri, dato una scorsa a quella descrizione in furia, non aveva bene inteso <lb></lb>il modo di contrapporre agli occhi, il Rastrello, o la Righetta, com&#039;ei la <lb></lb>chiama, e perciò tornava a scriver così al medesimo Galileo, pregandolo di <lb></lb>volersi dichiarar meglio e di avvisarlo. </s>

<s>“ Dalla prima vista della sua lettera <lb></lb>non ho ben compreso il modo di misurar le distanze coll&#039;Occhiale, ma forse, <lb></lb>col porre in opera lo Strumento, lo intenderò meglio. </s>

<s>Frattanto mi avvisi <lb></lb>se la Righetta và contro l&#039;occhio libero, perchè contro all&#039;occhio del Tele­<lb></lb>scopio non mi par che si possa accomodare ” (Alb. </s>

<s>X, 285). </s></p><p type="main">

<s>Galileo, benchè non ne siam certi, avrà fatte le necessarie dichiarazioni, <lb></lb>a avrà tolto via tutti i dubbii riguardo all&#039;uso dello strumento, come gli <lb></lb>aveva tolti, o piuttosto preveduti, riguardo alla pratica delle osservazioni, <lb></lb>facendo notar gli errori trascorsi nelle prime Effemeridi descritte nel Mes­<lb></lb>saggero celeste. </s>

<s>Son queste annotazioni di una certa importanza, e il Re­<lb></lb>nieri le trascrisse quali le ebbe di mano di Galileo, e come si leggono <lb></lb>da carte 26-29 del T. VI, P. III de&#039;Manoscritti galileiani, sotto il titolo: <lb></lb>“ Observationes Galilaei adnotatae, prout ipse propria manu descripsit. </s>

<s>” </s></p><p type="main">

<s>Come saggio di queste galileiane osservazioni sugli errori da notarsi <lb></lb>nelle prime descritte costituzioni gioviali; errori che dovevano fare accorto <lb></lb>a cansarli il Renieri, e che dovevano invitarlo ad emendarli col potente <lb></lb>aiuto de&#039;suoi Telescopii, trascriviamo dal Manoscritto questi due esempii: <lb></lb>“ Anno 1610 die 20 Januarii Paduae, in observatione horae 6 duae tantum <lb></lb>Stellae observatae sunt, ex quo intelligendum IV et III fuisse coniunctas. </s>

<s><lb></lb>Et licet latitudo inter ipsas magna fuerit, IV tamen ob exilitatem et pro­<lb></lb>prinquitatem III, et inexperientia observandi non fuit adnotata ........ <lb></lb>Die 12 Februarii apparuit in observatione quae habetur in Nuncio Sidereo <lb></lb>fuisse allucinationem. </s>

<s>In observationibus vero omnibus, quae in eo Libro <lb></lb>notantur, colligimus, ob inexperientiam et Instrumenti insufficientiam, Stel­<lb></lb>las mediceas conspectas non esse nisi dum essent remotae a centro Jovis <pb xlink:href="020/01/983.jpg" pagenum="426"></pb>sem. </s>

<s>3 ita notati ad diem 8 Februarii ” richiamandosi a quel risultato dei <lb></lb>moti medii calcolati sopra più corrette Radici, che pubblicò a pag. </s>

<s>287 del <lb></lb>suo Tomo V l&#039;Albèri. </s></p><p type="main">

<s>L&#039;eccellenza de&#039;Canocchiali, e la perizia acquistata dal Renieri ne&#039;cal­<lb></lb>coli e nelle osservazioni, facevano sperare a Galileo, il quale era stato così <lb></lb>prodigo delle sue fatiche e de&#039;suoi ammaestramenti, che sarebbero final­<lb></lb>mente uscite perfette le Tavole de&#039;moti gioviali. </s>

<s>Il Renieri stesso incorò <lb></lb>questa speranza, e la significava all&#039;amico Lettore delle sue prime Tavole <lb></lb>medicee pubblicate nel 1639. Il Cassini, avvertendo che nella seconda edi­<lb></lb>zione di quelle Tavole ampliate e corrette tace affatto l&#039;Autore intorno al­<lb></lb>l&#039;Effemeridi gioviali, che aveva già così solennemente promesse “ ce qui, <lb></lb>soggiunge, donne lieu de juger qu&#039;il y avoit trouvé plus de difficulté, qu&#039;il <lb></lb>n&#039;avoit supposé d&#039;abord ” (Hupoth. </s>

<s>cit., pag. </s>

<s>368). E par che voglia attri­<lb></lb>buire a questa difficoltà, piuttosto che a uno smarrimento o ai casi di una <lb></lb>morte immatura, l&#039;essere stata defraudata la scienza di quelle Effemeridi <lb></lb>aspettate con tanti desiderii. </s></p><p type="main">

<s>Era dall&#039;altra parte impossibile, chi ben rifiette, che non si trovasse il <lb></lb>Renieri implicato in gravissime difficoltà, le quali non gli erano punto, per <lb></lb>vero dire, appianate da Galileo, suggerendogli i suoi metodi empirici, con­<lb></lb>sigliandogli la pratica di operazioni astronomiche false e perciò disutili, po­<lb></lb>nendogli in mano strumenti impraticabili, e insinuandogli i suoi pregiudizii. </s></p><p type="main">

<s>Uno di così fatti pregiudizii galileiani de&#039;più dannosi era quello di man­<lb></lb>tenere, a dispetto del Keplero, le orbite circolari, non volendo in nulla rifor­<lb></lb>mare l&#039;architettura copernicana degli Eccentrici e degli Epicicli. </s>

<s>Conseguiva <lb></lb>da ciò, che essendo ne&#039;circoli il moto uniforme, per la più precisa misura <lb></lb>de&#039;tempi, non si teneva altro conto che della così detta <emph type="italics"></emph>Equazione de&#039;giorni <lb></lb>naturali,<emph.end type="italics"></emph.end> la quale consisteva nel ridurre i moti per l&#039;Ecclittica ai moti fatti <lb></lb>per l&#039;Equatore. </s>

<s>Il Renieri però, prevenendo di un secolo i progressi del­<lb></lb>l&#039;Astronomia, sentiva vivo il bisogno di aggiungere un&#039;altra <emph type="italics"></emph>equazione<emph.end type="italics"></emph.end> di­<lb></lb>pendente dal moto realmente variabile della Terra, nella sua orbita ellittica, <lb></lb>e sottoponeva così questo suo luminoso pensiero al giudizio di Galileo: </s></p><p type="main">

<s>“ Vedo l&#039;avvertimento che ella mi dà circa al crescer la Prostaferesi <lb></lb>dell&#039;Orbe più sensibilmente, ne&#039;tempi che Giove si trova opposto al Sole, <lb></lb>di quello che faccia ne&#039;punti delle massime digressioni nell&#039;Epiciclo, e ben­<lb></lb>chè io conosca che io non avea fatto sovra di ciò la debita considerazione, <lb></lb>per ogni modo non mi par dalle osservazioni passate poter in tutto levarmi <lb></lb>qualche scrupolo di questa anomalia del moto del Primo mobile, e pur vado <lb></lb>dubitando che in questi tempi, ne&#039;quali la Terra è più discosta dal Sole, il <lb></lb>moto diurno venga ad esser più tardo, che non è ne&#039;tempi del Perigeo so­<lb></lb>lare, e che, oltre la solita Equazione de&#039;giorni naturali, ve ne sia bisogno <lb></lb>di un&#039;altra cagionata dal mancar la velocità del moto diurno nello allonta­<lb></lb>narsi la Terra dal Sole apogeo, in cui risiede la virtù motrice ” (Alb. </s>

<s>X, 339) </s></p><p type="main">

<s>Soggiungeva il Renieri a Galileo che ci pensasse un poco, e poi glie ne <lb></lb>dicesse il suo parere, il quale a null&#039;altro giovò che a rintuzzare una pra-<pb xlink:href="020/01/984.jpg" pagenum="427"></pb>tica astronomica riconosciuta utilissima, e anzi necessaria dagli stranieri, che <lb></lb>perciò se ne attribuiron la gloria. </s>

<s>Un altro merito ha nonostante il Disce­<lb></lb>polo, sopra il Maestro che aveva trattata l&#039;Astronomia gioviale con metodi <lb></lb>puramente meccanici, ed è quella di avervi introdotta la Matematica. </s>

<s>Da <lb></lb>carte 41-59 del sopra citato Tomo dei Manoscritti galileiani si leggono au­<lb></lb>tografi del Renieri risoluti i principali problemi concernenti l&#039;Ecclissi de&#039;quat­<lb></lb>tro Satelliti gioviali. </s>

<s>E per̀chè ad essi problemi pare a noi che sian prin­<lb></lb>cipalmente raccomandati i meriti dell&#039;Astronomo genovese, è ben qui darne <lb></lb>qualche saggio alla luce, anche per mostrar che non tutto delle cose di lui <lb></lb>ne involarono i casi così variamente narrati, o la deplorata morte invidiosa: </s></p><p type="main">

<s>“ Rursum hic examinantur umbrae quantitates in transitu quatuor <lb></lb>Planetarum. </s>

<s>Ex observatione magis accurata anni 1641, die 23 Octobris, <lb></lb>∴ observatus est Pisis ingredi umbram hora 8, 17′ p. </s>

<s>m., exire autem <lb></lb>h. </s>

<s>11, 28′, unde, cum in Ecclipsi consumpserit horas 3, 11′, patet in dimi­<lb></lb>dia mora h. </s>

<s>1, 35′, 30″ consumptam fuisse, quo tempore ex semidiametro <lb></lb>Jovis ∴ metitur partes 49′, 38″. </s>

<s>Datur autem eo termpore locus Jovis cen­<lb></lb>tricus in 11°, 17′, 30″, Nodi in 3°, 5′, 28″, unde distantia a Nodo 8°, 12′, 2″, <lb></lb>et propterea inclinatio orbitae gr. </s>

<s>1, 15′. </s>

<s>Distat ergo umbrae centrum a plano <lb></lb><figure id="id.020.01.984.1.jpg" xlink:href="020/01/984/1.jpg"></figure></s></p><p type="caption">

<s>Figura 83.<lb></lb>quod ducitur per centrum Jovis Ecclipticae pa­<lb></lb>rallelum, partibus semid. </s>

<s>Jovis 17′, 45″. </s>

<s>” </s></p><p type="main">

<s>“ Sit igitur via ∴ in plano Ecclipticae pa­<lb></lb>rallelo AB (fig. </s>

<s>83) cuius dimidium AC, sitque <lb></lb>DC distantia centri umbrae D ab hoc plano. </s>

<s><lb></lb>Cum AC inventa sit partium 49′, 38″; DC, 18′, <lb></lb>15″ quarum semid. </s>

<s>Jovis est 60; ita AD umbrae <lb></lb>semidiametrum investigabimus. </s>

<s>” E risoluto il <lb></lb>triangolo ACD, trova AD=52′, 53″. </s></p><p type="main">

<s>“ Jam vero his ita repertis, quantitatem <lb></lb>axis coni umbrae Jovis et semidiametrum eius­<lb></lb>dem in transitu trium reliquorum ita venabimur. </s>

<s>Sit AB (fig. </s>

<s>84) semidia­<lb></lb>metrorum Jovis 14, prout pluribus observationibus compertum est ∴ ab Jove <lb></lb><figure id="id.020.01.984.2.jpg" xlink:href="020/01/984/2.jpg"></figure></s></p><p type="caption">

<s>Figura 84.<lb></lb>distare. </s>

<s>Erit ergo DF semidia­<lb></lb>metros umbrae Jovis in loco <lb></lb>transitus ∴, quae superius in­<lb></lb>venta est continere partes se­<lb></lb>midiametri Jovis 52′, 53″. </s>

<s>Au­<lb></lb>feratur DF aequalis AE et du­<lb></lb>catur EF. </s>

<s>Erit ergo EB partes 7′, 7″. </s>

<s>Cum ergo sit ut BE (7′, 7″) ad EF, <lb></lb>hoc est AD (14); ita AB (60) ad AC; propterea, in Regula trium, nota erit <lb></lb>AC semid. </s>

<s>Jovis 118, 2′. </s>

<s>Hinc denique, cognito axe AC 118, 2′, nota erit <lb></lb>umbrae semidiametros in loco transitus ∷, .. et ., ut si AC (118, 2′) ad <lb></lb>AB (60), ita DA semidiametrorum 26, distantia ∷, ad EB, scrup. </s>

<s>13′, <lb></lb>12″. </s>

<s>Et propterea AE, seu DF erit scr. </s>

<s>46′ 48″, sicut in . DF erit scr. </s>

<s>57′, <lb></lb>3″, in .. 55′, 3″, ” (ibi, c. </s>

<s>42). </s></p><pb xlink:href="020/01/985.jpg" pagenum="428"></pb><p type="main">

<s>Corse voce che non solamente le carte, alle quali furono consegnate <lb></lb>queste Teorie astronomiche, ma che ancora tutte le altre dov&#039;erano scritte <lb></lb>le Tavole de&#039;Medicei compiute, e alle quali le stesse Teorie astronomiche <lb></lb>già preparate dovevano esser premesse, erano andate irreparabilmente per­<lb></lb>dute. </s>

<s>La voce fu avvalorata dall&#039;autorità del Riccioli, che nel primo Tomo <lb></lb>dell&#039;Almagesto nuovo, raccontati i più minuti particolari di quello smarri­<lb></lb>mento, terminava la sua storia con le parole: <emph type="italics"></emph>dblenda profecto iactura.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Leggendo quivi Giovan Battista Hodierna pensò egli di riparare a così <lb></lb>dolorosa iattura, pubblicando nel 1656, in Palermo, un libro intitolato “ Me­<lb></lb>nologiae Jovis compendium, seu Ephemerides Mediceorum ” libro che fu dal <lb></lb>suo Autore diviso in tre parti. </s>

<s>Nella prima tratta del numero, dellla serie, <lb></lb>delle digressioni, de&#039;congressi e de&#039;Periodi de&#039;Medicei; nella seconda, delle <lb></lb>variabilità delle Latitudini, e nella terza dà le Tavole astronomiche e i ca­<lb></lb>noni da calcolarle. </s></p><p type="main">

<s>Dal Nunzio Sidereo in fuori non aveva il nostro Palermitano altri pre­<lb></lb>decessori che il Mario e lo Schirleo, ad ambedue i quali però non prestava <lb></lb>gran fede, e specialmente allo Schirleo, il quale fra&#039;molti altri suoi sogni <lb></lb>ed errori aveva detto che i Satelliti gioviali scintillavano di luce propria <lb></lb>come le Stelle. </s>

<s>“ Haec mihi non placuerunt, dice l&#039;Hodierna, nam si lucem <lb></lb>sibi innatam satellites Jovis habent, praesertim Primus et Penextimus, quo­<lb></lb>modo seipsos ad invecem eclypsare indubitatum esse dicit? </s>

<s>” (ibi, pag. </s>

<s>70). </s></p><p type="main">

<s>Un tale errore lo aveva sostenuto pure il Liceti, concludendolo dal prin­<lb></lb>cipio metafisico delle intelligenze governatrici, mentre lo Schirleo lo aveva <lb></lb>invece concluso dal fatto fisico del vedere i Satelliti risplendere intorno a <lb></lb>Giove non men vivamente di quel che si facciano in cielo le Stelle fisse. </s>

<s><lb></lb>Galileo aveva pensato a confutar quell&#039;errore con argomenti che dovevano <lb></lb>inserirsi nella <emph type="italics"></emph>Lettera sul candore lunare,<emph.end type="italics"></emph.end> ma che poi rimasero, a quel che <lb></lb>sembra, fra le carte scritte a dettatura dal Viviani. </s>

<s>Qualcuno di quegli ar­<lb></lb>gomenti è ricavato da osservazioni volgari, come sarebbe questo: “ Se il <lb></lb>risplendere è segno di maggior nobiltà e perfezione, le lucciole e alcuni <lb></lb>vermi saranno più perfetti d&#039;infiniti altri animali, che nulla risplendono, e <lb></lb>quei legni, ch&#039;essendo prima tenebrosi si fanno poi risplendenti, non cam­<lb></lb>minano come V. S. e comunemente si crede alla corruzione e allo infradi­<lb></lb>ciarsi, ma al perfezionarsi e nobilitarsi ” (MSS. Gal., P. III, T. VII, c. </s>

<s>135). </s></p><p type="main">

<s>Alcuni altri argomenti poi sa ben Galileo trarli da più alte e più sot­<lb></lb>tili considerazioni, che noi vogliamo in parte far qui note ai Lettori. </s>

<s>“ Ve­<lb></lb>ramente il pensier di V. S. (così aveva fatto intenzione di dire al Liceti) <lb></lb>dello stimare i tre Pianeti superiori essere per sè stessi lucidi, come quelli <lb></lb>che da più nobili e perfette intelligenze sono generati, mi è parso mirabile <lb></lb>e degno di essere abbracciato e ritenuto, tuttavolta però che mi venissero <lb></lb>rimossi alcuni scrupoli, e risolute certe difficoltà, delle quali per mia debo­<lb></lb>lezza non so ridurre la soluzione alle Intelligenze, ed essendo che, conforme <lb></lb>al pronunziato sicurissimo di Aristotile, <emph type="italics"></emph>qui dat esse dat consequentia ad <lb></lb>esse,<emph.end type="italics"></emph.end> dando l&#039;Intelligenza lo splendore per esempio a Giove, deve in con-<pb xlink:href="020/01/986.jpg" pagenum="429"></pb>seguenza contenere le cagioni delle varietà, che nello splendore di Giove si <lb></lb>scorgono, delle quali ben pare a me di ritrovare apertamente e indubitabil­<lb></lb>mente le cagioni, mentre che io costituisco Giove per sè naturalmente te­<lb></lb>nebroso, e solo lucido per l&#039;illuminazione del Sole. </s>

<s>” </s></p><p type="main">

<s>“ Si rivolgono in cerchi differenti e diseguali, concentrici però al cen­<lb></lb>tro di Giove, quattro minori Stelle, le quali in statuti e preveduti tempi <lb></lb>restano in tutto prive di lume, e come ecclissate. </s>

<s>Tale accidente non pati­<lb></lb>scono esse se non vicine a Giove, e costituite nella parte superiore de&#039;cer­<lb></lb>chi loro, ma nella parte inferiore vengono a congiungersi e a separarsi dal­<lb></lb>l&#039;istesso Giove, senza patire ecclisse alcuna. </s>

<s>Inoltre si nascondono nelle <lb></lb>tenebre, alcune volte, avanti che arrivino al contatto di Giove, ed altre volte, <lb></lb>dopo l&#039;essersi con esso corporalmente congiunte, non tornano a dimostrarsi <lb></lb>risplendenti, se non in distanze notabili dal disco di Giove, e queste distanze <lb></lb>si fanno in alcuni tempi maggiori, e in altri minori, e di tutta questa di­<lb></lb>versità puntualissima rispondenza se n&#039;ha dalla diversa costituzione e aspetto <lb></lb>di Giove col Sole. </s>

<s>” </s></p><p type="main">

<s>“ Di più, tal perdita di&#039;lume, e con tali regole accadente, a me pare <lb></lb>che ci assicuri che sola la metà del disco di Giove che risguarda verso il <lb></lb>Sole sia luminosa, restando l&#039;altro suo emisfero privo di luce. </s>

<s>Che quando <lb></lb>egli risplendesse, gli suoi Satelliti, essendogli tanto vicini, riterrebber lume <lb></lb>bastante a farli cospicui, nè potrebbe il cono dell&#039;ombra di Giove dal tuttto <lb></lb>denigrarli. </s>

<s>Oltre che accade talvolta che uno di essi, che in grandezza su­<lb></lb>pera gli altri, offusca col piccol cono della sua ombra uno che gli è supe­<lb></lb>riore. </s>

<s>Come poi tali diverse apparenze possino trarre origine dalla Intelli­<lb></lb>genza, la quale in genere infonde lo splendore nel corpo di Giove, veramente <lb></lb>non so io capire, senza porre varietà e mutazioni nella stessa Intelligenza, <lb></lb>e però volentieri sentirei come tali corde potessero accordarsi col tenore <lb></lb>della corda principale ” (ivi, c. </s>

<s>135, 36). </s></p><p type="main">

<s>Ma, per tornare all&#039;Hodierna, egli pensò a imporre a ciascun Satellite <lb></lb>un nome proprio. </s>

<s>Galileo gli voleva nominare a principio tutti insieme <emph type="italics"></emph>Pla­<lb></lb>netae cosmici,<emph.end type="italics"></emph.end> come infatti si legge in una bozza autografa delle ultime pa­<lb></lb>role scritte nell&#039;Avviso Sidereo (MSS. Gal., P. III, T. III, c. </s>

<s>26). Poi consi­<lb></lb>gliato dal Vinta, per far partecipe della nuova apoteosi non il solo granduca <lb></lb>Cosimo, ma tutta insieme la famiglia, gli denominò <emph type="italics"></emph>Planetae Medicaei<emph.end type="italics"></emph.end> (Vo­<lb></lb>linski, Lett. </s>

<s>inedite di Galileo, Firenze 1874, pag. </s>

<s>19). In particolare poi gli <lb></lb>designava con numeri di ordine, cominciando a contar dal più intimo, o con <lb></lb>punti disposti in linea retta, come si vede per esempio a c. </s>

<s>43 del T. V, <lb></lb>P. III de&#039;Manoscritti. </s>

<s>Il Renieri, come si vide dianzi nel passo trascritto, gli <lb></lb>distingueva con punti configurati. </s></p><p type="main">

<s>Un nome proprio pareva più comodo per la trattazione e l&#039;Hodierna, <lb></lb>giacchè l&#039;uso, che si voleva far de&#039;Medicei per la ricerca delle Longitudini, <lb></lb>veniva a costituirli in cielo quasi altrettante luci di <emph type="italics"></emph>Fari,<emph.end type="italics"></emph.end> a&#039;radicali delle <lb></lb>prime quattro lettere dell&#039;alfabeto greco dava una medesima desinenza tolta <lb></lb>dal nome <emph type="italics"></emph>faro,<emph.end type="italics"></emph.end> componendone così i nomi di Alfifaro, Bitifaro, Cappifaro e <pb xlink:href="020/01/987.jpg" pagenum="430"></pb>Deltifaro. </s>

<s>Brutti nomi, nè per aver convertite le lettere greche nelle per­<lb></lb>sone del granduca Ferdinando, del padre di lui, della moglie e del principe <lb></lb>ereditario, i nuovi nomi trasformati in Ferndifaro, Cosmifaro, Vittrifaro e <lb></lb>Princifaro, riuscirono per verità punto più belli. </s></p><p type="main">

<s>Potrebbe esser questa una prova dell&#039;amoroso studio posto intorno a <lb></lb>ciò dall&#039;Hodierna, del quale studio avremmo a dir vero potuto fare un giu­<lb></lb>dizio più sicuro, se ci avesse piuttosto descritti gli strumenti, e il partico­<lb></lb>lar modo di usarli nelle sue osservazioni. </s>

<s>Egli per esempio asserisce “ nun­<lb></lb>quam Jovis diametrum excedere secunda 45 ” (Menologia cit., pag. </s>

<s>11) ma <lb></lb>non dice in che modo abbia tolta quella scrupolosa misura. </s></p><p type="main">

<s>A pagine 27 e 28, 29 e 30 della Terza parte della sua Menologia si <lb></lb>vede, per ciascun Satellite in particolare e co&#039;moduli proprii alle loro mas­<lb></lb>sime digressioni, impressa “ Orbitae circumscriptio et Orbis dimensiones, <lb></lb>per singulas circumferentiae partes, ad auspicandas a centro Jovis digres­<lb></lb>siones, quae mira facilitate promptissime explicantur. </s>

<s>” Chi vi getta sopra <lb></lb>lo sguardo si sovvien facilmente di quelli <emph type="italics"></emph>Schematismi de&#039;seni,<emph.end type="italics"></emph.end> che usava <lb></lb>Galileo per misurare a occhio le distanze de&#039;Pianetini dal centro di Giove, <lb></lb>se non che son dall&#039;Hodierna quelli stessi Schematismi ordinati a risolvere <lb></lb>graficamente, oltre a quello delle distanze, alcuni altri problemi di Astrono­<lb></lb>mia gioviale. </s></p><p type="main">

<s>Nè qui possiamo lasciar di notare che improprio sembra a noi il nome <lb></lb>di <emph type="italics"></emph>Giovilabio<emph.end type="italics"></emph.end> dato a questi <emph type="italics"></emph>Schematismi,<emph.end type="italics"></emph.end> quasi fossero strumenti meccanici <lb></lb>ingegnosamente composti di organi materiali, e di una nuova invenzione di <lb></lb>Galileo. </s>

<s>Ma lasciando il questionar del nome, a noi par che l&#039;Albèri, e chi <lb></lb>senza discrezione lo segue, propriamente ne frantendano l&#039;uso. </s></p><p type="main">

<s>Del resto, un autorevolissimo giudizio dell&#039;Opera astronomica dell&#039;Ho­<lb></lb>dierna fu dato così dal Cassini, nelle sue Effemeridi bolognesi: “ Non de­<lb></lb>fuit Joanni Baptistae Hodiernae siculo studium ad Tabularum Mediceorum <lb></lb>Syderum constructionem, sed cum observationibus annorum tantummodo <lb></lb>quinque eas fundarit, quam citissime, magnum a Ccelo dissidium exhibuere. </s>

<s><lb></lb>Praesertim vero latitudinis Canones, prioribus suis observationibus correspon­<lb></lb>dentes ceu perpetuos edidit, quos panlo post agnovit a succedentibus valde <lb></lb>et manifeste dissentire, nec tamen eorum reformationem aggressus est, cum <lb></lb>latitudinis mutationem observationibus deprehenderet, eius vero modum ra­<lb></lb>tionemque minime perciperet ” (Bononiae 1668, pag. </s>

<s>5). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Aveva dunque l&#039;Hodierna fatto un passo importante ad occuparsi delle <lb></lb>variazioni delle Latitudini, di che nè Galileo, nè il Castelli, nè lo stesso Re­<lb></lb>nieri ebbero alcun sospetto. </s>

<s>E poniamo che ciò fosse non piccolo merito, il <lb></lb>Cassini pretendeva di più di voler sapere il modo e la ragione di così fatte <pb xlink:href="020/01/988.jpg" pagenum="431"></pb>variazioni Qui stava l&#039;importanza della nuova scoperta astonomica, e qui <lb></lb>consistevano le principali difficoltà, a superar le quali s&#039;attendeva nell&#039;Ac­<lb></lb>cademia del Cimento, tre anni prima che fossero pubblicate le Effemeridi <lb></lb>bolognesi. </s></p><p type="main">

<s>Giuseppe Campani aveva lavorato per il Granduca un eccellentissimo <lb></lb>Canocchiale, con cui, nell&#039;estate del 1665, il Borelli incominciò a osservare <lb></lb>Saturno e poi Giove. </s>

<s>Sovvenendosi allora di aver fra le mani quella Tavola <lb></lb>delle Radici, che andava sotto il nome di Galileo, benchè vi avesse avuto <lb></lb>gran parte il Castelli, da cui n&#039;ebbe copia quando forse da giovane fre­<lb></lb>quentava la sua scuola; si sentì con sì propizia occasione eccitato a riscon­<lb></lb>trare i dati di quella Tavola co&#039;nuovi calcoli istituiti. </s>

<s>Gli era allieviata la <lb></lb>fatica delle osservazioni e dei calcoli dai dotti colloqui che intratteneva, sulle <lb></lb>ore vespertine, col principe Leopoldo, e con altri Accademici convenuti nelle <lb></lb>sale de&#039;Pitti, dove frattanto “ quamplurima de motibus, positionibusque Me­<lb></lb>diceorum disserebantur ” (Theoricae Medic. </s>

<s>cit., pag. </s>

<s>VI). </s></p><p type="main">

<s>La notizia, che nell&#039;Accademia fiorentina s&#039;attendeva a studiar le Teo­<lb></lb>riche de&#039;Medicei, si diffuse per tutta l&#039;Italia, e giunse alle orecchie di Ge­<lb></lb>miniano Montanari, da cui, come dall&#039;inventor del Micrometro, si poteva <lb></lb>con ogni buona ragione aspettar la scienza, se non forse teorie sublimi, esat­<lb></lb>tissime osservazioni. </s>

<s>Tale infatti, di risponder cioè all&#039;aspettativa, era l&#039;in­<lb></lb>tenzione dello stesso Montanari, il quale così scriveva da Bologna, il dì <lb></lb>25 Agosto 1665, ad Annibale Ranuzzi: </s></p><p type="main">

<s>“ Ecco a V. S. Ill.ma un poco d&#039;abbozzo dell&#039;Istrumento che, sino vi­<lb></lb>vente il signor marchese Cornelio Malvasia, felice memoria, avevo pensato <lb></lb>e cominciato di fabbricare, per rappresentare all&#039;occhio il sito de&#039;Pianeti <lb></lb>medicei e con facilità trovarne a qualsivoglia tempo le configurazioni con <lb></lb>Giove, data la loro ipotesi giusta, intorno alla quale avevo istituito qualche <lb></lb>studio. </s>

<s>Avendo perciò qualche numero d&#039;operazioni fatte vivente detto Si­<lb></lb>gnore e dopo morto lui ancora, ma distratto da tant&#039;altre cose, non l&#039;ho <lb></lb>proseguito, ed ora godo sentire da V. S. Ill.ma che il serenissimo signor <lb></lb>principe Leopoldo vi faccia studiare, e sia in prossimo d&#039;avere da que&#039;grandi <lb></lb>ingegni tutta la teoria de&#039;Medicei, al che più facile sarà loro d&#039;arrivare che <lb></lb>a me, la debolezza del cui talento non è da porre con essi a paragone. </s>

<s>” </s></p><p type="main">

<s>“ Certo che l&#039;Hodierna con tutto che forse, circa que&#039;tempi ch&#039;egli <lb></lb>stampò, le sue Tavole corrispondessero a un bel circa a&#039;tempi odierni, è <lb></lb>molto lontano, e le ipotesi sue hanno poco di quella sottigliezza, che a moti <lb></lb>così veloci e da noi lontani si richiede; oltre qualche non leggero suo in­<lb></lb>ciampo. </s>

<s>Se fosse per restar servito il serenissimo signor principe Leopoldo <lb></lb>mio signore d&#039;una scelta di quelle osservazioni, delle quali io faccio più ca­<lb></lb>pitale, fatte per lo più però col mio Canocchiale di 18 palmi colla Reticola, <lb></lb>mediante la quale misuravo assai esattamente le loro distanze ridotte però <lb></lb>sempre a diametri di Giove; io mi pregerei sommamente dell&#039;onore di ser­<lb></lb>virnelo. </s>

<s>Frattanto sto preparandomi a lavorare una lente di grandezza suf­<lb></lb>ficiente a veder molto meglio, e forse, se avrò luogo ove adoperarla, mi <pb xlink:href="020/01/989.jpg" pagenum="432"></pb>cimenterei a 40 o 50 palmi, e le osservazioni che potrò poi andar facendo <lb></lb>le parteciperò a V. S. Ill.ma, alla quale fo umilissima riverenza ” (MSS. Cim., <lb></lb>T. XXIV, c. </s>

<s>185). </s></p><p type="main">

<s>Chi sa quanto fosse il Montanari valoroso in ogni parte della Fisica <lb></lb>sperimentale, e specialmente nelle osservazioni astronomiche, essendo un <lb></lb>fatto che il Ramuzzi adempì l&#039;ufficio, domanda, desideroso, dopo questa let­<lb></lb>tura, se Leopoldo de&#039;Medici fece la consueta aspettata accoglienza alle Effe­<lb></lb>meridi de&#039;Medicei calcolate dal Discepolo del Malvasia. </s>

<s>Noi, per rispondere <lb></lb>alla domanda, non abbiamo documenti certi, ma se dovessimo andar per <lb></lb>congetture diremmo che il Principe dell&#039;Accademia fiorentina trascurò la <lb></lb>proposta, e ciò non per altro che per suggestione del Borelli, il quale pre­<lb></lb>gustava in cuore quelle amarezze contro il Montanari, che poi spremè, <lb></lb>quando questi pubblicò l&#039;osservazione delle attrazioni per capillarità de&#039;cor­<lb></lb>puscoli galleggianti, che il Borelli pretendeva fosse una sua scoperta fatta <lb></lb>dodici anni prima. </s>

<s>“ E perchè nel medesimo tempo, scriveva da Messina al <lb></lb>principe Leopoldo, dimorava a Firenze il detto Montanari, e praticava con <lb></lb>i signori Buoni, e da loro s&#039;informava di tutte le cose, non può allegare <lb></lb>ignoranza.... Ho ricordato questo a V. A. vedendo la troppa avidità di glo­<lb></lb>ria che ha questo giovane, e la poca gratitudine con i suoi maestri ” (MSS. <lb></lb>Cim., T. XIX, c. </s>

<s>96). </s></p><p type="main">

<s>Ma che veramente, vedendosi il Montanari così non curato, non solo <lb></lb>non proseguisse le sue osservazioni e i suoi calcoli intorno ai Medicei, ma <lb></lb>lasciasse andare a perdersi la miglior parte dei già fatti, è, ripetiamo, una <lb></lb>nostra congettura. </s>

<s>Del resto chi, cercando con più diligente pazienza e con <lb></lb>più comodità di quel che non abbiam potuto e saputo far noi, ritrovasse <lb></lb>quest&#039;altre Effemeridi bolognesi, avrebbe il merito di aggiungere un nuovo <lb></lb>splendido raggio di gloria alla già per sè gloriosa scienza gioviale italiana. </s></p><p type="main">

<s>Dicemmo essere un fatto che il Ranuzzi adempì fedelmente l&#039;ufficio <lb></lb>commessogli, e ciò si argomenta dal veder ch&#039;egli esibì, e consegnò nelle <lb></lb>mani del principe Leopoldo la lettera del Montanari, la quale fu raccolta fra <lb></lb>le altre carte appartenenti all&#039;Accademia, insiem colla descrizione dello Stru­<lb></lb>mento, di che si parla in principio della lettera stessa. </s>

<s>Di quella descrizione <lb></lb>frattanto non vogliamo defraudare il corredo dei documenti riccamente am­<lb></lb>manniti a questo capitolo della nostra Storia. </s></p><p type="main">

<s>“ A, A (fig. </s>

<s>85) cinque palline dorate rappresentanti Giove con li quat­<lb></lb>tro Medicei, delle quali la maggiore sta fitta in uno stile piantato in mezzo <lb></lb>allo strumento, e l&#039;altre sono sostenute da fili di ottone incurvati, e poste <lb></lb>in tanta distanza dalla maggiore, quanta è la maggior digressione di ciascun <lb></lb>Mediceo da Giove, e sono imperniate nello stilo di mezzo, mediante una lin­<lb></lb>guetta, che ha dall&#039;altro capo una punta, che mostra li gradi descritti nelle <lb></lb>rotelle a cui soprastano. </s>

<s>” </s></p><p type="main">

<s>“ B, B, quattro rotelle fitte stabili nel medesimo stilo di mezzo, intorno <lb></lb>le quali è la divisione del cerchio in 360 gradi, e ciascuna porta il suo Me­<lb></lb>diceo, come sopra. </s>

<s>” </s></p><pb xlink:href="020/01/990.jpg" pagenum="433"></pb><p type="main">

<s>“ C, C, linguette, per le quali stanno imperniati li Pianetini, la punta <lb></lb>delle quali segna i gradi nel cerchio delle rotelle. </s>

<s>” </s></p><p type="main">

<s>“ D, luogo determinato per vedere con l&#039;occhio la configurazione dei <lb></lb><figure id="id.020.01.990.1.jpg" xlink:href="020/01/990/1.jpg"></figure></s></p><p type="caption">

<s>Figura 85.<lb></lb>Pianeti medicei <lb></lb>con Giove, e que­<lb></lb>sto luogo si deve <lb></lb>far più basso e <lb></lb>più alto del pia­<lb></lb>no, nel quale si <lb></lb>muovono li Pia­<lb></lb>netini, oppure <lb></lb>stare in esso, con­<lb></lb>forme la di loro <lb></lb>latitudine richie­<lb></lb>de. </s>

<s>” </s></p><p type="main">

<s>“ E, asse po­<lb></lb>sta perpendico­<lb></lb>larmente avanti <lb></lb>l&#039;Istrumento per­<lb></lb>chè non si veg­<lb></lb>gano che le pal­<lb></lb>line, che potran­<lb></lb>no farsi apparire <lb></lb>avanti un panno azzurro, o nero come si vuole, per meglio imitare la ve­<lb></lb>duta del naturale. </s>

<s>” </s></p><p type="main">

<s>“ La divisione de&#039;cerchi nelle Rotelle deve cominciare in tutte al pari <lb></lb>una sotto l&#039;altra, e guardare precisamente il luogo d&#039;onde in cielo suppon­<lb></lb>ghiamo principiare il loro moto, ossia nell&#039;asse del cono dell&#039;ombra di Giove, <lb></lb>ossia nell&#039;asse della nostra vista, a piacere di chi fabbrica l&#039;ipotesi, e data <lb></lb>l&#039;ora per fare l&#039;osservazione, devesi calcolare ciascun Pianeta, in quel grado, <lb></lb>dove trovasi il suo circolo a quell&#039;ora ed ivi nello Strumento collocarlo, il <lb></lb>che fatto, dal luogo prefisso all&#039;occhio vedrassi la loro configurazione, quale <lb></lb>in tale ora dovrà vedersi in cielo. </s>

<s>” </s></p><p type="main">

<s>“ Potrebbonsi ancora disegnare nel muro o panno opposto alcune linee <lb></lb>parallele fra loro e perpendicolari all&#039;orizzonte, in distanza una dall&#039;altra <lb></lb>un diametro apparente della Pallina maggiore, e che una di esse corrispon­<lb></lb>desse all&#039;occhio, per lo centro di essa Palla maggiore, ad effetto di nume­<lb></lb>rare in un istante le distanze de&#039;Medicei da Giove in diametri di esso. </s>

<s>” </s></p><p type="main">

<s>“ Esponendosi in debito luogo un lume, a stanza serrata, si vedrebbe <lb></lb>qual de&#039;Pianeti e quando restasse ecclissato nell&#039;ombra della Palla mag­<lb></lb>giore, ossia corpo di Giove. </s>

<s>” </s></p><p type="main">

<s>“ Pensai ultimamente al modo, che non è difficile, di rappresentare le <lb></lb>medesime apparenze in un Orologio da pendolo, al moto del quale ciascuna <lb></lb>delle Palline facesse il proprio moto nel suo cerchio, e da un luogo prefisso <pb xlink:href="020/01/991.jpg" pagenum="434"></pb>se ne vedesse la configurazione, ma quando non vi sia ipotesi certissima del <lb></lb>loro moto, ogni anno per lo meno avrebbe bisogno di qualche correzione. </s>

<s><lb></lb>Per altro sarebbe molto più comodo lo Strumento se, aggiustato una volta, <lb></lb>camminasse lungo tempo da sè, per fuggire il tedio de&#039;calcoli. </s>

<s>” </s></p><p type="main">

<s>“ È però vero che stimavo necessario supporre ellittico il moto de&#039;Me­<lb></lb>dicei, così indotto da certe mie considerazioni sopra l&#039;osservazione di questi <lb></lb>tempi ed antichi, e però avevo pensato a farli camminare in una Ellisse <lb></lb>nello Strumento, facendo passare con le linguette C, C medesime un dente <lb></lb>che avessero sotto, per un canaletto ovato nella Rotella, o in altro de&#039;modi, <lb></lb>che può suggerire il Torno da ovati. </s>

<s>E finalmente in pratica molte altre <lb></lb>cose ponno aggiungersi per trarne comodo ed utilità maggiore, conforme <lb></lb>l&#039;occasion suggerisce ” (MSS. Cim., T. XXIV, c. </s>

<s>186). </s></p><p type="main">

<s>Ma intanto, mentre che il Montanari si sentiva così eccitato a ritornare <lb></lb>sopra i suoi studii gioviali, da que&#039;colloqui vespertini tenuti nell&#039;Accade­<lb></lb>mia de&#039;Pitti, e che furono occasione di quelli eccitamenti, ne nacque, dice <lb></lb>il Borelli, “ ut hoc Opusculum e manibus exciderit, quod, cum ostendissem <lb></lb>serenissimo sapientissimoque principi Leopoldo, eiusque acerrimo iudicio <lb></lb>submisissem, censuit ipse, pariterque alii amici, ut quam primum edere­<lb></lb>tur ” (Theoricae cit., pag. </s>

<s>VI, VII). </s></p><p type="main">

<s>Quell&#039;opuscolo conteneva le celeberrime <emph type="italics"></emph>Theoricae Mediceorum Pla­<lb></lb>netarum ex causis physicis deductae,<emph.end type="italics"></emph.end> divise in due libri, a proposito dei <lb></lb>quali scriveva l&#039;Autore, il dì 22 Gennaio 1665: “ Ho finito di tutto punto <lb></lb>il II libro delle dette mie teoriche delle Medicee ” (MSS. Cim., T. XVIII), <lb></lb>c. </s>

<s>90). Nonostante non fu il Manoscritto in ordine di esser mandato alla <lb></lb>stampa, che nel seguente mese di Ottobre. </s>

<s>Le vane paure dell&#039;Inquisitore <lb></lb>fecero indugiare all&#039;anno dopo la pubblicazione, che si doveva fare a Bo­<lb></lb>logna, affidandola alle cure del Montanari, le amarezze verso il quale si te­<lb></lb>nevano dal Borelli tuttavia segrete, ond&#039;è che avendo il motivo e l&#039;occa­<lb></lb>sione di rimproverarlo, “ non mi arrischio, diceva, di scrivergli nulla, perchè <lb></lb>ho provato in altre occasioni quanto mal volentieri egli riceva gli amiche­<lb></lb>voli avvertimenti, ed ora tanto più non vorrei alienarmelo, quando che avrei <lb></lb>bisogno dell&#039;opera sua per assistere alla correzione della stampa del mio <lb></lb>Libro ” (ivi, c. </s>

<s>93). </s></p><p type="main">

<s>Poi la stampa si fece in Firenze, per la fretta, della quale e della data <lb></lb>del Libro anticipata di un anno furon causa i Dialoghi fisici del Fabry “ il <lb></lb>quale mi ha reso attonito, scriveva lo stesso Borelli nel Febbraio del 1666 <lb></lb>al principe Leopoldo, per quel poco che ho veduto, perchè veggo che a quel <lb></lb>cervellaccio gli son sovvenuti concetti assai simili a&#039;miei, con i quali spiego <lb></lb>le cagioni fisiche de&#039;moti de&#039;Pianeti..... Ho stimato necessario stampar <lb></lb>furiosamente questa mia Opera costì a Firenze, non più a Bologna, .... per­<lb></lb>chè esca fuori presto sotto la data dell&#039;anno passato, quand&#039;io veramente <lb></lb>la presentai al serenissimo Granduca e gliela dedicai l&#039;Ottobre passato ” <lb></lb>(ivi, c. </s>

<s>111). </s></p><p type="main">

<s>De&#039;due Libri, in che, come dicemmo, è divisa l&#039;Opera del Borelli, nel <pb xlink:href="020/01/992.jpg" pagenum="435"></pb>primo s&#039;investigano le cause fisiche e meccaniche de&#039;moti; nel secondo si <lb></lb>danno le regole per le osservazioni. </s>

<s>Una delle principali cose che occorre <lb></lb>a notare è la conferma e dimostrazione fisica matematica delle Orbite ellit­<lb></lb>tiche, dal Montanari ammessa per induzione, e dalla prima Scuola galileiana <lb></lb>affatto negata, ed è altresì più notabile che le variazioni e le irregolarità os­<lb></lb>servate nei moti le attribuisca l&#039;Autore ai vari modi degl&#039;impulsi radiosi <lb></lb>del Sole, o a qualche cosa equivalente insomma all&#039;attrazion neutoniana, <lb></lb>ch&#039;egli rende ostensibile con ingegnose esperienze fondate sopra le proprietà <lb></lb>del Magnete. </s></p><p type="main">

<s>Rispetto alle osservazioni, quanto fossero arguti gli avvedimenti del Bo­<lb></lb>relli basterebbe a provarlo il cap. </s>

<s>III del Libro II, dove, in trattar delle va­<lb></lb>rietà dell&#039;Ecclissi, dimostra sperimentalmente, con Canocchiali via via di <lb></lb>maggiore ingrandimento, come nemmen co&#039;più grandi e più squisiti Stru­<lb></lb>menti si arriva a togliere affatto l&#039;irradiazione, cosa che pur sarebbe così <lb></lb>necessaria ad avvisar nell&#039;Ecclissi il tempo de&#039;precisi contatti. </s></p><p type="main">

<s>Altre dottrine di quest&#039;Opera insigne occorrerà di notarle fra poco, e <lb></lb>intanto è da saper che a&#039;colloqui vespertini, che si tenevano in Firenze alla <lb></lb>presenza del principe Leopoldo, uno de&#039;primi e principali convenutivi era <lb></lb>il Viviani. </s>

<s>A dissertar di Giove e de&#039;Medicei era per lui come un rinfre­<lb></lb>scare i più verdi e più gloriosi allori del suo adorato Maestro, nel quale ef­<lb></lb>fetto un acuto stimolo di rivalità, oltre al nobile amor della scienza, non gli <lb></lb>permetteva, a confronto del Borelli, di mostrarsi inoperoso. </s></p><p type="main">

<s>Ei non sa però dilungarsi da&#039;metodi praticati da Galileo, e perciò, co­<lb></lb>noscendo bene quanto importasse, nelle operazioni micrometriche del suo <lb></lb>Maestro, il sapere l&#039;ingrandimento del Canocchiale, ne immaginò, per mi­<lb></lb>surarlo più facilmente, questi tre modi: “ Io. </s>

<s>Sia AB (fig. </s>

<s>86) una tavoletta <lb></lb>tinta di nero, in mezzo di cui sia una striscia bianca uniforme di larghezza, <lb></lb>e in mezzo di questa un sottile ago fermato a piombo, sul quale si possano <lb></lb><figure id="id.020.01.992.1.jpg" xlink:href="020/01/992/1.jpg"></figure></s></p><p type="caption">

<s>Figura 86.<lb></lb>infilare dei cerchi di cartone tinti <lb></lb>neri, i diametri de&#039;quali abbiano <lb></lb>nota proporzione con la larghezza <lb></lb>della striscia. </s>

<s>E quivi, infilato or <lb></lb>un ed ora un altro de&#039;cerchi, si <lb></lb>osservi con l&#039;Occhiale posto a di­<lb></lb>rimpetto all&#039;asse qual di loro ap­<lb></lb>parirà all&#039;occhio accomodato all&#039;Oc­<lb></lb>chiale uguale alla larghezza della <lb></lb>fascia vista con l&#039;altro occhio li­<lb></lb>bero; che di qui si averà la proporzione dell&#039;ingrandimento. II

o. </s>

<s>Ovvero, <lb></lb>prese le distanze de&#039;fochi dell&#039;obiettivo e della lente oculare, quanto quella <lb></lb>si troverà maggiore di questa, di tanto l&#039;Occhiale accrescerà ogni larghezza <lb></lb>o altezza di oggetto. </s>

<s>IIIo. </s>

<s>Ovvero, fatti due cerchi uguali e neri, ed uno os­<lb></lb>servato con l&#039;Occhiale nella distanza che si vuole, in campo bianco, l&#039;altro <lb></lb>accostisi e discostisi finchè l&#039;occhio libero lo giudichi, nel medesimo campo, <pb xlink:href="020/01/993.jpg" pagenum="436"></pb>grande quanto l&#039;altro veduto coll&#039;Occhiale, e misurato quanto è dall&#039;occhio <lb></lb>al cerchio visto coll&#039;occhio libero, tante volte quanto questa distanza entra in <lb></lb>quell&#039;altra, tanto aggrandisce l&#039;Occhiale ” (MSS. Gal. </s>

<s>Disc., T. CXXXIV, c. </s>

<s>3). </s></p><p type="main">

<s>Così praticando il Viviani i metodi, che Galileo insegna nel Nunzio Si­<lb></lb>dereo per misurare le piccole distanze, e quegli altri che avrà suggerito a <lb></lb>voce al suo discepolo diletto, e assai poco difformi dagli esposti da noi di <lb></lb>sopra nel paragrafo I; ritrovò quegli elementi, che scrisse di sua propria mano <lb></lb>in una Tavola de&#039;moti de&#039;Satelliti di Giove. </s>

<s>“ Fere omnes Quatuor in eo­<lb></lb>dem plano circuitus suos absolvunt, declinante a Jovis orbita gradibus 2, 54′, <lb></lb>moventurque ab ortu in occasum in parte Jovis a nobis obversa. </s>

<s>Primus <lb></lb>omnium intimus distat a centro Jovis per semid. </s>

<s>Jovis 5 2/3, periodum suam <lb></lb>perficit spatio dierum 1, 18h, 22′. </s>

<s>Secundus a Jove distat per semid. </s>

<s>9 et <lb></lb>revolvitur 3d, 13h, 14. Tertius a Jovis centro distat per semid. </s>

<s>Jovis 14 et <lb></lb>paulo amplius, et periodum perficit d. </s>

<s>7, h. </s>

<s>3, 42′. </s>

<s>Quartus omnium exti­<lb></lb>mus distat a centro Jovis per semid. </s>

<s>25 1/3, et revolvitur per d. </s>

<s>16, h. </s>

<s>3, 2′ ” <lb></lb>(ivi, T. CXXXIX, c. </s>

<s>17). </s></p><p type="main">

<s>Qualunque però si fosse l&#039;esattezza di questi calcoli, ne&#039;quali è nota­<lb></lb>bile l&#039;inclinazione del piano delle orbite de&#039;Satelliti col piano dell&#039;orbita di <lb></lb>Giove, il Viviani vi tornò poi sopra altre volte, ora ricorrendo ai moti me­<lb></lb>dii, ora a nuove osservazioni dirette. </s>

<s>Ne ebbe qualche varietà di resultati, <lb></lb>come può vedersi dalla traduzione delle <emph type="italics"></emph>Osservazioni intorno al mondo<emph.end type="italics"></emph.end> del <lb></lb>Gadroy, dove il Viviani stesso, ch&#039;è il traduttore, destramente inserisce i <lb></lb>suoi nuovi numeri. </s>

<s>“ Egli (Galileo) si accorse che la Prima delle gioviali, <lb></lb>cioè la più prossima al corpo di Giove è lontana dal di lui centro cinque <lb></lb>semidiametri e 50 minuti, e gli gira intorno in tempo di un giorno, ore 18, <lb></lb>28′, 35″, 33tʹ, 14qʹ. </s>

<s>La seconda distante otto semidiametri e 50 minuti, e <lb></lb>compisce il suo corso in tre giorni e ore tredici 18′, 21″, 32tʹ, 20qʹ. </s>

<s>La Terza, <lb></lb>che in apparenza è la massima delle quattro, è lontana dal centro di Giove <lb></lb>tredici semid. </s>

<s>e 52 minuti, e termina il suo giro in sette giorni e due ore <lb></lb>27′, 25″, 57tʹ, 9qʹ. </s>

<s>E finalmente la Quarta, cioè la remotissima e che appa­<lb></lb>risce in grandezza la minima, ne è distante 24 semid. </s>

<s>e 35′, e fa il suo in­<lb></lb>tero periodo in sedici giorni e ore diciotto, minuti 7′, 12″, 21tʹ, 9qʹ ” (ivi, <lb></lb>T. CXLI, c. </s>

<s>202). </s></p><p type="main">

<s>Nel <emph type="italics"></emph>Discorso intorno al mondo<emph.end type="italics"></emph.end> lo stesso Viviani torna a trattar de&#039;Quat­<lb></lb>tro pianeti medicei, e riporta gli elementi stessi delle Tavole da noi di sopra <lb></lb>riferiti: “ Grande in vero ed utilissimo a noi abitatori della Terra si è il <lb></lb>nuovo scoprimento de&#039;quattro Pianeti fatto dalla più che lincea accortezza <lb></lb>del nostro Galileo, quali, in onore dell&#039;eroica prosapia della casa reale di <lb></lb>Toscana, volle che si appellassero Stelle medicee, affinchè la memoria e la <lb></lb>fama di Essa godesse della vita e della sorte degli stessi Pianeti. </s>

<s>Tre di <lb></lb>queste furono la prima volta osservate dal predetto Galileo il dì 7 Gen­<lb></lb>naio 1610, nella prima ora della notte, e il quarto nel 14 dell&#039;istesso mese, <lb></lb>e per molte osservazioni ch&#039;ei vi fece, si accorse che giravano intorno al <lb></lb>detto Pianeta. </s>

<s>Il più prossimo di tutti è lontano dal centro di Giove 5 2/3 <pb xlink:href="020/01/994.jpg" pagenum="437"></pb>semid. </s>

<s>del medesimo Giove, ed il suo periodo lo termina in un giorno e <lb></lb>ore 18, 22′. </s>

<s>Il secondo è lontano per 9 semidiametri, e compisce il suo pe­<lb></lb>riodo in giorni 3, ore 13, 14′. </s>

<s>Il terzo è lontano per più di 14 semid. </s>

<s>ed <lb></lb>il suo periodo lo termina in giorni 7, h. </s>

<s>3, 42′. </s>

<s>Il quarto più discosto di <lb></lb>tutti è lontano di più di 25 semid. </s>

<s>e compisce il suo periodo in giorni 16, <lb></lb>h. </s>

<s>3, 2′ ” (ivi, c. </s>

<s>277). </s></p><p type="main">

<s>In questo mentre che il Viviani attendeva così alle osservazioni e ai <lb></lb>calcoli de&#039;Medicei, il Cassini, eccitato anch&#039;egli dalla notizia di ciò che si <lb></lb>studiava nell&#039;Accademia fiorentina, mandò a lui manoscritte le Tavole dei <lb></lb>suoi <emph type="italics"></emph>Elementi.<emph.end type="italics"></emph.end> Aveva parecchi anni avanti, e prima che nascessero fra loro <lb></lb>le fiere e ostinate inimicizie, il Viviani stesso avuto copia dal Borelli di <lb></lb>quella Tavola delle Radici, di che abbiamo parlato più sopra, e intendendo <lb></lb>di promuovere la gloria di Galileo e di avvantaggiare la scienza, la mandava <lb></lb>il di 22 Dicembre 1665 al grande Astronomo di Bologna, accompagnata da <lb></lb>una sua Lettera dove diceva: “ L&#039;inclusa Tavola del Galileo è copiata da <lb></lb>una che anni sono m&#039;inviò di Messina il signor Borelli, e la quale io tra­<lb></lb>smetto a V. S. in ordine all&#039;intenzione che mi sovviene di averle data, che <lb></lb>sarebbe gratissimo che questa potesse in qualche parte conferire alla cor­<lb></lb>rezione delle osservazioni sue intorno alle Medicee, benchè io credo che in <lb></lb>oggi, mediante la maggior perfezione degli Occhiali, ed esquisitezza degli <lb></lb>Orologi, ed esattezza de&#039;modi ritrovati dopo per misurar le distanze di quelle <lb></lb>da Giove, si sia arrivati ancora a maggiore approssimazione nelle determi­<lb></lb>zioni di esse distanze e de&#039;moti medii de&#039;Pianetini, siccome delle loro ec­<lb></lb>centricità ” (ivi, T. CXLII, c. </s>

<s>107). </s></p><p type="main">

<s>Il Cassini rispondeva il dì 9 Gennaio seguente essergli stato carissimo <lb></lb>il Foglio de&#039;moti de&#039;Pianeti gioviali trasmessogli come opera di Galileo, e <lb></lb>confrontati que&#039;numeri co&#039;suoi, aveva trovato esser queste le più notabili <lb></lb>differenze: “ Ho veduto che i moti del signor Galileo sono presi dalla con­<lb></lb>giunzion superiore de&#039;Pianetini con Giove, mentre i miei sono presi dal <lb></lb>principio di Ariete, ma ridotti i miei all&#039;istesso principio trovo essere in ogni <lb></lb>Pianeta i moti medii più tardi di quelli del Galileo, almeno quindici secondi <lb></lb>il giorno, ed almeno un grado e mezzo l&#039;anno, il che dal tempo che si os­<lb></lb>serva importa almeno 84 gradi. </s>

<s>” </s></p><p type="main">

<s>“ E quanto alle Radici, la mia rappresenta nell&#039;istesso grado le Radici <lb></lb>del Galileo nel 1636 del III e del IV Pianeta; quella del II nel termine di <lb></lb>tre, e quella del I nel termine di gradi 20. Ma osservo che il primo era <lb></lb>allora vicinissimo allo Scorpione, niente opportuno a presentare dalle osser­<lb></lb>vazioni la sua Radice. </s>

<s>Nel 1616 i miei numeri rappresentano la Radice del <lb></lb>Galileo del I Pianetino nel termine di 11 gradi, il che dimostra che nel 1636 <lb></lb>sì gran differenza non può attribuirsi a difetto de&#039;miei numeri, perchè molto <lb></lb>maggiore sarebbe riuscita nel 1616, eppure è molto minore. </s>

<s>Ma nella Ra­<lb></lb>dice del II discordiamo 74 gradi, in quella del III 72, in quella del IV so­<lb></lb>lamente 5 gradi. </s>

<s>” </s></p><p type="main">

<s>“ Nella Radice del 1600 ci allontaniamo tutto il cielo, onde tengo per <pb xlink:href="020/01/995.jpg" pagenum="438"></pb>fermo che a quelle del Galileo sia stato apposto per errore l&#039;anno 1600, <lb></lb>invece dell&#039;anno 1610, perchè i miei numeri quell&#039;anno rappresentano i <lb></lb>predetti assai da vicino, cioè la Radice del I nel termine di gradi 8, del <lb></lb>II di gradi 14, del III di gradi 7, del IV di gradi 5, onde raccolgo che le <lb></lb>grandi differenze del 1616 nemmeno procedano da&#039;miei numeri, perchè riu­<lb></lb>scirebbero maggiori nel 1610. ” </s></p><p type="main">

<s>“ Le radici del 1610 e del 1615, non avendo aggiunta l&#039;ora, ho sup­<lb></lb>posto che siano ridotte al mezzogiorno dell&#039;ultimo dell&#039;anno precedente, nè <lb></lb>essendovi aggiunto il luogo non ho tenuto conto della differenza del meri­<lb></lb>diano, il che non so se fosse per portar maggiore o minor differenza. </s>

<s>” </s></p><p type="main">

<s>“ Le grandezze degli Orbi sono dentro a termini maggiori e minori, e <lb></lb>che si osservano in diversi tempi maggiori però di quelle che osservai l&#039;anno <lb></lb>passato, ed osservano le regole da me toccate nella Lettera delle ombre, cioè <lb></lb>sono quasi in continua proporzione, in modo che la proporzione de&#039;più este­<lb></lb>riori agli interiori vicini è sempre un poco maggiore di quella delli meno <lb></lb>esteriori agli altri suoi interiori. </s>

<s>Inoltre, paragonati con i loro moti perio­<lb></lb>dici, risplende quivi ancora prossimamente quella proporzione che, secondo <lb></lb>la regola de&#039;progetti, avrebbero, se avessero acquistato quell&#039;altezza con es­<lb></lb>sere stati progetti con tal velocità da Giove. </s>

<s>” </s></p><p type="main">

<s>“ Prego V. S. a confrontare con altri esemplari, se altri ve ne sono, i <lb></lb>numeri delle prime Radici ed avvisarmi se si trova differenza o no ” (ivi, <lb></lb>T. CXLV, c. </s>

<s>1, 2). </s></p><p type="main">

<s>Il Viviani mandò veramente un&#039;altra Nota delle Radici per confrontare <lb></lb>con quella prima, accennando al dubbio se fosse quella Nota propriamente <lb></lb>di Galileo o del Castelli, per cui il Cassini rispondeva ai di 3 Aprile di quel­<lb></lb>l&#039;anno 1666: “ Mi è anche stata carissima la Nota delle Radici delle Medi­<lb></lb>cee, siano del Galileo o del Castelli, le quali concordano con le prime man­<lb></lb>date, eccetto che nel 1600 in luogo di 1610 ” (ivi, c. </s>

<s>8). </s></p><p type="main">

<s>Nel 1668 que&#039;diligentissimi studii, che aveva fatto il Cassini intorno a <lb></lb>Giove, uscirono in Bologna alla luce sotto il titolo di <emph type="italics"></emph>Ephemerides bono­<lb></lb>nienses Mediceorum syderum,<emph.end type="italics"></emph.end> nè vogliamo chiamar altri a giudicarne che <lb></lb>il proprio Autore, il quale così soggiungeva nell&#039;opuscolo <emph type="italics"></emph>De l&#039;origine de <lb></lb>l&#039;Astronomie,<emph.end type="italics"></emph.end> dop&#039;aver accennato alla scoperta e alle osservazioni de&#039;Satel­<lb></lb>liti di Giove: “ On avoit déja donné au public des Tables de leur mouve­<lb></lb>ment, mais les erreurs imperceptibles, que l&#039;on n&#039;avoit pù y éviter, s&#039;étoient <lb></lb>tellement accumulées, dans la suite du tems, que ces Tables étoient deve­<lb></lb>nuës inutiles ” (Divers Ouvr. </s>

<s>d&#039;Astronom., Amsterdam 1736, pag. </s>

<s>44). </s></p><p type="main">

<s>Quegli errori, se il Cassini disse non aver potuto evitarli, doveva anche <lb></lb>averli presentiti in quelle discrepanze fra&#039;numeri delle massime digressioni, <lb></lb>che resultavano dalle misure prese in varie osservazioni; discrepanze che il <lb></lb>Borelli e poi il Newton attribuivano per la massima parte alla mancanza o <lb></lb>all&#039;imperfezione degli Strumenti micrometrici. </s>

<s>Nell&#039;opuscolo <emph type="italics"></emph>De mundi Sy­<lb></lb>stemate,<emph.end type="italics"></emph.end> volendo il celebre Inglese riscontrar nel piccolo Mondo gioviale la <lb></lb>legge delle forze attrattive in ragion reciproca de&#039;quadrati delle distanze <pb xlink:href="020/01/996.jpg" pagenum="439"></pb>riporta quelle medesime distanze misurate da Galileo, dal Mario, dal Cas­<lb></lb>sini e dal Borelli, prima dell&#039;invenzione del Micrometro, <emph type="italics"></emph>et post inventionem <lb></lb>Micrometri,<emph.end type="italics"></emph.end> quelle del Tounley e del Flamsteed. (Lausannae 1744, pag. </s>

<s>9). </s></p><p type="main">

<s>Ma i numeri, per quel che riguarda i nostri Italiani, se si eccettui il <lb></lb>Cassini che gli pose a pag. </s>

<s>15 delle Effemeridi bolognesi, non son derivati <lb></lb>da fonti sicure. </s>

<s>Le massime distanze da Giove, ritrovate da Galileo per i <lb></lb>primi tre Satelliti, il Newton le ricopia dall&#039;Hodierna, ma di dove questi le <lb></lb>ricavasse non l&#039;abbiamo potuto sapere. </s>

<s>A pag. </s>

<s>11 della citata Menologia fa <lb></lb>menzione di ciò che si legge “ in libro De maculis solaribus ” dove l&#039;Au­<lb></lb>tore ” in schemate Jovis et Satellitum asserit digressiones maximas Quar­<lb></lb>tae et supremae Stellae, quae tres alias circumambit, non trascendere duo­<lb></lb>decim apparentes Jovis diametros. </s>

<s>” Ma in verità non dice altro l&#039;Autore <lb></lb>delle Macchie solari se non che la IV Stella “ è lontana da Giove circa a <lb></lb>15 minuti, che tanto è il semidiametro del suo cerchio ” (Alb. </s>

<s>III, 497, 98). <lb></lb>Or perchè Galileo determinò come vedemmo l&#039;apparente grandezza di Giove <lb></lb>ora in 39, ora in 41, ora in 50 minuti secondi, la più piccola delle distanze <lb></lb>che ne risulterebbe sarebbe 18 diametri di Giove, e non 12 come pone <lb></lb>l&#039;Hodierna. </s></p><p type="main">

<s>Ma nemmeno le digressioni degli altri tre Satelliti, attribuite a Galileo <lb></lb>dall&#039;Hodierna e dal Newton, riscontrano con nessuna di quelle, che vera­<lb></lb>mente Galileo lasciò ne&#039;suoi scritti, ai tempi de&#039;due detti Astronomi non <lb></lb>conosciuti. </s>

<s>E perchè Galileo stesso si provò più volte e per varie vie a de­<lb></lb>finir più giustamente che fosse possibile quelle misure, avendone sempre un <lb></lb>resultato alquanto diverso, noi vogliamo nella Tavoletta seguente riferirle in <lb></lb>ordine, per maggiore comodità di riscontro, aggiungendovi quelle che ri­<lb></lb>trovò il Viviani proseguendo i metodi del suo Maestro. </s></p><p type="main">

<s>Noi designeremo i Satelliti co&#039;nomi che impose a loro il Cassini, rac­<lb></lb>comandandocegli alla memoria col verso <emph type="italics"></emph>Pallas, Juno, Themisque, Ceres <lb></lb>tibi Jupiter adstant.<emph.end type="italics"></emph.end> Dal n.o I al n.o IV si riferiscono i moduli presi da Ga­<lb></lb>lileo per i quattro varii Schematismì de&#039;seni (Alb. </s>

<s>V, 175, 76). Il n.o V ri­<lb></lb>ferisce le massime digressioni scritte in una Lettera al Castelli (ivi, VI, 319). <lb></lb>Il n.o VI quelle date come <emph type="italics"></emph>Rationes pro radiis Orbitarum<emph.end type="italics"></emph.end> (ivi, V, 248) e <lb></lb>il n.o VII quelle che il dì 14 Gennaio 1617 divisò di ridurre a nuove mi­<lb></lb>sure <emph type="italics"></emph>in gratiam superioris correctionis Tabularum<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>290). Di rin­<lb></lb>contro al n.o VIII si pongono le massime digressioni poste dal Viviani nella <lb></lb>Tavola di Giove (MSS. Gal. </s>

<s>Disc., T. CXL, c. </s>

<s>17) e in ultimo il n.o IX ri­<lb></lb>ferisce le&#039;dette misure inserite dallo stesso Viviani nelle Osservazioni del <lb></lb>Gadroy (ivi, T. CXLI, c. </s>

<s>202). <pb xlink:href="020/01/997.jpg" pagenum="440"></pb><figure id="id.020.01.997.1.jpg" xlink:href="020/01/997/1.jpg"></figure></s></p><p type="caption">

<s><emph type="italics"></emph>Raggi delle Orbite delle Medicee in semidiametri di Giove.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Chi rivolge lo sguardo su questa Tavola ritrova di fatto quelle discre­<lb></lb>panze, che misero il Borelli in gran pensiero e in gran sollecitudine di con­<lb></lb>ciliarle con la più vera misura, trovata per osservazioni più diligenti, e con <lb></lb>Istrumenti più esatti. </s>

<s>La VII posizione è quella che il Newton attribuisce <lb></lb>al Borelli, e ch&#039;ei chiama <emph type="italics"></emph>magis exacta,<emph.end type="italics"></emph.end> ma più esatta che mai è la VIII <lb></lb>del Viviani, la quale, da una piccola differenza in fuori nel III Satellite, ri­<lb></lb>scontra con quella ritrovata nel 1671 dal Cassini. </s></p><p type="main">

<s>Le massime distanze poste nelle Effemeridi bolognesi furono dall&#039;Au­<lb></lb>tore misurate in più modi, ma principalmente col Micrometro a reticolo del <lb></lb>Montanari, che trovò descritto nelle Effemerìdi del Malvasia, e per mezzo <lb></lb>del tempo, che impiega un Satellite, a passare o avanti o dietro il disco di <lb></lb>Giove, comparato al tempo che Giove stesso impiega a passar per un filo <lb></lb>teso perpendicolarmente alla direzione del suo moto diurno. </s>

<s>Ma egli avverti <lb></lb>una causa di errore nella variabilità de&#039;tempi de&#039;passaggi per ragion delle <lb></lb>latitudini de&#039;Satelliti, che perciò non sempre passano per il centro del Pia­<lb></lb>neta; causa di errore, ch&#039;egli poi destramente evitò, nell&#039;occasione presen­<lb></lb>tatasi l&#039;anno 1671, quando ritornando i Satelliti al loro Nodo boreale, le <lb></lb>congiunzioni riuscivano senza dubbio centrali. </s></p><p type="main">

<s>Da ciò che occorse al Cassini si comprende che le notate discrepanze <pb xlink:href="020/01/998.jpg" pagenum="441"></pb>dipendevano, oltre al difetto e all&#039;imperfezion del Micrometro, da un&#039;altra <lb></lb>causa, che è quella delle variabilità delle latitudini, intorno alle quali insor­<lb></lb>sero tali e sì importanti questioni, che non si vogliono lasciare addietro in <lb></lb>questa Storia. </s></p><p type="main">

<s>L&#039;Agucchia, nella Lettera altrove citata, dop&#039;aver descritti a Galileo i <lb></lb>tempi periodici delle Medicee da sè trovati, soggiunge: “ Mi è stato anche <lb></lb>avviso di comprendere che questa (la Medicea più lontana) retrogradi al­<lb></lb>quanto nella dimora o stazione sua occidentale, poichè due volte in trenta­<lb></lb>quattro dì tornò dai dieci alli otto minuti; onde mi ha fatto cadere nel pen­<lb></lb>siero che possa avere qualche cerchietto, quasi epiciclo, intorno al quale si <lb></lb>raggiri, e forse per simile ragione avviene che talora si sieno vedute pie­<lb></lb>gare all&#039;Ostro, talvolta a Tramontana ” (Alb. </s>

<s>VIII, 175). </s></p><p type="main">

<s>Galileo, ch&#039;era stato infin da principio nell&#039;opinione che i piani delle <lb></lb>orbite delle Stelle gioviali fossero paralleli al piano dell&#039;Ecclittica, a queste <lb></lb>parole cominciò a pensar meglio al fatto, ma non aveva modo di assicurar­<lb></lb>sene, infintanto che, inventato lo Strumento micrometrico descritto del Bo­<lb></lb>relli, sperò che potesse questo servir bene all&#039;uopo. </s>

<s>“ Nota quod si in Instru­<lb></lb>mento, quo distantiae capiuntur, notetur linea, quae illum secet secundum <lb></lb>angulum, quo ductus Eclypticae secat parallelum Aequatori, in loco Jovis; <lb></lb>per motum Jovis in hac linea cognoscetur numquid Medicei Planetae feran­<lb></lb>tur in planis Ecclipticae parallelis ” Alb. </s>

<s>V, 84). </s></p><p type="main">

<s>Se poi facesse anche quest&#039;uso dello Strumento, e qual resultato ne <lb></lb>avesse, è incerto: solamente sappiamo che nella II Lettera solare scriveva <lb></lb>al Velsero essergli note “ le cause del quando e perchè or l&#039;uno or l&#039;altro <lb></lb>de&#039;Satelliti declina o verso Borea o verso Austro in relazione a Giove ” <lb></lb>(Alb. </s>

<s>III, 395). Ma mentre s&#039;aspettava che Galileo dicesse quali fossero que­<lb></lb>ste cause, che al Velsero non dice, e mentre il Castelli francamente asseriva <lb></lb>di non essersi “ ingannato punto in notare le strane declinazioni di queste <lb></lb>stelle ” (MSS. Gal., P. III, T. VII, c. </s>

<s>28) Simon Mario pubblicava il suo <lb></lb><emph type="italics"></emph>Mundus Jovialis,<emph.end type="italics"></emph.end> dove esplicando nella II Parte il Fenomeno VI, così di­<lb></lb>ceva: “ Postquam vero mihi etiam de hoc phaenomeno constaret, nimirum <lb></lb>hos Joviales non semper in linea recta ducta per Jovem Ecclipticae paral­<lb></lb>lela versari, sed modo in Boream modo in Austrum ab hac deflectere, dif­<lb></lb>ferentia perceptibili; coepi etiam in hoc phaenomenon diligentius inquirere, <lb></lb>tandemque deprehendi hos Joviales, in maxima elongatione, semper in prae­<lb></lb>dicta linea parallela offendi, extra vero hos terminos semper ab hac decli­<lb></lb>nare, et in superiore quidem parte suae orbitae australes esse, in inferioro <lb></lb>vero boreales ” (Norimbergae 1614, pag. </s>

<s>42). </s></p><p type="main">

<s>Galileo indugiò dopo il Mario nove anni a dir ciò che pensava di que­<lb></lb>ste latitudini, e lo fece a principio del <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> negando contro lo stesso <lb></lb>Mario che i quattro cerchi delle Medicee inclinino dal piano dell&#039;Ecclittica, <lb></lb>e asserendo che “ anzi sono eglino ad esso sempre equidistanti ” (Alb. </s>

<s><lb></lb>IV, 151). Quanto poi al segno della declinazione de&#039;semicerchi superiori, <lb></lb>ossia di quelli che son più lontani dalla Terra, rispetto ai semicerchi infe-<pb xlink:href="020/01/999.jpg" pagenum="442"></pb>riori, che son più vicini; Galileo stabilisce questa regola per costante e per <lb></lb>generale: “ Quando Giove si troverà fuori del piano dell&#039;Ecclittica, acca­<lb></lb>derà che, se la sua latitudine sarà da esso piano verso Settentrione, restando <lb></lb>pure i quattro cerchi delle Medicee paralleli all&#039;Ecclittica, si rappresente­<lb></lb>ranno piegar verso Austro rispetto all&#039;inferiori, che ci si mostreranno più <lb></lb>boreali. </s>

<s>Ed all&#039;incontro, quando la latitudine di Giove sarà australe, le parti <lb></lb>superiori dei medesimi cerchietti ci mostreranno più settentrionali dell&#039;in­<lb></lb>feriori ” (ivi, pag. </s>

<s>152). </s></p><p type="main">

<s>Trovò tuttavia pendente la controversia fra l&#039;Astronomo nostro di Fi­<lb></lb>renze e quello di Brandeburgo l&#039;Hodierna, il quale preso ad esaminarla, <lb></lb>ebbe a concludere che tutt&#039;e due avevano il torto: Galileo a dire che le <lb></lb>Medicee non hanno sensibili latitudini, avendole anzi <emph type="italics"></emph>valde sensibiles,<emph.end type="italics"></emph.end> il Mario <lb></lb>a dire che ne&#039;semicerchi superiori le latitudini sono australi e negl&#039;inferiori <lb></lb>boreali “ nam, ex quo Mediceorum latitudines observare cepi, eos perpe­<lb></lb>tuo boreales in superioribus semicirculis, austrinas vero in inferioribus de­<lb></lb>prehendo ” (Menologia cit., pag. </s>

<s>32). </s></p><p type="main">

<s>Rimase a ciò stupito l&#039;Hodierna, non sapendo da prima persuadersi <lb></lb>come tanto grossamente si fossero ingannati due così valorosi Osservatori. </s>

<s><lb></lb>Poi, scoperto che le latitudini erano variabili, allo stupore sottentrò la ra­<lb></lb>gione a persuaderlo che, quando osservò Galileo, le latitudini dovevano es­<lb></lb>ser nulle; che quando osservò il Mario dovevano esser al modo da lui de­<lb></lb>scritto, finchè variando presero la contraria posizione, a quel modo ch&#039;esso <lb></lb>Hodierna le vide, concludendo essersi ambedue i grandi Astronomi ingan­<lb></lb>nati nell&#039;asserire il fatto costante. </s></p><p type="main">

<s>Concorda insomma in ciò con l&#039;Hodierna anche il Cassini, il quale ap­<lb></lb>parecchiandosi, nel cap. </s>

<s>V delle <emph type="italics"></emph>Hypotheses des Satellites de Jupiter,<emph.end type="italics"></emph.end> a dar <lb></lb>le regole delle latitudini, nota, a proposito degli Osservatori che lo avevano <lb></lb>preceduto, “ comme les uns les ont observées dans un temps, et les autres <lb></lb>dans un autre, chacun a supposé que les règles, qu&#039;il a trouvées par les <lb></lb>observations de son temps, estoient perpetuelles ” (edit. </s>

<s>cit., pag. </s>

<s>390). Nè <lb></lb>qui possiamo lasciar di proporre ai Lettori questa considerazione: Che il <lb></lb>Mario, nel fretteloso circolo delle sue osservazioni, non si accorgesse della <lb></lb>variabilità delle latitudini, s&#039;intende, ma come può intendersi che non se ne <lb></lb>assicurasse Galileo, il quale durò ad osservare i Medicei, con fatica atlantica, <lb></lb>per ben diciannov&#039;anni? </s>

<s>Intanto che si attende la risposta, la quale vorrà <lb></lb>ancora indugiare, noi ci affrettiamo ad aggiunger questo pure agli altri ar­<lb></lb>gomenti, per provar quanto le Effemeridi pubblicate dall&#039;Albèri fossero poco <lb></lb>accurate. </s></p><p type="main">

<s>Comunque sia, proseguendo il corso della Storia, prese dopo l&#039;Hodierna <lb></lb>a trattar la questione delle latitudini il Borelli, nel II Libro delle sue <emph type="italics"></emph>Theo­<lb></lb>ricae,<emph.end type="italics"></emph.end> e segnatamente ne&#039;quattro ultimi capitoli. </s>

<s>Egli confermò il fatto delle <lb></lb>variabilità di esse latitudini, investigando con sottilissima diligenza il periodo <lb></lb>della retrogradazione della linea de&#039;nodi, ch&#039;egli attribuiva a cause fisiche <lb></lb>e meccaniche assai somiglianti alle neutoniane. </s></p><pb xlink:href="020/01/1000.jpg" pagenum="443"></pb><p type="main">

<s>Il Cassini però, con riverenza di un <emph type="italics"></emph>homme si illustre et si consummé <lb></lb>dans le Mathematiques,<emph.end type="italics"></emph.end> crede di dover tenere altra via, e che sia perciò a <lb></lb>proposito “ de commencer par la distinction des apparences d&#039;optique, qui <lb></lb>se sont dans les orbes des Satellites à cause de la diversité des élevations <lb></lb>de nostre oeil sur le plan de l&#039;orbite de Jupiter, la quelle diversité est une <lb></lb>des causes principales de la difference, qu&#039;il y a entre les latitudes des Sa­<lb></lb>tellites vûês de la Terre, et celles qui en mesme temps seroient vûês du <lb></lb>Soleil, dont la connaissance est necessaire pour réduire les unes aux autres, <lb></lb>tant dans l&#039;établissement de leur theorie, que dans l&#039;usage, qu&#039;il en faut <lb></lb>faire ” (ivi, pag. </s>

<s>392). Ma il Newton, dimostrando poi esser causa princi­<lb></lb>pale della varietà delle latitudini l&#039;attrazion reciproca de&#039;Satelliti fra loro e <lb></lb>con Giove, parve decidere insieme che più vicina al vero fosse andata a co­<lb></lb>gliere la Meccanica del Borelli, che non l&#039;Ottica del Cassini. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;Ottica piuttosto che là dove si tratta di moti, ricorre qua più oppor­<lb></lb>tuna, dove si narra come variamente s&#039;appresentasse l&#039;aspetto di Giove ai <lb></lb>varii osservatori. </s>

<s>E per muover dai primi principii è da ritornar sopra quelle <lb></lb>parole, che scriveva il Cigoli a Galileo, e in cui gli diceva che Giove il Pas­<lb></lb>signano <emph type="italics"></emph>lo vede montuoso.<emph.end type="italics"></emph.end> Ciò in altre parole significava essere state vedute <lb></lb>alcune macchie nel disco del Pianeta, le quali si attribuivano all&#039;ombre git­<lb></lb>tate dai monti insolati, come nella Luna, e forse preluceva alla mente del <lb></lb><figure id="id.020.01.1000.1.jpg" xlink:href="020/01/1000/1.jpg"></figure></s></p><p type="caption">

<s>Figura 87.<lb></lb>nostro Passignano il concetto del Tilorier, che <lb></lb>credeva esser le fasce oscure lunghi e irsuti <lb></lb>gioghi di montagne. </s></p><p type="main">

<s>Comunque sia, eccitato Galileo da quelle <lb></lb>parole si dette più attentamente ad osservare, <lb></lb>e con schizzo in penna rappresentò l&#039;aspetto <lb></lb>generale di Giove come si vede ritratto qui <lb></lb>nella 87a figura. </s>

<s>Nel punto A gli appariva una <lb></lb><figure id="id.020.01.1000.2.jpg" xlink:href="020/01/1000/2.jpg"></figure></s></p><p type="caption">

<s>Figura 88.<lb></lb>macchia più distinta, <lb></lb>l&#039;apparenza della qua­<lb></lb>le volle più particola­<lb></lb>mente descriver nella <lb></lb>figura 88, in relazione a un tratto d&#039;ombra, sul­<lb></lb>l&#039;orlo della quale compariva più fosca. </s>

<s>Quella mac­<lb></lb>chia poi solitaria, che rassomiglia a un cratere, e <lb></lb>quell&#039;altre ombre, che rappresentano qualche dorso <lb></lb>e qualche vetta di monte, si vedono con diligenza <lb></lb>disegnate nelle figure 89, 90 e 91. </s></p><p type="main">

<s>Forse la penna, piuttosto che alla distinta visione telescopica, teneva <pb xlink:href="020/01/1001.jpg" pagenum="444"></pb>dietro alle lucide apprensioni della fantasia, nè l&#039;esser que&#039;disegni condotti <lb></lb>nel margine della carta 68 del T. V, P. III de&#039;Manoscritti galileiani, dove <lb></lb><figure id="id.020.01.1001.1.jpg" xlink:href="020/01/1001/1.jpg"></figure></s></p><p type="caption">

<s>Figura 89.<lb></lb><figure id="id.020.01.1001.2.jpg" xlink:href="020/01/1001/2.jpg"></figure></s></p><p type="caption">

<s>Figura 90.<lb></lb>son calcoli rela­<lb></lb>tivi alle Medicee, <lb></lb>è argomento cer­<lb></lb>to che si voglia in <lb></lb>quel modo raffi­<lb></lb>gurar l&#039;aspetto <lb></lb>propriamente di <lb></lb>Giove, macomun­<lb></lb>que sia, abbiam <lb></lb>sopra quelle figure voluto richiamar l&#039;attenzione de&#039;nostri Lettori, se cre­<lb></lb>dessero di servirsene come argomento da rispondere all&#039;Arago, il quale si <lb></lb><figure id="id.020.01.1001.3.jpg" xlink:href="020/01/1001/3.jpg"></figure></s></p><p type="caption">

<s>Figura 91.<lb></lb>maravigliava che Galileo non abbia fatta men­<lb></lb>zione mai delle Macchie gioviali, e domandava <lb></lb>con ghigno maliziosetto se “ les bandes n&#039;aura­<lb></lb>ient-elles pas existé du temps de cet immortal <lb></lb>observateur. </s>

<s>” </s></p><p type="main">

<s>Di quelle zone la Maestà di Giove si sarà <lb></lb>precinti i fianchi, infin da quando salì sul suo <lb></lb>trono reale, ma per vederle sotto quella distinta <lb></lb>figura ci bisognavano strumenti un poco più perfetti di quelli fabbricati da <lb></lb>Galileo. </s>

<s>Francesco Fontana nel 1630 (Novae Observ., 1646, pag. </s>

<s>110) fu primo <lb></lb>co&#039;suoi Canocchiali a notare una tal novità, ma dubitò non forse dovesse <lb></lb>“ crystalli vitio id accidere ” (pag. </s>

<s>107). Il Castelli in Roma vide due anni <lb></lb>dopo la stessa cosa, ma nemmen egli ne aveva certezza. </s>

<s>Intanto però l&#039;Ot­<lb></lb>tico napoletano, per dar credito alla fabbrica, divulgò la notizia che co&#039;suoi <lb></lb>nuovi Canocchiali vedevasi Giove “ fasciolis duabus ambitus ” (pag. </s>

<s>110). </s></p><p type="main">

<s>Giunse quella voce, circa il 1640, alle orecchie del Granduca in Pisa, <lb></lb>dove ne tenne discorso col Renieri, a cui sovvenne poco dopo un arguto <lb></lb>pensiero di servirsi delle mutazioni che avrebbero dovuto far quelle fasce, <lb></lb>come di nuovo argomento a confermar la verità del Sistema copernicano. </s>

<s>Ne <lb></lb>scrisse in proposito al principe Leopoldo, supposto che fosse stata verificata <lb></lb>la notizia venuta di Napoli, ma il Principe rispose che, non essendosi po­<lb></lb>tute vedere in Firenze quelle fascie gioviali, dubitava se l&#039;osservazione degli <lb></lb>Astronomi napoletani <emph type="italics"></emph>fosse stata fatta bene<emph.end type="italics"></emph.end> (Alb. </s>

<s>V, 368). </s></p><p type="main">

<s>In ogni modo, nel 1642 il Renieri medesimo si assicurò di ogni dub­<lb></lb>bio e lasciò nota a carte 53 de&#039;suoi Manoscritti raccolti nel T. VI della <lb></lb>P. III insieme co&#039;galileiani, dicendo di aver co&#039;suoi proprii occhi ve­<lb></lb>duto veramente Giove “ fasciolis duabus ambitus ” (Alb. </s>

<s>V, 366) come ave­<lb></lb>vano dato a intendere le voci venute di Napoli. </s>

<s>L&#039;anno appresso se ne as­<lb></lb>sicurò pure anche il Fontana, il quale anzi vide Giove non più “ duabus, <lb></lb>sed tribus fasciolis cinctus ” (Observ. </s>

<s>cit., pag. </s>

<s>112) e si persuase “ eas <lb></lb>vere in ipso Jovis corpore esse ” (ibi, pag. </s>

<s>107) e non un illusione ottica <pb xlink:href="020/01/1002.jpg" pagenum="445"></pb>delle lenti. </s>

<s>Pubblicando poi nel 1646 le sue <emph type="italics"></emph>Novae coelestium terrestrium­<lb></lb>que Rerum observationes,<emph.end type="italics"></emph.end> volle nel cap. </s>

<s>II del Trattato V descriver tuttociò <lb></lb>che da sedici anni aveva osservato in Giove, e dop&#039;aver detto delle fascie <lb></lb>soggiunge: “ haec deprehensio nova est ” (pag. </s>

<s>107). </s></p><p type="main">

<s>Que&#039;primi, che lessero ciò che così scriveva il povero Occhialaio, do­<lb></lb>mandavano all&#039;orgoglioso rivale di lui Matematico primario del Granduca: <lb></lb>— È co&#039;vostri Canocchiali si son vedute simili novità in Giove? </s>

<s>— A che <lb></lb>rispondeva il Torricelli, dicendo per sua scusa non si poter le fascie gio­<lb></lb>viali citar come prova della maggior potenza de&#039;Telescopi, essendo anzi state <lb></lb>vedute da&#039;primi Osservatori con Istrumenti assai mediocri. </s>

<s>“ Quanto al ve­<lb></lb>der le fasce in Giove, scriveva il di 10 Febbraio 1646 a Michelangiolo Ricci, <lb></lb>io non l&#039;ho mai vedute, perchè non si vedono sempre, e quando io ho avuto <lb></lb>l&#039;occasione di guardarlo, il che è stato da quattro o sei volte dopo che son <lb></lb>tornato in Firenze, non vi si vedevano. </s>

<s>Del resto, D. </s>

<s>Benedetto l&#039;ha vedute <lb></lb>in Roma in presenza mia, già sono circa 14 anni, con Occhiale mediocre. </s>

<s><lb></lb>Don Vincenzio Renieri l&#039;ha vedute, già sono sino a sei anni, con Occhiale <lb></lb>mediocre, ed altri le vedono continuamente con Occhiali, che non sono per­<lb></lb>fetti ” (MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>93). </s></p><p type="main">

<s>Fatta insomma e assicurata la scoperta delle Fasce gioviali si doman­<lb></lb>dava da che avessero origine. </s>

<s>Il Fontana dubitò che fossero profonde fes­<lb></lb>sure nel corpo di Giove. </s>

<s>“ Forsitan in Juppiteris corpore circulares rimae <lb></lb>existunt ” (Observ. </s>

<s>cit., pag. </s>

<s>107) e questa poteva stare insiem con altre <lb></lb>opinioni più strane fondate tutte nel supposto che le fasce dipendessero da <lb></lb>cause sempre stabilmente operanti. </s>

<s>Ma più accurate osservazioni vi fecero <lb></lb>scoprire una tale variabilità, che non si conciliava con quelle prime ipotesi. </s>

<s><lb></lb>L&#039;Huyghens, il quale aveva avvertito a quella instabilità di forme che sempre <lb></lb>presentano in Giove le fasce, descriveva nel suo <emph type="italics"></emph>Systema Saturnium<emph.end type="italics"></emph.end> il fatto <lb></lb>osservato con queste parole: “ Porro quae in Jove zonae seu fasciae qui­<lb></lb>busdam animadversae sunt non semper eadem forma praeditae, has ego et <lb></lb>qui mecum observarunt perspicue saepe animadvertimus reliquo Jovis cor­<lb></lb>pore magis lucidas, cum tamen alii obscuriores asserant, quibus forsitan in­<lb></lb>teriectum spatium inter binas zonas lucidiores pro una obscuriore fuerit. </s>

<s><lb></lb>Atque anno quidem 1656, multo maiori intervallo, quam sequentibus tri­<lb></lb>bus, illas a se mutuo distare comperimus ” (Op. </s>

<s>varia, Lgd. </s>

<s>Batav. </s>

<s>1724, <lb></lb>pag. </s>

<s>540). </s></p><p type="main">

<s>Il Cassini, per altre sue osservazioni fatte con un eccellente Canoc­<lb></lb>chiale del Campani, aggiungeva nuove particolarità al fatto osservato dal­<lb></lb>l&#039;Huyghens, che consistevano nell&#039;aver vedute le fasce di Giove anfrattuose <lb></lb>e variamente asperse d&#039;ombra e di luce, e nell&#039;avere scorto fra que&#039;due <lb></lb>campi anfrattuosi un sottil filo lucido, e splendente più delle rimanenti parti <lb></lb>del disco. (Campani, Ragguaglio ecc., Roma 1664, pag. </s>

<s>39). </s></p><p type="main">

<s>Sopra quelle sue osservazioni stabili dunque l&#039;Huyghens stesso una sua <lb></lb>ipotesi dell&#039;origine delle fasce gioviali, dedotta da cause meteorologiche si­<lb></lb>mili a quelle che si vedono operar sulla Terra. </s>

<s>Galileo aveva già in parti-<pb xlink:href="020/01/1003.jpg" pagenum="446"></pb>colare applicato a Giove l&#039;ipotesi di un&#039;ammosfera vaporosa, che secondo il <lb></lb>Moestlin involge ogni altro Pianeta. </s>

<s>Con ciò, sulla fine dell&#039;Avviso Sidereo, <lb></lb>spiegava in che modo i Satelliti ora appariscano più grandi ora minori; mi­<lb></lb>nori quando sono apogei per esser da noi veduti attraverso all&#039;ammosfera <lb></lb>vaporosa di Giove, minori quando son perigei “ per eiusdem orbis ablatio­<lb></lb>nem seu attenuationem ” (Alb. </s>

<s>III, 99). </s></p><p type="main">

<s>Parve questa ad alcuni una dimostrazione dell&#039;esser lo stesso Giove <lb></lb>soggetto a vicende meteorologiche somiglianti a quelle della nostra Terra, <lb></lb>ma venne a infirmar l&#039;argomento il Keplero, spiegando piuttosto il fatto di <lb></lb>quelle varie apparenze con attribuire ai Satelliti una figura discoide, pre­<lb></lb>sentandoci la quale in maestà si mostrassero più grandi che quando ce la <lb></lb>presentano per taglio. </s>

<s>“ Si quatuor hi Planetae disci forma plano ad Jovem <lb></lb>converso circumeant, ut ad excursus maximos nobis et Soli obiiciantur ut <lb></lb>lineae, supra et infra irradientur perpendiculariter videnturque magni et <lb></lb>forte diversicolores sint pro diversitate planitierum ” (Alb. </s>

<s>V, 436). Ebbe <lb></lb>anche Simon Mario idee alquanto simili a queste, ma nell&#039;esplicazione del <lb></lb>VII Fenomeno della Parte seconda và anche più per le sottili, attribuendo <lb></lb>principalmente la varietà di grandezza de&#039;Satelliti alla varietà delle loro fasi, <lb></lb>come si osserva avvenir della Luna, la quale è variamente illuminata dal <lb></lb>Sole e dalla Terra, a quel modo che variamente sono illuminati i Medicei, <lb></lb>o secondo l&#039;Autore i Brandeburgici, dal Sole stesso e da Giove. </s>

<s>“ Genuinam <lb></lb>igitur et veram causam incrementi et decrementi quantitatis apparentis ho­<lb></lb>rum Siderum hanc esse censeo: videlicet quod illuminentur a Sole, eo <lb></lb>modo quo Luna.... Judico etiam quatuor sidera Brandeburgica imitari plane <lb></lb>Lunam, et duplici modo illuminari et a Sole et a vicino Jove ” (Mundus <lb></lb>Jov. </s>

<s>cit., pag. </s>

<s>44). </s></p><p type="main">

<s>Erano in ogni modo, a mezzo il secolo XVII, così approvate dagli Astro­<lb></lb>nomi le idee degli antichi Pitagorici intorno alla fisica costituzion de&#039;Pia­<lb></lb>neti somigliante a quella della nostra Terra, che l&#039;Huyghens vide nella <lb></lb>variabilità delle fasce un effetto di meteorologia gioviale, da rassomigliarsi a <lb></lb>quello delle nuvole terrestri. </s>

<s>“ Qua ex instabilitate non male forsan colli­<lb></lb>gemus ad instar nubium nostrarum vapores quosdam vicinum Jovi aethe­<lb></lb>rem insidere, qui nunc his, nunc illis climatis crebri magis consertique exo­<lb></lb>riantur ” (Systema Sat., Op. </s>

<s>var. </s>

<s>cit., pag. </s>

<s>539, 40). </s></p><p type="main">

<s>Dicemmo come queste fasce fossero dal Passignano rassomigliate alle <lb></lb>ombre gittate da lunghi gioghi di monti, e come Galileo descrivesse alcune <lb></lb>macchie particolari, le quali sembra che s&#039;incominciassero a vedere più di­<lb></lb>stintamente verso il 1638. Il Cavalieri infatti il dì 2 Ottobre di quell&#039;anno <lb></lb>scriveva una lettera al Castelli, domandandogli s&#039;era vero quel che aveva <lb></lb>sentito dire, cioè che coi nuovi Telescopi napoletani “ si vegga Giove con <lb></lb>la inegualità delle macchie come la Luna “ (Alb. </s>

<s>X, 319). </s></p><p type="main">

<s>Galileo, come par voglia farci intendere da que&#039;muti disegni che si po­<lb></lb>nevano dianzi sotto gli occhi de&#039;nostri lettori, attribuiva quelle macchie a <lb></lb>cavità aperte sulla superficie di Giove o a valli insenate fra&#039;monti. </s>

<s>Si ri-<pb xlink:href="020/01/1004.jpg" pagenum="447"></pb>scontrarono poi in questa opinione alcuni altri Astronomi, infintanto che la <lb></lb>variabilità osservata in esse macchie non consigliò a riformare, almeno in <lb></lb>parte, l&#039;ipotesi, a quel modo che s&#039;era dovuto far per le zone. </s>

<s>“ Licet ergo, <lb></lb>scriveva il Cassini ammonendo coloro che volessero osservar Giove con le <lb></lb>sue Effemeridi bolognesi fra le mani, quaedam variationes ex maculis, quae <lb></lb>saepe advertimus circa medium Jovis discum oriri et revolutionem suam <lb></lb>cum aliis circa Jovis axem prosequi censeri possint opticae, ut si forte val­<lb></lb>les aut cavernae essent obliqueae, quae in ea revolutione vario modo nobis <lb></lb>exponerentur, quod doctissimo p. </s>

<s>Francisco Eschinardo S. J. nobiscum de <lb></lb>hac re et privatis literis in eruditissimo opere optico disserenti concedimus; <lb></lb>illae tamen mutationes, quae nullam habent cum huiusmodi revolutione, aut <lb></lb>cum alio motu connexionem, non possint nobis non censeri physicae ” (Edi­<lb></lb>tio cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Intorno alla causa fisica però di queste mutazioni fu disputato fra il <lb></lb>Cassini e l&#039;Huyghens, il quale contemplava in Giove le nuvole piovose ora <lb></lb>condensate, ora dissipate dai venti. </s>

<s>“ In Jovis planeta, scriveva nel lib. </s>

<s>I del <lb></lb>Cosmoteoro, nubium quidem mutabiles tractus cernuntur vapores aquamque <lb></lb>haud dubie continentes, quam aliunde quoque illic non deesse argumentis <lb></lb>adstruebamus. </s>

<s>Erunt ergo et imbres et venti, quia attractum a Sole humo­<lb></lb>rem recidere in terram necesse est, et calore soluti vapores ventorum causa <lb></lb>sunt, quorum flatus ex illa nubium iovialium mutabili facie cognoscitur ” <lb></lb>(Opera cit., pag. </s>

<s>681). </s></p><p type="main">

<s>In queste nubi, che ora velano, ora lasciano allo scoperto la superficie <lb></lb>di Giove, vedeva altresì l&#039;Huyghens la causa fisica della variabilità delle <lb></lb>macchie, e considerando come debbono esse nubi riflettere all&#039;occhio nostro <lb></lb>maggior copia di luce, di quel che non faccia la superficie aspra del Pia­<lb></lb>neta, a ciò attribuiva quel candore, dal Cassini attribuito invece alle nevi <lb></lb>che incanutiscono i monti. </s>

<s>“ Maculae vero, quae immutabiliter globo eius <lb></lb>inhaerere conspiciuntur, saepe longo tempore obtectae manent, nubibus vi­<lb></lb>delicet illis interceptae, e quibus deinde rursus emergunt. </s>

<s>Atque etiam nu­<lb></lb>bes in medio Jovis disco exoriri quandoque annotatum fuit, et maculas <lb></lb>quasdam minores existere reliquo corpore magis lucidas, neque eas diu su­<lb></lb>peresse, quas Cassinus ex nivibus esse coniectabat cacumina montium insi­<lb></lb>dentibus. </s>

<s>Mihi non improbabile videtur terrae regiones candidiores esse <lb></lb>superfusis nubibus plerumque occultatas, ac nonnunquam ab iis liberas ” <lb></lb>(ibi, pag. </s>

<s>656). </s></p><p type="main">

<s>Il Cassini però ebbe sopra l&#039;Huyghens l&#039;abilità e la destrezza di far <lb></lb>servir queste macchie a confermar non solo, ma a stabilir ne&#039;precisi ter­<lb></lb>mini una importantissima notizia intorno ai moti proprii di Giove. </s>

<s>Il dì <lb></lb>6 d&#039;Agosto 1667 scriveva da Parigi una lettera al Viviani, a cui mandando <lb></lb>in alcuni fogli descritte le configurazioni delle Medicee, per quel corrente <lb></lb>mese di Agosto e per il Settembre appresso, “ V. S., gli diceva, osserverà <lb></lb>che in questi fogli ho notato una macchia di Giove, ne&#039;giorni che arriverà <lb></lb>verso il mezzo del suo disco nel tempo delle osservazioni, che è quella da <pb xlink:href="020/01/1005.jpg" pagenum="448"></pb>cui appresi la rivoluzione di Giove attorno al suo asse, la quale, dopo la <lb></lb>prima discoperta seguita l&#039;anno 1664, è disparita due volte e ritornata a <lb></lb>farsi vedere altrettante, dopo essere stata più anni invisibile ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. CXLVI, c. </s>

<s>157). </s></p><p type="main">

<s>S&#039;ha in queste parole tratteggiata la storia della rotazione di Giove, la <lb></lb>quale il Cassini chiama una sua scoperta fatta nel 1664. Da cinquantaquat­<lb></lb>tr&#039;anni però gli Astronomi leggevano nella Dissertazion kepleriana sul Nun­<lb></lb>cio Sidereo queste notabilissime parole: “ Adeoque et hoc argutissime Wa­<lb></lb>ckerius iam monuit etiam Jovem circa suum volvi axem, ut nostram Tellurem, <lb></lb>ut ad illam convolutionem gyratio illa quatuor Lunarum sequatur, uti ad <lb></lb>nostrae Telluris gyrationem nostrae Lunae conversio in eamdem plagam se­<lb></lb>quitur, adeoque nunc demum se credere rationibus magneticis, quibus, in <lb></lb>nupero meo Fhisicae coelestis commentario, volutione Solis circa axem et <lb></lb>polos corporis causas motuum planetarum expedivi ” (Alb. </s>

<s>V, 431, 32). </s></p><p type="main">

<s>L&#039;anno dopo, nella Prefazione alla Diottrica, tornò il Keplero sopra que­<lb></lb>sto soggetto, e dall&#039;aver trovato il tempo periodico del III Satellite di otto <lb></lb>giorni, argomentando che al primo e più vicino due sarebbero bastati, sa­<lb></lb>gacemente, dietro le sue ragioni magnetiche, divinava “ etiam ipsum Jovis <lb></lb>globum convolvi rapidissime et procul dubio celerius quam in unius diei <lb></lb>nostratis spacio ” (Augustae Vindelic. </s>

<s>1611, pag. </s>

<s>14). </s></p><p type="main">

<s>Quando poi lo Schirleo Rheita, alle ragioni magnetiche del Keplero so­<lb></lb>stituendo le proprie fantasie, dette tempo a Giove di rivolgersi in sè stesso <lb></lb>284 ore, prima il nostro Torricelli e poi l&#039;Huyghens rammemorarono le <lb></lb>smarrite dottrine kepleriane, che servirono a loro di sicura guida a cansar <lb></lb>gli errori e a prevedere il vero. </s>

<s>Nella sopra citata Lettera a Michelangiolo <lb></lb>Ricci, dop&#039;avere il Torricelli detto della scoperta delle fasce di Giove, sog­<lb></lb>giunge le seguenti alle già da noi riferite parole: “ Quanto al girarsi in sè <lb></lb>io lo tengo per certo, senza vedervi altro contrassegno. </s>

<s>Ogni corpo lassù, <lb></lb>intorno al quale si girino altri corpi, V. S. dica pure che gira anch&#039;esso, <lb></lb>ma in tempo più breve che qualunque altro corpo che gli si muova intorno. </s>

<s><lb></lb>Però io credo che s&#039;inganneranno coloro, che pensano che Giove metta più <lb></lb>giorni in fare una rivoluzione sola ” (MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>93). </s></p><p type="main">

<s>L&#039;Huyghens poi par che anche più fedelmente del Torricelli ripeta, in­<lb></lb>sieme con le dottrine, le parole scritte nella prefazione alla Diottrica keple­<lb></lb>riana. </s>

<s>“ Rursus Tellus haec, egli dice nel Sistema Saturnio, diurno spatio <lb></lb>gyratur, quam Luna menstruo motu ambit. </s>

<s>Jovis autem Planetam quatuor <lb></lb>minores, hoc est totidem Lunae circumstant, eadem hac lege ut propiores <lb></lb>quae sunt celeriore cursu ferantur. </s>

<s>Unde Jupiter quidem breviori forsitan <lb></lb>tempore quam 24 horarum converti censendus est, cum citissime ei lunula­<lb></lb>rum minus biduo impendat ” (Opera cit., pag. </s>

<s>564). </s></p><p type="main">

<s>Così argomentavasi per induzione che dovesse anche Giove rivolgersi <lb></lb>sul proprio asse, e che in più breve tempo di un giorno ne dovesse com­<lb></lb>piere il moto revolutorio, ma non s&#039;aveva ancora una prova fisica nè del­<lb></lb>l&#039;un fatto nè dell&#039;altro. </s>

<s>Quanto alla rivoluzione di Giove in sè stesso il <pb xlink:href="020/01/1006.jpg" pagenum="449"></pb>Fontana fu forse il primo ad argomentarla dal variar le fasce d&#039;aspetto e <lb></lb>di figura. </s>

<s>“ Jovem etiam circa proprium centrum volvi atque rotari, haec <lb></lb>fasciarum nova deprehensio indicat, nam non semper omnes, nec eodem <lb></lb>modo, interdum enim convexae, nonnunquam concavae et aliquando rectae <lb></lb>apparent, ut supra dictum est, nec in eodem situ semper deprehenduntur.... <lb></lb>et sic dicerem praedictas fascias mutare figuras, situm atque occultari, quia <lb></lb>Juppiter circa proprium movetur centrum ” (Novae observat. </s>

<s>cit., pag. </s>

<s>108). </s></p><p type="main">

<s>Da così fatte apparenze veniva senza dubbio a dimostrarsi che anche <lb></lb>Giove, come la Terra e il Sole si rivolgeva in sè stesso, ma era difficile, <lb></lb>per la figura continuata delle zone, il definire il periodo a quella revolu­<lb></lb>zione, non potendosi computar giusto, se non che dal ritorno di un qualche <lb></lb>punto, ben distinto sulla superficie del Pianeta, al medesimo segno della <lb></lb>mira telescopica d&#039;onde s&#039;era partito. </s>

<s>Il Cassini fissò questo punto in una <lb></lb>delle macchie più cospicue, e trovò a questo modo che Giove, benchè così <lb></lb>corpulento, non penava più che 9 ore e 56 minuti a rivolgersi attorno. </s></p><p type="main">

<s>Attendeva il Cassini a queste sue diligenti osservazioni gioviali in Roma, <lb></lb>nell&#039;estate del 1664, e Giuseppe Campani lo assisteva. </s>

<s>La notte appresso al <lb></lb>dì 30 di Luglio, dop&#039;essere stato qualche ora intento e in silenzio contem­<lb></lb>plativo ad osservar Giove, si leva, e tutto lieto rivolto al Campani — guar­<lb></lb>date, gli dice, que&#039;due punti neri, che sono in mezzo alla fascia più larga. </s>

<s>— <lb></lb>Guarda, e a lui maravigliato della novità, per non poter esser quelle delle <lb></lb>solite macchie, il Cassini risponde: — Que&#039;due punti neri son l&#039;ombre proiet­<lb></lb>tate da due Satelliti sul disco di Giove, e se osservate attentamente vedrete <lb></lb>che non si muovono di pari passo con le altre macchie aderenti al Pianeta <lb></lb>e menate in volta da lui. </s>

<s>— </s></p><p type="main">

<s>Il Campani subito, in commemorazione della scoperta, fece stampare <lb></lb>una cartella, della quale fu mandata al principe Leopoldo una copia, che i <lb></lb>collettori inserirono a carte 48 del Tomo XII del Cimento. </s>

<s>Sotto un qua­<lb></lb>dretto, in mezzo al quale son finissimamente disegnati Saturno col suo anello, <lb></lb>e Giove con le sue fasce e con le due ombre de&#039;Pianetinì, come apparirono <lb></lb>in quella prima osservazione, si legge: “ Julii die 30 h. </s>

<s>2 1/2 noctis latio­<lb></lb>rem Jovis fasciam obscuram perambulabant maculae duae obscuriores quas, <lb></lb>celeberrimus astronomus Cassinus authori primum indigitavit, easque um­<lb></lb>bras Satellitum dixit Jovem subeuntium, qui deinde ab eius occiduo mar­<lb></lb>gine vere emergere visi sunt. </s>

<s>” </s></p><p type="main">

<s>Benchè, della sua scoperta così divulgata, il Cassini fosse sicuro, sen­<lb></lb>tiva nulladimeno, per dar fondamento ai calcoli, il bisogno di più diligenti <lb></lb>osservazioni, ch&#039;ei dovette indugiare fino all&#039;anno seguente. </s>

<s>In questa nota <lb></lb>che riferiamo s&#039;hanno di tali importantissime osservazioni descritti i più <lb></lb>minuti particolari. </s>

<s>“ A&#039;dì 9 Luglio 1665 in Roma, con un Occhiale del Cam­<lb></lb>pani di palmi 16 1/2, si cominciò ad osservare Giove la notte suddetta a h. </s>

<s>3, <lb></lb>m. </s>

<s>15 dell&#039;Orologio comune, e si scoperse l&#039;ombra del III Pianetino nel <lb></lb>centro preciso di quel Pianeta, sopra la terza fascia oscura che da esso ve­<lb></lb>niva toccata nell&#039;estremità. </s>

<s>Il suo moto era verso il margine occidentale vero <pb xlink:href="020/01/1007.jpg" pagenum="450"></pb>di Giove. </s>

<s>” E seguita a notar le osservazioni fatte a ore 4 1/8, a ore 4 1/4, <lb></lb>a ore 4, m. </s>

<s>52; ecc. (MSS. Cim., T. XII, c. </s>

<s>59). </s></p><p type="main">

<s>Nell&#039;Agosto, distratto dalla visita del Ponte Felice per ordine del Governo <lb></lb>“ dispiacemi estremamente, scriveva al Viviani, di non aver tempo di ap­<lb></lb>plicare ora al più esatto calcolo dell&#039;ombre de&#039;Pianetini, benchè a dire il <lb></lb>vero l&#039;aver essi, da che costituii l&#039;ipotesi, variato evidentemente le digres­<lb></lb>sioni, senza che io ne abbi fatta esatta misura, non mi lasci speranza di <lb></lb>conseguire ora molta sottigliezza ” (ivi, c. </s>

<s>151). </s></p><p type="main">

<s>Aveva nonostante il Cassini divisato l&#039;ordine di que&#039;calcoli, e accen­<lb></lb>nato all&#039;uso e alle conseguenze importanti in una lettera indirizzata all&#039;abate <lb></lb>Ottavio Falconieri, dove son notabili quelle leggi delle proporzionalità intra­<lb></lb>vedute fra le velocità de&#039;Satelliti e i raggi delle loro orbite, con che illu­<lb></lb>stravasi un concetto di Galileo, ma non s&#039;iniziava quella nuova Meccanica <lb></lb>celeste, alla quale attendeva in quel medesimo tempo il Borelli. </s></p><p type="main">

<s>Sottosignata “ di Roma lì 7 Ottobre 1665 ” comparve, quasi nello stesso <lb></lb>tempo che fu pubblicata la lettera del Cassini al Falconieri, un&#039;altra Let­<lb></lb>tera di Giuseppe Campani “ intorno alle ombre delle stelle Medicee nel volto <lb></lb>di Giove ed altri nuovi fenomeni celesti scoperti co&#039;suoi Occhiali, al signor <lb></lb>Gio. </s>

<s>Domenico Cassini, primario astronomo dell&#039;Archiginnasio di Bologna, ” <lb></lb>lettera stampata in folio in Roma da Fabio De Falco, e che può vedersi in­<lb></lb>serita da c. </s>

<s>285-93 nel T. XV de&#039;Manoscritti del Cimento. </s></p><p type="main">

<s>Avevano queste due lettere levato un gran rumore, e il Granduca e il <lb></lb>principe Leopoldo, mentre che il Borelli era tornato a Pisa, e il Viviani forse <lb></lb>se ne stava in campagna, vollero che si riscontrassero nell&#039;Accademia fio­<lb></lb>rentina le novità venute di Roma. </s>

<s>Risposero gli Accademici che il Cassini <lb></lb>s&#039;era ingannato, prendendo per ombre de&#039;Satelliti alcune delle solite mac­<lb></lb>chie inerenti al Pianeta, di che prova certissima era, secondo loro, il veder <lb></lb>quelle stesse ombre, che si dicevano proiettate, maggiori in diametro appa­<lb></lb>rente del corpo proietore. </s></p><p type="main">

<s>Il Granduca però e il principe Leopoldo, non s&#039;assicurando del parere <lb></lb>de&#039;loro Accademici, vollero averne sentenza più definitiva dal Borelli e dal­<lb></lb>l&#039;Huyghens, a cui nello stesso tempo si rendeva conto anche delle altre os­<lb></lb>servazioni e scoperte fatte dal Cassini intorno a Giove. </s>

<s>L&#039;Huyghens rispon­<lb></lb>deva così il dì 22 Giugno 1666 da Parigi: “ Quanto alla nuova osservazione <lb></lb>del Cassini dell&#039;ombre de&#039;Gioviali la m&#039;è paruta certamente bella e felice, <lb></lb>nè ho stimato doversi dubitar della verità del fatto, come intendo dubitar­<lb></lb>sene da altri, e meno ancora, dopo che io stesso ebbi manifestamente os­<lb></lb>servato, il dì 26 di Settembre del passato anno 1665, l&#039;ombra del III Com­<lb></lb>pagno quale aveva predetto il Cassini che doveva apparire. </s>

<s>Ma più bella <lb></lb>ancora è paruta quell&#039;altra sua osservazione del moto di Giove intorno al <lb></lb>suo asse, perchè quantunque altri disputino di aver viste le macchie in Giove <lb></lb>prima di lui, la gloria però principale a mio giudizio è state l&#039;averne, con <lb></lb>continuate osservazioni e perfetto discorso, cavato il tempo della circumvo­<lb></lb>luzione ” (MSS. Cim., T. XVIII, c. </s>

<s>316). </s></p><pb xlink:href="020/01/1008.jpg" pagenum="451"></pb><p type="main">

<s>Il Borelli poi rispondeva in termini ch&#039;eccitano in chi legge la curio­<lb></lb>sità di saperne qualche cosa più addentro. </s>

<s>“ Il serenissimo Granduca, scri­<lb></lb>veva al Principe Leopoldo, si è compiaciuto di farmi vedere una lettera del <lb></lb>Campani diretta al signor Cassini ultimamente stampata. </s>

<s>L&#039;ho letta con <lb></lb>quella stessa ammirazione, con la quale vidi l&#039;Epistola ultima del signor <lb></lb>Cassini, e finalmente concludo esser prudenza rimetterci e scapitarci qual­<lb></lb>che cosa del proprio, piuttosto che toccare o entrare in controversia con <lb></lb>persone tanto loquaci e fortificatori di sè medesimi. </s>

<s>Veggo poi in questa <lb></lb>Epistola far menzione di certi <emph type="italics"></emph>Dialoghi fisici<emph.end type="italics"></emph.end> stampati in Lione dal p. </s>

<s>Fa­<lb></lb>bry, dei quali ne cita alcuni brani in proposito della Fascia saturnia e del <lb></lb>sito degli Epicicli delle Medicee ” (ivi, c. </s>

<s>90). </s></p><p type="main">

<s>L&#039;errore del Fabry in tal proposito fu dimostrato falso dal Borelli in <lb></lb>una sua scrittura, che si legge da c. </s>

<s>14-16 del T. XIV del Cimento, e la <lb></lb>dimostrazione assai facile è dall&#039;Autore conclusa in queste parole: “ Segue <lb></lb>dunque che il centro di detti Pianetini precisamente sia il corpo di Giove, <lb></lb>il che bisognava dimostrare ” (ivi, c. </s>

<s>16). A c. </s>

<s>17 torna il Borelli sullo stesso <lb></lb>argomento contro il Fabry, il quale non aveva per verità gran bisogno di <lb></lb>essere confutato perchè dalle stesse “ osservazioni antichissime del signor <lb></lb>Galilei e del Castelli si convince evidentemente che il centro delle revolu­<lb></lb>zioni delle Medicee sia lo stesso corpo di Giove ” (ivi, c. </s>

<s>17). </s></p><p type="main">

<s>Ma quel che si diceva eccitar la curiosità di chi legge muove dalla prima <lb></lb>parte della lettera riferita, dove par che il Borelli non voglia concedere al <lb></lb>Cassini altro merito che di aver prima veduto ciò che i calcoli avevano a <lb></lb>lui stesso, al Borelli, mostrato dover essere in quel sito e in quel tempo <lb></lb>determinato. </s></p><p type="main">

<s>Una tale interpetrazione dall&#039;altra parte sembra esser confermata da <lb></lb>ciò che si legge nel cap. </s>

<s>III del II Libro delle <emph type="italics"></emph>Theoricae Mediceorum,<emph.end type="italics"></emph.end> dove, <lb></lb>dopo di aver confessato che furono le nuove ecclissi per la prima volta os­<lb></lb>servate in Roma <emph type="italics"></emph>ab eccellentissimo Cassini,<emph.end type="italics"></emph.end> soggiunge avergli fatto gran <lb></lb>maraviglia l&#039;udir che in Firenze erano state messe in dubbio “ nam licet <lb></lb>ego, ob visus debilitatem, videre eas non potuerim, alii docti viri, et acu­<lb></lb>tissimo visu praediti, in aula serenissimi Magni Ducis, eas conspexerunt, <lb></lb>iisdem temporibus et locis, quos culculus mihi designaverat ” (pag. </s>

<s>138), <lb></lb>anzi, prosegue a dire, fu di più osservata, da quegli stessi acutissimi osser­<lb></lb>vatori, la differenza di moto, che è fra tali ombrelle e le macchie aderenti <lb></lb>al Pianeta, <emph type="italics"></emph>differentia sane conspicua et perceptibilis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Del resto, l&#039;esser l&#039;ombre proiettate maggiori in diametro del corpo opaco <lb></lb>proiettore, e il non poter sempre, secondo il calcolo, il cono ombroso delle <lb></lb>Medicee giungere fino a toccar la superficie di Giove, non son tali difficoltà, <lb></lb>dice il Borelli, da dover mettere in dubbio le ecclissi cassiniane. </s>

<s>“ Hoc qui­<lb></lb>dem apud Opticos certum est, comprobaturque experientia, si parvus glo­<lb></lb>bulus M (fig. </s>

<s>92), filo tenui suspensus, exponatur radiis solis S atque pa­<lb></lb>pyrus G in parte eius adversa umbram globuli excipiat, removeaturque <lb></lb>papyrus a globulo ultra apicem coni umbrosi E ab integro disco solari ge-<pb xlink:href="020/01/1009.jpg" pagenum="452"></pb>niti. </s>

<s>Tunc quidem conspicitur in papyro G umbra quidem secundaria HI <lb></lb>circularis non valde obsura sed diluta, cuius diameter HI maior est diame­<lb></lb><figure id="id.020.01.1009.1.jpg" xlink:href="020/01/1009/1.jpg"></figure></s></p><p type="caption">

<s>Figura 92.<lb></lb>tro CD eiusdem globuli M, quia nimirum radii <lb></lb>penumbram, seu secundariam umbram termi­<lb></lb>nantes, ut sunt globum M tangentes AD et <lb></lb>BC decussati se mutuo secant in puncto F <lb></lb>inter solem S et pilam M positos, quare ab F <lb></lb>divergentes spatium HI umbrosum gignent <lb></lb>ampliorem quidem quam CD ” (pag. </s>

<s>138). </s></p><p type="main">

<s>Così le argomentazioni del Borelli e del­<lb></lb>l&#039;Huyghens, e i fatti meglio osservati, che ve­<lb></lb>nivano a confortarle di nuova autorità, valsero <lb></lb>a levar via tutti i dubbii; ond&#039;è che il Cas­<lb></lb>sini, trattando in quel suo Discorso <emph type="italics"></emph>De l&#039;ori­<lb></lb>gine de l&#039;Astronomie<emph.end type="italics"></emph.end> dell&#039;ecclissi de&#039;Satelliti <lb></lb>di Giove, potè francamente, innanzi agli Ac­<lb></lb>cademici parigini, pronunziare queste parole: <lb></lb>“ En faisant ces observations on découvrit une <lb></lb>nouvelle espece d&#039;éclipses, qui n&#039;est pas moins <lb></lb>admirabile, que celles dont on avoit déja con­<lb></lb>noissance, c&#039;est les éclipses que ces petite planettes font sur Juppiter en <lb></lb>passant entre son disque et celui du Soleil: on voit alors leurs petites om­<lb></lb>bres parcourir le disque de Jupiter d&#039;orient en occident, et l&#039;on peut deter­<lb></lb>miner la minute, que&#039;elles parviennent au milieu de ce disque. </s>

<s>On s&#039;est <lb></lb>servy de ces deux sortes d&#039;eclipses dans la correction des Tables ” (Divers <lb></lb>ouvr. </s>

<s>d&#039;Astronomie, Amsterdam 1736, pag. </s>

<s>44). </s></p><p type="main">

<s>Queste Tavole così corrette dovevano utilmente servire a sciogliere l&#039;im­<lb></lb>portantissimo, e da molti anni desiderato, problema delle Longitudini, delle <lb></lb>quali ci resta ora a parlare, nè può tanto stringerci la brevità, da passare <lb></lb>in silenzio l&#039;opera, che vi posero attorno, e i solleciti studii che vi dettero <lb></lb>i molti e illustri predecessori del Cassini. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il problema delle Longitudini fu in ogni tempo il desiderio de&#039;Geo­<lb></lb>grafi, desiderio che si accese allora ne&#039;loro animi più vivo, quando le ar­<lb></lb>dite navigazioni per lo sconfinato oceano fecero sentire più urgente il biso­<lb></lb>gno di risolvere quel difficile problema in qualche modo. </s>

<s>Non è perciò <lb></lb>maraviglia se, dimostratosi questo bisogno al primo grande scopritore del <lb></lb>Nuovo mondo, gli incorasse una certa fiducia di sodisfarlo per via di quel <lb></lb>maraviglioso Strumento magnetico, mandato come si diceva a salvar l&#039;uomo <lb></lb>pericolante in mare direttamente dal Cielo. </s></p><pb xlink:href="020/01/1010.jpg" pagenum="453"></pb><p type="main">

<s>Cristoforo Colombo fu il primo tra i naviganti ad osservar che la de­<lb></lb>clinazione magnetica variava al variar del meridiano, ed essendosi facilmente <lb></lb>persuaso che fosse quella variazione proporzionale al variar delle longitudini, <lb></lb>pensò che di queste fosse il Declinatorio la più giusta misura. </s>

<s>Fa di ciò te­<lb></lb>stimonianza Ferdinando, nel cap. </s>

<s>LXIII della Vita che scrisse di suo padre, <lb></lb>riferendo le parole stesse lasciate scritte da lui nell&#039;Itinerario. </s>

<s>“ E quan­<lb></lb>tunque fossero otto o dieci in quelle due caravelle, niun però di loro sapeva <lb></lb>ove fossero, ancorchè l&#039;Ammiraglio fosse certissimo che si ritrovavano al­<lb></lb>quanto più all&#039;occidente delle isole degli Astori, di che rendè la ragione nel <lb></lb>suo Itinerario, dicendo: <emph type="italics"></emph>Questa mattina le aguglie fiamminghe norvesta­<lb></lb>vano, come sogliono, una quarta, e le genovesi, che solevano conformarsi <lb></lb>con quelle, non norvestavano se non poco, e per l&#039;avvenire hanno a nor­<lb></lb>vestare andando il leste, che è segno che ci ritroviamo cento leghe o al­<lb></lb>quanto più all&#039;occidente delle isole degli Astori, perciocchè, quando fu­<lb></lb>rono appunto cento, allora era in mare poca cosa di ramoscelli sparsi, e <lb></lb>le aguglie fiamminghe norvestavano una quarta e le genovesi percotevano <lb></lb>la tramontana, e quando saremo più al leste norveste faranno alcuna <lb></lb>cosa.<emph.end type="italics"></emph.end> Il che si verificò subito la domenica seguente, a&#039;22 di Maggio. </s>

<s>Dal <lb></lb>quale indizio, e dalla certezza del suo punto, conobbe allora che si ritrovava <lb></lb>cento leghe lontano dall&#039;isola degli Astori ” (Traduz. </s>

<s>di A. Ulloa, Lon­<lb></lb>dra 1867, pag. </s>

<s>216, 17). </s></p><p type="main">

<s>Un altro illustre navigatore italiano, il fiorentino Filippo Sassetti, aveva <lb></lb>pure a principio conceputa l&#039;ardita speranza di avere a trovar le longitudini <lb></lb>per via della declinazion della Bussola, scrivendo così, il dì 8 Giugno 1550, a <lb></lb>Baccio Valori: “ Sarebbeci da fare un pieno trattato del reggimento della <lb></lb>Calamita, della quale son forse note fino a qui le minori virtù, dimostrando <lb></lb>non pure il polo, ma dando modo di trovare le longitudini ” (Lettere, Mi­<lb></lb>lano 1874, pag. </s>

<s>133). Due anni dopo però, dietro più attente considerazioni <lb></lb>e più precise esperienze, tornava così a scrivere allo stesso Valori de&#039;ser­<lb></lb>vigi che si potevano avere dalla Calamita: “ Servonsene i piloti per sa­<lb></lb>pere se sono presso alla terra o no, sapendo la differenza, ch&#039;ella fa in quel <lb></lb>luogo, dove e&#039;l&#039;hanno, ma per farne regola per trovare le longitudini, come <lb></lb>molti si stimano, è impossibile ” (ivi, pag. </s>

<s>182). </s></p><p type="main">

<s>Anche il Porta, nella prefazioncella al libro VII della Magia Naturale, <lb></lb>aveva esaltati i suoi magnetici esperimenti con dire: <emph type="italics"></emph>Ex his mundi longi­<lb></lb>tudo investigari potest,<emph.end type="italics"></emph.end> ma il Gilberto uscì incontro così a rintuzzare le <lb></lb>baldanzose speranze: “ Gratum hoc opus nautis esset, et Geographiae maxi­<lb></lb>mum incrementum adferret, sed spe vana et cogitatione illudetur B. Porta, <lb></lb>cap. </s>

<s>XXXVIII, lib. </s>

<s>VII. </s>

<s>Nam cum existimat quod, secundum motum per <lb></lb>meridianos, ordinem et proportionem sequeretur magneticum, ut quanto <lb></lb>proprinquis orienti fuerit, tanto magis versus orientem deviaret, quanto au­<lb></lb>tem versus occidentem perrexeris, eo ad occidentem ferrea cuspis vergeret, <lb></lb>quod omnino falsissimum est, putat se longitudinis verum invenisse indi­<lb></lb>cem, sed fallitur ” (De Magnete, Londini 1600, pag. </s>

<s>166, 67). </s></p><pb xlink:href="020/01/1011.jpg" pagenum="454"></pb><p type="main">

<s>Ma s&#039;ingannava anco Odoardo Wright, l&#039;amico del Gilberto, nell&#039;Epi­<lb></lb>stola premessa e indirizzata all&#039;Autor <emph type="italics"></emph>De Magnete,<emph.end type="italics"></emph.end> sperando di poter risol­<lb></lb>vere, per mezzo della Bussola, il problema delle Longitudini sul fondamento <lb></lb>di una proposizione ammessa come vera dal Gilberto, e dietro il modo dal <lb></lb>Gilberto stesso insegnato di ritrovar la latitudine coll&#039;Inclinatorio. </s>

<s>La pro­<lb></lb>posizione, che il Wright accetta per fondamento, è così formulata dall&#039;Au­<lb></lb>tor <emph type="italics"></emph>De Magnete: Variatio uniuscuiusque loci constans est<emph.end type="italics"></emph.end> (pag. </s>

<s>159). Ora, <lb></lb>se la declinazione (variatio) per ogni luogo è costante, argomentava il Wright, <lb></lb>e s&#039;è possibile a rinvenirsi, per mezzo dell&#039;Inclinatorio, la latitudine, come <lb></lb>dal Gilberto stesso s&#039;insegna al cap. </s>

<s>VIII del V libro “ problemati illi geo­<lb></lb>graphico de longitudine invenienda, quae tot saeculis doctissimorum Mathe­<lb></lb>maticorum ingenia exercuit, quodammodo satisfactum fore videatur, quia, <lb></lb>cognita uniuscuiusque loci maritimi variatione, idem postea ex eadem, quo­<lb></lb>ties opus fuerit, facillime, non ignota eiusdem loci latitudine, inveniri posset. </s>

<s>” </s></p><p type="main">

<s>Il metodo però così proposto dal Wright posava sopra due fondamenti, <lb></lb>che sebben fossero dal Gilberto tenuti per fatti certissimi, erano in realtà <lb></lb>due fallacie: quella del creder che le inclinazioni fossero proporzionali alle <lb></lb>latitudini, cosicchè le linee, che i moderni chiamano isocliniche, coincides­<lb></lb>sero sempre co&#039;meridiani, e l&#039;altra del suppor che sempre la declinazione, <lb></lb>in un medesimo luogo, si mantenga costante. </s></p><p type="main">

<s>Ai tempi del Gilberto e del Wright, per mancanza di osservazioni, ri­<lb></lb>manevano queste fallacie tuttavia occulte, come pure occulte, per le stesse <lb></lb>ragioni, rimasero a Galileo, il quale nonostante desiderava che fosse con di­<lb></lb>ligenza osservato (Alb. </s>

<s>VI, 52) se sia veramente, com&#039;ei supponeva, l&#039;in­<lb></lb>tensità magnetica reciprocamente proporzionale alle latitudini, o se in altre <lb></lb>parole le linee, così dette isodinamiche, propriamente coincidessero coi pa­<lb></lb>ralleli terrestri. </s>

<s>Qualche esperienza, che ha una certa relazione con questi <lb></lb>fatti, fu istituita dagli Accademici del Cimento, i quali però confessano di <lb></lb>non essersi “ finiti di sodisfare in ordine a molte particolarità, che riman­<lb></lb>gono tuttavia in pendente ” (Saggi di Natur. </s>

<s>esper., Firenze 1841, pag. </s>

<s>140). </s></p><p type="main">

<s>Come l&#039;altra fallacia del Gilberto, che consisteva nel creder la declina­<lb></lb>zione in un medesimo luogo mantenersi sempre costante, fosse scoperta e <lb></lb>dimostrata da più diligenti osservazioni fatte in diversi tempi e fra sè com­<lb></lb>parate, fu da noi detto nel § VI del cap. </s>

<s>VI di questo Tomo. </s>

<s>Qui rimane <lb></lb>però a soggiungere che il Gillibrando, nella sua scoperta, e il Petit, nella <lb></lb>sua speculazione, erano stati prevenuti dal nostro bolognese Cesare Marsili, <lb></lb>il quale aveva nel 1631 ritrovato “ che la Meridiana già scolpita nel pavi­<lb></lb>mento di San Petronio declina da quella, che di nuovo vi si trova ” (Alb. </s>

<s><lb></lb>IX, 229) e aveva spiegato un suo pensiero “ intorno alla Meridiana, ch&#039;ella <lb></lb>si muova, cioè che si muova il Polo del mondo, e perciò si varii la longi­<lb></lb>tudine e la latitudine delle città ” (ivi, pag. </s>

<s>230). Il Cassini stesso, il quale <lb></lb>vedemmo altrove così ritroso in consentire al Petit, che ripeteva inconsape­<lb></lb>vole il pensiero del nostro Marsili, ebbe finalmente a concludere, nel suo <lb></lb><emph type="italics"></emph>Discorso sul restauramento della Meridiana di San Petronio,<emph.end type="italics"></emph.end> esser cosa <pb xlink:href="020/01/1012.jpg" pagenum="455"></pb>evidentissima “ che nel medesimo luogo questa direzione della Calamita va­<lb></lb>ria talmente, che nello spazio di 25 anni l&#039;abbiamo veduta variare a Parigi <lb></lb>più di sette&#039;gradi ” (Bologna 1772, pag. </s>

<s>4). </s></p><p type="main">

<s>Cosi veniva finalmente a dimostrarsi coi fatti essere una vana speranza <lb></lb>quella del Wright, e di tutti gli altri, che proponevano la soluzione del pro­<lb></lb>blema delle longitudini, per mezzo della Bussola nautica, ed era questa dal­<lb></lb>l&#039;altra parte una persuasione ingeritasi molti anni prima nell&#039;animo del <lb></lb>nostro Sassetti, il quale, diffidato de&#039;metodi magnetici, non vedeva altra riu­<lb></lb>scibile via che negli astronomici. </s>

<s>Così infatti soggiungeva alle sopra citate <lb></lb>parole, nella lettera al Valori: “ Credomi che sia possibile e non molto dif­<lb></lb>ficile, a chi intende l&#039;uso dell&#039;Astrolabio, trovare la longitudine, di che l&#039;anno <lb></lb>passato (1581) trattai in Madrid col gentilissimo signor Lorenzo Canigiani, <lb></lb>figliolo del signor Ambasciatore, e adesso aspetto certa sua difficoltà per ve­<lb></lb>derne la risoluzione ” (Lettere cit., pag. </s>

<s>182). </s></p><p type="main">

<s>Importante sarebbe il conoscere qual fosse questo metodo proposto dal <lb></lb>Sassetti, ma noi non siamo in grado di darne la desiderata sodisfazione. </s>

<s>Es­<lb></lb>sendo però cosa certa che doveva quello essere un metodo astronomico, non <lb></lb>è difficile congetturare che dovesse, nella sostanza, non differir dai metodi <lb></lb>già proposti dal Werner nel 1514, poi da Appiano nel 1524, dal Fineo <lb></lb>nel 1529, dal Frisio nel 1530, dal Nunnez nel 1561 e dal Ruscelli final­<lb></lb>mente nell&#039;anno dopo. </s></p><p type="main">

<s>Questi metodi, in ogni modo, che non in altro consistevano se non in <lb></lb>argomentar la Longitudine dalla distanza della Luna da una e altra delle <lb></lb>stelle più conspicue e più vicine al Dragone, riconoscevano per primo e prin­<lb></lb>cipale autore Amerigo Vespucci, come dimostrò il Canovai, e fu confermato <lb></lb>da nuovi documenti venuti alla luce. </s>

<s>Il Baldelli, nella sua prefazione al Mi­<lb></lb>lione di Marco Polo, pubblicò una lettera, dove Amerigo, dopo aver detto a <lb></lb>Lorenzo di Pier Francesco Medici com&#039;avesse trovato, per mezzo dell&#039;Astro­<lb></lb>labio e del Quadrante, la latitudine giusta delle isole Fortunate, intorno alla <lb></lb>quale eran incorsi in grandi errori Tolomeo e tutti i geografi dopo di lui; cosi <lb></lb>soggiunge: “ La longitudine è cosa più difficile, che per pochi si può co­<lb></lb>noscere, salvo per chi molto vegghiò e guardò la congiunzione della Luna <lb></lb>co&#039;Pianeti. </s>

<s>Per causa delle dette longitudini ho perduti molti sonni, e ho <lb></lb>abbreviato la vita mia di<gap></gap>i anni, e tutto tengo per bene speso, perchè spero <lb></lb>venire in fama lungo secolo, se io torno con salute da questo viaggio. </s>

<s>Iddio <lb></lb>non me lo reputi a superbia, che ogni mio travaglio raddirizzerò al suo <lb></lb>santo servizio ” (Firenze 1827, pag. </s>

<s>LIV). </s></p><p type="main">

<s>Angelo Maria Bandini pubblicava un&#039;altra lettera di Amerigo allo stesso <lb></lb>Lorenzo, dove, come un bell&#039;esempio dell&#039;applicazion del suo metodo, di­<lb></lb>mostrava in che modo, dalla posizion della Luna con Marte, che, secondo <lb></lb>l&#039;Almanacco del Monteregio, dovevano il dì 23 Agosto 1499 congiungersi <lb></lb>insieme a mezzanotte, ritrovasse, osservando e calcolando, ch&#039;egli era in <lb></lb>luogo distante 82 gradi “ e tanto mi trovavo di longitudine dal meridiano <lb></lb>della città di Calis ” (Vita e lettere di A. Vespucci, Firenze 1745, pag. </s>

<s>72). </s></p><pb xlink:href="020/01/1013.jpg" pagenum="456"></pb><p type="main">

<s>Questo metodo del Vespucci era senza dubbio il più sicuro e il più <lb></lb>razionale, che si sapesse a que&#039;tempi, benchè riuscisse imperfetto princi­<lb></lb>palmente per non conoscersi con precisione i moti della Luna. </s>

<s>Nè più pre­<lb></lb>ciso di questo riusciva l&#039;altro metodo allora proposto di servirsi dell&#039;ecclissi <lb></lb>di luna “ imperocchè, quand&#039;ella incomincia a immergersi nel cono dell&#039;om­<lb></lb>bra terrestre, quell&#039;ombra è tanto tenue e sfumata, che l&#039;osservatore resta <lb></lb>perplesso, se la Luna abbia o no cominciato ad intaccarla ” (Alb. </s>

<s>VI, 241). <lb></lb>Sciveva così fatte parole Galileo, nella primavera dell&#039;anno 1616, proponendo <lb></lb>un suo nuovo metodo di trovare le longitudini alla Corte di Spagna, alla <lb></lb>quale soggiungeva di essere arrivato “ a scoprire nel cielo cose totalmente <lb></lb>incognite ai secoli passati, le quali equivalgono a più di mille ecclissi lunari <lb></lb>ogni anno, osservabili con minutissime precisioni, e quello che più importa <lb></lb>ridotte a tavole giustissime ed esquisite ” (ivi, pag. </s>

<s>242). </s></p><p type="main">

<s>Fallite le speranze con la corte di Spagna, tornò Galileo, vent&#039;anni dopo, <lb></lb>a far la medesima proposta agli Stati generali d&#039;Olanda, designando, nelle <lb></lb>osservazioni dello scoperto mondo gioviale, tre principali accidenti ben ac­<lb></lb>comodati ciascuno per l&#039;investigazione delle longitudini. </s>

<s>Primi fra questi acci­<lb></lb>denti annovera gli ecclissi, de&#039;quali si possono utilmente osservare le im­<lb></lb>mersioni e le emersioni nel cono dell&#039;ombra di Giove. </s>

<s>“ Oltre agli ecclissi <lb></lb>vi sono secondariamente le applicazioni dei loro corpi a quello di Giove,.... <lb></lb>come anche all&#039;incontro viene osservabile la loro separazione dal medesimo <lb></lb>disco..... Sono nel terzo luogo osservabili le ingiunzioni e separazioni tra <lb></lb>di loro dei medesimi Satelliti, li quali, mentre che con movimenti contrarii <lb></lb>si vanno ad affrontare, scorrendo questi la parte superiore dei loro cerchi, e <lb></lb>quelli l&#039;inferiore, si conducono all&#039;esatta congiunzione ” (Alb. </s>

<s>VII, 84). </s></p><p type="main">

<s>Queste pratiche però supponevano la cognizione esatta de&#039;moti de&#039;Sa­<lb></lb>telliti, intorno alla quale, non solo nel 1616, ma in sul primo intraprendere <lb></lb>l&#039;opera atlantica Galileo si confidava di esser giunto a segno “ di poter pre­<lb></lb>dire i siti e le disposizioni, che essi nuovi Pianeti siano per avere in ogni <lb></lb>tempo futuro, e abbiano anche avuto in ciascun tempo passato ” (Alb. </s>

<s>VI, 157). <lb></lb>Quanto vana però fosse questa confidenza i fatti narrati posson persuaderlo <lb></lb>a ciascuno, che saviamente ripensi da quante parti dovesse riuscir difettosa <lb></lb>l&#039;atlantica fatica di Galileo. </s></p><p type="main">

<s>Per questi difetti e per quella, che se non fosse uscita dalla fantasia di <lb></lb>un Galileo, si sarebbe tenuta per goffaggine, della sedia nautica del Besson, <lb></lb>e dell&#039;imperniatura del Cardano applicate al più comodo uso degli stru­<lb></lb>menti sulla nave ondeggiante; il nuovo metodo proposto di trovar le Lon­<lb></lb>gitudini riusciva inutile, ond&#039;è che parve una provvidenza, per la reputa­<lb></lb>zione e per la gloria di Galileo, la morte di que&#039;tre Olandesi deputati a <lb></lb>sperimentar s&#039;era riuscibile ciò che veniva proposto da Firenze. </s></p><p type="main">

<s>Una tal nuova soluzione del problema delle longitudini, per via de&#039;Sa­<lb></lb>telliti di Giove, rimase allora solamente nota fra persone private, e non ebbe <lb></lb>questo concetto di Galileo pubblicità che nel 1639, quando nella prefazione <lb></lb>alle prime Tavole medicee il Renieri scriveva del più sicuro e più facile <pb xlink:href="020/01/1014.jpg" pagenum="457"></pb>modo di emendar le longitudini: “ exhibent illud quatuor Jovis asseclae <lb></lb>quatuor Medicei planetae optici Tubi beneficio, per celebrem Virum hunc, <lb></lb>nostro saeculo reperti, qui quotidianas variant in coelo phases nunc iuncti, <lb></lb>nunc discedentes, nunc ecclipsim subeuntes, nunc a Jove contacti ” (Flo­<lb></lb>rentiae, pag. </s>

<s>IV). </s></p><p type="main">

<s>Sembra nonostante che, massime appresso gli scienziati stranieri, fosse <lb></lb>poco diffusa la notizia di questo progetto di Galileo. </s>

<s>L&#039;Herigonio, pubbli­<lb></lb>cando in Parigi nel 1644 il V Tomo del suo <emph type="italics"></emph>Corso matematico,<emph.end type="italics"></emph.end> vi aggiun­<lb></lb>geva “ Nova ac facilis methodus inveniendi locorum longitudines ” la pra­<lb></lb>tica del qual metodo dall&#039;Autore stesso s&#039;insegnava così: “ Observetur, ope <lb></lb>Telescopii, quota hora loci observationis aliquod Jovialium siderum appellat <lb></lb>ad lineam ab oculo intuentis per centrum Jovis transeuntem. </s>

<s>Deinde, si ope <lb></lb>Tabularum inquiratur quota hora diei illud sidus iungatur Jovi, differentia <lb></lb>horarum per observationem et Tabulas inventarum (reducta in gradus et <lb></lb>minuta graduum, multiplicando singulas horas per 15 gradus) erit quaesita <lb></lb>differentia longitudinum loci observationis, et loci ad quem constructae sunt <lb></lb>Tabulae ” (pag. </s>

<s>857). </s></p><p type="main">

<s>L&#039;Herigonio spacciava questa per una sua invenzione, ma quel Morin, <lb></lb>autor di un Trattato, nel quale, a giudizio di Galileo, il modo proposto di <lb></lb>trovare la longitudine, per via del moto della Luna, è una bella invenzione <lb></lb>in astratto, ma fallace e impraticabile in concreto (Alb. </s>

<s>VII, 199); quel Mo­<lb></lb>rin “ primo dicit Galilaeum esse inventorem methodi inveniendi locorum <lb></lb>longitudines per Jovialia sidera.... atque in hac civitate Parisiensi ab anno <lb></lb>iam elapso innotuisse Galilaeum illustrissimis Ordinibus Hollandiae hoc in­<lb></lb>ventum oblutisse. </s>

<s>” Il Gassendo, infatti, nella vita del Peiresc pubblicata a <lb></lb>Parigi nel 1641, dop&#039;aver narrato come venisse in mente ad esso Peiresc <lb></lb>di far uso de&#039;Satelliti di Giove, per emendar la Geografia, e per avvantag­<lb></lb>giar la Nautica, e com&#039;avesse altresì disposto di dar effetto a questo suo <lb></lb>pensiero “ eam curam deposuit, ratus aliunde Galileum Keplerumque in eam <lb></lb>curam incubituros, et pro sua solertia rem perfectius exsequturos. </s>

<s>Certe <lb></lb>non parum gavisus est, cum non ita pridem accepit venisse Galileo in men­<lb></lb>tem ut methodum perficeret, et cum Hollandis communicaret, a quibus ar­<lb></lb>canum Longitudinum est tantopere expetitum ” (pag. </s>

<s>133). </s></p><p type="main">

<s>Rispondeva l&#039;Herigonio di non aver nulla saputo di Galileo, <emph type="italics"></emph>ignotum­<lb></lb>que esse mihi adhuc an eodem modo, quo ego,<emph.end type="italics"></emph.end> proceda nel trattato con <lb></lb>gli Olandesi, <emph type="italics"></emph>ad corrigendum tantum errorem Horologii.<emph.end type="italics"></emph.end> Pretendeva in­<lb></lb>somma l&#039;Herigonio che fosse suo almeno il particolar modo di far uso delle <lb></lb>osservazioni gioviali, per le longitudini. </s>

<s>E Galileo glielo avrebbe facilmente <lb></lb>concesso, ma gli avrebbe detto nello stesso tempo che non era l&#039;invenzione <lb></lb>praticabile, in dodici anni, altro che due o quattro o sei volte, perchè ap­<lb></lb>punto, a cagion delle loro apparenti latitudini, i Satelliti, con tal rarità, in <lb></lb>tutta una rivoluzione, si congiungono al centro di Giove, se pure è possi­<lb></lb>bile, anche in tali rarissime congiunture, il discerner luce da luce. </s></p><p type="main">

<s>Invocava inoltre l&#039;Herigonio, a far testimonianza del vero, uomini degni <pb xlink:href="020/01/1015.jpg" pagenum="458"></pb>di fede “ qui asserent me illis communicasse meum inventum, biennio fere <lb></lb>antequam in lucem ederetur ” (Cursi mathem. </s>

<s>cit., T. V, pag. </s>

<s>873). Par <lb></lb>difficile a credere che in Parigi, dove ne parlavano il Beaugrand e il Morin, <lb></lb>e dove il Gassendo ne aveva scritto in pubblico, non fosse giunta alle orec­<lb></lb>chie dell&#039;Autor del Corso matematico la notizia del trattato di Galileo con <lb></lb>gli Olandesi, ma par che non fosse giunta nemmeno in Danzica, quando <lb></lb>l&#039;Hevelio scriveva la sua celebre Selenografia. </s>

<s>Egli infatti, dissertando ivi <lb></lb>delle osservazioni di Giove, credè essere stato il primo a descriverle in or­<lb></lb>dinata Effemeride. </s>

<s>La Menologia del nostro Hodierna usciva in Palermo alla <lb></lb>luce, in quel tempo che la Selenografia era in Danzica sotto i torchi, e il <lb></lb>Mondo gioviale del Mario, annunziato nel 1611 in quella lettera trascritta in <lb></lb>fine alla Diottrica kepleriana, dove lo stesso Mario dice de&#039;due estremi Sa­<lb></lb>telliti <emph type="italics"></emph>periodos iam indagavi tubulasque construxi;<emph.end type="italics"></emph.end> il Mondo gioviale, pub­<lb></lb>blicato tre anni dopo in fretta, per prevenir Galileo, parve, come poi al Cas­<lb></lb>sini, troppo povera cosa anche all&#039;Hevelio. </s></p><p type="main">

<s>E non solamente primo si credè il celebre Selenografo in dar opera alle <lb></lb>Effemeridi gioviali, ma par che si credesse primo altresì in proporle per la <lb></lb>invenzion delle Longitudini. </s>

<s>“ Hae observationes, egli dice, quotidie fuerunt <lb></lb>continuatae, quando per serenitatem coeli licuit, ita ut una nocte quinquies, <lb></lb>imo etiam sexies, quandoque has animadversiones reiteraverim. </s>

<s>Singulis ctiam <lb></lb>observationibus suum competens verumque tempus, una cum descriptione <lb></lb>situs Jovialium, addidi. </s>

<s>Id quod, quantum ego scio, post Galileum a nemine <lb></lb>adhuc in tali forma est praestitum. </s>

<s>Interim optandum esset serio ut eius­<lb></lb>modi observationes Jovialium antehac ab Astonomiae cultoribus saepius fuis­<lb></lb>sent institutae, et quotannis adhuc instituerentur. </s>

<s>Hoc namque pacto inter­<lb></lb>dum ex coniunctionibus Jovialium, praesertim Jovi viciniorum, quae fiunt <lb></lb>ex motu contrario, in diversis ac longe dissitis locis, et ex notatione tem­<lb></lb>poris occultationis alterius ab altera, id quod ex altitudine alicuius fixae <lb></lb>capta certe cognosci potest; longitudines locorum, ob velocem horum comi­<lb></lb>tum Jovis incessum, queunt investigari, vel minimum eorum motus exami­<lb></lb>nari et corrigi ” (Selenographia, Gedani 1647, pag. </s>

<s>45, 46). </s></p><p type="main">

<s>Il desiderio espresso in queste parole dell&#039;Hevelio fu sodisfatto alquanti <lb></lb>anni dopo dal Cassini, di cui già narrammo d&#039;onde gli venissero agli studii <lb></lb>gioviali gl&#039;impulsi. </s>

<s>Nel 1668 uscivano alla luce le Effemeridi bolognosi, nel <lb></lb>Proemio alle quali termina il cap. </s>

<s>I notando i particolari accidenti osservati <lb></lb>per uso delle longitudini: accidenti ch&#039;ei riduce agli ecclissi, alle congiun­<lb></lb>zioni, ai contatti, precisamente com&#039;avea proposto Galileo agli Stati generali. </s></p><p type="main">

<s>Una delle prime copie uscite dalla tipografia de&#039;Manolessi la spedì il <lb></lb>Cassini in ossequio al Viviani, il quale fece al libro tanta accoglienza, che <lb></lb>l&#039;Autore ebbe a rispondergli: “ È un effetto della sua gentilezza aver gra­<lb></lb>dito il mio libretto delle Medicee, nel quale V.S. riconoscerà la fretta nello <lb></lb>stampare, cagionata da un mio particolar domestico interesse, a cui sono stato <lb></lb>anco troppo tardo a provvedere ” (MSS. Gal. </s>

<s>Disc., T. CXLV, c. </s>

<s>69). </s></p><p type="main">

<s>Si studiò poi di emendare i trascorsi di quella fretta, tornando sull&#039;ar-<pb xlink:href="020/01/1016.jpg" pagenum="459"></pb>gomento in quelle ch&#039;egli intitolava “ Les hypotheses et les Tables des Sa­<lb></lb>tellites de Jupiter, reformées sur de nouvelles observations ” dove in sul <lb></lb>principio, a proposito dell&#039;ecclissi per servire ai progressi della Geografia e <lb></lb>della Idrografia, diceva “ qui n&#039;avoient jamais esté auparavant employées à <lb></lb>cet usage, quoy-qu&#039;on les eust supposées depuis long-temps tres-propres <lb></lb>pour servir à perfectionner la Geographie et la Navigation ” (Divers ou­<lb></lb>vres ecc., pag. </s>

<s>366). </s></p><p type="main">

<s>Parve ad alcuni che volesse con queste parole il Cassini attribuirsi le <lb></lb>prime parti nel propor l&#039;uso dell&#039;ecclissi gioviali nella Geografia e nella <lb></lb>Nautica, ciò che per verità sembra strano. </s>

<s>Sia pure infatti che non gli fos­<lb></lb>sero note le lettere di Galileo scritte agli Olandesi; egli aveva senza dubbio <lb></lb>letto il proemio alle Tavole del Renieri, dove si annoverano que&#039;tre acci­<lb></lb>denti accomodati, nelle osservazioni de&#039;Satelliti di Giove, a ritrovar con fa­<lb></lb>cilità le longitudini in mare, con parole estratte e compendiate dalle stesse <lb></lb>lettere galileiane. </s></p><p type="main">

<s>Ma pure, a meglio rimeditarle, s&#039;intende che le parole del Cassini as­<lb></lb>seriscono nessun altro prima di lui aver dato esecuzione al pensiero di ser­<lb></lb>virsi delle ecclissi de&#039;Satelliti di Giove, per uso delle longitudini; asserzione <lb></lb>dall&#039;altra parte verissima, com&#039;è pure verissimo quello ch&#039;egli soggiunge, <lb></lb>che cioè nessuno aveva prima di lui riconosciuta la peculiare utilità e il <lb></lb>vantaggio di quelle ecclissi, sopra gli altri varii accidenti osservati. </s></p><p type="main">

<s>Sulla fine del capitolo infatti par che voglio espressamente il Cassini <lb></lb>chiarire esser questo proprio il suo concetto, non sovvenutogli a caso, ma <lb></lb>dietro un gran numero di esperienze. </s>

<s>“ Ces expériences nous ont fait con­<lb></lb>noistre qu&#039;il faut préférer à toutes les autres phases les éclipses, que ces <lb></lb>Satellites souffrent en passant par l&#039;ombre de Jupiter, dont on peut obser­<lb></lb>ver l&#039;entrée et la sortie, et quelquefois l&#039;une et l&#039;autre, sans que deux ob­<lb></lb>servateurs soient in differend entr&#039;eux d&#039;un quart d&#039;une minute d&#039;heure.... <lb></lb>et que les éclipses de Premier Satellite, qui est plus viste, que les autres, <lb></lb>et qui entre plus diréctement dans l&#039;ombre, se peuvent déterminer encore <lb></lb>avec une plus grande precision ” (ivi, pag. </s>

<s>369). </s></p><p type="main">

<s>Aggiunse però, sopra gli annoverati da Galileo, il Cassini altri due ac­<lb></lb>cidenti, che sono quello delle ombre proiettate da&#039;Satelliti sul disco di Giove, <lb></lb>e l&#039;altro delle macchie su lui più visibili e permanenti, le quali, facendo la <lb></lb>circonvuluzione velocissima, offerirebbero sopra tutti gli altri fenomeni mag­<lb></lb>gior comodità di osservazioni, se il loro passaggio per il centro del Pianeta <lb></lb>si potesse determinar con la medesima precisione, come si fa delle immer­<lb></lb>sioni e delle emersioni de&#039;Satelliti dal cono dell&#039;ombra. </s></p><p type="main">

<s>Ma pur tanta esquisitezza era dal Cassini lasciata in un difetto, che ha <lb></lb>qualche cosa di notabile; difetto che consisteva nell&#039;aver trascurata la così <lb></lb>detta <emph type="italics"></emph>Equazion della luce,<emph.end type="italics"></emph.end> ponendo in dubbio la scoperta roemeriana, per <lb></lb>non averla potuta, nella Reale Accademia di Parigi, verificare colla sua pro­<lb></lb>pria esperienza. </s>

<s>S&#039;era questo però osservato, che i tempi di un numero con­<lb></lb>siderevole d&#039;immersioni d&#039;un medesimo Satellite erano notabilmente più <pb xlink:href="020/01/1017.jpg" pagenum="460"></pb>brevi de&#039;tempi di un pari numero d&#039;emersioni “ ce qui se peut expliquer, <lb></lb>soggiunge il Cassini, par l&#039;hypothese du mouvement successif de la lumiere: <lb></lb>mais cela ne lui a pas paru suffisant pour convaincre que le mouvement de <lb></lb>la lumiere est en effet successif, parceque l&#039;on n&#039;est pas cerain que cette <lb></lb>inegalité de tems ne soit pas produite ou par l&#039;excentricité du Satellite, ou <lb></lb>par l&#039;irregularité de son mouvement, ou par quelqu&#039;autre cause jusques ici <lb></lb>inconnuë, dont on pourra s&#039;éclaireir avec le tems ” (De l&#039;orig. </s>

<s>de l&#039;Astro­<lb></lb>nomie cit., pag. </s>

<s>46). </s></p><p type="main">

<s>Fu in ogni modo il Cassini il primo fra gl&#039;Italiani e gli stranieri a <lb></lb>mettere in atto ciò che sulla bocca di tanti non era stato altro che un bel <lb></lb>progetto, e perciò il Viviani, nel citato suo Discorso intorno al mondo, com­<lb></lb>pendiando questo tratto di Storia, che concerne l&#039;invenzion delle longitudini, <lb></lb>non ne riconosce e non ne commemora altri autori che Galileo e il Cassini. </s>

<s>“ E <lb></lb>dall&#039;osservare i periodi di questi Pianeti sì regolari, con la sua s̀olita perspi­<lb></lb>cuità, s&#039;accorse il Galileo che questi potevano esser l&#039;unico mezzo per ri­<lb></lb>trovare in ogni tempo le longitudini de&#039;luoghi, tanto per terra che per mare, <lb></lb>invenzione tanto desiderata dagli antichi e da&#039;moderni geografi, ed altret­<lb></lb>tanto utile alla Navigazione, non avendo per il passato altro modo, che quello <lb></lb>delle ecclissi del Sole e della Luna, che seguono poche volte l&#039;anno, e non <lb></lb>possono mai farsi con quell&#039;aggiustatezza, che richiedono tali osservazioni, <lb></lb>per poter dalla differenza del tempo del principio, mezzo e fine di tali ec­<lb></lb>clissi osservata in diversi luoghi della Terra, calcolare le longitudini di detti <lb></lb>luoghi: dove adesso, col mezzo di questi Pianeti, nell&#039;ecclissarsi nell&#039;om­<lb></lb>bra di Giove, ne possono, non solo farsi una o due, ma talora tre e quat­<lb></lb>tro osservazioni il giorno, e con tanta facilità ed esattezza di tempo, che <lb></lb>maggiore non può desiderarsi. </s>

<s>” </s></p><p type="main">

<s>“ Egli, nel tempo che fu a Roma nel 1620, per mezzo dell&#039;Ambascia­<lb></lb>tore di Spagna, la fece proporre alla Maestà Cattolica. </s>

<s>Di poi, nel 1636, alli <lb></lb>Stati di Olanda, i quali avevano deputato all&#039;esame di questa nuova inven­<lb></lb>zione l&#039;illustrissimo signor Lorenzo Realio, capitano generale e consigliere <lb></lb>di Stato, e i signori Martino Hortensio e il Blaw. </s>

<s>Ma per la morte di que­<lb></lb>sti, seguìta dentro il tempo di anni tre, e di poi del medesimo Galileo, ne <lb></lb>fu abbandonata per allora l&#039;impresa, la quale poi, essendo stata ben rico­<lb></lb>nosciuta l&#039;utilità di questa dal signor Domenico Cassini, primo astronomo <lb></lb>di S. M. Cristianissima, l&#039;ha posta in pratica, ed ha con questo mezzo ri­<lb></lb>trovato molti errori nelle carte geografiche ” (MSS. Gal. </s>

<s>Disc., T. CXLI, <lb></lb>c. </s>

<s>277). </s></p><p type="main">

<s>L&#039;invenzione del modo di trovar le longitudini ha questo di singolare, <lb></lb>e di comune a tutte le invenzioni credute più difficili, che poi uno è ve­<lb></lb>nuto a mostrar che invece erano di una facilità maravigliosa. </s>

<s>Nell&#039;Agosto <lb></lb>del 1659 sovvenne in mente al Borelli il modo facilissimo di misurar la dif­<lb></lb>ferenza de&#039;meridiani, per mezzo delle ore segnate da un Orologio e conver­<lb></lb>tite in gradi. </s>

<s>Gli parve questa invenzione sì ovvia, che temendo di non es­<lb></lb>sere prevenuto, volle deporla nelle mani del principe Leopoldo, a cui scrisse <pb xlink:href="020/01/1018.jpg" pagenum="461"></pb>il dì 2 Settembre una lettera pubblicata a pag. </s>

<s>64, 65 del T. II della rac­<lb></lb>colta di Lettere di uomini illustri, fatta in Firenze dal Fabbroni. </s></p><p type="main">

<s>Nè contento a ciò, scriveva in quel medesimo giorno un&#039;altra lettera <lb></lb>al Viviani, dove in proposito gli diceva: “ Quanto più ho pensato sopra <lb></lb>quella mia maniera di misurare le longitudini terrestri, tanto più ci ho posto <lb></lb>l&#039;amore, perchè ho fatto riflessione a tutte le difficoltà, che occorrono negli <lb></lb>altri modi finora considerati, e benchè io, per consiglio di V. S., abbia già <lb></lb>accennato questo mio concetto a Bologna, tuttavia ho stimato mettermi al <lb></lb>sicuro in mandare diverse copie attorno di tal lettera, o pur farlo in altra <lb></lb>maniera, ma prima è necessario ch&#039;io mi assicuri se l&#039;Evelio o il Riccioli <lb></lb>ne dicon qualche parola ed in che forma, credendo io fermamente che, se <lb></lb>ne dicon nulla, saranno parole generali, come quelle delli oracoli: tuttavia <lb></lb>è necessario vederli ” (MSS. Gal. </s>

<s>Disc., T. CXLIV, c. </s>

<s>135). </s></p><p type="main">

<s>Nella Salenografia e nella Cometografia dell&#039;Hevelio non avrà trovato <lb></lb>nulla in proposito, come nulla non avrà pure trovato nell&#039;Almagesto nuovo, <lb></lb>ma nella Geografia riformata, pubblicata nel 1672 in Venezia, a pag. </s>

<s>325 il <lb></lb>Riccioli cita il Biancani e il Kircher che proposero nella invenzion delle lon­<lb></lb>gitudini l&#039;uso dell&#039;Orologio. </s>

<s>In qualunque modo pubblicando l&#039;Huyghens <lb></lb>nel 1658 il suo <emph type="italics"></emph>Horologium,<emph.end type="italics"></emph.end> e dicendo delle grandi utilità, che sarebbe per <lb></lb>recare il nuovo Strumento, concludeva con queste parole: “ Ut iam de lon­<lb></lb>gitudinum quam vocant scientia dicere omittam, quae, si nunquam extitura <lb></lb>est, desideratumque tantopere cursui navigantium praebitura, non aliter quam <lb></lb>vectis per mare exquisitissimis atque omni errore vacuis Horologiis id obti­<lb></lb>nere posse multi nobiscum existimant ” (Op. </s>

<s>varia, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>6). </s></p><p type="main">

<s>Par che dunque il pensiero del Borelli fosse sovvenuto alquanti anni <lb></lb>prima in mente all&#039;Huyghens e ad altri, i quali però si avvidero che il pro­<lb></lb>getto era bellissimo, ma ch&#039;era difficile d&#039;eseguirlo per gli agitamenti della <lb></lb>nave che avrebbero arrestato il pendolo all&#039;Orologio. </s>

<s>Fu questa forse la dif­<lb></lb>ficoltà che attutì nel Borelli quel primo ardore della invenzione, la quale, <lb></lb>non potendosi praticare che in Terra, non s&#039;avvantaggiava di troppo sopra <lb></lb>quell&#039;altra del Viviani, che aveva proposto di servirsi de&#039;suoni a misurar le <lb></lb>distanze e le longitudini dei paesi. </s></p><p type="main">

<s>Ma se il Borelli si dette vinto alle difficoltà, l&#039;Huyghens volle rimaner <lb></lb>vincitore. </s>

<s>Nel 1664 furono fatte le prime esperienze nautiche con un Orolo­<lb></lb>gio ugeniano della prima forma, ch&#039;era però non a peso ma a molla, e la <lb></lb>clavicola che frena il pendolo, invece di avere uno sprone solo, ne aveva <lb></lb>due “ ne videlicet in gyrum evagari posset penduli motus, unde cessatio­<lb></lb>nis periculum ” (ibi, pag. </s>

<s>47). Il successo di questa prova fu felicissimo, ma <lb></lb>non fu tale però in altre, navigazioni, di che dice lo stesso Huyghens “ ne­<lb></lb>gligentia eorum, quibus Horologia commissa erant, quam ipsamet Automata <lb></lb>culpari possunt ” (ibi, pag. </s>

<s>48). </s></p><p type="main">

<s>Pervenuta la notizia in Italia, Michelangiolo Ricci scriveva il dì 25 Mag­<lb></lb>gio 1665 a Firenze al principe Leopoldo: “ Da Avignone mi viene scritto <lb></lb>che il signor Hugenio abbia l&#039;invenzione per trovar le longitudini, e che si <pb xlink:href="020/01/1019.jpg" pagenum="462"></pb>serva di un Oriolo a pendolo. </s>

<s>Il medesimo crede aver trovato, per la dot­<lb></lb>trina delle Meccaniche, ragione degli effetti più maravigliosi della Calamita ” <lb></lb>(MSS. Cim., T. XVIII, c. </s>

<s>188). A che il Principe, quasi un mese dopo, così <lb></lb>rispondeva: “ L&#039;invenzione di trovare la longitudine con il pendolo teorica­<lb></lb>mente ancora dal signor Galileo fu ritrovata, ma il trovare il modo che il <lb></lb>pendolo si adopri in mare, senza la perturbazione del moto che dovrebbe <lb></lb>avere uniforme, a voler conseguire l&#039;intento; questo non è stato trovato e <lb></lb>lo tengo per difficile, onde bellissima sarà l&#039;invenzione, se praticabile l&#039;avrà <lb></lb>ritrovata il signor Ugenio ” (ivi, T. XXII, c. </s>

<s>114). </s></p><p type="main">

<s>Che la bellissima invenzione poi fosse praticabile lo dimostrarono i fatti, <lb></lb>ond&#039;è che dopo l&#039;Huyghens s&#039;ingerì in tutti la persuasione che il problema <lb></lb>delle longitudini si sarebbe finalmente risoluto, non quando si fosse riusciti <lb></lb>a calcolare esattamente i moti delle Medicee, ma quando si fosse giunti a <lb></lb>costruire esattissimi e imperturbabili Orologi. </s></p><pb xlink:href="020/01/1020.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO XII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Di Saturno<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle prime osservazioni, e delle prime ipotesi degli Astronomi sul Sistema di Saturno, da Gali­<lb></lb>leo all&#039;Hevelio. </s>

<s>— II. </s>

<s>Della grande scoperta ugeniana dell&#039;Anello, e di quel che si pensò per <lb></lb>confermarla nell&#039;Accademia del Cimento. </s>

<s>— III. Dell&#039;origine, della fisica costituzione e del <lb></lb>moto dell&#039;Anello saturnio, secondo gli Accademici del Cimento. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La scoperta del nuovo Mondo gioviale destò, in tutti quei che n&#039;eb­<lb></lb>bero l&#039;annunzio, la maraviglia e in alcuni, come sempre suol delle cose <lb></lb>nuove, la diffidenza, la quale poi ne&#039;più ragionevoli s&#039;acquietò facilmente, <lb></lb>ripensando come in somma tutto quel che di straordinario s&#039;era scoperto in <lb></lb>Giove consisteva nel tirarsi dietro, rivolgentisi attorno, quattro Lune invece <lb></lb>d&#039;una, come si vede fare alla nostra Terra. </s>

<s>Altre novità però presentava Sa­<lb></lb>turno, delle quali non s&#039;era per l&#039;innanzi avuto l&#039;esempio, ond&#039;è che se il <lb></lb>Sistema gioviale, da qualche ostinato peripatetico in fuori, persuase presto <lb></lb>e fece riposare nella certezza le menti degli Astronomi, il Sistema saturnio <lb></lb>invece le tenne, per un mezzo secolo, agitate ne&#039;dubbii più penosi, infin­<lb></lb>tanto che non si scoperse il vero di quelle strane apparenze per la perfe­<lb></lb>zione introdottasi negli strumenti, e per la sagacia, a cui si venivano edu­<lb></lb>cando gli osservatori. </s></p><p type="main">

<s>Alla fine del Luglio 1610 Galileo da Padova scriveva così a Firenze, in <lb></lb>una lettera indirizzata a Belisario Vinta: “ Ho scoperto un&#039;altra stravagan­<lb></lb>tissima maraviglia, la quale desidero che sia saputa dalle LL. AA. e da V. S. <lb></lb>tenendola però occulta, finchè nell&#039;Opera che ristamperò sia da me pubbli-<pb xlink:href="020/01/1021.jpg" pagenum="464"></pb>cata, ma ne ho voluto dar conto alle LL. AA. Serenissime, acciò, se altri <lb></lb>l&#039;incontrasse, sappiano che niuno l&#039;ha osservata avanti di me, sebben tengo <lb></lb>per fermo che niuno la vedrà, se non dopo che ne l&#039;avrò fatto avvertito. </s>

<s><lb></lb>Questo è che la stella di Saturno non è una sola, ma un composto di tre, <lb></lb>le quali quasi si toccano, nè mai tra di loro si muovono o mutano e sono <lb></lb>poste in fila secondo la lunghezza del Zodiaco, essendo quella di mezzo <lb></lb>circa tre volte maggiore dell&#039;altre due laterali, e stanno situate in questa <lb></lb>forma <figure id="id.020.01.1021.1.jpg" xlink:href="020/01/1021/1.jpg"></figure> ” (Alb. </s>

<s>VI, 114, 15). </s></p><p type="main">

<s>Vedendo così Galileo il suo strumento rivelatore fecondo di nuove sco­<lb></lb>perte, era incerto se faceva un&#039;altra edizione del Nuncio Sidereo con nuove <lb></lb>aggiunte, o se scriveva un libro a parte delle <emph type="italics"></emph>Novità celesti.<emph.end type="italics"></emph.end> Intanto che <lb></lb>prendeva seco stesso e con gli amici consiglio intorno al modo più conve­<lb></lb>niente di annunziare al pubblico le sue scoperte celesti, con un accortezza <lb></lb>tante volte ammirata e lodata dal Keplero, diffondeva la notizia di Saturno <lb></lb>in enimma, che mandato a Praga eccitò a interpetrarlo la curiosità nel­<lb></lb>l&#039;animo dello stesso Keplero. </s>

<s>“ Annus iam vertitur (scriveva nel 1611 nella <lb></lb>prefazione alla Diottrica) ex quo Galilaeus Pragam perscripsit, se novi quid <lb></lb>in coelo praeter priora deprehendisse. </s>

<s>Et ne existeret qui obtrectationis stu­<lb></lb>dio priorem se spectatorem ventitaret, spacium dedit propalandi quae quis­<lb></lb>quis nova vidisset. </s>

<s>Ipse interim suum inventum literis transpositis in hunc <lb></lb>modum descripsit..... Ex hisce literis ego versum confeci semibarbarum, <lb></lb>quem Narratiuncula mea inserui, mense septembri superioris anni: <emph type="italics"></emph>Salve <lb></lb>umbistineum geminatum Martia proles.<emph.end type="italics"></emph.end> Sed longissime a sententia litera­<lb></lb>rum aberravi: nihil illa de Marte continebat. </s>

<s>Et ne te lector detineam, en <lb></lb>detectionem Gryphi ipsius Galilaei authoris verbis ” (Augustae, Vindelic, <lb></lb>pag. </s>

<s>13). E quì prosegue trascrivendo la lettera a don Giuliano de&#039;Medici, <lb></lb>dove Galileo stesso riduce così la mostruosità del Grifo alle forme naturali. <lb></lb><emph type="italics"></emph>Altissimum planetarum tergeminum observavi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Persuaso che tale, cioè tergemina, fosse la nativa e invariabile faccia <lb></lb>di Saturno, nella quale infino a tutto l&#039;Aprile 1612 <emph type="italics"></emph>non s&#039;era scorta mu­<lb></lb>tazione alcuna<emph.end type="italics"></emph.end> (Alb. </s>

<s>III, 396), Galileo, per l&#039;esperienza che aveva di tutti <lb></lb>gli altri movimenti delle stelle, si rendeva certo che oramai non dovrebbe <lb></lb>Saturno fare altra mutazione nemmeno per l&#039;avvenire “ perchè, ragionava, <lb></lb>quando in tali stelle fosse movimento alcuno simile ai movimenti delle Me­<lb></lb>dicee, o di altre stelle, già doveriano essersi separate o totalmente congiunte <lb></lb>colla principale stella di Saturno, quando anco il movimento loro fosse mille <lb></lb>volte più tardo di qualsivoglia altro di altra stella che vada vagando per lo <lb></lb>cielo ” (ivi). </s></p><p type="main">

<s>Riposava con più tranquillità che mai Galileo in tal certezza, vedendo <lb></lb>Saturno seguitar tuttavia a mostrarsi tricorporeo infino all&#039;Estate, dopo la <lb></lb>quale, intermesse le osservazioni, non tornò a riprenderle che sulla fin di <lb></lb>Novembre. </s>

<s>Rimase stupefatto: sparite le due stelle laterali, Saturno era di­<lb></lb>ventato monosferico come Giove. </s>

<s>Datone avviso a Federigo Cesi, rispose que­<lb></lb>sti da Roma la novità di Saturno parergli tanto più strana “ quanto che <pb xlink:href="020/01/1022.jpg" pagenum="465"></pb>V. S. qui mi disse non avere i suoi laterali moto alcuno, e nella prima Let­<lb></lb>tera solare dice non essersi in essa scorta mutazione alcuna, nè dovervisi <lb></lb>vedere ” (Alb. </s>

<s>VIII, 244). </s></p><p type="main">

<s>Dicevano in simil modo anche tutti gli altri che vedevano smentirsi da <lb></lb>sè stesso l&#039;oracolo di Galileo, il quale mutando tenore al responso confes­<lb></lb>sava così in pubblico che s&#039;era ingannato; e che non aveva tanto ingegno <lb></lb>da penetrare l&#039;arcano. </s>

<s>“ Ora che si ha da dire in così strana metamorfosi? </s>

<s><lb></lb>forse si sono consumate le due minori stelle al modo delle macchie so­<lb></lb>lari? </s>

<s>forse sono sparite e repentinamente fuggite? </s>

<s>forse Saturno si ha di­<lb></lb>vorato i propri figli, oppure è stata illusione e fraude l&#039;apparenza, colla <lb></lb>quale i cristalli hanno per tanto tempo ingannato me con tanti altri, che <lb></lb>meco molte volte gli osservarono? </s>

<s>È forse ora venuto il tempo di rinver­<lb></lb>dir la speranza, già prossima al seccarsi, in quelli che retti da più profonde <lb></lb>contemplazioni hanno penetrato tutte le nuove osservazioni esser fallacie, <lb></lb>nè potere in veruna maniera sussistere? </s>

<s>Io non ho che dire cosa risoluta <lb></lb>in caso così strano, inopinato e nuovo: la brevità del tempo, l&#039;accidente <lb></lb>senza esempio, la debolezza dell&#039;ingegno e il timore dell&#039;errore mi rendono <lb></lb>grandemente confuso ” (Alb. </s>

<s>III, 506, 7). </s></p><p type="main">

<s>Nonostante non si volle dar Galileo per vinto. </s>

<s>Incominciò a pensare che <lb></lb>forse i due Satelliti immobili al fianco di Saturno cangiavano aspetto dipen­<lb></lb>dente dal moto proprio del Pianeta combinato col moto della Terra, cosic­<lb></lb>chè ora si vedono i detti Satelliti in maestà, e Saturno si mostra tricor­<lb></lb>poreo; ora si vedono in profilo o in isbieco, in modo che l&#039;anteriore proietti <lb></lb>il lume e si confonda colla vista del Pianeta, e il posteriore ne rimanga <lb></lb>dietro occultato, e il Pianeta stesso si mostra allora monosferico e solitario. </s>

<s><lb></lb>Sopra una tal conclusione, che Galileo confessa non aver nessuna certezza, <lb></lb>predisse così al Velsero, infine alla III Lettera solare, le fasi che sarebbe, <lb></lb>dopo il 1612, per mostrar Saturno ai curiosi osservatori: “ Le due minori <lb></lb>Stelle saturnie, le quali di presente stanno celate, forse si scopriranno un <lb></lb>poco per due mesi intorno al solstizio estivo dell&#039;anno prossimo futuro 1613, <lb></lb>e poi si asconderanno, restando celate sin verso il brumal solstizio del­<lb></lb>l&#039;anno 1614, circa al qual tempo potrebbe accadere che di nuovo per qual­<lb></lb>che mese facessero di sè alcuna mostra, tornando poi di nuovo ad ascon­<lb></lb>dersi sin presso all&#039;altra seguente bruma, al qual tempo credo bene con <lb></lb>maggior risolutezza che torneranno a comparire, nè più si asconderanno, se <lb></lb>non che nel seguente solstizio estivo, che sarà dell&#039;anno 1615, accenne­<lb></lb>ranno alquanto di volersi occultare, ma non però credo che si asconderanno <lb></lb>interamente, ma ben tornando poco dopo a palesarsi, le vedremo distinta­<lb></lb>mente e più che mai lucide e grandi, e quasi risolutamente ardirei di dire <lb></lb>che le vedremo per molti anni, senza interrompimento veruno ” (Alb. </s>

<s>III, 507). </s></p><p type="main">

<s>Di queste predizioni di Galileo però non se ne vide avverar compiuta­<lb></lb>mente nessuna; nemmen quella che, essendosi Saturno divorato il pasto nè <lb></lb>avendolo per vecchiezza potuto ben masticare, sarebbe appunto per renderlo <lb></lb>così intero come l&#039;avea trangugiato (Alb. </s>

<s>VIII, 248), imperocchè, invece dei <pb xlink:href="020/01/1023.jpg" pagenum="466"></pb>due soliti globetti, vide sulla fin dell&#039;Agosto 1616 (ivi, 390) Galileo stesso <lb></lb>dare a Saturno fuori come due mitre o orecchioni “ che rendono tutto il <lb></lb>composto di figura ovale, simile a un&#039;oliva. </s>

<s>” Dopo le quali parole imme­<lb></lb>diatamente soggiunge: “ Si distingue però tra le due mitre il globo di mezzo <lb></lb>perfettamente rotondo, e non di figura ovata, e nel mezzo delle attaccature <lb></lb>delle mitre al globo di mezzo si veggono due macchie oscure assai ” (ivi, <lb></lb>VII, 228). In similissimo aspetto, cioè ovale “ ac tum duabus maculis ro­<lb></lb>tundis ad utrumque verticem ” dice, nel cap. </s>

<s>VII, lib. </s>

<s>XV <emph type="italics"></emph>De mundi fa­<lb></lb>brica,<emph.end type="italics"></emph.end> di avere osservato Saturno, dalla fin di Ottobre 1616 al Novembre 1619, <lb></lb>il padre Biancani. (Mutinae 1635, pag. </s>

<s>155). </s></p><p type="main">

<s>Disegnò di sua propria mano Galileo questa nuova fase saturnia a tergo <lb></lb>della carta 94 di quel Tomo, ch&#039;è in ordine numerico il IV della Parte III <lb></lb>de&#039;Manoscritti galileiani, e il disegno stesso lucidato dall&#039;originale si rap­<lb></lb>presenta qui nella figura 93 sotto gli occhi de&#039;nostri Lettori. </s>

<s>Tutto il com­<lb></lb><figure id="id.020.01.1023.1.jpg" xlink:href="020/01/1023/1.jpg"></figure></s></p><p type="caption">

<s>Figura 93.<lb></lb>posto mostrasi chiaramente configurato, come diceva Ga­<lb></lb>lileo, in somiglianza di oliva, e da&#039;due lati del Globo sa­<lb></lb>turnio perfettamente rotondo escono i due orecchioni o le <lb></lb>due mitre, ciascuna colle sue macchie assai oscure nel mezzo. </s></p><p type="main">

<s>Si rende così a tutti i riguardanti manifesta la vera intenzione di chi <lb></lb>tratteggiò quella figura colla penna, ma quando l&#039;Albèri annunziò con tromba <lb></lb>sonora ai quattro venti la scoperta delle Effemeridi contenute manoscritte <lb></lb>nel sopra citato Volume, e i curiosi concorsero d&#039;ogni parte a Firenze a <lb></lb>veder con gli occhi e a toccar con mano il Codice avventuroso, fu ad uno <lb></lb>di essi trattenuto lo sguardo sulla detta figura, e vedendoci senz&#039;altro Sa­<lb></lb>turno inanellato, tanti anni prima che dall&#039;Hugenio, esultò come di una <lb></lb>scoperta più maravigliosa di quella, che diceva d&#039;aver fatto lo stesso Albèri. </s></p><p type="main">

<s>Quest&#039;<emph type="italics"></emph>homme d&#039;un gran savoir<emph.end type="italics"></emph.end> diffuse la notizia della sua scoperta a <lb></lb>Parigi, dove allora stanziava Guglielmo Libri, il quale subito nel Giugno <lb></lb>del 1844 dette mano a scrivere, nel <emph type="italics"></emph>Journal des Savants,<emph.end type="italics"></emph.end> un articolo, in <lb></lb>cui, dopo di aver diffidato se quella specie di Giornale messo fuori dall&#039;Al­<lb></lb>bèri, dove interpolate alle osservazioni celesti si notano le spese fatte in cu­<lb></lb>cina, contenesse veramente l&#039;atlantica fatica di Galileo, così soggiunge: “ Il <lb></lb>parait cependant qu&#039;on trouve dans ces notes un fait extremement remar­<lb></lb>quable, qui a echappé a M.r Albèri; savoir, le dessin fait par Galilée de Sa­<lb></lb>turne avec son anneau. </s>

<s>Si ce fait, qui nous est attesté par des hommes <lb></lb>d&#039;un gran savoir, se confirme, c&#039;est là une veritable découverte qu&#039;on aura <lb></lb>fait dans les papiers de Galilée ” (Alb. </s>

<s>V, 34). </s></p><p type="main">

<s>Al rimprovero d&#039;essersi così lasciata scappar di mano una scoperta <lb></lb>tant&#039;ovvia, eppur sì <emph type="italics"></emph>extremement remarquable,<emph.end type="italics"></emph.end> l&#039;Albèri si risentì, ma non <lb></lb>rispose, com&#039;avrebbe potuto, alle parole inconsiderate. </s>

<s>Avrebbe infatti po­<lb></lb>tuto opporre che il disegno manoscritto lo fece incidere Galileo nella pa­<lb></lb>gina 217 della prima impressione del <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> fatta da Giacomo Mascardi <lb></lb>in Roma nel 1623, cosicchè stette per trentasei anni l&#039;immagine di Saturno <lb></lb>con l&#039;anello sotto gli occhi del Viviani e del Borelli, tanto stupidi da non <pb xlink:href="020/01/1024.jpg" pagenum="467"></pb>s&#039;avveder che il loro Galileo aveva scoperto, molto tempo prima, quel che, <lb></lb>come cosa nuova, ammiravano nell&#039;Hugenio. </s>

<s>Stette di più quello stesso di­<lb></lb>segno per altri cento e ottantacinque anni scolpito nelle molteplici edizioni <lb></lb>dell&#039;opere galileiane, sotto gli occhi di tutti gli Astronomi di Europa, senza <lb></lb>che in nessuno si ritrovasse ancora quel <emph type="italics"></emph>gran savoir<emph.end type="italics"></emph.end> necessario a far la <lb></lb>scoperta annunziata dal Libri. </s></p><p type="main">

<s>Chi non si fa caso di tanta inconsideratezza, in uomini reputati di sì <lb></lb>gran sapere, compatirà al nostro Targioni Tozzetti, il quale accennò in una <lb></lb>nota a piè della pag. </s>

<s>385 del T. </s>

<s>I delle sue <emph type="italics"></emph>Notizie degli aggrandimenti ecc.<emph.end type="italics"></emph.end><lb></lb>che il Beriguardi nel 1643, sedici anni prima della pubblicazione del <emph type="italics"></emph>Sy­<lb></lb>stema saturnium,<emph.end type="italics"></emph.end> lodava la scoperta ugeniana dell&#039;anello. </s>

<s>L&#039;errore è tanto <lb></lb>grosso, che non par credibile in uno storico della scienza, ma che pure ha <lb></lb>la stessa radice di quell&#039;altro, che si svelò da noi a pag. </s>

<s>450 del I Tomo, <lb></lb>in ambedue i quali errori incorse il Targioni per non avere, in cosa di sì <lb></lb>facile sospetto, dubitato punto che l&#039;edizione de&#039;<emph type="italics"></emph>Circoli pisani,<emph.end type="italics"></emph.end> fatta nel 1643, <lb></lb>non fosse in tutto simile all&#039;altra fatta nel 1661, vivente tuttavia l&#039;Autore, <lb></lb>e quando già le grandi scoperte del Torricelli e dell&#039;Huyghens avevano della <lb></lb>loro fama riempiuto il mondo. </s></p><p type="main">

<s>Ma passando sopra gli altrui errori con quella indulgente pietà, con cui <lb></lb>vorremmo che si passasse sui nostri, rivolgiamo l&#039;attenzione a quella im­<lb></lb><figure id="id.020.01.1024.1.jpg" xlink:href="020/01/1024/1.jpg"></figure></s></p><p type="caption">

<s>Figura 94.<lb></lb>magine saturnia fatta imprimere da Galileo stesso nella <lb></lb>citata pagina del <emph type="italics"></emph>Saggiatore.<emph.end type="italics"></emph.end> Noi l&#039;abbiamo di là lu­<lb></lb>cidata e la rappresentiamo nella figura 94 sotto gli occhi <lb></lb>de&#039;nostri Lettori perchè, riscontrandola colla precedente, <lb></lb>ne verifichino da sè stessi la sostanziale somiglianza. </s></p><p type="main">

<s>Attendendo dunque (benchè mute sieno le due figure, così qui nella <lb></lb>stampa, come là nel manoscritto) si sa d&#039;altre fonti sicure che voleva Ga­<lb></lb>lileo rappresentare in que&#039;disegni Saturno co&#039;suoi due orecchioni da cia­<lb></lb>scun lato, e una macchia oscura nel loro mezzo. </s>

<s>A questo punto si tacque <lb></lb>il primo scopritor dell&#039;altissimo Pianeta tergemino, nè ebbe ardire o spe­<lb></lb>ranza d&#039;avvincer nelle sue reti quel Proteo multiforme, che tante volte gli <lb></lb>era uscito di mano. </s>

<s>Vedremo come il costrutto lasciato a questo punto in­<lb></lb>terrotto da Galileo fosse poi ripreso dall&#039;Hodierna, che si studiò di ridurre <lb></lb>questa fase saturnia ultimamente osservata a sistema. </s>

<s>Ma perchè quel si­<lb></lb>stema accenna piuttosto a un regresso, giova proseguire a diritto il filo di <lb></lb>quella via che avrebbe finalmente condotto alla desiderata scoperta. </s></p><p type="main">

<s>La prima mossa, benchè così dalla lontana, venne allor che il Gassendi <lb></lb>e il Peiresc, osservando, con un Canocchiale mandato a loro da Galileo, l&#039;ul­<lb></lb>tima fase saturnia rappresentata nel <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> dubitarono; se la figura fosse <lb></lb><emph type="italics"></emph>macchiata,<emph.end type="italics"></emph.end> come diceva Galileo, o <emph type="italics"></emph>forata<emph.end type="italics"></emph.end> piuttosto come pareva a loro (Alb. </s>

<s><lb></lb>X, 193). Nel 1646 il Fontana pubblicò le nuove osservazioni fatte co&#039;suoi <lb></lb>Canocchiali. </s>

<s>La fase del 1630, che rappresenta Saturno rotondo con due pic­<lb></lb>cole stelle rotonde ai lati (Novae Observ., pag. </s>

<s>119) è quella che poi illuse <lb></lb>anche l&#039;Hevelio, ma l&#039;altra del 1633 descritta dallo stesso Fontana a pag. </s>

<s>131 <pb xlink:href="020/01/1025.jpg" pagenum="468"></pb>del suo libro, è mostruosa. </s>

<s>Più conformi al vero sono le osservazioni del 1634 <lb></lb>(pag. </s>

<s>133) e del 1636 (pag. </s>

<s>134), le quali dettero occasione all&#039;Hevelio di <lb></lb>immaginare il suo sistema, ma poi, nel passare a descrivere le fasi del 1644 <lb></lb>(pag. </s>

<s>137) e del 1645 (pag. </s>

<s>139 e 141) ritornò il Fontana alle mostruosità, <lb></lb>immaginandosi che i due punti estremi e laterali della figura, vivamente ir­<lb></lb>radianti, fossero quelle stesse stelle della prima osservazione, che si tenes­<lb></lb>sero congiunte al pianeta come per due redini di luce. </s></p><p type="main">

<s>Ma intanto si veniva con sì fatte rappresentazioni a decidere i dubbi <lb></lb>del Gassendo e del Peiresc se quelle, che si vedevano in mezzo a&#039;due orec­<lb></lb>chioni di Galileo, erano macchie o fori. </s>

<s>Così, il Boulliaud scriveva al prin­<lb></lb>cipe Leopoldo de&#039;Medici di aver nel Dicembre del 1648 osservato Saturno <lb></lb>con due lati ben distinti in modo, da non aver più dubbio che non sieno i <lb></lb>due laterali di qua e di là disgiunti dal globo del Pianeta. </s>

<s>Per mezzo di <lb></lb>un Canocchiale eccellente donatogli dal Granduca “ Saturnum conspexi, dice <lb></lb>il Boulliaud, mense Decembri superiori dum Terrae vicinus erat hac forma <lb></lb>(fig. </s>

<s>95): ita ut acutiores cernerentur partes AB <lb></lb><figure id="id.020.01.1025.1.jpg" xlink:href="020/01/1025/1.jpg"></figure></s></p><p type="caption">

<s>Figura 95.<lb></lb>quam circuli circumferentia ferre possit, sed <lb></lb>ad ellipticam figuram propius accedebat: distin­<lb></lb>ctae apparebant partes O, O, tamquam hiatus <lb></lb>tenebrosus utrinque globum Saturni a latero­<lb></lb>nibus disiungens ” (MSS. Cim., T. XVI, c. </s>

<s>21). </s></p><p type="main">

<s>Quest&#039;apparenza descritta dal Boulliaud, e nella quale si correggeva ciò <lb></lb>che v&#039;aveva di fantastico introdotto il Fontana, rappresentatasi più scolpita <lb></lb>che mai all&#039;oculatissimo Hevelio, servi a inspirargli quell&#039;animo di comporre <lb></lb>un Sistema saturnio, che le strane metamorfosi osservate avevano prima fatto <lb></lb>smarrire a Galileo. </s>

<s>Nel 1656 pubblicava in Danzica una dissertazione col <lb></lb>titolo “ De nativa Saturni facie eiusque variis phasibus certa periodo re­<lb></lb>deuntibus ”, dove non dissimulando le gravissime difficoltà, e anzi aperta­<lb></lb>mente confessando i dubbi che gli tenevano agitata la mente, s&#039;introduce a <lb></lb>trattar dell&#039;arduo soggetto con queste parole: “ Ego hucusque, licet indefesse <lb></lb>in isto negotio, ab anno 1642 continue, multorum perfectissimorum tam <lb></lb>nostra quam aliorum artificum sedula manu elaboratorum Telescopiorum <lb></lb>beneficio desudaverim; nullo tamen modo recte phaenomenon hocce assequi <lb></lb>et perscrutari potuerim, haerens plane utrum Saturnus sit rotundus,. an <lb></lb>vero ellipticus, utrum simplex corpus an vero tricorporeus ” (pag. </s>

<s>2). </s></p><p type="main">

<s>Dopo più mature considerazioni, parvegli nonostante di potere stabi­<lb></lb>lire le tre cose seguenti; “ Primo itaque Saturnum cum plerisque Astro­<lb></lb>philis a Sole illuminari quidem statuo..... Secundo, pro certo habeo Sa­<lb></lb>turnum non semper esse uniformem .... sed variam faciem nobis ostentare, <lb></lb>diversasque exhibere phases..... Tertio, Saturnum pono revera esse tricor­<lb></lb>poreum et omnino talis speciei qualis est num. </s>

<s>1° adumbratus, medium <lb></lb>nempe corpus non esse rotundum sed ellipticum; duo laterones eius non <lb></lb>esse globosa ac pecularia circa Saturnum mobilia, sed firmiter circa partes <lb></lb>superiores et inferiores adhaerentia corpora, instar brachiorum figurae fere <pb xlink:href="020/01/1026.jpg" pagenum="469"></pb>hyperbolicae, ac certo et immutabili interstitio circa medium a medio cor­<lb></lb>pore remoto, mobilia tamen una cum corpore intermedio circa unicam axem <lb></lb>certa periodo ” (pag. </s>

<s>3, 4). </s></p><p type="main">

<s>Le figure ombreggiate, di che fa cenno l&#039;Autore, sono in numero di <lb></lb>sei impresse tutte insieme e per ordine numerate in una Tavola a rappre­<lb></lb>sentar la successione delle principali fasi saturnie, che si distinguono cia­<lb></lb>scuna col nome proprio di <emph type="italics"></emph>Saturnus elliptico-ansatus plenus, S. ellipticus <lb></lb>ansatus diminutus, S. sphaerico-ansatus, S. sphaerico-cuspidatus, S. tri­<lb></lb>corporeus, S. monosfaericus.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Prototipa è la prima figura, la quale nell&#039;intenzion dell&#039;Hevelio rap­<lb></lb>presenta Saturno composto di un globo ellittico nel mezzo, con un&#039;ansa <lb></lb>attaccata di qua e di là dalle due parti. </s>

<s>Supponeva l&#039;Autore che tutto il <lb></lb>sistema facesse in 30 anni una rotazione intiera intorno al suo asse minore <lb></lb>perpendicolarmente eretto e stabile sul piano dell&#039;orbita planetaria, e così <lb></lb>sperava che sarebbero regolarmente apparite le varietà delle fasi secondo <lb></lb>l&#039;ordine divisato. </s>

<s>Ma presto si videro i fatti non approvar l&#039;ipotesi, impe­<lb></lb>rocchè, secondo la predizion dell&#039;Hevelio, la fase rotonda del 1656 doveva <lb></lb>mantenersi infino al Settembre dell&#039;anno appresso, e nonostante infin dal <lb></lb>dì 13 d&#039;Ottobre di quell&#039;anno 1656 si vide Saturno riapparire coll&#039;anse, <lb></lb>mantenendosi in quella medesima apparenza anche dopo. </s></p><p type="main">

<s>Fallace il Sistema heveliano si dimostrava altresì dal riscontro delle fasi <lb></lb>antecedentemente osservate, fra le quali insigni nella storia del Pianeta erano <lb></lb>quelle descritte, nella III Lettera velseriana, da Galileo. </s>

<s>Nel solstizio del­<lb></lb>l&#039;anno 1612, quando Saturno era nei 18° 22′ de&#039;Pesci, Galileo l&#039;osservò tri­<lb></lb>corporeo, mentre sarebbe dovuto per le Tavole dell&#039;Hevelio comparire ro­<lb></lb>tondo; e similmente, nel Dicembre di quell&#039;anno 1612, essendo Saturno in <lb></lb>11° 27′ de&#039;Pesci, Galileo l&#039;osservò rotondo, mentre si doveva per l&#039;Hevelio aspettare trisferico. </s></p><p type="main">

<s>Ma se in ogni modo per prototipo delle altre fasi stabilivasi quella de­<lb></lb>signata col nome di <emph type="italics"></emph>ellittico ansata piena,<emph.end type="italics"></emph.end> non si vedeva come potessero <lb></lb>da questa sola derivarsi tutte le varie apparenze del Pianeta. </s>

<s>Sia infatti nella <lb></lb>figura 96 ABCD il globo ellissoideo di Saturno, a cui sieno attaccate le anse <lb></lb>EF, GH e si volga tutto il sistema attorno all&#039;asse BD. </s>

<s>Non v&#039;ha dubbio <lb></lb><figure id="id.020.01.1026.1.jpg" xlink:href="020/01/1026/1.jpg"></figure></s></p><p type="caption">

<s>Figura 96.<lb></lb>che da chiunque stesse di faccia a riguar­<lb></lb>dare le apparenti mutazioni di figura pre­<lb></lb>sentate da questo moto, si vedrebbero le <lb></lb>anse andar via via sempre più ad acco­<lb></lb>starsi al globo centrale, e così potrebbe <lb></lb>Saturno in questa ipotesi mostrarsi sotto <lb></lb>l&#039;aspetto di ellittico ansato diminuito, e di <lb></lb>sferico ansato. </s>

<s>Seguitando poi tutto il si­<lb></lb>stema a volgersi regolarmente attorno, giunto a presentar l&#039;asse maggiore <lb></lb>in direzione del raggio visuale, potrebbe altresi pigliar la forma monosferica, <lb></lb>ma dovendo secondo il supposto dell&#039;Hevelio, le altezze EF, GH mantenersi <pb xlink:href="020/01/1027.jpg" pagenum="470"></pb>sempre e in qualunque caso invariabili, non potrebbero perciò mai tanto <lb></lb>comprimersi da mostrar le due fasi sferico cuspidata e trisferica. </s></p><p type="main">

<s>Mentre che così discutevasi dagli Astronomi intorno alla possibilità del <lb></lb>Sistema heveliano, che per queste ragioni principalmente rimaneva molto <lb></lb>dubbioso, l&#039;Huyghens dall&#039;Aja pubblicava, in data del dì 5 Marzo 1656, <lb></lb>una breve nota contenente la scoperta di una nuova Luna, la quale, come <lb></lb>le Medicee intorno a Giove, si rivolgeva in sedici giorni intorno a Saturno. </s>

<s><lb></lb>Accennava ivi inoltre a una cosa ben più nuova e più importante, che cioè <lb></lb>la scoperta di quella Luna “ viam aperuit, tandemque causam rescivimus, <lb></lb>cur interdum inter binas velut ansas Saturnus medius teneatur, alias recta <lb></lb>quasi brachia protendat, tum nonnunquam, omnibus amissis, rotundus in­<lb></lb>veniatur ” (Opera Varia, Vol. </s>

<s>II, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>525). A che si <lb></lb>riducesse quella causa intorno alla quale, fra tutti gli Astronomi, il solo <lb></lb>Hevelio aveva allora allora e non troppo felicemente pronunziata la sua sen­<lb></lb>tenza, l&#039;Huyghens lo accennò alla fine di detta nota in enimma o per grifo, <lb></lb>imitando le previdenti accortezze di Galileo. </s></p><p type="main">

<s>La curiosità di scioglier l&#039;enimma frugò tutti gli Astronomi, ma due <lb></lb>soli vi si provarono, il Roberval in Francia, e l&#039;Hodierna in Italia. </s>

<s>S&#039;im­<lb></lb>maginava il primo che dalla zona torrida di Saturno si sollevassero vapori <lb></lb>condensati dal freddo, i quali vapori, se riempiono tutta intorno e molto <lb></lb>spessi la zona, danno a noi che gli vediamo irraggiati dal Sole l&#039;apparenza <lb></lb>ellittica. </s>

<s>Se sono men densi, e non si vedono perciò che là, dove per pro­<lb></lb>spettiva appariscono cumulati, cioè dalle due parti, presentano la fase an­<lb></lb>sata. </s>

<s>Se poi Saturno è sereno, precipitatasi qualunque esalazion vaporosa sopra <lb></lb>la superficie del suo Globo, ci apparisce come Giove perfettamente rotondo. </s></p><p type="main">

<s>Questa ipotesi robervalliana era senza dubbio semplicissima, ma non <lb></lb>essendosi ancora osservati i ritorni matematicamente regolari delle fasi, non <lb></lb>si poteva ripudiar per il semplice motivo della capricciosa variabilità delle <lb></lb>stagioni. </s>

<s>Se veramente però dipende questa variabilità da cause meteorolo­<lb></lb>giche somiglianti a quelle della nostra Terra, la quale è più nuvolosa ai poli <lb></lb>che no all&#039;Equatore, non s&#039;intende, opponevasi al Roberval, come debba in <lb></lb>Saturno avvenir così tutto al contrario. </s></p><p type="main">

<s>L&#039;Hodierna, fisso nella contemplazione della fase saturnia descritta nel <lb></lb><emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> e ch&#039;ei ci volle rappresentar sott&#039;occhio in quella Tavola, dove <lb></lb>all&#039;esemplare del Sistema gioviale aggiunse le apparenze degli altri fenomeni <lb></lb>celesti; ritornò in dietro a considerare con Galileo e col Biancani Saturno <lb></lb>ovale tinto delle due macchie nere alla sua superficie. </s>

<s>Segnando nel sistema <lb></lb>dell&#039;Hevelio questo regresso, approvò del resto l&#039;ipotesi di lui, sperando di <lb></lb>aver così colto nel segno in decifrar l&#039;enimma ugeniano. </s>

<s>Ma l&#039;Hugenio stesso <lb></lb>gli fece poco dopo capire che non includeva l&#039;enimma per nulla o la prugna <lb></lb>o l&#039;uovo maculato, col quale, se potevansi rappresentar le fasi monosferi­<lb></lb>che due volte sole in 30 anni, rimaneva però tuttavia inesplicato come tante <lb></lb>altre volte mostrasse quello stesso aspetto il Pianeta, non potendo ciò fare <lb></lb>se non che ascondendo, ma non si vedeva dove, quelle due macchie nere. </s></p><pb xlink:href="020/01/1028.jpg" pagenum="471"></pb><p type="main">

<s>Nel Luglio del 1659 comparve finalmente il <emph type="italics"></emph>Systema Saturnium<emph.end type="italics"></emph.end> dedi­<lb></lb>cato al principe Leopoldo de&#039;Medici, e fu allora dall&#039;oracolo stesso del­<lb></lb>l&#039;Huyghens svelato l&#039;arcano, che ridestò in generale una lieta maraviglia, <lb></lb>e in alcuni pochi un impotente prurito di contradizione. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nel <emph type="italics"></emph>Systema Saturnium<emph.end type="italics"></emph.end> narra da sè stesso l&#039;Autore la storia della sua <lb></lb>insigne scoperta, la quale si compendia così in queste parole: “ Quand&#039;ebbi, <lb></lb>egli dice, ritrovato che il periodo del nuovo Pianeta era di 16 giorni, pen­<lb></lb>sai che si sarebbe anche Saturno stesso revoluto intorno al suo asse. </s>

<s>Im­<lb></lb>perocchè sul suo asse si rivolge la nostra Terra, sul suo asse il Sole e pro­<lb></lb>babilmente anche Giove in un periodo di tempo che, secondo me, è più <lb></lb>breve di ventiquattr&#039;ore. </s>

<s>Persuaso dunque così per induzione che dovesse <lb></lb>Saturno rigirarsi in sè stesso, ne conclusi che avrebbe seco menato in volta <lb></lb>anche gli altri corpi circostanti, con tanto maggior velocità quanto gli an­<lb></lb>davano più vicini. </s>

<s>” </s></p><p type="main">

<s>“ M&#039;occorse d&#039;osservare il Pianeta nel 1655, quando mostrava le sue <lb></lb>braccia sporte lungo una linea retta, come se fosse trafitto e trapassato nel <lb></lb>mezzo da una clava con le sue estremità più grosse e più chiare da una <lb></lb>parte e dall&#039;altra. </s>

<s>Quum itaque quotidie eamdem hanc speciem prae se <lb></lb>ferret, intellexi id alia ratione fieri non posse, siquidem tam brevis esset <lb></lb>Saturni, eorumque quae illi cohaerent circuitus, nisi ut globus Saturni a <lb></lb>corpore alio aequaliter undique cinctus poneretur, atque ita ANNULUS qui­<lb></lb>dam medium eum ambiret ” (Op. </s>

<s>varia cit., pag. </s>

<s>565). </s></p><p type="main">

<s>“ Così, col supposto di questo Anello mi veniva bene quella fase spie­<lb></lb>gata: bisognava però spiegare anche le altre, ciò che m&#039;avvenne presto <lb></lb>avvertendo che la linea delle braccia saturnie intersecava l&#039;Ecclittica con un <lb></lb>angolo maggiore di venti gradi, d&#039;onde ne stabilii che tale, sulla stessa Ec­<lb></lb>clittica, dovess&#039;esser pure l&#039;inclinazion del piano di quello Anello, ch&#039;io <lb></lb>m&#039;ero immaginato. </s>

<s>Ne seguiva di qui ch&#039;essendo veduto da noi sotto varii <lb></lb>aspetti dovesse ora apparirci in figura di un&#039;ellissi più o meno aperta, e <lb></lb>ora anche in esquisita linea retta. </s>

<s>La fase ansata poi la spiegavo assai facil­<lb></lb>mente ammettendo che fra il giro interiore dell&#039;Anello e il globo del Pia­<lb></lb>neta intercedesse qualche spazio vuoto. </s>

<s>” </s></p><p type="main">

<s>Le più minute particolarità che illustrano questa storia, con altre di­<lb></lb>gressioni sopra soggetti nuovi e importantissimi, si leggevano in Firenze <lb></lb>dagli Accademici del Cimento, al principe de&#039;quali dedicava l&#039;Autore il suo <lb></lb>libro, non per cortigianesca adulazione, ma perchè fosse diligentemente esa­<lb></lb>minato e imparzialmente giudicato da quei, che sopra gli altri reputava au­<lb></lb>torevoli nella scienza. </s>

<s>In ordine a che non solo ne furono sodisfatti i desi­<lb></lb>derii, ma ebbe di più l&#039;Huyghens a professar gratitudine verso i nostri<pb xlink:href="020/01/1029.jpg" pagenum="472"></pb>fiorentini, i quali rimossero le difficoltà e confermarono il vero Sistema sa­<lb></lb>turnio in un modo ingegnosissimo, riducendo sotto i nostri occhi le appa­<lb></lb>renze di ciò, che la Natura opera in un mondo così smisuratamente lontano <lb></lb>da noi. </s></p><p type="main">

<s>Una delle prime e più forti di quelle difficoltà si riduceva a dire che <lb></lb>essendosi a moltissimi osservatori, dopo Galileo, mostrato Saturno con due <lb></lb>stelle disgiunte e laterali, non si vedeva come si potesse ridur questa fase <lb></lb>alla figura dell&#039;anello. </s>

<s>Rispose l&#039;Huyghens che questa di Saturno tricorpo­<lb></lb>reo era una illusione dei troppo deboli strumenti usati da que&#039;suoi prede­<lb></lb>cessori, ma non seppe dimostrar di fatto come sparissero le illusioni e ap­<lb></lb>parisse il vero, usando strumenti più perfetti. </s></p><p type="main">

<s>La dimostrazione sperimentale di ciò, che pareva impossibile, fu ritrovata <lb></lb>nell&#039;Accademia fiorentina dall&#039;ingegno del Borelli, il quale fece fabbricare <lb></lb>una macchinetta a rappresentare il Globo di Saturno col suo Anello, nelle <lb></lb>puntuali proporzioni stabilite dall&#039;Hugenio. </s></p><p type="main">

<s>“ Costituita detta Macchina in testa ad una galleria lunga 128 braccia, <lb></lb>ed illuminata da quattro Torce, collocate in modo che rimanessero nascoste <lb></lb>all&#039;occhio dell&#039;Osservatore, si notò che quanto minore era l&#039;angolo de&#039;raggi <lb></lb>visuali sopra il piano della Fascia, tanto più andava restringendosi l&#039;appa­<lb></lb>rente Ellisse, infin tanto che i tratti GF, CD (fig. </s>

<s>97) ad un Occhiale im­<lb></lb>perfetto si facevano invisibili, e pur tuttavia con esso si seguitavano a sco­<lb></lb><figure id="id.020.01.1029.1.jpg" xlink:href="020/01/1029/1.jpg"></figure></s></p><p type="caption">

<s>Figura 97.<lb></lb>prire i due estremi B, E, che per la <lb></lb>lontananza e debolezza della luce per­<lb></lb>fettamente si rotondavano, a tale che <lb></lb>l&#039;apparenza della Macchina in tal costi­<lb></lb>tuzione corrispondeva alla prima delle <lb></lb>Tavole dell&#039;Hugenio, che è di tre sfer e, <lb></lb>la di mezzo maggiore e l&#039;altre due mi­<lb></lb>nori, per breve tratto disgiunte dal disco <lb></lb>di Saturno. </s>

<s>Variavasi bene quest&#039;ap­<lb></lb>parenza riguardando l&#039;istessa Macchina, <lb></lb>non punto alterata dalla sua prima po­<lb></lb>sizione e lontananza, con un Occhiale <lb></lb>di un braccio e un terzo ma d&#039;esquisito <lb></lb>lavoro, mostrandosi allora Saturno non più in mezzo delle due stelle B, E, <lb></lb>ma coronato dalla zona lucida BCDEFG, mercè delle braccia luminose nuo­<lb></lb>vamente resegli dall&#039;esquisitezza del secondo Occhiale ” (Targioni, Noti­<lb></lb>zie ecc., T. I, pag. </s>

<s>741). </s></p><p type="main">

<s>Un&#039;altra non men grave difficoltà, ad approvare il Sistema ugeniano, <lb></lb>nasceva dalla fase monosferica, e l&#039;Huyghens stesso l&#039;avea già prevenuta con <lb></lb>dire che, sebben l&#039;Anello stia anche allora intorno al Pianeta, è nonostante <lb></lb>invisibile a noi perchè, trovandosi il prolungamento del nostro raggio vi­<lb></lb>suale sul piano di esso Anello, non ci mostra di sè che l&#039;esteriore super­<lb></lb>ficie convessa, o come si direbbe l&#039;esergo. </s></p><pb xlink:href="020/01/1030.jpg" pagenum="473"></pb><p type="main">

<s>Bisognava però qui rendere la ragione di una tale invisibilità, la quale <lb></lb>si poteva credere che dipendesse dal ritrovarsi in quella così espansa figura <lb></lb>annulare troppo assottigliata la materia. </s>

<s>Ma l&#039;Huyghens nega che possa es­<lb></lb>ser questa la ragione cercata, perchè l&#039;Anello dee avere una certa mate­<lb></lb>rial grossezza resa evidente nell&#039;ombra proiettata da lui sul disco del Pia­<lb></lb>neta, che lo sega attraverso con una linea oscura. </s>

<s>Perciò conclude che la <lb></lb>ragione di una tale invisibilità dee non in altro consistere che nell&#039;esser <lb></lb>l&#039;esergo dell&#039;Anello composto di qualche particolar materia inetta, come <lb></lb>l&#039;acqua, a render più vivamente la luce ne&#039;moltiplicati riflessi. </s>

<s>“ Alioquin <lb></lb>vel illud forsitan dici possit materiam quandam aquae similem aut certe <lb></lb>laevi et splendida superficie praeditam, extrema Annuli praecingere, quae <lb></lb>unico tantum veluti puncto Solis radios reflectens nequaquam nobis conspi­<lb></lb>cua erit ” (Opera cit., pag. </s>

<s>577). </s></p><p type="main">

<s>Il Borelli, nell&#039;Accademia del Cimento, confermò questa fase con l&#039;espe­<lb></lb>rienza, situando innanzi alla Macchinetta l&#039;occhio nel piano della Fascia <lb></lb>“ nel qual caso, perdendosi per la loro sottigliezza i suoi contorni esterni, <lb></lb>rimaneva l&#039;apparenza di una sfera perfettamente rotonda ” (Targioni, cit., <lb></lb>pag. </s>

<s>743). L&#039;esperienza stessa però non parve di voler secondar così bene <lb></lb>la ragione della invisibilità resa dall&#039;Huyghens, perchè non fu potuto dagli <lb></lb>Accademici veder la linea nera proiettata sul disco del Pianeta, e dando al­<lb></lb>l&#039;anello artificiale della Macchina una qualche sensibile grossezza non si potè <lb></lb>far mai che non si rendesse in qualche modo cospicuo. </s>

<s>“ Ci siamo perciò <lb></lb>attenuti, lasciarouo quegli stessi Accademici scritto, a formar l&#039;anello di no­<lb></lb>tabile sottigliezza, parendoci che questa ci sottragga da altre difficoltà in­<lb></lb>contrate nel costituirlo altrimenti ” (ivi, pag. </s>

<s>743). </s></p><p type="main">

<s>Essendo così nell&#039;Accademia richiamata l&#039;attenzione sull&#039;ombre che dal­<lb></lb>l&#039;Anello irraggiato dal Sole si debbono necessariamente, essendo opaco, <lb></lb>proiettare sul disco del Pianeta, si riconobbe la necessità di un&#039;altra zona <lb></lb>ombrosa, la quale dee nascere “ non dall&#039;aspetto della superficie cilindrica <lb></lb>convessa, ma dallo sbattimento della larghezza dell&#039;istesso Anello, per lo che <lb></lb>dee variare anch&#039;ella di sito, ed alcune volte interamente perdersi ” (ivi). </s></p><p type="main">

<s>Dalla considerazione di questi fatti il Borelli fu condotto a trovare la <lb></lb>più decisiva conferma del Sistema ugeniano in certe apparenze, che s&#039;ad­<lb></lb>ducevano da alcuni per una delle più forti ragioni a doverlo negare. </s>

<s>Fu <lb></lb>osservata una volta dagli Accademici, fra quelle così mutabili apparenze. </s>

<s><lb></lb>una delle più singolari, e affatto nuova nella storia delle metamorfosi fino <lb></lb>allora narrate dagli Astronomi: Saturno appariva per l&#039;appunto come se <lb></lb>fosse un cappello candido di tesa larga, volato via per l&#039;aria di capo a qual­<lb></lb>cuno. </s>

<s>Il Borelli allora dimostrò come quella fase, nella quale vedevasi più <lb></lb>che in altra mai cancellata l&#039;immagine dell&#039;Anello, dipendeva anzi dall&#039;Anello <lb></lb>stesso e da un gioco non avvertito della sua ombra. </s></p><p type="main">

<s>“ E prima di finir questa parte, scriveva al principe Leopoldo, non so <lb></lb>se io mi debba arrischiare a palesare certa mia fantasia, della quale forse <lb></lb>l&#039;Hugenio ne farebbe qualche stima. </s>

<s>Le sere passate con eccellenti Telescopi <pb xlink:href="020/01/1031.jpg" pagenum="474"></pb>fu osservato in Palazzo il globo di Saturno collocato no nel mezzo precisa­<lb></lb>mente della sua Ciambella, ma collocato un poco all&#039;in su, in maniera che <lb></lb>molti di quei signori l&#039;assomigliavano a un cappello da cardinali. </s>

<s>Io qui non <lb></lb>dico che l&#039;anterior parte XV (fig. </s>

<s>98) della ciambella di Saturno doverebbe <lb></lb>apparire più larga e più allontanata dal centro del medesimo Saturno, che <lb></lb><figure id="id.020.01.1031.1.jpg" xlink:href="020/01/1031/1.jpg"></figure></s></p><p type="caption">

<s>Figura 98.<lb></lb>la parte posteriore RS, perchè, con tutto <lb></lb>che questo sia vero, in tanta lontananza <lb></lb>non può cadere sotto i nostri sensi, ma <lb></lb>avverto bene che in questa ipotesi è ne­<lb></lb>cessario che la parte anteriore XV della <lb></lb>Ciambella produca certa ombra nell&#039;infe­<lb></lb>rior porzione del disco di Saturno. </s>

<s>E per­<lb></lb>chè i raggi della nostra vista sono assai <lb></lb>inclinati ai raggi del Sole, perchè ora la <lb></lb>prostaferesi dell&#039;orbe è massima, sarà l&#039;inferior parte del disco di Saturno <lb></lb>adombrata esposta alla nostra vista, la qual ombra, coprendo quasi tutto <lb></lb>quell&#039;estremo orlo del disco di Saturno posto sotto la Ciambella XV, non <lb></lb>ce lo lascia vedere, ma la parte superiore rimane spiccata e rilevata, per <lb></lb>non essere coperta da ombra veruna, e però deve rappresentarsi in forma <lb></lb>di cappello. </s>

<s>Sicchè, come vede V. A., quella esperienza, che mostrava per­<lb></lb>turbare l&#039;ipotesi dell&#039;Hugenio, la favorisce mirabilmente ” (MSS. Cim., <lb></lb>T. XII, c. </s>

<s>56). </s></p><p type="main">

<s>Un&#039;altra particolarità fu osservata dagli Accademici del Cimento, ed era <lb></lb>che una delle anse, senza saper perchè, non s&#039;andava ad attaccare perfet­<lb></lb>tamente al disco di Saturno. </s>

<s>Allora il Borelli dimostrò che in quel punto, <lb></lb>in cui l&#039;ansa stessa pareva rotta, andava a proiettarsi l&#039;ombra oscura del <lb></lb>Pianeta. </s>

<s>“ Con gran mia meraviglia intesi l&#039;osservazione di Saturno fatta <lb></lb>le sere passate da V. A. S. nella quale si vide che uno dei manichi che ab­<lb></lb>braccian Saturno non si unisce perfettamente al disco luminoso dello stesso <lb></lb>Saturno, ma vi s&#039;interpone un piccolo interstizio tenebroso. </s>

<s>Cercai subito <lb></lb>con gran curiosità in qual sito cadesse la detta ombra, e fui assicurato, che <lb></lb>cadeva dalla parte superiore verso oriente. </s>

<s>Ora, perchè quest&#039;esperienza ma­<lb></lb>ravigliosamente confermerebbe l&#039;ipotesi d&#039;Ugenio, ho stimato bene inviarne <lb></lb>la dimostrazione a V. A. S., insieme con il pronostico delle variazioni, che <lb></lb>dovrà fare la detta ombra per i mesi seguenti ” (ivi, c. </s>

<s>57); dimostrazione <lb></lb>e pronostici che furono inseriti nel <emph type="italics"></emph>Parere<emph.end type="italics"></emph.end> pubblicato dal Targioni, dove si <lb></lb>leggono nel Tomo sopra citato a pag. </s>

<s>345, 46. </s></p><p type="main">

<s>Intanto che così nell&#039;Accademia fiorentina si confermava e s&#039;illustrava <lb></lb>tanto sapientemente il Sistema ugeniano, il padre Onorato Fabry in Roma <lb></lb>meditava le sue lepidezze. </s>

<s>Egli faceva dal suo cervello scaturire intorno a <lb></lb>Saturno quattro globi, due bianchi e due neri, che messi opportunamente <lb></lb>in gioco, col loro chiaro e con l&#039;ombra, supplissero a rappresentar le fasi <lb></lb>stesse che rappresenta l&#039;Anello. </s>

<s>Fu il nuovo Sistema pubblicato dallo stesso <lb></lb>Fabry sotto il nome di Eustachio Divini, col titolo di <emph type="italics"></emph>Brevis annotatio in<emph.end type="italics"></emph.end><pb xlink:href="020/01/1032.jpg" pagenum="475"></pb><emph type="italics"></emph>Systema saturnium Christiani Hugenii,<emph.end type="italics"></emph.end> e fu pure questa Annotazione in­<lb></lb>titolata al principe Leopoldo. </s></p><p type="main">

<s>L&#039;Huyghens che ai fatti, con laboriose vigilie osservati, si vide contrap­<lb></lb>porre così strane chimere, ne rimase maravigliato e in una breve scrittura, <lb></lb>che indirizzò al medesimo principe di Toscana, col titolo di <emph type="italics"></emph>Brevis assertio <lb></lb>Systematis saturnii sui,<emph.end type="italics"></emph.end> disse che in somma a sentirsi parlar di que&#039;globi, <lb></lb>che ora appariscon bianchi ora neri, gli pareva di trovarsi presente a un <lb></lb>gioco di bussolotti. </s>

<s>“ Videor mihi circolatorium quemdam calculorum lu­<lb></lb>dum videre, alios ibi albos, alios nigros esse; nunc hos, nunc illos ostendi <lb></lb>abscondique vicissim ” (Op. </s>

<s>cit., pag. </s>

<s>633). </s></p><p type="main">

<s>Il principe Leopoldo, innanzi al quale i due dissenzienti avevano por­<lb></lb>tato a decidere la questione, fece esaminare nell&#039;Accademia il libro del Di­<lb></lb>vini, che si lesse nell&#039;adunanza del dì 17 Luglio 1660 (Targioni, Notizie ecc., <lb></lb>T. I, pag. </s>

<s>132), e il Borelli ne fece un estratto, riducendo a sommi capi i <lb></lb>luoghi, sopra i quali dovevano gli Accademici particolarmente rivolgere le <lb></lb>loro attenzioni, per profferirne poi i loro giudizi. </s>

<s>Nel dì 7 dell&#039;Agosto se­<lb></lb>guente, adunatasi di nuovo l&#039;Accademia per sentir que&#039;giudizi intorno al <lb></lb>decider del vero Sistema saturnio, tra quello che proponeva l&#039;Huyghens, e <lb></lb>l&#039;altro che il Fabry gli veniva contrapponendo, non par che leggessero se <lb></lb>non che il Borelli e il Dati. </s>

<s>La Scrittura del Borelli, gittata in bozza da <lb></lb>c. </s>

<s>99-107 del T. XII de&#039;Manoscritti del Cimento, e poi ridotta in assai ni­<lb></lb>tida copia da c. </s>

<s>15-20 del T. XXX, s&#039;intitolava “ Annotazioni sopra l&#039;Apo­<lb></lb>logia di Eustachio Divini contro il Sistema saturnio del signor Cristiano <lb></lb>Ugenio. </s>

<s>” </s></p><p type="main">

<s>Le risposte alle principali difficoltà promosse dal Fabry contro il Si­<lb></lb>stema ugeniano son quelle che, prevenute già dall&#039;Huyghens stesso, erano <lb></lb>state date nel sopra riferito <emph type="italics"></emph>Parere<emph.end type="italics"></emph.end> letto nell&#039;Accademia dal Borelli, il quale <lb></lb>in queste Annotazioni ci torna sopra confermandole in altra maniera. </s>

<s>Come <lb></lb>argomento de&#039;più concludenti però v&#039;aggiunge l&#039;esperienza, la quale se <lb></lb>aveva allora, in quel primo Discorso, mirabilmente approvata l&#039;ipotesi del­<lb></lb>l&#039;Huyghens, veniva ora a riprovar la opposta del Fabry colla medesima evi­<lb></lb>denza di fatto. </s></p><p type="main">

<s>“ Finalmente, conclude le sue parole il Borelli, secondo l&#039;ordine di <lb></lb>V. A., si fabbricò una Macchina, che rappresentava il Sistema di Saturno <lb></lb>secondo le posizioni del p. </s>

<s>Fabri, e disposta in debita lontananza, adoprando <lb></lb>il lume di quattro torce, con Telescopi di varie grandezze e perfezioni, non <lb></lb>fu possibile rappresentare al vivo con essa, se non la prima e seconda figura <lb></lb>della Tavola di Eustachio, e di più l&#039;apparenza di Saturno solitario ” (MSS. <lb></lb>Cim., T. XXX, c. </s>

<s>18). </s></p><p type="main">

<s>L&#039;altro Discorso del Dati fu inserito, da pag. </s>

<s>66-69, nel II Tomo delle <lb></lb>Lettere d&#039;uomini illustri, dal Fabbroni, che l&#039;attribuì per errore al Borelli; <lb></lb>discorso dove, più dalla naturalezza del senno, che dalla profondità della <lb></lb>scienza, si decide a favor dell&#039;Hugenio. </s>

<s>Non è noto a noi se in quella adu­<lb></lb>nanza accademica, dove il Borelli e il Dati lessero i loro discorsi, fosse in-<pb xlink:href="020/01/1033.jpg" pagenum="476"></pb>tervenuto anche il Viviani, il quale non par che prendesse in queste astro­<lb></lb>nomiche controversie gran parte, e in ogni modo rimase indietro al Borelli <lb></lb>nell&#039;attività e nel fervore. </s>

<s>Scriveva nonostante nel Settembre del 1660 al <lb></lb>principe Leopoldo, a Pisa, che al ritorno di S. A. avrebbe spiegato per mezzo <lb></lb>di figure un concetto sovvenutogli intorno all&#039;apparir solitario di Saturuo <lb></lb>“ non so, diceva, se avvertito dall&#039;Ugenio ” e concludeva così quella sua <lb></lb>lettera: “ Scrivo in fretta, per non essere appresso l&#039;A. V. prevenuto dal <lb></lb>sig. </s>

<s>Borelli, al quale tengo per certo che sia per sovvenire l&#039;istesso che <lb></lb>dirò all&#039;A. V. e forse molto più ” (MSS. Cim., T. XVII, c. </s>

<s>69). </s></p><p type="main">

<s>Fra que&#039;concetti, che facevano a gara a proporre al principe i due ri­<lb></lb>vali, n&#039;era uno che tendeva a rispondere ad una difficoltà promossa dal Di­<lb></lb>vini, il quale asseriva che, attraverso al vuoto lasciato tra l&#039;anello e il globo <lb></lb>di Saturno, si sarebbe dovuto vedere il cielo del suo colore, e di quando in <lb></lb>quando trasparire le stelle. </s>

<s>Non essendosi queste mai potute vedere, sov­<lb></lb>venne al Borelli e al Viviani che ciò dipendesse dall&#039;esser troppo poveri di <lb></lb>esse stelle que&#039;punti del cielo trasparenti attraverso all&#039;Anello, ciò che non <lb></lb>sarebbe avvenuto quanto s&#039;abbattesse Saturno a navigar per Galassia Le <lb></lb>ardite speranze le significava il principe Leopoldo all&#039;Huyghens, nel ren­<lb></lb>dergli conto delle osservazioni sul sistema di Saturno e delle scoperte fatte <lb></lb>ai mesi addietro nella sua Accademia. </s>

<s>“ E non meno curioso sarà, diceva, <lb></lb>l&#039;osservare Saturno, quando si troverà in alcuno spazio della Via lattea, e <lb></lb>mi saria sommamente grato l&#039;intendere se V. S. creda che, per quelli spazi <lb></lb>che appariscono esservi fra l&#039;Anello e il Globo di Saturno, vi abbia a tra­<lb></lb>sparire al nostro occhio alcuna delle infinite stelle di quella gran Via ” (Tar­<lb></lb>gioni, Notizie cit., T. I, pag. </s>

<s>384). </s></p><p type="main">

<s>Qual si fosse la risposta che venne in tal proposito dall&#039;Huyghens non <lb></lb>sapremmo dire precisamente, nè potremmo asserir se davvero avvenisse quel <lb></lb>che sperava Michelangiolo Ricci, che cioè dai discorsi degli Accademici fio­<lb></lb>rentini “ potrà molto cavare il signor Ugenio per illustrare e difendere la <lb></lb>sua posizione ” (MSS. Cim., T. XVII, c. </s>

<s>92). In ogni modo, qualunque si <lb></lb>fosse l&#039;animo dell&#039;altero Olandese verso i Nostri, è un fatto che lo stabili­<lb></lb>mento del Sistema saturnio fu principalmente opera di loro, nè si sarebbe <lb></lb>l&#039;Olanda assicurata così presto della sua gloria, se non fosse venuta a fer­<lb></lb>marle la corona in fronte, con tanto zelo, l&#039;Italia. </s>

<s>Anzi da quella parte che <lb></lb>il Fabry moveva i suoi assalti, contro i quali nè l&#039;Huyghens per sè, nè i <lb></lb>nostri Accademici in alleanza con lui non avevano sicura difesa, a confer­<lb></lb>mare il sistema di Saturno, i nuovi aiuti vennero principalmente essi pure <lb></lb>d&#039;Italia. </s></p><p type="main">

<s>Quell&#039;attentato del Fabry, che pareva simile a una mina insidiosa atta <lb></lb>a sovvertire il Sistema ugeniano dalle sue fondamenta, si concludeva nel <lb></lb>breve giro delle seguenti parole: “ Turbinatio Saturni, vel illius annuli, <lb></lb>licet enim Sol hoc vertiginis motu agatur circa suum centrum, ut evinci­<lb></lb>tur ex illius maculis, aliis tamen planetis nulla huiusmodi, vel alia quae­<lb></lb>piam probatio suffragatur ” (In Op. </s>

<s>var. </s>

<s>Hug. </s>

<s>cit., pag. </s>

<s>615). </s></p><pb xlink:href="020/01/1034.jpg" pagenum="477"></pb><p type="main">

<s>Contro un tale attentato dicemmo non aver nè l&#039;Huyghens nè i fau­<lb></lb>tori di lui nessuna difesa, perchè la turbinazion di Saturno s&#039;ammetteva <lb></lb>solo per induzione dietro quel principio formulato dal Torricelli, che cioè, <lb></lb>se intorno a un corpo, negli spazii celesti, girano altri corpi, si può tener <lb></lb>per certo che gira anch&#039;esso. </s>

<s>Or perchè s&#039;era trovato girare intorno a Sa­<lb></lb>turno una Luna, si teneva per fermo che dovesse turbinare in sè stesso anche <lb></lb>il Pianeta, ma non se ne aveva ancora nessuna prova di fatto. </s>

<s>Anzi non <lb></lb>s&#039;aveva prova di questo fatto (e in ciò si faceva forte il Fabry) in nessun <lb></lb>altro de&#039;Pianeti che circondano il Sole, quando, come dicemmo, venne il <lb></lb>Cassini a dar la prima e più evidente dimostrazione di ciò che dal Fabry <lb></lb>stesso mettevasi in dubbio, per le macchie apparenti sulla faccia di Giove. </s></p><p type="main">

<s>Confermavasi così mirabilmente dai fatti il teorema astratto del moto <lb></lb>vertiginoso di un corpo, che mena seco in volta altri corpi: teorema, il quale <lb></lb>com&#039;aveva un&#039;applicazione certa nel Sole, nella Terra e in Giove, non la­<lb></lb>sciava nulla a dubitare nemmen rispetto a Saturno. </s>

<s>Ma il Cassini, proce­<lb></lb>dendo nelle sue scoperte glorioso, dimostrò di più che la turbinazion de&#039;pia­<lb></lb>neti in sè stessi era una loro proprietà generale, indipendentemente dal <lb></lb>principio meccanico professato già dal Keplero e promosso poi dal Torri­<lb></lb>celli. </s>

<s>Conforme infatti a questo principio pareva che si dovesse negare o che <lb></lb>si dovesse almeno mettere in gran dubbio, se Marte, Venere e Mercurio, <lb></lb>intorno ai quali non si vedevano rivolgersi altri corpi, rimanessero in sè <lb></lb>stessi non convertibili e immoti. </s></p><p type="main">

<s>Fu però quel dubbio, prima, rispetto a Marte, tolto via dal Cassini, il <lb></lb>quale, se applaudiva alle metafisiche congetture, che avevano così felicemente <lb></lb>divinato i turbinamenti di Saturno e di Giove, pensava in ogni modo che <lb></lb>l&#039;Astronomia era scienza di osservazione. </s>

<s>Osservando dunque il moto di al­<lb></lb>cune macchie sulla faccia di Marte, si assicurò che anch&#039;egli si rivolgeva, <lb></lb>come Giove, in sè stesso, in un periodo di tempo diligentemente prestabilito. </s>

<s><lb></lb>Dava della scoperta così avviso al Viviani per lettera del dì 3 Aprile 1666 <lb></lb>da Bologna: “ Ho nuovamente ritrovata la rivoluzione di Marte intorno al <lb></lb>proprio asse, da alcune macchie apparentissime, che seco si raggirano, le <lb></lb>quali però, essendo simili in varie e quasi opposte parti della superficie, e <lb></lb>difficilissime a distinguersi immediatamente le une dalle altre, poteano ca­<lb></lb>gionare qualche confusione. </s>

<s>Ciascuna di esse ritorna da un dì all&#039;altro <lb></lb>40 minuti più tardi, e le seconde succedono alle prime otto ore dopo. </s>

<s>Ne <lb></lb>ho voluto dar questo saggio a V. S. che mi farà grazia di parteciparlo <lb></lb>a S. A. S. ” (MSS. Gal. </s>

<s>Disc., T. CXLV, c. </s>

<s>8). Dava poco di poi al pub­<lb></lb>blico la importante notizia in una scrittura stampata in folio in quel mede­<lb></lb>simo anno 1666 in Bologna col titolo: <emph type="italics"></emph>Martis circa proprium axem revo­<lb></lb>lubilis, observationes bononienses,<emph.end type="italics"></emph.end> dove concludevasi che Marte si rivolge in <lb></lb>sè stesso in 24 ore e 39 minuti. </s></p><p type="main">

<s>Ricevuta il principe Leopoldo dal Viviani la notizia, e poco di poi dal­<lb></lb>l&#039;Autore stesso questo foglio, che pubblicamente la confermava, ne scrisse <lb></lb>in proposito all&#039;Huyghens, il quale rispondeva così il dì 22 Giugno 1666 da <pb xlink:href="020/01/1035.jpg" pagenum="478"></pb>Parigi: “ Ho anche visto poi quel ch&#039;è stato pubblicato dal Cassini e da <lb></lb>Eustachio Divini sopra il moto di Marte, ed ho trovato che il moto perio­<lb></lb>dico stabilito dal Cassini è prossimamente il medesimo, che io stesso, la fin <lb></lb>del Settembre 1659, mosso dalle osservazioni, avevo congetturato che fosse <lb></lb>di quattro giorni, trovando io notato nel mio <emph type="italics"></emph>Libro de&#039;ricordi<emph.end type="italics"></emph.end> che ogni re­<lb></lb>voluzione del Pianeta si fa, presso a poco, in ore 24. La forma però delle <lb></lb>macchie, delle quali io osservavo il ritorno, non appariva del tutto simile <lb></lb>alla forma di quelle, che furono osservate in Roma e in Bologna. </s>

<s>E in ve­<lb></lb>rità, perchè mi avvedevo che quelle forme non mi si rappresentavano ba­<lb></lb>stantemente distinte, giudicai di non dover per allora pronunziare alcuna <lb></lb>cosa senza fondamento, ma d&#039;aspettare fintanto che avessi Telescopi migliori. </s>

<s><lb></lb>E ora, non racconto a V. A. queste cose, perchè pretenda che mi sia dato <lb></lb>in questo fatto tantin di lode, ma perchè colla mia approvazione, qualunque <lb></lb>ella si sia, venga confermato il periodo determinato dal Cassini ” (MSS. <lb></lb>Cim., T. XVIII, c. </s>

<s>317). </s></p><p type="main">

<s>Anche il Divini, commemorato dall&#039;Huyghens in principio di questo <lb></lb>passo di lettera, osservò le macchie in Marte, e, avendone indi argomentato <lb></lb>alla rotazione, pretendeva o di aver prevenuto o di avere almeno concorso <lb></lb>col Cassini nella scoperta. </s>

<s>Il merito però di Eustachio, che annunziò il sem­<lb></lb>plice fatto, non solo non è da paragonar col merito del Cassini, che ne de­<lb></lb>finì il periodo, ma, se per l&#039;esattezza delle osservazioni è alquanto superiore, <lb></lb>rispetto al tempo è inferiore al Fontana, il quale già, in fin dal 1638, da <lb></lb>una <emph type="italics"></emph>pillola<emph.end type="italics"></emph.end> osservata sulla faccia di Marte, era venuto in sospetto della sua <lb></lb>girazione. </s>

<s>“ Martis pilula vel niger conus intuebatur distincte ad circuli ipsum <lb></lb>ambientis deliquium proportionaliter deficere, quod fortasse Martis gyratio­<lb></lb>nem circa proprium centrum significat ” (Novae observat. </s>

<s>cit., pag. </s>

<s>106). </s></p><p type="main">

<s>La stessa cosa che in Marte s&#039;immaginò il Fontana di avere osservato <lb></lb>in Venere, e perchè gli pareva che quelle pillole notassero sulla superfice <lb></lb>di lei, come i pesci nel mare, ne inferiva che non dovesse essa Venere ri­<lb></lb>manere inchiodata nel cielo, ma che, sospesa nello spazio, si rivolgesse, pur <lb></lb>come Marte, intorno al suo centro. </s>

<s>“ Huiusmodi autem Veneris pilulae non <lb></lb>semper in eodem deprehenduntur situ, sed huc illucque, tanquam in mari <lb></lb>pisces, transmigrare, ex quo inferri potest eodem modo Venerem ipsam mo­<lb></lb>veri, et non esse alicui coeli parti alligatam ” (ibi, pag. </s>

<s>91). </s></p><p type="main">

<s>Venne a questa fantasia, alquanti anni dopo, il Cassini a dar saldezza <lb></lb>di vero. </s>

<s>Invece che nelle pillole stravaganti ei fermò l&#039;attenzione sopra le <lb></lb>macchie apparenti, ma difficile era l&#039;osservazione in un Pianeta, che così <lb></lb>breve sull&#039;orizzonte, e così indistinta, per i vivi splendori, faceva la sua <lb></lb>comparsa. </s>

<s>I tentativi nonostante che fece, per riuscir nell&#039;intento, e i resul­<lb></lb>tati che n&#039;ebbe, gli descrisse in una lettera al Petit, dove gli rendeva conto <lb></lb>di varii altri suoi studi. </s>

<s>Fu quella Lettera pubblicata nel <emph type="italics"></emph>Journal des Sa­<lb></lb>vans<emph.end type="italics"></emph.end> del 1667, e in Amsterdam, nel 1676, se ne pubblicò in francese un <lb></lb>estratto concernente la scoperta della rotazione di Venere col titolo: <emph type="italics"></emph>Extrait <lb></lb>d&#039;une Lettere de M. Cassini, professeur d&#039;Astronomie dans l&#039;Université de<emph.end type="italics"></emph.end><pb xlink:href="020/01/1036.jpg" pagenum="479"></pb><emph type="italics"></emph>Boulogne, a M. </s>

<s>Petit .... touchant la decouverte qu&#039;il a faite du mou­<lb></lb>vement de la Planete Venus à l&#039;entour de son axe, du Juin 1667.<emph.end type="italics"></emph.end> Una <lb></lb>bella copia a mano della Lettera intera, che ha l&#039;indirizzo <emph type="italics"></emph>Clarissimo doctis­<lb></lb>simoque viro Petro Petit, Regis christianissimi Arcibus muniendis Prae­<lb></lb>fecto, Jo. </s>

<s>Dominicus Cassinus S. P. D.<emph.end type="italics"></emph.end> ordinò che ne fosse fatta il prin­<lb></lb>cipe Leopoldo, ed è quella che, inserita da c. </s>

<s>227-29 del T. XIII del Cimento, <lb></lb>da noi si tiene sott&#039;occhio. </s></p><p type="main">

<s>La più importante parte di storia che si contiene in questa Lettera cas­<lb></lb>siniana, sì quanto alle difficoltà incontrate nell&#039;osservazione, e sì quanto ai <lb></lb>resultati ottenuti da esse, concludesi dall&#039;Autore nelle seguenti parole: <lb></lb>“ Tamque altius se attollente a terra Venere multo difficilior erat huiusmodi <lb></lb>apparentiarum observatio. </s>

<s>De his vero longe timidius iudicium fero, quam <lb></lb>de maculis Jovis et Martis. </s>

<s>Has quippe totam noctem, circa oppositiones cum <lb></lb>Sole, attente contemplari licebat, earumque motus aliquot horarum spatio <lb></lb>inspicere, atque ex regularibus restitutionibus decernere eaedemque ne an <lb></lb>diversae essent, quae obiicerentur maculae, earumdemque versari periodos. </s>

<s><lb></lb>At huiusmodi Veneris apparentiae tam brevi temporis spatio conspiciuntur, <lb></lb>ut minus tute de earumdem restitutione decernere liceat. </s>

<s>Eadem si semper <lb></lb>fuerit lucida Veneris particula, huius praesertim anni observationibus obvia, <lb></lb>suam seu revolutionem seu librationem absolvit spatio minore unius diei, <lb></lb>ita quidem ut, spatio horarum circiter 23, ad eumdem proxime in Venere <lb></lb>situm circa eamdem horam restitutam, quod tamen non sine aliqua pro­<lb></lb>cedit irregularitate ” (c. </s>

<s>29). Conclude esser nonostante rimasto nell&#039;incer­<lb></lb>tezza, se quello era un moto seguente di circolazione, o se un&#039;andata o un <lb></lb>ritorno di librazione, e il determinare in ogni modo il periodo di questo, <lb></lb>qualunque si fosse moto, lo teneva per difficilissimo. </s></p><p type="main">

<s>Il periodo della rotazione di Venere, prefinito così dal Cassini in 23 ore <lb></lb>in circa, veniva approvato dagli Astronomi, quando mons. </s>

<s>Francesco Bian­<lb></lb>chini, ch&#039;ebbe, per la munificenza del cardinale di Polignac, strumenti della <lb></lb>maggior perfezione, a cui fosse giunta l&#039;arte di Giuseppe Campani, pub­<lb></lb>blicò, nel 1728 in Roma, un&#039;opera in folio, col titolo: <emph type="italics"></emph>Hesperi et Phosphori <lb></lb>phaenomena, sive observationem circa planetam Veneris.<emph.end type="italics"></emph.end> Non deve far me­<lb></lb>raviglia, ivi dice l&#039;Autore, una sì gran differenza che passa fra questo nuo­<lb></lb>vamente assegnato e il periodo cassiniano “ neque enim definire poterat, ex <lb></lb>ordinata mutatione seu progressu macularum supra discum Veneris, num <lb></lb>intra horas 23 an potius intra dies 24 integra rotatio absolveretur, nisi obser­<lb></lb>vandi Planetae copia talis daretur in eiusdem proximo accessu ad Terrae <lb></lb>globum, ut tribus horis solidis ante ortum, vel post occasum Solis, esset <lb></lb>supra horizzontem conspicuus. </s>

<s>Ad hoc demonstrandum accedimus in obser­<lb></lb>vatis anni 1726, quibus deprehendimus, non horis 23, sed totis diebus 24 <lb></lb>unicam rotationem globi Veneris circa axem proprium compleri ” (pag. </s>

<s>60). </s></p><p type="main">

<s>Così il Bianchini, come il Cassini stesso, s&#039;erano ingannati intorno al­<lb></lb>l&#039;apparenza di quelle macchie di Venere, ma più notabilmente s&#039;era ingan­<lb></lb>nato il Bianchini, il quale si propose nel Cap. </s>

<s>IV di divisarle e d&#039;imporre <pb xlink:href="020/01/1037.jpg" pagenum="480"></pb>a ciascuna il suo nome, com&#039;aveva fatto il Riccioli per le macchie della <lb></lb>Luna. </s>

<s>“ Exhibetur Celidographia seu descriptio macularum, in globo Vene­<lb></lb>ris observatarum, et illarum praecipuis partibus aptantur nomina ” (pag. </s>

<s>38). <lb></lb>Non fa perciò maraviglia se il periodo stabilito da lui in 24 giorni aberrasse <lb></lb>più dal vero di quello delle 23 ore in circa, stabilito già dal Cassini. </s>

<s>Non <lb></lb>essendo in fatti in Venere macchie stabili, e distintamente riconoscibili nel <lb></lb>loro ritorno, conveniva attenersi ad altri segni, i quali si offersero comodi <lb></lb>in alcuni vertici delle più alte montagne illuminati in mezzo alle valli om­<lb></lb>brose, mentre che il Pianeta si mostra a noi falcato come la Luna. </s>

<s>Così ne <lb></lb>fu precisato il periodo della restituzione, che si trovò differir di pochi mi­<lb></lb>nuti da quello del Cassini. </s></p><p type="main">

<s>Non rimaneva dunque al grande Astronomo nostro inesplorato altro che <lb></lb>Mercurio, in cui le difficoltà stesse incontrate in Venere si rendevano anche <lb></lb>maggiori. </s>

<s>Ma non vedendosi oramai ragione perchè il pianeta più vicino al <lb></lb>Sole s&#039;avesse ad appartare da tutti gli altri, se ne stabili senz&#039;altro la re­<lb></lb>gola generale che i Pianeti, o menino in volta o no altri corpi, si rivolgono <lb></lb>tutti in sè stessi, e così l&#039;argomento d&#039;analogia veniva ritorto a dimostrar <lb></lb>contro il Fabry esser ragionevolissima l&#039;ipotesi ugeniana della rotazion di <lb></lb>Saturno. </s></p><p type="main">

<s>Vedemmo come i principii a questa ipotesi venissero dalla scoperta di <lb></lb>un nuovo Satellite intorno al Pianeta. </s>

<s>Or avendo il Cassini scoperto altri <lb></lb>satelliti, e avendo perciò ampliato il mondo saturnio, conferiva anche da que­<lb></lb>sta parte efficacemente a confermarne il Sistema. </s>

<s>Verso la fine del mese di <lb></lb>Ottobre 1671, rivolto un Canocchiale del Campani di 17 piedi a Saturno, lo <lb></lb>trovò circondato da tre piccole stelle non più vedute. </s>

<s>Le osservazioni, pro­<lb></lb>seguite dal 25 di Ottobre al primo di Novembre, lo fecero accorto due di <lb></lb>tali stelle esser fisse e l&#039;altra un Pianeta, com&#039;appariva dal suo moto “ le <lb></lb>quel est tres-manifeste à l&#039;égard des etoiles fixes, mais moins sensible à <lb></lb>l&#039;égard de Saturne ” (Découverte de deux nouv. </s>

<s>plan., Paris 1673, pag. </s>

<s>6) <lb></lb>Il centro di questo moto era manifestamente Saturno, e il nuovo Satellite <lb></lb>doveva senza dubbio essere esterno, facendo le sue massime digressioni tri­<lb></lb>ple di quelle del Satellite ugeniano. </s></p><p type="main">

<s>Interrotte le osservazioni, non potè il Cassini riprenderle che sulla fine <lb></lb>di Dicembre, quando s&#039;incontrò in una nuova Stella, che veduta il dì 10 di <lb></lb>Gennaio 1673 ritornare alla medesima posizione rispetto a Saturno, riconobbe <lb></lb>facilmente per un pianeta. </s>

<s>Stette alquanto in dubbio se fosse quello il pia­<lb></lb>neta medesimo dianzi scoperto, ma preso di maraviglia per alcune partico­<lb></lb>larità osservate, ebbe presto a riconoscerlo così per un satellite nuovo. </s></p><p type="main">

<s>“ Ce qui nous donna de l&#039;admiration, fut d&#039;avoir trouvé trois fois de <lb></lb>suite cette petite Etoile entre Saturne et le Satellite ordinaire, toùjours en <lb></lb>distance presque égale de l&#039;un et de l&#039;autre. </s>

<s>Mais nostre admiration cessa <lb></lb>a là quatrieme observation, qui fut faite le 15 de Janvier, dans la quelle le <lb></lb>Satellite ordinaire estoit oriental, et le nouveau estoit occidental, comme il <lb></lb>avoit esté dans l&#039;observation precedente, mais un peu plus proche de Sa-<pb xlink:href="020/01/1038.jpg" pagenum="481"></pb>turne. </s>

<s>Nous eùmes ce soir-là assez/de temps pour observer attentivement <lb></lb>cette Planete une heure de suite, pendant laquelle nous apperceùmes qu&#039;elle <lb></lb>s&#039;approchoit de Saturne vers l&#039;occident, et par consequent qu&#039;elle estoit dans <lb></lb>la partie superieure de son cercle; ce qui nous confirma entierement dans <lb></lb>la supposition, à laquelle nous panchions, que c&#039;estoit un Satellite interieur, <lb></lb>dont la revolution estoit plus vite que celle du Satellite ordinaire ” (pag. </s>

<s>10). </s></p><p type="main">

<s>Della <emph type="italics"></emph>Découverte de deux nouvelles planetes autour de Saturne,<emph.end type="italics"></emph.end> stam­<lb></lb>pata in folio e dedicata a Luigi di Francia, XIV nel numero de&#039;Re, come <lb></lb>XIV era il Saturnio ultimamente scoperto nel numero de&#039;Pianeti; ne furono <lb></lb>inviati alquanti esemplari a Firenze al cardinale Leopoldo accompagnati da <lb></lb>una lettera scritta dal Cassini stesso il dì 6 di maggio 1673 da Parigi (MSS. <lb></lb>Cim., T. XX, c. </s>

<s>117). </s></p><p type="main">

<s>Que&#039;fiorentini, i quali non credevano che potesse aver veduti tanti <lb></lb>mondi lontani colui, che non valeva a leggere una lettera di carattere di­<lb></lb>stintissimo senza gli occhiali, squadernando i fogli dispensati a loro dal prin­<lb></lb>cipe della Sperimentale Accademia, v&#039;ebbero poca fede, la quale non sa­<lb></lb>premmo dire se si spengesse affatto, o se piuttosto si ravvivasse nel 1684, <lb></lb>quando il Cassini stesso tornò ad annunziar la scoperta d&#039;altri due più in­<lb></lb>timi Satelliti saturnii. </s></p><p type="main">

<s>In ogni modo, non ne dubitò mai l&#039;Huyghens, il quale anzi vaticinava <lb></lb>che si sarebbero scoperte altre Lune saturnie, oltre alla sua e alle quattro <lb></lb>cassiniane. </s>

<s>“ Imo praeter harum numerum alias quoque, vel unam vel plu­<lb></lb>res latere suspicari licet, non deest ratio ” (Cosmot., Op. </s>

<s>var. </s>

<s>cit., pag. </s>

<s>698); <lb></lb>vaticinio che poi fu pienamente avverato. </s></p><p type="main">

<s>Non ne dubitò nemmeno quel sagace uomo e scevro da pregiudizii, che <lb></lb>fu il Viviani, il quale, in un capitolo del suo <emph type="italics"></emph>Discorso<emph.end type="italics"></emph.end> altre volte citato <emph type="italics"></emph>in­<lb></lb>torno al Mondo,<emph.end type="italics"></emph.end> trattando delle apparenze di Saturno, dop&#039;avere accennato <lb></lb>alla storia del Pianeta, infino alla grande scoperta di Cristiano Huyghens, <lb></lb>soggiunge che fu egli il primo “ ad osservare intorno a Saturno un Pia­<lb></lb>neta che compisce il suo periodo in giorni 15, 22h, 40′. </s>

<s>Altri quattro Pianeti <lb></lb>ne ha osservati il signor Cassini, primo Astronomo di S. M. Cristianissima, <lb></lb>che uno termina il suo giro in un giorno 21h, 18′; il secondo in giorni 2, <lb></lb>17h, 3′; il terzo in giorni 4, 13h, 47′; il quarto in giorni 79, 7h, 53′ ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXLI, c. </s>

<s>278). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La figura vera di Saturno e le varie apparenze di lei, felicemente ri­<lb></lb>velatesi alla perspicacia dell&#039;Hugenio, venivano insomma, per le ingegnose <lb></lb>esperienze degli Accademici del Cimento, ridotte a una dimostrazione di <lb></lb>fatto, e il Cassini aveva colle sue scoperte confermato da più parti il prin­<lb></lb>cipio, a cui s&#039;informava quella dimostrazione. </s>

<s>Ma pure intorno a cose che <pb xlink:href="020/01/1039.jpg" pagenum="482"></pb>tanto uscivano fuori dell&#039;ordinario venivano tentati di diffidenza anche gli <lb></lb>animi più sinceri, e le menti più sicure non potevano deliberarsi dai dub­<lb></lb>bii. </s>

<s>Com&#039;è possibile, domandavano, che un anello materiale e pesante si <lb></lb>regga in sè sempre così regolarmente in equilibrio e, senz&#039;esservi allegato <lb></lb>da nulla, seguiti fedel compagno il suo pianeta? </s>

<s>L&#039;Huyghens aveva già ri­<lb></lb>sposto a questa difficoltà dicendo che si reggerebde pure, per consenso di <lb></lb>alcuni, una volta, e senza alcun sostegno, quando fosse possibile continuarla <lb></lb>per tutto l&#039;ambito della Terra. </s>

<s>“ Plane sicuti quidam contemplati sunt, quod <lb></lb>si continuum fornicem per totum terrarum ambitum extrui possibile esset, <lb></lb>is, absque ullo fulcimento semetipsum esset sustentaturus ” (Syst. </s>

<s>Sat., Op. </s>

<s><lb></lb>varia cit., pag. </s>

<s>567). </s></p><p type="main">

<s>Pochissimi però, quand&#039;erano così ancora rannuvolate le idee della gra­<lb></lb>vitazione dei corpi sui loro centri attrattivi, potevano comprendere la forza <lb></lb>di questo argomento, e dall&#039;altra parte occorreva a fare sul Sistema satur­<lb></lb>nio tante altre questioni, le quali, perchè forse erano dall&#039;Huyghens stimate <lb></lb>più curiose che importanti, ei lasciò a disputar liberamente agli Astronomi. </s>

<s><lb></lb>Nella Sperimentale Accademia fiorentina però, affinchè il nuovo misterioso <lb></lb>mondo di Saturno, com&#039;era stato dottamente illustrato per quel che riguarda <lb></lb>la parte fisica, così non mancasse della sua Filosofia speculativa, non si vol­<lb></lb>lero lasciare indietro quelle questioni, e si trattarono anzi in modo, da fare <lb></lb>alla semplice curiosità prender abito d&#039;importanza. </s></p><p type="main">

<s>Fu il difficile argomento svolto in due discorsi diretti al serenissimo <lb></lb>Principe dell&#039;Accademia, e ne furono autori due, tanto differenti in età, <lb></lb>quanto nell&#039;indole e nell&#039;ingegno, il Magalotti e il Borelli. </s>

<s>Il Discorso del <lb></lb>primo non è altro in sostanza che un ingegnoso commento del Sistema ro­<lb></lb>bervalliano, ma pur è tanto l&#039;Autore infervorato del suo soggetto, che non <lb></lb>si ricorda più delle censure fattegli pubblicamente dall&#039;Hugenio. </s>

<s>Il Maga­<lb></lb>lotti, che non aveva concetti suoi propri, sa vagamente adornare concetti al­<lb></lb>trui, tirandoli con destrezza ingegnosa da varie parti al proposito di Saturno. <lb></lb></s>

<s>È notabile fra questi concetti quello riferito da Galileo, che disperso negli <lb></lb>insegnamenti orali del gran Maestro ebbe salva la vita in questo stesso <lb></lb>Discorso. </s></p><p type="main">

<s>E qui sia lecito a noi studiosi d&#039;intendere in tutta la sua integrità, e <lb></lb>nel vero esser suo la mente di un uomo, intorno alla quale, quasi come a <lb></lb>cardine si volge la nostra Storia, fare una breve digressione per dire che <lb></lb>male si persuadono di provvedere a quella integrità coloro, che vanno so­<lb></lb>lamente a ricercarla ne&#039;Manoscritti galileiani. </s>

<s>Idee, dimostrazioni e inven­<lb></lb>zioni del loro Maestro rimangono in gran parte commemorate negli scritti <lb></lb>de&#039;suoi numerosi e zelantissimi Discepoli, e chi le andasse qua e là racco­<lb></lb>gliendo con intelligenza ed amore, potrebbe a giusta ragion vantarsi di averci <lb></lb>date le opere di Galileo veramente complete. </s></p><p type="main">

<s>Di quelle idee intanto ne offre una delle più elette il Magalotti nel suo <lb></lb>Discorso. </s>

<s>Da raccogliersi fra le dimostrazioni sarebbe quella della Cicloide, <lb></lb>distesa da Galileo in una lettera al Cavalieri; Lettera, che il padre Stefano An-<pb xlink:href="020/01/1040.jpg" pagenum="483"></pb>geli scrisse al Viviani di aver inutilmente cercata per Roma, ad istanza del <lb></lb>Dati (MSS. Cim., T. XVII, c. </s>

<s>176), che suppose esser capitata nelle mani <lb></lb>del Magiotti o del Ricci, il contenuto della quale, se non la dicitura, non <lb></lb>sarebbe difficile a ricomporre dietro i cenni fattine da coloro, che intesero <lb></lb>o lessero, intorno a quel soggetto geometrico, il pensiero galileiano. </s></p><p type="main">

<s>Da raccoglier poi fra le invenzioni sarebbe quella, di cui così parla il <lb></lb>Magiotti in una lettera al Torricelli: “ Ho caro la congiuntura del sig. </s>

<s>Vin­<lb></lb>cenzio Viviani, dal quale desidererei il modo del sig. </s>

<s>Galileo di tirare in <lb></lb>prospettiva le superficie ed i corpi, per via di due corpi che s&#039;interpongono. </s>

<s><lb></lb>Questa mi mostrò il sig. </s>

<s>Aggiunti, e so che molti in Firenze l&#039;usano, ma <lb></lb>io non me ne ricordo, ed ho promesso ad un cavaliere amico mio di far­<lb></lb>mela venire ” (MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>71). </s></p><p type="main">

<s>Ma perchè dimostrazioni e invenzioni di questo genere son propriamente <lb></lb>aliene dal nostro Tema, ci sia permesso d&#039;invitare i nostri lettori a com­<lb></lb>prendere in uno sguardo di considerazione altre idee, altre dimostrazioni e <lb></lb>altre invenzioni appartenenti alle scienze sperimentali, da noi già notate, e <lb></lb>parecchie altre che si noteranno, da aggiunger com&#039;eletta corona alle opere <lb></lb>stampate e manoscritte di Galileo. </s></p><p type="main">

<s>E per non indugiar di troppo ad aggiungere a quella corona il pro­<lb></lb>messo fiore, e con ciò ritornare a Saturno, ecco la miglior parte del Di­<lb></lb>scorso del Magalotti, trascritto da una copia, che si legge da c. </s>

<s>70-75 del <lb></lb>T. XXX del Cimento, nitida di carattere, ma scorretta in più luoghi da noi <lb></lb>emendati, e con lacune da noi supplite col riscontro dell&#039;autografo, inserito <lb></lb>da c. </s>

<s>80-84 del T. XII della medesima collezione. </s></p><p type="main">

<s>“ Serenissimo principe,...... applicandosi il Robervallio a costituirsi <lb></lb>l&#039;idea di un ipotesi, con la quale salvar si potessero le stravaganti appa­<lb></lb>renze, che in Saturno s&#039;osservano; si va immaginando sollevarsi dalla zona <lb></lb>torrida di quel Pianeta in gran copia i vapori, i quali, per la loro grossezza <lb></lb>ed intensità, divengano specchi potentissimi della riflessione solare, e sì la <lb></lb>diversità degli aspetti derivarsi dalla difformità di queste esalazioni, le quali, <lb></lb>se per ogni intorno vengono egualmente spirate, apparirà continuata l&#039;el­<lb></lb>lisse lucida; se solo da alcune parti, l&#039;apparenza delle due Stelle compa­<lb></lb>gne; e se finalmente manchi la pioggia ascendente di detti vapori, rimarrà <lb></lb>sferico e solitario il Pianeta. </s>

<s>” </s></p><p type="main">

<s>“ Era così facile e puro questo concetto, che a gran fatica credetti po­<lb></lb>tersene trovar altro che l&#039;agguagliasse, camminando anch&#039;io con quella in­<lb></lb>vecchiata credenza esser proprio alla Natura l&#039;attenersi ai modi piu facili <lb></lb>nel suo operare. </s>

<s>Considerando nulladimeno quanto si avesse giustamente <lb></lb>usurpato la fede universale questo concetto, mi venne in mente un pen­<lb></lb>siero nobilissimo del signor Galileo, pel quale rimasi certo regolarsi altri­<lb></lb>menti nelle sue Opere la Natura, da quello che noi, col nostro corto vedere, <lb></lb>la ci figuriamo. </s>

<s>” </s></p><p type="main">

<s>“ È così facile, dice egli, la formazione di una sfera che, se in una pia­<lb></lb>stra piana di metallo duro si caverà un vacuo circolare, dentro al quale si <pb xlink:href="020/01/1041.jpg" pagenum="484"></pb>vada rivolgendo casualmente qualsivoglia solido assai grossamente tondeg­<lb></lb>giato, per sè stesso, senz&#039;altro artifizio, si ridurà in figura sferica più che <lb></lb>sia possibile perfetta, purchè quel tal solido non sia minore della sfera, che <lb></lb>passasse per quel cerchio. </s>

<s>E quel che v&#039;è ancora di più degno di conside­<lb></lb>razione, è che dentro a quel medesimo incavo si formeranno sfere di di­<lb></lb>verse grandezze. </s>

<s>Attendiamo ora a quel che vi voglia, per ridurre alla so­<lb></lb>miglianza del vero un cavallo o una locusta, e ritroveremo che non v&#039;harà <lb></lb>al mondo scultore così industrioso, che sia valevole a farlo. </s>

<s>Perchè, siccome <lb></lb>la grandezza, nel formar la sfera, deriva dalla sua assoluta semplicità ed <lb></lb>uniformità; così la somma irregolarità rende difficilissimo l&#039;introdurre altre <lb></lb>figure, e perciò anco la figura d&#039;un sasso, rotto casualmente con un mar­<lb></lb>tello o spiccato da un masso o arrotato in un letto di un fiume, sarà delle <lb></lb>difficili ad introdursi, essendo essa ancora irregolare, forse più di quella del <lb></lb>cavallo. </s>

<s>Eppure è forza dire quella figura ch&#039;egli ha, qualunque ella si sia, <lb></lb>averla così perfetta, che alcun altra sì puntualmente non le s&#039;assesti. </s>

<s>” </s></p><p type="main">

<s>“ Infin qui col signor Galileo: ma applicando al mio proposito, se delle <lb></lb>figure irregolari, e perciò difficili a conseguirsi, pur se ne trovano infinite <lb></lb>in natura perfettissimamente ottenute, come in ogni sasso ci si rappresenta, <lb></lb>e delle perfette sferiche o niuna o radissime fra essi ne troveremo; con qual <lb></lb>ragione dovremo noi figurarcela così avara e infingarda, che tenga sì stretto <lb></lb>conto di risparmio a fatica nella fabbrica delle sue maraviglie più rare, e <lb></lb>non dir piuttosto tutte le operazioni, benchè ammirabili, esserle egualmente <lb></lb>agevoli, nè regolarsi ella dalla bassezza di nostra forza, che ci finghiamo <lb></lb>difficile ad essa o insolita la costruzione di una Macchina, che troppo da&#039;no­<lb></lb>stri concetti sì lievi? </s>

<s>” </s></p><p type="main">

<s>“ Fatto ardito da questa riflessione, mi sovvenne il principio, che at­<lb></lb>tribuisce Renato Des-Cartes, nel cap. </s>

<s>IX delle sue <emph type="italics"></emph>Meteore,<emph.end type="italics"></emph.end> all&#039;apparenza <lb></lb>di quegli Aloni, che intorno al Sole ed alle Stelle talvolta si coloriscono. </s>

<s><lb></lb>Dice egli essere sparse le regioni più fredde della nostr&#039;aria di alcuni va­<lb></lb>pori addiacciati, a guisa di stelline minutissime, le quali, abbattendosi in <lb></lb>gran copia tra alcune Stelle e la nostra vista, di quelle, oltre alla piramide <lb></lb>diretta che viene a ferir l&#039;occhio, molti eziandio di que&#039;raggi, che per altri <lb></lb>dove si spargono, con le loro superficie rifrangono, e sì all&#039;intorno di essa <lb></lb>dipingono l&#039;apparenza di un Iride. </s>

<s>Checchessia della verità di questo di­<lb></lb>scorso, discorrerò così: ” </s></p><p type="main">

<s>“ Se intorno alla nostra Terra vegghiamo continuamente sollevarsi va­<lb></lb>pori, e di quelli, arrivati ad una tal distanza, altri rammassarsi in acqua, <lb></lb>altri ripiovere in rugiade, altri in nevi e gragnole; non è egli molto pro­<lb></lb>babile che l&#039;ammosfera di Saturno, tanto più lontana dal Sole, sia sempre <lb></lb>gravida di vapori grossissimi, anzi, che per l&#039;eccessivo freddo a fatica sol­<lb></lb>levati, non passino pe&#039;gradi di rugiade, di piogge e di nevi, ma ben presto <lb></lb>si gelino in diaccioli minutissimi, quali sarebbero le stille delle nostre ru­<lb></lb>giade, se s&#039;addiacciassero? </s>

<s>” </s></p><p type="main">

<s>“ E notisi che, quantunque esalino per ogni intorno del globo di Sa-<pb xlink:href="020/01/1042.jpg" pagenum="485"></pb>turno i vapori, non perciò, sollevati che e&#039;sono, gli formeranno all&#039;intorno <lb></lb>una perfetta sfera vaporosa, conciossiachè, intorno all&#039;equinoziale ed alla zona <lb></lb>torrida, saran molto più tenui che verso i poli, onde ascenderanno ad equi­<lb></lb>librarsi più in alto, che in altri paralleli, e si circonderanno il Pianeta, a <lb></lb>guisa d&#039;uno sferoide prolato, rivolgendosi intorno ai suoi poli, cioè intorno <lb></lb>all&#039;asse minore della loro ellisse. </s>

<s>Sarà dunque assai probabile che, dopo <lb></lb>inalzati ad una determinata altezza, finalmente, come dicemmo, si gelino, <lb></lb>ma quei che sono intorno all&#039;equinoziale, come più tenui, s&#039;addiaccino in <lb></lb>stelline più minute, onde agevolmente s&#039;equilibrino, al contrario di quei più <lb></lb>densi, addiacciati di qua e di là dall&#039;Equatore per notabile spazio verso i Poli, <lb></lb>i quali per la loro gravezza saranno più facili a ricadere. </s>

<s>Sicchè, spiccandosi <lb></lb>di qua e di là all&#039;asse maggiore dello sferoide vaporoso due porzioni di esso, <lb></lb>rimane, per notabilissimo spazio, intorno all&#039;Equatore, una zona di minu­<lb></lb>tissime stelle di diaccio. </s>

<s>” <lb></lb>… </s></p><p type="main">

<s>“ Proseguendo tuttavia il conceputo entusiasmo, mi sforzerò di mo­<lb></lb>strare non esser tanto lontano dal poter congetturarsi, anche in altri Pia­<lb></lb>neti, effetti somiglianti, benchè meno osservabili, a proporzione della maggior <lb></lb>vicinanza col Sole. </s>

<s>” </s></p><p type="main">

<s>“ Scrive l&#039;Ugenio, a c. </s>

<s>6 del suo libro del Nuovo sistema, aver egli <lb></lb>bene spesso osservato le fasce di Giove più lucide del rimanente del suo <lb></lb>disco. </s>

<s>Asseriva in oltre d&#039;averle vedute alterare nella loro forma, ed in di­<lb></lb>versi tempi accostarsi e discostarsi fra loro per qualche tratto; ond&#039;egli <lb></lb>molto probabilmente inferisce, e dalla riflession più viva e dall&#039;incostanza <lb></lb>di figura e di sito, esser materia assai simile alle nostre nuvole generate or <lb></lb>qua or là dalla elevazion de&#039;vapori, che or in questo or in quel clima si <lb></lb>condensino. </s>

<s>” </s></p><p type="main">

<s>“ Anche di Marte riferisce una simile apparenza d&#039;una fascia ombrosa, <lb></lb>che lo cinge, ma questa oscurità dev&#039;attendersi per esser forse quei vapori, <lb></lb>come più vicini al Sole di quei di Saturno e di Giove, più tenui, e perciò <lb></lb>di riflessione più debole. </s>

<s>” </s></p><p type="main">

<s>“ Dov&#039;io noto l&#039;aspetto di queste fasce mostrarsi sempre ai dintorni <lb></lb>dell&#039;equinoziale, nè mai vagare in vicinanza dei poli. </s>

<s>Non potrebb&#039;egli dun­<lb></lb>que esser la cagione produttrice di tali maravigliose apparenze somigliante <lb></lb>a quella istessa, che resa più valida, a quella proporzione dell&#039;immensa lon­<lb></lb>tananza dal Sole, le produce in Saturno sì facilmente osservabili? </s>

<s>” </s></p><p type="main">

<s>“ Ardirò di più: chi sa che quel tratto di cielo, che intorno alla no­<lb></lb>stra Terra, sì costantemente nuvoloso, cotanto affligge, con le sue vampe, <lb></lb>gli abitatori del nostro Equinoziale, e quelle nebbie sì folte, che dagli 85 <lb></lb>gradi di latitudine rendon sì fosca e caliginosa l&#039;aria del polo, non ricono­<lb></lb>scano una somigliante cagione, e si costituiscasi ne&#039;Pianeti una scala, dirò <lb></lb>così, della densità dei vapori, mostrandosi massima in Saturno, minore, ma <lb></lb>però assai osservabile più che in ogni altro in Giove, meno in Marte, mi­<lb></lb>nima nella Terra, non essendo del certo così ferma e stabile quella striscia <pb xlink:href="020/01/1043.jpg" pagenum="486"></pb>di nuvole intorno all&#039;Equinoziale, che talvolta, almeno per alcuni tratti, non <lb></lb>isparisca; e finalmente nulla in Venere ed in Mercurio, vagando quelli vi­<lb></lb>cinissimi al Sole, sotto la pioggia profusissima de&#039;suoi raggi? </s>

<s>” </s></p><p type="main">

<s>“ Non è già ragionevole il dirsi che una luce così accesa, quale ci <lb></lb>manda la fascia di Saturno, e forse più viva di quella del di lui disco, sia <lb></lb>una semplice refrazione, quale supponemmo i colori di quell&#039;Iride cingente <lb></lb>le stelle, le quali, benchè a noi vicinissime, pur di colori assai slavati e lan­<lb></lb>guidi si coloriscono. </s>

<s>Sarà dunque assai probabile illuminarsi la fascia col <lb></lb>riflettere, non col rifrangere i raggi solari, e se ad alcuno, per un riperco­<lb></lb>timento sì vivo, non giudicasse bastevole la sostanza trasparente di quelle <lb></lb>stelle di diaccio, potrebbe dirsi che, siccome l&#039;acqua per la sua fluidità non <lb></lb>ubbidisce perfettamente al moto della nostra Terra, quando mai si movesse, <lb></lb>come nei flussi e reflussi è manifesto; così forse l&#039;aria ambiente Saturno, <lb></lb>particolarmente intorno al suo equinoziale dove ha il movimento rapidissimo, <lb></lb>non obbedisce interamente al moto del suo Pianeta, e tanto men se s&#039;ab­<lb></lb>battessero intorno a quell&#039;Equatore pianure e tratti grandi di mari, dove <lb></lb>liberamente vagasse, senza venir portata tra&#039;seni di montagne altissime. </s>

<s>Ne <lb></lb>abbiamo <gap></gap> li ciò l&#039;esempio in quel vento costante, che da oriente in occi­<lb></lb>dente spira nei nostri mari, attribuito divinamente dal signor Galileo a que­<lb></lb>sta cagione. </s>

<s>” </s></p><p type="main">

<s>“ Non sarà dunque maraviglia che quelle stelline di diaccio galleggianti <lb></lb>nell&#039;aria, tanto quanto contumaci alla vertigine del Pianeta, anch&#039;elleno, in <lb></lb>quei flussi e riflussi aerei, non essendo tenacemente fra loro collegate, per <lb></lb>essere di superficie tersissime, variamente urtandosi, ed insieme arrotandosi, <lb></lb>si stritolino, e si divengano atte alla riflessione del lume, come vegghiamo <lb></lb>accadere al diaccio, al cristallo, al vetro triti e pesti che, di trasparenti, <lb></lb>bianchissimi divengono, nè più s&#039;imbevono, anzi ribattono, con la molti­<lb></lb>plicità delle loro minime superficie, in larghissima copia, per ogni parte, <lb></lb>la luce. </s>

<s>” </s></p><p type="main">

<s>“ Così sarebbesi generata intorno all&#039;equatore di Saturno una fascia <lb></lb>obbedientissima al moto circolare in sè stessa, ch&#039;essendo la di lei super­<lb></lb>fice interna, per quei stritolamenti, asprissima, avrebbe molti attacchi per <lb></lb>esser portata in giro dall&#039;aria, che a lei contigua fa vortice intorno all&#039;asse <lb></lb>della revoluzione dell&#039;istesso Saturno. </s>

<s>” </s></p><p type="main">

<s>Il troppo ossequio alle dottrine di Galileo dette occasione a questa ul­<lb></lb>tima congettura del Magalotti, la quale è una futilità e un regresso nella <lb></lb>scienza comparata a quel che sapientemente aveva detto l&#039;Huyghens del­<lb></lb>l&#039;anello gravitante al centro di Saturno, e partecipante al moto rotatorio di <lb></lb>lui, come ne partecipano, benchè non materialmente congiunti, i corpi gra­<lb></lb>vitanti al centro della nostra Terra. </s>

<s>“ Porro, quum certo satis colligi posse <lb></lb>videatur, ob similitudinem ac cognationem magnam quae Saturno cum Tel­<lb></lb>lure nostra intercedit, illum perinde ut haec in medio sui vorticis situm <lb></lb>esse, centrumque eius versus omnia natura sua tendere, quae illic gravia <lb></lb>habentur, inde necessario quoque efficitur, annulum istum omnibus sui par-<pb xlink:href="020/01/1044.jpg" pagenum="487"></pb>tibus aequali vi ad centrum nitentem, hoc ipso ita consistere ut undequa­<lb></lb>que pari intervallo a centro absit ” (Syst. </s>

<s>Sat., Op. </s>

<s>cit., pag. </s>

<s>567). </s></p><p type="main">

<s>Ma il Boreili, nel suo Discorso, anche più chiaramente dell&#039;Huyghens, <lb></lb>dimostrò la causa del moto dell&#039;Anello risiedere in una attrazion magnetica <lb></lb>di Saturno, non dissimile punto da quella, che Giove esercita su i suoi <lb></lb>quattro Pianeti. </s>

<s>Non così felice però fu il Borelli stesso nel risolvere alcune <lb></lb>altre questioni concernenti la possibilità e la persistenza dell&#039;Anello, per di­<lb></lb>pender così fatte questioni dalla qualità della materia componente esso Anello, <lb></lb>intorno a che si credeva che non si potesse da ingegno umano formar pro­<lb></lb>babile congettura. </s>

<s>Eppure le naturali osservazioni celesti, comparate con <lb></lb>quell&#039;altre ingegnosamente propostesi nella Macchina artificiale, pareva che <lb></lb>avessero dovuto condurre a diritto il Borelli a congetturar la solidità del­<lb></lb>l&#039;Anello, da quegli stessi indizii ch&#039;ebbero dell&#039;aspra superfice montagnosa <lb></lb>di lui Astronomi più recenti. </s>

<s>Leggiamo infatti ciò ch&#039;egli scrisse in quel suo <lb></lb><emph type="italics"></emph>Parere<emph.end type="italics"></emph.end> sul sistema ugeniano in proposito del rappresentarsi, per mezzo della <lb></lb>Macchina, Saturno solitario. </s></p><p type="main">

<s>“ Avvertirò bene una fallacia, della quale nel suo primo apparire fu <lb></lb>intesa la cagione e subitamente rimossa, col rastiare dal piano della Fascia <lb></lb>quelle scabrosità di gesso lasciatevi a fine di renderla più atta a ripercuo­<lb></lb>tere per ogni banda il lume, poichè, per minime che esse si fossero, certo <lb></lb>è che a quella piccola Macchinetta avevano sempre proporzione sì fatta, <lb></lb>quale non hanno alla Terra montagne altissime, e sì, quantunque l&#039;occhio <lb></lb>cadesse nel piano dell&#039;Anello, le dette prominenze vi cadevano perpendico­<lb></lb>lari, ed essendo illuminate rappresentavano fallacemente, con una linea lu­<lb></lb>cida, la superfice esteriore convessa della Fascia, benchè sottilissima, illu­<lb></lb>minata “ (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>742). </s></p><p type="main">

<s>Or essendo un fatto che nell&#039;osservar Saturno s&#039;erano gli Accademici <lb></lb>accorti, come dianzi accennava il Magalotti, apparir l&#039;Anello più vivamente <lb></lb>splendido dello stesso Globo saturnio da lui precinto; pareva facilissimo, pa­<lb></lb>ragonando gli effetti dell&#039;arte con quelli della Natura, a sovvenire il pen­<lb></lb>siero che il più vivo splendor dell&#039;Anello naturale fosse dovuto a scabrosità <lb></lb>montagnose, rappresentate da que&#039;minuzzoli di gesso rimasti sull&#039;anello ar­<lb></lb>tificiale. </s>

<s>Ma fu impedimento alla facilità di quel pensiero un concetto, che <lb></lb>il Borelli aveva letto e apprezzato nell&#039;Hugenio, il quale, per ispiegare in <lb></lb>che modo si mantenesse l&#039;anello oscuro e invisibile, benchè riguardasse il <lb></lb>Sole con tale obliquità, da poter esserne alquanto illuminato; disse che <lb></lb>l&#039;anello stesso doveva essere di superficie non aspra ma levigata. </s>

<s>“ Qua ta­<lb></lb>men in re illud ante omnia statuere necesse est, superficiem Annuli non <lb></lb>esse asperam montibusque obsitam, veluti maxima ex parte Lunae nostrae <lb></lb>est superficies, sed aequalem planamque ” (Syst. </s>

<s>Sat., Op. </s>

<s>cit., pag. </s>

<s>583). </s></p><p type="main">

<s>Per conformarsi a un tal concetto il Borelli raschiò le asperità del gesso <lb></lb>dalla sua Macchina, la quale, non rappresentando perciò più il vero natu­<lb></lb>rale, lo tenne in dubbio se la materia dell&#039;anello fosse solida o fluida, sic­<lb></lb>chè stimando ugualmente probabile tanto l&#039;una cosa quanto l&#039;altra, andò <pb xlink:href="020/01/1045.jpg" pagenum="488"></pb>accomunando alle due varie ipotesi, con docilità, le sue speculazioni. </s>

<s>Non <lb></lb>mancano certamente queste speculazioni di quell&#039;ingegno, ch&#039;era tutto pro­<lb></lb>prio del Borelli, ed essendo in ogni modo primizie d&#039;Astronomia fisica non <lb></lb>dispiacerà ai Lettori di vedersele presentare innanzi dall&#039;Autore stesso nel <lb></lb>suo Discorso, che noi trascriviamo da una copia inserita da c. </s>

<s>66-69 del <lb></lb>T. XXX de&#039;Manoscritti del Cimento; copia che fu riveduta dal Magalotti. </s></p><p type="main">

<s>“ Serenissimo Principe, così grande e tanto ammirabile è la ricchezza <lb></lb>della Natura, che con gran difficoltà e dubbiezza arriva l&#039;intelletto umano <lb></lb>a comprenderne il magistero, ed a profferirne le cagioni. </s>

<s>Siccome adunque <lb></lb>non si dee chiamar temerario chi si mette a speculare sopra le opere di <lb></lb>essa più ammirande, e per vie non battute tenta di salvare insolite e nuove <lb></lb>apparenze del cielo, da noi separate per sì gran tratto; così ancora non si <lb></lb>dee ascrivere a viltà, nè a soverchio timore, se altri si protesta, in tanta <lb></lb>incertezza, di propor solo dubbiosamente il suo parere, senza mai asserire <lb></lb>cosa veruna. </s>

<s>Richiesto adunque della mia opinione circa la nuova posizione <lb></lb>di Saturno, prima di pronunziare quanto mi è passato per l&#039;intelletto, ri­<lb></lb>cordo alla discretezza di chi legge questa mia breve scrittura che, se ad al­<lb></lb>cuno paressero troppo arditi e nuovi questi miei pensieri, nuovo e strano <lb></lb>è ancora il problema, di cui si tratta; e se ad altri troppo dubbioso e irre­<lb></lb>soluto il mio parere, troppo alta ed oscura è similmente la verità, che da <lb></lb>noi si ricerca. </s>

<s>” </s></p><p type="main">

<s>“ Dico pertanto che l&#039;ipotesi della Fascia o Ciambella sottile, la quale <lb></lb>circonda Saturno, staccata però dalla superficie di quello, sodisfa, se non in <lb></lb>tutto, alla maggior parte delle apparenze. </s>

<s>Ma resta tuttavia da esaminare la <lb></lb>fisica possibilità di tal posizione, cioè in primo luogo se l&#039;esistenza e la ge­<lb></lb>nerazione di detta Ciambella sia possibile o no. </s>

<s>Secondo, se possa durare <lb></lb>e conservarsi perpetuamente. </s>

<s>Terzo, se possa obedire e secondare il moto <lb></lb>di Saturno, mentr&#039;egli scorre per l&#039;etere fluido. </s>

<s>” </s></p><p type="main">

<s>“ Quanto al primo, può essere la sostanza di detta Ciambella, o di ma­<lb></lb>teria dura e consistente, o fluida. </s>

<s>Se si volesse conceder dura, non vi scorgo <lb></lb>impossibilità, nè, perchè questa è cosa senza esempio, adunque ne segue che <lb></lb>non si possa dare in natura, perchè del tesoro inesausto ed infinito della <lb></lb>Natura la maggior parte rimane a noi ignota, e però, scoprendosi di mano <lb></lb>in mano qualcheduno degli effetti di essa, saranno la prima volta, senza <lb></lb>esempi, non conosciuti e non intesi i fini, ai quali la Natura gli adopera. </s>

<s>” </s></p><p type="main">

<s>“ Ma chi volesse credere esser la sostanza di detta Ciambella fluida, <lb></lb>non so vedere che vi siano repugnanze in natura, che la rendano impos­<lb></lb>sibile, perchè potrebbe ella generarsi da vapori eruttati da voragini, simili <lb></lb>ai nostri vulcani e mongibelli, i quali fussero collocati lungo l&#039;equinoziale <lb></lb>di Saturno, nè è impossibile che somiglianti vapori, arrivati a quella tale <lb></lb>altezza dell&#039;aria o etere ambiente Saturno, dove vengono ridotti all&#039;equili­<lb></lb>brio, si fermino senza passar più oltre, e posto che attorno a Saturno non <lb></lb>vi spirino venti, il che anche non è impossibile, non ci è ragione perchè <lb></lb>debbano uscir dal piano dell&#039;Equinoziale. </s>

<s>” </s></p><pb xlink:href="020/01/1046.jpg" pagenum="489"></pb><p type="main">

<s>“ Di più, perchè è assai probabile, non che possibile, che Saturno si <lb></lb>rivolga intorno al proprio asse, che è parallelo all&#039;asse del Mondo e del no­<lb></lb>stro Equinoziale, e che tal vertigine sia partecipata dai corpi aderenti al <lb></lb>medesimo sistema, dentro al quale verrà ad essere inclusa la detta Ciam­<lb></lb>bella vaporosa; potrà in ogni modo, come fluida, non effettivamente secon­<lb></lb>dare la vertigine di Saturno, e così verranno a riempirsi li spazi della sua <lb></lb>latitudine, onde venga a perfezionarsi ed a contornarsi la superfice piana <lb></lb>della detta Ciambella. </s>

<s>Oltre a ciò, perchè i detti vapori, nella densità e gra­<lb></lb>vità, non sono similari, possono i meno gravi equilibrarsi più di un diame­<lb></lb>tro lontani da Saturno, ed i più gravi è possibile che si equilibrino con <lb></lb>l&#039;ambiente fluido poco più di un semidiametro lontani dallo stesso Sa­<lb></lb>turno. </s>

<s>” </s></p><p type="main">

<s>“ Con maggior facilità potrebbe generarsi la detta Ciambella fluida, <lb></lb>senz&#039;avere a condurre tutta la materia vaporosa, che compone la detta Ciam­<lb></lb>bella, dallo stesso corpo di Saturno in tanta lontananza. </s>

<s>Trovansi non pochi <lb></lb>fluidi, che dalla mistura di poche gocciole d&#039;altro liquore si trasformano, da <lb></lb>trasparente in opaco, e per il contrario, d&#039;opaco ch&#039;egli era, divien traspa­<lb></lb>rente, il che frequentemente d&#039;osserva in tutte l&#039;acque forti ripiene di me­<lb></lb>talli e minerali da esser corrosi, quali poche gocciole d&#039;olio di tartaro o <lb></lb>d&#039;altra cosa simile tolgono loro la trasparenza, e le fanno divenire opache, <lb></lb>niente manco di un marmo. </s>

<s>Anzi questo medesimo effetto nell&#039;orina lo fa <lb></lb>la semplice freddezza, che di trasparente la fa divenire opaca, e per il con­<lb></lb>trario il calore la rischiara. </s>

<s>” </s></p><p type="main">

<s>“ Supposto questo, se la regione aerea ambiente Saturno fusse d&#039;una <lb></lb>tal natura analoga all&#039;acqua stillata in piombo, o alle acque forti incorpo­<lb></lb>rate d&#039;argento, e se lungo l&#039;Equinoziale saturnino svaporassero pochissimi <lb></lb>fumi analoghi a quelle poche gocce d&#039;olio di tartaro, facilissimamente si po­<lb></lb>trebbe intorbidare attorno a Saturno. </s>

<s>E perchè, come s&#039;è detto, si può sup­<lb></lb>porre quella regione non soggetta all&#039;agitazione de&#039;venti, rimane il detto <lb></lb>Anello nello stesso sito. </s>

<s>Ne è maraviglia che, lungo l&#039;Equinoziale saturnino, <lb></lb>si vomitine de&#039;vapori, e non d&#039;altrove, conforme non da tutte le parti del­<lb></lb>l&#039;animale e della Terra svaporano, ed escono alcuni determinati vapori e <lb></lb>liquori. </s>

<s>” </s></p><p type="main">

<s>“ Secondo, circa la perseveranza e durazione di detta Ciambella, quando <lb></lb>ella si supponga solida e dura, non ha difficoltà che possa considerarsi come <lb></lb>gli altri corpi mondani. </s>

<s>Ma se ella non è dura, potrà in ogni modo conti­<lb></lb>nuarsi, quando il pabulo continuamente gli venga somministrato, come la <lb></lb>regione vaporosa e crepuscolina della nostra Terra dura sempre, perchè suc­<lb></lb>cessivamente si rimette quel che si consuma. </s>

<s>Ma chi ne volesse un effetto <lb></lb>somigliantissimo nella nostra Terra, consideri la zona fredda, compresa dal <lb></lb>Cerchio artico, l&#039;aria sovrastante nella quale è quasi sempre ingombrata <lb></lb>da&#039;vapori acquei, i quali per lungo tratto sono già agghiacciati in forma di <lb></lb>neve, che per il suo poco peso, con gran lentezza movendosi allo in giù, ma <lb></lb>la medesima avvicinandosi a terra si dissolve, e di nuovo riducesi in forma <pb xlink:href="020/01/1047.jpg" pagenum="490"></pb>fluida acquea, ma per tutto lo spazio superiore, nel quale si manteneva in <lb></lb>forma di neve, era bianchissima, e però, efficacemente riflettendo il lume <lb></lb>ripercosso, dovrebbe, a chi da lontano riguardasse tal regione trasversal­<lb></lb>mente, rappresentare come un anello opaco e bianchissimo attorno quella <lb></lb>Terra settentrionale, staccato dalla superficie terrestre. </s>

<s>E perchè somigliante <lb></lb>generazione di vapori e di nevi, in quella regione, è perpetua, per rimet­<lb></lb>tersi successivamente quello che va perdendosi; adunque non è impossibile <lb></lb>che attorno Saturno si mantenga una somigliante generazione, conservata da <lb></lb>un successivo pabulo, che dal corpo di Saturno le venga somministrato. </s>

<s>” </s></p><p type="main">

<s>“ Non v&#039;è pericolo che la figura di detta Ciambella possa variamente <lb></lb>figurarsi, perchè si suppone tutta la regione fluida attorno a Saturno, per <lb></lb>grande spazio, aver naturale inclinazione d&#039;accostarsi, gravare e mantenersi <lb></lb>aderente a Saturno, ed anche si suppone che in tal regione non vi siano <lb></lb>venti, ma sia sommamente tranquilla. </s>

<s>Adunque, cessando la cagione d&#039;in­<lb></lb>torbidamento e variazion di figura, e perseverando la gravità naturale a man­<lb></lb>tenere tutta la detta regione unita ed aderente a Saturno, non potrà in niuna <lb></lb>maniera la figura di detta Ciambella alterarsi o mutar sito. </s>

<s>Un effetto so­<lb></lb>migliante osservasi in una boccia di vetro, nella quale l&#039;acqua, il vino ed <lb></lb>altri liquori si mantengon separati, anzi striscie di varii colori, nella stessa <lb></lb>acqua, perseverano nello stesso sito, positura e figura, tutta volta che l&#039;acqua <lb></lb>si mantenga tranquilla, e non punto agitata da onde o da altri interni mo­<lb></lb>vimenti. </s>

<s>” </s></p><p type="main">

<s>“ Restaci l&#039;ultimo punto da considerare: in che maniera, girando Sa­<lb></lb>turno per l&#039;etere fluido, la sua Ciambella non resti indietro o si ripieghi <lb></lb>od acquisti altra figura, come succede alla fiamma di una torcia velocemente <lb></lb>girata, la quale lascia una coda, come la Cometa, e finalmente si dissipa. </s>

<s>E <lb></lb>qui è da considerare che la fiamma della torcia commossa può essere ac­<lb></lb>compagnata mai sempre da una medesima porzione di aria, ed in questo <lb></lb>caso non può nè piegarsi nè smorzarsi, come si vede in quei lumi, che son <lb></lb>chiusi dentro una lanterna, ma allora solamente può ripiegarsi e spengersi, <lb></lb>quando la medesima fiamma incontra ed urta nell&#039;aria immobile. </s>

<s>Ora, se la <lb></lb>regione che circonda Saturno fosse più alta della Ciambella, com&#039;è credi­<lb></lb>bile, per essere annessa a Saturno, in virtù della sua gravità o forza ma­<lb></lb>gnetica o d&#039;altra cagione somigliante, che tenacemente la mantenesse ade­<lb></lb>rente a Saturno, sicchè tutto insieme venisse a formarsi un sistema; verrebbe <lb></lb>la detta Ciambella di Saturno ad esser coperta e difesa dagli urti dell&#039;etere <lb></lb>immobile, ed in conseguenza non potrebbe nè piegarsi nè dissiparsi. </s>

<s>” </s></p><p type="main">

<s>“ Ma che occorre cercare altre ragioni consimili? </s>

<s>Non bast&#039;egli veder <lb></lb>sensatamente che la Natura opera nel cielo effetti somigliantissimi, anzi me­<lb></lb>desimi appunto? </s>

<s>Giove si rivolge pur nell&#039;etere fluido, nè i suoi quattro <lb></lb>pianeti Medicei che lo circondano hanno punto di difficoltà a secondare il <lb></lb>suo moto, e mai occorre che restino indietro, per gli urti e impedimenti <lb></lb>dell&#039;etere immobile. </s>

<s>Venere e Mercurio è pur vero che non mai abbando­<lb></lb>nano il Sole, nè la Stella nuovamente scoperta in Saturno rimane addietro. <pb xlink:href="020/01/1048.jpg" pagenum="491"></pb>Adunque, se noi concederemo una somigliante virtù, potrà con la medesima <lb></lb>facilità girar con Saturno stabilmente la sua Ciambella. </s>

<s>E però, se la virtù <lb></lb>che rapisce seco le Medicee risiede in Giove, diremo parimente che la forza, <lb></lb>che trasporta la Ciambella di Saturno, risieda nel medesimo Pianeta, e chi <lb></lb>stimasse ch&#039;ella fosse propria de&#039;Pianetini medicei, o cosa analoga a gra­<lb></lb>vità o virtù magnetica, lo stesso appunto si può dire della Ciambella satur­<lb></lb>nina, sicchè sarà lecito a lei, non meno che ai Pianeti gioviali, essere tra­<lb></lb>sportata insieme con Saturno. </s>

<s>” </s></p><p type="main">

<s>“ Questo basti per ora, in cosa tanto nuova ed incerta, con ferma spe­<lb></lb>ranza che il tempo e le future osservazioni sieno per somministrarci più <lb></lb>evidenti, e più solidi discorsi. </s>

<s>” </s></p><p type="main">

<s>Di tutto ciò che s&#039;era letto nell&#039;Accademia, a proposito di Saturno, fu <lb></lb>spedito copia in Olanda all&#039;Huyghens, e non si mancò di fargli recapitare <lb></lb>anche questi due Discorsi, i quali pure furono mandati a Roma a Miche­<lb></lb>langiolo Ricci. </s>

<s>Il Magalotti, nella qualità sua di segretario, accompagnava il <lb></lb>plico con una lettera, nella quale incomincia a ringraziare esso Ricci di aver <lb></lb>liberato l&#039;Accademia dal fastidio del Fabry, fecondo sempre di nuovi e stra­<lb></lb>vaganti discorsi per accomodar Saturno al suo sistema. </s>

<s>Poi, entra più par­<lb></lb>ticolarmente delle due Scritture sopra la possibilità della costituzione fisica <lb></lb>dell&#039;anello, qualificando le idee ivi espresse, e dandole “ come voli permessi <lb></lb>a due intelletti annoiati oramai di rigirarsi, per si lungo tempo, tra gli an­<lb></lb>gusti limiti di calcoli e di figure. </s>

<s>” </s></p><p type="main">

<s>“ Il primo, immediatamente il Magalotti soggiunge, è del Borelli. </s>

<s>Quanto <lb></lb>al secondo sono così interessato nella reputazione dell&#039;Autore, che non do­<lb></lb>vrei farle, come suol dirsi, il nome. </s>

<s>Ma ella se l&#039;è già immaginato, e avrà <lb></lb>ripresa a quest&#039;ora la mia temerità. </s>

<s>Che vuol ch&#039;io le dica? </s>

<s>Questo è, si­<lb></lb>gnor Michelangiolo, quel vantaggio deplorabile, che serve a consolarmi bene <lb></lb>spesso nelle frequenti meditazioni della mia da me ben conosciuta ignoranza; <lb></lb>l&#039;essermi lecito il profferire ogni mio concetto; libertà da non usurparsi da <lb></lb>coloro, i quali dal proprio sapere vengono costituiti debitori a sè medesimi, <lb></lb>anzi all&#039;opinione del mondo, della propria fama. </s>

<s>Qual pregiudizio adunque <lb></lb>dovrò io temere dal paragone formidabile dei pensieri del signor Borelli, <lb></lb>se egli, in venticinque anni confirmati in letture pubbliche, con applauso <lb></lb>universale delle più celebri Università d&#039;Italia; conta ben tre anni di pro­<lb></lb>fessione più di quel che io mi conti di vita? </s>

<s>” (Lettere famil., T. II, Fi­<lb></lb>renze, 1769, pag. </s>

<s>2, 3). </s></p><p type="main">

<s>E nonostante, non par che avrebbe temuto il Magalotti di venire a con­<lb></lb>fronto col gran Borelli, non solo privatamente ne&#039;giudizii degli Accademici, <lb></lb>dell&#039;Huyghens e del Ricci, ma pubblicamente nel giudizio universale degli <lb></lb>scienziati, essendo suo manifesto desiderio “ di mettere in sicuro tutto quello <lb></lb>che l&#039;anno 1660 si speculò, e si operò nell&#039;Accademia intorno a Saturno, <lb></lb>essendoci accorti che insensibilmente, quando uno e quando un altro, va <lb></lb>facendosi bello della maggior parte delle nostre cose ” (Targioni, Notizie cit, <lb></lb>T. I, pag. </s>

<s>385). </s></p><pb xlink:href="020/01/1049.jpg" pagenum="492"></pb><p type="main">

<s>Fra questi usurpatori intendeva il Magalotti di comprender principal­<lb></lb>mente Giuseppe Campani, il quale, nel suo <emph type="italics"></emph>Ragguaglio di due nuove Os­<lb></lb>servazioni,<emph.end type="italics"></emph.end> parlò, come di sua propria invenzione, di una “ Macchinuccia <lb></lb>che a somiglianza del celeste Saturno composi, egli dice, d&#039;un globo bianco <lb></lb>cinto d&#039;un cerchio piano, della stessa materia, che con l&#039;aiuto d&#039;un fil di <lb></lb>ferro, che gli fa diametro e passa pel centro del Globo, può abbassarsi ed <lb></lb>elevarsi, sempre segando il globo per mezzo, perocchè, locato questo Stru­<lb></lb>mento in opportuna distanza e abbastanza illuminato, osservandosi con un <lb></lb>piccol Canocchiale,.... rappresenta mirabilmente l&#039;apparenza del vero Sa­<lb></lb>turno ” (Roma 1664, pag. </s>

<s>19, 20). </s></p><p type="main">

<s>Il Borelli simulò una certa noncuranza dell&#039;usurpazione, contentandosi <lb></lb>di richiamarsene appresso il principe Leepoldo, a cui Michelangiolo Ricci, <lb></lb>ch&#039;era stato messo di mezzo in questo negozio, rispondeva da Roma: “ Fi­<lb></lb>nalmente, dell&#039;invenzione da mostrare Saturno con quel Cerchio intorno, <lb></lb>credo di potere indurre il Campani, in altra scrittura, che ne additi il vero <lb></lb>e primiero Autore ” (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>748). </s></p><p type="main">

<s>Quella simulazione poi, in un uomo dell&#039;indole del Borelli, veniva con­<lb></lb>sigliata dal timor che aveva di non trovarsi implicato in una question col <lb></lb>Cassini, il quale era dello strumento del Campani anima e vita, e spirito <lb></lb>che parlava per quella lingua. </s>

<s>Rivelasi un tal sentimento da queste parole, <lb></lb>che il Borelli stesso scriveva al principle della fiorentina Accademia: “ Rendo <lb></lb>umilissime grazie a V. A. del foglio delle figure del Campani, nelle quali <lb></lb>veggo chiaramente che egli vi aggiunge qualche cosa di più di quello, che <lb></lb>veramente ha potuto vedere in Saturno, imperocchè è impossibile che si <lb></lb>allarghi tanto quell&#039;ombra, che egli mostra nel disegno quarto delle sue <lb></lb>figure, il che facilmente si può dimostrare, ma questa sorta di genti, che <lb></lb>hanno più caro l&#039;adulazione che i sinceri avvertimenti, è bene lasciarli stare ” <lb></lb>(MSS. Cim., T. XVIII, c. </s>

<s>92). </s></p><p type="main">

<s>Or, ritornando al proposito di mettere al sicuro le scoperte fatte nel­<lb></lb>l&#039;Accademia, ne fu distolto il Magalotti dallo stesso Borelli, il quale preten­<lb></lb>deva che tutto ciò, che fu operato e speculato intorno a Saturno, fosse opera <lb></lb>sua, e perciò voleva che andasse fuori particolarmente sotto il suo nome, <lb></lb>pensando forse fin d&#039;allora di raccogliere anche queste speculazioni astro­<lb></lb>nomiche fra le cose geometriche e filosofiche, in varii tempi speculate, e <lb></lb>delle quali intendeva di comporre un nuovo libro (ivi, T. XX, c. </s>

<s>49). Ma <lb></lb>perchè il nuovo libro, qualunque poi se ne fosse la ragione, non fu com­<lb></lb>posto, l&#039;opera saturnia fatta nell&#039;Accademia fu posta al sicuro, come si por­<lb></lb>rebbe al sicuro un tesoro, nascondendolo sotto terra, che nè arricchisce i <lb></lb>rapaci usurpatori, nè fruttifica ai legittimi eredi. </s></p><pb xlink:href="020/01/1050.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO XIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle Stelle fisse e delle Comete<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del luogo e del moto, della sostanza e della generaziono delle Stelle nuove nel cieìo. </s>

<s>— II. </s>

<s>Delle <lb></lb>osservazioni telescopiche delle Stelle fisse; della scintillazione, e della loro parallasse. </s>

<s>— <lb></lb>III. </s>

<s>Delle varie ipotesi intorno alla natura e all&#039;essere delle Comete. </s>

<s>— IV. </s>

<s>Della teoria pla­<lb></lb>netaria delle Comete. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Saturno ingemmato dell&#039;Anello, come sposo ch&#039;esca fuor del suo ta­<lb></lb>lamo, Giove seduto sulla maestà del suo trono, con le quattro elette e fedeli <lb></lb>scorte all&#039;intorno, s&#039;appresentavano a que&#039;primi fortunati osservatori tranquil­<lb></lb>lamente veleggiar per i sereni eterni, come per le placide acque di un oceano <lb></lb>immenso, che mandi scintille vive dal suo seno profondo. </s>

<s>Il Canocchiale of­<lb></lb>friva uno spettacolo nuovo e maraviglioso: que&#039;punti lucidi apparivano assai <lb></lb>più spessi che all&#039;occhio nudo, e impiccoliti raggiavan più fieri, com&#039;acqua <lb></lb>che per le angustiate vie più forte e chiara zampilli, o come pupilla, che <lb></lb>più ristrinta guardando, più sorride amorosa. </s>

<s>La gioia ineffabile di così fatto <lb></lb>spettacolo spira dalle pagine del Messaggero celeste di Galileo, se non che la <lb></lb>severità del Filosofo la tempera alquanto, e l&#039;essere state le stelle ampio e <lb></lb>fecondo oggetto di contemplazioni alla vista nuda degli Astronomi la mino­<lb></lb>rava, come a chi assiste all&#039;inaspettato splendor delle seconde scene in una <lb></lb>festa già cominciata. </s></p><p type="main">

<s>Dir come cominciasse quella, a cui si dette dall&#039;artificioso linguaggio <lb></lb>degli Astronomi il nome proprio e particolare di Astroscopia, non si saprebbe <lb></lb>far così in fretta, e non sarebbe dall&#039;altra parte conforme col nostro isti-<pb xlink:href="020/01/1051.jpg" pagenum="494"></pb>tuto, ma non possiamo noi Italiani, esaltati al canto dell&#039;Alighieri, non tor­<lb></lb>nare indietro con la memoria a que&#039;tempi, quando il Divino cantor dei tre <lb></lb>Regni, rappresentandosi alla fantasia nuove inesplorate terre e nuovi mari, <lb></lb>vedeva nelle loro acque specchiarsi quattro risplendentissime stelle non viste <lb></lb>mai fuor che alla prima gente. </s></p><p type="main">

<s>Un altro fiorentino, Amerigo Vespucci, fece poi corporalmente quel viag­<lb></lb>gio, che aveva fatto in spirito l&#039;Alighieri, e osservando da Astronomo le <lb></lb>fiammelle, di che pareva godere il polo meridionale “ mi ricordai, così scrive <lb></lb>in una lettera a Lorenzo di Pier Francesco de&#039;Medici, d&#039;un detto del no­<lb></lb>stro Dante, del quale fa menzione nel primo Capitolo del <emph type="italics"></emph>Purgatorio,<emph.end type="italics"></emph.end> quando <lb></lb>finge di salire di questo emisfero e trovarsi nell&#039;altro, che volendo descri­<lb></lb>vere il Polo antartico dice: <emph type="italics"></emph>Io mi volsi a man destra e posi mente ecc.<emph.end type="italics"></emph.end> che <lb></lb>secondo me mi pare che il Poeta in questi versi voglia descrivere per le <lb></lb>quattro stelle il Polo dell&#039;altro firmamento, e non mi diffido fino a qui che <lb></lb>quello che dice non valga la verità, perchè io notai quattro stelle, figurate <lb></lb>come una mandorla, che tenevano poco movimento ” (Bandini, Vita e let­<lb></lb>tere, Firenze 1745, pag. </s>

<s>70). </s></p><p type="main">

<s>Che se aveva Dante compassionato al nostro emisfero, per esser vedovo <lb></lb>di così splendide luci, soggiunge il Vespucci che avrebbe il settentrionale da <lb></lb>invidiar ben altre nuove bellezze al cielo meridionale “ vaghissimamente <lb></lb>adorno di alcune stelle che non sono da noi conosciute, delle quali io asse­<lb></lb>gnatamente ne ho tenuto memoria, e annoveraine forse venti di tanta chia­<lb></lb>rezza, di quanta sono appresso di noi le stelle di Venere e di Giove. </s>

<s>Con­<lb></lb>siderai anche il loro circuito, e i varii movimenti, e misurai la lor circon­<lb></lb>ferenza e diametro assai facilmente, avendo io notizia della Geometria ” (ivi, <lb></lb>pag. </s>

<s>113). Trovò, facendo uso de&#039;suoi strumenti ch&#039;erano il Quadrante e <lb></lb>l&#039;Astrolabio, non esser tra le nuove scoperte stella “ che tenessi men che <lb></lb>dieci gradi di movimento all&#039;intorno del firmamento, di modo che non re­<lb></lb>stai sodisfatto di me medesimo di nominar nessuna, essendo il polo del Me­<lb></lb>ridione, a causa del gran circolo che facevano intorno al firmamento ” (ivi, <lb></lb>pag. </s>

<s>70). </s></p><p type="main">

<s>Le osservazioni astronomiche sopra le stelle, e sopra le costellazioni del <lb></lb>cielo meridionale dice Amerigo stesso di averle diligentemente descritte, e <lb></lb>rappresentate in figure nel suo libro delle <emph type="italics"></emph>Quattro giornate;<emph.end type="italics"></emph.end> libro ch&#039;ei <lb></lb>commemora nelle sue lettere più volte e in modo, da accendere in noi vi­<lb></lb>vissimo desiderio di sè, benchè senza speranza oramai che venga sodisfatto. </s></p><p type="main">

<s>Quel nonostante, che raccogliesi dalle sue lettere e da altre sue scrit­<lb></lb>ture rimaste, basta a noi Italiani perchè possiamo qualificare il Vespucci <lb></lb>come l&#039;alba che, sotto il ciel di Firenze, precede al sole di Galileo, il quale <lb></lb>iniziò col disputar delle stelle quella scienza, che l&#039;avrebbe poi fatto coro­<lb></lb>nare di tanta gloria. </s></p><p type="main">

<s>Aveva appresso gli stranieri Galileo senza dubbio precursori più imme­<lb></lb>diati di quel che non fosse il Vespucci, e Ticone, a capo di una numerosa <lb></lb>schiera di astronomi, era tra que&#039;precursori de&#039;più celebri e de&#039;più dili-<pb xlink:href="020/01/1052.jpg" pagenum="495"></pb>gentemente operosi. </s>

<s>Ebbe a mostrar particolarmente la sua operosità nelle <lb></lb>svariate osservazioni fatte all&#039;Uraniburgo, e la sua diligenza all&#039;occasione che <lb></lb>si vide apparire in cielo, sui principii del Novembre 1572, una stella nuova. </s>

<s><lb></lb>Determinata la posizione di lei, sì quanto alla longitudine e alla latitudine, <lb></lb>come quanto alla declinazione e all&#039;ascensione retta, la trovò immobile ri­<lb></lb>spetto alle altre stelle fisse, e senz&#039;alcuna sensibile parallasse. </s>

<s>Confermatosi <lb></lb>ciò dagli altri astronomi, più esercitati ne&#039;calcoli e nelle osservazioni, ve­<lb></lb>niva a concludersi che la nuova apparita si doveva sublimar su fino alla <lb></lb>vòlta stellata, e senza dubbio molto al di là della sfera di Saturno. </s></p><p type="main">

<s>Singolar cosa che a una tal conclusione, tanto contraria alla fede in­<lb></lb>valsa della incorruttibilità de&#039;cieli, non si riscntissero i Peripatetici, almeno <lb></lb>con quell&#039;ardore come fecero, specialmente in Italia, 32 anni dopo, quando <lb></lb>apparve il di 10 Ottobre del 1604 un&#039;altra stella nuova. </s>

<s>Galileo, professore <lb></lb>allora nello studio di Padova, fece alla scolaresca, o meglio al pubblico con­<lb></lb>venutovi numerosissimo, tre Lezioni su quel soggetto, per rinsavire colla <lb></lb>ragione la popolare frenetica fantasia. </s>

<s>Il principio della prima fra quelle Le­<lb></lb>zioni, a cui Galileo stesso accennò nella <emph type="italics"></emph>Difesa contro il Capra<emph.end type="italics"></emph.end> (Alb. </s>

<s>XI, 363), <lb></lb>fu pubblicato nella II Parte delle <emph type="italics"></emph>Memorie ecc.<emph.end type="italics"></emph.end> dal Venturi (Modena 1821, <lb></lb>pag. </s>

<s>331, 32), e si rileva da questo come il Trattato galileiano fosse distinto <lb></lb>in due parti: nella prima matematica, dove si dimostrava il luogo e il moto <lb></lb>della Stella nuova, e nell&#039;altra fisica, dove si congetturava l&#039;origine acciden­<lb></lb>tale di lei, l&#039;essere e la sostanza. </s>

<s>“ Quod mei muneris praecipuum est af­<lb></lb>feram quidquid de motu et loco demonstrative constabit; quid autem ad <lb></lb>substantiae indagationem horum accidentium conferunt praecognitio,.... nostis <lb></lb>omnes ” quanto sia difficile di quaggiù aver notizia degli avvenimenti celesti. </s></p><p type="main">

<s>Per quel che riguarda la prima parte dimostrativa non fece altro Ga­<lb></lb>lileo che applicare a questa stella il metodo usato già da Ticone e dal <lb></lb>Moestlin, per assicurarsi della immobilità e deficienza di parallasse della <lb></lb>stella del 1572; metodo che Galileo stesso rammemora al Capra, il quale lo <lb></lb>aveva dimenticato, benchè celebrasse la scrittura moestliniana sopra la detta <lb></lb>stella “ il cui sito, immobilità e carenzia di parallasse con altro egli non os­<lb></lb>servò che con un filo, trovandola sempre in linea retta con due coppie di <lb></lb>stelle fisse ” (Alb. </s>

<s>XI, 368). Ora avendò anche il nostro professore di Pa­<lb></lb>dova osservato mantenersi la Nuova apparita sempre in linea retta con la <lb></lb>prima stella delle tre nella coda dell&#039;Orsa maggiore, e con la Lucida della <lb></lb>Corona (ivi, pag. </s>

<s>369 e V, 395) ne concluse dover quella apparenza venirci <lb></lb>da una regione superiore alla elementare. </s></p><p type="main">

<s>Questo del “ dimostrare il sito della Nuova stella essere e esser som­<lb></lb>pre stato molto superiore all&#039;orbe lunare ” fu, dice Galileo, “ il principale <lb></lb>scopo delle mie lezioni “ (Alb. </s>

<s>VI, 26), ond&#039;è che la parte fisica, concer­<lb></lb>nente l&#039;origine e la sostanza di quel fatto straordinario, fu toccata appena <lb></lb>per le difficoltà e per l&#039;incertezza, innanzi a cui s&#039;arretrava prudentemente <lb></lb>la scienza. </s>

<s>Gli era a principio venuto in mente che si potessero tali appa­<lb></lb>rizioni ed occultazioni salvar “ per via di epicicli o di qualsivogliano movi-<pb xlink:href="020/01/1053.jpg" pagenum="496"></pb>menti circolari ” (ivi, II, 301), ma trovato di fatto esser la stella immobile, <lb></lb>Galileo ebbe a rinunziare a questo primo pensiero, rivolgendosi ad alcun <lb></lb>altro che non riusci però a sodisfarlo. </s></p><p type="main">

<s>Intanto i Peripatetici fedeli al loro domma insorsero, non propriamente <lb></lb>contro Galileo, ma contro Ticone, contro il Moestlin, contro tutti gli Astro­<lb></lb>nomi, che avevano colle loro osservazioni e coi calcoli insegnato a Galileo <lb></lb>stesso la via e il modo di dimostrar che la Stella nuova s&#039;era ingenerata <lb></lb>negli incorruttibili spazi celesti. </s>

<s>Fu de&#039;primi fra costoro Antonio Lorenzini, <lb></lb>il quale, facendo quel conto delle matematiche dimostrazioni che delle fisi­<lb></lb>che ipotesi, volle provar che le osservazioni di Ticone e degli altri Astro­<lb></lb>nomi erano fallacie, e i loro calcoli sbagli, ma che corretti gli uni e le altre <lb></lb>com&#039;egli vuole, concludevano evidentemente il luogo della Stella nuova dover <lb></lb>essere sullunare. </s></p><p type="main">

<s>Altri Peripatetici però più prudenti, mettendo da parte la Matematica, <lb></lb>la quale non lascia all&#039;ingegno i suoi liberi voli, si riducevano ne&#039;campi <lb></lb>della Fisica, più facilmente trattabili per sè stessi, e già preparati, nel libro <lb></lb>degli Omocentrici del Fracastoro, a questo nuovo genere di cultura. </s>

<s>Dice <lb></lb>l&#039;Autore, nel Cap. </s>

<s>VIII della Sezione II, che egli, oltre all&#039;aria e al vapore <lb></lb>acqueo riconosce un altro mezzo, attraverso a cui passano le apparenze degli <lb></lb>astri; mezzo che consiste nella maggiore o minor densità delle varie parti <lb></lb>del cielo. </s>

<s>“ Ergo, ne conclude da questa ipotesi il Fracastoro, quod eiusmodi <lb></lb>novumque appareant stellae, causa interdum non in aere sed in coeli par­<lb></lb>tibus quod modo crassiores, modo tenuiores quibusdam stellis subiiciuntur ” <lb></lb>(Op. </s>

<s>omnia, Venetiis 1584, c. </s>

<s>13). </s></p><p type="main">

<s>Applicarono questa ipotesi fracastoriana al caso della Nuova apparita <lb></lb>nel 1604 Lodovico Delle Colombe e Giovanni Heckio, ma Raffaello Gualtie­<lb></lb>rotti suppose che alcuni vapori esalati dalla Terra si fossero sublimati nelle <lb></lb>regioni celesti, e che ivi illuminati dal Sole mostrassero per riflesso a noi <lb></lb>quella luce in somiglianza di stella. </s></p><p type="main">

<s>Or chi il crederebbe? </s>

<s>A Galileo, che non aveva ancora saputo trovare <lb></lb>ipotesi che lo sodisfacesse, piacque questo pensiero del Gualtierotti, e si pose <lb></lb>dietro a cercare argomenti che lo rendessero più probabile e a rispondere <lb></lb>alle obiezioni. </s>

<s>Di questo solitario lavorìo di mente s&#039;hanno le vestigia im­<lb></lb>presse ne&#039;Manoscritti galileiani, i quali raccolti per le carte disperse spec­<lb></lb>chian pure in qualche modo il pensiero, come può specchiarsi l&#039;immagine <lb></lb>di una fiammella ne&#039;frantumi accozzati di un cristallo. </s></p><p type="main">

<s>Si trovano cotesti frammenti in parte scritti da c. </s>

<s>10-13 del T. II, P. III, <lb></lb>in parte da c. </s>

<s>12-15 del T. VI, P. IV. L&#039;Albèri, che ne pubblicò qualche <lb></lb>cosa, e coloro che ci vengono ora ripetendo ciò che fu detto e fatto da lui, <lb></lb>danno quelle note di Galileo come brani o come appunti presi per servir­<lb></lb>sene a distendere le tre Lezioni sopra la stella nuova. </s>

<s>Ma è facile provar <lb></lb>che debbono essere quelle note posteriori al 1604, accennandovisi a un&#039;os­<lb></lb>servazione fatta <emph type="italics"></emph>die 3 Febraurii 1605<emph.end type="italics"></emph.end> (MSS. Gal., P. III, T. II, c. </s>

<s>10), e ci­<lb></lb>tandovisi il trattato <emph type="italics"></emph>De stella nova<emph.end type="italics"></emph.end> del Keplero (ivi, c. </s>

<s>11) stampa&#039;o nel 1606. <pb xlink:href="020/01/1054.jpg" pagenum="497"></pb>Dall&#039;altra parte, se fossero stati veramente svolti, al modo che suol Galileo, <lb></lb>i pensieri accennati in quegli appunti, non sarebbe stato più vero che il <lb></lb>principale intento delle tre Lezioni fosse stato quello solo di dimostrar dove <lb></lb>avesse il luogo, o se si movesse la Stella. </s></p><p type="main">

<s>Con queste note insomma non intendeva Galileo di far altro, che di rac­<lb></lb>cogliere argomenti da provar la probabilità dell&#039;ipotesi del Gualtierotti, la <lb></lb>quale veniva così in certo modo a far sua, e come tale poi l&#039;avrebbe di­<lb></lb>stesa in un Discorso, di cui questa era la trama: s&#039;incominciava ad esami­<lb></lb>nare, per rifiutarle, tutte quelle ipotesi, che parevano meno probabili, delle <lb></lb>quali però non si trovano nel Manoscritto notate che queste due: “ Quod <lb></lb>Stella nova non sit pars Lactei circuli patet quia non dissolveretur, sicut <lb></lb>ipse Circulus non dissolvitur, adversus Ticonem ” (MSS. Gal., P. III, T. II, <lb></lb>c. </s>

<s>13). “ Stella nova non fuisse incendium patet ex eo quod quae citissime <lb></lb>incendunt brevi quoque extinguntur ” (Alb. </s>

<s>V, 395). Si concludeva questa <lb></lb>prima parte del Discorso colle parole: “ Et haec fere sunt quae meo iudi­<lb></lb>cio non sunt ” (ivi, pag. </s>

<s>393). </s></p><p type="main">

<s>“ Restat modo (così doveva cominciarsi la seconda parte) ut quod tan­<lb></lb>dem de hac admiranda apparitione sentiam in medium afferam ” (ivi) e dopo <lb></lb>essersi scusato se, per la difficoltà, non fossero i lettori rimasti sodisfatti <lb></lb>della sua opinione, passava ad annunziarla con queste parole: “ Quod circa <lb></lb>Terram eleventur vapores qui ascendentes Solis lumen reflectant, saepissime <lb></lb>apparet ” (ivi) e ne adduce gli esempi de&#039;crepuscoli e delle Aurore boreali, <lb></lb>e avrebbe poi voluto aggiungervi l&#039;esempio di quel cerchio che talvolta ap­<lb></lb>parisce intorno alla Luna e ch&#039;è dovuto al lume riflesso dai vapori conden­<lb></lb>sati (ivi, pag. </s>

<s>334). A rifletter poi il lume del Sole e a dar l&#039;apparenza di <lb></lb>stella, doveva dimostrarsi che bastava qualunque condensazione anche più <lb></lb>leggiera, e si potea desumer l&#039;argomento della dimostrazion dalle nuvole <lb></lb>“ quae veluti vastissimi montes in aere pendentes a Sole supra Lunam et <lb></lb>stellas omnes illuminantur, ita ut condensatio longe minor posset supra stel­<lb></lb>las illuminari ” (ivi). </s></p><p type="main">

<s>Esposta così l&#039;ipotesi e dimostratane la probabilità con questi e con altri <lb></lb>argomenti, che sarebbero via via sovvenuti, si doveva nella III Parte del <lb></lb>Discorso rispondere alle obiezioni, e prima di tutto persuader coloro, i quali <lb></lb>falsamente credevano non poter la luce venir riflessa che da qualche soli­<lb></lb>dissimo corpo (ivi, pag. </s>

<s>395). </s></p><p type="main">

<s>Agli altri che domandavano come potesse la Terra somministrar tanta <lb></lb>smisurata mole di esalazioni, quanta ne sarebbe stata necessaria a comporre <lb></lb>la Stella nuova, doveva rispondersi non aver ciò nulla dell&#039;impossibile “ vi­<lb></lb>demus enim aerem serenissimum, dicto citius expleri nubibus, et ex viridi <lb></lb>ligno exposito ad ignem, nulla sensibili eius facta diminutione, ingens fieri <lb></lb>in fumum evaporatio ” (ivi). </s></p><p type="main">

<s>A chi poi fosse curioso di saper come mai, evaporando sempre la Terra, <lb></lb>non si sieno nonostante vedute mai apparir le stelle circa e vicino a lei, <lb></lb>pensava di rispondere in questa maniera: “ Alcuni fuochi, che da lontano ap-<pb xlink:href="020/01/1055.jpg" pagenum="498"></pb>pariscono splendentissimi, da vicino non si veggono niente per la loro te­<lb></lb>nuità. </s>

<s>Così la Stella nuova può essere una esalazione illuminata, e chi vi <lb></lb>fosse vicino non la vedrebbe, e apparirebbe solo come i vapori elevati e illu­<lb></lb>minati la notte ” (ivi). </s></p><p type="main">

<s>Il discorso sopra l&#039;origine e l&#039;essere della Stella nuova, che doveva in­<lb></lb>tessersi da Galileo con questo ordito, fu lasciato da parte e non riman di <lb></lb>lui altro che queste fila. </s>

<s>Si potrebbe credere che ripensandoci meglio avesse <lb></lb>riconosciuta la mostruosità dell&#039;ipotesi del Gualtierotti, il quale facendo della <lb></lb>Stella uno strano composto di celeste e di terreno non poteva andare a ge­<lb></lb>nio nè ai seguaci di Aristotile, nè a quelli del Gilberto, meravigliati che il <lb></lb>professor di Padova non sentisse come prima e principale difficoltà contro <lb></lb>l&#039;ipotesi da lui favorita fosse quella dell&#039;essere affatto impossibile che una <lb></lb>materia terrea estravaghi così dalla sua sfera attrattiva. </s></p><p type="main">

<s>È un fatto però che Galileo non pensò mai a queste sfere attrattive, <lb></lb>nemmen quando l&#039;ipotesi della Stella nuova venne solennemente nel <emph type="italics"></emph>Sag­<lb></lb>giatore<emph.end type="italics"></emph.end> ad applicarla alla Cometa, e non sentendo perciò le difficoltà, che <lb></lb>gli si movevano contro dalla nuova scienza magnetica, lasciò di dare alle note <lb></lb>scritte forma di discorso, perchè era persuaso di avere incontrato in altra <lb></lb>diversa opinione “ che non abbia evidenti contradizioni e che perciò possa <lb></lb>esser vera ” (Alb. </s>

<s>VI, 27). </s></p><p type="main">

<s>La curiosità ci fruga e la importanza della cosa c&#039;invita a ricercar qual <lb></lb>fosse questo sentimento di Galileo circa la sostanza e generazione della Stella <lb></lb>nuova, per assicurarsi del qual sentimento soggiunge nel luogo sopra citato <lb></lb>“ mi è bisognato aspettare il ritorno di essa Stella in oriente, dopo la se­<lb></lb>parazione dal Sole, e di nuovo osservare con gran diligenza quali mutazioni <lb></lb>abbia fatto, sì nel sito, come nella visibile grandezza e qualità del lume. </s>

<s>E <lb></lb>continuando la speculazione sopra questa maraviglia, sono finalmente venuto <lb></lb>in credenza di poterne sapere qualche cosa di più di quello, in che la sem­<lb></lb>plice coniettura finisce. </s>

<s>E perchè questa mia fantasia si tira dietro o piut­<lb></lb>tosto si mette avanti grandissime conseguenze e conclusioni, però ho riso­<lb></lb>luto di mutar le Lezioni in una parte di Discorso, che intorno a questa <lb></lb>materia vo distendendo ” (ivi). </s></p><p type="main">

<s>Or qui nasce una nuova curiosità di sapere se quel Discorso fu vera­<lb></lb>mente disteso, e qual sia e dove si trovi. </s>

<s>Noi, che interpetriamo nel signi­<lb></lb>ficato di <emph type="italics"></emph>Dialogo<emph.end type="italics"></emph.end> quella parola <emph type="italics"></emph>Discorso,<emph.end type="italics"></emph.end> ritroviam questa <emph type="italics"></emph>parte di Dialogo<emph.end type="italics"></emph.end><lb></lb>autografa da c. </s>

<s>4-13 del T. II, P. IV de&#039;Manoscritti galileiani, e da c. </s>

<s>14-23 <lb></lb>del T. II, P. III troviam quegli appunti e quelle note, che sempre era so­<lb></lb>lito di preparar Galileo, prima di dar mano a distendere qualche scrittura. </s>

<s><lb></lb>Che tali appunti si riferiscano a questo soggetto se ne persuade facilmente <lb></lb>chiunque legge così a c. </s>

<s>23: “ Nota delle osservazioni fatte dai 13 Astro­<lb></lb>nomi, dove sono notate le altezze polari e le altezze della Stella nuova, tanto <lb></lb>le minime quanto le massime, prese nel meridiano. </s>

<s>” E chiunque attende a <lb></lb>quest&#039;altra nota, non dubita che non sieno scritte per dialogizzarsene il con­<lb></lb>cetto queste parole, che di Dialogo presentano già scolpitissime le forme: <pb xlink:href="020/01/1056.jpg" pagenum="499"></pb>“ Notabili belli: tutte le prove, che rendono le stelle sopra le fisse, sono <lb></lb>emendabili, non è vero? </s>

<s>— Sì. </s>

<s>— E le emendazioni le hanno a ritirare in <lb></lb>giù, non è vero? </s>

<s>— Sì. </s>

<s>— Ma nel ritornare in giù prima hanno a passar <lb></lb>per le fisse e poi per i Pianeti, avanti che vengano agli elementi.... ” <lb></lb>(ivi, c. </s>

<s>15 v.). </s></p><p type="main">

<s>Quel Dialogo dunque incomincia così nel Manoscritto sopra citato: <emph type="italics"></emph>“ Sa­<lb></lb>gredo.<emph.end type="italics"></emph.end> Ma che ci dice il signor Salviati in proposito delle Stelle nuove, son <lb></lb>elleno veramente state trasportate di cielo in queste più basse regioni, in <lb></lb>virtù de&#039;calcoli dell&#039;Autore prodotto dal signor Simplicio? </s>

<s>” E termina con <lb></lb>quest&#039;altre parole poste pure in bocca allo stesso Sagredo: “ E perchè mi <lb></lb>pare che assai chiaramente si sia dimostrata la differenza grande, che è tra <lb></lb>i motivi di quelli Astronomi e di questi loro oppugnatori, sarà bene che la­<lb></lb>sciata questa parte torniamo alla nostra principal materia. </s>

<s>” </s></p><p type="main">

<s>Chiunque getti lo sguardo sopra questa Scrittura, non esita a ricono­<lb></lb>scerla per una parte de&#039;Dialoghi dei due Massimi Sistemi, dove fu vera­<lb></lb>mente inserita nella III Giornata, da pag. </s>

<s>302-48 della edizione dell&#039;Albèri. </s>

<s><lb></lb>Nè il saperne l&#039;origine storica è da reputar di lieve importanza, prima perchè <lb></lb>ci si rende così la ragione come mai del Manoscritto degli stessi Due mas­<lb></lb>simi sistemi sien rimaste queste sole nove carte in anticipazione e separate <lb></lb>dal rimanente; poi, perchè di qui s&#039;argomenta che Galileo aveva infin da <lb></lb>quel tempo, non solo pensato a scrivere il suo libro sul Sistema del mondo, <lb></lb>ma che ne avea già scelti i personaggi interlocutori del Dialogo, a cui aveva <lb></lb>divisata la forma e l&#039;andamento. </s></p><p type="main">

<s>Essendo così, non s&#039;intende come non si sieno dati o non si diano final­<lb></lb>mente pace coloro, che rimpiangono la iattura delle tre Lezioni, avendo in­<lb></lb>teso dalla bocca dello stesso Galileo ch&#039;ei volle mutarle in un Discorso, da <lb></lb>lui poi inserito in un&#039;Opera, che non ha temuto fin qui nè temerà pericolo <lb></lb>di smarrimento o di morte. </s>

<s>Vero è che in quella parte di Discorso, scritto <lb></lb>propriamente contro il Lorenzini, e col solo intento di dimostrar che non <lb></lb>erano sbagliati i calcoli e le osservazioni, per le quali veniva il luogo della <lb></lb>Stella nuova a costituirsi nelle regioni stellari; non si legge nulla che ri­<lb></lb>guardi la generazione e la sostanza di essa stella, ma non è di questa iat­<lb></lb>tura da sentirne dolore, avendo Galileo provveduto alla sua gloria, prima, col <lb></lb>lasciare informe nei presi appunti quel Discorso, nel quale egli intendeva di <lb></lb>sostener la mostruosa ipotesi del Gualtierotti, e poi col non pensar più a <lb></lb>riformar quella ipotesi, che non sarebbe forse per questo riuscita punto mi­<lb></lb>gliore, mutando lo stesso primo Discorso latino in parte dello splendido dia­<lb></lb>logo italiano. </s></p><p type="main">

<s>Che qualunque altra ipotesi immaginata da Galileo non dovesse riuscir <lb></lb>punto migliore di quella, da lui già approvata, delle esalazioni terrestri su­<lb></lb>blimate in cielo e illuminate dal Sole, s&#039;argomenta dall&#039;esaminar le ipotesi <lb></lb>sovvenute in mente agli altri celebri Astronomi contemporanei, tutte per man­<lb></lb>canza di esperienza in qualche parte repugnanti alla natura dei fatti, non <lb></lb>eccettuata quella dello stesso Keplero, che asserì il nuovo splendore apparito <pb xlink:href="020/01/1057.jpg" pagenum="500"></pb>in cielo “ flammam fuisse quia ut flamma consumpta est quasi deficiente <lb></lb>alimento ” (De Stella nova, Pragae 1606, pag. </s>

<s>97). </s></p><p type="main">

<s>Benchè sempre si proceda (e come sarebbe stato possibile altrimenti?) <lb></lb>per vie congetturali, pure ipotesi alquanto più ragionevoli di quelle di Ga­<lb></lb>lileo e del Keplero, per tacere degli altri, incominciarono ad apparire nella <lb></lb>storia della scienza col Boulliaud, a cui succede, nel difficile magistero, il <lb></lb>nostro Montanari. </s>

<s>In un suo Discorso astronomico sopra la sparizione di al­<lb></lb>cune stelle, posto com&#039;appendice all&#039;Astrologia convinta di falso, dop&#039;aver <lb></lb>rifiutate le opinioni degli antichi, e le più recenti altresì del Cartesio e del <lb></lb>Riccioli, così soggiunge: </s></p><p type="main">

<s>“ E giacchè le Stelle fisse, a guisa di tanti Soli, di propria luce sono <lb></lb>dotate, come oggimai consentono tutti gli Astronomi da irrefragabili argo­<lb></lb>menti persuasi, io non veggo alcun inconveniente per dire che debbano esse <lb></lb>ancora soggiacere all&#039;incursione di queste macchie, che talora in molta quan­<lb></lb>tità crescendo loro attorno le oscurino, le impiccoliscano e le rinchiudano <lb></lb>affatto, ora per lunghissimi tempi, ora per brevi intervalli, ed ora a vicende, <lb></lb>giusta che la materia di cui si compongono in molta o poca copia si ra­<lb></lb>guna. </s>

<s>Se dunque d&#039;improvviso s&#039;adunano tali corpi intorno a una stella, <lb></lb>che per molti secoli esente da tali oscurità scintillò agli occhi nostri, eccola <lb></lb>impiccolire, eccola eziandio sparire dal cielo. </s>

<s>Se alcuna, che per l&#039;avanti <lb></lb>n&#039;ebbe sempre attorno di sè una quantità così costante, che per lungo tempo <lb></lb>fu stimata per esempio di quarta grandezza, d&#039;improvviso se ne sgombra la <lb></lb>faccia, eccola tutta rilucente prenden luogo fra quelle di seconda e di prima <lb></lb>maestà. </s>

<s>Se taluna, condannata per molti secoli ad un&#039;oscura carcere fra que­<lb></lb>ste macchie, rompe talora i ceppi, sboccando il rinchiuso fuoco, eccola nuova <lb></lb>e non più veduta Stella agli occhi nostri palesarsi illustrando d&#039;inusitati <lb></lb>raggi quella parte del Cielo. </s>

<s>E se di nuovo, aggregandosi tali macchie, alle <lb></lb>primiere tenebre viene ristretta, eccone perdute le vestigia, eccone annichi­<lb></lb>lato il fulgore. </s>

<s>Che se da una sola parte del di lei corpo s&#039;apre luogo al­<lb></lb>l&#039;interno fulgore, ed abbia intorno al proprio centro un moto periodico, la <lb></lb>vedrete, non men di quella del Bullialdo nella Balena, a determinati tempi <lb></lb>apparire, fino a tanto che nuove aggregazioni di macchie o nuova aper­<lb></lb>tura delle medesime alcuna inaspettata varietà v&#039;introduca ” (Venezia 1685, <lb></lb>pag. </s>

<s>21, 22). </s></p><p type="main">

<s>Così alla felice ipotesi inspirata al Boulliaud dal principio kepleriano, <lb></lb>che ruotino le stelle fisse in sè stesse, come ruota il Sole, e per la quale <lb></lb>non si spiegava altro che il loro apparire e disparire in certi periodi di <lb></lb>tempo; il nostro Montanari ne sostituiva un&#039;altra non men ragionevole ipo­<lb></lb>tesi, per la quale si spiegano i fatti più curiosi, che ora in crescere ora in <lb></lb>diminuir di grandezza, senz&#039;ordine apparente, presentano alcune Stelle agli <lb></lb>attenti osservatori. </s>

<s>E perchè a questa ipotesi hanno fatto plauso gli stessi <lb></lb>Astronomi plù recenti, si può dir che qui rimanesse assoluta questa parte <lb></lb>di Fisica stellare, oggetto di tanta maraviglia al volgo, e occasione di tante <lb></lb>strane congetture al Filosofo. </s>

<s>È da passar perciò ora a vedere gli impulsi <pb xlink:href="020/01/1058.jpg" pagenum="501"></pb>che vennero, e i progressi che fece l&#039;Astronomia in contemplar la celeste <lb></lb>vòlta stellata, quando s&#039;apri un nuovo spettacolo alla vista dal portentoso <lb></lb>artificio del Canocchiale. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Primo a riferire ai mortali questo stupendo spettacolo, contemplato nel <lb></lb>cielo, fu Galileo, il quale ebbe a notar come cosa inaspettata che le Stelle <lb></lb>fisse osservate col Telescopio non ricrescevano in grandezza a quella pro­<lb></lb>porzione che tutti gli altri oggetti sogliono, non eccettuata la Luna. </s>

<s>Intese <lb></lb>che ciò dipendeva dall&#039;irradiazione ascitizia, gli effetti della quale in alterar <lb></lb>l&#039;apparente grandezza delle stelle furono soggetto di diligenti studii agli <lb></lb>astronomi, quando il progredir delle scienze accese in loro più che mai vivo <lb></lb>il desiderio di farsi almeno un&#039;idea di ciò che siano, rispetto al piccolo no­<lb></lb>stro, quegli smisurati lucenti mondi lontani. </s></p><p type="main">

<s>Galileo aveva, dall&#039;esperienza fatta del suo debole strumento, concluso: <lb></lb>“ fixae vero Stellae periphaeria circulari nequaquam terminatae conspiciun­<lb></lb>tur sed veluti fulgores quidam radios circumcirca vibrantes ” (Alb. </s>

<s>III, 74) <lb></lb>e il vederle terminate in circoli e senza raggi dipendeva da certi artificii, <lb></lb>che sovvennero poi più tardi in mente agli Astronomi. </s>

<s>L&#039;Huyghens faceva <lb></lb>consistere uno di questi semplici artificii nel tinger leggermente l&#039;oculare <lb></lb>di un color nero o di filiggenne o di brace, in cui veniva così a spengersi <lb></lb>intorno all&#039;occhio la luce erratica, che le stelle apparivano quasi come punti <lb></lb>matematici senza sensibile grandezza. </s></p><p type="main">

<s>Ma si debbono allo stesso Huyghens ben altri più laboriosi artificii, da <lb></lb>lui inventati, per dar sodisfazione tutt&#039;insieme a chi volesse contemplar le <lb></lb>Stelle per suo diletto, e a chi volesse osservarle con intendimento di scienza. </s>

<s><lb></lb>Descrisse quegli artificii in una sua operetta latina, che ha il titolo di <emph type="italics"></emph>Astro­<lb></lb>scopia compendiaria Tubi optici molimine liberata,<emph.end type="italics"></emph.end> della quale il Viviani, <lb></lb>da c. </s>

<s>136-47 del Tomo CXXXVIII de&#039;Discepoli di Galileo, lasciò manoscritta <lb></lb>una bella traduzione italiana. </s></p><p type="main">

<s>Incomincia l&#039;Autore dell&#039;Astroscopia a dire com&#039;essendosi tutte le spe­<lb></lb>ranze di coloro, che attendevano al perfezionamento dei Canocchiali, appun­<lb></lb>tate nel fabbricare oggettivi di gran distanza focale, per la quale bisogna­<lb></lb>vano lunghissimi tubi, difficilissimi, anche coi macchinamenti inventati in <lb></lb>Firenze dal Del Buono e dal Campani in Roma, a maneggiarsi; egli avesse <lb></lb>rimossa ogni difficoltà, posando la lente oggettiva sopra una lunga antenna, <lb></lb>e accomodando l&#039;oculare presso all&#039;osservatore, in un tubo collocato a con­<lb></lb>veniente distanza. </s>

<s>Il modo di volgere e addirizzare a piacere il cristallo, per <lb></lb>mezzo di carrucole e di fili, che venissero alla mano dello stesso osserva­<lb></lb>tore, son dall&#039;Huyghens particolarmente descritti, ma quel che più importa <pb xlink:href="020/01/1059.jpg" pagenum="502"></pb>è ciò che riguarda l&#039;oculare preparato per le osservazioni più squisite così, <lb></lb>come riferiscono tradotte dal Viviani le parole seguenti: </s></p><p type="main">

<s>“ Ma adesso aggiungeremo altro di più, per cui rendere più perfetto <lb></lb>questo nostro modo di osservare, benchè se si tralasciasse non pregiudiche­<lb></lb>rebbe punto, ma però non deve disprezzarsi dal curioso osservator delle <lb></lb>stelle. </s>

<s>E pertanto, mentre io cercavo con maggior diligenza i Pianeti cassi­<lb></lb>niani di Saturno, e che difficilmente io gli trovava, in particolare nelle notti <lb></lb>non oscurissime, m&#039;accorsi avvenir ciò da una certa debole luce, che dal­<lb></lb>l&#039;aria veniva all&#039;occhio, non già quella che viene per la lente maggiore, <lb></lb>ma quella che scappa fuori dalle bande. </s>

<s>Per escludere questa tale impor­<lb></lb>tuna luce io sapeva che avrebbe alquanto giovato, se qui ancora intorno <lb></lb>alla lente maggiore avessi posto quel cerchio di carta, di cui io mi serviva <lb></lb>nell&#039;osservare la Luna. </s>

<s>Ma stando applicato a ciò, mi sovvenne un altro più <lb></lb>efficace rimedio, da unirsi a quello, cioè coll&#039;apporvi una lamina bucata, <lb></lb>acciò la pupilla dell&#039;occhio venisse a restringersi, quando per altro ella è <lb></lb>solita nelle tenebre di dilatarsi molto. </s>

<s>Di che, subito che io feci sperienza, <lb></lb>veddi chiaramente tutt&#039;e tre le Stelle di Saturno, che poi, levato quel pic­<lb></lb>col foro, non ne vedevo altro che la mia di mezzo ” (c. </s>

<s>130). </s></p><p type="main">

<s>Dalla semplice osservazione de&#039;fatti, che mostravano quanto nocesse alla <lb></lb>visione distinta delle stelle, e quanto ne alterasse l&#039;apparente grandezza l&#039;ir­<lb></lb>radiazione avventizia, si passò ad istituire particolari esperienze per misurar <lb></lb>quanto, in un Canocchiale di una lunghezza data, ricrescesse l&#039;immagine, <lb></lb>per effetto della stessa irradiazione. </s>

<s>Il Picart, con un Telescopio di tre piedi, <lb></lb>osservava, a una distanza di 191,382 di que&#039;piedi, una fiamma di latitudine <lb></lb>tripedale, e la trovò sottendere un angolo di 8″, mentre che non sarebbe <lb></lb>dovuto quell&#039;angolo riuscir maggiore di 3″, 14tʹ. </s>

<s>Fu questa esperienza delle <lb></lb>prime, che servirono al Newton per confermar la sua teoria, la quale con­<lb></lb>cludevasi in dire che, per l&#039;ineguale refrangibilità della luce, tutti i punti <lb></lb>luminosi occupano nel foco dell&#039;obiettivo uno spazio circolare di tal lar­<lb></lb>ghezza, che è quasi la cinquantesima parte dell&#039;apertura del vetro. </s>

<s>“ Ita ta­<lb></lb>men, soggiunge, ut lux in circuitu rarissima vix, aut ne vix quidem sen­<lb></lb>tiatur, in medio vero, ubi constipatior est, sensumque satis ferit, lucidum <lb></lb>constituat circellum, cuius latitudo pro splendore puncti lucentis varia sit, <lb></lb>ac tertiam circiter, quartamve, aut quintam fere partem latitudinis totius, <lb></lb>ut plurimum, adaequet ” (De Mundi systemate, Opuscul., T. II, Lausan­<lb></lb>nae 1744, pag. </s>

<s>15, 16). </s></p><p type="main">

<s>Così veniva in qualche modo a spiegarsi, ne&#039;principii del secolo XVIII, <lb></lb>come punti quasi matematici si rendessero alla retina del nostro occhio sen­<lb></lb>sibili, e come sopr&#039;essa retina operando que&#039;punti lucidi con alternati moti, <lb></lb>che si direbbero di sistole e di diastole, apparissero scintillanti. </s></p><p type="main">

<s>Che sia la scintillazione propria alle Stelle fisse erasi riconosciuto già <lb></lb>anche dall&#039;occhio nudo, ma Galileo se ne assicurò meglio col Telescopio, <lb></lb>che gli mostrava que&#039;raggi vibrarsi tutto intorno dal nucleo della Stella <lb></lb>“ atque admodum scintillantes ” (Alb. </s>

<s>III, 75). Nè qui nel Nunzio sidereo <pb xlink:href="020/01/1060.jpg" pagenum="503"></pb>però, nè altrove, per le varie opere galileiane stampate, ci sovvien d&#039;aver <lb></lb>letto nulla in proposito della ragione del fenomeno misterioso. </s>

<s>Solo a c. </s>

<s>11 <lb></lb>del T. II, P. III, ci siamo abbattuti a leggere questa nota manoscritta: “ Kep­<lb></lb>plerus <emph type="italics"></emph>De stella nova<emph.end type="italics"></emph.end> car. </s>

<s>95 de scintillatione ait fieri posse ex rotatione <lb></lb>fixarum. </s>

<s>Et licet ad ipsas Sol insensibilis omnino sit, ut a nobis eo consti­<lb></lb>tutis nulla ratione videri possit; tamen non evanescit ipsis, nam et consi­<lb></lb>derat quod multo citius evanescit illuminatio corporis lucidi, quam conspectus <lb></lb>eiusdem, et sic a longissima distantia videmus facem ardentem, quae cor­<lb></lb>pora nobis adiacentia non illustrat. </s>

<s>” </s></p><p type="main">

<s>Si potrebbe dubitar se avesse Galileo presa quella nota per confutare <lb></lb>il detto del Keplero o per approvarlo, ma riscontrando che la considerazione <lb></lb>ivi fatta, per salvar dalle opposizioni quella ipotesi, non è propriamente del <lb></lb>Keplero, si può argomentar che Galileo la commentasse, coll&#039;intenzione di <lb></lb>professarla. </s>

<s>Giova poi di vedere in che quel commento particolarmente con­<lb></lb>sista, perchè di qui ne scende una conclusione importante ed è, che Gali­<lb></lb>leo partecipava a quel tempo in tutto colle idee singolari professate dall&#039;Au­<lb></lb>tor del trattato <emph type="italics"></emph>De Stella nova,<emph.end type="italics"></emph.end> al Cap. </s>

<s>VIII del quale vien perciò richiamata <lb></lb>la nostra attenzione. </s></p><p type="main">

<s>Aveva già lo Scaligero esercitato le sottigliezze del suo ingegno anche <lb></lb>intorno al fenomeno della scintillazione, riducendolo a cinque cause conco­<lb></lb>mitanti, che son per lui la grandezza, lo splendore e il moto della Stella, <lb></lb>il mezzo dell&#039;aria, e il moto della luce, che è in tempo e no in istante. </s>

<s>Parve <lb></lb>al Keplero di dover tenere altra via più facile e più naturale, che gli si <lb></lb>presentò in un fatto occorsogli ad osservare in que&#039;festoni (<emph type="italics"></emph>uniones<emph.end type="italics"></emph.end>), e in <lb></lb>que&#039;pendagli di cristallo, di che si sogliono ornar le lumiere. </s>

<s>Stava una sera <lb></lb>seduto tutto solo nell&#039;anticamera del palazzo imperiale, e attentamente guar­<lb></lb>dava quel cangiar di colore, e quello scintillare che facevano i prismi cri­<lb></lb>stallini, velocemente rotando intorno al loro punto di sospensione, per il <lb></lb>moto impresso, nell&#039;accendersi, alla lumiera. </s>

<s>Ecco disse allora spiegato il fatto: <lb></lb>le stelle son di una sostanza diafana, cristallina e angolosa, e rotando in sè, <lb></lb>illuminate dal Sole, presentano la varietà di colori e lo scintillamento, come <lb></lb>i pendagli della stessa lumiera. </s>

<s>“ Quare non metuo ut perpetua esse non <lb></lb>possint corpora stellarum, si angulose aut si intus inaequaliter densa sunt, <lb></lb>ut solent <emph type="italics"></emph>Uniones<emph.end type="italics"></emph.end> partibus aliis aliter pellucidi..... Tum autem ipsa per <lb></lb>se rotatio fixarum magna probabilitate, magnis exemplis nititur. </s>

<s>Sed exem­<lb></lb>plum solus Copernicus dederit hanc nostram Tellurem quae, ut undequa­<lb></lb>que Soli conspectu frui possit, rotatur in dies singulos, seseque quasi assat <lb></lb>ad hunc ignem. </s>

<s>Credibile est igitur et Planetas et fixas omnes quosque in <lb></lb>suis rotari spatiis, ne sit aliquid in Mundo quod centri nobilissimi corporis, <lb></lb>radiis vitalibus et lumine splendidissimo, penitus privetur ” (Pragae 1606, <lb></lb>pag. </s>

<s>94, 95). </s></p><p type="main">

<s>V&#039;erano queste grandi difficoltà però, che guastavano la seducente fa­<lb></lb>cilità dell&#039;ipotesi: l&#039;azione del Sole dee per l&#039;immensa lontananza riuscire <lb></lb>insensibile sopra le Stelle, le quali, essendo dall&#039;altra parte così corpulente, <pb xlink:href="020/01/1061.jpg" pagenum="504"></pb>non possono convertirsi in sè stesse tanto veloci, quanto mostra il vederle <lb></lb>ad ogni istante cangiar colori. </s>

<s>Alla prima delle quali difficoltà rispondeva il <lb></lb>Keplero: “ Non enim evanescit Sol ipsi rerum naturae.... quia forte, et <lb></lb>omnino quidem nostris oculis illic constitutis evanesceret, nec enim aequum <lb></lb>est, nostra visus hebetudine, vim aestimare et acumen Naturae ” (ibi, pag. </s>

<s>95). <lb></lb>Rispondeva alla seconda: “ Si multas habent partes eiusmodi, quales dixi­<lb></lb>mus scintillationibus et coloribus servire.... iam non est necesse ut quo­<lb></lb>ties una emicat scintillatio, toties una integra sit absoluta rotatio, sed, ut <lb></lb>rota multos clavos, sic haec corpora multos angulos, multa fulgura, unica <lb></lb>rotatione exserere videntur ” (ibi). </s></p><p type="main">

<s>E giacchè il Keplero non dà per risposta alle due difficoltà altro che <lb></lb>queste due ragioni, è un commento dunque di Galileo la considerazione, che <lb></lb>più presto svanisce al nostr&#039;occhio l&#039;illuminazione degli oggetti circostanti, <lb></lb>che non l&#039;aspetto lontano del corpo illuminante. </s>

<s>Quanto erano lontani i due <lb></lb>grandi uomini dal sollevare ancora a quelle alture, a cui sollevarono poi l&#039;ala <lb></lb>del potentissimo ingegno! Chi crederebbe che gli Autori dell&#039;<emph type="italics"></emph>Epitome Astro­<lb></lb>nomiac copernicanae,<emph.end type="italics"></emph.end> e de&#039;Dialoghi intorno i due Massimi Sistemi, dentro <lb></lb>il primo decennio del secolo XVII, professassero idee così basse intorno al­<lb></lb>l&#039;essere delle Stelle, rassomigliate a cristalli sfaccettati, che rotano intorno <lb></lb>al Sole, per goder d&#039;ogni parte i benefici raggi della sua luce e del suo ca­<lb></lb>lore? </s>

<s>Vero è bene che Galileo, quando si persuase che le stelle avevano luce <lb></lb>propria, e che non era perciò più accettabile l&#039;ipotesi del Keplero, si ridusse a <lb></lb>dire che le stelle stesse scintillano, perchè a differenza dei Pianeti “ fulgorem <lb></lb>ab intra emittunt ” (Alb. </s>

<s>XIV, 331 e VI, 154), ma, oltre che non si rendeva <lb></lb>così la ragione del cangiare ad ogni istante colore, rimaneva a saper come <lb></lb>mai l&#039;emetter la luce <emph type="italics"></emph>ab intra<emph.end type="italics"></emph.end> producesse quell&#039;irrequieto scintillare sì vivo. </s>

<s><lb></lb>Sembra insomma a noi questo secondo passo di Galileo un ritrarsi indietro, <lb></lb>e anzi quasi un delirare dal vero, la diritta via del quale era segnata già <lb></lb>dallo Scaligero, e un altro italiano, Maestro insigne di fisica sperimentale, vi <lb></lb>aveva impresse orme così profonde, che, dietro a quelle procedendo i mo­<lb></lb>derni, riuscirono finalmente a sapere perchè, guardate attraverso alla no­<lb></lb>str&#039;aria vaporosa, si veggano in cielo coruscare le Stelle. </s></p><p type="main">

<s>Giovan Battista Benedetti, nelle sue Disputazioni <emph type="italics"></emph>De quibusdam placitis <lb></lb>Aristotelis,<emph.end type="italics"></emph.end> così, a Galileo e al Keplero che non vollero ascoltarlo, insegnava <lb></lb>la ragione dello scintillar delle fisse, non cavata dalle finzioni della mente, <lb></lb>ma dall&#039;analogia che passa tra il fenomeno celeste, e alcuni fatti naturali at­<lb></lb>tentamente osservati. </s>

<s>“ Ubi Aristotiles ait scintillationem stellarum fieri ra­<lb></lb>tione aspectus nostri, ob maximam distantiam, maximum errorem committit, <lb></lb>ut etiam facit cum putat visionem fieri extramittendo, contra id quod alio <lb></lb>loco, immo contra veritatem ipsam, asseruit. </s>

<s>Scintillatio ergo stellarum, ne­<lb></lb>que aspectus nostri ratione, neque alicuius mutationis earumdem stellarum, <lb></lb>sed ab inaequalitate motus corporum diaphanorum mediorum nascitur, que­<lb></lb>madmodum clare cernitur, quod si inter aliquod obiectum et nos alliquis <lb></lb>fumus, qui ascendat, intercesserit, videbimus obiectum illud quasi tremere. <pb xlink:href="020/01/1062.jpg" pagenum="505"></pb>Hoc autem tanto magis fiet, quanto magis distabit obiectum ab ipso fumo, <lb></lb>unde admirationi locus non erit, si stellas fixas magis scintillare quam er­<lb></lb>rantes cernamus. </s>

<s>Lumen stellae ad oculum nostrum accedens perpetuo per <lb></lb>diversas diaphaneitates penetrat, medio continuorum motuum corporum me­<lb></lb>diorum, unde continuo eorum lumen variatur, et hoc in longinquis, magis <lb></lb>quam in proprinquis stellis, apparet, quemadmodum ab exemplo de fumo <lb></lb>allato, et etiam ab aliquibus vitris, ex superficie non plana sed irregu­<lb></lb>lari constantibus, quilibet cognoscere potest ” (Speculationum Liber, Vene­<lb></lb>tiis 1599, pag. </s>

<s>186). </s></p><p type="main">

<s>Lasciando considerare ai lettori quanto fossero feconde di verità queste <lb></lb>speculazioni del Fisico veneziano, a dimenticar le quali ebbero gl&#039;Italiani i <lb></lb>perniciosi esempi da Galileo, è da tornare a dir di un altro magnifico spet­<lb></lb>tacolo, che le Stelle osservate col Canocchiale offersero di sè, e che lo stesso <lb></lb>Galileo fu per avventura de&#039;primi a riferire agli attoniti mortali: “ Perspi­<lb></lb>cilli beneficio, egli dice, maiores et clariores apparent, quam magnitudinis <lb></lb>secundae Sidera acie naturali visa. </s>

<s>Ut autem de inopinabili fere illarum fre­<lb></lb>quentia unam alteramve attestationem videas, Asterismos duos subseribere <lb></lb>placuit, ut ab eorum exemplo de caeteris iudicium feras ” (Alb. </s>

<s>III, 75). </s></p><p type="main">

<s>Il primo di quegli Asterismi rappresenta la costellazione di Orione, che <lb></lb>aveva in animo di rappresentare intera “ verum ab ingenti stellarum copia, <lb></lb>temporis vero inopia obrutus, aggressionem hanc in aliam occasionem di­<lb></lb>stuli ” (ibi). Nè mancò Galileo al proposito, ripigliando con più cura a de­<lb></lb>scrivere quello stesso Asterismo di Orione, specialmente rispetto a quelle <lb></lb>stelle che sono intorno al Cingolo, e le rappresentò in una Mappa, inserita <lb></lb>a c. </s>

<s>12 del T. VI, P. IV, scrittovi in fronte di propria mano “ Circa cingu­<lb></lb>lum Orionis. </s>

<s>” </s></p><p type="main">

<s>Il secondo degli Asterismi, descritti nel Nunzio Sidereo, è quello delle <lb></lb>Pleiadi, e benchè si contenti il frettoloso Autore di dar questi due soli per <lb></lb>saggi, parecchi altri se ne trovano qua e là dispersi pe&#039;Manoscritti. </s>

<s>Noi ci <lb></lb>contenteremo di citar quelli, che si veggono disegnati nelle c. </s>

<s>2, 18 e 28 <lb></lb>del T. VI, P. IV, senz&#039;alcuna indicazione, e l&#039;altro a c. </s>

<s>29 del medesimo <lb></lb>Tomo, che porta di mano dell&#039;Autore scritto il nome della <emph type="italics"></emph>Canicula.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>A tergo della c. </s>

<s>32, T. III, P. III, è un altro Asterismo, distinto di punti <lb></lb>semplici, a rappresentare le stelle minori, e di punti irraggiati a rappresen­<lb></lb>tar le maggiori, e l&#039;Autore stesso lo notò colle parole <emph type="italics"></emph>exquisita descriptio.<emph.end type="italics"></emph.end><lb></lb>Tanto lavoro è rimasto ora senza frutto per noi, e senza merito per chi lo <lb></lb>fece, eppure quelle Mappe, collazionate colle moderne, potrebbero tornare <lb></lb>utilissime alla scienza, e in ogni modo le dovrebbe la Uranografia tenere in <lb></lb>pregìo e aver care, come la Geografia tiene in pregio e ha care le relazioni, <lb></lb>benchè imperfette, de&#039;primi esploratori. </s>

<s>Galileo s&#039;era forse proposto di rac­<lb></lb>cogliere quelle Mappe, e il frutto delle sue fatiche, nel libro delle <emph type="italics"></emph>Novità <lb></lb>celesti,<emph.end type="italics"></emph.end> ma perchè al suo proposito, qualunque se ne fosse la causa, venne <lb></lb>meno l&#039;Autore, pareva che v&#039;avesse dovuto supplire l&#039;amorosa sollecitudine <lb></lb>degli editori. </s></p><pb xlink:href="020/01/1063.jpg" pagenum="506"></pb><p type="main">

<s>Benchè questi Asterismi, e specie l&#039;ultimo citato, sieno stati tutti esqui­<lb></lb>sitamente descritti, e degli stessi due primi riferiti nel Nunzio si dica “ in­<lb></lb>terstitia, quo exactius licuit, servavimus ” (Alb. </s>

<s>III, 75) furono nonostante <lb></lb>quegli interstizi presi a occhio, e anzi a occhio tutte intere ritratte in dise­<lb></lb>gno le Mappe. </s>

<s>A tergo però della c. </s>

<s>31 del Tomo manoscritto ultimamente <lb></lb>citato, si vede indicata una stella colle parole: “ canem minorem credo ” <lb></lb>e sotto si legge la nota: “ Stella A absque Specillo non cernitur, attamen <lb></lb>Specillo inspecta, apparet tantae magnitudinis, ut infra ipsam aliae secun­<lb></lb>dae, tertiae, et quartae magnitudinis conspiciantur. </s>

<s>” Presso a questo Aste­<lb></lb>rismo, nella medesima carta, si vede disegnato l&#039;altro del Cane maggiore, <lb></lb>con le precise misure delle distanze delle stelle minori dalla maggiore, e <lb></lb>colla dichiarazione: “ Circa Canem, praeter alias, extant stellulae 7, in con­<lb></lb>simili configuratione (fig. </s>

<s>99) quarum maxima a Cane distantia non supe­<lb></lb>rat minuta 20. ” </s></p><p type="main">

<s>Queste misure in minuti di grado furono senza dubbio prese da Gali­<lb></lb>leo col primo strumento micrometrico, descritto nel <emph type="italics"></emph>Nunzio,<emph.end type="italics"></emph.end> e i tentativi <lb></lb><figure id="id.020.01.1063.1.jpg" xlink:href="020/01/1063/1.jpg"></figure></s></p><p type="caption">

<s>Figura 99.<lb></lb>che bisognava fare, e il tempo che si dovea per­<lb></lb>dere, per trovar qual fosse quell&#039;apertura di foro <lb></lb>nella lamina, che rispondesse per l&#039;appunto all&#039;os­<lb></lb>servazione, ci rispondono perchè non si trovi de­<lb></lb>signata, colle misure precise delle distanze, altro <lb></lb>che questa poca parte dell&#039;Asterismo del Cane. </s>

<s>Ma <lb></lb>quando ebbe pensato a quell&#039;altro strumento mi­<lb></lb>crometrico, col quale si potevano misurar gl&#039;inter­<lb></lb>stizi fra stella e stella, per mezzo del Rastrello o <lb></lb>del Reticolo, contrapposto alla mira del Canocchiale, e allora Galileo meditò <lb></lb>un gran progetto, ed era quello di ridurre in Mappe tutta una estesa re­<lb></lb>gione del Cielo. </s>

<s>A collaborare all&#039;opera aveva chiamato il Castelli, a cui <lb></lb>insegnò l&#039;uso dello Strumento, e a cui riuscì di por qualche rimedio a uno <lb></lb>de&#039;maggiori inconvenienti, che presentava esso Strumento, accomodando la <lb></lb>lanterna da illuminare il Reticolo in modo, che non abbagliasse la vista al­<lb></lb>l&#039;osservatore, e che si potessero perciò discerner da lui anco le più pic­<lb></lb>cole stelle. </s></p><p type="main">

<s>A questo negozio, di non lieve importanza nella storia della scienza, ac­<lb></lb>cennava il Castelli stesso così con queste parole, in una lettera indirizzata a <lb></lb>Galileo, il dì 7 Gennaio 1617 da Pisa: “ Per l&#039;osservazione della Canicola <lb></lb>ho ritrovato un luogo, nel quale si potrà collocare il lumicino, e di poi al­<lb></lb>lontanarsi 150 braccia in circa per osservare, e quanto prima il tempo mi <lb></lb>dia licenza, mi metterò all&#039;opera. </s>

<s>Venere lavora tuttavia, ma non è ancora <lb></lb>ridotta al semicircolo. </s>

<s>Non manco d&#039;andare in busca di Stelle fisse, ma non <lb></lb>trovo cosa al proposito, fuorchè la avvisata nella passata. </s>

<s>Desidererei che <lb></lb>V. S. E., concedendoglielo la sanità, una sera desse un&#039;occhiatina a quella <lb></lb>stella di mezzo, delle tre che sono nella coda dell&#039;Orsa maggiore, perchè è <lb></lb>una delle più belle cose che sia in cielo, e non credo che per il nostro ser-<pb xlink:href="020/01/1064.jpg" pagenum="507"></pb>vigio si possa desiderar di meglio in quelle parti ” (MSS. Gal., P. III, T. VII, <lb></lb>Sez. </s>

<s>II, c. </s>

<s>62). </s></p><p type="main">

<s>Della raccolta de&#039;frutti, che sì prometteva ubertosa, non sappiamo dir <lb></lb>niente. </s>

<s>Solo a tergo della c. </s>

<s>31, T. III, P. III, si trova preparato un Reti­<lb></lb>colo, esteso da 24 a 34 gradi di latitudine, <lb></lb>e da 46 a 54 gradi di longitudine, nelle ma­<lb></lb><figure id="id.020.01.1064.1.jpg" xlink:href="020/01/1064/1.jpg"></figure></s></p><p type="caption">

<s>Figura 100.<lb></lb>glie del quale però non si trovano situate <lb></lb>al loro luogo altro che pochissime stelle, <lb></lb>come nella rappresentazione della fig. </s>

<s>100 <lb></lb>si vede. </s>

<s>Ma dovevano esser capitate in mano <lb></lb>al Viviani altre carte galileiane, dove l&#039;Au­<lb></lb>tore stesso descriveva lo strumento micro­<lb></lb>metrico, descritto poi dal Borelli, e dove <lb></lb>altresì insegnava a far uso di quello stesso <lb></lb>strumento per misurar gli interstizi fra stella <lb></lb>e stella, con qualche altro saggio forse di <lb></lb>così fatta applicazione. </s>

<s>Di quelle carte è <lb></lb>veramente a doler la jattura, e non di tante <lb></lb>altre scritture galileiane, perdute perchè <lb></lb>non fatte, o perdute solamente di nome, <lb></lb>ma delle quali non san darsi pace i ciechi adoratori del Divino filosofo. </s></p><p type="main">

<s>Il Viviani del contenuto in quelle carte galileiane, ch&#039;egli ebbe in mano, <lb></lb>e che sono ora smarrite, ne conferi una volta col Cassini, a cui rifiorirono <lb></lb>quelle idee nella memoria e rinverdirono le speranze, quando sentì vivo il <lb></lb>bisogno di una diligente descrizion delle stelle, per riscontrarne le miste­<lb></lb>riose vicende, e investigar la causa del Ioro mutar grandezza, e ora appa­<lb></lb>rire improvvise in cielo, ora nuovamente sparire. </s></p><p type="main">

<s>“ Quando eramo insieme a veder Saturno, scriveva il Cassini stesso al <lb></lb>Viviani da Bologna il di 6 Agosto 1661, notai che non appariva più in cielo <lb></lb>la stella risorta nel petto del Cigno. </s>

<s>Ma giunto in Bologna in tempi sere­<lb></lb>nissimi l&#039;ho veduta ridotta alla piccolezza delle tre stelline prossime nel prin­<lb></lb>cipio del collo, nello stesso sito, come per due anni l&#039;ho osservata, e dove <lb></lb>nel tempo della prima apparizione fu descritta dal Keplero e dal Baiero. </s>

<s>Es­<lb></lb>sendo scemata, dall&#039;anno passato in qua, dalla terza alla quinta grandezza, <lb></lb>è probabile che abbi di nuovo a sparire, come già un&#039;altra volta ha fatto <lb></lb>in questo secolo, onde non sarebbe inutile seguitarla con esquisitissimi oc­<lb></lb>chiali, per rintracciare al possibile la cagione di questa singolarità. </s>

<s>Spero <lb></lb>che anco dalle stelle fisse abbiamo ad imparare novità non più immaginate. </s>

<s><lb></lb>E però di qui prendo occasione d&#039;animar V. S. alla perfezione del gran di­<lb></lb>segno, abbozzato da Galileo ne&#039;Manoscritti che mi conferi, intorno l&#039;esatta <lb></lb>osservazione di esse, giacchè sotto la protezione de&#039;Serenissimi principi non <lb></lb>le può mancare tutte le più desiderabili comodità di sodisfarsi a pubblico <lb></lb>beneficio ” (MSS. Gal. </s>

<s>Disc., T. CXLIV, c. </s>

<s>193). </s></p><p type="main">

<s>Che si potesse, del resto, anche dalle Stelle fisse imparar novità non <pb xlink:href="020/01/1065.jpg" pagenum="508"></pb>più immaginate lo avevano, assai prima del Cassini, riconosciuto Galileo e <lb></lb>il Castelli, i quali, sopra a tutto quel che si potesse sperare dall&#039;Astronomia, <lb></lb>chiamarono quelle stesse Fisse, non men dei Pianeti e del Sole “ a com­<lb></lb>parire in giudizio a render testimonianza del moto a favor della Terra ” <lb></lb>(Alb. </s>

<s>I, 415). </s></p><p type="main">

<s>A c. </s>

<s>10 del T. VI, P. IV de&#039;Manoscritti galileiani, si trovano autografe <lb></lb>due notarelle, chi legge le quali riman sorpreso di maraviglia, che Galileo <lb></lb>si sia trattenuto in cose tanto elementari, come son queste: “ Polis con­<lb></lb>versionis diurnae in Terra immutabilibus et fixis existentibus, immutabilis <lb></lb>permanet Aequinoctialis, et ad eumdem terrestris superficiei punctum neuter <lb></lb>Aequatoris polorum attollitur aut deprimitur unquam, sed invariabilis sem­<lb></lb>per remanet eiusdem loci eadem elevatio poli, quae solummodo mutatur dum <lb></lb>in superficie Terrae ad Aequatorem vel ad Polum accedimus. </s>

<s>— Extenso <lb></lb>terrestris Aequatoris plano et axe usque ad fixas, si quae fixa in axe stete­<lb></lb>rit, et si stellae in plano Aequatoris reperiantur, circulum maximum desi­<lb></lb>gnare videbuntur, reliquarum vero unaquaeque circulum describere appa­<lb></lb>rebit, eo minorem quo ab ipso Aequatoris plano remotior fuerit, et quae ad <lb></lb>aliquem locum verticales fuerint, semper verticales erunt, quamdiu ad pla­<lb></lb>num Aequatoris elongationem servabunt. </s>

<s>” </s></p><p type="main">

<s>Fa maraviglia, ripetiamo, il trovar fra le peregrine speculazioni di Ga­<lb></lb>lileo queste cose notissime agli stessi fanciulli, ma la maraviglia cesserà in <lb></lb>chi intende non esser questo se non che il principio a un discorso, che si <lb></lb>voleva concludere in questo modo: Se la Terra è immobile sul suo asse e <lb></lb>ne&#039;suoi poli, son tali le semplicissime apparenze di moto, che presentan le <lb></lb>Stelle fisse nella loro sfera. </s>

<s>Ma se, rimanendo io fermo nel medesimo luogo <lb></lb>della superficie terrestre, la Terra stessa, movendosi in giro, seco mi tra­<lb></lb>sporta? </s>

<s>“ Si manente me in eadem terrestris superficiei loco tota Terra <lb></lb>transponatur?.... ” (ibi). </s></p><p type="main">

<s>La risposta non fu data, se non da poi che il Castelli venne così a <lb></lb>mettere sotto altra forma la domanda: “ Ho osservata la Stella settentrio­<lb></lb>nale delle tre della fronte dello Scorpione, quale ha una stellina vicinissima, <lb></lb>più settentrionale d&#039;essa, nella continuazione dell&#039;arco delle tre della fronte, <lb></lb>in questa maniera: <figure id="id.020.01.1065.1.jpg" xlink:href="020/01/1065/1.jpg"></figure> V. S. mi faccia grazia di scrivermi che gioco doverà <lb></lb>fare movendosi la Terra, caso che lei sia assai più lontana dalla Terra del­<lb></lb>l&#039;altra compagna visibile con la vista naturale ” (Campori, Carteggio galil., <lb></lb>Modena 1881, pag. </s>

<s>260). </s></p><p type="main">

<s>Allora Galileo, a cui il di 7 Agosto 1627 venivano dirette queste pa­<lb></lb>role da Roma, riprese a&#039;suoi pensieri il filo rimasto in quelle due notarelle <lb></lb>interrotto, e delle speculazioni, provocate e promosse dalle stesse parole <lb></lb>scritte in quella lettera del Castelli, arricchì la III Giornata dei Due Mas­<lb></lb>simi Sistemi. </s>

<s>“ Io non credo, pone ivi in bocca al Salviati, che le Stelle <lb></lb>siano sparse in una sferica superficie egualmente tutte distanti da un cen­<lb></lb>tro, ma stimo che le loro lontananze da noi siano talmente varie, che al­<lb></lb>cune ve ne possano essere due o tre volte più remote di alcune altre, talchè, <pb xlink:href="020/01/1066.jpg" pagenum="509"></pb>quando si trovasse col Telescop̀io qualche piccolissima stella vicinissima ad <lb></lb>alcuna delle maggiori, e che però quella fosse altissima, potrebbe accadere <lb></lb>che qualche sensibile mutazione succedesse tra di loro, rispondente a quella <lb></lb>de&#039;Pianeti superiori ” (Alb. </s>

<s>I, 415). E proseguendo a dimostrare qual di­<lb></lb>versità di aspetto o parallasse debban fare a cagion del moto della Terra le <lb></lb>Stelle fisse, conclude dover essere questa stessa parallasse “ maggiore o mi­<lb></lb>nore secondo che le stelle osservate sono più o meno vicine al polo del­<lb></lb>l&#039;Ecclittica, sicchè finalmente delle stelle che sono nell&#039;Ecclittica stessa, tal <lb></lb>diversità si riduce a nulla ” (ivi, pag. </s>

<s>417). </s></p><p type="main">

<s>Bel pensiero senza dubbio quello del Castelli, belle speculazioni queste <lb></lb>di Galileo, ma bisognava che venissero confermate dai fatti, senza che le <lb></lb>Stelle fisse, chiamate in giudizio, sarebbero rimaste muti testimoni a favor <lb></lb>del moto della Terra, e anzi avrebbero col loro silenzio, come poi fecero al <lb></lb>Riccioli, fatto a tutti argomentar del contrario. </s></p><p type="main">

<s>Fu de&#039;primi Giovanni Pieroni che, sulla fine del 1640, credesse di avere <lb></lb>col Canocchiale osservato il moto delle Stelle fisse di alquanti minuti se­<lb></lb>condi; fatto che, come dimostrativo del moto della Terra, da Francesco Ri­<lb></lb>nuccini riferito a Galileo (Alb. </s>

<s>VII, 360), questi che pareva ne dovesse esul­<lb></lb>tare a sentir che le sue ipotesi eran confermate dal vero, pose invece le <lb></lb>cose nuovamente osservate dal Pieroni in tal dubbio, da equivalere a una <lb></lb>aperta negazione, concludendo esser vana speranza il voler raccogliere “ una <lb></lb>delicatissima e sottilissima osservazione da esperienze grossolanissime, ed anco <lb></lb>impossibili a farsi ” (ivi, pag. </s>

<s>363). </s></p><p type="main">

<s>Queste parole è vero le dettava Galileo al Viviani in mezzo all&#039;accora­<lb></lb>mento che sentiva, ripensando alle sorti del suo <emph type="italics"></emph>Dialogo sfortunato,<emph.end type="italics"></emph.end> ma pure <lb></lb>anche a mente serena si sarebbe persuaso che i moti, nella III Giornata pre­<lb></lb>scritti a fare alle Stelle fisse, in conseguenza del moto della Terra, erano <lb></lb>matematiche speculazioni difficilissime, se non impossibili, a esemplifiare <lb></lb>ne&#039;fatti. </s>

<s>I discepoli e i seguaci se ne persuasero poi anche più fermamente, <lb></lb>e il Borelli ripensava alla stella di mezzo del cingolo di Andromeda, e come, <lb></lb>se potesse verificarsi ch&#039;ella si fosse mossa, offrirebbe un bellissimo argo­<lb></lb>mento a favor del Copernico “ ma dubito, soggiungeva, che questa spe­<lb></lb>ranza ci fallirà, poichè dopo molte diligenze e speranze vane non riuscì, nean­<lb></lb>che coll&#039;aiuto del Telescopio, in altre fisse vicine, al Pieroni, e ad altri amici <lb></lb>di verificare una cosa simile ” (Fabbroni, Lettere ecc., T. I, Firenze 1773, <lb></lb>pag. </s>

<s>123). </s></p><p type="main">

<s>L&#039;espressione del Borelli però vuol esser alquanto rettificata: non è che <lb></lb>non fosse riuscito al Pieroni di verificare il moto delle stelle: è che non gli <lb></lb>riuscì di riscontrarci alcuna relazione col moto della Terra. </s>

<s>L&#039;osservazione poi <lb></lb>fatta da altri e la ferma persuasione che, se le stelle si muovono, non potesse <lb></lb>il loro moto apparente dipendere da altra causa che dalla parallasse annuale, <lb></lb>tennero lungamente gli Astronomi perplessi e confusi, infintantochè il Brad­<lb></lb>ley non dimostrò che i moti delle fisse non dipendono dalla parallasse, ma <lb></lb>dalla <emph type="italics"></emph>aberrazione.<emph.end type="italics"></emph.end> Così venne la grande inaspettata scoperta a confermare <pb xlink:href="020/01/1067.jpg" pagenum="510"></pb>due delle più importanti verità astronomiche, e delle più controverse; il moto <lb></lb>della Terra e il moto della Luce, che si compongono insieme a far dalla <lb></lb>nostra vista aberrare il luogo proprio delle stelle. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>È oramai più di un secolo e mezzo che s&#039;ammira da tutti il sottilis­<lb></lb>simo ingegno del Bradley, il quale non solo osservò il moto delle stelle fisse, <lb></lb>creduto da Galileo e da&#039;suoi seguaci impossibile, ma designò le vie di quel <lb></lb>moto in alcune stelle esser circoli, in altre ellissi più o meno allungate, ri­<lb></lb>ducendo la sua dimostrazione a tanta evidenza, a quanta può ridursi un teo­<lb></lb>rema di Meccanica, o una proposizione di Geometria. </s>

<s>Nè cessa l&#039;ammira­<lb></lb>zione verso il grande Astronomo inglese per sapersi che anche prima del <lb></lb>Newton conoscevano i Matematici, specialmente stranieri, il modo di com­<lb></lb>porre in un&#039;unica risultante due forze, non solamente ortogonali, ma qua­<lb></lb>lunque si fosse l&#039;angolo del loro concorso. </s></p><p type="main">

<s>Più grande ammirazione ridesta in ogni modo il sottilissimo ingegno del <lb></lb>nostro Borelli, il quale, prima del Newton, si studiò di ridurre a una dimo­<lb></lb>strazione meccanica le vie così apparentemente disordinate, che percorrono <lb></lb>in cielo le Comete. </s>

<s>Tale è la conclusionè, a cui tende questa seconda parte <lb></lb>del nostro capitolo, ma convien prima toccar brevemente delle varie ipotesi <lb></lb>fantasticate intorno all&#039;origine e all&#039;essere di quelle strane apparenze cele­<lb></lb>sti, che furono per lungo tempo il terrore del volgo, e la disperazion degli <lb></lb>Astronomi. </s></p><p type="main">

<s>Come s&#039;ingerisse negli uomini l&#039;opinione che fossero le Comete presa­<lb></lb>gio di pubbliche sventure non è del nostro istituto l&#039;investigare, ma come <lb></lb>dovessero frugar la curiosità degli Astronomi, e come riuscisse a loro diffi­<lb></lb>cile, di apparenze da noi tanto remote, indagar l&#039;origine e la ragione, è fa­<lb></lb>cilissimo a comprendere, tanto più ripensando al vezzo invalso tra Filosofi <lb></lb>di non fermarsi in quelle, tra così fatte ragioni, che paressero più semplici <lb></lb>e più naturali. </s></p><p type="main">

<s>Semplice e naturale era senza dubbio il concetto, che s&#039;erano delle Co­<lb></lb>mete formato i Pitagorici, i <emph type="italics"></emph>Placiti<emph.end type="italics"></emph.end> de&#039;quali venivano sapientemente divul­<lb></lb>gati da Plutarco, e da Seneca ne&#039;loro libri. </s>

<s>“ Alcuni de&#039;Pitagorici, riferiva <lb></lb>lo stesso Plutarco nel suo opuscolo, affermano essere la Cometa una stella <lb></lb>di quelle, che non sempre appariscono, ma dopo certo tempo determinato <lb></lb>ritornando in giro surgono dall&#039;orizzonte ” (Traduz. </s>

<s>ital., Milano 1829, T. V, <lb></lb>pag. </s>

<s>247). Simile riferisce Seneca nelle Questioni naturali essere stata l&#039;opi­<lb></lb>nione di Artemidoro. </s></p><p type="main">

<s>Di rincontro a questa semplicità di concetto sorsero gl&#039;ingegnosi com­<lb></lb>menti de&#039;Filosofi, il principe de&#039;quali insegnava, nel Libro delle Meteore, <lb></lb>essere la Cometa un&#039;esalazione terrena, che menata in volta dal concavo lu-<pb xlink:href="020/01/1068.jpg" pagenum="511"></pb>nare, ivi a cagion del rapido moto si accenda. </s>

<s>Così, in sull&#039;entrar del se­<lb></lb>colo XVII, erano fra&#039;Pitagorici e gli Aristotelici divise le opinioni, ma la <lb></lb>grande autorità di Ticone prevaleva a favor dei secondi, anche sulla mente <lb></lb>degli stessi Peripatetici. </s></p><p type="main">

<s>Le tre Comete apparite nell&#039;anno 1618 eccitarono il fermento delle di­<lb></lb>scussioni. </s>

<s>Si lesse sopra quel soggetto nel Collegio romano una Disputazione <lb></lb>astronomica, dove si concludeva essere stato il moto della Cometa per un <lb></lb>circolo massimo della sfera celeste, a somiglianza degli altri Pianeti. </s>

<s>“ Fuit <lb></lb>ergo, quod erat probandum, motus Cometae per circulum maximum ac mo­<lb></lb>tui Planetarum persimilis ” (Alb. </s>

<s>IV, 13). Quanto alla natura, dice essere <lb></lb>la Cometa “ non ex huius Terrae sordibus in aere succensa, sed coelestia <lb></lb>inter lumina sedem sortita ” (ibi) e non dubita, quanto al luogo di essa <lb></lb>Cometa, di assegnarlo probabilmente “ Solem inter ac Lunam ” (ibi). </s></p><p type="main">

<s>Così fatte idee pitagoriche, quanto al moto e all&#039;origine delle Comete, <lb></lb>non furono approvate da Galileo, il quale professò altre opinioni, non diret­<lb></lb>tamente per sè, ma per mezzo di Mario Guiducci, che recitò nell&#039;Accademia <lb></lb>fiorentina, su quel soggetto, una erudita ed eloquente Lezione. </s>

<s>Nega ivi <lb></lb>prima di tutto alle Comete qualunque somiglianza coi Pianeti “ imperocchè <lb></lb>i Pianeti avvicinandosi a poco a poco si fanno maggiori, sino a che fatti vi­<lb></lb>cinissimi ci appariscono nella maggior grandezza; quindi pian piano allon­<lb></lb>tanandosi si diminuiscono, e con quella stessa uniformità mantenuta nel­<lb></lb>l&#039;aggrandirsi si vedono aggiustatamente rappiccolire. </s>

<s>Ma la Cometa è grande <lb></lb>nel suo primo apparire, e indi poco o nulla o per brevissimo tempo ricre­<lb></lb>sce, diminuendosi poi in tutto il resto del tempo, fino a che fatta piccolis­<lb></lb>sima, per la sua tenuità, del tutto si perde ” (Alb. </s>

<s>IV, 23). Si nega in se­<lb></lb>condo luogo dal Guiducci alle Comete l&#039;essere sostanza celeste, e si torna <lb></lb>ad ammetter con Aristotile la loro origine da esalazioni terrene, non accese <lb></lb>però a quel modo che il Filosofo voleva, ma illuminate dal Sole, ai riflessi <lb></lb>del quale si debbono le apparenze del nucleo e della coda. </s></p><p type="main">

<s>L&#039;Autore della Disputazione astronomica, letta nel Collegio romano, per­<lb></lb>suaso, com&#039;era veramente, che le parole del Guiducci fossero inspirate da <lb></lb>Galileo, si rivolse contro questo direttamente a difendere le sue ragioni in <lb></lb>un libro, a cui pose il titolo di <emph type="italics"></emph>Libra astronomica.<emph.end type="italics"></emph.end> Uscì fuori questo libro <lb></lb>sotto il nome di Lotario Sarsi, anagramma di Orazio Grassi, divenuto fa­<lb></lb>moso per essere state le ragioni astronomiche di lui ponderate da Galileo, <lb></lb>non con una volgar <emph type="italics"></emph>Libra,<emph.end type="italics"></emph.end> ma con uno squisitissimo <emph type="italics"></emph>Saggiatore.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Poco prima che uscisse fuori questo <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> s&#039;era il padre Giuseppe <lb></lb>Biancani, collega del Grassi, studiato di ricomporre la controversia fra Pita­<lb></lb>gorici e Aristotelici, ch&#039;egli più volentieri distingue co&#039;nomi di Fisiologi e <lb></lb>di Astronomi, e vi s&#039;era studiato in modo, che se non provvedeva ai pro­<lb></lb>gressi della scienza, ne teneva nonostante aperte le vie, e non ne impediva <lb></lb>i progressi, come sventuratamente aveva fatto il Guiducci. </s></p><p type="main">

<s>“ Solent nonnulli Physiologi (scrive, nel Cap. </s>

<s>IV, Lib. </s>

<s>XVI <emph type="italics"></emph>De mundi <lb></lb>fabrica,<emph.end type="italics"></emph.end> il Biancani) cum Astronomis de Cometarum materia contendere. </s>

<s>Af-<pb xlink:href="020/01/1069.jpg" pagenum="512"></pb>firmant enim aliqui ex illis Cometas ex elementari materia constare, atque <lb></lb>etiam in elementari regione versari, quippe quae Cometas tantum de facie <lb></lb>norunt. </s>

<s>Cum enim eorum circuitus, vias, motus, parallaxes nec queant per­<lb></lb>severari, de iis tamen secundum vulgarem apparentiam iudicant. </s>

<s>Verentur <lb></lb>praeterea ne quam novitatis notam coelo inurant. </s>

<s>” </s></p><p type="main">

<s>“ Ex opposito Astronomi, qui praedicta Cometarum accidentia sagaciter <lb></lb>rimati sunt, eaque omnino rebus tantum coelestibus competere vident, eas non <lb></lb>elementares sed coelestes esse autumant. </s>

<s>Verum enim vero me ab utrisque <lb></lb>gratiam initurum confido, si qua ratione iis haec componi possit ostendero. </s>

<s>” </s></p><p type="main">

<s>“ Ratio igitur est si eorum opinionem sequemur, qui putant Cometas <lb></lb>coelestes esse ac continuo inter aeterna Mundi corpora perseverare, quamvis <lb></lb>raro conspicua evadant. </s>

<s>In qua sententia fuere olim Pythagorici, et Italo­<lb></lb>rum secta, sed et recentiores suas hypotheses ita Cometae accomodant, ut <lb></lb>cum antiquis consentire possint. </s>

<s>Dum enim eos in magno epiciclo revol­<lb></lb>vunt, omnes salvant apparentias, et praeterea eas in sublime coelum ita at­<lb></lb>tollunt, ut paulatim ad visum minuantur, ac tandem non pereant, sed non <lb></lb>apparent. </s>

<s>Hac enim ratione nihil novi in coelo inferunt, quod Physicis sic <lb></lb>contingat praecipuae curae est, nec eas elementares faciunt, quod Astronomi <lb></lb>magnopere aversantur. </s>

<s>Haec sit conciliatio ” (Mutinae 1635, pag. </s>

<s>160). </s></p><p type="main">

<s>Ma Galileo, avverso a ogni conciliazione proposta dal Gesuita collega del <lb></lb>Sarsi, esce fuori nel <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> contro lo stesso Sarsi, e rompe i cancelli <lb></lb>dei Pitagorici, proseguendo a sostener che il moto della Cometa non si fa <lb></lb>in un&#039;orbita simile a quella de&#039;Pianeti, o in eccentrici ed epicicli, ma in <lb></lb>linea retta dal centro della Terra, e rompe anche insieme i cancelli de&#039;Pe­<lb></lb>ripatetici, affermando che l&#039;esalazioni terrestri non son trattenute dal con­<lb></lb>cavo della Luna, ma penetrano attraverso al cielo liberamente, sublimandosi <lb></lb>nelle sue più alte regioni. </s></p><p type="main">

<s>Il <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> di Galileo, in parecchie esperienze e speculazioni, ricom­<lb></lb>pensava la Fisica degli sfregi, che veniva facendo all&#039;Astronomia; sfregi, che <lb></lb>liberamente riconosciuti e confessati dai discepoli, si pensò da essi sapien­<lb></lb>temente, per onor della scienza e della scuola italiana, ad emendarli. </s>

<s>Si dee <lb></lb>un tal pensiero principalmente al Borelli, il quale intanto che meditava di <lb></lb>ridurre il sistema pitagorico delle Comete, non solo alla maggior probabi­<lb></lb>lità di una opinione, ma alla certezza di una dimostrazione, chiamava da una <lb></lb>parte a collaborare all&#039;opera, e dall&#039;altra ad apparecchiarsi le vie uno de&#039;suoi <lb></lb>discepoli più valorosi, Alessandro Marchetti. </s>

<s>Di ciò, che questi allora intorno <lb></lb>a quel soggetto operava, dava il Borelli stesso parte da Pisa al principe Leo­<lb></lb>poldo per lettera del di 27 Aprile 1665. “ Intanto dò parte a V. A. S. come <lb></lb>il dottor Marchetti sta scrivendo un Trattato filosofico della Cometa, in lin­<lb></lb>gua toscana, molto elegante ed erudito ” (MSS. Cim., T. XVIII, c. </s>

<s>171). </s></p><p type="main">

<s>Questo trattato filosofico del Marchetti si legge autografo da c. </s>

<s>53-71 <lb></lb>del Tomo XIV del Cimento, in un fascicolo, a cui è premessa una carta <lb></lb>bianca coll&#039;occhietto: <emph type="italics"></emph>Dottor Marchetti, Sulle Comete, Scrittura.<emph.end type="italics"></emph.end> È divisa <lb></lb>questa scrittura in capitoli, nel I de&#039;quali si tratta “ Dei varii nomi delle <pb xlink:href="020/01/1070.jpg" pagenum="513"></pb>Comete, e delle loro derivazioni. </s>

<s>” Nel Cap. </s>

<s>II “ Delle varie opinioni intorno <lb></lb>alla natura ed essenza loro ” e vi si cita fra le altre, per confutarla, l&#039;opi­<lb></lb>nione dei Pitagorici. </s>

<s>Nel Cap. </s>

<s>VI “ si riferisce l&#039;opinione di Aristotile e dei <lb></lb>seguaci e diligentemente esaminandola si convince di falsità. </s>

<s>” </s></p><p type="main">

<s>L&#039;opinione di Aristotile, confutata già con ampia eloquenza nel <emph type="italics"></emph>Sag­<lb></lb>giatore,<emph.end type="italics"></emph.end> è dal Marchetti riferita nella forma seguente: “ Abbiamo finora, s&#039;io <lb></lb>non m&#039;inganno, sufficientemente provato contro agli antichi che le Comete <lb></lb>non siano uno ne&#039;più Pianeti. </s>

<s>Tempo è dunque che, scendendo dal cielo fra <lb></lb>gli elementi, esaminiamo il parere di Aristotile e dei seguaci, che le cre­<lb></lb>dettero abbruciamenti di terrestri esalazioni. </s>

<s>Egli dunque, imitando forse <lb></lb>Senofane, e per relazione di Seneca e di Epigene alcuni Stoici e Caldei, si <lb></lb>persuase che la Cometa altro non fosse che una esalazione terrena solle­<lb></lb>vata, da qualunque se ne sia la cagione, fino alla concava superficie della <lb></lb>Sfera lunare, che di materia simile è sempre piena, e da essa rapidissima­<lb></lb>mente portata in giro, onde tribbiandosi per la velocità del moto e, per così <lb></lb>dire, sminuzzandosi e stritolandosi le sue parti, ne concepisca calore e final­<lb></lb>mente si accenda, in quella guisa, dice egli, che per la stessa cagione veg­<lb></lb>ghiamo liquefarsi per aria il piembo di quelle frecce, che da gagliardo ar­<lb></lb>ciere vengon vibrate ” (c. </s>

<s>65). </s></p><p type="main">

<s>Riferisce poi nel Cap. </s>

<s>VII l&#039;opinion del Cartesio, che cioè non sieno le <lb></lb>Comete altro che Stelle fisse rimosse a viva forza dalle loro sedi, e scagliate <lb></lb>con violenza in varie parti; opinione da nominarsi piuttosto “ sogno d&#039;in­<lb></lb>fermi o fola di romanzi, che filosofica speculazione ” (c. </s>

<s>67). L&#039;ultimo capi­<lb></lb>tolo che è l&#039;VIII è riserbato a riferire l&#039;opinione propia dell&#039;Autore, e con­<lb></lb>tiene la parte, che più importa a noi, sì per la conclusione a cui tendiamo, <lb></lb>e sì per esservi riferite opinioni, che si sollevano al di sopra delle idee co­<lb></lb>muni a que&#039;tempi. </s></p><p type="main">

<s>“ Io dunque, scrive il Marchetti, avendo prima bene osservato con gli <lb></lb>occhi propri tutti i particolari accidenti delle due moderne Comete, ed oltre <lb></lb>a ciò attentissimamente, e con somma diligenza, esaminato intorno a cotal <lb></lb>materia gli scritti altrui, mi sono finalmente stabilito nell&#039;animo questo pa­<lb></lb>rere: cioè che, per investigare la loro natura, non sia punto sicuro lo allon­<lb></lb>tanarsi pur di un iota da quel tanto, che lasciò scritto, nel suo eruditissimo <lb></lb>ed elegantissimo Discorso accademico, il signor Mario Guiducci gentiluomo <lb></lb>fiorentino, e che fu prima speculato, e poi difeso contro al Sarsi nel <emph type="italics"></emph>Sag­<lb></lb>giatore,<emph.end type="italics"></emph.end> con dottrina ed eloquenza così mirabile, dal nostro gran Galileo. </s>

<s>Il <lb></lb>perchè stimo insieme con esso lui che, ritrovandosi unita insieme, in parte <lb></lb>dove non giunge l&#039;ombra piramidale del nostro Globo, una materia, qua­<lb></lb>lunque ella si sia, non del tutto trasparente, come il restante dell&#039;etere e <lb></lb>dell&#039;aria che la circonda, nè anco affatto opaca, come la Terra, la Luna e <lb></lb>tutti gli altri Pianeti, ed essendo questa percossa dai luminosi raggi del Sole, <lb></lb>parte di essi come opaca agli occhi nostri rifletta, onde il corpo si scorga <lb></lb>della Cometa, e ad altra parte come trasparente conceda libero passo, e gli <lb></lb>refranga, onde sia formata la coda. </s>

<s>” </s></p><pb xlink:href="020/01/1071.jpg" pagenum="514"></pb><p type="main">

<s>“ È il vero che, acciocchè questa da noi si vegga, non basta che i detti <lb></lb>raggi che si refrangono si diffondano nell&#039;aer puro, o per l&#039;etere limpidis­<lb></lb>simo, ma è necessario che incontrino ancora essi qualche materia, dalla quale <lb></lb>siano ripercossi. </s>

<s>Per la qual cosa immaginossi il Keplero, gran Filosofo ed <lb></lb>Astronomo del suo tempo, ed amico cordialissimo dello stesso Galileo, che <lb></lb>gli stessi raggi solari, penetranti per il corpo della Cometa, ne limino per <lb></lb>così dire continuamente, e portin seco alcune piccole particelle, dalle quali <lb></lb>e&#039;sian riflessi. </s>

<s>” </s></p><p type="main">

<s>“ Alcuni altri si sono creduti che la materia stessa, che da principio <lb></lb>si adunò insieme, vada da sè medesima separandosi, sfumandone di mano <lb></lb>in mano le parti più sottili per ogni banda, delle quali non pertanto quelle <lb></lb>solamente ci sian visibili, che si trovano opposte al Sole, per esser tutte <lb></lb>l&#039;altre disperse, quasi in un subito, e per l&#039;etere dissipate dal suo gran <lb></lb>lume: e v&#039;ebbe ancora chi, senza ammettere per necessaria alcuna interna <lb></lb>dissipazione, si pensò nondimeno di potere agevolmente salvare il tutto, figu­<lb></lb>randosi in quella vece che, nell&#039;unirsi insieme, mediante la simpatia loro <lb></lb>scambievole, le sue parti, cospirando a formare un globo e perciò premen­<lb></lb>dosi l&#039;una l&#039;altra e più e più calcandosi verso il centro, faccian quivi le <lb></lb>più vicine un quasi nocciolo molto denso, intorno al quale vadano poi va­<lb></lb>gando le più lontane e meno compresse, non altrimenti che far veggiamo <lb></lb>a&#039;nuovi sciami delle api, il principe delle quali, appena su qualche ramo <lb></lb>d&#039;albero arresta il volo, che la maggior parte di esse in un subito gli si <lb></lb>addossano, mentre il restante, qua e là svolazzando, d&#039;ogni intorno gli fan <lb></lb>corona. </s>

<s>” </s></p><p type="main">

<s>“ Di queste opinioni qual sia la migliore io al presente non mi curo <lb></lb>di esaminare, stimandole ugualmente tutte probabili, tutte belle, tutte de­<lb></lb>gne veramente di quei grandi uomini che l&#039;inventarono, nè avendo per av­<lb></lb>ventura alcuna difficoltà di ammetterle per vere tutt&#039;e tre insieme. </s>

<s>Ma, co­<lb></lb>munque si stia la cosa, a me basta che il Lettore resti avvertito ch&#039;io non <lb></lb>suppongo che la coda della Cometa sia una semplice refrazione, come poco <lb></lb>avvedutamente fece il Cardano, da noi perciò ragionevolmente nel Cap. </s>

<s>VI <lb></lb>confutato, ma congiungo con essa la riflessione, senza la quale al certo non <lb></lb>si vedrebbe ” (c. </s>

<s>70, 71). </s></p><p type="main">

<s>Benchè protesti il Marchetti, in riferir questa sua opinione delle Co­<lb></lb>mete, di non dilungarsi un iota dal Guiducci, nè perciò da Galileo, se ne <lb></lb>dilunga però sostanzialmente, supponendo che la materia atta a riflettere il <lb></lb>lume del Sole, e a dar così l&#039;apparenza del nucleo e della coda, non sia <lb></lb>parte delle fumosità terrestri, ma dell&#039;etere preesistente nelle alture de&#039;cieli. </s>

<s><lb></lb>Così veniva ad emendare uno de&#039;più gravi, e diciamolo francamente de&#039;più <lb></lb>vergognosi errori, che contenesse in sè l&#039;ipotesi galileiana, e benchè qui <lb></lb>non faccia nessun cenno l&#039;Autore di questa sua intenzione, non lasciò poi <lb></lb>di dichiararla apertamente, quando, ampliatane la materia, fu la prima scrit­<lb></lb>tura manoscritta ridotta in forma di Lettera a Francesco Redi, e nel 1684, <lb></lb>in Firenze, stampata. </s></p><pb xlink:href="020/01/1072.jpg" pagenum="515"></pb><p type="main">

<s>Ivi, verso la fine, dop&#039;aver concluso non poter le Comete esser pro­<lb></lb>dotte da aliti terrestri, si rivolge a confutar così la contraria opinione di <lb></lb>Galileo: </s></p><p type="main">

<s>“ O voi, signor Galileo, contro a quello che voi vi siete lasciato inten­<lb></lb>dere ne&#039;vostri Dialoghi, giudicate la Terrà essere immobile, e quasi centro <lb></lb>dell&#039;universo, o voi la credete mobile intorno all&#039;asse, e intorno al Sole. </s>

<s>Se <lb></lb>immobile, per tacere che voi a voi medesimo contradite, e come volete voi <lb></lb>salvare il moto diurno delle Comete, mediante il quale elleno, nel breve spa­<lb></lb>zio di un giorno solo naturale, si raggirano intorno a essa Terra da oriente <lb></lb>movendosi verso occidente, e di nuovo tornando nell&#039;oriente? </s>

<s>” <lb></lb>… </s></p><p type="main">

<s>“ Egli fa dunque pur di mestieri che voi dichiarate che essa Terra sia <lb></lb>quella, alla quale compete almeno il diurno rivolgimento. </s>

<s>Ma non vi sov­<lb></lb>viene egli di averci altrove avvertito, cioè in quella vostra divina Opera dei <lb></lb>due Massimi sistemi, che le materie che son parti di qualche globo, che si <lb></lb>muova circolarmente, non ponno, benchè staccate dal loro tutto, muoversi <lb></lb>di altro moto che circolare? </s>

<s>Certo si dee sovvenirvi, conciossiachè questo è <lb></lb>l&#039;unico fondamento, al qual si appoggia la dottrina de&#039;Pitagorici, da voi con <lb></lb>tanta altezza d&#039;ingegno, con tanta finezza di giudizio, e con tanta profon­<lb></lb>dità e singolarità di dottrina, per la più ragionevole, sostenuta. </s>

<s>” </s></p><p type="main">

<s>“ Ma se questo è vero, com&#039;è verissimo, adunque, ancorchè possa per <lb></lb>avventura difendersi come probabile che alcuna Cometa nel mentovato modo <lb></lb>si producesse, certo che voi ciò difendere in niun modo non potete, senza <lb></lb>incorrere in manifeste contradizioni e repugnanze alle più salde dottrine di <lb></lb>voi medesimo ” (pag. </s>

<s>86, 87). </s></p><p type="main">

<s>Noi abbiamo altrove dimostrato coi fatti che le dottrine di Galileo erano <lb></lb>anzi da questa parte assai vacillanti, non avendo egli penetrato il vero di <lb></lb>quella Filosofia magnetica, nella quale unicamente ritrovavasi a quelle stesse <lb></lb>dottrine la saldezza. </s>

<s>Ma non pare in ogni modo credibile che l&#039;Autor del <lb></lb><emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> non sentisse quelle contradizioni rinfacciategli poi così libera­<lb></lb>mente dal Marchetti; contradizioni, ch&#039;erano quelle medesime, in che s&#039;era <lb></lb>vent&#039;anni prima aggirato lo stesso Galileo, nel Discorso che s&#039;apparecchiava <lb></lb>a distendere sull&#039;origine della Stella nuova. </s></p><p type="main">

<s>S&#039;era fin d&#039;allora, per salvarsi da quelle contradizioni, offerto il partito <lb></lb>a cui poi, rispetto alle Comete, s&#039;attenne il Marchetti, e infatti Ticone e <lb></lb>altri insieme con lui avevano ritrovato in Galassia, a somministrar la ma­<lb></lb>teria a quelle vagabonde apparenze celesti, una ricca miniera. </s>

<s>Dicemmo per <lb></lb>quali ragioni Galileo rifiutasse questa ipotesi, rifiutata già dal Keplero, il <lb></lb>quale pensava essere atta a ingenerar nuove Stelle e nuove Comete qualun­<lb></lb>que parte del cielo. </s>

<s>“ Itaque potius in eo sum, ut credam coelum unde­<lb></lb>quaque aptum ad materiam hisce sideribus praebendam ” (De Stella nova <lb></lb>cit., pag. </s>

<s>112). </s></p><p type="main">

<s>Aveva il suo fondamento questa ipotesi kepleriana in quelle macchie <lb></lb>biancheggianti, che qua e là si vedevano variamente disperse per gli spazii <pb xlink:href="020/01/1073.jpg" pagenum="516"></pb>celesti, e alle quali si dava il nome di <emph type="italics"></emph>Nebulose.<emph.end type="italics"></emph.end> Si mostrò Galileo intorno <lb></lb>a ciò ritroso di seguitare il Keplero, perchè pensava delle Nebulose quel che <lb></lb>del Circolo latteo gli riferiva Plutarco, che cioè “ sia, secondo Democrito, <lb></lb>un unito splendore di molte minute stelle vicine l&#039;una all&#039;altra, che per la <lb></lb>spessezza rilucano insieme ” (Opus. </s>

<s>e Tomo cit., pag. </s>

<s>247); pensiero dal­<lb></lb>l&#039;altra parte introdotto nella scienza italiana dal divino canto dell&#039;Alighieri <lb></lb>(Par., C. XIV, t. </s>

<s>33). </s></p><p type="main">

<s>Quando poi il Canocchiale lo rese certo non essere altro veramente Ga­<lb></lb>lassia “ quam innumerarum Stellarum coacervatim consitarum congeries ” <lb></lb>(Alb. </s>

<s>III, 76), e le Nebulose “ Stellarum constipatarum coetum ” (ibi), e <lb></lb>allora si confermò più saldamente Galileo nella sua opinione non poter cioè <lb></lb>quella materia di già informata trasformarsi a comporre o Stelle nuove o <lb></lb>Comete. </s></p><p type="main">

<s>Si sono alcuni maravigliati che Galileo discorra in tal sentenza delle <lb></lb>Nebulose da far creder che tutte sieno allo stesso modo risolubili, come il <lb></lb>Circolo latteo, o il Capo di Orione, o il Presepe, e ne hanno concluso non <lb></lb>dover avere egli mai osservato le vere Nebulose non risolubili in Stelle. </s>

<s>La <lb></lb>conclusione però è prepostera, perchè, essendosi abbattuto Galileo ad osser­<lb></lb>var tali macchie albescenti nel cielo, piuttosto che crederle materia informe <lb></lb>pensò che rimanessero irresolubili, non per sè, ma per la debolezza del suo <lb></lb>Canocchiale. </s>

<s>E fu questo il pensiero che lo salvò dalle illusioni, che si fe­<lb></lb>cero altri Astronomi dopo di lui. </s></p><p type="main">

<s>L&#039;Huyghens, nel 1656, osservò nella spada di Orione risplendere quat­<lb></lb>tro stelle <emph type="italics"></emph>velut trans nebulam,<emph.end type="italics"></emph.end> la qual nebbia celeste in tre anni non mutò <lb></lb>sembianza. </s>

<s>Annunziò questo fenomeno <emph type="italics"></emph>a nemine hucusque, quod sciam, <lb></lb>animadversum,<emph.end type="italics"></emph.end> nel <emph type="italics"></emph>Systema Saturnium,<emph.end type="italics"></emph.end> dove concludeva esser la nuova <lb></lb>nebulosa di Orione di natura diversa dalle altre nebulose fino allora osser­<lb></lb>vate. </s>

<s>“ Nam caeterae Nebulosae olim existimatae, atque ipsa Via lactea, <lb></lb>perspicillo inspectae, nullas nebulas habere comperiuntur, neque aliud esse <lb></lb>quam plurium Stellarum congeries et frequentia ” (In oper. </s>

<s>var. </s>

<s>cit., Vol. </s>

<s>II, <lb></lb>pag. </s>

<s>541). </s></p><p type="main">

<s>Si tenne dagli Astronomi, questa descritta dall&#039;Huyghens, per la prima <lb></lb>scoperta fra le Nebulose così dette <emph type="italics"></emph>diffuse,<emph.end type="italics"></emph.end> ma Telescopii più squisiti mo­<lb></lb>strarono ch&#039;era anch&#039;essa, almeno in parte, risolubile come le altre, lasciando <lb></lb>i più assennati in una grande incertezza se quella, che apparisce in cielo <lb></lb>materia informe, sia veramente tale, oppure ci apparisca così, per non es­<lb></lb>sere gli strumenti, anche più perfetti che si sieno saputi fabbricare, atti a <lb></lb>rivelarci cose, che son da noi tanto remote. </s></p><p type="main">

<s>Dietro così fatte considerazioni s&#039;intende come fosse prudente consiglio <lb></lb>quello di Galileo del non volere ammettere, col Keplero, che le Stelle nuove <lb></lb>e le Comete siano ingenerate di materia celeste, ma non può però scusarsi <lb></lb>degli errori, in che egli cadde speculando di tali soggetti; errori del grave <lb></lb>danno de&#039;quali, come ora vedremo, fu largamente in Italia ristorata la scienza <lb></lb>astronomica per opera del Borelli. </s></p><pb xlink:href="020/01/1074.jpg" pagenum="517"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Gli errori detti intorno alle Comete, da noi sopra narrati, dipendevano <lb></lb>dall&#039;essersi smarrite le tradizioni dell&#039;antica scuola pitagorica italiana, alle <lb></lb>quali sapientemente tornava il Borelli in un suo Trattatello, incominciato a <lb></lb>scrivere in Pisa negli ultimi giorni del Gennaio 1665, terminato ivi il dì 10 <lb></lb>del Febbraio appresso, e pubblicato in forma di lettera al padre Stefano An­<lb></lb>geli, sotto il finto nome di Pier Maria Mutoli, col titolo: <emph type="italics"></emph>Del moto della Co­<lb></lb>meta apparsa il mese di Dicembre 1664.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Può distinguersi il Trattatello in tre parti: nella prima, nella quale, ac­<lb></lb>cennandosi alla generazione delle Comete, si rifiutano le opinioni del Gui­<lb></lb>ducci e di Galileo con tutti gli altri loro seguaci, che dicevano essere quegli <lb></lb>insoliti splendori esalazioni terrestri illuminate dal Sole, e anche talvolta dai <lb></lb>circostanti Pianeti. </s>

<s>Nella seconda, nella quale, volendosi rendere la ragione <lb></lb>de&#039;moti osservati nelle Comete, si prova che non si possono intendere quegli <lb></lb>stessi moti in altro sistema diverso dal copernicano, dall&#039;Autore chiamato <lb></lb>col nome di pitagorico. </s>

<s>Nella terza, nella quale si dimostra, per mezzo di <lb></lb>osservazioni simultanee fatte in luoghi diversi, che mancando la Cometa di <lb></lb>sensibile parallasse non può, come il Guiducci e Galileo dicevano, costituirsi <lb></lb>nella region sullunare. </s>

<s>E perchè l&#039;argomento della parallasse era infirmato <lb></lb>da&#039;peripatetici e segnatamente dal Chiaramonti e dal Riccioli, i quali dice­<lb></lb>vano quell&#039;argomento illusorio per essere le Comete vagabonde nel cielo, il <lb></lb>Borelli propone il metodo delle due osservazioni contemporanee, che non la­<lb></lb>sciavano a&#039;sani giudizi luogo a dubitare. </s></p><p type="main">

<s>Così veniva il Mutoli a sollevar le Comete, con gli antichi Pitagorici, <lb></lb>all&#039;essere e alla dignità degli altri Pianeti. </s>

<s>Non s&#039;era però pronunziato an­<lb></lb>cora intorno al decider della linea de&#039;loro moti, ciò che rende forse la ra­<lb></lb>gione del non essere le rinnovate dottrine riuscite colla piena approvazione <lb></lb>degli Astronomi. </s>

<s>S&#039;aggiungeva il non essersi avvertito il loro ritorno, ciò <lb></lb>che serviva a molti d&#039;argomento per confermarsi nella loro opinione non <lb></lb>essere le Comete altro che vane e transitorie apparenze, alle quali non si <lb></lb>potesse prescrivere un&#039;orbita come ai Pianeti. </s>

<s>S&#039;era all&#039;efficacia di un tale <lb></lb>argomento principalmente piegato Seth Ward, il quale, addetto all&#039;ipotesi <lb></lb>di Ticone, vedendo non potersi collocar le Comete nel medesimo cerchio, <lb></lb>per avere alcune i loro moti da levante a ponente, e altre da un polo al­<lb></lb>l&#039;altro, immaginò tanti cerchi massimi intorno al Sole, quante sono in nu­<lb></lb>mero le stesse Comete, e così supponeva farsi nel loro epiciclo una infles­<lb></lb>sione e variazione de&#039;Nodi, come una loro proprietà distinta da quella di <lb></lb>tutti gli altri Pianeti. </s></p><p type="main">

<s>L&#039;ipotesi del Ward fu approvata poi dall&#039;Auzout, e il Cassini la modi­<lb></lb>ficò alquanto, per ridurla al suo nuovo sistema. </s>

<s>Il Cassini era pure nel nu-<pb xlink:href="020/01/1075.jpg" pagenum="518"></pb>mero di coloro che, lontani dal sospettare il ritorno di una Cometa identica <lb></lb>e permanente nell&#039;esser suo, s&#039;era confermato nell&#039;idea che fossero tutte <lb></lb>le Comete evanescenti come quelle che pigliavan sostanza dalle esalazioni <lb></lb>della nostra Terra. </s>

<s>Primo a speculare intorno ai fenomeni della Luce zodia­<lb></lb>cale, e a dimostrar ch&#039;ell&#039;era dovuta a un anello di materia cosmica, illu­<lb></lb>minato dal Sole, pensò il Cassini, accostandosi col Ward, che un simile <lb></lb>anello di materia terrestre, e flessibile ne&#039;suoi Nodi, circolasse intorno al <lb></lb>nostro Globo, e presentasse ora il fenomeno di una, ora di altra Cometa, <lb></lb>secondo ohe un punto o l&#039;altro di esso anello interrotto rifletteva alla nostra <lb></lb>vista i raggi del Sole. </s></p><p type="main">

<s>Di un tal sistema cometario del Cassini così il Borelli scriveva il suo <lb></lb>parere al principe Leopoldo: “ Circa la teoria della Cometa, che egli (il <lb></lb>Cassini) pretende aver ritrovata, mi pare che sia nna cosa molto faticosa e <lb></lb>imbrogliata, dalla quale alla fine poco frutto ed utile se ne cava, il che mi <lb></lb>pare che egli faccia appostatamente, per mostrar che la sua teoria dell&#039;epi­<lb></lb>ciclo variabile e flessibile non l&#039;abbia tolta da Seto Wardo inglese ” (Fab­<lb></lb>broni, Lett. </s>

<s>cit., T. I, pag. </s>

<s>121). Il Borelli stesso ebbe, poco dopo la pub­<lb></lb>blicazione della Lettera del Mutoli, una polemica alquanto acerba coll&#039;Auzout, <lb></lb>il quale andava pure professando l&#039;ipotesi ticoniana modificata, o come di­<lb></lb>cevasi, perfezionata dal Wardo. </s></p><p type="main">

<s>In quella stessa Lettera del Mutoli non erasi ancora il Borelli, come <lb></lb>dicemmo, pronunziato intorno alla linea del moto della Cometa, ma poi ri­<lb></lb>pensando ch&#039;era questo uno de&#039;punti più vitali della nuova teoria cometa­<lb></lb>ria, si volse a speculare, aiutandosi de&#039;calcoli e delle esperienze, intantochè, <lb></lb>ai primi di Maggio, che vuol dir dopo tre mesi ch&#039;era stata pubblicata la Let­<lb></lb>tera del finto Mutoli, così scriveva al principe Leopoldo, da Pisa: “ Parmi <lb></lb>primieramente che il vero e real movimento della presente Cometa non possa <lb></lb>essere in niun conto fatto per linea retta, ma per una curva, tanto simile <lb></lb>a una parabola, che è cosa da stupire, e questo non solo lo mostra il cal­<lb></lb>colo, ma ancora un&#039;esperienza meccanica, che farò vedere a V. A. al mio <lb></lb>arrivo a Firenze ” (ivi, pag. </s>

<s>131). </s></p><p type="main">

<s>Un altro libro del Cassini, in proposito della Cometa, e nel quale veni­<lb></lb>vansi dall&#039;Autore a professare dottrine alquanto diverse dalle prime, benchè <lb></lb>sempre fondate sull&#039;ipotesi dell&#039;epiciclo flessibile, sollecitarono la partenza <lb></lb>del Borelli da Pisa, e una settimana dopo tornava a scrivere al Principe <lb></lb>nella seguente maniera: “ Mi giunge il libro del signor Cassini, il quale mi <lb></lb>tira di nuovo alla speculazione della Cometa, perchè egli, soverchiamente <lb></lb>invaghito dell&#039;epiciclo vastissimo, che attribuisce alla Cometa passata, vo­<lb></lb>lendo che ella si rivolga intorno alla Canicola, si compiace anche di toccare <lb></lb>qualche cosetta dell&#039;Epistola del Mutoli; cosa che ne poteva far di meno, <lb></lb>avendo poca ragione. </s>

<s>Però dubito che sarà bisogno entrare di nuovo in questa <lb></lb>materia, e scriver qualche altra cosa, forse in occasione di spiegar la figura <lb></lb>della linea del moto reale della Cometa presente, e penso d&#039;indirizzarla al <lb></lb>signor Bullialdo, spiegando con figure tutte le cose conforme egli desidera. </s>

<s>” </s></p><pb xlink:href="020/01/1076.jpg" pagenum="519"></pb><p type="main">

<s>“ Per questo bisognerà affrettar la mia partenza da Pisa, qualche giorno <lb></lb>prima di quello ch&#039;io pensava, per potermi quietamente porre a travagliare, <lb></lb>e liberarmi presto dai pensieri e disturbi della partenza. </s>

<s>Però supplico V. A. <lb></lb>che si compiaccia concedermi licenza di potermene venir, prima di Pasqua <lb></lb>(di Pentecoste), giacchè qui da ora innanzi in ogni modo la mia stanza, per <lb></lb>servigio dello Studio, è infruttuosa. </s>

<s>” </s></p><p type="main">

<s>“ Di più, avendo io commesso a diversi amici che mi trovassero qual­<lb></lb>che villuccia vicino alla città, oppur qualche casa sulla Costa a S. Giorgio, <lb></lb>non è stato finora possibile conseguire nè l&#039;una nè l&#039;altra. </s>

<s>Questo lo desi­<lb></lb>deravo io, non solo per liberarmi da quei martelli e strepiti, che si sentono <lb></lb>dalle stanze di Palazzo Vecchio, nelle quali poco si può dormire e meno stu­<lb></lb>diare e speculare, ma anche l&#039;avevo caro, per potere scoprire il cielo e poter <lb></lb>fare qualche osservazione. </s>

<s>Questo bisogno ora si accresce, comparendo la <lb></lb>Cometa prima del levare del Sole, la quale desidererei, se fosse possibile, <lb></lb>continuare ad osservare colla Macchina grande, che ultimamente ho fab­<lb></lb>bricata. </s>

<s>” </s></p><p type="main">

<s>“ Son dunque costretto di ricorrere al favore di V. A. S., e perchè io <lb></lb>non so se questo che mi è stato anteposto, sia impertinenza e temerità, però <lb></lb>lo propongo con le debite riserve, cioè, quando non sia domanda sproposi­<lb></lb>tata, perchè, in altra maniera, sia per non detto. </s>

<s>Mi dicono esservi la For­<lb></lb>tezza di S. Miniato, e quivi vicino il Convento dei padri zoccolanti, dai quali <lb></lb>luoghi si scopre l&#039;orizzonte orientale, e mi dicono che ambedue sono copiosi <lb></lb>di stanze vacue, ma nella Fortezza non so se sia lecito, nel Convento mi <lb></lb>sarebbe scomodo, non potendo avere il servigio della mia serva ” (MSS. Gal., <lb></lb>Filze Nelli, A, B, c. </s>

<s>391). </s></p><p type="main">

<s>Il principe Leopoldo dette generosamente al Borelli licenza di andare <lb></lb>nella Fortezza di S. Miniato, ch&#039;ebbe l&#039;onore di essere trasformata in una <lb></lb>delle prime Specule, che fossero per le osservazioni celesti state erette in <lb></lb>Italia. </s>

<s>Il nuovo Astronomo la corredò d&#039;importanti strumenti, fra&#039;quali la <lb></lb>gran Macchina, di che l&#039;abbiamo inteso parlare, e che consisteva in un Se­<lb></lb>stante di cinque braccia di raggio, costruito di regoli di legno, e che si de­<lb></lb>scrive a tergo della c. </s>

<s>368 nella Filza citata. </s></p><p type="main">

<s>Quel che più però al presente proposito importa, è che, ad una parete <lb></lb>di quelle stanze di S. Miniato, fu applicato lo strumento a dimostrare spe­<lb></lb>rimentalmente il corso parabolico della Cometa, com&#039;è attestato dallo stesso <lb></lb>Borelli in queste parole, che il dì 2 Aprile 1667 indirizzava al principe Leo­<lb></lb>poldo da Pisa, prima di abbandonar la Toscana, per tornarsene alla sua patria <lb></lb>Messina. </s>

<s>“ E perchè vado disponendo pian piano le cose per la partenza, <lb></lb>che non potrà essere prima di mezzo Maggio, ho pensato di offrire a V. A. <lb></lb>alcuni Strumenti e Macchine astronomiche, che stanno riposte nelle stanze <lb></lb>della Fortezza di S. Miniato, dove particolarmente vi è quella, che rappre­<lb></lb>senta al vivo la via parabolica che fece la prima Cometa di quelle ultime <lb></lb>che comparirono. </s>

<s>Vero è che, per essere fermamente accomodata al muro <lb></lb>d&#039;una delle dette stanze, vi sarà difficoltà al trasportarla in altro luogo, però <pb xlink:href="020/01/1077.jpg" pagenum="520"></pb>sarà bisogno che non la faccia toccare, prima che arrivino i dottori Marchetti <lb></lb>e Bellini, i quali sono informati del modo come si dovrà assettare ” (MSS. <lb></lb>Cim., T. XIX, c. </s>

<s>18). </s></p><p type="main">

<s>Ora il desiderio nostro e de&#039;nostri lettori sarebbe quello di aver par­<lb></lb>ticolarmente descritta quella macchina per l&#039;esperienza della Cometa, ma non <lb></lb>si può averne sodisfazione, perchè la macchina stessa dee essere andata <lb></lb>dispersa, e non se ne trova, per quel che si sappia da noi, negli scritti, me­<lb></lb>moria. </s>

<s>Si sperava che il Marchetti ne dicesse qualche cosa in proposito, o <lb></lb>nel Discorso manoscritto o nella Lettera stampata, ma non se ne trova per <lb></lb>verità fatto alcun cenno, essendo ciò dall&#039;altra parte alieno dal suo istituto, <lb></lb>ch&#039;era quello di confutare il sistema pitagorico. </s></p><p type="main">

<s>Intanto, nella mancanza di dati certi, non ci siamo rimasti di far qual­<lb></lb>che uso di congetture, per fondamento delle quali abbiamo prese quelle no­<lb></lb>tizie, che si son potute raccogliere, e fra le quali è da far primo conto di <lb></lb>quella, che ci assicura essere stato il Borelli scorto a concludere la sua teo­<lb></lb>ria cometaria da&#039;calcoli e dalle esperienze. </s>

<s>I calcoli non potevano esser cer­<lb></lb>tamente condotti se non che sopra i teoremi già conosciuti della Meccenica, <lb></lb>per cui, se doveva la Cometa descrivere per sua orbita una Parabola, con­<lb></lb>veniva riguardarla come soggetta all&#039;azione di due forze, una diretta verso <lb></lb>il centro, e l&#039;altra rifuggente dal centro stesso, in direzion tangenziale. </s></p><p type="main">

<s>Se avesse il Borelli, come udimmo, mantenuto il proposito di tornare <lb></lb>a trattar della Cometa in un&#039;altra scrittura, ch&#039;ei voleva indirizzare al Bul­<lb></lb>lialdo, si sarebbe lì veduta spiegar, per mezzo dell&#039;esperienza, la figura della <lb></lb>linea del moto, ma sembra che quella scrittura non avesse poi dall&#039;Autore <lb></lb>il suo effetto. </s>

<s>Il di 27 Aprile 1665 scriveva al principe Leopoldo: “ Quelle <lb></lb>parole del signor Bullialdo mi hanno stuzzicato a fare una mano di propo­<lb></lb>sizioni, per render ragione del movimento della Cometa secondo l&#039;ipotesi <lb></lb>pitagorica, le quali ho brevemente notato in scritto, per servirmene se farà <lb></lb>bisogno ” (MSS. Cim., T. XVIII, c. </s>

<s>171). Forse il bisogno non si presentò, <lb></lb>e le proposizioni, che si dovevano dimostrar coi calcoli e con l&#039;esperienze, <lb></lb>rimasero nella mente del loro Autore, o per meglio dire non presero quella <lb></lb>forma di scrittura diretta al Boulliaud, com&#039;era stata la prima intenzione. </s></p><p type="main">

<s>Quanto ai calcoli non è stata difficile la <lb></lb>congettura: quanto alle esperienze poi noi <lb></lb>richiamiamo l&#039;attenzione dei nostri lettori <lb></lb>sopra quella insigne così descritta nel II li­<lb></lb>bro delle Theoricae Mediceorum. </s>

<s>“ Sumatur <lb></lb><figure id="id.020.01.1077.1.jpg" xlink:href="020/01/1077/1.jpg"></figure></s></p><p type="caption">

<s>Figura 101. circulus ligneus ABC (fig. </s>

<s>101) cui diameter <lb></lb>aptetur pariter linea AB eius vero centro D <lb></lb>aptetur axiculus seu virga DE plano circuli <lb></lb>ABC erecta, ac eidem centro D apponatur <lb></lb>portio aliqua Magnetis F, cuius polus meri­<lb></lb>dionalis respiciat punctum A. </s>

<s>Deinde haec <lb></lb>omnia ita composita innatent in aqua sta-<pb xlink:href="020/01/1078.jpg" pagenum="521"></pb>gni RS. </s>

<s>In G autem adsit portio aliqua suberis supra quam sit globulus <lb></lb>aliquis ferreus I. </s>

<s>Possit autem huiusmodi suber simul cum ferreo globulo <lb></lb>supposito libere natare in ipsa aqua. </s>

<s>Deinde vero suber praedictum G admo­<lb></lb>veatur magneti F, quousque incidat in sphaeram activitatis eiusdem Magne­<lb></lb>tis, usque scilicet ad eum situm, ex quo ipse ferreus globulus incipit lente <lb></lb>approprinquari ipsi Magneti. </s>

<s>Tunc vero manu orizontaliter circumgiretur <lb></lb>extremum punctum E ipsius virgae ” (Florentiae 1665, pag. </s>

<s>48). E propone <lb></lb>che si giri con tale velocità, che la forza centrifuga contemperi l&#039;attrazione <lb></lb>magnetica. </s>

<s>Si vedrà così, dice l&#039;Autore, girare la palla di ferro intorno al <lb></lb>Magnete, come intorno al suo centro, benchè non sia fisicamente congiunta <lb></lb>con esso. </s></p><p type="main">

<s>Passa in seguito il Borelli a dir come si potrebbe rendere anche più <lb></lb>semplice l&#039;esperienza, rimovendo il Magnete, e facendo che la palla di ferro, <lb></lb>o di qualunque altra materia, sia impedita di scendere per natural gravità <lb></lb>al centro del circolo di legno, e rimanga sospesa nella scanalatura del rag­<lb></lb>gio, per la forza centrifuga eccitatavi dal rapidissimo moto. </s>

<s>Dietro le quali <lb></lb>esperienze poi così conclude: “ Quapropter si eodem modo concipiamus in <lb></lb>spatio aethereo Planeta in G (fig. </s>

<s>preced.) qui naturalem habeat instinctum <lb></lb>approprinquandi soli D, simulque in orbem feratur circa idem solare cen­<lb></lb>trum tali celeritate, quae sufficiat ad removendum Planetam, praecise tan­<lb></lb>tum, quantum ipse in unoquoque instanti Soli appropinquaret, dubium pro­<lb></lb>fecto non est quod hisce duobus motibus contrariis sese invicem compen­<lb></lb>santibus Stella G, neque admovebitur neque removebitur ab ipso Sole D <lb></lb>maiori spatio quam semidiameter DG, ideoque librata et innatans apparebit, <lb></lb>aut retenta ab aliquo firmo vinculo, quamvis sita sit in aethere fluidissimo, <lb></lb>nullique rei innitetur et a nulla substentetur ” (ibi, pag. </s>

<s>49). </s></p><p type="main">

<s>La somiglianza delle conclusioni rispetto al moto dei Pianeti e al moto <lb></lb>delle Comete ci apre la via a congetturar della somiglianza della esperienze. </s>

<s><lb></lb>Essendo, nell&#039;opinion del Borelli, la sostanza della Cometa materia cosmica <lb></lb>staccatasi da qualche Pianeta, ed errante per gli spazii eterei, la direzione <lb></lb>presa dal moto di essa materia doveva essere secondo la tangente dell&#039;or­<lb></lb>bita planetaria, d&#039;ond&#039;erasi distaccata, e sarebbe, per legge d&#039;inerzia, dovuta <lb></lb>seguitare a correre in quella direzione, se non fosse entrata nella sfera del­<lb></lb>l&#039;attrazione del Sole. </s>

<s>Ecco dunque le due componenti del moto parabolico. </s>

<s><lb></lb>L&#039;intensità delle due forze, dalla composizion delle quali il detto moto re­<lb></lb>sulta, o in altro modo il parametro della Parabola, era soggetto a quei cal­<lb></lb>coli, da cui dice il Borelli stesso che fu condotto alla sua conclusione. </s></p><p type="main">

<s>L&#039;esperienza poi propria, che poteva render visibili i resultati di que­<lb></lb>sti calcoli meccanici, noi ci diam facilmente a credere che avesse una gran <lb></lb>somiglianza con quella, con la quale dimostrava l&#039;Autore della Teorica de&#039;Me­<lb></lb>dicei il perpetuo circolar de&#039;Pianeti, librati nel libero etere intorno al Sole. </s>

<s><lb></lb>Consisteva insomma, secondo noi, l&#039;esperienza borelliana da dimostrare il <lb></lb>moto parabolico fatto dalla Cometa in sopreccitare in una palla di ferro la <lb></lb>forza centrifuga, e poi lasciarla fuggir lungo la tangente dell&#039;orbita, per la <pb xlink:href="020/01/1079.jpg" pagenum="522"></pb>quale avrebbe proseguito il suo corso, se non fosse stata attratta da un globo <lb></lb>magnetico opportunamente collocato nello Strumento. </s></p><p type="main">

<s>Quel che speculò e sperimentò il Borelli in questo importantissimo sog­<lb></lb>getto era rimasto dimenticato e sepolto nelle carte manoscritte di lui, e nelle <lb></lb>stanze della Fortezza di S. Miniato, quando, incontratosi ne&#039;medesimi con­<lb></lb>cetti l&#039;Hevelio, pubblicò in Danzica, nel 1668, la sua <emph type="italics"></emph>Cometografia.<emph.end type="italics"></emph.end> La ma­<lb></lb>teria delle Comete è, secondo l&#039;Autore, tenuissima ed evanescente, come <lb></lb>quella delle scorie notanti nella fotosfera, e che producono le macchie del <lb></lb>Sole. </s>

<s>Conclude di qui non poter le Comete moversi e rigirarsi in orbite <lb></lb>chiuse, essendo queste convenienti solo alla sempiterna sostanza dei Pianeti. <lb></lb></s>

<s>“ Cum igitur Cometae, ex tenuissima materia, atque minimis corpusculis <lb></lb>primum nascantur, ac successive in magnam excrescant molem, dum rursus <lb></lb>resolvuntur ac denique in subtilissimam aetheriam materiam rediguntur, si­<lb></lb>cut lib. </s>

<s>VII prolixe deduximus, neutiquam ergo Cometae sunt corpora per­<lb></lb>petua, sed potius temporanea, quibus autem motum assignare continuum a<gap></gap><lb></lb>perpetuum nimis absurdum esse videtur, nec suadet sane ratio corpora vi­<lb></lb>delicet caduca in circulo vel ellipsi perpetuo moveri, pariter atque Planetae, <lb></lb>qui corpora sunt aetherea, perfecta, aeterna, motum nunquam non conti­<lb></lb>nuum ac perpetuum exercentia ” (pag. </s>

<s>562). Perciò conclude, dietro queste <lb></lb>ragioni, non potere alle Comete competere altro moto che retto. </s>

<s>“ Gaudent <lb></lb>igitur Cometae, ex nostra sententia, hocce unico motu, fere recto ” (pag. </s>

<s>568). </s></p><p type="main">

<s>La direzione poi di questo moto è secondo la tangente dell&#039;orbita del <lb></lb>Pianeta, da cui si staccano le materie cometarie, ed uscite da quell&#039;ammo­<lb></lb>sfera, venendo attratte dal Sole, descrivono per la resultante di queste due <lb></lb>forze, una delle quali intrinseca e naturale, l&#039;altra estrinseca e violenta, <lb></lb>un&#039;orbita parabolica, a quel modo che la descrive un sasso cadente, dopo <lb></lb>essere uscito dalla vertigine della fionda. </s>

<s>“ Simili plane ratione etiam Co­<lb></lb>metas duos praecipuos motus favent, cuius alter est extrinsecus, et quasi <lb></lb>violentus, qui a vertigine atmosphaerae proficiscitur, mediante quo impetus <lb></lb>Cometae imprimitur (dum atmosphaera exit, et eam deserit, atque suae spon­<lb></lb>tis redditur) visque ei inditur se ulterius movendi, et quidem secundum <lb></lb>tangentem, seu lineam rectam, nisi alia causa impediens interveniat. </s>

<s>Alter <lb></lb>autem pariter naturalis et intrinsecus est, non quidem ex eo quod Come­<lb></lb>tis acque ac terrestribus gravitatem attribuam, sed alia huic non prorsus <lb></lb>dissimilis appetentia eis competat, ex qua Cometae omnes erga Solem, tan­<lb></lb>quam centrum Mundi,.... obvertuntur ” (pag. </s>

<s>666). </s></p><p type="main">

<s>Quest&#039;apparenza poi, che ha la materia cometaria, alla quale l&#039;Hevelio <lb></lb>assegna la figura uniforme e costante di un disco o di una tavola piana, la <lb></lb>rassomiglia alle attrazioni de&#039;due poli magnetici. </s>

<s>“ Haecque appetentia, sive <lb></lb>hic motus, cuius beneficio Cometae perpetuo altero lato plano ad centrum <lb></lb>Universi, altero opposito ad orbes Planetarum propendent, propemodum ae­<lb></lb>mulatur acum magneticam, quae alteram cuspidem indesinenter Aquilonem, <lb></lb>alteram Austrum versus obvertit, exporrigit, atque dirigit ” (pag. </s>

<s>667). </s></p><p type="main">

<s>Da questa parté però l&#039;Hevelio rimane molto indietro al Borelli, il quale, <pb xlink:href="020/01/1080.jpg" pagenum="523"></pb>oltre alla forza attrattiva, rassomigliata alla magnetica, aveva messo in gioco <lb></lb>la repulsiva delle forze centrifughe, e così approssimavasi di più alle sco­<lb></lb>perte del Newton, il quale soggettò finalmente le Comete all&#039;eterne leggi <lb></lb>dei moti planetari. </s>

<s>Si possono fare, egli dice in sulla fine del suo opuscolo <lb></lb><emph type="italics"></emph>De mundi systemate,<emph.end type="italics"></emph.end> intorno alle Comete&#039;tre ipotesi: o elle si generano e <lb></lb>si disfanno ogni volta, che appariscono e spariscono, o venendo dalle regioni <lb></lb>delle stelle fisse penetrano nel nostro sistema planetario, o finalmente si ri­<lb></lb>volgono in orbite molto eccentriche intorno al Sole. </s>

<s>Nel primo caso descri­<lb></lb>veranno una qualche sezione conica, la forma propria della quale sarà de­<lb></lb>terminata dal vario grado della velocità. </s>

<s>Nel secondo caso, descriveranno <lb></lb>un&#039;Iperbola, e nel terzo un&#039;Ellisse, tanto allungata da rassomigliarsi più <lb></lb>presto a una Parabola. </s>

<s>“ Orbes autem, si lex Planetarum servetur, haud <lb></lb>multum divaricabunt a plano Ecclipticae. </s>

<s>Et quantum hactenus animadver­<lb></lb>tere potui, casus tertius obtinet ” (Lausannae 1744, pag. </s>

<s>59, 60). </s></p><p type="main">

<s>Quanto alla fisica costituzione il Newton riguardò le code come pro­<lb></lb>dotte da materie esalate dal nucleo delle Comete, e respinte per circumpul­<lb></lb>sione dal centro del Sole, come sono respinti i fumi o altri corpi più leggeri <lb></lb>dell&#039;aria, per circumpulsione, dal centro della nostra Terra. </s>

<s>“ Ut in aere no­<lb></lb>stro fumus corporis cuiusvis igniti petit superiora, idque vel perpendicula­<lb></lb>riter, si corpus quiescat, vel oblique si corpus moveatur in latus; ita in <lb></lb>coelis, ubi corpora gravitant in Solem, fumi et vapores ascendere debent a <lb></lb>Sole ” (ibi, pag. </s>

<s>57). Così vennero finalmente a ridursi nel dominio della <lb></lb>scienza fisica e matematica quelli spettri paurosi, che s&#039;eran prima creduti <lb></lb>apparire di quando in quando nel cielo senz&#039;ordine e senza legge. </s></p><pb xlink:href="020/01/1081.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO XIV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>De&#039;moti dell&#039;Universo<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della scoperta delle Orbite ellittiche, e delle leggi del moto dei Piancti. </s>

<s>— II. </s>

<s>Delle forze centrali, <lb></lb>e dei decrementi delle loro intensità, in ragione delle distanze. </s>

<s>— III. </s>

<s>Delle leggi delle forze <lb></lb>centrali; dell&#039;attrazione universale; dell&#039;origine delle Orbite ellittiche. </s>

<s>— IV. </s>

<s>Delle varie ipo­<lb></lb>tesi proposte a spiegar la tendenza dei gravi ai loro centri. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi ripensa che, dopo tanti secoli e dopo tante aberrazioni, il Newton, <lb></lb>rispetto all&#039;essere e al moto delle Comete, confermò finalmente una verità, <lb></lb>lo splendor della quale, come raggio di stella in mezzo alle nubi, erasi già <lb></lb>rivelato alle menti degli antichi Pitagorici italiani, riman preso di tal mara­<lb></lb>viglia, che il pensiero di lui distende lietamente il volo a considerare altri <lb></lb>placiti di quella prima Filosofia, per concluderne all&#039;ultimo che non è l&#039;am­<lb></lb>mirata scienza moderna altro che un grande albero cresciuto, sotto un lun­<lb></lb>ghissimo inverno, da quell&#039;arbusto. </s>

<s>A persuadersi intanto di ciò, si dee sentir <lb></lb>l&#039;animo disposto chiunque ha per lungo tempo sentito, in discorrere del vero <lb></lb>sistema del mondo, chiamarlo indifferentemente col nome di Pitagorico e <lb></lb>di Copernicano, e chiunque altro, in legger la prefazione al libro delle Revo­<lb></lb>luzioni degli orbi celesti, udi il Copernico stesso commemorare con grande <lb></lb>onore, come suoi predecessori e maestri, Niceta da Siracusa e Filolao. </s></p><p type="main">

<s>Così veniva la lampada del Mondo a collocarsi al suo posto, in mezzo <lb></lb>al magnifico tempio, e così fiaccavasi il mostruoso orgoglio di quella Filo­<lb></lb>sofia, che insegnava il cielo essere stato creato in servigio della Terra. </s>

<s>Di <lb></lb>più toglievano affatto di mezzo i Pitagorici quella differenza, e anzi quel con-<pb xlink:href="020/01/1082.jpg" pagenum="525"></pb>trapposto fra Cielo e Terra, da una parte insegnando che la Terra era essa <lb></lb>pure celeste, e dall&#039;altra che i corpi stessi celesti partecipavano delle qua­<lb></lb>lità terrene. </s>

<s>Udimmo da Plutarco come si credeva che partecipasse di così <lb></lb>fatte qualità terrene la Luna, e i moderni, con l&#039;aiuto de&#039;Canocchiali, con­<lb></lb>fermarono pienamente i placiti pitagorici e gli estesero alla costituzione fisica <lb></lb>di tutti gli altri Pianeti, che trovarono montuosi come la Terra, e come la <lb></lb>Terra involti in una ammosfera variabile di aspetto fra il sereno e le nubi. </s></p><p type="main">

<s>Quando si giunse a intendere fra il Cielo e la Terra una tal cognazione, <lb></lb>e confermatesi per i fatti osservati le filosofiche speculazioni si ridusse ad <lb></lb>unità quel che prima. </s>

<s>era diviso, si compiacquero gli uomini di aver fatto <lb></lb>nella scienza del Cosmo un gran progresso. </s>

<s>Sperarono che sarebbe a un tal <lb></lb>progresso quasi costituito il suo termine, se si fosse riusciti a dimostrare <lb></lb>che, formando le varie membra un solo corpo fisico, da un unico principio <lb></lb>si dispensasse a questo corpo la vita: la qual vita, perciocchè manifestasi <lb></lb>nel moto, si comprese che sarebbe allora pienamente dimostrata l&#039;unità del­<lb></lb>l&#039;Universo, quando si vedesse tutto esser mosso da un medesimo impulso, <lb></lb>e tutto seguitare a moversi con una medesima legge. </s></p><p type="main">

<s>Le speranze che potesse la scienza dell&#039;uomo sollevarsi tanto alto, sulla <lb></lb>fine del secolo XVII, furono sodisfatte, ma colui, a cui toccò tanta gloria, <lb></lb>non s&#039;intende com&#039;avesse così potuto ignorare i placiti dell&#039;antichissima Fi­<lb></lb>losofia italica, da scrivere queste parole: “ Quibus vinculis Antiqui plane­<lb></lb>tas in spatiis liberis retineri, deque cursu rectilineo perpetuo retractos in <lb></lb>orbem regulariter agi docuere, non constat ” (Neutoni, Opusc. </s>

<s>De mundi <lb></lb>system., Lausannae 1744, pag. </s>

<s>6). Consta anzi fia Plutarco che dicevano que­<lb></lb>gli Antichi per questo ritenersi ne&#039;liberi spazii la Luna, perchè si muove <lb></lb>intorno alla Terra, come riman sospeso un sasso, o girato nella fionda o <lb></lb>scagliato liberamente nell&#039;aria. </s>

<s>Fa poi tanto più maraviglia l&#039;avere il Newton <lb></lb>ignorate le tradizioni dell&#039;antica Scuola italiana, vedendolo incominciare a <lb></lb>spiegare i suoi pensieri coll&#039;esempio stesso del sasso, il quale se si potesse, <lb></lb>ei dice, gittare con tanta forza da non lasciarlo cadere, s&#039;aggirerebbe an­<lb></lb>ch&#039;egli perpetuamente in orbe intorno alla Terra, come la Luna. </s></p><p type="main">

<s>Tra la Filosofia antica e questa nuova ci è senza dubbio una gran dif­<lb></lb>ferenza, la quale è il portato degli anni e della cultura. </s>

<s>E perchè veramente, <lb></lb>dai primi anni del secolo XVII, incominciò quella cultura ad essere frut­<lb></lb>tuosa, dee aver di lì principio questa parte di storia, nella quale si vuol da <lb></lb>noi brevemente narrare per quali vie si riuscisse a scoprir quell&#039;unica forza, <lb></lb>che dà legge di moto al sasso scagliato per l&#039;aria, e alle stelle erranti per <lb></lb>l&#039;etere immenso. </s></p><p type="main">

<s>S&#039;erano studiati i Filosofi antichi di ridurre all&#039;unità e alla semplicità <lb></lb>questo moto de&#039;corpi celesti, facendoli rigirar perpetuamente intorno a un <lb></lb>centro, in orbite circolari. </s>

<s>La desiderata semplicità però, in tali orbite, si <lb></lb>dovè confessare che non erasi conseguita, e quanto più l&#039;Astronomia faceva <lb></lb>progressi, e più ritrovava in quel mondano assettamento disordini e irrego­<lb></lb>larità da correggersi. </s>

<s>Nè a una tal correzione si trovarono sufficienti o la <pb xlink:href="020/01/1083.jpg" pagenum="526"></pb>complicata macchina degli Equanti e dei Deferenti di Tolomeo, o quella stessa <lb></lb>più semplice degli Eccentrici e degli Epicicli copernicani. </s></p><p type="main">

<s>Supposto moversi i Pianeti in orbite circolari, le discrepanze notabilis­<lb></lb>sime, che passavano fra i calcoli e le osservazioni, si fecero principalmente <lb></lb>sentire a quel Ticone, che in calcolare e in osservare i moti del cielo aveva <lb></lb>tutta consacrata la vita. </s>

<s>Sentitosi Giovanni Keplero chiamare a quel mede­<lb></lb>simo ministero in Germania, si doleva che la troppa lontananza dall&#039;Astro­<lb></lb>nomo danese gl&#039;impediva di frequentar quella Scuola, di che ebbe poi a <lb></lb>consolarsi, quando Ticone stesso venne in Boemia. </s>

<s>“ Eo igitur veni, sub <lb></lb>initium anni MDC, spe Planetarum correctas eccentricitates addiscendi ” (De <lb></lb>Stella Martis, Pragae 1909, pag. </s>

<s>53). Avvenne per divina disposizione, pro­<lb></lb>segue a dire il Keplero, che in quel tempo, che io venni in Boemia, le os­<lb></lb>servazioni del gran Maestro e de&#039;familiari di lui fossero tutte rivolte alla <lb></lb>Stella di Marte “ ex cuius motibus omnino necesse est nos in cognitionem <lb></lb>Astronomiae arcanorum venire, aut ea perpetuo nescire ” (ibi). </s></p><p type="main">

<s>Or quale arcana cognizione astronomica erasi rivelata al Keplero dai moti di <lb></lb>Marte? </s>

<s>Quella, rispondiamo, che le orbite de&#039;Pianeti non sono altrimenti cir­<lb></lb>colari, come avevano posto tutti gli Astronomi predecessori di lui, ma ellitti­<lb></lb>che, come veniva dimostrato dai fatti. </s>

<s>La dimostrazione della grande scoperta <lb></lb>kepleriana si conduce, e si conclude dall&#039;Autore nel suo Commentario <emph type="italics"></emph>De <lb></lb>Stella Martis,<emph.end type="italics"></emph.end> nella maniera che qui da noi compendiosamente si riferisce. </s></p><p type="main">

<s>Osservato Marte in tre diversi tempi, cioè ne&#039;di 31 Ottobre e 31 Di­<lb></lb>cembre dell&#039;anno 1590, e ne&#039;di 25 Ottobre dell&#039;anno 1595, fu trovato a tre <lb></lb>differenti distanze dal centro del Sole, le quali, ridotte al medesimo mese <lb></lb>di Qttobre e al medesimo anno 1590, venivano espresse dal numero 147750, <lb></lb>essendo Marte in 14°, 16′, 52″ del Tauro; dal numero 163100, essendo il <lb></lb>Pianeta in 5°, 24′, 21″ della Libbra, e dal numero 166255, essendo lo stesso <lb></lb>Pianeta in 8°, 19′, 4″ della Vergine. </s></p><p type="main">

<s>Ora, per rappresentarci queste varie po­<lb></lb>sizioni, sia, nella figura 102, A il Sole, e si <lb></lb><figure id="id.020.01.1083.1.jpg" xlink:href="020/01/1083/1.jpg"></figure></s></p><p type="caption">

<s>Figura 102.<lb></lb>conducano dal centro di lui le linee AK, AT, <lb></lb>in modo che sia l&#039;angolo KAT=114°, 2′, <lb></lb>12″, quanta è nel Zodiaco la distanza dal 14 <lb></lb>grado del Tauro all&#039;8° della Vergine. </s>

<s>Si con­<lb></lb>duca in oltre dal medesimo punto la linea AH <lb></lb>in modo, che l&#039;angolo KAH riesca uguale a <lb></lb>27°, 5′, 17″, quanto è dall&#039;8° del Tauro al 5° <lb></lb>della Libbra. </s>

<s>Se per i tre punti T, K, H si fa <lb></lb>passare un circolo, questo dovrebbe secondo <lb></lb>gli Astronomi segnar la via percorsa da Marte, <lb></lb>e se ciò è vero debbono le distanze AT, AK, <lb></lb>AH, ritrovate per l&#039;osservazione, corrispon­<lb></lb>dere a quelle che resultan dal calcolo, data la posizion del Pianeta e l&#039;ec­<lb></lb>centricità dell&#039;Orbita. </s></p><pb xlink:href="020/01/1084.jpg" pagenum="527"></pb><p type="main">

<s>Per la più giusta misura di tale eccentricità; dice il Keplero, le osser­<lb></lb>vazioni mi hanno dato modo di stabilire quel che avevo dall&#039;altra parte con­<lb></lb>cluso a priori, cioè la linea degli Apsidi “ non praeter Solem, ut artificibus <lb></lb>placet, sed per ipsum centrum corporis Solis transire ” (pag. </s>

<s>37). Sia dun­<lb></lb>que ED questa linea degli Apsidi, che pássa per il centro del Sole: sarà in <lb></lb>E l&#039;afelio, in D il perielio, e AG=14140 (pag. </s>

<s>209) misurerà l&#039;eccentri­<lb></lb>cità dell&#039;orbita. </s></p><p type="main">

<s>Condotte ora dal punto G le tre linee GT, GK, GH, i tre nuovi trian­<lb></lb>goli AGT, AGK, AGH che ne resultano, avendo per comun base il lato AG, <lb></lb>eccentricità nota, e di più noti i tre angoli ai vertici, che sono le equa­<lb></lb>zioni ottiche, e gli angoli intorno ad A, essendo dati dalle osservate posizioni <lb></lb>di Marte nel Zodiaco; potranno dunque risolversi, e risoluti danno le di­<lb></lb>stanze AK=166605, AH=163883, AT=148539, notabilmente differenti <lb></lb>come si vede dalle osservate. </s></p><p type="main">

<s>Che si dirà dunque, esce fuori con enfasi il Keplero, che tal differenza <lb></lb>è da attribuirsi al difetto delle osservazioni? </s>

<s>Ma a voi mi rivolgo, o periti <lb></lb>Astronomi “ qui sophistica effugia, caeteris disciplinis creberrima, in Astro­<lb></lb>nomia nulli patere scitis, vos appello ” (pag. </s>

<s>213). Voi vedete tanta essere <lb></lb>la differenza, che non può in nessun modo attribuirsi nè all&#039;imperizia nè <lb></lb>all&#039;incertezza dell&#039;osservare. </s></p><p type="main">

<s>Si dirà forse che convien ritirare l&#039;eccentrico, finchè non aggiunga alla <lb></lb>necessaria distanza? </s>

<s>Ma quanto si ritira da una parte, altrettanto vien man­<lb></lb>cando dall&#039;altra. </s>

<s>Che se si vuol tutto veramente aggiustare, supponete che <lb></lb>il circolo DTEH sia flessibile, e che tenuto fisso in D si debba allungare <lb></lb>verso E: l&#039;allungamento non sarà però possibile, se non a patto che il cir­<lb></lb>colo stesso si trasformi in ovale. </s>

<s>“ Itaque plane hoc est: Orbita Planetae <lb></lb>non est circulus, sed ingrediens ad latera utraque paulatim, iterumque ad <lb></lb>circuli amplitudinem in perigaeo exiens, cuiusmodi figuram itineris <emph type="italics"></emph>Ovalem<emph.end type="italics"></emph.end><lb></lb>appellitant ” (pag. </s>

<s>312, 14). </s></p><p type="main">

<s>Dimostrato così che l&#039;orbita planetaria è un Ellisse, il Keplero tornò a <lb></lb>considerare i tempi, in relazione alle porzioni del piano ellittico o dell&#039;aree <lb></lb>descritte dalla linea, che va dal Sole al Pianeta. </s>

<s>Aveva già dimostrato l&#039;Au­<lb></lb>tore che in qualunque Sistema o tolemaico o copernicano “ quo longius <lb></lb>abest Planeta a puncto illo, quod pro centro mundi assumitur, hoc debilius <lb></lb>illum incitari circa illud punctum ” (pag. </s>

<s>167) d&#039;onde ne conseguiva, anche <lb></lb>nell&#039;ipotesi delle orbite circolari “ partes plani metiri moras, quas Planeta <lb></lb>in partibus respondentis circumferentiae eccentricae trahat ” (pag. </s>

<s>214). </s></p><p type="main">

<s>Or perchè queste more o questi tempi sono egualmente bene misurati <lb></lb>dal piano dell&#039;orbita ellittica “ partes igitur plani diminuti aphelio et pe­<lb></lb>rihelio proximae metientur tempus maius, quia apud illas tenuis est dimi­<lb></lb>nutio, sed partes in longitudinibus mediis metientur minus tempus quam <lb></lb>antea, quia in illis accidit potissima totius plani diminutio. </s>

<s>Tam igitur, si <lb></lb>utamur hoc diminuto plano ad moderandas aequationes, fiet Planeta circa <lb></lb>aphelium et perihelium tardior, quam in priori vitiosa aequationum forma, <pb xlink:href="020/01/1085.jpg" pagenum="528"></pb>circa longitudines medias velocior, quia distantiae hic diminuuntur. </s>

<s>Morae <lb></lb>igitur hinc abstractae in aphelium et perihelium, sursum deorsumque com­<lb></lb>pensatione facta accumulabuntur, non secus ac si quis botellum ventrico­<lb></lb>sum in medio comprimat, eaque compressione minutal infarctum, e ventre <lb></lb>magis in utrasque extremitates infra supraque manum eminentes exprimat <lb></lb>et elidat ” (ibi). Ciò che tradotto in altre parole significa: <emph type="italics"></emph>Le aree descritte <lb></lb>dal raggio vcttore sono proporzionali ai tempi impiegati nel descriverle.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Questa era per il Keplero come una nota nuova nell&#039;armonia dell&#039;Uni­<lb></lb>verso, ma era una nota sola, che non modulavasi in aria di canto. </s>

<s>Non pago <lb></lb>perciò volle mettersi a ricercare l&#039;armonia fra due Pianeti, nelle relazioni <lb></lb>che passano fra gl&#039;intervalli delle orbite e i tempi periodici. </s>

<s>“ Inventis enim <lb></lb>veris orbium intervallis, scrive nel libro V <emph type="italics"></emph>Harmonices mundi,<emph.end type="italics"></emph.end> per obser­<lb></lb>vationes Brahei, plurimi temporis labore continuo, tandem, tandem genuina <lb></lb>proportio temporum periodicorum ad proportionem orbium <emph type="italics"></emph>sera quidem <lb></lb>respexit inertem, respexit tamen, et longo post tempore venit.<emph.end type="italics"></emph.end> Eaque, si <lb></lb>temporis articulos petis, 8 Martii huius anni millesimi sexcentesimi decimi <lb></lb>octavi animo concepta, sed infeliciter ad calculos vocata, eoque pro falsa <lb></lb>reiecta; denique, 15 Maii reversa, novo capto impetu expugnavit mentis meae <lb></lb>tenebras tanta comprobatione et laboris mei septem decennalis in observa­<lb></lb>tionibus braheanis, et meditationis huius in unum conspirantium, ut somniare <lb></lb>me et praesumere quaesitum inter principia primo crederem. </s>

<s>Sed res est <lb></lb>certissima exactissimaque quod <emph type="italics"></emph>Proportio quae est inter binorum quorum­<lb></lb>cumque Planetarum tempora periodica sit praecise sesquialtera proportio­<lb></lb>nis mediarum distantiarum, idest orbium ipsorum ”<emph.end type="italics"></emph.end> (Lincii 1619, pag. </s>

<s>189). <lb></lb>Questa è la terza delle mirabili armonie del mondo scoperte dal Keplero, e che <lb></lb>suole esprimersi così nel linguaggio moderno: <emph type="italics"></emph>I quadrati dei tempi periodici <lb></lb>dei diversi Pianeti sono fra loro come i cubi de&#039;grandi assi delle loro orbite.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Le nuove armonie kepleriane suonano dunque molto diverse dalle an­<lb></lb>tiche contemplate da Pitagora o da Platone, ai quali bastò supporre un im­<lb></lb>pulso iniziale dato ai Pianeti, perchè seguitassero a muoversi in sempiterna <lb></lb>uniformità di moto nelle loro orbite circolari. </s>

<s>Che se osservavansi alcune irre­<lb></lb>golarità di que&#039;moti, si davano facilmente a credere che ciò solo apparisse <lb></lb>rispetto a noi, a cui, per gli eccentrici e per gli epicicli, si fanno i Pianeti <lb></lb>ora più da presso ora più lontani. </s></p><p type="main">

<s>La Stella di Marte aveva invece rivelato al Keplero che quegli eccen­<lb></lb>trici e quegli epicicli non erano altro che immaginazioni, movendosi in realtà <lb></lb>il Pianeta ora più di lungi, ora più d&#039;appresso al centro de&#039;suoi moti, in <lb></lb>modo che la maggiore o la minore distanza da questo centro era la regola <lb></lb>de&#039;tempi, ora più lunghi ora più brevi. </s>

<s>Da ciò ne concluse argutamente il <lb></lb>Keplero ch&#039;essendo il centro di que&#039;moti il Sole, dovesse in esso e non in <lb></lb>altro risiedere la virtù motrice. </s>

<s>Ciò potevasi dall&#039;altra parte, ei soggiunge, <lb></lb>anco argomentare a priori dalla dignità e dalla prestanza dello stesso Sole <lb></lb>“ qui est fons vitae mundi .... qui est et lucis, quo totius Machinae constat <lb></lb>ornatus, qui itidem et caloris quo omnia vegetantur ” (pag. </s>

<s>169). </s></p><pb xlink:href="020/01/1086.jpg" pagenum="529"></pb><p type="main">

<s>Ma proseguiamo, dice l&#039;Autore del Commentario <emph type="italics"></emph>De Stella Martis,<emph.end type="italics"></emph.end> a <lb></lb>contemplare questa virtù motrice del Sole: ella non può essere la luce, la <lb></lb>quale non è forse altro che il veicolo o lo strumento, di che la stessa virtù <lb></lb>motrice si serve. </s>

<s>In qualunque modo, è una specie immateriata latitante nel <lb></lb>corpo del Sole, da cui esce e aderisce al Pianeta, come dall&#039;anima del get­<lb></lb>tatore esce il moto e aderisce alla pietra. </s>

<s>Ma la pietra segue il moto della <lb></lb>mano, secondo il quale o va in linea retta o va in giro. </s>

<s>Or perchè i Pia­<lb></lb>neti si muovono in giro, è necessario che in giro pure si muova la <expan abbr="vĩrtù">virrtù</expan> <lb></lb>motrice, cioè il Sole, ma no di spazio in spazio, come nel Sistema di To­<lb></lb>lomeo “ sed super suo centro, seu axe immobilibus, partibus eius de loco <lb></lb>in locum, in eodem tamen spacio toto corpore manente, transeuntibus ” <lb></lb>(pag. </s>

<s>173). </s></p><p type="main">

<s>Nasce però di qui una difficoltà ed è questa: se la virtù motrice è una <lb></lb>specie immateriata, che non può secondo la sua natura debilitarsi per la <lb></lb>distanza, com&#039;avviene che, ricevendo Saturno dal Sole la medesima impres­<lb></lb>sione di moto, si volga nonostante in giro tanto più lentamente di Mercu­<lb></lb>rio? </s>

<s>A che risponde il Keplero che, sebbene immateriata sia la virtù che <lb></lb>muove, materiati sono i Pianeti, e perciò inerti a muoversi, e dediti per na­<lb></lb>tura loro alla quiete. </s>

<s>“ Quarum rerum contentione cum nascatur pugna, su­<lb></lb>perat igitur plus ille Planeta qui in virtute imbecilliore consistit, eaque tardius <lb></lb>movetur, minus ille qui Soli propior. </s>

<s>Docet hinc analogia statuere omnibus <lb></lb>Planetis, ipsi etiam Mercurio humillimo, inesse vim materialem sese expli­<lb></lb>candi nonnihil ex orbe virtutis solaris. </s>

<s>Unde evincitur solaris corporis gyra­<lb></lb>tionem multo antevertere omnium Planetarum periodica tempora, ideoque <lb></lb>ad minimum, citius quam trimestri spacio, Solem semel in suo spacio gy­<lb></lb>rari ” (pag. </s>

<s>174, 75). </s></p><p type="main">

<s>Ma se non è la luce, che altro insomma è questa specie immateriata, <lb></lb>a cui s&#039;attribuisce la virtù di muovere, e contro la quale relutta la corpu­<lb></lb>lenza de&#039;Pianeti, come allo spirito relutta la materia? </s>

<s>Risponde il Keplero <lb></lb>che chi volesse farsene un&#039;idea guardi l&#039;esempio del Magnete “ cuius vir­<lb></lb>tus residet in universo corpore Magnetis, cum eiusdem mole crescit, cum <lb></lb>comminutione illius dividitur et ipsa. </s>

<s>Ita in Sole virtus movens tanto vide­<lb></lb>tur fortior, quod verisimile sit corpus eius esse totius mundi densissimum ” <lb></lb>(pag. </s>

<s>176). </s></p><p type="main">

<s>Si direbbe qui, di primo impeto, che fosse formulata in queste parole <lb></lb>la legge neutoniana delle forze proporzionali alle quantità di materia, se in <lb></lb>quel che il Keplero subito soggiunge, negata al Sole ogni virtù attrattiva, <lb></lb>non si vedesse paragonato al Magnete che per la sola virtù direttrice. </s>

<s>E <lb></lb>questo perchè? </s>

<s>Perchè altrimenti i Pianeti andrebbero a congiungersi col <lb></lb>Sole. </s>

<s>“ Credibile est in Sole non esse ullam vim Planetarum attractoriam, <lb></lb>ut in Magnete; accederent enim ad Solem tantisper, donec cum ipso coniun­<lb></lb>gerentur penitus, sed tantum directoriam ” (ibi). </s></p><p type="main">

<s>In ciò che abbiamo fin qui esposto insomma consiste l&#039;Astronomia <lb></lb>kepleriana, la quale, quanto avesse veramente ragione di essere detta <emph type="italics"></emph>Nuova,<emph.end type="italics"></emph.end><pb xlink:href="020/01/1087.jpg" pagenum="530"></pb>si comprende da tutti coloro, che la confrontano con l&#039;opera, non diciamo <lb></lb>di Ticone, ma dello stesso Copernico. </s>

<s>La novità introdotta nella scienza astro­<lb></lb>nomica dal Keplero ritorna da due parti: da una che si può dir matema­<lb></lb>tica, per distinguerla dall&#039;altra, che ha qualità più proprie alla Fisica. </s>

<s>La <lb></lb>matematica risulta dalla dimostrazione delle orbite ellittiche de&#039;Pianeti e <lb></lb>delle relazioni che ne conseguitano fra i tempi periodici e l&#039;aree e gli assi <lb></lb>delle stesse ellissi; la fisica consiste in quella importantissima conclusione <lb></lb>che il Sole non è un semplice punto, intorno a cui si circoscrivono i limiti <lb></lb>alle varie distanze de&#039;Pianeti, ma è un centro attivo, dall&#039;azion del quale <lb></lb>i Pianeti stessi ricevono i primi impulsi e la regola de&#039;loro moti. </s></p><p type="main">

<s>Benchè abbia una tal conclusione il carattere fisico, come s&#039;è detto, <lb></lb>scendendo nulladimeno per diritta via dalla natura delle orbite ellittiche, par­<lb></lb>tecipava pure della evidenza di una dimostrazione matematica, intantochè le <lb></lb>novità kepleriane parevano disposte a persuadere gl&#039;intelletti con quella <lb></lb>virtù, che è propria dell&#039;amabile Geometria. </s>

<s>Tutt&#039;altrimenti però da quel <lb></lb>che si sarebbe creduto, la Storia in questo fatto ci mostra un esempio no­<lb></lb>tabilissimo della ritrosia degli uomini ad accogliere le novità scoperte, anche <lb></lb>quando agli intelletti risplendano della più sincera luce del vero. </s>

<s>E affinchè <lb></lb>ci persuadiamo essere stato questo sempre un vizio comune, e non un pre­<lb></lb>giudizio di qualche setta, è da veder quale accoglienza facesse alla Nuova <lb></lb>astronomia kepleriana lo stesso Galileo. </s></p><p type="main">

<s>Avendo riscontrato di fatto che il Sole si rivolge intorno al suo asse, <lb></lb>come il Keplero aveva supposto, sembra che Galileo poco dopo quel tempo, <lb></lb>cioè nel 1614, approvasse anche la conseguenza, che derivava da quello stesso <lb></lb>supposto l&#039;Autor del Commentario della Stella di Marte. </s>

<s>“ Ho anco dimo­<lb></lb>strato, per le osservazioni continuate di tali materie tenebrose (scriveva al <lb></lb>Dini, nella Lettera sul Sistema copernicano) come il corpo solare per neces­<lb></lb>sità si rivolge in sè stesso, e di più accennato quanto sia ragionevole il cre­<lb></lb>dere che da tal rivolgimento dipendino i movimenti de&#039;Pianeti intorno al <lb></lb>medesimo Sole ” (Alb. </s>

<s>II, 25). </s></p><p type="main">

<s>Poco più tardi avendo a difendere il Sistema copernicano contro i Teo­<lb></lb>logi paripatetici, i quali adducevano il miracolo operato da Giosuè, per la <lb></lb>più certa prova del moto del Sole; Galileo col Keplero interpetrava il testo <lb></lb>biblico non del moto solare <emph type="italics"></emph>de spacio in spacium, sed super suo centro,<emph.end type="italics"></emph.end><lb></lb>mostrando come bene conseguisse l&#039;immobilità degli altri corpi celesti, ar­<lb></lb>restato il moto del Sole, che “ come ministro massimo della Natura, ed in <lb></lb>certo modo anima e cuore del Mondo, infonde agli altri corpi che lo cir­<lb></lb>condano, non solo la luce, ma il moto ancora col rigirarsi in sè medesimo ” <lb></lb>(ivi, pag. </s>

<s>61). </s></p><p type="main">

<s>Queste dottrine così espressamente professate da Galileo vedemmo come <lb></lb>fossero, secondo il Keplero, una legittima conseguenza delle orbite ellittiche, <lb></lb>ond&#039;è che ammettendosi per vera questa tal conseguenza, sembrava che per <lb></lb>vero pure si dovesse accettare il principio da cui derivava. </s>

<s>Forse a que&#039;tempi <lb></lb>Galileo professò questo principio, ma poi, ne&#039;Dialoghi de&#039;Due massimi si-<pb xlink:href="020/01/1088.jpg" pagenum="531"></pb>stemi, tornò co&#039;Pitagorici, con Platone e col Copernico alle orbite circolari, <lb></lb>riguardando il Sole non più come centro attivo e causa del moto de&#039;Pia­<lb></lb>neti, ma come un semplice termine di remozione, o punto saldo da cui mi­<lb></lb>surar le distanze: o in altro modo, come il centro delle oscillazioni di un <lb></lb>pendolo, le sensate esperienze del quale, dicesi nella Giornata IV, per bocca <lb></lb>del Salviati, “ si confermano con le esperienze dei movimenti celesti de&#039;Pia­<lb></lb>neti, ne&#039;quali si vede mantener l&#039;istessa regola, che quelli che si muovono <lb></lb>per cerchi maggiori più tempo consumano in passargli ” (Alb. </s>

<s>I, 489). </s></p><p type="main">

<s>Se non è dunque il Sole centro attivo, come aveva dimostrato il Keplero, <lb></lb>in che risiede la virtù che muove i Pianeti? </s>

<s>Galileo supplì alla negazione delle <lb></lb>cause fisiche proposte dallo stesso Keplero, e rispose poi più tardi nel IV Dialogo <lb></lb>delle Due nuove scienze, scoprendo in aspetto di verace storia le poetiche sem­<lb></lb>bianze di un concetto, degno veramente del gran Platone. </s>

<s>“ E&#039;mi pare assai <lb></lb>credibile, dicesi per bocca del Sagredo, che avendo noi per le dottrine astro­<lb></lb>nomiche assai competente notizia delle grandezze degli orbi e dei Pianeti, e <lb></lb>delle distanze loro dal centro, intorno al quale si raggirano, come ancora <lb></lb>delle loro velocità; possa il nostro Autore, al quale il concetto platonico non <lb></lb>era ascosto, aver talvolta per sua curiosità avuto pensiero di andare investi­<lb></lb>gando se si potesse assegnare una determinata sublimità, dalla quale, par­<lb></lb>tendosi come da stato di quiete i corpi dei Pianeti, e mossisi per certi spazii <lb></lb>di moto retto e naturalmente accelerato, convertendo poi la velocità acqui­<lb></lb>stata in moti equabili, si trovassero corrispondere alle grandezze degli orbi <lb></lb>loro, e ai tempi delle loro revoluzioni ” (Alb. </s>

<s>XIII, 238). </s></p><p type="main">

<s>Benchè una tal corrispondenza, qual&#039;è fra i tempi delle oscillazioni dei <lb></lb>pendoli e le lunghezze de&#039;loro fili, non fosse veramente ritrovata fra i tempi <lb></lb>periodici e i raggi delle orbite de&#039;Pianeti, nè fosse possibile, per esser con­<lb></lb>traria al vero, di ritrovarla; la platonica dottrina splendidamente rinnovel­<lb></lb>lata da Galileo, e secondo la quale attribuivasi a una virtù insita nel Pia­<lb></lb>neta l&#039;effetto di quel moto, che il Keplero diceva derivar principalmente dal <lb></lb>Sole, trovò buona accoglienza in uno de&#039;più valorosi astronomi della Fran­<lb></lb>cia. </s>

<s>Ma perchè, dall&#039;altra parte, il Boulliaud era per le proprie osservazioni <lb></lb>convinto che le orbite planetarie s&#039;aggiravano veramente in ellisse, invece <lb></lb>di ammettere con Galileo che i Pianeti acquistassero l&#039;uniformità del moto, <lb></lb>scendendo dalla quiete per linea retta, immaginò che facessero invece la loro <lb></lb>discesa in una spirale, sulla superficie di un cono scaleno disegnato dalla <lb></lb>fantasia dell&#039;Astronomo ìn mezzo allo spazio. </s></p><p type="main">

<s>“ Apprime equidem, dice l&#039;Autore dell&#039;Astronomia filolaica più chia­<lb></lb>ramente spiegata, Galileus Dialogo I (così, ma è il Dial. </s>

<s>IV delle Due nuove <lb></lb>scienze) contemplatur motus coelestes, et mota recte prius lata fuisse illa <lb></lb>corpora, ut velocitatis gradus determinatos acquirerent, qua per circulares <lb></lb>et in se redeuntes rovolutiones perpetuo deinceps ferrentur, validissimis ra­<lb></lb>tionibus adstruit: descensum sive casum a coni vertice etiam adstruimus, <lb></lb>sed etiam circa axem ipsius gyrationis adfuisse censemus ” (Parisiis 1657, <lb></lb>pag. </s>

<s>53). </s></p><pb xlink:href="020/01/1089.jpg" pagenum="532"></pb><p type="main">

<s>Sia ABC (fig. </s>

<s>103) questo cono, e sia la sua base BC, il suo asse AI. </s>

<s><lb></lb>Conducasi la linea EK in modo, che sia segata in X nel mezzo da una linea <lb></lb>VT parallelamente condotta alla base, e sulla stessa linea EK s&#039;immagini <lb></lb>elevarsi un piano perpendicolare al triangolo ABC, il qual <lb></lb><figure id="id.020.01.1089.1.jpg" xlink:href="020/01/1089/1.jpg"></figure></s></p><p type="caption">

<s>Figura 103.<lb></lb>piano disegnerà colla sua sezione l&#039;ellisse EQK sulla su­<lb></lb>perficie del cono. </s>

<s>Il punto M sarà un foco dell&#039;ellisse, e <lb></lb>presa XH=XM, sarà H l&#039;altro foco, dove si suppone <lb></lb>che risegga il Sole. </s></p><p type="main">

<s>Ora, essendo così disposte le cose, immagina il Boul­<lb></lb>liaud che, cadendo il Pianeta dal vertice A, quand&#039;è sceso <lb></lb>in E, abbia acquistati que&#039;precisi gradi di velocità pre­<lb></lb>scritti dal Creatore, e sia perciò rivolto <lb></lb>in quel punto ad aggirarsi con moto <lb></lb>equabile in un cerchio di raggio ES. </s>

<s><lb></lb>Immagina inoltre l&#039;Autore che il Pianeta <lb></lb>stesso, per avvicinarsi sempre più al <lb></lb>Sole, vada scendendo infino in P, e poi <lb></lb>risalga su fino in E, con vicenda inces­<lb></lb>sante, descrivendo innumerevoli circoli, <lb></lb>i raggi de&#039;quali sien compresi fra quello <lb></lb>della minima lunghezza ES, e quello <lb></lb>della massima PR. </s></p><p type="main">

<s>Così s&#039;intende, secondo l&#039;Autore <lb></lb>dell&#039;Astronomia filolaica, come sia el­<lb></lb>littica la via del Pianeta, e come nell&#039;afelio E, descrivendo un circolo di <lb></lb>minimo raggio, abbia la minima velocità, e l&#039;abbia massima nel perielio K, <lb></lb>dove il circolo stesso descritto ha invece il massimo raggio. </s>

<s>“ A vertice ita­<lb></lb>que coni intelligibilis creatum Planetae corpus a Creatore impulsum est, et <lb></lb>aequali circulationis motu, circa ipsius axem contortum, ita ut lineae spira­<lb></lb>lis circulationem unam vel plures describendo, per infinitos circulos magni­<lb></lb>tudine inaequales pertransierit, et gradus velocitatis acquisierit a primo illo <lb></lb>Agente determinatos. </s>

<s>In motum deinde perpetuum, ad quem decreto suo <lb></lb>alligaverat, Planetae corpus deflexit, viamque tenere fecit, cuius planum per <lb></lb>centrum Solis transiret. </s>

<s>Ut vero cum principio suo semper cohaereret ille <lb></lb>motus circa eumdem axem, quem initio impulsionis circumivit, perseverare <lb></lb>debuit; et quia perpetuus est, aequalibus temporibus aequales angulos ipsum <lb></lb>describere etiam conveniebat. </s>

<s>Et ut motum descensus quem in initio quo­<lb></lb>que habuerat, retineret, postquam in motum perpetuum per unum planum <lb></lb>deflexit, per aliquod spatium a vertice coni descendit, donec Soli, circa quem <lb></lb>etiam alligatus est, proximus factus esset. </s>

<s>Unde, propter motus perpetuita­<lb></lb>tem, digreditur, et rursum versus Coni verticcm ascendit. </s>

<s>Sicque ellipsim <lb></lb>describit Planeta ut observationes docent ” (ibi). </s></p><p type="main">

<s>Convinto da queste osservazioni il Boulliaud, non potè negare i fatti, i <lb></lb>quali egli accomodò piuttosto alle sue fantasie, che alle vere cause reali. </s>

<s>Il <pb xlink:href="020/01/1090.jpg" pagenum="533"></pb>merito di lui perciò, ne&#039;progressi dell&#039;Astronomia nuova, consiste principal­<lb></lb>mente nell&#039;aver confermata la verità delle orbite ellittiche. </s></p><p type="main">

<s>Mentre in Italia, in ordine a queste teorie planetarie, prevaleva ancora <lb></lb>l&#039;autorità di Galileo, sorse nella stessa Francia, contemporaneo al Boulliaud, <lb></lb>Francesco Blaise conte di Pagan, più comunemente conosciuto da&#039;Nostri <lb></lb>sotto il nome di conte Pagani. </s>

<s>Noi non avremmo creduto di dargli nome <lb></lb>nella Storia della scienza italiana, se non avessimo trovato che il Viviani lo <lb></lb>chiamò a parte di questo merito, col tradurre la <emph type="italics"></emph>Teoria de&#039;Pianeti, nella <lb></lb>quale tutti gli orbi celesti sono geometricamente ordinati contro la sen­<lb></lb>tenza degli Astronomi;<emph.end type="italics"></emph.end> libro pubblicato in francese nel 1657 a Parigi. </s></p><p type="main">

<s>Qual si fosse il motivo e l&#039;intento di questa versione italiana, rimasta <lb></lb>da c. </s>

<s>127-76 del Tomo CXLI de&#039;Discepoli di Galileo manoscritta, non sa­<lb></lb>premmo dire precisamente, ma forse, come parecchi altri libri di Autori stra­<lb></lb>nieri il Viviani prese a tradurli, per inserirvi le dottrine del suo Maestro; <lb></lb>così prese a tradurre questo libro del conte Pagani, per divulgare in Italia, <lb></lb>contro gl&#039;insegnamenti del suo stesso Maestro, la dottrina delle orbite ellit­<lb></lb>tiche, da più di un mezzo secolo di osservazioni dimostrate oramai come <lb></lb>una verità di fatto. </s></p><p type="main">

<s>In qualunque modo, alla nostra curiosità di sapere in che consistano <lb></lb>le novità introdotte nella Teoria de&#039;Pianeti dal Conte avignonese, risponde <lb></lb>così l&#039;Autore stesso nella sua Prefazione: “ Nella guisa, egli dice, che l&#039;Astro­<lb></lb>nomia era anticamente compresa nell&#039;Astrologia, così la teorica de&#039;Pianeti è <lb></lb>presentemente nell&#039;Astronomia. </s>

<s>Cleomede fu il primo fra i Greci a distin­<lb></lb>guere la cognizione delle stelle erranti dalle fisse. </s>

<s>Arato ed Ipparco furono <lb></lb>gl&#039;inventori della teorica de&#039;Pianeti, cioè delle Stelle erranti.... Guglielmo <lb></lb>landgravio d&#039;Hassia e Ticone Brahe, signori danesi, gli diedero l&#039;ultima <lb></lb>mano; io fui il primo a tor via le cause fisiche, e a rendere tutti li moti <lb></lb>geometrici. </s>

<s>Questi gran personaggi non poterono ritrovare negli Orbi delle <lb></lb>loro teoriche li veri moti de&#039;Pianeti. </s>

<s>I Deferenti e gli Epicicli non servi­<lb></lb>rono nulla alle loro intenzioni, e costretti a rilasciarli alle conietture della <lb></lb>Fisica, confondevano l&#039;Astronomia colla Filosofia. </s>

<s>Reinoldo e Keplero furono <lb></lb>i più famosi nello spiegare questo accomodamento, e stabilirono equazioni <lb></lb>fisiche, per accomodare ad esse l&#039;equazioni geometriche, e senz&#039;accorgersi <lb></lb>di un sì notabile inconveniente, ammessero queste falsità per principii na­<lb></lb>turali. </s>

<s>E fino ai nostri tempi nessuno potè giammai immaginarsi cadere er­<lb></lb>rore in sì grandi uomini. </s>

<s>” </s></p><p type="main">

<s>“ In quest&#039;Opera noi aviamo schiarito l&#039;oscurità delle loro teoriche, <lb></lb>togliendo via la confusione di tante cause diverse, ordinando tutti i moti <lb></lb>de&#039;Pianeti, e parimente quei della Luna, in termini di pura Geometria, ac­<lb></lb>comodando la semplicità de&#039;precetti alla sublimità della scienza, la facilità <lb></lb>delle supputazioni alle nuove scoperte dell&#039;Astronomia, ed una molto per­<lb></lb>fetta aggiustatezza ai moti di tutti i Pianeti, per via della cognizione delle <lb></lb>singolari proprietà degli ellissi, che felicemente aviamo scoperte ” (MSS. <lb></lb>cit., c. </s>

<s>128). </s></p><pb xlink:href="020/01/1091.jpg" pagenum="534"></pb><p type="main">

<s>Nel Cap. </s>

<s>III dell&#039;Opera si tratta di proposito <emph type="italics"></emph>Della natura degli ellissi,<emph.end type="italics"></emph.end><lb></lb>accomodati alle orbite de&#039;Pianeti, in un fuoco delle quali orbite ellittiche <lb></lb>disposto il Sole, s&#039;insegna il modo di determinare le varie anomalie pre­<lb></lb>sentate dal moto degli stessi Pianeti. </s>

<s>“ Tutti i Filosofi, dice quivi l&#039;Autore, <lb></lb>non gli hanno potuti giammai figurare che per cerchi perfetti. </s>

<s>Keplero fu <lb></lb>il primo, fra tanti savi e grandi personaggi, a ordinarli in ellissi. </s>

<s>Ciò non <lb></lb>fece che leggermente, e per l&#039;uso delle Tavole rodolfine, senza dimostra­<lb></lb>zione geometrica, e perfetta aggiustatezza, per la poca cognizione ch&#039;egli <lb></lb>teneva delle proprietà dell&#039;ellisse ” (ivi, c. </s>

<s>137). </s></p><p type="main">

<s>S&#039;intende insomma come l&#039;opera del conte Pagani era tutta geometrica, <lb></lb>e non si vede perciò come potesse sperarne sì gran progressi l&#039;Astronomia, <lb></lb>che non è scienza astratta di linee, ma di corpi materiali. </s>

<s>L&#039;insistere nono­<lb></lb>stante sulle proprietà dell&#039;Ellisse fu una geometria, che potè allora givare <lb></lb>alla combattuta fisica del Keplero, e il Viviani forse prese a far quella ver­<lb></lb>sione dal francese, per recar questo giovamento alla scienza italiana. </s>

<s>Ma la <lb></lb>scienza italiana, per tornar sulla dirittura di quella via, dalla quale Galileo <lb></lb>l&#039;aveva detorta, non ebbe punto bisogno di quel debole aiuto straniero. </s>

<s>Sorse <lb></lb>fra i discepoli dello stesso Galileo un grande ingegno, il quale tanto pro­<lb></lb>mosse l&#039;Astronomia nuova, istituita dal Keplero, che potè rimetterla al New­<lb></lb>ton in tal condizione, da non aver d&#039;altro bisogno che dell&#039;ultima mano. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quel discepolo di Galileo è Gian Alfonso Borelli, il celebre Autore delle <lb></lb><emph type="italics"></emph>Theoricae Mediceorum.<emph.end type="italics"></emph.end> Egli fu il primo fra gli Astronomi di Europa a sen­<lb></lb>tir quanto nuovo vigore di vita venisse a infondersi, dal Commentario della <lb></lb>Stella di Marte, nella Astronomia. </s>

<s>Che se non erasi in più di un mezzo se­<lb></lb>colo quel vigore ancora esplicato, riconobbe la principal ragione di ciò nel­<lb></lb>l&#039;essere stato depasciuto dalla falce di Galileo, e in non aver nel Boulliaud <lb></lb>ritrovato il necessario e opportuno fomento. </s>

<s>Alla deficienza di un tale aiuto <lb></lb>esterno conobbe il Borelli altresì che s&#039;aggiungevano alcuni impedimenti <lb></lb>d&#039;intrinseca natura a viziare le nuove idee kepleriane, e a insterilirne perciò <lb></lb>il natio rigoglio de&#039;germi. </s></p><p type="main">

<s>Il primo di questi vizi e de&#039;più nocivi, non in sè, ma nelle sue con­<lb></lb>seguenze, fu quello di aver negato, il Keplero, le qualità materiali alla luce. </s>

<s><lb></lb>Così, quella nuova e feconda verità scoperta, che cioè sia il Sole centro at­<lb></lb>tivo del moto de&#039;Pianeti, rimaneva rintuzzata dentro le menti, le quali non <lb></lb>si potevano dare a intendere in che modo potesse corporalmente operare <lb></lb>una virtù incorporea, o come dicevasi una specie immateriata. </s></p><p type="main">

<s>Persuaso dunque il Borelli che fosse il moto impartito dal Sole, per <lb></lb>mezzo de&#039;vortici kepleriani, non dubitò che gl&#039;impulsi radiosi di lui non <lb></lb>operassero corporalmente sopra i Pianeti. </s>

<s>Che poi i raggi della luce possano <pb xlink:href="020/01/1092.jpg" pagenum="535"></pb>veramente produrre effetti meccanici lo prova coll&#039;esempio di alcuni fiori <lb></lb>pratensi, che s&#039;agitano al tocco della stessa luce commossi, come a una leg­<lb></lb>gera aura di venti. </s>

<s>“ Videmus quoque flores plantarum motu locali cieri ab <lb></lb>iisdem radiis solaribus, ut videre est in floribus pratensibus ” (Theoricae <lb></lb>Medic., Florentiae 1665, pag. </s>

<s>61). </s></p><p type="main">

<s>Un tale impulso però non è nè può essere altro che debolissimo, e se <lb></lb>pure è sufficiente a commovere i gracili stami in un&#039;erba, non par possi­<lb></lb>bile che valga a trasportare di luogo in luogo, e con tanta velocità la smi­<lb></lb>surata mole, per esempio, di Giove o di Saturno. </s>

<s>A così fatta difficoltà ri­<lb></lb>sponde il Borelli opportunamente invocando certi principii di Meccanica che, <lb></lb>per non essere ancora noti, nè il VI Dialogo delle Nuove Scienze di Gali­<lb></lb>leo, nè le Lezioni accademiche del Torricelli, apparivano perciò nella scienza <lb></lb>affatto nuovi. </s>

<s>“ Radii solares, quamtumvis debiles supponantur, impellere <lb></lb>poterunt corpora Planetarum. </s>

<s>Et licet huiusmodi virtus motiva initio parvum <lb></lb>et insensibilem motum Planetis imprimere posse videatur, in progressu ta­<lb></lb>men motus ad insignem celeritatem augeri poterit, et ratio est, quia sup­<lb></lb>ponitur quod quolibet temporis instanti radii solares revoluti impellunt Pla­<lb></lb>netas, parum tamen et insensibiliter, et talis velocitatis gradus minimus non <lb></lb>extinguitur, sed remanet impressus, ut motus natura exigit. </s>

<s>Huic succedit <lb></lb>secundus impulsus debilissimus eorumdem radiorum solarium, qui impetum <lb></lb>Planetae duplum reddit: idipsum tertius impulsus facit, idipsum quartus, <lb></lb>caeterique alii insequentes ” (ibi). </s></p><p type="main">

<s>Galileo esemplificava questi principi meccanici nel fatto di colui, che <lb></lb>serra le porte di bronzo di S. </s>

<s>Giovanni (Alb. </s>

<s>XIII, 332), movendo un corpo <lb></lb>pesantissimo a forza di ripetere semplici e non molto valide spinte. </s>

<s>Ma il <lb></lb>Borelli trova un altro esempio, che meglio fa al caso suo, ed è quello di un <lb></lb>gran naviglio possibile a esser mosso per acqua a furia di ripetute tratte di <lb></lb>un filo sottilissimo, come potrebb&#039;essere un capello di donna. </s>

<s>Tanto poi, sog­<lb></lb>giunge, è più concludente l&#039;esempio trasportato ai Pianeti, in quanto che, <lb></lb>notando questi nel liquidissimo etere, non han da vincere la resistenza op­<lb></lb>posta dalla tenacità dell&#039;acqua. </s></p><p type="main">

<s>Veniva così all&#039;assurdo delle specie immateriate del Keplero più ragio­<lb></lb>nevolmente il Borelli a sostituire una causa fisica, e operativa nel Sole a <lb></lb>muovere efficacemente i Pianeti nelle loro orbite, e poniamo che non fosse <lb></lb>questa di tali moti planetari la causa vera, si faceva nonostante progredire <lb></lb>la scienza, sgombrando i pregiudizii inveterati che s&#039;avevano intorno alla <lb></lb>natura della luce, e all&#039;azione di lei su gli altri corpi. </s>

<s>In ogni modo però <lb></lb>è verissimo che poco, ai progressi della Meccanica celeste, conferirono que­<lb></lb>sti emendamenti introdotti dal Nostro nell&#039;ipotesi de&#039;vortici kepleriani. </s></p><p type="main">

<s>Altri emendamenti, che equivalevano ad efficacissimi impulsi al progre­<lb></lb>dire della scienza, furono dal Borelli stesso introdotti nella Nuova astrono­<lb></lb>mia da quella parte, che tendeva a rassomigliare la virtù del Sole alla virtù <lb></lb>del Magnete. </s>

<s>Udimmo come negasse al Sole magnetico il Keplero la virtù <lb></lb>di attrarre, attribuendogli quella sola del dirigere, e ciò per questa unica <pb xlink:href="020/01/1093.jpg" pagenum="536"></pb>ragione, perchè i Pianeti, sempre più prossimamente attratti, si sarebbero <lb></lb>andati all&#039;ultimo a congiungere col loro centro. </s></p><p type="main">

<s>Ben comprendeva il Borelli quanto fosse contrario alle più note pro­<lb></lb>prietà del Magnete il negargli la virtù di attrarre, e dall&#039;altra parte poniamo <lb></lb>che, per vederlo da Galileo così disprezzato, non facesse nessuna stima del <lb></lb>De Dominis, il quale aveva rassomigliato all&#039;attrazione magnetica l&#039;azione <lb></lb>esercitata sulle acque del mare dal Sole e dalla Luna; le sue proprie os­<lb></lb>servazioni sui fenomeni capillari, e sulla viscosità de&#039;liquidi, lo avevano con­<lb></lb>sigliato ad ammettere che si attraessero magneticamente insieme così due <lb></lb>gocciole di rugiada su un filo d&#039;erba, come due stelle negli smisurati spazii <lb></lb>del Cielo. </s>

<s>Al timore poi che le due stelle attratte non venissero finalmente <lb></lb>a congiungersi insieme, provvedeva introducendo una forza centraria, che <lb></lb>rifugga dal centro “ quemadmodum experimur in rotae, seu fundae gyro ” <lb></lb>(Theoricae Medic. </s>

<s>cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Come fossero i contrarii effetti delle due forze messi ingegnosamente <lb></lb>in gioco, e dimostrati dal Borelli stesso per mezzo della esperienza, fu de­<lb></lb>scritto nel capitolo precedente, a proposito del moto parabolico delle Co­<lb></lb>mete, e ora è da vedere come ne facesse l&#039;applicazione diretta alla sua nuova <lb></lb>teoria dei moti planetarii. </s></p><p type="main">

<s>“ Concipiatur itaque, egli dice, Solaris Globus qui convertatur circa <lb></lb>proprium axim ab occasu in ortum: deinde vero corpus unius Planetae, qui <lb></lb>naturali instinctu conetur directo motu approprinquari ipsi Soli, quemadmo­<lb></lb>dum videmus omnia gravia naturalem habere instinctum approprmquandi <lb></lb>Telluri nostrae, impulsu scilicet a vi gravitatis sibi connatnralis, et quemad­<lb></lb>modum quoque videmus ferrum directe moveri versus Magnetem ” (ibi, <lb></lb>pag. </s>

<s>76). Questo, egli poco appresso soggiunge, è il primo elemento ” ex <lb></lb>quo componi debet revolutio eccentrica Planetarum ” (ibi), ed è quello ele­<lb></lb>mento, a cui venne dato poi il nome di <emph type="italics"></emph>Forza centripeta.<emph.end type="italics"></emph.end> “ Secundo loco <lb></lb>supponamus praedictum Planetam a vertigine solarium radiorum in orbem <lb></lb>ferri circa Solem, per circulorum peripherias ab occasu ad ortum, et quo­<lb></lb>niam, ut dictum, motus circularis naturaliter quemdam imprimit impetum <lb></lb>ipsi mobili, quo mediante a centro removetur ” (ibi); e perciò questo è quel <lb></lb>secondo elemento del moto planetario, a cui fu dato il nome proprio di <lb></lb><emph type="italics"></emph>Forza centrifuga.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Dietro ciò così conclude la sua nuova teorica il Borelli: “ Ergo ex com­<lb></lb>positione dictorum motuum efficitur vis quaedam et impetus compositus, ex <lb></lb>quo pendet periodus celeritatis acquisitae a Planeta, quae a remotissimo ter­<lb></lb>mino usque ad propinquissimum augetur ea proportione, qua distantiae de­<lb></lb>crescunt ” (ibi, pag. </s>

<s>77). </s></p><p type="main">

<s>Riassumendo dunque, i principii che costituiscono questa nuova teoria bo­<lb></lb>relliana si riducono ai quattro capi seguenti: 1.° I Pianeti gravitano tendendo <lb></lb>al centro del Sole, come i corpi tendendo al centro della nostra Terra. </s>

<s>2.° La <lb></lb>forza, con la quale sono i Pianeti attratti verso il Sole. </s>

<s>decresce a proporzione <lb></lb>che aumentano le distanze. </s>

<s>3.° L&#039;impulso al moto viene ai Pianeti dai vortici <pb xlink:href="020/01/1094.jpg" pagenum="537"></pb>radiosi della luce del Sole; e 4.°, quel moto stesso risulta dalla composizione <lb></lb>di due forze opposte, una che tende al centro e l&#039;altra che ne rifugge. </s></p><p type="main">

<s>Le leggi del moto, che governano gli astri, venivano così dal Borelli <lb></lb>proposte alla scienza sotto forma d&#039;ipotesi, della verità o della falsità delle <lb></lb>quali avrebbero poi deciso i calcoli e i fatti. </s>

<s>Ma intanto quelle ipotesi ri­<lb></lb>chiamavano a sè gl&#039;ingegni speculativi, i quali si sentirono, dopo gl&#039;impulsi <lb></lb>venuti dal Keplero, sollevare alla contemplazione delle Armonie celesti, per <lb></lb>vie tutto affatto nuove e con voli più sicuri. </s>

<s>Quella sicurezza però, per la <lb></lb>natura del soggetto, e per le condizioni in che veniva proposto, dipendeva <lb></lb>principalmente dalla Matematica, piuttosto che dalla Fisica; dal calcolo, piut­<lb></lb>tosto che dalla esperienza. </s>

<s>Fu perciò che la scuola italiana, tutta dedita alle <lb></lb>esperienze e pochissimo esercitata ed esperta dell&#039;Analisi matematica, si trovò <lb></lb>insufficiente a condur l&#039;Opera, con sì fausti auguri dal Borelli iniziata. </s>

<s>D&#039;onde <lb></lb>avvenne che toccò all&#039;Inghilterra, patria di valorosi matematici quali erano <lb></lb>il Wren, l&#039;Hook, l&#039;Halley e il Newton sopra tutti, la gloria e l&#039;utile di rac­<lb></lb>cogliere il frutto da ciò che si era seminato in Italia. </s></p><p type="main">

<s>I tre primi ora commemorati furono de&#039;più solleciti, fra&#039;Matematici in­<lb></lb>glesi, a rivolgere la loro attenzione sopra que&#039;nuovi principii di Meccanica <lb></lb>celcste, che veniva a proporre alla scienza il nostro Borelli, e al Newton se­<lb></lb>guitò, come fra poco vedremo, un gran benefizio da quelle prime specula­<lb></lb>zioni de&#039;suoi illustri connazionali: ma era a lui solo riserbata la gloria di <lb></lb>dimostrar matematicamente in qual più riposto seno si asconda, e secondo <lb></lb>quali leggi si dispensi per l&#039;Universo la vita. </s></p><p type="main">

<s>Ripensava una sera di estate, sotto l&#039;aperto cielo sereno, a quel che <lb></lb>aveva letto nel libro del Fisico italiano di quell&#039;istinto con cui tendono ad <lb></lb>avvicinarsi <emph type="italics"></emph>Planetae Soli, Medicea vero sidera Jovi;<emph.end type="italics"></emph.end> istinto ivi rassomi­<lb></lb>gliato a quel medesimo, che hanno naturalmente <emph type="italics"></emph>omnia gravia approprin­<lb></lb>quandi Telluri nostrae impulsa scilicet a vi gravitatis sibi conaturalis.<emph.end type="italics"></emph.end> In <lb></lb>questi pensieri, solleva il Newton gli occhi, e fissandogli nella Luna, che <lb></lb>sul suo capo di pieno lume splendeva. </s>

<s>— Anche tu dunque, ei dice, pesi <lb></lb>costassù come quaggiù pesa una pietra, e anche tu, se nulla ti ritenesse, <lb></lb>come ogni altro corpo grave cadresti a Terra? </s>

<s>Sublime, stupenda contem­<lb></lb>plazione! Ma ma io vorrei saper s&#039;ella è vera. </s>

<s>— </s></p><p type="main">

<s>Pareva difficilissimo a sodisfare questo desiderio, ma il Newton pensò <lb></lb>che tutto si riduceva a calcolar, dal moto nell&#039;orbita, la velocità, con la quale <lb></lb>sarebbe caduta la Luna, e a paragonar quel moto con le oramai note leggi <lb></lb>del cader della pietra. </s>

<s>Il calcolo così tornava possibilissimo, non richieden­<lb></lb>dosi altro a condurlo, che la notizia del periodo lunare e della distanza della <lb></lb>stessa Luna dal centro della Terra. </s>

<s>Istituiti dal Newton i calcoli, e trovatili <lb></lb>non riscontrare, restò incerto se dovesse diffidar della verità dell&#039;ipotesi del <lb></lb>Borelli, o della sua sufficienza in dimostrarla. </s>

<s>Preponderò saggiamente il giu­<lb></lb>dizio di quà, riconoscendo per prima cosa l&#039;insufficienza da quella poco esatta <lb></lb>misura, che s&#039;aveva allora del grado del meridiano terrestre; misura ch&#039;era <lb></lb>il principal fondamento alla nuova supputazione. </s></p><pb xlink:href="020/01/1095.jpg" pagenum="538"></pb><p type="main">

<s>Ma quella poca esattezza geodetica avrebbe dovuto ridurre i calcoli a <lb></lb>più approssimati riscontri, di che il Newton si maravigliava, e anzi, per dir <lb></lb>più vero, si accorava, non vedendo come quel solo divario avesse dovuto <lb></lb>portare a tale disorbitanza. </s>

<s>Era tuttavia così radicato il pregiudizio che la <lb></lb>virtù motiva della luce o del magnete a cui rassomigliavasi il Sole, si de­<lb></lb>bilitasse a seconda delle semplici distanze, da non entrar nemmeno in so­<lb></lb>spetto al Newton che le disorbitanze riscontrate ne&#039;suoi calcoli potessero <lb></lb>dipendere da questo errore. </s>

<s>E ora che troppo ben si comprende quanto do­<lb></lb>vesse un tale errore tornare ai progressi della scienza dannoso, giova a noi <lb></lb>qui vederne l&#039;origine, e dir come disnebbiati finalmente ne venissero gl&#039;in­<lb></lb>telletti. </s></p><p type="main">

<s>L&#039;origine senz&#039;altro venne dal Keplero, il quale, nel suo primo Ottico <lb></lb>insegnamento, vedemmo al Cap. </s>

<s>I, § V di questo Tomo com&#039;egli ammet­<lb></lb>tesse nella luce una attenuazione <emph type="italics"></emph>in latum,<emph.end type="italics"></emph.end> o superficiale, e perciò un de­<lb></lb>crescere in lei l&#039;intensità a proporzione che crescono le semplici distanze. </s>

<s><lb></lb>Passando poi, nel Commentario <emph type="italics"></emph>De Stella Martis,<emph.end type="italics"></emph.end> a far l&#039;applicazione dei <lb></lb>principii ottici all&#039;Astronomia, si trovò aggirato in una penosa incertezza. </s>

<s><lb></lb>Sentiva bene che la diffusione superficiale era una ipotesi contraria ai fatti. <lb></lb></s>

<s>— Poniamo dunque, diceva il Keplero, che quella diffusione sia sferica: eb­<lb></lb>bene, come decrescerà l&#039;intensità della luce? </s>

<s>come crescono i quadrati delle <lb></lb>distanze? </s>

<s>anzi, piuttosto come i cubi, a me pare. </s>

<s>— “ Nam sphaerica su­<lb></lb>perficies ab Archimede demonstrata est quadrupla esse ad planum circuli <lb></lb>maximi, in sphaera scripti. </s>

<s>Omnino itaque corpus duplo distans longius vi­<lb></lb>detur octuplo obscurius lucere debuisse, non tantummodo duplo ” (De Stella <lb></lb>Martis cit., pag. </s>

<s>179). </s></p><p type="main">

<s>Abbandonata perciò, in tali e tante incertezze, l&#039;Ottica, il Keplero s&#039;af­<lb></lb>fidò tutto alla Meccanica, la quale gli dimostrava che le maggiori o minori <lb></lb>forze d&#039;impulso, che rendono ora più ora meno veloci i Pianeti, dipende­<lb></lb>vano dalle minori o dalle maggiori distanze di essi Pianeti dal centro del <lb></lb>Sole. </s>

<s>“ Intelligimus enim hinc quod Planetae pene ratione staterae seu vectis <lb></lb>moveantur. </s>

<s>Nam si Planeta, quo longior a centro, hinc difficilius, utique <lb></lb>tardius, a centri virtute movetur, equidem perinde est ac si dicerem pon­<lb></lb>dus, quo longius exeat ab hypomochlio, hoc reddi ponderosius, non seipso, <lb></lb>sed propter virtutem brachii substentantis in hac distantia. </s>

<s>Utrinque nam­<lb></lb>que, et hic et in Statera seu vecte, et illic in motu Planetarum, haec debi­<lb></lb>litas sequitur proportionem distantiarum ” (ibi, pag. </s>

<s>168). </s></p><p type="main">

<s>Il Boulliaud nel suo Trattato <emph type="italics"></emph>De natura lucis<emph.end type="italics"></emph.end> venne poi a togliere tutte <lb></lb>quelle incertezze, nelle quali s&#039;erano, insiem col Keplero, aggirati gli Ot­<lb></lb>tici, e rifiutata la diffusione superficiale, e avendo fatto osservar che la luce <lb></lb>nella diffusione sferica si muove in superfice e non in corpo, avea senza <lb></lb>ambagi concluso che l&#039;attenuazione della luce stessa è proporzionale ai qua­<lb></lb>drati delle distanze. </s>

<s>Rimase in quel Trattato il Boulliaud dentro i termini <lb></lb>dell&#039;Ottica, ma nell&#039;<emph type="italics"></emph>Astronomia philolaica,<emph.end type="italics"></emph.end> riguardando la luce come forza <lb></lb>impulsiva, a modo del Keplero, fece rilevar gli errori, in ch&#039;era incorso l&#039;Au-<pb xlink:href="020/01/1096.jpg" pagenum="539"></pb>tore del Commentario di Marte, e ne notò argutamente i paralogismi. </s>

<s>“ Vir­<lb></lb>tus autem illa, qua sol prehendit seu harpagat Planetas, corporalis quae ipsi <lb></lb>pro manibus est, lineis rectis in omnem mundi amplitudinem emissa, quasi <lb></lb>species Solis cum illius corpore rotatur. </s>

<s>Cum ergo sit corporalis, imminui­<lb></lb>tur, et extenuatur in maiori spatio et intervallo. </s>

<s>Ratio autem huius immi­<lb></lb>nutionis eadem est ac luminis, in ratione nempe dupla intervallorum, sed <lb></lb>eversa. </s>

<s>Hoc non negavit Keplerus, attamen virtutem motricem in simpla tan­<lb></lb>tum ratione intervallorum contendit imminui ” (Parisiis 1645, pag. </s>

<s>23). </s></p><p type="main">

<s>Noi vedemmo dianzi da che fosse condotto il Keplero a rifiutar la legge <lb></lb>de&#039;quadrati, che non negò alla luce, come non le negò quella de&#039;cubi, ma <lb></lb>il Boulliaud procede oltre a notare il paralogismo, che si commetteva dallo <lb></lb>stesso Keplero in concluder che la luce, operando per contatto di superficie, <lb></lb>debiliti nonostante la sua virtù a proporzione che crescono le semplici di­<lb></lb>stanze. </s>

<s>“ Illa virtus agit per contactum speciei solaris, quae cum virtute <lb></lb>motrice a Sole defluit. </s>

<s>Species autem illa tangit corpus Planetae ut super­<lb></lb>ficies superficiem, ergo et virtus eodem modo tanget, quippe quae eodem <lb></lb>modo a Sole defluit. </s>

<s>Ipsam igitur in ratione dupla intervallorum, ut speciem, <lb></lb>imminui necesse est ” (ibi). </s></p><p type="main">

<s>Si trova nell&#039;Astronomia filolaica un&#039;altra importantissima applicazione <lb></lb>dell&#039;Ottica, la qual consiste in determinare la quantità di luce, che riceve <lb></lb>ciascun Pianeta, secondo la sua maggiore o minor distanza dal Sole. </s>

<s>Gli <lb></lb>Astronomi precedenti s&#039;erano contentati di dire così indeterminatamente, <lb></lb>come dall&#039;altra parte è suggerito anco al volgo dall&#039;esperienza comune, che <lb></lb>i Pianeti tanto ricevon meno di luce dal Sole quanto ne son più lontani. </s>

<s><lb></lb>Ma il Boulliaud, con immediata applicazione delle leggi della diffusion della <lb></lb>luce, da sè già dimostrate, concluse che l&#039;intensità dell&#039;illuminazion de&#039;Pia­<lb></lb>neti è in ragion reciproca delle loro distanze quadratiche dal Sole. </s></p><p type="main">

<s>“ Inquisita (dice, al cap. </s>

<s>X del libro I, l&#039;Autore dell&#039;Astronomia filo­<lb></lb>laica) apparente diametro Solis in distantiis omnium Planetarum ab ipso, <lb></lb>inquirenda est deinceps proportio, sub qua imminuitur illuminatio illius, in <lb></lb>unaquaque distantia. </s>

<s>Omnis autem illuminatio, etsi a corpore lucido produ­<lb></lb>catur, non tamquam a corpore trinam dimensionem possidente producta con­<lb></lb>siderari debet, sed quatenus a superficie illius perficitur, et quatenus etiam <lb></lb>in superficiem corporis illustrati incidunt radii. </s>

<s>Cum itaque luminis effluxus <lb></lb>sphaerici sint, in superficie sphaerae angustioris consertiores sunt radii, quam <lb></lb>in ampliore. </s>

<s>Quare in minori distantia a lucido plures radii erunt in una <lb></lb>aliqua superficie, in maiori vero elongatione in eadem pauciores: rarescit <lb></lb>enim lumen digrediens a lucido. </s>

<s>Quare, cum lux superficie terminetur et <lb></lb>illuminet, ut se habebit quadratum diametri sphaerae unius, ad quadratum <lb></lb>sphaerae alterius; ita illuminatio ad illuminationem, seu ut potentia distan­<lb></lb>tiae Planetae unius a Sole, ad potentiam distantiae alterius, ita illuminatio <lb></lb>ad illuminationem, analogia inversa. </s>

<s>Sed est etiam eadem ratione alterna, ut <lb></lb>distantia ad distantiam, ita diameter apparens ad diametrum apparentem. </s>

<s>Ab <lb></lb>aequali ergo, ut quadratum semidiametri apparentis unius, ad quadratum <pb xlink:href="020/01/1097.jpg" pagenum="540"></pb>alterius, ita illuminatio ad illuminationem, ratione alterna ” (Parisiis 1645, <lb></lb>pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Noi che prestiamo oramai il nostro assenso ai Teoremi del Boulliaud, <lb></lb>come alle cose che più certamente sien dimostrate per vere, crederemmo <lb></lb>che si dovess&#039;essere la medesima persuasione ingerita nelle menti degli <lb></lb>Astronomi, a cui furono quegli stessi Teoremi, dopo la prima metà del se­<lb></lb>colo XVII, così solennemente annunziati. </s>

<s>Eppure, chi il crederebbe? </s>

<s>furon <lb></lb>tutte le orecchie sorde a quest&#039;annunzio del vero, a persuadere il quale vi <lb></lb>bisognarono altri fatti, di cui ci rimane ora a narrar brevemente la storia. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Erano già vent&#039;anni, che si leggeva in pubblico l&#039;Astronomia filolaica, <lb></lb>quando il Borelli meditava la sua teoria de&#039;Pianeti. </s>

<s>Egli che aveva, dopo il <lb></lb>Boulliaud, riconosciuto l&#039;error del Keplero riguardo alla natura della luce, <lb></lb>sembrava che avrebbe, altresì dopo il Boulliaud, dovuto riconoscere l&#039;altro <lb></lb>errore, detto pur dal Keplero riguardo alla diffusion della stessa luce; ond&#039;è <lb></lb>che supponendo l&#039;Autor della Teorica de&#039;Medicei venire impresso il moto <lb></lb>ai Pianeti dagl&#039;impulsi radiosi del Sole, pareva che ne avesse dovuto con­<lb></lb>cludere, conforme a ciò ch&#039;era stato dimostrato, che le forze di tali impulsi <lb></lb>solari s&#039;indeboliscono via via a proporzione che crescono i quadrati delle <lb></lb>distanze. </s>

<s>S&#039;accennò già com&#039;avesse infelicemente il Borelli eletto piuttosto <lb></lb>il falso antico, che nò il vero nuovo, di che egli e tutti gli altri, che aber­<lb></lb>rarono con lui per altri vent&#039;anni, non trovano forse scusa che in una con­<lb></lb>siderazione ed è questa: L&#039;incertezza, ch&#039;ereditarono dal Keplero gli Ottici <lb></lb>e gli Astronomi, rispetto al decider se, concessa la diffusion della luce in <lb></lb>sfera, l&#039;intensità luminosa sia reciproca ai quadrati o ai cubi de&#039;raggi, ve­<lb></lb>niva tolta dal Boulliaud coll&#039;asserir semplicemente che la stessa luce si dif­<lb></lb>fonde non in solido, ma in superficie, senza dar però niuna prova della sua <lb></lb>asserzione. </s></p><p type="main">

<s>La più bella prova sarebbe stata quella dell&#039;esperienza, la quale non <lb></lb>si capirebbe com&#039;avesse indugiato ancora parecchi altri anni, se non si ri­<lb></lb>pensasse che, almeno fra noi, s&#039;erano in questo proposito e a tale impor­<lb></lb>tantissimo effetto, tentate esperienze di un altr&#039;ordine, e per la loro appa­<lb></lb>rente facilità seduttrici. </s>

<s>Giacchè la virtù del Sole, in dare impulso ai Pianeti, <lb></lb>si rassomigliava alla virtù del Magnete, e s&#039;era questa stessa virtù dal Bo­<lb></lb>relli principalmente riconosciuta nell&#039;attrazione, s&#039;argomentava che l&#039;acce­<lb></lb>lerazione di un ferro verso il Magnete stesso attraente fosse la ragione, colla <lb></lb>quale si accelererebbero i Pianeti attratti verso il centro del Sole. </s>

<s>Ora, ben­<lb></lb>chè il Kircker non avesse saputo affermar altro in proposito, se non che <lb></lb>“ Aaequalibus spaciis inaequalia fiunt in propagatione Magnetismi decre­<lb></lb>menta ” (De Magnete, Romae 1654), e benchè dalle prime esperienze fatte <pb xlink:href="020/01/1098.jpg" pagenum="541"></pb>nell&#039;Accademia del Cimento si ricavasse questo solo fatto, che cioè “ Un <lb></lb>ferro posto notante sull&#039;acqua, ovvero su una tavola, alzato da un pezzo di <lb></lb>Calamita, se gli accosta con moto sempre più accelerato ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXXXIX, c. </s>

<s>28); si volle in altre esperienze accademiche, dirette dallo <lb></lb>stesso Borelli, ricercar la legge di questo acceleramento, che sarebbe stata <lb></lb>la legge medesima, con cui cresce la virtù motrice, avvicinandosi i Pianeti <lb></lb>sempre più al Sole. </s>

<s>Ma rimasero le belle speranze deluse, come attesta un <lb></lb>Diario, in cui si legge la nota seguente: “ A&#039;dì 5 Luglio 1657. Si durò per <lb></lb>lo restante del mese a osservare e provare in varii modi, se si potesse tro­<lb></lb>vare in che proporzione un ago galleggiante in acqua accelerasse il suo moto, <lb></lb>per unirsi alla Calamita posta nella massima distanza, nella quale lo tira, <lb></lb>misurando i tempi co&#039;quali passava spazii uguali con le vibrazioni di un <lb></lb>pendolo molto esatto, nè fu mai possibile riconoscervi proporzione alcuna ” <lb></lb>(MSS. Cim., T. II, c. </s>

<s>249). </s></p><p type="main">

<s>La difficoltà si fece poi sentire anche ad altri valorosi sperimentatori, <lb></lb>per cui il Newton ritrasse da certe sue osservazioni, da lui stesso ricono­<lb></lb>sciute per grossolane, che la forza magnetica “ in recessu a Magnete de­<lb></lb>crescit in ratione distantiae, non duplicata, sed fere triplicata ” (Principia <lb></lb>mathem., Lib. </s>

<s>III, Genevae 1742, pag. </s>

<s>41). Solo fu riserbato più tardi, a <lb></lb>quello squisitissimo strumento della <emph type="italics"></emph>Bilancia di torsione,<emph.end type="italics"></emph.end> il dimostrar ch&#039;es­<lb></lb>sendo veramente la ragion delle distanze duplicata, il Newton era in errore. </s></p><p type="main">

<s>Non fa perciò maraviglia se il Borelli, a cui mancavano gli strumenti <lb></lb>inventati tanto tempo dopo, lasciate per le difficoltà incontratevi le fluttuanti <lb></lb>vie dell&#039;esperienza, cercò di ridursi a quel più sicuro porto della scienza <lb></lb>Meccanica, che gli era stato additato dallo stesso Keplero. </s>

<s>“ Nunc superest, <lb></lb>egli dice nel lib. </s>

<s>I delle <emph type="italics"></emph>Theoricae Mediceorum,<emph.end type="italics"></emph.end> ut ostendamus quomodo et <lb></lb>qua ratione motiva facultas, quae in Sole, vel in Jove reperitur, cum sit per­<lb></lb>petuo eiusdem gradus et sibi ipsi uniformis, possit tamen modo maiorem <lb></lb>modo minorem celeritatem tribuere eidem Planetae, prout ipse magis mi­<lb></lb>nusve approprinquat vel removetur a Sole vel Jove. </s>

<s>Hoc autem facillimo <lb></lb>negotio absolvetur ex aliquibus principiis mechanicis ” (Florentiae 1665, <lb></lb>pag. </s>

<s>63). </s></p><p type="main">

<s>Questi principii meccanici son quelli della stadera o del vette, i quali <lb></lb>avendo esposti al Lettore, il Borelli così prosegue: “ Concipiatur solare vel <lb></lb>ioviale corpus AS (fig. </s>

<s>104) torqueri circa proprium centrum S, globus vero <lb></lb><figure id="id.020.01.1098.1.jpg" xlink:href="020/01/1098/1.jpg"></figure></s></p><p type="caption">

<s>Figura 104.<lb></lb>eiusdem Planetae modo sit proprinquum <lb></lb>Soli in B, modo vero remotum in C. </s>

<s><lb></lb>Quoniam vis qua Sol operatur move­<lb></lb>turque Planetam, a suorum radiorum <lb></lb>potentia mensuratur, qui semper iidem <lb></lb>et eiusdem energiae sunt, et a celeritate <lb></lb>propriae vertiginis, quae pariter manet <lb></lb>inalterata ac ex ambobus hisce eius momentum componitur, cum debeat hoc <lb></lb>momentum aequari duabus resistentiis eiusdem Planetae in B et in C; ne-<pb xlink:href="020/01/1099.jpg" pagenum="542"></pb>cesse est ut contra minorem Planetae resistentiam in B maiori operetur <lb></lb>efficacia, ideoque ipsum maiori celeritate convertat ea qua utitur contra <lb></lb>maiorem resistentiam eiusdem Planetae siti in maiori distantia C, quem <lb></lb>proinde tardiori motu torquebit ea proportione quam reciproce habent re­<lb></lb>sistentiae seu distantiae ” (ibi, pag. </s>

<s>65). </s></p><p type="main">

<s>Tale, così conclusa dalle Meccaniche, era la legge che sopraffece quel­<lb></lb>l&#039;altra dal Boulliaud dimostrata dietro i principii dell&#039;Ottica, e tale, cioè <lb></lb>delle semplici distanze, era la legge professata allora anche dai matematici <lb></lb>d&#039;Inghilterra, quando l&#039;Hook si sentì vivamente eccitato dalle nuove teo­<lb></lb>rie delle forze centrali proposte alle speculazioni degli Astronomi dal nostro <lb></lb>Borelli. </s></p><p type="main">

<s>Intese l&#039;arguta mente del Filosofo inglese quello essere piuttosto sog­<lb></lb>getto da Matematica, che no da esperienza, e notò che l&#039;Italiano autore delle <lb></lb>nuove teorie, così ritroso ad accettare il principio della composizione del <lb></lb>moto, confondeva la forza centrifuga con la forza tangenziale. </s>

<s>Intorno alle <lb></lb>leggi delle forze centrifughe stesse non si conosceva altro a quel tempo, se <lb></lb>non quel poco, e misto ad errori, che ne&#039;Dialoghi del Sistema del Mondo <lb></lb>ne aveva scritto il Galileo, quando si pubblicarono, nel 1673, i teoremi del­<lb></lb>l&#039;Hugenio. </s>

<s>Allora l&#039;Hook, posto il principio che la forza centrifuga è da una <lb></lb>parte direttamente proporzionale alla mole e al raggio dell&#039;orbita dal mobile <lb></lb>descritta, ed è dall&#039;altra in ragion recipreca del quadrato del tempo perio­<lb></lb>dico; suppo sto inoltre che l&#039;azione esercitata dal Sole sui Pianeti sia pro­<lb></lb>porzionale alle loro moli, calcolò i moti di due degli stessi Pianeti, per pa­<lb></lb>ragonarli fra loro, e applicata la terza legge kepleriana, che cioè i quadrati <lb></lb>de&#039;tempi periodici son proporzionali ai cubi delle distanze, trovò che il Sole <lb></lb>esercitava sulle moli mosse una virtù reciprocamente proporzionale ai qua­<lb></lb>drati di quelle stesse distanze. </s></p><p type="main">

<s>Allora tornò l&#039;Hook indietro col pensiero sulla dimenticata Astronomia <lb></lb>filolaica, e il teorema fotometrico applicato ai Pianeti, e la legge con cui il <lb></lb>Sole dispensa a distanza i suoi impulsi radiosi, gli apparvero nella verità <lb></lb>della loro sembianza. </s>

<s>L&#039;Ottica e l&#039;Astronomia proseguirono da quel punto <lb></lb>affrettatamente il loro corso, come a rimuovere un gran macigno, che abbia <lb></lb>tutto ingombrato l&#039;alveo alle ringorgate acque di un fiume. </s></p><p type="main">

<s>La gloriosa opera di condurre il corso a coteste acque, in che scen­<lb></lb>deva con incredibile impeto il fiume della scienza, fu riserbata principal­<lb></lb>mente al Newton sollecitatovi dall&#039;Hook stesso, dal Wren e dall&#039;Halley. </s>

<s>Nello <lb></lb>Scolio alla proposizione IV del Lib. </s>

<s>I l&#039;Autor de&#039;Principii matematici di <lb></lb>Filosofia naturale confessa pubblicamente di essere stato preceduto da que­<lb></lb>sti tre suoi illustri connazionali (ediz. </s>

<s>cit., pag. </s>

<s>103), i quali avevano intanto <lb></lb>raccolto un tal preziosissimo frutto dal connubio delle speculazioni del Bo­<lb></lb>relli coi teoremi ugeniani. </s></p><p type="main">

<s>Non fu il Newton troppo sollecito di tornare alla dimostrazione dell&#039;ipo­<lb></lb>tesi borelliana, persuaso che alla precision del calcolo della caduta della Luna <lb></lb>nuocesse principalmente la poco esatta misura assunta di un grado del me-<pb xlink:href="020/01/1100.jpg" pagenum="543"></pb>ridiano terrestre. </s>

<s>Ma quando nel 1682 il Picard, nell&#039;Accademia francese, <lb></lb>ebbe ricercata quella misura con tanta diligenza, e l&#039;ebbe trovata tale da <lb></lb>poterci affidar sopra i calcoli alla sicura, e allora con questo nuovo dato e <lb></lb>supposto, com&#039;avevano concluso l&#039;Hook, e il Wren e l&#039;Halley d&#039;accordo con <lb></lb>lui, che la forza con cui la Terra attrae la Luna s&#039;indebolisca a proporzione <lb></lb>che aumentano i quadrati delle distanze, il Newton riprese le abbandonate <lb></lb>supputazioni, delle quali, nell&#039;opuscolo <emph type="italics"></emph>De mundi systemate,<emph.end type="italics"></emph.end> e nella pro­<lb></lb>posizione IV del Lib. </s>

<s>III de&#039;Principii, ne furono lasciati impressi i vestigi. </s></p><p type="main">

<s>Assunta la distanza media della Luna 60 semidiametri terrestri, il pe­<lb></lb>riodo lunare, rispetto alle stelle fisse, prefinito in 27 giorni, 7 ore e 43 mi­<lb></lb>nuti, e posto che l&#039;ambito della Terra corrisponda a 123,249,600 piedi pa­<lb></lb>rigini “ uti a Gallis mensurantibus definitum est, si Luna motu omni privari <lb></lb>fingatur ac dimitti, ut urgente vi illa omni, qua in orbe suo retinetur, de­<lb></lb>scendat in Terram, haec spatio minuti unius primi cadendo describit pedes <lb></lb>parisienses 15 1/12 ” (Principia cit., Lib. </s>

<s>III, pag. </s>

<s>26, 27). </s></p><p type="main">

<s>Supposto poi dall&#039;altra parte che la Luna stessa venga attratta fin presso <lb></lb>alle nostre regioni, con una forza crescente in ragion reciproca de&#039;quadrati <lb></lb>delle distanze, la rivoluzione di lei intorno alla Terra si compirebbe in un&#039;ora, <lb></lb>24 minuti primi e 27 secondi, non tenuto conto della resistenza dell&#039;aria, per <lb></lb>cui “ sublato motu suo circolari, et urgente eadem vi centripeta ac prius, <lb></lb>describeret cadendo pedes parisienses 15 1/12, tempore minuti unius secundi <lb></lb>(De mundi syst. </s>

<s>cit., pag. </s>

<s>12). Or perchè quello stesso spazio in piedi pa­<lb></lb>rigini fu sperimentalmente ritrovato dall&#039;Huyghens esser passato da un grave, <lb></lb>che sulla superficie della Terra cada liberamente in un minuto secondo, e <lb></lb>perciò il Newton così conclude la sua dimostrazione: “ Et propterea vis, qua <lb></lb>Luna in orbe suo retinetur, si descendatur in superficiem Terrae, aequalis <lb></lb>evadit vi gravitatis apud nos, ideoque est illa ipsa vis quam nos gravitatem <lb></lb>dicere solemus ” (Principia cit., pag. </s>

<s>29). </s></p><p type="main">

<s>L&#039;ipotesi del Borelli veniva dunque così matematicamente dimostrata, <lb></lb>rispetto al caso particolare della Luna, ma l&#039;Autor delle Teoriche de&#039;Medi­<lb></lb>cei aveva esteso quell&#039;ardita ipotesi a tutti i sistemi, e avea detto che non <lb></lb>solo, come una pietra sulla Terra, gravita sulla Terra stessa la Luna, ma <lb></lb>che gravitano pure allo stesso modo i Pianeti sul Sole, e i Satelliti su Giove, <lb></lb>e che insomma la gravitazione era legge universale. </s></p><p type="main">

<s>Rimaneva perciò al Newton a dimostrar la universalità dell&#039;ipotesi bo­<lb></lb>relliana, ciò che egli fece nelle prime proposizioni del I libro dei Principii, <lb></lb>trattando delle proprietà generali di un corpo, che si rivolga intorno ad un <lb></lb>centro, in conformità delle leggi scoperte dal Keplero, e mostrando che quelle <lb></lb>proprietà competono così bene al moto della Luna intorno alla Terra, come <lb></lb>al moto de&#039;Pianeti intorno al Sole, e de&#039;Satelliti intorno a Giove, cosicchè <lb></lb>“ Si tempora periodica sint in ratione sesquiplicata radiorum ” per qualun­<lb></lb>que corpo rivolgentesi in quelle condizioni nella sua orbita “ vires centri­<lb></lb>petae erunt reciprocae ut quadrata temporum ” (Principia cit., pag. </s>

<s>98). Dun­<lb></lb>que, le forze centripete di qualunque corpo girante intorno a un centro di <pb xlink:href="020/01/1101.jpg" pagenum="544"></pb>attrazione nel Cosmo, operano secondo le leggi della gravità terrestre; dun­<lb></lb>que la gravità o l&#039;attrazione, non è per una particolare e mutua corrispon­<lb></lb>denza che passi fra la Terra e la Luna, ma è legge di moto universale. </s>

<s>La <lb></lb>qual legge universale, universalmente applicata, confermò le ragioni date già <lb></lb>dal De Dominis del flusso marino, dimostrò la causa della precessione degli <lb></lb>equinozii, della nutazione de&#039;poli, e svelò insomma i più ascosti misteri del­<lb></lb>l&#039;antica Filosofia. </s>

<s>Questa sola cosa rimaneva ancora a sapere come mai la <lb></lb>Natura avesse eletto di comporre le sue celesti armonie, non sopra la per­<lb></lb>fezione de&#039;circoli, come si persuadevano gli antichi, ma sopra le irregolarità <lb></lb>delle ellissi. </s></p><p type="main">

<s>Il problema si proponeva curiosamente a risolvere sotto quest&#039;altra <lb></lb>forma: come mai i Pianeti non si tengano sempre dal centro de&#039;loro moti <lb></lb>ugualmente lontani, ma ora se ne dilunghino di più, ora gli vadano più <lb></lb>d&#039;appresso. </s>

<s>Il Keplero immaginò nel Sole un polo attrattivo e un polo re­<lb></lb>pulsivo, come nel Magnete, cosicchè il Pianeta nel perielio fosse attratto, e <lb></lb>nell&#039;afelio invece venisse respinto. </s>

<s>Ma perchè sentiva che sarebbe accusato <lb></lb>di contradizione, per aver negata allo stesso Sole la virtù di attrarre, si stu­<lb></lb>dia di discolparsene nella guisa seguente: “ Ego vero supra, Cap. </s>

<s>XXXIX, <lb></lb>de Sole negavi vim Planetarum attractricem: intelligebatur tamen tantum­<lb></lb>modo mere attractrix, ut ex usurpato argumento patet. </s>

<s>Hic autem ponitur <lb></lb>simul attractrix, simul alio situ repultrix. </s>

<s>Vel etiam hoc ponatur ut Sol <lb></lb>instar ferri nondum imbuti, tantummodo petatur, non vicissim petat, cum <lb></lb>ipsius filamenta supra fuerint circularia, Planetarum vero hic ponantur recta ” <lb></lb>(De Stella Martis cit., pag. </s>

<s>275). Non cessa però per questo di rimaner l&#039;ipo­<lb></lb>tesi kepleriana tuttavia involta in una caligine così densa, che attraverso a <lb></lb>lei il Sole della verità rompe ogni raggio. </s></p><p type="main">

<s>Vedemmo come a tale intento principalmente, cioè a rendere la ragione <lb></lb>delle orbite ellittiche, fosse architettato dal Boulliaud quel suo cono scaleno. </s>

<s><lb></lb>Ma oltre che questa sembrava una fedelissima imitazione de&#039;fantastici mac­<lb></lb>chinamenti di Tolomeo, non s&#039;intendeva come dovessero i Pianeti avvolgersi <lb></lb>con tant&#039;ordine intorno a una linea retta immaginaria, e tanto irregolar­<lb></lb>mente riguardare il Sole, che è centro fisico e reale del moto. </s></p><p type="main">

<s>Il Borelli, a cui non piacque questa Geometria del Boulliaud, sperò nella <lb></lb>Fisica di trovare soccorso, ma era ad ogni modo un medesimo lavorare di <lb></lb>fantasia, benchè il campo fosse diverso. </s>

<s>Immaginò che i Pianeti galleggias­<lb></lb>sero nel liquido etere, come un cilindro di legno galleggia nell&#039;acqua. </s>

<s>E a <lb></lb>quel modo che, lasciato verticalmente cader quel cilindro, per impulso di <lb></lb>gravità si profonda alquanto al di sotto del livello conveniente alle leggi idro­<lb></lb>statiche, e risospinto se ne solleva altrettanto, reciprocando le oscillazioni, <lb></lb>che diverrebbero perpetue, rimosse tutte le resistenze; così il Pianeta reci­<lb></lb>proca ondeggiando nell&#039;etere simili oscillazioni, d&#039;ond&#039;è ch&#039;eccedendo ora <lb></lb>da una parte ora dall&#039;altra del centro, l&#039;orbite non son circolari, ma confi­<lb></lb>gurate in ellisse. </s>

<s>Con tal meccanismo facilmente si spiega, secondo il Bo­<lb></lb>relli, l&#039;origine e la natura delle orbite planetarie, perchè basta supporre che <pb xlink:href="020/01/1102.jpg" pagenum="545"></pb>il Creatore nell&#039;inizio del moto avesse collocato ciascun Pianeta nel suo pro­<lb></lb>prio afelio. </s>

<s>“ Supponamus divinam Sapientiam, ob eius altissimos et inscru­<lb></lb>tabiles fines, decrevisse motum Planetarum circa Solem eccentricum efficere <lb></lb>ac figurae non circularis sed ellipticae: tunc nihil aliud necessarium fuisset <lb></lb>quam summo compendio ab initio creare locareque Planetam in remotissimo <lb></lb>puncto ” (Theoricae medic. </s>

<s>cit., pag. </s>

<s>78). </s></p><p type="main">

<s>A noi per dir vero sembran queste ragioni fisiche del gran Borelli un <lb></lb>romanzo, eppure ei se ne compiacque, e quando vide che simili fantasie <lb></lb>erano uscite fuori da quel cervellaccio del Fabry, piuttosto che concluderne <lb></lb>dover essere le sue stesse parto di un cervellaccio, pensò di preparare fu­<lb></lb>riosamente la stampa delle Teoriche de&#039;Medicei, per non parere di essersi <lb></lb>servito delle altrui invenzioni. </s>

<s>“ Ho ricevuto oggi (scriveva da Pisa il dì <lb></lb>18 Febbraio 1665 al principe Leopoldo) alle 22 ore, il libro del p. </s>

<s>Fabri <lb></lb>(cioè i Dialoghi fisici) il quale mi ha reso attonito per quel poco che ho ve­<lb></lb>duto, perchè veggo che a quel cervellaccio gli son sovvenuti concetti assai <lb></lb>simili ai miei, con i quali spiego le cagioni fisiche de&#039;moti de&#039;Pianeti, e <lb></lb>benchè quest&#039;uomo dia al solito suo in spropositi, tuttavia non vorrei che <lb></lb>altri potessi sospettare che io mi fossi servito delle sue invenzioni ” (MSS. <lb></lb>Cim., T. XVIII, c. </s>

<s>110). </s></p><p type="main">

<s>Del libro delle Teoriche, appena che ne fu eseguita furiosamente la <lb></lb>stampa in Firenze, ne mandò in dono lo stesso principe Leopoldo una copia <lb></lb>al Boulliaud, il quale rispose una lettera al donatore, dicendo avrebbe de­<lb></lb>siderato che l&#039;Autor di quelle teoriche gli dimostrasse le cause fisiche dei <lb></lb>Pianeti, perchè altrimenti le avrebbe tenute per una semplice congettura, <lb></lb>non punto più probabile della sua. </s>

<s>Il Borelli rispose allo stesso Principe, <lb></lb>che gli aveva fatto recapitare la lettera venuta da Parigi: “ Ho letto l&#039;epi­<lb></lb>stola del sig. </s>

<s>Bullialdo, e mi son maravigliato prima, che egli richiegga da <lb></lb>me dimostrazione delle cause fisiche de&#039;moti de&#039;Pianeti da me assegnate, <lb></lb>quando io espressi in più luoghi che le propongo per coniettura e proba­<lb></lb>bilità; secondo, che egli stimi tanto probabile le ragioni fisiche da lui im­<lb></lb>maginate quanto le mie. </s>

<s>Ma pure io ho manifestato l&#039;impossibilità della sua <lb></lb>opinione ” (ivi, c. </s>

<s>339). </s></p><p type="main">

<s>La dimostrazione richiesta dal Boulliaud, e che doveva così dissipar la <lb></lb>sua propria ipotesi geometrica, come l&#039;altra fisica del Borelli, era riserbata <lb></lb>un po&#039;più tardi al valore matematico del Newton, il quale si volse tutto a <lb></lb>considerare gl&#039;impulsi iniziali, da cui dovea principalmente dipendere la na­<lb></lb>tura delle orbite de&#039;Pianeti. </s>

<s>Si persuase per prima cosa che non potevano <lb></lb>quegl&#039;impulsi iniziali derivare dai vortici kepleriani, rinnovellati dalla fisica <lb></lb>del Borelli, e ciò con facile dimostrazione posta poi per Scolio alla propo­<lb></lb>sizione LIII del II Libro de&#039;<emph type="italics"></emph>Principii.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sia in S il Sole (fig. </s>

<s>105) a cui si circoscriva il circolo CF del vortice <lb></lb>radioso, il qual vortice, perciocchè si suppone descriver le aree proporzio­<lb></lb>nali ai tempi, si moverà dovunque con moto uniforme. </s>

<s>Sieno AD, BE due <lb></lb>orbite eccentriche e in D, E si costituiscano i perielii, in A, B poi gli afelii. <pb xlink:href="020/01/1103.jpg" pagenum="546"></pb>Ora, per legge astronomica, negli afelii i Pianeti debbono andare più lenti, <lb></lb>e nonostante per legge meccanica hanno più validi impulsi, perch&#039;essendo <lb></lb><figure id="id.020.01.1103.1.jpg" xlink:href="020/01/1103/1.jpg"></figure></s></p><p type="caption">

<s>Figura 105.<lb></lb>le velocità de&#039;fluidi in ragion reci­<lb></lb>proca delle sezioni, per gli spazii AB, <lb></lb>BC, più angusti degli spazii DE, FE, <lb></lb>la materia vorticosa deve moversi più <lb></lb>veloce. </s>

<s>“ Quae duo repugnant inter <lb></lb>se ” (Editio cit., pag. </s>

<s>421). </s></p><p type="main">

<s>Gl&#039;impulsi iniziali secondo l&#039;ipo­<lb></lb>tesi platonica, rinverdita di nuove <lb></lb>fronde da Galileo, non si poteva ora­<lb></lb>mai più ammettere, essendo stato di­<lb></lb>mostrato di fatto che i moti de&#039;Pia­<lb></lb>neti non sono uniformi ne&#039;circoli <lb></lb>perfetti, e dall&#039;altra parte non aveva <lb></lb>alcuna specie di probabilità l&#039;ipotesi <lb></lb>immaginata dal Boulliaud de&#039;circoli equanti. </s>

<s>Fu perciò che il Newton pensò <lb></lb>felicemente di tornare alle antiche idee pitagoriche, secondo le quali il moto <lb></lb>e la traiettoria della Luna si rassomigliava al moto e alla traiettoria della <lb></lb>pietra gittata. </s>

<s>“ Lapis proiectus, urgente gravitate sua, deflectitur de cursu <lb></lb>rectilineo et curvam lineam in aere describendo, tandem cadit in Terram. </s>

<s><lb></lb>Si motu velociore proiiciatur, pergit longius. </s>

<s>Augendo velocitatem fieri pos­<lb></lb>set ut arcum describeret milliaris unius, duorum, quinque, decem, centum, <lb></lb>mille, ac tandem ut pergendo ultra terminos Terrae non amplius in Terram <lb></lb>caderet ” (De Mundi syst. </s>

<s>cit., pag. </s>

<s>6, 7). </s></p><p type="main">

<s>Lo splendor del pensiero, che balena condensato dentro queste parole, <lb></lb>si riflette, come luce di specchio in specchio, da una in altra delle varie <lb></lb>proposizioni dimostrate nel Lib. </s>

<s>I dei Principii matematici di Filosofia na­<lb></lb>turale. </s>

<s>Data la forza equabile di proiezione e l&#039;acceleratrice verso il centro, <lb></lb>in modo però che gli additamenti d&#039;impulso sieno costantemente proporzio­<lb></lb>nali ai tempi, e perciò, per le brevi distanze prese sulla superficie terrestre, <lb></lb>dato che le forze attrattive sieno invariabili, il proietto scagliato descrive una <lb></lb>parabola. </s>

<s>“ Hoc est theorema Galilaei ” (Propos. </s>

<s>X, pag. </s>

<s>149). </s></p><p type="main">

<s>Supponiamo ora, seguitava così a ragionare il gran Filosofo, di avere <lb></lb>una Forza onnipotente, la quale sia capace di gettar la Luna o altro più <lb></lb>ponderoso Pianeta per l&#039;immensità del Cielo, come la nostra mano getta <lb></lb>una pietra per l&#039;aria. </s>

<s>Supponiamo inoltre che quello smisurato Globo così <lb></lb>lanciato, per esser tanto lontano dal centro del proprio moto, vi sia attratto, <lb></lb>non con forza costante, ma variabile reciprocamente ai quadrati delle di­<lb></lb>stanze. </s>

<s>Descriverà egli ancora una parabola, come nel teorema di Galileo, o <lb></lb>una curva diversa? </s>

<s>E la risposta, conclusa da alcune proposizioni prece­<lb></lb>dentemente dimostrate, era questa: ” Movebitur hoc corpus in aliqua sectio­<lb></lb>num conicarum, umbilicum habente in centro virium ” (Prop. </s>

<s>XIII, pag. </s>

<s>161). </s></p><p type="main">

<s>Quel corpo dunque, come in una parabola, così potrebbe rivolgersi bene <pb xlink:href="020/01/1104.jpg" pagenum="547"></pb>in una ellissi o in una iperbola. </s>

<s>Or in quali casi propriamente avverrà che, <lb></lb>poste certe condizioni, il proietto descriva o l&#039;una curva o l&#039;altra? </s>

<s>Una così <lb></lb>fatta domanda si formulò dall&#039;Autore nella seguente proposizione, che è la <lb></lb>XVII del libro sopra citato: “ Posito quod vis centripeta sit reciproce pro­<lb></lb>portionalis quadrato distantiae locorum a centro, et quod vis illius quantitas <lb></lb>absoluta sit cognita, requiritur linea quam corpus describit in loco dato, cum <lb></lb>data velocitate, secundum datam lineam egrediens ” pag. </s>

<s>170). </s></p><p type="main">

<s>Il quesito è nella sua prima parte così risoluto: “ Figura erit ellipsis ” <lb></lb>(pag. </s>

<s>173). Nella quale ellisse, dati i fochi, e da quello di questi due, di­<lb></lb>verso dal foco di attrazione, e che sia designato con H, condotto un raggio <lb></lb>alla traiettoria nel punto P del proietto, se tanta sarà la forza impressa che <lb></lb>la lunghezza PH riesca infinita “ figura erit parabola.... Quod si corpus <lb></lb>maiori adhuc cum velocitate de loco suo P exeat, capienda erit longitudo PH <lb></lb>ad alteram partem tangentis; ideoque, tangente inter umbilicos pergente, <lb></lb>erit hyperbola ” (pag. </s>

<s>173). </s></p><p type="main">

<s>Ecco risoluto così felicemente l&#039;arduo problema delle traiettorie. </s>

<s>In ge­<lb></lb>nerale sono esse ellittiche, come si osserva in tutti i Pianeti, e ciò, non per <lb></lb>una special disposizione del Creatore, a quel modo che s&#039;immaginavano il <lb></lb>Boulliaud e il Borelli, ma come conseguenza dell&#039;impulso iniziale e delle <lb></lb>leggi prescritte al moto degli stessi Pianeti. </s>

<s>Le Comete in particolare pos­<lb></lb>sono descrivere o l&#039;una o l&#039;altra sezione del cono. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le idee pitagoriche, le quali erano pure balenate alla mente di Galileo <lb></lb>(Alb. </s>

<s>VII, 61), avevano così nella matematica del Newton ritrovato il più <lb></lb>splendido commento, e la scienza esultò a veder che l&#039;ipotesi del Borelli <lb></lb>s&#039;era, oltre ogni umana speranza, stabilita nella fermezza del vero. </s>

<s>Parve <lb></lb>allora all&#039;uomo orgoglioso esser quasi divenuto simile a Dio, quando seppe <lb></lb>che a Giove e a Saturno, lanciati per gl&#039;immensi spazii del cielo da una <lb></lb>Mano onnipotente, erano state prescritte le vie con quelle medesime leggi, <lb></lb>che son prescritte a un sasso gettato per l&#039;aria dalla mano di un fanciullo. </s>

<s><lb></lb>Ma quell&#039;orgoglio presto si rintuzzò nel petto, al prurito di sodisfare a un&#039;al­<lb></lb>tra brama irrequieta. </s>

<s>È una gran conquista, dicevasi, della nostra scienza <lb></lb>quell&#039;unità di legge governatrice dell&#039;Universo, e secondo la quale i Pianeti <lb></lb>intorno al Sole e i Satelliti intorno a Giove, e la Luna intorno alla Terra <lb></lb>gravitano ai loro centri, come un pomo maturo che penda dal suo ramo, <lb></lb>ma che cos&#039;è questa forza, che fa piegare il ramo, e ne stacca il pomo, fa­<lb></lb>cendolo finalmente cadere sulle zolle del campo? </s>

<s>Tanto rimaneva ancora a <lb></lb>sapere, perchè fossero sodisfatti i desiderii dell&#039;uomo, e la nuova scienza <lb></lb>del Cosmo riuscisse assoluta, e a tanto attesero studiosamente i Filosofi, con <pb xlink:href="020/01/1105.jpg" pagenum="548"></pb>quale effetto però lo mostrerà quest&#039;ultima pagina della presente parte di <lb></lb>Storia. </s></p><p type="main">

<s>Fu primo tra que&#039;Filosofi il Gilberto, il quale rassomigliò la tendenza <lb></lb>dei corpi gravi al centro della Terra all&#039;appetito, con cui il ferro vien tratto <lb></lb>al Magnete. </s>

<s>Più alto poi sublimando le idee, disse che non la Terra sola, <lb></lb>ma tutti i corpi celesti esercitavano una loro virtù magnetica sui corpi cir­<lb></lb>costanti, cosicchè intorno alla Luna, al Sole, ai Pianeti circoscrivesi una <lb></lb>ammosfera di quegli effluvii attrattivi. </s>

<s>“ Circumfusa effluvia omnia et in <lb></lb>illis gravia quovis modo vi pulsa, simul cum Tellure generali cohaerentia <lb></lb>uniformiter procedunt. </s>

<s>Quod etiam fit in omnibus primariis corporibus, Sole, <lb></lb>Luna, Tellure, partibus ad sua principia et fontes sese conferentibus, qui­<lb></lb>bus eadem appetentia annectuntur ut terrena Telluri, quae gravia nos no­<lb></lb>minamus. </s>

<s>Sic lunaria appellunt Lunam, solaria solem intra effluviorum suo­<lb></lb>rum orbes ” (De Magnete, Londini 1600, pag. </s>

<s>229). </s></p><p type="main">

<s>La fecondità delle speculazioni che derivò dalla Filosofia magnetica, e <lb></lb>l&#039;argomento che si trovò in lei a sollevare, o a dir più vero a diradare il <lb></lb>velo de&#039;più ascosti misteri della Natura, sono cose notissime oramai, e per <lb></lb>quel che riguarda la scienza particolare del Cosmo è noto pure quanta luce <lb></lb>di pensiero si derivò dal libro del Gilberto in quelli di Galileo, del De Do­<lb></lb>minis e del Borelli, per non accennar che ad alcuni de&#039;più insigni fra i <lb></lb>nostri Italiani. </s></p><p type="main">

<s>Le idee del Borelli vedemmo quanto riuscissero efficaci sulle menti degli <lb></lb>stranieri, per cui nasce la curiosità di sapere se riuscissero affatto sterili fra <lb></lb>noi. </s>

<s>Ma che veramente sterili non riuscissero, potrebbesi dimostrare per varii <lb></lb>esempii, fra&#039;quali basti a noi in tanta fretta citarne uno solo dal Magalotti; <lb></lb>notabile esempio, se si ripensi in che modo egli discorra dell&#039;attrazione uni­<lb></lb>versale e degli effetti di lei, quando ancora, almeno in Italia, non si cono­<lb></lb>scevano le teorie neutoniane. </s></p><p type="main">

<s>“ Suppongo, egli scrive nella IV delle Lettere scientifiche, essere il Globo <lb></lb>terrestre una gran Calamita, la quale spirando per ogni parte la sua virtude, <lb></lb>egualmente i corpi e gli elementi tutti ne attragga..... Stabilito ciò, dico <lb></lb>la virtù della Terra non estendersi in infinito, ma solo diffondersi per un <lb></lb>determinato spazio, e questa tale sfera della sua potenza porre il termine <lb></lb>all&#039;ammosfera di ciascun Pianeta. </s>

<s>Se poi s&#039;abbatterà che due Pianeti siano <lb></lb>fra loro per tanto spazio lontani, che la sfera della potenza magnetica del­<lb></lb>l&#039;uno non confini colla sfera dell&#039;altro; questo tratto intermedio o sarà voto, <lb></lb>o sparso per avventura di fuoco, di luce o d&#039;etere o d&#039;altro mezzo più te­<lb></lb>nue, ed un corpo quivi collocato non avrà inclinazione al moto, ma tratterrassi <lb></lb>immobile. </s>

<s>Se le sfere magnetiche di due Pianeti saranno confinanti, allora <lb></lb>io considero fra l&#039;un Pianeta e l&#039;altro una linea immaginaria, la quale io <lb></lb>chiamerò comune distanza, e secondo che un corpo sarà collocato di qua o <lb></lb>di là da cotal linea, entrerà nella sfera dell&#039;un Pianeta o dell&#039;altro, e sì ve­<lb></lb>nendone attratto, in questo o in quello anderà a cadere. </s>

<s>Se un Pianeta, gi­<lb></lb>randosi nell&#039;orbe suo, s&#039;incontrerà ad abbracciare colla sua sfera di potenza <pb xlink:href="020/01/1106.jpg" pagenum="549"></pb>magnetica un corpo, collocato immobile in uno spazio intermedio fra le sfere <lb></lb>di due pianeti, seco lo porterà ” (Firenze 1721, pag. </s>

<s>27-29). Applica poi <lb></lb>questi stessi principii al caso degli aereoliti, con gran maraviglia di coloro, <lb></lb>che trovan qui la soluzione antica a un problema nuovo. </s></p><p type="main">

<s>Gran sodisfazione trovò senza dubbio la scienza in quelle intravedute <lb></lb>somiglianze tra l&#039;attrazione magnetica e la terrestre, che è quella stessa, la <lb></lb>quale opera nell&#039;universale, ma in che consiste, si domandava, quella virtù, <lb></lb>per cui il ferro viene attratto al Magnete? </s>

<s>E in provarsi a rispondere alla <lb></lb>domanda, si conobbe che il mistero cosmico nella Filosofia magnetica rima­<lb></lb>neva tuttavia, e che nelle mani di lei non altro fece in sostanza che mu­<lb></lb>tar velo. </s></p><p type="main">

<s>Si sentì perciò il bisogno di procedere per altra via, e l&#039;Huyghens fu <lb></lb>il primo, che risalì col pensiero ad applicare al Cosmo quelli, che si direb­<lb></lb>bero ludi della Natura. </s>

<s>Un fatto volgarissimo aveva richiamata la sua atten­<lb></lb>zione, e fu quello de&#039;corpuscoli galleggianti, che si vedono attratti al centro <lb></lb>di qualche vortice, formatosi qua o là nel correre, sulla superficie dell&#039;acqua. </s>

<s><lb></lb>L&#039;ipotesi di un etere fluidissimo, che di sè tutto riempia lo spazio, era ora­<lb></lb>mai divenuta comune, e il Keplero, nella rotazione del Sole partecipata allo <lb></lb>stesso etere ambiente, aveva ritrovato il principio ai supposti moti vertigi­<lb></lb>nosi. </s>

<s>Dato ciò, bastava, secondo l&#039;Huyghens, che un Pianeta si trovasse nel <lb></lb>vortice, che s&#039;aggira intorno al Sole, perchè ne dovesse essere attratto. </s></p><p type="main">

<s>Una tale ipotesi intorno alla causa prima, che produce la gravitazione, <lb></lb>si trova accennata già dall&#039;Huyghens nel <emph type="italics"></emph>Systema Saturnium,<emph.end type="italics"></emph.end> là dove in­<lb></lb>tende a dimostrar come l&#039;Anello, benchè staccato, segua senza mai rima­<lb></lb>nere indietro il moto del suo Pianeta, perchè gravita sulla superficie di lui, <lb></lb>a quel modo che i corpi gravi sospesi assecondano il moto della nostra Terra. <lb></lb></s>

<s>“ Porro quum certo satis colligi posse videatur, ob similitudinem ac cogna­<lb></lb>tionem magnam quae Saturno cum Tellure nostra intercedit, illum perinde <lb></lb>ut haec in medio sui vorticis situm esse, centrumque eius versus omnia na­<lb></lb>tura sua tendere, quae illic gravia habentur, inde necessario quoque effici­<lb></lb>tur. </s>

<s>Annulum istum omnibus sui partibus aequali vi ad centrum nitentem, <lb></lb>hoc ipso, ita consistere ut undiquaque pari intervallo a centro absit ” (Opera <lb></lb>varia, Vol. </s>

<s>II, Lugduni Batav. </s>

<s>1724, pag. </s>

<s>567). </s></p><p type="main">

<s>Par che insomma l&#039;ipotesi de&#039;vortici fosse stata speculata dall&#039;Huy­<lb></lb>ghens infino dal 1659, parecchi anni prima che il Borelli e il Newton pub­<lb></lb>blicassero le loro teorie. </s>

<s>In un&#039;apposita scrittura poi, che intitolò <emph type="italics"></emph>Diatriba,<emph.end type="italics"></emph.end><lb></lb>lo stesso Huyghens spiegò intorno a quella ipotesi i suoi particolari concetti, <lb></lb>e vi tornò sopra alla fine del II libro del Cosmoteoro. </s>

<s>Quivi è l&#039;Autore in <lb></lb>gran sollecitudine di notar quanto differisca il suo dal sistema cartesiano, <lb></lb>ch&#039;egli chiama <emph type="italics"></emph>commentatio levibus rationibus contexta,<emph.end type="italics"></emph.end> e soggiunge es­<lb></lb>sersi spesso maravigliato <emph type="italics"></emph>tantum operae in talibus concinnandis figmentis <lb></lb>eum impendere potuisse ”<emph.end type="italics"></emph.end> (Cosmotheoros in Op. </s>

<s>cit., pag. </s>

<s>721). </s></p><p type="main">

<s>Una delle differenze più notabili fra il sistema ugeniano e il cartesiano <lb></lb>consiste in ciò, che il Cartesio suppone moversi la materia del vortice tutta <pb xlink:href="020/01/1107.jpg" pagenum="550"></pb>insieme, e dalla medesima parte, mentre a volere spiegare i fatti, secondo <lb></lb>l&#039;Huyghens, bisogna “ vorticem turbinemve materiae coelestis circa Solem <lb></lb>converti, non totum in easdem partes, sed ita ut variis motibus, iisque ce­<lb></lb>lerrimis, in omne latus secundum diversas sui portiones rapiatur, nec tamen <lb></lb>dilabi possit, propter circumstantem aetherem, qui non tali nec tam celeri <lb></lb>motu agitetur ” (ibi, pag. </s>

<s>720). E semplifica il fatto in que&#039;vortici, che si <lb></lb>formano qua e là sulla superficie di un lago, per la forte agitazione del <lb></lb>remo “ et sicut horum motus nequaquam ab unis ad alios perveniunt, nec <lb></lb>proinde sese mutuo impediunt, ita quoque coelestium vorticum motus cir­<lb></lb>cum astra aut Soles se habere existimo ” (ibi, pag. </s>

<s>721). </s></p><p type="main">

<s>Trattò senza dubbio l&#039;Huyghens de&#039;vortici da geometra, mentre il Car­<lb></lb>tesio ne avea trattato piuttosto da romanziere o da poeta, ma non cessò per <lb></lb>questo di apparire il sistema stesso de&#039;vortici ugeniani un lavoro di fanta­<lb></lb>sia. </s>

<s>Il Newton, ne&#039;suoi Principii di Filosofia naturale, essendosi severamente <lb></lb>imposto di non toccar questione, che non si potesse risolvere nella certezza <lb></lb>di una verità matematica, dimostrando l&#039;esistenza e le leggi della gravita­<lb></lb>zione universale, lasciò a disputare ai Filosofi delle cause ultime produt­<lb></lb>trici di quella forza. </s>

<s>Ma là dove s&#039;apre un campo a parte per questionare <lb></lb>di tutto ciò, che non è dimostrabile o per matematiche ragioni o per espe­<lb></lb>rienza, non tacque di dir ciò ch&#039;egli pensava esser causa della gravitazione <lb></lb>universale, ricorrendo anch&#039;egli all&#039;etere, considerato però in condizioni sta­<lb></lb>tiche differenti dalle dinamiche dell&#039;Hugenio. </s></p><p type="main">

<s>“ Annon hoc medium, prosegue a dir dell&#039;etere cosmico nella XXI Que­<lb></lb>stione, multo rarius est intra corpora densa Solis, Stellarum, Planetarum et <lb></lb>Cometarum, quam in vacuis spatiis coelestibus interiectis? </s>

<s>Et a corporibus <lb></lb>istis ad usque ingentia intervalla, annon densius perpetuo densiusque eva­<lb></lb>dit, eoque pacto efficit ut et magna ista corpora erga se invicem gravia sint, <lb></lb>et ipsorum partes singulae erga ipsa corpora, omnibus nimirum corporibus, <lb></lb>qua parte medium densius est, ea ex parte recedere conantibus in partes <lb></lb>rariores? </s>

<s>Etenim si hoc medium rarius sit intra corpus Solis quam in <lb></lb>eiusdem superficie, et in ipsa superficie rarius quam interiecto extrinsecus <lb></lb>centesimae partis unciae unius a corpore Solis intervallo, et hoc postremo <lb></lb>in loco rarius quam in orbe Saturni; equidem nihil causae video quamo­<lb></lb>brem increscenti densitati usquam locorum ullus constitutus sit finis, quo­<lb></lb>minus per omnia intervalla, et a Sole ad Saturnum, et adhuc usque porri­<lb></lb>gatur. </s>

<s>Quae quidem densitas, quanquam ingentibus interiectis intervallis, <lb></lb>fortasse lentissimis augeatur accrementis, poterit tamen, si quidem vis ela­<lb></lb>stica huius medii admodum sit magna, corpora vi ea omni quam gravitatem <lb></lb>appellamus a densioribus partibus medii ad rariores versus impellere. </s>

<s>Valde <lb></lb>autem magnam esse medii huiusce vim elasticam ex vibrationum suarum <lb></lb>celeritate est colligere ” (Optices, Lib. </s>

<s>III, Patavii 1773, pag. </s>

<s>143). </s></p><p type="main">

<s>Due secoli son passati da che l&#039;Huyghens e il Newton proposero que­<lb></lb>ste loro ipotesi, e benchè l&#039;Autore del Cosmoteoro terminasse il suo libro <lb></lb>con dire ch&#039;egli stimava le ragioni ultime de&#039;moti dell&#039;Universo <emph type="italics"></emph>nequa-<pb xlink:href="020/01/1108.jpg" pagenum="551"></pb>quam humano ingenio cxcogitari, aut coniecturis attingi posse,<emph.end type="italics"></emph.end> non volle <lb></lb>nonostante la scienza così progredita lasciar di fare i suoi sforzi. </s>

<s>E perchè <lb></lb>nell&#039;elettricità principalmente si trovò aver fatti que&#039;suoi seducenti pro­<lb></lb>gressi, nell&#039;elettricità pose ogni speranza di giungere a rivelarsi gli ascosti <lb></lb>misteri. </s></p><p type="main">

<s>Benchè a vero dire siasi in ciò da&#039;moderni preso altro indirizzo, l&#039;ap­<lb></lb>plicazione delle virtù elettriche alle forze, che danno anima al Cosmo, risale <lb></lb>infino a Ottone di Guericke. </s>

<s>Accennammo ad altro proposito la fecondità <lb></lb>delle speculazioni, che derivarono al Filosofo di Magdeburgo, da quella sua <lb></lb><emph type="italics"></emph>Terrella elettrica,<emph.end type="italics"></emph.end> in che vedeva come in un punto solo contratta e rappre­<lb></lb>sentata al vivo l&#039;immagine della gran Terra, e fu il primo frutto di così <lb></lb>fatte speculazioni quello di concludere che dovesse, nel gran Globo terrestre <lb></lb>e naturale, risiedere la virtù medesima di attrarre e di respingere, che i <lb></lb>fatti dimostravano esser propria al piccolo artificiale globo di zolfo. </s></p><p type="main">

<s>Risalendo più su ad applicare ai corpi celesti i fatti particolari con lo <lb></lb>stesso Globo sulfureo sperimentati, in quel seguitar che fa dovunque la <lb></lb>piuma esso Globo, sempre tenendo verso lui rivolta la medesima parte, vide <lb></lb>Ottone rappresentarsi in immagine la Luna, che segue fedel compagna nel <lb></lb>suo viaggio annuale la Terra, a cui tien pure sempre rivolta la medesima <lb></lb>faccia. </s>

<s>“ Causam constantiae lunaris faciei naturalem esse detegit simul Glo­<lb></lb>bus ille sulphureus, qui plumulam, a se semel expulsam, una semper facie <lb></lb>in orbe virtutis retinet, in quamcumque etiam partem circumducatur ” <lb></lb>(Experimenta nova magd., Amstelodami 1672, pag. </s>

<s>179). E come la piuma, <lb></lb>benchè non rimanga mai indietro al globo, pur seguitandolo, alquanto tituba <lb></lb>e vacilla; così tituba e vacilla per conseguenza anco la Luna (ivi). </s></p><p type="main">

<s>Poi l&#039;Hawksbee, quando vide i fili elettrometrici di mussolina ora es­<lb></lb>sere con sì costante ordine attratti, ora respinti dal centro del globo torna­<lb></lb>tile di vetro “ ho scoperto, annunziava esultando al pubblico, alcune pro­<lb></lb>prietà di questa materia elettrica, che possono parere maravigliose a quelli <lb></lb>che minutamente le considereranno, conciossiachè somministrano una sorta <lb></lb>di rappresentazione de&#039;grandi fenomeni dell&#039;Universo ” (Esper. </s>

<s>fisico mecc, <lb></lb>traduz. </s>

<s>ital., Firenze 1716, pag. </s>

<s>44). </s></p><p type="main">

<s>Le idee del Guericke e dell&#039;Hawksbee erano nuove, ma non si faceva <lb></lb>altro per esse che rassomigliare alle attrazioni e alle repulsioni elettriche i <lb></lb>moti cosmici, che il Gilberto e il Keplero avevano già rassomigliato alle <lb></lb>virtù del Magnete. </s>

<s>La rappresentazione dei fenomeni dell&#039;Universo ne&#039;fatti <lb></lb>elettrici, per la varietà delle loro forme più facilmente accomodabili, pareva <lb></lb>sodisfare alquanto meglio che non la monotonia de&#039;magnetici, ma il mistero, <lb></lb>benchè si mostrasse sotto altro aspetto, rimaneva tuttavia coperto da un&#039;im­<lb></lb>penetrabile velo, a rimuovere il quale, baldanzosi de&#039;progressi fatti dalla <lb></lb>scienza elettrica, si provarono i fisici moderni. </s>

<s>Da giudici imparziali però <lb></lb>non può darsi altra sentenza delle nuove speculate ipotesi, se non dicendo <lb></lb>ch&#039;elle sono un elaborato e assai prolisso commento delle antiche, conside­<lb></lb>randovisi l&#039;etere elettrico, diffuso in tutto il cosmo, in quelle condizioni sta-<pb xlink:href="020/01/1109.jpg" pagenum="552"></pb>tiche, in che il Newton lo considerò, secondo la sopra riferita Questione. </s>

<s><lb></lb>L&#039;etere, dicono insomma i Fisici novelli, che della sua ammosfera circonda <lb></lb>le molecole dei corpi, variando in densità colla distanza, produce nel ridursi <lb></lb>all&#039;equilibrio una pressione, e dalla pressione ha origine il conato, e pro­<lb></lb>ducesi il moto. </s></p><p type="main">

<s>Ma perchè dee variare in densità l&#039;etere? </s>

<s>si domanda. </s>

<s>Questa in ogni <lb></lb>modo o rimane un&#039;ipotesi gratuita, o volendo rispondere, non si può dire <lb></lb>altro se non che l&#039;etere è variamente denso, perchè variamente attratto al <lb></lb>suo centro, ma si assumerebbe così per principio della spiegazione, e per <lb></lb>argomento, il fatto stesso che si voleva spiegare. </s></p><p type="main">

<s>Confessando dunque anche noi coll&#039;Huyghens che l&#039;origine de&#039;moti <lb></lb>cosmici è inescogitabile, consideriamo il processo, che per tre secoli ha te­<lb></lb>nuto la scienza nell&#039;investigar l&#039;origine e la natura della forza. </s>

<s>Vedemmo <lb></lb>che ne furono ricercate e intravedute l&#039;orme o nella luce o nel fluido ma­<lb></lb>gnetico o nell&#039;elettrico, e in qualche altra cosa insomma di più sottile, che <lb></lb>siasi saputa immaginare, e che sia più aliena dal partecipare delle qualità <lb></lb>più comuni della crassa materia. </s>

<s>Gli antichi Filosofi dicevano perciò che <lb></lb>principio della forza sia lo spirito, ond&#039;è che non vedendo come si potes­<lb></lb>sero movere altrimenti i Pianeti, o davano ad essi un&#039;anima o gli commet­<lb></lb>tevano al governo delle intelligenze celesti. </s>

<s>In tempi più prossimi a noi, e <lb></lb>ne&#039;quali la presente scienza fisica ebbe i suoi inizii, il Gilberto pensò che <lb></lb>la virtù magnetica fosse animata, e il Keplero, nelle varie sue opere, tornò <lb></lb>più volte a parlar dell&#039;anima, e degli organi animali, di ch&#039;è compaginata <lb></lb>la Terra. </s></p><p type="main">

<s>Le forze animastiche furono finalmente bandite dalla scienza del Cosmo, <lb></lb>per opera del Borelli, che sapientemente vi sostituì le forze fisiche. </s>

<s>Ma, ben­<lb></lb>chè fosse questo un progresso effettivo, e una reale conquista del vero, da <lb></lb>nessuno s&#039;è saputo poi, in tanto tempo, penetrare addentro alla natura fisica <lb></lb>di quelle forze. </s></p><p type="main">

<s>Si saprà forse in avvenire? </s>

<s>A ciò risponderà la storia, scritta in qual­<lb></lb>che capitolo di quest&#039;altro Tomo, dove si narreranno i progressi fatti dalla <lb></lb>scienza sperimentale nello studio della vita e degli organi dei sensi, misu­<lb></lb>ratori angusti del nostro acume e dei nostri voli. </s></p><pb xlink:href="020/01/1110.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICI<emph.end type="center"></emph.end><pb xlink:href="020/01/1111.jpg"></pb></s></p><pb xlink:href="020/01/1112.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE DEI CAPITOLI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Della luce diretta e della luce riflessa.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I De&#039;primi e principali cultori dell&#039;Òttica <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 7 </s></p><p type="main">

<s>II Della legge fondamentale della luce riflessa. </s>

<s>” 12 </s></p><p type="main">

<s>III De&#039;corpi diafani e degli opachi; delle ombre e delle penombre ” 20 </s></p><p type="main">

<s>IV Di alcune esperienze singolari sulle ombre; del passaggio della luce attraverso a pic­<lb></lb>coli fori ” 26 </s></p><p type="main">

<s>V Delle leggi della intensità luminosa. </s>

<s>” 32 </s></p><p type="main">

<s>VI Della velocità della luce ” 39 </s></p><p type="main">

<s>VII Delle ipotesi delle ondulazioni eteree, e dell&#039;emissione ” 46 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Della luce rifratta.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle prime teorie speculate intorno alla natura delle rifrazioni, e de&#039;primi tentativi <lb></lb>fatti per iscoprirne le leggi <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 53 </s></p><p type="main">

<s>II Del Teorema dello Snellio, e della legge diottrica indi formulatane dal Cartesio ” 60 </s></p><p type="main">

<s>III Della legge diottrica dimostrata dall&#039;Herigonio; del principio delle cause finali introdotto <lb></lb>in quella dimostrazione, e come il Newton ritornasse ai principii meccanici ” 68 </s></p><p type="main">

<s>IV Della scienza delle rifrazioni in Italia ” 75 </s></p><p type="main">

<s>V Delle rifrazioni astronomiche ” 86 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Della luce diffratta e de&#039;colori.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Dell&#039;esperienze, da cui fu condotto il Grimaldi a professar che la luce, come i liquidi, <lb></lb>si diffrange <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 96 </s></p><p type="main">

<s>II Come il Newton confermasse le verità de&#039;fenomeni grimaldiani, e come v&#039;applicasse <lb></lb>a spiegarli il principio dell&#039;attrazione ” 103 </s></p><p type="main">

<s>III Delle teorie de&#039;colori ” 108 </s></p><p type="main">

<s>IV De&#039;colori, e delle varie apparenze dell&#039;Iride celeste ” 115 </s></p><p type="main">

<s>V Delle Corone e de&#039;Parelii. </s>

<s>” 123 </s></p><pb xlink:href="020/01/1113.jpg" pagenum="556"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del calore.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Dell&#039;antica teoria degl&#039;ignicoli rinnovata da Galileo: della questione del freddo posi­<lb></lb>tivo o privativo <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 132 </s></p><p type="main">

<s>II Di alcune speculazioni, e sperienze meno note, fatte intorno al calore dagli Accademici <lb></lb>del Cimento ” 142 </s></p><p type="main">

<s>III Del calore di comunicazione, e del calorico raggi<gap></gap>ate ” 151 </s></p><p type="main">

<s>IV Degli effetti del calore negli agghiacciamenti ” 160 </s></p><p type="main">

<s>V Degli effetti del calore nelle evaporazioni ” 170 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del suono.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della diffusione del suono per l&#039;aria <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 177 </s></p><p type="main">

<s>II Delle varie esperienze ordinate a dimostrar la diffusione, e a misurar la velocità del <lb></lb>suono per l&#039;aria ” 187 </s></p><p type="main">

<s>III Delle prime fisiche ragioni date delle consonanze ” 198 </s></p><p type="main">

<s>IV Di ciò che, intorno al risonar delle corde, fu dimostrato da Galileo ” 203 </s></p><p type="main">

<s>V Di un trattato fisico matematico, che preparava Niccolò Aggiunti sui tremori armonici <lb></lb>nelle corde ” 212 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del Magnete.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle più antiche osservazioni, e delle prime esperienze fatte intorno al Magnete <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 223 </s></p><p type="main">

<s>II Di ciò che, a promuovere la Filosofia magnetica, si cooperò dal Gilberto, dal Sarpi, e <lb></lb>da Galileo ” 230 </s></p><p type="main">

<s>III Delle teorie magnetiche, e di ciò che particolarmente ne pensarono i Filosofi inglesi ” 238 </s></p><p type="main">

<s>IV Dell&#039;ipotesi de&#039;due fluidi sostanziali, e del loro modo di operar nel Magnete, secondo <lb></lb>A. Nardi. </s>

<s>e F. M. </s>

<s>Grimaldi ” 245 </s></p><p type="main">

<s>V Delle variazioni della declinazione magnetica ” 251 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dell&#039;Elettro.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle prime esperienze elettriche, e delle ipotesi del Gilberto e del Cabeo; delle espe­<lb></lb>rienze del Guericke, e degli Accademici del Cimento <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 262 </s></p><p type="main">

<s>II De&#039;fuochi elettrici dell&#039;Hawksbee, dell&#039;elettricità per comunicazione, dell&#039;elettricità vi­<lb></lb>trea e resinosa, e dell&#039;elettricità positiva e negativa ” 269 </s></p><p type="main">

<s>III Di ciò che, a promuovere la scienza elettrica, fu cooperato in Italia, principalmente dal <lb></lb>Beccaria e dal Volta. </s>

<s>” 275 </s></p><p type="main">

<s>IV Dell&#039;elettricità, e degli effetti di lei nell&#039;ammosfera. </s>

<s>” 284 </s></p><pb xlink:href="020/01/1114.jpg" pagenum="557"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Delle Meteore.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle sublimazioni de&#039;vapori vescicolari, e de&#039;loro condensamenti in pioggia <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 294 </s></p><p type="main">

<s>II Dell&#039;origine de&#039;venti in generale, e in particolare de&#039;venti tropicali ” 305 </s></p><p type="main">

<s>III Delle variazioni, che subisce il Barometro al vario stato del cielo ” 316 </s></p><p type="main">

<s>IV Delle Effemeridi meteorologiche del Ramazzini; delle variazioni barometriche prodotte <lb></lb>dallo spirare de&#039;venti, e dall&#039;appressarsi delle procelle. </s>

<s>” 324 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del sistema del Mondo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Del sistema del Mondo immaginato dagli antichi Peripatetici; della Sintassi platonica <lb></lb>e della Copernicana, e quali fossero i loro primi incontri appresso gli stranieri <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 331 </s></p><p type="main">

<s>II Del Sistema copernicano in Italia, e segnatamente di Galileo Galilei. </s>

<s>” 341 </s></p><p type="main">

<s>III Del Dialogo galileiano sopra i due Massimi sistemi del Mondo ” 351 </s></p><p type="main">

<s>IV Delle avventure del Copernicismo dai tempi di Galileo alla fine del secolo XVII ” 363 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO X.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del Sole e della Luna.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle prime osservazioni intorno alle macchie solari fatte in Italia, e descritte da Galileo. <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 372 </s></p><p type="main">

<s>II Delle controversie insorte tra lo Scheiner e Galileo: dell&#039;essere e della natura delle <lb></lb>Macchie solari ” 381 </s></p><p type="main">

<s>III Delle macchie, e di varie altre apparenze nel cerchio della Luna ” 389 </s></p><p type="main">

<s>IV Del Candore lunare, e particolarmente della Lettera di Galileo sopra questo argomento. </s>

<s>” 398 </s></p><p type="main">

<s>V Del color rosso nelle Ecclissi di Luna ” 405 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO XI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Di Giove.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della scoperta de&#039;quattro Pianeti medicei; de&#039;metodi usati da Galileo per definirne i <lb></lb>tempi periodici, e le massime digressioni <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 411 </s></p><p type="main">

<s>II Degli studii intorno al Sistema gioviale proseguiti dal Castelli, dal Renieri e dall&#039;Ho­<lb></lb>dierna. </s>

<s>” 423 </s></p><p type="main">

<s>III Di ciò che, a perfezionare le osservazioni e a dimostrare le teoriche de&#039;Medicei, coope­<lb></lb>rarono il Montanari e il Borelli, il Viviani e il Cassini ” 430 </s></p><p type="main">

<s>IV Dell&#039;aspetto di Giove, e della fisica costituzione di lui. </s>

<s>” 443 </s></p><p type="main">

<s>V Del problema delle Longitudini, e della particolar soluzione di lui, per mezzo delle Ef­<lb></lb>femeridi gioviali ” 452 </s></p><pb xlink:href="020/01/1115.jpg" pagenum="558"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO XII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Di Saturno.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle prime osservazioni, e delle prime ipotesi degli Astronomi sul sistema di Saturno, <lb></lb>da Galileo all&#039;Hevelio <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 463 </s></p><p type="main">

<s>II Della grande scoperta ugeniana dell&#039;Anello, e di quel che si pensò, per confermarla, <lb></lb>dagli Accademici del Cimento ” 471 </s></p><p type="main">

<s>III Dell&#039;origine, della fisica costituzione, e del moto dell&#039;Anello saturnio, secondo gli Acca­<lb></lb>demici del Cimento ” 481 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO XIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Delle Stelle fisse e delle Comete.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Del luogo e del moto, della sostanza e della generazione delle stelle fisse nel cielo <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 493 </s></p><p type="main">

<s>II Delle osservazioni telescopiche delle stelle fisse; della scintillazione, e della loro pa­<lb></lb>rallasse ” 501 </s></p><p type="main">

<s>III Delle varie ipotesi intorno all&#039;essere e alla natura delle Comete. </s>

<s>” 510 </s></p><p type="main">

<s>IV Della teoria planetaria delle Comete ” 517 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO XIV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>De&#039;moti dell&#039;Universo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della scoperta delle Orbite ellittiche, e delle leggi del moto dei Pianeti <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 524 </s></p><p type="main">

<s>II Delle forze centrali, e dei decrementi delle loro intensità, in ragione delle distanze. </s>

<s>” 534 </s></p><p type="main">

<s>III Delle leggi delle forze centrali; dell&#039;attrazione universale; dell&#039;origine delle Orbite el­<lb></lb>littiche ” 540 </s></p><p type="main">

<s>IV Delle varie ipotesi proposte a spiegar la tendenza dei gravi ai loro centri ” 547 </s></p><pb xlink:href="020/01/1116.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE ALFABETICO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEGLI AUTORI E DELLE COSE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Co&#039;numeri s&#039;accenna alle pagine.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Accademici del Cimento<emph.end type="bold"></emph.end> fanno inutile prova delle attrazioni elettriche nel vuoto 268, sperimentano <lb></lb>il poter della fiamma sull&#039;ambra 269. </s></p><p type="main">

<s><emph type="bold"></emph>Accolti Pietro<emph.end type="bold"></emph.end> spiega la ragione della penombra 24, come spieghi il circoleggiar dell&#039;immagine del <lb></lb>Sole passata attraverso a qualunque irregolarità di foro 31. </s></p><p type="main">

<s><emph type="bold"></emph>Aggiunti Niccolò,<emph.end type="bold"></emph.end> proposizioni meccaniche di lui sulla trazion delle corde 215, sue teorie ed espe­<lb></lb>rienze della diffusione del suono ne&#039;solidi e ne&#039;liquidi 217, sue proposizioni acustiche dimo­<lb></lb>strate 220, traduce in latino il Discorso di Galileo sul flusso del mare 350. </s></p><p type="main">

<s><emph type="bold"></emph>Agucchia Giovan Batista<emph.end type="bold"></emph.end> ritrova i tempi periodici della circolazion de&#039;Satelliti intorno a Giove 417. </s></p><p type="main">

<s><emph type="bold"></emph>Aguilonio,<emph.end type="bold"></emph.end> come fosse presso a trovare, e come smarrisse la diretta via, nell&#039;investigar la legge del <lb></lb>decrescere l&#039;intensità della luce, a proporzione che crescono le distanze 34. </s></p><p type="main">

<s><emph type="bold"></emph>Alighieri Dante,<emph.end type="bold"></emph.end> come dimostrò le due leggi fondamentali della Catottrica 13, ammette Venere e <lb></lb>Mercurio inferiori 336. </s></p><p type="main">

<s><emph type="bold"></emph>Ancora della Calamita,<emph.end type="bold"></emph.end> origine di questo nome e uso 236. </s></p><p type="main">

<s><emph type="bold"></emph>Anello di ghiaccio<emph.end type="bold"></emph.end> immaginato dal Cartesio a spiegare il modo come si dipingono i Parelii 126. </s></p><p type="main">

<s><emph type="bold"></emph>Anello di Saturno,<emph.end type="bold"></emph.end> come sperimentalmente si dimostri essere montagnoso 487, se sia possibile 488, <lb></lb>come possa esser durabile 489, come seguiti il moto del Pianeta 490. </s></p><p type="main">

<s><emph type="bold"></emph>Apelle,<emph.end type="bold"></emph.end> sue Lettere sulle Macchie solari 375. </s></p><p type="main">

<s><emph type="bold"></emph>Archibugio a vento,<emph.end type="bold"></emph.end> da chi ritrovato 179. </s></p><p type="main">

<s><emph type="bold"></emph>Aria,<emph.end type="bold"></emph.end> come si trovi nell&#039;acqua 162, come nel mercurio dello Strumento torricelliano 164, ricerche <lb></lb>inutili del Montanari, per veder d&#039;onde ella entri nel mercurio del Barometro 165, è il veicolo <lb></lb>ordinario del suono 188. </s></p><p type="main">

<s><emph type="bold"></emph>Aristotile,<emph.end type="bold"></emph.end> per quali ragioni neghi la mobilità della Terra 333, sua opinione delle Comete 513. </s></p><p type="main">

<s><emph type="bold"></emph>Asterismi<emph.end type="bold"></emph.end> varii disegnati ne&#039;Manoscritti di Galileo 505. </s></p><p type="main">

<s><emph type="bold"></emph>Astri,<emph.end type="bold"></emph.end> come spieghi Galileo il loro apparire sull&#039;orizzonte più grandi 90, come spiegato da Leonardo <lb></lb>da Vinci 91, come dal Fracastoro 91. </s></p><p type="main">

<s><emph type="bold"></emph>Astroscopia dell&#039;Huyghens<emph.end type="bold"></emph.end> tradotta dal Viviani 501. </s></p><p type="main">

<s><emph type="bold"></emph>Attrazione universale,<emph.end type="bold"></emph.end> come dimostrata 543. </s></p><p type="main">

<s><emph type="bold"></emph>Attrazioni e repulsioni elettriche,<emph.end type="bold"></emph.end> come spiegate dal Nollet 279. </s></p><p type="main">

<s><emph type="bold"></emph>Aurore boreali,<emph.end type="bold"></emph.end> loro origine secondo Galileo 290, secondo il Franklin 291, secondo il Beccaria 292, <lb></lb>secondo il Bondioli, non però secondato dal Volta 292. </s></p><p type="main">

<s><emph type="bold"></emph>Bacone Francesco,<emph.end type="bold"></emph.end> sue esperienze sull&#039;origine dei venti 306. </s></p><p type="main">

<s><emph type="bold"></emph>Baliani Giovan Batista<emph.end type="bold"></emph.end> crede falso il problema delle ombre proposto dal Gassendo 408. </s></p><p type="main">

<s><emph type="bold"></emph>Bardi Pietro<emph.end type="bold"></emph.end> propone a risolvere a Galileo un problema termico 134. </s></p><p type="main">

<s><emph type="bold"></emph>Barometro,<emph.end type="bold"></emph.end> se risenta alcuna variazione nel flusso e riflusso 355. </s></p><p type="main">

<s><emph type="bold"></emph>Bartoli Daniele<emph.end type="bold"></emph.end> muove difficoltà contro la teoria galileiana delle risonanze 206. </s></p><p type="main">

<s><emph type="bold"></emph>Beccaria Giovan Batista<emph.end type="bold"></emph.end> scopre la legge del moto ne&#039;flussi elettrici 277, dà la teoria delle punte <lb></lb>elettriche 278, dà la teoria della Macchina elettrica 279, dimostra sperimentalmente come le at­<lb></lb>trazioni elettriche avvengano anche nel vuoto 280, primo a sperimentare in Italia l&#039;elettricità <lb></lb>ammosferica ne&#039;pali frankliniani 288. </s></p><pb xlink:href="020/01/1117.jpg" pagenum="560"></pb><p type="main">

<s><emph type="bold"></emph>Benedetti Giovan Batista,<emph.end type="bold"></emph.end> come dimostri la legge dell&#039;intensità calorifica sulle superflcie variamente <lb></lb>inclinate 157, sue speculazioni intorno alla generazione del suono 182, conosce la vera causa dei <lb></lb>venti 305, approva il sistema copernicano 343, ragioni che rende del rosso negli ecclissi di <lb></lb>Luna 405, dello scintillar delle stelle 504. </s></p><p type="main">

<s><emph type="bold"></emph>Biancani Giuseppe<emph.end type="bold"></emph.end> si studia di ricomporre la controversia insorta fra Pitagorici e Aristotelici intorno <lb></lb>all&#039;origine delle Comete 511. </s></p><p type="main">

<s><emph type="bold"></emph>Bianchini Francesco<emph.end type="bold"></emph.end> definisce il tempo della rotazione di Venere 479. </s></p><p type="main">

<s><emph type="bold"></emph>Bianconi Lodovico<emph.end type="bold"></emph.end> dimostra la variabile velocità del suono, nell&#039;estate e nell&#039;inverno 197. </s></p><p type="main">

<s><emph type="bold"></emph>Borelli Gian Alfonso<emph.end type="bold"></emph.end> pensa a un&#039;esperienza, da concluder se la luce si muove con tempo 43, ri­<lb></lb>prova le dottrine kepleriane, ma non promuove la Diottrica 68, pensa a un&#039;esperienza dimostra­<lb></lb>tiva delle astronomiche rifrazioni 94, come dimostri gli effetti dell&#039;acqua nell&#039;agghiacciarsi 164, <lb></lb>diffonde in Toscana la notizia delle proprieta de&#039;suoni nel loro diffondersi per l&#039;aria, scoperte <lb></lb>dal Mersenno 192, sue esperienze e ragioni del v<gap></gap>nto ne&#039;cammini accesi 307, narra la scoperta, <lb></lb>e dice le ragioni delle variazioni barometriche, secondo il vario stato del cielo 320, dietro alle <lb></lb>proprie osservazioni trova insufficiente la dottrina del Keplero a render la ragione del lume nella <lb></lb>Luna ecclissata 400, suo metodo per trovare le longitudini, con gli orologi 460, sua teoria de&#039;moti <lb></lb>planetarii 536. </s></p><p type="main">

<s><emph type="bold"></emph>Borro Girolamo<emph.end type="bold"></emph.end> scrive del flusso e riflusso marino 352, sua ipotesi delle Macchie lunari 391. </s></p><p type="main">

<s><emph type="bold"></emph>Bottiglia di Leyda,<emph.end type="bold"></emph.end> sua teoria data dal Franklin 276. </s></p><p type="main">

<s><emph type="bold"></emph>Boulliaud Ismaele,<emph.end type="bold"></emph.end> suo teorema fotometrico dimostrato 38, sue teorie plauetarie 531, primo a dimo­<lb></lb>strar che gl&#039;impulsi radiosi del Sole, in movere i Pianeti, si debilitano a proporzione che cre­<lb></lb>scono i quadrati delle distanze 539, primo ad applicare la legge fotometrica alla illuminazione <lb></lb>de&#039;Pianeti 539. </s></p><p type="main">

<s><emph type="bold"></emph>Branca Giovanni,<emph.end type="bold"></emph.end> libro <emph type="italics"></emph>Delle machine<emph.end type="italics"></emph.end> 173. </s></p><p type="main">

<s><emph type="bold"></emph>Cabeo Niccolò,<emph.end type="bold"></emph.end> come spieghi le attrazioni elettriche 266. </s></p><p type="main">

<s><emph type="bold"></emph>Calamita,<emph.end type="bold"></emph.end> come ne fosse da Galileo perfezionata l&#039;armatura 236, come si sperasse per essa di tro­<lb></lb>vare le longitudini 453. </s></p><p type="main">

<s><emph type="bold"></emph>Calcolo del Cartesio<emph.end type="bold"></emph.end> intoruo ai raggi rifratti osservati già dallo Snellio 62. </s></p><p type="main">

<s><emph type="bold"></emph>Calore,<emph.end type="bold"></emph.end> sua varia conducibilità nelle varie nature de&#039;corpi, da chi prima sperimentata 152, se si dif­<lb></lb>fonda in sfera 155, leggi della intensità del riscaldamento 157, come variamente assorbito dalle <lb></lb>superfìcie bianche e dalle nere 158. </s></p><p type="main">

<s><emph type="bold"></emph>Campani Giuseppe<emph.end type="bold"></emph.end> si usurpa l&#039;invenzione della Macchinetta, da rappresentare le fasi di Saturno 492. </s></p><p type="main">

<s><emph type="bold"></emph>Candore lunare,<emph.end type="bold"></emph.end> principio delle controversie insorte fra Galileo e il Liceti 399, su questo argomento <lb></lb>scrive Galileo un principio di Lettera al Liceti 400, torna, nel seguito di quella Lettera, a rivol­<lb></lb>gere il discorso al principe Leopoldo 401, pensieri importanti di Galileo su questo argomento 402, <lb></lb>riepilogo del principale argomento contro il Liceti 404. </s></p><p type="main">

<s><emph type="bold"></emph>Cappello,<emph.end type="bold"></emph.end> fase presentata in tal figura da Saturno 474. </s></p><p type="main">

<s><emph type="bold"></emph>Cartesio Renato,<emph.end type="bold"></emph.end> come dimostri geometricamente la legge dell&#039;uguaglianza fra gli angoli dell&#039;inci­<lb></lb>denza e quelli di riflessione 15, dimostra la relazione costante, che passa fra i seni degli angoli <lb></lb>dell&#039;incidenza e i seni degli angoli della rifrazione 63, come e quando s&#039;intese che le leggi diot­<lb></lb>triche spiegate da lui erano state prima dimostrate dallo Snellio 65, ragione perchè si creda pro­<lb></lb>babile ch&#039;egli conoscesse il Teorema diottrico dello Snellio 67, questioni da lui proposte intorno <lb></lb>al Magnete 240. </s></p><p type="main">

<s><emph type="bold"></emph>Cassini Gian Domenico,<emph.end type="bold"></emph.end> quel che risponda al Petit nel negar la variabilità della declinazione ma­<lb></lb>gnetica 257, riscontra le radici de&#039;Medicei calcolate da Galileo 437, sue Effemeridi bolognesi 438, <lb></lb>determina il periodo della rotazione di Giove 449, scopre le ombre de&#039;Satelliti proiettate sul disco <lb></lb>di Giove 449, propone le sue Effemeridi gioviali per la soluzione del problema delle Longitu­<lb></lb>dini 459, sua teoria delle comete 518. </s></p><p type="main">

<s><emph type="bold"></emph>Castelli Benedetto,<emph.end type="bold"></emph.end> suo Teorema di Fotometria dimostrato 37, suo discorso sopra la Calamita 238, <lb></lb>dà opera, insieme con Galileo, alle osservazioni gioviali 424, collaboratore a Galileo nell&#039;osser­<lb></lb>vare le stelle 506. </s></p><p type="main">

<s><emph type="bold"></emph>Cavalieri Bonaventura<emph.end type="bold"></emph.end> medita intorno al problema delle ombre proposto dal Gassendo 26, come <lb></lb>ignorasse la legge della diffusione del suono 183, sue idee singolari intorno all&#039;origine dei <lb></lb>venti 311, concorda con Galileo intorno alla ragione del vedersi ancora la Luna nelle ecclissi 408. </s></p><p type="main">

<s><emph type="bold"></emph>Ceralacca,<emph.end type="bold"></emph.end> se si elettrizzi di elettricità simile a quella dell&#039;ambra 273. </s></p><p type="main">

<s><emph type="bold"></emph>Cervo volante,<emph.end type="bold"></emph.end> macchina da esplorare l&#039;elettricità ammosferica 287. </s></p><p type="main">

<s><emph type="bold"></emph>Cesalpino Andrea<emph.end type="bold"></emph.end> ammette il moto diurno della Terra 342, sua opinione intorno alle macchie della <lb></lb>Luna 391. </s></p><p type="main">

<s><emph type="bold"></emph>Cilindretti di vetro<emph.end type="bold"></emph.end> immaginati dall&#039;Huyghens, per spiegare come si dipingano le corone e i parelii 128. </s></p><pb xlink:href="020/01/1118.jpg" pagenum="561"></pb><p type="main">

<s><emph type="bold"></emph>Colombo Cristoforo,<emph.end type="bold"></emph.end> primo a osservare la declinazione dell&#039;ago magnetico 225, primo a proporre il <lb></lb>modo di trovar la longitudine, per mezzo della Bussola 453. </s></p><p type="main">

<s><emph type="bold"></emph>Colori,<emph.end type="bold"></emph.end> loro natura secondo i Peripatetici 108, secondo il De Dominis 109, loro generazione per ri­<lb></lb>frazione, secondo il Maurolico 110, secondo il Grimaldi 111, loro teoria, secondo il Cartesio 112, <lb></lb>loro analogie coll&#039;armonie de&#039;suoni, secondo il Grimaldi 113, dipendono, secondo il Castelli, dalla <lb></lb>maggiore o minore velocità del raggio emesso 113, loro teoria, secondo il Newton 114, loro com­<lb></lb>posizione nell&#039;occhio, secondo il Montanari 115. </s></p><p type="main">

<s><emph type="bold"></emph>Comete,<emph.end type="bold"></emph.end> loro orbita parabolica dimostrata sperimentalmente 520, loro natura planetaria dimostrata <lb></lb>dal Newton 523. </s></p><p type="main">

<s><emph type="bold"></emph>Condensazione dell&#039;acqua<emph.end type="bold"></emph.end> dimostrata impossibilc 163. </s></p><p type="main">

<s><emph type="bold"></emph>Contradizioni<emph.end type="bold"></emph.end> alle leggi diottriche del Cartesio 64. </s></p><p type="main">

<s><emph type="bold"></emph>Copernico Niccolò,<emph.end type="bold"></emph.end> da che venisse inspirato alle contemplazioni de&#039;fenomeni celesti 335, suo si­<lb></lb>stema 336, pubblicazione de&#039;sei libri <emph type="italics"></emph>De revolutionibus<emph.end type="italics"></emph.end> 337. </s></p><p type="main">

<s><emph type="bold"></emph>Cornelio Tommaso<emph.end type="bold"></emph.end> ritrova falso un principio assunto da Galileo, per risolvere un problema ter­<lb></lb>mico 135, come si provi a risolvere lo stesso problema 136, avverte, prima del Pecquet, l&#039;ela­<lb></lb>sticità dell&#039;aria 180. </s></p><p type="main">

<s><emph type="bold"></emph>Corone,<emph.end type="bold"></emph.end> come si dipingano intorno al Sole, secondo Ferrante Imperato 124, come, secondo il Car­<lb></lb>tesio 125. </s></p><p type="main">

<s><emph type="bold"></emph>Cristalli del ghiaccio,<emph.end type="bold"></emph.end> come spiegati dal Keplero 166, come dal Cartesio 167, loro modo di formarsi, <lb></lb>secondo il Baliani e il Borelli 168, secondo il Rossetti 169. </s></p><p type="main">

<s><emph type="bold"></emph>Dalibard<emph.end type="bold"></emph.end> mette in esecuzione il progetto frankliniano de&#039;parafulmini 287. </s></p><p type="main">

<s><emph type="bold"></emph>De Dominis,<emph.end type="bold"></emph.end> suoi errori intorno al fatto delle rifrazioni 59, risolve le principali questioni intorno al <lb></lb>flusso del mare 358. </s></p><p type="main">

<s><emph type="bold"></emph>Declinatorio magnetico<emph.end type="bold"></emph.end> sperimentato dal Sagredo 235. </s></p><p type="main">

<s><emph type="bold"></emph>Decreto<emph.end type="bold"></emph.end> nella sacra Congregazione romana contro il Copernico 347. </s></p><p type="main">

<s><emph type="bold"></emph>Del Buono Paolo<emph.end type="bold"></emph.end> esperimenta la generazione dell&#039;aria dall&#039;acqua 163. </s></p><p type="main">

<s><emph type="bold"></emph>Del Papa Giuseppe,<emph.end type="bold"></emph.end> come risolva un problema termico male risoluto da Galileo 137. </s></p><p type="main">

<s><emph type="bold"></emph>Diafani e opachi,<emph.end type="bold"></emph.end> da che dipendano 23. </s></p><p type="main">

<s><emph type="bold"></emph>Diffrazione della luce<emph.end type="bold"></emph.end> scoperta dal Grimaldi 100. </s></p><p type="main">

<s><emph type="bold"></emph>Digestore<emph.end type="bold"></emph.end> papiniano, e sua teoria data dal Newton 173. </s></p><p type="main">

<s><emph type="bold"></emph>Digressioni<emph.end type="bold"></emph.end> de&#039;Satelliti di Giove trovate da Galileo 416. </s></p><p type="main">

<s><emph type="bold"></emph>Diottrica,<emph.end type="bold"></emph.end> trattata dall&#039;Huyghens, e storia della sua pubblicazione 81. </s></p><p type="main">

<s><emph type="bold"></emph>Disegno<emph.end type="bold"></emph.end> dell&#039;anello di Saturno fatto a penna da Galileo 466. </s></p><p type="main">

<s><emph type="bold"></emph>Du-Hamel<emph.end type="bold"></emph.end> nega, contro l&#039;autorità del Pascal e del Borelli, che l&#039;aria nuvolosa pesi più della se­<lb></lb>rena 322. </s></p><p type="main">

<s><emph type="bold"></emph>Effemeridi<emph.end type="bold"></emph.end> prime di Galileo 412. </s></p><p type="main">

<s><emph type="bold"></emph>Elasticità dell&#039;aria,<emph.end type="bold"></emph.end> quando e come fosse conosciuta 179. </s></p><p type="main">

<s><emph type="bold"></emph>Elba,<emph.end type="bold"></emph.end> isola, se abbia alcuna influenza in alterar la direzione dell&#039;ago calamitato 227. </s></p><p type="main">

<s><emph type="bold"></emph>Elettriche,<emph.end type="bold"></emph.end> forze, rassomigliate alle forze cosmiche 551. </s></p><p type="main">

<s><emph type="bold"></emph>Elettricità<emph.end type="bold"></emph.end> per comunicazione scoperta dal Gray, e confermata dal Dufay 272, vitrea e resinosa 273, <lb></lb>Elettricità vindice 283, Elettricità ammosferica, sua origine secondo il Franklin 285, come di­<lb></lb>mostrata dal Volta 289, Elettricità per eccesso, sua origine nell&#039;aria 290. </s></p><p type="main">

<s><emph type="bold"></emph>Empoli (da) Giovanni<emph.end type="bold"></emph.end> specula sulle proprietà della Calamita 225. </s></p><p type="main">

<s><emph type="bold"></emph>Equazion della luce<emph.end type="bold"></emph.end> nelle osservazioni de&#039;Satelliti di Giove 459. </s></p><p type="main">

<s><emph type="bold"></emph>Esalazioni ascendenti,<emph.end type="bold"></emph.end> causa secondo Galileo delle evaporazioni 172. </s></p><p type="main">

<s><emph type="bold"></emph>Esperienza<emph.end type="bold"></emph.end> proposta dal Borelli per misurar la velocità della luce 43, di Euclide sulle rifrazioni 53, <lb></lb>esperienza con cui prima il Grimaldi scopri il fenomeno della diffrazione 98, altra esperienza <lb></lb>per questo effetto 99, esperienza della luce, che aggiunta a luce fa ombra 101, esperienza im­<lb></lb>maginata dal Borelli, per dimostrar come l&#039;aria carica di vapori faccia sollevar di più la co­<lb></lb>lonna barometrica 317. </s></p><p type="main">

<s><emph type="bold"></emph>Esperienze acustiche<emph.end type="bold"></emph.end> di Galileo, che non rispondono alle prove 2<gap></gap>8, 211, esperienze magnetiche de­<lb></lb>scritte dal Porta, nel VII libro della Magia naturale 229, esperienze della Calamita nel vuoto 251. </s></p><p type="main">

<s><emph type="bold"></emph>Euclide,<emph.end type="bold"></emph.end> suo trattato di Prospettiva 8, come dimostri che l&#039;angolo dell&#039;incidenza è uguale all&#039;an­<lb></lb>golo della riflessione 12. </s></p><p type="main">

<s><emph type="bold"></emph>Fabry Onorato,<emph.end type="bold"></emph.end> suo sistema saturnio 475, sue opposizioni fatte contro quello dell&#039;Huyghens 476. </s></p><p type="main">

<s><emph type="bold"></emph>Fasce di Glove,<emph.end type="bold"></emph.end> da chi prima osservate 445, loro origine 446. </s></p><pb xlink:href="020/01/1119.jpg" pagenum="562"></pb><p type="main">

<s><emph type="bold"></emph>Fata morgana,<emph.end type="bold"></emph.end> come spiegata co principii ottici neutoniani 19. </s></p><p type="main">

<s><emph type="bold"></emph>Fermat<emph.end type="bold"></emph.end> si oppone alla legge diottrica dimostrata dal Cartesio 64, come, partendo dal principio delle <lb></lb>cáuse finali, s&#039;incontrasse nella legge diottrica formulata dal Cartesio 71. </s></p><p type="main">

<s><emph type="bold"></emph>Ferroni Giuseppe,<emph.end type="bold"></emph.end> come spieghi che l&#039;aria serena preme più sul Barometro, che non la nuvolosa 322. </s></p><p type="main">

<s><emph type="bold"></emph>Fiamma,<emph.end type="bold"></emph.end> come scoperta conduttrice dell&#039;Elettricità 273. </s></p><p type="main">

<s><emph type="bold"></emph>Fontana Francesco,<emph.end type="bold"></emph.end> sue osservazioni sul pianeta di Saturno 468. </s></p><p type="main">

<s><emph type="bold"></emph>Foro,<emph.end type="bold"></emph.end> per cui passa la luce e si proietta su un diaframma: fenomeni relativi spiegati 30. </s></p><p type="main">

<s><emph type="bold"></emph>Fracastoro Girolamo,<emph.end type="bold"></emph.end> suo sistema degli Omocentrici 341, sua ipotesi intorno all&#039;apparizione delle <lb></lb>stelle nuove 496. </s></p><p type="main">

<s><emph type="bold"></emph>Franklin Beniamino,<emph.end type="bold"></emph.end> sua teoria dell&#039;Elettricità vitrea e resinosa 275. </s></p><p type="main">

<s><emph type="bold"></emph>Freddo,<emph.end type="bold"></emph.end> se sia positivo: questione insorta fra il Dati e il Rucellai 139. </s></p><p type="main">

<s><emph type="bold"></emph>Fulmini,<emph.end type="bold"></emph.end> loro natura, secondo il Montanari 284. </s></p><p type="main">

<s><emph type="bold"></emph>Fuoco elettrico,<emph.end type="bold"></emph.end> sua differenza dal fuoco ordinario 270. </s></p><p type="main">

<s><emph type="bold"></emph>Galilei Alessandro,<emph.end type="bold"></emph.end> sua macchina a vapore 175. </s></p><p type="main">

<s><emph type="bold"></emph>Galileo Galilei,<emph.end type="bold"></emph.end> sue proposizioni di Fotometria 61, suo errore nel misurar l&#039;intensità del lume di <lb></lb>Luna 39, propone l&#039;esperienza, per decider se la luce si muove in istante 41, sua ambiguità <lb></lb>nell&#039;ammettere le rifrazioni, e d&#039;ond&#039;ella dipendesse 93, rinnova le dottrine de&#039;Filosofi antichi <lb></lb>intorno al calore 133, come errasse nel paragonare la diffusione della luce con quella del ca­<lb></lb>lore 154, leggi del risonar delle corde da lui scoperte 209, come spieghi le attrazioni elettriche 265, <lb></lb>osserva col Canocchiale i vapori ascendenti, e pensa alle ragioni della pioggia 295, sua prima <lb></lb>professione di Copernicismo 344, scrive il Discorso del flusso e riflusso 348, vicende della pub­<lb></lb>blicazione del suo Dialogo copernicano 349, quale efficacia, sulla marea, attribuisse alla Luna 354, <lb></lb>se fosse il primo a pensare alle fasi di Venere, per confermare il Sistema copernicano 358, os­<lb></lb>serva <emph type="italics"></emph>averso vultu<emph.end type="italics"></emph.end> le macchie del Sole 374, è incoerente a sè medesimo, nell&#039;assegnar la data <lb></lb>della scoperta delle Macchie solari 374, sua incoerenza nell&#039;ammettere l&#039;inversione delle imma­<lb></lb>gini nel Canocchiale, e no nell&#039;occhio 381, ciò che, riguardo all&#039;osservazione e alla filosofia delle <lb></lb>macchie solari, attingesse dal Passignani e dal Castelli 381, sua ipotesi intorno alle stelle nuove 496, <lb></lb>suo Dialogo intorno a questo soggetto 498, quale accoglienza facesse alla Nuova astronomia keple­<lb></lb>riana 530. </s></p><p type="main">

<s><emph type="bold"></emph>Gassendi Pietro,<emph.end type="bold"></emph.end> suo problema dell&#039;ombre 26, ammette il freddo positivo 138, sue proposizioni in­<lb></lb>torno alle proprietà de&#039;suoni, verificate dagli Accademici del Cimento 194, compendia la storia <lb></lb>del Magnete 239. </s></p><p type="main">

<s><emph type="bold"></emph>Ghiacclo,<emph.end type="bold"></emph.end> causa del ricrescimento della sua mole 161. </s></p><p type="main">

<s><emph type="bold"></emph>Giamblico,<emph.end type="bold"></emph.end> come racconti la stoma pitagorica de&#039;suoni musicali 199. </s></p><p type="main">

<s><emph type="bold"></emph>Gilberto Guglielmo,<emph.end type="bold"></emph.end> racconta come e da chi fosse prima osservata la direzione dell&#039;ago magne­<lb></lb>tico 224, non fa il Magnetismo e l&#039;Elettricità due cose della stessa natura, come pretendono al­<lb></lb>cuni 282, in che riconosca la causa della variazione della declinazione magnetica 253, accresce <lb></lb>il numero de&#039;corpi elettrici 263, investiga le ragioni delle attrazioni elettriche 264, le fa consi­<lb></lb>stere nell&#039;umido copulatore 265, suoi argomenti fisici in favore del moto terrestre 339. </s></p><p type="main">

<s><emph type="bold"></emph>Giove,<emph.end type="bold"></emph.end> misura del diametro apparente del Pianeta 418, sue macchie 443, sue zone, da chi prima os­<lb></lb>servate 444, sua rotazione, come scoperta 448. </s></p><p type="main">

<s><emph type="bold"></emph>Grandi Guido<emph.end type="bold"></emph.end> applica un teorema ugeniano a dimostrar la legge diottrica cartesiana, col principio <lb></lb>delle cause finali 72. </s></p><p type="main">

<s><emph type="bold"></emph>Grandine,<emph.end type="bold"></emph.end> origine della sua formazione, secondo il Volta 293. </s></p><p type="main">

<s><emph type="bold"></emph>Gray<emph.end type="bold"></emph.end> scopre l&#039;Elettricità per comunicazione 272. </s></p><p type="main">

<s><emph type="bold"></emph>Gravi<emph.end type="bold"></emph.end> tendono al centro della Terra, come il ferro al Magnete 548. </s></p><p type="main">

<s><emph type="bold"></emph>Gravità,<emph.end type="bold"></emph.end> che tiene aderente a Saturno il suo anello 486. </s></p><p type="main">

<s><emph type="bold"></emph>Grimaldi Franc. </s>

<s>Maria,<emph.end type="bold"></emph.end> come fisicamente dimostri la legge dell&#039;uguaglianza, che passa fra gli an­<lb></lb>goli d&#039;incidenza e di riflessione 16, se professasse l&#039;ipotesi delle ondulazioni 50, censura l&#039;ipo­<lb></lb>tesi assunta dal Cartesio per la sua diottrica dimostrazione 82, come renda la ragione dell&#039;ac­<lb></lb>costarsi il raggio rifratto, e discostarsi dalla perpendicolare 83, come dimostri la legge diottrica, <lb></lb>tenendo una via, da quella del Cartesio, diversa 84, sua importante teoria magnetica 248, suoi <lb></lb>esperimenti magnetici 249. </s></p><p type="main">

<s><emph type="bold"></emph>Guericke Ottene,<emph.end type="bold"></emph.end> sue esperienze elettriche 267, dimostra artificialmente come faccia il cielo a ran­<lb></lb>nuvolarsi, piovere, e tornar sereno 304. </s></p><p type="main">

<s><emph type="bold"></emph>Guglielmini,<emph.end type="bold"></emph.end> rispetto alla luce professa l&#039;ipotesi delle ondulazioni 51. </s></p><p type="main">

<s><emph type="bold"></emph>Guiducci Mario<emph.end type="bold"></emph.end> espone il sistema magnetico del Gilberto 231. </s></p><p type="main">

<s><emph type="bold"></emph>Guy Tachart<emph.end type="bold"></emph.end> primo a osservare la variazione magnetica diurna 261. </s></p><pb xlink:href="020/01/1120.jpg" pagenum="563"></pb><p type="main">

<s><emph type="bold"></emph>Hawkabee Francesco<emph.end type="bold"></emph.end> ripete l&#039;esperienza del Lowthorp, per dimostrare la rifrazion della luce, che <lb></lb>dal vuoto passa nell&#039;aria 95, sue esperienze, per dimostraro da che dipenda il galleggiar dei <lb></lb>corpi ne&#039;mezzi specificamente più leggeri 303, conferma coll&#039;esperienza un concetto sovvenuto al <lb></lb>Viviani 323, dimostra sperimentalmente l&#039;efflcacia de&#039;venti, in alterar lo stato barometrico 320. </s></p><p type="main">

<s><emph type="bold"></emph>Herigonio Pietro,<emph.end type="bold"></emph.end> suo Corso matematico 68, come dimostri la proporzione costante, che passa fra&#039;seni <lb></lb>degli angoli dell&#039;incidenza, e i seni degli angoli delle rifrazioni 69, propone il modo di trovare <lb></lb>le longitudini, per via della congiunzione de&#039;Satelliti col centro di Giove 457. </s></p><p type="main">

<s><emph type="bold"></emph>Hevelio Giovanni<emph.end type="bold"></emph.end> propone di risolvere il problema delle longitudini, per via delle Effemeridi de&#039;Sa­<lb></lb>telliti di Giove 458, suo sistema saturnio 469, sua teoria del moto parabolico delle Comete 522. </s></p><p type="main">

<s><emph type="bold"></emph>Hodierna Giovan Batista,<emph.end type="bold"></emph.end> sua Menologia di Giove 428, impone i nomi ai Satelliti gioviali 429. </s></p><p type="main">

<s><emph type="bold"></emph>Hook Roberto<emph.end type="bold"></emph.end> conferisce col Viviani i suoi studii intorno al Magnete 243, come riuscisse a conclu­<lb></lb>dere la legge delle forze centrali 512. </s></p><p type="main">

<s><emph type="bold"></emph>Huyghens Cristiano,<emph.end type="bold"></emph.end> notizie intorno alla pubblicazione della sua Diottrica 127, sua applicazione di <lb></lb>uno strumento inventato dal Lecuwenoeck 370, narra come scoprisse l&#039;anello di Saturno 471. </s></p><p type="main">

<s><emph type="bold"></emph>Inclinazione dell&#039;ago magnetico,<emph.end type="bold"></emph.end> da chi prima osservata 233. </s></p><p type="main">

<s><emph type="bold"></emph>Innominato Autore<emph.end type="bold"></emph.end> dell&#039;Elettricismo, sua teoria de&#039;vortici elettrici 274. </s></p><p type="main">

<s><emph type="bold"></emph>Iride<emph.end type="bold"></emph.end> si fa per refrazione, secondo i placiti de&#039;Filosofi antichi riferiti da Plutarco e da Dante 115, <lb></lb>come si dipinga nelle nubi, secondo Vitellione 116, Iride primaria e secondaria, come spiegata da <lb></lb>Ferrante Imperato 117, teorie del Maurolico 118, del De Dominis 119, del Cartesio 121. </s></p><p type="main">

<s><emph type="bold"></emph>Irradiazlone,<emph.end type="bold"></emph.end> effetti di lei nella falce della Luna 395. </s></p><p type="main">

<s><emph type="bold"></emph>Kepier Giovanni,<emph.end type="bold"></emph.end> è il primo a dar la dimostrazione geometrica dell&#039;uguaglianza, che passa tra gli <lb></lb>angoli incidenti, formati dai raggi di luce, e i reflessi 14, come spieghi il rotondarsi dello spettro <lb></lb>del Sole passato attraverso a un foro irregolare 30, sue proposizioni di fotometria 33, ammette <lb></lb>che l&#039;intensità della luce scemi al crescere delle semplici distanze 35, applica alle rifrazioni il <lb></lb>principio della composizion delle forze 56, come narri la storia della scoperta delle astronomiche <lb></lb>rifrazioni 86, primo a osservare i cristallini del ghiaccio 166, a qual numero riducesse le conso­<lb></lb>nanze 200, osserva il Sole e la Luna, <emph type="italics"></emph>averso vultu<emph.end type="italics"></emph.end> 373, quando osservasse le Macchie solari col <lb></lb>Canocchiale 383, sua opinione intorno alla natura delle Macchie solari 386, leggi planetarie da <lb></lb>lui scoperte 528, da che fosse condotto ad ammettere che le forze centrali si debilitano secondo <lb></lb>le semplici distanze 538. </s></p><p type="main">

<s><emph type="bold"></emph>Hircker Atanasio,<emph.end type="bold"></emph.end> ragioni rese da lui della variazione della declinazione magnetica 254. </s></p><p type="main">

<s><emph type="bold"></emph>Latitudini de&#039;Gioviali,<emph.end type="bold"></emph.end> controversia insorta fra il Mario e Galileo 442. </s></p><p type="main">

<s><emph type="bold"></emph>Leibniz Gotifredo<emph.end type="bold"></emph.end> dimostra, col principio delle cause finali, l&#039;uguaglianza che passa fra gli angoli <lb></lb>d&#039;incidenza e di riflessione 20, dimostra, con lo stesso principio delle cause finali, il teorema <lb></lb>diottrico cartesiano 73, suo strumento meccanico adattato a rappresentar le variazioni barome­<lb></lb>triche, variando lo stato del cielo 326. </s></p><p type="main">

<s><emph type="bold"></emph>Leeuwenhoeck Antonio,<emph.end type="bold"></emph.end> sua esperienza per dimostrare il moto della Terra 369. </s></p><p type="main">

<s><emph type="bold"></emph>Libri Guglielmo<emph.end type="bold"></emph.end> e il disegno galileiano dell&#039;anello di Saturno 466. </s></p><p type="main">

<s><emph type="bold"></emph>Liceti Fortunio,<emph.end type="bold"></emph.end> come risolva ii problema delle ombre proposto dal Gassendo 27. </s></p><p type="main">

<s><emph type="bold"></emph>Longitudine,<emph.end type="bold"></emph.end> modo di ritrovarla proposto da Galileo 446. </s></p><p type="main">

<s><emph type="bold"></emph>Luce,<emph.end type="bold"></emph.end> se sia materiale: opinion degli antichi 40, sua velocità come misurata dal Roemer 46, luce ag­<lb></lb>giunta a luce, fa ombra 101, come possa produrre effetti meccanici 535. </s></p><p type="main">

<s><emph type="bold"></emph>Lucerna di Herone,<emph.end type="bold"></emph.end> come operasse 180. </s></p><p type="main">

<s><emph type="bold"></emph>Luna,<emph.end type="bold"></emph.end> rossore di lei negli ecclissi, da che secondo il Vossio dipenda 2<gap></gap>, da che dipenda, secondo il <lb></lb>Benedetti 28, s&#039;irraggia anch&#039;essa come le stelle 396, perchè si mostri maggiore all&#039;orizzonte 397, <lb></lb>origine del candor di lei nelle congiunzioni 398, paragonata nel candore alla pietra lucifera 406. </s></p><p type="main">

<s><emph type="bold"></emph>Macchie del Sole<emph.end type="bold"></emph.end> osservate direttamente coll&#039;occhio 376, descritte da Galileo 377, Galileo dimostra <lb></lb>che non sono stelle 378, controversia insorta fra lo Scheiner e Galileo, come si decida 385, opi­<lb></lb>nioni varie intorno alla loro origine ed essenza 388, Macchie di Giove osservate e descritte da <lb></lb>Galileo 443, loro origine 447. </s></p><p type="main">

<s><emph type="bold"></emph>Macchina inventata<emph.end type="bold"></emph.end> dal Borelli a rappresentar l&#039;immagine, e le fasi di Saturno 472. </s></p><p type="main">

<s><emph type="bold"></emph>Magalotti Loren<gap></gap>o,<emph.end type="bold"></emph.end> come rappresenti la struttura de&#039;pori nelle superficie nere, per assorbir meglio <lb></lb>il calore 159, sue notabili idee intorno all&#039;attrazione universale 548. </s></p><p type="main">

<s><emph type="bold"></emph>Magnete,<emph.end type="bold"></emph.end> esperienze dell&#039;attrazione di lui a varie distanze 541. </s></p><p type="main">

<s><emph type="bold"></emph>Maraldi Giacomo Filippe,<emph.end type="bold"></emph.end> sue esperienze sull&#039;ombre, a fin di spiegare i fenomeni degli ecclissi di <lb></lb>Luna 29. </s></p><pb xlink:href="020/01/1121.jpg" pagenum="564"></pb><p type="main">

<s><emph type="bold"></emph>Marchetti Alessandro,<emph.end type="bold"></emph.end> sua scrittura manoscritta sopra le Comete, e sua opinione intorno a queste <lb></lb>apparenze 513, confuta l&#039;opinione di Galileo 515. </s></p><p type="main">

<s><emph type="bold"></emph>Mari nella Luna,<emph.end type="bold"></emph.end> se più chiari o scuri debbano apparire de&#039;continenti 393. </s></p><p type="main">

<s><emph type="bold"></emph>Mario Simone<emph.end type="bold"></emph.end> pretende alla priorità della scoperta de&#039;Satelliti di Giove 423. </s></p><p type="main">

<s><emph type="bold"></emph>Marsili Cesare<emph.end type="bold"></emph.end> osserva la variazione della declinazione magnetica 454. </s></p><p type="main">

<s><emph type="bold"></emph>Marte,<emph.end type="bold"></emph.end> sue prime fasi osservate dal Castelli 361, periodo della rivoluzione in sè stesso 477, dà oc­<lb></lb>casione al Keplero a instituir l&#039;Astronomia nuova 526. </s></p><p type="main">

<s><emph type="bold"></emph>Mattonata,<emph.end type="bold"></emph.end> scrittura del Castelli relativa al vario grado di assorbimento del calore incidente sopra <lb></lb>superficie o bianche o nere 158. </s></p><p type="main">

<s><emph type="bold"></emph>Mattoni<emph.end type="bold"></emph.end> troppo cotti, alterano la declinazione magnetica 257. </s></p><p type="main">

<s><emph type="bold"></emph>Maurolico Francesco,<emph.end type="bold"></emph.end> suo Teorema sulla penombra 24, suoi Teoremi fotometrici 32, suoi Teoremi <lb></lb>sulle rifrazioni 57. </s></p><p type="main">

<s><emph type="bold"></emph>Mazzoni Jacopo<emph.end type="bold"></emph.end> legge in Pisa, insieme con Galileo, il libro delle Speculazioni del Benedetti 343. </s></p><p type="main">

<s><emph type="bold"></emph>Medici Leopoldo,<emph.end type="bold"></emph.end> ciò che pensasse intorno alla causa delle variazioni meteorologiche del Baro­<lb></lb>metro 319. </s></p><p type="main">

<s><emph type="bold"></emph>Mersenno Marino,<emph.end type="bold"></emph.end> come dimostri l&#039;ipotesi cartesiana del diffondersi il lume dal corpo luminoso 47, <lb></lb>fu primo a misurar la velocità del suono 190, applica il suono alla misura delle distanze 191. </s></p><p type="main">

<s><emph type="bold"></emph>Michelotti Pierantonio<emph.end type="bold"></emph.end> difende il Leibniz dalle accuse mossegli contro dal Desaguliers 327. </s></p><p type="main">

<s><emph type="bold"></emph>Montanari Geminiano,<emph.end type="bold"></emph.end> legge fotometrica da lui prima sperimentalmente dimostrata 39, come fosse <lb></lb>condotto a professar, rispetto alla luce, l&#039;ipotesi delle ondulazioni eterce 51, come spieghi il modo <lb></lb>dell&#039;operar del vento, nel sollecitar l&#039;evaporazione 174, attende alle Tavole de&#039;Satelliti di Giove 431, <lb></lb>descrive uno strumento, da rappresentare i moti di Giove 432, sua ipotesi dell&#039;apparizione e spa­<lb></lb>rizione delle stelle 500. </s></p><p type="main">

<s><emph type="bold"></emph>Monti<emph.end type="bold"></emph.end> nella circonferenza della Luna, da chi prima osservati 394. </s></p><p type="main">

<s><emph type="bold"></emph>Moto e calore,<emph.end type="bold"></emph.end> concetti degli antichi e de&#039;moderni 160. </s></p><p type="main">

<s><emph type="bold"></emph>Muro scabro,<emph.end type="bold"></emph.end> perchè apparisca più luminoso di uno specchio levigato 21. </s></p><p type="main">

<s><emph type="bold"></emph>Musschenbrock Pietro<emph.end type="bold"></emph.end> accusa di poco accurati i nostri Accademici fiorentini intorno all&#039;esperienza <lb></lb>del suono 188. </s></p><p type="main">

<s><emph type="bold"></emph>Mutoli,<emph.end type="bold"></emph.end> pseudonomo del Borelli, suo Discorso della Cometa 517. </s></p><p type="main">

<s><emph type="bold"></emph>Nardi Antonio,<emph.end type="bold"></emph.end> sua teoria delle attrazioni magnetiche 245. </s></p><p type="main">

<s><emph type="bold"></emph>Nebulose,<emph.end type="bold"></emph.end> come e da chi prima osservate 516. </s></p><p type="main">

<s><emph type="bold"></emph>Newton Isacco,<emph.end type="bold"></emph.end> come dimostri, per le leggi della Meccanica, l&#039;uguaglianza che intercede, fra gli angoli <lb></lb>formati dai raggi incidenti della luce, e dai riflessi 18, sue Questioni intorno alla natura e alla <lb></lb>diffusion della luce 48, suoi principii meccanici applicati a dimostrare il Teorema diottrico del <lb></lb>Cartesio 75, s&#039;introduce allo studio de&#039;colori 103, esamina il fenomeno grimaldiano della diffra­<lb></lb>zione 105, come perfezionasse la teoria dell&#039;Iride celeste, esposta dal De Dominis e dal Carte­<lb></lb>sio 123, suo giudizio sull&#039;ipotesi proposta dall&#039;Huyghens, per spiegare il modo del dipingersi gli <lb></lb>Aloni e i Parelii 130, come dimostri la speculazione del Benedetti, che cioè il suono si produce <lb></lb>dai condensamenti e dalle rarefazioni dell&#039;aria 183, come dimostri il propagarsi del suono attra­<lb></lb>verso agli ostacoli 184, suo processo matematico, per misurar la velocità della diffusione del <lb></lb>suono 195, ripensa alla possibile caduta della Luna sopra la Terra 537, suo calcolo della velocità, <lb></lb>con cui la Luna sarebbe caduta sulla Terra 543, sua ipotesi intorno alle cause della gravita­<lb></lb>zione 550. </s></p><p type="main">

<s><emph type="bold"></emph>Nollet,<emph.end type="bold"></emph.end> non fu il primo a far l&#039;esperienza della diffusione de suoni nell&#039;acqua 189. </s></p><p type="main">

<s><emph type="bold"></emph>Ombre,<emph.end type="bold"></emph.end> se fosse stato il Vossio il primo a trattarne 23, ombre proiettate dai Satelliti sul disco di <lb></lb>Giove negate dagli Accademici fiorentini 450, confermate dalle osservazioni dell&#039;Huyghens e del <lb></lb>Borelli 451. </s></p><p type="main">

<s><emph type="bold"></emph>Onde eteree<emph.end type="bold"></emph.end> diffusive della luce professate in Italia, prima dal Montanari 51, diffusive del calore, pro­<lb></lb>fessate dal Montanari stesso e dal Guglielmini 155. </s></p><p type="main">

<s><emph type="bold"></emph>Opachi e diafani,<emph.end type="bold"></emph.end> qual sia la causa che gli produce 23. </s></p><p type="main">

<s><emph type="bold"></emph>Orbite elettriche,<emph.end type="bold"></emph.end> loro causa fisica, secondo il Borelli 544, loro causa matematica, secondo il New­<lb></lb>ton 546. </s></p><p type="main">

<s><emph type="bold"></emph>Orologi,<emph.end type="bold"></emph.end> per uso delle longitudini 461. </s></p><p type="main">

<s><emph type="bold"></emph>Ovale,<emph.end type="bold"></emph.end> orbita di Marte, dimostrata dal comparare i calcoli con le osservazioui 527. </s></p><p type="main">

<s><emph type="bold"></emph>Pagani Francesco,<emph.end type="bold"></emph.end> sua teoria de&#039;Pianeti 533. </s></p><p type="main">

<s><emph type="bold"></emph>Parafulmini,<emph.end type="bold"></emph.end> loro primo concetto sovvenuto al Franklin 286. </s></p><p type="main">

<s><emph type="bold"></emph>Parallasse<emph.end type="bold"></emph.end> delle stelle fisse 509. </s></p><pb xlink:href="020/01/1122.jpg" pagenum="565"></pb><p type="main">

<s><emph type="bold"></emph>Pardies,<emph.end type="bold"></emph.end> sue opposizioni alle teorie ottiche neutoniane 104. </s></p><p type="main">

<s><emph type="bold"></emph>Pascal Biagio,<emph.end type="bold"></emph.end> primo a sperimentare le variazioni meteorologiche del Barometro 316. </s></p><p type="main">

<s><emph type="bold"></emph>Passignani Domenico<emph.end type="bold"></emph.end> osserva e specula sulle macchie del Sole 380, sue controversie con Galileo 387. </s></p><p type="main">

<s><emph type="bold"></emph>Pendolo,<emph.end type="bold"></emph.end> suo moto applicato al moto de&#039;Pianeti 531. </s></p><p type="main">

<s><emph type="bold"></emph>Petit Pietro,<emph.end type="bold"></emph.end> sue osservazioni e studii intorno alla variazione della declinazione magnetica 253, a <lb></lb>qual causa attribuisse un tale effetto 254, sua lettera al Sauval 255. </s></p><p type="main">

<s><emph type="bold"></emph>Pianeti,<emph.end type="bold"></emph.end> leggi de&#039;loro moti scoperte dal Keplero 528. </s></p><p type="main">

<s><emph type="bold"></emph>Ploggie,<emph.end type="bold"></emph.end> loro origine secondo il Borelli 296, secondo il Cartesio 299, secondo il Baliani 300. </s></p><p type="main">

<s><emph type="bold"></emph>Pitagorici,<emph.end type="bold"></emph.end> loro opinione intorno alle Comete 510. </s></p><p type="main">

<s><emph type="bold"></emph>Piatone,<emph.end type="bold"></emph.end> suo sistema del Mondo 333. </s></p><p type="main">

<s><emph type="bold"></emph>Piutarco,<emph.end type="bold"></emph.end> sua teoria della Luna 389, ne attribuisce le macchie alle ombre de&#039;monti, e a&#039;seni ripieni <lb></lb>di acque nereggianti 390, ammirato e seguito dal Keplero 391. </s></p><p type="main">

<s><emph type="bold"></emph>Porta Giovan Batista<emph.end type="bold"></emph.end> racconta come e da chi fosse osservata la direzione dell&#039;ago magnetico 224, <lb></lb>sue esperienze magnetiche giudicate dal Gilberto 228. </s></p><p type="main">

<s><emph type="bold"></emph>Portavoce,<emph.end type="bold"></emph.end> come il Newton ne spiegasse gli effetti 184. </s></p><p type="main">

<s><emph type="bold"></emph>Presagi del tempo<emph.end type="bold"></emph.end> dedotti dal Barometro, secondo il Borelli 328, secondo il Guericke 329, secondo <lb></lb>il Vossio 330. </s></p><p type="main">

<s><emph type="bold"></emph>Principio<emph.end type="bold"></emph.end> delle cause finali riprovato nella Diottrica 74. </s></p><p type="main">

<s><emph type="bold"></emph>Questioni varie<emph.end type="bold"></emph.end> di Ottica risolute dal Newton, dietro l&#039;ipotesi dell&#039;emissione 49. </s></p><p type="main">

<s><emph type="bold"></emph>Ramazzini Bernardino,<emph.end type="bold"></emph.end> sue Effemeridi modanesi 324, sua nuova ipotesi di Meteorologia barometrica, <lb></lb>in sostituzione di quella del Borelli 325. </s></p><p type="main">

<s><emph type="bold"></emph>Renieri Vincenzio,<emph.end type="bold"></emph.end> sua opinione intorno al color rosso nella Luna ecclissata 407, 409, ammaestrato <lb></lb>da Galileo intorno al modo di osservare i satelliti di Giove 424, tien conto di alcune annotazioni <lb></lb>manoscritte di Galileo 425, sente la necessità di ammettere le orbite ellittiche 426, suoi problemi <lb></lb>astronomici intorno agli ecclissi de&#039;Satelliti di Giove 427. </s></p><p type="main">

<s><emph type="bold"></emph>Rifrazioni,<emph.end type="bold"></emph.end> loro leggi fondamentali 54, d&#039;onde avessero i loro principii dimostrativi 58, primi ten­<lb></lb>tativi sperimentali fatti intorno ad esse 59, secondo Galileo e altri, son riflessioni interne 76, <lb></lb>come fossero tardi studiate in Italia 77. </s></p><p type="main">

<s><emph type="bold"></emph>Rinaldini Carlo,<emph.end type="bold"></emph.end> pensa a un&#039;esperienza da dimostrare il moto della luce 44, ciò che pensasse in­<lb></lb>torno alle rifrazioni 81, sua singolare esperienza, per decider se il freddo del ghiaccio operi po­<lb></lb>sitivamente 141. </s></p><p type="main">

<s><emph type="bold"></emph>Risonanze<emph.end type="bold"></emph.end> sperimentate dagli Accademici del Cimento 207. </s></p><p type="main">

<s><emph type="bold"></emph>Roberval,<emph.end type="bold"></emph.end> suo Aristarco Samio 364, suo sistema saturnio 470. </s></p><p type="main">

<s><emph type="bold"></emph>Rosa Ursina<emph.end type="bold"></emph.end> dello Scheiner 382. </s></p><p type="main">

<s><emph type="bold"></emph>Rotazione<emph.end type="bold"></emph.end> di Giove 448 </s></p><p type="main">

<s><emph type="bold"></emph>Rothmann Cristoforo,<emph.end type="bold"></emph.end> sue controversie con Ticone intorno aile astronomiche rifrazioni 87, come ri­<lb></lb>sponde agli argomenti promossi da Ticone contro il moto della Terra 338. </s></p><p type="main">

<s><emph type="bold"></emph>Rucellai Orazio,<emph.end type="bold"></emph.end> suo Discorso contro il freddo positivo 140. </s></p><p type="main">

<s><emph type="bold"></emph>Sagredo Giovan Francesco<emph.end type="bold"></emph.end> fu il primo a far l&#039;esperienza del suono nel vuoto 187. </s></p><p type="main">

<s><emph type="bold"></emph>Sarpi Paolo<emph.end type="bold"></emph.end> conferisce, intorno allo strumento inclinatorio, con Galileo 234. </s></p><p type="main">

<s><emph type="bold"></emph>Sassetti Filippo<emph.end type="bold"></emph.end> specula intorno alle proprietà dell&#039;ago magnetico 226, propone il modo di trovar la <lb></lb>longitudine, per mezzo della calamita 453. </s></p><p type="main">

<s><emph type="bold"></emph>Satelliti<emph.end type="bold"></emph.end> di Giove e i Pianeti non hanno luce propria 428, causa della loro apparente grandezza 446. <lb></lb>Satelliti di Saturno scoperti dal Cassini 480. </s></p><p type="main">

<s><emph type="bold"></emph>Saturno,<emph.end type="bold"></emph.end> prime osservazioni fatte da Galileo su questo Pianeta 464, sue fasi divinate 465, Sistema <lb></lb>robervalliano illustrato dal Magalotti 483. </s></p><p type="main">

<s><emph type="bold"></emph>Saussure,<emph.end type="bold"></emph.end> sue osservazioni microscopiche sul vapore vescicolare 303. </s></p><p type="main">

<s><emph type="bold"></emph>Scaleno,<emph.end type="bold"></emph.end> cono, immaginato dal Boulliaud, per spiegar l&#039;origine delle orbite ellittiche 532. </s></p><p type="main">

<s><emph type="bold"></emph>Scaligero Giuseppe<emph.end type="bold"></emph.end> dimostra con buone ragioni che il moto della luce non può essere in stante 45. </s></p><p type="main">

<s><emph type="bold"></emph>Scatola<emph.end type="bold"></emph.end> delle rifrazioni, per farne l&#039;esperienza, inventata dal Viviani 79. </s></p><p type="main">

<s><emph type="bold"></emph>Scheiner Cristoforo<emph.end type="bold"></emph.end> osserva il Sole ellittico, e ne riconosce la causa dalle rifrazioni 88, è il primo a <lb></lb>proporre il modo come si possano, per rifrazione, dipingere le Corone e i Parelii 125, narra a <lb></lb>quale occasione si volgesse a osservar le macchie del Sole 384. </s></p><p type="main">

<s><emph type="bold"></emph>Schelhamer<emph.end type="bold"></emph.end> oppositore in Meteorologia barometrica al Ramazzini 325. </s></p><p type="main">

<s><emph type="bold"></emph>Scintillazione<emph.end type="bold"></emph.end> delle stelle fisse 502, loro causa, secondo il Keplero 503, secondo Galileo e il Bene­<lb></lb>detti 504. </s></p><p type="main">

<s><emph type="bold"></emph>Scrittura santa,<emph.end type="bold"></emph.end> argomenti da lei addotti contro il moto della Terra 346. </s></p><pb xlink:href="020/01/1123.jpg" pagenum="566"></pb><p type="main">

<s><emph type="bold"></emph>Seneca,<emph.end type="bold"></emph.end> come spieghi il trapassar del suono attraverso alle pareti di un muro 185. </s></p><p type="main">

<s><emph type="bold"></emph>Sinclaro Giorgio<emph.end type="bold"></emph.end> discute intorno alle ragioni del Copernicismo 366. </s></p><p type="main">

<s><emph type="bold"></emph>Sismoseopio,<emph.end type="bold"></emph.end> sua prima invenzione del Grimaldi 186. </s></p><p type="main">

<s><emph type="bold"></emph>Snellio Willebrod,<emph.end type="bold"></emph.end> sua legge delle rifrazioni formulata 61. </s></p><p type="main">

<s><emph type="bold"></emph>Sole ellittico,<emph.end type="bold"></emph.end> come spiegato da Galileo nel <emph type="italics"></emph>Saggiatore<emph.end type="italics"></emph.end> 91, come nelle Operazioni astronomicbe 93. </s></p><p type="main">

<s><emph type="bold"></emph>Sovero Bartolommeo<emph.end type="bold"></emph.end> non è inventore dell&#039;armatura delle calamite 237. </s></p><p type="main">

<s><emph type="bold"></emph>Southwell Roberto<emph.end type="bold"></emph.end> riferisce al Viviani gli studii e l&#039;esperienze fatte dall&#039;Hook e dall&#039;Halley intorno <lb></lb>al Magnete 242. </s></p><p type="main">

<s><emph type="bold"></emph>Specchi levigati,<emph.end type="bold"></emph.end> perchè appariscan più bui di un muro aspro 21, come abbiano la virtù ustoria, con­<lb></lb>figurati in qualunque genere di parabola 153. </s></p><p type="main">

<s><emph type="bold"></emph>Speeie immateriata,<emph.end type="bold"></emph.end> secondo il Keplero, motrice del Sole 529. </s></p><p type="main">

<s><emph type="bold"></emph>Spuma dell&#039;acqua,<emph.end type="bold"></emph.end> perchè apparisca bianca 22. </s></p><p type="main">

<s><emph type="bold"></emph>Stoici<emph.end type="bold"></emph.end> rassomigliavano le onde del suono alle onde, che si forman nell&#039;acqua intorno a un corpo <lb></lb>grave, che sopra vi cada 178. </s></p><p type="main">

<s><emph type="bold"></emph>Strumento micrometrico<emph.end type="bold"></emph.end> di Galileo descritto dal Borelli 420. </s></p><p type="main">

<s><emph type="bold"></emph>Suono<emph.end type="bold"></emph.end> si credeva prodotto dalla collisione de&#039;corpi 181, legge della sua intensità, come fosse tardi <lb></lb>conosciuta 183, facilità della sua trasmissione 186. </s></p><p type="main">

<s><emph type="bold"></emph>Tavola<emph.end type="bold"></emph.end> delle orbite de&#039;Medicei in semidiametri di Giove 440. </s></p><p type="main">

<s><emph type="bold"></emph>Teoriche<emph.end type="bold"></emph.end> de&#039;Medicei del Borelli, quando stampate 434. </s></p><p type="main">

<s><emph type="bold"></emph>Termostatiei<emph.end type="bold"></emph.end> o pesatori del caldo inventati dal Borelli e dal Viviani 149. </s></p><p type="main">

<s><emph type="bold"></emph>Terrella<emph.end type="bold"></emph.end> elettrica 267. </s></p><p type="main">

<s><emph type="bold"></emph>Ticone,<emph.end type="bold"></emph.end> sue controversie col Rothmann intorno alle astronomiche rifrazioni 87, suoi argomenti con­<lb></lb>tro la mobilità della Terra 338. </s></p><p type="main">

<s><emph type="bold"></emph>Torricelli Evangelista,<emph.end type="bold"></emph.end> suo giudizio intorno all&#039;Aristarco Samio del Robervallio 364. </s></p><p type="main">

<s><emph type="bold"></emph>Umidità<emph.end type="bold"></emph.end> nociva alle esperienze elettriche 271. </s></p><p type="main">

<s><emph type="bold"></emph>Unisono<emph.end type="bold"></emph.end> di due corde, una delle quali vibrata e l&#039;altra quieta, come fosse spiegato dal Keplero 200, <lb></lb>come dal Fracastoro 201, come da Guidubaldo Del Monte 201, come da Galileo 204, come Galileo <lb></lb>illustri la teoria fracastoriana 205. </s></p><p type="main">

<s><emph type="bold"></emph>Vapori<emph.end type="bold"></emph.end> condensati nell&#039;aria e sulle fredde superficie de&#039;corpi, come spiegati dal Benedetti 170, non <lb></lb>si sollevano perchè attratti dal Sole, ma perchè divenuti più leggeri 171. </s></p><p type="main">

<s><emph type="bold"></emph>Venere,<emph.end type="bold"></emph.end> rotazione intorno al suo asse 478, difficoltà di definirne il periodo 479. </s></p><p type="main">

<s><emph type="bold"></emph>Venti,<emph.end type="bold"></emph.end> loro effetti nelle evaporazioni, come spiegati 174, loro origine secondo il Cartesio 306, secondo <lb></lb>il Redi e il Del Papa 308, secondo il Montanari 209, secondo il Torricelli 310, venti tropicali come <lb></lb>spiegati da Galileo 312, come gli facesse il Guericke argomento a dimostrare il moto della <lb></lb>Terra 315, ioro effetti in alterar lo stato del Barometro 328. </s></p><p type="main">

<s><emph type="bold"></emph>Vento<emph.end type="bold"></emph.end> fatto da&#039;corpi velocemente girati attorno, a che lo attribuisca il Galileo 313. </s></p><p type="main">

<s><emph type="bold"></emph>Vescicole<emph.end type="bold"></emph.end> vaporose dell&#039;acqua, come salgano in mezzo all<gap></gap>aria, secondo il Baliani 300, come secondo <lb></lb>il Montanari 301, come secondo il Guglielmini 302, come secondo il Del Papa 302, come secondo il <lb></lb>Volta 303. </s></p><p type="main">

<s><emph type="bold"></emph>Vespucci Amerigo,<emph.end type="bold"></emph.end> suo metodo astronomico per la ricerca delle Longitudini 455, osserva da astro­<lb></lb>nomo le Stelle 494. </s></p><p type="main">

<s><emph type="bold"></emph>Vinei (da) Leonardo,<emph.end type="bold"></emph.end> come dimostri il calore diffondersi in modo, che l&#039;intensità scemi col crescere <lb></lb>de&#039;quadrati delle distanze 154. </s></p><p type="main">

<s><emph type="bold"></emph>Vista,<emph.end type="bold"></emph.end> fenomeni presentati da lei nel guardare gli oggetti 9. </s></p><p type="main">

<s><emph type="bold"></emph>Vitellione,<emph.end type="bold"></emph.end> pollacco, riprova il principio platonico dell&#039;emissione de&#039;raggi dagli occhi 9, giudizio sopra <lb></lb>l&#039;Ottica di lui 10, applica alla rifrazione il principio della composizion delle forze 55. </s></p><p type="main">

<s><emph type="bold"></emph>Viviani Vincenzio,<emph.end type="bold"></emph.end> sue speculazioni e sperienze intorno al moto della luce 42 e 44, come gli venisse <lb></lb>a mano la Diottrica del Cartesio 78, come ne rimanesse ammirato 79, sue esperienze intorno alle <lb></lb>rifrazioni 80, sue esperienze per provar che un raggio di luce si refrange, passando dall&#039;aria nel <lb></lb>vuoto 94, suo giudizio intorno alla Relazione dell&#039;Huyghens sull&#039;alone osservato a Parigi 129, <lb></lb>spiega in un suo Discorso il concetto di Galileo intorno alla natura del calore 143, illustra un <lb></lb>passo del I Dialogo delle Nuove Scienze, relativo agli effetti del calore 146, pone i principii alla <lb></lb>Termometria 150, come rispondesse alle varie domande fattegli dal Granduca intorno ai suoni 192, <lb></lb>sue corrispondenze scientifiche con la R. </s>

<s>Accademia di Londra 241, come giudichi un problema me­<lb></lb>teorologico, che non sapeva essere stato risoluto da Galileo 314, esamina le condizioni delle va­<lb></lb>riazioni barometriche, in ordine allo stato del cielo 318, suo argomento a provare il moto della <pb xlink:href="020/01/1124.jpg" pagenum="567"></pb>Terra, dedotto dal moto de&#039;pendoli 367, se prevenisse l&#039;esperienza del Foucault 368, suoi metodi <lb></lb>proposti per misurar l&#039;ingrandimento del Canocchiale 435, suo Tavole de&#039;moti di Giove 436. </s></p><p type="main">

<s><emph type="bold"></emph>Volta Alessandro<emph.end type="bold"></emph.end> spiega le attrazioni elettriche, per mezzo de&#039;principii neutoniani 282. </s></p><p type="main">

<s><emph type="bold"></emph>Vortici kepleriani,<emph.end type="bold"></emph.end> repugnanze che si trovano in questa ipotesi 545, vortici eterei, secondo l&#039;Huy­<lb></lb>ghens 549. </s></p><p type="main">

<s><emph type="bold"></emph>Vossio Isacco<emph.end type="bold"></emph.end> è il primo a pubblicare lo notizie dell&#039;Ottica manoscritta dello Snellio 66, propone a <lb></lb>risolvere una difficoltà contro l&#039;esistenza de&#039;monti della Luna 395, dimostra esser falsa la ra­<lb></lb>gione data dal Keplero della visibilità della Luna ecclissata 410. </s></p><p type="main">

<s><emph type="bold"></emph>Wright,<emph.end type="bold"></emph.end> propone di risolvere il problema delle Longitudini, per mezzo della Bussola 454. </s></p><pb xlink:href="020/01/1125.jpg"></pb><p type="main">

<s>Finito di stampare in Bologna presso la <lb></lb>Libreria Editrice Forni nel Marzo 1970 <pb xlink:href="020/01/1126.jpg"></pb></s></p><pb xlink:href="020/01/1127.jpg"></pb></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Editor-in-Chief: Harry Woolf<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Willis K. </s>

<s>Shepard Professor of the History of <lb></lb>Science, The Johns Hopkins University<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/1128.jpg"></pb><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph><emph type="italics"></emph>Storia del Metodo <lb></lb>Sperimentale in Italia<emph.end type="italics"></emph.end><emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>by RAFFAELLO CAVERNI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>in Six Volumes<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Volume III<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE, NO. 134 <lb></lb>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>NEW YORK LONDON 1972<emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/1129.jpg"></pb><p type="main">

<s><emph type="center"></emph>Reproduced here is the Florence edition of 1891-1900.<emph.end type="center"></emph.end></s></p><figure id="id.020.01.1129.1.jpg" xlink:href="020/01/1129/1.jpg"></figure><p type="main">

<s><emph type="center"></emph>Copyright © 1972 by Johnson Reprint Corporation All rights reserved <lb></lb>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></s></p><p type="main">

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<s><emph type="center"></emph><emph type="italics"></emph>Printed in Italy<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/1130.jpg"></pb><p type="main">

<s><emph type="center"></emph>DEL METODO SPERIMENTALE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>APPLICATO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>ALLA STORIA NATURALE<emph.end type="center"></emph.end><pb xlink:href="020/01/1131.jpg"></pb></s></p><pb xlink:href="020/01/1132.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dell&#039;Anatomia nello studio della vita animale<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle Istituzioni anatomiche di Galeno, e delle prime instaurazioni dell&#039;arte, per opera del Beren­<lb></lb>gario e del Vesalio. </s>

<s>— II. Dell&#039;Anatomia descrittiva, istituita dal Falloppio e proseguita dal­<lb></lb>l&#039;Eustachio, dall&#039;Acquapendente e dal Casserio. </s>

<s>— III. </s>

<s>Delle vivisezioni praticate da Realdo <lb></lb>Colombo, e come s&#039;incominciasse ad applicare le leggi della Fisica a spiegar le funzioni della <lb></lb>vita. </s>

<s>— IV. Dell&#039;Anatomia nella Scuola iatromeccanica. </s>

<s>— V. </s>

<s>Della Scuola iatromatematica ita­<lb></lb>liana, e de&#039;limiti naturalmente imposti ai progressi dell&#039;Anatomia. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La Fisica, della quale narrammo i più notabili progressi fatti con gli <lb></lb>argomenti dell&#039;arte sperimentale, si propone per oggetto lo studio della na­<lb></lb>tura, e il modo dell&#039;operar de&#039;corpi secondo le loro proprietà generali; co­<lb></lb>sicchè indaga le leggi per esempio della luce, del calore, del suono, e attende <lb></lb>al manifestarsi dei moti nel Magnete, nell&#039;Elettro, e nella materia univer­<lb></lb>sale, senza nulla curarsi di quel particolar corpo che luce, che riscalda, che <lb></lb>suona, che ora attrae, ora respinge altri corpi. </s>

<s>Ma pure anche il saper le <lb></lb>particolari e individue proprietà, per cui un corpo si distingue e si ricono­<lb></lb>sce da tutti gli altri, era oggetto di curiosità agli uomini, a&#039;quali furono <lb></lb>ovvie le prime differenze che passano fra gli animali e le piante e i mine­<lb></lb>rali. </s>

<s>La scienza della Natura perciò si può dire che avesse di qui i suoi <lb></lb>principii, e quando le altre parti di lei non avevano ancora nessun cultore, <lb></lb>si leggevano con ammirazione e con diletto i libri di Aristotile e di Plinio, <lb></lb>per tacere di tanti altri minori. </s></p><p type="main">

<s>Questa però per vero dire non era scienza: posta la volgar distinzione <lb></lb>fra ciò che pareva non aver moto, e fra ciò che mostrava di nutrirsi e di <pb xlink:href="020/01/1133.jpg" pagenum="8"></pb>vegetar solamente, o di più muoversi con ispontaneità d&#039;atto e sentire, si <lb></lb>stavano contenti quegli Autori a descrivere le esteriori apparenze e gli usi <lb></lb>di un minerale, la figura e le natìe abitudini di una pianta, gli organi della <lb></lb>locomozione e dei sensi di un animale, i costumi e la patria. </s>

<s>S&#039;intende da <lb></lb>ciò com&#039;avesse, e come ben rispondesse all&#039;intenzione degli scrittori e agli <lb></lb>stessi fatti il nome dato a coteste naturali descrizioni di <emph type="italics"></emph>Storia.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Se, come è rimasto il nome, fosse così rimasto a un tal genere di let­<lb></lb>teratura quel primo semplice carattere descrittivo, non si vedrebbe perchè <lb></lb>dovessero gli studii di lei entrar nella nostra trattazione, ufficio della quale <lb></lb>è di non narrar solamente quel che si notò osservando l&#039;esterior faccia della <lb></lb>Natura, ma quel che si scoprì nel suo più intimo seno, per via di più stu­<lb></lb>diose osservazioni e di più laboriosi cimenti, di cui non conobbero l&#039;arte <lb></lb>quei Naturalisti antichi. </s></p><p type="main">

<s>Ne sentirono però il bisogno, infin da quando si provarono a divisare <lb></lb>l&#039;ordine, secondo il quale si sarebbero più convenientemente collocate le <lb></lb>innumerevoli varietà componenti ciascuno dei tre grandi Regni: perchè, do­<lb></lb>vendo quel collocamento dipendere dalla dignità gerarchica, per così dire, <lb></lb>conveniva conoscer le ragioni del merito onde una specie e un genere aves­<lb></lb>sero a soprastare ad un altro genere e a un&#039;altra specie, e non era pos­<lb></lb>sibile far quella giusta ragione senza conoscere, in un animale o in una <lb></lb>pianta, la prestanza degli organi e delle funzioni. </s></p><p type="main">

<s>Ma gli organi poco o nulla porgono a conoscer di sè, nelle loro parti <lb></lb>esterne e superficiali, non escluso lo stesso tatto universalmente diffuso per <lb></lb>gli involucri del corpo. </s>

<s>La semplice Anatomia descrittiva perciò si sentì, per <lb></lb>mancanza di esperienze e di strumenti, impotente a penetrare addentro nella <lb></lb>composizione degli organi, a vederne le relazioni co&#039;principii della sensibi­<lb></lb>lità e della vita, e a intendere gli uffici, a cui i membri che stanno intorno <lb></lb>agli stessi organi furono dalla Natura variamente ordinati. </s>

<s>Di qui s&#039;intende <lb></lb>come quella, che ha tuttavia serbato il nome di <emph type="italics"></emph>Storia naturale,<emph.end type="italics"></emph.end> entrasse <lb></lb>nel suo progredire a far parte di questa scienza, che s&#039;aiuta delle esperienze <lb></lb>e degli strumenti a ciò necessarii, e che è il soggetto proprio del nostro <lb></lb>storico discorso. </s></p><p type="main">

<s>Il processo del qual discorso perciò, chi volesse intanto saperlo, si ri­<lb></lb>duce a narrare per sommi capi, prima, come dall&#039;esercizio dell&#039;arte speri­<lb></lb>mentale fosse condotta la scienza a conoscer l&#039;intima composizione dei corpi <lb></lb>e le varie funzioni della vita, poi, come fosse quella stessa arte utilmente <lb></lb>applicata a investigar ciò che è proprio di un animale o di un altro, di <lb></lb>una o altra pianta o minerale che sia, perchè nell&#039;ordinare i tre Regni <lb></lb>della Natura ciascuna famiglia, specie, genere o classe abbia il suo colloca­<lb></lb>mento, non eletto a caso o per le notate differenze di caratteri superficiali, <lb></lb>ma quale egli vien portato dall&#039;intrinseca varietà degli organi e delle fun­<lb></lb>zioni, delle membra compaginate e delle parti. </s></p><p type="main">

<s>In questo filosofico ordinamento, che s&#039;intendeva fare degli esseri innu­<lb></lb>merevoli di che è popolata la Terra, primi a considerare occorsero gli ani-<pb xlink:href="020/01/1134.jpg" pagenum="9"></pb>mali. </s>

<s>E perchè le varietà presentate al di fuori era facile intendere che <lb></lb>dovessero dipendere da più intime varietà della loro costituzione, furono i <lb></lb>primi passi che si fecero dalla scienza, a conseguire il fine desiderato, quelli <lb></lb>di dinudar l&#039;animale stesso della sua prima veste, sotto la quale apparvero <lb></lb>i muscoli, sotto i muscoli le ossa, e dentro l&#039;ossa i visceri e gli organi prin­<lb></lb>cipali dei sensi. </s>

<s>Così ebbe principio quella, a cui fu dato il nome di Ana­<lb></lb>tomia, la quale fu coltivata con grande ardore e con gran diligenza infino <lb></lb>dagli antichi tempi della civiltà greca, non semplicemente per promovere lo <lb></lb>studio della Storia naturale, ma per il desideratissimo intento di riconoscere <lb></lb>l&#039;occulta origine de&#039;morbi, e d&#039;apprestarvi i più efficaci rimedii. </s></p><p type="main">

<s>Ippocrate, per la gran distanza da cui si guarda, e per esserci perve­<lb></lb>nute le sue dottrine in gran parte negli insegnamenti tradizionali, s&#039;è trasfor­<lb></lb>mato quasi in simbolo a rappresentar l&#039;arte medica, e i nomi di Erofilo, di <lb></lb>Polibo, di Erasistrato ci vengono riflessi alle orecchie da&#039;libri di coloro, che <lb></lb>ne raccolsero i placiti, e principalmente da quelli di Galeno, che riconosce <lb></lb>e venera cotesti antichi per suoi primi autori e maestri. </s>

<s>Maestro però alla <lb></lb>nuova civiltà rimase co&#039;suoi libri lo stesso Galeno, il quale si acquistò nelle <lb></lb>descrizioni anatomiche, e ne&#039;precetti dell&#039;arte medica, tanta autorità e tanta <lb></lb>fama, che fu tenuto come un oracolo, il contradire al quale reputavasi te­<lb></lb>merità e quasi una ribellione contro la verità stessa. </s></p><p type="main">

<s>Per formarsi un&#039;idea di ciò, che il greco Maestro descrisse concernente <lb></lb>l&#039;anatomica costituzione del corpo umano, converrebbe svolgere i suoi vo­<lb></lb>lumi e i commenti che ne fecero gli studiosi, i quali forse non ritrarreb­<lb></lb>bero nella loro profusione così viva l&#039;immagine dello scrittore, come ce la <lb></lb>rappresenta il seguente passo estratto dal Cap. </s>

<s>XVI del I Libro <emph type="italics"></emph>De usu par­<lb></lb>tium,<emph.end type="italics"></emph.end> dove, professando l&#039;Autore di trattar dell&#039;utilità, a cui servono le varie <lb></lb>membra animali, accenna ai discorsi fatti altrove intorno alle loro funzioni: <lb></lb>“ De actionibus vero venarum et arteriarum et nervorum et musculorum <lb></lb>et tendonum neque consentitur, neque apparet quidquam, ac propterea ser­<lb></lb>mone indiget longiori. </s>

<s>Sed non est nunc tempus de actionibus disquirendi. </s>

<s><lb></lb>Non enim de ipsis, sed de utilitatibus propositum est nobis dicere. </s>

<s>Neces­<lb></lb>sarium igitur est, ex iis quae alicubi demonstrata sunt, et nunc et per <lb></lb>omnem futurum nobis sermonem, conclusiones demonstrationum, tamquam <lb></lb>aliquas suppositiones accipiendo, ita hunc perficere sermonem. </s>

<s>Quod igitur <lb></lb>principium nervorum omnium cerebrum est et spinalis medulla, et quod <lb></lb>ipsius rursus spinalis medullae cerebrum: arteriarum vero omnium cor, ve­<lb></lb>narum autem hepar: et quod nervi quidem a cerebro animalem virtutem, <lb></lb>arteriae vero a cordis pulsatione: venae autem ab hepate naturalem acci­<lb></lb>piunt, in libris de Hippocratis et Platonis dogmatibus demonstratum est. </s>

<s><lb></lb>Erit itaque nervorum utilitas facultatem sensus et motus a principio in par­<lb></lb>tes deducere. </s>

<s>Arteriarum autem custodire eam natura est caliditatem et nu­<lb></lb>trire spiritum animalem. </s>

<s>Sanguinis autem generandi simul et in omnes fe­<lb></lb>rendi gratia venae factae sunt. </s>

<s>At vero et de tendonibus et nervis et liga­<lb></lb>mentis quomodo differant in libris de musculorum motu dictum est. </s>

<s>Palam <pb xlink:href="020/01/1135.jpg" pagenum="10"></pb>autem quod et de natura musculorum in illis dictum est, et quod sunt or­<lb></lb>gana motus voluntarii, et quod eorum aponevrosis, hoc est derivatio, nomi­<lb></lb>natur ” (Lugduni Batav. </s>

<s>1550, pag. </s>

<s>36, 37). </s></p><p type="main">

<s>L&#039;anatomia e la fisiologia galenica, condensate e specchiate in queste <lb></lb>brevi parole, erano universalmente seguite senza nulla aggiungervi e nulla <lb></lb>levare, come quelle che erano stimate rappresentar vivo e vero il sapientis­<lb></lb>simo magistero della natura nella mirabile fabbrica del corpo animale. </s>

<s>In <lb></lb>tanto ferma e indubitata fede non osavasi di far pure a Galeno una domanda <lb></lb>ingenua, ed era se l&#039;anatomia degli animali, che s&#039;intraprese a principio <lb></lb>per promovere lo studio della Storia naturale, si poteva così in tutto appro­<lb></lb>priare all&#039;uomo, da servire a investigar l&#039;occulta origine de&#039;suoi morbi e a <lb></lb>curarli, come insegnavano a fare quegli antichi Maestri. </s>

<s>Non facevasi la do­<lb></lb>manda, perchè si teneva certa la risposta, che cioè le fonti della vita nel­<lb></lb>l&#039;uomo fossero con perfettissima somiglianza rappresentate da quelle del cane <lb></lb>e della scimmia. </s>

<s>Una tal risposta dall&#039;altra parte sodisfaceva, perchè sem­<lb></lb>brava dispensare dall&#039;insozzarsi della sanie de&#039;cadaveri umani, e dal provar <lb></lb>quel ribrezzo, che mette addosso a ciascuno il violar con mano crudelmente <lb></lb>sacrilega la pace del sepolcro. </s></p><p type="main">

<s>Quando nel secolo XVI, specialmente nella nostra Italia, l&#039;ardente de­<lb></lb>siderio di sapere vinse quel ribrezzo, e sanamente si ragionò che un atto <lb></lb>intrapreso per amor della scienza, e che non offendeva se non ciò che era <lb></lb>stato già offeso dalla morte, non poteva imputarsi a sacrilegio; s&#039;intese al­<lb></lb>lora, sezionando cadaveri umani, come notabilmente e per moltissime parti <lb></lb>differissero le membra degli uomini da quelle de&#039;bruti, e come non fosse <lb></lb>stata da&#039;Medici la vera arte anatomica ancora ben conosciuta. </s></p><p type="main">

<s>Primo a fare il gran passo, tentato già dal Mondino, per uscir fuori <lb></lb>degli alloggiamenti galenici, dove s&#039;eran da secoli ricoverati con sicurtà tutti <lb></lb>i Filosofi e i Medici, fu Iacopo Berengario da Carpi, il quale pubblicò per <lb></lb>la prima volta in Bologna, nel 1521, le sue nuove descrizioni anatomiche, in <lb></lb>un libro intitolato <emph type="italics"></emph>Commentaria cum amplissimis additionibus super Ana­<lb></lb>tomia Mundini, una cum textu eiusdem in pristinum et verum nitorem <lb></lb>redacto.<emph.end type="italics"></emph.end> È dedicato il libro al cardinale di S. </s>

<s>Lorenzo in Damaso, Giulio <lb></lb>de&#039;Medici, con lettera che comprende le carte II, III, seguenti alla prima <lb></lb>del frontespizio disegnato in un elegantissimo antiporto, con lo stemma me­<lb></lb>diceo sull&#039;architrave, e impressovi il nome di Leon X. </s></p><p type="main">

<s>A pag. </s>

<s>IV incomincia l&#039;<emph type="italics"></emph>Expositio Anatomiae Mundini cum additioni­<lb></lb>bus Carpi,<emph.end type="italics"></emph.end> e l&#039;intenzione, ch&#039;ebbe nello scriverla l&#039;Autore, viene espressa <lb></lb>nella seguente forma ai lettori: “ Visis tot et tantis altercationibus inter <lb></lb>scribentes de Anatomia, placuit mihi, qui longa experientia vidi secando et <lb></lb>vivorum et mortuorum corpora et qui longa lectione quaesivi, per viam Com­<lb></lb>menti in unum breviori quodam summario perstringere. </s>

<s>Et dux meus erit <lb></lb>optimus Mundinus bononiensis, qui inter omnes sapientes Medicinae in bre­<lb></lb>viori quodam catalogo omnia de cognitione organicorum membrorum perstrin­<lb></lb>git, cuius merito primus Anatomes habetur. </s>

<s>Cuius librum exponere intendo, <pb xlink:href="020/01/1136.jpg" pagenum="11"></pb>quamvis etiam ipsius litera quasi clara sit. </s>

<s>In qua expositione aliqua notatu <lb></lb>digna, iunioribus non inutilia, addam, duce semper sensu et divini Galeni <lb></lb>auctoritatibus et rationibus quibusdam, et libri titulus erit <emph type="italics"></emph>Expositio ana­<lb></lb>lomica Mundini cum additionibus Carpi. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Tanta fu l&#039;accoglienza fatta a quest&#039;Opera dagli studiosi, i quali ascol­<lb></lb>tavano dopo tanti secoli discorrer d&#039;Anatomia a un uomo vivo, che l&#039;Autore <lb></lb>pensò di farne un Isagoge o un compendio, impresso in Venezia nel 1535, <lb></lb>e dedicato al suo signor naturale Alberto Pio. </s>

<s>A lui rivolgendosi il Beren­<lb></lb>gario, dop&#039;aver detto come gli fosse felicemente riuscita la sezione di un ani­<lb></lb>male vivo, soggiunge le seguenti parole: </s></p><p type="main">

<s>“ Tanta, testor Deos immortales, ex illo tempore Anatomiae dulcedo <lb></lb>mentem animumque meum tenuit, ut omnem aetatem iis Medicinae elemen­<lb></lb>tis non minori bonorum professorum utilitatem, quam privata voluptate con­<lb></lb>tribuerim: libros huiusce disciplinae quam plurimos sed indigestos lectitan­<lb></lb>dos, quos eorum authores, ad alia transferentes volumina, fabulas potius <lb></lb>quam Anatomiam tribuere videbantur, quo factum est ut pauci vel nulli <lb></lb>hac nostra tempestate tam necessariae ac preciosissimae artis finem nove­<lb></lb>rint. </s>

<s>Accedebat insuper ad eius ignorationem, sic mea fert opinio, foeda ac <lb></lb>multis stomacosa membrorum sectio creberrimaque illorum attrectatio. </s>

<s>Et <lb></lb>quum ego quamplurima centena cadaverum secuerim, quam pauci aetatis <lb></lb>nostrae Medici hanc artem noverint intellexi. </s>

<s>Quare, praesenti ac futuro sae­<lb></lb>culo prodesse cupiens, non minus pium quam saluberrimum fore putavi <lb></lb>Commentarii quaedam et digressiones super anatomia Mundini componere, <lb></lb>quae antiquorum Philosophorum pariter et Medicorum sapienter scripta de <lb></lb>humani corporis admirabili mole demonstrant, illaque copiose tradita, a quam­<lb></lb>plurimis Medicinae studiosissimis viris rogatus, in lucem dedi ” (Isagoge bre­<lb></lb>ves, Venetiis 1535, ad Albertum Pium). </s></p><p type="main">

<s>In queste parole del Berengario, chi bene addentro penetra al loro senso, <lb></lb>si scopre un segreto artificio di conciliare il passato col presente, accennando <lb></lb>da una parte alle cose scritte sapientemente da&#039;Filosofi e da&#039;Medici prede­<lb></lb>cessori, ch&#039;egli accoglie nel suo libro e commenta, e santenziando dall&#039;altra <lb></lb>che, dal sezionar cadaveri umani, s&#039;era accorto <emph type="italics"></emph>quam pauci aetatis nostrae <lb></lb>Medici hanc artem noverint.<emph.end type="italics"></emph.end> Si proponeva così dunque dall&#039;Autore un&#039;arte <lb></lb>nuova, e tacitamente insinuavasi, colla proposta, che la insegnata da Galeno <lb></lb>non era l&#039;arte anatomica vera, e fra&#039;medici che s&#039;accusavano d&#039;avere <lb></lb>ignorato una tal arte era necessariamente incluso anco il Maestro. </s>

<s>Procede <lb></lb>però il Berengario, nel proporre le sue novità, con tal riserbo, che nes­<lb></lb>suno si sente offeso di quella accusa. </s>

<s>Da un altro canto, non consistendo <lb></lb>quelle novità che in descrivere alcune parti, le quali non si leggevano nel <lb></lb>testo galenico, era pronto il rifugio da salvar la dignità del Maestro, con <lb></lb>dire ch&#039;egli trascurò quelle cose, perchè non le credeva importanti, o forse <lb></lb>egli non le trascurò veramente, ma le descrisse in altri libri che ora sono <lb></lb>smarriti. </s></p><p type="main">

<s>L&#039;anatomico di Carpi sarà stato di parere diverso da questo degli ido-<pb xlink:href="020/01/1137.jpg" pagenum="12"></pb>latri di Galeno, ma in ogni modo egli che non erasi trattenuto, con tutta <lb></lb>quella diligenza che bisognava, a comparar, per rilevarne le differenze, l&#039;ana­<lb></lb>tomia de&#039;bruti con quella dell&#039;uomo; non si sentiva tanto autorevole da sen­<lb></lb>tenziar che i difetti notati, e gli errori dell&#039;anatomia galenica derivassero <lb></lb>dall&#039;aver sezionati cadaveri, e dall&#039;aver perciò descritte per umane le mem­<lb></lb>bra dei bruti. </s>

<s>Ma iniziati intanto così felicemente i progressi dell&#039;Anatomia, <lb></lb>l&#039;opera del nostro Carpense fu animosamente proseguita da Andrea Vesalio, <lb></lb>da cui comincia l&#039;Anatomia comparata. </s></p><p type="main">

<s>Risultò veramente da quelle comparazioni intraprese con una fiera gio­<lb></lb>vanile baldanza, che Galeno aveva attribuite all&#039;uomo le membra, come sono <lb></lb>configurate ne&#039;cani e nelle scimmie. </s>

<s>E giacchè si trattava di fatti, ch&#039;egli <lb></lb>sottoponeva, nell&#039;anfiteatro della Scuola padovana, alla testimonianza degli <lb></lb>occhi della numerosissima scolaresca, e di chiunque altro se ne fosse voluto <lb></lb>assicurare; l&#039;accusa contro Galeno non aveva oramai più difesa: il tempio <lb></lb>era profanato, e si volevano i sacerdoti dispersi. </s></p><p type="main">

<s>Dalla ristretta cerchia dell&#039;insegnamento orale si diffuse nel pubblico <lb></lb>lo spirito della rivolta, per mezzo della pubblicazione di un libro, che s&#039;in­<lb></lb>titolava: <emph type="italics"></emph>Andreae Vesalii bruxellensis Scholae medicorum Patavinae pro­<lb></lb>fessoris, de humani corporis fabrica, Basileae M.D.XLIII.<emph.end type="italics"></emph.end> Incomincia <lb></lb>nella prefazione dal rimproverare i Medici, per aver sempre tenuto con tanta <lb></lb>fedeltà dietro a Galeno, da non dilungarsene <emph type="italics"></emph>ne latum quidem unguem,<emph.end type="italics"></emph.end><lb></lb>stimando che nulla sia ne&#039;libri di lui da riprendere. </s>

<s>Eppure è un fatto, sog­<lb></lb>giunge il Vesalio, che Galeno stesso “ se frequenter corrigit, suamque ne­<lb></lb>gligentiam quibusdam libris commissam in aliis postea, exercitatior redditus, <lb></lb>non semel indicat contrariamque frequenter docet. </s>

<s>” Comunque sia, lasciando <lb></lb>le parole e venendo ai fatti “ nobis modo, ex renata dissectionis arte dili­<lb></lb>gentique Galeni librorum praelectione et in plerisque locis eorumdem non <lb></lb>poenitenda restitutione, constat nunquam ipsum nuper mortuum corpus hu­<lb></lb>manum resecuisse. </s>

<s>” Si lasciò sedurre, prosegue a dir l&#039;ardente Brussel­<lb></lb>lese, dalle sue scimmie, nè si sa perchè. </s>

<s>Se non sempre pronti a sezionare <lb></lb>aveva cadaveri freschi, da studiarvi le viscere e le altre parti molli, vi erano <lb></lb>le aride ossa, le quali poteva Galeno sempre a suo agio esaminare, e avve­<lb></lb>dersi delle notabilissime differenze che passano fra le stesse ossa umane e <lb></lb>quelle delle scimmie. </s></p><p type="main">

<s>Svolgendo i sette libri, in che tutta l&#039;Opera è divisa, si può dir che il <lb></lb>Vesalio non passa descrizione di membra umane, che non si trattenga a no­<lb></lb>tar baldanzosamente gli errori, e le improprietà della storia di Galeno. </s>

<s>E fu <lb></lb>giusto questa baldanza che nocque all&#039;Autore, e nocque ai progressi, ai qual i <lb></lb>il Berengario aveva tranquillamente avviata la scienza. </s>

<s>Nocque all&#039;Autore, <lb></lb>per le fiere persecuzioni che gli si suscitarono incontro da tutti coloro, che <lb></lb>tenevano esser ne&#039;libri galenici i precetti dell&#039;arte medica divinamente ri­<lb></lb>velati: nocque ai progressi della scienza, perchè, mentre pareva che si vo­<lb></lb>lessero liberar gl&#039;ingegni dalla servitù antica, si tentava destramente di sog­<lb></lb>giogarli a una servitù nuova. </s></p><pb xlink:href="020/01/1138.jpg" pagenum="13"></pb><p type="main">

<s>Qual decisa intenzione e qual consapevolezza fosse in questi tentativi <lb></lb>non si potrebbe affermare, ma che si studiasse il Vesalio di ridurre a sè <lb></lb>tutto il merito dell&#039;Anatomia nuova, e tutta l&#039;autorità di nuovo maestro, <lb></lb>apparisce chiaro dalla citata prefazione, nella quale egli si vanta che l&#039;arte <lb></lb>del dissettare sia per la sola opera sua, a&#039;suoi tempi, rinata. </s>

<s>Fà cechi ado­<lb></lb>ratori e seguaci di Galeno non solamente Oribasio, Teofilo e gli Arabi, ma <lb></lb>tutti quanti i moderni, i quali trattando di cose anatomiche “ nihil umquam <lb></lb>minus aggressi videntur quam humani corporis sectionem. </s>

<s>” Il Mondino, e <lb></lb>il Berengario, che aveva da sè solo dissecato centinaia di cadaveri umani, <lb></lb>non erano certamente del numero di coloro, che così venivano accusati, e il <lb></lb>Vesalio, tacendo de&#039;due instauratori dell&#039;arte anatomica italiana, nè potendo <lb></lb>allegare ignoranza, dà giusto motivo di sospettare che ciò facesse, per attri­<lb></lb>buire a sè tutto il merito di quella restaurazione. </s>

<s>Aristotile prima, e poi <lb></lb>Galileo e il Cartesio, che vollero apparire al mondo di naturale Filosofia primi <lb></lb>e soli maestri, danno anch&#039;essi l&#039;esempio di aver rinnegate le tradizioni dei <lb></lb>loro maggiori, e parve succeder felicemente l&#039;intenzione al Vesalio, com&#039;era <lb></lb>felicemente riuscita all&#039;antico Maestro e duce di coloro che sanno. </s></p><p type="main">

<s>Ma fra que&#039;giovani studenti, i quali ascoltavano le fervorose declamazioni <lb></lb>fatte contro Galeno dal Brussellese venuto a insegnare a Padova, n&#039;erano <lb></lb>due nati sotto il cielo d&#039;Italia, e non molto di lungi dalla patria di Iacopo <lb></lb>Berengario, i quali sarebbero divenuti in anatomia celeberrimi maestri, e pro­<lb></lb>fessandosi amici di Galeno e del Vesalio, ma fermi sopra ogni cosa di voler <lb></lb>essere amici del vero, liberata la scienza dal giogo antico e dal nuovo, avreb­<lb></lb>bero dimostrato col loro esempio che argomento unico all&#039;Anatomia per pro­<lb></lb>gredire erano le osservazioni e l&#039;esperienze. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Que&#039;due giovani, che stavano tranquillamente ad ascoltare, mentre l&#039;altra <lb></lb>scolaresca applaudiva scompostamente al Maestro, erano Gabbriello Falloppio <lb></lb>e Realdo Colombo. </s>

<s>Se non fosse rimasto altro che quella turba fremente e <lb></lb>plaudente, l&#039;Anatomia arrestava senza dubbio nel Vesalio i progressi, i quali <lb></lb>si componevano di tre passi: del primo, che si arrestò in Galeno, e in cui si <lb></lb>descrisse l&#039;anatomia de&#039;bruti; del secondo fatto dal Berengario e da cui inco­<lb></lb>minciò l&#039;anatomia del corpo umano, e del terzo ultimamente promosso dallo <lb></lb>stesso Vesalio, che dal felice connubio delle due precedenti anatomie raccolse <lb></lb>il frutto ubertoso. </s>

<s>Che fosse tutto intero quel frutto, possibile a raccogliersi <lb></lb>da&#039;nuovi studii, veramente raccolto dal divino Brussellese, lo andavano ripe­<lb></lb>tendo i suoi adoratori, mentre volevano dall&#039;altra parte i fierissimi nemici <lb></lb>di lui persuadere ognuno che quella nuovamente aperta era una scuola di <lb></lb>errori e di bestemmie. </s></p><p type="main">

<s>Tali due impedimenti opposti ai progressi dell&#039;Anatomia furono vinti <pb xlink:href="020/01/1139.jpg" pagenum="14"></pb>animosamente dal Falloppio, il quale narra nelle sue Osservazioni anatomi­<lb></lb>che le battaglie ch&#039;ebbe a combattere nella mente, per conseguire la diffi­<lb></lb>cile vittoria, e come a scoprir cose nuove, rimaste occulte a Galeno stesso <lb></lb>e al Vesalio, aprisse a sè e a&#039;suoi seguaci largamente la via. </s></p><p type="main">

<s>“ Avevo fatto proposito, così scrive rivolgendo il discorso al suo ami­<lb></lb>cissimo Pietro Manna, di non mai esercitare la penna intorno a cose spet­<lb></lb>tanti all&#039;Anatomia, e ciò perchè parevami che il Vesalio avesse resa l&#039;opera <lb></lb>quasi compiuta, non vedendosi quel che aggiungere o quel che si potesse <lb></lb>desiderare di più delle ammirabili descrizioni ch&#039;egli fa delle parti del corpo <lb></lb>umano. </s>

<s>Di qui è ch&#039;io mi dava a credere perpetuo dover durare quel mo­<lb></lb>numento del divino ingegno, e tali esser le cose dette, da non poterle dire <lb></lb>di meglio, nè in altro modo diverso da lui porgerle, senza venir meritamente <lb></lb>deriso. </s>

<s>Stetti in questa persuasione più anni, infin tanto che divenuto più <lb></lb>esperto negli esercizii dell&#039;arte, e reso dall&#039;esempio stesso del Vesalio più <lb></lb>audace, incominciai a pensare e a voler decidere fra me chi de&#039;due o Ga­<lb></lb>leno o il Vesalio si fosse più d&#039;appresso avvicinato a conoscere il vero. </s>

<s>In <lb></lb>hoc itaque studio quamvis non negarim me illud unum observasse, nempe <lb></lb>quod optimus anatomicus Andreas Vesalius, veluti exercitus victoriae ardore <lb></lb>ac impetu actus, saepe aliquid tentat quod minus aut ad gloriam propriam <lb></lb>conducit aut optimis ducibus ac imperatoribus satisfacit, Galenum aliquando <lb></lb>in verbis, potius quam in sententiis capit, aliquando mutilum quod facere <lb></lb>debuerat minime excusat, ac saepe indignius, quam anatomicum philoso­<lb></lb>phum ac medicum tam insignem deceret, carpit et accusat ” (Observationes <lb></lb>anat. </s>

<s>in Op. </s>

<s>omn., Francofurti 1584, pag. </s>

<s>398). </s></p><p type="main">

<s>Nonostante, prosegue a dire il Falloppio, tenni più dalla parte del Ve­<lb></lb>salio, che non da quella di Galeno, come possono farne testimonianza tutti <lb></lb>coloro, che m&#039;intesero descriver le parti del corpo umano dalle pubbliche <lb></lb>cattedre di Pisa e di Padova. </s>

<s>“ Post autem hoc iudicium, confirmatis adhuc <lb></lb>magis animi viribus, quaerere coepi an in hac arte in qua Hippocrates pri­<lb></lb>mum, deinde Aristotiles, praeterea Erasistratus, Marinus ac Hierophilus, et <lb></lb>tandem Galenus erravit, solus Vesalius reperiatur, qui nihil unquam dormi­<lb></lb>tando, non solum hos diversos scriptores, sed etiam Homerum ipsum ali­<lb></lb>quando, ut fertur in adagio, dormitantem superavit, seu potius aliquid sit <lb></lb>ab ipso praetermissum, vel non satis integre enarratum, seu aliquid distor­<lb></lb>tum, vel ab historia partium corporis humani discrepans in illius volumine <lb></lb>anatomico reperiatur. </s>

<s>In hoc multum revera varias ob causas sudavi, pri­<lb></lb>mum quia tentavi rem per se difficillimam, secundum, quia in verbis ma­<lb></lb>gistri iuratus, atque illius auctoritati plurimum tribuens, non audebam ex <lb></lb>iis carceribus quos ipse arti imposuit egredi, tertium, quod et gravissimum <lb></lb>est, quod publicam notam pertimescebam, momosque etiam ipsos auribus <lb></lb>meis oggannientes iam tum audire videbar. </s>

<s>Haec tamen omnia satis strenue <lb></lb>superavi. </s>

<s>Nam rei difficultatem summo studio, labore et vigiliis plurimis vici. </s>

<s><lb></lb>Magistri reverentiam et timorem ipsius exemplo lenivi. </s>

<s>Quoniam uti Vesa­<lb></lb>lius, non in scholis quidem vivae vocis auditor, sed in Musaeo factus, non <pb xlink:href="020/01/1140.jpg" pagenum="15"></pb>ipsius auctoritate deterritus est quin plurima arti adderet, quae a praeceptore <lb></lb>eius praetermissa erant; ita et ego in illius schola, quia eius scripta dili­<lb></lb>genter legerim versatus, alacrius in hoc pariter artem curare tentavi ” (ibi, <lb></lb>pag. </s>

<s>398, 99). </s></p><p type="main">

<s>I frutti di questi tentativi, così felicemente riusciti, furono dal Fallop­<lb></lb>pio raccolti nelle sue <emph type="italics"></emph>Osservazioni,<emph.end type="italics"></emph.end> nelle quali, occorrendogli per prima cosa <lb></lb>a descrivere le mascelle, tocca della controversia insorta fra Galeno, che de­<lb></lb>scrisse esse mascelle come composte di due pezzi, e il Vesalio, che asseriva <lb></lb>invece esser salde e composte di un osso solo. </s>

<s>Il Falloppio osserva che, ri­<lb></lb>dotte in due pezzi attaccati insieme, si trovano veramente le mascelle negli <lb></lb>infanti e ne&#039;piccoli nati delle scimmie, per cui concludeva, a difesa di Ga­<lb></lb>leno e a temperar le fiere accuse avventategli dal Vesalio, che l&#039;antico padre <lb></lb>e Maestro dell&#039;Anatomia avea descritte le mascelle quali si ritrovano ne&#039;te­<lb></lb>neri fanciulli e nò negli adulti. </s>

<s>“ Quamobrem pro Galeno dici posset ipsum <lb></lb>de tenerrima maxilla locutum fuisse. </s>

<s>Quod si adversarius respondeat non de­<lb></lb>cere dogmata de imperfectis partibus assumere, sed de perfectis esse tractan­<lb></lb>dum, addas hac quoque causa errasse omnes anatomicos, qui de appendici­<lb></lb>bus ita diffuse loquti sunt, cum illae in imperfectis tantum ossibus non <lb></lb>autem in adultis reperiantur ” (ibi, pag. </s>

<s>413). </s></p><p type="main">

<s>Più avanti, descrivendo il Falloppio i vasi arteriosi che ricorrono sulla <lb></lb>superficie del cervello, e s&#039;insinuano alquanto al di sotto della sostanza cor­<lb></lb>ticale, facendone vibrar la membrana al ritmo della loro pulsazione “ doleo, <lb></lb>egli dice, et mirum in modum doleo quod divinus Vesalius, quem amo atque <lb></lb>uti praeceptorem colo venerorque, aliquando, dum acrius accusat Galenum <lb></lb>ac alios anatomicos, ipse erret, quod ipsi accidit in vasis describendis, quae <lb></lb>ad sinus ipsius membranae durioris cerebri pertingunt. </s>

<s>Nam accusat Gale­<lb></lb>num ac reliquos anatomicos, qui non viderint sinus dictos pulsantes cum <lb></lb>illud manifestissime faciant. </s>

<s>Deinde non invenerint arterias una cum venis <lb></lb>ad eiusdem sinus pertingentes. </s>

<s>Quorum utrumque mihi videtur aliquantisper <lb></lb>ab historiae veritate recedere ” (ibi, pag. </s>

<s>449). </s></p><p type="main">

<s>Proseguendo colla solita libertà, dimostra il Falloppio, nelle sue <emph type="italics"></emph>Istitu­<lb></lb>zioni anatomiche,<emph.end type="italics"></emph.end> essersi ingannato il Vesalio, attribuendo all&#039;uomo le pro­<lb></lb>prietà del muscolo cremastere de&#039;cani (ivi, pag. </s>

<s>490), come pure dimostra <lb></lb>avere il Vesalio stesso errato nel descriver come convenienti all&#039;uomo i ca­<lb></lb>nini muscoli intercostali (pag. </s>

<s>495). Perciò il Falloppio, a proposito de&#039;mu­<lb></lb>scoli locomotori dell&#039;occhio, per la descrizione de&#039;quali il Vesalio sezionò la <lb></lb>scimmia, rimprovera a lui il difetto stesso e gli ritorce incontro lo strale <lb></lb>acutissimo e avvelenato, ch&#039;egli avventò contro Galeno. </s>

<s>“ Circa hos muscu­<lb></lb>los quid dixerit Vesalius iudicent studiosi, cum ipsos in diversis partibus <lb></lb>artos in diversas partes insertos ita collocet, ut cuivis ipsius positionem consi­<lb></lb>deranti appareat musculos hos, nisi ita se haberent atque ipse ait, profecto <lb></lb>in eamdem partem ambo oculum traherent nullo interim oculum ad mediam <lb></lb>regionem retrahente. </s>

<s>Superaddit his omnibus septimum alium musculum <lb></lb>Vesalius una cum Galeno, <gap></gap> quem ipse eamdem notam patietur, quam <pb xlink:href="020/01/1141.jpg" pagenum="16"></pb>saepissime imputat Galeno, dum ipsum suis delusum simiis multa afferre et <lb></lb>comminisci ait quae, si humana cadavera secuisset, aliter protulisset ” (ibi, <lb></lb>pag. </s>

<s>510). </s></p><p type="main">

<s>Così veniva chiaramente dimostrato dai fatti che tanto Galeno quanto <lb></lb>il Vesalio erano due uomini, come tutti gli altri, soggetti ad errori; onde <lb></lb>avendosi per cosa certa essere stata l&#039;Anatomia fino a quel tempo coltivata <lb></lb>da uomini e non da Dei, nell&#039;imperfezione umana, in ch&#039;era rimasta, dava <lb></lb>certissima speranza a tutti e prometteva il merito debito a chiunque ne fa­<lb></lb>vorisse i progressi, per cui il Falloppio stesso, ad avvivar la speranza di con­<lb></lb>seguir più facilmente un tal merito, dettava a chi si volesse dare agli eser­<lb></lb>cizii dell&#039;arte i precetti seguenti: </s></p><p type="main">

<s>“ I. </s>

<s>Quae non connata sunt facile ac leviter dividi. </s>

<s>II. </s>

<s>Quae connata <lb></lb>sunt difficillime, nisi maxima adhibita diligentia, dividenda esse. </s>

<s>III. </s>

<s>Nihil <lb></lb>lacerandum. </s>

<s>IV. </s>

<s>Quod summe est necessarium et difficile ut sciamus quae <lb></lb>sit una pars, quae vero plures: ne plures partes simul iunctas constituamus <lb></lb>unam esse, nec ex una plures faciamus. </s>

<s>V. </s>

<s>Quis sit ordo in dissectione obser­<lb></lb>vandus: possumus enim vario modo incipere et mutare ordinem. </s>

<s>Aut enim <lb></lb>habemus rationem dignitatis, et tunc incipimus a dignioribus ut a corde, a <lb></lb>cerebro; aut dirigimus ordinem ad duiturnitatem materiae, et incipimus ab <lb></lb>iis partibus quae citius pereunt et putrescunt, aut respicimus collocationem <lb></lb>et situm partium, ut quando extimas prius secamus servato ordine usque <lb></lb>ad intimas, aut spectamus usum toti corpori exhibitum, et tunc a duriori­<lb></lb>bus incipit ars, utpote ac quae totum corpus fulciunt. </s>

<s>VI. </s>

<s>Ut cognoscamus <lb></lb>quibus instrumentis nunc haec particula nunc illa sit dividenda, cui adhi­<lb></lb>bendi opera ministri, cui minime. </s>

<s>VII. </s>

<s>Ut cognoscamus quae particulae sint <lb></lb>dividendae et inspiciendae in vivis animalibus, quae vero in mortuis et qua <lb></lb>ratione; quaedam enim partes etiam mortuae omnia integra reservant, quae­<lb></lb>dam vero vel nihil vel parum admodum retinent illius quod sensu est per­<lb></lb>cipiendum “ (Institutiones anatom. </s>

<s>inter Op. </s>

<s>omnia cit., pag. </s>

<s>521). </s></p><p type="main">

<s>Nella duplice opera delle <emph type="italics"></emph>Osservazioni<emph.end type="italics"></emph.end> anatomiche e delle <emph type="italics"></emph>Istituzioni,<emph.end type="italics"></emph.end><lb></lb>si rendeva dunque per due conti il Falloppio benemerito de&#039;progressi del­<lb></lb>l&#039;Anatomia: prima, per aver salvato dagli attentati del Vesalio, che voleva <lb></lb>reciderle, le più antiche tradizioni galeniche della scienza; poi, per aver mo­<lb></lb>strato che alla via gloriosamente corsa dallo stesso Vesalio non era posto il <lb></lb>termine nelle scoperte di lui, ma che restava molto ancora a scoprire a chi <lb></lb>vi si fosse rivolto con studio amoroso, com&#039;egli ne&#039;suoi due libri anatomici <lb></lb>insegnava coi fatti e coi precetti. </s></p><p type="main">

<s>Ma i precetti a dir vero accennano all&#039;arte già progredita, la quale si <lb></lb>studia di giungere alla sua perfezione per quella via già segnata dai primi <lb></lb>maestri, senza cercare o saper trovar modo da renderla più diritta e più <lb></lb>aperta. </s>

<s>Vedremo di ciò l&#039;esempio ne&#039;principali Anatomisti, che successero <lb></lb>al Falloppio, mettendo in pratica i precetti di lui, mentre che Realdo Co­<lb></lb>lombo, il quale porgeva nuovi argomenti all&#039;Anatomia per progredire, ri­<lb></lb>maneva incompreso e per lungo tempo dimenticato. </s></p><pb xlink:href="020/01/1142.jpg" pagenum="17"></pb><p type="main">

<s>Que&#039;nuovi argomenti consistevano nelle esperienze, che aggiungevansi <lb></lb>alle osservazioni semplici del Vesalio, e delle quali insegnava unicamente a <lb></lb>far uso il Falloppio. </s>

<s>In quelle brevi parole di avvertimento al lettore, che <lb></lb>preparava Realdo per premetterle ai suoi XV libri <emph type="italics"></emph>De re anatomica,<emph.end type="italics"></emph.end> inco­<lb></lb>mincia a dire che il fine, per cui prese a scrivere, fu quello di riferire <emph type="italics"></emph>quae <lb></lb>observavi<emph.end type="italics"></emph.end> non solo, ma <emph type="italics"></emph>et cum rei natura consentire experimento didici.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ecco proposta una nuova autorità superiore a quella di Galeno e del <lb></lb>Vesalio, l&#039;autorità dell&#039;esperienza, e le fiere contese fra due uomini, che si <lb></lb>reputavano ugualmente divini, si portavano a decidere dalla natura, vera­<lb></lb>mente divina, dei fatti. </s>

<s>È perciò che Realdo non ha paura di offendere nè <lb></lb>d&#039;incontrar le inimicizie di nessuno, anteponendo la verità alle sentenze <lb></lb>scritte ne&#039;libri del Vesalio, e benchè protesti di venerar Galeno <emph type="italics"></emph>tamquam <lb></lb>numen,<emph.end type="italics"></emph.end> promette nostante a&#039;suoi buoni lettori che dalle esperienze fatte <lb></lb>sul cuore palpitante di un cane apprenderanno più in un&#039;ora, e con più <lb></lb>gran diletto, che rileggendo per tre mesi interi il trattato <emph type="italics"></emph>De pulsibus<emph.end type="italics"></emph.end> dello <lb></lb>stesso Galeno. </s></p><p type="main">

<s>E che cosa potevano rispondere a queste parole i Galenisti, i quali si <lb></lb>erano così furiosamente levati contro le critiche del Vesalio? </s>

<s>Eppure il no­<lb></lb>stro Anatomico cremonese non è men rigido censore di quel che si fosse <lb></lb>l&#039;Anatomico brussellese, a persuadersi di che basta leggere il libro XIV <emph type="italics"></emph>De <lb></lb>re anatomica,<emph.end type="italics"></emph.end> dove s&#039;incomincia a dire che Galeno, per questo solo si <lb></lb>astenne dal sezionar cadaveri umani, perchè per le infami crudeltà de&#039;suoi <lb></lb>predecessori fu severamente divietato dalle leggi civili. </s>

<s>“ Sed, bone Galene, <lb></lb>soggiunge Realdo, si tibi crudele nimis videbatur vivum hominem secare, <lb></lb>si animus horrescebat, si reformidabas, vel si tibi neque vel mortuum homi­<lb></lb>nem secare per Principum edicta aut inveteratam consuetudinem non lice­<lb></lb>bat; quo pacto licebat tibi simias secanti veteribus contradicere quos humana <lb></lb>corpora secuisse, tu ipse testis es locupletissimus? ... Multis in locis vete­<lb></lb>res reprehendis, cum tute maiore his dignus sis reprehensione. </s>

<s>Nam et si­<lb></lb>mia simile quid habeat homini, simia tamen est, non homo neque eius com­<lb></lb>pago hominis fabricae omni ex parte respondet, partesque nonnullas in <lb></lb>homine conspicies, de quibus veteres anatomici loquebantur, quibus simia <lb></lb>caret ” (Venetiis 1559, pag. </s>

<s>256). </s></p><p type="main">

<s>Qui non si ricorre alle gentili furberie del Falloppio, ma si riprende <lb></lb>apertamente Galeno, come faceva il Vesalio, di cui pure non è parte ne&#039;libri <lb></lb>di Realdo, dove non si scopran francamente gli errori. </s>

<s>Eppure è notabilis­<lb></lb>simo che non ne facessero risentimento ne&#039;Galenisti, ne&#039;Vesaliani. </s>

<s>Si po­<lb></lb>trebbe ciò attribuire all&#039;essere uscito il trattato <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> postumo, <lb></lb>se non si fossero veduti i Vesaliani, stessi non risparmiarla dopo morto al <lb></lb>Falloppio. </s></p><p type="main">

<s>Di Spagna, facendo il Vesalio viaggio a Gerusalemme, passò per Ve­<lb></lb>nezia, e alcuni de&#039;principali medici della città, adoratori del nome di lui, <lb></lb>erano convenuti insieme per salutarlo nella bottega del libraio Francesco <lb></lb>de&#039;Franceschi, dove sapevano ch&#039;ei recapitava. </s>

<s>Ivi gli domandarono que&#039;me-<pb xlink:href="020/01/1143.jpg" pagenum="18"></pb>dici che fosse avvenuto delle critiche fatte alle <emph type="italics"></emph>Osservazioni<emph.end type="italics"></emph.end> del Falloppio, <lb></lb>in quella scrittura che avevan sentito dire essere stata affidata a Paolo Tie­<lb></lb>polo, ambasciatore veneto a Madrid, perchè la recasse nel suo ritorno a Pa­<lb></lb>dova. </s>

<s>Rispose allora il Vesalio che, dovutosi trattenere per le guerre galli­<lb></lb>che civili il Tiepolo in Catalogna, era trascorsa l&#039;occasion della pubblicazione, <lb></lb>perchè il Falloppio in quel tempo era morto. </s>

<s>Saputo ciò que&#039;medici ricor­<lb></lb>sero al Tiepolo stesso, e avutone da lui il manoscritto, lo consegnarono al <lb></lb>detto Franceschi stampatore, che nel 1564 lo die fuori alla luce. </s></p><p type="main">

<s>Il titolo del libro era questo: <emph type="italics"></emph>Andreae Vesalii Anatomicarum Gabrie­<lb></lb>lis Falloppii Observationnm Examen,<emph.end type="italics"></emph.end> e lo spirito che l&#039;informava era quello <lb></lb>di dimostrar che il Falloppio non aveva veramente scoperto in anatomia nulla <lb></lb>di nuovo, e che non fosse già o esplicitamente o in germe contenuto nei <lb></lb>VII libri della Fabbrica del corpo umano. </s>

<s>Del Colombo non vi si fa men­<lb></lb>zione altro che per incidenza, e si sfoga indirettamente l&#039;ira contro il Val­<lb></lb>verda, il quale è accusato d&#039;inesperienza delle dissezioni e d&#039;ignoranza delle <lb></lb>mediche discipline. </s>

<s>Del libro ch&#039;egli scrisse in lingua spagnuola, principal­<lb></lb>mente per divulgare fra&#039;suoi connazionali le scoperte anatomiche del Colombo, <lb></lb>è detto che non fece ivi altro l&#039;Autore che assumersi l&#039;ufficio d&#039;interpetre, <lb></lb><emph type="italics"></emph>turpis quaestus causa.<emph.end type="italics"></emph.end> (Venetiis 1564, pag. </s>

<s>72). </s></p><p type="main">

<s>I Vesaliani trionfarono, dandosi a credere che venisse da questo Esame <lb></lb>annichilato il Falloppio coi discorsi, e il Colombo coi silenzii, ma è da dire, <lb></lb>per onor dell&#039;Italia e della scienza, che sebbene la prematura istituzione <lb></lb>sperimentale dell&#039;Autor <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> non trovasse allora seguaci, i pre­<lb></lb>cetti intorno al modo di sezionare i cadaveri e di osservarne le parti, che <lb></lb>il Falloppio dettava dalle cattedre di Pisa e di Padova, e poi diffondeva nei <lb></lb>libri, educarono all&#039;arte valorosissimi ingegni, i quali trovarono ancora ab­<lb></lb>bondante pascolo da nutrirsi in quell&#039;albero, che si diceva aver per solo il <lb></lb>Vesalio menato i suoi fiori e i suoi frutti. </s></p><p type="main">

<s>Vien primo per tempo e per eccellenza tra il fiore di quegl&#039;ingegni <lb></lb>italiani Bartolommeo Eustachio, il quale a descriver le parti del corpo umano <lb></lb>si servì più volentieri dell&#039;arte del disegno, prestatagli, come si dice, dal <lb></lb>celebre Tiziano, che di quella della parola. </s>

<s>Ma le Tavole anatomiche del <lb></lb>gran Maestro rimasero lungamente in Roma nella biblioteca vaticana, senza <lb></lb>profitto degli studiosi, infintantochè sotto il pontificato di Clemente XI non <lb></lb>furono, col seguente titolo, pubblicate da Giovanni Maria Lancisi: “ Tabu­<lb></lb>lae anatomicae clarissimi viri Bartholommaei Eustachii, quas a tenebris tan­<lb></lb>dem vindicatas et Sanctissimi Domini Clementis XI Pont. </s>

<s>Max. </s>

<s>munificentia <lb></lb>dono acceptas, praephatione notisque illustravit, ac ipso suae Bibliotechae <lb></lb>dedicationis die publici iuris fecit Jo. </s>

<s>Maria Lancisius, intimus cubicularius <lb></lb>et Archiater pontificius. </s>

<s>Romae 1714. ” </s></p><p type="main">

<s>A saper solo che il libro usciva fuori per cura del Lancisi, e con pre­<lb></lb>fazione e note scritte da lui, basterebbe per dover forse tenerne in più gran <lb></lb>pregio la pubblicazione, che se fosse stata fatta dal suo proprio autore. </s>

<s>Ma <lb></lb>perchè sempre i grandi ingegni sono modesti, diffidando il Lancisi di sè in <pb xlink:href="020/01/1144.jpg" pagenum="19"></pb>condur la difficile impresa, volle aiuti e consigli da&#039;più valorosi medici ita­<lb></lb>liani d&#039;allora, e principalmente dal Pacchioni e dal Morgagni. </s>

<s>“ Et quoniam, <lb></lb>egli così scrive nella Prefazione, ne frequens locorum obscuritas me in er­<lb></lb>rorem duceret saepe maximeque sum veritus, idcirco in laboris honesti so­<lb></lb>cietatem vocavi D. </s>

<s>Antonium Pacchionum medicum romanum, et in rebus <lb></lb>potissimum anatomicis apprime versatum, quo, cum singulas Tabulas ite­<lb></lb>rum ad examen revocare non detrectavi, atque ubi vel minimus scrupulus, <lb></lb>quod interdum accidit, nobis iniectus est, statim imaginem cum archetypo, <lb></lb>nempe iconem cum dissecto cadaveris membro contulimus et comparavimus, <lb></lb>in partem quoque diligentiee curaeque accito Francisco Soldato, iuvene qui­<lb></lb>dem medicis studiis cadaverumque sectionibus magnopere exercito. </s>

<s>Neque <lb></lb>vero, cum opportunum censuimus, per epistolas quoque in consilium admit­<lb></lb>tere praetermisimus eximios viros Joannem Fantonium et Joannem Bapti­<lb></lb>stam Morgagnum nostrae aetatis in Italia experientissimos anatomicos ” <lb></lb>(pag. </s>

<s>XIV). </s></p><p type="main">

<s>Ciascuno iconismo delle numerose Tavole è dichiarato, nelle sue parti, <lb></lb>per lettere di richiamo, nella pagina di rincontro, cosicchè si rendono agli <lb></lb>occhi degli attenti osservatori que&#039;disegni anatomici quasi parlanti. </s>

<s>Nono­<lb></lb>stante però che s&#039;usassero tante diligenze, e vi si applicasse con tanto amo­<lb></lb>roso studio di scienza e di arte, l&#039;Albino notò nell&#039;opera del Lancisi alcune <lb></lb>imperfezioni, che lo consigliarono a fare una nuova edizione delle Tavole <lb></lb>eustachiane uscite in luce in Leida nel 1744. Così in ogni modo si diffuse più <lb></lb>largamente la notizia di ciò che, da quasi due secoli, s&#039;era osservato nella <lb></lb>fabbrica del corpo umano in Italia, e se non si giovò molto oramai ai pro­<lb></lb>gressi dell&#039;anatomia, s&#039;offerse uno de&#039;suoi più solenni documenti alla storia. </s></p><p type="main">

<s>L&#039;Eustachio apparisce in questi documenti come uno de&#039;primi che, non <lb></lb>abbarbagliato dall&#039;aureola posta da&#039;fanatici in fronte a Galeno e al Vesalio, <lb></lb>facesse sull&#039;esempio del Falloppio progredire l&#039;anatomia descrittiva, ma non <lb></lb>fu il solo: a lui si aggiunsero, osservatori diligenti de&#039;precetti falloppiani, <lb></lb>Girolamo Fabrizi d&#039;Acquapendente, e il piacentino Giulio Casserio. </s></p><p type="main">

<s>Far l&#039;Acquapendente in anatomia discepolo del Falloppio non sembrerà <lb></lb>punto alieno dal vero a chi considera ch&#039;egli è forse l&#039;unico, che in scusare <lb></lb>gli errori di Galeno, per non provocarsi l&#039;ire de&#039;galenisti, imiti l&#039;arte gen­<lb></lb>tilissima del maestro. </s>

<s>Si può citar come esempio di ciò il fatto che, dalle <lb></lb>somiglianze notate fra le parti componenti le mani e i piedi, Galeno stesso <lb></lb>ne argomentava la somiglianza dell&#039;uso. </s></p><p type="main">

<s>L&#039;Acquapendente conferma per altri riscontri questa galenica analogia, <lb></lb>soggiungendo: “ Nam sicuti pedis duplex est actio, innixus et apprehensio, <lb></lb>similiter et manu ” (De motu locali Patavii 1618, pag. </s>

<s>92), colla qual mano <lb></lb>si può così ben calcare, per mezzo della palma, come per mezzo della pianta <lb></lb>e del calcagno del piede. </s>

<s>Così dicendo non sembra aver l&#039;autore altra in­<lb></lb>tenzione che di rimover l&#039;accusa di paradosso, di che altri imputerebbe il <lb></lb>discorso galenico. </s>

<s>“ Si igitur omnes apprehensiones ut in manu et in pede <lb></lb>similiter fiunt, non est ulterius ambigendum neque ullo modo credendum <pb xlink:href="020/01/1145.jpg" pagenum="20"></pb>Galenum paradoxum protulisse, cum dixit pedem esse instrumentum ap­<lb></lb>prehensionis ” (ibi, pag. </s>

<s>93). </s></p><p type="main">

<s>Il Vesalio sarebbe uscito qui, colla solita baldanza, a far notare a Ga­<lb></lb>leno che somiglianti son le parti, e perciò anche gli usi, delle mani e dei <lb></lb>piedi nelle scimmie, non però nell&#039;uomo. </s>

<s>Ma l&#039;Acquapendente trova modo <lb></lb>a scusar l&#039;errore concludendo così il suo ragionamento: “ Natura igitur in <lb></lb>pede construendo respexit superficiem corporis et corpora ipsa super quibus <lb></lb>facere innixum oportebat. </s>

<s>Quae cum varia essent penes figuram aut an­<lb></lb>gularem aut planam aut rotundam aut curvam, tum per reliquas dissimi­<lb></lb>laris corporis differentias, ut tutus super omnia iam dicta corpora innixus <lb></lb>fiat, factum est ut innixus multiplex sit multipliciterque fiat. </s>

<s>Cum vero ge­<lb></lb>neraliter omnis innixus comprimendo fiat, tamen a calcaneo et planta sim­<lb></lb>pliciter solaque compressione et comprimendo; a cavo pedis tum compres­<lb></lb>sione tum incurvatione; a digitis postremo tum compressione tum apprehen­<lb></lb>sione absolvitur. </s>

<s>Quo fit ut Galenus pedes instrumenta apprehensionis esse <lb></lb>dixerit, quod nonnisi ratione digitorum contingit, qui, tam comprimendo <lb></lb>quam apprehendendo, tutum praestant innixum ” (ibi, pag. </s>

<s>96). </s></p><p type="main">

<s>Abbiamo detto che, in questo modo di procedere verso Galeno, l&#039;Acqua­<lb></lb>pendente imitò le arti del Falloppio, e le chiamiamo arti, perchè crediamo <lb></lb>che gli sviscerati ossequi de&#039;Galenisti, in que&#039;liberi petti, non fossero sin­<lb></lb>ceri. </s>

<s>Frutto di questa libertà nello stesso Acquapendente fu quello di avere <lb></lb>introdotto nell&#039;Anatomia un metodo nuovo da distinguere e nominare i mu­<lb></lb>scoli dalle loro azioni. </s>

<s>Prima di lui, così Galeno come il Vesalio, non ave­<lb></lb>vano trattato la Miologia, se non che così materialmente, descrivendo i mu­<lb></lb>scoli secondo che l&#039;uno si mostrava succedere all&#039;altro, o era l&#039;uno all&#039;altro <lb></lb>contiguo o consociato. </s>

<s>Ma il Nostro, non badando all&#039;ordine e alla mate­<lb></lb>riale disposizion delle fibre, ne considera gli effetti de&#039;moti, e descrive i <lb></lb>muscoli secondo che agiscono in uno o in altro modo sulle leve degli ossi, <lb></lb>a cui come potenza vengono applicati. </s>

<s>Di qui nacque nell&#039;Anatomia muscu­<lb></lb>lare una importante riforma, la quale volle essere così notata dal nostro <lb></lb>Autore, affinchè i lettori non ne prendessero maraviglia: </s></p><p type="main">

<s>“ Miraberis forsitan, lector, quod musculos non describam ut Vesalius <lb></lb>in toto suo opere, et Galenus in libro De adm. </s>

<s>anat. </s>

<s>fecit, qui ordinem seu <lb></lb>commodam dissectionem respicientes eos descripsere, quoniam ii tantum­<lb></lb>modo eorum dissectionem, prout unus alteri succedit et contiguus est asso­<lb></lb>ciaturque, nobis saltem ob oculos ponere et monstrare voluerunt. </s>

<s>At nos, <lb></lb>qui scopum habemus docere, per ea quae insunt musculis, earum actiones <lb></lb>et usus, merito alio ordine concedendum duximus, qui procul dubio nos <lb></lb>ducit ad notitiam casuum musculorum et articulorum. </s>

<s>Nam si quis simpli­<lb></lb>cem dissectionem inquirat, et primum, secundum, tertium et sequentes hoc <lb></lb>modo numeret, potius confusionem quam notitiam, utilitatem musculorum <lb></lb>consequetur. </s>

<s>At, quando nos eorum quae insunt musculis causas inquirimus, <lb></lb>tunc usum inquirimus, et musculorum numerum exactius memoriae man­<lb></lb>damus ” (ibi, pag. </s>

<s>82). </s></p><pb xlink:href="020/01/1146.jpg" pagenum="21"></pb><p type="main">

<s>Proseguendo l&#039;Acquapendente con questo nuovo metodo razionale le sue <lb></lb>ricerche miologiche, narra come fosse, nel 1599, condotto alla scoperta dei <lb></lb>muscoli gemelli (pag. </s>

<s>83, 84) e a riconoscer la vera natura e gli uffici del <lb></lb>lungo estensor comune delle dita de&#039;piedi, notando tre capitalissimi errori, <lb></lb>in ch&#039;era caduto il Vesalio (ivi, pag. </s>

<s>103, 4). </s></p><p type="main">

<s>Discepolo e familiare dell&#039;Acquapendente, il Casserio, parve compren­<lb></lb>dere in sè tutte insieme le virtù de&#039;suoi illustri predecessori, non eccet­<lb></lb>tuato il Colombo, il quale egli imita nel dar di Galeno que&#039;liberi giudizi, <lb></lb>intorno a che l&#039;Acquapendente stesso e il Falloppio tanto timidi s&#039;erano di­<lb></lb>mostrati, da parer quasi servili. </s>

<s>Basti di quella filosofica libertà dell&#039;Anato­<lb></lb>mico piacentino recar questo esempio dal cap. </s>

<s>XI del libro IV <emph type="italics"></emph>De auris <lb></lb>auditus organi structura,<emph.end type="italics"></emph.end> dove si tratta dei tre ossicini. </s>

<s>Dal non trovarli in <lb></lb>Galeno descritti s&#039;era incominciato a dire che gli aveva il gran Maestro igno­<lb></lb>rati: risposero allora solleciti i Galenisti ch&#039;era di ciò la ragione, o per es­<lb></lb>sere andati alcuni libri galenici smarriti, o perchè, nel libro <emph type="italics"></emph>De ossibus,<emph.end type="italics"></emph.end> si <lb></lb>dichiara l&#039;Autore di aver per brevità lasciate indietro alcune delle più mi­<lb></lb>nute descrizioni. </s>

<s>Ma il Casserio non trovava punto ragionevoli queste scuse. <lb></lb></s>

<s>“ Enimvero, scriveva, prior coniectura levis admodum est et rationi parum <lb></lb>consona, posterior vero ratio omnino non satisfacit, nam quemadmodum excu­<lb></lb>satione dignus videri potest, si in compendioso libro, cuiusmodi est qui <emph type="italics"></emph>De <lb></lb>ossibus<emph.end type="italics"></emph.end> inscribitur, exacte et minute omnia et praesertim difficilia non expli­<lb></lb>cat; ita iusta reprehensione carere nequit quod in aliis tractationibus longis <lb></lb>et copiosis nullam de his ossiculis mentionem facit. </s>

<s>Idcirco ego sane mihi <lb></lb>persuadeo Galenum non in aliis animalibus quam in simia, si forte non sint <lb></lb>alia quae ossiculis illis carent, auditus organum interius collustrasse. </s>

<s>Nam in <lb></lb>simia nulla intus in osse petroso ossicula reperiuntur ” (De quinque sens., <lb></lb>Venetiis 1609, pag. </s>

<s>205). </s></p><p type="main">

<s>Che poi il discepolo e il familiare dell&#039;Acquapendente ritenga in sè le <lb></lb>virtù di osservare e di descrivere le parti, colla diligenza insegnata dal Fal­<lb></lb>loppio, e della quale così splendidi esempi dava l&#039;Eustachio, basta senz&#039;altro <lb></lb>a provarlo il fatto che fu egli, il Casserio, il primo che osservò e delineò <lb></lb>l&#039;artificiosissimo magistero de&#039;muscoli così detti da lui <emph type="italics"></emph>penniformi.<emph.end type="italics"></emph.end> Ma oltre <lb></lb>al comprendere in sè le virtù de&#039;maggiori ha il nostro Piacentino qualche <lb></lb>cosa, che lo distingue da tutti gli altri, e che sentita nella propria coscienza <lb></lb>fa sì ch&#039;egli si dia, fra gli Autori di que&#039;tempi, oltre a quello di medico <lb></lb>il titolo di filosofo. </s>

<s>Egli infatti non si contenta solo di osservare, come il <lb></lb>Vesalio e il Falloppio e l&#039;Eustachio, e di descrivere, ma applicando il me­<lb></lb>todo dell&#039;Acquapendente non a soli i muscoli, sì a tutti gli organi, filosofa <lb></lb>intorno ai fini, per cui furono dalla Natura essi organi ordinati, e non <lb></lb>lascia di descriver parte del corpo umano, che non tratti degli usi. </s>

<s>È in ciò <lb></lb>forse imitator di Galeno, più di quel ch&#039;egli stesso non si creda, ma l&#039;aver <lb></lb>prediletto di trattar de&#039;sensi, e particolarmente di quello dell&#039;udito, lo fa <lb></lb>sollevare a questioni metafisiche intorno all&#039;origine delle idee; origine ch&#039;egli <lb></lb>crede esser da quegli stessi sensi, con anatomico stile aperti a svelarne i misteri. </s></p><pb xlink:href="020/01/1147.jpg" pagenum="22"></pb><p type="main">

<s>È sembrato ad alcuni che questo nuovo modo di filosofare segni nella <lb></lb>scienza un progresso, ma comunque sia, egli è ancora troppo affrettato, e <lb></lb>scavalca per così dire a un altro passo, che nel regolare andamento delle <lb></lb>idee si sarebbe dovuto premettere, e che, sebben si arrestasse nelle sue <lb></lb>prime mosse, era stato con valido impulso dato già da Realdo Colombo. </s>

<s>Il <lb></lb>metodo sperimentale, applicato da lui allo studio della fabbrica del corpo <lb></lb>umano, iniziò quella che ora propriamente si dice <emph type="italics"></emph>Fisiologia,<emph.end type="italics"></emph.end> e per la quale <lb></lb>veniva la semplice arte del dissettare i cadaveri a sollevarsi all&#039;essere e alla <lb></lb>dignità di scienza. </s>

<s>Più conveniente perciò, e più conducevole al desiderato <lb></lb>perfezionamento, sarebbe riuscita l&#039;opera del Casserio, se piuttosto che di <lb></lb>filosofo fosse stata di fisiologo, ma non era venuta ancora la stagione oppor­<lb></lb>tuna a indossar quell&#039;abito nuovo, benchè le aure che si sentivano spirare <lb></lb>l&#039;annunziassero vicina. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Come spirassero quell&#039;aure sotto il cielo d&#039;Italia, e giungessero a fe­<lb></lb>condare un ingegno straniero, è da rimeditar con pensiero degno della Fi­<lb></lb>losofia della storia. </s>

<s>Realdo Colombo dicemmo che aveva felicemente appli­<lb></lb>cato il metodo sperimentale alle dissezioni anatomiche, d&#039;ond&#039;ebbe origine <lb></lb>fra le altre la dimostrata scoperta delle funzioni fisiologiche del cuore nella <lb></lb>piccola circolazion polmonare. </s>

<s>Istitutor di quel nuovo metodo il Colombo, in <lb></lb>principio dalla cattedra e poi nel trattato <emph type="italics"></emph>De re anatomica,<emph.end type="italics"></emph.end> ne dettava le <lb></lb>regole, che si leggono nel XIV libro, a cui si dà il titolo <emph type="italics"></emph>De viva sectione.<emph.end type="italics"></emph.end><lb></lb>Prescrive prima di tutto che si scelgano ad immolare sull&#039;altar di Minerva <lb></lb>i cani, maschi o femmine che siano, ma giovani, principalmente perchè la­<lb></lb>trando più forte danno modo a conoscere qual sia veramente l&#039;organo della <lb></lb>voce. </s>

<s>È anche questa scoperta un frutto del nuovo metodo istituito dal no­<lb></lb>stro Cremonese, e benchè sia importante, non è quella ancora, sopra la quale <lb></lb>ha da rivolgersi la nostra considerazione. </s></p><p type="main">

<s>Insegnato il modo di legare sopra una tavola il cane vivo, affinchè non <lb></lb>si muova e non morda, si vede, aperto il ventre, come i polmoni circondano <lb></lb>il cuore e come respirando l&#039;animale giochi il Diaframma. </s>

<s>“ Ad haec pul­<lb></lb>cherrima visu illud quoque accedit, motus scilicet cordis quemadmodum am­<lb></lb>plificetur atque arctetur. </s>

<s>Item qualis sit motus arteriarum in viva Anatome, <lb></lb>si lubuerit, conspicaberis; numquid idem sit vel oppositus motui cordis. </s>

<s><lb></lb>Comperies enim dum cor dilatatur constringi arterias et rursus in cordis <lb></lb>constrictione dilatari. </s>

<s>Verum animadvertas, dum cor sursum trahitur et tu­<lb></lb>mefieri videtur, tunc constringitur: cum vero se exerit, quasi relaxatus deor­<lb></lb>sum vergit. </s>

<s>Atque eo tempore dicitur cor quiescere, estque tunc cordis <lb></lb>systole, propterea quod facilius suscipit minoreque labore, at cum transmittit <lb></lb>maiori opus est robore. </s>

<s>Neque hoc floccifacias, etenim non paucos reperias <pb xlink:href="020/01/1148.jpg" pagenum="23"></pb>qui eo tempore cor dilatari certo opinantur, quo vere constringitur ” (Edi­<lb></lb>tio cit., pag. </s>

<s>257). </s></p><p type="main">

<s>Nè queste sole, soggiunge poco appresso il Colombo, son le cose che <lb></lb>si possono imparare dalla viva voce della Natura, piuttosto che dalla lettera <lb></lb>morta di Galeno, ma si intenderà inoltre per quanto lunga via errassero i <lb></lb>Peripatetici, dietro il loro principe Aristotile, il quale osò dire tre essere i <lb></lb>ventricoli del cuore, nel destro de&#039;quali il sangue accolto è caldissimo, nel <lb></lb>sinistro è freddissimo, e nel mezzarìo mediocre. </s>

<s>“ Tu vero dextro cordis ven­<lb></lb>triculo inciso si digitum immiseris, calor tepidus tibi occurret, at in sinistro <lb></lb>tantus, ut ferre vix possis. </s>

<s>Illud insuper, quod saepe in disquisitionem venit, <lb></lb>quo pacto vere se habeat experieris an in arteria venali aer et vapor ille, quem <lb></lb>capinosum quasi fumidum dicunt, vel sanguis contineatur ” (ibi, pag. </s>

<s>259). </s></p><p type="main">

<s>All&#039;utilità che veniva alla scienza dal mostrarsi in che modo si potesse <lb></lb>toccar con mano il vero, lungamente rimasto ne&#039;libri de&#039;filosofi antichi an­<lb></lb>nebbiato, aggiungeva l&#039;Autore il diletto, per cui i cruciati infelicissimi di <lb></lb>que&#039;poveri animali vuol che sieno da dire piuttosto felici, offerendo uno spet­<lb></lb>tacolo misto di una dolce pietà, e d&#039;incredibile stupore. </s></p><p type="main">

<s>Era in sul morire la madre di alcuni cagnolini, che allora allora la mano <lb></lb>dell&#039;esperto anatomico aveva dall&#039;utero estratti, e l&#039;amore dei figli pareva <lb></lb>superare i dolori e le agonie della morte. </s>

<s>Perchè se tu provavi a toccare <lb></lb>uno di que&#039;cagnolini latrava, se tu glielo appressavi alle labbra, metteva <lb></lb>fuori la lingua e lo lambiva con grandissimo affetto. </s>

<s>Che se invece tu pre­<lb></lb>sentavi alla paziente, lacerata dal ferro anatomico, qualche altro oggetto di­<lb></lb>verso, lo mordeva con rabbia disperata. </s>

<s>“ Quem naturae amore, atque adeo <lb></lb>parentum in liberos incredibilem charitatem in publicis theatris maxima <lb></lb>spectatorum admiratione saepius ostendi, Patavii praesertim, cum adesset <lb></lb>illustrissimus ac reverendissimus Rainutius Farnesius ” (ibi, pag. </s>

<s>258) e <lb></lb>dopo aver nominati molti altri signori, che assisterono allo spettacolo in­<lb></lb>sieme col Farnese, così il Colombo sogiunge: “ Hi omnes, item alii multi <lb></lb>summa cum voluptate huic vivae canis sectioni interfuerunt, et illud insi­<lb></lb>gne exemplum de ingenti amore vel brutorum in filios se nunquam obli­<lb></lb>turos asseverabant, neque has duntaxat discendi voluptates quas hactenus <lb></lb>memoravi ” (ibi, pag. </s>

<s>258, 59). </s></p><p type="main">

<s>Un Autore che, trattando di Anatomia, sa in fare la descrizione delle <lb></lb>n uove cose scoperte instillar nell&#039;animo di chi lo ascolta la voluttà dell&#039;im­<lb></lb>parare, sembrava che dovess&#039;essere secondato e universalmente applaudito, <lb></lb>come sempre avviene a colui, che sa mescere l&#039;utile al dolce. </s>

<s>Eppure è un <lb></lb>fatto che Realdo Colombo, col suo nuovo metodo e con le sue insigni sco­<lb></lb>perte, non figura nella storia anatomica del secolo XVI, se non come una <lb></lb>splendida apparizione svanita, senza lasciar di sè vestigio nell&#039;aria o negli <lb></lb>occhi di chi con subita ammirazione l&#039;avea riguardata. </s>

<s>La fisiologia del <lb></lb>cuore, per tacer di tante altre verità anatomiche scoperte negli animali vivi <lb></lb>per via di osservazioni e di esperienze, rimase una istituzione morta nelle <lb></lb>pagine di un libro, e il Falloppio stesso ne&#039;suoi scritti pubblicati dopo <pb xlink:href="020/01/1149.jpg" pagenum="24"></pb>il 1559 e l&#039;Eustachio e l&#039;Acquapendente, che vuol dire insomma i più so­<lb></lb>lenni maestri di allora, intorno alla piccola circolazion del sangue e alle fun­<lb></lb>zioni del cuore e dei polmoni, ripeterono gli errori del Vesalio. </s></p><p type="main">

<s>A commemorare que&#039;nomi, ai quali son da aggiungere il Casserio, il <lb></lb>Vidio, l&#039;Aranzio, insieme con parecchi altri, la scienza italiana si esalta, ve­<lb></lb>dendo in essi così numerosa e poderosa oste congiurata insieme a cacciar <lb></lb>dalle nostre contrade il maggiore de&#039;nostri nemici, l&#039;errore, ma si umilia <lb></lb>dall&#039;altra parte a pensar che quei valorosi, a cui il Colombo avea presen­<lb></lb>tato un nuovo vessillo, da conquistar con esso in mano nuove inesplorate <lb></lb>provincie, si mostrassero tanto poco sollecitamente avveduti, da lasciarselo <lb></lb>rapire, venuto per avventura in mezzo a loro, da un sagace straniero. </s></p><p type="main">

<s>Guglielmo Harvey fu colui che, venuto d&#039;Inghilterra in Italia, non tanto <lb></lb>imparò dalla viva voce dell&#039;Acquapendente, quanto dai libri scritti più di <lb></lb>un mezzo secolo prima da Realdo Colombo. </s>

<s>Di quelle pagine, le quali erano <lb></lb>state oramai dagl&#039;Italiani dimenticate, fece il giovane inglese la sua lettura <lb></lb>prodiletta, e vi apprese la nuova arte, rimasta per tutto quel tempo incolta, <lb></lb>di studiare i moti del cuore nella vivisezione. </s>

<s>Tornato in patria, ebbe nel­<lb></lb>l&#039;aula di Giorgio I animali in copia e di varie specie, che si allevavano nei <lb></lb>ricchi parchi reali, e ch&#039;egli con più esperta mano sezionava vivi, larga­<lb></lb>mente applicandovi i metodi del Colombo, da cui tenne per dimostrata la <lb></lb>piccola circolazion polmonare. </s>

<s>Proseguendo oltre per l&#039;aperto cammino, riu­<lb></lb>scì a indovinare e a segnar le intralciate vie, per cui il sangue va dal cuore <lb></lb>a irrigare le membra pe&#039;rami delle arterie, e vi torna con perpetuo circolo <lb></lb>ricondottovi dalle vene. </s>

<s>Nel 1628 pubblicò la sua scoperta in un libro, a cui <lb></lb>diè il titolo di esercitazione anatomica <emph type="italics"></emph>De motu cordis et sanguinis,<emph.end type="italics"></emph.end> libro <lb></lb>che non si potrebbe meglio qualificare, che con chiamarlo il più splendido <lb></lb>commento fatto al Trattato <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> del nostro Cremonese, da cui, <lb></lb>come da albero diligentemente coltivato, il fortunato Britanno trasse unico <lb></lb>le invidiate dovizie del frutto. </s></p><p type="main">

<s>I due trattati perciò <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> e <emph type="italics"></emph>De motu cordis<emph.end type="italics"></emph.end> che non vanno <lb></lb>disgiunti, perchè quello mancherebbe del suo seguito, e questo del suo prin­<lb></lb>cipio, segnano nella storia dell&#039;Anatomia un periodo distinto e un notabi­<lb></lb>lissimo progresso, il quale consiste, come accennammo, nell&#039;aver congiunto <lb></lb>con le anatomiche osservazioni lo studio degli organi sorpresi in quell&#039;atto <lb></lb>stesso, ch&#039;esercitano le funzioni della vita. </s>

<s>Ebbe da quegli studi la sua prima <lb></lb>origine la Fisiologia, la quale sarebbesi però rimasta sterile, senza il con­<lb></lb>nubio con un&#039;altra scienza, solerte indagatrice delle proprietà generali della <lb></lb>materia, e fu il Pecquet che dette il primo solenne esempio di quel connu­<lb></lb>bio nella sua Dissertazione anatomica <emph type="italics"></emph>De circulatione sanguinis et chyli <lb></lb>motu.<emph.end type="italics"></emph.end> L&#039;Anatomia del Diepeo ha giusto titolo d&#039;esser chiamata nuova, per­<lb></lb>chè non descrive solamente le parti, com&#039;avevan fatto tutti i più gran mae­<lb></lb>stri dell&#039;arte, dal Vesalio all&#039;Acquapendente, nè osserva solamente o descrive <lb></lb>i moti vitali come avevan fatto il Colombo e l&#039;Harvey, ma applicando le <lb></lb>leggi della Fisica si studia di rendere la ragion di que&#039;moti. </s></p><pb xlink:href="020/01/1150.jpg" pagenum="25"></pb><p type="main">

<s>Abbiam detto che fu il Pecquet il primo a dar solenne esempio di que­<lb></lb>sta applicazione delle leggi fisiche allo studio della vita animale, ma consi­<lb></lb>derando poi che la Fisica pecqueziana si riduce tutta nell&#039;esperienza del <lb></lb>Torricelli, il quale pure insiem col Magiotti non aveva lasciato, ne&#039;privati <lb></lb>esercizi, di tentar felicemente simili applicazioni, abbiam creduto d&#039;essere <lb></lb>giusti giudici a non attribuire all&#039;Anatomico francese altro merito, da quello <lb></lb>in fuori d&#039;essere egli stato il primo a render pubblicamente noti i nuovi <lb></lb>esperimenti. </s></p><p type="main">

<s>Fu il Torricelli, senza dubbio, l&#039;istitutore della moderna fisica speri­<lb></lb>mentale, ma lo avevano preceduto il Benedetti e Galileo, e le applicazioni <lb></lb>della Fisica alla scienza della vita, d&#039;ond&#039;ebbe origine quella che propria­<lb></lb>mente oggidì si chiama Fisiologia, son più antiche non di quelle sole isti­<lb></lb>tuite dal Pecquet, ma dal Torricelli stesso e dal Magiotti, i quali fecero poi <lb></lb>del Borelli il fondatore di quella scuola, che indifferentemente si chiama o <lb></lb>Iatromatematica o Italiana. </s>

<s>Giacchè dunque l&#039;aver promossa a questo grado <lb></lb>la semplice arte di descriver le parti del corpo umano, e di compararle con <lb></lb>quelle de&#039;bruti, è opera principalmente dei nostri Italiani, giova considerarne <lb></lb>in uno sguardo i principii e i progressi. </s></p><p type="main">

<s>Risalgono que&#039;principii propriamente al Santorio, che facendo uso di <lb></lb>uno strumento volgarissimo, qual&#039;è la Stadera, dimostrò l&#039;insensibile traspi­<lb></lb>razione del corpo dell&#039;uomo, e ne fece il fondamento a un sistema medico, <lb></lb>che è il primo, a cui si possa dar veramente il titolo di razionale. </s>

<s>Egli primo <lb></lb>invocò la Fisica e la Meccanica a inventare Termometri, Pulsilogi, e altri <lb></lb>nuovi strumenti, tutti applicabili agli usi della Medicina. </s></p><p type="main">

<s>Galileo che fu al Fisico giustinopolitano amico e collega, e che sali più <lb></lb>volte, per fare esperienza della traspirazione del suo proprio corpo, sulla Sta­<lb></lb>dera medica (Alb. </s>

<s>VIII, 368), derivò da lui e dall&#039;Acquapendente un certo <lb></lb>amore per le cose mediche e per l&#039;Anatomia, com&#039;apparisce da&#039;suoi stessi <lb></lb>Dialoghi, che sembrano da sì fatte materie esser più alieni. </s>

<s>Nell&#039;aforismo V <lb></lb>della II Sezione della Medicina statica accenna il Santorio all&#039;uso dell&#039;Areo­<lb></lb>metro, per conoscer fra le acque le più o meno leggere, e sceglier così le <lb></lb>più convenienti allo stomaco de&#039;malati. </s>

<s>“ Quantum sit aquae ponderositas <lb></lb>facile intelligitur, si grave perpendatur in aqua: illa enim est levior et per <lb></lb>consequens salubrior, in qua grave magis gravitat: illa vero, in qua minus <lb></lb>est ponderosior, est insalubrior ” (Opera Omnia, T. III, De statera medica, <lb></lb>Venetiis 1660, pag. </s>

<s>8). E Galileo, nel I Dialogo delle due nuove scienze, <lb></lb>dop&#039;aver descritti i giochi fatti da una palla di cera immersa in acqua di <lb></lb>varia gravità specifica, “ Non è cotesta esperienza, soggiunge, priva di uti­<lb></lb>lità, perchè trattandosi dai Medici in particolare delle diverse qualità di acque <lb></lb>e tra le altre principalmente della leggerezza e gravità più di questa che di <lb></lb>quella, con una simil palla aggiustata, sì che resti ambigua per così dire <lb></lb>tra lo scendere e il salire in un&#039;acqua, per minima che sia la differenza di <lb></lb>peso tra due acque, se in una tal palla scenderà, nell&#039;altra che sia più grave, <lb></lb>salirà ” (Alb. </s>

<s>XIII, 72). </s></p><pb xlink:href="020/01/1151.jpg" pagenum="26"></pb><p type="main">

<s>Quanto all&#039;Anatomia, dice Galileo stesso nella Giornata II de&#039;Due mas­<lb></lb>simi Sistemi, per bocca del Sagredo, di essersi trovato in Venezia a veder <lb></lb>le sezioni fatte da un diligente e pratico Notomista, un giorno che s&#039;andava <lb></lb>ricercando l&#039;origine de&#039;nervi, per decidere l&#039;antica controversia insorta fra <lb></lb>Galenisti e Peripatetici (Alb. </s>

<s>I, 121), e voleva forse con questa reminiscenza, <lb></lb>accomodata alla persona del Patrizio veneziano, accennare alle tante altre <lb></lb>volte che in Padova, in quel celebre anfiteatro eretto nelle stanze attigue a <lb></lb>quelle dove dettava le sue lezioni, avrà assistito alle anatomie dell&#039;Acquapen­<lb></lb>dente. </s>

<s>In ogni modo è ragionevolissimo il supporre che il trattato <emph type="italics"></emph>De motu <lb></lb>locali<emph.end type="italics"></emph.end> di costui invogliasse Galileo ad applicar le leggi della meccanica ai <lb></lb>movimenti animali, per la quale applicazione era indispensabile la notizia <lb></lb>dell&#039;anatomia de&#039;muscoli e dell&#039;ossa. </s></p><p type="main">

<s>Essendo cosa certa che, infin dal 1628, aveva l&#039;Harvey pubblicata la <lb></lb>sua Esercitazione anatomica del moto del cuore e del circolo del sangue, <lb></lb>nasce una viva curiosità di sapere in questo proposito qual si fosse l&#039;acco­<lb></lb>glienza fatta da Galileo a un libro, in cui s&#039;annunziava una novità di tanta <lb></lb>importanza. </s>

<s>Dovremo intorno a ciò in altro capitolo intrattenere, non così <lb></lb>come ora in fretta, il discorso, ma, per sodisfare intanto alle prime curio­<lb></lb>sità, basti il dire che la notizia della scoperta arveiana fu recata in Italia <lb></lb>nel 1637 da un medico tedesco, che faceva in Roma anatomiche dimostra­<lb></lb>zioni, alle quali interveniva fra gli altri Raffaello Magiotti. </s>

<s>La circolazione, <lb></lb>che fa il sangue in noi, e che sembrava al Magiotti stesso “ bastante a ri­<lb></lb>volgere tutta la medicina, siccome l&#039;invenzione del Telescopio ha rivolta <lb></lb>tutta l&#039;Astronomia, la Bussola l&#039;economia e l&#039;Artiglieria tutta l&#039;arte mi­<lb></lb>litare ” (Alb. </s>

<s>X, 207) ei la descriveva in una lettera del dì 25 Aprile di <lb></lb>quell&#039;anno 1637 a Famiano Michelini, perchè la riferisse a Galileo, il quale, <lb></lb>per non dire addirittura che poca fede aveva nell&#039;annunziata scoperta, fece <lb></lb>intendere di averla letta <emph type="italics"></emph>con qualche gusto<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>209). Lo stesso Mi­<lb></lb>chelini ne dette parte anche al Baliani, il quale più francamente di Galileo <lb></lb>rispose all&#039;amico che, se gli avesse detto i motivi per cui teneva così sicura <lb></lb>l&#039;opinion dell&#039;Arveo, forse gli avrebbe addotto qualche cosa in contrario ” <lb></lb>(Targioni, Notizie degli aggrandimenti ecc., T. I, Firenze 1780, pag. </s>

<s>204). </s></p><p type="main">

<s>Si par chiaro di qui che la grande innovazione degli studi anatomici e <lb></lb>fisiologici, introdottasi nella scienza dopo la scoperta dell&#039;Harvey, fu pro­<lb></lb>mossa in Italia principalmente per opera del Magiotti e del Michelini, il <lb></lb>quale ebbe una grande efficacia sulla mente del Borelli, a cui fu maestro <lb></lb>ed amico. </s>

<s>Non è però da negare che più d&#039;alto vennero quegli efficacissimi <lb></lb>impulsi, da Galileo cioè e dal Castelli, perchè, sebbene non sentisse esso Ga­<lb></lb>lileo quell&#039;alito di verità, che spirava dalle pagine arveiane, e che si sarebbe <lb></lb>così largamente diffuso a fecondare di sè la scienza, avevano egli e il Ba­<lb></lb>liani, così esperti de&#039;metodi sperimentali, qualche ragionevole motivo di <lb></lb>dubitar di un fatto, che si rendeva, per tanti bene ordinati e concludenti <lb></lb>argomenti probabilissimo, ma che non veniva in verità dimostrato certo da <lb></lb>nessuna sensata esperienza. </s></p><pb xlink:href="020/01/1152.jpg" pagenum="27"></pb><p type="main">

<s>I primi esempii insomma dell&#039;applicazione delle leggi fisiche a spiegare <lb></lb>i varii fatti e le varie passioni della vita, così vegetativa come animale; <lb></lb>esempii ai quali s&#039;informò poi la scuola così detta iatromatematica o iatro­<lb></lb>meccanica, furono dati da Galileo e dal Castelli, veri padri e maestri di ogni <lb></lb>disciplina, ch&#039;ebbe dai loro valenti e numerosi discepoli così larga e fio­<lb></lb>rente cultura. </s>

<s>Non vogliamo di quegli esempii addurne altro che uno, ma <lb></lb>valevole per tutti gli altri, come quello che più a vivo di tutti gli altri ri­<lb></lb>trae le qualità proprie di quella istituzione, ed è l&#039;esempio dell&#039;aria, che ora <lb></lb>restringendosi ora dilatandosi, a seconda che in lei manca o cresce il calore, <lb></lb>fa salire o scendere il liquido in una caraffella, il lungo e sottil collo della <lb></lb>quale, con la sua bocca aperta, in quello stesso liquido s&#039;immerga. </s></p><p type="main">

<s>Galileo applicò il fatto fisico al moto dell&#039;ascesa e della discesa de&#039;suc­<lb></lb>chi nutritizi negli alberi, per l&#039;avvicendarsi dei giorni calorosi con le frigide <lb></lb>notti, e così spiegava in che modo granissero le biade e maturassero i frutti <lb></lb>(Alb. </s>

<s>XIV, 335). Il Castelli poi trovò, in quello stesso fatto fisico, modo a <lb></lb>spiegare un fatto patologico ben più nuovo e più curioso. </s>

<s>Erano a un po­<lb></lb>ver&#039;uomo ferito nel ventre usciti dall&#039;apertura gl&#039;intestini, che rigonfiandosi <lb></lb>gli producevano acerbissimi dolori. </s>

<s>Chiamato a curarlo Giovanni Trullo, <lb></lb>espertissimo chirurgo, che operò anche intorno agli occhi di Galileo, “ ve­<lb></lb>duto ch&#039;ebbe il paziente (dice il Castelli stesso in una lettera al Cesarini, <lb></lb>pubblicata da D. B. Boncompagni) con gran franchezza e risoluzione prese <lb></lb>un&#039;ago, e pungendo in diverse parti quell&#039;intestina, scappando via quel flato <lb></lb>rinchiuso, subito sgonfiarono..... Il caso fu bello ed il rimedio facilissimo <lb></lb>ed intelligibile, ma io rimasi da una difficoltà sopraggiunto, la quale mi ha <lb></lb>dato che pensare assai a questo fatto, poichè alcuni giorni sono, discorrendo <lb></lb>col medesimo signor Trullo di questa cura, egli mi disse che sempre in si­<lb></lb>mili ferite, coll&#039;uscita dell&#039;intestina, seguiva l&#039;istesso accidente del rigon­<lb></lb>fiarsi, e di più che sempre il ferito veniva da crudelissimi dolori tormentato. </s>

<s><lb></lb>In questo mi sovvenne un&#039;esperienza fattami vedere, già più di trentacin­<lb></lb>que anni sono, dal nostro signor Galileo ” (Bullettino di Bibl. </s>

<s>e di Stor. </s>

<s><lb></lb>matem. </s>

<s>ecc., T. XI, Roma 1878, pag. </s>

<s>645). </s></p><p type="main">

<s>L&#039;esperienza è quella della caraffina già detta, e la ragion de&#039;fatti os­<lb></lb>servati nel cannellino di vetro intendeva il Castelli di applicarla ai nuovi <lb></lb>fatti osservati nel tubo dell&#039;intestino. </s>

<s>Se non che vedeva la cosa avvenire <lb></lb>tutto al contrario, perchè l&#039;aria, raffreddandosi nell&#039;intestino uscito fuori del <lb></lb>ventre, avrebbe dovuto produr piuttosto uno sgonfiamento che un tumore. </s>

<s><lb></lb>Allora il nostro primo Iatromeccanico pensò così ragionando di conciliar la <lb></lb>fisica con la fisiologia. </s>

<s>“ Perchè tutte le budella dello stesso animale comu­<lb></lb>nicano senza dubbio una con altra, e con esse gli altri meati di altri vasi <lb></lb>del vivente, come mostrano chiaramente gli Anatomisti, e questa tale comu­<lb></lb>nicanza continuando fino alla respirazione dell&#039;animale, però venendo l&#039;aria, <lb></lb>rinchiusa nelle intestina uscite dal ventre, raffreddata, di necessità vien con­<lb></lb>densata. </s>

<s>E perchè nelle altre intestina e vasi dell&#039;animale si trovano molti <lb></lb>flati, i quali sono facilissimi ad esser mossi o forse cercano l&#039;esito; però <pb xlink:href="020/01/1153.jpg" pagenum="28"></pb>questi flati entrano nelle uscita intestina e le rigonfiano. </s>

<s>Che se io non du­<lb></lb>bitassi in queste difficilissime materie di Medicina d&#039;inciampare, non essendo <lb></lb>mia professione, direi di più che, stante la ferita, accendendosi nel corpo <lb></lb>dell&#039;animale il calor febbrile, ancora questo calore può cooperare al rigon­<lb></lb>fiamento delle budella fuori del ventre, imperocchè, riscaldandosi di sover­<lb></lb>chio le parti interne dell&#039;animale, è necessario che cagionino la dilatazione <lb></lb>de&#039;flati rinchiusi nel ventre. </s>

<s>Quindi con maggior forza ed impeto trapassano <lb></lb>nelle parti delle intestina di già uscite e le rigonfiano ” (ivi, pag. </s>

<s>648). </s></p><p type="main">

<s>Un altro esempio notabilissimo di questa applicazione dei fatti fisici a <lb></lb>spiegar le più misteriose funzioni della vita, ad imitazione di ciò che gli <lb></lb>aveva insegnato a fare il suo maestro Castelli, ce l&#039;offre il Magiotti, il quale <lb></lb>appena ebbe scoperta la renitenza certissima dell&#039;acqua alla compressione, <lb></lb>ed ebbe inventato il vario e graziosissimo modo di que&#039;suoi giochetti idro­<lb></lb>statici, vide nel pronto operar del dito sui boccioli pieni d&#039;acqua il segreto <lb></lb>artificio, con cui la volontà e gl&#039;istinti degli animali operano sui nervi e sui <lb></lb>muscoli a muovere in una o in altra parte, a piacere, le varie membra. </s>

<s>Il <lb></lb>Borelli ritrovò in questo stesso fatto idrostatico uno de&#039;principali fondamenti <lb></lb>alla sua teoria fisica de&#039;moti muscolari, ma prima di venire a veder più <lb></lb>d&#039;appresso e a comprendere tutta in uno sguardo l&#039;opera di chi istituì la <lb></lb>scuola iatromeccanica, giova commemorare altri suoi più immediati maestri, <lb></lb>e valutar l&#039;efficacia, ch&#039;ebbero in quella nuova istituzione i loro insegna­<lb></lb>menti e i loro esempi. </s></p><p type="main">

<s>Primo e principale fra que&#039;maestri, dopo Galileo e il Castelli, sarebbe <lb></lb>da annoverare il Torricelli, per questa sola ragione, perchè fu egli che <lb></lb>instaurò la Fisica sperimentale. </s>

<s>Ma perchè egli stesso applicò direttamente <lb></lb>le sue esperienze a soggetti varii di storia naturale, e perchè nelle inven­<lb></lb>zioni de&#039;suoi strumenti ebbe di mira l&#039;applicazione anche agli usi medici, <lb></lb>ha perciò un particolar diritto e un merito speciale d&#039;entrar nel numero <lb></lb>de&#039;precursori iatromeccanici. </s></p><p type="main">

<s>Che veramente applicasse il Torricelli le sue esperienze del vuoto a <lb></lb>varii e importantissimi soggetti di Storia naturale ne fanno pubblica testi­<lb></lb>monianza gli Accademici del Cimento, i quali lasciarono così scritto: “ Infin <lb></lb>dal tempo che il Torricelli inventò la prima esperienza dell&#039;argentovivo, ebbe <lb></lb>anche pensiero di rinchiudere nello spazio voto diversi animali, per osser­<lb></lb>vare in essi il moto, il volo, il respiro ed ogni altro eccidente che quivi pa­<lb></lb>tissero. </s>

<s>Vero è che, non avendo egli per allora strumenti a proposito per <lb></lb>questa prova, si contentò di farla com&#039;ei potette ” (Saggi di natur. </s>

<s>esper., <lb></lb>Firenze 1841, pag. </s>

<s>67). </s></p><p type="main">

<s>Fu questa notizia senza dubbio suggerita al Segretario dell&#039;Accademia <lb></lb>dal Borelli, il quale, non potendo attingerla altronde, la raccolse da quelle <lb></lb>cartucce disperse, che trovò in Roma uniche e desolate fra la spazzatura <lb></lb>della casa, dov&#039;era infelicemente morto di peste Raffaello Magiotti. </s>

<s>Attesta <lb></lb>il Borelli stesso che si contenevano in quelle carte notate quasi tutte l&#039;espe­<lb></lb>rienze del vuoto fatte poi dagli Accademici del Cimento, ond&#039;è lecito, dietro <pb xlink:href="020/01/1154.jpg" pagenum="29"></pb>questi accenni, immaginar come cosa vera una grande operosità nel Torri­<lb></lb>celli, che da Firenze suggeriva l&#039;esperienze, e nel Magiotti, che in Roma <lb></lb>le eseguiva. </s>

<s>Considerando poi l&#039;inclinazione e il grande amore, con cui il <lb></lb>Magiotti stesso prediligeva gli studi anatomici e fisiologici, è lecito altresì <lb></lb>pensare che molte più e di più vario argomento delle commemorate dagli <lb></lb>Accademici fiorentini fossero l&#039;esperienze da&#039;due amici tentate in soggetto <lb></lb>di Storia naturale. </s>

<s>Che se di tanta operosità fosse rimasto qualche pubblico <lb></lb>documento, non aveva forse a gloriarsi il Pecquet d&#039;essere stato il primo <lb></lb>ad illustrar la scienza anatomica e fisiologica co&#039;suoi nuovi applauditi espe­<lb></lb>rimenti. </s></p><p type="main">

<s>Che poi il Torricelli, nell&#039;inventare i suoi varii strumenti, non avesse <lb></lb>solo in mira di compiacere al granduca Ferdinando, ma di provvedere alla <lb></lb>pubblica utilità, per ciò che più particolarmente concerne la cura degl&#039;in­<lb></lb>fermi, lo attesta una scrittura, forse composta dal Viviani, e in ogni modo <lb></lb>copiata dalla propria mano di lui, e che s&#039;intitola “ Fabbrica ed uso degli <lb></lb>strumenti di vetro inventati dal serenissimo granduca Ferdinando II per <lb></lb>esaminar l&#039;aria, l&#039;acqua, i vini e per altre curiosità ” (MSS. Cim., T. X, <lb></lb>c. </s>

<s>227). Gli strumenti quivi descritti si riducono alle varie maniere di Pe­<lb></lb>saliquori e di Termometri, e alcuni di questi s&#039;applicano all&#039;uso di cono­<lb></lb>scere quando l&#039;uova sono in punto per darsi a bevere a chi è infermo o di <lb></lb>stomaco troppo delicato. </s></p><p type="main">

<s>Dop&#039;aver descritti “ gli strumentini serrati con migliarole di piombo <lb></lb>dentro, e col collo diviso in gradi 35 ad uso di conoscere le maggiori o mi­<lb></lb>nori gravità in specie de&#039;vini, che vengono dimostrate dal maggiore o minor <lb></lb>numero di gradi, che sopravanzano al livello di essi vini ” (ivi) così, nella <lb></lb>citata Scrittura, si soggiunge: “ Gli strumentini serrati, col collo diviso in <lb></lb>gradi 60, servono a questo che, ponendo a cuocere in acqua fredda del­<lb></lb>l&#039;uova, benchè senza bucare, con immergervi nell&#039;istesso tempo uno di que­<lb></lb>sti strumenti, quando il liquore in esso contenuto sarà salito, per mezzo del <lb></lb>calor dell&#039;acqua, al minore de&#039;due numeri di gradi segnati di bianco in <lb></lb>cima a detto strumento, allora l&#039;uova saranno da bere. </s>

<s>E quando ascenderà <lb></lb>al maggior numero, allora saranno bazzotte, cioè nello stato mezzano tra le <lb></lb>lattate e le sode ” (ivi). </s></p><p type="main">

<s>Di un&#039;altra foggia di Termometro, accomodato ad uso di conoscere l&#039;in­<lb></lb>tensità del calor febbrile, si dice: “ Gli strumenti fatti a foggia di botticina, <lb></lb>con sei palline dentro, legati al braccio di un febbricitante, dimostrano, col <lb></lb>maggiore o minor numero di palline che discendono, il maggiore o minor <lb></lb>calore del paziente ” (ivi, c. </s>

<s>229). </s></p><p type="main">

<s>Eccitato dalle parole, che scrivevagli da Roma il Magiotti, e stimolato <lb></lb>da questi esempii del Torricelli, che apparivano tanto più luminosi, in quanto <lb></lb>venivano dati nella stessa aula del Granduca, il Michelini, presi per fonda­<lb></lb>mento i tre fatti oramai dimostrati dell&#039;insensibile traspirazione, del moto <lb></lb>del chilo, e del circolo del sangue, instituì un nuovo sistema di medicina <lb></lb>e d&#039;igiene. </s>

<s>Fosse per non essere entrato bene addentro nella struttura ana-<pb xlink:href="020/01/1155.jpg" pagenum="30"></pb>tomica del corpo umano, o per adattarsi alla capacità delle intelligenze <lb></lb>volgari, presentando la Fisiologia sotto forma di apologo, egli usa un lin­<lb></lb>guaggio figurato. </s>

<s>“ Io suppongo, egli dice, che il nostro corpo sia uno stru­<lb></lb>mento composto d&#039;innumerabili canali grandi, piccoli e minimi. </s>

<s>Suppongo <lb></lb>ancora esservi una cosa, che li muova tutti, e questi io chiamo i lavoranti, <lb></lb>ed i canali grandi e piccoli le botteghe. </s>

<s>Certi pezzi di carne, come il fegato, <lb></lb>il cuore, il pancreas chiamo strumentini da lavorare, stritolare e muovere, <lb></lb>e fare scorrere le robe lavorate d&#039;una in altra bottega ” (Targioni, Noti­<lb></lb>zia cit., T. II, P. I, pag. </s>

<s>223). </s></p><p type="main">

<s>Come si potesse ridurre questo sistema, che tanto si rassomiglia a un <lb></lb>romanzo, alla precisione geometrica, non è per verità così facile intendere, <lb></lb>ma pure il Michelini seriveva al principe Leopoldo che andava “ riducendo <lb></lb>la Filosofia medica, come le cose matematiche o di Euclide, dai primi prin­<lb></lb>cipii ” (ivi, T. I, pag. </s>

<s>200). In qualunque modo, piglia lo stesso apologo nel <lb></lb>Michelini la forma iatromatematica, per quel che di vero e di reale hanno <lb></lb>i fatti fisiologici della circolazione del sangue e del moto del chilo ivi adom­<lb></lb>brati, e quando non si volesse attribuire all&#039;Autore altro merito, non si po­<lb></lb>trebbe negar ch&#039;egli fu de&#039;primi in Italia, ch&#039;ebbe fede nella scoperta ar­<lb></lb>veiana, e che sentì la grande efficacia che avrebbe avuto in ridur l&#039;arte <lb></lb>medica a qualche grado di scienza. </s>

<s>Ripensando ora alla reputazione ch&#039;ebbe <lb></lb>in matematica don Famiano, e al magistero ch&#039;esercitò sul Borelli infino <lb></lb>alla morte, si giudicherà qual parte di merito gli competa in quella istitu­<lb></lb>zione iatromeccanica, la quale occorse al discepolo, scendendogli da più <lb></lb>parti, come rivi d&#039;acque correnti, che vanno a riversarsi insieme nell&#039;alveo <lb></lb>d&#039;un gran fiume. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Discepolo affezionatissimo del Castelli, come poi del Michelini, a cui <lb></lb>venne da Pisa a consolare le agonie della morte, ammiratore dell&#039;ingegno, <lb></lb>e inquisitor diligente degli studii del Torricelli e del Magiotti, il Borelli trovò <lb></lb>ne&#039;loro insegnamenti il principio a quelle dottrine, che avrebbe poi larga­<lb></lb>mente svolte nella grande Opera Dei moti animali. </s>

<s>Doveva esser questa la <lb></lb>corona della sua vita e de&#039;suoi studii, e infatti egli morì appena preparato <lb></lb>il manoscritto da servir per la stampa, a cui si legge con mesto pensiero <lb></lb>premessa la dedica alla Regina di Svezia, sotto signata dal Collegio delle <lb></lb>Scuole Pie in S. </s>

<s>Pantaleone di Roma, nel Dicembre del 1679. Divisa l&#039;Opera <lb></lb>in due Parti, gli Scolopi, che ospitaron l&#039;Autore, e poi ne furono eredi, <lb></lb>pubblicarono nella stessa Roma la prima parte nel 1680, e la seconda nel­<lb></lb>l&#039;anno appresso. </s></p><p type="main">

<s>Che veramente, come della vita, così fosse il trattato <emph type="italics"></emph>De motu anima­<lb></lb>malium<emph.end type="italics"></emph.end> la corona degli studii del Borelli, si può asseverar dal sapere che, <pb xlink:href="020/01/1156.jpg" pagenum="31"></pb>nella stessa intenzione di lui, non furono gli altri libri presi a scrivere per <lb></lb>altro fine, che per prepararsi a quest&#039;ultimo, a cui da più che vent&#039;anni <lb></lb>s&#039;appuntavano tutti i suoi pensieri. </s>

<s>Dall&#039;altra parte i teoremi di Meccanica <lb></lb>dimostrati nel trattato <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> che è il primo di que&#039;due libri <lb></lb>preparatorii, e i principii della Fisica ricercati ed esposti nel trattato <emph type="italics"></emph>De mo­<lb></lb>tionibus naturalibus,<emph.end type="italics"></emph.end> che è il secondo di que&#039;libri, dicono abbastanza chiaro <lb></lb>che il fine dell&#039;Autore era quello di applicare alla nuova scienza della vita <lb></lb>animale le leggi de&#039;moti già dimostrate, e i fatti già sperimentati nella ma­<lb></lb>teria bruta. </s></p><p type="main">

<s>Era in ogni modo necessario conoscere la fabbrica del corpo animale, <lb></lb>a che non tornarono sufficienti le descrizioni, com&#039;erano state fatte dagli <lb></lb>Anatomici fino a que&#039;tempi, ma ci volevano anatomie particolari, che servis­<lb></lb>sero di fondamento ai nuovi studii e di conferma alle nuove speculazioni. </s>

<s>E <lb></lb>perchè il Borelli non si sentiva per sè stesso inclinato a trattare i ferri, si <lb></lb>servì della mano di altri, a cui suggeriva i suoi stessi pensieri, e cosi venne <lb></lb>educando, nella sua propria casa, una scuola, che fece non solamente pro­<lb></lb>gredire, ma dette abito nuovo all&#039;Anatomia. </s></p><p type="main">

<s>Il bolognese Carlo Fracassati fu uno de&#039;primi e principali, che fioris­<lb></lb>sero in quella scuola, ed egli stesso confessa nelle sue Dissertazioni l&#039;effi­<lb></lb>cacia che, a fargli in anatomia scoprir cose nuove, ebbero i pensieri, di che <lb></lb>sempre era feconda la gran mente del Borelli. </s>

<s>Nella Esercitazione epistolica <lb></lb><emph type="italics"></emph>De cerebro,<emph.end type="italics"></emph.end> raccolta fra le Opere del Malpighi, descritta ch&#039;egli ivi ha la <lb></lb>struttura anatomica delle branchie de&#039;pesci, e le parti in esse ordinate a ri­<lb></lb>cevere i vasellini sanguigni “ ut pluries, soggiunge, apud excellentissimum <lb></lb>Borellum Pisis, qui rerum novarum repertor, sectiones anatomicas promovet <lb></lb>et perdite peperit, sum expertus ” (Lugduni Batav. </s>

<s>1687, T. II, pag. </s>

<s>143). </s></p><p type="main">

<s>In questa stessa esercitazione <emph type="italics"></emph>De cerebro,<emph.end type="italics"></emph.end> nella quale, senza volere ap­<lb></lb>parire, il Fracassati aggiunge all&#039;anatomia di quel viscere molte e impor­<lb></lb>tantissime cose lasciate indietro dal Malpighi, accenna alla invenzione del <lb></lb>coagulare il sangue nel cuore e nelle vene, da che tanti vantaggi si ripro­<lb></lb>metteva l&#039;Anatomia, la Fisiologia e la Medicina. </s>

<s>Ei ne attribuisce, con esem­<lb></lb>pio rarissimo nella storia, il merito principale a Silvestro Bonfiglioli, ch&#039;egli <lb></lb>chiama il suo Oreste, e non piglia per sè altra parte a quel merito, che di <lb></lb>aver messo in esecuzione, nell&#039;anfiteatro pisano, il ritrovato del carissimo <lb></lb>suo concittadino ed amico (ivi, pag. </s>

<s>158). Il Borelli però ci rivela il vero <lb></lb>Autore dell&#039;invenzione, scrivendo così in una lettera del dì 6 Marzo 1665, <lb></lb>diretta da Pisa al principe Leopoldo: “ Il signor Fracassati ha speculato ed <lb></lb>esperimentato il modo d&#039;accagliare il sangue nel cuore e nelle vene, e con <lb></lb>tale artifizio non solo si scoprono i vasi lattei ed altre cose minutissime .... <lb></lb>ma altri stravaganti effetti ” (MSS. Cim., T. XVIII, c. </s>

<s>126). </s></p><p type="main">

<s>Si sente per queste relazioni la premura e la compiacenza, che prova­<lb></lb>vano il Principe e il Maestro in promovere nell&#039;Ateneo toscano gli studii <lb></lb>anatomici, e il Borelli dà spesso nelle sue lettere sfogo a quei sentimenti, <lb></lb>trattenendovisi, a somiglianza degli agricoltori, a riguardar l&#039;ubertà de&#039;frutti <pb xlink:href="020/01/1157.jpg" pagenum="32"></pb>maturati sui rami a questo e a quell&#039;altro albero irrorati tutti dalle stille <lb></lb>del cielo, e dai propri sudori. </s>

<s>Uno di questi alberi più ubertosi infino dalla <lb></lb>giovanezza allevato dal Borelli fu il Bellini, di cui così scrive il dì 17 Mag­<lb></lb>gio 1662 allo stesso Principe, dopo varie altre notizie: “ Do poi nuova a <lb></lb>V. A. come Lorenzo Bellini ha finito di comporre le sue esercitazioni ana­<lb></lb>tomiche della struttura ed uso de&#039;Reni ” (ivi, T. XVII, c. </s>

<s>170). </s></p><p type="main">

<s>Diremo a suo luogo quale efficacia avesse esso Borelli sul coltello ana­<lb></lb>tomico menato dal Bellini intorno alla lingua, per iscoprirvi il vero organo <lb></lb>del gusto, ma non è da tacere intanto di un illustre straniero, Claudio Au­<lb></lb>bery, il quale, benchè fosse pubblico professore di Anatomia nella scuola <lb></lb>antica pisana, risentì nulladimeno i benefici influssi, che venivano sull&#039;arte <lb></lb>del dissecare dalle speculazioni di chi istituiva fra noi una scuola nuova. </s>

<s>In <lb></lb>casa di lui, in Pisa, uel 1657, mostrò l&#039;Aubery la struttura e gli organi se­<lb></lb>cretori ne&#039;didimi del cinghiale, essendovi presente anche il Malpighi. </s>

<s>“ Postea <lb></lb>idem Auberius meo suasu pulcherrimam hanc observationem typis excudit, <lb></lb>addita eleganti aenea figura Florentiae eodem anno ” (De Motu anim., Pars II, <lb></lb>Romae 1681, pag. </s>

<s>342). </s></p><p type="main">

<s>Quel Malpighi però, che vien così in ultimo luogo commemorato, è il <lb></lb>primo per meriti fra coloro, che s&#039;educarono alle discipline anatomiche nella <lb></lb>nuova scuola istituita dal Borelli. </s>

<s>Narra il Malpighi stesso nella sua <emph type="italics"></emph>Auto­<lb></lb>biografia<emph.end type="italics"></emph.end> com&#039;essendo venuto in Pisa coabitasse con Girolamo Barbato, che <lb></lb>insegnava in quel fiorente studio toscano la medicina pratica. </s>

<s>Egli era, il <lb></lb>Barbato, attaccatissimo alle dottrine di Galeno e de&#039;più antichi Maestri, e <lb></lb>benchè ne&#039;privati e familiari colloqui s&#039;attentasse di propor talvolta inda­<lb></lb>gini nuove, pareva nonostante ch&#039;egli facesse ciò per confutare i placiti al­<lb></lb>trui, piuttosto che consolidare i suoi proprii. </s>

<s>“ Interea, prosegue a dire il <lb></lb>Malpighi, pro exercenda exponendaque. </s>

<s>Anatomia clarissimus D. </s>

<s>Claudius <lb></lb>Uberius Patavio Pisas evocatur, qui doctissimi D. </s>

<s>Borelli domi frequentes <lb></lb>habebat animalium sectiones, inter quas celebris est ea qua, me praesente, <lb></lb>innotuit testium structura intestinalis compaginata, in Apro deprehensa, et <lb></lb>sub nomine Vavelii Dathirii Bonclari evulgata. </s>

<s>Tunc pariter in Serenissi­<lb></lb>mis M. D. et principibus ingens excitata est curiositas rerum anatomicarum <lb></lb>et physicarum, unde quotidianae in Aula ipsa exercitationes Anatomiae in <lb></lb>variis brutis exercebantur, quibus interpositis graviores politicae curae tem­<lb></lb>perabantur. </s>

<s>Hinc famosa celebrisque Cimenti Academia excitata est ” (Opera <lb></lb>posthuma, Londini 1697, pag. </s>

<s>4). </s></p><p type="main">

<s>Che da tale occasione avesse origine la celebre Accademia è credibilis­<lb></lb>simo, e verrebbe solennemente da questo fatto testimoniato il carattere pro­<lb></lb>prio della istituzione borelliana, nella quale l&#039;Anatomia si disposava colla <lb></lb>Fisica. </s>

<s>Come poi prevalesse nelle sessioni accademiche l&#039;esercizio delle espe­<lb></lb>rienze a quello delle dissezioni, non è difficile intenderlo dietro ciò che si <lb></lb>disse nel nostro Discorso preliminare, a cui rimandando i lettori, pensiam <lb></lb>dì ritornare al Malpighi promotore validissimo della scienza, intorno alla <lb></lb>quale ha da trattenersi la nostra Storia. </s></p><pb xlink:href="020/01/1158.jpg" pagenum="33"></pb><p type="main">

<s>Abbiamo udito dalla sua propria bocca come si sentisse chiamato al­<lb></lb>l&#039;Anatomia dalle dissezioni vedute fare all&#039;Aubory nelle case del Borelli, a <lb></lb>cui, tornato a Bologna, dedicò la prima insigne scoperta delle vescicole e <lb></lb>delle cellule de&#039;polmoni. </s>

<s>Presto però si alienarono gli animi, intorno a che <lb></lb>lasciò così scritto il Malpighi nella sopra citata autobiografia. </s>

<s>“ Miraberis, <lb></lb>lector, doctissimum Joannem Alphonsum Borellum, quem nuper amice mea­<lb></lb>rum Epistolarum editionem sollicitantem audivimus, nunc contradicentem <lb></lb>castigantemqque erumpere. </s>

<s>Huius autem impulsiva causa ea fuit quoniam, <lb></lb>intermisso a me litterario cum ipso commercio, ita in me meaque indigna­<lb></lb>bundus exarsit, ut in his quae ultimo senio composuit, qualia sunt De ani­<lb></lb>malium motu, occasionem arripuerit mea infirmandi ” (ibi, pag. </s>

<s>5). </s></p><p type="main">

<s>Che fosse questo il solo o il principal motivo, per cui il Borelli alienò <lb></lb>e convertì l&#039;animo iroso contro il Malpighi, non è da credere in un tal uomo: <lb></lb>stillavano quelle amarezze da fonti più segrete, che il nostro Autobiografo <lb></lb>o non sospettò, o non si curò di ricercare, ma che non è molto difficile a <lb></lb>noi di penetrarle. </s>

<s>Le nuove cose, che in Anatomia andava scoprendo il Mal­<lb></lb>pighi, e le speculazioni, ch&#039;egli ammanniva dietro a quelle scoperte, lo vol­<lb></lb>gevano per una via diversa, da quella che il Borelli avea prescritta alla sua <lb></lb>scuola, e sulla quale s&#039;erano sempre tenuti, il Fracassati e il Bellini. </s>

<s>Il Mi­<lb></lb>croscopio, felicemente applicato ad osservar le parti dissecate ne&#039;cadaveri <lb></lb>degli animali e ne&#039;tronchi degli alberi, fece penetrare il Malpighi addentro <lb></lb>alla composizione degli organi, per cui, risalendo di costì a filosofare intorno <lb></lb>alle funzioni della vita, sentì vivamente il bisogno di un&#039;arte più sottile di <lb></lb>quel che non fosse la Fisica borelliana. </s>

<s>Si fece sentir cotesto bisogno in sul <lb></lb>primo entrare alle microscopiche scoperte fatte intorno alla compagine dei <lb></lb>polmoni, e la natura delle vescicole, rivelando l&#039;azione immediata dell&#039;aria <lb></lb>sul sangue, dette luogo a speculare sull&#039;ematosi, intorno a che nacque fra <lb></lb>il Borelli e il Malpighi una delle principali divergenze. </s></p><p type="main">

<s>È giusto da queste divergenze che si rivela come il Malpighi incli­<lb></lb>nasse a invocare la iatrochimica, la quale derivava dal Cartesio, come la <lb></lb>iatrofisica professata dal Borelli derivava da Galileo. </s>

<s>Non è già che il grande <lb></lb>Anatomico di Bologna, e che aveva in Pisa imbevuti i principii della scienza <lb></lb>nelle case del Borelli, intendesse di disertare dalla Scuola italiana, ma vo­<lb></lb>leva, con consiglio che si dee dire sapiente, delibar anche dalla Filosofia del <lb></lb>Cartesio quel che ci avesse di buono o che facesse al bisogno. </s>

<s>È perciò che <lb></lb>nella Autobiografia, dop&#039;aver raccontato come Ovidio Montalbani persuadesse <lb></lb>il Rettore dell&#039;Università di Torino a proporre ai giovani dottorandi in me­<lb></lb>dicina questa formula di giuramento: “ iurabis doctrinam eam te servatu­<lb></lb>rum et defensurum esse quae publice praelegitur in archigymnasio bono­<lb></lb>niensi, aliisque in studiis famosis, secundum eos Auctores a tot saeculis iam <lb></lb>approbatos, qui explicandi et declarandi per Gymnasiarchas doctoribus et <lb></lb>professoribus ipsis proponuntur, Aristotilem nempe, Galenum et Hippocra­<lb></lb>tem ” (ibi, pag. </s>

<s>21), il Malpighi brevemente toccando de&#039;progressi, che aveva <lb></lb>fatto la scienza nel succedersi di tanti secoli, protesta anch&#039;egli di volerla <pb xlink:href="020/01/1159.jpg" pagenum="34"></pb>coltivare a quel modo, che avevano ultimamente insegnato il Cartesio e il <lb></lb>Castelli. </s>

<s>“ Haec itaque a Graecis exculpta, subsequentibus Arabum Barba­<lb></lb>rorumque dogmatibus inquinata iacuit, donec vigentibus hoc saeculo iterum <lb></lb>Anatomicis studiis incrementum coepit, et mechanicis firmata fortiori talo <lb></lb>stare coepit. </s>

<s>Cum igitur Graecorum et antiqua Italorum sapientia apud Si­<lb></lb>culos olim floruerunt et novis Cartesii Castellique inventis vigere coeperit, <lb></lb>hanc eamdem excolendam me professurum pollicitus sum ” (ibi, pag. </s>

<s>25). </s></p><p type="main">

<s>La nuova Fisica insomma e la nuova Meccanica applicate alle scienze <lb></lb>mediche le riconosceva il Malpighi derivar da due fonti, dal Castelli o da <lb></lb>Galileo e dal Cartesio, il quale coltivando a preferenza la fisica sottile o mo­<lb></lb>lecolare, ch&#039;era un&#039;ombra della chimica moderna, secondava molto il genio <lb></lb>di quello stesso Malpighi investigator così acuto de&#039;sottilissimi stami, di che <lb></lb>s&#039;intesse la vita. </s>

<s>S&#039;aggiunga di più che il Cartesio aveva insegnato a filoso­<lb></lb>fare intorno all&#039;uomo e intorno alle passioni di lui da fisiologo, mentre che <lb></lb>Galileo si rimase indifferente alle grandi scoperte dell&#039;Asellio e dell&#039;Harveio, <lb></lb>e il Castelli non ebbe appena messo il piede in quel campo, che lo ritrasse, <lb></lb>protestando non esser quella la sua professione. </s></p><p type="main">

<s>Il Cartesio recò anche nell&#039;Anatomia i suoi vizii filosofici, i quali prin­<lb></lb>cipalmente consistono nel volere accomodare i fatti alla ragione. </s>

<s>Distingue <lb></lb>nella fabbrica del corpo umano due parti: una visibile, la quale egli dice si <lb></lb>può ciascuno far mostrare ai periti dell&#039;arte; un&#039;altra invisibile, di che egli <lb></lb>solo intende farsi a tutti gli altri maestro. </s>

<s>“ Non haereo, scriveva nell&#039;in­<lb></lb>troduzione al trattato <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end> in describendis ossibus, nervis, musculis, <lb></lb>venis, arteriis, stomacho, iecore, corde, cerebro et partibus omnibus aliis.... <lb></lb>quas curare quis potest sibi demonstrari a perito Anatomico..... Et quan­<lb></lb>tum ad partes, quae ob parvitatem suam visibiles non sunt, eas facilius et <lb></lb>clarius potero notas facere, tractando de motibus qui pendent inde ” (Fran­<lb></lb>cofurti ad M. 1692, pag. </s>

<s>2). </s></p><p type="main">

<s>Passando infatti, nella seconda parte del libro a trattare de&#039;moti mu­<lb></lb>sculari, egli immaginò che spiri dal cervello un vento, il quale entrando e <lb></lb>uscendo per opportune valvole ne&#039;muscoli ora gli fa inturgidire, ora sgon­<lb></lb>fiare. </s>

<s>I condotti di quel vento e le valvole nessuno Anatomico le aveva po­<lb></lb>tute vedere, ma ciò non vuol dir niente, rispondeva il Cartesio, perchè ho <lb></lb>detto che sono invisibili, e da un&#039;altra parte come potrebbe meglio operar <lb></lb>la Natura di quel che la mia Filosofia così sottilmente le insegna? </s>

<s>— Or, <lb></lb>queste al Borelli, discepolo de&#039;discepoli di Galileo, sembravan pazzie, nè po­<lb></lb>teva perciò patire che nessuno Italiano disertasse dalle sapienti instituzioni <lb></lb>della sua propria scuola, per andar dietro alle follie della scuola straniera. </s>

<s><lb></lb>Tanto meno poteva ciò sopportare quell&#039;uomo sdegnoso nel Malpighi, a cui <lb></lb>aveva egli stesso instillati gli schietti principii della Filosofia galileiana. </s></p><p type="main">

<s>I vizii propri al razionalismo cartesiano, che aveva si può dire sedotto <lb></lb>il mondo filosofico di que&#039;tempi, venivan nonostante palliati agli occhi degli <lb></lb>Anatomici dal vedere il Cartesio stesso lasciar da parte le finzioni della <lb></lb>mente, per risolversi a toccar con mano i fatti concernenti i moti del cuore, <pb xlink:href="020/01/1160.jpg" pagenum="35"></pb>e poi rivolgersi a quella grande autorità dell&#039;Harvey, per dirgli che stavano <lb></lb>in tutt&#039;altro modo da ciò che gli avea descritti. </s>

<s>Vedremo a suo luogo come, <lb></lb>anche in questi seducenti modi di argomentare dalle esperienze e dai fatti <lb></lb>osservati nelle vivisezioni, fossero riconosciuti i soliti vizii filosofici, i quali <lb></lb>forse potevansi scusare in quel trattato, dove insegnavasi per la prima volta <lb></lb>a studiar l&#039;uomo, non nelle metafisiche astrattezze, ma nella fisiologia degli <lb></lb>organi del corpo, e nell&#039;anatomia di quegli strumenti, di che si serve l&#039;anima <lb></lb>per impossessarsi del mondo, e per esercitare il pensiero. </s>

<s>Molte altre son <lb></lb>le fisiologiche dottrine che ricorrono nel trattato <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end> e che sono in­<lb></lb>fette non solamente di errori, ma di vizii proprii al razionalismo peripate­<lb></lb>tico cartesiano, e nonostante il vederle assunte dal Filosofo, che le riveste <lb></lb>dell&#039;affascinante splendore della sua eloquenza, invitava a ricever le inspi­<lb></lb>razioni da lui e a pigliar l&#039;abito di quel suo filosofare molti, anche di quei <lb></lb>che attendevano allo studio del corpo umano e delle sue funzioni. </s>

<s>Si distinse <lb></lb>fra costoro in Italia Tommaso Cornelio, il quale coltivò l&#039;Anatomia e la Fi­<lb></lb>siologia in quell&#039;Accademia di Napoli, dove Luca Antonìo Porzio instaurava <lb></lb>con tanto zelo la Fisica del Cartesio. </s>

<s>Notabile che il Cornelio si professi di­<lb></lb>scepolo di Michelangiolo Ricci, e dedichi una sua scrittura in segno di ami­<lb></lb>cizia al Borelli, il quale forse non lo avversò come avversava il Malpighi, <lb></lb>perchè lo sentiva meno potente a infirmare la sua istituzione, lo zelo verso <lb></lb>la quale veniva sollecitato dall&#039;amor proprio, che gli suggeriva dover egli <lb></lb>solo costituirsi principe della Scuola iatromeccanica. </s>

<s>Fu perciò ch&#039;egli ebbe <lb></lb>a studiarsi di far dimenticare l&#039;opera di alcuni suoi predecessori, e come ciò <lb></lb>gli succedesse felicemente, così per i meriti propri, come per gli eventi na­<lb></lb>turali, è ciò che intorno al presente soggetto ora a noi resta a narrare. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Antonio Deusing pubblicava in Croninga, nel 1661, le sue esercitazioni <lb></lb><emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> dove tratta particolarmente del moto de&#039;muscoli e <lb></lb>della respirazione. </s>

<s>Egli però, ferventissimo Galenista e ritroso ad ammettere <lb></lb>qualunque novità si volesse introdur nella scienza, non fa, rispetto ai moti <lb></lb>animali, altro che commentare e svolgere a suo modo i concetti meditati sui <lb></lb>libri del suo antico Maestro. </s>

<s>Il Muller e lo Charletton, contro i quali prin­<lb></lb>cipalmente insorge il Deusingio, intendevano di sostituire allo spiritalismo <lb></lb>galenico la fisica del fluido nerveo, iniziando così le ipotesi, che verrebbero <lb></lb>sotto tanto varie forme proposte da&#039;Fisiologi successori, ma Niccolò Stenone <lb></lb>riconobbe esser quelle ipotesi troppo affrettate, e che bisognava apparec­<lb></lb>chiarvisi con una più diligente Anatomia muscolare. </s>

<s>A tale intento pubblicò <lb></lb>in Amsterdam, nel 1664, il suo Saggio di osservazioni <emph type="italics"></emph>De musculis et glan­<lb></lb>dulis,<emph.end type="italics"></emph.end> dove l&#039;arte del sezionare par da quelle descrizioni che sia giunta <pb xlink:href="020/01/1161.jpg" pagenum="36"></pb>oramai alla sua maggior perfezione. </s>

<s>Venuto in Toscana, per le virtù e per <lb></lb>la scienza si rese in pregio e amabilissimo ai principi Medicei, e ai dotti <lb></lb>che fiorivano nella loro Accademia e nella Università di Pisa, dove infin d&#039;al­<lb></lb>lora il Borelli, dietro esperienze instituite sopra ogni genere di animali, <lb></lb>speculava intorno a quella ch&#039;egli era solito dire sua nuova e maravigliosa <lb></lb>Filosofia. </s></p><p type="main">

<s>Tra gli Accademici del Cimento, co&#039;quali si legò lo Stenone in più in­<lb></lb>tima amicizia, fu Vincenzio Viviani, il quale, concorrendo a gara col Borelli <lb></lb>in ogni altra delle varie parti in che si distingueva la scienza naturale, per <lb></lb>questa sola si sentiva rimanere indietro, che concerne gli organi degli ani­<lb></lb>mali, non avendo avuto occasione d&#039;esercitarvisi, nè comodità di servirsi <lb></lb>della mano de&#039;Notomisti pisani. </s>

<s>Ma quand&#039;ei ritrovò nello Stenone, intrat­<lb></lb>tenuto seco ai servigi di corte in Firenze, quel che aveva in Pisa il Borelli <lb></lb>ritrovato nell&#039;Aubery, nel Fracassati e nel Bellini, e allora fu che, trasfor­<lb></lb>matesi le prime emulazioni in fierissime inimicizie, pensò a fare ogni opera <lb></lb>perchè si avesse a disdire chi, colle parole, senza ancora mostrare in pub­<lb></lb>blico i fatti, si diceva primo Autore e maestro di una nuova Filosofia ma­<lb></lb>tematica applicata agli organi e alle funzioni della vita. </s></p><p type="main">

<s>Discorrevano ne&#039;frequenti colloqui lo Stenone e il Viviani de&#039;loro stu­<lb></lb>dii, cosicchè la Geometria dell&#039;uno, riscontrandosi con l&#039;Anatomia dell&#039;altro, <lb></lb>strinsero, senz&#039;avvedersene, insieme un maraviglioso connubio. </s>

<s>Fermo l&#039;Ana­<lb></lb>tomico danese nel suo primo proposito, che cioè fosse necessario descrivere <lb></lb>i muscoli con più diligenza di quel che non si fosse fatto per lo passato, si <lb></lb>studiava di ridurli alle loro proprie forme distinte, sotto gli occhi del Vi­<lb></lb>viani, che intravedeva in quelle stesse forme il sapiente magistero della geo­<lb></lb>metrizzante Natura. </s>

<s>Ebbe di qui origine lo <emph type="italics"></emph>Specimen Myologiae,<emph.end type="italics"></emph.end> ossia la <lb></lb>Descrizione geometrica de&#039;muscoli, e perchè, venendo pubblicato e dedicato <lb></lb>il libro al granduca Ferdinando II a nome dello Stenone, non fosse il Vi­<lb></lb>viani defraudato della sua parte, si conclude dall&#039;Autore stesso con queste <lb></lb>parole: “ Ne vero quisquam ingenio, potius quam experientiae, haec attri­<lb></lb>buat, amicissimum mihi Vincentium Viviani Serenissimi Magni Ducis Mathe­<lb></lb>maticum testem appello, qni hisce aliisque praesenti libro contentis plusquam <lb></lb>spectator adfuit ” (Florentiae 1667, pag. </s>

<s>119). </s></p><p type="main">

<s>Il libro dunque dell&#039;Anatomico di Coppenhagen, informato alla Geome­<lb></lb>tria del matematico di Firenze, usciva fuori come cosa nuova e nuove suo­<lb></lb>navano alle orecchie dei più quelle parole scritte nella dedica al Granduca, <lb></lb>e nelle quali si diceva ch&#039;essendo il nostro corpo un organo composto di <lb></lb>mille altri organi chi presumeva di volerne aver qualche cognizione, senza <lb></lb>l&#039;uso delle Matematiche, faceva conto d&#039;avere a investigare una materia <lb></lb>senza estensione, o un corpo senza figura. </s>

<s>Nè altra si soggiungeva esser <lb></lb>l&#039;origine di quegli innumerevoli errori, che insozzano la storia del corpo <lb></lb>umano “ quam quod Matheseos leges Anatome hactenus indignata fuerit. </s>

<s>” </s></p><p type="main">

<s>Recalcitravano alle novità gli Aristotelici e i Galenisti, i quali non sa­<lb></lb>pevano comprendere come c&#039;entrasse la Matematica nella loro arte, non usa <pb xlink:href="020/01/1162.jpg" pagenum="37"></pb>a sottostare ad altra disciplina, che all&#039;autorità de&#039;suoi primi istitutori, e <lb></lb>tacitamente si mostrava avverso per gelosia, vedendo esser messa la falce <lb></lb>nella proda di quel campo, che largamente coltivava, il Borelli co&#039;valorosi <lb></lb>seguaci della sua scuola: cosicchè la Miologia geometrica dello Stenone ri­<lb></lb>mase senza i favori così di chi amava le novità, come di chi le aborriva. </s></p><p type="main">

<s>Il Viviani si sentiva più dello stesso Stenone accorato di questo repu­<lb></lb>dio, per parte massimamente di coloro che secondavano i progressi della <lb></lb>scienza, e conoscendo l&#039;animosità del Borelli consigliava il principe Leopoldo <lb></lb>a interpellare il giudizio de&#039;matematici al Borelli stesso non ossequenti, <lb></lb>fra&#039;quali era uno de&#039;primi il padre Stefano Angeli. </s>

<s>Nel mese dunque di <lb></lb>Maggio del 1667 il Principe spedì a lui una copia della Miologia stenoniana <lb></lb>accompagnata da una lettera, nella quale si lamentava la poco favorevole <lb></lb>accoglienza, che avevano ritrovato nel pubblico i nuovi studii. </s>

<s>L&#039;Angeli, il <lb></lb>dì 4 di Giugno di quel medesimo anno 1667, rispondeva così da Venezia: </s></p><p type="main">

<s>“ Mi ha consolato indicibilmente il signore Stenone, vedendo con quanta <lb></lb>sottigliezza dilata li termini della Geometria, facendo egli anche nell&#039;Anato­<lb></lb>mia conoscere quanto sia impossibile poter senza Geometria filosofare in qual <lb></lb>si sia cosa. </s>

<s>Lo compatisco però in estremo, mentre vedo che il suo Libro, <lb></lb>quantunque sia di materia professata da tanti de&#039;quali sono proprietà <emph type="italics"></emph>hone­<lb></lb>ste vestiri, gloriose mentiri<emph.end type="italics"></emph.end> ecc., nulladimeno è per incontrare pochissima <lb></lb>fortuna. </s>

<s>” </s></p><p type="main">

<s>“ La Geometria, anche ne&#039;suoi principii, è intesa da pochi, e sprezzata <lb></lb>per lo più dai signori medici, ad alcuni de&#039;quali avendo io lodato il libro <lb></lb>del signore Stenone l&#039;hanno sprezzato come innovatore, e giurato, per la <lb></lb>loro veneranda e prolissa barba e corti capelli, di non lo voler nè anco <lb></lb>vedere. </s>

<s>” </s></p><p type="main">

<s>“ Tale però non è il signor Molinetto nostro anatomico di Padova, che <lb></lb>da me di ciò informato mi risponde con una lettera, che sebbene scritta con <lb></lb>quella familiarità che fra noi passa, invio a V. A. S. </s>

<s>Il Molinetto è uomo di <lb></lb>pronto ingegno: ha una facondia e prontezza straordinaria. </s>

<s>Nella cattedra, <lb></lb>per la sua franchezza di dire, chiarezza e galanteria d&#039;esprimere i suoi sensi, <lb></lb>ha pochi pari. </s>

<s>Non intende però Geometria, quantunque abbi talenti atti ad <lb></lb>ogni cosa. </s>

<s>Fra&#039;molti discorsi, cha ho avuti seco quante alli muscoli, non mi <lb></lb>pare molto lontano da&#039;pensieri del signore Stenone. </s>

<s>Solo, non avendo co­<lb></lb>gnizione di Geometria, non crede abbi geometrizzato sopra essi, riducendo <lb></lb>la parte media a parallelepipedo, e li tendini a prismi tetragonali. </s>

<s>” </s></p><p type="main">

<s>“ Io ho letto il libro del signore Stenone ed inteso quello dice, ma <lb></lb>non posso accertarmi di quel che dice con li miei occhi, essendo senza al­<lb></lb>cuna cognizione di Anatomia, impedito sempre dalla mia schifa natura, che <lb></lb>non permette veder cosa alcuna in questo proposito senza nausea, scon­<lb></lb>volgimento di stomaco e inappetenza per molti giorni. </s>

<s>” (MSS. Cim., T. XIX, <lb></lb>c. </s>

<s>27). </s></p><p type="main">

<s>L&#039;avversione del Borelli alle novità stenoniane, alle quali aveva presa <lb></lb>così gran parte l&#039;odiato Viviani, accennammo essere stata segreta, e benchè <pb xlink:href="020/01/1163.jpg" pagenum="38"></pb>sia certa, considerata l&#039;indole dell&#039;uomo, non abbiamo però a provarla, se <lb></lb>non che argomenti negativi dedotti dal trattato <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> dove <lb></lb>o si tace o si rappresentano i fatti in modo da levare una parte del merito <lb></lb>all&#039;opera dello Stenone. </s>

<s>Nella proposizione XXXVII della P. II, per esem­<lb></lb>pio, si tratta dal Borelli della struttura del cuore, ma fra coloro, ch&#039;eser­<lb></lb>citarono lo stile per quegli intricatissimi laberinti, non si commemora se non <lb></lb>che il Malpighi, il Lower e il Bellini, mentre fu forse lo Stenone che smarrì <lb></lb>meno la via di tutti gli altri. </s></p><p type="main">

<s>Nella proposizione LXXX della I Parte, si propone il Borelli di dimo­<lb></lb>strare a priori che i muscoli radiosi si debbono necessariamente comporre <lb></lb>di più muscoli penniformi, cosa ch&#039;era stata già dimostrata di fatto dallo <lb></lb>Stenone nella elegantissima fabbrica del Muscolo deltoide, rappresentata in <lb></lb>scolpitissimo disegno nella III Tavola della Miologia. </s>

<s>Or perchè questa volta <lb></lb>l&#039;Anatomico era necessario invocarlo a confermare le speculazioni del Filo­<lb></lb>sofo, nello scolio alla citata proposizione il Borelli stesso scriveva: “ Hanc <lb></lb>musculorum radiosorum structuram, quam mechanicum ratiocinium mihi <lb></lb>suaserat, experimentis confirmare non licuit, nisi imperfecte in locustis ma­<lb></lb>rinis et gammaris. </s>

<s>Postea valde gavisus sum cum viderem diligentissimos et <lb></lb>praeclaros anatomicos Stenonem et Loverium in humano musculo Deltoide <lb></lb>belle et exacte eamdem structuram observasse et diligentissime delineatam <lb></lb>edidisse ” (Editio cit., pag. </s>

<s>161). </s></p><p type="main">

<s>Ma benchè in ogni modo la Miologia dello Stenone avesse posto come <lb></lb>dicemmo la falce per le prode del campo, rimaneva al Borelli intatta la più <lb></lb>larga e più fruttuosa cultura di esso, e dall&#039;altra parte non doveva la nuova <lb></lb>Filosofia borelliana trattenersi solamente a ridurre i muscoli alle forme geo­<lb></lb>metriche, ma co&#039;principii matematici dimostrarne la legge dei moti. </s>

<s>Poteva <lb></lb>per queste ragioni il Borelli assicurarsi che l&#039;Opera sua tornava nuova e <lb></lb>non adombrare per parer che l&#039;avessero prevenuta lo Stenone stesso e il <lb></lb>Viviani. </s></p><p type="main">

<s>Se c&#039;era stato qualcuno che avesse veramente prevenuta l&#039;opera <emph type="italics"></emph>De <lb></lb>motu animalium<emph.end type="italics"></emph.end> era costui piuttosto Guglielmo Croone, il quale, essendo <lb></lb>amico e connazionale dello Stenone, e avendo conferito più volte con lui <lb></lb>intorno al difficilissimo soggetto dei moti musculari, deliberò di dare alla <lb></lb>luce in Amsterdam il suo trattatello <emph type="italics"></emph>De ratione motus musculorum,<emph.end type="italics"></emph.end> in quel <lb></lb>tempo che aveva sentito dire essere sotto i torchi la Miologia stenoniana. </s>

<s>È <lb></lb>quel trattatello, secondo noi, notabilissimo nella storia, perchè vi si dà il <lb></lb>primo saggio della vera Meccanica animale, e il difficile problema della po­<lb></lb>tenza de&#039;muscoli nel braccio dell&#039;uomo, sui dati dell&#039;esperienza, si risolve <lb></lb>con l&#039;aiuto dell&#039;Analisi matematica. </s></p><p type="main">

<s>Per quanto abbia importanza storica il trattatello del Croone, non de­<lb></lb>trasse però nulla all&#039;opera del Borelli, la quale, in quella sua ampiezza di <lb></lb>trattazione, informata a un&#039;unità di principio, apparve a tutti nuova e ma­<lb></lb>ravigliosa. </s>

<s>Tale giova credere che apparisse anche al giudizio del Viviani, a <lb></lb>cui i padri Scolopi di Roma davano, per lettera del dì 19 Aprile 1681, an-<pb xlink:href="020/01/1164.jpg" pagenum="39"></pb>nunzio della pubblicazione della I Parte <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> e dicevano di <lb></lb>far ciò, per secondare la volontà dell&#039;Autore “ il quale, nel passare che fece <lb></lb>all&#039;altra vita in questa nostra casa di S. Pantaleone, caldamente ci racco­<lb></lb>mandò che, subito terminata la stampa, quale egli stava in procinto di co­<lb></lb>minciare, ne facessimo partecipi i professori di tali materie ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. CXLVI, c. </s>

<s>235). </s></p><p type="main">

<s>L&#039;istituzione del Borelli doveva poi, non al Viviani solo ma a tutti, e <lb></lb>specialmente agli Italiani apparire meravigliosa, anche per questo, perchè <lb></lb>non furono avversate le novità di lei, come furono avversate le novità della <lb></lb>istituzione cartesiana ne&#039;due più insigni fautori che avesse fra noi, Tommaso <lb></lb>Cornelio e Marcello Malpighi. </s></p><p type="main">

<s>Del primo di questi due ne abbiamo il ritratto in una lettera di Gio­<lb></lb>vanni Fink, anatomico nello studio di Pisa, e mandato da&#039;principi Medicei, <lb></lb>insiem con Tommaso Baines, a viaggiare pel Napoletano e per i dintorni di <lb></lb>Roma, perchè vi facessero diligente raccolta di oggetti di storia naturale, di <lb></lb>libri di Anatomia e di Medicina, e perchè prendessero notizia degli scien­<lb></lb>ziati, che avessero per quelle parti più rinomanza. </s>

<s>“ A Napoli, riferiscono <lb></lb>al principe Leopoldo i due viaggiatori, abbiamo avuto particolarissima no­<lb></lb>tizia del signor Tommaso Cornelio, matematico e medico di grande grido ed <lb></lb>amico del signor Michelangiolo Ricci. </s>

<s>Lui ha scritto un libro intitolato <emph type="italics"></emph>Pro­<lb></lb>gymnasmata physica:<emph.end type="italics"></emph.end> è stampato a Venezia, ed una parte di esso dedicata <lb></lb>al signor D. </s>

<s>Alfonso Borelli. </s>

<s>Lui è cartesiano, e molto difensore delle cose <lb></lb>nuove, onde viene a Napoli ad essere odiato da quelli, che giurano fedeltà <lb></lb>alli loro maestri. </s>

<s>Quel signore dice in suo libro che lui sia stato inventore <lb></lb>della ipotesi della compressione dell&#039;aria e della forza elastica di quella innanzi <lb></lb>Pecqueto ed ogni altro. </s>

<s>È della nazione calabrese, uomo vivo ed acuto, ma, <lb></lb>come la maggior parte di quella, molto caldo ” (MSS. Cim., T. XVII, <lb></lb>c. </s>

<s>224). </s></p><p type="main">

<s>Nè meno odiato del Cornelio, com&#039;abbiamo udito dal Fink, era il Mal­<lb></lb>pighi, il quale faceva il Microscopio rivelatore, ne&#039;succhi delle piante e nel <lb></lb>sangue, de&#039;misteri della chimica cartesiana. </s>

<s>Se la presero perciò i suoi fu­<lb></lb>riosi nemici anche col Microscopio, ond&#039;è ch&#039;egli, il Malpighi, ebbe a di­<lb></lb>fenderne l&#039;uso e a mostrare i servigi che aveva resi alla scienza, come fa, <lb></lb>per recare un esempio curioso, quando spiega in che modo l&#039;ortica battuta <lb></lb>sopra la nostra pelle si faccia urente. </s>

<s>Il Microscopio svela, egli dice, che ciò <lb></lb>dipende dalle spine, di che si vedono essere irsute le foglie dell&#039;ortica; spine <lb></lb>tutte piene di un sugo attivo, che s&#039;inocula nel sangue. </s>

<s>“ E perchè è assai <lb></lb>verosimile, prosegue a dire, che il sugo che si trova negli utricoli trasver­<lb></lb>sali e nelle fibre, le quali compongono il caule e le foglie dell&#039;ortica, sia <lb></lb>dell&#039;istessa natura, di qui ne nasce che il Microscopio può portare qualche <lb></lb>lume non solo al mal prodotto dalle spine, ma anche al modo d&#039;operare <lb></lb>che fa il sugo dell&#039;ortica fermentando prima e poi fissando, come fa lo spi­<lb></lb>rito di vetriolo infuso nelle vene ” (Opera posth. </s>

<s>cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Si dirà che i nemici del Cornelio e del Malpighi, ne&#039;quali due soli ab-<pb xlink:href="020/01/1165.jpg" pagenum="40"></pb>biamo voluto rappresentare tutti coloro, che trattavano le scienze fisiologi­<lb></lb>che coi principii della Filosofia cartesiana, crano peripatetici, ma questa che <lb></lb>pareva una opposizione è invece una conferma al nostro argomento, perchè <lb></lb>essendo costoro, per istituto della loro scuola, inclinati ad avversare così il <lb></lb>Cartesio come il Borelli, se tanto furiosamente si sollevarono contro quello, <lb></lb>e non contro questo, ripetiamo che, sebbene abbia ciò la sua ragion natu­<lb></lb>rale, è pure un fatto, che ha l&#039;apparenza di maraviglioso. </s>

<s>Quella ragion na­<lb></lb>turale è forse a investigarsi più difficile di quel che a primo aspetto non <lb></lb>sembrerebbe, e perciò lasciando il carico di farlo a chi è più acuto di noi, <lb></lb>ci contenteremo di concludere che, non essendo la nuova Filosofia del Bo­<lb></lb>relli avversata da&#039;Peripatetici, e venendo dall&#039;altra parte con tanto favore <lb></lb>accolta da chi attendeva con più sano giudizio agli studii, potè solidamente <lb></lb>instaurarsi a benefizio comune della scienza, e, in mezzo alle rivalità carte­<lb></lb>siane e alle ingerenze straniere, apparir d&#039;origine e mantenersi schiettamente <lb></lb>italiana. </s></p><p type="main">

<s>Tale, quale si conclude dal nostro discorso, fu il principio, e tali furono <lb></lb>le avventure della scuola iatromatematica, da non lasciarsi qui da noi senza <lb></lb>un breve esame, che ne riveli l&#039;indole e ci faccia estimare i meriti della <lb></lb>nuova istituzione. </s>

<s>Le funzioni della vita si riducono per essa, nelle piante <lb></lb>e negli animali, alle leggi della Fisica. </s>

<s>Così per esempio l&#039;ascendere della <lb></lb>linfa su per i vasellini de&#039;tronchi e de&#039;rami s&#039;attribuisce a quella forza <lb></lb>fisica, che fa risalire il liquido su per i tubi capillari: il corso del sangue <lb></lb>per le arterie e per le vene si regola, nella velocità del suo moto, dietro le <lb></lb>leggi idrauliche, e la forza de&#039;muscoli nel contrarsi si paragona alla forza <lb></lb>di trazione che s&#039;esercita, imbevute che sieno d&#039;umidità, nelle funi. </s>

<s>L&#039;oc­<lb></lb>chio si riguarda come uno strumento ottico fabbricato dall&#039;arte, e l&#039;orec­<lb></lb>chio come uno strumento acustico. </s></p><p type="main">

<s>Chi ben considera, comprenderà quanto dovess&#039;essere seducente questa <lb></lb>nuova Filosofia, quando a svelare i misteri della vita o non s&#039;avevano ra­<lb></lb>gioni, o quelle che s&#039;adducevano si conoscevano troppo bene da&#039;savi per <lb></lb>sogni di romanzi. </s>

<s>Il sostituire le cause fisiche a que&#039;sogni si reputò come <lb></lb>uno de&#039;più grandi progressi, che avesse fatto la scienza, ed ebbero di qui <lb></lb>origine i vittoriosi trionfi della istituzion borelliana. </s></p><p type="main">

<s>S&#039;incominciarono però presto a raffreddare que&#039;primi fervori, quando <lb></lb>l&#039;Anatomia, giunta alla sua ultima perfezione, tanto riuscì ad assottigliare <lb></lb>la punta dello stile e l&#039;acume della vista, da penetrare addentro al più se­<lb></lb>greto magistero degli organi de&#039;sensi. </s>

<s>Il Valsalva, il Morgagni, il Cotugno <lb></lb>e lo Scarpa, per non commemorare fra&#039;nostri che i principali, descrissero <lb></lb>così la fabbrica dell&#039;orecchio e dell&#039;occhio, e si sollevarono da quelle de­<lb></lb>scrizioni a filosofare intorno a que&#039;due nobilissimi organi tant&#039;alto, che di <lb></lb>lassù volgendosi indietro videro quanto gli strumenti acustici e la camera <lb></lb>ottica, tutte cose morte, fossero per sè miseri a rappresentar, nell&#039;udito e <lb></lb>nella vista, lo spirito che v&#039;infonde la vita. </s>

<s>Poi, per più diligenti esperienze <lb></lb>condotte principalmente dall&#039;Haller e dallo Spallanzani, si trovò che il moto <pb xlink:href="020/01/1166.jpg" pagenum="41"></pb>del sangue nelle arterie e nelle vene non segue precisamente le leggi idrau­<lb></lb>liche, e che il correre della linfa ne&#039;vasellini organici dipende da bene altra <lb></lb>forza vitale e più attiva di quella forza fisica che sospinge i liquidi su per <lb></lb>i tubi capillari. </s>

<s>Quando si giunse a conoscere per esperienze sensate e libere <lb></lb>dalle prime apprensioni di una frettolosa immaginazione, che i muscoli e il <lb></lb>cuore nel contrarsi induriscono e scortano, senz&#039;ammettere nella loro so­<lb></lb>stanza carnosa un liquido straniero, che gli faccia ricrescere di mole, e al­<lb></lb>lora ben s&#039;intese che non si potevano attribuire le forze delle loro fibre <lb></lb>traenti all&#039;effervescenze de&#039;liquidi commisti, nè paragonare alle trazioni delle <lb></lb>fila di canapa inumidite, e attorte in fune o comunque sia aggomitolate. </s></p><p type="main">

<s>La iatromatematica, ch&#039;era stata accolta da tutti con sì gran festa, si <lb></lb>dovè allora e per tali giuste ragioni abbandonarla, cosicchè poco durarono <lb></lb>i suoi trionfi, e lievi con precipitoso giudizio se ne dissero i benefizi. </s>

<s>Licen­<lb></lb>ziata però che fu dai servigi della scienza, non si seppe chi chiamare a so­<lb></lb>stituirla. </s>

<s>La scoperta di Luigi Galvani, per quel che particolarmente con­<lb></lb>cerne i moti muscolari, solleticò le speranze di molti, che si credettero aver <lb></lb>dalla nuova Fisica elettrica migliori servigi che non dalla Fisica antica. </s>

<s>Ma <lb></lb>poi presto si conobbe per esperienza che lo stesso spirito elettrico non era <lb></lb>altro che una lusinghiera immagine dello spirito della vita. </s></p><p type="main">

<s>E ora da quale altra scienza si potrebbe questo spirito rivelare? </s>

<s>Le dis­<lb></lb>sezioni operate dall&#039;esperto taglio del coltello anatomico aprirono mirabil­<lb></lb>mente la via agli studii biologici, dal Vesalio al Malpighi. </s>

<s>Il Microscopio, <lb></lb>applicato dal Malpighi stesso e da&#039;suoi successori, scoprì un mondo nuovo <lb></lb>nella testura delle parti solide del corpo organico, e nella composizione dei <lb></lb>liquidi che ricircolano in esso, intanto che s&#039;ebbe infin d&#039;allora notizia si <lb></lb>può dir compiuta di ciò che si può toccare e vedere nel corpo animale. </s>

<s>La <lb></lb>macchina de&#039;polmoni aveva fatto conoscere, non a soli i Filosofi antichi, ma <lb></lb>allo stesso volgo che, oltre ai solidi e ai liquidi, entrano anche gli aeriformi <lb></lb>a farsi ministri della vita, e poi la Chimica fece meglio conoscere la natura <lb></lb>di que&#039;corpi che, sebbene sfuggevoli alle sottigliezze del coltello anatomico <lb></lb>e invisibili a qualunque acume di Microscopio, potevano come gli altri corpi <lb></lb>trattarsi e farsene soggetto di sperimenti. </s>

<s>All&#039;ultimo il Galvani ebbe indizio <lb></lb>che, oltre ai solidi, ai liquidi e agli aeriformi, entrasse a compor la mac­<lb></lb>china animale anche l&#039;etere, non arrendevole a qualunque industria del­<lb></lb>l&#039;arte, e solo rivelantesi a noi negli effetti dell&#039;elettricità, sotto le più mi­<lb></lb>steriose sembianze. </s>

<s>E perchè quel sottilissimo etere, meglio della materia <lb></lb>crassa di che si componpongono i muscoli e le ossa e il sangue, si conosce <lb></lb>organo acconcio ai più intimi servigi della vita, là dove se ne sentiva più <lb></lb>vivamente il bisogno, l&#039;Anatomia ci abbandona, confessandosi, a sodisfare ai <lb></lb>nostri desiderii, impotente. </s></p><p type="main">

<s>A questo scoglio si frangono davvero i flutti spumosi dell&#039;orgogliosa <lb></lb>Filosofia. </s>

<s>Il Cartesio, il quale sagacemente indovinò non essere le parti vi­<lb></lb>sibili nel corpo animale nè i soli nè i principali organi della vita, suppose <lb></lb>l&#039;esistenza di parti invisibili, per aprirsi il campo a una Anatomia immagi-<pb xlink:href="020/01/1167.jpg" pagenum="42"></pb>naria, qual&#039;è quella degli sfiatatoi del vento, che ne&#039;muscoli esala dal cer­<lb></lb>vello. </s>

<s>Così il Filosofo, che orgogliosamente credeva di superar quello scoglio, <lb></lb>ne fu vergognosamente ributtato più indietro, e possono perciò dall&#039;esem­<lb></lb>pio di lui i lettori, che ci seguiteranno, conoscere quali sieno i limiti pre­<lb></lb>scritti al progresso degli studii, di cui siamo per narrare la storia. </s>

<s>Prepa­<lb></lb>rativa di quegli studii è l&#039;Anatomia, le cose della quale fin qui dette e <lb></lb>concluse ce la fanno rassomigliare a una nave, impotente per la sua corpu­<lb></lb>lenza a condurci infin là, dove le sottili acque, spirate da un agilissimo soffio, <lb></lb>giungono a toccare il lontanissimo lido. </s></p><pb xlink:href="020/01/1168.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dei moti muscolari<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle prime ipotesi proposte a rendere la ragione dei moti muscolari, e particolarmente dell&#039;ipo­<lb></lb>tesi del Cartesio. </s>

<s>— II. </s>

<s>Di altre varie ipotesi, principalmente speculate dai nostri Italiani. </s>

<s>— <lb></lb>III. </s>

<s>Dei moti volontarii e dei naturali. </s>

<s>— IV. </s>

<s>Della meccanica dei moti muscolari. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;impotenza dell&#039;Anatomia a scoprirci, co&#039;suoi materiali strumenti, i <lb></lb>seni, dove s&#039;asconde quello spirito che vivifica le membra, si manifesta ai <lb></lb>primi passi di chi si studia di porre il piede in quegl&#039;intimi penetrali. </s>

<s>Esce <lb></lb>da que&#039;penetrali la vita, e si rivela ne&#039;moti, i quali soli sono a noi indizio <lb></lb>ch&#039;ella veramente risegga negli organi mossi. </s>

<s>Comprendesi perciò assai fa­<lb></lb>cilmente come il primo problema che si proponesse a sciogliere la scienza, <lb></lb>e che nelle prime ovvie manifestazioni presentasse difficoltà insuperabili, fu <lb></lb>quello di rendere in qualche modo la ragione di que&#039;moti volontarii e istin­<lb></lb>tivi, che sono il primo e principale argomento per noi da riconoscere la <lb></lb>morte e la vita. </s></p><p type="main">

<s>Chiunque sappia essere stata da Aristotile scritta la prima Storia na­<lb></lb>turale degli animali, che pure è tenuta anche dai moderni in qualche re­<lb></lb>putazione, s&#039;immagina che il gran Filosofo non abbia fra gli altri lasciato <lb></lb>indietro di trattar questo soggetto de&#039;moti muscolari. </s>

<s>Egli ha infatti, fra le <lb></lb>opere appartenenti a cose naturali, un trattatello che s&#039;intitola <emph type="italics"></emph>De incessu <lb></lb>animalium,<emph.end type="italics"></emph.end> a cui vollero alcuni dar la medesima importanza, che agli altri <lb></lb>libri, ne&#039;quali descrive lo Stagirita la Storia universale degli animali. </s></p><p type="main">

<s>Aristotile però, volendo esser conseguente a suoi principii di Anatomia <pb xlink:href="020/01/1169.jpg" pagenum="44"></pb>e di Fisiologia, si trovava nella impossibilità di trattar della Meccanica ani­<lb></lb>male, non potendovi esser macchina senza composizione di organi o conge­<lb></lb>gno di parti. </s>

<s>Questi organi infatti e questi congegni rimasero per Aristotile <lb></lb>affatto inconsiderati, insegnando che l&#039;anima muove da sè immediatamente <lb></lb>il corpo, per via degli spiriti, che partendosi dal cuore si partecipano ai nervi, <lb></lb>e di lì alle flessure degli articoli e agli ossi. </s>

<s>Che se gli avesse domandato <lb></lb>qualcuno come mai spiriti così tenui valessero a muover moli tanto ponde­<lb></lb>rose, quali son quelle per esempio degli elefanti, era pronto a rispondere <lb></lb>che la Natura sa, con piccole forze, l&#039;arte di produrre effetti straordinarii. </s>

<s><lb></lb>Aristotile insomma non aveva inteso a che fare stessero nel corpo animale <lb></lb>quelle fibre carnose e quelle durissime funi, che tanto artificiosamente si <lb></lb>legano agli ossi. </s></p><p type="main">

<s>Primo a conoscere l&#039;importante ufficio, a cui vennero dalla Natura or­<lb></lb>dinati i muscoli, i tendini e i ligamenti, fu Galeno, il quale ci lasciò fra le <lb></lb>sue Opere scritto un trattatello <emph type="italics"></emph>De motu musculorum,<emph.end type="italics"></emph.end> diviso in due libri. </s>

<s><lb></lb>Il meccanismo della vita stravolto da Aristotile, che poneva nel cuore il prin­<lb></lb>cipio de&#039;nervi, fu riordinato sapientemente da esso Galeno, che riconobbe <lb></lb>avere i nervi principio dal cervello e dalla midolla spinale, d&#039;onde vanno a <lb></lb>insinuarsi e a partecipare la loro maravigliosa virtù a tutti i muscoli. </s>

<s>Che <lb></lb>sia veramente così “ cognosces, egli dice, ex passionibus, nam incisus, op­<lb></lb>pressus, contusus, laqueo interceptus, scirrhis affectus et putrefactus nervus <lb></lb>aufert musculo omnem motum et sensum. </s>

<s>Quin et nervo inflammato non <lb></lb>pauci spasmo correpti sunt et mente alienati, quorum quidam sic affecti, <lb></lb>cum sapientiorem medicum nacti essent, nervo inciso statim spasmo et men­<lb></lb>tis alienatione liberati sunt, sed postea musculum, in quem nervus insertus <lb></lb>erat, insensilem atque inutilem ad motum habuerunt. </s>

<s>Adeo certe magna <lb></lb>quaedam vis est in nervis superne a magno principio affluens, non enim ex <lb></lb>seipsis eam, neque innatam habent. </s>

<s>Cognoscere etiam potes hinc maxime, <lb></lb>si incideris quemcumque istorum nervorum aut spinalem ipsam medullam. </s>

<s><lb></lb>Quantum enim superius est incisione, continuum cerebro, id quidem adhuc <lb></lb>conservabit principii vires: omne autem quod inferius est, neque sensum, <lb></lb>neque motum ulli praebere poterit. </s>

<s>” Dai quali fatti Galeno è condotto alla <lb></lb>seguente importantissima conclusione: “ Nervi tanquam rivorum in morem a <lb></lb>cerebro, ceu ex quodam fonte, deducunt musculis vires, quos, cum primum <lb></lb>attigerint, scinduntur multip<gap></gap>iciter in aliam subinde atque aliam sectionem, <lb></lb>tandemque, in tenues et membranaceas fibras toti soluti, totum sic musculi <lb></lb>corpus intertexunt ” (Galeni librorum I Classis, Venetiis 1597, pag. </s>

<s>309). </s></p><p type="main">

<s>La Meccanica animale aveva fatto così, per Galeno, un gran passo, non <lb></lb>posando il piè sulla mobilità delle filosofiche speculazioni, ma fermandolo <lb></lb>sulla solidità delle esperienze, dalle quali veniva dimostrato essere il cer­<lb></lb>vello e i nervi che conducono la forza nei muscoli. </s>

<s>Ma perchè la sete di <lb></lb>sapere, che pare a un tratto spenta, accende nuova sete più viva, si voleva <lb></lb>di più intendere in che mai consista quella virtù, e in che modo operino <lb></lb>il cervello e i nervi per indur ne&#039;muscoli una tal prontezza di moti. </s>

<s>Il Mae-<pb xlink:href="020/01/1170.jpg" pagenum="45"></pb>stro antico lasciò il carico di rispondere ai suoi successori, il primo e più <lb></lb>savio de&#039;quali, incontratosi in un gran mistero, non ebbe ardire o speranza <lb></lb>di riuscire a toglierli il velo. </s>

<s>Il Berengario infatti, contento ad ammettere <lb></lb>con Galeno essere i muscoli gli organi dei moti volontarii, ecco tutto quel <lb></lb>ch&#039;egli dice della meccanica di que&#039;moti: “ Voluntas, cum mittit virtutem <lb></lb>animalem ad nervum versus lacertum suum, volens per illum plicare ali­<lb></lb>quod membrum, retrahitur ille lacertus circa sui principium, et statim pli­<lb></lb>catur membrum. </s>

<s>Et similiter, cum voluerit quod membrum extendatur et <lb></lb>erigatur, extendit voluntas illum lacertum cum lacerto sibi opposito, et ten­<lb></lb>duntur simul, et cum cessat operatio voluntatis universaliter, nec mittit ad <lb></lb>lacertum virtutem, omnino remanet lacertus similis caeteris rebus congela­<lb></lb>tus, et tendit per suam ponderositatem naturalem cum eo cui adhaeret ad <lb></lb>inferius, tamquam membrum mortuum ” (Commentaria super Anat. </s>

<s>Mun­<lb></lb>dini, Bononiae 1521, fol. </s>

<s>LXXVI a tergo). </s></p><p type="main">

<s>Che possano però le membra morire e resuscitare, quante volte è in <lb></lb>piacere dell&#039;animale, non parve un concetto de&#039;più felici, fra&#039;tanti sovve­<lb></lb>nuti alla mente anatomica del Berengario. </s>

<s>Dall&#039;altra parte potevano anche <lb></lb>coloro, che non approvan l&#039;audacia di certi Filosofi, accusarlo d&#039;essersi troppo <lb></lb>ritenuto lontano dall&#039;adempire agli uffici di scienziato, riducendo la ragione <lb></lb>de&#039;moti muscolari, e concludendola in dire che la volontà manda verso i <lb></lb>lacerti ai nervi la sua virtù motrice. </s>

<s>Questa, ch&#039;è contro i Peripatetici dot­<lb></lb>trina di Galeno, si poteva dire nel secolo XVI anche dottrina volgare, e <lb></lb>perciò il Vesalio, in quel risorgere che faceva allora per lui la scienza, sentì <lb></lb>che i placiti antichi volevano essere dichiarati con nuovi commenti. </s></p><p type="main">

<s>Come la vena, egli dice, serve a nutrire il muscolo, e l&#039;arteria a fo­<lb></lb>mentarlo; così il nervo lo ricrea degli spiriti animali, di che mai non lo <lb></lb>lascia digiuno. </s>

<s>Con ciò il Brussellese, che ammetteva l&#039;influsso nerveo pe­<lb></lb>renne, emendava l&#039;errore del nostro Carpense, ma va anche più oltre a dire <lb></lb>quale egli creda esser causa efficiente dei moti muscolari; causa ch&#039;egli ri­<lb></lb>conosce tutt&#039;insieme e nella virtù dello spirito animale, e nella particolare <lb></lb>struttura del muscolo. </s>

<s>“ Deinde spiritus animalis, vi et debitae peculiarisque <lb></lb>musculi constructionis gratia, musculum contrahi laxarique sentio ” (De <lb></lb>humani corp. </s>

<s>fabrica, Basileae 1543, pag. </s>

<s>222). </s></p><p type="main">

<s>Come l&#039;occhio è l&#039;organo della vista, l&#039;orecchio dell&#039;udito, la lingua <lb></lb>del gusto, così il Vesalio crede che i muscoli siano gli organi dol moto. </s>

<s>E <lb></lb>come un solo e medesimo spirito, entrando nell&#039;occhio e trovandolo a quel <lb></lb>modo disposto, fa vedere, e nell&#039;orecchio udire, e nella lingua gustare; così <lb></lb>entrando nel muscolo, per essere a quell&#039;effetto costruito dalla Natura, lo <lb></lb>fa muovere come si vuole. </s>

<s>“ Non enim alius animalis spiritus oculo, aut <lb></lb>linguae, aut auditus organo, quam musculis, diffunditur. </s>

<s>Verum suae con­<lb></lb>structionis ratione, et accedente spiritu, oculus videt, lingua gustat, au­<lb></lb>ditus organum sonos percipit, et sane musculus ipse voluntariis motibus <lb></lb>praeest ” (ibi). </s></p><p type="main">

<s>Ma perchè l&#039;anatomia rivela che il muscolo si compone di più fibre <pb xlink:href="020/01/1171.jpg" pagenum="46"></pb>raccolte, e in un fascio legate insieme, qual&#039;è in questo membro, così com­<lb></lb>posto di più parti, il precipuo organo del moto? </s>

<s>E risponde il Vesalio es­<lb></lb>sere la carnosità delle stesse fibre muscolari. </s>

<s>“ Atque hanc carnem praeci­<lb></lb>puum motus organum esse existimo, et nequaquam dumtaxat fibrarum <lb></lb>thorum et fulcimentum ” (ibi). Come però operi propriamente la carne mu­<lb></lb>scolare per rendersi organo precipuo del moto, l&#039;Autore qui non lo dice, <lb></lb>ma nell&#039;Esame delle Osservazioni anatomiche del Falloppio si spiegò meglio, <lb></lb>facendo intendere che l&#039;allungare e lo scorciar del muscolo dipende dalla <lb></lb>carne che s&#039;aggroppa in esso o si snoda. </s>

<s>“ Hac namque collectione, et ve­<lb></lb>luti conglobatione, musculum breviorem reddi: itaque movere existimo, et <lb></lb>quum is illam collectionem brevitatemque relaxat, ipsum motam prius partem <lb></lb>suo veluti arbitrio, relinquere mihi persuadeo ” (Venetiis 1564, pag. </s>

<s>118). </s></p><p type="main">

<s>Si direbbe che quel conglobarsi e distendersi della sostanza carnosa <lb></lb>fosse, secondo la mente del Vesalio, principalmente governato dall&#039;influsso <lb></lb>dello spirito animale, se non si sapesse ch&#039;egli stesso, <emph type="italics"></emph>parum in hoc Ana­<lb></lb>tomicus,<emph.end type="italics"></emph.end> come giustamente lo accusa il Colombo, sentenziò che v&#039;erano molti <lb></lb>muscoli, dentro i quali non entravano nervi. </s>

<s>Intendeva con ciò il rivoltoso <lb></lb>Spirito brussellese di contradire a Galeno, di cui dianzi si riferivano in pro­<lb></lb>posito le dottrine, e non si avvedeva, nell&#039;ardore della passione, che preci­<lb></lb>devasi cosi ogni via ai progressi della scienza, e che si rendeva impossibile <lb></lb>a investigar la causa de&#039;moti muscolari. </s>

<s>Benemerito perciò di que&#039;progressi <lb></lb>è da dire il Colombo, il quale, avendo confermato il principio galenico, che <lb></lb>sieno cioè i muscoli organi del moto volontario, soggiunge contro il Vesa­<lb></lb>lio, e a restaurar le vere dottrine dell&#039;antichissimo Maestro, che nessun mu­<lb></lb>scolo manca de&#039;suoi nervi “ et cum ad musculum nervum ferri dico, non <lb></lb>ita intelligo prope musculos nervos ferri, aut per illorum medium recta <lb></lb>praeterire, ed per musculorum substantiam aio nervos disseminari ” (De re <lb></lb>anatom., Venetiis 1559, pag. </s>

<s>119). </s></p><p type="main">

<s>Il Falloppio con la sua scuola, tutti dediti all&#039;Anatomia descrittiva, toc­<lb></lb>carono appena la difficile questione, la quale, nel risorgere della scienza spe­<lb></lb>rimentale, si rimase a quel punto in cui l&#039;avevano lasciata il Colombo, o <lb></lb>diciam meglio Galeno. </s>

<s>Il Cartesio, ch&#039;entrò primo a filosofare di queste cose, <lb></lb>trovò dunque essersi prima di lui insegnato che la virtù di muovere viene <lb></lb>ai muscoli dal cervello, il quale manda a loro il suo spirito, per via de&#039;nervi, <lb></lb>dentro la stessa muscolare sostanza largamente dispersi. </s>

<s>Si sentiva però an­<lb></lb>cora frugata la filosofica curiosità di saper queste cose: che sia e d&#039;onde <lb></lb>abbia origine quello spirito vitale; come operi propriamente sui muscoli a <lb></lb>produrre i vari moti animali. </s></p><p type="main">

<s>Alla prima domanda non avea sodisfatto il Colombo, proponendo una <lb></lb>sua ipotesi, che a noi pare indegna di lui, bench&#039;egli se ne compiaccia come <lb></lb>di una bella invenzione, per cui rispondeva così il Cartesio, fondando sul­<lb></lb>l&#039;anatomia e sulla fisiologia del cervello il suo discorso: “ Quantum ad par­<lb></lb>tes sanguinis, quae usque in cerebrum penetrant, haec ibi non nutriendae <lb></lb>ac reficiendae tantum illius substantiae inserviunt, sed imprimis quoque <pb xlink:href="020/01/1172.jpg" pagenum="47"></pb>subtilissimum quemdam halitum, aut potius valde mobilem et puram flam­<lb></lb>mam producunt, quae animalium spirituum nomine venit. </s>

<s>Sciendum enim <lb></lb>est arterias, quae hunc sanguinem a corde ad cerebrum deferunt, primo in <lb></lb>infinitos tenuissimos ramulos dividi et componere parva illa reticula, quae <lb></lb>tapetorum instar in fundo ventriculorum cerebri expansa sunt, ac denuo <lb></lb>coire circum exiguam quandam glandulam, quae circiter in media cerebri <lb></lb>substantia sita est, in ipso ventriculorum introitu, atque ibi valde multos <lb></lb>exiguos poros habere, per quos subtilissimae sanguinis quem continent par­<lb></lb>ticulae effluere possint in hanc glandulam, non vero crassiores, eo quod ni­<lb></lb>mis angusti sint pori isti ” (De Homine, Francofurti ad M. 1692, pag. </s>

<s>21). </s></p><p type="main">

<s>Ammesso così che lo spirito o la fiammella della vita sia un vapore del <lb></lb>sangue esalato nel passar che fa, come per un cribro, attraverso ai pori <lb></lb>della ghiandola pineale, viene il Cartesio a dire come quello spirito deriva <lb></lb>dal suo principio ne&#039;muscoli per la via diretta de&#039;nervi, ch&#039;egli immagina <lb></lb>esser fabbricati a guisa di un gran tubo membranoso involgente altri più <lb></lb>piccoli tubi tutti pieni di una certa sostanza midollore, che però non serve <lb></lb>a muover le membra, e che è composta di molti sottilissimi filamenti. </s>

<s>Rap­<lb></lb>presenta l&#039;Autore questa immaginata anatomia de&#039;nervi in disegno, illu­<lb></lb>strato da queste parole: “ Vides igitur hunc nervum A, cuius exterior tu­<lb></lb>nica, instar magni tubi est, continentis in se plures minores tubulos .... <lb></lb>ex interiori tunica compositos.... Insuper notandum in his singulis tubulis <lb></lb>esse quasi medullam quandam compositam ex plurimis tenuissimis filamen­<lb></lb>tis a propria cerebri substantia deductis ” (ibi, pag. </s>

<s>25). </s></p><p type="main">

<s>Son questi tubi nervei lo spiracolo della fiamma vitale, che con per­<lb></lb>petuo circolo va e torna dal cervello ai muscoli, quando questi però stanno <lb></lb>in riposo. </s>

<s>Ma quando hanno a muoversi, vi sono agl&#039;ingressi e agli egressi <lb></lb>nella sostanza muscolare certe valvole, che impediscono allo spirito il suo <lb></lb>libero corso, e fanno sì che un muscolo s&#039;enfi più del suo antagonista, per <lb></lb>cui quello vincendola sopra questo lo tira alla sua parte, verso la quale di­<lb></lb>rigesi la resultante del moto. </s>

<s>Il fantasticato <lb></lb><figure id="id.020.01.1172.1.jpg" xlink:href="020/01/1172/1.jpg"></figure></s></p><p type="caption">

<s>Figura 1.<lb></lb>macchinamento è tale, che non può descri­<lb></lb>versi chiaramente senza l&#039;aiuto delle figure, <lb></lb>come fa il Cartesio stesso, il quale esem­<lb></lb>plifica così il suo sistema ne&#039;muscoli motori <lb></lb>dell&#039;occhio: </s></p><p type="main">

<s>“ Nota inter duos tubos <emph type="italics"></emph>bf, ef<emph.end type="italics"></emph.end> (fig. </s>

<s>1) <lb></lb>dari pelliculam quandam H <emph type="italics"></emph>fi,<emph.end type="italics"></emph.end> quae duos <lb></lb>hos tubos <emph type="italics"></emph>bf<emph.end type="italics"></emph.end> et <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> seiungit, iisque inservit <lb></lb>tanquam porta quae duas habet plicas G <lb></lb>et <emph type="italics"></emph>i,<emph.end type="italics"></emph.end> tali modo dispositas, ut cum spiritus <lb></lb>animales, qui a <emph type="italics"></emph>b<emph.end type="italics"></emph.end> ad H descendere conan­<lb></lb>tur, maiorem vim habent iis qui conantur adscendere ab <emph type="italics"></emph>c<emph.end type="italics"></emph.end> versus <emph type="italics"></emph>i<emph.end type="italics"></emph.end> depri­<lb></lb>mant et aperiant hanc pelliculam, adeoque occasionem praebeant iis, qui in <lb></lb>musculo E sunt, una cum ipsis celerrime versus D fluendi. </s>

<s>Ubi vero spi-<pb xlink:href="020/01/1173.jpg" pagenum="48"></pb>ritus, qui ascendere nituntur ab <emph type="italics"></emph>e<emph.end type="italics"></emph.end> versus <emph type="italics"></emph>i<emph.end type="italics"></emph.end> fortiores sunt, aut saltem aeque <lb></lb>fortes ac alii, pelliculam H <emph type="italics"></emph>fi<emph.end type="italics"></emph.end> attollunt clauduntque, atque ita semetipsos im­<lb></lb>pediunt, quominus exeant ex musculo F; cum alias, si utrimque satis vi­<lb></lb>rium non habeant ad eam pellendam, naturaliter semiaperta maneat. </s>

<s>Et <lb></lb>denique si spiritus contenti in musculo D egredi aliquando conentur per <lb></lb><emph type="italics"></emph>dfe,<emph.end type="italics"></emph.end> aut <emph type="italics"></emph>dfb,<emph.end type="italics"></emph.end> plica H distendi et viam ipsis praecludere potest. </s>

<s>Et eodem <lb></lb>prorsus modo inter duos tubos <emph type="italics"></emph>eg,<emph.end type="italics"></emph.end> et <emph type="italics"></emph>dg,<emph.end type="italics"></emph.end> pellicula seu valvula <emph type="italics"></emph>g<emph.end type="italics"></emph.end> reperitur <lb></lb>praecedenti similis, quae naturaliter semiaperta manet et claudi potest a <lb></lb>spiritibus venientibus a tubulo <emph type="italics"></emph>dg,<emph.end type="italics"></emph.end> et ab iis qui veniunt a <emph type="italics"></emph>cg<emph.end type="italics"></emph.end> aperiri ” (ibi, <lb></lb>pag. </s>

<s>40). </s></p><p type="main">

<s>Descritti così gli organi principali, ecco come sono, in questa fantastica <lb></lb>macchina cartesiana, messe in gioco le forze, perchè possano i muscoli dare <lb></lb>all&#039;occhio, a cui sono applicati, quella loro così pronta varietà di moti. </s>

<s>“ Unde <lb></lb>haud difficulter intelligi potest quod si spiritus animales, qui in cerebro sunt, <lb></lb>prorsus nullum aut fere nullum conatum habeant per tubulos <emph type="italics"></emph>bf, cg<emph.end type="italics"></emph.end> affluendi, <lb></lb>duas pelliculas seu valvulas <emph type="italics"></emph>f<emph.end type="italics"></emph.end> et <emph type="italics"></emph>g<emph.end type="italics"></emph.end> semiapertas manere, atque ita musoules D <lb></lb>et E flaccidos et actione destitutos fore, quandoquidem contenti in ipsis ani­<lb></lb>males spiritus libere ab uno in alium transeunt, ab E per <emph type="italics"></emph>f<emph.end type="italics"></emph.end> versus D, et <lb></lb>reciproce a D per <emph type="italics"></emph>g<emph.end type="italics"></emph.end> versus E. </s>

<s>At si spiritus qui in cerebro sunt, cum vi <lb></lb>aliqua conentur ingredi tubos <emph type="italics"></emph>bf, cg,<emph.end type="italics"></emph.end> et haec vis ab utraque parte aequalis <lb></lb>sit, statim claudunt duas valvulas <emph type="italics"></emph>g<emph.end type="italics"></emph.end> et <emph type="italics"></emph>f,<emph.end type="italics"></emph.end> et duos musculos D et E quan­<lb></lb>tum possunt distendunt. </s>

<s>Uude fit ut sistatur oculus et immotus teneatur in <lb></lb>eo situ quem tunc habet. </s>

<s>Deinde, ubi spiritus a cerebro venientes, maiori <lb></lb>vi fluere nituntur per <emph type="italics"></emph>bf<emph.end type="italics"></emph.end> quam per <emph type="italics"></emph>cg<emph.end type="italics"></emph.end> claudunt pelliculam <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> et aperiunt <emph type="italics"></emph>f,<emph.end type="italics"></emph.end><lb></lb>idque magis aut minus prout lenius vel vehementius agunt. </s>

<s>Qua ratione spi­<lb></lb>ritus musculo E contenti se conferunt ad musculum D per meatum <emph type="italics"></emph>ef,<emph.end type="italics"></emph.end> idque <lb></lb>celerius vel tardius, prout valvula <emph type="italics"></emph>f<emph.end type="italics"></emph.end> magis vel minus aperta est. </s>

<s>Adeo ut <lb></lb>musculus D, ex quo egredi non possunt, in spiritus contrahatur et E exten­<lb></lb>datur, atque ita oculus versus D conversus est. </s>

<s>Sicut ex adverso, ubi spi­<lb></lb>ritus, qui in cerebro sunt, maiori vi fluere nituntur per <emph type="italics"></emph>cg,<emph.end type="italics"></emph.end> quam per <emph type="italics"></emph>bf,<emph.end type="italics"></emph.end><lb></lb>claudunt pelliculam <emph type="italics"></emph>f<emph.end type="italics"></emph.end> et aperiunt <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> adeo ut spiritus musculi D statim re­<lb></lb>deant per meatum <emph type="italics"></emph>dg<emph.end type="italics"></emph.end> in musculum E, qui hac ratione contrahitur, et ocu­<lb></lb>ìum iterum ad se trahit ” (ibi, pag. </s>

<s>41). </s></p><p type="main">

<s>Chi sa quale efficacia avesse sopra le menti di allora la seducente elo­<lb></lb>quenza di Renato, non si maraviglierà di veder queste fantasie approvate e <lb></lb>seguite, non da&#039;soli metafisici o da&#039;filosofi razionali, ma dagli stessi cultori <lb></lb>delle scienze mediche. </s>

<s>Da un&#039;altra parte la fortunata scoperta dell&#039;Harvey <lb></lb>aveva così disposti gl&#039;ingegni ad ammetter negli animali, a somiglianza del <lb></lb>circolo del sangue, il circolo cartesiano degli spiriti vitali, che Enrico Regiò, <lb></lb>amico a Tommaso Bartholin, il quale riferisce il fatto nel suo Spicilegio <lb></lb>de&#039;vasi linfatici, si lusingò di aver co&#039;suoi proprii occhi veduto questo cir­<lb></lb>colo andar daì ventre al capo attraverso alle cellule trasparenti di una Lu­<lb></lb>maca. </s>

<s>E a proposite degli stessi vasi linfatici il Glisson costituì nel corpo <lb></lb>animale un altro circolo somigliantissimo a quello arveiano, in cui facevano <pb xlink:href="020/01/1174.jpg" pagenum="49"></pb>que&#039;vasi, a somiglianza delle vene, tornar la linfa alla sua fonte, dalla quale <lb></lb>i nervi, col Cartesio creduti tubulari, come le arterie il sangue, l&#039;avevano <lb></lb>attinta, per nutrir di un alimento tutto proprio di lei le varie membra. </s></p><p type="main">

<s>Non tutti però, per amor del vero, furono sedotti dalle eloquenti fan­<lb></lb>tasie del Filosofo: si trattava di cose naturali, in cui le speculazioni, per <lb></lb>quanto ingegnose, non potevano aver virtù di persuadere, se non venivano <lb></lb>confermate dai fatti, quali si rivelano all&#039;osservazione e son dimostrati dalle <lb></lb>esperienze. </s>

<s>Il Cartesio, e dietro lui il Glisson, supponevano che i nervi fos­<lb></lb>sero tubulari, e il Bartholin gli richiama alle osservazioni anatomiche, dalle <lb></lb>quali, perciocchè non vedevasi confermato il supposto, cosi con veemenza <lb></lb>contro ad essi conclude: “ Non igitur audiendi qui nervos vasorum instar <lb></lb>cavos nobis obtrudunt. </s>

<s>Monstrent intento digito ut assentiamur, nam manus <lb></lb>nobis sunt oculatae. </s>

<s>Quotquot nervos accurato oculo inspexere, nullam in­<lb></lb>venerunt cavitatem ” (Spicilegium ex vasis lymphat., Amstelodami 1660, <lb></lb>pag. </s>

<s>21). </s></p><p type="main">

<s>Eransi immaginati i nervi tubulari dal Cartesio, per dar libero passag­<lb></lb>gio agli spiriti; dal Glisson per servire al circolo della linfa: il Bartholin <lb></lb>gli richiamò all&#039;esperienze, le quali dimostrano che per i nervi non iscorre <lb></lb>nessuna spiritosa o liquida sostanza. </s>

<s>“ Quidquid sit, nullum motum seu spi­<lb></lb>ritus seu liquoris possumus in nervis expiscari. </s>

<s>Tentavi duplici ligatura <lb></lb>iniecta nervumque vidi inter vincula nihil intumescere, nec discissum liquo­<lb></lb>rem stillare; unde existimavi nihil humoris contineri, quia regredi non po­<lb></lb>tuit propter superius vinculum, nec elective trahi pellique, propter inferius <lb></lb>vinculum. </s>

<s>Quorsum evasit succus inter ligaturas contentus? </s>

<s>” (ibi, pag. </s>

<s>32). </s></p><p type="main">

<s>Vedremo com&#039;avesse il Malpighi da simili esperienze resultati diversi, <lb></lb>ma in oghi modo a dover tenere l&#039;ipotesi cartesiana per non più che per <lb></lb>una ingegnosa finzione, basti il saper che nessuno Anatomico, nemmen con <lb></lb>l&#039;aiuto del più artificioso Microscopio, è riuscito a veder quelle pieghe mem­<lb></lb>branose o quelle valvole poste nell&#039;ingresso de&#039;muscoli dalla fantasia del <lb></lb>Cartesio. </s>

<s>È anzi a notare che le immaginate valvole sono incompatibili col <lb></lb>fatto della diramazione de&#039;nervi nella sostanza di tutti i muscoli, secondo <lb></lb>aveva il Colombo dimostrato contro il Vesalio, per cui il Cartesio, ammet­<lb></lb>tendo che il nervo venga reciso in tronco nell&#039;entrare del muscolo, contra­<lb></lb>dice al fatto anatomico più manifesto. </s>

<s>Tutti i più savi perciò, persuasi non <lb></lb>potersi fingere il corpo animale a nostro modo, ma doversi tener quale le <lb></lb>osservazioni e l&#039;esperienze ce lo mostrano fabbricato dalla Natura, ben co­<lb></lb>nobhero che non si poteva, in ordine al render la ragione de&#039;moti musco­<lb></lb>lari, seguitar la Filosofia cartesiana, e ch&#039;era necessario in ogni modo te­<lb></lb>nere altra via. </s>

<s>Furono per avventura fra que&#039;savi i nostri Italiani, de&#039;quali <lb></lb>è da narrar le speculazioni e l&#039;esperienze, di che s&#039;aiutarono studiosamente <lb></lb>per risolvere il difficilissimo problema. </s></p><pb xlink:href="020/01/1175.jpg" pagenum="50"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Giovan Batista Baliani che si studiò, per quanto valessero le sue forze, <lb></lb>di emular Galileo nella scienza del moto e che, con più amoroso studio di <lb></lb>lui, coltivò questa stessa scienza nelle applicazioni, che potevan farsene al <lb></lb>moto degli animali; ha fra le sue opere diverse, raccolte in Genova dal Ca­<lb></lb>lenzani, una breve scrittura, nella quale proponesi di rendere la ragione <lb></lb><emph type="italics"></emph>Quomodo animal moveatur.<emph.end type="italics"></emph.end> Il carattere proprio dì questa scrittura è piut­<lb></lb>tosto quello di una nota, scritta forse con intenzione di tornare a disten­<lb></lb>derla in più larga forma, per sodisfare ai lettori meglio, che con quell&#039;arida <lb></lb>e concisa argomentazione, con la quale si affretta a concludere il suo di­<lb></lb>scorso. </s>

<s>Benchè pubblicata nel 1666, ella dee essere di parecchi anni ante­<lb></lb>riore, e perchè dettata in tempi, ne&#039;quali non si sapeva a qual genere di <lb></lb>macchina, fra quelle semplici descritte dalla Scienza meccanica, rassomigliar <lb></lb>quella messa, nell&#039;economia animale, in opera dalla Natura; e perciò hanno <lb></lb>da questa parte le dottrine del Baliani, che ora sembrano sì comuni, qual­<lb></lb>che cosa in sè per que&#039;tempi di notabile. </s></p><p type="main">

<s>Ecco dunque come, ammessa l&#039;ipotesi degli spiriti vitali, si rende la <lb></lb>ragion del muoversi, a ubbidire alla volontà o a secondare gl&#039;istinti, secondo <lb></lb>il Baliani, la varie membra. </s>

<s>“ Animal movetur per animam, anima movet <lb></lb>spiritum, spiritus nervos, nervus muscolos, musculi tendines, tendines ossa, <lb></lb>membra, inde etiam totum corpus.... Dices quomodo spiritus potest mo­<lb></lb>vere corpus grave? </s>

<s>Respondeo spiritus etiam est corpus, quamvis tenue, <lb></lb>divisum in tot partes, quot sunt nervi subtilissimi, et proinde quilibet ipso­<lb></lb>rum a suo spiritu interno facile ad libitum ducitur, unde plures partes spi­<lb></lb>ritus facile ducunt plures nervos in eodem musculo dispositos, ex quo totus <lb></lb>musculus de facili movetur et suo motu, mediis tendinibus, ossa et inde <lb></lb>membra movet: hinc spiritus movet totum corpus, quod explicandum fuit ” <lb></lb>(pag. </s>

<s>274). </s></p><p type="main">

<s>Ma queste in ogni modo sono asserzioni, le quali, benchè si possano <lb></lb>senza difficoltà tener per vere, mancano nonostante di quelle ragioni e di <lb></lb>quelle prove, che le rendano dimostrate: nè col sentenziare assoluto s&#039;adem­<lb></lb>piono gli uffici della scienza. </s>

<s>Dall&#039;altra parte, se non si potevano quegli uf­<lb></lb>fici adempire altrimenti da quel che fece il Cartesio, fu prudente consiglio <lb></lb>del nostro Baliani l&#039;andar più cauto ne&#039;malagevoli passi. </s></p><p type="main">

<s>Venne però tempo in Italia, in cui i progrediti-studii sperimentali e la <lb></lb>seducente applicazione delle leggi fisiche ai fatti fisiologici incorarono una <lb></lb>certa baldanzosa speranza di avere a giungere al vero desiderato, più d&#039;ap­<lb></lb>presso di quel che non vi fossero giunti i predecessori, in altri tempi e con <lb></lb>aiuti più scarsi. </s>

<s>Intanto che le nuove studiate ipotesi maturavano nella mente, <pb xlink:href="020/01/1176.jpg" pagenum="51"></pb>volle il Borelli, per assicurarsi della loro verità o falsità, richiamare a sot­<lb></lb>tile esame quelle ch&#039;erano state proposte prima di lui. </s></p><p type="main">

<s>La più antica e universalmente ammessa da Galeno al Cartesio era <lb></lb>quella degli spiriti perennemente scorrenti dalla fonte del cervello, per i ri­<lb></lb>voli de&#039;nervi. </s>

<s>L&#039;antico Maestro della scienza della vita non par che si spie­<lb></lb>ghi bene intorno all&#039;essere di quegli spiriti, se gli creda cioè composti di <lb></lb>materia simile all&#039;aria, o di più sottile sostanza impercettibile ai sensi. </s>

<s>Qual­<lb></lb>che schiarimento alle idee comincia a venirci da Realdo Colombo, il quale <lb></lb>fa distinzione fra spiriti vitali, così detti secondo lui perchè sono un alito <lb></lb>purissimo della vita, e spiriti animali risultanti di una miscela di essi spi­<lb></lb>riti vitali e d&#039;aria. </s>

<s>Si fa questa miscela, secondo l&#039;Anatomico cremonese, <lb></lb>ne&#039;ventricoli superiori del cervello, per il moto de&#039;plessi <emph type="italics"></emph>coriformi,<emph.end type="italics"></emph.end> ch&#039;egli <lb></lb>più volentieri chiama <emph type="italics"></emph>reticulari.<emph.end type="italics"></emph.end> L&#039;aria entra poi ne&#039;detti ventricoli attrat­<lb></lb>tavi dal naso, attraverso ai forellini dell&#039;Etmoide. </s>

<s>Una tal confezione dello <lb></lb>spirito animale vuole il Colombo che sia una sua nuova scoperta, e perciò <lb></lb>invita i lettori a seguirlo in questo passo con più diligenza che mai. </s>

<s>“ Per <lb></lb>hos superiores cerebri ventriculos feruntur plexus coriformes, quos reticu­<lb></lb>lares appellavimus. </s>

<s>Usus autem horum est animalium spirituum generatio. </s>

<s><lb></lb>Atque hoc quod nunc dicam, quoniam meum inventum est, diligenter at­<lb></lb>tende. </s>

<s>Horum ventriculorum origo est supra os sphaenoides ethmoides ver­<lb></lb>sus. </s>

<s>Aer autem per nares attractus in frontis cunealisque cavitate aliquando <lb></lb>conservatur. </s>

<s>Alteratus deinde ad hos binos ventriculos, quos ego superiores <lb></lb>appellavi, per foramina ethmoidis ascendit, at in his ventriculis, ob assi­<lb></lb>duum tum cerebri tum huius reticularis plexus motum, miscetur cum vi­<lb></lb>talibus spiritibus aer. </s>

<s>Itaque spiritus animales evadunt ex aere, eo quo di­<lb></lb>ximus modo praeparato, et ex vitalibus dictis spiritibus, quae res a nemine <lb></lb>ante me observata fuit ” (De re anat. </s>

<s>cit., pag. </s>

<s>191). </s></p><p type="main">

<s>Se dunque lo spirito animale si compone in parte di aria comune, e <lb></lb>se al dir dello stesso Cartesio è un&#039;aereosa sostanza esalata dal sangue, si <lb></lb>dovrebbe, quando veramente scorresse dentro i tubi de&#039;nervi, rivelar come <lb></lb>l&#039;aria stessa ne&#039;suoi effetti pneumatici, e manifestarsi all&#039;occhio nell&#039;appa­<lb></lb>renza delle solite bolle, aperto il nervo o il muscolo inturgidito sott&#039;acqua. </s>

<s><lb></lb>Ora il Borelli, fatta diligentemente questa esperienza, vide che nulla galloz­<lb></lb>zolava per l&#039;acqua stessa, d&#039;ond&#039;ei ne concluse non venire i muscoli dagli <lb></lb>spiriti animali nè enfiati nè mossi. </s>

<s>“ Sectis enim in longum musculis vi­<lb></lb>ventis animalis, intra aquam demersis, in qua ob dolorem vehementissime <lb></lb>agitantur, in tam grandi, copioso et vehementi fervore et ebullitione illius <lb></lb>aurae spiritosae in musculis excitata erumperent, et ascenderent a cicatrice <lb></lb>innumerabiles bullae aereae per aquam, ut in aheno ferventi contingit, quod <lb></lb>prorsus non apparet. </s>

<s>Igitur non a spiritibus corporeis musculi inflantur et <lb></lb>moventur ” (De motu anim., P. II, Romae 1681, pag. </s>

<s>36). </s></p><p type="main">

<s>Altri chiarissimi Fisiologi dicevano che i muscoli s&#039;enfiano inturgiditi <lb></lb>dal sangue stillatovi dalle arterie e non potuto risorbir dalle vene. </s>

<s>Il Borelli <lb></lb>dimostrò ch&#039;era anche questa ipotesi falsa e lo fece prima con argomenti <pb xlink:href="020/01/1177.jpg" pagenum="52"></pb>conclusi da principii anatomici e fisiologici, e poi ricorrendo in ultimo al­<lb></lb>l&#039;esperienza. </s>

<s>Se è vero, diceva, che i muscoli mossi inturgidiscono di san­<lb></lb>gue ivi stagnante, dovrebbero nell&#039;esercizio pesar più che quando si riman­<lb></lb>gono in quiete. </s>

<s>Perciò fatto giacere un&#039;uomo sopra una tavola, in modo che <lb></lb>l&#039;umbilico, in cui risiede il centro della gravità, risponda esattamente sul <lb></lb>taglio del prisma o coltello da bilance, sopra il quale si suppone che la ta­<lb></lb>vola stessa sia equilibrata; se comincerà quell&#039;uomo a mettere in moto le <lb></lb>gambe, inturgiditi di sangue, secondo l&#039;ipotesi, i muscoli, dovrebbesi veder <lb></lb>preponderare il corpo da quella parte, <emph type="italics"></emph>quod tamen,<emph.end type="italics"></emph.end> fattane l&#039;esperienza, dice <lb></lb>il Borelli, <emph type="italics"></emph>non contigit<emph.end type="italics"></emph.end> (ibi, pag. </s>

<s>39). </s></p><p type="main">

<s>Essendo il cuore come il primo mobile del sistema animale, o secondo <lb></lb>l&#039;espression dell&#039;Harvey, come il Sole nel Microcosmo, pensarono altri che <lb></lb>anco ai moti muscolari i primi e più validi impulsi venissero da lui. </s>

<s>Il Bo­<lb></lb>relli dimostrò che nemmeno una tale ipotesi potevasi dimostrare, e ciò, fra <lb></lb>le altre principalmente per questa ragione, perchè le arterie coronarie fa­<lb></lb>cendo con le respettive vene un circolo a parte, ricevono anch&#039;esse, come <lb></lb>la grande Aorta, l&#039;impulso dal cuore, ed è perciò l&#039;iniezione del sangue <lb></lb>fra&#039;pori de&#039;muscoli cardiaci un effetto prodotto dalle pulsazioni del mede­<lb></lb>simo cuore. </s>

<s>Ma non potendo l&#039;effetto produr la sua propria causa, sarà im­<lb></lb>possibile che per l&#039;iniezione del sangue si commovano i muscoli, di che il <lb></lb>cuore s&#039;intesse “ unde deducitur quod neque caeteri musculi animalis in­<lb></lb>flari possint a sanguine ” (ibi, pag. </s>

<s>42). </s></p><p type="main">

<s>Ai seguaci della Scuola iatrofisica era facile sovvenisse il pensiero che <lb></lb>si potesse l&#039;inturgidire e lo scortar de&#039;muscoli, insinuandosi dentro alle loro <lb></lb>fibre il sangue, dimostrar per l&#039;esempio di ciò che si vede avvenir nelle <lb></lb>funi inumidite. </s>

<s>Forse questo stesso pensiero s&#039;appresentò anche alla mente <lb></lb>del Borelli, ma ei dovette presto riconoscerne la fallacia, principalmente per­<lb></lb>chè, bene osservando, tutt&#039;altro che somigliarsi insieme le funi e i muscoli <lb></lb>tengono nell&#039;operare modi fra loro opposti. </s>

<s>La fune infatti rigonfia e scorta, <lb></lb>quand&#039;è imbevuta d&#039;umido, e quand&#039;è arida s&#039;assottiglia ed allunga, men­<lb></lb>tre il muscolo invece quand&#039;è inaridito è più teso e più corto. </s>

<s>S&#039;ha di ciò <lb></lb>l&#039;esempio nel cuore che contrattosi impallidisce e disteso torna a rosseg­<lb></lb>giare, e s&#039;ha la dimostrazione nel fatto che, ferito un muscolo mentre è <lb></lb>lasso, manda sangue più in copia che quando è turgido e duro. </s></p><p type="main">

<s>Non avendo, così, trovato il Borelli da sodisfarsi di nessuna delle varie <lb></lb>ipotesi proposte a rendere la ragione dei moti muscolari, si volse con ogni <lb></lb>studio a specularne una sua nuova, che non patisse le difficoltà notate, e <lb></lb>che, senza presumere di darla per cosa certa, avesse pure qualche maggior <lb></lb>probabilità di tutte l&#039;altre. </s>

<s>Gli fu suggerito il principio a quella nuova spe­<lb></lb>culazione da Raffaello Magiotti, il quale avendo trovato per esperienza che, <lb></lb>premendo con un dito sulla bocca di un vaso cilindrico pieno d&#039;acqua den­<lb></lb>tro alla quale fossero galleggianti le figurine da lui descritte nel Discorso <lb></lb>sopra la Renitenza dell&#039;acqua alla compressione, si potevano, a talento dello <lb></lb>sperimentatore, ora mettere in un istante in moto quelle stesse figurine, e <pb xlink:href="020/01/1178.jpg" pagenum="53"></pb>ora nuovamente farle posare; pensò che per qualche modo simile a questo <lb></lb>potesse l&#039;anima operare sul corpo, e mettere in moto le varie membra. <lb></lb></s>

<s>“ Considero, egli dice, in questo cilindro quell&#039;angustissimo e capacissimo <lb></lb>vaso della Memoria, con acqua per altri limpida e spiritosa, per altri flem­<lb></lb>matica e torbida. </s>

<s>Considero le figurine or più grandi or più piccole, or ab­<lb></lb>bagliate or distinte, con diverse operazioni, e quand&#039;una figurina più avanti <lb></lb>m&#039;impedisce un&#039;altra più indietro, qual&#039;io vorrei pur vedere, con una lieve <lb></lb>scossa di Cilindro, cioè a dire con una grattata di capo, bene spesso conse­<lb></lb>guirò l&#039;intento. </s>

<s>Ma fuor di burla .... se il volere e principiar la compres­<lb></lb>sione può essere nel medesimo istante, e come un atto solo dell&#039;Anima, <lb></lb>essendo il dito o polpa della mano congiunto con l&#039;acqua, non potrà abbas­<lb></lb>sarsi il dito se l&#039;acqua nel medesimo tempo non sale per le Caraffine, e <lb></lb>quelle non cominciano diversi giochi. </s>

<s>Adunque il volere e principiar la com­<lb></lb>pressione e salir dell&#039;acqua, e cominciar diversi giochi a talento e gusto <lb></lb>dell&#039;Anima, sarà un atto solo di lei, quale averà in un certo modo ampliata, <lb></lb>per quanto è lungo il Cilindro, la sfera dell&#039;attività sua. </s>

<s>” </s></p><p type="main">

<s>“ Di più, quella notabil differenza tra liquidi e solidi svanisce nei mu­<lb></lb>scoli, nervi, tendini, cartilagini, ecc., come in materia nè liquida, nè solida, <lb></lb>della quale si serve l&#039;anima per fare ad un tempo diverse operazioni. </s>

<s>Bene <lb></lb>è ragione che, se la virtù impressa nell&#039;acqua, corpo molto grave, può nel <lb></lb>medesimo istante dare il moto ad altre figurine in giu, ad altre in su, ed <lb></lb>altre fermare in equilibrio; così, e meglio, possa tutta ad un tempo l&#039;Anima, <lb></lb>che è incorporea, cominciare a toccare, a vedere, a pensare, e fare altre di­<lb></lb>verse operazioni. </s>

<s>Così nel medesimo punto può muovere il Musico la bat­<lb></lb>tuta, la tastata e la voce. </s>

<s>Così può l&#039;Anima, nel medesimo tempo, attuar <lb></lb>l&#039;istesso umido e chilo nutricando tutte le nostre membra, trasmutandolo in <lb></lb>diverse sostanze e figure, non alterando con l&#039;umido e suoi minimi la simme­<lb></lb>tria. </s>

<s>Dove, se ella si servisse dei solidi, tutte le membra senza alcuna pro­<lb></lb>porzione darebbero nel rotondo e nel simile. </s>

<s>” (Targioni, Notizie degli <lb></lb>aggr. </s>

<s>ecc., T. II, P. I, Firenze 1780, pag. </s>

<s>190, 91). </s></p><p type="main">

<s>Era facile, dietro questi concetti e dietro gli apparecchiamenti fatti dal­<lb></lb>l&#039;ipotesi cartesiana, sovvenisse il pensiero che, stillando il cervello un li­<lb></lb>quido, piuttosto ch&#039;esalare un&#039;aura, e riempiendosi i canaletti de&#039;nervi di <lb></lb>questo liquido, si potesse la pronta comunicazione di moto ai muscoli attri­<lb></lb>buire alla volontà, che per mezzo di qualcuno dei tanti organi cerebrali, <lb></lb>de&#039;quali non conoscesi l&#039;uso, faccia l&#039;effetto stesso del dito sulla bocca del <lb></lb>cilindro, nelle esperienze idrostatiche del Magiotti. </s>

<s>Rintuzzavano però i ri­<lb></lb>gogliosi germogli a questo pensiero l&#039;esperienze autorevoli di Tommaso Bar­<lb></lb>tholin, il quale aveva, come dicemmo, o credeva di aver dimostrato, per <lb></lb>mezzo delle allacciature, che nessuna aereosa o liquida sostanza scorre nel­<lb></lb>l&#039;interiore cavità dei nervi. </s>

<s>Ma poi il Malpighi, facendo più diligente ana­<lb></lb>tomia microscopica del cervello, credè di averlo trovato composto di ghian­<lb></lb>dole secernenti un umore, che di lassù scoli attraverso alle fibrille nervee, <lb></lb>e stimò fosse il fatto messo fuor di ogni dubbio dallo stillicidio, che seguita <pb xlink:href="020/01/1179.jpg" pagenum="54"></pb>dopo il taglio nelle ultime propaggini. </s>

<s>Alle esperienze del Bartholin, che <lb></lb>parevano dimostrar tutto il contrario, rispondeva il Malpighi che il non ve­<lb></lb>dersi inturgidire il nervo, fra le allacciature, non era argomento concludente, <lb></lb>perchè il liquido trova nelle numerose diramazioni libero quel passaggio, che <lb></lb>gli era stato prima impedito nel tronco. </s></p><p type="main">

<s>Narra esso Malpighi, nella Autobiografia più volte da noi citata, come <lb></lb>fosse giunto alla scoperta delle novità anatomiche nel cervello, e facendo <lb></lb>distinzione fra ciò che si poteva dimostrar come certo, e ciò che potevasi <lb></lb>mettere in controversia, così a proposito del succo nerveo, ci lasciò scritto: <lb></lb>“ Nervei succi existentia apud plures controvertitur, vel saltem eius natura <lb></lb>diversimode exponitur, sicut et usus, ita ut nil fere obscurius occurrat apud <lb></lb>Auctores. </s>

<s>Illud tamen mihi videtur in hac re maximum habere momentum <lb></lb>quod, sectis extremis nervorum tubuli, ubi in ultimas solvuntur propagines, <lb></lb>succus erumpat. </s>

<s>In cauda bovis et similium hinc inde nervus excurrit tri­<lb></lb>bus vel quatuor fistulis coagmentatus: in his itaque, facta extremo digiti <lb></lb>ungue compressione, humoris motus intra exaratas fistulas contenti deprehen­<lb></lb>ditur et successiva turgentia, qui tandem per excitatum foramen exit, the­<lb></lb>rebinthinae instar, fluidus enim est et glutinosus. </s>

<s>In nervis, immediate a <lb></lb>spinali medulla erumpentibus, cum ob mollitiem compressi lacerantur, non <lb></lb>ita facile succus occurrit eiusque motus manifestatur, quare solidiores extre­<lb></lb>mique nervi lustrandi sunt. </s>

<s>Nec obstat nervum ligatura facta non turgere, <lb></lb>cum lateraliter propagines habeat reticulariter propaginatas, in qua idem suc­<lb></lb>cus, impedito ulteriori progressu, derivari potest: languidus enim est impe­<lb></lb>tus, quem a cerebro recipit nerveus succus, unde ex quocumque impedi­<lb></lb>mento comprimente et vetante, ulteriorem insinuationem retardari, sisti, et <lb></lb>ad latera derivari potest ” (Opera posthuma cit., pag. </s>

<s>27). Queste esperienze <lb></lb>furono poi dopo il Malpighi ripetute dal Bellini, il quale tenne come cosa <lb></lb>di fatto che “ il liquido dei nervi scorre sempre incessantemente e tien sem­<lb></lb>pre pieni di sè i suoi canali ” (Discorsi di Anat., Milano 1837, pag. </s>

<s>15), e <lb></lb>il Lancisi concludeva alla necessità di quel succo, per mettere in moto i <lb></lb>muscoli, osservando “ quod ligato nervo .... ad musculum aliquem pertin­<lb></lb>gente, eius motus deficit, tamdemque, flaccescente musculo, penitus cessat ” <lb></lb>(De motu cordis, Romae 1728, pag. </s>

<s>9). </s></p><p type="main">

<s>Quel pensiero di applicare alla trasmissione del moto nei muscoli il <lb></lb>principio idrostatico del Magiotti, dappoichè il Malpighi ebbe contro il Bar­<lb></lb>tholin dimostrata l&#039;esistenza di un liquido fluente dal cervello dentro i tu­<lb></lb>buli de&#039;nervi; quel pensiero diciam dunque, per ridurci colà d&#039;onde mosse <lb></lb>il discorso, essere principalmente sovvenuto al Borelli, che lo pose per fonda­<lb></lb>mento a questa parte della sua Meccanica animale. </s>

<s>Egli suppone infatti che la <lb></lb>prima causa eccitante il moto ne&#039;muscoli sia il succo nerveo, il quale è fatto <lb></lb>dal cervello stillare in essi muscoli, per un moto di compressione delle fibre <lb></lb>cerebrali; moto che si comunica nell&#039;istante fino alle ultime diramazioni <lb></lb>nervose, per quella medesima ragione idrostatica, per cui la pression del dito <lb></lb>nell&#039;esperienze del Magiotti si comunica nell&#039;istante dalla bocca al fondo del <pb xlink:href="020/01/1180.jpg" pagenum="55"></pb>Cilindro, e da una estremità all&#039;altra di un tubo membranoso pien d&#039;acqua, <lb></lb>come, per esempio, nel lungo tubo di un intestino. </s>

<s>“ Et sicuti videmus in <lb></lb>intestino aqua repleto, et utrimque clauso, quod uno eius extremo impulso, <lb></lb>compresso et leviter percusso, subito commotio et concussio ad oppositum <lb></lb>terminum intestini turgidi communicatur, quatenus fluidae partes inter se <lb></lb>contiguae, longo ordine se consequentes una alteram impellendo et concu­<lb></lb>tiendo motionem diffundunt usque ad extremam intestini partem; sic pari­<lb></lb>ter a quacumque levi compressione, ictu, aut irritatione facta in principiis <lb></lb>canaliculatarum fibrarum nervearum in ipso cerebro existentibus, necesse <lb></lb>est ut ipsae fibrae concussae et agitatae instillent guttas aliquas illius succi, <lb></lb>quo turgent internae eorum spongiosae substantiae intra musculorum car­<lb></lb>neam molem ” (De motu animal. </s>

<s>cit., P. II, pag. </s>

<s>58, 59). </s></p><p type="main">

<s>Ma benchè la facile e subitanea trasmissione del moto ne&#039;liquidi avesse <lb></lb>fatto ritrovare al Borelli la probabile ragion fisica della rapida trasmissione <lb></lb>dei moti volontari, infino all&#039;estreme propaggini dei nervi, questo solo però <lb></lb>non bastava, ma conveniva di più spiegare in che modo così fatte stille di <lb></lb>sacco nerveo avessero potuto indurre ne&#039;muscoli quella sì facile e repen­<lb></lb>tina contrazione, dalla quale immediatamente dipendono i moti delle mem­<lb></lb>bra. </s>

<s>Si risovvenne allora dell&#039;effervescenza, in che si commovono a un tratto <lb></lb>due liquidi mescolati insieme nelle chimiche ampolle, e immaginò che una <lb></lb>simile effervescenza venga a mettersi nel sangue e nella linfa de&#039;muscoli, <lb></lb>quando scende a stillar sopr&#039;essi il liquido spiritoso de&#039;nervi. </s>

<s>Ond&#039;è che, <lb></lb>esaminate altre cause e trovatele tutte insufficienti a spiegare il fatto “ re­<lb></lb>stat solummodo, egli conclude, ut ex mistione succi nervei cum lympha, vel <lb></lb>cum sanguine, fermentatio et ebullitio oriatur similis eis, quae passim in <lb></lb>chimicis elaborationibus observantur ” (ibi, pag. </s>

<s>63). </s></p><p type="main">

<s>Questa ipotesi dei moti muscolari, benchè si pubblicasse nel 1681, l&#039;aveva <lb></lb>nulladimeno speculata il Borelli parecchi anni avanti, e forse prima che Gu­<lb></lb>glielmo Croone si fosse incontrato in que&#039;medesimi pensieri, ch&#039;ei pubblicò <lb></lb>in Amsterdam, nel 1667, in un Trattatello intitolato <emph type="italics"></emph>De ratione motus mu­<lb></lb>sculorum.<emph.end type="italics"></emph.end> Premessa una diligente anatomia delle fibre e una nuova fisiologia <lb></lb>de&#039;loro atti vitali in contrarsi e in dilatarsi, vien l&#039;Autore a proporre la sua <lb></lb>ipotesi, intorno alla quale, sentite le gravissime difficoltà, confessa di non <lb></lb>avere, in cosa tanto oscura, ad affermare nulla di certo. </s>

<s>Ma comunque sia, <lb></lb>egli dice, per quell&#039;impulso, che riceve l&#039;estremità del nervo nel cervello, <lb></lb>si scuote tutta la serie delle fibre, infino alle loro estreme diramazioni per <lb></lb>entro la sostanza dei muscoli, dove stillano quel loro liquido spiritoso. </s>

<s>“ Cum <lb></lb>enim iam satis probatum sit vim quamdam a cerebro per nervos advehi in <lb></lb>musculum, nec, si oculis fides habenda sit, quicquam in nervis appareat, <lb></lb>quod huic usui magis convenire queat, quam opulentissimus ac spirituosus <lb></lb>iste succus, qui constanti circuitu per omnes nervos traducitur; quid obsecro, <lb></lb>magis verisimile est, quam vim illam cum hoc liquore deferri, aut potius <lb></lb>esse hunc ipsum liquorem, sive spiritum animalem fibrarum impetu a ner­<lb></lb>vorum ramulis excussum? </s>

<s>Quod si sit, illud quoque admodum probabile <pb xlink:href="020/01/1181.jpg" pagenum="56"></pb>erit ex admistione liquoris huiusce, sive spiritus cum spiritibus sanguinis, <lb></lb>continuo spirituosarum omnium particularum, quae in vitali motus musculi <lb></lb>succo insunt, magnam agitationem contingere, uti cum spiritus vini spiritui <lb></lb>sanguinis humani admiscetur. </s>

<s>Namque omnem animantis partem vivifico <lb></lb>quodam ac spirituoso liquore turgescere, supra quidem monui, ac omnibus <lb></lb>est in confesso, ac nemo fere tam in Chymia hospes est, qui nesciat quanta <lb></lb>particularum commotio ac agitatio ex variis inter se permistis liquoribus ac­<lb></lb>cidere soleat ” (pag. </s>

<s>23). </s></p><p type="main">

<s>Prese risoluzione il Croone, com&#039;egli stesso dice nella lettera al Com­<lb></lb>melin, di dare alla luce questa sua nuova ipotesi de&#039;moti muscolari, in quel <lb></lb>tempo che gli era venuto avviso in Parigi come lo Stenone aveva sotto i <lb></lb>torchi i suoi Elementi di miologia. </s>

<s>Apparvero veramente quegli Elementi alla <lb></lb>luce in Firenze, in quel medesimo anno 1667, e l&#039;Autore, dimostrando geo­<lb></lb>metricamente la proposizione “ in omni musculo, dum contrahitur, tumorem <lb></lb>contingere, etiamsi musculus contractus aequalis maneret musculo non con­<lb></lb>tracto ” (pag. </s>

<s>16) rovesciava dalle fondamenta, senza saperlo, l&#039;ipotesi messa <lb></lb>dallo stesso Croone, in quel medesimo tempo, alla luce, e insieme anche <lb></lb>l&#039;altra simile, che avrebbe pubblicata il Borelli quattordici anni dopo. </s></p><p type="main">

<s>Scendeva come corollario da quella proposizione che nessuna estranea <lb></lb>materia s&#039;insinua a ingrossare le fibre muscolari, per indurvi le contrazioni, <lb></lb>intorno a che lo Stenone si dichiara nella lettera al Thevenot, non osando <lb></lb>però di decider nulla di certo, ma facendo osservare che lo stillarsi il succo <lb></lb>nerveo in mezzo alle fibre muscolari, e il produrre una subita effervescenza <lb></lb>nella linfa e nel sangue, di che sono esse fibre sempre imbevute, erano ipotesi <lb></lb>deboli di per sè, e non confortate da nessuna esperienza: parole insomma e <lb></lb>non fatti. </s>

<s>“ Spiritus animales, subtiliorem sanguinis partem, vaporem eius, et <lb></lb>nervorum succum multi nominant, sed verba haec sunt, nihil exprimentia. </s>

<s><lb></lb>Qui ulterius pergunt salinas, sulphureasque partes, vel spiritui vini analo­<lb></lb>gum quid adferunt, quae vera forsan sed nec certa nec satis distincta. </s>

<s>Ab <lb></lb>assumpto vini spiritu restitui exhaustas vires experientia docet, sed ipsi hoc <lb></lb>humori, quem spiritum vocamus, an alii materiae adscribendum, quae spi­<lb></lb>ritum fluidum reddit, aut aliam forte ob causam illi iuncta est, quis deter­<lb></lb>minaverit? (ibi, pag. </s>

<s>63). </s></p><p type="main">

<s>Il Borelli non mancò di rispondere a queste difficoltà promosse dallo <lb></lb>Stenone, e se l&#039;effervescenza dentro le fibre de&#039;muscoli non si vede, non <lb></lb>importa diceva, vedendosene così manifesti gli effetti. </s>

<s>Alla proposizione ste­<lb></lb>noniana, nella quale provavasi che i muscoli, mentre che si contraggono, <lb></lb>non ricrescon di mole, contrapponeva un&#039;altra proposizione che è la XV della <lb></lb>II Parte <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> e nella quale il Borelli stesso dimostrava non <lb></lb>esser possibile che il muscolo inturgidisca, senza che vi si insinui una ma­<lb></lb>teria estranea, la quale faccia dentro i pori delle fibre l&#039;effetto meccanico <lb></lb>de&#039;cunei, e perciò concludeva esser impossibile che il muscolo indurisca e <lb></lb>non rigonfi. </s>

<s>“ Talis autem inflatio esset impossibilis, nisi particulae corpo­<lb></lb>ris advenientis ad instar cuneorum insinuarentur intra porositates earum-<pb xlink:href="020/01/1182.jpg" pagenum="57"></pb>dem fibrarum, aut illa spatia, vi percussiva expanderent, quae actio pariter <lb></lb>ad vim et actionem cunei reducitur ” (Editio cit., pag. </s>

<s>30). </s></p><p type="main">

<s>Giovanni Bernoulli, cercando un soggetto da porre a nuovo cimento la <lb></lb>già sperimentata virtù del Calcolo differenziale, lo trovò in questi moti mu­<lb></lb>scolari, intorno ai quali scrisse una Dissertazione, che seguita com&#039;appen­<lb></lb>dice al trattato <emph type="italics"></emph>De separatione liquidorum<emph.end type="italics"></emph.end> del Michelotti. </s>

<s>Ivi è il Bernoulli <lb></lb>fedel seguace dell&#039;ipotesi del Borelli, e quanto al teorema dello Stenone, in <lb></lb>cui dimostravasi che il muscolo si contrae, non per aggiunta di materia, ma <lb></lb>per la sola mutazion di figura, trasformandosi da un parallelogrammo obli­<lb></lb>quangolo in retto, sentenziò che quella era opinione “ prorsus ridicula, et <lb></lb>pro mero lusu ingenii Authoris habenda ” (Venetiis 1721, pag. </s>

<s>4). Eppure <lb></lb>Fisiologi più recenti, facendo contrarre i muscoli sott&#039;acqua e notando se <lb></lb>scorgevasi alcuna variazion di livello, benchè non ne concludessero nulla di <lb></lb>certo, pur parvero l&#039;esperienze inclinare a favore dello Stenone. </s></p><p type="main">

<s>Erasi in ogni modo il Borelli acquistata tanta autorità in così fatte que­<lb></lb>stioni di Meccanica animale, che resisterono le sue dottrine a tutte le con­<lb></lb>tradizioni di allora, e istituitasi la Scuola iatromatematica i discepoli si stu­<lb></lb>diarono di migliorarle, per renderle così nell&#039;universale più accette. </s>

<s>Il Bellini, <lb></lb>che fu tra que&#039;discepoli uno de&#039;più valentemente operosi, commemorando <lb></lb>nel suo trattato <emph type="italics"></emph>De motu cordis<emph.end type="italics"></emph.end> in che modo avesse dimostrato il Borelli la <lb></lb>ragione dei moti muscolari, soggiunge con gran compiacenza che la mede­<lb></lb>sima cosa “ nos alia via longe diversa et magis naturali demonstramus ” <lb></lb>(Op. </s>

<s>omnia, P. II, Venetiis 1708, pag. </s>

<s>161). Consiste questa ipotesi più na­<lb></lb>turale nell&#039;ammettere che le fibre muscolari sieno composte di villi natu­<lb></lb>ralmente contrattili, cosicchè non ci sia d&#039;altro bisogno a farle effettivamente <lb></lb>contrarre, che dell&#039;azione degli stimoli esterni. </s>

<s>Egli osserva che la virtù di <lb></lb>contrarsi non è propria solo ai tessuti organici, ma a tutta la materia, di <lb></lb>che cerca le prove in moltissimi fatti naturali, e fra questi nel conglobarsi <lb></lb>delle gocciole liquide, ammirando la potenza di quella forza di contrazione, <lb></lb>che vince le resistenze opposte dal pesantissimo argento vivo. </s></p><p type="main">

<s>Egli ammette col Malpighi che sia il cervello una glandula secernente <lb></lb>un umore spiritoso, che stilla in mezzo alle fibre muscolari per il condotto <lb></lb>dei nervi, e ammette col Borelli che, mescendosi quell&#039;umor nerveo alla <lb></lb>linfa e al sangue delle stesse fibre, vi produca una subita effervescenza, e <lb></lb>così le faccia contrarre. </s>

<s>Ma mentre che il Borelli riduceva la causa imme­<lb></lb>diata di così fatte contrazioni alle bollicelle sollevatesi nell&#039;effervescenza, le <lb></lb>quali insinuandosi fra le porosità della sostanza fibrosa operano meccani­<lb></lb>camente in dilatarle, come tanti cunei ficcatisi in mezzo per forza; il Bel­<lb></lb>lini ammetteva ne&#039;villi, di che s&#039;intessono i muscoli, una nativa loro irri­<lb></lb>tabilità, ad eccitar la quale le bollicelle sollevatesi nella effervescenza operino <lb></lb>come stimoli accidentalmente sopravvenuti di fuori. </s></p><p type="main">

<s>Alla raccolta delle Opere belliniane, da noi sopra citata e alla quale <lb></lb>sopraintese Giovanni Bohn con tanto amorose e sapientissime cure, è pre­<lb></lb>messa una Sinopsi, nella quale i principii, a cui s&#039;informa l&#039;ipotesi dell&#039;Au-<pb xlink:href="020/01/1183.jpg" pagenum="58"></pb>tore, son ridotti a sommi capi, quasi essenze stillate dalla polpa di squisi­<lb></lb>tissimi pomi, e infuse dentro a varie piccole ampolle. </s>

<s>Per quel che riguarda <lb></lb>il moto del liquido dentro i nervi, i principii belliniani si riducono sostan­<lb></lb>zialmente ai tre capi seguenti: “ I. </s>

<s>Datur liquidum in nervis igne concre­<lb></lb>scens. </s>

<s>II. </s>

<s>Eiusmodi liquido nervi semper in statu naturali sunt pleni. </s>

<s>III. </s>

<s>Vis <lb></lb>praecipua, qua liquidum nervorum a cerebri glandulis exprimitur, et per <lb></lb>ipsos influxum agitur, est pressio proveniens a dilatatione arteriarum Piam <lb></lb>matrem intexentium, et etiam intime totum cerebrum intercurrentium. </s>

<s>” </s></p><p type="main">

<s>Per quel che poi più particolarmente concerne i moti de&#039;muscoli, così <lb></lb>necessarii che volontarii, le dottrine del Bellini si trovano sostanzialmente <lb></lb>comprese ne&#039;seguenti principii: “ I. </s>

<s>Licet ad imperium voluntatis aut ap­<lb></lb>petitus cresceret impetus et copia liquidi per nervos quantum libet, non ta­<lb></lb>men id esse potest incrementum, quod satis sit subitae ac vehementi con­<lb></lb>tractioni villi. </s>

<s>II. </s>

<s>Subita ac violenta villi contractio, nisusque in oppositos <lb></lb>terminos, fit per influxum liquidi subito rarescentis aut quaquaversum se se <lb></lb>cum impetu in bullas innumeras effundentis. </s>

<s>Oportet autem liquidum in­<lb></lb>fluens sit tantae molis, ut cum rarescit aut in bullas effunditur, ipsius par­<lb></lb>tes per universam villi longitudinem amplitudinemque se premant. </s>

<s>III. </s>

<s>Motus <lb></lb>villi rarescente intra ipsum, aut se in bullas effundente, liquido componitur <lb></lb>ex contractione per longitudinem et distractione per amplitudinem: cum vil­<lb></lb>lus in suam longitudinem restituitur, contrahitur per amplitudinem, et causa <lb></lb>huius contractionis breviter iudicatur. </s>

<s>” </s></p><p type="main">

<s>Udimmo dianzi il Bellini compiacersi di questa sua ipotesi e a para­<lb></lb>gone di quella del Borelli vantarla per più naturale, cioè più conforme alla <lb></lb>Natura, la quale non opera ne&#039;muscoli con forze morte, come nelle mac­<lb></lb>chine, ma con le proprie e particolari virtù della vita. </s>

<s>Tanto parve ragione­<lb></lb>vole questo perfezionamento introdotto nell&#039;ipotesi borelliana, che Alberto <lb></lb>Haller accolse il fondamento delle idee belliniane nel suo trattato di Fisio­<lb></lb>logia. </s>

<s>Svolgendo infatti il libro XI, alla terza Sezione, vi si trova insegnato <lb></lb>che la forza contrattile è insita al muscolo, e che, sebben non sempre ve­<lb></lb>dasi in atto, pur si può mettere anche artificialmente per via degli stimoli, <lb></lb>che vi producono una irritazione. </s>

<s>Questa irritazione, nelle parti vive, diffe­<lb></lb>risce da quella che osservasi nella morte, e non si può confondere con la <lb></lb>facoltà del sentire. </s>

<s>“ Laurentius Bellinius vim contractilem naturalem fuse <lb></lb>exposuit, quae ab acribus excitata se causa molestiae liberet, musculos mo­<lb></lb>veat, sanguinis motum acceleret .... mechanice omnia ex hypothesi citra <lb></lb>experimentum. </s>

<s>Praeterea et ipse Vir clarissimus, et qui eum sunt secuti, <lb></lb>contractionem vivam a mortua, hanc a nervosa non satis videntur distinxisse ” <lb></lb>(Elem. </s>

<s>Physiol., T. IV, Lausannae 1766, pag. </s>

<s>461). </s></p><p type="main">

<s>S&#039;argomenta assai facilmente da queste parole quali fossero i perfezio­<lb></lb>namenti introdotti dall&#039;Haller nelle dottrine del Bellini, d&#039;onde ne nacque <lb></lb>quella celebre Scuola halleriana, ch&#039;ebbe così numerosi e valenti seguaci <lb></lb>nella Svizzera, in Francia e anche fra noi in Italia. </s>

<s>Il Fisiologo di Berna <lb></lb>accusa il Nostro di avere speculata la sua ipotesi senza il fondamento del-<pb xlink:href="020/01/1184.jpg" pagenum="59"></pb>l&#039;esperienze, ma le stesse esperienze halleriane servono benissimo a far di­<lb></lb>stinguere fra le vie da tenersi l&#039;una dall&#039;altra; rischiarano altresì quella <lb></lb>ch&#039;è la più diretta; fino a un certo punto però, oltre il quale si trovano <lb></lb>immersi nelle tenebre più profonde i desiderosi di veder il termine del fa­<lb></lb>ticoso cammino. </s>

<s>Fu perciò che molti deliberarono di tornarsene indietro, a <lb></lb>somiglianza di chi, presumendo di avere in ogni modo a trovare la riu­<lb></lb>scita, si lusinga di avere smarrita la via, a cui cerca altra più pratica scorta <lb></lb>e più fida. </s></p><p type="main">

<s>È notabile esempio nel numero di costoro Stefano Hales, il quale in sul <lb></lb>cominciar del secolo XVIII ritornò indietro a cercare fra le ipotesi proposte <lb></lb>da&#039;Fisiologi che lo avevano preceduto se qualcuna per avventura sodisfaces­<lb></lb>segli meglio delle più recenti. </s>

<s>Rivolse più particolarmente la sua attenzione <lb></lb>all&#039;ipotesi di coloro, da&#039;quali s&#039;attribuivano i moti muscolari all&#039;impulso, <lb></lb>che viene al sangue dal cuore, e non arretrato dalla grande autorità nè dalle <lb></lb>ragioni, con ch&#039;era stata confutata una tale ipotesi dal Borelli, volle sotto­<lb></lb>porla all&#039;esame di nuovi e più delicati esperimenti. </s>

<s>“ Sono già ventisette <lb></lb>anni, scriveva, che leggendo le congetture poco sodisfacenti degli Autori, che <lb></lb>trattano del moto muscolare, mi posi a fare sperienze sugli animali viventi, <lb></lb>per iscoprire se il sangue, col solo suo moto meccanico, avesse una forza <lb></lb>bastevole a dilatare le fibre muscolose, e a scemare per tal via in loro lun­<lb></lb>ghezza, e produrre i grandi effetti del moto muscolare. </s>

<s>Questo si fu il mo­<lb></lb>tivo che m&#039;indusse ad entrare nel vasto campo delle esperienze che ho fatto ” <lb></lb>(Statica animale, traduz. </s>

<s>ital., Napoli 1750, pag. </s>

<s>66). Ebbe però da così fatte <lb></lb>laboriose esperienze ragionevolmente a concludere “ che la forza del sangue <lb></lb>ch&#039;entra ne&#039;muscoli è molto piccola in agguaglio di quel che dovrebb&#039;es­<lb></lb>sere per produrre il moto muscolare ” (ivi, pag. </s>

<s>65). </s></p><p type="main">

<s>Rimaneva da questa alesiana conclusione sperimentale rovesciata dalle <lb></lb>sue fondamenta anche un&#039;altra ipotesi macchinata da Giorgio Baglivi, e già <lb></lb>da sè stessa vacillante, per la troppo debole struttura. </s>

<s>Incomincia dal con­<lb></lb>siderare il celebre Archiatro pontificio la grande efficacia del sangue nei moti <lb></lb>muscolari; efficacia dimostrata da un&#039;esperienza dello Stenone, che allac­<lb></lb>ciando l&#039;arteria magna vide gli arti posteriori rimanere immobili in un cane; <lb></lb>confermata dal veder tuttavia seguitare a pulsare il cuore estratto dalle rane, <lb></lb>e più concludentemente dagli aneurismi, che inducono il torpore nelle parti <lb></lb>non più irrigate. </s>

<s>Ripensando poi in che modo possa esercitare il sangue <lb></lb>questa sua efficacia, ricorre a quelle particelle solide di zolfo “ salium varii <lb></lb>generis, terrae, globulorum rubrorum, striarum nutritiarum et mille aliarum <lb></lb>particularum ” che il sangue stesso “ ab aere, fossilibus, et vegetabilibus <lb></lb>continuo haurit, et in sinu fovet ” (Opera omnia, Dissertatio De motu musc., <lb></lb>Lugduni 1710, pag. </s>

<s>404). </s></p><p type="main">

<s>Queste particelle solide fanno sopra le fibre muscolari l&#039;effetto stesso <lb></lb>dei <emph type="italics"></emph>curri<emph.end type="italics"></emph.end> applicati a muovere i pesi. </s>

<s>“ Et quia velociter currunt impresso <lb></lb>illis a corde pulsante vehementissimo impetu, necesse est ut fibrarum fila <lb></lb>ad contactum globulorum currentium premantur, et undulando veluti cri-<pb xlink:href="020/01/1185.jpg" pagenum="60"></pb>spentur, quae crispatura, quoniam maxime sensibilis est in medio musculi, <lb></lb>ubi sanguis velocius currit, sequitur inde, ut extrema fibrarum singula­<lb></lb>rum versus medium contrahantur, brevìora fiant et apposita sublevent ossa ” <lb></lb>(pag. </s>

<s>405). </s></p><p type="main">

<s>A ciò semplicemente ridurrebbesi l&#039;effetto prodotto dalle particelle so­<lb></lb>lide contenute nel sangue, quand&#039;elle fossero perfettamente sferiche. </s>

<s>Ma se <lb></lb>sono irregolari, allungate più per un verso che per un altro, si produrranno <lb></lb>nelle fibre de&#039;muscoli moti più complicati, sinuosi e vermicolari, come quelli <lb></lb>per esempio degli intestini. </s>

<s>Una tale irregolarità poi nelle particelle solide <lb></lb>del sangue, è, soggiunge il Baglivi, prodotta dalla virtù propria del succo <lb></lb>nerveo, il quale “ cum sit summopere tenue, elasticum, et radiis lucis affine, <lb></lb>incredibili celeritate a phantasia impulsum, cum sanguine musculi iam iam <lb></lb>movendi miscetur, et quadam elastica irradiatione, cum proportione tamen <lb></lb>et aequilibrio, minima eius mutat et alterat, mutataque minimorum figura, <lb></lb>mutantur etiam diametri ” (pag. </s>

<s>406). Di qui nasce, secondo lo stesso Ba­<lb></lb>glivi, che se non ci fossero gli antagonisti, i moti muscolari sarebbero con­<lb></lb>tinui, come veramente continui son quelli del cuore e degli intestini. </s>

<s>Per <lb></lb>conseguenza, dal mancare un così fatto antagonismo, si risolve ogni difficoltà, <lb></lb>e si rende la ragion chiarissima delle differenze, che passano tra i moti na­<lb></lb>turali e i volontari (ivi, pag. </s>

<s>406, 7). </s></p><p type="main">

<s>Il mancare a così fatta ipotesi ogni buon fondamento di fisica e di mec­<lb></lb>canica la fece facilmente repudiare ai Fisiologi, sopra i quali tanto più tornò <lb></lb>inefficace l&#039;autorità del&#039;grande Archiatro, ripensando alla sopra riferita con­<lb></lb>clusione alesiana. </s>

<s>L&#039;Hales stesso, veduto che, per le tante vie fino allora <lb></lb>tentate, non si riusciva a dare quella così lungamente desiderata ragionevole <lb></lb>soluzione al problema dei moti muscolari, piegò anch&#039;egli con molti altri le <lb></lb>vele a ricevere le aure, che si sentivano spirare da un nuovo oriente. </s>

<s>I primi <lb></lb>aliti, benchè insensibili a molti, movevano incerti dal libro delle Questioni <lb></lb>neutoniane, nella XXIV delle quali si leggevano queste parole: “ Annon <lb></lb>motus animalis medii eiusdem actherei efficitur, vibrationibus quae in cere­<lb></lb>bro potestate voluntatis excitantur, indeque per solida, pellucida et unifor­<lb></lb>mia nervorum capillamenta in muscolos eorum contrahendorum ac dilatan­<lb></lb>dorum gratia propagentur? </s>

<s>Nervorum capillamenta singula solida esse pono <lb></lb>et uniformia, ut motus vibrans medii aetherei per ea uniformiter et non in­<lb></lb>terrupte ab usque uno extremo ad alterum propagetur ” (Optices Lib. </s>

<s>III <lb></lb>Quaestiones, Patavii 1773, pag. </s>

<s>144). </s></p><p type="main">

<s>I pensieri del Newton, ch&#039;erano appariti sì oscuri, ebbero a un tratto <lb></lb>uno splendido commento nelle scoperte di Stefano Gray, dalle quali s&#039;ar­<lb></lb>gomentava che, come l&#039;etere elettrico diffondevasi da un capo all&#039;altro di <lb></lb>una corda bagnata, così poteva similmente diffondersi dall&#039;una all&#039;altra estre­<lb></lb>mità del nervo. </s>

<s>L&#039;Hales perciò inclinava a preferire questa nuova ipotesi a <lb></lb>tutte le altre, che s&#039;erano dal Cartesio in poi sotto varie forme proposte, e <lb></lb>a renderla anche più probabile citava fatti fisiologici e patologici, come per <lb></lb>esempio quello che, grattandosi talvolta le bolle in alcuna parte del corpo, <pb xlink:href="020/01/1186.jpg" pagenum="61"></pb>si sente in altre parti lontane risvegliarsi punture, che si succedono al metro <lb></lb>del menare delle unghie. (Statica anim. </s>

<s>cit., pag. </s>

<s>65). </s></p><p type="main">

<s>Così, l&#039;etere neutoniano, riconosciuto simile negli effetti all&#039;elettrico, si <lb></lb>applicò alle funzioni della vita animale sotto il nome di <emph type="italics"></emph>fluido biotico,<emph.end type="italics"></emph.end> e le <lb></lb>antiche teorie meccaniche del Borelli parvero essere allora dalla Fisiologia <lb></lb>licenziate per sempre. </s>

<s>Ma come talvolta l&#039;aria combattuta da venti contrarii <lb></lb>si rischiara da una parte, in quel medesimo tempo che si oscura dall&#039;altra, <lb></lb>e come, dietro una subitanea luce abbagliante, le tenebre si fanno più fitte; <lb></lb>così avvenne alla scienza, quando lieta di avere scoperto nell&#039;elettricità i mi­<lb></lb>steriosi spiriti della vita, si domandò d&#039;onde avesse cotesta vitale elettricità <lb></lb>l&#039;origine, e com&#039;ella operasse a produrre i moti muscolari. </s>

<s>E perchè s&#039;am­<lb></lb>metteva con facilità da tutti non potere essere altrove quell&#039;origine che nel <lb></lb>cervello, sentivasi una viva curiosità di sapere in qual modo quel viscere, <lb></lb>in apparenza inerte, potesse rassomigliarsi ai globi tornatili di zolfo o di vetro <lb></lb>conosciuti allora dell&#039;artificiosa elettricità le sole possibili sorgenti. </s>

<s>Inteso ciò, <lb></lb>era men difficile intendere l&#039;azione elettrica sui muscoli, ridotta facilmente <lb></lb>dall&#039;Haller a uno de&#039;più efficaci stimoli esterni. </s></p><p type="main">

<s>Era a questo punto del suo faticoso cammino giunta la scienza, quando <lb></lb>occorse la memoranda scoperta di Luigi Galvani. </s>

<s>E perch&#039;è un fatto sto­<lb></lb>rico che i germi di novità scientifiche più fecondi sono quasi sempre sboc­<lb></lb>ciati sotto il cielo d&#039;Italia, e un&#039;occulta cognazione, inconsapevole anche a sè <lb></lb>stessi, è sempre fra i grandi ingegni, specialmente della medesima nazione; <lb></lb>non vogliamo lasciar di notare in queste pagine di storia un singolare esem­<lb></lb>pio della detta cognazione che passa inconsapevole fra il Galvani stesso e il <lb></lb>Borelli. </s>

<s>Chi legge nel trattato <emph type="italics"></emph>De motu animalium<emph.end type="italics"></emph.end> la proposizione CCXIII <lb></lb>della Parte II riman sorpreso di gran maraviglia, trovando ivi descritta in­<lb></lb>torno alle rane scorticate quell&#039;esperienza, che conteneva in sè come in fonte <lb></lb>nascosto i fiumi delle dottrine galvaniche non solo, ma di quelle stesse del <lb></lb>Volta. </s>

<s>“ Videmus autem quod talis irritatio efficitur in nervis cruralibus <lb></lb>Ranarum exenteratarum quotiescumque acu punguntur, vel succo salino <lb></lb>tanguntur ” (Editio cit., pag. </s>

<s>433). </s></p><p type="main">

<s>Mentre insomma che la Scienza fisiologica confessava d&#039;ignorar come <lb></lb>avesse origine quell&#039;elettricità animale, che dietro le speculazioni del Newton <lb></lb>e l&#039;esperienze del Gray tenevasi più per certa oramai che per probabile, <lb></lb>usciva fuori il Galvani a dimostrar che i muscoli e i nervi componevano, a <lb></lb>somiglianza di quei ritrovati dall&#039;arte, un nuovo apparecchio elettrico della <lb></lb>vita. </s>

<s>“ Huius peculiare nec antea cognitum ingenium esse videtur ut a mu­<lb></lb>sculis ad nervos vel ab his potius ad illos tendat vehementer, subeatque <lb></lb>illico vel arcum, vel hominum catenam vel quaecumque alia deferentia cor­<lb></lb>pora, quae a nervis ad musculos breviori et expeditiori ducant itinere, ce­<lb></lb>lerrimeque per eadem ab illis ad hos excurrat. </s>

<s>Ex hoc autem duo maxime <lb></lb>profluere videntur, duplicem scilicet in his partibus electricitatem esse, po­<lb></lb>sitivam aliam, ut credere est, aliam negativam, atque alteram ob altera pe­<lb></lb>nitus esse natura seiunctam, secus enim, aequilibrio habito, nullus motus, <pb xlink:href="020/01/1187.jpg" pagenum="62"></pb>excursus electricitatis nullus, nullum muscularis contractionis phaenomenon ” <lb></lb>(A. Galvani, De viribus electric., Mutinae 1792, pag. </s>

<s>39). </s></p><p type="main">

<s>Ammesso però che la sede dell&#039;elettricità sia nel muscolo, e che perciò <lb></lb>il cervello non dia ma riceva del fluido elettrico, difficilissima riusciva la <lb></lb>ragione dei moti volontari. </s>

<s>Così fatta difficoltà era ben sentita dallo stesso <lb></lb>Galvani, ma tanta parvegli essere la certezza, che veniva dai fatti sperimen­<lb></lb>tati, da non doversi dubitar se il circolo sia veramente dal muscolo al nervo. </s>

<s><lb></lb>Quando poi il Volta, fatte nuove e più diligenti esperienze, ritrovò che l&#039;elet­<lb></lb>tricità veramente fluiva, come pareva più conveniente, dal nervo al muscolo, <lb></lb>e allora al Galvani non dispiacque di aver errato, e anzi parve che in certo <lb></lb>modo se ne compiacesse nella risposta ch&#039;ei diresse a Bassiano Carminati, <lb></lb>il quale lo aveva da Pavia informato delle prime scoperte elettriche fatte <lb></lb>ivi dal Volta. </s></p><p type="main">

<s>“ Gli esperimenti di lui, scriveva del Volta il Galvani, chiaro dimostre­<lb></lb>rebbono potersi avere i moti muscolari, diretto il fluido elettrico, non solo <lb></lb>dal muscolo al nervo, siccome io supponeva, ma eziandio dal nervo al mu­<lb></lb>scolo, e potersi avere, non solo per mezzo della scarica, ma ancora per una <lb></lb>sopraccarica forzata ed impetuosa della supposta boccia muscolare, lo che <lb></lb>ammesso, chi non vede quanto riesca felice la spiegazione de&#039;moti musco­<lb></lb>lari volontarii? </s></p><p type="main">

<s>“ L&#039;anima, per eccitar questi, non deve che dal cervello ov&#039;ella risiede, <lb></lb>colla maravigliosa sua ed incomprensibil forza ed impero, determinare una <lb></lb>maggior copia di fluido elettrico animale nel cervello raccolto pel nervo con­<lb></lb>duttore al muscolo; oppure dar forse un impulso maggiore a quello che na­<lb></lb>turalmente in esso nervo esiste. </s>

<s>Si avranno allora le contrazioni non altri­<lb></lb>menti che si ebbero dal celebratissimo signor Volta, allorchè egli aggiunse <lb></lb>all&#039;elettricità animale del nervo un pochino di artifiziale elettricità, e crebbe <lb></lb>in conseguenza l&#039;impulso e l&#039;azione di quella, che nell&#039;interna superficie <lb></lb>della fibra muscolare si stava in una specie di inerzia o di ozioso equilibrio. </s>

<s><lb></lb>Ma allorchè si aggiunge elettricità ad una superficie di una Boccia di Ley­<lb></lb>den, ne esce dall&#039;opposta, per la legge dell&#039;uguaglianza e dell&#039;equilibrio <lb></lb>delle due superficie, e tanta ne esce da una quanto se ne aggiunge all&#039;altra; <lb></lb>dunque avvependo lo stesso nella supposta boccia muscolare, quanto di fluido <lb></lb>nerveo elettrico accorrerà dal cervello pel nervo all&#039;interna parte, ossia su­<lb></lb>perficie del muscolo, tanto ne escirà dall&#039;opposta superficie, ossia parte <lb></lb>esterna del medesimo, che è già sempre irrigata da fluidi conduttori atti a <lb></lb>disperderla, e a portarla fuori del corpo, e quindi luogo darassi sempre a <lb></lb>una nuova copia e carica..... ” </s></p><p type="main">

<s>“ Ammesso un tale costante ingresso ed egresso del detto fluido ner­<lb></lb>veo dal muscolo, per leggi note e costanti, chi non vede tosto essere facile <lb></lb>lo spiegare come costantemente corra il suddetto fluido al muscolo, senza <lb></lb>che se ne accumuli in esso all&#039;eccesso, e in modo che impedisca l&#039;aggiunta <lb></lb>di nuovo copia o naturalmente fluente dal cervello al medesimo muscolo o <lb></lb>dall&#039;anima determinatavi? </s>

<s>Fenomeno che certo in niuno de&#039;sistemi finora <pb xlink:href="020/01/1188.jpg" pagenum="63"></pb>inventati facilmente intendesi ” (Appandice al trattato De virib. </s>

<s>electric. </s>

<s>cit., <lb></lb>pag. </s>

<s>72, 73). </s></p><p type="main">

<s>Ma poco dopo venne il Volta a tentare colle sue valide forze di distrug­<lb></lb>gere il bello architettato edifizio, dimostrando come quella che si credeva <lb></lb>essere un&#039;elettricità propria e intrinseca all&#039;animale, non era altro che uno <lb></lb>stimolo esterno, sopravveniente dall&#039;elettricità naturale eccitatasi dal contatto <lb></lb>di due diversi metalli. </s>

<s>Il Galvanismo ebbe al poderoso incorso a cedere il <lb></lb>campo, il quale si provò di riconquistar più volte con l&#039;aiuto di valorosi Fi­<lb></lb>siologi, che vennero in sua difesa, ma le vicende di questa lotta e la vit­<lb></lb>toria non bene ancora decisa stanno ad attestare quanto sia ottuso l&#039;ingegno <lb></lb>dell&#039;uomo a penetrare addentro ai misteri della vita. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le studiose esercitazioni fatte da tanti e si valorosi Fisiologi, che si <lb></lb>trasmisero dall&#039;uno all&#039;altro l&#039;ufficio di render sodisfazione ai curiosi di <lb></lb>saper la causa dei moti muscolari, tornarono insomma inutili, come conclu­<lb></lb>desi dalla passata storia, e l&#039;infelice frutto che se ne raccolse fu di accen <lb></lb>dere, in chi ricorreva a quelle fonti desideroso, una sete più viva. </s>

<s>Ma l&#039;infe­<lb></lb>licità di questi studii, che parevano per verità meritevoli d&#039;altro premio, si <lb></lb>giudica dal considerar di più come, anco quando quelli così ingegnosamente <lb></lb>divisati fossero stati i modi, secondo i quali opera la Natura sui muscoli a <lb></lb>produrre i moti volontarii, rimanevasi nonostante inesplicato il modo dei moti <lb></lb>necessarii, che procedono indipendenti affatto o dalla volontà o dagli istinti <lb></lb>animali. </s>

<s>Il cuore, per esempio, pulsa ne&#039;suoi moti di sistole e di diastole, <lb></lb>anche in chi dorme, e l&#039;intestino reciproca le sue peristaltie e l&#039;antiperi­<lb></lb>staltie o voglia o non voglia l&#039;animale. </s>

<s>Non par però che i processi mecca­<lb></lb>nici, immaginati a spiegare in che modo faccia la volontà convellere le fibre <lb></lb>nervee e spremere il loro succo nelle fibre muscolari, perchè debbano a un <lb></lb>tratto contrarsi; si possano applicare al moto di que&#039;visceri sempre continuo, <lb></lb>e ne&#039;naturali suoi ordini non mai perturbato. </s></p><p type="main">

<s>Il Cartesio, descrivendo nel suo trattato <emph type="italics"></emph>De homine<emph.end type="italics"></emph.end> gli organi, per <lb></lb>mezzo de&#039;quali si muove la macchina animale, non par che si curi se non <lb></lb>che di rendere la ragione dei moti volontarii. </s>

<s>Il moto dèl cuore è secondo <lb></lb>lui necessario, com&#039;è necessario il restringersi e il dilatarsi di tutti i corpi, <lb></lb>ai quali scemino o s&#039;accrescano i gradi del calore. </s>

<s>Questo calore però non <lb></lb>è nativo del cuore, ma gli vien partecipato dal sangue, il quale entra in una <lb></lb>subita calorosa effervescenza, mescolandosi quel poco rimasto ne&#039;ventricoli <lb></lb>con l&#039;altro che sopravviene per l&#039;arteria venosa. </s>

<s>“ Paulum vero illud rare­<lb></lb>facti sanguinis, quod in ventriculis eius restabat, se illi, qui recens ingre­<lb></lb>ditur statim immiscens, est fermenti cuiuspiam loco, sanguinem illum re­<lb></lb>pente calefacientis et dilatantis, qua opera cor intumescit et durescit, et <pb xlink:href="020/01/1189.jpg" pagenum="64"></pb>mucro nonnihil accedit ad basin “ (Editi cit., pag. </s>

<s>163). Ma dappoichè il <lb></lb>sangue così rarefatto ha cominciato a correre per le arterie “ cor continuo <lb></lb>detumescit mollescitque eiusque mucro recedit a base, quia scilicet non re­<lb></lb>manet ipsi parum sanguinis in ventriculis eius ” (ibi). </s></p><p type="main">

<s>Benchè questa ipotesi cartesiana fosse anch&#039;ella, come le altre imma­<lb></lb>ginaria, pur non conoscendosi ancora bene le funzioni della respirazione, e <lb></lb>gli uffici de&#039;polmoni, non avevansi argomenti ragionevoli per confutarla. </s>

<s>Si <lb></lb>diceva che non erano allora ben conosciute le funzioni della respirazione, <lb></lb>perchè il Cartesio ebbe qualche sentore del vero, osservando che l&#039;aria, <lb></lb>nell&#039;atto che l&#039;animale respira, si mescola in qualche modo col sangue, e <lb></lb>serve ad accrescergli l&#039;intensità del calore (ivi, pag. </s>

<s>80). Ma perchè, co­<lb></lb>munque sia, ritenevasi per secondario quello, che era il fatto principale, e <lb></lb>s&#039;ignorava perciò la fisiologia polmonare, non si poteva allora o ripudiare <lb></lb>o confutare l&#039;ipotesi del Cartesio, nè con la certezza dei fatti, nè con l&#039;au­<lb></lb>torità delle ragioni. </s></p><p type="main">

<s>Cotesta certezza e cotesta autorità nella scienza erano però venute ai <lb></lb>tempi del Borelli, il quale si avvide bene che la sua ipotesi dei moti mu­<lb></lb>scolari non si poteva applicare ai moti del cuore, o che almeno per appli­<lb></lb>carvela bisognavano nuovi commenti industriosamente da lui stesso condotti <lb></lb>ed esposti nel Cap. </s>

<s>VI della II Parte Dei moti animali. </s>

<s>Incomincia prima di <lb></lb>tutto a distinguere, fra le cause motive del cuore, una immediata e l&#039;altra <lb></lb>mediata, e mentre vuol nella proposizione LXXVII dimostrar che la prima <lb></lb>di queste cause non differisce da quella medesima, che muove i muscoli vo­<lb></lb>lontari, conclude nella proposizione seguente che la differenza non è altro <lb></lb>che nella seconda; vale a dire nella causa mediata. </s></p><p type="main">

<s>Essendo che dunque i muscoli volontari si contraggono “ inflatis vexi­<lb></lb>culis eorum pororum ” e dall&#039;altra parte il modo di operare della Natura <lb></lb>è nell&#039;ordine e negli strumenti sempre consimile a sè medesimo, “ sic quo­<lb></lb>que immediata causa tensionis cordis erit inflatio vexicularum pororum eius <lb></lb>facta a fermentativa ebullitione tartarearum partium sanguinis a succo spi­<lb></lb>rituoso ex orificiis nervorum instillato ” (Editio cit., pag. </s>

<s>151). </s></p><p type="main">

<s>La causa prima e mediata però che muove il cuore, prosegue nelle sue <lb></lb>dimostrazioni il Borelli, non può essere in nessum modo quella stessa degli <lb></lb>altri muscoli che muovon le membra, perchè mentre un braccio o una <lb></lb>gamba, per esempio, si muove quando, e come e dove io voglio, il cuore <lb></lb>“ non obsequitur voluntatis praecepto, sed non secus ac moletrina sem­<lb></lb>per movetur, sive velimus, sive nolimus, etiam dormientibus nobis ” (ibi, <lb></lb>pag. </s>

<s>152). Di più, non è lecito al cuore, come ai muscoli che muovono le <lb></lb>sopra dette membra, perseverare lungamente nel moto o cessare a talento <lb></lb>“ sed caeca quadam necessitate efficit vehementissimos ac fere momenta­<lb></lb>neos ictus alternis vicibus interceptis, pausis et morulis aeque temporaneis, <lb></lb>nec unquam, donec animal vivit et non aegrotat, talem obstinatam metho­<lb></lb>dum operandi interrumpit ” (ibi). </s></p><p type="main">

<s>Essendo così, è da cercar dunque, seguita il Borelli il suo ragiona-<pb xlink:href="020/01/1190.jpg" pagenum="65"></pb>mento, qual sia la causa prima e immediata che fa muovere il cuore con <lb></lb>metro sì regolato, e indipendentemente da qualunque deliberata volontà del­<lb></lb>l&#039;animale. </s>

<s>Che si possa un tal metro rassomigliare a quello del pendolo non <lb></lb>sembra, perchè converrebbe immaginare un&#039;organo, come sarebbe una val­<lb></lb>vola, che aprendosi e chiudendosi con moto sempre equitemporaneo, ora ri­<lb></lb>tenga gli spiriti animali dentro il cervello, e ora gli anmetta. </s>

<s>Ma oltre che <lb></lb>non si vedono queste valvole, e nessuno ne ha potuto osservare mai il gioco, <lb></lb>resterebbe s sapere qual sia la causa, che le apre e le chiude sempre in <lb></lb>tempo così ben regolato. </s>

<s>“ Alia igitur organica structura inquiri debet, quae <lb></lb>nedum possibilis et facilis sit, sed praeterea passim in naturalibus operatio­<lb></lb>nibus observetur, et sufficiens sit ad superius phaenomena pulsationum cor­<lb></lb>dis salvanda ” (ibi, pag. </s>

<s>155). </s></p><p type="main">

<s>Di così fatta struttura organica parve al Borelli di aver trovato l&#039;esem­<lb></lb>pio in quei filtri, o in quelle sottilissime fistole di vetro, le quali, benchè <lb></lb>sieno di liquido tutte piene, lo fanno nonostante cadere a gocciole, che si <lb></lb>succedono l&#039;una all&#039;altra con pause quasi uguali. </s>

<s>Immagina perciò che i <lb></lb>nervi sieno simili a quelle fistole, sempre pieni di un umor viscido, che <lb></lb>ha nel cervello la fonte. </s>

<s>L&#039;ordine regolare, secondo il quale si succedono <lb></lb>quelle gocciole insinuandosi tra le fibre del cuore, è secondo il Borelli, una <lb></lb>conseguenza delle leggi idrauliche. </s>

<s>Perchè mantenendosi sempre a un ugual <lb></lb>livello il liquido nella cavità cerebrale, e permanendo i nervi sempre nello <lb></lb>stesso calibro, la quantità e la velocità del flusso proseguono sempre con <lb></lb>una medesima legge tanto inalterabile, che si può col moto dei flussi liquidi, <lb></lb>poste quelle condizioni che pur si verificano nell&#039;organo cerebro nervoso, <lb></lb>dar regola di moto agli stessi orologi. </s></p><p type="main">

<s>È questa, secondo il Borelli, la speculata ragione delle pulsazioni del cuore: <lb></lb>che se non si vedono così ugualmente pulsare i muscoli, ne&#039;quali s&#039;aprono <lb></lb>in modo simile gli orifici dei nervi, dipende egli dice da ciò che quegli orifici, <lb></lb>quando gli spiriti hanno a servire al moto dei muscoli, non si possono aprire, <lb></lb>se non che dall&#039;atto imperioso della volontà, che ne scuote le fibre. </s>

<s>Ma quando <lb></lb>hanno a servire ai meti del cuore, trovano il passaggio facile e aperto, senza <lb></lb>che quelle stesse fibre sentano altrimenti il bisogno di essere vellicate. </s></p><p type="main">

<s>Immaginata così e descritta la struttura organica, creduta sufficiente a <lb></lb>salvare il fenomeno delle pulsazioni del cuore, ritornandovi sopra col pen­<lb></lb>siero, parve all&#039;Autore stesso quella essere una speculazione non troppo fe­<lb></lb>lice, e perciò ne soggiunge un&#039;altra, che commove i lettori colla novità, <lb></lb>forse perchè si presenta nelle sembianze di un paradosso. </s>

<s>“ Non erit su­<lb></lb>pervacaneum videre an adsint rationes dubitandi utrum cordis motus fieri <lb></lb>possit, non a mera naturali mechanica necessitate, sed ab eadem animae <lb></lb>facultate, a qua omnes alii musculi moventur ” (ibi, pag. </s>

<s>458). Il dubbio si <lb></lb>risolve nell&#039;appresso proposizione LXXX, nella quale il Borelli intende di <lb></lb>dimostrare esser possibile che il moto deì cuore si faccia dalla medesima <lb></lb>facoltà animale conoscitiva, ma senza alcuna avvertenza, per la consuetudine <lb></lb>e per l&#039;abito inveterato. </s></p><pb xlink:href="020/01/1191.jpg" pagenum="66"></pb><p type="main">

<s>Nel trattato <emph type="italics"></emph>De motu animalium<emph.end type="italics"></emph.end> avevano avuto questi concetti relativi <lb></lb>alle pulsazioni del cuore una preparazione dalle proposizioni antecedente­<lb></lb>mente dimostrate, e specie dalla XXV di questa stessa Parte II, dove l&#039;abi­<lb></lb>tuale perizia, con cui gli spiriti animali si ammettono dalla volontà a com­<lb></lb>movere certi determinati nervi invece di altri, s&#039;attribuisce, non alla Natura <lb></lb>ma all&#039;esercizio e all&#039;esperienza acquistata infino dall&#039;infanzia, la quale sto­<lb></lb>lida, smemorata e studiosa più dell&#039;utile che del sapere “ fit ut nobis insciis <lb></lb>retineamus postea altius impressam artem et habitum, quo spiritus in cere­<lb></lb>bro moveri debent, ut certas artium motiones exequi valeant ” (ibi, pag. </s>

<s>62). </s></p><p type="main">

<s>Da una simile esperienza crede il Borelli che sieno da principio gover­<lb></lb>nati i moti del cuore, i quali in seguito divengono abituali, e anzi necessarii <lb></lb>di modo che non ci può poi più la volontà col suo imperio. </s>

<s>Ne reca di ciò <lb></lb>varii esempii, qual sarebbe quello de&#039;muscoli delle palpebre, i quali benchè <lb></lb>sieno volontarii pur giungono a coprire e ad aprire gli occhi, per un&#039;abi­<lb></lb>tudine contratta infin dalla infanzia, intanto che talvolta, non avendosi al­<lb></lb>cun timore di offesa, pur chiudiam le palpebre, come facciamo quando ve­<lb></lb>diam per esempio moversi al nostro viso un&#039;amica mano, che ci accarezza. <lb></lb></s>

<s>“ Non est igitur impossibile ut dici possit actio voluntaria illa quae habitù <lb></lb>fit, et nos non advertimus eam vòluisse, imo putamus eam nolle. </s>

<s>Quia nempe <lb></lb>talis habitus non acquiritur nisi praecedant plurimi et frequentes actus a <lb></lb>voluntate imperati, a quibus tandem, ob exercitium spiritus, peritiam quan­<lb></lb>dam acquirunt et instrumenta organica quasi laevigantur, et promptiores <lb></lb>redduntur ad operandum, et in hoc consistere videtur vis et potentia con­<lb></lb>suetudinis ” (ibi, pag. </s>

<s>160). </s></p><p type="main">

<s>S&#039;opporrà in contrario, così prevede il Borelli, che il cuore estratto da <lb></lb>una testuggine seguita per più ore a pulsare, ma seguitano, si risponde, a <lb></lb>contrarsi, dop&#039;essere stati recisi da un serpente, anche i muscoli del suo <lb></lb>dorso, i quali servonc senza dubbio ai moti volontarii. </s>

<s>Ciò avviene perchè <lb></lb>rimangono ivi gli organi e le cause efficienti del moto volontario, anche <lb></lb>dopo la scissione, ond&#039;è da dire del cuore, tuttavia palpitante bench&#039;estratto <lb></lb>vivo dal petto, quel che si dice della coda recisa in un serpente (ivi, pag. </s>

<s>161). </s></p><p type="main">

<s>Tali essendo le ipotesi proposte dal Borelli a sciogliere il tanto difficile <lb></lb>e controverso problema dei moti muscolari, o governati dalla necessità o <lb></lb>dall&#039;arbitrio, il giudizio che se ne può dare dagl&#039;imparziali è che le sopra <lb></lb>riferite proposizioni si concludono sull&#039;esempio di fatti fisici, che mal si con­<lb></lb>vengono colle funzioni della vita animale. </s>

<s>Quell&#039;entrare che fa l&#039;Autore in <lb></lb>tanti e tanto minuti particolari distrae più presto che condurre alla persua­<lb></lb>sione, perchè nessuno che si sia formato un giusto concetto della dignità <lb></lb>degli organi ordinati agli esercizi della vita, può, per esempio, patir di udirsi <lb></lb>rassomigliare il cervello alto sgocciolare di una Clessidra. </s>

<s>I seguaci perciò <lb></lb>della stessa Scuola borelliana evitarono di entrare in così fatte minutaglie, <lb></lb>che parevano un volere spendere la propria ignoranza in moneta spicciola, <lb></lb>e sentita la terribilità del mistero, che si parava ai loro occhi, stettero mo­<lb></lb>desti a supporre che un fluido stilli dal cervello nei muscoli per la via di-<pb xlink:href="020/01/1192.jpg" pagenum="67"></pb>retta dei nervi. </s>

<s>Colla modesta semplicità del principio si resero anche più <lb></lb>chiare e più accettabili le conclusioni, di che ne porge un&#039;esempio notabi­<lb></lb>lissimo fra tutti gli altri il Lancisi. </s></p><p type="main">

<s>Egli chiama tonici in generale tutti quei moti che si dicevano neces­<lb></lb>sarii o naturali, e suppone che questi si producano da un continuo e pe­<lb></lb>renne influsso del liquido cerebrale, per esempio, ne&#039;muscoli del cuore o <lb></lb>nelle fibre della tunica membranosa degl&#039;intestini. </s>

<s>Quel perenne influsso lo <lb></lb>ricevono altresi i muscoli motori delle membra, ma essi non si muovono, <lb></lb>se non per aggiunta di liquido, che alla loro nativa inerzia dia nuovo ecci­<lb></lb>tamento; aggiunta, che può farsi o non farsi ad arbitrio, e per la quale si <lb></lb>determina nelle varie membra o la quiete o il moto. </s></p><p type="main">

<s>Questa semplicissima ipotesi la proponeva il Lancisi nella sua Disser­<lb></lb>tazione <emph type="italics"></emph>De structura et usu Gangliorum,<emph.end type="italics"></emph.end> la quale, perciocchè ha il discorso <lb></lb>rivolto al Morgagni, fu com&#039;appendice inserita nell&#039;<emph type="italics"></emph>Adversaria anatomica <lb></lb>Quinta<emph.end type="italics"></emph.end> di lui. </s>

<s>“ In hoc enim, scrive l&#039;Autore di quella Dissertazione, mo­<lb></lb>tus tonicos a superadditis differre arbitramur, quod illi a continuo perenni­<lb></lb>que influxu liquidorum musculares lacertos villosque tendentium oriantur; <lb></lb>hi secus a temporaria immissione, vel saltem ab aucto nuper influxu eorum­<lb></lb>dem liquidorum excitantur, ac tandiu perdurant, donec idem recens addi­<lb></lb>tus influxus perseveraverit. </s>

<s>Hoc sane in singulis artefactis machinis, quae <lb></lb>per decursum, impetumque aquarum, statis temporibus moventur, usuve­<lb></lb>nire comperimus: in cartariis enim aliisque hydraulicis certum quoddam <lb></lb>sufflamen praesto est, cuius contrariis motibus laticum illapsus artificis ar­<lb></lb>bitrio, prout res postulat, promoveri vel prohiberi solet ” (Patavii 1719, <lb></lb>pag. </s>

<s>113). </s></p><p type="main">

<s>Scorto da un sì felice pensiero, si dette il Lancisi con ogni sollecitu­<lb></lb>dine a cercare se nulla fosse nei nervi che si potesse credere far l&#039;ufficio <lb></lb>di quei moderatori del flusso, che si sogliono applicare agli edifizii idraulici. </s>

<s><lb></lb>Per trovar ciò conveniva rivolgersi alle osservazioni anatomiche, alle quali <lb></lb>il diligentissimo Falloppio aveva da un secolo e mezzo dati gl&#039;inizii. </s>

<s>Descri­<lb></lb>vendo il sesto paio, “ Verum unum notetur, egli scrive nelle <emph type="italics"></emph>Osservazioni,<emph.end type="italics"></emph.end><lb></lb>quod maximi momenti est, in hoc sexto pari, quod tunica vel membrana <lb></lb>illa qua vestitur, dum per forameu elabitur, aliquando manifeste adsorbens <lb></lb>aliquot fibrillas istius nervi, aliquando etiam immanifeste, cum extra calva­<lb></lb>riam est producit quoddam <emph type="italics"></emph>corpus oblongum olivaris figurae,<emph.end type="italics"></emph.end> aliquando <lb></lb>simplex, aliquando geminum in utroque latere, quod colore carneum vide­<lb></lb>tur, ac substantia nerveum durumque admodum est. </s>

<s>Hoc corpus olivare in <lb></lb>quamdam desinit fibram nerveam, quae per cervicem declinans propagini­<lb></lb>bus quibusdam nervorum, qua cervice oriuntur, a primo scilicet et secundo <lb></lb>pari et quarto et quinto et sexto, vel a primo, secundo, quinto sexto et <lb></lb>septimo copulata est, veluti reticulum aut complicationem quamdam effor­<lb></lb>mat, quae per totam cervicem in unoquoque latere anteriori descendit, atque <lb></lb>in ista complicatione nova alia corpora olivaria aliquando concrescunt, in­<lb></lb>certo tamen numero, quae nulla alia substantia quam nervea, et quasi in <pb xlink:href="020/01/1193.jpg" pagenum="68"></pb>callum concrescente, constant. </s>

<s>Cum ego primus talem nervorum copulam <lb></lb>observarim, primum quoque nomine imposito <emph type="italics"></emph>plexum sexti paris<emph.end type="italics"></emph.end> appellabo ” <lb></lb>(Francofurti 1584, pag. </s>

<s>456). </s></p><p type="main">

<s>Descrive così il Falloppio, il quale ne fu veramente il primo osserva­<lb></lb>tore, com&#039;egli dice, quel nervo che si presenta come un lungo cordone di­<lb></lb>steso dalla base del cranio al coccige, e che è oggidì fra gli Anatomici co­<lb></lb>nosciuto sotto il nome di <emph type="italics"></emph>Gran simpatico<emph.end type="italics"></emph.end> o d&#039;<emph type="italics"></emph>Intercostale.<emph.end type="italics"></emph.end> Rigonfia quel <lb></lb>nervo di qnando in quando nel suo decorso in alcuni nodi rassomigliati dal <lb></lb>Falloppio nella loro forma alle olive, e perciò detti da lui <emph type="italics"></emph>corpi olivari,<emph.end type="italics"></emph.end> e <lb></lb>ricevendo radicelle nervose da ogni punto dell&#039;asse cerebro spinale e som­<lb></lb>ministrandole alla sua volta, dà luogo a formarsi quei <emph type="italics"></emph>plessi,<emph.end type="italics"></emph.end> i filamenti dei <lb></lb>quali attraversano pel loro mezzo qua e là nuovi corpi olivari, dal Fallop­<lb></lb>pio stesso ivi diligentemente descritti. </s></p><p type="main">

<s>A que&#039;corpi olivari fu dato poi il nome proprio di <emph type="italics"></emph>Gangli,<emph.end type="italics"></emph.end> e benchè al <lb></lb>grande Anatomico modenese non isfuggisse nulla che concernesse la loro <lb></lb>intima costituzione, non sa però o non dice almeno quale, nell&#039;intenzione <lb></lb>della Natura, ne potesse esser l&#039;uso. </s>

<s>Il Vesalio che, per detrarre qualche <lb></lb>parte del merito al suo rivale, riduceva le olive falloppiane al numero di <lb></lb>quelle ghiandolette descritte già da Galeno, rassomigliandole ai nodi delle <lb></lb>canne, disse ch&#039;erano ordinate alla robustezza del nervo, come pure al fine <lb></lb>di tener bene in posto esso nervo credè che fossero dalla Natura ordinati <lb></lb>que&#039;così artificiosi intrigamenti dei plessi. </s>

<s>“ Ut ligamentosam substantiam <lb></lb>musculis quibusdam nunc ad opportunum exortum, nunc ad innexum inser­<lb></lb>tionemve, nunc roboris occasione imprimis accedere mihi habeo persuasis­<lb></lb>simum; sic membraneam substantiam propriae nervorum qui procul sunt <lb></lb>ducendi substantiae ad robur conferre una est docendum. </s>

<s>Uti ad substan­<lb></lb>tiae illius augmentum et robur illae etiam conducunt Glandulae, quas a Ga­<lb></lb>leno in ultimo De partium usu libro pertractatas esse mox subiiciam ” (Gabr. </s>

<s><lb></lb>Falloppii Observ. </s>

<s>Examen, Venetiis 1564, pag. </s>

<s>100). </s></p><p type="main">

<s>Dell&#039;uso de&#039;Gangli non furono, in un secolo e mezzo decorso dalla loro <lb></lb>scoperta, dette da nessuno cose importanti infino al Lancisi, il quale sotto­<lb></lb>postili a nuova e più diligente anatomia credè di aver ritrovato in essi quel­<lb></lb>l&#039;organo moderatore del flusso nerveo, preveduto sì necessario a intendere <lb></lb>il vario governo de&#039;moti naturali e dei volontarii. </s>

<s>“ Perspicis, Morgagni <lb></lb>praeclarissime, Gangliorum usum, tametsi alii quoque inferioris notae con­<lb></lb>siderari possint, praecipuum esse ut eadem nervis admota atque intertexta, <lb></lb>sint veluti moderatores, rectoresve eorum animalium motuum, qui vel ar­<lb></lb>bitrio obsecundant vel ipso arbitrio celerius moveri aut retardari debent ” <lb></lb>(Dissertatio in loco cit., pag. </s>

<s>113). </s></p><p type="main">

<s>Si confermava il Lancisi in questa supposizione dal veder che i nervi, <lb></lb>i quali servono ai sensi, procedono oltre liberi senz&#039;essere interrotti da gan­<lb></lb>gli moderatori, perchè debbono essere come porte sempre aperte a ricevere <lb></lb>le impressioni, che a loro vengono d&#039;ogni parte dagli oggetti, per i sottili <lb></lb>mezzi interposti. </s>

<s>“ Nervos qui sensibus ancillantur, ut olfactorios, opticos etc. <pb xlink:href="020/01/1194.jpg" pagenum="69"></pb>nullis gangliis munitos esse reperio. </s>

<s>Id vero tu, Vir praeclarissime, haud <lb></lb>frustra Naturam molitam esse intelligis, siquidem cum organa sensuum exci­<lb></lb>piendis externis pulsibus aeque semper exposita esse debeant, ut non tam <lb></lb>ad agendum quam ad patiendum sint comparata, par erat ut spiritus anima­<lb></lb>les, et quidquid cum iisdem fluitat, per apertos obviorum nervorum ductus <lb></lb>aequabili tenore influerent. </s>

<s>Sunt enimvero sensus in corpore quasi quaedam <lb></lb>viae, ut Tullius ait, ad oculos, ad aures a sede animi perforatae. </s>

<s>Nulla idcirco <lb></lb>in iis aut repagula aut incitamenta addenda vel interponenda erant ” (ibi, <lb></lb>pag. </s>

<s>112). </s></p><p type="main">

<s>In conclusione hanno per il Lancisi i Gangli un uso importantissimo e <lb></lb>nuovo: gli riguarda come altrettanti piccoli cervelli collocati fuori del cra­<lb></lb>nio, o come tante sentinelle avanzate ad avvisar del subitaneo incorrere dei <lb></lb>nemici il Re, che se ne sta rinchiuso nella sua Rocca. </s>

<s>“ Quamobrem per­<lb></lb>pendenti olim mihi detectam structuram menteque conceptum officium Gan­<lb></lb>gliorum, subiit animo suspicari an eadem in cerebri subsidium ita sint com­<lb></lb>parata ut appellari possint exigua quaedam ac peculiaria cerebella, voluntariis <lb></lb>tamen ac superadditis dumtaxat motibus excitandis hic, illic, extra calvariam, <lb></lb>per corpus dispersa ac distributa, veluti militares quaedam stationes ad su­<lb></lb>bitos hostium incursus collocatae ” (ibi, pag. </s>

<s>114). </s></p><p type="main">

<s>L&#039;ipotesi del Lancisi intorno all&#039;uso de&#039;Gangli fu accolta con gran fa­<lb></lb>vore da Fisiologi e da Notomisti e perciocchè le ben concepite idee son fe­<lb></lb>conde di altre idee che, sebben sempre non raggiungano il vero, pur vi <lb></lb>tendono con sospiri di desiderio; s&#039;assegnò agli stessi Gangli un altr&#039;uso <lb></lb>tutto loro particolare, qual&#039;è quello di presiedere alla vita organica e vege­<lb></lb>tativa, ond&#039;è che lo Chaussier chiamò il Grande simpatico <emph type="italics"></emph>Sistema nervoso <lb></lb>della vita organica,<emph.end type="italics"></emph.end> e il Bichat <emph type="italics"></emph>Sistema nervoso vegetativo.<emph.end type="italics"></emph.end> Così veniva a <lb></lb>intendersi come non solo i moti ritmici del cuore e i vermicolari degl&#039;in­<lb></lb>testini fossero indipendenti dalla volontà, ma e le funzioni stesse che in vario <lb></lb>modo s&#039;esercitano dall&#039;organismo animale. </s></p><p type="main">

<s>Faceva a principio qualche difficoltà contro l&#039;ipotesi lancisiana il veder <lb></lb>che da Gangli son pure interrotti i nervi, che presiedono ai moti volontarii, <lb></lb>come i nervi cervicali e gli spinali, ma poi una più diligente anatomia, mo­<lb></lb>strando la differenza che passa fra questi e quelli nella loro intima strut­<lb></lb>tura, lasciò libertà di supporre che non tutti essi Gangli moderassero gl&#039;im­<lb></lb>peti della volontà a un modo, ma variamente, secondo che più o men <lb></lb>contengono e son rimpolpati di materia grigia, o secondo che son le fibre <lb></lb>sensorie in maggiore o minor copia conteste con le fibre motrici. </s></p><p type="main">

<s>Comunque sia, avevano gli Halleriani trovato così facile e semplice il <lb></lb>modo di sciogliere il problema de&#039;moti necessarii e de&#039;volontarii nelle dot­<lb></lb>trine del loro Maestro, che non si vollero dipartire da esse, per seguir l&#039;ipo­<lb></lb>tesi del Lancisi, nella quale non pareva a loro possibile spiegare come mai <lb></lb>impedissero i Gangli il corso al fluido nerveo diretto dalla volontà, e non <lb></lb>impedissero il passaggio alla corrente elettrica capace di eccitar nell&#039;animale <lb></lb>dolorosissime sensazioni. </s></p><pb xlink:href="020/01/1195.jpg" pagenum="70"></pb><p type="main">

<s>L&#039;Haller dunque, posto il principio che i muscoli si muovono per irri­<lb></lb>tazione, sempre che sopravvengono a loro gli stimoli proporzionati, diceva <lb></lb>non far nessuna maraviglia che il cuore, il ventricolo, gl&#039;intestini si muo­<lb></lb>vano di continuo e spontaneo moto, non mancando mai a loro il sangue, <lb></lb>l&#039;aria, il cibo stimolatori. </s>

<s>I muscoli poi delle membra ora si muovono, ora <lb></lb>si rimangono in quiete, perchè la volontà ora manda a loro e ora gli tien <lb></lb>digiuni del necessario liquido stimolante. </s>

<s>“ Omnes musculi a stimulo ad <lb></lb>motum cientur, sed viribus vìtalibus et involuntariis ut agant, stimulos na­<lb></lb>tura adplicat: cordi sanguinem et arteriis; aerem, cibum ventriculo, inte­<lb></lb>stinis; urinam vesicae urinariae. </s>

<s>Nunc si stimulantur ii musculi, necesse est <lb></lb>agere, nam et voluntarii si forent, stimulo sibi admoto operarentur. </s>

<s>Procte­<lb></lb>rea haec organa, certe cor et eius potissimum auriculae et intestinum, sti­<lb></lb>muli esse impatientissima, diutissime in motu perseverare, et musculos in­<lb></lb>voluntarios ea in praerogativa superare per experimenta ostendimus. </s>

<s>Etsi <lb></lb>etiam aliquoties musculi voluntarii contrahi visi sunt, quando cor et inte­<lb></lb>stina quieverant, rarum id tamen est.... Si ergo vehementer irritabilia sunt <lb></lb>haec organa, et si perpetuo irritantur, nihil omnino miri est si moventur <lb></lb>perpetuo ” (Elem. </s>

<s>Physiol., T. IV, Lausannae 1766, pag. </s>

<s>534). </s></p><p type="main">

<s>Per quel che poi riguarda i muscoli volontarii, prosegue a dir l&#039;Haller, <lb></lb>essi essendo meno irritabili, e venendo dalle contrarie forze antagonistiche <lb></lb>contemperati, non possono uscire in atto di cospicui moti. </s>

<s>“ Iidem tamen <lb></lb>stimulo admoto, veneni, radentis chalybis, electrici torrentis, acrimoniae <lb></lb>cuiuscumque perinde in contractiones involuntarias cientur. </s>

<s>Pro stimulo au­<lb></lb>tem videntur in voluntatis imperio spirituum nervosorum quamcumque ef­<lb></lb>ficaciam a natura adhiberi. </s>

<s>Dum stimulus superest, contrahuntur, ac sub­<lb></lb>ducto quiescunt. </s>

<s>Nihil adeo in discrimine musculorum involuntariorum a <lb></lb>reliquis arbitrio mentis subiectis musculis nodi est, quod anima vindice <lb></lb>egeat ” (ibi, pag. </s>

<s>535), </s></p><p type="main">

<s>Questa ipotesi halleriana veniva con gran semplicità e facilità conclusa <lb></lb>dall&#039;ipotesi degli spiriti vitali scorrenti dal cervello ne&#039;muscoli per la via <lb></lb>de&#039;nervi, ed era ugualmente bene applicabile o si facessero consistere essi <lb></lb>spiriti nel succo nerveo o nel fluido elettrico, bastando che, qualunque si <lb></lb>fosse la loro natura, si riconoscesse il loro operare a modo di stimolo esterno. </s>

<s><lb></lb>L&#039;elettricità galvanica modificò alquanto l&#039;ipotesi halleriana, ma l&#039;efficacia <lb></lb>della causa stimolante fu anche dal Galvani approvata e seguita, sol ch&#039;egli <lb></lb>faceva questa causa intima alla compage organica, e compartecipe della vita. </s></p><p type="main">

<s>“ Haec autem si concedantur, soggiungeva il Galvani dop&#039;aver descritte <lb></lb>l&#039;esperienze, dalle quali voleva concluder l&#039;esistenza dell&#039;elettricità animale, <lb></lb>aditus forte aperietur aliquis ad explicandos musculares motus, qui in vi­<lb></lb>vente animali fiunt, quosque considerare nunc aggredimur. </s>

<s>Nam ad volun­<lb></lb>tarios quod attinet, poterit forte animus, mira sua vi, aut in cerebrum, ut <lb></lb>proclivius est credere, aut extra idem, in eum quem sibi libuerit nervum, <lb></lb>impetum quasi quemdam facere, quo fiet ut nerveo-electricum fluidum a <lb></lb>respondente musculo confestim ad eam nervi partem confluat, ad quam <pb xlink:href="020/01/1196.jpg" pagenum="71"></pb>fuerit per impulsum revocatum, quo cum perventum erit, cohibenti nerveae <lb></lb>substantiae parte per auctas tunc vires superata, ab eaque exiens excipie­<lb></lb>tur, aut ab extrinseca nervi humiditate, aut a membranis, aut a contiguis <lb></lb>aliis deferentibus partibus, per easque, ceu per arcum, ad musculum a quo <lb></lb>discessit restituetur, ut nempe, iuxta aequilibrii legem, ad negativae muscu­<lb></lb>larium fibrarum electricam partem ea copia tandem confluat, qua a positiva <lb></lb>electrica earumdem parte, per impulsum in nervo, ut opinari placuit, antea <lb></lb>effluxerit ” (De viribus electric. </s>

<s>comment. </s>

<s>cit., pag. </s>

<s>52). </s></p><p type="main">

<s>Ammessa questa ipotesi de&#039;fluidi eccitatori governati dalla volontà a <lb></lb>produrre interrottamente i moti delle membra, restava al Galvani molto più <lb></lb>facile a spiegare i moti naturali, ne&#039;quali le cause stimolanti son continua­<lb></lb>mente regolate dalle necessarie leggi della Natura. </s>

<s>“ Non dissimili forte, <lb></lb>immo minus difficili, si quid iudico, ratione expediri res poterit in invitis <lb></lb>et praeternaturalibus motibus, acribus scilicet, et stimulantibus principiis <lb></lb>nervos vel spinalem medullam vel cerebrum irritantibus, nerveumque simul <lb></lb>fluidum advocantibus, ut a deferentibus partibus exceptum ad musculos tan­<lb></lb>dem tamquam per arcum restituatur ” (ibi, pag. </s>

<s>53). </s></p><p type="main">

<s>Il Volta usciva fuori poco tempo dopo con la sua <emph type="italics"></emph>Prima Memoria sopra <lb></lb>l&#039;Elettricità animale,<emph.end type="italics"></emph.end> e nella prima parte di essa, esaminando l&#039;opinione di <lb></lb>que&#039;Fisiologi, i quali si rìducevano a considerare i nervi in certo modo quali <lb></lb>conduttori degli spiriti animali, come i metalli son conduttori del fluido elet­<lb></lb>trico; concludeva non esser quelle altro che idee vaghe e indeterminate. </s>

<s><lb></lb>Comprendeva altresì in quella sua sentenza anche il Sauvages con i suoi <lb></lb>numerosi seguaci, i quali confortavano principalmente la loro opinione col <lb></lb>fatto sperimentato della grande efficacia del fluido elettrico e della sua at­<lb></lb>tività in far, senza altro stimolo, repentinamente contrarre le fibre musco­<lb></lb>lari. (Opere, T. II, P. I, Firenze 1816, pag. </s>

<s>25-28). </s></p><p type="main">

<s>Nella seconda parte di quella Memoria procedeva più oltre il Volta a <lb></lb>scoprire un errore, in che era incorso il Galvani, il quale, avendo rassomi­<lb></lb>gliato i muscoli all&#039;armatura e i nervi al conduttore di una Bottiglia di <lb></lb>Leyda, aveva detto che il circolo si fa dal di dentro di esso muscolo al di <lb></lb>fuori, mentre è il vero ch&#039;essendo l&#039;elettricità negativa nell&#039;interior super­<lb></lb>ficie muscolare e positiva nell&#039;esterna, come per l&#039;Elettrometro aveva riscon­<lb></lb>trato lo stesso Volta, il flusso elettrico si fa con circolo diretto dal di fuori <lb></lb>al di dentro, se qualche scarica avvenga o spontanea o naturale (ivi, pag. </s>

<s>41). </s></p><p type="main">

<s>Dato avviso di ciò a Bologna, per mezzo del Carminati, come altrove <lb></lb>accennammo, il Galvani ridusse le nuove osservazioni del Volta a render più <lb></lb>semplice la sua spiegazione dei moti volontarii, ma l&#039;Autor della <emph type="italics"></emph>Memoria <lb></lb>seconda sull&#039;Elettricità animale,<emph.end type="italics"></emph.end> esce a dichiararsi apertamente come quelle <lb></lb>sue osservazioni, tutt&#039;altro che porgersi ai servigi del Galvanismo, medita­<lb></lb>vano di condurlo passo passo in rovina. </s>

<s>Si dimostrava infatti nella detta <lb></lb><emph type="italics"></emph>Memoria<emph.end type="italics"></emph.end> che il fluido elettrico non agisce direttamente sui muscoli che sono <lb></lb>gli organi del moto, ma termina la sua azione immediata nel nervo, ond&#039;è <lb></lb>che venivano così disperse al vento le belle speranze di tutti coloro, che <pb xlink:href="020/01/1197.jpg" pagenum="72"></pb>nell&#039;elettricità stimolante le fibre muscolari si lusingavano di aver finalmente <lb></lb>scoperta la misteriosa causa dei moti animali (ivi, pag. </s>

<s>81-85). </s></p><p type="main">

<s>Nè quel mistero è stato ancora svelato dopo un altro secolo di pro­<lb></lb>gressi, ed è tale la sua natura, tale l&#039;ottusità de&#039;sensi dell&#039;uomo a penetrare <lb></lb>addentro ne&#039;più segreti organi componenti la macchina animale, che di so­<lb></lb>disfare a quei desiderii è ne&#039;prudenti creduta vana ogni speranza. </s>

<s>Così la <lb></lb>Fisiologia è costretta a confessar ora la sua impotenza, come la confessava <lb></lb>verso la metà del secolo XVII, quando poche erano tuttavia l&#039;esperienze delle <lb></lb>difficoltà, che s&#039;incontravano per conseguire il fine desiderato. </s>

<s>Noi vogliamo <lb></lb>qui di quella ingenua confessione recare un documento, e tanto ciò più vo­<lb></lb>lentieri facciamo, in quanto che è da una parte un riepilogo delle cose già <lb></lb>dette, e dall&#039;altra un avviamento a quelle che ci rimangono a dire. </s></p><p type="main">

<s>È il documento accennato una scrittura, della quale il Viviani fra&#039;suoi <lb></lb>manoscritti ci conservò la copia, e porta il titolo di <emph type="italics"></emph>Pareri diversi circa <lb></lb>varie materie avute da varie persone letterate.<emph.end type="italics"></emph.end> Dop&#039;essersi ivi accennato <lb></lb>ad altre varie questioni di Fisica, si passa a dire in che modo sciogliesse il <lb></lb>Borelli alcuni curiosi problemi di Meccanica animale, aiutandosi del fatto <lb></lb>dell&#039;insensibile traspirazione. </s>

<s>Poi si soggiunge: “ Ma perchè nello sciogli­<lb></lb>mento che si è di sopra apportato, cioè che rimanendo nel nostro corpo <lb></lb>questi avanzi d&#039;escrementi, essendoli impedito il traspirare, s&#039;internino nei <lb></lb>nostri muscoli, e gl&#039;impediscano il potere esercitare ad arbitrio le forze; <lb></lb>non sarà affatto fuor di proposito il dire in qual maniera si generino tanti <lb></lb>e tanti movimenti nel nostro corpo, altri per un verso, altri per un altro, <lb></lb>e conforme la volontà ci detta. </s>

<s>” </s></p><p type="main">

<s>“ Per intenderne dunque qualche cosa, oppure, per averne qualche <lb></lb>lume benchè oscuro, bisogna immaginarsi o per dir meglio tener per certo <lb></lb>che, dove i movimenti si fanno, vi sono alcuni mobili attaccamenti, che si <lb></lb>chiamano giunture, poichè in uno stinco non si farà moto nessuno, perchè <lb></lb>non vi è giunture. </s>

<s>Per intelligenza di che descrivasi la linea AB (fig. </s>

<s>2), e <lb></lb><figure id="id.020.01.1197.1.jpg" xlink:href="020/01/1197/1.jpg"></figure></s></p><p type="caption">

<s>Figura 2.<lb></lb>nel punto A attacchisi la linea AC in maniera tale, <lb></lb>che possa girare e muoversi ora in AE, ora in AF <lb></lb>o dove più gli aggrada: certa cosa è che se io la <lb></lb>tirerò verso D, con la linea DC, ella seguirà la me­<lb></lb>desima linea DC. </s>

<s>Restar dunque chiari potremo <lb></lb>i movimenti che si fanno nel nostro corpo tutti farsi per alcune linee o cor­<lb></lb>dicelle o altro che tirino. </s>

<s>” </s></p><p type="main">

<s>“ Inteso questo, veniamo all&#039;esperienze, e se io vorrò muovere una <lb></lb>mano o un dito, mossa che io l&#039;avrò, sentirò che ingrossato mi s&#039;è ed as­<lb></lb>sodato un muscolo nel braccio, talchè per questa esperienza è necessario <lb></lb>dire che questo moto non possa seguire senza l&#039;ingrossamento del muscolo, <lb></lb>perchè tanto quanto resti piegata la mano, tanto durerà a star sodo il mu­<lb></lb>scolo, ed abbiamo di sopra visto che il moto non dipende da altro, che da <lb></lb>alcune cordicelle tirate. </s>

<s>” </s></p><p type="main">

<s>“ Ora vediamo dunque in che maniera possa questo muscolo assodan-<pb xlink:href="020/01/1198.jpg" pagenum="73"></pb>dosi far forza a tirare, e non altrimenti dico io ciò possa fare, che come fa <lb></lb>il canapo bagnato, il quale, non solo doventa più grosso e più sodo, ma <lb></lb>s&#039;accorcia per non poche braccia. </s>

<s>La ragione di ciò è che quelle particelle <lb></lb>dell&#039;acqua, che penetrano per il canapo, vogliono anch&#039;esse luogo, onde son <lb></lb>causa che il canapo sia forzato ad alzarsi e fargli luogo, ond&#039;egli viene a <lb></lb>ritirare i suoi filamenti e per conseguenza ad accorciarsi: e, se esso sarà <lb></lb>ancora attaccato, a far non poca forza a ciò che lo trattiene, come dal Ga­<lb></lb>lileo chiaramente ed apertamente è provato. </s>

<s>” </s></p><p type="main">

<s>“ Altra non diremo dunque esser la causa di questo tiramento de&#039;mu­<lb></lb>scoli, che stanno attaccati passato le giunture, vedendosi uno di quelli in­<lb></lb>grossarsi, quando segue il movimento, se non che penetri dentro ai medesimi <lb></lb>muscoli qualche umore o altro che, facendoli ingrossare, faccia che mediante <lb></lb>loro ne segua il ritiramento. </s>

<s>Ma perchè si vede che i muscoli sono un ag­<lb></lb>gregato di fila tutte ad una medesima dirittura condotte, e sto per dire pa­<lb></lb>rallele, senza punto attorcigliarsi come il canapo, si potrebbe dubitare che <lb></lb>non ne dovesse seguire il medesimo effetto. </s>

<s>Senza dubbio però il medesimo <lb></lb>effetto ne segue, come in un canapo, poichè, se piglieremo un budello o <lb></lb>qualsivoglia altra cosa composta di lineamenti non attorcigliati, gonfiandoli <lb></lb>e facendoli venir grossi, si vedrà che raccorceranno. </s>

<s>” </s></p><p type="main">

<s>“ Ma è ora da investigarsi da noi ciò che sia questo, che ne fa diven­<lb></lb>tar grosso questo muscolo, e se io, dal signor dottor Borelli persuaso, ne <lb></lb>dovessi assegnare il mio parere, direi liberamente che non lo so. </s>

<s>Alcuni vo­<lb></lb>gliono che sia sangue, ma a me si rende difficile l&#039;intendere dove stia que­<lb></lb>sto sangue, che ha da servire per questo effetto, non ne vedendo vasi, o <lb></lb>altro dove si ricoveri, quando sta fuora de&#039;muscoli. </s>

<s>Altri vogliono che sia <lb></lb>uno spirito purissimo, che penetri là di dentro. </s>

<s>Basta: ciò che si sia, l&#039;es­<lb></lb>sere spirito o sangue non mi capacita. </s>

<s>Siccome ancora in che maniera ad <lb></lb>un semplice atto della mia volontà abbia io a muovere tutto il corpo, que­<lb></lb>sto ancora non l&#039;intendo, e confesso che non è cosa per me il dirmi che <lb></lb>è una potenza dell&#039;anima e non altro. </s>

<s>Neppure mi sodisfa, poichè io vorrei <lb></lb>saper come fa, in che maniera; cose tutte difficilissime a spiegarsi. </s>

<s>” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>13, 14). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Si diceva che il documento ora trascritto avrebbeci avviato a quel che, <lb></lb>in ordine alla Storia scientifica dei moti muscolari, ci rimaneva a narrare in <lb></lb>questa ultima parte. </s>

<s>Abbiamo ivi letto in principio a che insomma si ridu­<lb></lb>cesse la macchina produttrice di que&#039;moti, intorno a che, sebben si avessero <lb></lb>nelle Meccaniche i principii già dimostrati, s&#039;eran pure, infino alla metà <lb></lb>del secolo XVII, detti di gravissimi errori. </s>

<s>A diffondere con maggiore am­<lb></lb>piezza e lucidità que&#039;meccanici principii, avevano efficacemente conferito <pb xlink:href="020/01/1199.jpg" pagenum="74"></pb>gl&#039;insegnamenti di Galileo, il quale fu de&#039;primi a farne l&#039;applicazione al <lb></lb>muoversi degli animali. </s>

<s>Ma in quel tempo che Galileo stesso, già professore <lb></lb>nello studio di Padova, scriveva al Vinta d&#039;aver tra mano materiali da com­<lb></lb>porre un opuscolo <emph type="italics"></emph>de Animalium motibus<emph.end type="italics"></emph.end> (Alb. </s>

<s>VI, 98), Girolamo Fabricio <lb></lb>d&#039;Acquapendente speculava intorno a quel medesimo soggetto, e otto anni <lb></lb>dopo, nel 1618, ne pubblicava, pure in Padova, un trattato col titolo <emph type="italics"></emph>De <lb></lb>motu locali animalium secundum totum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sarebbe senza dubbio curiosa la nostra storia d&#039;investigare quali com­<lb></lb>merci d&#039;idee passassero fra il Matematico e l&#039;Anatomico, e benchè non si <lb></lb>sappia intorno a ciò dire nulla di certo, pur è lecito, e anzi ragionevolis­<lb></lb>simo, l&#039;immaginare che Galileo, frequentando l&#039;Anfiteatro dove sezionava il <lb></lb>Fabricio, ne ritornasse erudito di quella scienza anatomica, che gli era ne­<lb></lb>cessaria a confutar gli errori di Aristotile e de&#039;ciechi settatori di lui. </s></p><p type="main">

<s>Ma infin di qui comincia intanto a trasparire una qualche notabile dif­<lb></lb>ferenza fra le intenzioni de&#039;due celebri Professori padovani, imperocchè, <lb></lb>sebbene il Fabricio venisse via via scoprendo in Anatomia cose nuove, era <lb></lb>però sollecito di dimostrare come tali novità non si opponevano agl&#039;inse­<lb></lb>gnamenti aristotelici, nè importava se, per una tale dimostrazione, si sen­<lb></lb>tiva costretto a cadere in contradizioni o ad avvolgersi in paralogismi. </s>

<s>Il <lb></lb>Fabricio insomma, ch&#039;è pure così benemerito della Storia naturale, non aveva <lb></lb>avuto il coraggio di disertare dalla scuola dello Stagirita, e perciò, se po­<lb></lb>teva essere a Galileo congiunto in amichevoli affetti, doveva esser fra loro <lb></lb>un divorzio negli scientifici pensieri. </s></p><p type="main">

<s>Comunque sia, apparisce di un tal divorzio un argomento certissimo <lb></lb>nella presente trattazione de&#039;moti animali, in cui l&#039;Acquapendente, riducen­<lb></lb>dosi a far l&#039;ufficio di semplice Anatomico descrittivo, non partecipa in nulla <lb></lb>delle speculazioni meccaniche di Galileo. </s>

<s>Fintantochè infatti si tratta di de­<lb></lb>scrivere un muscolo o l&#039;inserzione tendinosa di lui in un osso, per eserci­<lb></lb>tarvi ora l&#039;una ora l&#039;altra specie di moto, e fintantochè non intendevasi che <lb></lb>a notar le differenze tra gli organi della locomozione negli uomini e negli <lb></lb>animali, il Fabricio è il più eccellente di quanti l&#039;han preceduto, da Galeno <lb></lb>in poi. </s>

<s>Ma quando si passa a determinare in qual modo i muscoli eserci­<lb></lb>tino meccanicamente il moto, il novello Professore null&#039;altro sa ripetere, col <lb></lb>suo Maestro antico Galeno, se non che il tendine è quasi un vette. </s>

<s>E pro­<lb></lb>vandosi di applicare e di dare qualche estensione al pensiero galenico, si <lb></lb>trova impacciato nell&#039;assegnare il punto di appoggio del vette stesso, e del­<lb></lb>l&#039;applicazione della potenza, l&#039;effetto meccanico prodotto dalla quale ei non <lb></lb>sa misurarlo dalla lunghezza del vero vette, ch&#039;è nell&#039;osso, ma dalla lun­<lb></lb>ghezza del muscolo e del tendine, per cui conclude che questi organi danno <lb></lb>moti tanto più gagliardi, quanto sono più lunghi. </s></p><p type="main">

<s>“ Quaeritur, così propriamente dice l&#039;Autore, cur hic musculus est lon­<lb></lb>gus, cum tamen hi motus omnes breves sint. </s>

<s>Respondetur quod longi mu­<lb></lb>sculi interdum dant robustos motus nequaquam longos, eomodo quo pondera <lb></lb>quae manibus movere non possumus, vectibus adhibitis moliri comperimus, <pb xlink:href="020/01/1200.jpg" pagenum="75"></pb>aut similiter fune adhibita et longius trahente pondus, quod alioquin mani­<lb></lb>bus trahi non poterat, facile trahitur et movetur. </s>

<s>Aut forte melius dicamus <lb></lb>carnosam musculorum partem longam et brevem, ut puta quae contrahitur <lb></lb>et aut breviatur, dare longos aut breves motus: tendineam vero, ut puta <lb></lb>quae tenditur et obduratur, breves aut longos motus non exhibere, sed ro­<lb></lb>bustos. </s>

<s>Musculus autem propositus brevem omnino carnosam partem obti­<lb></lb>net, longam vero tendineam, quae, cum se habeat ut vectis et ut funis <lb></lb>longius a pondere trahens, ideo hac ratione robustum motum perficit. </s>

<s>Sum­<lb></lb>matim, ut carnosus brevem, ut tendineus longus robustum dat motum ” (De <lb></lb>motu locali, Patavii 1618, pag. </s>

<s>105). </s></p><p type="main">

<s>Nè dopo l&#039;Acquapendente seppero i Filosofi investigar nulla di meglio, <lb></lb>in ordine al determinare i veri organi della locomozione animale. </s>

<s>Il Gas­<lb></lb>sendo, persuaso esso pure di ciò che anticamente aveva affermato Galeno, <lb></lb>che cioè quegli organi appartenessero alla natura dei vetti, si dette studio­<lb></lb>samente a ricercar nel corpo animale la materia e la forma propria di que­<lb></lb>gli strumenti, ma non gli parve di trovarci altro che funi nelle fibre mu­<lb></lb>scolari e ne tendini, o troclee nelle estremità arrotondate degli ossi. </s>

<s>Egli <lb></lb>ridusse perciò ogni maniera di macchinamento animale al modo di operar <lb></lb>delle taglie o dei polispasti, ne&#039;quali s&#039;accresce l&#039;effetto della forza col mol­<lb></lb>teplice ritessersi delle fila traenti. </s>

<s>Così lusingavasi di avere in qualche modo <lb></lb>a intendere la ragione e l&#039;uso di quella grande matassa di fibre, in che si <lb></lb>avvolgono e di che si compongono i muscoli. </s></p><p type="main">

<s>Altri asserirono lo stesso, ma con diversa ragione, e dissero che le fibre <lb></lb>muscolari e i tendini agiscono a modo di una macchina, perchè con la pic­<lb></lb>cola virtù degli spiriti vitali valgono pure a sollevare di grandissimi pesi. </s>

<s><lb></lb>Sembra che rimanessero costoro infetti di quell&#039;errore, così acutamente sco­<lb></lb>perto da Galileo, relativo all&#039;utilità delle macchine, la quale si faceva con­<lb></lb>sistere in poter mover gran pesi con pochissima forza. </s>

<s>E tanto fu contagioso <lb></lb>quell&#039;error meccanico, che ne rimasero infetti Fisiologi valentissimi, fra&#039;quali <lb></lb>basti a noi citare quel Croone che, inconsapevole di ciò che speculavasi in <lb></lb>Toscana, prevenne le ipotesi e le teorie del Borelli. </s></p><p type="main">

<s>Egli, prima dello stesso Borelli, misurò la forza di alcuni muscoli in <lb></lb>sostener varii gradi di peso, e perch&#039;erano le sue misure dirette a provar <lb></lb>che la forza principalmente risiede ne&#039;tendini, di che i muscoli non man­<lb></lb>cano mai, fece particolar soggetto alle sue esperienze quel muscolo, che serve <lb></lb>a tirare indietro la coscia e a piegar la gamba, detto, per mancar di carne <lb></lb>e per esser in gran parte tendinoso, <emph type="italics"></emph>Gracile<emph.end type="italics"></emph.end> dagli antichi e dal Soemme­<lb></lb>ring, ma conosciuto più comunemente oggidì sotto il nome di <emph type="italics"></emph>Retto interno.<emph.end type="italics"></emph.end><lb></lb>“ De fibris autem tendinosis, dice il Croone, tria summopere notanda sunt: <lb></lb>Primo, ex iis potissimum musculos constare, quod ex eo liquet quod octo­<lb></lb>ginta librarum pondo alligatum istius musculi tendini, quam <emph type="italics"></emph>Gracilem in­<lb></lb>ternum<emph.end type="italics"></emph.end> in homine vocant, ab humo sublatum facile sustinuerim, altera mu­<lb></lb>sculi extremitate manu apprehensa ” (De ratione motus muscul. </s>

<s>cit., pag. </s>

<s>14). </s></p><p type="main">

<s>Ma quando passa il Croone a considerar quella forza muscolare, in <pb xlink:href="020/01/1201.jpg" pagenum="76"></pb>quanto ella opera a produrre i moti nelle membra dell&#039;animale, fonda an­<lb></lb>ch&#039;egli la sua dimostrazione sul principio che la Natura, con pochissima <lb></lb>forza vitale, non solo muova le membra, ma altri gravi pesi che sieno a loro <lb></lb>attaccati. </s>

<s>“ Accedo iam ad demonstrandum huiusmodi intumescentia mu­<lb></lb>sculi, quantum exigua fingatur, non tantum satis valere ad quodlibet cor­<lb></lb>poris membrum attollendum, sed etiam ad aliud quodcumque pondus ten­<lb></lb>dini appensum ” (ibi, pag. </s>

<s>14). </s></p><p type="main">

<s>Primo a riconoscer l&#039;errore così comunemente invalso, e a dimostrar <lb></lb>che la cosa era tutt&#039;al contrario di quel che prima di lui s&#039;era creduto, fu <lb></lb>il Borelli, il quale non si fa punto maraviglia che fosse rispetto a ciò da <lb></lb>tutti seguito il falso, avendo la verità ch&#039;egli prende a dimostrare le appa­<lb></lb>renti sembianze di un assurdo. </s>

<s>“ Etsi hoc absurdum iure censetur, qui fieri <lb></lb>poterit ut Natura sapientissima, quae ubique compendia, simplicitatem et <lb></lb>facilitatem quaerit, tanta industria machinas in organis animalis elaborave­<lb></lb>rit, non ut parva virtute magna pondera, sed e contra immenso propemo­<lb></lb>dum robore parva pondera moveat; hoc quidem, licet videatur monstrum <lb></lb>et contra communem sententiam, non diffiteor me posse evidentissime de­<lb></lb>monstrare, et petita prius venia ostendere contrariae sententiae assertores <lb></lb>hallucinatos fuisse ” (De motu anim., P. I, Romae 1780, pag. </s>

<s>18). </s></p><p type="main">

<s>L&#039;evidenza delle dimostrazioni, dal Borelli promessa in queste parole, <lb></lb>risulta necessariamente dai processi matematici da lui seguiti, ma Giovanni <lb></lb>Bernoulli trovò un difetto nella ipotesi, su cui si fondano i calcoli borel­<lb></lb>liani, difetto ch&#039;egli attribuisce, non all&#039;uomo, ma ai tempi, quando ancora <lb></lb>del Calcolo differenziale non conoscevasi bene nè la natura nè l&#039;uso. </s>

<s>Il Bo­<lb></lb>relli, per esempio, dà agli elementi, di che si compongono le fibre musco­<lb></lb>lari, la figura di rombi, ma essendo molti e d&#039;ogni parte ugualmente com­<lb></lb>pressi, dimostra il nuovo Calcolo non poter configurarsi quegli elementi o <lb></lb>quelle macchinette, come al Borelli stesso piaceva chiamarle, in altra forma <lb></lb>diversa dalla circolare. </s>

<s>Nel preloquio dell&#039;Autore alla sopra citata Disserta­<lb></lb>zione <emph type="italics"></emph>De motu musculorum,<emph.end type="italics"></emph.end> il Bernoulli infatti scriveva: “ Jo: Alphonsi <lb></lb>Borelli vestigiis insistemus, amplectendo eius hypothesim, quam tamen ni­<lb></lb>mis oscitanter applicuisse ostendemus, quando suis machinulis vel vesiculis <lb></lb>fibrarum muscularium figuram rhomboidalem attribuit, ubi simul apparebit <lb></lb>hance figuram rectilineam prae aliis ipsis assignasse, tum facilitatis ergo, <lb></lb>nimirum ut commodiori calculo relationes virium dilatantium ad resistentias <lb></lb>supputaret, tum etiam quia iustam et debitam figuram, quam circularem <lb></lb>esse ex natura pressionis liquidorum demonstrabimus, et quae exinde emer­<lb></lb>gunt vires distendentes, non potuit non ignorare sine novo nostro calculo <lb></lb><emph type="italics"></emph>Integralium<emph.end type="italics"></emph.end> verbo appellato, qui tum profundissima caligine adhuc tectus <lb></lb>latitabat, cuiusque prima stamina magno Geometrae G. G. </s>

<s>Leibnitio de­<lb></lb>bemus. </s>

<s>” </s></p><p type="main">

<s>Per via del calcolo degl&#039;Integrali, soggiunge il Bernoulli di aver tro­<lb></lb>vato che le forze traenti i muscoli non operano, secondo il supposto borel­<lb></lb>liano, a modo di cunei, ma come tante infinite particelle elastiche, che tutte <pb xlink:href="020/01/1202.jpg" pagenum="77"></pb>con egual forza agendo contro le vescicole muscolari faranno ad esse pi­<lb></lb>gliar, non la figura de&#039;rombi “ sed aliam curvilineam conciliabunt, quam <lb></lb>nunc indagabimus ” (ibi, pag. </s>

<s>11) e ch&#039;egli dice resultar similissima alla <lb></lb><emph type="italics"></emph>Velaria.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Un altro grave difetto, non notato qui dal Bernoulli nella Meccanica <lb></lb>borelliana, e di cui non si può addurre nessuna scusa, consiste nell&#039;aver ri­<lb></lb>pudiato come falso il principio herigoniano della composizione delle forze. </s>

<s><lb></lb>Ma perchè dovremo intorno a ciò trattenersi di proposito altrove, passeremo <lb></lb>senz&#039;altro a delibar qualche cosa de&#039;tanti e insigni teoremi dal Borelli di­<lb></lb>mostrati, e relativi alla meccanica dei moti muscolari. </s></p><p type="main">

<s>È il primo di que&#039;Teoremi così formulato: “ Motus articulorum flexi­<lb></lb>vus sphaericus est, vel circularis, aut in superficie conica, circa centrum <lb></lb>imaginarium factus ” (De motu anim. </s>

<s>Pars I cit., pag. </s>

<s>18). Questo stesso <lb></lb>Teorema, che è il fondamento a tutto il nuovo edifizio della Meccanica mu­<lb></lb>scolare, era stato già dimostrato da Galileo nella seconda Giornata de&#039;Due <lb></lb>massimi sistemi. </s>

<s>Ivi infatti il Salviati, volendo rispondere alle strane obie­<lb></lb>zioni di un certo Filosofo peripatetico contro il moto annuale della Terra, <lb></lb>così gli dice: “ Voi primieramente ammettete per vero che la Natura abbia <lb></lb>fatto gli articoli, le flessure e snodature degli animali, acciocchè si possano <lb></lb>muovere di molti e diversi movimenti, e io vi nego questa proposizione, e <lb></lb>dico che le flessioni son fatte, acciocchè l&#039;animale possa muovere una o più <lb></lb>delle sue parti, restando immobile il resto, e dico che, quanto alle spezie e <lb></lb>differenze dei movimenti, quelli sono di una sola, cioè tutti circolari, e per <lb></lb>questo voi vedete tutti i capi degli ossi mobili esser colmi o cavi, e di que­<lb></lb>sti altri sono sferici, che son quelli che hanno a muoversi per tutti i versi, <lb></lb>come fa nella snodatura della spalla il braccio dell&#039;alfiere nel maneggiar <lb></lb>l&#039;insegna, e dello strozziere nel richiamar col logoro il falcone, e tale è la <lb></lb>flessura del gomito, sopra la quale si gira la mano nel forar col succhiello. </s>

<s><lb></lb>Altri son circolari per un sol verso, e quasi cilindrici, che servono per le <lb></lb>membra, che si piegano in un sol modo, come le parti delle dita l&#039;una sopra <lb></lb>l&#039;altra. </s>

<s>Ma senza più particolari incontri un solo general discorso ne può <lb></lb>far conoscere questa verità: e questo è che di un corpo solido che si muova, <lb></lb>restando uno de&#039;suoi estremi senza mutar luogo, il moto non può esser se <lb></lb>non circolare, e perchè nel muover l&#039;animale uno delle sue membra non <lb></lb>lo separa dall&#039;altro suo conterminale, adunque tal moto è circolare di ne­<lb></lb>cessità ” (Alb, I, 282). </s></p><p type="main">

<s>Premesso dunque quel Teorema fondamentale, così da Galileo premo­<lb></lb>strato, passa il Borelli alla dimostrazione di altri Teoremi di Meccanica <lb></lb>astratta “ quasi lemmata utilia ad robur, seu momentum musculorum de­<lb></lb>monstrandum ” (Loco cit., pag. </s>

<s>26). Il volere entrare addentro a queste sot­<lb></lb>tili speculazioni, per farne la storia, ci condurrebbe troppo al di là degii an­<lb></lb>gusti limiti, che ci sono prescritti, e perciò, lasciando indietro l&#039;esame di <lb></lb>questi importantissimi Lemmi, e di quegli altri pure, co&#039;quali incomincia il <lb></lb>cap. </s>

<s>XVI, ci contenteremo di dire come la conclusione, a cui tendono tutte <pb xlink:href="020/01/1203.jpg" pagenum="78"></pb>le hellissime proposizioni, è quella in principio da lui promessa, che cioè, <lb></lb>calcolate le potenze de&#039;muscoli e le resistenze degli ossi, quelle si trovano <lb></lb>sempre a queste di molto superiori. </s></p><p type="main">

<s>Infino a tutto il cap. </s>

<s>XVII della prima parte del suo Trattato, posti <lb></lb>que&#039;teoremi fondamentali già da noi detti, e applicando i Lemmi meccanici <lb></lb>via via dimostrati, il Borelli tratta della Dinamica dei moti animali. </s>

<s>Nel <lb></lb>cap. </s>

<s>XVIII, con cui si termina la soluzione dei problemi più generali, si <lb></lb>tratta poi dall&#039;Autore della Statica animale, e intorno ad essa pure si sco­<lb></lb>prono molte nuove verità e si correggono antichi errori. </s>

<s>Basti all&#039;intento <lb></lb>nostro recar come saggio di queste nuove dottrine statiche la soluzione di <lb></lb>quel problema enunciato nella proposizione CXLIII, e formulato con que­<lb></lb>ste parole: “ Quare stando alternis pedibus, perpendiculariter innixis, mi­<lb></lb>nus fatigamur. </s>

<s>quam quando a duobus simul operantibus fulcimur ” (ibi, <lb></lb>pag. </s>

<s>233). </s></p><p type="main">

<s>Erasi il problema stesso assai prima proposto dall&#039;Acquapendente a scio­<lb></lb>gliere sotto quest&#039;altra forma: “ Cur ambobus cruribus stando, magis la­<lb></lb>boramus, quam uno tantum crure stante et altero ocioso et nihil agente, <lb></lb>cum contrarium potius evenire deberet, quod uni cruri stanti totum corpo­<lb></lb>ris pondus commissum sit, post dicemus ” (De motu loc. </s>

<s>cit., pag. </s>

<s>13). Poco <lb></lb>più sotto infatti, applicandosi a sciogliere il promesso problema, così l&#039;Acqua­<lb></lb>pendente stesso scriveva: “ Videamus primo quomodo se habent ambo crura <lb></lb>in statione. </s>

<s>Quando ambo crura stant, etsi nullus ad oculum apparet in eis <lb></lb>musculorum motus, revera omnes musculi moventur et agunt. </s>

<s>Qui sane <lb></lb>motus ad sensum latens <emph type="italics"></emph>tonicus,<emph.end type="italics"></emph.end> idest quasi extensus appellatur. </s>

<s>Est enim <lb></lb>tonicus motus ille, in quo brachium, aut crus, aut aliud membrum exten­<lb></lb>sum detinetur, propter musculos omnes, tum flectentes quam extendentes, <lb></lb>in eo operantes, videlicet tensos redditos, quem Galenus, <emph type="italics"></emph>De motu musc. </s>

<s><lb></lb>cap. </s>

<s>VIII,<emph.end type="italics"></emph.end> declarans dicit: Concipias aliquem aliquod pondus, ut puta lapi­<lb></lb>dem aut lignum, chorda trahentem: si alius alia chorda ponderi appensa ad <lb></lb>contrariam partem trahat, sed minori robore, dubio procul pondus versus <lb></lb>priorem tractum movebitur, sed difficilius et minus quam si non adesset se­<lb></lb>cundus trahens. </s>

<s>At si primus et secundus trahens aequalis sint roboris, non <lb></lb>movebitur pondus, utcumque uterque totis viribus trahat. </s>

<s>Sic est in motu <lb></lb>tonico: utrique musculi, tam flectentes quam extendentes, ita trahunt ut <lb></lb>neuter alterum superet. </s>

<s>In quo casu membrum extensum et immobile ad <lb></lb>sensum apparet, quamvis omnes musculi tensi et contracti ad extremum <lb></lb>sint. </s>

<s>Ubi igitur amborum crurum statio se se offert, tunc crura motu tonico <lb></lb>moventur et agunt, licet motus sensu non percipiatur, neque homo locum <lb></lb>mutet. </s>

<s>Quia vero in hoc tonico motu omnes musculi agunt, et agunt non <lb></lb>moderate sed validissimo et extremo motu; ideo multum laborant, impen­<lb></lb>seque defatigantur quam in alio quovis motu ” (ibi, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Ma il Borelli, dop&#039;aver riferita questa dottrina dell&#039;Acquapendente, senza <lb></lb>però nominarlo, e confondendolo con altri, i quali andavano ripetendo il detto <lb></lb>già da Galeno e da lui, argutamente così osserva, prima di dar del problema <pb xlink:href="020/01/1204.jpg" pagenum="79"></pb>la vera risoluzione sicura: “ At non animadvertunt hi praeclari Viri falsi­<lb></lb>tatem assumpti eorum. </s>

<s>Verum est minori labore, nempe sub duplo, ab una <lb></lb>manu dextra pondus decem librarum sustineri, quam si aliae decem librae <lb></lb>a sinistra quoque suspenderentur, nam tunc duae manus duplum pondus <lb></lb>20 libr. </s>

<s>elevarent, quam una manus sola. </s>

<s>At falsum est quod idem pon­<lb></lb>dus 20 libr. </s>

<s>facilius ab unica manu sustineatur, quam si subdiviso onere <lb></lb>10 librae a singulis manibus suspenderentur. </s>

<s>Eodem modo fatigari magis <lb></lb>deberent musculi unius pedis, duplum pondus totius hominis sustinendo, <lb></lb>quam subdiviso onere super duobus pedibus, ita ut medietas ab unoquoque <lb></lb>fulciri deberet ” (De motu anim. </s>

<s>P. cit., pag. </s>

<s>233, 34). </s></p><p type="main">

<s>Così è di fatti, conforme a ciò che detta la ragion naturale, che cioè <lb></lb>un piede solo, sopportando il peso di tutto il corpo, deve più affaticarsi che <lb></lb>ripartendolo con quell&#039;altro. </s>

<s>Ma come dunque va che tante volte facciam <lb></lb>questo gioco di appoggiarsi su un piede solo, parendo che s&#039;allievi a quel <lb></lb>modo in noi la stanchezza? </s>

<s>A che il Borelli risponde, invocando in propo­<lb></lb>sito la dottrina galileiana della vera causa, che induce in noi stessi e negli <lb></lb>altri animali il senso della stanchezza. </s>

<s>“ Lo stancarsi il corpo dell&#039;animale, <lb></lb>dice Galileo, deriva per mio credere dall&#039;impiegare una parte sola per muo­<lb></lb>vere sè stessa e tutto il resto del corpo, come v. </s>

<s>g. </s>

<s>per camminare s&#039;im­<lb></lb>piegano le cosce e le gambe solamente per portar loro stesse e tutto il ri­<lb></lb>manente ” (Alb. </s>

<s>I, 295). Tale essendo la ragione della stanchezza, il Borelli <lb></lb>soggiunge, e così conclude la sua dimostrazione: “ Cum e contra actione <lb></lb>interrupta, pausis interpositis minus molesta pondera graviora sustineamus, <lb></lb>sicuti stando maiorem lassitudinem patimur quam leniter deambulando; quare <lb></lb>patet quod alterna positura et innixio modo super unum, modo super alium <lb></lb>pedem est quaedam commutatio similis deambulationi ” (De motu anim. </s>

<s><lb></lb>Pars cit., pag. </s>

<s>234). </s></p><p type="main">

<s>Perchè, stando per qualche tempo in piedi sentiamo maggiore stanchezza <lb></lb>che passeggiando per tutto quel tempo, è un altro curioso problema di Mec­<lb></lb>canica animale, che il Borelli cita nelle sopra riferite parole, com&#039;esempio, <lb></lb>senza curarsi di darne la soluzione. </s>

<s>Chi fosse però desideroso di saperla può <lb></lb>sodisfarsene leggendola in quei <emph type="italics"></emph>Pensieri diversi circa varie materie,<emph.end type="italics"></emph.end> cho noi <lb></lb>citammo più sopra, dove troverebbe altresì risolute altre questioni in simile <lb></lb>soggetto. </s>

<s>E perchè il discorso non è poi tanto lungo, e può da un&#039;altra <lb></lb>parte servir di complemento alle dottrine borelliane, benchè non sieno gli <lb></lb>argomenti per verità rigorosamente desunti da principii meccanici; pen­<lb></lb>siamo di trascriver qui le relative parole, per sodisfare al desiderio dei no­<lb></lb>stri Lettori: </s></p><p type="main">

<s>“ Nel ritrovarsi un giorno, mentre si celebravano gli uffici della Set­<lb></lb>timana santa, nella Chiesa del Duomo di Pisa, nel rizzarsi che fece uno dal <lb></lb>luogo dove stava a sedere, disse: io son più stracco, che se tutt&#039;oggi io <lb></lb>avessi camminato. </s>

<s>A questo proposito furono proposti dall&#039;Ecc.mo Sig. </s>

<s>Bo­<lb></lb>relli due graziosissimi teoremi: l&#039;uno è perchè, stando v. </s>

<s>g. </s>

<s>ritto senza muo­<lb></lb>vermi una mezz&#039;ora, mi stracco assai più che se per mezz&#039;ora io passeggiassi. <pb xlink:href="020/01/1205.jpg" pagenum="80"></pb>Certa cosa è che passeggiando io duro la medesima fatica, che richiedesi per <lb></lb>stare in piedi, ed oltre a questo duro la fatica nel muovermi e nel portare <lb></lb>il corpo. </s>

<s>Dovrebbesi dunque dire che, durandosi in uno degli atti assai mag­<lb></lb>gior fatica che nell&#039;altro, più si dovesse stancare in quello che nell&#039;altro: <lb></lb>eppure il contrario apertamente se ne vede seguire. </s>

<s>” </s></p><p type="main">

<s>“ Con l&#039;occasione d&#039;esaminarsi questo, un altro più curioso ne pro­<lb></lb>pose, e fu: due v. </s>

<s>g. </s>

<s>d&#039;ugual valore concordano di trovarsi a duello tra <lb></lb>quattro giorni. </s>

<s>Uno di essi, volendo risparmiare le forze per la giornata <lb></lb>prefissa, tutt&#039;e quattro i giorni consuma in dormire o nel letto: l&#039;altro in <lb></lb>quei quattro giorni, non curante di riposo, tutto il giorno in varie cose si <lb></lb>esercita. </s>

<s>Si domanda chi di loro dovrebbe essere più valoroso o chi riposò <lb></lb>o chi si affaticò? </s>

<s>” </s></p><p type="main">

<s>“ Pareva ridicolo il dire che quello che s&#039;affaticò fosse stato più pode­<lb></lb>roso, per l&#039;esempio di quello, che avendo a fare una cena sontuosa, in cam­<lb></lb>bio di avanzarsi in danari, gettasse via e piatti e tavole e danari, e tuttociò <lb></lb>che poteva servire per la cena. </s>

<s>Così questo che doveva fare il duello, in­<lb></lb>vece di avanzarsi in forze, e non le spendere nei quattro giorni antecedenti, <lb></lb>le getta, si strapazza e si affatica, sicchè parrebbe doversi dire che quello <lb></lb>che stette in ozio dovesse essere il più valoroso: eppure, per l&#039;esperienza, <lb></lb>tutto segue il contrario. </s>

<s>” </s></p><p type="main">

<s>“ Per intelligenza di che due bellissimi esempi possono addursi: l&#039;uno <lb></lb>è che se v. </s>

<s>g. </s>

<s>da un pozzo, ancorchè d&#039;acqua perfettissima, si starà lungo <lb></lb>tempo senza trarne acqua, il pozzo resta guasto e l&#039;acqua putrida. </s>

<s>Il me­<lb></lb>desimo ancora si vede seguire in uno scalpello, ancorchè di tempra ottimo, <lb></lb>che se lascerassi stare per molto tempo, senza punto adoperarsi, tutto ir­<lb></lb>rugginito andrà a male, nè potrà di quello alcuno servirsi, se prima, o con <lb></lb>la ruota o con altro consumandolo, non lo ridurrà netto e pulito. </s>

<s>Dubbio <lb></lb>veruno non vi è che, se il medesimo scalpello fosse stato adoprato, consu­<lb></lb>mato non si fosse, ma nello stesso consumarsi veniva a restar pulito e netto <lb></lb>da quella ruggine, che l&#039;ha reso inabile al fendere, e del tutto inutile per <lb></lb>quello che fu fatto. </s>

<s>” </s></p><p type="main">

<s>“ Così ancora dir si potrà di quello, che stette ritto senza punto muo­<lb></lb>versi, e durò meno fatica di quello, che camminò, ed era più stracco. </s>

<s>Im­<lb></lb>perocchè non vi è dubbio alcuno che quello che cammina fa più forza di <lb></lb>quello, che resta semplicemente ritto, ma è ben vero anche che quello che <lb></lb>cammina dura assai meno fatica in far più forza, che dura quello che sta <lb></lb>ritto in far meno forza, poichè quel primo, nella forza che fa, si vien anco <lb></lb>a mondare da quella ruggine, che impedisce al secondo adoperare a suo pia­<lb></lb>cere la forza. </s>

<s>Imperocchè nel moto che fa, aprendosi i meati della carne, <lb></lb>traspira facilmente certa materia, la quale imprigionata dentro, entrando per <lb></lb>i muscoli, cagiona non poco impedimento per esercitar le forze. </s>

<s>” </s></p><p type="main">

<s>“ Sicchè verissimo stimo io che quello posando nel letto getti via meno <lb></lb>forza di quello, che tutto il giorno si esercita, ma è anco vero ch&#039;ei, con lo <lb></lb>stare ozioso, non dà luogo alla traspirazione, onde ne seguita che il giorno <pb xlink:href="020/01/1206.jpg" pagenum="81"></pb>prefisso al duello egli resti di forze svantaggiato. </s>

<s>Nè paia cosa ciò fuori di <lb></lb>proposito, cioè che le semplici traspirazioni per i meati possano essere giu­<lb></lb>sta e adeguata ragione per lo scioglimento delle predette difficoltà. </s>

<s>Poichè, <lb></lb>se noi prenderemo tuttociò che si mangia ed esattissimamente lo peseremo, <lb></lb>messo poi insieme tutti gli escrementi mandati fuora o per orina o per se­<lb></lb>cesso o per sputo, pesandoli, troveremo questi essere molto minori di peso <lb></lb>di quello, che sopra si ponderò mangiato. </s>

<s>Avvertasi però che la detta espe­<lb></lb>rienza non si deve fare nè in un giorno nè in due o poco più, ma per mesi <lb></lb>continui, per torre molte difficoltà, che potrebbero alterare l&#039;esattezza del­<lb></lb>l&#039;esperienza fatta tanto bene dal Santorio e dal Michelini. </s>

<s>” </s></p><p type="main">

<s>“ Se dunque si troverà tanto svantaggio o diminuimento di forze del <lb></lb>peso secondo, dove potrà essere andato il peso che non si trova? </s>

<s>Nè si può <lb></lb>dire che vada tutto per accrescimento del corpo, poichè in breve tempo re­<lb></lb>steremmo così grassi e corpulenti, dovendoci avanzare e crescere di raggua­<lb></lb>gliato quasi una libbra al giorno, che appena ci potremmo muovere, oppure <lb></lb>di statura così dell&#039;ordinaria superiore, che in quarant&#039;anni e più che cor­<lb></lb>rono di vita, da che l&#039;uomo finisce di crescere, avanzeremmo i Morganti e <lb></lb>i Rodomonti, che dettero materia di favoleggiare a più di uno. </s>

<s>Sicchè, per <lb></lb>concludere, altro non resta a dire, se non che l&#039;avanzo del peso è traspi­<lb></lb>rato per i meati ed i pori della nostra carne, ed in questa maniera, con­<lb></lb>frontandosi con l&#039;esperienza, si salveranno tutte le altre apparenze ed ef­<lb></lb>fetti. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>10-12). </s></p><p type="main">

<s>Essendo queste cose dette dal Borellli in una conversazione di amiei, <lb></lb>i quali non tutti erano matematici, s&#039;intende come, per adattarsi all&#039;intelli­<lb></lb>genza di ognuno, ricorresse a cercare le prove del suo discorso negli esempi <lb></lb>volgari e nel fatto allora notissimo dell&#039;insensibile traspirazione, trascurando <lb></lb>que&#039;principii meccanici di Galileo, ch&#039;egli sapientemente deriva nel trattato <lb></lb><emph type="italics"></emph>De motu animalium<emph.end type="italics"></emph.end> alle sue intenzioni, e dell&#039;applicazion de&#039;quali giova, <lb></lb>a&#039;riferiti di sopra, aggiungere qualche altro esempio. </s></p><p type="main">

<s>Nel secondo Dialogo delle Due nuove scienze, dopo la dimostrazione del <lb></lb>Teorema VIII della resistenza de&#039;solidi allo spezzarsi, Galileo, così por modo <lb></lb>di corollario o di scolio, compendiava una scienza nuova dell&#039;equilibrio delle <lb></lb>macchine animali: “ Or vedano come dalle cose sin qui dimostrate aperta­<lb></lb>mente si raccoglie l&#039;impossibilità del poter, non solamente l&#039;arte, ma la Na­<lb></lb>tura stessa crescer le sue macchine a vastità immensa.... Disegnai già la <lb></lb>figura di un osso allungato solamente tre volte, ed ingrossato con tal pro­<lb></lb>porzione, che potesse nel suo animale grande far l&#039;ufficio proporzionato a <lb></lb>quel dell&#039;osso minore dell&#039;animal più piccolo, e le figure son queste .... <lb></lb>dove vedete sproporzionata figura che diviene quella dell&#039;osso ingrandito. </s>

<s><lb></lb>Dal che è manifesto che chi volesse mantenere in un vastissimo gigante le <lb></lb>proporzioni, che hanno le membra in un uomo ordinario, bisognerebbe o <lb></lb>trovar materia molto più dura e resistente per formare le ossa, ovvero am­<lb></lb>mettere che la robustezza sua fosse a proporzione assai più fiacca, che negli <lb></lb>uomini di statura mediocre: altrimente, crescendoli a smisurata altezza, si ve-<pb xlink:href="020/01/1207.jpg" pagenum="82"></pb>drebbono dal proprio peso opprimere e cadere. </s>

<s>Dovecchè all&#039;incontro si vede, <lb></lb>nel diminuire i corpi, non si diminuire con la medesima proporzione le <lb></lb>forze, anzi nei minori crescer la gagliardia con proporzion maggiore ” <lb></lb>(Alb. </s>

<s>XIII, 128, 29). </s></p><p type="main">

<s>Il Borelli applica destramente queste dottrine galileiane alla meccanica <lb></lb>del salto, concludendo che per la ponderosità del corpo i grandi son assai <lb></lb>meno agili de&#039;piccoli animali. </s>

<s>“ Demonstravit eximius Galileus, <emph type="italics"></emph>De motu <lb></lb>locali,<emph.end type="italics"></emph.end> quod in corporibus animalium proportionaliter decrescentium minui­<lb></lb>tur pondus in maiori proportione, nempe duplicata resistentiae et roboris <lb></lb>eorum, et ideo ossa maiorum animalium crassiora fieri debebant, ut suo ro­<lb></lb>bore incrementum ponderis sustentare valerent. </s>

<s>Et hinc fit ut animalia vasta, <lb></lb>quae corpus valde ponderosum habent, minus vivacia et minus agilia sint <lb></lb>quam exigua animalia. </s>

<s>Quare verum est quod minus ponderosa animalia <lb></lb>maiores saltus respectu sui corporis efficiunt ” (De motu anim. </s>

<s>Pars cit., <lb></lb>pag. </s>

<s>282). </s></p><p type="main">

<s>Di questa curiosità di meccanica muscolare, vogliam dire del salto, erasi <lb></lb>pure occupato Galileo, come apparisce da quella Selva di Problemi varii, <lb></lb>che raccolse il Viviani. </s>

<s>“ Assai manco si salterebbe, ivi si legge, a piè giunti, <lb></lb>se minor fosse la lunghezza del piede, e forse il salto sarebbe nullo, se si <lb></lb>posasse sopra la punta di due coni ” (Alb. </s>

<s>XIV, 322). Ma il Borelli dette <lb></lb>di queste particolarità di moto ne&#039;varii animali la teoria assoluta, che poi <lb></lb>osarono d&#039;infirmare due stranieri, il Barthez e il Dumas. </s>

<s>Dicevano costoro <lb></lb>che non può, come fa il nostro Italiano, paragonarsi il salto dell&#039;uomo al <lb></lb>rimbalzar di una molla, perchè le ossa e tutte le altre parti componenti la <lb></lb>macchina umana non hanno quell&#039;elasticità, che fa risalire le molle. </s>

<s>Vin­<lb></lb>cenzio Brunacci però prese a difendere valorosamente, in un suo Discorso <lb></lb>accademico, le dottrine borelliane, dimostrando che i due suddetti Fisiologi <lb></lb>stranieri le posero in dubbio, per non averle troppo bene comprese, essen­<lb></lb>dochè “ il Borelli al fenomeno del balzo prodotto dalla elasticità de&#039;corpi <lb></lb>riferisce la spiegazione del salto, non perchè la macchina rimbalzi in virtù <lb></lb>di una elasticità a lei propria,... ma perchè, come accade nel risalto dei <lb></lb>corpi, il centro di gravità della macchina, obbligato a prendere un moto di <lb></lb>direzione verticale, fa distaccare la macchina umana dal suolo ” (Discorsi <lb></lb>accadamici, Milano 1827, pag. </s>

<s>178, 79). </s></p><p type="main">

<s>Ritornando ora alle dottrine meccaniche di Galileo, intorno alle condi­<lb></lb>zioni di naturale equilibrio fra le parti componenti le moli animali, contro <lb></lb>i principii esposti nel Dialogo del Salviati, e da noi già riferiti, promuove <lb></lb>Simplicio una difficoltà, sovvenutagli dal pensare alle smisurate moli de&#039;ce­<lb></lb>tacei. </s>

<s>Quella difficoltà, risponde ivi lo stesso Salviati, lo fa accorto di una <lb></lb>condizione lasciata addietro nel primo discorso; condizione potente a far sì <lb></lb>“ che i giganti ed altri animali vastissimi potessero consistere e agitarsi, <lb></lb>non meno che i minori, e ciò seguirebbe, quando non solo si aggiugnesse <lb></lb>gagliardia all&#039;ossa ed all&#039;altre parti, ufficio delle quali è il sostenere il pro­<lb></lb>prio e sopravveniente peso, ma lasciata la struttura delle ossa con le me-<pb xlink:href="020/01/1208.jpg" pagenum="83"></pb>desime proporzioni, pur nell&#039;istesso modo, anzi più agevolmente consiste­<lb></lb>rebbono le medesime fabbriche, quando con certa proporzione si diminuisse <lb></lb>la gravità della materia delle medesime ossa, e quella della carne o di altro <lb></lb>che sopra l&#039;ossa si abbia ad appoggiare, e di questo secondo artifizio si è <lb></lb>prevalsa la Natura nella fabbrica dei pesci, facendogli le ossa e la polpa non <lb></lb>solamente assai leggere, ma senza veruna gravità ” (Alb. </s>

<s>XIII, 130). </s></p><p type="main">

<s>Dottrine galileiane son queste, che il Borelli ebbe a ripetere con lo <lb></lb>stesso costrutto di discorso, se non colle medesime parole: “ Et idoo pisces, <lb></lb>egli dice nella citata Parte prima della Meccanica animale, non indigent pe­<lb></lb>dibus, sicut terrestria et volatilia. </s>

<s>Secundo, non fatigantur, neque ullam las­<lb></lb>situdinem percipiunt stando, quia membra aequilibrata, non gravitant, neque <lb></lb>comprimunt partes subiectas. </s>

<s>Tertio, vastiora esse possunt corpora piscium <lb></lb>quam terrestrium animalium, ut docuit Galileus, quia pisces non coguntur <lb></lb>sustinere proprium pondus, quod nullam vim compressivam exercent, ob <lb></lb>aequilibrium cum aqua ” (pag. </s>

<s>332). </s></p><p type="main">

<s>Altre bellissime speculazioni di Meccanica applica Galileo a interpetrare <lb></lb>il sapiente magistero della Natura in fabbricare il corpo, e particolarmente <lb></lb>le ossa a varie qualità di animali; speculazioni largamente illustrate dal Bo­<lb></lb>relli, e sulle quali ritorneremo in altro capitolo di questa terza parte della <lb></lb>nostra Storia. </s>

<s>Ma non vogliamo intanto lasciarci sfuggir l&#039;occasione di far <lb></lb>notare un singolar merito, che dee giustamente attribuirsi a Galileo, benchè <lb></lb>gli stessi cechi adoratori di lui non ne facciano il debito conto, ed è che fu <lb></lb>egli veramente il primo ad applicare le leggi dell&#039;equilibrio e del moto dei <lb></lb>solidi alle leggi dell&#039;equilibrio e del moto de&#039;corpi animali. </s></p><p type="main">

<s>Qual efficacia avesse in avviare questa nuova parte di Filosofia natu­<lb></lb>rale l&#039;Acquapendente, lo abbiamo qua e là accennato più volte, e qui in <lb></lb>ultimo, per compendio, s&#039;aggiunge che la massima parte de&#039;problemi gali­<lb></lb>leiani, accennati nella <emph type="italics"></emph>Selva<emph.end type="italics"></emph.end> e risoluti ne&#039;Dialoghi del mondo e in quegli <lb></lb>altri del moto, furono proposti dallo stesso Acquapendente, ma perch&#039;egli <lb></lb>ci andò con gli errati principii di Meccanica aristotelica, Galileo fu che ne <lb></lb>dette per il primo la vera soluzione. </s></p><p type="main">

<s>Il soggetto accomodatissimo a ricreare gl&#039;ingegni, di che quell&#039;uomo <lb></lb>di natura conversevole e gioviale si compiaceva, ebbe maggior cultura di <lb></lb>quel che non possa apparire dalle due massime Opere di lui, e la detta <lb></lb><emph type="italics"></emph>Selva<emph.end type="italics"></emph.end> messa insieme dal Viviani lo attesta, e lo attestano con più efficacia <lb></lb>i pensieri galileiani fatti rivivere dal Borelli, non solo nella grande Opera <lb></lb>sua, ma in altre scritture pochissimo conosciute, alcune delle quali s&#039;indi­<lb></lb>cheranno presentandocisi l&#039;occasione. </s></p><pb xlink:href="020/01/1209.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dei moti del cuore<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della struttura muscolare del cuore; de moti di sistele e di diastole. </s>

<s>— II. </s>

<s>Delle forze motive del <lb></lb>cuore, e della loro misura; del moto del sangue per le arterie e per le vene. </s>

<s>— III. </s>

<s>Delle leggi <lb></lb>idrauliche applicate al moto del sangue. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Se la vita è moto, i muscoli, che son le potenze applicate a muovere <lb></lb>la macchina animale, si dovevan rappresentare alla mente de&#039;Fisiologi an­<lb></lb>tichi come primi e principali organi di quella stessa vita, che per tutte le <lb></lb>esperienze e con universale consenso si concepiva avere il suo principio, e <lb></lb>quasi la sua fonte, nel cuore. </s>

<s>Non fa perciò maraviglia se colui, ch&#039;è tra&#039;Fi­<lb></lb>siologi conosciuto per il più antico, scorto dalla luce naturale di questo con­<lb></lb>cetto, sentenziò senza timor di dubbio che il cuore è un muscolo molto forte. </s>

<s><lb></lb>Non dubitava Ippocrate della verità di questa sua sentenza, vedendo essere <lb></lb>il cuore stesso quasi un lago, da cui muovono con impeto i fiumi del san­<lb></lb>gue a irrigare le membra, riseccato il quale, irreparabilmente l&#039;uomo sen <lb></lb>muore. </s>

<s>“ Cor musculus est valde fortis, non nervo, sed densitate ac con­<lb></lb>strictione carnis, et duos ventriculos habet discretos in uno amiculo, ab utra­<lb></lb>que parte unum.... Hi fontes sunt humanae naturae, et hic flumina sunt, <lb></lb>quibus totum corpus irrigatur, atque hi etiam vitam homini conferunt, et, <lb></lb>ubi resiccati fuerint, homo moritur ” (Opera, Lib. </s>

<s>De corde, Venetiis 1619, <lb></lb>fol. </s>

<s>25). </s></p><p type="main">

<s>Il concetto sbocciato così nella mente d&#039;Ippocrate, come un vergine <lb></lb>fiore in balza solitaria, fu nella sua natia bellezza e nella soavità della fra-<pb xlink:href="020/01/1210.jpg" pagenum="85"></pb>granza guasto e corrotto, quando Galeno lo traspose ne&#039;suoi orti accademici, <lb></lb>per esercitarvi attorno un&#039;artificiosa cultura. </s>

<s>È uno de&#039;più fiorenti fra que­<lb></lb>sti orti galenici quello che è inscritto <emph type="italics"></emph>De anatomicis demonstrationibus,<emph.end type="italics"></emph.end><lb></lb>nel VII libro del quale il capitolo VIII è intitolato: <emph type="italics"></emph>De substantia et motu <lb></lb>cordis adversus antiquos.<emph.end type="italics"></emph.end> Il cuore non può, ragiona ivi l&#039;Autore, essere un <lb></lb>muscolo, perchè ne differisce sostanzialmente nelle funzioni: il muscolo in­<lb></lb>fatti si muove ad arbitrio, ed il cuore non cessa mai. </s>

<s>“ Etenim cordis mo­<lb></lb>tus non arbitrarius esse, nec cessare, quoad animal ita fruitur, potest: mu­<lb></lb>sculorum autem functio subinde quiescit, ac rursus excitatur, animantis <lb></lb>arbitrio subserviens ” (Venetiis 1597, fol. </s>

<s>95). Nè dee far maraviglia, sog­<lb></lb>giunge Galeno, che il cuore e i muscoli differiscano nelle funzioni, essendo <lb></lb>così notabilmente differenti nella sostanza. </s>

<s>“ Quapropter neque musculi eam­<lb></lb>dem cum corde functionem habent, quoniam neque substantiam. </s>

<s>Certe, si <lb></lb>quis cor et musculum quemlibet pariter coctum utrumque gustare voluerit, <lb></lb>hand mediocrem ipsorum gustu differentiam deprehendet;.... cor quovis <lb></lb>musculo durius est, et fibrarum varietate sic colore palam discrepat ” (ibi). </s></p><p type="main">

<s>Per poi meglio persuadere della diversità, che passa tra le funzioni del <lb></lb>cuore e dei muscoli, Galeno richiama l&#039;attenzione al principio dei moti vitali <lb></lb>rivelatoci chiaramente dall&#039;esperienza. </s>

<s>Quel principio risiede nei nervi, recisi <lb></lb>i quali, dovrebbe così rimanersi inerte il muscolo come il cuore: ma si vede <lb></lb>a questo anche dopo l&#039;incisione durare il polso “ quare superest vim pul­<lb></lb>satilem ex ipsius cordis corpore oriri: non autem oriretur, si viscus eam­<lb></lb>dem cum totius corporis musculis naturam obtineret ” (ibi, fol. </s>

<s>96). Ond&#039;è <lb></lb>che, dietro questo e dietro gli altri sopra addotti argomenti, Galeno così con­<lb></lb>clude: “ Horum igitur ignari nobis videntur qui cor musculum esse exi­<lb></lb>stimant, non intelligentes actionis ipsius excellentiam ex sua visceri substan­<lb></lb>tia necessario inèsse, quapropter maxime errant qui cor musculum esse <lb></lb>censent ” (ibi). </s></p><p type="main">

<s>Ecco, fra&#039;tanti, un altro esempio storico de&#039;tristi effetti della Filosofia, <lb></lb>la quale bene spesso, piuttosto ch&#039;educare il Vero, nato spontaneo nelle <lb></lb>menti, lo sradica per imporvi in quella vece le sue finzioni. </s>

<s>Il buon senso <lb></lb>dell&#039;uomo, se il Filosofo non glielo avesse suggerito, non avrebbe pensato <lb></lb>mai che la Natura tanto aristocratica procedesse nelle sue leggi, da non per­<lb></lb>metter che il nobilissimo cuore s&#039;avesse a scambiare, anco nell&#039;apparenza, <lb></lb>con gli altri muscoli plebei. </s>

<s>Ma era facilissimo rispondere a Galeno che male <lb></lb>avrebbe provveduto la Natura a far nella fabbrica de&#039;muscoli e del cuore <lb></lb>una così onorevole distinzione, se poi voleva condannar tanto questo che <lb></lb>quelli alla medesima servilità degli uffici. </s>

<s>Questo, a cui poi riducesi nella sua <lb></lb>nativa semplicità il concetto ippocratico, fu scorta ai Fisiologi per non smar­<lb></lb>rir del tutto la via, facilmente persuadendosi che se sono i muscoli gli or­<lb></lb>gani del moto, non può il cuore, che è il primo mobile, non essere anch&#039;egli <lb></lb>un muscolo schietto. </s>

<s>Da questo ragionamento scorto anche il Berengario, <lb></lb>benchè non qualifichi addirittura il cuore per un muscolo, pur, come ve­<lb></lb>dremo tra poco, insinua la cosa indirettamente, dando al viscere, nelle no-<pb xlink:href="020/01/1211.jpg" pagenum="86"></pb>tabili differenze di struttura che passano tra lui stesso e gli altri muscoli, <lb></lb>un&#039;attribuzione de&#039;medesimi uffici. </s></p><p type="main">

<s>Venuto il tempo della nuova instaurazione dell&#039;Anatomia, il Vesalio esce <lb></lb>con più libertà fuori de&#039;cancelli preclusi a lei da Galeno, e benchè senta <lb></lb>con l&#039;antico Maestro quanto abbia d&#039;importanza, in costituirsi la differenza <lb></lb>tra il cuore e i muscoli, il veder che quello si muove per necessità e que­<lb></lb>sti ad arbitrio; pure egli è il primo a notar che essi hanno, que&#039;due or­<lb></lb>gani dei moti animali, una somiglianza notabilissima nella struttura delle <lb></lb>fibre carnee, di che son contessuti. </s>

<s>“ Ut enim in musculis fibrae, ne rum­<lb></lb>perentur, carnem undique habent circumpositam; sic et cordis fibrae pecu­<lb></lb>liari ipsis carne continentur uniunturque..... Dein, quemadmodum cordis <lb></lb>fibrae cum musculorum fibris nonnulla consequntur communia, sic etiam ut <lb></lb>et illae motui famulantur, sed prorsus diversa: musculorum enim motus ar­<lb></lb>bitrarius est, cordis vero naturalis ” (De humani corp. </s>

<s>fabrica, Basileae 1543, <lb></lb>pag. </s>

<s>587). Si sentirebbe da queste considerazioni sospinto il Vesalio a tor­<lb></lb>nare indietro a consentir con Ippocrate, ma egli non s&#039;attenta di dichia­<lb></lb>rarsene aperto, e gli emuli successori poi rintuzzarono ogni conato di lui <lb></lb>confermandosi piuttosto, come in solido fondamento, ne&#039;placiti di Galeno. </s>

<s>Il <lb></lb>Colombo, per esempio, sentenziò, come se fosse sicuro di pronunziare un <lb></lb>oracolo: “ nullo pacto potest cor inter musculos connumerari, quamvis di­<lb></lb>vinus Hippocrates in Libro <emph type="italics"></emph>De corde<emph.end type="italics"></emph.end> ipsum musculum esse dicere non eru­<lb></lb>buerit “ (De re anat., Venetiis 1559, pag. </s>

<s>176, 77). </s></p><p type="main">

<s>L&#039;importanza, che sempre e da tutti fu riconosciuto avere il cuore nelle <lb></lb>funzioni della vita, facevano vivamente sentire il bisogno di decider della <lb></lb>natura di un organo sì principale, e la decisione dipendeva, com&#039;è facile <lb></lb>comprendere, da una più diligente anatomia del cuore stesso e de&#039;muscoli; <lb></lb>anatomia, che per le difficoltà naturali incontrate, sopraggiunta l&#039;imperizia <lb></lb>dell&#039;arte e l&#039;imperfezione degli strumenti, indugiò fino ai tempi dello Ste­<lb></lb>none. </s>

<s>Egli pubblicò in Amsterdam nel 1664 un trattato col titolo <emph type="italics"></emph>De mu­<lb></lb>sculis et glandulis,<emph.end type="italics"></emph.end> dove incomincia a narrare come, nella primavera del <lb></lb>precedente anno 1663, si fosse dato con ogni industria, per compiacere al <lb></lb>suo proprio genio e agli amici, a fare anatomia del cuore, e come gli venis­<lb></lb>sero da una tal prima dissezione rivelati questi tre fatti importanti: I, non <lb></lb>esser nel cuore altro paranchima diverso dalle fibre; II, non andar nessuna <lb></lb>fibra a diritto, ma tutte intorte; III, non esser l&#039;andamento delle stesse <lb></lb>fibre, nè retto nè circolare, ma incurvato alquanto nel mezzo. </s>

<s>Soggiunge <lb></lb>poco appresso l&#039;Autore come, proseguendo a esercitare intorno a sì difficile <lb></lb>soggetto lo stile, vedesse sopra quella stessa luce apparitagli d&#039;oriente, sten­<lb></lb>dersi nuove tenebre inaspettate “ ad quas discutiendas nullum, nisi ab mu­<lb></lb>sculorum cognitione remedium ” (pag. </s>

<s>3). </s></p><p type="main">

<s>Datosi dunque a esaminare i muscoli ordinati al moto di varii organi, <lb></lb>per conoscerne le differenze, lo Stenone così conclude: “ Quae hic de mu­<lb></lb>sculis proposita, si cordi applicentur, sufficiunt propositae initio demonstran­<lb></lb>dae propositioni: <emph type="italics"></emph>Cor vere musculum esse ”<emph.end type="italics"></emph.end> (pag. </s>

<s>24). Promette di tornare <pb xlink:href="020/01/1212.jpg" pagenum="87"></pb>in altro libro a dimostrare più profusamente la verità di questa annunziata <lb></lb>proposizione, ma intanto qui riduce a tre i principali argomenti formulati <lb></lb>nell&#039;ordine e nel modo che segue: “ I. </s>

<s>In universa cordis substantia nihil <lb></lb>occurrit sequentia praeter arterias, venas, nervos, fibras, membranas. </s>

<s>Sed nec <lb></lb>in musculo praeter dicta occurrunt alia (pag. </s>

<s>24). II. </s>

<s>Inter cordis fibras nulla <lb></lb>scrutanti mihi obvenit, quae non medio carnosa, extremis utrinque tendi­<lb></lb>nosa: id quod et omnibus musculorum fibris commune. </s>

<s>In corde, non mi­<lb></lb>nus ac in alio musculo, villorum uniformis est ductus (pag. </s>

<s>25). III. </s>

<s>Mem­<lb></lb>brana cordi propria, transverso fibrarum ductu, cordis secat fibras, eodemque <lb></lb>inter illas se insinuat ritu, nec aliud in musculi occurrit membrana ” (pag. </s>

<s>29) <lb></lb>Essendo così dimostrato, conclude all&#039;ultimo lo Stenone che, tutti gli attri­<lb></lb>buti de&#039;muscoli competendo con egual ragione anche al cuore, <emph type="italics"></emph>vere cor mu­<lb></lb>sculi nomine salutandum,<emph.end type="italics"></emph.end> ed è perciò verissima e confermata dai fatti os­<lb></lb>servati la sentenza dell&#039;antichissimo Ippocrate. </s></p><p type="main">

<s>Così parve finalmente decisa la questione, che insorta fra i due più an­<lb></lb>tichi greci Maestri dell&#039;Anatomia si rinnovellò ai tempi del Vesalio in Italia. </s>

<s><lb></lb>Ma benchè lo Stenone fosse espertissimo in esercitare lo stilo, e oculatissim<gap></gap><lb></lb>in osservare quel che dalla punta di lui gli veniva scoperto, tante erano nul­<lb></lb>ladimeno le difficoltà, che presentava il cuore nel districare l&#039;implicata tes­<lb></lb>situra delle sue fibre, che àlcuni lo trovarono oscuro in descriverle, altr<gap></gap><lb></lb>difettoso in esaminarle. </s>

<s>Di qui è che, verso la metà del secolo XVII, dura­<lb></lb>vano tuttavia nelle menti i dubbi, in che, infino dai restauramenti dell&#039;arte, <lb></lb>s&#039;erano incontrati i primi Anatomisti. </s></p><p type="main">

<s>Il Berengario confessò ch&#039;essendo il cuore così sodo non potevano com­<lb></lb>prendersi dal senso le varietà delle fibre, di ch&#039;è intessuto, ma dalle opera­<lb></lb>zioni di lui, che consistono principalmente in dilatarsi per attrarre, e ind<gap></gap><lb></lb>ritenere ed espellere il sangue, congetturava che di tre ordini dovesser es­<lb></lb>sere quelle stesse fibre: lunghe cioè, disposte nell&#039;interno del viscere, per <lb></lb>servire all&#039;attrazione; trasverse, collocate nel mezzo, per meglio ritenere l<gap></gap><lb></lb>stesso sangue; larghe, ricorrenti sull&#039;esterior superficie, per esser più vali<gap></gap><lb></lb>a spremerlo fuori e ad irrigarne tutte le membra. </s>

<s>“ Non sunt tales inu<gap></gap><lb></lb>in corde, sicut in musculis, in situ neque in substantia, quia situs istorun, <lb></lb>villorum in corde .... sunt absque ordine, et non sunt sic in musculis. </s>

<s>Prima <lb></lb>namque operatio cordis, teste Galeno <emph type="italics"></emph>V. </s>

<s>De iuvamentis membrorum,<emph.end type="italics"></emph.end> e<gap></gap><lb></lb>dilatare, et sic attrahit, et attractioni deserviunt villi, et in unoquoque men<gap></gap><lb></lb>bro villi longi deserviunt attractioni, et consiti sunt in interiori parte; <gap></gap><lb></lb>retentioni deserviunt transversi, qui necessario sunt siti in medio, scilic<gap></gap><lb></lb>supra istos; et expulsioni deserviunt lati, qui necessario sunt exteriores. </s>

<s>In <lb></lb>corde tamen, propter suam soliditatem, talis diversitas non potest ad sensum <lb></lb>comprehendi, et fuerunt in corde praedictae speties villorum, quia in eo ne­<lb></lb>cessario sunt diversi motus ” (Commentaria super Anat. </s>

<s>Mundini, Bono­<lb></lb>niae 1521, fol. </s>

<s>CCCXXXIX). </s></p><p type="main">

<s>Il Vesalio non sembra aver fatto altro in questo proposito che comme<gap></gap><lb></lb>tare i detti del Notomist<gap></gap> di Carpi. </s>

<s>Se tu prendi, egli dice, a esaminare u<gap></gap><pb xlink:href="020/01/1213.jpg" pagenum="88"></pb>muscolo, e o cotto o crudo, tu lo discerpi col coltello o coll&#039;unghie, ti si <lb></lb>rivela senza difficoltà la struttura delle sue fibre. </s>

<s>“ At cordis quidem caro <lb></lb>fibris compactissimis et inter se plurimum differentibus oppleta videtur. </s>

<s>Quae <lb></lb>vero earumdem situs differentiarumque sit ratio, coniectura potius quam <lb></lb>sectione assequimur ” (De hum. </s>

<s>corporis fabrica cit., pag. </s>

<s>586). </s></p><p type="main">

<s>La congettura si riduce, ad esempio del nostro Berengario, ad ammet­<lb></lb>tere un triplice ordine di fibre, le più intime delle quali facciano l&#039;ufficio <lb></lb>di attrarre, le mezzane di ritenere e l&#039;esterne di espellere il sangue. </s>

<s>Però <lb></lb>soggiunge che non si può propriamente assegnare a quelle stesse fibre un <lb></lb>ordine certo o una collocazione determinata, mescolandosi insieme dovunque <lb></lb>le rette con le oblique e con le transverse. </s>

<s>“ Sectio ipsa triplex hoc fibra­<lb></lb>rum genus invicem commisceri ostendit, et nunc rectas, nunc obliquas, nunc <lb></lb>transversas, et rursus rectas et obliquas et transversas quodammodo com­<lb></lb>mostrat, quasi tres priores differentiae singulis ventriculis peculiares essent, <lb></lb>posteriores vero toti cordi ambobusque ventriculis dedicarentur. </s>

<s>Appello au­<lb></lb>tem in corde rectas fibras quas in eo, per quam elixato, ex ipsius basi ad <lb></lb>mucronis usque ipsius centrum deduci, tam per cordis ventriculorum septum, <lb></lb>quam reliquam sedem, conspicimus; transversas autem, quae orbiculatim cor <lb></lb>ventriculosque ambiunt; obliquas vero, quae quidem orbiculatim cor ven­<lb></lb>triculosque ambiunt, at oblique, secundum cordis longitudinem, procedunt ” <lb></lb>(ibi, pag. </s>

<s>587). </s></p><p type="main">

<s>Quelle fibre rette ammesse dal Vesalio e nelle sue descrizioni accolte <lb></lb>dal Colombo (De re anat. </s>

<s>pag. </s>

<s>176), benchè si possano salvare nell&#039;anato­<lb></lb>mia di alcuni bruti, son però cosa affatto immaginaria, se si tratti del cuore <lb></lb>dell&#039;uomo. </s>

<s>Pure, anche il Lower poi ripetè lo stesso, e il Morgagni, per ta­<lb></lb>cere di altri, confessò che avendo diligentemente tenuto dietro alla rettitu­<lb></lb>dine di quelle fibre “ numquam videre potuisse, ob eamque causam facile <lb></lb>crediderim a diligentissimo anatomico Vieussenio in fibrarum cordis descrip­<lb></lb>tione esse praetermissas ” (Adversaria anat. </s>

<s>V, Patavii 1719, pag. </s>

<s>21). </s></p><p type="main">

<s>Ma, ripigliando il filo della nostra storia, quando lo Stenone pubblicava <lb></lb>nel suo trattato <emph type="italics"></emph>De musculis et glandulis<emph.end type="italics"></emph.end> di aver trovato il dutto delle fibre <lb></lb>del cuore non esser nè retto nè circolare, “ sed tantum circa medium sui <lb></lb>nonnihil incurvatum ” (pag. </s>

<s>2), il Borelli in Pisa aveva tredici anni prima <lb></lb>con pari diligenza osservato di esse fibre cardiache la configurazione e la <lb></lb>struttura, e non essere dirette nè parallele, ma curve e spirali; non intes­<lb></lb>sute come i giunchi nelle cestelle, secondo che parve al Vesalio, ma dispo­<lb></lb>ste con artificio assai più maraviglioso. </s>

<s>“ Immediate enim sub externa cor­<lb></lb>dis membrana a basi cordis et ab orificiis circularibus tendinosis, in quibus <lb></lb>desinunt venae cavae et pulmonaris auriculae, nec non a principiis arteria­<lb></lb>rum Aortae et Pulmonaris, propagatur stratum fibrarum carnosarum, quae <lb></lb>fere aequidistantes sunt inter se et directe a basi versus cordis mucronem <lb></lb>tendentes, ubi varie inflexae et contextae reflectuntur versus internas cavi­<lb></lb>tates ventriculorum. </s>

<s>Huic strato succedunt alia fibrarum strata oblique et <lb></lb>spiraliter descendentia, quorum fibrae semper magis ac magis inclinatae, pa-<pb xlink:href="020/01/1214.jpg" pagenum="89"></pb>riter versus mucronem tendentes, antequam apicem attingant, decussantur, <lb></lb>et texuntur inter se, et cum aliis ordinibus fibrarum, et inde interius reflec­<lb></lb>tuntur, et partim spiris obliquis et transversis, veluti fasciis, ad basim cordis <lb></lb>reflectuntur; partim internas columnas componere videntur, quibus funiculi <lb></lb>valvularum tricuspidum et mitralium alligantur; partim transverse contextae, <lb></lb>sinum ventriculi dextri efformant ” (De motu anim. </s>

<s>cit., P. II, pag. </s>

<s>89). </s></p><p type="main">

<s>Dopo di avere il Borelli descritta questa così mirabile struttura, occor­<lb></lb>sagli a vedere nel 1657 in Pisa, soggiunge di aver sentito dire che poi altri <lb></lb>avevano osservato lo stesso, e voleva senza dubbio alludere allo Stenone, il <lb></lb>quale pubblicò i suoi trattati anatomici parecchi anni prima che uscisse alla <lb></lb>luce la grande opera intorno ai Moti animali. </s>

<s>Noi, che non abbiamo ragioni <lb></lb>da smentirla, crediamo perciò sincera la confessione che il Borelli stesso fa <lb></lb>colle seguenti parole: “ Hanc mirabilem structuram primum mihi videri <lb></lb>contigit Pisis, adstante clarissimo Malpighio, anno 1657. Postea novi alios <lb></lb>eadem adnotasse: tandem clariss. </s>

<s>Lower et Laurentius Bellinus exactam cor­<lb></lb>dis contexturam indagarunt, dissolvendo fibrarum perplexam colligationem <lb></lb>ad instar glomi ” (ibi, pag. </s>

<s>90). </s></p><p type="main">

<s>Al Malpighi però non parve troppo esatta, nè conforme alla verità delle <lb></lb>cose la storia della scoperta delle fibre spirali del cuore, così esposta. </s>

<s>E per­<lb></lb>ciò, sul principio della sua <emph type="italics"></emph>Antobiografia,<emph.end type="italics"></emph.end> narra com&#039;essendo stato, nel 1656, <lb></lb>eletto dal Granduca professore di Medicina teorica nella Università di Pisa, <lb></lb>vi conobbe ed ebbe familiarità con uomini dottissimi, fra&#039;quali il Borelli, con <lb></lb>cui teneva frequentemente colloqui intorno a cose di Anatomia. </s>

<s>“ Ut autem, <lb></lb>mutuis officiis eximiae tanti Viri curiositati satisfacerem, eius domi frequen­<lb></lb>ter anatomicas moliebar sectiones, inter quas, dum incocto maceratoque corde <lb></lb>fibrarum inclinationem indagabam, spiralis ipsarum tractus occurrit, quem <lb></lb>ipsi primo ostendi, licet, in suo posthumo libro <emph type="italics"></emph>De motu anim.,<emph.end type="italics"></emph.end> me exara­<lb></lb>tae observationis testem tantum enunciet ” (Opera postuma cit., pag. </s>

<s>2). </s></p><p type="main">

<s>Dopo la pubblicazione dell&#039;Opera del Borelli altri valorosi anatomici <lb></lb>esercitarono lo stilo intorno al cuore, e son fra questi a commemorare, per <lb></lb>diligenza fra&#039;primi, Raimondo Vieussens e il nostro Lancisi. </s>

<s>Questi, nel suo <lb></lb>trattato postumo <emph type="italics"></emph>De motu cordis,<emph.end type="italics"></emph.end> intitolava così la XXVIII proposizione: <lb></lb>“ Ostenditur cor esse musculum quadricavum suis tendinibus instructum ” <lb></lb>(Romae 1728, pag. </s>

<s>46). </s></p><p type="main">

<s>Fu il Lancisi de&#039;primi a far particolare attenzione ai muscoli cavi, e ad <lb></lb>interpetrarne il sapiente magistero della Natura, applicandovi le dottrine mec­<lb></lb>caniche di Galileo. </s>

<s>Nel primo dialogo delle Due nuove scienze proponesi dal <lb></lb>Salviati a sciogliere questo problema: “ Come possano i filamenti di una <lb></lb>corda, lunga cento braccia, sì saldamente connettersi insieme, non essendo <lb></lb>ciascheduno di essi lungo più di due o tre, che gran violenza ci voglia a <lb></lb>dissepararli ” (Alb. </s>

<s>XIII, 12). E si risolve con dire ch&#039;essendo, per la tor­<lb></lb>tura, i fili della canapa tenuti stretti in tutta la loro lunghezza, converrebbe <lb></lb>sbarbarli, facendoli strisciar l&#039;uno sopra l&#039;altro, ciò che sarebbe più diffi­<lb></lb>cile assai che romperli. </s></p><pb xlink:href="020/01/1215.jpg" pagenum="90"></pb><p type="main">

<s>Il Lancisi dunque, osservando che i muscoli cavi son tessuti a una certa <lb></lb>similitudine delle funi, congettura che la Natura abbia voluto provvedere in <lb></lb>quel modo alla solidità, contorcendone le fibre e rendendole così più diffi­<lb></lb>cili a rompersi, con l&#039;artificio che si rendono, secondo Galileo, difficili a <lb></lb>rompersi le stesse funi. </s>

<s>“ Quadricavus cordis musculus, egli scrive, non ex <lb></lb>una, eaque simplici carnearum ac tendinearum fibrarum advolutione, sed <lb></lb>ex mirabili complexione, tum glomi, tum viminei contextus, assurgit et so­<lb></lb>lidascit. </s>

<s>Inter multiplices modos cohaerentium partium in animalibus ille, <lb></lb>meo quidem iudicio, magis est inspiciendus, quo Natura, in coagmentandis <lb></lb>cavis musculis, utitur. </s>

<s>Hi enim compinguntur ex varia, circum determinatas <lb></lb>capacitates villorum fibrarumque, contorsione, ac prius minus spirali prae­<lb></lb>sertim advolutione, cuius quanta sit facultas et vis prius docuit Galiìeus, u<gap></gap><lb></lb>conficiendae funis artificium expendit ” (De motu cordis cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Si può dir che nel Lancisi in sostanza si compiessero le notizie, ch&#039;era <lb></lb>possibile avere dell&#039;anatomia del cuore, intorno alla quale per questo s&#039;è <lb></lb>intrattenuta la nostra storia, perchè dipende principalmente da quelle noti­<lb></lb>zie la più esatta cognizione delle pulsazioni di lui. </s>

<s>La necessità di premettere <lb></lb>l&#039;Anatomia a rischiarare tante difficoltà, in che si trovò avvolta la scienza <lb></lb>di questi moti, fu sentita già dal Berengario, il quale si compiacque d&#039;es­<lb></lb>sersi, per via dello studio che fece sulla testura de&#039;villi nel cuore, chiarito <lb></lb>di un fatto, da pochissimi medici allora conosciuto. </s>

<s>“ Ex praedicto textu in­<lb></lb>telligitur qualiter per villos aperiatur cor et qualiter claudatur, et qualiter <lb></lb>inter istos motus est quies.... Istam quietem in pulsu rari sunt Medict <lb></lb>qui eam cognoscant: tamen, ni falìor, ego comprehendo per intellectum <lb></lb>minimum temporis esse inter dyastolem et systolem ” (Commentaria cit., <lb></lb>fol. </s>

<s>CCCXL). </s></p><p type="main">

<s>Un esempio a questo contrario, e per cui si dimostra come gli erro<gap></gap><lb></lb>nell&#039;anatomia del cuore condussero ad errare altresì intorno ai moti di lu<gap></gap><lb></lb>ce lo porge il Vesalio, il quale, come dicemmo, descrisse le fibre rette, ch<gap></gap><lb></lb>dalla base ricorrono all&#039;apice, e che il Morgagni ed altri, perchè veramen<gap></gap><lb></lb>non ci sono, attestarono di non aver mai vedute. </s>

<s>S&#039;immaginò dunque esse <lb></lb>Vesalio, sul fondamento di quelle immaginate fibre rette, che fosse il cuore <lb></lb>contessuto dalla parte di fuori a guisa di un canestro, in cui, essendo dalla <lb></lb>parte del taglio legati i giunchi intorno intorno a un cerchio, fossero da<gap></gap><lb></lb>l&#039;altra parte delle punte raccolti e legati insieme, da far prendere al cane­<lb></lb>stro stesso la figura di un cono, o come dicevasi allora di una piramide <lb></lb>Così essendo, suppongasi che sia attaccata al vertice di questa piramide una <lb></lb>cordicella, e che si tiri, facendola attraversare il centro del cerchio: il c<gap></gap><lb></lb>nestro si schiaccerà divenendo più capace. </s>

<s>E così il cuore, a cui si ass<gap></gap><lb></lb>miglia nella forma e nella testura, quando la sua punta si avvicina all<gap></gap><lb></lb>base, si dilata e divien così più capace ad attrarre in quell&#039;atto il sangu<gap></gap><lb></lb>“ Porro cordis dilatationem, qua mucronis ipsius ad basis centrum est a<gap></gap><lb></lb>tractio et omnium latorum cordis distentio, rectae efficiunt fibrae, mucronen <lb></lb>versus basìm contrahentes. </s>

<s>Quod sane ita perficitur, ac si vimineo circu<gap></gap><pb xlink:href="020/01/1216.jpg" pagenum="91"></pb>orbiculatim eademque serie complurimas iuncorum scirporumve radices con­<lb></lb>necteres, et capitibus illorum simul collectis velut pyramidem quamdam <lb></lb>efformares, ac demum funiculum ex mucronis medio per circuli centrum <lb></lb>dimitteres: quo, deorsum tracto, pyramis brevior intusque multo capacior <lb></lb>redderetur ” (De hum. </s>

<s>corp. </s>

<s>fabrica cit., pag. </s>

<s>587). </s></p><p type="main">

<s>Quando insomma la punta si avvicina alla base, il cuore, secondo il <lb></lb>Vesalio, si dilata: riceve allora in sè il sangue, e si ritrova in quella fase <lb></lb>del suo moto, che si disse <emph type="italics"></emph>Diastole.<emph.end type="italics"></emph.end> Queste cose però, e il Vesalio stesso lo <lb></lb>confessa, sono congetturate e non dedotte da quella osservazione de&#039;fatti, <lb></lb>che fu riserbata poco più tardi a Realdo Colombo. </s>

<s>Egli, proseguendo quel <lb></lb>sicuro metodo della vivisezione da sè istituito, trovò che gli stessi fatti erano <lb></lb>tutt&#039;al contrario di quel che il divino Brussellese aveva congetturato. </s></p><p type="main">

<s>Ritorniamo al trattato <emph type="italics"></emph>De re anatomica,<emph.end type="italics"></emph.end> e leggiamo nel libro XIV. Ivi, <lb></lb>dop&#039;avere insegnato il modo di preparare il cane, per disseccarlo vivo, sog­<lb></lb>giunge l&#039;Autore ciò che può vedersi, aperto il ventre, in quelle viscere pal­<lb></lb>pitanti, e fra le altre cose bellissime, ei dice “ illud quoque accedit motus <lb></lb>scilicet cordis quemadmodum amplificetur atque arctetur: item qualis sit <lb></lb>motus arteriarum in viva Anatome, si lubuerit, conspicaberis: numquid idem <lb></lb>sit vel oppositus motui cordis. </s>

<s>Comperies enim, dum cor dilatatur, constringi <lb></lb>arterias, et rursus, in cordis constrictione, dilatari. </s>

<s>Verum animadvertas, dum <lb></lb>cor sursum trahitur et tumefieri videtur, tunc constringitur: cum vero se <lb></lb>exerit, quasi relaxatus deorsum vergit, atque eo tempore dicitur cor quie­<lb></lb>scere: estque tunc cordis <emph type="italics"></emph>Systole,<emph.end type="italics"></emph.end> propterea quod facilius suscipit minore <lb></lb>labore. </s>

<s>At cum transmittit, maiori opus est robore ” (Editio cit., pag. </s>

<s>257). </s></p><p type="main">

<s>L&#039;osservazione dei fatti nell&#039;animale vivo insegna dunque che, avvici­<lb></lb>nandosi la punta alla base, il cuore non si dilata, come diceva il Vesalio, ma <lb></lb>si contrae, e non è allora in diastole ma in sistole. </s>

<s>Avviene il contrario <lb></lb>quando la punta si abbassa, nel qual tempo il cuore si posa ed è in dia­<lb></lb>stole, benchè nel testo si legga <emph type="italics"></emph>sistole,<emph.end type="italics"></emph.end> forse per inavvertenza di chi curò <lb></lb>questa edizione postuma. </s>

<s>Il Colombo descrive i fatti senza però accennare <lb></lb>che fanno contro al Vesalio, e perchè prevedeva che la grande autorità di <lb></lb>quell&#039;uomo reputato divino avrebbe fatto prevalere il falso congetturato al <lb></lb>nuovo vero scoperto, si raccomanda ai Lettori che quel ch&#039;egli dice dei moti <lb></lb>del cuore non lo ritengan per cosa di lieve importanza. </s>

<s>“ Neque hoc flocci­<lb></lb>facias: etenim non paucos reperias, qui, eo tempore cor dilatari certo opi­<lb></lb>nantur, quo vere constringitur ” (ibi). </s></p><p type="main">

<s>Le parole sopra citate dal XIV libro <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> a noi parrebbe <lb></lb>che potrebbero inscriversi per testo alla prima parte del celebre trattato del­<lb></lb>l&#039;Harvey, che è di quelle stesse parole del Colombo il più splendido e il più <lb></lb>glorioso commento. </s>

<s>Anche l&#039;Inglese, proseguendo le vie segnategli dall&#039;ita­<lb></lb>liano Maestro, incomincia a descrivere i moti del cuore quali gli si rappre­<lb></lb>sentarono agli occhi nelle sezioni de&#039;vivi, ond&#039;è ch&#039;egli si propone perciò <lb></lb>di dimostrare nel cap. </s>

<s>II <emph type="italics"></emph>De motu cordis.<emph.end type="italics"></emph.end> “ Ex vivorum dissectione qualis <lb></lb>sit cordis motus ” (Lugduni Batav. </s>

<s>1737, pag. </s>

<s>24). </s></p><pb xlink:href="020/01/1217.jpg" pagenum="92"></pb><p type="main">

<s>Nelle viscere palpitanti aperte, no nel ventre de&#039;soli cani o di altri ani­<lb></lb>mali a sangue caldo, ma e de&#039;pesci, delle rane e di altri così fatti animali <lb></lb>freddi, osservando dunque l&#039;Harvey i moti del cuore, si assicurò esser vero <lb></lb>quel che aveva detto il Colombo, e lo confermò con l&#039;esperienza e con la <lb></lb>ragione. </s>

<s>Prese per fondamento del suo argomentare gli altri muscoli, e <lb></lb>com&#039;egli vedeva mettersi questi in moto, accorciandosi nelle estremità e in­<lb></lb>turgidendo nel mezzo; così diceva avvenir nel cuore che, accorciandosi dal­<lb></lb>l&#039;apice verso la base, intumidisce ne&#039;ventricoli, i quali perciò divengono più <lb></lb>angusti e premono il sangue. </s>

<s>Di qui coglieva occasione di notare in che avesse <lb></lb>preso errore il Vesalio, il quale non ebbe un&#039;idea chiara della fabbrica del <lb></lb>cuore, nè seppe applicare ad essa la meccanica muscolare. </s></p><p type="main">

<s>Uno de&#039;più notabili tra questi fatti meccanici è che, quando il muscolo <lb></lb>è in forze, indurisce, stringendosi più fortemente le une addosso all&#039;altre <lb></lb>le fibre; ond&#039;è che, come una fune bagnata e attorta indurisce essa pure <lb></lb>e spreme fuori l&#039;umore, così il muscolo spreme il sangue e ne dà segno <lb></lb>con l&#039;impallidire. </s>

<s>Quando poi succede la quiete, torna, per il sangue che ri­<lb></lb>sorbe di nuovo, a porporeggiare, cosicchè, se anche il cuore è un muscolo <lb></lb>come gli altri, si potrà facilmente conoscere quand&#039;egli è in quiete o in <lb></lb>moto dal suo stesso colore. </s>

<s>Questo continuo cangiar di colore è visibilissimo <lb></lb>negli animali a sangue freddo, nel cuor de&#039;quali può confermarsi il fatto col <lb></lb>ferire il ventricolo, dopo che si vede che, mentre il cuore biancheggia, il <lb></lb>sangue non esce, ma spiccia con viva forza quando torna a porporeggiare. </s></p><p type="main">

<s>“ Ex quibus observatis, conclude l&#039;Harvey, rationi consentaneum est, <lb></lb>Cor eo quo movetur tempore et undique constringitur, et secundum parie­<lb></lb>tes incrassescit: secundum ventriculos coarctari et contentum sanguinem <lb></lb>protrudere, quod ex quarta observatione satis patet, cum in ipsa tensione <lb></lb>sua, propterea quod sanguinem in se prius contentum expresserit, albescit, <lb></lb>et denuo, in laxatione et quiete, subingrediente de novo sanguine in ven­<lb></lb>triculum, redit color purpureus et sanguineus cordi. </s>

<s>Verum nemo amplius <lb></lb>dubitare poterit, cum, usque in ventriculi cavitatem inflicto vulnere, singu­<lb></lb>lis motibus, sive pulsationibus cordis, in ipsa tensione, prosilire cum impetu <lb></lb>foras contentum sanguinem viderit ” (ibi, pag. </s>

<s>26). </s></p><p type="main">

<s>Si veniva da tutti questi fatti osservati a dimostrare la falsità dell&#039;opi­<lb></lb>nione comune, concludendosi non essere il moto proprio del cuore la dia­<lb></lb>stole, come si credeva, ma la sistole, nel qual tempo la punta si avvicina <lb></lb>alla base, i muscoli si mettono in forza intorno ai ventricoli, che perciò spre­<lb></lb>mono fuori il sangue. </s>

<s>Il Cartesio insorse allora contro le innovazioni arve­<lb></lb>iane, e mentre diceva da una parte lo Scopritore del circolo del sangue <emph type="italics"></emph>pro <lb></lb>tam utili inventu numquam satis laudandum,<emph.end type="italics"></emph.end> notava dall&#039;altra che non solo <lb></lb>era contrario alla comune opinione dei Medici, ma ripugnante all&#039;ordinario <lb></lb>giudizio degli occhi l&#039;affermar che nella Sistole consiste il moto del cuore. </s>

<s><lb></lb>Degli argomenti del Medico inglese il Filosofo bretone non fa nessun conto, <lb></lb>anzi glie ne suggerisce uno in apparenza più concludente di tutti gli altri. <lb></lb></s>

<s>“ Et hoc quidem poterat, soggiunge il Cartesio, dop&#039;aver commemorati gli <pb xlink:href="020/01/1218.jpg" pagenum="93"></pb>argomenti dell&#039;Harvey, adhuc valde specioso experimento confirmari, nempe <lb></lb>si canis vivi mucro cordis abscindatur et per incisionem inferatur digitus in <lb></lb>alterutrum ventriculorum eius, quoties mucro cordis accedet ad basim, ma­<lb></lb>nifeste sentietur digitum comprimi, desinetque pressio quoties recedet ” (De <lb></lb>homine cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Il Lower e il Bellini si servirono poi di questa bellissima esperienza <lb></lb>per confermare i fatti osservati dal Colombo e dall&#039;Harvey, che cioè strin­<lb></lb>gendosi il cuore dall&#039;apice verso la base, il ventricolo si fa più angusto, ed <lb></lb>è allora in sistole, e spreme il sangue. </s>

<s>Ma il Cartesio gli perveniva dicendo <lb></lb>che ciò null&#039;altro prova “ nisi quod ipsa experimenta nobis saepe halluci­<lb></lb>nandi occasionem offerunt, si quidem illorum causas omnes possibiles non <lb></lb>satis expendamus ” (ibi, pag. </s>

<s>168). </s></p><p type="main">

<s>Coloro che, dopo tanti esempi fin qui offerti dalla nostra Storia, dubi­<lb></lb>tano tuttavia se il Cartesio procedesse ne&#039;metodi sperimentali e quel modo, <lb></lb>che da noi si disse nel nostro primo <emph type="italics"></emph>Discorso,<emph.end type="italics"></emph.end> rimeditino le citate parole, <lb></lb>che ritraggono in immagine viva l&#039;indole della Filosofia cartesiana. </s>

<s>Si diceva <lb></lb>essere una tale indole quella di accomodare, come facevano i Peripatetici, <lb></lb>alle speculazioni filosofiche i fatti naturali: e in verità, nell&#039;esempio che ab­<lb></lb>biamo fra mano, il Cartesio professa che a nulla valgono gli sperimenti, <lb></lb>quando non si sappia trovar delle cose le cause possibili. </s>

<s>Che vuol egli dire <lb></lb>il potersi toccar con mano che i ventricoli del cuore, quando la punta si <lb></lb>avvicina alla base si restringono, se la Filosofia investigatrice delle cause <lb></lb>possibili ci conclude invece che si debbono dilatare? </s></p><p type="main">

<s>I filosofici argomenti, che il Cartesio contrapponeva ai fatti sperimen­<lb></lb>tali dell&#039;Harvey, si fondano sull&#039;osservazione che il sangue esce dal cuore <lb></lb>molto più caldo che non è quando c&#039;entra. </s>

<s>Ma s&#039;è natura del calore il di­<lb></lb>latare, dunque, quando il cuore manda fuori di sè il sangue, si dilata ne­<lb></lb>cessariamente e non si ristringe. </s>

<s>Che se il calore stesso indurisce le fibre, <lb></lb>e nell&#039;indurirle anche le distende “ fieri potest ut digitum in ventriculis <lb></lb>positum comprimatur, quamvis inde ventriculi nihilo magis coartentur, sed <lb></lb>potius dilatentur ” (ibi, pag. </s>

<s>169). </s></p><p type="main">

<s>Tanto poi si compiacque il Cartesio di aver così trovato nel calore la <lb></lb>causa motrice del cuore, della quale l&#039;Harvey, con tutta la sua scienza spe­<lb></lb>rimentale, non aveva fatta alcuna menzione, che si maraviglia della gran po­<lb></lb>tenza della sua propria Filosofia, dalla quale fu scorto a una tale e così <lb></lb>nuova scoperta. </s>

<s>“ Quapropter valde miror quod, quamvis ab omni aevo no­<lb></lb>tum fuerit plus esse caloris in corde quam in cactero corpore, sanguinem­<lb></lb>que posse calore rarefieri; nemo tamen hactenus repertus sit, qui cordis <lb></lb>motum ab hac sola rarefactione proficisci animadverterit. </s>

<s>Nam quamquam vi­<lb></lb>detur Aristotiles de hoc cogitasse, cum libri <emph type="italics"></emph>De respiratione,<emph.end type="italics"></emph.end> cap. </s>

<s>XX, dicit <lb></lb><emph type="italics"></emph>motum hunc esse similem actioni liquoris vi caloris bullientis,<emph.end type="italics"></emph.end> atque etiam <lb></lb>causam pulsus <emph type="italics"></emph>esse quod succus ciborum quos manducavimus, in cor per­<lb></lb>petuo ingrediens, ultimam eius membranam elevet;<emph.end type="italics"></emph.end> tamen, quia nullam <lb></lb>ibi sanguinis mentionem facit, aut structurae cordis, liquet illum casu tan-<pb xlink:href="020/01/1219.jpg" pagenum="94"></pb>tum in aliquid a vero non alienum et sine ulla cogitatione certa incidisse. </s>

<s><lb></lb>Et certe haec eius sententia sectatores nullos invenit ” (ibi, pag. </s>

<s>169). </s></p><p type="main">

<s>Ma questa è una lusinga, che si faceva il Cartesio, a cui sarebbero sa­<lb></lb>liti nel viso i rossori della vergogna e i livori del dispetto, se gli avesse al­<lb></lb>cuno aperto sotto gli occhi le <emph type="italics"></emph>Questioni peripatetiche<emph.end type="italics"></emph.end> del Cesalpino, là dove, <lb></lb>commentando la sentenza aristotelica, si dice che il cuore, sorgente del calor <lb></lb>vitale, è simile a una pignatta che bolle, intorno alla quale, perchè il san­<lb></lb>gue contenutovi andando in spuma non trabocchi, son posti i flabelli dei <lb></lb>polmoni. </s>

<s>“ Ut igitur sufficiens maneret vasorum tensio, ignis autem interim <lb></lb>non suffocaretur, remedium molita est Natura modica ferventis sanguinis re­<lb></lb>frigeratione iuxta principium, quemadmodum ii faciunt qui ollae ferventis <lb></lb>tumorem cohibent insufflando: modica enim hac refrigeratione non impedi­<lb></lb>tur coctio, sed solum intumescentis humoris nimius fastus ” (Venetiis 1571, <lb></lb>fol. </s>

<s>111). </s></p><p type="main">

<s>Ma l&#039;effervescenza e il calore, dice il Cesalpino, producono moto, ed <lb></lb>hanno di qui principio i moti del cuore. </s>

<s>Movendosi così per la turgenza il <lb></lb>cuore si muovono tutt&#039;insieme anche l&#039;arterie. </s>

<s>“ Cum enim pulsatio cor­<lb></lb>dis et arteriarum sit accidens quoddam quod ex necessitate insequitur hu­<lb></lb>moris in corde effervescentiam, qua sanguinis generatio perficitur, ut in cae­<lb></lb>teris quae igne elixantur accidit, intumescente corde necesse est simul omnes <lb></lb>arterias dilatari, in quas derivatur fervor ” (ibi, fol. </s>

<s>109). </s></p><p type="main">

<s>Forse nessuno avrà rammemorato al Filosofo, che tutta la scienza fa­<lb></lb>ceva scaturire dal suo proprio cervello, questo passo del nostro Peripatetico <lb></lb>italiano, ma l&#039;Harvey stesso, verso la fine della seconda esercitazione ana­<lb></lb>tomica <emph type="italics"></emph>De circulatione sanguinis,<emph.end type="italics"></emph.end> mentre da una parte ringrazia come di <lb></lb>una gran degnazione il Cartesio <emph type="italics"></emph>ob mentionem sui nominis honorificam,<emph.end type="italics"></emph.end><lb></lb>conclude liberamente dall&#039;altra che quell&#039;acutissimo ingegno e tutti gli altri <lb></lb>con lui, i quali quando il cuore “ erigitur, attollitur et vigoratur, ampliari, <lb></lb>aperiri, ventriculosque suos exinde capaciores esse autumant, haud recte me­<lb></lb>cum observant ” (ibi, pag. </s>

<s>164). </s></p><p type="main">

<s>Il Cartesio nonostante, com&#039;era da aspettarsi da quella sua indole, ri­<lb></lb>mase, contro la verità dimostrata dai fatti, ostinato nella sua filosofica sen­<lb></lb>tenza, di che presero poi maraviglia i Cartesiani stessi anco più infervorati. </s>

<s><lb></lb>Tommaso Cornelio, nel suo Proginnasma VII <emph type="italics"></emph>De vita,<emph.end type="italics"></emph.end> dopo aver riferita <lb></lb>l&#039;opinion del Filosofo, secondo la quale il sangue entrato ne&#039;ventricoli gli <lb></lb>dilata col suo calore, ch&#039;è perciò la causa efficiente del moto “ sed nescio, <lb></lb>soggiunge, quomodo Vir clarissimus contra autopsiam obstinatione quadam <lb></lb>sententiae pugnaverit. </s>

<s>Enimvero, seu vena cava ligetur ut nullus omnino <lb></lb>sanguis permanare possit in cor, sive cor ipsum ita vulneretur, ut influens <lb></lb>in eiusdem ventriculos sanguis totus pene effluat, videbimus quidem etiam <lb></lb>tum cor ut ante mobiliter palpitare, alterneque astringi, atque laxari “ (Nea­<lb></lb>poli 1688, pag. </s>

<s>271). </s></p><p type="main">

<s>Tanto erano questi e altri simili fatti offerti dall&#039;autopsia evidenti, che, <lb></lb>nonostante la seducente eloquenza del Filosofo, trionfò il vero osservato prima <pb xlink:href="020/01/1220.jpg" pagenum="95"></pb>dal Colombo e dimostrato poi dall&#039;Harveio. </s>

<s>Proseguendo questi con la solita <lb></lb>diligenza le sue osservazioni intorno ai moti del cuore, ebbe a notar gli er­<lb></lb>rori in ch&#039;erano incorsi due uomini reputati dottissimi e peritissimi del­<lb></lb>l&#039;arte, Gaspero Bauhino e Giovanni Riolano, i quali ammettevano quattro <lb></lb>essere que&#039;moti distinti di tempo e di luogo. </s>

<s>Osservava l&#039;Harvey che una <lb></lb>tal distinzione potevasi bene far quanto al luogo, non però quanto al tempo <lb></lb>“ simul enim ambae auriculae movent et simul ambo ventriculi, ut quatuor <lb></lb>loco motus distincti sunt, duobus tantum temporibus, atque hoc se habet <lb></lb>modo: Duo sunt quasi eodem tempore motus, unus auricularum, alter ipso­<lb></lb>rum ventriculorum; nec enim simul omnino fiunt, sed praecedit motus au­<lb></lb>ricularum ” (De motu cordis cit., pag. </s>

<s>31). </s></p><p type="main">

<s>Questi due moti però si seguono l&#039;uno all&#039;altro con ritmo sì misurato, <lb></lb>che appariscono all&#039;occhio essere un moto solo, d&#039;ond&#039;ebbero occasione gli <lb></lb>inganni di parecchi osservatori. </s>

<s>Ma che in ogni modo il moto delle orrec­<lb></lb>chiette preceda quello dei ventricoli, il Borelli, nella proposizione LV della <lb></lb>II Parte <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> lo dimostra come una necessaria conseguenza <lb></lb>della particolare struttura della macchina del cuore, nella quale, quando il <lb></lb>moto del ventricolo precedesse o coincidesse con quello della orecchietta, le <lb></lb>valvole tricuspidali o sarebbero inutili o produrrebbero effetti contarii a quelli <lb></lb>intesi dalla Natura (pag. </s>

<s>113, 14). </s></p><p type="main">

<s>Di queglì inganni, che si diceva conseguitar dalle difficoltà dell&#039;osser­<lb></lb>vazione, ne offerse un esempio notabilissimo il Lancisi, il quale formulava <lb></lb>così la XL sua proposizione <emph type="italics"></emph>De motu cordis.<emph.end type="italics"></emph.end> “ Ex vivorum sectionibus <lb></lb>ostenditur contractionem auricularum non esse vere alternam cum ventri­<lb></lb>culis, sed nonnihil antevertere, citiusque desinere ac propterea magna ex <lb></lb>parte synchronam esse ” (Editio cit., pag. </s>

<s>88). Ammetteva il Lancisi certe <lb></lb>diciamo così consonanze nel ritmo cardiaco, che i Fisiologi dissero non esi­<lb></lb>stere in natura, ond&#039;è che l&#039;Haller riserbò il § XXII, Sezione IV del IV libro <lb></lb>del suo grande trattato di Fisiologia, per confutare l&#039;opinion lancisiana (T. I, <lb></lb>Lausannae 1757, pag. </s>

<s>418-20). </s></p><p type="main">

<s>Così, per amor del vero e per l&#039;autorità dell&#039;Haller, si tornò a profes­<lb></lb>sare l&#039;alterna contrazione de&#039;ventricoli e delle orecchiette, specialmente in <lb></lb>Italia, dove il Bellini aveva dato un&#039;ingegnosissima spiegazione di quel per­<lb></lb>petuo alternarsi di moti. </s>

<s>Egli, come già sappiamo, riteneva che i nervi ec­<lb></lb>citino il moto ne&#039;muscoli e nello stesso cuore, stillandovi il loro succo, di <lb></lb>che sempre hanno pieni i canali, cosicchè, nella contrazione de&#039;ventricoli, <lb></lb>le orecchiette si rilasciano perchè, restando compressi i nervi, non ricevono <lb></lb>da loro il succo necessario par mettersi in moto. </s>

<s>Quando poi i nervi son <lb></lb>compressi dal contrarsi delle orecchiette, i ventricoli si rilasciano, perchè non <lb></lb>stilla più fra le loro fibre il succo eccitatore. </s>

<s>A questa ipotesi dava il Bel­<lb></lb>lini stesso forma di proposizione, ch&#039;è la prima del suo trattato <emph type="italics"></emph>De motu <lb></lb>cordis<emph.end type="italics"></emph.end> ed è così formulata: “ Si liquidum nervorum est illud, quod prae­<lb></lb>cipue facit ad contractionem musculorum, datur de facto tempus quo eius­<lb></lb>modi liquidum ita cessat ab influxu in musculis auricularum et ventriculo-<pb xlink:href="020/01/1221.jpg" pagenum="96"></pb>rum cordis, ut, quo tempore influit in musculum auricularum, iam influxus <lb></lb>erit in musculum ventriculorum; et, quo tempore influit in musculum <lb></lb>ventriculorum, iam influxerit in musculum auricularum ” (Venetiis 1732, <lb></lb>pag. </s>

<s>106). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La macchina del cuore, che agisce con alterno moto a quel modo, e per <lb></lb>quelle ragioni immaginatesi dal Bellini, fu rassomigliata a uno de&#039;com<gap></gap><lb></lb>strumenti idraulici, i quali da una parte aspirano il liquido, e dall&#039;altra lo <lb></lb>premono e lo sollevano in alto. </s>

<s>Nello stringersi e nel dilatarsi de&#039;ventricoli <lb></lb>vedevano l&#039;immagine dello stantuffo, che scorre su e giù per il corpo di <lb></lb>tromba, e nelle vene e nelle arterie i canali da attingere e da sospingere il <lb></lb>sangue. </s>

<s>Questa analogia però, nella quale bene applicata, contenevasi la sco­<lb></lb>perta della circolazione, fu intraveduta assai tardi, ma in ogni modo che, <lb></lb>specialmente le arterie, fossero vasi comunicanti col cuore e dipendenti da <lb></lb>lui, fu con assai facilità conosciuto anche dagli antichi. </s>

<s>Fu riconosciuto al­<lb></lb>tresì per facile esperienza che dai moti di sistole e di diastole dipendono i <lb></lb>polsi, ma si errava comunemente nell&#039;assegnare l&#039;ordine di queste dipen­<lb></lb>denze, credendosi che l&#039;arteria pulsi, quando pulsa il ventricolo sinistro. </s>

<s>Non <lb></lb>vedendosi chiara ancora la somiglianza che passa fra gli strumenti idraulici <lb></lb>dell&#039;arte e quello della Natura, non si comprendeva l&#039;impossibilità che fosse <lb></lb>nello stesso tempo pieno di liquido il corpo di tromba, e il canale irrigatore. </s></p><p type="main">

<s>La via perciò da conoscere il vero, che pareva chiusa d&#039;ogni parte alle <lb></lb>filosofiche speculazioni, fu aperta alle osservazioni anatomiche, quando Realdo <lb></lb>Colombo raccomandò, come fecondissimo organo di scoperte, e insegnò le <lb></lb>regole della vivisezione. </s>

<s>Come caparra di tali promesse l&#039;Autor <emph type="italics"></emph>De re ana­<lb></lb>tomica<emph.end type="italics"></emph.end> citava quel ch&#039;egli stesso, proseguendo il metodo propostosi, era riu­<lb></lb>scito a scoprire, e fra le altre nuove e mirabili cose, che invita a vedere <lb></lb>nelle viscere palpitanti di un cane, questa è fra le principali, perchè scopre <lb></lb>agli occhi di qualunque persona volgare l&#039;inganno che s&#039;eran fatto i Filo­<lb></lb>sofi speculando con la mente sublime: <emph type="italics"></emph>comperies enim, dum cor dilatatur, <lb></lb>constringi arterias, et rursus in cordis constrictione dilatari.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Tanto poi sentiva il Colombo essere l&#039;importanza di questa verità sco­<lb></lb>perta contro l&#039;errore così universalmente invalso, che non contento di quella <lb></lb>prima preparazione anatomica vuol, per meglio persuadere i Filosofi in libris, <lb></lb>e chi giura sulla veneranda autorità de&#039;loro fogli, immolare un&#039;altro cane, <lb></lb>e apertogli egli prima il torace, invita i desiderosi d&#039;imparare il vero dalla <lb></lb>Natura, a proseguire la vivisezione. </s>

<s>“ Thorace igitur huius secundi canis <lb></lb>primum aperto per rectam lineam in cartilaginem: sed illum confestim aperi <lb></lb>atque una pericardion. </s>

<s>Deinde, abdomine quoque aperto, magnae arteriae <lb></lb>manum admoveto: diligenterque, quoad eius fieri poterit, considera an illa <pb xlink:href="020/01/1222.jpg" pagenum="97"></pb>dilatetur dum constringitur cor, vel opposito modo se res habeat, ibique <lb></lb>differentias omnes pulsium sub oculos intueberis in rem praesentem de­<lb></lb>ductos, magnos, longos, latos, veloces, latos celeres, frequentes, parvos. </s>

<s>Ne­<lb></lb>que hos modo, sed veloces quidem tardosve, aut frequentes sed interpola­<lb></lb>tos, item frequentissimos, minimos, tardissimos, undosos et formiculares ” <lb></lb>(De re anat. </s>

<s>cit., pag. </s>

<s>261). </s></p><p type="main">

<s>Non insegna dunque l&#039;Harvey, nel suo cap. </s>

<s>III <emph type="italics"></emph>De motu cordis,<emph.end type="italics"></emph.end> nulla <lb></lb>di nuovo, e nel dimostrare il vero <emph type="italics"></emph>contra communia dogmata<emph.end type="italics"></emph.end> non fu giu­<lb></lb>sto il tacere che quella stessa dimostrazione l&#039;aveva data, ottant&#039;anni prima, <lb></lb>Realdo Colombo. </s>

<s>Così sembra che null&#039;altro merito competasi, rispetto a ciò, <lb></lb>al Fisiologo inglese, da quello in fuori di aver con nuove esperienze con­<lb></lb>fermati i fatti osservati dal Nostro. </s>

<s>L&#039;esperienza arveiana, in proposito di <lb></lb>dimostrar che, quando il cuore è in sistole, le arterie invece vanno in dia­<lb></lb>stole; son semplicissime, e nello stesso tempo concludentissime, come vedesi <lb></lb>per l&#039;esempio della prima, che consiste nell&#039;incidere un&#039;arteria, e nell&#039;os­<lb></lb>servar che, quando il ventricolo sinistro si ristringe, ella gitta allora il san­<lb></lb>gue con maggior forza. </s>

<s>Altre esperienze a conferma di ciò furono dall&#039;Har­<lb></lb>vey fatte sul cuore dei pesci, e in ultimo richiama l&#039;attenzione sui varii <lb></lb>casi, che, nel far risalire il sangue ora più ora meno lontano, presenta l&#039;ar­<lb></lb>teriotomia. </s>

<s>“ Ex his videtur manifestum, poi ne conclude, contra communia <lb></lb>dogmata, quod arteriarum diastole fit eo tempore, quo cordis systole, et ar­<lb></lb>terias repleri et distendi propter sanguinis a constrictione ventriculorum cor­<lb></lb>dis immissionem et intrusionem; quin etiam distendi arterias, quia replentur <lb></lb>ut utres aut vesica, non repleri, quia distenduntur ut folles ” (De motu cor­<lb></lb>dis cit., pag. </s>

<s>29). </s></p><p type="main">

<s>Con queste ultime parole s&#039;accenna a una questione importantissima, <lb></lb>della quale aveva avanti l&#039;Harvey trattato nel Proemio al suo libro. </s>

<s>Era una <lb></lb>tal questione con Galeno, il quale scrisse appositamente un libro, per rispon­<lb></lb>dere a Erasistrato, e a chi con lui dubitava <emph type="italics"></emph>An sanguis in arteriis natura <lb></lb>contineatur.<emph.end type="italics"></emph.end> E dopo avere in sette capitoli dimostrato che veramente le ar­<lb></lb>terie son tutte piene di sangue, nel cap. </s>

<s>VIII intitola la seguente proposi­<lb></lb>zione: “ Motrix facultas a corde in tunicas arteriarum venit qua se pandunt <lb></lb>omnes simul et spiritum attrahunt ” (Opera I Classis, Venetiis 1597, fol. </s>

<s>62 <lb></lb>ad terg.). Incomincia Galeno a dire com&#039;essendosi, nelle proposizioni prece­<lb></lb>denti, dimostrato che nelle arterie contienesi il sangue, potrebbe sembrare <lb></lb>alquanto difficile a intendere come mai gli spiriti sieno dispensati per tutto <lb></lb>il corpo dal cuore. </s>

<s>“ Quocirca, cum ambigunt quo modo spiritus in totum <lb></lb>corpus a corde feratur, si plenae sanguinis arteriae sint, difficile non est <lb></lb>eiusmodi dubitationem solvere, et dicere, non ferri, sed trahi spiritum in <lb></lb>arteriis nec a corde solo sed undequaque..... Vim tamen, quae arterias <lb></lb>extendit a corde, ceu fonte quodam manare, a nobis est in aliis libris expli­<lb></lb>catum ” (ibi). </s></p><p type="main">

<s>Qui, prosegue a dire Galeno per dimostrar che le arterie son veramente <lb></lb>mosse dalla forza del cuore, che le distende come un mantice, e apre così <pb xlink:href="020/01/1223.jpg" pagenum="98"></pb>libera la via al sangue; addurrò una esperienza, ed è tale: “ Arteriam unam, <lb></lb>e magnis et conspicuis quempiam, si voles, nudabis, primoque pelle remota <lb></lb>ipsam ab adiacenti suppositoque corpore tamdiu separare non graveris, quoad <lb></lb>filum circum immittere valeas. </s>

<s>Deinde, secundum longitudinem, arteriam in­<lb></lb>cide, calamumque, et concavum et pervium, in foramen intrude, vel aeneam <lb></lb>aliquam fistulam, qua et vulnus obturetur, et sanguis exilire non possit. </s>

<s><lb></lb>Quoadusque sic se arteriam habere conspicies, ipsam totam pulsare videbis: <lb></lb>cum primum vero obductum filum in laqueum contrahens arteriae tunicas <lb></lb>calamo obstrinxeris, non amplius arteriam ultra laqueum pulsare videbis, <lb></lb>etiamsi spiritus et sanguis ad arteriam quae est ultra filum, sicuti prius <lb></lb>faciebat, per concavitatem calami feratur. </s>

<s>Quod si propterea pulsabant arte­<lb></lb>riae, pulsarent et nunc partes quae sunt ultra laqueum, sed non pulsant, <lb></lb>igitur perspicuum est quoniam moveri posse desinunt, non per spiritum, in <lb></lb>concavitatibus discurrentem, sed ob virtutem in tunicam transmissam arte­<lb></lb>rias a corde moveri ” (ibi). </s></p><p type="main">

<s>Altre esperienze avevano, come vedemmo, dimostrato all&#039;Harvey essere <lb></lb>il sangue, che sospinto con impeto nella sistole del cuore, distende e fa pul­<lb></lb>sare le arterie, le quali perciò s&#039;empiono come un otre: e non è il sangue <lb></lb>che v&#039;entra per l&#039;aperta via, trovandole distese dal cuore stesso con la sua <lb></lb>forza, come un mantice. </s>

<s>Conveniva in ogni modo però conciliar queste con <lb></lb>la esperienza galenica, a far che l&#039;Harvey medesimo si trovò in grande im­<lb></lb>paccio, per uscir dal quale disse che quella esperienza ei non l&#039;aveva fatta, <lb></lb>reputandola impossibile a farsi nell&#039;animale vivo, per la impetuosa incur­<lb></lb>sione del sangue, e per esser difficile, senza le legature, a turar la ferita; <lb></lb>dall&#039;altra parte, soggiungeva, è tanto concludente dimostrazione quella tolta <lb></lb>dall&#039;arteriotomia, che lo stesso sperimento di Galeno, quando fosse pratica­<lb></lb>bile, non potrebbe far altro che confermarla. </s>

<s>“ Nec ego feci experimentum <lb></lb>Galeni, nec recte posse fieri, vivo corpore, ob impetuosi sanguinis ex arte­<lb></lb>riis eruptionem, puto, nec obturabit sine ligatura vulnus fistula: et per fistu­<lb></lb>lae cavitatem ulterius prosilire sanguinem non dubito. </s>

<s>Tamen hoc experi­<lb></lb>mento et probare videtur Galenus facultatem pulsificam per tunicas arteriarum <lb></lb>a corde manare, et quod arteriae, dum distenduntur ab ìlla facultate pul­<lb></lb>sifica, repleantur, quia distenduntur ut folles, non distendantur, quia replen­<lb></lb>tur ut utres. </s>

<s>Sed et in arteriotomia et vulneribus contrarium manifestum <lb></lb>est ” (De motu cordis cit., Proemium, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Nella seconda Esercitazione anatomica però, <emph type="italics"></emph>ad Riolanum,<emph.end type="italics"></emph.end> torna l&#039;Har­<lb></lb>vey a trattare di questo soggetto, e dice che, a fine d&#039;investigare il vero, <lb></lb>consigliò Galeno agli studiosi quel suo sperimento, e lo prescrisse poi pure <lb></lb>a loro anche il Vesalio “ sed neque Vesalius neque Galenus dicit experi­<lb></lb>mentum hoc fuisse ab illis, sicut a me, probatum ” (ibi, pag. </s>

<s>129). La prova <lb></lb>però, impossibile all&#039;arte, venne preparata all&#039;Harvey dalla Natura, nella <lb></lb>ossificazione delll&#039;arteria crurale di un suo malato, nella quale la fistola ossea <lb></lb>della ciste faceva le veci del calamo, nello sperimento galenico. </s>

<s>In questo <lb></lb>caso dunque, a conferma del vero e a confutazione dell&#039;error di Galeno, <pb xlink:href="020/01/1224.jpg" pagenum="99"></pb>dice esso Harvey: “ Inferiores arterias, trans hoc tale aneurisma, pulsare <lb></lb>valde exiliter senties, quando superius, et praesertim in aneurismate ipso, <lb></lb>pulsus magni et vehementer apparent ” (ibi, pag. </s>

<s>130). </s></p><p type="main">

<s>Quando poi i Fisiologi e i Chirurgi acquistarono maggior pratica nel­<lb></lb>l&#039;operare, e si trovarono forniti di più squisiti strumenti, si persuasero che <lb></lb>non dovess&#039;essere lo sperimento galenico d&#039;impossibile riuscita, e il Flou­<lb></lb>rens, nelle sue Ricerche sperimentali sulle proprietà e le funzioni del si­<lb></lb>stema nervoso, si compiacque di averlo messo in pratica nell&#039;arteria magna <lb></lb>di un montone (Paris 1842, pag. </s>

<s>368). </s></p><p type="main">

<s>Il Fisiologo francese però era stato preceduto, di ben cento ottant&#039;anni, <lb></lb>da un nostro Italiano, il quale fu, contro l&#039;opinion dell&#039;Harvey, persuaso <lb></lb>che lo sperimento della fistola inserita nell&#039;arteria incisa fosse possibile, e <lb></lb>che Galeno non lo avesse solamente proposto agli studiosi, ma che lo avesse <lb></lb>altresì praticato, benchè, per le gravi difficoltà, prendesse abbaglio nell&#039;os­<lb></lb>servare. </s>

<s>Così infatti scriveva, nel 1661, Tommaso Cornelio, in quel suo <lb></lb>VII Proginnasma, che s&#039;intitola <emph type="italics"></emph>De vita:<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Harveius autem, quum multis et gravibus argumentis docuisset ar­<lb></lb>terias ab impulsu sanguinis distendi, ausus est Galeni experimentum in du­<lb></lb>bium vocare. </s>

<s>Scripsit enim nec a se eius rei periculum factum esse, nec <lb></lb>recte in vivis animantibus fieri posse, ob vim sanguinis ex maioribus arte­<lb></lb>riis magno impetu erumpentis, sibi verisimile videri ut vulnus calamo obduci <lb></lb>sine ligamine possit. </s>

<s>” </s></p><p type="main">

<s>“ Atqui ego non omnem Galeno fidem in hacre derogandam velim, <lb></lb>quippe mihi haec aliquando licuit experiri. </s>

<s>Ligata utrinque hinc et illinc <lb></lb>arteria, spatioque inter vincula diffiso, fistulam per vulnus in arteriam inse­<lb></lb>rui, ac discissam arteriae partem praetenui filo fistulae alligavi. </s>

<s>Tum, disru­<lb></lb>ptis confestim prioribus vinculis, sanguis per fistulam permanabat in ulte­<lb></lb>riorem arteriae partem. </s>

<s>At interea videre erat arteriam ultra vinculum, sed <lb></lb>paulo obscurius, pulsantem. </s>

<s>” </s></p><p type="main">

<s>“ Quod autem eiusmodi motum Galenus non animadverterit, causam <lb></lb>fuisse suspicor calami crassitudinem qui, quoniam exiguo pertusus erat fo­<lb></lb>ramine, traiectioni sanguinis officere potuit. </s>

<s>Ad haec accedit quod sanguis <lb></lb>intra fistulam facile coit atque densatur, quapropter tale experimentum no­<lb></lb>vum industriumque postulat observatorem ” (Neapoli 1688, pag. </s>

<s>274-76). </s></p><p type="main">

<s>Conclude il Cornelio a favor dell&#039;Harvey la descrizione di questo suo <lb></lb>esperimento, dicendo: “ Arterias igitur ab impulsu sanguinis moveri, atque <lb></lb>micare, palam fit ab ipso Galeni experimento ” (ibi, pag. </s>

<s>276). Veniva così <lb></lb>d&#039;ogni parte confermato quel che l&#039;Harvey stesso intendeva di dimostrare, <lb></lb>che cioè le arterie vanno in diastole e danno il polso, per solo impulso del <lb></lb>sangue e non per una qualche innata virtù pulsifica o partecipata a loro <lb></lb>dal cuore. </s>

<s>La pulsante onda del sangue poi nelle arterie l&#039;assomigliava al­<lb></lb>l&#039;acqua sollevata, a ogni colpo di sifone, nelle fistole plumbee. </s>

<s>“ Quemad­<lb></lb>modum cum aqua, vi et impulsu syphonis, per fistulas plumbeas in altum <lb></lb>cogitur, singulas compressiones instrumenti, per multa licet stadia distent, <pb xlink:href="020/01/1225.jpg" pagenum="100"></pb>in ipso aquae exeuntis fluxu, singulorum ictuum ordinem, principium, in­<lb></lb>crementum, finem, vehementiam, observare et distinguere possumus; ita ex <lb></lb>abscissae arteriae orificio ” (Exercitatio anat. </s>

<s>II app. </s>

<s>De motu cordis cit., <lb></lb>pag. </s>

<s>158, 59). </s></p><p type="main">

<s>S&#039;attribuiva allora ai sifoni una duplice azione, quella di premere e l&#039;al­<lb></lb>tra di attrarre, e una tale duplice azione è dall&#039;Harvey attribuita pure anche <lb></lb>al cuore. </s>

<s>Nell&#039;ultimo capitolo del suo trattato, dove anatomicamente descrive <lb></lb>gli organi del moto del cuore, e il modo com&#039;essi esercitano le loro forze <lb></lb>sul sangue; conclude dall&#039;Embriologia comparata un&#039;avvertenza importante, <lb></lb>ed è che l&#039;orecchietta destra è la prima a pulsare, <emph type="italics"></emph>primum vivens, ulti­<lb></lb>mum moriens,<emph.end type="italics"></emph.end> e vien perciò da lei il primo impulso al moto del sangue <lb></lb>stesso, il quale è trasfuso nel ventricolo sottoposto. </s>

<s>“ Qui ventriculus, poi <lb></lb>soggiunge, continuo seipsum contrahendo, iam ante in motu existentem san­<lb></lb>guinem commodius elidat, et violentius propellat, ut cum ludas pila a re­<lb></lb>verberatione, fortius et longius percutiendo quam simpliciter proiiciendo, <lb></lb>impellere poteris. </s>

<s>Quin etiam contra vulgarem opinionem, quia neque cor <lb></lb>neque aliud quidpiam seipsum distendere sic potest, ut in seipsum attrahere <lb></lb>sua diastole quicquam possit, nisi ut spongia, vi prius compressa, dum redit <lb></lb>ad constitutionem suam ” (pag. </s>

<s>97). </s></p><p type="main">

<s>Dopo la grande esperienza dimostrativa del peso dell&#039;aria, come il Ba­<lb></lb>liani e il Torricelli avevano rimossa la forza attrattiva del vacuo dalla Fi­<lb></lb>sica, così fu il Pecquet de&#039;primi a rimoverla dalla Fisiologia. </s>

<s>Nel cap. </s>

<s>VII <lb></lb>della sua Dissertazione anatomica <emph type="italics"></emph>De circulatione sanguinis,<emph.end type="italics"></emph.end> s&#039;introduce ad <lb></lb>esaminar le due forze, alle quali principalmente s&#039;attribuiva prima di lui il <lb></lb>moto del sangue; l&#039;intrinseco impulso cioè della sistole, e l&#039;attrazione della <lb></lb>diastole. </s>

<s>E riferiti que&#039;celebri esperimenti del vuoto, ne conclude con dire <lb></lb>che l&#039;azione attribuita ai corpi di attrarre niente altro era in verità che una <lb></lb>pressione sopravveniente in essi dal peso dell&#039;aria. </s>

<s>E perch&#039;egli credeva non <lb></lb>potersi ridurre la forza d&#039;impulsione, se non che nella naturale gravità del <lb></lb>sangue, e perchè, scoperta essere una fallacia l&#039;attrazione, vedeva andare <lb></lb>svanita quella forza, a cui commettevasi la diastole; “ superest, dice il <lb></lb>Pecquet, ut vasorum constrictionem et eorumdam a vicinarum partium agi­<lb></lb>tatione, vel etiam pondere, compressionem expendamus ” (Parisiis 1654, <lb></lb>pag, 73). E dop&#039;aver ponderato il momento di queste forze di contrazione <lb></lb>e di compressione de&#039;vasi, così conclude: “ Ergo triplici pronuntio sangui­<lb></lb>nem incitabulo circumrolvi: systoles videlicet impulsione, vasorum seu spon­<lb></lb>tanea seu violenta contractione, atque, ab adiacentium connixu partium, va­<lb></lb>sorum eorumdem compressione: tribus invicem ita dispositis, ut aliqua semper <lb></lb>aliarum defectus, etsi lentiuscule, quidem officii perseverantia compenset ” <lb></lb>(ibi, pag. </s>

<s>75, 76). </s></p><p type="main">

<s>La compressione però, se da una parte può promuovere il corso del <lb></lb>sangue, gli serve dall&#039;altra d&#039;impedimento, e anzi il Borelli notò che que­<lb></lb>sto impedimento era insigne. </s>

<s>“ Et noto quod resistentia contra impulsum <lb></lb>sanguinis, quae exercetur, ut viae aperiantur inter carnes et intra viscera, <pb xlink:href="020/01/1226.jpg" pagenum="101"></pb>est insignis, quia sanguis terebrare debet porositates partium corporis ani­<lb></lb>malis solidarum, grandi impetu ” (De motu anim. </s>

<s>cit., P. II, pag. </s>

<s>149). Fu <lb></lb>perciò che il Borelli stesso, de&#039;tre incitamenti che a promuovere il corso <lb></lb>del sangue annoverava il Pecquet, non ne ritenne altro che due: la forza <lb></lb>del cuore e la contrazion delle arterie, rassomigliate al moto peristaltico <lb></lb>degl&#039;intestini (ivi, pag. </s>

<s>147). Ma alle fibre muscolari del cuore attribuiva il <lb></lb>massimo effetto, e fu egli il primo che si provò di ridurlo a misura. </s></p><p type="main">

<s>Ammesso che la potenza di un muscolo sia proporzionale al peso, per­<lb></lb>ciocchè la mole carnosa del cuore uguaglia quella di uno de&#039;muscoli tem­<lb></lb>porali e di un messetere, la potenza di questi due sarà dunque uguale alla <lb></lb>potenza dello stesso cuore. </s>

<s>E perchè si trova per l&#039;esperienze che le fibre <lb></lb>tutte insieme riunite dei due muscoli sopraddetti possono sostenere un peso <lb></lb>maggiore delle tremila libbre “ igitur elicere possumus quod vis quam exer­<lb></lb>cent omnes minimae fibrae cordis, simul sumptae, si impellerent radium <lb></lb>externum librae, bifariam in centro sectae, superare potest pondus 3000 li­<lb></lb>brarum ” (ivi, pag. </s>

<s>134). </s></p><p type="main">

<s>Messa questa potenza muscolare in azione nella macchina idraulica del <lb></lb>cuore, dimostra il Borelii che la forza motiva di lui, a tutta la forza con la <lb></lb>quale il sangue nelle arterie resiste all&#039;espulsione, sta come uno a sessanta. </s>

<s><lb></lb>Di qui, e dai dati precedenti, si deduce con facilità la cercata misura. </s>

<s>“ Quia <lb></lb>vis absoluta, quam exercet musculus cordis inflando vexiculas omnes po­<lb></lb>rosas eius, tam grandis est, ut immediate et absque machina superare pos­<lb></lb>set pondus maius quam 3000 librarum: at eadem vis motiva ad eiusdem <lb></lb>momentum, seu ad vim, qua sanguinis motus in arteriis impeditur, eamdem <lb></lb>proportionem habet quam 1 ad 60; ergo vis absoluta, a qua sanguinis mo­<lb></lb>tus in arteriis impeditur, et quam cordis potentia superat, maior est vi pon­<lb></lb>deris 180,000 librarum ” (ibi, pag. </s>

<s>143). </s></p><p type="main">

<s>Questa non è altro però che la forza, la quale dee superarsi dal cuore, <lb></lb>per empir le arterie fino alla turgenza. </s>

<s>Ma perchè possa fuori di loro uscire <lb></lb>il sangue, il quale ha da aprirsi la via tra la porosità de&#039;muscoli e il pa­<lb></lb>renchima de&#039;visceri, vi bisogna una nuova forza, che il Borelli giudica non <lb></lb>potere esser minore delle 135 mila libbre. </s>

<s>Di qui è che, per empir le ar­<lb></lb>terie e per sopraggiunger nuov&#039;impulso al sangue che n&#039;esca, conviene al <lb></lb>cuore, secondo questi calcoli, superar tutto insieme una resistenza, ch&#039;equi­<lb></lb>vale al peso di 315 mila libbre. </s>

<s>“ Stupenda profecto, esclama qui il Borelli, <lb></lb>est tam vasta vis et incredibilis omnino esset, nisi adesset energia percus­<lb></lb>sionis, quae ex sui natura superare potest quamcumque finitam resistentiam <lb></lb>quiescentem ” (ibi, pag. </s>

<s>150). </s></p><p type="main">

<s>La infinita forza della percossa, invocata qui dal Borelli in questi cal­<lb></lb>coli di meccanica animale, ci fa sovvenir dell&#039;esempio della palla, che per­<lb></lb>cossa, dop&#039;essersi riflessa, si manda più di lungi che a semplicemente get­<lb></lb>tarla: esempio recato al medesimo proposito dall&#039;Harvey, ma in ogni modo <lb></lb>i resultamenti di que&#039;calcoli borelliani parvero esagerati. </s></p><p type="main">

<s>L&#039;esagerazione dall&#039;altra parte rendevasi manifesta a comparar la po-<pb xlink:href="020/01/1227.jpg" pagenum="102"></pb>tenza meccanica messa in esercizio, con l&#039;effetto utile da lei prodotto, il <lb></lb>quale effetto si può per l&#039;arteriotomia riconoscer tutto negli zampilli verti­<lb></lb>cali, e ne&#039;getti parabolici del sangue. </s>

<s>Quegli zampilli e que&#039;getti si vedono <lb></lb>similmente prodursi ne&#039;vasi pieni d&#039;acqua, forati nel fondo, con impeti <lb></lb>uguati e forse maggiori di quel che non avvenga nel sangue: eppure, la <lb></lb>potenza che gli produce, tutt&#039;altro ch&#039;essere infinita, riducesi alla semplice <lb></lb>pressione, che fa il liquido soprincombente al centro del foro. </s></p><p type="main">

<s>Questi pensieri passavano per la mente a Jacopo Keill, a cui parve anzi <lb></lb>che la questione, promossa dal Borelli intorno alla misura delle forze del <lb></lb>cuore, si potesse facilmente risolvere coi principii noti dell&#039;Idrometria. </s>

<s>È <lb></lb>anche il cuore, secondo lui, un vaso che contiene un liquido, e benchè ne <lb></lb>esca fuori con forza violenta, pur si può ridurre a una forza naturale. </s>

<s>È anzi <lb></lb>questo l&#039;intendimento, che principalmente si propone il Keill nel III de&#039;suoi <lb></lb><emph type="italics"></emph>Tentamina medico-hpysica,<emph.end type="italics"></emph.end> dove, comparata la velocità del sangue nell&#039;aorta <lb></lb>alla velocità del flusso in un vaso pieno d&#039;acqua, applica la misura della <lb></lb>forza, che produce un tal flusso, alla misura della forza del cuore stesso. <lb></lb><figure id="id.020.01.1227.1.jpg" xlink:href="020/01/1227/1.jpg"></figure></s></p><p type="caption">

<s>Figura 3.</s></p><p type="main">

<s>Un gran maestro di scienza idrometrica al mon­<lb></lb>do era, specialmente in Inghilterra, patria del Keill, <lb></lb>riconosciuto il Newton, il quale, dop&#039;aver definito, <lb></lb>nella proposizione XXXVI del II libro dei Principii <lb></lb>matematici di Filosofia naturale, il moto dell&#039;acqua <lb></lb>fluente dal foro EF (fig. </s>

<s>3) aperto in fondo a un <lb></lb>vaso cilindrico, in cui sia GI la distanza che passa <lb></lb>dal centro del foro stesso alla superficie AB di li­<lb></lb>vello; soggiunge il seguente corollario II: “ Et vis, <lb></lb>qua totus aquae exilientis motus generari potest, <lb></lb>aequalis est ponderi cylindricae columnae aquae, cu­<lb></lb>ius basis est foramen EF, et attitudo 2 GI ” (Ge­<lb></lb>nevae 1711, pag. </s>

<s>291). </s></p><p type="main">

<s>Applicando perciò il Keill questo Teorema, e rappresentandosi nel vaso <lb></lb>AF il ventricolo sinistro del cuore, nel foro EF l&#039;apertura dell&#039;aorta, e in <lb></lb>GI l&#039;altezza, a cui dovrebbe livellarsi il sangue, per produr naturalmente <lb></lb>nell&#039;aorta stessa quella velocità violentemente prodotta dalla sistole, e che <lb></lb>con i dati sperimentali si suppone essere stata già misurata; la forza pro­<lb></lb>duttrice di una tal velocità, ch&#039;è la forza impulsiva del cuore, conclude es­<lb></lb>sere uguale alla pressione di una colonna di sangue, alta quant&#039;è il doppio <lb></lb>di GI, e larga quant&#039;è EF nella sua base. </s>

<s>Il peso premente di una tal co­<lb></lb>lonna sanguigna, ch&#039;è, come si disse, la misura della pressione del cuore, <lb></lb>trovò il Keill stesso non esser più che cinq&#039;once. </s>

<s>“ Haec altitudo, bis sum­<lb></lb>pta, dat 1,48, sive digitos 17,76, et haec est altitudo cylindri sanguinis pleni, <lb></lb>cuius basis aequalis est Aortae orificio, quod 0,4187 aequale esse posuimus. </s>

<s><lb></lb>Solidum itaque contentum est 7,436112, cuius pondus vi cordis absolutae <lb></lb>est aequale. </s>

<s>Hoc pondus est pondus quinque unciarum. </s>

<s>Cordis itaque vis <lb></lb>quinque unciarum ponderi est aequalis ” (Lucae 1756, pag. </s>

<s>57). </s></p><pb xlink:href="020/01/1228.jpg" pagenum="103"></pb><p type="main">

<s>La nuova via idrometrica aperta, e che prometteva del problema delle <lb></lb>forze del cuore dare una più facile e più certa soluzione di quella, che per <lb></lb>via meccanica avea data il Borelli; fu proseguita da quel solertissimo spe­<lb></lb>rimentatore, che fu Stefano Hales, il quale, fatto accorto dal Michelotti che <lb></lb>si potevano scansare alcune delle più gravi opposizioni, che incontrò il cal­<lb></lb>colo del Keill, vide che si poteva dallo zampillo verticale dedur la quantità <lb></lb>del sangue premente sulle pareti del ventricolo sinistro del cuore, applican­<lb></lb>dovi direttamente il teorema idrostatico del Torricelli. </s>

<s>Incisa l&#039;arteria cru­<lb></lb>rale a un cane, trovò che lo zampillo verticale risaliva a sei piedi e otto <lb></lb>pollici, e che risaliva pure a una tale altezza il sangue dall&#039;incisa arteria <lb></lb>carotide sinistra. </s>

<s>Fattavi dentro l&#039;iniezione di cera, trovò che la superficie <lb></lb>interna del ventricolo sinistro era di undici pollici quadrati, ond&#039;è che mol­<lb></lb>tiplicando questo numero per la trovata altezza verticale dello zampillo, con­<lb></lb>cludeva che il prodotto dei 180 pollici che ne resulta esprimeva i pollici <lb></lb>cubi del sangue “ i quali premono sopratutto le interne pareti di quello <lb></lb>stesso ventricolo, quand&#039;è contratto giusto quanto debb&#039;esserlo, per soste­<lb></lb>nere ed eguagliare la forza del sangue nell&#039;aorta ” (Statica degli anim., <lb></lb>trad. </s>

<s>ital., T. I, Napoli 1750, pag. </s>

<s>39). </s></p><p type="main">

<s>Passando poi ad applicare lo stesso metodo sperimentale a misurar la <lb></lb>forza della resistenza, che supera ne&#039;suoi moti di sistole il cuore dell&#039;uomo, <lb></lb>“ supponiamo, dice l&#039;Hales, com&#039;è verisimile, che il sangue di una carotide <lb></lb>umana, in un cannello ad essa verticalmente applicato, s&#039;inalzerebbe all&#039;al­<lb></lb>tezza di piedi 7,5 e che la superficie interna del ventricolo sinistro del cuore <lb></lb>sia di 15 pollici quadrati. </s>

<s>Moltiplicando questi per quell&#039;altezza, avremo il pro­<lb></lb>dotto di 1350 pollici cubi di sangue, che premono questo ventricolo, quando <lb></lb>comincia a stringersi, ed uguagliano il peso di libbre 51,5 ” (ivi, pag. </s>

<s>42). </s></p><p type="main">

<s>La differenza che passa fra questi calcoli dell&#039;Hales e quelli del Keill, <lb></lb>e le disorbitanze che si notano, fra&#039;numeri dati da questi due sperimenta­<lb></lb>tori e quelli prima conclusi dal Borelli, posero alcuni in gran diffidenza degli <lb></lb>usi e delle applicazioni, che s&#039;intendeva far delle leggi della Meccanica e <lb></lb>della Idrostatica allo studio della Fisiologia. </s>

<s>Altri, più zelanti del metodo <lb></lb>iatromatematico e più savi, facevano notare che i vizii non erano da attri­<lb></lb>buirsi a esso metodo, ma a chi partiva da principii non certi, e da suppo­<lb></lb>sti reputati falsi, e trascurava la massima parte di quei coefficienti neces­<lb></lb>sarii per ridurre i calcoli, e per averli più giusti. </s></p><p type="main">

<s>L&#039;Haller, per esempio, osserva che si può molto dubitare dell&#039;ipotesi <lb></lb>assunta dal Borelli, che cioè le potenze de&#039;muscoli sieno proporzionali ai <lb></lb>pesi, potendovi essere in diversi muscoli fibre di diverse virtù, come si può <lb></lb>congetturar facilmente dal veder che alcune son più irritabili alla luce che <lb></lb>all&#039;aria, altre più all&#039;aria che all&#039;acqua. (Elem. </s>

<s>Fhysiologiae cit., T. I, <lb></lb>pag. </s>

<s>448). Francesco de Sauvages pose in dubbio l&#039;assunto dall&#039;Hales, che <lb></lb>cioè il tempo della sistole sia un terzo di quello della diastole, parendo più <lb></lb>ragionevole che dovesser essere que&#039;due tempi uguali, ma contro i calcoli <lb></lb>del Keill uno de&#039;più fervorosi a insorgere fu il Michelotti. </s></p><pb xlink:href="020/01/1229.jpg" pagenum="104"></pb><p type="main">

<s>Nota in que&#039;calcoli dell&#039;Inglese il Nostro che non si fa differenza fra la <lb></lb>tenacità dell&#039;acqua e quella del sangue, nè si tien conto degli attriti, che su­<lb></lb>bisce il sangue stesso, in rasentar le pareti, e in passar per le volte e le <lb></lb>rivolte dei vasi. </s>

<s>Gli errori però, che seguitano nel calcolo dal trascurar que­<lb></lb>ste cose, sono un nulla, soggiunge il Michelotti, rispetto a quelli che deri­<lb></lb>vano dall&#039;ammetter per vera quella proposizion neutoniana della legge dei <lb></lb>flussi, sopra la quale il calcolo stesso ha il suo principal fondamento. </s>

<s>“ Hanc <lb></lb>vero propositionem absolute falsam esse eo liquet quod velocitas aquae, ex <lb></lb>foramine vasis effluentis, ea omnino sit quam grave libere cadendo ex alti­<lb></lb>tudine aquae supra foramen acquireret. </s>

<s>Nam, quum infra videbimus, eius­<lb></lb>modi velocitatem aquae ex vase effluentis acceptam referre totam debeamus <lb></lb>pressioni aquae foramini incumbentis, nimirum ponderi columnae aquae, <lb></lb>cuius basis est foramen et altitudo aequalis altitudini supremae superficiei <lb></lb>aquae supra foramen; evidens est vim illam, per quam fluidum ex orificio <lb></lb>alicuius canalis effluens certam velocitatem acquirit, eam nempe quam grave <lb></lb>acquireret ex altitudine AB delapsum, esse aequalem ponderi cylindri eius­<lb></lb>dem fluidi, cuius basis aequalis est orificio, per quod fluidum egreditur, al­<lb></lb>titudo vero aequalis ipsi simplae AB, non autem huius duplae, quemadmo­<lb></lb>dum existimat clariss. </s>

<s>Keillius, fidenter eminentem geometram Js. </s>

<s>Neuto­<lb></lb>num in hac re secutus ” (De separat. </s>

<s>fluid. </s>

<s>Venetiis 1721, pag. </s>

<s>112). </s></p><p type="main">

<s>Il dir le ragioni, per le quali il Michelotti credeva che la proposizione, <lb></lb>in cui dal Newton si dimostrava il moto de&#039;flussi liquidi da un foro aperto <lb></lb>in un vaso, era falsa, vien riserbato ad altra parte di questa storia, e perciò <lb></lb>confessandosi, per la varietà de&#039;resultati numerici, le difficoltà incontrate, <lb></lb>qualunque metodo si tenesse in definir la più giusta misura della forza del <lb></lb>cuore; tutti i Fisiologi erano concordi in ammetter che, o piccola o grande <lb></lb>si tenesse quella forza, non era in ogni modo per sè sola sufficiente a so­<lb></lb>spingere il sangue infino alle ultime e più lontane diramazioni delle arterie, <lb></lb>non composte di pareti rigide, ma cedevoli e molli. </s></p><p type="main">

<s>Questo elaterio delle tuniche arteriose era stato posto in evidenza da <lb></lb>quelle belle esperienze, con le quali l&#039;Harvey dimostrava contro Galeno che <lb></lb>l&#039;arterie stesse pulsano perchè violentemente dilatate dall&#039;onda del sangue, <lb></lb>passata la quale, ritornano al loro primo stato. </s>

<s>L&#039;efficacia poi di quell&#039;ela­<lb></lb>terio in promuovere il circolo sanguigno fu sperimentalmente dimostrata dal <lb></lb>Pecquet, legando un&#039;arteria e osservando che al di là del vincolo rimaneva <lb></lb>esausta, senza dubbio, perchè la molla delle sue fibre spremeva il liquido <lb></lb>contenuto (Dissertatio anat. </s>

<s>De circul. </s>

<s>sang. </s>

<s>cap. </s>

<s>VII, edit. </s>

<s>cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Ma il moto del sangue per l&#039;arterie, e i particolari accidenti di lui, e <lb></lb>l&#039;inturgidirsi e il restituirsi delle tuniche arteriose, che sono in parte causa <lb></lb>e in parte effetto di quello stesso moto, furono più che da altri mai diligen­<lb></lb>temente studiati da Domenico Guglielmini, nella mente del quale preluce­<lb></lb>vano le dimostrate ragioni del moto delle acque correnti dentro i canali. </s></p><p type="main">

<s>Consideriamo, incomincia egli così il suo ragionamento, il sangue nel­<lb></lb>l&#039;atto che, per la contrazione del sinistro ventricolo, è spremuto dentro <pb xlink:href="020/01/1230.jpg" pagenum="105"></pb>l&#039;Aorta dal cuore. </s>

<s>Egli avrà una determinata velocità iniziale, che dipende <lb></lb>in parte dal tempo più o meno breve intercedente fra una diastole e il fine <lb></lb>di una sistole, e in parte dalla capacità dell&#039;Aorta. </s>

<s>Imperocchè, rimanendo <lb></lb>in questa sempre la sezione costante, se più veloci saranno i moti del cuore <lb></lb>più veloci saranno altresì i moti del sangue. </s>

<s>Ma se rimanendo invariabile il <lb></lb>tempo, in cui il cuore passa da una diastole all&#039;altra, l&#039;Aorta varia la sua <lb></lb>sezione, e divien per esempio minore, anche per ciò il sangue si moverà <lb></lb>più veloce. </s>

<s>Questi fatti si succedono così indubitatamente, supposto che in <lb></lb>qualunque sistole sia uguale la quantità emessa del sangue, ma se questa <lb></lb>è diversa, la velocità sarà pure alterata, anche per questa terza cagione. </s></p><p type="main">

<s>“ Itaque, prosegue a ragionare il Guglielmini, exit a corde in arteriam <lb></lb>aortam sanguis determinata velocitate, quam quidem, si retineret in toto suo <lb></lb>usque ad extrema arteriarum excursu, nulla fieret earumdem arteriarum <lb></lb>extrusio. </s>

<s>Verum hoc impossibile est; aflrictus enim, quem habet sanguis ad <lb></lb>latera arteriarum, necessario aliquid velocitatis subtrahit sanguini pertran­<lb></lb>seunti, in quo duo subsequi necesse est: primum, quod sanguis fluens per <lb></lb>arterias non uniformi feratur velocitate, sed minori quidem qui versus cir­<lb></lb>cumferentiam est, maiori vero, qui per medium tubuli arteriosi, et veluti <lb></lb>per eius axem, fluit; alterum, quod cum velocitas retardetur, ob supra dic­<lb></lb>tam rationem, non potest totus sanguis, a corde expulsus, per eiusdem <lb></lb>multo minus per minoris diametri arterias pertransire. </s>

<s>Ideo eius pars qui­<lb></lb>dem per longum arteriosi tubuli iter suum prosequitur, altera vero in eius­<lb></lb>dem arteriae capacitate subsistit, locum sibi quaerens ad extra, ex quo oritur <lb></lb>arteriae ad latera extrusio, idest dilatatio. </s>

<s>” </s></p><p type="main">

<s>“ Cumque, quo maior est recessus sanguinis a corde versus partes, sem­<lb></lb>per plures offendantur resistentiae, non modo affrictus, de quo supra, verum <lb></lb>etiam divisionis, curvitatis et obliquitatis vasorum, sequitur quod, quo maior <lb></lb>est via sanguinis a corde, eo maior fiat velocitatis amissio, et consequenter <lb></lb>quod minori impetu afficiatur sanguis praecedens, maiori vero succedens. </s>

<s><lb></lb>Igitur sanguis, subsequenti systole a corde extrusus, duplicem invenit, vel <lb></lb>ipso sui motus initio, in arterias resistentiam: alteram affrictus vasorum, al­<lb></lb>teram antecedentis sanguinis. </s>

<s>Ideoque, sui velocitate ab affrictu reliqua, par­<lb></lb>tim urgebit antecedentem sanguinem, partim contra arteriarum membranas <lb></lb>nitetur, quas idcirco dilatabit in ampliorem diametrum, absque eo quod ta­<lb></lb>men, quod observabile, cesset in toto sanguine fluxus per arteriarum longi­<lb></lb>tudinem ” (De sanguinis natura, Venetiis 1701, pag. </s>

<s>7-9). </s></p><p type="main">

<s>Assai più gravi difficoltà presentava a intendersi il moto del sangue <lb></lb>nelle vene, non più aiutato, come dianzi per le arterie, dalla macchina im­<lb></lb>pellente del cuore, ond&#039;è che, non vedendoci nulla di violento, furono i Fi­<lb></lb>siologi costretti ad affidare tutta quella forza d&#039;impulso alla gravità naturale. </s>

<s><lb></lb>Dicevano che le vene con le arterie, come per esempio la Cava discendente <lb></lb>con l&#039;Aorta ascendente, componevano un sifone, e che perciò il sangue, per <lb></lb>legge d&#039;equilibrio idrostatico, tanto discendeva in quella, quanto in questa <lb></lb>ascendeva. </s>

<s>Il Pecquet riserbò il cap. </s>

<s>VI della citata Dissertazione anatomica <pb xlink:href="020/01/1231.jpg" pagenum="106"></pb><emph type="italics"></emph>De circulatione sanguinis<emph.end type="italics"></emph.end> a confutare una così fatta opinione, dimostran­<lb></lb>done da più parti la falsità con le ragioni e con l&#039;esperienze. </s></p><p type="main">

<s>La prima di quelle ragioni è che, dovendo i liquidi ne&#039;rami di un sifone <lb></lb>ascendere e discendere nel medesimo tempo, perchè se non operassero con­<lb></lb>temporaneamente le due forze non potrebbero comporsi in equilibrio, conver­<lb></lb>rebbe, applicato quello strumento idrostatico al sangue, che si facessero nello <lb></lb>stesso tempo dal medesimo mobile due moti contrarii, che son nel caso <lb></lb>nostro la sistole e la diastole del cuore. </s>

<s>“ Patebit tum quam sit incongrua <lb></lb>Siphonis cum sanguineo motu iugis fluendi successio, nam eodem instanti <lb></lb>et in cor influeret sanguis et ex corde deflueret ” (pag. </s>

<s>45). </s></p><p type="main">

<s>La falsità dell&#039;ipotesi del Sifone, prosegue a dire il Pecquet, è confer­<lb></lb>mata dall&#039;osservazione sui cadaveri, e dall&#039;esperienza su gli animali vivi. </s>

<s><lb></lb>Imperocchè, se per mantener l&#039;equilibrio idrostatico debbono mantenersi i <lb></lb>due rami sempre di liquido ugualmente pieni “ qui fiat ut in cadavere mors <lb></lb>turgidis venis arterias prorsus exhauriat? </s>

<s>” (ibi). La vena guigulare rap­<lb></lb>presenta un sifone con la curvatura superiore. </s>

<s>“ Hanc, dice il Pecquet, cum <lb></lb>in collo ligavi, nihilominus per ascendentes arterias sursum immissus est <lb></lb>sanguis ” (ibi). Altre esperienze, che seguita l&#039;Autore a descrivere, confer­<lb></lb>mavano l&#039;insufficienza del sifone, ond&#039;è che ridusse tutta la macchina del <lb></lb>moto sanguineo dentro le vene alla nativa contrattilità delle loro fibre. </s></p><p type="main">

<s>Il Borelli poi conobbe che bisognava con più diligenza studiare questo <lb></lb>meccanismo, e ne considerò distintamente l&#039;opera in tre tempi diversi: nel­<lb></lb>l&#039;atto, in cui il sangue arterioso entra per le bocche aperte delle vene ca­<lb></lb>pillari; quando entratovi segue un primo tratto della sua via lungo questi <lb></lb>stessi capillari; e in ultimo, quando avvicinandosi più al cuore vi scende <lb></lb>per canali venosi sempre più larghi. </s></p><p type="main">

<s>Il primo atto, che è dell&#039;ingresso del sangue arterioso nelle estremità <lb></lb>capillari delle vene, presentava la massima difficoltà sopra gli altri, perchè, <lb></lb>sebbene ai tempi in che fu pubblicata o forse anche scritta dal Borelli que­<lb></lb>sta Parte dei moti animali, avesse il Malpighi veduto co&#039;suoi eccellenti mi­<lb></lb>croscopi continuarsi le estremità arteriose con le venose in alcuni organi <lb></lb>secretori delle rane, rimasero tuttavia, anche lungo tempo dopo, in dubbio <lb></lb>i Fisiologi di queste anastomosi, parendo forse a loro, come parve al Pe­<lb></lb>cquet, più naturale ammettere un&#039;estravasamento del sangue, con che ren­<lb></lb>devasi assai più facile a intendere la nutrizione. </s></p><p type="main">

<s>Comunque sia, il Borelli stesso, nella XXXII proposizione della II Parte <lb></lb><emph type="italics"></emph>De motu anim.,<emph.end type="italics"></emph.end> confessò che la ragion meccanica del moto del sangue nelle <lb></lb>vene non è così chiara, principalmente per ciò che concerne il modo come <lb></lb>si sugge il sangue arterioso dalle ultime venuzze capillari. </s>

<s>“ Nam venae ca­<lb></lb>pillares, egli dice, non uniuntur cum extremis arteriolis per anastomosin, et <lb></lb>ideo sanguis immitti non potest immediate ab arteriis ad venas, cum haec <lb></lb>vasa sint separata ad invicem. </s>

<s>Et licet opinemur adesse communicationem <lb></lb>quandam inter extrema orificia arteriarum et venarum capillarium, per in­<lb></lb>termediam spongiosam substantiam carnium, viscerum, aut per cribrosam <pb xlink:href="020/01/1232.jpg" pagenum="107"></pb>substantiam ossium, tamquam per pumicis porositates; attamen non perci­<lb></lb>pimus a qua vi motiva insinuari sanguis possit intra capillares venas. </s>

<s>Primo, <lb></lb>quia vis impulsiva, qua systole cordis sanguinem intra arterias immittit, con­<lb></lb>sentaneum est ut sensim debilitetur, et tandem langueat in angustiis illis <lb></lb>extremorum vasorum et porositatum intermediarum. </s>

<s>Secundo, quia orificia <lb></lb>venularum non possunt semper dilatata et aperta permanere, cum earum <lb></lb>consistentia non sit dura ut ossea, sed membranosa, mollis et lubrica, et <lb></lb>ideo facile elaudantur et ingressum novi sanguinis impedire possint. </s>

<s>Tertio, <lb></lb>neque ad compressionem viscerum et carnium recurrere possumus, a qua <lb></lb>per expressionem sanguis ibidem insinuatur ” (Editio cit., pag. </s>

<s>79, 80). </s></p><p type="main">

<s>Questa terza ragione è manifestamente contro l&#039;ipotesi del Pecquet, la <lb></lb>quale dice il Borelli è insufficiente a spiegar la causa del sofficcarsi così il <lb></lb>sangue arterioso nelle bocchuzze delle vene, vedendosi avvenir ciò non solo <lb></lb>quando i muscoli enfiandosi esercitano la loro compressione, ma quando al­<lb></lb>tresì riposano e rimangono affatto relassati. </s></p><p type="main">

<s>Quella ipotesi del Pecquet, soggiunge il Borelli, è di più insufficiente <lb></lb>a spiegare in che modo, imboccato il sangue, proceda con impeto per tutto <lb></lb>il tratto delle venuzze capillari, vedendolo procedere con quel medesimo <lb></lb>impeto anche attraverso alla stessa dura sostanza, non punto compressibile, <lb></lb>degli ossi. </s>

<s>E qui il nostro Italiano introduce com&#039;efficiente di quel moto <lb></lb>una causa, rimasta incognita agli stranieri, infin dopo la prima metà del se­<lb></lb>colo XVII, benchè Andrea Cesalpino avesse attribuita ad essa l&#039;ascendere della <lb></lb>linfa nelle piante. </s>

<s>Niccolò Aggiunti, morto come sappiamo nel 1635, riduce <lb></lb>a una occulta virtù, che poi fu detta di capillarità, il moto de&#039;liquidi per <lb></lb>gli angusti meati de&#039;corpi, e specialmente per le venuzze degli animali, men­<lb></lb>tre, nel 1651, il Pecquet non sapeva attribuire ad altra causa che alle com­<lb></lb>pressioni e agli agitamenti del torace e de&#039;muscoli intercostali, nell&#039;atto <lb></lb>della respirazione, il moto così veloce del chilo per i vasi aselliani. </s></p><p type="main">

<s>I fenomeni capillari furono, come narreremo a suo tempo, uno de&#039;primi <lb></lb>soggetti intorno ai quali s&#039;intrattennero l&#039;esperienze de&#039;nostri Accademici <lb></lb>del Cimento, e il Borelli ne fa qui una insigne applicazione alla Meccanica <lb></lb>animale, rassomigliando i primi moti del sangue, che s&#039;insinua nelle aperte <lb></lb>boccuzze delle vene, all&#039;insinuarsi dell&#039;acqua ne&#039;pori aperti delle spugne, <lb></lb>de&#039;filtri, delle funi, o nell&#039;interno di sottilissimi cannellini, per intrinseco <lb></lb>impulso, non punto diverso da quello della gravità universale. </s>

<s>“ Sic vis mo­<lb></lb>tiva gravitatis, qua sanguis carere non potest, ad instar aquae, cum offendit <lb></lb>canaliculos patulos capillarium venarum, eo quod nunquam a conniventia <lb></lb>membranosa tam stricta et tenaci clausura constringi possunt, ut aditus aliqui <lb></lb>non remaneant, ut in funium porulis patet; necesse est ut, energia motiva <lb></lb>qua pollent, inertem angustiarum resistentiam superet, et proinde actione <lb></lb>simili filtrationi sanguis intra capillares venulas insinuetur ” (ibi, pag. </s>

<s>80). <lb></lb>Insinuatosi così, per l&#039;impulso iniziale, procede nel suo moto oltre sospinto <lb></lb>dal sangue che sussegue “ ut videmus aquam a filtro exuctam a suprema <lb></lb>finbria reclinata et pendula percolari ” (ibi, pag. </s>

<s>81). </s></p><pb xlink:href="020/01/1233.jpg" pagenum="108"></pb><p type="main">

<s>All&#039;ultimo, proseguendo il sangue nelle vene il suo corso, dagli angu­<lb></lb>sti seni de&#039;capillari trapassa nelle più aperte vie de&#039;tronchi venosi; ond&#039;è <lb></lb>che, accresciutasi ivi la sezione, la velocità naturalmente diminuisce. </s>

<s>“ Ideo <lb></lb>deinceps auxiliaribus manibus indiget ut promoveri ulterius possit ” (ibi). <lb></lb>Consistono principalmente questi ausiliari, soggiunge tosto il Borelli, nel <lb></lb>moto vermicolare o peristaltico delle vene, a cui s&#039;aggiungono la compres­<lb></lb>sione dell&#039;aria ambiente, e l&#039;elasticità dell&#039;interna, nonchè il moto de&#039;mu­<lb></lb>scoli, de&#039;visceri e de&#039;fluidi nel corpo animale continuamente scorrenti. </s></p><p type="main">

<s>Non occorre entrar nella questione dell&#039;aria contenuta nel sangue, ma <lb></lb>è da notar come il Borelli, annoverando fra i coefficienti del moto la pres­<lb></lb>sion dell&#039;aria ambiente le vene, emendava uno de&#039;più gravi difetti della <lb></lb>meccanica pecqueziana, la quale, contenta a escludere il nome vano dell&#039;at­<lb></lb><figure id="id.020.01.1233.1.jpg" xlink:href="020/01/1233/1.jpg"></figure></s></p><p type="caption">

<s>Figura 4.<lb></lb>trazione del vacuo, non attribuì nessuna efficacia in sol­<lb></lb>lecitare il moto del sangue a quel grave peso dell&#039;am­<lb></lb>mosfera, sotto il torchio del quale gemono, o in quiete o <lb></lb>in moto che sieno, tutti i corpi terrestri. </s></p><p type="main">

<s>Mentre dunque così il Borelli da una parte emen­<lb></lb>dava la meccanica animale del Pecquet, la compieva dal­<lb></lb>l&#039;altra, attribuendo al gioco delle valvole principalmente <lb></lb>l&#039;impulso a proseguire oltre verso il cuore, il sangue, <lb></lb>nelle vene più grosse. </s>

<s>Rappresenti il cilindro KLHI <lb></lb>(fig. </s>

<s>4) un grosso tronco di vena, e nelle interne pareti <lb></lb>di lui sieno apposte le due valvole membranose AONMP, <lb></lb>BONQR. </s>

<s>Ecco in che modo il Borelli descrive il mecca­<lb></lb>nismo delle valvole, in protrudere innanzi il sangue verso <lb></lb>il ventricolo destro del cuore: </s></p><p type="main">

<s>“ Intelligatur eadem portio HMQL sanguine repleta, <lb></lb>et quia a fibris circularibus eius, et ab ambientibus mu­<lb></lb>sculis et visceribus stringitur una pars post aliam, oportet <lb></lb>ut eius laterales parietes S, T ad sese propius accedant <lb></lb>versus V, et tunc vena restricta cylindricam formam amit­<lb></lb>tet, transformabiturque in duo infundibula HVL, MVQ, <lb></lb>quae minus capacia sunt ipso cylindro, et proinde san­<lb></lb>guis, qui continebatur in spatiis VHS et VLT expelletur <lb></lb>extra orificium HL: reliqua vero moles sanguinis contenta in spatiis VSM, <lb></lb>VQT eiicietur extra orificium MQ versus IK. ” </s></p><p type="main">

<s>“ Patet igitur quod ex praedicta compressione parietum venae expri­<lb></lb>mitur sanguis, pelliturque aequali copia ad partes oppositas, et hoc contin­<lb></lb>geret, si valvulae non adessent. </s>

<s>At quia, in internis parietibus MP, QR ve­<lb></lb>nae, appositae sunt valvulae, seu sacculi membranosi superius expositi, <lb></lb>necesse est ut sanguis impulsus a compressione facta in ST insinuetur per <lb></lb>rimam NO, quia fluidum cedens in sacculis contentum, ab adveniente san­<lb></lb>guine contusum, constringitur, evacuaturque, et ideo latera valvularum NO <lb></lb>ab invicem recedendo patulam viam relinquunt, per quam sanguineus fluor <pb xlink:href="020/01/1234.jpg" pagenum="109"></pb>ab MSTQ adveniens insinuari potest, et pertransire ultra AB. Porro, post­<lb></lb>quam sanguis confinia valvularum PO, RO transgressus est, necessario subse­<lb></lb>quitur spontanea restrictio et clausura rimulae NO, nam ipse sanguis, mole <lb></lb>sua gravi et propensione fluida, replere debet sacculos valvularum, et ideo <lb></lb>latera mollia eorum dilatata, quousque se mutuo exacte tangant, rimulam NO <lb></lb>arcte claudere debent ” (ibi, pag. </s>

<s>82, 83). </s></p><p type="main">

<s>Quando ancora non s&#039;è restituita nel suo primo stato la parte venosa <lb></lb>T, S, incomincia, proseguendo il moto peristaltico, a contrarsi la porzion <lb></lb>superiore F, E, e il sangue contenuto nell&#039;infondibolo GBA, trovando di sotto <lb></lb>le valvole chiuse, non retrocede però, ma vien oltre sospinto verso DC “ non <lb></lb>secus ac pila lusoria parieti illisa ” (ibi). Nello stesso tempo è spinto pure <lb></lb>per la medesima via il sangue contenuto negli spazii EDG, FCG, cosicchè, <lb></lb>dello stesso sangue sospinto in quella medesima compressione, doppia viene <lb></lb>ad esser la mole. </s>

<s>E perchè doppia mole produce doppia velocità, è questo, <lb></lb>conclude il Borelli, un altro singolar benefizio delle valvole delle vene (ivi). </s></p><p type="main">

<s>La difficoltà d&#039;investigar la causa e la ragion meccanica del moto del <lb></lb>sangue nelle vene pareva in questo modo assai ingegnosamente superata, e <lb></lb>poniamo che rimanga tuttavia occulto quel che ad esaltare i moti puramente <lb></lb>meccanici vi conferisce lo spirito della vita, non si potevano i Fisiologi aspet­<lb></lb>tar nulla di più sottile di queste borelliane speculazioni. </s>

<s>In ogni modo, per­<lb></lb>ciocchè la forza che si cercava (la quale essendo vitale dev&#039;esser semplicis­<lb></lb>sima) si lusingavano gli Iatromatematici che dovesse resultare di compo­<lb></lb>nenti non tutte computabili dalle deboli forze del nostro ingegno, credettero <lb></lb>che, per far concorrere in più gran numero possibile le stesse componenti <lb></lb>più conosciute, si potesse riuscire ad avere almeno per approssimazione il <lb></lb>valore della forza resultante. </s></p><p type="main">

<s>Una tal tendenza della scienza fisiologica, specialmente in Italia, dove <lb></lb>la scuola iatromatematica avendo avuto la sua prima istituzione, ebbe anche <lb></lb>maggior cultura; vien rappresentata dalla dottrina del Guglielmini, il quale, <lb></lb>dopo aver divisate come vedemmo le ragioni meccaniche del moto del san­<lb></lb>gue nelle arterie, passa a considerar le cause efficienti di quello stesso moto <lb></lb>nelle estremità capillari delle vene, e ne&#039;loro tronchi. </s></p><p type="main">

<s>Che un moto, simile a quello discorrente per le arterie, lo abbia altresì <lb></lb>il sangue per le vene, può dimostrarsi, egli dice, da ciò “ quod non aliunde <lb></lb>sanguis venis subministretur quam ab arteriarum osculis, vel, quod proba­<lb></lb>bilius, a porosis carnium meatibus, in quos sanguis arteriosus, tum nutri­<lb></lb>tionis, tum motionis musculorum, tum aliorum usuum causa effunditur. </s>

<s>In <lb></lb>hos enim hiantia tum arteriarum tum venarum ora illa vehunt, haec, quod <lb></lb>superest revehunt. </s>

<s>Ideoque, qua ratione exit ab arteriis sanguis, eadem et <lb></lb>carnium interstitia perluere et venas subingredi cogitur ” (De sanguinis na­<lb></lb>tura cit, pag. </s>

<s>13). </s></p><p type="main">

<s>Se dunque, ne conclude il Guglielmini, vien rapito dal cuore per le ar­<lb></lb>terie un fiume non interrotto di sangue; un fiume non interrotto di sangue <lb></lb>è pur necessario che sia rimenato al cuore dalle vene. </s>

<s>Favoriscono questo <pb xlink:href="020/01/1235.jpg" pagenum="110"></pb>ricorso, ei soggiunge, più cause coefficienti e son quelle considerate già dal <lb></lb>Borelli e da altri Fisiologi nostrali e stranieri. </s>

<s>Ma prima di veder il nostro <lb></lb>Autore ridurre in ordine e annoverare le ragioni altrui, non vogliamo la­<lb></lb>sciare inavvertito che in quelle parole: <emph type="italics"></emph>si igitur per arterias, non inter­<lb></lb>rupto flumine, vehitur, id etiam per venas contingere necesse est,<emph.end type="italics"></emph.end> conclu­<lb></lb>desi la principal causa del moto del sangue per le vene, qui dal Guglielmini <lb></lb>accennata, ma che, nella II delle sue <emph type="italics"></emph>Lettere idrostatiche,<emph.end type="italics"></emph.end> ha il più chiaro <lb></lb>e più pieno commento. </s>

<s>Ivi dimostra le vere leggi del moto dell&#039;acqua den­<lb></lb>tro i sifoni, e osserva che una parte del fluido si tira necessariamente die­<lb></lb>tro, con la stessa velocità, l&#039;altra parte che addietro la segue, per non poter <lb></lb>rimanervisi spazii vuoti interposti. </s>

<s>D&#039;onde segue che il moto dello stesso <lb></lb>fluido non è naturale ma violento, come quello che necessariamente sog­<lb></lb>giace alla prepotente pressione di tutta l&#039;ammosfera. </s>

<s>La continuità del cir­<lb></lb>colo mette il sangue in queste medesime condizioni idrostatiche, ond&#039;è im­<lb></lb>possibile che il sangue stesso sgorghi dalla vena Cava, ch&#039;è l&#039;estremità del <lb></lb>sifone, dentro il ventricolo destro, senza che quel che gli è dietro tutto in­<lb></lb>sieme lo segua, con la velocità conveniente alle sezioni. </s></p><p type="main">

<s>Accennata questa, che è la causa principale del ricorso del sangue nelle <lb></lb>vene “ Huic autem recursui, soggiunge il Guglielmini, opem ferunt, tum <lb></lb>impetus sanguini a corde et arteriis communicatus a parte post partem ab <lb></lb>arterioso sanguine in venosum transiens; tum ratio aequilibrii in ascenden­<lb></lb>tibus venis. </s>

<s>Sicuti enim in recurvis syphonibus fluida ad eamdem altitudi­<lb></lb>nem aequilibrantur, et per unum syphonis crus tantum ascendunt, quantum <lb></lb>per alterum descenderunt, etiam precisa quacumque vi externa; ita consi­<lb></lb>milis aequilibrii ratione irruens per Aortam descendentem eiusque propagi­<lb></lb>nes, sanguis, qui uti in viventi animali fluidus est, ita et reliquorum flui­<lb></lb>dorum naturam sequitur, per minores ramulos a Cava descendente prognatos <lb></lb>primo, mox in eius truncum adscendere cogitur usque ad cor, etiam si huius <lb></lb>vis subtraheretur. </s>

<s>Quanto ergo magis si legibus aequilibrii copuletur altera <lb></lb>vis extrinseca, scilicet cordis et arteriarum constrictiva facultas! ” </s></p><p type="main">

<s>“ Aliquando etiam regressui sanguinis in cor suffragatur eiusdem gra­<lb></lb>vitas, ut in venis descendentibus. </s>

<s>Protrusus enim per Aortam ascendentem <lb></lb>in caput sanguis, ubi minima lustraverit cerebri vascula et in venulas com­<lb></lb>mearit, quae in cavam ascendentem hiant, huius declivitas et perpendicularis <lb></lb>situs efficit ut nullo externo indigeat sanguis auxilio ut ad priora reverta­<lb></lb>tur contubernia. </s>

<s>Addunt alii peristalticum venarum motum et valvularum, <lb></lb>quae in iis sunt adiumentum: ille enim motum sanguinis promovet, hoc <lb></lb>versus certam partem determinat, ut obstendit praeclarissimus Borellus ” <lb></lb>(ibi, pag. </s>

<s>14, 15). </s></p><pb xlink:href="020/01/1236.jpg" pagenum="111"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi bene attende all&#039;indole delle esposte dottrine del Guglielmini, ci <lb></lb>vede profondamente impresse le vestigia di quella scienza idraulica, nella <lb></lb>quale egli fu così insigne Maestro. </s>

<s>Potremo fra poco, da quello stesso trat­<lb></lb>tato <emph type="italics"></emph>De sanguinis natura,<emph.end type="italics"></emph.end> desumere di ciò altri più chiari esempi, ma in­<lb></lb>tanto è da considerare ch&#039;essendo quell&#039;indole tutta propria alla istituzione <lb></lb>iatromatematica, il Guglielmini stesso doveva avere appreso di là i nuovi <lb></lb>modi, seguendo l&#039;orme dell&#039;applauditissimo Istitutore. </s></p><p type="main">

<s>Anche prima di averne la riprova dei fatti, si prevede facilmente da <lb></lb>ognuno che il Borelli, discepolo dell&#039;Autore <emph type="italics"></emph>Della misura delle acque cor­<lb></lb>renti,<emph.end type="italics"></emph.end> doveva prevalersi delle leggi idrauliche a investigar le cause e le ra­<lb></lb>gioni del moto del sangue: e fu di fatto così, com&#039;accennava già la storia <lb></lb>passata, e come si dimostrerà meglio dalla presente. </s>

<s>S&#039;asserisce anzi di più <lb></lb>che il Borelli stesso fu il primo a far, tra l&#039;Idraulica e la Fisiologia, quel <lb></lb>connubio, che parve ai successori così fecondo, e se una tale fecondità ha <lb></lb>nessuna ragion di merito, il merito di ciò principalmente, e forse tutto, è <lb></lb>da attribuirsi alla scuola italiana. </s></p><p type="main">

<s>È vero che l&#039;Harvey rassomigliò il cuore a quella macchina artificiale <lb></lb>da attrar l&#039;acqua dalle cisterne e da sollevarla, da lui chiamata <emph type="italics"></emph>Sifone,<emph.end type="italics"></emph.end> ma <lb></lb>egli che professava allora, insiem coi filosofi de&#039;suoi tempi, il principio del­<lb></lb>l&#039;attrazion del vuoto, era troppo di lungi dall&#039;intendere la ragione di ciò <lb></lb>ch&#039;esemplificava, non intendendo la ragion dell&#039;esempio. </s>

<s>Il Pecquet stesso, <lb></lb>che fu il primo a cacciare dalla meccanica del cuore il falso principio di <lb></lb>quell&#039;attrazione, non seppe progredire più oltre, e anzi, sotto le macerie del <lb></lb>vecchio edifizio da lui distrutto, rimase sepolto e dimenticato anche l&#039;esem­<lb></lb>pio del Sifone recato dall&#039;Harveio. </s></p><p type="main">

<s>Ch&#039;ei non progredisse veramente più oltre, il Pecquet, e che non gli <lb></lb>sovvenisse di applicare alla scienza delle cause e delle ragioni del moto <lb></lb>de&#039;fluidi nel corpo animale la scienza delle cause e delle ragioni del moto <lb></lb>dell&#039;acqua ne&#039;tubi, scienza fuori allora non coltivata come in Italia, si di­<lb></lb>chiara per alcuni fatti occorsi al Pecquet stesso, nella storia della celebre <lb></lb>scoperta del Canale toracico. </s>

<s>Gli dinegava il Riolano la verità di quella sco­<lb></lb>perta, perch&#039;essendo, ei diceva, sproporzionata la capacità del ricettacolo ai <lb></lb>due condotti, che sboccano nelle vene succlavie, non poteva il chilo essere <lb></lb>ne&#039;due vasi ugualmente veloce, nè perciò continuarvi il suo moto. </s></p><p type="main">

<s>Avrebbe il Pecquet, ricorrendo all&#039;Idraulica, potuto fare avvertire al <lb></lb>Riolano che la stessa quantità d&#039;acqua passa in un ruscello per i più lar­<lb></lb>ghi seni, e fra i più avvicinati margini delle sue sponde, proseguendo a di­<lb></lb>ritto e non interrotto il suo corso, eppure, soggiogato per una parte dalle <lb></lb>difficoltà, e per l&#039;altra assicurato dal fatto, non sa come meglio rispondere <pb xlink:href="020/01/1237.jpg" pagenum="112"></pb>che col dire che la medesima sproporzione, notata fra il Ricettacolo e i ca­<lb></lb>naletti chiliferi, si trovava fra le vene del mesenterio e i pori epatici, per i <lb></lb>quali, secondo lo stesso Riolano, il chilo trasformato in sangue è portato alla <lb></lb>vena Cava dalla vena Porta diramatasi nel fegato attraverso al suo paren­<lb></lb>chima. (Epistolae, Parisiis 1654, pag. </s>

<s>213). </s></p><p type="main">

<s>Come dunque, trattando del moto del chilo, non seppe vedervi il Pecquet <lb></lb>la causa, che fa scorrere i liquidi ne&#039;tubi capillari; così, abbattendosi a dover <lb></lb>notare alcune accidentali anomalie di quel moto, non seppe vedervi la con­<lb></lb>formità con le leggi delle acque correnti. </s>

<s>Queste leggi dimostrate per i primi <lb></lb>dagl&#039;Italiani trapassarono dal campo delle Matematiche in quello della Fisio­<lb></lb>logia per opera del Borelli, il quale, ripigliando il dimenticato concetto ar­<lb></lb>veiano, dimostrò come il cuore si conformasse veramente nell&#039;operare alle <lb></lb>leggi idrauliche del Sifone. </s></p><p type="main">

<s>Il capitolo V della II Parte <emph type="italics"></emph>De motu animalium<emph.end type="italics"></emph.end> è tutto riserbato dal­<lb></lb>l&#039;Autore a esporre in varie proposizioni questa nuova dimostrazione, ed è <lb></lb>reputato uno de&#039;luoghi più insigni dell&#039;Opera borelliana. </s>

<s>Dopo avere sneb­<lb></lb>biate le menti dei dannosi errori vesaliani, e dop&#039;aver fatto notare che le <lb></lb>cavità del cuore si restringono, non perchè s&#039;accorcino le lunghezze dei ven­<lb></lb>tricoli, ma perchè c&#039;accostano l&#039;una all&#039;altra le pareti laterali (prop. </s>

<s>I, edit. </s>

<s><lb></lb>cit., pag. </s>

<s>103) passa a dimostrar che l&#039;azione propria dei muscoli, di ch&#039;è <lb></lb>contessuto lo stesso cuore “ est constrictio ventriculorum eius et compressio <lb></lb>et expressio sanguinis in eis contenti, ad instar praeli facta ” (ibi, pag. </s>

<s>105). </s></p><p type="main">

<s>Per dimostrare l&#039;azion meccanica di questo torchio sul sangue s&#039;appa­<lb></lb>recchia il Borelli la via, configurando uno strumento idraulico a somiglianza <lb></lb>del cuore, e dimostrando le relazioni che passano tra la potenza e la resi­<lb></lb>stenza, supposto che lo strumento stesso venga applicato a spingere e a sol­<lb></lb>levar l&#039;acqua dentro una fistola, per la quale intende poi di rappresentare <lb></lb>l&#039;Aorta. </s>

<s>La dimostrazione è sotto questa forma annunziata: “ Vis utrem <lb></lb>aqua plenum stringens, ad resistentiam aquae per fistulam ei annexam expul­<lb></lb><figure id="id.020.01.1237.1.jpg" xlink:href="020/01/1237/1.jpg"></figure></s></p><p type="caption">

<s>Figura 5.<lb></lb>sae, eamdem proportionem habet quam <lb></lb>amplitudo utris ad amplitudinem fistu­<lb></lb>lae ” (ibi, pag. </s>

<s>121). </s></p><p type="main">

<s>Suppongasi, per comodità della di­<lb></lb>mostrazione, che così la fistola come <lb></lb>l&#039;otre siano ridotti alla perfetta geome­<lb></lb>trica figura dei cilindri, e sia rappresen­<lb></lb>tato con ABCD l&#039;otre (fig. </s>

<s>5) e con IGH <lb></lb>la fistola annessa, dentro alla quale è <lb></lb>sospinto il liquido dall&#039;embolo LM. </s>

<s>A <lb></lb>chi volesse sapere qual relazione passa <lb></lb>in questo meccanico esercizio, fra la potenza P dell&#039;embolo, e la forza R, <lb></lb>con cui resiste la mole liquida alla pressione, risponde il Borelli dicendo <lb></lb>“ potentiam P ad R se habere ut amplitudo circuli AD ad amplitudinem <lb></lb>circuli IG ” (ibi). </s></p><pb xlink:href="020/01/1238.jpg" pagenum="113"></pb><p type="main">

<s>Il teorema, dimostrato da Galileo nel Discorso intorno alle galleggianti <lb></lb>col principio delle velocità virtuali, è dal Borelli concluso da un altro prin­<lb></lb>cipio, che per conformarsi al linguaggio degli scienziati moderni si può enun­<lb></lb>ciar sotto questa forma: “ Allochè due pesi o due altre potenze son dispo­<lb></lb>ste in maniera, che l&#039;una non possa muoversi, senza far muover l&#039;altra, se <lb></lb>lo spazio che deve percorrere uno de&#039;pesi, secondo la sua direzione propria <lb></lb>e naturale, stia allo spazio che deve percorrer l&#039;altro nel medesimo tempo, <lb></lb>secondo la sua direzione propria e naturale, reciprocamente come quest&#039;ul­<lb></lb>timo peso sta al primo; questi due pesi staranno in equilibrio. </s>

<s>” </s></p><p type="main">

<s>Analiticamente il Teorema, nel caso particolare contemplato qui dal <lb></lb>Borelli, viene espresso dalle seguenti equazioni: AB:HG=......... <lb></lb>HGXIG:ABXAD; P:R=ABXAD:GHXIG, onde avremo, nel caso <lb></lb>e nella supposizione dell&#039;equilibrio, P:R=HG:AB=AD:IG. “ Igitur <lb></lb>potentia P ad resistentiam R se habet ut GH velocitas ipsius R ad AB ve­<lb></lb>locitatem ipsius P, seu ut amplitudo circularis AD ad amplitudinem cir­<lb></lb>culi IG ” (ibi). </s></p><p type="main">

<s>Dal medesimo principio è pure conclusa la seguente proposizione LIX, <lb></lb>che dà le leggi meccaniche tra la potenza e la resistenza nelle utilissime ap­<lb></lb>plicazioni del Torchio idraulico, a cui rassomigliasi dal Borelli il cuore nella <lb></lb>sua potenza e nella resistenza oppostagli dal sangue: “ Si intra fistulam <lb></lb>aquam continentem, a maiori tubo, nova aqua embolo impellatur, vis embo­<lb></lb>lum impellens ad resistentiam aqueae molis praeesistentis et de novo im­<lb></lb>pulsae intra fistulam, eamdem proportionem habebit quam amplitudo orificii <lb></lb>tubi ad amplitudinem orificii fistulae ” (ibi, pag. </s>

<s>122). </s></p><p type="main">

<s>Come fu il primo e il più studioso il Borelli d&#039;applicare in queste, e <lb></lb>in altre simili proposizioni, le leggi idrauliche ai moti del cuore, così fu <lb></lb>primo ad applicarle ai moti del sangue, parendogli che, dovendo anch&#039;esso <lb></lb>partecipare della natura di tutti i fluidi, non potesse sottrarsi dalle leggi ge­<lb></lb>nerali dimostrate già dal Castelli. </s></p><p type="main">

<s>È la fondamentale di queste leggi che le quantità son proporzionali alla <lb></lb>velocità moltiplicata per la sezione, d&#039;onde ne segue che, duplicandosi la <lb></lb>quantità e rimanendo la sezione costante, la velocità è pure anch&#039;essa ne­<lb></lb>cessariamente duplicata. </s>

<s>Applica questa legge idraulica il Borelli al moto del <lb></lb>sangue nelle vene, per le valvole apposte alle quali sospingendosi innanzi, <lb></lb>nella medesima compressione e nel medesimo tempo, una doppia quantità <lb></lb>dello stesso sangue, convien che si cacci in corso doppiamente veloce. </s>

<s>“ Cum­<lb></lb>que ab eadem compressione sanguis qui continebatur in spatiis EDG, FCG <lb></lb>(fig. </s>

<s>4 preced.) propellatur ultra DC, igitur dupla moles sanguinis, eodem <lb></lb>tempore quo fit compressio, expellitur per idipsum ostium DC. </s>

<s>Sed quando <lb></lb>dupla fluidi moles, eodem tempore, per idem orificium emittitur, excurrere <lb></lb>debet velocitate dupla, igitur, per machinam valvularum, compressiones ve­<lb></lb>narum duplo velociori motu sanguinem versus cor protrudunt, non fluxu <lb></lb>continuo, sed interpositis morulis et velocitatibus inaequalibus ” (ibi, pag. </s>

<s>83). </s></p><p type="main">

<s>Se le quantità stanno in ragion composta della velocità e della sezione, <pb xlink:href="020/01/1239.jpg" pagenum="114"></pb>conforme alla sopra detta legge fondamentale, ne segue che rimanendo le <lb></lb>sezioni uguali le quantità stanno in semplice ragione delle velocità, e ciò <lb></lb>vuol dire che da un vaso sgorga, in un medesimo tempo, tanto maggior <lb></lb>quantità di liquido quant&#039;è più veloce. </s>

<s>Or proponendosi il Borelli di enar­<lb></lb>rare i preclari effetti che si producono dalla velocità del circolo sanguigno <lb></lb>per far comprendere la gran quantità del sangue, con cui la Natura prov­<lb></lb>vede alla nutrizione dell&#039;animale, applica il corollario di quella legge delle <lb></lb>acque correnti. </s>

<s>“ In unaquaque cordis pulsatione grandis copia sanguinis a <lb></lb>subtilissimis arteriosis canaliculis effunditur et eiaculatur, quia eo maior <lb></lb>copia fluoris ab eisdem canalibus effluit, quanto velociori motu per eos mo­<lb></lb>vetur, ut B. </s>

<s>Castellus demonstravit, et proinde sanguis, ad instar pleni et <lb></lb>rapidissimi torrentis, intra spongiosas carnium et viscerum porositates im­<lb></lb>mittitur ” (ibi, pag. </s>

<s>85). </s></p><p type="main">

<s>Consegue altresì da quella sopra citata legge fondamentale delle quan­<lb></lb>tità in relazione colle velocità e colle sezioni, ch&#039;essendo le velocità o i tempi <lb></lb>uguali, le quantità tornano proporzionali alle semplici sezioni. </s>

<s>Trovò anche <lb></lb>questo corollario un&#039;applicazione ai moti animali, avendolo il Borelli pre­<lb></lb>messo come lemma alla proposizione CXCVII, nella quale vuol dimostrare <lb></lb>come la quantità del sangue, ch&#039;esce dalla vena splenica, è presso a poco <lb></lb>la quarta parte del fluido, che nel tempo di una intera circolazione viene <lb></lb>espulso dalla vena mesenterica. </s></p><p type="main">

<s>Il lemma dunque, che si premette dal Borelli in servigio di dimostrar <lb></lb>la citata proposizione, è così formulato: Da due fistole molli inegualmente <lb></lb><figure id="id.020.01.1239.1.jpg" xlink:href="020/01/1239/1.jpg"></figure></s></p><p type="caption">

<s>Figura 6.<lb></lb>ampie, ugualmente turgide, e dalla stessa potenza compresse, <lb></lb>fluiscono nello stesso tempo due moli ineguali, che hanno <lb></lb>fra loro la proporzione stessa degli orifizi. </s>

<s>E ciò appunto per <lb></lb>questa ragione: “ quia duae fistulae humore plenae ab eadem <lb></lb>potentia, scilicet ab eadem vi impulsiva, eodemque tempore <lb></lb>comprimuntur, ergo eodem impetu et eadem velocitate ex­<lb></lb>primuntur, et exiliunt fluores ex orificiis AC, DF (fig. </s>

<s>6). <lb></lb>Sed moles fluidae, effusae eadem velocitate eodemque tem­<lb></lb>pore, eamdem proportionem habent quam orificia,.... ergo <lb></lb>moles fluidi egressa ex fistula AB, ad eam quae profluit ex <lb></lb>DE, se habet ut orificium AC ad DF ” (ibi, pag. </s>

<s>405). </s></p><p type="main">

<s>La nuova via aperta così dal celebratissimo Maestro in­<lb></lb>vitava a proseguirla alacremente i discepoli, uno de&#039;più stu­<lb></lb>diosi fra i quali fu, come sappiamo, il Bellini. </s>

<s>Gli esercizi <lb></lb>dell&#039;arte medica, fra&#039;quali era d&#039;uso frequente la flebotomia, facevangli fa­<lb></lb>cilmente risovvenir, fra gli zampilli del sangue, degli zampilli delle acque <lb></lb>da&#039;fori aperti ne&#039;vasi, e le emissioni sanguigne diligentemente raccolte e <lb></lb>ridotte a giusta misura, secondo l&#039;abito degli infermi e le condizioni della <lb></lb>malattia, potevano in questi casi direttamente condurre un Iatromatematico <lb></lb>dell&#039;indole del Nostro a fare, intorno al sangue raccolto ne&#039;salassi, l&#039;ufficio <lb></lb>sperimentale dell&#039;Idrometra. </s></p><pb xlink:href="020/01/1240.jpg" pagenum="115"></pb><p type="main">

<s>La quantità del sangue emesso, ripensava il Bellini tutto piena la mente <lb></lb>di quelle applicazioni delle leggi idrauliche alla Fisiologia, che aveva appresa <lb></lb>dalla viva voce del Borelli; dipende dalla velocità moltiplicata per la sezione. </s>

<s>E <lb></lb>perchè questa, aperta che sia la vena, riman nel tempo del flusso sempre la <lb></lb>stessa, è dunque la velocità unica regolatrice della quantità di quel flusso. </s>

<s>Or <lb></lb>egli considerava come non era possibile che tutto il sangue uscito in un dato <lb></lb>tempo dalla ferita, fosse uguale a quello, che sarebbe passato in quel mede­<lb></lb>simo tempo per la vena chiusa, procedendo a diritto per la sua via: la quan­<lb></lb>tità gli pareva dover esser maggiore, e ciò necessariamente importava una <lb></lb>maggior velocità nel sangue stesso, che d&#039;ogni parte affluisce al varco aperto. </s></p><p type="main">

<s>Forse il rassomigliar che faceva il Borelli il circolo sanguigno a un <lb></lb>pieno e rapidissimo torrente dette occasione al Bellini di considerar ciò che <lb></lb>segue, rompendosi l&#039;argine ai fiumi, e di rassomigliarne a quelli della rotta <lb></lb>vena gli effetti. </s>

<s>In qualunque modo il Guglielmini, annoverando per primo <lb></lb>tra quegli effetti <emph type="italics"></emph>Lo scemarsi repentino della piena nelle parti superiori <lb></lb>del fiume,<emph.end type="italics"></emph.end> dop&#039;aver detto esser la ragion di ciò che le ripe, facendo resi­<lb></lb>stenza, indugiano il corso dell&#039;acqua, la quale perciò tolti quegl&#039;impedimenti <lb></lb>si rende anche nelle parti superiori necessariamente più veloce, così sog­<lb></lb>giunge: “ Effetto simile è stato dimostrato dal signor Lorenzo Bellini, in­<lb></lb>signe medico e matematico fiorentino e famosissimo per le sue opere rice­<lb></lb>vute dal mondo con tanto applauso, dovere succedere nella cavata del san­<lb></lb>gue dalle vene e dalle arterie degli animali, avendo una grande analogia il <lb></lb>corso del sangue per li proprii vasi a quello dell&#039;acque per gli alvei dei <lb></lb>fiumi, ed equivalendo l&#039;apertura della vena alla rottura di un argine, siccome <lb></lb>con questo simbolizzano le tuniche de&#039;vasi predetti ” (Della natura de&#039;fiumi, <lb></lb>Vol. </s>

<s>II, Milano 1821, pag. </s>

<s>172). </s></p><p type="main">

<s>Fra le opere del Bellini, ricevute dal mondo con tanto applauso, prin­<lb></lb>cipale si è quella che intitolò <emph type="italics"></emph>De sanguinis missione,<emph.end type="italics"></emph.end> distinta in proposi­<lb></lb>zioni, per conformarsi anche nelle parti accessorie ai metodi dimostrativi del <lb></lb>Borelli. </s>

<s>È nella prima di quelle proposizioni, che si dimostra il velocitarsi <lb></lb>del circolo per l&#039;aperta vena, concludendo la dimostrazione dal principio che <lb></lb>la quantità del sangue fluente dalla ferita è maggiore di quella che passe­<lb></lb>rebbe in egual tempo addiritto per la vena illesa, e per l&#039;arteria contigua. <lb></lb></s>

<s>“ A quacumque vena mittatur sanguis, per totum spatium temporis quo <lb></lb>mittitur, quantitates eius singulis contractionibus cordis influens in truncum <lb></lb>arteriae, cuius aliquis ramus continuus sit venae a qua mittitur sanguis; <lb></lb>maiorem proportionem habet ad quantitatem eodem tempore influentem in <lb></lb>truncum alterum, quam quantitates eodem tempore in eosdem truncos homo­<lb></lb>loge influentes, quando nihil sanguinis mittitur, sed totus fluit per canales <lb></lb>suos ” (Opera omnia, Pars I, Venetiis 1708, pag. </s>

<s>64). </s></p><p type="main">

<s>La maggior quantità del sangue emesso, rispetto a quello che proce­<lb></lb>derebbe per i suoi canali addiritto, non poteva, secondo la legge del Ca­<lb></lb>stelli, dipendere da altro che da un incremento della velocità, e perciò bi­<lb></lb>sognava ritrovar la causa di questo incremento, perchè venisse dimostrata <pb xlink:href="020/01/1241.jpg" pagenum="116"></pb>la verità della proposizione. </s>

<s>Considerava a tale effetto il Bellini che le tu­<lb></lb>niche venose fanno resistenza al sangue, no nei soli punti adiacenti, ma in <lb></lb>quelli altresì che li precedono: e no nelle vene sole, ma e nelle diramazioni <lb></lb>delle arterie influenti, nelle quali il sangue fa uno sforzo continuo sul san­<lb></lb>gue che precede; sforzo ch&#039;esce poi in azione di libero moto, quando aperta <lb></lb>la vena le resistenze opposte sono in parte diminuite. </s></p><p type="main">

<s>“ Quoniam sanguis fluens per arterias mittitur in sanguinem fluentem <lb></lb>per venas, et sanguis per venas praecedens impedimento est sanguini per <lb></lb>easdem succedenti; amoto igitur impedimento succedenti per venas sanguini, <lb></lb>idem sanguis continue per venas succedens fluet velocius, adeoque sanguis <lb></lb>per arterias in ipsum nitens, quoties impedimentum illud remotum erit, mi­<lb></lb>norem resistentiam a sanguine venarum patietur. </s>

<s>Sed facto emissario in qua­<lb></lb>libet vena, ita ut sanguis possit effluere et reipsa effluat, fit, ut sanguini <lb></lb>per venas succedenti nihil obsistat sanguis per easdem praecedens, cum liber <lb></lb>illi pateat effluxus in nihil repugnantem aera; facto igitur in qualibet vena <lb></lb>emissario, sanguis per arterias in venis continuas fluens et in earumdem <lb></lb>sanguinem nitens, minori resistentiae occurret. </s>

<s>Est autem sanguis per omnes <lb></lb>arterias sibi ipsi continuus, et succedens per ipsas nititur in praecedentem. </s>

<s><lb></lb>Igitur nisus sanguinis fluentis per arterias omnes continuus est in sangui­<lb></lb>nem fluentem per venas quaslibet, adeoque, facto emissario in vena quali­<lb></lb>bet, ita ut sanguis effluat, minuetur resistentia, non solum sanguini per <lb></lb>summas arterias venae illi continuas, sed per earumdem ramos maiusculos, <lb></lb>maiores, ac demum truncum ad usque cor ” (ibi, pag. </s>

<s>65). </s></p><p type="main">

<s>Ritrovarono queste applicazioni iatromatematiche del Bellini tanto ap­<lb></lb>plauso, segnatamente appresso i medici, che altri valorosi si sentirono ani­<lb></lb>mati a proseguire per que&#039;sentieri, per i quali il Borelli aveva con tanta <lb></lb>gloria avviata la sua nuova scuola. </s>

<s>Il Guglielmini, infin da quando pubbli­<lb></lb>cava la sua prima opera idraulica <emph type="italics"></emph>Aquarum fluentium mensura,<emph.end type="italics"></emph.end> promet­<lb></lb>teva ai lettori che avrebbe trasportate quelle sue considerazioni “ al moto <lb></lb>sì naturale come violento de&#039;fluidi tutti, oltre i confini delle Matematiche, <lb></lb>sino cioè alli studi più ascosi dell&#039;arte medica ” (Prefazione al Trattato nella <lb></lb>raccolta degli Idraulici, T. I, Firenze 1765, pag. </s>

<s>317). E nel trattato <emph type="italics"></emph>Della <lb></lb>natura de&#039;fiumi,<emph.end type="italics"></emph.end> dopo aver commemorate le somiglianze che riscontrò il <lb></lb>Bellini tra l&#039;accelerarsi della piena, rotto l&#039;argine, e l&#039;accelerarsi del san­<lb></lb>gue aperta la vena ” il che ho voluto, soggiunge, in questo luogo motivare, <lb></lb>acciò paia non essere così disparate le dottrine idrostatiche dalle mediche, <lb></lb>anco pratiche, come altri per avventura si crede, anzi essere affatto neces­<lb></lb>sarie le prime a chi vuol bene intendere in molte parti le seconde, come <lb></lb>spero di far vedere a suo tempo, applicando molte notizie desunte da que­<lb></lb>sto Trattato alla Fisiologia medica ed alla dottrina de&#039;mali particolari ” <lb></lb>(Tomo cit., pag. </s>

<s>172, 73). Nel 1701 infatti, mantenendo le sue promesse, <lb></lb>pubblicava il trattato <emph type="italics"></emph>De sanguinis natura,<emph.end type="italics"></emph.end> dove alcune delle leggi princi­<lb></lb>pali che governano il moto delle acque sono applicate, come rilevasi dagli <lb></lb>stessi luoghi da noi dianzi riferiti, al moto del sangue. </s></p><pb xlink:href="020/01/1242.jpg" pagenum="117"></pb><p type="main">

<s>Della splendida triade iatromatematica composta del Borelli, del Bellini <lb></lb>e del Guglielmini, si gloriava compiacente la scienza italiana, quando la cri­<lb></lb>tica inesorabile venne a turbare la tranquillità di quella compiacenza. </s>

<s>Pie­<lb></lb>ranton Michelotti, che fu di tanta autorità in quella stessa Scuola, ammirava <lb></lb>gli egregi studi di que&#039;tre, ch&#039;ei chiama <emph type="italics"></emph>Italorum medicorum principes,<emph.end type="italics"></emph.end><lb></lb>ma poi soggiunge: “ Verum plura ab ipsis praetermissa, quaedam non ani­<lb></lb>madversa, quaedam imperfecte tractata, et nonnulla non rite fuisse deter­<lb></lb>minata quilibet experiri poterit, cui fuerit in animo motiones fluidorum <lb></lb>omnium per canales animantium haudquaquam aequabiles, sed mille modis <lb></lb>variantes, geometrico mechanica methodo pervestigare ” (De separat. </s>

<s>liquid. </s>

<s><lb></lb>cit., pag. </s>

<s>82). E concludeva che, a voler trattare e per arte di computo <lb></lb>svolgere il difficile tema “ desunt experimenta, sive sufficientia data ” (ibi, <lb></lb>pag. </s>

<s>82). </s></p><p type="main">

<s>La critica del Michelotti non riguardava dunque altro che la scienza in <lb></lb>sè stessa, o nel metodo geometrico meccanico delle sue speculazioni. </s>

<s>Ma per­<lb></lb>chè quelle speculazioni erano applicabili, e da alcuni applicate di fatto agli <lb></lb>usi medici, al dubbio degli errori innocenti della mente s&#039;aggiungeva il pe­<lb></lb>ricolo dei danni alla salute e alla vita degli uomini. </s>

<s>Nel Filosofo insomma <lb></lb>era zelo del vero, mentre nel Medico era un coscienzioso dovere di esami­<lb></lb>nare le novelle dottrine, e specialmente quelle che proponeva il Bellini. </s></p><p type="main">

<s>Se infatti è vero che si acceleri nel salasso il corso del sangue, anche <lb></lb>per le arterie corrispondenti alla vena incisa, posto che le malattie infiamma­<lb></lb>torie, alle quali riducevansi la frenesia e la pleurisia, sien malattie delle ar­<lb></lb>terie, avrebbe avuto buon fondamento la speranza del Boerhaave e de&#039;se­<lb></lb>guaci di lui, che aprendosi una vena si provocasse il corso del sangue <lb></lb>ristagnante nella parte infiammata, e così disostruendosi le estremità arte­<lb></lb>riose restituire al sangue stesso la sua fluidità primitiva. </s>

<s>Ma se il teorema <lb></lb>belliniano è falso, la cura del Boerhaave si comprendeva con facilità che sa­<lb></lb>rebbe per riuscir disutile, e anzi sempre più o meno dannosa. </s></p><p type="main">

<s>L&#039;occasione d&#039;esaminar di proposito quanto fosse di vero nelle applau­<lb></lb>ditissime dottrine del Bellini venne quando il Silva, in Parigi, sul fonda­<lb></lb>mento di quelle stesse dottrine, pubblicava il suo trattato <emph type="italics"></emph>De la saignée.<emph.end type="italics"></emph.end> Il <lb></lb>Quesnay, e una più grande autorità fisiologica e medica, il Senac, negarono <lb></lb>assolutamente che il sangue dalla vena incisa fluisca più veloce, d&#039;onde av­<lb></lb>venne un gran dissidio fra i pratici della Facoltà medica parigina. </s></p><p type="main">

<s>In questo tempo l&#039;Haller attendeva nella stessa Parigi agli esercizi del­<lb></lb>l&#039;Anatomia, e di tanta importanza gli parve, che si dette studiosamente a <lb></lb>cercare il modo di decidere la questione. </s>

<s>Conveniva bene col Michelotti che <lb></lb>non si sarebbe potuti giungere a quella così desiderata decisione finale, altro <lb></lb>che per via delle esperienze, ma come penetrare addentro a misurare il <lb></lb>moto del sangue, per le vie gelosamente chiuse dell&#039;animale vivo? </s>

<s>Si ri­<lb></lb>sovvenne allora che il Malpighi e il Lecuwenhoeck avevano pur veduto il <lb></lb>circolo del sangue attraverso ai vasi trasparenti delle rane e dei pesci, e <lb></lb>incorò di lì una viva speranza che i globuli del sangue, in così fatti ani-<pb xlink:href="020/01/1243.jpg" pagenum="118"></pb>mali, avrebbero potuto far l&#039;ufficio e prestare i servigi dell&#039;Idrometro a <lb></lb>galleggiante. </s></p><p type="main">

<s>Di qui ebbero occasione le due Memorie <emph type="italics"></emph>Sur le mouvement du sang,<emph.end type="italics"></emph.end><lb></lb>che risvegliarono nello Spallanzani il desiderio di nuove osservazioni, e fe­<lb></lb>cero sì che si arricchisse di nuove e importantissime scoperte la scienza ita­<lb></lb>liana. </s>

<s>L&#039;Haller dunque sui vasi sanguiferi delle rane, e lo Spallanzani sui <lb></lb>vasi delle salamandre, verificarono con maraviglia universale in che il moto <lb></lb>del sangue sia conforme, in che difforme dalle leggi idrauliche, d&#039;onde si <lb></lb>venne per l&#039;uno a pronunziare e per l&#039;altro a confermare questa sentenza, <lb></lb>che servì di canone utilissimo alla nuova Fisiologia: “ Non ideo repudian­<lb></lb>das leges crediderim, quibus extra corpus animale vires motrices regun­<lb></lb>tur: id volo nunquam transferendas ad nostras animati corporis machinas, <lb></lb>nisi experimentum consenserit ” (Haller, Elem. </s>

<s>Physiol. </s>

<s>Praefatio, Lausan­<lb></lb>nae 1757, pag. </s>

<s>VI). </s></p><p type="main">

<s>Procedendo dunque per questa sicura via sperimentale, dopo aver l&#039;Hal­<lb></lb>ler riferiti i nomi illustri di quei Francesi, che negarono fede al teorema <lb></lb>belliniano, “ Pour moi j&#039;ai vû très souvent, et aussi souvent que je l&#039;ai <lb></lb>voulu voir, puisque le resultat a toujours êtê le même, j&#039;ai vû, disje, que <lb></lb>quelle que fut la directions du sang dans la veine que j&#039;ouvrois, soit qu&#039;il <lb></lb>allat naturellement du coté du coeur, soit que par un mouvement retro­<lb></lb>grade il fut porté vers les intestins, soit qu&#039;il se balançat, ou qu&#039;il fut en <lb></lb>repos, soit enfin qu&#039;on eut arraché le coeur, ou liè, ou coupé les aortes, le <lb></lb>sang dans tous ces cas sortoit de la veine coupée, avec une vitesse beau­<lb></lb>coup plus grande que celle qu&#039;il a dans aucune veine entiere, et même plus <lb></lb>vite qu&#039;il ne par court les arteres ” (Lausanne 1756, pag. </s>

<s>99, 100). </s></p><p type="main">

<s>Questa verificazione però, che l&#039;Haller dice in nota essere stata fatta <lb></lb>pure dall&#039;Heide, riguardava più la scienza astratta che la pratica medica, <lb></lb>per la quale sarebbe stato assai più importante il sapere se, come affermava <lb></lb>il Bellini, l&#039;aumento della velocità del sangue fluente dalla vena provocasse <lb></lb>una corrispondente velocità nelle arterie. </s>

<s>Ma questa seconda verificazione, <lb></lb>dice lo stesso Haller, è più difficile della prima a farsi per via dell&#039;espe­<lb></lb>rienze. </s>

<s>“ Leur resultat n&#039;a pas toujours été le même, et celle que j&#039;ai faits <lb></lb>sur moi même, ne repondit point à mon attente ” (ivi, pag. </s>

<s>106). </s></p><p type="main">

<s>Più felice dell&#039;Haller fu il nostro Spallanzani, il quale, sperimentando <lb></lb>sopra le salamandre piuttosto che sopra le rane, verificò del Teorema bel­<lb></lb>liniano no quella parte sola che riguardava la scienza astratta, ma quella al­<lb></lb>tresì, che più importava alla pratica medica. </s>

<s>Nella Dissertazione quarta in­<lb></lb>fatti <emph type="italics"></emph>Sui fenomeni della circolazione,<emph.end type="italics"></emph.end> esponendo i resultati dell&#039;esperienze <lb></lb>fatte e descritte nella Dissertazion precedente, dice che vien per essi con­<lb></lb>fermata una delle più importanti verità mediche, ed è questa: “ Aperta una <lb></lb>vena, il sangue di lei, quello delle vene vicine e quello dell&#039;arteria che loro <lb></lb>somministra il sangue, acquista un novello grado di velocità, e si precipita <lb></lb>alla ferita. </s>

<s>Cotal verità, che dopo di essere stata scoperta dal celebre Bellini, <lb></lb>ha avuto tanti oppositori, è stata infine comprovata dal fatto, mercè le spe-<pb xlink:href="020/01/1244.jpg" pagenum="119"></pb>rienze del De Heide, ma assai più dall&#039;Haller nel mesenterio delle rane. </s>

<s><lb></lb>Imperocchè ferita una delle sue vene, la trasparenza delle membrane gli ha <lb></lb>conceduto di vedere quali cangiamenti nascono allora nella circolazione, ed <lb></lb>ha trovato essere que&#039;dessi, ch&#039;erano stati asseriti dal prelodato Bellini. </s>

<s><lb></lb>Quanto dunque ha scoperto l&#039;Haller nel mesenterio delle rane ho avuto il <lb></lb>piacere di vederlo confermato ne&#039;vasi delle salamandre, e quel che è più <lb></lb>ne&#039;vasi degli animali caldi, cioè del pulcino ” (Opere, Vol. </s>

<s>IV, Milano 1826, <lb></lb>pag. </s>

<s>418). </s></p><p type="main">

<s>Da queste osservazioni sopra gli animali caldi risulta principalmente <lb></lb>l&#039;eccellenza del Nostro sopra il fisiologo di Berna, la quale eccellenza in tal <lb></lb>proposito si misura non solamente dall&#039;aver veduto lo Spallanzani veloci­<lb></lb>tarsi il sangue anche nell&#039;arteria contigua alla vena incisa, ciò che l&#039;Haller <lb></lb>confessò di non aver potuto sperimentare, ma dall&#039;aver ne&#039;varii casi parti­<lb></lb>colari verificato se alle leggi idrauliche si conformava il moto del sangue, <lb></lb>secondo le speculazioni de&#039;nostri Italiani. </s></p><p type="main">

<s>Il Borelli tenne, come vedemmo, per cosa certa che il sangue, restrin­<lb></lb>gendosi la vena e riducendo alla metà la sua sezione, vi corresse doppiamente <lb></lb>veloce, a somiglianza di quel che vedesi fare all&#039;acqua corrente ne&#039;canali. </s>

<s><lb></lb>Lo Spallanzani, nella sua Dissertazione <emph type="italics"></emph>Dell&#039;azione del cuore ne&#039;vasi san­<lb></lb>guigni,<emph.end type="italics"></emph.end> verificò il fatto in questo modo. </s>

<s>“ Avendo, egli stesso dice, un giorno <lb></lb>sott&#039;occhio una vena del mesenterio formata di due rami, trovai esser que­<lb></lb>sta, non so per qual vizio, ristretta talmente in un sito, che quantunque <lb></lb>prima e dopo il cilindro del sangue fosse assai grosso, pure ivi non ne potea <lb></lb>passare che un filetto alla volta. </s>

<s>In siffatta angustia il suo acceleramento si <lb></lb>facea tale, che appena l&#039;occhio vi potea tener dietro. </s>

<s>All&#039;opposito, passato <lb></lb>lo stretto, il sangue riacquistava il primiero movimento ” (ivi, pag. </s>

<s>127). </s></p><p type="main">

<s>Questo principio idraulico delle velocità reciprocamente proporzionali <lb></lb>alle sezioni ebbe un&#039;altra applicazione ai moti e alle funzioni del sangue, di <lb></lb>non lieve importanza nella storia della Fisiologia. </s>

<s>Guglielmo Cole, ripen­<lb></lb>sando alle funzioni della nutrizione, la quale non è altro secondo lui “ nisi <lb></lb>congruae cuiusdam substantiae partibus in deperditae locum appositio ” in­<lb></lb>cominciò a dubitare di quel che si credeva comunemente, che cioè la stessa <lb></lb>quantità di sangue si contenesse ne&#039;grossi tronchi e nelle ultime dirama­<lb></lb>zioni arteriose, parendogli che non dovesse esser questa sufficiente a nutrir <lb></lb>le parti, e non avere il sangue stesso il tempo necessario per trattenersi a <lb></lb>dispensare a ciascuna il suo vitale alimento. </s></p><p type="main">

<s>Benchè fosse il Cole un inglese, egli ebbe pure molta familiarità con <lb></lb>la scienza italiana, e trovò modo a risolvere i dubbi nelle dottrine apprese <lb></lb>dal trattato <emph type="italics"></emph>Della misura delle acque correnti.<emph.end type="italics"></emph.end> Ivi, al corollario XI, scopre <lb></lb>il Castelli l&#039;errore, in che era incorso Giovanni Fontana, il quale, avendo <lb></lb>fatto misurar tutti i fossi e i fiumi che mettevano al Tevere, e avendo tro­<lb></lb>vato che la somma delle loro sezioni era doppia di quella del Tevere stesso <lb></lb>al ponte Quattrocapi, ne aveva concluso che si dovesse render doppiamente <lb></lb>largo l&#039;alveo del fiume, perchè potesse in ogni caso ricever la piena. </s>

<s>Il Ca-<pb xlink:href="020/01/1245.jpg" pagenum="120"></pb>stelli notava che l&#039;errore dell&#039;Architetto romano consisteva nel credere che <lb></lb>le misure dell&#039;acque, prese negli alvei de&#039;fossi e de&#039;fiumi, dovessero man­<lb></lb>tenersi le medesime nel Tevere, mentre è il vero che “ se l&#039;aeque ridotte <lb></lb>nel Tevere crescono di velocità, scemano di misura ” (Bologna 1660, pag. </s>

<s>16). </s></p><p type="main">

<s>Ora il Cole, applicando queste dottrine al moto del sangue nelle arte­<lb></lb>rie, ne concludeva che la somma delle sezioni de&#039;rami dovess&#039;esser mag­<lb></lb>giore della sezione del tronco principale. </s>

<s>Congetturava inoltre che avesse <lb></lb>provveduto, con sì fatto artificio, la sapiente Natura ad aumentar la misura <lb></lb>del sangue ne&#039;vasi capillari, e a rattemperare i primi impeti ricevuti dal <lb></lb>cuore, per modo da poter con pace dispensare alle parti il necessario ali­<lb></lb>mento. </s>

<s>“ Isthaec vero vitari possunt incommoda supposito quod vasorum <lb></lb>istorum capillaria, proportione ad truncum aucta, fabricavit Natura: satis <lb></lb>enim placide sic movebitur sanguis ut adhibita singulis partibus esca sup­<lb></lb>peditetur ” (De secretione anim., Oxon. </s>

<s>1674, pag. </s>

<s>101). </s></p><p type="main">

<s>Il supposto del Cole era dunque fondato sopra ciò che sapeva essere <lb></lb>stato osservato sui fiumi, e il Guglielmini, che aveva ridotte quelle osserva­<lb></lb>zioni a regola generale, sentenziando che “ se si misureranno le larghezze <lb></lb>di tutti i fiumi, che unendosi formano un fiume maggiore, si troverà infal­<lb></lb>libilmente che esse insieme unite supereranno quella del fiume maggiore ” <lb></lb>(Della natura de&#039;fiumi cit., Vol. </s>

<s>II, pag. </s>

<s>120) non dubitò, trasportando la <lb></lb>legge idraulca al moto del sangue, di approvare per vere le dottrine del Fi­<lb></lb>siologo inglese. </s>

<s>È anzi da notare, a questo proposito, come sembrasse allo <lb></lb>stesso Guglielmini tanto più certo il fatto del diminuirsi la velocità, come <lb></lb>più il sangue si dilunga dal cuore, che da ciò conclude dover essere la se­<lb></lb>zion dell&#039;Aorta minore delle sezioni dei rami arteriosi tutte sommate in­<lb></lb>sieme. </s>

<s>“ Cum eaeteri violenti motus, quo magis a movente elongantur, eo <lb></lb>semper languidiores fiant,.... sequitur velocitatem sanguinis semper debi­<lb></lb>liorem evadere, quo sanguis longius a corde spatium emensus est, unde in <lb></lb>arteriarum finibus languidissimus erit sanguinis circulantis motus. </s>

<s>Cumque, <lb></lb>ex Hydrometricis, fluentium liquorum sectiones debeant velocitatibus esse <lb></lb>reciprocae, oritur, ut quam rationem habet velocitas versus cor ad veloci­<lb></lb>tatem in extremis arteriarum, eamdem habere debeant omnia oscula extre­<lb></lb>marum arteriarum, simul sumpta, ad sectionem Aortae prope cor. </s>

<s>Ideoque <lb></lb>si, ut ostensum est, velocitas sanguinis in finibus arteriarum longe minor <lb></lb>est velocitate eiusdem in Aorta prope cor, necessarìo omnia oscula arteria­<lb></lb>rum simul sumpta multo ampliora erunt orificio, aut sectione Aortae prope <lb></lb>cor, ut optime ex aliis rationibus colligit Guglielmus Cole, in libro <emph type="italics"></emph>De se­<lb></lb>cretione animali ”<emph.end type="italics"></emph.end> (De sang. </s>

<s>nat. </s>

<s>cit., pag. </s>

<s>19). </s></p><p type="main">

<s>Questo processo dimostrativo del Guglielmini rende ragione dell&#039;ordine, <lb></lb>che presero gli studi sperimentali de&#039;Fisiologi posteriori, i quali, tenendosi <lb></lb>certi che il sangue si velociti come tutti gli altri fluidi in ragion reciproca <lb></lb>delle sezioni, si rivolsero tutti a ricercar s&#039;era vero, e in qual precisa pro­<lb></lb>porzione aumentassero le luci de&#039;rami arteriosi, rispetto a quella della grande <lb></lb>Aorta. </s>

<s>Il Keill, prendendo a fondamento delle sue esperienze e de&#039;suoi cal-<pb xlink:href="020/01/1246.jpg" pagenum="121"></pb>coli i vasi dello scheletro, da Guglielmo Cowper ripieni di cera, trovò, come <lb></lb>lasciò scritto nel IV de&#039;suoi <emph type="italics"></emph>Tentamina<emph.end type="italics"></emph.end> “ arteriae cuiusvis ramos simul <lb></lb>sumptos ipsa arteria maiores esse ” (Lucae 1756, pag. </s>

<s>90). Quanto alle pro­<lb></lb>porzioni di questa maggioranza “ Aortae ratio, egli scrive, ad ramos trunco <lb></lb>suo immediate propagatos, est ut 100,000 ad 120,740, et quasi Naturae pro­<lb></lb>posito in bilis secretione haud sufficeret haec ratio, arteriam mesentericam <lb></lb>multo magis superant sui rami. </s>

<s>Huius arteriae medium Mesenterium tran­<lb></lb>seuntis, et unum et viginti ramos emittentis talis est forma, interque trun­<lb></lb>cum et ramos sequentes rationes obtinere deprehendi ” (ibi). E dopo aver <lb></lb>qui ordinata una tavoletta numerica “ Ex his rationibus palet, egli sog­<lb></lb>giunge, ramorum summam arteriae mesentericae truncum plus duplo axce­<lb></lb>dere, adeoque in his suae velocitatis dimidium amittit sanguis ” (ibi, pag. </s>

<s>100). </s></p><p type="main">

<s>Che se questa è la maggior diminuzione trovata, par che s&#039;ingannas­<lb></lb>sero il Cole e il Guglielmini a credere che il sangue nelle estremità arte­<lb></lb>riose <emph type="italics"></emph>languidissimus erit.<emph.end type="italics"></emph.end> L&#039;Hales poi tenne altra via, e iniettando nelle <lb></lb>arterie di un cadavere l&#039;acqua, la quale si vedeva nelle diramazioni perdere <lb></lb>una notabile parte della sua prima velocità, ne congetturava che maggiore <lb></lb>dovess&#039;essere quella perdita subita dal sangue. </s>

<s>“ Quindi vediamo, così con­<lb></lb>clude dalle sue esperienze intorno alle arterie de&#039;muscoli, quanto la velo­<lb></lb>cità dell&#039;acqua si scema, quando questa dal tronco di un&#039;arteria grande passa <lb></lb>a scorrere nelle sue ramificazioni di diverso ordine, nonostante che la somma <lb></lb>delle sezioni di questi rami sia molto maggiore delle sezioni del loro tronco. </s>

<s><lb></lb>La velocità del sangue dee dunque in tal passaggio maggiormente scemarsi, <lb></lb>perchè questo fluido è molto più dell&#039;acqua grosso e viscoso, ma dee sopra <lb></lb>tutto la velocità del sangue scemarsi, per cagione delle divisioni rettango­<lb></lb>lari delle arteriuzze, il cui diametro giunge ad essere di una sola mille se­<lb></lb>cen ventesima parte di pollice, di maniera che i globetti del sangue non pos­<lb></lb>sono passarvi più che uno per volta ” (Statica anim. </s>

<s>cit., pag. </s>

<s>62). </s></p><p type="main">

<s>Erano anche questi però sentieri tentati al buio, che si riconobbero <lb></lb>tortuosi, quando venne a sicura guida del passo la chiara luce degli occhi. </s>

<s><lb></lb>Nella dissertazion I De&#039;fenomeni della circolazione, lo Spallanzani scriveva <lb></lb>così sotto l&#039;esperienza XXI: “ In più salamandre sonomi singolarmente pre­<lb></lb>fisso di osservare se il sangue, in passando dai tronchi polmonari ai rami, <lb></lb>scema di velocità, ed ho trovato che no, qualunque siasi l&#039;angolo del ramo <lb></lb>col tronco ” (Opere cit., T. IV, pag. </s>

<s>175). E perchè lo Spallanzani stesso <lb></lb>ci faceva di sopra veder con gli occhi che anche il sangue, passando attra­<lb></lb>verso alle angustie di un vaso, velocità come l&#039;acqua il suo moto, si do­<lb></lb>vrebbe egli forse dubitare della verità del teorema del Cole, o della esattezza <lb></lb>dell&#039;esperienze e dei calcoli del Keill? </s>

<s>Ma è pure lo Spallanzani che di quella <lb></lb>verità e di quella esattezza ci assicura, nell&#039;appresso esperienza XXXIII, di­<lb></lb>cendo che anche nelle arterie mesenteriche delle salamandre osservate “ la <lb></lb>somma de&#039;lumi ne&#039;rami è sempre maggiore del lume del loro tronco ” (ivi, <lb></lb>pag. </s>

<s>184). </s></p><p type="main">

<s>Là dunque il sangue si conforma alle leggi idrauliche, e qui rompe <pb xlink:href="020/01/1247.jpg" pagenum="122"></pb>l&#039;ordine di quelle leggi. </s>

<s>Ma vi sono di ciò altri notabili esempii. </s>

<s>Il Gugliel­<lb></lb>mini fu primo a congetturare che il sangue, verso il centro della sezion di <lb></lb>un suo vaso, dovess&#039;essere più veloce che presso alla circonferenza, per <lb></lb>l&#039;esempio di ciò che si vede fare all&#039;acque correnti ne tubi, le pareti dei <lb></lb>quali indugiano al liquido il moto, per via degli attriti. </s>

<s>Or venne a confer­<lb></lb>mare una tal congettura l&#039;oculata osservazione dei fatti. </s>

<s>“ L&#039;ampiezza dei <lb></lb>vasi medii venosi del Mesenterio, scriveva lo Spallanzani nella citata disser­<lb></lb>tazione Dell&#039;azion del cuore ne&#039;vasi sanguigni, rivolgendo all&#039;Heller il suo <lb></lb>discorso; mi diede agio di esaminare un problema, che ha esercitata la vo­<lb></lb>stra industria. </s>

<s>Ei concerne il sapere se più rapido sia il movimento del san­<lb></lb>gue lungo l&#039;asse dei vasi, che ai lati, come trovato avete da alcune vostre <lb></lb>esperienze. </s>

<s>La colonna sanguigna, siccome assai ampia, poteva essere oppor­<lb></lb>tunissima al caso, ma qui pure è mestiere prendere il destro, in cui la Na­<lb></lb>tura parla all&#039;osservatore. </s>

<s>Essendo il circolo del sangue vigorosissimo, la <lb></lb>rapidità dei globetti è tale, che l&#039;occhio quantunque attentissimo non può <lb></lb>notare se siavi tal differenza. </s>

<s>Bisogna dunque aspettare che si calmi un poco <lb></lb>il suo impeto. </s>

<s>Allora veramente comincia a scoprirsi che il sangue dell&#039;asse <lb></lb>gode di un movimento un po&#039;poco maggiore che quello dei lati. </s>

<s>Ma per <lb></lb>averne il netto, con più sicurezza, fa d&#039;uopo aspettare che la sua cor­<lb></lb>rente divenga lentissima. </s>

<s>Allora non può cader dubbio su tal verità ” (ivi, <lb></lb>pag. </s>

<s>125, 26). </s></p><p type="main">

<s>Non essendovi dunque dubbio che l&#039;attrito del sangue contro le pareti <lb></lb>dei vasi ne indugia il moto, chi non giurerebbe che un uguale attrito, e <lb></lb>perciò un simile indugio, non dovess&#039;esser prodotto da quel così spesso e <lb></lb>repentino mutar via di quegli stessi vasi? </s>

<s>Raccogliendo la quantità di <lb></lb>acqua fluita da due uguali lunghezze e luci di tubi, ma l&#039;uno diritto e <lb></lb>l&#039;altro ritorto, si trova che in ugual tempo il lìquido erogato da questo è <lb></lb>minore dell&#039;altro, segno evidentissimo dell&#039;accresciuta resistenza, per l&#039;at­<lb></lb>trito maggiore incontrato in quelle sinuosità, per cui indugiasi maggior­<lb></lb>mente il moto. </s>

<s>Chi dunque s&#039;aspettava per cosa certa che così pure dovesse <lb></lb>avvenire, per la resistenza incontrata dal sangue nelle curvature de&#039;vasi, <lb></lb>sarebbe tolto d&#039;inganno da questa e da altre esperienze dello Spallanzani: <lb></lb>“ Un&#039;arteriuzza, egli dice delle salamandre osservate, veniva giù per il me­<lb></lb>senterio, facendo da undici in dodici curvature, ed un suo delicatissimo ramo <lb></lb>si stendeva alla regione degli intestini, su cui si diramava in altri più esili, <lb></lb>non conducenti ciascuno che una serie di globetti. </s>

<s>Questi ultimi ramicelli, <lb></lb>col ripiegar verso il mesenterio, generavano una vena, la quale diveniva un <lb></lb>ramo di una maggiore, che varcato il mesenterio, riconduceva il sangue al <lb></lb>cuore: le curvature nulla toglievano di velocità al sangue ” (ivi, pag. </s>

<s>193). <lb></lb>E più sotto dice risultare da un&#039;altra esperienza “ che ad onta di venticin­<lb></lb>que rivolgimenti, che fa una venina posta su di un budello, il sangue non <lb></lb>rallenta punto il moto ” (ivi, pag. </s>

<s>199). </s></p><p type="main">

<s>Parecchie altre bellissime osservazioni in proposito si potrebbero rac­<lb></lb>cogliere da quelle CLXVI, di che l&#039;insigne professor di Pavia arricchì la <pb xlink:href="020/01/1248.jpg" pagenum="123"></pb>sua prima dissertazione <emph type="italics"></emph>De&#039;fenomeni della circolazione osservata nel giro <lb></lb>universale dei vasi,<emph.end type="italics"></emph.end> ma giova piuttosto trattenersi a meditar sulla conclu­<lb></lb>sione ultima, ch&#039;egli trae sapientemente dai numerosi fatti sperimentali. </s></p><p type="main">

<s>“ Il resultato, egli dice, di questi e degli antecedenti fatti mette dun­<lb></lb>que in buon lume la teoria concernente il genuino andamento del sangue <lb></lb>dal principio delle arterie, fino alle loro estremità, la qual teoria, siccome <lb></lb>per l&#039;addietro mancante delle necessarie osservazioni, non è maraviglia se <lb></lb>è stata fino al presente poco più che congetturale, e conseguentemente sot­<lb></lb>toposta all&#039;incomodo delle dispute. </s>

<s>” </s></p><p type="main">

<s>“ Da questi fatti ridonda pure un altro vantaggio, cioè la conferma di <lb></lb>quanto saviamente stabilisce l&#039;Haller intorno al diffidare dell&#039;applicazione <lb></lb>de&#039;principii idraulici al corpo animale, mancandovi l&#039;appoggio dell&#039;espe­<lb></lb>rienza confermatrice. </s>

<s>E di vero se questi principii qui avessero dominato, <lb></lb>come non dovevano le menzionate cagioni ritardare considerabilissimamente <lb></lb>la corrente sanguigna, a quel modo che considerabilissimamente ritardano i <lb></lb>fluidi scorrenti per entro i canali? </s>

<s>Non è già che tali cagioni, anche nel <lb></lb>corpo animale, non producano, quanto è ad essa, ritardamento nel sangue, <lb></lb>ma dir bisogna che questo ritardamento venga sminuito da contrarie cagioni <lb></lb>residenti ne&#039;vasi animali, e concorrenti ad accrescere il moto del sangue, <lb></lb>qualunque poi esse sieno, le quali cagioni non hanno luogo ne&#039;canali idrau­<lb></lb>lici ” (ivi, pag. </s>

<s>288, 89). </s></p><p type="main">

<s>In queste ultime parole si compendia il più sapiente giudizio, che sia <lb></lb>stato mai dato dalla Scuola iatromatematica, la quale non si avvide che la <lb></lb>vita sublima, diciam così, nelle sue alture i fatti fisici da trasformarne bene <lb></lb>spesso la prima loro natura. </s>

<s>Giova inoltre considerare, nel nostro particolar <lb></lb>proposito, che il moto dell&#039;acqua ne&#039;tubi è naturale, ossia non soggetto che <lb></lb>alle sole leggi di gravità, mentre il moto del sangue è violento, governato <lb></lb>dalle forze vitali di quella macchina maravigliosa, che appellasi Cuore. </s>

<s>E <lb></lb>un&#039;ultima considerazione da farsi, e più importante di tutte, è questa: che <lb></lb>ne&#039;fatti fisici il soggetto dell&#039;esperienza è sempre una materia definita, o <lb></lb>acqua o aria, o insomma qualche altra trattabile sostanza, mentre ne&#039;fatti <lb></lb>fisiologici tante sottilissime essenze, da noi, per non saperne altro, chiamate <lb></lb>eteree, e dalle quali efficientemente dipendono le funzioni animali, sono sco­<lb></lb>nosciute, perchè affatto sfuggevoli ai nostri sensi, d&#039;onde hanno origine i <lb></lb>misteri della vita, e d&#039;onde è derivata la sentenza, che umilia l&#039;orgoglio <lb></lb>de&#039;Filosofi, ed è che que&#039;misteri all&#039;uomo non saranno mai rivelati. </s></p><pb xlink:href="020/01/1249.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del circolo del sangue<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del circolo polmonare. </s>

<s>— II. </s>

<s>Del circolo universale. </s>

<s>— III. </s>

<s>Delle esperienze e delle osservazioni, <lb></lb>che dimostrano la verità del circolo universale. </s>

<s>— IV. </s>

<s>Del sistema arveiano in Italia, e della <lb></lb>trasfusione del sangue. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi torna addietro sul capitolo precedente, e la varietà delle cose ivi <lb></lb>discorse comprende in uno sguardo solo, ritrova che s&#039;incominciava la sto­<lb></lb>ria de&#039;moti del cuore con Ippocrate, il quale rassomigliava il viscere a una <lb></lb>fonte perenne, da cui scaturiscono i fiumi del sangue a irrigare tutto il <lb></lb>corpo dell&#039;animale, e si terminava pure col rassomigliare lo stesso sangue <lb></lb>ai fiumi, che scorrono dentro i loro alvei ristretti, ora con qualche varietà, <lb></lb>e ora con perfetta uniformità di leggi. </s>

<s>Aristotile, anzi altri Scrittori più an­<lb></lb>tichi, e per i divini inspirati concetti ben assai più autorevoli, vedevano in <lb></lb>quel perpetuo correre de&#039;fiumi un perpetuo ricircolare di moti, essendo che <lb></lb>vanno le loro acque a scender nel mare, dove non hanno pace, ma solle­<lb></lb>vate in vapori per l&#039;aria, di lassù cadono, per andare a correre nuovamente <lb></lb>ne&#039;fiumi. </s></p><p type="main">

<s>Il simbolico pensier degli antichi venne a incarnarsi, tanti secoli dopo, <lb></lb>nella mente di Guglielmo Harvey, quando rappresentandosi per l&#039;acqua cor­<lb></lb>rente ne&#039;fiumi il sangue, che corre dentro le vene, e pel mare rappresen­<lb></lb>tandosi il cuore, da cui, al calor della vita, si solleva lo stesso sangue, per <lb></lb>tornar, come l&#039;acqua sollevata dal calor del sole, alla sua origine prima; <lb></lb>esultò d&#039;aver ritrovato che la Natura, nel gran mondo delle Meteore e nel <lb></lb>piccolo mondo animale, somigliava nell&#039;operare a sè stessa, e quel mede-<pb xlink:href="020/01/1250.jpg" pagenum="125"></pb>simo nome di <emph type="italics"></emph>circolo<emph.end type="italics"></emph.end> dagli antichi imposto al perpetuo moto dell&#039;acqua che <lb></lb>irriga la Terra, lo applicò al perpetuo moto del sangue, che irriga agli ani­<lb></lb>mali le membra. </s>

<s>“ Quem motum <emph type="italics"></emph>circularem<emph.end type="italics"></emph.end> eo pacto nominare liceat, quo <lb></lb>Aristoteles aerem et pluviam circularem superiorum motum aemulatus est. </s>

<s><lb></lb>Terra enim madida a Sole calefacta evaporat: vapores sursum elati conden­<lb></lb>sant: condensati in pluvias rursum descendunt, terram madefaciunt, et hoc <lb></lb>pacto sunt hic generationes et similiter tempestatum et metereorum ortus, <lb></lb>a Solis circulari motu accessu et recessu ” (De motu cordis cit., pag. </s>

<s>56). <lb></lb>E che altro è in fatti il Cuore, prosegue a dire l&#039;Harvey, se non che <emph type="italics"></emph>Sol <lb></lb>Microcosmi,<emph.end type="italics"></emph.end> per virtù del quale il sangue si muove, si perfeziona, e si pre­<lb></lb>serva dalla corruzione? </s>

<s>Ei dispensa i suoi benefizi a tutto il corpo, “ Lar <lb></lb>iste familiaris, fundamentum vitae, author omnium ” (ibi, pag. </s>

<s>57). </s></p><p type="main">

<s>Questa sublime comparazione arveiana, tra il cuore nel Microcosmo, e <lb></lb>il Sole nell&#039;immenso Mondo creato, dette occasione ad alcuni di rassomi­<lb></lb>gliar piuttosto il circolo del sangue al circolo de&#039;Pianeti, e di attribuire al­<lb></lb>l&#039;Harvey stesso in promuovere la scienza un merito non punto inferiore a <lb></lb>quello, che s&#039;attribuiva al Copernico. </s>

<s>È infatti cosa degna della considera­<lb></lb>zion del Filosofo la mirabile analogia, che passa tra l&#039;ordine de&#039;moti car­<lb></lb>diaci, e l&#039;ordine dei moti celesti, non che tra i processi della mente del­<lb></lb>l&#039;uomo in investigar le ragioni degli uni e degli altri. </s>

<s>Tre sono i circoli <lb></lb>del sistema solare: quello de&#039;due pianeti inferiori, quello di tutto insieme <lb></lb>l&#039;ordine planetario, quello del Sole in sè stesso, ai quali tre circoli corri­<lb></lb>spondono nel sistema della vita animale il circolo polmonare, il circolo nel <lb></lb>giro universale dei vasi, e finalmente il circolo coronario. </s>

<s>Come della circo­<lb></lb>lazione de&#039;due Pianeti inferiori s&#039;ebbero dagli orti e dagli occasi i primi <lb></lb>indizii, così del circolo polmonare, dall&#039;andar della vena arteriosa e dal tor­<lb></lb>nar al cuore dell&#039;arteria venosa, s&#039;ebbero le prime persuasioni. </s>

<s>Gli Astro­<lb></lb>nomi egiziani, col loro sistema introdotto in Italia da Marziano Capella e <lb></lb>divulgato dall&#039;Alighieri, mossero i primi passi per quella via, per la quale <lb></lb>il Copernico avrebbe fatto si gran progresso, come Galeno e il Colombo e <lb></lb>il Cesalpino iniziarono la scoperta, alla quale avrebbe dato glorioso compi­<lb></lb>mento l&#039;Arveio. </s>

<s>Ultimo a rivelarsi, dopo il circolo universale de&#039;Pianeti, fu <lb></lb>il circolo del Sole in sè stesso, come, dopo il circolo del sangue nel giro <lb></lb>universale dei vasi, ultimo a dimostrarsi fu il circolo coronario. </s>

<s>I passaggi <lb></lb>dalla luce all&#039;ombra servirono a quello, come l&#039;alternarsi il pallor della si­<lb></lb>stole al purpureo della diastole servi a questo, e fu il Canocchiale a Galileo <lb></lb>ministro della scoperta, com&#039;allo Spallanzani fu il Microscopio. </s></p><p type="main">

<s>Ma come l&#039;Harvey, dop&#039;avere eloquentemente accennato alle ragioni, <lb></lb>per cui il cuore può dirsi il Sole nel Micromosmo, a quel modo che il Sole <lb></lb>stesso può dirsi il cuore del Mondo, soggiunge tosto: “ sed de his conve­<lb></lb>nientius, cum de huiusmodi motus causa finali speculabimur ” (ibi); così <lb></lb>noi soggiungiamo che più convenientemente s&#039;intenderanno le divisate ana­<lb></lb>logie nell&#039;ordine particolare de&#039;fatti, de&#039;quali entriamo senz&#039;altro a narrare <lb></lb>la storia. </s></p><pb xlink:href="020/01/1251.jpg" pagenum="126"></pb><p type="main">

<s>E giacchè l&#039;Harvey, come vedemmo, commemorava Aristotile, nell&#039;atto <lb></lb>d&#039;imporre il nome alla sua grande scoperta, al lungo ordine delle idee, che <lb></lb>si svolgerebbero nel decorrere di tanti secoli, conviene in Aristotile stesso <lb></lb>appiccare le prime fila. </s>

<s>Il gran Maestro della scienza universale non lasciò <lb></lb>indietro la descrizione delle membra degli animali, e ne compose quel Trat­<lb></lb>tato diviso in quattro libri col titolo <emph type="italics"></emph>De partibus animalium,<emph.end type="italics"></emph.end> da cui prin­<lb></lb>cipalmente imparassero i discepoli il sapiente magistero della Natura nella <lb></lb>fabbrica del corpo dell&#039;uomo. </s>

<s>Ma in realtà la Natura, qui come in altre <lb></lb>parti di scienza naturale, conforma que&#039;suoi magisteri alle speculazioni del <lb></lb>Filosofo, di che il cap. </s>

<s>IV del III libro ne porge fra&#039;tanti altri un notabile <lb></lb>esempio. </s>

<s>Ivi si conclude che il cuore è il principio delle vene. </s>

<s>“ Cor autem <lb></lb>venarum principium est, ex hoc enim venae et per hoc esse videntur ” (Ope­<lb></lb>rum Tomus sextus, Venetiis 1560, fol. </s>

<s>231). Infatti, ei soggiunge, tutti gli <lb></lb>altri visceri son corsi dalle vene, fuor che il cuore, il quale è cavo, per <lb></lb>contenere il sangue da sè generato, e per dispensarlo al corpo per la via <lb></lb>delle vene: è spesso “ ut principium caloris servare possit ” (ibi). — Ma an­<lb></lb>che il Fegato è tutto pieno di sangue: or perchè non potrebb&#039;egli esserne <lb></lb>il generatore, e il principio delle vene invece del cuore? </s>

<s>— Risponde Aristo­<lb></lb>tile, non dietro le osservazioni anatomiche o l&#039;esperienze, ma dietro i sug­<lb></lb>gerimenti della sua propria ragione, ch&#039;egli vuole imporre alla Natura per <lb></lb>legge, e dice che tanta eccellenza si conviene al cuore, perch&#039;egli è collo­<lb></lb>cato nel mezzo: “ in medio enim positum est. </s>

<s>” Al Fegato non potrebbe <lb></lb>convenirsi una tale eccellenza, nè perciò dirsi il principio o di tutto il corpo <lb></lb>o del sangue, perch&#039;ei non è collocato nel luogo principale. </s>

<s>“ Jecur etiam <lb></lb>omnibus sanguine praeditis inest, sed nemo id censuerit esse principium <lb></lb>vel corporis totius, vel sanguinis, situs enim nequaquam obtinet principa­<lb></lb>lem ” (ibi). </s></p><p type="main">

<s>Quando, cinque secoli dopo, i fatti anatomici osservati parvero persua­<lb></lb>dere a molti che la Natura esercita un magistero tutto suo proprio, e molto <lb></lb>differente da quello impostole dalla ragion di Aristotile, Galeno tolse dalla <lb></lb>sedia principale il Cuore, per porvi il Fegato, e fatta distinzione fra arterie <lb></lb>e vene disse che queste avevano dal Fegato stesso gl&#039;inizii, come quelle <lb></lb>lo avevano invece dal Cuore. </s>

<s>“ Nam quemadmodum venae ab Hepate, ita <lb></lb>Arteriae a Corde ducunt initium ” (De usu partum, Lugduni 1550, pag. </s>

<s>335). <lb></lb>L&#039;innovazione galenica segnava senza dubbio un regresso dal termine, a <lb></lb>cui doveva giunger la scienza, per scoprire il circolo del sangue, ma ciò <lb></lb>dipendeva piuttosto dalla naturale imperfezione dell&#039;uomo, che dal metodo <lb></lb>sperimentale o di osservazione sostituito dall&#039;Anatomico al metodo raziona­<lb></lb>listico del Filosofo. </s>

<s>Che ciò sia il vero vien dimostrato dal veder che quel <lb></lb>metodo di osservazione condusse direttamente Galeno stesso a scoprire il cir­<lb></lb>colo polmonare. </s>

<s>Le vene, secondo il Medico di Coo, vanno dal Fegato a in­<lb></lb>figgersi nelle cavità destre del cuore, e le arterie muovono dalle cavità si­<lb></lb>nistre come da loro principio. </s>

<s>Quel vaso dunque, che va dalla parte destra <lb></lb>del cuore al polmone, è una vena, ma perchè ha costituzione di arteria vuol <pb xlink:href="020/01/1252.jpg" pagenum="127"></pb>perciò appellarsi <emph type="italics"></emph>Vena arteriosa.<emph.end type="italics"></emph.end> L&#039;altro vaso, che va al Polmone stesso <lb></lb>dalla parte sinistra del Cuore, è una arteria, ma perchè ha costituzione di <lb></lb>vena dovrà dunque dirsi <emph type="italics"></emph>Arteria venosa.<emph.end type="italics"></emph.end> Fu appunto per la diligente os­<lb></lb>servazione di questi due vasi singolari, che Galeno si condusse alla sua <lb></lb>scoperta. </s></p><p type="main">

<s>Nel VI libro <emph type="italics"></emph>De usu partium<emph.end type="italics"></emph.end> il cap. </s>

<s>X s&#039;intitola, secondo l&#039;interpe­<lb></lb>trazione del medico calabrese Niccolò Regio, “ Vena ad pulmonem per­<lb></lb>veniens arterialis est et arteria è converso ” (ibi, pag. </s>

<s>323). Incomincia ivi <lb></lb>a dire l&#039;Autore che per gli scambievoli beneficii fra que&#039;due visceri, organi <lb></lb>principalissimi della vita animale, il polmone è nutrito direttamente dal <lb></lb>Cuore, e non essendo conveniente che gli fosse mandato il sangue nutri­<lb></lb>tizio per la vena Cava, la sapiente Natura ordinò a quell&#039;effetto un&#039;apposita <lb></lb>vena, a cui dette, per renderla singolare, costituzione propria di arteria. <lb></lb></s>

<s>“ Nam ut aliud nihil in omnibus animantibus, ita in ipso Pulmone, utique <lb></lb>sapiens Natura temere nihil neque sine causa quidquam fecit. </s>

<s>Commutavit <lb></lb>autem vasorum tunicas, venam quidem faciens arteriosam, arteriam vero <lb></lb>venosam. </s>

<s>In aliis vero omnium partibus, cum arteria sit aequabilis tunica­<lb></lb>rum, tamen crassitudo non est eadem, sed tantum utique differt, quantum <lb></lb>Herophilus recte collegisse videtur, qui arteriam venae crassitudine sexcu­<lb></lb>plam esse definierit ” (ibi). </s></p><p type="main">

<s>Fatta l&#039;osservazione di questo notabile scambio fra arterie e vene, trat­<lb></lb>trandosi che il cuore doveva direttamente e per sè nutrire il polmone, Ga­<lb></lb>leno passa a investigare e ad esporre <emph type="italics"></emph>quamobrem Natura,<emph.end type="italics"></emph.end> in così fatto <lb></lb>modo, <emph type="italics"></emph>machinata est,<emph.end type="italics"></emph.end> spendendo tutto quanto il capitolo in così fatta inve­<lb></lb>stigazione, per apparecchiarsi alla quale dice esser conveniente premettere <lb></lb>quest&#039;altra ricerca: perchè cioè la Natura abbia contessute le arterie di fibre <lb></lb>più robuste delle vene. </s>

<s>Ciò egli dice <emph type="italics"></emph>longa egere oratione non arbitror,<emph.end type="italics"></emph.end><lb></lb>essendo che le vene, ordinate a condurre un sangue crasso, grave e pigro, <lb></lb>bastava che fossero rivestite di una semplice tunica, ma era conveniente il <lb></lb>raddoppiarla per contener, come fanno le arterie, un sangue ch&#039;è tutto spi­<lb></lb>ritoso, tutto mobile e diffusivo. </s>

<s>Ora, perchè il polmone composto di sostanza <lb></lb>spiritosa voleva esser nutrito di un sangue raffinato e pur anch&#039;esso spiri­<lb></lb>toso, ecco che la sapiente Natura glielo manda per una vena, la quale ha <lb></lb>la costituzione e la compagine propria di un&#039;arteria. </s></p><p type="main">

<s>Il cap. </s>

<s>XI del citato libro galenico è così intitolato: “ Arteriosum vas <lb></lb>aut eius generis membranas ex vena cava produci non potuisse docet osten­<lb></lb>diturque utilitatem dextri ventriculi cordis ” (ibi, pag. </s>

<s>332). La dimostra­<lb></lb>zione si conclude all&#039;ultimo colle parole seguenti: “ Ex quibus intelligi po­<lb></lb>test multo melius fuisse pulmonem a corde nutriri. </s>

<s>Porro cum vas alterum <lb></lb>quod tunica simplici constat in cor infigatur, alterum vero quod duplici ex <lb></lb>ipso producatur, communem utrique locum, quasi lacunam quamdam, pa­<lb></lb>rari necesse fuit. </s>

<s>Ad quam pertinentibus utrisque, per alterum quidem tra­<lb></lb>datur sanguis, per reliquum vero immittatur. </s>

<s>Atque hic dexter cordis ven­<lb></lb>triculus est pulmonis causa, quemadmodum demonstravimus, comparatus. <pb xlink:href="020/01/1253.jpg" pagenum="128"></pb>Quocirca quae animalia pulmonem non habent, eadem neque in corde duos <lb></lb>habent ventriculos, sed illis solis is inest, qui motus arteriis omnibus dux <lb></lb>est ” (ibi, pag. </s>

<s>335). </s></p><p type="main">

<s>Si raccoglie da così fatti documenti essere stata intenzione principalis­<lb></lb>sima di Galeno quella di dimostrar che il Polmone veniva direttamente nu­<lb></lb>trito dal Cuore, e in qual modo venisse quello a ricever da questo il vitale <lb></lb>suo nutrimento. </s>

<s>Includeva in sè un tal processo dimostrativo la descrizione <lb></lb>de&#039;vasi particolari ordinati a quel nutrimento, e delle comuni relazioni, che <lb></lb>hanno quegli stessi vasi fra loro e col cuore, in che consiste insomma la <lb></lb>scoperta galenica del circolo polmonare. </s></p><p type="main">

<s>Era come vedemmo dottrina insegnata dall&#039;antico Maestro che le vene <lb></lb>avessero tutte la loro origine dal Fegato, e che le non portassero altro che <lb></lb>sangue crasso, per nutrir le membra di tutto il corpo animale, dal Polmone <lb></lb>in fuori, il quale veniva direttamente irrigato dal destro ventricolo di pu­<lb></lb>rissimo sangue spiritoso. </s>

<s>E perchè giusto appunto doveva esser quel sangue <lb></lb>di sostanza spiritosa, ordinò la Natura che la vena irrigatrice avesse consi­<lb></lb>stenza di arteria. </s>

<s>Non potendosi però tutto il sangue portato da questa vena <lb></lb>esaurire in alimentare il polmone, il superfluo fu fatto ritornare al cuore, <lb></lb>non per la medesima via indietreggando, perchè ne sarebbe potuto seguire <lb></lb>un tumultuoso flusso e riflusso, ma per la via della vena arteriosa lasciata <lb></lb>aperta nelle bene apposte anastomosi. </s></p><p type="main">

<s>Per meglio conseguire un tale effetto, la stessa sapientissima Natura <lb></lb>apparecchiò le opportune valvole, tanto nel principio della vena arteriosa, <lb></lb>perch&#039;entrato il sangue non ne dovesse uscire, quanto pure allo sbocco del­<lb></lb>l&#039;arteria venosa, perchè uscito non dovesse rientrare. </s>

<s>Per il gioco dunque <lb></lb>delle valvole il sangue dalla vena è costretto a passar nell&#039;arteria, e la forza <lb></lb>d&#039;impulso nasce dai moti del torace, che ampliandosi dilata i vasi, i quali <lb></lb>perciò attraggono più facilmente, restringendosi gli comprime, e sforza così <lb></lb>il sangue a passare attraverso alle troppo anguste anastomosi. </s>

<s>“ Fieri nun­<lb></lb>quam potuisset ut per invisibilia, atque exigua ossilla, sanguis in arterias <lb></lb>transumetur..... Cum autem thorax contrahitur pulsae atque intro com­<lb></lb>pressae undique, quae in pulmone sunt venosae arteriae, exprimunt quidem <lb></lb>quam celerrime qui in seipsis est spiritus. </s>

<s>Transumunt autem per subtilia <lb></lb>illa ossilla sanguinis portionem aliquam, quod numquam accidisset profecto, <lb></lb>si sanguis per maximum os retro remeare potuisset ” (ibi, pag. </s>

<s>336). </s></p><p type="main">

<s>Benchè insomma Galeno non avesse compresa la vera intenzione della <lb></lb>Natura nel condurre il sangue al Polmone, e nel ridurlo poi al Cuore, ei <lb></lb>descrisse pure il circolo polmonare con tanta precisione, da servir come ve­<lb></lb>dremo di esempio alla grande scoperta dell&#039;Harveio. </s>

<s>Sarebbe forse, prose­<lb></lb>guendo per l&#039;aperta via, riuscito più d&#039;appresso a conoscere il circolo uni­<lb></lb>versale del sangue quell&#039;antico Maestro, se il negare al Cuore il principato <lb></lb>aristotelico non glielo avesse impedito. </s>

<s>Illuso dal sistema della vena Porta <lb></lb>e dal parenchima sanguinolento del Fegato, attribuì a questo viscere le fun­<lb></lb>zioni generative del sangue, e riconobbe da lui solo l&#039;origine di tutte le <pb xlink:href="020/01/1254.jpg" pagenum="129"></pb>vene. </s>

<s>Così, il circolo, che la Natura aveva fatto continuo, si veniva dal Fi­<lb></lb>losofo a rendere spezzato, dando al sangue venoso altro principio diverso <lb></lb>dal sangue arterioso; altre qualità, altre funzioni. </s>

<s>Le numerose vene eran <lb></lb>secondo Galeno disperse per tutte le membra a recarvi il necessario ali­<lb></lb>mento, e la Cava scendeva nell&#039;orecchietta destra per colar di lì nel sotto­<lb></lb>posto ventricolo il sangue, che dovevasi dispensare in due parti: l&#039;una <lb></lb>andando ad alimentare il Polmone, e l&#039;altra attraverso al setto medio pene­<lb></lb>trando nel ventricolo sinistro, dove acquistava qualità spiritose, e i conce­<lb></lb>puti spiriti, entrando per l&#039;Arteria magna ed esalando per le numerose <lb></lb>anastomosi, facevano pulsar le membra e infondevano in esse i balsami <lb></lb>della vita. </s></p><p type="main">

<s>Come onde, benchè interrotte qua e là da qualche ostacolo, si propa­<lb></lb>garono per un lungo ordine di secoli queste dottrine, infin tanto che non <lb></lb>arrivarono al Berengario da Carpi. </s>

<s>O illuso dalla propria esperienza o sog­<lb></lb>giogato dall&#039;autorità di coloro, che asserivano di aver veduto ne&#039;cadaveri <lb></lb>l&#039;arteria venosa vuota di sangue, dubitò da questo lato della verità delle dot­<lb></lb>trine galeniche, e ripensando a quale altro fine fosse ivi tra il Polmone e <lb></lb>il Cuore disposto quel vaso, immaginò che rassomigliasse alla gola di un <lb></lb>cammino, attraverso alla quale passassero i fumi filigginosi sollevatisi dal <lb></lb>ventricolo sinistro nella concozione del sangue. </s>

<s>“ In isto etiam ventre sini­<lb></lb>stro est aliud orificium in basi cordis, in quo incipit arteria venalis, dicta <lb></lb>arteria quia vaporem portat, vel, ut inquit Galenus VII <emph type="italics"></emph>De iuvamentis,<emph.end type="italics"></emph.end><lb></lb>quia pulsat. </s>

<s>Et dicitur venalis quia tantum unam habet tunicam, per quam <lb></lb>transit extra corpus fumus capnosus ” (Comment. </s>

<s>in Anat. </s>

<s>Mundini cit., <lb></lb>fol. </s>

<s>CCCL). </s></p><p type="main">

<s>Del resto, negata la verità del circolo polmonare, il Berengario segue <lb></lb>fedelmente Galeno. </s>

<s>Diligentissimo nel descrivere il setto medio, dice che le <lb></lb>cavità aperte in esso, dalla parte che guarda il ventricolo destro, si vanno <lb></lb>sempre più restringendo, infino a ridursi in sottilissimi pori, che vanno a <lb></lb>sboccare nel ventricolo sinistro. </s>

<s>Questo ei lo crede un artificio della Natura <lb></lb>perchè attraverso allo stesso setto medio il sangue quasi si cribra e si as­<lb></lb>sottiglia, disponendosi intanto a pigliar quella spirituosità, che gli sarà im­<lb></lb>partita dalle forze proprie del Cuore, prima di esser dispensato alle memhra <lb></lb>per la via dell&#039;Aorta. </s>

<s>“ Visis ventriculis lateralibus cordis, scilicet dextro et <lb></lb>sinistro, ad ventriculum medium cordis me converto. </s>

<s>Et dico in pariete, qui <lb></lb>est communis ventriculo dextro et sinistro, qui est in medio cordis....esse <lb></lb>certas concavitates, seu foramina, quae ut supra dixi notabiles sunt in cor­<lb></lb>dibus magnorum bouum,.... quae foramina dicuntur a Medicis Venter me­<lb></lb>dius cordis, et ipsa foramina pertranseunt parietem praedictum, a dextro <lb></lb>ventriculo incipiendo usque ad concavitatem ventriculi sinistri, et talia fora­<lb></lb>mina sunt latiora et ampliora versus ventriculum dextrum quam sunt ver­<lb></lb>sus ventrem sinistrum. </s>

<s>Et haec foramina reperiuntur semper ad magis <lb></lb>strictum procedere, usquequo transeant totum praedictum parietem,.... et <lb></lb>ita per talia foramina transit sanguis a ventre dextro ad sinistrum, qui con-<pb xlink:href="020/01/1255.jpg" pagenum="130"></pb>tinue in transitu subtiliatur et sie praeparatur ad spirituositatem ” (ibi, <lb></lb>fol. </s>

<s>CCCLI). </s></p><p type="main">

<s>Così, diligentemente illustrata quella parte che conteneva il falso, im­<lb></lb>provvidamente negata quell&#039;altra che dimostrava il vero, tramandavasi ai <lb></lb>posteri dal Berengario la dottrina, che intorno al circolo del sangue avea <lb></lb>insegnata Galeno. </s>

<s>Al modesto Anatomico di Carpi successe, non molti anni <lb></lb>dopo, il vanitoso Anatomico brussellese, il quale essendo riuscito a far cre­<lb></lb>dere ch&#039;egli era proceduto senza maestro, com&#039;uomo apparito al mondo <lb></lb>senza padre e senza madre, s&#039;acquistò il titolo di divino. </s>

<s>Maravigliosa è da <lb></lb>dir senza dubbio quella virtù, che valse a indurre nelle menti una tal per­<lb></lb>suasione, per cui sempre e in ogni modo appariranno uomini maravigliosi <lb></lb>Aristotile, e Galileo e il Cartesio, ma pure hanno i più savii sempre pensato <lb></lb>che com&#039;è impossibile non riconoscere un padre nella generazione animale, <lb></lb>così è impossibile nella generazione intellettuale non riconoscere un maestro. </s>

<s><lb></lb>Il Vesalio ebbe a suoi principali maestri Galeno e il Berengario, benchè, per <lb></lb>non apparire discepolo di nessuno, questo copra sotto l&#039;ombra de&#039;silenzii, e <lb></lb>quello sotto la mora degl&#039;insulti. </s></p><p type="main">

<s>Non ingrato allo studioso, nè disutile alla storia riuscirebbe il percor­<lb></lb>rere i VII libri <emph type="italics"></emph>De humani corporis fabrica,<emph.end type="italics"></emph.end> per notar come e quanto ivi <lb></lb>ritragga l&#039;Autore dai libri di Galeno, e dai Commentarii del Berengario, di <lb></lb>che quello che ci occorrerà ora a notare, in proposito della fisiologia del <lb></lb>sangue, può valer per esempio. </s>

<s>Si pongano di grazia sotto gli occhi i let­<lb></lb>tori il cap. </s>

<s>X del VI libro <emph type="italics"></emph>De usu partium,<emph.end type="italics"></emph.end> che incomincia <emph type="italics"></emph>Mutuam enim <lb></lb>cor pulmoni gratiam referre.....<emph.end type="italics"></emph.end> e lo vengano insiem con noi riscon­<lb></lb>trando col cap. </s>

<s>XI del libro VI dell&#039;Anatomia del Vesalio, se vogliono ve­<lb></lb>dere com&#039;essendo in ambedue quegli Autori ugualmente difettosa la Fisio­<lb></lb>logia, la Rettorica dell&#039;uno sia inferiore a quella dell&#039;altro, quant&#039;esser può <lb></lb>inferiore la studiata maniera di un Barbaro alla nativa eleganza di un Greco. </s></p><p type="main">

<s>“ Pulmo enim, così scrive il Vesalio, qui instar promptuarii cordi cir­<lb></lb>cumponitur ut id ab illo aerem perpetuo allicere queat, rarus, fungosus, <lb></lb>levis, ac ad thoracis motus sequacissimus fieri debuit. </s>

<s>Neque eiusmodi pro­<lb></lb>fecto suis functionibus idoneo nutrimento ali potuit, nisi privatim illi san­<lb></lb>guis ex eo quem Cava continet, levis, aereus, spumosus, expurgatus, nihilque <lb></lb>minus quam foeculentus, ab alio organo praepararetur, atque ita ipsi pul­<lb></lb>moni ad opportunam nutritionem deduceretur. </s>

<s>At nullum organum corde <lb></lb>ipso calidissimo et pulmoni proximo viscere ad id munus erat aptum. </s>

<s>Neque <lb></lb>etiam aliud omnino iustius pulmoni hac in re famulari poterat, quandoqui­<lb></lb>dem nimis quam ingratum Cor habendum foret, si Pulmoni tam amice ae­<lb></lb>rem, quo nisi ilico concidere emorique velit, perpetuo indiget, ipsius nomine <lb></lb>attrahenti ac obsequentissimi famuli ritu praeparanti, et illius potissimum <lb></lb>gratia fabricanti, nullas vices referendas putaret, ac non modis omnibus cor, <lb></lb>ut gratiam reponeret pulmoni, opportunum alimentum, cum id citra incom­<lb></lb>modum possit, conficere praeparareque studeret ” (De hum. </s>

<s>corp. </s>

<s>fabrica, <lb></lb>Basileae 1543, pag. </s>

<s>596). </s></p><pb xlink:href="020/01/1256.jpg" pagenum="131"></pb><p type="main">

<s>Tale è il tratto di Rettorica uscito dalla penna anatomica del Vesalio <lb></lb>per dimostrare, a imitazion di Galeno, che il polmone vuol essere diretta­<lb></lb>mente alimentato dal cuore. </s>

<s>Ma perchè Galeno stesso non lasciò le froude <lb></lb>dell&#039;eloquenza vuote affatto de&#039;frutti della Filosofia, argutamente deducendo <lb></lb>che le due destre cavità cardiache erano poste in servigio de&#039;polmoni, per­<lb></lb>chè gli animali privi della respirazion polmonare hanno il cuore mancante <lb></lb>di quelle parti: anche il Vesalio non trascura di mandar all&#039;ultimo la sua <lb></lb>dimostrazione condita di questo galenico sale. </s>

<s>“ Pulmonis igitur occasione <lb></lb>dexter cordis ventriculus creatus est, quod etiam liquidissimo animalia con­<lb></lb>firmant pulmone carentia, ac ob id dextro cordis ventriculo destituta ” (ibi) </s></p><p type="main">

<s>Dall&#039;osservazione di questi fatti però Galeno fu condotto a scoprire il <lb></lb>circolo polmonare, ma il Vesalio abbandona a questo punto l&#039;antica guida, <lb></lb>per seguir piuttosto quella del Berengario. </s>

<s>Da lui ritrae l&#039;anatomia del setto <lb></lb>medio poroso e la fisiologia del ventricolo destro, esprimendosi con queste <lb></lb>parole: “ Hic namque ventriculus, in animalibus quae illo donantur, a vena <lb></lb>Cava, quoties Cor dilatatur ac distenditur, magnam sanguinis vim attrahit, <lb></lb>quem adiuvantibus ad hoc ventriculi foveis excoquit, ac suo calore atte­<lb></lb>nuans levioremque et qui aptius impetu postmodum per arterias ferri pos­<lb></lb>sit reddens, maxima portione per ventriculorum cordis septi poros in sini­<lb></lb>strum ventriculum desudare sinit. </s>

<s>Reliquam autem eius sanguinis partem, <lb></lb>dum cor contrahitur, arctaturque, per venam arterialem in pulmonem de­<lb></lb>rivat ” (ibi). </s></p><p type="main">

<s>Dal Berengario derivò pure il Vesalio la dottrina delle funzioni del <lb></lb>sinistro ventricolo e dell&#039;arteria venosa, la quale ei non credè che fosse or­<lb></lb>dinata a portare il sangue avanzato alla nutrizion del polmone, com&#039;aveva <lb></lb>detto l&#039;antico Maestro di Coo, ma a condur fumi e aria, com&#039;aveva pensato <lb></lb>il Maestro nuovo da Carpi. </s>

<s>“ Quemadmodum enim dexter ex Cava sangui­<lb></lb>nem trahit, ita quoque sinister, aerem ex pulmone in arteriam venalem at­<lb></lb>tractum ad se dilatato, corde allicit, illoque ad caloris innati refrigerationem <lb></lb>et substantiae ipsius enutritionem spiritumque vitalem utitur, hunc aerem <lb></lb>excoquens et praeparans, ut is una cum sanguine, qui ex dextro ventriculo <lb></lb>in sinistrum, per ventriculorum septum copiosius resudavit, in magnam Ar­<lb></lb>teriam totumque adeo corpus delegari possit ” (ibi, pag. </s>

<s>598). </s></p><p type="main">

<s>La grande autorità del Vesalio aveva rese approvatissime nel giudizio <lb></lb>de&#039;più queste dottrine galeniche riformate dal Berengario, quando Realdo <lb></lb>Colombo si propose di volere investigare il vero nella Natura e no ne&#039;libri. </s>

<s><lb></lb>Dando dunque effetto a questo savio proposito, per le dissezioni de&#039;cada­<lb></lb>veri e degli animali vivi, si assicurò che l&#039;arteria venosa conteneva vera­<lb></lb>mente sangue, com&#039;aveva detto Galeno, e non fumi e aria com&#039;avevano in­<lb></lb>segnato poi il Berengario e il Vesalio. </s>

<s>Nel riferire al pubblico la verità <lb></lb>dimostrata dai fatti anatomici, contro gli errori vesaliani, il Colombo è ar­<lb></lb>gutissimo perchè, senza nominar nessuno, scopre non solo quegli errori, ma <lb></lb>ciò che più doveva cuocere al superbo Brussellese, l&#039;origine di quegli er­<lb></lb>rori, ripetizioni inconsiderate dei detti altrui. </s>

<s>Egli percìò insiste sopra quei <pb xlink:href="020/01/1257.jpg" pagenum="132"></pb>fumi fuligginosi usciti dalla penna del buon Berengario, e si ride di quegli <lb></lb>anatomici, a cui tanto piacque questa finzione “ quippe qui certo existimant <lb></lb>in corde ea fieri, quae in caminis assolent, quasi in corde viridia ligna exi­<lb></lb>stant, quae, dum cremantur, fumum edant ” (De re anat. </s>

<s>cit., pag. </s>

<s>178). </s></p><p type="main">

<s>Ma è il vero, soggiunge tosto il Colombo, che l&#039;arteria venale è fatta <lb></lb>“ ut sanguinem cum aere a pulmonibus mixtum afferant ad sinistrum cor­<lb></lb>dis ventriculum. </s>

<s>Quod tam verum est, quam quod verissimum, nam non <lb></lb>modo si cadavera inspicis, sed si viva etiam animalia hanc arteriam in omni­<lb></lb>bus refertam invenies, quod nullo pacto eveniret, si ob aerem duntaxat et <lb></lb>vapores constructa foret ” (ibi). Ma perchè il fatto dimostrato nella vena <lb></lb>dell&#039;animale, mentre respira e mentre che la vita dà moto al sangue, do­<lb></lb>veva riuscire più concludente, il Colombo stesso, là dove tratta delle fun­<lb></lb>zioni del polmone, invita i suoi lettori e gli scongiura che ricorrano alle vi­<lb></lb>visezioni, e che tocchino da sè stessi con mano se quello ch&#039;egli asserisce <lb></lb>è vero; se è vero cioè che l&#039;arteria venosa è anch&#039;essa piena di sangue, <lb></lb>come tutte le altre vene, “ quemadmodum peroptume maximus Galenus <lb></lb>probat eo libello <emph type="italics"></emph>An sanguis in arteriis contineatur,<emph.end type="italics"></emph.end> contra Erasistratum ” <lb></lb>(ibi, pag. </s>

<s>224). </s></p><p type="main">

<s>Ma d&#039;onde atting&#039;ella il sangue quest&#039;arteria venosa? </s>

<s>Da quello, ri­<lb></lb>sponde il Colombo, riversato nel Polmone dalla vena arteriosa, e sopravan­<lb></lb>zato al nutrimento del viscere, il qual sangue rimescolandosi ivi con l&#039;aria <lb></lb>diventa spiritoso e così confezionato entra per le diramazioni dell&#039;arteria ve­<lb></lb>nosa, dalla quale è portato al ventricolo sinistro. </s>

<s>“ Vena enim haec arte­<lb></lb>rialis, praeterquam quod sanguinem pro sui alimento defert, adeo ampla est, <lb></lb>ut alius usus gratia deferre possit. </s>

<s>Sanguis huiusmodi, ob assiduum pulmo­<lb></lb>num motum, agitatur, tenuis redditur, et una cum aere miscetur, qui et <lb></lb>ipsa in hac collisione refractioneque praeparatur, ut simul mixti sanguis et <lb></lb>aer per arteriae venalis ramos suscipiantur, tamdemque per ipsius truncum <lb></lb>ad sinistrum cordis ventriculum deferantur ” (ibi, pag. </s>

<s>223). </s></p><p type="main">

<s>È dunque il Colombo così condotto dagli esercizii della vivisezione a <lb></lb>descrivere quel circolo polmonare del sangue, che il Berengario aveva ne­<lb></lb>gato a Galeno, sostituendovi ipotesi dannosamente diffuse dall&#039;autorità del <lb></lb>Vesalio. </s>

<s>Tanto poi diritte furon le vie, che condussero l&#039;Anatomico cremo­<lb></lb>nese alla sua conclusione, e tanto si fissò la mente di lui in cacciare i fumi <lb></lb>fuligginosi del Berengario, piaciuti al Vesalio, che non, pensando a Galeno, <lb></lb>a cui giovò come une de&#039;più validi strumenti il principio delle cause finali, <lb></lb>si compiacque di avere scoperto il vero con gli schietti metodi e co&#039;legit­<lb></lb>timi strumenti sperimentali. </s></p><p type="main">

<s>Ma il Vesalio, che aveva bene inteso come quel rimprovero agli Ana­<lb></lb>tomici, a&#039;quali piacque tanto la comparazione del Berengario tra il sangue <lb></lb>nel cuore e le legna verdi gittate ad ardere ne&#039;cammini, era scritto per lui, <lb></lb>se ne risentì fieramente, e nell&#039;<emph type="italics"></emph>Esame del Falloppio<emph.end type="italics"></emph.end> accusò il Colombo e <lb></lb>il Valverda, scolare di lui, di non aver mai letto Galeno, di che fanno prova, <lb></lb>egli dice, que&#039;luoghi nel trattato <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> “ quibus subinde glo-<pb xlink:href="020/01/1258.jpg" pagenum="133"></pb>riatur a se compertum esse venalem arteriam sanguinem continere, cum <lb></lb>scilicet id tam diffuse vereque a Galeno, multisque insuper aliis fuerit per­<lb></lb>tractatum ” (Venetiis 1564, pag. </s>

<s>93). </s></p><p type="main">

<s>Parrebbe di qui che, confessandosi per vera la sentenza galenica del­<lb></lb>l&#039;arteria venale piena di sangue e non d&#039;aria fumosa, il Vesalio avesse poi <lb></lb>riformata la sua dottrina intorno al circolo polmonare, ma sventuratamente, <lb></lb>più che gli emendati insegnamenti, ebbe grande efficacia in diffondere i <lb></lb>falsi, intantochè la piccola circolazione del sangue, anche nel primo venten­<lb></lb>nio del secolo appresso, come fra poco vedremo, o era dimenticata, o ve­<lb></lb>niva messa in dubbio, dimenticate oramai le speculazioni anatomiche del lon­<lb></lb>tano Galeno, e le vivisezioni del più vicino Colombo. </s></p><p type="main">

<s>Ciò che poi fa più maravigliare di questa dimenticanza, specialmente <lb></lb>in Italia, si è che il Cesalpino aveva confermata la scoperta anatomica del <lb></lb>Colombo, e fu anzi egli il primo che impose al giro del sangue il nome di <lb></lb><emph type="italics"></emph>Circolo,<emph.end type="italics"></emph.end> e che tolse di mezzo quel bisticcio di Arteria venosa e di Vena ar­<lb></lb>teriosa, dicendo che il vaso, da cui è portato il sangue al polmone, è un&#039;ar­<lb></lb>teria addirittura, perchè pulsa, e l&#039;altro vaso, da cui il sangue è riportato <lb></lb>al cuore, è una vera vena, facendo ella gli ufficii, ed essendo fabbricata al <lb></lb>modo consueto delle altre vene. </s>

<s>I Medici, egli dice nella III delle Questioni <lb></lb>peripatetiche, usi a chiamar vene i vasi che sboccano nella parte destra, e <lb></lb>arterie quelli che sboccano nella parte sinistra del cuore, escogitarono molte <lb></lb>finzioni e molte assurdità per intenderne l&#039;uso. </s>

<s>“ Pulsat igitur in pulmone <lb></lb>vas dextri ventriculi, hoc enim a corde accipit ut Arteria magna, et simi­<lb></lb>liter fabricatum est eius corpus. </s>

<s>Vas autem sinistri ventriculi non pulsat, <lb></lb>quia introducit tantum, et eius corpus simile est reliquis venis ” (Vene­<lb></lb>tiis 1571, fol. </s>

<s>111 a tergo). </s></p><p type="main">

<s>Le nuove idee, ch&#039;esalano fragranti dalla novità del linguaggio, traspor­<lb></lb>tano in un mondo intellettuale, in cui il cielo è più limpido e più aperto, <lb></lb>perchè il Cesalpino aveva felicemente sgombrata quella nuvola, che faceva <lb></lb>ombra alla vista del vero. </s>

<s>Come fosse quella nuvola sgombrata dal nostro <lb></lb>Peripatetico lo vedremo in quest&#039;altro capitolo, e intanto ascoltiamo come <lb></lb>per lui si metta il circolo polmonare in tal nuova luce, da veder chiari in <lb></lb>essa gli albori del nascente Sole arveiano. </s>

<s>“ Idcirco Pulmo, per venam ar­<lb></lb>teriis similem, ex dextro cordis ventriculo fervidum hauriens sanguinem, <lb></lb>eumque per anastomosim arteriae venali reddens qua in sinistrum cordis <lb></lb>ventriculum tendit, transmisso interim aere frigido per asperae arteriae ca­<lb></lb>nales qui iuxta arteriam venalem protenduntur, non tamen osculis commu­<lb></lb>nicantes, ut putavit Galenus, solo tactu temperat. </s>

<s>Huic sanguinis <emph type="italics"></emph>circulationi<emph.end type="italics"></emph.end><lb></lb>ex dextro cordis ventriculo per pulmones in sinistrum eiusdem ventriculum <lb></lb>optime respondent ea quae in dissectione apparent. </s>

<s>Nam duo sunt vasa in <lb></lb>dextrum ventriculum desinentia, duo etiam in sinistrum Duorum autem <lb></lb>unum intromittit tantum, alterum educit, membranis eo ingenio constitutis. </s>

<s><lb></lb>Vas igitur intromittens vena est magna, quidem in dextro, quae Cava ap­<lb></lb>pellatur: parva autem in sinistro ex pulmone intraducens, cuius unica est <pb xlink:href="020/01/1259.jpg" pagenum="134"></pb>tunica ul caeterarum venarum. </s>

<s>Vas autem educens arteria est magna, qui­<lb></lb>dem in sinistro, quae Aorta appellatur: parva autem in dextro ad pulmo­<lb></lb>nes derivans, cuius similiter duae sunt tunicae ut in caeteris arteriis ” (ibi). </s></p><p type="main">

<s>Così, nella storia della risorta Anatomia, lasciato in dimenticanza l&#039;an­<lb></lb>tico Galeno, si poteva dire e si diceva veramente da alcuni essere stato il <lb></lb>Colombo che prima del Cesalpino o di qualunque altro o italiano o stra­<lb></lb>niero avesse descritto il circolo polmonare, quando il Morgagni, per citare <lb></lb>uno storico de&#039;più autorevoli, insorse contro una tale asserzione scrivendo <lb></lb>“ non Columbum, sed .... hispanum medicum Michaelem Servetum, sex et <lb></lb>viginti annis ante Columbum, minorem illum circuitum sanguinis diserte <lb></lb>tradidisse ” (Epistolae anat. </s>

<s>Lugduni Batav. </s>

<s>1728, pag. </s>

<s>95). </s></p><p type="main">

<s>Cita il Morgagni, in questa Epistola anatomica prima, il Sievert, che <lb></lb>nella sua dissertazione <emph type="italics"></emph>De morbis<emph.end type="italics"></emph.end> trascrisse il luogo da quell&#039;esemplare del <lb></lb>libro <emph type="italics"></emph>De Christianismi restitutione,<emph.end type="italics"></emph.end> che si dice esser unico rimasto salvo <lb></lb>dalle fiamme di quel rogo, in mezzo alle quali fu l&#039;Autore stesso bruciato <lb></lb>vivo. </s>

<s>Altri citano il Wotton, che fece la trascrizione da quel medesimo esem­<lb></lb>plare, bench&#039;ei lo dica edito, no nel 1533, ma venti anni dopo, cosicchè lo <lb></lb>Spagnolo avrebbe preceduto, non di 26 anni come il Morgagni sulla fede <lb></lb>del Sievert dice, ma di soli 6 il nostro Italiano. </s>

<s>Anche Lodovico Dutens, nel <lb></lb>II Tomo <emph type="italics"></emph>Dell&#039;origine delle scoperte,<emph.end type="italics"></emph.end> tradotto in italiano e stampato prima <lb></lb>in Napoli, e poi in Venezia nel 1789, riferì in nota al § 191 il passo del <lb></lb>Sievert relativo alla circolazione del sangue, dicendo di averlo fedelmente tra­<lb></lb>scritto dalle <emph type="italics"></emph>Riflessioni<emph.end type="italics"></emph.end> del Wotton <emph type="italics"></emph>sopra gli Antichi e i Moderni.<emph.end type="italics"></emph.end> Ma verso <lb></lb>la metà del secolo presente un illustre Fisiologo francese venne ad assicu­<lb></lb>rarci di ogni impostura e di ogni inganno col dire: “ J&#039;ai vu, j&#039;ai touché <lb></lb>le livre de Servet ” (Flourens, Histoire da la decouverte de la circulation <lb></lb>du sang, Paris 1854, pag. </s>

<s>138). </s></p><p type="main">

<s>Racconta ivi il Flourens come l&#039;esemplare del libro, da lui veduto e <lb></lb>toccato, fu quello medesimo, ch&#039;ebbe sotto gli occhi il Colladon per esami­<lb></lb>narlo, e per dar la crudele sentenza provocata dalla invidiosa empietà di <lb></lb>Calvino. </s>

<s>Venuto il libro alle mani di Riccardo Mead, il Mead lo donò al <lb></lb>Boze, e dagli eredi di lui lo comprò la Biblioteca reale di Parigi, dove tut­<lb></lb>tavia si conserva. </s>

<s>Egli è, soggiunge il Flourens, questo <emph type="italics"></emph>malheureux exem­<lb></lb>plaire,<emph.end type="italics"></emph.end> di una autenticità <emph type="italics"></emph>irrecusable.<emph.end type="italics"></emph.end> “ Plusieurs pages sont en partie rous­<lb></lb>sies et consumées par le feu. </s>

<s>Il ne fut sauvé du bucher où l&#039;on brulait à <lb></lb>la fois le livre et l&#039;auteur, que lorsque l&#039;incendie avait dejà commencé ” <lb></lb>(ivi, pag. </s>

<s>138, 39). </s></p><p type="main">

<s>In appendice a questa <emph type="italics"></emph>Histoire<emph.end type="italics"></emph.end> trascrive l&#039;Autore da pag. </s>

<s>202-14 il <lb></lb>passo estratto dal libro <emph type="italics"></emph>Christianismi Restitutio, Viennae Allobrogorum, <lb></lb>MDLIII,<emph.end type="italics"></emph.end> nè la trascrizione di quel passo si limita solamente a ciò che con­<lb></lb>cerne la circolazione del sangue, ma altre parti importanti di Fisiologia. </s></p><p type="main">

<s>Tolta dunque da così autorevoli testimonianze ogni ragion di sospetto <lb></lb>intorno all&#039;autenticità del documento, e alla fedeltà della trascrizione, non <lb></lb>abbiamo potuto escludere dalla nostra Storia il Servet, e anzi, esaminando <pb xlink:href="020/01/1260.jpg" pagenum="135"></pb>quel ch&#039;egli speculò della circolazione del sangue, siamo stati costretti di <lb></lb>confessare, con grande nostra sorpresa, aver lui già scoperte tutte quelle <lb></lb>novità, che si lessero poi scoperte dal Colombo. </s>

<s>Egli avverte prima di tutto, <lb></lb>il Medico spagnolo, che sarà per intendere facilmente le cose solamente colui, <lb></lb><emph type="italics"></emph>qui in Anatome fuerit exercitatus.<emph.end type="italics"></emph.end> Poi passa a distinguere la trinità degli <lb></lb>spiriti: il naturale nel fegato e nelle vene, il vitale nel cuore e nelle arte­<lb></lb>rie, l&#039;animale nel cervello e nei nervi. </s>

<s>Lo spirito vitale si genera propria­<lb></lb>mente nel ventricolo sinistro del cuore, ma perchè vi son misti insieme <lb></lb>aria, acqua e fuoco, concorrono molto a quella generazione i polmoni, che <lb></lb>somministrano l&#039;aria al sangue. </s>

<s>“ Generatur ex facta in pulmonibus mix­<lb></lb>tione inspirati aeris cum elaborato subtili sanguine, quem dexter ventricu­<lb></lb>lus cordis sinistro communicat. </s>

<s>Fit autem communicatio haec, non per pa­<lb></lb>rietem cordis medium, ut vulgo creditur, sed magno artificio a dextro cordis <lb></lb>ventriculo longo per pulmones ductu agitatur sanguis subtilis. </s>

<s>A pulmoni­<lb></lb>bus praeparatur, flavus efficitur, et a vena arteriosa in arteriam venosam <lb></lb>transfunditur ” (Flourens, Histoire cit., pag. </s>

<s>203, 4). </s></p><p type="main">

<s>Quel che soggiunge il Servet a rendere questa sua descrizione del cir­<lb></lb>colo cardiaco polmonare originale, sopra quella datane da Galeno, lo vedremo <lb></lb>tra poco, ma intanto è da concludere che la scoperta, e nelle morte pagine <lb></lb>dell&#039;eterodosso Spagnuolo e nelle vive del Colombo e del Cesalpino, era stata <lb></lb>fatta e diffusa tra gli studiosi della scienza. </s>

<s>Si giudicherebbe perciò che sopra <lb></lb>l&#039;errore del Berengario, protetto dall&#039;autorità del Vesalio, la vera dottrina <lb></lb>galenica suffragata dall&#039;autorità del Colombo e del Cesalpino dovesse avere <lb></lb>compiuta vittoria, almeno in Italia, ma è pure un fatto degno di nota quel <lb></lb>che s&#039;accennava di sopra, che cioè rimase fra la verità e l&#039;errore una lotta, <lb></lb>nella quale parve questo sventuratamente prevalere su quella. </s></p><p type="main">

<s>Il Falloppio, tutto intento alle descrizioni anatomiche, e tutto in cerca <lb></lb>di quelle squisitezze sfuggite all&#039;occhio e all&#039;acutissimo stilo del Vesalio, <lb></lb>poco dice delle funzioni del cuore o del moto del sangue, e in quel poco <lb></lb>non si dilunga insomma dalla fisiologia del Berengario. </s>

<s>L&#039;Acquapendente <lb></lb>pure, come se il Colombo e il Cesalpino non avessero insegnato dalle mag­<lb></lb>giori cattedre d&#039;Italia, e come se avessero le loro dottrine segnate sull&#039;arena, <lb></lb>e non impresse sopra la carta, nel discorrere, come fa per esempio nel <lb></lb>cap. </s>

<s>VIII. <emph type="italics"></emph>De formato foetu,<emph.end type="italics"></emph.end> delle funzioni del cuore e del polmone, non <lb></lb>aggiunge nulla di nuovo a ciò che tutti apprendevano dall&#039;Oracolo brus­<lb></lb>sellese. </s></p><p type="main">

<s>Benchè così fervorosamente, come vedemmo, raccomandasse il Colombo <lb></lb>le vivisezioni a chi volesse assicurarsi di fatto se l&#039;arteria venosa contenesse <lb></lb>dentro sè sangue o aria, il Vidio scriveva nel cap. </s>

<s>IV del VI libro <emph type="italics"></emph>De ana­<lb></lb>tome corporis humani:<emph.end type="italics"></emph.end> “ Sed utrum cum aere sanguis, per hanc arteriam <lb></lb>feratur, dubium est. </s>

<s>Veteres solum aerem per ipsam ferri dixerunt.... re­<lb></lb>centiores asserunt sanguinem in ea secundum naturam contineri ” (Vene­<lb></lb>tiis 1611, pag. </s>

<s>298). Vero è bene che nel capitolo appresso, persuaso oramai <lb></lb>che “ nullum foramen conspicitur in septo medio inter dextrum et sinistrum <pb xlink:href="020/01/1261.jpg" pagenum="136"></pb>ventriculum cordis ” non vede altra via aperta al sangue che per l&#039;arteria <lb></lb>venale “ quae cum aere affert aliquid sanguinis ad sinistrum ventriculum <lb></lb>cordis, quem sanguinem arteria venalis in pulmone accipit a vena arteriali ” <lb></lb>(ibi, pag. </s>

<s>302) ma anche sopra la verità qui riconosciuta soffia il vento freddo <lb></lb>dei dubbii dalle pagine precedenti. </s></p><p type="main">

<s>Inutile potrebbe sembrare oramai recare altre testimonianze, ma noi vo­<lb></lb>gliamo condurre i nostri lettori proprio infin sulle soglie della scoperta ar­<lb></lb>veiana, dove vedremo l&#039;Autore di un&#039;altra insigne scoperta così parlare del <lb></lb>circolo del sangue, come se avendo la storia da Galeno, anzi da Aristotile <lb></lb>al Vidio e all&#039;Aranzio, fatto naufragio, si guardasse attraverso al cupo fondo <lb></lb>delle acque, o si studiasse di tirarne a galla qualche frammento, con gli <lb></lb>ami della memoria. </s></p><p type="main">

<s>Gaspero Asellio, tutto in filosofica contemplazione de&#039;maravigliosi arti­<lb></lb>ficii, con cui la Natura dà alla macchina animale continuo moto di vita, ri­<lb></lb>pensa al sangue, e com&#039;egli possa trapassare dall&#039;una all&#039;altra parte del <lb></lb>cuore. </s>

<s>“ Quid igitur prohibet, poi dice, riscossosi da quella contemplazione, <lb></lb>talis quoque e dextro cordis sinu in sinistrum per septum eius, cum Ga­<lb></lb>leno, ob eas quas adducit rationes, statuere? </s>

<s>Accedit quod istae viae, etsi in <lb></lb>mortuis ut aliae plurimae cernuntur, quod in his, ut Galenus ibidem ait, <lb></lb>omnia sunt perfrigerata et densata, in vivis tamen quis praestabit aut nul­<lb></lb>las eas esse aut non manifestas et patentes? </s>

<s>” (De lactibus ecc., Medio­<lb></lb>lani 1627, pag. </s>

<s>16). </s></p><p type="main">

<s>Ma sia pure, prosegue a dire l&#039;Asellio, che non si trovino nel setto <lb></lb>medio que&#039;fori intraveduti da Galeno, “ neque sic tamen deerit fortassis <lb></lb>alia et commodior via sanguini venoso a dextro in sinistrum ventriculum <lb></lb>traducendo. </s>

<s>Mihi sane nequaquam absurdum videtur eum sanguinem, qui <lb></lb>per venam arteriosam in pulmones e dextro cordis sinu effunditur, ibi assi­<lb></lb>duo eorum verbere extenuatum cum aere, altera vitalis spiritus materia, in <lb></lb>ventriculum sinistrum relabi, quam viam forte nec Galenus ignoravit ” (ibi). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;anno dopo che uno de&#039;più insigni investigatori de&#039;segreti della vita <lb></lb>animale divulgò queste parole in Italia, dove s&#039;erano dimenticate le antiche <lb></lb>e le più recenti tradizioni della scienza, Guglielmo Harvey pubblicava in <lb></lb>Francfort la sua esercitazione anatomica <emph type="italics"></emph>De motu cordis.<emph.end type="italics"></emph.end> L&#039;occasione e il <lb></lb>diritto al merito della grande scoperta, e tutt&#039;insieme le ragioni, per cui <lb></lb>gl&#039;Italiani se la lasciarono carpire a uno straniero, sono eloquentemente <lb></lb>espresse nel cap. </s>

<s>VII della detta Esercitazione, dove scrive l&#039;Autore di es­<lb></lb>sersi sentito fecondare l&#039;ingegno dal rimeditar sopra quella così chiara de­<lb></lb>scrizione del circolo polmonare, della quale udimmo dianzi l&#039;Asellio parlar <lb></lb>con tanta oscitanza. </s>

<s>“ Quod argumentum Galenus pro transitu sanguinis per <pb xlink:href="020/01/1262.jpg" pagenum="137"></pb>dextrum ventriculum de vena Cava in pulmones adducit, eodem nobis rec­<lb></lb>tius pro transitu sanguinis de venis per cor in arterias, mutatis tantum ter­<lb></lb>minis, liceat ” (Lugd. </s>

<s>Batav. </s>

<s>1737, pag. </s>

<s>53). </s></p><p type="main">

<s>Confessa insomma l&#039;Harvey che la via, dalla quale fu condotto ad ar­<lb></lb>gomentar la verità del circolo universale, fu quella, da cui fu condotto Galeno <lb></lb>ad argomentar l&#039;esistenza del circolo polmonare. </s>

<s>Ripensava l&#039;arguto Inglese <lb></lb>che, per la gran copia, e per la grande velocità del sangue, non sarebbe <lb></lb>stato possibile che le arterie non si rompessero o che non rimanessero le <lb></lb>vene esinanite, se a queste il fluido sanguigno non ritornasse da quelle, e <lb></lb>ripensando al modo come ciò potesse avvenire, “ coepi egomet mecum co­<lb></lb>gitare, egli dice, an motionem quamdam, quasi in circulo haberet, quam <lb></lb>postea veram esse reperi, et sanguinem a corde per arterias in habitum <lb></lb>corporis et omnes partes protrudi et impelli a sinistri cordis ventriculi pulsu, <lb></lb>quemadmodum in pulmones, per venam arteriosam a dextris; et rursus, per <lb></lb>venas, in venam Cavam et usque ad auriculam dextram remeari, quemad­<lb></lb>modum ex pulmonibus, per arteriam dictam venosam, ad sinistrum ventri­<lb></lb>culum ” (ibi, pag. </s>

<s>56). </s></p><p type="main">

<s>Sopra lo storico dei pensamenti altrui grandissima efficacia dovrebbe <lb></lb>aver senza dubbio la fede, che ne fa di sè stesso l&#039;Autore. </s>

<s>Ma perchè può <lb></lb>esser benissimo che manchi della necessaria sincerità e interezza quella con­<lb></lb>fessione, abbiamo perciò il dovere di esaminarla. </s>

<s>Attesta dunque l&#039;Harvey <lb></lb>che il Circolo galenico gli fece ripensare al Circolo da sè poi felicemente <lb></lb>scoperto. </s>

<s>Chi ben riflette però trova che questo è troppo gran salto, e non <lb></lb>par credibile, secondo le leggi degli svolgimenti dell&#039;umano pensiero, che <lb></lb>la lontana scintilla del Fisiologo greco, senz&#039;altra esca mediata, abbia nella <lb></lb>mente del Fisiologo inglese suscitato quel grandissimo incendio. </s></p><p type="main">

<s>Per potere infatti legittimamente indurre il Circolo universale dal Cir­<lb></lb>colo polmonare, la copia e la velocità del sangue ne&#039;vasi non sarebbe stato <lb></lb>argomento efficace, senz&#039;esser certi che il setto medio è imperforato, che <lb></lb>non hanno le vene la loro origine dal Fegato, e che il circolo fra la vena <lb></lb>arteriosa e l&#039;arteria venosa non è ordinato a nutrire il polmone. </s>

<s>La descri­<lb></lb>zione galenica era come vedemmo viziata da tutti questi errori, e perchè <lb></lb>non dice l&#039;Harvey di essere stato egli il primo a scoprirli, e tacitamente <lb></lb>insinua essere stato fatto ciò per opera di altri, la sua scoperta dunque dovette <lb></lb>aver, per questi altri, una mediata preparazione più prossima di quella di <lb></lb>Galeno. </s></p><p type="main">

<s>Nel cap. </s>

<s>VII <emph type="italics"></emph>De motu cordis<emph.end type="italics"></emph.end> s&#039;accenna è vero al Colombo <emph type="italics"></emph>peritissimo <lb></lb>doctissimoque Anatomico<emph.end type="italics"></emph.end> (pag. </s>

<s>50), ma poi, sul principio del capitolo ap­<lb></lb>presso, si dà, rispetto alla descrizione del circolo polmonare, per un sem­<lb></lb>plice ripetitore dei detti dell&#039;antico Maestro, e se nel Proemio non si de­<lb></lb>frauda di aver notato che il sangue della vena arteriosa è alla nutrizion del <lb></lb>polmone soverchio, si fa in un&#039;asciutta parentesi e sotto voce. </s>

<s>Eppure noi <lb></lb>ripetiamo qui quel che dicemmo altrove, ed è che l&#039;Harvey apprese dalle <lb></lb>vivisezioni del Colombo ad osservare nella Natura i moti del cuore e del <pb xlink:href="020/01/1263.jpg" pagenum="138"></pb>sangue, e la ragione, che indusse il Discepolo a tacere com&#039;avesse il Mae­<lb></lb>stro per il primo osservato che alla sistole dell&#039;arteria corrisponde la dia­<lb></lb>stole del cuore, fu forse la ragion medesima, che lo indusse a tacer in che <lb></lb>modo facesse l&#039;Autor <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> progredire così le dottrine galeniche <lb></lb>intorno al giro del sangue, da renderle più prossime e più efficaci inspira­<lb></lb>trici della grande scoperta. </s>

<s>Se dunque è trasmesso a noi il dovere ed è af­<lb></lb>fidato l&#039;ufficio di parlare, diremmo che tra Galeno e l&#039;Harvey tramezzano le <lb></lb>speculazioni e le scoperte del Colombo e del Cesalpino, che sono i due no­<lb></lb>stri Italiani, da&#039;quali, come da sotterranea radice, scoppiarono al fortunato <lb></lb>Inglese i verdi allori. </s></p><p type="main">

<s>Dalle remote rive di Coo, quale onda malefica rinforzata dal Berengario <lb></lb>e dal Vesalio, s&#039;era come vedemmo diffuso l&#039;errore che il sangue trovasse <lb></lb>aperto un passaggio dal destro al sinistro ventricolo del cuore, attraverso al <lb></lb>setto medio, quando ad arrestare quell&#039;onda, che pur seppe vincere e tra­<lb></lb>passare l&#039;ostacolo, sorse il Colombo, tutto compiacente d&#039;essere stato egli <lb></lb>il primo ad annunziare al mondo una verità rimasta occulta per tanto tempo. <lb></lb></s>

<s>“ Inter hos ventriculos, egli dice, septum adest, per quod fere omnes exi­<lb></lb>stimant sanguini a dextro ventriculo ad sinistrum aditum patefieri, id ut fiat <lb></lb>facilius in transitu, ob vitalium spirituum generationem, tenuem reddi, sed <lb></lb>longa errant via, nam sanguis per arteriosam venam ad pulmonem fertur, <lb></lb>ibique attenuatur. </s>

<s>Deinde cum acre una, per arteriam venalem, ad sini­<lb></lb>strum cordis ventriculum defertur, quod nemo hactenus aut animadvertit, <lb></lb>aut scriptum reliquit, licet maxime sit ab omnibus animadvertendum ” (De <lb></lb>re anat. </s>

<s>cit., pag. </s>

<s>177). </s></p><p type="main">

<s>Sarebbe però il Colombo dovuto rimaner sorpreso di gran maraviglia, <lb></lb>se gli avesse il Flourens aperto sotto gli occhi il libro del Servet, additan­<lb></lb>dogli questo passo: “ Fit autem communicatio haec, non per parietem cor­<lb></lb>dis medium, ut vulgo creditur, sed magno artificio a dextro cordis ventri­<lb></lb>culo.... (Histoire cit., pag. </s>

<s>203), seguitando a descrivere il circolo polmonare <lb></lb>con parole molto simili a quelle ora trascritte dal VII libro <emph type="italics"></emph>De re ana­<lb></lb>tomica.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il fatto, benchè sia notabile, pur si potrebbe attribuire a qualche for­<lb></lb>tuito riscontro d&#039;idee, se si fossero i due Autori riscontrati in quel punto <lb></lb>solo, ma perchè son que&#039;punti tutti quelli, ne&#039;quali si tratta del circolo del <lb></lb>sangue, nasce un gran sospetto che l&#039;uno abbia ripetuto quel che aveva <lb></lb>letto o udito dire dall&#039;altro. </s>

<s>E perchè meglio si senta la ragione di questo <lb></lb>sospetto, confrontiamo le idee e le speculazioni del Nostro con le idee e con <lb></lb>le speculazioni dello Spagnolo. </s></p><p type="main">

<s>Una dalle più importanti osservazioni fatte dal Colombo, l&#039;utilità della <lb></lb>quale, in promovere le dottrine galeniche verso la scoperta del circolo uni­<lb></lb>versale del sangue, nemmen l&#039;Harvey potè negare, fu quella che la vena <lb></lb>arteriosa era troppo grande, per dover solamente dispensare il necessario <lb></lb>alimento al polmone, d&#039;onde argutamente ne concludeva che dovess&#039;esser <lb></lb>lo stesso circolo polmonare ordinato, non in servigio di quel viscere solo, <pb xlink:href="020/01/1264.jpg" pagenum="139"></pb>ma di tutte le membra. </s>

<s>“ Vena arteriosa haec, quam diximus, magna est <lb></lb>satis, immo vero multo maior quam necesse fuerit, si sanguis ad pulmones <lb></lb>supra cor exiguo intervallo deferendus duntaxat erat ” (De re anat. </s>

<s>cit., <lb></lb>pag. </s>

<s>178). Alle quali parole fanno esatto riscontro quest&#039;altre del Servet: <lb></lb>“ Confirmat hoc magnitudo insignis venae arteriosae, quae nec talis, nec tanta <lb></lb>facta esset, nec tantam a corde ipso vim purissimi sanguinis in polmones <lb></lb>emitteret, ob solum suum nutrimentum ” (Flourens, Histoire cit., pag. </s>

<s>204). </s></p><p type="main">

<s>Dop&#039;avere il Colombo, per le dette ragioni, argomentato che il circolo <lb></lb>polmonare doveva servire agli usi di tutto il corpo, determina particolar­<lb></lb>mente questi usi, e dice che consistono in preparare gli spiriti, da dispen­<lb></lb>sarsi poi, per mezzo del cuore e delle arterie, a tutte le membra. </s>

<s>“ Est <lb></lb>autem praeparatio et pene generatio vitalium spirituum, qui postmodum in <lb></lb>corde magis perficiuntur. </s>

<s>Aerem namque per nares et os inspiratum su­<lb></lb>scipit, nam asperae arteriae vehiculo per universum pulmonem fertur. </s>

<s>Pulmo <lb></lb>vero aerem illum una cum eo sanguine miscet, qui a dextro cordis ven­<lb></lb>triculo profectus per arterialem venam deducitur. </s>

<s>Vena enim haec arterialis, <lb></lb>praeter quam quod sanguinem pro sui alimento defert, adeo ampla est ut <lb></lb>alius usus gratia deferre possit. </s>

<s>Sanguis huiusmodi, ob assiduum pulmonum <lb></lb>motum, agitatur et una cum aere miscetur, qui et ipse in hac collisione <lb></lb>refractioneque praeparatur, ut simul mixti sanguis et aer per arteriae ve­<lb></lb>nalis ramos suscipiantur, tamdemque per ipsius truncum ad sinistrum cor­<lb></lb>dis ventriculum deferantur. </s>

<s>Deferuntur vero tam belle mixti atque atte­<lb></lb>nuati ut cordi exiguus praeterea labor supersit. </s>

<s>Post quam exiguam elabo­<lb></lb>rationem, quasi extrema imposita manu, vitalibus hisce spiritibus reliquum <lb></lb>est ut illos, ope arteriae ahorti, per omnes corporis partes distribuat ” (De <lb></lb>re anat. </s>

<s>cit., pag. </s>

<s>223) </s></p><p type="main">

<s>Benchè dica con gran fidanza il Colombo esser questo nuovo uso dei <lb></lb>polmoni tale, <emph type="italics"></emph>quem nemo Anatomicorum hactenus somniavit,<emph.end type="italics"></emph.end> pure è un <lb></lb>fatto che nel Servet si trovano, con mirabile fedeltà, espresse tutte le più <lb></lb>minute particolarità di quei concetti. </s>

<s>“ Est prius intelligenda substantialis <lb></lb>generatio ipsius vitalis spiritus, qui ex aere inspirato et subtilissimo san­<lb></lb>guine componitur et nutritur. </s>

<s>Vitalis spiritus in sinistro cordis ventriculo <lb></lb>suam originem habet, iuvantibus maxime pulmonibus ad ipsius generatio­<lb></lb>nem.... Generatur ex facta in pulmonibus mixtione inspirati aeris cum ela­<lb></lb>borato subtili sanguine, quem dexter ventriculus cordis sinistro communi­<lb></lb>cat. </s>

<s>” E dopo aver detto che la comunicazione si fa per via del circolo <lb></lb>polmonare, soggiunge: “ Deinde in ipsa arteria venosa inspirato aeri mi­<lb></lb>scetur.... atque ita tandem a sinistro cordis ventriculo totum mixtum <lb></lb>attrahitur, apta supellex ut fiat spiritus vitalis ” (Flourens, Histoire cit., <lb></lb>pag. </s>

<s>203, 4). </s></p><p type="main">

<s>Il Colombo, come ad altro proposito avvertimmo, dice che questi spi­<lb></lb>riti vitali si strasformano in animali ne&#039;plessi coroidei, da lui più volentieri <lb></lb>chiamati <emph type="italics"></emph>retiformi,<emph.end type="italics"></emph.end> per il moto de&#039;quali “ miscetur cum vitalibus spiritibus <lb></lb>aer. </s>

<s>Itaque spiritus animales evadunt ex aere eo quo diximus modo prae-<pb xlink:href="020/01/1265.jpg" pagenum="140"></pb>parato, et ex vitalibus dictis spiritibus ” (De re anat. </s>

<s>cit., pag. </s>

<s>191). Ora, <lb></lb>benchè immediatamente soggiunga queste parole: <emph type="italics"></emph>quae res a nemine ante <lb></lb>me observata fuit,<emph.end type="italics"></emph.end> il Servet, fedelmente riscontrandosi col Colombo anche <lb></lb>nel chiamar retiforme il plesso coroideo, così scrive: “ Hic itaque spiritus <lb></lb>vitalis a sinistro cordis ventriculo in arteriis totius corporis deinde tran­<lb></lb>sfunditur, ita ut qui tenuior superiora petat, ubi magis adhuc elaboratur, <lb></lb>praecipue in <emph type="italics"></emph>plexu retiformi,<emph.end type="italics"></emph.end> sub basi cerebri sito, in quo ex vitali fieri <lb></lb>incipit animalis ” (Flourens, Histoire cit., pag. </s>

<s>205). </s></p><p type="main">

<s>Queste somiglianze, così ripetutamente notate fra le idee e le stesse <lb></lb>espressioni, son tali, che anche i nostri lettori saranno oramai persuasi non <lb></lb>si potere attribuire al caso, ond&#039;è necessità concludere o che il Servet ap­<lb></lb>prese quelle dottrine in Italia dalla viva voce del Colombo, mentre pubbli­<lb></lb>camente insegnava dalle cattedre di Padova, di Pisa e di Roma, o che il <lb></lb>Colombo stesso ebbe fra le mani e imparò l&#039;Anatomia dal libro teologico <lb></lb>del Serveto. </s>

<s>Cosicchè ogni volta che nel Trattato <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> si legge <lb></lb><emph type="italics"></emph>questa cosa prima di me nessuno l&#039;aveva detta,<emph.end type="italics"></emph.end> oppure: <emph type="italics"></emph>nessun altro ana­<lb></lb>tomico l&#039;aveva nemmen sognata,<emph.end type="italics"></emph.end> non faccia altro l&#039;Autore se non che ri­<lb></lb>petere una gran menzogna. </s></p><p type="main">

<s>Chi si forma un giusto giudizio de&#039;due uomini, ripensando principal­<lb></lb>mente che tutti gli Spagnuoli, a&#039;quali era per legge ecclesiastica e civile <lb></lb>proibito di sezionar cadaveri umani, si trovavan costretti o ad imparare <lb></lb>l&#039;Anatomia sui libri o a venire a scuola in Italia; e chi pone a confronto <lb></lb>il Teologo fanatico col Padre dell&#039;Anatomia sperimentale, non esita a dar di <lb></lb>ciò sentenza definitiva. </s>

<s>Questa sentenza poi è nuova e importante per la <lb></lb>Storia della Fisiologia in Italia, rivendicandosi per essa, con giuste ragioni, <lb></lb>al Colombo il merito di aver egli anatomicamente e fisiologicamente descritto <lb></lb>per il primo il circolo polmonare, e dimostrato quanto si fossero ingannati <lb></lb>gli Anatomici prima di lui a creder nel cuore aperti al sangue que&#039;fori, che <lb></lb>ne attraversano il setto medio. </s></p><p type="main">

<s>Le illustrate galeniche dottrine e i rimossi errori preparavano così le <lb></lb>vie alla gloria dell&#039;Harvey, ma rimaneva ancora un grande ostacolo al li­<lb></lb>bero progredire per quelle vie, ostacolo che il Colombo non valse a sgom­<lb></lb>brare. </s>

<s>Malaugurato seguace de&#039;falli di Galeno asseverò che il Fegato doveva <lb></lb>annoverarsi “ inter principes nostri corporis partes ” (De re anat., pag. </s>

<s>163. <lb></lb>Egli è, soggiunge, il viscere dedicato alla sanguificazione, e in verità non <lb></lb>altrove che in lui e da lui e non dal cuore, come Aristotile scrisse, si ge­<lb></lb>nera il sangue. </s>

<s>“ Est igitur Jecur omnium venarum caput, fons, origo et <lb></lb>radix ” (ibi, pag. </s>

<s>164). </s></p><p type="main">

<s>Il Fegato e il Cuore son nel microcosmo il Sole e la Terra dell&#039;uni­<lb></lb>verso: s&#039;aspettava perciò che sorgesse anche alla Fisiologia il suo Coper­<lb></lb>nico, il quale riordinasse i moti, e riponesse il cuore nella sua sede. </s>

<s>È sin­<lb></lb>golare che nella storia della Fisiologia e dell&#039;Astronomia, scambiate le parti, <lb></lb>un Aristotelico esca fuori a far gli uffici del Copernico, e Aristotile stesso <lb></lb>scambi l&#039;abito con Niceta di Siracusa o con Aristarco. </s></p><pb xlink:href="020/01/1266.jpg" pagenum="141"></pb><p type="main">

<s>Quell&#039;Aristotelico, che venne a restaurare il principato del cuore, come <lb></lb>il Copernico avea restaurato il principato del Sole, è Andrea Cesalpino. </s>

<s>Egli <lb></lb>è il primo, nella risorta Anatomia, il quale osa di contrapporre all&#039;oracolo <lb></lb>di Galeno la sentenza che il cuore e non il Fegato è il principio del san­<lb></lb>gue. </s>

<s>“ Quod si cor principium est sanguinis, venarum quoque et arteria­<lb></lb>rum principium esse debet; vasa enim haec sanguini sunt destinata ” (Quae­<lb></lb>stiones perip., Venetiis 1571, fol. </s>

<s>102 ad terg.). </s></p><p type="main">

<s>Sarà dunque il cuore invece del Fegato l&#039;organo della sanguificazione? </s>

<s><lb></lb>No, risponde il Cesalpino: quest&#039;organo risulta da tutto insieme il sistema <lb></lb>venoso, che egli appella col nome di <emph type="italics"></emph>Viscere,<emph.end type="italics"></emph.end> e al quale attribuisce le fun­<lb></lb>zioni dagli anatomici precursori attribuite al Fegato stesso. </s></p><p type="main">

<s>Il sangue insomma così raccolto e continuamente restaurato dalle vene <lb></lb>mesenteriche, che assorbono il chilo, ha, secondo il Cesalpino, due moti <lb></lb>opposti <emph type="italics"></emph>ad instar Euripi,<emph.end type="italics"></emph.end> uno nello venuzze capillari diretto alle parti per <lb></lb>nutrirle, e l&#039;altro ne&#039;più grossi tronchi venosi diretto al cuore. </s>

<s>Questa se­<lb></lb>conda direzione, che va al cuore opposta all&#039;altra del sangue che va alle <lb></lb>parti, la dimostra il Nostro per via delle allacciature. </s>

<s>“ Sed illud specula­<lb></lb>tione dignum videtur propter quid ex vinculo intumescunt venae ultra locum <lb></lb>apprehensum, non citra, quod experimentum sciunt qui venam secant, vin­<lb></lb>culum enim adhibent citra locum sectionis, non ultra, quia tument venae <lb></lb>ultra vinculum, non citra. </s>

<s>Debuisset autem opposito modo contingere, si mo­<lb></lb>tus sanguinis et spiritus a <emph type="italics"></emph>Visceribus,<emph.end type="italics"></emph.end> fit in totum corpus ” (Quaestionem <lb></lb>medicarum, Venetiis 1593, pag. </s>

<s>234). </s></p><p type="main">

<s>Il fine poi, per cui il sangue scende nel cuore, è quello di concocersi <lb></lb>nel ventricolo destro, ch&#039;è la fucina del calore. </s>

<s>Così concetto e purificato <lb></lb>passa attraverso al setto medio nel ventricolo sinistro, ma perchè sarebbe <lb></lb>troppo fervente, una parte, invece di attraversare il setto, va a refrigerarsi <lb></lb>per la vena arteriosa nel polmone, d&#039;onde così refrigerato torna, per l&#039;ar­<lb></lb>teria venosa, nel ventricolo sinistro a mescolarsi con l&#039;altro sangue, dive­<lb></lb>nuto più sincero e tutto spiritoso. </s>

<s>“ Cum enim fervere oporteret in corde <lb></lb>sanguinem ut fieret alimenti perfectio, primo quidem in dextro ventriculo, <lb></lb>in quo crassior adhuc continetur sanguis, deinde autem in sinistro, ubi sin­<lb></lb>cerior iam sanguis est, partim per medium septum, partim per medios pul­<lb></lb>mones, refrigerationis gratia, ex dextro in sinistrum transmittitur ” (Quae­<lb></lb>stiones perip. </s>

<s>cit., fol. </s>

<s>112). </s></p><p type="main">

<s>Il sangue nel ventricolo sinistro, divenuto così spiritoso, è, per la ela­<lb></lb>sticità degli stessi spiriti, diffusivo. </s>

<s>Si diffonde di fatti attraverso all&#039;Aorta <lb></lb>per l&#039;estreme diramazioni arteriose, dove giunto lo spirito esala, lasciando <lb></lb>come per sedimento la materia del sangue, che serve a nutrire ogni parte <lb></lb>del corpo in cui rimane. </s>

<s>“ Motus igitur continuus a corde in omnes cor­<lb></lb>poris partes agitur, quia continua est spiritus generatio, qui sua amplifica­<lb></lb>tione diffundi celerrime in omnes partes aptus est. </s>

<s>Simul autem alimentum <lb></lb>nutritivum fert, et auctivum ex venis elicit, per osculorum communionem, <lb></lb>quem Graeci <emph type="italics"></emph>anastomosim<emph.end type="italics"></emph.end> vocant. </s>

<s>Tandem vero, spiritu in aerem ambien-<pb xlink:href="020/01/1267.jpg" pagenum="142"></pb>tem difflante, alimenti corpulentia remanet partim frigore, partim calore <lb></lb>coagulata ” (ibi, fol. </s>

<s>109). </s></p><p type="main">

<s>Chi bene attende a questi chiarissimi sensi facilmente si persuade es­<lb></lb>sere stata vana l&#039;opera, e inutilmente avere spese tante parole tutti coloro, <lb></lb>i quali vollero al Cesalpino rivendicare la scoperta del circolo universale. </s>

<s><lb></lb>Perchè, lasciamo stare ch&#039;egli, non dando fede al Colombo, ripetè l&#039;antico <lb></lb>errore galenico del passaggio del sangue attraverso al setto medio, disse, <lb></lb>com&#039;apparisce chiaro dall&#039;ultimo luogo citato, che il sangue arterioso non <lb></lb>ritorna alle vene, ma che si esaurisce tutto nelle estremità capillari, parte <lb></lb>dissipandosi in esalazioni, e parte rimanendo a nutrire le parti. </s>

<s>Anzi, tut­<lb></lb>t&#039;altro che ricevere le vene dalle arterie, il sistema arterioso <emph type="italics"></emph>elicit alimen­<lb></lb>tum auctivum ex venis per osculorum communionem,<emph.end type="italics"></emph.end> ossia per i contatti, <lb></lb>che le due diverse specie di vasi hanno qua e là lungo i loro decorsi. </s></p><p type="main">

<s>Il Cesalpino insomma non conobbe formalmente il circolo universale, <lb></lb>benchè, tolto di mezzo il Fegato, avesse materialmente descritta la continua­<lb></lb>zione di tutto il sistema de&#039;vasi sanguiferi, e la loro riunione nel cuore, <lb></lb>dando così (nè piccolo ne dovrebhe essere perciò il merito) la più prossima <lb></lb>e immediata preparazione alla grande scoperta arveiana. </s>

<s>Che altro in vero <lb></lb>rimaneva a fare all&#039;Harvey, dopo il Colombo e il Cesalpino, se non che ri­<lb></lb>conoscere la vanità degli spiriti nella sostanza del sangue, il quale perciò <lb></lb>uon esala dagli estremi vasi arteriosi, ma ritorna tutto alle vene? </s></p><p type="main">

<s>Quella vanità degli spiriti poi non era difficile lo scoprirla, imparando <lb></lb>l&#039;arte da chi per esperienza l&#039;aveva confermata. </s>

<s>Il Colombo infatti, in trat­<lb></lb>tar della vivisezione di un cane aveva scritto: “ Si arteriam asperam, inter <lb></lb>annulum et annulum, secueris, et arundinem immiseris, si eam ori admo­<lb></lb>veris et buccis infles, pulmones illico attolluntur et cor ipsum amplexabun­<lb></lb>tur, et paulo post pulsus immutabitur seipso maior factus ” (De re anat., <lb></lb>pag. </s>

<s>261) attribuendo questa frequenza di polso alla maggior copia d&#039;aria <lb></lb>passata dal polmone nell&#039;arteria venosa e nel cuore. </s>

<s>L&#039;Harvey, dopo aver os­<lb></lb>servato che all&#039;ingresso e all&#039;egresso dell&#039;aria si sarebbero dovute opporre <lb></lb>le valvole tricuspidali e semilunari, ripetè l&#039;esperienza, ch&#039;ei dà com&#039;ese­<lb></lb>cuzion di un progetto di Galeno, e non come un fatto del Colombo, con­<lb></lb>cludendone contro lo stesso Colombo che dal polmone insufflato non passa <lb></lb>punto d&#039;aria nella vena polmonare, nè nel ventricolo sinistro. </s>

<s>“ Si quis <lb></lb>experimentum Galeni faceret et cani adhuc viventi tracheam incideret, et <lb></lb>follibus pulmones aere impleret per vim et distentos ligaret fortiter, idem <lb></lb>mox dissecto pectore multam aeris copiam in pulmonibus usque ad extre­<lb></lb>mam illorum tunicam invenerit, sed neque in arteria venosa, neque in si­<lb></lb>nistro ventriculo cordis quidquam ” (De motu cordis cit., pag. </s>

<s>18). </s></p><p type="main">

<s>Or essendo i fatti così, come da noi sono stati narrati, domandiamo ai <lb></lb>nostri Lettori se credono sincera la confessione fattaci dall&#039;Harvey, che cioè <lb></lb>unico inspiratore alla sua scoperta sia stato il circolo polmonare descritto <lb></lb>da Galeno. </s>

<s>Chi sa che Galeno ritenne essere il setto medio perforato, e aver <lb></lb>le vene la loro origine dal Fegato, domanderà ancora, prima di rispondere, <pb xlink:href="020/01/1268.jpg" pagenum="143"></pb>se fu egli il primo l&#039;Harvey che emendò que&#039;galenici errori, e fatto certo che <lb></lb>non fu così, dovrà concluderne essere per lo meno sospetta la confessione ar <lb></lb>veiana, parendo assai più naturale il riuscir felicemente al termine col fare <lb></lb>un passo solo, che col dare un gran salto smisurato. </s>

<s>E veramente dal Ce­<lb></lb>salpino è un passo, e da Galeno all&#039;Harvey è un salto tale, che si direbbe <lb></lb>impossibile alle più snelle gambe di un uomo. </s></p><p type="main">

<s>Comunque sia, che troppo in lungo ci porterebbe il discorso, uno stra­<lb></lb>niero, e sia pur se così vuolsi che ne fosse inconsapevole, sentì viva nella <lb></lb>mente quell&#039;efficacia delle tradizioni scientifiche italiane, alla quale gl&#039;Ita­<lb></lb>liani stessi rimasero ottusi, e a lui toccò il merito di dar l&#039;ultima perfezione <lb></lb>alle idee del Cesalpino, sentenziando il sangue arterioso non restar nelle <lb></lb>estremità capillari, nè esser le vene dello stesso sangue riproduttrici e re­<lb></lb>stauratrici, ma “ ab unoquoque membro ipsas venas hunc sanguinem per­<lb></lb>petuo retroducere ad cordis locum ” (De motu cordis cit., pag. </s>

<s>58). La ve­<lb></lb>rità della qual sentenza è provata nel suo libro dall&#039;Harvey con argomenti <lb></lb>di vario genere, nell&#039;ammannire i quali e nel convalidarli ebbero, come ve­<lb></lb>dremo nella seguente storia, grandissima parte i nostri Italiani. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Che il sangue abbia nelle vene il suo corso diretto verso il cuore si <lb></lb>prova dall&#039;Harvey prima di tutto per via delle allacciature, nel modo stesso <lb></lb>indicato dal Cesalpino, ed è questo anzi l&#039;argomento, di che si fanno prin­<lb></lb>cipalmente forti gl&#039;inconsiderati zelanti, che vorrebbero sopra l&#039;Inglese al <lb></lb>Nostro rivendicare la gloriosa scoperta. </s>

<s>L&#039;altra prova sperimentale è dal­<lb></lb>l&#039;Autore <emph type="italics"></emph>De motu cordis<emph.end type="italics"></emph.end> dedotta dalle valvole, la scoperta delle quali è ivi <lb></lb>attribuita o al Fabricio d&#039;Acquapendente o a Giacomo Sylvio, come vuole <lb></lb>il Riolano. </s>

<s>Ma perchè veramente il Sylvio non ha gran parte in quella sco­<lb></lb>perta, e il Fabricio, benchè ve n&#039;abbia grandissima, non può pretendersi i <lb></lb>primi onori, convien che, in cosa di tanto momento, la nostra storia risalga <lb></lb>a investigar del fatto i primi principii. </s></p><p type="main">

<s>Ritrovandosi in Ratisbona don Francesco d&#039;Este gravemente infermo, <lb></lb>fu da Ferrara mandato a curarlo Giovan Batista Canani, archiatro ducale. </s>

<s><lb></lb>O fosse chiamato a consulto o si trovasse ivi per caso, visitava col Canani <lb></lb>l&#039;infermo anche il Vesalio, e i due Medici, trovandosi nella medesima ca­<lb></lb>mera insieme, vi si trattenevano a colloquio di cose anatomiche. </s>

<s>Era sui primi <lb></lb>anni della pubblicazione della grande opera <emph type="italics"></emph>De corporis humani fabrica,<emph.end type="italics"></emph.end><lb></lb>e il nostro Ferrarese, lieto di poter significare la sua ammirazione alla pre­<lb></lb>senza del celebre Autore, rivolse un giorno il discorso sopra ciò che, in <lb></lb>principio del cap. </s>

<s>IV del III libro, aveva letto della fabbrica delle vene e <lb></lb>delle arterie, riassumendo il senso di queste parole, stampate a pag. </s>

<s>261 <lb></lb>della prima edizione dell&#039;Opera vesaliana fatta nel 1543 in Basilea. </s>

<s>“ Sicut <pb xlink:href="020/01/1269.jpg" pagenum="144"></pb>Natura venae et arteriae, praeter proprias ipsarum tunicas, aliam subinde <lb></lb>membranam circumdedit, cuius beneficio opportune conterminis partibus <lb></lb>alligatur, tuteque prorepat; sic quoque, cum minime ignoraret unumquod­<lb></lb>que vas inibi noxiis opportunius expositum esse, ubi in ramos discinditur, <lb></lb>tutae fixionis gratia, praeter eiusmodi membranas, substantiam quamdam <lb></lb>mediocriter mollem modiceque cedentem condidit, qua nodorum in arbori­<lb></lb>bus ritu vasorum divaricationes sic passim replent. </s>

<s>” </s></p><p type="main">

<s>Soggiungeva il Canani di avere altre singolarità scoperto nelle vene, e <lb></lb>specialmente nel principio della vena azygos o <emph type="italics"></emph>senza pari,<emph.end type="italics"></emph.end> nelle vene renali, <lb></lb>e in quelle adiacenti alla parte più elevata dell&#039;osso sacro, ed erano quelle <lb></lb>nuove cose scoperte alcune membrane similissime nella struttura e nella <lb></lb>disposizione a quelle, che si osservano ne&#039;principii della vena arteriale e <lb></lb>della grande arteria, l&#039;ufficio proprio delle quali membrane credeva il Ca­<lb></lb>nani che fosse quello d&#039;impedire il reflusso del sangue. </s>

<s>Udito ciò e tornan­<lb></lb>dogli cosa nuova, si sentì il Vesalio frugato da una viva curiosità di veri­<lb></lb>ficarla, tanto più, quando nel 1547 Amato Lusitano divulgò la scoperta dello <lb></lb>stesso Canani, aggiungendovi di suo per confermarla un&#039;esperienza, la quale <lb></lb>essendo manifestamente falsa, anzi mendace, tinse della sua pece il vero, <lb></lb>che fu perciò dagli Anatomici, per tutto il rimanente secolo XVI, con fiera <lb></lb>ostinazione perseguitato. </s></p><p type="main">

<s>L&#039;esperienza del Lusitano consisteva nel soffiar nella Vena senza pari, <lb></lb>e nell&#039;asseverare che il fiato, nonchè il sangue, per l&#039;impedimento oppo­<lb></lb>stogli dalle valvole non andava a riuscire nella vena Cava. </s>

<s>Il Vesalio dun­<lb></lb>que, datosi a far più diligente anatomia, e non trovando segni evidenti della <lb></lb>figura di quelle valvole, e dall&#039;altra parte facilmente scoperta la menzogna <lb></lb>del Lusitano, ne concluse che tutti coloro, i quali dopo il Canani dicevano <lb></lb>di avere osservate le dette valvole in tutte le vene del corpo, e particolar­<lb></lb>mente delle braccia e delle gambe, dovevano essere stati allucinati da quelle <lb></lb>membrane, che la Natura appose qua e là ne vasi sanguiferi per loro rin­<lb></lb>forzo. </s>

<s>Nella seconda edizione perciò della sua Opera anatomica, al capitolo <lb></lb>sopra citato aggiunse queste parole: “ Venarum haec crassior substantia, <lb></lb>quum venae sanguine inanitae intus conspiciuntur, flaccidaeque secundum <lb></lb>ipsarum ductum dissectae propendent; ita versus venarum amplitudinem <lb></lb>connivet, ut inter secandum astantium nonnulli eam instar membranei cor­<lb></lb>poris procreatam aliquando contenderint, quod urinam in meatibus hanc a <lb></lb>renibus in vesicam deferentes refluere, retrudive prohibet. </s>

<s>Ubi etiam nonnun­<lb></lb>quam eminentem illam venarum corporis substantiam membranis compa­<lb></lb>rare studuerunt, quae magnae arteriae et venae arterialis, ubi haec e corde <lb></lb>prodeunt spectantur orificiis, perinde sane ac si, e vena sine pari et e venis <lb></lb>brachia caput, renes et crura adeuntibus, eiusmodique compluribus venis <lb></lb>sanguinem in Cavae caudicem, vel in sanguinis missione et variis animi mo­<lb></lb>tibus, eiusmodique occasionibus, remeare refluereve, secus multo quam ego <lb></lb>existimo, foret impossibile, qui crassiorem eam venae corporis, in ipsa ra­<lb></lb>morum dissectione occurrentem substantiam, roboris cuiusdam gratia e Na-<pb xlink:href="020/01/1270.jpg" pagenum="145"></pb>tura procreatam esse in scholis contendere soleo, pravi quorundam iudicio <lb></lb>haud ignarus, qui, integris venis, ne flatum quidem, e vena pari carente in <lb></lb>Cavae caudicem, duci posse turpiter confingunt ” (Basileae 1555, pag. </s>

<s>278). </s></p><p type="main">

<s>A così fiero risentimento, espresso in queste ultime parole contro il <lb></lb>Lusitano, fece eco il Falloppio, il quale anzi rincrudeli l&#039;accusa dicendo <lb></lb>quello essere non un pravo giudizio, nè una turpitudine, ma un vero de­<lb></lb>litto. </s>

<s>Nelle Osservazioni anatomiche infatti, dop&#039;aver riferito ciò che lo stesso <lb></lb>Lusitano dice delle valvole nella vena azygos, e in altre, soggiunge che co­<lb></lb>stui, presente alle dissezioni del Canani, non dovette aver nè bene veduto <lb></lb>i fatti, nè bene intese le parole di quel dottissimo e venerabile uomo, l&#039;at­<lb></lb>tribuire al quale i proprii errori era un rendersi colpevole del delitto della <lb></lb>calunnia. </s>

<s>“ Quare ego in Amatum, virum alioquin doctum, potius culpam <lb></lb>huius criminis reiicerem, quoniam non ita recte omnia, quae ad Anatomen <lb></lb>pertinent, aut viderit aut intellexerit, ut recte sunt a Canano explicata ” <lb></lb>(Opera omnia, Francofurti 1584, pag. </s>

<s>443). </s></p><p type="main">

<s>Fu da queste parole che, passando il Vesalio ad esame ogni detto del <lb></lb>Falloppio, prese occasione di compendiar la storia da noi narrata in princi­<lb></lb>pio del presente discorso. </s>

<s>“ Ratisbonae, quum dom. </s>

<s>Franciscum Estensem <lb></lb>aegrum cum ipso Canano viserem, is mihi retulit se in Venae coniuge ca­<lb></lb>rentis initio, et idem in venarum renes adeuntium, et in sectionum venae, <lb></lb>iuxta elatiorem sacri ossis sedem occurrentium orificiis, membranas eiusmodi <lb></lb>observare, quales in Venae arterialis et Magnae arteriae occurrunt princi­<lb></lb>piis, hasque sanguinis refluxui obstare asseruit. </s>

<s>Unde aliam hinc occasio <lb></lb>afferebatur ut rem num ita se haberet mox sectione expedirem. </s>

<s>Cumque <lb></lb>Amatum insuper in Canani comperirem esse sententia, illumque ex huius <lb></lb>iudicio pendere legerem, fini capitis illius, quo qui natura venarum robori <lb></lb>in distributione prospexit, prosequor, satis dilucide addidi quidnam de eius­<lb></lb>modi membranis veniat statuendum: has nemque non reperi ” (Anatomi­<lb></lb>carum Gabr. </s>

<s>Falloppii Observat. </s>

<s>Examen, Venetiis 1564, pag. </s>

<s>83). </s></p><p type="main">

<s>Il Colombo pure, tacendone, sembra che non le trovasse ne&#039;tronchi e <lb></lb>ne&#039;rami delle altre vene, fuor che nelle meseraiche, là dove s&#039;aprono a sug­<lb></lb>gere dagli intestini il chilo, dicendo essere state con grand&#039;arte dalla Natura <lb></lb>ivi apposte “ ut chylum facile suscipere possent, ne autem egrediatur mem­<lb></lb>branulae illae prohibent “ (De re anat. </s>

<s>cit., pag. </s>

<s>165). Sulla fine del se­<lb></lb>colo XVI Giovan Batista Carcano e Andrea Laurent, per citar due de&#039;più <lb></lb>celebri anatomici fra gl&#039;Italiani e gli stranieri di que&#039;tempi, negarono essi <lb></lb>pure l&#039;esistenza delle valvole, intorno a che il Laurent stesso ha queste <lb></lb>espresse parole: “ Quas autem in azygos ramis somniavit membranulas, <lb></lb>velut hostiola sanguinis refluxum impedientia, Amatus Lusitanus, nobis nec <lb></lb>cuiquam adhuc vidisse contigit ” (Historia anat. </s>

<s>corporis hum., Parisiis 1599, <lb></lb>pag. </s>

<s>92). </s></p><p type="main">

<s>Come se la storia de&#039;fatti fin qui narrati fosse stata cancellata dai libri, <lb></lb>il Fabricio d&#039;Acquapendente un giorno del 1574 preme a caso col dito una <lb></lb>vena, e vede formarsi in essa un rigonfiamento, senza dubbio per un ri-<pb xlink:href="020/01/1271.jpg" pagenum="146"></pb>stagno di sangue: frega in giù col dito sulla stessa vena, e vede farsi lo <lb></lb>stesso. </s>

<s>Non sapendo in sull&#039;istante qual si fosse la causa di ciò, gli occorse <lb></lb>poi sezionando di trovar le vene attraversate qua e là dalle valvole, alle quali <lb></lb>non ebbe dubbio di attribuire quell&#039;osservato ristagno. </s>

<s>Che tal si fosse ve­<lb></lb>ramente l&#039;origine della scoperta lo dice da sè l&#039;Autore, con queste parole: <lb></lb>“ Si enim premere, aut deorsum fricando adigere sanguinem tentes, cursum <lb></lb>ipsius ab ipsis ostiolis intercipi remorarique aperte videbis, neque enim ali­<lb></lb>ter ego in huiusmodi nolitiam sum deductus ” (De vunarum ostiolis, Pa­<lb></lb>duae 1603, pag. </s>

<s>2). </s></p><p type="main">

<s>Contento per allora il Fabricio a diffonder con la viva voce negli sco­<lb></lb>lari la sua scoperta, Salomone Alberto, tedesco, ne scrisse il primo, nel 1579, <lb></lb>per le stampe, divulgandola fra&#039;suoi nazionali, col darne la debita gloria allo <lb></lb>scopritore, ciò che fece risolverlo finalmente a pubblicare in Padova quel­<lb></lb>l&#039;opuscolo <emph type="italics"></emph>De venarum ostiolis,<emph.end type="italics"></emph.end> dedicato all&#039;inclita nazione germanica, e <lb></lb>dove più efficacemente delle brevi parole parlano le bellissime otto grandi <lb></lb>tavole aggiunte. </s>

<s>Chi ha letto la storia sopra narrata non può certamente <lb></lb>capacitarsi come nel 1603 il Fabricio potesse così scrivere, nell&#039;introdursi a <lb></lb>trattare di quell&#039;argomento. </s>

<s>“ De his itaque in praesentia locuturi, subit <lb></lb>primum mirari quomodo ostiola haec, ad hanc usque aetatem, tam priscos <lb></lb>quam recentiores Anatomicos adeo latuerint, ut non solum nulla prorsus <lb></lb>mentio de ipsis facta sit, sed neque aliquis prius haec viderit, quam anno <lb></lb>Domini septuagesimo quarto supra millesimum et quingentesimum, quo a <lb></lb>me summa cum laetitia inter dissecandum observata fuere ” (pag. </s>

<s>1). </s></p><p type="main">

<s>Un altro fatto riman pure incompreso in questa storia, ed è che, osti­<lb></lb>natamente negata la scoperta delle valvole al Canano, fosse poi creduta al­<lb></lb>l&#039;Acquapendente da tutti senza contradizione. </s>

<s>Si potrebbe forse attribuire <lb></lb>la cosa al progresso, fatto dal pensiero scientifico in più di un mezzo secolo <lb></lb>di tempo, ma v&#039;ebbe forse gran parte l&#039;antipatia al Lusitano, ebreo, e la <lb></lb>simpatia per l&#039;Acquapendente, venerabile vecchio. </s></p><p type="main">

<s>Da questo, che giusto è detto <emph type="italics"></emph>venerabilis senex,<emph.end type="italics"></emph.end> confessa di aver avuto <lb></lb>la scoperta l&#039;Harvey, nè gli giova chiamare in parte del merito il Sylvio, <lb></lb>posteriore al Canano, e complice di quel crimine, di che facevasi terribile <lb></lb>accusatore il Falloppio. </s>

<s>Poco più tardi s&#039;incominciò a dare all&#039;Acquapen­<lb></lb>dente un altro competitore in Paolo Sarpi, alla qual voce dovette aver ag­<lb></lb>giunto non poco credito il Peiresc, che a proposito della scoperta arveiana, <lb></lb>discorrendo delle valvole, si ricordava, secondo che riferisce il Gassendi nella <lb></lb>Vita di lui, esserne stato <emph type="italics"></emph>inventorem primum Sarpium servitam<emph.end type="italics"></emph.end> (Pari­<lb></lb>siis 1641, pag. </s>

<s>222). Ma perchè i fanatici non seppero poi confermar la sen­<lb></lb>tenza coi documenti, non rimane ai savii a ragionare in altro modo da quel <lb></lb>che insegnava il Morgagni, a cui non pareva possibile che un fraticello no­<lb></lb>vizio di 22 anni si facesse dimostratore a un vecchio e peritissimo anato­<lb></lb>tomico. </s>

<s>Nè val che l&#039;Acquapendente ricordi il Sarpi nell&#039;osservazione della <lb></lb>pupilla, che si dilata e si restringe secondo che la luce è debole o viva, <lb></lb>“ haec autem, bene avverte lo stesso Morgagni, non quae ad corporis struc-<pb xlink:href="020/01/1272.jpg" pagenum="147"></pb>turam, sed quae ad actiones attinebant; non quae ad scalpellum require­<lb></lb>bant, sed quae per se ante oculos posita erant; non quae Sarpius primum, <lb></lb>sed quae alii antea animadverterant ” (Epistolae anat., T. II, Venetiis 1740, <lb></lb>pag. </s>

<s>155). </s></p><p type="main">

<s>Comunque sia, nè l&#039;Acquapendente nè il Sarpi conobbero l&#039;uso delle <lb></lb>membrane applicate alle interiori pareti delle vene, e quelli stessi primi, che <lb></lb>riconobbero un tal uso nel proibire il reflusso del sangue, credendone di­<lb></lb>retto il moto dal cuore alle parti, interpetrarono al contrario del vero le in­<lb></lb>tenzioni della Natura. </s>

<s>Che il vero ufficio delle valvole consistesse nel pro­<lb></lb>durre un effetto, contrario a quello creduto dal Canani e dai seguaci di lui; <lb></lb>che consistesse insomma nel facilitare l&#039;ingresso, e no nell&#039;impedire il re­<lb></lb>gresso del sangue nel cuore, fu primo a intenderlo l&#039;Harvey, il quale anzi <lb></lb>lo rese visibile per via dello spicillo, che intromesso dalle radici ai rami non <lb></lb>passa impedito dalle valvole, mentre passa con facilità intromesso dai rami <lb></lb>alle radici. </s>

<s>“ Ego illud saepissime in dissectione venarum expertus sum, si <lb></lb>a radice venarum initio facto versus exiles venarum ramos spicillum mitte­<lb></lb>rem, quanto potuerim artificio, ob impedimentum valvularum longius im­<lb></lb>pellere non potuisse: contra vero forinsecus, a ramulis radicem versus, fa­<lb></lb>cillime ” (De motu cordis cit., pag. </s>

<s>78). </s></p><p type="main">

<s>Così, con questo nuovo efficace argomento confermandosi la verità <lb></lb>insegnata dal Cesalpino, che cioè il sangue nelle vene non va dal cuore <lb></lb>alle parti, ma dalle parti, attinto alle arterie, ritorna nel cuore; si rendeva <lb></lb>probabilissimo il fatto del circolo universale del sangue, che nel 1628 ve­<lb></lb>niva in pubblico a proporre ai Fisiologi Guglielmo Harvey. </s>

<s>Abbiamo detto <lb></lb>che si rendeva probabilissimo quel fatto, non però ancora con certezza di­<lb></lb>mostrato, rimanendo per avere una tal certezza a verificarsi due supposti <lb></lb>dell&#039;Harvey, il primo de&#039;quali era che il sangue della Vena porta mettesse <lb></lb>nella Cava, e il secondo che il sangue entrato nelle estremità venose fosse <lb></lb>veramente quello uscito dalle arteriose. </s></p><p type="main">

<s>Il primo supposto derivò, come vedemmo, nell&#039;Harvey dal Cesalpino, <lb></lb>il quale ne dette una dimostrazione a suo modo, per cui sarebbe allo stesso <lb></lb>Harvey bisognato ridurre gli argomenti peripatetici a prove sperimentali. </s>

<s>Ma <lb></lb>perch&#039;ei non volle o non seppe farlo, si trovò senza difesa assalito dalle <lb></lb>armi del Riolano, che propugnando gli antichi errori non negava il circolo <lb></lb>universale, ma lo rompeva in due, uno che avesse per centro il Fegato e <lb></lb>l&#039;altro il Cuore. </s>

<s>Tenne quel poderoso assalto vacillante la dottrina arveiana, <lb></lb>infin tanto che il Pecquet non venne coll&#039;esperienza a riconfermarla. </s>

<s>Es­<lb></lb>sendo egli ben persuaso che quel profluvio di sangue della Vena porta si <lb></lb>affretta di scendere alla Cava, se ne assicurò soffocando con un laccio il <lb></lb>ramo della stessa Cava, ch&#039;entra sotto alla gibbosità del Fegato, “ ac tum <lb></lb>ad vinculum sanguis proruens, ingurgitato supramodum a Jecore ramo, do­<lb></lb>cuit Portae cum Cava manifestum commercium, quamque apposite doctis­<lb></lb>simus inter anglos medicos Io. (sic) Harveius universi motum sanguinis <lb></lb>dixerit circularem ” (Dissertatio de circul. </s>

<s>sang., Parisiis 1654, pag. </s>

<s>33). </s></p><pb xlink:href="020/01/1273.jpg" pagenum="148"></pb><p type="main">

<s>L&#039;altro supposto arveiano, che cioè il sangue estravasato dalle arterie <lb></lb>ritornasse tutto alle vene, era anche di più difficile dimostrazione. </s>

<s>Galeno <lb></lb>aveva insegnato che ne&#039;polmoni le estremità capillari dell&#039;arteria venosa <lb></lb>avevano comunicazione diretta, per via delle anastomosi, colle estremità della <lb></lb>vena arteriosa “ sed nec ipse Galenus, dice lo stesso Harvey, neque ulla <lb></lb>experientia unquam sensibiles anastomoses conspexerunt aut ad sensum <lb></lb>ostendere potuerunt ” (Exercitatio Ia De circulat. </s>

<s>sanguinis, in appendice <lb></lb>all&#039;Exercit. </s>

<s>De motu cordis cit., pag. </s>

<s>124). Nè ciò asserisce per le relazioni <lb></lb>altrui, ma per la testimonianza degli occhi suoi proprii, perchè, avendo con <lb></lb>laboriosa diligenza esplorate quelle galeniche anastomosi, non gli era mai <lb></lb>riuscito di rinvenirle. </s>

<s>“ Ego qua potui diligentia perquisivi, et non parum <lb></lb>olei et operae perdidi in anastomosi exploranda, nusquam autem invenire <lb></lb>potui vasa invicem, arterias scilicet cum venis per orificia copulari ” (ibi). <lb></lb>Non per questo, con quella modesta saviezza ch&#039;è propria de&#039;grandi inge­<lb></lb>gni, credè di dovere assoluta<gap></gap>ente negare il fatto, ma tenendo per cosa certa <lb></lb>che il sangue in ogni modo dalle arterie tornava alle vene, lasciò indeciso <lb></lb>se ciò avvenisse “ per anastomosin immediate, vel mediate per carnis po­<lb></lb>rositates ” (De motu cordis cit., pag. </s>

<s>66). </s></p><p type="main">

<s>Il Pecquet, non potutosi poi nemmen egli assicurare, per esperienza sua <lb></lb>propria, di quella immediata comunicazione tra&#039;vasi, teneva che fosse molto <lb></lb>più probabile un estravasamento del sangue arterioso, e con ciò, forse senza <lb></lb>saperlo, emendava le idee del Cesalpino, e le riduceva al senso arveiano, <lb></lb>asserendo col nostro Peripatetico che una parte di quello stesso sangue ar­<lb></lb>terioso estravasato rimaneva per nutrimento delle parti, e che l&#039;altra non <lb></lb>esalava, ma, rimescolata colla fluidità del siero, tornava alle vene. </s>

<s>“ Imo po­<lb></lb>tius autumarem, per anastomoseis extra arteriarum claustra, transcolandam <lb></lb>in carnes exuberare sanguinis partem, ut inde, quod exactiori coctione dispo­<lb></lb>situm est, in similarium sidet nutrimentum; quidquid vero minus digestum, <lb></lb>cum fluidiori sero in venas, a foris in interiora circumquaque pervias, re­<lb></lb>fugiat. </s>

<s>Nam si perpetuus intra vasa fluor nullnm extra sanguinem effundat, <lb></lb>unde corporeae molis augmentum? </s>

<s>et si sit in iugi motu corporearum par­<lb></lb>tium substantia, unde tabidam fatiscentium maciem instaurari? </s>

<s>” (Disser­<lb></lb>tatio anat. </s>

<s>de circ. </s>

<s>sang. </s>

<s>cit., pag. </s>

<s>39). </s></p><p type="main">

<s>Erano dunque XXIII anni passati, da che aveva l&#039;Harvey pubblicate le <lb></lb>sue esercitazioni anatomiche <emph type="italics"></emph>De circulatione sanguinis,<emph.end type="italics"></emph.end> e il gran fatto fisio­<lb></lb>logico, benchè si tenesse da&#039;più savii per certo, non era però d&#039;ogni sua <lb></lb>parte tanto ben dimostrato, da levare ai dubbiosi ogni motivo, e ai contra­<lb></lb>dittori ogni pretesto. </s>

<s>Nel 1661 esercitava il Malpighi la sua perizia anatomica <lb></lb>intorno ai polmoni, e tra l&#039;esame del paranchima, che gli fruttò tante nuove <lb></lb>e gloriose scoperte, non volle lasciare inesplorate quelle anastomosi, che <lb></lb>aveva a Galeno <emph type="italics"></emph>nimis forsan audacter<emph.end type="italics"></emph.end> negato lo stesso Harvey. </s>

<s>Dando il <lb></lb>primo esempio ai Fisiologi futuri, fu esso Malpighi che si servì per quella <lb></lb>esplorazione delle iniezioni, scegliendo a principio il mercurio, che vedeva <lb></lb>trasparire in un bell&#039;albero di argento, e poi dell&#039;acqua tinta di nero. </s>

<s>Ma <pb xlink:href="020/01/1274.jpg" pagenum="149"></pb>i trasudamenti attraverso ai pori de&#039;vasellini rendevano difficile a discer­<lb></lb>nere, fra tante intricate vie, qual fosse la più immediata e diretta, cosicchè <lb></lb>nulla venivasi da tali delicatissime esperienze a decider di certo intorno alle <lb></lb>anastomosi desiderate. </s>

<s>“ An haec vasa in sinibus vel alibi mutuam habeant <lb></lb>anastomosim, ita ut sanguis a vena resorbeatur continuato tramite, an vero <lb></lb>hient omnes in pulmonum substantiam, dubium quod adhuc mentem meam <lb></lb>torquet, pro quo enodando incassum licet plura et plura molitus sum aere <lb></lb>et liquidis varie tinctis. </s>

<s>Saepius enim immissam aquam nigram syphone per <lb></lb>arteriam pulmonarem, a pluribus erumpentem vidi partibus, nam facta levi <lb></lb>compressione solet exsudare a membrana investiente, partim etiam coacer­<lb></lb>vari in interstitiis, maior vero copia cum immixto sanguine erumpit per ve­<lb></lb>nam pulmonarem, et quod mirabilius est per tracheam diluta et minus co­<lb></lb>lore tincta cum levi spuma ” (Opera omnia, Londini 1687, pag. </s>

<s>136). </s></p><p type="main">

<s>Anche dopo queste prime esperienze, che promettevano di riuscire così <lb></lb>concludenti, il sistema arveiano dunque si trovava in quelle medesime con­<lb></lb>dizioni, che ritrovavasi il sistema copernicano, quando ancora nessuno, in <lb></lb>Venere falcata o in Marte scantonato, se n&#039;era assicurato con gli occhi. </s>

<s>Il <lb></lb>Copernico rilasciava questa gloria a Galileo, e una gloria simile al Malpighi <lb></lb>la rilasciava l&#039;Harveio. </s></p><p type="main">

<s>Nella Lettera seconda al Borelli sull&#039;anatomia de&#039;polmoni incomincia <lb></lb>a dir l&#039;Autore di aver nella prima lasciata indietro la soluzione di due im­<lb></lb>portantissimi problemi: “ Primum erat quodnam sit rete illud descriptum, <lb></lb>quo singulae vesicae et sinus quodammodo vinciuntur in pulmonibus: al­<lb></lb>terum erat an pulmonum vasa mutua anastomosi iunganlur an vero hient <lb></lb>in communem pulmonum substantiam et sinus: problemata quae soluta <lb></lb>maioribus sibi viam agent, et ob oculos Naturae operationes clarius sunt po­<lb></lb>situra, pro quibus enodandis fere totum ranarum genus perdidi, quod non <lb></lb>contingit in effera illa Homeri Batrachomyomachia. </s>

<s>In ranarum enim ana­<lb></lb>tome, quam favente excellentissimo D. </s>

<s>Carolo Fracassato collega meo insti­<lb></lb>tueram, ut certior fierem circa membraneam pulmonum substantiam, talia <lb></lb>mihi videre contingit ut non immerito illud Homeri usurpari possim ad rem <lb></lb>praesentem melius: <emph type="italics"></emph>Magnum certum opus oculis video.<emph.end type="italics"></emph.end> Nam in hac, propter <lb></lb>structurae simplicitatem vasorumque et fere totius diaphanitatem quae ocu­<lb></lb>los in penitiora admittit, evidentius res ita demonstrantur, ut caeteris obscu­<lb></lb>rioribus lucem sint tandem allaturae ” (ibi, pag. </s>

<s>140, 41). </s></p><p type="main">

<s>Ecco dunque lo spettacolo, meglio di quello divinamente descritto da <lb></lb>Omero, degno di poema eroico e di storia: ecco il sistema del Microcosmo, <lb></lb>rivelato già al Copernico inglese, fatto finalmente veder con gli occhi dal <lb></lb>nuovo Galileo di Bologna: “ Aperto igitur ranarum abdomine, et retracto <lb></lb>mesenterio, appensisque intestinis, motum sanguinis in ramis Venae portae <lb></lb>et sociae arteriae reliquorumque infimi ventris vasis contemplatus, haec fre­<lb></lb>quentius succedere observavi. </s>

<s>Sanguis itaque in venis movetur a peripheria <lb></lb>corporis ex ramis minimis in minores, et successive in truncos et postremo <lb></lb>in cor ” (M. Malpighi, Opera postuma cit., pag. </s>

<s>91). </s></p><pb xlink:href="020/01/1275.jpg" pagenum="150"></pb><p type="main">

<s>A diffondere però la scoperta, invitando i Naturalisti ad assicurarsi della <lb></lb>verità lungamente desiderata, e i curiosi a ricrearsi del giocondo spettacolo <lb></lb>maraviglioso, efficacemente concorsero i discepoli del Malpighi, fra&#039;quali <lb></lb>Giorgio Baglivi, che nel 1696, pubblicando i suoi Esperimenti anatomici, in­<lb></lb>titolava l&#039;XI di essi <emph type="italics"></emph>De circulatione sanguinis in Rana.<emph.end type="italics"></emph.end> Dava quivi l&#039;Au­<lb></lb>tore alcune importanti notizie taciute dal suo Maestro, relative alle qualità <lb></lb>de&#039;Microscopii da usarsi, avvertendo che non voglion essere composti di due <lb></lb>lenti, come quelli fabbricati dal Divini, ma di una lente sola, tenuta colla <lb></lb>mano destra per osservare al sole la Rana presa con le dita della sinistra. <lb></lb></s>

<s>“ Ad haec experimenta peragenda utendum est Mycroscopio unius lentis, <lb></lb>quod dextra manu tenendum: e contra Rana sinistrae manus digitis ac­<lb></lb>curate prehensa, lumini Solis obiiciatur ” (Opera omnia, Lugduni 1710, <lb></lb>pag. </s>

<s>680). </s></p><p type="main">

<s>La notizia delle nuove cose osservate in Italia si diffuse ben presto al­<lb></lb>l&#039;intorno, e il Leuwenhoeck, in quel medesimo anno 1696 che il Baglivi <lb></lb>pubblicava il suo sperimento anatomico sopra la Rana, scriveva di aver fatte <lb></lb>le medesime osservazioni sopra la coda di alcune piccole anguille. </s>

<s>“ Hisce <lb></lb>anguillis, Mycroscopio appositis oculisque demissis in pinnam caudalem,.... <lb></lb>cum voluptate vidi sanguinis periodum ” (Arcanorum Naturae continuatio, <lb></lb>Lugduni Batav. </s>

<s>1722, pag. </s>

<s>131) e lo fece poi vedere all&#039;amico suo Cristiano <lb></lb>Huyghens, il quale così solennemente commemorò nella sua <emph type="italics"></emph>Dioptrica<emph.end type="italics"></emph.end> il filo­<lb></lb>sofico piacere provato in quella naturale contemplazione: “ In his (cioè nei <lb></lb>Microscopi semplici da lui detti <emph type="italics"></emph>batavici,<emph.end type="italics"></emph.end> e dai nostri Fiorentini <emph type="italics"></emph>della per­<lb></lb>lina<emph.end type="italics"></emph.end>) est observatio manifesta circularis motus sanguinis, quem, monstrante <lb></lb>A. </s>

<s>Lewenoechio nostro diligentissimo horum investigatore, in angnillae cauda <lb></lb>summa cum voluptate conspeximus. </s>

<s>Est enim perlucida ac sanguis, globulis <lb></lb>subrubentibus constans, celeri motu per canaliculos arteriarum, qui venis <lb></lb>continuantur, discurrit. </s>

<s>Quod haud dubio in caeteris quoque animalibus ani­<lb></lb>madverteretur, sed non facile partes luci perviae in his reperiuntur. </s>

<s>Anguil­<lb></lb>lulam vivam in tubum vitreum demiserat, aqua semiplenum, cui extrinse­<lb></lb>cus Mycroscopium applicabat, ea parte, qua cauda extrema vitrum tangebat ” <lb></lb>(Lugduni Batav. </s>

<s>1703, pag. </s>

<s>226, 27). </s></p><p type="main">

<s>L&#039;argomento dall&#039;analogia, di che fa uso qui l&#039;Huyghens, era senza <lb></lb>dubbio ragionevole: era ragionevole cioè che le cose osservate in Italia sopra <lb></lb>le rane e in Olanda sopra le anguille, <emph type="italics"></emph>in caeteris quoque animalibus ani­<lb></lb>madverterentur,<emph.end type="italics"></emph.end> ma pur v&#039;era anche ragionevole motivo di dubitarne, po­<lb></lb>tendo il sangue caldo, più denso e più coagulabile, non passar così facil­<lb></lb>mente per i minimi vasi, come vi si vedeva passare il sangue freddo. </s>

<s>Fu <lb></lb>questa forse la ragione per cui, nonostante le osservazioni del Malpighi sopra <lb></lb>le rane, il Borelli e il Guglielmini, come si par dai passi altrove recati, ri­<lb></lb>masero tuttavia in dubbio delle anastomosi negli animali a sangue caldo, e <lb></lb>inclinarono ad ammettere col Pecquet un estravasamento del sangue arte­<lb></lb>rioso nelle porosità della carne, d&#039;onde attingessero le vene ciò che v&#039;era <lb></lb>d&#039;avanzo per la nutrizione. </s></p><pb xlink:href="020/01/1276.jpg" pagenum="151"></pb><p type="main">

<s>A voler che dunque la dimostrazione del circolo arveiano risultasse da <lb></lb>ogni parte completa, conveniva anch&#039;estenderla agli animali a sangue caldo. </s>

<s><lb></lb>Ma l&#039;opacità delle tuniche de&#039;vasi, e il sangue che così facilmente si rap­<lb></lb>piglia nell&#039;aperto ventre dell&#039;animale, sotto le impressioni dell&#039;aria, avevano, <lb></lb>infino a qualche anno dopo la prima metà del secolo XVIII, resa inutile <lb></lb>ogni più sollecita industria. </s>

<s>Perciò l&#039;Haller scriveva nel I Tomo della sua <lb></lb>grande Fisiologia: “ Primus Guilielmus Cowper in fele iuniori, in mesen­<lb></lb>terio canino et in omento felis rete arteriolarum et venularum sibi lnoscu­<lb></lb>latarum delineavit, raro certe felicitatis exemplo. </s>

<s>Mihi enim in calidi san­<lb></lb>guinis animalibus hactenus ne motum quidem sanguinis, et multo minus <lb></lb>circuitum, conspicuum videre datum est ” (Lausannae 1757, pag. </s>

<s>238). </s></p><p type="main">

<s>Ma le osservazioni del Cowper intorno agli animali caldi, essendo ri­<lb></lb>strette all&#039;accennare il semplice moto de&#039;globetti sanguigni ne&#039;vasi più sot­<lb></lb>tili, parvero al caso troppo piccola cosa allo Spallanzani, il quale si sentiva <lb></lb>ardere di quella nuova sete di scienza, nè aveva ancora potuto spengerla, <lb></lb>quando inaspettatamente dalla sua buona ventura si trovò condotto sul verde <lb></lb>margine di una fonte nascosta. </s></p><p type="main">

<s>“ Un giovane medico (così egli stesso nell&#039;introduzione al libro <emph type="italics"></emph>De&#039;fe­<lb></lb>nomeni della circolazione<emph.end type="italics"></emph.end> ci narra questa importantissima storia) valente in <lb></lb>Anatomia, il signor dottor Rezia comasco, ripetendo per utile suo svaga­<lb></lb>mento le sensate osservazioni dell&#039;Haller <emph type="italics"></emph>Sulla formazione del pulcino,<emph.end type="italics"></emph.end> volle <lb></lb>farmene partecipe col mostrarmi giornalmente i progressi di quell&#039;uccello <lb></lb>racchiuso ancora nell&#039;uovo. </s>

<s>Un giorno portommi uno di quest&#039;uova covate, <lb></lb>rotto ed aperto nella parte ottusa del guscio, il qual uovo era più rimarca­<lb></lb>bile delle altre per mostrare in maniera più distinta e più risentita il cuo­<lb></lb>ricino, che spessamente batteva, l&#039;orditura dell&#039;embrione e la membrana <lb></lb>ombelicale tutta intrecciata di bellissimi vasi sanguigni. </s>

<s>Siccome da molto <lb></lb>tempo io ardeva dal desiderio di scoprir pure negli animali caldi la circo­<lb></lb>lazione, e di scoprirla con quell&#039;ampiezza di giro, con cui l&#039;aveva scoperta <lb></lb>negli animali di freddo temperamento; così que&#039;vasi, per appartenere ad <lb></lb>animale di simil fatta, più d&#039;ogni altro a sè rapirono i miei sguardi, e m&#039;in­<lb></lb>vitarono a contemplarli. </s>

<s>La camera ov&#039;io mi trovava, non avendo luce che <lb></lb>bastasse, e volendo pure in qualche maniera render paga la mia curiosità, <lb></lb>mi appigliai al partito di esaminar l&#039;uovo all&#039;aperto ed immediato lume del <lb></lb>sole. </s>

<s>Apprestatolo adunque alla macchinetta del Lyonet, di subito l&#039;impun­<lb></lb>tai con la lente, e nonostante la gran luce ond&#039;era attorniato, potei, purchè <lb></lb>aguzzassi ben gli occhi, nettamente veder correre il sangue per l&#039;intiero cir­<lb></lb>cuito de&#039;vasi ombelicali, arteriosi e venosi. </s>

<s>Preso allora da gioia inaspettatta, <lb></lb>credetti quell&#039;una volta di poter dire anch&#039;io <emph type="italics"></emph>evreca, evreca.<emph.end type="italics"></emph.end> La scoperta <lb></lb>la feci nel maggio 1771, e nell&#039;estive vacanze di quell&#039;anno m&#039;ingegnai di <lb></lb>svolgerla come conveniva ” (Opere, T. IV, Milano 1826, pag. </s>

<s>155). </s></p><p type="main">

<s>Questa singolarissima osservazione microscopica nel sistema del cuore <lb></lb>s&#039;assomiglia all&#039;osservazione telescopica di Mercurio nel sistema del Sole, e <lb></lb>come si rendeva per questa d&#039;ogni parte assoluta la dimostrasione dell&#039;or-<pb xlink:href="020/01/1277.jpg" pagenum="152"></pb>dine de&#039;moti nell&#039;Universo, così per quella si rendeva per ogni parte asso­<lb></lb>luta la dimostrazione dell&#039;ordine dei moti nel Microcosmo. </s>

<s>Ma era allo stesso <lb></lb>Spallanzani riserbata un&#039;altra gloria, ch&#039;è quella d&#039;esser egli stato il primo <lb></lb>ad osservare il circolo coronario. </s>

<s>La difficoltà di una tale osservazione con­<lb></lb>sisteva nel color sanguigno del cuore, che non facendo discernere il color <lb></lb>sanguigno de&#039;vasi non dava perciò speranza di vedervi correre il sangue, <lb></lb>altro che nel pallor della sistole. </s>

<s>In questa fase del cuore di una salaman­<lb></lb>dra vide esso Spallanzani certe piegoline rosse, che facevano credere di esser <lb></lb>vasi, dentro i quali corresse il sangue. </s>

<s>“ Un giorno, egli scrive nella dis­<lb></lb>sertazione <emph type="italics"></emph>Dell&#039;azione del cuore ne&#039;vasi sanguigni,<emph.end type="italics"></emph.end> considerando il cuore <lb></lb>d&#039;una grossa salamandra, ebbi il piacer di conoscere che giusti erano i miei <lb></lb>sospetti. </s>

<s>Le rosse piegoline si convertirono in altrettanti vasetti. </s>

<s>Nell&#039;atto <lb></lb>che restringevasi il cuore, per questi scorreva il sangue rapidamente, ma <lb></lb>dilatandosi egli di nuovo, sminuivasi a vista la velocità del sangue ” (Opere <lb></lb>e Tomo cit., pag. </s>

<s>120, 21). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Giunti al termine di un viaggio fatto attraverso a tanti secoli, quanti <lb></lb>sono da Aristotile allo Spallanzani, è bene tutto in uno sguardo conside­<lb></lb>rarne l&#039;andamento, come fa colui che le smisurate distanze da un punto <lb></lb>all&#039;altro della terra si rappresenta in brevi tratti disegnate sopra una mappa. </s>

<s><lb></lb>Ci rivela facilmente un tale sguardo, comprensivo di tutta la storia fin qui <lb></lb>narrata, come la scoperta della circolazione del sangue ebbe in Italia la sua <lb></lb>più prossima preparazione, e in Italia l&#039;ultima mano. </s>

<s>Resta però ancora <lb></lb>una curiosità da sodisfare, ed è in che modo gl&#039;Italiani, che non seppero <lb></lb>concludere il vero dalle dottrine premesse dagli avi, accettassero poi quella <lb></lb>conclusione, quando venne ad annunziarla al mondo l&#039;Harvey. </s>

<s>Ma perchè <lb></lb>ciò accenna necessariamente a un risveglio, giova, a meglio intenderne le <lb></lb>circostanze e gli atti, investigare l&#039;origine di quel sonno. </s></p><p type="main">

<s>A noi par che una tale origine sia da Girolamo Fabricio d&#039;Acquapen­<lb></lb>dente, il quale tenendosi affatto fuori da quelle battaglie insorte fra il Ve­<lb></lb>salio e il Colombo e il Falloppio, come se tante valide forze si fossero so­<lb></lb>lamente impiegate a distruggere, ridusse tutto il progredir della scienza ai <lb></lb>commenti da sè fatti agli insegnamenti galenici, i quali perciò sulla fine del <lb></lb>secolo XVI si diffusero, sotto questa nuova forma, a dominare per le Scuole <lb></lb>d&#039;Italia. </s>

<s>Se dunque nel 1574 esso Fabricio, ch&#039;era per farsi maestro e prin­<lb></lb>cipe di questa Scuola, si maraviglia che nessuno abbia fatto mai menzione <lb></lb>delle valvole delle vene, non è una menzogna detta per farsene credere egli <lb></lb>primo discopritore, ma è perchè non si curò di leggere, almeno con atten­<lb></lb>zione e tutti interi, que&#039;libri dove il Falloppio e il Vesalio tanto passiona­<lb></lb>tamente avevano scritto del Canani e del Lusitano. </s></p><pb xlink:href="020/01/1278.jpg" pagenum="153"></pb><p type="main">

<s>Reciso così il filo delle tradizioni scientifiche, principalmente per ciò che <lb></lb>riguardava il Colombo, e rimasto involto nella forfora peripatetica il Cesal­<lb></lb>pino, la scienza italiana, in proposito della fisiologia del cuore e del moto <lb></lb>del sangue, come ramo reciso dal suo tronco, cadde in un languore di vita <lb></lb>e in un torpore di sonno, in mezzo a cui la realtà, ch&#039;era presso a sboc­<lb></lb>ciare, si sciupava in larve stranamente mostruose. </s>

<s>Come la circolazion pol­<lb></lb>monare, così esattamente descritta dal Colombo e dal Cesalpino, si trasformi <lb></lb>in quelle mostruosità nella mente di Girolamo Fabricio, può vedersi dal <lb></lb>cap. </s>

<s>VIII della II Parte <emph type="italics"></emph>De formato faetu,<emph.end type="italics"></emph.end> dove si trova spenta anche quella <lb></lb>scintilla di vero, che attraverso al fondo buio de&#039;secoli traspariva lieta <lb></lb>dalle pagine di Galeno. </s>

<s>Tre sono i vasi, ivi si legge, cbe si diramano <lb></lb>nel polmone: l&#039;aspera arteria, che v&#039;introduce l&#039;aria, la vena arteriosa, <lb></lb>che per nutrimento del viscere vi spinge il purissimo sangue, e l&#039;arteria <lb></lb>venosa, che mena la stessa aria inspirata nel ventricolo sinistro, dove si <lb></lb>trasforma in spirito, e tutto insieme refrigera il cuore. </s>

<s>“ Pulmones, cum <lb></lb>publicum usum corpori praebent, tria illa vasorum genera in sui substan­<lb></lb>tiam disseminatam, scilicet asperam arteriam, venam arterialem, et arteriam <lb></lb>venalem hoc modo administrant: Per asperam arteriam aerem respiratione <lb></lb>attractum primo rapiunt, et recipiunt qui postea a cordis pulsu per arteriam <lb></lb>venalem in sinistrum cordis sinum defertur conquoquendum, et in spiritum <lb></lb>vitalem commutandum, refrigeriumque cordi praestandum. </s>

<s>Per tertium vero <lb></lb>vas quod vena arterialis dicitur pulmones purissimo tenuissimoque sanguine <lb></lb>enutriuntur. </s>

<s>Itaque hoc tempore pulmo nutritur vase quod arteriae corpus <lb></lb>obtinet, tum vero spiritum suscipit per vias quod venae substantiam obti­<lb></lb>net ” (Venetiis 1600, pag. </s>

<s>138). </s></p><p type="main">

<s>Seguace delle dottrine di quella Scuola, e disposto per acume d&#039;inge­<lb></lb>gno a specularne altre da sè, e per indole a rimanersi nella libertà del pro­<lb></lb>prio pensiero, era Paolo Sarpi, che avendo saputo l&#039;arte di tacere, lasciò che <lb></lb>tanto ne parlassero gli altri. </s>

<s>E ora non son molti anni, che il Bianchi Gio­<lb></lb>vini gli fa rompere dalla tomba que&#039;lunghi silenzii, si vuol che non faccia <lb></lb>scomparire gli encomiatori, in ogni modo approvando i loro detti, benchè <lb></lb>nient&#039;altro in realtà si provi da quel frammento di lettera pubblicato da <lb></lb>esso Giovini, se non che egli, e tutti coloro che vorrebbero a fra Paolo sal­<lb></lb>vare il merito della scoperta del circolo sanguigno e delle valvole, si sono <lb></lb>ingannati, come que&#039;fanciulli, che credono le nebbie esser monti scesi mi­<lb></lb>racolosamente a colmare le valli. </s></p><p type="main">

<s>Noi leggiamo quel frammento di lettera sarpiana, in francese, nella <lb></lb>Storia altre volte citata del Flourens, dove il Sarpi, ringraziato un amico <lb></lb>che gli aveva donato l&#039;opera anatomica dell&#039;illustre Vesalio, così prosegue: <lb></lb>“ Il y a réellement une grande analogie entre les choses déja remarquées <lb></lb>et notées par moi, à l&#039;égard du mouvement du sang dans le corps animal, <lb></lb>et de la structure ainsi que de l&#039;usage des valvules ” (Histoire de la circulat. </s>

<s><lb></lb>du sang cit., pag. </s>

<s>124). Se un tal documento è autentico, la questione è <lb></lb>dunque decisa: il Sarpi credeva come il Vesalio che il sangue passasse at-<pb xlink:href="020/01/1279.jpg" pagenum="154"></pb>traverso ai pori del setto medio dal vetricolo destro nel sinistro, e che fosse <lb></lb>l&#039;arteria venosa, come la gola di un cammino, per dar esito ai fumi filig­<lb></lb>ginosi. </s>

<s>E perchè passa una analogia fra queste e le mostruosità dell&#039;Acqua­<lb></lb>pendente, è da concluder che il Sarpi avesse della circolazion polmonare <lb></lb>idee simili a quelle che scrisse il suo amico, e che noi trascrivemmo di <lb></lb>sopra dal libro <emph type="italics"></emph>De formato foetu.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Che se lo stesso Sarpi teneva anche delle valvole opinioni analoghe a <lb></lb>quelle del Vesalio, e il Vesalio le credeva membrane apposte alle tuniche <lb></lb>delle vene, per invigorirne la natural debolezza, è pur anche da questa parte <lb></lb>decisa la questione, ond&#039;è che se, prima del Giovini, si credeva che fra Paolo <lb></lb>l&#039;avesse dimostrate all&#039;Acquapendente, ora è da dire invece ch&#039;ei le negò <lb></lb>allo stesso Acquapendente, che le aveva scoperte, come il Vesalio le aveva <lb></lb>già negate al Canani. </s>

<s>Da questa controversia forse prese l&#039;Autore <emph type="italics"></emph>De vena­<lb></lb>rum ostiolis<emph.end type="italics"></emph.end> occasione di osservare con più diligenza, e di render pubbli­<lb></lb>camente noto ciò che per l&#039;avanti o non aveva pensato, o non s&#039;era atten­<lb></lb>tato di fare; unico merito rivendicato al Sarpi dal documento pubblicato <lb></lb>nel 1838 sulla <emph type="italics"></emph>Revue de Londres<emph.end type="italics"></emph.end> dal Bianchi Giovini. </s></p><p type="main">

<s>Giorgio Ent, nelle sue <emph type="italics"></emph>Metamorfosi di Apolline ed Esculapio,<emph.end type="italics"></emph.end> vuol che <lb></lb>il Sarpi sia stato il primo in Italia ad aver notizia della scoperta arveiana, <lb></lb>prima della sua pubblicazione, e ciò per mezzo del Legato veneto, che di <lb></lb>Londra nel 1619 tornava in patria. </s>

<s>È certo che in quell&#039;anno faceva l&#039;Har­<lb></lb>vey la circolazione universale del sangue soggetto alle sue pubbliche lezioni, <lb></lb>e che nel 1622, un&#039;anno prima della morte del Sarpi, aveva presentato il <lb></lb>manoscritto a Gaspero Hofmann, che tanto freddamente lo accolse, da di­<lb></lb>sanimar l&#039;Autore e da indugiarne per altri sei anni la pubblicazione. </s>

<s>Per <lb></lb>cui, ripensando che il detto Frate italiano teneva dietro a tutte le novità <lb></lb>straniere, l&#039;opinione dell&#039;Ent ha del probabile. </s>

<s>Ma noi siam persuasi che <lb></lb>anche al Sarpi, imbevuto delle idee dell&#039;Acquapendente e di analoghe a <lb></lb>quelle del Vesalio, le cose dette dall&#039;Harvey saranno sembrate così nuove <lb></lb>e inaudite “ ut non solum ex invidia quorumdam metuam malum mihi, sed <lb></lb>verear ne habeam inimicos omnes homines: tantum consuetudo aut semel <lb></lb>inibibita doctrina altisque defixa radicibus, quasi altera natura apud omnes <lb></lb>valet! ” (De motu cordis cit., pag. </s>

<s>55). </s></p><p type="main">

<s>I presentiti giusti timori, fondati sull&#039;esperienza degli uomini, si sa­<lb></lb>ranno dissipati dall&#039;animo dell&#039;Harvey, quando vide il Cartesio fare alle <lb></lb>nuove idee così lieta e inaspettata accoglienza. </s>

<s>Che se lo stesso favorevole <lb></lb>incontro avessero avuto in Galileo, per l&#039;autorità dei due Principii della <lb></lb>scienza, era spettatore esso Harvey in vita de&#039;suoi più pieni e più gloriosi <lb></lb>trionfi. </s>

<s>Ma Galileo alieno da quegli studii, e da tutto ciò che non promet­<lb></lb>teva di renderlo il primo ed il solo, si mostrò verso il Copernico inglese <lb></lb>tanto freddo, quanto s&#039;era mostrato fervente verso il vero Copernico prus­<lb></lb>siano, cosicchè nè a luì nè al Sarpi è da attribuire alcun merito in restau­<lb></lb>rare i perturbati ordini naturali ne&#039;moti del Microcosmo. </s>

<s>Que&#039;meriti si <lb></lb>debbon tutti a due nostri Toscani, i quali, benchè sieno nella Repubblica <pb xlink:href="020/01/1280.jpg" pagenum="155"></pb>scientifica pochissimo conosciuti, pur furono essi veramente i primi, che ap­<lb></lb>plicassero allo studio della vita animale i metodi galileiani, rendendo dei <lb></lb>nuovi frutti negletti dall&#039;Istitutore ubertoso l&#039;albero della scienza italiana. </s></p><p type="main">

<s>Il dì 31 Marzo 1637 Raffaello Magiotti scriveva a Galileo da Roma in <lb></lb>una lettera queste parole: “ Quà si trova un Medico tedesco, anatomista <lb></lb>raro, quale mostra in fatto assaissimi errori <emph type="italics"></emph>De natura anim.<emph.end type="italics"></emph.end> e quand&#039;io <lb></lb>li contai del cavallo del Gattamelata, che sta sopra due gambe dalla mede­<lb></lb>sima banda, contro il detto di Aristotile, rise veramente di tutto cuore, ed <lb></lb>ogni giorno porta qualche luogo per farci sempre più ridere ” (MSS. Gal., <lb></lb>P. VI, T. XIII, c. </s>

<s>14). </s></p><p type="main">

<s>Quel Medico tedesco, chiunque egli sia, dimostrava in Roma, in mezzo <lb></lb>alle sue anatomie, il circolo universale del sangue, cosicchè fu egli il primo <lb></lb>a diffondere in Italia le dottrine arveiane già diffuse nelle libere città ger­<lb></lb>maniche, in una delle quali, piuttosto che nella patria dell&#039;Hofmann e del <lb></lb>Riolano, fece l&#039;Autore stampare il suo libro <emph type="italics"></emph>De motu cordis.<emph.end type="italics"></emph.end> Erano a quelle <lb></lb>anatomie del Tedesco spettatori assidui Raffaello Magiotti e Antonio Nardi, <lb></lb>i duumviri della Scienza sperimentale, secondo Galileo, rimasti in Roma dopo <lb></lb>la partenza del Torricelli. </s>

<s>Il Nardi, nella veduta Ia della Scena VIII, dava <lb></lb>così la prima pietosa mano a rivestir del nuovo abito inglese le nudità, e <lb></lb>anzi lo squallore a ch&#039;era stata ridotta la Fisiologia italiana dai discepoli <lb></lb>dell&#039;Acquapendente: </s></p><p type="main">

<s>“ Ora, seguendo, dico come le orecchie del cuore sono una natura di <lb></lb>mezzo ed un certo legame tra il cuore ed i vasi venali ed arteriali: anche <lb></lb>sono le prime e l&#039;ultime a vivere e muoversi tra le parti solide dell&#039;ani­<lb></lb>male. </s>

<s>Battono, non in virtù propria, ma del sangue spiritoso, il quale come <lb></lb>fuoco artifiziosissimo ha movimento ed atto perpetuo, insino che resta san­<lb></lb>gue. </s>

<s>Al battere delle orecchie segue il restringersi o allargarsi del cuore, <lb></lb>poichè riempito di sangue il ventricolo destro dalla Vena cava, e dalla de­<lb></lb>stra orecchia, restringesi per il soverchio caldo, e discaccia il sangue per i <lb></lb>vasi, e di nuovo ritornando al primiero e naturale stato torna a riempirsi <lb></lb>alternamente, e così un certo moto circolare e perpetuo formasi del sangue, <lb></lb>mentre dal destro ventricello se ne passa per i condotti al polmone, e quindi <lb></lb>se ne ritorna al sinistro, a che ancora il moto del polmone serve. </s>

<s>Ed osser­<lb></lb>visi che il cuore non solo ha il movimento suddetto di restringersi ed al­<lb></lb>largarsi, ma anche l&#039;arterie, massime maggiori, ed anche la Vena cava presso <lb></lb>il cuore, e questo seconda per consenso quello del cuore. </s>

<s>Quindi ancora il <lb></lb>sangue per le vene passa dalle parti al cuore, e per le arterie dal cuore <lb></lb>passa alle parti, e l&#039;uno spinge l&#039;altro. </s>

<s>E&#039;non è dubbio che questa moderna <lb></lb>osservazione del moto circolare del sangue non sia una delle belle cose, che <lb></lb>si sia mai trovata nell&#039;arte, onde moltissime considerazioni farsi potrebbono, <lb></lb>di che vedasi l&#039;Harveio ” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>1097). </s></p><p type="main">

<s>Il Magiotti, per lettera del 25 Aprile 1637, rendeva così noto a don Fa­<lb></lb>miano Michelini il grandissimo gusto, che aveva delle anatomie del Tedesco, <lb></lb>e così gli descriveva la circolazione che fa il sangue in noi, scoperta a <pb xlink:href="020/01/1281.jpg" pagenum="156"></pb>que&#039;tempi e bastante, com&#039;ei si esprimeva, a rivolgere tutta la medicina, <lb></lb>siccome l&#039;invenzione del Telescopio ha rivolta tutta l&#039;Astronomia, la Bus­<lb></lb>sola l&#039;economia, e l&#039;Artiglieria tutta l&#039;arte militare: </s></p><p type="main">

<s>“ Sono molti anni che un Medico milanese osservò negli animali, pa­<lb></lb>sciuti di fresco e poi ammazzati, massime nei cani, che nel mesenterio sono <lb></lb>molte vene lattee, quali da tutti gl&#039;intestini tirano succo, ovvero chilo, alla <lb></lb>volta del panereas e per quello al fegato ed alla Vena cava, per la quale <lb></lb>finalmente s&#039;annida, si riscalda e concuoce dentro al destro ventricolo del <lb></lb>cuore. </s>

<s>Di quivi, dalla vena arteriosa, passa a refrigerarsi nel polmone per <lb></lb>meglio concuocersi, e dal polmone, per l&#039;arteria venosa torna nel sinistro <lb></lb>ventricolo del cuore, dove si fa l&#039;ultima concozione. </s>

<s>Di là, per l&#039;arteria ma­<lb></lb>gna, e da lei per tutte l&#039;arterie, si sparge il sangue spiritoso per tutto il <lb></lb>corpo, e così si diffondono gli spiriti e il calore, e così il moto del pulsare <lb></lb>a tutte le membra. </s>

<s>Dalle membra tutte succhiano le vene capillari il san­<lb></lb>gue, quale era stato portato dalle arterie per nutrire le parti, come se fos­<lb></lb>sero tante radiche e barbe, e riconducono il sangue così con pochissimi spi­<lb></lb>riti al cuore per la Vena porta, acciò là di nuovo con qualche porzione di <lb></lb>nuovo chilo, per opera delle vene lattee, si riscaldi e concuocia.... ” (Opere <lb></lb>di Gal., Alb. </s>

<s>X, 207). </s></p><p type="main">

<s>Il Michelini tanto conforto sentì all&#039;ingegno di questa nuova rivelazione, <lb></lb>che avendo avuto ordine dal Magiotti di rivelarla al signor Galileo, non <lb></lb>mancò di adempire all&#039;ufficio. </s>

<s>E non si potendo persuadere come colui, <lb></lb>ch&#039;era con tanto ardire concorso a infrangere l&#039;idolo aristotelico, si mo­<lb></lb>strasse ora così irresoluto contro il galenico, ch&#039;era ai progressi delle scienze <lb></lb>sperimentali e dell&#039;arte medica tanto più dannoso, rivolsesi a cercar nuovi <lb></lb>conforti al suo giudizio nel giudizio di Giovan Batista Baliani, tenuto per la <lb></lb>seconda autorità, che dopo lo stesso Galileo si conoscesse allora in così fatto <lb></lb>scientifico magistero. </s>

<s>Ma, contro ogni espettativa del Michelini, il Baliani da <lb></lb>Genova così gli rispondeva: “ Rispetto alla circolazione del sangue, se mi <lb></lb>dicesse i motivi che le hanno fatta stimare sicura l&#039;opinione dell&#039;Arveo, <lb></lb>forse che le addurrei qualche cosa in contrario ” (Targioni, Notizie degli <lb></lb>aggrandimenti ecc., T. I, Firenze 1780, pag. </s>

<s>204). </s></p><p type="main">

<s>Quali fossero veramente quelle ragioni in contrario noi non sappiamo, <lb></lb>ma dovettero esser tali da persuaderlo a preferire alle verità arveiane le <lb></lb>mostruosità invalse nell&#039;universale, per l&#039;autorità del Vesalio, e in Italia in <lb></lb>particolare per quella non punto minore dell&#039;Acquapendente; persuasione <lb></lb>che il Baliani stesso rivela in quel trattato che scrisse <emph type="italics"></emph>Della pestilenza.<emph.end type="italics"></emph.end> Ivi <lb></lb>incomincia con ragioni fisiche, per que&#039;tempi del tutto nuove, a dimostrar <lb></lb>che i miasmi contagiosi si producono nell&#039;aria, e dipoi passa a indagar le <lb></lb>vie segrete, per le quali s&#039;inoculano così fatti miasmi nel sangue ricirco­<lb></lb>lante nel corpo a nutrire e a vivificare le parti al modo che segue: </s></p><p type="main">

<s>“ Presuppongo io primieramente, egli scrive, insieme con molti, an­<lb></lb>corchè altri che sono già in credito sentano in contrario, che qualora, per <lb></lb>essersi fatta la diastole, il cuore si sia gonfiato e i suoi vani, seni o ventri-<pb xlink:href="020/01/1282.jpg" pagenum="157"></pb>coli che gli chiamino, aggranditi e ripieni, esso per naturale istinto con la <lb></lb>sistole si restringa, e che allora il sangue del seno diritto, perciò fortemente <lb></lb>compresso, non solo sia spinto per la vena arteriale nel polmone, ma che <lb></lb>una porzione più sottile ne sia cacciata per li meati del tramezzo, forse in­<lb></lb>sensibili sol nel cadavere, nel seno manco. </s>

<s>Il che essendo vero, parmi con­<lb></lb>seguentemente di veder chiaramente che tal porzione di sangue, per passare <lb></lb>a forza per quei pori sottilissimi, ritrovando il vano, anzi per così dire spruz­<lb></lb>zatovi, si sparga in minutissimi zampilli, che per restar privi per la loro <lb></lb>piccolezza di attività e di vigor bastante a resistere all&#039;azione del calore che <lb></lb>vi ritruovano e che gli penetra, si riducano subitamente in vapore e bolli­<lb></lb>cini, che gonfiandosi e con gran celerità dilatandosi sforzino e spingano le <lb></lb>pareti del ventricolo, e con nuova diastole l&#039;aggrandiscano. </s>

<s>Parmi inoltre <lb></lb>a ciò, non potendo esse bolle sanguigne per la forma loro sferica termi­<lb></lb>narsi co&#039;termini altrui, acciocchè spazio vuoto non ci rimanga, che con ra­<lb></lb>gione vi supplisca la Natura con preparare una materia arrendevole, pronta <lb></lb>a sottentrarvi, e acconcia a riempire i vani che tra&#039;detti bollicini si ritro­<lb></lb>vano, cioè a dir l&#039;aria portatavi dall&#039;arteria venale, di quella che inspirata <lb></lb>risiede nel polmone, non ad altro uso per avventura stato da essa Natura <lb></lb>formato, e tal composto di bolle sanguigne e d&#039;aria è al creder mio quella <lb></lb>sostanza che spirito vitale si domanda ” (Savona 1647, pag. </s>

<s>61-63). </s></p><p type="main">

<s>Ma il Michelini sentì la verità più potente degli autorevoli pregiudizi <lb></lb>di Galileo e del Baliani, e tra il 1645 e il 47 compose, sulle scoperte del­<lb></lb>l&#039;Asellio e dell&#039;Harvey, quel nuovo sistema di medicina razionale, che la­<lb></lb>sciò abbozzato in alcune lettere pubblicate più di un secolo dopo dal Tar­<lb></lb>gioni (Notizie cit., T. II, P. I, pag. </s>

<s>221-25). Scoperto il canal toracico, fece <lb></lb>anche questa terza notizia entrare in quel sistema d&#039;Igiene, che, rimasto di­<lb></lb>menticato infino al 1780, fu dato alla prima luce dallo stesso Targioni (T. III, <lb></lb>pag. </s>

<s>329-45). </s></p><p type="main">

<s>Chi legge ora quelle cose le giudica una meschinità, non ripensando <lb></lb>che da queste aride stille fu rinfrescata a novella vita la Medicina in Italia, <lb></lb>che per opera del Michelini prese abito e complessione di scienza, e fu per <lb></lb>lui solo introdotta nella scuola galileiana. </s>

<s>Basti il dire che fu inspirato a <lb></lb>quelle meschinità il gran Borelli, che vi ritrovò, come ne&#039;cotiledoni del <lb></lb>germe, quel vital nutrimento da cui crebbe a tanto maravigliosa grandezza, <lb></lb>e in sì breve tempo, la nuova Fisiologia. </s>

<s>Quando nel 1661 il Malpighi, che <lb></lb>discende esso pure direttamente dal Michelini per la linea dello stesso Bo­<lb></lb>relli, rese il circolo del sangue visibile agli occhi di tutti, e allora gl&#039;Ita­<lb></lb>liani si riscossero dal loro sonno, e per rifarsi di un tesoro perduto anda­<lb></lb>rono, con la speranza di metterle in corso, a ricercar le arrugginite monete <lb></lb>rimaste chiuse nelle arche degli avi. </s></p><p type="main">

<s>Il Fracassati, per citar qualche esempio, nella sua dissertazione <emph type="italics"></emph>De ce­<lb></lb>rebro,<emph.end type="italics"></emph.end> accolta fra le opere del Malpighi, a provar che il mondo è tante volte <lb></lb>ingiusto dispensator del merito, “ sanguinis circulatio, scrive, Galaxia in mi­<lb></lb>crocosmo humano, scilicet via chyli ad cor, nonne Caesalpinum agnoscit <pb xlink:href="020/01/1283.jpg" pagenum="158"></pb>auctorem, ac Eustachium <emph type="italics"></emph>De vena sine pari?<emph.end type="italics"></emph.end> et tamen solos in scholis <lb></lb>auctores crepant anglos Harveos, ac diepenses Pecquetos ” (Operum, T. II, <lb></lb>Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>138). Tommaso Cornelio, acceso dal medesimo zelo, <lb></lb>venne a rammemorare a&#039;suoi che il moto del sangue descritto dall&#039;Harvey <lb></lb>era stato già conosciuto da Paolo Sarpi, e anzi molto tempo prima dal Ce­<lb></lb>salpino. </s>

<s>“ Motum sanguinis ab Harveio descriptum iampridem agnoverat et <lb></lb>amicis indicaverat Paulus Sarpi venetus, quin etiam illum multo ante de­<lb></lb>signaverat Andreas Caesalpinus ” (Progymnasmata physica, Neapoli 1688, <lb></lb>pag. </s>

<s>296). </s></p><p type="main">

<s>Di qui ebbero principio e vennero gli esempii a que&#039;profluvii di scrit­<lb></lb>ture insulse, che si rassomigliano ai pugni dati in aria, e agli urli di chi, <lb></lb>ridestatosi a un tratto dal lungo sonno, si mette a gridare al ladro al vi­<lb></lb>cino, che ha operosamente vegliato, benchè il Borelli avesse dato agl&#039;Ita­<lb></lb>liani altri esempi di più assennati giudizi. </s>

<s>“ Inveatum profecto admirabile, <lb></lb>egli dice della circolazione del sangue, partim a Cesalpino, sed postea exac­<lb></lb>tissime ab Harveio nuper mortalibus tanta evidentia demonstratum, ut nemo <lb></lb>supersit qui de eius veritate adhuc dubitet ” (De motu anim., P. II, Ro­<lb></lb>mae 1681, pag. </s>

<s>77). </s></p><p type="main">

<s>La vana loquacità dei tanti scrittori, che si dettero a seguir gli esempi <lb></lb>del Fracassati e del Cornelio, piuttosto che del Borelli, si manifesta anche <lb></lb>dal fatto che, mentre vogliono glorificare i loro connazionali di finti meriti, <lb></lb>non si curano poi di ricercarne i meriti veri. </s>

<s>Benemeriti della Fisiologia ar­<lb></lb>veiana sono tutti coloro, che la confermarono con vario genere di argomenti, <lb></lb>fra&#039;quali è anche da annoverare la trasfusione del sangue, splendido pen­<lb></lb>siero, benchè malaugurato negli effetti. </s>

<s>Prima dell&#039;Harvey ebbero quel pen­<lb></lb>siero Pico della Mirandola, Girolamo Cardano, e Giovanni Colle fra&#039;nostri, <lb></lb>e in mezzo a loro Andrea Libavio, lusingato di poter per via di tubi tra­<lb></lb>sfondere il sangue e trasformare un vecchio in un giovane, come s&#039;era lu­<lb></lb>singato d&#039;aver, per via de&#039;processi alchimici, a trasformare il peltro in <lb></lb>purissimo oro. </s>

<s>Nel cap. </s>

<s>XVI <emph type="italics"></emph>De motu cordis,<emph.end type="italics"></emph.end> dove il circolo del sangue dal <lb></lb>cuore alle parti e dalle parti al cuore si mostra dai veleni e dai morsi ve­<lb></lb>lenosi, che inducono rapidamente il malore per tutte le membra, si conte­<lb></lb>neva in germe la possibile trasfusione del sangue, ma Francesco Folli sog­<lb></lb>giunge che concorse in quell&#039;inspirazione la viva voce della Natura. </s>

<s>Egli è <lb></lb>storico diligentissimo di sè stesso, e perciò a lui ci convien cedere la parola. </s></p><p type="main">

<s>“ Nell&#039;anno 1652 lessi il libretto di Guglielmo Arveo, inglese, che tratta <lb></lb>del moto del cuore e del sangue, la qual lettura, con qualche notizia che <lb></lb>aveva dell&#039;innestar le piante, produsse nella mia fantasia questo terzo pro­<lb></lb>blema, che data la circolazione del sangue fosse possibile la trasfusione, con <lb></lb>la quale si potesse non solo curare alcuni mali, ma ringiovanire e ingigan­<lb></lb>tire ancora, come l&#039;accennai nel mio libretto <emph type="italics"></emph>Della cultura della vite,<emph.end type="italics"></emph.end> che <lb></lb>non pubblicai per altro, che per far palese a tutti che la trasfusione del <lb></lb>sangue era da me stata inventata, e fin dall&#039;anno 1654 manifestata al Se­<lb></lb>renissimo Ferdinando II, granduca..... ” </s></p><pb xlink:href="020/01/1284.jpg" pagenum="159"></pb><p type="main">

<s>“ Scorsero undici anni, nè mai intesi novella alcuna di questo problema, <lb></lb>nè per allora io abitava in Fiorenza, come fo adesso, ma timido quanto cu­<lb></lb>rioso non sapeva qual mezzo termine prendere per averne notizia. </s>

<s>Determi­<lb></lb>nai scrivere la mia <emph type="italics"></emph>Recreatio physica,<emph.end type="italics"></emph.end> la quale, e dal geroglifico del fron­<lb></lb>tespizio e dalla materia che vi tratto, potrà ciascuno leggendola riconoscere <lb></lb>che in grazia della trasfusione fu scritta, e anco dedicata al medesimo gran­<lb></lb>duca Ferdinando, acciocchè presentandogliela, come feci nel 1665, mi pale­<lb></lb>sasse qualche cosa di essa. </s>

<s>Ma esso tacendo supposi o che non ne avesse <lb></lb>fatta fare esperienza alcuna, oppure avendone fatte non volesse che fossero <lb></lb>note, e restando nella medesima ingnoranza di prima non ardiva di sco­<lb></lb>prirmi con alcuno. </s>

<s>Ma quando meno vi pensava, mi fu detto da ser Ippo­<lb></lb>lito Tei da Bibbiena, mio amico e che allora dimorava in casa dell&#039;illustris­<lb></lb>simo signor marchese Filippo Niccolini, come in Inghilterra avevano trovato <lb></lb>una bellissima invenzione di ringiovanire, col trasfondere del sangue di gio­<lb></lb>vanetti nelle vene de&#039;vecchi. </s>

<s>” </s></p><p type="main">

<s>“ Quale io restassi a tale avviso, lo lascio considerare a chi ha aspet­<lb></lb>tato un tempo, e poi conseguito all&#039;improvviso una buonissima nuova, ac­<lb></lb>coppiata con un dolore altrettanto grande, quanto fusse l&#039;allegrezza, per <lb></lb>perdere nell&#039;istesso momento l&#039;onore, che sperava e credeva acquistato. </s>

<s>Poi­<lb></lb>chè non sapeva se era accaduto ad altri nell&#039;istesso secolo il medesimo pen­<lb></lb>siero, oppure di Toscana avesse navigato in Londra. </s>

<s>Mi lusingava però che, <lb></lb>per essere stati qui alla corte di Firenze alcuni virtuosi Inglesi, e presenti <lb></lb>ancora a molte esperienze, come l&#039;attesta il signor Redi, fra&#039;quali era il <lb></lb>signor Finchio, che al presente si ritrova ambasciator residente alla Porta <lb></lb>ottomana per la corona d&#039;Inghilterra, potessero averla in questa corte in­<lb></lb>tesa, e trasportata poi alla patria. </s>

<s>S&#039;aggiunga a questo verisimile che di <lb></lb>tutte le altre belle invenzioni, che di là sieno venute, si è anco inteso il <lb></lb>nome dell&#039;autore, eccetto che di questa. </s>

<s>” </s></p><p type="main">

<s>“ Ma impaziente non volli star più celato, e pigliando scusa di scri­<lb></lb>vere della cultura della vita, mi scopersi per inventore di essa, chiaman­<lb></lb>done in testimonio il prefato serenissimo Ferdinando II, che in quel tempo <lb></lb>viveva, nè mai ho saputo che altri si sia detta invenzione arrogata. </s>

<s>Con <lb></lb>ragione adunque posso chiamarla mia. </s>

<s>” (Stadera medica, Firenze 1680, <lb></lb>pag. </s>

<s>35-38). </s></p><p type="main">

<s>Non erano questi però del Folli altro che progetti: egli stesso confessa <lb></lb>nel suo <emph type="italics"></emph>Dialogo intorno alla cultura della vite<emph.end type="italics"></emph.end> di non averne mai fatta <lb></lb>esperienza (Firenze 1670, pag. </s>

<s>44). Le prime prove della trasfusione del <lb></lb>sangue furono, secondo l&#039;Haller, fatte in Inghilterra da Timoteo Klarke <lb></lb>nel 1657 (Elementa physiol. </s>

<s>cit., T. I, pag. </s>

<s>233), tre anni dopo la proposta <lb></lb>fatta dallo stesso Folli al Granduca, e il Senac dice che l&#039;anno dopo furono <lb></lb>anche dall&#039;Hansbau così fatte nuove esperienze tentate in Francia (Della <lb></lb>struttura del cuore, traduz. </s>

<s>ital., T. III, Brescia 1783, pag. </s>

<s>58). Ma perchè <lb></lb>non sono così fatte testimonianze di questi celebri scrittori confortate di do­<lb></lb>cumenti, che a volerli sottoporre ad esame non basterebbo forse un intero <pb xlink:href="020/01/1285.jpg" pagenum="160"></pb>volume, noi sceglieremo, fra tutte le altre, per vera la più diritta e più spe­<lb></lb>dita via, che a nostro giudizio ci si presenta. </s></p><p type="main">

<s>Ne&#039;principii dell&#039;anno 1665 Carlo Fracassati in Pisa proponeva la sua <lb></lb>nuova <emph type="italics"></emph>Medicina infusoria.<emph.end type="italics"></emph.end> Consisteva questo nuovo metodo nell&#039;iniettare <lb></lb>per le incise vene alcune sostanze, che restituissero le perdute sue buone <lb></lb>qualità al sangue. </s>

<s>In mezzo a questi pensieri sovvenne all&#039;inventore un altro <lb></lb>pensiero assai più seducente, che gli ragionava come parendo probabile di­<lb></lb>pendere la causa dell&#039;apoplessia da un improvviso coagulo sopravvenuto nel <lb></lb>sangue, si potessero i colpiti da così fatto accidente, coll&#039;iniezione di alcuni <lb></lb>solventi, ridonare felicemente alla vita. </s>

<s>Il granduca Ferdinando, a cui il Fra­<lb></lb>cassati aperse questo pensiero, lo incoraggiò, e lo consigliò a diffonderne la <lb></lb>notizia, ciò che fece subito l&#039;Autore in quella sua Epistola <emph type="italics"></emph>De cerebro<emph.end type="italics"></emph.end> di­<lb></lb>retta al Malpighi, e stampata, dentro quello stesso anno 1665, in Bologna. <lb></lb></s>

<s>“ Cum Pisis, ivi egli scrisse, in theatrum anatomicum curassem inventum <lb></lb>conglaciationis sanguinis,.... subiit mentem posse hoc experimentum multa <lb></lb>docere: videbatur enim pari passu sanguinis solutionem nos fuisse deprehen­<lb></lb>suros, dum concretionem tenebamus, quae infusa per iugularem ac simul <lb></lb>etiam cruralem venam aqua forti communi succedebat. </s>

<s>Quare sanguinis re­<lb></lb>putans congelationes, quod in apoplecticis aperit autopsia, credidi non male <lb></lb>nos esse consulturos laborantibus si, secta statim vena, dissolvens aliquod <lb></lb>iniceretur. </s>

<s>Propterea cogitationes meas novit Ser. </s>

<s>M. D., cui inventum pa­<lb></lb>tefeceram, et fassus est posse inde multa innotescere ” (Inter Opera M. Mal­<lb></lb>pighi, T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>158, 59). </s></p><p type="main">

<s>La notizia da Pisa e da Bologna giunse presto a Londra e ad Oxford, <lb></lb>e Riccardo Lower fu de&#039;primi ad accoglierla e ad eseguire il progetto, prima <lb></lb>che sugli uomini, sopra vario genere di animali. </s>

<s>Anzi egli applicò il metodo <lb></lb>del Fracassati non a infonder solo liquori medicinali, ma varie sorta di suc­<lb></lb>chi nutritizi, d&#039;onde ei confessa essergli spontaneamente sovvenuto il pen­<lb></lb>siero di iniettare lo stesso sangue. </s>

<s>“ Complures anni sunt (così scrive nel <lb></lb>cap. </s>

<s>II del trattato <emph type="italics"></emph>De corde<emph.end type="italics"></emph.end> pubblicato per la prima volta in Londra <lb></lb>nel 1669) cum alios Oxonii viderim, et ipse, experiendi causa, varios liquo­<lb></lb>res opiatos emeticos, in vivorum animalium venas iniecerim.... Cum vero <lb></lb>insuper plures alimentares succos simili modo infuderim, atque cum variis <lb></lb>vini tum cerevisiae iniectionibus sanguinem diversorum animalium satis apte <lb></lb>et amice congruere vidissem; animum mox subiit experiri an non multo <lb></lb>magis sanguis diversorum animalium inter se conveniret, et sine periculo <lb></lb>aut lucta commisceretur.... Quare spem hinc animo concipiens, ad expe­<lb></lb>rimentum eius tentandum animum et manus adhibui ” (In Mangctì Biblio­<lb></lb>theca anat., T. II, Genevae 1685, pag. </s>

<s>108). </s></p><p type="main">

<s>Preparate fistole, e tutt&#039;altro che occorreva per l&#039;esperienza, “ quo­<lb></lb>circa, prosegue il Lower a dire, cum ex voto omnia expectationi respon­<lb></lb>derent, tandem Oxonii, sub finem Februarii anni 1665, praesentibus doctis­<lb></lb>simis viris doct. </s>

<s>Johanne Wallis, dom. </s>

<s>Thoma Millington, aliisque medicis, <lb></lb>experimentum hoc novum, iucundo sane spectaculo atque optimis auspiciis, <pb xlink:href="020/01/1286.jpg" pagenum="161"></pb>exhibui ” (ibid.) e prosegue a descrivere la trasfusione del sangue da un <lb></lb>cane in un altro. </s>

<s>Poi all&#039;ultimo così conclude: “ Horum fama, cum mox <lb></lb>Londinum pervolaret, aecepta epistola a clariss. </s>

<s>Boyleo, impense rogatus sum <lb></lb>ut totius experimenti methodum Societati regiae impertirem, quod non ita <lb></lb>multo post a me praestitum in philosoficis eiusdem Societatis Transactio­<lb></lb>nibus, Decembri insequente anno 1666, publici iuris factum est. </s>

<s>Et tum ru­<lb></lb>mor eius ad exteras gentes et Galliam pervagatus est, ubi mox, rei novi­<lb></lb>tate allecti, diligentius illam prosequi et aliis subinde experimentis augere, <lb></lb>illustrare; quodque ego solum in brutis perfeceram, ad hominis usum ac­<lb></lb>commodare coeperunt, uti in scriptis illorum, sequenti martio anni 1667 <lb></lb>tunc primum editis, apparet ” (ibid.). </s></p><p type="main">

<s>Il rumore di questi francesi esperimenti, giunto presto in Italia, riscosse <lb></lb>gli animi dei concittadini del Folli. </s>

<s>Il cardinale Leopoldo de&#039;Medici, non po­<lb></lb>tendo fare eseguir l&#039;esperienza nella sede dell&#039;Accademia, per essere gli <lb></lb>accademici dispersi, ne mostrò desiderio al Montanari, che si dette all&#039;opera <lb></lb>in Bologna insieme col Cassini. </s>

<s>Le prove riuscirono con non poco provento, <lb></lb>ond&#039;è che il Cassini stesso, in quella celebre lettera al Petit del dì 18 Giu­<lb></lb>gno 1667, dop&#039;aver riferite le osservazioni fatte intorno a Venere, per defi­<lb></lb>nirne il periodo della rotazione, passando a dire degli altri suoi studi, così <lb></lb>soggiunge: “ Experimenta multa de transfusione sanguinis ab uno in aliud <lb></lb>animal, exemplo eorum quae apud vos habita sunt, deque ipsius sanguinis <lb></lb>motu saepius fecimus, non parum proventu ” (MSS. Cim., T. XIII, c. </s>

<s>228). </s></p><p type="main">

<s>L&#039;anno dopo, avendo il Montanari dovuto abbandonare Bologna e an­<lb></lb>dare in Udine per suoi negozii, non lasciò le intraprese esperienze, una delle <lb></lb>quali, che consisteva nella trasfusione del sangue da un agnello in un cane <lb></lb>decrepito, gli riuscì tanto lusinghiera, che ne scrisse una breve relazione <lb></lb>indirizzata al Cassini. </s>

<s>La relazione però, qualunque se ne fosse la forma, <lb></lb>apparteneva all&#039;Accademia del Cimento, al Principe della quale ne fu man­<lb></lb>data dall&#039;Autore una copia, accompagnata da una lettera sottoscritta in Bo­<lb></lb>logna il dì 13 di Giugno 1668 (MSS. Cim., XIX, c. </s>

<s>184), e l&#039;accluso foglio, <lb></lb>acciocchè lo sappiano anche i nostri lettori, così diceva: </s></p><p type="main">

<s>“ La trasfusione del sangue d&#039;un animale nelle vene d&#039;un altro, l&#039;espe­<lb></lb>rienze di cui in tante parti del mondo già fatte sono oramai rese famose, è <lb></lb>materia, e per sè stessa e per le conseguenze che seco porta, così degna del­<lb></lb>l&#039;attenzione de&#039;Filosofi, che non potrà cred&#039;io riuscire discara a V. S. Ecc.ma<lb></lb>una succinta narrativa, che le farò con la presente, d&#039;una prova che ulti­<lb></lb>mamente ne fu fatta in Udine del Friuli, quando m&#039;ero colà recato per varii <lb></lb>affari, ma principalmente per riverire e godere i favori dell&#039;illustrissimo <lb></lb>signor conte Girolamo Savorgnano del Monte, cavaliere principalissimo di <lb></lb>quelle parti e mio stimatissimo signore. </s>

<s>” </s></p><p type="main">

<s>“ Ci trovassimo dunque, il dopo pranzo del giorno di Pentecoste, 20 di <lb></lb>Maggio 1668, il predetto illustrissimo sig. </s>

<s>conte Girolamo, l&#039;Ecc.mo sig. </s>

<s>dot­<lb></lb>tore Giov Batista Coris nostro bolognese ed io, in casa gli Ecc.mi signori <lb></lb>dottori Antonio e Giuseppe Griffoni, gentiluomini di quella città, presenti i <pb xlink:href="020/01/1287.jpg" pagenum="162"></pb>quali e con l&#039;assistenza ancora del sig. </s>

<s>Andrea Ceraffini, eccellente cerusico <lb></lb>che ne favorì non solo de&#039;suoi ferri ma in gran parte dell&#039;opera diligentis­<lb></lb>sima delle sue mani, preparammo in primo luogo un agnello, di cui sco­<lb></lb>perta l&#039;arteria crurale e fattevi le debite legature, delle quali quella che ri­<lb></lb>guardava la parte verso il cuore era a laccio scorrente, v&#039;adattammo dentro <lb></lb>con ogni possibile diligenza il cannellino, che avevamo preparato rivolto con <lb></lb>l&#039;orificio verso il cuore, e sopra di quello legammo assai bene l&#039;arteria me­<lb></lb>desima. </s>

<s>Dopo di che scopersimo la vena iugulare d&#039;un cane bracco, di cui <lb></lb>fra poco racconterò le condizioni, e legatala a laccio scorrente in due luo­<lb></lb>ghi, nello spazio di mezzo, aperto con lancetta, inserimmo un altro cannello <lb></lb>rivolto pure con l&#039;orificio verso il cuore, ed attorno di lui legammo suffi­<lb></lb>cientemente la vena. </s>

<s>Poscia adattando in sito proporzionato l&#039;agnello, inne­<lb></lb>stassimo insieme i cannellini, il che fatto sciogliemmo in primo luogo la <lb></lb>legatura della vena del cane, che riguardava verso il cuore, ed osservammo <lb></lb>che non ne venne perciò, nel cannellino ch&#039;era di vetro, porzione alcuna <lb></lb>di sangue, ma sciolta la legatura dell&#039;arteria dell&#039;agnello, dalla parte pur <lb></lb>verso il di lui cuore, scorse d&#039;improvviso il sangue per lo cannellino sino <lb></lb>nella vena del cane, ed in quella trasfondendosi, slegassimo subito anche la <lb></lb>legatura della vena del cane, che riguardava il capo, dalla quale lasciammo <lb></lb>uscire il sangue di lui, sebbene non così continuo come per lo cannellino <lb></lb>entrava, poichè considerato essere quella vena assai più grossa dell&#039;arteria <lb></lb>dell&#039;agnello, ad effetto che non uscisse molto maggiore copia di quello che <lb></lb>v&#039;entrava, si comprimeva talvolta col dito. </s>

<s>E finalmente, quando ci parve <lb></lb>che poco più ne restasse nell&#039;agnello venuto meno, rilegassimo l&#039;una e <lb></lb>l&#039;altra legatura della vena del cane, e ne estraessimo i cannellini. </s>

<s>Dopo di <lb></lb>che ricucimmo in parte la piaga, lasciando un poco d&#039;apertura, perchè po­<lb></lb>tesse purgandosi guarire, e dall&#039;agnello estraessimo quanto di sangue po­<lb></lb>temmo di vantaggio, che non empì un guscio d&#039;uovo. </s>

<s>” </s></p><p type="main">

<s>“ È però da avvertire che qualche poco del sangue dell&#039;agnello nel­<lb></lb>l&#039;operazione estravasava dai cannellini, a cagione che questi non s&#039;erano <lb></lb>potuti così bene innestare insieme, come si desiderava, perchè in difetto di <lb></lb>più adattati avevamo scelto un pezzo di cannello, staccato da uno di que&#039;stru­<lb></lb>menti di vetro, che usano le donne lattanti per votarsi le poppe, sebbene <lb></lb>andammo così riparando col dito, che non giudicammo esserne uscito un&#039;on­<lb></lb>cia per questa via, onde il rimanente di tutto l&#039;agnello si trasfuse nel cane. </s>

<s>” </s></p><p type="main">

<s>“ Era questo cane bracco barbone, allevato in casa di que&#039;signori Grif­<lb></lb>foni, non molto grande fra gli altri di quella specie, vecchio di tredici anni <lb></lb>e più, sordo affatto, già più di tre anni, sicchè per rumore, fischio o chia­<lb></lb>mata ad alta voce non dava cenno, pur con gli occhi, di udire. </s>

<s>Pochissimo <lb></lb>camminava, e non potendo per la debolezza alzare i piedi, gli strascicava in <lb></lb>modo, che ne faceva sentire il rumore per le stanze con lo strascino delle, <lb></lb>unghie sul suolo. </s>

<s>Poco e di poca voglia mangiava, e già da molto tempo <lb></lb>aveva tralasciato il costume di far carezze, neppure col moto della coda, ai <lb></lb>padroni. </s>

<s>” </s></p><pb xlink:href="020/01/1288.jpg" pagenum="163"></pb><p type="main">

<s>“ Dopo la trasfusione, sciolto dalla croce di legno ove s&#039;era legato, restò <lb></lb>per un&#039;ora in circa sulla medesima tavola, dove s&#039;era fatta l&#039;operazione, <lb></lb>nel qual tempo, essendo noi discesi in altre stanze, comparve egli final­<lb></lb>mente, avendo da sè discesa la tavola e la scala, ma non volle cibo, che <lb></lb>quindi ad un&#039;altr&#039;ora. </s>

<s>” </s></p><p type="main">

<s>“ Li due giorni seguenti, ne&#039;quali andai per diporto a vedere la for­<lb></lb>tezza d&#039;Osopo ed altre terre di giurisdizione di quell&#039;Illustriss. </s>

<s>sig. </s>

<s>conte <lb></lb>Girolamo, mi riferirono que&#039;signori Griffoni che aveva incominciato a stare <lb></lb>più sollevato d&#039;assai, anzi, che il martedì egli era uscito di casa, e contro <lb></lb>suo solito postosi a correre con altri cani per la piazza, non più strasci­<lb></lb>cando i piedi come prima soleva, ma fatto manifestamente più robusto. </s>

<s>Tor­<lb></lb>nato a casa, fece insolite carezze ai padroni, e quel che più ci parve consi­<lb></lb>derabile, oltre il mangiare più e con più avidità di prima, incominciò a dar <lb></lb>segni manifesti di recuperar l&#039;udito, perchè infatti molte volte al fischio e <lb></lb>alla voce de&#039;padroni si voltava, sebbene il sesto e settimo giorno, comin­<lb></lb>ciando a suppurare gagliardamente la ferita, egli paresse reso di nuovo più <lb></lb>malinconico e debole, il che s&#039;attribuiva ai sintomi che dalla ferita mede­<lb></lb>sima le provenissero. </s>

<s>” </s></p><p type="main">

<s>“ Partii poscia da quelle parti, ed ora mi trovo in Bologna, aspettando <lb></lb>giornalmente da quegli Eccellentiss. </s>

<s>signori Griffoni altre relazioni di ciò <lb></lb>che sarà seguito..... Bologna, 8 Giugno 1668. ” (MSS. Cim., T. XIX, <lb></lb>c. </s>

<s>180, 81). </s></p><p type="main">

<s>Di quest&#039;altre relazioni non abbiamo trovato il documento, dal quale <lb></lb>forse si concluderebbe che la gioventù renduta al cane dei signori Griffoni <lb></lb>di Udine non era che un&#039;illusione. </s>

<s>Illusioni simili apparvero nelle trasfu­<lb></lb>sioni del sangue negli uomini, che perciò furono severamente proibite dalle <lb></lb>leggi civili, ma l&#039;invenzione del Folli e le esperienze del Montanari, benchè <lb></lb>disonorate da certi medici cerretani, rimasero pure una delle più belle di­<lb></lb>mostrazioni del circolo del sangue, rendendosi evidente non andar egli alle <lb></lb>parti, se non che per la via del cuore. </s></p><pb xlink:href="020/01/1289.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della respirazione<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle cause motive, degli organi e dei modi della respirazione. </s>

<s>— II. Dell&#039;azione dell&#039;aria inspi­<lb></lb>rata sul sangue dei polmoni. </s>

<s>— III. </s>

<s>Della respirazione dei neonati: del problema arveiano. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il cuore posto in grembo ai polmoni, i quali anzi, quasi incubandolo, <lb></lb>par che lo tengano sotto le loro ali, dava facile indizio di quegl&#039;intimi com­<lb></lb>merci, che passano tra lui e il viscere che lo circonda nell&#039;economia della <lb></lb>vita animale. </s>

<s>Risoneranno forse ancora nelle orecchie dei nostri lettori gli <lb></lb>idillii, ne&#039;quali Galeno e il Vesalio cantarono del cuore, che nutrisce e mi­<lb></lb>nistra da sè stesso ai polmoni, e de&#039;polmoni che per contraccambio sono in <lb></lb>assiduo moto per refrigerare gli ardori del cuore; tant&#039;oltre procedendo in <lb></lb>questa amorosa corrispondenza, da non isguagliarsi i polsi dai moti del to­<lb></lb>race: Comunque siasi, è pur vero che sono i due visceri tra loro tanto stretti <lb></lb>consorti, che l&#039;aver parlato dell&#039;uno porta necessariamente che si parli anche <lb></lb>dell&#039;altro, e insaparabili nelle più alte funzioni della vita non vogliono andar <lb></lb>disgiunti ne&#039;fasti della Storia. </s></p><p type="main">

<s>I fatti però che passiamo a narrare hanno vicende alquanto diverse <lb></lb>dalle narrate, perchè prima di tutto, per ciò che concerne il tempo, si può <lb></lb>dire che, quando la scienza del cuore era già compiuta, quella de&#039;polmoni <lb></lb>invece era appena cominciata. </s>

<s>La ragione di ciò non è difficile investigarla, <lb></lb>essendo che, a bene intendere i moti del sangue, non era necessario pre­<lb></lb>cedesse altra scienza, mentre, a bene intendere i moti dell&#039;aria nella respira­<lb></lb>zione e gli effetti di lei sullo stesso sangue, conveniva precorressero la Mec-<pb xlink:href="020/01/1290.jpg" pagenum="165"></pb>canica e la Chimica de&#039;corpi aeriformi; due nuove scienze, la prima delle <lb></lb>quali, incominciata sull&#039;entrar del secolo XVII, verso la metà di lui fu quasi <lb></lb>assoluta, e la seconda non comparve che verso il terminar del secolo XVIII. </s></p><p type="main">

<s>È perciò che, non dovendo pretergredire i limiti posti alla nostra Sto­<lb></lb>ria, non resta a dir altro a noi se non che de&#039;presentimenti, che s&#039;ebbero <lb></lb>dell&#039;azione chimica dell&#039;aria sul sangue, ond&#039;è insomma che il frutto noi <lb></lb>dobbiam presentarlo ai lettori sotto le forme dell&#039;ovario chiuso intorno in­<lb></lb>torno e adombrato dalle foglie del fiore. </s>

<s>Ma tutta dentro il nostro campo <lb></lb>rinchiusa riman la meccanica dei moti respiratorii, progredita col progredire <lb></lb>della Pneumatica, nella quale si possono segnare questi tre passi: Il primo, <lb></lb>che termina col secolo XVI, quando s&#039;aveva della natura dell&#039;aria e delle <lb></lb>proprietà fisiche di lei un&#039;idea vaga e indistinta, fra ciò che si concepisce <lb></lb>come spirito, e ciò che si concepisce come materia; il secondo, che da&#039;primi <lb></lb>anni del secolo giunge fino al 1644, quando, per opera del Porta, del Keplero <lb></lb>e di Galileo, si dimostrò che l&#039;aria essendo pesante era materia, non diffe­<lb></lb>rente da tutta l&#039;altra, fuor che nell&#039;apparenza; il terzo finalmente, che <lb></lb>dal 1644 passa oltre alla metà del secolo, quando per via del celebre Stru­<lb></lb>mento del Torricelli e delle Macchine del Gueriche e del Boyle, si fece espe­<lb></lb>rienza che, oltre all&#039;esser l&#039;aria pesante, è elastica e perciò operativa di <lb></lb>tutti quegl&#039;innumerevoli effetti naturali, che parvero agli antichi altrettanti <lb></lb>misteri. </s></p><p type="main">

<s>Se sempre la Fisiologia fosse stata sollecita di giovarsi delle scoperte <lb></lb>della Fisica, a que&#039;tre passi, segnati ne&#039;progressi della Pneumatica, corri­<lb></lb>sponderebbero esattamente i progressi fatti dalla scienza de&#039;moti respiratorii. </s>

<s><lb></lb>Ma perchè le solite ritrosie ad accettare le novità, e una certa natural pi­<lb></lb>grizia del pensiero, in distendere e sollevare le ali, ora indugiarono que&#039;con­<lb></lb>nubii, e ora consigliarono a seguitar di fornicare con gli antichi errori; quei <lb></lb>tre passi non procedono, nella Pneumatisa e nella Fisiologia, sincroni, ma <lb></lb>perturbati, come vibrazioni di pendoli, che pur soggiacendo alle leggi gene­<lb></lb>rali della Meccanica si risentono de&#039;primi impulsi più o meno gagliardi, e <lb></lb>del più o men temperato influsso delle stagioni. </s>

<s>Che se il veder gl&#039;intrecci <lb></lb>di più pendoli, e il precedere e il susseguire de&#039;moti diletta i curiosi, e <lb></lb>porge soggetto di utili considerazioni ai Filosofi; di non minor utilità e di­<lb></lb>letto sarà per riuscire questa parte di storia a chi, nelle diversioni e nelle <lb></lb>stesse retrogressioni del pensiero, sa riconoscer la legge provvidamente im­<lb></lb>posta a&#039;suoi progressi. </s></p><p type="main">

<s>Incominciando dunque dal primo passo sopra segnato, l&#039;aria in sè stessa <lb></lb>riguardavasi come qualche cosa di spiritoso o di etereo, se non che la coin­<lb></lb>quinano necessariamente materie terree e fuligginose. </s>

<s>S&#039;attribuivano a così <lb></lb>fatte materie gli effetti sensibili dell&#039;aria stessa, come i moti ventosi e la <lb></lb>varia temperatura, e la facoltà di alimentare o di estinguer la fiamma. </s>

<s>Que­<lb></lb>sta idea della composizione dell&#039;aria applicata alle funzioni respiratorie, tra­<lb></lb>sparisce distinta nel Vesalio sotto una tal forma: “ Ex faucibus enim aerem, <lb></lb>per nares aut os attractum, recta in pulmonem ducit (aspera arteria), hunc <pb xlink:href="020/01/1291.jpg" pagenum="166"></pb>per universum pulmonis corpus ita numerosa ipsius serie distribuens, ut <lb></lb>pulmonis substantia hunc prompte alteret, atque cordis muneribus aptum <lb></lb>reddat. </s>

<s>Caeterum quod pulmonis proprium sit munus, suo dicemus loco, <lb></lb>nunc etiam sat est asperam arteriam, ita efformatam, innuere quod aptis­<lb></lb>sime aerem dum respiramus pulmoni deferat, ac rursus omnem, qui cordi <lb></lb>inutilis est, una cum fuliginosis ipsius excrementis inter expirandum reddat. </s>

<s><lb></lb>Neque arteriae venalis usus nulli incognitus est, cum is praecipuus sit ut <lb></lb>aerem cordi aptum, ac a pulmonis substantia in asperae arteriae ramis con­<lb></lb>fectum, in se pelliciat ipsiusque interventu cor eumdem in sinistrum ven­<lb></lb>triculum attrahat ” (De corporis hum. </s>

<s>fabrica, Basileae 1543, pag. </s>

<s>577 e 583). </s></p><p type="main">

<s>Di qui ebbero origine le varie ipotesi degli ufficii dell&#039;aria nella respi­<lb></lb>razione. </s>

<s>Coloro, che la riguardarono in sè stessa o nella sua purità eterea, <lb></lb>la fecero genitrice degli spiriti animali; quegli altri, che la considerarono <lb></lb>come necessariamente commista con parti terree, le attribuirono l&#039;ufficio di <lb></lb>rinfrescare il cuore, ventilatagli intorno dalle ali del Polmone. </s></p><p type="main">

<s>L&#039;ipotesi della generazion degli spiriti dall&#039;aria entrata per la trachea <lb></lb>ne&#039;polmoni, ipotesi professata già dagli antichi, il Colombo si lusingò come <lb></lb>vedemmo di averla ridotta alla certezza dei fatti, per via dell&#039;esperienza, la <lb></lb>quale fu primo il Cesalpino a riconoscer per falsa, e a dir perciò che l&#039;aria, <lb></lb>artificialmente insufflata per l&#039;aspera arteria, non passa nella sostanza de&#039;pol­<lb></lb>moni, e tanto meno nel ventricolo sinistro del cuore. </s>

<s>L&#039;ipotesi degli spiriti <lb></lb>veniva così ragionevolmente repudiata, ond&#039;è che il Cesalpino stesso non <lb></lb>seppe vedere a quale altro uso dovesse entrar l&#039;aria nel petto, se non che <lb></lb>a temperare il soverchio calor del sangue. </s>

<s>“ Transmisso interim aere fri­<lb></lb>gido per asperae arteriae canales, qui iuxta arteriam venalem protenduntur, <lb></lb>non tamen osculis communicantes, ut putavit Galenus, solo tactu temperat ” <lb></lb>(Quaestiones perip., Venetiis 1571, fol. </s>

<s>111 ad terg.). </s></p><p type="main">

<s>Se l&#039;aria dunque non attraversa i polmoni, come possono questi refri­<lb></lb>gerare il cuore? </s>

<s>Mosso da tal ragione, è sollecito il Cesalpino di emendar <lb></lb>quell&#039;errore invalso nell&#039;insegnamento di alcuni, e di mostrar come il re­<lb></lb>frigerio non va direttamente al cuore stesso, che non ne ha il bisogno, ma <lb></lb>al sangue, uscito così fervente dal ventricolo destro attraverso alla vena ar­<lb></lb>teriale. </s>

<s>Ecco perciò qual&#039;è l&#039;ufficio proprio dal nostro Autore assegnato ai <lb></lb>polmoni: “ Maximo igitur ingenio Natura fabricata est pulmones in pede­<lb></lb>stribus, et branchias in aquatibus, ut sanguinis fervorem moderaretur, illaeso <lb></lb>corde. </s>

<s>Nam cordi ad tutelam pericardium membranam circumduxit, tam­<lb></lb>quam eius capsulam: ferventem autem in eo sanguinem ad pulmones aut <lb></lb>branchias derivaus, iterumque cordi restituens. </s>

<s>Interim in transitu, ex aeris <lb></lb>frigidi aut aquae contactu, refrigerationem molita est ” (ibi). </s></p><p type="main">

<s>Noi non possiamo con certezza asserire che fosse proprio il Cesalpino <lb></lb>inspirator dell&#039;Arveo, ma pure è un fatto che, negatosi dal Nostro il passag­<lb></lb>gio dell&#039;aria attraverso alla sostanza del polmone, il Fisiologo inglese vol­<lb></lb>sesi a ripetere l&#039;esperienza del Colombo, e provato che, soffiandosi col man­<lb></lb>tice nella trachea, non si trova dell&#039;aria <emph type="italics"></emph>neque in arteria venosa, neque in<emph.end type="italics"></emph.end><pb xlink:href="020/01/1292.jpg" pagenum="167"></pb><emph type="italics"></emph>sinistro ventriculo cordis quidquam,<emph.end type="italics"></emph.end> fu dalle ragioni medesime del Cesal­<lb></lb>pino condotto a negar che la respirazione fosse propriamente ordinata alla <lb></lb>generazione degli spiriti animali. </s>

<s>Ond&#039;è che, trovandosi costretto a ricono­<lb></lb>scere in altro quell&#039;uso, venne, o fosse caso o fosse tacito e consapevole <lb></lb>consenso di idee, nella sentenza dello stesso Cesalpino. </s>

<s>“ Unde quoque pro­<lb></lb>babile foret pulmonum expirationem esse qua his efflatis eventaretur et de­<lb></lb>puraretur sanguis: atque inspirationem esse ut sanguis, pertranseundo inter <lb></lb>ventriculos duos cordis, contemperetur ambientis frigore, ne excandescens et <lb></lb>intumescens quadamque fermentatione inflatus, sicuti effervescens mel et lac, <lb></lb>adeo distenderet pulmonem, ut suffocaretur animal ” (Exercitatio I. </s>

<s>De circul. </s>

<s><lb></lb>sang. </s>

<s>post tractatum <emph type="italics"></emph>De motu cordis<emph.end type="italics"></emph.end> cit., pag. </s>

<s>139). </s></p><p type="main">

<s>Anche il Cartesio, il quale dopo il Cesalpino rinnovò l&#039;errore aristote­<lb></lb>lico del maggior calore, che è dentro il cuore, rispetto a quello delle altre <lb></lb>membra, e per cui il sangue esce dal ventricolo destro così bollente, da dis­<lb></lb>siparsi facilmente in vapore; anche il Cartesio, come l&#039;Harvey, nell&#039;asse­<lb></lb>gnare l&#039;ufficio proprio del polmone, revocò a sè l&#039;ipotesi dello stesso Ce­<lb></lb>salpino. </s>

<s>“ Et praecipuus quidem pulmonis usus (scrive nella Descrizione del <lb></lb>corpo umano, posta per appendice al trattato <emph type="italics"></emph>De homine<emph.end type="italics"></emph.end>) in hoc solum <lb></lb>consistit, quod aeris quem spiramus ope, sanguinem ex dextro cordis ven­<lb></lb>triculo affluentem condenset et temperet, antequam in sinistrum ingredia­<lb></lb>tur ” (Francofurti ad M. 1692, pag. </s>

<s>165). </s></p><p type="main">

<s>L&#039;ipotesi degli spiriti animali, direttamente generati dalla parte eterea <lb></lb>dell&#039;aria, introdotta nel sangue per opera immediata della respirazione, ve­<lb></lb>niva così bandita dalla Fisiologia, e dopo i primi esempi dati dal Cesalpino <lb></lb>si confermò il bando, allorchè, dimostratosi per l&#039;esperienza esser l&#039;aria in sè <lb></lb>stessa ponderosa, si riguardò come uno degli altri corpi, atta perciò a produrre <lb></lb>effetti naturali. </s>

<s>Fu allora che resuscitò tra&#039;Fisiologi una questione rimasta <lb></lb>alquanto sopita: se cioè i moti respiratorii dipendano dal polmone enfiato <lb></lb>per la corpulenza dell&#039;aria, o dall&#039;alterno sollevarsi e abbassarsi del torace. </s></p><p type="main">

<s>Le origini della controversia risalgono al Berengario, ne&#039;primi impulsi <lb></lb>che vennero da lui al risorgere della scienza. </s>

<s>Egli entra a discutere se i <lb></lb>moti de&#039;polmoni sieno necessarii o volontarii, e dopo aver riferite le altrui <lb></lb>opinioni. </s>

<s>“ Ego tamen credo, soggiunge, quod pulmo interdum habeat so­<lb></lb>lum motum naturalem per proprios villos, qui sunt in suis venis et arteriis, <lb></lb>qui tamen motus dependet a motu cordis, et sic motus pulmonis est acci­<lb></lb>dentalis; nam in corde, de consensu omnium, conceditur motus naturalis, <lb></lb>a quo motu fit aeris attractio, et etiam sanguinis, at ita etiam a motu na­<lb></lb>turali fit aeris, capnosorum fumorum et sanguinis et spirituum expulsio. </s>

<s>Cum <lb></lb>autem iste aer attractus a corde prius ingrediatur pulmonem, et ipsum in­<lb></lb>flet, necessario movet eum.... Huic motui naturali necessario obediunt mu­<lb></lb>sculi qui sunt inter costas et etiam diafragma, et moventur, quia pectus <lb></lb>necessario debet dilatari ad ampliationem et inflationem pulmonis propter in­<lb></lb>gressum aeris in ipso ” (Commentarium super Anat. </s>

<s>Mundini, Bononiae 1521, <lb></lb>fol. </s>

<s>CCCXXVIII ad terg.). </s></p><pb xlink:href="020/01/1293.jpg" pagenum="168"></pb><p type="main">

<s>Quando la sperimentata ponderosità dell&#039;aria dette quasi si direbbe corpo <lb></lb>a queste dottrine, i fautori si studiarono di confermarle sul fondamento di <lb></lb>una esperienza, che fu primo a farla il Vesalio; ripetuta poi da tanti quando <lb></lb>si pensò di applicarla a soccorrere gli annegati, e attribuita comunemente <lb></lb>all&#039;Hook. </s>

<s>Consisteva quella maravigliosa vesaliana esperienza nell&#039;insnfflare <lb></lb>i polmoni di un animale rimasto morto, e nel restituirgli nuovamente la <lb></lb>vita “ Ut vero vita animali quodammodo restituatur, foramen in asperae <lb></lb>arteriae caudice tentandum est, cui canalis ex calamo aut arundine indetur, <lb></lb>isque inflabitur ut pulmo assurgat, ac ipsum animal quodammodo aerem <lb></lb>ducat. </s>

<s>Levi enim inflatu in vivo hoc animali pulmo tantum quanta thoracis <lb></lb>erat cavitas intumet, corque vires denuo assumit et motus differentia pul­<lb></lb>chre variat ” (De corp. </s>

<s>hum. </s>

<s>fabrica cit., pag. </s>

<s>658). È dunque ne&#039;polmoni <lb></lb>e no nel torace il principio ai moti della respirazione. </s></p><p type="main">

<s>I fautori però dell&#039;altra sentenza, che poi era la vera, non potevano <lb></lb>persuadersi come i polmoni, privi affatto di organi motori, valessero a dare <lb></lb>impulso al torace fornito di tanti muscoli, e credettero meglio che, al dila­<lb></lb>tarsi e al restringersi del torace stesso, l&#039;aria entrasse ed uscisse dal petto, <lb></lb>com&#039;entra ed esce nel mantice al distendersi e al ripiegarsi delle sue pelli. </s>

<s><lb></lb>Ebbe, nell&#039;instaurare questa più sana dottrina, grande efficacia il Cartesio, <lb></lb>il quale, dop&#039;aver nel trattato <emph type="italics"></emph>De homine<emph.end type="italics"></emph.end> descritto il gioco de&#039;muscoli pet­<lb></lb>torali, conclude col dire che essi operano in modo “ ut spatium quo pul­<lb></lb>mones continentur reddatur amplius, quo fit ut aer in eos ingrediatur, eo <lb></lb>prorsus modo quo in follem ingreditur, quando illum aperimus. </s>

<s>Ubi vero <lb></lb>horum musculorum antagonistae inflantur, spatium illud fit angustius, atque <lb></lb>ideo aer iterum egreditur ” (Editio cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Il Van Horne, in quel suo libretto intitolato il <emph type="italics"></emph>Microcosmo,<emph.end type="italics"></emph.end> e nel quale <lb></lb>si rendevano in facile ed elegante modo popolari l&#039;Anatomia e la Fisiologia <lb></lb>di que&#039;tempi, diffuse fra gli Olandesi la dottrina, che la respirazione “ non <lb></lb>contingit a pulmonis propria virtute, sed a thoracis distentione et coarcta­<lb></lb>tione, ope potissimum diafragmatis ” (Lugduni Batav. </s>

<s>1665, pag. </s>

<s>78). E il <lb></lb>Deusingio fra&#039;Tedeschi commemorò, invece delle cartesiane moderne, le più <lb></lb>antiche tradizioni aristoteliche, insegnando che il torace si distende per virtù <lb></lb>sua propria “ ac dum distenditur, et quia distenditur, ingreditur aer. </s>

<s>Sicque <lb></lb>verissimum est quod dicit Aristotelis, <emph type="italics"></emph>De respiratione c. </s>

<s>XXI,<emph.end type="italics"></emph.end> cum attollitur <lb></lb>pectus eodem, perinde ut in folles, aerem externum influere necesse est ” <lb></lb>(Exercitationes de Respir., Croningae 1661, pag. </s>

<s>99). </s></p><p type="main">

<s>Tra gl&#039;Inglesi Natanaele Ighmor, amicissimo del Boyle, si dette, con <lb></lb>più sollecito e amoroso studio de&#039;predecessori e de&#039;contemporanei, a trattar <lb></lb>la questione dei moti respiratorii, consacrando a ciò il Cap. </s>

<s>III della P. III <lb></lb>Lib. </s>

<s>II della sua <emph type="italics"></emph>Disquisizione anatomica del corpo dell&#039;uomo.<emph.end type="italics"></emph.end> Incomincia <lb></lb>ivi dal sottoporre a un diligente esame le ipotesi di coloro, che attribuivano <lb></lb>ai polmoni una virtù propria di respirare, e dimostratane con argomenti di <lb></lb>fatto e di ragione la falsità, così all&#039;ultimo conclude: “ A motu itaque tho­<lb></lb>racis motum pulmonum dependere statuendum est. </s>

<s>Quando scilicet thorax <pb xlink:href="020/01/1294.jpg" pagenum="169"></pb>dilatatur, pulmones ad implendam eius cavitatem, ob vacui fugam, attollun­<lb></lb>tur, et internae eius superficiei undique se applicantes illorum porosas ca­<lb></lb>vitates etiam distendunt, in quas, ne daretur vacuum, per bronchias aer ir­<lb></lb>ruit. </s>

<s>Laxatis vero thoracis fibris, et cavitate hoc modo constricta, proprio <lb></lb>gravati pondere, pulmones sponte decidunt, aeremque, spongiosos illorum <lb></lb>poros comprimendo, expirant ” (Hagae comitis, 1651, pag. </s>

<s>186). </s></p><p type="main">

<s>Fin qui però l&#039;Igmoro niente altro fa che le parti di sapiente Filosofo, <lb></lb>ma perchè sentiva che sarebbero l&#039;esperienze riuscite molto più concludenti <lb></lb>delle ragioni, spogliato il pallio filosofale e impugnato il coltello anatomico, <lb></lb>tanto vi si esercitò, da credere di aver dispersa in quegli atti tutta intera <lb></lb>la razza dei cani, “ quibus, egli dice, in vivorum dissectionibus semper usi <lb></lb>sumus. </s>

<s>” </s></p><p type="main">

<s>Ferito dunque il torace, i polmoni presentavano all&#039;attento osservatore <lb></lb>fatti diversi. </s>

<s>Se la ferita facevasi nel mezzo, si venivano bene spesso a vio­<lb></lb>lare le membrane del Mediastino, cosicchè l&#039;aria, liberamente entrando dalle <lb></lb>due parti nel petto “ vacui metum tollat, ideoque cum thoracis cavitas di­<lb></lb>stendatur non assurgunt pulmones, dempta necessitate illos ad motum co­<lb></lb>gente ” (ibi, pag. </s>

<s>188). Lo stesso avviene quando, aperti ambedue i lati con <lb></lb>larghe e profonde ferite, l&#039;aria a furia d&#039;ogni parte v&#039;irrompe. </s>

<s>Se però <lb></lb>feriscasi un lato solo, rimanendosi l&#039;altro inviolato, qui osservammo, egli <lb></lb>dice, che il polmone seguita a muoversi, mentre là rimane affatto inerte. </s>

<s><lb></lb>La ragione è “ quia Mediastinum exacte cavitatem illaesi lateris claudit, adeo <lb></lb>ut aer externus necessitatem illam movendi in pulmonibus demere nequeat, <lb></lb>quia omnino excluditur ” (ibi). </s></p><p type="main">

<s>Stava tutto ciò a dimostrar chiaramente all&#039;Igmoro che il moto dei pol­<lb></lb>moni dipende dal torace, quando venne una difficoltà a dare improvviso as­<lb></lb>salto alla sua persuasione. </s>

<s>Ferito leggermente il cane in petto, in modo che <lb></lb>l&#039;aria non irrompa a furia, ma vi trapeli appena, “ aliquando motus illorum <lb></lb>loborum continuatur, imo saepe tam violento agitantur motu, ut etiam extra <lb></lb>vulnus evolare saepe cernantur ” (ibi). Ciò pareva confermar l&#039;ipotesi di co­<lb></lb>loro, che attribuivano al polmone un moto proprio, ma <emph type="italics"></emph>post longam con­<lb></lb>templationem frequentesque observationes,<emph.end type="italics"></emph.end> l&#039;Igmoro stesso scopri l&#039;inganno, <lb></lb>e intese da che veramente dipendeva quel fatto: “ quod scilicet lobi pulmo­<lb></lb>num lateris illaesi et integri, ob vacui fugam, moventes, ut supra dictum <lb></lb>est, aerem externum confertim arripiant, quam violentam attractionem plus <lb></lb>aeris sequitur quam in illis contineri queat. </s>

<s>Ideoque, cum ad lobos utriusque <lb></lb>lateris per eumdem canalem aer feratur, et lobi lateris integri repleti sint, <lb></lb>adeo ut totum illud aeris commoti quod insequitur recipere non possint; <lb></lb>ille vero incitatus non statim a motu desistit, sed qua patet via ruit, se­<lb></lb>quensque priorem urget, et cum in parte attrahente spatium non invenit, <lb></lb>in bronchias patentes loborum iam fatiscentium, qui a thorace non moven­<lb></lb>tur, irruit, eosque, ob levitatem eximiam, paululum attollit et motum quen­<lb></lb>dam languidum aliquandiu efficit ” (ibi, pag. </s>

<s>189). </s></p><p type="main">

<s>Chi legge oggidi queste parole, scritte dopo sette anni da ch&#039;era stata <pb xlink:href="020/01/1295.jpg" pagenum="170"></pb>fatta l&#039;esperienza del Torricelli, si maraviglia che, a intendere il fatto sopra <lb></lb>descritto, bisognassero all&#039;Igmoro lunghe contemplazioni, e si maraviglia <lb></lb>anche di più ehe frutto di osservazioni frequenti fosse la sopra riferita con­<lb></lb>clusione. </s>

<s>Consegue però da una tal maraviglia una notizia importante, ed è <lb></lb>che l&#039;arguto Anatomico inglese aveva della respirazione risoluto il problema <lb></lb>meccanico, ma no il pneumatico, lasciando ancora a spiegare in che modo, <lb></lb>dilatandosi e restringendosi il torace, l&#039;aria entri ed esca dal petto. </s></p><p type="main">

<s>La notizia delle scoperte italiane non era ancora penetrata in quelle <lb></lb>estranee regioni, nelle quali dominava piuttosto la Filosofia cartesiana, in <lb></lb>conformità de&#039;placiti della quale s&#039;ammetteva che il petto attraesse l&#039;aria a <lb></lb>sè prossima, la quale fosse spinta dalla contigua, e questa dalla precedente <lb></lb>via via per una serie continuata di moti, rimasta nota nella storia sotto il <lb></lb>nome di <emph type="italics"></emph>circolo cartesiano.<emph.end type="italics"></emph.end> L&#039;Igmoro applicò questo circolo alla più com­<lb></lb>piuta soluzion del problema de&#039;moti del polmone dalla parte del petto leg­<lb></lb>germente ferito, e rimasto nell&#039;altra parte inviolato. </s>

<s>“ Sic cum pulmonum <lb></lb>lobi in latere illaeso et integro moveantur, ac in aere motum quemdam ra­<lb></lb>pidum excitent, particulae aeris quae primo attrahuntur a subsequentibus <lb></lb>etiam impelluntur, hae ab aliis, illae a subsequentibus, illas aliae promovent, <lb></lb>adeo ut lobos elatos copiose infarcientes ad flaccidam etiam et immotam pul­<lb></lb>monum partem aer commotus, per eamdem canalem, irruat, illamque paulo <lb></lb>attollat ac distendat, perinde ac vesica quae per tubulum inflatur ” (ibi, <lb></lb>pag. </s>

<s>189). Nè è a passare in tal propòsito senza nota che l&#039;Autore, quat­<lb></lb>tordici anni dopo la pubblicazione de&#039;Dialoghi galileiani delle Due nuove <lb></lb>scienze, ammetta in quel circolo d&#039;aria inspirata un velocitarsi di moto dalla <lb></lb>bocca infino al polmone, somigliante a quello che produce, secondo il Pe­<lb></lb>reirio, il velocitarsi de&#039;corpi gravi cadenti. </s>

<s>“ Huius motus exemplum in <lb></lb>motu lapidis ab excelso descendentis habemus, cuius progressus in aere, in <lb></lb>fine velocior est quam in principio, ob aerem scilicet illum subsequentem <lb></lb>et promoventem, referente Pereirio, cap. <emph type="italics"></emph>De motu.<emph.end type="italics"></emph.end> Delabente enim lapide <lb></lb>partes aeris proxime inferiores, plus a lapide pulsae ac divulsae, ut locum <lb></lb>ab illo relictum occupent, magno impetu et celaritate ad terga lapidis con­<lb></lb>currunt, ipsumque impellunt ac ulterius promovent, et quo plures fuerint <lb></lb>aeris particulae, maiorique nixu impulsae ac maiori vi confluentes, lapidem <lb></lb>a tergo vehementius urgent et protrudunt, ac lapis velocius descendit ” (ibi, <lb></lb>pag. </s>

<s>188). </s></p><p type="main">

<s>Ebbe l&#039;Igmoro in quella ipotesi del circolo cartesiano molti consorti, <lb></lb>fra&#039;quali è da citar lo Charletton, di cui le dottrine trovarono nelle contro­<lb></lb>versie col Deusingio un commento. </s>

<s>Essendo un fatto oramai certo che l&#039;aria <lb></lb>entra, come nel mantice, nella cavità del torace, si disputava se ciò avve­<lb></lb>nisse per attrazione o per impulsione, a che rispondeva il Deusingio che <lb></lb>poteva essere e nell&#039;un modo e nell&#039;altro. </s>

<s>“ Nempe, dum dilatatur thorax, <lb></lb>pellitur aer circumstans ab ipso thorace se distendente: is vero aerem vi­<lb></lb>cinum propellit. </s>

<s>Cumque nullibi vacuum detur in rerum natura.... neces­<lb></lb>sum omnino est aerem sic pulsum, quasi circulatione quadam facta, thora-<pb xlink:href="020/01/1296.jpg" pagenum="171"></pb>cem subire.... Sed et vicissim dum dilatatur thorax, amplior redditur interior <lb></lb>eius cavitas in quam necessitate quadam, cum vacuum dari nequeat, subin­<lb></lb>trat aer, ipsumque spatium replet, sicque aer videtur attractione in cavum <lb></lb>thoracis subire ” (Exercitatio de respir. </s>

<s>cit., pag. </s>

<s>99, 100). </s></p><p type="main">

<s>Che di alquanti anni varcata la metà del secolo XVII si durasse così fra <lb></lb>gli stranieri a commentare il circolo cartesiano, e a pronunziare quelle insi­<lb></lb>gnificanti parole di <emph type="italics"></emph>fuga del vacuo,<emph.end type="italics"></emph.end> fa senza dubbio gran maraviglia, ma <lb></lb>più gran maraviglia fa Giovanni Swammerdam, che pretese di dimostrare <lb></lb>la propulsione dell&#039;aria ne&#039;polmoni per mezzo dell&#039;esperienza. </s></p><p type="main">

<s>Nel 1667, diciannove anni dopo le pubbliche esperienze torricelliane fatte <lb></lb>dal Pascal a Roano e a Parigi, e tredici anni dopo che il Pecquet avea pub­<lb></lb>blicato quegli stessi esperimenti, fatti pure in Parigi, intorno alle proprietà <lb></lb>elastiche dell&#039;aria; il celebre Medico olandese, che frequentava la Francia, <lb></lb>instaurava la sua fisiologia della respirazione sopra la dottrina “ de rare­<lb></lb>factione et condensatione iuxta nobilissimi et subtilissimi Cartesii fundamenta <lb></lb>firmissima et inconcussae veritatis ” (De respiratiene usuque pulmonum, <lb></lb>Lugduni Batav. </s>

<s>1667, pag. </s>

<s>119). Gli esperimenti poi, che secondo lo Swam­<lb></lb>merdam rendono quelle cartesiane verità fermissime ed inconcusse, son varii, <lb></lb>ma notabile fra gli altri è quello delle due ampolle disegnate a pag. </s>

<s>55 della <lb></lb>citata edizione, e riprodotte da noi <lb></lb>nella fig. </s>

<s>7, che per i nostri lettori <lb></lb>non ha bisogno d&#039;altra dichiarazione. </s>

<s><lb></lb>I moti dello stantuffo GH, che aspi­<lb></lb>rando o premendo l&#039;aria nella storta <lb></lb>A fanno zampillare il liquido ora dal <lb></lb>beccuccio D, ora dall&#039;altro C, rap­<lb></lb>presentano i moti del petto, e gli ef­<lb></lb>fetti dell&#039;espulsione e dell&#039;impulsione <lb></lb><figure id="id.020.01.1296.1.jpg" xlink:href="020/01/1296/1.jpg"></figure></s></p><p type="caption">

<s>Figura 7.<lb></lb>dell&#039;aria ne&#039;polmoni; effetti che si vedono, dice l&#039;Autore, seguire allo stesso <lb></lb>modo, se al collo della storta, invece d&#039;applicarvi uno stantuffo ” iungantur <lb></lb>totidem tubuli aenei oblongi, qui in asperam alicuius canis arteriam succes­<lb></lb>sive immittantur, arcteque huic alligentur ” (ibi, pag. </s>

<s>58). </s></p><p type="main">

<s>La nuova scienza pneumatica, istituita dal Torricelli, fu primo il Pecquet <lb></lb>ad applicarla sapientemente alla Fisiologia, mettendo in piena evidenza quella <lb></lb>singolar proprietà che ha l&#039;aria di dilatarsi spontaneamente; proprietà ri­<lb></lb>masta, prima dello sperimento torricelliano, inconsiderata. </s>

<s>Ma il Pecquet, ben­<lb></lb>chè avesse aperti gli occhi dei Fisiologi intorno all&#039;errore della suzione e <lb></lb>dell&#039;attrazione, e avesse nelle sue Dissertazioni anatomiche sentenziato che <lb></lb>“ folles aerem non attrahunt exuguntve, sed intrusum externa vi coguntur <lb></lb>excipere ” (Parisiis 1654, pag. </s>

<s>66); non si curò di applicare questa teoria <lb></lb>pneumatica dai mantici ai polmoni, lasciandone tutto il merito al Boyle, che <lb></lb>sperimentando la vita degli animali nel vuoto della sua Macchina, prese di <lb></lb>li occasione a dimostrar come l&#039;aria, spontaneamente e senz&#039;altro esteriore <lb></lb>impulso, entra a riempire l&#039;aperta cavità del torace. </s></p><pb xlink:href="020/01/1297.jpg" pagenum="172"></pb><p type="main">

<s>Dal XLI de&#039;suoi Nuovi esperimenti fisico-meccanici fa una digressione, <lb></lb><emph type="italics"></emph>in qaa dubitationes nonnullae de respiratione continentur,<emph.end type="italics"></emph.end> e dopo avere <lb></lb>accennato all&#039;ipotesi del circolo cartesiano, e alle esperienze immaginate per <lb></lb>confermarlo, e alle ragioni da alcuni addotte in centrario; “ huic autem diffi­<lb></lb>cultati, soggiunge il Boyle, Machina nostra facilem nobis suppeditat solutio­<lb></lb>nem, cum ex multis superioribus pateat experimentis quod in re de qua <lb></lb>agitur nulla omnino sit necessaria, quamvis verum sit in usitata respiratione <lb></lb>aliquam istiusmodi fieri solitam, ex thoracis vel abdominis dilatatione, aeris <lb></lb>in pulmones propulsio: quod quidem a sola thoracis dilatatione, interni istius <lb></lb>aeris seu halituosae substantiae spira, quae cavitatem possidere solet, quo­<lb></lb>usque a pulmonibus non adimpletur, plurimum debilitata, externus et con­<lb></lb>tiguus aer necessario per apertam arteriam asperam in pulmones irrumpit, <lb></lb>quoniam illic minorem quam alibi reperit oppositam sibi contranitentiam ” <lb></lb>(Opera omnia, T. I, Venetiis 1697, pag. </s>

<s>103). </s></p><p type="main">

<s>Così, nel 1659, entrava animosamente il Boyle in mezzo a quel grande <lb></lb>scompiglio d&#039;idee provocato dal vizioso fermento della Filosofia cartesiana, <lb></lb>e le riduceva sapientemente negli ordini del vero. </s>

<s>Il sale depurativo, per <lb></lb>così dire, delle false dottrine accolte nella sua patria e altrove le aveva il <lb></lb>grande Fisico inglese attinte dallo sperimento torricelliano, intanto che non <lb></lb>poca parte del merito è per i giusti giudici da attribuirsi all&#039;Italia. </s>

<s>Nè qui <lb></lb>è a tacere che, a confronto dell&#039;attività degli stranieri, i Nostri appariscono <lb></lb>inerti, di che non è difficile intraveder le ragioni, la prima e principal delle <lb></lb>quali è da riconoscersi in quella severità degl&#039;istituti galileiani, che non per­<lb></lb>mettevano di coltivare altra scienza, da quella in fuori che ha il fondamento <lb></lb>nelle matematiche, e nell&#039;osservazione dei fatti naturali. </s>

<s>È degno nonostante <lb></lb>di considerazione che fu il Malpighi, che dette al Bartholin occasione di di­<lb></lb>mostrare, nel Cap. </s>

<s>V <emph type="italics"></emph>De pulmonibus,<emph.end type="italics"></emph.end> “ Aerem a thorace non pelli in pulmo­<lb></lb>nes contra Cartesium ” (Inter Malpighii Opera, T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, <lb></lb>pag. </s>

<s>372-79). </s></p><p type="main">

<s>Col trattato <emph type="italics"></emph>De homine<emph.end type="italics"></emph.end> applicava il Cartesio la sua Filosofia allo stu­<lb></lb>dio del corpo umano, per cui egli ebbe grande efficacia e dette valido im­<lb></lb>pulso a promovere la Fisiologia; impulso che mancò agli Italiani, i quali, <lb></lb>riguardando il cartesianismo come un contagio, rimasero da questa parte <lb></lb>lungamente indietro agli stranieri. </s>

<s>La maravigliosa fecondità della scoperta <lb></lb>torricelliana, applicabile a ogni ordine di scienza, veniva debolmente colti­<lb></lb>vata fra noi dal Michelini e dal Magiotti, non anatomici per verità nè fisio­<lb></lb>logi, i quali non porsero ai loro connazionali, come al Boyle l&#039;Igmoro, il <lb></lb>Bartholin, il Willis e tanti altri, un subietto preesistente da instaurarvi, sulle <lb></lb>ipotesi immaginate, i nuovi fatti scoperti. </s></p><p type="main">

<s>Narrammo in altra parte della nostra Storia come quella, che si può <lb></lb>chiamare Filosofia nuova torricelliana, rimanesse per alquanti anni in Italia <lb></lb>inculta e quasi dimenticata, è com&#039;ella solamente risorgesse nell&#039;Accademia <lb></lb>del Cimento, quando già il Pascal, il Guericke e il Boyle l&#039;avevano con tanto <lb></lb>splendore diffusa tra le più studiose nazioni di Europa. </s>

<s>I nostri accademici <pb xlink:href="020/01/1298.jpg" pagenum="173"></pb>fiorentini dunque ripeterono gli esperimenti degli animali nel vuoto, sopra <lb></lb>i quali il Borelli fondò poi la sua teoria della respirazione divisa in due <lb></lb>parti, nella prima delle quali tratta <emph type="italics"></emph>De motu respirationis,<emph.end type="italics"></emph.end> e nell&#039;altra <emph type="italics"></emph>De <lb></lb>usu respirationis primario.<emph.end type="italics"></emph.end> Delle dottrine borelliane, che concernono questa <lb></lb>seconda parte, diremo nel paragrafo appresso, per trattenerci qui solamente <lb></lb>a riferir ciò che concerne la pneumatica e la meccanica de&#039;moti respiratorii. </s></p><p type="main">

<s>È questa de&#039;moti respiratorii, incomincia a dire il Borelli, una cogni­<lb></lb>zione assai perplessa ed oscura, non essendo noi certi quali sieno le vere <lb></lb>cause motive, quali gli strumenti, e quali i modi veri della respirazione. </s>

<s>No­<lb></lb>nostante egli è certamente dimostrato nella propos. </s>

<s>LXXXII della P. II <emph type="italics"></emph>De <lb></lb>motu anim.<emph.end type="italics"></emph.end> che nè l&#039;aria, nè i polmoni sono cause effettive della respira­<lb></lb>zione, ma che solo passivamente concorrono a produrre quegli atti. </s>

<s>Il pro­<lb></lb>cesso dimostrativo è semplice e spedito, imperocchè, non avendo l&#039;aria altra <lb></lb>forza motiva che nella sua gravità e nel suo elaterio, non può perciò pro­<lb></lb>durre nessuna azione, mentre che il fluido si rimane in mezzo all&#039;atmosfera <lb></lb>in equilibrio, perchè ugualmente d&#039;ogni parte compresso. </s>

<s>“ Quare est im­<lb></lb>possibile, dum in quiete persistit, ut tanta violentia dilatet pulmones, eos­<lb></lb>que repleat, et postea motu contrario eosdem constringat ut aufugiat ” (Ro­<lb></lb>mae 1681, pag. </s>

<s>155). Che non sieno poi causa effettiva della respirazione i <lb></lb>polmoni è chiaro, non essendo essi composti di fibre muscolari, per cui non <lb></lb>si possono muovere da sè stessi (ivi). </s></p><p type="main">

<s>Cause efficienti della respirazione, soggiunge nella proposizione appresso <lb></lb>il Borelli, son le forze de&#039;muscoli, che allargano il torace, e il peso con­<lb></lb>giunto alla forza elastica dell&#039;aria. </s>

<s>Rispetto al designare i muscoli, ai quali <lb></lb>sono stati propriamente dalla Natura commessi quegli uffici, gli Anatomici, <lb></lb>anco ai tempi del Borelli, non si trovavano pienamente concordi, ma pure <lb></lb>il Vidio fra&#039;Nostri, ne aveva scritto con assai precisione. </s>

<s>Dopo aver detto <lb></lb>che s&#039;inspira, quando il torace si dilata, e si espira, quand&#039;egli si contrae, <lb></lb>“ quamobrem, soggiunge, quicumque musculi thoracem dilatant ad inspira­<lb></lb>tionem pertinent, quicumque contrahuut, ad expirationem. </s>

<s>Sed cum utra­<lb></lb>que et naturaliter fiat et cum quadam vi, plures musculi concurrunt ad eam <lb></lb>quae fit cum vi, quam ad eam quae naturaliter. </s>

<s>In naturali respiratione di­<lb></lb>latando thoraci sufficit septum transversum duntaxat. </s>

<s>Sed in ea quae fit <lb></lb>cum vi, thorax necesse est dilatetur, non tantum a septo transverso, sed <lb></lb>etiam a primo ex musculis,.... qui inter costas sibi fibras habent superne <lb></lb>deorsum tendentes: hi autem sunt externi in omnibus spaciis inter costas. </s>

<s><lb></lb>Expirationem naturalem satis praestat per se gravitas thoracis qui, relaxato <lb></lb>septo transverso, descendit et ita contrahitur, sed ubi cum vi expiramus con­<lb></lb>currunt ad eum contrahendum musculi, qui siti inter costas fibras habent <lb></lb>ab inferiori parte sursum ascendentes ” (De anat. </s>

<s>corp. </s>

<s>hum., Venetiis 1611, <lb></lb>pag. </s>

<s>201, 2). Il Borelli pure, approvando in sostanza queste dottrine del Vidio, <lb></lb>concludeva la sua LXXXIV proposizione col dire che i moti respiratori, così <lb></lb>placidi e naturali come violenti, si compiono dai soli muscoli intercostali e <lb></lb>dal diaframma insieme operanti (De motu anim. </s>

<s>Pars cit., pag. </s>

<s>171). </s></p><pb xlink:href="020/01/1299.jpg" pagenum="174"></pb><p type="main">

<s>L&#039;altra causa efficiente della respirazione, aggiunge il Borelli, consiste <lb></lb>nel peso e nella elasticità dell&#039;aria, ciò che, senza ricorrere alle artificiali <lb></lb>esperienze del Boyle, semplicemente dimostra per l&#039;esempio del mantice, <emph type="italics"></emph>qui <lb></lb>utrem inclusum habeat,<emph.end type="italics"></emph.end> nel quale otre si rappresenta il polmone contenuto <lb></lb>nella cavità del torace (ivi, pag. </s>

<s>167). </s></p><p type="main">

<s>Venivano così dimostrate le vere cause motive e gli strumenti della re­<lb></lb>spirazione: rimaneva a dire dei modi, ciò che il Borelli fa nella proposi­<lb></lb>zione XC, premesse altre cinque per lemmi, in cui le costole si rappresen­<lb></lb>tano per archi semiellittici, con le loro estremità imperniate in una colonna <lb></lb>fissa, che rende immagine della colonna vertebrale. </s>

<s>Sollevandosi quegli archi, <lb></lb>la capacità compresa fra essi e la colonna aumenta, e abbassandosi diminui­<lb></lb>sce, d&#039;onde all&#039;ultimo il nostro Autore ne conclude, facendone l&#039;applicazione <lb></lb>ai moti respiratorii del petto: “ contractis musculis intercostalibus, una cum <lb></lb>diaphragmate, necessario pectoris cavitas ampliari et aer inspirari debet <lb></lb>“ (ibi, pag. </s>

<s>176). </s></p><p type="main">

<s>Bench&#039;entrasse il Borelli in questa trattazione, com&#039;udimmo, con passo <lb></lb>incerto, pur ne uscì fuori fiancheggiato dal vero, che i Fisiologi insomma <lb></lb>hanno poi confermato. </s>

<s>La teoria meccanica della respirazione, iniziata dal <lb></lb>Boyle fra gli stranieri, ebbe così l&#039;ultima mano in Italia, dove si sarebbe <lb></lb>creduto che dovess&#039;essere universalmente accolta, sì per la grande autorità <lb></lb>del Maestro che l&#039;insegnava, e sì per le patrie scientifiche tradizioni, che, <lb></lb>dopo aver lungamente esulato, un Italiano riduceva quasi trionfali nella sua <lb></lb>patria. </s>

<s>Eppure il Baglivi, tanto autorevole a que&#039;tempi, mostruosamente ac­<lb></lb>coppiando il vero dimostrato col falso già confutato, scriveva in una delle <lb></lb>sue Dissertazioni ch&#039;entrando l&#039;aria nel petto, col proprio peso e con la pro­<lb></lb>pria elasticità dà moto ai polmoni, a cui necessariamente conseguitano i moti <lb></lb>del torace. </s>

<s>“ Et videtur probabile motum thoracis ab inflatis aere pulmoni­<lb></lb>bus pendere, thoracemque dilatari ut locum det pulmonibus aere se expan­<lb></lb>dentibus; nam primo succedit aeris ingressus, deinde dilatatio thoracis. </s>

<s>” <lb></lb>(Opera omnia, Lugduni 1710, pag. </s>

<s>455). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Male però giudicherebbe de&#039;progressi, dalla Fisiologia fatti in Italia <lb></lb>sulla fine del secolo XVII, per impulso principalmente della grande opera <lb></lb>del Borelli, colui che volesse pigliar l&#039;esempio da Giorgio Baglivi. </s>

<s>A lui, <lb></lb>divenuto celebre nella prassi medica, troppo gran difetto facevano i prin­<lb></lb>cipii della Fisica e della Matematica, nè reca maraviglia che ripetesse in­<lb></lb>torno agli organi della respirazione gli errori confutati un mezzo secolo prima <lb></lb>dall&#039;Igmoro egli, che preferiva in astronomia Tolomeo a Galileo, e in chi­<lb></lb>mica al Boyle l&#039;Helmontio. </s></p><p type="main">

<s>Nella prima parte insomma del suo trattato della respirazione si può <pb xlink:href="020/01/1300.jpg" pagenum="175"></pb>dir che il Borelli ne dava la teoria, per ogni sua parte assoluta, e univer­<lb></lb>salmente approvata dagli stranieri e dai nostri, che secondavano i progressi <lb></lb>della scienza. </s>

<s>Ma quanto era certo che l&#039;aria entra spontaneamente ne&#039;pol­<lb></lb>moni, per la propria elasticità e pel proprio peso, altrettanto era dubbio qual <lb></lb>ne fosse nell&#039;economia della vita l&#039;uso primario. </s>

<s>“ Nec tandem, si sentiva <lb></lb>costretto di confessar lo stesso Borelli, usus eius primarius exacte perceptus <lb></lb>est ” (De motu anim., P. II cit., pag. </s>

<s>162). </s></p><p type="main">

<s>Quel <emph type="italics"></emph>tandem<emph.end type="italics"></emph.end> accenna a un qualche laborioso esercizio della mente dei <lb></lb>Fisiologi precursori, in investigare un tal uso, che dal Nostro si riduce al <lb></lb>refrigerio del calor del cuore, alla ventilazione della fiamma vitale, e all&#039;espul­<lb></lb>sione delle materie filigginose; usi tutti che il Borelli, con assai facili ra­<lb></lb>gioni rifiuta, ma però tace di altre ipotesi più sottili, nelle quali ei non senti <lb></lb>sventuratamente la fragranza di quel fior del vero, che sarebbe in terra stra­<lb></lb>niera, e dopo lunga stagione, allegato nel frutto. </s>

<s>Noi dobbiamo dunque in­<lb></lb>trattenerci alquanto sopra sì fatte ipotesi, tanto più che possiamo da un Ita­<lb></lb>liano pigliare i principii alla nostra storia. </s></p><p type="main">

<s>Potrebbe essere quell&#039;Italiano l&#039;Acquapendente, il quale, nel cap. </s>

<s>IV, <lb></lb>libro I <emph type="italics"></emph>De respiratione,<emph.end type="italics"></emph.end> prendeva sapientemente la Fisica per sicura scorta <lb></lb>alla Fisiologia, e diceva l&#039;aria generare e conservare gli spiriti animali a <lb></lb>quel modo, che genera e conserva la fiamma; ond&#039;è che, a voler conoscere <lb></lb>fra le varie opinioni quale sia la vera, “ quomodo tum generetur tum con­<lb></lb>servetur omnis flamma indagandum est ” (Opera omnia, Lugd. </s>

<s>Batav 1738, <lb></lb>pag. </s>

<s>163). Ma seguendo in così fatte indagini, l&#039;Autore, piuttosto l&#039;autorità <lb></lb>di Galeno che l&#039;esperienza, ne lasciava perciò il primo merito, un mezzo <lb></lb>secolo dopo, a un altro Medico italiano. </s></p><p type="main">

<s>Nel 1661 Tommaso Cornelio meditava seriamente sopra i più difficili <lb></lb>problemi della vita. </s>

<s>Fautor del Cartesio, da lui creduto professare una Filo­<lb></lb>sofia, “ quae a rebus incertis assensionem cohibendo, ea tantum admittat, <lb></lb>quae cognita plane fuerint penitusque perspecta ” (Progymnasmata, 1688, <lb></lb>pag. </s>

<s>279), ebbe a riconoscere di quando in quando di essersi ingannato, e <lb></lb>specialmente udendo il suo Autore farsi seguace di Aristotile e dire che il <lb></lb>cuore è negli animali tanto fervente, da non potersegli tener sopra la mano, <lb></lb>per cui entratovi dentro il sangue si leva subito in gran bollore. </s>

<s>— Ma come <lb></lb>poteva persuadersi di ciò il gran Filosofo, pensa il Cornelio, se a toccare il <lb></lb>cuore e a intingervi, come tante volte ho fatt&#039;io, il dito, non si sente punto <lb></lb>più caldo delle altre viscere? </s>

<s>— </s></p><p type="main">

<s>Veduta perciò di qui la necessità di abbandonare il Maestro, fu per­<lb></lb>suaso esso Cornelio che il calore sia nò nel cuore ma nel sangue, a cui si <lb></lb>comunichi e in cui si conservi in virtù del continuo moto, a produrre il <lb></lb>quale occorsegli per prima cosa al pensiero che fosse principalmente ordi­<lb></lb>nata la respirazione. </s>

<s>“ Quippe sanguis ille, qui e dextero cordis ventriculo <lb></lb>in pulmones, per venam ut vocant, arteriosam, propellitur, nequit in sini­<lb></lb>strum ventriculum permanare, nisi aer spiritu ductus arteriae asperae sur­<lb></lb>culos inflet atque distendat. </s>

<s>Hinc enim fit ut venae arteriosae ramuli com-<pb xlink:href="020/01/1301.jpg" pagenum="176"></pb>primantur atque adeo conclusus in his sanguis protrudatur in surculos <lb></lb>arteriae venosae ” (ibi, pag. </s>

<s>283). </s></p><p type="main">

<s>Qui, proseguendo il Cornelio le sue meditazioni, sentiva sollevarsi nella <lb></lb>mente un dubbio, che così gli ragionava: — Se la respirazione a questo <lb></lb>principale effetto di promuovere il circolo del sangue è comparata, come <lb></lb>mai un uomo non può lungamente vivere chiuso per esempio in un orcio, <lb></lb>che non abbia da nessuna parte il traspiro? </s>

<s>O perchè ci dovrebb&#039;egli al­<lb></lb>lora esser bisogno che l&#039;aria da respirarsi tratto tratto sia rinnovata? </s>

<s>Anzi <lb></lb>nè ogni sorta di aria, atta per il suo peso e per la sua elasticità a dare im­<lb></lb>pulso di moto al sangue, è buona alla respirazione, come si vede per l&#039;esem­<lb></lb>pio di quella, che traspira dalle cave del carbon fossile o ch&#039;esala dai cre­<lb></lb>pacci di alcune caverne. </s></p><p type="main">

<s>— Io ho avuto a questo proposito, seguita a dire il Cornelio, a far <lb></lb>osservazione di un fatto singolare, ed è che quell&#039;aria, la quale soffoca gli <lb></lb>uomini, è quella stessa ch&#039;estingue la fiamma. </s>

<s>So ben che l&#039;Hobbes im­<lb></lb>maginò un terzo genere di corpi, che non siano nè aria nè umore, ma qual­<lb></lb>che cosa di mezzana natura, e che sebben sieno come l&#039;aria stessa così <lb></lb>trasparenti, riescon pure in ogni modo nocivi al petto degli animali. </s>

<s>Ma che <lb></lb>ci è egli bisogno d&#039;immaginar cose nuove e straordinarie, quando possiamo <lb></lb>ricorrere alle comuni? </s>

<s>— (ivi, pag. </s>

<s>287-89). </s></p><p type="main">

<s>Di qui passa il Cornelio a dire che molte cose egli aveva pensate delle <lb></lb>qualità dell&#039;aria, e degli usi di lei nella respirazione, ma che essendosi pro­<lb></lb>posto di trattarne particolarmente in un suo libro, quì nel Proginnasma che <lb></lb>abbiam sott&#039;occhio <emph type="italics"></emph>De vita,<emph.end type="italics"></emph.end> si contenta solo di farne un breve cenno. </s>

<s>Que­<lb></lb>sto cenno crediamo che sia il solo rimasto delle speculazioni del Medico co­<lb></lb>sentino, le quali se fossero veramente venute alla luce esposte in un volume, <lb></lb>davano nell&#039;Autore anche agli Italiani per tempo il loro Pascal, il loro Boyle <lb></lb>e il loro Guericke: nè d&#039;essere il seme della sua scorperta con men solle­<lb></lb>cito amore coltivato fra&#039;suoi che fra gli stranieri, si sarebbe potuto giusta­<lb></lb>mente dolere lo spirito superstite del Torricelli. </s></p><p type="main">

<s>Il Nostro, il Filosofo inglese e l&#039;altro di Magdeburgo mirabilmente si <lb></lb>riscontrano, quasi allo stesso tempo, insieme in assegnare il vero uso del­<lb></lb>l&#039;aria nella respirazione, argomentandolo dal fatto sperimentale del morir <lb></lb>gli animali al mancare dell&#039;aria stessa, e dell&#039;estinguersi, in ugual modo e <lb></lb>per somiglianti cagioni, la fiamma. </s>

<s>“ Mihi itaque persuasum in primis est, <lb></lb>scrive il Cornelio, parem esse aeris necessitatem, quum ad animalium vitam, <lb></lb>tum ad ignem conservandum: ad utrumque vero utilis esse videtur aer ille, <lb></lb>qui nec valde rarus sit nec valde densus, item neque praeter modum com­<lb></lb>pressus neque distractus. </s>

<s>Quare si ignis in laterna conclusus ardeat, at e <lb></lb>foramine, quod in ipsius laternae fundo est, spiritus exugatur, statim flamma <lb></lb>contrahi ac languescere incipiet, et brevi tandem extinguetur. </s>

<s>Idem prorsus <lb></lb>continget, si per illud ipsum foramen in laternam aer copiosius inspiretur ” <lb></lb>(ibi, pag. </s>

<s>289, 90). </s></p><p type="main">

<s>L&#039;esperienza fatta naturalmente coll&#039;aspirar delle guance, e senz&#039;al-<pb xlink:href="020/01/1302.jpg" pagenum="177"></pb>tr&#039;uso di Macchina pneumatica, non è molto precisa, e non son perciò troppo <lb></lb>precise nemmen le idee derivate da quella. </s>

<s>Ottone di Guericke, estraendo <lb></lb>con la pompa da sè nuovamente macchinata l&#039;aria da un pallone di vetro, <lb></lb>dentro il quale era accesa una candela, vedeva la fiamma a poco a poco <lb></lb>impiccolire, infintanto che, ridottasi a una hollicina di color ceruleo a fior <lb></lb>del lucignolo, non si spengeva. </s>

<s>Di qui ne conclude non poter rendersi altra <lb></lb>ragione del fatto “ nisi quod cogitarem ignem ex aere aliquid alimenti ac­<lb></lb>cipere, ac proinde aerem consumere, et sic propter defectum ulterius vivere <lb></lb>non posse ” (Experimenta nova magdeb., Amstelodami 1672, pag. </s>

<s>90). Tolta <lb></lb>la candela e posto in quella vece nel pallone di vetro un passero, simil­<lb></lb>mente concluse dai nuovi fatti osservati che, per difetto d&#039;aria, s&#039;estingueva <lb></lb>intorno al cuore la vita, <emph type="italics"></emph>veluti spiritus vini flamma.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Veniva così il Guericke a rispondere a un importante quesito, che pro­<lb></lb>posto dal Cornelio era nonostante da lui lasciato irresoluto: onde avvenga <lb></lb>cioè che l&#039;animale non possa lungamente vivere in un vaso chiuso, se l&#039;aria <lb></lb>di quando in quando non si rinnova. </s>

<s>Esso Guericke dunque aveva sagace­<lb></lb>mente riconosciuto che la candela, mentre arde, e l&#039;animale, mentre respira, <lb></lb>prendono qualche cosa dall&#039;aria circostante, che serve ad alimentare la luce <lb></lb>e la vita, ma rimaneva tuttavia nella incertezza rispetto a un punto della <lb></lb>questione, il quale era se l&#039;estinguersi e il morire dipendesse perchè l&#039;aria <lb></lb>stessa si fosse consumata, o trasformatasi piuttosto in qualche altra crassa <lb></lb>o terrea sostanza, inabile a fare gli ufficii di prima. </s>

<s>“ Posterius, poi con­<lb></lb>clude, credo verum esse, quanquam sit adeo exile, ut nullo modo percipien­<lb></lb>dum ” (ibi, pag. </s>

<s>91). </s></p><p type="main">

<s>La medesima questione si parò pure per prima cosa alla mente del <lb></lb>Boyle, quando nel digredire dal suo XLI esperimento si dette ad applicare <lb></lb>i fatti fisici pneumatici osservati alla respirazione degli animali. </s>

<s>Tanto par­<lb></lb>vegli quel soggetto importante, da trovar qualche cosa di serio nelle stesse <lb></lb>stramberie del Paracelso, il quale diceva, secondo riferisce lo stesso Boyle, <lb></lb>“ quod, uti ventriculus alimenta conquoquit, partemque in usum corporis <lb></lb>convertit, aliamque partem reiicit; ita pulmo partem aeris consumit, aliam­<lb></lb>que proscribit. </s>

<s>Adeo ut, iuxta hermeticum hunc philosophum, sic enim secta <lb></lb>illius eum compellari voluit, supponamus licet aliquid in aere esse vitalis <lb></lb>eiusdem elixiris, sit verbo venia, quod refrigerandis restaurandisque vita­<lb></lb>libus nostris spiritibus inserviat, cui usui, cum crassior et ultra compara­<lb></lb>tionem maior aeris pars incommoda sit, mirum videri non debet ” (Opera <lb></lb>omnia, T. I, Venetiis 1697, pag. </s>

<s>109). </s></p><p type="main">

<s>Così intendesi, per questa ermetica dottrina, soggiunge il Boyle, come <lb></lb>l&#039;animale abbia bisogno che gli sia continuamente rinnovata l&#039;aria, della <lb></lb>quale ei solamente consuma la parte vitale, rimanendo l&#039;altra quasi come <lb></lb>feccia o come sedimento. </s></p><p type="main">

<s>Insieme con le dottrine, che secondo i Filosofi reputati di senno ave­<lb></lb>vano dello strano, si tirava dentro alla questione un fatto, che teneva del <lb></lb>portentoso, e l&#039;Autore de&#039;Nuovi esperimenti fisici-meccanici lo veniva, in <pb xlink:href="020/01/1303.jpg" pagenum="178"></pb>mezzo alle alte speculazioni della scienza, a raccontare al visconte di Dun­<lb></lb>garvan suo nipote, tale quale lo aveva avuto da persona non punto volgare, <lb></lb>sperando che sarebbe a Sua Signoria riuscito caro saperlo “ potissimum cum <lb></lb>idem ab alio scriptore commemoratum haud repererim ” (ibi, pag. </s>

<s>110). </s></p><p type="main">

<s>Il fatto dunque divulgato per la prima volta dal Boyle, in proposito <lb></lb>della necessità dell&#039;aria e degli usi di lei nella respirazione, è questo: Cor­<lb></lb>nelio Drebbellio, divenuto per le invenzioni meccaniche e per le scoperte <lb></lb>chimiche a&#039;suoi tempi famoso, si diceva che fra le tante sue opere ammi­<lb></lb>rande avesse costruita una nave sottomarina, della quale fece, presente lo <lb></lb>stesso re Giacomo, esperienza nel Tamigi con successo stupendo. </s>

<s>Il naviglio <lb></lb>era fatto vogare dalle robuste braccia di dodici remiganti, da uno de&#039;quali, <lb></lb>rimasto infino a queste presente anno 1659 unico superstite, riseppe il fatto <lb></lb>un Matematico di gran nome, <emph type="italics"></emph>a quo,<emph.end type="italics"></emph.end> attesta il Boyle, <emph type="italics"></emph>ego ipse accepi<emph.end type="italics"></emph.end> (ibi, <lb></lb>pag. </s>

<s>110). </s></p><p type="main">

<s>Chi fosse quel gran Matematico l&#039;Autore non dice, ma il Cavalieri, da <lb></lb>Bologna, in una sua lettera del primo Agosto 1645, dop&#039;aver dato al Tor­<lb></lb>ricelli notizia di varie curiosità scientifiche, soggiunge: “ In altro proposito <lb></lb>dirò del nostro buon padre Mersenno. </s>

<s>Mi bisognò sentire una farraggine di <lb></lb>cose.... Tra le altre mi maravigliai molto di quel suo navigar sott&#039;acqua, <lb></lb>del quale ha riempito ogni luogo dov&#039;è passato ” (MSS. Gal., T. XLI, c. </s>

<s>224). <lb></lb>Potrebb&#039;esser perciò che quel Matematico di gran nome, di cui fa menzione <lb></lb>il Boyle, fosse lo stesso Mersenno, il quale sentendosi costretto ad essere <lb></lb>con gl&#039;Inglesi più sincero, che con i nostri Italiani, avesse anche là susci­<lb></lb>tata la memoria di un ritrovato non suo, ma abbellito dalla sua viva imma­<lb></lb>ginazione, e commentato dal suo poco giudizio. </s></p><p type="main">

<s>Comunque sia, rimase il Boyle in udir ciò stupefatto, ed entrò allora <lb></lb>in gran curiosità di sapere come mai potessero gli uomini star così lunga­<lb></lb>mente sott&#039;acqua, senza rimanervi affogati. </s>

<s>E perchè sembra che quel gran <lb></lb>Matematico non gli avesse intorno a ciò data la richiesta sodisfazione, si mise <lb></lb>dietro a interrogare i parenti dello stesso Drebbellio, e specialmente un me­<lb></lb>dico ingegnoso, che aveva sposata una figliola di lui, dal qual medico gli <lb></lb>fu risposto “ putasse Drebbellium non totum aeris corpus at certam illius <lb></lb>partem efficere ut respirationi inserviat, qua consumpta, crassius quod reli­<lb></lb>quum est corpus, sive cadaver, sit verbo veniam, aeris vitalem flammam in <lb></lb>corde residentem fovere non valet ” (ibi). </s></p><p type="main">

<s>Così, per quanto mi fu possibile intendere, prosegue il Boyle la sua <lb></lb>narrazione, oltre all&#039;avere inventato il macchinamento del naviglio, trovò il <lb></lb>Drebbellio il modo di confezionare un qualche chimico liquore, nell&#039;uso del <lb></lb>quale principalmente consistesse il segreto di quella sottomarina navigazione. <lb></lb></s>

<s>“ Quotiescumque enim puriorem aeris partem consumptam vel nimium re­<lb></lb>spiratione depravatam, et eorum effluviis qui navigarunt saturatam animad­<lb></lb>vertit, recluso vase illo liquore completo, derepente turbato aeri talem vi­<lb></lb>talium partium proportionem restituit, qualis efficere potuit ut respirationi <lb></lb>aliquamdiu subserviret ” (ibi). </s></p><pb xlink:href="020/01/1304.jpg" pagenum="179"></pb><p type="main">

<s>Questa notizia però m&#039;accese, soggiunge lo stesso Boyle, nuova ardente <lb></lb>sete di saperne un&#039;altra, qual cioè si fosse quel così stupendo liquore, che <lb></lb>avesse virtù di purgare dalle infezioni e di render nuovamenre respirabile <lb></lb>l&#039;aria corrotta. </s>

<s>Mi fu risposto esser questo un segreto, che il Drebbellio non <lb></lb>aveva voluto mai rivelare a nessuno: anzi ei non fece vedere. </s>

<s>e ciò solo <lb></lb>materialmente, altro che ad uno, quella sostanza ristoratrice, e fu quell&#039;uno <lb></lb>colui “ qui me de ipsa rei veritate fecit certiorem ” (ibi). </s></p><p type="main">

<s>Ma il Digby, comunque poi se ne fosse assicurato, affermò che qnella <lb></lb>misteriosa sostanza, ristoratrice dell&#039;aria già viziata dai respiranti sott&#039;acqua <lb></lb>nel naviglio drebbelliano, consisteva nel sal nitro, ch&#039;ei rassomiglia nel suo <lb></lb>trattato <emph type="italics"></emph>De plantarum vegetatione<emph.end type="italics"></emph.end> al magnete, perchè ha virtù di attrarre un <lb></lb>altro sale simile, <emph type="italics"></emph>quo aer redditur foecundus<emph.end type="italics"></emph.end> (Amstelodami, 1669, pag. </s>

<s>54). <lb></lb>Questo stesso sale, poi soggiunge l&#039;Autore, è l&#039;alimento dei polmoni e il <lb></lb>nutrimento degli spiriti vitali. </s>

<s>“ Cornelius Drebbellius, contracta magna <lb></lb>huiusce salis quantitate in angustum quoddam spatium, suos animo defi­<lb></lb>cientes hospites, in sua angusta domo sub aqua, postquam omne balsamum <lb></lb>in secluso aere, in quo et ipsi seclusi erant consumpserant; aperiendo quam­<lb></lb>dam phialam, quae per istum vetustum, depravatum et exhaustum aerem <lb></lb>novos infundebat spiritus, recreare et rofocillare potuit ” (ibi, pag. </s>

<s>54, 55). </s></p><p type="main">

<s>Questa però del Digby dee in ogni modo essere stata una congettura, <lb></lb>fondata sulle nozioni che della Chimica si potevano avere a que&#039;tempi, nè <lb></lb>il Boyle era uomo da rimanere indietro agli altri. </s>

<s>Ma perchè sentiva a quelle <lb></lb>stesse congetture de&#039;commentatori del Drebbellio, e alle opinioni del Para­<lb></lb>celso, mancare ogni buon fondamento di scienza, ei si protesta di averle <lb></lb>semplicemente commemorate, senza approvarle, inclinando piuttosto a con­<lb></lb>sentir con coloro, che dicevano, come dall&#039;altra parte sembrava lo sconfer­<lb></lb>massero l&#039;esperienze, che l&#039;aria è necessaria a ventilare e a fomentar nel <lb></lb>cuore la fiamma vitale. </s>

<s>“ Quapropter aliquando iis consentire propensus fui, <lb></lb>quibus visus est aer necessarius ventilandae fovendaeque vitali flammae, <lb></lb>quam in corde sine intermissione ardentem suspicantur. </s>

<s>Videre est enim <lb></lb>quod in Machina nostra flamma lampadis, post aeris exuctionem, haud mul­<lb></lb>tum diutius quam vita animalis perdurabit ” (Opera et T. cit., pag. </s>

<s>110). </s></p><p type="main">

<s>Così gli assennati consigli rintuzzavano all&#039;ingegno quelli che parevano <lb></lb>arditi, ed eran pure liberi voli, nè si avvedeva il Boyle che più del balsamo <lb></lb>e dell&#039;elixir della vita, contenuto nell&#039;aria, era strana cosa rassomigliare il <lb></lb>cuore a una lampada accesa. </s>

<s>Tommaso Willis e Giovanni Mayow, in ciò più <lb></lb>sagaci, riconobbero nelle idee del Paracelso un simbolo del vero, che nella <lb></lb>storia del Drebbellio prende forma di poemetto. </s>

<s>E benchè non riuscissero <lb></lb>a sostituire alle immaginate le cose reali, sanno pur sollevarsi al di sopra <lb></lb>degli altri, e sono i primi fra gli estranei all&#039;Italia, in cui si veda la chi­<lb></lb>mica della respirazione balenare da&#039;loro pensieri, come luce che rivela im­<lb></lb>provviso un nuovo mondo, e poi subito lo nasconde. </s>

<s>Il precipuo fine per <lb></lb>cui, secondo il Willis, l&#039;aria si accoglie ne&#039;polmoni “ est ut sanguis veno­<lb></lb>sus a circuitu redux, chymo recenti dilutus, proindeque crudus et veluti <pb xlink:href="020/01/1305.jpg" pagenum="180"></pb>semiextinctus, tum perfectius misceatur, et velut subigatur, tum potissimum, <lb></lb>ut secundum omnes suas partes, ab aere nitroso de novo accendatur ” (Phar­<lb></lb>maceutices ration. </s>

<s>P. II, Opera omnia, T. II, Lugduni 1681, pag. </s>

<s>22). E il <lb></lb>Mayow, ricercando nel suo trattato <emph type="italics"></emph>De respiratione<emph.end type="italics"></emph.end> qual sia quell&#039;elemento <lb></lb>aereo, che è così necessario a noi per condurre la vita, “ verisimile est, egli <lb></lb>dice, particulas quasdam indolis nitrosalinae easque valde subtiles, agiles, <lb></lb>summeque fermentativas, ab aere, pulmonum ministerio, secerni, inque cruo­<lb></lb>ris massam transmitti ” (In Mangeti Bibliotheca anat., T. I, Genevae 1699, <lb></lb>pag. </s>

<s>1063). </s></p><p type="main">

<s>Dicemmo il Willis e il Mayow essere stati i primi fra gli stranieri a <lb></lb>sentir che l&#039;aria dovea avere un&#039;azione chimica sul sangue dei polmoni, <lb></lb>perchè in quello stesso tempo in Italia si speculava sottilmente intorno a <lb></lb>quel medesimo soggetto da due de&#039;più insigni cultori della scienza, e le loro <lb></lb>comuni speculazioni son, ne&#039;docili consensi e ne&#039;liberi dissensi, argomento <lb></lb>importantissimo di storia. </s></p><p type="main">

<s>Verso il 1660 il Borelli, per farsi via dalla vita vegetativa a introdursi <lb></lb>ne&#039;più astrusi misteri della vita animale, meditava intorno al modo, che <lb></lb>tengono nel nutrirsi le piante, e domandava per qual miracolo le materie <lb></lb>terree, introdotte dall&#039;acqua nelle radici, potessero trasformarsi in tanta lus­<lb></lb>suria di foglie, in tanta eleganza di fiori, e in tanta dolcezza di frutti. </s>

<s>Il mi­<lb></lb>racolo offerto dalla Natura, pensava, non è molto differente da quello così <lb></lb>spesso provocato dall&#039;arte, quando s&#039;inocula una verbena domestica sul <lb></lb>tronco di qualche albero agreste; ciò che non può spiegarsi altrimenti se <lb></lb>non con dire che i succhi agresti, entrando per i vasi dell&#039;albero domestico, <lb></lb>prendono ivi altra configurazione e abito nuovo. </s>

<s>Questa trasformazione il <lb></lb>Borelli l&#039;attribuiva tutta alla virtù de&#039;vasi, i quali danno a&#039;succhi la loro <lb></lb>impronta, ed essi la ricevono in sè, come cedevole materia che docilmente <lb></lb>s&#039;adatti alla nuova forma. </s></p><p type="main">

<s>Simili speculazioni erano dal nostro Autore applicate al modo del nu­<lb></lb>trirsi le piante, per mezzo delle radici, il qual modo ei dice di aver dopo <lb></lb>lunga meditazione riconosciuto non poter consistere in altro, se non in quelle <lb></lb>configurazioni, che acquistano le particole nutritizie in passar per gli acco­<lb></lb>modati orifizii delle radici, “ unde fluores illi percolati et transpositi in planta <lb></lb>inducunt configurationem et indolem illius plantae propriam ” (De motu <lb></lb>anim. </s>

<s>P. II cit., pag. </s>

<s>253). Riguardava insomma il Borelli le boccuzze aperte <lb></lb>nelle innumerevoli fibrille radicellari come i fori di un cribro, per i quaii <lb></lb>passano diverse e determinate particelle fluide; o in altre parole, passano in <lb></lb>ciascuna radicella quelle parti del succo, che trovano meglio adattato l&#039;ori­<lb></lb>ficio al loro ingresso (ivi, pag. </s>

<s>371). </s></p><p type="main">

<s>Non vedeva però ancora il nostro Fisiologo come si potessero queste <lb></lb>speculazioni applicare alla nutrizione degli animali, quando il Malpighi gli <lb></lb>venne a dare avviso della sua nuova scoperta intorno alla testura de&#039;pol­<lb></lb>moni, la quale tanto parve al Borelli importante, che sollecitò l&#039;Autore a <lb></lb>pubblicarla, e per lettera del di 18 Gennaio 1661 tornava di nuovo ad in-<pb xlink:href="020/01/1306.jpg" pagenum="181"></pb>culcargli si risolvesse di farlo, e di farlo presto “ perchè altrimenti l&#039;anderà <lb></lb>a bordello, oppure altri se ne accorgerà e la darà fuori, perchè la cosa è di <lb></lb>tanta importanza, che merita comparire in pubblico, ancorchè fosse un mezzo <lb></lb>foglio ” (Malpighi, Opera postuma, Londini 1677, pag. </s>

<s>6). Il Malpighi dun­<lb></lb>que, così calorosamente eccitato, dette mano a scrivere e a pubblicare la <lb></lb>sua Prima epistola <emph type="italics"></emph>De pulmonibus,<emph.end type="italics"></emph.end> indirizzata allo stesso Borelli. </s></p><p type="main">

<s>Ivi non si sta contento l&#039;Autore a far la semplice parte di Anatomico, <lb></lb>descrivendo quelle <emph type="italics"></emph>vescicole,<emph.end type="italics"></emph.end> che per unanime consenso furon poi dette <emph type="italics"></emph>mal­<lb></lb>pighiane,<emph.end type="italics"></emph.end> ma trapassa a far da Fisiologo, speculando sull&#039;uso del Polmoni, <lb></lb>i quali egli dice essere a questo principalmente fabrefatti dalla Natura, cioè <lb></lb><emph type="italics"></emph>ad sanguinariae molis miscelam<emph.end type="italics"></emph.end> (Londini 1687, pag. </s>

<s>136). Per sangue poi, <lb></lb>soggiunge, io non intendo quell&#039;aggregato di quattro elementi volgarmente <lb></lb>riconosciuti, “ sed totam illam corporaturam, quae per venas et arterias con­<lb></lb>tinuo fluit, quae licet pene infinitis constet particulis, omnes tamen sub du­<lb></lb>plici parte comprehendi posse videntur ad rudem nostrum sensum quodam­<lb></lb>modo similari; sub alba scilicet, quae vulgo dicitur serum, et sub rubra ” <lb></lb>(ibi, pag. </s>

<s>137). </s></p><p type="main">

<s>I polmoni insomma son per il Malpighi fatti a mantenere, fra il siero <lb></lb>e la parte rossa del sangue, una conveniente miscela, ciò ch&#039;essi, com&#039;adat­<lb></lb>tato strumento, eseguiscono per i moti d&#039;inspirazione e d&#039;espirazione, nei <lb></lb>quali, empiendosi e votandosi d&#039;aria le vescicole, in quel continuo andare <lb></lb>e venire contundono il sangue, e avvien qualche cosa di simile a ciò che <lb></lb>tutti i giorni si vede, “ dum farina in massam impingitur; ut enim eam <lb></lb>exacte misceamus, crebra tundimus manu ” (ibi, pag. </s>

<s>138). E come mesco­<lb></lb>landosi la farina, per l&#039;intruso fermento, nello stesso tempo anche si ri­<lb></lb>scalda; così avviene del sangue, e di qui ha l&#039;origine il suo calore. </s>

<s>“ Eodem <lb></lb>tempore ex deducta materia, intercedente fermentatione, sanguineae massae <lb></lb>instauratio contingit, calor emergit, et maior et maior inducitur particula­<lb></lb>rum libertas ” (ibi). Concorre, soggiunge il Malpighi, efficacemente a pro­<lb></lb>durre una tal fermentazione l&#039;aria, ma non tutta: sì bene una parte di lei, <lb></lb>che vien secreta dalle vescicole, e attraverso a&#039;loro pori continuamente ri­<lb></lb>versata nel sangue. </s></p><p type="main">

<s>Queste idee malpighiane intorno alle funzioni fisiologiche del polmone <lb></lb>erano state tacitamente approvate dal Borelli, infino dalla prima lettura del <lb></lb>manoscritto, e benchè sentisse che non consonavano in tutto con le sue, ri­<lb></lb>manendo queste tuttavia involte quasi negli inviluppi dell&#039;embrione, non <lb></lb>aveva nulla di pronto da contrapporre. </s>

<s>Ma la stessa Epistola del Malpighi, <lb></lb>rimeditata, venne presto a fare gli ufficii di ostetricante. </s>

<s>In quella compli­<lb></lb>catissima rete di vasi capillari, che ricorrono per il parenchima polmonare, <lb></lb>vide il Borelli una grandissima somiglianza con le fibrille delle radici degli <lb></lb>alberi, ed esultò per gran compiacenza vedendosi allora inaspettatamente <lb></lb>aperta la via di applicare al sangue quelle sue prime speculazioni intorno <lb></lb>al succo delle piante; cosa, che lungamente desiderata, non era ancora riu­<lb></lb>scito a conseguire. </s></p><pb xlink:href="020/01/1307.jpg" pagenum="182"></pb><p type="main">

<s>Le particelle del sangue venoso, deformate e perturbate dalla miscela <lb></lb>col chilo e colla linfa, vanno, secondo questa teoria borelliana, a riordinarsi <lb></lb>e a conformarsi nuovamente coi loro prototipi nelle sottilissime fibrille della <lb></lb>vena polmonare che si ramificano “ ad instar extremitatum radieum ar­<lb></lb>borum. </s>

<s>Ab hisce villosis fistulis suscipiuntur determinati liquores, nempe in <lb></lb>unaquaque illi qui figurae orificii vasculi aptari et ingredi possunt ” (De <lb></lb>motu anim. </s>

<s>P. II cit., pag. </s>

<s>256). Così riordinata ciascuna particola sangui­<lb></lb>gna, e tutte vivificate dagli spiriti, son riversate nel ventricolo sinistro del <lb></lb>cuore, d&#039;onde si dispensano a nutrir le varie parti del corpo animale. </s></p><p type="main">

<s>Questi pensieri sovvenuti ingegnosamente al Borelli che, tutto iatromec­<lb></lb>canico, aborriva dalla chimica della fermentazione; pensieri che poi furono <lb></lb>espressi e pubblicati nella proposizione CXXIX <emph type="italics"></emph>De motu anim.,<emph.end type="italics"></emph.end> vennero <lb></lb>proposti in sostituzione de&#039;suoi al Malpighi, il quale rimase maravigliato di <lb></lb>quel cambiamento. </s>

<s>Si direbbe anzi che ne rimase di più mortificato, come <lb></lb>trasparisce da un luogo della sua Autobiografia, in cui, dopo aver detto <lb></lb>come fosse la Prima epistola <emph type="italics"></emph>De Pulmonibus<emph.end type="italics"></emph.end> in tutto e per tutto approvata <lb></lb>dal Borelli, “ qui, soggiunge, mutato consilio, instetit ut, castigatis quibus­<lb></lb>dam, novum pulmonum usum ab eodem propositum, exponerem, quod al­<lb></lb>tera Epistola, ut plenissime eidem satisfacerem, libens executus sum ” (Opera <lb></lb>posth. </s>

<s>cit., pag. </s>

<s>6). </s></p><p type="main">

<s>Nella seconda Epistola infatti, che il Malpighi diresse al Borelli, <emph type="italics"></emph>De pul­<lb></lb>monibus,<emph.end type="italics"></emph.end> dop&#039;aver descritto il circolo del sangue, dal Microscopio rivelato <lb></lb>all&#039;occhio che l&#039;osserva con dolcissima maraviglia attraverso ai vasi traspa­<lb></lb>renti delle rane, passa a investigare a che fine sia quel perpetuo circolo <lb></lb>disposto dalla Natura, e non volendo, per fare ossequio al Maestro, contra­<lb></lb>dire a sè stesso, approva che un tal uso, oltre a quello della miscela del <lb></lb>sangue accennato nell&#039;Epistola precedente, possa essere anche l&#039;altro sug­<lb></lb>geritogli dallo stesso Borelli, a cui rivolge così il discorso: “ In quem vero <lb></lb>finem haec omnia fiant ultra ea quae superiori Epistola tetigi de pulmo­<lb></lb>naria miscela, tu ipse visus es apprime deprehendisse, nec celeberrimo tuo <lb></lb>hoc inventu mens est fraudanda, quod humanitate tua ad me exaratis lite­<lb></lb>ris commisisti, quibus subtiliter philosopharis mira in vegetabilibus portenta <lb></lb>Naturae observando, dum miramur poma ex trunco non suo pendere.... <lb></lb>Miri huius effectus tua philosophandi methodo secretum aperis: existimare <lb></lb>enim debemus eatenus massilici mali acidum succum in meri naturam dul­<lb></lb>cescere, quatenus particulae illius succi, licet feliciter excurrant per exiles <lb></lb>meatus proprii trunci, non eodem tamen modo possunt continuatos vitis tu­<lb></lb>bulos subire, hinc suo percitae motu et subsequentium impulsu extra suum <lb></lb>ordinem divulsae et fractae, necesse est ut ad superinductam meatus figu­<lb></lb>ram se componant, et novam induant naturam, qua et vitis et iesminum <lb></lb>producitur. </s>

<s>Similem operationis modum in pulmonibus Natura perficit: redit <lb></lb>enim ab ambitu corporis viduatus alibilibus particulis turbatus sanguis, cui <lb></lb>novus e vena subclavia humor additur alteriori naturae actione perficiendus. </s>

<s><lb></lb>Hic igitur ut in particularum carnis, ossis, nervis etc., disponatur et prae-<pb xlink:href="020/01/1308.jpg" pagenum="183"></pb>paretur, dum subit pulmonarium vasculorum myriades, velut in diversa mi­<lb></lb>nima stamina ducitur, et ita sanguineis particulis conciliatur nova figura, <lb></lb>situs et motus, quibus carnes, ossa et spiritus possint efformari. </s>

<s>Cumulatur <lb></lb>tui dicti fides a consimili seminalium vasorum structura, ac si animantis <lb></lb>nutritio quaedam esset eiusdem regeneratio ” (Opera omnia cit., pag. </s>

<s>143). </s></p><p type="main">

<s>Di queste ossequiosissime approvazioni però, e di questo splendido com­<lb></lb>mento fatto alle sue dottrine, il Borelli non rimase punto sodisfatto. </s>

<s>Voleva <lb></lb>che il Malpighi si disdicesse di tutto ciò, che aveva scritto intorno alla mi­<lb></lb>scela del sangue, e alle fermentazioni indotte in lui dall&#039;aria, secreta dalle <lb></lb>vescicole polmonari. </s>

<s>Pretendeva insomma che, rinnegasse ogni idea chimica, <lb></lb>per professare quella schietta teoria meccanica della respirazione, ch&#039;egli in­<lb></lb>segnava. </s>

<s>Ma perchè il Malpighi sentiva che a lasciarsi imporre prepotente­<lb></lb>mente il giogo a quel modo era una viltà, che digradava troppo un Filosofo, <lb></lb>proseguì con dignitosa libertà per la sua via, lungo la quale il Borelli, fie­<lb></lb>ramente sdegnato, gli si mise dietro le spalle a perseguitarlo. </s></p><p type="main">

<s>Tutto il capitolo VIII della II Parte <emph type="italics"></emph>De motu anim.<emph.end type="italics"></emph.end> è contro i chimisti <lb></lb>seguaci specialmente del Willis e del Mayow, i quali “ proferre non ve­<lb></lb>rentnr aerem habere nitrosam naturam, quae a caliditate agitata sanguinis <lb></lb>motum promovet ” (Editio cit., pag. </s>

<s>221). Ma è particolarmente rivolto quello <lb></lb>stesso capitolo a confutar le dottrine accennate nella I Epistola <emph type="italics"></emph>De Pulmo­<lb></lb>nibus,<emph.end type="italics"></emph.end> a sovvertir le quali s&#039;apparecchian dal Borelli le mine in quelle dieci <lb></lb>proposizioni precedenti alla CVIII, la quale finalmente esplode in questa sen­<lb></lb>tenza: “ Est impossibile ut in pulmonibus partes sanguinis etherogeneae, <lb></lb>quamtumvis contusae, misceantur exacte inter se ” (ibi, pag. </s>

<s>207). </s></p><p type="main">

<s>Confutate dunque le dottrine dell&#039;azione chimica dell&#039;aria nitrosa e fer­<lb></lb>mentativa sul sangue, vuole il Borelli instaurare le sua teoria meccanica <lb></lb>della respirazione, richiamando prima di tutto l&#039;attenzion de&#039;Fisiologi sopra <lb></lb>i fatti sperimentati dal Boyle, o meglio dagli Accademici del Cimento, che <lb></lb>sono ben più decisivi, dimostrandosi per essi che, al mancare a un tratto <lb></lb>l&#039;aria nel recipiente del vuoto torricelliano, l&#039;animale ivi dentro rinchiuso <lb></lb>si vede a un tratto cader moribondo. </s>

<s>Si comprende di qui come l&#039;aria è la <lb></lb>causa potissima della vita, per cui ella dee necessariamente penetrare nel <lb></lb>sangue, ma com&#039;ella ciò faccia è dubbio, essendo dimostrato da antiche espe­<lb></lb>rienze che, insufflata per l&#039;aspera arteria, non penetra nel polmone. </s>

<s>Io so, <lb></lb>prosegue a dire il Borelli, tacendo al solito il nome del Malpighi, che al­<lb></lb>cuni hanno detto essere, nelle tuniche de&#039;vasi polmonari e delle vescicole, <lb></lb>pori simili a quelli della cute, per i quali possa traspirar l&#039;aria insensibil­<lb></lb>mente, ma è ciò contrario all&#039;esperienza, vedendosi ben entrare ed uscire <lb></lb>attraverso ai pori di una membrana i liquidi, ma no l&#039;aria stessa. </s>

<s>“ Sicuti <lb></lb>ergo aer per praedictas membranas porosas non penetrat, sic per poros ve­<lb></lb>narum non transibit ” (ibi, pag. </s>

<s>217). </s></p><p type="main">

<s>Ma perchè in ogni modo è necessario che l&#039;aria inspirata si mescoli <lb></lb>col sangue ne&#039;polmoni, il Borelli in proposito ripensa che sempre son le ve­<lb></lb>scicole malpighiane ripiene di qualche succo acqueo o sieroso, ivi dentro stil-<pb xlink:href="020/01/1309.jpg" pagenum="184"></pb>lato, il quale si fa menstruo all&#039;aria, e penetrando attraverso ai pori mem­<lb></lb>branosi, com&#039;è proprietà dimostrata de&#039;liquidi, traduce seco l&#039;aria stessa nel <lb></lb>sangue. </s>

<s>“ Atque talis aquea serositas conquassata a vento aeris inspirati in <lb></lb>spumas proculdubio facesset, et hinc aqua illa impraegnatur a particulis <lb></lb>aeris. </s>

<s>Cumque eadem aqua per poros venarum facile exudare et penetrare <lb></lb>valeat, fieri non potest quin secum deferat ei inclusas aeris particulas easque <lb></lb>sanguini immisceat ” (ibi, pag. </s>

<s>219). </s></p><p type="main">

<s>Come si concilino queste dottrine con quell&#039;altre professate nella pro­<lb></lb>posizione CXXIX, nella quale, per confutar più direttamente la teoria chi­<lb></lb>mica dei fermenti sostenuta dal Malpighi, si dice che nei polmoni “ nulli <lb></lb>succi fermentitii repositi sunt, cum vesiculae malpighianae solo aere replean­<lb></lb>tur ” lo lasciamo al giudizio di chi sa che il passionato amor de&#039;sistemi fa <lb></lb>travedere anche i più grandi ingegni, trapassando piuttosto a dire a quale <lb></lb>uso credesse il Borelli che fosse l&#039;aria trasportata in circolo per le arterie. </s></p><p type="main">

<s>Quell&#039;uso, come oramai ci aspettiamo di udire dal Nostro, è puramente <lb></lb>meccanico, consistente negli effetti delle minime particelle aeree “ quae sunt <lb></lb>machinae spirales, quae comprimi a vi externa possunt, et deinceps sponte <lb></lb>resilire, ad instar arcus ” (ibi, pag. </s>

<s>225). Introdotte queste macchinette nel <lb></lb>sangue, e spiegando per le angustie de&#039;vasi il loro elaterio, concepiscono un <lb></lb>moto oscillatorio “ ad instar penduli ” (ibi, pag 228) e così inducono una <lb></lb>tremola commozione vitale in tutto il corpo. </s>

<s>“ Hinc forsan spirituum, seu <lb></lb>succi nervei et musculorum agitatio, saltem ex parte, dependet ” (ibi). </s></p><p type="main">

<s>Questo era per verità un ritornare più di un secolo indietro a rinnovar <lb></lb>la dottrina della generazione degli spiriti, insegnata da Realdo Colombo. </s>

<s>Il <lb></lb>Malpighi, nella tranquillità del suo senno, ben comprese le aberrazioni, melle <lb></lb>quali l&#039;ira e l&#039;amor proprio avevano sospinta quella gran mente, e l&#039;acco­<lb></lb>ramento che ne provò lo espresse in alcune belle pagine della sua Autobio­<lb></lb>grafia. </s>

<s>Ivi egli prende ad esaminare le dottrine, con tanta animosità dal Bo­<lb></lb>relli contrapposte alle sue, e con esempio, in casi simili raro, dimenticando <lb></lb>le offese e compatendo alle umane debolezze, con sereno giudizio ne fa no­<lb></lb>tare i difetti gravissimi, e gl&#039;incredibili errori. </s>

<s>All&#039;ultimo, confermatosi sem­<lb></lb>pre meglio nel suo pensiero, che cioè l&#039;aria abbia sul sangue un&#039;azione <lb></lb>paragonabile a quella che produce i fermenti, così conclude con memora­<lb></lb>bili parole la maggior probabilità, ch&#039;egli crede avere la sua ipotesi chimica <lb></lb>della respirazione sopra quella meccanica del Borelli: “ Externum vero et <lb></lb>turbativum principium ab aere perpetuo separatur, media membranea pul­<lb></lb>monum substantia, et pertranseunti sanguini ubique miscetur et affunditur. </s>

<s><lb></lb>Et licet doctissimus Vir admittat minimas particulas spirales aeris sanguinem <lb></lb>ingredi, probabilius tamen est quid latitans in aere et aquae etiam, summe <lb></lb>mobile et activum separari, quod fortasse luminis naturam sapit ” (Opera <lb></lb>posthuma cit, pag. </s>

<s>16). </s></p><p type="main">

<s>A questa misteriosa sostanza sommamente mobile ed attiva e che il <lb></lb>sangue separa continuamente dall&#039;aria, il Paracelso dava il nome metafo­<lb></lb>rico di <emph type="italics"></emph>elixir della vita.<emph.end type="italics"></emph.end> Il Willis e il Mayow, nel linguaggio chimico di <pb xlink:href="020/01/1310.jpg" pagenum="185"></pb>que&#039;tempi, l&#039;appellarono <emph type="italics"></emph>aria nitrosa,<emph.end type="italics"></emph.end> balbuziendo così una parola, che un <lb></lb>secolo e mezzo dopo la bene snodata lingua del Lavoisier pronunziò colla <lb></lb>voce di <emph type="italics"></emph>ossigeno.<emph.end type="italics"></emph.end> Allora finalmente fu dimostrata la vera analogia, che passa <lb></lb>fra la candela che arde e l&#039;animal che respira, e com&#039;avesse ragione il Mal­<lb></lb>pighi di rassomigliare quel non so che sommamente attivo e vivificatore del <lb></lb>sangue alla natura medesima della luce. </s>

<s>Ma perchè ebbe quella dimostra­<lb></lb>zione a patir così lungo indugio, è da accennar brevemente quali fossero <lb></lb>le dottrine seguite specialmente in Italia, dopo il Borelli e il Malpighi e <lb></lb>prima del Lavoisier, intorno alla respirazione. </s></p><p type="main">

<s>Le divise opinioni de&#039;due insigni Maestri ebbero, com&#039;è facile a pre­<lb></lb>vedere, una grande influenza sui discepoli, alcuni de&#039;quali si studiarono in­<lb></lb>gegnosamente di tirarsi fuori d&#039;ogni controversia, mentre altri o professa­<lb></lb>rono le schiette teorie meccaniche, o le accoppiarono alle chimiche, quasi <lb></lb>credessero che da due cause concomitanti ne dovesse riuscire più pieno e <lb></lb>più approvato l&#039;effetto. </s>

<s>Il primo di questi esempii ci è offerto da Lorenzo <lb></lb>Bellini, il quale studiando la respirazione dell&#039;uovo, e osservando gli effetti <lb></lb>dell&#039;aria sopra gli svolgimentì embrionali del pulcino, applicò fuori di ogni <lb></lb>controversia i nuovi fatti osservati alla respirazione polmonare. </s>

<s>Egli non di­<lb></lb>scute se, intorno al modo d&#039;introdursi l&#039;aria nel sangue, abbia ragione il <lb></lb>Borelli o il Malpighi, ma “ quemadmodum certum est aerem folliculi obtu­<lb></lb>sum ovi verticem occupantis, aut aliquid ab eodem aere separatum derivari, <lb></lb>ex eodem folliculo, in cavitatem amnii et liquidum eius; ita certum erit, ex <lb></lb>modo praemissis, aerem e pulmonibus in cavitatem canalium pulmonarium <lb></lb>et eorum sanguinem derivari ” (A propos. </s>

<s>VIII <emph type="italics"></emph>De motu cordis,<emph.end type="italics"></emph.end> Digressio <lb></lb><emph type="italics"></emph>De ovo,<emph.end type="italics"></emph.end> etc., Operum Pars II, Vanetiis 1703, pag. </s>

<s>142). </s></p><p type="main">

<s>Nè degli usi dell&#039;aria occorre pure di questionare; ella fa, dice il Bel­<lb></lb>lini, sopra i liquidi rimescolati col sangue dei polmoni quel ch&#039;ella fa sopra <lb></lb>i liquidi stessi, che riempiono l&#039;uovo. </s>

<s>“ Sed ille illa mutat in liquida pri­<lb></lb>mae et succedentibus fermentationibus apta, igitur aer pulmonis mutabit <lb></lb>memorata liquida in illa liquida quae sunt apta continuae fermentationi ani­<lb></lb>malis, hoc est conservationi eiusdem. </s>

<s>Sed hoc dicitur producere sangui­<lb></lb>nem, igitur sanguis in pulmonibus per admistionem aeris producitur ” (ibi, <lb></lb>pag. </s>

<s>143). </s></p><p type="main">

<s>Esempio di chi si dette fra noi a seguitar le dottrine schiettamente <lb></lb>meccaniche ce lo porge il Baglivi, il quale pensò che fosse la respirazione <lb></lb>a questo principale effetto ordinata “ ut huius magni follis motibus tota <lb></lb>fluidorum moles solidorumque compages in vivida veluti vibratione perma­<lb></lb>neat ” (Opera omnia, Dissertatio IV <emph type="italics"></emph>De experimentis circa sanguinem,<emph.end type="italics"></emph.end><lb></lb>Lugduni 1710, pag. </s>

<s>458). Che se in ordine a ciò sembra il nostro Autore <lb></lb>inspirarsi al Borelli, in assegnar poi altri usi all&#039;aria inspirata approva opi­<lb></lb>nioni dal Borelli stesso dimostrate per false. </s>

<s>Dice infatti il Baglivi che un <lb></lb>altro degli effetti della respirazione è quello di promovere ne&#039;polmoni e nel <lb></lb>cuore il corso del sangue, divenuto oramai troppo crasso e torpido per la <lb></lb>subita miscela colla linfa e col chilo. </s>

<s>“ Quare ut per ingentem pulmonum <pb xlink:href="020/01/1311.jpg" pagenum="186"></pb>molem pertransire possit, et ad sinistrum thalamum pervenire, valido forti­<lb></lb>que impellente, et nunquam cessaturo, indigebat, quod nonnisi aer, vi ela­<lb></lb>stica gravitateque sua, poterat absolvere ” (ibi, pag. </s>

<s>457). </s></p><p type="main">

<s>Domenico Guglielmini, nel suo trattato <emph type="italics"></emph>De sanguinis natura et consti­<lb></lb>tutione,<emph.end type="italics"></emph.end> distendendo le idee più al largo forse di tutti i Fisiologi suoi con­<lb></lb>temporanei, invoca l&#039;aiuto delle dottrine meccaniche e delle chimiche a <lb></lb>rivelargli i segreti misteri della vita, che per lui consistono principalmente <lb></lb>nel sangue. </s>

<s>È una follia, egli dice, la fiamma vitale suggerita all&#039;immagi­<lb></lb>nazione di molti da certi fatti di fosforescenza, che si osservano talvolta nelle <lb></lb>carni putrescenti de&#039;pesci, nelle uova delle lucertole, nelle nottiluche, ecc. </s>

<s><lb></lb>Sorgente unica di calore nel corpo animale è il sangue, che si riscalda pel <lb></lb>continuo moto e per le particelle sulfuree, che in sè contiene. </s>

<s>Di qui facil­<lb></lb>mente s&#039;intende come sia tanto più caldo intorno al cuore e ai polmoni <lb></lb>“ ubi magis a respiratione et attractis aeris particulis agitatur; ubi celeriore <lb></lb>a corde recepto motu urgetur ” (Venetiis 1701, pag. </s>

<s>93). Che maraviglia fa <lb></lb>dunque che sia sempre il cuore così fervente? </s>

<s>“ id quod fefellit vitalis flam­<lb></lb>mae propugnatores qui ab excedenti caliditate in corde necessitatem arden­<lb></lb>tis in eo fomitis deduxere ” (ibi, pag. </s>

<s>94). Ma il vero è, conclude il Gu­<lb></lb>glielmini, che null&#039;altro fomite è veramente nel cuore “ praeter sanguinem <lb></lb>transeuntem ” (ibi). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi ripensa a quello splendore d&#039;idee, che simile a raggio di sole attra­<lb></lb>verso a una squarciata nube trasparisce dalle parole del Willis e del Mayow, <lb></lb>del Malpighi e del Guglielmini, ammmira la sagacia di quegli ingegni, che <lb></lb>videro così viva la immagine del vero in ciò che si rappresentava agli occhi <lb></lb>di tutti gli altri sotto forma di larva mostruosa, e considerando poi quanto <lb></lb>fosse ancora lontana la scienza dal dare una dimostrazione certa di quelle <lb></lb>argutissime congetture, ben comprende come quel sottil filo di luce dovesse <lb></lb>andar facilmente disperso in mezzo alle comuni tenebre dell&#039;errore. </s>

<s>A que­<lb></lb>sta natural condizione s&#039;aggiungevano, per rintuzzar con più forza i pro­<lb></lb>gressi delle idee, gli efficacissimi influssi della Filosofia cartesiana, la quale, <lb></lb>per non ismentir mai l&#039;indole propria, sostituendo ai fatti naturali le ar­<lb></lb>guzie dell&#039;ingegno, come nella immaginata effervescenza del sangue rico­<lb></lb>nobbe la ragione de&#039;moti del cuore, così vi ritrovò pure i fini e gli usi <lb></lb>refrigeranti della respirazione. </s></p><p type="main">

<s>Questa cartesiana dottrina dall&#039;altra parte veniva confermata dalla grande <lb></lb>autorità dell&#039;Harvey, il quale, come vedemmo, nelle sue prime Esercitazioni <lb></lb>intorno alla circolazione, approvò l&#039;ipotesi del Cesalpino, che disse esser <lb></lb>l&#039;uso precipuo de&#039;polmoni quello di ventilare e di depurare il sangue. </s>

<s>Poi, <lb></lb>negli ultimi tempi della sua vita, ai quali si riferiscono quelle esercitazioni <pb xlink:href="020/01/1312.jpg" pagenum="187"></pb><emph type="italics"></emph>De partu,<emph.end type="italics"></emph.end> che Giorgio Ent pubblicò in appendice alle altre esercitazioni <emph type="italics"></emph>De <lb></lb>generatione animalium,<emph.end type="italics"></emph.end> tornato esso Harvey a meditar più di proposito <lb></lb>sopra i misteriosi ufficii dell&#039;aria inspirata, parve dubitare di quella sua <lb></lb>prima opinione. </s>

<s>“ Verum num refrigerii gratia respiratio instituta sit, an in <lb></lb>alium finem, alibi plenius ex observationibus nostris disputabimus ” (Lugduni <lb></lb>Batav. </s>

<s>1737, pag. </s>

<s>353). </s></p><p type="main">

<s>Quelle osservazioni e quelle disputazioni arveiane <emph type="italics"></emph>De respiratione<emph.end type="italics"></emph.end> an­<lb></lb>darono sventuratamente disperse, ma intanto qui soggiunge l&#039;Autore un fatto <lb></lb>singolarissìmo, ch&#039;ei confessa di non sapere spiegare, e che gli fu prima e <lb></lb>principale occasione di dubitar se l&#039;aria sia propriamente inspirata per re­<lb></lb>frigerare gli ardori del cuore. </s>

<s>Il fatto è così proposto, sotto forma di pro­<lb></lb>blema, per chiederne ai Fisiologi la soluzione: “ Qui fit ut foetus in lucem <lb></lb>editus, ac membranis integris opertus, et etiamnum in aqua sua manens, <lb></lb>per aliquot horas, citra suffocationis periculum, superstes sit; idem tamen <lb></lb><emph type="italics"></emph>secundis<emph.end type="italics"></emph.end> exutus, si semel aerem intra pulmones attraxerit, postea ne mo­<lb></lb>mentum quidem temporis absque eo durare possit sed confestim moria­<lb></lb>tur? </s>

<s>” (ibi). Intanto ch&#039;egli attende la desiderata risposta, l&#039;Harvey si serve <lb></lb>del fatto stesso per concluder che se l&#039;aria, una volta inspirata, è così dal <lb></lb>neonato avidamente richiesta “ fervor in eo ab aere accenderetur, potius <lb></lb>quam restingueretur ” (ibi). </s></p><p type="main">

<s>Lasciata dunque da parte la question dell&#039;uso dell&#039;aria ne&#039;polmoni, pro­<lb></lb>mossa poi più utilmente dall&#039;esperienze del Guericke e del Boyle, e dalle <lb></lb>speculazioni del Borelli e del Malpighi, meglio che dalle esercitazioni del­<lb></lb>l&#039;Harvey; è da veder come i Fisiologi si studiassero di risolvere il proposto <lb></lb>problema. </s>

<s>Ci vien di qua aperto l&#039;adito a una trattazione storica di non <lb></lb>lieve importanza, perchè avendo noi fin ora riferito le dottrine, che concer­<lb></lb>nono gli organi, i modi e gli usi della respirazion negli adulti, ci conduce <lb></lb>a narrare i progressi della scienza nello studio di quelle funzioni, che in <lb></lb>particolar maniera s&#039;esercitano nei neonati. </s>

<s>La stretta cognazione inoltre, <lb></lb>ch&#039;è fra il cuore e i polmoni, dà estensione, e aggiunge nuova importanza <lb></lb>a questa parte di storia, per quel che riguarda i modi della circolazione del <lb></lb>sangue nel feto, a cui furono deputati dalla Natura organi speciali, che nel­<lb></lb>l&#039;adulto, divenuti inutili, non lasciano di sè vestigi. </s>

<s>Alla storia fisiologica <lb></lb>perciò delle funzioni precede la storia anatomica delle parti, che ci fa risa­<lb></lb>lire a Galeno, e ce lo fa salutare, con giusta compiacenza de&#039;galenisti, per <lb></lb>il primo e più sagace maestro di anatomia fetale. </s></p><p type="main">

<s>Lasciati da parte altri luoghi parecchi delle varie opere galeniche, dove <lb></lb>si tratta di questo soggetto, basta per noi trattenerci sul cap. </s>

<s>VI del XV libro <lb></lb><emph type="italics"></emph>De usu partium,<emph.end type="italics"></emph.end> che s&#039;intitola <emph type="italics"></emph>De ordine generationis in foetu.<emph.end type="italics"></emph.end> Ivi è tutto <lb></lb>intento l&#039;Autore in contemplare il magistero ammirabile esercitato dalla Na­<lb></lb>tura intorno a quel corpicciolo, che vive una vita non sua in grembo all <lb></lb>madre, e principalmente ammira in tal natural magistero i modi e le vie, <lb></lb>per le quali il sangue va a somministrar materia conveniente a formarsi il <lb></lb>polmone. </s>

<s>Il quale, essendo organo così importante alla vita e così delicato, <pb xlink:href="020/01/1313.jpg" pagenum="188"></pb>riceve non di quel sangue comune, che vien dalla Vena cava, ma di un <lb></lb>sangue purificato, e perciò trasmessogli da un&#039;arteria, che ha natura venosa. </s>

<s><lb></lb>Così essendo a questo stesso vaso commesso un ufficio, che è proprio delle <lb></lb>vene, fu necessario rimanesse a fare all&#039;altro l&#039;ufficio delle arterie, ond&#039;ei <lb></lb>venne messo in diretta comunicazione con l&#039;Arteria magna. </s>

<s>“ Cum autem <lb></lb>id was venae officium huic visceri praestaret, necesse fuit alterum vas in <lb></lb>arteriae usum transmutari, quocirca Natura id quoque in magnam Arteriam <lb></lb>pertudit. </s>

<s>Verum, cum hic vasa inter se aliquantum distarent, aliud <emph type="italics"></emph>tertium <lb></lb>vas esiguum,<emph.end type="italics"></emph.end> quod utrumque coniungeret, effecit. </s>

<s>In reliquis vero duobus, <lb></lb>cum haec quoque mutuo sese coniungerent, velut <emph type="italics"></emph>foramen quoddam<emph.end type="italics"></emph.end> utri­<lb></lb>que commune fecit. </s>

<s>Tum membranam quamdam in eo, instar operculi <gap></gap><lb></lb>machinata, quae ad pulmonis vas facile resupinaretur, quo sanguini a Vena <lb></lb>cava impetu affluenti cederet quidem, prohiberet autem ne sanguis rursum <lb></lb>in venam cavam reverteretur ” (Opera, T. I, Venetiis 1597, fol. </s>

<s>212). </s></p><p type="main">

<s>Venivan così con mirabile chiarezza descritte le particolarì disposizioni <lb></lb>de&#039;vasi, e i vasi stessi aggiunti per servire al proprio modo della circolazion <lb></lb>del sangue nel feto, in cui la vena cava comunica con la vena polmonare, <lb></lb>per mezzo di un foro, e l&#039;arteria polmonare è congiunta all&#039;Aorta per mezzo <lb></lb>di un <emph type="italics"></emph>piccolo condotto.<emph.end type="italics"></emph.end> Nel rinnovamento della scienza anatomica al Beren­<lb></lb>gario sfuggirono queste galeniche osservazioni fetali, e furono perciò dimen­<lb></lb>ticate dal divino Vesalio, a cui il Berengario stesso, che in molte cose gli <lb></lb>serviva di guida, non le aveva rammemorate. </s>

<s>Sfuggirono altresì, forse per <lb></lb>simili ragioni, all&#039;oculatissimo Colombo, che se ne passa in quel trattar che <lb></lb>egli fa, nel XII libro della sua Anatomia, <emph type="italics"></emph>De formatione foetus.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Primo a resuscitare, benchè solamente in parte, quelle antiche spente <lb></lb>memorie, fu nelle sue Anatomiche osservazioni il Falloppio, il quale mara­<lb></lb>vigliato, in ritesser ch&#039;egli fa la storia delle arterie, raccogliendo le tante <lb></lb>fila lasciate indietro, domanda: “ Qua ratione factum sit quod Anatomici <lb></lb>fere omnes tam negligenter observaverint partem illam canalis vel arteriae, <lb></lb>qua iungitur vena arterialis circa basim cordis ipsi Aortae, cum in foetu <lb></lb>tam aperte pateat, tantusque sit aditus ab Aorta ad venam arterialem ” <lb></lb>(Opera omnia, Francofurti 1584, pag. </s>

<s>447). La maraviglia, poi soggiunge il <lb></lb>Falloppio stesso, tanto più mi cresce, e tanto più cresce insieme la ragione <lb></lb>di rimproverar la negligenza degli anatomici miei predecessori, in quanto <lb></lb>che quel canale arterioso “ qua iungitur vena arterialis circa basim cordis <lb></lb>ipsi Aortae ” benchè <emph type="italics"></emph>paucissimis verbis,<emph.end type="italics"></emph.end> pur fu chiaramente descritto da <lb></lb>Galeno nel cap. </s>

<s>VI del XV libro <emph type="italics"></emph>De usu partium.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sentì il Vesalio che que&#039;rimproveri di negligenza venivano direttamente <lb></lb>a lui, e per iscolparsene, in quell&#039;Esame ch&#039;egli prese a fare delle Osser­<lb></lb>vazioni falloppiane, raccontò come desiderando Francesco Rota di veder, nella <lb></lb>grande Opera <emph type="italics"></emph>De humani corporis fabrica,<emph.end type="italics"></emph.end> l&#039;anatomia comparata tra il feto <lb></lb>e l&#039;adulto, di che ivi affatto si tace, per compiacere ai desiderii dell&#039;amico <lb></lb>e di tutti gli studiosi, si volgesse con gran diligenza a rimeditar sui passi <lb></lb>di Galeno, per illustrarli. </s>

<s>“ Adinvento itaque connexu, prosegue a dire il <pb xlink:href="020/01/1314.jpg" pagenum="189"></pb>Vesalio, mox in foetu venae cavae caudicem, ubi connatam habet dextram <lb></lb>cordis auriculam, et qua illi transversim subiicitur ea venalis arteriae por­<lb></lb>tio, quae dextram pulmonis sedem petit, longa sectione secundum rectitu­<lb></lb>dinem operui. </s>

<s>Hic sese tum nihil manifestius mihi obtulit quam maximum <lb></lb>venae cavae in venalem arteriam pertinens <emph type="italics"></emph>foramen,<emph.end type="italics"></emph.end> vasorumque elegans <lb></lb>unio, ex quo specillum in omnem venalis arteriae seriem protrudere erat <lb></lb>promptissimum. </s>

<s>Ut vero membranea mihi illa observaretur substantia, quam <lb></lb>instar materiae, qua foramen nunc dictum et <emph type="italics"></emph>ovata praeditum effigie<emph.end type="italics"></emph.end> in <lb></lb>foetu iam in lucem edito promptius et ocyus obsignaretur; hic subsistere <lb></lb>prius monui ” (Venetiis 1664, pag. </s>

<s>91, 92). </s></p><p type="main">

<s>Questo lo fa il Vesalio per dire ch&#039;egli aveva osservato qualche cosa <lb></lb>di più del Falloppio, e per ritorcere contro lui stesso l&#039;accusa di negligenza. </s>

<s><lb></lb>Ma poi soggiunge di aver anch&#039;egli ritrovato il canale arterioso descritto da <lb></lb>Galeno, e di averlo esaminato come il forame ovale, e con pari artificio. <lb></lb></s>

<s>“ Pari artificio venae arterialis caudicem, qua is anteriori magnae Arteriae <lb></lb>sedi adnascitur, et secundum posteriorem huius sedem dextra parte sua ad <lb></lb>dextram pulmonis regionem contorquetur, longa etiam sectione patefeci, cau­<lb></lb>dicisque illius cum magna Arteria unionem et mutuum foramen observavi ” <lb></lb>(ibi, pag. </s>

<s>92). </s></p><p type="main">

<s>Quel Francesco Rota, persona dall&#039;altra parte di non gran nominanza, <lb></lb>si può facilmente sospettar che fosse introdotto dal Vesalio nel suo racconto, <lb></lb>per non avere a coefessare che, a fargli rivolgere l&#039;attenziono sul testo ga­<lb></lb>lenico, fosse stata necessaria quella frugata di gomito, che gli veniva a dare <lb></lb>il Falloppio. </s>

<s>Ma comunque sia, egli fu il primo fra&#039;nuovi anatomici che, fa­<lb></lb>cendo emenda della sua propria e della negligenza dello stesso Falloppio, <lb></lb>descrisse e impose il nome di <emph type="italics"></emph>forame ovale<emph.end type="italics"></emph.end> a quella apertura, che mette <lb></lb>nel cuor del feto in comunicazione la vena cava con la vena polmonare. </s>

<s><lb></lb>Queste osservazioni fetali occorsero al Vesalio poco dopo la pubblicazione <lb></lb>delle Osservazioni anatomiche del Falloppio, ma per le vicende altrove da <lb></lb>noi narrate non comparvero alla luce prima del 1564. </s></p><p type="main">

<s>Frattanto Giulio Cesare Aranzio, medico bolognese, chiamato spesso <lb></lb>dalle partorienti, “ et quandoque in huiusmodi occasiones casu incidens, <lb></lb>perbelle, sensu ipso observare et examinare potui quomodo scilicet quae <lb></lb>scribimus sese habeant, quod aliis peritissimis in Anatome viris, ut admi­<lb></lb>rabili Andreae Vesalio, aliisque recentioribus raro contigit ” (pag. </s>

<s>46), e di <lb></lb>qui ebbe origine quel trattatello <emph type="italics"></emph>De humano foetu,<emph.end type="italics"></emph.end> da cui si son trascritte <lb></lb>queste parole, e che vide la prima luce in Bologna in quel medesimo <lb></lb>anno 1564, in cui il Franceschi in Venezia pubblicava il manoscritto del­<lb></lb>l&#039;Esame fatto dal Vesalio alle Osservazioni anatomiche del Falloppio. </s></p><p type="main">

<s>Benchè l&#039;Aranzio si proponga di scriver le cose conforme ai fatti os­<lb></lb>servati, ei si protesta nonostante difensore acerrimo di Galeno (ivi, pag. </s>

<s>7) <lb></lb>e perciò, trattando nell&#039;ultimo capitolo della congiunzione de&#039;vasi del cuore, <lb></lb>dice di non far altro intorno a ciò che spiegare, e dar pubblica dimostra­<lb></lb>zione di quel che si legge nel XV libro <emph type="italics"></emph>De usu partium,<emph.end type="italics"></emph.end> maravigliandosi <pb xlink:href="020/01/1315.jpg" pagenum="190"></pb>molto che il Falloppio citi questo stesso testo galenico in quel luogo “ in <lb></lb>quo de utraque coniunctione pertractat, duo tamen maxima observatione <lb></lb>digna, ibidem exposita interim praetermittat: iam dictam scilicet Cavae cum <lb></lb>venali arteria coniunctionem, et enarrata ostiola. </s>

<s>Sed quandoque bonus dor­<lb></lb>mitat Homerus ” (ibi, pag. </s>

<s>75). </s></p><p type="main">

<s>L&#039;Aranzio insomma, nell&#039;illustrare il canale arterioso e il forame ovale, <lb></lb>si riscontra con ciò che, nello stesso tempo o non molto prima, aveva fatto <lb></lb>il Vesalio, di cui, s&#039;è men minuto, è forse però più preciso. </s>

<s>Ma il Nostro <lb></lb>sul Brussellese ha il vantaggio di aver notate alcune imperfezioni, in che <lb></lb>descrivendo incorse Galeno, il quale scrisse, come udimmo, che l&#039;arteria <lb></lb>polmonare, perchè molto distante dall&#039;Aorta, voleva essergli congiunta per <lb></lb>mezzo di un canale, mentr&#039;essendo la Vena cava alla vena polmonare con­<lb></lb>tigua, potevan facilmente comunicarsi insieme per via di un semplice foro. </s>

<s><lb></lb>Ma l&#039;Aranzio osserva che le cose stanno tutte al contrario. </s>

<s>“ Cava enim <lb></lb>multum abest ab Arteria venali, et sub corde latenter ad eam reptat ca­<lb></lb>nalis coniungens, et propterea dissecanti minus conspicua quam coniunctio <lb></lb>altera, quae in superficie est sita. </s>

<s>Aorta vero venae arteriali ita vicina po­<lb></lb>sita fuit, ut brevissimo ductu ad coniunctionem et continuationem sit opus ” <lb></lb>(ibi, pag. </s>

<s>77, 78). </s></p><p type="main">

<s>Si venivano così tutto insieme a correggere dall&#039;Aranzio le imperfette <lb></lb>osservazioni del Vesalio, a cui parve che l&#039;arteria polmonare e l&#039;Aorta fos­<lb></lb>sero quasi contigue, per cui si maraviglia molto che Galeno le abbia vedute <lb></lb>distare per qualche notabile intervallo, a ricongiungere il quale sia stato bi­<lb></lb>sogno alla Natura di apporvi un terzo vaso distinto. </s>

<s>Per ciò, dopo aver detto <lb></lb>che per esaminar meglio le cose avea aperta la vena arteriale <emph type="italics"></emph>longa sectione,<emph.end type="italics"></emph.end><lb></lb>così il Vesalio stesso soggiunge: “ Quod cum facerem, videremque in hac <lb></lb>unione connexioneve nullum insigne medium esse intervallum, quo vasa illa <lb></lb>ab invicem dehiscunt, miratus fui quamobrem Galenus hic tam dilucide vasis <lb></lb>privatim meminit, quo vena arterialis in magnam arteriam pertinet, cum <lb></lb>scilicet nisi mutua quaedam hic consurgat citra manifestum, aut saltem ali­<lb></lb>quousque eductum vasis canalisve progressum, vasorum arteriae corpore con­<lb></lb>stantium apertio ” (Examen cit., pag. </s>

<s>92). L&#039;Aranzio dunque definì in que­<lb></lb>sto proposito che l&#039;arteria polmonare e l&#039;Aorta non si toccano, come parve <lb></lb>al Vesalio, nè si ricongiungono per un notabile tratto, come diceva Ga­<lb></lb>leno, ma per un <emph type="italics"></emph>brevissimo dutto.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Mentre che dai nuovi Embriologi si pubblicavano queste descrizioni in <lb></lb>Venezia e in Bologna, un nostro piemontese, Leonardo Botallo, passato in <lb></lb>Francia ad esercitarvi la medicina pratica, attendeva per suo diletto a qual­<lb></lb>che cosa di Anatomia. </s>

<s>Prediligeva tra&#039;nuovi Maestri il Colombo, di cui forse <lb></lb>fu discepolo, e la circolazion polmonare da lui mirabilmente descritta sen­<lb></lb>tiva esser contrariata da molti Galenisti, i quali asserivano avere il sangue <lb></lb>passaggio dal destro al sinistro ventricolo del cuore, attraverso ai pori del <lb></lb>setto medio. </s>

<s>Rimasto così il Botallo in tal penosa incertezza, gli occorse un <lb></lb>giorno di avere un cuore da sezionare, in cui tenendo dietro al corso della <pb xlink:href="020/01/1316.jpg" pagenum="191"></pb>vena polmonare, là dove ella si insinua addentro nel viscere, osservò una <lb></lb>assai cospicua apertura, che metteva in comunicazione l&#039;orecchietta destra <lb></lb>con la sinistra. </s>

<s>Ecco, disse allora esultando, trovata finalmente la via vera <lb></lb>del sangue molto diversa da quella designata da Galeno e dal Colombo: <lb></lb>ecco a tuttte le arterie scoperta l&#039;origine prima e la radice. </s>

<s>Raccolse que­<lb></lb>sta, insieme con altre poche osservazioni anatomiche, in un libretto pubbli­<lb></lb>cato in sedicesimo, dopo i “ Commentarioli duo, alter de medici, alter de <lb></lb>aegroti munere ” stampati in Lione nel 1565. </s></p><p type="main">

<s>Il Van Horne, pubblicando poi in Leyda, nel 1660, tutte le opere del <lb></lb>Medico astigiano, vi raccolse anche le Osservazioni anatomiche, nella terza <lb></lb>e ultima delle quali, intitolata <emph type="italics"></emph>Vena arteriarum nutrix a nullo antea no­<lb></lb>tata,<emph.end type="italics"></emph.end> si legge così la scoperta del passaggio del sangue dalla destra alla si­<lb></lb>nistra parte del cuore: “ Diebus iis proximis peractis, cum Galenum atque <lb></lb>Columbum dissentire viderem de via qua in Cor sanguis qui per arterias <lb></lb>vagatur, fertur, asserente Galeno hunc in Cor transfundi per parva forami­<lb></lb>nula cordis, septo insita, Columbo vero per alia ad arteriam venosam quae, <lb></lb>etsi frustra olim perquisiverim, nuper tamen denuo eidem inquisitioni me <lb></lb>tradens, cor dividere occepi, ubi paulo supra coronalem, quam stephanoidem <lb></lb>appellant Graeci, satis conspicatum reperi ductum iuxta auriculam dextram, <lb></lb>qui statim in sinistram aurem recto tramite fertur, qui ductus vel vena iure <lb></lb>arteriarum vitaliumque spirituum nutrix dici potest, ob id quod per hanc <lb></lb>feratur sanguis arterialis in cordis sinistrum ventriculum, et consequenter <lb></lb>in omnes arterias, non autem per septum vel venosam arteriam, ut Gale­<lb></lb>nus vel Columbus putaverunt ” (Leonardi Botalli, Opera omnia, Lugduni <lb></lb>Batav. </s>

<s>1660, pag. </s>

<s>66-69). </s></p><p type="main">

<s>Il foro osservato dal Botallo è senza dubbio il forame ovale del feto, <lb></lb>rimasto per qualche caso singolare aperto nel cuor dell&#039;adulto, ma pur, non <lb></lb>si trattando qui d&#039;Anatomia fetale, è notahilissimo che i Francesi, fra&#039;quali <lb></lb>ebbe grandissima fama il Nostro, incominciassero allora, e durino tuttavia a <lb></lb>chiamare <emph type="italics"></emph>Trou de Botal<emph.end type="italics"></emph.end> quello stesso forame ovale, commettendo due impro­<lb></lb>prietà di linguaggio: una fisiologica, perchè il Botallo non tratta del feto ma <lb></lb>dell&#039;adulto, e una storica, perchè la scoperta del forame ovale era stata fatta <lb></lb>mille quattrocento anni prima, e l&#039;anno avanti che il Botallo stesso pubbli­<lb></lb>casse in Lione i suoi <emph type="italics"></emph>Commentarioli,<emph.end type="italics"></emph.end> erano usciti alla pubblica luce in Ve­<lb></lb>nezia e in Bologna i commenti fatti all&#039;Embriologia galenica dal Vesalio e <lb></lb>dall&#039;Aranzio. </s></p><p type="main">

<s>Ma come sempre suole avvenire, l&#039;improprietà del linguaggio portò un <lb></lb>disordine nelle idee, di cui s&#039;ha l&#039;esempio nello stesso Van Horne, il quale <lb></lb>in una nota al testo rimprovera al Botallo quel che doveva rimproverar piut­<lb></lb>tosto ai francesi, e a sè, che l&#039;avevan franteso. </s>

<s>Con pace d&#039;uomo sì egre­<lb></lb>gio, leggesi in quella nota, “ dixerim caecutiisse, dum pro nova observatione <lb></lb>et peculiaris nobis obtrudit, quam Galenus, abhine plusquam mille quin­<lb></lb>gentis annis, praedicit ” (ibi, pag. </s>

<s>67). </s></p><p type="main">

<s>Nè che cecuzzisse il Botallo fa dall&#039;altra parte gran maraviglia, con-<pb xlink:href="020/01/1317.jpg" pagenum="192"></pb>fessando di avere insieme con lui, e per le medesime ragioni, cecuzzito pa­<lb></lb>recchi anni dopo il grandissimo Arveo, il quale, dop&#039;aver detto nel cap. </s>

<s>VI <lb></lb><emph type="italics"></emph>De motu cordis<emph.end type="italics"></emph.end> che il forame ovale riman talvolta per qualche mese aperto <lb></lb>dopo la nascita, anzi per qualche anno, e per tutto il tempo della vita, in <lb></lb>alcun caso più straordinario, “ quae res imposuit, soggiunge, forsan Botallo <lb></lb>se novum transitum sanguini de vena cava in sinistrum ventriculum cordis <lb></lb>invenisse, et fateor me quoque, cum in mure maiori iam adulto hoc reperi, <lb></lb>tale quid statim existimasse ” (Editio cit., pag. </s>

<s>46). </s></p><p type="main">

<s>Un altro anche più notabile esempio del disordine, che portarono nel <lb></lb>giudizio filosofico i pregiudizi popolari, ce l&#039;offre il Flourens, il quale ingan­<lb></lb>nato forse dal vederne tutte insieme raccolte e pubblicate le opere nel 1660, <lb></lb>fa apparire la scoperta del Botallo parecchi anni dopo il Vesalio e l&#039;Aranzio <lb></lb>non solo, ma e dopo Giovan Batista Carcano, e, congegnate le molle alle <lb></lb>parti del suo discorso, ne fa con francese arguzia scattare il ridicolo, scri­<lb></lb>vendo che dopo essere divulgate le nuove osservazioni fetali e i commenti <lb></lb>fatti all&#039;antico testo galenico da que&#039;tre valentissimi e celebratissimi Ana­<lb></lb>tomici, “ Botal s&#039;imagina qu&#039;il venait de faire la plus grande découverte qui <lb></lb>pû être faite ” (Histoire de la circul. </s>

<s>du sang, Paris 1854, pag. </s>

<s>49). </s></p><p type="main">

<s>Ma che accecati veramente e illusi fossero, invece del Nostro, i due stra­<lb></lb>nieri che presero a giudicarlo, senza esaminarne il processo, apparirà chiaro <lb></lb>a chi pensa ch&#039;essendo la osservazion del Botallo pubblicata nel 1565 dovea <lb></lb>necessariamente essere stata fatta qualche tempo avanti, quando non era pos­<lb></lb>sibile che fossero ancora capitati in Francia l&#039;Esame del Vesalio al Fallop­<lb></lb>pio o il trattatello embriologico dell&#039;Aranzio, e tanto meno il <emph type="italics"></emph>De cordis <lb></lb>vasorum in foetu unione<emph.end type="italics"></emph.end> di Giovan Batista Carcano, pubblicato in Pavia <lb></lb>nel 1574. </s></p><p type="main">

<s>Cosicchè, quando il Botallo osservò nel cuore quel foro che mette in <lb></lb>comunicazione le due orecchiette, per riscontrar se qualcuno de&#039;più recenti <lb></lb>Maestri ne aveva parlato, non c&#039;era da consultar altri che il Berengario, il <lb></lb>Vesalio nella grande opera anatomica, il Colombo e il Falloppio, i quali tutti <lb></lb>trovatili tacere intorno a quel punto, aveva dunque diritto il nostro Asti­<lb></lb>giano di scrivere in fronte alla sua anatomica osservazione: <emph type="italics"></emph>a nullo antea <lb></lb>notata.<emph.end type="italics"></emph.end> E tanto più ne aveva diritto in quanto che dallo stesso Galeno non <lb></lb>era stato notato quel foro altro che nel feto, e senza intenzione di ridurlo <lb></lb>a dimostrar le vie del sangue nell&#039;adulto, intanto che il Botallo è il terzo <lb></lb>degl&#039;Italiani, dopo il Colombo e l&#039;Acquapendente, introdotto in quel dramma <lb></lb>arveiano, che ebbe per sua finale risoluzione la grande scoperta. </s>

<s>Nè Colui, <lb></lb>che si meritò dall&#039;Harvey un tanto onore, è quel presuntuoso che ci è di­<lb></lb>pinto dal Flourens, il quale se ne sarebhe facilmente persuaso se avesse <lb></lb>lette queste parole con cui si termina dall&#039;Autore l&#039;osservazione anatomica, <lb></lb>che poteva a que&#039;tempi parere una vera scoperta, della vena nutrice delle <lb></lb>arterie: “ Haec obiter dicta sint monitionis gratia, non ut Galenum vel Ve­<lb></lb>salium, Columbumve vel alios si qui sint, qui probe de rebus anatomicis <lb></lb>scripserunt, redarguere putemus, nam iis sane nos et tota posteritas pluri-<pb xlink:href="020/01/1318.jpg" pagenum="193"></pb>mum debemus. </s>

<s>Verum incidit interdum ut qnicquam in quavis arte a mi­<lb></lb>nus exercitato retegatur, quod ab exercitatissimis non fuerit antea cogni­<lb></lb>tum ” (Opera cit., pag. </s>

<s>70). </s></p><p type="main">

<s>Ma perchè l&#039;origine prima e la radice de&#039;falsi giudizii del Flourens <lb></lb>intorno al Botallo è dall&#039;avere ignorato il tempo, in cui il Botallo stesso <lb></lb>pubblicò le sue anatomiche Osservazioni, e ciò forse per essere i <emph type="italics"></emph>Commen­<lb></lb>tarioli duo<emph.end type="italics"></emph.end> citati, divenuti assai rari, eccone il preciso titolo com&#039;apparve <lb></lb>la prima volta alla luce: “ Leonardi Botalli astensis, medici regii, Commen­<lb></lb>tarioli duo, alter de medici, alter de aegroti munere. </s>

<s>Huic accedit admonitio <lb></lb>fungi strangulatorii. </s>

<s>Lugduni apud Antonium Gryphium 1565. ” Nel tergo <lb></lb>di questa carta è impressa la nota de&#039;saguenti opuscoli aggiunti “ eiusdem <lb></lb>Auctoris et ab eodem recogniti: De chatarro, in cuius fine addita est figura <lb></lb>monstruosorum renum in cadavere repertorum. </s>

<s>Ostenditur etiam locus, per <lb></lb>quem fertur sanguis in sinistrum cordis ventriculum, nondum antea cogni­<lb></lb>tus (che comprende le pag. </s>

<s>180-82). De lue venerea, De vulneribus sclo­<lb></lb>petorum. </s>

<s>” </s></p><p type="main">

<s>Lasciando ora il Botallo, che in virtù di un motto pronunziato con ele­<lb></lb>ganza francese si trovò intruso, senza merito e senza colpa, nella storia della <lb></lb>Embriologia, diciamo che a mezzo il secolo XVI, quanto erasi resa dimo­<lb></lb>strativa l&#039;anatomia galenica del feto, altrettanto misteriosa ne rimaneva la <lb></lb>fisiologia. </s>

<s>A qual fine, si domandava, fu lasciato aperto quel foro o aggiun­<lb></lb>tovi quel condotto? </s>

<s>Galeno lasciò scritto per risposta che, avendo bisogno il <lb></lb>polmone nel feto solamente di crescere, la Natura gli somministrò un pu­<lb></lb>rissimo sangue; “ cum vero ad motum fuit translatum, carnem levem instar <lb></lb>alae cuiusdam fecit, ut facile a thorace dilataretur ac comprimeretur. </s>

<s>Ob eam <lb></lb>igitur causam in foetibus vena cava in arteriam venosam est pertusa. </s>

<s>Cum <lb></lb>autem id vas venae officium huic visceri praestaret, necesse fuit alterum <lb></lb>vas in arteriae usum transmutari, quocirca Natura id quoque in magnam <lb></lb>arteriam protrudit ” (Opera cit., fol. </s>

<s>212). Questo era quel solo che poteva <lb></lb>dirne il Maestro: a chi ne avesse voluto saper di più, rispondeva che, a <lb></lb>intendere a qual fine sieno state fatte quelle cose, <emph type="italics"></emph>humani ingenii captum <lb></lb>superat<emph.end type="italics"></emph.end> (ibi). </s></p><p type="main">

<s>L&#039;Aranzio vollesi provare a spiegare un po&#039;meglio i concetti di Galeno, <lb></lb>ma gl&#039;intricò più che mai, com&#039;era da aspettarsi da chi credeva che am­<lb></lb>bedue i vasi polmonari recassero sangue, l&#039;uno per somministrar le materie <lb></lb>necessarie a formarsi la carne dei polmoni, l&#039;altro “ ut eorum caro, ex spi­<lb></lb>rituum rarefacientium multitudine, exinde magis rara reddatur, et eius san­<lb></lb>guinis calore vivat, hocque beneficium ei libenti animo Cor per aortam <lb></lb>affert, eam forte ob causam, quia postea parem gratiam, inspirando et refri­<lb></lb>gerando, cum infans esset in lucem editus, erant relaturi pulmones ” (De <lb></lb>hum. </s>

<s>foetu cit., pag. </s>

<s>76). </s></p><p type="main">

<s>La circolazione del sangue nel feto era per episodio riserbata alla grande <lb></lb>epopea arveiana, nel cap. </s>

<s>VI della quale si trova descritta. </s>

<s>La vena e l&#039;ar­<lb></lb>teria polmonare, secondo le nuove rivelazioni, rimangono nel loro proprio <pb xlink:href="020/01/1319.jpg" pagenum="194"></pb>essere di vena e di arteria anche nell&#039;adulto, nè si scambiano ufficio, come <lb></lb>insegnava Galeno, il quale distingueva le due specie di vasi, non principal­<lb></lb>mente dalla direzione del moto, ma dalla qualità del sangue in essi conte­<lb></lb>nuto. </s>

<s>La vena polmonare induce e l&#039;arteria educe ugualmente nel feto e <lb></lb>nell&#039;adulto: ci è la sola differenza che, in questo, i due vasi appartengono <lb></lb>a un circolo sanguigno proprio e distinto, mentre in quello rientrano nel <lb></lb>sistema generale della Vena cava, con cui la vena polmonare comunica at­<lb></lb>traverso al forame ovale, e rientrano nel sistema generale dell&#039;Aorta, a cui <lb></lb>l&#039;arteria polmonare, per via del canale arterioso, è ricongiunta. </s>

<s>Il passag­<lb></lb>gio insomma dal destro nel sinistro ventricolo del cuore, senza l&#039;intermezzo <lb></lb>de&#039;polmoni, si fa, secondo l&#039;Harvey, in questo modo: “ Dexter, sanguinem <lb></lb>ab auricula recipiens, inde per venam arteriosam et progaginem suam, ca­<lb></lb>nalem arteriosam dictam, in magnam Arteriam propellit. </s>

<s>Similiter sinister, <lb></lb>eodem tempore, mediante auriculae motu, recipit sanguinem, in illlam si­<lb></lb>nistram auriculam diductum scilicet per foramen ovale e Vena cava, et ten­<lb></lb>sione sua et constrictione, per radicem Aortae, in magnam itidem Arteriam <lb></lb>simul impellit ” (De motu cordis cit., pag. </s>

<s>46). Nel cuor dell&#039;embrione <lb></lb>perciò, come nel cuore degli animali che non hanno polmoni, non giocano <lb></lb>che un&#039;orecchietta e un ventricolo solo. </s>

<s>Quando poi il feto è venuto alla <lb></lb>luce, e comincia a respirare, il forame ovale che si richiude, e il canale ar­<lb></lb>terioso, che si oblitera, riducono i ricettacoli del sangue a quattro: due inser­<lb></lb>vienti alla circolazion polmonare, e i due altri al circolo nel giro universale <lb></lb>dei vasi. </s></p><p type="main">

<s>Era stata fatta da alquanti anni alla scienza fisiologica questa nuova <lb></lb>rivelazione, quando fu proposto a risolvere il problema arveiano. </s>

<s>Primo a <lb></lb>entrar nello stadio fu il Boyle, il quale, digredendo da&#039;suoi fisici meccanici <lb></lb>esperimenti, scrisse che sebbene “ tam difficili problemati solvendo nos im­<lb></lb>pares esse fatemur, hoc autem de eo experimentum fecimus ” (Opera omnia, <lb></lb>T. I, Venetiis 1697, pag. </s>

<s>111). A una cagna, ch&#039;era per partorire, aperse <lb></lb>il ventre e n&#039;estrasse quattro cagnolini. </s>

<s>Ne scelse uno che, appena liberato <lb></lb>dalle membrane involgenti, lo vide aprire la bocca all&#039;aria, muover la lin­<lb></lb>gua, respirare insomma. </s>

<s>Poco dopo, apertogli il petto e dissecatogli il dia­<lb></lb>framma, lo vide nonostante seguitare a tentare il respiro, e a dimenare in <lb></lb>modo maraviglioso la lingua. </s>

<s>Poi svolse gli altri tre cagnolini rimasti “ in <lb></lb>quibus dissectis, tantum spiritus vitalis non invenimus, et qui ulli in corde <lb></lb>eorum motui perceptibili producendo sufficeret, cum tamen alterius catuli <lb></lb>cor, qui respirationem semel exercuisset, tam diu pulsum continuavit ut <lb></lb>nos ipsi auriculam pulsare quinque vel sex horas postea observaverimus. </s>

<s>” <lb></lb>E conclude con dire: “ super hac observatione cum doctoris Harvei pro­<lb></lb>blemate collata, cogitationes suas exercere aliis relinquo ” (ibi). </s></p><p type="main">

<s>In ogni modo s&#039;intende che il Boyle riduceva tutta la soluzione del <lb></lb>problema arveiano ai moti del cuore, ch&#039;eccitato una volta dagli spiriti, ossia <lb></lb>dall&#039;aria inspirata, prosegue spontaneo a muoversi, nè riprende il suo primo <lb></lb>esercizio se per caso gli sia stato interrotto. </s>

<s>La falsità di questa soluzione <pb xlink:href="020/01/1320.jpg" pagenum="195"></pb>però veniva, lasciamo stare le tante altre ragioni, dimostrata dai fatti citati <lb></lb>dallo stesso Harvey contro coloro, i quali dicevano, come par che credesse <lb></lb>il Boyle, il cuor nell&#039;embrione non muoversi punto, ma rimanersi in per­<lb></lb>fetto riposo, “ cum in ovo, cui gallina incubuit, et in embryonibus recenter <lb></lb>ex utero crectis, autopsia patet cor movere, sicut in adultis ” (De motu cor­<lb></lb>dis cit., pag. </s>

<s>45). </s></p><p type="main">

<s>Non fa perciò maraviglia se lo Swammerdam ripose anche questa del <lb></lb>Boyle fra le altre nenie. </s>

<s>Incomincia il Fisiologo olandese il suo trattato <emph type="italics"></emph>De <lb></lb>respiratione<emph.end type="italics"></emph.end> coll&#039;accusar la negligenza di coloro, che non considerarono il <lb></lb>primo moto de&#039;polmoni nel feto, “ hoc enim percepto, de ipso qui in adul­<lb></lb>tis fit motu iudicare erit facillimum. </s>

<s>Sed quis circa foetus respirationem <lb></lb>praeter naenias nobis obtrusit? </s>

<s>” (Lugduni Batav. </s>

<s>1667, pag. </s>

<s>2, 3). E sog­<lb></lb>giunge che solo l&#039;Arveo propose intorno a ciò un problema, ch&#039;ei lasciò <lb></lb>irresoluto, promettendo di farlo in un trattato da pubblicarsi intorno alla <lb></lb>respirazione, il qual trattato, perchè ancora non s&#039;è veduto, dice lo Swam­<lb></lb>merdam, ho pensato bene di supplirvi io stesso con questo mio. </s>

<s>Così leg­<lb></lb>gesi nella prefazione, e nella conclusione dell&#039;opera, tornando l&#039;Autore in­<lb></lb>dietro sopra ciò che aveva dimostrato intorno al maraviglioso modo come <lb></lb>incomincia la respirazione nel feto, “ in qua explicanda, tutto compiacente <lb></lb>egli scrive, nos primi glaciem fregimus, cum Autores praeter chimeras nihil <lb></lb>nobis obtruserint ” (ibi, pag. </s>

<s>119). </s></p><p type="main">

<s>I giudici imparziali però non trovano troppo giuste ragioni a quella <lb></lb>compiacenza, non avendo fatto altro ivi lo Swammerdam che dimostrare <lb></lb>come la cavità del petto nel feto è tutta piena di umori, e l&#039;aria che prima <lb></lb>v&#039;entra, con l&#039;acrimonia de&#039;suoi sali, rimescolatisi col sangue, irrita i nervi <lb></lb>e i muscoli, che perciò incominciano a mettere in moto il diaframma e il <lb></lb>torace. </s>

<s>“ Hisce bene consideratis, evidenter patebit quomodo motus pectoris <lb></lb>primo incipiat, atque postmodum, ob musculorum respirationi inserventium <lb></lb>alternatam continuatamque contractionem, necessario continuetur ” (ibi, <lb></lb>pag. </s>

<s>76). Di qui concludesi, secondo il Fisiologo d&#039;Amsterdam, la soluzione <lb></lb>del problema arveiano, che non differisce da quella data dal Boyle, se non <lb></lb>che più ragionevolmente si considera l&#039;aria come prima eccitatrice de&#039;mu­<lb></lb>scoli del torace, piuttosto che delle fibre del cuore. </s></p><p type="main">

<s>Un altro degli atleti, sceso a esercitare le forze in questo agone, fu il <lb></lb>nostro Borelli, il quale avendo ammesso per vero che l&#039;aria “ quae vitae sal <lb></lb>nuncupari potest ” sia così necessaria che l&#039;animale “ ne momentum quidem <lb></lb>vivere potest absque respiratione ” (De motu anim., Pars II cit., pag. </s>

<s>232); <lb></lb>disse che nel feto è supplito il bisogno dalla respirazion della madre. </s>

<s>Contro <lb></lb>una tal soluzione però veniva un fatto già notato, nel proporre il problema, <lb></lb>dallo stesso Harvey, il qual fatto è che “ in sectione caesarea foetus horis <lb></lb>complusculis post matris obitum eximitur, vitalis tamen reperitur, et intra <lb></lb>secundas sepultus, aeris nihil indigus, superest ” (De partu cit., pag. </s>

<s>353), <lb></lb>nel qual caso il feto non riman certamente superstite, per essergli stata <lb></lb>mantenuta la vita, come il Borelli diceva, dalla respirazione materna. </s></p><pb xlink:href="020/01/1321.jpg" pagenum="196"></pb><p type="main">

<s>A pensar che un Harvey, un Boyle, uno Swammerdam, un Borelli o <lb></lb>non vi si vollero nemmen provare, atterriti dalle difficoltà, o provativisi non <lb></lb>riuscirono a risolvere il problema, convien dire ch&#039;ei fosse davvero d&#039;im­<lb></lb>possibile risoluzione. </s>

<s>Ma l&#039;impossibilità, che non era nella cognizione dei <lb></lb>fatti, veniva messa agl&#039;ingegni dallo stesso Harvey, il quale insomma pro­<lb></lb>poneva a dimostrare una cosa falsa. </s>

<s>E il non avvedersi di ciò l&#039;Harvey stesso, <lb></lb>e il non avvedersene que&#039;grandi ingegni, è uno de&#039;più notabili fatti di que­<lb></lb>sta Storia. </s></p><p type="main">

<s>Era fra&#039;supposti del problema arveiano che, ammessa la prima aria nel <lb></lb>petto del neonato, non ne potesse poi far senza, nemmeno un momento, <emph type="italics"></emph>sed <lb></lb>confestim moriatur, illico suffocetur.<emph.end type="italics"></emph.end> Suppor ciò era un supporre insieme <lb></lb>che il forame ovale <emph type="italics"></emph>confestim<emph.end type="italics"></emph.end> si chiuda, ed <emph type="italics"></emph>illico<emph.end type="italics"></emph.end> si obliteri il canale arte­<lb></lb>rioso. </s>

<s>Ora era questo un supposto contrario alla ragione, all&#039;autorità de&#039;mag­<lb></lb>giori, e all&#039;esperienza, com&#039;è per persuadercene facilmente il discorso. </s></p><p type="main">

<s>Che fosse contrario alla ragione è approvato da ognuno, che sa come <lb></lb>nulla dalla Natura s&#039;operi nell&#039;istante. </s>

<s>Che fosse quel supposto contrario <lb></lb>all&#039;autorità de&#039;maggiori, è chiaramente dimostrato dai documenti, per primo <lb></lb>dei quali occorre anche questa volta a citar quello lasciatoci dall&#039;antico Ga­<lb></lb>leno. </s>

<s>Nel passo da noi sopra citato dal lib. </s>

<s>XV <emph type="italics"></emph>De usu partium,<emph.end type="italics"></emph.end> dop&#039;aver <lb></lb>descritta la valvola del forame ovale, “ haec quidem omnia, esclama il con­<lb></lb>templativo Antore, Naturae opera sunt admiranda. </s>

<s>Superat vero omnem admi­<lb></lb>rationem praedicti foraminis haud ita multo post conglutinatio. </s>

<s>Etenim, cum <lb></lb>primum animans in lucem est editum, aut ante unum vel duos dies, in qui­<lb></lb>busdam vero ante quatuor aut quinque vel plures, membranam quae est ad <lb></lb>foramen coalescentem reperias nondum tum coaluisse. </s>

<s>Cum autem animal <lb></lb>perfectum fuerit, aetateque iam floruerit, si locum hunc ad unguem densa­<lb></lb>tum inspexeris, negabis fuisse aliquod tempus, in quo fuerit pertusus, multo <lb></lb>autem magis in iis, quae adhuc utero geruntur, aut in nupero genitis mem­<lb></lb>branam conspicatus ad solam quidem radicem firmatam, reliquum vero to­<lb></lb>tum corpus in vasorum cavitate pendulum; existimabis fieri non posse ut <lb></lb>ipsa unquam perfecte coalescat.... Pari modo id vas quod magnam arteriam <lb></lb>venae, quae fertur ad pulmonem connectit, cum aliae omnes animalis par­<lb></lb>ticulae augeantur, non modo non augetur, verum etiam tenuius semper ef­<lb></lb>fici conspicitur, adeo ut, tempore procedente, penitus tabescat atque exice­<lb></lb>tur ” (Opera cit., fol. </s>

<s>212). </s></p><p type="main">

<s>Galeno dunque stimava che il forame ovale si richiudesse dopo due o <lb></lb>tre giorni o più dalla nascita, e il canale arterioso si obliterasse <emph type="italics"></emph>tempore <lb></lb>procedente.<emph.end type="italics"></emph.end> Ma il Vesalio, benchè non assegni nessun tempo determinato, <lb></lb>par nonostante che ammetta una maggiore prontezza. </s>

<s>Quella membrana, che <lb></lb>dallo stesso Galeno era stata descritta come una valvola applicata al forame <lb></lb>ovale, perchè il sangue sospinto nella vena polmonare non dovesse refluir <lb></lb>nella Cava; il Vesalio, che rifiutava nelle vene ogni artificio di valvole, la <lb></lb>credeva materia preparata dalla Natura, per otturar prontamente nel cuore <lb></lb>del neonato l&#039;apposto forame. </s>

<s>“ Observatio in nascendis proxime foetibus <pb xlink:href="020/01/1322.jpg" pagenum="197"></pb>est promptissimam huic operationi orbiculatim adnatam esse illam tenuis­<lb></lb>simae membranae substantiam, quae superius <emph type="italics"></emph>promptae<emph.end type="italics"></emph.end> post nativitatem <lb></lb>occlusioni foraminis accommoda censebatur ” (Examen Falloppii cit., pag. </s>

<s>92). </s></p><p type="main">

<s>Queste osservazioni intorno al tempo impiegato dalla Natura, per tra­<lb></lb>sformare gli organi della circolazion fetale negli organi della circolazion pol­<lb></lb>monare, trascurate dall&#039;Harvey, posero il Boyle, lo Swammerdam e il Bo­<lb></lb>relli nell&#039;impossibilità di risolvere il proposto problema. </s>

<s>Ma il Cartesio, in <lb></lb>raccomandare alla sua scuola queste dottrine, s&#039;espresse con una chiarezza <lb></lb>e con una precisione maravigliosa. </s>

<s>“ Experientia enim comportum est, egli <lb></lb>scrive, infantes, qui dum in utero matris sunt, nequeant respirare, duas <lb></lb>habere in corde aperturas, quae in adultioribus non reperiuntur. </s>

<s>Et quidem, <lb></lb>per unam ex his aperturis, sanguinem Venae cavae, una cum arteriae ve­<lb></lb>nosae sanguine, in sinistrum cordis ventriculum fluere, per alterum vero, <lb></lb>quae ad instar exigui tubi facta est, partem sanguinis ex dextro ventriculo <lb></lb>defluentis transire ex vena arteriosa in magnam arteriam, neque pulmonem <lb></lb>usquam ingredi. </s>

<s>Compertum est etiam hasce duas aperturas in natis infan­<lb></lb>tibus <emph type="italics"></emph>ultro paulatim occludi, postquam respirationis usum adepti sunt ”<emph.end type="italics"></emph.end><lb></lb>(De homine cit., pag. </s>

<s>166). </s></p><p type="main">

<s>Tommaso Cornelio, imbevuto a queste cartesiane dottrine, dal saper che <lb></lb>il foro ovale si chiude a poco a poco, ne congetturava che dunque, infin­<lb></lb>tantochè non siasi esso foro richiuso affatto, l&#039;infante, benchè privato d&#039;aria <lb></lb>non dee morire, circolando nel cuore di lui liberamente il sangue, anche <lb></lb>senza passare attraverso al polmone. </s>

<s>Una tal congettura s&#039;opponeva diret­<lb></lb>tamente al supposto dell&#039;Harvey, e scoprendone la falsità, spiegava final­<lb></lb>mente in che modo il problema embriologico, che proponeva ai Fisiologi, <lb></lb>fosse trovato di così difficile, anzi impossibile risoluzione. </s>

<s>Era perciò impor­<lb></lb>tantissima cosa il verificare quella congettura, per mezzo dell&#039;esperienza, e <lb></lb>il Cornelio la verificò negli infanti, e l&#039;espresse così, nel 1661, nel suo Pro­<lb></lb>ginnasma <emph type="italics"></emph>De vita.<emph.end type="italics"></emph.end> “ Videmus recens natos pueros posse aliquandiu, sine <lb></lb>vitae valetudinisque incommodo, respiratione privari, quia scilicet in eisdem <lb></lb>patent viae ductusque, per quos, praecluso pulmonum transitu, sanguis per­<lb></lb>labitur ” (Neapoli 1668, pag. </s>

<s>287). </s></p><p type="main">

<s>Di qui, ripensando il nostro Fisiologo calabrese a quel <emph type="italics"></emph>Cola,<emph.end type="italics"></emph.end> famoso <lb></lb>palombaro, che, dallo star lungamente sott&#039;acqua senza riceverne offesa, ebbe <lb></lb>il soprannome di <emph type="italics"></emph>Pesce,<emph.end type="italics"></emph.end> spiegò il portento col dire che doveva il cuor di <lb></lb>quell&#039;uomo, come di quell&#039;altro sezionato già dal Botallo, aver serbato il <lb></lb>forame ovale tuttavia aperto. </s>

<s>Passò poi da questa considerazione a imma­<lb></lb>ginare arditamente che si potessero i fanciulli educare alla vita amfibia; <lb></lb>inconsiderata proposta, che tornò un mezzo secolo dopo l&#039;Ettmuller a ri­<lb></lb>mettere in campo, nel suo trattatello <emph type="italics"></emph>De circulatione sanguinis in foetu.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>L&#039;esperienze però fatte dal Cornelio sopra gl&#039;infanti, essendo perico­<lb></lb>lose, si pensò di farle poi con più sicurtà sopra gli animali. </s>

<s>Il Mery speri­<lb></lb>mentò che i neonati possono senza offesa rimanere lungamente nel vuoto, e <lb></lb>il Bohn vide un feto, che aveva aperta la bocca ai primi respiri, rimaner <pb xlink:href="020/01/1323.jpg" pagenum="198"></pb>per alquante ore sotterrato, senza morire, e senza morire vide pure alcuni <lb></lb>animali nati di fresco star per ventiquattr&#039;ore intere co&#039;bronchi intasati. </s>

<s><lb></lb>L&#039;Haller fece una gentile esperienza: prese un cagnolino, che aveva comin­<lb></lb>ciato a respirare, e osservò che visse sommerso per mezz&#039;ora in un&#039;acqua <lb></lb>tiepida. </s>

<s>“ Vidi catellum, qui semel respiraverat, et cuius pulmo in aqua na­<lb></lb>tavit, tamen per dimidiam horam in tepida vixisse. </s>

<s>Vidit Bohonius, et bis <lb></lb>vidit, fetum, qui respiraverat et vivebat, aliquot horis sub ipsa terra, absque <lb></lb>aere, vixisse. </s>

<s>Sed etiam, bronchio intercepto, nuper nata animalia vivunt, et <lb></lb>totis 24 horis supersunt ” (Elem. </s>

<s>physiol., T. III, Lausannae 1766, pag. </s>

<s>314). </s></p><p type="main">

<s>Ma non solo il forame ovale si ottura negli animali così assoggettati <lb></lb>alle esperienze, e il canale arterioso si oblitera a poco a poco: lo stesso Haller <lb></lb>sperimentò che non tutti a un tratto si spiegano nemmeno i polmoni, quasi <lb></lb>ali, che si addestrino a poco a poco ai liberi voli della vita. </s>

<s>Preso il pol­<lb></lb>mone di un uccello, che aveva fatte alcune respirazioni, trovò che non gal­<lb></lb>leggiava nell&#039;acqua, segno che non tutte ancora si erano ripiene d&#039;aria le <lb></lb>sue vescichette. </s>

<s>“ In avibus ostendimus etiam, post plusculas respirationes, <lb></lb>pulmonem ne natare quidem, non adeo continuo mutari ” (ibi). </s></p><p type="main">

<s>Ecco dimostrato così dalle esperienze esser falso che il feto, attratta <lb></lb>l&#039;aria nel primo respiro, <emph type="italics"></emph>ne momentum quidem temporis absque eo durare <lb></lb>possit,<emph.end type="italics"></emph.end> ed ecco insomma scoperta l&#039;impossibilità del problema arveiano, non <lb></lb>avvertita nè da chi lo propose, nè riconosciuta poi da que&#039;grandi ingegni, <lb></lb>che tanto s&#039;affaticarono per trovarne la soluzione. </s>

<s>Più fidando nell&#039;autorità <lb></lb>di un uomo, che nell&#039;esperienza dei fatti naturali, non pensarono che la <lb></lb>vita non si accende improvvisa, nè improvvisa si estingue, ma come fiac­<lb></lb>cola, che sorge su su lambendo infino al sommo gli stami, e crepitando <lb></lb>scintilla, prima di sparire. </s></p><pb xlink:href="020/01/1324.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della nutrizione<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle varie dottrine professate dai Fisiologi intorno alla digestione, e delle esperienze in proposito <lb></lb>di Lazzero Spallanzani. </s>

<s>— II. </s>

<s>Della scoperta delle vie del chilo, per le vene lattee del Mesen­<lb></lb>terio. </s>

<s>— III. </s>

<s>Della scoperta del Ricettacolo del chilo, e del Canale toracico. </s>

<s>— IV. </s>

<s>Della sco­<lb></lb>perta de&#039;vasi linfatici; dell&#039;esequie al Fegate defunto. </s>

<s>— V. Dell&#039;opera data particolarmente <lb></lb>dai nostri Italiani allo studio dei vasi bianchi. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La storia delle cose passate, intorno all&#039;importantissimo soggetto della <lb></lb>respirazione, ci dimostra come, dopo lunghi e penosi errori, finalmente i Fi­<lb></lb>siologi riconoscessero che l&#039;aria inspirata dai polmoni agisce direttamente <lb></lb>sul sangue. </s>

<s>Si discuteva se fosse quell&#039;azione puramente meccanica o chi­<lb></lb>mica; non si sapeva decidere se tutta l&#039;aria concorresse insieme a produr <lb></lb>l&#039;effetto, o una sola parte di lei, nella quale consistesse quella mirabile effi­<lb></lb>cacia attribuita poi più tardi all&#039;ossigeno; ma in ogni modo, sul finir del <lb></lb>secolo XVIII, apparvero agl&#039;ingegni speculativi, sotto le amabili sembianze <lb></lb>del vero, i pensieri del Willis, del Mayow e del Malpighi, che rivelarono <lb></lb>com&#039;ha propriamente l&#039;aria un&#039;azione chimica e vitale sul sangue. </s></p><p type="main">

<s>Così fatte dottrine però erano il portato di altre dottrine, frutto di lun­<lb></lb>ghe e laboriose esperienze, per le quali tanto strabocchevolmente s&#039;arricchì, <lb></lb>in un secolo, il tesoro delle <expan abbr="scieñze">sciennze</expan> così scarso ereditato dagli <lb></lb>avi. </s>

<s>Quando <lb></lb>si credeva che le vene compartissero l&#039;alimento alle membra come le arte­<lb></lb>rie, e il sangue di queste non si sapeva per altro che per esterne qualità <lb></lb>distinguere dal sangue di quelle, non era possibile riconoscer nello stesso <lb></lb>sangue il bisogno che aveva di ristorarsi, fuor che per la quantità, delle per-<pb xlink:href="020/01/1325.jpg" pagenum="200"></pb>dite subite in nutrire le parti, ciò che si diceva effettuarsi dalle vene del <lb></lb>mesenterio, che suggono avidamente il chilo dagli intestini. </s>

<s>E poichè la con­<lb></lb>versione d&#039;esso chilo in sangue si affidava tutta al Fegato, non era possi­<lb></lb>bile pensare all&#039;aria introdottasi ne&#039;polmoni, alla quale perciò, come sap­<lb></lb>piamo, s&#039;attribuivano gli ufficii più inverosimili e strani. </s></p><p type="main">

<s>La grande, e veramente innovatrice scoperta arveiana, dimostrò che il <lb></lb>sangue si dispensa per le arterie alle membra, di dove, assorbito dalle estreme <lb></lb>diramazioni venose, va a confluire in un vaso solo, che sbocca nel cuore. </s>

<s><lb></lb>Allora fu facile pensar che il sangue arterioso avesse perduto qualche cosa <lb></lb>di sè, piuttosto nella qualità che nella quantità, per cui a ristorarsene s&#039;af­<lb></lb>frettasse così di ritornar per le vene. </s>

<s>S&#039;aggiungeva a confermare questo pen­<lb></lb>siero il perduto ufficio sanguificatore del Fegato, che nonostante si seguitò <lb></lb>a fare il ricettacolo del chilo. </s>

<s>Ma quando scopertesi le vene lattee, e dimo­<lb></lb>stratosi il canale toracico, s&#039;intese che il chilo si riversa immediatamente <lb></lb>nella Vena cava, per andare a diritto col sangue di lei nel cuore, e allora <lb></lb>quel pensiero, che ragionava ai Fisiologi aver necessità il sangue venoso di <lb></lb>ristorarsi, per divenir nuovamente atto alla nutrizione, prese forme anche <lb></lb>più scolpite. </s>

<s>Il luogo e il modo di quel ristoro non fu poi molto difficile a <lb></lb>indovinarlo, vedendo che il sangue venoso mescolato col chilo era mandato <lb></lb>al polmone. </s>

<s>Il luogo dunque, dove il sangue ripiglia vita e si rifà delle per­<lb></lb>dite col chilo che ha raccolto per via, è senza dubbio lo stesso polmone. </s>

<s>— E <lb></lb>il modo? </s>

<s>— Che altro modo può avere il polmone d&#039;operar sul sangue, fuor <lb></lb>che per via dell&#039;aria, da lui messa in moto con sì assidua faccenda? </s></p><p type="main">

<s>La teoria della respirazione insomma si vede ben di qui essere una <lb></lb>conseguenza della scoperta del circolo del sangue, e degli organi ordinati <lb></lb>alla nutrizione. </s>

<s>Per rendere perciò compiuta, almeno nelle cose più sostan­<lb></lb>ziali, questa prima parte della nostra storia, ci rimane a narrare da chi e <lb></lb>come furono scoperti e dimostrati quegli organi, e ciò che, dietro la sicura <lb></lb>scorta dell&#039;esperienza, giunsero a intendere i Fisiologi di una funzione, che <lb></lb>è il primo e principal fondamento posto dalla Natura all&#039;economia animale. </s></p><p type="main">

<s>Principio alla nutrizione, e non ci voleva troppa scienza ad accorger­<lb></lb>sene, è il cibo, che per la bocca introdotto nello stomaco si riduce in chimo, <lb></lb>da cui com&#039;essenza distillasi il chilo. </s>

<s>Questa funzione dello stomaco, nel lin­<lb></lb>guaggio degli scienziati e dal popolo, s&#039;appella col nome di <emph type="italics"></emph>digestione,<emph.end type="italics"></emph.end> in­<lb></lb>torno alla quale i filosofi e i medici antichi non trovarono molte difficoltà, <lb></lb>rassomigliandola alle cozioni artificiali de&#039;cibi, per far lo stomaco da reci­<lb></lb>piente, il calore innato da fuoco, e i liquidi animali da acqua di elissazione. </s>

<s><lb></lb>Così avevano insegnato Ippocrate e Aristotile ne&#039;loro libri, ma Erasistrato <lb></lb>v&#039;aggiunse l&#039;azion meccanica dell&#039;attrito, che subiscono fra le angustie del <lb></lb>ventricolo i cibi, ivi dentro continuamente agitati dai muscoli, e quasi pesti. </s></p><p type="main">

<s>Nel rinnovamento della scienza uno de&#039;primi e de&#039;più autorevoli Mae­<lb></lb>stri, che si studiò d&#039;insegnar cose nuove intorno alle funzioni digestive, sol­<lb></lb>levandole coll&#039;ingegno da quelle bassezze, in cui le avean lasciate gli anti­<lb></lb>chi, fu il Cartesio, il quale rassomigliò il decomporsi de&#039;cibi nello stomaco, <pb xlink:href="020/01/1326.jpg" pagenum="201"></pb>in cui è sempre qualche umore, al disfarsi della calce viva a contatto del­<lb></lb>l&#039;acqua, e notò di più che alcune delle sostanze alimentari hanno la pro­<lb></lb>prietà di decomporsi spontaneamente, e di riscaldarsi, come si vede avvenir <lb></lb>del fieno, se talvolta è riposto nelle capanne o è ammontato nelle biche non <lb></lb>secco. </s>

<s>A queste cause chimiche aggiunta l&#039;azion meccanica degl&#039;intestini e <lb></lb>delle loro fibre, che tengono i cibi ingesti continuamente agitati e compressi, <lb></lb>ben s&#039;intenderà, dice il Cartesio, come si possano i cibi stessi concocere e <lb></lb>spremersene i necessari succhi nutritizi. </s></p><p type="main">

<s>“ In primis, in machinae huius stomacho, cibi digeruntur vi liquorum <lb></lb>quorumdam, qui cum interfluunt ciborum partes separant, agitant et cale­<lb></lb>faciunt eas, ut communis aqua in calce viva, et aqua fortis in metallis fa­<lb></lb>cit. </s>

<s>Cui adde quod hi liquores quam celerrime a corde per arterias advecti <lb></lb>non possint non valde calidi esse. </s>

<s>Imo ipsi cibi eius plerumque naturae sunt, <lb></lb>ut etiam soli et per se corrumpi et incalescere possint, quemadmodum foe­<lb></lb>num recens in horreo facit, quando satis siccum non est. </s>

<s>Et quod notan­<lb></lb>dum, agitatio quam incalescendo accipiunt hae ciborum particulae, iuncta <lb></lb>cum motu stomachi et iutestinorum quibus continentur, ac cum dispositione <lb></lb>omnium filamentorum, ex quibus intestina componuntur, in causa est ut, <lb></lb>quamprimum facta fuerit concoctio, aliqua paulatim descendant versus duc­<lb></lb>tum illum, quo partes crassiores excerni debent ” (De homine cit., pag. </s>

<s>4). </s></p><p type="main">

<s>Vedremo quale efficacia avessero così fatte dottrine sulla mente di quei <lb></lb>Fisiologi, che professarono la Filosofia cartesiana, ma intanto il celebratis­<lb></lb>simo Harvey richiamava l&#039;attenzione degli studiosi sopra un singolar modo, <lb></lb>che nel digerire i cibi tengon gli uccelli. </s>

<s>Essi hanno un doppio ventricolo: <lb></lb>l&#039;<emph type="italics"></emph>ingluvie,<emph.end type="italics"></emph.end> nella quale ritengono i grani interi or ora divorati, gli ammolli­<lb></lb>scono, gli macerano e gli fanno di li passar nel <emph type="italics"></emph>ventriglio<emph.end type="italics"></emph.end> propriamente detto, <lb></lb>dove come sotto una macina si riducono in minutissimi frantumi. </s>

<s>È per aiu­<lb></lb>tar l&#039;opera di questo trituramento, prosegue a dire l&#039;Harvey, che quasi tutti <lb></lb>i pennati ingollano pietruzze aspre e dure, che poi vengono fortemente agi­<lb></lb>tate e sconvolte da que&#039;due robustissimi muscoli di che il ventriglio stesso <lb></lb>è composto. </s>

<s>Che se tali pietruzze sì riducano per il lunge attrito ad es­<lb></lb>sere levigate, e tornino perciò inabili a triturare, que&#039;sagaci animali le vo­<lb></lb>mitano, per ingollarne altre, che scelgono tentandone prima colla lingua la <lb></lb>scabrosità e la durezza. </s>

<s>Eleggono talvolta a quest&#039;uso anche il ferro, e l&#039;ar­<lb></lb>gento, ch&#039;io, dice, ho trovato nel ventriglio di alcuni struzzi, d&#039;onde fu cre­<lb></lb>duto dal volgo, vedendoli così consumati dal forte attrito, che valessero quei <lb></lb>voraci animali a digerire gli stessi metalli. </s>

<s>“ Hoc pacto alimenta conficiunt <lb></lb>et chylificant, posteaque compressione facta, quemadmodum ex herbis aut <lb></lb>fructibus contusis succum vel pulticulum exprimere solemus, pars mollior <lb></lb>et liquidior sursum attollitur, eamque in principium intestinorum, quod in <lb></lb>illis iuxta ingressum gulae, in ventriculi parte superiore collocatur, transfe­<lb></lb>runt ” (De generatione anim., Lugduni Batav. </s>

<s>1737, pag. </s>

<s>27). </s></p><p type="main">

<s>Si diceva dianzi che sopra queste curiosità naturali fu richiamata l&#039;at­<lb></lb>tenzione degli studiosi, e a chi ripensa alla grande autorità, che s&#039;era oramai <pb xlink:href="020/01/1327.jpg" pagenum="202"></pb>nella scienza acquistato l&#039;Harvey, non farà punto maraviglia che, per i non <lb></lb>curanti e i disprezzatori della Filosofia cartesiana, s&#039;incominciassero da quelle <lb></lb>arveiane osservazioni gli esercizii sperimentali intorno alla digestione. </s>

<s>Furono <lb></lb>que&#039;primi esercizii fra noi intrapresi, nel secondo periodo della fiorentina <lb></lb>Accademia, in Pisa dal Borelli, il quale, dopo aver nella propos. </s>

<s>CLXXXIX <lb></lb>della II P. <emph type="italics"></emph>De motu anim.,<emph.end type="italics"></emph.end> ripetuto con l&#039;Autore inglese esser l&#039;ufficio dei <lb></lb>sassolini nel ventriglio degli uccelli quello di contundere i cibi, così prov­<lb></lb>vidamente supplendo al natural difetto dei denti; “ Hoc verissimum esse, <lb></lb>soggiunge, expertus sum Pisis, iussu Sereniss. </s>

<s>M. D. </s>

<s>Ferdinandi secundi: <lb></lb>globulos enim vitreos, seu vesiculas vacuas, et tubulos plumbeos pariter exca­<lb></lb>vatos et ligneas pyramidulas, et alia plurima intra gallorum indicorum in­<lb></lb>gluviem per os immisi, et die sequenti plumbeas massas contusas et ero­<lb></lb>sas, vitra pulverizata, et sic reliqua ingesta reperi ” (Editio cit., pag. </s>

<s>395). </s></p><p type="main">

<s>Nel terzo splendido periodo dell&#039;illustre Accademia furono, sotto la di­<lb></lb>rezione dello stesso Borelli, ripetute simili esperienze sopra le galline e le <lb></lb>anatre, e si lasciò fatto di esse questo breve cenno in fine al libro dei <emph type="italics"></emph>Saggi:<emph.end type="italics"></emph.end><lb></lb>“ Mirabile è la forza, con la qual s&#039;opera la digestione delle galline e delle <lb></lb>anatre, le quali imbeccate con palline di cristallo massicce (il Redi notò che <lb></lb>dovea dirsi <emph type="italics"></emph>vuote,<emph.end type="italics"></emph.end> come leggesi a pag. </s>

<s>49 del T. II delle Opere di lui, stam­<lb></lb>pate a Napoli nel 1741) sparate da noi in capo di&#039;parecchie ore, ed aperti i <lb></lb>loro ventrigli al sole, parevano foderati d&#039;una tunica rilucente, la qual ve­<lb></lb>duta col microscopio si conobbe non esser altro che un polverizzamento finis­<lb></lb>simo ed impalpabile di cristallo. </s>

<s>In alcune, imbeccate parimente con palle <lb></lb>di cristallo ma vote e forate sottilmente, ci siamo abbattuti a veder delle <lb></lb>suddette palle altre già peste e macinate, ed altre solamente incominciate a <lb></lb>fendersi, e ripiene di certa materia bianca, simile al latte rappreso, entra­<lb></lb>tavi per quel piccolissimo foro, ed abbiamo sottosopra osservato che quelle <lb></lb>macinano meglio dell&#039;altre, che hanno ne&#039;loro ventrigli maggior copia di <lb></lb>sassolini inghiottiti. </s>

<s>Quindi con minor maraviglia stritolano e pestano .... <lb></lb>i noccioli delle olive, i pinocchi durissimi ed i pistacchi fatti loro ingollar <lb></lb>con la buccia. </s>

<s>Le palle di pistola, in capo di ventiquattr&#039;ore, le abbiamo <lb></lb>trovate schiacciate notabilmente, e di alcuni quadrelli di stagno voti parte <lb></lb>ne trovammo graffiati e storti, e parte sfondati da parte a parte ” (Saggi <lb></lb>di natur. </s>

<s>esper., Firenze 1841, pag. </s>

<s>174, 75). </s></p><p type="main">

<s>Questi mirabili effetti meccanici al Borelli, che si studiava di ridurre a <lb></lb>soli effetti meccanici tutte le funzioni della vita animale, arrisero in modo, <lb></lb>da fargli stabilire quella sua teoria meccanica della digestione, che invalse <lb></lb>a principio nelle scuole italiane. </s>

<s>Studiata, per impulso avutone dall&#039;Harvey, <lb></lb>sugli uccelli, egli intendeva applicarla a tutti gli animali a ventricolo mem­<lb></lb>branoso, ne&#039;quali l&#039;effetto della triturazione, in che principalmente consi­<lb></lb>stono per lui le funzioni digestive, producesi dalla mola dei denti. </s>

<s>Ne&#039;pesci <lb></lb>soli, che non han denti nè ventricolo musculoso, il Borelli s&#039;indusse ad am­<lb></lb>mettere l&#039;opera di un fermento, eccitato sui cibi ingesti da un succo cor­<lb></lb>rosivo, secreto da certe ghiandole sparse per le membrane ventricolari. </s>

<s>Di <pb xlink:href="020/01/1328.jpg" pagenum="203"></pb>questo succo però, in cui fu poi dimostrato risiedere principalmente l&#039;effi­<lb></lb>cacia della digestione, il Borelli stesso non fece nessun conto negli altri ani­<lb></lb>mali, come pure ei non fece nessun conto di quella materia bianca, simile <lb></lb>al latte, entrata per i fori delle palline e dei tubi fatti ingollare alle anatre, <lb></lb>e ai galli indiani; osservazioni importantissime, che rimasero per le carte <lb></lb>del <emph type="italics"></emph>Cimento<emph.end type="italics"></emph.end> come lucerna spenta, infintanto che, riaccesa dalla mano indu­<lb></lb>stre dello Spallanzani, non gli servì di luminosa guida in quelle sue mara­<lb></lb>vigliose esperienze, che si riguardarono da tutti come altrettante scoperte. </s></p><p type="main">

<s>Quando il celebre professor di Pavia intraprese le sue esperienze in­<lb></lb>torno alla digestione, incominciando dal ripetere quelle del Borelli, era nella <lb></lb>scienza fisiologica sorto primo Maestro Ermanno Boerhaave, di cui quasi <lb></lb>universalmente si seguivano le dottrine. </s>

<s>Ma quelle dottrine del celebratis­<lb></lb>simo Medico straniero, intorno alle funzioni digestive, erano prettamente <lb></lb>italiane, e Tommaso Cornelio, inspiratosi alla filosofia cartesiana, le aveva <lb></lb>insegnate infino dal 1661 fra noi, dev&#039;ebbe seguaci anche coloro, che per <lb></lb>amor del vero sentirono nella coscienza il dovere di disertar dalla scuola <lb></lb>dello stesso Borelli. </s></p><p type="main">

<s>Il Proginnasma VI del nostro Fisiologo calabrese è tutto dedicato a trat­<lb></lb>tare di questo importantissimo soggetto, e s&#039;intitola perciò <emph type="italics"></emph>De nutricatione.<emph.end type="italics"></emph.end><lb></lb>Incomincia dal dimostrare l&#039;impossibilità che sieno i cibi concotti nello sto­<lb></lb>maco dal calore animale, secondo l&#039;opinion degli antichi, osservando che i <lb></lb>pennati digeriscono corpi tanto duri, che non si potrebbero disfare a un <lb></lb>debol fuoco, nè infusi nell&#039;acqua stessa più fervente. </s>

<s>Il ricorrere alle qua­<lb></lb>lità occulte, prosegue il Cornelio, è un non far altro insomma che un con­<lb></lb>fessare la propria ignoranza. </s>

<s>“ Quapropter ad similitudinem veri propius ac­<lb></lb>cedere videtur illorum sententia, qui censent ciborum concoctionem fieri a <lb></lb>succis quibusdam mordacibus, in animalium ventriculos distillantibus, qui <lb></lb>instar menstrui, ita chymici eiusmodi liquores appellant, escam comminuant, <lb></lb>dissolvantque, ut inde particulae ad alendum idoneae extrahi, secernique <lb></lb>possint ” (Progynnasmata physica, Neapoli 1688, pag. </s>

<s>211). </s></p><p type="main">

<s>Se non che, così procede l&#039;Autore nel suo discorso, avendo i menstrui <lb></lb>virtù diverse, converrebbe ammettere nel ventricolo la secrezione di tanti <lb></lb>succhi distinti, quante sono le innumerevoli varietà dei cibi, ciò che non c&#039;in­<lb></lb>duciamo facilmente a pensare, per essere contrario alla semplicità degli or­<lb></lb>dini naturali, ond&#039;è che, ad esplicare il modo della digestione de&#039;cibi, con­<lb></lb>viene speculare altre ragioni. </s>

<s>“ Ego vero, ut quid ipse sentiam exponam, <lb></lb>arbitror in unam ciborum confectionem plures convenire causas, nempe et <lb></lb>ipsam escam fermentari debere, et calidorum spirituum, halitumque expira­<lb></lb>tione foveri, et rursus ventriculi motu pressuque misceri, cogi atque con­<lb></lb>fundi, ac demum apto humore irrorari atque dilui, ut hac ratione confecta <lb></lb>per peculiares ductus distribuatur ” (ibi, pag. </s>

<s>213). </s></p><p type="main">

<s>Passa quindi il Cornelio a spiegare particolarmente ciascuna di queste <lb></lb>cause concorrenti a produrre la digestione, ma prima si trattiene a descri­<lb></lb>vere la struttura del ventricolo, notandovi certe cose che da nessuno, egli <pb xlink:href="020/01/1329.jpg" pagenum="204"></pb>dice, “ quod sciam, animadversa hactenus fuere. </s>

<s>” Queste anatomiche os­<lb></lb>servazioni concernono la tunica interiore trapunta, come da un ago, da innu­<lb></lb>merevoli forellini, intorno ai maggiori de&#039;quali stanno alcune ghiandolette <lb></lb>lenticolari che, leggermente compresse, stillano nel ventricolo un certo umor <lb></lb>biancheggiante. </s>

<s>A queste osservazioni anatomiche soggiunge poi la descri­<lb></lb>zione del moto vermicolare degl&#039;intestini, dopo di che ritorna a dire della <lb></lb>confezione de&#039;cibi. </s></p><p type="main">

<s>La prima funzione del ventricolo è quella di concuocere l&#039;esca, la quale <lb></lb>perciò incomincia a fermentare, essendovi disposta per sua natura. </s>

<s>Concorre <lb></lb>all&#039;opera il calore animale, co&#039;suoi aliti, l&#039;efficacia de&#039;quali in ammollire i <lb></lb>cibi si può facilmente argomentare da quelle essenze distillate dai Chimici, <lb></lb>e che rinchiuse dentro le ampolle rodono il sughero de&#039;loro otturamenti. </s>

<s><lb></lb>Aperto molte volte lo stomaco agli animali vivi, mentre che i cibi ingesti <lb></lb>son presi dai fermenti, abbiam sentito, egli dice, sempre esalarne certi va­<lb></lb>pori tanto acri, da fare zuffa col naso e con gli occhi. </s>

<s>Gustate allora quelle <lb></lb>sostanze, si trovano di sapore ingrato, come le materie che incominciano a <lb></lb>putrefarsi, ond&#039;è che non a torto Empedocle e Plistonico annoverarono la <lb></lb>stessa putrefazione fra le cause, che concorrono alla confezione de&#039;cibi. </s></p><p type="main">

<s>Si trasformano essi cibi, così conclude il Cornelio le sue dottrine in­<lb></lb>torno alla digestione, specialmente negli uomini, in una sostanza di color <lb></lb>bianco, a produrre il qual colore efficacemente concorre quel succo “ quem <lb></lb>e vasis a nobis primum notatis intra ventriculum influere praemonuimus ” <lb></lb>(ibi, pag. </s>

<s>221). È poi la principale utilità di un tal succo quella di diluire <lb></lb>gli alimenti, e di ridurli in parti così minute, che possano facilmente entrare <lb></lb>per le boccuzze aperte dei vasi. </s></p><p type="main">

<s>Il Fisiologo cosentino avviava così, per altri sentieri diversi da quelli <lb></lb>designati dalla Scuola fiorentina, le dottrine della digestione, per la qual <lb></lb>funzione animale diceva non esser sufficiente la meccanica triturazione, ma <lb></lb>bisognarvi di più qualche altra cosa, che assottigli i cibi già macinati, e gli <lb></lb>converta in chilo. </s>

<s>Erano dall&#039;altra parte quelle dottrine dell&#039;Autore de&#039;Pro­<lb></lb>ginnasmi così confortate di ragioni e di esperimenti, che le predicate ve­<lb></lb>rità del Cornelio prevalsero anche fra noi sulla grande autorità del Borelli, <lb></lb>e degli Accademici del Cimento. </s></p><p type="main">

<s>Primo a darne il coraggioso esempio fu Francesco Redi, il quale avendo <lb></lb>occasione, in mezzo alle sue <emph type="italics"></emph>Esperienze intorno a cose naturali,<emph.end type="italics"></emph.end> di toccare <lb></lb>anche delle funzioni digestive, intanto che raccomandava come degno e uti­<lb></lb>lissimo da leggersi in questo proposito il dottissimo Proginnasma <emph type="italics"></emph>De nutri­<lb></lb>catione<emph.end type="italics"></emph.end> scritto da Tommaso Cornelio, così, dop&#039;aver riferite l&#039;esperienze dei <lb></lb>suoi Fiorentini, e aver fatto particolare attenzione a quella materia di color <lb></lb>bianco entrata nelle palline ingollate dai polli, ne esponeva compendiosa­<lb></lb>mente, accettandole per verosimili, le dottrine: “ D&#039;onde possa scaturire que­<lb></lb>sto così fatto liquor bianco io per me crederei che fosse spremuto da quelle <lb></lb>infinite papille, le quali son situate in quella parte interna dell&#039;esofago di <lb></lb>tutti gli uccelli, la quale è attaccata alla bocca superiore del ventricolo, e <pb xlink:href="020/01/1330.jpg" pagenum="205"></pb>tanto più lo crederei, quanto che in altre simili esperienze ho posto mente <lb></lb>che le palline piene solamente di tal liquore, senz&#039;altra mistura di cibo, le <lb></lb>ho trovate sempre nella bocca superiore del ventriglio. </s>

<s>Le altre ch&#039;eran piene <lb></lb>e di cibo e di liquor bianco l&#039;ho trovate nell&#039;interna cavità di esso ventri­<lb></lb>glio. </s>

<s>Se poi a questo liquor bianco se ne mescoli qualcun altro, che gli co­<lb></lb>munichi l&#039;amarezza, è facile il congetturarlo, siccome è facile il rinvenire <lb></lb>qual sia il suo ufficio. </s>

<s>Io tengo che la digestione ne&#039;ventrigli degli uccelli <lb></lb>non sia fatta e perfezionata totalmente dalla triturazione, come alcuni hanno <lb></lb>voluto, ma che dopo di essa ci voglia ancora un mestruo per fermentare, <lb></lb>dissolvere, assottigliare e convertire il cibo di già macinato in chiìo ” (Opere, <lb></lb>T. II, Napoli 1741, pag. </s>

<s>50, 51). </s></p><p type="main">

<s>I seguaci di quella fiorente Scuola toscana fondata dal Redi, rifiutata ad <lb></lb>imitazion del Maestro la teoria meccanica degli Accademici del Cimento, si <lb></lb>volsero a professare intorno alla digestione dottrine più confacenti a quelle <lb></lb>introdotte dal Cornelio in Italia, di che può per tutti gli altri servire d&#039;esem­<lb></lb>pio il Vallisnieri, che nel descrivere l&#039;anatomia dello struzzo, volendo deci­<lb></lb>dere se sia conforme alla verità la comune opinione, ch&#039;ei digerisca il ferro, <lb></lb>“ se io ho da parlare colla solita ingenuità, ne conclude, io giudico che ve­<lb></lb>ramente vengano assaliti (i metalli ingesti) dallo stomacale fermento, come <lb></lb>da un&#039;acqua forte, prodigiosa,.... e vengano così corrosi e ridotti in mi­<lb></lb>nutissimi e impalpabili tritoli ” (Opere, T. I, Venezia 1733, pag. </s>

<s>242). </s></p><p type="main">

<s>La persona però di Tommaso Cornelio, che fu primo a introdurre così <lb></lb>fatte nuove dottrine nella scienza della digestione, disparve anche agli occhi <lb></lb>degli stessi Italiani, quando quel medesimo abito del nostro Cosentino s&#039;ac­<lb></lb>comodò al dosso di uno straniero, che abbagliava collo splendore del volto, <lb></lb>innanzi a cui il mondo chinava riverente le ciglia, come alla presenza di un <lb></lb>Nume adorato. </s>

<s>Vedemmo come esso Cornelio ammettesse a produr la dige­<lb></lb>stione più cause concomitanti, le quali si riducono per lui alla fermentazion <lb></lb>naturale, e alla spontanea putrefazione de&#039;cibi, che si diluiscono nel chilo <lb></lb>agitati dal moto vermicolare dei vasi digerenti. </s>

<s>Ermanno Boerhaave propose, <lb></lb>dopo un mezzo secolo, nelle sue celebri Istituzioni mediche, dove a princi­<lb></lb>pio tratta <emph type="italics"></emph>De oeconomia animalis,<emph.end type="italics"></emph.end> quelle medesime dottrine italiane, sotto <lb></lb>queste forme: “ Cibi et potus deglutiti ventriculo clauso, humido, calidoque <lb></lb>excepti, diluti, aere commisti, sponte in hoc loco pro diversitate materiae <lb></lb>fermentescere inciperent vel putrescere: utroque vero modo mire mutari vel <lb></lb>in acescentem vel in alcalescentem, vel in rancidam, aut in glutinosam de­<lb></lb>nique massam...... Si consideres ad cibos hos eo loci salivam magna copia <lb></lb>assidue fluere ex ore et oesophago, ventriculum eos transudante humore di­<lb></lb>luere perpetuo, reliquias prioris alimenti iis permistas eos agitare, aerem iis <lb></lb>subactum eos intime movere calorem loci cuncta haec excitare, videbis ef­<lb></lb>fectus hic praestitos esse: macerare, diluere, in tumorem attollere, attenuare, <lb></lb>fermentationem inchoare, dissolvere, meatibus et humoribus corporis nostri <lb></lb>adaptare ingesta ” (Opera omnia medica, Venetiis 1722, pag. </s>

<s>11). </s></p><p type="main">

<s>Così spiega il Boerhaave il modo come si digeriscono i cibi più molli <pb xlink:href="020/01/1331.jpg" pagenum="206"></pb>e più facili a disfarsi: per la digestion de&#039;più solidi invoca, com&#039;ausiliare <lb></lb>delle sopra dette cause, l&#039;azion meccanica de&#039;muscoli adiacenti al ventri­<lb></lb>colo, non che de&#039;vasi arteriosi ivi con ripetuto continuo moto pulsanti. </s>

<s>“ Ne­<lb></lb>que tamen hinc videris quomodo solidiores cibi non admodum mansi, feli­<lb></lb>citer digerantur in ventriculo..... Ut vero causa haec quaesita inveniatur, <lb></lb>speculeris fabricam muscularem ventriculi, expendesque quaenam inde actio <lb></lb>pendeat ” (ibi, pag. </s>

<s>11, 12). </s></p><p type="main">

<s>Queste del Cornelio assunte nella gloria del Boerhaave erano le dot­<lb></lb>trine, che universalmente si seguivano intorno alla digestione, quando Laz­<lb></lb>zero Spallanzani, lasciate addietro le ipotesi e non soggiogato dall&#039;autorità <lb></lb>di un uomo, pose mano alle esperienze, risalendo alle prime dimenticate tra­<lb></lb>dizioni della scienza italiana. </s>

<s>“ Nell&#039;anno 1777, egli stesso scrive, io ripeteva <lb></lb>a&#039;miei uditori le famose sperienze dell&#039;Accademia del Cimento, riguardanti <lb></lb>la mirabile forza, con la quale le galline e l&#039;anitre macinano in poche ore <lb></lb>e polverizzano ne&#039;loro ventrigli le palline vote di cristallo. </s>

<s>Trovato avendo <lb></lb>veracissime tali esperienze, m&#039;invogliai di estenderle ad alcuni altri di que­<lb></lb>gli uccelli, che a guisa delle galline e dell&#039;anatre diconsi di ventricolo mu­<lb></lb>scoloso. </s>

<s>Queste furono le prime linee d&#039;un lavoro, al quale allora non avrei <lb></lb>mai pensato, e che poi è andato crescendo a proporzione che cresceva in <lb></lb>me la curiosità in un argomento sì bello e sì utile, come si è quello che <lb></lb>riguarda la grand&#039;opera della digestione ” (Dissertazioni di Fisica anim., T. I, <lb></lb>Modena 1780, pag. </s>

<s>1). </s></p><p type="main">

<s>Furono i frutti di un tal lavoro tutti insieme raccolti e in bell&#039;ordine <lb></lb>esposti al pubblico in sei eloquentissime Dissertazioni. </s>

<s>Nella prima s&#039;illu­<lb></lb>strano le esperienze degli Accademici fiorentini intorno alla potenza del ven­<lb></lb>tricolo dei gallinacei, per dimostrare i quali portentosi effetti lo Spallanzani <lb></lb>operava nel modo che segue: “ Dentro a tubetti di latta, della lunghezza <lb></lb>ciascheduno di otto linee e del calibro di quattro, io cacciava varie qualità <lb></lb>di semenze, conficcandone in ciascuna un dato numero proporzionale alla <lb></lb>maggiore o minore grandezza di esse. </s>

<s>Le due estremità de&#039;tubi le lasciava <lb></lb>aperte, a riserva di essere attraversate da più filetti di ferro, che taglian­<lb></lb>dosi in croce venivano a formare una specie d&#039;ingraticolamento, che non im­<lb></lb>pediva a<gap></gap> succhi del ventriglio di entrare ne&#039;tubi, e che vietava alle sostanze <lb></lb>rinchiuse in essi di uscire..... Per dar poi maggiore adito a codesti liquidi, <lb></lb>oltre al continuare a lasciare aperte le estremità, feci fare una moltitudine <lb></lb>di fori alle pareti de&#039;suddetti tubi, cosicchè i succhi gastrici vi potessero <lb></lb>piover dentro da tutte le parti ” (ivi, pag. </s>

<s>4, 5). </s></p><p type="main">

<s>Fatti ingollare cotesti tubi alle galline nostrali, alle anatre, ai galli d&#039;India <lb></lb>e a simili altri, ed estrattili dopo parecchie ore, non si potè mai accorgere <lb></lb>che le semenze ivi dentro rinchiuse, benchè ammorbidite, avessero incomin­<lb></lb>ciato a disciogliersi. </s>

<s>D&#039;ond&#039;ei ne raccolse per cosa già dimostrata che il tri­<lb></lb>turamento negli uccelli granivori “ non può essere che un effetto della ga­<lb></lb>gliarda pressione e di ripetuti violenti urti delle interne pareti del ventriglio, <lb></lb>mediante i robustissimi muscoli ond&#039;è corredato ” (ivi, pag. </s>

<s>6). </s></p><pb xlink:href="020/01/1332.jpg" pagenum="207"></pb><p type="main">

<s>Essendo così, penseremo noi, prosegue a dire lo Spallanzani “ che da <lb></lb>questa azione dipenda anche la digestione dei cibi dentro al ventricolo, di <lb></lb>maniera che, in grazia della triturazione, arrivino essi in fine a convertirsi <lb></lb>in quella pultacea sostanza, che chiamasi <emph type="italics"></emph>chimo?<emph.end type="italics"></emph.end> O più veramente che que­<lb></lb>sta sostanza si generi mediante i succhi preparati o raccolti nel ventriglio, <lb></lb>e che la triturazione aiuti bensì con lo spezzamento de&#039;cibi, ma non pro­<lb></lb>duca la digestione? </s>

<s>” (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Per rispondere efficacemento a così fatta importantissima domanda pensò <lb></lb>lo Spallanzani di metter dentro i tubi già descritti alcune sostanze alimen­<lb></lb>tari, come sarebbe mollica di pane, la quale trovò che veramente era stata <lb></lb>consunta, per aver soggiaciuto all&#039;azione del succo gastrico nel ventriglio di <lb></lb>una gallina. </s>

<s>Ma perchè con sostanze non solubili l&#039;esperienze sarebbero riu­<lb></lb>scite più concludenti, riempiè i medesimi tubetti con carne di vitella smi­<lb></lb>nuzzata, ed estrattala dai ventrigli osservò che quella carne, dov&#039;era venuta <lb></lb>a contatto col succo gastrico, avea cangiato di colore, e acquistati tutti i segni <lb></lb>caratteristici di una vera digestione. </s></p><p type="main">

<s>Così fatte esperienze erano senza dubbio per sè concludenti, ma perchè <lb></lb>riuscissero anche più decisive venne in mente allo Spallanzani di sperimen­<lb></lb>tare se il succo gastrico mantenesse quella sua vitale virtù di sciogliere i <lb></lb>cibi, anche fuor de&#039;ventrigli. </s>

<s>L&#039;abbondanza di liquido, che vedeva secer­<lb></lb>nersi dagli organi digerenti delle galline d&#039;India e dell&#039;oche, gl&#039;incorò buona <lb></lb>speranza d&#039;avere a riuscir nell&#039;intento, e perciò ne riempiè due piccoli tubi <lb></lb>di vetro serrati ermeticamente da una parte, e con ceralacca dall&#039;altra, dopo <lb></lb>aver posto in uno de&#039;pezzettini di carne di castrato, e in quell&#039;altro varii <lb></lb>grani spezzati di frumento. </s>

<s>Si la carne poi che i grani aveva lasciato ma­<lb></lb>cerar prima nel gozzo di un gallo d&#039;India, perchè avessero dalla Natura <lb></lb>quelle disposizioni, che in così fatti animali precedono sempre alla digestione. <lb></lb></s>

<s>“ E siccome il calore del ventriglio, così propriamente scrive lo stesso Spal­<lb></lb>lanzani, era probabilmente una condizione richiesta allo scioglimento de&#039;cibi, <lb></lb>così pensai di supplirvi col far provare ai tubi un grado di caldo presso a <lb></lb>poco consimile, mettendomeli tutti e due sotto le ascelle. </s>

<s>Li lasciai interpo­<lb></lb>latamente in tal sito tre giorni, indi apertili e visitato prima il tubetto dei <lb></lb>grani di frumento, la maggior parte di questi non aveva più che la nuda <lb></lb>scorza, essendone già uscita la polpa farinosa, che nel fondo del tubetto for­<lb></lb>mato aveva un sedimento grigio bianchiccio e densetto. </s>

<s>La carne poi del­<lb></lb>l&#039;altro tubo, senza dare il minimo odor di putredine, era in massima parte <lb></lb>sciolta ed incorporatasi al succo gastrico, fattosi quindi più torbido e denso. </s>

<s><lb></lb>I pochi avanzi di lei perduto avevano il rosso naturale, e si eran fatti tene­<lb></lb>rissimi. </s>

<s>Rimessi quegli avanzi nel proprio tubetto, che empiuto avea di no­<lb></lb>vello succo gastrico, e ripetuta la prova sotto l&#039;ascella, dopo un altro giorno, <lb></lb>quel resto di carne sciolto erasi interamente ” (ivi, pag. </s>

<s>41). </s></p><p type="main">

<s>Confermatasi così per le digestioni artificiali l&#039;efficacia del succo gastrico <lb></lb>nelle digestioni naturali de&#039;gallinacei e degli uccelli, che tutti hanno il ven­<lb></lb>tricolo muscoloso, passa lo Spallanzani a dimostrar che lo stesso avviene <pb xlink:href="020/01/1333.jpg" pagenum="208"></pb>nelle digestioni degli animali a ventricolo membranoso, come sono le rane, <lb></lb>le salamandre, le bisce terrestri e le acquatiche, le vipere, i pesci, le pecore, <lb></lb>i buoi e i cavalli. </s>

<s>Rimaneva ancora a sperimentare sull&#039;uomo. </s>

<s>Vero è bene <lb></lb>che avendo anch&#039;egli ventricolo membranoso si potevano dedurre dai fatti <lb></lb>sperimentati sopra gli altri animali argomenti probabilissimi di analogia: in <lb></lb>ogni modo però, non se ne conseguiva l&#039;assoluta certezza. </s>

<s>Ma fare ingollare <lb></lb>a un uomo, com&#039;ai galli, tubetti di latta o palline di vetro pareva pericoloso, <lb></lb>e dall&#039;altra parte si paravano innanzi alla fantasia dell&#039;Autore esempi di corpi <lb></lb>non digeribili, che inavvedutamente ingollati dai fanciulli avevano in essi ec­<lb></lb>citato molesti urti di stomaco, e altri funestissimi effetti. </s>

<s>Altri fatti in con­<lb></lb>trario però, quali erano il veder che i noccioli durissimi delle ciriegie, delle <lb></lb>susine, ecc., ingoiati pure così spesso dagl&#039;ingordi fanciulli erano innocua­<lb></lb>mente renduti per secesso, gl&#039;infusero coraggio, e vinta ogni repugnanza de­<lb></lb>liberò di fare esperienza su sè medesimo, così almeno per saggio. </s></p><p type="main">

<s>“ Consisteva questo saggio, scrive esso Spallanzani, nel prender per <lb></lb>bocca una borsetta di tela, entrovi una porzione di pane masticato, del peso <lb></lb>di cinquantadue grani. </s>

<s>La prova fu da me fatta di mattino dopo l&#039;esser le­<lb></lb>vato, trovandomi a stomaco digiuno, e queste furono le circostanze, che ac­<lb></lb>compagnarono sempre l&#039;altre susseguenti esperienze. </s>

<s>La borsetta stette den­<lb></lb>tro di me ventitre ore, senza ch&#039;io ne provassi il più piccolo male, e rimandata <lb></lb>che fu, trovossi spogliata interamente di pane. </s>

<s>Il refe, che strettamente cu­<lb></lb>civa insieme i due lembi della borsetta, non si era nè rotto nè guasto, e lo <lb></lb>stesso era di quello, che ne serrava la gola perchè il pane non uscisse. </s>

<s>Non <lb></lb>si vide tampoco sdrucitura di sorta nella tela stessa, e però era patente che <lb></lb>tanto nel mio ventricolo quanto negli intestini la piccola borsa non era stata <lb></lb>niente pregiudicata. </s>

<s>Io non posso esprimere al Lettore la confidenza, in che <lb></lb>mi pose il buon esito di questa esperienza, per intraprenderne altre. </s>

<s>Non <lb></lb>indugiai pertanto a ripeterla con due altre borsette della medesima tela con­<lb></lb>tenenti ciascuna l&#039;istessa dose di pane masticato, variata soltanto la circo­<lb></lb>stanza che una delle borsette era formata di due invogli di tela, e l&#039;altra di <lb></lb>tre. </s>

<s>Per le cose dette altrove egli è facile l&#039;indovinare il motivo di tal va­<lb></lb>riazione, ch&#039;era quello di vedere se, a norma del crescente numero degl&#039;in­<lb></lb>vogli, rendevasi più difficile la digestione del pane. </s>

<s>E questo effettivamente <lb></lb>successe. </s>

<s>Imperocchè, uscite essendo dal mio corpo le due piccole borse, <lb></lb>dopo ore ventisette non ben compiute, il pane, quantunque fosse stato di­<lb></lb>gerito del tutto nella borsetta dai due invogli, ne rimaneva però una pie­<lb></lb>cola quantità in quella dai tre. </s>

<s>Tal quantità, quantunque in parte perduto <lb></lb>avesse del proprio sugo, riteneva però la natura di pane ” (ivi, pag. </s>

<s>194, 95). </s></p><p type="main">

<s>Restava così d&#039;ogni parte ben dimostrato che la digestionè è opera uni­<lb></lb>camente del succo gastrico. </s>

<s>Ma perchè riuscisse la dimostrazione anco più <lb></lb>compiuta, conveniva persuadere i seguaci del Boerhaave non essere in quel <lb></lb>fatto fisiologico nulla che si possa attribuire ai fermenti o alla putredine. </s>

<s><lb></lb>Quanto ai fermenti, prima di venire alla prova delle esperienze, osserva lo <lb></lb>Spallanzani che i cibi ingesti non hanno il tempo sufficiente per passare <pb xlink:href="020/01/1334.jpg" pagenum="209"></pb>via via da uno in altro di quegli stati necessarii, perchè possa la materia <lb></lb>subire le sue complete trasformazioni. </s>

<s>Quanto poi alla putredine dimostrò <lb></lb>lo stesso Spallanzani che anzi il succo gastrico è antisettico, concludendo ciò <lb></lb>dall&#039;osservazione di questi fatti: “ Due piccoli vasi di vetro pieni di succo <lb></lb>gastrico, l&#039;uno corvino l&#039;altro canino, entrovi carne di vitella e di pecora, <lb></lb>restarono in tempo d&#039;inverno in una stanza per l&#039;intervallo di trentasette <lb></lb>giorni, senza che si avesse mai soluzione nè infracidamento, nonostante che <lb></lb>dette carni, tenute con acqua in altri due simili vasi, verso il settimo giorno <lb></lb>cominciassero a puzzare, e nel vigesimo fossero già degenerate in una feten­<lb></lb>tissima corruttela ” (ivi, pag. </s>

<s>263). </s></p><p type="main">

<s>Quando vennero queste sei Dissertazioni dell&#039;illustre professor di Pavia <lb></lb>alla luce, i Fisiologi ne rimasero ammirati, e ciò che più importa persuasi <lb></lb>di quel che ivi si dimostrava coi fatti. </s>

<s>Insorsero è vero contradittori, e fra <lb></lb>questi alcuni, come l&#039;Hunter, valorosissimi, ma non fecero altro le discus­<lb></lb>sioni che confermare le verità nuovamente rivelate da quelle, che tutti, ma <lb></lb>specialmente gli stranieri, predicavano per maravigliose esperienze di Fisica <lb></lb>animale del nostro Spallanzani. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Verso la fine del secolo XVIII era dunque la Scienza fisiologica, dopo <lb></lb>tante aberrazioni, giunta a intendere in che modo si facesse la digestione, <lb></lb>e come il cibo nello stomaco si riducesse in chimo, da cui poi gl&#039;intestini <lb></lb>ricevessero il chilo. </s>

<s>Che tutto quel sostanzial nutrimento rimanesse in ser­<lb></lb>vigio de&#039;soli visceri, dentro i quali erasi generato, fu antica opinione di al­<lb></lb>cuni di grossolano ingegno, ma i più seguivano gl&#039;insegnamenti di Galeno, <lb></lb>il quale aveva nel IV libro <emph type="italics"></emph>De usu partium<emph.end type="italics"></emph.end> lasciato scritto: “ Prius elabo­<lb></lb>ratum in ventricolo alimentum venae ipsae deferunt ad aliquem concoctio­<lb></lb>nis locum communem totius animalis, quem Hepar nominamus ” (Opera, <lb></lb>T. I, Venetiis 1597, fol. </s>

<s>135). </s></p><p type="main">

<s>Quelle vene son secondo Galeno le meseraiche, le quali come radici d&#039;al­<lb></lb>bero si partono dagl&#039;intestini, e vanno a riunirsi in un tronco solo, che è <lb></lb>quello della <emph type="italics"></emph>Vena,<emph.end type="italics"></emph.end> la quale entra per la <emph type="italics"></emph>porta<emph.end type="italics"></emph.end> del Fegato, a cui fuor che <lb></lb>per essa non giunge nulla, <emph type="italics"></emph>quemadmodum in urbes nihil, nisi per portas, <lb></lb>invehi potest.<emph.end type="italics"></emph.end> “ Colligens vero Natura, ut in arboribus, exiguas illas radi­<lb></lb>ces in crassiores, ita in animalibus vasa minora in maiora, et ea rursus in <lb></lb>alia maiora, idque semper agens usque ad Hepar in unam omnia venam <lb></lb>coegit, quae ad portas sita est ” (ibi, fol. </s>

<s>141). </s></p><p type="main">

<s>Tali erano le vie da Galeno prescritte al chilo, per giungere al Fegato, <lb></lb>dove fomentato dal calor naturale del viscere si trasforma in sangue “ ve­<lb></lb>luti vinum ipsum in doleo mustum ” (ibi, fol. </s>

<s>136), e tali, in conformità di <lb></lb>quelle del Maestro, furono le opinioni cecamente seguite in tal proposito dai <pb xlink:href="020/01/1335.jpg" pagenum="210"></pb>Medici, infintantochè, nel risvegliarsi che fece la scienza per opera del Be­<lb></lb>rengario, revocatesi quelle galeniche dottrine ad esame, non incominciarono <lb></lb>i dubbii a sottentrare alla fede. </s>

<s>Com&#039;è possibile, si domandava, che le vene <lb></lb>meseraiche portino il chilo, se si vedono sempre rosseggiare di sangue, o <lb></lb>come si può credere che lo succhino dagl&#039;intestini, se non si vedono entrare <lb></lb>nel loro interno con le bocche aperte? </s></p><p type="main">

<s>Il dubbio era ragionevole; nessuno però lo sapeva risolvere, intanto che <lb></lb>Giovanni Fernelio trovatosi, come si dice, alle strette, uscì a dire che in ogni <lb></lb>modo al senso doveva in questo caso prevaler la ragione. </s>

<s>Il cap. </s>

<s>II del <lb></lb>VI libro della sua Fisiologia, pubblicata la prima volta in Parigi nel 1538, <lb></lb>s&#039;intitola così: “ Ut e ventriculo per intestina et venas meseraicas in iecur <lb></lb>fiat alimenti distributio. </s>

<s>” Ricerca ivi il Fernelio quali possano essere i vasi <lb></lb>proprii deputati dalla Natura a suggere il chilo, e pensa per prima cosa non <lb></lb>poter essere le arterie, che vanno, e s&#039;inseriscono negl&#039;intestini, le quali, se <lb></lb>pur possono suggere qualche poco di umore, “ id omnino perexiguum esse <lb></lb>debet, quod crassior illic succus existat, sintque arteriae spiritui halitiuque <lb></lb>trahendo accommodatae ” (Johannis Fernelii Universa medicina, Lugduni 1602, <lb></lb>pag. </s>

<s>155, 56). </s></p><p type="main">

<s>Non possono esser dunque i vasi chiliferi, così, prosegue il Fernelio <lb></lb>stesso a ragionare, altro che le vene del mesenterio: e benchè elle non sem­<lb></lb>brino far quest&#039;ufficio a giudizio del senso, nonostante la ragione ci persuade <lb></lb>non poter aversi dagl&#039;intestini al Fegato altra via diversa, nè che sia meglio <lb></lb>accomodata di quella. </s>

<s>“ Qui unum sensum aestimatorem iudicemque adhi­<lb></lb>buerit, mesenterii venas ventriculi et intestinorum nutricationi, non autem <lb></lb>succorum distributioni, destinatas esse contendet, quod omnes semper rubro, <lb></lb>nunquam albo succo, confertae videntur, quodque in ventriculi et intestino­<lb></lb>rum substantiam se figant, neque ad interiorem capacitatem apertae sint. </s>

<s><lb></lb>Verumtamen, quoniam aliae nusquam viae ex intestinis in iecur directae <lb></lb>feruntur, per quas alimentum influat; ratio, magis quam sensus, convincit <lb></lb>eas etiam ad distributionem accommodari ” (ibi, pag. </s>

<s>156). </s></p><p type="main">

<s>Intanto che il senso durava ancora, ne&#039;seguaci del Fernelio, a conten­<lb></lb>dere coll&#039;intelletto, il Colombo usciva fuori ad annunziare in questo propo­<lb></lb>sito una sua nuova scoperta; non è vero che le vene meseraiche, negligen­<lb></lb>temente fin qui osservate, non penetrino nella cavità intestinale; elle anzi <lb></lb>vanno ad aprirvi dentro le loro bocche, alle quali l&#039;industriosa Natura ap­<lb></lb>pose alcune ingegnose valvole, perchè assorbito il chilo non dovesse ritor­<lb></lb>narsene indietro. </s>

<s>Nel VI libro <emph type="italics"></emph>De re anatomica,<emph.end type="italics"></emph.end> dop&#039;aver descritto il quinto, <lb></lb>il sesto e il settimo ramo della Vena porta, così il Colombo stesso prosegue: <lb></lb>“ Ex quibus tres illi, quos ad intestina ferri diximus, cum in mesenterium <lb></lb>pervenere, in meseraicas dictas venas innumeras, ac pene infinitas, scindun­<lb></lb>tur, quae intestina, non modo amplectuntur, sed etiam ad internam usque <lb></lb>cavitatem perforant, quo loco Natura sagax extremae unicuique harum mem­<lb></lb>branam apposuit, qualem in vesicae cavitate extremis ureteris apposuit, quae <lb></lb>lotio ad vesicam descendenti aditum praebent, prohibentque ne ad superiora <pb xlink:href="020/01/1336.jpg" pagenum="211"></pb>amplius revertatur. </s>

<s>Idem in extremitate harum mesaraicarum, quas innume­<lb></lb>ras diximus, effecit Natura: quod a nemine, quod sciam, adhuc animadver­<lb></lb>sum est. </s>

<s>Licet omnes uno ore dicant factas fuisse meseraicas ut chylum ab <lb></lb>intestinis exugerent, in eo tamen parum diligentes fuere quod finem earum <lb></lb>persequi neglexerint, ut magnam Naturae industriam facile perspicerent, <lb></lb>quanta scilicet arte effecerit ut hae venae chylum facile suscipere possent, <lb></lb>ne autem egrediatur, membranulae illae prohibent ” (Venetiis 1559, pag. </s>

<s>165). </s></p><p type="main">

<s>Nè il Colombo però nè i suoi contemporanei riconobbero la maggiore <lb></lb>importanza di quella scoperta, anzi non par che la riconoscesse nemmeno <lb></lb>lo stesso Asellio, il quale intese, o volle intendere, che Realdo avesse de­<lb></lb>scritte le meseraiche volgate, per argomento di che adduceva la disposizion <lb></lb>delle valvole, diversa nelle meseraiche stesse comunemente conosciute, e nelle <lb></lb>lattee, da sè nuovamente scoperte. </s>

<s>Diceva insomma l&#039;Asellio che le valvole <lb></lb>del Colombo s&#039;aprono dal di fuori al di dentro, in che son dissomiglianti <lb></lb>dalle nuove scoperte, le quali si aprono invece dal di dentro al di fuori. <lb></lb></s>

<s>“ Hac tamen inter utrasque constituta dissimilitudine et differentia, ut illae <lb></lb>Columbi foris intro ferantur, nostrae contra intus foris spectent ” (De lacti­<lb></lb>bus, Mediolani 1627, pag. </s>

<s>39). </s></p><p type="main">

<s>Ma s&#039;è veramente tale la disposizion delle valvole, secondo il Colombo, <lb></lb>com&#039;avrebbero potuto servire a far entrar dentro ai vasi deferenti il chilo, <lb></lb>e a proibire a lui <emph type="italics"></emph>ne egrediatur?<emph.end type="italics"></emph.end> L&#039;Asellio dunque frantese, e fu causa del <lb></lb>suo inganno l&#039;aver sentito rassomigliare le valvole, apposte alle estremità <lb></lb>delle meseraiche, alla valvola applicata all&#039;estremità dell&#039;uretere, la quale <lb></lb>veramente s&#039;apre dal di fuori al di dentro, affinchè non ringorghi il liquido, <lb></lb>che ha da scendere nella vescica. </s></p><p type="main">

<s>Il desiderio forse, che aveva esso Asellio di non esser costretto a rico­<lb></lb>noscere nessun prossimo premostratore della sua scoperta, non gli lasciò li­<lb></lb>bertà di pensare che il Colombo rassomigliava i due organi nell&#039;ufficio, ma <lb></lb>no nel proprio e particolar modo di esercitarlo. </s>

<s>Se poi si ripensi che il si­<lb></lb>stema della Vena porta è privo di valvole, e che le valvole descritte nel <lb></lb>VI libro. <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> hanno la medesima disposizione delle aselliane, <lb></lb>non si avrà nessuna difficoltà ad ammettere che il Colombo osservasse le <lb></lb>vere lattee, e non le meseraiche <emph type="italics"></emph>alterius et vulgati generis,<emph.end type="italics"></emph.end> come l&#039;Asellio <lb></lb>stesso facilmente si lusingava (ivi). Ma il trovarle così esili, e incerte quanto <lb></lb>al liquido contenuto, precise la via della scoperta, fatta poi gloriosamente <lb></lb>dal più giovane suo concittadino, al vecchio Anatomico di Cremona, il quale, <lb></lb>mentre pareva esser giunto così dappresso a toccare la riva, si rituffò nel <lb></lb>più profondo gorgo de&#039;comunali errori, così scrivendo nel cap. </s>

<s>IV del sopra <lb></lb>citato libro, presso a finir di descrivere l&#039;anatomia del ventricolo: “ Venae <lb></lb>vero, tum illi nutrimentum deferunt, tum chylo suscepto illum ad iecur de­<lb></lb>ferunt ” (227). </s></p><p type="main">

<s>Tanto però sembrava impossibile darsi in natura un canale, in cui due <lb></lb>liquidi diversi avessero moto contrario, che alcuni si ridussero ad ammettere <lb></lb>nelle meseraiche due ordini distinti: uno che portasse il sangue, e l&#039;altro <pb xlink:href="020/01/1337.jpg" pagenum="212"></pb>che asportasse il chilo, e forse era questa l&#039;intenzion del Colombo. </s>

<s>Ma il <lb></lb>non essersi bene spiegato gli tolse il merito di aver preparate le vie alla <lb></lb>scoperta aselliana, meglio di Erofilo, di Galeno, di Polluce, di Rhasis e di <lb></lb>quanti altri fra gli antichi si commemorano dalla Storia. </s></p><p type="main">

<s>Contro tutti costoro però, che volendo essere più ragionevoli ammette­<lb></lb>vano nel Mesenterio i due sopra detti ordini di vasi, insorse il lodigiano Gio­<lb></lb>vanni Costèo, il quale pubblicò in Venezia, nel 1565, un libretto così inti­<lb></lb>tolato: “ De venarum mesaraicarum veteris opinionis confirmatione adversus <lb></lb>eos, qui chyli in iecur distributionem fieri negant per mesaraicas venas. </s>

<s>” <lb></lb>Ma perchè il Costèo non dimostrava il suo assunto coll&#039;esperienze, ma col­<lb></lb>l&#039;autorità e co&#039;ragionamenti, non fu perciò ascoltato dai savii, dalla mente <lb></lb>de&#039;quali non si potè rimovere l&#039;assurdo che nasceva dal far le meseraiche <lb></lb>tutt&#039;insieme conduttrici del sangue che va, e del chilo che viene. </s></p><p type="main">

<s>Andrea Cesalpino, quand&#039;ebbe riconosciuta la vera direzione del san­<lb></lb>gue venoso, venne a togliersi una delle maggiori difficoltà, che si paravano <lb></lb>innanzi agli altri, e dall&#039;avere scoperto che il sangue stesso e il chilo vanno <lb></lb>nelle meseraiche pel medesimo verso, fu condotto a dare una nuova solu­<lb></lb>zione al difficilissimo problema. </s>

<s>Quel che va, disse, per le vene del mesen­<lb></lb>terio non è sangue, ma è chilo, e, se mostra di color rosso, è perchè le <lb></lb>arterie, che si anastomizzano con le vene stesse meseraiche, v&#039;infondono il <lb></lb>loro sangue, ond&#039;è che il chilo si tinge di quel colore, come fa l&#039;acqua alla <lb></lb>quale si mescola il vino. </s>

<s>“ Cum enim necesse sit omnes partes nutriri san­<lb></lb>guine, venae meseraicae non possunt illis sanguinem tribuere, quia datae <lb></lb>sunt ut sugant chylum et ferant ad hepar. </s>

<s>Simul autem per easdem ferri <lb></lb>sursum chylum et sanguinem deorsum absurdum est, neque diversis tem­<lb></lb>poribus, nunquam enim venae meseraicae repertae sunt chylo plenae, sed <lb></lb>semper sanguine. </s>

<s>Quomodo igitur sugunt chylum ut omnes fatentur?.... <lb></lb>Quod autem sanguis semper reperiatur in vasis istis, nunquam autem ma­<lb></lb>teria alba, causa est quia arteriae cum venis delatae, per anastomosin san­<lb></lb>guinem in venas transfundunt, unde chyli fit conversio in sanguinem ut vi­<lb></lb>num facit aquae mixtum ” (Artis medicae, Lib. </s>

<s>VII, Romae 1603, pag. </s>

<s>9). </s></p><p type="main">

<s>L&#039;ingegnosa ipotesi del Cesalpino però non ebbe accoglienza nel pub­<lb></lb>blico, così alieno allora dal professare le innovatrici dottrine di lui intorno <lb></lb>alla natura e alla direzione del sangue nelle vene, ond&#039;è che Gaspero Asel­<lb></lb>lio si confermò sempre più nella sua opinione che avesse la Natura ordi­<lb></lb>nati a condurre il chilo vasi appropriati, e che la risoluzione del gran pro­<lb></lb>blema consistesse tutta in trovarli. </s>

<s>Datosi perciò alle autopsie, anco per <lb></lb>seguire il consiglio di Galeno che raccomandava di creder solo <emph type="italics"></emph>propriis ocu­<lb></lb>lis. </s>

<s>non libris<emph.end type="italics"></emph.end> (Praefatio in dissert. </s>

<s>De lact. </s>

<s>cit.), non era ancora riuscito a <lb></lb>trovar nulla, quando quello, che gli era stato così ostinatamente negato dallo <lb></lb>studio, gli fu spontaneamente offerto dalla fortuna. </s>

<s>“ Casu magis, ut verum <lb></lb>fatear, quam consilio aut data in id peculiari opera ” (De lactibus cit., pag. </s>

<s>18). </s></p><p type="main">

<s>Adducono alcuni questa ingenua confessione come un esempio di sin­<lb></lb>golare modestia, ma è la sincera espressione della verità, che vuole avere <pb xlink:href="020/01/1338.jpg" pagenum="213"></pb>un commento dalla storia. </s>

<s>Questo commento poi si conclude tutto nella ri­<lb></lb>sposta a una tale domanda: come mai tanti valorosi Anatomisti, con tanti <lb></lb>solleciti studi, non riuscirono a vedere quel che, premostrante poi l&#039;Asellio, <lb></lb>tutti videro senza difficoltà nel mesenterio degli animali o vivi o morti? </s>

<s>Par­<lb></lb>rebbe si potesse rispondere esser facile avvertire la presenza di un oggetto <lb></lb>in un luogo, dop&#039;averci qualcuno assicurato che guardandoci noi ve lo tro­<lb></lb>veremo di certo, ma non farebbe questa risposta per l&#039;Asellio, nella mente <lb></lb>di cui e nell&#039;animo si vuol penetrare, e non s&#039;intenderebbe come, fuor <lb></lb>d&#039;ogni modestia, egli avesse attribuita la sua scoperta al caso. </s></p><p type="main">

<s>A intender ciò giova osservare che, da poi che il Colombo, dettando le <lb></lb>regole per le vivisezioni, consigliò di praticarle sui cani, i cani furono, prima <lb></lb>e dopo l&#039;Asellio, quasi i soli immolati, e gli esempi del Pecquet e dell&#039;Igmoro <lb></lb>possono valere per tutti gli altri. </s>

<s>Ma la fame dei cani è proverbiale, a che <lb></lb>s&#039;aggiungeva che i dissettori gli tenevano ad arte digiuni più che mai, perchè <lb></lb>i poveri animali, lasciandosi andar, fra gli spasimi, a deporre il superfluo <lb></lb>del ventre, non dovessero gli assistenti allo spettacolo rimanere offesi dalla <lb></lb>schifezza, e ammorbati dal fetore. </s></p><p type="main">

<s>Aveva dunque anche l&#039;Asellio sempre praticato così, e una volta che <lb></lb>ebbe a incidere un cane, non secondo il solito digiuno, ma anzi benissimo <lb></lb>pasciuto, ebbe ragione di attribuire il fatto a un benefizio singolare della <lb></lb>fortuna. </s>

<s>Che tali fossero davvero i sentimenti dell&#039;avventuroso primo dimo­<lb></lb>stratore delle vene lattee, è confessato nella storia, da lui stesso descrittaci <lb></lb>con mirabile grazia e naturalezza, e nella quale s&#039;incomincia così a raccon­<lb></lb>tare a quale occasione, e in che modo gli occorresse di fare l&#039;inaspettata <lb></lb>scoperta. </s></p><p type="main">

<s>“ Canem, ad diem Julii 23 eiusdem anni (1622) bene habitum, beneque <lb></lb>pastum incidendum vivum sumpseram, amicorum quorumdam rogatu, qui­<lb></lb>bus recurrentes nervos videre forte placuerat. </s>

<s>Ea nervorum demonstratione <lb></lb>perfunctus cum essem, visum est eodem in cane, eadem opera, diaphragma­<lb></lb>tis quoque motum observare. </s>

<s>Hoc dum conor, et eam in rem abdomen ape­<lb></lb>rio, intestinaque cum ventriculo, collecta in unum deorsum manu, impello, <lb></lb>plurimos repente, eosque tenuissimos candidissimosque ceu funiculos, per <lb></lb>omne mesenterium et per intestina, infinitis propemodum propaginibus di­<lb></lb>spersos, conspicor. </s>

<s>Eos primo aspectu nervos esse ratus, non magnopere mi­<lb></lb>ratus sum, sed mox falsum me cognovi, dum nervos, qui ad intestina per­<lb></lb>tinent, distinctos a funiculis illis et longe diversos esse, ac seorsim praeterea <lb></lb>ferri, animadverti. </s>

<s>Quare, rei novitate perculsus, haesi aliquamdiu tacitus, <lb></lb>cum menti varia occurrerent, quae inter Anatomicos versantur de venis me­<lb></lb>seraicis et eorum officio, plenae non litium minus quam verborum contro­<lb></lb>versiae. </s>

<s>Et forte fortuna congruerat ut, paucis ante diebus, quendam de hoc <lb></lb>argumento proprie scriptum a Joanne Costaeo libellnm evolverem. </s>

<s>Ut me <lb></lb>collegi experiundi causa, adacto acutissimo scalpello, unum ex illis, et ma­<lb></lb>iorem funiculum pertundo. </s>

<s>Vix bene ferieram, et confestim liquorem album, <lb></lb>lactis aut cremoris instar, prosilire video. </s>

<s>Quo viso, cum tenere laetitiam non <pb xlink:href="020/01/1339.jpg" pagenum="214"></pb>possem, conversus ad eos qui aderant, ad Alexandrum Tadinum, et Sena­<lb></lb>torem Septalium .... <emph type="italics"></emph>evreca,<emph.end type="italics"></emph.end> inquam cum Archimede, et simul ad rei tam <lb></lb>insolitae, tam iucundum spectaculum invito eius novitate ipsos quoque com­<lb></lb>motos ” (De lactibus cit., Cap. </s>

<s>IX, pag. </s>

<s>19, 20). </s></p><p type="main">

<s>I beneficii però della fortuna, con tanto affetto poi commemorati, non <lb></lb>furono dall&#039;Asellio riconosciuti, se non da poi ch&#039;esalati il cane gli ultimi <lb></lb>spiriti vide dall&#039;aperto abdome sparire l&#039;incantevole scena di quei sottilis­<lb></lb>simi cordoncini lattei. </s>

<s>Per tornar dunque a godere le voluttà dello spetta­<lb></lb>colo, si volse a por le mani sopra un altro cane, il quale eletto di qualità <lb></lb>conformi al desiderio dei male accorti dissettatori, era magro e digiuno. </s>

<s>Ma <lb></lb>aperto con tanta avidità il ventre, e messa la rete del mesenterio allo sco­<lb></lb>perto, rimase! “ Nullum prorsus, vel minimum album vasculum, quanta­<lb></lb>cumque etiam diligentia perquirenti, in conspectu sese dabat. </s>

<s>Et iam abiici <lb></lb>animo coeperam, ac cogitare ne quae in cane illo primo se obtulissent mihi, <lb></lb>ex illis assent quae raro spectari in anatome solebat Galenus dicere ” (ibi, <lb></lb>pag. </s>

<s>20). Riprese poi presto animo, quando pensò al digiuno, e procuratosi <lb></lb>ad arte un terzo cane, come quello primo che gli era stato offerto dal caso, <lb></lb>benissimo pasciuto, fu nuovamente consolato dello spettacolo, e riconobbe <lb></lb>allora quanta parte del merito avesse avuto la Fortuna in quella scoperta, <lb></lb>e ne fece commemorazione solenne nel capitolo VIII, che serve di proemio <lb></lb>a questa storia. </s></p><p type="main">

<s>Fatto così certo l&#039;Asellio della scoperta, e ripensando che i quadrupedi <lb></lb>son dalla Natura formati sopra lo stesso stampo, sperò di ritrovar le vene <lb></lb>lattee in tutti essi ugualmente come ne&#039;cani. </s>

<s>Le trovò di fatto, diligente­<lb></lb>mente cercandole, nei gatti, negli agnellini di latte, e ne&#039;più adulti, nelle vac­<lb></lb>che, nei porci e in un cavallo comperato a questo unico intento, e sventrato <lb></lb>vivo. </s>

<s>Quanto poi all&#039;uomo, sebbene Erasistrato ed Erofilo non temessero d&#039;in­<lb></lb>ciderlo, “ non incidi, fateor, nec incidam qui nefas et piandum morte, cum <lb></lb>Celso, existimo praesidem salutis humanae artem pestem alicui, eamque atro­<lb></lb>cissimam, inferre. </s>

<s>Ita nihilominus, idque pro certo statuo, quae in tot bru­<lb></lb>tis visa mihi sunt, iis fieri nullo modo posse unus et solus homo ut defi­<lb></lb>ciatur ” (ibi, pag 20). </s></p><p type="main">

<s>Chiunque in ogni modo loda l&#039;Asellio, per essersi astenuto dall&#039;incidere <lb></lb>un uomo vivo, si maraviglia ch&#039;ei non tentasse di farlo sui cadaveri, ai quali <lb></lb>sempre erano ricorsi gli Anatomici, per esplorare e descriverne fedelmente <lb></lb>le altre parti. </s>

<s>Cessa ogni maraviglia però in chi ripensa che l&#039;Asellio stesso, <lb></lb>al veder le vene lattee sparire a un tratto fuggitive insiem colla vita, si per­<lb></lb>suase che non fossero visibili ne&#039;cadaveri, dove il chilo non va a riempirle <lb></lb>di sè, sospinto innanzi dall&#039;impulso de&#039;moti vitali. </s></p><p type="main">

<s>Ma l&#039;Igmoro poi riconobbe, per ripetute esperienze, che non sempre il <lb></lb>suceo latteo fugge dalle vene del cane, al fuggir della vita. </s>

<s>“ At vero cum <lb></lb>anima lacteus ile succus a vasis non semper fugit, sed saepissime post inspec­<lb></lb>tionem motuum pulmonum et cordis, imo diu postquam animam efflavit <lb></lb>canis, illas venas lacteas inveni ” (Corporis hum. </s>

<s>disquisitio anat. </s>

<s>cit., pag. </s>

<s>38). <pb xlink:href="020/01/1340.jpg" pagenum="215"></pb>Dal veder le lattee esser dopo morte rimaste impresse nel mesenterio dei <lb></lb>bruti, incorò l&#039;Igmoro una buona speranza di averle a ritrovare altresì ne&#039;ca­<lb></lb>daveri umani, e nel 1639 scrisse di avervele ritrovate di fatto. </s>

<s>Anzi aggiunge <lb></lb>che un medico suo amico gli aveva dato avviso di essersi due anni prima <lb></lb>incontrato ad osservare la medesima cosa in un uomo, la notte e gran parte <lb></lb>del giorno dopo ch&#039;era spirato. </s>

<s>“ Mihi amicissimus Medicus oxoniensis idem <lb></lb>haec scripturo enunciavit quod, in dissectione corporis humani, anno 1637, <lb></lb>apparuerunt lacteae, postquam expirasset animam per spatium totius noctis <lb></lb>et partis maioris diei. </s>

<s>Idem et ipse, in dissectione humani corporis, anno 1639, <lb></lb>perlustravi, licet perfectam illarum disquisitionem copia pinguedinis obnu­<lb></lb>bilavit: illarum tamen plurimas chylo refertas adstantibus demonstravi. </s>

<s>Non <lb></lb>itaque statim post mortem semper evanescunt ” (ibid). </s></p><p type="main">

<s>Di queste anatomiche ispezioni, fatte in Inghilterra sui cadaveri umani, <lb></lb>non s&#039;ebbe però pubblica notizia prima del 1651, quando comparve alla luce <lb></lb>all&#039;Aja l&#039;opera dell&#039;Igmoro. </s>

<s>Ma dodici anni prima un nostro Anatomico ve­<lb></lb>neziano, Cecilio Folli, aveva nella sua città nativa pubblicato un libretto <lb></lb>in 4° col titolo: “ Sanguinis a dextro in sinistrum cordis ventriculum de­<lb></lb>fluentis facilis reperta via, cui non vulgaris in lacteas nuper patefactas ve­<lb></lb>nas animadversio proponitur, Venetiis 1639. ” Ivi dice l&#039;Autore di avere <lb></lb>osservate e di avere altresì in pubblico dimostrate le vene lattee ne&#039;cada­<lb></lb>veri umani, in quel frattempo che asserirono poi di avervele scoperte i due <lb></lb>anatomici stranieri. </s></p><p type="main">

<s>Ha il Folli, in quel suo libretto, considerazioni intorno alle lattee di <lb></lb>qualche pregio, come sarebbe per esempio quella che i vasi chiliferi vanno <lb></lb>tutti a confluire in un tronco, di che è da alcuni attribuito al Nostro il me­<lb></lb>rito di aver additato, benchè dalla lontana, il Ricettacolo pecqueziano. </s>

<s>Ma <lb></lb>nocque alla pubblica stima di lui l&#039;aver, dopo l&#039;Harvey, creduto essere le <lb></lb>vie vere del sangue attraverso alla cavità del cuore quelle, che tanti anni <lb></lb>prima avevano sedotto il Botallo. </s>

<s>Per questa ragione, fra le altre, quando <lb></lb>nel 1641 comparve la Vita di Niccolò Fabrizi di Peiresc, s&#039;ebbe fede e si <lb></lb>accettò per più autentico documento di storia la testimonianza, che ne fece <lb></lb>il celebre biografo di lui Pietro Gassendo, il quale narra com&#039;esso Peiresc, <lb></lb>desideroso di osservare le vene lattee nell&#039;uomo, e disperato di averle a tro­<lb></lb>var ne&#039;cadaveri, dietro ciò che aveva scritto l&#039;Asellio, tentasse in ogni modo, <lb></lb>nel 1634, la prova sul cadavere di un uomo condannato alle forche. </s>

<s>“ Quamo­<lb></lb>brem damnatum suspendio procuravit primum, antequam iudicium capitale <lb></lb>pronunciaretur, secure et egregie pasci, ut nempe esset unde chylus lacte­<lb></lb>sceret, quo tempore requireretur, ac inde, non nisi hora cum semisse post <lb></lb>suspendium expectata, cadaver devehi curavit in anatomicum theatrum. </s>

<s>Prae­<lb></lb>stitum est vero ea diligentia ut aperto abdomine venae albescentes apparue­<lb></lb>rint, utque ex nonnullis resectis colligi potuerit liquor lacteus, quod profecto <lb></lb>visum est mirum ” (Petri Gassendi, Fabricii De Peiresc Vita, Parisiis 1641, <lb></lb>pag. </s>

<s>283). </s></p><p type="main">

<s>Narra ivi lo stesso Gassendo come, avuta il Peiresc la notizia della sco-<pb xlink:href="020/01/1341.jpg" pagenum="216"></pb>perta dell&#039;Asellio, si procurasse varii esemplari del libro “ quae in medicos <lb></lb>amicos distribuit “ (pag. </s>

<s>222) e così, infin dal 1628, alquanti mesi dopo la <lb></lb>pubblicazione, si diffuse in Francia la novella scoperta italiana, dal Peiresc <lb></lb>stesso, e da&#039;suoi molti e valorosi amici in ogni genere di animali, e nel­<lb></lb>l&#039;uomo stesso, come vedemmo, non molti anni dipoi, verificata. </s></p><p type="main">

<s>Non par però che fosse fra quegli amici il Cartesio, il quale insegnando <lb></lb>nel suo trattato <emph type="italics"></emph>De homine<emph.end type="italics"></emph.end> in che modo il ventricolo digerisca il cibo, dice <lb></lb>che le particelle di lui più sottili attraversano i minutissimi pori intestinali <lb></lb>“ per quos fluunt in ramos magnae cuiusdam venae quae ad hepar eas de­<lb></lb>fert, nec non in alias venas, quae eas alio deferunt ” (Editio cit., pag. </s>

<s>4). </s></p><p type="main">

<s>Avverte il De-la-Forge in nota (pag. </s>

<s>6) che il non aver qui il Cartesio <lb></lb>fatto menzione delle vene lattee è sicuro argomento dell&#039;essere il trattato <lb></lb><emph type="italics"></emph>De homine<emph.end type="italics"></emph.end> più antico della dissertazione <emph type="italics"></emph>De lactibus,<emph.end type="italics"></emph.end> ciò che per verità a <lb></lb>noi non sembra, dando manifesta prova dell&#039;essere quel trattato cartesiano <lb></lb>stato scritto dopo il 1628 la circolazione del sangue, ivi professata a modo <lb></lb>dell&#039;Harvey, e sapendo che in quel medesimo anno il Peiresc si fece ban­<lb></lb>ditore solenne in Francia della scoperta aselliana. </s>

<s>Noi crediamo piuttosto es­<lb></lb>sere quel silenzio in conformità del genio di Renato, che presumeva essere, <lb></lb>appetto alle sue, tutte quelle degli altri scoperte da nulla, bastando dall&#039;al­<lb></lb>tra parte alle sue funzioni la macchina umana, com&#039;ei l&#039;aveva filosoficamente <lb></lb>congegnata. </s>

<s>Che se fa grazia all&#039;Harvey è un miracolo, e l&#039;Harvey stesso <lb></lb>glie ne professa riconoscenza: e il medesimo crediamo avrebbe fatto, se ne <lb></lb>fosse stato in tempo, il Gilberto. </s></p><p type="main">

<s>Che se il repudio della tanto aspettata scoperta fa maraviglia in un filo­<lb></lb>sofo, quale era creduto il Cartesio, più gran maraviglia fa in un Fisiologo <lb></lb>qual&#039;era di fatto l&#039;Harvey. </s>

<s>Egli ha per aperto e dimostrato il chilo, in tutti <lb></lb>gli animali che si nutriscono “ ex intestinis per venas mesaraicas deferri, <lb></lb>nec opus esse ut novum iter, venas lacteas scilicet, inquiramus ” (De gene­<lb></lb>ratione anim. </s>

<s>cit., pag. </s>

<s>221). Così il sospiro di tanti anatomici, succedutisi <lb></lb>senza interruzione, dal Fernelio in poi, non era stato per l&#039;Harvey che un <lb></lb>vano inutile desiderio. </s></p><p type="main">

<s>Molti commenti hanno fatto gli storici intorno alla strana sentenza del <lb></lb>celeberrimo uomo. </s>

<s>Vollero dire alcuni che fu disprezzo delle cose italiane: <lb></lb>altri che fu gelosia e dispetto del non esser stato egli il primo eletto ad ac­<lb></lb>cogliere le divine aure, che incominciavano a commoversi allora, inspiratrici <lb></lb>di un nuovo stupendo genere di scoperte. </s>

<s>La dissertazione <emph type="italics"></emph>De lactibus<emph.end type="italics"></emph.end> in­<lb></lb>fatti comparve in pubblico un anno prima della Esercitazione anatomica <emph type="italics"></emph>De <lb></lb>motu cordis,<emph.end type="italics"></emph.end> e le valvole, che promuovono e dirigono il chilo, troppo gran <lb></lb>somiglianza hanno colle valvole, che promovono e dirigono il sangue, da ama­<lb></lb>reggiare alquanto la compiacenza in chi aveva scritto che lo scopritor delle <lb></lb>valvole nelle vene non ne conobbe l&#039;uso “ nec alii addiderunt ” (De motu <lb></lb>cordis cit., pag. </s>

<s>77). </s></p><p type="main">

<s>Usi a vedere su questa terra tanto più in basso umiliarsi le valli, quanto <lb></lb>in alto più si erigono i monti, non fa a noi maraviglia il veder quel sublime <pb xlink:href="020/01/1342.jpg" pagenum="217"></pb>ingegno dell&#039;Harvey, ch&#039;era pure un uomo di questa terra, scendere così <lb></lb>in basso fra le passioni volgari e gli errori. </s>

<s>Nonostante diremmo che l&#039;aver <lb></lb>egli negata la necessità delle vene lattee, così vivamente sentita da tutti nel­<lb></lb>l&#039;economia animale, fosse una legittima conseguenza di ciò che gli era oc­<lb></lb>corso a osservare nell&#039;uovo incubato, e di alcune ipotesi da lui stesso fon­<lb></lb>date sopra l&#039;ordine di quegli ammirati svolgimenti embrionali. </s>

<s>All&#039;albume, <lb></lb>che nutrisce il pulcino chiuso dentro nell&#039;uovo, vide sostituito il chilo, che <lb></lb>lo nutrisce escluso. </s>

<s>E siccome quell&#039;albume è portato dalle vene meseraiche <lb></lb>al Fegato, che lo riduce in sostanza meglio atta e più disposta a nutrire; <lb></lb>così pensò che i medesimi vasi diramati pel mesenterio, non potendo rima­<lb></lb>nere ivi inutili e come fuor di servigio, esaurito l&#039;albume dell&#039;uovo, e il <lb></lb>pulcino escluso, di li in poi servissero invece a trasportare il chilo. </s>

<s>“ Porro <lb></lb>cum dicta vasa in ovo in albumen paritèr ac vitellum spargantur, non ali­<lb></lb>ter quam plantae radices in terram solent; constat utrumque hunc liquorem <lb></lb>pro nutrimento foetui esse, eundemque per vasa illa ad hunc deferri..... <lb></lb>Absumitur equidem primo albumen et vitellus sero tandem pro cibo est, <lb></lb>lactisque vicem in iam natis animalibus supplet..... Manifestum igitur est <lb></lb>pullum iam exclusum, dum adhuc tenellus est, vitello nutriri. </s>

<s>Et quemad­<lb></lb>modum is intra ovum, partim ab albumine, partim ex vitello alitur, prae­<lb></lb>cipue vero ab albuminibus, quae et maiore copia adsunt, et citius absu­<lb></lb>muntur; ita similiter, iam exclusus, cui omne adveniens alimentum iecur <lb></lb>pertransit, et ibidem ulterius praeparatur, partim vitello partim chylo ex in­<lb></lb>testinis hausto nutritur, praesertim autem chylo, quem plures venarum me­<lb></lb>saraicarum ramuli ad se rapiunt ” (ibi, pag. </s>

<s>219, 20). </s></p><p type="main">

<s>Lasciamo andare che l&#039;albume e il chilo non si rassomigliano in altro <lb></lb>che nell&#039;ufficio di nutrire e nel colore, ma che pensiamo rispondesse l&#039;Har­<lb></lb>vey a quell&#039;antica difficoltà, mossa contro coloro che, come lui, dicevano le <lb></lb>meseraiche essere conduttrici del chilo, mentre si vedon sempre rosseggiare <lb></lb>di sangue? </s>

<s>Forse chi sa che non avesse pronta la risposta del Cesalpino. </s>

<s><lb></lb>Sarebbe allora anche questo da annoverar fra&#039;molti silenziosi incontri di <lb></lb>que&#039;due uomini, dall&#039;altra parte così diversi, non solo per età e per patria, <lb></lb>ma per educazione d&#039;ingegno; incontri, che darebbero, a chi non avesse <lb></lb>fretta come noi, soggetto importantissimo a un altro nuovo capitolo di storia. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Ma perchè siam consigliati di proseguire addiritto il nostro cammino, <lb></lb>riprendiamo le mosse da quell&#039;Harveio, che abbiamo ora lasciato. </s>

<s>Il celebre <lb></lb>e valoroso Fisiologo ripeteva, nella prima metà del secolo XVII, intorno al­<lb></lb>l&#039;economia della nutrizione, le dottrine stesse insegnate dall&#039;antico Galeno: <lb></lb>le vene meseraiche, come le radici degli alberi dalla terra, suggono il chilo <lb></lb>dagl&#039;intestini, e confluendo tutte insieme alla Porta, lo riversan nel Fegato, <lb></lb>che lo rende colla sua virtù perfetto alimento. </s></p><pb xlink:href="020/01/1343.jpg" pagenum="218"></pb><p type="main">

<s>Tanto aveva il Fegato, con la sua mole superiore a quella di molti <lb></lb>altri visceri, con la sua sede che è fra le più cospicue nell&#039;interno del bene <lb></lb>architettato edifizio, col suo colore e col suo tessuto, a cui par che il san­<lb></lb>gue stesso abbia prestato le fila, sedotta la fantasia degli anatomici, per di <lb></lb>più commossa dalle epopee galeniche, ricantate da tanti; che l&#039;Asellio stesso, <lb></lb>come se ce le avesse vedute entrare, tenne per cosa certa che le lattee, dopo <lb></lb>aver confluito insieme nella Ghiandola pancreatica, s&#039;inserissero nel Fegato, <lb></lb>per riversare in lui il chilo, come frumento nel prontuario di una città ben <lb></lb>munita. </s></p><p type="main">

<s>Nè dopo parecchi anni ancora di esercitazioni e di studii, aveva il Fe­<lb></lb>gato lasciato sugli anatomici o rimesso punto della sua affascinatrice potenza. </s>

<s><lb></lb>Fra&#039;molti, basti a noi citare due esempii, che possono valere per tutti gli <lb></lb>altri, e sia primo quello di Giovanni Veslingio, nel <emph type="italics"></emph>Sintagma anatomico<emph.end type="italics"></emph.end><lb></lb>pubblicato la prima volta in Padova nel 1641, e poi in Amsterdam nel 1666 <lb></lb>coi commenti di Gerardo Blasio. </s>

<s>Trattando l&#039;Autore nel citato <emph type="italics"></emph>Syntagma<emph.end type="italics"></emph.end><lb></lb>particolarmente del Pancreas e del suo ufficio, “ suscipit, egli dice, chilum, <lb></lb>susceptumque iecori subministrat, non per venas ullas a Porta descendentes <lb></lb>aut arterias, sed per singulares ductus, quos ob similitudinem aliquam, tum <lb></lb>conformationis, tum distributionis, venas Asellius nuncupavit, easque lac­<lb></lb>teas.... Longa autem sunt et tereta vascula.... a Pancreate sursum circa <lb></lb>descendentis Venae portae truncum ad iecur, deorsum vero ad intestina mi­<lb></lb>nutissimis propaginibus dispersa.... Colligere easdem in communem aliquem <lb></lb>truncum, ob latitudinem Pancreatis insignem, divino Conditori non placuit ” <lb></lb>(Amstelodami 1666, pag. </s>

<s>56). </s></p><p type="main">

<s>L&#039;altro esempio di coloro che, ingannati dalle nuove rivelazioni del Pan­<lb></lb>creas, e sedotti dall&#039;ossequio antico al principato del Fegato, ripeterono e <lb></lb>confermarono le dottrine dell&#039;Asellio, ci è porto dal famoso Riolano salu­<lb></lb>tato principe degli Anatomici, a que&#039;tempi, in Francia, e per tutto il mondo. </s>

<s><lb></lb>Nel suo <emph type="italics"></emph>Enchiridio,<emph.end type="italics"></emph.end> dove tutti apprendevano in compendio la scienza ana­<lb></lb>tomica dettata per gli studiosi dal nuovo Galeno, trattando, al cap. </s>

<s>XVIII <lb></lb>del II libro, <emph type="italics"></emph>De mesenterio,<emph.end type="italics"></emph.end> così profferiva l&#039;Autore la sua sentenza: “ Quar­<lb></lb>tum genus vasorum, quae Venae lacteae dicuntur ab Asellio inventore, adiec­<lb></lb>tum fuit, de quo non est amplius dubitandum, cum sit iam vulgatum et ac­<lb></lb>ceptum. </s>

<s>Hoc unum multos anxios tenet distributionis diversitas. </s>

<s>Nam in <lb></lb>animali vivente, saturo et aperto, notantur quidem istae venae lacteae spar­<lb></lb>sae per mesenterium, sed aliae ad Pancreas progrediuntur, aliae ad Hepar, <lb></lb>aliae ad truncum. </s>

<s>Cavae derivantur, nullae ad lienem. </s>

<s>Nec, more venarum, <lb></lb>Portae in unum caudicem coeunt: videntur potius radicem et fundamentum <lb></lb>habere in Pancreate, et inde hinc et illinc dispergi ” (Lugduni Batavo­<lb></lb>rum 1649, pag. </s>

<s>109). </s></p><p type="main">

<s>Aveva di poco l&#039;Oracolo parigino profferita questa sentenza, quand&#039;esce <lb></lb>fuori un giovane sconosciuto, venuto di Dieppe a Parigi, a sentenziare au­<lb></lb>dacemente contro il Maestro: “ non ad Hepar, non ad venas Portae, non <lb></lb>ad cavam prope emulgentes derivari chylum, sed ab intestinis ad <emph type="italics"></emph>Recepta-<emph.end type="italics"></emph.end><pb xlink:href="020/01/1344.jpg" pagenum="219"></pb><emph type="italics"></emph>culum<emph.end type="italics"></emph.end> quoddam ” e soggiungeva con giuramento che chiunque, sezionando <lb></lb>con arte, si mettesse diligentemente a cercare, troverebbe che così era, come <lb></lb>egli asseverava di fatto. </s></p><p type="main">

<s>Rimase il Riolano di tanta giovanile baldanza, e brontolando andava ag­<lb></lb>girandosi per l&#039;aula magna dell&#039;Accademia, e diceva non esser quelle sco­<lb></lb>perte da giovani, e che in ogni modo conveniva, com&#039;avea fatto del suo ca­<lb></lb>nale il Virsungo, interrogare i seniori della scuola parigina, e un principiante <lb></lb>inesperto, com&#039;era quel Giovanni Pecqueto, docilmente accettarne l&#039;infalli­<lb></lb>bile responso. </s>

<s>“ Non ita Pecquetus, nec anatomicorum Principi persolvit <lb></lb>tributum: haec belli causa, haec ratio in lacteas thoracicas Riolanum arma­<lb></lb>vit ” (Brevis destructio responsionis Riolani, inter Opera Pecqueti, Pari­<lb></lb>siis 1654, pag. </s>

<s>197). </s></p><p type="main">

<s>Ma la navicella del pellegrino ingegno ha oramai spiegate le vele, e le <lb></lb>celesti aure la sospingono innanzi così fortemente veloce, che la remora del <lb></lb>Riolano è non men ridicolmente impotente di quella del favoloso pesciolino <lb></lb>di mare. </s>

<s>Il felice corso di quella nave nel profondo pelago della vita, e le <lb></lb>lunghe durate fatiche e il conquistato premio della scoperta son raccontati <lb></lb>così dallo stesso Nauclero, appena ritornato trionfale dal suo viaggio: </s></p><p type="main">

<s>“ Post acquisitam ante annos aliquot, ex cadaverum sectione, mutam <lb></lb>alioqui frigidamque sapientiam, placuit et ex vigenti vivarum animantium <lb></lb>harmonia veram sapientiam exprimere. </s>

<s>Et quia hae ab illis solo propemo­<lb></lb>dum differunt motu, cuius in corde praecipua sedes, consilium fuit eundem, <lb></lb>expedito involucris, avulsoque corde, manifestius contemplari. </s>

<s>” </s></p><p type="main">

<s>“ Ergo diffissa viventis, quae media est, alvo molossi, inchoo extispi­<lb></lb>cium. </s>

<s>Nec mora: cor, rescissis quibus reliquo adhaeret corpori, vasculorum <lb></lb>retinaculis, avello. </s>

<s>Tum exhausta, quae statim restagnaverat, spectantisque <lb></lb>confuderat oblutus, copia cruoris, albicantem subinde lactei liquoris, nec <lb></lb>certe parum fluidi scaturiginem intra Venae cavae fistulam, circa dextri se­<lb></lb>dem ventriculi, miror effluere. </s>

<s>” </s></p><p type="main">

<s>“ ..... Venam cavam a Diaphragmate ad iugulum aperio: apparuit <lb></lb>illico nivei humoris, omni tum cruoris expurgatum mixtura, fluentulum. </s>

<s>A <lb></lb>ramis usque subclaviis ad pericardium, intra Venam, subsidebat candidus <lb></lb>apprime liquor, et effuso per Mesenterium chylo simillimus, sicut inter utrum­<lb></lb>que collatos invicem et nitor et odor et sapor et consistentia nullum inesse <lb></lb>discrimen ostenderint. </s>

<s>” </s></p><p type="main">

<s>“ Extinctus animalis exenterati motus, stiterat fluorem, nec, qua lac­<lb></lb>teus erupisset, aut quo scaturiisset ab ubere latex, sinebat quies interno­<lb></lb>scere. </s>

<s>Tamen, gliscente reconditioris doctrinae desiderio, thymum comprimo, <lb></lb>collum stringo, ipsos etiam anteriorum partium artus, si qua forte albicantis <lb></lb>substantiae residuum ex vasculosis stillaret anfractibus, sollicito. </s>

<s>Sed inde <lb></lb>sanguinis tantum effluxerunt aliquot guttulae, nihil lacteum in Cavam ir­<lb></lb>rupit. </s>

<s>” </s></p><p type="main">

<s>“ Ergo, quod unicum industriae meae superfuit, Mesenterii lacteas, quid <lb></lb>hanc sibi iuris in rem obtinerent, pondere digiti gravitantis, adigo com-<pb xlink:href="020/01/1345.jpg" pagenum="220"></pb>monstrare. </s>

<s>Parent urgenti, nam e ramis subclaviis tanta succi, quem obser­<lb></lb>vabam, copia profunditur, ut per eiusdem esse lacteas originem agnoverim, <lb></lb>et a chylo diversum putare duxerim insanissimum. </s>

<s>” </s></p><p type="main">

<s>“ Ne tamen quid inexploratum relinqueretur, cum e superioribus ra­<lb></lb>morum eiusmodi partibus praeceps rueret, has in longum, una cum caeta­<lb></lb>ris colli et artuum anteriorum venis, diffindo, compressaque mox inferioris <lb></lb>alvi capacitate, et exerto in apertos iuxta claviculas alveos obtutu, ecce com­<lb></lb>pletorio mei voti exitu, indubitato iam tum in superiores ramorum subcla­<lb></lb>viorum partes utrinque chylus redundavit. </s>

<s>” </s></p><p type="main">

<s>“ <foreign lang="grc">Εχβολ<gap></gap>ς</foreign> noto pronas oculis et spectantibus manifestas scaturigines, <lb></lb>foraminula scilicet, paulo infra iugulares venas et axillarum cataractas, nu­<lb></lb>merosis ostiolis hiscentla. </s>

<s>Sed et iugularium illic valvulas observo ruituro <lb></lb>in cordis gurgitem chylo faciles ascensu penitus interdicere. </s>

<s>” </s></p><p type="main">

<s>“ Verum, qua tandem via, quibus meatibus eo chylus devolveretur, non <lb></lb>licuit, ob exhaustum animalis iamdudum mactati mesenterium, evanescen­<lb></lb>tibus plane lacteis cum expressi liquoris effluxu deprehendere. </s>

<s>” </s></p><p type="main">

<s>“ ..... Suffecissem illico, in demortui locum, quem mihi tum ex im­<lb></lb>proviso fors canem obtulerat..... Ergo illaqueatum canem .... subigo, et <lb></lb>cum ieiunii moras largissima dape compensassem, demum, hora circiter a <lb></lb>saturitate quarta, extorum accingimur examini. </s>

<s>Summa consilii fuit.... toto <lb></lb>studio in thoracem incumbere.... Observo surculos Cavae: omnes livebant. </s>

<s><lb></lb>Nullus ascendentium arteriarum ramus ad lactea foramina, quae recens in­<lb></lb>veneram, emicabat. </s>

<s>Sexti paris sequor propagines, quarum hae diaphragmatis <lb></lb>obice sistebantur, illas imus venter absorbebat. </s>

<s>Tandem exerto in suprema <lb></lb>vertebrarum dorsi latera contuitu, nescio quid albedinis, instar chylosi cana­<lb></lb>liculi, oculos meos moratur. </s>

<s>Sinuoso aliquantisper et ad spinam impacto ser­<lb></lb>pebat volumine. </s>

<s>Dubium an, ex similitudine, nervus, an foret vasculum, <lb></lb>quale sollicitus vestigabam. </s>

<s>Ergo subducto paulo infra claviculas vinculo, cum <lb></lb>a ligatura sursum flaccesceret, superstite deorsum turgentis alveoli tumore, <lb></lb>dubium meum penitus enervavit. </s>

<s>” </s></p><p type="main">

<s>“ ..... Num chyli ductus quispiam aut ad caput exiliret, aut ad artus <lb></lb>derivaretur anteriores, eorumdem incumbit scrutandum hortamine. </s>

<s>Sed cum <lb></lb>amputatum caput, truncatosque artus nihil lactis, ne compressu quidem in­<lb></lb>ferioris alvi sequeretur, ex illa quae se receperat intra Cavam chylosae sub­<lb></lb>stantiae copia, argumentor neque ad caput, neque ad anteriores artus diver­<lb></lb>tere chylum, sed totum in ramos subclavios confluere. </s>

<s>” </s></p><p type="main">

<s>“ ..... Redeo ad vincula..... Quarta vertebra coeuntes sustentabat, <lb></lb>reliquum ad decimam spatium bifidos anfractibus disiunxerat, fluvialium <lb></lb>more, tortuosis. </s>

<s>Pari tumore diffluebant transversis non raro incilibus, ve­<lb></lb>lut ad opem mutuam, oblique colligati. </s>

<s>Confuso demum vado, rursusque <lb></lb>distracto flumine, in ampullatos alveos sensim excrescentes, ad diaphragmatis <lb></lb>centrum intumuerant, non leve vicinorum, unde per thoracem in subclavias <lb></lb>venas immittitur chylus, fontium argumentum. </s>

<s>” </s></p><p type="main">

<s>“ Ergo, cum et ipsum diaphragma, ut extremo quod sperabam desine-<pb xlink:href="020/01/1346.jpg" pagenum="221"></pb>ret obesse scrutinio, satagerem a lacteis vasis seiungere, lacerata forte sini­<lb></lb>strorsum, ad duodecimam circiter dorsi vertebram, ampulla, cuius est apprime <lb></lb>tenuis membranula, restagnantem demiratus lactis effusi copiam, suspicor <lb></lb>non exiguum illic eiusdem liquoris occuli <emph type="italics"></emph>Receptaculum.<emph.end type="italics"></emph.end> Sed manus im­<lb></lb>prudentia stitit laborem et reliquum ad resegmina cadaver amandavit .... ” </s></p><p type="main">

<s>“ Commodum ad cibum canis, quem pransum opipare, post horas ali­<lb></lb>quot, in anatomicum edo Theatrum..... Lacteos mesenterii rivulos quaqua­<lb></lb>versum exploravi, nullus ad iecur porrigi inventus est. </s>

<s>Portam diffidi, sple­<lb></lb>nicum aperui meatum, nec ipsi mesenterio peperci .... et omni ex parte <lb></lb>cruor effusus est, nulla chyli scaturigo male creditam viam dealbavit. </s>

<s>” </s></p><p type="main">

<s>“ ..... Tantis testimoniis enucleata veritate, <emph type="italics"></emph>non ad hepar videlicet <lb></lb>chylum, non ad venas Portae, non ad Cavam prope emulgentes derivari,<emph.end type="italics"></emph.end><lb></lb>lustrata viscera quarendus alibi chylus .... praecepit. </s>

<s>Tum frustatim ad cau­<lb></lb>telam revulso diaphragmate, licuit residuum, qui sub eius apophysibus de­<lb></lb>litescebat, Aortae truncum et nostras in propatulo lacteas contueri. </s>

<s>” </s></p><p type="main">

<s>“ Hac sinistrorsum pariter sub Aorta .... ampullescentem alveum expli­<lb></lb>cabant.... Illic, res mira! gravitanti digito facile stratum seipsum ultro com­<lb></lb>planabat, arguente subsultim mollitie delitescentem sub mesenterico centro, <lb></lb>non exiguae capacitatis chyli vesicam. </s>

<s>Demum celantia, parcente scalpello, <lb></lb>dissipo involucra.... Sic tandem patuit optatissimum reconditi chyli penus, <lb></lb>et tantis laboribus quaesitum <emph type="italics"></emph>Receptaculum. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb>… </s></p><p type="main">

<s>“ Ita, mi lector, habes exactam Lactearum venarum historiam. </s>

<s>Intra <lb></lb>triplicis dissectionis spatium assiduum semel trium annorum (dal 1648 <lb></lb>al 1651, anno, sui principii del quale fu per la prima volta pubblicata in <lb></lb>Parigi questa stessa storia) laborem coarctavi, quia tantilli temporis dispen­<lb></lb>dio potes ab erroribus desciscere. </s>

<s>Trinum tibi ut expono canicidium dabit, <lb></lb>quod mihi centena plusquam vivarum animantium exenteratione, vix tandem <lb></lb>concessum est. </s>

<s>” (Experimenta nova anat., Parisiis 1654, pag. </s>

<s>4-17). </s></p><p type="main">

<s>L&#039;anno dopo ch&#039;era stata in Parigi divulgata la nuova storia, comparve <lb></lb>in Leyda, dalla tipografia di Francesco Hack, un libretto di 36 pagine in 4°, <lb></lb>intitolato <emph type="italics"></emph>Novus ductus chyliferus, nunc primum delineatus.<emph.end type="italics"></emph.end> L&#039;Autore era <lb></lb>Giovanni Van-Horne che, rivolgendosi ai Provveditori della leidese Accade­<lb></lb>mia, diceva di aver, per quella sua scoperta, tratto dagli stessi penetrali della <lb></lb>natura <emph type="italics"></emph>novam et inauditam doctrinam.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>È il trattatello, dopo una breve prefazione, diviso in due parti: nella <lb></lb>prima, storica e anatomica, e nella seconda, dottrinale e fisiologica. </s>

<s>Narra, <lb></lb>quanto alla storia, come ne&#039;primi mesi dell&#039;anno 1652 gli occorresse a caso <lb></lb>di sezionare un cane, e come, sollevando verso il rene sinistro, sopra le ap­<lb></lb>pendici del diaframma, la duplicatura del peritoneo, che separa i reni, la <lb></lb>vena cava e l&#039;aorta dalle altre viscere dell&#039;addome; gli venissero veduti al­<lb></lb>cuni tenuissimi vasi membranosi, dai quali rotti fluiva il chilo. </s>

<s>“ Haec prima <lb></lb>fuit novi inventi occasio ” imperocchè nessuno aveva trovato così fatti vasi <lb></lb>bianchi altro che nel mesenterio. </s>

<s>— Ma che sieno davvero vene lattee? </s>

<s>— <pb xlink:href="020/01/1347.jpg" pagenum="222"></pb>cominciò a dubitare il Van-Horne, e se ne assicurò dal veder che comuni­<lb></lb>cavano direttamente col Pancreas leggermente premuto. </s>

<s>Gli venne allora de­<lb></lb>siderio d&#039;investigar le segrete vie di quella comunicazione, e da principio <lb></lb>non gli riusciva trovarle. </s>

<s>“ Tandem audacior factus, ipsum quoque dia­<lb></lb>phragma discindere aggressus sum, sopra quod, intra thoracis cavitatem, <lb></lb>apparuit <emph type="italics"></emph>vas aliquod lacte turgidum ”<emph.end type="italics"></emph.end> (pag. </s>

<s>14). </s></p><p type="main">

<s>Strinto questo vaso per via di un filo, permise l&#039;intumescenza di po­<lb></lb>terne più facilmente seguitar, ne&#039;canali inferiori, il decorso, e trovò che <lb></lb>questo terminava negli intestini. </s>

<s>Ciò valse a confermarlo meglio nella prima <lb></lb>opinione che appartenessero veramente que&#039;vasi alle vene lattee falsamente <lb></lb>credute dall&#039;Asellio convenire nel Pancreas, e di li, senza progredire più <lb></lb>oltre, andare al Fegato, da cui invece escono, per diramarsi in varii modì. </s>

<s><lb></lb>Di alcuni di questi rami seguendo diligentemente il progresso, trovò che <lb></lb>dopo molti giri andavano a riunirsi in un tronco, della grandezza di una <lb></lb>penna da scrivere, il quale, trapassato sopra le vertebre lombari il diaframma, <lb></lb>penetra nella cavità del torace, e lì, nello spazio che resta di mezzo fra la <lb></lb>colonna vertebrale e l&#039;Aorta, incomincia a salire. </s>

<s>“ Ascendit itaque ductus <lb></lb>hic, uti dictum est, per thoracis longitudinem, sensim tenuior evadens, atque <lb></lb>ubi cor superavit, quo loco alius observatus fuit ramus versus cor tendens, <lb></lb>non amplius aortae accumbit, sed oesophago incumbens, ad axillares usque <lb></lb>ramos pertingit, quantum primo intuitu licet cognoscere. </s>

<s>Sed vero diligen­<lb></lb>tius inquirenti manifestum evadet ad iugularem internam sinistri lateris de­<lb></lb>ferri, praecipuo suo ramo inseri sub thymo glandula, in illam Venae cavae <lb></lb>partem, quae claviculis subiaciens, in homine ab illis subclavia denomina­<lb></lb>tur ” (pag. </s>

<s>16, 17). </s></p><p type="main">

<s>Nella seconda parte del trattatello, intitolata <emph type="italics"></emph>Ductus officium,<emph.end type="italics"></emph.end> dimostra <lb></lb>essere un tale ufficio quello di condurre il chilo a riversarsi nel sangue. </s>

<s>Di <lb></lb>qui, presa occasione di notar l&#039;errore, in ch&#039;erano caduti gli antichi, ne con­<lb></lb>clude non solo non andare al Fegato nessuna porzione dell&#039;alimento, ma <lb></lb>esser questo affatto impossibile, per trovar d&#039;ogni parte d&#039;andare al Fegato, <lb></lb>il chilo chiuse le vie. </s></p><p type="main">

<s>Era questa la nuova, e inaudita dottrina <emph type="italics"></emph>ex ipsis Naturae penetrali­<lb></lb>bus eruta,<emph.end type="italics"></emph.end> che veniva dal Van-Horne a&#039;suoi Accademici, solennemente, per <lb></lb>la prima volta, annunziata, e si credeva che dovesse come a loro così a tutto <lb></lb>il mondo veramente apparir cosa nuova e inaudita, quando giunse a Enrico <lb></lb>Born, professore di Leyda, una lettera da Parigi, nella quale si diceva ma­<lb></lb>ravigliarsi che il Van-Horne avesse data per nuova la scoperta del dutto <lb></lb>chilifero, che da due anni in Francia si sapeva da tutti: si consigliava <lb></lb>l&#039;Horne stesso a fare la sua pubblica ritrattazione, se non voleva essere in­<lb></lb>criminato di plagio, e si concludeva al Born stesso raccomandandogli “ ut <lb></lb>virum doctissimum caute officii sui admoneret ” (In Pecqueti Experim. </s>

<s><lb></lb>anat. </s>

<s>cit., pag. </s>

<s>180). </s></p><p type="main">

<s>L&#039;Horne, uomo retto, non volle entrare in questioni, e dall&#039;altra parte <lb></lb>davan vinta al Pecquet la causa del primato i numerì, colla irresistibile <pb xlink:href="020/01/1348.jpg" pagenum="223"></pb>forza della loro fredda eloquenza. </s>

<s>Nel § 37 del <emph type="italics"></emph>Microcosmo<emph.end type="italics"></emph.end> infatti, senza <lb></lb>fare il minimo accenno agli inventori e alle loro controversie, dice esser uf­<lb></lb>ficio delle vene lattee “ ut chyli laudabilior portio per illas quidem defera­<lb></lb>tur, porro in <emph type="italics"></emph>Receptaculum,<emph.end type="italics"></emph.end> et hinc ascendendo, per ductum chyliferum ” <lb></lb>(Lugd. </s>

<s>Batav. </s>

<s>1655, pag. </s>

<s>54). </s></p><p type="main">

<s>Gli Olandesi però stettero fermi in riconoscer per loro premostratore <lb></lb>del Canale toracico il Professore leidese, e fu tra quelli uno de&#039;più zelanti <lb></lb>quel Gerardo Blasio, che facendo notare nel commentario al Veslingio come <lb></lb>il chilo non va al pancreas, nè al fegato, secondo diceva il suo Autore con <lb></lb>l&#039;Asellio, ma a un certo ricettacolo nuovamente scoperto; “ Hac de re, sog­<lb></lb>giunge, consule primum eius, hisce in oris, inventorem in canibus, Johannem <lb></lb>Van-Horne, anatomicum leidensem exercitatissimum ” (Editio cit., pag. </s>

<s>53). </s></p><p type="main">

<s>Fra gli estranei varii furono del caso singolare i giudizii, ma richiama <lb></lb>a sè particolarmente la nostra attenzione ciò che scrive in proposito, nel suo <lb></lb>primo libro <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end> il padre Onorato Fabry. </s>

<s>“ Forte alter, egli dice del <lb></lb>Pecquet e del Van-Horns, ab altero accepit, forte uterque legitimus inven­<lb></lb>tor, sed hanc litem non definio. </s>

<s>Utut sit, modica locorum distantia, cursores <lb></lb>publici, qui singulis hebdomadis ultro citroque commeant, librariorum com­<lb></lb>mercium, novi inventi publica fama, aemula eiusdem artis professorum cu­<lb></lb>riositas, et alias huiusmodi aliquam plagii suspicionem movere possent, sed <lb></lb>neminem iudico ” (Parisiis 1666, pag. </s>

<s>216). </s></p><p type="main">

<s>Par che sia in queste parole espressa una conoscenza delle cose del <lb></lb>mondo, che si direbbe troppo maliziosa, ma chi penetrasse in quel cervel­<lb></lb>laccio, anche più addentro, vi troverebbe ascosto un senso di dispetto, per <lb></lb>aver trovato un altro, ch&#039;era entrato col Pecquet a roder quell&#039;osso. </s>

<s>Altri­<lb></lb>menti il padre Onorato si sarebbe aperto, coi denti e colla lingua, un varco <lb></lb>da entrar là, dove s&#039;era il Van-Horne fatto largo, esercitandovi la mano ana­<lb></lb>tomica e il ferro. </s>

<s>Danno saldo fondamento a sospettar così alcuni altri fatti, <lb></lb>fra&#039;quali, per non uscir dal presente soggetto, ch&#039;è intorno a cose anato­<lb></lb>miche e fisiologiche, basti addur questi due. </s></p><p type="main">

<s>Nella proposizione II del citato libro <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end> dove spiega la circo­<lb></lb>lazion del sangue, dop&#039;aver commemorato l&#039;Harvey e il Cartesio e il Pecquet, <lb></lb>che ne illustrarono la scoperta, “ Ego verissimam esse, prosegue, semper <lb></lb>putavi, eamque, antequam libellus Harvei prodiret, publice docui, iam ab <lb></lb>anno 1638, qui certe longo post tempore in meas manus venit, quod ad <lb></lb>ostentationem non dico ” (ibid., pag. </s>

<s>204). Ma, con buona pace, è questa <lb></lb>una vera ostentazione o di gran malizia o di grande ignoranza, essendochè <lb></lb>nel 1638 il libro dell&#039;Harvey era, da ben dieci anni, per le mani di tutti. </s></p><p type="main">

<s>Nella proposizione XVII spiega la secrezione del sangue ne&#039;reni, e dopo <lb></lb>aver ripetute, intorno alla struttura e alle funzioni di quelle glandule, le <lb></lb>nuove cose scoperte, e infin dal 1662 divulgate nella esercitazione anato­<lb></lb>mica <emph type="italics"></emph>De structura et usu renium<emph.end type="italics"></emph.end> da Lorenzo Bellini, “ Haec iam, dice il <lb></lb>Fabry, a multis annis scripseram, cum forte incidi in elegantissum opuscu­<lb></lb>lum a Laurentio Bellino florentino in publicam lucem datum, dignum sane <pb xlink:href="020/01/1349.jpg" pagenum="224"></pb>quod a Philosophis et Medicis legatur, in quo eadem fere quae supra repe­<lb></lb>ries ” (ibid., pag. </s>

<s>237). </s></p><p type="main">

<s>E giacchè questo Gesuita francese, dimorante a Roma, è quasi fatto da <lb></lb>alcuni Accademico del Cimento, e in ogni modo è come attore entrato nella <lb></lb>altre parti della nostra Storia, diremo qui tutto insieme quel poco, che anche <lb></lb>per questa parte lo riguarda, imitando colui, che fa tutt&#039;in una volta i conti <lb></lb>di saldo con certi creditori, o troppo importuni, o troppo esigenti. </s></p><p type="main">

<s>Il trattato <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end> che abbiamo dianzi citato, è il secondo dopo un <lb></lb>altro, che ha per soggetto le piante e la generazione degli animali. </s>

<s>I nostri <lb></lb>Lettori hanno oramai, per questi e per gli altri esempi da noi recati ne&#039;pre­<lb></lb>cedenti due Tomi, riconosciuta l&#039;indole del Gesuita straniero corrispondente <lb></lb>coi nostri Accademici fiorentini, la quale era di sfiorare ogni loro scoperta, <lb></lb>per adornarsene, e apparire in pubblico il primo. </s>

<s>Aveva da Michelangiolo <lb></lb>Ricci inteso come il Borelli attendeva in Pisa a instituire la sua nuova Fi­<lb></lb>losofia degli animali e delle piante, e come il principe Leopoldo ve lo ecci­<lb></lb>tava con grande ardore, ben conoscendo quanto, da un tant&#039;uomo e in sì <lb></lb>importante e nuovo soggetto, sarebbe per venir gloria agli studii toscani, e <lb></lb>benefizio universale alla scienza. </s></p><p type="main">

<s>Il Fabry dunque, per prevenir l&#039;opera, colla facilità di chi, a volere sve­<lb></lb>lare i più reconditi misteri della Natura, non ha a far altro che consultare <lb></lb>il proprio cervello, dette mano a scrivere i due trattati, e a farli da Fran­<lb></lb>cesco Muguet frettolosamente imprimere in Parigi. </s>

<s>Il Ricci dava a Firenze <lb></lb>notizie della stampa, e come uno de&#039;libri del II trattato avesse per soggetto <lb></lb>particolare il moto degli animali. </s>

<s>Si può immaginar quanto ciò dovesse fru­<lb></lb>gare la curiosità del Borelli, per soddisfare alla quale il principe Leopoldo, <lb></lb>anch&#039;egli divenuto di ciò curioso, scrisse al Bigot a Parigi, il dì 18 Giu­<lb></lb>gno 1666, che desiderando di averlo, gli mandasse il libro, colà stampato, <lb></lb>del p. </s>

<s>Fabry (MSS. Cim., T. XXIII, c. </s>

<s>133). Ma poco dopo venne a offrir­<lb></lb>glielo in dono lo stesso Autore, di che il Principe lo ringraziò, per lettera <lb></lb>del dì 19 Ottobre di quel medesimo anno (ivi, c. </s>

<s>141), e data una scorsa, <lb></lb>spedì al Borelli a Pisa la copia. </s>

<s>Il Borelli, il dì 19 Dicembre, così rispon­<lb></lb>deva: “ Subito che ricevetti l&#039;onore fattomi da V. A. del libro del p. </s>

<s>Fabri, <lb></lb>mi posi con grandissima avidità a leggerlo, e primieramente vidi tutto quello, <lb></lb>che egli scrive intorno ai movimenti degli animali, dove non vi trovai altre <lb></lb>cose che le comuni e dozzinali, tolto che alcune sue osservazioni sopra lo <lb></lb>starnuto e la tosse ” (ivi, T. XVIII, c. </s>

<s>368). Avremo dato dunque al Fabry, <lb></lb>in questo saldo finale, quella parte del merito che gli compete, salutandolo <lb></lb>Fisiologo dello starnuto e della tosse, di che, non richiedendovisi tanta ana­<lb></lb>tomia, si fece più facilmente credere autore, che non del Canale toracico, da <lb></lb>lui perciò lasciato alle libere contenzioni fra il Pecquet e il Van-Horne. </s></p><p type="main">

<s>Come i fatti decidevano dunque a favore del Pecquet, primo a intra­<lb></lb>prendere le esercitazioni anatomiche, e primo a pubblicare la scoperta indi <lb></lb>seguitane; così, a favore del Pecquet, ha deciso oramai il giudizio dei po­<lb></lb>steri. </s>

<s>Ma sarebbe una calunnia l&#039;accusare il. </s>

<s>Van-Horne di plagio, come fu <pb xlink:href="020/01/1350.jpg" pagenum="225"></pb>una tirannia quella del Pecquet, che lo voleva costringere a una ritratta­<lb></lb>zione. </s>

<s>Chi legge la scoperta del Nuovo dutto chilifero, e la confronta con <lb></lb>quella descritta negli Esperimenti nuovi anatomici, sente che ambedue le <lb></lb>storie sono ugualmente originali, e i loro incontri inconsapevoli, e no studiati. </s></p><p type="main">

<s>Che poi l&#039;uno Anatomico non si sia vestito dell&#039;abito dell&#039;altro, si con­<lb></lb>clude dal veder che ognuno porta quello, ch&#039;è tagliato bene al suo dosso. </s>

<s><lb></lb>Il Pecquet è più giovane e più poeta; il Van-Horne è più positivo. </s>

<s>Chi <lb></lb>getta lo sguardo, ora sull&#039;una ora sull&#039;altra delle due tavole, dove ciascuno <lb></lb>Autore esibisce in disegno le cose vedute por l&#039;aperte viscere dell&#039;animale, <lb></lb>non ha, a persuadersene, bisogno d&#039;altre parole. </s>

<s>Nel Pecquet, per esempio, <lb></lb>il Canal toracico è doppio, e i due rami comunicano, lungo il loro decorso, <lb></lb>per frequenti anastomosi, finchè uno non va a terminare nella giugulare de­<lb></lb>stra, e l&#039;altro nella sinistra. </s>

<s>Nel Van-Horne il dutto chilifero è semplice e <lb></lb>schietto, e sbocca nella giugulare sinistra. </s></p><p type="main">

<s>I fautori del Pecquet dissero che sezionando s&#039;era incontrato a caso a <lb></lb>veder nel cane quell&#039;anomalia, e ciò si potrebbe credere se si trattasse di <lb></lb>un esempio solo. </s>

<s>Ma perchè il Pecquet ebbe a trucidare un gran numero <lb></lb>di cani, è egli credibile ostentassero tutti quel fatto anomalo, che il Masca­<lb></lb>gni quasi si doleva non essergli mai toccato a vedere in tanti cadaveri se­<lb></lb>zionati di uomini e di bruti? </s></p><p type="main">

<s>Più ragionevole perciò è il dire che, dove sfugge al Pecquet la vista, <lb></lb>soccorre pronta a supplirvi la fantasia, ond&#039;il Van-Horne, che seppe aste­<lb></lb>nersi da quel vizio, riesce tanto più preciso e più vero. </s>

<s>Si direbbe che giovò <lb></lb>a una tal precisione l&#039;essere prevenuto, se non si riconoscesse piuttosto come <lb></lb>il portato dell&#039;esercizio, e se non ci persuadesse l&#039;Anatomico olandese, col <lb></lb>suo discorso, che così a lui come al Pecquet sufficiente preparazione era la <lb></lb>scoperta dell&#039;Asellio. </s></p><p type="main">

<s>Ebbe di qui origine quel sentimento di riconoscenza e di ammirazione, <lb></lb>che spira verso il nostro Italiano dalle pagine de&#039;due celebri Notomisti stra­<lb></lb>nieri, i quali se lo proposero per imitabile esempio di scienza non solo, ma <lb></lb>di morale. </s>

<s>Il Pecquet, dop&#039;avere annoverate le varie specie di animali, nei <lb></lb>quali tutti ritrovò il ricettacolo del chilo, “ homines non dixi, soggiunge <lb></lb>tosto, quia thoanteos ritus execror, mitioribus sacris innutritus.... Fugienda <lb></lb>est medicina, quam docet crudelitas, et abominanda sapientia, quam parit <lb></lb>homicidium ” (Experimenta nova anat. </s>

<s>cit., pag. </s>

<s>18). Si contenta perciò di <lb></lb>creder per analogia l&#039;esistenza del Canale toracico nell&#039;uomo, imitando anche <lb></lb>in questi particolari il modo di argomentar dell&#039;Asellio, benchè citi l&#039;autopsia <lb></lb>del Peiresc, e dalla notizia che soggiunge paresse esser consigliato ad imi­<lb></lb>tarla: “ Huic et interfuit Gassendus spectaculo, quod ipse pridem mihi, dum <lb></lb>Parisiis degeret, viva voce confirmavit ” (ibi). </s></p><p type="main">

<s>Il Van-Horne poi è dell&#039;Asellio imitatore anche più espresso. </s>

<s>“ At hic <lb></lb>non levis exoritur de homine dubitatio, num similiter in illo existat ” dice <lb></lb>dopo aver descritto il dutto chilifero di un cane. </s>

<s>” Equidem hac in parte <lb></lb>idem fatum experietur Ductus hic cum lacteis Asellii, quas cum in homine <pb xlink:href="020/01/1351.jpg" pagenum="226"></pb>non viderit idem, quia nefas existimavit vivum hominem incidere, necessa­<lb></lb>ria tamen sequela intulit fieri vix posse ut unus et solus homo iis desti­<lb></lb>tuatur, quae in tot brutis, ob similem necessitatem, reperiuntur ” (Novus <lb></lb>ductus delineatus cit, pag. </s>

<s>17, 18). Benchè, prosegue a dire l&#039;Autore, dan­<lb></lb>dosi l&#039;opportunità di avere a sezionare il cadavere di un uomo, morto di <lb></lb>morte subitanea nel levarsi da mensa, sarebbe men difficile osservar questo <lb></lb>Dutto, che le vene aselliane. </s>

<s>“ Et siquidem ullo unquam tempore eiusmodi <lb></lb>contigerit subiectum, quo omnis hac de re lis terminetur, nostrae non deeri­<lb></lb>mus diligentiae ” (ibi). </s></p><p type="main">

<s>Ma fu prevenuto dalla sollecitudine di Tommaso Bartholin, il quale, <lb></lb>avendo avuto da suo fratello Erasmo notizia della scoperta pecqueziana, e <lb></lb>datosi con Michele Lyser suo amicissimo a verificarla, s&#039;avvide che le con­<lb></lb>trazioni spasmodiche dell&#039;animale inciso vivo erano quelle, che facevano spa­<lb></lb>rire i vasi chiliferi più presto. </s>

<s>Pensava perciò che più opportuni all&#039;estispicio <lb></lb>dovessero essere gli animali strangolati, fra&#039;quali anche l&#039;uomo. </s>

<s>“ Meditato <lb></lb>consilio, scrisse nel trattato <emph type="italics"></emph>De lacteis thoracicis,<emph.end type="italics"></emph.end> pubblicato la prima volta <lb></lb>nel 1652, optatus eventus adspiravit, plurimisque in canibus factis experi­<lb></lb>mentis, humano tandem cadavere ex voto publico, serenissimo rege Fride­<lb></lb>rico III annuente, rotae alioquin et perpetuae cruci adiudicato, beneque pasto, <lb></lb>nacti in singula accuratius tam in publico theatro anatomico solemni de­<lb></lb>monstratione, quam privata opera, tanto maiori studio inquisivimus, quod <lb></lb>primi haec in homine tentaverimus ” (In Mangeti Bibliotheca anat. </s>

<s>cit., T. II, <lb></lb>pag. </s>

<s>660). Soggiunge che fu fatta l&#039;autopsia in due cadaveri, il primo di un <lb></lb>infanticida scorbutico e macilento, l&#039;altro di un ladro obeso, ben fatto e di <lb></lb>perfetta salute. </s></p><p type="main">

<s>Fu tratto il primo, narra più particolarmente lo stesso Bartholin nella <lb></lb>storia LIII della I Centuria, nel Teatro anatomico il dì 19 Febbraio del­<lb></lb>l&#039;anno 1652, dove essendosi prima diligentemente esaminate le altre viscere, <lb></lb>quanto al ricettacolo del chilo così dice: “ Reclinatis ad latus intestinis, vidi <lb></lb>novum receptaculum lacteum in suo situ, ipsis vertebris lumbaribus instra­<lb></lb>tum, inter Cavam descendentem et Aortam, in angulo fere, quem emulgens <lb></lb>dexter cum Cava efformat. </s>

<s>Candidum illud exque eo rami lactei ad mesen­<lb></lb>terium et pancreas eius derivari. </s>

<s>Ablatis prorsus intestinis, et Cava ad su­<lb></lb>periora reclinata, et Aorta quoque ad latus nonnihil diducta, apparuit re­<lb></lb>ceptaculum non unum, nec una cavitate praeditum, sicut in brutis, sed ex <lb></lb>glandulis duabus longioribus, invicem superpositis, variisque lacteis surculis <lb></lb>commeantibus ultro citroque ” (Historiarum anat. </s>

<s>rariorum Cent. </s>

<s>I, Amste­<lb></lb>lodami 1654, pag. </s>

<s>80). </s></p><p type="main">

<s>Fu dell&#039;altro cadavere fatta nel Teatro anatomico l&#039;autopsia il dì 24 Marzo <lb></lb>di quel medesimo anno, e aperta l&#039;ascellare, narra il Bartholin nell&#039;appresso <lb></lb>storia LIV, “ vidimus osculum eius unicum sub internae iugularis ingres­<lb></lb>sum, et valvulam circularem tenerrimam osculo praefixam, quae, pro vario <lb></lb>flatus impulsu, modo elevabatur, modo concidebat. </s>

<s>Reliqua, quae de lacteis <lb></lb>thoracicis primi in homine observavimus, operosius in <emph type="italics"></emph>Historia<emph.end type="italics"></emph.end> nostra <emph type="italics"></emph>ana-<emph.end type="italics"></emph.end><pb xlink:href="020/01/1352.jpg" pagenum="227"></pb><emph type="italics"></emph>tomica De lacteis thoracicis,<emph.end type="italics"></emph.end> publice diducta, lector curiosus inveniet ” (ibid., <lb></lb>pag. </s>

<s>85). </s></p><p type="main">

<s>Era tale il progresso fatto fino al 1652 nella scoperta de&#039;vasi chiliferi <lb></lb>dopo l&#039;Asellio, quando l&#039;anno appresso comparve in Vuesterat (Arosiae) un <lb></lb>libretto in 4° di Olao Rudbeck, intitolato <emph type="italics"></emph>Nova exercitatio anatomica, exhi­<lb></lb>bens ductus hepaticos aquosos.<emph.end type="italics"></emph.end> Nel cap. </s>

<s>III, dopo avere osservato che il <lb></lb>Veslingio e l&#039;Igmoro, persuasi della verità degli antichi insegnamenti gale­<lb></lb>nici intorno alle funzioni epaietiche, s&#039;erano ingannati descrivendo per vasi <lb></lb>chiliferi diretti al Fegato quelli che forse non erano altro che nervi; “ anxie­<lb></lb>tas haec, soggiunge l&#039;Autore, quae iamdiu multos tenuerat, discussa est anno <lb></lb>millesimo sexcentesimo quinquagesimo dum, nescio quo casu, vituli macta­<lb></lb>tionem inspicere contingebat.... ut aperto thorace motum cordis, post eva­<lb></lb>cuatum sanguinem, pernoscerem ” (In Mangeti Bibliotheca anat., cit., pag. </s>

<s>702). </s></p><p type="main">

<s>Vede fluire dalla vena giugulare un succo simile al siero del latte!... <lb></lb>Gli entra allora una gran curiosità di sapere d&#039;onde avesse origine, e com­<lb></lb>prato dal beccaio il vitello, e fattoselo portare a casa, trovò il canale che <lb></lb>conduceva quel siero, ma per essere lacerate l&#039;interiora, non ne potè rin­<lb></lb>tracciar la radice. </s></p><p type="main">

<s>Per quell&#039;anno, distratto da altre cure, non potè attendere a fare ana­<lb></lb>tomie. </s>

<s>L&#039;anno seguente preso un gatto, dopo cinque ore ch&#039;era stato pa­<lb></lb>sciuto, gli aprì il ventre, e perchè il chilo non si dissipasse così tosto, allacciò <lb></lb>le vene lattee in due luoghi: sopra il pancreas, e là dove il mesenterio si <lb></lb>collega col dorso. </s>

<s>Sezionato poi il torace, e tolto lo sterno, rivide quel me­<lb></lb>desimo canale, l&#039;anno avanti scoperto nel vitello, e lo allacciò in quel punto, <lb></lb>che risponde sotto il cuore. </s>

<s>Sciolti poi i due detti legami intorno alle lat­<lb></lb>tee, “ tunc chylus aliquibus ramulis, sive venulis contentus, Vesiculam quan­<lb></lb>dam inter diaphragma et renes, sub vena cava et arteria aorta sitam, patuit <lb></lb>unde tumescebat ” (ibid., pag. </s>

<s>703). </s></p><p type="main">

<s>Quella Vessica è il ricettacolo del Pecquet, da Olao così felicemente <lb></lb>scoperto. </s>

<s>Rimaneva a verificare se da quella stessa vessica e dal canale an­<lb></lb>nesso, che ricevono il chilo dal mesenterio, derivasse quell&#039;umor latteo ve­<lb></lb>duto la prima volta fluire dalle giugulari del macellato vitello. </s>

<s>Lega a tale <lb></lb>intento le vene ascellari insieme e le giugulari, e aperto il destro ventricolo <lb></lb>del cuore spreme col dito da que&#039;vasi sotto la legatura il sangue. </s>

<s>Rimasti <lb></lb>così esausti, scioglie il filo, con che il canale chilifero era stato allacciato, <lb></lb>“ et chylus citissime axillarem ad coniunctionem eius cum iugulari ingre­<lb></lb>diebatur ” (ibid.). Non rimaneva all&#039;ultimo da verificare se non se il chilo, <lb></lb>dalla giugulare, scendesse per la Cava addìritto nel cuore, ciò che fu dimo­<lb></lb>strato in quel medesimo istante, imperocchè vedevasi, attraverso all&#039;apertura, <lb></lb>il sinistro ventricolo rimaner sotto quel profluvio di chilo tutto imbiancato. <lb></lb></s>

<s>“ Tandem per Cavam superius resistentibus valvulis descendens, dextrum <lb></lb>cordis ventriculum dealbavit ” (ibid.). </s></p><p type="main">

<s>La vessicola chilosa fu dallo Svedese inventore dimostrata in pubblico <lb></lb>nell&#039;Aprile del medesimo anno 1652, alla presenza della Maestà di quella <pb xlink:href="020/01/1353.jpg" pagenum="228"></pb>vergine Cristina, a cui dedicava il nostro Borelli, poco prima di morire, la <lb></lb>grande opera dei Moti animali. </s>

<s>Ma costì, mentre Olao faceva le sue pubbli­<lb></lb>che dimostrazioni, i regii medici gli sussurrano nelle crecchie esser venuto <lb></lb>il Pecquet stesso a Stockolm a divulgare le sue esperienze, e il Tonson li­<lb></lb>braio aver venali, nella sua bottega, il libretto del Nuovo dutto chilifero del <lb></lb>Van-Horne, e il trattato Delle lattee del Torace, dove Tommaso Bartholin <lb></lb>attesta di aver veduta la vescicola del chilo anche nell&#039;uomo. </s>

<s>Ma Olao, che <lb></lb>più della sua gloria amava la scoperta del Vero, vuol dir dunque, rispose <lb></lb>tranquillamente a que&#039;medici, che dalla concorde testimonianza di tanti scrit­<lb></lb>tori verrà meglio confermata questa importantissima verità: “ Hepar non <lb></lb>esse primarium sanguificationis organum ” (ibid.). </s></p><p type="main">

<s>Quel fortuito incontro de&#039;tre inventori separati fra loro qua da monti <lb></lb>e là da mari, ha senza dubbio qualche cosa di maraviglioso, e poniamo che <lb></lb>ricevessero tutt&#039;e tre uguale impulso dalla scoperta del nostro Asellio, ri­<lb></lb>man tuttavia a maravigliare come mai si trovassero tutt&#039;e tre ispirati nel <lb></lb>medesimo tempo. </s>

<s>Nonostante, per la perizia dell&#039;arte e per l&#039;amore agli <lb></lb>studii, furono di quella inspirazione tutti ugualmente degni, e la Sapienza, <lb></lb>nell&#039;eleggerli a sedere al suo convito, non seppe usar quella preferenza, di <lb></lb>che, scrivendo le loro storie, si resero colpevoli i giudizi degli uomini appar­<lb></lb>tenenti alle tre varie nazioni. </s></p><p type="main">

<s>Ma se que&#039;tre furono chiamati al convito, non mancarono altri, che vi <lb></lb>s&#039;intromisero di furto, e sotto vesti mentite, o non proprie d&#039;uomo sapiente. </s>

<s><lb></lb>Basti di ciò addurre due esempi, e sia primo quello di Lodovico Bils. </s>

<s>Ba­<lb></lb>rone di Koppensdam, ebbe il prurito di fare il Notomista, e per non insoz­<lb></lb>zare il decoro della tunica baronale, avea trovato un balsamo emostatico, <lb></lb>intantochè riuscivano le sue dissezioni incruente. </s>

<s>Fin qui avrebbe potuto <lb></lb>utilmente giovare, se non in altro, ai comodi dell&#039;arte, ma si fu il male che <lb></lb>volle riformare a suo modo la scienza. </s>

<s>Il chilo, che da tutti si credeva esser <lb></lb>per le vene lattee del mesenterio e del torace riversato nel ricettacolo pecque­<lb></lb>ziano, ei lo chiama <emph type="italics"></emph>rugiada,<emph.end type="italics"></emph.end> e vuol che, attinto questo rugiadoso umore agli <lb></lb>intestini, confluisca nel <emph type="italics"></emph>Dutto rorifero,<emph.end type="italics"></emph.end> che per lui si divide in due rami, <lb></lb>uno de&#039;quali va alla glandula affissa alla Vena porta, l&#039;altro al ricettacolo <lb></lb>glanduloso del mesenterio. </s>

<s>Insorsero contro una tale scempiataggine il Van­<lb></lb>Horne e Paolo Barbette, ai quali il Bils rispose, o per meglio dire, essendo <lb></lb>illitterato, fece rispondere una scrittura pubblicata in Rotterdam nel 1661. </s></p><p type="main">

<s>Par che tutto il nervo delle sue ragioni e tutta l&#039;arte della difesa la <lb></lb>faccia consistere nel notar la differenza, che passa fra il suo Dutto rorifero <lb></lb>e il chilifero del Van-Horne, per concluderne poi, da un tal confronto, quanto <lb></lb>egli fosse più veridico interpetre della Natura. </s>

<s>A una tavola perciò, che esi­<lb></lb>bisce il disegno del dutto bilsiano, fa seguirne un&#039;altra, ch&#039;esibisce il dise­<lb></lb>gno del dutto horniano, “ unde videre licet magnam differentiam, quae in­<lb></lb>tercedit inter huius chyliferum et roriferum nobilissimi D. D. </s>

<s>Ludovici de <lb></lb>Bils ” (Responsio ad admonitiones J. ab Horne etc., Roterodami 1661, pag. </s>

<s>11). </s></p><p type="main">

<s>L&#039;altro esempio, che si diceva, è quello di Giovanni Finck, venuto d&#039;In-<pb xlink:href="020/01/1354.jpg" pagenum="229"></pb>ghilterra a insegnare anatomia nello studio di Pisa, il quale inglese dimo­<lb></lb>strò alla presenza del Granduca, facendola credere una sua nuova scoperta, <lb></lb>come il chilo va per le vene lattee a riversarsi in un dutto; e di lì, per le <lb></lb>giugulari e per la Vena cava, nel cuore. </s>

<s>È Claudio Beriguardo, come si ve­<lb></lb>drà meglio nell&#039;ultima parte di questo capitolo, che in uno de&#039;suoi Circoli <lb></lb>pisani ci dà una tale inaspettata notizia. </s>

<s>Il Targioni che, a pag. </s>

<s>272 del <lb></lb>I Tomo de&#039;suoi Aggrandimenti delle scienze fisiche in Toscana, cita dal libro <lb></lb>del Beriguardo il passo, letto senza dubbio nella seconda edizione fatta in <lb></lb>Padova nel 1661, senza niente sospettar che fosse un&#039;aggiunta alla prima <lb></lb>edizione del 1643; ne conclude un&#039;altra notizia, che giunge anche più ina­<lb></lb>spettata, ed è che il Finck avesse scoperto il Canale toracico prima di quel­<lb></lb>l&#039;anno 1643, che vuol dir quando ancora il Pecquet era in Mompellieri sco­<lb></lb>lare. </s>

<s>La semplicità del Targioni è maggiore di quella di un fanciullo, ed <lb></lb>essendo la terza volta, che da quella semplicità o difetto di critica è con­<lb></lb>dotto in errore, intorno a questioni storiche di così facile risoluzione, e di <lb></lb>tanto grave importanza; non crediamo di esser troppo rigidi a giudicarlo <lb></lb>immeritevole di ogni scusa. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dappoichè Giovanni Pecquet ebbe scoperto che le vene lattee del me­<lb></lb>senterio non conducono il chilo al Fegato, ma al Ricettacolo e al Canale <lb></lb>toracico, per riversarlo, mediante la Vena cava, nel ventricolo destro del <lb></lb>cuore; gli Anatomici incominciarono a dubitare intorno all&#039;essere e all&#039;uso <lb></lb>di certi vasi, che apparivano della natura stessa de&#039;lattei, e che senza dub­<lb></lb>bio penetravano addentro al Fegato, e si diramavano nel suo parenchima. </s>

<s><lb></lb>Il Veslingio aveva trovato così fatti vasi nel feto, e l&#039;Igmoro gli avea dili­<lb></lb>gentemente descritti. </s>

<s>Olao Rudbeck, che fu de&#039;primi a rivolgere la sagacia <lb></lb>del proprio ingegno sopra quelle anatomiche descrizioni, perciocchè non <lb></lb>erano i nuovi vasi, da que&#039;Notomisti pur così valorosi, esplorati nè collo <lb></lb>stilo, nè per via delle legature o delle insufflazioni, e non davano dall&#039;altra <lb></lb>parte indizio che vi scorresse dentro alcun umore, pensò non fossero altro <lb></lb>che nervi. </s>

<s>“ Quae autem Veslingius, scrisse nel cap. </s>

<s>III della sua Nuova eser­<lb></lb>citazione anatomica, in figura foetus dissecti apposuit, et Nathanael Hygmo­<lb></lb>rus elegantissimis delineamentis illustravit, nervulos fuisse existimo, quippe <lb></lb>cum illa, nec stylo, nec inflatione, nec ligatura, nec denique motu humoris <lb></lb>probaverint ” (In Mangeti Bibliotheca cit., pag. </s>

<s>702). </s></p><p type="main">

<s>Ma frugava più vivamente che mai la curiosità del Rudbeck la seconda <lb></lb>Tavola dell&#039;Asellio, nella quale son designati colle lettere N. N. due vasi assai <lb></lb>cospicui, con questa dichiarazione in margine: “ Progressus Lactearum ex <lb></lb>pancreate ad Hepar. </s>

<s>” Se non son que&#039;due vasi, pensava, immaginari, la <lb></lb>sentenza del Pecquet non si può tenere assolutamente per vera. </s></p><pb xlink:href="020/01/1355.jpg" pagenum="230"></pb><p type="main">

<s>A decidere una questione di tanta importanza, un giorno allaccia in­<lb></lb>sieme la Vena porta e il canal coledoco, e osserva un fatto singolare: i cre­<lb></lb>duti vasi aselliani si vedevano, tra il Fegato e la legatura, inturgidire, e vo­<lb></lb>tarsi al di sotto. </s>

<s>Era da ciò manifesto che non portavano, ma estraevano <lb></lb>anzi umore dal viscere, e tra per questa ragione, e per trovarli pieni di un <lb></lb>liquido, non più bianco e denso come il latte, ma liquido e sciolto come <lb></lb>l&#039;acqua, si persuase esser quelli vasi di un nuovo genere, differenti da&#039;lat­<lb></lb>tei dell&#039;Asellio per la strutura e per l&#039;uso. </s>

<s>La scoperta occorse, come narra <lb></lb>lo stesso Autore, fra il 1650 e il 1651, in mezzo a quelle dissezioni del vi­<lb></lb>tello e del gatto da noi sopra narrate, e per cui si rivelarono all&#039;Anatomico <lb></lb>svedese, nel tempo stesso che al Diepeo, il Canal toracico e la vescicola del <lb></lb>chilo. </s>

<s>“ Dum anno 1650 et 1651 in venarum lactearum originem et inser­<lb></lb>tionem inquirendam versabar, iniectaque supra venam Portae cum ductibus <lb></lb>cholidocis ligatura, non semel apparuere ductus manifeste ab Hepate ad liga­<lb></lb>turam intumescentes, infra evanescentes, quos venas esse lacteas minime <lb></lb>sum arbitratus ” (ibid., pag. </s>

<s>701). Essendo vasi nuovamente scoperti, ci vo­<lb></lb>leva anche un nome nuovo per designarli, e fu dal Rudbeck scelto quello <lb></lb>di <emph type="italics"></emph>Dutti epatico acquosi.<emph.end type="italics"></emph.end> “ Et quidem <emph type="italics"></emph>Ductuum<emph.end type="italics"></emph.end> hepaticorum quum et hu­<lb></lb>morem ferant ac ducant, et quod illum ab Hepate accipiant, indeque suam <lb></lb>originem depromant; deinde <emph type="italics"></emph>aquosorum,<emph.end type="italics"></emph.end> quod tali humore ipsorum cavitas <lb></lb>infarta sit ” (ibid.). </s></p><p type="main">

<s>Proseguendo attentamente il Rudbeck il decorso di questi dutti epatico <lb></lb>acquosi, da sè così felicemente scoperti, trovò che i più, e anzi quasi tutti, <lb></lb>“ glandulam quandam ingrediuntur, ramulis dispersis, atque deinde, cum <lb></lb>reliquis eandem praetervectis, in Vesiculam chyli, sitam inter renes sub Vena <lb></lb>cava et arteria aorta, sese insinuant ” (ibid.). </s></p><p type="main">

<s>Dà l&#039;Autore a queste ghiandole, esse pure nuovamente scoperte almeno <lb></lb>per quel che riguarda le loro relazioni co&#039;dutti epatico acquosi, il nome di <lb></lb><emph type="italics"></emph>Vasi ghiandolari sierosi,<emph.end type="italics"></emph.end> perchè gli parve che contenessero un liquido più <lb></lb>denso, e in certo modo simile al chilo. </s>

<s>Il qual siero pensò che venisse tra­<lb></lb>sudato dagl&#039;intestini e dagli altri visceri, tanto più dopo ch&#039;egli ebbe a <lb></lb>notar questo fatto, “ quod mihi ter, egli dice, videre contigit: manifestam <lb></lb>anastomosin hosce inter ductus epaticos et duas vel tres lactearum venas <lb></lb>dari ” (ibid.). D&#039;onde gli fu facile congetturare che l&#039;uso di tali ghiandole <lb></lb>sierose fosse quello di confezionar meglio il chilo, e di rimandarlo così ela­<lb></lb>borato al comun Ricettacolo. </s></p><p type="main">

<s>Così, tra il 1650 e il 1651, era stata fatta la scoperta di que&#039;nuovi or­<lb></lb>gani della vita animale, conosciuti poi sotto il nome di <emph type="italics"></emph>Vasi<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>ghiandole <lb></lb>linfatiche,<emph.end type="italics"></emph.end> ma l&#039;Autore non si curò di pubblicare la sua scoperta, già mo­<lb></lb>strata nel 1652 sotto gli occhi della Regina, quando a proposito della Ve­<lb></lb>scicola del chilo <emph type="italics"></emph>hos quoque ductus in medium adduxit;<emph.end type="italics"></emph.end> se non che nel­<lb></lb>l&#039;anno appresso, in un libretto in 4°, a cui dette il titolo: “ Nova exercitatio <lb></lb>anatomica exhibens ductus hepaticos aquosos, et Vasa glandularum serosa ” <lb></lb>e stampato in Vuesterat (Arosiae) piccola città della Svezia. </s></p><pb xlink:href="020/01/1356.jpg" pagenum="231"></pb><p type="main">

<s>In quel medesimo anno 1652, in cui il Rudbeck fece alla regina Cri­<lb></lb>stina e ai regii medici la sua solenne dimostrazione, Tommaso Bartholin pub­<lb></lb>blicava in Coppenaghen (Hafniae) la sua Storia anatomica <emph type="italics"></emph>De lacteis thora­<lb></lb>cicis.<emph.end type="italics"></emph.end> Venne all&#039;Autore l&#039;impulso ai nuovi studii da quella parte stessa, che <lb></lb>era venuta al Rudbeck, imperocchè, avendogli la scoperta del Pecquet, tante <lb></lb>volte verificata, dimostrato che il chilo non và al Fegato, ma al Ricettacolo <lb></lb>e di li al cuore, stava pensando che cosa potess&#039;essere, nella Tavola III del­<lb></lb>l&#039;Asellio, quella vena designata colla lettera N e qualificata per una lattea <lb></lb>“ iuxta Cavam ascendens ad Hepar, et ad Venam Portae propagatam eamque <lb></lb>coronans. </s>

<s>” </s></p><p type="main">

<s>Il primo consiglio, che gli fu suggerito dalla sua propria saviezza e dal <lb></lb>buon metodo sperimentale, fu quello di verificar se i vasi descritti dall&#039;Asel­<lb></lb>lio intorno alla Vena porta erano una realtà o una immaginazion dell&#039;Au­<lb></lb>tore, o altro simile inganno. </s>

<s>Preso perciò un cane, alla presenza di varii <lb></lb>Medici amici, così il Bartolino stesso racconta nella storia XLVIII della <lb></lb>II centuria, “ quarta hora a pastu aperui, die 25 Decembris 1651. Viso re­<lb></lb>ceptaculo chyli pecquetiano, aliisque huc spectantibus, ad Hepar oculorum <lb></lb>cultrique aciem convertimur. </s>

<s>Ecce multi comparebant ductus pinguedini im­<lb></lb>mersi prope Hepar portam amplexantes, non candidi, lacteorum more, sed <lb></lb>splendentes colore hydatidum..... Nihil de novis vasis cogitans, quanquam <lb></lb>lacteas Asellii esse venas humor contentus dissuadebat, pro lacteis tamen <lb></lb>habui .... chylumque evanidum seri speciem induisse suspicabar. </s>

<s>9 Jan. </s>

<s>se­<lb></lb>quentis anni 1652, in cane adhuc maiore, esperimentum feci..... Insciis <lb></lb>oculis iidem ductus aquosi ultro se obtulerunt, annuli in morem, Portam <lb></lb>cingentes, limpida aqua tumentes, qua et Receptaculum et vasa thoracica, <lb></lb>alias lactea, scatebant ” (Histor. </s>

<s>anatom. </s>

<s>rariorum Cent. </s>

<s>II cit., pag. </s>

<s>225, 26). </s></p><p type="main">

<s>Nel dì 28 Febbraio di quel medesimo anno 1652 fece, aiutato dal suo <lb></lb>fedele amico Michele Lyser, altre dissezioni, per le quali venne sempre me­<lb></lb>glio confermato che i vasi descritti intorno alla Porta dall&#039;Asellio eran reali, <lb></lb>e non punto, come si sospettava, immaginarii. </s>

<s>Ebbe di qui a concludere il <lb></lb>Bartolino che la sentenza del Pecquet non era assolutamente vera, e fu da <lb></lb>questo fatto osservato condotto a intitolare il cap. </s>

<s>XV <emph type="italics"></emph>De lacteis:<emph.end type="italics"></emph.end> “ Non <lb></lb>omnem chylum per thoracicas lacteas ad cor ferri, sed aliquem ad hepar <lb></lb>per lacteas mesenterii. </s>

<s>“ (In Mangeti Bibl. </s>

<s>cit., pag. </s>

<s>667). Vuol l&#039;Autore, <lb></lb>fra gli antichi e i recenti Anatomisti, entrare mediatore di pace “ ne hepati <lb></lb>tot saeculis opere sanguificationis gloriose defuncto plane eamus exsequias. </s>

<s>” <lb></lb>Se ho da pronunziar dunque una sentenza che concilii le due parti e fac­<lb></lb>cia andare pecqueziani e galenisti ugualmente contenti, “ existimo, dice il <lb></lb>Bartholin, operas inter se partiri hepar et cor, ut vel promiscuos humores <lb></lb>alimentarios admittat uterque, vel diviso munere hoc tenuem, illud cras­<lb></lb>sum ” (ibid.). </s></p><p type="main">

<s>Dop&#039;aver così solennemente pronunziato questo giudizio, senza dir nè <lb></lb>come nè quando gli occorresse di dover riformarlo, prende in fretta la <lb></lb>penna, <emph type="italics"></emph>celerrimo calamo<emph.end type="italics"></emph.end> com&#039;egli stesso si esprime, per scrivere una Sto-<pb xlink:href="020/01/1357.jpg" pagenum="232"></pb>ria nuova <emph type="italics"></emph>Vasorum lymphaticorum,<emph.end type="italics"></emph.end> pubblicata in Coppenaghen in quello <lb></lb>stesso anno 1653, in cui il Rudbeck avea divulgata fra&#039;suoi, fatta già da due <lb></lb>anni, la sua propria scoperta. </s>

<s>Il Bartholin, che avea fin allora tenuti per lattei <lb></lb>que&#039;vasi aselliani coronanti la Vena porta, ha scoperto che son vasi di nuovo <lb></lb>genere, e che, invece di portare, estraggono dal fegato quel loro umore sie­<lb></lb>roso. </s>

<s>“ Vidimus quippe vasa illa prope hepar sui esse generis .... ex hepate <lb></lb>ad Receptaculum aquam inferre, ligataque intumescere prope hepar ” (ibid, <lb></lb>pag. </s>

<s>699). </s></p><p type="main">

<s>E qui “ dans un petit accès de gaieté savante ” diremo anche noi col <lb></lb>Flourens (Histoire de la circul. </s>

<s>du sang, Paris 1854, pag. </s>

<s>94), si spoglia la <lb></lb>prima toga di avvocato, per indossar l&#039;abito pontificale, e cantare al Fegato <lb></lb>l&#039;esequie solenni. </s>

<s>Mi duole, egli dice, d&#039;aver dovuto così cambiar veste, ma <lb></lb>son le solite vicende del mondo; è questa la sorte propria dei grandi Eroi; <lb></lb>ora nella polvere, ora sopra gli altari. </s>

<s>“ Ego interim, antiquae venerationis <lb></lb>memor, ne sine publico monumento tot saeculorum abdominis nostri Rector <lb></lb>ignotus iam busto inseratur, in perpetuam bene feliciterque, per bis octo <lb></lb>saecula administrati ac cruenti imperii memoriam, donec panegyris conda­<lb></lb>tur, hanc ultimae devotionis inscriptionem tumulo illius conservavi: SISTE <lb></lb>VIATOR.CLAUDITUR HOC TUMULO QUI.TUMULAVIT.PLURIMOS.PRINCEPS COR­<lb></lb>PORIS TUI COCUS.ET ARBITER.HEPAR NOTUM SAECULIS.SED.IGNOTUM NA­<lb></lb>TURAE.QUOD NOMINIS MAIESTATEM ET.DIGNITATIS.FAMA FIRMAVIT.OPINIONE <lb></lb>CONSERVAVIT.TAMDIU COXIT.DONEC.CUM CRUENTO IMPERIO.SEIPSUM.DE­<lb></lb>COXERIT.ABI SINE IECORE VIATOR.BILEMQUE HEPATI CONCEDE.UT SINE BILE <lb></lb>BENE.TIBI COQUAS ILLI PRECERIS ” (ibid.). </s></p><p type="main">

<s>Furono queste cose, come nella storia XLVIII citata il Bartolino stesso <lb></lb>ci attesta, pubblicate in Coppenaghen nelle calende di Maggio del 1653, <lb></lb>“ partim ne Naturae faventis sprevisse viderer indulgentiam, partim ne in­<lb></lb>ventum nostrum fama hinc inde divulgatum .... scioli alii suffurarentur ” <lb></lb>(pag. </s>

<s>231). Ma giunse in quel punto da Vuesterat la Nuova esercitazione <lb></lb>anatomica, per la quale si scopriva, e anzi si dimostrava coi fatti, essere il <lb></lb>ladrò il Bartolino stesso che temeva dei ladri. </s></p><p type="main">

<s>Si dimostrava coi fatti, dicendovisi che il Rudbeck nel 1651 aveva sco­<lb></lb>perto, e nel 1652 dimostrato in pubblico ai regii medici e alla stessa Regina, <lb></lb>i nuovi dutti, che trasportano il loro umor sieroso dal Fegato, di che il Bar­<lb></lb>tholin, per confessione sua propria, non s&#039;accorse che l&#039;anno dopo. </s>

<s>Ma come <lb></lb>se n&#039;accorse? </s>

<s>Ei non lo dice, per tenere il furto nascosto, ma noi abbiamo <lb></lb>tutte le buone ragioni di sospettare che la notizia delle pubbliche dimostra­<lb></lb>zioni, fatte nella reggia di Svezia, con sollecitudine si diffondesse nella vi­<lb></lb>cina Danimarca. </s>

<s>In che altro modo infatti si spiegherebbe quella trasforma­<lb></lb>zione del Bartholin che di avvocato del Fegato diventa a un tratto sacer­<lb></lb>dote delle sue esequie? </s>

<s>Ma come spesso avviene de&#039;rei, patrocinatori della <lb></lb>causa propia, ei si tradisce da sè medesimo. </s>

<s>Nel II capitolo infatti della <emph type="italics"></emph>Histo­<lb></lb>ria nova,<emph.end type="italics"></emph.end> ripensendo ai nomi più convenienti ai dutti nuovamente scoperti, <lb></lb>“ fuere, egli dice, qui <emph type="italics"></emph>serosa vasa<emph.end type="italics"></emph.end> indiderint quod serum contineant ” (In <pb xlink:href="020/01/1358.jpg" pagenum="233"></pb>Mangeti Bibliotheca cit., pag. </s>

<s>694). Se prima dunque avevano avuto un nome, <lb></lb>dovevano essere stati anche prima scoperti, e il Rudbeck fu giusto quello, <lb></lb>che aveva imposto alle ghiandole linfatiche il nome di vasi sierosi. </s></p><p type="main">

<s>Diffusasi più largamente in pubblico la notizia della scoperta dei dutti <lb></lb>epatico acquosi, e delle ghiandole sierose, venuta di Svezia, il Bartholin, che <lb></lb>voleva in ogni modo far sua legittima proprietà quella, che all&#039;acuto giu­<lb></lb>dizio altrui non appariva che un furto, sperò che avesse l&#039;oratoria a far di­<lb></lb>menticare la storia. </s>

<s>Scrisse perciò con grand&#039;enfasi ed eloquenza, nella Cen­<lb></lb>turia II, i più minuti particolari della scoperta dei vasi linfatici “ propter <lb></lb>quod inventum, omni saeculo invisum, hecatomben promisimus ” (pag. </s>

<s>228). <lb></lb>Soggiungeva non essere ostentazione il magnificar ch&#039;egli fa la propria sco­<lb></lb>perta, ma un render lode a Dio creatore, <emph type="italics"></emph>et patriae nostrae celebritatem<emph.end type="italics"></emph.end><lb></lb>(pag. </s>

<s>231). </s></p><p type="main">

<s>Ma perchè sentiva minaccioso dalla lontana mormorarsi il nome di Olao <lb></lb>Rudbeck, vuole il Bartholin aver parlato della nuova scoperta “ paucis ver­<lb></lb>bis cap. </s>

<s>VI, et XII et XV <emph type="italics"></emph>De lacteis thoracicis,<emph.end type="italics"></emph.end> Hafniae, 5 Maii 1652, edi­<lb></lb>tis ” (pag. </s>

<s>231). Troppo debole provvedimento però era questo alla difesa, <lb></lb>perchè, se nell&#039;avere osservati vasi bianchi intorno al fegato e in altre parti <lb></lb>consistesse la scoperta de&#039;vasi linfatici, ne sarebbero da dire piuttosto Au­<lb></lb>tori il Veslingio, il Van-Horne, l&#039;Igmoro, anzi il Falloppio, anzi Galeno stesso, <lb></lb>o qualcun altro de&#039;più antichi anatomici greci. </s></p><p type="main">

<s>Più tardi uscì in mezzo fra il Rudbeck e il Bartholin un altro compe­<lb></lb>titore, e ne fu dagli Inglesi a Francesco Glisson affidata la gelosa tutela. </s>

<s><lb></lb>Nel cap. </s>

<s>XXXI <emph type="italics"></emph>De anatomia hepatis,<emph.end type="italics"></emph.end> accennando esso Glisson ai vasi acquosi <lb></lb>nuovamente scoperti, “ incidi primum in eorum notitiam, egli ivi dice, in­<lb></lb>ditio D. Jolivii, idque anno 1652, sub initium Junii, quo tempore ille, docto­<lb></lb>ratus gradum adepturus, me Cantabrigiae in eum finem convenerat ” (Amste­<lb></lb>lodami 1659, pag. </s>

<s>319). Ma perchè il Giolivio non aveva nulla lasciato scritto, <lb></lb>rimaneva franco il Rudbeck, e il Bartolino difeso. </s>

<s>Al qual Bartolino, benchè <lb></lb>avesse due altri casi valorosi competitori, riuscì nulladimeno di conseguire <lb></lb>il trionfo. </s></p><p type="main">

<s>Di questo, ch&#039;è dei più notabili fra&#039;tanti altri ingiusti giudizii degli uo­<lb></lb>mini, chi volesse ricercar le ragioni, le troverebbe facilmente nell&#039;essere stato <lb></lb>il Bartholin più eloquente, e più procacciante del Rudbeck, e nell&#039;aver tro­<lb></lb>vato, tanta è la potenza delle parole, ne&#039;<emph type="italics"></emph>Vasi linfatici<emph.end type="italics"></emph.end> un nome più facile <lb></lb>a pronunziarsi di quello di <emph type="italics"></emph>Dutti epatico acquosi.<emph.end type="italics"></emph.end> Ma forse più di ogni altra <lb></lb>cosa giovarono a fermargli in fronte la corona i risentimenti fieri de&#039;Gale­<lb></lb>nisti, che in quella parodia del Fegato si vedevano amaramente derisi. </s>

<s>Il <lb></lb>gran Riolano, che non s&#039;era anoora riavuto delle fatiche durate, prima con­<lb></lb>tro l&#039;Harvey, poi contro il Pecquet, per mantener saldo il combattuto regno <lb></lb>galenico, si trova di fronte il Bartholin, che aggiunge alla punta acuta del­<lb></lb>l&#039;armi il ridicolo più pungente degli insulti. </s>

<s>Fa i suoi risentimenti col bi­<lb></lb>sbetico brontolio e con l&#039;ira impotente dei vecchi, ma non lascia intanto di <lb></lb>meditar ragioni, o affinare arguzie, per salvare al Fegato il suo primo e no-<pb xlink:href="020/01/1359.jpg" pagenum="234"></pb>bilissimo ufficio. </s>

<s>Danno mano alla pietosa opera, come animosi soldati in­<lb></lb>torno al capitano, Iacopo De Back, Isacco Cattier, Carlo Le Noble, Claudio <lb></lb>Tardy, a uno a uno redarguiti dal Bartolino stesso, nel suo Spicilegio secondo. </s></p><p type="main">

<s>Ma in tutti i sopra commemorati era l&#039;ardor passionato d&#039;una setta, <lb></lb>piuttosto che il sereno amor della scienza, il quale, per onor degli uomini <lb></lb>e del vero, non mancò d&#039;inspirare alcuni animi eletti. </s>

<s>È de&#039;principali fra <lb></lb>questi da annoverare il Van-Horne, il quale, amicissimo del Bartholin, non <lb></lb>si lasciò tanto dalla passione o dall&#039;affetto annuvolare il giudizio, da non co­<lb></lb>noscer che quel piccolo accesso di gaietà, da cui fu condotto a cantar l&#039;ese­<lb></lb>quie al Fegato, non era stato sapiente. </s>

<s>Fece l&#039;Autore della Storia nuova <lb></lb>de&#039;vasi linfatici il viscere defunto da&#039;suoi primi ufficii, perchè i vasi, invece <lb></lb>di portarvelo, n&#039;estraevano quell&#039;umore, che si diceva dover essere trasfor­<lb></lb>mato in sangue. </s>

<s>Ma il rifondere un liquido, ragionava giustamente il Van­<lb></lb>Horne, è anzi argomento certissimo che vi sia nel vaso stato prima infuso, <lb></lb>ond&#039;è che, se dal Fegato esce un umor nutritizio, è di necessità che in qual­<lb></lb>che modo siavi entrato. </s>

<s>Nè fa difficoltà il veder l&#039;umore che esce aver ap­<lb></lb>parenza o natura diversa da quello che entra, imperocchè il viscere ha virtù <lb></lb>di concuocere il chilo, per mandarlo così confezionato, attraverso ai vasi lin­<lb></lb>fatici, al Canal toracico, e al cuore. </s>

<s>Queste insomma erano le funzioni asse­<lb></lb>gnate dal Rudbeck alle ghiandole sierose, e il Van-Horne le estese al Fe­<lb></lb>gato, quasi esso fosse una grande ghiandola sierosa, e le stesse ghiandole <lb></lb>seriose non fossero altro che tanti piccoli fegati. </s></p><p type="main">

<s>Non era dunque, secondo queste idee, il Rettore e il principe delle vi­<lb></lb>scere animali affatto defunto: se gli era tolto il dignitoso ufficio di fattore <lb></lb>del sangue, gliè ne rimaneva un altro, non punto meno importante, qual era <lb></lb>quello di elaborare un umor nutritizio atto a ristorare il sangue. </s>

<s>Così il <lb></lb>Van-Horne, non per amor di Galeno, ma per amor del vero tanto più an­<lb></lb>tico, attendeva a rivendicare il Fegato dagli insulti del Bartholin, e il Rud­<lb></lb>beck dalle usurpazioni. </s></p><p type="main">

<s>La fisiologia epatica nuova, insiem coi liberi giudizii intorno al primo <lb></lb>inventore dei vasi linfatici, vengon lucidamente esposti nel <emph type="italics"></emph>Microcosmo,<emph.end type="italics"></emph.end> e <lb></lb>son parte, in questo presente articolo di storia, di non lieve importanza. </s>

<s><lb></lb>Parve all&#039;Autore la struttura del viscere, tanto avvilito dal Bartholin, ma­<lb></lb>ravigliosa, ond&#039;ebbe a concluderne “ usum eius haud vulgarem esse ” <lb></lb>(Lugduni Batav., pag. </s>

<s>56). Quest&#039;uso poi ei lo riconobbe nella elaborazione <lb></lb>di quella parte di chilo più crasso, che non va per i vasi aselliani al Ca­<lb></lb>nale toracico. </s></p><p type="main">

<s>La rete del mesenterio è, secondo il Van-Horne, intessuta di un du­<lb></lb>plice ordine di vene: lattee, e rosse, “ quod in hunc finem factum arbitror, <lb></lb>ut chyli laudabilior portio per illas quidem deferatur, porro in Receptacu­<lb></lb>lum, et hinc, ascendendo per Ductum chyliferum, infundatur venae axil­<lb></lb>lari aut iugulari; per has vero una cum sanguine ab intestinis remeante <lb></lb>devehatur ad Portae truncum, e sima parte hepatis erumpentem ” (ibid., <lb></lb>pag. </s>

<s>54, 55). </s></p><pb xlink:href="020/01/1360.jpg" pagenum="235"></pb><p type="main">

<s>Entrato il chilo insieme col sangue nel Fegato, attraverso alla Vena <lb></lb>porta, si distribuisce per le numerose propaggini di lei, che lo riversano <lb></lb>dentro le porosità del viscere, d&#039;onde viene assorbito dai rami della Vena <lb></lb>cava ivi dispersi, per i quali è direttamente condotto al cuore. </s>

<s>“ Atque in <lb></lb>hac chyli et sanguinis traductione unum Jecoris officium consistit ” (ibid., <lb></lb>pag. </s>

<s>59). Dell&#039;altro ufficio, che è quello di secerner la bile, promette il Van­<lb></lb>Horne di parlarne in seguito, per trattenersi a descriver le vie di quell&#039;al­<lb></lb>tra porzione di chilo schietto, ch&#039;e per le vene lattee riversato “ in Vesi­<lb></lb>culam chylo aquoso, hoc est lympha, permixto repletam ” (ibid., pag. </s>

<s>61). <lb></lb>E qui, a proposito de&#039;nuovi dutti acquosi, sentenzia da giusto giudice, e <lb></lb>sicuro di pronunziare il vero, che elegantemente gli delineò “ et erudito <lb></lb>orbi communicavit Olaus Rudbeck in tractatu suo De ductibus hepaticis <lb></lb>aquosis ” (ibid.) e riprendendo più sotto il Bartholin, che avesse nell&#039;uomo <lb></lb>sostituito alla Vescicola del chilo e al Canal pecqueziano le ghiandole lom­<lb></lb>bari, “ sed ego, soggiunge, cum doctissimo Rudbeckio, horum naturae ar­<lb></lb>canorum scrutatori maximo, in homine vesiculam inveni ” (ibid., pag. </s>

<s>63). </s></p><p type="main">

<s>Nonostante, ebbe il Bartholin assai maggiore efficacia del Rudbeck in <lb></lb>diffondere con gli stessi scritti apologetici la notizia, e in promuovere lo <lb></lb>studio di questi nuovi dutti scoperti, il quale studio versava principalmente <lb></lb>intorno alla ragione del moto dell&#039;umore in essi dutti contenuto, e dell&#039;uso, <lb></lb>a cui furono dalla Natura i nuovi organi preparati. </s>

<s>Quanto alla direzion di <lb></lb>quel moto, furono sempre sicura scorta le valvole, a fare attenzione alle <lb></lb>quali fu primo, con sua dolce maraviglia, l&#039;Asellio. </s>

<s>“ In his, dice nella ci­<lb></lb>tata dissertazione <emph type="italics"></emph>De venis lacteis,<emph.end type="italics"></emph.end> illud admiratione dignum, quod pluribus <lb></lb>valvulis, sive ostiolis, interstinctae sunt sive intercisae, quas ego valvulas, <lb></lb>saepius vanescente iam chylo,.... animadverti ” (pag. </s>

<s>38, 39). </s></p><p type="main">

<s>Aperta così dal Nostro la via, per la quale gloriosamente s&#039;introdusse <lb></lb>l&#039;Harvey, che fece delle valvole argomento a dimostrare il corso del sangue <lb></lb>per le vene; il Pecquet, sulle orme dell&#039;anatomico Italiano e dell&#039;Inglese, <lb></lb>fece le stesse valvole argomento a dimostrar che il chilo ha il suo moto <lb></lb>diretto per le vene lattee al Ricettacolo comune. </s>

<s>Consisteva la dimostrazione <lb></lb>in allacciare una delle dette vene, e in osservar che, premuta col dito fra <lb></lb>l&#039;allacciatura e il Ricettacolo stesso, il chilo non ritorna indietro verso l&#039;in­<lb></lb>testino, ciò che manifestamente prova, così esprimesi il Pecquet, “ esse intra <lb></lb>Receptaculi cavitatem valvularum obiectacula in mesentericarum ostiis, ad <lb></lb>excubias seu regressus interdictum, constituta ” (Opera anat., Parisiis 1654, <lb></lb>pag. </s>

<s>121). E perchè nessun dubitasse esser forse questa una conclusione <lb></lb>troppo affrettata, “ certe mihi, soggiunge lo stesso Pecquet, non sunt explo­<lb></lb>ratae minus eiusmodi valvulae, quam quas in venis descripsit Fabricius ab <lb></lb>Aquapendente ” (ibid). </s></p><p type="main">

<s>Quando il Rudbeck, dal veder quelle manifeste anastomosi fra i dutti <lb></lb>epatici e due o tre delle vene lattee, ebbe indizio che, comunicandosi in­<lb></lb>sieme i vasi, anche gli umori passerebbero dagli uni negli altri, fu a lui <lb></lb>altresì facilissimo a congetturare che, essendo fornite di valvole le vene lat-<pb xlink:href="020/01/1361.jpg" pagenum="236"></pb>tee, i dutti acquosi non ne andrebbero esenti. </s>

<s>Davano fondamento alle con­<lb></lb>getture quelle nodosità, di che i dutti stessi gli si mostravano involti, e ne <lb></lb>ebbe all&#039;ultimo certezza di dimostrazione dallo stile introdotto nelle cavità, <lb></lb>e dalle insufflazioni. </s>

<s>Descrivendo perciò, nella sua citata Nuova esercitazione <lb></lb>anatomica, i nuovi vasi scoperti, “ figuram, egli dice, ipsis rotundam, fistu­<lb></lb>losam, ac mirabiliter nodosam, ob contentas valvulas concessit Natura ” <lb></lb>(pag. </s>

<s>702). </s></p><p type="main">

<s>Tanto poi parvero al Rudbeck queste valvole certe, nella loro esistenza <lb></lb>e nell&#039;ufficio, che non si curò di far del suo metodo delle insufflazioni altro <lb></lb>che un lieve accenno. </s>

<s>Ma perchè alcuni, fra&#039;quali quel Bils, non si sa se <lb></lb>più famoso per le sue invenzioni o per le sue pazzie, non mancarono di ne­<lb></lb>gare assolutamente ciò ch&#039;era meno aperto agli occhi che all&#039;intelletto, si <lb></lb>trovarono i Fisiologi costretti a far delle stesse valvole de&#039;linfatici più evi­<lb></lb>dente dimostrazione. </s></p><p type="main">

<s>Attese a questo studio con singolare zelo lo Swammerdam, il quale, <lb></lb>soffiando entro esilissimi tubettini metallici a quest&#039;uso proprio fabbricati, <lb></lb>pose le valvole e la direzione del moto da esse indicata sotto gli occhi dei <lb></lb>curiosi osservatori. </s>

<s>“ Asserimus, egli dice, quod iam, anno 1664, 19 Junii, <lb></lb>Salmurii in Gallia, praesentibus variis Medicinae doctoribus celeberrimis, tu­<lb></lb>bulorum aeneorum ac tenuissimorum ope,.... valvulas in vasis lymphati­<lb></lb>cis, motum iam adsignatum lymphae ad oculum quoque confirmantes, obser­<lb></lb>vaverimus, figuris illustraverimus, atque amicorum nostrorum curiosioribus, <lb></lb>tum alibi, tum praesertim Amstelodami degentibus, communicaverimus. </s>

<s>Quas <lb></lb>figuras delineatas, una cum praeparandi modo, postquam a nobis accepisset <lb></lb>clariss. </s>

<s>D. Blasius,.... easdem adiunxit Commentariis suis in Veslingii syn­<lb></lb>tagma ” (De respiratione, Lugd. </s>

<s>Batav. </s>

<s>1667, pag. </s>

<s>90). </s></p><p type="main">

<s>Ma perchè il Bils seguitava nonostante a strepitare e a dire che avrebbe <lb></lb>voluto veder le valvole dentro i vasi con gli occhi, e che nessuno ancora <lb></lb>gliele aveva sapute mostrare, Federigo Ruysch uscì fuori, nel 1665, con un <lb></lb>libretto in 12°, appositamente intitolato <emph type="italics"></emph>Dilucidatio valvularum in vasis <lb></lb>lymphaticis et lacteis,<emph.end type="italics"></emph.end> dove esprimeva così nel proemio la speranza di aver <lb></lb>finalmente vinta, colle sue lucide dimostrazioni, la ritrosia del nobilissimo e <lb></lb>lungamente ostinato oppositore: “ Bilsius, per multos annos, obstrepere non <lb></lb>cessavit neminem sibi posse ostendere in vasis lymphatìcis valvulas has in <lb></lb>rerum natura extare neganti. </s>

<s>Ego e contra, eas, non solum in rerum na­<lb></lb>tura extare assero, ast illi quoque luculenter demonstravi ” (In Mangeti Bi­<lb></lb>bliotheca anat. </s>

<s>cit., pag. </s>

<s>712). </s></p><p type="main">

<s>La dimostrazione dall&#039;altra parte non era troppo difficile, trattandosi di <lb></lb>fatti. </s>

<s>Ma ben più difficile riusciva a intendere a che fine servisse un umore, <lb></lb>a dispensare il quale equabilmente e con moto non interrotto, aveva la Na­<lb></lb>tura macchinata quell&#039;artifiziosa struttura di valvole, che si vedono ne&#039;dutti <lb></lb>acquosi ricorrere così frequenti. </s>

<s>Il Bartholin, nella Storia nuova dei vasi <lb></lb>linfatici, riserbò il cap. </s>

<s>VII a trattare appositamente de&#039;loro usi, che furono <lb></lb>da lui ridotti a questi due principali: “ I ut nutriendas partes onere inu-<pb xlink:href="020/01/1362.jpg" pagenum="237"></pb>tilis sibi aquae levent; II ut aquam aliis partibus certos in fines apportent, <lb></lb>in primis cordi, sive ad sanguinem alioquin crassiorem nonnihil diluendum, <lb></lb>sive calidiorem temperandum, sive ad sanguinis concoctionem promovendam ” <lb></lb>(In Mangeti Bibliotheca cit., pag. </s>

<s>697). </s></p><p type="main">

<s>Il Pecquet, che fu de&#039;più fervorosi ad applaudire alla scoperta, perchè <lb></lb>essendo il suo Ricettacolo sempre in faccenda di ricever la linfa aveva che <lb></lb>rispondere a coloro, i quali opponevano ch&#039;esso Ricettacolo negli animali <lb></lb>digiuni si rimaneva inutile e ozioso; immaginò che l&#039;umore acqueo fosse <lb></lb>dalla Natura ordinato nell&#039;economia animale per rilavare i vasi, e tenerli <lb></lb>liberi dalle ostruzioni. </s>

<s>“ Adde, poi soggiunge, virtuti lotivae, ex aciduloso <lb></lb>succo sanguinis ipsius aut chyli fermentativam. </s>

<s>In intestinis diffunditur ut <lb></lb>bilis mordacem reprimat impetum ” (Opera cit., pag. </s>

<s>117). </s></p><p type="main">

<s>Il Glisson approvò alcuni di questi usi dell&#039;umore acquoso, e ne esco­<lb></lb>gitò altri de&#039;nuovi: “ Nimirum sanguinis coagulationem probibet, et cum <lb></lb>maxima illius pars iam antea ad volatilitatem, sive exhalationem perducta <lb></lb>sit, spiritibus vitalibus socium sibi adiungit, sanguinisque micationem pro­<lb></lb>movet ” (Anatomie hepatis cit., pag. </s>

<s>552). Era opinione però dell&#039;illustre <lb></lb>Anatomico di Cambridge che male s&#039;indovinerebbero gli usi della linfa, senza <lb></lb>prima determinarne bene l&#039;origine e la natura. </s>

<s>Il Pecquet, nel luogo ulti­<lb></lb>mamente citato, aveva espressa una sua opinione, che cioè l&#039;umore acqueo <lb></lb>portato dai nuovi vasi bartoliniani fosse un escremento del sangue. </s>

<s>“ Et licet <lb></lb>excrementum sanguinis aqueum eiusmodì liquorem existimem, non eum ta­<lb></lb>men suspìcer inutilem usquequaque. </s>

<s>” Ma il Glisson negò alla linfa la na­<lb></lb>tura di escremento, perchè saviamente ragionava, se fosse tale, si sarebbe <lb></lb>dovuta espellere come tutti gli altri escrementi del corpo, e non farla tor­<lb></lb>nar di nuovo a rimescolarsi col sangue. </s>

<s>“ Non est sanguinis excrementum, <lb></lb>quoniam denuo in venas regreditur, et cum sanguine remiscetur ” (ibid., <lb></lb>pag. </s>

<s>483, 84). </s></p><p type="main">

<s>Hanno una gran somiglianza, argutamente pensava il Glisson stesso, il <lb></lb>sangue arterioso e la linfa: ambedue reflui dalle varie parti del corpo, per <lb></lb>appositi canali forniti di valvole, e ambedue influenti nel ventricolo destro <lb></lb>del cuore. </s>

<s>Che se si assomigliano così, i due generi di vasi e gli umori in <lb></lb>essi contenuti, nel termine, debbono altresì rassomigliarsi ne&#039;principii. </s>

<s>I prìn­<lb></lb>cipii delle vene son dalle estremità arteriose, alle quali esse vene attingono <lb></lb>il sangue, che ha servito alla nutrizione. </s>

<s>È probabile perciò che anche i lin­<lb></lb>fatici attingano il loro umore avanzato ad altri vasi, che hanno portato alle <lb></lb>membra qualche altra sorta di nutrimento differente dal sangue arterioso. </s></p><p type="main">

<s>Or il Glisson si mise tutto in sollecitudine di cercar quali fossero que­<lb></lb>sti vasi, che sarebbero come le arterie dei dutti acquosi, e gli parve di tro­<lb></lb>varli ne&#039;nervi, che perciò furono da lui costituiti, nella economia animale, <lb></lb>a far gli ufficii di un quinto e nuovo genere di condotti. </s>

<s>“ Sunt etiam co­<lb></lb>niecturae probabiles quae suadeant haud esse uspiam quinti generis vasa <lb></lb>communia, hactenus ignota, quae liquorem succulentum in partes illas omnes <lb></lb>immittant ” (ibid., pag. </s>

<s>486). </s></p><pb xlink:href="020/01/1363.jpg" pagenum="238"></pb><p type="main">

<s>Le congetture poi che persuadevan l&#039;Autore dover essere quel quinto <lb></lb>genere di vasi i nervi, avevano il loro fondamento sull&#039;osservazione di quei <lb></lb>tanti rami nervosi, mandati alle viscere e alle numerose ghiandole conte­<lb></lb>nute nell&#039;abdome. </s>

<s>Qual&#039;è dunque l&#039;ufficio proprio di cotesti nervi, che non <lb></lb>è certo quello di presiedere alla sensazione o al moto? </s>

<s>E prendeva il Glis­<lb></lb>son per particolare esempio la milza, i nervi della quale, perciocchè non <lb></lb>servono alla glandola per sentire o per muoversi, “ nulli insigni usui, ne <lb></lb>conclude, destinari videntur, nisi quidpiam, vel ad lienem adferant, vel ab <lb></lb>eodem auferant. </s>

<s>Non autem existimandum est quicquam eorum adminiculo <lb></lb>ad lienem apportari, quoniam neque id huic ex usu fuerit, nec vas excre­<lb></lb>torium ullum adest, per quod ingestus humor egeratur foras. </s>

<s>Ideoque opor­<lb></lb>tet aliquid e liene educant, quod deinde in superiorem abdominis plexum <lb></lb>transferant, unde postea data occasione, vel immediate per nervos sexto pari <lb></lb>connexos, vel mediantihus cerebro et medulla spinali, in omnes totius cor­<lb></lb>poris nervos distribuatur ” (ibid., pag. </s>

<s>520, 21). Applica il medesimo ragio­<lb></lb>namento alle altre ghiandole, e specialmente a quelle del mesenterio, le quali <lb></lb>“ prae caeteris, egli dice, ad propositum nostrum maxime spectant ” (ibid., <lb></lb>pag. </s>

<s>530). </s></p><p type="main">

<s>Il nuovo inaudito ufficio, commesso dal Glisson ai nervi, levò gran ro­<lb></lb>more fra i Fisiologi, e il Bartholin fu primo a insorgere contro l&#039;Anatomico <lb></lb>inglese, che aveva introdotto nella scoperta de&#039;vasi linfatici, in persona del <lb></lb>Giolivio, un terzo odioso competitore. </s>

<s>Altri però non dubitarono di segui­<lb></lb>tar le ipotesi glissoniane o schiette, com&#039;avevale proposte l&#039;Autore, o mo­<lb></lb>dificate, secondo un notabile esempio, che tra poco vedremo, offertoci dal <lb></lb>Borelli. </s></p><p type="main">

<s>E qui il sentire, dopo lungo silenzio, risonarci alle orecchie il nome di <lb></lb>un Italiano, rallegra, e dall&#039;altra parte accora, per vederlo comparire all&#039;ul­<lb></lb>timo, e come personaggio, se non estraneo, certamente secondario in que­<lb></lb>st&#039;amplissima scena, che apertasi pure in Italia passò in Francia, e andò a <lb></lb>chiudersi in Svezia e in Danimarca. </s>

<s>Il Pecquet, il Rudbeck e il Bartholin, <lb></lb>inspirati dall&#039;Asellio, ne compierono la gloriosa scoperta, verso la quale gli <lb></lb>Italiani si mostrarono inoperosi, come inoperosi s&#039;erano mostrati nelle sco­<lb></lb>perte del Colombo e del Cesalpino, compiute poi non meno gloriosamente <lb></lb>dall&#039;Harveo. </s>

<s>Intorno a che lasciamo per un poco meditabondi i nostri let­<lb></lb>tori Italiani, per poi ripigliar con essi il cammino, che dopo lunga peregri­<lb></lb>nazione ci riconduce in patria. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Siamo nelle sale anatomiche del liceo di Pisa, dove Giovanni Finck eser­<lb></lb>cita il suo coltello per dimostrare, ai curiosi ivi convenuti e allo stesso <lb></lb>Granduca, una cosa nuova: il Canale cioè che prende il chilo dalle vene <pb xlink:href="020/01/1364.jpg" pagenum="239"></pb>mesenteriche, e per la giugulare destra lo riversa nella Vena cava, d&#039;onde <lb></lb>egli scende a diritto nel cuore. </s>

<s>È Claudio Beriguardo che, nel VII della <lb></lb>III Parte de&#039;suoi Circoli pisani, ci attesta il fatto con queste espresse pa­<lb></lb>role, dop&#039;avere accennato alla scoperta delle vene lattee: “ Illae ab intesti­<lb></lb>nis, per mesenterium dispersae, quamplurimae immittunt ramos ad pancreas, <lb></lb>iugularem dextram, et inde ad cor per ductus, quos praeclare ostendit <lb></lb>Jo. </s>

<s>Finchius, nobilis anglus, in Lyceo pisano anatomicus ordinarius, ut et <lb></lb>multa alia scitu dignissima coram serenissimo Magno Duce ” (Patavii 1661, <lb></lb>pag. </s>

<s>617). Che poi riuscisse l&#039;Anatomico inglese a far credere quella una <lb></lb>sua nuova scoperta, s&#039;argomenta pure dalle espressioni dello stesso Beri­<lb></lb>guardo, che soggiunge aversi perciò il Finchio meritata non minor lode e <lb></lb>gloria “ quam Guilielmus Harveius, decus inclitae suae nationis, cuius et <lb></lb>ille spes altera dici potest ” (ibid.). </s></p><p type="main">

<s>Si prova da questo documento più cose degne di considerazione, e prin­<lb></lb>cipalmente che, in uno de&#039;più fiorenti Studii italiani, s&#039;ignorava così la sco­<lb></lb>perta pecqueziana, che uno straniero potè dimostrarla in pubblico per sua. </s>

<s><lb></lb>Nè, in secondo luogo, è da lasciare inconsiderato che, non il Finchio solo, <lb></lb>ma molti degli Anatomici pisani di que&#039;tempi erano stranieri, e particolar­<lb></lb>mente inglesi: l&#039;Aubery, il Tilmann, il Fava, il Baines e altri. </s>

<s>È ciò un <lb></lb>argomento certo della penuria, che s&#039;aveva allora in Italia, dove il campo <lb></lb>anatomico era rimasto isterilito dalle viete discipline galeniche instaurate dal­<lb></lb>l&#039;Acquapendente, il quale s&#039;interpose fra il Cesalpino, che preparava le vie <lb></lb>alla scoperta del circolo del sangue, e l&#039;Asellio, che iniziava le scoperte del <lb></lb>Canal toracico e de&#039;vasi linfatici, come argine attraversato al fiume della <lb></lb>scienza italiana, che fece impaludar l&#039;alveo di sopra, e rimaner vuoto l&#039;alveo <lb></lb>di sotto. </s></p><p type="main">

<s>A riempir dunque cotesto vuoto si chiamarono in Italia, e segnatamente <lb></lb>in Pisa, stranieri, infintantochè non fu istituita la nuova scuola anatomica <lb></lb>del Borelli, la quale cresceva su rigogliosa, a pigliare il suo posto, e a ri­<lb></lb>vendicar la patria del patito servaggio e dell&#039;onta. </s></p><p type="main">

<s>Una delle più notabili fra queste rivendicazioni, e che più strettamente <lb></lb>s&#039;attiene al presente argomento storico, è quella relativa alla scoperta del <lb></lb>canale toracico. </s>

<s>L&#039;opuscolo, pubblicato dal Pecquet in Parigi nel 1651, non <lb></lb>s&#039;introdusse così facilmente in Toscana, dove piuttosto che l&#039;anatomia si <lb></lb>coltivava la fisica, diciamo così, torricelliana. </s>

<s>Ma quando il solitario opuscolo <lb></lb>disperso s&#039;aggiunse alle altre Dissertazioni pecqueziane, dove quella stessa <lb></lb>Fisica trovava così nuova e sì importante cultura, non potè non essere pre­<lb></lb>murosamente ricercato dai professori Pisani, chiamati intanto in Firenze dal <lb></lb>principe Leopoldo ai nuovi accademici consessi. </s></p><p type="main">

<s>Quelle pecqueziane Dissertazioni, alle quali precedevano gli Sperimenti <lb></lb>nuovi anatomici, furono pubblicate nel 1654 in Parigi, e benchè non sia fa­<lb></lb>cile determinare il tempo, in che ne giunse in Firenze e in Pisa la notizia, <lb></lb>è certo nulladimeno che, nel Luglio del 1657, erano state esaminate nell&#039;Ac­<lb></lb>cademia del Cimento, in un Diario della quale, sotto il di 13 di quel mese, <pb xlink:href="020/01/1365.jpg" pagenum="240"></pb>di mano del Rinaldini, si legge: “ Si fece l&#039;esperienza del Roberval<gap></gap>e della <lb></lb>vescica di pesce, che si gonfia nel vacuo, proposta dal signor Borelli ” (MSS. <lb></lb>Cim., T. II, P. I, c. </s>

<s>49). </s></p><p type="main">

<s>Al comparire del documento, che faceva autentica testimonianza del <lb></lb>primo inventore del Canale toracico, ebbe a rimanere svergognato il Fin­<lb></lb>chio, e quell&#039;uggia segreta, sentita dalla vecchia scuola inglese verso la nuova <lb></lb>italiana, fu allora che proruppe in aperti dissidii. </s>

<s>In mezzo a così fatti dis­<lb></lb>sidii s&#039;ebbe quel singolare esempio di rivendicazione, che si diceva di sopra, <lb></lb>e il quale consisteva nel pretendere e nel dimostrar, che facevano i Nostri, <lb></lb>come il primo a scoprire il Canal toracico non era stato nè il Finchio e nè <lb></lb>il Pecquet stesso, ma un Anatomico italiano del secolo XVI, Bartolommeo <lb></lb>Eustachio. </s>

<s>A qual occasione, e qual parte avessero i dissenzienti stranieri in <lb></lb>resuscitare le sepolte tradizioni della scienza italiana, è notizia che non può <lb></lb>non essere desiderata dai curiosi d&#039;intendere questa storia. </s></p><p type="main">

<s>In Pisa, e poi anche in Messina, sotto la disciplina del Borelli, s&#039;edu­<lb></lb>cavano il Malpighi specialmente e il Fracassati a sezionar la più eletta parte <lb></lb>di quella pesca, che si faceva nel vicino mare, e ch&#039;era dalla munificenza <lb></lb>de&#039;Principi medicei offerta al Borelli stesso, perchè vi potesse studiare gli <lb></lb>organi e gli artificii del nuoto. </s>

<s>Quegli esperti e curiosi anatomici però non <lb></lb>lasciavano a quella occasione di esaminare anche le altre parti, fra le quali <lb></lb>il nervo ottico, che ne&#039;pesci spada, ne&#039;Tonni e in simili pesci più grossi, <lb></lb>apertamente mostrò, contro la comune opinione, d&#039;esser composto di una <lb></lb>larghissima membrana nervosa, gentilmente ristretta con pieghe simili a <lb></lb>quelle, che s&#039;usano nei fazzoletti. </s></p><p type="main">

<s>Fece la dimostrazione il Fracassati in Pisa, alla presenza del Granduca <lb></lb>e degli Anatomici inglesi, i quali a principio non mostrarono, racconta il <lb></lb>Borelli, che tal notizia giungesse loro nuova. </s>

<s>“ Poi si mutarono d&#039;opinione, <lb></lb>e di più dissero che, per esser tal nervo tenero e di sostanza midollare, fa­<lb></lb>cilmente poteva col coltello essere spianato in quella forma di membrana, e <lb></lb>con franchezza dissero quella esser tale, senza però averla voluta vedere ed <lb></lb>osservare diligentemente, il che se avessero fatto, non l&#039;avrebbero detto. </s>

<s>Dopo <lb></lb>tre giorni, quei medesimi signori Inglesi mostrarono al serenissimo Gran­<lb></lb>duca un libro (Opuscula anatomica) di Bartolommeo Eustachio, anatomico <lb></lb>italiano del secolo passato, il qual dice queste parole, nel trattato <emph type="italics"></emph>De ossi­<lb></lb>bus,<emph.end type="italics"></emph.end> pag. </s>

<s>227 (Venetiis 1564): <emph type="italics"></emph>Tam cito admiratio illa evanuit quam ner­<lb></lb>vum visorium, in eo animali, quod cognitum nunc habes, tibi ac pluri­<lb></lb>mis aliis movisse praedicabas, qui nervus, veluti tenuissimum matronarum <lb></lb>linteum, in innumeras rugas aequales, et pari serie distributas complica­<lb></lb>tus, tuniculasque illas ambiente coactus, hanc eadem incisa evolvi sese <lb></lb>permittebat, et in amplam membranam totum explicari atque estendi. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb>(Inter M. Malpighi, Opera posthuma, Londini 1697, P. II, pag. </s>

<s>1, 2). </s></p><p type="main">

<s>Così gl&#039;Inglesi, svergognati alla presenza del Granduca per l&#039;accusa di <lb></lb>plagio del Canale toracico, s&#039;erano vendicati degl&#039;Italiani, accusandoli in­<lb></lb>nanzi allo stesso Granduca di manifesto plagio della struttura del nervo ot-<pb xlink:href="020/01/1366.jpg" pagenum="241"></pb>tico. </s>

<s>Ma i Nostri non erano in verità d&#039;altro colpevoli, che di aver troppo <lb></lb>trascurate le tradizioni della scienza italiana, e di aver mostrato di non co­<lb></lb>noscere, altro che forse di nome, Bartolommeo Eustachio. </s>

<s>Si può credere <lb></lb>allora se la curiosità gli spinse a ricercare il libro dell&#039;Anatomico italiano, <lb></lb>e attentamente leggendolo, s&#039;abbatterono a notar, nell&#039;opuscolo <emph type="italics"></emph>De vena <lb></lb>sine pari,<emph.end type="italics"></emph.end> là nell&#039;antigramma XIII, queste parole, che seguono alla descri­<lb></lb>zione del tronco giugulare sinistro, osservato dall&#039;Autore stesso nell&#039;anato­<lb></lb>mia di un cavallo: “ Itaque, in illis animantibus, ab hoc ipso insigni trunco <lb></lb>sinistro iuguli, qua posterior sedes radicis venae internae iugularis spectat, <lb></lb>magna quaedam propago germinat, quae, praeter quam quod in eius origine <lb></lb>hostiolum semicirculare habet, est etiam alba, et aquei humoris plena, nec <lb></lb>longe ab ortu in duas partes scinditur, paulo post coeuntes in unam, quae <lb></lb>nullos ramos diffundens, iuxta sinistrum vertebrarum latus, penetrato septo <lb></lb>transverso, deorsum ad medium usque lumborum fertur. </s>

<s>Quo loco latior <lb></lb>effecta, magnamque arteriam circumplex, obscurissimum finem, mihique <lb></lb>adhuc non bene perceptum, obtinet ” (Opuscula anat. </s>

<s>cit., pag. </s>

<s>301). </s></p><p type="main">

<s>Non vi è dubbio che quella vena bianca, piena di un umore acquoso, <lb></lb>la quale, penetrato il diaframma presso i lombi, si allarga, non sia il Canal <lb></lb>pecqueziano col suo Ricettacolo, ma l&#039;Eustachio non la riconosce punto per <lb></lb>tale, nè nel principio nè nel termine o nell&#039;uso, e tutt&#039;altro che stimarla <lb></lb>uno degli organi primarii nell&#039;economia animale, crede che sia una prov­<lb></lb>videnza della natura tutta propria al cavallo. </s></p><p type="main">

<s>Nonostante, gli Anatomici pisani, a capo de&#039;quali era il Fracassati, esul­<lb></lb>tarono della scoperta, e inconsideratamente uscirono fuori a vantarsi che, <lb></lb>quasi un secolo prima del Pecquet, il Canal toracico e il Ricettacolo del chilo <lb></lb>erano stati scoperti, e pubblicamente descritti da un Italiano. </s>

<s>Anzi, in quel <lb></lb>fervore, e in quel risvegliarsi che faceva la scienza anatomica fra&#039;Nostri, <lb></lb>quasi dolce lusinga escusatrice de&#039;lunghi sonni, e riparatrice di perduti <lb></lb>acquisti, a quel modo che si volevano i meriti del Pecquet rivendicare al­<lb></lb>l&#039;Eustachio, si pretese di attribuire al Cesalpino gli onori conquistati dal­<lb></lb>l&#039;Harveo. </s></p><p type="main">

<s>Sedussero queste lusinghe così l&#039;animo degli Italiani, che il Borelli e <lb></lb>il Malpighi ebbero a dar mano alla penna per consigliare ai loro stessi amici, <lb></lb>discepoli e connazionali, più giusti e più assennati giudizi. </s>

<s>Fu a quest&#039;unico <lb></lb>intendimento composta dal Borelli, nel 1664, una scrittura, la quale il Mal­<lb></lb>pighi inseri a principio della II parte delle sue Opere postume, da noi sopra <lb></lb>citate. </s>

<s>Egli ivi invita i troppo fervorosi zelanti del nome italiano a conside­<lb></lb>rare più cose: “ Prima, che se questo fosse lecito, per una sola parola in­<lb></lb>cidentemente detta a modo di enimma, privar tutti gli inventori delle cose <lb></lb>nuove di quella gloria che loro si deve; darebbero troppo vantaggio questi <lb></lb>signori a coloro, che hanno voluto privar l&#039;Harveio della gloria della in­<lb></lb>venzione della circolazione del sangue. </s>

<s>La qual cosa, non parendomi giusta <lb></lb>nè ragionevole, mi sforza a distendermi qualche poco sopra questo parti­<lb></lb>colare. </s>

<s>” <pb xlink:href="020/01/1367.jpg" pagenum="242"></pb>… </s></p><p type="main">

<s>“ Egli è bene applicar questo discorso al proposito nostro: Scrisse il Cesal­<lb></lb>pino espressamente che il sangue girava dal destro ventricolo del cuore per li <lb></lb>polmoni, passando dalla vena arteriosa nell&#039;arteria venosa, conducendosi al si­<lb></lb>nistro ventricolo del cuore, e quivi finisce, nè ebbe tanta accortezza di cono­<lb></lb>scere che gran tesoro gli era venuto alle mani, ma trapassa questa cosa come <lb></lb>se niente importasse. </s>

<s>Successe poi l&#039;Harveio, e con maravigliosa accortezza e <lb></lb>profondo giudizio conobbe non solo la circolazione per i polmoni, ma l&#039;ampliò <lb></lb>a tutto il resto del corpo, e la dimostrò evidentemente con l&#039;esperienza. </s>

<s>” </s></p><p type="main">

<s>“ Similmente Bartolommeo Eustachio racconta di aver ne&#039;cavalli osser­<lb></lb>vato certo canale pieno di una materia bianca aderente alla schiena, ch&#039;egli <lb></lb>stesso non sa se sia sangue o acqua o altra materia, nè intese il principio, <lb></lb>nè il fine di detto condotto, nè che fosse il Canale del chilo, che si condu­<lb></lb>cesse dagl&#039;intestini direttamente al cuore, nè niun altro di quegli usi ma­<lb></lb>ravigliosi, che da tale invenzione si sono cavati. </s>

<s>Venne poi quel fortunato <lb></lb>giovane Pecqueto, il quale, da un semplice indizio di vedere uscir dal cuore <lb></lb>un liquor bianco, si mosse a cercar l&#039;origine del detto vaso, e mostrò evi­<lb></lb>dentemente tutto il suo progresso ed uso, e non solo riconobbe una cosa <lb></lb>tanto preziosa, ma ancora la sparse, e comunicò a noi tutti questa recondita <lb></lb>e preziosissima verità. </s>

<s>Or chi non vede che l&#039;invenzione d&#039;Eustachio di questo <lb></lb>dutto fu casuale, dubbiosa, incerta, non conosciuta nè apprezzata da lui stesso, <lb></lb>nè da niuno de&#039;posteri in maniera, che si assomiglia piuttosto agli enimmi <lb></lb>degli antichi, li quali s&#039;intendono solamente dop&#039;esser seguito l&#039;effetto, e <lb></lb>piuttosto si attribuisce a loro credulamente quel significato che non avevano, <lb></lb>nè gli autori di essi se l&#039;avevano immaginato nè sognato? </s>

<s>” (pag. </s>

<s>2, 3). </s></p><p type="main">

<s>Il Malpighi, in più concise parole, ripeteva gli stessi concetti. </s>

<s>Posto il <lb></lb>principio che “ in artibus et scientiis inventor is dicendus est, qui Naturae <lb></lb>arcanum per suas causas patefecit, rationum et experimentorum cumulatis <lb></lb>argumentis firmavit, et usum Naturae congruum dilucide exposuit, ” ne <lb></lb>faceva scendere per legittima conclusione esser l&#039;Harvey “ sanguinis circu­<lb></lb>lationis inventor, et Pecquetus Thoracici ductus auctor ” (ibid, pag. </s>

<s>7). </s></p><p type="main">

<s>I giudizii del Borelli e del Malpighi eran giusti, ma non era la sola se­<lb></lb>renità della mente che gli guidava. </s>

<s>Dall&#039;aver dimostrato che la scoperta del <lb></lb>Canal toracico fu all&#039;Eustachio casuale, intendevano di concluderne che fosse <lb></lb>pure casuale, incerta e non intesa, la scoperta del nervo ottico, e così di­<lb></lb>fendersi, appresso al Finchio e agli altri inglesi, dell&#039;accusa di plagio La <lb></lb>difesa per verità non era legittima, perchè l&#039;argomento da sostenerla era <lb></lb>quello di confessar liberamente che s&#039;erano dimenticate in Italia le patrie <lb></lb>tradizioni della scienza, e che perciò gli opuscoli eustachiani erano rimasti <lb></lb>per loro un tesoro nascosto. </s>

<s>Nè il Borelli però, nè il Malpighi, nè il Fra­<lb></lb>cassati vollero mai fare questa confessione. </s>

<s>Eppure in essa sola è dato in­<lb></lb>tendere le ragioni storiche, per cui le due massime scoperte della circola­<lb></lb>zione del sangue e delle vie del chilo, cominciate in Italia, andarono a <lb></lb>compiersi in terra straniera. </s></p><pb xlink:href="020/01/1368.jpg" pagenum="243"></pb><p type="main">

<s>Ma perchè sempre gli uomini preferiscono le deboli scuse alle ingenue <lb></lb>confessioni, furono presto dimenticati in Italia i giudizii del Borelli e del <lb></lb>Malpighi, e sui principii del secolo XVIII risorsero i fanatici a tor via le <lb></lb>corone dai simulacri dell&#039;Harvey e del Pecquet, per riporle in fronte al Ce­<lb></lb>salpino e all&#039;Eustachio. </s>

<s>Rispetto al Sanseveritano, fu la nuova sommossa, <lb></lb>rivendicatrice de&#039;meriti di lui, capitanata dal Lancisi, quando pubblicò in <lb></lb>Roma, nel 1714, le Tavole eustachiane, e nella prefazione al libro fece il <lb></lb>panegirico dell&#039;Autore. </s>

<s>Ivi, dop&#039;aver dall&#039;Antigramma XIII <emph type="italics"></emph>De vena sine <lb></lb>pari<emph.end type="italics"></emph.end> trascritte le parole stesse da noi sopra citate, “ quid clarius, conclude <lb></lb>il Lancisi, de canali toracico Pecquelus? </s>

<s>” (pag. </s>

<s>XI). </s></p><p type="main">

<s>I savii Italiani nonostante seguitarono a riconoscere, col Borelli e col <lb></lb>Malpighi, nel Pecquet il vero autore della scoperta, nè si ostinarono a ri­<lb></lb>vendicarla alla loro patria, costretti in ogni modo a confessare che, per ciò <lb></lb>che rende quella stessa scoperta compiuta, va la scienza anatomica debitrice <lb></lb>alla sola opera degli stranieri. </s></p><p type="main">

<s>Come non sì sollecito ai Nostri giunse l&#039;opuscolo pecqueziano di Parigi, <lb></lb>così indugiarono anche di più a giungere, da Vuesterat e da Copenaghen, <lb></lb>gli opuscoli del Rudbeck e del Bartholin. </s>

<s>Da un&#039;altra parte la vecchia scuola <lb></lb>inglese era in decadenza, e la nuova non coltivava l&#039;Anatomia pe sè, ma in <lb></lb>servigio della fisica e della meccanica animale. </s>

<s>Da ciò s&#039;intende come gli <lb></lb>Anatomici borelliani non si mostrassero così solleciti di tener dietro alla <lb></lb>nuova scoperta dei vasi linfatici, che insieme con gli altri vasi bianchi s&#039;in­<lb></lb>cominciarono a studiare verso il 1664, come par che si provi da queste pa­<lb></lb>role, scritte il dì 26 dicembre di quell&#039;anno, in una lettera del Bellini al <lb></lb>Borelli. </s>

<s>“ Delle cose, gli dice, ch&#039;ella desidera di sapere, non ce n&#039;è che <lb></lb>meriti gran racconto ed osservazione. </s>

<s>Solo pochi giorni sono si ammazzò <lb></lb>una cerva viva, idest si tagliò viva. </s>

<s>Vi si veddero le vene lattee, il canal to­<lb></lb>racico del Pecqueto, e i vasi linfatici grossissimi “ (Targioni, Notizie cit., <lb></lb>T. I, pag. </s>

<s>287). </s></p><p type="main">

<s>Si diceva dianzi che tardi giunse ai Nostri la notizia delle nuove cose <lb></lb>scoperte in Svezia e in Danimarca, e ora soggiungiamo che quella prima <lb></lb>notizia giunse indirettamente col libro <emph type="italics"></emph>Anatomia Hepatis<emph.end type="italics"></emph.end> di Francesco Glis­<lb></lb>son. </s>

<s>Capitato in Pisa alle mani del principe Leopoldo, lo dette ad esaminare <lb></lb>al Borelli, a cui parvero le cose ivi scritte una nuova rivelazione, o come si <lb></lb>diceva in schietta frase toscana, uno scoprir paese, specialmente per ciò che <lb></lb>vi si diceva delle ghiandole, intorno alle quali vi si commemorava con gran <lb></lb>lode l&#039;opera anatomica del Warthon. </s></p><p type="main">

<s>Ma ciò che più sedusse il Borelli fu quel quìnto ordine di vasi, per cui <lb></lb>si venivano i nervi a costituire arterie del chilo, delle quali i linfatici fos­<lb></lb>sero le vene. </s>

<s>Il cap. </s>

<s>XI del II Tomo <emph type="italics"></emph>De motu animalium<emph.end type="italics"></emph.end> è in gran parte <lb></lb>inspirato a cotesta ipotesi glissoniana, la quale, se parve nell&#039;Inglese ardita, <lb></lb>il Nostro vi giocò intorno forse più arditamente col proprio ingegno. </s>

<s>Dal ve­<lb></lb>der quell&#039;immensa copia di rami nervosi andare all&#039;addome, ai visceri, alle <lb></lb>ghiandole, anche il Borelli, che non pensava aver la vita vegetativa essa <pb xlink:href="020/01/1369.jpg" pagenum="244"></pb>pure bisogno d&#039;innervazione, si persuase facilmente che l&#039;uso di que&#039;nervi <lb></lb>fosse quello di concorrere, col loro succo instillato, a comporre il chilo, a <lb></lb>confezionarlo, “ et per consequens ad nutritionem partium ” (Romae 1681, <lb></lb>pag. </s>

<s>318). E perchè quel succo vien dal cervello alle parti, e dalle parti <lb></lb>ritorna al cervello, l&#039;Autor De&#039;moti animali, che aveva esclusa l&#039;opera dei <lb></lb>vasi linfatici, non dubitò di dimostrar come cosa possibile “ Spiritus per <lb></lb>eosdem canales nerveos contrariis motibus agitari ” (ibid., pag. </s>

<s>319). </s></p><p type="main">

<s>Chiamato dunque dal Principe a render relazione del libro del Glisson, <lb></lb>il Borelli ne parlò con tanta lode, che il Principe stesso lo commendò a&#039;suoi <lb></lb>Accademici di Firenze, ai quali, scrivendo da Pisa come un Notomista in­<lb></lb>glese aveva osservato che i linfatici pigliano il ritorno di quell&#039;umor nutri­<lb></lb>tivo, che i nervi suggono dalle ghiandole del ventre, per dispensarlo alle <lb></lb>parti; lasciava, come se venisse a proporre a loro la soluzione di un nuovo <lb></lb>importante problema, che ne indovinassero il resto. </s></p><p type="main">

<s>Ardente di gioventù e desideroso di gloria era fra quegli accademici il <lb></lb>Magalotti, che lusingandosi di poter colla fantasia e con l&#039;ingegno supplire <lb></lb>al difetto della scienza anatomica, si fecè innanzi a distendere su quel tema <lb></lb>un discorso. </s>

<s>Non avendo un&#039;idea chiara degli ufficii e degli usi de&#039;vasi lat­<lb></lb>tei e de&#039;linfatici, al sentir che riducevano il loro umore nel cuore, pensò <lb></lb>che, no nell&#039;interno di lui ciò facessero, rimescolandosi col sangue, ma nel­<lb></lb>l&#039;esterno, cosicchè fosse il ricettacolo della linfa no il ventricolo, ma il pe­<lb></lb>ricardio. </s>

<s>Non pare ch&#039;egli avesse nemmeno uso del linguaggio anatomico, <lb></lb>designando le parti destra e sinistra del cuore, non secondo la positura che <lb></lb>hanno nell&#039;interno dell&#039;animale, relativamente alle altre membra, ma secondo <lb></lb>che corrispondono alla mano di chi le osserva al di fuori. </s></p><p type="main">

<s>Il discorso del Magalotti insomma, anatomicamente considerato, è da dire <lb></lb>addirittura uno scorbio, e l&#039;Autore stesso lo riconosce e lo confessa. </s>

<s>Ma certe <lb></lb>notizie, come sarebbe quella della nuova foggia di Barometro elegantissimo <lb></lb>inventato dal Viviani, ce lo rendono importante, e più importante che mai <lb></lb>si rende per sè medesimo come documento che attesti qual si fosse, verso <lb></lb>il 1661, la cognizione, che avevasi dell&#039;anatomia e delle funzioni dei vasi <lb></lb>bianchi, dalla più eletta parte dei cultori delle scienze sperimentali in Italia. </s>

<s><lb></lb>Speriamo perciò che non dispiacerà ai nostri Lettori d&#039;intendere quel Di­<lb></lb>scorso, da noi fedelmente trascritto da una copia ritoccata qua e là dalla <lb></lb>stessa penna del Magalotti: </s></p><p type="main">

<s>“ Fui avvisato dal serenissimo principe Leopoldo che si era veduto in <lb></lb>Pisa un libro di certo Notomista inglese, il quale scriveva di avere osser­<lb></lb>vato come i vasi linfatici pigliano il ritorno di quell&#039;umore, che circolando <lb></lb>per i nervi fa nel corpo umano un corso a noi novello d&#039;acqua, come per <lb></lb>le arterie e le vene lo fa il sangue, onde in un certo modo vengono ad es­<lb></lb>sere i nervi come arterie dei suddetti vasi. </s>

<s>” </s></p><p type="main">

<s>“ Altro non mi fu comunicato dall&#039;A. S., come apparisce dalle seguenti <lb></lb>parole, che sono l&#039;istesse della sua lettera: <emph type="italics"></emph>È ben vero che un Inglese ana­<lb></lb>tomista ha stampato un librettino, che scopre paese, e tratta quello di os-<emph.end type="italics"></emph.end><pb xlink:href="020/01/1370.jpg" pagenum="245"></pb><emph type="italics"></emph>servare le ghiandole, che sono nel corpo umano, e fra le altre cose mostra <lb></lb>che le vene linfatiche servono a riportar l&#039;umido, che viene da quello, <lb></lb>che circola per i nervi, e così scopre una nuova circolazione, facendo le <lb></lb>vene linfatiche una parte simile a quella, che fanno le vene; e li nervi, <lb></lb>simile a quella che fanno le arterie. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Questa però è troppo scarsa notizia per poter sensatamente discor­<lb></lb>rere sopra questa novità, onde vi vorrebbero molte e molte esperienze e <lb></lb>tagli replicati, e sì chiarirsi di alcune particolarità essenzialissime, per fon­<lb></lb>dare un mio debole discorso, il quale voglio nondimeno qui brevemente ac­<lb></lb>cennare, per quei rispetti che ho già comunicati al serenissimo Principe. </s>

<s>” </s></p><p type="main">

<s>“ Crederei che tutta l&#039;acqua dei vasi linfatici metta nel pericardio, come <lb></lb>fa il sangue nel cuore. </s>

<s>Ma come poi dal pericardio sia succhiata dai nervi <lb></lb>(se pure è vero ciò che mi si suppone che per quelli si trovi circolare) <lb></lb>questo stimo io difficilissimo a rinvenirsi, sì per non sapersi se bea quivi <lb></lb>alcun ramoscello di essi, sì per la difficoltà che avrebbe quell&#039;acqua a im­<lb></lb>penetrare per le cavità sue, conciossiachè si dubiti ancora se gli spiriti, che <lb></lb>per essi meano, o per angustissimi fori come per canale scorrendo, o a <lb></lb>grande stento cacciandosi tra filo e filo della fibrosa sostanza loro, vi cor­<lb></lb>rano come per le ritorte di una corda umore. </s>

<s>” </s></p><p type="main">

<s>“ Ma siasi di ciò quel che vuole, bisogna qui assicurarsi se veramente <lb></lb>arrivi al pericardio alcun tronco o ramo di nervi, e come il tronco della <lb></lb>grande arteria nel destro ventricolo si ribee il sangue; così questo risorbi­<lb></lb>sce l&#039;acqua versata dai vasi linfatici, della quale vi si fa conserva. </s>

<s>” </s></p><p type="main">

<s>“ Ma quando questo vi si ritrovi, si cerca il modo col quale possa que­<lb></lb>st&#039;acqua penetrarvi, poichè, se il sangue passa nell&#039;Arteria, ciò accade per­<lb></lb>chè, stringendosi il destro ventricolo nel moto costrittivo del cuore, e quello <lb></lb>trovandosi pieno di sangue, lo caccia a forza dentro all&#039;Arteria, dalla quale <lb></lb>non può ricadere nella cavità del ventricolo, benchè questo sotto se gli apra, <lb></lb>perocchè riman chiuso dalle valvole, che sono in essa. </s>

<s>Ma il pericardio, non <lb></lb>avendo tal moto di sistole e di diastole, come potrà schizzare ne&#039;nervi quel­<lb></lb>l&#039;acqua, che in sè contiene? </s>

<s>Nè mi si dica non esservi a forza cacciata <lb></lb>l&#039;acqua, ma naturalmente sollevarvisi, come fa pe&#039;cannelli sottilissimi di cri­<lb></lb>stallo, perchè ciò si rende impossibile, per la grande strettezza della cavità <lb></lb>interna de&#039;nervi, se pur son forati, e direi piuttosto che non vi salga l&#039;acqua, <lb></lb>ma che s&#039;attragga da&#039;filamenti, che la nervosa sostanza compongono, come <lb></lb>da un lucignolo, da un capo tuffato nell&#039;acqua, succhiarlasi veggiamo e dal­<lb></lb>l&#039;altra gemerla. </s>

<s>” </s></p><p type="main">

<s>“ Ma supponiamo pure esser forati i nervi, il che ha molto del vero­<lb></lb>simile, e mi ricordo aver sentito raccontare dal p. </s>

<s>Fabri una cotale espe­<lb></lb>rienza: Prese egli un grosso nervo, tagliato da un castrato allora aperto e <lb></lb>fumante, e messolo sur una padella di ferro d&#039;un braciere, dov&#039;era però <lb></lb>dianzi stato il fuoco, rigonfiò sì pel calore, che adoprandovi il Microscopio <lb></lb>vi scorse nel mezzo il foro, e se ben mi rammento, tentò di ritrovare il suo <lb></lb>seno con un sottilissimo fil di vetro, e potè farlo. </s>

<s>” </s></p><pb xlink:href="020/01/1371.jpg" pagenum="246"></pb><p type="main">

<s>“ Questo foro però è così piccolo e stretto, che forse l&#039;acqua non vi <lb></lb>può penetrare, se non vi è cacciata con gran violenza. </s>

<s>Io gliela dava uguale <lb></lb>a quella, con cui viene scagliato il sangue nell&#039;arteria, anzi l&#039;istessa appunto, <lb></lb>e ricordandomi di certa esperienza veduta già del signor Vincenzio Viviani, <lb></lb>adattandola al mio proposito, discorreva così: ” </s></p><p type="main">

<s>“ Se al fondo della boccia A (fig. </s>

<s>8) sarà attaccata ad un fil di seta <lb></lb>la vescica B, non interamente gonfia d&#039;aria, ma tutta quella che v&#039;è sia <lb></lb><figure id="id.020.01.1371.1.jpg" xlink:href="020/01/1371/1.jpg"></figure></s></p><p type="caption">

<s>Figura 8.<lb></lb>presa al fondo di qual­<lb></lb>che torre, ed essa ve­<lb></lb>scica nuoti nell&#039;acqua <lb></lb>arzente, la quale non <lb></lb>solo riempia tutta la <lb></lb>boccia A, ma si sollevi <lb></lb>in C, C, C, nei sotti­<lb></lb>lissimi cannellini di <lb></lb>cristallo, i quali per <lb></lb>di sopra sieno tutti <lb></lb>aperti; certissima co­<lb></lb>sa è che, se tal boc­<lb></lb>cia si porterà in alto, <lb></lb>più e più s&#039;andrà sol­<lb></lb>levando l&#039;acqua nei <lb></lb>cannellini, e ciò, non <lb></lb>perchè si sollevi l&#039;a­<lb></lb>cqua per sè medesi­<lb></lb>ma, ma perchè, di <lb></lb>mano in mano che <lb></lb>più si va in alto, sce­<lb></lb>ma la pressione dell&#039;aria ne&#039;cannellini, onde quella che si conserva nella <lb></lb>vescica, senza alterarsi dallo stato di sua natural pressione, tanto acquista <lb></lb>quanto quella perde, e respirando, in mezzo a quell&#039;acqua che la circonda, <lb></lb>è forza che se la discacci d&#039;intorno, e discacciandola la sollevi. </s>

<s>” </s></p><p type="main">

<s>“ Si metta ora, in cambio della vescica, in mezzo della boccia il cuore, <lb></lb>sospeso nel mezzo del pericardio pien d&#039;acqua, la qual tocchino e vi si ba­<lb></lb>gnino le bocche de&#039;ramicelli nervosi figurati da&#039;medesimi cannellini, e si <lb></lb>consideri che quel medesimo schizzar d&#039;acqua, che si fa in essi dalla vescica <lb></lb>per il suo dilatarsi, quell&#039;istesso si fa dal cuore, nel dilatarsi che anch&#039;egli <lb></lb>fa, per lo continuo moto che l&#039;agita, detto da&#039;greci sistole e diastole, e quindi <lb></lb>avviene che, nella diastole del cuore, viene discacciata l&#039;acqua ne&#039;nervi, con <lb></lb>quella stessa forza, che poi nella sistole si scaglia nell&#039;arteria il sangue, e <lb></lb>in questo tempo che si restringe il cuore, gemono per avventura i vasi lin­<lb></lb>fatici per altre docce nel pericardio la loro acqua, in quella stessa guisa che, <lb></lb>stringendosi il destro ventricolo, il sinistro s&#039;apre, e riceve il sangue, che <lb></lb>vi trasmette la Vena cava ” </s></p><pb xlink:href="020/01/1372.jpg" pagenum="247"></pb><p type="main">

<s>“ Molte altre bellissime conietture possono dedursi da quest&#039;acqua di­<lb></lb>scorrente pe&#039;nervi, ne&#039;quali, se pure è vero che stiano gli spiriti, questo <lb></lb>adacquarli che fa la Natura dimostra che debbono essere un vino molto po­<lb></lb>tente, e quell&#039;acqua che lo tempera non avrebbe ad essere un&#039;acqua pazza, <lb></lb>come suol dirsi. </s>

<s>” </s></p><p type="main">

<s>“ Altre speculazioni possono farsi sopra quest&#039;acqua, la quale mi per­<lb></lb>suado che di qui avanti dovrà essere molto risguardata ne&#039;mali, e nella pa­<lb></lb>ralisia e idropisia particolarmente. </s>

<s>Rimane per ultimo che io mi protesti di <lb></lb>aver disteso questo mio concetto, con quella pura semplicità ch&#039;ei nacque, <lb></lb>ond&#039;è che, riconoscendolo sottoposto ad infiniti errori, mi dichiaro non me­<lb></lb>ritare che se ne faccia alcun conto, infinchè le diligenti osservazioni e le <lb></lb>replicate esperienze non istabiliscano il fondamento a più saldi discorsi. </s>

<s>” <lb></lb>(MSS. Cim., T. IX, c. </s>

<s>59-62). </s></p><p type="main">

<s>Chi volesse da questo Discorso del Magalotti pigliare argomento da giu­<lb></lb>dicare della cultura, che intorno a cose anatomiche e fisiologiche avevasi <lb></lb>dagli Accademici fiorentini, verrebbe ad una conclusione troppo sfavorevole <lb></lb>ad essi ed ingiusta. </s>

<s>Ma è pure un fatto, per ciò che particolarmente concerne <lb></lb>i vasi bianchi, che poco si promosse quella cultura dalla scuola del Borelli, <lb></lb>il quale, senza fare nemmeno un cenno degli organi nuovamente scoperti <lb></lb>dagli stranieri, se ne passa in quelle sue meccaniche speculazioni intorno <lb></lb>alla nutrizione, esposte nella II parte dei Moti animali. </s></p><p type="main">

<s>La nuova Fisiologia perciò, così splendidamente iniziata dall&#039;Asellio, si <lb></lb>può dir che incominciasse a coltivarsi in Italia alquanti anni dopo la prima <lb></lb>metà del secolo XVII, per opera di due insigni Naturalisti, il primo de&#039;quali, <lb></lb>ch&#039;è Tommaso Cornelio, erasi ridotto in disparte dagli altri suoi connazio­<lb></lb>nali, per professar solitario la Filosofia cartesiana, e l&#039;altro, ch&#039;è Marcello <lb></lb>Malpighi, e che, per riconquistarsi la filosofica libertà, era quasi disertato <lb></lb>dalla scuola del Borelli. </s></p><p type="main">

<s>Il Cornelio trattando, nel citato proginnasma VI, <emph type="italics"></emph>De nutricatione,<emph.end type="italics"></emph.end> tut­<lb></lb>t&#039;altro che astenersene, com&#039;avea fatto il Borelli, entra animosamente in <lb></lb>mezzo alle questioni suscitate nella scienza dalle nuove scoperte, ed è an­<lb></lb>ch&#039;egli uno degli insorti a difendere la causa del Fegato, che il Bartholin <lb></lb>voleva, <emph type="italics"></emph>iocosis monimentis,<emph.end type="italics"></emph.end> defunto. </s>

<s>“ Compertum quidem est nobis, egli <lb></lb>asserisce con gran confidenza, vel omne alimentum, vel certe maximam <lb></lb>eiusdem partem, per vulgares ventriculi, et mesenterii venas ad iecur con­<lb></lb>fluere ” (Progymnasmata cit., pag. </s>

<s>232). </s></p><p type="main">

<s>Le ragioni, che mossero il Cornelio ad asserir così contro l&#039;opinion <lb></lb>pecqueziana, son presso a poco quelle del Van-Horne, se non che, mentre <lb></lb>l&#039;Olandese credeva che l&#039;umor nutritizio passasse dal Fegato nel Canal chi­<lb></lb>lifero, il Nostro, compiacendosene come di una sua propria scoperta, lo fa­<lb></lb>ceva ritornare agl&#039;intestini, e di li nuovamente al Fegato, <emph type="italics"></emph>iterato saepe cir­<lb></lb>cuitu,<emph.end type="italics"></emph.end> infin tanto che tutta la sostanza nutritizia non si fosse, così tessendo <lb></lb>e ritessendo le medesime vie, consumata. </s>

<s>“ Nemo tamen hactenus animadver­<lb></lb>tit liquorem hunc ab intestinis et alvo, una cum succo alibili, ad iecur aliasve <pb xlink:href="020/01/1373.jpg" pagenum="248"></pb>partes lapsum, magnam partem ad intestina relabi, easdemque vias saepius <lb></lb>iterare, donec alimentum omne fuerit transumptum ” (ibid., pag. </s>

<s>245). </s></p><p type="main">

<s>Rivendicata così la dignità del Fegato, con attribuirgli l&#039;importantissimo <lb></lb>ufficio di confezionare il chilo, e di stillar la bile, tanto necessaria per la <lb></lb>buona distribuzione dell&#039;alimento; passa il Cornelio a investigar le origini <lb></lb>della linfa, “ cui, secondo egli crede, praecipua liquandi diluendique chyli <lb></lb>vis inest ” (ibid., pag. </s>

<s>245). Ei riconosce quella origine non d&#039;altronde es­<lb></lb>sere che dal cibo e dalla bevanda, e i vasi, ordinati dalla Natura a condurre <lb></lb>quell&#039;alimento, partono dal Fegato, come fu primo ad osservarli il Fallop­<lb></lb>pio, e poi a descriverli Natanaele Igmoro. </s>

<s>“ Tandem vero Thomas Bartho­<lb></lb>linus, cum haec ipsa vasa diligentius contemplaretur, observavit in illis con­<lb></lb>tineri aqueum liquorem ” (ibid., pag. </s>

<s>246). Di questo liquore, <emph type="italics"></emph>ab alimento <lb></lb>secretus,<emph.end type="italics"></emph.end> è il destino, conclude così il Cornelio la sua linfatica fisiologia, che, <lb></lb>com&#039;è partito dagl&#039;intestini, “ ad intestina relabatur ” (ibid., pag. </s>

<s>248). </s></p><p type="main">

<s>Se questo, insiem con gli altri Proginnasmi del nostro Fisiologo cosen­<lb></lb>tino, che portan la data di Napoli 1661, ma che furono pubblicati tutti in­<lb></lb>sieme in Venezia nel 1663; giungessero alla notizia del Bartholin, non si <lb></lb>saprebbe da noi dimostrare, ma, quando pure gli fossero pervenuti, non <lb></lb>avrebbero forse sodisfatta l&#039;ambizione di chi voleva esser creduto primo <lb></lb>inventore de&#039;vasi linfatici, punto meglio di quel che l&#039;avesse sodisfatta il <lb></lb>Van-Horne, il quale liberamente attribuiva al Rudbeck quell&#039;ambita in­<lb></lb>venzione. </s></p><p type="main">

<s>In ogni modo non è credibile che quell&#039;uomo, il quale, con l&#039;opera <lb></lb>propria e con quella degli amici, s&#039;era dato tanta faccenda di diffondere <lb></lb>negli scienziati, e di persuaderli che la scoperta de&#039;linfatici era sua; non <lb></lb>sentisse dispiacere degl&#039;Italiani, che l&#039;avessero così negletta, e che non fosse <lb></lb>ancora sorto fra loro a parlarne altro che il Cornelio, in maniera non troppo <lb></lb>degna di sè, nè della scienza. </s></p><p type="main">

<s>Per la mediazione di Erasmo Bartholin, suo fratello, che teneva amici­<lb></lb>zia e corrispondenza epistolare col Viviani, entrò in relazione con gli Acca­<lb></lb>demici del Cimento, e Carlo Dati, per offerire all&#039;illustre straniero un sag­<lb></lb>gio di ciò, che intorno a cose anatomiche s&#039;era scoperto in Italia, gli mandò <lb></lb>l&#039;Epistole malpighiane <emph type="italics"></emph>De pulmonibus.<emph.end type="italics"></emph.end> L&#039;Anatomico danese, tutto dedito <lb></lb>allora allo studio de&#039;vasi lattei, rimase maravigliato, e tanta riconobbe es­<lb></lb>sere la novità, tanta la bellezza del soggetto e l&#039;importanza, che dette mano <lb></lb>a scrivere quella eruditissima dissertazione <emph type="italics"></emph>De pulmonum substantia et <lb></lb>motu,<emph.end type="italics"></emph.end> la quale fu, nel II Tomo delle opere raccolte in Leyda nel 1687, in­<lb></lb>serita dopo le Epistole dello stesso Malpighi. </s>

<s>La principale intenzione però, <lb></lb>ch&#039;ebbe l&#039;Autore in distendere quella scrittura, fu “ ut illam gratiam labo­<lb></lb>ribus aliorum et feliciter inventis exhiberet ” ch&#039;egli sperava avrebbero gli <lb></lb>Italiani retribuita a&#039;suoi Linfatici, a che far disponeva gli animi loro con <lb></lb>questi encomii: “ Debemus plurimum Italorum ingeniis et humanitati, nec <lb></lb>unquam patiar ut tantae gentis gloria apud nostros taceatur. </s>

<s>Mater studio­<lb></lb>rum Bononia has <emph type="italics"></emph>De pulmonibus<emph.end type="italics"></emph.end> observationes per Malpighium peperit, <pb xlink:href="020/01/1374.jpg" pagenum="249"></pb>florentissima Pisa, per Borellum, suscepit, Florentia cultissima pluribus vo­<lb></lb>luit, per Datum, esse communes “ (pag. </s>

<s>336). </s></p><p type="main">

<s>Le intenzioni del Bartholin non andarono a vuoto, imperocchè il Mal­<lb></lb>pighi ben conoscendo come la parte del sistema linfatico, che più aveva bi­<lb></lb>sogno di essere illustrata, era quella delle glandole, si rivolse con gran di­<lb></lb>ligenza a quello studio, e nel 1668 pubblicò la sua Epistola <emph type="italics"></emph>De structura <lb></lb>glandularum conglobatarum.<emph.end type="italics"></emph.end> Riconobbe quella struttura essere di vasi san­<lb></lb>guigni e di nervi, ai quali s&#039;implica un nuovo genere di vasi escretori, che <lb></lb>sono i linfatici, e benchè trovasse molto difficile, per l&#039;esilità delle parti e <lb></lb>per la friabilità della sostanza, l&#039;usarvi attorno il coltello; credè nulladimeno <lb></lb>di poter asserire: “ quamlibet conglobatam glandulam lymphaticis ditari ” <lb></lb>(Lugduni Batav. </s>

<s>1668, pag. </s>

<s>7). A conferma di che vide per mezzo delle <lb></lb>iniezioni, che il liquido passava da una ghiandola all&#039;altra, attraverso ai vasi <lb></lb>sierosi, per andare indi a riversarsi nel Ricettacolo pecqueziano. </s></p><p type="main">

<s>Altri importantissimi problemi erasi proposto di risolvere in sì difficile <lb></lb>soggetto il Malpighi, e fra questi, che da&#039;Fisiologi erano più desiderati, i tre <lb></lb>seguenti: I. </s>

<s>Se le prime origini de&#039;vasi linfatici sieno dalle ghiandole mi­<lb></lb>nori, come da fonti. </s>

<s>II. </s>

<s>Qual sia l&#039;origine de&#039;linfatici, che ricorrono intorno <lb></lb>agl&#039;intestini, e particolarmente nel fegato e nella milza. </s>

<s>III. </s>

<s>Se sia qualche <lb></lb>organo applicato alle estreme diramazioni de&#039;vasi, mediante il quale sia se­<lb></lb>greta la linfa. </s>

<s>Ma trovò la cosa tanto difficile, ch&#039;ebbe, dopo lunghi e dili­<lb></lb>gentissimi studii, e confessare: “ nec adhuc quid certi enunciare mihi <lb></lb>licet ” (ibid.). </s></p><p type="main">

<s>I problemi, lasciati così nella loro prima incertezza dal Malpighi, furono <lb></lb>non infelicemente risoluti dagli anatomici e da&#039;fisiologi posteriori, ma ne ri­<lb></lb>manevano altri ancora a risolversi, e ch&#039;esercitarono l&#039;ingegno dei nostri <lb></lb>Italiani. </s>

<s>Venuti tardi a sedersi al convito ripararono i Nostri alla negligenza <lb></lb>col mandarvi que&#039;due validissimi commensali, che furono il Morgagni e il <lb></lb>Mascagni, e che soli basterebbero per tutti gli altri. </s>

<s>L&#039;opera loro, di che <lb></lb>troppo lungo sarebbe a parlare, basti a noi qui accennarla con qualche <lb></lb>esempio. </s></p><p type="main">

<s>Fra&#039;più curiosi problemi intorno ai linfatici era quello degli usi, a cui <lb></lb>furono le numerose ghiandole riserbate, e con tanta frequenza disposte lungo <lb></lb>il decorso dei vasi. </s>

<s>Il Morgagni sagacemente notò che quella frequenza era, <lb></lb>dagli arti inferiori verso il centro del Dutto toracico, maggiore negli uomini <lb></lb>che ne&#039;bruti. </s>

<s>Ripensando sopra le ragioni di ciò, gli parve di ritrovarla nel­<lb></lb>l&#039;aver l&#039;uomo positura eretta, e i bruti inclinata, per cui si condusse facil­<lb></lb>mente a congetturare, dietro questa comparazione, che l&#039;uso delle ghiandole <lb></lb>fosse quello di promuovere il corso della linfa, e di sostenerla di grado in <lb></lb>grado contro la tendenza della gravità naturale. </s>

<s>“ Porro ex eiusdem obser­<lb></lb>vatione quod vasa lymphatica, ab artubus inferioribus versus thoracici ductus <lb></lb>initium pergentia, plures in homine quam in brutis conglobatas glandulas <lb></lb>subeant; ego illum istarum usum confirmari posse animadverto, quod vide­<lb></lb>licet lymphae motum iuvent, qui quoniam in nobis, ob erectum corporis <pb xlink:href="020/01/1375.jpg" pagenum="250"></pb>positum, multo est per ea vasa difficilior, quam in brutis; ideo plures glan­<lb></lb>dulas et brevioribus intervallis distributas videtur requisivisse ” (Adversaria <lb></lb>anat. </s>

<s>omnia, Patavii 1719, pag. </s>

<s>88). </s></p><p type="main">

<s>Un altro de&#039;più curiosi e de&#039;più importanti problemi da risolversi in­<lb></lb>torno ai linfatici, e che gli stessi Fisiologi moderni confessano non essere <lb></lb>stato ancora ben risoluto, è quello della causa meccanica, che sì agevolmente <lb></lb>sospinge la linfa ne&#039;vasi. </s>

<s>Dopo il Pecquet, che riconobbe quella causa prin­<lb></lb>cipalmente nella compression del torace e nelle pulsazioni arteriose, l&#039;Haller <lb></lb>v&#039;applicò la sua ipotesi degli stimoli e delle azioni irritanti. </s>

<s>Ma il Mascagni <lb></lb>dubitò di questa ipotesi, vedendo gli stessi vasi spontaneamente espellere le <lb></lb>materie iniettate, anche ne&#039;cadaveri, e alla irritabilità alleriana sostitui la <lb></lb>naturale elasticità delle fibre. </s>

<s>“ Cum aquam calentem, seu imbutam colore <lb></lb>seu destitutam, in vasa sanguinea iniecissem ” trovai, egli scrive, che anche <lb></lb>i linfatici apparivano inturgiditi, e passato oltre il liquido, sparivano di nuovo. <lb></lb></s>

<s>“ Itaque vis huiusmodi, dietro ciò ne conclude, qua lymphaticorum humor <lb></lb>propellitur, non solum in cadaveribus post multos a morte horas, iamque <lb></lb>frigefactis, perdurat, sed et per annos servatur, quae tanta activitatis diutur­<lb></lb>nitas, num cum irritabilitate conveniat, Hallerus diudicet..... Porro vim ita <lb></lb>agentem in elasticitate tunicarum esse reponendam ex eo patet, quod vis eius­<lb></lb>modi in hoc prorsus consistit quod partes compressae, flexae ac distractae, in <lb></lb>statum a quo recesserant redire conentur, statimque redeant ubi vis distra­<lb></lb>hens removeatur ” (Vasorum lymphatic. </s>

<s>Historia, Senis 1787, pag. </s>

<s>27, 28). </s></p><p type="main">

<s>Il magnifico volume, ora citato, è degno della grandezza regia di quel <lb></lb>Pietro Leopoldo, granduca di Toscana, a cui volle il Mascagni che fosse de­<lb></lb>dicato, nelle numerose Tavole aggiunte al quale chi guarda, non sa se più <lb></lb>debba ammirare il magistero della Natura in condur quelle sottilissime e <lb></lb>intricatissime reti di vasi, per ogni membro del corpo umano, o la perizia <lb></lb>di chi seppe far di loro così splendida apparizione, col quasi magico soffio <lb></lb>della sua bocca. </s></p><pb xlink:href="020/01/1376.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dei sensi<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del tatt<gap></gap> del gusto e dell&#039;odorato: — II. Dell&#039;organo dell&#039;udito: dell&#039;o<gap></gap>cchio medio. </s>

<s>ossia della <lb></lb>Cassa del timpano. </s>

<s>— III. Dell&#039;orecchio interno, ossia del Labirinto. </s>

<s>— IV. </s>

<s>Del senso dell&#039;udito. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi nello studio degli svolgimenti embrionali attende a que&#039;sottilissimi <lb></lb>innumerevoli vasi, che s&#039;insinuano nell&#039;albume e nel vitello dell&#039;uovo, o <lb></lb>nella placenta aderente all&#039;utero, per dispensare il necessario alimento al <lb></lb>pulcino e al feto, non esita punto in ammettere come verissime le somi­<lb></lb>glianze, tante volte notate dagli Embriologi, tra gli animali e le piante, nelle <lb></lb>quali le innumerevoli radicelle suggono gli alimenti dalla terra, come le in­<lb></lb>numerevoli venuzze suggon gli umori alibili dall&#039;uovo stesso o dall&#039;utero <lb></lb>della madre. </s></p><p type="main">

<s>Ma la pianta si riman perpetuamente in quella sua prima e natia con­<lb></lb>dizione, mentre per l&#039;animale non è che precaria. </s>

<s>Schiuso l&#039;uovo e aperto <lb></lb>l&#039;utero, riceve il nuovo nato in altri modi, e per altre vie l&#039;alimento: si <lb></lb>suggellano le fonti de&#039;vasi umbilicali, e s&#039;apre al sacco dello stomaco e degli <lb></lb>intestini la bocca. </s>

<s>L&#039;albume e il latte simulano da principio i modi della <lb></lb>prima nutrizione fetale, ma poi vien tempo che quel nutrito di latte si rende <lb></lb>indipendente anche dalle mammelle, divenuto atto d&#039;andar per sè medesimo <lb></lb>in cerca del cibo. </s>

<s>Gli organi, che lo pongono in così fatte nuove condizioni, <lb></lb>sono princìpalmente quelli del moto, per i quali si pone in volontaria e spon­<lb></lb>tanea relazione coi corpi circostanti, per ridurli a sodisfare ai bisogni, e alle <lb></lb>comodità della vita. </s></p><pb xlink:href="020/01/1377.jpg" pagenum="252"></pb><p type="main">

<s>La locomozione spontanea però, alla quale servono i muscoli degli arti <lb></lb>e le ossa, aveva bisogno di qualche guida, dall&#039;animale ritrovata fedelissima <lb></lb>nei sensi, e principalmente in quello del tatto, che perciò è sì squisito nelle <lb></lb>mani e ne&#039;piedi, e, per tutto l&#039;integumento esposto a ricevere le prime <lb></lb>esterne impressioni del moto, largamente diffuso. </s></p><p type="main">

<s>La superficialità del tatto era dunque così benissimo accomodata a ser­<lb></lb>vire all&#039;animale di guida, in quel libero aggirarsi che fa per lo spazio pieno <lb></lb>di tanti altri corpi, de&#039;quali era necessario conoscere le relazioni di posi­<lb></lb>zione, per cercarli con amore o per rifuggire da essi con odio. </s>

<s>Primo e prin­<lb></lb>cipale oggetto di questo amore e di quest&#039;odio erano que&#039;corpi buoni a ser­<lb></lb>vire di cibo, de&#039;quali era necessario avesse l&#039;animale stesso conoscenza più <lb></lb>che superficiale, e fu a questo scopo dalla provvidente Natura ordinato l&#039;or­<lb></lb>gano del gusto. </s></p><p type="main">

<s>Si può dire che sia il gusto un finissimo tatto di ciò che hanno i corpi <lb></lb>alibili, no nella loro esterior superficie, ma nell&#039;intima loro sostanza, che ha <lb></lb>da trasformarsi nella sostanza stessa dell&#039;animale, e perciò si sciolgono quei <lb></lb>corpi sopra la lingua, come in mestruo nella saliva, per rendersi così a più <lb></lb>intimo contatto colle papille nervee, più squisitamente elaborate di quelle <lb></lb>disperse sopra la cute. </s></p><p type="main">

<s>I due detti sensi perciò sono il fondamento della vita di relazione, per <lb></lb>conferma di che si osserva che ne partecipano in qualche modo anche le <lb></lb>piante. </s>

<s>Del tatto danno indizio alcune foglie che si risentono, o toccate da <lb></lb>qualche corpo solido, o ripercosse dagli stessi raggi di luce, ma questa pro­<lb></lb>prietà non è visibile che in alcuni casi particolari. </s>

<s>S&#039;ha più manifesto indi­<lb></lb>zio e universale esempio di ciò nelle radicelle, le quali si vedono andar sotto <lb></lb>terra a cercare, e, come avessero gusto, a scegliere gli alimenti, preferendo, <lb></lb>se libera, la più facile via e più spedita, o divertendo il passo, se qualche <lb></lb>ostacolo s&#039;interponga o dall&#039;arte o dalla Natura. </s></p><p type="main">

<s>L&#039;animale però, che appartiene ad un ordine superiore, è fornito di altri <lb></lb>sensi, di che mancano affatto le piante, e patiscono difetto gli stessi animali <lb></lb>inferiori. </s>

<s>L&#039;eccellenza de&#039;nuovi sensi sopra il tatto ed il gusto si rivela prin­<lb></lb>cipalmente da ciò, che mentre in questi non si produce la sensazione, se <lb></lb>non sia l&#039;oggetto immediatamente applicato al sensorio, in quelli agisce l&#039;og­<lb></lb>getto stesso anche a distanza, o per una diffusione di sè o per un qualche <lb></lb>mezzo interposto. </s></p><p type="main">

<s>Sono i corpi, individualmente e nella mondana composizione, in vario <lb></lb>modo di sè diffusivi, cosicchè un&#039;aura circonda ogni oggetto particolare sopra <lb></lb>la terra; un&#039;aura circonda tutta insieme la terra stessa in sè conglobata; <lb></lb>un&#039;aura circonda l&#039;universo. </s>

<s>Ogni corpo terreno perciò si trova continua­<lb></lb>mente immerso in tre distinte ammosfere, le quali, oltre ad avere un&#039;azione <lb></lb>fisica sulle cose circondate, hanno un&#039;azione specifica sopra gli organi del­<lb></lb>l&#039;animale. </s>

<s>L&#039;esalazione di alcuni corpi particolari agisce sull&#039;odorato; l&#039;esa­<lb></lb>lazione della terra, ossia l&#039;aria, agisce specificamente sull&#039;udito, e l&#039;esalazione <lb></lb>dell&#039;Universo, ossia l&#039;etere, agisce sopra la vista. </s></p><pb xlink:href="020/01/1378.jpg" pagenum="253"></pb><p type="main">

<s>Nell&#039;annoverare i sensi, l&#039;odorato ricorre per ordine nel mezzo, e ve­<lb></lb>ramente partecipa della qualità e della natura de&#039;due antecedenti, e de&#039;due <lb></lb>conseguenti. </s>

<s>Ne differisce però da questi notabilmente perchè, mentre l&#039;aura <lb></lb>odorosa è sostanziale dell&#039;oggetto, l&#039;aria e l&#039;etere nell&#039;orecchio e nell&#039;oc­<lb></lb>chio non hanno altra ragion che di segno, i caratteri del quale sono i tre­<lb></lb>mori armonici, la luce, l&#039;ombra, i colori. </s></p><p type="main">

<s>Passar dal segno al significato è opera tutta propria dell&#039;intelligenza, <lb></lb>la quale par che abbia ne&#039;due nobilissimi sensi i principali strumenti del <lb></lb>suo esercizio, e che ritrovi in essi le necessarie condizioni al suo magistero. <lb></lb></s>

<s>È perciò che i due organi sono elaborati con arte maravigliosa, dalla quale, <lb></lb>piuttosto che dal cervello, si può trarre argomento de&#039;gradi dell&#039;intensità <lb></lb>di luce intellettuale, che si accendono ne&#039;diversi individui, e nei diversi or­<lb></lb>dini animali. </s></p><p type="main">

<s>Quella luce dall&#039;altra parte, ch&#039;è splendore di vita, è per noi chiusa in <lb></lb>tenebre profonde: per noi, che non abbiamo della vita stessa altro argo­<lb></lb>mento, che dai moti delle membra e dalle impressioni, che fanno in noi i <lb></lb>corpi, o applicati immediatamente alla cute, alla lingua, alla pituitaria, o <lb></lb>trasmessi all&#039;orecchio, e resi parventi all&#039;occhio attraverso al mezzo dell&#039;aria <lb></lb>che circonda la terra, o dell&#039;etere che circonda l&#039;universo. </s>

<s>Che se i tremori <lb></lb>armonici e le ondulazioni eteree si trovarono involte nel mistero, quando si <lb></lb>considerarono sotto il semplice aspetto fisico, pensiamo che dovrà essere, <lb></lb>quando si vengano a riguardare sotto l&#039;aspetto fisiologico; quando si pre­<lb></lb>tende cioè di avere scienza del modo, come un increspamento d&#039;aria diventi <lb></lb>udito, o un ondeggiare di etere vista. </s></p><p type="main">

<s>Si dovrebbe da queste considerazioni concludere che lo studio della fisio­<lb></lb>logia dei sensi non è soggetto d&#039;esperienza, e che perciò non entra nella <lb></lb>nostra Storia, se non fosse vero dall&#039;altra parte che son di ogni senso esterno <lb></lb>strumenti fisiologici un organo proprio e un sensorio, e che oggetto di ogni <lb></lb>percezion sensitiva è un corpo, il quale fisicamente agisce, benchè l&#039;azione <lb></lb>fisica si trasformi, esaltata in azion fisiologica, in un certo modo per noi mi­<lb></lb>sterioso. </s>

<s>Ma l&#039;organo e il sensorio son soggetti di anatomiche osservazioni, <lb></lb>e la Fisiologia può illustrarsi con fisiche esperienze, come fa per esempio <lb></lb>l&#039;Acustica, rispetto all&#039;udito, e l&#039;Ottica rispetto alla vista. </s></p><p type="main">

<s>Non è dunque il metodo sperimentale inutile in questo studio, e anzi <lb></lb>a lui solo si deve se nulla s&#039;è inteso, specialmente intorno al modo come <lb></lb>si rappresentano le immagini nell&#039;occhio per apprenderne la vista; come i <lb></lb>tremori armonici risveglino l&#039;udito; quali siano gli organi proprii dell&#039;odo­<lb></lb>rato, del gusto e del tatto. </s>

<s>Ampio soggetto è questo di narrazioni, benchè <lb></lb>la brevità ci consigli di restringer le molte cose da dire nelle poche pagine, <lb></lb>in che si svolge questo insiem col seguente capitolo di Storia. </s></p><p type="main">

<s>Incominciando dal tatto, che a giudizio dei più è il senso fondamentale, <lb></lb>chi avesse domandato agli antichi qual ne fosse di lui lo strumento, si sa­<lb></lb>rebbe sentito rispondere: “ Tactus instrumentum esse quiddam intus in cor­<lb></lb>pore abditum, quod potestate tale est, quale actu est tangibile. </s>

<s>” L&#039;enim-<pb xlink:href="020/01/1379.jpg" pagenum="254"></pb>matico responso è in qualche modo interpetrato dal Cesalpino nella V delle <lb></lb>sue Peripatetiche questioni, così esplicando le teorie aristoteliche: “ Ob haec <lb></lb>igitur solum instrumentum tactus internum est, reconditum; caeterorum sen­<lb></lb>suum sensoria exteriora sunt et quodammodo media: unum enim est pri­<lb></lb>mum omnium sensorium sanguinem. </s>

<s>Sanguineam quoque esse oportet eorum <lb></lb>naturam, non enim receptio sine materia fit, sine spiritu, qui in sanguine <lb></lb>est ” (Venetiis 1571, pag. </s>

<s>115). </s></p><p type="main">

<s>Quando poi Galeno dimostrò che la sensibilità non appartiene al sangue <lb></lb>ma ai nervi, i quali hanno la loro origine, no dal cuore ma dal cervello, e <lb></lb>allora s&#039;incominciò a dire più saviamente che lo strumento del tatto era la <lb></lb>cute, ma non se ne seppe, infin a mezzo il secolo XVII, riconoscere l&#039;or­<lb></lb>gano speciale. </s>

<s>Fu primo il Malpighi a fare quella scoperta, la quale è, se <lb></lb>altra mai, per sè e per le sue conseguenze, degna di storia. </s></p><p type="main">

<s>Attendeva l&#039;insigne Fisiologo bolognese a studiare la composizione ana­<lb></lb>tomica della lingua, e diligentemente osservando col microscopio quella dei <lb></lb>bovi, delle capre, delle pecore e dell&#039;uomo stesso, ne ritrovò la superfice <lb></lb>sparsa di piccole eminenze coniche, o di papille, differenti così tra loro, nella <lb></lb>struttura e nella grandezza, da poterle con facilità distinguere in tre classi. <lb></lb></s>

<s>“ Observantur enim aliquae grandiores, quae ad latera praecipue apicis lin­<lb></lb>guae situantur inter infra exarandas. </s>

<s>In area etiam superiori linguae qua­<lb></lb>drato ordine disponuntur: circa mediam regionem, ubi albescit lingua, rarae <lb></lb>observantur: in basis autem lateribus aliquae et insigniores. </s>

<s>Haec, substantia <lb></lb>et figura, videntur aemulari cornua emissilia et conductilia, quae in limacibus <lb></lb>conspiciuntur; ... exordium habent a nervoso et papillari corpore.... Succe­<lb></lb>dunt alterius ordinis papillae copiosiores exaratis: quot enim cornua exterius <lb></lb>linguam tegunt, tot etiam huius generis nerveae papillae intus reperiuntur. </s>

<s><lb></lb>Hae, exortae a communi papillari corpore, in mediocrem altitudinem elevan­<lb></lb>tur, et ab extremo capite nerveas propagines ulterius emittunt, quae subin­<lb></lb>trant iam exaratos sinus, et eorum radiclbus occorrunt.... Circa basim lin­<lb></lb>guae, in cornuum situ, papillae nerveae enarratae foras eminentes mutant <lb></lb>figuram, et obtusiores, mox subrotundae et depressiores fiunt, et harum insi­<lb></lb>gniores non valde absimiles sunt iis, quae ad radices dentium in buccis obser­<lb></lb>vantur ” (Opera Omnia, De lingua, Londini 1687, pag. </s>

<s>15, 16). </s></p><p type="main">

<s>A quale uso possono mai servire queste papille, che debbon essere senza <lb></lb>dubbio una espansione dei nervi? </s>

<s>incominciò a domandare a sè medesimo <lb></lb>il Malpighi. </s>

<s>Sarebb&#039;egli vero, che qui risegga l&#039;organo del gusto? </s>

<s>L&#039;idea. </s>

<s><lb></lb>che tale dovess&#039;essere veramente il fine, per cui furono dalla Natura impo­<lb></lb>sti sopra la lingua que&#039;corpi papillari ora nuovamente scoperti; si rappre­<lb></lb>sentava al discopritore sotto il più lusinghiero aspetto della verità, ripen­<lb></lb>sando a ciò che, intorno allo speciale strumento del gusto, era stato detto <lb></lb>da&#039;suoi predecessori. </s>

<s>Il Bartholin e il Veslingio, forse per l&#039;opinione che <lb></lb>avevano non trovarsi in tutto il corpo carne che si somigli con quella della <lb></lb>lingua, credettero che il senso del gusto non avesse altr&#039;organo che la so­<lb></lb>stanza di lei carnosa. </s>

<s>Il Warthon, avendo trovato alcune glandole alla radice <pb xlink:href="020/01/1380.jpg" pagenum="255"></pb>della lingua, sospettò che fosse in esse la sede propria del senso, ma poi lo <lb></lb>Stenone dimostrò che appartenevano al genere delle glandole salivali, e che <lb></lb>erano perciò ordinate a secernere e no a sentire. </s>

<s>Nè punto più ragionevole <lb></lb>di queste sembrava al Malpighi l&#039;opinion di coloro, che attribuivano la fa­<lb></lb>coltà di gustare alla membrana, da cui superficialmente è rivestita la lingua, <lb></lb>perchè “ si exteriores membranae gustandi munus haberent, Natura forte <lb></lb>sinuosas non abdidisset vias in binis exterioribus involucris exculptas, qui­<lb></lb>bus videtur ulteriorem aditum permittere sapidis corporibus ” (ibid., pag. </s>

<s>18). </s></p><p type="main">

<s>Di qui ne trae il Malpighi una conclusione, che riesce nuova nella storia <lb></lb>della Fisiologia, ed è che il senso del gusto consista in quel vellicar che <lb></lb>fanno, le particelle sapide, le papille nervee disperse sopra la lingua, a quel <lb></lb>modo che, dal vellicar che fanno l&#039;aria e la luce, co&#039;loro tremori, il tim­<lb></lb>pano e la retina, si produce la sensazion dell&#039;udito e della vista. </s>

<s>“ Quare, <lb></lb>cum dictis meatibus insignibus occurrant papillaria corpora, probabilius est <lb></lb>in his ultimo, ex subintranti sapido humore, titillationem et mordicationem <lb></lb>quamdam fieri, quae gustum efficiat. </s>

<s>Fusa enim salia et consimilia, salivae <lb></lb>vel alteri humori commixta, proprio pondere, vel prementis aeris ope, sinus <lb></lb>mox expositos, substantia, nerveas papillas diversimode feriunt, vel blando <lb></lb>quodam motu ipsas demulcent, ita ut, ex diversa figura ingredientis salini <lb></lb>corporis, eiusque vario motu et insinuatione, diversae corporum species na­<lb></lb>turae cognatae vel eidem aversae emergant ” (ibid., pag. </s>

<s>18). Hanno di qui <lb></lb>origine le varie impressioni del gusto, le quali possono talvolta ridursi a do­<lb></lb>lorose, come racconta il Cardano di quell&#039;Augusto Corbetta, che sentiva do­<lb></lb>iore a toccar la lingua col pepe, “ nam ex pipere quidem subintrante lace­<lb></lb>rabantur nerveae papillae, unde dolor. </s>

<s>Non aderat autem saporis sensus, quia <lb></lb>prima radix nervosi corporis ad gustum destinati non consentiebat, vel non <lb></lb>commovebatur blanda illa motione et affectione qua gustum edit, sicut in au­<lb></lb>ditu et visu contingit, organum plus iusto concutiente vel vellicante obiecto ” <lb></lb>(ibid., pag. </s>

<s>19, 20). </s></p><p type="main">

<s>Come nella scoperta dell&#039;organo del gusto, e nelle ipotesi speculate per <lb></lb>rendere la ragione della varietà de&#039;sapori, s&#039;incontrassero quasi nel mede­<lb></lb>simo tempo il Bellini e il Fracassati, lo diremo tra poco, per non interrom­<lb></lb>pere il filo della storia, dalla quale ha da mostrarsi in che modo la scoperta <lb></lb>delle papille nervee sopra la lingua, ad uso del gusto, conducesse il Malpi­<lb></lb>ghi stesso alla scoperta delle papille nervee sopra la cute, ad uso generale <lb></lb>del tatto. </s>

<s>Quella storia poi è così narrata dall&#039;Autore medesimo in questa <lb></lb>forma a Giacomo Ruffo, visconte di Francavilla: </s></p><p type="main">

<s>“ Mens de ambiguo usu, pyramidalibus in lingua descriptis papillis assi­<lb></lb>gnato, anxia torquebatur. </s>

<s>Mens igitur aciem microscopio munitam veluti auxi­<lb></lb>liares convocat copias, et quia brutorum non aderant illico perquirenda mem­<lb></lb>bra, extremum digiti lustro apicem, et dum attentive inaequales illas rugas <lb></lb>quasi in gyrum vel in spiras ductas contemplor, eo e quibusdam alveolis et <lb></lb>finibus subrotunda, ac veluti diaphana emergunt corpora, miro ordine per <lb></lb>interiorem totius digiti faciem copiose dispersa. </s>

<s>Exultavit animus rei novi-<pb xlink:href="020/01/1381.jpg" pagenum="256"></pb>tate laetabundus, et praecipiti subitoque quodam iudicio in eum venit sen­<lb></lb>sum exigua haec corpora eandem naturam et usum cum pyramidalibus lin­<lb></lb>guae papillis sortiri, latumque philosophandi campum mihi videbar aperuisse. </s>

<s><lb></lb>Sed breve conceptae hoc felicitatis momentum ocyus effluxit, dum enim lon­<lb></lb>giori iterum indagine perquiro papillas, deterso digiti apice, frustra eas quaero <lb></lb>mox sensim erumpentes compresso digito auctiores, et diaphanas reddo, et <lb></lb>tandem mutata figura effluere, non sine animi moerore, ut verum tibi fa­<lb></lb>tear, intueor, atque iterum absterso digito humoris instar eas abire conspexi. </s>

<s><lb></lb>His tamen nequaquam fractus animus ex concepto in utrisque papillis usu, <lb></lb>quo sibi maxime complacuerat, aliena iubet rimari ex inaequalitate cutis <lb></lb>quae in nobis etiam observatur, latens aliquod papillae consimile se reper­<lb></lb>turum confidens ” (Ibid., De externo tactus organo, pag. </s>

<s>22). E in fatti se­<lb></lb>zionando i piedi a varii animali, e diligentemente osservando, ritrovò quello <lb></lb>che gli era prima apparito e poi scomparso nel suo proprio dito, intorno al <lb></lb>quale non si poteva con troppa confidenza esercitare il ferro anatomico. </s></p><p type="main">

<s>Andò il sagace investigatore a posare a dirittura la sua attenzione sui <lb></lb>piedi, parendogli esser quelli gli organi, che meglio corrispondessero nei <lb></lb>bruti alle mani degli uomini, ma poi ripensando che dev&#039;essere ne&#039;palpi <lb></lb>delle labbra più che altrove squisitissimo il tatto, si volse ad esaminar quelle <lb></lb>parti con grandissima diligenza, e vi trovò in gran numero papille simili a <lb></lb>quelle scoperte già sulla lingua. </s>

<s>“ Sed quia brutorum aliqua, praecipue qua­<lb></lb>drupedia, superiori labro et externis naricibus, veluti manibus, terram et <lb></lb>obiecta alimenta explorare solent, necessarium duxi inquirere an in huius­<lb></lb>modi consimilem structuram molita fuerit Natura. </s>

<s>Bovis igitur labrum ad <lb></lb>trutinam revoco, et in superiori praecipue parte, elatae quaedam areae, di­<lb></lb>versae tamen figurae in cuticula sese offerunt; nigriores tamen papillas in <lb></lb>singulis areis copiose dispersas reperio, inter quae latiora quaedam hiant <lb></lb>foramina, quae salivam sive sudorem, compressa narium mole, pleno ore <lb></lb>eructant. </s>

<s>Dum interim externum involucrum evellitur, ecce papillarum pe­<lb></lb>dunculos abripi disrumpique video. </s>

<s>Hi autem erumpunt, ut mos est, a re­<lb></lb>ticulari et mucoso corpore, et tandem altas habent radices in subiecta cute, <lb></lb>sub qua copiosissimae locantur glandulae proprio vase excretorio ditatae, ad <lb></lb>exposita orificia desinente. </s>

<s>In sue etiam eandem fere structuram adinveni ” <lb></lb>(Ibid., pag. </s>

<s>25). </s></p><p type="main">

<s>Passa con più diligenza che mai ad esaminare la mano, e ne trova <lb></lb>l&#039;epidermide composta di una membrana muccosa e di una reticolare, nelle <lb></lb>fitte areole della quale s&#039;annidano le papille nervee, insiem con altre di più <lb></lb>fosco aspetto (dalle quali ei crede dipendere la nigrizia degli Etiopi) e le <lb></lb>ghiandole sudorifere. </s>

<s>In quelle papille-nervee disperse tutto intorno per la <lb></lb>cute, ma più condensatamente in alcune parti di lei, riconobbe il Malpighi <lb></lb>il precipuo organo del tatto, il quale opera secondo lui a produrre la sen­<lb></lb>sazione in un modo simile a quello delle papille nervee ricorrenti sopra la <lb></lb>lingua. </s>

<s>“ Haec repetitis sectionibus deprehendi, ex quibus non improbabi­<lb></lb>liter deducam, sicuti ex grandioribus et elatioribus papillis, alias a me in <pb xlink:href="020/01/1382.jpg" pagenum="257"></pb>lingua observatis, gustus organum elicitur ex peculiari situ et nervorum pro­<lb></lb>tractu; ita, ex copiosa harum papillarum congerie et copiosiori grandiorique <lb></lb>earum proventu in organis, ubi maxime animalia tactus motione afficiuntur, <lb></lb>ex earundem etiam propagine in reliquo ambitu, ubi tactus vires etiam exe­<lb></lb>rit, adaequatum tactus organum sufficienter haberi ” (Ibid., pag. </s>

<s>23). </s></p><p type="main">

<s>Così la scoperta delle papille nervee sopra la lingua condusse il Malpi­<lb></lb>ghi all&#039;altra simile scoperta delle papille nervee sopra la cute, e l&#039;organo <lb></lb>del tatto gli si rivelò, in questo modo per analogia, dall&#039;organo del gusto, <lb></lb>dove le dette papille nervee, essendo in più ristretta superficie raccolte e <lb></lb>perciò più notabili, davano anche più facile indizio de&#039;loro ufficii. </s>

<s>Ciò rende <lb></lb>forse la ragione di un fatto singolarissimo nella storia, ed è che concorsero <lb></lb>col Malpighi nella scoperta dell&#039;organo del gusto il Bellini, che la divulgò <lb></lb>nel suo trattato <emph type="italics"></emph>Gustus Organum,<emph.end type="italics"></emph.end> e il Fracassati, che dottamente la com­<lb></lb>mentò nella sua esercitazione epistolica <emph type="italics"></emph>De lingua<emph.end type="italics"></emph.end> indirizzata allo stesso <lb></lb>Malpighi. </s></p><p type="main">

<s>Il Bellini, ch&#039;ebbe primo a notare la singolarità, alla quale abbiamo ac­<lb></lb>cennato, qualificò il fatto per una vittoria riportata cogli amici in comune, <lb></lb>della quale sarebbe indegna cosa sentire invidia. </s>

<s>Dove altri ne avrebbe pro­<lb></lb>vato dispiacere, egli anzi ne godeva. </s>

<s>“ Gaudeo tamen, tum quia alienam mihi <lb></lb>sapientiam obfuturam non iudico, tum quia observationi non easdem forte <lb></lb>meditationes aptamus, sed quisque suas pro genio; tum quia, cum res inter <lb></lb>amicos peracta sit, communia quoque dicenda, potius quam propria, hac <lb></lb>in re videntur; tum denique quod, si de hoc communi invento dolerem, aut <lb></lb>invidus aut arrogans audirem, quorum utrumque cane peius et angue sem­<lb></lb>per odi, utpote quae et a societatibus expellunt, et humanitate spoliant, et <lb></lb>nos ridiculos faciunt, quibus quid homini accidere iniucundius potest, quid <lb></lb>miserabilius? </s>

<s>” (Gustus org. </s>

<s>Bononiae 1665, pag. </s>

<s>243, 44). </s></p><p type="main">

<s>Nonostante, non possono non sentirsi i lettori frugare a una viva cu­<lb></lb>riosità di sapere in che modo occorresse al Bellini di fare la scoperta del­<lb></lb>l&#039;organo del gusto, entrando quasi dentro i reconditi pensieri, che s&#039;agita­<lb></lb>vano per la mente al Malpighi. </s>

<s>E giacchè il Bellini stesso si esibisce spontaneo <lb></lb>a sodisfare a quella curiosità, ascoltiamone le parole da noi così liberamente <lb></lb>tradotte dal citato trattatello latino: </s></p><p type="main">

<s>“ M&#039;incontrai un giorno in Firenze in Gian Alfonso Borelli, mio aman­<lb></lb>tissimo Maestro, e dopo averlo salutato gli domandai: — Che cosa ci è di <lb></lb>nuovo? </s>

<s>— Oh! ci ho una bellissima nuova da darti, ei mi rispose allora, <lb></lb>non però da parte mia, ma da parte del nostro signor Marcello. </s>

<s>Leggi ciò <lb></lb>che il nostro accuratissimo osservatore ha ultimamente scoperto sopra la lin­<lb></lb>gua elissata: — e ponendomi in mano la lettera seguitava a dire: — Medita <lb></lb>attentamente quel che ci è scritto, e ci troverai una novità elegantissima. <lb></lb></s>

<s>— Allora io, benchè non conoscessi di persona il Malpighi, ma solo per i suoi <lb></lb>scritti, mosso dalla grande stima che avevo di quell&#039;uomo, mi detti avida­<lb></lb>mente a leggere tutto quel trattato, nel quale, ritrovando così particolarmente <lb></lb>descritta la muccosa della lingua, a cui nessuno prima di lui aveva pensato; <pb xlink:href="020/01/1383.jpg" pagenum="258"></pb>— e noi, dissi fra me, ci staremo cosi oziosi ad ascoltare le belle cose sco­<lb></lb>perte dagli altri? </s>

<s>Perchè non diam mano all&#039;opera, e sulle orme segnateci <lb></lb>da Marcello non ci mettiamo a consultar la Natura, per comprovar con l&#039;ora­<lb></lb>colo di lei quel ch&#039;egli ha asserito? </s>

<s>— S&#039;aggiungevano intanto gli stimoli <lb></lb>che mi venivano dal Borelli, cosicchè datomi alacremente allo studio anato­<lb></lb>mico della lingua in varii animali, ritrovai finalmente tutto quello, e anzi <lb></lb>qualche cosa di più, in quell&#039;organo del gusto, non scoperta dallo stesso <lb></lb>Malpighi. </s>

<s>” </s></p><p type="main">

<s>“ Mentre che così fatte cose seguivano in Firenze, anche al signor Carlo <lb></lb>Fracassati, mio amicissimo, è partecipata dal Borelli la medesima notizia, solo <lb></lb>però accennandogli così in generale che il Malpighi aveva ritrovata qualche <lb></lb>importante novità sopra la lingua. </s>

<s>Quell&#039;uomo perspicacissimo allora, non <lb></lb>sospettando qual fosse propriamente la nuova scoperta malpighiana, datosi <lb></lb>alacremente allo studio di quel membro, mi scrive pochi giorni dopo da Bo­<lb></lb>logna in tali termini, che io mi avvidi essersi egli abbattuto a fare la mia <lb></lb>medesima scoperta. </s>

<s>Ci rallegrammo a vicenda, compiacendoci che, simili es­<lb></lb>sendo nel genio, riuscissimo compagni nella fortuna. </s>

<s>” </s></p><p type="main">

<s>“ Stavano le cose in questi precisi termini, quand&#039;ecco venir di Mes­<lb></lb>sina nuove lettere del Malpighi, le quali annunziavano la scoperta stessa <lb></lb>delle papille nervee disseminate sulla muccosa linguale, ch&#039;era occorsa a <lb></lb>fare a me in Firenze e al Fracassati in Bologna, E perchè l&#039;epistola mal­<lb></lb>pighiana era stata di Messina mandata apposta perchè dovessesi pubblicare, <lb></lb>aveva fatto proposito di bruciare le mie scritture come inutili oramai e anzi <lb></lb>come dispregevoli, imperocchè chi poteva mettersi a correre il palio con quel <lb></lb>genio di Marcello Malpighi, senza farsi o deridere dal volgo o compassionare <lb></lb>dai dotti? </s>

<s>” (Gustus Organum cit., pag. </s>

<s>177-80). </s></p><p type="main">

<s>Nonostante, forse ai conforti dello stesso Malpighi, deliberò di dare alla <lb></lb>luce in Bologna il suo trattatello, dove s&#039;illustravano le teorie della sensa­<lb></lb>zione, affermandosi che le varie affezioni sensitive dipendono dalle varie forme <lb></lb>cristalline de&#039;corpi “ et nihil aliud esse saporem quam ipsum sal determina­<lb></lb>tis linguae partibus applicatum, in quibus et ratione figurarum ipsius, et <lb></lb>ratione conformationis partium linguae, illa passio excitetur, ex qua dolor <lb></lb>aut delectatio determinata proveniens dicatur iucunda vel iniucunda gustatio, <lb></lb>suavis aut insuavis, talis ac talis sapor ” (ibid., pag. </s>

<s>44). </s></p><p type="main">

<s>L&#039;anno dopo la pubblicazione del trattato del Bellini usciva fuori, pure <lb></lb>in Bologna, l&#039;esercitazione epistolica <emph type="italics"></emph>De lingua<emph.end type="italics"></emph.end> del Fracassati, in principio <lb></lb>della quale narra l&#039;Autore come esaminando la lingua elissata di un vitello <lb></lb>rimanesse preso di maraviglia dal trovar che sotto quelle piccole eminenze <lb></lb>coniche, che la rendono tutta scabrosa, si ascondevano le estremità papillari­<lb></lb>di tanti funicoli nervosi, che scaturivano di sotto dalla sostanza carnosa della <lb></lb>stessa lingua. </s>

<s>Mentre pensava tutto fra sè a che cosa potessero mai servire <lb></lb>quelle così cospicue e numerose papille nervee, gli giunge la lettera nella <lb></lb>quale il Borelli, come al Bellini, dava anche a lui la notizia della nuova sco­<lb></lb>perta del Malpighi. </s>

<s>Conobbe allora il Fracassati di essersi egli pure incon-<pb xlink:href="020/01/1384.jpg" pagenum="259"></pb>trato in quella medesima scoperta, ond&#039;è che scriveva nella citata Esercita­<lb></lb>zione epistolica allo stesso Borelli, come mosso da quell&#039;avviso, “ ad primam <lb></lb>meam redeo perfunctoriam observationem ” dalla quale si vide allora spa­<lb></lb>rire ogni dubbio. </s>

<s>“ Credo enim, poi immediatamente soggiunge, posse non <lb></lb>valde ab amici invento nostrum, qualecumque sit, abludere, adeo ut ambo­<lb></lb>rum circa rem eamdem, licet impari successu, idem forte sit futurus cona­<lb></lb>tus ” (Inter Malpighi Opera, T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>176). E prose­<lb></lb>gue a illustrare l&#039;anatomia dell&#039;organo e le speculazioni del Malpighi e del <lb></lb>Bellini intorno alle forme cristalline de&#039;sali, che variamente impressionando <lb></lb>la lingua son causa del sentirsi in essa le varietà de&#039;sapori. </s></p><p type="main">

<s>La scoperta dei tre nostri insigni anatomici riuscì molto proficua ai pro­<lb></lb>gressi della Fisiologia dei sensi, perchè dimostrava, anche per il tatto e per <lb></lb>il gusto, esser organo primario, non la cute o la sostanza carnosa della lin­<lb></lb>gua, ma il nervo, che fu perciò riconosciuto per il sensorio comune. </s>

<s>Nono­<lb></lb>stante però che fossero queste cose dimostrate per certe, nei principii del <lb></lb>secolo XVIII disputavasi tuttavia qual fosse il nervo che presiedesse all&#039;ol­<lb></lb>fatto, alcuni attribuendo quel particolare ufficio alle diramazioni del primo, <lb></lb>altri a quelle del quinto paio. </s></p><p type="main">

<s>Ma ben più antichi erano i dubbii agitati intorno all&#039;organo, distrigan­<lb></lb>dosene tutti facilmente col dire che quell&#039;organo era il naso, il quale attra­<lb></lb>verso ai cribri dell&#039;osso etmoide mette in comunicazione con l&#039;aria esterna <lb></lb>il cervello. </s>

<s>Fu anzi questa ipotesi, la quale fece credere a Galeno e agli <lb></lb>stessi suoi predecessori che gli effluvii odorosi agissero immediatamente sui <lb></lb>processi mamillari. </s></p><p type="main">

<s>I grandi nostri Italiani restauratori della scienza anatomica ripeterono <lb></lb>queste medesime dottrine. </s>

<s>Realdo Colombo descrivendo, sulla fine del cap. </s>

<s>V <lb></lb>del I libro <emph type="italics"></emph>De re anatomica,<emph.end type="italics"></emph.end> l&#039;osso etmoide, così detto dai Greci <emph type="italics"></emph>quod ima­<lb></lb>ginem cribri referat,<emph.end type="italics"></emph.end> “ per quae foramina, soggiunge, patere solet ascensus <lb></lb>odoribus cerebrum petentibus, cuius rei argumentum inde sumimus, quod <lb></lb>coriza, vel gravi destillatione laborantes odorandi facultatem interim amit­<lb></lb>tunt, opplentur enim foraminula haec pituita spirituum gravitate detenta, <lb></lb>atque olfactiva organa ita impediuntur, ut ne ullum quidem odorem sentire <lb></lb>queant, aut sensili virtuti suggerere ” (Venetiis 1559, pag. </s>

<s>25). E nel cap. </s>

<s>II <lb></lb>del libro VIII, proponendosi di descrivere gli organi e i nervi dell&#039;odorato, <lb></lb>incomincia a dire che nella parte anteriore del cervello, verso la sua base, <lb></lb>occorrono ad osservarsi due corpi bislunghi detti processi mamillari, ai quali <lb></lb>due organi “ odores per nares attracti ascendunt: itaque distinguimus quae <lb></lb>bene, quae male oleant, propterea odoratus instrumenta merito appellari pos­<lb></lb>sunt ” (ibid., pag. </s>

<s>194). </s></p><p type="main">

<s>Un mezzo secolo dopo non aveva ancora la scienza progredito di un <lb></lb>passo, nemmen per opera di Colui, che si applicò con speciale amore allo <lb></lb>studio dei cinque sensi, e ne riportò la gloria di varie scoperte. </s>

<s>Intendiamo <lb></lb>dire del piacentino Giulio Casserio, il quale, dal considerar che gli odori na­<lb></lb>turalmente salgono in alto, argomentando che le parti del cerebro meglio <pb xlink:href="020/01/1385.jpg" pagenum="260"></pb>esposte a riceverne le impressioni <emph type="italics"></emph>ad os cribrosum locatae esse debuerunt, <lb></lb>ut tamquam fidelissimi exploratores quidquid aeris ingreditur examinent;<emph.end type="italics"></emph.end><lb></lb>si persuase facilmente con Galeno e con Aristotile esser organo dell&#039;olfatto <lb></lb>i processi mamillari. </s>

<s>A così fatta opinione poi soggiunge “ unusquisque <lb></lb>acquiescet facilius, si ubi ossa colatoria obstructa sunt olfactum impediri <lb></lb>meminerit, signum profecto id quod statim post haec ossa occurrit verum <lb></lb>olfactus organum censeri debere ” (De quinque sensibus, Venetiis 1609, <lb></lb>pag. </s>

<s>137). </s></p><p type="main">

<s>Ma non avevano le questioni per solo argomento il sensorio e l&#039;organo: <lb></lb>si disputava altresì intorno all&#039;oggetto, perchè, sebben tutti facilmente ap­<lb></lb>prendiamo gli odori pel senso, non a tutti è facile definire in che consista <lb></lb>la loro natura. </s>

<s>I Fisiologi per lo più, o per crederlo difficile o per crederlo <lb></lb>inutile, si passano sopra questo argomento, e non sarà perciò discaro agli <lb></lb>studiosi che si riferiscano in tal proposito i pensieri di uno scrittore pochis­<lb></lb>simo noto; pensieri che dall&#039;altra parte ci rivelano in poche parole la fe­<lb></lb>condità e, se non l&#039;importanza, la curiosità almeno di questo soggetto. </s>

<s>An­<lb></lb>tonio Nardi, nella veduta XXX della scena I, è colui che verso il 1640 ci <lb></lb>lasciava manoscritti così, intorno all&#039;odorato e agli odori, quelli che si di­<lb></lb>ceva suoi filosofici pensieri: </s></p><p type="main">

<s>“ Risolvonsi tutte le composte sostanze a poco a poco in minime par­<lb></lb>ticelle, mediante gli universali o particolari movimenti e momenti, e così ve­<lb></lb>diamo dentro delle camere volare infiniti corpicelli, per il raggio del sole, <lb></lb>quali dal pavimento, dalle vesti, dai libri e da ogni quasi cosa esalano. </s>

<s>Molto <lb></lb>più facilmente esala dall&#039;acqua il vapore, massime se rotta ella sia o assot­<lb></lb>tigliata, mentre s&#039;imbeve dalla terra, e così l&#039;umido, il freddo e il ventoso <lb></lb>di lei sentiamo. </s>

<s>Dal vino ancora e dalle vivande apprendiamo gli odori simili <lb></lb>ai sapori, ma più sottili, come quelli che per l&#039;aria vanno vagando. </s>

<s>Di nuovo <lb></lb>più di questi sottili sono gli altri odori, i quali non convengono coi sapori, <lb></lb>se non per analogia. </s>

<s>” </s></p><p type="main">

<s>“ Diciamo pertanto che l&#039;aria principalmente è il mezzo rimoto, per cui <lb></lb>gli animali sentono gli odori, ma i più grossi odori anco nell&#039;acqua s&#039;ap­<lb></lb>prendono dai pesci in grazia del cibo, e così molti pesci odorano senza naso, <lb></lb>quasi che le branchie, ove talora terminano i condotti proporzionali a quelli <lb></lb>del naso, siano a loro per attrar gli odori bastevoli. </s>

<s>” </s></p><p type="main">

<s>“ Il prossimo strumento dell&#039;odorato sono i processi mamillari, ma i <lb></lb>canaletti che a quelli conducono, e l&#039;aria che in essi sta, servono di con­<lb></lb>dotto e di mezzo all&#039;odore, il quale per essi tirato più valentemente penetra <lb></lb>il senso. </s>

<s>” </s></p><p type="main">

<s>“ Io m&#039;immagino che, siccome il sapore, così anche l&#039;odore sia in uni­<lb></lb>versale dall&#039;uomo squisitamente appreso, per esser questo temperatissimo e <lb></lb>perfettissimo animale, di maniera che molte più differenze di sapori e di <lb></lb>odori conosce che gli altri. </s>

<s>È ben vero che qualcuno di questi animali più <lb></lb>esattamente e più di lontano conosce qualche odore, conforme alla tempe­<lb></lb>ratura sua, a che giova molto l&#039;attenzione, la consuetudine, il portare il naso <pb xlink:href="020/01/1386.jpg" pagenum="261"></pb>per terra, e la lunghezza dei canali. </s>

<s>Ma l&#039;uomo, poichè molti più sono gli <lb></lb>odori che offendono che quei che giovano, viene a liberarsi dalle molestie <lb></lb>col portar da terra alto il viso. </s>

<s>Ora, che gli animali molte meno differenze <lb></lb>di odori conoscano che l&#039;uomo, scorgesi chiaramente, poichè per lo solo nu­<lb></lb>drirsi e moltiplicarsi osserviamo odorar gli animali. </s>

<s>” </s></p><p type="main">

<s>“ È poi l&#039;odore diffusione nell&#039;ambiente fatta dalla cosa odorifera e sue <lb></lb>particelle esalanti. </s>

<s>Il fiore dunque più odorar si sente, mentre le sue sotti­<lb></lb>lissime particelle diffonde d&#039;ogni intorno. </s>

<s>Ora, in quanto alla natura di essi <lb></lb>odori, non è dubbio che hanno questi molta somiglianza con le focose na­<lb></lb>ture, e così dall&#039;aria premuti vengono d&#039;ogni intorno. </s>

<s>” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XX, pag. </s>

<s>149, 50). </s></p><p type="main">

<s>Benchè il Nardi segua, rispetto all&#039;organo dell&#039;odorato, l&#039;opinione del <lb></lb>Colombo e del Casserio, accenna nulladimeno a certe squisitezze nell&#039;organo <lb></lb>stesso trascurate da quegli insigni Anatomici, che l&#039;avevano preceduto. </s>

<s>Par <lb></lb>ch&#039;egli senta la Natura, stata così semplice negli organi del tatto e del gu­<lb></lb>sto, incominciare ora nel naso a dare un saggio di quello squisitissimo la­<lb></lb>voro, con cui sarebbe poi per condurre l&#039;orecchio e l&#039;occhio. </s>

<s>Quell&#039;elabo­<lb></lb>rato apparecchio strumentale, di che dà nel naso la Natura il primo esempio, <lb></lb>lo riconosceva il Nardi in que&#039;canaletti dell&#039;osso cribroso, per i quali, tirato <lb></lb>più valentemente l&#039;odore, penetra il senso. </s></p><p type="main">

<s>Lo spiegar però come mai le fistole ossee servano ad attrar più valen­<lb></lb>temente gli odori era riserbato a un valoroso anatomico e fisiologo pado­<lb></lb>vano, Antonio Molinetti, il quale rassomigliava lo strumento dell&#039;olfatto a <lb></lb>quello dell&#039;udito e della vista, e diceva che, siccome i suoni passano per la <lb></lb>finestra ovale, e i colori per la finestra dell&#039;uvea; così passavano gli odori <lb></lb>per la finestra aperta fra le pinne delle narici. </s>

<s>E a quel modo che i cana­<lb></lb>letti spirali del laberinto moltiplicano il suono, e la lente cristallina accre­<lb></lb>sce intensità alla luce; così le fistole, che serpeggiano dentro l&#039;osso cribroso, <lb></lb>servono a condensare gli odori, che perciò più fortemente s&#039;imprimono sul <lb></lb>nervo. </s>

<s>“ Pinnas narium fistulae statim excipiunt ex squamis tenuissimis, in <lb></lb>ossea structura narium et faciei, compositae circinato quodam modo, aut po­<lb></lb>tius spirali se mutuo pervadentes, ita dispositae, ut labyrintheum iter pan­<lb></lb>dant corpusculis odorum delatoribus, non secus ac sonum excipiunt, et acuunt <lb></lb>Labyrinthi aurium spirales canaliculi, et lumen unit ac compingit in conum <lb></lb>lens illa oculi crystallina. </s>

<s>Foras enim hiantes fistulae ad instar tubarum an­<lb></lb>gustantur interius, magis magisque, quo propius accesserint ad nervum. </s>

<s>Hinc <lb></lb>sequitur quod pyramis odora illico incipiat acui et inspissari ac cogi com­<lb></lb>pingenda iterum in fistulis superioribus, ut spissior vel crebrior appulsus <lb></lb>evadat corpusculorum odor abilium in nervum, organum scilicet odoratus <lb></lb>formale ” (Dissertationes anat., Patavii 1669, pag. </s>

<s>59). </s></p><p type="main">

<s>All&#039;ultimo, in quel modo che l&#039;affezion della luce non termina nella re­<lb></lb>tina, nè le vibrazioni dell&#039;aria nel nervo acustico, ma per la continuità degli <lb></lb>spiriti si propagano infino al Sensorio comune, che ha la sua sede nella mi­<lb></lb>dolla allungata, designata dall&#039;Autore col nome proprio di <emph type="italics"></emph>Ponte;<emph.end type="italics"></emph.end> “ ita affec-<pb xlink:href="020/01/1387.jpg" pagenum="262"></pb>tus, seu contactus odorabilium in mamillari non desinit, verum per spiritus, <lb></lb>qui in nervo, primum in ventriculos cerebri, postea in ipsius medullam se <lb></lb>insinuat, eo quidem vehementius, quod corpuscula producta ulterius impe­<lb></lb>tum semper maiorem concipiant, agitentque validius spiritus illos, qui in <lb></lb>fonte suo haerent ” (ibid., pag. </s>

<s>61). </s></p><p type="main">

<s>Le opinioni de&#039;Fisiologi intorno all&#039;organo dell&#039;olfatto e alle vie, per le <lb></lb>quali giungono gli odori al sensorio, erano fondate sull&#039;ipotesi che i forellini <lb></lb>dell&#039;osso cribroso fossero vuoti. </s>

<s>Ma il Berengario, e dietro lui il Vesalio, ave­<lb></lb>vano da gran tempo dimostrato che invece erano pieni, e perciò coloro che <lb></lb>facevano quegli stessi forellini gli scolatoi del mucco, di che si ripurga il <lb></lb>cervello, pensarono di trovare altre vie perchè potessero così fatti umori giun­<lb></lb>gere al naso. </s>

<s>Il Molinetti stesso asseriva che vi giungevano “ per forami­<lb></lb>nula in angulis internis oculorum patentia primum in nares ” (ibid.) ma <lb></lb>non perciò crede di dover riformare la sua opinione intorno al sensorio, se­<lb></lb>guitando a riconoscerlo ne&#039;processi mamillari, ai quali giungono gli odori <lb></lb>attraverso all&#039;umido, di che appunto la Natura riempì l&#039;ossa nasali “ ut acu­<lb></lb>men plerumque nimium odorabilium, motusque spirituum, ex appulsu eorum­<lb></lb>dem nimis concitatos, humore interiecto compesceret ac moderaretur ” (ibid.). </s></p><p type="main">

<s>Ma benchè fossero queste speculazioni del Molinetti ingegnose, il vero <lb></lb>strumento dell&#039;olfatto era stato scoperto già da Currado Vittorio Schneider <lb></lb>nella seconda sezione del III libro <emph type="italics"></emph>De catarrhis,<emph.end type="italics"></emph.end> pubblicato in Wittemberg <lb></lb>nel 1661, e dove si descrive così dall&#039;Autore la membrana pituitaria, che <lb></lb>glien&#039;è attribuito il merito della scoperta. </s>

<s>Nè si vuol da noi qui contender­<lb></lb>gliela, permettendoci solo di far osservare ch&#039;esaminando il Falloppio le fosse <lb></lb>nasali, e con molta diligenza descrivendo i seni frontali e gli sfenoidali, nè <lb></lb>lasciando indietro i mascellari, che poi furono detti <emph type="italics"></emph>Antri dell&#039;Igmoro,<emph.end type="italics"></emph.end> dice <lb></lb>che son tutti questi seni rivestiti, “ tenuissima quadam membrana aut pel­<lb></lb>licola ” (Observat. </s>

<s>anat. </s>

<s>inter Opera omnia cit., pag. </s>

<s>410), nella quale hanno <lb></lb>voluto alcuni riconoscere la pituitaria. </s></p><p type="main">

<s>In qualunque modo si dissiparono dopo lo Schneider tutti gli antichi <lb></lb>errori, e in quel che egli insegnò si continua tuttavia a riconoscere da&#039;Fi­<lb></lb>siologi le rivelate sembianze del vero. </s>

<s>Ma gli odori seguitarono ancora a ri­<lb></lb>maner misteriosi più della luce e de&#039;suoni, e parendo dall&#039;altra parte cosa <lb></lb>tutta soggettiva, pochissimi si curarono di studiarla nel proprio oggetto. </s>

<s>Non <lb></lb>possono perciò in tanta penuria, a noi che teniamo particolarmente d&#039;occhio <lb></lb>la Scuola toscana, sfuggire dimenticate quelle due <emph type="italics"></emph>Lettere scientifiche<emph.end type="italics"></emph.end> dal <lb></lb>Magalotti scritte intorno agli odori. </s></p><p type="main">

<s>Le idee è vero son vaporose, e il discorso è risonante di molte parole, <lb></lb>nel fluir delle quali son pur da raccogliere non poche perle. </s>

<s>Pare a noi una <lb></lb>delle più pregevoli tra queste l&#039;osservazione che, mentre il tatto è il più in­<lb></lb>fallibile de&#039;sensi, l&#039;odorato è il più dubbioso di tutti. </s>

<s>Dell&#039;infallibilità del <lb></lb>tatto basta dire, osserva il Magalotti, ch&#039;ella si piglia per traslato dell&#039;evi­<lb></lb>denza, essendo che, per assicurar altri della verità di una cosa, si suol dire <lb></lb>ch&#039;ella si tocca con mano. </s>

<s>Conferma l&#039;osservazione coll&#039;esempio dei ciechi, <pb xlink:href="020/01/1388.jpg" pagenum="263"></pb>i quali suppliscono col tatto al difetto della vista, e commemora in propo­<lb></lb>sito il famoso Cieco di Gambassi, che a forza di brancicare faceva somiglian­<lb></lb>tissimi i ritratti nella creta, e quell&#039;altro non men famoso Cieco che, pure <lb></lb>a toccarli, co&#039;polpastrelli delle dita, sapeva dire alla granduchessa Vittoria <lb></lb>di Toscana di che colore fossero i nastri, i veli, le vesti e altri oggetti mes­<lb></lb>sigli innanzi. </s></p><p type="main">

<s>“ A proposito di quel modo di dire <emph type="italics"></emph>questa è una verità che si tocca <lb></lb>con mano,<emph.end type="italics"></emph.end> osservate, soggiunge il Magalotti, che da tutti i cinque senti­<lb></lb>menti cavandosi varie graduazioni d&#039;espressioni di maggiore o minore evi­<lb></lb>denza d&#039;una verità, l&#039;infima e la più meschina di tutte è quella che si de­<lb></lb>duce dal testimonio del naso, tanto è generalmente riconosciuto il poco accerto <lb></lb>de&#039;suoi giudizi. </s>

<s>Di grazia osservate. <emph type="italics"></emph>Questa cosa si tocca con mano:<emph.end type="italics"></emph.end> ecco <lb></lb>il sommo dell&#039;indubitabilità. <emph type="italics"></emph>Questa cosa si vede con gli occhi:<emph.end type="italics"></emph.end> comincia a <lb></lb>poterci essere della fallacia. <emph type="italics"></emph>Questa cosa si sente bisbigliare:<emph.end type="italics"></emph.end> ci è il caso di <lb></lb>frantendere. <emph type="italics"></emph>Questa cosa si comincia a assaporare:<emph.end type="italics"></emph.end> siamo indietro assai. <lb></lb><emph type="italics"></emph>Questa cosa si subodora:<emph.end type="italics"></emph.end> non se ne può saper manco ” (Firenze 1721, <lb></lb>pag. </s>

<s>82). </s></p><p type="main">

<s>Un&#039;altra notabile osservazione del Magalotti, per tacere delle altre, è <lb></lb>che il senso dell&#039;odorato si raffina anche indipendentemente dall&#039;organo, <lb></lb>ossia dalla maggiore o minor perfezione di “ quelle due laminette cartilagi­<lb></lb>nose, che abbiamo fitte per punta di qua e di là nel naso, alle radici del­<lb></lb>l&#039;osso cribroso, nella tunica che investe le quali pare che resti convinto for­<lb></lb>marsi il senso dell&#039;odorato ” (ivi). Di qui s&#039;argomenta essersi largamente <lb></lb>diffusa in Italia la scoperta sneideriana emendatrice di quegli errori antichi, <lb></lb>per liberarsi dai quali faceva come si vide gli ultimi conati fra noi Antonio <lb></lb>Molinetti. </s></p><p type="main">

<s>Ma se il Molinetti e la maggior parte dei successori studiarono l&#039;organo <lb></lb>secondario, e specularono intorno al più squisito modo come possa l&#039;aura <lb></lb>odorosa agir sopra lui, si passarono con qualche negligenza sull&#039;organo pri­<lb></lb>mario o sulla distribuzione delle filamenta nervose ordinate a ricevere il <lb></lb>senso. </s>

<s>Fu questo importantissimo studio lasciato alle indagini di Antonio <lb></lb>Scarpa, delle quali rendeva conto al pubblico in un suo libro intitolato <emph type="italics"></emph>De <lb></lb>organo olfactus praecipuo, deque nervis nasalibus interioribus e pari quinto <lb></lb>nervorum cerebri.<emph.end type="italics"></emph.end> Avendo osservato l&#039;Autore che pochi sono i filamenti ner­<lb></lb>vosi dispersi ne&#039;turbinati, “ quam ob rem, ei soggiunge, non temere pro­<lb></lb>nunciare posse videor organum olfactus praecipuum septo narium late su­<lb></lb>perinductum esse, quandoquidem et confertae admodum fere undique supra <lb></lb>septum nervi olfactorii fibrillae sunt, et quibusdam in sedibus ad imam <lb></lb>usque septi basim exporrectae ” (Ticini Regii 1785, pag. </s>

<s>51). </s></p><p type="main">

<s>Che se altri credesse invece di dover circoscrivere la sede del senso nei <lb></lb>seni pituitarii, si contrapporrebbero all&#039;opinione di lui i fatti, che i fanciulli <lb></lb>tutti hanno l&#039;odorato squisito, e l&#039;hanno anche alcuni adulti, ne&#039;quali pure <lb></lb>o mancano questi seni, o non vi sono altro che rudimentari. </s>

<s>“ Et quoniam, <lb></lb>all&#039;ultimo conclude, suadente Anatome, spongiosum os inferius nihil conferre <pb xlink:href="020/01/1389.jpg" pagenum="264"></pb>videtur ad distributionem nervi olfactorii; ideo haud spernendam esse cen­<lb></lb>seo illorum sententiam, qui docuerunt spongiosa ossa non una atque unica <lb></lb>de causa, nempe pro distributione nervi olfactilis esse creata, sed illud quo­<lb></lb>que utilitatis et commodi narium cavitatem apte angustando praestare, ut <lb></lb>respirationi et quae ab hac pendent functionibus famulentur, utque timenda <lb></lb>pulmonibus e magna narium amplitudine, magneque inde irruentis aeris <lb></lb>flumine, pericula avertant ” (ibid., pag. </s>

<s>52). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dicemmo che nell&#039;olfatto dava la Natura il primo esempio di un organo <lb></lb>elaborato, ma la fabbrica insomma era assai semplice, come quella che non <lb></lb>aveva altro fine, da quello in fuori di far percepire al senso la varietà delle <lb></lb>aure odorose. </s>

<s>Ben assai però più sottili e più difficili ad approdare al sen­<lb></lb>sorio erano le onde sonore e l&#039;eteree, per cui bisognava elaborare un organo <lb></lb>più gentile e squisito, tanto più che l&#039;oggetto, secondo che osservammo, <lb></lb>non si riduceva, come ne&#039;tre primi sensi, alle sole particelle materiali o so­<lb></lb>lide o vaporose, ma pigliava, per dirla coi Filosofi, forma intelligibile di <lb></lb>segno. </s>

<s>Se un finissimo magistero perciò conveniva s&#039;esercitasse dalla Natura <lb></lb>nel fabbricar l&#039;orecchio e l&#039;occhio de&#039;bruti, doveva quello stesso natural ma­<lb></lb>gistero giungere alla sua massima eccellenza nell&#039;uomo. </s>

<s>Per quali lunghe e <lb></lb>penose vie giungessero gli Anatomici a riconoscere questa eccellenza è ciò <lb></lb>che ci proponiam di narrare nella seguente parte di storia, la quale, per pro­<lb></lb>cedere con l&#039;ordine oramai preso, prima che dell&#039;occhio tratta dell&#039;anatomia <lb></lb>e delle funzioni dell&#039;orecchio. </s></p><p type="main">

<s>Galeno, cosa notabilissima, non descrisse propriamente nessun organo <lb></lb>auditivo, cosicchè la vecchia Anatomia mancò affatto di questa parte di scienza <lb></lb>nuovamente instituita dal Mondino e dal Berengario. </s>

<s>Il XXXVII Testo mun­<lb></lb>diniano infatti, citato e commentato dal Berengario stesso, dop&#039;avere accen­<lb></lb>nato al foro esterno e alle cavernosità che s&#039;aprono nella parte interiore del­<lb></lb>l&#039;orecchio, soggiunge: “ eius foramen vel cavernositates cooperit panniculus <lb></lb>subtilis contextus ex villis nervorum auditus ” (Carpi, Commentaria super <lb></lb>Anat. </s>

<s>Mundini, Bononiae 1521, fol. </s>

<s>CCCCLXXVI). </s></p><p type="main">

<s>Questo <emph type="italics"></emph>pannicolo sottile<emph.end type="italics"></emph.end> è dunque il primo organo auditivo descritto <lb></lb>nella risorta Anatomia, la quale progredì presto in altre più nuove e più <lb></lb>insigni scoperte, innanzi di venire alle quali giova intrattenersi su questa <lb></lb>prima mundiniana. </s>

<s>Ella di fatto accusava Galeno di negligenza, e perciò, <lb></lb>mentre da una parte infervorava i novatori, metteva dall&#039;altra in gran sol­<lb></lb>lecitudine i conservatori degli ordini antichi, i quali disperati di trovare un <lb></lb>testo galenico che parlasse chiaro, accennavano a que&#039;barlumi, che vedevano <lb></lb>i loro cupidi occhi trasparire dal cap. </s>

<s>VI dell&#039;VIII libro, e dal XII del li­<lb></lb>bro XI <emph type="italics"></emph>De usu partium.<emph.end type="italics"></emph.end> Fu in questo sollecito studio de&#039;primi l&#039;Acquapen-<pb xlink:href="020/01/1390.jpg" pagenum="265"></pb>dente, il quale ardendo di gran desiderio, com&#039;egli stesso si esprimeva, di <lb></lb>dimostrar “ Galeno et Aristotili nihil occultum extitisse ” (De Aure, Opera <lb></lb>omnia, Lugd. </s>

<s>Batav. </s>

<s>1738, pag. </s>

<s>250), non potendo salvar Galeno, si com­<lb></lb>piaceva che Aristotile e anzi Ippocrate prima di lui avessero conosciuto già <lb></lb>quel che si credeva essere stato primo a insegnare il Mondino. </s>

<s>Dal libello <lb></lb>ippocratico infatti <emph type="italics"></emph>De carnibus<emph.end type="italics"></emph.end> traduceva così: “ Pellicula in aure iuxta os <lb></lb>durum tenuis est, veluti aranearum tela et omnium pellicularum siccis­<lb></lb>sima “ (ibid.). </s></p><p type="main">

<s>Più importante, per l&#039;efficacia ch&#039;ebbero sopra molti le teorie, è il <lb></lb>testo 83, che l&#039;Acquapendente cita dal II libro aristotelico <emph type="italics"></emph>De anima.<emph.end type="italics"></emph.end> Ivi <lb></lb>dice il Filosofo che l&#039;aria per sè medesima è insonora, essendo naturalmente <lb></lb>dissipabile, e non si fa altrimenti il suono che quando ne sia proibita così <lb></lb>fatta dissipazione. </s>

<s>Ciò avviene appunto, dice Aristotile, nell&#039;orecchio, “ hic <lb></lb>autem aer inaedificatus est, ad hoc ut immobilis sit, quatenus certe sentiat <lb></lb>omnes differentias motus ” (Operum, T. VII, Venetiis 1560, fol. </s>

<s>66). Che <lb></lb>poi il suono non sia prodotto nell&#039;aria dissipabile esterna, ma in quella che <lb></lb>è nell&#039;interno immobilmente implantata, lo prova lo Stagirita dal fatto che <lb></lb>si ode bene anche sott&#039;acqua, e si diventa sordi quando “ membrana labo­<lb></lb>ret, sicut cum quae super pupillam est pellis laborat ” (ibid.) perchè allora <lb></lb>l&#039;aria immobile divien dissipabile attraverso alla stessa membrana lesa. </s></p><p type="main">

<s>Non è dubbio dunque che la pellicola di Empedocle, e la membrana di <lb></lb>Aristotile rassomigliata alla cornea, non siano la medesima cosa che il pan­<lb></lb>nicolo sottile del Mondino. </s>

<s>Ma chi ripensa che, dimenticato il vecchio Ippo­<lb></lb>crate, e non curato, anzi dai più disprezzato Aristotile, non riconoscevano <lb></lb>gli Anatomici altro Maestro che Galeno, si persuaderà facilmente che la prima <lb></lb>notizia della membrana tesa come sipario tra il meato esterno e l&#039;interna <lb></lb>cavità dell&#039;orecchio fu nell&#039;Anatomia intradotta dal nostro Bolognese, ed ha <lb></lb>perciò il merito di una vera scoperta. </s></p><p type="main">

<s>Divulgatasi quella scoperta da&#039;Commentari e dalle Isagogi del Beren­<lb></lb>gario, il Vesalio esaminò la membranula mundiniana con maggior diligenza <lb></lb>e la trovò <emph type="italics"></emph>prorsus pellucida,<emph.end type="italics"></emph.end> per cui, adombrando un poco tra quella che <lb></lb>fu poi detta Corda del timpano e il manico del martello, disse che questo <lb></lb>“ intus transversum insternitur, quemadmodum in <emph type="italics"></emph>tympanis<emph.end type="italics"></emph.end> fidem unam <lb></lb>atque alteram crassiorem membranae obtendi conspicimus ” (De hum. </s>

<s>corp. </s>

<s><lb></lb>fabrica, Basileae 1543, pag. </s>

<s>35). Questa espressione suggerì l&#039;altra al Co­<lb></lb>lombo, intendendo della parte più grossa del Martello: “ illam ipsam <emph type="italics"></emph>Mem­<lb></lb>branam tympani<emph.end type="italics"></emph.end> modo quatit ” (De re anat. </s>

<s>cit., pag 26) e di lì in poi <lb></lb>quella, che Ippocrate chiamava <emph type="italics"></emph>pellicola,<emph.end type="italics"></emph.end> Aristotile <emph type="italics"></emph>membrana<emph.end type="italics"></emph.end> e il Mondino <lb></lb><emph type="italics"></emph>pannicolo,<emph.end type="italics"></emph.end> ebbe il nome proprio e sacro oramai nella scienza di <emph type="italics"></emph>Membrana <lb></lb>del timpano.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il Falloppio, a cui parvero le cose relative all&#039;organo dell&#039;udito “ ab <lb></lb>aliquot Anatomicis satis imperfecte, ab aliquot vero false descriptae ” da­<lb></lb>tosi con incredibile ardore al nuovo studio, incominciò dalla membrana del <lb></lb>timpano, ch&#039;ei ritrovò tesa a un apposito anello osseo, non perpendicolar-<pb xlink:href="020/01/1391.jpg" pagenum="266"></pb>mente, ma un po&#039;inclinata: “ Extenditur autem ipsa, non per transversum <lb></lb>sed oblique ” (Observat. </s>

<s>anat. </s>

<s>inter, Op. </s>

<s>omn. </s>

<s>cit., pag. </s>

<s>409). E ciò per ri­<lb></lb>cever minore offesa dai colpi dell&#039;aria, “ Ictus enim obliquus minus loedit <lb></lb>quam qui recta fertur ” (ibid.). </s></p><p type="main">

<s>Nelle figure 12 e 13, impresse nella Tavola apposta al suo trattato <emph type="italics"></emph>De <lb></lb>aure auditus organo,<emph.end type="italics"></emph.end> l&#039;Acquapendente disegnò con molta diligenza l&#039;anello <lb></lb>osseo descritto dal Falloppio, e notò inoltre che il setto membranoso tesovi <lb></lb>intorno non era perfettamente piano, “ sed in medio centroque quodam­<lb></lb>modo interius incurvatum et gibbum, extra cavum, ita ut concinne herbam <lb></lb>cymbalitidem, seu umbilicum veneris, prae se ferat ” (Op. </s>

<s>omn. </s>

<s>cit., pag. </s>

<s>250). </s></p><p type="main">

<s>Un&#039;altra osservazione importantissima ha, in proposito della membrana <lb></lb>del timpano, l&#039;Acquapendente, ed è che talvolta, benchè di rado, suole in­<lb></lb>nanzi a quella stessa membrana, dalla parte esterna, “ tunica quaedam cras­<lb></lb>sior praeter naturam adnasci opponique, quam ego in pueris bis deprehendi ” <lb></lb>(ibid.). Quel che fu però dall&#039;Autore creduto preternaturale venne poi ri­<lb></lb>conosciuto per cosa ordinaria, e il Molinetti perciò descriveva così la mem­<lb></lb>brana del timpano composta di due pagine soprapposte: “ Una quidem per <lb></lb>se est, cui tamen altera supertenditur, tractu temporis tendo futura musculi <lb></lb>externi, quam et in nuper natis semper reperimus; quare seminalem utram­<lb></lb>que esse non dubito. </s>

<s>Atque interiorem quidem tenuiorem altera, et magis <lb></lb>transparentem videmus; crassiorem secundam, quae marginibus externi cir­<lb></lb>culi ossei circumtensa, dum succrescunt ossa, vel extenduntur ad construen­<lb></lb>dum meatum auditorium, cum iisdem obtenditur ut ea intrinsecus vestiat; <lb></lb>mox, acceptis filamentis aliquot carneis ab iisdem ossibus, speciem musculi <lb></lb>induit, non sine motu et actione aliqua musculorum propria, siquidem dum <lb></lb>corripitur, contractis more reliquarum filamentis illis carneis, pars ultima <lb></lb>superstrata Tympano nonnihil contrahitur, simulque cum illa subiecta Tym­<lb></lb>pani membrana tenditur ” (Dissertationes anat. </s>

<s>cit, pag. </s>

<s>48). </s></p><p type="main">

<s>Nonostante che tali fossero la tradizioni della scienza, le quali anzi ri­<lb></lb>salgono al Vidio, che sebben senz&#039;altra dichiarazione asserì <emph type="italics"></emph>duplice<emph.end type="italics"></emph.end> essere <lb></lb>la membrana del timpano (De anat. </s>

<s>corp. </s>

<s>hum., Venetiis 1611, pag. </s>

<s>322); <lb></lb>il Valsalva, sul principio del cap. </s>

<s>II del suo celebre trattato <emph type="italics"></emph>De aure hu­<lb></lb>mana,<emph.end type="italics"></emph.end> dop&#039;aver descritta come cosa nuova la membrana stessa doppiamente <lb></lb>compaginata, “ a qua, conclude, usque adhuc ignota compositione, ex Durae <lb></lb>matris scilicet et cutis membraneis expansionibus, considerabilis membranae <lb></lb>tympani firmitas et robur dependet ” (Venetiis 1740, pag. </s>

<s>18). </s></p><p type="main">

<s>Questa nuova anatomia e questa sentenza dettero occasione al Morga­<lb></lb>gni, in principio della sua Epistola anatomica V, di esaminare più diligen­<lb></lb>temente la cosa, comparando le osservazioni sue proprie con quelle già de­<lb></lb>scritte dal Ruysch, dal Kerckring, dal Du-Verney e da altri Anatomici illustri. </s>

<s><lb></lb>E giacchè aveva detto il Valsalva essere la composizione della membrana del <lb></lb>timpano nel feto umano patente, su quel soggetto il Morgagni stesso eser­<lb></lb>citando l&#039;industria, scoprì essere essa membrana composta di tre pagine di­<lb></lb>stinte, procedendo nell&#039;amministrazione anatomica nel modo che segue: </s></p><pb xlink:href="020/01/1392.jpg" pagenum="267"></pb><p type="main">

<s>“ Aggressus igitur a cavo tympani, cum aliquo huius pariete investien­<lb></lb>tem membranam sensim attollendo, ad proximam usque tympani membranam <lb></lb>deduxissem, eadem porro ratione pergens, praeclare vidi continuari illam ac <lb></lb>produci in laminam per huius posteriora se se extendentem. </s>

<s>Qua detracta, <lb></lb>continuo ad alteram sive exteriorem faciem oculos manumque transtuli. </s>

<s>Cum­<lb></lb>que in ultimo auditorii meatus recessu quidquid erat integumentorum dili­<lb></lb>genter attollere coepissem, sensimque ad tympani membranam reducerem, <lb></lb>et avellere per hanc pergerem, alteram ab hac quoque facie, et facilius qui­<lb></lb>dem et aequalius, laminam dempsi, et duabus lamellis constantem, quarum <lb></lb>exterior nihil erat aliud nisi materia sebacea, interior autem reapse erat <lb></lb>membranea, in quam se integumenta auditorii meatus evidentissime pro­<lb></lb>ducebant. </s>

<s>Hac quoque altera ablata lamina, etiam tum in sua sede restabat <lb></lb>tertia, quae inter utramque media fuerat, ut, nulla adhibita maceratione, <lb></lb>mihi esset manifestum tribus laminis compactam tympani membranam ap­<lb></lb>parere ” (Epist. </s>

<s>anat. </s>

<s>XXII, Venetiis 1740, pag. </s>

<s>89, 90). </s></p><p type="main">

<s>Colla macerazione però fu trovata quella compagine di quattro lamine <lb></lb>distinte provenienti dall&#039;epidermide, dalla cute del meato auditivo, dal pe­<lb></lb>riostio dello stesso meato, e dal periostio del timpano. </s>

<s>“ Inter secundam et <lb></lb>tertiam, prosegue a dir l&#039;Haller, conspicua cellulosa tela est, cum vasculis <lb></lb>illis elegantibus, arbusculum referentihus: alia similis inter tertiam et quar­<lb></lb>tam.... Qui duas tantum laminas numerarunt, aut tres, ii vel cutem omi­<lb></lb>serunt ex eo numero, vel epidermidem ” (Elementa Physiol, T. V, Lausan­<lb></lb>nae 1769, pag. </s>

<s>201) </s></p><p type="main">

<s>Tale infino alla metà del secolo XVIII è la storia compendiosa della <lb></lb>scoperta fatta dal Mondino, “ sed ultra ea quae dicuntur a Mundino de au­<lb></lb>ribus, soggiunge il Berengario, aliquid a nobis est dicendum. </s>

<s>” La princi­<lb></lb>pale di queste cose da dire è che al panniculo mundiniano “ adiacent duo <lb></lb>ossicula parva, quae moventur ab aere moto, et se invicem percutiunt, et <lb></lb>secundum aliquos sunt illa quae, propter suum motum, causant sonum in <lb></lb>aure, et ista est res in rei veritate notatu digna a paucis visa ” (Comment. </s>

<s><lb></lb>cit., fol. </s>

<s>CCCCLXXVI ad t.). </s></p><p type="main">

<s>Ecco scoperti altri due organi che si credettero allora gli efficienti del­<lb></lb>l&#039;udito, benchè non ne fossero poi riconosciuti che per sole elegantissime ed <lb></lb>essenzialissime parti. </s>

<s>Ma il Vesalio, secondando il suo genio d&#039;apparire in <lb></lb>ogni cosa il primo e il solo, s&#039;appropriò quelle scoperte, illustrandole con la <lb></lb>sua arte e diffondendole colla sua autorità, tanto superiore a quella del no­<lb></lb>stro Carpense. </s>

<s>Il cap. </s>

<s>VIII del I libro <emph type="italics"></emph>De humani corporis fabrica<emph.end type="italics"></emph.end> è con­<lb></lb>sacrato a descrivere le interne cavità dell&#039;orecchio, una delle quali, egli dice, <lb></lb>è orbicolare e piana “ et osseo circulo parumper extuberante septa. </s>

<s>Ad huius <lb></lb>circuli quinti paris nervo obducti exteriorem atque auri proximam sedem <lb></lb>ossiculum observatur, quod duobus tenuibus acutisque processibus tanquam <lb></lb>cruribus huic osseo circulo adstabilitur, superius, ubi crura ipsius coeunt, <lb></lb>spissus crassiusque, incudis instar effectum.... Caeterum si hoc ossiculum, <lb></lb>quia tantum binis donatur cruribus, incudi assimilare minus placuerit, nihil <pb xlink:href="020/01/1393.jpg" pagenum="268"></pb>profecto obstiterit molari denti duabus tantum radicibus ornato id conferre. </s>

<s><lb></lb>Alterum ossiculum auditus organi fabricam ingrediens a iam commemorato <lb></lb>plurimum variat, et alteri membranae innascitur ” (Basileae 1543, pag. </s>

<s>34, 35). <lb></lb>Alla qual membrana, che è quella del timpano, fu quell&#039;ossicino saldamente <lb></lb>fermato per via di un lungo e sottile processo. </s>

<s>“ Hunc processum liceret <lb></lb>femoris ossis parti comparari, quae ab ipsius processibus, quae rotatores vo­<lb></lb>camus, ad inferiora usque femoris capita pertinet ... A membrana intror­<lb></lb>sum abscedit in rotundum caput desinens, quod laeve minimeque asperum <lb></lb>est, et superiori parti alterius ossiculi, quod molari denti aut incudi assi­<lb></lb>milavimus, ita tenuissimarum membranarum interventu committitur, ac si <lb></lb>malleus incudi laxe alligaretur, non secus quam si ossiculum postremo enar­<lb></lb>ratum malleoli praestaret munus, alterum vero incudis vicem gereret ” (ibid., <lb></lb>pag. </s>

<s>35). </s></p><p type="main">

<s>Di qui vennero imposti i nomi di <emph type="italics"></emph>Martello<emph.end type="italics"></emph.end> e d&#039;<emph type="italics"></emph>Incudine<emph.end type="italics"></emph.end> ai due ossi­<lb></lb>cini innominati del Berengario, che rimase in questa vesaliana descrizione <lb></lb>affatto dimenticato. </s>

<s>L&#039;orgoglioso Conquistatore straniero si vide però presto <lb></lb>insorgere incontro uno stuolo di prodi a rivendicare l&#039;onore degli avviliti <lb></lb>fratelli. </s>

<s>Si componeva quello stuolo del Colombo e del Falloppio, che usa­<lb></lb>rono verso il Vesalio una certa gentilezza di modi, e del Massa e dell&#039;Eu­<lb></lb>stachio più sdegnosi e più fieri. </s>

<s>Io vorrei volentieri, dice il Colombo, rico­<lb></lb>noscere per primo inventore di questi ossicini il Vesalio, “ nisi Carpus de <lb></lb>his ante illum suis scriptis meminisset ” (De re anat. </s>

<s>cit., pag. </s>

<s>26). E il <lb></lb>Falloppio solennemente rammemora che primo a dare di quegli ossicini no­<lb></lb>tizia “ fuit Jacobus Carpensis, primus quoque, procul dubio anatomicae artis, <lb></lb>quam Vesalius postea perfecit, restaurator ” (Observ. </s>

<s>anat. </s>

<s>Op. </s>

<s>omnia cit., <lb></lb>pag. </s>

<s>409). </s></p><p type="main">

<s>Niccolò Massa, non osando pronunziare quel nome tremendo, — que­<lb></lb>sta gente, badava a dire in una sua Epistola che noi non abbiamo potuto <lb></lb>consultare nelle sue fonti, come si è arrogata la mia, così arrogandosi le <lb></lb>scoperte degli altri, si crede d&#039;essere stata la prima a ritrovare e a descri­<lb></lb>vere i due ossicini dell&#039;udito, ma è certo che erano stati già ritrovati dagli <lb></lb>Anatomici infin dai tempi di Alessandro Achillini, e di Jacopo da Carpi. </s>

<s>— <lb></lb>“ Haec ossicula Anatomici, tempore Alexandri Achillini viri in omni scien­<lb></lb>tiarum genere eminentissimi, ut ex eius scriptis clarissime videre est, inve­<lb></lb>nerunt. </s>

<s>Quare non ab istis sunt primo inventa, nec ostensa, cum etiam Ja­<lb></lb>cobus Carpensis loca istorum ossiculorum invenire doceat. </s>

<s>Mitto quae a me <lb></lb>inventa sibi arrogant ” (Morgagni, Epist. </s>

<s>VI cit., pag. </s>

<s>114). </s></p><p type="main">

<s>Ben assai più del Massa è l&#039;Eustachio fieramente sdegnoso contro Colui <lb></lb>che, sebbene abbia detto tanti e sì grossi errori, <emph type="italics"></emph>anatomicae hodie artis <lb></lb>inventor et quasi architectus ab omnibus pene creditur;<emph.end type="italics"></emph.end> contro Colui, che <lb></lb>ingratissimo, dop&#039;avere espilato il Carpense, non si vergognò di avvilirlo <lb></lb>chiamandolo la feccia de&#039;Notomisti. </s>

<s>“ Caeterum, quantum ipse scio, haec <lb></lb>duo ossìcula primi indicarunt Alexander Achillinus hononiensis, philosophus <lb></lb>insignis, et Jacobus Carpensis, chirurgus et anatomicus non ita contemnen-<pb xlink:href="020/01/1394.jpg" pagenum="269"></pb>dus, quanquam eum ingratissimi quìdam, postquam expilarunt, ut ab omni­<lb></lb>bus parvifieret, anatomicorum faeciem nominare non erubuerunt: neuter ta­<lb></lb>men eorum sibi tantum sumpsit, ut inventionis sibi palmam vindicaret ” <lb></lb>(Opusc. </s>

<s>anat. </s>

<s>Venetiis 1564, De auditus org., pag. </s>

<s>153). </s></p><p type="main">

<s>Trovatosi il Vesalio così colto in fallo circondato da tante e sì valorose <lb></lb>armi vendicative, cercava di uscirne per la via più spedita, — e io, diceva, <lb></lb>non so nulla io nè de&#039;vostri Achillini, nè de&#039;vostri Carpensi: questo solo <lb></lb>so che, rimondando un giorno un cranio, vidi a caso uno degli ossicini cader <lb></lb>dall&#039;orecchio, aperto il quale vi trovai dentro anche quell&#039;altro, e come gli <lb></lb>trovai gli descrissi. </s>

<s>“ Quum enim mihi inter mundandum ad sceleti appa­<lb></lb>ratum calvariam casu ossiculum quoddam ex aure procidisset, auditus orga­<lb></lb>num in cruda calvaria aperui, et cum illo ossiculo secundum insuper quod­<lb></lb>dam reperi, remque ut tum mihi occurrit descripsi ” (Falloppi Examen, <lb></lb>Venetiis 1564, pag. </s>

<s>24). </s></p><p type="main">

<s>Come si rende per questi documenti chiaro essere stati i due primi os­<lb></lb>sicini dell&#039;udito ritrovati e resi noti, molti anni prima che venisse il Vesalio, <lb></lb>altrettanto incerto rimane il nome proprio dell&#039;inventore. </s>

<s>L&#039;Achillini e il <lb></lb>Carpense, commemorati dal Massa e dall&#039;Eustachio, fecero andare il Valsalva <lb></lb>a pronunziare questo giudizio: “ Malleus et Incus primum Anatomicis inno­<lb></lb>tuere, inventore Carpo, aut potius Achillino ” (De aure hum. </s>

<s>cit., pag. </s>

<s>21). <lb></lb>Ma perchè il Massa dice che la scoperta fu fatta non dall&#039;Achillini, ma ai <lb></lb>tempi dell&#039;Achillini, e l&#039;Eustachio soggiunge che nè esso Achillini nè il Be­<lb></lb>rengario ardirono d&#039;attribuirsene il merito dell&#039;invenzione, l&#039;Haller, migliore <lb></lb>interpetre dei due citati scrittori, si limitò a pronunziare così fatta sentenza: <lb></lb>“ Circa ultimam partem saeculi XV innotuit, dice del Martello, non quidem <lb></lb>inventore Jacobo Berengario, sed teste ” (Elem. </s>

<s>Phys., T. V, cit., pag. </s>

<s>208). </s></p><p type="main">

<s>Il giudiziosissimo uomo esclude a ragione l&#039;Achillini, il quale, tutt&#039;altro <lb></lb>che Anatomista, era un peripatetico sottilissimo commentator di Aristotile, <lb></lb>e perciò avverso o non curante di Galeno. </s>

<s>Amico, concittadino e collega del <lb></lb>Berengario, è probabile che avesse avuto da lui la notizia della scoperta, e <lb></lb>ch&#039;ei la divulgasse col suo autorevole magistero a viva voce nella sua scuola. </s>

<s><lb></lb>Diciamo a viva voce perchè, cominciando dal Massa e dall&#039;Eustachio, tutti <lb></lb>coloro che predicano il Filosofo bolognese o inventore o primo relatore degli <lb></lb>ossicini non citano nè le parole nè il luogo degli scritti di lui. </s>

<s>Noi per cu­<lb></lb>riosità, consultando la raccolta delle Opere ristampate nel 1568 in Venezia da <lb></lb>Girolamo Scoto, al leggere fra gli altri impressi nel frontespizio anche il titolo <lb></lb><emph type="italics"></emph>De physico auditu,<emph.end type="italics"></emph.end> siamo andati desiderosi a squadernare al luogo accen­<lb></lb>nato il volume in folio, e abbiamo trovato che di tutt&#039;altro vi si tratta che <lb></lb><emph type="italics"></emph>De physico auditu.<emph.end type="italics"></emph.end> Chi avesse il coraggio di mettersi a frugare per tutti i <lb></lb>seni di quell&#039;immenso mare peripatetico, e s&#039;abbattesse per fortuna a ritro­<lb></lb>varvi la perla preziosa, si persuaderebbe forse averla in ogni modo il Filosofo <lb></lb>dovuta ripescar con l&#039;amo di qualche Notomista. </s></p><p type="main">

<s>Potrebb&#039;essere questo Notomista facilmente il Berengario, e non cono­<lb></lb>scendosi a que&#039;tempi nessun altro più valoroso di lui, noi daremmo la cosa <pb xlink:href="020/01/1395.jpg" pagenum="270"></pb>come certa, se non avessimo in contrario, per non curarsi di tutti gli altri, <lb></lb>i giudizii autorevolissimi dell&#039;Haller e del Morgagni. </s>

<s>Ripensando poi che <lb></lb>non hanno que&#039;giudizii altro fondamento che sopra le parole dell&#039;Eustachio, <lb></lb>si vorrebbe sapere quali fossero le ragioni, per le quali s&#039;indusse l&#039;Anato­<lb></lb>mico sanseveritano a sentenziare che Jacopo da Carpi, divulgando la noti­<lb></lb>zia degli ossicini dell&#039;udito, non se ne rivendicò per questo la palma del­<lb></lb>l&#039;invenzione. </s></p><p type="main">

<s>Non possono quelle ragioni avere altro argomento che nel modo di <lb></lb>esprimersi dello stesso Carpense, il quale disse i due piccoli ossicini esser <lb></lb>cosa <emph type="italics"></emph>a paucis visa.<emph.end type="italics"></emph.end> Ma chi seguita a leggere, al sentirsi citare le opinioni <lb></lb>varie di tanti intorno all&#039;uso di quegli ossicini, direbbe che que&#039;<emph type="italics"></emph>pochi<emph.end type="italics"></emph.end> si <lb></lb>riducono a <emph type="italics"></emph>molti,<emph.end type="italics"></emph.end> e par che la cosa nuova abbia dato luogo a tante dispute <lb></lb>quanto una verità da lungo tempo già conosciuta. </s>

<s>Nelle espressioni del Be­<lb></lb>rengario insomma, per que&#039;<emph type="italics"></emph>pauci<emph.end type="italics"></emph.end> s&#039;intende <emph type="italics"></emph>nessuno,<emph.end type="italics"></emph.end> e le parole <emph type="italics"></emph>aliqui vo­<lb></lb>lunt, aliqui dicunt<emph.end type="italics"></emph.end> si traducono in quell&#039;altre: <emph type="italics"></emph>si potrebbe credere da alcuni, <lb></lb>si potrebbe dire da altri ....<emph.end type="italics"></emph.end> Chi ha pratica del linguaggio usato dall&#039;Autore <lb></lb>in tutto il suo libro se ne persuade assai facilmente, e l&#039;Eustachio s&#039;ingannò <lb></lb>forse, per aver più badato alla sostanza che alla forma dell&#039;espressione. </s></p><p type="main">

<s>Il Colombo ebbe però tempo d&#039;avvedersi dell&#039;inganno e di confessarlo, <lb></lb>e perciocchè il modo più conveniente di far quella confessione gli fu divie­<lb></lb>tato dalla morte, ingiustamente il Morgagni lo accusò di essere stato <emph type="italics"></emph>sibi <lb></lb>parum constans<emph.end type="italics"></emph.end> (Epist. </s>

<s>VI cit., pag. </s>

<s>115). Nel I libro infatti <emph type="italics"></emph>De re anat.,<emph.end type="italics"></emph.end><lb></lb>parlando degli ossicini, “ quis tamen inventor fuerit, dice, me plane latet ” <lb></lb>(pag. </s>

<s>26) perchè ciò non appariva chiaro dalle parole del Berengario. </s>

<s>Poi, <lb></lb>ripensandoci meglio e interpetrando nel loro vero significato le espressioni <lb></lb>dell&#039;Autore de&#039;commentarii sopra Mondino, scrivendo alcuni anni dopo il <lb></lb>libro VIII pubblicato insieme con gli altri postumo, non dubitò di asserire <lb></lb>che i due ossicini <emph type="italics"></emph>Carpus primum invenit<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>196). E perchè in­<lb></lb>somma a questa sentenza si riducono, e in ogni modo non contradicono <lb></lb>l&#039;espressioni del Massa e del Falloppio, crediamo anche noi con questi grandi <lb></lb>uomini aver primo di tutti scoperto il Martello e l&#039;Incudine nella cavità del­<lb></lb>l&#039;orecchio Jacopo Berengario. </s></p><p type="main">

<s>Aperta dai due nostri Bolognesi alle gloriose scoperte dell&#039;organo del­<lb></lb>l&#039;udito la via, rimasta sempre chiusa infin da Galeno, si trovò che que&#039;due <lb></lb>primi ossicini componevano nella mediana cavità dell&#039;orecchio una catena <lb></lb>continua, a cui s&#039;aggiungevano altri due anelli, intorno alla invenzione dei <lb></lb>quali ha da esercitarsi non poco la nostra Storia. </s></p><p type="main">

<s>Lodovico Collado pubblicava nel 1555 un suo libro col titolo: <emph type="italics"></emph>In Ga­<lb></lb>leni lib. </s>

<s>De ossibus ad tirones enarrationes,<emph.end type="italics"></emph.end> dove, dopo di aver nel cap. </s>

<s>I <lb></lb>trattato de&#039;due primi ossicini conosciuti da qualche tempo in Italia, “ ego, <lb></lb>soggiunge, una cum Cosmo Medina, in inclyta Academia salmanticensi nunc <lb></lb>publico Anatomes professore longe doctissimo, discipulo meo mihi carissimo, <lb></lb>aliud os reperi, cui, quod simile esset equitandi instrumento quo pades fir­<lb></lb>mantur, <emph type="italics"></emph>stapedae<emph.end type="italics"></emph.end> nomen imposui ” (Valentiae, pag. </s>

<s>12). </s></p><pb xlink:href="020/01/1396.jpg" pagenum="271"></pb><p type="main">

<s>Quattro anni dopo vedeva la luce, molto tempo prima meditata e scritt<gap></gap><lb></lb>l&#039;opera del Colombo, nel I libro della quale al cap. </s>

<s>VII, dopo aver l&#039;Au <lb></lb>tore descritti gli ossicini del Martello e dell&#039;Incudine, “ his tertium accedi <lb></lb>soggiunge, nemini quod sciam ante nos cognitum. </s>

<s>Jacet hoc vel latitat po <lb></lb>tius in cavernula quadam ferme rotunda intra sinum auditorium exculpta <lb></lb>quo fit, ut ad organi auditus fabricam non pertinere non possit. </s>

<s>Cavum es <lb></lb>et perforatum, egregie ferrei instrumenti naturam imitatur, quod <emph type="italics"></emph>Staphan<emph.end type="italics"></emph.end><lb></lb>novo vocabulo nuncupamus, in quo equorum sellis insidentes pedes sistunt <lb></lb>(De re anat. </s>

<s>cit., pag. </s>

<s>27). </s></p><p type="main">

<s>Ma quando, due anni dopo da che erano state divulgate queste notizi<gap></gap><lb></lb>comparvero le Osservazioni anatomiche del Falloppio, vi si lesse dentro un <lb></lb>storia, dalla quale appariva essere stato il Colombo, nello scrivere a que <lb></lb>modo, o menzognero od illuso. </s>

<s>Quella storia, per la quale dimostravasi in <lb></lb>vece essere stato il primo a scoprire la Staffa il siciliano Filippo Ingrassia <lb></lb>è così particolarmente narrata dall&#039;Autore a Pietro Manna: </s></p><p type="main">

<s>“ Anno Domini millesimo quingentesimo quadragesimo octavo, quo eg <lb></lb>primum Pisis profiteri coepi, cum neque a Vesalio qui multo antea, nequ <lb></lb>a Columbo cive tuo, qui anno proxime superiori Anatomen Pisis tractave <lb></lb>rat, nulla fuisset facta mentio istius ossis, dum eam ego celebrarem, ad m <lb></lb>venit quidam auditor meus iuvenis doctissimus, qui si recte memini docto <lb></lb>ratus ornamento iam insignis erat, Ingrassiaeque affinitate coniunctus, nome<gap></gap><lb></lb>nunc memoria haud retineo, hicque me monuit Joannem Philippum tertium <lb></lb>ossiculum in tympano invenisse, quod <emph type="italics"></emph>Stapedis<emph.end type="italics"></emph.end> nomine et figura appellarit <lb></lb>Ego hac re commotus, adhibito maiori studio, ossiculum laetus inveni, sta <lb></lb>timque publice protuli, omnibus admirantibus. </s>

<s>Atque praeterea Bartholom <lb></lb>maeo Madio, sanctissimae memoriae, medico doctissimo ac celeberrimo pe <lb></lb>epistolam communicavi. </s>

<s>Scripsi etiam de hac re quibusdam amicis qui Ro <lb></lb>mae erant de quo, et rescripsere, a Columbo qui paulo ante Anatome<gap></gap><lb></lb>tractarat, nihil audiverant, neque ab ullo alio, cum in Italia tunc temporis <lb></lb>uno excepto Johanne Baptista Canano medico et Anatomico celeberrimo <lb></lb>nullus alius praeter dictos reperiatur, qui docte Anatomen publicam docer<gap></gap><lb></lb>potuisset ” (Op. </s>

<s>omnia cit., pag. </s>

<s>409). </s></p><p type="main">

<s>Ferirono queste parole come saetta acuta la coscienza a Bartolomme<gap></gap><lb></lb>Eustachio, che insegnava pure allora in Roma, e che si sentiva tante supe­<lb></lb>riore a Bartolommeo Maggi e a Giovan Batista Canani. </s>

<s>Risolutosi perciò d <lb></lb>render conto al pubblico di ciò che aveva scoperto intorno all&#039;organo del­<lb></lb>l&#039;udito, dette mano a scrivere quella sua Epistola a Francesco Alciato, sot­<lb></lb>toscritta negl&#039;idi di Ottobre del 1562, nella quale accennando all&#039;invenzione <lb></lb>della Staffa e alla Storia del Falloppio, “ sed referat eam quisque, conclude<gap></gap><lb></lb>cui mavult acceptam. </s>

<s>Ego quidem scio me neque edoctum, neque monitum <lb></lb>ab aliquo, multo antequam ipsi scribant, id ossiculum novisse, Romaequ<gap></gap><lb></lb>non paucis ostendisse, atque in aes incidendum curasse ” (Opusc. </s>

<s>anat. </s>

<s>cit., <lb></lb>pag. </s>

<s>154). </s></p><p type="main">

<s>Il Falloppio, il quale aveva enfaticamente conclusa la storia della Staffa <pb xlink:href="020/01/1397.jpg" pagenum="272"></pb>con le parole: “ Deus tamen gloriosus scit Ingrassiae fuisse inventum ” fa <lb></lb>quella invenzione anteriore al 1548, e l&#039;Eustachio afferma di averla fatta <lb></lb><emph type="italics"></emph>multo antequam ipsi scribant.<emph.end type="italics"></emph.end> Il tempo però che non fu scritto da costoro <lb></lb>preciso, non si seppe prima del 1604 quando in Palermo comparve postumo <lb></lb>il libro dell&#039;Ingrassia <emph type="italics"></emph>De ossibus commentaria in Galenum,<emph.end type="italics"></emph.end> dove dice l&#039;Au­<lb></lb>tore di avere scoperta la Staffa nel 1546. Ma perchè fu questo libro mani­<lb></lb>festamente scritto dopo la pubblicazione degli Opuscoli dell&#039;Eustachio, e dopo <lb></lb>la morte dell&#039;Autore, avvenuta nel 1580, da un nipote di lui fu pubblicato; <lb></lb>non rimane altro documento ad attestar della scoperta del Medico siciliano <lb></lb>che le parole, e la fede avuta alle parole altrui dal Falloppio. </s></p><p type="main">

<s>Se devesi dunque la storia appoggiare sopra la fede, primi a scoprire <lb></lb>la Staffa furono l&#039;Eustachio e l&#039;Ingrassia; se si deve appoggiare ai pubblici <lb></lb>documenti, furon primi invece il Collado e il Colombo. </s>

<s>Così le storie pri­<lb></lb>vate però che le pubbliche a nulla conducono senza la critica, che può sola <lb></lb>decidere del vero o espresso nelle parole o impresso sopra le carte. </s>

<s>Un ca­<lb></lb>none di critica giustissima ce lo suggerisce molto a proposito l&#039;Eustachio, <lb></lb>il quale, dop&#039;avere asserito che fu il terzo ossicino da lui scoperto in Roma, <lb></lb><emph type="italics"></emph>neque edoctum neque monitum ab aliquo,<emph.end type="italics"></emph.end> soggiunge che della verità della <lb></lb>sua asserzione faranno testimonianza le cose, che sarà per dire, dalle quali <lb></lb>decideranno i lettori, “ num propria ego industria auditus organa investi­<lb></lb>garim et invenerim, an potius aliorum opera usus ” (De auditus org. </s>

<s>cit., <lb></lb>pag. </s>

<s>154). </s></p><p type="main">

<s>Seguendo questo criterio, si dovrebbe escludere dal merito dell&#039;inven­<lb></lb>zione il Collado, spagnolo, e riporre nel primo luogo il Colombo, il quale è <lb></lb>probabilissimo che avesse scoperta, e, nonostante le relazioni avute in con­<lb></lb>trario dal Falloppio, dimostrata nelle sue scuole la Staffa molti anni prima <lb></lb>che fosse pubblicato il suo libro. </s>

<s>Chi ripensa all&#039;egual valore di quegli Ana­<lb></lb>tomici, e che, scoperto il Martello e l&#039;Incudine, era naturalissimo il ritrovar <lb></lb>la catena degli ossicini continuata nella Staffa, non avrà nessuna difficoltà <lb></lb>a credere che il Colombo, l&#039;Eustachio e l&#039;Ingrassia, così studiosi dell&#039;organo <lb></lb>dell&#039;udito, s&#039;incontrassero tutti e tre insieme e inconsapevoli nella scoperta <lb></lb>di quel terzo ossicino. </s>

<s>Tanta poi era manifesta agli occhi di tutti la somi­<lb></lb>glianza fra l&#039;esemplare e l&#039;esemplato, che non fa maraviglia se tutti e tre, <lb></lb>senza nulla saper l&#039;uno dell&#039;altro, convennero nell&#039;imporre a quello stesso <lb></lb>ossicino il nome di <emph type="italics"></emph>Staffa.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>I tre ossicini così, innanzi alla prima metà del secolo XVI, scoperti for­<lb></lb>marono l&#039;ammirazione degli Anatomici seguenti, i quali si dettero con amo­<lb></lb>roso studio a contemplarli in sè stessi Desiderosi di descriverli nelle loro <lb></lb>vere sembianze, aguzzarono gli occhi nelle loro minuzie più sfuggevoli, tra <lb></lb>le quali ne notarono una in quella parte, che il processo dell&#039;Incudine si <lb></lb>articola colla Staffa. </s>

<s>Dissero che cotesta articolazione si faceva per l&#039;inter­<lb></lb>medio di un osso distinto, che perciò sarebbe in ordine il quarto, e che va­<lb></lb>riamente presentandosi all&#039;occhio dell&#039;osservatore ebbe vario nome, secondo <lb></lb>l&#039;apparente varietà delle sue forme. </s>

<s>Anche questo, ch&#039;è il più piccolo degli <pb xlink:href="020/01/1398.jpg" pagenum="273"></pb>ossicini dell&#039;udito, ha una storia sua propria, che non vuol essere nel pre­<lb></lb>sente argomento taciuta. </s></p><p type="main">

<s>Aveva già il Vesalio da lungo tempo osservato che l&#039;estrema gamba <lb></lb>dell&#039;Incudine andava a terminare “ quasi in unculum ” (De corp. </s>

<s>hum. </s>

<s>fa­<lb></lb>brica cit., pag. </s>

<s>35) ciò che l&#039;avrebbe potuto mettere in sospetto dell&#039;esi­<lb></lb>stenza di un terzo ossicino, a cui quell&#039;uncinetto servirebbe di attacco. </s>

<s>Ma <lb></lb>al Colombo, nella serie completa degli ossicini da lui osservata, si presentò <lb></lb>quel punto di attacco sotto la forma di un capolino di spillo collocato nella <lb></lb>staffa ossea al posto dell&#039;anello in cui, nelle staffe da cavalcare, s&#039;infila la <lb></lb>correggia pendente dalla sella. </s>

<s>“ Una re tamen a stepede differt quod caret <lb></lb>eo foramine in quod lora immittuntur ad stapedem sellae utrinque alligan­<lb></lb>dam. </s>

<s>At huius loco capitulum quoddam extat rotundum, quo ad incudis <lb></lb>processum accedit ” (De re anat. </s>

<s>cit., pag. </s>

<s>27). Fu questo capolino descritto <lb></lb>poi anche dall&#039;Aranzio, come fece notare il Morgagni a pag. </s>

<s>122 dell&#039;Epi­<lb></lb>stola anatomica VI da noi più volte citata, e nostante, sulla fine della prima <lb></lb>metà del secolo XVII, formò per alcuni Anatomici, com&#039;apparirà dal rac­<lb></lb>conto che segue, il vanto di una nuova scoperta. </s></p><p type="main">

<s>Visitando Tommaso Bartholin l&#039;Italia e i più eccellenti professori del­<lb></lb>l&#039;arte, ch&#039;ei coltivava con tanta fama, giunto in Venezia, s&#039;introdusse in <lb></lb>casa di Cecilio Folli, che volle onorar l&#039;ospite col mostrargli certe sue pre­<lb></lb>parazioni degli ossicini auditivi, fra&#039;quali glie ne additava uno, compiacen­<lb></lb>dosi di averlo egli il primo da poco tempo scoperto. </s>

<s>— Ma cotesto, disse <lb></lb>allora il Bartholin, è il quarto ossicino scoperto, già sono alcuni anni, dal <lb></lb>mio amico Francesco Sylvio, e ch&#039;io stesso, dietro la notizia avutane da lui, <lb></lb>pure scopersi e descrissi in una mia dissertazioncella anatomica, della quale, <lb></lb>se vi piace, posso mandarvi una copia. </s>

<s>— Restò il Folli a queste parole <lb></lb>senza fiato, nè lo riebbe, se non che dalla speranza espressa al Bartholino <lb></lb>che quell&#039;osso sylviano potess&#039;essere qualche cosa di differente dal suo. </s></p><p type="main">

<s>In questo, l&#039;Ospite che vedeva non esser quello nè il luogo nè il tempo <lb></lb>di entrare in dispute, si congedò per andare a Padova, di dove mandò a <lb></lb>Venezia la promessa Dissertazione, accompagnata da una lettera sottoscitta <lb></lb>il dì 25 di Ottobre 1644, nella quale, a proposito degli ossicini dell&#039;udito, <lb></lb>così al Folli diceva: “ Auditus ossicula nitida erant quae nobis ostendebas. </s>

<s><lb></lb>Quod vero quartum Os sylvianum diversum a tuo diceres, mirum mihi vi­<lb></lb>debatur. </s>

<s>Quaeso per otium auditus instrumenta, tuo more separata, et si <lb></lb>quid circa illa dignum memoria notasti, nobis communica ” (T. Barthol., <lb></lb>Epistolarum medic. </s>

<s>Centuria I, Hagae Comitum 1740, pag. </s>

<s>249, 50). </s></p><p type="main">

<s>Il Folli infatti rispose il dì 19 di Novembre appresso poche parole, con <lb></lb>le quali accompagnava al Bartholin sei figure rappresentative de&#039;varii stru­<lb></lb>menti dell&#039;organo dell&#039;udito, semplicemente dichiarate con lettere di ri­<lb></lb>chiamo. </s>

<s>Nella figura II, quella parte disegnata colla lettera <emph type="italics"></emph>l<emph.end type="italics"></emph.end> si dichiara così: <lb></lb>“ Stapedis osseus quidam globulus Thomae Bartholino in Anatomia Paren­<lb></lb>tis descriptus ” (ibid., pag. </s>

<s>258). Par di qui che il Folli rinunziasse al me­<lb></lb>rito della scoperta, ma nella seguente figura III, benchè il piccolo strumento <pb xlink:href="020/01/1399.jpg" pagenum="274"></pb>indicato colla lettera <emph type="italics"></emph>g<emph.end type="italics"></emph.end> si dichiari nuovamente: “ Stapedis osseus globulus ” <lb></lb>(ibid., pag. </s>

<s>259) in disegno apparisce diverso dalla forma globulare, e rap­<lb></lb>presenta piuttosto quella <emph type="italics"></emph>squamula oblonga,<emph.end type="italics"></emph.end> a cui ben lo rassomigliava il <lb></lb>Molinetti nel cap. </s>

<s>IX delle sue <emph type="italics"></emph>Dissertazioni<emph.end type="italics"></emph.end> (ediz. </s>

<s>cit., pag. </s>

<s>52). Questa era <lb></lb>forse la diversità che il Folli diceva passare fra il suo e l&#039;Osso sylviano, ma <lb></lb>poi sembra si persuadesse non esser la forma di lui squamosa ma globu­<lb></lb>lare, non avvedendosi nè egli nè il Bartholin che il Sylvio era stato di quasi <lb></lb>un secolo prevenuto dal Colombo e dall&#039;Aranzio. </s>

<s>Gli Anatomici poi, asse­<lb></lb>gnando al quarto ossicino la figura lenticolare, dichiarano che il Folli avrebbe <lb></lb>fatto meglio a non si lasciar persuadere al Bartholino, e a dichiarare, come <lb></lb>aveva rappresentato in disegno, il piccolissimo strumento, intorno al quale <lb></lb>nonostante si disputa se sia un osso distinto o un apofisi del più lungo pro­<lb></lb>cesso dell&#039;Incudine, e la lite è sotto il giudice ancora. </s></p><p type="main">

<s>In quella III figura, dove il Folli disegnò gli ossicini, il Martello è rap­<lb></lb>presentato con tre processi, il maggiore e il minore già da lungo tempo co­<lb></lb>nosciuti e descritti, e un altro più minuto, ch&#039;esso Folli dichiara <emph type="italics"></emph>a nemine <lb></lb>antea observatus<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>259). Ma a che fine usar la Natura tant&#039;arte in <lb></lb>così sfuggevoli minuzie? </s>

<s>Era questa una domanda che, tutto in contempla­<lb></lb>zione di quelle maraviglie, si faceva un giorno l&#039;Eustachio. </s>

<s>Sospettò che <lb></lb>dovessero que&#039;processi servire di attacco a qualche muscolo, e dall&#039;altra <lb></lb>parte, se gli ossicini si muovono, come da tutti s&#039;ammette per certo, qual&#039;è <lb></lb>il principio e lo strumento del moto? </s></p><p type="main">

<s>Dietro la scorta di queste idee, incidendo il peritissimo Anatomico l&#039;osso <lb></lb>“ quod petram refert, eo loco, quo linea minime alte penetrante exculptum <lb></lb>est et versus tenuiorem ossis temporis sedem in anteriorem partem magis <lb></lb>eminet, eiusque squammam accurate detrahens ” gli venne trovato un mu­<lb></lb>scolo “ qui etsi omnium minimus sit, elegantia tamen et constructionis ar­<lb></lb>tificio nulli cedit. </s>

<s>Oritur a substantia ligamentis simili qua parte os, quod <lb></lb>cuneum imitatur cum temporis osse committitur, indeque carneus evadens <lb></lb>redditur sensim ad medium usque aliquanto latior, deinde vero angustior <lb></lb>effectus tendinem gracillimum producit qui, in maiorem apophysim ossiculi <lb></lb>malleo comparati, fere e regione minoris apophysis eiusdem inseritur ” (De <lb></lb>auditus org. </s>

<s>cit., pag. </s>

<s>158). </s></p><p type="main">

<s>Poco però al moto parve un muscolo solo, l&#039;inserzion del quale lasciava <lb></lb>inutili gli altri processi. </s>

<s>L&#039;Eustachio forse intravide la necessità di altri pic­<lb></lb>coli muscoli, che servissero a quell&#039;armonica corrispondenza di moti, in che <lb></lb>si dovevano mettere gli ossicini, ma oltre quel primo non potè nell&#039;interno <lb></lb>dell&#039;orecchio ritrovarvene altri. </s>

<s>Il dì 7 di Marzo del 1593 la ventura toccò <lb></lb>poi al Casserio, che fece in quel tempo incidere il nuovo muscolo felice­<lb></lb>mente scoperto a perpetua memoria, aspettando l&#039;occasione propizia d&#039;an­<lb></lb>nunziarlo pubblicamente in iscritto. </s>

<s>Stava intanto in gran trepidazione che <lb></lb>qualcuno non lo prevenisse, e avendo saputo che Andrea Laurent attendeva <lb></lb>in Parigi alla stampa della sua <emph type="italics"></emph>Anatomia,<emph.end type="italics"></emph.end> volle per mezzo degli amici del­<lb></lb>l&#039;Autore spiare se nulla vi dicesse di questo secondo muscolo interno del-<pb xlink:href="020/01/1400.jpg" pagenum="275"></pb>l&#039;orecchio, e n&#039;ebbe per risposta che il Laurent accennava solo essere or­<lb></lb>gani delle pulsazioni auditive i tre ossicini e alcuni muscoli, senza designarli <lb></lb>però nè nel numero nè nella specie. </s></p><p type="main">

<s>Il Relatore, chiunque egli fosse, come sbagliò nell&#039;indicare il titolo del­<lb></lb>l&#039;Opera, così sbagliò nell&#039;indicare il libro e il capitolo, dove l&#039;Anatomico <lb></lb>parigino trattava dell&#039;udito, ond&#039;è che il Casserio così citava, dietro le poco <lb></lb>esatte informazioni, il volume tuttavia inedito, come se fosse già venuto alla <lb></lb>luce. </s>

<s>“ Andreas Laurentius philos. </s>

<s>e med. </s>

<s>celeberrimus, suorum operum <lb></lb>anat., lib. </s>

<s>IV, cap. </s>

<s>XVIII, scribit pulsationi, quam concussis invicem audi­<lb></lb>tus organi ossiculis quidam pro efficienda auditione fieri opinantur, exiles <lb></lb>dicatos esse musculos. </s>

<s>An autem duo tantum sint an plures, et ubi consi­<lb></lb>stant, unde orti, quomodo progrediantur, ubi inseruntur non docet.... Cae­<lb></lb>terum musculum hunc consistentem in auditorio meatu ego anno millesimo <lb></lb>quingentesimo nonagesimo tertio, mense martio die septima, in praesentia <lb></lb>excellentissimi Domini Christofori Malvicini .... et plurium studiosorum, ... <lb></lb>observavi, et statim ab honorabili viro Josepho Mureto germano pictore, tunc <lb></lb>temporis mihi, pro pingendis figuris anatomicis cohabitanti, delineari in per­<lb></lb>petuam memoriam curavi ” (De auris auditus organii historia, Ferrariae 1600, <lb></lb>pag. </s>

<s>79). </s></p><p type="main">

<s>In quell&#039;anno, che appariva in Ferrara questo trattato del Casserio alla <lb></lb>luce, il Laurent pubblicava in Parigi la sua <emph type="italics"></emph>Historia anatomica humani <lb></lb>corporis,<emph.end type="italics"></emph.end> nell&#039;XI libro della quale, al cap. </s>

<s>XIII, si leggevano queste parole: <lb></lb>“ Stapes enim superiorem fenestram claudens ab Incude movetur. </s>

<s>Incus a <lb></lb>Malleo, Malleus a membrana aeris externi appulsu percussa. </s>

<s>Haec igitur pul­<lb></lb>sationis sunt organa: ossicula tria, chorda et musculi ” (pag. </s>

<s>428). </s></p><p type="main">

<s>Ma in quel medesimo anno 1600 comparve alla luce in Venezia anche <lb></lb>il trattato <emph type="italics"></emph>De aure auditus organo<emph.end type="italics"></emph.end> dell&#039;Acquapendente, nella Prima parte <lb></lb>del quale, al cap. </s>

<s>VI, dop&#039;aver descritto il muscolo eustachiano, si soggiunge: <lb></lb>“ Praeterea hoc anno 1599 musculum invenire visus sum in meatu audito­<lb></lb>rio, qui extra membranam est, exiguus, carneus, non expers tendinis ” <lb></lb>(Opera omnia cit., pag. </s>

<s>251). È questa come ognuno vede la descrizione del <lb></lb>muscolo che il Casserio, discepolo dell&#039;Acquapendente, diceva di avere sco­<lb></lb>perto sei anni prima, e che l&#039;Albino stesso liberamente confessava essere <lb></lb>stato più diligentemente descritto dal discepolo che dal maestro (Ibid., Al­<lb></lb>bini praefatio De Hier. </s>

<s>Fabricio). </s></p><p type="main">

<s>Quella diligenza però verrà anche meglio apprezzata, considerando le <lb></lb>difficoltà dell&#039;invenzione, per le quali, appresso a molti Anatomici posteriori, <lb></lb>andò affatto dimenticato quel nuovo muscolo casseriano, che si sta tutto invi­<lb></lb>sibilmente nascosto sotto il corpo dell&#039;Incudine e il Meato auditorio. </s>

<s>Fu <lb></lb>perciò che il Valsalva credè necessario d&#039;insegnare il più facile modo di <lb></lb>farne l&#039;indagine “ cum multi ex Recentioribus eumdem musculum omni­<lb></lb>fariam sileant, quasi nunquam hunc docuisset Casserius, .... immo quasi <lb></lb>nunquam hic musculus in aure extitisset ” (De aure hum. </s>

<s>cit., pag. </s>

<s>22). </s></p><p type="main">

<s>Da questo zelo trasportato aumentò lo stesso Valsalva il numero di que-<pb xlink:href="020/01/1401.jpg" pagenum="276"></pb>sti muscoli interni, assegnandone uno a ciascun de&#039;processi da lui distinti <lb></lb>col nome di <emph type="italics"></emph>processo maggiore<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>processo minore<emph.end type="italics"></emph.end> dato ai due primi an­<lb></lb>ticamente conosciuti, e col nome di <emph type="italics"></emph>processo minimo<emph.end type="italics"></emph.end> dato a quello scoperto <lb></lb>dal Folli. </s>

<s>“ Musculus processus minimi, a pariete Tympani faciem spectante <lb></lb>incipiens et per hunc progrediens, inflectitur, deinde, et Tympani chordam <lb></lb>subtermeans, in Mallei partem praecedentis musculi insertioni quasi oppo­<lb></lb>sitam, nempe in processum minimum, insertum se venit, et sic Malleus ex <lb></lb>utraque parte, ope huius et praecedentis musculi, firmatus consistit, non sic <lb></lb>tamen ut immobilis sit, verum ut in ipsorum insertis extremitatibus hypo­<lb></lb>mochlium in propriis motibus habeat ” (ibid.). Ma gli Anatomici posteriori, <lb></lb>fra&#039;quali lo stesso Morgagni, messero in dubbio questo terzo muscolo appli­<lb></lb>cato dal Valsalva a fermare e a servire d&#039;ipomoclio al Martello. </s></p><p type="main">

<s>Essendo questo primo ossicino, conforme alla più comune opinione di <lb></lb>quei tempi, il principio del moto, si poteva facilmente credere che non aves­<lb></lb>sero gli altri nessun bisogno di muscoli motori, ma il Casserio ne ritrovò <lb></lb>uno applicato alla staffa nell&#039;orecchio di un cavallo, e fra le figure della Ta­<lb></lb>vola IX lo disegnò nella XXIV colla lettera C così dichiarata: “ Musculus <lb></lb>internus alter, a nemine hactenus inventus et observatus, suo tendine te­<lb></lb>nuissimo Stapedi adiunctus ” (De auris historia cit., pag. </s>

<s>56). </s></p><p type="main">

<s>Il Riolano, a cui non riuscì di ritrovare il muscolo equino descritto e <lb></lb>disegnato nelle sue Tavole dal Casserio, sentenziò con gran confidenza che <lb></lb>egli era fittizio: molti lo negarono affatto nell&#039;uomo. </s>

<s>Lo Schelhammer ha <lb></lb>nel suo trattato <emph type="italics"></emph>De auditu<emph.end type="italics"></emph.end> queste espresse parole: “ Huie etiam ossiculo <lb></lb>(alla staffa) musculum destinatum esse Dn. </s>

<s>Lamy asserit, in quo fortassis <lb></lb>fallitur ” (Lugd. </s>

<s>Batav. </s>

<s>1684, pag. </s>

<s>47). Ma pure que&#039;grandi Anatomici ita­<lb></lb>liani del secolo XVI non erano così facili ad ingannarsi, e il Vidio accen­<lb></lb>nava a un filo <emph type="italics"></emph>seu chorda tenuissima,<emph.end type="italics"></emph.end> che passa attraverso alla Finestra ro­<lb></lb>tonda “ pertinetque ad commissuram incudis cum stapede ” (De Anatome <lb></lb>corp. </s>

<s>hum., Venetiis 1611, pag. </s>

<s>322). Il Varolio poi riconobbe (De resolu­<lb></lb>tione corp. </s>

<s>hum., Francofurti 1591, pag. </s>

<s>28) essere quella corda tenuissima <lb></lb>il tendine di un muscolo, che il Valsalva liberò da tutte le contradizioni di­<lb></lb>mostrando avere il suo corpo carnoso annidato “ in curvo canali osseo late­<lb></lb>raliter, circa mediam falloppiani Aquaeductus partem, insculpto ” (De aure <lb></lb>hum. </s>

<s>cit., pag. </s>

<s>25). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La storia descrittiva di quelle corde, sopra le quali cantano i loro idillii <lb></lb>le divine Sirene mollemente sedute sopra gli orli della Conca auditiva, è <lb></lb>ormai giunta al suo termine, e non resta altro a noi che di scendere nel <lb></lb>profondo di quella Conca, per i riposti anfratti, per i seni tortuosi e per gli <lb></lb>intricati labirinti a narrare ciò che di nuovo e di maraviglioso v&#039;ha scoperto <lb></lb>l&#039;industria dell&#039;uomo. </s></p><pb xlink:href="020/01/1402.jpg" pagenum="277"></pb><p type="main">

<s>Gli Anatomici antichi impaurirono timorosi di smarrire la via, e i primi <lb></lb>restauratori dell&#039;arte s&#039;affacciarono appena alla bocca dell&#039;antro misterioso, <lb></lb>sollevando la prima lapide che la chiudeva. </s>

<s>Realdo Colombo dice del piè della <lb></lb>staffa, in cui ci si rappresenta l&#039;immagine di quella lapide: “ Jacet, vel la­<lb></lb>titat potius, in cavernula quadam, ferme rotunda, intra sinum auditorium <lb></lb>exculpta “ (De re anat. </s>

<s>cit., pag. </s>

<s>27), e quel seno auditorio è dall&#039;Autore <lb></lb>vagamente descritto come vacuo “ ac diversis veluti speluncis excavatum ” <lb></lb>(ibid., pag. </s>

<s>23). È da notare, altrove soggiunge, fra quelle spelonche un pro­<lb></lb>cesso “ ad cerebri basim, qui in iugi modum extenditur in acutum desi­<lb></lb>nens, cavernamque intus habet instar labyrinthi ” (ibid., pag. </s>

<s>26), penetrar <lb></lb>nel quale non era a nessuno permesso, che non avesse avuto il filo d&#039;Arianna. </s></p><p type="main">

<s>Aveva perciò ragione il Falloppio a dire delle cavità scolpite nell&#039;osso <lb></lb>temporale per uso dell&#039;udito, “ hae ab aliquot Anatomicis satis imperfecte, <lb></lb>ab aliquot vero falso descriptae sunt. </s>

<s>Igitur, soggiunge tosto a Pietro Manna, <lb></lb>quales sint audi ” (Observat. </s>

<s>anat. </s>

<s>in loco cit., pag. </s>

<s>409). E dop&#039;essersi di­<lb></lb>ligentemente ed eruditamente trattenuto intorno alla membrana e agli ossi­<lb></lb>cini, entra addentro a esplorare la cavità da lui detta il Timpano “ ob eam <lb></lb>quam habet cum militari tympano similitudinem ” e la trova insigne per <lb></lb>due cavità, e per un canale, a cui piacegli d&#039;imporre il nome di <emph type="italics"></emph>Acquedotto.<emph.end type="italics"></emph.end><lb></lb>Le due cavità pure non vuol lasciarle senza un nome distinto, ch&#039;è quello <lb></lb>di <emph type="italics"></emph>Finestre<emph.end type="italics"></emph.end> e così le descrive: “ Altera elatior, et quasi in media concame­<lb></lb>ratione Tympani collocata, quam Stapedis basis claudit. </s>

<s>Figura istius ovalis <lb></lb>penitus est, quae aperta desinit in secundam cavitatem, quam <emph type="italics"></emph>Labyrinthum<emph.end type="italics"></emph.end><lb></lb>nominabo. </s>

<s>Altera vero humilior est rotundaque et ad posteriora cavitatis <lb></lb>declinans, quae per os penetrans in geminum canalem aut viam fenditur, <lb></lb>quarum viarum unam in dictum labyrinthum, alteram in tertiam cavitatem <lb></lb>cochlearem vel <emph type="italics"></emph>Cochleam<emph.end type="italics"></emph.end> a me dictam tendit. </s>

<s>Haec secunda fenestella nullo <lb></lb>osse clauditur, cum tamen prior Stapedis basi semper clausa maneat ” (ibid.). </s></p><p type="main">

<s>Aperti così una volta gli occhi a contemplare ciò ch&#039;era prima sfuggito <lb></lb>all&#039;attenzione di tutti, gli Anatomici posteriori al Falloppio esaminarono con <lb></lb>più diligenza quelle due finestre, e trovarono che v&#039;era qualche cosa da cor­<lb></lb>reggere nella figura e nelle parti annesse. </s>

<s>Il Vidio, il Plater e il Casserio <lb></lb>disegnarono, nelle loro Tavole, rotonda quella più alta finestra, com&#039;era stata <lb></lb>veduta dallo stesso Falloppio, ma l&#039;Acquapendente, nella figura XIX illustra­<lb></lb>tiva del suo trattato <emph type="italics"></emph>De aure,<emph.end type="italics"></emph.end> la dipinse in forma più tendente al triangolo <lb></lb>che al cerchio, e tale, in più casi, ebbe veramente a ritrovarla il Morgagni. <lb></lb></s>

<s>“ Nam quod ego in pluribus, ne dicam in plerisque auribus, continenter <lb></lb>inspectis animadverteram, rotundam Fenestram ad trianguli magis, cuius <lb></lb>vertex sit ad superiora conversus, quam ad circuli figuram accedere, id olim <lb></lb>a Fabricio nostro expressum video ” (Epist. </s>

<s>anat. </s>

<s>XXII cit., pag. </s>

<s>175). </s></p><p type="main">

<s>La lode però, come giustamente osserva lo Scarpa, è immeritata, perchè <lb></lb>l&#039;Acquapendente dipinse a caso quella figura “ cui tamen nullam explica­<lb></lb>tionem adiecit, quia, sicuti ex eius verbis colligitur, rem non adhuc sibi <lb></lb>satis cognitam delincabat ” (De structura Fenestrae rotundae, Mutinae 1772, <pb xlink:href="020/01/1403.jpg" pagenum="278"></pb>pag. </s>

<s>26). Le parole, a cui qui accenna lo Scarpa, sono principalmente quelle <lb></lb>scritte nel cap. </s>

<s>VII della I Parte <emph type="italics"></emph>De aure auditus organo,<emph.end type="italics"></emph.end> dalle quali ve­<lb></lb>ramente si conclude che il celebre Autore non descrisse dell&#039;orecchio, sul­<lb></lb>l&#039;esempio degli Anatomici antichi, altro che la parte esterna. </s>

<s>Quanto all&#039;in­<lb></lb>terna cavità, egli dice, è piena di così innumerevoli seni “ ut assequi ac <lb></lb>denumerare possibile non sit ” (Opera omnia cit., pag. </s>

<s>252). E benchè citi <lb></lb>il Falloppio “ cui in rebus abstrusis maximam fidem adhibeo, utque prae­<lb></lb>ceptorem colo ” nonostante dice che i canali semicircolari, in cui si raggira <lb></lb>il labirinto, son tali e tanti, che si possono bene ammirare “ dinumerare <lb></lb>autem seu ad ordinem quemdam redigere aut dirigere non est ut quisquam <lb></lb>tentet ” (ibid.) dimenticò, a quel che pare, che il Falloppio stesso avea ri­<lb></lb>dotti quegli innumerevoli canali a tre, e come gli avea distintamente veduti, <lb></lb>così gli avea in pubblico diligentemente descritti. </s></p><p type="main">

<s>Queste osservazioni, alle quali ha dato occasione il giudizio autorevolis­<lb></lb>simo di Antonio Scarpa, servano a difendere noi contro i ciechi ammiratori <lb></lb>di Girolamo Fabricio, ai quali sarà forse dispiaciuto che si sia in varie pa­<lb></lb>gine di questa storia fatto apparire il celebre uomo come un ostacolo al li­<lb></lb>bero progredire della scienza in Italia. </s></p><p type="main">

<s>Ritornando ora alla così detta <emph type="italics"></emph>Finestra rotonda,<emph.end type="italics"></emph.end> trovò il Cotunnio da <lb></lb>correggere anche la figura stessa descritta dal Morgagni, e disse che quel <lb></lb>forame “ lumine gaudet non plane circulari, sed potius parabolico, et poste­<lb></lb>riora versus integre patente ” (De Aquaeductibus etc., Neapoli 1775, pag. </s>

<s>20). <lb></lb>Questa correzione in ogni modo fatta dagli Anatomici posteriori alla prima <lb></lb>descrizion del Falloppio è una squisitezza anatomica, ma vi erano in quelle <lb></lb>stesse descrizioni altre cose da correggere, che dovevano avere per la teoria <lb></lb>della percezione de&#039;suoni una non lieve importanza. </s></p><p type="main">

<s>Nel passo, da noi sopra citato dalle <emph type="italics"></emph>Osservazioni<emph.end type="italics"></emph.end> falloppiane, si conclu­<lb></lb>deva dall&#039;Autore la descrizione delle due Finestre, così dicendo in partico­<lb></lb>lare della Rotonda: “ Haec secunda fenestella nullo osse clauditur, cum <lb></lb>tamen prior Stapedis basi semper clausa maneat. </s>

<s>” Ma perchè non par che <lb></lb>il Falloppio avesse posto mente alle membrane che rivestono le interne ca­<lb></lb>vità dell&#039;orecchio, dicendo della Finestra rotonda <emph type="italics"></emph>nullo osse clauditur,<emph.end type="italics"></emph.end> in­<lb></lb>tendeva ch&#039;ella fosse del tutto aperta. </s>

<s>Il Vidio però, nel suo Manoscritto <lb></lb>edito molto tardi, dava così de&#039;seni interni auriculari, il primo dopo il Fal­<lb></lb>lopio, una descrizione assai più precisa: “ At basis Stapedis foramen unum <lb></lb>claudit ex duobus sitis in primo sinu, ad quem iam aggredimur. </s>

<s>Unum ova­<lb></lb>tam figuram habens situm est ad superiorem ac mediam partem sinus, te­<lb></lb>nuissimaque membrana clauditur ambiente universum sinum: clauditur au­<lb></lb>tem a basi Stapedis. </s>

<s>Alterum versus pesteriorem atque inferiorem partem <lb></lb>est rotundum, atque eadem membrana obductum ” (De Anatome, Vene­<lb></lb>tiis 1611, pag. </s>

<s>322). </s></p><p type="main">

<s>La Finestra rotonda non è dunque aperta, ma è per il Vidio chiusa da <lb></lb>una membrana, che è la continuazione del periostio del Timpano. </s>

<s>Il Casse­<lb></lb>rio pure riconobbe questo opercolo, ma lo descrisse come proveniente in-<pb xlink:href="020/01/1404.jpg" pagenum="279"></pb>vece dalla parte membranacea della lamina spirale, ossia dal periostio del <lb></lb>Laberinto. </s>

<s>Dop&#039;aver detto infatti che l&#039;elice consta di due lamine, una ossea <lb></lb>e l&#039;altra membranacea, “ quam ea format, soggiunge, membrana quae du­<lb></lb>plex hoc antrum vestiens utramque obserat fenestram ” (De auris historia <lb></lb>cit., pag. </s>

<s>59). Questa apparente contradizione poi tra il Vidio e il Casserio <lb></lb>fu riconciliata dallo Scarpa, il quale dimostrò che la membrana, dalla quale <lb></lb>è chiusa la Finestra rotonda, “ ex tenui periostio Tympani et tenuissimo La­<lb></lb>byrinthi componitur ” (De fenestra rotunda cit., pag. </s>

<s>56). </s></p><p type="main">

<s>Così insomma la diligenza, dagli Anatomici usata intorno all&#039;esame della <lb></lb>struttura delle due finestre, aveva supplito al difetto delle prime descrizioni <lb></lb>del Falloppio, il quale, oltre ai due detti forami, ritrovò nella cavità del Tim­<lb></lb>pano un terzo organo insigne, a cui piacquegli, come dicemmo, d&#039;imporre <lb></lb>il nome di <emph type="italics"></emph>Acquedotto.<emph.end type="italics"></emph.end> “ Tertium, quod ego observatione dignum existimo, <lb></lb>così scrive nelle sopra citate <emph type="italics"></emph>Osservazioni,<emph.end type="italics"></emph.end> canalis quidam osseus est, qui <lb></lb>tecto huius cavitatis quasi subtenditur, exitque extra calvariam post radicem <lb></lb>calcaris inter illam ac mamillarem processum: principium autem ipsius est <lb></lb>intra calvariam. </s>

<s>Nam si recte inspicias videbis quintum par nervorum a re­<lb></lb>liquis Anatomicis ita vocatum extendi ad medium ferme processuum ossis <lb></lb>temporum, quem internum atque petrosum appellamus. </s>

<s>Illuc tensum hoc <lb></lb>par ingreditur in canalem quemdam insculptum in quo latens in duas fin­<lb></lb>ditur partes, alteram quidem magnam, alteram vero parvam et gracilem <lb></lb>valde duroriemque. </s>

<s>Haec posterior, perforato osse occulto quodam canali, <lb></lb>versus anteriora capitis serpit, deinde reflexa Tympanumque ingressa pro­<lb></lb>prio hoc canali osseo deorsum et posteriora versus ad pinnae ipsius auri­<lb></lb>culae radicem erumpit et disseminatur. </s>

<s>Via igitur istius nervi canalis hic est <lb></lb>de quo loquor, et <emph type="italics"></emph>Aquaeductum<emph.end type="italics"></emph.end> a similitudine appello ” (pag. </s>

<s>410). </s></p><p type="main">

<s>La similitudine però, com&#039;ebbe a fare osservare il Cotunnio (loco cit., <lb></lb>pag. </s>

<s>14), non era tolta dall&#039;opinione che il nervo menasse seco un umore <lb></lb>acquoso, ma dall&#039;essere quell&#039;osso scavato a somiglianza de&#039;canali aperti <lb></lb>ne&#039;sotterranei, o sostenuti dagli archi nelle città, e che gli antichi Architetti <lb></lb>romani chiamavano giusto col nome di Acquedotti. </s>

<s>Ma, oltre a questo ca­<lb></lb>nale, l&#039;Eustachio, che attendeva a studiar l&#039;interno dell&#039;orecchio in quel <lb></lb>medesimo tempo e con ugual diligenza del Falloppio, ne scoprì un altro che <lb></lb>metteva in aperta comunicazione l&#039;aria esterna attinta dalle fauci con quella <lb></lb>implantata nelle cavernosità dell&#039;osso petroso. </s>

<s>“ A caverna ossis lapidei in <lb></lb>quam meatus auditorius conchion appellatus finitur, via in narium cavitatem <lb></lb>perforata est. </s>

<s>Ab illa enim meatus alter oritur, rotundo canaliculo similis, <lb></lb>et instar tenuioris calami amplius, qui oblique ad anterius interiusque basis <lb></lb>capitis latus procedens, in medio quatuor foraminum totum istud os pene­<lb></lb>trat atque perfodit.... Caeterum hunc meatum, de quo sermo est, arbitra­<lb></lb>bitur fortasse quispiam eo loco desinere: res autem non ita se habet, sed <lb></lb>alterius generis substantia auctum, inter duos faucium seu gulae musculos, <lb></lb>a paucis hucusque bene cognitos, secundum paulo ante memoratae fissurae <lb></lb>ductum ulterius procedit, et iuxta radicem internae partis apophysis ossis <pb xlink:href="020/01/1405.jpg" pagenum="280"></pb>alis vespertilionum similis in alteram narium cavitatem terminatur ” (De <lb></lb>auditus org. </s>

<s>cit., pag. </s>

<s>161, 62). </s></p><p type="main">

<s>Anche a questo canaliculo, che il suo Inventore lasciò senza un nome <lb></lb>proprio, gli Anatomici posteriori, come l&#039;Acquapendente, dettero sull&#039;esem­<lb></lb>pio del Falloppio il nome di acquedotto: “ meatusque est, quem veluti aquae­<lb></lb>ductum dixeris ” (De aure cit., pag. </s>

<s>252). La somiglianza de&#039;nomi dette in­<lb></lb>tanto occasione a certi Anatomici, in ciò pochissimo diligenti, di confonder <lb></lb>le cose, scambiando il primo Acquedotto descritto dal Falloppio con questo <lb></lb>secondo scoperto dall&#039;Eustachio, che si rimase per molti ignorato. </s>

<s>Ciò fu che <lb></lb>accese fieramente lo zelo dello Schelhammer, il quale deplorava che a&#039;suoi <lb></lb>tempi le anatomiche dimostrazioni fosser fatte “ ad pompam potius, quam <lb></lb>usum ” (De auditu cit., pag. </s>

<s>57). E al veder che quell&#039;errore da lui detto <lb></lb>sozzissimo, s&#039;era introdotto nell&#039;Anatomia riformata, per l&#039;autorità di un <lb></lb>Bartholin, padre, e di un Riolano, disperava di poterlo oramai sradicare dalle <lb></lb>giovani menti: “ adeoque hic error nostrae iuventuti nec evitari quidem <lb></lb>potest ” (ibid.). </s></p><p type="main">

<s>Il Valsalva però prese la cosa con pace, e lasciate le declamazioni si <lb></lb>volse a trovare e ad applicare efficacemente i rimedii. </s>

<s>Riconosciuto che l&#039;er­<lb></lb>rore aveva avuto origine dal mancare il canaliculo scoperto dall&#039;Eustachio <lb></lb>di un nome proprio, incominciò a chiamarlo <emph type="italics"></emph>Tuba eustachiana.<emph.end type="italics"></emph.end> “ Tubam <lb></lb>eustachianam appellabo ” (De aure hum. </s>

<s>cit., pag. </s>

<s>30) e gli Anatomici una­<lb></lb>nimi ne seguirono l&#039;esempio. </s>

<s>E perchè il mancar quell&#039;organo di un nome <lb></lb>proprio e l&#039;averlo avuto comune con quell&#039;altro scoperto dal Falloppio dette <lb></lb>origine a quella confusione, così deplorata dallo Schelhammer, il Valsalva scolpì <lb></lb>nella Tavola VII la figura V a questo fine principalmente “ ut cuicumque <lb></lb>constare possit aliud esse aquaeductum Falloppii, aliud Tubam eustachianam, <lb></lb>cum alioqui a multis, saltem nomine, haec duo confundantur ” (ibid., pag. </s>

<s>103). </s></p><p type="main">

<s>Fu per questi motivi che il Morgagni disse il Valsalva della scoperta <lb></lb>eustachiana “ plusquam instauratorem existimandum esse ” (Epist. </s>

<s>anat. </s>

<s>XXII <lb></lb>cit., pag. </s>

<s>187) ma una più vera ragione del merito è da riconoscersi nell&#039;aver <lb></lb>lo stesso Valsalva con più diligenza di nessun altro esaminata la figura, la <lb></lb>composizione e i muscoli della Tuba instaurata. </s>

<s>Ei l&#039;assomigliò a due coni <lb></lb>d&#039;ineguale altezza, che si tocchino per gli apici troncati. </s>

<s>“ Eius cavitatis <lb></lb>figura assimilari potest duobus contrapositis inaequalis altitudinis conis, com­<lb></lb>pressiorem ellypsim pro basi habentibus, et antequam in apices desinant <lb></lb>coeuntibus ” (De aure hum. </s>

<s>cit., pag. </s>

<s>30); disse esser composta “ ex parte <lb></lb>ossea, membranacea cartilaginea atque carnea ” (ibid., pag. </s>

<s>31), e la trovò <lb></lb>fornita di un nuovo muscolo, “ a quo, ubi opus sit, eadem potest dilatari. </s>

<s><lb></lb>Quod assertum sicut in anatomicis scholis novum est, ita mihi, quem diutina <lb></lb>conquisitio et improbus labor id docuere, inter ea, de quibus certiores su­<lb></lb>mus, videtur reponendum ” (ibid., pag. </s>

<s>32). </s></p><p type="main">

<s>Le scuole anatomiche ritennero infatti così questa come le altre novità <lb></lb>ritrovate dal Valsalva intorno alla Tuba per cosa certissima, e accoppiando <lb></lb>l&#039;erudizione alla scienza si misero dietro a investigare del restaurato organo <pb xlink:href="020/01/1406.jpg" pagenum="281"></pb>la prima storia. </s>

<s>Lo Schelhammer, da cui ebbe quella restaurazione l&#039;im­<lb></lb>pulso, aveva scritto: “ Fuit autem Aristoteli hic ductus non ignotus ” (De <lb></lb>auditu cit., pag. </s>

<s>54); espressione ripetuta poi dal Valsalva (De haure hum. </s>

<s><lb></lb>cit., pag. </s>

<s>30) e dal Morgagni, incerto se l&#039;invenzione si dovesse dir propria <lb></lb>dell&#039;Eustachio “ vel potius Aristotelis. </s>

<s>” Così scrisse nella VII delle XXII <lb></lb>Epistole anatomiche a pag. </s>

<s>185, ma nella prima delle <emph type="italics"></emph>Epistolae anatomi­<lb></lb>cae duae<emph.end type="italics"></emph.end> riferì, dal cap. </s>

<s>XI del I libro dell&#039;<emph type="italics"></emph>Historia animalium,<emph.end type="italics"></emph.end> le parole <lb></lb>proprie di Aristotile stesso, le quali suonano così: “ in oris palatum usque <lb></lb>semita pertendit ” movendo dalla parte più interna dell&#039;orecchio (Lugd. </s>

<s><lb></lb>Batav. </s>

<s>1728, pag. </s>

<s>109). </s></p><p type="main">

<s>La sentenza aristotelica dall&#039;altra parte era vera, perchè fondata sopra <lb></lb>un esperimento, che può secondo il Vesalio facilmente ripetersi da ciascuno <lb></lb>di noi “ si attracto in os aere, illum quasi per aures propellere conemur ” <lb></lb>(De humani corp. </s>

<s>fabrica cit., pag. </s>

<s>40). Eppure nè il Vesalio nè il volgo <lb></lb>hanno preteso mai d&#039;appropriarsi la scoperta eustachiana, come s&#039;intende di <lb></lb>appropriarla ad Aristotile, che non andò punto più là del Vesalio e del volgo. </s></p><p type="main">

<s>Forse lo Schelhammer, e dopo lui il Valsalva e il Morgagni, messero <lb></lb>lo Stagirita a parte dell&#039;invenzione eccitati dall&#039;esempio dello stesso Eusta­<lb></lb>chio, a cui piacque piuttosto di citare Alcmeone, e non par si accorgessero <lb></lb>que&#039;valentuomini della finissima satira, con la quale l&#039;Anatomico sanseveri­<lb></lb>tano derideva le sciocche pretensioni di coloro che tutte le cose nuove “ a <lb></lb>maioribus nostris inventa atque instituta esse semper praedicant ” (De au­<lb></lb>ditus organis cit., pag. </s>

<s>156). Dal non aver penetrato addentro a cotesti sensi <lb></lb>satirici ebbe origine l&#039;inganno di quegli altri, i quali attribuirono a mode­<lb></lb>stia l&#039;aver esso Eustachio riconosciuto Empedocle inventor della Chiocciola, <lb></lb>com&#039;avea riconosciuto Alcmeone primo inventor della Tuba, egli che dall&#039;al­<lb></lb>tra parte, ammirando il naturale artificio, senza tanta modestia, lo disse <emph type="italics"></emph>a <lb></lb>me inventum<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>162). Nel particolare esempio della Chiocciola però <lb></lb>il sale era mescolato col fiele, di cui volle l&#039;Autor <emph type="italics"></emph>De auditus organis<emph.end type="italics"></emph.end> asper­<lb></lb>gere il Falloppio suo odiato rivale. </s></p><p type="main">

<s>Nelle Osservazioni anatomiche dunque, alle quali dobbiam ora tornare, <lb></lb>dop&#039;aver l&#039;Autore diligentemente descritto il Timpano, passa all&#039;altra cavità <lb></lb>contigua assai minore, la quale avvolgendosi per tante intricate sinuosità, <lb></lb>“ merito Labyrinthus dicetur, in quam prospicit Fenestra ovalis clausa a Sta­<lb></lb>pede, et altera orbicularis, quae etiam in caecam cavitatem tendit, de qua <lb></lb>iam loquar. </s>

<s>Est itaque tertia dicta cavitas insculpta in eodem processu pe­<lb></lb>troso, in latere ipsius anteriori, interque hanc et canalem illum, in quem <lb></lb>primum quinti paris nervi gemini, durus scilicet et mollis, integri ingrediun­<lb></lb>tur, tenuissimum quoddam interstitium continetur. </s>

<s>Nam in eodem situ pa­<lb></lb>res sunt, verum canalis in medio processu cavitas in anteriori ipsius latere <lb></lb>est collocata, quae duobus aut tribus gyris in morem cochleae constat, ne­<lb></lb>que exitum habet. </s>

<s>Unde <emph type="italics"></emph>Cochlea,<emph.end type="italics"></emph.end> vel cochlearis cavitas, vel caeca etiam est <lb></lb>dicenda. </s>

<s>Haec in intima superficie, velut etiam secunda cavitas, ut cuniculi <lb></lb>eiusdem, et omnes etiam dentium naturales cavitates, membranula quadam <pb xlink:href="020/01/1407.jpg" pagenum="282"></pb>mollissima ac tenuissima vestiuntur, quae an sit nervus expansus an aliud <lb></lb>non refert ” (Opera omnia cit., pag. </s>

<s>410). </s></p><p type="main">

<s>L&#039;Eustachio, a leggere queste cose scritte come diceva da gente che si <lb></lb>inspira al divino Vesalio, e che nonostante si vanta di rendere inutili le fa­<lb></lb>tiche di tutti coloro, “ qui operam dederint ut inventis suis addant aliquid ” <lb></lb>(De auditus org., pag. </s>

<s>156), pensò di avvilire l&#039;iattanza col mettere il Fal­<lb></lb>loppio a pari di Empedocle “ qui auditum impulsione spiritus fieri docuit, <lb></lb>qui cochleae simile intra aurem, tintinnabuli instar suspensum, percutit atque­<lb></lb>pulsat, cui etiam Aristotiles assentire videtur ” (ibid., pag. </s>

<s>161). </s></p><p type="main">

<s>La satira è sanguinosa, e fa gran maraviglia che il Morgagni non l&#039;ab­<lb></lb>bia intesa. </s>

<s>Nella prima infatti delle <emph type="italics"></emph>Epistolae anatomicae duae<emph.end type="italics"></emph.end> si mette <lb></lb>dietro sul serio a riceroare i passi di Empedocle e di Aristotile, ai quali ne <lb></lb>aggiunge un&#039;altro di Celso, e dal leggere in quegli Autori descritta l&#039;orec­<lb></lb>chia <emph type="italics"></emph>in modum cochleae obvolutam,<emph.end type="italics"></emph.end> e dal sentir dire a esso Celso che il <lb></lb>meato uditorio, dop&#039;essersi flessuosamente prolungato “ iuxta cerebrum in <lb></lb>multa et tenuia foramina diducitur, per quae facultas audiendi est ” (De re <lb></lb>medica, Parisiis 1529, fol. </s>

<s>116 ad t.); ne argomenta essere stata la chioc­<lb></lb>ciola del laberinto nota agli antichi, anche prima che venisse a descriverla <lb></lb>il Falloppio (Lugd. </s>

<s>Batav. </s>

<s>1728, pag. </s>

<s>108). </s></p><p type="main">

<s>Non pensò il Valentuomo che le due cose non si riscontrano veramente <lb></lb>altro che nel nome, rassomigliando Empedocle e Aristotile e Celso alla forma <lb></lb>del ben noto mollusco, non quell&#039;organo ch&#039;è riposto nella più interna ca­<lb></lb>vità dell&#039;orecchio, ma il più patente di lui meato esterno. </s>

<s>In conferma di <lb></lb>che può addursi la testimonianza del Berengario, che più saviamente del <lb></lb>Morgagni e di tanti scrittori moderni interpetrò il testo aristotelico. </s>

<s>“ Fi­<lb></lb>gura aurium, egli dice nel citato Commentario al Mundino, omnibus nota <lb></lb>est: suum foramen est anfractuosum ut conchilia testa, sensu et teste Arist., <lb></lb>primo <emph type="italics"></emph>De Historia ”<emph.end type="italics"></emph.end> (fol. </s>

<s>CCCCLXXVII ad t.). </s></p><p type="main">

<s>La Chiocciola del Laberinto insomma, sconosciuta agli Antichi, fu primo <lb></lb>a descriverla il Falloppio, ma egli, dice l&#039;Eustachio, la descrisse così super­<lb></lb>ficialmente, come descrisse Empedocle il suo campanello, che dallo spirar <lb></lb>dell&#039;aria è fatto sonare. </s>

<s>Quell&#039;elegantissimo organo, poi soggiunge, non è <lb></lb>così semplice nè così volgare, che debba vergognarsi di venire rassomigliato <lb></lb>alle palustri lumache, dovendosi saper che l&#039;osso, rappresentante nella Rocca <lb></lb>petrosa una tal figura, si compone di un doppio genere di spire, “ quorum <lb></lb>alterum ab ossea substantia admodum tenui, sicca et quae facile teritur, <lb></lb>creatur: alterum vero, omnibus Anatomicis adhuc ignotum, ex materia qua­<lb></lb>dam fit molli et mucosa, firma tamen, et quae nescio quid arenosi per­<lb></lb>mixtum habet, oriturque ex medio spacio priorum spirarum tamquam ex <lb></lb>ampliore basi, sensimque extenuatum in aciem desinit. </s>

<s>Comparari potest <lb></lb>appositissime eius forma testae cochlearum, exteriore prius ex ea superficie <lb></lb>rotunda detracta, et parte interiore quae in spiras contorquetur reservata. </s>

<s><lb></lb>Qua autem substantia posteriores hae spirae efficiantur fateor me ignorare ” <lb></lb>(De aud. </s>

<s>org. </s>

<s>cit., pag. </s>

<s>160). </s></p><pb xlink:href="020/01/1408.jpg" pagenum="283"></pb><p type="main">

<s>Conoscere queste sottigliezze, ignorate dall&#039;Eustachio, era riserbato ai <lb></lb>progressi, che sarebbe per fare l&#039;Anatomia più di un secolo dopo, ma in <lb></lb>sostanza la composizione della cavità cocleare scolpita nel Laberinto è vera­<lb></lb>mente quella così descritta dal nostro Sanseveritano. </s>

<s>Di quell&#039;altra cavità, <lb></lb>di che il Labirinto stesso si rende insigne, e che risulta dei così detti <emph type="italics"></emph>Ca­<lb></lb>nali semicircolari,<emph.end type="italics"></emph.end> l&#039;Eustachio se ne passa con assai brevità, quasi suo mal­<lb></lb>grado confessando che nulla era da aggiungere alla descrizione, datane in <lb></lb>questi precisi termini dal Falloppio: “ Ab hac cavitate tres cuniculi oriun­<lb></lb>tur, et in eamdem redeunt, circulares penitus, a quibus nomen accepit ipsa <lb></lb>cavitas. </s>

<s>Quorum unus est inferior, qui ab anteriori parte cavitatis divertens <lb></lb>versus exteriora, ac deinde reflexus in eamdem cavitatem, per posteriorem <lb></lb>angulum recurrit. </s>

<s>Alter cuniculus oritur ab eodem anterioris cavitatis an­<lb></lb>gulo, sursumque elatus quasi ad hortogonion facto semicirculo, iterum in <lb></lb>cavitatem, per angulum posteriorem, regreditur. </s>

<s>Tertius oritur et occidit, aut <lb></lb>sinit in posteriori angulo cavitatis; nam inde ortus, perforatoque osse cir­<lb></lb>culari quodam canali, exteriora versus illuc item revertitur ” (Observat. </s>

<s><lb></lb>anat. </s>

<s>inter. </s>

<s>Op. </s>

<s>omnia cit., pag. </s>

<s>410). </s></p><p type="main">

<s>A questa falloppiana descrizione dei Canali semicircolari il diligente <lb></lb>Vidio, e il diligentissimo Casserio non trovarono da aggiunger nulla di nuovo <lb></lb>nè di più preciso, sia quanto alle parole, sia quanto ai disegni, i quali anzi <lb></lb>rimasero trascurati o non condotti con le debite cure infino al 1644, quando <lb></lb>venne primo ad esibirli al Bartholin, nella sopra citata Epistola anatomica, <lb></lb>Cecilio Folli. </s>

<s>La Figura prima “ quae ostendit Cochleam, Labyrinthum, fo­<lb></lb>ramina ovale et rotundum, nec non Aquaeductum Falopii ” (Thomae Bartho­<lb></lb>lini Epist. </s>

<s>medic. </s>

<s>Centuria I cit., pag. </s>

<s>256), e la Figura quarta “ quae habet <lb></lb>Cochleam inversam ut videatur cavitas cum propriis foraminibus et loco ner­<lb></lb>vorum ” (ibid., pag. </s>

<s>260), son reputate sufficientemente precise, e in ogni <lb></lb>modo hanno il pregio di esser delle prime a comparire nella storia dell&#039;Ana­<lb></lb>tomia. </s></p><p type="main">

<s>Quel Laberinto in conclusione, intorno a cui s&#039;erano gli Anatomici an­<lb></lb>tichi smarriti, col filo ammannito già dal Falloppio, era stato, verso la prìma <lb></lb>metà del secolo XVII, specialmente da&#039;Nostri così diligentemente esplorato, <lb></lb>che poco più rimaneva a saper di lui quanto alla figura o agli andamenti <lb></lb>delle vie scolpite nell&#039;Osso petroso. </s>

<s>Una così fatta esplorazione però non era <lb></lb>completa, sfuggendo anche ai più attenti osservatori certe parti essenzialis­<lb></lb>sime dell&#039;organo auditivo, le quali o per esser molli s&#039;erano staccate dagli <lb></lb>ossi duri, o per esser liquide erano col tempo esalate, o le avevano avida­<lb></lb>mente imbevute, nel riseccarsi, le spugnose pareti. </s>

<s>Un esempio notabilissimo <lb></lb>di ciò ce l&#039;offire il muscolo della Staffa, il quale fu soggetto di tante contra­<lb></lb>dizioni, perchè chi lo negava non aveva ancora osservata la struttura del­<lb></lb>l&#039;orecchio ne&#039;cadaveri freschi. </s></p><p type="main">

<s>Primi a confermar l&#039;esistenza di quel muscolo nell&#039;uomo furono il Val­<lb></lb>salva e il Cotunnio, i quali furono anche i primi a notomizzare l&#039;organo <lb></lb>nelle orecchie recenti, da che venne a loro porta l&#039;occasione di scoprir que-<pb xlink:href="020/01/1409.jpg" pagenum="284"></pb>gli umori, che trasudano dalle interne membrane, e che poi vanno a riem­<lb></lb>pir di sè ogni più riposto seno del Laberinto. </s>

<s>“ Porro huius cavitatis coro­<lb></lb>nide, così termina il Valsalva la prima parte del suo trattato, scire iuvat <lb></lb>Labyrinthum humore quodam aqueo, et hoc copioso, intus madefactum re­<lb></lb>periri, unde contentae membranae humescunt, de quo nulli fecere mentio­<lb></lb>nem. </s>

<s>Humor hoc in recenti aure observatur ” (De aure hum. </s>

<s>cit., pag. </s>

<s>51). </s></p><p type="main">

<s>Passa poi il Valsalva a proporre alcune questioni intorno all&#039;origine, e <lb></lb>intorno alla natura di quell&#039;umore; questioni ch&#039;ei lascia irresolute, perchè <lb></lb>dice mancargli la necessaria preparazione delle osservazioni e degli esperi­<lb></lb>menti. </s>

<s>Furono le parole di un tant&#039;uomo eccitamento al Cotunnio, il quale <lb></lb>intanto, ripensando che la scoperta era stata fatta sui cadaveri freschi, fu <lb></lb>sollecito di sezionare subito dopo la morte. </s>

<s>Rimuove leggermente la Staffa <lb></lb>dalla Finestra ovale; “ totum Vestibulum aqua plenissimum observatur ” <lb></lb>(De aquaeduc. </s>

<s>cit., pag. </s>

<s>38). Prende uno de&#039;Canali semicircolari, lo rompe <lb></lb>di un colpo; “ lumen aqua plenissimum ostendit, quod in Cochlea discissa <lb></lb>manifestissimum est ” (ibid.). Maravigliato che nessun&#039;altro avesse notato <lb></lb>questa cosa, intese poi che tutto dipendeva dallo stato del cadavere: fre­<lb></lb>schissimo ha il Laberinto tutto pieno di umore, come a lui stesso era per <lb></lb>la prima volta occorso di osservarlo. </s>

<s>Poi, a poco a poco quell&#039;umore esa­<lb></lb>lando, lascia però ancora impregnate di sè le membrane, e in tale stato sco­<lb></lb>prì l&#039;orecchio il Valsalva. </s>

<s>Resta all&#039;ultimo tutto asciutto e secco, cosicchè <lb></lb>all&#039;umidità sottentra l&#039;aria, e in tale stato, cioè d&#039;una cavità tutta piena <lb></lb>d&#039;aria secca, fu sempre osservato il Labirinto da tutti gli Anatomici ante­<lb></lb>riori allo stesso Valsalva. </s></p><p type="main">

<s>Il Cotunnio perciò, nell&#039;atto di pubblicare la sua scoperta, trepidava, <lb></lb>ripensando che aveva a persuadere una gente per tanti secoli rimasta ingan­<lb></lb>nata, e nell&#039;opinion della quale era ingerito che mezzo naturale della trasmis­<lb></lb>sione dei suoni fosse l&#039;aria e non l&#039;acqua. </s>

<s>“ Hoc est primum paradoxon, <lb></lb>quod in medium afferre videbor, in tanta quidem Anatomicorum omnium, <lb></lb>quod sciam, consensione existimantium madescere quidem, non ad amussim <lb></lb>impleri hoc umore Labyrinthum, et aerem a Tympano venientem simul <lb></lb>continere ” (ibid., pag. </s>

<s>37). </s></p><p type="main">

<s>La scoperta del Valsalva, alla quale in queste parole s&#039;accenna, aveva <lb></lb>predisposte le menti ad accogliere con docilità la scoperta del Cotunnio, e <lb></lb>perchè i fatti, così nell&#039;uomo come negli animali, erano in ogni modo pa­<lb></lb>tenti, s&#039;acconsentì che il nervo acustico ricevesse le impressioni, mediante <lb></lb>il liquido in cui trovasi immerso. </s></p><p type="main">

<s>A compiere poi le gloriose scoperte degli Italiani venne il Breschet colla <lb></lb>sua <emph type="italics"></emph>otoconia,<emph.end type="italics"></emph.end> ma chi ripensa a quel <emph type="italics"></emph>quid avenosi,<emph.end type="italics"></emph.end> di che disse l&#039;Eustachio <lb></lb>essere permista la sostanza molle e muccosa, che s&#039;aggira in lamina spirale <lb></lb>intorno alla Chiocciola, s&#039;avvedrà avere avuti i suoi principii in Italia anco <lb></lb>quest&#039;ultima scoperta straniera. </s></p><pb xlink:href="020/01/1410.jpg" pagenum="285"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La descrizione dell&#039;organo dell&#039;udito ci ha mostra<gap></gap>o fin qui, nella sua <lb></lb>storia, le grandi difficoltà incontrate dagli Anatomici: eppure non dipende­<lb></lb>vano da altro quelle difficoltà, che dall&#039;artificiosa struttura delle parti, a bene <lb></lb>esaminar le quali, e a descriverle, facevano spesso difetto l&#039;acume degli os­<lb></lb>servatori, e l&#039;imperfezione degli strumenti. </s>

<s>Di qui è che, col tempo e con <lb></lb>l&#039;esercizio, si fecero i sopra narrati progressi dal Berengario al Cotunnio. </s>

<s><lb></lb>Quando poi dalla semplice e material descrizione si volle passare a inten­<lb></lb>dere del complicatissimo organo le funzioni, e allora le difficoltà si fecero <lb></lb>sentir tanto maggiori, da non sperar di vincerle col tempo e con lo studio. </s>

<s><lb></lb>Si sapeva esser quello, così sottilmente notomizzato, l&#039;organo dell&#039;udito, ma <lb></lb>dove abbia la sua propria sede l&#039;udito, e come un oggetto materiale che <lb></lb>agisce sopra uno strumento materiale si sublimi negli atti del senso e della <lb></lb>vita, questo si voleva sapere, ma ne tornò l&#039;acuta fame dell&#039;uomo sempre <lb></lb>digiuna. </s>

<s>Alla Fisiologia perciò, trovatasi così involta nella nuvola del mi­<lb></lb>stero, non rimaneva altra via di progredire che quella apertale innanzi dal­<lb></lb>l&#039;Anatomia, ond&#039;è che, secondo le venivano più precise notizie intorno alla <lb></lb>composizione dell&#039;organo, più probabili, intorno alle funzioni di lui, e meno <lb></lb>estranee dal vero si rendevano via via le congetture. </s>

<s>Ciò è appunto dimo­<lb></lb>strato dai fatti, che siam per narrare nel presente paragrafo di storia. </s></p><p type="main">

<s>Empedocle, che credeva tutto l&#039;organo consistere nell&#039;orecchio esterno, <lb></lb>dalla figura, nella quale materialmente gli si rappresentava la conca, disse <lb></lb>ch&#039;ell&#039;era un campanello sospeso di qua e di là dagli ossi delle tempia. </s>

<s>Ai <lb></lb>tempi di Aristotile, entrati più addentro, s&#039;era osservata la membrana del <lb></lb>Timpano, e il Timpano stesso tutto pieno di aria, la quale perciò si fece <lb></lb>principale e immediato strumento della sensazione. </s>

<s>Ma quando il Berenga­<lb></lb>rio scoprì in quella cavità i due primi ossicini, i quali non dovevano certa­<lb></lb>mente esser fatti per altro che per servire all&#039;udito, incominciò, in quel primo <lb></lb>risorgere della scienza, il desiderio d&#039;intender quegli usi, per i quali si ve­<lb></lb>nivano o a correggere o ad illustrare i concetti de&#039;Filosofi antichi. </s>

<s>“ Sunt <lb></lb>aliqui, scrisse lo stesso Berengario, qui volunt quod illa ossicula moveant <lb></lb>aerem intra stantem et pelliculam praedictam, sicut pene vel digiti movent <lb></lb>cordas citarae, et aerem complantatum in citara. </s>

<s>Sunt tamen aliqui alii, qui <lb></lb>volunt quod cordae in citara sint loco illorum ossiculorum, et quod pene <lb></lb>vel digiti sint loco aeris exterioris meventis ossicula, et quod isto modo cum <lb></lb>aere implantato fiat sonus. </s>

<s>Et dicunt aliqui alii quod pellicula praedicta non <lb></lb>moveatur, sed quod est ibi ut teneat cavernam ante dictam clausam, in qua <lb></lb>est aer implantatus ” (Commentaria cit., fol. </s>

<s>CCCCLXXVII ad t.). Così si­<lb></lb>gnificava il Berengario le varie ipotesi, che avrebbero potuto fare i Filosofi, <pb xlink:href="020/01/1411.jpg" pagenum="286"></pb>speculando sopra la sua invenzione, e, non decidendosi nè per l&#039;una nè per <lb></lb>l&#039;altra, le proponeva come questioni a risolversi da&#039;suoi successori. </s></p><p type="main">

<s>Se i lunghi processi però e la continuata catena degli ossicini avevano <lb></lb>suggerito al Carpense l&#039;immagine delle corde di una cetra, le loro estre­<lb></lb>mità e le loro congiunzioni, rappresentando più scolpitamente al Vesalio gli <lb></lb>esempi del martello e dell&#039;incudine, gli fecero balenare al pensiero che fosse <lb></lb>il suono udito prodotto piuttosto dalla percussione interna dei due stru­<lb></lb>menti. </s>

<s>Ma la difficoltà d&#039;intendere il modo e la ragion dell&#039;udire, e il ri­<lb></lb>pensar che troppo poco conoscevasi ancora della costruzione dell&#039;organo, gli <lb></lb>fecero prudentemente sospendere il giudizio. </s>

<s>“ Num autem ossicula Incudis <lb></lb>et Malleoli officia ita fungantur, quemadmodum sane formam referunt, .... <lb></lb>a me haudquaquam assertum velim, quandoquidem auditus rationem non <lb></lb>satis ex sententia percipiam. </s>

<s>Non quod mihi animo exciderit commune illud <lb></lb>Medicorum ad partium temporum asylum, et aeris gyri, quos ex huius per­<lb></lb>cussu in aurem ferri et quandam membranam ferire, vulgo nobis e lapil­<lb></lb>lorum in aquam iactu persuademus; interim organi huius constructionis <lb></lb>ignari ” (De hum. </s>

<s>corp. </s>

<s>fabrica cit., pag. </s>

<s>35). </s></p><p type="main">

<s>Ma perchè, lette queste cose, incominciò il Colombo a pensare, non dee <lb></lb>il suono interno prodursi dal percotere del Martello sopra l&#039;Incudine? </s>

<s>A che <lb></lb>altro fine avrebbe allora la Natura dato agli ossicini quella tal forma, o per­<lb></lb>chè gli avrebbe così ben disposti l&#039;un sotto l&#039;altro a dare e a ricevere i <lb></lb>colpi? </s>

<s>“ Nam cum ex aeris motu auditio fiat, ictus aeris in meatum ad haec <lb></lb>ossicula defertur, fitque ibi quaedam repercussio ad eum ciendum sonitum <lb></lb>qui sentitur. </s>

<s>Haec igitur ossicula cedente membrana moveri, atque invicem <lb></lb>confricari necesse est, ut cum primum os aeris ictu percussum in alterum <lb></lb>impingat, illudque feriat, merito malleoli, secundum vero incudis, officio pa­<lb></lb>riter et vocabulo donatum est ” (De re anat. </s>

<s>cit., pag. </s>

<s>27). </s></p><p type="main">

<s>Così decidevansi con troppa fretta i dubbi del Vesalio, il quale sagace­<lb></lb>mente era entrato in sospetto contenersi dentro a quel misterioso Laberinto <lb></lb>organi dell&#039;udito più importanti de&#039;due ossicini, e de&#039;quali, ignorando l&#039;es­<lb></lb>sere e la natura, era impossibile che si conoscessero gli usi. </s>

<s>Il Colombo <lb></lb>però, con minor considerazione e con più baldanza, a che altro diceva pos­<lb></lb>sono servire quelle molteplici aggirate cavità che a riflettere i colpi dell&#039;aria, <lb></lb>e a rendere così più sensibile il suono? </s>

<s>“ Adest quidem processus alius <lb></lb>iuxta hunc ipsum in longum protuberans interiore calvariae parte, in quo <lb></lb>effingitur Labyrinthus, reflectendis aeris ictibus quam appositissimus ” (ibid., <lb></lb>pag. </s>

<s>23). </s></p><p type="main">

<s>Quando quelle cieche tenebrose cavità entrò colla sua face il Falloppio <lb></lb>a illuminarle, si sarebbe creduto che l&#039;ardito esploratore avesse più da presso <lb></lb>assistito a que&#039;misteri che si celebravano dalla Natura ne&#039;gelosi penetrali, <lb></lb>ma par ch&#039;egli non intendesse nulla di meglio di quel che, stando di fuori, <lb></lb>s&#039;era immaginato il Colombo. </s>

<s>Vero è bene ch&#039;egli si confidava di dire la <lb></lb>sua sentenza intorno al suono, e di chiaramente spiegare “ quis sit usus <lb></lb>istorum ossium, et fortasse verum ” (Observat. </s>

<s>anat. </s>

<s>in loco cit., pag. </s>

<s>411), <pb xlink:href="020/01/1412.jpg" pagenum="287"></pb>ma perchè, nè qui nè altrove mantiene le sue promesse, l&#039;Eustachio disse <lb></lb>esser quelle delle solite vanitose parole del suo orgoglioso rivale, impotente, <lb></lb>per i suoi errori detti specialmente intorno alla costruzion della Coclea, a <lb></lb>penetrare i segreti della Natura. </s>

<s>E giacchè nessuno aveva ancora proposto <lb></lb>un ragionevole modo a spiegare l&#039;udito, egli crede di potere insegnarlo an­<lb></lb>che a coloro “ in quos hodie oculi coniecti sunt omnium anatomicae facul­<lb></lb>tatis studiosorum ” (De aud. </s>

<s>org. </s>

<s>cit., pag. </s>

<s>156). </s></p><p type="main">

<s>La freccia è principalmente appuntata al Falloppio, ma viene indiretta­<lb></lb>mente a ferire anche il Colombo, col quale tutti convenivano allora nel dire <lb></lb>“ aerem, qui dum sonus editur, tanquam unda fluctuat, membranam audi­<lb></lb>torio meatu obductam pulsare; ab illa deinceps consecutione quadam illa <lb></lb>ossicula moveri. </s>

<s>At quid obsecro, argomenta contro le comuni dottrine l&#039;Eu­<lb></lb>stachio, oportebat ad hunc rudem motum obeundum sapientissimum ani­<lb></lb>mantium Opificem tantum studium adhibere, et de horum ossiculorum figura, <lb></lb>articulatione ac positione esse tam sollicitum, quando aere irruente mem­<lb></lb>brana quae tympano similis est, sine tali organorum apparatu, percuti aut <lb></lb>ossiculo aut aliquo solidiori corpore, nulla arte elaborato, poterat? </s>

<s>” (ibid., <lb></lb>pag. </s>

<s>157). </s></p><p type="main">

<s>Non è dunque, ragionevolmente concludeva contro il Colombo e contro <lb></lb>i seguaci di lui esso Eustachio, prodotto il suono dal percotere del martello <lb></lb>sulla membrana del Timpano o sull&#039;incudine, e non sono i tre ossicini gli <lb></lb>organi principali dell&#039;udito, come parve di credere il Falloppio, il quale, se <lb></lb>avesse più diligentemente esaminato il Laberinto, e se, specialmente della <lb></lb>Coclea, avesse inteso il sapientissimo magistero, non avrebbe egli col Co­<lb></lb>lombo assegnato a quelle cavità l&#039;ignobile ufficio di riflettere e di moltipli­<lb></lb>care i colpi dell&#039;aria. </s>

<s>Non è propriamente la Coclea un canale a fondo cieco, <lb></lb>nè le spire, in ch&#039;ella si avvolge, mancano, come nelle lumache terrestri, <lb></lb>del loro forame, “ Sed in medio, ea nimirum parte cui spirae innituntur, <lb></lb>a principio ad extremum usque, angusto et recto meatu est pervium, et ab <lb></lb>eo foramine, cui triangulum ossiculum praeest, via aperta est, quae in maio­<lb></lb>rem huius ossis spiram desinit. </s>

<s>Etenim, si cavitas caeca esset, percussus aer <lb></lb>nervo occurrere nullo modo posset. </s>

<s>Sed quia, ita ut dixi res, se habet, ar­<lb></lb>bitror ipse aerem a Tympano et ab ossiculis agitatum, eo quo exposui iti­<lb></lb>nere, ad maiorem ossis spiram pervenire, indeque ad minorem reflecti, mox <lb></lb>per medium foramen rectum ad nervum ascendere ” (ibid., pag. </s>

<s>160). </s></p><p type="main">

<s>Accennando così l&#039;Eustachio al più intimo organo dell&#039;udito, avente la <lb></lb>sede sua principale nel Laberinto, dentro il quale i tremori dell&#039;aria entrano <lb></lb>a impressionare il nervo, attraverso a quella finestra, innanzi a cui sta pa­<lb></lb>rato l&#039;osso triangolare, ossia la Staffa; apriva il primo le vie ai progressi <lb></lb>della scienza. </s>

<s>Si misero per quelle vie poco dopo il Vidio e l&#039;Ingrassia, ma <lb></lb>perchè i loro libri postumi videro la luce quasi un mezzo secolo da poi che <lb></lb>furono scritti, la buona sementa, sparsa con frettolosa mano nella Epistola <lb></lb>eustachiana a Francesco Alciato, rimase soffocata da que&#039;voraci prunai ari­<lb></lb>stotelici trapiantati nel campo della nuova scienza dal malefico magistero <pb xlink:href="020/01/1413.jpg" pagenum="288"></pb>dell&#039;Acquapendente. </s>

<s>Fermo in quella sua strana opinione che sia la scienza <lb></lb>rimasta stagnante ne&#039;libri di Aristotile e di Galeno, e che perciò non faccia <lb></lb>e non abbia bisogno di far progressi, perciocchè il Filosofo insegnava esser <lb></lb>l&#039;aria materia del suono, che si diffonde ed è portato da essa “ sensorium <lb></lb>audiendi aeris esse fatemur ” ciò che dall&#039;altra parte conferma Galeno in­<lb></lb>segnando “ aereum constituendum esse auditus sensorium, quia sonos qui <lb></lb>vehuntur aere, ipsiusque aeris sunt affectiones, ipsum suscipere oportebat ” <lb></lb>(De aure auditus org. </s>

<s>cit., pag. </s>

<s>256). </s></p><p type="main">

<s>A che dunque giovarono alla scienza le scoperte del Berengario, del <lb></lb>Falloppio e dell&#039;Eustachio? </s>

<s>A null&#039;altro, risponde l&#039;Acquapendente, che ad <lb></lb>illustrare le dottrine di Aristotile e di Galeno. </s>

<s>Gli ossicini essendo duri, densi <lb></lb>e politi sono attissimi <emph type="italics"></emph>ad soni receptionem et delationem,<emph.end type="italics"></emph.end> ciò che egli prova <lb></lb>per l&#039;esperienza di una lunghissima trave, all&#039;una estremità della quale, egli <lb></lb>dice, se tu farai stare qualcuno, mettendoti tu dall&#039;altra, “ tum percutias <lb></lb>digito partem tuam ita leniter, ut ictus vix a te percipiatur, alter vero ex <lb></lb>altero fine trabis collocatus; si aurem propius ei admoverit, quamvis longis­<lb></lb>sime a te dissitus, exquisitius tamen ictus percipiet atque tu, qui aurem non <lb></lb>admoveris, utcumque ictui propior fueris ” (ibid., pag. </s>

<s>262). </s></p><p type="main">

<s>O di quel Laberinto, così dal Falloppio artificiosamente descritto, qual <lb></lb>si fu l&#039;intenzione della Natura? </s>

<s>E risponde l&#039;Acquapendente che, ne&#039;colpi <lb></lb>forti e terribili, il suono troppo grand&#039;impeto farebbe nella Miringe (così <lb></lb>egli chiama la membrana del timpano) da lacerarla, se non entrasse per <lb></lb>quelle cavità a scaricarsi, e a sfogar la sua possa. </s>

<s>“ Nunc vero in haec fo­<lb></lb>ramina, in prima cavitate exculpta, sonus suapte natura sese insinuat et in­<lb></lb>greditur, et ita anaclasis soni, sive reverberatio aut repercussus repulsusque <lb></lb>et echo prohibetur ” (ibid., pag. </s>

<s>265). </s></p><p type="main">

<s>Se poi tu mi domandi, prosegue l&#039;Acquapendente, la ragione dell&#039;am­<lb></lb>piezza e della lunghezza di que&#039;laberintici canali, io ti rispondo che son per <lb></lb>ammettere le differenze de&#039;suoni. </s>

<s>“ Nam amplum gravem, angustum acu­<lb></lb>tum sonum admittit. </s>

<s>Ratio ex Arist. </s>

<s>desumitur in Problem. </s>

<s>Copiosus igitur <lb></lb>aer et gravis sonus amplum foramen exposcit ut ingrediatur: contra acu­<lb></lb>tus..... Longitudo ad eam soni differentiam sese accommodat, quae per <lb></lb>magnum et parvum variat..... Itaque maior sonus longiores, minor brevio­<lb></lb>res cavernulas exposcit ” (ibid.). </s></p><p type="main">

<s>L&#039;ingegno, ch&#039;era pur grande, di Girolamo Fabricio si perde tutto, come <lb></lb>si vede, nell&#039;adattar le vecchie masserizie a un edificio nuovo, la qual no­<lb></lb>vità però per lui non consiste nella sostanza, ma negli accessorii. </s>

<s>Egli è <lb></lb>convinto che i canali semicircolari, la Coclea e tutto il laberinto sieno le ca­<lb></lb>vità dell&#039;orecchie <emph type="italics"></emph>antiquis cognitae<emph.end type="italics"></emph.end> (ibid.). Che fosse pur cognita a loro la <lb></lb>Tuba eustachiana l&#039;Acquapendente, sull&#039;autorità di Aristotile e di Galeno, <lb></lb>non ne dubita, ma è qui, nell&#039;assegnare gli usi di lei, dove il prurito di far <lb></lb>tutta la scienza tanto ringorgare indietro da confondersi col mare aristote­<lb></lb>lico, che lo mette in impaccio. </s>

<s>Come può infatti conciliarsi la dottrina del­<lb></lb>l&#039;aria ingenita e immobile con questo, che è uno degli ufficii che l&#039;Autore <pb xlink:href="020/01/1414.jpg" pagenum="289"></pb>assegna al meato <emph type="italics"></emph>a concha in palatum pertuso?<emph.end type="italics"></emph.end> “ Itaque praedictus mea­<lb></lb>tus ventilationem respirationemque simul et refectionem aeri complantato <lb></lb>adhibet ” (ibid., pag. </s>

<s>267). Far complice Aristotile di una tal contradizione <lb></lb>è, a volere esser giusti, una calunnia, perchè egli veramente non seppe nulla <lb></lb>di quel meato. </s>

<s>Ma pur parve un sì fatto organo, dopo la scoperta dell&#039;Eu­<lb></lb>stachio, di tanta importanza, da far grande onore all&#039;Idolo venerato, per cui <lb></lb>libero l&#039;Acquapendente prosegul per la nuova via aperta, ostinandosi a cre­<lb></lb>dere di camminar per la vecchia. </s></p><p type="main">

<s>Era oramai divulgata esperienza che alcuni difettosi dell&#039;udito sentis­<lb></lb>sero con facilità i corpi sonori, mettendoli in comunicazione colla bocca per <lb></lb>mezzo di una verga rigida stretta fra&#039;denti. </s>

<s>Il Porta raccolse anche questa <lb></lb>fra le maraviglie scritte nella sua Magia naturale in quattro libri, e termina <lb></lb>pazzamente l&#039;articolo inserito nel cap. </s>

<s>XXV del II libro con dire, che da <lb></lb>quel fatto si dimostrava non sentirsi per l&#039;udito ma per il gusto: “ dicique <lb></lb>poterit non auditus sensu sed gustu percipere ” (Neapoli 1558, pag. </s>

<s>99). </s></p><p type="main">

<s>Anche l&#039;Ingrassia, ne&#039;suoi Commentarii al trattato <emph type="italics"></emph>De ossibus<emph.end type="italics"></emph.end> di Ga­<lb></lb>leno, cap. </s>

<s>I, Testo VIII, raccontava di un suo amico, bravo sonatore di ce­<lb></lb>tra, il quale divenuto sordo si consolava di poter tornare ad udire il dolce <lb></lb>suono, mordendo, mentr&#039;ei ne toccava le corde, il lungo manico dello stru­<lb></lb>mento. </s>

<s>Ma l&#039;Acquapendente fu il primo che, invocando gli usi della Tuba <lb></lb>eustachiana, spiegò questo non solo, ma anche altri fatti più curiosi, come <lb></lb>per esempio perchè, quando un discorso ci diletta stiamo ad ascoltarlo, se­<lb></lb>condo che proverbialmente si dice, a bocca aperta. </s>

<s>“ Quarta et ultima prae­<lb></lb>dicti meatus utilitas est ut si forte fortuna membrana laedatur, unde audi­<lb></lb>tus difficilior obtusiorque reddatur, per hanc viam sonus per os ingressus <lb></lb>ad aurium intima pertingat, atque hac ratione surdastris subveniatur. </s>

<s>Nam <lb></lb>et illi, ut exquisitius audiant, hiante ore, voces et sonos excipere consueve­<lb></lb>runt. </s>

<s>Neque modo surdastri sed alii quoque, cum quidpiam obscure audiunt, <lb></lb>ore adaperto melius percipere videntur. </s>

<s>Idem quoque testantur musica in­<lb></lb>strumenta, quae, si utraque aure diligenter obturata, baculo quem dentibus <lb></lb>apprehenderis contingas, exquisitius pulsari audies. </s>

<s>Sic et qui in via, noctu <lb></lb>potissimum, alicuius procul advenientis strepitum captant, si baculi aut ensis <lb></lb>alterum extremum terrae affigant, alterum vero dentibus apprehendant, e <lb></lb>longinquo magis audiunt, idque potissimum contingit, quando via duris saxis <lb></lb>operta est ” (ibid., pag. </s>

<s>267). </s></p><p type="main">

<s>I Fisiologi approvarono poi tutti unanimi questi usi della Tuba eusta­<lb></lb>chiana, non avvertiti dal suo proprio inventore, il quale riconobbe il nuovo <lb></lb>organo utile solamente “ ad rectum medicamentorum usum ” (De aud. </s>

<s>org. </s>

<s><lb></lb>cit., pag. </s>

<s>163). Lo spirito dell&#039;Eustachio forse avrebbe, del benefizio, sen­<lb></lb>tito riconoscenza verso l&#039;Acquapendente, se ne fosse stato da lui riconosciuto <lb></lb>per inventore. </s>

<s>Ma non fu questo il legame che ricongiunse i due ingegni, <lb></lb>così opposti nelle opinioni: fu il trovarsi consorti nella scoperta de&#039;musco­<lb></lb>lini auditivi interni. </s>

<s>L&#039;Autore dell&#039;epistola all&#039;Alciato si condusse da una <lb></lb>tale scoperta ad emettere una sua idea, che nella novità aveva qualche cosa <pb xlink:href="020/01/1415.jpg" pagenum="290"></pb>dello strano. </s>

<s>“ Cum instituisset Natura, egli scrive, auditus organa arbitrio <lb></lb>voluntatis moveri, articulationem quoque ac musculum, sine quibus fieri is <lb></lb>motus nequit, tribuere illis voluit ” (ibid., pag. </s>

<s>157, 58). Nè si spiega più <lb></lb>da vantaggio, ma l&#039;Acquapendente, ripigliando il costrutto eustachiano ri­<lb></lb>masto interrotto, lo concludeva in questo argomento: “ Quod sì motus est <lb></lb>a musculo et per dearticulationem factus, dubio procul voluntarius est ” (De <lb></lb>aure cit., pag. </s>

<s>251). </s></p><p type="main">

<s>A togliere la maraviglia dalla mente di coloro, che reluttassero ad am­<lb></lb>mettere una sentenza tanto nuova, l&#039;Acquapendente ricorre a certi esempii, <lb></lb>ch&#039;egli stesso confessa esser di difficile persuasione, perchè si tratta di fe­<lb></lb>nomeni subiettivi. </s>

<s>Pur fatta in sè medesimo esperienza di poter a volontà <lb></lb>suscitar nell&#039;orecchio uno strepito, e fermo in credere e in insegnare che <lb></lb>l&#039;udito è arbitrario. </s>

<s>“ Hic igitur motus ille est arbitrarius quem in auribus <lb></lb>meis percipio, et alteri ostendere aut docere aliter non possum, quia intus <lb></lb>in auribus fit et exiguus, sed tamen evidens est motus, et sicuti in constrin­<lb></lb>genda manu decipi non possum, sic neque in hoc decipior. </s>

<s>Hoc dico prop­<lb></lb>terea quod aliqui sunt, qui cum observare in seipsis non possint praedictum <lb></lb>motum, illum negare audent, sed tamen multos semper in publicis theatris <lb></lb>reperi, qui illum exploraverint et confessi sunt ” (ibid.). </s></p><p type="main">

<s>Benchè il trattato dell&#039;Acquapendente, in cui si professano così fatte <lb></lb>dottrine, vedesse la luce nel medesimo anno di quello del Casserio, è certo <lb></lb>nulladimeno che all&#039;uno autore debbono essere state note le idee dell&#039;altro, <lb></lb>o le avesse attinte nella scuola o ne&#039;familiari colloqui, o gli fosse dato di <lb></lb>leggerle nel manoscritto. </s>

<s>È in ogni modo un fatto che il Piacentino confuta <lb></lb>alcune teorie fisiologiche esposte nel libro <emph type="italics"></emph>De aure<emph.end type="italics"></emph.end> del suo Maestro, di cui, <lb></lb>perchè non profferisce il nome, crediamo che ciò si faccia da lui per rive­<lb></lb>renza, vedendolo spesso passare dalle confutazioni ai commenti. </s></p><p type="main">

<s>Confuta l&#039;idea che il sensorio consista nell&#039;aria ingenita, perchè, do­<lb></lb>vend&#039;essere organo della sensazione un corpo vivente, “ vivere ipsum aerem <lb></lb>dici non potest ” (De auris aud. </s>

<s>org. </s>

<s>Historia anat. </s>

<s>cit., pag. </s>

<s>82), ma poi <lb></lb>egli ammette, con Aristotile e con l&#039;Acquapendente, l&#039;aere ingenito, e con­<lb></lb>sente ch&#039;egli sia libero e quieto, come quello che “ ad soni extrinsecus in­<lb></lb>trantis receptionem aptissimum est, at e contra inquietum a motu aliquo <lb></lb>agitatum ineptissimum ratio dictitat, et quotidiana experientia comprobat ” <lb></lb>(ibid., pag. </s>

<s>121). L&#039;ufficio però di un tal aere ingenito interno è, secondo <lb></lb>il Casserio, quello di rispondere all&#039;unisono coll&#039;esterno, che fa vibrare la <lb></lb>membrana del Timpano “ atque consimilem soni speciem in actum indu­<lb></lb>cit ” (ibid., pag. </s>

<s>85). </s></p><p type="main">

<s>Contradice inoltre esso Casserio al Maestro intorno all&#039;uso degli ossicini, <lb></lb>pensando che non sieno ordinati a condurre i suoni, ma “ ad stabiliendum <lb></lb>et defendendum Tympanum, ne, dum aer internus aut externus vehemen­<lb></lb>tius in illud irruat, divellatur ” (ibid., pag. </s>

<s>118), però consente nell&#039;ammet­<lb></lb>tere che i muscolini governino a volontà del senziente i moti del Martello. <lb></lb></s>

<s>“ Porro fuit illud munus cohibendi motum Mallei musculis et voluntariis <pb xlink:href="020/01/1416.jpg" pagenum="291"></pb>instrumentis commissum, ut sicuti variae sunt aeris ad membranas impul­<lb></lb>siones, sic cohibitio ac distantia motus Mallei varia fieret. </s>

<s>Ad hanc sane <lb></lb>functionem non ligamenta, eodem semper tenore agentia, sed musculi vo­<lb></lb>luntarii motus organa et qui cum quadam analogia et mensura operantur, <lb></lb>et plus minusve, prout opus est, contrahendo sese et laxando, aeris variis <lb></lb>impulsionibus, quarum quidem varietas in maioris minorisve ratione con­<lb></lb>sistit, vario motu resistere poterant ” (ibid., pag. </s>

<s>120). </s></p><p type="main">

<s>S&#039;è d unque al Casserio, come all&#039;Acquapendente, appiccato in far l&#039;udito <lb></lb>arbitrario il contagio dell&#039;Eustachio, con cui, ambedue insieme rivaleggiando, <lb></lb>si compiacciono d&#039;essere stati, nell&#039;invenzione de&#039;muscoli auditivi interni, <lb></lb>fortunati consorti. </s>

<s>Ma da questo contatto in poi, i due Anatomici più recenti <lb></lb>si dilungano troppo dal Sanseveritano, nelle idee del quale contenevansi <lb></lb>come avvertimmo principii più sani e più fecondi. </s></p><p type="main">

<s>Nal 1604 comparvero i Commentarii a Galeno dell&#039;Ingrassia. </s>

<s>Egli è ve­<lb></lb>ramente il primo che, sebben non sia amico all&#039;Eustachio, sente quanto le <lb></lb>dottrine di lui sieno più conformi al vero delle puerilità del Colombo. </s>

<s>Ma <lb></lb>l&#039;Autore <emph type="italics"></emph>De auditus organis,<emph.end type="italics"></emph.end> insegnando che i tremori armonici entrano <lb></lb>nel Labirinto per la Finestra ovale, non diceva a che fine fosse aperta nella <lb></lb>volta del vestibolo la Finestra rotonda. </s>

<s>Or perchè non è credibile che la Na­<lb></lb>tura la lasciasse ivi oziosa, si dette l&#039;Ingrassia a specularne gli usi, da che <lb></lb>fu condotto a immaginare che l&#039;aria compressa dal piè della Staffa, dopo <lb></lb>aver risonato in quelle cavità senza fondo, echeggi sulle soglie della stessa <lb></lb>Finestra rotonda, dalla quale ritorni nella cassa del Timpano, d&#039;ond&#039;era par­<lb></lb>tita. </s>

<s>“ Stapha sic deorsum compressa, sua quidem basi sub se contentum a <lb></lb>naturaque insitum in Labyrintho aerem alium comprimit, percutitque, qui <lb></lb>sic denique commotus verberatusque, per cavernulas, anfractus ac gyros <lb></lb>secundae et tertiae cavitatis decurrens, ad quos auditorius quinti paris ner­<lb></lb>vus terminatur, in membranulas quasdam dissolutus extenuatusque illos <lb></lb>obliniens, ibique tintinnans, quamdam veluti echo facit per aliam fenestram, <lb></lb>in eamdem primam cavitatem resiliens ” (De ossibus, commentaria in Ga­<lb></lb>lenum, Panormi 1604, pag. </s>

<s>45). </s></p><p type="main">

<s>Quest&#039;uso, prosegue a dire l&#039;Ingrassia, assegnato alla seconda Finestra, <lb></lb>ossia alla Rotonda, è importante, perchè, se l&#039;aria condensata non potesse <lb></lb>tornare indietro, non diverrebbe atta a risonare, “ membranulasque illas <lb></lb>intercipientes cavernulisque illitas frangeret ” (ibid.). La teorica però era <lb></lb>fondata sull&#039;ipotesi che la Finestra rotonda, come l&#039;avea descritta il Fallop­<lb></lb>pio, rimanesse aperta: ma il Vidio che trovò sopra lei teso il periostio del <lb></lb>Timpano, ebbe a svolgere in altri termini i concetti dell&#039;Eustachio. </s>

<s>Disse <lb></lb>che i tremori del suono si propagano dal Timpano nel Labirinto attraverso <lb></lb>alle membrane che chiudono le due finestre, come la comune esperienza ci <lb></lb>dimostra che si propagano attraverso alle chiuse pareti da una stanza all&#039;al­<lb></lb>tra. </s>

<s>Sebben egli confessi esser difficilissimo a noi l&#039;intendere il meccanismo <lb></lb>dell&#039;udito, “ illud tamen in aperto est quod, ubi agitatur Membrana, agita­<lb></lb>tur etiam Malleus, per manubriolum Membranae illigatum, et propterea In-<pb xlink:href="020/01/1417.jpg" pagenum="292"></pb>cus et Stapes, et ita aperitur ovatum foramen, adeo ut sonus, per hoc et <lb></lb>per alterum rotundum, penetrare ad alios sinus possit obductos membranula <lb></lb>ex nervulo quinti paris dilatato, ubi domicilium est facultatis audiendi ce­<lb></lb>rebro transmissae ” (De anatome corp. </s>

<s>humani, Venetiis 1611, pag. </s>

<s>323). </s></p><p type="main">

<s>Scritte queste cose, certamente prima del 1567, anno in cui il Vidio <lb></lb>morì, quando comparvero in Venezia alla luce, le dottrine dell&#039;Acquapen­<lb></lb>dente da undici anni tenevano soggiogati alla loro autorità la maggior parte <lb></lb>dei dotti, resi oramai indocili ad attemperare l&#039;ingegno a più razionali prin­<lb></lb>cipii. </s>

<s>I magisteri del Casserio dall&#039;altra parte si rimanevano inefficaci, sì <lb></lb>perchè le sue confutazioni si notavano d&#039;ingratitudine verso il venerabile <lb></lb>Maestro e l&#039;insigne benefattore; sì perchè non seppe mettere in evidenza <lb></lb>l&#039;azion dell&#039;aria risonante sul nervo, ignorati e negletti gli ufficii principa­<lb></lb>lissimi del Laberinto. </s>

<s>L&#039;Ingrassia e il Vidio poi, quasi dopo un mezzo secolo, <lb></lb>tornavano a parlar dalla tomba a gente, che non era ad essi legata nè coi <lb></lb>vincoli dell&#039;affetto, nè con quelli della memoria, per cui non fa maraviglia <lb></lb>se i più celebri Anatomici fioriti nella prima metà del secolo XVII costituis­<lb></lb>sero sensorio dell&#039;udito l&#039;aria ingenita, con fanciullesco inganno inghiot­<lb></lb>tendo l&#039;errore aristotelico confettato dall&#039;esperte mani dell&#039;Acquapendente. </s></p><p type="main">

<s>Altri è vero professarono, come per esempio il Deusing, che proprio <lb></lb>organo dell&#039;udito “ non est Tympanum, nec aer insitus, nec ossiculorum <lb></lb>aliqua compages, sed ipse nervus auditorius ” (Exercitatio De sensuum func­<lb></lb>tionibus, Croningae 1661, pag. </s>

<s>273), ma non ci voleva altro che l&#039;autorità <lb></lb>del Cartesio, alla scuola del quale furono addetti tutti costoro, a preva­<lb></lb>lere, benchè per piccoli momenti, sopra quella di Girolamo Fabricio. </s>

<s>Nella <lb></lb>IV Parte dei <emph type="italics"></emph>Principia Philosophiae,<emph.end type="italics"></emph.end> là dove l&#039;Autore tratta dei sensi e dei <lb></lb>nervi deputati alle loro particolari funzioni, “ Duo alii nervi, egli dice, in <lb></lb>intimis aurium cavernis reconditi excipiunt tremulos et vibratos totius aeris <lb></lb>circumiacentis motus. </s>

<s>Aer enim membranulam Tympani concutiens sub­<lb></lb>iunctam trium ossiculorum catenulam, cui isti nervi adhaerent, simul quatit, <lb></lb>atque ab horum motuum diversitate diversorum sonorum sensus oriuntur ” <lb></lb>(Amstelodami 1650, pag. </s>

<s>293). </s></p><p type="main">

<s>La Scuola cartesiana fu dunque da questa parte benemerita della Fisio­<lb></lb>logia, ma se potè ridursi ne&#039;retti sentieri, per que&#039;vizii ingeniti a lei, che <lb></lb>hanno la loro radice nell&#039;orgoglioso ripudio delle tradizioni, rimase debole <lb></lb>in dare alla scienza per progredire gl&#039;impulsi. </s>

<s>Primo, dopo la metà del se­<lb></lb>colo XVII, a risalire alle tradizioni eustachiane, fu Antonio Molinetti, il quale <lb></lb>riconosceva nell&#039;orecchio quell&#039;eccellenza di squisito natural magistero, che <lb></lb>tutti ammiravano nell&#039;occhio. </s>

<s>Rassomigliava perciò la finestra ovale alla pu­<lb></lb>pilla, il cristallino, dove la luce si refrange, ai Canali semicircolari, dove il <lb></lb>suono si riflette, e il nervo espanso sul fondo della Coclea alla Retina espansa <lb></lb>sul fondo del globo oculare. </s>

<s>“ Cochlea primum suscipit perque cochleares, <lb></lb>idest spirales suos ambitus multum diffundi cogit, non sine roboris incre­<lb></lb>mento atque impulsus, demum in tunicam perducit simillimam Retinae, pro­<lb></lb>ductam ab expansa substantia molli nervi auditorii, osseos parietes ipsius <pb xlink:href="020/01/1418.jpg" pagenum="293"></pb>obliniente, non aliter ac Retina extimam Vitrei superficiem. </s>

<s>Quis autem du­<lb></lb>bitet quin durities illa plusquam ossea parietum et canaliculorum Cochleae <lb></lb>mirum in modum conducat ad determinandum sonum, non secus atque ni­<lb></lb>ger choroidis color ad sistendum progressum luminis illudque terminandum <lb></lb>in Retina? </s>

<s>Ea igitur percussa soni sensus excitatur qui antea non erat, nec <lb></lb>quicquam omnino, praeter aerem agitatum ab externo movente. </s>

<s>Fit autem <lb></lb>hoc communicatis vibrationibus, quibus substantia nervi afficitur, et cum <lb></lb>illa spiritus per ipsam diffusus cerebro spiritibusque successive continuis, <lb></lb>usque in principium nervi ” (Dissert. </s>

<s>anat. </s>

<s>cit., pag. </s>

<s>44). </s></p><p type="main">

<s>E perchè, rinnovellando così di nuove fronde il gentile arbusto pian­<lb></lb>tato nel campo della scienza dall&#039;Eustachio, fosse meglio difeso dal soffiar <lb></lb>di quel vento, che lo poteva inaridire, il Molinetti risolve la questione del­<lb></lb>l&#039;udito arbitrario, liberando anche da questa parte la scienza dagl&#039;impacci <lb></lb>frapposti ai liberi passi di lei dall&#039;Acquapendente. </s>

<s>“ Neque hic oportet im­<lb></lb>peria voluntatis quaerere, cuius instrumenta musculi esse perhibentur, eadem <lb></lb>enim necessitas, quae ciliaria dicta ligamenta in oculo producit ut corripian­<lb></lb>tur vel laxentur, quo luminis exuberantiae excludantur, aut eiusdem de­<lb></lb>fectui occurratur; eadem musculum auris suscitat, ad motus varios obeun­<lb></lb>dos, pro appulsibus soni diversis ad membranam Tympani ” (ibid., pag. </s>

<s>50). </s></p><p type="main">

<s>Le grandi scoperte delle vene lattee, del circolo del sangue, del Canale <lb></lb>toracico e de&#039;vasi linfatici troppo avevano agitata e commossa la scienza, da <lb></lb>farla superare quegli argini, dentro i quali la voleva ritenere stagnante Colui, <lb></lb>che insignito di una duplice autorità, scientifica e morale, era dal grande <lb></lb>Harvey salutato col nome di <emph type="italics"></emph>Venerabile vecchio.<emph.end type="italics"></emph.end> Ma benchè fosse il magi­<lb></lb>stero del Molinetti secondato dall&#039;influsso dei tempi, egli ha pure il merito <lb></lb>di aver ritirata la fisiologia dell&#039;udito ai suoi veri principii. </s></p><p type="main">

<s>Ai quali principii ritornando Guntero Cristoforo Schelhammer badava a <lb></lb>ripensare fra sè in che maniera l&#039;Eustachio, non facendo nessun conto della <lb></lb>Finestra rotonda, ch&#039;ei certamente dovea col Falloppio credere affatto aperta, <lb></lb>dicesse che i tremori armonici passano nel Labirinto attraverso alla Fine­<lb></lb>stra ovale “ cui triangulum ossiculum praeest. </s>

<s>” Potrebbe quella parola <lb></lb><emph type="italics"></emph>praeest<emph.end type="italics"></emph.end> dar luogo a interpetrare che il piè della Staffa stia innanzi al suo <lb></lb>forame, senza chiuderlo esattamente, ma forse non fu questa l&#039;intenzione <lb></lb>dell&#039;Autore. </s>

<s>Nelle <emph type="italics"></emph>Osservazioni<emph.end type="italics"></emph.end> falloppiane (in loco cit., pag. </s>

<s>410) erasi già <lb></lb>divulgata l&#039;esperienza che, traforando la membrana del Timpano colla punta <lb></lb>di un ago, e toccando il capolino del Martello, il moto si propagava alla <lb></lb>Staffa, cosicchè, facendo vibrare la mano armata di quella punta, si sentiva <lb></lb>a quel tenore vibrare essa Staffa. </s>

<s>Di qui era facilissimo immaginare che, <lb></lb>operando simili effetti le onde sonore, facessero aprire e chiudere la Fine­<lb></lb>stra ovale con tal moto oscillatorio, molto opportuno a diffonder non solo, <lb></lb>ma a produrre le risonanze. </s></p><p type="main">

<s>Questa dall&#039;altra parte era l&#039;interpetrazione, che de&#039;sensi eustachiani <lb></lb>avea data il Vidio, le teorie e le scoperte del quale, o ignorate o ripudiate <lb></lb>dallo Schelhammer, lo fecero andare in quella falsa opinione che la Fine-<pb xlink:href="020/01/1419.jpg" pagenum="294"></pb>stra ovale rimanesse chiusa sempre dalla Staffa, e la Rotonda invece sem­<lb></lb>pre aperta, nè perciò velata da nessuna membrana. </s>

<s>Di qui ne scendeva che <lb></lb>la via dei suoni per entrare nel Labirinto fosse necessariamente questa, e <lb></lb>non quella. </s>

<s>Nel venir però a una tal conclusione ebbe facilmente a com­<lb></lb>prendere che l&#039;Eustachio non fece per l&#039;ammissione del suono nessun conto <lb></lb>della Finestra rotonda, perch&#039;ella si rimane in disparte dalla membrana del <lb></lb>Timpano, d&#039;onde giungono i tremori esterni, mentre la Finestra ovale torna <lb></lb>a quella stessa membrana in diritto. </s>

<s>Ma pur, sempre fermo in quella sua <lb></lb>opinione della struttura delle due Finestre, pensò lo Schelhammer a togliere <lb></lb>le difficoltà ricorrendo alle riflessini de&#039;suoni. </s></p><p type="main">

<s>Gli Assiomi <emph type="italics"></emph>De sono,<emph.end type="italics"></emph.end> posti nel II cap. </s>

<s>della I Parte <emph type="italics"></emph>De auditu,<emph.end type="italics"></emph.end> non <lb></lb>son tutti ammissibili come certi, e i Teoremi perciò non rimangono con <lb></lb>certezza dimostrati, tanto più che bene spesso alla scienza si sostituisce l&#039;au­<lb></lb>torità del Kircher o di altri così fatti. </s>

<s>Ma pure egli è benemerito, lo Schel­<lb></lb>hammer, per aver primo tentate queste nuove vie di fisica matematica, ap­<lb></lb>plicando l&#039;Acustica alla Fisiologia dell&#039;udito. </s>

<s>Volendo aver di queste appli­<lb></lb>cazioni qualche esempio, nel Teorema ultimo che è il XXIII si propone <lb></lb>l&#039;Autore di dimostrare: “ Sonus in cochleis maximas vires obtinet ” (editio <lb></lb>cit., pag. </s>

<s>157), e nel cap. </s>

<s>V della Parte II ne fa, così dicendo, l&#039;applica­<lb></lb>zione al moltiplicarsi per naturale artificio il suono nella Chiocciola dell&#039;orec­<lb></lb>chio: “ Hic igitur incomparabile prorsus et stupendum Naturae artificium <lb></lb>depraedicandum venit. </s>

<s>Comprehendit enim in parvo spatio quicquid ad so­<lb></lb>num et multiplicandum in immensum et sistendum unquam poterat exco­<lb></lb>gitari. </s>

<s>Quantum enim valeat ad sonum in infinitum multiplicandum tubus <lb></lb>cochleatus disci potest ex ultimo theorematum, quod ex Athanasio Kirchero <lb></lb>excripsimus ” (ibid., pag. </s>

<s>237). </s></p><p type="main">

<s>Così fatti moltiplicati riflessi si fanno, secondo lo Schelhammer, nella <lb></lb>Coclea dai raggi sonori, similmente riflessi dalla cassa del Timpano nella Fi­<lb></lb>nestra rotonda, a quest&#039;uso principalmente creduta dallo stesso Schelham­<lb></lb>mer aperta. </s>

<s>Debbono senza dubbio avere avuto qualche efficacia, sopra que­<lb></lb>sta opinione del Fisiologo tedesco, le parole, nelle quali il nostro Molinetti <lb></lb>diceva comunicar liberamente l&#039;aria del labirinto colla timpanica “ per fo­<lb></lb>ramen rotundum, hoc nomine puto praecipue apertum ” (Dissert. </s>

<s>anat. </s>

<s>cit., <lb></lb>pag. </s>

<s>53). Ma perchè il Vidio e il Casserio avevano oramai da lungo tempo <lb></lb>dimostrato che quel forame è chiuso dal periostio, che riveste le due più <lb></lb>intime cavità auricolari, cadevano le teorie infrante dalla forza dei fatti, e <lb></lb>dall&#039;altra parte escludere dall&#039;ufficio d&#039;intromettere i suoni la Finestra ovale, <lb></lb>come intendeva lo Schelhammer, pareva men ragionevole ch&#039;escludere la <lb></lb>Finestra rotonda, com&#039;avea fatto l&#039;Eustachio, perchè altrimenti a qual fine <lb></lb>congegnar così sapientemente la Natura la catena dei tre ossicini? </s></p><p type="main">

<s>Persuasi perciò i Fisiologi che dovessero i due forami essere ugual­<lb></lb>mente utili, si volsero a speculare di quella utilità le ragioni. </s>

<s>Nel 1683 com­<lb></lb>pariva in Parigi un libretto in 12° di Giuseppe Duverney intitolato <emph type="italics"></emph>Traité <lb></lb>de l&#039;organe de l&#039;ouiė,<emph.end type="italics"></emph.end> e perchè vi si trattava di cose non comuni, il Man-<pb xlink:href="020/01/1420.jpg" pagenum="295"></pb>get lo raccolse, tradotto in latino, nella sua Biblioteca anatomica da cui noi <lb></lb>lo citiamo. </s></p><p type="main">

<s>Che le speculazioni del Francese, come quelle del Tedesco sopra com­<lb></lb>memorato, avessero impulso da quelle del nostro Anatomico veneziano a noi <lb></lb>par credibile, imperocchè, dop&#039;aver detto il Molinetti che i suoni si molti­<lb></lb>plicano nel Labirinto, soggiunge che nella Coclea “ quo magis aer in spiris <lb></lb>minoribus coarctatur, in nervum mollem impingitur oblinientem ultimam <lb></lb>partem Cochleae, quem vibrationibus similibus etiam movet ” (ibid., pag. </s>

<s>54). </s></p><p type="main">

<s>Anche il Duverney dunque ammette che la sede dell&#039;udito sia nel La­<lb></lb>birinto, e segnatamente nel nervo espanso, dentro la Coclea stessa, in quella <lb></lb>che, scoperta già dall&#039;Eustachio, si chiamò <emph type="italics"></emph>Lamina spirale.<emph.end type="italics"></emph.end> Rimaneva però <lb></lb>ancora a decidere per quali porte s&#039;intromettessero i suoni, e perchè la ra­<lb></lb>gion suggeriva che ciò si dovesse fare in amichevole società dai due forami, <lb></lb>il Duverney fu il primo a specularne i modi. </s>

<s>La lamina spirale divide tutto <lb></lb>il dulto cocleare in due scale, che si appoggiano allo stesso modiolo, di modo <lb></lb>che la superiore non comunica colla inferiore. </s>

<s>La finestra rotonda si apre <lb></lb>in questa, e l&#039;Ovale in quella, e i tremori armonici passano ugualmente bene <lb></lb>comunicati alle membrane chiudenti l&#039;una e l&#039;altra di quelle stesse Fine­<lb></lb>stre, “ atque ita spiralis laminae, cum ipsa utrinque verberetur, tremuli mo­<lb></lb>tus vividiores et fortiores esse debent ” (In Biblioth. </s>

<s>anat. </s>

<s>cit., T. II, Ge­<lb></lb>nevae 1685, pag. </s>

<s>436). </s></p><p type="main">

<s>Così il Fisiologo parigino, dop&#039;avere svolte le idee del Molinetti, esplicava <lb></lb>i sensi del Vidio, e proseguendo nelle sue speculazioni passava ad illustrar <lb></lb>l&#039;ipotesi dell&#039;Acquapendente intorno all&#039;uso de&#039;canali più o meno lunghi, e <lb></lb>più o meno larghi in modulare i tuoni, rassomigliando anch&#039;egli l&#039;organo <lb></lb>dell&#039;udito a quelle trombe, co&#039;loro tubi avvolti in spira fra&#039;musicali stru­<lb></lb>menti. </s>

<s>Anzi, perchè quella varietà di armonie dev&#039;essere immediatamente <lb></lb>sentita dal sensorio primario, ei crede che la stessa Lamina spirale, vibrando <lb></lb>ora nella parte più stretta ora nella più larga, sia a questo principale effetto <lb></lb>disposta di rappresentare i tuoni gravi e gli acuti. </s>

<s>“ Lamina haec aeris mo­<lb></lb>tus tremulos recipere non tantum apta est, sed ipsius structura eam omni­<lb></lb>bus eorumdem motuum differentibus caracteribus respondere posse argu­<lb></lb>mento esse debet. </s>

<s>Cum enim in primae suae revolutionis principio quam in <lb></lb>ultimae extremo, ubi veluti in cuspidem desinit, latior est, cum aliae itidem <lb></lb>ipsius partes quoad latitudinem proportionaliter minuantur; dicere possumus <lb></lb>partes latiores, quandoquidem immotis reliquis, commoveri possunt tremulis <lb></lb>motibus, seu vibrationibus lentioribus, quae sonis proinde gravibus respon­<lb></lb>deant aptas duntaxat esse, et e contra, ubi angustiores ipsius partes verbe­<lb></lb>rantur, earum vibrationes celeriores esse, et sonis acutis ideo respondere ” <lb></lb>(ibid., pag. </s>

<s>437). </s></p><p type="main">

<s>Le dottrine del Duverney raccolte dai varii Autori italiani, via via nel <lb></lb>nostro discorso commemorati, e in bell&#039;ordine esposte, apparvero e furono <lb></lb>ricevute come nuove, plaudendo i dotti all&#039;Autore. </s>

<s>Anche il Valsalva si vide <lb></lb>a quella luce così condensata e riflessa rischiarare le vie, ma desideroso di <pb xlink:href="020/01/1421.jpg" pagenum="296"></pb>andar da sè in cerca della perfezione, costituì primario sensorio, insiem colla <lb></lb>Lamina spirale, le zone contenute ne&#039;Canali semicircolari “ unde, cum ipsae <lb></lb>quidem nil aliud sint quam mollis auditorii nervi expansiones, sensatio exci­<lb></lb>tatur ” (De aure hum. </s>

<s>cit., pag, 79). </s></p><p type="main">

<s>Ma perchè la Natura, sentiva domandarsi, commise l&#039;ufficio a tre, piut­<lb></lb>tosto che a una zona sola? </s>

<s>Per rispondere alla qual domanda l&#039;Autore in­<lb></lb>voca il fatto notissimo del mettersi spontanea a risonare una corda non <lb></lb>tocca, e tesa all&#039;unisono di un altro strumento. </s>

<s>“ Haec cum ita sint, poi <lb></lb>soggiunge, iam aliquem suspicari posse: cum tam varii soni a nobis audiri <lb></lb>et distincte percipi debuerint, per impressiones quidem ab illis in membra­<lb></lb>nulam demum factas, ut eorum perceptio vividior esset curasse Naturam ut <lb></lb>singuli non utcumque membranulam attingerent, sed quam possent maio­<lb></lb>rem impressionem in eamdem facerent. </s>

<s>At sicuti varii toni non possunt <lb></lb>omnes facere maiorem impressionem in unam aut unius conditionis chor­<lb></lb>dam, sed singuli variae conditionis chordas exposcunt; ita neque varios so­<lb></lb>norum tonos in unam simplicemve membranulam potuisse requisitam maio­<lb></lb>rem impressionem facere. </s>

<s>Ideo non unum canalem unamque membranulam <lb></lb>sive zonam, sed plures canales, et plures zonas Naturam posuisse, et istas <lb></lb>quidem variae conditionis, saltem quo ad longitudinem attinet, nam maior <lb></lb>una, minor altera, tertia vero minima est ” (ibid., pag. </s>

<s>79, 80). </s></p><p type="main">

<s>Si può anche questo tenere per un bello e ingegnoso commento alle <lb></lb>dottrine di Girolamo Fabricio, ma il desiderio di tentar cose nuove condusse <lb></lb>il Valsalva a un esito non troppo felice quando, dal Duverney che avea, ri­<lb></lb>spetto agli usi delle due Finestre seguito il Vidio, si dilungò per rinnovel­<lb></lb>lare l&#039;opinion dell&#039;Eustachio. </s></p><p type="main">

<s>I suoni dunque secondo l&#039;Autore, non si comunicano dal meato udito­<lb></lb>rio esterno al Labirinto, acusticamente ne&#039;tremori attraverso alla cavità del <lb></lb>Timpano, ma giunti ivi alle soglie operano meccanicamente sopra la mem­<lb></lb>brana, e il moto meccanico si propaga attraverso alla catena degli ossicini <lb></lb>infino alla Staffa, la quale, comprimendo l&#039;aria contenuta nel Labirinto, la <lb></lb>mette in moto di risonanza. </s>

<s>S&#039;indusse il Valsalva, contro le più comuni opi­<lb></lb>nioni, a creder così, per gl&#039;impedimenti che troverebbero le onde sonore in <lb></lb>propagarsi per la cavità del Timpano imperturbate; “ scilicet, non solum <lb></lb>membrana ipsius Tympani, sed hinc stapes ovalem fenestram obturans, illinc <lb></lb>membrana Fenestram rotundam claudens, nec non situs eiusdem Fenestrae, <lb></lb>advenientibus sonoris motibus, non adversae, sed lateralis ” (ibid., pag. </s>

<s>60). </s></p><p type="main">

<s>Persuaso così che i moti aerei apportatori dei suoni operino meccani­<lb></lb>camente sopra la Staffa, il Valsalva, che par non conoscesse le proprietà <lb></lb>elastiche dei fluidi aeriformi, disse non potere alla stessa Staffa ceder l&#039;aria <lb></lb>il suo luogo, se non a patto o di trovar da ricoverarsi altrove, o di aver <lb></lb>qualche sfogo. </s>

<s>Questo secondo caso però non è possibile, perchè ammette <lb></lb>col Duverney anche il Nostro, che la Scala inferiore, ossia del Timpano, non <lb></lb>abbia alcuna comunicazione colla Scala superiore, ossia del Vestibolo; ond&#039;è <lb></lb>che l&#039;aria contenuta in questa dee necessariamente trovare altro luogo, nè <pb xlink:href="020/01/1422.jpg" pagenum="297"></pb>s&#039;intende come potesse trovarlo altrove che nella cuna della Lamina spirale, <lb></lb>o della Zona incurvata per la pressione. </s>

<s>Ne è da temer che oppongasi a <lb></lb>questa incurvatura, soggiunge l&#039;Autore, la resistenza dell&#039;aria, di che è piena <lb></lb>quell&#039;altra Scala, la quale aria trova da rifarsi dello spazio perduto, pre­<lb></lb>mendo e facendo così rigonfiare verso la cavità del Timpano la sottile e fles­<lb></lb>sibile membrana, che chiude la Finestra rotonda. </s>

<s>“ Aer enim Scalae Vesti­<lb></lb>buli propulso non obstat, cum ipse propellere illum possit, qui in Tympani <lb></lb>Scala continetur, non quidem per poros aut certam aliquam communicatio­<lb></lb>nem, ut quidam suspicari visus est, sed per ipsius tenuis Zonae, qua utra­<lb></lb>que Scala distinguitur, compressionem. </s>

<s>Nam rursus aer iste, qui in Tympani <lb></lb>Scala continetur, compressae Zonae facile cedit, non dico in Tympanum per <lb></lb>Fenestram rotundam prorumpendo, ut idem Auctor, hanc membrana claudi <lb></lb>non advertens, credidit, sed istam eandem membranam, quoad opus est (exi­<lb></lb>guo autem spatio opus est) versus Tympanum urgendo atque curvando ” <lb></lb>(ibid., pag. </s>

<s>81). </s></p><p type="main">

<s>Tale è, secondo il Valsalva, l&#039;uso della Finestra rotonda, non avendo <lb></lb>propriamente la Natura assegnato per l&#039;ammissione del suono altro che la <lb></lb>Finestra ovale. </s>

<s>Che se così rinnovellava l&#039;Autore l&#039;opinion dell&#039;Eustachio, <lb></lb>dall&#039;altra parte la peggiorava, attribuendo agli ossicini un ufficio non acu­<lb></lb>stico, ma meccanico, come, rinnovellando altresì l&#039;opinione del Molinetti, in <lb></lb>conformità della quale l&#039;aria sonora agisce sul nervo, premendolo, volgeva <lb></lb>in peggio le idee proposte dal Duverney per illustrarla. </s></p><p type="main">

<s>Mentre che così fatte considerazioni tenevano fra la grande stima che <lb></lb>si faceva dell&#039;uomo, e le irragionevolezze e gli errori, in questo particolar <lb></lb>proposito della teoria dell&#039;udito, il pubblico dei dotti perplesso, fu instanta­<lb></lb>neamente decisa la questione da un colpo dato dal Cotunnio a uno de&#039;ca­<lb></lb>naletti semicircolari, a vedere il quale pieno d&#039;acqua e non d&#039;aria. </s>

<s>“ Quid <lb></lb>zonae sonorae, esclama, a Valsalva propositae? </s>

<s>Aliquid in quo bonus dor­<lb></lb>mitavit Homerus. </s>

<s>Quid aer ille, ingenitus Aristoteli dictus, et toti prope an­<lb></lb>tiquitati acceptus, cui tantum Anatomici et Physici videntur tribuisse? </s>

<s>” <lb></lb><emph type="italics"></emph>Patet,<emph.end type="italics"></emph.end> risponde a sè medesimo, da questo umore che cola (De aquaeducti­<lb></lb>bus auris. </s>

<s>hum. </s>

<s>cit., pag. </s>

<s>39). </s></p><p type="main">

<s>E giacchè, dopo tanti secoli, era toccato a lui il primo finalmente a <lb></lb>scoprire il mistero, intese perchè l&#039;aria non all&#039;aria ma a un liquido comu­<lb></lb>nichi i suoi tremori. </s>

<s>Le ossa dure, dentro alle quali s&#039;accoglie il più intimo <lb></lb>organo dell&#039;udito, sono, ei pensa, attissime a ricevere e a conservare i tre­<lb></lb>mori, “ oportuit tamen nervos humore inundari, ne si ab ipso immediato <lb></lb>ossium contactu deberent sibi tremorem comparare, nimium pro teneritudine <lb></lb>sua lacessirentur. </s>

<s>Humor etenim intermedius leniter inundans, ob acceptum <lb></lb>ab ossibus impulsum, concutit nervos, sed molli nec aspero contactu ” (ibid., <lb></lb>pag. </s>

<s>40). </s></p><p type="main">

<s>Quanto al meccanismo della funzione non ha il Cotunnio difficoltà di <lb></lb>seguire il Valsalva, sull&#039;esempio del quale, dall&#039;altra parte, procede sicuro <lb></lb>di non contradire alle leggi della Fisica, essendo propriamente i liquidi ane-<pb xlink:href="020/01/1423.jpg" pagenum="298"></pb>lastici e incompressibili. </s>

<s>Ma egli ebbe in quel meccanismo a ritrovare gli <lb></lb>usi di due canaletti da sè nuovamente scoperti, uno de&#039;quali, facendosi via <lb></lb>attraverso all&#039;osso petroso, deriva dal Vestibolo in tempi prestabiliti l&#039;umore <lb></lb>nel prossimo seno laterale della dura madre, e l&#039;altro che dalla Chiocciola <lb></lb>deriva un simile umore nelle cavità del cranio. </s>

<s>Dà al primo il nome di <lb></lb><emph type="italics"></emph>Acquedotto del Vestibolo,<emph.end type="italics"></emph.end> e al secondo quello di <emph type="italics"></emph>Acquedotto della Chioc­<lb></lb>ciola,<emph.end type="italics"></emph.end> e da questi due organi, ai quali principalmente accomoda la sua nuova <lb></lb>teoria dell&#039;udito, intitola il Cotunnio il suo classico libro. </s></p><p type="main">

<s>La Staffa dunque, secondo l&#039;Autore, messa meccanicamente in moto <lb></lb>dalle onde sonore pulsanti la membrana del Timpano, comprime l&#039;umore <lb></lb>del Labirinto, che dalla cavità anteriore del Vestibolo, per via del canale <lb></lb>esterno, passa alla cavità posteriore, e indi, per il canal comune, ritorna alla <lb></lb>medesima cavità anteriore, quasi compiendo un circolo (ivi, pag. </s>

<s>57). A que­<lb></lb>sto moto circolare, a cui s&#039;opporrebbe l&#039;incompressibilità naturale del liquido, <lb></lb>e l&#039;impenetrabilità del corpo, favorisce la membrana della Finestra rotonda, <lb></lb>che dà, cedendo, luogo a ricoverarsi dentro la sua cavità l&#039;umore spostato, <lb></lb>e favoriscono altresì gli Acquedotti, che danno a quello stesso umore un <lb></lb>esito, ristorato poi dalle arterie esalanti, delle quali è sì ricca la cavità del <lb></lb>Labirinto (ivi, pag. </s>

<s>105). </s></p><p type="main">

<s>Tale insomma è, secondo il Cotunnio, il meccanismo dell&#039;umore, che <lb></lb>dee partecipare i tremori armonici ai nervi. </s>

<s>“ Integra igitur perceptio soni <lb></lb>in singulorum tremorum a sonante corpore editorum perceptione consistit, <lb></lb>atque anima tum integrum aliquem sonum percipit, cum plenum eius tre­<lb></lb>morum numerum agnoscit. </s>

<s>Ita similes dicimus sonos quoties eumdem in <lb></lb>utroque tremorum numerum percipimus. </s>

<s>Sunt igitur nervi acustici quasi <lb></lb>chordae in singulo tremore sonori corporis semel oscillantes, totque, cum <lb></lb>audimus, impressiones cerebro numeratim impertientes, quot numero sunt <lb></lb>sonori corporis vibrationes ” (ibid., pag. </s>

<s>103). </s></p><p type="main">

<s>L&#039;organo generale della percezione del suono è il setto membranoso, <lb></lb>che divide il Vestibolo. </s>

<s>“ Hoc enim Septum amplam firmamque chordam, <lb></lb>sive seriem tot chordarum paralellorum, quot nervosa fila complectitur, re­<lb></lb>praesentat, quae moto a Stapede humori, undique opponuntur eiusque vim <lb></lb>integram accipiunt ” (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>I Canali semicircolari, le zone contenute ne&#039;quali son, come sopra nar­<lb></lb>rammo, fatte dal Valsalva strumenti principali dell&#039;audizione, non hanno per <lb></lb>il Cotunnio altro che un ufficio secondario, ed è quello di dirigere così il <lb></lb>corso all&#039;umore, che non debba il Setto rimanersene in secco. </s></p><p type="main">

<s>Ma s&#039;è questo Setto l&#039;organo della percezion generale, qual&#039;è lo stru­<lb></lb>mento della particolar percezione de&#039;suoni? </s>

<s>E risponde il Cotunnio essere <lb></lb>la Chiocciola “ in qua series chordarum paralellarum tensarumque cymbalo <lb></lb>similis absconditur, cuius in zona Cochleae sedes est, quae fila nervosa a spi­<lb></lb>rali lamina accepta et parallela continet longitudinis variae. </s>

<s>Harum ego chor­<lb></lb>darum minimam in zonae origine pono, prope orificium Scalae Tympani, <lb></lb>ubi arctissima zona est, maximam vero versus zonae hamulum. </s>

<s>Quemadmo-<pb xlink:href="020/01/1424.jpg" pagenum="299"></pb>dum ergo, edito sono aliquo etiam vocis humanae, observatur ex tot cym­<lb></lb>bali chordis unam tremere, quae in eodem unisono cum sono dato est; ita <lb></lb>in quovis dato sono, intra Cochleam, quae cymbalum nostrum est, propria <lb></lb>unisone respondens chorda datur, quae unisone contremiscens eius soni ani­<lb></lb>mae distinctionem exhibet ” (ibid., pag. </s>

<s>105). E conclude questa fisiologia <lb></lb>dell&#039;udito, che è la più filosoficamente bella che sia stata pensata: “ Septo <lb></lb>igitur sonum percipimus, Cochlea tonos discernimus ” (ibid.). </s></p><p type="main">

<s>La teoria del Cotunnio fondata sopra la sua scoperta dell&#039;umore, di <lb></lb>ch&#039;è tutto ripieno il Labirinto, fu accolta universalmente, e si fece plauso <lb></lb>ai nuovi usi assegnati al Setto del Vestibolo, ai Canali semicircolari e alla <lb></lb>Chiocciola. </s>

<s>Quanto alla Finestra rotonda, dell&#039;utilità della quale i Fisiologi, <lb></lb>dai tempi dell&#039;Eustachio in poi, erano rimasti sì incerti, volle esso Cotun­<lb></lb>nio insignirla di un duplice ufficio, di quello acustico cioè attribuitole dal <lb></lb>Duverney, e di quell&#039;altro meccanico del Valsalva. </s>

<s>“ Duplex mihi videtur <lb></lb>ratio esse. </s>

<s>Prima, ut eo tempore quo Tympani membranam sonora unda <lb></lb>impellit, aer Tympani percussus tremorem acceptum membranae communi­<lb></lb>caret Fenestrae rotundae, quae oscillatione sua proximum humorem Scalae <lb></lb>Tympani agitaret, et per orificium Cochleae aquaeductus eodem tempore <lb></lb>expelleret, quo Vestibuli humor a Stapede movetur.... Alteram, ut qui Fe­<lb></lb>nestram rotundam premit humor, tempore quo nova quantitas ex vestibulo <lb></lb>advehitur, non in superpositam Cochleae zonam, etsi breviorem hic robu­<lb></lb>stioremque, totus ageret, sed in cedentem hanc Rotundae Fenestrae mem­<lb></lb>branam impulsus partem perderet ” (ibid., pag. </s>

<s>83). </s></p><p type="main">

<s>Parvero questi usi della Finestra rotonda ad Antonio Scarpa poco pro­<lb></lb>babili, e in un suo trattatello si studiò di dimostrar che quell&#039;organo era <lb></lb>un sussidiario del Timpano, per cui ei lo designò col nome di <emph type="italics"></emph>Timpano <lb></lb>secondario.<emph.end type="italics"></emph.end> Il modo proprio di operare di lui si rassomiglia dallo stesso <lb></lb>Scarpa al Corno acustico “ quo instrumento, egli dice, nihil similius est <lb></lb>provido artificio, quod in Secundarii Tympani commodum Natura elabora­<lb></lb>vit. </s>

<s>Id enim boni quod oscillans membrana ad basim instrumenti posita prae­<lb></lb>stat membranae Tympani in aure, illud idem membrana isthaec primarii <lb></lb>Tympani membranae Secundarii conciliat ” (De structura Fenestrae rotun­<lb></lb>dae auris, et de Tympano secundario, Mutinae 1772, pag. </s>

<s>79). </s></p><p type="main">

<s>Assegnando lo Scarpa questo nuovo uso alla membrana della Finestra <lb></lb>rotonda, e alla cavità del Timpano annessa, intendeva di perfezionare il si­<lb></lb>stema del Cotunnio, ch&#039;ei del resto approva, come lo approvarono i Fisio­<lb></lb>logi più insigni del secolo XVIII, fa&#039;quali l&#039;Haller, che sciolse le difficoltà <lb></lb>di alcuni ritrosi ad ammettere la somiglianza fra le fila nervose e le corde <lb></lb>dei musici strumenti (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V cit., pag. </s>

<s>294), e dette al nostro <lb></lb>Napoletano il titolo di <emph type="italics"></emph>Sommo.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/1425.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Ancòra Dei sensi.<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>I. Dell&#039;organo della vista; delle membrane dell&#039;occhio. </s>

<s>— II. </s>

<s>Degli umori di refrangenza nell&#039;occhio.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>III. </s>

<s>Del senso della vista<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le analogie fra il modo come funziona l&#039;Orecchio, e il modo come fun­<lb></lb>ziona l&#039;Occhio, sagacemente riscontrate dal Molinetti, e le più strette rela­<lb></lb>zioni, che si riconobbe con general maraviglia passare fra i due organi, <lb></lb>quando primo il Cotunnio dimostrò ch&#039;erano ambedue ripieni di umori, <lb></lb>aprono le vie a intendere un fatto, che ci occorre a notare, nel dar princi­<lb></lb>pio a questa nuova parte di storia. </s>

<s>Il fatto notabile è questo: che maggiori <lb></lb>difficoltà trovarono gli Anatomici nell&#039;investigar la struttura dell&#039;organo del­<lb></lb>l&#039;udito, che non di quello della vista; ond&#039;è che, mentre gli Antichi in quello <lb></lb>non andaron più là della superficial descrizione del meato uditorio esterno, <lb></lb>di questo si può dir che abbiamo la storia compiuta ne&#039;libri di Galeno. </s>

<s>Ma <lb></lb>quanto la cosa è per sè certa, altrettanto perplesse ne rimangono le ragioni, <lb></lb>perchè, se da una parte si direbbe che l&#039;udito è più eccellente della vista, <lb></lb>essendo quello quasi l&#039;ostetrico e il maestro dell&#039;intelligenza, per cui l&#039;uomo <lb></lb>sordo si ridurrebbe in istato inferiore a quello del bruto; dall&#039;altra, essendo <lb></lb>l&#039;aria, ch&#039;è il veicolo del suono, più materiale dell&#039;etere, ch&#039;è il veicolo <lb></lb>della luce, pareva che dovesse servire a quello un organo più grossolano e <lb></lb>più trattabile dagli argomenti dell&#039;arte. </s></p><p type="main">

<s>Ma è giusto nelle diverse proprietà de&#039;due elementi, che si trova la ra­<lb></lb>gione della varia struttura degli organi, e delle maggiori o minori difficoltà, <pb xlink:href="020/01/1426.jpg" pagenum="301"></pb>ch&#039;ebbe l&#039;arte a trovare in divisar dell&#039;uno e dell&#039;altro le parti. </s>

<s>Perchè, <lb></lb>dovendo l&#039;aria comunicare i suoi tremori ai nervi, conveniva fosse servita <lb></lb>da corpi atti a risentirsi con facilità a quegli stessi tremori, e perciò ebbe <lb></lb>la Natura a rinchiudere il setto, la lamina spirale e le zone dentro i duris­<lb></lb>simi ossi del Vestibolo, della Chiocciola e dei Canali semicircolari. </s>

<s>La luce <lb></lb>invece, avendo l&#039;aria non per veicolo ma per semplice mezzo, richiedeva che <lb></lb>gli umori della sua refrangenza si trovassero a contatto con quello stesso <lb></lb>mezzo, e che perciò l&#039;organo fosse esterno. </s>

<s>Di qui è che, mentre per l&#039;udito <lb></lb>si scavò dentro la Rocca petrosa quell&#039;inestricabile Labirinto, che fece di­<lb></lb>sperare i primi Anatomici di poter entrarvi addentro a esplorarlo, per la <lb></lb>vista s&#039;aprì sotto l&#039;osso frontale quelle due semplici orbite, dentro alle quali, <lb></lb>come tutto intero fu posto l&#039;occhio dalla Natura per servire al senso, così <lb></lb>tutto intero e raccolto potè estrarlo l&#039;arte, per istudiarne il maraviglioso <lb></lb>magistero. </s></p><p type="main">

<s>Que&#039;primi Anatomici, che o sui bruti o sull&#039;uomo si dettero a un tale <lb></lb>studio, ebbero a trovar facilmente che tutta la fabbrica del preziosissimo or­<lb></lb>gano si riduceva a membrane involgenti alcuni trasparentissimi umori; nè <lb></lb>men difficile era a loro avvedersi che quelle stesse membrane dipendevano <lb></lb>dal nervo ottico, il quale uscito dal suo foro s&#039;apre innanzi e si espande. </s>

<s><lb></lb>Distinguere e annoverare queste soprapposte espansioni, riconoscere la na­<lb></lb>tura diversa degli umori, la grandezza, la figura, l&#039;ordine che tengon fra <lb></lb>loro e le relazioni, erano agli Anatomici soggetto di studii, che non presen­<lb></lb>tarono grandi difficoltà, infin tanto che la scienza si contentò di aver del­<lb></lb>l&#039;Occhio una descrizione sommaria, ma quando volle investigarne quelle più <lb></lb>minute particolarità, che si comprendeva non dover essere a caso, e allora <lb></lb>s&#039;incontrarono dubbii, e incominciarono le dispute a dar soggetto alla storia. </s></p><p type="main">

<s>Quelle dispute poi e que&#039;dissensi, per ciò che specialmente concerne <lb></lb>l&#039;origine, il numero e la natura delle membrane, ebbero occasione dal con­<lb></lb>siderar le cose sotto aspetti diversi, e dal riguardar uno tutto insieme con­<lb></lb>giunto quel che un altro invece voleva separato e distinto. </s>

<s>“ Numerus tuni­<lb></lb>carum oculi, osserva a questo proposito l&#039;Acquapendente, non est apud omnes <lb></lb>certus et definitus, sed variat, non quidem re, ut dicit Galenus, sed potius <lb></lb>quia alii quasdam partes tunicis annumerant, alii seiungunt. </s>

<s>Propterea septem, <lb></lb>sex, quinque, quatuor, tres, duae denique oculorum tunicae a quibusdam re­<lb></lb>censentur ” (De oculo visus organo, Opera omnia cit., pag. </s>

<s>188). </s></p><p type="main">

<s>Celso infatti, dietro Herofilo e gli altri Anatomici greci, due dice essere <lb></lb>le tuniche degli occhi; la Cheratoide cioè e la Ragoide, in latino Uvea, alle <lb></lb>quali aggiunge l&#039;Aracnoide, per la quale intende forse la Retina, e una mem­<lb></lb>brana propria involgente il Vitreo, e poi detta Gialloidea, benchè l&#039;Autore la <lb></lb>lasci innominata. </s>

<s>“ Oculus summas habet duas tunicas, ex quibus superior <lb></lb>a Graecis <emph type="italics"></emph>Cheratoides<emph.end type="italics"></emph.end> vocatur. </s>

<s>Ea, qua parte alba est satis crassa, pupillae <lb></lb>loco extenuatur. </s>

<s>Huic inferior adiuncta est, media parte qua pupilla est, mo­<lb></lb>dico foramine concava, circa tenuis, ulterioribus partibus ipsa quoque pla­<lb></lb>nior, quae Ragoides a Graecis nominatur..... Deinde infra rursus tenuis-<pb xlink:href="020/01/1427.jpg" pagenum="302"></pb>sima tunica, quam Herophilus Aracnoides nominavit. </s>

<s>” E dopo aver descritto <lb></lb>l&#039;umor vitreo, “ id autem, soggiunge, superveniens ab interiore parte mem­<lb></lb>branula includit ” (De re medica, Parisiis 1529, fol. </s>

<s>100 ad t.). </s></p><p type="main">

<s>Galeno, che più diligentemente de&#039;suoi predecessori anatomizzò l&#039;occhio <lb></lb>nelle altre sue parti, per quel che concerne le membrane ne vide, fra la <lb></lb>Cheratoide e la Ragoide, un&#039;altra distinta col nome proprio di Coroide, e <lb></lb>così ridusse a quattro quegli involucri, specificando l&#039;Aracnoide di Herofilo <lb></lb>col nome di Corpo retiforme. </s></p><p type="main">

<s>Gli Arabi poi, per natura propria e per gl&#039;istituti aristotelici, usi a smi­<lb></lb>nuzzare la scienza, applicando i loro metodi all&#039;esame anatomico dell&#039;occhio, <lb></lb>fecero delle tre più intime membrane distinzione, fra quella parte che riman <lb></lb>di dietro, e l&#039;altra che si protende in avanti, e così colla Congiuntiva, che <lb></lb>sola riguardarono andantemente circondar tutto il globo, ridussero quelle <lb></lb>stesse membrane a sette, così, seguendo gli Arabi, dal nostro Berengario <lb></lb>annoverate per ordine e descrite: “ Prima harum..... <emph type="italics"></emph>Coniunctiva.<emph.end type="italics"></emph.end> Se­<lb></lb>cunda, diaphana et lucida ut cornu, et ideo dicitur communiter <emph type="italics"></emph>Cornea.....<emph.end type="italics"></emph.end><lb></lb>Post Corneam,.... versus latera et versus retro, correspondit una tunica <lb></lb>ipsi Corneae alligata et continua, quae vocatur <emph type="italics"></emph>Schlerotica.....<emph.end type="italics"></emph.end> Cornea et <lb></lb>schlerotica oriuntur a dura Matre..... Post istas tunicas ante est una alia <lb></lb>tunica, quae vocatur <emph type="italics"></emph>Uvea,<emph.end type="italics"></emph.end> quae occupat ante medictatem oculi tendendo <lb></lb>retro versus, et aliam medietatem occupat una tunica, quae correspondet <lb></lb>huic versus retro quae vocatur <emph type="italics"></emph>Secundina<emph.end type="italics"></emph.end> (la Coroide di Galeno), et istae <lb></lb>duae tunicae sunt simul continuae, et oriuntur ambae duae a pia Matre..... <lb></lb>Post istas tunicas, ante versus, est una alia tunica, quae vocatur <emph type="italics"></emph>Aranea,<emph.end type="italics"></emph.end><lb></lb>quia est subtilissima, cui retro correspondet una alia tunica posterior dicta <lb></lb><emph type="italics"></emph>Rhetina ”<emph.end type="italics"></emph.end> (Commentaria cit., fol CCCCLXVIII). </s></p><p type="main">

<s>Tale era la descrizione delle parti involgenti gli umori dell&#039;occhio, che <lb></lb>il Berengario tramandava al Vesalio, “ quem, esclamano ancora i lettori col <lb></lb>Colombo, mirum est in membri adeo nobilis descriptione tantopere lapsum <lb></lb>esse ” (De re anat. </s>

<s>cit., pag. </s>

<s>220). Vedremo di questi lassi nella nostra breve <lb></lb>storia gli esempii, ma perchè il Colombo stesso, nel principio del suo lib. </s>

<s>X <lb></lb><emph type="italics"></emph>De oculis,<emph.end type="italics"></emph.end> accusa di più il Vesalio anche di negligenza, si può in questo rie­<lb></lb>pilogo veder le non ingiuste ragioni di quella accusa. </s>

<s>“ Fuit itaque haec <lb></lb>Oculi partium series: humor chrystallinus; tunicula cepis pelliculae tenuis­<lb></lb>simae modo pellucida, anteriorique Chrystallini humoris sedi adnata, humor <lb></lb>vitreus in posteriori oculi sede tantum positus; tunica, in quam visorii nervi <lb></lb>substantia resolvitur, ac posteriorem humoris vitrei sedem tantum amplecti­<lb></lb>tur; tunica Uvea a tenui Cerebri membrana principium ducens; tunica, seu <lb></lb>Orbis araneae telae modo tenuis et nigricans, et interstitium vitrei humoris <lb></lb>ab aqueo; tunica dura, quae in anteriori oculi sede, cornu modo pellucida, <lb></lb>redditur; aqueus humor; septem Oculum moventes musculi; tunica adhae­<lb></lb>rens, se alba, anteriori tantum Oculi sede obnata; palpebrae, et demum ve­<lb></lb>nae et arteriae ” (De hum. </s>

<s>corporis fabrica cit., pag. </s>

<s>649). </s></p><p type="main">

<s>Più però che questa negligenza, la quale apparisce manifesta nella stessa <pb xlink:href="020/01/1428.jpg" pagenum="303"></pb>disordinata enumerazion delle parti, è disposto il Colombo a scusar l&#039;errore, <lb></lb>ch&#039;egli attribuisce all&#039;aver piuttosto il Vesalio sezionato l&#039;occhio del bruto, <lb></lb>che non quello dell&#039;uomo, la vera descrizion del quale, forse dimentico del <lb></lb>Berengario, si vanta d&#039;essere stato a darla egli il primo. </s>

<s>“ Scito praeterea <lb></lb>neminem ante me hominis oculum descripsisse, sed omnes belluinum ocu­<lb></lb>lum describere, magno et turpi errore ” (De re anat. </s>

<s>cit., pag. </s>

<s>215). </s></p><p type="main">

<s>Proponendosi dunque di dar la prima e nuova descrizione dell&#039;occhio <lb></lb>umano, distingue il Colombo sei membrane, ch&#039;egli così annovera e de­<lb></lb>scrive: “ Prima exterior est, pluribus nominibus insignita, nam Adnata, <lb></lb>Alba, Adhaerens et Coniunctiva appellatur..... Secunda oculi membrana <lb></lb>nomine caret, neque id mirum est cum hactenus incognita fuerit..... Mem­<lb></lb>brana tertia Ceratois, idest Cornea, duraque dicitur..... Arabes autem Ana­<lb></lb>tomici, unica fidelia duos parietes dealbantes, partem anteriorem Corneam, <lb></lb>quod instar cornu pelluceat, posteriorem Sclerotica, a duritie, appellarunt. </s>

<s><lb></lb>Sed una duntaxat est, non duae..... Quarta oculi membrana Uvea dici­<lb></lb>tur..... Uveae nomen sortita est, eo quod uvae granum videatur esse..... <lb></lb>Quinta oculi membrana Amphiblistroides, hoc est Retina dicta..... Sexta <lb></lb>membrana, Arachnois graece, latine Aranea dicitur, nam aranei telam prae se <lb></lb>ferre videtur ” (ibid., pag. </s>

<s>217, 18). </s></p><p type="main">

<s>Il Falloppio non si dilungò molto da questa enumerazione, e così il Pla­<lb></lb>ter, ch&#039;esplicando la figura dell&#039;occhio disegnata nella Tavola XLIX, distinse <lb></lb>le due tuniche proprie involgenti il Vitreo e il Cristallino; la Hialoides e <lb></lb>la Chrystalloides (De corporis hum. </s>

<s>structura, Basileae 1603): e così il Vidio, <lb></lb>che aggiunse alle sei del Colombo una <emph type="italics"></emph>Tunica ciliare,<emph.end type="italics"></emph.end> per cui si riducono a <lb></lb>sette, così annoverate: “ Arachnoides, Retiformis, Ciliaris, Uvea, Cornea, Al­<lb></lb>bum oculi, et ea quae oritur a chordis musculorum ” (De anat. </s>

<s>cit., pag. </s>

<s>321). <lb></lb>Ma l&#039;Acquapendente ritornò alla prima semplicità, riducendo le membrane <lb></lb>a tre: alla Sclerotica, alla quale è congiunta la Cornea, alla Coroide, dalla <lb></lb>quale dipende l&#039;Iride, e alla Retina, che si trasforma, intorno al Cristallino, <lb></lb>nella tunica Aranea. </s></p><p type="main">

<s>Non fu però questa sapiente semplicità seguita da tutti: il Molinetti per <lb></lb>esempio ritornò presso a poco alla enumerazion del Colombo, e vi tornò il <lb></lb>Ruysch, che oltre alla Vitrea e alla Cristallina, entrate già nella enumerazion <lb></lb>del Platero, aggiungendovene un&#039;altra nuova da sè scoperta, ridusse in tutte <lb></lb>quelle tuniche a otto: “ I. Adnata, seu Coniunctiva, II. Tendinea, III. Schle­<lb></lb>rotica, IV. Choroidea, V. Ruyschiana, VI. Retina, VII Vitrea, VIII. </s>

<s>Chrystal­<lb></lb>lina ” (De Oculorum tunicis, Epistola ad Christ. </s>

<s>Wedelium, Amstelodami 1720, <lb></lb>pag. </s>

<s>10). </s></p><p type="main">

<s>Verso la metà del secolo XVIII Giovanni Gotifredo Zinn, che arricchì <lb></lb>la scienza della più compiuta descrizione anatomica dell&#039;Occhio umano, ve­<lb></lb>duta la confusione, la quale nasceva forse più dalla capricciosa varietà dei <lb></lb>nomi che dalla reale distinzion delle parti, ritornò con sapiente consiglio alla <lb></lb>semplicità proposta dall&#039;Acquapendente, riconoscendo anch&#039;egli nell&#039;occhio <lb></lb>tre principali membrane, delle quali quelle, da altri descritte come distinte, <pb xlink:href="020/01/1429.jpg" pagenum="304"></pb>non sieno più che parti integranti. </s>

<s>E perchè l&#039;esempio del Zinn è oramai <lb></lb>imitato da tutti coloro, che nella semplicità ritrovano la chiarezza, noi segui­<lb></lb>remo quello stesso ordine tenuto da lui nell&#039;espor brevemente, delle tre tu­<lb></lb>niche e delle loro parti componenti, la storia. </s></p><p type="main">

<s>Fu il Colombo il primo a dare autorità a una certa opinione, che cioè <lb></lb>fossero sopra la Sclerotica distese due altre membrane, una detta Congiun­<lb></lb>tiva, e l&#039;altra rimasta Innominata, “ cum hactenus, dice esso Colombo, inco­<lb></lb>gnita fuerit ” (De re anat. </s>

<s>cit., pag. </s>

<s>217), e generata, secondo ch&#039;egli tien <lb></lb>per certo, “ a nerveis musculorum Oculi tenuitatibus ” (ibid.). I principali <lb></lb>Anatomici, succeduti nel secolo XVI a Realdo, senza disputar se la cosa fosse <lb></lb>veramente nuova, ammisero l&#039;esistenza di quella Tunica tendinosa, e il Vidio <lb></lb>fra gli altri così la descriveva: “ Vestit praedictam tunicam alia, quam effi­<lb></lb>ciunt chordae musculorum Oculum moventium, non tamen totam vestit, sed <lb></lb>usque ad nigrum oculi duntaxat, qua Schlerotica dicitur ” (De anat. </s>

<s>corp. </s>

<s><lb></lb>humani cit., pag. </s>

<s>320). Ma il Casserio e il Riolano, sui principii del se­<lb></lb>colo XVII, dop&#039;avere osservato che Galeno, nel cap. </s>

<s>II del libro X <emph type="italics"></emph>De usu <lb></lb>partium,<emph.end type="italics"></emph.end> lasciò scritto i tendini dei quattro muscoli retti “ ad anteriora Oculi <lb></lb>in unum circulum lati tendinis convenire, et propriam ibi membranam con­<lb></lb>stituere ” (Op. </s>

<s>cit., T. I, fol. </s>

<s>177), e che Carlo Stefano avea sulla Sclerotica <lb></lb>riconosciuta una tunica, nata dalle aponeurosi muscolari; negarono assolu­<lb></lb>tamente di quella stessa Tunica l&#039;esistenza. </s>

<s>Nonostante, per tutto il se­<lb></lb>colo XVII, prevalse a quella del Casserio e del Riolano la più antica auto­<lb></lb>rità del Colombo. </s>

<s>Il Molinetti fra&#039;Nostri descriveva come sottoposta imme­<lb></lb>diatamente alla Congiuntiva l&#039;Innominata “ quam expansio musculorum <lb></lb>tendinosa, protensa usque ad terminos Iridis, componit ” (Dissert. </s>

<s>anat. </s>

<s>cit., <lb></lb>pag. </s>

<s>24), e lo Spigelio e il Veslingio, fra gli stranieri, la illustrarono con <lb></lb>figure, e il Winslow le impose il nome di <emph type="italics"></emph>Albuginea<emph.end type="italics"></emph.end> accettato da molti, spe­<lb></lb>cialmente francesi. </s>

<s>Sui principii però del secolo XVIII il Senac e il Leiu­<lb></lb>taud incominciarono a dubitare, e il Zinn ebbe per cosa certa i tendini <lb></lb>“ nunquam in unum iungi, aut propriam tunicam continuam constituere <lb></lb>posse ” (Descriptio anat. </s>

<s>cit., pag. </s>

<s>15). In Italia il Valsalva, che dietro le <lb></lb>sue proprie osservazioni anatomiche sentenziava: “ Tunicam innominatam <lb></lb>nullam esse ” (Dissertatio anat. </s>

<s>II, Venetiis 1740, pag. </s>

<s>142) avrebbe rassi­<lb></lb>curato le menti, se non fosse poco dopo venuto il Morgagni a mettere scru­<lb></lb>poli con dire che se i tendini, presso alla Cornea, non si avvicinano così da <lb></lb>comporre una membrana continua, “ multo tamen propius quam putemus ” <lb></lb>(Epistola anat. </s>

<s>XVI cit., pag. </s>

<s>195). Nonostante gli Anatomici poi si assicu­<lb></lb>rarono non esser da mettere in dubbio le sentenze del Valsalva e del Zinn, <lb></lb>ma, se negarono la membrana tendinea, riconobbero collo Stenone la Scle­<lb></lb>rotica “ magna ex parte ex fibrarum motricium tendinibus esse compo­<lb></lb>sitam, quandoquidem, non modo durae tunicae vere tendineae sit conti­<lb></lb>nua, sed etiam tendines vere excipiat ” (Elem. </s>

<s>Myologiae, Florentiae 1667, <lb></lb>pag. </s>

<s>103). </s></p><p type="main">

<s>E perchè la notizia della composizion della Sclerotica dipende in mas-<pb xlink:href="020/01/1430.jpg" pagenum="305"></pb>sima parte dalla notizia dell&#039;origine di lei, è da saper che furono fra gli <lb></lb>Anatomici, intorno a questo punto, di gran dissensioni. </s>

<s>Tutti per lungo <lb></lb>tempo ritennero consenzienti con Galeno che la Sclerotica derivasse dalla <lb></lb>dura madre. </s>

<s>I dissensi propriamente cominciarono dai Francesi, in sui prin­<lb></lb>cipii del secolo XVIII, quando il Winslow e il Senac, avendo trovato colla <lb></lb>macerazione ch&#039;eran diverse le fila, di che s&#039;intesse la Sclerotica, da quelle <lb></lb>con le quali la dura Madre si compila; dissero che essa Sclerotica era una <lb></lb>membrana propria e peculiare dell&#039;Occhio, strettamente congiunta coll&#039;invo­<lb></lb>lucro che, derivato dalla dura madre stessa, accompagna e invagina il nervo. </s></p><p type="main">

<s>Il Valsalva uscì fuori in mezzo a quei dissensi con una nuova propo­<lb></lb>sta, dicendo che dal concorso di tutte le fibre de&#039;muscoli motori dell&#039;Occhio <lb></lb>si componeva un anello tendineo carnoso, da cui il nervo, nel suo primo <lb></lb>ingresso nell&#039;orbita, e la Pia madre, che all&#039;esterno l&#039;investe, sono con <lb></lb>stretto vincolo legati insieme. </s>

<s>Di qui ne deduce tre conseguenze “ iis omnino <lb></lb>contraria, quae ab Anatomicis fere passim in scholis traduntur ” la seconda <lb></lb>delle quali è “ Scleroticam non a dura matre, sed a tendinibus musculorum <lb></lb>oculi, et a pia Meninge ortum ducere ” (Dissertatio II cit., pag. </s>

<s>142). </s></p><p type="main">

<s>Ripensando il Zinn a queste novità introdotte nell&#039;Anatomia dell&#039;occhio <lb></lb>dal nostro insigne Italiano, ebbe, dietro alle sue diligentissime osservazioni, <lb></lb>a confessare non essere i limiti tra la vagina del nervo ottico e l&#039;origine <lb></lb>della Sclerotica così insensibili e oscuri, da lasciar luogo ai dubbi. </s>

<s>“ Scle­<lb></lb>rotica enim in fundo crassior, non ex mutata et sensim incrassata dura <lb></lb>matre nascitur, sed leniter prominulo, rotundo, nervum versus convexo, ad <lb></lb>minimum octies crassiori involucro nervi, circa eius insertionem oritur, nervo, <lb></lb>quem uti annulus digitum, arcte complectitur ” (Descriptio oculi hum. </s>

<s>cit., <lb></lb>pag. </s>

<s>10, 11). Per quel poi riguarda l&#039;origine dalla pia Meninge, si studia <lb></lb>il Zinn di interpetrare le idee del Valsalva, come divinatrici della tunica sco­<lb></lb>perta da Niccolò Le Cat, il quale affermava che la pia madre, dopo la con­<lb></lb>trazione del nervo ottico, si divide in due lamine, una delle quali va alla <lb></lb>Coroide e l&#039;altra si applica alla solida interna faccia della Sclerotica e la <lb></lb>tappezza. </s>

<s>“ Num Valsalva, son le parole proprie dell&#039;Anatomico di Gottinga, <lb></lb>forte iam simile quid vidit, ubi Scleroticam, non ex dura matre, sed ex pia <lb></lb>meninge tendinibusque musculorum oriri scripsit? </s>

<s>” (ibid., pag. </s>

<s>13). </s></p><p type="main">

<s>Galeno, nel cap. </s>

<s>III del X libro <emph type="italics"></emph>De usu partium,<emph.end type="italics"></emph.end> in ciò consenziente <lb></lb>con gli Anatomici suoi predecessori, aveva detto che la Sclerotica, giunta a <lb></lb>mezzo l&#039;occhio, dalla parte anteriore s&#039;assottiglia, e divien più spessa e pel­<lb></lb>lucida come un corno. </s>

<s>“ Cum enim crassa quidem esset admodum haec tu­<lb></lb>nica, sed densa minus quam usus flagitabat, tenuiorem simul ac densiorem <lb></lb>coepit producere. </s>

<s>Post autem paulatim promovens, partem eius maxime me­<lb></lb>diam longe tenuissimam ac densissimam efficit. </s>

<s>Apte diceres eam cornibus <lb></lb>admodum extenuatis similem, unde ei nomen ” (Op. </s>

<s>omnia cit., f. </s>

<s>178). </s></p><p type="main">

<s>Questa connessione e questa origine della Cornea dalla Sclerotica era <lb></lb>tenuta certa dalla maggior parte degli Anatomici, quando venne il Falloppio <lb></lb>a metterla in dubbio, dicendo non si poter persuadere “ Corneam esse tu-<pb xlink:href="020/01/1431.jpg" pagenum="306"></pb>nicae durioris partem, quae a dura cerebri meninge erigitur, cum non so­<lb></lb>lum substantia, sed et crassitie et figura differat ” (Observat. </s>

<s>an., Op. </s>

<s>omnia <lb></lb>cit., pag. </s>

<s>478). L&#039;autorità del grande Anatomico tenne per lungo tempo in­<lb></lb>certa la scienza, infin tanto che gli Accademici parigini, sui principii del <lb></lb>secolo XVIII, non dimostrarono chiaramente congiungersi la Cornea colla <lb></lb>Sclerotica negli occhi di un lupo cerviero. </s>

<s>Non si erano ancora diffusi gli <lb></lb>atti dell&#039;Accademia, nè s&#039;era ancora divulgato il trattato del Brisseau in <lb></lb>Italia, quand&#039;occorse al Morgagni di far negli occhi de&#039;bovi, e poi anche <lb></lb>degli uomini, quella stessa scoperta. </s>

<s>“ Haud scio an res adhuc satis de­<lb></lb>scripta fuerit, sed ego certe, priusquam de ipsa aliquid ex Commentariis <lb></lb>Regiae scientiarum Academiae parisiensis intellexissem, nam cl. </s>

<s>Brissaei vi­<lb></lb>dere tractatum nondum potui, in boum oculis, communibus scleroticae et <lb></lb>corneae perlustratis finibus, sic inveneram opacam ibi illius substantiam <lb></lb>huius pellucidae substantiae impositam, utramque autem sensim, quo magis <lb></lb>progreditur, eo magis extenuatam, sic inter se committi, ut quantum exte­<lb></lb>rius Sclerotica excrescit ad corneam ellypticis oris contegendam, tantum in­<lb></lb>terius producatur Cornea ad Scleroticam circulari ambitu occupandam ” (Epi­<lb></lb>stola anat. </s>

<s>XVII, pag. </s>

<s>251, 52). </s></p><p type="main">

<s>Queste osservazioni, confermate poi da tanti altri, rendevano certi della <lb></lb>identità di natura che passa fra la Sclerotica e la Cornea, ma restava di <lb></lb>sodisfare alla curiosità di chi avrebbe voluto sapere in che modo, dall&#039;opa­<lb></lb>cità dell&#039;una si passasse alla perfetta trasparenza dell&#039;altra. </s>

<s>Il fatto noto di <lb></lb>alcuni corpi che imbevuti di acqua divengon diafani, avrebbe potuto pre­<lb></lb>parar la risposta, ma intanto non se ne vide l&#039;analogia, nè si pensò di farne <lb></lb>l&#039;applicazione all&#039;occhio, se non che verso la metà del secolo XVIII, dopo <lb></lb>essersi fatta della cornea una più sottile anatomia. </s>

<s>La struttura lamellare di <lb></lb>lei fu riconosciuta infino dagli antichissimi tempi, cosicchè l&#039;Acquapendente, <lb></lb>nel darne l&#039;appresso descrizione, citava Ruffo Efesino. </s>

<s>“ Et quamvis, egli <lb></lb>dice giusto della Cornea, tenuis sit tunica, ut diaphana sit, non tamen sim­<lb></lb>plex censenda est, sed triplex, quadruplexque conspicitur, quasi ex pluribus <lb></lb>corticibus constare videatur, cum laminae, quarum una alteri superposita est <lb></lb>valdeque adhaeret, multae sint ” (De oculo cit., pag. </s>

<s>189). </s></p><p type="main">

<s>La prima e importante novità scoperta in tal proposito dagli Anatomici <lb></lb>più recenti è dovuta allo Stenone, il quale dice nel suo trattato <emph type="italics"></emph>De muscu­<lb></lb>lis et glandulis:<emph.end type="italics"></emph.end> “ Semel iterumque in Cornea observavi, non sine admi­<lb></lb>ratione, poros quandam aquei humoris transmittentes partem ” (Amstelo­<lb></lb>dami 1664, pag. </s>

<s>49). Il Leuwenoeck poi confermò la scoperta stenoniana, <lb></lb>dimostrando che la cornea compressa trasuda un umor rugiadoso che l&#039;ap­<lb></lb>panna. </s>

<s>Nè egli però, nè lo stesso Stenone seppero decider se fosse un tale <lb></lb>umore espresso dalla sostanza della Cornea, o vi trapelasse dall&#039;interno del­<lb></lb>l&#039;occhio. </s>

<s>“ Vidi quidem per poros exeuntem humorem, sed ipsine tunicae <lb></lb>adscribendus substantiae, an ab inclusa aqua deducendus, non facile ante <lb></lb>ulterius examen determinavero ” (ibid.). </s></p><p type="main">

<s>Se questo ulteriore esame fosse poi fatto non sappiamo, ma è certo in <pb xlink:href="020/01/1432.jpg" pagenum="307"></pb>ogni modo che rimase dubbia la scienza intorno all&#039;origine di quell&#039;acqua <lb></lb>trasudata dalla Cornea compressa, infino a che il Morgagni, esaminando certe <lb></lb>schedule lasciate dal Valsalva, non vi trovò scritto: “ Corneam ex diversa <lb></lb>duplici constare substantia, tenuibus membranis duabus eiusdem naturae, et <lb></lb>substantia his interiecta, quae videtur spongiosa ” (Epistola anat. </s>

<s>XVI cit., <lb></lb>pag. </s>

<s>200). In questa così fatta sostanza spugnosa pensò allora lo stesso Mor­<lb></lb>gagni che risedesse l&#039;umor veduto stillare dallo Stenone, e più copiosamente <lb></lb>espresso dal Leuwenoeck, di cui volle ripetere l&#039;esperienze: “ Quod si forte <lb></lb>quaeras de hoc humore quid ipse adnotaverim, respondere possum in plu­<lb></lb>ribus humanis oculis expertum esse an comprimendo exprimerem, ex illis­<lb></lb>que omnibus expressisse: ad singulas enim compressiones madore quodam, <lb></lb>quasì opaco velo, corneae facies obducebatur, qui mox abstersus, continuo <lb></lb>ad novam compressionem redibat ” (ibid., pag. </s>

<s>201). </s></p><p type="main">

<s>A qual fine però introdusse la natura, fra le lamelle cornee, quella so­<lb></lb>stanza cellulare o spugnosa atta a imbevere e a ritenere in sè l&#039;acqua, fu <lb></lb>primo a investigarlo il Zinn, il quale riuscì per questa via a sciogliere il pro­<lb></lb>blema della trasparenza della Cornea. </s>

<s>“ A qua ipsa cellulosa, aqua ebria, <lb></lb>egli dice, pelluciditatem corneae unice pendere fere crediderim ” (Descriptio <lb></lb>Oculi cit., pag. </s>

<s>20). </s></p><p type="main">

<s>La cornea è per la sua trasparenza, diciamo così, quasi la porta mae­<lb></lb>stra che introduce nell&#039;interno dell&#039;occhio, dove son la Coroide e la Retina <lb></lb>deputati principali ministri a celebrare i naturali misteri. </s>

<s>I più antichi Ana­<lb></lb>tomici greci, confondendo questa seconda membrana coll&#039;Aracnoide, distin­<lb></lb>sero la prima col nome di Ragoide, che insieme colla Sclerotica, alla quale <lb></lb>immediatamente soggiace, forma per essi il principale involucro dell&#039;occhio. </s>

<s><lb></lb>Anche Celso, seguendo queste dottrine, dop&#039;aver descritta la Cheratoide, <lb></lb>soggiunge: “ Huic inferior adiuncta est, media parte qua pupilla est, medio <lb></lb>foramine concava, circa tenuis, ulterioribus ipsa quoque plenior, quae Ra­<lb></lb>goides a graecis nominatur ” (De re med. </s>

<s>cit., fol. </s>

<s>100 ad t.). </s></p><p type="main">

<s>Il nome proprio di Coroide par che fosse primo a introdurlo nel lin­<lb></lb>guaggio scientifico Galeno, il quale designava con esso tutta la parte poste­<lb></lb>riore della tunica, riserbando il nome di Ragoide a sola quella parte anteriore, <lb></lb>che Ruffo appellò <emph type="italics"></emph>Iride,<emph.end type="italics"></emph.end> ed egli <emph type="italics"></emph>Tunica cerulea.<emph.end type="italics"></emph.end> “ Ibi nam Tunicam cae­<lb></lb>ruleam, Ragoide dico, hoc est viniformem seu vineam pertudit. </s>

<s>Appellant <lb></lb>autem ipsam ita, acino uvae levitatem eius externam et asperitatem inter­<lb></lb>nam opinor comparantes ” (De usu partium, Op. </s>

<s>omnia cit., fol. </s>

<s>179). La <lb></lb>comparazione però tra la buccia, o il fiocino dell&#039;uva, proprissima nelle de­<lb></lb>scrizioni di Herofilo e di Celso, nelle descrizioni galeniche diventa impropria, <lb></lb>e da questa improprietà nacquero alcune confusioni, che dai semplici nomi <lb></lb>passarono nelle cose. </s>

<s>Coloro infatti, che prendevano a rigore la compara­<lb></lb>zione tra l&#039;Uvea e la Coroide, intendevano che l&#039;Iride fosse una continua­<lb></lb>zione della Coroide stessa, mentre quegli altri, che pur seguitarono a chia­<lb></lb>mar uvea la sola parte anteriore, la quale veramente, presentandosi sotto <lb></lb>l&#039;aspetto di un cerchio, non rende altra immagine del fiocino dell&#039;uva, se <pb xlink:href="020/01/1433.jpg" pagenum="308"></pb>non forse nel colore; passarono facilmente a riguardarla come una mem­<lb></lb>brana distinta. </s></p><p type="main">

<s>Le novità che introdusse il Mariotte nell&#039;organo della visione, resero, <lb></lb>verso la metà del secolo XVII, di grande importanza la sentenza data da <lb></lb>tutti gli Anatomici concordi intorno alla origine della Coroide dalla pia madre <lb></lb>del nervo. </s>

<s>E perchè, quando fosse stata quella sentenza falsa, tutto il si­<lb></lb>stema del Mariotte cadeva, si dettero i fautori ogni più sollecito studio di <lb></lb>confermarla. </s>

<s>Porse uno de&#039;principali argomenti a cotesta conferma Federico <lb></lb>Ruyschio, il quale, iniettando un giorno le arterie coroidee, sentì colla mano <lb></lb>la tela de&#039;vasi staccarsi da un&#039;altra tela. </s>

<s>“ Hoc a me viso, scrive nella ci­<lb></lb>tata Epistola XIII a Cristiano Wedelio, suspicari coepi annon Tunica cho­<lb></lb>roidea esset gemina, et artificio quodam in duas lamellas separabilis. </s>

<s>Hoc <lb></lb>ex voto bis successit, et portionem satis magnam a Choroidea separabam, <lb></lb>per quam, aeque bene ac per Choroidem, observabam arterias peculiares di­<lb></lb>verso reptatu repantes esse dispersas ” (pag. </s>

<s>13). Facendo poi di ciò pub­<lb></lb>blica dimostrazione, sentì il bisogno che aveva la nuova tunica scoperta di <lb></lb>un nome. </s>

<s>“ Itaque filius meus Henricus proponebat nomen <emph type="italics"></emph>Tunicae ruy­<lb></lb>schianae,<emph.end type="italics"></emph.end> cui calculum apponebam ” (ibid.). </s></p><p type="main">

<s>A una tale scoperta dunque esultarono i seguaci del Mariotte, perchè <lb></lb>là dove prima nell&#039;assegnar le origini della Coroide pareva che rimanesse <lb></lb>l&#039;Aracnoide inutile, ora s&#039;intendeva come, derivando da questa la sola pa­<lb></lb>gina esterna, ossia la Coroide propria, dalla pia madre schietta si produ­<lb></lb>cesse la Ruischiana. </s>

<s>Come al Mariotte però così al Ruyschio non mancarono <lb></lb>contradittori, fra&#039;quali uno de&#039;più fieri fu il Rau, ma perchè in cosa di non <lb></lb>lieve importanza parevano le contese riuscir troppo dannose ai progressi <lb></lb>della scienza, si levarono alcuni autorevoli giudici, fra&#039;quali il nostro Mor­<lb></lb>gagni. </s>

<s>Egli, accennando a Francesco Sylvio e al Casserio, ch&#039;ebbero della <lb></lb>Ruischiana qualche presentimento, rammemorava che il Guenellon, infino <lb></lb>dal 1686, aveva trovata duplice la membrana coroidea ne&#039;pesci, e narrando <lb></lb>le esperienze sue proprie fatte sui bovi, e sopra simili altri animali, “ non <lb></lb>difficulter, ei dice, eae laminae sunt divulsae. </s>

<s>Et divulsarum facies, quam­<lb></lb>vis non omnino, sic satis tamen fuerunt aequales, ut proclive esset intelli­<lb></lb>gere eam separationem, si peculiare aliquod accederet anatomicum artifi­<lb></lb>cium, longe melius esse successuram. </s>

<s>Quo facilius adducor ut credam, excel­<lb></lb>lenti in eiusmodi administrationibus Ruyschio, aliisque eius viam rationemque <lb></lb>callentibus, rem hanc felicissime provenire ” (Epist. </s>

<s>anat. </s>

<s>XVII cit., pag. </s>

<s>243). <lb></lb>Queste parole però, se persuasero tutti potersi la Coroide sdoppiare nei bruti, <lb></lb>lasciavano riguardo all&#039;uomo alcuni ragionevoli dubbii, ond&#039;è che il Zinn fra <lb></lb>gli altri confessò non potersi ancora persuadere “ in oculo humano Choroi­<lb></lb>dem ex duabus lamellis aut pluribus esse compositam ” (Descriptio oculi <lb></lb>cit., pag. </s>

<s>53), e di qui incominciò la Ruischiana ad andare in dimenticanza. </s></p><p type="main">

<s>La dubbiosa scoperta del Ruysch ebbe, per coloro che la tennero certa, <lb></lb>una grande efficacia rispetto al determinar le origini dell&#039;Iride, e dei Corpi <lb></lb>ciliari, dicendo esser quella una propaggine della pagina coroidea esterna, e <pb xlink:href="020/01/1434.jpg" pagenum="309"></pb>questi una continuazione della pagina interna. </s>

<s>Ma quelle due appendici della <lb></lb>Coroide, i corpi ciliari vogliam dire e l&#039;iride, hanno tanta importanza come <lb></lb>organi della vista, che non può tacersi da noi la loro particolare storia. </s></p><p type="main">

<s>Scrisse Galeno, come cosa avuta da&#039;suoi predecessori, che dalla Coroide <lb></lb>si partono <emph type="italics"></emph>tenues quaedam productiones, et araneae similes,<emph.end type="italics"></emph.end> le quali giun­<lb></lb>gono a toccare il cristallino, a cui fanno da ligamento. </s>

<s>Tu diresti, ei sog­<lb></lb>giunge, che fossero que&#039;sottilissimi processi altrettanti vasellini da recare <lb></lb>allo stesso cristallino il necessario alimento, se non si vedessero ritornare <lb></lb>indietro alla loro prima inserzione. </s>

<s>“ Revertitur nam immensam vasorum <lb></lb>tenuium sibi ipsis proprinquorum copiam quandam afferens, cum quibus <lb></lb>omnibus sursum in superiorem productionem inseritur, ut eorum insertio <lb></lb>palpebrarum pilis persimilis esse videatur. </s>

<s>Sic enim comparant, idque meo <lb></lb>iudicio non absurde, qui Naturae opera studiosius perscrutantur.... Cum <lb></lb>enim praedicta insertio in medium crystallinum, quod rotundum est, undi­<lb></lb>que facta sit, circulus necessarius est factus, qui certe maximus est in chry­<lb></lb>stallino, ipsumque in duo dividit ” (De usu partium, Op. </s>

<s>omnia, T. </s>

<s>I cit., <lb></lb>fol. </s>

<s>178). </s></p><p type="main">

<s>Nella risorta Anatomia, tacendosi dal Berengario di questo anello ci­<lb></lb>liare, che tutto intorno circonda il cristallino, fu primo a rinnovellarne la <lb></lb>memoria il Vesalio. </s>

<s>Raffigurando mostruosamente l&#039;Occhio in un circolo, <lb></lb>alla circonferenza del quale è, quasi per due anse, ricongiunto un altro cer­<lb></lb>chio concentrico, assai minore, e per cui viene inteso il cristallino; son quelle <lb></lb>due anse, colla lettera di richiamo K, così dichiarate: “ Tunica ab Uvea <lb></lb>initium ducens, et ciliis seu palpebrarum pilis imagine correspondens, ac <lb></lb>interstitium pariter vitrei humoris ab aqueo ” (De hum. </s>

<s>corp. </s>

<s>fabrica cit., <lb></lb>pag. </s>

<s>643). </s></p><p type="main">

<s>Al sentir così i processi ciliari qualificarsi per una tunica, che fa da <lb></lb>tramezzo all&#039;umor vitreo e all&#039;acqueo, il Colombo disse che il Vesalio aveva <lb></lb>sognato, non essendo quelli presi per cigli altro che rughe impresse nel­<lb></lb>l&#039;Aracnoide, da quella parte che involge il cristallino. </s>

<s>“ Atque hae solae <lb></lb>sunt verae oculi membranae; quare ne expectetis dum ego de illa loquar <lb></lb>membrana instar ciliorum, quam Vesalius somniavit, nam lineae illae, quae <lb></lb>humorem cristallinum circumstant, in hac, quam paulo ante descripsimus <lb></lb>Aranea, collocantur ” (De re anat. </s>

<s>cit., pag. </s>

<s>218). </s></p><p type="main">

<s>Ma il Falloppio esaminò la cosa con più diligenza, e benchè convenisse <lb></lb>col Colombo non esser quella descritta dal Vesalio una tunica vera, la ri­<lb></lb>conobbe nonostante per un corpo reale intessuto di fila, da rassomigliarsi <lb></lb>benissimo ai cigli impiantati sulle palpebre, che servissero a tener legate <lb></lb>insieme l&#039;uvea e la membrana estrema del cristallino. </s>

<s>“ In ciliari corpore <lb></lb>illo, quod inter uveam et humorem crystallinum ac vitreum intercedit, a di­<lb></lb>vino Vesalio discrepo. </s>

<s>Quia tunica minime est, sed potius nexus aut liga­<lb></lb>mentum, quo Uvea iungitur extremae membranae crystallini. </s>

<s>Ideo non est <lb></lb>dicendum tunica, neque pro tunica numerandum, sed potius pro ligamento <lb></lb>quod nos <emph type="italics"></emph>Ciliare<emph.end type="italics"></emph.end> vocabimus ” (Observat. </s>

<s>anat, Op. </s>

<s>omnia cit., pag. </s>

<s>479). </s></p><pb xlink:href="020/01/1435.jpg" pagenum="310"></pb><p type="main">

<s>Anche l&#039;Eustachio, nelle figure 8 e 9 della Tavola XL, disegnò, per cor­<lb></lb>reggere l&#039;errore del Vesalio, i corpi ciliari, a quel modo che gli aveva de­<lb></lb>scritti il Falloppio, ma l&#039;Acquapendente, non approvando così fatte novità, <lb></lb>tornò col Colombo a dire che quegli immaginati corpi ciliari non son altro <lb></lb>che le vestigia delle fibre nere dell&#039;uvea lasciate impresse sulla tunica re­<lb></lb>tina, meglio che sul cristallino. </s>

<s>“ Comminiscuntur nescio quam ciliarem tu­<lb></lb>nicam Anatomici circa crystallinum, quae circulus et copula tunicarum est, <lb></lb>quae nulla alia sunt quam nigra uveae tunicae fibrarum vestigia in crystal­<lb></lb>linum, aut potius in retinam tunicam impressa ” (De oculo, Op. </s>

<s>omnia cit., <lb></lb>pag. </s>

<s>190). </s></p><p type="main">

<s>Parve il Casserio a parole consentire coll&#039;Acquapendente, ma poi nelle <lb></lb>figure 7 e 9 della Tavola V dipinse, in ciò molto superiore all&#039;Eustachio, <lb></lb>con mirabile verità, e il primo fra gli Anatomici, i corpuscoli oblonghi, dai <lb></lb>quali, disposti a modo di raggi, s&#039;intesse il corpo ciliare, e che più tenui <lb></lb>dalla parte convessa del giro, e dalla parte concava più crassi, danno allo <lb></lb>stesso corpo ciliare quasi la composizion di due anelli. </s>

<s>Non essendo però <lb></lb>gl&#039;Iconismi dichiarati da nessuna parola, e quelle espresse nel testo facendo <lb></lb>l&#039;Autore consenziente col Colombo e col Fabrizio, si rimase la cosa inespli­<lb></lb>cata, infintantochè non l&#039;avvertì il Morgagni, riscontrando quegli stessi cas­<lb></lb>seriani iconismi nell&#039;autopsia. </s>

<s>“ Quarum rerum omnium, cum Auctor nul­<lb></lb>lam, non modo descripsisset, verum ne indicasset quidem, non ante illas <lb></lb>animadverti quam in bovillis oeulis ipse adnotassem ” (Epist. </s>

<s>anat. </s>

<s>XVII <lb></lb>cit., pag. </s>

<s>253, 54). </s></p><p type="main">

<s>Ma forse avea prima del Morgagni avvertite queste stesse cose Giovan <lb></lb>Batista Verle, che venuto da Venezia ai servigi della Corte medicea, nel ve­<lb></lb>der lo Stenone sezionare alla presenza del granduca Ferdinando II l&#039;occhio <lb></lb>di un coniglio, s&#039;invogliò dello studio di quel mirabile organo, intorno al <lb></lb>quale scrisse un opuscolo di poche pagine, pubblicato nel 1679 in Firenze <lb></lb>col titolo <emph type="italics"></emph>Anatomia artifiziale dell&#039;occhio umano.<emph.end type="italics"></emph.end> Fu la novità ricevuta con <lb></lb>tanto applauso, che per diffonderla anche fra gli stranieri si pensò di tra­<lb></lb>durre il detto opuscolo in latino, e il Mangeto lo reputò meritevole d&#039;essere, <lb></lb>sotto questa forma, inserito nella sua scelta Biblioteca. </s></p><p type="main">

<s>Anche il Verle dunque disegnò e descrisse con molta verità i corpi ci­<lb></lb>liari, anzi andò tanto per le minute da contarne a una a una le fibre e le <lb></lb>semifibre, riducendole al preciso numero di ottanta (Anatomia artif. </s>

<s>cit., <lb></lb>pag. </s>

<s>33 e 35). </s></p><p type="main">

<s>Il Morgagni però, poco curandosi di così fatte minuzie, ne&#039;§§ XI-XVI <lb></lb>dell&#039;Epistola anatomica XVII, insegnò molte cose nuove e utilissime intorno <lb></lb>al vero sito, alla connessione, all&#039;origine de&#039;corpi ciliari e alla loro strut­<lb></lb>tura, descrivendoli particolarmente nell&#039;uomo come circondanti il Cristallino <lb></lb>a guisa di una elegantissima corona, da non potersi rassomigliar meglio che <lb></lb>al disco di un fiore raggiato, in cui sieno tutti i petali della stessa lunghezza. <lb></lb></s>

<s>“ Quin etiam interdum accidit, idque in homine, ut depositum cum vitreo <lb></lb>humorem crystallinum elegantissima corona, quasi radiati floris discum, ae-<pb xlink:href="020/01/1436.jpg" pagenum="311"></pb>qualibus omnibus et consimillimis oblongis petalis circumcirca ornatum, <lb></lb>conspexerim ” (Epist. </s>

<s>cit, pag. </s>

<s>255). </s></p><p type="main">

<s>Rivendicata così dunque alla scienza la verità di quella corona di cigli, <lb></lb>che avevano intorno al cristallino descritta gli Anatomici antichi, si doman­<lb></lb>dava qual fosse di que&#039;cigli la propria e particolare struttura. </s>

<s>Vedemmo come <lb></lb>Galeno gli qualificasse per vasi, ma l&#039;ufficio e la denominazione di lega­<lb></lb>mento, dato a loro poi dal Falloppio, gli fece facilmente credere di natura <lb></lb>muscolosa a coloro che, per la teorica della visione, introdussero nel cristal­<lb></lb>lino una certa mutabilità di sito e di figura. </s>

<s>Le autorità del Keplero e del <lb></lb>Cartesio erano sì grandi, e le loro teorie ottiche apparivano così seducenti, <lb></lb>che si tennero i corpi ciliari per un composto di fibre muscolose inserite <lb></lb>nel cristallino, senza troppo controversie, infino ai tempi del Bocrhaave, il <lb></lb>quale affermò di aver più volte vedute e riconosciute nell&#039;occhio quelle stesse <lb></lb>fibre (Institutiones med., Venetiis 1722, pag. </s>

<s>65). Il Winslow incominciò a <lb></lb>dubitarne, e l&#039;Hoow, non punto timoroso di tornare all&#039;antico Galeno, disse <lb></lb>esser que&#039;cigli intorno al cristallino, non fibre muscolari, ma vasi. </s>

<s>L&#039;Haller <lb></lb>secondò in principio la dottrina del venerato Maestro, poi parve esitare, e <lb></lb>all&#039;ultimo, trattando nel Tomo V degli Elementi di Fisiologia del corpo ci­<lb></lb>liare, sentenziò: “ Musculosi nihil quidquam habet ” (Editio cit., pag. </s>

<s>382). </s></p><p type="main">

<s>Così i Ruischiani, che facevano i ciliari e l&#039;iride derivare dalla Coroide, <lb></lb>come tutti coloro, che vedevano, in ogni modo fra&#039;due organi una grande <lb></lb>somiglianza di struttura, pigliarono argomento di negar l&#039;esistenza delle fibre <lb></lb>muscolose in essi corpi ciliari, perchè vedevano mancarne l&#039;Iride stessa. </s>

<s>Que­<lb></lb>sta, ne&#039;misteriosi silenzi eloquente rivelatrice de&#039;più intimi affetti, prima di <lb></lb>lasciarsi lacerare al ferro invitò sempre gli Anatomici a contemplarne le di­<lb></lb>vine bellezze. </s>

<s>Dalla più rimota antichità, che risale oltre a Ruffo, ebbe il <lb></lb>nome di Iride “ a coelestis Iridis, dice il Colombo, similitudine translatum ” <lb></lb>(De re anat. </s>

<s>cit., pag. </s>

<s>217), e Galeno, che fu de&#039;più infervorati in quelle <lb></lb>estetiche contemplazioni, fu de&#039;primi altresì a filosofarvi attorno, esponendo <lb></lb>un certo suo singolare concetto, che trovò poi nel Vidio il più fedele com­<lb></lb>mento. </s>

<s>“ Scire autem licet circulum illum, qui in priore parte Oculi, inter <lb></lb>album et nigrum, deprehenditur, a coloris varietate Iridem appellari. </s>

<s>Effi­<lb></lb>ciunt hanc varietatem septem substantiae, quae ibi inter se committuntur: <lb></lb>prima, ut ab externa parte incipias, est album oculi, secunda est tunica orta <lb></lb>a chordis musculorum, tertia cornea, quarta uvea, quinta retiformis, sexta <lb></lb>humor crystallinus, septima humor vitreus ” (De anat. </s>

<s>corp. </s>

<s>hum. </s>

<s>cit., <lb></lb>pag. </s>

<s>321) </s></p><p type="main">

<s>Ma il primo a dare delle colorate apparenze dell&#039;Iride una spiegazione <lb></lb>originale crediamo sia stato il Molinetti, il quale attribuisce quella diversità <lb></lb>di colori alle varie riflessioni subite dalla luce nell&#039;incontrarsi in quelle mol­<lb></lb>teplici superficie presentate dai ligamenti ciliari. </s>

<s>“ Decernendum est discri­<lb></lb>mina huiusmodi oriri.... ex diversa proportione superficierum, in quas lu­<lb></lb>men incidit, aut etiam quas traiiciit, non alia certe ratione quam columbarum <lb></lb>collo refulgentes observamus varios colores ” (Dissertationes anat. </s>

<s>cit., pag. </s>

<s>23). </s></p><pb xlink:href="020/01/1437.jpg" pagenum="312"></pb><p type="main">

<s>Il Valsalva, secondo riferisce il Morgagni, tutto intento alla contempla­<lb></lb>zione di quella mirabile rete di vasi, che ricorrono per tutta la sostanza della <lb></lb>Coroide, credeva “ non exiguam Iridis portionem et coloris varietatem haud <lb></lb>aliunde quam a varia sanguiferorum vasculorum divisione ac complicatione <lb></lb>esse repetendam ” (Epist. </s>

<s>anat. </s>

<s>XVII cit., pag. </s>

<s>244). Ma l&#039;Haller, dop&#039;aver <lb></lb>descritti que&#039;fiocchi, che si vedono vivamente fiammeggiare sulla lamina este­<lb></lb>riore dell&#039;Iride, e che dice essere di una sorprendente bellezza, “ ab his <lb></lb>flocculis ostendimus, ne conclude, colores Iridis pendere ” (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V <lb></lb>cit., pag. </s>

<s>369). </s></p><p type="main">

<s>Prende parte a variare il tuono di cotesti colori il pigmento disteso sulla <lb></lb>lamina interiore dell&#039;Iride, e che è comune ai corpi ciliari e a tutta la Co­<lb></lb>roidea. </s>

<s>Tal pigmento, osservò l&#039;Acquapendente, non solo tinge e macchia <lb></lb>del suo color nero, “ sed etiam, si abluatur, nigrities fere omnis abolitur, <lb></lb>et membrana cui inhaeret alba evadit, ut proinde non alium quam adsciti­<lb></lb>tium huiusmodi nigrum colorem, si velis, nominare possis. </s>

<s>Cui quidem illud <lb></lb>rarius accidit quod hic color niger adscititius ubique non est. </s>

<s>Nam qua parte <lb></lb>Uvea et Choroides crystallinum, aqueum, corneam et omnino diaphana pu­<lb></lb>raque oculorum corpora respiciunt, nigrities apparet, potius innata quam <lb></lb>apposita.... Unde tota Choroides hac parte tantum tingit qua Sclerotica con­<lb></lb>tigua est. </s>

<s>Uvea vero neutrobique, cum interna facie aqueum humorem, <lb></lb>externa vero corneam respiciat contingatque ” (De oculo, Op. </s>

<s>omnia cit., <lb></lb>pag. </s>

<s>226). </s></p><p type="main">

<s>Il Morgagni, che avrebbe desiderato fosse veramente così, perchè allora <lb></lb>s&#039;intenderebbe come, in tanto rimescolarsi dell&#039;umor acqueo per le sue ca­<lb></lb>mere, non rimanesse tinto di nero, trovò per esperienza che anche sull&#039;Iride <lb></lb>il pigmento era ascitizio, per cui credè bene d&#039;accostarsi con coloro che di­<lb></lb>cevano “ nigram materiam non extrinsecus insidere Choroidi, sed laminae <lb></lb>exteriori subiectam, per hanc translucere ” (Epist. </s>

<s>cit., pag. </s>

<s>254, 55). </s></p><p type="main">

<s>Stimò l&#039;Acquapendente che fosse l&#039;atramento coroideo escreto come fec­<lb></lb>cia dal sangue, e non ritrovandosi nell&#039;occhio manifesti organi secretori, ri­<lb></lb>mase lungamente quella origine incerta, infintantochè il Zinn non la rico­<lb></lb>nobbe in quei filamenti fioccosi, ch&#039;ei vide scaturire dalla faccia interna della <lb></lb>Membrana. </s>

<s>“ Quae cum ita sint, coniectura non parum inde confirmare vi­<lb></lb>detur ex iisdem flocculis secerni pigmentum nigrum Choroidi obductum ” <lb></lb>(Descriptio oculi cit., pag. </s>

<s>48). </s></p><p type="main">

<s>Questo è ciò che riconobbero i Filosofi contemplativi intorno alla ele­<lb></lb>gante varietà dei colori, che dipingono all&#039;occhio il sottoposto ovario e gli <lb></lb>aperti petali del suo fiore. </s>

<s>Ma quando s&#039;accorsero che quel fiore ora apriva, <lb></lb>ora chiudeva la sua corolla, per consolar gl&#039;interiori spiriti sensitivi d&#039;una <lb></lb>più soave temperanza dì luce, e allora non perdonarono alla punta del ferro <lb></lb>anatomico, che ne ricercò la più intima testura delle fibre. </s>

<s>Perchè dunque <lb></lb>fu questa anatomia dell&#039;Iride principalmente provocata dal singolar fatto <lb></lb>osservato della mobilità della pupilla, sotto le varie impressioni della luce, <lb></lb>giova toccar qui di quel fatto brevemente la storia. </s></p><pb xlink:href="020/01/1438.jpg" pagenum="313"></pb><p type="main">

<s>Nel capitolo V del X libro <emph type="italics"></emph>De usu partium<emph.end type="italics"></emph.end> dice Galeno di avere osser­<lb></lb>vato che, chiudendo un occhio e tenendo l&#039;altro aperto, questo ha la pupilla <lb></lb>più dilatata di quello. </s>

<s>Benchè sieno in sè le parole assai chiare, parve no­<lb></lb>nostante il testo galenico a tutti oscuro, e ciò perchè la naturale osserva­<lb></lb>zione non si descriveva secondo la verità, come quella che veniva male in­<lb></lb>formata dalla filosofica teoria. </s>

<s>Portava infatti questa teoria, che Galeno si <lb></lb>studiò di convalidare coll&#039;esperienza, insufflando l&#039;occhio estratto dall&#039;orbita <lb></lb>dalla parte di dietro, e avvertendo che all&#039;impeto del fiato l&#039;Iride si con­<lb></lb>traeva; portava, diciamo, che a moderar l&#039;apertura del foro pupillare concor­<lb></lb>resse esclusivamente la quantità degli spiriti animali. </s>

<s>Or perchè all&#039;occhio <lb></lb>aperto dovevano questi spiriti affluire in maggior copia che al chiuso, e perciò <lb></lb>se ne concludeva, contro l&#039;esperienza dei fatti, ch&#039;era la pupilla più ristretta <lb></lb>in questo caso che in quello. </s></p><p type="main">

<s>Ma Colui, che fu tra gli antichi il più valido promotore del metodo spe­<lb></lb>rimentale, riguardando l&#039;Occhio, non come subietto anatomico ma come or­<lb></lb>gano delle osservazioni celesti, ebbe occasione di riconoscere, secondo il vero <lb></lb>esser loro, i moti pupillari, quando insegnò nell&#039;Arenario il modo di misu­<lb></lb>rar con la più scrupolosa esattezza l&#039;apparente diametro del Sole. </s>

<s>Benchè <lb></lb>però le parole “ porro quoniam visus non respicit ab uno puncto, sed ab <lb></lb>aliqua quantitate ” e la prescrizione, che tosto si soggiunge, di adattare a <lb></lb>questa maggiore o minor quantità “ aliqua magnitudo teres non minor visu ” <lb></lb>(Archimedis Opera, Parisiis 1615, pag. </s>

<s>453), insinuino e presuppongano la <lb></lb>mobilità della pupilla, rimase in quella universale decadenza degli studii la <lb></lb>gentile osservazione obliata, infintantochè gli ecclissati splendori archimedei <lb></lb>non tornarono a illuminare le riaperte vie ai progressi delle scienze speri­<lb></lb>mentali, rivelandosi all&#039;ingegno di Paolo Sarpi. </s>

<s>Egli, rimeditando sui libri <lb></lb>del Matematico di Siracusa, e com&#039;era suo uso riducendo le speculazioni <lb></lb>all&#039;esperienza, trovò, nell&#039;adattare i diametri de&#039;cilindri torniti all&#039;apertura <lb></lb>della pupillla, che questa da un momento all&#039;altro variava nella grandezza. </s>

<s><lb></lb>Della quale maravigliosa variabilità ricercando la causa, non seppe altro ve­<lb></lb>dere se non ch&#039;ella dipendeva dalla varia intensita della luce. </s></p><p type="main">

<s>Giovan Batista Porta, in quel tempo, come s&#039;ha dalla prefazioncella al <lb></lb>VII libro della Magia naturale “ Venetiis eodem studio invigilans, cognovit <lb></lb>R. M. </s>

<s>Paulum Venetum, a quo aliqua didicisse fatetur ” (Lugd. </s>

<s>Batav. </s>

<s>1651, <lb></lb>pag. </s>

<s>287). Un giorno dunque fra Paolo, sedendo coll&#039;amico fra le chiuse <lb></lb>pareti della sua cella, presso a por fine al dotto colloquio tenuto con lui, lo <lb></lb>invita per curiosità a guardargli la pupilla degli occhi, e a stimarne la gran­<lb></lb>dezza dell&#039;apertura. </s>

<s>Poi si leva movendosi verso la finestra e, stato alquanto <lb></lb>a riguardare l&#039;aperto cielo-vivamente irraggiato dal Sole, invita nuovamente <lb></lb>il Porta a guardar quel medesimo occhio, in cui la pupilla, che appariva <lb></lb>dianzi grande quanto una lente, ora agguagliava appena il capo di uno spillo. </s>

<s><lb></lb>Sorpreso dalla novità, il Fisico napoletano pubblicò nel suo ottico trattato <lb></lb><emph type="italics"></emph>De refractione<emph.end type="italics"></emph.end> il fatto in tal forma, da lasciarvi impresse visibilmente le <lb></lb>vestigie della secreta storia ora svelata. </s>

<s>“ Si amici oculos, egli dice, aper-<pb xlink:href="020/01/1439.jpg" pagenum="314"></pb>tos intentosque vehementius solis lumini obiectos contemplaberis, adeo pu­<lb></lb>pillam coarctari videbis, ut per angustissimum foramen vix tenuis acus aciem <lb></lb>admitteret. </s>

<s>Eosdem, si in obscuro cubiculo convertat, parvo temporis curri­<lb></lb>culo foramen adeo dilatari conspicies, ut fere lentem capiat.... Huins rei <lb></lb>instrumento certius fies compos quod Archimedes in dignoscenda solis quan­<lb></lb>titate usus est ” (Neapoli 1593, pag. </s>

<s>74). </s></p><p type="main">

<s>Poco dopo avvenute queste cose, occorse all&#039;Acquapendente, che non <lb></lb>ne sapeva ancora nulla, di maravigliarsi della variabilità della pupilla osser­<lb></lb>vata ne&#039;gatti. </s>

<s>E vedendola passare in quelle alterne vicende di maggiore e <lb></lb>di minor grandezza, in così brevi intervalli di tempo, pensò a principio che <lb></lb>fossero que&#039;moti volontarii. </s>

<s>Non vedendoci però muscoli atti a far ciò, ri­<lb></lb>mase in dubbio. </s>

<s>Comunicata intanto l&#039;osservazione al suo amico Paolo Sarpi, <lb></lb>gli fu da lui risposto che egli aveva osservato avvenir ciò nella pupilla degli <lb></lb>uomini stessi, com&#039;aveva già detto e fatto vedere al Porta. </s>

<s>Ma l&#039;osserva­<lb></lb>zione dell&#039;Acquapendente invogliò fra Paolo a fare altre numerose espe­<lb></lb>rienze, dalle quali finalmente concluse che il restringersi la pupilla a una <lb></lb>luce più intensa, e il dilatarsi a una luce più rimessa, era una proprietà <lb></lb>dell&#039;occhio in tutti gli animali. </s>

<s>“ Res igitur, così l&#039;Acquapendente stesso <lb></lb>racconta, cum amico quodam nostro communicata, ille tandem forte id obser­<lb></lb>vavit, scilicet non modo in cato, sed in homine et quocumque animali, fo­<lb></lb>ramen Uveae in maiori luce contrahi, in minori dilatari. </s>

<s>Quod arcanum <lb></lb>observatum est, et mihi significatum a Rev. </s>

<s>patre magistro Paulo Veneto.... <lb></lb>mathematicarum disciplinarum, praecipueque Optices, maxime studioso ” (De <lb></lb>oculo, Opera omnia cit., pag. </s>

<s>229). </s></p><p type="main">

<s>Fecero osservare alcuni però che a quell&#039;arcano erasi Galeno stesso stu­<lb></lb>diato di togliere la più densa parte del velo, e che l&#039;osservazione del dila­<lb></lb>tarsi e del restringersi la pupilla ne&#039;gatti l&#039;avea il Cardano accennata nei <lb></lb>suoi libri <emph type="italics"></emph>De subtilitate<emph.end type="italics"></emph.end> parecchi anni prima dell&#039;Acquapendente. </s>

<s>Giovan <lb></lb>Batista Ruschi, anatomico pisano, così infatti scriveva in un suo trattato <emph type="italics"></emph>De <lb></lb>visus organo<emph.end type="italics"></emph.end> pubblicato in Pisa nel 1631: “ Pupillae motum, nec mille lin­<lb></lb>guis exprimendus, quam obscure Galenus agnovit?... Catos existimat Hye­<lb></lb>ronimus Cardanus, in libris <emph type="italics"></emph>De subtilitate,<emph.end type="italics"></emph.end> oculos voluntarie contrahere ac <lb></lb>laxare ” (pag. </s>

<s>42). </s></p><p type="main">

<s>Quando nonostante, nel 1632, Galileo pubblicò i Dialoghi dei due mas­<lb></lb>simi Sistemi, volle far credere l&#039;osservazione dei moti della pupilla, e l&#039;ap­<lb></lb>plicazione di lei a ritrovar l&#039;angolo del concorso de&#039;raggi secondo il metodo <lb></lb>archimedeo sapientemente illustrato dal Sarpi, per cosa del tutto nuova. </s>

<s>In <lb></lb>colorir tali novità, noi svelammo a varie occasioni la scaltrissima arte del­<lb></lb>l&#039;Autore, ma perchè l&#039;Acquapendente non seppe entrare per la nuova via <lb></lb>de&#039;progressi, e l&#039;opera del Porta fu repressa e avvilita dalla prepotente vit­<lb></lb>toria del suo rivale, si può creder vero quel che il Salviati dice, che cioè <lb></lb>“ tra mille, che hanno osservato ne&#039;gatti stringersi e allargarsi assaissimo <lb></lb>la pupilla dell&#039;occhio, non ve ne sono due nè forse uno che abbia osser­<lb></lb>vato un simile effetto farsi nelle pupille degli uomini ” (Alb. </s>

<s>I, 394); come <pb xlink:href="020/01/1440.jpg" pagenum="315"></pb>dall&#039;altra parte è verissimo che si diffusero da que&#039;Dialoghi, insiem con <lb></lb>questa ch&#039;è il soggetto del presente discorso, moltissime altre notizie, le <lb></lb>quali apparvero e furono credute per nuove, perchè rimaste immote nelle <lb></lb>neglette pagine di pochi dotti. </s></p><p type="main">

<s>Ripensando poi a questa larga diffusion della scienza, per opera de&#039;Dia­<lb></lb>loghi galileiani; considerando che aveva il Sarpi lasciate vive ancora in Ve­<lb></lb>nezia le tradizioni de&#039;suoi ritrovati; che il trattato dell&#039;Acquapendente fu <lb></lb>pubblicato in Padova e quel del Ruschi in Pisa; fa certo maraviglia che il <lb></lb>Verle veneziano scrivesse in Firenze di avere osservato i moti della pupilla <lb></lb>farsi solo nei bambini, e ne&#039;fanciulli dai quattro ai quindici anni, che hanno <lb></lb>l&#039;iride di color celestino, concludendo: “ Nelle pupille poi, d&#039;altro colore <lb></lb>che de&#039;suddetti, non ho fatta fin qui considerazione se ciò succeda o altri­<lb></lb>menti ” (Anat. </s>

<s>artifiz. </s>

<s>cit., pag. </s>

<s>38). </s></p><p type="main">

<s>Diminuisce però quella maraviglia ripensando che il Verle era uomo <lb></lb>pratico, e che la storia dell&#039;Anatomia non aveva avuto ancora i suoi eruditi <lb></lb>e diligenti cultori, i quali, quando in sul cominciar del secolo XVIII si det­<lb></lb>tero a quello studio, ritrovarono compiacenti che l&#039;osservazione, la quale <lb></lb>Galileo scommetteva non essere stata fatta a&#039;suoi tempi che forse da uno <lb></lb>solo, si leggeva in numerosi e antichissimi autori. </s></p><p type="main">

<s>Il Morgagni, nell&#039;<emph type="italics"></emph>Adversaria anatomica I,<emph.end type="italics"></emph.end> annunziava di aver trovato <lb></lb>rivelato l&#039;arcano nelle Annotazioni anatomiche dell&#039;Achillini, dalle quali tra­<lb></lb>scrive in calce queste parole: “ Uvea, cuius foramen est pupilla, aperitur <lb></lb>in mediocri lumine, excessivo constringitur in suo foramine ” (Patavii 1719, <lb></lb>pag. </s>

<s>54). Noi non abbiamo potuto consultare queste <emph type="italics"></emph>Annotationes<emph.end type="italics"></emph.end> del Filo­<lb></lb>sofo bolognese, le quali del resto non si trovano inserite nell&#039;<emph type="italics"></emph>Opera omnia <lb></lb>in unum collecta<emph.end type="italics"></emph.end> da Panfilio Monti, e per la seconda volta nel 1568 pub­<lb></lb>blicate in Venezia; ciò che ingerisce in noi qualche dubbio, reso anche più <lb></lb>forte dall&#039;essere esse Annotazioni postume. </s>

<s>Il saper dall&#039;altra parte che <lb></lb>l&#039;Achillini, tutto involto nel lezzo peripatetico, non era anatomico, ci fa so­<lb></lb>spettar che avesse avuto la notizia dalla viva voce di Leonardo da Vinci, il <lb></lb>quale, nel dipinger dal vero gli occhi, badando ad ogni minuzia, disse di <lb></lb>essersi accorto che l&#039;apertura della pupilla, secondo le varie luci, strana­<lb></lb>mente variava di grandezza. </s></p><p type="main">

<s>Nell&#039;Epistola anatomica XVII poi soggiunse lo stesso Morgagni ch&#039;era <lb></lb>tra gli osservatori del fatto da annoverar non solo l&#039;Achillini, “ sed ipsum <lb></lb>Rhazen longe antiquiorem, et locupletiorem testem ” da cui trascrive le se­<lb></lb>guenti parole: “ Constringìtur enim cum lumen est multum, et dilatatur <lb></lb>cum est in obscuro. </s>

<s>Hoc autem foramen est pupilla ” (Editio cit, pag. </s>

<s>248). <lb></lb>L&#039;Haller (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V sit., pag. </s>

<s>374) aggiunse a Rhazen e ad Avi­<lb></lb>cenna anche Areteo: altri eruditi potrebbero con facilità arricchir la storia <lb></lb>di altri nomi forse più antichi, ma no certo più illustri di quello di Archi­<lb></lb>mede, dall&#039;Arenario del quale zampillarono le tradizioni com&#039;acqua viva, che <lb></lb>viene da lontane sorgenti a riversarsi nel fiume della scienza. </s></p><p type="main">

<s>Se il Sarpi, che fu il primo ad accogliere queste tradizioni, oltre all&#039;os-<pb xlink:href="020/01/1441.jpg" pagenum="316"></pb>servare il fatto attendesse a specularne le cause, per verità non sappiamo, <lb></lb>ond&#039;è che riman solo per noi l&#039;Acquapendente, il quale persuaso dal difetto <lb></lb>di muscoli non dover essere i moti della pupilla volontarii, e dall&#039;altra parte <lb></lb>considerando non poter quegli stessi moti esser causati, come Galeno inse­<lb></lb>gnava, dagli spiriti affluenti, che produrrebbero effetti necessariamente con­<lb></lb>trarii: rassomigliò il restringersi e il dilatarsi dell&#039;iride alla sistole e alla <lb></lb>diastole del cuore, o meglio alla flaccidità e alla turgenza de&#039;corpi caver­<lb></lb>nosi. </s>

<s>“ Quocirca dicere satius est motus huius efficientem causam proficisci <lb></lb>a propria Uveae tunicae facultate, quae hunc motum efficiendi vim a Na­<lb></lb>tura habeat, perinde ac cor dilatandi se et contrahendi potentiam obtinet. </s>

<s><lb></lb>Melius autem forte fuerit virilis pudendi motui uveae foraminis motum assi­<lb></lb>milare ” (De oculo, Op. </s>

<s>omnia cit., pag. </s>

<s>230). </s></p><p type="main">

<s>Poco dopo, il Cesalpino attribuì i moti della pupilla a certe speculate <lb></lb>ragioni, che rimaste soffocate ne&#039;libri di lui dalla lussuria d&#039;immaginati si­<lb></lb>stemi, quando questi dovettero inaridire, quelle tornarono nuovamente alla <lb></lb>luce. </s>

<s>“ Causa dilatationis, egli dice nel cap. </s>

<s>XLVI del V libro <emph type="italics"></emph>Artis me­<lb></lb>dicae,<emph.end type="italics"></emph.end> est Uveae repletio aut a spiritu, aut ab humoribus collectis intra <lb></lb>Uveam..... Constrictionis causa est inanitio ” (Romae 1603, pag. </s>

<s>284). </s></p><p type="main">

<s>Gl&#039;immaginati sistemi che si diceva son quelli del Cartesio. </s>

<s>Che vuole <lb></lb>egli dire se l&#039;Acquapendente non ha trovato nulla nell&#039;iride di muscolare, <lb></lb>nè perciò di volontario? </s>

<s>Il Filosofo ha arbitrio di prescrivere alla Natura <lb></lb>quel che gli fa bisogno per la sua teoria. </s>

<s>Dunque il forame della pupilla <lb></lb>“ speciem exigui musculi habet, qui diducitur aut contrahlitur, prout obiecta <lb></lb>quae contuemur vel propius vel longius absunt, vel magis aut minus illu­<lb></lb>minantur, vel prout magis aut minus curiose illa contemplari animus est ” <lb></lb>(Dioptrices, cap. </s>

<s>III, Francofurti ad M. 1692, pag. </s>

<s>54). Dunque lo sfintere, <lb></lb>che ha da fare al Filosofo così fatti servigi, bisogna che sia necessariamente <lb></lb>un muscolo volontario “ licet ut plurimum nobis ignorantibus peragatur, <lb></lb>quemadmodum labiorum et linguae motus, pronuntiationi inserviens, volun­<lb></lb>tarius dicitur, quoniam loquendi voluntatem sequitur, licet saepissime igno­<lb></lb>remus qualem singulae literae requirant ” (Ibid., pag. </s>

<s>54, 55). </s></p><p type="main">

<s>Quando Ernesto Sthal introdusse nelle questioni fisiologiche il fermento <lb></lb>della Filosofia cartesiana, soggiogata la scienza da due così prepotenti auto­<lb></lb>rità, per seguir le speculate teorie non si curarono le osservazioni dei fatti. </s>

<s><lb></lb>Anche i più liberi ingegni, e quelli stessi che facevano scuola da sè, nel <lb></lb>particolar proposito dei moti della pupilla, convennero che doveva al difetto <lb></lb>delle sensate esperienze supplir l&#039;acume filosofico della mente. </s>

<s>Il Ruyschio <lb></lb>parlò chiaro, e disse le fibre orbicolari, necessarie per la reale esistenza <lb></lb>dello sfintere cartesiano, “ non tam luculenter conspici posse, quin oculi <lb></lb>mentis in auxilium sint vocandi ” (Epist. </s>

<s>ad Wedelium cit., pag. </s>

<s>10). E il <lb></lb>Boerhaave, immaginandosi che le fibre della Coroide, entrate nell&#039;Uvea, di­<lb></lb>ventino muscolari, movendo dalla circonferenza esterna e intessendosi a <lb></lb>compor lo stesso sfintere cartesiano intorno al lembo orbicolare, che circo­<lb></lb>scrive il foro della pupilla; “ Unde patet, ne conclude, orbiculares constrin-<pb xlink:href="020/01/1442.jpg" pagenum="317"></pb>gere, longitudinales dilatare foramen pupillae ” (Institutiones med. </s>

<s>cit., <lb></lb>pag. </s>

<s>65). </s></p><p type="main">

<s>In Italia, in grazia degli istituti e dell&#039;opera de&#039;discepoli di Galileo, ri­<lb></lb>maste più che altrove salve le menti dal contagio cartesiano, indipendente­<lb></lb>mente da ogni autorità, si vollero esaminare i fatti. </s>

<s>Fu de&#039;primi il Valsalva, <lb></lb>il quale, al riferir del Morgagni, distesa l&#039;iride sopra un vetro, benchè vi <lb></lb>vedesse apparir le fibre da lui credute muscolari andar dalla circonferenza <lb></lb>esterna alla orbicolare della pupilla, “ nullas autem in annuli modum cir­<lb></lb>cumductas adnotavit ” (Epist. </s>

<s>anat. </s>

<s>XVII cit., pag. </s>

<s>244). Il Morgagni stesso <lb></lb>poi con le osservazioni sue proprie confermò quelle del suo Maestro, asse­<lb></lb>verando che tra le fibre dell&#039;iride, diligentemente osservate attraverso a una <lb></lb>lamina di vetro, non ne aveva potuto avvertir nessuna, che si rigirasse in­<lb></lb>torno alla pupilla a guisa di anello. </s>

<s>“ Cum has, sive fibrillas sive vascula, <lb></lb>non in eo tantum sed et in compari oculo ad eumdem modum conspexissem, <lb></lb>nulla usquam annularia filamenta potui animadvertere ” (ibid., pag. </s>

<s>250). </s></p><p type="main">

<s>A confermare anche meglio ciò che, intorno alle musculose fibre orbi­<lb></lb>colari della pupilla, avevano affermato i due insigni nostri Italiani, concor­<lb></lb>sero poco dopo il Duvernoi e il Weitbrecht: poi il Zinn appose a quelle affer­<lb></lb>mazioni l&#039;autorevole suo suggello, dicendo: “ Neque ipse certe crediderim <lb></lb>fibras musculares unquam ullo microscopio demonstrari posse ” (Descriptio <lb></lb>oculi cit., pag. </s>

<s>91). Ond&#039;è che potè coll&#039;Haller la scienza de&#039;fatti contro le <lb></lb>immaginazioni del Cartesio finalmente sentenziare: “ Circulus in Uvea con­<lb></lb>strictor nullus est ” (Elem. </s>

<s>Physiol. </s>

<s>T. </s>

<s>V cit., pag. </s>

<s>378). </s></p><p type="main">

<s>Ma pure il Cartesio stesso aveva preteso che le sue filosofiche dottrine <lb></lb>fossero non immaginazioni ma fatti, richiamando i dubbiosi alle esperienze. <lb></lb></s>

<s>“ Et fidem huic rei pueri oculus cuivis dubitanti astruere poterit. </s>

<s>Nam sì <lb></lb>iusseris ut vicinum aliquod obiectum attente respiciat, videbis aliquanto <lb></lb>arctius pupillam eius contrahi, quam si aliud multo remotius.... Et obser­<lb></lb>vandum hunc motum voluntarium esse dicendum ” (Dioptrices cap. </s>

<s>cit., <lb></lb>pag. </s>

<s>54). I Cartesiani poi, specialmente seguaci dello Stahl, aggiunsero fra <lb></lb>le molte altre cose essere in arbitrio del fanciullo il restringere la pupilla <lb></lb>e il dilatarla, benchè poi gli adulti dimentichino questo gioco. </s>

<s>Ai quali final­<lb></lb>mente rispose la vera scienza sperimentale, per bocca del medesimo Haller: <lb></lb>“ Verum haec omnia nimia sunt et facillime experimentis refutantur. </s>

<s>Im­<lb></lb>peret sibi ipsi homo ut vel constringat pupillam vel relaxet: nihil efficiet, <lb></lb>dum idem erit luminis vigor ” (Elem. </s>

<s>Phys. </s>

<s>cit., pag. </s>

<s>378). </s></p><p type="main">

<s>Francata così dunque la scienza dal giogo degli immaginati sistemi, si <lb></lb>apparecchiò a investigare il mistero dei moti pupillari, esaminando con gran <lb></lb>diligenza l&#039;Iride nella sua vera struttura. </s>

<s>L&#039;esame cominciò dal Valsalva, il <lb></lb>quale, al riferir del Morgagni, osservando l&#039;iride elegantissima di una lepre, <lb></lb>notò che tutta era intessuta di fibre “ quae ab ambitu centrum versus fe­<lb></lb>runtur ” (Epist. </s>

<s>anat. </s>

<s>XVII cit., pag. </s>

<s>244). Il Morgagni stesso poi descrisse <lb></lb>quell&#039;intrecciamento di fibrille fosche “ ad convexum zonulae ambitum, quam <lb></lb>minorem illum esse Ruyschii circulum non dubitavi ” (ibid., pag. </s>

<s>250). </s></p><pb xlink:href="020/01/1443.jpg" pagenum="318"></pb><p type="main">

<s>Ma della fabbrica striata dell&#039;Iride non fu il bellissimo spettacolo da <lb></lb>nessun altro meglio descritto che dal Zinn, contemplandolo col microscopio in <lb></lb>un occhio recente. </s>

<s>“ In annulo enim maiori apparent fibrae innumerae ma­<lb></lb>gis minusve albidae et gryseae, aliae maiores, quae plerumque magis can­<lb></lb>didae, aliae minores et tenuiores minusque diluti coloris, omnes parallelae <lb></lb>et densissimo ordine sibi appositae ut plures recipere non posse videatur. </s>

<s><lb></lb>Ab ipso ergo ambitu exteriori Iridis versus annulum minorem convergunt, <lb></lb>serpentino flexu incedentes, eo maioribus flexionibus quo iris angustior et <lb></lb>pupilla amplior fuerit..... Ubi autem ad zonulam, quae pupillam proxime <lb></lb>ambit, sive ad annulum minorem ventum est, fibrae maiores saepe in duos <lb></lb>ramos abire videntur, qui ad angulum satis obtusum discedunt.... Ex mu­<lb></lb>tua ergo coniunctione trunculorum inter se ad angulos acutos coeuntium, <lb></lb>et per arcus sibi unitorum formari videtur circulus serratus et flexuosus.... <lb></lb>Ex ora illa serrata, quae circuli instar maiorem annulum terminat, et inpri­<lb></lb>mis ex convexitate arcuum, ex duobus trunculis inter se unitis factorum, <lb></lb>oriuntur plurimae fibrae tenuissimae, parallelae fere, rectae in radiorum mo­<lb></lb>dum versus centrum pupillae convergentes, rariores et saepe intervallo quo­<lb></lb>dam inter se disiunctae, subtilissima cellulositate inter se connexae, quae <lb></lb>annulum interiorem foramine circulari pertusum constituunt ” (Descriptio <lb></lb>cit., pag. </s>

<s>86-88). </s></p><p type="main">

<s>Tali essendo gli organi inservienti al moto dell&#039;Iride, si domandavano <lb></lb>le ragioni di que&#039;moti. </s>

<s>E giacchè l&#039;Acquapendente gli aveva rassomigliati <lb></lb>aìla sistole e alla diastole del cuore si domandava a qual fase dell&#039;Iride cor­<lb></lb>rispondesse la diastole, ossia lo stato naturale, e rispondevasi comunemente <lb></lb>che al restringimento di lei, ossia alla dilatazione della pupilla. </s>

<s>Pareva con­<lb></lb>fermassero questa opinione i fatti osservati in caso di sincope o di morte, <lb></lb>ma il Zinn trovò che ciò avveniva infintantochè l&#039;occhio si lasci nel suo sito <lb></lb>naturale, ma estratto dal cadavere, “ iteratis experimentis edoctus fui, egli <lb></lb>dice, pupillam post mortem sensim angustiorem factam fuisse.... Cum an­<lb></lb>tem ad explicandum hoc phaenomenon neque vires contractiles fibrarum <lb></lb>orbicularium, neque vis irruens humorum in animale diu ante mortuo in <lb></lb>auxilium vocari possint, parum abest quin ad credendum adducar dilatatio­<lb></lb>nem multum omnino pendere ab elasticitate fibrarum Iridis longitudinalium, <lb></lb>contractionem autem fere esse naturalem et sponte sequi, si fibrae longitu­<lb></lb>dinales plane relaxatae, et a puncto fixo cui adnectuntur divisae fuerint ” <lb></lb>(ibid., pag. </s>

<s>102). </s></p><p type="main">

<s>Così tornavasi a ripetere la sentenza antica del Cesalpino: <emph type="italics"></emph>Constrictio­<lb></lb>nis causa est inanitio.<emph.end type="italics"></emph.end> Se non che non pareva credibile che la vivacissima <lb></lb>attività della luce si dovesse all&#039;ultimo ridurre ad una semplice inanizione. </s>

<s><lb></lb>Non fa perciò maraviglia se i Fisiologi non convennero col Zinn, reputando <lb></lb>più ragionevole interpetrare a dovere un concetto sovvenuto all&#039;Acquapen­<lb></lb>dente, il quale, risaputo dal Sarpi il fatto che la pupilla si restringeva al­<lb></lb>l&#039;aperta luce e si dilatava nell&#039;ombra, disse che avrebbe creduto dovere avve­<lb></lb>nire tutto al contrario, “ quod lucis natura potius sit disgregare, dilatareque, <pb xlink:href="020/01/1444.jpg" pagenum="319"></pb>tenebrarum vero constringere, densare et comprimere ” (De oculo, Op. </s>

<s>omnia <lb></lb>cit., pag. </s>

<s>229). </s></p><p type="main">

<s>Ma i Fisiologi trovarono la verità in quel che aveva dato occasione di <lb></lb>dubitare all&#039;Acquapendente, il quale non pensò che il dilatamento della pu­<lb></lb>pilla era una conseguenza necessaria della restrizione dell&#039;Iride. </s>

<s>Ammesso <lb></lb>perciò come vero che la luce, colla sua propria attività, spieghi le pliche <lb></lb>serpentinose delle fibre, e distenda le cellule delle strie, confermarono con­<lb></lb>tro il Zinn la più comune opinione, che cioè sia la pupilla dilatata e non <lb></lb>ristretta nello stato suo naturale. </s>

<s>“ Videtur, scrisse l&#039;Haller, potius causa <lb></lb>esse in irritante luce, quae, excitatis viribus, iridem introrsum pellat, evo­<lb></lb>lutis plicis serpentinis vasorum et striarum cellulosarum, ut in rectitudinem <lb></lb>conversae iridem dilatent.... Naturalis ergo status Iridis foret angustia et <lb></lb>pupillae latitudo ” (Elem. </s>

<s>Phys. </s>

<s>T. cit., pag. </s>

<s>378). </s></p><p type="main">

<s>Così, essendo naturalmente aperte, chiude da sè la luce le gelose cor­<lb></lb>tine nell&#039;entrare addentro al riposto talamo, sopra cui ella trova mollemente <lb></lb>distesa quella tela, in filar la quale e in lavorarla la Natura usò la sua mas­<lb></lb>sima industria. </s>

<s>Che fosse la sottilissima orditura veramente filata dalle più <lb></lb>intime viscere del cervello, lo dissero gli Anatomici più antichi, e furono i <lb></lb>loro detti solennemente confermati da Galeno, il quale anzi dubitò se con­<lb></lb>venisse a quel nobilissimo e principale organo della vista il nome di mem­<lb></lb>brana “ cum, si exemptam ipsam seposueris, in unum acervum coniiciens, <lb></lb>tibi plane videbere videre cerebri portionem quamdam exemptam ” (De usu <lb></lb>partium, Opera omnia cit., T. I, fol. </s>

<s>177); espressione fra&#039;tanti altri ripe­<lb></lb>tuta da Realdo Colombo (De re anat. </s>

<s>cit., pag. </s>

<s>218). </s></p><p type="main">

<s>La rassomigliarono a principio alle tele di ragno per la testura, e perciò <lb></lb>la chiamarono Aracnoidea: poi, rispetto principalmente alla figura dell&#039;am­<lb></lb>bito e del fondo, la paragonarono o a un uovo dimezzato o a una rete da <lb></lb>pescatori. </s>

<s>“ Est enim hoc involucrum, dice il Vesalio, forma dimidiato tan­<lb></lb>tum ovo comparandum, aut minori piscatorum reti, quod uni accomodatur <lb></lb>baculo, et ex ampla basi dimidiati globi modo in obtusum mucronem fer­<lb></lb>tur. </s>

<s>Ab huiusmodi enim retis imagine arbitror praesens involucrum Graecis <lb></lb><emph type="italics"></emph>amphiblistroides<emph.end type="italics"></emph.end> muncupatum fuisse ” (De hum. </s>

<s>corp. </s>

<s>fabrica cit., pag 647). </s></p><p type="main">

<s>Questo nome di Amfiblistroide, derivato <emph type="italics"></emph>a circumiiciendo,<emph.end type="italics"></emph.end> indica che il <lb></lb>paragone toccava semplicemente la figura della Retina distesa e applicata <lb></lb>sull&#039;umor vitreo, ma Herofilo, come notò l&#039;Acquapendente (De oculo cit., <lb></lb>pag. </s>

<s>191), aveva inteso di rassomigliarla alle stesse reti anche nella testura <lb></lb>delle maglie. </s>

<s>Notabile che sotto questa forma reticolare fosse la membrana <lb></lb>descritta da tutti gli Anatomici per tanti secoli, infino al Valsalva, il quale <lb></lb>uscì inaspettatamente a dire: “ Sciatis hanc non in retis formam construc­<lb></lb>tam esse, ut communiter docent Anatomes magistri. </s>

<s>Verum res ita se habet: <lb></lb>Nervus opticus interna sui substantia oculi cameram ingreditur, dimissa prius <lb></lb>pia meninge pro tunica sclerotica, arachnoide vero pro coroide. </s>

<s>Statim au­<lb></lb>tem ac ingressus est, radiatim expanditur in quamplurima filamenta, quae <lb></lb>versus peripheriam excurrunt usque ad unionem lentis crystallinae cum vi-<pb xlink:href="020/01/1445.jpg" pagenum="320"></pb>treo humore, quibus duobus, una cum ciliari processu, firmiter adhaeret ” <lb></lb>(Dissertationes anat. </s>

<s>cit., pag. </s>

<s>142). </s></p><p type="main">

<s>La testura dell&#039;Amfibilistroide in ogni modo, o reticolare come la dice­<lb></lb>vano gli Anatomici, o raggiata come la descrisse il Valsalva, dipendeva dalla <lb></lb>struttura del nervo ottico, dalla sostanza midollare del quale convenivano <lb></lb>tutti che si espanda. </s>

<s>Una lunga questione ebbero però gli Anatomici del se­<lb></lb>colo XVI e XVII intorno alla struttura di quel nervo, ordinato a riferire le <lb></lb>impressioni degli oggetti illuminati al cervello. </s>

<s>Herofilo disse di avere osser­<lb></lb>vato in ciascun nervo ottico reciso due pori, che Cicerone, nel III libro <emph type="italics"></emph>De <lb></lb>natura Deorum,<emph.end type="italics"></emph.end> chiamò le vie, per le quali gli spiriti visivi giungono dalle <lb></lb>più intime sedi dell&#039;anima agli occhi. </s>

<s>Confermata l&#039;osservazione di Herofilo <lb></lb>da Galeno, il Berengario disse che, sebbene i nervi ottici, “ secundum ali­<lb></lb>quos sint notabiliter perforati, hoc tamen negat sensus in mortuo animali ” <lb></lb>(Isagogae breves, Venetiis 1535, fol. </s>

<s>52). E il Vesalio negò assolutamente il <lb></lb>fatto ne&#039;vivi e nei morti. </s></p><p type="main">

<s>Consentirono in ciò col Vesalio il Colombo, il Valverde e il Falloppio, <lb></lb>ma l&#039;Eustachio insorse a rivendicare Galeno in quell&#039;<emph type="italics"></emph>Examen Ossium et <lb></lb>de motu capitis,<emph.end type="italics"></emph.end> che dette tanta occasione di mormorar contro l&#039;Autore <lb></lb>agl&#039;infervorati seguaci del divino Brussellese. </s>

<s>Dicevano ch&#039;egli sviava la fa­<lb></lb>cile gioventù dal secondare i progressi della scienza, e che s&#039;era messo a <lb></lb>difender Galeno, non punto per amor del vero, ma per una odiosa rivalità <lb></lb>col Vesalio. </s>

<s>Dalle quali accuse si difendeva l&#039;Eustachio innanzi al suo ca­<lb></lb>rissimo Fabio Amicio, citandogli, fra&#039;varii esempii non di parole ma di fatti, <lb></lb>che stavano a confermar contro le moderne le dottrine più antiche, anche <lb></lb>quello de&#039;nervi ottici, i quali, in alcuni grandi pesci, mostrano evidente­<lb></lb>mente d&#039;essere perforati. </s>

<s>“ Nonne, soluto prius oculo in singulas sui mem­<lb></lb>branas, quod vix animus capere potest, foramen nervi visorii tibi et aliis, <lb></lb>vel multis reclamantibus, ante oculos sexcenties exposui? </s>

<s>Iam cito admira­<lb></lb>tio illa evanuit quam nervum visorium, in eo animali quod cognitum nunc <lb></lb>habes, tibi ac plurimis aliis movisse praedicabas, qui nervus, veluti tenuis­<lb></lb>simum matronarum linteum, in innumeras rugas aequales et pari serie di­<lb></lb>stributas complicatus, tuniculaque illas ambiente coactus, hac eadem incisa, <lb></lb>evolvi sese permittebat, et in amplam membranam totum explicari atque <lb></lb>extendi ” (Examen ossium, inter Opuscula anat. </s>

<s>cit., pag. </s>

<s>227). </s></p><p type="main">

<s>La questione pareva che dovess&#039;essere così finalmente decisa, ma alle <lb></lb>dispute fervorose sottentrati i placidi esami, nel secolo XVII si seguitò col <lb></lb>Vesalio a negar l&#039;esistenza dei pori erofiliani. </s>

<s>Allora, come se l&#039;opuscolo <lb></lb>eustachiano non fosse mai stato scritto, il Malpighi tornò a dimostrar la par­<lb></lb>ticolare struttura del nervo ottico nelle Xifie e in altri simili pesci, conclu­<lb></lb>dendone anch&#039;egli come cosa nuova: “ Ex his omnibus aliquid colligere <lb></lb>poteris ad solvendum illud, quod antiquos et neotericos diu vexavit, num <lb></lb>scilicet optici perforati sint ” (De Cerebro, Operum, T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, <lb></lb>pag. </s>

<s>121). </s></p><p type="main">

<s>Ma il nuovo, e nella esperienza in sè stessa e nelle applicazioni di lei, <pb xlink:href="020/01/1446.jpg" pagenum="321"></pb>a decider le controversie riscontra così coll&#039;antico, che fu da alcuni il Mal­<lb></lb>pighi accusato di plagio. </s>

<s>“ Verum, risponderemo anche noi coll&#039;Haller, Mal­<lb></lb>pighius alienis non egebat divitiis ” (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V cit., pag. </s>

<s>353), ma <lb></lb>il fatto in ogni modo è notabile, e fa gran maraviglia come potesse la scuola <lb></lb>anatomica del Borelli così aver dimenticata la più eletta parte delle patrie <lb></lb>tradizioni. </s></p><p type="main">

<s>Comunque sia però, nè l&#039;Eustachio nè il Malpighi, insinuando che i <lb></lb>fori ottici son prodotti dalle pieghe del nervo linteolare, tolsero affatto i <lb></lb>dubbi, imperocchè, se potevano da coteste pieghe pigliare apparenza i pori <lb></lb>più minuti, rimaneva tuttavia incerta l&#039;origine di quel forame più grande, <lb></lb>che, reciso presso l&#039;occhio il nervo per traverso, veniva oramai a rivelarsi <lb></lb>come cosa fuor d&#039;ogni dubbio alle più diligenti inspezioni dei moderni. </s></p><p type="main">

<s>Il Zinn dimostrò che cotesto foro niente altro era che la luce aperta <lb></lb>dell&#039;arteria centrale, e perchè, sopra l&#039;inserzione di essa arteria il nervo è <lb></lb>solido e non presenta alcun vestigio di pori, si studia di conciliar Galeno <lb></lb>col Vesalio, dicendo che il primo dovette aver reciso il nervo dopo, e il se­<lb></lb>condo prima della detta inserzione. </s>

<s>“ Pori autem vacui in medio nervo nul­<lb></lb>lum reperitur vestigium supra insertionem ipsius arteriae centralis, ubi ner­<lb></lb>vus solidus plane apparet, ut inde facile diversae opiniones Galeni, qui nervum <lb></lb>foramine pertundi asserit, et Vesalii, qui foramen illud negat, conciliari posse <lb></lb>videantur ” (Descriptio oculi cit., pag. </s>

<s>194). </s></p><p type="main">

<s>Se, così, il Morgagni, dal veder que&#039;misteriosi meati impediti sempre <lb></lb>“ membranea quadam structura, quasi cellulosa ” (Epist. </s>

<s>anat. </s>

<s>XVII cit., <lb></lb>pag. </s>

<s>301), ne aveva concluso contrariar questo solo fatto l&#039;ipotesi degli An­<lb></lb>tichi delle vie di diretta comunicazione fra il cervello e gli occhi; il Zinn, <lb></lb>rivelando il mistero, confinò quella ipotesi per sempre nella reggia de&#039;sogni, <lb></lb>con avvantaggio di quella più ragionevole Filosofia della visione, che formerà <lb></lb>il soggetto della nostra storia, dopo questa dell&#039;organo, a completar la quale <lb></lb>ci rimane ancora a dir degli umori. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Gli Anatomici anteriori a Galeno non conobbero che l&#039;umor vitreo e il <lb></lb>Cristallino. </s>

<s>Celso infatti, nel § 13 del VII libro <emph type="italics"></emph>De re medica,<emph.end type="italics"></emph.end> dop&#039;aver de­<lb></lb>scritta la Retina, ch&#039;ei con Herofilo chiama Aracnoidea, “ ea media, sog­<lb></lb>giunge, subsidit, eaque cavo continet quiddam quod, a vitri similitudine, <lb></lb>Jaloides graeci vocant.... Sub his gutta humoris est, ovi albo similis: Chry­<lb></lb>stalloides a graecis nominatur ” (Editio cit., fol. </s>

<s>100). Ma sotto la cornea <lb></lb>“ qua parte pupilla est, locus vacuus est ” (ibid.). </s></p><p type="main">

<s>Si direbbe, pensava l&#039;Haller, che gli Antichi non avessero inciso altro <lb></lb>che l&#039;occhio de&#039;pesci, ne&#039;quali l&#039;umor acqueo è scarsissimo, “ cum planis­<lb></lb>sima cornea iridi incumbat ” (Elem. </s>

<s>Phys. </s>

<s>T. </s>

<s>V cit., pag. </s>

<s>409), ma forse, <pb xlink:href="020/01/1447.jpg" pagenum="322"></pb>non avendo diligenza di scegliere per le dissezioni occhi freschi, quello stesso <lb></lb>umore o era stato assorbito o esalato. </s>

<s>In qualunque modo, Galeno, nel cap. </s>

<s>IV <lb></lb>del libro X <emph type="italics"></emph>De usu partium,<emph.end type="italics"></emph.end> pensò che la previdente Natura, affinchè non <lb></lb>dovesse il Cristallino moversi e patire attrito, facesse protuberare la cornea, <lb></lb>non lasciando lo spazio interposto vuoto, ma riempiendolo di un certo umor <lb></lb>viscido, somigliante all&#039;albume dell&#039;uovo. </s>

<s>“ Simul autem providit humorem <lb></lb>quendam tenuem ac sincerum, cuiusmodi in ovis reperitur, crystallino cir­<lb></lb>cumfundens, ac tertio praeter haec spiritu aereo ac splendido omnem pu­<lb></lb>pillae locum opplens ” (Op. </s>

<s>omnia cit., T. I, fol. </s>

<s>179). </s></p><p type="main">

<s>Da queste ultime parole si comprende che dovette Galeno aver trovato <lb></lb>quell&#039;umore albugineo così scarso, da non rimanerne totalmente piena la <lb></lb>camera dell&#039;occhio, nel vuoto della quale, secondo lui, vivamente splendeva <lb></lb>lo spirito aerio. </s>

<s>Così veniva a partecipar con l&#039;inganno de&#039;suoi predeces­<lb></lb>sori, occasionato senza dubbio dal non aver avuto, come quelli non ebbero, <lb></lb>l&#039;accortezza di sezionar occhi freschi. </s></p><p type="main">

<s>Non mancò poi, nel risorgere degli studii anatomici, questa accortezza <lb></lb>a Jacopo Berengario, il quale dice di aver tante volte esaminata e riesami­<lb></lb>nata la composizione dell&#039;organo, “ modo in oculo humano, modo in oculis <lb></lb>brutorum, modo dequoquendo oculos, modo capiendos ipsos crudos ” (Com­<lb></lb>mentaria super Mund. </s>

<s>cit., fol. </s>

<s>CCCCLXIX), e di aver trovato, dietro un tale <lb></lb>diligentissimo esame, che fra la cornea e il cristallino lo spazio è tutto pieno <lb></lb>di umore, concedendo nonostante che si possa, alla parte di questo stesso <lb></lb>umore che sta innanzi alla pupilla, per esser più che altrove splendente, <lb></lb>dare il nome di <emph type="italics"></emph>etereo.<emph.end type="italics"></emph.end> “ Post tunicas dicendum est de humoribus, qui sunt <lb></lb>communiter tres: Primus quorum est albugineus, qui est inter corneam et <lb></lb>uveam tunicam,.... qui quidem humor albugineus, in directo pupillae ten­<lb></lb>dendo ab humore crystallino seu ab aranea tunica usque ad corneam, vo­<lb></lb>catur ab aliquibus etereus, quia est clarus et lucidus sicut eter..... Est <lb></lb>unus alter humor in oculo vitreus dictus, qui est in quantitate maior aliis <lb></lb>duobus,.... et in medio eius, non in centro sed circa medium eius, in parte <lb></lb>anteriori, est situs ille alter humor, qui dicitur crystallinus, quia lucet ad <lb></lb>instar crystalli ” (ibid., fol. </s>

<s>CCCCLXVIII). </s></p><p type="main">

<s>Così veniva, per opera del Berengario, alla sua sommaria integrità, e alle <lb></lb>sue più ragionevoli proporzioni ridotta la descrizione dell&#039;occhio. </s>

<s>Ma il Vesalio <lb></lb>non seppe giovarsi degli studii, per via de&#039;quali riuscì il nostro Carpense ad <lb></lb>emendare gli errori antichi, e, come Galeno, condotto anch&#039;egli dalla scarsezza <lb></lb>dell&#039;umor acqueo ad ammettere l&#039;esistenza di uno spirito aereo repletivo <lb></lb>della camera anteriore dell&#039;occhio, ne esagerò così l&#039;ampiezza, da farla uguale <lb></lb>allo spazio occupato in dietro dall&#039;umor vitreo. </s>

<s>Fu l&#039;errore messo in più ver­<lb></lb>gognosa mostra, che dalle parole, da quel malaugurato iconismo impresso al <lb></lb>cap. </s>

<s>XIV del VII libro <emph type="italics"></emph>De humani corporis fabrica,<emph.end type="italics"></emph.end> alla pagina altrove citata. </s></p><p type="main">

<s>Diciamo quell&#039;iconismo malaugurato, perchè gli offesi dalle soverchianze <lb></lb>orgogliose dell&#039;Autore si gittarono a quella vista sopra lui, come cani in <lb></lb>caccia sulla preda ferita. </s>

<s>Chi non sente spirare la voluttà della vendetta da <pb xlink:href="020/01/1448.jpg" pagenum="323"></pb>queste parole, colle quali il Colombo termina il suo X libro? </s>

<s>“ Errores Ve­<lb></lb>salii deprehendes, qui tota errat via, existimans cristallinum humorem in <lb></lb>centro oculi exquisite situm esse, item tantum humoris aquei quantum vi­<lb></lb>trei reperiri ” (De re anat. </s>

<s>cit., pag. </s>

<s>220). </s></p><p type="main">

<s>Giovanni Valverde spagnolo che nel 1559 ridusse in compendio l&#039;ana­<lb></lb>tomia del Colombo, e che con quella traduzione italiana del suo libro, fatta <lb></lb>per lui l&#039;anno dopo da Antonio Tabo, conferì a diffondere le nozioni più <lb></lb>elementari della scienza in chi non la professava, scrivendo nel V libro <emph type="italics"></emph>Degli <lb></lb>occhi,<emph.end type="italics"></emph.end> dop&#039;aver detto della cornea e dell&#039;iride, così soggiungeva: “ Lo spa­<lb></lb>zio tra queste due tele è pieno di un umore chiamato Hialoydes, che vuol <lb></lb>dire acquoso, per esser simile all&#039;acqua. </s>

<s>Altri il chiamarono albugineo, per <lb></lb>esser simile al chiaro dell&#039;uovo, il quale non è tanta quantità quanta si <lb></lb>pensò il Vesalio, perchè aprendo l&#039;occhio, ancor che sia finito di morir <lb></lb>l&#039;uomo, non escono più di sei o sette gocciole d&#039;acqua ” (Anatomia del <lb></lb>corpo umano, Roma 1560, pag. </s>

<s>113). </s></p><p type="main">

<s>Il Falloppio, sempre più gentile ne&#039;modi, anche più efficacemente cor­<lb></lb>resse gli errori del Vesalio, descrivendo con la maggior diligenza il vero, e <lb></lb>lasciando che altri ne facessero a loro piacere il confronto o ne rilevassero <lb></lb>il contrapposto. </s>

<s>Perciò nell&#039;<emph type="italics"></emph>Examen observationum<emph.end type="italics"></emph.end> il Brussellese risponde, <lb></lb>piuttosto che al Falloppio, al Colombo e al Valverde, e rispondendo, esem­<lb></lb>pio raro, confessa il suo errore, di cui par che voglia addur per sua scusa <lb></lb>l&#039;esempio dello stesso Galeno, che per simili cause, come sopra osservammo, <lb></lb>s&#039;era pure ingannato. </s>

<s>“ Quum enim oculum, così leggesi nel citato <emph type="italics"></emph>Exa­<lb></lb>men,<emph.end type="italics"></emph.end> frequentius mea vulgari illa, quam in meis libris descripsi, admini­<lb></lb>stratione, solebam secare, omnes tres simul humores in volam ex oculo pro­<lb></lb>cidebant, et quando tum duae aut tres tantum aquei humoris se offerebant <lb></lb>guttulae, universum illud spatium, quod illi humori in oculo adscribimus, <lb></lb>etiam spiritu oppleri existimabamus. </s>

<s>Et quamvis impar omnino aquei hu­<lb></lb>moris cum vitreo videbatur tum proportio, spirituum tamen illorum et oculi <lb></lb>mox a morte anteriore in sede collapsus, ac curationis denique, quam in <lb></lb>suffusionum depressionibus acu molimur, occasionem, cristallinum humorem, <lb></lb>magis quam oportuit, in posteriora retrusi, quemadmodum etiam iusta vi­<lb></lb>trei humoris moles a me non est explicata ” (Venetiis 1564, pag. </s>

<s>162). </s></p><p type="main">

<s>Cosicchè, se l&#039;errore del Vesalio si disse da una parte malaugurato, si <lb></lb>può chiamar dall&#039;altra felice, avendo non solamente fruttato il merito di que­<lb></lb>sta confessione, ma dato impulso a quel più diligente esame anatomico, e <lb></lb>a quella più acconcia amministrazione dell&#039;occhio, della quale il Berenga­<lb></lb>rio avea dato l&#039;esempio. </s>

<s>Il Colombo e il Falloppio insegnarono con gli scritti: <lb></lb>l&#039;Eustachio, di quelle dissoluzioni delle parti componenti l&#039;organo della vi­<lb></lb>sta, da sè fatte con tant&#039;arte, <emph type="italics"></emph>quod vix animus capere potest;<emph.end type="italics"></emph.end> lasciò che <lb></lb>ne parlassero gl&#039;iconismi. </s>

<s>Da questi tre insigni Autori, insieme col Beren­<lb></lb>gario, ebbe propriamente principio lo studio anatomico dell&#039;occhio dell&#039;uomo, <lb></lb>come lo dimostrava dianzi la storia delle membrane, e come lo confermerà <lb></lb>ora quella, che siam per dar brevemente, dei tre umori in particolare. </s></p><pb xlink:href="020/01/1449.jpg" pagenum="324"></pb><p type="main">

<s>Gli antichi non si espressero chiaramente intorno al definir la quantità <lb></lb>dell&#039;umor vitreo, rispetto agli altri due: il Berengario si limitò a dire che <lb></lb>è “ in quantitate maior aliis duobus ” (Comment. </s>

<s>cit., fol. </s>

<s>CCCCLXIX), e, <lb></lb>nell&#039;Isagoge, che “ est longe maior cristallino ” (editio cit., fol. </s>

<s>52), ciò che <lb></lb>dette occasione al Vesalio di dir nelle sue ritrattazioni: “ Nulla nemque vi­<lb></lb>trei cum aqueo est proportio, isque magis quam ad mediam oculi sedem <lb></lb>antrorsum ducitur ” (Examen cit., pag. </s>

<s>162). </s></p><p type="main">

<s>Primo a definire quelle proporzioni fu il Colombo, il quale scrisse che <lb></lb>l&#039;ialoide è di tal mole “ ut ex quatuor oculi partibus tres occupet ” (De re <lb></lb>anat., cit., pag. </s>

<s>219). L&#039;Acquapendente lo disse “ fere quadruplo crystal­<lb></lb>loidem exsuperantem ” (De oculo cit., pag. </s>

<s>193) e il Casserio quadruplo <lb></lb>del cristallino, e quasi doppio dell&#039;acqueo. </s>

<s>“ Maximus omnium est humor <lb></lb>vitreus et crystallinum quadruplo, albugineum duplo fere superans ” (Pen­<lb></lb>taestheseion, Venetiis 1609, pag. </s>

<s>289). Ma per la diffluente mollizie essendo <lb></lb>difficile a determinarsi quelle precise misure, anche all&#039;arte peritissima dei <lb></lb>moderni, si contentarono questi d&#039;affermar così in generale col Zinn: “ hu­<lb></lb>more vitreo longe maximam cavitatis oculi partem occupari ” (Descriptio <lb></lb>oculi cit., pag. </s>

<s>118). </s></p><p type="main">

<s>La fisica costituzion dell&#039;umore, che lo fece infino dagli antichissimi <lb></lb>tempi rassomigliare al vetro fuso, rivelò con facilità l&#039;esistenza di quella, al­<lb></lb>trimenti sfuggevole, membrana che gli serve da recipiente. </s>

<s>“ Id, scrisse <lb></lb>Celso dell&#039;ialoide, neque liquidum neque aridum est, sed quasi concretus <lb></lb>humor..... Id autem, superveniens ab interiore parte, membranula inclu­<lb></lb>dit ” (De re medica cit., fol. </s>

<s>100). Pretermessa negligentemente questa mem­<lb></lb>branula nelle sue descrizioni dal Vesalio, fu il Falloppio il primo a rinfre­<lb></lb>scarne la perduta memoria, annoverandola fra le altre tuniche dell&#039;occhio. <lb></lb></s>

<s>“ Verum enim vero tunica, quae vitreum humorem ambit, et in illa cavi­<lb></lb>tate crystallo dicata, et in reliqua totius humoris superficie a Vesalio prae­<lb></lb>termissa, procul omni dubio addi debet ” (Observat. </s>

<s>anat., Op. </s>

<s>omnia cit., <lb></lb>pag. </s>

<s>479). Nonostante il Vesalio stesso disse, nel poco fa citato <emph type="italics"></emph>Esame,<emph.end type="italics"></emph.end> di <lb></lb>non aver avuto ancora tanti occhi, “ ut peculiarem quandam tunicam, a me <lb></lb>non descriptam, vitreo humori tribuere valeam ” (pag. </s>

<s>163). Il Plater però non <lb></lb>ebbe alcun dubbio di designar, nella Tavola XLIX illustrativa del suo trat­<lb></lb>tato <emph type="italics"></emph>De corporis humani structura,<emph.end type="italics"></emph.end> fra le tuniche anche l&#039;<emph type="italics"></emph>ialoides,<emph.end type="italics"></emph.end> ma il <lb></lb>Vidio assegnò propriamente alla Retina l&#039;ufficio d&#039;involgere l&#039;umor vitreo <lb></lb>“ a posteriori parte et a priori ” (De anatome cit., pag. </s>

<s>320), e tale si fu <lb></lb>pure l&#039;opinione dell&#039;Acquapendente che, designando le tre membrane del­<lb></lb>l&#039;occhio, la scleroide, la coroide e la Retina, dice che si espandono in emi­<lb></lb>sferio, “ humorem vitreum intus posteriusque complexae ” (De oculo cit., <lb></lb>pag. </s>

<s>187). </s></p><p type="main">

<s>Giovan Batista Ruschi, benchè affermasse essere stata la ialoide cono­<lb></lb>sciuta da suo padre, che però la confuse coll&#039;aracnoide, nel passare a farne, <lb></lb>nel cap. </s>

<s>XI del II libro del suo <emph type="italics"></emph>Visus organo,<emph.end type="italics"></emph.end> una particolar descrizione, <lb></lb>la riguardò come cosa di poco momento, per non essere altro in sostanza <pb xlink:href="020/01/1450.jpg" pagenum="325"></pb>che la superficie dello stesso umor vitreo. </s>

<s>“ Videtur autem fere ipsa vitrei <lb></lb>substantia: corpora enim omnia in superficie quasi pellicula vel crustula <lb></lb>obducuntur, etsi, hac etiam dissecta tunica, si tunica meretur nominari, vi­<lb></lb>treum nihilominus consistat ” (editio cit., pag. </s>

<s>46). </s></p><p type="main">

<s>Questa opinione del Ruschi fu, per tacere di tanti altri, seguita dal <lb></lb>Briggs, nel cap. </s>

<s>III della sua Ottalmografia, tra gli stranieri, e fra&#039;nostri <lb></lb>dal Molinetti, il quale disse avere la ialoidea origine dallo stesso umore “ su­<lb></lb>perficie scilicet ipsius crassescente in tunicam, prout plerisque probabile vi­<lb></lb>sum est ” (Dissert. </s>

<s>anat. </s>

<s>cit., pag. </s>

<s>22). </s></p><p type="main">

<s>Ma perchè le probabilità e i pareri altrui non fanno scienza, si volle <lb></lb>ricorrere alle esperienze. </s>

<s>Il Morgagni, estratto l&#039;umor vitreo dagli occhi di <lb></lb>varii animali, e per sessant&#039;ore tenutolo esposto all&#039;aria, non vide perciò <lb></lb>“ crassiorem pelliculam ostendisse ” (Epist. </s>

<s>XVII cit., pag. </s>

<s>274). Altre espe­<lb></lb>rienze fatte dal Desmours dimostrarono, contro l&#039;asserzione del Ruschi, che <lb></lb>ferita la membrana si vede uscir l&#039;umore per la rottura, e anzi trasudare <lb></lb>spontaneamente attraverso ai pori naturali, lasciata all&#039;aria essa membrana <lb></lb>illesa. </s>

<s>Del resto il vederla, iniettandovi il fiato, rigonfiare e staccarsi dal­<lb></lb>l&#039;umor sottoposto, fu tale conclusiva esperienza, da togliere anche l&#039;ombra <lb></lb>del dubbio. </s></p><p type="main">

<s>Fra il vitreo e il cristallino era naturalissimo veder che passava una <lb></lb>strettissima relazione, e benchè distinti di forma e di natura si trovavano, <lb></lb>a qualunque più ovvio esame, sempre fra loro amichevolmente congiunti in­<lb></lb>sieme. </s>

<s>Il Berengario disse che il legame di così fatta congiunzione consi­<lb></lb>steva nella retina, che dalla parte anteriore si trasforma nell&#039;aranea. </s>

<s>“ Et <lb></lb>hic cristallinus humor, absque aliquo medio, ante habet tunicam araneam, <lb></lb>et sic tunica aranea, rethina et cristallinus humor cum vitreo sunt ligati ” <lb></lb>(Commentaria cit., fol. </s>

<s>CCCCLXIX). </s></p><p type="main">

<s>Il Colombo fece poi dell&#039;aranea una membrana distinta, sottilissima e <lb></lb>trasparente come i veli delle cipolle, l&#039;ufficio della quale fosse “ ut humo­<lb></lb>res vitreum et cristallinum complecteretur ” (De re anat. </s>

<s>cit., pag. </s>

<s>218). È <lb></lb>tutta andantemente, soggiunge, una membrana sola “ licet ea parte, quae <lb></lb>ante cristallinum locatur, paulo crassior sit quam in reliquis partibus ” (ibid.). </s></p><p type="main">

<s>Nonostante il Ruschi, tornando indietro al Berengario, disse che, giunta <lb></lb>la retina alla circonferenza del cristallino, in quel punto che questo emerge <lb></lb>dal vitreo, “ in duplicem abit tenuissimam tunicam, quae a dicto circulo <lb></lb>orta tenuiori sui parte inferius dimidietatem crystallini vitreo mersam inve­<lb></lb>stit, altera nonnihil crassiori emergentem dimidietatem obvolvit, ita ut undi­<lb></lb>quaque hac eadem membrana crystallinus investiatur, quae, cum tenuissima <lb></lb>sit, araneae nomen sortita est ” (De visus org. </s>

<s>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Queste dimenticate osservazioni del nostro Anatomico pisano, sui prin­<lb></lb>cipii del secolo XVIII, quando l&#039;esperienze avevano oramai dimostrata l&#039;esi­<lb></lb>stenza della gialloidea, rifiorirono in Francia, dove il Petit, riconoscendo in <lb></lb>essa gialloidea quella divisione in due lamine, che aveva il Ruschi descritta <lb></lb>nella Retina o nell&#039;Aranea, scoprì che, nel punto della loro separazione, la-<pb xlink:href="020/01/1451.jpg" pagenum="326"></pb>sciavano uno spazio vuoto, da cui veniva a formarsi un certo canale distinto <lb></lb>col nome di <emph type="italics"></emph>Canal godronnė<emph.end type="italics"></emph.end> dall&#039;inventore, ma che più volentieri gli Ana­<lb></lb>tomici designarono poi col nome di <emph type="italics"></emph>Canal del Petit.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La curiosa scoperta richiamò a sè l&#039;attenzione degli Anatomici, uno <lb></lb>de&#039;più studiosi fra&#039;quali fu il Zinn, a cui occorse di scoprire o di mettere <lb></lb>in maggiore evidenza, in tale occasione, una parte distinta di quell&#039;organo, <lb></lb>che lega insieme il vitreo col cristallino. </s>

<s>“ Dum enim, così egli stesso rac­<lb></lb>conta, in oculis et humanis et bubulis in fabricam Canalis petitiani inquiro, <lb></lb>iteratis experimentis, demum edoctus fui in eodem plano, ubi corpus ciliare <lb></lb>ex choroide producitur, ex tunica vitrea oriri membranulam aut zonulam ” <lb></lb>(Descriptio oculi cit., pag. </s>

<s>122). </s></p><p type="main">

<s>Si risovvenne allora che questa zonula era quella medesima, che il Mor­<lb></lb>gagni trovò fra le schedule del Valsalva descritta come veduta separarsi dal <lb></lb>cristallino “ ad formam plani circularis, quae solam tegat partem ipsius an­<lb></lb>teriorem ” (Epist. </s>

<s>XVII cit., pag. </s>

<s>272), e impose a quello stesso piano, che <lb></lb>a guisa di collare circonda la lente, il nome di <emph type="italics"></emph>Corona ciliare:<emph.end type="italics"></emph.end> “ nomine <lb></lb>Coronae ciliaris mihi dicta ” benchè gli Anatomici oggidì comunemente la <lb></lb>chiamino <emph type="italics"></emph>Zona del Zinn.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La membrana dunque, che involge il <emph type="italics"></emph>Canal godronnė,<emph.end type="italics"></emph.end> non è una con­<lb></lb>tinuazione della gialloidea, come si dette a credere il Petit, ma è quella <lb></lb>Zona, che porse al Zinn nello scoprirla occasion di descrivere il canal pe­<lb></lb>titiano più diligentemente del suo stesso inventore. </s>

<s>Uscita dalla gialloidea, <lb></lb>dice esso Zinn, e rimasta da lei libera, benchè contigua, la <emph type="italics"></emph>Corona,<emph.end type="italics"></emph.end> da quella <lb></lb>parte che s&#039;insinua tra il corpo vitreo e il corpo ciliare, “ sensim, quo pro­<lb></lb>pius ad lentem accedit, eo magis a corpore vitreo dimovetur, et in conve­<lb></lb>xitate demum anteriori lentis ultra circulum maximum capsulae illius inse­<lb></lb>ritur, ut adeo spatium nascatur naturale exiguum triangulare curvilineum <lb></lb>inter humorem vitreum et hanc modo dictam membranulam, cuius trianguli <lb></lb>basin sistit illa portio convexitatis anterioris lentis, inter circulum maximum <lb></lb>et insertionem eius membranulae intermedia. </s>

<s>Illa autem zonula, a prima <lb></lb>origine ex tunica vitrea ad insertionem in lentem usque, percurritur fibris <lb></lb>fortioribus transversis, et ipsa membrana multo brevioribus, quae illam per <lb></lb>intervalla sic stringunt et contrahunt, ut per vulnusculum membranulae illi <lb></lb>inflictum, flatu in spatium illud triangulare immisso, canalis se sistat con­<lb></lb>tinuus, et lentem undique ambiens, spatiis alternis immisso flatu turgenti­<lb></lb>bus et contractis, qui, si comparationem instituere liceat, figuram fere expri­<lb></lb>mere videtur intestini coli flatu repleti, a ligamentis longitudinalibus intestino <lb></lb>brevioribus in rugas contracti ” (ibid., pag. </s>

<s>123). </s></p><p type="main">

<s>La facile esperienza poi, per la quale si dimostrava che, insuffiato l&#039;in­<lb></lb>volucro della lente, il fiato non passava dentro il Canale, mentre veniva a <lb></lb>confermare il fatto non potere, come dicevasi, un tale involucro nascere <lb></lb>dalla duplicatura della gialloidea, dimostrava nel tempo stesso quel ch&#039;era <lb></lb>stato così lungamente controverso, che cioè essa lente cristallina era involta <lb></lb>da una capsula sua propria. </s>

<s>La ragione di così fatte controversie, che du-<pb xlink:href="020/01/1452.jpg" pagenum="327"></pb>rarono fino ai primi anni del secolo XVIII, non è difficile trovarla nella te­<lb></lb>nuità e trasparenza di quel velo, che, sfuggevole a ogni vista più acuta, si <lb></lb>rivelò solo allora che si vide mobile al fiato. </s></p><p type="main">

<s>Fu questa stessa trasparenza anche causa del non poter gli Anatomici <lb></lb>così per tempo riconoscere la particolare struttura dell&#039;umor cristallino. </s>

<s>Lo <lb></lb>Stenone, sezionando l&#039;occhio delle Carcarie e di molti altri pesci, fu il <lb></lb>primo che trovasse in essi la lente affaldata nel mezzo di lamelle, come le <lb></lb>tuniche nelle cipolle, circondate da una materia glutinosa, sopra la quale <lb></lb>galleggiava un liquido affatto simile all&#039;acqua. </s>

<s>“ Crystallini humoris substan­<lb></lb>tia triplex erat: media dura, et ex lamellis composita; huic undique adhae <lb></lb>rens alia multum glutinosa; tertia, tunicae proxima, omnino aquea ” (Ele­<lb></lb>mentorum myol. </s>

<s>specimen cit., pag. </s>

<s>80). </s></p><p type="main">

<s>Il difficile esame anatomico dello Stenone rimase per parecchi anni senza <lb></lb>riscontro, infino al Morgagni, il quale trovò che la struttura lamellare del <lb></lb>nucleo era propria al cristallino di tutti gli animali. </s>

<s>Trovò di più che le la­<lb></lb>mine si fanno dall&#039;interno all&#039;esterno sempre più molli, infino a ridursi in <lb></lb>quella sostanza glutinosa già descritta dallo stesso Stenone. </s>

<s>“ Illud tamen <lb></lb>constantius observare consuevi, non modo in piscibus, verum etiam in cae­<lb></lb>teris animalibus, crystallini corpus, quo magis ab interiore medio nucleo re­<lb></lb>cedit, eo magis magisque mollescere, quod et in resiccato lamellae ostendunt <lb></lb>eo magis friabiles quo exteriores, et in recenti substantia exterior, gelatinam <lb></lb>quasi quandam et interdum vitraei humoris consistentiam aemulans, quod <lb></lb>neque intermediae et multo minus intimae substantiae convenit, plane con­<lb></lb>firmat ” (Adversaria anat., Patavii 1719, pag. </s>

<s>90). </s></p><p type="main">

<s>Del terzo strato acqueo, descritto dallo Stenone, il Morgagni pure am­<lb></lb>mise l&#039;esistenza, affermando “ tunica incisa, humorem quendam aqueum <lb></lb>prodire ” (ibid.). Mossi da una tale affermazione gli Anatomici dettero a quel <lb></lb>liquido acqueo il nome di <emph type="italics"></emph>Umor del Morgagni,<emph.end type="italics"></emph.end> ma l&#039;Haller fu, se non <lb></lb>de&#039;primi, de&#039;più autorevoli senza dubbio in negarne l&#039;esistenza. </s>

<s>“ Nullam, <lb></lb>egli dice nel citato Tomo degli Elementi di Fisiologia, in crystallina lente <lb></lb>aqulam reperi ” (pag. </s>

<s>405) e quella trovatavi dal Morgagni la crede un&#039;esa­<lb></lb>lazion vaporosa, condensatasi nel cadavere, provvidamente ordinata dalla Na­<lb></lb>tura a impedir l&#039;adesione della capsula con la lente. </s>

<s>“ Nam ea aquula, <lb></lb>emissa lens crystallina, collabitur, sicca fit et opaca, et suae capsulae adhae­<lb></lb>ret ” (ibid., pag. </s>

<s>406). </s></p><p type="main">

<s>Più facile che la struttura pareva a definire della lente cristallina la <lb></lb>forma, eppure quanto furono intorno a ciò varii i giudizii degli Anatomici, <lb></lb>da&#039;più antichi infino ai moderni! Anzi Galeno stesso, nelle varie sue opere, <lb></lb>dà di quella stessa forma giudizii diversi, imperocchè, mentre nel cap. </s>

<s>II del <lb></lb>libro X <emph type="italics"></emph>De usu partium,<emph.end type="italics"></emph.end> al fol. </s>

<s>178 del I Tomo delle Opere più volte ci­<lb></lb>tato, dice del cristallino <emph type="italics"></emph>quod rotundum est,<emph.end type="italics"></emph.end> e ch&#039;egli nuota nel vitreo <lb></lb>“ quasi semisecta quaepiam sphaera in aqua, ” nel cap. </s>

<s>VIII del VII libro <lb></lb><emph type="italics"></emph>De&#039;placiti d&#039;Ippocrate e di Ptatone<emph.end type="italics"></emph.end> lo rappresenta invece a somiglianza di <lb></lb>un globo compresso. </s>

<s>Gli Arabi si accostarono con Ruffo Efesio e con Teofilo, <pb xlink:href="020/01/1453.jpg" pagenum="328"></pb>che fecero il cristallino dalla parte anteriore men convesso e quasi piano; <lb></lb>ciò che fu poi confermato dalle osservazioni del Berengario. </s>

<s>“ Sua figura, <lb></lb>egli scrive, non est totaliter sphaerica: sphaerica tamen est versus anterius <lb></lb>cum aliquali planitie.... et ideo Hali vocat suam partem anteriorem sub­<lb></lb>planam ” (Comment. </s>

<s>cit., fol. </s>

<s>CCCCLXXIV). </s></p><p type="main">

<s>Nella instaurazione della nuova Anatomia il Vesalio ripetè ciò che, nei <lb></lb>Placiti sopra citati, avea detto Galeno, rappresentando il cristallino non come <lb></lb>esattamente rotondo, “ sed et anteriori et posteriori parte leviter non secus <lb></lb>compressum, quam si lignei globi medio, secundum lineas aequidistantes, <lb></lb>orbem crassiusculum serra exemisses, et dein duas globi partes denuo con­<lb></lb>glutinasses.... ad lentis similitudinem ” (De hum. </s>

<s>corp. </s>

<s>fabrica cit., pag. </s>

<s>646). <lb></lb>Ma il Colombo convenne piuttosto col Berengario, dicendo esser l&#039;umor cri­<lb></lb>stallino conglobato sì in sfera, però compressa, dalla parte che guarda l&#039;umor <lb></lb>acqueo, in modo, “ ut lentis formam referat ” (De re anat. </s>

<s>cit., pag. </s>

<s>219). <lb></lb>La quale affermazione confortata dall&#039;altra del Falloppio, che scrisse essere <lb></lb>il cristallino sferico dalla parte posteriore, “ in anteriori vero depressus <lb></lb>ita, ut haec facies parum a plana distet ” (Observat. </s>

<s>anat., Op. </s>

<s>omnia cit., <lb></lb>pag. </s>

<s>479), valse a far dimenticare la descrizione, che ne aveva fatta il Ve­<lb></lb>salio “ a Galeno assumens ” (ibid.). </s></p><p type="main">

<s>L&#039;Acquapendente fu il primo a comparar la figura dell&#039;umore ne&#039;varii <lb></lb>generi di animali, e ne&#039;pesci la trovò esattamente rotonda, ma negli uo­<lb></lb>mini, ne&#039;bovi e in altri simili “ non usquequaque et ad unguem perfecta <lb></lb>rotunditas apparet, sed quidem, qua vitreum contingit in eumque mergitur, <lb></lb>perfectam habet rotunditatem, Galeno ignotam. </s>

<s>Anterius autem ad aqueum <lb></lb>humorem depressus est, et lenticulae extuberantiam refert, unde haec pars <lb></lb>lenticularis a Ruffo est appellata ” (De oculo, Op. </s>

<s>omnia cit., pag. </s>

<s>192). </s></p><p type="main">

<s>Più minute osservazioni in proposito furono poi fatte, al riferir del Gas­<lb></lb>sendo, dal Peirese, il quale è il primo che abbia tentato di misurare se­<lb></lb>condo qual ragione stieno, ne&#039;varii animali, i raggi di curvatura delle due <lb></lb>faccie della lente, benchè confessi di non aver potuto da così fatte misure <lb></lb>concluder nulla, in ordine al determinar la vera figura geometrica della <lb></lb>stessa lente, “ praesertim quia mortuo animali humor flaccescit collabitur­<lb></lb>que, et seu a digitis tractetur, seu suspensus teneatur, seu supra papyrum <lb></lb>resideat, vix potest non deflectere a nativa sua figura ” (Vitae, lib. </s>

<s>V, Pa­<lb></lb>risiis 1641, pag. </s>

<s>279). </s></p><p type="main">

<s>Nascevano così fatte difficoltà naturalmente dall&#039;esame anatomico dei <lb></lb>fatti, ma i Diottrici si lusingarono di poterle superare, prescrivendo alla <lb></lb>stessa Natura quelle leggi, che avevano con l&#039;aiuto della geometria presta­<lb></lb>bilite nelle loro astratte speculazioni. </s>

<s>Il Keplero, nel § I del cap. </s>

<s>V de&#039;Pa­<lb></lb>ralepomeni a Vitellione, assegnò al cristallino, da quella parte che riguarda <lb></lb>l&#039;acqueo, la figura di un conoide ellissoideo, e da quell&#039;altra, che riguarda <lb></lb>il vitreo, la figura di un conoide iperbolico. </s>

<s>“ Chrystallinus, ea facie quae <lb></lb>aqueo immergitur, figuram accepit aut sphaericam aut sphaeroidis lenticu­<lb></lb>laris portionem circumducta ellipsi per axem divisa;.... a posteriore parte, <pb xlink:href="020/01/1454.jpg" pagenum="329"></pb>quae vitreo immergitur, figura ipsi est conoides hyperbolica ” (Franco­<lb></lb>furti 1604, pag. </s>

<s>167). Nella Diottrica accennò poi che così fatta figura <emph type="italics"></emph>con­<lb></lb>stat experientia Anatomicorum,<emph.end type="italics"></emph.end> ma ch&#039;ella fosse dedotta piuttosto dalle <lb></lb>teorie, lo tradisce il processo stesso delle dimostrazioni. </s>

<s>Dop&#039;avere infatti <lb></lb>nella propos. </s>

<s>LIX dimostrato: “ Superficies densi, quae parallelos per cor­<lb></lb>pus venientes, post corpus refractione facta, perfecte concurrere facit, est <lb></lb>hyperbolicae adfinis ” (Augustae Vindel. </s>

<s>1611, pag. </s>

<s>2); passa immediata­<lb></lb>mente a farne l&#039;applicazione all&#039;umor cristallino dell&#039;occhio, scrivendo: <lb></lb>“ Chrystallinus humor oculi est lens convexa forma hyperbolae ” (ibid.). </s></p><p type="main">

<s>Era una tal maniera di argomentare dalle teorie ai fatti conformissima <lb></lb>al genio del Cartesio, il quale avendo nella Diottrica dimostrato che la linea <lb></lb>del perfetto concorso non è nè l&#039;iperbola nè la parabola, ma l&#039;ellisse, ne <lb></lb>concluse che dovesse avere la lente cristallina, dalle due facce, una figura <lb></lb>ellissoidea. </s>

<s>Vedesi questa figura esquisitamente rappresentata negli iconismi <lb></lb>impressi nel cap. </s>

<s>III della Diottrica, e nel trattato <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end> dov&#039;essen­<lb></lb>dosi designata la lente per la lettera L vien nel testo dichiarata con queste <lb></lb>parole: “ Figura humoris L, qui <emph type="italics"></emph>crystallinus<emph.end type="italics"></emph.end> dicitur, similis est illi figurae <lb></lb>vitrorum, quam in tractatu de Dioptrica descripsi, quorum interventu omnes <lb></lb>radii, ab uno quodam puncto venientes, coeunt in puncto quodam alio ” <lb></lb>(Francofurti ad M. 1692, pag. </s>

<s>62). </s></p><p type="main">

<s>Mentre gli Anatomici rimanevano tuttavia incerti de&#039;loro esami, non <lb></lb>mancarono nel secolo XVII alcuni, che si confidarono meglio delle specu­<lb></lb>late teorie de&#039;Diottrici, e il Philippeau, riferente lo Stenone “ crystallini <lb></lb>figuram ex duabus hyperbolis in homine compositam credit ” (Elem. </s>

<s>Myol. </s>

<s><lb></lb>specimen cit., pag. </s>

<s>82), e il Molinetti vide colla mente “ crystallinum bina <lb></lb>superficie praeditum, utraque ad ellipsim vergente ” (Dissertat. </s>

<s>anat. </s>

<s>cit., <lb></lb>pag. </s>

<s>18), dietro i dimostrati teoremi cartesiani. </s></p><p type="main">

<s>Svaporati nel secolo XVIII i fumi di quella inebriatrice Filosofia car­<lb></lb>tesiana, e più sanamente radicatasi l&#039;opinione non si dare altra scienza in <lb></lb>natura, da quella infuori che resulta dall&#039;osservazione dei fatti e dalla espe­<lb></lb>rienza; si potè nel presente proposito concluderne questo solo, che cioè la <lb></lb>convessità, nella parte anteriore della lente, è sempre maggior che nella po­<lb></lb>steriore. </s>

<s>“ Omnes certe meae observationes in eo consentiunt, scrisse il <lb></lb>Zinn, lentis convexitatis anterioris sectionem ad maioris circuli ambitum, <lb></lb>quam posterioris attinere,.... semperque mihi contigit videre utramque fa­<lb></lb>ciem, habita ratione ad diametrum transversalem, eo esse convexiorem quo <lb></lb>propior homo est origini, ut in fetu aut infante recens nato ad figuram fere <lb></lb>sphaericam accedere, et diameter ab anterioribus ad posteriora parum a dia­<lb></lb>metro transversali abludere videatur, quae lens in utraque facie eo planior <lb></lb>deprehenditur, quo homo adultior fuerit: post annum tamen tricesimum <lb></lb>figura lentis parum amplius mutari ” (Descriptio oculi cit., pag. </s>

<s>128, 29). </s></p><p type="main">

<s>Venivano da queste osservazioni a conciliarsi le varie sentenze degli <lb></lb>Anatomici, specialmente più antichi, essendo facile che le varie figure da <lb></lb>essi notate nel cristallino dipendessero in gran parte dalle varie età degli <pb xlink:href="020/01/1455.jpg" pagenum="330"></pb>individui, gli occhi de&#039;quali si sottoponevano all&#039;anatomico esame, ma per <lb></lb>nulla rendevasi da tuttociò probabile che la Natura usi in lavorar la lente <lb></lb>dell&#039;occhio l&#039;arte usata dagli uomini in fabbricare e configurare i vetri da <lb></lb>servire ai loro diottrici strumenti. </s>

<s>Comunque siasi però, non potè per gli <lb></lb>usi della vista naturale negarsi, nè agli antichi nè ai moderni, l&#039;eccellenza <lb></lb>del cristallino sopra gli altri due umori, e specialmente sopra l&#039;acqueo, la <lb></lb>storia del quale si riduce per noi a pochi e semplici fatti. </s></p><p type="main">

<s>Dopo Galeno, i primi studii a noi noti incominciano col Berengario, il <lb></lb>quale descrivendo quell&#039;umore, che si rassomigliava all&#039;albume dell&#039;uovo, <lb></lb>e dicendolo invece “ fluxibilis ut aqua ” (Comment. </s>

<s>cit., fol. </s>

<s>CCCCLXX), <lb></lb>conferì a fargli, nel linguaggio degli Anatomici posteriori, scambiar l&#039;antico <lb></lb>e improprio nome di albugineo in quello di <emph type="italics"></emph>acqueo.<emph.end type="italics"></emph.end> Il Colombo, che fu dei <lb></lb>primi ad usare quella nuova denominazione, la quale poi si rese comune, <lb></lb>raccomanda alla memoria de&#039;suoi lettori un fatto singolare, che fu in tal <lb></lb>proposito da lui stesso osservato: “ Hoc quod dicam, obsecro lector, ne exci­<lb></lb>dat me certa coniectura deprehendisse humorem hunc instar excrementi <lb></lb>esse: nam ego bis hisce oculis vidi totum prorsus effusum esse ob vulnera, <lb></lb>tamen spatio temporis renatum, ita ut eodem oculo cernere deinceps potu­<lb></lb>erit ” (De re anat. </s>

<s>cit., pag. </s>

<s>219). Dello stesso fatto, che reputavasi allora <lb></lb>maraviglioso, tornò un mezzo secolo dopo a pigliar nuova esperienza il padre <lb></lb>di Giovan Batista Ruschi, così commemorato nel cap. </s>

<s>II del III libro <emph type="italics"></emph>De <lb></lb>visus organo:<emph.end type="italics"></emph.end> “ Egregiam habeo ac iuxta vulgi opinionem admirabilem pa­<lb></lb>tris mei observationem, qui cuidam ex vulnere aqueum humorem viderat <lb></lb>excidisse, ac ita visionem interceptam, eodem regenerato, non multo tem­<lb></lb>pore restitutam ” (editio cit., pag. </s>

<s>49). </s></p><p type="main">

<s>Andate queste tradizioni della scienza in dimenticanza, un altro mezzo <lb></lb>secolo dopo il Redi, che tante favolose storie degli antichi ridusse alla ve­<lb></lb>rità dei fatti naturali, avendo letto in Dioscoride e in Plinio che l&#039;erba ce­<lb></lb>lidonia fu ritrovata dalle Rondini, per usarla come medicina intorno agli <lb></lb>occhi lacerati de&#039;loro pulcini, si assicurò per ripetute esperienze esser ca­<lb></lb>gionata quella guarigione dalla sola Natura, senz&#039;altro medicamento, “ come <lb></lb>potrà esser manifesto ad ognuno che voglia aver curiosità di forar gentil­<lb></lb>mente, o con ago o con lancetta da cavar sangue, gli occhi alle rondini o <lb></lb>a qualsivoglia altro uccello. </s>

<s>Io n&#039;ho fatta la prova ne&#039;colombi, nelle galline, <lb></lb>nell&#039;oche, nelle anatre e ne&#039;galli d&#039;India, e gli ho veduti spontaneamente <lb></lb>guarire in meno di ventiquattr&#039;ore ” (Esper. </s>

<s>intorno a cose nat., Opere, <lb></lb>T. II, Napoli 1741, pag. </s>

<s>10). </s></p><p type="main">

<s>Capitato questo Discorso del Redi alle mani del Naturalista empolese <lb></lb>Ippolito Neri, volle provare se per fortuna avvenisse la stessa guarigione <lb></lb>negli occhi de&#039;quadrupedi. </s>

<s>“ E di fatto, scrive Giuseppe Zambeccari in una <lb></lb>sua elegantissima descrizione d&#039;<emph type="italics"></emph>Esperienze intorno a diverse viscere ta­<lb></lb>gliate,<emph.end type="italics"></emph.end> e intitolata allo stesso Redi, avendogli V. S. illustrissima sommini­<lb></lb>strate tutte le cose necessarie, sdrucì gentilmente tutt&#039;e due gli occhi, con <lb></lb>una lancetta da cavar sangue, ad un cane, e ne fece uscire tutto quanto <pb xlink:href="020/01/1456.jpg" pagenum="331"></pb>l&#039;umido acquoso a segno tale, che gli occhi rimasero come due borselli voti <lb></lb>e grinzi. </s>

<s>Lasciato poscia il cane a benefizio di natura, si conobbe eviden­<lb></lb>tissimamente, sei ore dopo e forse in più breve tempo, che gli occhi si erano <lb></lb>ripieni e tornati nel loro stato naturale col segno solamente della cicatrice, <lb></lb>ed il cane era festoso ed allegro, come se non gli fosse fatto male veruno, <lb></lb>e quel che più importa non era rimasto cieco, ma ci vedeva benissimo.... <lb></lb>Si ritentò di nuovo la stessa esperienza in diversi altri cani, e ne&#039;conigli <lb></lb>ancora, e ne&#039;porcellini d&#039;India, ed in un agnello, e sempre con grandissima <lb></lb>felicità guarirono tutti in poche ore, senza che veruno di essi rimanesse mai <lb></lb>cieco. </s>

<s>Galeno, nel cap. </s>

<s>II del I libro <emph type="italics"></emph>Delle cagioni de&#039;sintomi,<emph.end type="italics"></emph.end> ancorchè <lb></lb>affermasse che era difficilissimo, anzi quasi impossibile, il non perder la <lb></lb>vista dopo che per ferita era uscito l&#039;umor acqueo fuori dell&#039;occhio, nondi­<lb></lb>meno pur al fine confessa che una volta un fanciullo non ne rimase cieco.... <lb></lb>Se ne potranno vedere altri esempi in diversi animali, se si leggerà il cap. </s>

<s>VI <lb></lb>del XXIX libro di Plinio, ancorchè non se ne dichiari, ma attribuisca forse <lb></lb>quelle sanazioni ad alcune ridicolose cerimonie e superstizioni in quel ca­<lb></lb>pitolo descritte. </s>

<s>Or siccome bella opera della sola Natura si è la rigenera­<lb></lb>zione dell&#039;umor acqueo negli occhi degli animali, così ancora della stessa <lb></lb>Natura è opera la rigenerazione dell&#039;umor vitreo e del cristallino ” (Fi­<lb></lb>renze 1680, pag. </s>

<s>26-28). </s></p><p type="main">

<s>Della rigenerazione di questi due umori promette il Zambeccari di trat­<lb></lb>tarne ad altra occasione. </s>

<s>Se avesse mantenuta la sua promessa, benchè noi <lb></lb>non sappiamo dirlo, avrebbe fatto cosa di grande importanza per la noso­<lb></lb>logia e per la operazione della cateratta, da che fecesi poco dopo vivamente <lb></lb>sentire il bisogno di definire la relativa grandezza delle così dette <emph type="italics"></emph>Camere <lb></lb>dell&#039;occhio.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Galeno dicendo, nel cap. </s>

<s>IV del citato libro X <emph type="italics"></emph>De usu partium,<emph.end type="italics"></emph.end> che <lb></lb>affinchè il cristallino non patisse attrito contro la cornea, la quale potrebbe <lb></lb>giungere facilmente a toccarlo attraverso al foro della pupilla, la previdente <lb></lb>Natura gli avea circumfuso “ humorem quendam tenuem ac sincerum cuius­<lb></lb>modi in ovis reperitur ” (fol. </s>

<s>179); mostrò chiaramente di aver riconosciute <lb></lb>le due Camere distinte e separate fra loro per l&#039;intermezzo dell&#039;Iride. </s>

<s>Il <lb></lb>Berengario poi ne avea data una descrizione assai più chiara e più minuta, <lb></lb>dicendo che l&#039;albugineo riempie non quello spazio solo, ch&#039;è fra la cornea <lb></lb>e l&#039;uvea, ma quell&#039;altro eziandio, ch&#039;è più indietro, non occupato dall&#039;ara­<lb></lb>nea tela e dalla retina. </s>

<s>“ Primus est albugineus, qui est inter corneam et <lb></lb>uveam tunicam, et est etiam hic humor intra uveam versus araneam et re­<lb></lb>thinam tunicam, et tota illa pars quae est ante, quae non est occupata ab <lb></lb>aranea tela nec a rethina, est plena isto humore albugineo ” (Comment. </s>

<s>cit., <lb></lb>fol. </s>

<s>CCCCLXVIII). </s></p><p type="main">

<s>Vedemmo com&#039;avesse il Vesalio esagerata così la grandezza della ca­<lb></lb>mera posteriore, da ridurla a mezza la cavità dell&#039;occhio, ma il Colombo, <lb></lb>dal trovar l&#039;umor acqueo così scarso, andato nell&#039;errore contrario, non par <lb></lb>che riconosca altro che la camera anteriore compresa in quell&#039;angusto spa-<pb xlink:href="020/01/1457.jpg" pagenum="332"></pb>zio, ch&#039;è tra l&#039;Uvea e la Cornea. </s>

<s>“ Aqueum Natura anteriore in parte lo­<lb></lb>cavit inter membranam uveam corneamque: qui humor paucus admodum <lb></lb>est ” (De re anat. </s>

<s>cit., pag. </s>

<s>219). </s></p><p type="main">

<s>Gli Anatomici posteriori al Colombo e al Valverde riconobbero in ge­<lb></lb>nerale che l&#039;umor acqueo era d&#039;assai maggior quantità, che di poche stille, <lb></lb>e che perciò rimaneva da lui inondato l&#039;occhio anche a tergo dell&#039;Iride. </s>

<s>Ma <lb></lb>dissentivano grandemente intorno al definir la capacità delle parti inondate, <lb></lb>dipendendo i dissensi dal vario modo di disegnar la cornea, e l&#039;iride, e i <lb></lb>processi ciliari, d&#039;onde venivano a variarsi notabilmente gli spazii interpo­<lb></lb>sti e circoscritti. </s>

<s>Quei per esempio, che facevano la cornea di raggio uguale <lb></lb>e concentrica con la sclerotica, diminuivano notabilmente la capacità della <lb></lb>camera anteriore, e quegli altri, i quali facevano l&#039;Iride concava e piani i <lb></lb>corpi ciliari, accrescevano la capacità della Camera posteriore. </s></p><p type="main">

<s>Questo punto di storia, con più concisa chiarezza che dalle parole, ci <lb></lb>viene enodato dagli Iconismi, e specialmente da quegli impressi ne&#039;varii <lb></lb>trattati di Ottica, perchè dovendosi gli Autori rivolgere agli Anatomici, e <lb></lb>trovando fra loro tanti dissensi, ebbero a studiarsi d&#039;attenersi al meglio o <lb></lb>a ciò che aveva maggiori suffragi. </s></p><p type="main">

<s>Quando nel 1554 il Vesalio esercitava sopra la scienza il suo pacifico <lb></lb>dominio, il Maurolico, che scriveva in quel tempo i suoi <emph type="italics"></emph>Photismi,<emph.end type="italics"></emph.end> rappre­<lb></lb>sentò a pag. </s>

<s>72 la figura dell&#039;occhio col cristallino nel centro, e coi corpi <lb></lb>ciliari, che separano le due uguali capacità riempite dall&#039;acqueo e dal vi­<lb></lb>treo, secondo le descrizioni da lui lette nel VII libro <emph type="italics"></emph>De humani corporis <lb></lb>fabrica.<emph.end type="italics"></emph.end> “ Haec, egli dice dopo la dichiarazione della detta figura, ex Ana­<lb></lb>tomia Andreae Vesalii bruxellensis, viri actate nostra perspicacissimi, excer­<lb></lb>psimus ” (Photismi De lumine, Neapoli 1611, pag. </s>

<s>72), non accettando però <lb></lb>la forma vesaliana della lente, che anch&#039;egli disegna compressa sì, “ sed a <lb></lb>parte anteriori compressior ” (ibid., pag. </s>

<s>69). </s></p><p type="main">

<s>L&#039;Aguilonio, disegnando l&#039;occhio a pag. </s>

<s>3 del suo grande trattato in <lb></lb>folio (Antuerpiae 1613), si giovò degl&#039;iconismi del Plater e del Vidio, con­<lb></lb>dotti sopra le descrizioni del Colombo e del Falloppio, ma la verità natu­<lb></lb>rale parve non essere stata da nessun altro meglio rappresentata che dal <lb></lb>Cartesio, a pag. </s>

<s>54 della Diottrica, e a pag. </s>

<s>62 del trattato <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end><lb></lb>nelle edizionì da noi citate. </s>

<s>Il Molinetti anatomico non trovò nulla da cor­<lb></lb>reggere nel Filosofo, di cui con gran fedeltà, a pag. </s>

<s>21 delle sue <emph type="italics"></emph>Disserta­<lb></lb>tiones,<emph.end type="italics"></emph.end> ricopia la figura, nella quale il Briggs ammirò tanta esattezza, da <lb></lb>creder che il Cartesio l&#039;avesse ritratta dallo stesso esemplare dell&#039;occhio <lb></lb>consolidato dal ghiaccio (Ophtalmographia, in Mangeti Biblioth. </s>

<s>anat. </s>

<s>cit, <lb></lb>T. II, pag. </s>

<s>363). </s></p><p type="main">

<s>Rimaste poi, specialmente in Italia, più libere le menti, e osservando <lb></lb>che il Cartesio stesso non pretendeva di farla da anatomico, rimandando <lb></lb>anzi per le più particolari descrizioni dell&#039;occhio i suoi lettori ai trattati di <lb></lb>Anatomia, ne&#039;quali “ plura circa hanc materiam notari solent ” (Dioptriees, <lb></lb>cap. </s>

<s>III cit., pag. </s>

<s>55); si giudicò che il modo di congelar l&#039;occhio, secondo <pb xlink:href="020/01/1458.jpg" pagenum="333"></pb>il Briggs consueto al Cartesio, <emph type="italics"></emph>in votis potius quam in more fuisse.<emph.end type="italics"></emph.end> Que­<lb></lb>sto giudizio è del Morgagni (Epist. </s>

<s>XVII cit., pag. </s>

<s>261), che trovò nel tea­<lb></lb>tro anatomico padovano l&#039;uso di congelar l&#039;occhio sì antico, da creder che <lb></lb>risalisse ai tempi dell&#039;Acquapendente. </s>

<s>Come altrimenti avrebb&#039;egli infatti, <lb></lb>argomenta lo stesso Morgagni, potuto rappresentar nelle loro vere sedi i tre <lb></lb>umori, secondo che vedesi in quell&#039;Iconismo impresso al cap. </s>

<s>VIII del III li­<lb></lb>bro <emph type="italics"></emph>De oculo,<emph.end type="italics"></emph.end> con intenzione di giovare agli Ottici “ ut accurate observare <lb></lb>possint progressum varium radiorum, dum ab uno in alium humorem tran­<lb></lb>seunt, atque angulos refractionis dimetiri? </s>

<s>” (Op. </s>

<s>omnia cit., pag. </s>

<s>235). </s></p><p type="main">

<s>Parve quell&#039;Iconismo all&#039;Autore delle Epistole anatomiche così rappre­<lb></lb>sentativo del vero, da non trovarsi di meglio, ei dice, se non forse nei tempi <lb></lb>moderni. </s>

<s>“ Attamen, poi soggiunge, si quaedam paulo diligentius essent re­<lb></lb>praesentata, quaedam, Irisque praesertim, paulo amplius expressa, nihil aliis, <lb></lb>nihil mihi ipsi laboris relictum erat ” (Epist. </s>

<s>cit., pag. </s>

<s>461). Ond&#039;è ch&#039;ei <lb></lb>crede di aver ragione di maravigliarsi e di deplorare una così bell&#039;opera <lb></lb>del Fabricio <emph type="italics"></emph>a posteris fere neglectam.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Voleva dire insomma il Morgagni che se non fosse stata dimenticata <lb></lb>la figura dell&#039;occhio delineata e impressa dal Fabricio, si dovevano a que­<lb></lb>sta tributare le prime lodi, per esser ritratta conforme alla verità naturale, <lb></lb>meglio di quella del Cartesio. </s>

<s>Ma con riverenza di un tant&#039;uomo ei s&#039;in­<lb></lb>gannava, bastando mettere a riscontro i due iconismi, per dover persuadersi <lb></lb>che il Cartesiano è di quel del Fabricio assai più perfetto, non solo nel rap­<lb></lb>presentar l&#039;iride, e le altre parti dal Morgagni desiderate, ma, ciò che più <lb></lb>importa, nel dipingere l&#039;inserzione del nervo fuori dell&#039;asse ottico. </s></p><p type="main">

<s>Da questa parte dunque aveva ragione il Briggs, ma s&#039;ingannava an­<lb></lb>ch&#039;egli nel credere che così fatti perfezionamenti fossero stati nell&#039;icono­<lb></lb>grafia ottica introdotti dal Cartesio E perch&#039;era facile avvedersi che il Filo­<lb></lb>sofo speculava sul fondamento dei fatti da qualche Anatomico prima osservati, <lb></lb>sarebbe stato bisogno ricercar chi fosse quell&#039;Anatomico, il quale perfezionò <lb></lb>l&#039;opera dell&#039;Acquapendente. </s>

<s>La ricerca non fu fatta dal Briggs, persuaso che <lb></lb>quell&#039;anatomico fosse lo stesso Cartesio, e non fu fatta dal Morgagni, fissa <lb></lb>la mente nelle pagine del Fabricio, delle quale non fu, secondo lui, dipinto <lb></lb>mai meglio. </s>

<s>Che se avessero que&#039;due valentuomini aperto per caso il libro <lb></lb>dello Scheiner intitolato <emph type="italics"></emph>Oculus,<emph.end type="italics"></emph.end> e gettato lo sguardo sopra quell&#039;iconismo <lb></lb>impresso a pag. </s>

<s>17 (Oeniponti 1619), non bisognava altro per riconoscerlo <lb></lb>similissimo a quello del Cartesio. </s>

<s>In ogni modo è da questo Autore, negletto <lb></lb>dal Briggs e dal Morgagni, che vien rischiarato questo tratto di storia, avendo <lb></lb>lo Scheiner, reputato non più che un semplice Ottico, avuto gran parte ai <lb></lb>progressi dell&#039;iconografia anatomica dell&#039;occhio. </s>

<s>Fu per servire alla maggior <lb></lb>precisione di questa iconografia che si dette a misurar la quantità dell&#039;umor <lb></lb>acqueo, rispetto al cristallino, e trovò che quella stava a questa in propor­<lb></lb>zion sesquialtera, ossia come uno e mezzo sta ad uno, o come nove sta a <lb></lb>sei. </s>

<s>“ Ego oculum taurinum adhuc calentem caute aperui, aqueumque hu­<lb></lb>morem provide in sphaerulam vitream excepi, quam semel totam deinde <pb xlink:href="020/01/1459.jpg" pagenum="334"></pb>dimidiam ex eo implevi: tum intrusi humorem cristallinum ex eodem oculo, <lb></lb>et spharulam praecise totam occupavit. </s>

<s>Itaque aqueus humor esset ad cri­<lb></lb>stallinum in proportione sexquialtera ” (Oculus cit., pag. </s>

<s>16). </s></p><p type="main">

<s>Così riuscì a definir la grandezza delle Camere, e lo spazio occupato <lb></lb>dal cristallino, lasciando tutto il rimanente al vitreo. </s>

<s>Ma l&#039;iconografia schei­<lb></lb>neriana è come accennammo superiore a quelle de&#039;predecessori, non eccet­<lb></lb>tuato il Fabricio, specialmente per ciò che riguarda il punto dell&#039;inserzione <lb></lb>del nervo “ qui non iacet in axe optico, sed sinistrorsum vergit in oculo <lb></lb>dextro, dextrorsus in sinistro. </s>

<s>Docet hoc experientia in oculo bovino, ovili, <lb></lb>caprino, suili et similium brutorum, cuius ego rei periculum coram aliis <lb></lb>frequentissimum feci.... Neque dicas ex eo quod nullus Anatomicorum hoc <lb></lb>asseruerit, probabile non videri id in hominis oculo verum esse, nam etiam <lb></lb>nullus id vel observavit vel affirmavit de oculo bestiae ” (ibid., pag. </s>

<s>18). </s></p><p type="main">

<s>Descritti gli umori, le tuniche e l&#039;inserzione del nervo, vuol lo Scheiner <lb></lb>sodisfare ai curiosi di sapere in che modo, per ritrarlo più esattamente, si <lb></lb>fosse preparato l&#039;esemplare in natura, e dice che prendeva un bulbo fresco <lb></lb>e che lo lasciava essiccare all&#039;aria, tenuto per lo stesso nervo sospeso a un <lb></lb>filo. </s>

<s>“ Et sic ideam oculi talem dedi qualem natura fabricante didici, qua­<lb></lb>lem etiam Hyeronymus Fabricius ab Aquapendente, anno 1600, quem post <lb></lb>meam inquisitionem gratulabundus sum nactus, inventam posteritati com­<lb></lb>mendavit ” (Ibid., pag. </s>

<s>20). </s></p><p type="main">

<s>Non aveva dunque ragione di lamentarsi della negligenza dei posteri il <lb></lb>Morgagni, se rivisse l&#039;Acquapendente nello Scheiner, l&#039;iconismo del quale, <lb></lb>delineato dalla stessa penna del Viviani (MSS. Cim., T. X, c. </s>

<s>34), tennero <lb></lb>sotto gli occhi gli Accademici fiorentini. </s>

<s>I Cartesiani credettero quella opera <lb></lb>del loro Maestro e benchè s&#039;ingannassero conferirono efficacemente in dif­<lb></lb>fondere la invenzione pubblicata nel 1600 da un nostro Italiano, e da un <lb></lb>successore di lui nella cattedra padovana, dopo più di un secolo perfezio­<lb></lb>nata, “ cum, petente anatomico praestantissimo Heistero, dice il Morgagni, <lb></lb>humanum iterum oculum delineandum curavi ” (Epist. </s>

<s>cit., pag. </s>

<s>261). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;organo è dunque, in tutte le sue parti più minute, delineato dalla <lb></lb>più esperta mano che si possa desiderare, ciò che accende in noi il desi­<lb></lb>derio, e incora la speranza di sapere com&#039;ei funziona. </s>

<s>Ma la via è lunga e <lb></lb>penosa, e le fatiche, dalla mente durate in percorrerla, non sono all&#039;ultimo <lb></lb>consolate dal dolce riposo. </s>

<s>Ci rimane in ogni modo a dire, con la solita bre­<lb></lb>vità, quali frutti si raccogliessero dalle esperienze dei Fisici, e dalle specu­<lb></lb>lazioni dei Filosofi, in riconoscer l&#039;organo primario, e in penetrare le mi­<lb></lb>steriose funzioni della vista. </s></p><p type="main">

<s>Galeno aveva, nel cap. </s>

<s>I del libro X <emph type="italics"></emph>De usu partium,<emph.end type="italics"></emph.end> lasciato scritto <pb xlink:href="020/01/1460.jpg" pagenum="335"></pb>essere il cristallino <emph type="italics"></emph>primum videndi instrumentum<emph.end type="italics"></emph.end> (Op. </s>

<s>omnia cit., T. I, <lb></lb>fol. </s>

<s>177), e fra&#039;seguaci dell&#039;antico Maestro alcuni interpetrarono quella sen­<lb></lb>tenza come assoluta, altri più savii dissero che voleva essere commentata <lb></lb>con altre dottrine, espresse nel medesimo testo, e per le quali si rendeva <lb></lb>la mente dell&#039;Autore compiuta. </s></p><p type="main">

<s>Que&#039;primi dunque attribuirono allo stesso cristallino la virtù di sentire, <lb></lb>come si par dal nostro Berengario, che ne&#039;citati Commentarii sopra Mundino <lb></lb>riferisce una tale opinione, invalsa già fra gli Arabi, ed egli pure la segue. <lb></lb></s>

<s>“ Hali vocat partem anteriorem cristallini subplanam, ut occurrat plurimae <lb></lb>quantitati eorum quae sentit. </s>

<s>Si enim esset haec pars rotunda perfecte, non <lb></lb>sentiret parva corpora, et non sentiret pariter, neque stabiliter, quia rotunda <lb></lb>figura non recipit in se, nisi vix aliqua fixa, cuius oppositum facit planities ” <lb></lb>(fol. </s>

<s>CCCCLXXIV). </s></p><p type="main">

<s>Quegli altri però che, più da savii, erano ben persuasi non poter la <lb></lb>virtù di sentire riseder che solo nei nervi, ritrovarono questa verace dot­<lb></lb>trina chiaramente espressa dallo stesso Galeno, là dove nel cap. </s>

<s>II del ci­<lb></lb>tato libro, discorrendo della retina, disse: “ Porro utilitas ipsius, prima qui­<lb></lb>dem ac maxima, propter quam superne fuit demissa, est ut, cum crystallinus <lb></lb>alteratur, id sentiat ” (De usu partium, in loco cit., fol. </s>

<s>177). Non è dun­<lb></lb>que, secondo Galeno, il cristallino che sente, ma le alterazioni prodotte in <lb></lb>lui dalle specie impresse, son tradotte al cervello per via della retina, che <lb></lb>perciò <emph type="italics"></emph>superne fuit demissa.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Molti furono gl&#039;interpetri di Galeno, che professarono così fatte dot­<lb></lb>trine, in mezzo ai quali s&#039;annovera uno de&#039;primi, fra gli Arabi stessi, Alha­<lb></lb>zen, anche in ciò fedelmente seguito da Vitellione, che per la concavità, in <lb></lb>cui spandesi il nervo ottico, intendendo la retina, scrisse come le immagini <lb></lb>degli oggetti, attraverso all&#039;umor vitreo, giungessero infino a lei. </s>

<s>“ Quoniam <lb></lb>formae rerum visibilium, quando perveniunt in corpus humoris vitrei, exten­<lb></lb>ditur sensus ab illo in corpus sentiens extensum in concavo nervi, conti­<lb></lb>nuati inter visum et anterius cerebri ” (Optices libri, Norimbergae 1535, <lb></lb>pag. </s>

<s>60). </s></p><p type="main">

<s>Così, nella prima metà del secolo XVI, rimaneva il campo della scienza <lb></lb>diviso fra gli stessi seguaci di Galeno, alcuni de&#039;quali professavano col Be­<lb></lb>rengario bastare alla visione il cristallino, altri con Vitellione dicevano che <lb></lb>esso cristallino riceve solo le immagini degli oggetti, delle quali poi rimette <lb></lb>l&#039;impressione alla retina, che sola è atta a sentire. </s>

<s>Fra gli Autori delle nuove <lb></lb>instaurazioni il Vesalio dubitò se fosse veramente il cristallino organo pri­<lb></lb>mario, liberamente confessando “ hac in parte quod sanum undique sit a <lb></lb>me non adferri posse ” (De humani corporis fabrica cit., pag. </s>

<s>649). Ma per­<lb></lb>chè il dubbio e le difficoltà incontrate in risolverlo supponevano l&#039;opinione <lb></lb>di quei Galenisti, che davano al cristallino la virtù tutto insieme di ricevere <lb></lb>e di sentire; il Maurolico se ne deliberò, da una parte ammettendo che <lb></lb>l&#039;umor glaciale sia quello “ in quo visiva virtus tanquam in sede consistit ” <lb></lb>(Photismi cit., pag. </s>

<s>69), e dicendo dall&#039;altra che, ricevute le specie, esso <pb xlink:href="020/01/1461.jpg" pagenum="336"></pb>umor glaciale “ per opticum nervum ad communis sensus indicium defert ” <lb></lb>(ibid., pag. </s>

<s>70). </s></p><p type="main">

<s>Questa era come vedemmo dottrina comunemente professata dai migliori <lb></lb>interpetri di Galeno. </s>

<s>Non essendo però il Maurolico notomista, e rimaste per <lb></lb>lungo tempo le sue speculazioni ottiche sconosciute, il Colombo ripetè con <lb></lb>gli Arabi e col Berengario essere il cristallino “ praecipuum ac pene princeps <lb></lb>videndi instrumentum ” (De re anat. </s>

<s>cit., pag. </s>

<s>219), nè in sentenza punto <lb></lb>diversa andò il Falloppio, che, per essere esso cristallino diafano, “ facil­<lb></lb>lime, disse, colorum species suscipit ” (Instit. </s>

<s>anat., Op. </s>

<s>omnia cit., pag. </s>

<s>511). </s></p><p type="main">

<s>Ma così gli uni come gli altri seguaci di Galeno, che rimasero nelle <lb></lb>opinioni, come s&#039;è veduto, infino ai tempi del Falloppio, divisi, lasciavano <lb></lb>a desiderar molte cose, e intorno al modo come il cristallino sente, e intorno <lb></lb>a quella parte, o a quella trasformazione del nervo ottico, che ha da rice­<lb></lb>vere la sensazione. </s>

<s>L&#039;Acquapendente fu tra&#039;Galenisti il primo, che pretese <lb></lb>di dimostrare com&#039;essendo la retina opaca, e perciò inalterabile alla luce, <lb></lb>era in tanto solo atta a ricevere le impressioni visive, in quanto ella si tra­<lb></lb>sforma nell&#039;aranea lucida, che riveste il cristallino dalla sua parte anteriore. <lb></lb></s>

<s>“ Natura tunicam retinam opacam et corpulentam fecit, nequaquam diapha­<lb></lb>nam, quo fit ut a luce affici immutarique minime possit.... Quod si non <lb></lb>afficitur, neque etiam sentire potest.... Igitur retina quatenus a nervi me­<lb></lb>dulla et cerebri substantia exorta, eatenus sentientem secum defert faculta­<lb></lb>tem, quatenus insuper ad crystallinum progressa, eatenus ad araneae gene­<lb></lb>rationem sese offert ” (De oculo, Op. </s>

<s>omnia cit., pag. </s>

<s>235). </s></p><p type="main">

<s>In questa e in altre dottrine di Fisiologia ottica, esposte nel trattato <lb></lb>dell&#039;Acquapendente, ritrovava la scienza galenica il suo massimo svolgimento. </s>

<s><lb></lb>Ma rimaneva il modo come si fa la vista tuttavia oscuro, non appagando la <lb></lb>mente quel che si diceva delle specie impresse nel cristallino diafano, e nel­<lb></lb>l&#039;aranea lucida, che ne trasmette le impressioni al sensorio comune. </s>

<s>Dal­<lb></lb>l&#039;altra parte si disputava tra&#039;Filosofi, seguaci di Aristotile e di Platone, se <lb></lb>quelle specie venivano dagli oggetti all&#039;occhio, o s&#039;era l&#039;occhio stesso che <lb></lb>le mandava agli oggetti. </s></p><p type="main">

<s>A dare a intendere il modo come si fa la vista, e a decidere fra gli <lb></lb>aristotelici e i platonici la lunga questione, soccorse opportunissima un&#039;espe­<lb></lb>rienza, che risale al secolo XV, trovandosene ne&#039;manoscritti di Leonardo da <lb></lb>Vinci, per quanto se ne sappia, la più antica memoria. </s>

<s>“ La sperienzia (così <lb></lb>leggesi in una di quelle note vinciane pubblicate da Guglielmo Libri) che <lb></lb>mostra come li obietti mandino le loro spezie, ovvero similitudini, interse­<lb></lb>gate dentro all&#039;occhio nello umore albugineo, si dimostra quando, per al­<lb></lb>cuno piccolo spiracolo rotondo, penetreranno le spezie delli obietti allumi­<lb></lb>nati in abitazione forte oscura. </s>

<s>Allora tu riceverai tale spezie in una carta <lb></lb>bianca, posta dentro a tale abitazione alquanto vicina a esso spiracolo, e ve­<lb></lb>drai tutti li predetti obbietti in essa carta colle lor proprie figure e colori, <lb></lb>ma saran minori, e fieno sottosopra, per causa della detta intersegazione ” <lb></lb>(Histoire des sciences mathem., T. IV, Paris 1841, pag. </s>

<s>305, 6). </s></p><pb xlink:href="020/01/1462.jpg" pagenum="337"></pb><p type="main">

<s>Se si potesse penetrare addentro alle tenebre di quei tempi, si vedreb­<lb></lb>bero i dimenticati Fisiologi contemporanei di Leonardo disputare fra loro <lb></lb>intorno all&#039;analogia, che si diceva passar fra la camera oscura e l&#039;occhio, <lb></lb>e alcuni più ritrosi negarla, per cagion delle immagini, che si rappresente­<lb></lb>rebbero a rovescio. </s>

<s>Gli amatori delle cose nuove, dall&#039;altra parte, si dovet­<lb></lb>tero studiar di vincere una tal ritrosia, e vi riuscirono, accomodando nello <lb></lb>strumento uno specchio concavo, che addirizzasse le immagini, e dicendo <lb></lb>che nell&#039;occhio era quello specchio rappresentato dalla retina, alla quale fa <lb></lb>da amalgama il pigmento coroideo. </s></p><p type="main">

<s>Di questo segreto lavorìo della scienza, dissipato nelle parole de&#039;dispu­<lb></lb>tanti, o consegnato a carte manoscritte, in parte dimenticate e in parte di­<lb></lb>sperse, n&#039;è rimasto qualche memoria nella prima Magia naturale scritta in <lb></lb>quattro libri dal Porta. </s>

<s>Nel II capitolo del III libro, dop&#039;aver l&#039;Autore de­<lb></lb>scritta la camera oscura, e il modo d&#039;accomodarvi lo specchio per dirizzar <lb></lb>le immagini, “ Hinc philosophis, soggiunge, et medicis patet quo fiat in ocu­<lb></lb>lis visus loco, ac intromittendi dirimitur quaestio sic agitata, nec alio prae­<lb></lb>stantius utrunque artificio demonstrari poterat. </s>

<s>Intromittitur enim idolum <lb></lb>per pupillam fenestrae instar, vicemque obtinet speculi parva magnae sphae­<lb></lb>rae portio ultimo locata oculi ” (Neapoli 1588, pag. </s>

<s>143, 44). Che poi per <lb></lb>questa piccola porzione della sfera grande si debba intendere il fondo del­<lb></lb>l&#039;occhio, ossia il concavo del nervo ottico espanso, come gli specchi artifi­<lb></lb>ciali anch&#039;egli impiombato dal pigmento coroideo, s&#039;argomenta da quelle <lb></lb>parole, che si leggono nel cap. </s>

<s>XVIII del IV libro, dove, dop&#039;avere inse­<lb></lb>gnato il modo come si pone agli specchi di vetro la piastra, soggiunge: <lb></lb>“ Hinc Natura, rerum omnino parens, oculum speculi instar composuit, <lb></lb>quippe a tergo pellucentibus partibus nigriorem quemdam apposuit, quo <lb></lb>sublato, et tolleretur videndi facultas ” (ibid., pag. </s>

<s>155). </s></p><p type="main">

<s>In questa teoria della visione però gli umori non fanno altro ufficio, che di <lb></lb>ricevere le immagini venute dal foro della pupilla, come le riceve il diaframma <lb></lb>posto di rincontro al foro della camera oscura. </s>

<s>Anzi non è propriamente <lb></lb>quell&#039;ufficio assegnato che all&#039;albugineo, secondo Leonardo, o al cristallino <lb></lb>secondo il Porta: dell&#039;uso particolare di ciascuno degli altri umori i nuovi <lb></lb>dimostratori della recezion delle immagini non ne intendono ancora nulla. </s></p><p type="main">

<s>Galeno aveva insegnato che l&#039;uso naturale dell&#039;umor vitreo era quello <lb></lb>di alimentare il cristallino. </s>

<s>“ Humori autem crystallino nutrimentum ei obti­<lb></lb>git, comparatumque ei a Natura fuit accomodatum humor vitreus ” (De usu <lb></lb>partium, Op. </s>

<s>omnia cit., T. I, fol. </s>

<s>177). L&#039;umor acqueo, secondo lo stesso <lb></lb>Galeno, non è nella parte anteriore dell&#039;occhio ad altro ufficio disposto, che <lb></lb>a impedire gli attriti, che potrebbe il cristallino patir dalla durezza della <lb></lb>cornea, attraverso al foro aperto della pupilla. </s>

<s>“ Ut igitur nec per hoc fo­<lb></lb>ramen tunica cornea aliquando crystallinum humorem tangeret, Opifex no­<lb></lb>stri providit, simul quidem portionem hanc corneae foras longius abducens, <lb></lb>simul autem humorem quendam tenuem ac sincerum, cuiusmodi in ovis <lb></lb>reperitur, crystallino circumfundens ” (ibid., fol. </s>

<s>179). </s></p><pb xlink:href="020/01/1463.jpg" pagenum="338"></pb><p type="main">

<s>Alhazen e Vitellione avevano fatto qualche cenno alle rifrazioni, che su­<lb></lb>bisce la luce attraverso agli umori dell&#039;occhio, prima di andar direttamente <lb></lb>a ferire il concavo del nervo. </s>

<s>Ma rimasero i germi delle loro idee sterili nel <lb></lb>campo de&#039;Galenisti, i quali facevano recettore delle specie e primario organo <lb></lb>della vista il cristallino. </s></p><p type="main">

<s>Nonostante, l&#039;Acquapendente, fra quegli stessi seguaci di Galeno, fu il <lb></lb>primo a riformare e a ridurre a miglior senso gli oramai invalsi placiti del­<lb></lb>l&#039;antico Maestro. </s>

<s>Egli assegnò il poter rifrangente alla cornea e all&#039;umor <lb></lb>acqueo, i quali fanno come una pila di vetro convergere e appuntare nel <lb></lb>cristallino i raggi visivi, che altrimenti andrebbero dispersi. </s>

<s>“ Cui rei aquei <lb></lb>humoris copià valde astipulatur, quae tanta est, quanta est necessaria ut <lb></lb>lux, unita et fortissima reddita, ad crystallinum pertingat, priusquam disper­<lb></lb>datur; ita ut punctum illud, in quo radiorum fit concursus, crystallinus sit ” <lb></lb>(De oculo cit., pag. </s>

<s>224). Nè il vitreo è, soggiunge l&#039;Acquapendente, ordi­<lb></lb>nato a nutrire il cristallino, come insegnava Galeno, ma gli fu posto dietro <lb></lb>questo diafano, affinchè i raggi non avessero a riflettersi sopra lo stesso umor <lb></lb>cristallino, incontrandosi in un corpo opaco, e tingendosi de&#039;colori di lui. <lb></lb></s>

<s>“ Propter hoc Natura diaphanum corpus, nimirum vitreum, post crystalloi­<lb></lb>dem locavit, ne lux crystallinum transverta statim, ab opacis coloratisque <lb></lb>corporibus foedata, ad crystallinum revertatur ” (ibid., pag. </s>

<s>236). </s></p><p type="main">

<s>In ogni modo, benchè così riformata la teoria galenica della visione, non <lb></lb>sodisfaceva i migliori ingegni speculativi, ai quali arridevano piuttosto le <lb></lb>analogie ricavate dall&#039;esperienza. </s>

<s>Pochi anni dopo che l&#039;Acquapendente scri­<lb></lb>veva, furono quelle analogie messe dal Keplero nella più chiara luce, ma <lb></lb>alla storia dell&#039;Ottico alemanno ne precede un&#039;altra schiettamente italiana, <lb></lb>della quale dobbiamo ora far qualche cenno, riappiccando il filo del nostro <lb></lb>discorso colà, dove in Leonardo e nel Porta lo lasciammo interrotto. </s></p><p type="main">

<s>Que&#039;Filosofi che accolsero le speculazioni, delle quali l&#039;Artista da Vinci <lb></lb>e il Fisico di Napoli ci porgevano dianzi i documenti, dovettero ripensare a <lb></lb>qual uso fossero così ben disposti gli umori, i quali non potevano starvi <lb></lb>inutili, come pareva insinuarsi dalle esperienze della prima Camera oscura, <lb></lb>e non potevano dall&#039;altra parte essere, come si diceva, recettori delle imma­<lb></lb>gini, per esser queste in ogni diafano dissipabili. </s></p><p type="main">

<s>Or occorse, in mezzo a questi pensieri che, per rendere anche più <lb></lb>stretta la somiglianza fra l&#039;organo naturale e lo strumento artificioso, si <lb></lb>adattasse al foro di questo una lente biconvessa, che faceva le veci del cri­<lb></lb>stallino. </s>

<s>Le immagini, che apparivano sul diaframma più distinte, fecero gli <lb></lb>osservatori accorti del poter rifrangente che dovevano avere, in rendere la <lb></lb>vista più distinta, gli umori, e l&#039;analogia fra il modo del rappresentarsi le <lb></lb>immagini nella Camera oscura, e nell&#039;occhio, riuscì per ogni parte mirabil­<lb></lb>mente compiuta. </s></p><p type="main">

<s>Chi primo avesse così ingegnosamente, ne&#039;giochi dell&#039;arte, scoperti i <lb></lb>segreti della Natura, non si potrebbe additar da noi con certezza. </s>

<s>Ma perchè <lb></lb>nel Libro delle speculazioni di Giovan Batista Benedetti, nel 1580, se ne <pb xlink:href="020/01/1464.jpg" pagenum="339"></pb>trova fatta di ciò la prima menzione, non dubitiamo di riconoscerne il Ma­<lb></lb>tematico veneziano per primo Autore. </s>

<s>“ Ratio unde fiat ut videamus di­<lb></lb>stincte omnes colores, egli dice, cum in qualibet aeris parte, quo lumina <lb></lb>reflexa possunt pervenire, mixta sint et non distincta, oritur a parvitate <lb></lb>ipsius pupillae oculorum, et a magna expansione virtutis visivae in super­<lb></lb>ficie concava orbis continentis humores diaphanos oculorum, per ramuscu­<lb></lb>los nervi optici remote ab ipsa pupilla. </s>

<s>Et quamvis radii luminosi frangan­<lb></lb>tur ab unoquoque humore diversimode, hoc nihilominus maxime iuvat ad <lb></lb>distinctionem radiorum, sed et si directe procederent idem fere eveniret, non <lb></lb>tamen suis locis. </s>

<s>Cogita ex. </s>

<s>gr. </s>

<s>lineam AUE (fig. </s>

<s>9) ut communis sectio <lb></lb><figure id="id.020.01.1464.1.jpg" xlink:href="020/01/1464/1.jpg"></figure></s></p><p type="caption">

<s>Figura 9.<lb></lb>cuiusdam plani secantis sphaeram <lb></lb>oculi, per centrum ipsius et pupillae, <lb></lb>et O punctum sit proximum centro <lb></lb>ipsius pupillae, sed interius aliquan­<lb></lb>tulum: extra autem oculum sint varii <lb></lb>colores, ut C, N, T in dicto diaphano. </s>

<s><lb></lb>Iam nulli dubium est quod lumina, <lb></lb>quae producuntur ab C, N, T ad O, in <lb></lb>ipso O mixta et non distincta. </s>

<s>Procedendo igitur ulterius ipsi radii citra O, <lb></lb>tunc disgregantur et separantur ad invicem, et cum parveniunt ad lineam <lb></lb>AUE, sentiuntur distincti alii ab aliis ” (Speculationum Liber, Venetiis 1599, <lb></lb>pag. </s>

<s>296, 97). </s></p><p type="main">

<s>In queste speculazioni però si sollevava così l&#039;Autore sopra la scienza <lb></lb>de&#039;suoi tempi, che non fa maraviglia se rimase incompreso. </s>

<s>Avendo letto <lb></lb>il Plater in Realdo Colombo che, estratto il cristallino dall&#039;occhio, e avvi­<lb></lb>cinatolo ai caratteri scritti, questi apparivano più grandi e più distinti, e che <lb></lb>perciò credeva di qui “ specillorum inventionem originem duxisse ” (De re <lb></lb>anat. </s>

<s>cit., pag. </s>

<s>219); immaginò che lo stesso cristallino, in ingrandir gli og­<lb></lb>getti alla retina, facesse da occhiale, e lo scrisse nel III libro <emph type="italics"></emph>De corporis <lb></lb>humani structura,<emph.end type="italics"></emph.end> pubblicato la prima volta nel 1583 in Basilea, con que­<lb></lb>ste parole, che noi però trascriviamo dalla seconda edizione: “ Cristallinus <lb></lb>humor, qui perspicillum est nervi visorii, atque ante ipsum et pupillae fo­<lb></lb>ramen collocatus species oculo illabentes veluti radios colligit, et in ambi­<lb></lb>tum totius retiformis nervi diffundens, res maiores illi, ut commodius eas <lb></lb>perciperet, perspicilli penitus modo, repraesentat ” (Basileae 1603, pag. </s>

<s>187). </s></p><p type="main">

<s>Nè punto meglio del Plater seppe interpetrare il Libro delle Specula­<lb></lb>zioni il Porta, il quale, nel riformar che fece nel 1585 e ridurre in XX libri <lb></lb>la Magia naturale, descritta la Camera oscura, co&#039;perfezionamenti introdot­<lb></lb>tivi dal Benedetti, passa a farne l&#039;applicazione alla vista, e là dove prima <lb></lb>aveva detto far le veci dello specchio il fondo dell&#039;occhio, ora si corregge <lb></lb>scrivendo tener luogo del diaframma recettor delle immagini il cristallino. <lb></lb></s>

<s>“ Vicemque obtinet tabulae crystallinae sphaerae portio in medio ocnli lo­<lb></lb>cata ” (Magiae natur., libri XX, Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>590). </s></p><p type="main">

<s>Volle la mala ventura che capitassero al Keplero, invece delle Specula-<pb xlink:href="020/01/1465.jpg" pagenum="340"></pb>zioni del Benedetti, i commenti che, senza intenderle, ne avevano fatti il <lb></lb>Plater e il Porta. </s>

<s>E quanto al primo parve all&#039;Autore de&#039;Paralipomeni a <lb></lb>Vitellione che l&#039;ufficio di amplificare le immagini, attribuito al cristallino, <lb></lb>fosse cosa tutta aliena dal proposto negozio, imperocchè “ haec amplificatio <lb></lb>literarum per crystallinum, vel ei analogon quippiam, in oculo, non infor­<lb></lb>mat visionem ” (Francofurti 1604, pag. </s>

<s>208). </s></p><p type="main">

<s>Quanto al Porta, che chiama eccellente investigatore de&#039;misteri della <lb></lb>Natura, al sentirgli spiegare il modo della visione per mezzo della Camera <lb></lb>ottica, dirimendo così le antiche liti fra i seguaci di Aristotile e quelli di <lb></lb>Platone, <emph type="italics"></emph>equidem beasti nos,<emph.end type="italics"></emph.end> esclama il Keplero. </s>

<s>“ Caeterum de modo vi­<lb></lb>sionis, poi prosegue, paulo accuratius verba tua, Porta, consideranda sunt. <lb></lb><emph type="italics"></emph>Hinc,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>patet quonam fiat visus loco.<emph.end type="italics"></emph.end> Et postea explicans, <emph type="italics"></emph>transmit­<lb></lb>titur,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>idolum per pupillam fenestrae foraminis instar, vicemque <lb></lb>obtinet tabulae crystallinae sphaerae portio.<emph.end type="italics"></emph.end> Ergo, si te bene capio, tu si <lb></lb>interrogeris quo loco visio fiat respondebis in superficie crystallini ceu in <lb></lb>tabula..... Sane si hic scopum fixum habes, si non ultra crystallinum de­<lb></lb>scendis, errasti sententia..... Itaque, ut concludam, si hoc unum, Porta so­<lb></lb>lertissime, tuae sententiae addideris: picturam in crystallino adhuc confusam <lb></lb>esse admodum, praesertim dilatato foramine uveae, nec fieri visionem per <lb></lb>coniunctionem lucis cum crystallino, sed descendere in retinam, descensu­<lb></lb>que eo et magis separari diversorum et coniungi eiusdem puncti radiatio­<lb></lb>nes, inque ipsa retina locum esse collectionis ad punctum, quae evidentiam <lb></lb>picturae praestat, fierique et per illam intersectionem ut imago fiat eversa, <lb></lb>et per hanc collectionem ut distinctissima sit et evidentissima; hoc, in­<lb></lb>quam, si addideris, tuae sententiae plane absolveris visionis modum ” (ibid., <lb></lb>pag. </s>

<s>210, 11). </s></p><p type="main">

<s>Se avesse il Keplero letto il libro del Benedetti, <emph type="italics"></emph>equidem beasti nos<emph.end type="italics"></emph.end><lb></lb>avrebbe detto a lui con più ragione, per essere stato lui veramente che, <lb></lb>dietro le analogie colla camera ottica, insegnò che la visione si faceva sulla <lb></lb>retina per modo di pittura. </s>

<s>Ma rimasto fra gli stessi Italiani dimentico il <lb></lb>Matematico di Venezia, l&#039;onore dell&#039;invenzione andò tutto intero all&#039;Astro­<lb></lb>nomo di Praga. </s></p><p type="main">

<s>Ad eccitar più che mai viva la curiosità de&#039;Filosofi intorno a cotesta <lb></lb>invenzione concorse efficacemente la scoperta del Telescopio, il modo del­<lb></lb>l&#039;operar del quale reputandosi affatto simile a quello dell&#039;occhio, faceva spe­<lb></lb>rare che insiem con l&#039;uno si rivelerebbe anche l&#039;altro mistero. </s>

<s>Fu tra co­<lb></lb>loro, che ingerirono una sì lusinghiera speranza, Gian Francesco Sagredo, <lb></lb>gentiluomo veneziano, che il dì 2 Giugno 1612 così scriveva in una sua let­<lb></lb>tera a Galileo: “ Versa ora la mia speculazione sopra il modo come si faccia <lb></lb>la vista, e come gli occhiali, così gli ordinarii come questi della nuova in­<lb></lb>venzione, siano di aiuto per accrescerla. </s>

<s>E perchè, come V. S. E. sa, io sono <lb></lb>matematico di nome e niente di essenza e verità, perciò, non avendo ve­<lb></lb>duto nè Vitellione nè altri Autori che trattano della Prospettiva, io non ho <lb></lb>in testa altra dottrina che quella che mi ha dettata il mio proprio discorso ” <pb xlink:href="020/01/1466.jpg" pagenum="341"></pb>(Alb. </s>

<s>VIII, 204). Nella verità del qual discorso riposerebbe tranquillo, se <lb></lb>non gli fosse contrariato da Agostino Mula e da Paolo Sarpi, i quali si fa­<lb></lb>cevano forti dell&#039;autorità degli scrittori. </s>

<s>“ E perchè, prosegue a dire il Sa­<lb></lb>gredo a Galileo, io stimo più lei e il suo giudizio che quello degli scrittori, <lb></lb>in particolare la prego scrivermi sommariamente la sua opinione ” (ivi). </s></p><p type="main">

<s>Galileo ricusò di compiacere all&#039;amico, il quale tornò così a fare istanza, <lb></lb>come un povero affamato, che chieda la carità di un po&#039;di pan secco a qual­<lb></lb>che ricco avaro: “ Giacchè ella non vuol significarmi la sua opinione, in­<lb></lb>torno al modo che si fa la vista, almeno la prego a scriver la volgata per <lb></lb>modo storico, senza dimostrazioni ” (ivi, pag. </s>

<s>213). </s></p><p type="main">

<s>La lettera, in cui si scrivevano queste parole, fu data da Venezia quat­<lb></lb>tordici giorni dopo la precedente, nel qual tempo sembra che fosse per la <lb></lb>prima volta capitato alle mani del Sagredo il trattato <emph type="italics"></emph>De radiis visus et lucis<emph.end type="italics"></emph.end><lb></lb>di Marc&#039;Antonio De Dominis, del quale il Sagredo stesso ne parlava in que­<lb></lb>sti termini a Galileo: “ Io non so se ella abbia veduto un trattato dell&#039;Ar­<lb></lb>civescovo di Spalatro circa l&#039;Occhiale. </s>

<s>Se costì non si trova, mi avvisi che <lb></lb>glielo manderò subito, perchè mi sarebbe caro intendere il giudizio di V. S. <lb></lb>sopra esso trattato ” (ivi). </s></p><p type="main">

<s>Ma verso la fine del mese, benchè Galileo ch&#039;era allora tutto dietro a <lb></lb>far sua quella ch&#039;ei chiamava <emph type="italics"></emph>istituzione circa la vista,<emph.end type="italics"></emph.end> promettesse d&#039;in­<lb></lb>segnare il modo di misurare il concorso degli angoli visuali, avuto riguardo <lb></lb>alla maggiore o minore apertura della pupilla, che il mondo tutto da tanti <lb></lb>anni aveva imparato da Archimede; quanto al dar giudizio del trattato del <lb></lb>De Dominis era ancora rimasto in silenzio, per cui il Sagredo così tornava <lb></lb>a sollecitarlo: “ Io sto con gran desiderio attendendo la sua istituzione circa <lb></lb>la vista, e mi sarà caro che ella non si scordi di scrivermi il suo parere <lb></lb>sopra il libro intitolato <emph type="italics"></emph>De radiis visus et lucis<emph.end type="italics"></emph.end> dell&#039;Arcivescovo di Spala­<lb></lb>tro, il quale a carte 15 confuta con assai familiarità la mia opinione, che <lb></lb>cioè la vista si faccia dentro l&#039;occhio, per le rifrazioni che fanno le spezie, <lb></lb>passando per l&#039;umore cristallino ” (ivi, pag. </s>

<s>217). </s></p><p type="main">

<s>Sanno i nostri Lettori oramai quanto fosse alieno dal professar così fatti <lb></lb>sani principii di Fisiologia ottica quel Galileo, che credeva co&#039;Platonici nel­<lb></lb>l&#039;emission delle specie; che faceva concorrere i raggi visuali dietro l&#039;occhio <lb></lb>irrefratti e non decussati; che teneva co&#039;Galenisti essere il cristallino sensi­<lb></lb>tivo, e recettore delle immagini. </s>

<s>Vinto dall&#039;importunità, scrisse finalmente <lb></lb>intorno alla vista una tal sua opinione, ch&#039;era l&#039;impasto di tutti questi er­<lb></lb>rori, e alla quale il Sagredo francamente si oppose: “ Quanto a quello, che <lb></lb>ella mi scrive dei raggi visivi e delle spezie, io non so trattare della diffe­<lb></lb>renza tra loro, poichè io non credo che vi sieno raggi visivi, nè per ancora <lb></lb>comprendo come questi sieno necessarii per vedere. </s>

<s>Ma siccome il suono <lb></lb>nelle nostre orecchie si fa, per la percussione causata dall&#039;aere nel timpano, <lb></lb>senza che da esso timpano parta cosa alcuna; così credo che succeda al­<lb></lb>l&#039;occhio. </s>

<s>E circa a quello che mi scrive della inversione delle macchie del <lb></lb>sole, che si vedono nella carta, io non metto dubbio che l&#039;istesso non oc-<pb xlink:href="020/01/1467.jpg" pagenum="342"></pb>corra nell&#039;occhio, il quale, per essere avvezzo ad apprendere tutte le spezie <lb></lb>rovescie, le giudica dirette ” (Alb. </s>

<s>XVI, 59). </s></p><p type="main">

<s>In queste idee del gentiluomo, che non faceva professione di scienza, <lb></lb>concorse in quel medesimo tempo un Artista, amico anch&#039;egli e familiare <lb></lb>di Galileo. </s>

<s>Lodovico Cigoli, dop&#039;aver descritta nella sua Prospettiva pratica <lb></lb>la camera oscura, sul diaframma della quale si dipingono le immagini degli <lb></lb>oggetti a rovescio. </s>

<s>“ Nel medesimo modo, egli dice, le immagini esterne <lb></lb>vengono riportate, e non sopra la sfera dell&#039;occhio, perchè, quando si fa <lb></lb>qualche concorso di materia fra il cristallino e la cornea, ci par di vedere <lb></lb>per l&#039;aria, alquanto lontano, qualche cosa di simile alle tele del ragno, e <lb></lb>così di colore oscuro, perch&#039;essendo tal materia illuminata dalla parte este­<lb></lb>riore, e veduta dalla parte interiore ch&#039;è l&#039;ombrosa, perciò ci apparisce <lb></lb>oscura. </s>

<s>Il che ci fa manifesto che la sensazione è più interna dell&#039;umore <lb></lb>acqueo, e non pare possa essere nel centro del cristallino, perchè come cen­<lb></lb>tro non è capace delle diverse quantità. </s>

<s>Ma piuttosto, passando i raggi per <lb></lb>il centro di esso, come per lo esempio della stanza e formando un angolo <lb></lb>alla cima, si dirà che faccino la base nella superficie del nervo ottico, dove <lb></lb>s&#039;imprimono le specie ad esempio della stanza, e di tanto maggiore squisi­<lb></lb>tezza, quanto le requìsite condizioni si trovano in più squisito grado ” (MSS. <lb></lb>Gal. </s>

<s>Contemporanei, T. VIII, c. </s>

<s>25). </s></p><p type="main">

<s>Il Cigoli e il Sagredo che ritrovano così la scienza della visione non <lb></lb>ne&#039;libri ma nel loro proprio discorso, mentre Galileo veniva ostinatamente <lb></lb>ripetendo i più vieti errori letti ne&#039;libri di Platone e di Galeno, dimostrano <lb></lb>che le dottrine del Benedetti, divulgate dal Keplero, si presentavano sotto <lb></lb>l&#039;aspetto di verità naturali, rintuzzate dall&#039;aculeo dei sofismi, e adombrate <lb></lb>dalle caligini dei pregiudizii. </s>

<s>Dicevasi che la retina, essendo opaca, non era <lb></lb>atta a specchiare in sè le immagini degli oggetti. </s>

<s>Ma rispondeva a questa <lb></lb>difficoltà il Santorio nella questione CXXIII de&#039;suoi Commentarii sopr&#039;Avi­<lb></lb>cenna, facendo notare che, appunto per ritenere le immagini, deve essa re­<lb></lb>tina essere opaca, perchè altrimenti, come tutti i diafani sogliono, diffonde­<lb></lb>rebbe la luce e ne disperderebbe i raggi in altri mezzi. </s>

<s>“ In illa parte debet <lb></lb>fieri visio, in qua obiecta non transferuntur in aliena loca, sed hic est quod <lb></lb>refractiones, quae fiunt in aqueo, crystallino et vitreo, reducant visibile in <lb></lb>aliena loca, ergo in ipsis non fiet visio. </s>

<s>Retina vero cogit omnes radios re­<lb></lb>fractos, impeditque ne ulterius penetrare possint, itaque firmantur ” (Opera <lb></lb>omnia, T. III, Venetiis 1660, pag. </s>

<s>1065). </s></p><p type="main">

<s>Faceva inoltre difficoltà la manifesta inversione delle immagini sul dia­<lb></lb>framma della Camera oscura, mentre l&#039;occhio vede gli oggetti diretti. </s>

<s>“ Omnia <lb></lb>cernuntur inversa, scriveva il De Dominis, quia radii sese in illo angusto <lb></lb>foramine intersecant, quod in oculo neque contingit neque contingere po­<lb></lb>test: visio enim fit valde prope foramen uveae, antequam sese radii possent <lb></lb>intersecare, et quia visio debet fieri in unico puncto, qui sit vertex coni <lb></lb>visivi, illa vero simulacra occupant magnum spatium ” (De radiis visus et <lb></lb>lucis, Venetiis 1611, pag. </s>

<s>15). </s></p><pb xlink:href="020/01/1468.jpg" pagenum="343"></pb><p type="main">

<s>Il Cigoli aveva invece dimostrato che la visione dee farsi molto più in­<lb></lb>dietro dell&#039;Uvea, e il Sagredo aveva detto che l&#039;occhio giudica esser tutti <lb></lb>gli oggetti diritti, per essere avvezzo ad apprenderne le specie tutte a ro­<lb></lb>vescio. </s>

<s>A questa spiegazione del fatto singolare, che parve anche ai moderni <lb></lb>la più filosofica di tutte, si riduce quell&#039;altra dello Scheiner, il quale dice <lb></lb>che perciò le immagini dipinte sulla retina a rovescio si vedon diritte “ quod <lb></lb>nimirum visus rem eo loco esse apprehendat, quo radius formaliter visorius, <lb></lb>si produceretur, exiret ” (Oculus cit., pag. </s>

<s>192). </s></p><p type="main">

<s>Il Baliani più tardi, in quel suo trattatello <emph type="italics"></emph>De visione,<emph.end type="italics"></emph.end> raccolto fra le <lb></lb>Opere diverse pubblicate in Genova dal Calenzani, nel 1666, era, a spiegare <lb></lb>il fatto, ricorso ai varii poteri rifrangenti del vitreo e del cristallino da lui <lb></lb>stesso sperimentati sui cadaveri (pag. </s>

<s>321), ma il Santorio non aveva ve­<lb></lb>duto miglior partito di togliersi d&#039;ogni impaccio che col negar la supposta <lb></lb>inversione delle immagini, dicendo che queste venivano raddirizzate sopra <lb></lb>la retina dalle seconde rifrangenze del vitreo. </s>

<s>“ Sicuti uno vitro convexo, <lb></lb>scrive nella sopra citata Questione, species visibilis in charta non erigitur, <lb></lb>sed duobus vitris erigitur.... quia crystallinus est unum vitrum convexum, <lb></lb>vitreus vero humor est aliud, sic in retina figurae eriguntur ” (Op. </s>

<s>omnia <lb></lb>cit., pag. </s>

<s>1065). </s></p><p type="main">

<s>L&#039;errore del Santorio si veniva a scoprir facilmente dalle sopra accen­<lb></lb>nate esperienze del Baliani, ma perchè queste erano difficili troppo, e su­<lb></lb>periori alla perizia, che in tal genere d&#039;arte sperimentale poteva aversi a <lb></lb>que&#039;tempi, non c&#039;era migliore argomento dimostrativo che quello dei fatti. </s>

<s><lb></lb>Lo Scheiner aveva opportunamente citato l&#039;esempio di quell&#039;uomo, a cui es­<lb></lb>sendo rimasta la pupilla annuvolata, fuor che per un breve tratto da rasso­<lb></lb>migliarsi a una sottil falce di luna, non vedeva gli oggetti se non che quando <lb></lb>i loro raggi v&#039;entravano obliqui (Oculus cit., pag. </s>

<s>36). </s></p><p type="main">

<s>Chi fosse propriamente il primo ad osservare sul fondo dell&#039;occhio, come <lb></lb>sul diaframma di una Camera ottica preparata dalle stesse mani della Na­<lb></lb>tura, le immagini rovesciate, crediamo non si poter con fiducia asserirlo. </s>

<s><lb></lb>Uno fra costoro in ogni modo, se ha da credersi al Gassendo, sarebbe stato <lb></lb>il Peiresc, il quale, persuaso che la retina amalgamata a tergo dalla coroide <lb></lb>faccia nell&#039;occhio l&#039;ufficio degli specchi, che raddirizzan le immagini, rin­<lb></lb>novellò nel 1634 l&#039;ipotesi invalsa a mezzo il secolo XVI, e riferita, come <lb></lb>vedemmo dal Porta in uno di quei quattro libri, di che compose la sua <lb></lb>prima Magia Naturale. </s>

<s>Per dar dunque il Peiresc fondamento alla sua ipo­<lb></lb>tesi, volle osservare quel che realmente avviene nell&#039;occhio, in cui gli ap­<lb></lb>parì “ posticam illam interioremque circumductionem oculi speculum esse <lb></lb>concavum, propter inversam, tam candelae quam aliorum quorumlibet obiecto­<lb></lb>rum, refiexionem ” (Vita cit., pag. </s>

<s>275). </s></p><p type="main">

<s>Chi ripensa a quello zelante fervore del Peiresc in diffondere così le <lb></lb>proprie come le altrui scoperte, più efficacemente forse che per mezzo degli <lb></lb>scritti, per via de&#039;familiari colloqui co&#039;più dotti amici, convenuti dalla non <lb></lb>lontana Parigi nelle sue case, e intrattenuti in privati accademici consessi; <pb xlink:href="020/01/1469.jpg" pagenum="344"></pb>intenderà che anche di questa esperienza delle immagini, che si vedono di­<lb></lb>pinte a rovescio sul fondo dell&#039;occhio, si dovesse facilmente divulgar la no­<lb></lb>tizia, e dalle tradizioni orali passare ne&#039;libri. </s>

<s>Comunque sia, il Cartesio, nel <lb></lb>cap. </s>

<s>V della Diottrica, suggerì pubblicamente di servirsi dell&#039;occhio stesso per <lb></lb>osservar in lui di fatto quel che gli era prima stato attribuito per conget­<lb></lb>ture fondate sopra semplici argomenti di analogia. </s>

<s>“ Omnia tamen, sog­<lb></lb>giunge dop&#039;avere accennato alla Camera oscura, magis explorata et certa <lb></lb>erunt, si evulsum recens defuncti hominis, aut, si illius copia non sit, bovis <lb></lb>vel alterius magni alicuius animalis oculum, ita secemus, ut ablata ea parte <lb></lb>trium eius membranarum, quae cerebro obversa est, satis magna pars hu­<lb></lb>moris vitrei appareat nuda, nec tamen iste humor effundatur, sed continea­<lb></lb>tur charta, vel ovi putamine vel alia quavis materia alba et tam tenui, ut, <lb></lb>quamvis non sit pellucida, omnem tamen luminis transitnm non excludat ” <lb></lb>(editio cit., pag. </s>

<s>59). </s></p><p type="main">

<s>Il Briggs consigliò poi di servirsi degli occhi delle civette, “ quod expe­<lb></lb>rimentum, egli dice, luculentius, ut mihi videtur, quam illud Cartesii mo­<lb></lb>dum visionis explicat, cum partes hoc more ìn situ naturali et integrae <lb></lb>conspiciantur ” (Ophtalmographia in loco cit., pag. </s>

<s>363). E infatti si dif­<lb></lb>fuse così quel piacevole esperimento, che il Malpighi lo commemorava come <lb></lb>il più bello e il più facile modo di persuadere ognuno della pittura delle <lb></lb>immagini rovesciate sopra la retina. </s>

<s>“ La propagazione delle specie alla Re­<lb></lb>tina inversa, tanto controversa, con l&#039;occhio della civetta usato come un ca­<lb></lb>nocchiale, per essere la parte posteriore della cornea diafana, si stabilisce ” <lb></lb>(Opera posthuma cit., P. II, pag. </s>

<s>151). </s></p><p type="main">

<s>Questa stessa diafaneità poi delle membrane negli occhi delle civette <lb></lb>suggerì al Morgagni uno de&#039;più efficaci argomenti, per confutare una no­<lb></lb>vità, che avendo, poco dopo passato mezzo il secolo XVII, levato così gran <lb></lb>romori nel campo dell&#039;Ottica fisiologica, non può da noi passarsi senza qual­<lb></lb>che cenno da inserirsi in questo tratto di storia. </s></p><p type="main">

<s>Dopo lo Scheiner par che fosse Edmondo Mariotte il primo ad atten­<lb></lb>dere con diligenza alla inserzione eccentrica del nervo nell&#039;occhio, per cui <lb></lb>le immagini, che si dipingono simmetriche intorno all&#039;asse ottico, vanno a <lb></lb>dipingersi necessariamente fuor di quella inserzione. </s>

<s>Ripensando sopra ciò <lb></lb>il Mariotte, fu preso da una curiosità di sapere qual effetto facessero i raggi <lb></lb>della luce, quando ad arte si facessero cadere sul punto proprio del nervo, <lb></lb>e nel 1668 istitui le opportune esperienze, delle quali, in una <emph type="italics"></emph>Lettre a mon­<lb></lb>sieur Pecquet,<emph.end type="italics"></emph.end> così descriveva i modi particolari, e dava conto all&#039;amico e <lb></lb>al collega dei resultati: “ J&#039;avois souvent observé, par l&#039;Anatomie tant des <lb></lb>hommes que des animaux, que iamais le nerf-optique ne repond iustement <lb></lb>au milieu du fond de l&#039;oeil, c&#039;est a-dire, à l&#039;endroit ou se fait la peinture <lb></lb>des objets, qu&#039;on regard directement; et que dans l&#039;homme il est un peu <lb></lb>plus haut, et a coté tirant vers le nez. </s>

<s>Pour faire donc tomber les rayons <lb></lb>d&#039;un objet sur le nerf-optique de mon oeil, et éprouver ce qui en arrive­<lb></lb>rait, j&#039;attachai sur un fond obscur, environ à la hauteur de mes yeux, un <pb xlink:href="020/01/1470.jpg" pagenum="345"></pb>petit rond de papier blanc, pour me servir de point de vûë fixe; et cepen­<lb></lb>dant j&#039;en fis tenir un autre à coté vers ma droite, à la distance d&#039;environ <lb></lb>deux pieds, mais un peu plus bas que le premier, afin qu&#039;il pût donner sur <lb></lb>le nerf-optique de mon oeil droit, pendant que je tiendrois le gauche fermé. </s>

<s><lb></lb>Je me plaçai vis-à-vis du premier papier, et m&#039;en eloignai peu à peu, te­<lb></lb>nant toujours mon oeil droit arrité dessus; et lorsque je fus à la distance <lb></lb>d&#039;environ neuf pieds, le second papier, qui étoit grand de près de quatre <lb></lb>pouces, me disparut entierement ” (Nouvelle decouverte touchante la vûe, <lb></lb>Ouvres, T. II, A la Haye 1740, pag. </s>

<s>496). </s></p><p type="main">

<s>Il fatto inaspettato si verificò privatamente da alcuni amici, e poi l&#039;Au­<lb></lb>tore stesso lo dimostrò in pubblico consesso in Parigi nella Biblioteca del <lb></lb>Re, dove depositò una scrittura, che conteneva la spiegazione. </s>

<s>Si diceva che <lb></lb>organo essenziale della visione non doveva esser la Retina, come da tutti <lb></lb>s&#039;era creduto e si credeva, ma la Coroide, la quale perchè “ part des bords <lb></lb>de nerf-optique, et n&#039;en couvre point le mileu ” (ivi, pag. </s>

<s>497) rende la ra­<lb></lb>gion chiarissima del perchè il punto dello stesso nervo sia cieco. </s></p><p type="main">

<s>Gli argomenti con cui il Mariotte si studiava, nella citata scrittura, di <lb></lb>dimostrare una cosa tanto nuova, che cioè organo primario della vista fosse <lb></lb>la Coroidea, erano diversi, ma questi due s&#039;annoverano fra&#039;principali: <emph type="italics"></emph>I, que <lb></lb>la retine ne penétré point dans le cerveau, comme fait la Choroide, qui <lb></lb>enveloppe le nerf-optique au-delà de l&#039;oeil, et l&#039;accompagne jusqu&#039;un mi­<lb></lb>lieu du cerveau; II, que la Choroide, étant fort déliée et opaque, elle <lb></lb>peut recevoir en un point les rayons d&#039;un méme point lumineaux<emph.end type="italics"></emph.end> (ivi, <lb></lb>pag. </s>

<s>500, 503). </s></p><p type="main">

<s>Il Pecquet, a cui aveva il Mariotte indirizzata la sua prima lettera de­<lb></lb>scrittiva dell&#039;esperienza chiedendone l&#039;autorevole giudizio di lui intorno al <lb></lb>modo tenuto nello spiegarla, negò che fosse la Coroide <emph type="italics"></emph>le principal organe <lb></lb>de la vision,<emph.end type="italics"></emph.end> nè le ragioni addotte dallo stesso Mariotte gli parevano con­<lb></lb>cludenti. </s>

<s>Quanto alla prima di quelle ragioni, diceva che la pia madre, di <lb></lb>ch&#039;è composta la Coroide, può bene impartire un senso di dolore a questa, <lb></lb>come a tutte le altre membrane, “ mais non pas celui de la vûe, qui de­<lb></lb>mande une autre impression que celle qui fait la douleur ” (ivi, pag. </s>

<s>501). <lb></lb>Quanto alla seconda poi delle sopra riferite ragioni conveniva che la Coroide <lb></lb>opaca avrebbe potuto ritenere in sè l&#039;impressione dei raggi luminosi, quando <lb></lb>però la Retina non fosse ella pure sufficientemente opaca da impedire il <lb></lb>passo libero a quegli stessi raggi (ivi, pag. </s>

<s>503). </s></p><p type="main">

<s>Un altro, non men valido nè meno autorevole oppositore contro l&#039;opi­<lb></lb>nione del Mariotte, sorse in seno alla stessa Accademia parigina nella per­<lb></lb>sona di Claudio Perrault, il quale avendo stabilito che “ la polissure et <lb></lb>l&#039;exacte égalité de la surface de la membrane, qui doit etre reputée l&#039;organe <lb></lb>de la vision, est une condition, sans la quelle on ne peut concevoir que la <lb></lb>vision se puisse faire ” (ivi, pag. </s>

<s>518); n&#039;ebbe a concluder che il difetto <lb></lb>di una tal requisita uguaglianza di superficie nella stessa Coroide è ciò che <lb></lb>“ la rend mal-propre a recevoir l&#039;impression des espèces ” (ivi, pag. </s>

<s>519). </s></p><pb xlink:href="020/01/1471.jpg" pagenum="346"></pb><p type="main">

<s>Nè fuori dell&#039;Accademia parigina mancarono al Mariotte oppositori, <lb></lb>fra&#039;quali non è da trascurare il Briggs, che propostisi ad esaminare quei <lb></lb>principali da noi sopra riferiti argomenti rispondeva a loro così in contra­<lb></lb>rio con queste ragioni: “ Ad prius argumentum respondeo quod, licet hi <lb></lb>colores per fibrarum interstitia transluceant, ipsas tamen fibras non adeo <lb></lb>permeant, praesertim versus nervi optici exitum, ubi densius agglomerantur, <lb></lb>quin hae, fere instar chartae purissimae et diaphanae, ad sistendas species <lb></lb>sufficiant. </s>

<s>Obiectio secunda facile refellitur ex eo quod tunica retiformis <lb></lb>eiusdem substantiae cum cerebro existat, quod tamen ad omnes obiectorum <lb></lb>impressiones, tam retinendas quam alio deferendas, idoneum esse reperi­<lb></lb>tur ” (Ophtalmog. </s>

<s>cit., pag. </s>

<s>358). </s></p><p type="main">

<s>In Italia la risoluzione della questione si trovava preparata già dal San­<lb></lb>torio, il quale aveva dimostrato, come vedemmo, che la Retina ha la pellu­<lb></lb>cidità necessaria, per ritenere le immagini, simile a quella della carta bianca <lb></lb>o della pelle d&#039;uovo, sopra cui poi il Cartesio, detratte le naturali membrane, <lb></lb>riceveva le pitture degli oggetti venute attraverso agli umori dell&#039;occhio. </s>

<s><lb></lb>Galileo avrebbe, così di questa come di ogni altra parte d&#039;Ottica fisiologica, <lb></lb>lasciata digiuna la sua scuola, se non ci avessero provveduto il Castelli col <lb></lb>suo <emph type="italics"></emph>Discorso sopra la vista,<emph.end type="italics"></emph.end> e il Baliani col suo trattatello <emph type="italics"></emph>De visione,<emph.end type="italics"></emph.end> com­<lb></lb>mentando le teorie del Keplero, ch&#039;erano insomma schiettamente italiane, <lb></lb>per aver avuto, come si dimostrò, i principii non dalle giocose fantasie del <lb></lb>Porta, ma dalle matematiche speculazioni del Benedetti. </s></p><p type="main">

<s>È notabile che in tanta penuria di scienza ottica, in ch&#039;era lasciata la <lb></lb>Scuola galileiana, il sopra citato <emph type="italics"></emph>Discorso<emph.end type="italics"></emph.end> rimanesse lungamente inedito, ed <lb></lb>è più notabile che si risolvesse il cardinale Leopoldo de&#039;Medici di farlo pub­<lb></lb>blicare, insiem con gli altri Opuscoli filosofici del Castelli, nel quarto pe­<lb></lb>riodo dell&#039;Accademia del Cimento. </s>

<s>Essendo questa risoluzione avvenuta nel­<lb></lb>l&#039;anno 1669 è facile congetturare che fosse provocata dai rumori sollevati <lb></lb>dal Mariotte in Francia. </s>

<s>In ogni modo però è cosa certa che il principe del­<lb></lb>l&#039;Accademia fiorentina fece in Parigi diligente ricerca delle famose Lettere <lb></lb>sopra la <emph type="italics"></emph>Nouvelle decouverte touchant la vûe,<emph.end type="italics"></emph.end> nè fu sua colpa, se venne <lb></lb>mal servito dal gesuita Bertet, il quale gli scriveva da Lione, il dì 3 d&#039;Ot­<lb></lb>tobre di quell&#039;anno 1669, in tali termini, da far chiara mostra di non avere <lb></lb>inteso nulla di quel che si trattava, scambiando fra le altre la sclerotica colla <lb></lb>coroidea. </s>

<s>“ Lasciai partendo da Parigi a uno de&#039;nostri padri la nuova sco­<lb></lb>perta del sig. </s>

<s>Mariotte intorno all&#039;organo del viso, ch&#039;egli prova essere la <lb></lb>sclerotide..... ” (MSS. Cim., T. XIX, c. </s>

<s>274). </s></p><p type="main">

<s>Che dunque il Principe e gli Accademici del Cimento rivolgessero i loro <lb></lb>studii intorno all&#039;organo della visione, proponendosi per loro testo gli Opu­<lb></lb>scoli del Castelli, è cosa dimostrata dai documenti, ma noi non sappiamo i <lb></lb>particolari di quegli studii, cosicchè a insorgere contro le innovazioni del <lb></lb>Mariotte, alquanti anni dopo, apparisce primo fra noi il Morgagni. </s>

<s>L&#039;Epi­<lb></lb>stola anatomica XVII, dal § 35 alla fine, s&#039;intrattien tutta in dimostrare che <lb></lb>non può la Coroide essere organo primario della vista, confutando le ra-<pb xlink:href="020/01/1472.jpg" pagenum="347"></pb>gioni del Mariotte con argomenti, che hanno le radici nella scienza più adden­<lb></lb>tro di quelli addetti dal Pecquet, dal Perrault e da altri stranieri. </s>

<s>Sentì bene <lb></lb>il Morgagni che tutto il forte di quelle ragioni stava nella composizion della <lb></lb>retina, e risalendo alle tradizioni della scienza italiana commemorò il Cas­<lb></lb>serio, che ripensando da una parte alla gran sensibilità di essa retina, e <lb></lb>dall&#039;altra alla stupidità della polpa cerebrale, congetturò che dovess&#039;essere <lb></lb>la membrana, organo precipuo della visione, intessuta di filamenti derivati <lb></lb>dalla pia madre. </s>

<s>Or si propose il Morgagni di ridurre le congetture ai fatti, <lb></lb>dai quali soli si poteva sperare che sarebbero bandite per sempre dalla <lb></lb>scienza le irragionevoli innovazioni francesi. </s>

<s>Ma la cosa era tanto difficile <lb></lb>che, non osando ripromettersi dimostrazioni, si contentava d&#039;indizi. </s>

<s>“ Idcirco <lb></lb>videndum est nobis possitne res demonstrari, aut, si non possit, ullane sal­<lb></lb>tem ex anatome indicia existant, quae, si quis in re difficillima sequatur, is <lb></lb>minus a veri similitudine, quam qui non sequantur, discedat ” (editio cit., <lb></lb>pag. </s>

<s>288). E gl&#039;indizii dell&#039;esser veramente la Retina intessuta di filamenti <lb></lb>derivati dalla pia madre furono tali, da aver in sè quella verosimiglianza <lb></lb>che si poteva desiderare. </s></p><p type="main">

<s>Quanto alla seconda delle sopra riferite ragioni, che il Mariotte addu­<lb></lb>ceva per conferma della sua opinione, il Morgagni invocava il fatto speri­<lb></lb>mentato dal Briggs negli occhi della civetta, ne&#039;quali, perciocchè le imma­<lb></lb>gini si vedevano così bene dipingersi sopra tutte le membrane soprapposte, <lb></lb>ne concludeva che l&#039;attitudine di ritener le pitture degli oggetti, dallo stesso <lb></lb>Mariotte attribuita alla sola Coroide, era propria, non che alla retina che si <lb></lb>diceva mancare della necessaria pellucidità, alla stessa scleroide (ivi, pag. </s>

<s>286). </s></p><p type="main">

<s>La gloria della <emph type="italics"></emph>Nouvelle decouverte,<emph.end type="italics"></emph.end> combattuta dagli stessi Francesi <lb></lb>nel suo primo fiore, fu per opera del Morgagni finalmente divelta dalle sue <lb></lb>radici, cosicchè tutti ritennero come vero che si facesse la vista per la pit­<lb></lb>tura degli oggetti sopra la Retina, secondo avevano insegnato il Benedetti <lb></lb>e il Keplero. </s>

<s>Questa dottrina però sembrava implicare in sè il supposto che <lb></lb>sien quasi nel cervello due occhi intenti a contemplare le immagini, ciò che, <lb></lb>giudicandosi inconveniente dal Cartesio, lo fece andare ad ammetter l&#039;ipo­<lb></lb>tesi che ciascun punto delle immagini muova diversamente i filamenti ner­<lb></lb>vosi espansi sopra la retina, dai quali si traducono le impressioni al cer­<lb></lb>vello. </s>

<s>“ Licet autem haec pictura sic transmissa in cerebrum semper aliquid <lb></lb>similitudinis ex obiectis a quibus venit, retineat, non tamen ob id creden­<lb></lb>dum est hanc similitudinem esse, quae facit ut illa sentiamus, quasi denuo <lb></lb>alii quidam oculi in cerebro nostro forent, quibus illam contemplari posse­<lb></lb>mus. </s>

<s>Sed potius motus esse, a quibus haec pictura componitur, qui imme­<lb></lb>diate in animam nostram agentes, quatenus illa corpori unita est, a natura <lb></lb>instituti sunt ad sensus tales in ea excitandos ” (Dioptrices, cap. </s>

<s>VI, edit. </s>

<s><lb></lb>cit., pag. </s>

<s>66). </s></p><p type="main">

<s>L&#039;ingegnosa ipotesi cartesiana però ebbe a cadere, quando l&#039;Anatomia <lb></lb>dimostrò non essere il nervo ottico composto di filamenti distinti, e quando <lb></lb>l&#039;osservazione del ristringimento dello stesso nervo persuase il Malpighi che, <pb xlink:href="020/01/1473.jpg" pagenum="348"></pb>se fosse vero quel che insegna il Cartesio, non si potrebbe veder altro che <lb></lb>poca e determinata parte dell&#039;oggetto. </s>

<s>“ Antequam retinae fiat expansio <lb></lb>tam arcte constringitur extrema optici latitudo, ut necessario intestinulorum <lb></lb>et fibrarum, si quae sint, intima fiat connexio et nodus..... Si autem sin­<lb></lb>gula illa intestinula unici filamenti vicem gererent, paucas et numero deter­<lb></lb>minatas tantum obiecti partes intueremur ” (Malpighi, Operum, T. II, Lugd. </s>

<s><lb></lb>Batav. </s>

<s>1687, pag. </s>

<s>123). </s></p><p type="main">

<s>Quell&#039;Anatomia però, che aveva col coltello del Malpighi uccisa l&#039;ipo­<lb></lb>tesi cartesiana, non seppe sostituirvene un&#039;altra, che avesse del vero miglior <lb></lb>sembianza, infintantochè non venne a fare intorno a ciò nuove prove del <lb></lb>suo ingegno il Valsalva. </s>

<s>Scoperta ch&#039;egli ebbe la testura raggiata della re­<lb></lb>tina, immaginò che gli spiriti visivi, tendendo più o meno cotesti raggi, pro­<lb></lb>ducessero più o meno viva nel sensorio l&#039;impression degli oggetti. </s>

<s>Confor­<lb></lb>tava questa sua ipotesi con una esperienza, ch&#039;ei diceva di avere appresa <lb></lb>da un suo Collega, e che consisteva nel ricever le immagini venute attra­<lb></lb>verso al foro di una Camera oscura sopra una pelle bagnata, sulla quale <lb></lb>si osserva che le pitture di esse immagini appariscono sempre più distinte, <lb></lb>secondo che, rasciugandosi via via la pelle, viene tutto insieme ad essere <lb></lb>anco più tesa. </s>

<s>“ Quod autem, iuxta diversam retinae dispositionem, obiecto­<lb></lb>rum impressiones variari possint, experimento evincitur, quod a doctissimo <lb></lb>Sodali accepi: nimirum si in Camera optica, ad terminandas obiectorum vi­<lb></lb>sibilium impressiones, adhibeatur pellis illa, qua in ducendis bracteis utun­<lb></lb>tur auri malleatores, obiecta ipsa satis vivida et satis distincta apparebunt, <lb></lb>modo ea pellis arida sit; quod si aqua fuerit madefacta, languida fiet obiec­<lb></lb>torum pictura ” (Dissertatio anat. </s>

<s>II cit., pag. </s>

<s>143). Ma perchè questa ipo­<lb></lb>tesi si divulgò quando la scienza, tutta intenta alle prime scoperte elettri­<lb></lb>che, incominciava a negar fede all&#039;antica esistenza degli spiriti vitali, non <lb></lb>trovò ne&#039;Fisiologi accoglienza, ond&#039;è che le intravedute analogie fra la Ca­<lb></lb>mera ottica e l&#039;occhio, apparite da principio così lusinghiere, si conobbe poi <lb></lb>che non toglievano in tutto il velo al mistero. </s></p><p type="main">

<s>I dubbi erano incominciati già infin da quando, sapendosi che per la <lb></lb>più precisa pittura nello strumento artificiale vuol l&#039;oggetto avere una po­<lb></lb>situra determinata rispetto alla lente, si pensò che nell&#039;organo naturale in­<lb></lb>vece s&#039;accomoda così bene la vista alle più avariate distanze. </s>

<s>Aveva già il <lb></lb>Keplero presentita questa difficoltà alle sue teorie, ed ebbe a fare perciò <lb></lb>ricorso all&#039;azione de&#039;processi ciliari, sopra la quale non molto dopo lo Schei­<lb></lb>ner tornò con più spiegati concetti. </s>

<s>“ Hinc Natura, egli scrisse, motricem <lb></lb>facultatem, tam tunicae uveae, quam processibus ciliaribus attribuit, ut suo <lb></lb>astrictu, et specierum nimium affluxum castigarent, et humorem crystalli­<lb></lb>num aut conglobarent circumcirca comprimendo, aut attenuarent attractione: <lb></lb>vel in anteriora protruderent, seu denique introrsus regererent, quibus re­<lb></lb>bus, non tantum refractio maior aut minor evaderet, pro varia crystallini <lb></lb>effigiatione, verum etiam retina eidem vicinior longiorque constitueretur, et <lb></lb>sic, quantum fieri posset, basin communem semper arriperet ” (Oculus cit., <pb xlink:href="020/01/1474.jpg" pagenum="349"></pb>pag. </s>

<s>162, 63). E confermava questa sua congettura sul fatto che, nell&#039;aguz­<lb></lb>zar la vista e nella prolungata attenzione, s&#039;affaticano tanto i muscoli ciliari <lb></lb>da produrre un senso di dolore. </s></p><p type="main">

<s>Il Cartesio pure, nel trattato <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end> descrivendo i processi ciliari, <lb></lb>gli qualificava per tendini esigui “ quorum ope crystallini humoris figura <lb></lb>mutari potest, et paulo magis plana vel magis convexa reddi, prout usus <lb></lb>exigit ” (editio cit., pag. </s>

<s>62). Ma in così belle speculazioni si supponeva la <lb></lb>virtù motrice ne&#039;corpi ciliari e la elasticità nel cristallino, senza però esser <lb></lb>certi se ai supposti rispondessero i fatti. </s>

<s>La struttura di esso umor cristal­<lb></lb>lino, come descrivevasi allora, e la sperimentata incompressibilità dei liquidi <lb></lb>rendevano il secondo supposto più inverosimile del primo, e perciò il Mo­<lb></lb>linetti pensò di attribuire il gioco della trasformazion di figura sotto l&#039;azion <lb></lb>de&#039;muscoli a tutto il bulbo dell&#039;occhio, piuttosto che alla semplice lente. </s>

<s>Il <lb></lb>modo come ciò avviene, secondo l&#039;Autore, è questo: “ Ubi sese ciliarium <lb></lb>processuum filamenta corripiunt, bulbus oculi, qui sphaericus pene est, con­<lb></lb>tractus ad latera, in longum procurrit. </s>

<s>Ita fundus oculi et retina cum illo <lb></lb>deducitur a crystallino. </s>

<s>Contrarium vero accidit contrahentibus se musculis <lb></lb>exterius, quippe bulbus tractus ad latera undique dilatatur, et cum multo <lb></lb>maius tunc temporis spatium illud sit, quod est a latere ad latus, illo, quod <lb></lb>est a pupilla ad fundum; necessum est ut crystallinus et retina propiora <lb></lb>fiant, sive crystallinus ad illam accedat, sive haec ad illum ” (Dissert. </s>

<s>anat. </s>

<s><lb></lb>cit., pag. </s>

<s>19). </s></p><p type="main">

<s>In quel mentre che il Molinetti si disponeva a scrivere queste cose, lo <lb></lb>Stenone pubblicava le sue anatomiche descrizioni della struttura del cristal­<lb></lb>lino ne&#039;pesci, e dal trovarlo composto di un nucleo solido, circondato da una <lb></lb>materia cedevole e molle, prese occasione di confermar l&#039;ipotesi, ch&#039;egli at­<lb></lb>tribuisce al Philippeau, secondo la quale, cedendo per la sua esteriore mol­<lb></lb>lezza il cristallino alla pressione de&#039;muscoli ciliari, si trasforma anche nel­<lb></lb>l&#039;uomo così di figura, da accomodarsi a vedere gli oggetti a varia distanza. <lb></lb></s>

<s>“ Haec in crystallino substantiae diversitas ingeniosissimi Philippeau opinio­<lb></lb>nem confirmare videtur, qui et ipse, cum sine dubio in piscibus idem con­<lb></lb>firmasse, persuasit sibi processus ciliares crystallino humori undique anne­<lb></lb>xos, dum breviores fiunt, crystallini convexitatem tanto facilius deprimere, <lb></lb>quanto minus actioni illorum contenti fluidi mobilitas resistere poterit, eaque <lb></lb>ratione crystallini figuram, quam ille ex duabus hyperbolis in homine com­<lb></lb>positam credit, pro obiecti varia distantia varie mutari “ (Elementorum myol. </s>

<s><lb></lb>specimen cit., pag. </s>

<s>82). </s></p><p type="main">

<s>I Cartesiani esultarono, vedendo quel che pareva il più inverosimile <lb></lb>fra&#039;supposti del loro Maestro confermato dall&#039;autorità anatomica dello Ste­<lb></lb>none, alla quale più tardi s&#039;aggiunse quell&#039;altra del Morgagni. </s>

<s>Nell&#039;<emph type="italics"></emph>Adver­<lb></lb>saria anatomica VI,<emph.end type="italics"></emph.end> dop&#039;aver detto che la struttura stenoniana del cristal­<lb></lb>lino ne&#039;pesci era quella medesima, ch&#039;egli avea ritrovata negli uomini. <lb></lb></s>

<s>“ Mihi tamen, ne conclude nell&#039;Animadversione LXXI, in praesentia cum <lb></lb>illis facere satis est, qui ante me docuere istam crystallini exteriorem mol-<pb xlink:href="020/01/1475.jpg" pagenum="350"></pb>litudinem eius figurae mutationem multo faciliorem reddere. </s>

<s>Igitur proxi­<lb></lb>mae tunicae crystalloidi, nunc a ciliari ligamento contractae, nunc vicissim <lb></lb>sua vi elastica et interiorum lamellarum restituenti, cum sive iste crystal­<lb></lb>lini aqueus humor, sive ista aquosìor molliorque substantia non promptis­<lb></lb>sime obsequi, et sese veluti opus est non conformare non possit; haud video <lb></lb>sane qui plicae illae et corrugationes in crystallini superficie tunc adeo fa­<lb></lb>cile produci queant ” (Adversaria anat. </s>

<s>omnia, Patavii 1719, pag. </s>

<s>91). </s></p><p type="main">

<s>Ebbero questi argomenti, co&#039;quali confortava il Morgagni la sua opi­<lb></lb>nione, tanta efficacia sopra gl&#039;ingegni, che s&#039;ammetteva oramai da tutti <lb></lb>l&#039;ipotesi attribuita al Philippeau, lusingando dall&#039;altra parte così l&#039;apparente <lb></lb>struttura fibrosa de&#039;corpi ciliari, da farli facilmente credere muscolosi. </s>

<s>Ma <lb></lb>intanto, in mezzo ai lunghi dissensi che avevano avuto sempre quasi uguali <lb></lb>momenti, incominciava, poco dopo il Morgagni, a prevaler l&#039;opinione dalla <lb></lb>parte di coloro, che negavano a quelli stessi corpi ciliari la natura e l&#039;uffi­<lb></lb>cio di muscoli, infin tanto che, di pochi anni oltrepassata la prima metà del <lb></lb>secolo XVII, non uscì l&#039;Anatomia a pronunziare per bocca dell&#039;Haller quella <lb></lb>sua assoluta sentenza, che intorno al cristallino <emph type="italics"></emph>musculosi nil quidquam <lb></lb>habet.<emph.end type="italics"></emph.end> S&#039;ebbe allora a confessare che i morti strumenti fabbricati dall&#039;arte <lb></lb>erano ombre, le quali sparivano nell&#039;atto stesso che intendevasi dare a loro <lb></lb>un corpo rappresentativo de&#039;vivi organi della Natura. </s>

<s>S&#039;era la scienza umana, <lb></lb>dopo tanti secoli di studii faticosi, compiaciuta d&#039;aver finalmente ritrovate <lb></lb>le corde della lira nell&#039;orecchio, e il pennello del pittore nell&#039;occhio, ma al <lb></lb>domandar che poi si fece con quali organi s&#039;ascoltano tali suoni, o si con­<lb></lb>templano tali spettacoli, s&#039;ebbe a riconoscere nella risposta che quegli im­<lb></lb>maginati orecchi, e quegli occhi, che s&#039;attribuivano all&#039;anima, eran giusto <lb></lb>l&#039;organo dell&#039;udito e della vista, che si cercava. </s>

<s>La iatromatematica del Bo­<lb></lb>relli ebbe di qui l&#039;ultimo crollo, per cedere il suo luogo alle speculazioni <lb></lb>psichiche dello Stahl, le quali intanto ebbero seguaci, in quanto che lo stesso <lb></lb>enimmatico linguaggio pareva meglio conformarsi ai naturali misteri. </s></p><pb xlink:href="020/01/1476.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Degli ordinamenti naturali<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>I. Dell&#039;ordinamento degli animali. </s>

<s>— II. Dell&#039;ordinamento delle piante. </s>

<s><lb></lb>III. Dell&#039;ordinamento dei minerali.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Gli organi e le funzioni, intorno allo studio delle quali s&#039;è fin qui trat­<lb></lb>tenuta la nostra Storia, appartengono agli animali degli ordini superiori e <lb></lb>principalmente all&#039;uomo, che fu per questo appellato <emph type="italics"></emph>Microcosmo<emph.end type="italics"></emph.end> perchè in <lb></lb>lui tutta si compendia e sublimasi la Natura. </s>

<s>Perchè si sia la scienza ri­<lb></lb>volta con tanto ardore a meditare sulla gran Sintassi, non finendo il Ve­<lb></lb>salio di rimproverar Galeno, per avere inciso a preferenza i bruti, e il Co­<lb></lb>lombo e il Falloppio ritorcendo contro il Vesalio stesso le accuse, che al <lb></lb>Colombo e al Falloppio non mancò poi di raffacciare l&#039;Eustachio; non sa­<lb></lb>rebbe a dir nè sì facile nè sì spedito: ma fu in ogni modo provvido istinto <lb></lb>della stessa Scienza, la quale, avendo nell&#039;alta mente riposto di dare ordine <lb></lb>alle numerosissime e disperse varietà degli esseri naturali, sentì quanto fosse <lb></lb>per riuscir proficuo al suo intento il considerar que&#039;vari esseri nell&#039;uomo <lb></lb>solo tutti insieme riassunti. </s></p><p type="main">

<s>La necessità però di que&#039;naturali ordinamenti non fu così subito rico­<lb></lb>nosciuta, parendo che i tre grandi regni degli animali, delle piante e dei <lb></lb>minerali fossero dalla Natura stessa stabilmente definiti, e, quanto agli ani­<lb></lb>mali in particolare, vedendoli assai naturalmente ordinati e distinti in qua­<lb></lb>drupedi, in uccelli, in pesci e in insetti. </s>

<s>Le piante, per aver da una parte <lb></lb>troppe varietà fra loro, e dall&#039;altra troppe somiglianze, si trovò più difficile <pb xlink:href="020/01/1477.jpg" pagenum="352"></pb>a distribuirle, cosicchè gli antichissimi Naturalisti non s&#039;attentarono nemmen <lb></lb>di venire al cimento: difficile poi non solo, ma impossibile, si reputò il dar <lb></lb>convenevole ordine ai minerali. </s></p><p type="main">

<s>I primi conati dunque, che si fecero dalla scienza, furono intorno agli <lb></lb>animali, e incominciarono da Aristotile, a cui si fece anche per il primo <lb></lb>sentir la necessità di ordinare il più alto e supremo regno della Natura, <lb></lb>quando, dalle famiglie che popolavano l&#039;angusta Grecia, si passò a cono­<lb></lb>scerne tante altre disperse per le regioni dell&#039;aria, per i mari e per le terre, <lb></lb>di che si componevano gli smisurati imperi di Filippo e di Alessandro. </s></p><p type="main">

<s>Dallo Stagirita insomma incominciano i metodi, così dall&#039;altra parte con­<lb></lb>formi al genio particolare di quella Filosofia. </s>

<s>“ Animalium vero differentias <lb></lb>(scriveva nelll&#039;introdursi a trattar <emph type="italics"></emph>De historia animalium<emph.end type="italics"></emph.end>) aut per vitas, <lb></lb>aut per actiones, aut per mores, aut per partes constitui dignum est ” (To­<lb></lb>mus VI Operum, Venetiis 1560, fol. </s>

<s>84). Le fonti annoverate in ultimo luogo <lb></lb>erano le legittime, ma perchè troppo tornava difficile il desumere le diffe­<lb></lb>renze dagli organi, non troppo bene ancora conosciuti, tenendo pochissimo <lb></lb>conto de&#039;caratteri essenziali e intrinseci, s&#039;intrattien lungamente Aristotile <lb></lb>a notar quelle sole differenze fondate sopra caratteri accidentali ed esterni. </s></p><p type="main">

<s>La principal distinzione, che consegue da questo metodo, è in animali <lb></lb>acquatici e in terrestri. </s>

<s>La prima poi di tali due grandi classi si divide in <lb></lb>due ordini: “ alia enim in fluido degunt victumque petunt ex humore, quem <lb></lb>etiam humorem per vices recipiunt et reddunt, nec vivere possunt nisi ver­<lb></lb>sentur in humore, quod plurimae piscium parti evenire apertum est. </s>

<s>Alia <lb></lb>degunt quidem in fluido victumque inde emoliuntur, sed aerem non humo­<lb></lb>rem recipiunt, et foris patere solent. </s>

<s>Complura huius generis sunt partim <lb></lb>gressilia, ut lutris, latax, crocodilus; partim volucres, ut mergi, ut natrix ” <lb></lb>(ibid.). Si suddividono poi gli stessi acquatici, rispetto alle varie qualità degli <lb></lb>ambienti, in marini, in fluviatili e in lacustri. </s></p><p type="main">

<s>I terrestri pure son da Aristotile divisi in due grandi classi: in quelli <lb></lb>che respirano “ ut homo et quaecumque habent pulmonem ” (ibid., fol. </s>

<s>85); <lb></lb>e in quelli che non respirano “ ut vespae, apes et reliqua insecta, quo no­<lb></lb>mine ea appello, quorum corpus incisuris praecingitur ” (ibid.). Le due <lb></lb>grandi classi si dividono poi in ordini, e si suddividono in generi, desu­<lb></lb>mendo le loro distinzioni da differenze non punto meno accidentali, d&#039;ond&#039;è <lb></lb>condotto, volendo ridurre in un ordine quegli animali che convivono in so­<lb></lb>cietà, a ricongiungere insieme l&#039;uomo, l&#039;ape, la vespa, la formica e la grue. </s>

<s><lb></lb>Quando poi passa Aristotile a divisar le differenze, che nascono dalle parti, <lb></lb>non entra punto addentro alla composizione organica, ma nota di quelle <lb></lb>stesse parti le più esterne sole e più apparenti, dando così il primo esem­<lb></lb>pio ai futuri Naturalisti di quelli, che poi si chiamarono <emph type="italics"></emph>Metodi artificiali.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Da così fatti metodi informata procede, ne&#039;suoi dieci libri l&#039;<emph type="italics"></emph>Historia <lb></lb>animalium,<emph.end type="italics"></emph.end> che si ammirò e si studiò con amore dai dotti, infin tanto che <lb></lb>non sentì Plinio il bisogno di ampliarla, e di ridurla a quella universalità <lb></lb>di cose, a cui tendeva l&#039;indole e l&#039;ingegno di un Console dell&#039;imperio ro-<pb xlink:href="020/01/1478.jpg" pagenum="353"></pb>mano. </s>

<s>Degli ordinamenti naturali però l&#039;Autore della nuova Storia non si <lb></lb>prende troppo gran cura, e in quattro distinti libri, che son l&#039;VIII, il IX, <lb></lb>il X e l&#039;XI, trattando de&#039;quadrupedi, degli acquatici, degli uccelli e degli <lb></lb>insetti, non par che senta il dovere di rispondere a&#039;suoi lettori perchè dal <lb></lb>descrivere alcuni generi o alcune specie si passi a descriverne altre, che si <lb></lb>trovano bene spesso associate insieme, piuttosto nelle pagine del libro, che <lb></lb>nel regno della Natura. </s></p><p type="main">

<s>La varietà delle cose, e la semplice eleganza delle descrizioni, ne ren­<lb></lb>devano così piacevole la lettura, che le Storie naturali di Plinio divennero <lb></lb>la delizia degli eruditi. </s>

<s>Ma quando si scoprì il nuovo mondo, si trovaron <lb></lb>mancare di quella universalità, dall&#039;Autore stesso con sì grande studio cer­<lb></lb>cata, intantochè scriveva Amerigo Vespucci, in una sua lettera a Lorenzo di <lb></lb>Pier Francesco de&#039;Medici, che le cose descritte dallo stesso Plinio, benchè <lb></lb>fossero tante, pur non giungevano alla millesima parte di quelle, che gli era <lb></lb>occorso a vedere ne&#039;suoi Viaggi, o a scoprire ne&#039;nuovi paesi da sè sco­<lb></lb>perti. </s>

<s>“ Hanno molte perle, egli dice, e pietre preziose, com&#039;abbiamo ricor­<lb></lb>dato di sopra, le quali tutte cose, quand&#039;io volessi raccontar particolarmente, <lb></lb>per la gran moltitudine di esse e per la lor diversa natura, questa storia <lb></lb>diventerebbe troppo grande opera, perciocchè Plinio, uomo perfettamente <lb></lb>dotto, il quale compose istoria di tante cose, non giunse alla millesima parte <lb></lb>di questa, e se di ciascuna di loro egli avesse trattato averia, in quanto alla <lb></lb>grandezza, fatto opera molto maggiore, ma del vero perfettissima, e sopra <lb></lb>tutto porgono maraviglia non piccola le molte sorte di pappagalli di varii e <lb></lb>diversi colori. </s>

<s>Gli arbori tutti rendono odore tanto soave, che non si puote <lb></lb>immaginare, e per tutto mandano fuori gemme e liquori e sughi ” (Ban­<lb></lb>dini, Vita e Lettere di A. V., Firenze 1745, pag. </s>

<s>112, 13). </s></p><p type="main">

<s>Fra il secolo XIV e il XV dunque, mentre da una parte il regno della <lb></lb>Natura smisuratamente si ampliava, per le scoperte e per le descrizioni dei <lb></lb>Viaggiatori, specialmente Italiani, dall&#039;altra, a rappresentar meglio abiti e <lb></lb>forme nuove o non troppo domestiche, soccorreva opportuna alla Storia na­<lb></lb>turale l&#039;arte della pittura. </s>

<s>Di ciò, in Leonardo da Vinci che prestò l&#039;opera <lb></lb>sua ad Antonio Torriani, e nel Tiziano, che rappresentava in disegno ciò <lb></lb>che gli diceva di avere scoperto, nelle sue sottili anatomie, l&#039;Eustachio, ab­<lb></lb>biamo tali insigni esempii, che ci dispensano dal noverar que&#039;tanti altri, <lb></lb>per i quali si vedono con arte squisitissima disegnate dal vero piante e ani­<lb></lb>mali, da imprimersi ne&#039;libri per illustrare le descrizioni, che ne davano ì <lb></lb>Naturalisti. </s></p><p type="main">

<s>L&#039;arte in ogni modo poteva servire alla facilità delle descrizioni, ma <lb></lb>il cresciuto numero delle specie, oltre al dare maggior faccenda agli scrit­<lb></lb>tori, aumentava, ciò che più rileva, le difficoltà di bene ordinarle. </s>

<s>Succes­<lb></lb>sero, nella seconda metà del secolo XVI, all&#039;antico Plinio tre Autori, che <lb></lb>si ripartirono l&#039;opera laboriosa, benchè non si stendesse molto al di là del <lb></lb>sommo regno animale. </s>

<s>Guglielmo Rondelet trattò de&#039;pesci, Ulisse Aldovrandi <lb></lb>degli uccelli, e Currado Gesner de&#039;quadrupedi. </s></p><pb xlink:href="020/01/1479.jpg" pagenum="354"></pb><p type="main">

<s>Al primo entrare alla lettura del Rondelezio si sente sollecito l&#039;Autore <lb></lb>d&#039;andare in cerca di quelle note, per cui si differenziano tutte le cose ge­<lb></lb>nerate sopra la terra, e senza le quali “ notitia nulla haberi potest ” (De <lb></lb>piscibus marinis, Lugduni 1554, pag. </s>

<s>1). Quelle massime differenze però <lb></lb>confessa esser difficilissime a ritrovarsi, e dall&#039;altra parte non vede nessun <lb></lb>filosofo, di cui possa seguire gli esempii, da Aristotile in fuori, che perciò <lb></lb>prende a guida sicura per ordinare i suoi pesci. </s>

<s>“ Piscium igitur, ut cae­<lb></lb>terorum animalium, differentiae a vita vivendique consuetudine, a partibus, <lb></lb>ab actionibus, a moribus omnino sumuntur, et his, tanquam illustribus no­<lb></lb>tis, omnium quae in aqua vivunt animalium discrimina distinguemus. </s>

<s>Hanc <lb></lb>viam nobis indicavit Aristotiles, et ea animalium naturam est persequutus. </s>

<s><lb></lb>Eadem, in plantarum historia describenda, progressus est Theophrastus, ei­<lb></lb>dem et nos, in ea quae mare continet, penetrabimus ” (ibid., pag. </s>

<s>3). </s></p><p type="main">

<s>Il Rondelezio però è molto più diligente di Aristotile in ricercar le note <lb></lb>differenziali, che si desumono dall&#039;esame delle parti, e anzi è questo che lo <lb></lb>rende superiore a tutti i Naturalisti de&#039;suoi tempi, non eccettuato lo stesso <lb></lb>Aldovrandi. </s>

<s>L&#039;<emph type="italics"></emph>Ornithologia<emph.end type="italics"></emph.end> di lui, ch&#039;è l&#039;unica opera venuta in luce vivente <lb></lb>l&#039;Autore, è distribuita in venti libri compresi in tre grandi Tomi in folio, <lb></lb>il primo de&#039;quali fu pubblicato in Bologna nel 1599, ma noi non abbiamo <lb></lb>potuto avere sott&#039;occhio che l&#039;edizione fatta in Francfort nel 1610. </s></p><p type="main">

<s>Al primo de&#039;XII libri raccolti insieme in questo Tomo precedono i <emph type="italics"></emph>Pro­<lb></lb>legomeni,<emph.end type="italics"></emph.end> ne&#039;quali l&#039;Autore tratta fra le altre cose <emph type="italics"></emph>De ordine,<emph.end type="italics"></emph.end> nello sce­<lb></lb>gliere il quale, troppo indulgendo all&#039;indole cavalleresca dei tempi, s&#039;attiene <lb></lb>alle dignità, che nascono dall&#039;uso della forza o dal valore nelle armi, per <lb></lb>cui viene a costituirsi il primo ordine degli uccelli rapaci. </s>

<s>“ Cum itaque <lb></lb>particularem omnium avium, tam ab antiquis et recentioribus descriptarum, <lb></lb>quam nostris diuturnis observationibus conquisitarum, historiam contexen­<lb></lb>dam susceperim; in huius enarratione seriem dignitatis servare duxi, pri­<lb></lb>mumque rapacibus, tanquam nobilitate reliquis longe praeferendis, inter <lb></lb>omnes aves dare locum statui ” (Ornithol., Francof. </s>

<s>1610, pag. </s>

<s>4). E perchè, <lb></lb>fra gli stessi uccelli rapaci, di più nobile e generoso animo son quelli, che <lb></lb>vanno in aperta caccia di giorno, che non gli altri, i quali meditano nel­<lb></lb>l&#039;oscurità della notte insidie e tendono agguati; ne fa la prima e principal <lb></lb>divisione in diurni e notturni. </s>

<s>“ Carnivora autem isthaec, cum quaedam <lb></lb>diurna, quaedam nocturna habeantur; ego primum de diurnis, quod praedam <lb></lb>interdiu rapientia sensu et viribus aliis praepolleant, tractabo ” (ibid.). Nel <lb></lb>II Tomo, che comprende i libri XIII-XVIII, divide gli altri uccelli non ra­<lb></lb>paci in granivori, in baccivori e in vermivori, facendo questa volta giudici <lb></lb>delle dignità i cuochi ed i ghiotti, che gli mettono primi innanzi i pavoni, <lb></lb>le pavoncelle e i fagiani. </s>

<s>Ne&#039;libri XIX e XX del III Tomo, dedicato al car­<lb></lb>dinal di Montalto, e che noi leggiamo nell&#039;edizione fatta in Francfort nel 1613, <lb></lb>tratta degli uccelli acquatici, ai quali assegna l&#039;ultimo luogo, per essere più <lb></lb>ignobili e più insipidi di tutti gli altri. </s></p><p type="main">

<s>Si vede bene di qui che, in ordine alla ricerca delle note differenziali, <pb xlink:href="020/01/1480.jpg" pagenum="355"></pb>l&#039;Ornitologia dell&#039;Aldovrandi segna un regresso da Aristotile e dal Ronde­<lb></lb>lezio, i quali presero di mira il vario modo di vita, i costumi e le parti. </s>

<s>Ma <lb></lb>ben più manifesto e notabile è quel regresso nel Gesnero, che per levarsi <lb></lb>d&#039;impaccio, scambiando l&#039;abito di Naturalista in quello di Filologo, si mette <lb></lb>ad ordinare i suoi Quadrupedi vivipari secondo le lettere dell&#039;alfabeto, co­<lb></lb>sicchè in queste storie gesneriane (come del resto in tante altre storie, che <lb></lb>non hanno il titolo di naturali) toccano all&#039;Asino, e poi subito al Bue, le <lb></lb>prime dignità e i primi seggi. </s></p><p type="main">

<s>In quel medesimo tempo che l&#039;Aldovrandi e il Gesner, associando l&#039;opera <lb></lb>loro a quella del Rondelezio, rendevano quasi compiuta la Storia particolare <lb></lb>degli animali, Ferrante Imperato pensava a dare all&#039;Italia una storia più <lb></lb>compendiosa, ma comprensiva di tutte quelle parti, che si leggevano nel­<lb></lb>l&#039;Opera di Plinio, dalla quale toglie alle sue nuove trattazioni gli esempi. </s>

<s><lb></lb>Se non che poco si trattiene intorno agli animali e alle piante, per riser­<lb></lb>bare la maggior parte dei libri e dei capitoli alla descrizione dei minerali, <lb></lb>e alla risoluzione di problemi, fra&#039;quali alcuni importantissimi di Meteoro­<lb></lb>logia e di Geologia, cosicchè, piuttosto che <emph type="italics"></emph>Historia naturale,<emph.end type="italics"></emph.end> s&#039;intitolerebbe <lb></lb>il suo libro <emph type="italics"></emph>Fisica generale<emph.end type="italics"></emph.end> in preparazione alla scienza dei moderni. </s>

<s>“ Messi <lb></lb>mano, egli dice, a questa messe con restringermi nelle cose, o per l&#039;anti­<lb></lb>chità de&#039;scrittori e mutazioni di voci già sconosciute, oppur da quelli tra­<lb></lb>lasciate, ovvero imperfettamente e oscuramente trattate. </s>

<s>Questo fa che più <lb></lb>negli minerali, che nelle materie degli animali, e men di tutto nelle piante <lb></lb>mi sia disteso ” (Hist. </s>

<s>natur., Venezia 1672, pag. </s>

<s>1). Di qui è che Ferrante, <lb></lb>come Plinio, non si prende alcuna cura di ordinamenti, e dall&#039;altra parte <lb></lb>venivano a dispensarlo dal difficile assunto le scarsità delle specie descritte, <lb></lb>proponendosi di trattar solamente di quelle “ l&#039;istoria delle quali è stata <lb></lb>dagli altri meno osservata ” (ivi, pag. </s>

<s>654). </s></p><p type="main">

<s>Stando le cose in questi termini, aveva giusti motivi Francesco Bacone <lb></lb>di scrivere, nel cap. </s>

<s>III del II libro <emph type="italics"></emph>De augmentis scientiarum,<emph.end type="italics"></emph.end> che la sto­<lb></lb>ria Naturale “ tam inquisitione sua, quam congerie, nullo modo in ordine, <lb></lb>ad eum quem diximus finem, aptata est ” (Lugani, P. I, 1763, pag. </s>

<s>115). <lb></lb>Vedeva il Verulamio essa Storia com&#039;era stata dagli Autori trattata infino <lb></lb>a&#039;suoi tempi, perdersi piuttosto nelle superfluità degli iconismi, che fondarsi <lb></lb>in solide e diligenti osservazioni “ quare, ne concludeva, Historiam inducti­<lb></lb>vam desiderari pronunciamus ” (ibid.). </s></p><p type="main">

<s>Il generoso desiderio però non poteva essere così presto adempiuto, ri­<lb></lb>chiedendosi per quella induzione l&#039;esame di fatti particolari, smisurati di <lb></lb>numero, per esser tanti quante sono le specie dei vegetabili e degli animali; <lb></lb>difficilissimi ad essere riconosciuti nella loro propria natura e qualità di as­<lb></lb>sidui e fedeli ministri del senso e della vita. </s>

<s>L&#039;opera della mente dunque <lb></lb>trovava, in ordinar la Natura, tutt&#039;insieme difficoltà nelle varietà degli or­<lb></lb>gani, e nelle qualità delle funzioni. </s></p><p type="main">

<s>Per assegnare la dignità degli organi pareva giusto criterio quello della <lb></lb>così detta division del lavoro, di che, ne&#039;civili consorzii e nelle stesse umane <pb xlink:href="020/01/1481.jpg" pagenum="356"></pb>famiglie, si ha opportunissimo esempio. </s>

<s>A un piccolo proprietario bastano <lb></lb>pochi lavoratori delle sue terre: se la possessione cresce, e crescono i la­<lb></lb>voratori, ci vuol chi sopraintenda ad essi, ed abbia cura delle cantine e dei <lb></lb>granai. </s>

<s>Se cresce la possessione anche di più, quel fattore solo non basta: <lb></lb>ci vuol chi particolarmente abbia cura di confezionare e di conservare i vini, <lb></lb>chi di dispensare i grani, e chi attenda a tanti altri varii ufficii, che vo­<lb></lb>gliono esser via via ripartiti in più gran numero di persone, secondo che <lb></lb>al signore crescono le possessioni. </s></p><p type="main">

<s>Similmente, ad alcuni animali basta un gomitolino di fibre muscolari, <lb></lb>che faccia da cuore, ma in altri s&#039;intessono quelle fibre con assai maggiore <lb></lb>artificio, e dividono in due la interiore cavità del gomitolo. </s>

<s>Altri ne vogliono <lb></lb>tre, e risalendo ai più alti gradi, all&#039;ultimo, quelle interne cavità si molti­<lb></lb>plicano in quattro seni. </s>

<s>La varia struttura del cuore pareva dunque porgere <lb></lb>sufficiente argomento a costituire i varii seggi di dignità, dai crostacei, ai <lb></lb>mammiferi e agli uccelli; distinzione che risultava dall&#039;altra parte assai ma­<lb></lb>nifesta da quelle estrinseche note, sulle quali fermarono l&#039;attenzione Aristo­<lb></lb>tile e i suoi seguaci. </s></p><p type="main">

<s>Se l&#039;attendere ai soli organi bastasse, questo accennato sarebbe forse <lb></lb>il solo sufficiente, o almeno il principale de&#039;criterii da seguirsi nell&#039;ordinare <lb></lb>le varietà degli animali. </s>

<s>Ma convien di più al Naturalista tener conto delle <lb></lb>funzioni, le quali si mettono in atto da un organismo, che non cade sotto <lb></lb>i sensi, e che non è trattabile dal coltello anatomico. </s>

<s>Cotesto invisibile or­<lb></lb>ganismo si compone di elementi eterei, i quali non siamo certi se corri­<lb></lb>spondano proporzionalmente in numero, in qualità e in composizione agli <lb></lb>elementi materiali. </s>

<s>Danno buon fondamento al dubbio gl&#039;istinti, vedendosi <lb></lb>alcuni insetti, che son costituiti negl&#039;infimi gradi, esser rispetto a ciò tanto <lb></lb>superiori a molti mammiferi, com&#039;alle pecore, per esempio, le formiche e <lb></lb>le api. </s></p><p type="main">

<s>In ogni modo, essendo la proporzione tra l&#039;organismo etereo e il ma­<lb></lb>teriale un&#039;ipotesi impossibile a verificarsi, la scienza umana l&#039;ammette, e <lb></lb>ammette insieme per essenzial nota distintiva le parti, sicura che, quanto più <lb></lb>son queste elaborate, altrettanto ne resultino le funzioni più perfette. </s>

<s>Es­<lb></lb>sendo questa l&#039;unica via, che si parava innanzi alla mente per riuscire a <lb></lb>mettere in caratteri distinti e leggibili il volume immenso della Natura, s&#039;in­<lb></lb>tenderà come primi ad additar non solo, ma ad aprir quella stessa via fos­<lb></lb>sero coloro, che dettero opera alle dissezioni degli animali. </s>

<s>Furono così fatte <lb></lb>dissezioni, ai tempi di Galeno, principalmente rivolte all&#039;uso della medicina, e <lb></lb>si riducevan perciò tutte all&#039;Anatomia umana, la quale, risorgendo nel se­<lb></lb>colo XVI, si fece uno scrupoloso dovere di non dissecare che i soli cada­<lb></lb>veri dell&#039;uomo. </s>

<s>L&#039;istituto era senza dubbio ragionevole, trattandosi di voler <lb></lb>descrivere le sole parti del corpo umano, e di evitar di confonderle con <lb></lb>quelle delle belve, ma riusciva altresì proficuo ai progressi della storia Na­<lb></lb>turale, perchè, come s&#039;accennava sui principii di questo discorso, tutti gli <lb></lb>organismi inferiori si trovavano compresi insomma nella grande Sintassi. </s></p><pb xlink:href="020/01/1482.jpg" pagenum="357"></pb><p type="main">

<s>Perchè però riuscissero così fatti studii veramente proficui era neces­<lb></lb>sario far, nella sintesi, l&#039;analisi delle parti, e notar con gran diligenza le <lb></lb>differenze, che presenta un organo nell&#039;uomo e negli altri animali. </s>

<s>L&#039;Ana­<lb></lb>tomia comparata ebbe dal Vesalio, dal Colombo, dal Falloppio e dagli altri <lb></lb>insigni anatomici di quel tempo niuna o pochissima cultura, la quale pro­<lb></lb>priamente comincia con Girolamo Fabricio. </s>

<s>Questo nuovo instituto, che tra­<lb></lb>sparisce qua e là dalle varie opere dell&#039;Anatomico d&#039;Acquapendente, si ri­<lb></lb>vela più che mai esplicito in quel trattatello, ch&#039;egli intitolò <emph type="italics"></emph>De ventriculo, <lb></lb>intestinis et gula,<emph.end type="italics"></emph.end> dove si paragonano dall&#039;Autore questi organi della dige­<lb></lb>stione nelle varie classi degli animali, e se ne fanno rilevare le differenze. </s>

<s><lb></lb>Quanto ai ventricoli, per esempio, paragona quelli dei Ruminanti, che son <lb></lb>quattro, con quelli dei Pennati che son tre, e con quelli de&#039;pesci che si ri­<lb></lb>ducono in uno solo, e argutamente nota le differenze che presentano i sot­<lb></lb>toposti intestini. </s>

<s>“ Diversitas autem potissimum apparet in caeco intestino, <lb></lb>quod in homine tenuis oblongaque appendicula: in brutis quadrupedibus <lb></lb>oblongum, unicum et crassissimum: in piscibus nullum apparet caecum in­<lb></lb>testinum ” (Opera omnia cit., pag. </s>

<s>99). E da così fatte osservazioni, ini­<lb></lb>ziando l&#039;Acquapendente quell&#039;altra nuova scienza, che si disse Zoonomia, <lb></lb>passa a dire che da queste variazioni dell&#039;intestino ceco dipendono neces­<lb></lb>sariamente le varietà, che presenta il colon a lui prossimo. </s>

<s>“ Nam cui cae­<lb></lb>cum intestinum, ceu manca et exigua appendicula traditum est, ut homini, <lb></lb>huic per colon ei proximum et continuum, quod extuberans et amplissimum <lb></lb>in sui initio est, compensatum fuit. </s>

<s>Cui vero caecum amplissimum factum <lb></lb>est, ut quadrupedi, eidem coli in sui principio proposita amplitudo defecit. </s>

<s><lb></lb>Rursus, cui duo fuere comparata caeca intestina, ut pennato, eidem colon <lb></lb>universum denegatum est. </s>

<s>Denique piscium genus, quod caeco ex toto ca­<lb></lb>ruit, colo quoque caruisse patet ” (ibid.). </s></p><p type="main">

<s>Fu il nuovo istituto proseguito dal più insigne dei discepoli dell&#039;Acqua­<lb></lb>pendente, Giulio Casserio, il quale, nel descrivere gli organi dei sensi, pa­<lb></lb>ragona quelli dell&#039;uomo con gli altri dei varii bruti, e le differenze notate <lb></lb>parvero alla Scienza una nuova rivelazione. </s>

<s>Marc&#039;Aurelio Severino si mise <lb></lb>poi per quella nuova via aperta con tanto ardore che forse, come giudica­<lb></lb>rono aìcuni, esagerò nel designarne la riuscita, e nell&#039;esaltare sopra l&#039;Ana­<lb></lb>tomia umana la nuova Anatomia comparata, ma per lui intanto quella Zoo­<lb></lb>nomia, di che l&#039;Acquapendente e il Casserio avevano dati i primi esempii, <lb></lb>prese abito proprio e distinto di scienza; abito a cui la <emph type="italics"></emph>Zootomia,<emph.end type="italics"></emph.end> nella <lb></lb>quale ei fece e descrisse tante e sì notabili scoperte, porgeva solida se non <lb></lb>elegante corporatura. </s></p><p type="main">

<s>Conferì a dare eleganza a cotesta nuova scienza zootomica Francesco <lb></lb>Redi, il quale, dopo la prima metà del secolo XVII, in mezzo a tanti Ana­<lb></lb>tomici non in altro esercitanti il coltello che ne&#039;cadaveri umani, osservava <lb></lb>la differente struttura delle viscere ne&#039;varii animali. </s>

<s>Fa di ciò testimonianza <lb></lb>lo stesso Redi in una lettera da sè scritta a Jacopo del Lapo, a nome di <lb></lb>Alessandro Fregosi. </s>

<s>“ Fa di mestiere che io le dica che, nell&#039;essere am-<pb xlink:href="020/01/1483.jpg" pagenum="358"></pb>messo dal signor Redi, mi è paruto di entrare in un mondo nuovo, con­<lb></lb>ciossiachè nelle cose naturali ed anatomiche io non mi era esercitato mai, <lb></lb>se non in una diligente ricerca fatta ne&#039;cadaveri umani, ... e il signor Redi <lb></lb>solamente osserva per ora la differente struttura delle viscere degli uccelli e <lb></lb>de&#039;quadrupedi, e ne ha messo insieme grandissimi fasci di scritture ” (Opere, <lb></lb>T. IV, Napoli 1741, pag. </s>

<s>80). </s></p><p type="main">

<s>Comprendesi con facilità quai vantaggi fosse per recare, nel più sa­<lb></lb>piente ordinamento degli animali, il conoscere le differenze che passano <lb></lb>fra&#039;loro organi, per cui l&#039;Acquapendente, il Casserio, il Severino e il Redi <lb></lb>ci si presentano fra&#039;più benemeriti Autori della Storia naturale. </s>

<s>Ma troppo <lb></lb>erano ancora scarsi al profitto i soggetti comparati, nel più esteso studio <lb></lb>de&#039;quali aveva solo speranza la stessa Storia di ritrovar più efficace impulso <lb></lb>ai desiderati progressi. </s></p><p type="main">

<s>L&#039;Harvey, ripigliando la trattazione sopra la generazion degli animali <lb></lb>rimasta in Aristotile e nell&#039;Acquapendente interrotta, porgeva in sintesi quello <lb></lb>studio, intorno al quale poi si ripartiron l&#039;opera tanti e sì valorosi ingegni. </s>

<s><lb></lb>Fra&#039;Nostri, principe di una Scuola fecondissima di scoperte naturali ci si <lb></lb>presenta il Borelli, che primo ridusse alle leggi della Meccanica il passo <lb></lb>de&#039;quadrupedi, il volo degli uccelli, il nuoto de&#039;pesci, e a cui succede il <lb></lb>Malpighi, dal quale propriamente comincia la Fisiologia degl&#039;insetti. </s>

<s>E giac­<lb></lb>chè si può anche lo Stenone annoverare fra&#039;Nostri, a lui dobbiamo la de­<lb></lb>scrizione della struttura muscolare de&#039;pesci, e del loro organo della vista, <lb></lb>che tanto valse a illustrare il medesimo preziosissimo organo nell&#039;uomo. </s></p><p type="main">

<s>L&#039;efficacia della Scuola del Borelli in promovere la Storia naturale si <lb></lb>fece anche sentire nell&#039;Accademia del Cimento, dove si sperimentò nel vuoto <lb></lb>torricelliano la vita di varii animali più efficacemente di quel che non avesse <lb></lb>fatto, nel vuoto della sua macchina pneumatica, il Boyle. </s>

<s>L&#039;esperienze sulla <lb></lb>fosforescenza delle lucciole, che si fecero nel quarto periodo di essa Acca­<lb></lb>demia dietro gl&#039;impulsi avutine dallo stesso Boyle, conferirono alla soluzione <lb></lb>di uno de&#039;più curiosi problemi concernenti la fosforescenza degli animali. </s></p><p type="main">

<s>Il Segretario Lorenzo Magalotti, quando cominciò a dilettarsi dei viaggi, <lb></lb>imitando l&#039;esempio de&#039;più antichi Viaggiatori italiani, non trascurò, per ser­<lb></lb>vire alla Storia, le osservazioni delle cose naturali, ch&#039;ei descriveva elegan­<lb></lb>temente in varie lettere indirizzate a&#039;suoi amici di Firenze. </s>

<s>In una, data da <lb></lb>Amsterdam li 2 Dicembre 1667, terminava quelle sue descrizioni con que­<lb></lb>ste parole: “ Ho veduto uccelli dell&#039;India maravigliosi, e uno non più ca­<lb></lb>pitato in queste parti. </s>

<s>È venuto con un vascello, che vien d&#039;America, il <lb></lb>quale, trovandosi vicino alle Barbade, vedde venir questa bestia per l&#039;aria, <lb></lb>e tutta affannata posarsi sulla gabbia, onde, fatto forza di prenderla, si levò, <lb></lb>e non potendo reggersi cascò in mare, dove fu subito presa con le <emph type="italics"></emph>chaluppe.<emph.end type="italics"></emph.end><lb></lb>Il nome suo, come potete credere, non si sa, perchè non l&#039;ha saputo dire&#039; <lb></lb>non parlando ancora il fiammingo. </s>

<s>Si crede però che anche al suo paese <lb></lb>sia in stima, raffigurandosi per un uccello che si vede sulle pitture più <lb></lb>nobili, che vengono di quelle parti. </s>

<s>Non ve lo descrivo, perchè lo fo ri-<pb xlink:href="020/01/1484.jpg" pagenum="359"></pb>trarre in un quadro con diversi altri uccellacci inauditi ” (MSS. Cim., <lb></lb>T. XXXIII, c. </s>

<s>86). </s></p><p type="main">

<s>Apparteneva a quella stessa Accademia Francesco Redi, a cui va di <lb></lb>tante cose debitrice la storia naturale, e specialmente dell&#039;essersi liberata <lb></lb>dall&#039;errore delle generazioni equivoche, che per l&#039;esperienze di Antonio Valli­<lb></lb>snieri ebbe l&#039;ultima e più compiuta disfatta. </s>

<s>Il Redi, da cui non vogliono <lb></lb>separarsi Giuseppe Zambeccari, Giovan Batista Caldesi e Diacinto Cestoni, <lb></lb>insieme col Vallisnieri, pellegrinando per l&#039;immenso campo delle cose na­<lb></lb>turali, si soffermarono qua e là, dove il terreno o era sodo o era guasto, e <lb></lb>lo bonificarono e lo ridussero alla più nuova e più fiorente cultura. </s></p><p type="main">

<s>Quel Francesco Fontana, ch&#039;ebbe tanta parte nell&#039;invenzione del Mi­<lb></lb>croscopio, fu altresì de&#039;primi ad applicarlo alle osservazioni naturali, ma <lb></lb>Roberto Hook ne fece uso più esteso e rivelò nella sua <emph type="italics"></emph>Micrografia<emph.end type="italics"></emph.end> nuovi <lb></lb>popoli di viventi. </s>

<s>Antonio Leeuwenhoeck ridusse le osservazioni microsco­<lb></lb>piche ad arte, e così semplice artista com&#039;era, penetrando coll&#039;acume del­<lb></lb>l&#039;occhio armato per i più riposti seni della Natura, meritò d&#039;esser chiamato <lb></lb>a sedere in luogo distinto al convito della Scienza. </s></p><p type="main">

<s>Riducendoci ora tutta in uno sguardo l&#039;opera di tanti che, comparando <lb></lb>gli organi di una medesima funzione tra varii animali, descrivendo le parti, <lb></lb>gli abiti e i costumi proprii di tante varie specie, e ne&#039;viaggi pel grande e <lb></lb>per il piccolo mondo scoprendone delle nuove, facilitarono alla mente il modo <lb></lb>di porre ordine negli animali, non più secondo l&#039;arbitrio, ma secondo le <lb></lb>leggi della loro creazione; si direbbe che nel secolo XVIII si fosse la scienza <lb></lb>ridotta in grado di adempire i voti e di sodisfare ai filosofici desiderii del <lb></lb>toparca di Verulamio. </s></p><p type="main">

<s>In quel secolo infatti si diffuse il sistema proposto dal Linneo, il quale <lb></lb>ordinava tutti gli animali in sei classi, quadrupedi, uccelli, amfibii, pesci, <lb></lb>insetti e vermi. </s>

<s>Il Buffon giudicò questo ordinamento affatto arbitrario, e lo <lb></lb>riconobbe difettoso, per non trovarvi luogo molti animali: i serpenti per <lb></lb>esempio, le conchiglie e i crostacei. </s>

<s>Difettosa pure e arbitraria notò che riu­<lb></lb>sciva la division linneiana de&#039;quadrupedi, mettendovisi in società con l&#039;uomo <lb></lb>e con la scimmia la lucertola squammosa. </s></p><p type="main">

<s>Questo strano accozzamento di esseri così disparati avrebbe dovuto far <lb></lb>sovvenire alla mente del Buffon Aristotile, che associava all&#039;uomo le gru e <lb></lb>le formiche, e lo avrebbe dovuto far accorto che il sistema dello Stagirita <lb></lb>non era punto meno arbitrario di quello immaginato dal Naturalista svedese. </s>

<s><lb></lb>Eppure il valentuomo non se ne avvede, e Aristotile e Teofrasto e Plinio <lb></lb>sembrano a lui <emph type="italics"></emph>i primi e massimi Naturalisti,<emph.end type="italics"></emph.end> de&#039;quali perciò, sicuro di <lb></lb>non errare, segue gli esempii. </s>

<s>Tutto imbevuto del razionalismo aristotelico <lb></lb>vuol che s&#039;ordini la Natura secondo le relazioni, ch&#039;ella ha con l&#039;uomo, <lb></lb>da che segue, egli dice, nel suo primo <emph type="italics"></emph>Discorso intorno alla storia natu­<lb></lb>rale,<emph.end type="italics"></emph.end> che troveranno il primo luogo quegli oggetti, i quali s&#039;appresentano <lb></lb>all&#039;uomo stesso come più dilettevoli, o come più necessarii. </s>

<s>“ Per esempio <lb></lb>egli darà nell&#039;ordine degli animali la preferenza al cavallo, al cane, al bue, ecc. <pb xlink:href="020/01/1485.jpg" pagenum="360"></pb>e sarà sempre migliore conoscitore di quelli, che gli saranno più familiari. </s>

<s><lb></lb>In appresso si volgerà a quelli che, sebbene non sieno familiari, non la­<lb></lb>sciano però di abitare gli stessi luoghi, gli stessi climi, come i cervi, i lepri <lb></lb>e gli animali tutti selvatici e solo, dopo di avere acquistate tutte queste co­<lb></lb>gnizioni, sarà spinto dalla curiosità a ricercare che cosa siano essi gli ani­<lb></lb>mali de&#039;climi stranieri, come gli elefanti, i dromedarii, ecc Il simile sarà <lb></lb>de&#039;pesci, degli uccelli, degl&#039;insetti, delle conchiglie, delle piante, de&#039;mine­<lb></lb>rali e di tutte le altre produzioni della Natura. </s>

<s>Le studierà a proporzione <lb></lb>dell&#039;utile che spererà di ricavarne, le osserverà a misura che gli si faranno <lb></lb>più familiari, e le ordinerà nella sua mente secondo l&#039;ordine delle sue co­<lb></lb>gnizioni, poichè tale si è appunto l&#039;ordine, secondo cui le ha acquistate, e <lb></lb>secondo cui gl&#039;importa di osservarle. </s>

<s>Un ordine siffatto, che è fra tutti il <lb></lb>più naturale, è quello che noi creduto abbiamo di dover seguire ” (Opere, <lb></lb>Vol. </s>

<s>I, Venezia 1820, pag. </s>

<s>114). </s></p><p type="main">

<s>Che sembrasse questo metodo naturale a chi faceva con Aristotile l&#039;uomo <lb></lb>centro, e la ragione di lui legislatrice della Natura, non fa maraviglia. </s>

<s>Ma <lb></lb>chi tutt&#039;altrimenti credeva che la Natura stessa si governi con leggi pro­<lb></lb>prie, ebbe facilmente a persuadersi che gli ordinamenti di lei si dovevano <lb></lb>trovare in quelle stesse leggi, indipendenti dall&#039;arbitrio degli uomini. </s>

<s>Di li <lb></lb>solo poteva aversi speranza che que&#039;tanto desiderati ordinamenti riuscissero <lb></lb>veramente naturali, e fu Giorgio Cuvièr il primo che, escluse le note estrin­<lb></lb>seche e gli arbitrii, si studiò di costituire le varie dignità secondo gli organi <lb></lb>e le funzioni. </s>

<s>Così parvero i voti di Francesco Bacone adempiuti, e che la <lb></lb>Storia naturale avesse trovato il suo più convenevole assetto, quando usci­<lb></lb>rono gli evoluzionisti a dire essere inutile cercar distinzioni, non volute <lb></lb>dalla Natura. </s>

<s>Quel che credevasi la stabile gradinata di un edifizio è invece <lb></lb>l&#039;increspamento di un&#039;onda, che va, e che, andando, sempre più ingrossa. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi ripensa che le difficoltà, incontrate dai Naturalisti in ordinare gli <lb></lb>animali, dipendevano principalmente dalla difficoltà di conoscere e di com­<lb></lb>parare gli organi e le funzioni, intenderà quanto si dovessero quelle diffi­<lb></lb>coltà presentar maggiori in bene ordinare le piante, l&#039;anatomia e la fisio­<lb></lb>logia delle quali fu coltivata tanto più tardi. </s>

<s>Dall&#039;altra parte il vitto, le <lb></lb>medicine e le delizie stesse, che si ricavano dagli alberi e dall&#039;erbe, acce­<lb></lb>sero sempre negli uomini il desiderio di riconoscere i vegetabili, non men <lb></lb>vivamente di quel che avessero fatto gli animali, e per riconoscerli, in tanta <lb></lb>varietà e in tanta profusione, si fece molto per tempo sentire ai Botanici il <lb></lb>bisogno di un sistema, che, secondo l&#039;arguta espression del Linneo, è il <lb></lb>filo di Arianna “ sine quo chaos est res herbaria ” (Philosophia botanica, <lb></lb>Viennae Austriae 1763, pag. </s>

<s>102). </s></p><pb xlink:href="020/01/1486.jpg" pagenum="361"></pb><p type="main">

<s>Non fa perciò maraviglia se, a studiarsi di sodisfare in qualche modo <lb></lb>a questo bisogno, fosse primo quell&#039;antico Autore, di cui i libri due <emph type="italics"></emph>De <lb></lb>vegetabilibus<emph.end type="italics"></emph.end> si divulgarono sotto il nome, e si raccolsero perciò fra le altre <lb></lb>opere di Aristotile. </s>

<s>Il capitolo III del I libro è riserbato espressamente a <lb></lb>trattare <emph type="italics"></emph>De plantarum differentiis.<emph.end type="italics"></emph.end> Si possono queste differenze, secondo <lb></lb>l&#039;Autore, ricavare da moltissime parti, nell&#039;enumerar minutamente le quali <lb></lb>è notabile che comprendesse tutti quei sistemi scelti e proposti poi dai Bo­<lb></lb>tanici infino al Linneo, e che si qualificarono col nome di <emph type="italics"></emph>artificiali.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Le prime e più ovvie differenze ci fanno distinguere le piante in al­<lb></lb>beri, in frutici, in suffrutici e in erbe. </s>

<s>“ Plantarum aliae arbores sunt, aliae <lb></lb>inter arbores et herbas mediae, et frutices dicuntur, aliae herbae sunt, aliae <lb></lb>olera ” (Tomus VI operum Arist., Venetiis 1560, fol. </s>

<s>76). I varii generi, <lb></lb>appartenenti a queste tre grandi classi, si possono distinguere dalle foglie, <lb></lb>le quali per esempio, rispetto agli alberi, “ quarundam aspera sunt, qua­<lb></lb>rumdam levia. </s>

<s>Et aliorum folia sunt parva, aliorum scissa, ut vitis et ficuum. </s>

<s><lb></lb>Aliarum multas scissuras habent, ut pinus folia ” (ibid., fol. </s>

<s>77). Si possono <lb></lb>altresì distinguere dai frutti. </s>

<s>“ Succorum quoque, qui in fructibus sunt, alii <lb></lb>potabiles sunt, velut uvarum succus .... et aliorum unctuosi sunt, ut oli­<lb></lb>vae succus.... Aliorum item dulces, ut dactylorum,.... alii amari ut absin­<lb></lb>thii. </s>

<s>Quidam fructuum compositi ex carne sunt et osse, ut pruna, alii e <lb></lb>carne et grano ut cucumeros, quidam ex humore et granis, ut melagranata. </s>

<s><lb></lb>Et alii corticem foris habent, carnem intus, ut poma, pyra; quidam carnem <lb></lb>foris, os intus. </s>

<s>Sunt quoque alii, quibus statim semen fit cum tegumento <lb></lb>quo operiuntur, ut dactyli et amygdala; quidam non tales sunt..... Item <lb></lb>fructuum alii in siliquis sunt, velut fabae grana, alii in tegumentis et veluti <lb></lb>telis, ut triticum visitur, et caeteri; alii in carne, ut dactylorum fructus; <lb></lb>quidam velut in casis multis et tela ac testis, ut sunt nuces ” (ibid.). </s></p><p type="main">

<s>Le molte altre note distintive son prolissamente enumerate, e benchè <lb></lb>tutte sieno accidentali, è nonostante cosa meritevole di osservazione che per <lb></lb>certe piante, per le palme per esempio e per i fichi, assegni come nota da <lb></lb>distinguerle dalle altre i sessi. </s>

<s>“ In palmis quoque si folia vel foliorum pul­<lb></lb>vis, vel palmae masculinae cortex foliis foemellae palmae apponantur, ut <lb></lb>cohaerescant, cito maturescent eius fructus, casusque eorum prohibebitur.... <lb></lb>Alicubi vero ex aliquo horum, vel ex omnibus istud contingit. </s>

<s>Quod si forte <lb></lb>ex odore masculi abduxerit quippiam ventus ad foemellam, sic quoque ma­<lb></lb>turescent ipsius fructus, quemadmodum cum folia masculi ex illa fuerit <lb></lb>aspersa. </s>

<s>Ficus quoque sylvestres, per terram expansae, ficubus hortensibus <lb></lb>conferunt. </s>

<s>Eodem modo balaustia oleis conducunt, quando una plantan­<lb></lb>tur ” (ibid.). </s></p><p type="main">

<s>Si diceva che in questa prolissa enumerazione delle note da differen­<lb></lb>ziare le piante si comprendevano i varii sistemi, i quali dovevano in somma <lb></lb>consistere nella scelta di quelle, fra tali innumerevoli note, che fossero ri­<lb></lb>conosciute per più essenziali. </s>

<s>Ma qui stava la difficoltà, non alleviata punto <lb></lb>dall&#039;Autore aristotelico, il quale anzi faceva come chi, per saziar la sete a <pb xlink:href="020/01/1487.jpg" pagenum="362"></pb>uno, lo affogasse nell&#039;acqua. </s>

<s>Di che sentito il pericolo, i più si ritennero <lb></lb>sulla riva, contentandosi di quella massima e principal distinzione delle piante <lb></lb>in alberi, in frutici e in erbe, che appariva più manifesta. </s>

<s>Dioscoride ordinò <lb></lb>i generi appartenenti a queste grandi classi, secondo le loro virtù medici­<lb></lb>nali, e Teofrasto gli denominò dai loro luoghi nativi. </s></p><p type="main">

<s>Le difficoltà insomma di cogliere quelle note, che riducessero le piante <lb></lb>alle loro più vere somiglianze, e alle loro più sostanziali differenze, e dall&#039;al­<lb></lb>tra parte il non sentirne così grande il bisogno, per lo scarso numero delle <lb></lb>stesse piante, ch&#039;erano a que&#039;tempi meglio conosciute; fecero sì che gli <lb></lb>Antichi non s&#039;attentassero di proporre o di seguitare in Botanica nessun si­<lb></lb>stema, di cui i primi tentativi si videro far nel secolo XVI per Currado <lb></lb>Gesner. </s>

<s>Sembrò a lui, attentamente osservando e comparando, che le note <lb></lb>desiderate, e con tanta sollecitudine ricercate invano dagli studiosi di Ari­<lb></lb>stotile, non consistessero nelle foglie o in altro, ma ne&#039;fiori e ne&#039;frutti. </s>

<s><lb></lb>Preso questo per il filo di Arianna, riuscì a scoprire che alcune piante cre­<lb></lb>dute differenti, come per esempio le Stafisagrie e gli Aconiti, appartenevano <lb></lb>alla medesima famiglia, mentre altre invece, come la Melissa e l&#039;Ortica, che <lb></lb>sembrano sì vicine, esaminato bene il seme, si trova non aver fra loro nes­<lb></lb>suna parentela. </s>

<s>Nell&#039;Epistola a Teodoro Zuingger, dop&#039;avere stabilito per <lb></lb>fondamento alla distinzion delle piante il fiore e il frutto, “ ex his enim, <lb></lb>soggiunge, potius quam foliis, stirpium naturae et cognationes apparent. </s>

<s>His <lb></lb>notis Staphisagriam et Consolidam regalem, vulgo dictam Aconito, <foreign lang="grc">συμφυλους <lb></lb>εινχι βοτὰνας</foreign> facile deprehendi ” (Epistolae, Basileae 159, pag. </s>

<s>113). E ad <lb></lb>Adolfo Occone, medico di Augusta, scriveva in un&#039;altra Epistola: “ Melissa <lb></lb>costantinopolitana ad Lamium vel Urticam mortuam quodammodo videtur <lb></lb>accedere, seminis tamen, <emph type="italics"></emph>unde ego cognationes stirpium iudicare soleo,<emph.end type="italics"></emph.end><lb></lb>figura differt ” (ibid., pag. </s>

<s>65). </s></p><p type="main">

<s>Il fondamento a queste note però lo trovava il Gesner nella semplice <lb></lb>osservazione, ma il Cesalpino andò a ricercarlo più addentro nella fisiologia <lb></lb>delle piante, per cui, piuttosto che al Naturalista di Zurigo, si dee al Nostro <lb></lb>il merito di avere speculato, nel suo trattato <emph type="italics"></emph>De plantis,<emph.end type="italics"></emph.end> il primo sistema <lb></lb>botanico razionale. </s>

<s>“ Cum igitur omnis substantiae ratio, egli scrive, a fine <lb></lb>petatur (propter illum enim substantiae quoque sunt quae illius gratia haben­<lb></lb>tur) videndum est in plantis quae similitudo et dissimilitudo in iis fuerit, <lb></lb>quae primi animae operis gratia data sunt, deinde quae secundi, et si quae <lb></lb>alia sequantur deinceps ” (De plantis, Florentiae 1583, pag. </s>

<s>27). </s></p><p type="main">

<s>Dalle varie operazioni dunque, o manifestazioni dell&#039;anima vegetativa, <lb></lb>intende il Cesalpino di desumere le note essenziali, da servirgli per ordi­<lb></lb>nare le piante. </s>

<s>Di queste manifestazioni, soggiunge, alcune sono primarie, <lb></lb>altre secondarie. </s>

<s>Primarie sarebbero quelle, che appartengono alle funzioni <lb></lb>della nutrizione, secondarie le altre, che appartengono alle funzioni della ri­<lb></lb>produzione. </s>

<s>Le primarie perciò daranno la prima e più grande distribuzione <lb></lb>delle piante in alberi, in frutici, in suffrutici e in erbe; e le secondarie ser­<lb></lb>viranno per distinguere i varii generi in quelle stesse prime classi compresi. </s></p><pb xlink:href="020/01/1488.jpg" pagenum="363"></pb><p type="main">

<s>E perchè è questa la distinzion più importante, dai frutti, dice il Ce­<lb></lb>salpino, si desumeranno le note. </s>

<s>“ Secundum autem vegetativi opus est <lb></lb>generare sibi simile, quod et perfectione prius est, cuius gratia dati sunt <lb></lb>fructus et partes ad fructificationem facientes. </s>

<s>Cum igitur id non omnibus <lb></lb>insit, sed perfectioribus, pro fructificationis similitudine et dissimilitudine, <lb></lb>posteriora genera, tum in genere arboreo, tum in humiliori materia, consti­<lb></lb>tuenda erunt..... Et merito ex modo fructificandi multa emersunt planta­<lb></lb>rum genera. </s>

<s>In nullis enim aliis partibus tantam organorum multitudinem <lb></lb>et distinctionem Natura molita est, quanta in fructibus condendis spectatis ” <lb></lb>(ibid., pag. </s>

<s>27, 28). </s></p><p type="main">

<s>Al Cesalpino successe, in sul finir del secolo XVI, un altro insigne <lb></lb>cultore della Botanica in Fabio Colonna. </s>

<s>Giovane di XXV anni, pubblicò <lb></lb>nel 1592 il suo primo libro, che intitolava <foreign lang="grc">ΦΥΤΟΒΑΣΑΝΟΣ</foreign>, perchè vi si met­<lb></lb>tevano le varie piante a tortura di rivelare il vero esser loro. </s>

<s>Gli fu il fine <lb></lb>prìncipale dell&#039;opera suggerito dal bisogno di dichiarare il testo di Diosco­<lb></lb>ride, dalla lettura del quale nascevano tante oscurità e tante incertezze, per <lb></lb>esser dall&#039;Autore una medesima pianta chiamata con più nomi, che pote­<lb></lb>vano ridursi a diversi significati. </s>

<s>Il principal merito perciò del <emph type="italics"></emph>Fitobasano<emph.end type="italics"></emph.end><lb></lb>consiste nell&#039;avere introdotta nella scienza botanica la proprietà del linguag­<lb></lb>gio; merito che si apprezzerà da coloro, i quali sanno quanto in una nu­<lb></lb>merosa società d&#039;individui sia necessario, per riconoscerli, evitare le incer­<lb></lb>tezze e le confusioni dei nomi. </s></p><p type="main">

<s>Del resto, non par che il giovane Botanico avesse ancora pensato a <lb></lb>comporre un sistema suo proprio, o a seguire gli esempii del Gesnero e del <lb></lb>Cesalpino, perchè, occorrendogli di assegnare il luogo proprio a una pianta <lb></lb>di quelle da sè nuovamente scoperte, la riduce fra le varietà delle Trache­<lb></lb>lie, non guardando alla forma del fiore, ma alla polpa delle foglie e al sa­<lb></lb>pore. </s>

<s>“ Non e florum forma, natali loco, annique tantum tempore quo floret, <lb></lb>sed et a lactis copia, substantia foliorum, et sapore totius plantae, Trache­<lb></lb>liorum varietati (sic a recentioribus, quia tracheae locisque vicinis medea­<lb></lb>tur, appellatarum) reddenda est haec nova planta, in D. M. </s>

<s>Virginis Monte, <lb></lb>sic vulgo dicto, exoriens ” (<foreign lang="grc">Φυτοβ<gap></gap>σανος</foreign>, cui accessit adnotat. </s>

<s>auctore Iano <lb></lb>Planco, Florentiae 1744, pag. </s>

<s>118). </s></p><p type="main">

<s>Pubblicato il Fitobasano, e fatto Fabio da Marzio Colonna vice-principe <lb></lb>di Zagarola, si dette a perlustrare i monti della Puglia, dove fece diligente <lb></lb>raccolta di molte piante o meno note o affatto sconosciute, ch&#039;egli poi de­<lb></lb>scrisse in un libro stampato col seguente titolo, in Roma, nel 1606, da Gu­<lb></lb>glielmo Facciotti. </s>

<s>“ Fabii Columnae Lyncei minus cognitarum rariorumque <lb></lb>nostro coelo orientium stirpium <foreign lang="grc">ΕΚΦΠΑΣΙ<gap></gap></foreign>, qua non paucae ab antiquiori­<lb></lb>bus Theophrasto, Dioscoride, Plinio, Galeno aliisque descriptae, praeter illas <lb></lb>etiam in <foreign lang="grc">ΦΥΤΟΒΑΣΑΝΩ</foreign> editas, disquiruntur ac declarantur. </s>

<s>” Ma nemmen <lb></lb>qui il Colonna segue una ragion certa, in ordinar le piante antiche e le <lb></lb>nuove ch&#039;egli descrive. </s></p><p type="main">

<s>Proseguendo però con più ardore che mai nell&#039;intrapreso studio, aveva <pb xlink:href="020/01/1489.jpg" pagenum="364"></pb>nel 1616 aggiunta un&#039;altra parte all&#039;Ecfrasi, la quale fu, insiem colla prima, <lb></lb>pubblicata in quel medesimo anno in Roma coi tipi di Giacomo Mascardi. <lb></lb></s>

<s>È giusto in questo libro, che s&#039;intitola: “ Fabii Columnae Lyncei, minus <lb></lb>cognitarum stirpium <emph type="italics"></emph>Pars altera,<emph.end type="italics"></emph.end> in qua non tam novae plures plantae <lb></lb>eaeque rariores a nemine hactenus aut animadversae aut descriptae nunc <lb></lb>primum proponuntur, quam nonnullae aliae apud antiquos dubiae atque <lb></lb>obscurae dilucidantur; ” è in questo libro diciamo che l&#039;Autore stabilisce, <lb></lb>in conferire i generi, per note specifiche, non quelle desunte dalle foglie, <lb></lb>ma dal seme e dai fiori. </s>

<s>“ Foliorum effigiem in conferendis generibus parvi <lb></lb>fecimus. </s>

<s>Non enim ex foliis, sed ex flore seminisque conceptaculo, et ipso <lb></lb>potius semine plantarum, affinitatem diudicamus, respondente praesertim <lb></lb>sapore in reliqua plantae parte ” (pag. </s>

<s>62). </s></p><p type="main">

<s>Fors&#039;ebbero in questa deliberazione di lasciar le foglie, per seguir le <lb></lb>note differenziali offerte dai fiori e dai semi, non poca efficacia sul Colonna <lb></lb>gli esempii del Gesner e del Cesalpino, ma perchè sempre i fatti hanno più <lb></lb>virtù delle parole, crediamo che la diversità delle idee, espresse nel Fito­<lb></lb>basano e nell&#039;Ecfrasi seconda, dipendesse dall&#039;uso, che incominciò l&#039;Autor <lb></lb>di questa a fare allora del Microscopio. </s>

<s>Egli, sì amante de&#039;nomi greci, fu <lb></lb>che suggerì un tal nome a Federigo Cesi, principe di que&#039;Lincei, fra&#039;quali <lb></lb>ebbe il nuovo strumento la prima e più feconda applicazione alle scienze <lb></lb>naturali. </s>

<s>Il Colonna dunque, mettendosi ad osservar diligentemente col Mi­<lb></lb>croscopio la composizione de&#039;fiori e de&#039;semi, ebbe a persuadersi esser vero <lb></lb>il detto del Cesalpino, che cioè non potrebbe, per conferire i generi, ritro­<lb></lb>varsi in altre parti della pianta tanta moltitudine di organi e tante di­<lb></lb>stinzioni. </s></p><p type="main">

<s>Fu un tal principìo sistematico applicato dall&#039;Autore, non solo in or­<lb></lb>dinar le piante descritte nell&#039;Ecfrasi II, ma in quelle erudite illustrazioni <lb></lb>altresì, ch&#039;egli fece alla Storia di Francesco Hernandez, a cui aveva il re <lb></lb>di Spagna ordinato che descrivesse tutto ciò, che di applicabile alla fisica e <lb></lb>alla medicina si trovasse nel Regno messicano. </s>

<s>La morte impedì all&#039;Her­<lb></lb>nandez di dar forma ai numerosi e pregevolissimi materiali raccolti, di che <lb></lb>fu la cura dallo stesso Re commessa a Nard&#039;Antonio Recchi, il quale di­<lb></lb>stese le storie messicane in X libri. </s>

<s>Morto il Recchi, il manoscritto venne <lb></lb>alle mani di un nipote di lui da parte di sorella, Marc&#039;Antonio Petilio, da <lb></lb>cui l&#039;ebbe il principe Cesi. </s>

<s>Esaminata l&#039;Opera, la trovò degna che v&#039;eser­<lb></lb>citassero l&#039;ingegno attorno i suoi Lincei, fra&#039;quali scelse Giovanni Terrenzio <lb></lb>di Cosenza, e Giovanni Faber bambergese e medico del Papa, perchè illu­<lb></lb>strassero particolarmente la Zoologia, e dette a Fabio Colonna ordine che <lb></lb>illustrasse la Botanica, ciò ch&#039;egli fece in quelle Note, nelle quali il sistema <lb></lb>d&#039;ordinar le piante, secondo la distinzion del fiore e del frutto, trova larga <lb></lb>e sapiente applicazione. </s></p><p type="main">

<s>Ma queste Note, già finite di scrivere nel 1628, videro la prima luce <lb></lb>insiem col testo nell&#039;anno 1648, e nel 1651 con aggiunte, per opera di Cas­<lb></lb>siano del Pozzo e di Francesco Stelluti, i due soli Lincei rimasti in quel <pb xlink:href="020/01/1490.jpg" pagenum="365"></pb>tempo superstiti, e dall&#039;altra parte l&#039;Ecfrasi e gli altri libri furono, vivente <lb></lb>l&#039;Autore, così poco diffusi, che non fa maraviglia se, tra per l&#039;una e per <lb></lb>l&#039;altra ragione, non avendo avuto, nella prima metà del secolo XVI, il Co­<lb></lb>lonna lettori, non ebbe delle sue dottrine perciò nè seguaci. </s></p><p type="main">

<s>Così essendo, non rimaneva ai Botanici, amatori dei progressi della <lb></lb>scienza, altro che la scuola del Cesalpino, alla quale si ascrissero molti, e <lb></lb>fra questi Paolo Hermann, che ordinò la sua <emph type="italics"></emph>Flora batavica<emph.end type="italics"></emph.end> sull&#039;esame dei <lb></lb>soli frutti, e Giovanni Ray, che nel cap. </s>

<s>XX del I libro <emph type="italics"></emph>De historia plan­<lb></lb>tarum,<emph.end type="italics"></emph.end> trattando delle loro specifiche differenze, scriveva queste parole: “ Ut <lb></lb>plantarum numerus iniri possit, et earumdem divisio recte instititui, oportet <lb></lb>ut notas aliquas, seu indicia specificae distintionis, investigemus. </s>

<s>Nobis au­<lb></lb>tem diu multumque indagantibus nulla certior occurrit, quam distincta pro­<lb></lb>pagatio ex semine..... Quae plantae ex alterius semine non proveniunt, nec <lb></lb>unquam semine satae transmutantur in se invicem, eae demum specie di­<lb></lb>stinctae sunt ” (Londini 1686, pag. </s>

<s>40). </s></p><p type="main">

<s>Ma queste note di specifica distinzione, che il Ray teneva per così certe, <lb></lb>parvero a Pietro Magnol per lo meno insufficienti, nè che valesse a com­<lb></lb>pierle l&#039;aggiungere all&#039;esame de&#039;semi quello de&#039;fiori. </s>

<s>Gli si veniva a di­<lb></lb>mostrare una tale insufficienza dai fatti, osservando, per esempio, che, fra <lb></lb>trifogli congeneri, altri erano monopetali, e altri invece polipetali, e che tra <lb></lb>le stesse vere e proprie Linarie n&#039;erano alcune col seme piano, altre col <lb></lb>seme rotondo. </s>

<s>Perciò pensava il Magnol che le note specifiche non si do­<lb></lb>vessero ridurre a una sola o a due, ma a più, raccolte da varie parti e da <lb></lb>qualità anche accidentali, purchè accennino a quelle somiglianze fra le varie <lb></lb>piante, che hanno fra sè i membri di una stessa famiglia. </s></p><p type="main">

<s>Esprimeva queste idee nella Prefazione al Catalogo delle piante del­<lb></lb>l&#039;Orto regio di Mompellieri, nella qual prefazione, dop&#039;aver detto che dal Ca­<lb></lb>talogo stesso, ch&#039;è per dare alla luce, resulterà la smisurata varietà delle <lb></lb>piante raccolte insieme e disposte nel giardino reale; così soggiunge: “ At <lb></lb>vero quandoquidem, dum tractatur de plantis, cavendum est ne infinito pene <lb></lb>earum numero memoria obruatur, et suboriantur errores ex nominum di­<lb></lb>versitate et mutatione, id unum mihi cordi fuit, non modo ut ad certas <lb></lb>quasi familias et classes revocarentur, sed etiam ut ad pauciora, quantum <lb></lb>fieri potest, genera reducerentur. </s>

<s>Quantum inquam fieri potest, nec enim <lb></lb>puto certos omnino dari posse plantarum caracteres, quibus varia earum <lb></lb>genera perfecte, certo et semper, a se invicem distinguerentur ” (Hortus <lb></lb>regius monspelliensis, Monspelii 1697, pag. </s>

<s>VII). </s></p><p type="main">

<s>Questo è ciò che fu più volte tentato da peritissimi Botanici, ma an­<lb></lb>cora, prosegue a dire il Magnol, non par che si sia da-nessuno conseguito <lb></lb>l&#039;intento. </s>

<s>“ Nec mirum, nam desumi non potest huiusmodi caracter, nisi <lb></lb>ex floribus, vel ex capsulis, vel ex seminibus. </s>

<s>Atqui ex iis desumi semper <lb></lb>non posse et experientia certo constat, et uno aut altero exemplo sic de­<lb></lb>monstro: Quippe, si trifoliorum aut limoniorum flores spectes, habent alii <lb></lb>monopetalon alii polypetalon: congeneres tamen esse species quis neget? <pb xlink:href="020/01/1491.jpg" pagenum="366"></pb>Inter veras et genuinas Linarias recensere necesse est tum eas quae semen <lb></lb>planum, tum eas quae rotundum habent, et, sive lotus habeat siliquas cel­<lb></lb>lulis distinctas, sive non habeat, germanae sunt loti species. </s>

<s>Ex quibus luce <lb></lb>clarius conficitur neque ex floribus, neque ex seminibus, neque ex capsulis <lb></lb>semper argui posse generum diversitatem ” (ibid., pag. </s>

<s>VIII). </s></p><p type="main">

<s>A coloro però i quali, per essere alcuni tentativi riusciti infelici, non <lb></lb>avevano perduta la speranza di cogliere le vere note specifiche delle piante, <lb></lb>parve questa conclusione del Magnol dedotta da principii non veri, o almeno <lb></lb>non troppo precisi, imperocchè, se il Cesalpino e il Colonna avevano pro­<lb></lb>posto l&#039;esame de&#039;semi, non intendevano che si dovesse il Botanico fermare <lb></lb>sulla loro apparente figura, o sopra le varie accidentalità de&#039;loro inviluppi, <lb></lb>ma sopra l&#039;intima composizione degli organi. </s></p><p type="main">

<s>Giuseppe Pitton di Tournefort fu il più valoroso fra gli oppositori usciti <lb></lb>contro il Magnol, e rimeditando sopra la ragione di ordinare le piante, espo­<lb></lb>sta dal Cesalpino, disse ch&#039;era la sola “ inter Herbarios philosopho dignam ” <lb></lb>(Institutiones rei herbariae, Parisiis 1719, pag. </s>

<s>66). Confermava la verità <lb></lb>di una tal sua sentenza mostrando che la Filosofia delle piante propriamente <lb></lb>comincia col nostro Aretino, il quale paragonò i semi agli ovi, e affermò <lb></lb>che simili erano negli uni e negli altri le virtù e i modi dei loro svolgi­<lb></lb>menti. </s>

<s>“ Fuit insuper Caesalpinus in rebus physicis, ut ferebant illa tem­<lb></lb>pora, multum versatus, seminaque plantarum cum animantium ovis et vim, <lb></lb>qua ovi partes explicantur, cum fermentatione conferre non dubitavit ” (ibid.). </s></p><p type="main">

<s>Dice che fu dotto in Fisica il Cesalpino secondo i suoi tempi, perchè <lb></lb>intanto era venuto il Malpighi, filosofo prestantissimo e sottile indagatore <lb></lb>delle opere della Natura, “ qui veram Plantarum anatomen instituit, et opus <lb></lb>admirationis plenum exegit “ (ibid., pag. </s>

<s>54). Egli, soggiunge, fu primo a <lb></lb>dimostrar che le piante si compongono di cellule e che son fornite di un <lb></lb>doppio ordine di vasi, gli uni per servire al nutrimento, e gli altri alla re­<lb></lb>spirazione. </s></p><p type="main">

<s>La fiducia dunque che aveva il Tournefort di poter riuscire a quel che <lb></lb>il Magnol disperava, era fondata sulla nuova scienza anatomica e fisiologica <lb></lb>istituita dal Malpighi, e della quale aveva nel Cesalpino sagacemente intra­<lb></lb>veduti i principii. </s>

<s>Scorto da queste nuove scienze, esamina diligentemente <lb></lb>le piante, per desumer dalla loro intima struttura le note specifiche, e ne <lb></lb>conclude che i semi soli son per sè insufficienti, se non si congiungono ai <lb></lb>fiori. </s>

<s>Riconosciuto perciò difettoso il sistema del Cesalpino, la ragione ana­<lb></lb>litica lo conduce ad approvar piuttosto l&#039;opinione del Gesner e del Colonna. <lb></lb></s>

<s>“ Analiticam rationem adhibui, quae mox patebit, coegit me ad Gesneri et <lb></lb>Columnae sententiam amplectendam. </s>

<s>Quod ingenii bonitate tanti viri conse­<lb></lb>cuti sunt, arte explorandi acquisivi ” (ibid.). </s></p><p type="main">

<s>Seguendo dunque quest&#039;arte sperimentale, nella quale il Tournefort ri­<lb></lb>conosce per maestro il Malpighi, si condusse a ricercare i particolari organi <lb></lb>e le funzioni, e ne concluse dalla dimostrazione dei fatti, meglio che dall&#039;au­<lb></lb>torità dei detti, non si potere i generi delle piante stabilire altrimenti, che <pb xlink:href="020/01/1492.jpg" pagenum="367"></pb>esaminando insieme i fiori e i frutti. </s>

<s>“ Haec cum ita sint, genera planta­<lb></lb>rum statui non posse liquet nisi flores simul et fructus adhibeantur. </s>

<s>Eamque <lb></lb>methodum vim fere demonstrationis habere existimo ” (ibid., pag. </s>

<s>57). </s></p><p type="main">

<s>Le regole poi di questo dimostrato metodo, dalle quali si professa di <lb></lb>non declinare se non per cause gravi, le riduce il Tournefort a sei, ma le <lb></lb>principali fra le altre son le quattro seguenti: “ I. </s>

<s>Plantae quae floribus et <lb></lb>fructibus, vel alterutro carent, in genera redigi debent ratione rerum magis <lb></lb>insignium, perinde ac illae, quarum flores et fructus solo microscopio pate­<lb></lb>fiunt. </s>

<s>II. </s>

<s>Floris simul et fructus structurae ratio semper habenda est ad <lb></lb>constituenda genera plantarum, quae floribus et fructibus donantur. </s>

<s>III. </s>

<s>Flo­<lb></lb>ribus simul et fructibus standum est, cum abunde sufficiunt ad genera di­<lb></lb>stinguenda. </s>

<s>IV. </s>

<s>Non solum caeterae omnes plantarum partes, sed earum <lb></lb>affectiones, crescendi modus, habitus et facies exterior in auxilium vocari <lb></lb>debent, cum flos simul et fructus non sufficiant ad genera recte distin­<lb></lb>guenda ” (ibid., pag. </s>

<s>61). </s></p><p type="main">

<s>Secondo queste regole ordina il Tournefort le sue XXII classi, incomin­<lb></lb>ciando dalla prima, nella quale son riposte l&#039;erbe e i suffrutici a fiori mo­<lb></lb>nopetali campaniformi, infino all&#039;ultima, che comprende gli alberi e i fru­<lb></lb>tici a fiori papiglionacei. </s>

<s>Il nuovo ordinamento, fatto con tanto studio d&#039;arte <lb></lb>e di scienza sperimentale, fu accolto con plauso, e ne fu approvato il me­<lb></lb>todo, che veramente, come sperava di aver fatto l&#039;Autore, <emph type="italics"></emph>caeteras omnes <lb></lb>antecellit,<emph.end type="italics"></emph.end> infintantochè non venne a commovere la scienza una scoperta <lb></lb>inaudita. </s>

<s>Andrea Cesalpino aveva detto che le piante nascono come gli ani­<lb></lb>mali, e dopo un secolo e mezzo Carlo Linneo soggiungeva che si fecondano <lb></lb>altresì, con distinzione di sessi, come gli stessi animali. </s>

<s>La sentenza com­<lb></lb>mosse, perchè riusciva inaspettata. </s>

<s>E infatti quel Tournefort, che tanto aveva <lb></lb>richiamata l&#039;attenzione degli studiosi sopra le forme de&#039;fiori, e che unico <lb></lb>fra Sistematici era dietro il Malpighi entrato così addentro a penetrarne le <lb></lb>funzioni; ripeteva quel che aveva imparato dagli altri, che cioè son gli uf­<lb></lb>ficii del fiore quelli di preparare l&#039;alimento al formarsi e allo svolgersi dei <lb></lb>semi. </s>

<s>“ Flores autem sunt veluti viscera quaedam, in quibus alimentum <lb></lb>multiplici circuitu ad primam ovi formationem vel amplificationem aptius <lb></lb>evadit ” (ibid., pag. </s>

<s>68). </s></p><p type="main">

<s>Il Linneo invece dimostrò che ufficio proprio de&#039;fiori era quello, non <lb></lb>di servire al nutrimento, ma alla fecondazione, organi femminei della quale <lb></lb>sono i pistilli, e organi maschili gli stami. </s>

<s>Secondando meno la profondità <lb></lb>del Tournefort, che la superficialità de&#039;Sistematici suoi predecessori, il Lin­<lb></lb>neo pensò d&#039;istituire, sopra quella distinzione d&#039;organi sessuali da sè sco­<lb></lb>perta, un metodo nuovo, che fece a molti dimenticare quell&#039;altro dal Tour­<lb></lb>nefort stesso, quarant&#039;anni prima, con tanto studio e con tanta scienza <lb></lb>elaborato. </s></p><p type="main">

<s>La <emph type="italics"></emph>Philosophia botanica<emph.end type="italics"></emph.end> è una mirabile sintesi della mente linneana <lb></lb>non solo, ma della scienza. </s>

<s>Pubblicati già i libri <emph type="italics"></emph>Classes plantarum,<emph.end type="italics"></emph.end> e <emph type="italics"></emph>Spon­<lb></lb>salia plantarum,<emph.end type="italics"></emph.end> “ reliquas sectiones fundamentorum, dice l&#039;Autore rivol-<pb xlink:href="020/01/1493.jpg" pagenum="368"></pb>gendo <emph type="italics"></emph>Lectori botanico<emph.end type="italics"></emph.end> il suo discorso, coniunctim cum prioribus in unum <lb></lb>opus compingere, et auctas novis exemplis, observationibus, demonstratio­<lb></lb>nibus, sub <emph type="italics"></emph>Philosophiae botanicae<emph.end type="italics"></emph.end> titulo edere diu animo volvi ” (editio <lb></lb>cit., pag. </s>

<s>3). </s></p><p type="main">

<s>Alla parte scientifica dell&#039;Opera fa erudito corredo la parte storica, nella <lb></lb>quale, dop&#039;aver contratti in poche parole e in pochi numeri i sistemi del <lb></lb>Cesalpino, del Morison, dell&#039;Hermann, del Ray, del Tournefort e del Ma­<lb></lb>gnol, per tacere degli altri meno importanti, ma che pur non sono in que­<lb></lb>sto Specchio dimenticati; “ Ego, ne conclude, sexuale Systema secundum nu­<lb></lb>merum, proportionem et situm staminum cum pistillis, elaboravi ” (pag. </s>

<s>28). <lb></lb>E dalle Monandrie alle Poliandrie, dalle Didinamie alle Tetradinamie, dalle <lb></lb>Monadelfie alle Poliadelfie, dalle Singenesie alle Ginandrie, dalle Monoecie <lb></lb>alle Diecie, dalle Poligame alle Crittogame, ne annovera ordinatamente le <lb></lb>classi (ibid., pag. </s>

<s>28, 29). </s></p><p type="main">

<s>Questo nuovo sistema però, per quanto seducesse i Botanici, non fu <lb></lb>trovato esente da gravi difetti. </s>

<s>Il numero degli stami, per esempio, e così <lb></lb>variabile nelle diverse specie d&#039;uno stesso genere, che spesso spesso è a <lb></lb>certe piante assegnato dal Linneo il loculo, che meno a loro appartiene. </s>

<s><lb></lb>Senza che, difficilissimo è riconoscere i sessi, e perciò il modo della fecon­<lb></lb>dazione, di certi fiori, come per esempio, di quelli delle Singenesie. </s></p><p type="main">

<s>Dietro queste considerazioni si giudicò il sistema linneano non meno <lb></lb><emph type="italics"></emph>artificiale<emph.end type="italics"></emph.end> di quelli prima elaborati, e l&#039;Autore stesso sentì nella sua pro­<lb></lb>pria coscienza la verità di quei giudizii, ai quali sembra che volesse ritro­<lb></lb>vare una scusa col dire, che le classi artificiali eran necessarie nelle pre­<lb></lb>senti condizioni della Scienza, come succedanee alle naturali. </s>

<s>Che se aveva <lb></lb>seguìto piuttosto l&#039;arte che la Natura, aveva ciò fatto per non perdere, come <lb></lb>gli pareva fosse avvenuto al Morison e al Ray, il filo di Arianna. </s>

<s>“ Artifi­<lb></lb>ciales classes succedaneae sunt naturalium, usquedum omnes naturales sint <lb></lb>detectae, quas plura genera nondum detecta revelabunt, et tum limites <lb></lb>classium difficillimi evadant. </s>

<s>Cavendum ne imitando Naturam filum ariad­<lb></lb>neum amittamus uti Morisonus, et Rajus ” (ibid., pag. </s>

<s>104, 5). </s></p><p type="main">

<s>Riconosce nulladimeno il Linneo e confessa che il carattere naturale è <lb></lb>veramente quello, che può porgere stabile fondamento alle classificazioni <lb></lb>delle piante “ quo destitutus, nullus de genere rite iudicabit, adeoque abso­<lb></lb>lutum fundamentum cognitionis plantarum est, et erit ” (ibid., pag. </s>

<s>135). <lb></lb>Questi eran però precetti, piuttosto che fatti, intorno ai quali lasciò l&#039;Au­<lb></lb>tore della Filosofia botanica che si travagliassero i suoi successori. </s>

<s>Vennero <lb></lb>essi non molto dopo, e furono Bernardo e Lorenzo di Jussieu e Michele <lb></lb>Adanson, riconosciuti da tutti per i più laboriosi e fortunati architettori di <lb></lb>Metodi naturali. </s></p><pb xlink:href="020/01/1494.jpg" pagenum="369"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le piante, nelle quali trovò a principio l&#039;uomo da sodisfare alle prime <lb></lb>necessità della vita, educarono l&#039;arte dell&#039;agricoltura, che ha il suo princi­<lb></lb>pal fondamento nella cognizione delle varie qualità dei terreni, meglio atti <lb></lb>a ricevere, e a far lietamente prosperare i surculi e i semi. </s>

<s>Ma non si po­<lb></lb>teva l&#039;industre opera condurre senza l&#039;uso di opportuni strumenti, i quali <lb></lb>furono ritrovati a principio in quelle pietre sparse qua e là, consistenti in <lb></lb>sè stesse, e ritrose a lasciar l&#039;apparente irregolarità delle loro forme. </s></p><p type="main">

<s>S&#039;intende facile di qui come la prima e più natural distinzione, che <lb></lb>occorresse a fare delle sostanze dette ora da noi minerali, fosse quella di <lb></lb>Terre e di Pietre, le varie specie delle quali si desumevano, come da note <lb></lb>caratteristiche, dalle varie attitudini alla cultura, e dalla durezza. </s>

<s>In seguito <lb></lb>si scoprì il ferro che, sostituito alla pietra in que&#039;primi rozzi strumenti, <lb></lb>dette insieme con la perfezionata agricoltura mirabile incremento a tutte le <lb></lb>arti fabbrili. </s>

<s>Furono poi dopo il ferro conosciute altre sostanze, che gli so­<lb></lb>migliavano nella durezza e nello splendore, e alle Terre e alle Pietre quegli <lb></lb>antichissimi mineralogisti, che descrivevano la Natura secondo le prime ap­<lb></lb>prensioni dei sensi, aggiunsero anche i Metalli. </s></p><p type="main">

<s>Vennero dopo lungo tempo ad esercitar l&#039;intelletto intorno a quelle <lb></lb>prime sensate apprensioni i Filosofi, il principe de&#039;quali, nel seno della gran <lb></lb>madre Terra investigando le origini, insegnò a distinguere i minerali se­<lb></lb>condo la varietà dei loro nascimenti. </s>

<s>Il terzo Libro meteorologico si conclude <lb></lb>da Aristotile in trattar di quelle cose, che si generano dentro la Terra, e <lb></lb>dice ch&#039;essendo due le esalazioni, come antecedentemente crede di aver ben <lb></lb>dimostrato, dalla fumosa hanno origine i Fossili, e dalla vaporosa i Metalli. <lb></lb></s>

<s>“ Sicca igitur exhalatio igniens facit fossibilia omnia ut lapidum genera inae­<lb></lb>liquabilia, et Sandaracam et Ochram et Minium et Sulfur et alia talia. </s>

<s>Plu­<lb></lb>rima autem fossibilium sunt, haec quidem pulvis coloratus, illa autem lapis, <lb></lb>ex tali consistentia factus, velut Cinnabari. </s>

<s>Exhalationis autem vaporosae <lb></lb>quaecumque metallica sunt, et sunt aut fusibilia aut ductilia ut ferrum, au­<lb></lb>rum, aes. </s>

<s>Facit autem haec omnia exhalatio vaporosa cum includitur, et <lb></lb>maxime in lapidibus, propter siccitatem, in unum coarctatur et concrescit, <lb></lb>velut ros aut pruina ” (Tomus VI, Operum cit., fol. </s>

<s>57). </s></p><p type="main">

<s>Termina Aristotile così il riassunto del suo discorso: ” Communiter <lb></lb>igitur dictum est de omnibus his, sigillatim autem considerandum intenden­<lb></lb>tibus circa unumquodque genus ” (ibid, fol. </s>

<s>58). Ma chi attendeva all&#039;agri­<lb></lb>coltura, come per esempio Columella, considerò particolarmente i generi delle <lb></lb>terre coltivabili; chi attendeva alla medicina, come Galeno, considerò quei <lb></lb>generi di minerali, che servono per medicamenti, e Plinio nell&#039;ampiezza del <lb></lb>suo soggetto vi comprese altresì que&#039;varii generi di minerali, che porgono <pb xlink:href="020/01/1495.jpg" pagenum="370"></pb>materia alla costruzione degli edifizii, o che si ricercano per l&#039;esercizio <lb></lb>delle arti. </s></p><p type="main">

<s>Una considerazione perciò bene ordinata intorno alle varie specie di <lb></lb>minerali, ch&#039;era il desiderio della Scienza, non si vide apparir che sulla fine <lb></lb>del secolo XVI, per opera di Andrea Cesalpino. </s>

<s>S&#039;aggiungeva in quel tempo, <lb></lb>ad accendere più che mai vivo un tal desiderio, la curiosità di trovar la so­<lb></lb>luzione a un problema, che s&#039;era incominciato allora a propor con più <lb></lb>instanza intorno all&#039;origine delle lapidefatte reliquie marine, che si trovano <lb></lb>sparse per le alte cime dei monti. </s>

<s>Attribuivano i più cotesta origine al Di­<lb></lb>luvio universale, ma perchè in Aristotile non si trovavano, intorno a una <lb></lb>tale universale inondazion della Terra, i testi chiari, molti Peripatetici in­<lb></lb>vocavano i superni influssi celesti, e anzi alcuni affermavano con gran fidu­<lb></lb>cia che le reliquie fossili dei monti, tutt&#039;altro ch&#039;essere ivi deposte dal mare, <lb></lb>v&#039;erano addirittura piovute dal cielo. </s>

<s>Uno di costoro scrisse in tal proposito <lb></lb>un libro nel quale, perciocchè davasi maggiore autorità ad Aristotile che alla <lb></lb>Bibbia, fu condannato dalla Chiesa Romana. </s></p><p type="main">

<s>Benchè sembrasse un tal libro al Cesalpino scritto <emph type="italics"></emph>diligentissime atque <lb></lb>eleganter,<emph.end type="italics"></emph.end> non potè nonostante patir l&#039;offesa, che veniva a riceverne ingiu­<lb></lb>stamente la Filosofia peripatetica, attribuendo a menzogna o ad ignoranza il <lb></lb>dire che Aristotile non ammetteva che un diluvio parziale. </s>

<s>A riparar dun­<lb></lb>que a una tale offesa, deliberò il Cesalpino di darsi allo studio dei minerali, <lb></lb>e di pubblicare un suo trattato, nel quale interpetrerebbe Aristotile in vero <lb></lb>senso ortodosso, e si ridurrebbe la questione degli avanzi fossili ritrovati sui <lb></lb>monti all&#039;ordine dei fatti naturali. </s>

<s>Nel dedicar quel trattato, col titolo <emph type="italics"></emph>De <lb></lb>metallicis,<emph.end type="italics"></emph.end> a papa Clemente VIII, esprimeva in questa forma lo stesso Au­<lb></lb>tore le sue prese deliberazioni, e i suoi intendimenti: “ Materia metallica, <lb></lb>beatissime Pater, philosophiae studiosis valde expetita, nec non medicis ap­<lb></lb>prime necessaria, quamvis nuper diligentissime atque eleganter fuerit tra­<lb></lb>dita, duo tamen impulerunt me ut opus idem aggrederer: Primum, quod <lb></lb>multa in ea traditione reperiantur principiis philosophiae minus congruam, <lb></lb>et peripateticam doctrinam evertentia; alterum quod Auctor, utpote a sancta <lb></lb>romana Ecclesia expulsus, haberi nequaquam concedatur. </s>

<s>Cum. </s>

<s>igitur plan­<lb></lb>tarum historiam edidissem, visum fuit opere praecium, eadem methodo, cor­<lb></lb>porum metallicorum explicationem adiungere. </s>

<s>” </s></p><p type="main">

<s>E come nel dar la storia delle piante, ritenuta la comune e naturale <lb></lb>distinzione d&#039;alberi, di frutici, di suffrutici e d&#039;erbe, aveva nel diligente <lb></lb>esame dei frutti ritrovato il modo di ordinarle in generi e in specie; così <lb></lb>nel dar la storia dei minerali, ritenuta la natural distinzione di terre, di pie­<lb></lb>tre e di metalli, a ciascuna delle quali differenze consacra un libro del suo <lb></lb>tripartito discorso; ora dalle generazioni per via di soluzione o di sublima­<lb></lb>zione, e ora da qualità e proprietà fisicamente specifiche desume le note <lb></lb>opportune per ridur la molteplice e infino allora confusa varietà di sostanze <lb></lb>ai loro più convenevoli ordinamenti. </s></p><p type="main">

<s>Le prime differenze delle Terre si desumono dalla varietà dei loro sol-<pb xlink:href="020/01/1496.jpg" pagenum="371"></pb>venti, che sono acqua o olio. </s>

<s>Solubili nell&#039;acqua sono le terre propriamente <lb></lb>dette, i sali, gli allumi e altri corpi a questi assaì somiglianti. </s>

<s>“ Terra igi­<lb></lb>tur, ut a simplicioribus ordiamur, ea proprie appellatur, quae sicca cum sit <lb></lb>sine humore non cohaeret, sed pulveris modo diffluit: humore autem ma­<lb></lb>defacta glutinatur in lutum..... Multae autem sunt terrarum differentiae <lb></lb>pro ariditate, aut pinguedine, densitate, raritate, asperitate, levitate, tenaci­<lb></lb>tate, fragilitate et aliis huiusmodi: item coloribus et saporibus..... Quoniam <lb></lb>autem ad diversos usus petuntur ab artificibus, secundum hos, diversa no­<lb></lb>mina imposita sunt speciebus. </s>

<s>Agricolae enim suas terras quaerunt, alias <lb></lb>figuli et plastici, alias fullones, alias pictores, alias medici ” (De metallicis, <lb></lb>Romae 1596, pag. </s>

<s>25). </s></p><p type="main">

<s>Dei sali ne riconosce con Dioscoride tre generi: fossile, marino e la­<lb></lb>custre. </s>

<s>“ Ad salem reducuntur spuma salis, muria, et flos salis ” (ibid., <lb></lb>pag. </s>

<s>43). Gli allumi son, per la veemenza del sapore astringente, dai Greci <lb></lb>chiamati <emph type="italics"></emph>stipterii,<emph.end type="italics"></emph.end> e gli antichi ne annoverarono varie specie, riguardandoli <lb></lb>o come efflorescenze della Terra o come concrezioni di varia figura. </s>

<s>“ Multa <lb></lb>alia hodie recensent inter alumina, ut alumen plumae, quod amiantum esse <lb></lb>diximus, alumen scaliolum, qui Lapis est specularis inter genera gypsi, alu­<lb></lb>men Catinum quod vulgo sodam vocant inter nitra factitia, alumen faecis, <lb></lb>quae faex vini est combusta inter nitra factitia, alumen zuccharinum..... <lb></lb>Alumen iamenum Arabes intelligunt scissile Dioscoridis ” (ibid., pag. </s>

<s>55). </s></p><p type="main">

<s>Le sostanze terrose, che si sciolgon nell&#039;olio, son per il Cesalpino il <lb></lb>solfo, i bitumi “ et congenera his ” (pag. </s>

<s>62) quali sarebbero l&#039;Arsenico, <lb></lb>la Sandracca, l&#039;Asfaltide, la Canfora e l&#039;Ambra, i quali due ultimi corpi gli <lb></lb>riguarda “ ut genera Bituminis odorata ” (pag. </s>

<s>71). E con la descrizione <lb></lb>delle proprietà naturali relative a ciascuna di queste recensite sostanze, e <lb></lb>de&#039;loro usi o nella pratica medicina o nell&#039;esercizio delle arti, termina il <lb></lb>nostro Autore il suo primo libro <emph type="italics"></emph>De metallicis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il secondo, come si disse, è consacrato a trattar delle sostanze lapidee, <lb></lb>che il Cesalpino, seguendo l&#039;uso volgare, distingue in marmi, in sassi, in <lb></lb>gemme preziose e in pietre propriamente dette. </s>

<s>“ Quatuor autem genera <lb></lb>summa lapidum traduntur vulgo nota: marmora, saxa, gemmae, lapides ” <lb></lb>(pag. </s>

<s>81). I generi de&#039;marmi, soggiunge, non è facile, in tanta moltitudine <lb></lb>e in tanta varietà di colori, annoverarli, non essendovi luogo che non abbia i <lb></lb>suoi proprii. </s>

<s>“ Nos tamen breviter ex numero colorum colligemus ” (pag. </s>

<s>89). <lb></lb>E passa a descrivere il Marmo pario, il Numidico, le Ofiti, le Serpentine, <lb></lb>le Porfiriti, le Terebintine. </s></p><p type="main">

<s>In due sommi generi ripartisce i sassi, in Tufi e in Silici: queste du­<lb></lb>rissime, e quelli molli. </s>

<s>La silice, che fu tra le pietre, egli osserva, ritrovata <lb></lb>la prima per servir così bene ad uso di macina, quando sia cotta al fuoco <lb></lb>perde la sua prima durezza, e si trasforma in calce o in gesso; ond&#039;è che <lb></lb>quelle specie d&#039;essa silice, che si scelgono a quest&#039;usi particolari, si distin­<lb></lb>guono con nomi proprii. </s>

<s>“ Saxum, unde calx excoquitur, calcariam dici po­<lb></lb>test.... Cognata res calci Gypsum est ” (pag. </s>

<s>85). </s></p><pb xlink:href="020/01/1497.jpg" pagenum="372"></pb><p type="main">

<s>Gemme si dicono quelle pietre insignemente dure, che dilettano per la <lb></lb>loro chiarezza e per il loro splendore, e s&#039;usano ad ornamento degli anelli <lb></lb>e dei monili. </s>

<s>Si distinguono in chiare, in colorite e in opache. </s>

<s>“ Perspicuae <lb></lb>aliae sola claritate oblectant, ut Crystallus, Adamas: aliae colorum quoque <lb></lb>pulchritudine ut Smaragdus, Carbunculus; opacae solo splendere et colorum <lb></lb>pulchritudine ” (pag. </s>

<s>96). </s></p><p type="main">

<s>Le pietre all&#039;ultimo propriamente dette si dividono in Coti e in Arene. </s>

<s><lb></lb>Delle Coti alcune sono Aquarie, perchè non hanno per aguzzare altro biso­<lb></lb>gno che d&#039;esser bagnate con acqua, come le Naxie e le Armenie; altre <lb></lb>sono oleari, come le Cretiche e le Laconiche. </s>

<s>“ Quaedam aqua et oleo in­<lb></lb>digent ut Ciliciae, quaedam hominis saliva, sed mollissimae, ut Flammini­<lb></lb>tanae ex Hispania citeriore ” (pag. </s>

<s>87). Delle arene, che son sassi stritolati <lb></lb>e ridotti in minutissime parti, ne assegna il Cesalpino, sull&#039;esempio di Pli­<lb></lb>nio, tre generi: le fossili, le fluviatili e le marine (ivi). </s></p><p type="main">

<s>Il terzo libro è dall&#039;Autore riserbato ai metalli, fra&#039;quali, repudiata <lb></lb>com&#039;arbitraria la comun distinzione in sette specie annoverate secondo l&#039;or­<lb></lb>dine e denominate dai sette Pianeti, riconosce due primi e massimi generi, <lb></lb>di fusibili e di duttili. </s>

<s>Dai metalli poi distingue quelle parti ch&#039;escono dagli <lb></lb>stessi metalli, alcune delle quali, egli dice, hanno origine nelle fornaci, come <lb></lb>le scorie, altre fuori, come la ruggine. </s>

<s>Alle stesse scorie in ultimo riduce <lb></lb>anche il vetro “ substantia enim similis est scoriis metallorum ” (pag. </s>

<s>212). </s></p><p type="main">

<s>Il libro, in cui venivano dal Cesalpino in questo modo ordinate, e se­<lb></lb>condo le loro proprietà fisiche descritte le varie sostanze metalliche, è il <lb></lb>primo documento, che avesse, in quella nuova instaurazione delle scienze <lb></lb>sperimentali in Italia, la Mineralogia. </s>

<s>Ma un valoroso discepolo dell&#039;Autore <lb></lb>dava in quel medesimo tempo in Roma opera a quegli stessi studii, di che <lb></lb>il Maestro non punto di ciò geloso, ma anzi tutto compiacente faceva, nella <lb></lb>citata dedica a Clemente VIII, questa commemorazione solenne: “ Sed ecce, <lb></lb>quamprimum Romam petii ut medicinam publice profiterer, comperi ean­<lb></lb>dem provinciam a reverendissimo ac perillustri Michaele Mercato viro doctis­<lb></lb>simo susceptam eamque, cum is mihi communicasset tanquam praeceptori <lb></lb>suo, quo usus est dum Pisis Simplicia profiterer, incredibili laetitia affectus <lb></lb>sum, quod discipulum praeclarissimum ex schola mea tanquam ex proprio <lb></lb>ventre prodeuntem adeo profecisse viderem ut toto orbe admirabilis redde­<lb></lb>retur. </s>

<s>Inter caeteras enim lucubrationes <emph type="italics"></emph>Metallothecam vaticanam<emph.end type="italics"></emph.end> miro or­<lb></lb>dine construxit, loculis propriis singula corpora distribuens, ut ingens eorum <lb></lb>turba, absque ulla turbatione, intuentibus praesto esset. </s>

<s>Eorumdem imagi­<lb></lb>nes aeneis typis imprimendas curavit, adiuncta enarratione facundissima ex <lb></lb>omnibus auctoribus tam priscis quam posterioribus collecta, ut desiderari <lb></lb>quid amplius nequiret. </s>

<s>” </s></p><p type="main">

<s>Pareva per queste ragioni, prosegue a dire il Cesalpino, che dovesse <lb></lb>riuscir superflua l&#039;opera nostra, ma sventuratamente il Mercati aveva appena <lb></lb>disteso il primo Tomo, dove tratta delle Terre, de&#039;Sali, degli Allumi, de&#039;Solfi <lb></lb>e di altri simili, quando la morte sopravvenutagli gl&#039;impedì di proseguire il <pb xlink:href="020/01/1498.jpg" pagenum="373"></pb>bene incamminato lavoro, lasciandolo così, con grave danno della scienza, <lb></lb>imperfetto. </s>

<s>“ Deest enim de Marmoribus tractatio et de gemmis et metallis, <lb></lb>quorum sylvam esse quidem apud se in fragmentis quibusdam asserebat, <lb></lb>sed minus elaboratam. </s>

<s>” </s></p><p type="main">

<s>Questo elogio dell&#039;Autore e dell&#039;Opera fatto da un tal giudice, qual&#039;è <lb></lb>il Cesalpino, invoglia di saperne più avanti i nostri lettori, per sodisfare ai <lb></lb>quali diciamo che negli ultimi giorni di Settembre dell&#039;anno 1666 fu veduto <lb></lb>da certi pescatori alla Gorgona presso Livorno un gran pesce andar placi­<lb></lb>damente leccando la spalmatura di una tartana, ond&#039;è che gli si potè facil­<lb></lb>mente avventare un laccio intorno al capo e trarlo, benchè dopo grandis­<lb></lb>sima resistenza, dentro la barca. </s>

<s>Il capo di questo pesce, conosciuto dai <lb></lb>Naturalisti di allora sotto il nome di <emph type="italics"></emph>Lamia,<emph.end type="italics"></emph.end> fu fatto dal Granduca venire <lb></lb>a Firenze per consegnarlo a Niccolò Stenone, che ne facesse diligente ana­<lb></lb>tomia. </s></p><p type="main">

<s>I Fiorentini accorsero curiosi a vedere questa nuova maraviglia: ai lon­<lb></lb>tani trovò modo di sodisfar Carlo Dati, mandando quella stessa testa dise­<lb></lb>gnata con finissimo intaglio. </s>

<s>Chi vide cotesta immagine andare attorno, pochi <lb></lb>giorni dopo che fu chiappato il pesce, prese a far forse maggiori maraviglie <lb></lb>di quegli altri, ch&#039;ebber agio di saziar la vista nell&#039;oggetto reale, non in­<lb></lb>tendendo come potess&#039;essere che in sì breve tempo fosse stato condotto in <lb></lb>Firenze sul rame un sì squisito lavoro. </s></p><p type="main">

<s>Fra i maravigliati di ciò era in Roma Ottavio Falconieri, a cui il Dati <lb></lb>stesso, che gli aveva mandato pochi giorni innanzi il disegno, rispondeva <lb></lb>così rivelandogli il mistero. </s>

<s>“ Agli anni passati io comprai la <emph type="italics"></emph>Metalloteca <lb></lb>vaticana<emph.end type="italics"></emph.end> manoscritta con tutti i suoi rami intagliati mirabilmente, descritta <lb></lb>da mons. </s>

<s>Michele Mercati, con pensiero di farla una volta stampare, perchè <lb></lb>veramente è opera insigne. </s>

<s>Il detto Autore, con occasione di trattare delle <lb></lb>glossopetre, dice che elle sono tanto simili ai denti del pesce Lamia, che da <lb></lb>alcuni sono spesse volte scambiate, e dop&#039;averne assegnate le differenze pone <lb></lb>il disegno del capo di questo pesce. </s>

<s>Mi sovvenne di ciò, e trovando il rame, <lb></lb>ne ho fatti tirare dodici soli, per non offendere l&#039;intaglio che è gentilis­<lb></lb>simo, risparmiandolo per la stampa dell&#039;opera ” (Lettere di C. Dati, Fi­<lb></lb>renze 1825, pag. </s>

<s>56, 57). </s></p><p type="main">

<s>“ Di mons. </s>

<s>Michele Mercati, dice il Dati stesso in un&#039;altra sua lettera <lb></lb>al medesimo Falconieri, non perdo tempo a darle notizia, perchè il valore <lb></lb>di esso e l&#039;opera <emph type="italics"></emph>Degli obelischi<emph.end type="italics"></emph.end> l&#039;ha reso celebre e particolarmente in co­<lb></lb>testa città di Roma. </s>

<s>Anzi io spero da lei a suo tempo qualche aiuto per <lb></lb>fare di questo Letterato un breve elogetto storico. </s>

<s>Fra gli altri studii di que­<lb></lb>sto. </s>

<s>Prelato fu quello delle cose naturali, e specialmente delle metalliche, <lb></lb>onde, mentr&#039;era al servizio di Sisto V P. M., formò nel Vaticano una co­<lb></lb>copiosissima Metalloteca, la quale poi descrisse in lingua latina secondo l&#039;or­<lb></lb>dine col quale era disposta, trattando le principali materie con eguale cu­<lb></lb>riosità, erudizione ed eleganza, e adornolla di figure intagliate in rame con <lb></lb>estrema finezza, senza guardare a spesa o diligenza veruna. </s>

<s>Prevenuto dalla <pb xlink:href="020/01/1499.jpg" pagenum="374"></pb>morte, non potette pubblicar detta opera, che già era riveduta e passata <lb></lb>da&#039;Superiori e resa famosa dal testimonio dell&#039;Eminentissimo card. </s>

<s>Baronio <lb></lb>nel primo tomo degli <emph type="italics"></emph>Annali ecclesiastici.<emph.end type="italics"></emph.end> Restarono adunque presso agli <lb></lb>eredi il manoscritto e i rami con grandissimo pericolo d&#039;andar male, e fu­<lb></lb>rono più volte in cimento d&#039;andar portati oltre i monti. </s>

<s>Agli anni passati, <lb></lb>avendone io qualche precedente cognizione, procurai di veder l&#039;uno e gli <lb></lb>altri, e talmente me ne invogliai, che avanti di restituirgli negoziai e con­<lb></lb>clusi la compra con qualche mio scomodo per la somma di settanta dop­<lb></lb>pie..... Mi mossi a far questa spesa, a me veramente sproporzionata, per <lb></lb>desiderio che quest&#039;Opera si pubblicasse, ma essendo per me, com&#039;è noto <lb></lb>ad ognuno, corsi molti anni disastrosi, non è possibile che io faccia sì grande <lb></lb>sborso quanto sarebbe necessario a volerla stampar nobilmente..... Tal­<lb></lb>mente che senza qualche buono aiuto mi son perduto d&#039;animo, e in Olanda, <lb></lb>dove avrei occasione di mandarla, non voglio, per non mettere a risico <lb></lb>i rami. </s>

<s>” </s></p><p type="main">

<s>“ Per essere questa Galleria stata eretta in Vaticano, e perciò <emph type="italics"></emph>Vaticana<emph.end type="italics"></emph.end><lb></lb>intitolata, a diletto e spese d&#039;un Sommo Pontefice, il mio concetto era pub­<lb></lb>blicandola consacrarla al nome glorioso del regnante Pontefice Ottimo Mas­<lb></lb>simo, e riempire i voti dell&#039;armi pontificie con l&#039;insegne trionfali di casa <lb></lb>Ghigi. </s>

<s>Le lettere dedicatorie, prefazione, vita dell&#039;Autore, indici, assistenza, <lb></lb>correzione, ecc., tutto son pronto a fare. </s>

<s>E siccome fui pronto al primo <lb></lb>sborso, così farei al restante, se i miei negozii non fossero andati in ma­<lb></lb>lora. </s>

<s>Ma nello stato presente non mi resta se non un buon desiderio e un <lb></lb>godimento d&#039;avere assicurata quest&#039;opera degnissima, perchè altri, quando <lb></lb>che sia, abbia miglior fortuna di pubblicarla ” (ivi, pag. </s>

<s>62-66). </s></p><p type="main">

<s>Da queste espressioni, fatte in una lettera del dì 6 Novembre 1666, <lb></lb>collazionate con quelle che si leggono nella precedente del dì 17 Settem­<lb></lb>bre, e nella quale il Dati pregava il Falconieri che si volesse far mediatore <lb></lb>appresso Alessandro VII per la stampa dell&#039;opera del Mercati, si raccoglie <lb></lb>che non doveva avere avuto lo stesso Dati troppo buone speranze di riu­<lb></lb>scire per quella via all&#039;intento. </s>

<s>E infatti ei morì, lasciando il manoscritto <lb></lb>e i rami in eredità a&#039;suoi figli, i quali gli presentarono in dono a Cle­<lb></lb>mente XI, per secondare i desiderii del padre. </s></p><p type="main">

<s>Di ciò che prometteva di fare il Dati stesso intorno alla edizione, per­<lb></lb>chè riuscisse corredata di tutte le sue parti, e corretta, dette cura Clemente <lb></lb>al suo Archiatro Giovan Maria Lancisi, il quale pubblicò l&#039;Opera in Roma <lb></lb>nel 1717 col titolo seguente: “ Michaelis Mercati Metallotheca Opus postu­<lb></lb>mum, Auctoritate et munificentia Clementis XI e tenebris in lucem eductum, <lb></lb>Opera autem et studio Joannis Mariae Lancisii illustratum. </s>

<s>” Due anni dopo <lb></lb>a un certo numero di copie si reimpresse, pure in Roma dallo stesso Lan­<lb></lb>cisi, il titolo dell&#039;Opera “ cui accessit appendix cum XIX recens inventis <lb></lb>iconibus. </s>

<s>” </s></p><p type="main">

<s>Apparisce dai fatti fin qui narrati che le notizie tramandate intorno alla <lb></lb>Metalloteca vaticana dal Cesalpino non sono molto precise, imperocchè le <pb xlink:href="020/01/1500.jpg" pagenum="375"></pb>immagini de&#039;loculi e delle figure dei metalli non rimanevano <emph type="italics"></emph>aeneis typis <lb></lb>imprimendae,<emph.end type="italics"></emph.end> ma erano già state impresse, e il Dati scrive che “ fatta di­<lb></lb>ligente rassegna de&#039;rami finiti, abbozzati e rifatti, in tutto sono cento trenta ” <lb></lb>(ivi, pag. </s>

<s>64). </s></p><p type="main">

<s>Se poi fosse vero quel che dianzi udimmo dire dallo stesso Dati, che <lb></lb>cioè il manoscritto della Metalloteca era stato riveduto e passato dai Supe­<lb></lb>riori, parrebbe si dovesse dubitare anche del Cesalpino là dove dice essere <lb></lb>stata l&#039;Opera lasciata dal suo Autore imperfetta. </s>

<s>In ogni modo è vero che <lb></lb>manca, nella pubblicazion del Lancisi, il trattato delle gemme e dei metalli, <lb></lb>e quel de&#039;marmi è manifestamente interrotto ne&#039;suoi principii. </s>

<s>Ma suppli­<lb></lb>sce il Mercati al difetto coll&#039;introdurre nella sua trattazione tre nuovi sog­<lb></lb>getti, de&#039;quali il Cesalpino non tocca, e per cui l&#039;opera del discepolo vien <lb></lb>principalmente a pigliare importanza sopra quella dello stesso Maestro. </s></p><p type="main">

<s>È tutta insieme la Metalloteca dunque magnificamente ordinata in <emph type="italics"></emph>Ar­<lb></lb>madi,<emph.end type="italics"></emph.end> eretti intorno intorno alle pareti di una delle grandi sale del Vati­<lb></lb>cano. </s>

<s>Primo e principal pensiero dell&#039;Autore è quello di far sì che i varii <lb></lb>oggetti trovino da collocarsi in un medesimo Armadio, coi loro congeneri, <lb></lb>specificati ciascuno ne&#039;loculi convenienti. </s>

<s>Prende l&#039;Autore a guida de&#039;suoi <lb></lb>pensieri Aristotile, il dilungarsi dal quale egli stima pericoloso, per l&#039;esem­<lb></lb>pio di un Autore, che l&#039;aveva di poco preceduto, e di cui dice che “ peri­<lb></lb>patetica luce orbatus, nil mirum si in graves incidit errores ” (pag. </s>

<s>5). E <lb></lb>perch&#039;è per lui di grande autorità Teofrasto, fedel discepolo di Aristotile, si <lb></lb>studia di conciliarlo col Maestro, ripudiando senza esitare Galeno, che pro­<lb></lb>poneva di ordinar le varie sostanze minerali in pietre, in corpi metallici e <lb></lb>in terre coltivabili, e insiem con lui Avicenna, che le stesse sostanze distri­<lb></lb>buiva tutte in pietre, in metalli, in solfori e in sali. </s>

<s>“ Sed ne videamur inu­<lb></lb>tilia persequi, poi tosto soggiunge dop&#039;aver dimostrato essere difettoso ogni <lb></lb>altro ordinamento, che si dilunghi dagl&#039;insegnamenti aristotelici, ad nostrum <lb></lb>institutum revertamur ab iis incipientes, quae a sicca exhalatione fiunt, quo­<lb></lb>rum alia humore solubilia sunt, ut terrae proprie vocatae quae in lutum <lb></lb>transeunt, sales qui in aquam, sulphur quod in oleum. </s>

<s>Alia insolubilia, ut la­<lb></lb>pides illiquabiles. </s>

<s>Postremo explicabuntur quae humida exhalatione constant: <lb></lb>haec autem igne liquabilia sunt aut ductilia ” (ibid.). </s></p><p type="main">

<s>Qui l&#039;Editore avverte esser nel manoscritto una lacuna, lasciatavi se­<lb></lb>condo noi dal trovarsi incerto e pensoso l&#039;Autore, per vedersi innanzi smar­<lb></lb>rite a un tratto l&#039;orme del suo fedele Aristotile, negli ordinamenti del quale <lb></lb>non pareva che trovassero luogo proprio le sostanze lapidee innate negli ani­<lb></lb>mali, o che presentano figure simili a quelle di corpi o di membra animali. </s>

<s><lb></lb>Ebbe perciò all&#039;ultimo a deliberarsi di assegnare a questi corpi di natura <lb></lb>e di forme singolari due Armadi distinti, da collocarsi fra le sostanze lapi­<lb></lb>deo terrose e i marmi. </s>

<s>Il discorso dell&#039;Autore intorno a questi ultimi si ri­<lb></lb>duce a tre soli capitoli, nel primo de&#039;quali tratta delle definizioni, e nel <lb></lb>secondo delle differenze, ch&#039;egli desume da più numerose note di quelle, <lb></lb>alle quali sole avevano atteso i suoi primi Maestri. </s>

<s>“ Differentiae marmo-<pb xlink:href="020/01/1501.jpg" pagenum="376"></pb>rum aliae oriuntur a substantiae temperamento, aliae a compositione par­<lb></lb>tium, nonnullae a magnitudine corporis a qua gignuntur, quaedam a duri­<lb></lb>tia, quaedam a nitore, sed plures a colore et specie macularum et locis <lb></lb>natalibus ” (pag. </s>

<s>353). </s></p><p type="main">

<s>Di qui preparavasi ampia la trattazione de&#039;marmi, la quale invece si <lb></lb>assolve tutta ne&#039;principii del cap. </s>

<s>III, in cui, proponendosi il Mercati di trat­<lb></lb>tare del Marmo pario, si divaga in descrivere le statue antiche del Laocoonte, <lb></lb>dell&#039;Apollo e dell&#039;Antinoo, collocate per ornamento de&#039;giardini vaticani, e <lb></lb>scolpite in quella stessa elettissima qualità di marmo bianco. </s>

<s>Dovevasi qui <lb></lb>insieme co&#039;marmi trattare anche delle gemme, nelle quali e ne&#039;metalli pro­<lb></lb>priamente detti si lasciò veramente, come il Cesalpino diceva, la Metalloteca <lb></lb>vaticana imperfetta. </s></p><p type="main">

<s>Secondo che dunque potè raccogliersi dal manoscritto, la Metalloteca <lb></lb>stessa si lasciò così dal Mercati ordinata in X distinti Armadi. </s>

<s>Nel I si ri­<lb></lb>ponevano le Terre, nel II i sali e i Nitri, nel III gli Allumi, nel IV i Suc­<lb></lb>chi acri (crisocolla, ruggine, arsenico, sandracca), nel V i Succhi pingui <lb></lb>(solfo, bitumi, succino), nel VI le sostanze d&#039;origine marina (coralli, spugne, <lb></lb>pomici), nel VII <emph type="italics"></emph>Lapides terrae similes<emph.end type="italics"></emph.end> (calamina, manganese, tufo, mica, <lb></lb>magnetide, pietra speculare, amianto, ematite), nell&#039;VIII <emph type="italics"></emph>Lapides animali­<lb></lb>bus innati<emph.end type="italics"></emph.end> (bezoar, bufoniti, chelonie, perle, ecc.). </s></p><p type="main">

<s>Fra la ricca raccolta delle varie produzioni naturali se ne trovava il <lb></lb>Mercati a mano di quelle, alle quali, neanche fermandosi sulle note fisiche, <lb></lb>si sarebbe saputo trovare il luogo conveniente, simulando l&#039;origine vera la <lb></lb>loro apparente figura ora per esempio di ova o di lingue, ora di rami d&#039;al­<lb></lb>beri o di code di serpenti. </s>

<s>Disputavasi se avessero veramente codesti og­<lb></lb>getti nascimento dagli animali, o se fossero, come le altre pietre, prodotti <lb></lb>dalla terra. </s>

<s>Ond&#039;è che risolutosi il Mercati di seguire questa seconda opi­<lb></lb>nione, riserbò un Armadio distinto, ch&#039;è in ordine il IX, a que&#039;particolari <lb></lb>oggetti da lui stesso insigniti del nome d&#039;<emph type="italics"></emph>Idiomorfi<emph.end type="italics"></emph.end> “ idest peculiari forma <lb></lb>praediti ” (pag. </s>

<s>215). Trovarono in cotesto Armadio dove riporsi le ooliti, <lb></lb>le ammoniti, le ofiti, i lepidoti, le dendriti, le glossopietre e simili, che hanno <lb></lb>dato appresso al volgo origine a tante favole francamente derise dal nostro <lb></lb>Autore. </s>

<s>L&#039;ultimo Armadio, ch&#039;è il X, era stato appena aperto per riporvi <lb></lb>i marmi, ma l&#039;inesorabile morte fece sì che, dal primo loculo in fuori si <lb></lb>rimanesse del resto vuoto. </s></p><p type="main">

<s>Chi ripensa a questi ordinamenti dei minerali, proposti sulla fine del <lb></lb>secolo XVI, contemporaneamente dal Cesalpino e dal Mercati, non può non <lb></lb>apprezzarne il sollecito studio e l&#039;ammirabile industria. </s>

<s>L&#039;averli anzi ten­<lb></lb>tati, quando la smisurata varietà sbigottiva gl&#039;ingegni, e le difficoltà d&#039;in­<lb></lb>vestigar le prime origini, e di penetrare addentro alla più intima natura <lb></lb>de&#039;corpi, non eran vinte ancora dalla scienza o dall&#039;arte; forma tutt&#039;insieme <lb></lb>la ragion del merito e la scusa dei difetti, che si trovan nell&#039;opera de&#039;due <lb></lb>nostri Autori. </s>

<s>Se la Mineralogia infatti ha potuto oggidì proporre ordina­<lb></lb>menti più razionali non v&#039;è per altro riuscita, che per esser venute in va-<pb xlink:href="020/01/1502.jpg" pagenum="377"></pb>lido soccorso di lei la Geologia, la Cristallografia e la Chimica; tre scienze <lb></lb>che, ai tempi del Cesalpino e del Mercati, o non erano nate o si trovavano <lb></lb>nella loro prima infanzia. </s></p><p type="main">

<s>La Geologia ponendo mente ai varii strati sedimentarii, in che il ter­<lb></lb>restre globo s&#039;affalda, potè con certezza di fatto dimostrar l&#039;opera e l&#039;effi­<lb></lb>cacia di quelle inondazioni, che si appellarono col nome di diluvii, e presa <lb></lb>per sua ancella la Paleontologia dare un giusto criterio da distinguer le pie­<lb></lb>tre fossili dalle reliquie animali. </s>

<s>Così veniva a espurgarsi delle Glossopetre, <lb></lb>e di tanti altri Idiomorfi, il IX Armadio mineralogico del Mercati. </s></p><p type="main">

<s>La Cristallografia dimostrando che non alla sola figura sessangola, ma <lb></lb>a varii tipi più semplici si riducono le forme primigenie de&#039;cristalli, apriva <lb></lb>largo campo a raccogliere nuove note specifiche del più gran numero di <lb></lb>minerali, mentre nel tempo stesso soccorreva opportuna la Chimica a sve­<lb></lb>lar l&#039;inganno, in ch&#039;erano inevitabilmente caduti tutti gli Antichi, mostrando <lb></lb>che bene spesso, sotto un simile abito esterno, s&#039;ascondon corpi tanto fra <lb></lb>sè diversi d&#039;origine e di sostanza. </s></p><p type="main">

<s>Così essendo la Chimica, a conoscere la testura de&#039;corpi bruti, stru­<lb></lb>mento meglio proporzionato di quel che non fosse, a investigar la trama <lb></lb>organica, l&#039;Istologia, si può dire che gli ordinamenti de&#039;Minerali, a princi­<lb></lb>pio appariti tanto difficili, e perciò venuti più tardi, si trovarono fondati sopra <lb></lb>più stabili principii, che non gli ordinamenti degli altri due regni superiori. </s></p><p type="main">

<s>In ogni modo furon tali, quali si son potuti accennare in questo capi­<lb></lb>tolo, i laboriosi studii fatti dalla Scienza, per ridurre in convenevole ordine <lb></lb>i tre grandi eserciti, che militano su questa Terra. </s>

<s>Ond&#039;ora non rimane a <lb></lb>noi che a delibare il frutto delle sensate osservazioni e delle artificiose espe­<lb></lb>rienze nello studio degli organi e delle funzioni proprie ai varii generi di <lb></lb>animali; della struttura delle piante, e della vita vegetativa; dell&#039;origine, <lb></lb>delle forme e delle proprietà, che distinguono le varie sostanze minerali. </s></p><pb xlink:href="020/01/1503.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO X.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>De&#039;Mammiferi e degli Uccelli<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della generazione dagli svolgimenti embrionali dell&#039;uovo. </s>

<s>— II. De&#039;moti locali: del passo e del <lb></lb>volo. </s>

<s>— III. </s>

<s>Di alcune questioni concernenti le funzioni digestive ne&#039;quadrupedi ruminanti e <lb></lb>negli uccelli gallinacei: delle vescicole pneumatìche negli uccelli. </s>

<s>— IV. </s>

<s>Di certe più notabili <lb></lb>differenze negli organi dei sensi: degli strumenti della voce e del canto. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Gli organi e le funzioni di quelli animali, che appartengono agli ordini <lb></lb>superiori, e che o s&#039;appellano <emph type="italics"></emph>Mammiferi<emph.end type="italics"></emph.end> dal modo del loro allevamento, o <lb></lb><emph type="italics"></emph>Quadrupedi<emph.end type="italics"></emph.end> dagli strumenti della locomozione, non differiscono sostanzial­<lb></lb>mente dagli organi e dalle funzioni animali dell&#039;uomo. </s>

<s>Essendosi perciò, <lb></lb>nella serie de&#039;capitoli precedenti intrattenuta la nostra Storia in narrar ciò <lb></lb>che, per via dell&#039;arte sperimentale, riuscì la scienza a intendere della strut­<lb></lb>tura del corpo umano e della vita di lui, viene a restringersi il soggetto <lb></lb>della narrazione che resta in que&#039;più notabili particolari, per cui i bruti <lb></lb>hanno una storia naturale a loro propria. </s>

<s>Che se nel Microcosmo, come ci <lb></lb>occorse di osservare altra volta, si trova la Natura tutta insieme raccolta e <lb></lb>sublimata, riducesi dunque ogni officio, che incombe al nuovo studio, in <lb></lb>comparare l&#039;anatomia e la fisiologia dell&#039;uomo coll&#039;anatomia, e colla fisio­<lb></lb>logia de&#039;varii sottoposti ordini animali, e in osservare e sperimentare che <lb></lb>sia ciò che gli differenzia, e che gli costituisce ne&#039;gradi, dalla Natura stessa <lb></lb>a ciascun di loro assegnati. </s></p><p type="main">

<s>Intorno al resultato insomma di quelle comparazioni, ch&#039;ebbero a scorta <lb></lb>l&#039;osservazione e l&#039;esperienza, ha da trattenersi il nostro Discorso, alle prime <pb xlink:href="020/01/1504.jpg" pagenum="379"></pb>mosse del quale si fanno incontro gli Anatomici del secolo XVI fieramente <lb></lb>disputanti fra loro. </s>

<s>E perchè dalla risoluzione di quelle dispute viene a de­<lb></lb>cidersi se i primi documenti della comparata Anatomia si trovino per i libri <lb></lb>galenici, e se l&#039;antico Maestro descrivesse la struttura del corpo umano o <lb></lb>del belluino, ci consiglia il soggetto che prendiamo a trattare di soffermarci <lb></lb>brevemente su questo punto. </s></p><p type="main">

<s>Che il Vesalio, per le numerose pagine della sua Anatomia descrittiva <lb></lb>della fabbrica del corpo umano, non s&#039;abbattesse a descriver parte, d&#039;onde <lb></lb>non pigliasse avida occasione di coglier Galeno in fallo, s&#039;è detto e ripe­<lb></lb>tuto più volte anche da noi. </s>

<s>Il Colombo pure, benchè fosse nelle accuse più <lb></lb>mite, ebbe a riconoscere che molte delle galeniche descrizioni, volutesi da <lb></lb>lui appropriare all&#039;uomo, ritraevan piuttosto la particolare struttura degli <lb></lb>organi dei cani e delle scimmie; ond&#039;è che insorsero fieramente i Vesaliani <lb></lb>ad accusare i Galenisti d&#039;avere spacciata per l&#039;anatomia dell&#039;uomo quella, <lb></lb>ch&#039;è piuttosto propria del bruto. </s></p><p type="main">

<s>Erasi il campo della contesa particolarmente restrinto nell&#039;esame degli <lb></lb>ossi, intorno a che s&#039;esercitarono il Falloppio e l&#039;Ingrassia, scrivendone par­<lb></lb>ticolari trattati che, divulgatissimi per le più celebri scuole d&#039;Italia, furono <lb></lb>ambedue pubblicati postumi. </s>

<s>Quel del Falloppio, dato in luce nel 1570 da <lb></lb>Francesco Michino, è il più importante, e com&#039;ebbe maggiore autorità del­<lb></lb>l&#039;altro in compor gli animi de&#039;disposti alla pace, così dette nuovo motivo <lb></lb>ai dissidenti di sostener, con più ardore che mai, le loro già pregiudicate <lb></lb>opinioni. </s></p><p type="main">

<s>Il trattato falloppiano, che porta il titolo di <emph type="italics"></emph>Observationes in librum <lb></lb>Galeni de ossibus,<emph.end type="italics"></emph.end> è un&#039;introduzione allo studio dell&#039;Anatomia, della quale <lb></lb>l&#039;Autore dà la definizione, e investiga l&#039;origine, riconoscendola co&#039;Platonici <lb></lb>nella naturale curiosità di sapere. </s>

<s>Nota poi che la nuova scienza ebbe in­<lb></lb>cremento per opera d&#039;Ippocrate e di Democrito mosso, da coloro che lo de­<lb></lb>ridevano, a cercar ne&#039;dutti biliari le riposte sorgenti della pazzia. </s></p><p type="main">

<s>Come introduzione perciò incomincia il Falloppio dagli ossi, e descrive <lb></lb>lo scheletro, comparando via via le osservazioni sue proprie con le descri­<lb></lb>zioni, che si leggono ne&#039;libri di Galeno. </s>

<s>Nel cap. </s>

<s>XXII per esempio tratta <lb></lb>dell&#039;osso sacro, e relativamente alla figura delle parti che lo compongono <lb></lb>scrive: “ Observandum est quod spina in osse sacro est similis spinae alia­<lb></lb>rum vertebrarum secundum Galenum, quod quidem verum est in canibus <lb></lb>et simiis, sed in hominibus est exilis et fere non conspicua. </s>

<s>” (Venetiis, apud <lb></lb>Karera, 1570, fol. </s>

<s>54). Rispetto al numero poi di quelle parti, dop&#039;aver letto <lb></lb>nel testo galenico che son tre, soggiunge: “ Quot sint partes ossis sacri <lb></lb>nunc docet Galenus, sed haec descriptio multum differt ab ossibus humanis. </s>

<s><lb></lb>Ascribit nam illi tres partes, cum tamen sint sex. </s>

<s>Quibus tribus partibus, <lb></lb>tanquam propriis vertebris, adiungit %o%%<foreign lang="grc">υγα</foreign> ” (ibid., fol. </s>

<s>55). </s></p><p type="main">

<s>Così proseguendo il Falloppio il suo diligente esame, per tutte le altre <lb></lb>parti, veniva a concludersene che Galeno avesse piuttosto descritto lo sche­<lb></lb>letro delle scimmie. </s>

<s>Sorse Bartolommeo Eustachio a confutare una tal con-<pb xlink:href="020/01/1505.jpg" pagenum="380"></pb>clusione, dimostrando anzi che l&#039;antico Maestro non poteva aver avuto sot­<lb></lb>t&#039;occhio altro che la struttura delle ossa dell&#039;uomo. </s>

<s>Quanto al sacro, osservava <lb></lb>che nell&#039;Autor greco la confusione nasce tutta dai nomi, perch&#039;egli del re­<lb></lb>sto, dando al coccige tre parti, viene insomma a dire che, tutto insieme, esso <lb></lb>osso sacro si compone di sei. </s>

<s>“ Quantum ego penetrare ad sensum opinio­<lb></lb>nemque Galeni possum, rudi linea ipse nobis abumbravit, quando in libro <lb></lb><emph type="italics"></emph>De ossibus,<emph.end type="italics"></emph.end> et in illis, quos <emph type="italics"></emph>De administratione anatomica<emph.end type="italics"></emph.end> inscripsit, os <lb></lb>sacrum in tres portiones et totidem os coccygis partiri docuit ” (Opusc. </s>

<s><lb></lb>anat., Venetiis 1564, Ossium examen, pag. </s>

<s>220, 21). Argomenta dall&#039;altra <lb></lb>parte l&#039;Eustachio che dee aver veramente Galeno descritte le parti dell&#039;osso <lb></lb>sacro nell&#039;uomo, perchè se le avesse osservate nelle scimmie “ dubio procul <lb></lb>eas nominare vertebras, sicut profecto sunt, non praetermisisset ” (ibid., <lb></lb>pag. </s>

<s>221). </s></p><p type="main">

<s>Nel secolo XVIII uno de&#039;più valorosi Naturalisti della Francia, atten­<lb></lb>dendo con particolare studio all&#039;anatomia <emph type="italics"></emph>De l&#039;Orang-outang et de quel­<lb></lb>ques autres especes de singes,<emph.end type="italics"></emph.end> ben comprese quanto fosse importante il de­<lb></lb>cider l&#039;antica questione, insorta fra gli Anatomici del secolo XVI, le contrarie <lb></lb>parti de&#039;quali venivano rappresentate dalle due grandi autorità del Fallop­<lb></lb>pio e dell&#039;Eustachio. </s>

<s>E dal riscontro delle osservazioni sue proprie con le <lb></lb>descrizioni galeniche ebbe, con imparziale giudizio, a dar sentenza finale: <lb></lb>“ Que jamais Galien n&#039;a disséquė de cadavres humains, ou que du moins <lb></lb>il ne s&#039;en est pas servi pour composer ses ouvrages ” (Oeuvres de Pierre <lb></lb>Camper, T. I, Paris 1803, pag. </s>

<s>43). </s></p><p type="main">

<s>Si vien ora da così fatta decisiva sentenza del Camper a concludere che <lb></lb>trovasi da&#039;Galenisti antichi già descritta l&#039;anatomia di quegli animali di <lb></lb>ordine superiore, il trattar de&#039;quali è parte del presente capitolo di storia. </s>

<s><lb></lb>Non vuol tacersi però che gli argomenti del Naturalista francese, benchè <lb></lb>fondati sopra un maggior numero di osservazioni, sono in sostanza quegli <lb></lb>stessi, di che s&#039;era due secoli prima servito il Falloppio, il quale inoltre, <lb></lb>comparando l&#039;anatomia dell&#039;uomo e delle scimmie ne&#039;feti, e facendone no­<lb></lb>tare la somiglianza, si studiò di compor la lite col dire che Galeno s&#039;in­<lb></lb>gannò talvolta, per aver creduto che gli organi embrionali si mantenessero <lb></lb>invariabili in ogni più minuta particolarità delle loro forme, anche negli <lb></lb>adulti. </s></p><p type="main">

<s>Poi più tardi, svolgendosi nel progredir della scienza il fecondo concetto <lb></lb>falloppiano, si riconobbe che quelle somiglianze intravedute ne&#039;feti s&#039;allar­<lb></lb>gano mirabilmenle considerate negli ovi, da che s&#039;ebbe a concluderne che <lb></lb>i Mammiferi hanno origine da un principio simile a quello degli Uccelli. </s>

<s>Ma <lb></lb>vien qui a rappresentarcisi un soggetto nuovo di tale importanza, che non <lb></lb>può non concederglisi convenevole luogo fra le stesse angustie, a cui ci ri­<lb></lb>duce il vicin termine prescritto a questa terza Parte della nostra Storia. </s></p><p type="main">

<s>Aristotile, nel secondo capitolo del VI libro <emph type="italics"></emph>De historia animalium,<emph.end type="italics"></emph.end><lb></lb>iniziava l&#039;Embriologia, descrivendo le trasformazioni osservate nelle uova <lb></lb>delle galline rese feconde, e incominciando dal loro primo concepimento, <pb xlink:href="020/01/1506.jpg" pagenum="381"></pb>“ concipit, egli dice, foemina quae coierit ovum superius ad septum tran­<lb></lb>sversum, quod ovum primo minutum et candidum cernitur, mox rubrum <lb></lb>cruentumque, deinde increscens luteum et flavum efficitur totum ” (T. VI, <lb></lb>operum, Venetiis 1560, fol. </s>

<s>138). </s></p><p type="main">

<s>Stettero lungamente queste dottrine aristoteliche per infallibile docu­<lb></lb>mento di scienza, infin tanto che Ulisse Aldovrandi non pensò di riscon­<lb></lb>trarle colle naturali esperienze, dalle quali tornò maravigliato che avesse il <lb></lb>Filosofo trascurata la descrizion di quell&#039;organo, dentro cui l&#039;uova stesse <lb></lb>hanno la loro ultima perfezione. </s>

<s>“ Atque isthaec est doctrina Aristotilis, sed <lb></lb>mirum quod uteri non meminerit, in quo tamen ovum perficitur, etsi extra <lb></lb>eum primo propriae substantiae habeat rudimenta, sed formam absolutissi­<lb></lb>mam in eo recipit. </s>

<s>Locus itaque inchoationis, quae ab Aristotilis Interpetre <lb></lb><emph type="italics"></emph>conceptio<emph.end type="italics"></emph.end> dicitur, est ventris inferioris superior ac media pars ad septum <lb></lb>transversum. </s>

<s>Dixit enim: <emph type="italics"></emph>faeminae concipiunt ova ad septum transversum.<emph.end type="italics"></emph.end><lb></lb>Hoc addimus nos, ex anatomica inspectione, esse supra ipsam spinam ad <lb></lb>divaricationem vasorum, quae in crura descendunt. </s>

<s>Locus vero perfectionis <lb></lb>est ipse uterus, cuius forma plurimum differt ab utero viviparorum ” (Or­<lb></lb>nithologiae, lib. </s>

<s>XIV, Francofurti 1610, pag. </s>

<s>99). </s></p><p type="main">

<s>Ma perchè il maraviglioso naturale artificio nella concezione degli ovi <lb></lb>non si può intendere, se non da chi con gli occhi suoi proprii lo contem­<lb></lb>pla, io, prosegue a dir l&#039;Aldovrandi, per provvedere alla comune utilità degli <lb></lb>studiosi, mi rivolsi a quell&#039;eccellentissimo auatomico ch&#039;è Antonio Ulmo, <lb></lb>perchè mi facesse la dissezione di alquante galline. </s>

<s>Ei disegnò diligentemente <lb></lb>le cose come le vide stare in natura, e io vi rappresento, o lettori, sott&#039;oc­<lb></lb>chio quegli stessi disegni nelle cinque figure, che troverete impresse nella <lb></lb>mia Tavola quarta. </s>

<s>“ Prior icon, quae Tab. </s>

<s>IV num. </s>

<s>9 extat, ovorum sub <lb></lb>septo conceptorum magnitudinem et locum per quem in uterum descendunt, <lb></lb>item in quo luteum ab albumine ambitur, nec non etiam ubi testae duri­<lb></lb>tiem acquirunt, aliosque demonstrat locos generationi destinatos.... Alterae <lb></lb>tres subsequentes eiusdem Tabulae, nn. </s>

<s>10, 11 et 12, isthaec fere omnia <lb></lb>sed dilucidius ostendunt; nempe qua magnitudine ova a septo in matricem <lb></lb>descendant, nec non et uteri protensionem. </s>

<s>Ultima num. </s>

<s>13 dictae Tabulae <lb></lb>solius uteri figura est, demonstratque utrunque eius orificium, per quod <lb></lb>scilicet ova sub septo contenta recipiat, item per quod ea postremo exclu­<lb></lb>dat ” (ibid.). </s></p><p type="main">

<s>Quest&#039;ultima figura, secondando le generose intenzioni dell&#039;Aldovrandi, <lb></lb>com&#039;apparirà dal processo della presente storia, giovò davvero moltissimo <lb></lb>agli studiosi, specialmente da poi che Girolamo Fabricio venne colle sue elo­<lb></lb>quenti parole ad illustrarla. </s>

<s>Nel principio del suo trattato <emph type="italics"></emph>De formatione ovi <lb></lb>et pulli<emph.end type="italics"></emph.end> l&#039;Anatomico d&#039;Acquapendente, per supplire anche meglio al difetto <lb></lb>aristotelico, dà il nome di utero, non a quell&#039;organo solo in cui l&#039;uova si <lb></lb>perfezionano, ma a quell&#039;altro aziandio in cui si concepiscono, e ch&#039;ei de­<lb></lb>scrive com&#039;un acervo di ovicini attaccati per un pedunculo al ramo, come <lb></lb>i grani dell&#039;uva. </s>

<s>A quest&#039;organo, ossia all&#039;Ovaia, dà l&#039;Autore il nome di <pb xlink:href="020/01/1507.jpg" pagenum="382"></pb><emph type="italics"></emph>utero primo<emph.end type="italics"></emph.end> e <emph type="italics"></emph>superiore,<emph.end type="italics"></emph.end> a cui soggiace l&#039;altr&#039;utero rappresentato nella <lb></lb>quinta figura dell&#039;Aldovrandi, e che l&#039;Acquapendente rassomiglia a una <lb></lb>tromba col suo padiglione, o infundibolo com&#039;ei lo chiama. </s>

<s>“ Hoc enim fo­<lb></lb>ramen tubae et infundibulo est simile, quam ob causam <emph type="italics"></emph>infundibulum<emph.end type="italics"></emph.end> ap­<lb></lb>pello ” (Op. </s>

<s>omnia cit., pag. </s>

<s>2). </s></p><p type="main">

<s>Questo Trattato del nostro Italiano, venuto postumo alla luce nel 1621, <lb></lb>richiamò a sè l&#039;attenzione di Guglielmo Harvey, che si sentì da quegli esempii <lb></lb>eccitato a studiare gli svolgimenti embrionali nell&#039;uova delle galline, seguendo <lb></lb>l&#039;orme di Aristotile fra gli antichi, e del Fabricio d&#039;Acquapendente fra&#039;re­<lb></lb>centi, da lui tenuti “ illum tanquam <emph type="italics"></emph>Deum,<emph.end type="italics"></emph.end> hunc ut <emph type="italics"></emph>Praemonstratorem. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb>Così fatte espressioni, che si leggono in sul finir della prefazione alle Eser­<lb></lb>citazioni anatomiche <emph type="italics"></emph>De generatione animalium,<emph.end type="italics"></emph.end> rivelano l&#039;occulta radice <lb></lb>de&#039;difetti più notabili in quest&#039;Opera arveiana, la quale tanto ritrae dalla <lb></lb>viziata mente di Aristotile nelle filosofiche speculazioni, e de&#039;fallaci instituti <lb></lb>del Fabricio nelle naturali esperienze, che, se fosse soppresso il nome del­<lb></lb>l&#039;Autore nel titolo del libro, difficilmente si crederebbe questo fratello al­<lb></lb>l&#039;altro <emph type="italics"></emph>De motu cordis.<emph.end type="italics"></emph.end> S&#039;aggiungono ai vizii della materia i difetti della <lb></lb>forma, i quali però trovano una ragionevole scusa ne&#039;tumulti delle guerre <lb></lb><emph type="italics"></emph>plusquam civilia,<emph.end type="italics"></emph.end> nelle quali si trovò involto l&#039;Harveio, com&#039;ei deplora in <lb></lb>fine alla sua LXVIII Esercitazione, e nell&#039;essere stato il manoscritto rimesso <lb></lb>insieme da Giorgio Ent e dato in luce da lui in Londra nel 1651, senza che <lb></lb>se ne volesse prendere alcuna cura l&#039;Autore, già vecchio, e disgustato ora­<lb></lb>mai de&#039;tempi, degli uomini e di sè stesso. </s></p><p type="main">

<s>Rimangono in ogni modo queste nuove esercitazioni arveiane monu­<lb></lb>mento solenne della scienza, perchè, lasciato il suo <emph type="italics"></emph>Dio<emph.end type="italics"></emph.end> sul lido, e spiegate <lb></lb>le vele innanzi al suo <emph type="italics"></emph>Premostratore,<emph.end type="italics"></emph.end> si mette tutto solo a correre un nuovo <lb></lb>mare. </s>

<s>Lo studio dell&#039;uovo gallinaceo non termina per l&#039;Harveio, come per <lb></lb>Aristotile e per l&#039;Aldovrandi, in sè stesso, ma viene a questo principale in­<lb></lb>tento prescelto, perchè, nella generazione degli animali d&#039;ordine superiore, <lb></lb>possa servire come di più facile e trattabile chiave ad aprire il mistero. </s>

<s>“ Cur <lb></lb>ab ovo gallinaceo documentum sumerem, iampridem dictum est: nempe quod <lb></lb>illud parvo veniret, et ubique obviam esset.... In viviparorum autem ge­<lb></lb>neratione cognoscenda eadem facilitas non occurrit. </s>

<s>Ab humani enim uteri <lb></lb>dissectione fere omnino excludimur: in equis vero, bobus, capris caeteris­<lb></lb>que pecoribus, aliquid ad hanc rem experiri, citra ingentem laborem et im­<lb></lb>pendium haud exiguum, non licet ” (De generat. </s>

<s>anim. </s>

<s>Lugd. </s>

<s>Batav. </s>

<s>1737, <lb></lb>pag. </s>

<s>287, 88). Ma la munificenza del re Carlo, giovane amante della caccia <lb></lb>specialmente de&#039;cervi, liberò l&#039;Harveio da ogni spesa, e da ogni sollecitu­<lb></lb>dine di cercare animali vivipari, permettendogli di sezionar le damme ridotte <lb></lb>dalle selve de&#039;monti inglesi ne&#039;rinchiusi cancelli del suo parco reale. </s>

<s>Par <lb></lb>che il frutto di così fatte esperienze l&#039;abbia l&#039;Herveio stesso voluto tutto <lb></lb>concludere in seno a queste parole: “ Fabricius ab Aquapendente, tanquam <lb></lb>omnis viviparorum conceptus ovum quoddam esset, ab hoc tractatum auspi­<lb></lb>catur.... Nos vero, in observationum harum vestibulo, cuncta animalia quo-<pb xlink:href="020/01/1508.jpg" pagenum="383"></pb>dammodo ex ovo nasci affirmavimus ” (ibid., 288). Chi credesse che in que­<lb></lb>ste osservazioni si contenga una scoperta, s&#039;ingannerebbe, perch&#039;elle in verità <lb></lb>non son altro che una fallacia, per scoprir la quale non debbonsi le sen­<lb></lb>tenze dell&#039;Acquapendente e dell&#039;Harveio riguardare a parte, ma nel com­<lb></lb>plesso della Storia, che vuol perciò risalire a&#039;suoi primi principii. </s></p><p type="main">

<s>Ippocrate dava autorità alla comune opinione invalsa, che cioè si gene­<lb></lb>rassero gli uomini e gli altri animali affini dal seme virile commisto al <lb></lb>femineo, il quale operasse dentro l&#039;utero come il caglio sul latte. </s>

<s>Aristotile, <lb></lb>a cui parve questa teoria troppo semplice, la sublimò colle arguzie del suo <lb></lb>ingegno su per le regioni metafisiche, dicendo che il sangue menstruo som­<lb></lb>ministra al feto la materia, che poi riceve dal virile atto la forma. </s>

<s>Ma a qual <lb></lb>uso, si domandava, stanno allora i <emph type="italics"></emph>testes<emph.end type="italics"></emph.end> in seno alle femmine? </s>

<s>Dall&#039;altra <lb></lb>parte quel profluvio di umore, che vien dall&#039;utero alla vagina, nell&#039;atto stesso <lb></lb>del concepire, era tale esperienza in favor d&#039;Ippocrate, da poter sugl&#039;inge­<lb></lb>gni più efficacemente delle aristoteliche teorie. </s>

<s>Come, dall&#039;altra parte, si co­<lb></lb>nosceva da cotesti creduti testicoli femminei l&#039;origine di quell&#039;umore, che <lb></lb>vien per l&#039;utero alla vagina; così immaginavasi che i ligamenti uterini cre­<lb></lb>duti vuoti, servissero a quello stesso umore da&#039;canicoli conduttori. </s>

<s>Di così <lb></lb>fatte immaginate ipotesi informavasi l&#039;anatomia descrittiva degli organi mu­<lb></lb>liebri, che la nuova scienza risorta, non reluttando i Peripatetici stessi, ac­<lb></lb>colse docilmente dalle lezioni del nostro Jacopo da Carpi. </s></p><p type="main">

<s>Ei descrive l&#039;utero, o il ricettacolo come lo chiama, di forma quadran­<lb></lb>golare, <emph type="italics"></emph>cum aliquali rotunditate,<emph.end type="italics"></emph.end> che ha verso la cervice, di qua e di là, <lb></lb>attaccati due freni o ligamenti simili alle corna delle lumache. </s>

<s>Intorno a <lb></lb>queste, che perciò si chiamano corna dell&#039;utero, sta un testicolo da una parte <lb></lb>e dall&#039;altra <emph type="italics"></emph>durior et minor quam in mare,<emph.end type="italics"></emph.end> non perfettamente rotondo, ma <lb></lb>compresso a guisa di mandorla, e in cui <emph type="italics"></emph>generatur sperma.<emph.end type="italics"></emph.end> “ Istis testibus <lb></lb>implantantur vasa seminaria, quae a chili et ab Aorta et ab emulgentibus <lb></lb>descendunt, dicta <emph type="italics"></emph>praeparantia.<emph.end type="italics"></emph.end> Inde alia vasa <emph type="italics"></emph>deportantia<emph.end type="italics"></emph.end> nominata, con­<lb></lb>tinue se dilatando, usque ad receptaculum tendunt, et intra matrices con­<lb></lb>cavitatem sperma ducunt ” (Isagogae, Venetiis 1535, fol. </s>

<s>20 ad t.). </s></p><p type="main">

<s>Il Vesalio e il Colombo non lasciarono ne&#039;loro libri descrizioni punto <lb></lb>più felici, poco dopo apparite nel Falloppio, il quale ebbe a notare ne&#039;suoi <lb></lb>predecessori una gran confusione, principalmente rispetto ai vasi, che vanno <lb></lb>alla matrice. </s>

<s>Quell&#039;organo, che il Berengario rassomigliava alle corna delle <lb></lb>lumache, disse il Falloppio aver piuttosto le sembianze di una <emph type="italics"></emph>tromba,<emph.end type="italics"></emph.end> la <lb></lb>quale, movendo dalle così dette corna dell&#039;utero, “ cum parum recesserit <lb></lb>ab eo, latior sensim redditur, et capreoli modo crispat se, donec veniat prope <lb></lb>finem. </s>

<s>Tunc, demissis capreolaribus rugis, atque valde latus redditus, finit <lb></lb>in extremum quoddam quod membranosum, carneumque ob colorem ru­<lb></lb>brum videtur, extremumque lacerum valde et attritum est, veluti sunt pan­<lb></lb>norum attritorum fimbriae, et foramen amplum habet, quod semper clausum <lb></lb>iacet, concidentibus fimbriis extremis, quae tamen, si diligenter aperiantur <lb></lb>ac dilatentur, <emph type="italics"></emph>tubae<emph.end type="italics"></emph.end> cuiusdam aeneae extremum orificium exprimunt. </s>

<s>” Da <pb xlink:href="020/01/1509.jpg" pagenum="384"></pb>che è condotto a dar a quel <emph type="italics"></emph>classico organo<emph.end type="italics"></emph.end> il nome di <emph type="italics"></emph>Tuba.<emph.end type="italics"></emph.end> “ Ideo a me <lb></lb>uteri <emph type="italics"></emph>Tuba<emph.end type="italics"></emph.end> vocatus est ” (Op. </s>

<s>omnia, Observ. </s>

<s>anat., Francof. </s>

<s>1584, pag. </s>

<s>472). </s></p><p type="main">

<s>Ma perchè alcuni Anatomici davano a così fatta Tuba dell&#039;utere, rico­<lb></lb>nosciuta dal Berengario per un ligamento, l&#039;ufficio di canal deferente il se­<lb></lb>minale umore femmineo, questa è cosa, disse il Falloppio, <emph type="italics"></emph>quod minime <lb></lb>placet,<emph.end type="italics"></emph.end> e ciò per più ragioni. </s>

<s>Prima di tutto perchè, ne&#039;supposti testicoli <lb></lb>femminei, non ho trovato mai indizio di sperma. </s>

<s>“ Vidi quidem in ipsis <lb></lb>quasdam veluti vesicas, aqua vel humore aquaeo, alias luteo, alias vero lim­<lb></lb>pido turgentes, sed nunquam semen vidi, nisi in vasis ipsis spermaticis, vel <lb></lb>delatoriis vocatis ” (ibid.). </s></p><p type="main">

<s>In secondo luogo, quando pure si fossero così fatte vesciche ritrovate <lb></lb>piene di umor seminale, sarebbe impossibile che stillassero quel loro umore <lb></lb>nell&#039;utero per la via delle tube, come per appositi meati seminarii “ quo­<lb></lb>niam nunquam observare potui meatus istos seminarios coninnctos cum te­<lb></lb>stibus.... Si igitur non connascuntur, vide an verum illud sit quod dixerim, <lb></lb>dogmata aliquot, quae ad generationem seminis pertinent, valdene titubent, <lb></lb>laborare ” (ibid.). </s></p><p type="main">

<s>Veniva da queste ragioni e da questi fatti veramente l&#039;ipotesi ippocra­<lb></lb>tica a ricevere un colpo tale, che troppo grande sforzo sarebbevi bisognato, <lb></lb>per reggersi in piedi in quel gran titubare. </s>

<s>Ma se il Falloppio dava da una <lb></lb>parte il crollo all&#039;edifizio antico, confessava dall&#039;altra di non sapervene so­<lb></lb>stituire un altro nuovo, a cui primo a por mano fu senza dubbio l&#039;Harveio. </s>

<s><lb></lb>Sezionando le damme allevate nel parco reale, al ritrovarne i testicoli dopo <lb></lb>il coito non punto inturgiditi, e anzi di nulla alterati dalla loro solita co­<lb></lb>stituzione, volle argomentarne, confermando i sospetti del Falloppio, che <lb></lb>quegli organi non servono a generare, e ch&#039;è loro ufficio proprio quello di <lb></lb>“ stabilire venarum divaricationes, et humorem lubricandis partibus conser­<lb></lb>vare ” (Exercit. </s>

<s>De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>299). </s></p><p type="main">

<s>Un&#039;altra nuova osservazione gli occorse a fare in proposito confermata <lb></lb>dalle esperienze e fu che l&#039;utero delle damme, com&#039;anche delle pecore, <lb></lb>delle vacche e delle capre, è così chiuso, da dar bene esito ai menstrui, ma <lb></lb>da non ammettere nulla dal di fuori, non eccettuata l&#039;aria stessa. </s>

<s>“ Debuit <lb></lb>namque statui sanguini menstruo, aliisque humoribus excernendis, via pa­<lb></lb>tefacere, verum autem externarum, etiam minimarum, aeris puta aut semi­<lb></lb>nis ingressui, omnino praecludi ” (ibid., pag. </s>

<s>295). E infatti non trovò nel­<lb></lb>l&#039;utero delle damme, aperto a tale intento, nessuna traccia di questo seme, <lb></lb>ciò che avendo fatto osservare e credere al Re, i custodi del parco e i cac­<lb></lb>ciatori andavano dicendo che quello era un inganno, e che il fatto dipen­<lb></lb>deva solo dal fresco delle piogge, per cui s&#039;era indugiato il tempo degli <lb></lb>amori. </s>

<s>“ Postea vero, cum coeundi tempus praeteriisse cernerent, egoque <lb></lb>idem usque assererem, constanter affirmabant et me deceptum esse et a me <lb></lb>Regem ipsum, debereque necessario aliquid conceptus in utero reperiri, do­<lb></lb>nec propriis oculis, rem ut erat perscrutati, summa cum admiratione de lite <lb></lb>desisterent ” (ibid., pag. </s>

<s>306). </s></p><pb xlink:href="020/01/1510.jpg" pagenum="385"></pb><p type="main">

<s>Ritenute queste cose per vere, l&#039;ipotesi di Ippocrate non solo, ma quella <lb></lb>altresì di Aristotile venivano ambedue ugualmente dimostrate per false, non <lb></lb>potendosi l&#039;umor virile, che non è ammesso altrimenti nell&#039;utero, nè com­<lb></lb>mescersi col seme femmineo, nè col sangue menstruo. </s>

<s>“ Adeo ut explora­<lb></lb>tum habeam non ex spermate maris aut foeminae, nec ex ambobus simul <lb></lb>mistis, neque ex sanguine menstruo, conceptus aliquid necessario constitui ” <lb></lb>(ibid., pag. </s>

<s>307). </s></p><p type="main">

<s>Come si costituisce dunque al concepimento il principio? </s>

<s>E rispondono <lb></lb>all&#039;Harveio le proprie osservazioni fatte nello stesso utero delle damme, den­<lb></lb>tro cui ebbe a vedere “ mucosa quaedam filamenta, quae simul iuncta mem­<lb></lb>branosam seu mucilaginosam tunicam, sive <emph type="italics"></emph>manticam<emph.end type="italics"></emph.end> vacuam referunt ” <lb></lb>(ibid, 308). Questo sacchetto vide poi empirsi di un umore albuminoso, non <lb></lb>dissimile da quello dell&#039;uovo, da che fu condotto a sentenziare aver tutti <lb></lb>gli animali anche vivipari origine dall&#039;uovo: sentenza che, in sè stessa è <lb></lb>vera, ma che nella mente dell&#039;Harveio, come s&#039;accennava dianzi, contiene <lb></lb>una gran fallacia. </s>

<s>Domandandogli infatti da che ha origine quell&#039;uovo, ei <lb></lb>risponde dall&#039;utero. </s>

<s>“ Nos autem brevitati studentes, ut facile concedimus <lb></lb>uteri officium et usum procreandis ovis destinatum esse, ita efficiens adae­<lb></lb>quatum et immediatum in ovo ipso contineri asseveramus, ovumque non ab <lb></lb>utero, sed ab interno principio naturali sibique proprio, tum generari tum <lb></lb>augeri censemus ” (ibid., pag. </s>

<s>34). Viene quella virtù di procrear l&#039;uovo a <lb></lb>riceverla l&#039;utero dall&#039;umore prolifico, il quale “ citra tactum agit ” (ibid., <lb></lb>pag. </s>

<s>5), e opera perciò “ per spiritualem substantiam et irradiationem ” <lb></lb>(pag. </s>

<s>179). </s></p><p type="main">

<s>Avevano così fatte dottrine la natura schietta di paradosso, facilmente <lb></lb>riconoscibile dagli scienziati di Londra, se era stata già riconosciuta dagli <lb></lb>stessi custodi del parco reale. </s>

<s>Pure, era tanta l&#039;autorità dell&#039;Harveio, che <lb></lb>non fa maraviglia se ne rimasero vinti tutt&#039;insieme la scienza e il senso co­<lb></lb>mune. </s>

<s>Dall&#039;altra parte è da ripensare che, dopo la distruzione avvenuta per <lb></lb>opera del Falloppio, era questa arveiana la prima restaurata teoria della ge­<lb></lb>nerazione. </s>

<s>Il Cartesio, in appendice al suo trattato <emph type="italics"></emph>De homine,<emph.end type="italics"></emph.end> s&#039;era pro­<lb></lb>vato a render la ragione <emph type="italics"></emph>De formatione animalis;<emph.end type="italics"></emph.end> ragione ch&#039;egli riduce <lb></lb>ai due sessuali umori commisti, i quali si fanno da fermento a vicenda, co­<lb></lb>sicchè dal calore che ne consegue “ nonnullae eorum particulae dilatentur <lb></lb>premantque alias, hacque ratione illas paulatim eo disponant modo, qui ad <lb></lb>membra formanda requiritur ” (Francof. </s>

<s>ad M. 1692, pag. </s>

<s>173). Ma l&#039;antica <lb></lb>teoria ippocratica così rinnovellata, succisa già dal coltello anatomico del Fal­<lb></lb>loppio, veniva affatto diradicata dalle esperienze dell&#039;Harveio, nelle quali forse <lb></lb>riducesi l&#039;unico benefizio da lui recato all&#039;Ovologia. </s>

<s>Egli francamente asse­<lb></lb>riva che l&#039;umor vaginale non ha natura di seme, e che perciò non è ne­<lb></lb>cessario alla generazione. </s>

<s>“ Novi enim plurimas quae, citra talem eiectio­<lb></lb>nem, foecundae satis essent ” (Exercit. </s>

<s>de gener. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>127). </s></p><p type="main">

<s>Avvenne, per tutte queste ragioni, che seguaci de&#039;paradossi dell&#039;Harveio <lb></lb>si facessero anche alcuni Cartesiani, fra&#039;quali è notabile per noi Tommaso <pb xlink:href="020/01/1511.jpg" pagenum="386"></pb>Cornelio. </s>

<s>Il proginnasma V s&#039;intitola per lui <emph type="italics"></emph>De generatione hominis,<emph.end type="italics"></emph.end> e in <lb></lb>mezzo a sì felte tenebre, non trovata altra guida, s&#039;atiene all&#039;Harveio, con­<lb></lb>forme alle dottrine del quale, da un suo ragionamento più abbondante di <lb></lb>parole che ricco d&#039;idee, così ne conclude: “ Quare superest ut dicamus ge­<lb></lb>niturae vim omnem positam esse in substantia quadam prorsus <emph type="italics"></emph>insensili,<emph.end type="italics"></emph.end><lb></lb>quae materiam a foemina collatam subigens, generationis sit efficiens ” (Pro­<lb></lb>gymnasm. </s>

<s>phys., Neapoli 1688, pag. </s>

<s>177, 78). Dall&#039;esser l&#039;atto virile sulla <lb></lb>genitura <emph type="italics"></emph>insensile<emph.end type="italics"></emph.end> ne veniva per conseguenza che si potesse anche senza gli <lb></lb>organi materiali esercitare; altro paradosso che pareva dovesse risvegliar la <lb></lb>mente a riconoscer quel primo. </s>

<s>Eppure il Cornelio con tutta confidenza <lb></lb>scrive: “ Mihi vero experientia compertum est canem, cui testes fueront <lb></lb>abscissi, filios generasse ” (ibid., pag. </s>

<s>165). </s></p><p type="main">

<s>Ma queste son sentenze pronunziate in un momento di sonnolenza o di <lb></lb>ebbrezza, dalle quali passioni riavutasi felicemente la scienza, riconobbe che, <lb></lb>nella dottrina della generazione animale, s&#039;era l&#039;Harveio dimostrato inferiore <lb></lb>a sè stesso e al portato del tempo. </s>

<s>Le strane dottrine conseguivano da os­<lb></lb>servazioni poco diligenti, e dal vizio aristotelico di voler fare alle precon­<lb></lb>cette teorie servire le naturali esperienze. </s>

<s>Egli ingannò veramente con sè <lb></lb>stesso il re Carlo, affermando che non si trovava nell&#039;utero traccia di sperma, <lb></lb>mentre il Falloppio lo avea già ritrovato infin dentro alle Tube. </s>

<s>“ Testes <lb></lb>enim mihi adfuere plurimi fide digni spectatores quod saepius in his mea­<lb></lb>tibus semen exquisitissimum repererim ” (Observ. </s>

<s>anat. </s>

<s>inter. </s>

<s>Op. </s>

<s>omnia <lb></lb>cit, pag. </s>

<s>472). </s></p><p type="main">

<s>Quella borsettina ripiena di un umore albuminoso la vide l&#039;Harveio nel­<lb></lb>l&#039;utero, dopo quindici giorni e più dall&#039;atto fecondativo, e senza ricercar se <lb></lb>potesse esservi venuta d&#039;altrove, pensa che sia ivi prodotta nell&#039;utero come <lb></lb>le galle, e i vermi contenutivi dentro, son prodotti dall&#039;anima vegetativa <lb></lb>delle piante. </s>

<s>Ma l&#039;esser la manteca fetale, nella cavità uterina, erratica <lb></lb>avrebbe dovuto far sospettare al grand&#039;uomo che non poteva essere indi na­<lb></lb>tiva, e se avesse pensato di servirsi per quelle osservazioni delicatissime del <lb></lb>Microscopio, come se ne servì per osservare gl&#039;insetti (De motu cordis, <lb></lb>cap. </s>

<s>XVII), avrebbe potuto riconoscer meglio l&#039;essere e la natura di quel <lb></lb>primo concetto, a cui dava a caso, e fuor del suo proprio significato, il nome <lb></lb>di uovo. </s></p><p type="main">

<s>Eran tali quelle giuste considerazioni e quelle libere censure che, ol­<lb></lb>trepassata la prima metà del secolo XVII, si facevano all&#039;opera dell&#039;Har­<lb></lb>veio dagli Embriologi, avviando l&#039;Ovologia per più diritti sentieri. </s>

<s>Lo Ste­<lb></lb>none, per meglio confermare e illustrare le osservazioni fatte dagli amici <lb></lb>intorno all&#039;origine degli animali dall&#039;uovo, si dette a sezionar varie specie <lb></lb>di vivipari, e in render conto, innanzi all&#039;Accademia medica di Koppena­<lb></lb>ghen, dell&#039;esito de&#039;suoi studii, fu primo a chiamare i testicoli femminili <lb></lb><emph type="italics"></emph>ovari<emph.end type="italics"></emph.end> e le tube falloppiane <emph type="italics"></emph>ovidutti.<emph.end type="italics"></emph.end> “ Ovi autem nomine intelligo, non <lb></lb>modo rotundas vesiculas humore plenas, testiculorum magnam partem consti­<lb></lb>tuentes, sed et chorion cum omnibus suis contentis. </s>

<s>Utor plerumque ter-<pb xlink:href="020/01/1512.jpg" pagenum="387"></pb>minis solitis, per testiculos faemellarum ovaria, per tubas cornuaque et ute­<lb></lb>ros oviductus intelligo ” (Observationes anat. </s>

<s>in Mangeti biblioth., T. I, <lb></lb>Genevae 1685, pag. </s>

<s>483). Si convengono, soggiunge l&#039;Autore, a quegli or­<lb></lb>gani nomi simili, perchè si rassomigliano perfettamente nelle funzioni. </s>

<s>“ Ova­<lb></lb>ria, scilicet testiculi, dant ovis principium, oviductus autem seu uteri vel <lb></lb>cornua cum tubis dant quidquid requiritur ad perfectum incrementum foe­<lb></lb>tus ” (ibid.). </s></p><p type="main">

<s>La poca diffusione ch&#039;ebbero queste idee, rimaste per alquanto tempo <lb></lb>chiuse nelle sale di un&#039;Accademia, fece sì che altri, forse inconsapevoli di <lb></lb>quel che s&#039;era detto in Danimarca, le annunziassero al pubblico, al cospetto <lb></lb>del quale Giovanni Van-Horne si presentò il primo di tutti. </s>

<s>Pigliando dal­<lb></lb>l&#039;Harveio l&#039;occasione e l&#039;impulso ai suoi nuovi studi, esaminò diligentemente <lb></lb>col microscopio quel che l&#039;Autore <emph type="italics"></emph>De generatione animalium<emph.end type="italics"></emph.end> avea descritto <lb></lb>come una piccola borsa chiusa gettata a caso dentro la cavità dell&#039;utero, e <lb></lb>non esitò a riconoscere cotesto corpicciolo per un uovo propriamente detto, <lb></lb>ritrovandolo simile a una vescichetta rivestita di una pellicola, dalla quale <lb></lb>scaturiva un certo liquido albuminoso. </s>

<s>E giacchè tutto lo persuadeva non <lb></lb>poter essere quell&#039;uovo all&#039;utero nativo, pensava fra sè d&#039;onde mai potes­<lb></lb>s&#039;essere venuto. </s></p><p type="main">

<s>Le vescicole, di che diceva il Falloppio esser composti i <emph type="italics"></emph>testes foemi­<lb></lb>nei,<emph.end type="italics"></emph.end> avendo a sè richiamata l&#039;attenzione del Van-Horne, gli fecero nascere <lb></lb>il sospetto che si fosse staccato di lì il misterioso ovicino embrionale, ma <lb></lb>non vedeva come potess&#039;esser passato alla matrice. </s>

<s>Nelle tube non era al­<lb></lb>cuna speranza di trovar quel veicolo, per queste ragioni: perchè l&#039;infondi­<lb></lb>bulo si credeva chiuso, e i <emph type="italics"></emph>testes<emph.end type="italics"></emph.end> segregati da esso. </s>

<s>Una tal chiusura però <lb></lb>si teneva sulla autorità del Falloppio, il quale, potendosi essere ingannato, <lb></lb>lasciava il fatto a decidersi dalle esperienze. </s>

<s>Il Van-Horne dunque, ammet­<lb></lb>tendo il fiato e iniettando un liquido, trovò che la Tuba era aperta, con che <lb></lb>veniva a togliere alla sua ipotesi la prima e principale delle due difficoltà <lb></lb>sopra dette. </s></p><p type="main">

<s>Rimaneva l&#039;altra, la quale pure o posava o rallentava l&#039;arco, contrappo­<lb></lb>nendole alla mira il confronto fra le Tube, descritte dal Falloppio ne&#039;vivipari, <lb></lb>e le Tube disegnate da Antonio Ulmo nelle tavole dell&#039;Aldovrandi, con questo <lb></lb>stesso nome di <emph type="italics"></emph>Tube<emph.end type="italics"></emph.end> appellate dall&#039;Acquapendente, nel trattar della generazione <lb></lb>ovipara degli Uccelli. </s>

<s>Avendo avuto que&#039;due organi, pensava il Van-Horne, <lb></lb>ne&#039;due varii ordini di animali, nomi uguali dall&#039;arte e figura simile dalla <lb></lb>Natura, perchè non potrebbero dalla stessa Natura essere stati deputati al <lb></lb>medesimo ufficio? </s>

<s>Perchè facendo la Tuba ulmiana da ovidutto non potrebbe <lb></lb>da ovidotto fare ugualmente bene anche la Falloppiana? </s>

<s>Se dall&#039;altra parte <lb></lb>gli organi, che stanno intorno al padiglione de&#039;due varii generi di Tube, <lb></lb>hanno strettissima somiglianza fra loro nella situazione e nella figura, perchè <lb></lb>non converranno insieme nell&#039;essere e nella denominazione di ovaie e di ova? </s>

<s><lb></lb>E se queste cascano, staccate da quelle, dentro l&#039;infondibulo delle tube negli <lb></lb>uccelli, perchè non farebbero il simile nel ventre degli animali superiori? </s></p><pb xlink:href="020/01/1513.jpg" pagenum="388"></pb><p type="main">

<s>Il ragionamento era bello e la conclusione gloriosamente lusinghiera, nè <lb></lb>mancava altro che confortarla di nuove esperienze, e metterla in forma di <lb></lb>trattato. </s>

<s>Mentre a far ciò alacremente attendeva il Van-Horne, giunge in <lb></lb>Leida una lettera stampata, nella quale Regnero De Graaf dava, il dì 20 di <lb></lb>Febbraio del 1668, notizia a Francesco de la Boe Sylvio <emph type="italics"></emph>De nonnullis circa <lb></lb>partes genitales inventis novis.<emph.end type="italics"></emph.end> Il Van-Horne stesso allora, perchè diceva <lb></lb>meglio prevenire ch&#039;esser prevenuti, pubblicò una lettera indirizzata a Guer­<lb></lb>nero Rolfinck, la quale era come il Prodromo al trattato sulla struttura degli <lb></lb>organi ne&#039;due sessi, e sul sistema della generazione, che da lungo tempo <lb></lb>fra sè meditava. </s>

<s>Fra le varie cose in quel Prodromo annunziate la più ru­<lb></lb>morosamente nuova era quella delle ovaie muliebri sostituite agli antichi <lb></lb>testicoli, i quali non sono inutili organi, come l&#039;Hoffman seguendo l&#039;Harveio, <lb></lb>nel cap. </s>

<s>XLIV del II libro delle Istituzioni insegna, “ imo ab ipsis totum <lb></lb>generationis opus materiale dependet: quod enim est ovarium in oviparis, <lb></lb>sunt testes muliebres, utpote qui perfecta ova intra se contineant ” (Inter <lb></lb>opera omnia Regneri de Graaf, Lugd. </s>

<s>Batav. </s>

<s>1677, pag. </s>

<s>439). E soggiunge <lb></lb>che son quest&#039;uova ne&#039;loro ovarii fecondate dall&#039;umor virile, il quale giunge <lb></lb>dalla matrice infin là attraverso alle Tube falloppiane. </s></p><p type="main">

<s>Lette queste cose il Graaf, divulgò in quel medesimo anno 1668 per <lb></lb>le stampe, e dispensò fra gli amici il suo trattato <emph type="italics"></emph>De virorum organis ge­<lb></lb>nerationi inservientibus,<emph.end type="italics"></emph.end> nella prefazione al quale confutava la descrizione <lb></lb>horniana dell&#039;arteria spermatica, dicendo ch&#039;ella procede a diritto, e non si <lb></lb>contorce in sè stessa a formare il Corpo piramidale. </s>

<s>“ Quibus clariss. </s>

<s>Van­<lb></lb>Horne, racconta il Graaf stesso, per annum quo supervixit et dimidium, licet <lb></lb>ab aliis professoribus atque medicis aliquoties rogatus, nihil omnino respon­<lb></lb>dit. </s>

<s>Interea temporis, quantum per otium mihi licuit, mulierum organa ge­<lb></lb>nerationi inserventia, maiori quam ante diligentia, examini subieci, nec non <lb></lb>figuras aliquas delineare coepi, quarum primarias anno 1670 Swammerdamio <lb></lb>me invisenti amice demonstravi, cui figurae illae ita placuerunt, ut anno 1671 <lb></lb>me ad divulgandas adhortaretur ” (Partium genit. </s>

<s>Defensio, Op. </s>

<s>omnia cit, <lb></lb>pag. </s>

<s>441, 42). </s></p><p type="main">

<s>Premessa infatti un&#039;Epistola a Luca Schacht, sottoscritta il dì 30 Mag­<lb></lb>gio 1671, usciva alla luce in Leida l&#039;anno dopo il trattato nuovo <emph type="italics"></emph>De mu­<lb></lb>lierum organis generationi inservientibus,<emph.end type="italics"></emph.end> nel quale a dir vero, rispetto alla <lb></lb>generazione dell&#039;uomo dall&#039;uovo, niente altro fa il Graaf ch&#039;esplicare e con­<lb></lb>fermare i concetti del Van-Horne. </s>

<s>Dal Prodromo di lui confessa di volere <lb></lb>accettare le denominazioni di uova date agli organi muliebri (Op. </s>

<s>omnia cit., <lb></lb>pag. </s>

<s>298), e così conclude, in sentenza dello stesso Van-Horne: “ Commu­<lb></lb>nis itaque foemellarum testiculorum usus est generare, fovere et ad matu­<lb></lb>ritatem promovere, sic ut in mulieribus eodem quo volucrum ovario mu­<lb></lb>nere fungantur ” (ibid., pag. </s>

<s>302). </s></p><p type="main">

<s>Quell&#039;argomento d&#039;analogia, che aveva condotto il Van-Horne ad am­<lb></lb>mettere la possibilità non solo, ma la natural facilità nell&#039;uova muliebri di <lb></lb>cader nelle tube falloppiane, a quel modo che l&#039;uova delle galline cadono <pb xlink:href="020/01/1514.jpg" pagenum="389"></pb>nelle tube ulmiane; è quello stesso argomento che alle asserzioni del Graaf <lb></lb>dà valore. </s>

<s>“ Quod tanto liberius asserimus, cum in variis quadrupedibus <lb></lb>extremam tubarum expansionem eiuscemodi, ut oviductus infundibulum, <lb></lb>quod in avibus vitellos excipit, efformatam offenderimus ” (ibid., pag. </s>

<s>351). </s></p><p type="main">

<s>Il Prodromo horniano prometteva che nella trattazione distesa si sa­<lb></lb>rebbe non solo spiegato <emph type="italics"></emph>quomodo haec ova intra uterum suscipiantur,<emph.end type="italics"></emph.end> ma <lb></lb>come altresì vengano attuate <emph type="italics"></emph>a semine virili<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>439). Ma perchè <lb></lb>per la sua crassizie non pareva ad alcuni possibile che, almeno in ogni caso, <lb></lb>il viril seme risalisse su per le tube, s&#039;argomentò il Graaf di togliere la <lb></lb>difficoltà col dire che non era punto necessario “ quod semen ipsum ad <lb></lb>uterum aut tubas ascendat, sed sufficere quod seminalis aura, illa loca per­<lb></lb>transeundo, ad testiculorum ova pertingat ” (ibid., pag. </s>

<s>346). </s></p><p type="main">

<s>Benchè sia questo il tradizional magistero delle dottrine antropogeni­<lb></lb>che esposte dal Graaf, ei si studiò nonostante di dare a loro tal forma, da <lb></lb>farle apparir per la massima parte originali. </s>

<s>Ma lo Swammerdam d&#039;amico <lb></lb>per rivalità e per invidia divenuto nemico, pubblicando pochi mesi dopo il <lb></lb>suo <emph type="italics"></emph>Miraculum naturae, seu uteri muliebris fabrica,<emph.end type="italics"></emph.end> dimostrava che nel <lb></lb>trattato del Graaf non era parte, che non avesse tolta a sè, al Van-Horne, <lb></lb>e prima che a loro due allo Stenone. </s>

<s>Di che il pover uomo, o si credesse <lb></lb>scoperto in fallo o calunniato, nonostante la difesa fatta innanzi alla grande <lb></lb>Società regia anglicana, provò tanto accoramento, che dicono ne morisse. </s></p><p type="main">

<s>Comunque sia le speculate teorie e le istituite esperienze intorno al­<lb></lb>l&#039;oviparismo dell&#039;uomo e degli animali affini pervennero d&#039;oltremonti in <lb></lb>Italia, per mezzo del <emph type="italics"></emph>Trattato nuovo<emph.end type="italics"></emph.end> del Graaf dedicato al granduca Co­<lb></lb>simo III di Toscana. </s>

<s>I Nostri, che riconobbero nelle dottrine straniere lo <lb></lb>svolgimento di que&#039;germi posti nella scienza embriologica dagli avi, non re­<lb></lb>luttarono alle novità, ma le vollero sottoporre a un più diligente esame. </s>

<s>Il <lb></lb>Malpighi scelse per soggetto di quell&#039;esame gli organi delle vacche, e non <lb></lb>dubitò di qualificare per vere ovaie quelle “ quae, come dice nella sua Dis­<lb></lb>sertazione epistolica di vario argomento a Giacomo Spon, antiquitus testes <lb></lb>censebantur ” (Operum, T. II, Lugd. </s>

<s>Batav. </s>

<s>1787, pag. </s>

<s>202). “ In vaccis, <lb></lb>soggiunge, in quibus ampla et manifesta extant, obducta membrana fibris <lb></lb>carneis firmata, ambiuntur. </s>

<s>Qua ratione ovum ab ovario emergat et in Tu­<lb></lb>bas transducatur, solicita multaque eget indagine. </s>

<s>Quae tamen ex fortuitis <lb></lb>ovarii in vaccis lustrationibus colligere potui tibi brevibus aperiam ” (ibid.). <lb></lb>E l&#039;esposizione che segue è una delle più sapienti illustrazioni, e delle più <lb></lb>autorevoli conferme del sistema degli Ovaristi. </s>

<s>Il Redi pure concorreva nel <lb></lb>medesimo effetto, sperimentando che poste a bollire nell&#039;acqua si conden­<lb></lb>sano e si rappigliano quell&#039;uova, che si trovano ne&#039;testicoli femminili o <lb></lb>ovaie de&#039;quadrupedi “ conforme, egli scrive nel trattato <emph type="italics"></emph>Degli animali vi­<lb></lb>venti negli animali viventi,<emph.end type="italics"></emph.end> ho osservato nelle uova delle leonesse, dell&#039;orse, <lb></lb>delle vacche, delle bufale, dell&#039;asine, delle daine, delle cerve e di altri ani­<lb></lb>mali quadrupedi ” (Opere, T. I, Napoli 1741, pag. </s>

<s>74). </s></p><p type="main">

<s>Del resto esso Redi, benchè non componesse in tal soggetto un trattato <pb xlink:href="020/01/1515.jpg" pagenum="390"></pb>disteso, ne toccò qua e là ne&#039;suoi scritti in modo, da illustrare con argo­<lb></lb>menti, e da confermare, con esperienze nuove allo stesso Graaf, i concetti <lb></lb>horniani. </s>

<s>Teodoro Kerkring nella sua <emph type="italics"></emph>Antropogenia iconografica,<emph.end type="italics"></emph.end> pubblicata <lb></lb>in Amsterdam nel 1671, approvava e difendeva la generazione umana dal­<lb></lb>l&#039;uovo, ma sosteneva che fanno da ovidutti i vasi deferenti degli antichi, e <lb></lb>no le tube del Falloppio. </s>

<s>“ Non son uomo, entra qui a dire il Redi, da po­<lb></lb>ter dar sentenze, ma se a me toccasse di far la parte di giudice, sentenzie­<lb></lb>rei a favore delle Tube falloppiane. </s>

<s>E per dar fuora di ciò i motivi, dico che <lb></lb>nel fondo della cavità interna dell&#039;utero non sono se non due soli forami <lb></lb>aperti, per i quali si possa introdurre uno stile o una tenta, e questi forami <lb></lb>riescono nelle Tube falloppiane, sicchè, introdotto per essi forami lo stile, <lb></lb>ei passa nelle Tube, e pel contrario, introdotto lo stile nelle Tube, penetra <lb></lb>per essi forami nella cavità dell&#039;utero. </s>

<s>Inoltre, gonfiato l&#039;utero con uno <lb></lb>schizzatoio a vento, si gonfiano ancora le Tube falloppiane, e si vede uscir <lb></lb>l&#039;aria per l&#039;apertura che è in quella parte, che confina co&#039;testicoli femmi­<lb></lb>nili, ovvero ovaie ” (Lettere nel T. IV dell&#039;Opere cit., pag. </s>

<s>63, 64). </s></p><p type="main">

<s>Alla gran difficoltà promossa dal Falloppio, e che nasceva dal non aver <lb></lb>mai potuto veder le Tube <emph type="italics"></emph>coniunctas cum testibus,<emph.end type="italics"></emph.end> rispondeva il Graaf che <lb></lb>simile si osserva negli uccelli, ma il Redi notava di più che quella congiun­<lb></lb>zione si fa ne&#039;quadrupedi mediante una certa espansione membranosa del­<lb></lb>l&#039;infondibulo della stessa Tuba; espansione che nella donna è sostituita “ da <lb></lb>certe fimbrie intagliate a guisa di foglie, onde l&#039;uovo maturo e fecondo, <lb></lb>mentre è cascato fuor dell&#039;ovaia tra le pieghe di queste fimbrie, va ad en­<lb></lb>trare nell&#039;ovidutto ” (Istorie mediche, nel T. VI dell&#039;Op. </s>

<s>cit., pag. </s>

<s>142). </s></p><p type="main">

<s>L&#039;ovarismo poi tutto intero nel suo sistema veniva dallo stesso elegan­<lb></lb>tissimo Redi esposto agl&#039;Italiani in questa forma: “ Le uova della donna <lb></lb>non si formano nell&#039;utero, ma si formano e si conservano nelle proprie e <lb></lb>determinate ovaie, le quali dagli antichi Notomisti fu creduto che fossero i <lb></lb>testicoli femminili. </s>

<s>Congiungendosi insieme, passa il seme del maschio ad <lb></lb>imbrattare le pareti uterine, e da questo imbrattamento si solleva un&#039;aura <lb></lb>seminale, o uno spirito fecondatore, il quale, penetrando per li canali delle <lb></lb>Tube falloppiane, trapassa all&#039;ovaia, e quivi feconda e galla un uovo e tal­<lb></lb>volta più d&#039;uno. </s>

<s>L&#039;uovo fecondato e gallato si stacca dall&#039;ovaia, ed entrando <lb></lb>poscia per quel forame, che è nell&#039;estremità più larga delle Tube fallop­<lb></lb>piane, spinto dal moto peristaltico di esse Tube, se ne cala giù pel loro ca­<lb></lb>nale, ed entra nelle cavità dall&#039;utero, e quivi s&#039;inzuppa di quel liquore. </s>

<s>Da <lb></lb>tale inzuppamento, crescendo l&#039;uovo, si comincia nell&#039;interna sua cavità a <lb></lb>formare il fanciullo ” (Consulti medici, T. VI cit., pag. </s>

<s>80, 81). </s></p><p type="main">

<s>Nonostante, non mancarono molti, più forse fra gli stranieri che fra&#039;no­<lb></lb>stri, i quali, adombrando ad ogni novità, ripetevano, per mantenere gli or­<lb></lb>dini antichi, che le femmine secernono di fatto il loro umor seminale, nel­<lb></lb>l&#039;atto stesso che concorrono all&#039;opera della generazione. </s>

<s>Non curando punto <lb></lb>costoro nè le osservazioni anatomiche del Falloppio, nè le sensate esperienze <lb></lb>dell&#039;Harveio, si facevano forti dell&#039;autorità dì Galeno, confermata da tanti <pb xlink:href="020/01/1516.jpg" pagenum="391"></pb>insigni anatomici più recenti, quali erano il Fernelio, il Varolio, il Laurent <lb></lb>e sopra tutto il gran Riolano. </s>

<s>Ma il Redi, che leggeva il libro della Natura <lb></lb>piuttosto che quelli degli uomini, sgombrava de&#039;loro ostinati errori alla <lb></lb>scienza, così scrivendo, i sentieri: “ Quanto poi a&#039;vasi deferentì degli An­<lb></lb>tichi, pe&#039;quali essi credevano che il seme femminile scendesse nell&#039;utero, <lb></lb>io me ne rimetto all&#039;esperienza se sieno <emph type="italics"></emph>in rerum natura<emph.end type="italics"></emph.end> o se non sieno; <lb></lb>se sieno aperti e scanalati, oppure se sieno solidi. </s>

<s>Io so bene che Galeno <lb></lb>fu il primo che fece menzione di questi vasi deferenti, e scrisse che ave­<lb></lb>vano un ramo solo, il quale metteva capo nel fondo dell&#039;utero. </s>

<s>Dopo di Ga­<lb></lb>leno il Fernelio e il Laurenzio, l&#039;Higmoro, il Plagzonio e il Varolio dissero <lb></lb>che non un sol ramo ma due ve ne avea, uno de&#039;quali andava, come disse <lb></lb>Galeno, a scaricarsi nel fondo dell&#039;utero, e l&#039;altro nel collo o nella imboc­<lb></lb>catura di esso utero. </s>

<s>Per quel ramo, che metteva capo nel fondo dell&#039;utero, <lb></lb>crederono ch&#039;entrasse nell&#039;utero il seme delle donne non gravide, per quel <lb></lb>ramo, che imboccava nel collo dell&#039;utero, crederono ch&#039;entrasse e si spar­<lb></lb>gesse il seme delle donne gravide. </s>

<s>Or vengane per terzo Rodomonte, e que­<lb></lb>sto Rodomonte sia il famoso dottissimo Riolano, il quale, oltre i due sud­<lb></lb>detti rami de&#039;vasi deferenti, ne volle inventare ancora un altro, che fosse <lb></lb>il terzo, ma io però non ho mai saputo vedere queste ramificazioni, e se <lb></lb>pure per disgrazia vi fossero, dico che non sono vasi deferenti, nè possono <lb></lb>introdurre cosa solida dentro la cavità dell&#039;utero, perch&#039;essi non vi pene­<lb></lb>trano e non v&#039;imboccano, e questa cosa consta di fatto ” (Lettere, T. IV <lb></lb>dell&#039;Op. </s>

<s>cit., pag. </s>

<s>64). </s></p><p type="main">

<s>Ma perchè pur costava di fatto la secrezione di quell&#039;umor femmineo, <lb></lb>si domandava dunque da che avesse origine, se non scendeva dagli organi <lb></lb>seminali. </s>

<s>Il Van-Horne aveva detto nel suo Prodromo che scaturiva cotesto <lb></lb>umore “ ex ipsa glandulosa osculi uteri interni substantia, per multos mi­<lb></lb>nutosque meatus ” (loco cit., pag. </s>

<s>439); meati più diligentemente descritti <lb></lb>dal Graaf, in fine al cap. </s>

<s>XIII <emph type="italics"></emph>De mulierum organis.<emph.end type="italics"></emph.end> Il Diemerbroeck no­<lb></lb>nostante non ne restava capace, e a Gasparo Bartholin, figlio di Tommaso, <lb></lb>dimostratore zelante dell&#039;uova muliebri in Coppenaghen, in Leida, in Parigi, <lb></lb>in Firenze e in Roma, proponeva i suoi dubbi. </s>

<s>Il Bartholin gli riconobbe <lb></lb>non irragionevoli, perchè veramente i dutti cechi descritti dal Graaf al com­<lb></lb>messo ufficio non parevano sufficienti. </s>

<s>Datosi dunque a un più diligente <lb></lb>esame anatomico sopra le vacche, ritrovò che “ ad latera vaginae, non pro­<lb></lb>cul ab urethrae exitu, utrinque glandula insignis canalem emittit, qui conspi­<lb></lb>cuo et in papilla, quando premitur glandula, protuberante ostio intra vul­<lb></lb>vam, aperitur ” (De ovariis mulierum, Florentiae 1700, pag. </s>

<s>18). È da questa <lb></lb>ghiandola compressa da certe fibre carnose, che si costringono <emph type="italics"></emph>in actu ve­<lb></lb>nereo,<emph.end type="italics"></emph.end> dimostrò che scaturisce l&#039;umor vaginale. </s></p><p type="main">

<s>Pareva così l&#039;Ovarismo rimasto de&#039;suoi nemici nella scienza embriolo­<lb></lb>gica vittorioso, quando una strana inaspettata scoperta venne a dargli nuovo <lb></lb>e valido assalto. </s>

<s>Antonio Leuwenoeck, appuntando un giorno un suo squi­<lb></lb>sitissimo microscopio sopra il seme maschile, ebbe a restar maravigliato di <pb xlink:href="020/01/1517.jpg" pagenum="392"></pb>vedervi dentro guizzar vivacissime innumerevoli anguillette “ cuius delinea­<lb></lb>tionem, scrisse in una di quelle lettere, di che compilasi la <emph type="italics"></emph>Continuatio ar­<lb></lb>canorum Naturae,<emph.end type="italics"></emph.end> ego anno 1677 ad regiam Societatem londinensem misi, <lb></lb>quamque celeberrimi eius Collegii socii aeri incidi fecerunt, ac, cum aliquot <lb></lb>ex litevis meis excerptis, latino idiomata, inter Acta philosophica no 141, <lb></lb>pag. </s>

<s>1049 orbi erudito communicarunt, atque illic fig. </s>

<s>II et III exhibue­<lb></lb>runt ” (Lugd. </s>

<s>Batav. </s>

<s>1722, pag. </s>

<s>22). </s></p><p type="main">

<s>Prima però di darne formale notizia alla Società di Londra, aveva pri­<lb></lb>vatamente fatto vedere il Leuwenoeck gli animalucci spermatici a Cristiano <lb></lb>Huyghens, il quale, da quel gran filosofo ch&#039;egli era, pensò che dovessero <lb></lb>avere un ufficio importantissimo nell&#039;opera della generazione. </s>

<s>Esprimeva <lb></lb>così i suoi pensieri, nel riferir la nuova scoperta olandese ai colleghi suoi <lb></lb>Accademici parigini: “ Quae in animalium semine deteguntur, translucida <lb></lb>omnia sunt, celerrime moventur, et ranis, antequam horum pedes formen­<lb></lb>tur, similia sunt. </s>

<s>Haec animalcula in Hollandia primum fuere observata, et <lb></lb>horum inventio admodum mihi utilis videtur, et quae opus suppeditabit <lb></lb>illis, qui in animalium genesim inquirunt ” (Opera varia, Lugd. </s>

<s>Batav., <lb></lb>T. IV, 1724, pag. </s>

<s>765). </s></p><p type="main">

<s>Ripensando poi l&#039;Huyghens in che consistesse quella particolare utilità, <lb></lb>non dubitò di credere che gli spermatozoi entrassero nell&#039;uova delle fem­<lb></lb>mine, per costituire al nascituro gl&#039;inizi. </s>

<s>Esponeva questa sua ipotesi, che <lb></lb>gli arrideva in aria di certezza, nella Diottrica, là dove, trattando del Mi­<lb></lb>croscopio e delle applicazioni di lui, così dice accennando alla scoperta delle <lb></lb>anguillette seminali: “ quae animalcula intrare ova faeminarum, atque esse <lb></lb>ipsorum animalium inde excludendorum initia, vix mihi dubitandum vide­<lb></lb>tur ” (Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>228). </s></p><p type="main">

<s>L&#039;ipotesi erasi divulgata dalla viva voce, prima che per le stampe; e <lb></lb>perchè la persona dell&#039;Huyghens non appariva, s&#039;attribuì al Leuwenoeck e <lb></lb>si disse che voleva sostituirla all&#039;Ovarismo. </s>

<s>Le idee, che venivano a dare <lb></lb>tanta importanza alla scoperta, furono accolte non solo, ma applaudite dal­<lb></lb>l&#039;Autore di essa scoperta, il quale non le aveva però ancora professate in <lb></lb>pubblico, come pareva volesse far credere uno scrittore. </s>

<s>“ Est liber, son pa­<lb></lb>role dello stesso Leuwenoeck, in quo notor quasi eo tempore (nell&#039;anno 1677) <lb></lb>iam statuissem ex animalculo seminis virilis oriri hominem, cum tamen e <lb></lb>contrario meam circa eam rem sententiam nunquam aperuerim ” (Arcana <lb></lb>Naturae detecta, Lugd. </s>

<s>Batav. </s>

<s>1722, pag. </s>

<s>27). </s></p><p type="main">

<s>Perchè potesse la nuova ipotesi prevalere sull&#039;ovarismo, sentiva l&#039;Au­<lb></lb>tore degli scoperti arcani della Natura il bisogno di dimostrare che anche <lb></lb>gli spermazoi, come l&#039;uova, costituiscono gl&#039;inizii alla generazione d&#039;ogni <lb></lb>sorta d&#039;animali. </s>

<s>A un&#039;altra curiosità si voleva che sodisfacesse la scienza, <lb></lb>ed era quella d&#039;assegnar l&#039;origine de&#039;due sessi. </s>

<s>Il Falloppio, dimostrando <lb></lb>che tutte le membra del maschio si contengono nella femmina, non eccet­<lb></lb>tuati i muscoli sospensori del pene, e che tutte le parti della femmina si con­<lb></lb>tengon nel maschio, non eccettuate le mammelle, porgeva il più ragionevole <pb xlink:href="020/01/1518.jpg" pagenum="393"></pb>modo di sodisfare alla curiosità, ammettendo per verosimile che si dispon­<lb></lb>gano le parti nell&#039;embrione secondo un certo dimorfismo, cosicchè la fem­<lb></lb>mina venga quasi ad essere un&#039;allotropia del maschio. </s>

<s>Ma perchè molti ri­<lb></lb>ducevano le osservazioni del Falloppio a quelle del Berengario, il quale <lb></lb>anch&#039;egli diceva esser le membra a&#039;due sessi comuni “ sed membra viro­<lb></lb>rum sunt completa extra.... foeminarum vero sunt diminuta intra ” (Isa­<lb></lb>gogae cit., fol. </s>

<s>20 ad t.), d&#039;onde venivasi a confermar l&#039;esistenza de&#039;testi­<lb></lb>coli femminili; gli Ovaristi, scansando il pericoloso incontro, si contentaron <lb></lb>di dire altre essere uova di femmine, altre di maschi. </s>

<s>Il Leuwenoeck voleva <lb></lb>poter dir questo stesso delle anguillette, e perchè le due ipotesi non solo <lb></lb>concorressero insieme, ma l&#039;una potesse prevalere sull&#039;altra, sentiva il bi­<lb></lb>sogno di mostrar in quelle stesse anguillette qualche manifesto indizio delle <lb></lb>varietà sessuali. </s>

<s>Avendo perciò ritrovato veramente il medesìmo brulicare <lb></lb>anguifero in tutti i semi, e lusingandosi d&#039;aver notati in un medesimo seme <lb></lb>due generi d&#039;animali diversi, credè il Leuwenoeck che fosse venuto il tempo <lb></lb>di potere apertamente professare quella ipotesi ugeniana, che veniva a pro­<lb></lb>movere tant&#039;alto la sua scoperta. </s>

<s>“ Sed iam, ubi etiam in seminibus mascu­<lb></lb>linis animalium quadrupedum, avium, piscium, imo etiam insectorum repe­<lb></lb>rio animalcula, multo certius statuo quam antea hominem, non ex ovo sed <lb></lb>ex animalculo in semine virili contento oriri, ac praesertim cum reminiscor <lb></lb>me in semine masculino hominis, et etiam canis, vidisse duorum generum <lb></lb>animalcula. </s>

<s>Hoc videns, mihi imaginabar alterum genus mares, alterum foe­<lb></lb>minas esse ” (Arcana Naturae cit., pag. </s>

<s>27, 28). </s></p><p type="main">

<s>E perchè non sembrasse esser dall&#039;amor proprio, piuttosto che dal­<lb></lb>l&#039;amore del vero, condotto a far nell&#039;Embriologia questa innovazione, diceva <lb></lb>il Leuwenoeck non si poter persuadere che sia l&#039;uovo attratto e tradotto <lb></lb>per le Tube falloppiane sì anguste. </s>

<s>“ Credere non possum Tubam fallop­<lb></lb>pianam ovum ab ovario posse exsugere sive trahere, ac illud traducere per <lb></lb>meatum adeo angustum ” (ibid., pag. </s>

<s>26, 27). Che se alcuno gli avesse do­<lb></lb>mandato a che fine dunque ha la Natura nelle galline e in altri simili ani­<lb></lb>mali disposto l&#039;uovo, rispondeva che a somministrar l&#039;alimento e la materia <lb></lb>necessaria alla formazion del pulcino. </s>

<s>“ Omnem enim illam materiam, quae <lb></lb>in ovis gallinarum aliorumve animalium continetur,.... nulli alii fini in­<lb></lb>servire censeo, quam alendo intra ovum galli gallinacei semini eique in pul­<lb></lb>lum formando “ (ibid., pag. </s>

<s>66). </s></p><p type="main">

<s>Gli Ovaristi non videro migliore argomento per rifiutare la nuova ipo­<lb></lb>tesi che negar l&#039;esistenza de&#039;vermicelli spermatici, ma il Leuwenoeck rispose <lb></lb>francamente ad essi che tutto dipendeva dal non averli saputi vedere, non <lb></lb>conoscendo nè la fabbrica nè l&#039;uso de&#039;Microscopii, e un nostro illustre Na­<lb></lb>turalista ebbe a confessare che il Micrografo olandese così dicendo aveva ra­<lb></lb>gione. </s>

<s>“ Anch&#039;io candidamente confesso, scriveva il Vallisnieri a proposito <lb></lb>degli spermatozoi, sono stato lungo tempo ostinato nel non volergli conce­<lb></lb>dere.... ma quando ebbi la sorte d&#039;avere ordigni, a tali fini fabbricati da <lb></lb>peritissime mani maestre, i quali con evidenza veder me gli fecero, non <pb xlink:href="020/01/1519.jpg" pagenum="394"></pb>ebbi vergogna nè ribrezzo alcuno di mutare consiglio ” (Istoria della gene­<lb></lb>razione dell&#039;uomo e degli animali, Venezia 1721, pag. </s>

<s>48). </s></p><p type="main">

<s>Benchè però il Vallisnieri vedesse così distintamente que&#039;vermi, da non <lb></lb>poter negarne in verità l&#039;esistenza, non approvava che fossero gl&#039;inizi fetali <lb></lb>del nascituro. </s>

<s>Gli pareva che l&#039;Ovarismo fosse bene oramai dimostrato dalle <lb></lb>osservazioni dell&#039;Aldovrandi, dell&#039;Acquapendente e dell&#039;Harvey, le quali ve­<lb></lb>nivano ad aver la più solenne e autorevole conferma dalla sentenza del Mal­<lb></lb>pighi: “ pulli stamina in ovo praeesistere ” (De formatione pulli in ovo, <lb></lb>Operum T. II, Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>54). Il fatto però non riguardava che <lb></lb>sole le ova fecondate, ma il Malpighi stesso volle anche di più esamìnar le <lb></lb>parti, che si offerissero a notar nelle suvventanee, e trovò che, non molto <lb></lb>lungi dal centro, “ globòsum candidumque corpus, seu cinereum, quasi mola <lb></lb>locabatur, quod laceratum nullum peculiare exhibebat corpus a se diversum. </s>

<s><lb></lb>Appendices reticulares habebat, quarum spatia diversas referebant figuras, <lb></lb>non raro ovales, diaphanoque replebantur colliquamento; denique tota haec <lb></lb>moles, iridis instar, plurimis circumdabatur circulis ” (ibid.). D&#039;onde ragio­<lb></lb>nevolmente argomentava così il Vallisnieri: “ Se il verme spermatico deve <lb></lb>entrare nella cicatrice, e non far altro se non crescere e manifestarsi, a qual <lb></lb>fine ci è quel <emph type="italics"></emph>corpo globoso e candido o cinereo, quasi mola,<emph.end type="italics"></emph.end> con tutto <lb></lb>quell&#039;altro grande apparato d&#039;intorno che vien descritto? </s>

<s>Bastava un sem­<lb></lb>plice e puro sacchetto con un poco di liquore, dove avesse potuto spogliarsi <lb></lb>e nuotare. </s>

<s>Ma quel <emph type="italics"></emph>quasi mola,<emph.end type="italics"></emph.end> con tutti gli altri ordigni circondatori, mo­<lb></lb>stra che in quella fosse il feto, di fibre ancor diafane e dilicatissime com­<lb></lb>posto, che aspettasse il moto e l&#039;ultimo sviluppo dallo spirito del maschil <lb></lb>seme ” (Istoria della generaz. </s>

<s>cit., pag. </s>

<s>81). </s></p><p type="main">

<s>In queste parole del Vallisnieri si conclude la verità scoperta per l&#039;espe­<lb></lb>rienza, ma prudentemente lasciata tuttavia sotto un velo di naturale mistero. </s>

<s><lb></lb>Filosofi più audaci pretesero di spiegare in che modo il maschil seme opera <lb></lb>sull&#039;uovo, e non riuscendovi ricorsero a una virtù attiva insita nella Na­<lb></lb>tura, per la quale si plasmano gl&#039;inizii fetali, che nell&#039;utero della madre ri­<lb></lb>cevono poi gl&#039;incrementi. </s>

<s>Fondavano la loro ipotesi sopra l&#039;esperienze de­<lb></lb>gl&#039;infusorii, ma lo Spallanzani, nel suo <emph type="italics"></emph>Saggio di osservazioni microscopiche <lb></lb>concernenti il sistema della generazione dei signori di Needham e Buffon,<emph.end type="italics"></emph.end><lb></lb>dimostrò che quelli animalucci non hanno origine dalla virtù vegetatrice <lb></lb>della Natura, ma da&#039;germi, che altri simili animalucci avevano prima de­<lb></lb>posti nelle varie materie assoggettate alle infusioni. </s>

<s>Così rimase nel suo più <lb></lb>sincero splendore, a scorta dell&#039;Embriologia, la sentenza del Malpighi, che <lb></lb>cioè gli stami del pulcino e di ogni altro animale preesistan nell&#039;uovo, da <lb></lb>cui si svolgono in virtù dell&#039;atto fecondatore a noi misterioso. </s></p><pb xlink:href="020/01/1520.jpg" pagenum="395"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;ipotesi del Needham ora commemorata si posava sul fondamento che <lb></lb>gl&#039;infusorii, e con essi anche i vermi spermatici, fossero veri e proprii ani­<lb></lb>mali. </s>

<s>Lo Spallanzani perciò, nell&#039;istituire le sue microscopiche esperienze <lb></lb>col fine di confutar quella ipotesi, ebbe prima a decidere della supposta ani­<lb></lb>malità, ch&#039;egli pure si persuase esser manifesta da certi atti, in apparenza <lb></lb>instintivi, e da certi moti che mostravano d&#039;essere spontanei. </s>

<s>“ Quel pren­<lb></lb>der di mira, egli dice, e dolcemente ferire co&#039;loro beccucci le briciole dei <lb></lb>vegetabili disperse nelle infusioni; quel raccogliersi mancando il fluido e <lb></lb>unirsi in calca, dove questo più tardi finisce; quel passar dalla quiete a un <lb></lb>movimento veloce, senza apparenza di corpi, che ne li sospingano e caccino; <lb></lb>quell&#039;andar tante volte al contrario della corrente; quel saper così bene schi­<lb></lb>far sè stessi, non meno nell&#039;affacciarsi, che gli ostanti imbarazzi che incon­<lb></lb>tran per via; quel finalmente variar d&#039;improvviso di direzione e determi­<lb></lb>narsi ad opposito movimento, sono tutti segnali manifestissimi ed innegabili <lb></lb>di un tal principio animale ” (Dissertaz. </s>

<s>varie, T. II, Milano 1826, pag. </s>

<s>275). </s></p><p type="main">

<s>Forse lo Spallanzani s&#039;ingannava, non sospettando che la luce e l&#039;elet­<lb></lb>tricità, per tacere di altri più materiali e incomputabili agenti, possono con <lb></lb>minimo momento turbar così l&#039;equilibrio di quell&#039;esigue particelle solide <lb></lb>sospese in mezzo al liquido, da farle facilmente credere animate, ma in ogni <lb></lb>modo è il moto per noi il più sicuro argomento della vita. </s>

<s>Le questioni <lb></lb>sarebbero state fra&#039;Micrografi senza dubbio decise, quando fossesi potuto di­<lb></lb>mostrare che le lunghe code degli infusorii son, come ne&#039;pesci, organi della <lb></lb>locomozione, ma rimarrebbe anche così tuttavia incerto se dipenda il vivace <lb></lb>guizzar d&#039;esse code da intrinseca attività, o piuttosto da esterno impulso. </s>

<s><lb></lb>Per la final decisione in ogni modo sarebbe convenuto dimostrar la ragione <lb></lb>di un tal moto, coniugando la Fisiologia alla Meccanica, come si fa del re­<lb></lb>sto rispetto agli animali degli ordini superiori, che in grazia del moto locale <lb></lb>hanno apposite e distinte membra. </s>

<s>Ma pure nell&#039;esercizio di queste rimase <lb></lb>quella ragion meccanica per lungo tempo oscura e involta nell&#039;errore, come <lb></lb>apparirà dalla seguente storia, la quale, limitandosi per ora al passo de&#039;qua­<lb></lb>drupedi e al volo degli uccelli, dispone intanto gl&#039;ingegni a riconoscere nelle <lb></lb>inaspettate difficoltà quelli, che in esseri semoventi e d&#039;invisibili membra, <lb></lb>alla lusingata scienza dell&#039;uomo torneranno misteri. </s></p><p type="main">

<s>Della meccanica del passo nessuno frà gli Antichi aveva fatto il soggetto <lb></lb>a filosofiche speculazioni prima di Aristotile, il quale ci lasciò fra le Opere <lb></lb>un trattatello intitolato <emph type="italics"></emph>De animalium incessu.<emph.end type="italics"></emph.end> Proponendosi nel cap. </s>

<s>XII <lb></lb>d&#039;insegnare in che modo si faccia l&#039;incesso de&#039;quadrupedi, non dubitò di <lb></lb>affermare che i piedi s&#039;incrociano così, che al destro posteriore corrisponde <lb></lb>sempre, e nella quiete e nel moto, il sinistro anteriore, e un tale alternato <pb xlink:href="020/01/1521.jpg" pagenum="396"></pb>metro osservano gli altri due. </s>

<s>“ Moventur autem posteriora ad priora per <lb></lb>diametrum: post enim dextrum prius, sinistrum movet posterius. </s>

<s>Ita sini­<lb></lb>strum prius, post illud autem dextrum posterius ” (Tomus VI, Oper., Ve­<lb></lb>netiis 1560, fol. </s>

<s>277). </s></p><p type="main">

<s>Se questo gioco veramente riscontri coll&#039;esperienza è inutile fatica al <lb></lb>Filosofo l&#039;investigarlo, non potendo essere altrimenti da quel che la ragione <lb></lb>prescrive alla Natura. </s>

<s>Imperocchè, se non per la diagonale, dice Aristotile, <lb></lb>si facesse l&#039;incesso del quadrupede, ma per i lati del quadrangolo, manche­<lb></lb>rebbe al centro di gravità il suo sostegno, e il moto dell&#039;animale evidente­<lb></lb>mente sarebbe ruinoso. </s>

<s>Il medesimo inconveniente ne seguirebbe, ei sog­<lb></lb>giunge, se movesse insieme i piè d&#039;avanti e poi quelli di dietro. </s>

<s>“ Causa <lb></lb>autem est quoniam, si priora simul et prius, distraheretur sane aut prae­<lb></lb>cidua esset ambulatio.... Si autem utrisque dextris primis, extra sane ful­<lb></lb>crorum fierent sustentacula ” (ibid.). </s></p><p type="main">

<s>Dopo gl&#039;istauramenti della scienza primo a rivolgere le sue speculazioni <lb></lb>sopra questo argomento fu Girolamo Fabricio, il quale, nel suo libro <emph type="italics"></emph>De <lb></lb>motu locali animalium secundum totum,<emph.end type="italics"></emph.end> riserbò a trattar <emph type="italics"></emph>De gressu qua­<lb></lb>drupedum<emph.end type="italics"></emph.end> in particolare poche parole, che ripetevano ai nuovi risvegliati <lb></lb>dal lungo sonno le sentenze dell&#039;antico Aristotile. </s>

<s>“ Fit itaque ambulatio <lb></lb>altero crure ad terram firmato, altero autem translato.... Ex quatuor cru­<lb></lb>ribus bina anteriora dum incedunt ita quidem constitui et moveri ut alte­<lb></lb>rum transferatur, alterum innitatur. </s>

<s>Quo tempore duo posterius posita, et <lb></lb>ipsa quoque idem praestantia, alterum eorum transferatur, alterum innita­<lb></lb>tur, ita tamen ut ei quod transfertur anterius non respondeat ex eodem la­<lb></lb>tere quod posterius est in translatione,.... ita ut ipsius quadranguli dia­<lb></lb>metri sint similes, hoc est crus anterius et posterius nequaquam sibi invi­<lb></lb>cem per latus respondentia, sed tantum inter se vicissim, per diametrum <lb></lb>opposita, similem habeant constitutionem ” (Opera omnia, Lug. </s>

<s>Batav. </s>

<s>1738, <lb></lb>pag. </s>

<s>371). L&#039;Acquapendente però, quasi volesse mostrare di aver anch&#039;egli <lb></lb>risentiti i tepori della nuova stagione, si lusingava di confermar così fatte <lb></lb>dottrine con l&#039;esperienze, le quali, sebbene egli dice esser difficili a farsi, <lb></lb>per la loro celerità, ne&#039;cani e ne&#039;cavalli, “ in testudine id non difficulter <lb></lb>observatur ” (ibid.). </s></p><p type="main">

<s>L&#039;aristotelismo rinnovellato dall&#039;Acquapendente seduceva così gl&#039;inge­<lb></lb>gni, non solamente disposti a mantenere gli ordini antichi, ma liberi nel­<lb></lb>l&#039;accogliere le novità, che s&#039;aggiunge anche questo fra&#039;tanti altri esempii <lb></lb>di quella seduzione, dimostratici dalla storia. </s>

<s>Pier Gassendo restò dalle ra­<lb></lb>gioni di Aristotile, e dall&#039;esperienze dello stesso Acquapendente, così ben <lb></lb>persuaso moversi i piè dei quadrupedi, per usar le sue proprie parole, <emph type="italics"></emph>com­<lb></lb>mutatione in crucem facta,<emph.end type="italics"></emph.end> che stando un giorno in Parigi nella chiesa di <lb></lb>S. </s>

<s>Martino a vedere il cavallo, su cui siede il celeste Guerriero, co&#039;due piè <lb></lb>sinistri posati e co&#039;due destri sollevati da terra, ebbe a dare al pittore il <lb></lb>titolo di sciocco. </s>

<s>“ Et quo proinde intelliges quam fuerit Pictor ille ineptus, <lb></lb>qui Parisiis, in alteram alam organorum S. Martini, ita equum pinxit, ut <pb xlink:href="020/01/1522.jpg" pagenum="397"></pb>terrae insistens duobus sinistris pedibus, duos dextros elatos in aerem ha­<lb></lb>beat ” (Syntagma philosophicus, Operum, T. II, Florentiae 1727, pag. </s>

<s>469). </s></p><p type="main">

<s>Forse in quel medesimo tempo, che nella chiesa di S. </s>

<s>Martino a Pa­<lb></lb>rigi, si rappresentava una scena molto diversa in una sala anatomica di <lb></lb>Roma. </s>

<s>Quel Medico tedesco, che dicemmo altrove essere stato il primo a <lb></lb>dimostrare in Italia il circolo del sangue, si studiava argutamente, sezionando <lb></lb>cadaveri, di scoprire alla presenza de&#039;discepoli e degli amici ivi convenuti <lb></lb>gli errori astotelici, in ciò tanto dando nel genio a Raffaello Magiotti. </s>

<s>Que­<lb></lb>sti, caduto un giorno il discorso sull&#039;incesso degli animali, rammemorava <lb></lb>allo stesso tedesco Maestro il cavalllo del Gattamelata, che era sulla piazza <lb></lb>di Padova con due gambe dalla medesima parte, contro il precetto del Fi­<lb></lb>losofo, il quale perciò ambedue insieme tanto deridevano, lodando l&#039;arte <lb></lb>dello Scultore italiano, quanto il Gassendo lo venerava, rimproverando l&#039;igno­<lb></lb>ranza del Pittor parigino. </s></p><p type="main">

<s>E qui s&#039;offrirebbe largo e fecondo campo di osservazioni intorno alla <lb></lb>storia dell&#039;arte in relazione colla storia naturale, dalle quali verrebbe a con­<lb></lb>fermarsi quel che altrove dicemmo di Leonardo da Vinci, dai dipinti del <lb></lb>quale si raccoglierebbe un trattato <emph type="italics"></emph>De animalium incessu<emph.end type="italics"></emph.end> dimostrativo del <lb></lb>vero naturale meglio di quelli stessi scritti dai Filosofi ne&#039;loro libri. </s>

<s>Ma, per <lb></lb>non interrompere il filo alla nostra storia, diciamo che le confutazioni del ra­<lb></lb>zionalismo aristotelico, ritrovate da quell&#039;Anatomice tedesco nell&#039;osservazione <lb></lb>dei fatti naturali, fecero al Magiotti risovvenire che Galileo, anche in quel <lb></lb>particolar soggetto <emph type="italics"></emph>De natura animalium,<emph.end type="italics"></emph.end> aveva con grande zelo intrapreso <lb></lb>il medesimo istituto, per cui non potè in quel filosofico fervore tenersi di <lb></lb>prendere la penna in mano, per eccitare il suo valoroso Maestro a prose­<lb></lb>guirlo. </s>

<s>“ Godo in estremo, gli scriveva da Roma il dì 31 Marzo 1637, che <lb></lb>Ella si occupi intorno al moto de&#039;proietti, e tanto più quanto meno mi dà <lb></lb>sodisfazione Aristotile. </s>

<s>Per fine la prego quanto so e posso a non lasciare <lb></lb>indietro le speculazioni <emph type="italics"></emph>De incessu animali,<emph.end type="italics"></emph.end> acciò con questo tutta ancora <lb></lb>si sbarbi quella opinionaccia, che questo Autore sia in tutto e per tutto un <lb></lb>oracolo.... Mi è sovvenuto questo, perchè qua si trova un Medico tedesco, <lb></lb>anatomista raro, quale mostra in fatto assaissimi errori <emph type="italics"></emph>De natura anima­<lb></lb>lium,<emph.end type="italics"></emph.end> e quand&#039;io li contai del cavallo del Gattamelata, che sta sopra due <lb></lb>gambe dalla medesima banda, contro il detto di Aristotile, rise veramente <lb></lb>di tutto cuore, ed ogni giorno porta qualche luogo per farci sempre più ri­<lb></lb>dere ” (MSS. Gal., P. VI, T. XIII, c. </s>

<s>14). </s></p><p type="main">

<s>Il trattato <emph type="italics"></emph>De motu locali animalium,<emph.end type="italics"></emph.end> pubblicato dall&#039;Acquapendente <lb></lb>in Padova nel 1618, aveva eccitato Galileo a rivolgere la mente anche su <lb></lb>questa curiosa parte della Meccanica, e nella <emph type="italics"></emph>Selva di problemi varii<emph.end type="italics"></emph.end> (Alb. </s>

<s><lb></lb>XIV, 319) si trovano appunti relativi a questo tema, non preso ancora a <lb></lb>svolgere dall&#039;Autore nel 1637. L&#039;esortazioni del Magiotti par che avessero <lb></lb>avuto efficacia, perchè non molto tempo dopo lo stesso Galileo si deliberò <lb></lb>di dettare a Francesco Renuccini, se non la forma, la sostanza a un discorso <lb></lb><emph type="italics"></emph>Intorno il camminare del cavallo,<emph.end type="italics"></emph.end> di cui il Venturi e poi l&#039;Alberi pubbli-<pb xlink:href="020/01/1523.jpg" pagenum="398"></pb>carono l&#039;introduzione. </s>

<s>Si confuta ivi Aristotile, dicendo che la Natura non <lb></lb>ha così limitato l&#039;adoperare i piedi al cavallo, che debbano necessariamente <lb></lb>venire come ad incrociarsi, ma chi si piglierà la briga d&#039;andare a qualun­<lb></lb>que cavallerizza potrà da sè stesso “ osservare in quanti modi mova, ad un <lb></lb>fischio di bacchetta, il cavallo i piedi obbedienti ” (ivi, pag. </s>

<s>310). </s></p><p type="main">

<s>I concetti galileiani, rimasti in quel saggio del Rinuccini per lungo <lb></lb>tempo dimenticati, avevano avuto più dotta esplicazione e più solenne pub­<lb></lb>blicità per opera del Borelli, il quale riserbò il cap. </s>

<s>XX della I Parte <emph type="italics"></emph>De motu <lb></lb>animalium<emph.end type="italics"></emph.end> a trattare dell&#039;incesso de&#039;quadrupedi. </s>

<s>La proposizione CLXV si <lb></lb>legge così formulata: “ Gressum quadrupedum non fieri motis alternatim <lb></lb>duobus pedibus diagonaliter oppositis, reliquis duobus quiescentibus ” (Ro­<lb></lb>mae 1680, pag. </s>

<s>263). Della qual proposizione sembrano all&#039;Autore le prove <lb></lb>così evidenti, che si fa maraviglia come Aristotile e i suoi seguaci non si <lb></lb>sieno avveduti dell&#039;assurdità della contraria. </s>

<s>Imperocchè se negano moversi <lb></lb>il cavallo co&#039;piè commutati secondo il lato del quadrangolo, perchè cadendo <lb></lb>il centro di gravità sopra una linea l&#039;equilibrio riuscirebbe instabile, non <lb></lb>s&#039;intende come possano persuadersi d&#039;accomodar le partite, ricorrendo alla <lb></lb>commutazione de&#039;piè per diametro, il quale pure essendo una linea rende­<lb></lb>rebbe l&#039;equilibrio instabile per la stessa, stessissima ragione. </s>

<s>“ Sed quid <lb></lb>quaerimus rationes, conclude il Borelli, quando experientiae reclamant? </s>

<s><lb></lb>Observa equum lento motu gradientem: nunquam videbis duos pedes dia­<lb></lb>gonaliter oppositos simul tempore movèri, sed semper unicus pes a terra <lb></lb>elevatur, tribus reliquis firmis manentibus. </s>

<s>Idipsum postea, diligenti inspec­<lb></lb>tione, etiam observabis in gressu celeriori in omnibus quadrupedum specie­<lb></lb>bus ” (ibid., pag. </s>

<s>265). </s></p><p type="main">

<s>Nella seguente proposizione CLXVI passa l&#039;Autore a esporre il modo <lb></lb>come si fa l&#039;incesso de&#039;quadrupedi, e preconcetta già l&#039;opinione che tutta <lb></lb>la sicurtà di quell&#039;esercizio dipenda dal trovarsi il centro della gravità com­<lb></lb>preso dentro il perimetro di una superficie, dimostra essere quella super­<lb></lb>ficie o un triangolo o un parallelogrammo o un rombo o un trapezio, se­<lb></lb>condo che tre, nelle loro pose naturali, o quattro variamente spostate son <lb></lb>le colonne delle gambe insistenti sul suolo, per promuovere sempre più in­<lb></lb>nanzi la macchina animale. </s></p><p type="main">

<s>Abbiamo detto essere quella del Borelli un&#039;opinione preconcetta, se­<lb></lb>condo la quale si reputava impossibile che procedessero i cavalli co&#039;due piè <lb></lb>mossi dalla medesima parte. </s>

<s>Eppur la pittura e la statua equestre del S. </s>

<s>Mar­<lb></lb>tino e del Gattamelata son l&#039;immagine rappresentativa di una cosa natural­<lb></lb>mente vera, vedendosi propriamente ai cavalli movere sempre le gambe a <lb></lb>quel modo, quando vanno di trotto. </s>

<s>Fu questa verità di fatto conosciuta <lb></lb>bene da Galileo, affermando esser falso “ che i quadrupedi non possano <lb></lb>levar da terra nel medesimo tempo i due piedi dalla medesima banda ” <lb></lb>(Alb. </s>

<s>XIV, 319), e secondo che riferisce il Rinuccini rende altresì la ragione <lb></lb>del perchè, insistendo la gran macchina pure a quel modo sopra una linea, <lb></lb>non tema perciò il pericolo di cadere. </s>

<s>“ È forse vero che il cavallo cade-<pb xlink:href="020/01/1524.jpg" pagenum="399"></pb>rebbe, se movesse tutt&#039;a due i piedi dalla medesima banda, e nell&#039;istesso <lb></lb>tempo con intenzione di star fermo, ma si vede che così facendo piega a <lb></lb>quella parte, e con lui fa piegar chi ci è sopra, e se l&#039;aiuto degli altri due <lb></lb>indugiasse male ne avverrebbe ” (ivi, pag. </s>

<s>309). </s></p><p type="main">

<s>Si raccoglie da queste espressioni che Galileo, del non cadere il cavallo <lb></lb>mentre corre benchè posi sopra due piedi dalla medesima parte, rendeva una <lb></lb>duplice ragione: la prima ch&#039;egli piega sè e il cavaliere verso il lato ove <lb></lb>sono i piè fermi, e la seconda che per un attimo solo rimane in tale stato <lb></lb>così vacillante. </s>

<s>Quella prima ragione però vien contradetta dall&#039;esperienza, <lb></lb>andando il cavallo nel trotto così pari, che il cavaliere non sente il minimo <lb></lb>ondeggiamento, e quanto alla seconda converrebbe dire che fosse stata poco <lb></lb>provvida la Natura, se avesse messo in pericolo l&#039;animale anche per un mo­<lb></lb>mento solo. </s>

<s>Forse ebbe Galileo a sentir la forza dell&#039;argomento, e in quel <lb></lb>ch&#039;egli osserva <emph type="italics"></emph>che il cavallo cadrebbe se movesse tutt&#039;a due i piedi dalla <lb></lb>medesima banda e nell&#039;istesso tempo, con intenzione di star fermo,<emph.end type="italics"></emph.end> avrà <lb></lb>non difficilmente potuto ritrovar del fatto altra più verosimile spiegazione. </s>

<s><lb></lb>Sia pure che il cavallo in corsa possa reggersi per un brevissimo tempo <lb></lb>anche su due soli piedi, ma perchè non può tenersi a quel modo quand&#039;egli <lb></lb>è fermo nemmeno un istante? </s></p><p type="main">

<s>Il problema, che veniva così a proporsi, era similissimo a quell&#039;altro <lb></lb>meccanico problema, dallo stesso Galileo così formulato: “ Qual sia la ra­<lb></lb>gione che le trottole e le ruzzole girate si mantengono ritte, e ferme no ma <lb></lb>traboccano? </s>

<s>” (Alb. </s>

<s>XIV, 321). Nè la risoluzione era punto bisogno di ri­<lb></lb>cercarla, essendo già stata data dal Benedetti nel suo libro Delle specula­<lb></lb>zioni. </s>

<s>Egli ivi osserva, in un&#039;Epistola a Paolo Capra, che ne&#039;corpi mossi <lb></lb>velocemente attorno si ridesta una potente inclinazione di andare per linea <lb></lb>retta, che distrae i corpi stessi dalla naturale direzione dei gravi. </s>

<s>“ Ab eius­<lb></lb>modi inclinatione, poi soggiunge, rectitudinis motus partium alicuius corpo­<lb></lb>ris rotundi fit ut per aliquod temporis spacium trochus, cum magna vio­<lb></lb>lentia seipsum circumagens, omnino rectus quiescat super illam cuspidem <lb></lb>ferri quam habet, non inclinans se versus mundi centrum magis ad unam <lb></lb>partem quam ad aliam, cum quaelibet suarum partium in huiusmodi motu <lb></lb>non inclinet omnino versus mundi centrum, sed multo magis per transver­<lb></lb>sum ad angulos rectos cum linea directionis aut verticali aut orizontis axe, <lb></lb>ita ut necessario huiusmodi corpus rectum stare debeat ” (Venetiis 1599, <lb></lb>pag. </s>

<s>286). </s></p><p type="main">

<s>Che il corpo nella sua vertigine non inclini veramente al centro del <lb></lb>mondo argomentasi, prosegue il Benedetti, dal veder ch&#039;ei diventa più leg­<lb></lb>gero. </s>

<s>La palla infatti tanto più resiste per l&#039;aria al peso che la tira, secon­<lb></lb>dando la direzione della tangente, quant&#039;ella viene gittata con più gran forza. </s>

<s><lb></lb>Avrebbe agli esempi meccanici potuto l&#039;Autore soggiungere tante altre fisi­<lb></lb>che esperienze, per le quali si dimostra di fatto che i corpi in moto tanto <lb></lb>son più leggeri quanto vanno più veloci, ma in quel ridur le molte ragioni <lb></lb>alla sola meccanica de&#039;proietti intravediam l&#039;occasione, venuta di là a Ga-<pb xlink:href="020/01/1525.jpg" pagenum="400"></pb>lileo, d&#039;applicare il problema delle trottole e delle ruzzole al moto del ca­<lb></lb>vallo, sapendosi che il Magiotti lo richiamava su quel soggetto giusto in quel <lb></lb>tempo, ch&#039;egli attendeva a instituire la scienza nuova de&#039;proietti. </s>

<s>Comun­<lb></lb>que sia, la ragion meccanica per cui i moderni <emph type="italics"></emph>velocipedi,<emph.end type="italics"></emph.end> per esempio, ca­<lb></lb>dono quando stan fermi e si tengono così ben ritti quando sono in moto, <lb></lb>è quella stessa per cui il cavallo, che stando fermo cadrebbe, si regge anche <lb></lb>su due soli piedi dalla medesima parte, quando va di trotto. </s>

<s>Farebbe per­<lb></lb>ciò gran maraviglia se nè a Galileo nè a nessuno di que&#039;suoi tanti disce­<lb></lb>poli studiosi della meccanica non fosse sovvenuto di emendare gli errori ari­<lb></lb>stotelici, applicando all&#039;incesso de&#039;quadrupedi le nuove bellissime teorie del <lb></lb>Benedetti. </s></p><p type="main">

<s>Nè i settatori dunque di Aristotile nè i discepoli di Galileo, a quel che <lb></lb>par dalla storia, si sarebbero mai creduti che la Natura avesse così com­<lb></lb>plicato il passo de&#039;quadrupedi nelle più astruse leggi della Meccanica, da <lb></lb>renderne tanto difficile e faticoso lo studio de&#039;Filosofi; difficoltà e fatica, <lb></lb>che non s&#039;ebbe dall&#039;altra parte a incontrar punto minore, quando si volle <lb></lb>allo stesso modo filosofare intorno al volo degli uccelli. </s>

<s>Aristotile, nel cap. </s>

<s>X <lb></lb><emph type="italics"></emph>De animalium incessu,<emph.end type="italics"></emph.end> ne trattò con molta oscurità dipendente in parte <lb></lb>dalla concision del discorso, e in parte dalla difficoltà della cosa, che non lo <lb></lb>rendeva sicuro del vero naturale. </s>

<s>S&#039;intese nonostante ch&#039;ei volesse appro­<lb></lb>vare, e quasi colla sua autorità suggellar la comune opinione, che cioè fa­<lb></lb>cessero l&#039;ali l&#039;ufficio e producessero l&#039;effetto stesso dei remi. </s>

<s>Volendo in­<lb></lb>fatti rendere la ragione del perchè alcuni insetti abbiano un volo così tardo <lb></lb>e imbecille, dice che ciò da null&#039;altro dipende che dall&#039;aver l&#039;ali non pen­<lb></lb>nute ma membranose, o sproporzionate alla corpulenza del resto, cosicchè <lb></lb>avvien di esse quel che avviene de&#039;deboli remi, i quali abbiano da sospin­<lb></lb>gere innanzi una nave ponderosa. </s>

<s>“ Quemadmodum igitur si quis oneratam <lb></lb>navim remis tentet propellere, simili isthaec modo volatu utuntur, et ala­<lb></lb>rum naturae imbecillitas ad id non nihil facere videtur ” (T. VI, Operum <lb></lb>cit., fol. </s>

<s>275 ad t.). Ma gli uccelii, prosegue a ragionare il Filosofo, hanno <lb></lb>in generale un volo velocissimo, cosicchè le ali fanno in essi l&#039;ufficio dei <lb></lb>remi applicati a un&#039;agilissima nave. </s>

<s>Quell&#039;analogia insomma, che vedevasi <lb></lb>passare tra le ali e i remi, supponeva per cosa certa e già dimostrata che <lb></lb>fosse l&#039;uccello specificamente più leggero dell&#039;aria, come la nave è specifi­<lb></lb>camente più leggera dell&#039;acqua. </s></p><p type="main">

<s>Girolamo Fabricio, che nel suo trattato <emph type="italics"></emph>De motu locali animalium<emph.end type="italics"></emph.end> non <lb></lb>lasciò indietro il volo, dice cho questo si fa per via dell&#039;instancabile agitarsi <lb></lb>delle penne, le quali sospingono indietro l&#039;aria. </s>

<s>“ Ex quo motu, poi sog­<lb></lb>giunge, et aeris impulsu, contingit Volatile anterius locum mutare, non dis­<lb></lb>simili ratione ac, remigantibus aquam retro impellendo, navim antrorsum <lb></lb>moveri accidit ” (Opera omnia cit., pag. </s>

<s>375). Ma non poteva l&#039;Acquapen­<lb></lb>dente ammettere questa similitudine, senz&#039;ammettere insieme che l&#039;uccello <lb></lb>mentre vola galleggi sull&#039;aria soggiacente, come la nave stessa galleggia sul­<lb></lb>l&#039;acqua, cosicchè non incomba alle ali altro ufficio che di promovere il corpo <pb xlink:href="020/01/1526.jpg" pagenum="401"></pb>dell&#039;animale, senz&#039;avere il car|co di sostenerlo. </s>

<s>Tale infatti è l&#039;espressa opi­<lb></lb>nion dell&#039;Autore, che dice constar gli uccelli di duplice elemento, dell&#039;aereo <lb></lb>cioè e del terreo, essendo così disposti dalla Natura, da potere starsene ora <lb></lb>in aria, ora per terra. </s>

<s>“ Verumtamen, cum non perpetuo in aere esse sed <lb></lb>saepenumero ad terram dimitti esset commodum, idcirco Natura per pen­<lb></lb>nas leve quidem sed non ipso aere levius animal reddidit. </s>

<s>Ad id praestan­<lb></lb>dum leviusque aere ipsum reddendum, alarum potissimum caudaeque adiu­<lb></lb>tricis motus et expansio comparata est, ita ut, dum evolat levius redditum, <lb></lb>non impediatur volatus ab elementi terrei propensione ” (ibid., pag. </s>

<s>374). </s></p><p type="main">

<s>Se insomma galleggia secondo l&#039;Acquapendente l&#039;uccello sull&#039;aria, ciò <lb></lb>non è per altro che per l&#039;espansion delle penne delle ali e della coda. </s>

<s>Ma una <lb></lb>similitudine ch&#039;egli porta, per dar meglio a intendere come avvenga la cosa, <lb></lb>produce sulla mente di chi legge un effetto contrario. </s>

<s>La similitudine è tolta <lb></lb>dal lenzuolo, che ripiegato precipita dall&#039;alto, e disteso cade con lentissimo <lb></lb>moto. </s>

<s>Ma pur in ogni modo egli cade, e se ciò si avverasse dell&#039;uccello, colle <lb></lb>penne espanse, non sarebbe dunque più vero ch&#039;egli è assolutamente più <lb></lb>leggero dell&#039;aria, e che l&#039;ali non han da far altro che servire al volo. </s>

<s>Senti <lb></lb>perciò bene il Fabricio, per salvar l&#039;ipotesi aristotelica, il bisogno di ricor­<lb></lb>rere a qualche altro espediente, che fu quello della condensazione dell&#039;aria <lb></lb>fatta dentro il suo corpo dal volante, nell&#039;atto specialmente di sollevarsi da <lb></lb>terra. </s>

<s>“ Causa autem ob quam spiritus cohibitio ad suspendendum susti­<lb></lb>nendumque in aere volatile conferat, ea certe est quod spiritus cohibitio <lb></lb>aeris copiam intro in corpus coercet, constringit et continet, quae volatile <lb></lb>levius reddit ” (ibid., pag. </s>

<s>373). </s></p><p type="main">

<s>Diremo più qua come trovasse questa ipotesi, che ha in apparenza <lb></lb>qualche cosa di singolare, il suo fondamento nella particolare struttura degli <lb></lb>organi della respirazion degli uccelli, ma l&#039;Acquapendente non par che l&#039;ap­<lb></lb>poggi sopra questo principio fondamentale, ma su quell&#039;altro degli spiriti, <lb></lb>che muovono dal cervello come da fonte, e che per la via de&#039;nervi, come <lb></lb>per appositi canali, corrono e ricorrono a insufflare, e così a dar moto ai <lb></lb>muscoli. </s>

<s>Questa infatti è la dottrina galenica professata dal nostro Autore, <lb></lb>il quale, nella Parte seconda del suo trattato <emph type="italics"></emph>De musculis,<emph.end type="italics"></emph.end> così spiegava <lb></lb>l&#039;origine de&#039;loro moti. </s>

<s>“ Etenim a cerebro, seu spinali midulla, ceu prin­<lb></lb>cipio et fonte, et per nervos, ceu per canales et rivos, vim motoriam diffundi <lb></lb>in muscolos apparet ” (ibid., pag. </s>

<s>399). </s></p><p type="main">

<s>Narrammo a suo luogo come dimostrasse il Borelli per mezzo dell&#039;espe­<lb></lb>rienza che l&#039;ipotesi di quegli spiriti aerei non era altro che una immagina­<lb></lb>zione, ond&#039;essendo persuaso dalla scienza idrostatica e dai fatti che l&#039;uccello, <lb></lb>nemmeno per accidentalità, divien più leggero dell&#039;aria, n&#039;ebbe saviamente <lb></lb>a concludere che l&#039;antica teoria del volo, rinnovellata dall&#039;Acquapendente, <lb></lb>non si poteva oramai più salvare. </s>

<s>Se dunque le ali non operano a modo di <lb></lb>remi, e se l&#039;uccello ha bisogno d&#039;esser non solamente promosso ma soste­<lb></lb>nuto, qual può essere la nuova meccanica del volo? </s></p><p type="main">

<s>Il Borelli la riconosce principalmente nell&#039;elasticità dell&#039;aria, la quale <pb xlink:href="020/01/1527.jpg" pagenum="402"></pb>prima nell&#039;abbassarsi l&#039;ala, compressa, poi nel sollevarsi di lei si dilata, e <lb></lb>fa di sotto in su tale una corrente ventosa, da sostener con facilità la leg­<lb></lb>gera macchina volante. </s>

<s>Ma nello stesso tempo anche la promove, e a spie­<lb></lb>gar come ciò avvenga ricorre il nostro Autore <emph type="italics"></emph>De motu animalium<emph.end type="italics"></emph.end> all&#039;azion <lb></lb>meccanica del cuneo, in figura del quale dispone il volante stesso le ali sol­<lb></lb>levate sul dorso. </s>

<s>Consideriamo, egli dice, questo cuneo, che ha diretto il <lb></lb>taglio verso la coda, e la base rivolta alla parte del capo. </s>

<s>L&#039;aria prima com­<lb></lb>pressa, nello spiegar poi la sua elasticità, fa forza su&#039;due lati del cuneo <lb></lb>stesso, in che si sono disposte già l&#039;ali, e le caccia innanzi, presso a poco <lb></lb>come il nocciolo di ciliegia compresso dalle dita. </s>

<s>Il medesimo effetto mecca­<lb></lb>nico si produce quando le ali si abbassano, e ora il cuneo s&#039;appunta sotto, <lb></lb>come s&#039;appuntava dianzi sopra la coda. </s>

<s>“ Coacta igitur fuit Natura mirabili <lb></lb>solertia adhibere motum, qui eadem actione avem suspenderet, et eam hori­<lb></lb>zontaliter impelleret. </s>

<s>Hae quidem praestitit percutiendo aerem subiectum <lb></lb>perpendiculariter ad horizontem, sed obliquis ictibus, quod sola pennarum <lb></lb>flexibilitate consequitur. </s>

<s>Nam flabella alarum in actu percussionis formam <lb></lb>cunei acquirunt, a cuius expressione necessario avis anterius promoveri de­<lb></lb>bet ” (De motu anim., P. </s>

<s>I cit., pag. </s>

<s>311). </s></p><p type="main">

<s>In quel medesimo anno 1680, in cui in Roma appariva postuma alla <lb></lb>luce la prima Parte <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> il Coignard in Parigi pubblicava <lb></lb>i tre primi Tomi de&#039;Saggi di Fisica di Claudio Perrault, nel terzo de&#039;quali <lb></lb>è la <emph type="italics"></emph>Mechanique des animaux.<emph.end type="italics"></emph.end> Trattando ivi del volo dice l&#039;Autore che il <lb></lb>meccanismo n&#039;è maraviglioso, segnatamente per tre precauzioni prese in­<lb></lb>torno ad esso dalla Natura, e che sono: “ de rendre les instrumens du vol <lb></lb>tout-ensemble et legers et fermes; de leur donner une puissances suffisante <lb></lb>de se remuer fort vite; et de les disposer de sorte que ce mouvement soit <lb></lb>capable d&#039;elever l&#039;animal en l&#039;air ” (Oeuvres diverses de C. et P. Perrault, <lb></lb>a Leide 1721, pag. </s>

<s>377). </s></p><p type="main">

<s>Il primo effetto vien conseguito per via della particolare struttura delle <lb></lb>penne, che il Perrault minutamente descrive, e in ogni minima parte delle <lb></lb>quali s&#039;ammira la gran sapienza della Natura per renderle, più che sia pos­<lb></lb>sibile, leggere. </s>

<s>È pure il secondo effetto sapientemente conseguito con adat­<lb></lb>tar le penne delle ali alle braccia dell&#039;uccello messe in moto dai più robu­<lb></lb>sti muscoli di tutto il corpo. </s>

<s>L&#039;ultimo intento è dalla stessa sapientissima <lb></lb>Natura facilmente ottenuto col far che le ali, nell&#039;abbassarsi e nel solle­<lb></lb>varsi, prendano una disposizione diversa. </s>

<s>“ Cette differente disposition, così <lb></lb>esprimesi lo stesso Perrault, consiste en deux choses: la première est que <lb></lb>les plumes qui sont plates, lorsque l&#039;aile s&#039;abaisse, sont tournêes verticale­<lb></lb>ment lorsqu&#039;elles se levent, ce qui fait que l&#039;air qu&#039;elles coupent leur resiste <lb></lb>moins.... La seconde disposition, qui est toùjours iointe à la première, est <lb></lb>que les grandes plumes, qui sont au bout des ailes etant couchées les unes <lb></lb>sur les autres, elles se déplient et s&#039;elargissent, lorsque l&#039;oiseau frappe de <lb></lb>son aile, et se replient et se retrecissent, lorsqu&#039;il la leve ” (ivi, pag. </s>

<s>380, 81). </s></p><p type="main">

<s>In queste osservazioni, nelle quali si compendia dall&#039;Autore francese <pb xlink:href="020/01/1528.jpg" pagenum="403"></pb>tutta la meccanica del volo, possono i lettori trovare il criterio più giusto <lb></lb>per giudicar della differenza che passa fra la <emph type="italics"></emph>Mechanique des animaux<emph.end type="italics"></emph.end> e <lb></lb>il trattato <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> in cui le leggerezze della Fisica son corro­<lb></lb>borate dalla solidità della Geometria. </s>

<s>È il Borelli altresì superiore al Per­<lb></lb>rault per non aver come lui neglette le tradizioni della scienza antica, e per <lb></lb>aver anzi mostrato come da esse derivi la nuova, ciò che dall&#039;altra parte <lb></lb>molto conferisce a rendere la sua trattazione più autorevole di quella del <lb></lb>Francese e tutto insieme più piena. </s>

<s>Le prove di questa asserzione s&#039;hanno <lb></lb>dal seguito della storia, dalla quale intanto apparisce come il Borelli nella <lb></lb>scienza sua propria e in quella de&#039;suoi maestri ritrovasse, oltre alla gene­<lb></lb>rale ragion meccanica del volo, le speciali ragioni di certe accidentalità, in­<lb></lb>torno a che avevano errato gli antichi. </s></p><p type="main">

<s>Aristotile, nel cap. </s>

<s>VIII <emph type="italics"></emph>De animalium incessu,<emph.end type="italics"></emph.end> aveva detto che la coda <lb></lb>negli uccelli serve a dirigere il volo, come il timone delle navi, e perciò, in <lb></lb>quelle specie in cui la coda non così facile s&#039;inflette, come ne&#039;pavoni per <lb></lb>esempio e ne&#039;gallinacei, si vede il volo essere per lo più debole e affaticato. <lb></lb></s>

<s>“ Uropygium autem volatili inest generi ad dirigendos volatus, ut navigiis <lb></lb>gubernacula, quod necesse est etiam in ipsa inflecti adhaesione. </s>

<s>Quamobrem <lb></lb>et illa, quae discretas alas habent, verum uropygium ad eiùsmodi usum est <lb></lb>ineptum, ut pavones existunt et gallinacei ” (Operum, T. VI cit., fol. </s>

<s>275). </s></p><p type="main">

<s>Accolte per lungo tempo queste sentenze come vere da chi in venerar <lb></lb>l&#039;oracolo teneva gli occhi bassi, fu primo arditamente a sollevarli Ulisse <lb></lb>Aldovrandi, il quale non si poteva persuadere che dipendesse dalla coda il <lb></lb>debole volar de&#039;pavoni, vedendo ch&#039;essi, non solo l&#039;inflettono con facilità, <lb></lb>ma la riducono in forma di rota, ciò che non sanno fare gli uccelli stessi <lb></lb>anche più veloci. </s>

<s>“ Pavones et gallinas inter aves enumerat quae parum <lb></lb>volatu valent, et causam illius rei assignat quod uropygium ineptum, hoc <lb></lb>est, non actum flecti obtinent. </s>

<s>Uropygium enim ad dirigendos volatus a Na­<lb></lb>tura datum esse ait quemadmodum temones navigiis. </s>

<s>Verum cum Pavo cau­<lb></lb>dam non tantum flectat, ut reliquae volucres, verum etiam in rotae modum <lb></lb>erigat, itaque Aristotiles veram nobis rationem brevitatis huiusce volatus <lb></lb>nondum omnino expresserat ” (Ornithologiae, T. II cit., pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Osserva inoltre l&#039;Aldovrandi non esser troppo conforme all&#039;esperienza <lb></lb>de&#039;fatti la dottrina che la coda serva a dirigere il corso agli uccelli, come <lb></lb>il timone alle navi, vedendosi le Ardee per esempio e le Cicogne scodate <lb></lb>andar velocissime per diritto senza mai balenare. </s>

<s>“ Quod vero uropygium <lb></lb>volatus ut temon navem dirigat, ut ille ait, id quoque in omni avium ge­<lb></lb>nere locum non habet. </s>

<s>Siquidem multae, quales sunt Ardeae et Ciconiae, <lb></lb>cauda omnino destitutae, velocissimum tamen volatum exercent ” (ibid., <lb></lb>pag. </s>

<s>10). </s></p><p type="main">

<s>Ebbe la forza di questi argomenti a farsi sentire anche all&#039;intelletto <lb></lb>dell&#039;Acquapendente, il quale riconobbe la precipua causa delle varie dire­<lb></lb>zioni del volo nel vario moto delle ali. </s>

<s>Battute ambedue insieme e soave­<lb></lb>mente, quella direzione riesce orizzontale: concitate di più, la macchina vo-<pb xlink:href="020/01/1529.jpg" pagenum="404"></pb>lante si solleva, e rilassate un poco si abbassa: volgesi a destra o a sinistra, <lb></lb>secondo che l&#039;una delle stesse ali è battuta più forte o più veloce dell&#039;altra. <lb></lb></s>

<s>“ In quibus sane figuris et positionibus, soggiunge però l&#039;Acquapendente, <lb></lb>caudam quoque operari non est inficiandum, quam verisimile est navis gu­<lb></lb>bernaculum, ut dicit Aristotiles <emph type="italics"></emph>De anim. </s>

<s>incessu<emph.end type="italics"></emph.end> cap. </s>

<s>VIII, imitari ” (De <lb></lb>volatu, Op. </s>

<s>omnia cit., pag. </s>

<s>375). </s></p><p type="main">

<s>S&#039;intende bene che questa aggiunta alla precipua causa direttrice del <lb></lb>volo fu dall&#039;Acquapendente fatta solo in ossequio di Aristotile, ma Galileo <lb></lb>ne&#039;suoi liberi pensieri conobbe che la coda e le ali hanno ufficii tutt&#039;affatto <lb></lb>diversi, e che se queste, come diceva benissimo lo stesso Acquapendente, <lb></lb>servono a dirigere il volo da destra a sinistra, quella non può far altro che <lb></lb>volgerlo o in alto o in basso. </s>

<s>Di tali speculazioni di meccanica animale si <lb></lb>trova fra le opere galileiane la proposta, nella citata <emph type="italics"></emph>Selva di problemi varii,<emph.end type="italics"></emph.end><lb></lb>sotto questa forma: “ Del volar degli uccelli e qual sia l&#039;uso delle penne <lb></lb>della coda in questa operazione, e com&#039;essa coda non serva loro per timone, <lb></lb>e qual parte del corpo faccia l&#039;ufficio di timone ” (Alb. </s>

<s>XIV, 319). </s></p><p type="main">

<s>Il Discorso, disteso o dettato da Galileo per dimostrar l&#039;enunciato di <lb></lb>queste proposizioni, non si trova fra le opere di lui o stampate o mano­<lb></lb>scritte, ma il Borelli ne raccolse il concetto, e ne tramandò, benchè sotto <lb></lb>altra forma, ai posteri la memoria nella I Parte <emph type="italics"></emph>De motu animalium.<emph.end type="italics"></emph.end> La <lb></lb>proposizione CLXXXXVIII si legge dall&#039;Autore così formulata: “ Usus cau­<lb></lb>dae avium est flectere cursus volantium sursum et deorsum, non vero ad <lb></lb>dexterum et sinistrum latus ” (editio cit., pag. </s>

<s>311). Del quale asserto son <lb></lb>principalmente le prove dedotte dall&#039;esperienza, osservandosi che i colombi <lb></lb>per esempio o le rondini, quando vogliono piegare il volo o a destra o a <lb></lb>sinistra, non danno il minimo segno di mover la coda. </s></p><p type="main">

<s>Qual&#039;è dunque lo strumento che fa da timone al volante? </s>

<s>E il Borelli <lb></lb>stesso risponde così, dimostrando la proposizione che Galileo, nelle sopra <lb></lb>riferite parole, in secondo luogo enunciava: “ Ablato temone navis, si remi <lb></lb>dextri lateris flectantur, aquam impellendo versus puppim, sive navis quie­<lb></lb>scat sive directe moveatur, semper velocissime prora revolvetur versus si­<lb></lb>nistrum latum. </s>

<s>Idipsum continget si remi dextri lateris celerius quam sini­<lb></lb>stri retrorsum impellant.... Ergo eodem modo, dum avis in medio fluido <lb></lb>aeris innatat, volando aequilibrata in centro gravitatis eius, si sola dextra <lb></lb>ala deorsum sed oblique flectatur, aerem subiectum impellendo versus cau­<lb></lb>dam, necessario ad instar navis mox memoratae promovebitur latus eius <lb></lb>dextrum, quiescente aut tardius moto sinistro latere. </s>

<s>Ex quo fit ut avis pars <lb></lb>anterior, circa centrum gravitatis eius revoluta, flectatur versus sinistrum <lb></lb>latus ” (ibid., pag. </s>

<s>314). </s></p><p type="main">

<s>Si disse esser queste borelliane proposizioni un&#039;esplicazione dei concetti <lb></lb>di Galileo, di che, sebbene l&#039;Autore non faccia ivi alcun cenno, abbiamo non <lb></lb>probabili congetture ma certissimo documento. </s>

<s>Nel trattato <emph type="italics"></emph>De vi percussio­<lb></lb>nis<emph.end type="italics"></emph.end> aveva il Borellì stesso dimostrate alcune sue proposizioni relative agli <lb></lb>effetti, che produce il moto del timone sul moto della nave, pigliando in-<pb xlink:href="020/01/1530.jpg" pagenum="405"></pb>torno a ciò facile occasione di confutar le teorie meccaniche di Aristotile, il <lb></lb>quale riduceva il modo di operar del timone stesso al modo proprio d&#039;ope­<lb></lb>rare del vette. </s>

<s>I Peripatetici, al solito gelosi della dignità del Maestro, si ri­<lb></lb>sentirono, e il Borelli prese in una apposita scrittura a fare le sue difese. <lb></lb></s>

<s>“ Vengo finalmente, dice nell&#039;ultima parte di quella, a mostrare in qual <lb></lb>maniera e per qual cagione può esser vero in qualche caso che il timone <lb></lb>acquisti impeto di urtare e di spingere attraverso la poppa della barca. </s>

<s>Que­<lb></lb>sto dipende da una sottile sperienza del mio riverito Galileo, in proposito <lb></lb>di uno delli due timoni, che soglino adoperare i volatili, mentre scorrono <lb></lb>per l&#039;aria, e per brevità applicherò il suo discorso al caso nostro del timone <lb></lb>della nave. </s>

<s>” </s></p><p type="main">

<s>“ Intendasi alla barca CB (fig. </s>

<s>10) essere applicato un vasto timone CD, <lb></lb><figure id="id.020.01.1530.1.jpg" xlink:href="020/01/1530/1.jpg"></figure></s></p><p type="caption">

<s>Figura 10.<lb></lb>situato nella stessa direzione DCB <lb></lb>dell&#039;asse della barca CB, ed allora <lb></lb>sia tirata la barca dalla potenza M <lb></lb>(o sia spinta dal vento o dalla forza <lb></lb>de&#039;remi) per la stessa direzione da <lb></lb>C verso B, tirandosi dietro il timo­<lb></lb>ne CD. </s>

<s>Non ha dubbio che la barca <lb></lb>ed il timone, in virtù di detta spinta, <lb></lb>averanno acquistato un determinato grado d&#039;impeto, il quale a similitudine <lb></lb>de&#039;proietti seguiterà a spingerli da C verso B, anco dopo essere abbando­<lb></lb>nati dalla forza esterna, mentre dura e vige il detto moto impresso. </s>

<s>” </s></p><p type="main">

<s>“ Girisi il timone CD nel sito CE: è manifesto che il timone ripiegato <lb></lb>riterrà tuttavia l&#039;impeto di muoversi da C verso E, col quale è necessario. </s>

<s><lb></lb>Questa spinta, aggiunta alla forza dell&#039;urto dell&#039;acqua stagnante sopra il ti­<lb></lb>mone obliquo CE, farà che la poppa C della barca giri intorno al centro M, <lb></lb>verso la sinistra, con forza maggiore di quest&#039;ultima sola, e tale eccesso sarà <lb></lb>molto sensibile in questo caso che il timone è di notabile ed eccessiva gran­<lb></lb>dezza ” (MSS. Gal. </s>

<s>Disc., T. CXXXII, c. </s>

<s>86, 87). </s></p><p type="main">

<s>Da questa applicazione, fatta dal Borelli al timone delle navi, s&#039;intende <lb></lb>facilmente qual doves&#039;essere il discorso di Galileo intorno all&#039;ufficio della <lb></lb>coda in dirigere il volo degli uccelli, imperocchè, supposto che CB nella pre­<lb></lb>cedente figura rappresenti l&#039;asse del corpo dell&#039;animale, e che per CD debba <lb></lb>intendersi la coda, si vede che, sollevata in CE, la resistenza dell&#039;aria fa <lb></lb>nell&#039;urto verticale piegare in basso l&#039;animale stesso, come il timone faceva <lb></lb>dianzi, nell&#039;urto orizzontale, piegar la nave da lato. </s>

<s>Cosicchè l&#039;esperienza, <lb></lb>descritta dal Borelli nella proposizione CLXXXXVIII (ibid., pag. </s>

<s>313), è <lb></lb>sotto altre forme quella stessa che, ad esplicare il concetto galileiano, leg­<lb></lb>gesi nel passo da noi sopra trascritto. </s></p><p type="main">

<s>Il trattato borelliano però <emph type="italics"></emph>De volatu<emph.end type="italics"></emph.end> non si sta contento a discutere <lb></lb>quelle semplici questioni, che avea proposte Aristotile, e che dettero soggetto <lb></lb>agli studii dell&#039;Acquapendente e di Galileo, nè si rimane in quelle astratte <lb></lb>generalità di osservazioni, che fanno il merito principale della Meccanica del <pb xlink:href="020/01/1531.jpg" pagenum="406"></pb>Perrault, ma la statica e la dinamica vi son trattate in tutte le loro parti, <lb></lb>e con rigoroso ordine geometrico concluse dai loro principii. </s>

<s>Cosicchè in­<lb></lb>torno all&#039;azion de&#039;muscoli nella stazione, e ne&#039;tanti e svariati moti degli uc­<lb></lb>cèlli, si dimostrano teoremi, che trovan facile applicazione a risolvere pro­<lb></lb>blemi i più nuovi e più curiosi. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le cose fin qui storicamente da noi discorse mostrano come i quadru­<lb></lb>pedi differiscano dagli uccelli negli organi e negli atti della locomozione. </s>

<s>Ma <lb></lb>perchè sempre ogni abito esterno ha la sua ragione in qualche intimo prin­<lb></lb>cipio, la differenza ch&#039;è fra i piedi e le ali accenna a una più intrinseca dif­<lb></lb>ferenza nell&#039;organismo e nelle sue principali funzioni. </s>

<s>Son, rispetto alla vita <lb></lb>vegetativa, quelle principali funzioni le appartenenti alla nutrizione e alla <lb></lb>respirazione, e rispetto alla vita di relazione con quelle, che concernono i <lb></lb>sensi, e dalle quali massimamente dipende la superiorità del grado degli <lb></lb>animali. </s></p><p type="main">

<s>Nel fabbricare i varii organi, che dovevano servire a così fatte funzioni, <lb></lb>la Natura operò con mano alquanto diversa ne&#039;quadrupedi e negli uccelli, <lb></lb>presentando largo e fecondo campo a nuovi studii sperimentali, che non vo­<lb></lb>gliono esser passati senza un qualche cenno, benchè brevissimo, in questa <lb></lb>Storia. </s></p><p type="main">

<s>Lo stomaco è il principale organo della digestione, e gli Anatomici e i <lb></lb>Fisiologi più antichi ne intrapresero lo studio sugli uomini, sulle scimmie, <lb></lb>sui cani, e sopr&#039;altri così fatti, ne&#039;quali tutti si compone e funziona presso <lb></lb>a poco in simili modi. </s>

<s>Ma s&#039;ebbero in certi altri animali a notar differenze <lb></lb>di tal momento, che la struttura dell&#039;organo e la propria ragione degli usi <lb></lb>di lui dettero gran faccenda allo studio de&#039;Naturalisti. </s>

<s>Si distinse questo <lb></lb>particolar genere di animali col nome di <emph type="italics"></emph>ruminanti,<emph.end type="italics"></emph.end> e Aristotile, nel cap. </s>

<s>XIV <lb></lb>del III libro <emph type="italics"></emph>De partibus animalium,<emph.end type="italics"></emph.end> notò che son generalmente tutti cor­<lb></lb>nuti, e che mancano dei denti superiori. </s>

<s>Nonostante anche il Cammello, sog­<lb></lb>giunge il Filosofo, rumina, benchè non sia fornito di corna, avendo, ciò che <lb></lb>più importa, il ventre composto alla stessa maniera degli altri ruminanti. <lb></lb></s>

<s>“ Ruminat etiam Camelus more cornigerorum, quoniam ventres similes cor­<lb></lb>nigeris habeat. </s>

<s>Habent haec singula plures ventres, ut ovis, capra, cervus et <lb></lb>similia, ut cum officium oris non satis in molendo cibo adhibetur propter <lb></lb>inopiam dentium, munus ventrium expleat dum alius ab alio cibum reci­<lb></lb>pit, scilicet primus infectum, secundus aliquantulum confectum, tertius ple­<lb></lb>nius, quartus perquam plene confectum. </s>

<s>Ita fit ut genus hoc animalium <lb></lb>receptacula cibi habeat plura, quibus nomina haec, aut indita sunt, aut in­<lb></lb>dere licet: venter, arsineum, sive reticulum, omasum, abomasum ” (Ope­<lb></lb>rum, T. VI cit., fol. </s>

<s>245). </s></p><pb xlink:href="020/01/1532.jpg" pagenum="407"></pb><p type="main">

<s>I nomi imposti da Aristotile son generalmente usati anc&#039;oggidì dalla <lb></lb>scienza, la quale per verità imparò poco più oltre dal Maestro di coloro che <lb></lb>sanno, non avendo egli ivi nulla soggiunto nè del particolar modo, nè degli <lb></lb>organi più speciali della ruminazione. </s>

<s>Anche Galeno, nel III cap. </s>

<s>del VI li­<lb></lb>bro <emph type="italics"></emph>De anatomica administratione,<emph.end type="italics"></emph.end> lasciava digiuna di più saperne la sua <lb></lb>scuola, infin presso al terminar del secolo XVI, quando Girolamo Mercuriale <lb></lb>uscì a tentar qualche cosa di nuovo. </s>

<s>Egli fece una osservazione, la quale, <lb></lb>sebbene a noi possa sembrare ovvia, ha nonostante tutta l&#039;importanza e il <lb></lb>merito di una scoperta, e fu che il cibo ruminato non ritorna al gran ven­<lb></lb>tre, come parevano insinuare i testi aristotelici e i galenici, ma nel reticolo, <lb></lb>per una via tutta sua propria e differente dall&#039;altra. </s>

<s>“ Et ne quis dubitet <lb></lb>quomodo secunda vice in reticulum, non autem prima, labatur, sciendum est <lb></lb>foramen in gula esse satis angustum, quod pertingit in reticulum, et per <lb></lb>quod cibus prima vice, cum sit crassior et solidior, adhuc minime transire <lb></lb>potest; transit vero secunda vice, quando liquidus et mollis ita factus est, ut <lb></lb>iam transire queat ” (Variarum lectionum libri sex, Venetiis 1598, fol. </s>

<s>111). <lb></lb>Sarebbero da questo primo passo venuti facilmente aperti i sentieri a nuove <lb></lb>scoperte, se non fosse il Mercuriale stato per disavventura contradetto da <lb></lb>coloro, i quali si professavano amici di Aristotile e di Galeno più che del vero. </s>

<s><lb></lb>Non ebbe da quello stuolo peripatetico coraggio di disertare questa volta <lb></lb>nemmeno Ulisse Aldovrandi, che, ne&#039;Prolegomeni ai libri <emph type="italics"></emph>De quadrupedi­<lb></lb>bus bisulcis,<emph.end type="italics"></emph.end> trattando de&#039;ruminanti, così argomentava contro lo stesso Mer­<lb></lb>curiale: “ Vel Aristotiles foramen, quod ait Mercurialis pertingere in reti­<lb></lb>culum, non advertit, vel falsum est viam ab ore ad reticulum dari, quae non <lb></lb>prius ad primum ventrem pertingat. </s>

<s>Mihi eam viam minime necessariam <lb></lb>esse videtur ” (Bononiae 1621, editio secunda, pag. </s>

<s>2). </s></p><p type="main">

<s>La ragione di ciò, che ad esso Aldovrandi sembra probabilissima, è che <lb></lb>essendo il primo ventre irsuto, si trova perciò in bonissima condizione di <lb></lb>ritenere il cibo grossolano, ma ruminato ch&#039;e&#039;sia divien atto meglio a ri­<lb></lb>ceverlo il reticolo levigato, ond&#039;ei non è maraviglia se il bolo chimoso di­<lb></lb>rettamente scende in questo, piuttosto che in quello. </s>

<s>“ Utcunque tamen sit, <lb></lb>poi ne conclude, diligens anatomici inspectio controversiam dirimet ” (ibid.). </s></p><p type="main">

<s>Venivano così fatte parole a dar sollecito impulso all&#039;Acquapendente, <lb></lb>il quale per vero dire non seppe rispondere all&#039;invito, nè secondo i desi­<lb></lb>derii della scienza, nè secondo il bisogno. </s>

<s>Quell&#039;Anatomia, dalla quale si <lb></lb>doveva dirimere la lite, fu lasciata da lui qualche passo più indietro che non <lb></lb>dal Mercuriale, e la Fisiologia della ruminazione, che si legge nel suo nuovo <lb></lb>trattato, è un prolisso commentario ai concetti dell&#039;Aldovrandi. </s>

<s>Chi vuol per­<lb></lb>suadersene legga quella parte, che trovasi scritta sotto il titolo <emph type="italics"></emph>De varietate <lb></lb>ventriculorum,<emph.end type="italics"></emph.end> dove dall&#039;Autore s&#039;espongono tre ragioni del perchè il latte, <lb></lb>non solo si rinvenga di fatto, ma debba necessariamente rinvenirsi nell&#039;abo­<lb></lb>maso e no nell&#039;omaso, come diceva Aristotile. </s>

<s>Chi volesse poi risparmiarsi <lb></lb>la fatica, e vedere in poche parole conclusa la sostanza del lungo discorso, <lb></lb>ecco in proposito come si esprime l&#039;Autore stesso: “ Cum igitur cibus ru-<pb xlink:href="020/01/1533.jpg" pagenum="408"></pb>minatus vel mansus, beneficio oris, suam asperitatem et duritiam aliquo <lb></lb>modo deposuerit, secundus quoque ventriculus in ruminantibus minus asper <lb></lb>sit quam primus, utique probabile est credere cibum mansum et rumina­<lb></lb>tum potius in secundum quam in primum, propter suam similitudinem et <lb></lb>convenientiam descendere et ingredi, quemadmodum in lactantibus lac, non <lb></lb>in primo nec in secundo nec tertio, sed in quarto trahi et recipi videmus ” <lb></lb>(Opera omnia cit., pag. </s>

<s>137). </s></p><p type="main">

<s>Pochi anni dopo la pubblicazione di questo trattato dell&#039;Acquapendente, <lb></lb>fatta in Padova nel 1618, Giovanni Faber, venuto di Norimberga a farsi in <lb></lb>Roma d&#039;abito e di spiriti Italiano, si dette con più diligente amore allo stu­<lb></lb>dio della ruminazione, parendogli soggetto non indegno nè di medico nè di <lb></lb>filosofo. </s>

<s>Secondando l&#039;istituto di que&#039;Lincei, fra&#039;quali era stato chiamato dal <lb></lb>principe della nuova Accademia, Federigo Cesi, e sentendo che a dirimer le <lb></lb>liti insorte fra&#039;suoi predecessori l&#039;Aldovrandi invocava l&#039;autorità degli Ana­<lb></lb>tomici, attese ad apparecchiarsi le vie coll&#039;esperienze e colle anatomiche <lb></lb>dissezioni. </s>

<s>Che si raccolga il latte non altrove che nell&#039;abomaso lo riconobbe <lb></lb>come un fatto sì ovvio che, tutt&#039;altro che aver bisogno d&#039;esser provato co&#039;tre <lb></lb>argomenti speculativi dell&#039;Acquapendente, si maraviglia come fosse da Ari­<lb></lb>stotile ignorato quel che sapevasi benissimo “ a quovis e trivio pastore, vel <lb></lb>a quavis anicula caseorum fabra ” (Aliorum novae Hispaniae animalium <lb></lb>Nardi Antonii Recchi imagines et nomina, Johannis Fabri Lyncei exposi­<lb></lb>tione, Romae 1651, pag. </s>

<s>623). Scoprì inoltre che il cibo ruminato non va al <lb></lb>secondo ventricolo, come dietro il Mercuriale avevano creduto l&#039;Aldovrandi <lb></lb>e l&#039;Acquapendente, ma sì al terzo, di dove all&#039;ultimo scende nel quarto. </s></p><p type="main">

<s>L&#039;esperienze poi, congiunte colle anatomiche dissezioni, insegnarono al <lb></lb>Faber una cosa nuova, dalla quale fu poi condotto a scoprir le segrete vie, <lb></lb>per cui il chilo, scansando i due primi, va direttamente a infondersi ne&#039;due <lb></lb>ultimi ventricoli. </s>

<s>“ Didici enim, ex frequenti ventrium sive stomachorum <lb></lb>dissectione, tam vitulos quam haedos aliquando solo lacte frui ab uberibus <lb></lb>maternis facto, aliquando etiam, si foeni et herbarum copia detur, et haec <lb></lb>non illibenter carpere, atque ita, partim cibo tenerrimo, lacte scilicet quod <lb></lb>non ruminant, partim etiam duriore alimento, quod remandunt, vesci, et hoc <lb></lb>quidem in primum saeculum, illud in quartum ablegare, nullo itineris im­<lb></lb>pedimento facto ” (ibid., pag. </s>

<s>625). </s></p><p type="main">

<s>Di qui sentì il Faber frugarsi a una più viva curiosità di sapere in che <lb></lb>modo passando, come si credeva, per una medesima via le due diverse qua­<lb></lb>lità di cibo, riuscissero pure <emph type="italics"></emph>nullo itineris impedimento facto,<emph.end type="italics"></emph.end> a un termine <lb></lb>tanto diverso. </s>

<s>Quella specie di simpatia, ammessa dall&#039;Aldovrandi e dal­<lb></lb>l&#039;Acquapendente, fra l&#039;asprezza del gran ventricolo e la rigidezza del primo <lb></lb>cibo ingollato, come fra il secondo ventricolo di levigate interne pareti e il <lb></lb>più morbido cibo già ruminato; al Linceo, severo nell&#039;osservanza de&#039;canoni <lb></lb>sperimentali, non andava punto a genio. </s>

<s>Sentiva che gli si preparava pros­<lb></lb>sima una scoperta, e aiutato dal Microscopio tornò all&#039;autopsia. </s>

<s>Ecco final­<lb></lb>mente svelato il mistero. </s>

<s>Quell&#039;unica via dell&#039;esofago ora mette a un ter-<pb xlink:href="020/01/1534.jpg" pagenum="409"></pb>mine ora a un altro, perchè ora si trova più corta e ora invece diventa più <lb></lb>lunga; succedendo ciò per una maravigliosa semplicità di artificio, varia­<lb></lb>mente governato o dalla crassizie o dalla mollezza del cibo. </s>

<s>Sarebbe forse la <lb></lb>gentile invenzione, fra gli atti de&#039;Lincei rimasta dimenticata, se nell&#039;esporre <lb></lb>le immagini e i nomi di altri animali della Nuova Spagna, non scoperti dal­<lb></lb>l&#039;Hernandez e non descritti dal Recchi, non si fosse al Faber porta solenne <lb></lb>occasione di trattarne, a proposito di quel terribile ruminante appellato da <lb></lb>lui stesso col nome di <emph type="italics"></emph>Toro messicano.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ivi, dop&#039;avere diligentemente esaminate le dottrine de&#039;suoi predeces­<lb></lb>sori, e dimostrato in che modo e perchè riuscissero difettose, passa così a <lb></lb>descrivere, il nostro acuto Linceo, quel nuovamente scoperto artificio indu­<lb></lb>strioso della Natura. </s>

<s>“ In fine oesophagi, quem Itali <emph type="italics"></emph>il grumale<emph.end type="italics"></emph.end> vocant, hoc <lb></lb>est in superiore stomachi orificio, duo oblonga, et teretia veluti labia, mea­<lb></lb>tum illum obserant clauduntque, ut si cibus crassus densusque foenum, sar­<lb></lb>menta ac paleae aut similia semicommansa descendunt, haec labia carnosa <lb></lb>nimirum et membranosa facile cedant, et aditum graviori ac ponderosiori <lb></lb>cibo in saccum maiorem, primum nempe ventrem, permittant. </s>

<s>Ubi vero lac <lb></lb>ipsum liquidum delabitur, conniventia reperit haec oblonga corpora, quare <lb></lb>super hisce, tanquam super canali quodam declivi, currens, ad tertium im­<lb></lb>mediate ventrem labitur, et ex hoc ad quantum ” (ibid., pag. </s>

<s>622, 23). </s></p><p type="main">

<s>Scritte queste cose verso il 1625, e circa venticinqu&#039;anni dopo pubblicate, <lb></lb>si crederebbe che i Naturalisti avessero dovuto plaudire al Faber, e di una <lb></lb>insegnata verità, per tanti secoli rimasta a tutti occulta, riconoscerlo autore. </s>

<s><lb></lb>Eppure, presso al finir di quel secolo, Giovan Currado Peyer trattava degli <lb></lb>organi e delle funzioni della ruminazione come se fosse venuto a instituire <lb></lb>una scienza nuova, alla quale dava lo specioso titolo di <emph type="italics"></emph>Merycologia.<emph.end type="italics"></emph.end> Com­<lb></lb>memorando nel primo capitolo dell&#039;Opera tutti coloro, che lo avevano pre­<lb></lb>ceduto in quello studio, non lascia indietro i nomi del Mercuriale, dell&#039;Al­<lb></lb>dovrandi e dell&#039;Acquapendente, ma si tace affatto del Faber, e come se la <lb></lb>scoperta della duplice via esofogea, e specialmente di quella, dallo stesso ar­<lb></lb>guto inventore detta <emph type="italics"></emph>via lattea,<emph.end type="italics"></emph.end> fossero cose di nessuna novità e importanza, <lb></lb>Gian Giacomo Wepfer non riconosceva altri Naturalisti precursori del Peyer <lb></lb>che il Gesner e l&#039;Aldovrandi. </s>

<s>“ Quis enim horum, egli dice, accuratam ven­<lb></lb>triculorum descriptionem nobis tradidit, aut modum ruminationis explicuit? </s>

<s>” <lb></lb>(Merycologia, Basileae 1685, Appendix, pag. </s>

<s>273). E avrebbe avuto senza <lb></lb>dubbio ragione il Wepfer, quando a&#039;due scrittori da lui citati non fosse suc­<lb></lb>ceduto il Faber, di cui si tace anche qui il nome. </s>

<s>E perchè in uomini così <lb></lb>eruditi della storia scientifica non sembra che si possa ammettere ignoranza <lb></lb>della celebre opera dell&#039;Hernandez, e de&#039;famosi Lincei che la illustrarono, <lb></lb>la curiosità ci spinge a indagare il motivo, per cui la scienza che largamente <lb></lb>s&#039;attinge dalla descrizione del Toro messicano sia stata dai nuovi cultori <lb></lb>della Mericologia tenuta in sì poco pregio. </s></p><p type="main">

<s>Il Peyer lo dice chiaro: “ Neque Faber ipse rem exhausit, confessus <lb></lb>se quae ad Anatomen attinent, potius quam illa quae philosophica obscu-<pb xlink:href="020/01/1535.jpg" pagenum="410"></pb>raque ratione erui possent, indagaturum ” (ibid., pag. </s>

<s>200). Ma insomma <lb></lb>si riconosce in questo giudizio il merito anatomico del nostro Linceo, ond&#039;è <lb></lb>che non s&#039;intende come non fosse creduto degno d&#039;essere annoverato nem­<lb></lb>meno fra gli scrittori d&#039;infimo pregio, che trattarono della ruminazione. </s></p><p type="main">

<s>“ Ego denique, si soggiunge alle parole sopra citate, argumentum utro­<lb></lb>que modo pertractare allaboro ” cioè coll&#039;anatomia e colla fisiologia: cosic­<lb></lb>chè il Peyer tacitamente confessa di non aver fatto altro che compier l&#039;opera <lb></lb>e perfezionare la scoperta del Faber, il quale, dall&#039;altra parte, non trascurò <lb></lb>del tutto la fisiologia, come si potrà giudicar dalle cose di lui sopra nar­<lb></lb>rate, messe a riscontro con questi brevi cenni, che siam per dare dell&#039;opera <lb></lb>peieriana. </s></p><p type="main">

<s>Ne&#039;capitoli II, III, IV e V si descrivono i ventricoli, incominciando dal <lb></lb>primo infino al quarto, e una buona e diligente anatomia sornuota felice­<lb></lb>mente a un pelago di parole erudite. </s>

<s>Passando a trattar nel seguente capi­<lb></lb>tolo VII dell&#039;esofago nota che quel canale, chiamato dal Faber via lattea, è <lb></lb>improprio riguardarlo come una continuazione dello stesso esofago “ cum <lb></lb>reapse oriatur ex ipsa reticuli substantia, attollentibus se fibris et membra­<lb></lb>nis utrinque replicantibus, labrorum similitudine ” (ibid., pag. </s>

<s>168). </s></p><p type="main">

<s>Questi si può dire che sieno i tratti principali, per cui l&#039;anatomia del <lb></lb>Peyer s&#039;avvantaggia sopra quella del Faber. </s>

<s>Quanto alla Fisiologia ella si <lb></lb>riduce tutta nello spiegàre in che modo sia preso il cibo dal gran ventre e <lb></lb>dal reticolo, e come sia fatto risalire su in fino alla bocca, per esservi ru­<lb></lb>minato. </s>

<s>Il Faber è vero si contentò di ammettere il fatto senza nemmen <lb></lb>provarsi di renderne qualche ragione: “ quocumque id demum modo fiat, <lb></lb>haud disputo ” ciò che porse al Peyer il principale argomento per asserire <lb></lb>che l&#039;opera faberiana mancava di Filosofia, la quale dall&#039;altra parte, par <lb></lb>ch&#039;egli dica, era assai naturale. </s>

<s>Imperocchè la difficoltà, che trovasi nello <lb></lb>spiegare in che modo il cibo risalga dal ventre alla bocca nella ruminazione, <lb></lb>è quella medesima che trovasi nello spiegare in che modo il cibo stesso <lb></lb>salga dalla bocca al ventre, quando l&#039;animale pasce l&#039;erbe per terra col cello <lb></lb>inclinato. </s>

<s>Ciò non significa altro, dice l&#039;Autore della Filosofia mericologica, <lb></lb>se non che il moto del bolo lungo il canale esofageo è indipendente dalla <lb></lb>naturale propensione de&#039;gravi, intantochè si rassomiglierebbe piuttosto a <lb></lb>qualche moto violento, a cui è studio del Fisiologo il ricercare d&#039;onde venga <lb></lb>l&#039;impulso. </s>

<s>Il Peyer lo riconobbe nelle fibre muscolari, di che l&#039;esofago stesso <lb></lb>è così artificiosamente intessuto, le quali fibre contraendosi diversamente ser­<lb></lb>vono a produrre due moti, “ quorum altero pabulum ad ventrem impelli­<lb></lb>tur, altero in os repellitur, singulari ruminationis privilegio ” (ibid., pag. </s>

<s>164). </s></p><p type="main">

<s>A che altro uso infatti, argomenta l&#039;Autore, potrebbero essere state di­<lb></lb>sposte in quel modo le fibre? </s>

<s>Se dovesse l&#039;esofago servir da semplice canale <lb></lb>sarebbero state sufficienti le membrane, dalle quali egli è involto, ma dee <lb></lb>di più spingere e risospingere il bolo, e a ciò appunto servono i muscoli. <lb></lb></s>

<s>“ Meatum itaque dant membranae, potior autem pars musculosa motioni <lb></lb>subservit. </s>

<s>Quamprimum enim aliquid ex ore aut ventre in gulam immitti-<pb xlink:href="020/01/1536.jpg" pagenum="411"></pb>tur, fibrae, a re ingrediente dilatatae, allectis spiritibus animalibus, per or­<lb></lb>dinem naturae se protinus constringunt fortiter, pastumque promovent ocys­<lb></lb>sime, et sursum quidem, si motus infra a ventre incipiat, quod ruminatione <lb></lb>contingit et vomitu; deorsum vero, si supra ab ore ducatur exordium ” (ibid., <lb></lb>pag. </s>

<s>166). </s></p><p type="main">

<s>Questo moto insomma, prodotto dalle fibre muscolari nel canale esofa­<lb></lb>geo, sarebbe simile a quello vermicolare degl&#039;intestini o alle contrazioni pe­<lb></lb>ristaltiche delle Tube falloppiane, per cui possono, bench&#039;elle sieno si an­<lb></lb>guste, facilmente tradurre i germi dagli ovarii nella matrice. </s>

<s>Ma come gli <lb></lb>avversi all&#039;Ovarismo non concedevano punto volentieri allo Stenone, al Van­<lb></lb>Horne e al Graaf queste peristaltie negli ovidutti; così gli avversi alla nuova <lb></lb>Mericologia non le consentivano all&#039;Autore nella gola dei ruminanti, e ri­<lb></lb>correvano piuttosto a invocar l&#039;aiuto di quel semicanale, chiamato dal Faber, <lb></lb>come sopra udimmo, <emph type="italics"></emph>via lattea,<emph.end type="italics"></emph.end> perchè ordinato a condurre il latte: e per­<lb></lb>ch&#039;è altresì disposto a infondere ne&#039;ventricoli le bevande, appellato dal Peyer <lb></lb>col nome di <emph type="italics"></emph>acquedotto.<emph.end type="italics"></emph.end> Dicevano costoro, appropriandosi un pensiero ch&#039;era <lb></lb>allora allora venuto a suggerire ai Naturalisti un anonimo Autore della Fi­<lb></lb>losofia vecchia e nuova, “ tubum illum utroque margine, instar manus <lb></lb>cuiusdam, concessum videri a Natura, quo occluso, bolos stringi et sursum <lb></lb>deferri. </s>

<s>” </s></p><p type="main">

<s>Ma rispondeva esso Peyer, dop&#039;avere a pag. </s>

<s>167 trascritte queste pa­<lb></lb>role, contenervisi idee più speciose che meritevoli di fede, perchè la via lat­<lb></lb>tea o l&#039;acquidutto non è riposto nel primo ventre, ma nel secondo, in cui <lb></lb>l&#039;esperienza c&#039;insegna non ritrovarsi mai il cibo così male confezionato, da <lb></lb>aver bisogno d&#039;una nuova masticazione. </s>

<s>Soggiunge poi a questa altre così <lb></lb>fatte ragioni: “ Canalis porro angustiae proportione non respondent ascen­<lb></lb>dentium bolorum magnitudini, neque labra eius adeo sunt ductilia, ut re­<lb></lb>pente admodum expandi et captare cibum possint ” (ibid., pag. </s>

<s>167). </s></p><p type="main">

<s>Eppure i moderni, ritornando a fare in proposito esperienze più dili­<lb></lb>genti, hanno approvato il pensiero dell&#039;anonimo Autore della Filosofia, e <lb></lb>hanno insegnato che il pasto dentro il reticolo vien veramente preso dai <lb></lb>margini contrattili dell&#039;acquidotto, i quali palpano con moti simili a quelli <lb></lb>delle labbra nella stessa bocca, e dagli avvolgimenti di esse labbra, quasi <lb></lb>aggomitolato, per quel moto peristaltico peierrano, si riconduce il bolo su <lb></lb>dal ventre alla gola. </s>

<s>Notabile che alcuni francesi autori di Zoologia attri­<lb></lb>buiscano a un loro illustre Fisiologo del secolo XVIII questa teorica della <lb></lb>ruminazione, lusingandosi di aver dati gli sperimenti di lui per nuovi e da <lb></lb>nessuno prima tentati, mentre discendono, com&#039;abbiamo veduto, dalle lon­<lb></lb>tane tradizioni della scienza, specialmente italiana. </s></p><p type="main">

<s>Gli organi e le funzioni della digestione dei quadrupedi, che non appar­<lb></lb>tengono all&#039;ordine dei ruminanti, non porgono altro particolar soggetto di <lb></lb>discorso ai limitati intenti della nostra Storia, e perciò, passando ai pennuti, <lb></lb>rammemoriamo ai nostri lettori come incominciassero da essi gli studii dei <lb></lb>Fisiologi, fra&#039;quali l&#039;Acquapendente ci si presenta de&#039;primi. </s>

<s>Nel trattatello <pb xlink:href="020/01/1537.jpg" pagenum="412"></pb>di lui altre volte citato <emph type="italics"></emph>De varietate ventriculorum,<emph.end type="italics"></emph.end> dop&#039;aver detto dell&#039;in­<lb></lb>gluvie, ch&#039;è secondo Aristotile il prontuario dell&#039;alimento, passa a descri­<lb></lb>vere il secondo ventricolo “ exiguus, carnosus ac mollis, minumeque pon­<lb></lb>derosus ” e l&#039;ufficio proprio del quale è “ ad mollia potius concoquenda <lb></lb>cibaria ” (Op. </s>

<s>omnia cit., pag. </s>

<s>131). Gli soggiace immediatamente il ventri­<lb></lb>colo terzo, molto maggiore degli altri due, carnoso all&#039;esterno e rubicondo <lb></lb>come laveggio, che per meglio concocere il cibo sia tutto intorno circondato <lb></lb>dal fuoco. </s>

<s>Il qual fuoco è a lui tanto più necessario, in quanto che nella <lb></lb>sua interna concavità è freddo e duro “ et quadatenus aspera membrana <lb></lb>obducitur, ad consimiles cibos excipiendos accommodata. </s>

<s>Nam et lapilli non <lb></lb>pauci in hoc quoque ventre comperiuntur, quos conficere et chylum eva­<lb></lb>dere, ut in struthio camelo ferrum, consentaneum est ” (ibid.). </s></p><p type="main">

<s>Ebbe di qui principio fra&#039;Naturalisti una questione che, durata due se­<lb></lb>coli, fu risoluta finalmente, come siam per narrare, dall&#039;esperienze dello <lb></lb>Spallanzani. </s>

<s>Si credeva assai probabile dall&#039;Acquapendente che le pietruzze <lb></lb>ingollate dagli uccelli si trasformassero in chilo, perchè le riconosceva come <lb></lb>durabilissimo viatico alle lunghe pellegrinazioni intraprese da alcuni di essi, <lb></lb>come per esempio dalle Gru e dalle Cicogne, ma l&#039;Harvey nel suo senno <lb></lb>pensò che quello era un certo pane più che biscotto. </s>

<s>Non potendo dall&#039;altra <lb></lb>parte negar l&#039;esistenza di cotesti calcoli, ne&#039;ventrigli anserini, disse esser <lb></lb>loro ufficio proprio di servir come da macine per triturare il cibo, supplendo <lb></lb>opportunamente al naturale difetto dei denti. </s>

<s>“ Ut hoc modo, ceu duobus <lb></lb>lapidibus molaribus, binis invicem cardinibus colligatis, molere cibaria et <lb></lb>pinsere possint, vicemque dentium molarium, quibus carent, calculi sup­<lb></lb>pleant ” (De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>27). </s></p><p type="main">

<s>La nuova ingegnosa ipotesi tanto parve più ragionevole della prima, <lb></lb>che i migliori ingegni plaudirono all&#039;Harvey, anche fra gli stessi nostri Ita­<lb></lb>liani, e Tommaso Cornelio dimostrava la potenza meccanica del ventricolo <lb></lb>de&#039;pennuti con questa bella esperienza. </s>

<s>Prendeva delle monete o di rame <lb></lb>o di argento, le accartocciava, e poi le faceva ingollare a un gallo d&#039;India. </s>

<s><lb></lb>Estratte dopo una diecina di giorni, “ erat exterior, seu convexa illorum <lb></lb>superficies, insigniter attrita, at interior tamen seu concava omnimo integra <lb></lb>permanserat. </s>

<s>Unde palam est istiusmodi corpora in alitum ventriculis non <lb></lb>liquescere aut dissolvi, sed collisa potius exteri atque comminui ” (Pro­<lb></lb>gymnasmata, Neapoli 1688, De nutricatione, pag. </s>

<s>208). </s></p><p type="main">

<s>Anche gli Accademici del Cimento sperimentando intorno alla dige­<lb></lb>stione delle anatre, e dicendo di avere osservato che sottosopra “ quelle <lb></lb>macinano meglio delle altre, che hanno ne&#039;loro ventrigli maggior copia di <lb></lb>sassolini inghiottiti ” (Saggi di natur. </s>

<s>esp., Firenze 1841, pag. </s>

<s>175); mo­<lb></lb>strarono di approvar l&#039;ipotesi arveiana, e anzi ciò s&#039;asserisce come cosa certa <lb></lb>dal Redi, autorevole interpetre dei loro sensi. </s>

<s>Essendoglisi nelle <emph type="italics"></emph>Esperienze <lb></lb>intorno a cose naturali<emph.end type="italics"></emph.end> presentata l&#039;occasione di commentare un passo di <lb></lb>Eliano, forse aveva, egli dice, conosciuto il greco Scrittore “ che gli uccelli <lb></lb>mangiano le pietruzze, perch&#039;elle servon loro per far ben digerire il cibo, <pb xlink:href="020/01/1538.jpg" pagenum="413"></pb>il che poi è stato detto più chiaramente da&#039;moderni, e spezialmente da&#039;no­<lb></lb>stri Accademici del Cimento, da Guglielmo Arveo, e da Tommaso Cornelio, <lb></lb>i quali tengono che la digestione nello stomaco degli uccelli si faccia in gran <lb></lb>parte ovvero si aiuti per mezzo della triturazione, e che quelle pietruzze <lb></lb>sieno come tante macinette raggirate da quei due forti e robusti muscoli, <lb></lb>de&#039;quali è composto il ventriglio ” (Opere, T. II, Napoli 1741, pag. </s>

<s>47). </s></p><p type="main">

<s>Dieci anni da poi che il Redi aveva così storicamente riferite queste <lb></lb>opinioni altrui, intorno all&#039;uso delle pietruzze ne&#039;ventricoli de&#039;pennuti, senza <lb></lb>però pronunziare ancora in proposito nessun suo giudizio; uscì alla luce la <lb></lb>seconda parte <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> dove nel cap. </s>

<s>XIV si tratta giusto della <lb></lb>nutrizione. </s>

<s>Parve anche il Borelli secondare in principio il parer dell&#039;Har­<lb></lb>vey, confortato da lui colle teorie meccaniche, come l&#039;aveva il Cornelio con­<lb></lb>fermato prima colle semplici esperienze. </s>

<s>Perciocchè, egli dice nella CXCI pro­<lb></lb>posizione, l&#039;azione del ventricolo carnoso è simile a quella dei denti, “ igitur <lb></lb>coniiciere possumus vires motivas eorum aequales esse. </s>

<s>Verum ostensa fuit <lb></lb>vis musculorum humanam mandibulam stringentium maior potentia ponde­<lb></lb>ris librarum 1350. Igitur vis ventriculi galli indici non est minor potentia <lb></lb>librarum 1350 ” (Romae 1681, pag. </s>

<s>398). </s></p><p type="main">

<s>Riflettendo poi il Borelli che una tal misurata potenza era per sè me­<lb></lb>desima sufficiente a stritolare anche le pietre più dure, e osservando inoltre <lb></lb>che alcuni testacei marini, i quali vivono continuamente sotto l&#039;arena, non <lb></lb>possono d&#039;altronde ricavare il necessario nutrimento che pur da essa, in­<lb></lb>cominciò a persuadersi che l&#039;opinione dell&#039;Acquapendente non dovess&#039;es­<lb></lb>ser poi così strana, come a principio pareva. </s>

<s>Intitolava perciò la proposi­<lb></lb>zione CXCIV: “ Suspicari licet animalia pennata in sui nutrimentum assu­<lb></lb>mere lapillos quos tam avide vorant ” (ibid., pag. </s>

<s>401). </s></p><p type="main">

<s>Si fondava quel sospetto sopra l&#039;osservazione dei cigni trovati sempre <lb></lb>nell&#039;aperto ventre ripieni di copiosissima arena, senz&#039;alcun vestigio di so­<lb></lb>stanze o animali o vegetali, da qualche sottilissimo filo di erba in fuori, e <lb></lb>si fondava altresì sopra buone ragioni, imperocchè se si vuole, argomentava <lb></lb>il Borelli, che i sassolini non servano di cibo, ma di strumenti da macinare <lb></lb>il cibo, perchè gl&#039;ingollano così avidamente le galline domestiche e i co­<lb></lb>lombi nutriti sempre di morbido pane e di farina? </s>

<s>“ laborarent frustra, <lb></lb>contra naturae indigentiam, fere toto die ore prono lapillos colligendo, sicuti <lb></lb>nos non utimur dentibus quando pultam comedimus ” (ibid., pag. </s>

<s>403). Ne <lb></lb>conclude perciò che i gallinacei sciolgono nel ventricolo le pietruzze, per <lb></lb>servirsi del loro succo ad alimentar certe parti del corpo, che tengono del <lb></lb>lapideo e del lamellare, come sarebbero le ossa e le penne. </s></p><p type="main">

<s>La curiosità del soggetto e la grande autorità del Maestro fecero si che <lb></lb>il Redi si risolvesse di lasciare i libri e gli Autori, nelle sue prime <emph type="italics"></emph>Espe­<lb></lb>rienze intorno a cose naturali<emph.end type="italics"></emph.end> citati, per consultar piuttosto la Natura, dalla <lb></lb>quale fu accertato che quelle pietruzzole inghiottite dagli uccelli non confe­<lb></lb>riscono niente alla nutrizione. </s>

<s>“ Imperocchè, egli scrive nel trattato <emph type="italics"></emph>Degli <lb></lb>animali viventi negli animali viventi,<emph.end type="italics"></emph.end> in tempo di verno rinchiusi in una <pb xlink:href="020/01/1539.jpg" pagenum="414"></pb>gabbia un cappone, senza dargli mai nè da mangiare nè da bere, e passati <lb></lb>che furono cinque giorni interi si morì, siccome altri capponi, tenuti pur <lb></lb>senza mangiare e senza bere, non vissero più che sette, otto e nove giorni. </s>

<s><lb></lb>Eppure, aperti i loro ventrigli, vi trovai in tutti una considerabile quantità <lb></lb>di pietruzzole, che avevano inghiottite prima che fossero rinchiusi, ed in <lb></lb>tempo di così gran bisogno non si erano consumate nè passate in nutri­<lb></lb>mento ” (Opere, T. I, P. II, Napoli 1741, pag. </s>

<s>51). </s></p><p type="main">

<s>Queste e altre simili esperienze, che prosegue il Redi a descrivere nel <lb></lb>luogo citato, erano decisive contro la proposizion del Borelli, la quale poteva <lb></lb>però salvarsi con dire che non aveva inteso l&#039;Autore di dimostrare essere <lb></lb>il succo lapideo ristoratore di ogni parte del corpo, ma di sole le ossa e le <lb></lb>penne. </s>

<s>Non fa perciò meraviglia che in dubbio si rimanessero tuttavia molti, <lb></lb>e fra questi anche il Vallisnieri, il quale, giudicando che il ferro e altri corpi <lb></lb>più duri nello stomaco degli struzzi non siano meccanicamente consumati, <lb></lb>ma che quasi da un&#039;acqua forte prodigiosa vengano assaliti, “ se poi, dice, <lb></lb>cavino nutrimento da quelli è difficile da determinarsi, benchè il chiarissimo <lb></lb>G. </s>

<s>Alfonso Borelli affermi alcuni animali potersi forse nutrire di sola terra <lb></lb>arenosa, lo che certamente è verissimo de&#039;lombrichi terrestri. </s>

<s>Ma se ciò si <lb></lb>possa dire ancor degli uccelli, io non ardirei di francamente asserirlo, tanto <lb></lb>più che, per esperienze fatte dal Redi, morirono di fame alcuni capponi posti <lb></lb>in gabbia con acqua sola e pietruzze ” (Anatomia dello Struzzo, nel T. </s>

<s>I <lb></lb>delle Opere, Venezia 1733, pag. </s>

<s>243). </s></p><p type="main">

<s>Nonostante, sempre meglio chiarendosi le idee de Fisiologi intorno alla <lb></lb>nutrizione, la quale viene ad ogni parte dal sangue, continuamente risto­<lb></lb>rato dal chilo, furono l&#039;esperienze del Redi riconosciute come dimostrative <lb></lb>delle false opinioni del Borelli e dell&#039;Acquapendente. </s>

<s>Non potendosi dall&#039;al­<lb></lb>tra parte intendere a qual naturale uso si trovassero le pietruzze ingeste nei <lb></lb>ventrigli anserini, si tornò ad ammettere coll&#039;Harvey che facessero ivi l&#039;uf­<lb></lb>ficio di mole, opportunamente supplendo al difetto dei denti. </s></p><p type="main">

<s>Erano in tale stato le cose, quando lo Spallanzani si assicurò per espe­<lb></lb>rienza non esser vera nemmeno l&#039;ipotesi arveiana, unica, dopo tante vicende, <lb></lb>rimasta vittoriosa. </s>

<s>“ Alcuni piccioni terragnoli allora usciti dall&#039;uovo, così <lb></lb>scrive nelle sue <emph type="italics"></emph>Dissertazioni di fisica animale,<emph.end type="italics"></emph.end> non avevan come doveva <lb></lb>succedere pietruzze di sorta, e parecchi di essi mi presi io la pena di cu­<lb></lb>stodirli, tenendoli in sito caldo per tutto il tempo che erano ancora svestiti <lb></lb>di penne, e alimentandoli finchè atti fossero a mangiare da sè. </s>

<s>In seguito <lb></lb>li racchiusi in gabbia, apprestando loro il cibo seguente. </s>

<s>Da principio fu vec­<lb></lb>cia macerata nell&#039;acqua, indi veccia asciutta e dura che fu poi l&#039;alimento, <lb></lb>che proseguii sempre a somministrare ad essi. </s>

<s>Solamente, trascorso un mese <lb></lb>da che mangiavan da sè, io cominciai a framischiare al cibo di tanto in tanto <lb></lb>de&#039;corpi duri, come alcuni rari tubetti di latta, qualche vuota sferetta di <lb></lb>vetro, varie piccole schegge di vetro altresì, e a taluno de&#039;colombi non feci <lb></lb>prendere che uno di questi corpi. </s>

<s>Dopo due giorni furono tratti a morte. </s>

<s><lb></lb>Nessuno de&#039;colombi aveva nel ventriglio la minima pietruzza, eppure i tu-<pb xlink:href="020/01/1540.jpg" pagenum="415"></pb>betti di latta erano schiacciati, le sferette e le schegge di vetro rotte e smus­<lb></lb>sate..... Ecco dunque decisa una volta la famosa questione delle pietruzze <lb></lb>annidate ne&#039;ventrigli di varii uccelli, per sì lungo tempo dagli Autori agi­<lb></lb>tata, voglio dire che allo spezzamento de&#039;cibi più duri e de&#039;corpi stranieri <lb></lb>durissimi non sono esse punto necessarie, contro quello che è stato cre­<lb></lb>duto da tanti Naturalisti e Fisiologi sì moderni che antichi ” (Modena 1780, <lb></lb>pag. </s>

<s>18, 19). </s></p><p type="main">

<s>Ecco dunque l&#039;ipotesi dell&#039;Harvey e del Cornelio dimostrata falsa dal­<lb></lb>l&#039;esperienze dello Spallanzani, come l&#039;ipotesi dell&#039;Acquapendente e del Bo­<lb></lb>relli era stata dimostrata falsa dalle esperienze del Redi; ond&#039;è che, doman­<lb></lb>dando con gran curiosità, sulla fine del secolo XVIII, Naturalisti e Fisiologi <lb></lb>a che fine insomma si credesse che i gallinacei beccassero i sassolini, ri­<lb></lb>spondeva così, dop&#039;essersi consigliato con la sua propria scienza, lo stesso <lb></lb>Spallanzani: “ Io adunque sarei di parere che la ricchezza delle pietruzze, <lb></lb>che d&#039;ordinario s&#039;incontra ne&#039;ventrigli degli uccelli gallinacei, nascesse, non <lb></lb>già dall&#039;andarne essi in cerca e dal farne volontariamente raccolta, com&#039;è <lb></lb>sentimento di molti, ma piuttosto dal trovarsi non di rado questi estranei <lb></lb>corpiccioli mescolati a&#039;cibi che prendono ” (ivi, pag. </s>

<s>21). E così potrebbesi <lb></lb>saviamente rispondere rispetto all&#039;arida arena e al crasso limo, di che tro­<lb></lb>vasi ripieno il ventre ai testacei marini, e ai lombrichi terrestri. </s></p><p type="main">

<s>Da quello stesso Acquapendente, da cui mossero, sui principii del se­<lb></lb>colo XVII, le questioni relative alle funzioni digestive de&#039;ruminanti e dei <lb></lb>gallinacei, muove ora un&#039;altra non meno importante questione storica con­<lb></lb>cernente gli organi della respirazion negli uccelli. </s>

<s>Aristotile aveva detto, nel <lb></lb>cap. </s>

<s>X del III libro <emph type="italics"></emph>De partibus animalium,<emph.end type="italics"></emph.end> che son precinti del setto tra­<lb></lb>sverso o del diaframma tutti quegli stessi animali che son forniti di sangue <lb></lb>rosso, e che ciò era stato fatto dalla Natura per separar le più nobili parti <lb></lb>del corpo dalle più vili. </s>

<s>“ Habent hoc omnia quae sanguinem obtinent aeque <lb></lb>ut cor et iecur, cuius rei causa est quod ideo habetur, ut sedem cordis a <lb></lb>ventre dirimat, videlicet ut animae sentientis origo inoffensa servetur, nec <lb></lb>facile occupetur exhalatione cibi, et caloris adventitii copia. </s>

<s>Hac enim causa <lb></lb>Natura intercepit praecordiorum quasi parietis sepisque interventu, distin­<lb></lb>xitque partem nobiliorem ab ignobiliori ” (Operum, T. VI cit., fol. </s>

<s>243). </s></p><p type="main">

<s>Ma l&#039;Acquapendente osservò che gli uccelli, in così grande abbondanza <lb></lb>forniti di sangue rosso, non hanno questa siepe, la quale, perciocch&#039;egli cre­<lb></lb>deva non fosse data dalla Natura per dirimere il cuore dal ventre, ma per <lb></lb>servire alla respirazione, pensava che venisse negli stessi uccelli supplita dai <lb></lb>più validi moti delle coste. </s>

<s>Voleva questo primo pensiero però essere con­<lb></lb>fermato da più diligenti osservazioni, e un giorno entrato tutto in fervore <lb></lb>di ciò, mentre solitario meditava nel suo domestico studio, non avendo da <lb></lb>sezionare altri animali, mette le mani addosso al suo pappagallo, che pure <lb></lb>aveva carissimo, e coraggiosamente l&#039;immola al culto della scienza. </s>

<s>“ Quae <lb></lb>omnia, ac ea potissimum quae ad thoracis motum, dum obscure ita explico, <lb></lb>ac mihi ipsi vix satisfacio, ecce domi forte psittacus obiit, qui, etsi gratis-<pb xlink:href="020/01/1541.jpg" pagenum="416"></pb>simus erat, multo tamen gratius fuit per eum in exactam motus thoracis <lb></lb>notitiam, ni fallor, pervenisse ” (De respiratione, Op. </s>

<s>omnia cit., pag. </s>

<s>178). </s></p><p type="main">

<s>Sodisfatto così di sè medesimo, consigliava il Fabricio i Fisiologi che, <lb></lb>se volevano studiare i moti del torace, ricorressero agli uccelli, ne&#039;quali, <lb></lb>per la mancanza del diaframma, sono evidentissimi, “ cum in hominibus, <lb></lb>propter obscurum et exiguum motum, difficile admodum, et non nisi a <lb></lb>valde in re anatomica exercitatis et peritis, probe intelligi valeat ” ibid.). <lb></lb>Fu quel consiglio seguito in seno all&#039;Accademia parigina da Giovanni Mery, <lb></lb>il quale, confermando le osservazioni fatte prima dal Nostro sopra gli uc­<lb></lb>celli, conferì a chiarir molto le idee intorno all&#039;avvicendarsi de&#039;moti delle <lb></lb>coste nella respirazione, in quel tempo che più fervevano nella scienza le <lb></lb>controversie. </s>

<s>Nella storia accademica infatti del 1689 si trova così riferito <lb></lb>delle osservazioni del Mery <emph type="italics"></emph>sur la respiration.<emph.end type="italics"></emph.end> “ Pour rendre ce mouve­<lb></lb>ment plus sensible, on ferma, pendant quelque tems, le bec et les narines <lb></lb>et les ayant ensuite ouvertes, on vit manifestement que le ventre se com­<lb></lb>prime beaucoup, en dedans, que le sternum s&#039;éleva plus qu&#039;auparavant, et <lb></lb>que les còtes s&#039;eloignèrent davantage les unes des autres en s&#039;elevant. </s>

<s>On <lb></lb>observa au contraire, dans l&#039;expiration, que le sternum se rapprochoit des <lb></lb>vertebres, les còtes les unes des autres, et que le ventre s&#039;elevoit ” (Col­<lb></lb>lection de pièces acad., T. I, a Dijon 1754, pag. </s>

<s>146). </s></p><p type="main">

<s>Ma tornando all&#039;Acquapendente, nell&#039;introdursi ch&#039;ei fa a trattare <emph type="italics"></emph>De <lb></lb>formatione ovi,<emph.end type="italics"></emph.end> s&#039;imbatte al solito in Aristotile, che dice incominciarsi a <lb></lb>far l&#039;uovo nella gallina presso il setto trasverso. </s>

<s>“ Nos autem in Respira­<lb></lb>tionis tractatu negavimus pennata septum obtinere. </s>

<s>Solvitur dubium pennata <lb></lb>septo prorsus non destitui, quia membranam habent tenuem loco septi po­<lb></lb>sitam, quam Aristotiles cinctum et septum appellavit, sed non habent septum <lb></lb>quod musculus sit, et ad respirationem conferat, ut alia animalia. </s>

<s>Aristoti­<lb></lb>les autem musculum non agnovit ” (Op. </s>

<s>omnia cit., pag. </s>

<s>1, 2). </s></p><p type="main">

<s>Quando l&#039;Harvey s&#039;esercitava intorno a così fatte questioni di embrio­<lb></lb>logia, tenendo intorno a sè a man destra i libri di Aristotile, e dall&#039;altra <lb></lb>quelli dell&#039;Acquapendente, volle esaminar meglio quella tenue membrana, <lb></lb>che si diceva essere negli uccelli posta in luogo del diaframma, e trovò che <lb></lb>erano invece più membrane tese l&#039;une a distanza dall&#039;altre, fra gl&#039;inter­<lb></lb>stizi delle quali rimanevano certe cavità cellulari, senza dubbio ripiene d&#039;aria. </s>

<s><lb></lb>Incerto se quest&#039;aria era innata, o se veniva di fuori, si risovvenne di que­<lb></lb>ste parole, che aveva lette nel trattato <emph type="italics"></emph>De respiratione<emph.end type="italics"></emph.end> del suo Fabricio: <lb></lb>“ In pennatis igitur diaphragma non fuit appositum, ut non modo thorax, <lb></lb>sed etiam abdomen, per respirationem facile distendatur, attollaturque, tum <lb></lb>vero aere impleatur, atque hac ratione totus corporis truncus, qui sua na­<lb></lb>tura gravis et minus idoneus ad volandum erat futurus, levis omnino red­<lb></lb>datur ” (ibid., pag. </s>

<s>178). </s></p><p type="main">

<s>L&#039;aria nel ventre, a cui qui s&#039;accenna, pensava l&#039;Harvey, non può es­<lb></lb>sere altro che quella compresa fra&#039;sepimenti delle membrane, e se il Fa­<lb></lb>bricio dice che v&#039;entra <emph type="italics"></emph>per respirationem<emph.end type="italics"></emph.end> dee necessariamente venire dalla <pb xlink:href="020/01/1542.jpg" pagenum="417"></pb>trachea per i bronchi, attraverso ai polmoni. </s>

<s>Or perchè la decisione era ri­<lb></lb>serbata all&#039;esperienza, apre il becco a un uccello, vi soffia con un soffietto, <lb></lb>e ode il fremere del fiato che trapassa nel ventre. </s>

<s>Non contento, infila nella <lb></lb>trachea uno stilo, che trova dai polmoni nell&#039;abdome, con grandissima fa­<lb></lb>cilità, il passo aperto. </s>

<s>Volendo anche di più dar sodisfazione agli occhi, ne­<lb></lb>gletto il Microscopio, cerca uno degli uccelli più grossi, e trova nello Struzzo <lb></lb>i fori polmonari sì larghi, da ricever facilmente le punte delle dita. </s>

<s>Esultò <lb></lb>della scoperta, e nella III esercitazione <emph type="italics"></emph>De generatione animalium<emph.end type="italics"></emph.end> la ren­<lb></lb>deva nota al pubblico in questa forma: “ Perforatio pulmonum a me in­<lb></lb>venta haud obscura et caeca est, sed in pennatis praesertim patula admo­<lb></lb>dum adeo ut in struthiocamelo meatus plurimos repererim, qui digitorum <lb></lb>meorum apices facile exciperent. </s>

<s>In gallo indico et gallinaceo ipso, omni­<lb></lb>busque fere pennatis, immisso in tracheam stylo, transitus e pulmonibus in <lb></lb>cavitate abdominis apertos et patentes invenias. </s>

<s>Aer in eorum pulmones, <lb></lb>follium opera inspiratus, non sine impetu ad inferiora pertransit ” (Lugd. </s>

<s><lb></lb>Batav. </s>

<s>1737, pag. </s>

<s>6). </s></p><p type="main">

<s>Trent&#039;anni dopo la pubblicazione di questa scoperta Claudio Perrault, <lb></lb>perfezionata, la illustrava nel cap. </s>

<s>V della III Parte della sua <emph type="italics"></emph>Mechanique <lb></lb>des animaux,<emph.end type="italics"></emph.end> esibendo nella fig. </s>

<s>I della Tavola XVIII la disposizione delle <lb></lb>vescicole pneumatiche, situate quattro di qua e quattro di là nel petto dello <lb></lb>Struzzo, e due altre, una per parte, nel basso ventre. </s>

<s>“ Les quatre vessies <lb></lb>d&#039;en-haut ont quatre trous, qui reçoivent le vent du poumon. </s>

<s>La seconde <lb></lb>en a deux. </s>

<s>Celui d&#039;en-haut reçoit l&#039;air du poumon, celui d&#039;en-bas l&#039;envoye <lb></lb>à la vessie, qui est enfermée dans le bas ventre ” (ediz. </s>

<s>cit., pag. </s>

<s>464). </s></p><p type="main">

<s>In Italia, quasi nello stesso tempo, confermava queste osservazioni Fran­<lb></lb>cesco Redi, facendo così dire a Pietro Alessandro Fregosi, nel II Tomo del <lb></lb>supplemento al <emph type="italics"></emph>Giornale dei letterati:<emph.end type="italics"></emph.end> “ Ieri appunto (5 Dicembre 1682) <lb></lb>il signor Redi riscontrava le sue osservazioni intorno a&#039;polmoni degli uc­<lb></lb>celli, e con mia grandissima sodisfazione vidi che questi polmoni de&#039;volanti <lb></lb>non istanno liberi e sciolti, come quegli de&#039;quadrupedi e degli uomini, ma <lb></lb>sono fortemente attaccati alle costole e al groppone, e che di più son forati <lb></lb>da alcuni determinati e regolati forami, i quali forami sboccano in certe <lb></lb>particolari vesciche membranose che, moltiplicate fino in cinque, arrivano <lb></lb>l&#039;una dopo l&#039;altra infino a tutto il ventre inferiore ” (Opere, T. IV, Na­<lb></lb>poli 1741, pag. </s>

<s>81). </s></p><p type="main">

<s>Dall&#039;Anatomia, trapassando alla Fisiologia, si domandava qual potesse <lb></lb>essere l&#039;uso proprio di queste vescicole membranose. </s>

<s>Udimmo dalle sopra <lb></lb>riferite parole che l&#039;Acquapendente credeva conferissero alla leggerezza del <lb></lb>corpo, in grazia del più facile volo, ma l&#039;Harvey, considerando che il pol­<lb></lb>mone, dando transito all&#039;aria, non poteva perciò dirsi organo della respira­<lb></lb>zione adeguato, riguardò piuttosto quelle stesse vescicole membranose come <lb></lb>un polmone secondario. </s>

<s>“ Ita in pennatis pulmones potius transitus et via <lb></lb>ad respirationem videntur, quam huius adaequatum organum ” (De generat. </s>

<s><lb></lb>animal. </s>

<s>cit., pag. </s>

<s>5). </s></p><pb xlink:href="020/01/1543.jpg" pagenum="418"></pb><p type="main">

<s>Il Perrault illustrò benissimo questo concetto arveiano, dicendo che il <lb></lb>polmone degli uccelli si compone di due parti: una carnosa, come negli ani­<lb></lb>mali terrestri, e una membranosa. </s>

<s>Riconobbe in queste membrane l&#039;uso dei <lb></lb>muscoli nel basso ventre de&#039;quapredi; uso che non era sfuggito alla mente <lb></lb>dell&#039;Harvey: ma anche un altro volle aggiungervene, il Perrault, e fu quello <lb></lb>di comprimere gl&#039;intestini per la più equabile e non interrotta distribuzione <lb></lb>degli alimenti. </s>

<s>“ L&#039;usage de cette partie membraneuse est de suppleer au <lb></lb>défaut des muscles du bas ventre, qui sont tres petits dans le oiseaux, à <lb></lb>cause de la grandeur de l&#039;os de la poitrine, dont presque tout le ventre est <lb></lb>couvert, car ces muscles du bas ventre etant tres petits, et leur action pres­<lb></lb>que nulle, la compression importante, qu&#039;ils font sur les entrailles aux au­<lb></lb>tres animaux pour la coction et pour la distribution de la noutriture, auroit <lb></lb>manque aux oiseaux, si la partie membraneuse de leur poumon n&#039;y avoit <lb></lb>supplée “ (Mechanique cit., pag. </s>

<s>462). </s></p><p type="main">

<s>Il Redi poi, educato alla scuola galileiana, ripensando che dai principii <lb></lb>meccanici aveva Galileo (Alb. </s>

<s>XIII, 145) conclusa la ragione dell&#039;essere state <lb></lb>fatte le ossa degli uccelli fistolose, perchè riuscissero tutto insieme leggere <lb></lb>e resistenti, non credè doversi rigettare quello proposto dall&#039;Acquapendente <lb></lb>fra gli usi, alle vescicole pneumatiche nuovamente assegnati. </s>

<s>Perciò faceva <lb></lb>dire al medesimo Fregosi “ che l&#039;aria che entra per l&#039;aspera arteria non <lb></lb>si ferma ne&#039;polmoni, ma per quei forami de&#039;medesimi polmoni passa nelle <lb></lb>vesciche membranose e le gonfia, e gonfiandole fa crescere e dilatare le ca­<lb></lb>vità del ventre, onde l&#039;animale ne divien più tronfio e per così dire più <lb></lb>leggiero, e di più in questa dilatazione, venendo le viscere naturali ad es­<lb></lb>sere premute, elle possono, per via di questa alternata compressione, met­<lb></lb>tere in opera quegli ufizii, ai quali dalla natura sono state destinate ” <lb></lb>(Opere, Tomo cit., pag. </s>

<s>81). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Se, negli organi e nelle funzioni della digestione e della respirazione, <lb></lb>la feconda varietà del natural magistero aprì così largo campo d&#039;osserva­<lb></lb>zioni e d&#039;esperienze ai Naturalisti, non lo ridusse certo in termini punto <lb></lb>più circoscritti, per quel che concerne gli organi dei sensi. </s>

<s>Anzi quel sottil <lb></lb>lavorìo presenta tante e tali varietà nella trama e nell&#039;ordito, che sfuggono <lb></lb>alle più attente osservazioni, e dall&#039;altro lato l&#039;impossibilità di comprendere <lb></lb>i reconditi usi rende anche più difficile ogni diligenza in ricercar quelle mi­<lb></lb>nime differenze, che passano fra le parti. </s></p><p type="main">

<s>Questo, che può dirsi di tutti gli strumenti dei sensi, applicasi con più <lb></lb>ragione che mai alla vista e all&#039;udito, negli organi delle quali due princi­<lb></lb>palissime funzioni il cristallino per esempio e gli ossicini uditivi, sebben si­<lb></lb>mili nella sostanziale struttura in un medesimo genere, presentano pure va­<lb></lb>rietà notabili in ciascuna specie. </s>

<s>Essendo nonostante gli animali terrestri e <pb xlink:href="020/01/1544.jpg" pagenum="419"></pb>i volanti così fra loro diversi, non solo nella vita organica ma in quella di <lb></lb>relazione, non possono non intercedere fra gli organi de&#039;loro sensi differenze, <lb></lb>che debbano sfuggire, o comecchessia venir trascurate nella loro storia, e <lb></lb>intorno ad alcune di queste, o per meglio dire intorno ai validi aiuti, che <lb></lb>in riconoscerle ebbe la scienza della Natura dall&#039;arte sperimentale, si vuole <lb></lb>intrattener la presente limitata parte del nostro discorso. </s></p><p type="main">

<s>Rispetto agli occhi una delle più notabili differenze, che passano fra i <lb></lb>quadrupedi e gli uccelli, consiste in quel particolare organo, a cui fu dato <lb></lb>il nome di <emph type="italics"></emph>pettine.<emph.end type="italics"></emph.end> Fu primo ad esaminarlo il Petit, nelle memorie dell&#039;Ac­<lb></lb>cademia parigina del 1735, e poi l&#039;Haller ne fece una descrizione assai più <lb></lb>accurata, sì quanto alla sua origine dal nervo ottico, sì quanto alla sua forma <lb></lb>e alla sua struttura. </s>

<s>“ Parallelogramma fere membrana est, utriculosa, va­<lb></lb>sculosa, fusca et pene nigra, tenera, ad morem flabelli super seipsam pli­<lb></lb>cata, non similis bursae neque cavum aliquod continens, et quam maceratam <lb></lb>imperfectam planitiem explices ” (Elementa physiol., T. V, Lausannae 1769, <lb></lb>pag. </s>

<s>391). Il Petit pensò che il pettine servisse ad assorbire i raggi avven­<lb></lb>tizi, e a liberar l&#039;occhio dalle riflessioni irregolari, come il naturale pigmento <lb></lb>coroideo o quella tinta nera, che si dà intorno alle lenti degli strumenti no­<lb></lb>stri artificiali, ma l&#039;Haller “ mihi videtur, disse, similis arteriae albinianae <lb></lb>et bursulae piscium, advehere sanguinem lenti crystallinae ” (ibid.). </s></p><p type="main">

<s>L&#039;anatomia comparata e la fisiologia dell&#039;organo dell&#039;udito, se ci fosse <lb></lb>permesso più lungo discorso, porgerebbero alla nostra storia altro nuovo ar­<lb></lb>gomento, ma non è da far altro per noi che a delibare, anche da questo <lb></lb>pelago, qualche stilla di umore. </s>

<s>Non isfuggì nemmeno agli Antichi l&#039;osser­<lb></lb>vazione che l&#039;orecchia esterna è variamente configurata negli animali timidi <lb></lb>e nei feroci, e ch&#039;è altresì variamente disposta in quegli, che aspettano la <lb></lb>venuta del suono o di sotto o di sopra, o dalla parte d&#039;avanti del loro in­<lb></lb>corso, o da quella di dietro. </s>

<s>Il Porta, avendo a proporre, nel cap. </s>

<s>V del <lb></lb>XX libro della Magia naturale, uno strumento da udir di più lontano, si <lb></lb>inspirava sapientemente agli esempi della Natura. </s>

<s>“ Sancitum est enim in <lb></lb>Magiae naturalis praeceptis, quum aliqua nova investiganda sunt, Naturam <lb></lb>perscrutandam et imitandam censeamus. </s>

<s>Ut igitur animalia consideremus, <lb></lb>quae optimi auditus sunt, timida quaeramus oportet. </s>

<s>Natura enim eorum <lb></lb>saluti cavit ut quae minus viribus valerent saltem auditus praestantia fuga <lb></lb>saluti consulerent, ut cuniculus, lepus, cervus, asinus, bos et similia. </s>

<s>Haec <lb></lb>animalia aurita sunt, et aures apertas habent versus frontem, et hiatus di­<lb></lb>rigunt ex quo soni veniunt..... Quum erexere aures, acerrimi auditus, <lb></lb>quum remisere, timidi. </s>

<s>Et, ne per caetera animalia vagemur, quae aures am­<lb></lb>plas arrectas et apertas habent dicimus perfectissimum auditum habere. </s>

<s>Vi­<lb></lb>debimus nunc, contraria causa, quae parvas habent aures et obscuras obtu­<lb></lb>sioris esse auditus. </s>

<s>Magna piscium pars auribus caret, et qui solos meatus <lb></lb>habent et sine auriculis sensu hoc audiendi hebetiori esse necesse est. </s>

<s>Sunt <lb></lb>enim auriculae a Natura constructae ut veluti per eas in aures infundantur <lb></lb>soni ” (Lugd. </s>

<s>Batav. </s>

<s>1651, pag. </s>

<s>654, 55). </s></p><pb xlink:href="020/01/1545.jpg" pagenum="420"></pb><p type="main">

<s>Or perchè anche gli uccelli hanno i soli meati esterni, senza le auri­<lb></lb>cole, parrebbe che dovess&#039;essere in essi il senso non troppo squisito, ciò <lb></lb>che da un&#039;altra parte argomentavasi con più ragione da coloro, che vede­<lb></lb>vano mancare a quegli animali gli ossicini attaccati alla membrana, e altre <lb></lb>parti, che si reputavano di grand&#039;uso, nella cassa del timpano e nel labi­<lb></lb>rinto. </s>

<s>Non ebbe quella falsa opinione però altra origine che dall&#039;ignoranza <lb></lb>dell&#039;anatomia di questi organi, l&#039;esatta e compiuta descrizione de&#039;quali fu <lb></lb>a darla primo lo Scarpa. </s>

<s>Quand&#039;egli ebbe con tanti dotti argomenti dimo­<lb></lb>strato che l&#039;ufficio della finestra rotonda era quello di far da timpano se­<lb></lb>condario, passando alcuni a professare un&#039;opinione contraria a quella dianzi <lb></lb>accennata, e dicendo che l&#039;udito è anzi negli uccelli finissimo, benchè non <lb></lb>sia il suono rinforzato dalla finestra rotonda, negavano perciò che, quale ve­<lb></lb>niva a quest&#039;organo assegnato, tale veramente ne fosse l&#039;uso. </s>

<s>Lo Scarpa al­<lb></lb>lora si dette con gran diligenza a studiar l&#039;orecchio degli uccelli, e non solo <lb></lb>vi ritrovò la finestra rotonda, con tutto quell&#039;apparecchio acustico moltipli­<lb></lb>catore del suono, ma tante altre cose vi scoprì non più vedute, che il cap. </s>

<s>V <lb></lb>posto per appendice al trattato, e che s&#039;intitola <emph type="italics"></emph>Historia organi auditus <lb></lb>avium,<emph.end type="italics"></emph.end> apparve, presso a trent&#039;anni prima che terminasse il secolo XVIII, <lb></lb>come una nuova rivelazione alla scienza. </s></p><p type="main">

<s>Passa ivi l&#039;Autore ordinatamente dall&#039;esame dell&#039;orecchio esterno a quello <lb></lb>della Cassa del timpano e del Labirinto, ed esposta una sua ipotesi del per­<lb></lb>chè negli uccelli manchin le auricole, descrive in loro luogo nelle tempie <lb></lb>de&#039;Galli d&#039;India un organo che, sebbene egli dica essere ovvio “ nemo <lb></lb>hactenus animadvertit ” (De structura fen. </s>

<s>rotundae, Mutinae 1772, pag. </s>

<s>103). <lb></lb>Consiste quell&#039;organo in certi muscoli ordinatì a muovere una corona di <lb></lb>piume, di ch&#039;è interiormente orlato il margine del meato uditorio, e che <lb></lb>hanno co&#039;cigli delle palpebre una grandissima somiglianza nella disposizione, <lb></lb>ne&#039;movimenti e nell&#039;uso. </s></p><p type="main">

<s>Di più grande importanza era l&#039;esame della Cassa del timpano, nella <lb></lb>quale lo Scarpa osservò diligentissimamente quell&#039;unico ossicino, in cui par <lb></lb>si compendino i quattro proprii agli animali terrestri. </s>

<s>Lo Schelhammer, <lb></lb>dalla similitudine, l&#039;avea chiamato <emph type="italics"></emph>columna,<emph.end type="italics"></emph.end> e il Perrault, che nel suo trat­<lb></lb>tato <emph type="italics"></emph>Du bruit<emph.end type="italics"></emph.end> s&#039;era asciuttamente contentato di dire, che nell&#039;orecchia media <lb></lb>degli uccelli “ les osselets son reduits a un seul ” (Oeuvres, T. </s>

<s>I cit., <lb></lb>pag. </s>

<s>247), rappresentava poi nella figura II della Tavola VIII quest&#039;unico <lb></lb>ossicino come un sottile cilindro, che da una parte “ bouche le trou ova­<lb></lb>laire ” ed ha l&#039;altra, informemente rappresentata, “ attachée à la peau du <lb></lb>tambour ” (ivi, pag. </s>

<s>248). Ma il nostro Scarpa descrisse e fece nella sua ta­<lb></lb>vola II disegnare quell&#039;ossicino nella sua più vera e natural figura, ch&#039;è <lb></lb>a somiglianza del gambo e del cappello di un fungo. </s>

<s>“ Figura stilus fun­<lb></lb>giformis videtur: desinit enim in planam latamque ac fere triangularem su­<lb></lb>perficiem, quae ovalem fenestram, sicuti stapes in aure humana, penitus <lb></lb>claudit ” (De structura f. </s>

<s>rot. </s>

<s>cit., pag. </s>

<s>112). </s></p><p type="main">

<s>Per quel che poi più particolarmente riguarda il Labirinto, i tre canali <pb xlink:href="020/01/1546.jpg" pagenum="421"></pb>semicircolari erano a tutti patenti, ma “ au lieau du conduit spiral, diceva <lb></lb>il Perrault, il y a seulement un conduit court et droit en maniere d&#039;un pe­<lb></lb>tit sac ” (loc. </s>

<s>cit., pag. </s>

<s>247). Nonostante lo Scarpa più veramente rassomi­<lb></lb>gliava questo sacchetto all&#039;appendice vermiforme degl&#039;intestini. </s>

<s>“ Canales <lb></lb>semicirculares e directo prospicit Cocblea inferius producta, quae non ut in <lb></lb>homine et quadrupedibus convolvitur in spiram, sed canalem efficit non­<lb></lb>nihil recurvum et vermiformem intestinorum appendiculum simulantem ” <lb></lb>(De structura f. </s>

<s>r. </s>

<s>cit., pag. </s>

<s>124). </s></p><p type="main">

<s>La finestra rotonda, che dette occasione e fruttò alla scienza questo te­<lb></lb>soro di anatomia comparata, non riconosciuta ancora da nessuno de&#039;prede­<lb></lb>cessori, viene, insiem con la ovale, dallo Scarpa così descritta: “ Fenestra <lb></lb>ovalis, triangularem ferme figuram referens, superiorem partem occupat, et <lb></lb>a mobili capitulo ossiculi, tanquam a stapede, penitus obturatur. </s>

<s>Altera fe­<lb></lb>nestra, nempe rotunda, figura oblonga et inferius altera collocata, duplo <lb></lb>semper priore latior est, et in quibusdam avibus amplior. </s>

<s>Membrana ostium <lb></lb>fenestrae rotundae obtegit non intro convexa, ut in brutis ed homine, sed <lb></lb>plana distentaque admodum ut in tympano bellico et ad tremores aptis­<lb></lb>sima ” e a far perciò benissimo anche negli uccelli l&#039;ufficio di timpano se­<lb></lb>condario (ivi, pag. </s>

<s>121). </s></p><p type="main">

<s>È tale in compendio e nella sua più ridotta sostanza la storia ornito­<lb></lb>logica dell&#039;organo dell&#039;udito, per ciò che spetta gli strumenti ossei musco­<lb></lb>lari e membranosi. </s>

<s>“ Superest nunc, prosegue a dire lo stesso Scarpa, ad <lb></lb>eorum auditus historiam absolvendam, ut ea quoque addamus quae su­<lb></lb>sceptos soni tremores sensorio communi traducunt, nervum nempe acusti­<lb></lb>cum ” (ibid., pag. </s>

<s>125). Il Casserio, che fu primo a scoprire l&#039;ingresso di <lb></lb>un certo allungamento del cervelletto attraverso a un foro aperto fra la la­<lb></lb>mina ossea e interiore del cranio (Venetiis 1609, pag. </s>

<s>165), pensò che te­<lb></lb>nesse questo stesso processo cerebellare il luogo del nervo acustico. </s>

<s>Nè fu <lb></lb>molto differente da questo il parere dello Schelhammer, ma in verità, sog­<lb></lb>giunge lo Scarpa, non si vede mandare il cervelletto da quella sua sostanza <lb></lb>allungata nessun filamento che penetri nell&#039;interna parte del labirinto, e <lb></lb>non è perciò possibile che faccia le funzioni acustiche nel nervo. </s>

<s>“ Deest <lb></lb>ergo nervus acusticus? </s>

<s>Non sinunt observationes nostrae in hac sententia <lb></lb>morari. </s>

<s>Nervus enim acusticus, non tam in volucribus maioribus, sed in <lb></lb>aviculis etiam, perpetuus est et facile demonstrabilis. </s>

<s>Oritur enim ex oblon­<lb></lb>gata medulla, deinde statim in pluribus ramulis distinctus, nullo interposito <lb></lb>auditorio canale, extremam osseam labyrinthi laminam attingit, foraminibus <lb></lb>pertusam, per quae ad internam labyrinthi superficiem descendunt ” (ibid., <lb></lb>pag. </s>

<s>127). Ivi dentro penetrati così fatti ramuscoli nervei si trasformano in <lb></lb>quella sostanza polposa, che investe l&#039;uno e l&#039;altro vestibolo, i canali semi­<lb></lb>circolari e la chiocciola. </s></p><p type="main">

<s>Così intendesi come debba l&#039;orecchio degli uccelli riuscire organo per­<lb></lb>fettissimo dell&#039;udito. </s>

<s>“ Quare aves liquide audire necessario debent.... Fa­<lb></lb>tendum tamen est aliquod intercedere discrimen inter stridulas aves atque <pb xlink:href="020/01/1547.jpg" pagenum="422"></pb>canoras. </s>

<s>In istis enim quae exquisito auditu donantur, tria potissimum exhi­<lb></lb>bet auditus organum observatione dignissima: fenestram nempe rotundam <lb></lb>ovali triplo maiorem quam in stridulis volatilibus, vestibulum praesertim <lb></lb><emph type="italics"></emph>Tympani secundarii<emph.end type="italics"></emph.end> latius, ac denique cochleam longiorem magisque re­<lb></lb>curvam ” (ibid., pag. </s>

<s>130). D&#039;onde si conclude che l&#039;arte del canto è negli <lb></lb>uccelli educata dall&#039;orecchio; fatto del resto che si avvera in ogni genere <lb></lb>di animali, e in più eccellente modo nell&#039;uomo. </s>

<s>La stretta relazione perciò, <lb></lb>che passa fra&#039;due organi, ci consiglia a non trascurare un breve cenno sto­<lb></lb>rico dello strumento della voce, a complemento di quel che qui, e più lun­<lb></lb>gamente altrove, s&#039;è detto dell&#039;udito. </s></p><p type="main">

<s>In mezzo a tanti Vesaliani, dispregiatori dell&#039;antico Galeno, sorgeva Giu­<lb></lb>lio Casserio ad ammirare l&#039;intrepido petto di Colui “ qui contra Zenonem, <lb></lb>Stoicos, Diogenem, Babilonium et Chrysippum, pro ea vocis formatione de­<lb></lb>fendenda magnanimiter pugnavit. </s>

<s>Eorum autem alii a corde, ut Zeno, alii <lb></lb>a gutture vocem oriri putabant ” (De laringis hist. </s>

<s>anat., Ferrariae 1600, <lb></lb>pag. </s>

<s>148). Galeno invece sosteneva, per amor del vero, che aveva origine <lb></lb>la voce da uno strumento tanto simile al flauto, che dee il suo primo in­<lb></lb>ventore aver preso l&#039;esempio dalla stessa Natura. </s>

<s>“ Simile quidem est lin­<lb></lb>guae alicuius fistulae, potissimum si infernam ac supernam eius partem <lb></lb>spectes: infernam autem dico, ubi arteria et larinx inter sese connectun­<lb></lb>tur; supernam vero ad orificium quod fit a finibus, qui ibi sunt, arytenoi­<lb></lb>deos cartilaginis et scutiformis ” (De usu partium, lib. </s>

<s>VII, cap. </s>

<s>XIII, Lug­<lb></lb>duni 1550, pag. </s>

<s>406). Come però nel flauto organo precipuo del suono è la <lb></lb>linguetta, così nella laringe organo precipuo della voce è la glottide. </s>

<s>“ Ut <lb></lb>autem vocem edat animal indiget omnino etiam ea spiritus motione, quae <lb></lb>ab infernis repente simul erumpat. </s>

<s>Indiget autem nihil minus hac transitu <lb></lb>etiam angustiore, qui in larynge est. </s>

<s>Neque simpliciter angustiore, sed qui <lb></lb>paulatim quidem ex amplo ad strictius tendat, paulatim rursus ex strictiore <lb></lb>amplificetur. </s>

<s>Id quod penitus efficit corpus id, de quo nunc agimus, quod <lb></lb>lingulam et linguam laryngis nomino ” (ibid., pag. </s>

<s>407). </s></p><p type="main">

<s>Introdotte queste naturali verità nella nuova scienza risorta, per opera <lb></lb>d&#039;Iacopo Berengario, il quale aveva lasciato scritto esser la glottide “ prin­<lb></lb>cipalissimum vocis organum ” (Isag., Venetiis 1535, fol. </s>

<s>44); non per que­<lb></lb>sto crederono i Peripatetici di dover negar fede al loro Aristotile. </s>

<s>Dicevano <lb></lb>anzi che ciò ch&#039;egli insegnava della voce generata dal cuore veniva confer­<lb></lb>mato dall&#039;esperienze, vedendosi diventar fioco, e talvolta anche affatto muto, <lb></lb>allacciate le arterie carotidi, un animale. </s>

<s>Ma Realdo Colombo rispondeva <lb></lb>a costoro ciò dipendere dal venire offesa la laringe e no il cuore, perch&#039;è <lb></lb>troppo facile ad esser preso, insierne con la carotide, anche quel sottil nervo, <lb></lb>che dà spirito alla stessa laringe: nervo scoperto già da Galeno, e dagli Ana­<lb></lb>tomici poi detto <emph type="italics"></emph>ricorrente<emph.end type="italics"></emph.end> o <emph type="italics"></emph>reversivo,<emph.end type="italics"></emph.end> perchè “ per camdem revertitur <lb></lb>viam qua prius descenderat, ceu cursum reciprocans ” (De usu partium cit., <lb></lb>pag. </s>

<s>418). </s></p><p type="main">

<s>Per dimostrar di fatto che l&#039;afonia dipende dal nervo offeso, e non dal <pb xlink:href="020/01/1548.jpg" pagenum="423"></pb>cuore o da qualunque altro membro, esso Realdo ricorreva alla vivisezione. </s>

<s><lb></lb>Erano presenti, fra tanti altri filosofi e anatomici illustri, Girolamo Pontano, <lb></lb>Paolo Manilio e Giovanni Valverde, mentre il misero cane, legato sulla ta­<lb></lb>vola e colle viscere aperte, metteva lunghi urli acuti in mezzo a quegli spa­<lb></lb>simi atroci. </s>

<s>L&#039;espertissimo vivisettore mostra agli astanti un sottilissimo filo <lb></lb>bianco decorrere lungo l&#039;aspera arteria, e dice: questa è una propaggine <lb></lb>del nervo riversivo. </s>

<s>Tocca leggermente col dito quel nervo, e l&#039;urlo dalla <lb></lb>gola della vittima infelice esce fioco; lo preme di più, e&#039;cessa affatto. </s>

<s>Sa­<lb></lb>rebbe oggidì sembrato di assistere all&#039;esperienze della soneria elettrica, sul <lb></lb>filo conduttor della quale il dito facesse quel medesimo gioco. </s>

<s>È da creder <lb></lb>perciò se, vinta la pietà del dolore dalla curiosità del sapere, rimanessero <lb></lb>quegli astanti maravigliati dallo spettacolo, e l&#039;Autore stesso non potè te­<lb></lb>nersi di esclamare, dop&#039;averlo descritto: “ Profecto pulchrum est spectatu <lb></lb>consideratuque pulcherrimum quo pacto duo nervuli adeo parvuli tam bel­<lb></lb>lam edant actionem, qualis est vocis ipsius efformatio ” (De re anat. </s>

<s>cit., <lb></lb>pag. </s>

<s>259). L&#039;esperimento poi ripetuto da tanti, e con particolare eloquenza <lb></lb>descritto dal Casserio (De laryngis hist. </s>

<s>cit., pag. </s>

<s>67), fece sì che a quei <lb></lb>nervi si desse indifferentemente il nome di ricorrenti e di <emph type="italics"></emph>vocali.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Pareva così fatto argomento sperimentale sufficiente a disingannare i <lb></lb>Peripatetici, ma perchè, se non dovevano credere ad Aristotile, preferi­<lb></lb>vano le dottrine degli altri filosofi a quelle di Galeno, e perciò dicevano <lb></lb>che, se la voce non nasce dal cuore, può venir benissimo dalla gola e dai <lb></lb>polmoni. </s>

<s>In questo, apparve un Aristotelico autorevolissimo in Girolamo Fa­<lb></lb>bricio, il quale si trovò costretto a confessar dai fatti osservati che non si <lb></lb>potevano in nessun modo salvare le opinioni de&#039;filosofi antichi. </s>

<s>Prima, per­<lb></lb>ch&#039;essendovi bisogno a produr la voce dell&#039;elisione dell&#039;aria non hanno mu­<lb></lb>scoli per comprimerla nè i polmoni nè i bronchi; poi perchè si vede che, <lb></lb>incisa la trachea, passa bene il respiro, ma la voce cessa, e ritorna subito <lb></lb>allora che viene a richiudersi la ferita. </s>

<s>Da ciò conclude esso Fabricio esser <lb></lb>veramente organo della voce la laringe, o la glottide in lei che, vociferando <lb></lb>l&#039;animale, restringe la sua fessura. </s>

<s>Di che, egli soggiunge, ne&#039;polli, i quali <lb></lb>hanno quella stessa laringe così semplice, e collocata a sommo la trachea, <lb></lb>può aversi dimostrazione oculata. </s>

<s>“ Quod si etiam oculata fide id experiri <lb></lb>placet, gallinaceus pullus aut pennatum sumatur animal, et aperto ore vo­<lb></lb>ciferari cogatur: manifesto apparebit rem ita se habere, nam quando vocem <lb></lb>emittunt rimulam angustant, ubi vero abstinent, ipsam latiorem reddunt ” <lb></lb>(De larynge, Opera omnia cit., pag. </s>

<s>280). </s></p><p type="main">

<s>Dopo queste dimostrazioni, confermate da quell&#039;accuratissimo trattato, <lb></lb>che ne distendeva della laringe in quel medesimo tempo il Casserio; rimase <lb></lb>a pochi oramai più dubbio intorno alle verità galeniche, ma pur si voleva <lb></lb>sapere, per meglio acquietare la mente, come da così semplice disposizion <lb></lb>della glottide venisse a modularsi tanta varietà di note e di tuoni. </s>

<s>Lo stesso <lb></lb>Acquapendente, in quel suo curioso trattatello <emph type="italics"></emph>De brutorum loquela,<emph.end type="italics"></emph.end> ne <lb></lb>avea tanto più ardente acceso il desiderio, in quanto v&#039;avea scritto che il <pb xlink:href="020/01/1549.jpg" pagenum="424"></pb>passar la voce dal grave all&#039;acuto “ videtur ad animi affectus nuntiandos <lb></lb>non mediocriter conferre ” (ibid., pag. </s>

<s>323), no negli uomini soli, ma nei <lb></lb>bruti; anzi nelle stesse cose inanimate, come si vede per esempio nelle corde <lb></lb>tese all&#039;unisono, che si risentono quasi vive al suono di un altro strumento. </s></p><p type="main">

<s>L&#039;intraveduta somiglianza fra l&#039;organo musicale e quello animale por­<lb></lb>geva non difficile risoluzione al nuovo proposto problema, e infatti l&#039;Acqua­<lb></lb>pendente fu primo a insegnar che la voce si modula nella gola, a quel modo <lb></lb>che nel flauto stesso si modula il suono. </s>

<s>E come in tale strumento s&#039;ottien <lb></lb>dall&#039;arte il grave e l&#039;acuto, allargando e stringendo l&#039;apertura della lin­<lb></lb>guetta, e rendendo il tubo ora più ora meno largo, ora più ora meno lungo; <lb></lb>così opera la Natura nell&#039;organo animale per produrre il medesimo effetto. <lb></lb></s>

<s>“ Itaque tribus modis vox gravis acutaque perficitur, aut ex angustia, rimu­<lb></lb>lae maiore vel minore, aut ex longitudine et brevitate canalis, aut demum <lb></lb>ex eiusdem canalis latitudine maiore minoreque. </s>

<s>Nam ex minore rimulae <lb></lb>angustia, et canalis tum longitudine tum latitudine, maiore gravior, contra <lb></lb>vero acutior vox efficitur ” (De larynge cit., pag. </s>

<s>301). </s></p><p type="main">

<s>Il Casserio si diffonde prolissamente in descrivere le somiglianze, che <lb></lb>passano fra la laringe e i varii strumenti musicali a fiato, così in produr <lb></lb>la voce, come in modulare i varii tuoni, e per un secolo intero si ripete­<lb></lb>rono le dottrine di lui e dell&#039;Acquapendente, senza muover dubbio se fos­<lb></lb>sero vere. </s>

<s>Si venne però col tempo a riconoscere in quelle prime così se­<lb></lb>ducenti analogie qualche fallacia, perchè ogni strumento musicale a fiato si <lb></lb>compone di tre parti: di quella che manda l&#039;aria, di quella che produce il <lb></lb>suono, e della terza infine che produce la risonanza. </s>

<s>Ora nella teorica del­<lb></lb>l&#039;Acquapendente e del Casserio si davano alla trachea due ufficii fra sè <lb></lb>incompatibili, quali erano tutto insieme di mandare il fiato e di risonare. </s></p><p type="main">

<s>Denis Dodart nel 1700 fu primo a rivelare innanzi all&#039;Accademia pa­<lb></lb>rigina questa fallacia, e ritenuto essere la trachea semplice strumento pneu­<lb></lb>matico, esser la glottide precipuo organo acustico, si dette a ricercar quel­<lb></lb>l&#039;altro, che facesse nell&#039;animale da corpo di risonanza. </s>

<s>Riguardando dunque <lb></lb>prima di tutto la trachea come il tubo pneumatico della laringe, il Gassendo, <lb></lb>in trattar <emph type="italics"></emph>De voce animalium,<emph.end type="italics"></emph.end> avea posto il fondamento alle relative teorie <lb></lb>acustiche, con dir che l&#039;aria dee uscire dall&#039;aspera arteria con tanta velo­<lb></lb>cità, con quanta si vede esser necessario che si metta a vibrare una corda <lb></lb>sonora. </s>

<s>“ Et quanta quidem pernicitate aerem ex arteria prosilire necesse <lb></lb>sit, ut vox simpliciter creetur, intelligitur abunde ex iis, quae suo loco de <lb></lb>natura soni disserentes deduximus, cum esse eam non minorem oporteat <lb></lb>quam ituum et redituum fidis, quippe esse illos debere incredibiliter celeres <lb></lb>et crebros declaravimus ” (Syntagmatis philos., P. II, S. III, Operum T. II, <lb></lb>Florentiae 1727, pag. </s>

<s>457). </s></p><p type="main">

<s>Ripensando ora il Dedart a questa incredibile celerità, necessaria a pro­<lb></lb>dur la voce, ebbe a riconoscere, applicando all&#039;aria che passa per la tra­<lb></lb>chea la legge delle velocità de&#039;liquidi ne&#039;canali in ragion reciproca delle <lb></lb>sezioni, che dee l&#039;aria stessa risalir da&#039;bronchi alla laringe sempre più <pb xlink:href="020/01/1550.jpg" pagenum="425"></pb>lenta. </s>

<s>Anche Galeno, facilmente persuaso della necessaria celerità dell&#039;aria <lb></lb>in uscir dalla glottide, pare presentisse quella medesima difficoltà, che venne <lb></lb>tanti secoli dopo ad affacciarsi alla mente dell&#039;Accademico parigino, e sco­<lb></lb>perti dall&#039;antico padre dell&#039;Anatomia i ventricoli, rimasti ignoti a tutti i <lb></lb>suoi predecessori, pensò che in essi, chiusa la glottide, si comprimesse l&#039;aria, <lb></lb>la quale poi sfogandosi, quand&#039;essa glottide apre le labbra, entri in quella <lb></lb>celerità richiesta a produrre il suono. </s>

<s>“ Natura ventriculum apposuit non <lb></lb>parvum, ad quem, quum aer vias nactus amplas in animal ingreditur, rur­<lb></lb>susque exit, nihil in ventrem prosilire. </s>

<s>Porro, si transitus fuerit obstructus, <lb></lb>ibi tum arctatus aer pellitur violenter in obliquum lingulae, quae aperit <lb></lb>orificium, quod labiis applicatis clausum hactenus erat ” (De usu partium <lb></lb>cit., pag. </s>

<s>408). </s></p><p type="main">

<s>Anche l&#039;Acquapendente e il Casserio ripeterono esser questo assegnato <lb></lb>da Galeno il principale ufficio de&#039;ventricoli della laringe, ma il Dodart, in­<lb></lb>vocando la legge idraulica sopra accennata, dalla quale si conclude che la <lb></lb>celerità di ogni fluido che corre dentro un canale da null&#039;altro dipende che <lb></lb>dalla sezione, facilmente riconobbe che poteva la glottide così restringere la <lb></lb>sua apertura, e ridurla tanto minore rispetto a quella della trachea, da ba­<lb></lb>star questo solo a metter l&#039;aria in moto di risonanza. </s></p><p type="main">

<s>Emendati così questi errori colla scienza del moto de&#039;fluidi, ignota a <lb></lb>tutti coloro che avevano preceduto Benedetto Castelli, ciò che più impor­<lb></lb>tava al Dodart era quello di ritrovare il corpo della risonanza. </s>

<s>E giacchè <lb></lb>questo corpo, stando l&#039;organo sonoro nel mezzo, riesce ne&#039;musicali stru­<lb></lb>menti dalla parte opposta a quella che manda il fiato, dove in altro luogo <lb></lb>più acconcio, ragionava esso Dodart, può farsi la risonanza che nella cavità <lb></lb>del naso e della bocca? </s>

<s>“ On ne peut, selon cette analogie, attribuer le ton <lb></lb>qu&#039;à la bouche et aux narines, qui font le résonnement, ou à la glotte qui <lb></lb>fait le son; et comme tous les differens tons sont produits dans l&#039;homme <lb></lb>par le même instrument, il faut que la partie qui les produit soit capable <lb></lb>de changemens qui puissent y avoir rapport. </s>

<s>Pour un ton bas il faut plus <lb></lb>d&#039;air que pour un ton haut. </s>

<s>La trachée pour laisser passer cette plus grande <lb></lb>quantité d&#039;air se dilate, s&#039;accourcit, et en s&#039;accourcissant tire le canal de la <lb></lb>bouche et l&#039;allonge. </s>

<s>Au contraire pour un ton haut elle se resserre, s&#039;al­<lb></lb>longe et permet au canal de la bouche de s&#039;accourcir. </s>

<s>On pourroit donc <lb></lb>croire que le canal de la bouche plus long pour les tons graves, et plus <lb></lb>court pour les aigus, est iustement ce qu&#039;il faut pour la production des <lb></lb>tons ” (Collection académique, T. </s>

<s>I cit., pag. </s>

<s>497). </s></p><p type="main">

<s>Queste dottrine, in cui al flauto della voce animale si ritrovavan le più <lb></lb>giuste parti, dandosi a loro nello stesso tempo la disposizione più conve­<lb></lb>niente ai flauti musicali; furono accolte con gran plauso e approvate dai <lb></lb>più eletti ingegni del secolo XVIII, fra&#039;quali basti per noi poter citare il <lb></lb>Morgagni. </s>

<s>Se non che il grande Anatomico, più diligentemente esaminando <lb></lb>i ventricoli, ebbe a maravigliarsi che il Dodart, nella sua nuova instituzione, <lb></lb>non ne facesse alcun conto, di che riconobbe la causa nelle negligenti de-<pb xlink:href="020/01/1551.jpg" pagenum="426"></pb>scrizioni dell&#039;Acquapendente e del Casserio, i quali, in tanto assiduo studio <lb></lb>posto intorno alla laringe dell&#039;uomo, non si comprende come non fermas­<lb></lb>sero mai la loro attenzione in que&#039;seni ventricolari, per delinearne almeno <lb></lb>gli orificii. </s>

<s>Lo stesso Acquapendente, dop&#039;aver detto “ ventricolos obtinere <lb></lb>equum et porcum, ex iis quae novi ” (De larynge cit., pag. </s>

<s>292), si con­<lb></lb>tenta di soggiunger semplicemente: “ homines autem habent quidem, sed <lb></lb>non ita profundos ” (ibid.), e il Casserio, limitandosi all&#039;esame della laringe <lb></lb>porcina, “ opera horum ventriculorum, egli dice, porcos vocem illam, quam <lb></lb>grunnitum dicimus, absolvere verisimile est ” (De laryngis hist. </s>

<s>cit., pag. </s>

<s>183). </s></p><p type="main">

<s>Il Morgagni dunque, avendo riconosciuto che il poco diligente esame <lb></lb>dell&#039;organo era stato causa che ne fosse da&#039;suoi predecessori così poco ve­<lb></lb>rosimile designato l&#039;uso, cominciò a meditar di proposito intorno a ciò, e a <lb></lb>sospettar che i ventricoli servissero principalmente a modulare i suoni. </s>

<s>Dava <lb></lb>fondamento al suo sospetto l&#039;Acquapendente, il quale si ricordava aver os­<lb></lb>servato che fra le rane gracidano in tuono più grave di tutte l&#039;altre quelle <lb></lb>“ quae prope aures ex utraque parte foramen obtinent, membrana quadam <lb></lb>tenui ac laxissima obductum, per quod in expiratione aer egrediens, mem­<lb></lb>branam exterius impulsam utrinque inflat ampullam, veluti faciens ut ex <lb></lb>maiori facta cavitate gravior vox subsequatur ” (De larynge cit., pag. </s>

<s>304). </s></p><p type="main">

<s>Or pensava il Morgagni che i ventricoli della laringe, come si possono <lb></lb>facilmente restringere, così anche facilmente si possono dilatare: o perchè <lb></lb>dunque si negherebbe che quegli stessi ventricoli servano all&#039;uomo e agli <lb></lb>animali, come le vescicole alle rane, per far d&#039;uno in altro tuono passare <lb></lb>a talento la voce? </s>

<s>“ Sunt enim ventriculi, ut ante demonstrabam, statim <lb></lb>intra paris thyroarytaenoidaei atque adeo etiam intra thyroidis circumferen­<lb></lb>tiam constitutis, sic ut, his contractis aut relaxatis, illi quoque compriman­<lb></lb>tur vel amplientur. </s>

<s>Illud autem musculorum par, sicuti in acutis tonis, <lb></lb>constringendae glottidis gratia, contrahitur, unàquè, ob eandem causam, thy­<lb></lb>roides ab staphylo pharingaeis, atque a thyro pharingaeis coarctatur; ita <lb></lb>apposita de causa illud idem thyroarytaenoidaeum par, eademque cartilago <lb></lb>in tonis gravibus remittuntur ” (Adversaria anat. </s>

<s>omnia, Patavii 1719, pag. </s>

<s>18). </s></p><p type="main">

<s>La tranquilla meditazione intorno alla verosimiglianza di questa ipotesi, <lb></lb>che il Morgagni proponeva agli studiosi, venne a un tratto turbata dai ru­<lb></lb>mori sollevati da Antonio Ferrein in mezzo alla stessa Accademia di Parigi, <lb></lb>dove, leggendo nel 1741 una sua dissertazione <emph type="italics"></emph>De la formation de la voix <lb></lb>de l&#039;homme,<emph.end type="italics"></emph.end> sosteneva, contro il Dodart e contro tutti i Galenisti, che la <lb></lb>laringe non è uno strumento a fiato ma a corda; non è simile al flauto, ma <lb></lb>alla lira. </s>

<s>La cosa per verità non era nuova: l&#039;aveva accennata già nel <lb></lb>IV libro <emph type="italics"></emph>De resolutione corporis humani<emph.end type="italics"></emph.end> il Varolio, e più recentemente il <lb></lb>Perrault aveva, nel suo trattato <emph type="italics"></emph>De bruit,<emph.end type="italics"></emph.end> così lasciato scritto: “ Pour ce <lb></lb>qui regarde le ton de la voix, il est bas et grave quand la glotte fait une <lb></lb>sente bien longue: car alors la longueur de l&#039;une et de l&#039;autre membrane <lb></lb>qui composent la glotte rendant chaque membrane làche et peu rendue, <lb></lb>leurs ondoyemens sont rares et lents, d&#039;ou il s&#039;ensuit que les parties emùes <pb xlink:href="020/01/1552.jpg" pagenum="427"></pb>ne froissent les particules que loin à loin, ce qui fait le ton grave; le ton <lb></lb>aigu se fait par des causes opposées ” (Oeuvres cit., pag. </s>

<s>220). Nonostante <lb></lb>seppe così bene il Ferrein con esperienze nuove e con nuovi argomenti so­<lb></lb>stener l&#039;ipotesi antica, che molti, abbandonata quella del Dodart, si volsero <lb></lb>a professarla. </s>

<s>Ma l&#039;Accademia, esaminando le parti per decider se la laringe <lb></lb>operi come uno strumento a fiato o come uno strumento a corda, pronun­<lb></lb>ziò in giudizio, tuttavia approvato dai savii “ qu&#039;aucun instrument de mu­<lb></lb>sique artificial ne rassemble a la glotte ” (Collection académique, T. II, a <lb></lb>Diion 1754, pag. </s>

<s>426). </s></p><p type="main">

<s>Così, verso la metà del secolo XVIII, concludevasi, rispetto all&#039;organo <lb></lb>della voce nell&#039;uomo e ne&#039;quadrupedi, la sua storia cominciata già da Ga­<lb></lb>leno. </s>

<s>Per ciò poi che riguarda gli uccelli son le tradizioni assai meno lon­<lb></lb>tane, perchè propriamente muovono dall&#039;Aldovrandi. </s>

<s>Ripensava egli un giorno <lb></lb>a quella voce così forte e acuta, che mettono le anatre anche sott&#039;acqua, e <lb></lb>perch&#039;egli era di parere che si generasse essa voce dai polmoni, e che i <lb></lb>bronchi e la trachea facessero da corpi di risonanza, pensò di dover ritro­<lb></lb>vare, anatomizzando, in quegli organi qualche cosa, da cui si venisse a ren­<lb></lb>dere la ragione di un fatto, che gli recava stupore. </s>

<s>“ Vocem Anas cur tam <lb></lb>acutam atque magnam edat, tamquam sub aquam caput teneat, cum apud <lb></lb>meipsum mirarer, eam dissecui, causam eius scrutaturus haud dubio ex ar­<lb></lb>teriae asperae figura, quam sane diversam esse ab aliis reperi. </s>

<s>Quae igitur <lb></lb>bifariam divaricatur in pulmones vesicam quandam habet duram, cartilagi­<lb></lb>neam, concavam ubi maior apparet dextrorsum vergentem, eiusque bene­<lb></lb>ficio quae hactenus in ea stupebam obire iudicavi ” (Ornithologiae, T. III, <lb></lb>lib. </s>

<s>XIX, Francof. </s>

<s>1613, pag. </s>

<s>83). </s></p><p type="main">

<s>S&#039;ingerì da questa scoperta nella mente dell&#039;Aldovrandi l&#039;opinione, che <lb></lb>tutti quegli uccelli, i quali hanno voce più sonora o canto più dolce, sieno <lb></lb>anche serviti da qualche organo aggiunto alla semplice laringe superiore. </s>

<s><lb></lb>Trovò fra poeti e filosofi antichi una famosa controversia, dicendo questi che <lb></lb>il Cigno non canta, e quelli asserendo che anzi modula dolcissime armonie, <lb></lb>piene d&#039;una ineffabile mestizia, quando sentesi presso alla morte. </s>

<s>Riducen­<lb></lb>dosi perciò la cosa a una questione ornitologica, il nostro Autore nel cap. </s>

<s>I <lb></lb>del sopra citato libro ne tratta, prima eruditamente, e poi, inclinando a fa­<lb></lb>vorire i poeti, si rivolge all&#039;anatomia, la quale, gli rivelava ne&#039;Cigni organi <lb></lb>simili a quelli già scoperti nell&#039;Anatre, ma tanto più squisiti, da non si du­<lb></lb>bitar che servissero al canto. </s>

<s>“ Non modicam fidem faciet praeclara illa et <lb></lb>suspicienda arteriae asperae structura, ante hac a nullo alio, quod equidem <lb></lb>sciam, observata. </s>

<s>Ea enim, cum duplici reflexione tubae bellicae figuram <lb></lb>exactissime repraesentet, qua quamlibet tam acutorum quam gravium so­<lb></lb>norum varietatem modulantes tibicines effingere solent; Natura nihil frustra <lb></lb>facere neque etiam actionem illam sine idoneis functionique accomodatis <lb></lb>instrumentis obire soleat, minime vulgaris organi argumento; facile inducor <lb></lb>ut verisimiliorem eorum esse credam sententiam, qui dulce melos, praeser­<lb></lb>tim morte vicinos, Cycnos cantare dicunt ” (ibid., pag. </s>

<s>9). </s></p><pb xlink:href="020/01/1553.jpg" pagenum="428"></pb><p type="main">

<s>In quel medesimo tempo, che si pubblicava questa Ornitologia, il Cas­<lb></lb>serio e l&#039;Acquapendente attendevano ai loro particolari trattati intorno alla <lb></lb>laringe, ne&#039;quali, poco tempo dopo venuti alla luce, non facevasi nessun <lb></lb>cenno de&#039;nuovi organi scoperti dall&#039;Aldovrandi. </s>

<s>Cosicchè, dietro l&#039;autore­<lb></lb>volissimo magistero de&#039;due insigni Autori commemorati, si tenne general­<lb></lb>mente, e per quasi tutto il secolo XVII, esser organo del canto negli uc­<lb></lb>celli quella laringe, che lo stesso Acquapendente diceva esser sì facilmente <lb></lb>visibile nelle aperte fauci di tutti gli animali pennuti, e di così semplice <lb></lb>struttura, “ siquidem asperam arteriam in rimulam desinere in iis apparet ” <lb></lb>(De larynge cit., pag. </s>

<s>284) </s></p><p type="main">

<s>Se non che, ripensandoci in seguito meglio, pareva impossibile che in <lb></lb>certi uccelli un organo così semplice si prestasse a tanta mobile varietà, e <lb></lb>a tanta squisita arte di canto. </s>

<s>Fu perciò il Perrauìt uno de&#039;più studiosi in­<lb></lb>torno ai dimenticati organi scoperti dall&#039;Aldovrandi, e giovandosi della pro­<lb></lb>pria esperienza e del portato dei tempi fu assai più felice in riconoscerne <lb></lb>gli usi. </s>

<s>Ripudiatasi dal Nostro la scienza galenica, e credendo, come sopra <lb></lb>dicemmo, che la voce movesse dai polmoni, errava nel dire che quel du­<lb></lb>plice flesso, osservato nella trachea de&#039;Cigni, a ciò solo servisse “ ut ne <lb></lb>vox in tam longo arteriae spacio evanesceret, neve prolixo adeo itinere fa­<lb></lb>tisceret, sed in ipso revolutae arteriae angulo repercussa maiori cum clan­<lb></lb>gore erumperet, ac veluti morulae exiguae in eo anfractu quiete recreata <lb></lb>vires acquirat eundo ” (Ornithol., T. cit., pag. </s>

<s>9) </s></p><p type="main">

<s>Lette queste cose il Perrault non dubitò di credere che organo così <lb></lb>artificioso, piuttosto che a rinforzarla, servisse a produrre la voce, e che fosse <lb></lb>insomma una vera e propria laringe. </s>

<s>Era in ogni modo però necessario che <lb></lb>un&#039;idea tanto nuova fosse confermata dall&#039;esperienza. </s>

<s>Ripensando al modo <lb></lb>migliore di eseguirla, si sovvenne di aver letto nel trattato <emph type="italics"></emph>De larynge<emph.end type="italics"></emph.end> che, <lb></lb>mentre un giorno l&#039;Acquapendente esponeva in pubblico anfiteatro gli usi <lb></lb>di quell&#039;organo della voce, si levò un uditore a dire: — Maestro, a un uc­<lb></lb>cello morto soffiando per l&#039;aspera arteria, ho trevato che mandava la stessa <lb></lb>voce come se fosse vivo. </s>

<s>— Non apprezzando il Fabricio quanto si meri­<lb></lb>tava quella esperienza, si contentò di rispondere che si poteva da quel fatto <lb></lb>concluderne “ adesse cuique animali proprium organum, idest suam laryn­<lb></lb>gis constitutionem ” (De larynge cit., pag. </s>

<s>305). </s></p><p type="main">

<s>Ma il Perrault pensò che si poteva l&#039;esperienza dello scolare di Padova <lb></lb>bellamente e utilmente applicare al suo intento, ch&#039;era quello di mostrar <lb></lb>come l&#039;organo, posto al punto in cui la trachea si biforca negli uccelli, è <lb></lb>una vera laringe. </s>

<s>Se ucciso infatti l&#039;animale, col tagliargli la testa e col por­<lb></lb>targli via perciò la laringe superiore, in soffiare al modo che diceva colui <lb></lb>nell&#039;anfiteatro anatomico padovano, o in premere le vescicole pneumatiche <lb></lb>del ventre, la voce tuttavia si produce, qual più manifesta prova potrebbesi <lb></lb>desiderare dell&#039;aver veramente gli uccelli una laringe inferiore? </s></p><p type="main">

<s>Si fu tale il ragionamento, che condusse il Perrault a quella sua bella <lb></lb>e così ben dimostrativa esperienza, della quale così dice nella seconda parte <pb xlink:href="020/01/1554.jpg" pagenum="429"></pb>della sua <emph type="italics"></emph>Mechanique dex animaux,<emph.end type="italics"></emph.end> dop&#039;aver confermata la struttura della <lb></lb>trachea nell&#039;anatre, scoperta quasi un secolo prima dall&#039;Aldovrandi: “ L&#039;effet <lb></lb>de cette structure se peut aisement connoître, si ayant coupé la tète a ces <lb></lb>animaux, et le larynx leur etant ôté, on leur presse le ventre: car alors ils <lb></lb>ne laisseront pas de produire la même voix que lorsqu&#039;ils étoient vivans, <lb></lb>et qu&#039;ils avoient un larynx ” (Oeuvres, T. </s>

<s>I cit., pag. </s>

<s>394). </s></p><p type="main">

<s>L&#039;Haller trovò poi la laringe inferiore anche nei passeri e ne&#039;galli <lb></lb>(Elem. </s>

<s>physiol., T. III cit., pag. </s>

<s>435), ed avendo altri Naturalisti osservato <lb></lb>ch&#039;è con più sottil magistero elaborata negli uccelli canori, nessun dubitò <lb></lb>ch&#039;ella non sia veramente precipuo organo, in cui si forma la voce, e per <lb></lb>cui si modula il canto. </s></p><pb xlink:href="020/01/1555.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO XI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dei pesci<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>I. </s>

<s>Degli ergani e degli esercizi del nuoto. </s>

<s>— II. </s>

<s>Della respirazione branchiale e del circolo del sangne.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>III. </s>

<s>Degli organi dei sensi.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;ordine oramai preso in questa nostra storica trattazione porterebbe <lb></lb>che, dopo aver detto di ciò che i metodi sperimentali conferirono a far pro­<lb></lb>gredire la Storia naturale de&#039;Quadrupedi e degli Uccelli nella più esatta no­<lb></lb>tizia de&#039;loro precipui organi e delle loro funzioni, si passasse a far lo stesso <lb></lb>coi <emph type="italics"></emph>Rettili,<emph.end type="italics"></emph.end> che immediatamente succedono in grado e in dignità zoologica <lb></lb>agli stessi uccelli. </s>

<s>Ma perchè quei così fatti animali a sangue freddo in non <lb></lb>poche nè lievi cose s&#039;assomigliano ai pesci, nella storia di questi si vedrà <lb></lb>specchiata qualche immagine anche di quelli. </s>

<s>E dall&#039;altra parte non è pos­<lb></lb>sibile a noi, in questa general comprensione delle scienze sperimentali, come <lb></lb>campo immenso dato a mietere a una falce sola, cogliere che le poche spi­<lb></lb>ghe più mature, e perciò più eminenti. </s></p><p type="main">

<s>In conformità dei precedenti discorsi ci occorre per prima cosa a trat­<lb></lb>tar dei moti locali, trattazione che, in questo particolar soggetto, si riduce <lb></lb>alla storia degli organi e degli esercizi del nuoto. </s>

<s>Lusingavano così le pinne <lb></lb>e le ali, per le loro apparenti somiglianze con la struttura e con gli usi <lb></lb>de&#039;remi, che nessun dubitava non fossero le pinne stesse organo ai pesci di <lb></lb>qualunque loro movimento locale. </s>

<s>Come cosa ovvia perciò i Filosofi e i Na­<lb></lb>turalisti antichi non fecero nemmeno un cenno del meccanismo animale del <lb></lb>nuoto ne&#039;loro libri, e Plinio, che si trovò costretto a rendere la ragione per-<pb xlink:href="020/01/1556.jpg" pagenum="431"></pb>chè alcuni di essi pesci nuotino anche senza le pinne, come si vede far per <lb></lb>esempio alle pastinache e ai rombi, se ne spedì con dire che <emph type="italics"></emph>ipsa latitu­<lb></lb>dine natant.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Nell&#039;età del risorgimento, tacendosene il Rondelezio, fu primo l&#039;Acqua­<lb></lb>pendente che spendesse intorno al nuoto poche parole, proponendosi di ri­<lb></lb>solvere i tre seguenti problemi: “ I. </s>

<s>Quomodo pisces et pleraque alia anima­<lb></lb>lia, vel ponderosissima et maxime terrestria, in aqua innatando sustentantur. </s>

<s><lb></lb>II. </s>

<s>Quomodo natatus in aqua fiat. </s>

<s>III. </s>

<s>Qua ratione aquatile animal ad omnes <lb></lb>loci positiones permutatur ” (De natatu, Op. </s>

<s>omnia cit., pag. </s>

<s>377). E perchè <lb></lb>veramente tutta la meccanica del nuoto concludesi dentro questi tre pro­<lb></lb>blemi, si riduce l&#039;intento nostro a narrar brevemente come quando e da chi <lb></lb>venissero risoluti. </s></p><p type="main">

<s>Quanto al primo non è difficile, dice lo stesso Acquapendente, inten­<lb></lb>dere in che modo galleggino i pesci nell&#039;acqua, vedendovisi galleggiare gli <lb></lb>uomini stessi e i quadrupedi più ponderosi. </s>

<s>Di che, poi soggiunge, tanto più <lb></lb>facilmente ci persuaderemo pensando che hanno gli stessi pesci poche ossa, <lb></lb>carne floscia alleviata anche di più da quella vescica “ oblonga, ex tunica <lb></lb>tenuissima, et densissima aereque sola plena ” (ibid.). </s></p><p type="main">

<s>Poco dopo venne Galileo a illustrare co&#039;nuovi principii meccanici e idro­<lb></lb>statici questi concetti, cominciando dal dimostrare in che modo si possan <lb></lb>facilmente sostenere nell&#039;acqua moli di animali più smisurate di quelle <lb></lb>stesse, che si sostengono in aria. </s>

<s>La dimostrazione galileiana è conclusa dal <lb></lb>principio, che equilibrandosi i pesci dentro l&#039;acqua, per essere in loro il <lb></lb>peso dell&#039;ossa compensato dalla leggerezza della polpa, non sentono perciò <lb></lb>la propria gravezza. </s>

<s>“ Talchè negli acquatici avverrà l&#039;opposto di quel che <lb></lb>accade negli animali terrestri, cioè che in questi tocchi all&#039;ossa a sostenere <lb></lb>il peso proprio e quel della carne, e in quelli la carne regge la gravezza <lb></lb>propria, e quella dell&#039;ossa. </s>

<s>E però deve cessar la maraviglia come nell&#039;acqua <lb></lb>possano essere animali vastissimi, ma non sopra la terra, cioè nell&#039;aria ” <lb></lb>(Alb. </s>

<s>XIII, 131). </s></p><p type="main">

<s>Per ciò poi che riguarda l&#039;equilibrio idrostatico aveva l&#039;Acquapendente <lb></lb>osservato che, ne&#039;notanti per l&#039;acqua dolce, come nelle tinche, nei lucci, e <lb></lb>forse in altri, è affissa alla spina del dorso una vescica, perch&#039;essendo essa <lb></lb>acqua dolce più tenue della marina è anche perciò men valida a sostenere. </s>

<s><lb></lb>Il Rondelezio però aveva molto tempo prima pensato all&#039;uso di questa ve­<lb></lb>scica, e aveva detto servire a rendere più leggero il pesce e a facilitargli il <lb></lb>modo di risalire in alto. </s>

<s>“ Aspera igitur arteria, in iis piscibus qui pulmo­<lb></lb>nibus spirant, ducendi spiritus et respirandi gratia est constructa, eiusque <lb></lb>aliquando retinendi cohibendique, ut sursum facilius ferantur: aer enim re­<lb></lb>tentus velut suspendit in aqua, demergique prohibet. </s>

<s>Cuius utilitatis causa <lb></lb>vesicam aere plenam quibusdam branchias habentibus dedit Natura ” (De <lb></lb>piscibus marinis, Lugduni 1554, pag. </s>

<s>61). </s></p><p type="main">

<s>Quel ch&#039;era dunque per l&#039;Acquapendente uno strumento inerte, e quasi <lb></lb>diremo vanitoso, riusciva pel Rondelezio un organo attivo, facendone poì <pb xlink:href="020/01/1557.jpg" pagenum="432"></pb>Galileo rilevar meglio l&#039;attività coll&#039;attribuirgli l&#039;ufficio di mantenere il pe­<lb></lb>sce sempre equilibrato in mezzo a un liquido continuamente soggetto a va­<lb></lb>riar la sua propria gravità in specie. </s>

<s>“ I pesci, egli dice, ad arbitrio loro si <lb></lb>equilibrano, non solo con un&#039;acqua, ma con differenti notabilmente o per <lb></lb>propria natura o per una sopravvenente torbida o per salsedine, che fa dif­<lb></lb>ferenza assai grande; si equilibrano dico tanto esattamente che, senza punto <lb></lb>moversi, restano in quiete in ogni luogo, e ciò per mio credere fanno eglino, <lb></lb>servendosi dello strumento datogli dalla natura a cotal fine, cioè di quella <lb></lb>vescichetta che hanno in corpo, la quale per uno assai angusto meato ri­<lb></lb>sponde alla lor bocca, e per quello a posta loro o mandano fuori parte del­<lb></lb>l&#039;aria, che in dette vesciche si contiene, o, venendo col nuoto a galla, altra <lb></lb>ne attraggono, rendendosi con tale arte or più or meno gravi dell&#039;acqua, ed <lb></lb>a lor beneplacito equilibrandosegli ” (Alb. </s>

<s>XIII, 71, 72). </s></p><p type="main">

<s>Se quell&#039;angusto meato, che mette la vescica in comunicazion colla <lb></lb>bocca, non fosse stato da Galileo semplicemente supposto, la sua ingegnosa <lb></lb>ipotesi veniva del resto a verificarsi nell&#039;esempio di quei pesciolini artifi­<lb></lb>ciali, inventati e costruiti in Roma da Raffaello Magiotti, per dimostrar la <lb></lb>renitenza certissima dell&#039;acqua alla compressione, e tutt&#039;insieme a spetta­<lb></lb>colo dei curiosi. </s>

<s>Dop&#039;aver descritti i galleggianti i quali, alterandosi la den­<lb></lb>sità dell&#039;aria in essi inclusa col variarne la temperatura o la pressione, si <lb></lb>posson rendere a piacere più o men leggeri, e così farli imitatori de&#039;na­<lb></lb>turali moti di ascesa e di discesa de&#039;pesci dentro i vivai; “ sebbene è forza, <lb></lb>soggiunge esso Magiotti, con tutti i nostri artifizi, che questi pesci finti ce­<lb></lb>dano all&#039;esattezza dei veri, quali, ritenendo in certe vescichette più o meno <lb></lb>aria, sanno in ogni sorte d&#039;acqua ragguagliarsi e contrappesarsi a maravi­<lb></lb>glia ” (Targioni, Notizie degli aggrandimenti ecc., T. II, P. II, Firenze 1780, <lb></lb>pag. </s>

<s>187). </s></p><p type="main">

<s>Rimase perciò ai seguaci della scuola galileiana l&#039;ufficio di dimostrare <lb></lb>la reale esistenza del supposto canale di comunicazione tra la vescica de&#039;pe­<lb></lb>sci e la bocca, e intanto che s&#039;aspettava qualche esperto Anatomico per aver <lb></lb>da lui una decisione di fatto, gli Accademici del Cimento gli preparavano la <lb></lb>via con lo sperimentar se l&#039;aria trova propriamente il passo aperto, e collo <lb></lb>scoprir da qual parte ella esce dalle interiori viscere dell&#039;animale all&#039;esterno. </s>

<s><lb></lb>S&#039;accendeva ne&#039;nostri Accademici fiorentini tanto più vivo il desiderio di <lb></lb>questa ricerca, in quanto che Tommaso Cornelio aveva, in una sua Epistola, <lb></lb>già diffusa nel manoscritto prima che per le pubbliche stampe, dimostrato <lb></lb>per esperienze che l&#039;acqua si trasforma in aria dentro il corpo de&#039;pesci, co­<lb></lb>sicchè essendo essa aria in loro innata non hanno bisogno, come Galileo <lb></lb>diceva, d&#039;andare a cercarla a somma l&#039;acqua, ed è vano perciò supporre o <lb></lb>dar travaglio all&#039;Anatomia di scoprir nessun occulto meato, per cui qualche <lb></lb>cosa esca o venga di fuori. </s>

<s>“ Hinc patet, così concludeva il Cornelio quella <lb></lb>citata Epistola a Marc&#039;Aurelio Severino, non omnino opus esse piscibus <lb></lb>aliisque aquatilibus ad summam aquae superficicm eniti, ut inde hauriant <lb></lb>aerem qui passim invenitur in eorundem utriculis. </s>

<s>Potest enim aer ille in <pb xlink:href="020/01/1558.jpg" pagenum="433"></pb>ipsis piscium corporibus gigni, et exinde in praefatas vesiculas, tanquam in <lb></lb>propria conceptacula, deferri, siquidem facillime humor, uti iam dictum est, <lb></lb>vertitur in aerem ” (De cognatione aeris et aquae inter Progymnasm. </s>

<s>cit., <lb></lb>pag. </s>

<s>399). </s></p><p type="main">

<s>Per decider dunque se l&#039;aria negli utricoli de&#039;pesci era innata, o co­<lb></lb>municava coll&#039;esterno, posero i nostri Accademici un Barbio nel vuoto, e <lb></lb>trovarono poi esso utricolo nelle aperte viscere raggrinzato ed esausto. </s>

<s>As­<lb></lb>sicuratisi così che quell&#039;aria inclusa era uscita, non vedendo manifeste rot­<lb></lb>ture nella membrana artificialmente distesa col fiato, e dall&#039;altra parte si­<lb></lb>curi che dovesse aver l&#039;aria nell&#039;uscire in ogni modo trovato qualche varco; <lb></lb>sospettarono che ciò fosse nella più aguzza parte della vescica. </s>

<s>“ Quindi fu <lb></lb>pensato a far sì che l&#039;acqua medesima ce lo discoprisse. </s>

<s>Per lo che, fatta <lb></lb>cavare un&#039;altra vescica da un pesce vivo e sano, s&#039;involse in un brandello <lb></lb>di rete, e quella aggravata di conveniente peso si messe al solito in acqua, <lb></lb>sotto alla quale essendo rimasta, fatto il vuoto, si veddero uscire per la <lb></lb>parte aguzza molte gallozzole d&#039;aria, onde parve di poter verisimilmente cre­<lb></lb>dere esser quivi il meato naturale che la trasmette ” (Saggi di natur. </s>

<s>esper., <lb></lb>Firenze 1841, pag. </s>

<s>74). </s></p><p type="main">

<s>Restava, per più piena conferma del supposto galileiano, a dimostrar <lb></lb>che essa aria veniva veramente trasmessa alla bocca, e i nostri Accademici <lb></lb>non mancarono di farlo per via della seguente esperienza: “ Si rinvolse una <lb></lb>Lasca nella stessa rete, acciocchè, trattenuta in fondo dal peso attaccatole, <lb></lb>avesse per necessità a rimaner sott&#039;acqua. </s>

<s>Fattosi dunque il voto, se le <lb></lb>vedde fare grandissima copia d&#039;aria per bocca, la qual veniva in grossis­<lb></lb>sime bolle, nello stesso modo che s&#039;era veduta uscire dalla vescica som­<lb></lb>mersa ” (ivi). </s></p><p type="main">

<s>Messo così in piena evidenza il passaggio dell&#039;aria dalla vescica alla <lb></lb>bocca, Carlo Fracassati venne finalmente a rendere, colla sua sottile arte <lb></lb>anatomica, visibile agli occhi di ognuno quel canale di comunicazione indo­<lb></lb>vinato già da Galileo, gl&#039;insegnamenti del quale tornavano intanto d&#039;ogni <lb></lb>parte vittoriosi sopra quelli di Tommaso Cornelio. </s>

<s>“ Ipse quidem, scrive il <lb></lb>Fracassati nell&#039;Epistola <emph type="italics"></emph>De cerebro<emph.end type="italics"></emph.end> a Marcello Malpighi, ipse quidem de­<lb></lb>prehendi meatum ad folliculum aeris quo pisces perpetuo nataturi gaudent, <lb></lb>ex quo patet non ingenitum esse in utricolo natatorio aerem, sed ades se <lb></lb>quaedam commercia extrinseci, vel in aqua deliquescentis aeris cum illo ” <lb></lb>(M. Malpighi, Operum, T. II cit., pag. </s>

<s>144). </s></p><p type="main">

<s>Così venivano pienamente dimostrati gli usi, rimasti prima sì incerti, <lb></lb>della vescica dei pesci, la quale nessuno poi dubitò di chiamarla <emph type="italics"></emph>natatoria,<emph.end type="italics"></emph.end><lb></lb>dietro il primo esempio datone dal Fracassati. </s>

<s>L&#039;incertezza nasceva special­<lb></lb>mente dal parer che ella servisse piuttosto alla respirazione e al più al più <lb></lb>s&#039;ammetteva che potesse aver quell&#039;organo qualche ufficio secondario nel <lb></lb>nuoto. </s>

<s>L&#039;Harvey infatti rassomigliava la vescicola pneumatica de&#039;pesci alle <lb></lb>vescicole pneumatiche degli uccelli, nelle quali egli dice che si compie la <lb></lb>respirazione incominciatasi ne&#039;polmoni. </s>

<s>“ Quin etiam (quod tamen a nemine <pb xlink:href="020/01/1559.jpg" pagenum="434"></pb>hactenus observatum memini) earum bronchia, sive asperae arteriae fines <lb></lb>in abdomen perforantur, aeremque inspiratum intra cavitates illarum mem­<lb></lb>branarum recondunt, quemadmodum pisces et serpentes intra amplas vesi­<lb></lb>cas in abdomine positas eumdem attrahunt, et reservant, eoque facilius na­<lb></lb>tare existimantur ” (De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>5). </s></p><p type="main">

<s>Nel Mersenno, per citar l&#039;esempio di un&#039;altra grande autorità nella <lb></lb>scienza a que&#039;tempi, l&#039;incertezza se la vescica serva da polmone o da gal­<lb></lb>leggiante è anche più chiaramente espressa là dove, nel terzo Tomo delle <lb></lb>Nuove osservazioni, dice a proposito della respirazione esser dubbio se da <lb></lb>essa propriamente dipende la vita, vedendosi i pesci vivere senza respirare <lb></lb>“ nisi forte, poi però soggiunge, vim aliquam seu facultatem habeant qua <lb></lb>separent aerem ab aqua, eoque nobis nescientibus utantur. </s>

<s>Quod ex illorum <lb></lb>videtur confirmari follibus seu vesiculis aere inflatis, quales reperiuntur in <lb></lb>carpionibus et aliis piscibus, licet plerique censeant huiusmodi vesiculas illis <lb></lb>solum datas ut natare possint ” (Parisiis 1647, pag. </s>

<s>106). </s></p><p type="main">

<s>L&#039;esperienze dunque de&#039;nostri Accademici, alle quali s&#039;aggiungevano <lb></lb>quelle del Boyle, venivano a dissipare i dubbi del Mersenno e dell&#039;Harvey, <lb></lb>dimostrandosi per esse evidentemente che, votatasi ai pesci d&#039;ogni aria la <lb></lb>vescica, non era a loro più possibile sollevarsi, come prima facevano, a galla, <lb></lb>ma si vedevano dentro i vivai “ sempre andarsene terra terra notando con <lb></lb>la pancia rasente il fondo ” (Saggi cit., pag. </s>

<s>72). Dal vedere altresì in quelle <lb></lb>esperienze i pesci colla vescica esausta rivoltarsi supini, senza mai per qua­<lb></lb>lunque sforzo potersi riavere, veniva a dimostrarsi un altr&#039;uso importantis­<lb></lb>simo della stessa vescica, qual&#039;è quello di stabilire il centro della gravità nel <lb></lb>punto più conveniente alla natural posizione dell&#039;animale. </s></p><p type="main">

<s>Chi ripensa ora, dopo le cose narrate, che la massima parte dell&#039;espe­<lb></lb>rienze si facevano nell&#039;Accademia fiorentina sotto la direzione del Borelli, <lb></lb>in casa del quale in Pisa il Fracassati stesso, nella sopra citata Epistola <emph type="italics"></emph>De <lb></lb>cerebro<emph.end type="italics"></emph.end> (pag. </s>

<s>143), confessa d&#039;essersi esercitato intorno alle sue prime ana­<lb></lb>tomie dei pesci; anche prima di svolgere le pagine del libro s&#039;aspetta di <lb></lb>vedere stillato il succo di quelle dottrine e, come in suo proprio vaso, rac­<lb></lb>colto nell&#039;Opera dei moti animali. </s></p><p type="main">

<s>Nella proposizione CCXI infatti della Parte I, attendendo l&#039;Autore a ri­<lb></lb>cercar l&#039;organo per cui i pesci s&#039;equilibran nell&#039;acqua, lo ritrova facilmente <lb></lb>nella vescica, l&#039;aria della quale pensa che si potrebbe ora condensare e ora <lb></lb>dilatare per l&#039;azion delle fibre muscolari, di ch&#039;è intessuta la stessa mem­<lb></lb>brana, operanti a quel modo che nello sfintere dell&#039;ano o nella vescica uri­<lb></lb>naria. </s>

<s>Questo pensiero, che apparisce nuovo e tutto proprio al Borelli, ve­<lb></lb>niva confermato da quella esperienza degli Accademici del Cimento, per la <lb></lb>quale mostravasi che in un Barbio, stato prima nel vuoto, avevano le deli­<lb></lb>cate fibre della vescica nel violento sforzo così sofferto, da non essere ora­<lb></lb>mai più atte al loro ufficio. </s>

<s>Ond&#039;è che, sebbene al paziente si trovasse dopo <lb></lb>morto la vescica stessa “ gonfia come suol esser naturalmente ” l&#039;esser <lb></lb>però “ men dura a comprimersi che non son quelle degli altri pesci ” era <pb xlink:href="020/01/1560.jpg" pagenum="435"></pb>a quel Barbio causa che movendosi non potesse far altro che rasentar, senza <lb></lb>mai sollevarsene, il fondo del vivaio (Saggi cit., pag. </s>

<s>72). </s></p><p type="main">

<s>Nonostante riconobbe il Borelli esser questa operazione dello sfintere <lb></lb>della vescica d&#039;assai poco momento, e perciò, a spiegar in che modo i pesci <lb></lb>contemperino così destramente la loro propria gravità in specie a quella così <lb></lb>mutabile dell&#039;acqua, invocò come più efficaci delle sue nuove le dottrine <lb></lb>antiche di Galileo. </s>

<s>“ Haec autem vesicae aereae piscium dilatatio exigua esse <lb></lb>videtur, et ideo non sufficiet ad aequilibrium transmutandum in locis, in <lb></lb>quibus aqua dulcis est et parum gravis, et tunc puto quod pisces vi remi­<lb></lb>gatiouis sustinentur, et ad summitatem aquae perducuntur, ut novum aerem <lb></lb>deglutiendo minus graves in specie reddantur. </s>

<s>Qui postea, si superfluus fue­<lb></lb>rit in locis aquae profundioribus et gravioribus, evomitur per os, et solum <lb></lb>modo retinetur portio adaequata, ut absque laboriosa compressione aequili­<lb></lb>brata in fundo permanere et quiescere possint. </s>

<s>Quod postea aer praedictae <lb></lb>vesicae piscium multiplicari, novum aerem sorbendo, et minui, evomendo <lb></lb>superfluum, per os possit, prout necessitas aequilibrii eorum exigit, suade­<lb></lb>tur ex canali manifesto, licet subtili et stricto, praedictae vesicae, qui in <lb></lb>fundo stomachi desinit, et frustra factus esse non potest. </s>

<s>Imo per eum in <lb></lb>vacuo torricelliano talis vesica aere exinanitur, quando piscis per os mul­<lb></lb>tiplices spumosas ampullas eructat ” (De motu anim., P. I, Romae 1680, <lb></lb>pag. </s>

<s>338, 39). </s></p><p type="main">

<s>Il manifesto, benchè sottile e stretto canale, di che qui parla il Borelli, <lb></lb>è senza dubbio quello scoperto dal Fracassati, il quale dee essersi senza <lb></lb>altro abbattuto a sezionare una Cheppia, quando per la prima volta mo­<lb></lb>strò in Pisa quell&#039;organo tanto desiderato da&#039;Galileiani alla presenza dei <lb></lb>cortigiani medicei e degli amici convenuti insieme nelle case dello stesso Bo­<lb></lb>relli. </s>

<s>Nelle Cheppie infatti quel cannellino della vescica mette capo in fondo <lb></lb>allo stomaco e vien dal Fracassati, nell&#039;Epistola <emph type="italics"></emph>De Cerebro,<emph.end type="italics"></emph.end> così descritto: <lb></lb>“ In Clupea, postquam a ventriculi inferiori parte innumera pene intestinula <lb></lb>coeca prodierint, videtur totus ventriculus in hunc meatum abire, qui ad <lb></lb>bifidam aeream vesicam eadem prorsus implantatione progredetur ” (loco <lb></lb>cit., pag. </s>

<s>145). Or il Borelli credè che il termine del canaliculo nelle Chep­<lb></lb>pie fosse il medesimo che in tutti i pesci, e perciò sentenziò in generale <lb></lb>che <emph type="italics"></emph>in fundo stomachi desinit.<emph.end type="italics"></emph.end> Ma aveva già il Fracassati diligentemente <lb></lb>notato che <emph type="italics"></emph>variat meatus huius in aliis piscibus origo,<emph.end type="italics"></emph.end> e nella Tinca per <lb></lb>esempio non è dal fondo dello stomaco, ma dal principio. </s>

<s>“ In Tinca mea­<lb></lb>tus hic (quem antea ignotum fuisse credo) oritur ab initio stomachi ubi <lb></lb>dilatatur, et cavitatem infundibulo similem aemulatur. </s>

<s>Mox attenuatur, ac ad <lb></lb>medium utriculi illius ducitur, qui in medio se cogens, veluti duorum tur­<lb></lb>binum coalitu, clepsydram pulverariam refert, ibique implantatur ” (ibid., <lb></lb>pag. </s>

<s>144). </s></p><p type="main">

<s>Il Redi poi osservò che tale, quale il Fracassati la descrisse nella Tinca, <lb></lb>è la disposizione del canaliculo nella vescica della massima parte dei pesci, <lb></lb>e non potè con tutta la riverenza tenersi dallo svelare ai Naturalisti l&#039;er-<pb xlink:href="020/01/1561.jpg" pagenum="436"></pb>rore, che s&#039;ascondeva nelle sentenziose parole del Borelli. </s>

<s>“ Il famoso e ve­<lb></lb>ramente grandissimo Geometra Giovanni Alfonso Borelli (così egli scrive nel <lb></lb>trattato <emph type="italics"></emph>Degli animali viventi negli animali viventi<emph.end type="italics"></emph.end>) affermò che questo <lb></lb>suddetto canale, per cui può uscire ed entrare l&#039;aria nel notatoio o vescica, <lb></lb>partendosi da essa vescica, va ad insinuarsi e a metter capo nel fondo dello <lb></lb>stomaco de&#039;pesci: ma non in tutti i pesci mette capo quel canale nel fondo <lb></lb>dello stomaco, conforme per avventura parve a questo grand&#039;uomo, anzi per <lb></lb>dire il vero in una sola spezie di pesci ho trovato che nel fondo dello sto­<lb></lb>maco egli termina e s&#039;impianta, e questa è la spezie delle Lacce o Chep­<lb></lb>pie. </s>

<s>Nelle altre generazioni di pesci mette foce o nella gola o nel principio <lb></lb>dello stomaco, o nel mezzo della lunghezza dello stomaco medesimo. </s>

<s>Nè in <lb></lb>tutte queste generazioni è ugualmente manifesto questo canale, imperoc­<lb></lb>chè, se ne&#039;pesci di acqua dolce per lo più si vede e si trova a prima vista <lb></lb>e senza difficoltà veruna, pel contrario in molti pesci di mare non così su­<lb></lb>bito si trova e si ravvisa, e ci vuole una particolar premurosa diligenza e <lb></lb>pazienza per rinvenirlo, a segno tale che in alcuni, ancorchè sia probabi­<lb></lb>lissimo e certissimo ch&#039;e&#039;vi sia, io molte volte non ho saputo rinvenirlo, <lb></lb>ma da me medesimo ne incolpo la mia poca diligenza e destrezza con­<lb></lb>giunte forse con qualche mia insolita impazienza ” (Opere cit., T. I, P. II, <lb></lb>pag. </s>

<s>99, 100). </s></p><p type="main">

<s>Questa stessa difficoltà, così trovata dal Redi in ravvisare il canaliculo <lb></lb>di comunicazione fra l&#039;aria interna e l&#039;esterna in alcune generazioni di pe­<lb></lb>sci, fece forse sentenziare al Fracassati: “ in grandioribus piscibus haec ve­<lb></lb>sica deest ” (De cerebro, loco cit, pag. </s>

<s>145). Ma il Redi osservò che, seb­<lb></lb>ben di quell&#039;organo si trovino alcune specie di pesci veramente mancanti, <lb></lb>non è però questione nè di piccoli nè di grandi, come diceva il Fracassati, <lb></lb>nè di fluviatili o di marini com&#039;avevano infin dal 1658 pensato gli speri­<lb></lb>mentatori Accademici di Firenze (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>679). <lb></lb>Nel luogo sopra citato dal libro <emph type="italics"></emph>Degli animali viventi negli animali vi­<lb></lb>venti,<emph.end type="italics"></emph.end> annovera l&#039;Autore un lungo ordine di pesci, distinguendo quelli che <lb></lb>hanno il notatoio da tanti altri che non l&#039;hanno, d&#039;onde presero alcuni oc­<lb></lb>casione di dubitare se sia veramente la vescica il precipuo organo che serve <lb></lb>ad equilibrare il pesce nell&#039;acqua. </s>

<s>Il Fracassati però aveva già pensato a <lb></lb>risolvere il dubbio dicendo che ne&#039;pesci a cui manca la vescica supplisce <lb></lb>per notatoio l&#039;aria inclusa nelle cavità dell&#039;addome, e particolarmente quella, <lb></lb>ch&#039;è compresa fra le pagine di certe loro singolari membrane. </s>

<s>“ Putaverim <lb></lb>tamen totum abdomen sui cavitate illius munera implere (quando patere <lb></lb>possit aeris illuc aditus, quod nondum percipere potui) nam clausum est <lb></lb>suo diaphragmate. </s>

<s>In his tamen piscibus, qua in anterioribus dorsum sinua­<lb></lb>tus, videtur aer latitare, etenim, membrana a spina divulsa, latibulum ali­<lb></lb>quod aeris accusat ” (De cerebro cit. </s>

<s>p. </s>

<s>145). </s></p><p type="main">

<s>Il Redi poi trovò che, almeno in certe specie di pesci, si compone di <lb></lb>quella stessa membrana divulsa dalla spina la tunica alla vera e propria ve­<lb></lb>scica, ma la disposizione di lei in ogni modo era tale che, anche quando vi <pb xlink:href="020/01/1562.jpg" pagenum="437"></pb>fosse il canaliculo di comunicazion coll&#039;esterno, non potutosi sempre vedere <lb></lb>dal medesimo oculatissimo Redi, si rendeva nulladimeno assai difficile a in­<lb></lb>tendere come mai il pesce valga a deglutir l&#039;aria soprapposta all&#039;acqua in <lb></lb>tanta copia, da produr l&#039;effetto idrostatico voluto da Galileo. </s></p><p type="main">

<s>Fu la nuova difficoltà risoluta pure dal Fracassati, ammettendo che <lb></lb>l&#039;aria si trovi delitescente anche in mezzo all&#039;acqua, e che il pesce s&#039;equi­<lb></lb>libri non sempre coll&#039;aumentare o col diminuire il suo peso, ma talvolta <lb></lb>altresì coll&#039;espandere e col restringere la sua mole. </s>

<s>“ Pisces nataturi his <lb></lb>aecoliis utriculis utuntur: enatant enim ad superiora, si corpus laxaverint; <lb></lb>inferius subsistunt, si contracti corpore constringatur aer et ita gravius cor­<lb></lb>pus reddatur ” (ibid.). </s></p><p type="main">

<s>Fu così finalmente risoluto il primo dei tre problemi meccanici propo­<lb></lb>sti dall&#039;Acquapendente intorno al nuoto dei pesci. </s>

<s>Quanto agli altri due, <lb></lb><emph type="italics"></emph>quomodo natatus fiat, e qua ratione aquatile animal ad omnes loci po­<lb></lb>sitiones permutatur,<emph.end type="italics"></emph.end> dicemmo come l&#039;Autore seguisse la corrente opinione, <lb></lb>che riconosceva qual principale strumento del notare le pinne. </s>

<s>Un&#039;attenta <lb></lb>osservazione fece però indovinare all&#039;Acquapendente altri usi delle stesse <lb></lb>pinne, vedendo i lucci stare quasi a fior d&#039;acqua tenendole aperte e ferme, <lb></lb>per cui congetturò che servissero tutto insieme e a sostener la macchina <lb></lb>animale, e a fermarla in quel così lubrico posare sull&#039;acqua. </s>

<s>“ Propterea <lb></lb>lucios saepenumero prope aquae superficiem videbis ex toto corpore et pin­<lb></lb>nis, quasi alis immobilibus et latis extensisque, consistentes, ut propterea <lb></lb>hoc loco asseverandum sit extentas pinnas et ad oculum immobiles, non <lb></lb>modo ad sustinendos, sed imprimis ad firmandos in aqua pisces usum prae­<lb></lb>bere ” (De natatu, Op. </s>

<s>omnia cit., pag. </s>

<s>378). </s></p><p type="main">

<s>La direzione poi del nuoto, ch&#039;era il terzo problema, l&#039;Acquapendente <lb></lb>l&#039;affidava ai moti della coda rassomigliata al timone delle navi, concorren­<lb></lb>dovi la direzione più o meno obliqua delle pinne. </s>

<s>“ Oblique igitur ad ali­<lb></lb>quam loci differentiam volvi, revolvi, inclinare, permutarique, partim pinnae, <lb></lb>partim caudae munus esse constat, sed cauda privatim navis gubernaculum <lb></lb>exacte imitatur ” (ibid.). </s></p><p type="main">

<s>Se non fosse stato l&#039;Acquapendente soggiogato da quella sua ostinata <lb></lb>opinione che cioè si trovi tutta insieme la scienza raccolta ne&#039;libri dei Fi­<lb></lb>losofi e de&#039;Fisici antichi, veniva dalle sue proprie osservazioni intorno alla <lb></lb>meccanica animale del nuoto condotto a riconoscer quel vero, che poi così <lb></lb>facilmente si rivelò al più libero ingegno di Galileo. </s>

<s>Era infatti così ovvio <lb></lb>osservare, per le acque de&#039;fiumi e dei domestici vivai, non farsi da&#039;pesci <lb></lb>nessun più piccolo moto, senza che gli preceda il guizzo della coda; e dal­<lb></lb>l&#039;altra parte apparivano così sproporzionate le pinne ai remi delle navi nella <lb></lb>struttura e negli usi, ch&#039;esso Galileo non dubitò d&#039;affermare esser falso <lb></lb>che, per l&#039;effetto del nuoto, <emph type="italics"></emph>si servono i pesci delle ali che hanno sotto la <lb></lb>pancia.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>A queste semplici parole, che si leggono scritte sotto forma di fretto­<lb></lb>losa nota nella <emph type="italics"></emph>Selva di problemi varii<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIV, pag. </s>

<s>319), si riduce tutto <pb xlink:href="020/01/1563.jpg" pagenum="438"></pb>ciò ch&#039;è nelle pubbliche opere galileiane rimasto intorno a un tal soggetto <lb></lb>di meccanica animale. </s>

<s>Supplivano però alla mancanza delle scritture le tra­<lb></lb>dizioni, amorosamente secondo il solito raccolte, e ingegnosamente illustrate <lb></lb>dal Borelli. </s>

<s>Si diceva dunque in quelle orali tradizioni dell&#039;insegnamento <lb></lb>galileiano, mantenuto vivo con tanto zelo nella scuola fioritissima del Ca­<lb></lb>stelli, che la verità naturale era molto diversa da ciò che ne avea scritto <lb></lb>l&#039;Acquapendente, perchè tutt&#039;altro ch&#039;esser la coda organo secondario del <lb></lb>nuoto, e organo principale le pinne, sono anzi le pinne secondarie al prin­<lb></lb>cipale strumento del nuoto ch&#039;è la coda. </s>

<s>Di tutto ciò venne in mente al <lb></lb>Borelli di dar sodisfazione ai dubbiosi, per via di elegantissime esperienze, <lb></lb>fatte a&#039;di 25 Agosto 1662 innanzi al principe, e ai Colleghi dell&#039;Accademia <lb></lb>del Cimento, nelle carte della quale ne fu lasciata la seguente memoria: <lb></lb>“ Tagliate l&#039;ali ad un pesce, giva non pertanto notando per l&#039;acqua, ma <lb></lb>con gran fatica andava barcollando. </s>

<s>Tagliata ad un altro pesce la coda, per <lb></lb>moversi gli bisognavano forze grandissime, il che appariva dai continui e <lb></lb>violenti divincolamenti, onde andava sbattendosi ” (Targioni, Notizie e T. cit., <lb></lb>pag. </s>

<s>679). </s></p><p type="main">

<s>Queste prime esperienze, così felicemente riuscite sui piccoli pesci <lb></lb>d&#039;Arno, invogliarono il Borelli a proseguir lo studio della meccanica del <lb></lb>nuoto sopra pesci più grandi, e più svariatamente configurati, del mare, <lb></lb>ond&#039;è ch&#039;essendo nel Marzo 1663 obbligato a rimanere in Pisa, per atten­<lb></lb>dere alle lezioni, pregava don Famiano Michelini a sentire il principe Leo­<lb></lb>poldo “ se si compiace che la seguente settimana io venga a Livorno per <lb></lb>far quelle poche esperienze de&#039;pesci vivi, che io li accennai, e che averei <lb></lb>bisogno per capire perfettamente come si muovono e nuotano i pesci ” <lb></lb>(MSS. Cim., T. XVII, c. </s>

<s>188). </s></p><p type="main">

<s>Del resultato poi di così fatte esperienze rendeva il Borelli pubblico e <lb></lb>solenne conto in varie proposizioni, scritte nel cap. </s>

<s>XXII della I Parte <emph type="italics"></emph>De <lb></lb>motu animalium.<emph.end type="italics"></emph.end> La CCXII è volta a mostrar l&#039;errore di coloro, che face­<lb></lb>vano le pinne organo principale del nuoto, non considerando che, applicati <lb></lb>a una nave remi a proporzione così piccoli e flessibili come sono le pinne <lb></lb>stesse dei pesci, o non si moverebbe affatto o con tardissimo moto. </s>

<s>Sog­<lb></lb>giunge esser ciò benissimo confermato da quella esperienza, fatta già pri­<lb></lb>vatamente nella sperimentale Accademia fiorentina, e ora così resa in pub­<lb></lb>blica forma: “ Tandem hac experientia idipsum evidenter evincitur: forfi­<lb></lb>cibus resecui pinnas alarum piscium viventium usque ad earum radices, et <lb></lb>sic tonsos in piscina reposui, et vidi quod, etiam pinnis alarum carentes, <lb></lb>veloci cursu per aquam ferebantur sursum, deorsum et lateraliter. </s>

<s>Ergo non <lb></lb>a remigio pinnarum, sed ab alia causa pisces natando per aquam promo­<lb></lb>ventur ” (Editio cit., pag. </s>

<s>340). </s></p><p type="main">

<s>Non passa immediatamente il Borelli a dir qual&#039;è questa precipua causa <lb></lb>del nuoto, per trattenersi a contemplare e a descrivere il curioso spettacolo <lb></lb>offertogli da uno di que&#039;pesciolini, così tosato delle pinne del ventre, il <lb></lb>quale, quasi avesse a un tratto dimenticato l&#039;uso del nuoto, ora andava a <pb xlink:href="020/01/1564.jpg" pagenum="439"></pb>destra ora a sinistra “ sicut ebrii casuri et vacillantes inde incedere solent ” <lb></lb>(ibid.), da che venivano a confermarsi sperimentalmente i detti dall&#039;Acqua­<lb></lb>pendente, che cioè le ali servono talvolta, come i piedi, alla posa del pesce <lb></lb>e alla stazione. </s></p><p type="main">

<s>Dopo ciò vien l&#039;Autore a dimostrar, nella proposizione CCXIV, che lo <lb></lb>strumento con cui notano i pesci è propriamente la loro coda. </s>

<s>Desume la <lb></lb>prova di ciò dall&#039;esperienza delle navi, alla poppa delle quali se facciasi vi­<lb></lb>brare, come la coda dei pesci, un unico remo, si vedono pure velocemente <lb></lb>progredire per l&#039;acqua, come se fossero spinte dall&#039;azione concorde di più <lb></lb>remi laterali. </s>

<s>Il modo poi, soggiunge, di questa operazione, è tale: quel­<lb></lb>l&#039;unico remo, mentre si volge obliquamente intorno alla poppa, trovando <lb></lb>l&#039;acqua che gli fa resistenza, spinge necessariamente innanzi la navicella, <lb></lb>benchè il moto per verità sia per riuscirne balenante e tortuoso. </s>

<s>“ Verum, <lb></lb>quia talis declinatio subito corrigitur vel a motu contrario, vel a firma remi <lb></lb>retentione in situ obliquo, officium temonis exercendo, fit ut non advertan­<lb></lb>tur illae momentaneae declinationes, et sic solummodo directus motus con­<lb></lb>spicuus remanet ” (ibid., pag. </s>

<s>342). Parve al Borelli questa dimostrazione <lb></lb>così concludente, che trascurò di confermarla con quell&#039;altra esperienza, <lb></lb>fatta già nell&#039;Accademia del Cimento, e per la quale vedevansi come udimmo <lb></lb>i pesci colla coda tagliata far a sè stessi per moversi grandissima violenza. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Al <gap></gap>ilo storico della meccanica del nuoto, che, proceduto lungamente <lb></lb>uguale da Plinio all&#039;Acquapendente, va a risolversi senza tante vicende e a <lb></lb>confermarsi nella scuola di Galileo, succede una tela, sulla quale una mano <lb></lb>disfa il primo bene avviato lavoro, e poi vengono nuove mani, che tirano <lb></lb>innanzi alcune fila, e altre ne rivolgono indietro, studiandosi d&#039;intrecciarle <lb></lb>con assidua affannosa faccenda, durata lunghi secoli, prima che la sciolta <lb></lb>estrema orditura trovi nel vivagno la sua fermezza. </s>

<s>Intendiamo dire della <lb></lb>respirazione dei pesci, la scienza della quale, oltre a quella massima diffi­<lb></lb>coltà, ch&#039;ebbe comune colla respirazion de&#039;quadrupedi, e che dipendeva dal­<lb></lb>l&#039;ignorare gli antichi la chimica de&#039;nostri giorni, incontrò nuovi ostacoli <lb></lb>a&#039;suoi progressi dal non aver saputo veder bene addentro alla struttura ana­<lb></lb>tomica delle branchie, e dal non intender come possa l&#039;aria così facilmente <lb></lb>entrare per i chiusi penetrali dell&#039;acqua. </s>

<s>Ma la verità di questo secondo <lb></lb>fatto, che si nascose tante volte innanzi agli affaccendamenti dell&#039;arte e della <lb></lb>scienza moderna, s&#039;era felicemente rivelata ad alcuni antichissimi Filosofi, <lb></lb>quasi a quel modo che una cattura, non riuscita agli esperti, vien talvolta <lb></lb>alle mani di semplici fanciulli. </s>

<s>E chi non direbbe che fanciulleggiassero dav­<lb></lb>vero que&#039;buoni antichi, i quali, confondendo nella medesima voce <emph type="italics"></emph>pneuma<emph.end type="italics"></emph.end><lb></lb>l&#039;anima e l&#039;aria, intendevano che il respirar di questa fosse un continuo <pb xlink:href="020/01/1565.jpg" pagenum="440"></pb>infondere, e ristorare nell&#039;animale gli spiriti della vita? </s>

<s>Mirabile fanciullag­<lb></lb>gine, la balbuzie della quale noi così vecchi non abbiamo saputo dimenti­<lb></lb>care, e come chi, in mezzo all&#039;acquistata scienza, ammira le prime sponta­<lb></lb>nee rivelazioni della sua infanzia, anche noi ripensiamo con maraviglia a <lb></lb>Ippocrate e a Galeno, che indovinarono il respirar della cute, e a Demo­<lb></lb>crito abderita, che, dall&#039;avere spiriti animali, ne concludeva respirar neces­<lb></lb>sariamente non i pesci soli, ma anche gl&#039;insetti. </s>

<s>Conseguiva da questa <lb></lb>un&#039;altra necessità, ed era che lo pneuma, a vivificare gli stessi pesci, si do­<lb></lb>vesse, anticipatamente a qualunque fisica esperienza, trovare sciolto in mezzo <lb></lb>all&#039;acqua. </s>

<s>Anassagora diceva che, passando l&#039;acqua dalla bocca alle bran­<lb></lb>chie, vi sottentra a riempire il vuoto tant&#039;aria, che basta alla respirazione, <lb></lb>e Diogene, esplicando meglio il concetto, soggiungeva che per forza del va­<lb></lb>cuo s&#039;estrae l&#039;aria inesistente nell&#039;acqua. </s></p><p type="main">

<s>Ma questi teneri e rigogliosi germi di scienza venne presto a conco­<lb></lb>cerli il freddo fiato pestilenziale della Filosofia aristotelica, la quale senten­<lb></lb>ziò che le cose dette da Anassagora e da Diogene intorno alla respirazione <lb></lb>di pesci erano affatto impossibili. </s>

<s>“ Ait Anaxagoras quidem, cum emittunt <lb></lb>aquam per branchias, eum qui in ore sit aerem trahentes respirare pisces, <lb></lb>non enim esse vacuum ullum. </s>

<s>Diogenes autem, cum emittunt aquam per <lb></lb>branchias, ex circumstante circa os aqua trahere vacuo quod in ore aerem, <lb></lb>tanquam inexistento in aqua aere: haec autem sunt impossibilia ” (Arist., <lb></lb>Op. </s>

<s>T. VII, De respiratione, Venetiis 1560, fol. </s>

<s>270). </s></p><p type="main">

<s>Prosegue quivi Aristotile a dir le ragioni perch&#039;egli creda impossibile <lb></lb>che respirino i pesci, e poi, proponendo altrove dottrine ch&#039;egli giudica esser <lb></lb>le vere, dice che gli animali a sangue caldo non per altro hanno bisogno <lb></lb>dell&#039;aria che per refrigerio del calore innato, al quale effetto, ne&#039;pesci ba­<lb></lb>stando l&#039;acqua, son apposte le branchie invece dei polmoni. </s>

<s>“ Extrinsecus <lb></lb>autem vel aere vel aqua refrigerari necesse est, quamobrem piscium nullus <lb></lb>habet pulmonem, sed pro ea branchias obtinent: aqua enim refrigerantur ut <lb></lb>aere quae spirant ” (Arist., Op. </s>

<s>T. VI, De partibus anim., Venetiis 1560, fol. </s>

<s>238). </s></p><p type="main">

<s>A restaurare quel che Aristotile aveva distrutto venne provvidamente <lb></lb>Galeno, il quale, perchè il Filosofo aveva sostituito le branchie ai polmoni <lb></lb>per caso, da anatomico insegnò che i due diversi organi ne&#039;quadrupedi e <lb></lb>ne&#039;pesci servono veramente alle medesime funzioni. </s>

<s>Persuaso dalla scienza <lb></lb>de&#039;suoi predecessori che debbono necessariamente i pesci trovar da risto­<lb></lb>rare i loro spiriti anche in mezzo all&#039;acqua, vide in questa necessità, con <lb></lb>gli occhi della mente se non con quelli del corpo, esser le branchie fornite <lb></lb>di certi piccoli fori atti ad ammetter l&#039;aria, e ad escluder l&#039;acqua, come ad <lb></lb>ammetter l&#039;aria tenue e ad escluder la crassa hanno opportuni canaliculi i <lb></lb>polmoni. </s>

<s>“ Sed carum, quas <emph type="italics"></emph>branchias<emph.end type="italics"></emph.end> nuncupamus, constructio ipsis vice <lb></lb>pulmonis est. </s>

<s>Cum enim crebris ac tenuibus foraminibus sint branchiae hae <lb></lb>interceptae, aeri quidem et vapori perviis subtilioribus tamen quam pro mole <lb></lb>aquae, hanc quidem extra repellunt, illa autem prompte intromittunt ” (De <lb></lb>usu partium, Lugd. </s>

<s>1550, pag. </s>

<s>312). </s></p><pb xlink:href="020/01/1566.jpg" pagenum="441"></pb><p type="main">

<s>Qui e altrove avea promesso Galeno di trattenersi più di proposito in­<lb></lb>torno alla respirazione dei pesci, ma perchè non si videro, nelle opere di <lb></lb>lui rimaste salve dai naufragi del tempo, mantenute le promesse, supposto <lb></lb>che si fosse fatto ciò dall&#039;Autore in qualche libro smarrito, uno zelante di­<lb></lb>scepolo pensò di riparare alla iattura col libro <emph type="italics"></emph>De utilitate respirationis,<emph.end type="italics"></emph.end><lb></lb>studiandosi d&#039;indovinar nello scriverlo la mente del Maestro. </s>

<s>Si dubita dai <lb></lb>più, egli ivi dice, se i pesci respirino in mezzo all&#039;acqua, benchè sia que­<lb></lb>sta certissima cosa rispetto ai maggiori, i quali hanno manifestamente i pol­<lb></lb>moni. </s>

<s>“ Minores vero pisces, qui loco pulmonis branchias habent, spirant <lb></lb>intra aquam, spirantque aerem, qui modicus est intra aquam, per poros <lb></lb>branchiarum, qui sunt proportionales fistulis pulmonis. </s>

<s>Quemadmodum enim <lb></lb>fistulae pulmonis, ita similiter et pori branchiarum usque adeo angustantur <lb></lb>in ea parte, quae terminatur ad cor, ut non capiant aquam sed aerem so­<lb></lb>lum, qui per poros excolatur ab aqua, transiens ad cor ” (Spurii Galeno <lb></lb>ascripti libri, Venetiis 1609, fol. </s>

<s>64). </s></p><p type="main">

<s>Il più recente Autore galenico non ammette l&#039;aria ospitante nell&#039;acqua <lb></lb>in conseguenza di quell&#039;astratto principio psicologico, che informava la fisio­<lb></lb>logia di Anassagora e di Diogene, ma dietro ciò che si osserva nel fatto na­<lb></lb>turale del ghiaccio, in cui l&#039;aria che vi si occultava, restringendosi la mole, <lb></lb>si vede manifestamente separarsi dall&#039;acqua. </s>

<s>“ Quod autem aer sit intra <lb></lb>aquam probatur ex eo quod, cum congelatur aqua, fit minor, propter aeris <lb></lb>expressionem ” (ibid.). Notabili parole, che presentavano sotto il suo vero <lb></lb>aspetto la questione del gelo se sia acqua dilatata o condensata, per cui tanto <lb></lb>si contese ai tempi di Galileo. </s></p><p type="main">

<s>Sentendosi forte di una scienza sperimentale innanzi alle dominatrici <lb></lb>vanità filosofiche, l&#039;Autore di quello spurio libro galenico insorge ardita­<lb></lb>mente contro Aristotile, che vuol dar l&#039;acqua a refrigerare le branchie, <lb></lb>com&#039;aveva data l&#039;aria a refrigerare i polmoni, non avvedendosi che l&#039;aria <lb></lb>stessa, tutt&#039;altro che a refrigerio, è data a nutrimento del calore del san­<lb></lb>gue. </s>

<s>“ Aristotili visum est quod pisces, qui branchias habent loco pulmo­<lb></lb>nis, non attrahant aerem, sed aquam, ad refrigerandum calorem cordis. </s>

<s>Nam <lb></lb>et similiter de habentibus pulmonem dicit Aristotiles quod attrahunt aerem, <lb></lb>ad refrigerandum calorem cordis, cum ostensum sit aerem inspiratum prae­<lb></lb>stare nutrimentum calori cordis ” (ibid.). </s></p><p type="main">

<s>Ma per qualunque opposizione gli si facesse rimasto l&#039;Aristotelismo vin­<lb></lb>citore, aveva infino a mezzo il secolo XVI condotte le sue vittorie, quando <lb></lb>apparve sulla cattedra di Mompellieri Guglielmo Rondelezio. </s>

<s>Ei professa <lb></lb>questo principio, e lo raccomanda a&#039;suoi scolari, a cui dice: “ ut nunquam <lb></lb>temere a magnorum et vetustorum authorum sententiis discedendum esse; <lb></lb>sic eorum dicta omnia tanquam ex oraculo Apollinis pythii edita non esse <lb></lb>semper accipienda, sed omnia circumspicienda, diligenter observanda, expe­<lb></lb>rientia, quando licet, comprobanda ” (De piscibus mar. </s>

<s>cit., pag. </s>

<s>64). </s></p><p type="main">

<s>Seguendo questo sapientissimo canone di filosofia sperimentale, in tempi <lb></lb>ne&#039;quali i detti di Aristotile da una parte e di Galeno dall&#039;altra si tenevano <pb xlink:href="020/01/1567.jpg" pagenum="442"></pb>da tutti propriamente com&#039;oracoli pitii, trovò falso il Rondelezio che potes­<lb></lb>sero i pesci vivere anche senz&#039;aria, e che nelle branchie si trovin cribri, <lb></lb>per secernerla più facilmente dall&#039;acqua. </s>

<s>Dop&#039;aver nel cap. </s>

<s>IX del IV libro <lb></lb>risposto a uno a uno a tutti gli argomenti, co&#039;quali intendeva Aristotile di <lb></lb>dimostrare che le cose dette da Anassagora e da Diogene della respirazione <lb></lb>de&#039;pesci eran tutte impossibili; e dop&#039;avere invocato, per concludere la ne­<lb></lb>cessità di così fatta respirazione, il vitale spirito pitagorico, che infuso per <lb></lb>le membra tutta agita la gran mole, e perciò anco il piccolo corpo del pe­<lb></lb>sce; “ quoniam autem, all&#039;ultimo ei dice, iis quae sensibus evidentia et <lb></lb>perspicua sunt refragrari nemo potest, inde sumptam rationem unam aut <lb></lb>alteram superioribus adiungemus. </s>

<s>Si in vase angusti oris et aquae pleno <lb></lb>concludantur pisces, illic vivunt et natant, non dies aut menses, sed annos <lb></lb>aliquot. </s>

<s>Si vel manu, vel aliquo operculo, ita os vasis obtures, ut omnis aeri <lb></lb>aditus intercludatur, subito suffocantur: cuius rei ipse saepius periculum <lb></lb>feci ” (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Qual più evidente sensata dimostrazione di questa si potrebbe avere, <lb></lb>dice il Rondelezio, della falsa dottrina aristotelica? </s>

<s>Se bastasse infatti la sola <lb></lb>acqua per refrigerio del sangue, perchè rimarrebbero soffocati i pesci pri­<lb></lb>vati d&#039;aria? </s>

<s>Che poi dall&#039;altra parte, soggiunge esso Rondelezio, sia a quei <lb></lb>muti animali necessaria l&#039;aria per respirare, lo dimostra in essi stessi quella <lb></lb>contenziosa avidità, con la quale, se talvolta ne hanno difetto, si vedono an­<lb></lb>dare a cercarla. </s>

<s>“ Porro si in eodem vase, ad summum os non oppleto <lb></lb>neque obtecto, ut maior aeri locus sit, contineantur, illic natantes et luden­<lb></lb>tes pisciculos cum voluptate cernas. </s>

<s>Si manum ori vasis admoveas, tum <lb></lb>certatim alius alio superior in aqua esse contendit, ut modici aeris usura <lb></lb>fruantur ” (ibid.). </s></p><p type="main">

<s>Conclude perciò legittimamente l&#039;Autore da queste esperienze: <emph type="italics"></emph>quare <lb></lb>piscium genus omne respirat.<emph.end type="italics"></emph.end> Ma qual&#039;è l&#039;organo che serve a questa fun­<lb></lb>zione? </s>

<s>Galeno, e il galenico Autore del libro <emph type="italics"></emph>De utilitate respirationis,<emph.end type="italics"></emph.end> ave­<lb></lb>vano detto essere nelle branchie cribri da secernere l&#039;aria dall&#039;acqua: io <lb></lb>però, dice il Rondelezio, non ho saputo trovar nè fori nè canalicoli, che si <lb></lb>possa credere essere ivi disposti a quell&#039;uso. </s>

<s>“ In branchiis animadverti fo­<lb></lb>ramina nulla esse aut cavitates per se attrahendo aeri vel aquae, aut istis <lb></lb>attractis ad cor transmittendis accommodatas ” (ibid., pag. </s>

<s>64). Perciò presi <lb></lb>di qui occasione a dubitare, ei soggiunge, non sieno organi della respira­<lb></lb>zione gli opercoli ossei, piuttosto che le branchie. </s>

<s>“ Quae faciunt ut dubi­<lb></lb>tem num hiatus illius operculi ossei, dilatatione aperti et eiusdem compres­<lb></lb>sione occlusi, potius quam branchiarum beneficio, fiat respiratio ” (ibid.). </s></p><p type="main">

<s>Qual&#039;è dunque l&#039;uso delle branchie ne&#039;pesci? </s>

<s>Quello, risponde il Ron­<lb></lb>delezio, di far da sipario, e come da rete interposta fra l&#039;apertura della <lb></lb>bocca e quella dei così detti <emph type="italics"></emph>orecchi,<emph.end type="italics"></emph.end> affinchè il cibo imboccato non sfugga, <lb></lb>“ sed recta ad ventriculum delaberetur, et aqua, simul cum cibo hausta, <lb></lb>reiiceretur ” (ibid.). </s></p><p type="main">

<s>Perchè questo nuovo uso assegnato alle branchie (non vedendosi per <pb xlink:href="020/01/1568.jpg" pagenum="443"></pb>quali organi s&#039;insinui l&#039;aria direttamente nel sangue) rendeva inesplicabili <lb></lb>quelle stesse esperienze, che parevano così evidentemente dimostrare la ne­<lb></lb>cessità dell&#039;elemento aereo per la vita dei pesci; s&#039;intende come gli argo­<lb></lb>menti del Rondelezio, a convincere di falsità le peripatetiche dottrine, riu­<lb></lb>scissero inefficaci. </s>

<s>Quasi un secolo dopo si negava dunque la respirazione <lb></lb>branchiale, non solo dagli Aristotelici, ma dagli stessi addetti alla scuola di <lb></lb>Galileo, da cui avevano appreso non inesister l&#039;aria nell&#039;acqua, e non essere <lb></lb>quelle bollicelle gallezzolanti su dal liquido riscaldato altro che visibili atomi <lb></lb>di fuoco. </s></p><p type="main">

<s>In mezzo però a quell&#039;ardore di rivolta contro Aristotile, capitanato <lb></lb>dallo stesso Galileo, sorse Marc&#039;Aurelio Severino con animo d&#039;espugnar la <lb></lb>rocca anco da quella parte, dalla quale i Galileiani l&#039;avevano lasciata illesa. </s>

<s><lb></lb>Esaminando un giorno un pesce, dove la carena si rende molto concava, <lb></lb>vide il Severino ascondervisi dentro qualche cosa, che gli parve aver grande <lb></lb>analogia con le vescicole pneumatiche degli uccelli, le quali ei conobbe <lb></lb>che servivano alla respirazione, prima che venisse a insegnarlo al mondo <lb></lb>l&#039;Harvey. </s>

<s>Ecco, disse allora, i polmoni dei pesci: e que&#039;forellini aperti nelle <lb></lb>branchie, e annunziati già da Galeno, che altro mai possono esser fuorchè <lb></lb>le boccuzze di tanti sifoncini, alcuni de&#039;quali sien disposti ad assorbir l&#039;aria, <lb></lb>altri a rigettar l&#039;acqua? </s>

<s>Ed ecco così, ai polmoni de&#039;pesci, trovate anche le <lb></lb>trachee; due potentissime mine da far saltare all&#039;aria come una paglia l&#039;edi­<lb></lb>fizio aristotelico, e per accender le quali dette mano il Severino a scrivere <lb></lb>la sua <emph type="italics"></emph>Antiperipatias.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In mezzo a tanta esultanza però si sentiva l&#039;Autore rimproverare dai <lb></lb>suoi lettori, che non avesse sufficientemente dimostrato come potessero l&#039;aria <lb></lb>e l&#039;acqua fare insieme connubio, quando dall&#039;amicissimo suo Tommaso Cor­<lb></lb>nelio giunsegli il manoscritto dell&#039;epistola <emph type="italics"></emph>De cognatione aeris et aquae,<emph.end type="italics"></emph.end><lb></lb>nella quale, per varie esperienze, e particolarmente per quella dello schioppo <lb></lb>pneumatico, si dimostrava non essere altro l&#039;aria che una trasformazione <lb></lb>subita, per effetto del calore, dall&#039;acqua. </s>

<s>Il Severino allora, ch&#039;era per dare <lb></lb>alle stampe la già compiuta <emph type="italics"></emph>Antiperipatias,<emph.end type="italics"></emph.end> approvando, anzi accogliendo <lb></lb>con gioia la fisica del Cornelio, aveva seco medesimo deliberato d&#039;applicarla <lb></lb>a dimostrar più pienamente la respirazione de&#039;pesci in un supplemento al <lb></lb>libro, ma il fiero morbo pestilenziale del 1654 lo tolse alla scienza, e la <lb></lb>stessa <emph type="italics"></emph>Antiperipatias<emph.end type="italics"></emph.end> non vide la luce in Napoli se non cinque anni dopo. </s></p><p type="main">

<s>Al sentire i pesci inaspettatamente ridotti all&#039;ordine dei polmonati l&#039;Ittio­<lb></lb>logia ne rimase commossa, aspettando il giudizio che ne darebbero anato­<lb></lb>mici o più esperti del Severino, o colla mente più libera da pregiudizii. </s>

<s>In­<lb></lb>tanto, l&#039;esperienze fisiche del barometro ad acqua e gli esercizi della macchina <lb></lb>pneumatica avevano reso agli stessi occhi evidente sollevarsi di mezzo al­<lb></lb>l&#039;acqua bollicelle, da credersi facilmente ripiene d&#039;aria. </s>

<s>“ Dum tamen, disse <lb></lb>il Boyle nel XXII de&#039;suoi Esperimenti nuovi fisico-meccanici, suppetat no­<lb></lb>bis occasio plura de natura aeris faciendi experimenta, non isthoc fidenter <lb></lb>definiemus an aer corpus primigenium sit, eiusmodi scilicet ut nequeat vel <pb xlink:href="020/01/1569.jpg" pagenum="444"></pb>generari vel in aquam aliudve corpus transmutari ” (Op. </s>

<s>omnia, T. I, Ve­<lb></lb>netiis 1697, pag. </s>

<s>48). </s></p><p type="main">

<s>Qualunque sia però la natura e l&#039;origine dell&#039;aria nell&#039;acqua, crede il <lb></lb>Boyle che serva alla respirazione dei pesci, e all&#039;esperienze del Rondelezio, <lb></lb>e a quella così volgare del vedere morire i notanti ne&#039;vivai, quando l&#039;acqua <lb></lb>l&#039;inverno ghiaccia alla superficie, aggiunge l&#039;altra del vederli morire egual­<lb></lb>mente posti sotto la campana del vuoto. </s>

<s>“ Cepimus magnam anguillam (quia <lb></lb>nullum alium vivum piscem assequi tum potuimus) et ex vase, in quo ad <lb></lb>nos educta est, exemptam, magno recipienti immisimus, aeremque exhauriri <lb></lb>curavimus, observavimusque anguillam, post aliquam ultro citroque motio­<lb></lb>nem in vitro, aliquo modo affici videri. </s>

<s>Cumque aerem, obstinato et inde­<lb></lb>fesso conatu, exsussisemus, resupino se convertit ventre, quomodo mori­<lb></lb>bundi pisces solent, et ex eo tempore mortuae similis immota iacuit ” <lb></lb>(ibid., pag. </s>

<s>112). </s></p><p type="main">

<s>Anzi, a ridur più dappresso questa nuova Fisica pneumatica a servire <lb></lb>alla Fisiologia della respirazione, il Boyle stesso altrove si propone di scio­<lb></lb>gliere questo problema: “ Queritur quousque mereatur a nobis considerari <lb></lb>num ne in aqua communi tantum aeris lateat, qui usui frigidorum eiusmodi <lb></lb>animalium ut sunt pisces sufficiat, atque num separabilis ille sit ab aqua, <lb></lb>quae per branchias ipsorum percolatur ” (Nova experim. </s>

<s>pneum. </s>

<s>respira­<lb></lb>tionem spectanctia, in T. cit., pag. </s>

<s>433). Immagina, per riuscire al difficile <lb></lb>intento, varii strumenti, il più semplice e il meglio accomodato dei quali è <lb></lb>notabile che tanto si rassomigli a quelle caraffelle di lunghissimo collo gra­<lb></lb>duato, colle quali il nostro Paolo del Buono misurava la quantità dell&#039;aria, <lb></lb>generata da varie acque, o da una medesima acqua posta in diverse condi­<lb></lb>zioni di temperatura. (Targioni, Notizie cit., T. II, P. I, pag. </s>

<s>311-13). </s></p><p type="main">

<s>Benchè ritrovasse il Boyle questa misura dell&#039;aria risolutasi dall&#039;acqua <lb></lb>assai scarsa, la credè nulladimeno bastante, se non alla respirazione propria­<lb></lb>mente detta come ne&#039;quadrupedi e negli uccelli, a quella almeno che si fa <lb></lb>per via delle branchie, le quali “ non absurdum est dicere quamdam habere, <lb></lb>quoad usum saltem, cum pulmonibus analogiam ” (Experim. </s>

<s>physico-mecha­<lb></lb>nica in loco cit., pag. </s>

<s>112). Così, col non farne alcun conto, conferì più effi­<lb></lb>cacemente a bandire dalla Ittiologia le novità introdotte dal Severino, ma <lb></lb>non arrogandosi nessuna autorità di anatomico lasciava ad altri decidere se <lb></lb>siano veramente i pesci instrutti de&#039;polmoni, e se ricorrano per le branchie <lb></lb>canalicoli aerei, da rassomigliarsi negli usi a quelli de&#039;bronchi. </s></p><p type="main">

<s>Quando in Pisa il Borelli, per apparecchiarsi alla grande opera dei moti <lb></lb>animali, pensò d&#039;invocare l&#039;esperta mano anatomica dei discepoli suoi più <lb></lb>eletti, Carlo Fracassati attendeva ad esaminare con grandissima diligenza <lb></lb>quelle branchie, nelle quali, da Galeno al Severino, si ripeteva da tanti tro­<lb></lb>varvisi forellini da vagliar l&#039;aria, e sifunculi ordinati a recarla al cuore e <lb></lb>ai polmoni. </s>

<s>Ei tutt&#039;altrimenti le trovò composte di molteplici absidi ossei, <lb></lb>che hanno nella loro parte convessa infisse innumerevoli pinne radiate, e <lb></lb>scannellate in modo, che possano ricevere in sè e sostentare quei, che colà <pb xlink:href="020/01/1570.jpg" pagenum="445"></pb>mettono, numerosissimi vasellini sanguigni. </s>

<s>“ Branchiae sunt absides osseae <lb></lb>multiplices, scilicet in utroque latere octonarium numerum constituentes in <lb></lb>parte convexa, contra ac consuescat in rotis, pinnae quaedam radiorum instar <lb></lb>figuntur, quae ab implantatione assurgentes tenuantur in cuspides, et in <lb></lb>utroque latere striis quibusdam minimis exarantur, quae vascula sanguinea <lb></lb>admittunt, ut pluries apud excellentiss. </s>

<s>Borellum Pisis, qui rerum novarum <lb></lb>repertor, sectiones anatomicas promovet, sum espertus ” (De cerebro, Mal­<lb></lb>pighi, Operum T. II cit., pag. </s>

<s>143). </s></p><p type="main">

<s>Trovato così che il Severino avea da questa parte giocato d&#039;immagi­<lb></lb>nazione, si volse il Fracassati più curiosamente che mai ad esaminare que­<lb></lb>gli organi, ch&#039;esso Severino avea veduti addentro nella carena de&#039;pesci, <lb></lb>riguardandoli come i loro polmoni, e s&#039;accorse pur troppo che anche que­<lb></lb>sta visione era all&#039;Anatomico napoletano apparita in sogno. </s>

<s>Di ciò infatti che <lb></lb>potesse servire alla respirazione ivi non trovavasi indizio, e a tutti i segni <lb></lb>pareva piuttosto quella mole sanguigna, presa per parenchima polmonare, <lb></lb>una glandula conglobata, co&#039;suoi canaliculi escretori, che il Fracassati opinò <lb></lb>facesse l&#039;ufficio de&#039;reni. </s>

<s>“ Porro si spectemus substantias illas ad dorsum, <lb></lb>quas ipse pulmones autumat, quae literam T graphice affingunt, non quid <lb></lb>a veritate alienum protulit: si tamen illas continuo pulmones appellare non <lb></lb>libeat, has et ipse in thymno offendi, et sanguinem concretum statim dixis­<lb></lb>sem, ni vasorum plurium sobole substantiae illae affluerent. </s>

<s>Has potius re­<lb></lb>nem, aut emunctorium, sum arbitratus .... maxime cum videatnr recensi­<lb></lb>tus meatus aliquid recrementosum ab illis extra ventrem derivare ” (ibid., <lb></lb>pag. </s>

<s>144). </s></p><p type="main">

<s>Venivano dunque per queste anatomiche osservazioni degradati i pesci <lb></lb>da quella dignità, di che il Severino gli avea insigniti, ond&#039;essendo vero che <lb></lb>non è in essi vestigio d&#039;organi pneumatici si domandava al Fracassati che <lb></lb>cosa si dovesse pensare intorno alla gran questione della respirazione dei <lb></lb>pesci. </s>

<s>E il Fracassati rispondeva con argomenti che riducevan la causa, così <lb></lb>lungamente promossa e così fervidamente agitata, all&#039;antica sentenza ari­<lb></lb>stotelica. </s>

<s>Ei non negava l&#039;esistenza dell&#039;aria nell&#039;acqua: anzi si professava <lb></lb>seguace della fisica del Cornelio, che il Boyle stesso confessò non aver ra­<lb></lb>gioni di riprovarla. </s>

<s>Però essendo così, diceva il Fracassati, per separar l&#039;aria <lb></lb>dall&#039;acqua ci bisognano o le forze dissolutrici del calore o delle valide brac­<lb></lb>cia agitatrici della macchina pneumatica. </s>

<s>Ma dov&#039;è questo calore ne&#039;pesci, <lb></lb>o questa così gran forza nelle branchie? </s>

<s>“ Tanta egemus vi ut excludatur <lb></lb>ab aqua inditus aer, ut boyleano experimento validorum lacertorum robora <lb></lb>exigantur ” (ibid., pag. </s>

<s>143). È impossibile perciò, ne concludeva, che le <lb></lb>branchie abbian virtù d&#039;estrar l&#039;aria dall&#039;acqua, per servire alla respira­<lb></lb>zione. </s>

<s>Qual&#039;è dunque il loro uso? </s>

<s>e il Fracassati risponde esser quello di <lb></lb>far da sostegno ai vasellini sanguigni, i quali, premuti dall&#039;acqua, nel rin­<lb></lb>chiudersi che fanno gli opercoli, più facilmente promovono il sangue. </s>

<s>“ Sunt <lb></lb>igitur branchiae vasorum fulcra, quae dum moventur ac aqua interlabitur, <lb></lb>accedente operculi ossei pressione, motum sanguinis iuvant ” (ibid., pag. </s>

<s>144). <pb xlink:href="020/01/1571.jpg" pagenum="446"></pb>Così veniva a negarsi la respirazione de&#039;pesci, e le funzioni delle branchie <lb></lb>si riducevano tutte a quella semplice azion meccanica propria alle cartila­<lb></lb>gini e agli ossi. </s></p><p type="main">

<s>Non molto diversa da questa del Fracassati è facile congetturare che <lb></lb>fosse l&#039;opinione in proposito del Borelli. </s>

<s>Egli infatti, più savio del Cornelio <lb></lb>e men dubbioso del Boyle, supponeva, per spiegar la maravigliosa dilata­<lb></lb>zione dell&#039;acqua ghiacciata, che vi preesistessero molti atometti aerei “ o vi <lb></lb>siano stati cacciati i detti atometti aerei dentro l&#039;acqua dall&#039;agitazione e <lb></lb>vari movimenti dell&#039;aria contigua all&#039;acqua, o perchè continuamente dalle <lb></lb>parti inferiori terrestri traspirano molte parti aeree ” (Fabbroni, Lett. </s>

<s>ined., <lb></lb>Firenze 1773, T. I, pag. </s>

<s>103, 4). Non perciò credeva servissero queste parti <lb></lb>aeree nell&#039;acqua alla respirazione de&#039;pesci, i quali solennemente sentenziò <lb></lb>esser tali “ qui non respirant ” (De motu anim., P. II cit., pag. </s>

<s>215). </s></p><p type="main">

<s>Or essendo così, non può non venire, in chi legge queste storie, la cu­<lb></lb>riosità di saper come mai il Fracassati e il Borelli si volgessero a professar <lb></lb>dottrine tanto contrarie all&#039;esperienze fatte dal Rondelezio, e più recente­<lb></lb>mente, e in forma assai più dimostrativa, dal Boyle. </s>

<s>A che intendere senza <lb></lb>difficoltà basta osservare che il Fracassati, approvando l&#039;ipotesì della tra­<lb></lb>sformazione dell&#039;acqua in aria, diceva non provar punto l&#039;esperienze ronde­<lb></lb>leziane che, otturandosi il vaso, i pesci moiono per non succedere altr&#039;aria <lb></lb>alla già inspirata, ma perchè ne vengono impediti gli aerei effluvii dall&#039;acqua: <lb></lb>“ Hoc non probat omnino aeris succedentis defectu pisces interire, cum <lb></lb>cohibitum potius effluvium ipsos perimat ” (De cerebro cit., pag. </s>

<s>142). Così <lb></lb>fatti effluvii poi non servono alla respirazione, ma a riempir la vescicola na­<lb></lb>tatoria, ed è questo uno de&#039;precipui usi, per cui rendesi l&#039;aria tanto neces­<lb></lb>saria ai pesci. </s>

<s>“ Vel piscibus necessarius aer, qui medias incolunt aquas, <lb></lb>scilicet ut saltem natatorii repleantur utriculi ” (ibid., pag. </s>

<s>146). </s></p><p type="main">

<s>Di questa necessità poi era tanto ben persuaso il Borelli che, nella pro­<lb></lb>posizione CXII della II parte <emph type="italics"></emph>De motu anim.,<emph.end type="italics"></emph.end> dice esser cosa veramente <lb></lb>maravigliosa tanta avidità ne&#039;pesci d&#039;andare in cerca dell&#039;aria. </s>

<s>Non dubita, <lb></lb>come altri facevano, che sia quell&#039;avidità per riempir la vescica natatoria, <lb></lb>e così più facilmente equilibrarsi nell&#039;acqua, perchè ne&#039;morti sotto il ghiac­<lb></lb>cio ritrovò quella stessa vescica così sempre enfiata e piena, come ne&#039;vivi. </s>

<s><lb></lb>Ci dee esser dunque in quegli avidi animali qualche altra insigne necessità <lb></lb>“ quae alia non videtur esse posse, dice il Borelli, quam desiderium con­<lb></lb>servationis vitae ” (Editio cit., pag. </s>

<s>215). </s></p><p type="main">

<s>Ora, ai non pregiudicati intelletti, questo <emph type="italics"></emph>desiderio della conservazion <lb></lb>della vita<emph.end type="italics"></emph.end> parve un sofistico rifugio, per non confessar che i pesci respi­<lb></lb>rano, e il refugio stesso tanto apparve più manifesto, in quanto che quella <lb></lb>sopra citata borelliana proposizione si formulava: “ Aer, per respirationem <lb></lb>receptus, est causa potìssima vitae animalium ” (ibid., pag. </s>

<s>213). </s></p><p type="main">

<s>Comunque sia, i paralogismi del Fracassati e del Borelli, in proposito <lb></lb>della respirazione dei pesci, rimanevano impressi di tali note, ch&#039;ebbero fa­<lb></lb>cilmente a riconoscerli anche gli ammiratori di que&#039;due valorosi ingegni, <pb xlink:href="020/01/1572.jpg" pagenum="447"></pb>ond&#039;è che la stessa Scuola toscana si consigliò saviamente di disertare in­<lb></lb>torno a ciò dall&#039;insegnamento de&#039;suoi maggiori. </s>

<s>Il Redi così, sotto il nome <lb></lb>di Pier Alessandro Fregosi, diffondeva notizie, che parvero a molti dotti <lb></lb>nuove, e al volgo straordinarie: “ Oh questa non l&#039;avrei mai nè immagi­<lb></lb>nata nè creduta che i pesci avessero i polmoni negli orecchi, eppure il si­<lb></lb>gnor Redi me l&#039;ha fatto vedere manifestamente, e mi ha fatto, sto per dire, <lb></lb>toccar con mano che quel gran lavoro del giro e rigiro o circolazion del <lb></lb>sangue, che negli animali ragionevoli e quadrupedi si fa dal cuore a&#039;pol­<lb></lb>moni, e da&#039;polmoni al cuore, ne&#039;pesci si fa in quelle parti, che il popolo <lb></lb>le chiama <emph type="italics"></emph>orecchie,<emph.end type="italics"></emph.end> e dagli Scrittori della Storia naturale son chiamate lati­<lb></lb>namente <emph type="italics"></emph>branchiae ”<emph.end type="italics"></emph.end> (Opere, T. IV cit., pag. </s>

<s>83). </s></p><p type="main">

<s>Sarebbe stato desiderabilissimo che il Redi, lasciando l&#039;abito popolare, <lb></lb>e rivestendo quello scientifico, avesse particolarmente descritta, e non così <lb></lb>semplicemente accennata la circolazione branchiale, tanto più che si rimane <lb></lb>in dubbio se si tratta di osservazioni proprie e di scoperte originali, o non <lb></lb>si fa altro dal Nostro che ripetere e illustrare quel che aveva pubblicamente <lb></lb>detto il Perrault due anni avanti. </s>

<s>In qualunque modo, prima di passare a <lb></lb>vedere i progressi fatti dalla Scuola parigina, giova trattenersi sopra quelli <lb></lb>fatti, in tempi un poco anteriori, dalla Scuola nostra fiorentina, nella quale <lb></lb>sedeva allora sapientissimo maestro di queste cose, insiem col Redi, Niccolò <lb></lb>Stenone. </s>

<s>Questi aveva, infino dal 1664, pubblicato in Amsterdam, per ap­<lb></lb>pendice al trattatello <emph type="italics"></emph>De musculis et glandulis,<emph.end type="italics"></emph.end> un&#039;Epistola al medico Gu­<lb></lb>glielmo Pisone intorno all&#039;anatomia della <emph type="italics"></emph>Razza,<emph.end type="italics"></emph.end> dove si toccano le questioni <lb></lb>così vivamente agitate allora intorno alla respirazione de&#039;pesci. </s>

<s>De&#039;polmoni, <lb></lb>egli dice, non è, qui nella razza, nè più chiaro nè più oscuro che negli altri <lb></lb>pesci il vestigio, ma è veramente maravigliosa quella finissima tessitura di <lb></lb>vasi, di che vanno superbe le branchie. </s>

<s>Ora a quale altro fine potrebbe esser <lb></lb>ivi disposto un tale ordine di vasi, fuor che a fare al sangue subire una <lb></lb>mutazione “ sive id contingat de suo aliquid emittendo, sive recipiendo <lb></lb>externa, sive una et eadem opera utrunque praestando? </s>

<s>” (De raiae ana­<lb></lb>tome, Amstelodami 1664, pag. </s>

<s>70). </s></p><p type="main">

<s>Fra le tante cose a quei tempi pensate intorno alle misteriose funzioni <lb></lb>della respirazione, e intorno all&#039;azion dell&#039;aria sul sangue, che il Fracassati <lb></lb>dianzi diceva consister tutta nella virtù elastica di lei, “ qua circularis san­<lb></lb>guinis motus foveatur ” (pag. </s>

<s>141); questa dello Stenone è la sola, che mi­<lb></lb>rabilmente adombri il vero, un secolo e mezzo dopo messo dalla Chimica <lb></lb>della combustione allo scoperto. </s>

<s>S&#039;è infatti da questa nuova scienza ricono­<lb></lb>sciuto esser verissimo quel che lo Stenone diceva, che cioè, respirando l&#039;ani­<lb></lb>male, il sangue subisce una mutazione, rimettendoci del suo e tutto insieme <lb></lb>ricevendo qualche cosa dall&#039;esterno. </s></p><p type="main">

<s>Certo insomma di questo principìo filosofico, lo Stenone era dubbio in­<lb></lb>torno ai particolari, ond&#039;è che applicandolo alla respirazione dei pesci di­<lb></lb>ceva: “ quis scit anne idem illis praestet aqua quod nobis aer, subtiliora <lb></lb>suis amplexibus contenta corpora, quae quorundam sunt spiritus, illis lar-<pb xlink:href="020/01/1573.jpg" pagenum="448"></pb>giendo, si alias largiuntur quicquam, nam si tantum recipiunt egesta, res <lb></lb>facilis et nulli controversiae obnoxia est ” (De Raiae anat. </s>

<s>cit., pag. </s>

<s>71). </s></p><p type="main">

<s>Questa proposta facilità lusingò Stefano Lorenzini, che onorava in Fi­<lb></lb>renze la scuola anatomica dello Stenone e del Redi, dando mano a sezio­<lb></lb>nare le Torpedini, intorno alle quali scrisse quello, che l&#039;Haller, nel I Tomo <lb></lb>della sua Bibliografia anatomica, chiamava <emph type="italics"></emph>eximium opusculum<emph.end type="italics"></emph.end> (Tiguri 1774, <lb></lb>pag. </s>

<s>656). Il Lorenzini dunque, fra i varii partiti messigli innanzi dall&#039;insi­<lb></lb>gne Maestro, s&#039;attenne e quello, per cui si faceva consistere l&#039;azione del­<lb></lb>l&#039;ambiente esterno sul sangue in <emph type="italics"></emph>recipere egesta,<emph.end type="italics"></emph.end> ciò che da un&#039;altra parte <lb></lb>parevagli mirabilmente convenire con quella disposizione inversa, che lo Ste­<lb></lb>none argutamente notava aver le branchie convesse, rispetto ai polmoni con­<lb></lb>cavi, e per la quale inversa disposizione esse branchie, diceva l&#039;Autore <emph type="italics"></emph>De <lb></lb>Raiae anatome,<emph.end type="italics"></emph.end> “ ab ambiente possunt affici ” (pag. </s>

<s>73). </s></p><p type="main">

<s>Per adattar le branchie, che sono in luogo de&#039;polmoni, e l&#039;acqua che <lb></lb>è in luogo dell&#039;aria a quell&#039;uso di esportazione ne&#039;due diversi ordini di <lb></lb>animali, il Lorenzìni premette per fondamento al suo discorso alcuni prin­<lb></lb>cipii fisiologici, che hanno qualche cosa di notabile. </s>

<s>Per lui tutta la cute <lb></lb>respira, come i polmoni, vedendosi e comprendendosi troppo bene “ che le <lb></lb>angustie del ricettacolo sanguigno, che sono e nella cute e nei polmoni, sono <lb></lb>dell&#039;istesso genere, e che quelle che sono ne&#039;polmoni sono state radunate <lb></lb>in quel luogo, non per altro, che per supplire ed aiutare la separazione di <lb></lb>quell&#039;escremento, che si doveva separare per tutto l&#039;abito del corpo, cioè <lb></lb>per la cute, giacchè questa per sè stessa non era bastante a quest&#039;uso ” <lb></lb>(Osservazioni intorno alle Torpedini, Firenze 1678, pag. </s>

<s>94). E perchè il <lb></lb>massimo e principal benefizio della respirazione consiste nell&#039;ambiente, che <lb></lb>rilava e porta via gli escrementi del sangue, è quello stesso ambiente di varia <lb></lb>qualità e natura secondo i varii individui, ai quali deve servire. </s>

<s>“ Impe­<lb></lb>rocchè, siccome altri degl&#039;individui sono aerei ed altri acquatici, così anco <lb></lb>il fluido esterno, che serve per levar via l&#039;escremento da&#039;polmoni di questi <lb></lb>individui, altro è acqueo, altro è aereo, e di questi l&#039;aereo serve agli aerei, <lb></lb>cioè a quegli che vivono nell&#039;aria, e l&#039;acqueo agli acquei, cioè a quegli che <lb></lb>vivono nell&#039;acqua, servendo ambedue per un istesso fine, ma però in modo <lb></lb>diverso, imperocchè il fluido esterno aereo, per la medesima via che egli è <lb></lb>stato ammesso a toccare la superficie esterna de&#039;polmoni, per la medesima <lb></lb>egli è mandato fuori, cioè reciprocato, dove l&#039;acqueo è mandato fuori per <lb></lb>via diversa da quella, che egli è stato ammesso a toccare e radere la su­<lb></lb>perfice esterna de&#039;polmoni. </s>

<s>La ragione perchè questi due fluidi operano con <lb></lb>modo diverso si è perchè il fluido, che vien separato ne&#039;polmoni in diversi <lb></lb>animali, è diverso, imperocchè in quel luogo, dal quale è mandato fuora un <lb></lb>fluido tenace e viscoso, come ne&#039;polmoni de&#039;pesci, si ricerca che vi trapassi <lb></lb>con veemenza un fluido, che rada e lavi la superfice, e che per conseguenza <lb></lb>la superfice, ch&#039;egli ha da radere, sia convessa, altrimenti, se la superfice <lb></lb>che il fluido ha da radere e lavare fosse concava, ne seguirebbe che il fluido <lb></lb>non potrebbe trapassare con veemenza per fare l&#039;uffizio suo..... E di qui <pb xlink:href="020/01/1574.jpg" pagenum="449"></pb>si cava un argomento evidentissimo della sapienza e provvidenza del sommo <lb></lb>Artefice, conciossiachè egli ha disposto in ciascheduno animale gl&#039;istrumenti <lb></lb>del moto e a figura de&#039;vasi secondo la natura de&#039;fluidi de&#039;medesimi ani­<lb></lb>mali, imperocchè a quegli animali, che hanno l&#039;escremento più crasso, a <lb></lb>questi stessi egli ha dato la superfice esterna de&#039;polmoni, che è contigua al <lb></lb>fluido esterno, convessa, e vi ha aggiustato e adattato gl&#039;istrumenti in tal <lb></lb>forma, che essi strumenti potessero spingere, anzi spingessero continuamente <lb></lb>a quella superfice una nuova porzione di fluido esterno, dal qual fluido <lb></lb>esterno, sempre rinnovato, fosse essa superfice esterna de&#039;polmoni, come da <lb></lb>un fiume che sempre scorre, lavata .... ma agli altri animali, che hanno <lb></lb>l&#039;escremento de&#039;polmoni più rado e più dilatato, esso Divino Artefice fece <lb></lb>la superfice de&#039;polmoni, ch&#039;è contigua al fluido esterno, concava, e diede <lb></lb>loro istrumenti atti a reciprocare il moto del fluido esterno ” (ivi, pag. </s>

<s>95-98). </s></p><p type="main">

<s>Secondo il Lorenzini dunque il sangue ne&#039;polmoni de&#039;pesci, ossia nelle <lb></lb>branchie, non subisce altra mutazione che ripurgandosi, e dando del suo, <lb></lb>per ristoro di che, dice esso Lorenzini, bastare il chilo. </s>

<s>Ma lo Stenone aveva <lb></lb>più saviamente sospettato non venisse piuttosto quel ristoro, vivificatore dello <lb></lb>stesso chilo sanguificato, elargito dagli spiriti latenti nell&#039;acqua; concetto che <lb></lb>fu destramente preso dal Perrault e svolto nella Parte III della sua <emph type="italics"></emph>Mecha­<lb></lb>nique des animaux,<emph.end type="italics"></emph.end> là dove, nel cap. </s>

<s>V, tratta de&#039;polmoni e de&#039;vasi di di­<lb></lb>stribuzione del sangue. </s>

<s>“ L&#039;usage des branchies des poissons, egli ivi dice, <lb></lb>n&#039;est guere different de celui des poumons des animaux terrestres, puis­<lb></lb>qu&#039;elles sont faites pour la circulation du sang au travers des branchies .... <lb></lb>ou vrai-semblablement il reçoit une alteration pareille a celle qu&#039;il trouve <lb></lb>dans les poumons, y ayant appàrence qu&#039;il y a de l&#039;air mèlè parmi l&#039;eau, <lb></lb>qui peut agir au travers des branchies sur le sang que leurs vaisseaux con­<lb></lb>tiennent ” (Edizione cit., pag. </s>

<s>466). </s></p><p type="main">

<s>Il Perrault è de&#039;primi che, riguardate le branchie in relazione col cuore, <lb></lb>si sia studiato di descrivere in qualche modo la circolazione del sangue. </s>

<s>Lo <lb></lb>Stenone innanzi a lui, dop&#039;avere accennato alla somiglianza che passa tra <lb></lb>il circolo branchiale e il polmonare, sente disposti alcuni a negarla, per avere <lb></lb>il cuore un ventricolo solo. <emph type="italics"></emph>Nec haec tanti nobis erit,<emph.end type="italics"></emph.end> risponde, perchè, sia <lb></lb>pure che non tutto il sangue passi per le branchie: hanno osservato gli Ana­<lb></lb>tomici che anche in certi uomini adulti, essendo la via aperta dalla destra <lb></lb>alla sinistra orecchietta, non tutto il sangue perciò vien trasmesso dal cuore <lb></lb>ai polmoni. </s>

<s>“ Sed ne ab insolitis ad solita procedere videar, consideretur <lb></lb>quaeso illa sanguinis quantitas, quae per branchias transfertur, et patebit <lb></lb>sufficere illam ut cum reliquo inde sanguine in auricula concurrens ad con­<lb></lb>venientem omnia proportionem facile reducat ” (De Raiae anat. </s>

<s>cit., pag. </s>

<s>72). </s></p><p type="main">

<s>Or il Perrault attese a dimostrare questa conveniente proporzione che <lb></lb>passa tra la quantità del sangue trasportato alle branchie, e quell&#039;altro ri­<lb></lb>versato per l&#039;orecchietta nel ventricolo del cuore. </s>

<s>Ei rassomigliava esse bran­<lb></lb>chie a tante sottilissime fogliette cartilaginee, soprapposte le une alle altre, <lb></lb>tagliuzzate così, da mettere esilissimi filamenti, come le barbe delle penne. <pb xlink:href="020/01/1575.jpg" pagenum="450"></pb>Un osso, a cui sono queste barboline attaccate, serve a quelle stesse fo­<lb></lb>gliette di base, e ciascun filamento sostiene un&#039;arteriuzza capillare. </s>

<s>“ Le <lb></lb>coeur des poissons, qui n&#039;a qu&#039;un ventricule, a comme deux aortes, ou du <lb></lb>moins l&#039;aorte a deux troncs: car le premier s&#039;étant divise en plusieurs ra­<lb></lb>meaux, ces rameaux se rejoignent et produisent un second tronc, qui jette <lb></lb>d&#039;autres rameaux qui se distribuent dans tout le corps. </s>

<s>Or le premier tronc <lb></lb>de l&#039;aorte, qui sort du ventricule du coeur par son oreille superieure, jette <lb></lb>quatre rameaux de chaque còté, qui passent chacun dans la base d&#039;un des <lb></lb>fevillets des branchies. </s>

<s>Ces rameaux apres avoir jettè les petites arteres ca­<lb></lb>pillaires, qui se coulent dans les pointes de chacune des petites barbes, s&#039;as­<lb></lb>semblent deux à deux, et vont se joindre au second tronc de l&#039;aorte, qui <lb></lb>descend le long de l&#039;èpine, et se divise en plusieurs rameaux, qui portent <lb></lb>le sang par tout le corps. </s>

<s>Pour ce qui est des veines, il y en a aussi de <lb></lb>capillaires, qui accompagnent les petites arteres et qui rapportant le sang, <lb></lb>qu&#039;elles ont reçu, aboutissent à un rameau, qui accompagne aussi le rameau <lb></lb>de l&#039;artere, qui se coule dans la base du fevillet: ces quatre rameaux s&#039;as­<lb></lb>semblent aussi deux à deux, et forment un tronc qui rapporte le sang dans <lb></lb>le ventricule, s&#039;inserant à son oreille inferieure, dans la quelle deux autres <lb></lb>rameaux, qui rapportent le sang des parties inferieures, s&#039;inserent aussi. </s>

<s>” <lb></lb>E la descrizione è illustrata da due figure, che rappresentano il circolo san­<lb></lb>guigno per le arterie e per le vene branchiali di una Carpa. (Meccanica degli <lb></lb>anim. </s>

<s>cit., pag. </s>

<s>466, 67). </s></p><p type="main">

<s>Riguardando però attentamente i disegni, e considerando le parole, che <lb></lb>servono a dichiararli, si trova che tra il sangue arterioso e il venoso non <lb></lb>passa differenza per la sostanza, ma per i vasi, a cui s&#039;impongono nomi di­<lb></lb>versi: perchè, passando attraverso alle branchie il sangue del ventricolo, <lb></lb>ch&#039;è un sangue venoso, e ritornando per vasi, che dovrebbero avere ugual <lb></lb>nome de&#039;primi, essendo una continuazione di loro; quel che si dispensa ad <lb></lb>alimentare le membra non si può dir che sia vero e schietto sangue arte­<lb></lb>rioso. </s>

<s>Questo sarebbe un circolo, da meritarsi propriamente il titolo di vi­<lb></lb>zioso, non essendo forse utile ad altro, che a tenere in moto il liquido, per­<lb></lb>chè oziando non si corrompa. </s>

<s>Lo Stenone aveva sapientemente detto che <lb></lb>nella respirazione questo per prima cosa si richiede: “ ut ambiens, sive id <lb></lb>aqua fuerit, sive aer, semper novum ad vasorum feratur extrema ” (De <lb></lb>Raiae anat., pag. </s>

<s>71) perchè altrimenti non potrebbe il sangue subire al­<lb></lb>cuna trasformazione. </s>

<s>E affinchè pienamente l&#039;effetto si conseguisca, è ne­<lb></lb>cessario che il sangue stesso così trasformato passi in altri vasi distinti, e <lb></lb>non, come il Perrault disegna, prosegua addirittura per i medesimi. </s></p><p type="main">

<s>Quella dunque, che l&#039;Autore della Meccanica degli animali chiama aorta <lb></lb>ascendente, non è, per volerla ragguagliare con l&#039;organo dei polmonati, che <lb></lb>l&#039;arteria polmonare, la quale dai suoi capillari branchiali riversa il sangue <lb></lb>vivificato dall&#039;aria ne&#039;capillari di altri vasi distinti, e confluenti in un tronco <lb></lb>solo, che il Perrault chiama aorta discendente, ma ch&#039;è piuttosto analogo <lb></lb>alla vena polmonare. </s></p><pb xlink:href="020/01/1576.jpg" pagenum="451"></pb><p type="main">

<s>Qui s&#039;incontra una novità notabilissima, che fece adombrare l&#039;Ittiologo <lb></lb>francese: la vena polmonare, senza toccare il cuore, prosegue a diritto, e <lb></lb>si moltiplica in rami per andar, vera e propria aorta discendente, a vivifi­<lb></lb>care le membra inferiori del pesce. </s>

<s>Una semplice considerazione però ba­<lb></lb>stava a rimovere ogni ombra: Perchè infatti, si può domandare, la vena negli <lb></lb>animali aerei dal polmone ritorna al cuore? </s>

<s>Non mica perchè il sangue <lb></lb>acquisti qualche cosa nella sostanza, ma sì nella velocità del suo moto. </s>

<s>Or <lb></lb>dunque se si ammetta che quello stesso sangue esca dalle branchie con tale <lb></lb>velocità, da non aver bisogno, per giungere a&#039;suoi vasi estremi, che gli so­<lb></lb>praggiunga altro estrinseco impulso, s&#039;intenderà perchè al pesce non sia <lb></lb>altrimenti bisogno d&#039;avere al cuore nè l&#039;orecchietta nè il ventricolo sinistro. </s></p><p type="main">

<s>Ritornando ora con lo sguardo sulla pagina, e sopra gl&#039;iconismi del <lb></lb>Perrault, si vede che impropriamente è dato da lui alla radice dell&#039;arteria <lb></lb>branchiale il nome di <emph type="italics"></emph>orecchietta superiore.<emph.end type="italics"></emph.end> L&#039;orecchietta propriamente è <lb></lb>una sola, e in essa la vena cava superiore infonde il sangue raccolto per <lb></lb>ogni parte del capo, e la inferiore quello attratto da tutte le capillari arte­<lb></lb>riose, diramate per le membra inferiori del pesce. </s></p><p type="main">

<s>Queste considerazioni non era forse facile farle con lucidezza, prima che <lb></lb>fosse dimostrata la chimica azione dell&#039;aria sul sangue, e quando Giuseppe <lb></lb>Du-Verney nel 1699 n&#039;ebbe qualche rivelazione, i colleghi suoi Accademici <lb></lb>parigini stettero ad ascoltare le nuove cose proposte con qualche diffidenza. </s>

<s><lb></lb>Anche il Du-Verney dunque prese per soggetto de&#039;suoi studi le branchie <lb></lb>delle Carpe, ch&#039;ei trovò disposte in modo da ridur quasi l&#039;acqua a&#039;suoi mi­<lb></lb>nimi atomi. </s>

<s>Quel moto poi alternativo di dilatazione e di compressione l&#039;as­<lb></lb>somigliò negli effetti alle trombe idrauliche, le quali, perciocchè anch&#039;esse <lb></lb>ricevon l&#039;acqua quando si dilatano, e la rigettano allora che si comprimono; <lb></lb>“ il y a plus d&#039;apparence que c&#039;est dans l&#039;instant du reserrement qu&#039;elles <lb></lb>obligent l&#039;air exprimé de l&#039;eau à pénétrer les pores des petits vaisseaux san­<lb></lb>guins ” (Collection academique, T. </s>

<s>I cit., pag. </s>

<s>653). </s></p><p type="main">

<s>Così veniva il Du-Verney a ritrovar nelle branchie quella forza di aspi­<lb></lb>razione, non creduta possibile dal Fracassati, e s&#039;avviava a conoscere, più <lb></lb>distintamente di quel che non avesse fatto il Perrault, dai loro propri usi <lb></lb>la struttura dei vasi. </s>

<s>Se il cuore, domandava a sè stesso, non ha che un <lb></lb>ventricolo solo, e che una sola arteria, la quale si ramifica nelle branchie, <lb></lb>“ quels canaux arroseront le reste du corps, et porteront le sang vivifié par <lb></lb>le mêlange de l&#039;air? </s>

<s>” E rispondeva proponendo a considerar il fatto che, <lb></lb>come la vena polmonare uscendo dal cuore prende costituzione di arteria, <lb></lb>così la prende similmente la vena branchiale, nell&#039;uscir dalle stesse bran­<lb></lb>chie. </s>

<s>“ Apres que le sang des arterioles des ouïes s&#039;est chargé d&#039;air, il passe <lb></lb>par la loi de la circolation dans toutes le petites veines qui leur répondent. </s>

<s><lb></lb>Mais ce qui est fort singulier, c&#039;est que les veines des ouïes en étant une <lb></lb>fois sorties, devennient aussi-tot artéres, et vont se répandre dans toutes <lb></lb>les parties du corps, d&#039;ou d&#039;autres veines veritables rapportent le sang au <lb></lb>coeur ” (ivi). </s></p><pb xlink:href="020/01/1577.jpg" pagenum="452"></pb><p type="main">

<s>La diffidenza ingerita a principio da queste nuove dottrine, che avevano <lb></lb>apparentemente dello strano, si convertì presto in una piena fiducia, quando <lb></lb>la fisiologia chimica della respirazione dette l&#039;ultima conferma alla mecca­<lb></lb>nica della circolazione del sangue, e così per il Du-Verney incominciava, sul <lb></lb>terminar del secolo XVII, a decidersi conforme alla verità naturale, passata <lb></lb>per così lunghe vicende, la questione della respirazione dei pesci, che è forse <lb></lb>la più notabile nella loro storia, dopo quella degli organi de&#039;sensi, alla quale <lb></lb>riserbiamo quest&#039;altra parte del nostro discorso. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Che, essendo il tatto senso fondamentale, non ne mancassero i pesci, <lb></lb>nessun poteva dubitarne, ma quanto all&#039;organo si limitarono gli antichi a <lb></lb>dir così vagamente ch&#039;era la cute o qualunque se ne fosse l&#039;integumento <lb></lb>esteriore. </s>

<s>A ciò dall&#039;altra parte si riduceva tutto quel che sapevasi da quegli <lb></lb>stessi Filosofi antichi intorno all&#039;organo del tatto, negli animali d&#039;ordine su­<lb></lb>periore, non che nell&#039;uomo. </s>

<s>Lo studio anatomico della cute di questi co­<lb></lb>minciò dallo Stenone, il quale scoprì le ghiandole miliari coi loro nervi, e <lb></lb>i condotti sudoriferi coi loro vasi sanguigni. </s>

<s>Quando poi il Malpighi ebbe <lb></lb>nelle papille cutanee scoperto l&#039;organo essenziale del tatto, pensò che quelle <lb></lb>miliari ghiandolette stenoniane fossero ordinate a secernere il loro umore <lb></lb>“ ut madidae forte papillae nerveae reddantur ne arescant, et ne callo quo­<lb></lb>dam ex assiduo usu tententur ” (De externo tactus organo, Operum, T. II <lb></lb>cit., pag. </s>

<s>209) per cui argutamente notò che nelle parti, in cui il tatto è <lb></lb>più squisito, come nella pianta de&#039;piedi, per esempio, e sotto le ascelle, son <lb></lb>le ghiandolette miliari altresì più numerose, e il sudore perciò in più gran <lb></lb>copia vi si secerne. </s></p><p type="main">

<s>Esplorata ch&#039;ebbe lo Stenone la cute dell&#039;uomo e de&#039;quadrupedi, si <lb></lb>volse con pari diligenza a esplorare anche quella de&#039;pesci, per la quale, <lb></lb>nelle razze segnatamente, trovò dispersi certi piccoli fori ” unde viscidi hu­<lb></lb>moris prodeunt guttae ” (De musc. </s>

<s>et gland. </s>

<s>cit., pag. </s>

<s>39). Ritrovati poi <lb></lb>simili forellini in altri pesci, come in uno che prese a sezionare del genere <lb></lb>dei Cani, pensò che l&#039;untuoso umore, per cui si rendono così lubrici i pesci <lb></lb>tutti, non ad altro fine venisse in loro stillato, che per renderne, come la <lb></lb>spalmatura delle navi, più agevole il noto. </s>

<s>“ Patet inde Naturae solertis in­<lb></lb>dustria, quae superficiem piscium unxit, quo facilius obstantes aquas finde­<lb></lb>rent ” (Myologiae specimen, Florentiae 1667, pag. </s>

<s>112). </s></p><p type="main">

<s>Il Lorenzini, proseguendo sui pesci questi studii iniziati dall&#039;illustre <lb></lb>Maestro, trovò per la cute delle Torpedini altri più minuti forellini coi loro <lb></lb>respettivi canali, per i quali distillavasi il solito viscido umore. </s>

<s>Mettendosi <lb></lb>poi a ricercar l&#039;origine di un tale umore, non dubitò d&#039;attribuirla a certe <lb></lb>ghiandole, che si rassomiglierebbero alle miliari, dallo stesso Stenone sco-<pb xlink:href="020/01/1578.jpg" pagenum="453"></pb>perte in tutti i quadrupedi, e più abbondantemente nelle mani dell&#039;uomo. <lb></lb></s>

<s>“ Nelle torpedini dunque, scrive esso Lorenzini, ed in tutti gli altri pesci, <lb></lb>che hanno canali simili o rispondenti a questi, una buona quantità di quel­<lb></lb>l&#039;umore, che si separa dalle glandule miliari, si raduna in essi canali, e tutto <lb></lb>insieme al bisogno vien portato fuori per quei forami manifesti ” (Osser­<lb></lb>vazioni intorno alle Torp. </s>

<s>cit., pag. </s>

<s>30). </s></p><p type="main">

<s>Or la somiglianza della struttura portando ad argomentare somiglianza <lb></lb>uguale negli usi, fu lecito agl&#039;Ittiologi dire, sull&#039;esempio del Malpighi, che <lb></lb>l&#039;umor viscido de&#039;pesci rappresentante l&#039;umor sudorifico degli animali ter­<lb></lb>restri, sia, oltre al render lubrico il nuoto, destinato a mantener morbide <lb></lb>ne&#039;pesci le papille del tatto; ond&#039;è che, avendoci la Natura provveduto con <lb></lb>tal sollecitudine e con tanta solerzia, s&#039;ebbe ragionevolmente a concluderne <lb></lb>non potere in que&#039;taciturni animali il senso non essere in qualunque modo <lb></lb>esquisito. </s></p><p type="main">

<s>Fra&#039;sensi particolari il più distinto organo ne&#039;pesci, e che andò esente <lb></lb>da ogni controversia, è quello della vista, in cui si porse allo Stenone un <lb></lb>soggetto insigne da studiarvi la struttura lamellare del cristallino, propria <lb></lb>agli occhi di tutti gli altri animali. </s>

<s>Notarono anche gli Antichi che vi manca <lb></lb>l&#039;umor acqueo, e che la stessa lente cristallina è sferica in questi notanti <lb></lb>per l&#039;acqua, a differenza degli animali, che vivono in mezzo all&#039;aria. </s>

<s>Gli <lb></lb>Ittiologi riconobbero non difficile a intendere la ragione di così fatta parti­<lb></lb>colare struttura, e la significarono così per mezzo del Perrault: “ La figure <lb></lb>du crystallin est toujours sphérique aux poissons et lenticulare aux autres <lb></lb>animaux. </s>

<s>Cette difference vient de la differente nature du milieu de leur <lb></lb>vùe: car à l&#039;égard des poissons tout ce qni sert de milieu à leur vùe de­<lb></lb>puis l&#039;obiet jusqu&#039;au crystallin est aqueux, sçavoir, l&#039;eau dans laquelle ils <lb></lb>sont, et l&#039;humeur aqueuse de l&#039;oeuil qui est au devant du crystallin. </s>

<s>Mais <lb></lb>dans les autres animaux ce milieu est compose de l&#039;air et de l&#039;eau de leur <lb></lb>oeuil, laquelle commence la refraction, que le crystallin acheve avec l&#039;hu­<lb></lb>meur vitrée c&#039;est pourquoi il a fallu que le crystallin des poissons fùt sphe­<lb></lb>rique, ayant besoin d&#039;une refraction plus forte, puisqu&#039;il doit suppleer eelle <lb></lb>qui se fait aux autres animaux dans l&#039;humeur aqueuse, qui n&#039;est pas capa­<lb></lb>ble de faire de refraction dans les poissons, parce qu&#039;elle est de mème na­<lb></lb>ture que le reste du milieu ” (Mecanique des animaux cit., pag. </s>

<s>358). </s></p><p type="main">

<s>Negli occhi dunque dei pesci fu facilmente riconosciuta la struttura delle <lb></lb>parti, e dietro i noti principii d&#039;Ottica se ne intesero le differenze e gli usi. </s>

<s><lb></lb>Ma gli altri organi dei sensi presentarono tali e tante difficoltà da lasciar <lb></lb>dubbiose le menti, cosicchè i dubbi dettero tra&#039;Filosofi luogo a questioni, <lb></lb>della storia delle quali dobbiamo far argomento il presente nostro discorso. </s>

<s><lb></lb>Incominceremo dal senso del gusto, l&#039;organo del quale almeno, sebben non <lb></lb>colà dove si credeva da tutti, fu ritrovato nello stesso tempo e colla stessa <lb></lb>certezza, che furono anche per l&#039;integumento dei pesci scoperte le papille <lb></lb>nervee del tatto. </s></p><p type="main">

<s>Che sia veramente ne&#039;pesci il senso del gusto è dimostrato dalle più <pb xlink:href="020/01/1579.jpg" pagenum="454"></pb>volgari quotidiane esperienze, vedendoli fare scelta de&#039;cibi più saporiti, e <lb></lb>trarre con grande avidità all&#039;esca insidiosamente a loro offerta dagli ami. </s>

<s><lb></lb>Scorto perciò Aristotile dalla certa notizia di questi fatti, argomentò ragio­<lb></lb>nevolmente dall&#039;esistenza della funzione all&#039;esistenza dell&#039;organo corrispon­<lb></lb>dente, e perchè si credeva allora consistere un tal organo nella sostanza <lb></lb>carnosa della lingua, si mise con gran diligenza a ricercare essa lingua per <lb></lb>la bocca de&#039;pesci. </s>

<s>È facile che, preformato così il giudizio, si lusingasse di <lb></lb>avervela ritrovata, e infatti la descrisse come tale nella <emph type="italics"></emph>Storia degli ani­<lb></lb>mali,<emph.end type="italics"></emph.end> benchè dura e quasi irta di acute punte: anzi avvertì i Naturalisti <lb></lb>che ci era, sebben, rimasta talvolta aderente al palato, potesse facilmente <lb></lb>sfuggire alla loro vista. </s>

<s>“ Linguam autem ipsam duram, et pene spineam <lb></lb>habent, et adhaerentem, ut interdum carere lingua videantur ” (Operum, <lb></lb>T. VI cit., fol. </s>

<s>99). In un altro libro di questa stessa Storia degli animali <lb></lb>confessò che la lingua negli acquatici, sebben sia certo che vi sia, è nulla­<lb></lb>dimeno imperfetta, e soggiunge che in alcuni, ne&#039;quali ella par che affatto <lb></lb>vi manchi, come per esempio ne&#039;Ciprini, vi supplisce opportunamente il pa­<lb></lb>lato carnoso. </s>

<s>“ Aquatilium tamen generi, quos pisces vocamus, data quidem <lb></lb>est lingua, sed imperfecta incertaque: ossea enim nec absoluta. </s>

<s>Sed pa­<lb></lb>latum nonnullis carnosum pro lingua est, velut inter fluviales cyprino, ita <lb></lb>ut, nisi diligenter inspexeris, lingua id esse videatur ” (ibid., fol. </s>

<s>120). </s></p><p type="main">

<s>Il Rondelezio poi accolse queste dottrine aristoteliche, svolgendole e illu­<lb></lb>strandole nel III libro de&#039;suoi Pesci marini, là dove, nel cap. </s>

<s>IX, si riserba <lb></lb>a trattar di proposito della lingua e del palato. </s>

<s>Ammesso dunque con Ari­<lb></lb>stotile, e come gli pareva lo confermasse la sua propria osservazione, che <lb></lb>sia nella bocca de&#039;pesci la lingua, domanda il Rondelezio a quale uso possa <lb></lb>esser data a loro dalla Natura. </s>

<s>No certo per servire alla voce, essendo afoni, <lb></lb>nè per rivoltare i cibi e rimandarli in qua e in là sotto la mola de&#039;denti, <lb></lb>non masticando quegli animali, nè facendo altro essi denti colle punte ri­<lb></lb>volte verso lo stomaco, che ingerir più facilmente la preda, e proibir ch&#039;ella <lb></lb>scappi a loro di bocca. </s>

<s>“ Quare, ne conclude, alimentorum sapores ut di­<lb></lb>scernant linguam eis datam dicere necesse est ” (Editio cit., pag. </s>

<s>58). Man­<lb></lb>cano infatti, soggiunge l&#039;Autore, della lingua que&#039;pesci, che non hanno sa­<lb></lb>pori da scegliere, nutrendosi di sola acqua pura, come i testacei, o d&#039;acqua <lb></lb>limacciosa, come le carpe e le tinche, nelle quali nulladimeno, secondo os­<lb></lb>servò Aristotile, supplisce al difetto della stessa lingua il palato carnoso. </s></p><p type="main">

<s>Nessuno ancora degl&#039;Ittiologi aveva saputo metter dubbi negl&#039;insegna­<lb></lb>menti aristotelici, così dal Rondelezio autorevolmente confermati, quando, <lb></lb>per opera del Malpighi e del Bellini, scopertosi l&#039;organo del gusto in ogni <lb></lb>sorta di animali terrestri, venne al Fracassati curiosità di ricercarlo anche <lb></lb>nella bocca dei pesci. </s>

<s>Rivolgendo perciò l&#039;attenzione sopra la lingua, per <lb></lb>esplorare essa la prima, non sapeva risolversi a qual membro propriamente <lb></lb>attribuir questo nome. </s>

<s>Ma pur anch&#039;egli chiamando lingua quella parte, che <lb></lb>Aristotile e il Rondelezio avevano già designata per tale, non vi trovò vesti­<lb></lb>gio delle papille nervee, riconosciute oramai per essenziale organo del gusto <pb xlink:href="020/01/1580.jpg" pagenum="455"></pb>in tutti gli altri animali. </s>

<s>“ Quantumvis itaque lingua sit quod dubitavi pro <lb></lb>lingua habere, nullas tamen illa, saltem evidentes, exhibuit papillas ” (De <lb></lb>lingua in loco cit., pag. </s>

<s>178). </s></p><p type="main">

<s>Non perdutosi per questo d&#039;animo, il Fracassati pensò che, trapassando <lb></lb>il cibo celeremente per bocca, non fosse questa del gusto sede opportuna, <lb></lb>ma che si dovesse trovar riposta più addentro, là dove lo stesso cibo si trat­<lb></lb>tiene più a lungo ad eccitar nell&#039;ingordo animale le cupe voluttà del senso. </s>

<s><lb></lb>Dietro dunque la scorta di questi pensieri cercando, “ invenio membranam <lb></lb>expansam, quae initium oesophagi est. </s>

<s>Hanc papillulis refertam linguae vi­<lb></lb>cariam credidi, cum differat a continuato stomacho. </s>

<s>Palati etiam fornix ali­<lb></lb>quibus papillulis distinguebatur, et videbatur ad idem munus vocatus, al­<lb></lb>bescens tamen piscium caro minus conspicuas has nerveas notas reddebat ” <lb></lb>(ibid.). Esultò il Fracassati della scoperta, non solamente per sè ma perchè <lb></lb>veniva mirabilmente a confermare la scoperta del Malpighi e del Bellini, <lb></lb>vedendosi le papille nervee presiedere all&#039;organo del gusto anche nei pesci. <lb></lb></s>

<s>“ Quare, poi ne concludeva, cum fere omnia animantia haec papillaria ca­<lb></lb>pitula, in lingua vel in adiacentibus, promant, quid mirum si constans haec <lb></lb>structura, non tantum oculos, verum et mentem certiorem fecerit, in hac <lb></lb>scilicet circa gustum animantium linguae operationem, quae hactenus ana­<lb></lb>tomicis non innotuerat, sese manifestare? </s>

<s>” (ibid., pag. </s>

<s>179). </s></p><p type="main">

<s>Pochi infatti dubitarono della scoperta, alla quale erano insieme con­<lb></lb>corsi i tre illustri anatomici nostri italiani, ma le ultime osservazioni del <lb></lb>Fracassati dettero luogo a una curiosa questione fra gl&#039;Ittiologi, se cioè possa <lb></lb>dirsi che i pesci hanno la lingua. </s>

<s>Il Lorenzini non avendola trovata nelle <lb></lb>torpedini, la negò anche in tutti gli altri pesci, per la ragione che, non ser­<lb></lb>vendo nè alla voce nè alla masticazione de&#039;cibi, sarebbe stata inutile ingom­<lb></lb>bro nella bocca di così fatti animali. </s>

<s>E a chi gli opponeva col Rondelezio <lb></lb>essere utile la lingua a discernere i sapori, rispondeva ritorcendo così l&#039;ar­<lb></lb>gomento, e dicendo “ che quelle lingue, le quali non avranno così fatte pa­<lb></lb>pille, non saranno abili a discernere i sapori, e tali appunto sono quei corpi <lb></lb>dentro le bocche dei pesci, ai quali comunemente si vuol dare il nome di <lb></lb>lingua. </s>

<s>E che questi tali corpi non abbiano papille si rende chiarissimo e <lb></lb>dalla quotidiana esperienza, che se ne può fare, e dalle oculatissime osser­<lb></lb>vazioni del signor Fracassati, il quale non vide mai queste papille nella sup­<lb></lb>posta lingua de&#039;pesci, ma le vide bene e nel palato e nel principio dell&#039;eso­<lb></lb>fago, e nelle branchie. </s>

<s>Adunque quel corpo, che comunemente si chiama <lb></lb>lingua ne&#039;pesci, non essendo dotato di quelle papille, che sono l&#039;istrumento <lb></lb>della sensazione, non può gustare, e per conseguenza, non potendo gustare, <lb></lb>non si può chiamar lingua ” (Osservazioni intorno alle Torped. </s>

<s>cit., pag. </s>

<s>41). <lb></lb>Ma passiamo a questioni di ben altra importanza. </s></p><p type="main">

<s>Che i pesci odano, scrisse Aristotile nel IV libro della Storia degli ani­<lb></lb>mali, in quel cap. </s>

<s>VIII citato dianzi a proposito del gusto; è cosa a tutti <lb></lb>palese, imperocchè si vedono furiosamente fuggire a un rumore insolito, <lb></lb>com&#039;è per esempio quello dei remi agitati. </s>

<s>Di ciò dall&#039;altra parte soglion <pb xlink:href="020/01/1581.jpg" pagenum="456"></pb>prendere quotidiana esperienza i pescatori, che ora strepitando gli riducono <lb></lb>nella rete, e ora silenziosi gli van cogliendo ne&#039;loro nidi. </s>

<s>Nè men certo è, <lb></lb>soggiunge il Filosofo, che i pesci odorino, perchè non sono attratti a ogni <lb></lb>genere di esca, e i pescatori ora gli allettano, e ora gli deviano purchè in <lb></lb>ogni modo diano negli agguati, spargendo per l&#039;acqua sostanze, alcune delle <lb></lb>quali siano al senso de&#039;pesci odorose, altre fetenti. </s>

<s>Benchè però sian così <lb></lb>certi i fatti rispetto alle funzioni, “ auditus vero, dice Aristotile nel capi­<lb></lb>tolo sopra citato, olfactusve nullum continent membrum manifestum. </s>

<s>Quod <lb></lb>enim tale videri potest per loca narium id non ad cerebrum usque trans­<lb></lb>meat, sed partim obseptum et caecum mox desinit, partim ad branchias <lb></lb>fertur ” (fol. </s>

<s>120). </s></p><p type="main">

<s>Il Rondelezio in parte trovò queste aristoteliche dottrine vere, e in <lb></lb>parte, usandovi più diligente anatomia, le trovò false e le corresse, special­<lb></lb>mente per ciò che concerne le orecchie, intorno alle quali ha nel III libro <lb></lb><emph type="italics"></emph>De piscibus<emph.end type="italics"></emph.end> un capitolo insigne. </s>

<s>Son le orecchie, ivi egli dice, disposte nel­<lb></lb>l&#039;uomo a ricevere i suoni, e per esse a imbeversi delle erudite discipline, <lb></lb>e son date ne&#039;pesci a tutela e a conservazion della vita. </s>

<s>Atterriti infatti con <lb></lb>minaccioso strepito sen fuggono, e chiamati con dolce suono rispondono <lb></lb>“ ut nos frequenter in delphinis, luciis, aliisque huiusmodi experti sumus ” <lb></lb>(pag. </s>

<s>49). </s></p><p type="main">

<s>Si fa in questi pesci l&#039;udito, prosegue a dire l&#039;Autore, senza alcuna <lb></lb>esterna inspirazione, benchè siavi interiormente riposto l&#039;organo, il quale si <lb></lb>compone di alcune parti cartilaginose e di altre cutanee e secche, affinchè <lb></lb>possano più facilmente riflettere e fare echeggiare il suono per le più in­<lb></lb>terne parti turbinate e anfrattuose. </s>

<s>“ In osse lithoide foramen est insigne, <lb></lb>in quo veluti tympanum est: obtenditur enim membrana tenuissima et sim­<lb></lb>plicissima, cui ossicula duo alligantur, quorum unum incudis vicem gerit, <lb></lb>dentisque molaris figura est, et perforatum acus modo in terrestribus, in <lb></lb>piscibus sinuosum, quo foramine nervum ut acus filum recipit, eoque nervo <lb></lb>suspenditur simul et membranae interius alligatur. </s>

<s>Alterum malleoli offi­<lb></lb>cio fungitur, ex quorum percussu sonus ad cerebrum per nervum defer­<lb></lb>tur ” (ibid.). </s></p><p type="main">

<s>Ma perchè Aristotile aveva detto, nel cap. </s>

<s>XI del I libro <emph type="italics"></emph>De historia <lb></lb>animalium,<emph.end type="italics"></emph.end> che il Vitello marino ha manifesto il meato uditorio esterno, <lb></lb>di cui manca il Delfino, benchè anche in lui l&#039;udire sia certo, il Rondele­<lb></lb>zio pensava che senza comunicar col di fuori avrebbe inutilmente la Natura <lb></lb>scolpito l&#039;organo nell&#039;osso petroso. </s>

<s>“ Qua ratione impulsus, cum Delphini <lb></lb>cranium diligentissime contemplatus essem, manifestissimum audiendi mea­<lb></lb>tum, qui ad cerebrum usque patet, inveni e regione in vivi Delphini capite <lb></lb>foramen tam exiguum, ut fere oculorum aciem fugiat statim post oculum, <lb></lb>qui situs in causa est cur difficilius reperiatur: sunt enim oculi et foramina <lb></lb>illa in eadem fere linea cum oris scissura ” (ibid., pag. </s>

<s>465). </s></p><p type="main">

<s>Questo è ciò, conclude all&#039;ultimo il Rondelezio, che si è saputo di certo <lb></lb>dagli antichi e da me intorno alla funzione e all&#039;organo dell&#039;udito ne&#039;Ce-<pb xlink:href="020/01/1582.jpg" pagenum="457"></pb>tacei. </s>

<s>Quanto agli altri pesci poi “ vix constat qua parte audiant: nescias <lb></lb>enim an foramina ante oculos posita ad audiendum, an ad odorandum data <lb></lb>sint ” (ibid., pag. </s>

<s>49), perchè, com&#039;è certo che i pesci odorano, così è cer­<lb></lb>tissimo che, essendo ciechi que&#039;fori posti innanzi ai loro occhi, non pos­<lb></lb>sano perciò servire a trarre gli odori; intorno a che l&#039;Autore De&#039;pesci ma­<lb></lb>rini ripete le cose stesse, e quasi le stesse parole dell&#039;antico Autore della <lb></lb>Storia degli animali. </s></p><p type="main">

<s>Per le parole del Rondelezio trasmesso l&#039;eco delle dottrine aristoteliche <lb></lb>a quei grandi anatomici, che fiorirono sulla fine del secolo XVI, il Casserio, <lb></lb>dop&#039;avere atteso con si assiduo e diligente studio all&#039;anatomia degli organi <lb></lb>de&#039;sensi nell&#039;uomo, e nella maggior parte degli animali terrestri, “ omni <lb></lb>animi contentione, così narra di sè medesimo, ac insigni patientia, in plu­<lb></lb>ribus eius generis piscium, de quibus hucusque dubitatum est utrum per <lb></lb>foramina ante eorum oculos posita audirent av vero odorarent, exploravi per <lb></lb>quosnam meatus a foris sonus eiusque species intus deferreretur, ad quid­<lb></lb>nam recipiendi et diudicandi gratia intus fabricatum esset ” (De auditus <lb></lb>hist. </s>

<s>anat., Ferrariae 1600, pag. </s>

<s>95). Per la quale esplorazione, soggiunge, <lb></lb>mi si rivelarono agli occhi tali cose, da non lasciarmi alcun dubbio intorno <lb></lb>all&#039;uso di que&#039;forami, e da venirmi anzi di lì di tutte insieme le parti del­<lb></lb>l&#039;organo una notizia completa. </s></p><p type="main">

<s>Questa è come un&#039;avvertenza, dall&#039;Autore premessa all&#039;esplicazione <lb></lb>della terza figura con assai bel disegno impressa nel testo, e per la quale <lb></lb>si esibiscono le vescicole piene d&#039;acqua dentro il cranio del Luccio, e si rap­<lb></lb>presenta la posizione de&#039;nervi acustici, insieme con altri nervi propagati <lb></lb>dalla midolla spinale. </s>

<s>Per la lettera A si designa particolarmente una ve­<lb></lb>scicola “ ovalem figuram praeseferens, aqua plena, cui insunt duo corpu­<lb></lb>scula ossea discontinua, divisa, ac ob omni vinculo libera, super quam ve­<lb></lb>siculam duae nervorum propagines B, B, a spinali medulla ortae, instar <lb></lb>filamentorum tenuissimorum, progrediuntur, quibus quidem obiectorum so­<lb></lb>norum inditium concreditum est ” (ibid.). </s></p><p type="main">

<s>Ma la figura IV seguente sta per rappresentare agli occhi de&#039;lettori le <lb></lb>parti più distinte di quel medesimo organo, che ha da servir nel pesce a <lb></lb>due si diverse funzioni. </s>

<s>Le cavità de&#039;due forami, che son sotto gli occhi, <lb></lb>sono esternamente rivestite di una membrana rotonda, “ variis ac pene innu­<lb></lb>meris filamentis, quasi a circumferentia ad centrum, roboris gratia, ductis, <lb></lb>tympano auris aliorum animalium respondens, nec non auditui et olfactui <lb></lb>celebrando maxime deserviens ” (ibid.). Di costì partono due canali “ per <lb></lb>quos aer sonorus ad praecipuum audiendi organum comportatur; ” canali <lb></lb>che, dopo un breve tratto, confluiscono in un altro più largo, il quale va a <lb></lb>morire nella pia madre. </s></p><p type="main">

<s>Sopra queste e sopra le altre più minute nuove cose scoperte, racco­<lb></lb>gliendo il Casserio l&#039;animo e la mente, prende occasione di ammirare la <lb></lb>somma Arte e Provvidenza di Dio nella Natura, e ne fa argomento per con­<lb></lb>futar l&#039;errore di coloro, che tutto dicono nel mondo essere stato fatto dal <pb xlink:href="020/01/1583.jpg" pagenum="458"></pb>caso. </s>

<s>Chi, dopo queste anatomie, oserebbe dire esser fatto a caso l&#039;organo <lb></lb>dell&#039;udito nel Luccio? </s>

<s>“ Hic enim etiam tympanum, quamvis sepe, loco et <lb></lb>structura ab aliorum animalium tympano longe diversum, reperis; hic duc­<lb></lb>tum etiam admodum longum, mea sententia, olfactui et auditui communem <lb></lb>offendis; hic quoque mirabilis quorundam vinculorum aquam continentium, <lb></lb>capreolorumque ritu constructorum, plexus, nec non circumvolutiones con­<lb></lb>tueris; hic nonnulla corpora, aqua plena, figuram aut fructus olivae aut zi­<lb></lb>ziphi eleganter exprimentia, vides; hic demum ossicula magnitudine, figura, <lb></lb>positione dissimilia invenis ” (ibid.). </s></p><p type="main">

<s>L&#039;avere il Casserio piuttosto accennate che descritte tutte queste gran <lb></lb>cose, che dice di aver vedute nell&#039;organo auditorio del Luccio, e l&#039;aver la­<lb></lb>sciate le parti, trasportato dagli ardori dell&#039;eloquenza, senza determinarne <lb></lb>gli usi, conferirono, insieme con altre cause che si scopriranno nel processo <lb></lb>di questa storia, a far sì che venissero le novità di lui accolte da pochi, e <lb></lb>più ragionevolmente ripudiate da molti. </s>

<s>Marc&#039;Aurelio Severino e Pietro Gas­<lb></lb>sendo son di tanta celebrità, che possono servire a rappresentar, fino a mezzo <lb></lb>il secolo XVII, le contrarietà delle due parti. </s></p><p type="main">

<s>Il nostro Napoletano dunque non dubita di ammettere, persuaso dal­<lb></lb>l&#039;esperienze di Aristotile, del Rondelezio, e dalle sue proprie, che i pesci <lb></lb>odano, benchè, con que&#039;due Autori convenendo, anch&#039;egli ripeta: “ Nulla <lb></lb>tamen pars est manifesta, quae sensus ministrat audiendi ” (Antiperipatias, <lb></lb>Neapoli 1659, pag. </s>

<s>32). </s></p><p type="main">

<s>Il non esser però una cosa manifesta, ragionava il Severino, non vuol <lb></lb>dire che non ci sia, e da un&#039;altra parte è così chiaramente visibile l&#039;organo <lb></lb>interno, da far necessariamente argomentare all&#039;esistenza di un qualche invi­<lb></lb>sibile meato esterno. </s>

<s>Ma a un sì fatto modo di ragionare conseguiva il na­<lb></lb>tural desiderio di sapere qual, fra le tante parti di che si compone l&#039;organo <lb></lb>auditorio de&#039;pesci, fosse la principale, ciò che il Casserio aveva ai soli buoni <lb></lb>interpetri lasciato intendere, scrivendone tanto in confuso. </s>

<s>E perchè preva­<lb></lb>leva tuttavia la teoria meccanica, che insegnava risvegliarsi l&#039;udito nel tim­<lb></lb>pano dal risonar dell&#039;incudine percossa dal martello, vide il Severino ne&#039;cas­<lb></lb>seriani iconismi accennato a questi strumenti, in que&#039;due corpuscoli ossei <lb></lb>fra sè divisi, e chiusi in una vescicola, alla quale giungono le propaggini di <lb></lb>que&#039;nervi, <emph type="italics"></emph>quibus quidem obiectorum sonorum inditium concreditum est.<emph.end type="italics"></emph.end><lb></lb>Ecco infatti quali sono l&#039;espressioni proprie dell&#039;Autore dell&#039;<emph type="italics"></emph>Antiperipatias,<emph.end type="italics"></emph.end><lb></lb>là dove argomenta esser ne&#039;pesci la facoltà di udire, dal vederli dotati degli <lb></lb>organi principali, che servono a questa funzione: “ Facultatis auditoriae pi­<lb></lb>sces non sunt expertes, sed quantum horum natura capit participes, con­<lb></lb>stantibus auscultatorii organis internis apprime nobilibus, quorum unus, cum <lb></lb>sit lapillus malleo respondens sensus percussorio, hic, capite gestus, suam <lb></lb>facit audiendi promptitudinem ” (ibid, pag. </s>

<s>95). </s></p><p type="main">

<s>Il Gassendo, non anatomico nè zootomo come il Severino, ma fisico e <lb></lb>filosofo, ripudiava addirittura le novità introdotte dal Casserio negli organi <lb></lb>delle sensazioni dei pesci, perchè ripugnanti <emph type="italics"></emph>cum analogia aliorum omnium<emph.end type="italics"></emph.end><pb xlink:href="020/01/1584.jpg" pagenum="459"></pb><emph type="italics"></emph>animalium.<emph.end type="italics"></emph.end> Studiosissimo della fisica de&#039;suoni, argomentava che i pesci non <lb></lb>possono udire, perchè i tremori armonici non si profondan nell&#039;acqua. </s>

<s>Che <lb></lb>se pur odono i Cetacei, com&#039;è certo, avendo gli organi dell&#039;udito patenti, <lb></lb>ciò fanno solo, egli dice, quando sollevano il capo, e tengono le orecchie in <lb></lb>mezzo all&#039;aria. </s>

<s>“ Ad haec, scrive così trattando dei sensi in particolare nella <lb></lb>sezione III del suo <emph type="italics"></emph>Sintamma filosofico,<emph.end type="italics"></emph.end> utcumque perhibeant sonum pene­<lb></lb>trare per ipsam aquam, id tamen aut nihil, aut perexiguum est, et ad ipsam <lb></lb>quidem aquae superficiem duntaxat. </s>

<s>Nam primum quidem sonum aliquem <lb></lb>ex loco intra aquam advenire constat, cum corpora dura ac metallica prae­<lb></lb>sertim intra aquam collidimus, aut unum in alium demittimus, sed nimi­<lb></lb>rum id prope superficem..... At si moles aquae sit tanta, ut aut tremori <lb></lb>corporum obstet, aut ipsa non tremat, vel tremorem ita in orbem diffundat, <lb></lb>ut ad superficiem perveniens nullus pene sit, neque aerem movere sensi­<lb></lb>biliter posset; tunc nullus plane exauditur sonus ” (Operum, T. II, Flo­<lb></lb>rentiae 1727, pag. </s>

<s>319). </s></p><p type="main">

<s>Si opponevano a queste teoriche conclusioni l&#039;esperienze antiche, rife­<lb></lb>rite da Aristotile, e confermate dai quotidiani esercizi dei pescatori. </s>

<s>A che <lb></lb>trovò da rispondere ingegnosamente il Gassendo, cogliendo un concetto dal <lb></lb>libro del Rondelezio, il quale, dop&#039;aver detto che le ostriche, mancando degli <lb></lb>occhi, mancano senza dubbio anche degli orecchi, soggiunge che “ etsi sese <lb></lb>contrahunt, cum ferreis hamis appetuntur, agitatione aquae, potius quam <lb></lb>auditione admonita, id faciunt ” (De piscibus cit., pag. </s>

<s>49). Ai seguaci di <lb></lb>Aristotile dunque che, per provar l&#039;udito ne&#039;pesci, adducevano il fatto del <lb></lb>vederli fuggire allo strepito dei remi, rispondeva il Gassendo stesso, gene­<lb></lb>ralizzando quel concetto rondeleziano, e dicendo esser non i tremori sonori <lb></lb>dell&#039;aria eccitanti l&#039;udito, ma i moti ondosi dell&#039;acqua eccitanti il tatto, <lb></lb>quelli per cui si rendon cauti gli acquatici animali d&#039;evitare il pericolo. </s>

<s>Una <lb></lb>bella esperienza egli così racconta, per confermare il suo asserto: “ Tran­<lb></lb>siens alias prope piscinam cum quatuor aut quinque familiaribus, deprehen­<lb></lb>dimus Lucium in summa aqua soporatum: ille vero nullo aut pedum aut <lb></lb>sermonum nostrorum strepitu excitatus fuit, imo neque levioribus leviterque <lb></lb>aquam commoventibus festucis iniectis, sed solum, cum, paullo maiore con­<lb></lb>citatione, commovimus aquam: prorsus ut surdus, non strepitu, sed motu <lb></lb>solum excitatur ” (ibid., pag. </s>

<s>320). </s></p><p type="main">

<s>In ogni modo, tanto il Gassendo contradittore, quanto il Severino illu­<lb></lb>strator del Casserio avevano lasciata negli studiosi una viva curiosità di sa­<lb></lb>pere se quella membrana rotonda, designata con le lettere B, B nel sopra <lb></lb>citato IV iconismo casseriano, era veramente la membrana del timpano, e se <lb></lb>quei due canali C, C, confluenti nell&#039;unico canale D, servivano propriamente <lb></lb>a condurre al cervello i suoni e gli odori. </s>

<s>Si vide quella curiosità, che <lb></lb>aspettava qualche esperta mano anatomica, con grande maraviglia sodisfatta <lb></lb>nel 1667, quando lo Stenone, in appendice al suo libro <emph type="italics"></emph>Myologiae speci­<lb></lb>men,<emph.end type="italics"></emph.end> descrisse la storia anatomica di un pesce del genere dei Cani. </s>

<s>Dicemmo <lb></lb><emph type="italics"></emph>con gran maraviglia,<emph.end type="italics"></emph.end> perchè la membrana, che il Casserio rassomigliava al <pb xlink:href="020/01/1585.jpg" pagenum="460"></pb>timpano, compariva piuttosto analoga alla pituitaria; quei filamenti, creduti <lb></lb>posti ivi a rinforzar esso timpano, si descrivevano come tante lamelle, da <lb></lb>moltiplicar la superfice di contatto, ad esempio delle ossa turbinate; e i sup­<lb></lb>posti canali auditivi e olfattivi si vedevano, quasi per incanto, trasformati <lb></lb>ne&#039;processi mamillari. </s></p><p type="main">

<s>Venne poco dopo il Lorenzini a confermare queste nuove cose rivelate <lb></lb>agli Ittiologi dal Maestro, quando attese a descrivere più minutamente il cer­<lb></lb>vello delle Torpedini, tutta la mole del quale nuota, egli dice, in un certo <lb></lb>umore viscoso, che si racchiude per entro alla cavità della dura Madre (Os­<lb></lb>servazioni cit., pag. </s>

<s>99, 100). Non dubita che le membrane, delle quali son <lb></lb>rivestiti i forami posti sotto gli occhi, non servano veramente, anche nelle <lb></lb>Torpedini, al senso dell&#039;odorato, ricevendo esse i nervi olfattivi, che si ritro­<lb></lb>vano negli altri animali (ivi, pag. </s>

<s>12), i quali nervi si vedono, uno di qua <lb></lb>e uno di là, attaccati nella base di quel tubercolo grande, posto nella parte <lb></lb>anteriore del cervello (pag. </s>

<s>101). Per aggiunger nuove prove a dimostrare <lb></lb>che la moltiplicazione di superficie sia cagione dell&#039;acutezza dell&#039;odorato, <lb></lb>descrive minutamente le ossa turbinate nel naso di un orso, e riconoscendo <lb></lb>anch&#039;egli con lo Stenone quest&#039;ossa analoghe alle lamelle commesse sulla <lb></lb>membrana delle così dette narici dei pesci, ne conclude ch&#039;essendo così fatte <lb></lb>lamelle nelle Torpedini scarse, dee essere in loro l&#039;odorato assai ottuso <lb></lb>(pag. </s>

<s>12). </s></p><p type="main">

<s>Così essendo, non venne dunque il Perrault a dire in Ittiologia nulla <lb></lb>di nuovo, quando, facendo più finamente dello Stenone incidere, nella fig. </s>

<s>III <lb></lb>della tavola IX della sua Meccanica degli animali, il cervello e gli organi <lb></lb>dell&#039;odorato di un pesce, gli dichiarava alla mente de&#039;suoi lettori colle se­<lb></lb>guenti parole: “ La plus grande partie du cerveau des poissons est em­<lb></lb>ployée aux organes de l&#039;odorat. </s>

<s>Tout le cerveau, qui est recòuvert d&#039;une <lb></lb>pie-mere couchée immediatement sur la substance de cerveau est confermé <lb></lb>danse la dure-mere, qui est une espece de sac, rempli d&#039;une substance olea­<lb></lb>gineuse, dans laquelle le cerveau nage. </s>

<s>Les organes de l&#039;odorat, comme aux <lb></lb>animaux terrestres, eonsistent en un grand nombre de membranes, posant <lb></lb>les unes sur les autres, et composant deux masses de la figure d&#039;un oeuf. </s>

<s><lb></lb>Les productions du cerveau auxquelles ces masses sont attachées, qui sont <lb></lb>les apophyses mammillaires, sont creuses, et sont comme deux grands ven­<lb></lb>tricules ” (Oeuvres cit., T. I, pag. </s>

<s>409). </s></p><p type="main">

<s>Non aveva nulla ancora letto il Morgagni di queste nuove cose, sco­<lb></lb>perte ne&#039;pesci e pubblicamente descritte in Francia e in Italia dopo il Cas­<lb></lb>serio, col quale nonostante non conveniva, perchè avea conosciuto non poter <lb></lb>esser nervi acustici quelli, da lui delineati per tali, e perchè, scambiati i <lb></lb>processi mammillari in canali, non aveva nemmeno indicato all&#039;esistenza dei <lb></lb>nervi olfaltorii. </s>

<s>Desideroso dunque di ricercare i veri organi dell&#039;odorato nei <lb></lb>pesci, si dette il Morgagni a sezionarne alcuni di quei così detti Acipenseri, <lb></lb>e volgarmente chiamati <emph type="italics"></emph>porcelletti,<emph.end type="italics"></emph.end> ne&#039;quali riscontrò i forami, la cavità sot­<lb></lb>toposta e la membrana che la riveste. </s>

<s>“ Verum, soggiunge, neque hanc Cas-<pb xlink:href="020/01/1586.jpg" pagenum="461"></pb>serii auditoriis nervis subservire, neque caveam, ut Rondeletius aiebat, ad <lb></lb>branchias ferri, sed ad cerebrum, quod ille negabat, permeare, in acipen­<lb></lb>serum quidem utroque genere manifestum fuit ” (Epistol. </s>

<s>anat., T. II, Ve­<lb></lb>netiis 1740, pag. </s>

<s>294). </s></p><p type="main">

<s>Che la cavea fosse cieca e che mettesse alle branchie, piuttosto che al <lb></lb>cervello, l&#039;avea detto Aristotile, com&#039;apparisce dai passi di lui sopra alle­<lb></lb>gati, prima del Rondelezio, ma lo Stenone stesso, benchè dubitasse se l&#039;as­<lb></lb>serito da que&#039;due Autori era vero, confessò nonostante di non essersene po­<lb></lb>tuto assicurare. </s>

<s>“ An ex hoc foramine, egli così si esprime, in cavitatem <lb></lb>anfractuosam, cranio insculptam, via sit meatui auditorio analoga, necdum <lb></lb>observare mihi licuit ” (Myologiae specimen cit., pag. </s>

<s>112). </s></p><p type="main">

<s>Fatto dunque dal Morgagni questo primo passo nella desiderata ricerca <lb></lb>dell&#039;organo dell&#039;odorato, con l&#039;assicurarsi essere dai forami, che son per <lb></lb>naso dei pesci, veramente aperta la via nelle cavità anfrattuose scolpite nel <lb></lb>cranio; quel che maggiormente gl&#039;importava era di seguitare il corso del <lb></lb>nervo olfaltorio, e di osservarne il termine nell&#039;espandersi sulla membrana <lb></lb>rotonda. </s>

<s>Rivolgendo perciò l&#039;attenzione sopra quei sottilissimi filamenti, che <lb></lb>negli Acipenseri apparivano di un certo colore oscuro, si trovava penosa­<lb></lb>mente combattuto dal dubbio se fossero nervi o vasellini sanguigni, quando <lb></lb>gli capitò alle mani la Storia anatomica del pesce Cane sezionato dallo Ste­<lb></lb>none. </s>

<s>Al veder nella figura illustrativa que&#039;fili, che decorrono dal centro alla <lb></lb>circonferenza a modo di raggi, dichiarati così sotto la lettera di richiamo F: <lb></lb>“ nervea filamenta in tunicam narium a processibus mamillaribus diffusa ” <lb></lb>(ibid., pag. </s>

<s>114); il Morgagni, dietro l&#039;autorità di un tant&#039;uomo, o diciam <lb></lb>meglio dietro così chiara dimostrazione anatomica del vero, si trovò libero <lb></lb>d&#039;ogni dubbio, e si rese sempre più certo che nelle parti del suo Acipen­<lb></lb>sero, corrispondenti alle descritte dallo Stenone in quel suo pesce Cane, ri­<lb></lb>siede veramente l&#039;organo dell&#039;odorato. </s></p><p type="main">

<s>Vennero poi altre osservazioni a confermare l&#039;Anatomico padovano in <lb></lb>questa certezza, e furono la secrezione di un mucco, simile a quello del naso, <lb></lb>nella così detta <emph type="italics"></emph>Canicula,<emph.end type="italics"></emph.end> e la manifesta e unica inserzione dei nervi del <lb></lb>primo paio nella membrana rotonda di questo pesce: d&#039;onde trasse ragio­<lb></lb>nevole motivo a congetturare che, anche nel naso dell&#039;uomo, sebbene s&#039;in­<lb></lb>seriscano parecchi altri nervi, i preposti nulladimeno all&#039;odorato sieno pro­<lb></lb>priamente quelli del primo paio. </s>

<s>Dopo le quali cose, ritornando il Morgagni <lb></lb>al Casserio, d&#039;ond&#039;era mosso il discorso intorno all&#039;organo olfaltorio de&#039;pe­<lb></lb>sci, così riassume e conclude il § 41 della citata Epistola anatomica, dopo <lb></lb>aver confermata l&#039;analogia stenoniana fra le lamelle membranose, e le ossa <lb></lb>turbinate: “ Id quoque, et is de quo dicebam mucus, et potissimum Pri­<lb></lb>mum nervorum par, valde crassum, ad hanc pariter in Canicula caveam <lb></lb>perductum, ut nihil cum auditus, plurimum cum olfactus instrumento con­<lb></lb>veniunt; ita Casserii opinioni, utrumque hic organum coniungentis, inter <lb></lb>alia quae sciens praetereo, non obscure adversantur ” (pag. </s>

<s>295). </s></p><p type="main">

<s>Dimostratosi così con tanta evidenza dallo Stenone, e confermatosi dal <pb xlink:href="020/01/1587.jpg" pagenum="462"></pb>Lorenzini, dal Perrault, e più autorevolmente che mai dal Morgagni, non <lb></lb>convenire gli organi casseriani de&#039;pesci altro che all&#039;odorato, rimaneva negli <lb></lb>Ittiologi una viva curiosità di sapere qual si fosse dunque l&#039;organo dell&#039;udito <lb></lb>in quegli acquatici animali. </s>

<s>Vedemmo come il Morgagni stesso diffidasse ul­<lb></lb>timamente di riconoscer per nervo acustico quello, che nel capo del Luccio <lb></lb>avea fatto rappresentare in disegno l&#039;Anatomico piacentino, ma da un&#039;altra <lb></lb>grande autorità nella scienza era stato pronunziato, assai tempo prima, che <lb></lb>il nervo auditorio ne&#039;pesci, a&#039;suoi più diligenti esami, tuttavia rimaneva un <lb></lb>desiderio. </s>

<s>Tommaso Willis riserbò il cap. </s>

<s>V del suo trattato <emph type="italics"></emph>De cerebri ana­<lb></lb>tome<emph.end type="italics"></emph.end> a descrivere il cervello degli uccelli e de&#039;pesci, dove osserva che, seb­<lb></lb>bene il capo sia a proporzione delle altre membra maggiore ne&#039;pesci che <lb></lb>negli altri animali, il cervello è nulladimeno a loro il minimo di tutti. </s>

<s>“ Nam <lb></lb>duae moleculae anterius positae totum cerebri, ita proprie dicti, locum sub­<lb></lb>stinent. </s>

<s>Ex his duo nervi olfactorii insignes procedunt, qui longo et recto <lb></lb>itinere ad foramina, ex utroque oris latere excavata, quaeque instar narium <lb></lb>sunt, feruntur, atque piscibus singulare est.... Nervi auditorii hic deside­<lb></lb>rantur, licet Casserius placentinus hoc munus nervis olfactoriis attribuat ” <lb></lb>(In Mangeti, Bibliotheca anat., T. II, Genevae 1685, pag. </s>

<s>255 et 258). </s></p><p type="main">

<s>Quanto agli organi esterni, e a quegli altri più internamente scolpiti <lb></lb>nella cavità anfrattuosa del cranio, udimmo dianzi il Casserio eloquentemente <lb></lb>descrivere la membrana del timpano, e il meato uditorio, e i maravigliosi <lb></lb>plessi capreolari, e i lapilli olivari, e, varii di grandezza, di forma e di po­<lb></lb>situra, gli ossicini. </s>

<s>Al Perrault nonostante, guarda e riguarda, non riusci <lb></lb>mai di veder nulla di tutto ciò nella rocca petrosa de&#039;pesci, fuor che qual­<lb></lb>che cosa, da potersi senza dubbio rassomigliare ai canaliculi semicircolari. <lb></lb></s>

<s>“ Dans le poissons, egli dice nel trattato <emph type="italics"></emph>Du bruit,<emph.end type="italics"></emph.end> nous n&#039;avons point en­<lb></lb>core pù trouver ni de tambour, ni d&#039;osselets, ni de couduit dans le laby­<lb></lb>rinthe qui ait aucune analogie avec le limaçon: il y en a même beaucoup <lb></lb>où il ne se trouve point d&#039;ouverture au dehors qui soit visible. </s>

<s>Tout ce <lb></lb>qu&#039;on y void distinctement sont les conduits principalement du labyrinthe, <lb></lb>qui se trouvent en quelques poissons au nombre de trois comme aux oi­<lb></lb>seaux: il y en a où il ne s&#039;en trouve que deux ” (Oeuvres, T. </s>

<s>I cit., <lb></lb>pag. </s>

<s>247). </s></p><p type="main">

<s>Come potessero però questi canali semicircolari, senza nervo acustico, <lb></lb>senza nessuna apparente comunicazion coll&#039;esterno, rappresentare essi soli <lb></lb>l&#039;organo dell&#039;udito, riusciva difficile intenderlo ai più, i quali facilmente si <lb></lb>persuasero ch&#039;essendo muti i pesci fossero perciò da credere anche sordi. </s>

<s><lb></lb>Ma inaspettatamente, poco prima che il secolo XVIII giungesse a mezzo il <lb></lb>suo corso, si videro uscire in Danzica due volumi, con numerose bellissime <lb></lb>tavole ittiologiche, nel primo de&#039;quali Iacopo Teodoro Klein, che n&#039;era l&#039;Au­<lb></lb>tore, premetteva alla Storia de&#039;pesci un discorso intitolato <emph type="italics"></emph>De piscium au­<lb></lb>ditu.<emph.end type="italics"></emph.end> In quel tempo che l&#039;anatomia dell&#039;organo e la teoria della funzione <lb></lb>avevano già avuto tanti insigni cultori nello Schelhammer, nel Duverney, <lb></lb>nel Perrault, nel Valsalva, per tacer di tanti altri, nessun sarebbesi aspet-<pb xlink:href="020/01/1588.jpg" pagenum="463"></pb>tato fosse venuto un Naturalista a dire che il suono si produce nell&#039;orec­<lb></lb>chio dall&#039;incudine percossa dal martello. </s>

<s>Eppure il Klein si gloria principal­<lb></lb>mente di avere illustrate, co&#039;suoi nuovi studii, le oramai viete e meritamente <lb></lb>ripudiate teorie del Casserio, a cui egli attribuisce la prima palma nella sco­<lb></lb>perta de&#039;lapilli de&#039;pesci, l&#039;uso dei quali ei non dubita esser quello attri­<lb></lb>buito a loro dal Severino. </s>

<s>“ Casserius placentinus omnibus palmam prae­<lb></lb>ripuit, utpote qui primus tria paria lapillorum in cerebro Lucii detexit, et <lb></lb>si non adulari nullum involvit periculum audeamus dicere neminem Casse­<lb></lb>rio simul propius ad organa auditus piscium accessisse, via licet, quam pro <lb></lb>meatu auditorio elegit, plane regia non fuerit ” (Historiae piscium, P. I, <lb></lb>Gedani 1741, pag. </s>

<s>12). </s></p><p type="main">

<s>Cercando dunque il Klein questa nuova via regia, si compiacque di aver <lb></lb>fatto una scoperta, perchè, mentre il Casserio non avea veduto nel suo Luc­<lb></lb>cio altro che due soli forami, egli ebbe a ritrovarvene venti. </s>

<s>“ Ulterius Cas­<lb></lb>serii experimenta examinare cupidi, sumpsimus aliud Lucii maioris cranium, <lb></lb>cuius in superficiem mox offendimus decem paria foraminum, sive foramina <lb></lb>externa viginti: Casserius non nisi nares exhibet ” (ibid., pag. </s>

<s>13). Ma, se <lb></lb>non il Casserio, lo Stenone aveva descritto il rostro del suo Pesce cane “ mul­<lb></lb>tis undique foraminibus pertusum ” (Historia in Myol. </s>

<s>spec. </s>

<s>cit., pag. </s>

<s>112) <lb></lb>e il Lorenzini, a proposito delle Torpedini, avea così pubblicamente scritto, <lb></lb>illustrando e compiendo le osservazioni anatomiche de&#039;suoi due illustri mae­<lb></lb>stri: “ Tutta la pelle, che è sopra il dorso, è piena d&#039;infiniti forami, de&#039;quali <lb></lb>alcuni sono più grandi, altri più piccoli, e tanto i grandi quanto i piccoli <lb></lb>sono più numerosi in vicinanza del capo..... Questi stessi forami sono stati <lb></lb>osservati e descritti dal signore Stenone nel pesce chiamato Razza, con que­<lb></lb>sta differenza però che egli ha osservato una sola sorta di forami grandi, ed <lb></lb>io ho osservato i maggiori e i minori. </s>

<s>Il signor Francesco Redi, nel suo trat­<lb></lb>tato <emph type="italics"></emph>Delle anguille<emph.end type="italics"></emph.end> non ancora stampato, osservò ancor egli questa differenza <lb></lb>di forami maggiori e minori, e gli ha descritti diligentemente, e di più ha <lb></lb>osservato che, messa la setola per un forame e camminando lunghesso il <lb></lb>canale sottoposto, va la setola a uscire fuora del canale per la bocca del fo­<lb></lb>rame più vicino. </s>

<s>Inoltre egli ha osservato che, non solamente i pesci carti­<lb></lb>laginei e senza squame sono dotati di questi così fatti forami e canali, ma <lb></lb>ancora i pesci squamosi, come i Lucci, le Tinche, le Reine, le Trote ” (Os­<lb></lb>servazioni intorno alle Torp. </s>

<s>cit., pag. </s>

<s>7, 8). </s></p><p type="main">

<s>Non nuovo era dunque al Klein nemmen l&#039;artificio d&#039;esplorare le ri­<lb></lb>poste vie, e le loro riuscite, per mezzo delle setole porcine infilate in quegli <lb></lb>aperti forami, ma novissimo sarebbe riuscito al Redi e allo Stenone e al Lo­<lb></lb>renzini quel che lo stesso Klein diceva di avere scoperto, che cioè alcune di <lb></lb>quelle vie mettono al cervello, e che servono perciò al pesce in qualità di <lb></lb>meato uditorio esterno. </s>

<s>Così, mentre il Perrault non aveva saputo veder nel­<lb></lb>l&#039;osso litoide de&#039;pesci altro che i canali semicircolari, egli, il Klein, ci vide <lb></lb>tutto ciò che v&#039;avea veduto il Casserio, e ci vide anzi di più, oltre il mar­<lb></lb>tello e l&#039;incudine, la staffa e lo stesso osso lenticolare. </s>

<s>“ Quaenam vero di-<pb xlink:href="020/01/1589.jpg" pagenum="464"></pb>verticula sint, quae seta reflexa perrepserit, et utrum e fig. </s>

<s>III ossis petrosi <lb></lb>aut alius nescio, cuius vices subeat, peritiores, qui se anatomicos profiten­<lb></lb>tur, iudicent. </s>

<s>Similiter quid obstare possit quo minus maior lapillus pro <lb></lb>incude, proximus illi minor et longiusculus pro malleo, sive percussorio, <lb></lb>proximior vero et minimus orbicularis ac crenatus pro esse lenticulari Cas­<lb></lb>serii sive orbicolari, vel loco stapedis, foramina demum B, B figurae I pro <lb></lb>meatibus auditus externis, et vesicula ovalis figurae, diaphana, pro tympano <lb></lb>habenda? </s>

<s>” (Historiae piscium, P. </s>

<s>I cit., pag. </s>

<s>14). </s></p><p type="main">

<s>Questi in ogni modo furono giudicati sogni dagl&#039;Ittiologi del secolo XVIII, <lb></lb>i quali, essendo oramai ben persuasi che gli ossicini hanno un ufficio se­<lb></lb>condario, anche nell&#039;orecchio de&#039;quadrupedi e degli uccelli, non riconobbero <lb></lb>col Perrault ne&#039;pesci altr&#039;organo dell&#039;udito che i canali semicircolari. </s>

<s>L&#039;Hal­<lb></lb>ler diceva nel Tomo V della sua Fisiologia (pag. </s>

<s>292) che se si potesse aver <lb></lb>di ciò qualche certezza, si verrebbe a dar gran valore alla sentenza di co­<lb></lb>loro, che riponevano in quegli stessi canali la sede principale dell&#039;udito, ma <lb></lb>le nuove scoperte del Cotunnio avviavano la mente per ben altri sentieri. </s></p><p type="main">

<s>Se l&#039;orecchio infatti è tutto internamente pieno di umore, e se il nervo <lb></lb>riceve da questo, e non immediatamente dall&#039;aria, i tremori, i pesci, che vi­<lb></lb>vono in mezzo all&#039;acqua, non han dunque bisogno del risonar della dura <lb></lb>rocca petrosa, e perciò anche i canali semicircolari del Perrault si dubitava <lb></lb>che fossero da ripor nel numero de&#039;sogni casseriani. </s>

<s>Pensarono perciò sa­<lb></lb>viamente costoro tornasse piuttosto vera la sentenza del Gassendo, che cioè <lb></lb>al senso speciale dell&#039;udito ne&#039;pesci, come a quello della vista ne&#039;pipristelli <lb></lb>accecati dallo Spallanzani, supplisse il senso fondamentale del tatto, il quale <lb></lb>ha le sue papille continuamente immerse nell&#039;acqua, come sono continua­<lb></lb>mente immerse le filamenta nervose nell&#039;umor del Cotunnio. </s>

<s>Che dall&#039;altra <lb></lb>parte sia l&#039;acqua sensibilissimo e prontissimo mezzo di trasmissione di qua­<lb></lb>lunque minimo moto, lo dimostrano l&#039;esperienze del Magiotti, e i telegrafi <lb></lb>idraulici, fondati sul principio idrostatico dell&#039;uguaglianza delle pressioni. </s></p><p type="main">

<s>Un tal modo di ricevere i segni conviene oltresì col modo particolare <lb></lb>di emetterli, non sapendosi persuadere coloro, che accoglievano questi nuovi <lb></lb>pensieri, come si pretendesse che avessero i pesci organi da inspirar la voce, <lb></lb>non avendo strumenti da espirarla. </s>

<s>Come dunque i segni vengono a loro, <lb></lb>non dai moti acustici ma idrostatici dell&#039;acqua; così gli trasmettono per <lb></lb>questi stessi moti, e in tal maniera s&#039;intendono insieme, e vivono in comu­<lb></lb>nanza, e si partecipano a vicenda ora i minacciosi odii, ora i placidi amori. </s></p><pb xlink:href="020/01/1590.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO XII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Degl&#039;insetti<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della generazione spontanea e delle varie esperienze istituite per dimostrarla falsa. </s>

<s>— II. </s>

<s>Della <lb></lb>Micrografia e delle particolari applicazioni di lei alla scoperta degli organi della respirazione, <lb></lb>— III. </s>

<s>Degli organi dei sensi e particolarmente degli occhi. </s>

<s>— IV. De&#039;fenomeni di fosfore­<lb></lb>scenza, segnatamente nelle lucciole marine e nelle terrestri. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>A quella Filosofia che, secondo l&#039;animo proprio e la propria mente, fa­<lb></lb>ceva operatrice la Natura, parve quasi essere dalla sua dignità degradata, <lb></lb>quando, da contemplare i quadrupedi, gli uccelli e i pesci, la più parte dei <lb></lb>quali dominati dall&#039;uomo si porgevano docili e vinti a sodisfare alle neces­<lb></lb>sità della vita di lui e ai piaceri; abbassò lo sguardo su quell&#039;indiscipli­<lb></lb>nato indomabile esercito d&#039;innumerevoli animalucci, spesso nocivi, sempre <lb></lb>molesti, e ne&#039;quali, degradatasi la Natura stessa, non si riconosceva altra <lb></lb>immagine che della viltà e della abbiettezza. </s>

<s>Aristotile, gran Maestro di così <lb></lb>fatta Filosofia, nell&#039;introdursi a scrivere la Storia degli Animali, disse di <lb></lb>essere stato il primo a imporre a cotesti abietti esseri viventi il nome di <lb></lb><foreign lang="grc">έντομα ζω̄α</foreign>, che i Latini tradussero in <emph type="italics"></emph>Insecta animalia,<emph.end type="italics"></emph.end> e le lingue volgari <lb></lb>in <emph type="italics"></emph>Insetti.<emph.end type="italics"></emph.end> A pochi di costoro concesse il Filosofo l&#039;onore di riconoscere per <lb></lb>loro primo parente una gocciola d&#039;umor viscido e albuminoso, che avesse <lb></lb>qualche somiglianza con l&#039;uovo: i più disse essere ingenerati dalla pu­<lb></lb>tredine e dal fango: “ Procreantur porro insecta aut ex animalibus gene­<lb></lb>ris eiusdem, ut phalangia et aranei, ex phalangiis et araneis, ut bruci, lo­<lb></lb>custae, cicadae, aut non ex animalibus sed sponte, alia ex rore, qui frondibus <pb xlink:href="020/01/1591.jpg" pagenum="466"></pb>insudat, item alia ex coeno aut fimo putrescente ” (De historia anim, Ope­<lb></lb>rum, T. VI cit., fol. </s>

<s>132). </s></p><p type="main">

<s>I Filosofi posteriori si studiarono di nobilitare coteste generazioni, ri­<lb></lb>correndo alla indeficiente fecondità della madre Terra, sotto i benigni influssi <lb></lb>celesti, e Guglielmo Rondelezio, nel risorgere degli studi sperimentali, in­<lb></lb>troduceva i principii della Filosofia stoica nella Storia naturale, quando volle <lb></lb>ridurre a scienza lo spontaneo nascere di alcuni pesci. </s>

<s>A quel modo, egli <lb></lb>dice, che la Terra, in stabiliti tempi, senza seme e senz&#039;altr&#039;opera d&#039;uomo, <lb></lb>produce per sua propria virtù tant&#039;erbe e tanti animali; così medesima­<lb></lb>mente fa il Mare partecipe tutto insieme delle virtù dell&#039;umido, dell&#039;aereo <lb></lb>e del terreo, e perciò dispostissimo per sè a procreare. </s>

<s>“ Generantur ergo <lb></lb>in terra et in humore animantes et plantae, propterea quod in terra qui­<lb></lb>dem inest humidum, in humore spiritus, in universo autem calor animale, <lb></lb>ut quodammodo omnia anima plena sint ” (De piscibus cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Più immediato promotore della Storia naturale, che non il Rondelezio, <lb></lb>Girolamo Fabricio d&#039;Acquapendente non seppe far altro, per meglio confor­<lb></lb>marsi alle dottrine del Maestro, che ripetere verbo a verbo i detti sopra ri­<lb></lb>feriti di Aristotile, ai quali solo aggiunse, come per commento, di suo, dopo <lb></lb>avere annoverati i varii insetti che hanno varia generazion casuale, queste <lb></lb>parole: “ quorum nullum ex ovo, quod non preest, suam generationem <lb></lb>adipiscitur ” (De formatione ovi, Op. </s>

<s>omnia cit., pag. </s>

<s>25). E nell&#039;introdursi <lb></lb>a trattare della generazione, si proponeva di distinguere così in tre diversi <lb></lb>ordini le varie feture animali. </s>

<s>“ Animalium autem foetus alius ex ovo, alius <lb></lb>ex semine, alius ex putri gignitur, unde alia ovipara, alia vivipara, alia ex <lb></lb>putri, seu sponte naturae nascentia <foreign lang="grc">αυτόματα</foreign> graece dicuntur ” (ibid., pag. </s>

<s>1). </s></p><p type="main">

<s>Guglielmo Harvey, quando si dette con tanto ardore a proseguir l&#039;opera <lb></lb>dell&#039;Acquapendente, che avea così a soli alcuni animali assegnata la gene­<lb></lb>razione dall&#039;uovo, “ nos autem asserimus, gloriosamente scriveva, omnia <lb></lb>omnino animalia, etiam vivipara atque hominem adeo ipsum, ex ovo pro­<lb></lb>gigni ” (De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>2). E per accennare a un altr&#039;amo, a <lb></lb>cui rimasero presi alcuni, che delibarono qua e là qualche cosa del libro <lb></lb>dell&#039;Harvey, trattando in altra esercitazione, l&#039;Autore, de&#039;primordii oviformi <lb></lb>dai quali hanno origine le piante stesse, così interrompe il cominciato di­<lb></lb>scorso: “ Sed de his quoque generatim plura dicemus, cum multa anima­<lb></lb>lia, praesertim insecta, ab inconspicuis prae exiguitate principiis et seminibus, <lb></lb>quasi atomis in aere volitantibus, a ventis huc illuc sparsis ac disseminatis, <lb></lb>oriri ac progigni docebimus, quae tamen sponte, sive ex putredine orta, iu­<lb></lb>dicantur, quia eorum semina nusquam comparent ” (ibid., pag. </s>

<s>149). </s></p><p type="main">

<s>Per gli ami, de&#039;quali abbiam citato questi due esempii, vogliamo in­<lb></lb>tender l&#039;inganno di coloro, che crederono essere stato l&#039;Harvey il primo e <lb></lb>solenne maestro venuto fuori a insegnare la generazione di ogni animale <lb></lb>dall&#039;uovo, e che si dovesse perciò a lui principalmente il merito di aver <lb></lb>dimostrata la falsità della generazione spontanea. </s>

<s>I nostri lettori del passato <lb></lb>capitolo X, che sono stati oramai disingannati rispetto al primo punto, si <pb xlink:href="020/01/1592.jpg" pagenum="467"></pb>disinganneranno altresì con facilità rispetto al secondo, attendendo con noi, <lb></lb>per via di diligenti collazioni, al significato proprio, che dava l&#039;Harvey a <lb></lb>que&#039;semi, quasi atomi vaganti per l&#039;aria, e da&#039;quali s&#039;ingenerano que&#039;vi­<lb></lb>venti, che il volgo crede aver origine dalle materie putrefatte. </s>

<s>Non son mica <lb></lb>cotesti germi univoci, per usare il linguaggio proprio di que&#039;tempi, ma equi­<lb></lb>voci; ossia non vengono essi deposti dall&#039;utero di altri animali della mede­<lb></lb>sima specie, ma sono un fortuito accozzamento di atomi materiali, a cui si <lb></lb>dà promiscuamente il nome di <emph type="italics"></emph>uova<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>primordii vegetali.<emph.end type="italics"></emph.end> “ Liceat hoc <lb></lb>nobis <emph type="italics"></emph>primordium vegetale<emph.end type="italics"></emph.end> nominare, nempe substantiam quandam corpo­<lb></lb>ream vitam habentem potentia, vel quoddam per se existens, quod aptum <lb></lb>sit in vegetativam formam, ab interno principio operante, mutari. </s>

<s>Quale <lb></lb>nempe primordium ovum est et plantarum semen, tale etiam viviparorum <lb></lb>conceptus et insectorum vermis; diversa scilicet diversorum viventium pri­<lb></lb>mordia. </s>

<s>Pro quorum vario discrimine alii atque alii sunt generationis ani­<lb></lb>malium modi, qui tamen omnes in hoc uno conveniunt, quod a primordio <lb></lb>vegetali, tamquam e materia efficientis virtute dotata, oriantur. </s>

<s>Differunt <lb></lb>autem quod primordium hoc vel sponte et casu erumpit, vel ab alio preesi­<lb></lb>stente tanquam fructus erumpat, unde illa sponte nascentia, haec e paren­<lb></lb>tibus genita dicuntur ” (ibid., pag. </s>

<s>283). </s></p><p type="main">

<s>Parecchi altri sarebbero i passi, che si potrebbero collazionare, e nei <lb></lb>quali tutti si professa apertamente la generazione equivoca degli animali, con <lb></lb>questa sola differenza dalle idee degli Aristotelici che, invece di far di essi <lb></lb>animali immediata genitrice la putredine, si fanno i primordii vegetali o gli <lb></lb>archei. </s>

<s>Il Redi, dop&#039;aver citato alcuno di questi passi, accusava l&#039;Autore <lb></lb>piuttosto di oscurità che di errore, accagionandone i tumulti delle guerre <lb></lb>civili, ma lo Swammerdam, senza tanti riguardi, citato il testo, soggiunge: <lb></lb><emph type="italics"></emph>Hucusque Harveus: verum quot verba tot fere errores haec ipsius Disser­<lb></lb>tatio continet.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>E in verità rendevasi l&#039;errore manifesto considerandone la causa, che <lb></lb>vi conduceva necessariamente; causa, che riducevasi all&#039;aver l&#039;Hrvey, in <lb></lb>questo trattato <emph type="italics"></emph>De generatione animalium,<emph.end type="italics"></emph.end> abbandonate quelle sicure e di­<lb></lb>rette vie sperimentali, così felicemente proseguite nel trattato <emph type="italics"></emph>De motu cor­<lb></lb>dis,<emph.end type="italics"></emph.end> per tener dietro alle astrazioni della metafisica aristotelica corroborata <lb></lb>dello stoicismo e, a modo degli Scolastici, inoculata ne&#039;principii della Filo­<lb></lb>sofia cristiana. </s>

<s>Nella esercitazione XLV appoggia la ragione del generarsi <lb></lb>spontaneamente gli animali al principio, professato nel VII dei <emph type="italics"></emph>Matafisici<emph.end type="italics"></emph.end> di <lb></lb>Aristotile, che cioè <emph type="italics"></emph>materia potest a seipsa moveri,<emph.end type="italics"></emph.end> e nella esercitazione LVII <lb></lb>invoca que&#039;medesimi principii aristotelici, dai quali consegue poter avvenir <lb></lb>nella natura quel che nell&#039;arte, che cioè producasi fortuitamente talvolta <lb></lb>quel che è consueto d&#039;operarsi dall&#039;arte stessa, per applicar così tali meta­<lb></lb>fisici principii alle generazioni animali: “ Similiter se habet generatio quo­<lb></lb>rumlibet animalium, sive semen eorum casu adsit, sive ab agente univoco, <lb></lb>eiusdemque generis, proveniat. </s>

<s>Quippe etiam in semine fortuito inest prin­<lb></lb>cipium generationis motivum, quod ex se et per seipsum procreet idemque <pb xlink:href="020/01/1593.jpg" pagenum="468"></pb>quod in animalium congenerum semine reperitur, potens scilicet anima effor­<lb></lb>mare ” (ibid., pag. </s>

<s>253, 54). </s></p><p type="main">

<s>Il seme però fortuitamente composto non ha potenza di formar l&#039;ani­<lb></lb>male per virtù, che sia inerente alla materia, ma per una più alta virtù <lb></lb>partecipata a lei da quella Mente e da quello Spirito, che agita la gran mole <lb></lb>(ivi, pag. </s>

<s>115); Mente e Spirito, che altrove cristianeggiando l&#039;Harvey chiama <lb></lb>Dio creatore, Sommo e Onnipotente, e che è la Mente Divina di Aristotile, <lb></lb>l&#039;Anima del mondo di Platone, la Natura naturante, o il Saturno o il Giove <lb></lb>de&#039;pagani, “ vel potius, ut nos decet, Creatorem ac Patrem omnium quae <lb></lb>in coelis et terris, a quo animalia eorumque origines dependent, cuiusque <lb></lb>nutu, sive effato, fiunt et generantur omnia ” (ibid., gag. </s>

<s>228). </s></p><p type="main">

<s>Ma perchè riconoscevasi che questi nobili e sublimi concetti erano fuor <lb></lb>di luogo, trattandosi di una questione, che voleva essere risoluta per via di <lb></lb>diligenti osservazioni microscopiche, e di esatte esperienze, così dall&#039;Harvey <lb></lb>dannosamente neglette; ne&#039;primi congressi della prima Accademia speri­<lb></lb>mentale istituita in Europa si volle mettere a cimento quel che, filosofi e <lb></lb>volgo, credevano intorno al generarsi spontaneo di alcuni animali dal fango <lb></lb>e dall&#039;umido della terra. </s>

<s>In un registro infatti delle cose naturali, osservate <lb></lb>nell&#039;Accademia fiorentina sotto la presidenza del principe Leopoldo, si legge <lb></lb>questa nota colla data del dì 6 Settembre 1657. “ Non è vero che le botte <lb></lb>si generino dalla pioggia, ma allora si disascondono, come anco si è osser­<lb></lb>vato diligentemente in que&#039;luoghi, che in quel tempo ne paiono più abbon­<lb></lb>danti, la mattina escono fuori al fresco dell&#039;aurora, con tutto che per la <lb></lb>notte nessuna ne apparisca ” (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>680). </s></p><p type="main">

<s>Fra que&#039;filosofi peripatetici, così colti in fallo dagli Accademici fioren­<lb></lb>tini, erano i Gesuiti, che gelosi di mantenersi il principato della scienza te­<lb></lb>nevano gli occhi aperti sopra Firenze, per espiarne i segreti. </s>

<s>Forse erasi di <lb></lb>già divulgato il modo insegnato dal padre Atanasio Kircher, per ottenere una <lb></lb>nuova generazione di rane, con aspergere d&#039;acqua piovana la melma delle <lb></lb>paludi, e i nostri Accademici ne risero più facetamente di quel che, nelle <lb></lb>sue <emph type="italics"></emph>Esperienze intorno agl&#039;insetti,<emph.end type="italics"></emph.end> non facesse poi il Redi (Opera, T. I. cit., <lb></lb>pag. </s>

<s>91). In ogni modo i Gesuiti intesero che s&#039;ordinava nelle sale medicee <lb></lb>un valoroso esercito a combattere contro il loro peripatetico magistero, ond&#039;è <lb></lb>che minacciosi s&#039;armarono alle difese. </s>

<s>Di coteste minacce ebbe Carlo Ri­<lb></lb>naldini qualche sentore, e ne dava così avviso al principe Leopoldo, rivol­<lb></lb>gendosi direttamente al Viviani: “ Mi vien detto per cosa certissima che i <lb></lb>padri Gesuiti fanno strepito avanti il tempo, conciossiachè dicono che, se <lb></lb>nel <emph type="italics"></emph>Libro delle osservazioni naturali<emph.end type="italics"></emph.end> fatte costì, ci sarà cosa che possi toc­<lb></lb>care qualcheduno di loro, che averanno uomini, ai quali dà l&#039;animo di ri­<lb></lb>spondere, e che frattanto tutto che possono sapere delle cose fatte procu­<lb></lb>rano di sperimentare, e ne fanno un libro. </s>

<s>Deridono oltre a ciò molte cose <lb></lb>fatte da noi, come l&#039;esperienza delle botticine, dicendo di averla fatta con <lb></lb>porre dell&#039;arena nel lastricato, e vedute nascere al cader della pioggia. </s>

<s>E <lb></lb>molte altre cose, che per brevità tralascio..... Mi è parso bene di avvisare <pb xlink:href="020/01/1594.jpg" pagenum="469"></pb>il tutto a V. S. perchè, se stima bene, lo confidi al serenissimo Leopoldo, il <lb></lb>quale forse potrebbe creder ben fatto le cose che occorrono alla giornata non <lb></lb>doversi palesare, e restringere il negozio in pochi..... Pisa, 9 Marzo 1658 ” <lb></lb>(MSS. Cim., T. XXIV, c. </s>

<s>45). </s></p><p type="main">

<s>Lasciando considerare ai lettori l&#039;importanza di questo documento per <lb></lb>la storia dell&#039;illustre Accademia, e proseguendo addiritto il nostro ragiona­<lb></lb>mento, diciamo che, mentre gli Accademici insieme adunati si compiacciono <lb></lb>di aver così felicemente scoperto l&#039;inganno di coloro, che si davano a cre­<lb></lb>dere nascere spontaneamente le botticine dalla terra inumidita, vedono en­<lb></lb>trar nella sala un paggio, che recava a nome del Granduca alcune foglie di <lb></lb>olmo, perchè fosse esaminato col microscopio il contenuto dentro certe na­<lb></lb>scenze, che apparivano sopra le foglie stesse in guisa di boccioli o di ve­<lb></lb>scichette. </s>

<s>Del resultato di tali osservazioni si legge presa nota così nel so­<lb></lb>pra citato registro: “ Fra le foglie dei rami d&#039;olmo si trovano alcuni boc­<lb></lb>cioli, nei quali aprendosi si trova una quantità di vermi bianchissimi, i quali <lb></lb>col microscpio si veggono come trasparenti di cristallo, con alie simili alle <lb></lb>mosche, ed in mezzo ad essi si trova bene spesso una vescichetta bianca <lb></lb>piena d&#039;umore. </s>

<s>Col microscopio medesimo si ritrovò nascere dall&#039;uova, ve­<lb></lb>dendone alcuni non interamente usciti di esse ” (Targioni, Notizie, T. cit., <lb></lb>pag. </s>

<s>680, 81). </s></p><p type="main">

<s>Della natura e dell&#039;origine di cotest&#039;uova non si sa quel che propria­<lb></lb>mente ne pensassero gli Accademici, ma è probabile che avessero fin d&#039;al­<lb></lb>lora principio quelle controversie, tornate sett&#039;anni dopo, nel 1664, ad agi­<lb></lb>tarsi con più vivo ardore che mai, all&#039;occasione che ora diremo. </s>

<s>Quando il <lb></lb>Pontefice e il Granduca, a ricompor le controversie nate fra&#039;due stati per <lb></lb>causa delle Chiane, mandarono in visita l&#039;uno il Viviani e l&#039;altro Gian Do­<lb></lb>menico Cassini, questi trovò da consolare la solitudine della campagna atten­<lb></lb>tamente osservando la nascita e il progresso delle galle sopra la querce, e <lb></lb>de&#039;vermi che sempre, con sua gran maraviglia, vi trovò dentro nascosti. </s>

<s>Si <lb></lb>lusingò a principio che fosse l&#039;osservazione sua nuova, ma poco dopo s&#039;ab­<lb></lb>battè a leggere nel Mattioli, là dove, commentando il primo libro di Diosco­<lb></lb>ride, tratta nel capitolo CXXIV delle Galle, così fatte parole: “ Hanno le <lb></lb>galle in sè questa loro particolar virtù, che predicono ogni anno, con il <lb></lb>parto loro, la bontà o malizia dell&#039;anno futuro. </s>

<s>Perciocchè se, rompendosi <lb></lb>quelle che si ricolgono secche e non pertugiate, vi si ritrovano dentro mo­<lb></lb>sche, significa guerra; se ragni, peste, e se vermini, carestia. </s>

<s>Nè si mara­<lb></lb>vigli alcuno che delle galle nascano questi animali, perciocchè n&#039;ho veduto <lb></lb>io spessissime volte la esperienza, e poche o niuna se ne ritrova, che per­<lb></lb>tugiata non sia, e che di già non se ne sia uscito l&#039;animale che vi nasce, <lb></lb>che non si trovi pregna d&#039;uno di questi tre vermi. </s>

<s>Laonde si può dire che <lb></lb>la querce produce frutto e animale ” (Venezia 1555, pag. </s>

<s>131, 32). </s></p><p type="main">

<s>Ma perchè qui non si fa cenno della trasformazione del verme in in­<lb></lb>setto alato, rimase nel Cassini almeno la speranza di avere egli il primo os­<lb></lb>servata la metamorfosi, che subiscono gli animalucci nati dentro le galle, e <pb xlink:href="020/01/1595.jpg" pagenum="470"></pb>si compiacque di ciò col Viviani, discorrendone un giorno insieme. </s>

<s>Gli avrebbe <lb></lb>il Viviani potuto rispondere che di quel primato rimaneva la gloria tutta in­<lb></lb>tiera all&#039;Harvey, il quale aveva, tredici anni prima, lasciato così pubblica­<lb></lb>mente scritto nella esercitazione XVIII <emph type="italics"></emph>De generatione animalium:<emph.end type="italics"></emph.end> “ Appa­<lb></lb>ret nempe forma vermiculi sive galbae, sicut in frondibus arborum, corticum <lb></lb>pustulis, fructibus, floribus alibique vermium et erucarum primordia conspi­<lb></lb>cimus, praesertim vero in gallis quercinis, quarum in centro, intra crustu­<lb></lb>lam rotundam, seu nucleum, liquor limpidus continetur, qui sensim crasse­<lb></lb>scens et coagulatus subtilissimis lineamentis distinguitur, galbaeque formam <lb></lb>induit. </s>

<s>Manet autem aliquantisper immobilis, posteaque, motu et sensu prae­<lb></lb>ditus, fit animal, tandemque musca avolat ” (editio cit., pag. </s>

<s>80, 81). </s></p><p type="main">

<s>Ma il Viviani, o che non si sovvenisse di questo passo arveiano, o che <lb></lb>lo movesse più potentemente il desiderio di glorificare il Granduca e gli <lb></lb>Accademici suoi, disse al Cassini che di tutte quelle cose, da lui credute <lb></lb>nuove, era stata fatta sette anni prima in Firenze diligentissima osservazione <lb></lb>da Sua Altezza. </s>

<s>Nonostante, informatosi meglio esso Cassini e ritrovato, ciò <lb></lb>che dall&#039;altra parte facilmente dubitava, nelle risposte del Viviani molta <lb></lb>cortigianeria (non essendo state fatte veramente in Firenze altre osserva­<lb></lb>zioni che sulle vescicole delle foglie degli olmi) ne dette avviso a Ovidio <lb></lb>Montalbani, che promise di pubblicar le osservazioni fatte sulle querce delle <lb></lb>Chiane nella <emph type="italics"></emph>Dendrologia,<emph.end type="italics"></emph.end> la quale laboriosamente allora preparava per la <lb></lb>stampa sul manoscritto di Ulisse Aldovrandi. </s>

<s>Il Cassini infatti descrisse le <lb></lb>galle quercine e i vermi e le loro metamorfosi in una lettera latina, che il <lb></lb>Montalbani inserì, da pag. </s>

<s>220-21, nella detta Dendrologia pubblicata nel 1668 <lb></lb>in Bologna. </s></p><p type="main">

<s>Il Viviani intanto di ciò che aveva osservato e che pretendeva il Cas­<lb></lb>sìni dette subito avviso a Firenze, dipingendo la cosa come gliel&#039;avrà sug­<lb></lb>gerita quella inevitabile rivalità di due, che si trovavano a dover far le parti <lb></lb>d&#039;ingegneri periti fra due litiganti loro padroni. </s>

<s>Gli Accademici, già per sè <lb></lb>medesimi mal disposti verso il Cassini, ritornarono allora sull&#039;argomento dei <lb></lb>vermi nati sopra le piante, e vi si dedicarono in modo, che si venissero di <lb></lb>lì a colorire le ragioni di quel primato, che a rigor di giustizia era una <lb></lb>ingiusta pretesa. </s>

<s>E perchè ben comprendevano che sempre la Filosofia pri­<lb></lb>meggia sopra la Fisica, di ciò che prima avevano semplicemente osservato <lb></lb>si volsero a speculare le misteriose ragioni. </s>

<s>Il Cassini delle cause, che pro­<lb></lb>ducono i vermi, non aveva voluto dir nulla, discorrendone col Viviani, e <lb></lb>anche nella pubblica lettera, inserita nella Dendrologia dell&#039;Aldovrandi, se <lb></lb>ne scusa e se ne sbriga con dire che quelle cose derivano dalle più alte <lb></lb>fonti della Filosofia. </s>

<s>“ Harum productionum causas, quas meditatus sum, <lb></lb>hic non refero: eae enim sunt ut altius ex non vulgaris philosophiae prin­<lb></lb>cipiis sint petenda ” (Aldovrandi, Dendrol., pag. </s>

<s>221). </s></p><p type="main">

<s>Le ipotesi professate dai Filosofi precursori de&#039;nostri Accademici fio­<lb></lb>rentini, lasciando da parte l&#039;Harvey, che da&#039;suoi principii ne concludeva i <lb></lb>vermi ne&#039;frutti e nelle galle “ propria anima gubernari ” (De generat. <pb xlink:href="020/01/1596.jpg" pagenum="471"></pb>anim. </s>

<s>cit., pag. </s>

<s>112), si può dir che si riducevano a quelle derivate da Ari­<lb></lb>stotile, e a una affatto nuova derivata da Pietro Gassendo. </s>

<s>Gli Aristotelici, <lb></lb>fra&#039;quali va a rassegnarsi il sopra citato Mattioli, dicevano esser genitrice <lb></lb>dell&#039;animale la pianta, com&#039;è del frutto, concludendo una tal dottrina dal <lb></lb>testo del Filosofo, là dove, nel cap. </s>

<s>XIX del V libro <emph type="italics"></emph>De historia anima­<lb></lb>lium,<emph.end type="italics"></emph.end> descrivendo la vita delle farfalle, dice che “ nascuntur ex erucis, eru­<lb></lb>cae ex virentibus foliis ” (Operum, T. VI cit., fol. </s>

<s>132). Il Gassendo poi <lb></lb>il quale diceva nascere i vermi dentro i frutti dalle uova, che le madri pre­<lb></lb>gnanti avevan prima deposte ne&#039;fiori; rendeva applicabile ragionevolmete una <lb></lb>simile origine a questi vermi dentro le galle. </s></p><p type="main">

<s>Forse qualcuno degli Accademici propose qualche ipotesi sua propria, <lb></lb>ma dai documenti, che ci son rimasti, apparisce che furono nell&#039;Accademia <lb></lb>grandi contese fra chi faceva co&#039;Gassendisti genitori de&#039;vermi quercini un <lb></lb>altro simile verme, e chi non riconosceva con gli Aristotelici altra genitrice <lb></lb>di loro che la madre pianta. </s>

<s>Nel numero de&#039;primi era Antonio Uliva, e <lb></lb>fra&#039;secondi, calorosissimo peripatetico, il Magalotti, che scriveva così da Fi­<lb></lb>renze il dì 16 Settembre 1664 in una sua lettera familiare a Ottavio Fal­<lb></lb>conieri: “ Vedete, signor Ottavio, io rido di quelli che dicono che questi <lb></lb>bachi o mosche non sono così veri e legittimi parti della quercia, come le <lb></lb>ghiande e le medesime coccole, ma nati dal seme di simili animali cammi­<lb></lb>nati su&#039;fiori, onde nasce la coccola, o introdotti con qualche loro aculeo o <lb></lb>in altro modo nella medesima coccola dopo nata. </s>

<s>Mi dicano un po&#039;costoro, <lb></lb>se questo fosse, perchè avrebbono a esser tutti senza fallo della medesima <lb></lb>spezie, e sempre situati nel centro? </s>

<s>Niente meno mi rido dell&#039;opinion del­<lb></lb>l&#039;Uliva, il quale si dà ad intendere che di questa cosa se n&#039;abbia a fare un <lb></lb>grande scalpore fra&#039;peripatetici. </s>

<s>Fate conto, i&#039;sto per dire, ch&#039;e&#039;darebbe <lb></lb>l&#039;animo a me di salvare Aristotile, col quale, non essendo egli tenuto a te­<lb></lb>nere per soprannaturale l&#039;infusione della nostr&#039;anima, si potrebbe dire che <lb></lb>assai più maraviglioso passaggio è quello che si vede tuttodì dell&#039;umane ge­<lb></lb>nerazioni, dove la materia trapassa dal sensibile all&#039;intellettivo, che non è <lb></lb>questa, dove il passaggio solamente si fa dal vegetativo al sensibile ” (Let­<lb></lb>tere famil. </s>

<s>di L. Magalotti, Vol. </s>

<s>I, Firenze 1769, pag. </s>

<s>94, 95). </s></p><p type="main">

<s>Così fatta opinione peripatetica del Magalotti fu quella che prevalse nel­<lb></lb>l&#039;Accademia, e Angelo Fabbroni, editore delle Lettere familiari alle quali <lb></lb>appartiene anche questa ora citata, avverte in nota a pag. </s>

<s>92 del medesimo <lb></lb>Tomo I: “ L&#039;Uliva approvò poi l&#039;opinione del Magalotti, com&#039;ho veduto in <lb></lb>una sua lettera. </s>

<s>” </s></p><p type="main">

<s>Non ammesso ancora a far parte dell&#039;Accademia, Francesco Redi si <lb></lb>sentiva frugato da una viva curiosità di sapere quel che si faceva nelle se­<lb></lb>grete sale sperimentali di corte, e n&#039;era facilmente sodisfatto da que&#039;dotti <lb></lb>amici suoi cortigiani colleghi. </s>

<s>La questione de&#039;vermi delle galle secondava <lb></lb>più che altra mai quella sua potente inclinazione agli studii della Storia na­<lb></lb>turale, e considerata la grande importanza, ch&#039;ella aveva nella scienza, si <lb></lb>sentì nascere il desiderio d&#039;entrare egli in mezzo a deciderla. </s>

<s>Datosi perciò <pb xlink:href="020/01/1597.jpg" pagenum="472"></pb>a ricercar diligentemente gli Autori, le varie ipotesi de&#039;quali erano state <lb></lb>nell&#039;Accademia discusse, meditava attentamente quel che, nel <emph type="italics"></emph>Sintamma <lb></lb>filosofico,<emph.end type="italics"></emph.end> trattando il Gassendo della generazione degli animali, scrive nel <lb></lb>cap. </s>

<s>I di essi <emph type="italics"></emph>sponte nascentibus.<emph.end type="italics"></emph.end> La causa di così fatta spontanea genera­<lb></lb>zione, dice il Filosofo francese, è il seme stesso o la piccola anima ivi den­<lb></lb>tro infusa a far questo ufficio. </s>

<s>Ma perchè di tanto minima piccolezza risulti <lb></lb>una mole più grandicella e sensibile, è necessario che molte di quelle pic­<lb></lb>cole anime vivificanti gli atomi della materia si congiungano insieme. </s>

<s>An­<lb></lb>che negli animali di generazione equivoca la causa interna precipua e pros­<lb></lb>sima è nel detto principio seminale, come negli univoci, ciò che si prova, <lb></lb>dice il Gassendo, con molti argomenti, fra&#039;quali, dall&#039;esser varie le gene­<lb></lb>razioni secondo i climi e secondo gl&#039;incunabili, come si vede per esempio <lb></lb>che da varie sorta di legumi escono varie specie di insetti. </s>

<s>“ Neque obstare <lb></lb>debet quod propterea homo animalve aliud constet ex variorum animalium <lb></lb>seminibus, siquidem ut silex, quatenus est silex, constat ex ignis semini­<lb></lb>bus, quae atterendo se explicent; ita animal, quatenus animal, hoc est cor­<lb></lb>pus heterogeneum diversis, similibusque rebus connutritum, constitui potest <lb></lb>ex diversis animalium seminibus, quae putrescendo explicentur, ut per aesta­<lb></lb>tem, dum muscae depascuntur carnes, in iis vermes generant, videlicet eden­<lb></lb>tos ova, quae statim, prae caloris vehementia, excludantur in vermes, ex <lb></lb>quibus deinde grandiores muscae procreari, ut ex erucis per varias transmu­<lb></lb>tationes papiliones, possint: Ut vermes gignuntur intra pulpas fructuum, <lb></lb>quod muscae aut apes etc. </s>

<s>floribus insidentes reliquerint ova, quae fructi­<lb></lb>bus conclusa, accedente maturationis calore, excludantur: Ut muscae possint <lb></lb>impressisse herbarum et arborum foliis, quae a vaccis, capris, ovibus de­<lb></lb>pasta et lacte contenta caseoque conclusa, succescente et ab antiperistasi <lb></lb>incalescente substantia, in vermes formentur ” (Petri Gassendi, Operum, <lb></lb>T. II, Florentiae 1727, pag. </s>

<s>229). </s></p><p type="main">

<s>Sentì, a rimeditar queste cose, il Redi fecondarsi la mente, la quale gli <lb></lb>mostrava quanto fosse di vero in quelle nuove dottrine del Gassendo, nelle <lb></lb>quali insegnavasi che gl&#039;insetti, piuttosto che dalle sostanze imputridite, na­<lb></lb>scono dalle uova ivi dentro deposte da altri simili insetti. </s>

<s>Quel che dunque <lb></lb>il Filosofo francese avea concluso colla ragione, il nostro Naturalista attese <lb></lb>a dimostrarlo coll&#039;esperienze, particolarmente poi descritte in quel celebro <lb></lb>trattato <emph type="italics"></emph>Intorno agl&#039;insetti,<emph.end type="italics"></emph.end> indirizzato in forma di epistola a Carlo Dati. </s>

<s><lb></lb>Consistevano queste esperienze in lasciare imputridire varie materie, special­<lb></lb>mente carnami, e in osservar che non inverminavano mai, quando, dentro <lb></lb>vasi chiusi o sotto fitti veli, era proibito alle mosche gettarvisi sopra a pa­<lb></lb>scere e a deporvi, come in ben disposto nido, le loro uova. </s>

<s>Tanto parvero <lb></lb>anzi al Redi gli sperimentati fatti dimostrativi, che a questa immediata de­<lb></lb>posizione di uova attribuì l&#039;origine de&#039;vermi del cacio, senza que&#039;passaggi <lb></lb>accennati dal Gassendo. </s>

<s>“ Il sapientissimo Pietro Gassendo, egli dice, ac­<lb></lb>cenna che forse le mosche ed altri animali volanti, avendo impresse e disse­<lb></lb>minate le loro semenze sopra le foglie dell&#039;erbe e degli alberi, e quelle pa-<pb xlink:href="020/01/1598.jpg" pagenum="473"></pb>sciute poi dalle vacche, dalle capre e dalle pecore, possano introdurre nel <lb></lb>latte e nel formaggio quei semi abili in progresso di tempo a produrre i <lb></lb>vermi. </s>

<s>E certo tale opinione a molti non dispiace, nè io vo&#039;negare ora così <lb></lb>poter essere, ma tuttavia non so, colla dovuta riverenza che a questo gran­<lb></lb>dissimo e ammirabile filosofo io porto, non so, dico, in qual maniera quei <lb></lb>semi tritati dai denti degli animali, e nel loro stomaco cotti, abbiano potuto <lb></lb>conservar sana e salva la loro virtute. </s>

<s>Per lo che sarei forse di parere che <lb></lb>l&#039;inverminamento del latte, del formaggio e della ricotta abbia quella stessa <lb></lb>cagione da me soprammentovata nelle carni e ne&#039;pesci, cioè a dire che le <lb></lb>mosche ed i moscherini vi partoriscano sopra le loro uova, dalle quali na­<lb></lb>scano i vermi ” (Opere, T. </s>

<s>I cit., pag. </s>

<s>83, 84). </s></p><p type="main">

<s>Imbevuta la mente delle idee, ch&#039;eran prevalse fra gli Accademici del <lb></lb>Cimento, relative all&#039;origine de&#039;vermi nelle galle e dentro i frutti nasco­<lb></lb>sti, era il Redi da questi suoi esperimenti tentato a ripudiarle, per seguire <lb></lb>invece le idee del Gassendo, quando nuove difficoltà, nate da certe consi­<lb></lb>derazioni sue particolari, aggiungendo forza a quelle degli Accademici me­<lb></lb>desimi, lo fecero andar con essi a credere “ che quell&#039;anima o quella virtù, <lb></lb>la quale genera i fiori e i frutti nelle piante viventi, sia quella stessa che <lb></lb>generi ancora i bachi di esse piante ” (ivi, pag. </s>

<s>100), alle quali, per ridurre <lb></lb>alle ultime conseguenze i principii premessi già infino dal Mattioli, e pro­<lb></lb>fessati dai Fisici fiorentini, esso Redi, oltre alla vita vegetativa, attribuì an­<lb></lb>cora la sensibile, perchè “ le condizionasse e le facesse abili alla generazione <lb></lb>degli animali ” (ivi, pag. </s>

<s>104). </s></p><p type="main">

<s>A provar poi che dare il senso alle piante non era <emph type="italics"></emph>un gran peccato in <lb></lb>Filosofia,<emph.end type="italics"></emph.end> l&#039;Autore delle <emph type="italics"></emph>Esperienze intorno agl&#039;insetti<emph.end type="italics"></emph.end> profonde a larga <lb></lb>mano autorità di scrittori antichi e di Poeti “ pensando, dice a proposito il <lb></lb>Vallisnieri, che Virgilio, Dante e gli altri toscani Poeti, con quelle lor fa­<lb></lb>vole, volessero insegnarci che le piante non sono affatto prive di senso ” <lb></lb>(Esperienze ed osservazioni spettanti alla Storia Nat., Padova 1713, pag. </s>

<s>33). <lb></lb>Lo stesso peripatetico Filippo Bonanni scrisse nel suo libro <emph type="italics"></emph>Delle chiocciole<emph.end type="italics"></emph.end><lb></lb>che il citar le sentenze di Pitagora e di Empedocle, i quali credettero dav­<lb></lb>vero le piante aver senso, era “ piuttosto un rammentar i favolosi giardini <lb></lb>di Alcina e le boscaglie incantate del Berni ” (Roma 1681, pag. </s>

<s>55, 56), e <lb></lb>il Reaumur confessava essere una grande umiliazione al filosofico orgoglio <lb></lb>“ voir qu&#039;un si bel esprit ait pu adopter un sentiment si peu vraisemblabe, <lb></lb>ou pour trancher le mot si pitoyable ” (Memoires pour servir a l&#039;hist. </s>

<s>des <lb></lb>insectes, T. III, P. II, a Amsterdam 1738, pag. </s>

<s>269). </s></p><p type="main">

<s>Il Malpighi però, che comprendeva qual potenza dovesse avere sul gio­<lb></lb>vane ingegno del Redi l&#039;autorità degli Accademici fiorentini, sentitosi libero <lb></lb>da un tal giogo, proseguì a dirittura per quella via di esperienze, nella quale <lb></lb>erasi arretrato esso Redi, e dimostrò nel suo trattato <emph type="italics"></emph>De gallis<emph.end type="italics"></emph.end> che, com&#039;era <lb></lb>vero quel che avea detto il Gassendo dell&#039;uova deposte dalle mosche sulle <lb></lb>carni infradiciate, così era vero dell&#039;uova da simili mosche deposte nelle in­<lb></lb>cise cortecce degli alberi, e in seno agli aperti fiori, d&#039;onde hanno origine <pb xlink:href="020/01/1599.jpg" pagenum="474"></pb>i vermi, che si trovan chiusi dentro le galle quercine, e in mezzo ai pomi <lb></lb>maturi. </s>

<s>“ Ex hucusque instituta indagine, dice ivi dop&#039;aver descritte le par­<lb></lb>ticolarità delle galle nate sopra varie specie di alberi, patet exaratos qua­<lb></lb>rundam plantarum tumores reliquasque syderatas partes muscas et diversa <lb></lb>insectorum genera fovere et alere, donec emancipata viam sibi faciant. </s>

<s>Plura <lb></lb>enim insecta sua edunt ova omni fere auctivo succo destituta, quorum ali­<lb></lb>qua cortice privantur, ita ut mollis primaeva partium compages occurrat <lb></lb>sub specie quasi vermis. </s>

<s>Ut igitur inclusum animal debitam acquirat par­<lb></lb>tium manifestationem et soliditatem, uterum vel saltem ipsius vicariam opem <lb></lb>exigit, quam in plantis sagax insectorum natura perquirit ” (Op. </s>

<s>omnia, T. I, <lb></lb>Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>130). </s></p><p type="main">

<s>Di qui vedeva il Malpighi scendere spedita la soluzione a quelle diffi­<lb></lb>coltà che, promosse nell&#039;Accademia del Cimento dal Magalotti, duravano tut­<lb></lb>tavia a tenere i Peripatetici ritrosi contro il Gassendi. </s>

<s>Se la pianta infatti <lb></lb>serve come d&#039;utero all&#039;uova, porgendo a loro quell&#039;alimento, di che per sè <lb></lb>stesse hanno difetto, e se quell&#039;alimento è variamente richiesto, secondo la <lb></lb>varia natura di esse uova, si comprende come, scegliendo le sagaci madri <lb></lb>la cuna più convenevole alla maturazione de&#039;loro parti, abbiano in galle non <lb></lb>solo ma in parti uguali delle piante a ritrovarsi vermi sempre della mede­<lb></lb>sima specie. </s>

<s>” Quare, ex diversa ovorum contentorumque animalium indi­<lb></lb>gentia, a parentibus muscis varie diversis plantarum partibus ova commit­<lb></lb>tuntur vel deponuntur ” (ibid.). </s></p><p type="main">

<s>Così dal campo della Filosofia gassendistica veniva trapiantata in quello <lb></lb>della Storia naturale la vera generazione univoca de&#039;vermi delle piante, e <lb></lb>il Redi stesso nella sua ingenuità abiurò il proprio errore per professar la <lb></lb>sentenza del Malpighi. </s>

<s>“ Dominus Redius, ingenuitate sua, attenta propo­<lb></lb>sita a me observationum serie, in meam postea ivit sententiam ” (Opera <lb></lb>posthuma, Londini 1697, pag. </s>

<s>77). Scriveva queste cose esso Malpighi per <lb></lb>consolarsi degli assalti, che gli avea dato il Bonanni co&#039;suoi raggiri, degli <lb></lb>insulti vomitatigli contro dallo Sbaraglia, e delle petulanze del Trionfetti, che <lb></lb>si faceva forte del nome, più che della Filosofia, dell&#039;Harvey. </s>

<s>“ Resto ol­<lb></lb>tremodo scandalizzato e dolente, scriveva acceso di zelo il Vallisnieri, quando <lb></lb>nel leggere trovo Italiani contro Italiani in materie particolarmente di fatto, <lb></lb>attaccandosi piuttosto ad opinioni fantastiche d&#039;Autori stranieri, stimandole <lb></lb>come merci pellegrine più preziose e più care ” (Esper. </s>

<s>ed osservaz. </s>

<s>cit., <lb></lb>pag. </s>

<s>38). E intanto il Malpighi stesso, parlando dalla tomba di sè e delle <lb></lb>cose sue, rammentava agli oppositori suoi connazionali e colleghi un illu­<lb></lb>stre straniero venuto a confermar ciò che egli aveva osservato e scritto in­<lb></lb>torno alle galle. </s>

<s>“ Has autem morbosos tumores esse ortos ex intrusis a <lb></lb>parente musca ovis et tanquam in utero conclusis habui, quam positionem <lb></lb>plures exinde confirmarunt, et praecipue clarissimus Leewenoeck ” (Opera <lb></lb>posthuma cit., pag. </s>

<s>77). </s></p><p type="main">

<s>In una delle epistole infatti, di che si compagina il libro <emph type="italics"></emph>Arcana Na­<lb></lb>turae detecta<emph.end type="italics"></emph.end> il celebre Micrografo olandese tratta di proposito delle galle, <pb xlink:href="020/01/1600.jpg" pagenum="475"></pb>dimostrando anch&#039;egli, come il Malpighi, che irragionevolmente s&#039;eran cre­<lb></lb>dute un frutto della querce, essendo che pigliano incremento da certe spe­<lb></lb>cie di vermi originati da mosche, e in mosche nuovamente tornanti, i quali <lb></lb>rodendo le foglie sono col loro morso causa del formarsi così fatte morbose <lb></lb>escrescenze. </s>

<s>“ Ex observationibus hisce statui animalia haecce ita produci: <lb></lb>videlicet praedictum genus animalculorum sive muscarum ova sua in foliis <lb></lb>quercinis deponere, quibus in vasis folii depositis, vaseque folii ita a verme <lb></lb>ex ovulo exeunte perfosso ut liquor ex eodem effluat, succus ille coagula­<lb></lb>tur in globulos, simulque circulariter se se in vase dispergit, et ita produ­<lb></lb>citur galla exiensque hic in globulos coagulatus succus vermem excipit et <lb></lb>in medio collocat ” (Lugd. </s>

<s>Batav. </s>

<s>1722, pag. </s>

<s>213). </s></p><p type="main">

<s>Non men valoroso del Leeuwenoeck sorse poco dopo il Vallisnieri, il <lb></lb>quale, per dimostrarsi più innamorato del vero che affezionato al suo ca­<lb></lb>rissimo Maestro, mentre ne illustrava da una parte le dottrine, con rive­<lb></lb>renza dall&#039;altra ne faceva notare gli errori. </s>

<s>Egli il primo osservò che il ta­<lb></lb>glio, fatto dalle mosche sulle foglie e sulle cortecce degli alberi, era spalmato <lb></lb>di un succo lucido e viscosetto colato dietro le uova, per impedire che le <lb></lb>aperte labbra non ritornassero ad unirsi e rammarginarsi, e dalle varietà di <lb></lb>questi succhi crede abbiano origine, nella forma e nella struttura, quelle <lb></lb>così moltiplici varietà d&#039;escrescenze. </s>

<s>Egli fu altresì il primo ad osservare e <lb></lb>a descrivere lo strumento in forma di artificiosissima sega, con cui le mo­<lb></lb>sche incidono a&#039;rosai la buccia, per apprestare ai loro nascituri più comoda <lb></lb>cuna. </s>

<s>Studiando poi i costumi de&#039;così detti <emph type="italics"></emph>Convolvoli<emph.end type="italics"></emph.end> trovò che s&#039;era in­<lb></lb>gannato il Malpighi a credere che le foglie per esempio de&#039;pioppi e delle <lb></lb>viti rimangano accartocciate in virtù degli effluvii delle uova ivi dentro de­<lb></lb>poste “ essendo quello, dice il Vallisnieri, un industre lavorio della madre ” <lb></lb>(Esper. </s>

<s>ed osserv. </s>

<s>cit., pag. </s>

<s>55). </s></p><p type="main">

<s>S&#039;aggiunse non molti anni dopo a questa del Vallisnieri l&#039;opera del <lb></lb>Reaumur, il quale, nella sua IX Memoria per servire alla storia degl&#039;In­<lb></lb>setti, trattò dell&#039;escrescenze nate sulle foglie degli alberi, e la X riserbò <lb></lb>particolarmente alle galle. </s>

<s>Egli è senza dubbio uno de&#039;più valorosi promo­<lb></lb>tori delle dottrine insegnate dal Malpighi, di cui così scrive: “ M. </s>

<s>Malpi­<lb></lb>ghi nous a donné un curieux Traité de ces espèces de galles; mais je ne <lb></lb>fache point qu&#039;on ait encore fait attention, par rapport aux productions de <lb></lb>cette nature, à un fait qui en meritoit beaucoup; savoir qu&#039;il y a un genre <lb></lb>d&#039;insectes, qui comprend plusieurs especes, dont chaque mêre fait naitre sur <lb></lb>un arbre une galle, dans laquelle elle se laisse enfermer elle-même, et sem­<lb></lb>ble chercher à se faire renfermer de toutes parts pour y produire une nom­<lb></lb>breuse famille ” (A Amsterdam 1738, T. III, P. II, pag. </s>

<s>30). E prosegue <lb></lb>il Reaumur a notare altre parti delle dottrine malpighiane o men proprie o <lb></lb>difettose, ch&#039;egli sapientemente perfeziona colle sue proprie osservazioni, ed <lb></lb>emenda colla sua sagacia. </s></p><p type="main">

<s>Le osservazioni descritte nel trattato <emph type="italics"></emph>De gallis,<emph.end type="italics"></emph.end> con sì autorevole ma­<lb></lb>gistero confermate dal Vallisnieri e dal Reaumur, che valgono per tanti altri, <pb xlink:href="020/01/1601.jpg" pagenum="476"></pb>avevano efficacemente conferito a persuadere la sentenza del Redi, la quale <lb></lb>sarebbe altrimenti rimasta per una parte dubbiosa, cioè che la Terra, dalle <lb></lb>prime piante e dai primi animali, non abbia poi mai più spontaneamente <lb></lb>prodotto nessun vivente. </s>

<s>Ma pure parevano ancora pochi i fatti osservati e <lb></lb>descritti dai due grandi Naturalisti italiani, per indur di lì quell&#039;<emph type="italics"></emph>omne ani­<lb></lb>mal ab ovo,<emph.end type="italics"></emph.end> ch&#039;era la general conclusione, alla quale intendeva di perve­<lb></lb>nire la scienza. </s>

<s>Eravi una sorta di animali, che si riducevano allora nella <lb></lb>classe degl&#039;insetti, ma che si reputavano tanto più nobili di quelli generati <lb></lb>dalla putredine o dalle piante, e intorno alla generazione de&#039;quali non ave­<lb></lb>vano ancora insegnato nulla di certo nè il Redi nè il Malpighi. </s>

<s>Questi in­<lb></lb>setti, che sono i molluschi, specialmente testacei, ai quali appartengono le <lb></lb>preziose conchiglie margaritifere, si credevano dai Peripatetici esser gene­<lb></lb>rati dal limo della terra, così avendo insegnato a loro il Maestro nel cap. </s>

<s>XV <lb></lb>del V libro della Storia degli animali. </s>

<s>“ Universim omnia testacea sponte <lb></lb>Naturae in limo, diversa pro differentia limi, oriuntur, nam in caenoso Ostreae <lb></lb>in arenoso conchae ” (Operum, T. VI cit., fol. </s>

<s>130). Nè in quel primo ri­<lb></lb>svegliarsi della scienza dai sogni peripatetici seppe nulla insegnare di nuovo <lb></lb>il Rondelezio, il quale credeva che nascessero le conchiglie per una virtù <lb></lb>insita nell&#039;umore marino. </s>

<s>“ Quod si testis intecta diligentius consideres, ea <lb></lb>marini humoris vi, sine semine, sine mare et faemina procreari perspicue <lb></lb>cernes ” (De piscibus cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Corse voce ne&#039;principii del secolo XVII di alcune esperienze fatte in <lb></lb>Germania intorno alla generazione delle conchiglie margaritifere, che sem­<lb></lb>brava potess&#039;essere dalle semenze deposte, per opera delle madri, nella terra <lb></lb>o ne&#039;fiumi. </s>

<s>Giovanni Faber stimò ragionevolissime così fatte congetture, e <lb></lb>anzi sperò che si potessero col benefizio del Microscopio facilmente ricono­<lb></lb>scere le uova, sfuggevoli a qualunque attenzione dell&#039;occhio nudo. </s>

<s>“ Ego <lb></lb>prorsus nihil dubito si quis Microscopio ..... favaginem hanc examinare <lb></lb>posset, quin in hac ova testaceorum manifestissima reperturus esset..... <lb></lb>Accedit hae maximum probabilitatis indicium ostrea et conchas genitalia se­<lb></lb>mina terris committere et fluminibus, ex quibus nova soboles, sublatis ma­<lb></lb>tribus, paulatim renascantur. </s>

<s>Experti sunt id Germani nostri in conchis mar­<lb></lb>garitiferis ” (Revum medicarum Novae Hispaniae Thesaurus cit., pag. </s>

<s>757). </s></p><p type="main">

<s>Il Lister poi e il Willis ammisero le uova delle conchiglie come cosa <lb></lb>certa, e lo Stenone più sentenziosamente scriveva nel suo prodromo <emph type="italics"></emph>De so­<lb></lb>lido:<emph.end type="italics"></emph.end> “ Experientia constat ostrea et alia testacea ex ovis, non ex putredine <lb></lb>nasci ” (Florentiae 1669, pag. </s>

<s>58). Quali sieno però queste esperienze l&#039;Au­<lb></lb>tore non dice, cosicchè al peripatetico Bonanni rimaneva salva l&#039;autorità del <lb></lb>suo Aristotile, la quale ei contrapponeva come prevalente per tanti antichi <lb></lb>diritti sull&#039;autorità nuova dello Stenone. </s>

<s>Dietro il particolare esempio dei <lb></lb>così detti <emph type="italics"></emph>Ballani<emph.end type="italics"></emph.end> ammetteva esso Bonanni che la virtù di generar le con­<lb></lb>chiglie risiedesse non in solo l&#039;umore, come diceva il Rondelezio, ma negli <lb></lb>spiriti saligni altresì, e nella potenza prolifica del mare. </s>

<s>“ Converrà dunque <lb></lb>dire, scrive nel citato libro <emph type="italics"></emph>Delle chiocciole,<emph.end type="italics"></emph.end> che trovandosi nella terra al-<pb xlink:href="020/01/1602.jpg" pagenum="477"></pb>cune particelle primigenie atte alla formazione del Ballano, questo potrà sem­<lb></lb>pre nascere, quando non manchino altre concause e disposizioni necessarie <lb></lb>di un umido mescolato con spiriti saligni e prolifici del mare, e così pos­<lb></lb>sano fermentarsi, finchè giungano ad esser capaci della vita ” (pag. </s>

<s>57). </s></p><p type="main">

<s>A leggere queste cose Anton Felice Marsili, ch&#039;era per le osservazioni <lb></lb>sperimentali del Redi e del Malpighi rimasto persuaso della generazione dei <lb></lb>vermi dall&#039;uovo, si sentì assalire da un dubbio, che lo tenne per qualche <lb></lb>tempo in pene, infin tanto che non gli occorse di fare la scoperta, ch&#039;egli <lb></lb>stesso così racconta: “ Effodebantur bulbuli florum in hortulo nunc usui <lb></lb>simplicium a me destinato. </s>

<s>Dum terra removebatur, saepius accidit ut ali­<lb></lb>quot ovorum acervi reperirentur, quae primo non cognoscebam, nam licet <lb></lb>multa paterent, quod nondum perfectionem essent adepta, albumen merum <lb></lb>emittebant, nec poteram in illis reperire principium aliquod animalculi. </s>

<s>Tan­<lb></lb>dem vero factum est ut prope lapides cuiusdam horrei sese eorundem ovo­<lb></lb>rum tantus cumulus proderet, ut impleta manu facile mihi fuerit observare <lb></lb>quaedam eorum fractioni proxima, alia ad dimidiam sui partem, alia omni <lb></lb>ex parte iam fracta atque ex illis cochleolas exeuntes ” (De ovis cochl. </s>

<s><lb></lb>Malpighi, Operum, T. II cit., pag. </s>

<s>95, 96). Mostrò queste uova agli amici, <lb></lb>che si confermarono, insieme coll&#039;inventore, nella verità, con sì nuovo effi­<lb></lb>cace argomento dimostrata, della generazione univoca di tutti gl&#039;Insetti. </s></p><p type="main">

<s>Faceva eco ai Nostri fra gli stranieri Antonio Leewenoeck, che avendo <lb></lb>ripetute e confermate l&#039;esperienze del Redi e del Malpighi, sicuro di pro­<lb></lb>nunziare il vero così in una delle sue Epistole scriveva: “ Est apud me <lb></lb>ratum ac firmum nulla viventia animalia, sive demum vermem, sive mu­<lb></lb>scam, pulicem, pediculum, imo ne blatam quidem ex succo vel foliis ullius <lb></lb>arboris vel plantae, aut etiam putredine vel sudore produci posse ” (Arcana <lb></lb>Naturae, T. </s>

<s>I cit., pag. </s>

<s>215, 16). E così come scriveva in pubblico andava <lb></lb>fra gli amici ne&#039;familiari colloqui ripetendo, quando un giorno un Signore <lb></lb>assai dotto gli confessa aver certissima esperienza del generarsi da non altro <lb></lb>che dal sudore certi molesti ospiti, i quali avevano invaso il suo letto, sopra <lb></lb>cui una volta la settimana, e talora anche più spesso, si stendevano le len­<lb></lb>zuola di bucato. </s>

<s>Il Leewenoeck rispondeva poter ciò dipendere dalla gente <lb></lb>che rifà le camere, da che entrato quel signore in sospetto “ postea intel­<lb></lb>ligebam, così il Leewenoeck stesso termina il curioso racconto, quod ancil­<lb></lb>lam suam dimississet, quoniam pediculis undique scatebat ” (ibid., pag. </s>

<s>216). </s></p><p type="main">

<s>Queste del Naturalista olandese però sembra che fossero induzioni ra­<lb></lb>gionevoli, non conclusioni di fatti, osservati poi da altri Naturalisti, fra&#039;quali <lb></lb>è a commemorare il nostro Vallisnieri, storico di un altro insetto che, seb­<lb></lb>bene sia un po&#039;meno schifoso di quello ora detto, è in ogni modo ospite <lb></lb>all&#039;uomo e ai pelosi quadrupedi non punto meno molesto. </s>

<s>Aristotile aveva <lb></lb>intorno a ciò lasciata in gran confusione la sua scuola, insegnando nel cap. </s>

<s>I <lb></lb>del V libro della Storia degli animali che anche i due insetti, de&#039;quali pre­<lb></lb>ghiamo i lettori a sopportar un momento per amor della scienza le punture <lb></lb>e il prurito, hanno sessi distinti, e generano qualche cosa per sè ingenera-<pb xlink:href="020/01/1603.jpg" pagenum="478"></pb>bile, essendo la loro generazione dalla putredine: “ verbi gratia coitu pedi­<lb></lb>culorum lendes dictae procreantur, pulicum genus vermiculorum ovi spe­<lb></lb>ciem referens, ex quibus nec ea quae generant proveniunt ” (Op., T. VI cit., <lb></lb>fol. </s>

<s>124). Ma nel cap. </s>

<s>XXXI di questo medesimo libro poi dice “ pediculi <lb></lb>et pulices generant ea quae lendes vocantur ” (ibid., fol. </s>

<s>136), cosicchè gli <lb></lb>studiosi del Filosofo non sapevano raccapezzarsi se le pulci generano uova <lb></lb>(lendes) o vermiccioli molto simili all&#039;uova. </s>

<s>Parve l&#039;incertezza esser tolta <lb></lb>dalle osservazioni microscopiche di Francesco Fontana, il quale avendo fo­<lb></lb>rato colla punta di un ago il ventre a uno di quegli insetti, “ ex eius vul­<lb></lb>nere ova prosiluere et e vitiatis ovis pulli semiformes in lucem editi sunt ” <lb></lb>(Novae observationes, Neapoli 1646, pag. </s>

<s>149). </s></p><p type="main">

<s>I sagaci Naturalisti però riconobbero facilmente esser questa dell&#039;Oc­<lb></lb>chialaio napoletano una illusione, ond&#039;è che sui principii del secolo XVIII <lb></lb>s&#039;ignorava ancora la generazione de&#039;fastidiosi insetti, che perciò persiste­<lb></lb>vasi da molti a credere generati dal sudiciume, quando apparve alla luce la <lb></lb>Lettera del Vallisnieri, <emph type="italics"></emph>nella quale si dà notizia della nuova scoperta del­<lb></lb>l&#039;origine delle pulci dall&#039;uovo, contro i difensori de&#039;nascimenti sponta­<lb></lb>nei.<emph.end type="italics"></emph.end> Dalle accurate osservazioni dell&#039;insigne Naturalista resultò che i noti <lb></lb>insetti generano l&#039;uova, d&#039;onde schiudonsi i vermi, che stimolati si raggo­<lb></lb>mitolano così, da rendersi interpetri dell&#039;espressione aristotelica: <emph type="italics"></emph>genus ver­<lb></lb>miculorum ovi speciem referens.<emph.end type="italics"></emph.end> Giunti a maturità, così fatti vermi si fab­<lb></lb>bricano attorno un bozzoletto bianco, come quelli da seta. </s>

<s>“ La pulce, finat­<lb></lb>tantochè sta rinchiusa nel bozzolo, resta bianca lattata, ancorchè munita <lb></lb>delle sue gambe, ma due giorni avanti che deve uscire diventa colorata, si <lb></lb>indura e piglia forza, di modo che subito uscita salta addirittura ” (Esper. </s>

<s><lb></lb>ed osservaz. </s>

<s>cit., pag. </s>

<s>85). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Esaminando sottilmente il Vallisnieri in questo proposito i processi del <lb></lb>pensiero aristotelico, dice che il Filosofo s&#039;ingannò nel veder nascere dalle <lb></lb>mosche i vermi, credendo che sempre si rimanessero in tale stato, senza <lb></lb>ritornar mosche, e che perciò fosse quella loro una generazione imperfetta. <lb></lb></s>

<s>“ Sospettava inoltre, prosegue a dire l&#039;Autore della lettera all&#039;Andriani, che <lb></lb>si abbagliasse così al digrosso, perchè, fidandosi troppo dell&#039;ingegno suo, <lb></lb>sdegnò d&#039;abbassarsi tanto e pazientare fino al fine delle osservazioni mi­<lb></lb>nute, contentandosi di dare rozzamente una semplice e superficiale occhiata <lb></lb>alle prime cose, e supponendo vedere il restante colla propria acutissima <lb></lb>perspicacità, giudicò del non veduto egualmente che del veduto, e pensò non <lb></lb>poter succedere in altro modo una tale faccenda di quello s&#039;immaginava ” <lb></lb>(Esper. </s>

<s>ed osserv. </s>

<s>cit., pag, 87). </s></p><p type="main">

<s>Questo giudizio del Vallisnieri intorno al Filosofo è giusto, ma giova <pb xlink:href="020/01/1604.jpg" pagenum="479"></pb>aggiungere una considerazione, ed è che in quel caso l&#039;abuso dell&#039;ingegno <lb></lb>veniva in certo modo scusato dal difetto delle osservazioni, che, fatte così <lb></lb>com&#039;erano ad occhio nudo, non rappresentavano i piccoli insetti sotto altro <lb></lb>aspetto che d&#039;informi automi. </s>

<s>Il Microscopio perciò, rivelando anche in que­<lb></lb>gli spregevoli esseri gli organi e le funzioni proprie alla vita animale, giovò <lb></lb>molto a smentire il falso giudizio, che bastasse a ingenerarli il limo della <lb></lb>terra o altra cosa più vile. </s>

<s>Perciocchè dunque si fu tale il benefizio della <lb></lb>Micrografia, crediam bene di dover premettere un breve cenno di lei a ciò <lb></lb>che saremo per dire degli organi scoperti e delle funzioni, rivelate dal diot­<lb></lb>trico strumento nella Storia naturale degl&#039;Insetti. </s></p><p type="main">

<s>I primi inventori e tutti coloro, ai quali capitò in mano la prima volta <lb></lb>un Microscopio, non lasciarono di contemplar le maraviglie della Natura <lb></lb>nella fabbrica degl&#039;Insetti, ma era per una semplice curiosità, che fruttò <lb></lb>solo alla scienza qualche notizia delle più esterne apparenze di quegli ani­<lb></lb>mali. </s>

<s>Anche Galileo, benchè aprisse l&#039;adito alla meccanica animale, sco­<lb></lb>prendo l&#039;organo per cui possono le mosche così facilmente camminare at­<lb></lb>taccate agli specchi, si tratteneva a riguardare con gran compiacenza così <lb></lb>le bellissime zanzare e le tignole, come le orribilissime pulci (Alb. </s>

<s>Vl, 298). </s></p><p type="main">

<s>Delle applicazioni del Microscopio alla scienza entomologica ricorre il <lb></lb>primo e solenne documento nel trattato <emph type="italics"></emph>De motu cordis<emph.end type="italics"></emph.end> dell&#039;Harvey, là dove <lb></lb>nel cap. </s>

<s>XVII dice di aver osservato <emph type="italics"></emph>ope perspicilli multiplicantis<emph.end type="italics"></emph.end> (ediz. </s>

<s>cit., <lb></lb>pag. </s>

<s>91) un che pulsante nell&#039;interno delle api, delle mosche e de&#039;calabroni, <lb></lb>da potersi ragionevolmente credere sia quell&#039;organo il loro cuore. </s>

<s>Che se dee <lb></lb>darsi fede a ciò che si dice essere quelle Esercitazioni anatomiche, pubbli­<lb></lb>cate nel 1628, le Prelezioni recitate dodici anni prima dallo stesso Harvey <lb></lb>alla scolaresca di Londra; par che dunque le microscopiche osservazioni in­<lb></lb>torno al cuore pulsante degl&#039;insetti siano di qualche poco anteriori al 1616. <lb></lb>Notabile che il grand&#039;uomo non sentisse gli stupendi benefizii del nuovo <lb></lb>strumento, da abbandonarlo così presto anche colà, dove trattando <emph type="italics"></emph>De ge­<lb></lb>neratione animalium<emph.end type="italics"></emph.end> gli sarebbe servito di sicura scorta a evitar certi er­<lb></lb>rori, sopra i quali la storia getta uno sguardo di compassione. </s>

<s>Cosicchè se <lb></lb>l&#039;Harvey nella Micrografia entomologica primeggia per tempo, per l&#039;estesa <lb></lb>e intensa cultura rimane di gran lunga inferiore ai nostri Lincei. </s></p><p type="main">

<s>Tanto si rese familiare negli studii naturali de&#039;nostri Accademici il diot­<lb></lb>trico strumento, che abbisognando d&#039;esser chiamato con qualche nome Fa­<lb></lb>bio Colonna ellenista propose quello di <emph type="italics"></emph>Microscopio;<emph.end type="italics"></emph.end> nome approvato dal­<lb></lb>l&#039;Accademia, e di cui il Faber nelle sue pubbliche scritture fu primo a far <lb></lb>uso. </s>

<s>Esso Faber, nelle annotazioni al Recchi altre volte citate, commemora <lb></lb>l&#039;anatomia degli organi esterni delle api, fatta da Francesco Stelluti Linceo, <lb></lb>con l&#039;aiuto di un Microscopio “ quo res minutissimas triginta mille vicibus <lb></lb>et amplus grandiores quam in se sunt apparere solent ” (editio cit., pag. </s>

<s>757). <lb></lb>E altrove in queste stesse Annotazioni, a proposito del dito pollice de&#039;cani, <lb></lb>dice di aver trovato con suo grande stupore quell&#039;organo della prensione <lb></lb>anche negl&#039;insetti, e ciò per via di un eccellentissimo Microscopio, lavorato <pb xlink:href="020/01/1605.jpg" pagenum="480"></pb>e donatogli da due suoi Tedeschi. </s>

<s>“ In pediculo, foedo quodam animalculo, <lb></lb>hominis tamen non raro socio, non os modo oculosque, barbam et pretensa <lb></lb>duo in fronte cornicula, sed pedes insuper ex utroque latere ternos prae­<lb></lb>longos et articulatos, qui omnes ungues habebant recurvos duos, longum <lb></lb>unum, brevem alterum, et pollicis apprime locum supplentem, quibus et <lb></lb>cutem apprehendit, et serpendo gradum figit. </s>

<s>Tantum huic pollici aut cui­<lb></lb>piam particulae simili huius loco industria et nunquam deficiens Natura, in <lb></lb>minimis etiam et abiectissimis animalculis, studere voluit! ” (ibid., pag. </s>

<s>473). </s></p><p type="main">

<s>E qui il Faber, dop&#039;essersi compiaciuto di aver egli il primo mandato <lb></lb>in pubblico il Microscopio insignito di un nome proprio, accenna alla inven­<lb></lb>zione di lui nata gemella con quell&#039;altra del Telescopio, della teoria del <lb></lb>quale riconosce autore il Porta, e dell&#039;esecuzione alcuni occhialai tedeschi <lb></lb>ovvero olandesi. </s>

<s>Da giusto giudice al linceo collega suo Galileo non attri­<lb></lb>buisce altro merito che di aver il primo in Italia lavorate lenti diottriche, <lb></lb>non così però che ne sia defraudato il principe Cesi, il quale in quel me­<lb></lb>desimo tempo in Roma avea fatto, sull&#039;esempio degli Ottici stranieri, co­<lb></lb>struire Telescopi e Microscopi, colà diffusi qualche tempo prima che s&#039;avesse <lb></lb>notizia degli strumenti galileiani. </s>

<s>Per quel che poi riguarda la fabbrica del <lb></lb>Microscopio in particolare, loda il Faber l&#039;esperta mano di Galileo, che si <lb></lb>riman però molto inferiore a quella degli artefici tedeschi “ qui sedulam <lb></lb>in hoc nobis operam praestitere, nec pauca huiusmodi Microscopia, quae <lb></lb>Urbem totam in admirationem pertraxerunt, elaborata nobis exhibuerunt ” <lb></lb>(ibid., pag. </s>

<s>474). </s></p><p type="main">

<s>Prima però che fossero pubblicate queste Annotazioni del Faber alle <lb></lb>Storie naturali del Messico, Giovan Batista Hodierna s&#039;era co&#039;suoi <emph type="italics"></emph>Opuscoli<emph.end type="italics"></emph.end><lb></lb>acquistato uno de&#039;precipui meriti nella Micrografia entomologica, descrivendo <lb></lb>la mirabile struttura dell&#039;occhio delle mosche. </s>

<s>“ Or quanto, egli scrive, fin <lb></lb>qui ho detto intorno a questa nuova anatomia, l&#039;ho io scoverto, non con la <lb></lb>nuda vista dell&#039;occhio, ma col mezzo di un Occhialino, lavorato a vetri con­<lb></lb>vessi di figura semirotonda, più piena della lenticolare, simili a quelli dico <lb></lb>che oggi il volgo se ne serve per ammirare l&#039;ingrandimento apparente di <lb></lb>qualche bestiola, come d&#039;un pulce racchiuso, ma con doppio cristallo e con <lb></lb>artificio assai divario di quello, mentre per il mezzo di quei cristalli mi vien <lb></lb>rappresentato qualsivoglia piccolissimo granello d&#039;arena più di millecuplata <lb></lb>grandezza ” (Palermo 1644, pag. </s>

<s>16). </s></p><p type="main">

<s>Due anni però innanzi che fosse fatta la prima edizione delle Storie na­<lb></lb>turali del Recchi, e che perciò il Faber consacrasse in pubblico il nome di <lb></lb>Microscopio, seguitato a chiamar dall&#039;Hodierna, come udimmo, <emph type="italics"></emph>occhialino,<emph.end type="italics"></emph.end><lb></lb>Francesco Fontana, sull&#039;esempio del Gassendo nella Vita del Peiresc (Pa­<lb></lb>risiis 1641, pag. </s>

<s>186), denominava lo strumento diottrico da sè inventato <lb></lb>anch&#039;egli, o consapevole o no, conformandosi ai Lincei, <emph type="italics"></emph>Microscopio,<emph.end type="italics"></emph.end> ponendo <lb></lb>in appendice al suo nuovo trattato alcune osservazioni, fatte con quel va­<lb></lb>lido aiuto, intorno agli organi esterni e ai visceri di varii insetti. </s>

<s>Ma per­<lb></lb>ch&#039;egli non aveva avuta altra scuola che la bottega, e i Gesuisti napoletani, <pb xlink:href="020/01/1606.jpg" pagenum="481"></pb>che gli suggerivano la scienza, erano ostinatissimi peripatetici, non fa per­<lb></lb>ciò meraviglia se non vedessero sempre chiaro gli occhi del corpo attraverso <lb></lb>alle caligini della mente. </s></p><p type="main">

<s>Altro Artefice, che seppe però da sè medesimo educarsi l&#039;ingegno, e <lb></lb>sulle proprie ali sollevarsi alle più ardue cime della scienza, fu l&#039;inglese <lb></lb>Roberto Hook, autore di una Micrografia, dove, in mezzo alla molteplice va­<lb></lb>rietà delle cose, non isfuggono all&#039;osservazione gl&#039;insetti. </s>

<s>La prima edizione <lb></lb>fu fatta in Londra nel 1665, e nel primo Schematismo si rappresenta lo <lb></lb>strumento in tal modo, che al primo sguardo apparisce il sollecito studio <lb></lb>di moltiplicar, quanto fosse possibile, l&#039;effetto della vista, condensando sugli <lb></lb>oggetti per rifrazione il vivo lume di una candela. </s></p><p type="main">

<s>Eustachio Divini, altro semplice artefice, si studiò di conseguire per altre <lb></lb>vie questa tanto desiderata incontentabile moltiplicazione, lavorando con più <lb></lb>squisita arte le lenti, ch&#039;ebbero la fortuna di venire applicate ai veggentis­<lb></lb>simi occhi del Malpighi e del Redi. </s>

<s>Ma il Leewenoeck, per i particolari usi <lb></lb>delle osservazioni entomologiche, trovò molto opportuna un&#039;unica lente, la <lb></lb>quale, perciocchè faceva migliore effetto delle lenti composte, fu volentieri <lb></lb>adoperata dai Micrografi, che grati del servigio la insignirono, benchè così <lb></lb>nudo occhiale, del nome di <emph type="italics"></emph>Microscopio leuvenecchiano.<emph.end type="italics"></emph.end> Era insomma que­<lb></lb>sto il microscopio detto <emph type="italics"></emph>della perlina<emph.end type="italics"></emph.end> dai nostri Fiorentini, e <emph type="italics"></emph>batavo<emph.end type="italics"></emph.end> dagli <lb></lb>stranieri, adattato poi dal Lyonet, per l&#039;anatomia degli insetti, a quella sem­<lb></lb>plice macchinetta descritta dallo Spallanzani, e della quale si servì a mara­<lb></lb>viglia l&#039;insigne nostro Naturalista, per osservare la circolazione del sangue <lb></lb>nel giro universale dei vasi. (Dissertazione, T. I, Milano 1726, pag. </s>

<s>140, 41). </s></p><p type="main">

<s>Gli artificiosi strumenti e l&#039;acume delle osservazioni de&#039;Micrografi sopra <lb></lb>commemorati, ai quali sarebbero da aggiunger tanti altri, come per esem­<lb></lb>pio il Lister e lo Swammerdam, fanno presentire i maravigliosi progressi <lb></lb>dell&#039;Entomologia, dall&#039;Harvey allo Spallanzani, e quanto sarebbe soprabbon­<lb></lb>dante la messe da raccogliersi in questa storia. </s>

<s>Venendo però a noi pre­<lb></lb>scritti limiti sì angusti, ci contenteremo d&#039;accennare a ciò che il Microsco­<lb></lb>pio rivelò degli organi inservienti ad alcune delle principali funzioni della <lb></lb>vita animale degl&#039;insetti, e della loro vita di relazione. </s></p><p type="main">

<s>La principale fra quelle funzioni animali è senza dubbio il respiro, che <lb></lb>secondo i Filosofi antichi è il divino alito, da cui agile si ridesta nella ma­<lb></lb>teria, e perenne vi si mantiene la vita. </s>

<s>Aristotile nonostante, per confutar <lb></lb>Diogene, che sentenziava aver tutti gli animali necessità di respirare, addu­<lb></lb>ceva l&#039;esempio degl&#039;insetti, i quali che non respirino è provato, dice il Fi­<lb></lb>losofo, dal fatto che durano tuttavia a vivere, benchè tagliati in due o più <lb></lb>parti, come si vede nelle scolopendre: per cui domanda a Diogene stesso <lb></lb>in quali di queste parti, e in che modo occorra all&#039;insetto di trarre il re­<lb></lb>spiro: “ quae, qualiter aut in quonam contingit respirare? </s>

<s>” (De respir., <lb></lb>Operum, T. VII cit., fol. </s>

<s>270). </s></p><p type="main">

<s>Rimase a tale domanda muta la posterità infintanto che il Rondelezio <lb></lb>non isciolse la lingua, per dir liberamente ch&#039;ei si maravigliava come mai <pb xlink:href="020/01/1607.jpg" pagenum="482"></pb>quell&#039;Aristotile, il quale aveva scritto refrigerarsi tutti gli animali a sangue <lb></lb>freddo dall&#039;aria ambiente, facesse poi per gl&#039;insetti un&#039;eccezione particolare. </s>

<s><lb></lb>Ond&#039;è che posto il principio esser ogni corpo animato <foreign lang="grc">ἐιπνουν</foreign> et <foreign lang="grc">ε<gap></gap>πνουν</foreign>, cioè <lb></lb>inspiratore ed espiratore, così contro il Filosofo il Rondelezio stesso con­<lb></lb>clude: “ Cum igitur scolopendrae et aliorum insectorum partes dissectae <lb></lb>moventur et vivunt, tenuioris aeris aliquid undique inspirant et expirant ” <lb></lb>(De piscibus cit., pag. </s>

<s>101). </s></p><p type="main">

<s>Era venuto però il tempo che si voleva nelle cose naturali argomentar <lb></lb>dai fatti, e no dalle astratte speculazioni, e perciò l&#039;Acquapendente si trovò <lb></lb>costretto anch&#039;egli col Rondelezio d&#039;abbandonare il suo Aristotile, persuaso <lb></lb>che gl&#039;insetti respirano dagli anelli del ventre, per aver più volte osservato <lb></lb>che di li mandan vento. </s>

<s>“ Quo circa iis membrana tenuissima sub septo <lb></lb>transverso dimota, qua etiam murmur efficiunt et aerem paulum movent, <lb></lb>ad refrigerationem fit opportuna ” (Op. </s>

<s>omnia cit., pag. </s>

<s>165). </s></p><p type="main">

<s>Queste troppo frettolose osservazioni del Maestro viziate dai grossolani <lb></lb>errori aristotelici intorno alla respirazione, furon riprese a far con più dili­<lb></lb>genza che mai dall&#039;Harveio, il quale dall&#039;attendere a quel continuo allun­<lb></lb>garsi e contrarsi degli anelli del ventre, che ha tanta analogia coll&#039;anelar <lb></lb>delle coste del torace, venne a confermarsi nell&#039;opinione che gl&#039;insetti re­<lb></lb>spirino per la coda. </s>

<s>“ Crabrones et apes et alia insecta, non solum pulsum <lb></lb>habere sed et respirationem, in illa parte quam caudam nominant, experi­<lb></lb>mentis quibusdam me posse demonstrare arbitror, unde ipsam elongare e <lb></lb>contrahere contingit modo frequentius, modo rarius, prout anhelosi magis <lb></lb>videntur, et aere magis indigere ” (De motu cordis cit., pag. </s>

<s>96). I primi <lb></lb>esperimenti, di che qui si fa cenno, consistevano nel rendersi visibili gli <lb></lb>effetti di quel vento, che l&#039;Acquapendente avea detto spirar dagli anelli del­<lb></lb>l&#039;insetto, ma l&#039;Harvey se ne assicurò poi anche in un altro più evidente <lb></lb>modo, affogando gl&#039;insetti stessi o nell&#039;acqua o nell&#039;olio, e osservando che, <lb></lb>così sommersi, mandavano bolle d&#039;aria fuor dalla coda. </s>

<s>“ Hoc enim modo, <lb></lb>crabrones, vespas et huiusmodi insecta, in oleo demersa et suffocata, ultimo <lb></lb>aeris bullulas e cauda, dum emoriuntur, emittunt, unde ita respirare vivos <lb></lb>non est improbabile ” (ibid., pag. </s>

<s>141). </s></p><p type="main">

<s>Intanto eran venuti postumi alla luce in Bologna i sette libri <emph type="italics"></emph>De ani­<lb></lb>malibus insectis<emph.end type="italics"></emph.end> dell&#039;Aldovrandi, ne&#039;prolegomeni ai quali, trattando l&#039;Au­<lb></lb>tore degl&#039;insetti in genere, propone per question principale <emph type="italics"></emph>an respirent.<emph.end type="italics"></emph.end><lb></lb>Riferisce ivi eruditamente le varie opinioni scritte dagli antecessori in pro­<lb></lb>posito, e trattenutosi particolarmente a infirmare gli argomenti del Ronde­<lb></lb>lezio, si volge a professar la dottrina di Aristotile, perchè il ragionamento <lb></lb>di lui lo persuade. </s>

<s>Singolar cosa a notare è che fra gli scrittori neganti il <lb></lb>respirar degl&#039;insetti annovera l&#039;Aldovrandi Basilio Magno, da un Omelia del <lb></lb>quale sopra l&#039;Esaemerone trascrive queste parole: “ Cum volatilium ea con­<lb></lb>spexeris, quae insecta vocantur, ut apes et vespas, veniat tibi in mentem ea <lb></lb>praedita respiratione non esse, pulmoneque carere, sed totis omnia sui cor­<lb></lb>poris partibus nutriri aere. </s>

<s>Quapropter si oleo fuerint madefacta, occlusis <pb xlink:href="020/01/1608.jpg" pagenum="483"></pb>meatibus pereunt, sin aceto protinus asperseris, ea reclusis foraminibus re­<lb></lb>viviscunt ” (De anim. </s>

<s>insectis, Bononiae 1638, pag. </s>

<s>14). </s></p><p type="main">

<s>La bella esperienza, così commemorata, del Santo Padre della Chiesa <lb></lb>greca, fu letta in queste pagine dell&#039;Aldovrandi da Antonio Nardi, il quale, <lb></lb>in quella universal comprensione delle scienze naturali, attendendo alla sto­<lb></lb>ria degl&#039;insetti, s&#039;era, per le osservazioni dell&#039;Acquapendente e per l&#039;espe­<lb></lb>rienze dell&#039;Harvey, persuaso che quegli animali respirano, com&#039;ei si esprime, <lb></lb>dalle fasce del ventre. </s>

<s>Rivelava questa sua persuasione nella veduta I della <lb></lb>Scena VIII là dove, accennando alla circolazione del sangue, dop&#039;avere ap­<lb></lb>provata l&#039;opinione dello stesso Harveio, così soggiunge: “ È ben vero che <lb></lb>molto paradossa parrà l&#039;opinione di questo dottissimo uomo, mentre che nel­<lb></lb>l&#039;inferior ventre pensasi che le vespe ed altri somiglianti animali abbiano <lb></lb>il cuore, perchè, se dal battere una sua parte ciò si potesse argomentare, <lb></lb>seguiriane che gli animali più perfetti l&#039;avessino in capo, vedendosi il cer­<lb></lb>vello battere. </s>

<s>Alcuno piuttosto penserà che la parte battente nell&#039;inferior <lb></lb>ventre delle vespe siano i vasi seminali. </s>

<s>Nulla nondimeno affermo in mate­<lb></lb>ria così dubbia, perchè sperienza fatto non ne ho: nemmeno rifiuto il pa­<lb></lb>rere di tale Autore, quale concorda col mio, cioè che gl&#039;insetti spirino per <lb></lb>le fasce ” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>1098). </s></p><p type="main">

<s>Or avendo duuque il Nardi letto nelle parole trascritte dall&#039;Aldovrandi <lb></lb>che Basilio Magno diceva respirare gl&#039;insetti, non da sole le fasce, ma da <lb></lb>tutto il corpo, pensò di applicare l&#039;esperienza dell&#039;olio a decidere il dub­<lb></lb>bio. </s>

<s>Unti perciò gli anelli caudali a varie specie d&#039;insetti, lasciando le ri­<lb></lb>manenti parti del loro corpo scoperte, trovò che morivano. </s>

<s>E perch&#039;egli era <lb></lb>persuaso che ciò avvenisse per la tenacità dell&#039;untuosa materia, che intasa <lb></lb>le vie del respiro, ne concluse che sien dunque queste vie aperte, non in <lb></lb>tutta la superficie del corpo animale, ma fra le sole incisure del ventre. <lb></lb></s>

<s>“ Gli animali volatili insieme e intagliati, scrive nella veduta VII della <lb></lb>Scena IX, quali caldissimi sono e focosi, hanno più di tutti di respirare bi­<lb></lb>sogno, e così respirano, non solo dalla bocca, ma forse anco, quasi per tante <lb></lb>branchie, dalle commessure del ventre; il che si raccoglie dalla distanza, e <lb></lb>quasi separazione del petto dal ventre, quali parti talvolta non comunicano <lb></lb>se non per un lungo e sottilissimo canaletto, come negli Icneumoni, per cui <lb></lb>appena il cibo pare che trasmetter si possa. </s>

<s>Anco il suono che volando, e <lb></lb>talora anco fermi stando, fuori mandano gl&#039;insetti, argomenta, come nei <lb></lb>quaglieri avviene, frangasi per il moto l&#039;aria nei pori per d&#039;onde esce, poi­<lb></lb>chè il pensare che dal moto delle ali tal suono cagionisi, non parmi verisi­<lb></lb>mile. </s>

<s>Parimente il manifesto allargarsi e stringersi delle fasce, che loro cin­<lb></lb>gono il petto, tal mio parere conferma, quali ancora se d&#039;olio o d&#039;altra <lb></lb>grassezza vengano unti, muore l&#039;animale. </s>

<s>Il che forse non da altro nasce <lb></lb>che dall&#039;impedirsi alla respirazione il passaggio, e ciò non solo le vespe e <lb></lb>le api e gli altri insetti fanno, ma anco le mosche e tutti i sibilanti nel <lb></lb>suolo ” (ivi, pag. </s>

<s>1259, 60). </s></p><p type="main">

<s>Rimasti i concetti di Basilio Magno affogati nel mare peripatetico del-<pb xlink:href="020/01/1609.jpg" pagenum="484"></pb>l&#039;Aldovrandi, e l&#039;esperienza del Nardi sepolta ne&#039;manoscritti, a mezzo il <lb></lb>secolo XVII, da chi avea badato all&#039;espressioni, uscite per incidenza dalla <lb></lb>penna dell&#039;Harvey, si teneva la respirazion degl&#039;insetti per una probabile <lb></lb>congettura, senza ricercare più avanti. </s>

<s>Il Boyle, nel suo XL esperimento, <lb></lb>aveva osservate le mosche, le api e altri simili volanti in mezzo al vuoto <lb></lb>della sua macchina pneumatica; gli Accademici nostri fiorentini avevano in <lb></lb>mezzo al vuoto torricelliano sperimentato il fatto de&#039;grilli, delle mosche e <lb></lb>delle farfalle: e benchè resultasse da tutte queste esperienze avere anche <lb></lb>gl&#039;insetti per vivere bisogno dell&#039;aria, non si scorge negli sperimentatori <lb></lb>nessun intenzione d&#039;investigare in che modo soccorra l&#039;aria stessa a man­<lb></lb>tenere in questi animali la vita. </s></p><p type="main">

<s>Lo stesso Redi, tutto inteso allo studio degl&#039;insetti, non si prende altra <lb></lb>cura che di mettere a cimento del vero i detti di Galeno, di Luciano, di <lb></lb>Alessandro afrodisco, di Ulisse Aldovrando e di Giovanni Sperlingio affer­<lb></lb>manti che le mosche, se gustano dell&#039;olio o se con quello sono unte, si <lb></lb>moiono. </s>

<s>“ Ed in vero, egli scrive, che fattane da me l&#039;esperienza, ogni qual­<lb></lb>volta che io faceva che da una sola gocciola di olio fosse tocca ed inzup­<lb></lb>pata una mosca, in quello stesso momento ella cadeva fuor d&#039;ogni credere <lb></lb>morta ” (Esper. </s>

<s>intorno agl&#039;insetti, Op., T. </s>

<s>I cit., pag. </s>

<s>75). Ma non si fa <lb></lb>nemmeno un cenno che ciò accada per venir dall&#039;olio intasate le vie del <lb></lb>respiro. </s></p><p type="main">

<s>Mentre il Redi proseguiva questo genere di esperienze, non con altro <lb></lb>intendimento che di riscontrar coi fatti quel che si credeva dal volgo e dai <lb></lb>Filosofi intorno alla morte e alla resurrezione degl&#039;insetti, annegati in varie <lb></lb>sorte di liquidi; Marcello Malpighi dava assidua e diligente opera a noto­<lb></lb>mizzare i vermi da seta. </s>

<s>Nota sulla loro superficie alcune incisure, quasi <lb></lb><emph type="italics"></emph>stimmate<emph.end type="italics"></emph.end> impresse, dalle quali si propagano a modo di arterie alcuni vasi <lb></lb>che, quanto più si dilungano dal tronco, tanto si fanno più gracili e più <lb></lb>frequenti, intrecciandosi insieme a comporre una rete maravigliosa, da ras­<lb></lb>somigliarsi in qualche modo a quella formata dalle foglie degli alberi. </s>

<s>Una <lb></lb>tale diramazione, che avea fatto sovvenire al Malpighi quella osservata già <lb></lb>nella trachea e ne&#039;bronchi degli animali perfetti, finì di confermarlo nella <lb></lb>persuasione che i due organi, analoghi nella struttura, servissero ai mede­<lb></lb>simi usi, quando vide in quasi tutti i bruchi, e specialmente nei Cervi vo­<lb></lb>lanti, rigonfiarsi le estremità di que&#039;vasi in vescicole similissime alle polmo­<lb></lb>nari. </s>

<s>“ Unde, ex his et inferius dicendis, coniectatus sum tracheas esse, <lb></lb>quae suis productionibus pulmones efforment ” (De Bombycibus, Operum, <lb></lb>T. II cit., pag. </s>

<s>17). </s></p><p type="main">

<s>Essendo le stimmate bocche di così fatte trachee, dovrebbero essere <lb></lb>esse che ammettono l&#039;aria dentro i polmoni: per certificarsi di che il Mal­<lb></lb>pighi ricorse all&#039;antica esperienza dell&#039;olio, o di altre materie grasse, come <lb></lb>sarebbero il sevo ed il burro. </s>

<s>Intasate alcune delle superficiali incisure con <lb></lb>qualche stilla di queste appiccaticce sostanze, trovò che si rendevano para­<lb></lb>litiche le sole membra corrispondenti, ma che moriva immediatamente l&#039;ani-<pb xlink:href="020/01/1610.jpg" pagenum="485"></pb>male, quando l&#039;intasatura si faceva sopra tutte le stimme ugualmente. </s>

<s>Inno­<lb></lb>cue poi sperimentò che riuscivano sempre le unzioni, quando, salve esse <lb></lb>stimme, si facevano sul ventre, sul capo, intorno alla bocca o sul dorso. <lb></lb></s>

<s>“ Quare interitum ex oleo, eatenus contingere conieci, quatenus, occlusis <lb></lb>tracheae orificiis, suffocatio vel quid simile succedit ” (ibid., pag. </s>

<s>19). </s></p><p type="main">

<s>La verità, traveduta in ombra infin dai tempi di Basilio Magno, e del <lb></lb>suo più superficial velo scoperta da Antonio Nardi, aveva avuto nelle os­<lb></lb>servazioni anatomiche e nelle esperienze del Malpighi così piena dimostra­<lb></lb>zione, che per più di un mezzo secolo nessuno ebbe dubbio di ammettere <lb></lb>quel ch&#039;esso Malpighi avea concluso: “ aerem in haec bombycis vasa conti­<lb></lb>nuatim subingredi et egredi, ut in caeteris quibus insunt pulmones ” (ibid.). </s></p><p type="main">

<s>Parve però al Reaumur più conforme agli ordini naturali che si facesse <lb></lb>la respirazione dei bruchi, non a modo degli animali perfetti, ma piuttosto <lb></lb>a modo dei pesci, i quali inspirano l&#039;aria da una parte, e la espirano dal­<lb></lb>l&#039;altra. </s>

<s>“ Nous sommes donc conduits par les experiences (dice nella III <lb></lb>delle Memorie per servire alla storia degl&#039;insetti, compresa nella prima parte <lb></lb>del Tomo primo) à reconnoitre que la respiration complette, je veux dire <lb></lb>l&#039;inspiration et l&#039;expiration, se fait dans les Chenilles, et par consequent <lb></lb>dans un grand nombre d&#039;insectes, d&#039;une manière singuliere et tout-à-fait <lb></lb>differente de celle dont elle se fait dans les grands animaux ” (Amster­<lb></lb>dam 1737, pag. </s>

<s>172). </s></p><p type="main">

<s>Le diciotto stimmate scoperte e diligentemente annoverate nel bombice <lb></lb>dal Malpighi son, prosegue a dire il Reaumur, diciotto bocche “ qui don­<lb></lb>nent entrée à l&#039;air dans les principaux canaux, dans les plus gros troncs <lb></lb>des trachées, d&#039;ou il est conduit dans leurs differentes ramifications; il en­<lb></lb>file des canaux de plus étroits en plus êtroits, et c&#039;est par les dernières <lb></lb>extremités de ces canaux qu&#039;il s&#039;échappe; elles ont des ouvertures qui lui <lb></lb>permettent la sortie ” (ivi). </s></p><p type="main">

<s>L&#039;esperienze rivelatrici al Reaumur della verità di questi fatti son varie, <lb></lb>ma la prima e principale consiste nell&#039;avere immerso il bruco nell&#039;acqua, <lb></lb>e nell&#039;avere osservato che l&#039;aria esce in bollicelle dalla superficie dell&#039;ani­<lb></lb>male, fuor che dalle stimme, dalle quali anzi si sarebbe aspettato che do­<lb></lb>vesse vedersi uscire l&#039;aria stessa in forma di getto, se fosse stata vera l&#039;ipo­<lb></lb>tesi del Malpighi. </s>

<s>L&#039;anatomia sovveniva pure a conferma del medesimo fatto, <lb></lb>rivelando all&#039;occhio armato del Microscopio ch&#039;è la pelle del bruco tutta <lb></lb>trapunta da spessi e minutissimi pori. </s></p><p type="main">

<s>Questo modo di respirar degl&#039;insetti, ricevendo l&#039;aria per le stimmate <lb></lb>e rigettandola per gl&#039;innumerevoli pori aperti sopra la superficie del corpo, <lb></lb>rende la ragione, dice il Reaumur, di certi fatti, che si osservano avvenire <lb></lb>in questi animali in un modo assai diverso dagli animali degli ordini supe­<lb></lb>riori assoggettati all&#039;azione del vuoto pneumatico. </s>

<s>Le vesciche dei pesci, i <lb></lb>ventricoli delle rane, i polmoni degli uccelli inturgidiscono sempre più al <lb></lb>rarefarsi dell&#039;aria, intantochè si vede notabil<gap></gap> ricrescere sotto il reci­<lb></lb>piente tutta insieme la mole animale. </s>

<s>“ Il ne arrive tout autrement a nos <pb xlink:href="020/01/1611.jpg" pagenum="486"></pb>chenilles; on a eu beau epuiser d&#039;air le petit recipient ou elles étoient, leur <lb></lb>volume n&#039;a pas augmenté sensiblement, sans doute parce que l&#039;air de leur <lb></lb>corps trouve par-tout des passages pour s&#039;echapper ” (ivi, pag. </s>

<s>177). </s></p><p type="main">

<s>Un altro fatto singolare, e proprio a soli gl&#039;insetti, s&#039;osserva in questo <lb></lb>genere di esperienze, ed è che, sebbene estratta l&#039;aria s&#039;abbandonino come <lb></lb>morti, al riammetterla, anche dopo qualche giorno, riprendono la primiera <lb></lb>vivacità, e ciò non per altro avviene, dice il Reaumur, se non perchè l&#039;aria <lb></lb>facilmente uscendo da tutti i pori del corpo “ empêche qu&#039;il n&#039;y produise <lb></lb>des derangemens lorsqu&#039;il se raréfie ” (ivi). </s></p><p type="main">

<s>All&#039;assunto del Malpighi, ch&#039;era quello di dimostrare essere gli organi <lb></lb>da sè scoperti ne&#039;vermi da seta inservienti alla respirazione, i nuovi fatti, <lb></lb>dal Reaumur colla macchina pneumatica sperimentati, erano di una grande <lb></lb>importanza. </s>

<s>In fin dai tempi dell&#039;Accademia del Cimento dovea senza dub­<lb></lb>bio recar non poca maraviglia il veder che nel vuoto torricelliano morivano <lb></lb>immediatamente gli uccelletti, mentre i grilli vi si mantenevano “ per lo <lb></lb>spazio di un quarto d&#039;ora vivacissimi, movendosi sempre ma non saltando ” <lb></lb>(Saggi di natur. </s>

<s>esper. </s>

<s>cit., pag. </s>

<s>88); ciò che dovette avere grande effica­<lb></lb>cia sulla mente di coloro, che negavano agl&#039;insetti il respiro. </s>

<s>Il Malpighi <lb></lb>stesso non par che sentisse questa difficoltà, fidandosi delle esperienze degli <lb></lb>Accademici di Londra, i quali, avendo posti de&#039;bruchi sotto il recipiente <lb></lb>della macchina pneumatica, dalle troppo frettolose osservazioni conclusero <lb></lb>che “ orbata aere, interiere ” (De bombyc. </s>

<s>cit., pag. </s>

<s>19). Che il Reaumur <lb></lb>dall&#039;altra parte non avesse tolte le difficoltà dubitavasi ragionevolmente da <lb></lb>coloro, i quali comprendavano che poteva l&#039;aria trovar così facile esito per <lb></lb>le stimmate, come per i pori cutanei, nè si persuadevano come mai i mor­<lb></lb>tiferi effetti della privazione dell&#039;aria si riducessero a un <emph type="italics"></emph>derangemens<emph.end type="italics"></emph.end> degli <lb></lb>organi. </s></p><p type="main">

<s>Queste prime considerazioni invitarono ad entrar più addentro all&#039;esame <lb></lb>della questione Carlo Bonnet, il quale diligentemente bagnando il bruco, <lb></lb>prima di sommergerlo nell&#039;acqua, trovò che l&#039;aria non usciva altrimenti dai <lb></lb>pori cutanei, come pretendeva il Reaumur, ma dalle stimate, com&#039;avea detto <lb></lb>il Malpighi. </s>

<s>“ Queste esperienze, scrive lo Spallanzani in una nota alla sua <lb></lb>traduzione della <emph type="italics"></emph>Contemplazione della Natura,<emph.end type="italics"></emph.end> non mai pubblicate dal no­<lb></lb>stro Autore, che sono in buon numero e ingegnosamente variate, si con­<lb></lb>servano presso di me riserbandomi a darle fuori allora quando uscirà la mia <lb></lb>Opera sulle <emph type="italics"></emph>Riproduzioni animali ”<emph.end type="italics"></emph.end> (Tomo I, Modena 1759, pag. </s>

<s>279). </s></p><p type="main">

<s>Restava così dimostrato per queste bonnettiane esperienze che l&#039;aria <lb></lb>entra ed esce per le stimme dei vermi, come per la bocca degli animali <lb></lb>perfetti, ma non è da aspettarsi che in tempi, ne&#039;quali ignoravansi gli usi <lb></lb>dell&#039;aria nella respirazione, si potessero sciogliere così fatte proposte que­<lb></lb>stioni, le quali furono perciò dal Malpighi e dal Reaumur, come dallo stesso <lb></lb>Bonnet, lasciate alla progredita scienza dei Naturalisti del secolo seguente. </s></p><pb xlink:href="020/01/1612.jpg" pagenum="487"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Benchè la ignorata azione chimica dell&#039;aria sul sangue impedisse agli <lb></lb>Entomologi del secolo XVII e del XVIII di ridur compiuta la fisiologia della <lb></lb>respirazione, avevano nonostante avuto dal Microscopio così valido aiuto, da <lb></lb>scoprire gli organi inservienti a quella, che è la precipua funzione della vita <lb></lb>animale. </s>

<s>Si sarebbe sperato che il benefico diottrico strumento fosse venuto <lb></lb>a rivelare all&#039;occhio desideroso qualche apparenza almeno degli organi dei <lb></lb>sensi, invisibili per la piccolezza, non riconoscibili per la particolare strut­<lb></lb>tura. </s>

<s>Era per le più volgari esperienze noto che le api per esempio disperse <lb></lb>facilmente si convocano al risonar di un metallo percosso, e che le mosche <lb></lb>traggono d&#039;ogni parte nelle cucine all&#039;odore delle vivande, benchè nulla <lb></lb>apparisse in quegli insetti, che avesse qualche somiglianza con gli orecchi <lb></lb>e col naso nostro o deglì altri animali. </s>

<s>Tanto la così certa esistenza della <lb></lb>funzione provocava l&#039;intelletto ad argomentare all&#039;esistenza dell&#039;organo, che <lb></lb>del non averlo saputo ancora scoprire s&#039;accusava la debolezza della vista, <lb></lb>per cui venivano di qui ad incorarsi più vive le speranze riposte nel Mi­<lb></lb>croscopio. </s>

<s>Nè i primi imperfetti strumenti diottrici però, nè i più perfetta­<lb></lb>mente elaborati dipoi scoprirono negl&#039;insetti vestigio di organi, che si po­<lb></lb>tesse credere esser disposti dalla Natura per ricevere le impressioni de&#039;suoni <lb></lb>e degli odori. </s>

<s>Al Lyonet, che indicava le barboline intorno alla bocca per <lb></lb>organo dell&#039;olfatto, nessuno o pochissimi fra&#039;Naturalisti dettero fede, non <lb></lb>avendo una tal congettura miglior fondamento dell&#039;altra, che volesse rico­<lb></lb>noscer piuttosto l&#039;organo olfattorio ne&#039;peli del dorso, della testa o del ven­<lb></lb>tre. </s>

<s>Che se quelle barboline son palpi, non par che possano servire se non <lb></lb>al senso generale del tatto. </s></p><p type="main">

<s>Anche il Bonnet sospettò che servissero all&#039;odorato degl&#039;insetti le <emph type="italics"></emph>an­<lb></lb>tenne,<emph.end type="italics"></emph.end> per avverar la qual congettura lo Spallanzani proponeva ingegnosa­<lb></lb>mente di far questa esperienza: “ Sappiamo, egli dice, per l&#039;una parte che <lb></lb>la privazione delle antenne non toglie all&#039;insetto l&#039;esercitare le sue funzioni <lb></lb>corporee, e per l&#039;altra, che ci sono certi insetti, massime nel numero dei <lb></lb>volanti, i quali dalla sola forza dell&#039;odore sembrano avidamente essere por­<lb></lb>tati là dove giacciano materie acconce a fomentare, e a far nascere le uova, <lb></lb>che chiudono in seno, e delle quali hanno allora bisogno di sgravarsi. </s>

<s>Si <lb></lb>potrebbe dunque stare a osservare se tali insetti si determinano eziandio a <lb></lb>quella volta, mutilati essendo nelle antenne. </s>

<s>Se sì, bisogna dire che l&#039;or­<lb></lb>gano dell&#039;odorato non risegga nelle antenne; se no, abbiam motivo di cre­<lb></lb>dere il contrario ” (Traduz. </s>

<s>della Contemplazion della Natura, T. I, Mo­<lb></lb>dena 1769, in nota a pag. </s>

<s>85). Ma eseguitasi o no la proposta esperienza <lb></lb>rimasero gli Entomologi nella prima incertezza rispetto a ciò che, dell&#039;or­<lb></lb>gano olfattorio negli insetti, erasi dal Bonnet congetturato. </s></p><pb xlink:href="020/01/1613.jpg" pagenum="488"></pb><p type="main">

<s>Nessuno poi, nemmeno per congettura, osò d&#039;indicare un qualche or­<lb></lb>gano dell&#039;udito, benchè le sopra accennate esperienze ne facessero conclu­<lb></lb>der certa l&#039;esistenza nelle api, e la facoltà di emettere i suoni in tanti insetti <lb></lb>facesse necessariamente arguire a un sensorio da percepirli. </s>

<s>Il Casserio di­<lb></lb>ligentemente descrisse gli organi e il meccanismo di quel suono, che pro­<lb></lb>ducono, fregate insieme o percosse, le ali delle locuste e de&#039;grilli, e perchè <lb></lb>non si può credere che la Natura usasse un così sottil magistero per dare <lb></lb>all&#039;animale un&#039;inutile sollazzo, convien dire che abbia con più alto inten­<lb></lb>dimento così disposte le parti, per servire alla vita di relazione. </s></p><p type="main">

<s>“ Sonum locustarum genus alis edit, scrive il Piacentino nel suo trat­<lb></lb>tato <emph type="italics"></emph>De vocis organi historia anatomica,<emph.end type="italics"></emph.end> ita ut sibi invicem impositae mo­<lb></lb>veantur alae, quarum superior parte intima corpus habet subnigrum, durum, <lb></lb>per transversum locatum. </s>

<s>Inferior eiusdem substantiae corpusculum in extre­<lb></lb>mitate orae superioris, parte externa, cui adiacet perbellum tympanum. </s>

<s>Ho­<lb></lb>rum mutuo attritu stridor ille, imo et mortuis styli tactu excitatur, at multo <lb></lb>maior in vivente animali, ubi copiosior intercipitur aer et, natura monente, <lb></lb>validius alae colliduntur, non inutile membranae, quae admodum tensa cer­<lb></lb>nitur, opera ” (Ferrariae 1600, pag. </s>

<s>116). </s></p><p type="main">

<s>Più complicato di questo è l&#039;artificio, con cui la Natura condusse lo <lb></lb>stridulo organo delle Cicale, e il Casserio medesimo non trascurò, in quel <lb></lb>nuovo campo aperto all&#039;Entomologia, d&#039;esercitarvi l&#039;acume dello stilo ana­<lb></lb>tomico e dell&#039;occhio. </s>

<s>Chi, sodisfatta la curiosità nella lettura delle pagine <lb></lb>casseriane, passa a svolgere le <emph type="italics"></emph>Memorie<emph.end type="italics"></emph.end> del Reaumur, comprese nella prima <lb></lb>Parte del Tomo quinto, resta maravigliato in trovarvi scritto che il Ponte­<lb></lb>dera, a proposito del detto organe risonante “ assure avec raison qu&#039;il sem­<lb></lb>ble qu&#039;ils ont eté mal vus. </s>

<s>Il est certain au moins qu&#039;ils ont eté mal dé­<lb></lb>crits, et qu&#039;il y en a quelques-uns qui sont difficiles à decouvrir. </s>

<s>Quand on <lb></lb>observa du côte du ventre un mâle des Cigales on y remarque bientòt deux <lb></lb>assez grandez plaques écailleuses, qu&#039;on ne trouve point aux femelles ” <lb></lb>(Amsterdam 1741, pag. </s>

<s>199). E prosegue la descrizione, che i nostri Let­<lb></lb>tori possono confrontare con questa fatta dal nostro Anatomico piacentino <lb></lb>quasi un secolo e mezzo prima. </s>

<s>“ In cicada vero, plane mirabile sagacis Natu­<lb></lb>rae artificium, tympanum duplex sub thorace duplici obtegitur velut squama. </s>

<s><lb></lb>Thorax et abdomen magno excavata sunt antro, cuius superior pars, mem­<lb></lb>brana lutea tanquam fornice cincta, sonum excipit. </s>

<s>Hic a concusso aere, <lb></lb>resilit in amplam illam cameram. </s>

<s>Aerem autem quatiunt praedurae quaedam <lb></lb>membranulae, a lateribus sitae, quarum substantiam non obscure conferas <lb></lb>cum bracteris illis ex auricalcho, quae agitatae consimilem fere sonum fa­<lb></lb>ciunt. </s>

<s>Muniuntur hae suo cortice, ita tamen, ut omnino conclusae non sint, <lb></lb>sed liber aeri pateat aditus. </s>

<s>Voluntarie moventur duobus musculis, ab osse, <lb></lb>quod supremum ventrem cingit, ortis, validis ob motum respectu animalis <lb></lb>haud invalidum ” (De vocis hist. </s>

<s>cit, pag. </s>

<s>116). </s></p><p type="main">

<s>Ma insomma, benchè sia il canto ne&#039;maschi delle Cicale ordinato ad <lb></lb>allettare le femmine, non è stato possibile di riconoscere in queste nessun <pb xlink:href="020/01/1614.jpg" pagenum="489"></pb>vestigio d&#039;organo, da stare in silenzio ad ascoltar l&#039;amorosa canzone: co­<lb></lb>sicchè de&#039;sensorii, e non in tutti gl&#039;insetti, non s&#039;ebbe indizio altro che <lb></lb>degli occhi. </s>

<s>Gli antichi fondarono questi indizi sulla esterior lucentezza cri­<lb></lb>stallina, e sulla posizione, che hanno i due creduti globuli occellari rispetto <lb></lb>alla bocca, e rispetto alle altre parti analoghe a quelle degli animali supe­<lb></lb>riori, ma coll&#039;aiuto del Microscopio quegli stessi indizi, che avevano avuto <lb></lb>così debole fondamento, per la più intima somiglianza scoperta con gli oc­<lb></lb>chi veri vennero a farsi più probabili, e dopo lunghe discussioni, delle quali <lb></lb>accenneremo alla storia, si può dire anche certi. </s></p><p type="main">

<s>Incominciano i naturali avvenimenti storici anche questa volta in Italia, <lb></lb>dove Giovan Batista Hodierna, poco dopo il 1640, attendeva il primo ad os­<lb></lb>servare il maraviglioso spettacolo offertogli dall&#039;occhio delle mosche e degli <lb></lb>altri insetti. </s>

<s>“ Vedesi dunque, egli dice, per cominciare la descrizione di <lb></lb>questa singolare anatomia, da niuno prima, quant&#039;io sappia, che da me ten­<lb></lb>tata e scoverta, nell&#039;estrinseco dell&#039;occhio nella Mosca, e in qualsivoglia in­<lb></lb>dividuo delle specie annoverate sotto il genere degl&#039;insetti, o sia quello vo­<lb></lb>latile come la Mosca o pedestre come la formica, o aquatile come il gran­<lb></lb>chio; nella superfice convessa dell&#039;occhio, in quella dico che dalli periti <lb></lb>Anatomisti vien detta cornea tunica, dalla durezza che tiene e dall&#039;esser <lb></lb>trasparente come una laminetta di corno; dico nell&#039;estrinseca superfice della <lb></lb>cornea ambiente tutta la sostanza dell&#039;occhio, un grandissimo numero d&#039;or­<lb></lb>dinatissime sezioni designate e tirate per linee curve e circolari, che tra di <lb></lb>sè sono equidistanti e parallele, sicchè, attraversandosi gli uni con l&#039;altre ad <lb></lb>angoli retti, rendono tutta la convessità distinta in numero così grande, che <lb></lb>eccede il tremillesimo, rappresentando l&#039;ambito dell&#039;occhio un emisfero di­<lb></lb>stinto in tre mila piazzette quadre, che rassembra una vaghissima struttura <lb></lb>di mosaico ” (Opuscoli, Palermo 1644, pag. </s>

<s>9). </s></p><p type="main">

<s>Dalle semplici osservazioni risalendo l&#039;Hodierna col pensiero a scrutar <lb></lb>le intenzioni della provvida Natura, che contenta di dar due soli occhi agli <lb></lb>animali superiori ne fornisse poi gl&#039;insetti di tanto numero, da sembrare <lb></lb>alle menti volgari eccessivo; “ io intendo, prosegue a dire, che la Natura <lb></lb>nella fabbrica mirabile dell&#039;occhio dell&#039;insettile si sia servita, non a caso di <lb></lb>sì fatta struttura cotanto diversa dagli altri, ma acciò supplisca al bisogno, <lb></lb>che tengono questi animaletti nel vedere, qual bisogno parmi che avendo <lb></lb>tutti gli altri animali il capo mobile e volubile, mediante il collo che lo so­<lb></lb>stiene, eccettuandone il genere degl&#039;insetti, il quale, mancando di collo, tiene <lb></lb>il capo fisso e costante, senza poterlo piegare, e conseguentemente non può <lb></lb>menar l&#039;occhio per adattarlo agli obietti; la providente Natura dunque, per <lb></lb>supplire a tanto bisogno, l&#039;ha dotato d&#039;un occhio prominente, con attitudine <lb></lb>di poter discernerne tutti gli obietti circostanti, senza menare il capo, e senza <lb></lb>muovere l&#039;occhio ” (ivi, pag. </s>

<s>15). E di qui crede il nostro Entomologo di <lb></lb>poter formular la seguente legge zoonomica: che cioè tutti gli animali man­<lb></lb>canti di collo hanno occhi poliedrici, e al contrario, tutti quelli che si ve­<lb></lb>dono avere occhi poliedrici son mancanti di collo. </s></p><pb xlink:href="020/01/1615.jpg" pagenum="490"></pb><p type="main">

<s>Dopo l&#039;Hodierna, Francesco Fontana, nella sua VI Osservazione micro­<lb></lb>scopica, descriveva i ragni, che gli apparvero ferocemente armati di denti <lb></lb>come i cinghiali, e di unghie laceratrici, come quelle degli orsi. </s>

<s>“ Oculos <lb></lb>indicibili ordine distinctos habent, quatuor enim in fronte et binos in capi­<lb></lb>tis vertice, alterum a laeva, a dextera parte alterum, totam corporis imagi­<lb></lb>nem mirifice illustrantes, atqne horrendum reddentes lumen pellucide, ve­<lb></lb>lut ex nigricanti vitro, hispidis et longis setis septos ” (Novae observat. </s>

<s>cit., <lb></lb>pag. </s>

<s>150). Nel 1665 poi l&#039;Hooke, pubblicando in Londra la sua <emph type="italics"></emph>Microgra­<lb></lb>phia,<emph.end type="italics"></emph.end> tornava con più diligenza sulla scoperta pubblicata ventun&#039;anno prima <lb></lb>dal nostro Hodierna, e con migliore strumento osservando gli occhi delle <lb></lb>Mosche ne rappresentava, nel XXIV iconismo, i quattordicimila occhi, dei <lb></lb>quali, da pag. </s>

<s>175-80 della citata edizione, divisava i più minuti particolari, <lb></lb>in tal maraviglioso spettacolo della Natura, da sè contemplati. </s></p><p type="main">

<s>Benchè l&#039;Hodierna e l&#039;Hooke, se non il Fontana, fossero Micrografi e <lb></lb>uomini di tale ingegno, da creder che non si fossero così facilmente illusi, <lb></lb>riguardando i globuli lenticolari scoperti nella fronte degl&#039;insetti come oc­<lb></lb>chi; a confermar nonostante quella loro opinione s&#039;aggiunsero poco dopo <lb></lb>due delle più grandi autorità in Entomologia, il Malpighi e lo Swammer­<lb></lb>dam. </s>

<s>Il Nostro, nel rappresentare il Bombice nella fig. </s>

<s>XI della Tavola I, <lb></lb>dichiara que&#039;sei puntolini nereggianti, segnati colla lettera H, per gli ocelli <lb></lb>del bruco. </s>

<s>“ In anteriori parte, ad latera tamen, globuli H quidam, numero <lb></lb>sex, diaphani protuberant, qui oculi censentur ” (Tomus Operum cit., pag. </s>

<s>13). <lb></lb>E nella fig. </s>

<s>I della Tavola VII que&#039;due globuli diafani, segnati colla lettera B, <lb></lb>nella fronte dello stesso bruco, giudica che sieno propriamente gli occhi di <lb></lb>lui. </s>

<s>“ Diaphanos quosdam globulos B pro oculis habendos esse reor ” (ibid., <lb></lb>pag. </s>

<s>27) Nel descriver poi il capo della Farfalla rappresentato nella fig. </s>

<s>II <lb></lb>della Tavola IX, “ caput habet A, dice, exiguum tamen, in quo bini locan­<lb></lb>tur oculi B, ut in consimilibus observatur, qui semisphaeram multis segmen­<lb></lb>tis distinctam exhibent, unde innumeri, quasi intercepti assurgunt oculi ” <lb></lb>(ibid., pag. </s>

<s>34). </s></p><p type="main">

<s>Lo Swammerdam nel 1669 pubblicava in Utrecht nella patria lingua <lb></lb>un libro, che sedici anni dopo Enrico Cristiano Henning traduceva col titolo <lb></lb>d&#039;<emph type="italics"></emph>Historia generalis Insectorum.<emph.end type="italics"></emph.end> L&#039;Autore ivi non si contenta di riguar­<lb></lb>dare i trasparenti globuli malpighiani com&#039;occhi, ma, esercitando più adden­<lb></lb>tro la perita arte anatomica, trovò nelle vespe partirsi dal cervello a cia­<lb></lb>scuna cornea filamenti nervosi, da potersi riguardar come nervi ottici, e negli <lb></lb>emerobii, come già l&#039;Hooke nelle libellule, osservò che si espandeva così <lb></lb>esso nervo ottico, da emular la struttura e l&#039;ufficio della retina. </s>

<s>Si dee pure <lb></lb>allo Swammerdam la graziosa esperienza delle mosche che, bendati gli oc­<lb></lb>chi, non si risolvon di muoversi, e costrette si vedono andare con volo in­<lb></lb>certo, e come propriamente cieche urtar negl&#039;incontri. </s></p><p type="main">

<s>Mentre però si credeva che fosse l&#039;organo della vista negl&#039;insetti dimo­<lb></lb>strato, per le citate autorità e per le narrate esperienze, come cosa di fatto, <lb></lb>prevalsero così nella scienza le negazioni di alcuni rispetto all&#039;uso assegnato <pb xlink:href="020/01/1616.jpg" pagenum="491"></pb>ai due diafani globi maggiori, che Filippo De la Hire, appuntando un giorno <lb></lb>la lente microscopica sulla testa di una mosca, la posò esultando per andare <lb></lb>a riferire agli Accademici parigini colleghi suoi che avea in quegl&#039;insetti <lb></lb>scoperto il vero organo della vista. </s>

<s>E que&#039;Parigini, i quali s&#039;erano, come il <lb></lb>De la Hire, dimenticati che gli <emph type="italics"></emph>ocelli<emph.end type="italics"></emph.end> erano stati con gran solennità figurati <lb></lb>e descritti nel Bombice del Malpighi, in questa forma accademica furono <lb></lb>solleciti di divulgare la nazionale scoperta: “ Plusieurs personnes ont crû <lb></lb>que les mouches et la plupart des autres insectes volans n&#039;avoient point <lb></lb>d&#039;yeux. </s>

<s>La raison sur laquelle ils fondoient ce sentiment, est qu&#039;ils ne pou­<lb></lb>voient pas se persuader que les pelotons divises par quarrés ou exagones <lb></lb>qu&#039;ils ont au còté de la tête en fussent effectivement, n&#039;ayant autre rapport <lb></lb>à ceux des autres animaux que la situation. </s>

<s>M. de la Hire a trouvé que les <lb></lb>insectes en ont trois qui sont places entre les deux pelotons, sur la partie <lb></lb>la plus élevée de la tête, et sur une petite éminence, deux desquels regar­<lb></lb>dent en haut et un peu vers le côtés, et l&#039;autre regarde un peu de front. </s>

<s><lb></lb>Ils sont disposés en triangle. </s>

<s>Ces yeux ont des paupières que l&#039;on voit fort <lb></lb>bien..... Ces yeux sont ronds et fort polis, representant fort nettement les <lb></lb>obiets qui leur sont présentés, et leur partie opposée à la lumiere paroit <lb></lb>d&#039;un jaune doré, ce qui fait voir qu&#039;ils sont remplis d&#039;une humeur traspa­<lb></lb>rente, laquelle se séche aisément. </s>

<s>Ces remarques sont assez suffisantes, comme <lb></lb>il dit, pour nous persuader que ce sont des yeux ” (Collection acad., T. </s>

<s>I <lb></lb>cit., pag. </s>

<s>397). </s></p><p type="main">

<s>Non tutti però, nemmen nella stessa Accademia parigina, ingerirono <lb></lb>questa persuasione. </s>

<s>Uno anzi de&#039;più valorosi fra loro negò ogni probabilità <lb></lb>che i cristallini globi grandi e piccoli, o i così detti <emph type="italics"></emph>occhi<emph.end type="italics"></emph.end> e gli <emph type="italics"></emph>ocelli<emph.end type="italics"></emph.end> fos­<lb></lb>sero negl&#039;insetti occhi veri. </s>

<s>Claudio Perrault infatti terminava con queste <lb></lb>parole il cap. </s>

<s>I della I parte della Meccanica animale, proponendosi di di­<lb></lb>mostrar che gl&#039;insetti non hanno che un senso solo: “ Pour ce qui est des <lb></lb>parties qu&#039;on découvre dans les insectes avec le microscope, qui paroissent <lb></lb>être des yeux, et dont on en void trois sur la tête des mouches, et plus de <lb></lb>cent sur celle des Scorpions, on n&#039;est point convaincu qu&#039;elles soient des <lb></lb>yeux veritables ” (Oeuvres, T. </s>

<s>I cit., pag. </s>

<s>338). </s></p><p type="main">

<s>Il senso unico di che dice il Perrault esser dotati gl&#039;insetti è quello <lb></lb>del tatto, il quale è però in essi tanto squisito, che supera ogni nostra im­<lb></lb>maginazione. </s>

<s>Quando le mosche per esempio entrano in una cucina o in <lb></lb>una camera aperta non è la luce che serve a loro di scorta, ma il tiepor <lb></lb>dell&#039;ambiente; e così non è punto lo splendore, che attrae le farfalle, ma <lb></lb>il calor della fiamma. </s>

<s>Le stesse percezioni, prosegue a dire il Perrault, che <lb></lb>da noi si ricevono per il senso dell&#039;odorato, gl&#039;insetti lo ricevono per via <lb></lb>del tatto, come per esempio le mosche, che par sien tratte da gran distanza <lb></lb>all&#039;odore de&#039;putrescenti carcami, o le formiche, a cui par che in fin giù <lb></lb>ne&#039;riposti nidi giunga il lontano odore del grano. </s>

<s>“ Or quoique toutes ces <lb></lb>especes d&#039;animaux ne paroissent pas seulement avoir l&#039;usage de l&#039;odorat, mais <lb></lb>qu&#039;il semble aussi qu&#039;ils voyent et qu&#039;ils entendent, il est néanmoins, ce me <pb xlink:href="020/01/1617.jpg" pagenum="492"></pb>semble, plus aise de comprendre que la delicatesse de leur toucher peut <lb></lb>suffire à toutes ces connoissances; car tous les obiets des sens differens ne <lb></lb>se pouvant faire connoitre que par un certain mouvement particulier qui <lb></lb>les rend sensibles, il me semble qu&#039;il n&#039;est pas difficile de concevoir que les <lb></lb>insectes, qui sont tres petits, et qui par consequent ont les particules dont <lb></lb>l&#039;organe de leur sens est composé plus petites, et formant une substance, <lb></lb>s&#039;il faut ainsi dire, beaucoup plus fine que dans les grands animaux, ce sens <lb></lb>est plus aisément émù par le mouvement des obiects quelque delicat qu&#039;il <lb></lb>puisse être, et tout d&#039;une autre maniere que dans les grands animaux, ou <lb></lb>le toucher ne peut être ébranlè que par des mouvemens d&#039;une grandeur <lb></lb>considerable: et que de mème qu&#039;un mouvement, qui ne fait qu&#039;emouvoir <lb></lb>legerement le toucher d&#039;un grand animal, est capable d&#039;écraser un insecte, <lb></lb>il est croyable que ce qui émeut sensiblement un insecte ne cause aucun <lb></lb>sentiment à un grand animal ” (ivi, pag. </s>

<s>337, 38). </s></p><p type="main">

<s>L&#039;elegante novità di queste dottrine ebbe grande efficacia sulle menti <lb></lb>degli Entomologi, non solo in Francia, ma anche fra noi, dove il Vallisnieri, <lb></lb>disertando per un momento dalla scuola del Malpighi, inclinava col Perrault <lb></lb>a credere che negli insetti al senso particolar della vista soccorresse quello <lb></lb>universale del tatto. </s>

<s>“ Il vedere delle lumache, scriveva, e di molti vermi e <lb></lb>insetti è diverso dal nostro, e non consiste che nell&#039;allungamento delle loro <lb></lb>pieghevoli corna, o in altri di certe antenne, che fan l&#039;uffizio di spiare e <lb></lb>sentire col tatto la qualità degli oggetti che incontrano ” (Esperienze ed <lb></lb>osservaz. </s>

<s>cit., pag. </s>

<s>107). </s></p><p type="main">

<s>Chi conosce l&#039;indole del Vallisnieri, e il riverente amore che portava <lb></lb>al suo celebre Maestro, facilmente comprende che se non convenne con lui <lb></lb>essere i globuli trasparenti maggiori e minori nel bruco e nella farfalla del <lb></lb>Bombice occhi veri, ciò dovett&#039;essere per alcune forti ragioni. </s>

<s>Di dire in­<lb></lb>fatti queste ragioni non mancò esso Vallisnieri ne&#039;suoi <emph type="italics"></emph>Dialoghi,<emph.end type="italics"></emph.end> nelle sue <lb></lb><emph type="italics"></emph>Osservazioni intorno alla generazione dei vermi,<emph.end type="italics"></emph.end> e più di proposito nella <lb></lb><emph type="italics"></emph>Storia della nascita del verme nel naso delle pecore,<emph.end type="italics"></emph.end> dentro gli occhi del <lb></lb>qual verme “ osservai, scrive nella lettera a Giacinto Gemma sopra questo <lb></lb>argomento, con mio stupore una selva regolatissima di peli, che spuntava <lb></lb>fra l&#039;uno e l&#039;altro interstizio dalle graticole, il che pure notai negli occhi <lb></lb>di molti altri insetti, strabiliando come la sagacissima Natura offuschi di peli <lb></lb>un organo sì delicato e gentile, quando proviamo che un solo bruscolo così <lb></lb>stranamente l&#039;intorbida. </s>

<s>Nè è sola questa mosca, cui si veggano i peli negli <lb></lb>occhi suoi, mentre molti moscioni, certe api, alcune farfalle ed altri insetti gli <lb></lb>hanno manifestamente carichi de&#039;medesimi. </s>

<s>Quindi fu che allora sospettai <lb></lb>se veramente fossero occhi ” (ivi, pag. </s>

<s>106). Un&#039;altra ragione veniva a con­<lb></lb>fermare il sospetto del Vallisnieri, ed era che di que&#039;globi, onorati col titolo <lb></lb>di occhi, son forniti anche alcuni insetti, i quali, standosene continuamente <lb></lb>immobili e al buio, non par perciò che abbiano bisogno di vedere (pag. </s>

<s>108). </s></p><p type="main">

<s>In questo medesimo tempo che il Vallisnieri in Italia attendeva a de­<lb></lb>molire l&#039;edifizio fondato dall&#039;Hodierna, il Leeuwenoeck in Olanda lo rimet-<pb xlink:href="020/01/1618.jpg" pagenum="493"></pb>teva in onore, istituendo nuove regole, con l&#039;aiuto di dotti geometri amici <lb></lb>suoi, per computar più giusto il numero delle cornee oculari ridotte nella <lb></lb><emph type="italics"></emph>Mordella<emph.end type="italics"></emph.end> a 25,088. “ Sequitur Mordellam oculis 25,088 instructam esse. </s>

<s>Qui <lb></lb>numerus expectationem meam longe exsuperat, nam de muscarum oculis <lb></lb>disserens singulis illarum tunicis oculos inesse quater mille, atque adeo sin­<lb></lb>gulas muscas octo oculorum millibus praeditas esse statuebam ” (Epist. </s>

<s>phy­<lb></lb>siologicae, Delphis 1719, pag. </s>

<s>343). </s></p><p type="main">

<s>In questi calcoli supponeva il Leeuwenoeck che il maraviglioso organo <lb></lb>contemplato servisse alla vista, indottovi dall&#039;analogia e dalle prime tradi­<lb></lb>zioni della scienza, diffuse al di la dei monti dall&#039;Hooke, con più gagliardo <lb></lb>impulso che dall&#039;Hodierna. </s>

<s>Ma poi vennero a dimostrargli il supposto certe <lb></lb>osservazioni, dalle quali appariva essere una più intima somiglianza anche <lb></lb>nelle parti fra l&#039;occhio degl&#039;insetti e quello degli animali superiori. </s>

<s>“ Post <lb></lb>haec oculos Mordellae attentius quam ante visu examinavi, et singulis ocu­<lb></lb>lis exiguam maculam eamque translucidam, imo reliquis oculi partibus longe <lb></lb>lucidiorem inesse, animadverti..... Quod si istam oculorum fabricam cum <lb></lb>hominis et reliquorum animalium oculis conferamus, et corneas horum ocu­<lb></lb>lorum tunicas a partibus inferioribus separatas intueamur, nonne locum il­<lb></lb>lum rotundum, sive pupillam in humano oculo, quae radium opticum tran­<lb></lb>smittit, lucidiori quam dixi maculae respondere fatebimur? </s>

<s>Brevi, quidquid <lb></lb>artificii atque perfectionis oculis inest maiorum animalium, etiam inest <lb></lb>oculis minorum, licet in his, ob partium exiguitatem, visui nostro inconspi­<lb></lb>cuum ” (ibid., pag. </s>

<s>345). </s></p><p type="main">

<s>E in verità scopertasi dal Leeuwenoeck la pupilla, come s&#039;erano dallo <lb></lb>Swammerdam scoperti il nervo ottico e la retina, sembrava ragionevolissimo <lb></lb>l&#039;inferirne che s&#039;avessero a riscontrar negli occhi degli insetti anche le altre <lb></lb>parti corrispondenti a quelle degli animali maggiori, benchè riuscissero per <lb></lb>la loro esiguità invisibili a qualunque potenza di microscopi. </s>

<s>Il Vallisnieri <lb></lb>stesso, se non rimase da questi argomenti persuaso, rallentò nulladimeno <lb></lb>l&#039;arco al suo dubbio, com&#039;apparisce dalle seguenti espressioni uscitegli dalla <lb></lb>penna nel 1721, nel descriver la <emph type="italics"></emph>Storia della generazione dell&#039;uomo.<emph.end type="italics"></emph.end> “ E <lb></lb>se è vero che questi insetti abbiano un&#039;infinità di occhi, come ne induce <lb></lb>la figura e il sito di quelle membrane lucide e graticolate, e che a guisa <lb></lb>di tante finestrelle pare che ricevano il lume da tutte le parti; qual picco­<lb></lb>lezza averanno le immagini in questi innumerabili specchi a faccette? </s>

<s>” <lb></lb>(Opere, T. II, Venezia 1733, pag. </s>

<s>206). </s></p><p type="main">

<s>Il Reaumur poi, quel veramente <emph type="italics"></emph>princeps insectorum historicus,<emph.end type="italics"></emph.end> come <lb></lb>all&#039;Haller amico suo piacque di salutarlo (Bibliotheca an., T. II, Tiguri 1777, <lb></lb>pag. </s>

<s>61), colle ragioni e colla eloquenza finì così di dissipare le ombre, che <lb></lb>parve chiara agli occhi di tutti la luce, quando la videro come da specchio <lb></lb>riflessa dalla Memoria IV del citato Tomo I per servire alla storia degl&#039;in­<lb></lb>setti. </s>

<s>Ivi richiamasi dall&#039;Autore l&#039;attenzione de&#039;suoi lettori sulla spattacolosa <lb></lb>esperienza del Catelan ripetuta dal Leeuwenoeck e dal Puget, i quali, avendo <lb></lb>prima estratta e poi ben ben rinettata la cornea di un insetto, “ ont mis <pb xlink:href="020/01/1619.jpg" pagenum="494"></pb>et tenu cette cornée au foyer d&#039;un microscope, qu&#039;ils ont dirigé ensuite vers <lb></lb>quelque obiet, de maniere que les rayons qu&#039;il envoyoit a leurs yeux, pas­<lb></lb>soient par cette cornée, et par la lentille du microscope. </s>

<s>Il faut lire dans <lb></lb>M. </s>

<s>Puget même la description du spectacle qu&#039;il se donnoit, et qu&#039;il don­<lb></lb>noit à tous ceux qui vouloient avec lui admirer la Nature. </s>

<s>La cornée poin­<lb></lb>tée vis-a-vis un seul soldat faisoit voir une armée de pigmées: pointée vers <lb></lb>le arches d&#039;un pont, elle montroit une quantité de rangs d&#039;arches les unes <lb></lb>au-dessus des autres, qui surpassoit de beaucoup tout ce qui a jamais été <lb></lb>entrepris de plus grand pour la conduite des eaux. </s>

<s>La lumiere d&#039;une bou­<lb></lb>gie se multiplioit prodigieusement. </s>

<s>Jamais on n&#039;avra de verres à faccettes qui <lb></lb>multiplient autant les obiets, que ces cornées les moltiplient ” (pag. </s>

<s>265, 66). </s></p><p type="main">

<s>Proseguendo il Reaumur a descrivere eloquentemente la maravigliosa <lb></lb>struttura di queste cornee, all&#039;ultimo poi esclama: a che usar la Natura <lb></lb>tanto sottil magistero se non a lavorare un qualche organo del senso? </s>

<s>“ Et <lb></lb>à quelle sensation, dont nous ayons quelque idée, sont nécessaires des len­<lb></lb>tilles transparentes, des crystallins, qu&#039;a celle de la vue? </s>

<s>” (ivi, pag. </s>

<s>268). <lb></lb>Si fanno contro questo argomento alcune difficoltà, e quella così poderosa­<lb></lb>mente messa in campo dal Vallisnieri, quand&#039;ebbe scoperto esser gli occhi <lb></lb>degl&#039;insetti tutti ispidi e ingombri di peli, è, dice il Reaumur, <emph type="italics"></emph>une obiection <lb></lb>assez forte.<emph.end type="italics"></emph.end> È vero però, poi soggiunge, che quella selva di peli ingombre­<lb></lb>rebbe la vista, quando fosse un occhio solo, ma essendo più occhi distinti <lb></lb>quegli stessi peli, che s&#039;interpongono fra gli uni e gli altri, forse fanno l&#039;uf­<lb></lb>ficio di tante piccole palpebre. </s>

<s>In ogni modo è certo che “ ces poils qui <lb></lb>s&#039;elevent perpendicolairement sur le globe n&#039;empéchent pas des rayons d&#039;ar­<lb></lb>river à chaque petit oeil, à chaque crystallin ” (ivi, pag. </s>

<s>272). </s></p><p type="main">

<s>Passando poi da queste generalità, nel Tomo IV delle dette Memorie e <lb></lb>altrove, il Reaumur a descrivere particolarmente gli occhi di alcuni insetti, <lb></lb>fu primo a introdurre, in grazia del più chiaro e più spedito linguaggio, le <lb></lb>denominazioni di occhi <emph type="italics"></emph>a rezeau<emph.end type="italics"></emph.end> e di occhi <emph type="italics"></emph>lisci,<emph.end type="italics"></emph.end> date ai globi cristallini mag­<lb></lb>giori e minori. </s>

<s>Il Bonnet adottò nella <emph type="italics"></emph>Contemplazione della Natura<emph.end type="italics"></emph.end> questo <lb></lb>stesso linguaggio, che fu dallo Spallanzani tradotto in <emph type="italics"></emph>occhi a zigrino<emph.end type="italics"></emph.end> (T. </s>

<s>I <lb></lb>cit., pag. </s>

<s>81). E in nota, a piè della pagina ora citata e delle due seguenti, <lb></lb>si trattien brevemente il Traduttore intorno alla questione se quegli sieno <lb></lb>occhi veri, dove, dop&#039;avere accennato all&#039;esperienza della benda fatta dallo <lb></lb>Swammerdam sopra le mosche, e dal Reaumur ripetuta sopra le pecchie, <lb></lb>conclude all&#039;ultimo così il suo discorso: “ Siccome poi non solo i segmenti <lb></lb>emisferici, ma anche i piccoli corpi lisci sono in tutto soggetti a pari vi­<lb></lb>cende, quindi si ha solido fondamento di concludere che, non meno gli uni <lb></lb>che gli altri sieno negl&#039;insetti il verace organo della vista ” (pag. </s>

<s>83). </s></p><p type="main">

<s>Furono poi, dopo tante passate vicende, coronate le scoperte dell&#039;Ho­<lb></lb>dierna e del Malpighi del pacifico alloro della vittoria, quando l&#039;Haller in­<lb></lb>segnò dall&#039;alto della sua cattedra constare per esperienza i due grandi re­<lb></lb>ticolati e i tre più piccoli globi posti in fronte alle mosche “ veros esse et <lb></lb>ad videndum aptos oculos ” (Elem. </s>

<s>Physiol., T. </s>

<s>V cit., pag. </s>

<s>308), e quando, <pb xlink:href="020/01/1620.jpg" pagenum="495"></pb>colla medesima autorità di magistero, descrisse così l&#039;organo della vista nel­<lb></lb>l&#039;ape maggiore, da mostrar che nulla a lui manca in sostanza per doverlo <lb></lb>rassomigliare all&#039;occhio stesso di un animale perfetto (ivi, pag. </s>

<s>390). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Questi sopra narrati progressi fatti col potente aiuto del microscopio, <lb></lb>nella storia naturale degl&#039;insetti, furono, chi ben ripensa, i più efficaci ar­<lb></lb>gomenti da persuadere in tutto coloro, ne&#039;quali fosse ancora rimasto qual­<lb></lb>che piccolo dubbio intorno alla generazione di quegl&#039;infimi animali. </s>

<s>Impe­<lb></lb>rocchè, rivelando le microscopiche osservazioni all&#039;occhio maravigliato dei <lb></lb>Naturalisti organi inservienti alla vita vegetativa e a quella di relazione, non <lb></lb>punto meno elaborati negli spregiati automi, che negli animali stimati più <lb></lb>perfetti; dalla riconosciuta nobiltà della vita veniva giusta ragion di credere <lb></lb>alla nobiltà dell&#039;origine. </s></p><p type="main">

<s>Essendosi nonostante scoperta, col benefizio del medesimo diottrico stru­<lb></lb>mento, un&#039;altra popolazion di animali, là dove non si sarebbe aspettato nes­<lb></lb>suno che fosse segno di vita, ritornarono le peripatetiche ipotesi, con tante <lb></lb>e sì valorose armi cacciate via dal campo entomologico, ad applicarsi a spie­<lb></lb>gar la misteriosa generazione di questi nuovi viventi. </s>

<s>L&#039;irrequieto insorgere <lb></lb>di costoro, che non s&#039;erano ancora saputi terger l&#039;ingegno dall&#039;appiccatic­<lb></lb>cia pece aristotelica, fu ben presentito dall&#039;acutissimo Huyghens, quando, <lb></lb>alla descrizione degl&#039;infusorii del pepe fatta in una lettera indirizzata all&#039;Au­<lb></lb>tore del Diario parigino, soggiunse: “ Quis forte defendet animalcula haec <lb></lb>corruptione aut fermentatione generari ” (Opera varia, T. IV, Lugd. </s>

<s>Ba­<lb></lb>tav. </s>

<s>1724, pag. </s>

<s>764). </s></p><p type="main">

<s>S&#039;incominciarono infatti poco dopo a elaborare que&#039;filosofici sistemi, <lb></lb>ne&#039;quali rimettevansi in onore gli <emph type="italics"></emph>archei<emph.end type="italics"></emph.end> dell&#039;Helmont, o i <emph type="italics"></emph>primordii<emph.end type="italics"></emph.end> del­<lb></lb>l&#039;Harvey sotto il nuovo nome di <emph type="italics"></emph>forze plastiche<emph.end type="italics"></emph.end> o di <emph type="italics"></emph>forze attive,<emph.end type="italics"></emph.end> in virtù <lb></lb>delle quali in ogni modo asserivano il Nehedam e il Buffon che si generas­<lb></lb>sero gli animalucci delle infusioni. </s>

<s>Lo Spallanzani fece rispetto a questi quel <lb></lb>che avea fatto il Redi già rispetto agl&#039;insetti, e poniamo che fosse nell&#039;arte <lb></lb>sperimentale il valore dei due Naturalisti pari, parve nulladimeno il Profes­<lb></lb>sor di Pavia rimanere indietro al Medico aretino, per aver forse troppo con­<lb></lb>fidentemente creduto che il meccanico agitarsi dalle particelle, scioltesi dalle <lb></lb>materie infuse, fosse un moto vivace. </s></p><p type="main">

<s>Ma perchè non è lo scopo nostro quello di entrare in questioni, non <lb></lb>bene ancora definite o forse non definibili mai dalla scienza, faremo sog­<lb></lb>getto alla nostra storia un genere di animali, ch&#039;è per tale oggidì ben ri­<lb></lb>conosciuto, e che sta quasi di mezzo fra gl&#039;insetti propriamente detti e gli <pb xlink:href="020/01/1621.jpg" pagenum="496"></pb>infusorii; genere di animali ministro di quel lampeggiare di luce sull&#039;agi­<lb></lb>tata acqua marina, che fu un giorno il tormento della Filosofia antica, ed è <lb></lb>ora una gloria della moderna. </s>

<s>L&#039;esser poi questa gloria italiana ci ha con­<lb></lb>sigliato a scegliere, fra&#039;tanti altri che ci si presentavano innanzi, e tutti me­<lb></lb>ritevoli di storica trattazione, questo argomento, e a farlo risalire in fin là, <lb></lb>dove incomincia a ingrossare la sua sorgente. </s></p><p type="main">

<s>Volendo il Cartesio porre i principii della Filosofia a tutte le cose, an­<lb></lb>che più difficili a intendersi nella loro natura, com&#039;è la luce, non lascia <lb></lb>d&#039;adoprar la magica chiave del suo sistema ad aprire il mistero della fosfo­<lb></lb>rescenza marina. </s>

<s>Egli si confida di riuscirvi con gran facilità, dicendo che <lb></lb>le particelle rigide componenti l&#039;acqua, escono agili, commosse dalla tempe­<lb></lb>sta, a cacciare i globuli del secondo elemento, e così senz&#039;altro producono <lb></lb>quell&#039;apparenza di luce. </s>

<s>“ At in guttis aquae marinae, cuius naturam supra <lb></lb>explicuimus, facile est videre quo pacto lux excitatur. </s>

<s>Nempe dum illae <lb></lb>earum particulae, quae sunt flexiles, sibi mntuo manent implexae, aliae, quae <lb></lb>sunt rigidae ac laeves, vi tempestatis alteriusve cuiuslibet motus, ex gutta <lb></lb>excutiuntur et, spiculorum instar vibratae, facile ex eius vicinia globulos <lb></lb>secundi elementi expellunt, sicque lucem producunt ” (Principia Philos. </s>

<s><lb></lb>Amstelodami 1650, pag. </s>

<s>237). </s></p><p type="main">

<s>I Cartesiani avevano con gran docilità imbevuta, insieme con le altre <lb></lb>dottrine del Maestro, anche questa, ma i ritrosi di professar quella perico­<lb></lb>losa Filosofia confessavano piuttosto ingenuamente di non sapere intendere <lb></lb>come si potessero congiungere insieme due così contrari elementi, quali son <lb></lb>l&#039;acqua e il fuoco. </s>

<s>Quel languido e fuggitivo splendore però aveva, più che <lb></lb>di fuoco vero e di vera luce, sembianza di luce riflessa, ond&#039;è che il Bo­<lb></lb>relli, ricercando alle specchiate immagini l&#039;oggetto reale, riconobbe non si <lb></lb>potere in altro ritrovar che nelle stelle. </s>

<s>Troppo scarso nonostante parendo, <lb></lb>specie sotto ciel tempestoso, quel lume celeste, ricavò da certe sue sottilis­<lb></lb>sime osservazioni sul vapore vescicolare, che parvero nuove ad alcuni mo­<lb></lb>derni fisici stranieri, e da certe teorie ottiche apprese dagli scritti di Galileo <lb></lb>e dalla viva voce di Benedetto Castelli, la causa fisica della richiesta molti­<lb></lb>plicazione di quel fosforo marino, che, viaggiando una notte da Messina a <lb></lb>Catania, ed essendoglisi reso più che altre volte spettacoloso, lo indusse a <lb></lb>scriverne in questa forma a un amico: </s></p><p type="main">

<s>“ Del viaggio di Catania dovrei dir piuttosto i miei patimenti che l&#039;os­<lb></lb>servazioni fatte in quello, poichè io mi credevo sicuro di riportarne una in­<lb></lb>fermità pericolosissima, ma grazie a Dio me la sono passata con leggerissima <lb></lb>indisposizione. </s>

<s>Circa le osservazioni fatte nel navigare credo che mi sia suc­<lb></lb>cesso l&#039;avere intesa la cagione di un problema assai agitato, che è: onde <lb></lb>avvenga che nella notte più oscura, percotendosi il mare con li remi, ci si <lb></lb>vede un fulgore assai notabile. </s>

<s>Egli è indubitatamente riflessione del lume <lb></lb>delle stelle, mentre nel battere i remi nell&#039;acqua si conduce quantità d&#039;aria <lb></lb>nella profondità d&#039;essa acqua, la quale poi si risolve in minute particole, le <lb></lb>quali, circondate ognuna d&#039;acqua, pigliano figura sferica, e vanno lentamente <pb xlink:href="020/01/1622.jpg" pagenum="497"></pb>ascendendo verso la superfice dell&#039;aria. </s>

<s>E perchè da ognuna di queste sfe­<lb></lb>rette si suol riflettere all&#039;occhio il lume quasi di tutte le stelle, che ingom­<lb></lb>brano il nostro emisfero, ne avviene che la riflessione di tutta questa mol­<lb></lb>titudine di globetti, conducendosi all&#039;occhio, fa apparenza notabile. </s>

<s>” </s></p><p type="main">

<s>“ E ci è anco un altro particolare che, nello sbattere che si fa l&#039;acqua, <lb></lb>risaltano in aria moltitudine grande di stille d&#039;acqua, alcune delle quali, <lb></lb>com&#039;ho io diligentemente osservato, non solo mentre volano per la profon­<lb></lb>dità dell&#039;aria ritengono la figura sferica, ma anche arrivate che sono alla <lb></lb>superfice dell&#039;acqua ritengono per qualche tempo la medesima figura, prima <lb></lb>che confondersi col rimanente dell&#039;acqua, e ciò esser vero mi mostra il ve­<lb></lb>dere sdrucciolare questi medesimi globetti d&#039;acqua per qualche poco sopra <lb></lb>la superfice dell&#039;altr&#039;acqua. </s>

<s>Ora in questi, ne&#039;quali non so se ci sia inclusa <lb></lb>parte d&#039;aria, la riflessione si fa più che in altro vivacissima in modo, che <lb></lb>appariscono talvolta tanti carboncini accesi. </s>

<s>Intorno a che credo che ancora <lb></lb>lavori l&#039;accrescimento e moltiplicazione di lumi in essi globelti mercè della <lb></lb>rifrazione che si fa nel nostro occhio, come accade di tutti gli altri lumi <lb></lb>minuti, secondo la dottrina del Maestro. </s>

<s>Io non so se mi sono affrontato col <lb></lb>vero: lei parlando col padre don Benedetto se ne potrà assicurare ed avver­<lb></lb>tirmene della fallacia ” (MSS. Cim., T. XXV, c. </s>

<s>151). </s></p><p type="main">

<s>A scoprir la fallace applicazione delle bellissime e importantissime os­<lb></lb>servazioni fisiche qui descritte non c&#039;era per verità bisogno dell&#039;acume di <lb></lb>un Benedetto Castelli, essendo sufficiente notar che il mare non solo fosfo­<lb></lb>reggia, ma che fosforeggia anzi più vivamente, quando il cielo è privato di <lb></lb>stelle. </s>

<s>Cosicchè, anche quando si fosse divulgata questa ipotesi del Borelli, <lb></lb>non avrebbe facilmente riportata l&#039;approvazione dei Fisici, i quali si rima­<lb></lb>sero perciò intorno al curioso problema incerti, infin tanto che le recenti <lb></lb>scoperte elettriche non vennero colla loro solita baldanza a proporre una <lb></lb>nuova soluzione. </s></p><p type="main">

<s>Era un fatto, oramai da lunghe e non dubbie osservazioni confermato, <lb></lb>che il fosforeggiare è proprio di sole le ondose acque del mare, le quali, <lb></lb>perciocchè non si differenziano dalle dolci se non per i bitumi e per i sali, <lb></lb>che tengono in sè disciolti; fu perciò facile a pensare nient&#039;altro essere il <lb></lb>fosforo marino che una luce elettrica eccitata dal confricarsi insieme le par­<lb></lb>ticelle solide coll&#039;acqua stessa. </s>

<s>Fu primo a divulgare questo pensiero l&#039;Inno­<lb></lb>minato autore <emph type="italics"></emph>Dell&#039;elettricismo,<emph.end type="italics"></emph.end> il quale, avendo di più osservato che ri­<lb></lb>splendono allora l&#039;acque più vivamente, quando l&#039;aria soprastante è umida <lb></lb>e fredda, trovò in ciò una buona ragione da confermar la sua ipotesi col <lb></lb>dire ch&#039;essa aria umida si trova meglio disposta ad elettrizzarsi per comu­<lb></lb>nicazione, “ cioè più pronta a ricevere in sè la materia elettrica, che scappa <lb></lb>fuori ” (Napoli 1747, pag. </s>

<s>227). </s></p><p type="main">

<s>Riuscirono ai Fisici di que&#039;tempi queste dottrine così seducenti, che il <lb></lb>Franklin pensò di avvalorarle coll&#039;esperienze. </s>

<s>Prese una bottiglia d&#039;acqua, <lb></lb>v&#039;infuse sal marino, e si dette ad agitare fortemente il miscuglio. </s>

<s>Non vide <lb></lb>però farsi alcuna apparenza di luce, nè darsi altri segni di elettricismo, per <pb xlink:href="020/01/1623.jpg" pagenum="498"></pb>cui, ripetute l&#039;esperienze stesse più volte, e sempre trovandosi defraudato <lb></lb>della sua aspettazione, ebbe a concluderne che “ cette lumiere dans l&#039;eau <lb></lb>de la mer devoit être attribuée à quelques autres principes ” (Oeuvres, T. I, <lb></lb>Paris 1773, pag. </s>

<s>116). </s></p><p type="main">

<s>In quel tempo, che si pronunziava in faccia alla giovanile umiliata bal­<lb></lb>danza degli Elettricisti questa decisiva autorevole sentenza, Giuseppe Via­<lb></lb>nelli, medico di Chioggia e diligente osservatore dei fatti naturali, che gli <lb></lb>presentava a studiare la patria laguna, aveva già scoperto quel principio di <lb></lb>natura tutt&#039;affatto diversa dall&#039;elettrica, e in cui diceva il Franklin doversi <lb></lb>ricercar la causa della fosforescenza marina. </s>

<s>“ In una notte della state <lb></lb>del 1746, così racconta il Vianelli stesso la storia della sua scoperta, rac­<lb></lb>colsi con appropriato vaso buona quantità d&#039;acqua marina, ed in mia casa <lb></lb>avendola all&#039;oscuro riposta, osservai che, dibattuta e colle mie mani sovente <lb></lb>agitata, di questa brillantissima luce andava ricolma. </s>

<s>Poichè però la passai <lb></lb>per un panno lino ben tessuto, per quanto l&#039;andassi scotendo ed insieme <lb></lb>agitando, nientissimo affatto di cotal luce mandava fuori. </s>

<s>Tutta bensì la pri­<lb></lb>miera luce mi si rappresentava in minutissime particelle separata e divisa, <lb></lb>ed allo stesso panno lino attaccata. </s>

<s>Per la qual cosa ben francamente e fuor <lb></lb>d&#039;ogni dubbio potrei persuadermi che i luminosi corpiccioli erano qualche <lb></lb>cosa totalmente distinta dall&#039;acqua stessa. </s>

<s>” </s></p><p type="main">

<s>“ Mi rincrebbe allora altamente nell&#039;animo di non trovarmi in pronto <lb></lb>un de&#039;migliori vetri, che i piccoli oggetti vagliono ad ingrandire, per poter <lb></lb>subito farne paga la curiosità mia, rilevando che cosa mai questi <emph type="italics"></emph>fisici enti<emph.end type="italics"></emph.end><lb></lb>si fossero. </s>

<s>Cosa certamente che a cagione della loro piccolezza non mi riu­<lb></lb>scì con occhio disarmato di potere ottenere giammai, quantunque ben a <lb></lb>lungo aguzzassi le ciglia <emph type="italics"></emph>come vecchio sartor fa nella cruna. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Frattanto, avendo posto mente che i risplendenti corpicelli erano più <lb></lb>numerosi e vivaci sopra le foglie dell&#039;alga marina, un&#039;altra notte strappai <lb></lb>dal fondo dell&#039;acque una pianta dell&#039;alga stessa, la quale mi si diè subito <lb></lb>a divedere piena zeppa di questi brillantissimi lumicini. </s>

<s>Non ingrandisco <lb></lb>certo la cosa essendo che sopra una sola foglia di alga poteano contarsene <lb></lb>più di trenta. </s>

<s>Scuoter poi volli la foglia stessa, lusingandomi di poter al­<lb></lb>meno raccorne uno su d&#039;una bianca carta, che per quest&#039;uso avea apparec­<lb></lb>chiata. </s>

<s>Essendo che mi stava molto a cuore di farlo vedere agli amici miei <lb></lb>più cari, i quali dalle solite osservazioni mie mi stavano ansiosamente aspet­<lb></lb>tando. </s>

<s>” </s></p><p type="main">

<s>“ Nè dal divisato buon esito andò punto diversa la cosa. </s>

<s>Imperocchè <lb></lb>il luminoso corpicciolo sulla stessa carta raccolto, e fra le pieghe di quella <lb></lb>a bello studio nascosto, anche così rinserrato com&#039;erasi diede agli astanti <lb></lb>tutti a conoscere per la sua vaga luce, che da&#039;pori della carta mandava <lb></lb>fuori. </s>

<s>Del che poi ne potrebbe far certa testimonianza il signor Francesco <lb></lb>Cestari stimatissimo amico mio, e con esso lui moltissimi altri, che al gra­<lb></lb>zioso spettacolo furon presenti. </s>

<s>” </s></p><p type="main">

<s>“ Dispiegata poi la carta medesima, e diligentemente il lucidissimo cor-<pb xlink:href="020/01/1624.jpg" pagenum="499"></pb>picciolo riguardando, venni a scoprire che nella sua mole eguagliava appena <lb></lb>la metà d&#039;un sol pelo delle palpebre, che nel colore ad un croceo fosco <lb></lb>tendeva, e ch&#039;era d&#039;una assai tenera e fragil sostanza formato. </s>

<s>Buona sorte <lb></lb>però che allor mi trovava provveduto di un ottimo Microscopio, che per <lb></lb>quest&#039;uso a bella posta s&#039;era compiaciuto d&#039;inviarmi da Bologna l&#039;erudi­<lb></lb>tissimo signor dottore Pio Fantoni, dolcissimo amico mio, per mezzo del <lb></lb>quale potei rilevare che l&#039;esaminato brillantissimo lumicino si era un ele­<lb></lb>gante animaletto vivente. <emph type="italics"></emph>Io non potea da tal vista levarme,<emph.end type="italics"></emph.end> tanto egli mi <lb></lb>sembrava in tutte le sue parti e curioso e bizzarro. </s>

<s>E perciocchè sopra tutto <lb></lb>mi feriva la bella luce che tramandava fuori piacquemi di dargli il nome <lb></lb>di <emph type="italics"></emph>Cicindela<emph.end type="italics"></emph.end> o <emph type="italics"></emph>Luccioletta dell&#039;acqua marina ”<emph.end type="italics"></emph.end> (Nuove scoperte ecc., Ve­<lb></lb>nezia 1749, pag. </s>

<s>XVI-XX). </s></p><p type="main">

<s>Qui prosegue il Vianelli a descrivere la sua <emph type="italics"></emph>Luccioletta,<emph.end type="italics"></emph.end> ed è la de­<lb></lb>scrizione illustrata da due figure, impresse a tergo della pag. </s>

<s>XI della citata <lb></lb>Dissertazione. </s>

<s>Il Grisellini poi, tessendo una storia particolare dell&#039;insetto, <lb></lb>lo ridusse al genere delle Scolopendre, e gl&#039;impose il nome di <emph type="italics"></emph>Scolopendra <lb></lb>marina lucens<emph.end type="italics"></emph.end> (Observat. </s>

<s>sur le Scolopendre marine luisante. </s>

<s>Vened. </s>

<s>1751). <lb></lb>Tornò meglio provata da questa storia naturale l&#039;esistenza e la natura del <lb></lb>lucente insetto marino, così felicemente scoperto, ma perchè si potesse ra­<lb></lb>gionevolmente attribuire a lui, come a causa unica ed efficiente, la fosfore­<lb></lb>scenza della Laguna, rimaneva a sodisfare ancora a queste due domande: <lb></lb>prima perchè non fosforeggino altro che le acque del mare, e poi perchè <lb></lb>per lo più non fosforeggino quell&#039;acque stesse, se non che quando, o ad <lb></lb>arte come nel menare dei remi, o naturalmente, come nelle burrasche, ven­<lb></lb>gano agitate e sconvolte. </s></p><p type="main">

<s>Il Vianelli, studiando la storia naturale degl&#039;insetti scoperti, trovò modo <lb></lb>a rispondere adeguatamente ai due proposti quesiti, dimostrando che quei <lb></lb>marini animalucci non possono affatto vivere nell&#039;acque dolci, e che non <lb></lb>mandan luce al di fuori de&#039;loro corpiccioli, se non che quando o da in­<lb></lb>terne passioni o da esterni stimoli vengano in qualche modo irritati, cosic­<lb></lb>chè cessano di rappresentare il grazioso spettacolo, quando son morti. </s>

<s>Una <lb></lb>delle più concludenti fra le dimostrazioni sperimentali di questi fatti vien <lb></lb>così dall&#039;Autore stesso descritta in una sua lettera indirizzata da Chioggia, <lb></lb>ai dì 10 Settembre 1751, al conte Lodovico Barbieri: “ Ella avrà rilevato <lb></lb>di già dalla mia <emph type="italics"></emph>Dissertazione<emph.end type="italics"></emph.end> che questi piccoli viventi sono luminosi per <lb></lb>una certa agitazione o dibattimento delle parti de&#039;corpiccioli loro, e che <lb></lb>qualora si stanno quieti non mandano splendore di sorte. </s>

<s>Io adunque strap­<lb></lb>pai dal fondo della laguna buona quantità d&#039;alga pienissima di questi bril­<lb></lb>lantissimi insetti, e parte ne immersi subito in un vaso d&#039;acqua di fiume, <lb></lb>e parte in un altro d&#039;acqua marina. </s>

<s>Quella del primo vaso, appena che fu <lb></lb>attuffata nell&#039;acqua dolce, si fece luminosissima e costantemente per cinque <lb></lb>minuti conservò sempre la luce. </s>

<s>Se non che la luce medesima s&#039;andava <lb></lb>illanguidendo a poco a poco; e per modo che in cinque minuti s&#039;estinse <lb></lb>affatto. </s>

<s>Cosa che non mi successe di già nell&#039;altr&#039;alga posta nel secondo vaso <pb xlink:href="020/01/1625.jpg" pagenum="500"></pb>d&#039;acqua di mare, la quale si facea luminosa sol quando o io agitava l&#039;acqua, <lb></lb>o gli animaletti da se s&#039;agitavano, il che io ho potuto notare persino il giorno <lb></lb>dappoi. </s>

<s>” </s></p><p type="main">

<s>“ Che pare a Lei, illustrissimo signor mio, di questo grazioso feno­<lb></lb>meno? </s>

<s>Non si vede forse chiaramente che, dalla luce che mandano inces­<lb></lb>santemente le Lucciolette nell&#039;acqua dolce, sono in una continua molestis­<lb></lb>sima agitazione? </s>

<s>Che a misura che questo molesto ed improprio soggiorno <lb></lb>nell&#039;acqua dolce va togliendo loro la vita, vanno elleno svenendo e perdendo <lb></lb>co&#039;vitali moti la luce? </s>

<s>Non si vede forse, replico, fuor d&#039;ogni dubbio che <lb></lb>quelle povere bestiole nello spazio di cinque minuti si rimangono estinte <lb></lb>nell&#039;acqua dolce? </s>

<s>Io per me ne sono certo e persuaso del tutto. </s>

<s>E tanto più <lb></lb>perciocchè se, estinta che sia nell&#039;acqua dolce la luce dell&#039;alga, si voglia <lb></lb>tornare ad immergere l&#039;alga stessa nell&#039;acqua salsa, ella non acquista più <lb></lb>i primieri lumicini; segno evidentissimo che gli animaletti che cagionavano <lb></lb>la luce sono di già morti ” (Calogera, Raccolta di opuscoli, T. XLVII, Ve­<lb></lb>nezia 1752, pag. </s>

<s>336-38). </s></p><p type="main">

<s>Nell&#039;estate del 1749, quando avea già il Vianelli fatta da tre anni nelle <lb></lb>acque della Laguna la sua scoperta, soggiornava in Venezia il Nollet, il <lb></lb>quale, poco dopo ritornato a Parigi, raccontò a&#039;suoi che, maravigliato di <lb></lb>veder la notte lampeggiar l&#039;onde nel frangersi che facevano contro le mura <lb></lb>de&#039;palazzi veneti, e datosi a investigar di ciò la ragione, scoprisse che di­<lb></lb>pendeva da certi minutissimi insetti, de&#039;quali trovò gremite le foglie del­<lb></lb>l&#039;alga. </s>

<s>E perchè s&#039;era anche prima compiaciuto di una tale scoperta, nella <lb></lb>stessa Venezia, in casa il cardinale Quirini, e il Vianelli lo riseppe, nel pub­<lb></lb>blicar quella sua Dissertazione intitolata <emph type="italics"></emph>Nuova scoperta intorno le luci not­<lb></lb>turne delle acque marine, Venezia 1749,<emph.end type="italics"></emph.end> si lasciò nella prefazione uscir <lb></lb>dalla penna certe parole che venivano ad accusare il Nollet stesso di usur­<lb></lb>patore. </s>

<s>Dop&#039;avere ivi scritto esso Vianelli che non s&#039;era in tre anni riso­<lb></lb>luto ancora di stampar nulla, in proposito degli scoperti insetti fosforici, <lb></lb>impaurito dalle difficoltà che s&#039;incontrano da tutti coloro, i quali espongono <lb></lb>al pubblico giudizio i loro scritti; “ se non che, soggiunge, attrovandosi ai <lb></lb>passati mesi in Venezia il celebre signor abate Nollet, chiaro ornamento dei <lb></lb>Letterati francesi, e portando la congiuntura che seco lui tra&#039;virtuosi col­<lb></lb>loqui s&#039;intertenesse il nobil&#039;uomo signor Girolamo Giustiniani, al quale in <lb></lb>tempo del sempre glorioso suo reggimento di Chioggia essa scoperta mia <lb></lb>avea appalesata; egli non si recò a vile di umanamente ad esso signor Nol­<lb></lb>let significarla, invitandomi poscia con un molto cortese foglio perchè io vo­<lb></lb>lessi delle osservazioni mie qualche memoria recarne. </s>

<s>Posto adunque ogni <lb></lb>riguardo da parte, mi sono indotto, qualunque egli sia, esso scoprimento <lb></lb>mio a pubblicare ” (Nuove scoperte cit., pag. </s>

<s>X). </s></p><p type="main">

<s>Ma il Nollet, che pretendeva d&#039;essersi incontrato nella scoperta mede­<lb></lb>sima del Vianelli, senz&#039;averne avuto precedente avviso, nella XV delle <emph type="italics"></emph>Le­<lb></lb>zioni di Fisica<emph.end type="italics"></emph.end> che è <emph type="italics"></emph>Della luce,<emph.end type="italics"></emph.end> accennando l&#039;Autore ad alcuni insetti, che <lb></lb>consolan di lei infin le cupe acque del mare, “ una gran quantità se ne <pb xlink:href="020/01/1626.jpg" pagenum="501"></pb>vede, egli ivi scrive, sopratutto nelle lagune di Venezia, dovunque vi ha del <lb></lb>muschio o di quell&#039;erba, che <emph type="italics"></emph>alga marina<emph.end type="italics"></emph.end> vien detta. </s>

<s>Quivi ne feci la sco­<lb></lb>perta nel 1749, dopo di avere con grandissima sollecitudine ed assiduità ri­<lb></lb>cercato qual esser potesse la cagione di tanti fuochi, ch&#039;io vedeva brillar la <lb></lb>sera sotto a&#039;colpi de&#039;remi, all&#039;incontro delle gondole, e lungo le mura per­<lb></lb>cosse da&#039;flutti. </s>

<s>Io era già stato prevenuto, come il seppi dappoi, dal signor <lb></lb>Vianelli, dottore di medicina in Chioggia. </s>

<s>Si può vedere in un libretto, da <lb></lb>lui fatto stampare in Venezia alcuni mesi dopo la mia partenza, ed invia­<lb></lb>tomi dopo il mio ritorno in Francia. </s>

<s>In leggendo la prefazione di quest&#039;ope­<lb></lb>retta a pag. </s>

<s>10, potrebbe creder taluno che, in seguito alla relazione fattami <lb></lb>della scoperta del signor Vianelli, io avessi riconosciuto che la luce notturna <lb></lb>dell&#039;acqua di Venezia veniva cagionata dagl&#039;insetti. </s>

<s>Ma la verità si è che la <lb></lb>detta relazione non mi fu fatta se non dopo la mia osservazione, in casa <lb></lb>dell&#039;emin. </s>

<s>cardinal Quirini, ed alla presenza di otto o dieci persone, che me <lb></lb>ne renderebbono all&#039;occorrenza bonissima testimonianza. </s>

<s>Io son certo che <lb></lb>il signor Vianelli m&#039;avrebbe risparmiate queste parole, s&#039;egli avesse saputo <lb></lb>in qual modo eran passate le cose. </s>

<s>Anzi l&#039;avrei taciute io medesimo, quando <lb></lb>non avessi altro interesse che quello di conservarmi la parte, che posso avere <lb></lb>in questa scoperta. </s>

<s>Ma mi preme assaissimo che non si creda ch&#039;io me l&#039;ab­<lb></lb>bia voluta appropriare, come ragion si avrebbe di pensare, se fosse vero <lb></lb>ch&#039;io ne fossi stato istruito prima di osservare gl&#039;insetti luminosi, e se, <lb></lb>quando feci menzione della mia scoperta, nelle Memorie dell&#039;Accademia delle <lb></lb>scienze, 1759, pag. </s>

<s>50, non avessi resa sopra di ciò quella giustizia, che al <lb></lb>signor Vianelli si deve ” (Nollet, Lez. </s>

<s>di Fisica sperim., traduz. </s>

<s>ital., T. V, <lb></lb>Venezia 1762, pag. </s>

<s>20, 21). </s></p><p type="main">

<s>Dietro queste pubbliche e solenni dichiarazioni, che senza prove in con­<lb></lb>trario nessuno ha ragionevole diritto di credere menzognere, le accuse date <lb></lb>da alcuni scrittori italiani al Nollet sembrano a noi simili al prurito nella <lb></lb>gola di certi avvocati, che si fanno merito collo strepitoso declamare nella <lb></lb>causa dalle stesse parti già risoluta. </s>

<s>Che fosse poi la ragion del primato fra <lb></lb>gli stessi inventori già risoluta, non le parole sole nei riferiti documenti lo <lb></lb>attestano, ma lo attestano altresì, ciò che più importa, i fatti, non essendovi <lb></lb>nessuno, nemmeno fra gli stranieri, che dubitasse di riconoscere nella sco­<lb></lb>perta de&#039;fosforici insetti marini il primato del Vianelli. </s>

<s>Basti fra&#039;più cele­<lb></lb>bri di questi stranieri citare Carlo Linneo, il quale, in un suo opuscolo in­<lb></lb>titolato <emph type="italics"></emph>Noctiluca marina,<emph.end type="italics"></emph.end> incomincia a raccontare che, navigando per il <lb></lb>vasto e procelloso Mare chinese, si trovasse una notte co&#039;compagni in mezzo <lb></lb>alle acque così scintillanti, <emph type="italics"></emph>ut si in undis et flammis igneis navigaverimus.<emph.end type="italics"></emph.end><lb></lb>Poi soggiunge che nè a lui nè a nessun altro era ancora riuscito di sco­<lb></lb>prir la causa del portentoso spettacolo “ usque ad dominum Vianelli, qui <lb></lb>lumen hocce ex infinita minimorum vermium multitudine causari demon­<lb></lb>stravit ” (Upsaliao 1752, pag. </s>

<s>4). E di qui coglie il grand&#039;uomo occasione <lb></lb>a celebrare i Naturalisti italiani de&#039;suoi tempi, non degeneri dalle virtù dei <lb></lb>loro maggiori. </s></p><pb xlink:href="020/01/1627.jpg" pagenum="502"></pb><p type="main">

<s>Nacquero i dubbi piuttosto intorno alle applicazioni, che s&#039;intendeva <lb></lb>fare della scoperta, dicendo alcuni che delle frequenti e vive luci dell&#039;Oceano <lb></lb>non par che possano essere sufficiente causa que&#039;piccoli insetti, i quali ba­<lb></lb>stano ad accender l&#039;acqua fra gli angusti lidi e i bassi fondi della veneta <lb></lb>laguna. </s>

<s>Uno de&#039;primi fra noi ad accogliere questi dubbi fu il Beccaria, il <lb></lb>quale non rimase così vinto dall&#039;esperienze francliniane, che disperasse di <lb></lb>potere attribuire all&#039;elettricismo, fra le tante, anche questa nuova ingerenza <lb></lb>di render luminose le acque del mare, specialmente dell&#039;India, di cui il <lb></lb>Bourgez aveva descritti di poco gl&#039;insoliti splendori. </s>

<s>“ So bene (così scrive <lb></lb>in nota al cap. </s>

<s>VII della II parte dell&#039;<emph type="italics"></emph>Elettricismo naturale<emph.end type="italics"></emph.end>) simile luce <lb></lb>comparire altrove ancora. </s>

<s>Così nel 1707, navigando io da Savona a Livorno, <lb></lb>avvenne che una corda, con che la nostra barca era raccomandata e veleg­<lb></lb>giava d&#039;accordo con un&#039;altra barca, ogni volta che batteva l&#039;acqua secondo <lb></lb>tutta la lunghezza splendeva, e dava una luce veramente elettrica. </s>

<s>So inol­<lb></lb>tre che il diligente Vianelli da Chioggia ne ha esso il primo fatti divisare <lb></lb>gl&#039;insetti, che nella laguna di Venezia eccitano di notte una simile luce, ma <lb></lb>dalla relazione del p. </s>

<s>Bourgez pare ne risulti che nell&#039;Oceano tale luce sia <lb></lb>oltremodo frequente e viva, e che non debbasi altrimenti attribuire a simili <lb></lb>insetti ” (Torino 1753, pag. </s>

<s>217). </s></p><p type="main">

<s>Lo Spallanzani però, prima di terminare il cap. </s>

<s>XXVII de&#039;suoi <emph type="italics"></emph>Viaggi <lb></lb>alle due Sicilie,<emph.end type="italics"></emph.end> dove descrive le meduse fosforiche dello Stretto di Mes­<lb></lb>sina, dal ragionar della luce, che manda fuori un marino animale, prende <lb></lb>occasione di commemorare le lucciole scoperte nella laguna veneta dal Via­<lb></lb>nelli, e dice d&#039;aver di esse lucciole scoperto altre cinque specie nel medi­<lb></lb>terraneo, presso alla riviera di Genova. </s>

<s>Riferite poi le osservazioni proprie, <lb></lb>fatte intorno a queste nuove specie d&#039;insetti, così, terminando il capitolo, <lb></lb>soggiunge: “ Intanto dalle riferite osservazioni concludo non essere la sola <lb></lb>laguna di Venezia albergatrice di questi minutissimi viventi fosforici, ma sì <lb></lb>ancora il Mare ligustico e quello della Sicilia, e per dirlo innanzi tratto <lb></lb>eziandio l&#039;Arcipelago, il mare di Marmara, lo stretto di Costantinopoli <lb></lb>e il mar Nero, come apparirà dal mio <emph type="italics"></emph>Viaggio ”<emph.end type="italics"></emph.end> (Tomo III, Milano 1826, <lb></lb>pag. </s>

<s>38). </s></p><p type="main">

<s>Le scoperte dello Spallanzani insomma conferirono alla completa riso­<lb></lb>luzione di quel problema avviato dal Vianelli, e per cui fu rivelato alla <lb></lb>scienza il mistero della fosforescenza dei mari. </s>

<s>Ma l&#039;accresciuta famiglia degli <lb></lb>insetti splendenti accrebbe anche il desiderio di saper la causa e l&#039;origine <lb></lb>di cotesti vivi splendori, ond&#039;è che l&#039;istituto della nostra storia ci consiglia <lb></lb>a trattenerci brevemente, per dire quali fossero le prime esperienze e le <lb></lb>prime notizie indi raccolte intorno a que&#039;notissimi insetti che, svolazzando <lb></lb>nelle serate estive sui nostri campi, furono da qualche arguto ingegno ras­<lb></lb>somigliati alle stelle di questo basso cielo. </s></p><p type="main">

<s>Abbiamo certissimi documenti che quelle prime esperienze sopra le luc­<lb></lb>ciole terrestri furono istituite nell&#039;Accademia del Cimento, in quell&#039;ultimo <lb></lb>periodo, che non fu punto meno operoso degli altri, come basterebbero a <pb xlink:href="020/01/1628.jpg" pagenum="503"></pb>provarlo le cose che siam per dire, quando pure mancassero quegli argo­<lb></lb>menti da noi altrove accennati. </s>

<s>L&#039;occasione di sperimentare le lucciole nel <lb></lb>vuoto venne al cardinale Leopoldo dei Medici dalla notizia di una esperienza <lb></lb>del Boyle, diffusa in Italia dalla <emph type="italics"></emph>Gazzetta letteraria di Roma;<emph.end type="italics"></emph.end> la quale boie­<lb></lb>liana esperienza consisteva nel sottoporre le carni fosforescenti di alcuni pe­<lb></lb>sci alla campana della macchina pneumatica, e nel mostrar ch&#039;estratta l&#039;aria <lb></lb>si perde da esse carni ogni luminosa apparenza. </s>

<s>I nostri Accademici dun­<lb></lb>que riscontrarono il fatto nel vuoto torricelliano, di che sodisfattissimo il <lb></lb>Principe dava la lieta nuova al Borelli, in una lettera scritta sulla fine del <lb></lb>Giugno 1669 e indirizzata a Messina. </s>

<s>Il Borelli rispondeva il seguente 2 Lu­<lb></lb>glio: “ Rallegromi sommamente dell&#039;esperienza del Boyle, che V. A. ha <lb></lb>fatto confrontare, la quale veramente è mirabile e di gran conseguenza ” <lb></lb>(MSS. Cim., T. XIX, c. </s>

<s>263). Ma perchè, non recapitata questa responsiva <lb></lb>a Firenze, il Principe dubitò fosse andata smarrita la sua missiva, tornò a <lb></lb>scrivere il dì 25 Luglio “ per ogni caso che fosse andata male una lettera <lb></lb>che le scrissi per saper nuova di sua salute e di quello che sta operando. </s>

<s><lb></lb>Scrivo parte delle stesse cose .... che sono il desiderio d&#039;aver qualche par­<lb></lb>ticolare informazione delli accidenti del fuoco di Catania. </s>

<s>In oltre le diedi <lb></lb>conto di una esperienza fatta in Inghilterra e rifatta qui da me, la quale è <lb></lb>che mettendosi un pezzetto di pesce o interiora di quelle ch&#039;essendo vicine <lb></lb>a infradiciarsi fanno lume da sè stesse, dato il solito strumento del vacuo <lb></lb>e facendosi la consueta operazione di quello che comunemente si dice il <lb></lb>vacuo, il lume del pesce si perde, e facendo appresso un piccolo foro per <lb></lb>introdurvi l&#039;aria, all&#039;ingresso di quella, di nuovo ritorna a splendere il pez­<lb></lb>zetto di pesce. </s>

<s>Ed io ho già fatto l&#039;esperienza con un pezzetto di pesce <lb></lb>spada. </s>

<s>” </s></p><p type="main">

<s>“ Mi venne poi in mente di fare l&#039;esperienza stessa con le lucciole, le <lb></lb>quali ancora nel vuoto persero il lume. </s>

<s>È ben vero che all&#039;istante dell&#039;in­<lb></lb>trodursi dell&#039;aria si alluminò per brevissimo tempo tutto il vaso, ed io du­<lb></lb>bitando che questo splendore potesse procedere che, nel ricevere le lucciole <lb></lb>la consolazione del ritorno dell&#039;aria, facessero moto nel quale scoprissero la <lb></lb>parte luminosa, rifeci l&#039;esperienza, mettendo dentro nel vaso tutte le luc­<lb></lb>ciole morte, e nondimeno successe l&#039;istessa istantanea illuminazione del vaso <lb></lb>nell&#039;atto dell&#039;introdurre l&#039;aria per il solito piccolo foro formato da uno spillo. </s>

<s><lb></lb>Or è da sapersi di più che, dopo questa illuminazione, il lume che hanno <lb></lb>le lucciole è rimasto, sempre che si è fatta l&#039;operazione, meno vivace, ma <lb></lb>con tale differenza che non si è potuto mettere in dubbio che non sia così. </s>

<s><lb></lb>Questa è una esperienza facile e galante, ma tale che io credo che meriti <lb></lb>che vi si faccia riflessione ” (MSS. Cim., T. XXIII, c. </s>

<s>171, 72). </s></p><p type="main">

<s>Che avesse il Boyle notizia di queste fiorentine esperienze non ci sono <lb></lb>nè prove nè congetture, ma è certo in ogni modo che l&#039;esperienze inglesi <lb></lb>sopra le lucciole nel vuoto son di qualche anno posteriori alle nostre. </s>

<s>Si <lb></lb>trovano infatti non descritte prima che negli Esperimenti nuovi <emph type="italics"></emph>circa re­<lb></lb>lationem inter aerem et flammam vitalem animalium,<emph.end type="italics"></emph.end> a fine di confutar <pb xlink:href="020/01/1629.jpg" pagenum="504"></pb>l&#039;errore di coloro che, fautori di essa fiamma vitale, l&#039;additavano nel ven­<lb></lb>tre delle lucciole agli occhi degl&#039;increduli viva e vera. </s></p><p type="main">

<s>L&#039;istituto boileiano era importantissimo per sè medesimo, perchè ten­<lb></lb>deva a illustrare la teorica della respirazione, ma tornava altresì accidental­<lb></lb>mente importante, per il modo di fare il vuoto, diverso da quello tenuto <lb></lb>dagli Accademici fiorentini, d&#039;onde venivano a ricevere notabili varietà le <lb></lb>stesse osservazioni. </s>

<s>Nel vuoto torricelliano infatti la sparizione e la riappa­<lb></lb>rizione della luce erano istantanee, mentre nel vuoto boileiano si vedeva a <lb></lb>ogni colpo di stantuffo mirabilmente spengersi un grado di quel primiero <lb></lb>splendore. </s>

<s>“ Ad ipsam primam exsuctionem fieri coepit admodum manifesta <lb></lb>lucis diminutio, quae gradatim caliginosior evasit prout aer magis educeba­<lb></lb>tur, donec eadem tandem prorsus evanuit ” (Operum, T. III, P. II, Vene­<lb></lb>tiis 1697, pag. </s>

<s>170). E in altro esperimento: “ Per gradus aerem intromi­<lb></lb>simus et cum uno alterove intervallo ad observandum, ut et a nobis factum, <lb></lb>quod sicut diminutio lucis continuo maior erat, prout aer magis ac magis <lb></lb>exsugebatur; sic etiam rediens splendor gradatim intensior fiebat, quando <lb></lb>nobis libebat aerem magis ac magis in vermes immittere ” (ibid.). </s></p><p type="main">

<s>E qui vorremmo trattenerci più a lungo in una considerazione impor­<lb></lb>tante. </s>

<s>I Nostri fecero quasi sempre uso dello strumento torricelliano, piut­<lb></lb>tosto che della macchina boileiana, per mostrare di non aver bisogno di <lb></lb>ricorrere agli stranieri. </s>

<s>E poniamo che non fosse questo uno de&#039;più vir­<lb></lb>tuosi propositi albergati nell&#039;animo degli Accademici fiorentini, giovò nono­<lb></lb>stante alla scienza, trattandosi specie di sperimentare la vita degli animali, <lb></lb>la qual vita dipendere dall&#039;aria più ne&#039;polmonati che negli insetti veniva <lb></lb>efficacemente dimostrato da quel rimanere a un tratto e non a poco a poco <lb></lb>il recipiente esausto. </s>

<s>Il Boyle stesso provocato a rispondere al quesito se <lb></lb>giovasse meglio servirsi dello strumento torricelliano o del suo, confessò, nel <lb></lb>proemio agli Esperimenti nuovi <emph type="italics"></emph>circa relationem inter flammam et aerem,<emph.end type="italics"></emph.end><lb></lb>che trattandosi di piccoli corpi, operando a modo degl&#039;Italiani, “ exhaustio <lb></lb>expediri potest maiori cum celeritate et consequenter efficere ut effectus sit <lb></lb>magis conspicuus, quam usitata nostra experiendi via ” (Opsrum, T. III cit., <lb></lb>pag. </s>

<s>145). Ma trattandosi di corpi di non piccola mole, affermava il Boyle <lb></lb>esser molto più comodo servirsi della sua Macchina, nella quale dall&#039;altra <lb></lb>parte si può render quanto si vuole spedita l&#039;esaustione col diminuire la <lb></lb>capacità del recipiente. </s>

<s>Or perchè il Borelli non poteva negare che, ne&#039;casi <lb></lb>contemplati dal Boyle, la Macchina di lui s&#039;avvantaggiava sullo strumento <lb></lb>torricelliano, si dette, per non rimanere indietro, a immaginar quello ch&#039;ei <lb></lb>chiama <emph type="italics"></emph>Strumento del gran vacuo,<emph.end type="italics"></emph.end> e ch&#039;ei particolarmente descrive al prin­<lb></lb>cipe Leopoldo in una lettera da Messina, responsiva a quella, nella quale il <lb></lb>Principe stesso gli riferiva l&#039;esito dell&#039;esperienze fatte in Firenze sopra le <lb></lb>carni fosforescenti, e sopra il lume delle lucciole. </s>

<s>“ Io ebbi l&#039;onore della <lb></lb>lettera di V. A. delli 11 Giugno (1669), alla quale risposi la settimana se­<lb></lb>guente prolissamente intorno agli accidenti dell&#039;incendio di Catania, e di più <lb></lb>vi accompagnai una pianta a disegno delle montagne di detta città..... <pb xlink:href="020/01/1630.jpg" pagenum="505"></pb>Avevo io letto nella <emph type="italics"></emph>Gazzetta letteraria di Roma<emph.end type="italics"></emph.end> l&#039;esperienza del signor <lb></lb>Boyle, e mi pareva veramente mirabile, e però desideravo sommamente di <lb></lb>confrontarla, sicchè può giudicare quanta consolazione io abbia avuto, sen­<lb></lb>tendo che l&#039;A. V. l&#039;abbi sperimentata nella sua eruditissima Accademia, e <lb></lb>poi con tante belle circostanze di più di quelle che aveva osservato il Boyle: <lb></lb>però vorrei di nuovo supplicarla che ne facesse un&#039;altra con la pietra lu­<lb></lb>cifera di Bologna..... Ma perchè il modo antico di fare il vuoto, in vasi <lb></lb>grandi, è difficile e richiede lungo tempo, potrebbe l&#039;A. V. comandare che <lb></lb>si adoprasse lo strumento inventato da me ” e che il Borelli passa imme­<lb></lb>diatamente a descrivere. (MSS. Cim., T. XIX, c. </s>

<s>267). </s></p><p type="main">

<s>Forse anche queste esperienze furono eseguite dai Fiorentini nella loro <lb></lb>Accademia, ma per non dilungarci di più dal nostro argomento, ritorniamo <lb></lb>sopra quelle parole, colle quali il cardinale Leopoldo terminava di descri­<lb></lb>vere le sue esperienze sopra le lucciole, dicendo ch&#039;elle si meritavano <emph type="italics"></emph>vi si <lb></lb>facesse sopra reflessione.<emph.end type="italics"></emph.end> Il Borelli stesso riconobbe ch&#039;era cosa di <emph type="italics"></emph>gran <lb></lb>conseguenza,<emph.end type="italics"></emph.end> e ciò non per altro se non perchè veniva di li luce a scoprir <lb></lb>la natura del misterioso fosforo animale, vedendosi avere anche questo come <lb></lb>la fiamma bisogno dell&#039;alimento dell&#039;aria. </s>

<s>Ma la ignorata chimica della com­<lb></lb>bustione troncò il volo alle filosofiche riflessioni del cardinale Leopoldo, e <lb></lb>arrestò il corso a quelle scientifiche conseguenze, dalle quali sentivasi tra­<lb></lb>sportata la mente del sagace Borelli. </s></p><p type="main">

<s>Benchè sentisse pur troppo queste difficoltà anche il Malpighi, ei si con­<lb></lb>fidò nonostante che il suo microscopio e la perita arte, che oramai trovavasi <lb></lb>in mano, di sezionare gl&#039;insetti, gli avrebbero almeno in parte rivelato il <lb></lb>mistero. </s>

<s>Trovò che la sede del lume era nelle lucciole limitata alle due <lb></lb>estreme incisure del ventre, attraverso alle quali, con ritmo simile a quello <lb></lb>del cuore, si vedono frequentemente apparire e sparire i fulgori. </s>

<s>Talvolta, <lb></lb>benchè sia l&#039;animale integro e vivo, è pure spento d&#039;ogni suo lume, ma <lb></lb>emergono da un recondito succo certe bollicelle rotonde e lucide, le quali <lb></lb>ora si dissipano, e ora moltiplicandosi all&#039;improvviso fanno corruscare tutt&#039;a <lb></lb>un tratto la loro congerie, presso a poco come vampa, che si sollevi da un <lb></lb>mucchio di granelli di polvere pirica incendiata. </s>

<s>“ Vigente splendore, tre­<lb></lb>pidatio quaedam minimarum particularum evidenter observatur. </s>

<s>Extructus <lb></lb>huiusmodi succus ab animali adhuc lucet, absque tamen periodica corusca­<lb></lb>tione et si comprimatur ita ut lacteus ichor loco moveatur, lumen extendi­<lb></lb>tur et intenditur, et tamdiu durat lux quamdiu exaratus succus fluidus per­<lb></lb>manet, unde exsiccatus lumine orbatur. </s>

<s>Succus hic immersus aqua, aceto <lb></lb>et spiritu vini lumen conservat, sed diutius et intensius in aere lucet. </s>

<s>Splen­<lb></lb>dor in expositis animalculis succedit Maii mense et Junii medietate, qua <lb></lb>transacta, sensim deficit ” (Opera posthuma, Londini 1697, pag. </s>

<s>85). </s></p><p type="main">

<s>Descritti così gli organi della fosforescenza nelle lucciole, soggiunge to­<lb></lb>sto il Malpighi d&#039;aver con sua grande maraviglia scoperta una simile strut­<lb></lb>tura, e forse anco più evidente, nelle Farfalle. </s>

<s>“ Analogam structuram, et <lb></lb>forte evidentiorem, in consimilibus animalculis, pyraustis scilicet, vulgo <emph type="italics"></emph>Far-<emph.end type="italics"></emph.end><pb xlink:href="020/01/1631.jpg" pagenum="506"></pb><emph type="italics"></emph>falle<emph.end type="italics"></emph.end> dictis, admiratus sum ” (ibid.). E da ciò forse, più efficacemente che <lb></lb>dalle osservazioni della marchesa Sessi, fu indotto lo Spallanzani a studiare <lb></lb>la fosforescenza negli occhi delle stessse Farfalle. </s>

<s>I caratteri di questo fo­<lb></lb>sforo nuovamente scoperto son dal Traduttore della <emph type="italics"></emph>Contemplazione della <lb></lb>Natura<emph.end type="italics"></emph.end> ridotti a quattro, e così esposti in una nota illustrativa del testo: <lb></lb>“ I. </s>

<s>Il fosforo si manifesta tanto per la luce del giorno, quanto per quella <lb></lb>della candela, e ciò qualor la farfalla è vigorosa, perchè in caso diverso si <lb></lb>scopre il fosforo con la seconda luce, e non con la prima. </s>

<s>Anzi qualche <lb></lb>volta fa d&#039;uopo, essendo la farfalla languida, coprir con la mano il chiaro <lb></lb>della candela, se vuol vedersi detto fosforo. </s>

<s>E qui avvertasi come questo ca­<lb></lb>rattere distingua il fosforo presente dagli altri scoperti dal celebre Beccari, <lb></lb>la maggior parte de&#039;quali ha bisogno per risplendere dell&#039;immediato lume <lb></lb>del sole, e talor questo non basta. </s>

<s>Di più il fosforo delle farfalle è visibile <lb></lb>anche in mezzo alla luce, laddove i fosfori beccariani, per fare impressione <lb></lb>nell&#039;occhio, sogliono esigere interissima oscurità. </s>

<s>II. </s>

<s>La luce del fosforo è <lb></lb>accesa e tira al color di bragia pallida. </s>

<s>III. </s>

<s>Il fosforo non apparisce che negli <lb></lb>occhi delle farfalle vive. </s>

<s>Almeno di tante esaminate, dop&#039;essere state morte, <lb></lb>una sola ha dato qualche indizio di luce, lo che dà a temere che forse morta <lb></lb>non fosse interamente. </s>

<s>IV. </s>

<s>Gli occhi di tutte le farfalle non sono fosforici, <lb></lb>per quanto sinora si è rilevato, ma solamente quelli, che a proporzione della <lb></lb>grandezza degli occhi sono grossi, protuberanti e d&#039;un sol colore che tende <lb></lb>al nero. </s>

<s>” (Tomo I cit., pag. </s>

<s>83, 84). </s></p><p type="main">

<s>Ma se allo Spallanzani, quando scriveva queste note al Bonnet, per non <lb></lb>dire al Malpighi, che notomizzava gl&#039;insetti un secolo prima, fosse stato do­<lb></lb>mandato qual&#039;è la natura di così fatta luce animale, avrebbero questo solo <lb></lb>potuto rispondere: che è, a somiglianza delle luci artificiali, alimentata dal­<lb></lb>l&#039;aria, per cui nel vuoto, come fu primo a sperimentare il cardinale Leo­<lb></lb>poldo de&#039;Medici, anch&#039;essa si spenge. </s>

<s>Perchè però non sapevasi a que&#039;tempi <lb></lb>quali intime relazioni passassero fra l&#039;aria stessa e la fiamma, la combu­<lb></lb>stione diventava anche più misteriosa, trovandosi complicata colle più re­<lb></lb>condite funzioni della vita. </s></p><p type="main">

<s>Dall&#039;altra parte il principio della fiamma vitale, dall&#039;esperienze del Boyle, <lb></lb>e da più ragionevoli ipotesi proposte intorno all&#039;azion dell&#039;aria sul sangue, <lb></lb>era stato oramai relegato nel mondo delle follie, cosicchè non fa meravi­<lb></lb>glia se in tanta incertezza si rivolgessero gli occhi desiderosi a quell&#039;elet­<lb></lb>tricismo, che il Beccaria destramente ripose nel vuoto, rimasto fra le dot­<lb></lb>trine de&#039;Filosofi antichi. </s>

<s>Come questi infatti vedevano con gli occhi proprii <lb></lb>ardere attraverso alle trasparenti membrane delle lucciole la fiamma in­<lb></lb>teriore della vita; così il Beccaria vedeva con gli occhi proprii, nello splen­<lb></lb>dor di que&#039;medesimi insetti, il vapore elettrico, in cui s&#039;accende a ogni es­<lb></lb>sere animato la vita. </s>

<s>“ Quella luce di fosforo, che brilla in certe parti di <lb></lb>alcuni insetti, e che in alcuni non si fa vedere che alternativamente in certo <lb></lb>alternativo movimento del loro corpicciolo, non ne mostrerebbe in essi e <lb></lb>l&#039;esistenza e generalmente alcuna azione del vapore suddetto? </s>

<s>E questo va-<pb xlink:href="020/01/1632.jpg" pagenum="507"></pb>pore, che probabilmente esiste ed opera in tutti gli animali, non rendereb­<lb></lb>besi solo visibile in quelli, che avesssero alcune parti diafane, e in che si <lb></lb>potesse esso scorgere mentre si vibra attraverso ad esse parti meno elettri­<lb></lb>che per comunicazione, come scorgesi a lucere similmente il rado vapore <lb></lb>che attraversa un sottile strato di acqua? </s>

<s>” (Dell&#039;elettricismo cit., pag. </s>

<s>217). </s></p><p type="main">

<s>Tanto è ardente nell&#039;uomo la sete de<gap></gap> sapere che, se non trova acqua <lb></lb>da estinguerla, s&#039;acquieta in appressar le labbra anche a un arido sasso, <lb></lb>che specchi in sè gli oggetti come una fonte! </s></p><pb xlink:href="020/01/1633.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO XIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle piante<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle principali funzioni nutritive: delle forze concorrenti a produr l&#039;ascesa dei succhi; dell&#039;azione <lb></lb>e delle proprietà delle foglie. </s>

<s>— II. </s>

<s>Del circolo della linfa, e della respirazione. </s>

<s>— III. Dell&#039;uf­<lb></lb>ficio de&#039;fiori, della distinzione dei sessi, e della fecondazione dei semi. </s>

<s>— IV. </s>

<s>Della germina­<lb></lb>zione: dell&#039;uso dei lobi e delle foglie seminali: dell&#039;azione dell&#039;aria e de&#039;semi posti a ger­<lb></lb>mogliare nel vuoto. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi la passata storia commemorando ripensa a quell&#039;opinione dei Fi­<lb></lb>losofi antichi, ripullulata nel Redi, e secondo la quale si credeva possibile <lb></lb>che partecipasse la polpa vegetabile ai vermi il sentimento e la vita, già <lb></lb>conclude fra sè che dovessero quegli stessi Antichi far precellere, nelle na­<lb></lb>turali dignità, le piante agli insetti. </s>

<s>La maestosa sublimità degli alberi, il <lb></lb>decoro delle fronde, la gentilezza dei fiori, la soavità dei frutti erano dal­<lb></lb>l&#039;altra parte una continua attestazione all&#039;uomo, e quasi un documento, <lb></lb>messogli tutti i giorni a leggere sotto gli occhi, di quella nobiltà, di che <lb></lb>avea voluto, a preferenza degli abietti vermiccioli schifosi, insignir le piante <lb></lb>la munificente Natura. </s></p><p type="main">

<s>Non potevano nonostante que&#039;Filosofi negare a sè medesimi che il giu­<lb></lb>dizio, dato dell&#039;eccellenza di esseri immobili sopra i semoventi, non fosse, <lb></lb>meglio considerato, per apparire illusorio, e se ne sarebbero forse non dif­<lb></lb>ficilmente ricreduti, quando non avessero nelle piante stesse intraveduta una <lb></lb>viva immagine di quegli organi della vita animale, che non discernevano, <lb></lb>nè credevan possibili a riscontrarsi nella informe e compendiosa struttura <pb xlink:href="020/01/1634.jpg" pagenum="509"></pb>degl&#039;insetti. </s>

<s>Mentre questi infatti rappresentavansi ai loro occhi come una <lb></lb>particella di materia, che si muove da sè senza esser mossa, riconoscevano <lb></lb>nella terra l&#039;utero, nelle radici le vene, nel bulbo radicellare il cervello e <lb></lb>il cuore, nel midollo del tronco l&#039;asse cerebro spinale, e perfino i muscoli <lb></lb>stessi nelle fibre legnose. </s>

<s>Vedere la radicella andare in cerca dell&#039;alimento <lb></lb>industriosa, i rami sporgere verso la luce del sole desiderosi le braccia, e le <lb></lb>foglie mostrarsi spesso ritrose che altri le tocchi, parevano indizi certi di <lb></lb>una volontà elettiva, di un moto di desiderio nella ricerca del bene, di un&#039;at­<lb></lb>tenta e sollecita fuga dalle molestie. </s></p><p type="main">

<s>Il grazioso apologo s&#039;applica mirabilmente al nostro intelletto, il quale <lb></lb>anch&#039;egli, come gli alberi, non allega in frutto, se non è preceduto dal fiore. </s>

<s><lb></lb>E giacchè per frutto s&#039;intende le idee, e per fiore l&#039;immaginazione, la sto­<lb></lb>ria che siamo per accennare nel presente capitolo nient&#039;altro fa che dimo­<lb></lb>strar col fatto come, nelle immaginate analogie fra gli organi della vita ani­<lb></lb>male e quelli della vita vegetativa, allegasse via via il frutto della Fisiologia <lb></lb>delle piante. </s></p><p type="main">

<s>Incominciano per noi le istituzioni della nuova scienza da Andrea Ce­<lb></lb>salpino, il quale, sul declinar del secolo XVI, pubblicando i suoi XVI libri <lb></lb><emph type="italics"></emph>De plantis,<emph.end type="italics"></emph.end> trattava delle funzioni della loro vita, comparandole a quelle <lb></lb>degli animali. </s>

<s>“ Natura venarum, son fra le prime parole ch&#039;egli scrive, <lb></lb>quae alimentum ex ventre hauriunt, ut illud in universum corpus distri­<lb></lb>buant, aliqua in parte respondere videtur cum plantarum radicibus; nam <lb></lb>similiter hae ex terra, tamquam ex ventre cui implantantur, trahunt alimen­<lb></lb>tum ” (Florentiae 1583, pag. </s>

<s>1). Ma perchè le radici portano le raccolte so­<lb></lb>stanze nutritizie a concocersi nei ventricoli del cuore, non son di cuore perciò <lb></lb>sfornite nemmeno le piante, le quali lo hanno anzi opportunamente collo­<lb></lb>cato fra la radice e il tronco, come fra le membra superiori e le inferiori <lb></lb>lo hanno gli animali, in mezzo al loro corpo, convenientemente disposto. </s>

<s>E <lb></lb>perciocchè in questi il sangue è dal cuore stesso dispensato alle membra, <lb></lb>per via delle arterie; così a dispensar la linfa ricorrono per il tronco e per <lb></lb>i rami degli alberi vasi simili agli arteriosi. </s>

<s>Il Cesalpino, che non aveva an­<lb></lb>cora strumenti da poterli osservare con gli occhi, argomenta alla necessaria <lb></lb>esistenza di questi vasi, indifferentemente chiamati col nome di vene, dal <lb></lb>fatto delle viti tagliate o delle recise piante lattigginose. </s>

<s>“ Venas quoque <lb></lb>datas esse plantis, licet exiguas, argumento sunt illae quae lacte manant, <lb></lb>ut tithymalorum genus, et ficus .... quod et in vite maxime contingit, sed <lb></lb>propter meatuum exiguitatem cospici nequaquam possunt ” (ibid., pag. </s>

<s>4). </s></p><p type="main">

<s>Se non che rimaneva in queste analogie una cosa importantissima a <lb></lb>dimostrare: qual si fosse cioè la forza impulsiva della linfa, che sostituisce <lb></lb>la forza impulsiva del sangue. </s>

<s>A tale effetto richiamavasi il Cesalpino ai suoi <lb></lb>principii di fisiologia animale, secondo i quali non vien tanto al sangue l&#039;im­<lb></lb>pulso dai moti di sistole del cuore, quanto dall&#039;effervescenza del calore in­<lb></lb>nato. </s>

<s>Or di questo stesso calore innato non vuol che ne sia defraudato il cuore <lb></lb>della pianta, perchè il non rendersi a noi sensibile non è, egli dice, buona <pb xlink:href="020/01/1635.jpg" pagenum="510"></pb>ragione a negarlo. </s>

<s>“ Quamvis autem sensui immanifestus sit calor, non ob <lb></lb>id negandum est: quae enim minus calida sunt, quam tactus noster, frigida <lb></lb>iudicantur ” (ibid.). </s></p><p type="main">

<s>Ammessa dunque nella ceppaia dell&#039;albero l&#039;esistenza di un calore in­<lb></lb>nato, e osservando che non sono i canaliculi radicellari liberi e andanti come <lb></lb>le vene, ma tutti ingombri di villosità nel loro interno calibro, cosicchè il <lb></lb>liquido non sale in essi a modo che ne&#039;tubetti di vetro, ma a somiglianza <lb></lb>di quel che vede farsi ai canapi attorti; rassomiglia il Cesalpino l&#039;attra­<lb></lb>zione, che fan del succo nutritizio le radici dall&#039;utero della madre terra, <lb></lb>all&#039;attrazion dell&#039;olio fatta dal lucignolo di una lampada accesa. </s>

<s>“ Idcirco <lb></lb>eae non, ad venarum similitudinem, meatu quodam continuo perviae sunt, <lb></lb>sed potius instar nervorum ex villosa constant substantia. </s>

<s>Sic enim bibula <lb></lb>earum natura continue humorem ad principium caloris innati ducit, ut in <lb></lb>lucernarum luminibus videmus, funiculo enim quodam utuntur, quo oleum <lb></lb>continue ad flammam ducatur ” (ibid.). </s></p><p type="main">

<s>Concotti i succulenti umori nelle ceppaie, come il chilo nel cuore, deb­<lb></lb>bono per i vasi del tronco risalire su ai rami e alle foglie. </s>

<s>E qui invocasi <lb></lb>dal Cesalpino per questo moto di ascesa una forza simile alla precedente, se <lb></lb>non che il centro del calore attrattivo è su in alto, ne&#039;germi che si svol­<lb></lb>gono, e nei frutti che maturano, aggiuntovi il calore esterno del sole. </s>

<s>Così, <lb></lb>poi soggiunge, si spiega perchè comincino le piante ad andare in succhio, <lb></lb>quando germogliano di primavera, e continuino tutta l&#039;estate, infintanto che <lb></lb>non abbiano i loro frutti maturi. </s>

<s>“ Adiuvat autem hunc motum caliditas <lb></lb>innata humorem affluentem absumens in germina et fructus: necesse est <lb></lb>enim alium subinde consequi, absumpto priori, ob easdem causas, ut hi fa­<lb></lb>ciunt, qui penicillo in humore imposito ut altera eius pars extra vas pro­<lb></lb>pendeat, humorem a feculentia secernunt..... Ob id plantae pleraeque vere <lb></lb>et estate germinant magis et fructus edunt, quia a calore externo augetur <lb></lb>humoris attractio ” (ibid., pag. </s>

<s>4, 5). </s></p><p type="main">

<s>Nell&#039;allegar delle idee, ci si permetta anche questa volta l&#039;immagine, <lb></lb>che consuona dall&#039;altra parte col soggetto del discorso, avvien quello stesso <lb></lb>che nell&#039;allegare de&#039;fiori: le più esterne foglie e più appariscenti cadono e <lb></lb>vanno disperse, mentre le più riposte rimangono per trasformarsi nell&#039;ova­<lb></lb>rio e nel frutto. </s>

<s>Vedremo in seguito di queste cesalpiniane dottrine qual <lb></lb>fosse quella loro parte, che felicemente allegò nella scienza: ora è da notar <lb></lb>la sorte di que&#039;petali lussuriosi, che si dissiparono dal vento contrario alla <lb></lb>Filosofia peripatetica. </s>

<s>Il calore innato nel cuor della pianta fu quello appunto, <lb></lb>ch&#039;ebbe primo a subir questa sorte, tolto il qual calore all&#039;ipotesi del Ce­<lb></lb>salpino, veniva tutto insieme anche tolta la causa efficente dell&#039;ascesa del <lb></lb>succo dalle radici al tronco e alle fronde, come cessa il fluir dell&#039;olio at­<lb></lb>traverso al lucignolo, spenta che sia la fiamma della lucerna. </s></p><p type="main">

<s>Vero è bene che, avendo forse presentito il Cesalpino l&#039;insorgere di co­<lb></lb>loro, i quali gli sarebbero venuti a negare il calore nelle piante innato, per­<lb></lb>chè non si rende come negli animali sensibile al tatto; invocava sussidiario, <pb xlink:href="020/01/1636.jpg" pagenum="511"></pb>a spiegare il continuo moto di ascesa del succo, il fatto del vaso che si vuota <lb></lb>attraverso alle fila di un <emph type="italics"></emph>penicillo,<emph.end type="italics"></emph.end> come attraverso a un sifone, che travasi <lb></lb>il liquido con flusso non interrotto. </s>

<s>Ma a rispondere che questo era, a con­<lb></lb>ferma della proposta ipotesi, troppo debole aiuto, bastava semplicemente os­<lb></lb>servare, come poi fece il Borelli che, troncato il ramo a un albero, il succo <lb></lb>tuttavia stilla dalla cicatrice anche supina, mentre il penicillo non travasa <lb></lb>se, risalito all&#039;orlo del vaso, non ripiega in basso gli stillanti suoi stami. </s></p><p type="main">

<s>Sgombrate dunque le idee peripatetiche, non rimaneva a riconoscersi <lb></lb>dai seguaci del Cesalpino altra vera causa naturale dell&#039;ascesa del succo <lb></lb>nelle piante che il calore del sole. </s>

<s>Ma quale si fosse il modo dell&#039;operare di <lb></lb>questa causa non fu prima insegnato che nella privata scuola di Galileo. </s>

<s><lb></lb>Raccontano i biografi di lui ch&#039;e&#039;si tratteneva a coltivare di sua propria <lb></lb>mano l&#039;orticello attiguo alla sua casa di Arcetri, e di varii fatti, osservati <lb></lb>nella vita e nelle passioni delle piante, si studiava di ritrovare le fisiche ra­<lb></lb>gioni. </s>

<s>Uno di questi fatti per esempio sarebbe quello che “ alcune volte, <lb></lb>dopo una nebbia, scoprendosi il sole, le foglie di vite ed altre frondi diven­<lb></lb>gono aride e si seccano ” di che nel problema VII (Alb. </s>

<s>XIV, 328) dà Ga­<lb></lb>lileo una tale spiegazione, che fu nel secolo XVIII applicata da alcuni a ren­<lb></lb>dere la ragione de&#039;perniciosi effetti, che producono sui teneri polloni le <lb></lb>sferette del ghiaccio, quando appena son ferite dai raggi del sole. (Spallan­<lb></lb>zani, Pref. </s>

<s>alla traduzione della <emph type="italics"></emph>Contemplazion della Natura,<emph.end type="italics"></emph.end> T. </s>

<s>I cit., <lb></lb>pag. </s>

<s>29, 30). Concetto galileiano, inspiratogli dall&#039;Alighieri (Purg. </s>

<s>XXV, <lb></lb>v. </s>

<s>77), prolissamente illustrato dal Magalotti, e ripetuto con ammirazione da <lb></lb>tanti, perchè par che trovi nella moderna Chimica il suo commento, è che <lb></lb>“ il vino è un composto di umore e di luce ” (Magalotti, Lett. </s>

<s>scientif., Fi­<lb></lb>renze 1721, pag. </s>

<s>36-57). Ma più originalità e più sicurezza di scienza è in <lb></lb>quei dimostrati principii meccanici intorno alla resistenza dei solidi allo spez­<lb></lb>zarsi, ne&#039;quali trovò Galileo stesso la ragione del perchè un filo di paglia <lb></lb>sostenga una spiga più grave di tutto il gambo (Alb. </s>

<s>XIII, 145). </s></p><p type="main">

<s>Quel che però, in queste galileiane applicazioni delle forze fisiche alla <lb></lb>storia delle piante, si riferisce più strettamente all&#039;argomento, e di che dianzi <lb></lb>facevasi cenno, è la spiegazione del modo come operi il calor del sole sui <lb></lb>succhi nutritivi circolanti nel tronco e ne&#039;rami. </s>

<s>Chi si rammemora l&#039;espe­<lb></lb>rienza della caraffella, il lungo e sottilissimo collo della quale riceve più o <lb></lb>men di quell&#039;acqua in che tiene immersa la bocca, intende quanto fosse fa­<lb></lb>cile a sovvenire al pensiero di Galileo che il calor del sole produca nella <lb></lb>linfa delle piante un effetto molto analogo a quello, che produce nel Ter­<lb></lb>mometro ad aria. </s>

<s>Le ragioni particolari poi di così fatta analogia furono me­<lb></lb>glio spiegate e largamente diffuse ne&#039;suoi insegnamenti orali da Benedetto <lb></lb>Castelli, primo ad aprire in Roma una scuola di vera Fisica sperimentale, <lb></lb>nella quale il Borelli attesta, come fra poco vedremo, di avere attinti i prin­<lb></lb>cipii alla ragion meccanica del nutrirsi le piante e del germogliare. </s></p><p type="main">

<s>Di questa nuova scienza dei vegetabili, ch&#039;ebbe gl&#039;inizii da&#039;familiari <lb></lb>colloqui di Galileo già vecchio col Castelli, non è rimasto altro documento <pb xlink:href="020/01/1637.jpg" pagenum="512"></pb>che quello raccolto fra&#039;<emph type="italics"></emph>Pensieri<emph.end type="italics"></emph.end> galileiani, e in cui, per analogia dello <emph type="italics"></emph>Stru­<lb></lb>mento,<emph.end type="italics"></emph.end> e supposto esser le piante e i loro prodotti composti di vescicole o <lb></lb>di otricelli, come fu poi dimostrato vero dall&#039;anatomia del Malpighi, si rende <lb></lb>la ragion del crescere e del maturare le uve, i fichi, i pomi granati. </s>

<s>“ L&#039;uva <lb></lb>è composta di grani, o vogliamo dire vesciche, e questo si vede apparente­<lb></lb>mente nell&#039;uva, dove ogni grano è una vescica. </s>

<s>Il simile ne&#039;pomi granati, <lb></lb>fichi, cocomeri ed altri; onde tali vesciche, essendo piene di umore, venendo <lb></lb>il caldo del sole, le spreme e sgonfia, e mandano fuori parte di quell&#039;umore, <lb></lb>onde la sera son passe. </s>

<s>Ma nel sopraggiunger la notte e raffreddarsi l&#039;aria, <lb></lb>tali vesciche si vengono a riempire di nuovo umore, e maggior di quello <lb></lb>che il giorno avanti avevano mandato fuori, onde esse vesciche vengono a <lb></lb>molto più farsi capaci, e&#039;per questa alterazione si maturano, facendo l&#039;istesso <lb></lb>effetto che fa lo <emph type="italics"></emph>Strumento ”<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIV, 335). </s></p><p type="main">

<s>Secondo questa ipotesi la circolazione del succo nelle piante non sa­<lb></lb>rebbe dunque continua, ma si farebbe per accessi e per recessi, all&#039;alter­<lb></lb>narsi dei gioni e delle notti, com&#039;ora accede ora recede per cause simili il <lb></lb>liquido nello Strumento, ossia nel Termometro ad aria. </s>

<s>L&#039;ipotesi del Cesal­<lb></lb>pino corrispondeva meglio al fatto naturale, ma vedemmo da quali ragioni <lb></lb>Galileo e il Castelli, avversi alla Filosofia peripatetica, fossero indotti a ri­<lb></lb>fiutarla. </s>

<s>L&#039;avea per quelle stesse ragioni rifiutata pure un collega del Ca­<lb></lb>stelli, troppo presto rapito dalla morte agl&#039;incrementi delle scienze sperimen­<lb></lb>tali, Niccolò Aggiunti, il quale nonostante molto bene conobbe che il succo <lb></lb>vegetativo aveva impulso più simile a quello che fa ascendere l&#039;olio nel lu­<lb></lb>cignolo, che non all&#039;altro per cui l&#039;acqua va e viene nello Strumento. </s>

<s>Una <lb></lb>cosa sola però lo riteneva dal professar liberamente l&#039;ipotesi cesalpiniana, <lb></lb>ed era il credere con tutti gli altri che fosse il liquido nella lucerna attratto <lb></lb>in virtù del calor della fiamma. </s>

<s>Ma quando esso Aggiunti scoprì la vera <lb></lb>causa fisica universale di cotesti fenomeni di capillarità nel <emph type="italics"></emph>moto occulto<emph.end type="italics"></emph.end> del­<lb></lb>l&#039;acqua, non dubitò di applicarla alla vegetazion delle piante, lieto di poter <lb></lb>sostituire all&#039;immaginario calore innato la realtà di una causa fisica, e per <lb></lb>la quale veniva ad aversi del fatto una spiegazione più verosimile di quella <lb></lb>stessa insegnata dal Castelli o da Galileo. </s></p><p type="main">

<s>Ammessa insomma l&#039;esistenza de&#039;vasi capillari nel tronco delle piante, <lb></lb>il succo nutritizio, secondo l&#039;Aggiunti, vi ascende, non attratto dal calore <lb></lb>innato o dal calore del sole, ma per un moto occulto nell&#039;acqua e da cui <lb></lb>dipende altresì la ragione del “ perchè bisogni applicare nei nesti i surculi <lb></lb>e gemme, che corrispondano co&#039;lor meati a quelli del ramo innestato, e <lb></lb>l&#039;umore subentra in essi. </s>

<s>Ond&#039;ei non è maraviglia se, colla medesima di­<lb></lb>ligenza fatti, alcuni nesti si attaccano ed altri no, perchè, secondo che pochi <lb></lb>o molti meati, per i quali ha da passare il nutrimento, corrisponderanno con <lb></lb>quelli della pianta innestata, dalla quale vien somministrato il succo nutri­<lb></lb>tivo; succederà il fatto ” (Nelli, saggio di storia letter., Lucca 1759, pag. </s>

<s>95). </s></p><p type="main">

<s>Questa prima scoperta di fisica molecolare subì l&#039;infelice sorte del suo <lb></lb>Autore, rimanendo anch&#039;essa morta e seppellita co&#039;manoscritti di lui. </s>

<s>Quando <pb xlink:href="020/01/1638.jpg" pagenum="513"></pb>poi tornò a rivivere nell&#039;Accademia del Cimento, vedremo come l&#039;escludesse <lb></lb>il Borelli da ogni ingerenza nella fisiologia delle piante. </s>

<s>Intanto, oltrepas­<lb></lb>sata di poco la prima metà del secolo XVII, i germi di quella nuova scienza <lb></lb>fisiologica, posti da Galileo, dal Castelli e dall&#039;Agguinti, si videro a un tratto <lb></lb>in Italia e fuori giungere a maraviglioso incremento, quasi come all&#039;improv­<lb></lb>viso cader di una pioggia estiva sopra le inaridite zolle di un campo già <lb></lb>seminato. </s></p><p type="main">

<s>Furono cotesti maravigliosi effetti operati nel campo della nuova scienza <lb></lb>dalla Micrografia, quando l&#039;Ottica seppe fabbricare strumenti più squisiti, e <lb></lb>i laboriosi esercizi educaron l&#039;arte di bene usarli. </s>

<s>In Italia avevano dato i <lb></lb>Lincei i primi esempi, e in Italia, dove Eustachio Divini e Giuseppe Cam­<lb></lb>pani erano artefici peritissimi, ebbe la Fitologia microscopica la sua prima <lb></lb>e più sapiente cultura. </s>

<s>Federigo Cesi e Fabio Colonna si erano trattenuti <lb></lb>ad esaminar l&#039;esterna superfice de&#039;petali e delle foglie, per dedur di lì più <lb></lb>sicure note caratteristiche a distinguere la varietà delle piante: Marcello <lb></lb>Malpighi volle penetrare più addentro ad esaminar di tutte le parti, dalla <lb></lb>radice al tronco, dall&#039;arido seme al germoglio già sviluppato, l&#039;intima tes­<lb></lb>situra, per passar dalla notizia degli organi a investigare i misteri della vita <lb></lb>vegetativa. </s></p><p type="main">

<s>Ebbero principio questi suoi studi mentr&#039;era professore a Messina, e <lb></lb>gli venne l&#039;occasione d&#039;applicarvisi, trattenendosi spesso in campagna a vil­<lb></lb>leggiar col visconte Giacomo Ruffo. </s>

<s>“ Ruri interdum, racconta nell&#039;Auto­<lb></lb>biografia, non longe ab urbe, in villa illustrissimi vicecomitis d. </s>

<s>d. </s>

<s>Jacobi <lb></lb>Ruffi morans, plantarum structuram rimabar, et ibidem, in frustulo ligni <lb></lb>castaneae, ampli occurrere ductus aeris, seu <emph type="italics"></emph>tracheae,<emph.end type="italics"></emph.end> quas in aliis etiam <lb></lb>vegetabilibus adesse comperi. </s>

<s>Quare tantae rei clarissimum Borellum monui, <lb></lb>qui die XXVII aprilis 1663 haec mihi rescripsit: <emph type="italics"></emph>La ringrazio della repli­<lb></lb>cata sperienza delle fistole dell&#039;aria nelle piante. </s>

<s>L&#039;ho anch&#039;io fatta, ma <lb></lb>però la vista non mi aiuta. </s>

<s>Io però credo che siano l&#039;istesse fistole che <lb></lb>portano l&#039;umore e l&#039;aria e non differenti, fintantochè l&#039;esperienza non <lb></lb>mi dimostri altrimenti ”<emph.end type="italics"></emph.end> (Opera posthuma, P. I, Londini 1697, pag. </s>

<s>25). </s></p><p type="main">

<s>Lieto della scoperta delle trachee, occorsagli felicemente, com&#039;abbiamo <lb></lb>udito, nella primavera del 1663, si dette il Malpighi ad esaminare col mi­<lb></lb>croscopio degli alberi e dell&#039;erbe ogni parte, cosicchè nel 1671 avea tutta <lb></lb>esplorata la composizione anatomica delle piante, di cui dette in poche pa­<lb></lb>gine un&#039;<emph type="italics"></emph>Idea<emph.end type="italics"></emph.end> alla R. </s>

<s>Società di Londra. </s>

<s>Il segretario Enrico Holdenburg, <lb></lb>ricevute da Bologna le carte sottosignate il dì primo di Novembre di quel­<lb></lb>l&#039;anno 1671, rispondeva al Malpighi sotto il dì 14 Dicembre appresso, lo­<lb></lb>dandogli altamente, a nome delì&#039;Accademia, l&#039;opera, ed esortandolo a pro­<lb></lb>seguirla. </s>

<s>“ Hoc interim celare te nolim, vir praestantissime, poi soggiunge <lb></lb>lo stesso Segretario, quendam e societate regia Virum medicum nostratem, <lb></lb>idem illud argumentum tractandum suscepisse, quinimo ea qua hora, quod <lb></lb>forte miraberis, qua scriptum tuum a me proferebatur, libellum suum an­<lb></lb>glice iam editum laudatae Societati exhibuisse, in quo <emph type="italics"></emph>Plantarum anato-<emph.end type="italics"></emph.end><pb xlink:href="020/01/1639.jpg" pagenum="514"></pb><emph type="italics"></emph>men<emph.end type="italics"></emph.end> tum ab ipso arcessit semine, tum, singulis earum partibus earumque <lb></lb>vegetandi ratione consideratis, cum semine claudit ” (Epist. </s>

<s>circa tractatus <lb></lb>De Anat. </s>

<s>plant., Malpighi, Op. </s>

<s>omnia, T. I, Lugd. </s>

<s>Batav. </s>

<s>1687, pag. </s>

<s>164). </s></p><p type="main">

<s>Quel Medico inglese, a cui qui si accenna, era Neemia Grew, il quale <lb></lb>presentava stampato alla Società anglicana il suo libro <emph type="italics"></emph>The anathomy of <lb></lb>vegetlabes begun<emph.end type="italics"></emph.end> in quel medesimo giorno che il Malpighi presentava il ma­<lb></lb>noscritto della sua <emph type="italics"></emph>Anatomes plantarum idea.<emph.end type="italics"></emph.end> L&#039;opera inglese, divisa in <lb></lb>sette capitoli, ne&#039;quali, come abbiamo udito dire all&#039;Oldenburg, dal seme <lb></lb>che germoglia si giunge al frutto che allega, percorrendo tutto il ciclo della <lb></lb>vita vegetativa; fu poco dopo tradotta in latino col titolo di <emph type="italics"></emph>Anatomiae ve­<lb></lb>getabilium primordia,<emph.end type="italics"></emph.end> e inserita nelle Effemeridi de&#039;<emph type="italics"></emph>Curiosi della Natura<emph.end type="italics"></emph.end><lb></lb>in Germania, in appendice all&#039;anno VIII della I Decuria. </s></p><p type="main">

<s>Del fortuito incontro ce ne maravigliamo ora noi, ma più ebbero a far­<lb></lb>sene maraviglia gli Autori. </s>

<s>Il Malpighi, curiosissimo di vedere il libro del <lb></lb>suo concorrente, l&#039;ebbe nell&#039;originale inglese dopo il Marzo del 1672, e nei <lb></lb>primi giorni di Ottobre rispondeva d&#039;esserselo fatto da un suo amico tra­<lb></lb>durre in latino, e di averne inteso quanto faceva bisogno. </s>

<s>“ Gaudeo inte­<lb></lb>rim, poi soggiungeva, me cum accuratissimo Viro in quamplurimis obser­<lb></lb>vationibus et placitis convenire: reliqua autem, in quibus intercedere aliquid <lb></lb>diversitatis videtur, ulteriori instituta indagine, solertius examinabo, ne, quae <lb></lb>tanti Viri aciem effugere, illusione quadam languidae meae imponant fanta­<lb></lb>siae ” (ibid., pag. </s>

<s>166). </s></p><p type="main">

<s>Forse avrebbe il Grew con la pubblicazione del suo primo libro tenuta <lb></lb>l&#039;opera dell&#039;Anatomia delle piante per assoluta, e si sarebbe dolcemente <lb></lb>riposato sotto l&#039;ombra de&#039;conquistati allori, se il Malpighi, che operosamente <lb></lb>attendeva a colorire la sua proposta <emph type="italics"></emph>Idea,<emph.end type="italics"></emph.end> non fosse, con gli acuti stimoli <lb></lb>dell&#039;emulazione, venuto a turbargli i riposi. </s>

<s>Riguardando perciò anch&#039;egli, <lb></lb>il Grew, il suo libro come un&#039;<emph type="italics"></emph>Idea,<emph.end type="italics"></emph.end> o come i <emph type="italics"></emph>Primordii<emph.end type="italics"></emph.end> di ciò, che sarebbe <lb></lb>poi da fare nel larghissimo campo aperto; si propose, per non rimanere in­<lb></lb>dietro al Malpighi, di tornare all&#039;esame anatomico delle singole parti com­<lb></lb>ponenti le piante, e delle radici, del tronco, delle foglie, de&#039;fiori, de&#039;frutti e <lb></lb>de&#039;semi scrivere via via, di ciascuno, distintamente un trattato. </s></p><p type="main">

<s>Nel 1673 pubblicò in Londra il discorso fitologico delle radici col ti­<lb></lb>tolo <emph type="italics"></emph>An idea of a phytological hystory of roots,<emph.end type="italics"></emph.end> che i <emph type="italics"></emph>Curiosi della Na­<lb></lb>tura<emph.end type="italics"></emph.end> tradussero in latino col titolo <emph type="italics"></emph>Idea historiae phytologicae cum conti­<lb></lb>nuatione anatomiae vegetabilium, speciatim in radicibus,<emph.end type="italics"></emph.end> e che poi inse­<lb></lb>rirono in appendice agli anni IX e X della prima Decuria. </s>

<s>Nella prefazione <lb></lb>il Grew tocca cose riguardanti il Malpighi, delle quali, perchè sono impor­<lb></lb>tantissimo documento di storia, non bibliografica solo, ma che più importa <lb></lb>scientifica, trascriveremo nella sua integrità il discorso, come ce lo tradus­<lb></lb>sero gli Accademici leopoldini. </s></p><p type="main">

<s>“ Immediate ab harum publicatione (delle sette parti cioè in ch&#039;era <lb></lb>stato distinto il libro dei <emph type="italics"></emph>Primordii<emph.end type="italics"></emph.end>) discursus a doctissimo Malpighio, cu­<lb></lb>ius ingeniosissimae et accuratae industriae mundus obstrictissimus tenetur, <pb xlink:href="020/01/1640.jpg" pagenum="515"></pb>oblatus est regiae Societati de eodem subiecto 7 Dec. </s>

<s>1671, scriptus Bono­<lb></lb>niae 1° Nov. </s>

<s>1671. Cuius suffragio laetabar me videre veritatem observatio­<lb></lb>num mearum in universum omnium confirmatam, dum eius parum admo­<lb></lb>dum a meis differunt, licet ipse nbique usus fuerit Microscopio. </s>

<s>Exempli <lb></lb>gratia quod vasa aerea, quae illi dicuntur fistulae spirales, licet diu abhinc <lb></lb>eorum habuerim notitiam, utpote quae cum reliquis longe ampliora sint, fa­<lb></lb>cilius deteguntur, modum tamen spiralis eorum conformationis, nonnisi per <lb></lb>Microscopium observabilis, primo ab ipso didici, qui elegantissimam eorum <lb></lb>descriptionem dedit. </s>

<s>Quasdam suas <emph type="italics"></emph>De usu partium oeconomico<emph.end type="italics"></emph.end> cogitatio­<lb></lb>nes non comunicat. </s>

<s>Et nonnulla observatione digna de partibus floris, fructus <lb></lb>et seminis, ibi non reperiunda, ipsum inter alia secum reservasse possibile <lb></lb>est. </s>

<s>Optarem animitus edidisset suum Discursum, sed quoniam non vult an­<lb></lb>tequam ornatus sit figuris, ea de ratione aequum mihi visum est haec de <lb></lb>illo admonere ” (Acta Curios, Naturae Dec. </s>

<s>I, Ann. </s>

<s>IX et X, app. </s>

<s>Norim­<lb></lb>bergae 1674, pag. </s>

<s>104, 5). </s></p><p type="main">

<s>Quel che in questa storia concerne la scoperta delle trachee è veris­<lb></lb>simo, e vedremo in altra occasione il Grew addurre i documenti necessari <lb></lb>per dimostrarlo. </s>

<s>Ma in paragonare il rimanente dell&#039;opera sua con quella <lb></lb>del poderoso rivale gli molce l&#039;animo una dolce lusinga, incoratagli dalla <lb></lb>manifesta ragion del primato. </s>

<s>Quando infatti, ambedue seguitando d&#039;eserci­<lb></lb>tarsi nella medesima gloriosa palestra, si trovò il Grew stesso dal Malpighi <lb></lb>precorso, e allora quella prima compiacenza della concordia fra le idee si <lb></lb>trasformò nella sollecitudine di fare apparir tra loro un&#039;aperta discordia. </s></p><p type="main">

<s>Mentre intanto l&#039;Anatomico inglese presentava alla reale Società ma­<lb></lb>noscritto il suo III libro <emph type="italics"></emph>The anatomy of tuncks,<emph.end type="italics"></emph.end> dava il nostro Italiano, <lb></lb>il dì 20 Agosto 1674, una lettera all&#039;Oldenburg, con la quale della sua <emph type="italics"></emph>Ana­<lb></lb>tome plantarum<emph.end type="italics"></emph.end> accompagnavagli manoscritta la maggior parte trattante <lb></lb><emph type="italics"></emph>De cortice, De partibus caulem vel caudicem componentibus, De caudicis <lb></lb>augmento et nodis, De gemmis, De foliis, De floribus, De seminum gene­<lb></lb>ratione, De uterorum augmento et ipsorum succedente forma,<emph.end type="italics"></emph.end> e finalmente <lb></lb><emph type="italics"></emph>De secundinis et contento plantarum foetu.<emph.end type="italics"></emph.end> Non avendo però avuto ancora <lb></lb>della fatta spedizione il riscontro, tornava a scrivere il dì 27 Settembre ap­<lb></lb>presso: “ Mensis iam elapsus est, ex quo Anatomiam plantarum cum ico­<lb></lb>nismis capsula conclusam ad Ill.um Dom.um Ablegatum, Venetiis morantem, <lb></lb>transmisi, ut tibi tuta et opportuna occasione reddatur. </s>

<s>Tuis epistolis adeo <lb></lb>me sollicitatum vidi ut imperfectum, necdum absolutum, opus transmittere, <lb></lb>decreverim. </s>

<s>Plura enim <emph type="italics"></emph>De seminum vegetatione, Gallis, Radicibus et Spi­<lb></lb>nis<emph.end type="italics"></emph.end> delineanda mihi supersunt ” (Malp. </s>

<s>et Oldenb. </s>

<s>epistolae variae, Operum <lb></lb>T. </s>

<s>I cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Non molti mesi dopo, dato ordine anche a questi trattati, furono per la <lb></lb>medesima via spediti da Bologna a Londra. </s>

<s>Veniva così, per le due distinte <lb></lb>spedizioni, l&#039;opera malpighiana divisa in due parti, ma si comprende bene <lb></lb>come non era quella una divisione logica, avendo l&#039;Autore, sollecitato dalle <lb></lb>promesse e dagli stimoli dell&#039;emulazione, mandati prima quei quaderni, il <pb xlink:href="020/01/1641.jpg" pagenum="516"></pb>soggetto de&#039;quali non avea bisogno d&#039;ulteriore studio per parte dell&#039;Autore, <lb></lb>e per parte dell&#039;Artista era già terminato d&#039;illustrare dai relativi iconismi. </s></p><p type="main">

<s>Esaminati dall&#039;Accademia cotesti quaderni manoscritti, si consegnarono <lb></lb>al tipografo, il quale, tenuta la divisione delle due parti, com&#039;era venuta <lb></lb>fatta dalle due diverse consegne del procaccia veneto, gli compose secondo <lb></lb>gli venivano a mano, e gli dette in Londra alla luce nel 1675, senza che <lb></lb>fosse l&#039;opera manuale diretta da nessuna amorosa intelligenza. </s>

<s>Ebbe di qui <lb></lb>origine quel disordine, che si lamenta da tutti, e di che si può giustamente <lb></lb>rimproverar l&#039;Oldenburg e i suoi colleghi. </s></p><p type="main">

<s>Il leydese editore di tutte le Opere del Malpighi, raccogliendo nel primo <lb></lb>Tomo l&#039;Anatomia delle piante, si volle provare a dar miglior ordine ai di­<lb></lb>versi trattati, ma avendo anch&#039;egli mantenuta la prima duplice accidental <lb></lb>partizione, non s&#039;avvide come veniva in ogni modo l&#039;opera con tal disegno, <lb></lb>che avea, non solo dell&#039;informe, ma del mostruoso. </s>

<s>Si chiude infatti col <lb></lb>trattato <emph type="italics"></emph>De radicibus,<emph.end type="italics"></emph.end> rappresentando un albero capovolto in selva scompi­<lb></lb>gliata dalla tempesta. </s></p><p type="main">

<s>Se avesse l&#039;Oldenburg, prima di consegnare al tipografo il manoscritto, <lb></lb>consultato l&#039;Autore, forse avrebbe il Malpighi prescritto un tal ordine ai suoi <lb></lb>trattati. </s>

<s>Nel primo, <emph type="italics"></emph>Anatomes plantarum Idea,<emph.end type="italics"></emph.end> e <emph type="italics"></emph>De seminum vegetatione,<emph.end type="italics"></emph.end><lb></lb>che l&#039;assomiglierebbero al primo libro del Grew; nel secondo, <emph type="italics"></emph>De radici­<lb></lb>bus,<emph.end type="italics"></emph.end> che farebbe esatto riscontro col II libro dell&#039;Anatomia inglese; nel <lb></lb>terzo, <emph type="italics"></emph>De cortice, De partibus caulem, vel caudicem componentibus, De <lb></lb>caudicis augmento et nodis,<emph.end type="italics"></emph.end> soggetti di trattazioni, che rientrano nel III li­<lb></lb>bro <emph type="italics"></emph>Of trunks;<emph.end type="italics"></emph.end> nel quarto <emph type="italics"></emph>De gemmis, De foliis, De floribus, De seminum <lb></lb>generatione,<emph.end type="italics"></emph.end> distintamente delineati nel IV libro greviano. </s></p><p type="main">

<s>L&#039;Embriologia malpighiana descritta nelle dissertazioni <emph type="italics"></emph>De uterorum <lb></lb>augmento, et ipsorum succedente forma, De secundinis et contento plan­<lb></lb>tarum foetu;<emph.end type="italics"></emph.end> la Patologia, di che s&#039;ha un saggio insigne ne&#039;discorsi <emph type="italics"></emph>De <lb></lb>gallis, De variis plantarum tumoribus et excrescentiis;<emph.end type="italics"></emph.end> l&#039;Anatomia degli <lb></lb>organi accessorii e trasformati <emph type="italics"></emph>De pilis et spinis, De capreolis et consimi­<lb></lb>libus vinculis,<emph.end type="italics"></emph.end> e all&#039;ultimo quella più importante parte e più nuova <emph type="italics"></emph>De <lb></lb>plantis quae in aliis vegetant,<emph.end type="italics"></emph.end> non trovano ne&#039;trattati del Grew confronto, <lb></lb>per cui verrebbe, infin dell&#039;indice, quando specialmente fossero le materie <lb></lb>bene ordinate, a rivelarsi la maggiore estensione, che sopra quella dell&#039;ln­<lb></lb>glese ha l&#039;opera anatomica del Nostro. </s></p><p type="main">

<s>Alla pubblicazione di questa successe pochi mesi dopo la pubblicazione <lb></lb>della III parte di quella, col titolo <emph type="italics"></emph>The anatomy of trunks,<emph.end type="italics"></emph.end> tradotta dai <emph type="italics"></emph>Cu­<lb></lb>riosi della Natura,<emph.end type="italics"></emph.end> col titolo <emph type="italics"></emph>Comparativa anatomia truncorum.<emph.end type="italics"></emph.end> Dedicando <lb></lb>l&#039;Autore al presidente Brouncker il suo libro, torna per la seconda volta a <lb></lb>parlare in pubblico del Malpighi, la compiuta opera del quale si studiava <lb></lb>di comparare alla sua non ancora perfetta. </s>

<s>Rivendicava a sè la scoperta <lb></lb>delle trachee, delle quali nel cap. </s>

<s>II dei Primordii avea data la descrizione, <lb></lb>se non che, riserbando a un secondo conato le osservazioni microscopiche, <lb></lb>confessava di non avere scorto in quegli organi la struttura spirale. </s>

<s>“ Si-<pb xlink:href="020/01/1642.jpg" pagenum="517"></pb>mili ratione, poi soggiunge, eiusmodi observationes, quales D. </s>

<s>Malpighius <lb></lb>non inseruit libro suo primo, inventa sunt in primo meorum, ex. </s>

<s>gr. </s>

<s>de­<lb></lb>scriptio comae floridae in omnibus Corymbiferis et aliis floribus similari­<lb></lb>bus; de acetario in centro pyrorum omnis generis; de nucleo in prunis <lb></lb>omnis generis; de tertio quodam et interno integumento reperto in omni­<lb></lb>bus fere seminibus cuiuscumque generis analogo saepe secundinae; intume­<lb></lb>scentia prodigiosa involucrorum, in specie in fructibus cum nucleo, in gene­<lb></lb>ratione seminis, et post eorum contractio iuxta rationem uteri in quibusdam <lb></lb>animalibus, cum variis aliis, quorum quaedam non rcperiuntur in secundo <lb></lb>D. </s>

<s>Malpighi libro, et quaedam adhuc desiderantur..... Id imponam mode­<lb></lb>stiae notandae me a D. </s>

<s>Malpighio <emph type="italics"></emph>variare in omnibus,<emph.end type="italics"></emph.end> ut mihi videtur, exhi­<lb></lb>bitis exemplis ” (Appendix anni IX et X, Norimbergae 1676, pag. </s>

<s>228, 29). </s></p><p type="main">

<s>Da quali sentimenti fossero inspirate queste parole è troppo facile in­<lb></lb>tendere, ma convien dire che fosse ardentissimo il desiderio del Grew d&#039;ap­<lb></lb>parir superiore in certe cose al suo rivale, e in certe altre da&#039;pensieri di <lb></lb>lui indipendente, se s&#039;indusse a istituire il confronto fra un&#039;opera già com­<lb></lb>piuta e la sua propria lasciata a mezzo. </s>

<s>Gli rimaneva infatti a rivestire il <lb></lb>tronco di <emph type="italics"></emph>Fronde<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>Fiori;<emph.end type="italics"></emph.end> di fiori, che allegano in <emph type="italics"></emph>Frutti,<emph.end type="italics"></emph.end> di frutti che <lb></lb>concepiscono <emph type="italics"></emph>Semi.<emph.end type="italics"></emph.end> Le quattro trattazioni erano nel 1676 compiute, ma ne <lb></lb>fu indugiata dall&#039;Autore le stampa perchè, componendosi di esse il IV libro <lb></lb>dell&#039;Anatomia delle piante, voleva esser questo riunito agli altri tre libri, <lb></lb>che lo avevano di alcuni anni preceduto, per esibire al pubblico in un vo­<lb></lb>lume l&#039;opera tutta intiera. </s>

<s>Quel volume in folio apparve in fatti in Londra <lb></lb>nel 1682 col titolo: <emph type="italics"></emph>The anatomy of plants, with an idea of a philoso­<lb></lb>phical history of plants.<emph.end type="italics"></emph.end> Cosicchè quel che primo avea preso le mosse fu <lb></lb>l&#039;ultimo a toccare la meta. </s>

<s>Ma il Malpighi non se ne vantò, che si sappia, <lb></lb>e più prudente del Grew lasciò libero il giudizio ai posteri, l&#039;opinion dei <lb></lb>quali oramai è che ambedue gli Autori concorressero a instituire la Fitolo­<lb></lb>gia col fortuito riscontro delle idee, e più forse con le divergenze, d&#039;onde <lb></lb>venne occasione a ricercare il vero, per via di nuove osservazioni e di più <lb></lb>accurati esperimenti. </s>

<s>Non parve in ogni modo agl&#039;imparziali nè ingiusta nè <lb></lb>lusinghiera la sentenza di chi concluse esser l&#039;opera dell&#039;Italiano più estesa <lb></lb>e più profonda. </s></p><p type="main">

<s>In quel medesimo tempo in Francia due Fisici illustri, inconsapevoli <lb></lb>essi pure l&#039;uno dell&#039;altro, attendevano alla Fisiologia delle piante. </s>

<s>E perchè <lb></lb>il soggetto de&#039;loro studii era circoscritto a sole alcune particolari funzioni <lb></lb>dell&#039;Economia vegetabile, in dar pubblicità alle loro idee, per mezzo delle <lb></lb>accademiche relazioni, prevennero di qualche anno il Grew e il Malpighi. </s>

<s>Il <lb></lb>primo de&#039;commemorati Autori, che fra&#039;suoi <emph type="italics"></emph>Essais de Physique<emph.end type="italics"></emph.end> ha il primo <lb></lb>intitolato <emph type="italics"></emph>De la vegetation des plants,<emph.end type="italics"></emph.end> è il Mariotte, e il secondo è il Per­<lb></lb>rault, il quale così scrive in un avvertimento premesso al suo trattato <emph type="italics"></emph>De <lb></lb>la circulation de la seve des plantes:<emph.end type="italics"></emph.end> “ Celles d&#039;entre les experiences qui <lb></lb>sont novelles, ont été faites sur les Memoires que M. </s>

<s>Mariotte et moi avons <lb></lb>donnez: car cette pensée de la circulation de la seve des plantes nous ètoit <pb xlink:href="020/01/1643.jpg" pagenum="518"></pb>venue à tous deux sans nous l&#039;être communiquée. </s>

<s>La première fois qu&#039;on <lb></lb>en parla dans la Compagnie ce fut à l&#039;Assemblee du 15 Janvier 1667 ou <lb></lb>dans le Plan que je faifois d&#039;une Historie generale des plantes, au chapitre <lb></lb><emph type="italics"></emph>Des causes des plantes<emph.end type="italics"></emph.end> entre autres choses j&#039;expliquai les coniectures sur <lb></lb>lesquelles je fondois le nouveau paradoxe, et dont je ne croyois point que <lb></lb>personne eût jamais eu la pensé ” (Oeuvres, T. </s>

<s>I cit., pag. </s>

<s>69, 70). </s></p><p type="main">

<s>Il bisogno di provar l&#039;assunto, per via di esperienze, porse al Mariotte <lb></lb>e al Perrault occasione di applicar le leggi della fisica, non a sola la circo­<lb></lb>lazion del succo, ma a parecchie altre funzioni della vita vegetativa o male <lb></lb>intese o non ancora scoperte; cosicchè, aggiunta l&#039;opera de&#039;due citati Fran­<lb></lb>cesi a quella del Malpighi e del Grew, si può dir che toccasse in pochi anni <lb></lb>la storia delle piante quella perfezione, per raggiunger la quale avea tanti <lb></lb>secoli penato la storia degli animali. </s>

<s>Se avessimo alla storia della Botanica <lb></lb>potuto consacrare un libro, sarebbe stato ivi il luogo a descrivere le ragioni e <lb></lb>il modo di così mirabili progressi, ma essendo assegnata al soggetto la sola <lb></lb>prima angusta parte di questo capitolo, non è possibile che di qualche stilla, <lb></lb>attinta a quell&#039;ampio mare, soccorrere alla sete dei nostri Lettori. </s>

<s>E giac­<lb></lb>chè la causa dell&#039;ascesa della linfa ci si presentò nella storia come una delle <lb></lb>prime e principali investigazioni, a cui si volse la scienza, giova riappiccar <lb></lb>là dove fu lasciato interrotto il filo del nostro discorso, per accennare a <lb></lb>que&#039;progressi, che fece una sì astrusa e desiderata notizia in tempi, che la <lb></lb>Fisiologia delle piante ebbe, dall&#039;opera contemporanea degli Autori sopra <lb></lb>commemorati, così validi impulsi. </s></p><p type="main">

<s>Il Malpighi, scoperte le trachee delle piante, ch&#039;ei reputò servire come <lb></lb>negl&#039;insetti alla respirazione, applicò ad esse trachee legnose l&#039;ufficio se­<lb></lb>condario di promovere il succo, a quel modo che promovono il chilo e il <lb></lb>sangue ne&#039;vasi degli animali i moti alternativi del torace. </s>

<s>“ Et sicut in no­<lb></lb>bis, reliquisque sanguineis analogis respirationis motus, interpolatis impul­<lb></lb>sibus, promovet chyli et aliorum succorum motum, per lactea et consimilia <lb></lb>vasa; ita ex trachearum dilatatione, intus urgente aere, necessario urgentur <lb></lb>interceptae ligneac fibrae et horizontales utriculorum appendices, et ita pro­<lb></lb>babiliter fit contenti succi expressio in contiguas partes. </s>

<s>Remittente vero <lb></lb>tumore, laxiores redditi utriculi et fistulae ligneae, facilius novum admit­<lb></lb>tunt humorem ” (De cortice Op. </s>

<s>omnia, T. </s>

<s>I cit., pag. </s>

<s>34). </s></p><p type="main">

<s>Il Borelli però che, come udimmo, non consentiva col Malpighi intorno <lb></lb>all&#039;uso primario delle trachee, non consentiva nemmeno intorno a questo <lb></lb>particolare uso secondario, e in altre cause meccaniche ricercò nelle piante <lb></lb>la virtù impulsiva del succo. </s>

<s>Gli si presentavano alla mente in questa ri­<lb></lb>cerca le ipotesi dell&#039;Aggiunti e del Castelli, mantenute vive ne&#039;tradizionali <lb></lb>insegnamenti di que&#039;due primi e valorosi discepoli di Galileo, e suoi stima­<lb></lb>tissimi Maestri; ma perchè gli sembrava che alcuni fatti non favorissero <lb></lb>l&#039;ipotesi dell&#039;ascesa della linfa per cause capillari, si volse ad applicare a <lb></lb>quell&#039;effetto la meccanica del Termometro santoriano. </s>

<s>Significò questi suoi <lb></lb>pensieri al Malpighi, il quale, per non irritarsi l&#039;animo di quell&#039;uomo sde-<pb xlink:href="020/01/1644.jpg" pagenum="519"></pb>gnoso, dop&#039;aver fatto qualche segno di secondarli, pensò bene di togliersi <lb></lb>d&#039;ogni impaccio col dire che lasciava la dimostrazione di quelle cose ai sa­<lb></lb>gaci Meccanici. </s>

<s>“ Subintrans itaque humor sursum ascendit et quasi suspen­<lb></lb>ditur. </s>

<s>Singula namque portio quae invicem fibrarum frustula unit cum pa­<lb></lb>rum interius emineat valvulae vices supplet, et ita minima quaelibet guttula <lb></lb>veluti per funem, seu per gradus ad ingens deducitur fastigium. </s>

<s>Hunc au­<lb></lb>tem ascensum non tantum fistularum interior asperitas iuvat, sed et succes­<lb></lb>siva aeris temperies, calida scilicet et frigida ex diei noctisque variis crasibus, <lb></lb>eiusque elasticus motus qui exteriora corticis involucra urgens contentorum <lb></lb>liquorum motum superiora versus promovere et iuvare potest: quae singula <lb></lb>sagacioribus Mechanicis demonstranda relinquo ” (ibid., pag. </s>

<s>22, 23). </s></p><p type="main">

<s>Queste ultime parole accennano senza dubbio al Borelli, il quale rispose <lb></lb>all&#039;invito nel capitolo XIII della II parte <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> dove, intro­<lb></lb>ducendosi a trattar della generazione e vegetazion delle piante, dop&#039;avere <lb></lb>accennato al Malpighi che, coll&#039;aiuto del microscopio, dette della struttura <lb></lb>di esse piante esattissima cognizione, “ ego tantum proferam theoricam, poi <lb></lb>soggiunge, quam ex B. </s>

<s>Castello praeceptore didici, et quae deinceps medi­<lb></lb>tatus sum ” (Editio cit., pag. </s>

<s>358). </s></p><p type="main">

<s>Descritto nella proposizione CLXXV quello, da Galileo chiamato <emph type="italics"></emph>Stru­<lb></lb>mento<emph.end type="italics"></emph.end> e da lui, discepolo del Castelli, <emph type="italics"></emph>Termometro santoriano,<emph.end type="italics"></emph.end> passa a farne <lb></lb>l&#039;applicazione, dicendo che il cannello di vetro rappresenta le fistole spu­<lb></lb>gnose delle piante, su per le quali, facendo esse spugnosità da valvole, il <lb></lb>succo ascende per gradi, succedendo al calore rarefacente del giorno la con­<lb></lb>densatrice frigidità della notte. </s>

<s>“ Ergo inflando vesciculas porosas molles <lb></lb>tota moles augebitur. </s>

<s>Postea, superveniente refrigeratione nocturna, aut a <lb></lb>vento facta, aer in spongioso spatio contentus denuo condensabitur, et proinde <lb></lb>aqua ulterius promovebitur, et sic novis vicissitudinibus priori similibus ” <lb></lb>(ibid., pag. </s>

<s>359). </s></p><p type="main">

<s>Il Borelli escluse come accennammo l&#039;attrazion capillare perchè, reciso <lb></lb>un ramo, seguita a stillar l&#039;umore sul tronco eretto dalla cicatrice supina <lb></lb>(ibid., pag. </s>

<s>372), ma il Mariotte non invocava altre forze attrattive che quelle <lb></lb>stesse capillari, ritornando a vita, e dando autorità all&#039;abbandonata ipotesi <lb></lb>dell&#039;Aggiunti. </s>

<s>“ Cette première entrée de l&#039;eau dans les racines, scrive nel <lb></lb>Saggio fisico <emph type="italics"></emph>De la vegetation des plantes,<emph.end type="italics"></emph.end> se fait par una loi de la nature, <lb></lb>car par-tout ou il y a des tuyaux tres-étroits, qui touchent l&#039;eau, elle y <lb></lb>entre, et même elle y monte contre sa pente naturelle de descendre ” (Oeu­<lb></lb>vres, T. </s>

<s>I cit., pag. </s>

<s>130). E prosegue a descrivere la notissima esperienza <lb></lb>dell&#039;acqua, che ascende su per i sottilissimi tubi di vetro, applicandola non <lb></lb>a sole le radici ma ai vasi del tronco. </s></p><p type="main">

<s>Il Perrault dall&#039;altra parte elaborò così l&#039;ipotesi del Castelli, da darle <lb></lb>quasi una impronta di originalità, assegnando a spiegare il fatto del passare <lb></lb>il succo dalle radici ai rami le due cause seguenti: “ l&#039;un est l&#039;impulsion, <lb></lb>l&#039;autre est l&#039;ouverture des conduits, qui doivent recevoir et donner passage <lb></lb>à ce qui est pouffé. </s>

<s>L&#039;un et l&#039;autre se fait par la rarefaction, qui est capa-<pb xlink:href="020/01/1645.jpg" pagenum="520"></pb>ble non seulement de dilater les conduits et les pores des racines, mais aussi <lb></lb>de faire gonfler le suc contenu dans la terre, lorsque par la chaleur du <lb></lb>dehors, iointe à celle qui est dans la terre, et par celle de la fermentation <lb></lb>qu&#039;il conçoit à l&#039;attouchement des racines, qui en contiennent le principe, il <lb></lb>souffre une dilatation qui lui fait avoir besoin d&#039;un lieu plus spacieux pour <lb></lb>s&#039;étendre: car cette dilatation le force à s&#039;insinuer dans les conduits qu&#039;il <lb></lb>rencentre ouverts, soit dans la racine, soit dans le tronc et dans les branches, <lb></lb>jusqu&#039;à l&#039;extrémité de la plante ” (De la circol. </s>

<s>de la seve, Ouvres cit., pag. </s>

<s>77). </s></p><p type="main">

<s>In tutte queste ipotesi però fin qui recensite non si rendeva chiaro a <lb></lb>intendere quel così continuo e regolare afflusso del succo dalla radice alle <lb></lb>foglie, che il Cesalpino vedeva tanto bene rappresentato dall&#039;immagine della <lb></lb>fiamma, alla quale regolarmente affluisce l&#039;olio della lucerna. </s>

<s>Le splendide <lb></lb>analogie cesalpiniane si dovettero come inutili e anzi nocive ripudiare dalla <lb></lb>Fisica nuova, infintanto che non venne a sostituirsi una causa reale all&#039;im­<lb></lb>maginario calore innato de&#039;germogli che si svolgono, e dei frutti che ma­<lb></lb>turano, come una causa reale era stata dall&#039;Aggiunti sostuita all&#039;immaginato <lb></lb>calor del cuore vegetativo, che attira il succo dalle radici. </s>

<s>E perchè questa <lb></lb>reale causa fisica risiedeva propriamente colà dove il Cesalpino l&#039;aveva un <lb></lb>po&#039;in confuso indicata, cioè nelle foglie, a compier l&#039;opera dell&#039;Aggiunti <lb></lb>conveniva aver quella esatta notizia della fisiologia delle stesse foglie, che <lb></lb>s&#039;ebbe solo un secolo dopo che l&#039;anatomia del Malpighi dette instituto e <lb></lb>impulso di progredire alìa nuova scienza. </s>

<s>Apparvero notabilissimi questi pro­<lb></lb>gressi nel secolo XVIII, quando Stefano Hales, Enrico Lodovico Du-Hamel <lb></lb>e Carlo Bonnet raccolsero ne&#039;loro libri i frutti di tante varie e ingegnose <lb></lb>esperienze. </s>

<s>Hanno molte di quelle esperienze per soggetto le foglie, e giac­<lb></lb>chè elle sono un organo principalissimo, a cui fra le altre funzioni della vita <lb></lb>vegetativa è attribuita anche quella di promovere efficacemente l&#039;ascesa del <lb></lb>succo nutritizio; per le relazioni coll&#039;argomento che trattiamo, e per l&#039;im­<lb></lb>portanza che ha in sè medesimo, sopra le foglie intratterremo il discorso. </s></p><p type="main">

<s>S&#039;acquistarono dagli antichi le foglie il titolo di lussuriose, e tutto al <lb></lb>più si ammetteva che fossero in sì bell&#039;ordine disposte sui rami, per ripa­<lb></lb>rare dai soverchi ardori del sole la delicata giovanezza dei frutti. </s>

<s>Ma quando <lb></lb>il Malpighi notomizzandole trovò in esse tutti insieme raccolti i varii organi, <lb></lb>da rappresentarglisi come in compendio tutta intera la pianta, s&#039;avvide che <lb></lb>dovevano quelle fronde calunniosamente credute una lussuria esser precipue <lb></lb>e insigni parti integranti degli alberi e dell&#039;erbe. </s>

<s>Ripensava a quale impor­<lb></lb>tante ufficio fossero dunque ordinate, e vedendo che ne&#039;germoglianti semi <lb></lb>quell&#039;ufficio è di nutrire, ebbe a congetturarne perciò che, serbando le fo­<lb></lb>glie adulte la medesima natura delle seminali, dovessero proseguire altresì <lb></lb>i medesimi ministeri. </s>

<s>“ Taliter excitata folia videntur a Natura fabrefacta <lb></lb>ut coctioni alimenti, quae praecipua est, inserviant..... Probabilem nutri­<lb></lb>titii succi in foliis coctionem indicare videtur seminalis ptantulae structura: <lb></lb>hanc constare geminis foliis evidens est, quae propriis vasculis et utriculis <lb></lb>succo turgidis ditantur ” (De foliis, Op. </s>

<s>omnia cit., pag. </s>

<s>54). </s></p><pb xlink:href="020/01/1646.jpg" pagenum="521"></pb><p type="main">

<s>In quel medesimo tempo che l&#039;Anatomia al Malpighi, l&#039;esperienze fisi­<lb></lb>che rivelavano al Mariotte e al Perrault l&#039;importanza grandissima delle fo­<lb></lb>glie nell&#039;economia vegetabile. </s>

<s>S&#039;era il secondo di questi Autori trattenuto <lb></lb>più volte innanzi a que&#039;grandi alberi, che sorgono dal lastricato delle piazze <lb></lb>cittadine, per domandar come mai, non andando una stilla di pioggia alle <lb></lb>loro radici, potessero pur così lietamente vivere e prosperare. </s>

<s>Si credette <lb></lb>averne per risposta che mantenevansi in quella loro giovanile freschezza <lb></lb>“ par le moyen des humiditez qu&#039;ils reçoivent de l&#039;air des pluyes et des ro­<lb></lb>sees ” (De la circ. </s>

<s>cit., pag. </s>

<s>92). Anche il Malpighi, accennando, nella <emph type="italics"></emph>Ve­<lb></lb>getazione dei semi,<emph.end type="italics"></emph.end> ai cotiledoni, che ora sono <emph type="italics"></emph>ipogei,<emph.end type="italics"></emph.end> come oggidi si dice, <lb></lb>ora sono <emph type="italics"></emph>apogei,<emph.end type="italics"></emph.end> sospettò che giusto rimanessero questi sopra terra per at­<lb></lb>trar l&#039;umore dell&#039;aria ambiente, e somministrarlo alla tenera pianticella. <lb></lb></s>

<s>“ Longe a terra locantur et post primos incubationis dies humor a terreno <lb></lb>utero per caulem communicatur, ni velimus suspicari ab ambiente aere iis <lb></lb>subministrari ” (Oper., T. </s>

<s>I cit., pag. </s>

<s>111). Ma il Mariotte se ne assicurò <lb></lb>per una bella esperienza, ch&#039;egli, nel sopra citato <emph type="italics"></emph>Saggio della vegetazion <lb></lb>delle piante,<emph.end type="italics"></emph.end> così descrive: “ Si l&#039;on coupe une petite branche d&#039;arbre ou <lb></lb>de quelque herbe, comme du persil, cerfevil, etc., ou il y ait quelque bran­<lb></lb>chette à côté, et qu&#039;on trempe l&#039;extrémité des fevilles dans de l&#039;eau, lais­<lb></lb>sant la tige avec la branchette sur le bord du vaisseau ou sera l&#039;eau, cette <lb></lb>branchette se conservera verte trois ou quatre jours..... Au lieu que si on <lb></lb>met d&#039;autres herbes ou petites branches d&#039;arbre semblables sur le bord du <lb></lb>vaisseau, sans toucher à l&#039;eau, elles se fletriront et secheront en peu de <lb></lb>tems. </s>

<s>” D&#039;onde con certezza di fatto ne conclude che: “ le primier suc qui <lb></lb>vient de dehors, n&#039;entre pas seulement par la racine dans les plantes, mais <lb></lb>aussi par les fevilles et par les branches, et elles le reçoivent de la rosée <lb></lb>ou de la pluie, ou des vapeurs dont l&#039;air est toujours rempli ” (Oeuvres <lb></lb>cit., pag. </s>

<s>133). </s></p><p type="main">

<s>Il nuovo fatto così, verso il 1667, scoperto in Francia e dimostrato, fu <lb></lb>quasi il primo talento trasmesso a que&#039;valorosissimi Fisici botanici del se­<lb></lb>colo XVIII che, coltivandolo n&#039;ebbero a ricavare un sì largo frutto. </s>

<s>L&#039;Hales <lb></lb>lo confermò per via di una diligentissima esperienza, descritta nel cap. </s>

<s>IV <lb></lb>della sua Statica de&#039;vegetabili, tagliando un grosso ramo di melo, e tenen­<lb></lb>dolo capovolto colla punta immersa nell&#039;acqua di una caraffella di vetro. </s>

<s>“ In <lb></lb>tre giorni e due notti, egli dice, attrasse in questa maniera e traspirò quat­<lb></lb>tro libbre e due once e mezzo di acqua, e le fronde si conservarono verdi, <lb></lb>mentre quelle d&#039;un altro ramo, nell&#039;istesso tempo separato dall&#039;istesso al­<lb></lb>bero, senza metterlo nell&#039;acqua, invizzirono quarant&#039;ore prima ” (Traduz. </s>

<s><lb></lb>ital., Napoli 1756, pag. </s>

<s>107). </s></p><p type="main">

<s>La dimostrata importanza delle foglie, nella nutrizione degli alberi e <lb></lb>dell&#039;erbe, invogliò a mezzo il secolo XVIII Carlo Bonnet a far quegli or­<lb></lb>gani soggetto di uno studio particolare. </s>

<s>Avendo notata la differenza grande <lb></lb>che passa negli alberi, fra la superficie inferiore di esse foglie e la supe­<lb></lb>riore, la prima cosa che gli occorse al pensiero fu quella d&#039;investigare il <pb xlink:href="020/01/1647.jpg" pagenum="522"></pb>fine, ch&#039;ebbe di far così la sapiente Natura. </s>

<s>Avvertendo perciò che le ru­<lb></lb>giade salgono da terra incominciò a dubitare se i peli e altre scabrosità fos­<lb></lb>sero date alla pagina fogliacea inferiore, per ritener più facilmente l&#039;umi­<lb></lb>dità, che incontro a lei sale. </s>

<s>“ L&#039;experience démontre que la rosée s&#039;éleve <lb></lb>de la terre. </s>

<s>La surface inferieure des fevilles auroit-elle été principalement <lb></lb>destinée à pomper cette vapeur, et à la transmettre dans l&#039;interieur de la <lb></lb>plante? </s>

<s>La position des fevilles relativement à la terre et le tissu de leur <lb></lb>surface inferieure semblent l&#039;indiquer ” (Recherches sur l&#039;usage des fevil­<lb></lb>les a Neuchatel 1779, pag. </s>

<s>19, 20). Furono poi i dubbi confermati dall&#039;espe­<lb></lb>rienze, osservando che molto più s&#039;imbeve una foglia posata sull&#039;acqua colla <lb></lb>superfice inferiore, in che trovava altresì il Bonnet la ragione perchè le umili <lb></lb>erbe immerse nella rugiada abbiano le due pagine delle loro foglie disposte <lb></lb>a sorbir l&#039;umido ugualmente. </s>

<s>Il vento e le mani dell&#039;agricultore fanno so­<lb></lb>vente cangiar direzione alle foglie, cosicchè si trovano com&#039;animale supino <lb></lb>fuori della loro posizion naturale. </s>

<s>Ma elle, tanto importa alla loro prospera <lb></lb>vita, “ savent la rependre d&#039;elles-mèmes, par un mouvement qui leur est <lb></lb>propre, et qui paroit presque aussi spontane que ceux que se donnent di­<lb></lb>vers animaux pour des fins analogues ” (ivi, pag. </s>

<s>11). </s></p><p type="main">

<s>Le foglie assorbiscono dunque come la cute: e perchè da un secolo e <lb></lb>mezzo d&#039;esperienze veniva dimostrato ch&#039;essa cute, mentre da una parte <lb></lb>riceve dal di fuori, dall&#039;altra lo rimanda, si volle saper se le piante abbiano <lb></lb>con gli animali comune anche la virtù di traspirare. </s>

<s>Il Malpighi dal trovar <lb></lb>nelle foglie vasi sudoriferi, simili ai cutanei, aveva già congetturato in esse <lb></lb>l&#039;esistenza di questa funzione. </s>

<s>“ In folia, compendio quodam singula vasa <lb></lb>tracheae scilicet, fistulae ligneae et peculiaria vascula desinunt extremis fini­<lb></lb>bus, nec desinunt sudoris vascula et transpiratus, quare credidi cutis seu <lb></lb>corii munia subire ” (De foliis in loco cit., pag. </s>

<s>54). </s></p><p type="main">

<s>Primo a dimostrare sperimentalmente il supposto sembra fosse il Mu­<lb></lb>schenbroeck, operando in un modo simile a quello descritto nella XVII fra <lb></lb>le statistiche esperienze halesiane. </s>

<s>“ Avendo dalle precedenti esperienze co­<lb></lb>nosciuto evidentemente che le piante gran copia attraggono e respirano <lb></lb>d&#039;umido, volli tentar di raccogliere la materia della loro traspirazione, e <lb></lb>per venirne a capo presi diverse storte di vetro, delle quali feci entrare in <lb></lb>ciascuna un ramo per sorte di diversi alberi colle sue frondi sopra, chiu­<lb></lb>dendo l&#039;apertura con vescica ben legata intorno al collo della storta. </s>

<s>Ed in <lb></lb>questa maniera molt&#039;once raccolsi della respirazione della vite, del fico, del <lb></lb>melo, ecc. </s>

<s>” (Traduz. </s>

<s>cit., pag. </s>

<s>45). </s></p><p type="main">

<s>Benchè non fosse l&#039;Hales il primo a far l&#039;esperienza fu però il primo <lb></lb>ad applicarla alla causa dell&#039;ascesa del succo, dimostrando che la traspira­<lb></lb>zione fa l&#039;effetto appunto della fiamma sull&#039;olio della lucerna. </s>

<s>“ Dall&#039;an­<lb></lb>zidette osservazioni e sperienze vien dimostrato, egli dice, che le foglie danno <lb></lb>un grandissimo aiuto alla vegetazion delle piante, poichè servono per dir <lb></lb>così come tante trombe per sollevar le particelle nutritive e per farle giun­<lb></lb>gere fino alla sfera d&#039;attrazione del frutto ” (ivi, pag. </s>

<s>255). Sopra queste <pb xlink:href="020/01/1648.jpg" pagenum="523"></pb>halesiane dottrine sperimentalmente dimostrate il Du-Hamel, nel <emph type="italics"></emph>Traité des <lb></lb>arbres fruitiers,<emph.end type="italics"></emph.end> formulò la sua VII proposizione: “ Les fevilles influent tal­<lb></lb>lement sur la quantité et le mouvement de la seve, qu&#039;elle augmente ou <lb></lb>diminue a proportion de leur nombre et de leur êtat ” (Paris 1782, pag. </s>

<s>122). <lb></lb>Così un fatto fisico veniva un&#039;altra volta a sostituirsi all&#039;immaginario calore <lb></lb>innato del Cesalpino, e se non l&#039;unico era senza dubbio ritrovato all&#039;ascesa <lb></lb>del succo nutritizio il più valido impulso. </s>

<s>Il Bonnet poi chiamò tutte insieme <lb></lb>a concorso le varie forze, proposte a produr quell&#039;ascesa dai varii Autori <lb></lb>che lo avevano preceduto; ciò che in cosa di tanta difficoltà, e soggetta a <lb></lb>tanti differenti giudizii, trovò lode ne&#039;successori e imitazion dell&#039;esempio. <lb></lb></s>

<s>“ L&#039;estrema finezza dei condotti del succo, leggesi nella <emph type="italics"></emph>Contemplazione <lb></lb>della Natura,<emph.end type="italics"></emph.end> che li fa essere in certo modo capillari, l&#039;azione dell&#039;aria <lb></lb>sulla lama elastica delle trachee, e l&#039;impressione di queste sulle fibre legnose <lb></lb>che abbracciano, o da cui sono abbracciate, il calore che rarefà il succo, <lb></lb>quel calore massimamente che agendo sulla superfice delle foglie vi attrae <lb></lb>il superfluo del succo nutritivo, e vi produce lo svaporamento; sembrano <lb></lb>essere le cagioni principali dell&#039;ascendere di questo fluido dentro le piante ” <lb></lb>(Traduz. </s>

<s>cit., T. I, pag. </s>

<s>188). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le singolarissime esperienze fisiche, per via delle quali s&#039;incominciò a <lb></lb>riconoscere la grande importanza fisiologica delle foglie, furono intraprese <lb></lb>dal Mariotte e dal Perrault per servir d&#039;argomento a dimostrare una loro <lb></lb>opinione, secondo la quale si pretendeva che circolasse la linfa nelle piante, <lb></lb>come circola il sangue negli animali. </s>

<s>Vedeva di questa circolazione il Per­<lb></lb>rault ricorrergli all&#039;immaginoso pensiero due esempi: quello dell&#039;acqua, che <lb></lb>si solleva in aria, dove sciolti i sali infin lassù sollevati ritorna con essi in <lb></lb>pioggia a deporli sopra la terra; e quello dell&#039;aratura, l&#039;effetto della quale <lb></lb>è di rivoltare continuamente le zolle in modo, che la parte di sopra, fecon­<lb></lb>data dal sole, dall&#039;aria e dalle piogge torni di sotto a partecipar la sua fe­<lb></lb>condità alle radici degli alberi, e alle barboline dei semi. </s></p><p type="main">

<s>“ Il semble donc que ces circulations dans les êtres non-vivans ont <lb></lb>quelque rapport avec celle que l&#039;on estime se devoir faire dans les plantes, <lb></lb>quoiqu&#039;elles se fassent d&#039;une maniere opposée a celle des plantes et des ani­<lb></lb>maux: car de même que les eaux de la pluye descendent sur la terre pour <lb></lb>y laisser ce qu&#039;elles ont contracté de gras et de propre a nourrir dans ces <lb></lb>regions superieures, et qu&#039;elles en ressortent maigres et steriles lorsqu&#039;elles <lb></lb>en sont élevées, c&#039;est à-peu-pres de la même maniere que l&#039;humidité, dont <lb></lb>les plantes sont nourries, sortant de la racine monte dans la tige, dans les <lb></lb>branches, et dans les fevilles, avec des qualitez convenables à chacune de <lb></lb>ces parties, et apres y avoir laissé ce qu&#039;elle a de propre pour leur nour-<pb xlink:href="020/01/1649.jpg" pagenum="524"></pb>riture et pour leur accroissement, le reste qui est inutile descend dans la <lb></lb>racine, pour y ètre cuit et préparé de nouveau, et la étant iointe à l&#039;autre <lb></lb>suc que la racine reçoit de la terre, ce suc remonte dans les parties supe­<lb></lb>rieures de la plante, et l&#039;on supposé que cela se fait de la mème façon que <lb></lb>dans les animaux, ou le sang arteriel sortant du coeur, qui est à leur égard <lb></lb>ce que la partie la plus noble de la racine est dans les plantes, se distribue <lb></lb>dans tout le corps, qui ayant retenu ce que ce sang a de propre pour l&#039;en­<lb></lb>tretenir, renvoye le reste au coeur, afin qu&#039;étant joint au suc que les veines <lb></lb>lactées ont reçu des intestins, qui sont aux animaux ce que la terre est aux <lb></lb>plantes, il retourne dans toutes les parties du corps, pour entretenir une <lb></lb>circulation continuelle ” (Oeuvres, T. </s>

<s>I cit., pag. </s>

<s>73). </s></p><p type="main">

<s>L&#039;Autore, a cui sovvennero questi concetti, se ne compiacque nel pub­<lb></lb>blicarli come di una scoperta, in parte della quale sentì con suo grande <lb></lb>rammarico che fosse venuto il Mariotte. </s>

<s>Diremo fra poco i giudizi che ne <lb></lb>dettero i più savi di que&#039;tempi e del secolo appresso, ma perchè molti fra <lb></lb>i concorsi nell&#039;opinione di un continuo circolo del succo dalle radici ai rami <lb></lb>e dai rami alle radici ammettono terzo dopo i due Francesi il nostro Mal­<lb></lb>pighi, giova esaminare quali idee avesse in proposito il sapiente Maestro <lb></lb>dell&#039;anatomia delle piante. </s></p><p type="main">

<s>Il rumore che se ne fece in Francia, per la cosa in sè stessa e per le <lb></lb>contese fra&#039;due celebri rivali è facilissimo che giungesse a Bologna. </s>

<s>Ma a <lb></lb>richiamar l&#039;attenzion del Malpighi sull&#039;argomento bastava il pensare alla <lb></lb>gloriosa scoperta dell&#039;Harvey, rammemoratagli dalle intravedute analogie fra <lb></lb>la vita delle piante e degli animali: analogie intorno alle quali si trovava <lb></lb>egli stesso, insieme co&#039;due Francesi, prevenuto da Daniele Major, medico di <lb></lb>Hambourg, che aveva infino dal 1665 pubblicato il suo libro <emph type="italics"></emph>De planta <lb></lb>monstrosa gottorpiensi, et circulatione succi nutrititii.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Comunque sia, nel chiudere quelle sì dotte pagine descrittive dell&#039;ana­<lb></lb>tomia delle piante s&#039;appresentò al giudizio del Malpighi quel circolo della <lb></lb>linfa <emph type="italics"></emph>sursum et deorsum,<emph.end type="italics"></emph.end> di che s&#039;era trattato in Hambourg e in Parigi, e <lb></lb>tutt&#039;altrimenti da quel che si dice sentenziò sembrargli molto dubbioso. <lb></lb></s>

<s>“ Quaenam sit alimenti semita et an ab extremis plantarum apicibus re­<lb></lb>fluat succus ad imas partes, et iuxta indigentiam in omnem peripheriam <lb></lb>sursum et deorsum protrudatur, dubium est ” (De radicibus, Op. </s>

<s>omn. </s>

<s>cit., <lb></lb>pag. </s>

<s>159). Le ragioni di questo dubbio le ritrova il Nostro nell&#039;osservazione <lb></lb>dei fatti, dai quali si dimostra che non ha il succo un moto regolare e an­<lb></lb>dante, ma fa talvolta anche viaggio ritroso, come per esempio, quando pian­<lb></lb>tato un ramo d&#039;albero mette sotto terra le sue radici. </s>

<s>Dall&#039;altra parte non <lb></lb>si vedono aver le fistole delle piante, a dare un corso determinato alla linfa, <lb></lb>valvole, com&#039;hanno le vene a dirigere il moto del sangue. </s>

<s>“ Radices ab <lb></lb>extremis ramorum apicibus erumpentes, contento succo inversum iter, no­<lb></lb>vumque motum praescribunt: nullae enim interseruntur valvulae, determi­<lb></lb>natum inducentes motum (ibid.). </s></p><p type="main">

<s>I principali argomenti, addotti poi contro il circolo del Perrault, si ri-<pb xlink:href="020/01/1650.jpg" pagenum="525"></pb>ducono a questi: tanto è falso che fosse il Malpighi fautore delle dottrine <lb></lb>francesi! Ma pure egli, il nostro Bolognese, volle investigare qual sia il vero <lb></lb>viaggio, che fa nelle viscere della pianta la linfa, alla quale investigazione, <lb></lb>egli dice, “ aliquid lucis praebent ea quae in diversis arboribus tentavi. </s>

<s>” <lb></lb>L&#039;esperienze notabilissime son dall&#039;Autore così appresso descritte: “ In va­<lb></lb>riis itaque surculis et ramis, horizontalem sectionem in cortice feci, ablata <lb></lb>eiusdem et libri annulari portione, ita ut subiectum lignum denudatum pa­<lb></lb>teret. </s>

<s>In opii ramis, prunorum, mali Cydoniae, quercus, salicis, populi, avel­<lb></lb>lanae, etc., excitata huiusmodi circulari sectione pars superior surculi, seu <lb></lb>caudicis supra sectionem brevi vegetans ita excrescit ut longe turgida red­<lb></lb>datur: cortex enim, in quercu praecipue, in prunis et cydonia malo hori­<lb></lb>zontales utriculorum ordines ita elongat, ut frequenter appendices proman­<lb></lb>tur, quibus denudata ligni portio cooperitur, et facta denuo mutua anastomosi <lb></lb>cum inferiori secti corticis labio continuus redditur cortex. </s>

<s>Rami quoque <lb></lb>portio ultra sectionem ligneo superexcrescente circulo, et involucro impense <lb></lb>crassa protuberat. </s>

<s>Denudata vero lignea portio adhuc subsistit nullo vigente <lb></lb>incremento, quod reliquo quoque surculi infra sectionem contingit. </s>

<s>Idem <lb></lb>mihi saepius accidit facta spirali sectione in pomis et prunis ” (ibid.). </s></p><p type="main">

<s>Da ciò parve al Malpighi fosse evidentemente dimostrato che il succo <lb></lb>alimentare scende veramente dai rami fra il legno e la corteccia. </s>

<s>Se non <lb></lb>che venne a turbargli la pace della mente un dubbio che così gli ragionava: <lb></lb>non potrebb&#039;esser che il succo ascendente, costretto a passar fra gli angu­<lb></lb>sti vasi del legno snudato, poi trovato da respirare più al largo, si espan­<lb></lb>desse tutto intorno a produrre quell&#039;escrescenza sopravvenuta alla legatura? </s>

<s><lb></lb>Per assicurarsi di ciò incise in giro la buccia a un querciolo in modo, che <lb></lb>rimanesse al di sopra dell&#039;incisione poca parte del ramo, e trovò che non <lb></lb>si produceva il solito tumore. </s>

<s>A uno poi di quegli alberi adulti, che avea <lb></lb>veduto protuberare, fece l&#039;incisione annulare in modo che la buccia di sopra <lb></lb>continuasse con quella di sotto, per via di una listerella sottile quanto un&#039;un­<lb></lb>ghia, e trovò che l&#039;ipertrofia avveniva nella listerella lasciata e nell&#039;orlo su­<lb></lb>periore della corteccia incisa. </s>

<s>“ Quare ex his probabilius conieci nutrititii <lb></lb>succi motum a superioribus etiam ad inferiora promoveri ” (ibid., pag. </s>

<s>160). </s></p><p type="main">

<s>La descrizione dunque del viaggio che fa la linfa, secondo il Malpighi, <lb></lb>è questa: ascende per la parte legnosa del tronco infino alle foglie, dentro <lb></lb>alle quali si concuoce e si elabora: torna poi così elaborata a scendere fra <lb></lb>lo stesso legno e la buccia, e ivi tutta si consuma a produrre quegli an­<lb></lb>nuali strati incrementizi, resi così ben visibili dalla sega menata perpendi­<lb></lb>colarmente all&#039;asse di atterrati alberi antichi, e ne&#039;quali strati concentrici <lb></lb>annoverati si può legger l&#039;età della pianta, scrittavi dallo stesso infallibile <lb></lb>dito della Natura. </s></p><p type="main">

<s>Si comprende bene come questo malpighiano non è propriamente un <lb></lb>circolo, ma se pur vuolsi in qualche modo rassomigliare al circolo del san­<lb></lb>gue, diremmo ch&#039;egli è il circolo harveiano, il circolo grande. </s>

<s>Vi son poi <lb></lb>tanti altri piccoli circoli quante sono le parti della pianta, le quali, se vege-<pb xlink:href="020/01/1651.jpg" pagenum="526"></pb>tano tutte insieme e in comune nel composto, posson anche separate avere <lb></lb>una vita, e una individualità loro propria. </s>

<s>Questo fatto notissimo ai pratici <lb></lb>agricultori, che di quasi ogni frustolo di legno traggon gli <emph type="italics"></emph>ovoli,<emph.end type="italics"></emph.end> da cui nasce <lb></lb>un albero novello, era per scienza notissimo al Malpighi, il quale avea ri­<lb></lb>trovati ripetuti in ogni parte gli organi, che servono alla vita di tutta la <lb></lb>pianta. </s></p><p type="main">

<s>Ma mentre il valent&#039;uomo poneva alla fisiologia de&#039;vegetabili per fon­<lb></lb>damento le anatomiche dissezioni, e instituiva una scienza, il Perrault a imi­<lb></lb>tazion del Cartesio accomodava la Natura al suo ingegno, e fabbricava si­<lb></lb>stemi. </s>

<s>Chi credesse essere questo giudizio da noi dato dell&#039;illustre Accade­<lb></lb>mico parigino troppo severo legga là in fine alla seconda parte del trattato <lb></lb><emph type="italics"></emph>De la circulation de la seve,<emph.end type="italics"></emph.end> dove l&#039;Autore descrive l&#039;esperienza delle due <lb></lb>spugne, una imbevuta d&#039;olio essenziale, e l&#039;altra d&#039;acqua pura, e ambedue <lb></lb>poste nell&#039;alambicco “ pour donner une idee par analogie de quelle maniere <lb></lb>les differens sucs montent dans les plantes, et comment les utiles sont re­<lb></lb>tenus, lorsque les inutiles retournent à la racine ” (Oeuvres cit., pag. </s>

<s>104). </s></p><p type="main">

<s>Ma è superfluo e pericoloso l&#039;ingerire il nostro e il giudizio de&#039;nostri <lb></lb>lettori in una questione, che il pubblico scienziato ha oramai da lungo tempo <lb></lb>decisa. </s>

<s>L&#039;esperienze descritte dal Malpighi in fine all&#039;ultimo suo trattato <emph type="italics"></emph>De <lb></lb>radicibus plantarum,<emph.end type="italics"></emph.end> rimangono tuttavia il filo arianneo, a cui s&#039;attengono <lb></lb>anche i moderni per non andare smarriti nell&#039;intricatissimo laberinto, men­<lb></lb>tre l&#039;esperienze del Perrault, che trovarono ragionevoli oppositori infino dal <lb></lb>loro nascere, per le poderose argomentazioni del Magnol, dell&#039;Hales e del <lb></lb>Bonnet rimasero inconcludenti. </s>

<s>Basti fra l&#039;esperienze halesiane citare la LXV, <lb></lb>la quale è forse nella sua semplicità più efficacemente dimostrativa, perchè <lb></lb>se nel ramoscello più alto, al di sopra dell&#039;incisione annulare della cortec­<lb></lb>cia, circolasse veramente la linfa che ritorna alla radice, poniamo pure che <lb></lb>fosse come vuol lo stesso Perrault inutile a nutrire, dovrebbe almeno essere <lb></lb>utile a tener fresche le foglie, ciò che in farne esperienza dice l&#039;Hales “ non <lb></lb>avvenne, anzi nemmeno nel punto dell&#039;incisione vi fu segno alcuno di umi­<lb></lb>dità ” (Traduz. </s>

<s>cit., pag. </s>

<s>117). </s></p><p type="main">

<s>Il Bonnet, nella quinta delle sue <emph type="italics"></emph>Recherches sur l&#039;usage des fevilles,<emph.end type="italics"></emph.end><lb></lb>facendo alcune osservazioni contro l&#039;opinione della circolazion del succo, in­<lb></lb>fonde novelli spiriti di vita nelle sapienti dottrine del Malpighi. </s>

<s>“ Les plan­<lb></lb>tes n&#039;ont point de parties qui repondent, par leur structure ou par leur jeu, <lb></lb>a celles qui opèrent la circulation du sang dans les grands animaux. </s>

<s>Elles <lb></lb>n&#039;ont ni coeur, ni arteres, ni veines. </s>

<s>Leur structure est tres-simple et tres­<lb></lb>uniforme. </s>

<s>Les fibres lignenses, les utricules, les vases propres, les trachees <lb></lb>composent le systeme entier de leurs visceres; et ces visceres sont répan­<lb></lb>dus universellement dans tout le corps de la plante: on les retrouve jus­<lb></lb>ques dans les moindres partiee. </s>

<s>Les vaisseaux séveux n&#039;ont point de valvu­<lb></lb>les destinées à favoriser l&#039;ascension de la seve et à en empecher la retro­<lb></lb>gradation. </s>

<s>Quand ces valvules échapperoient au microscope, l&#039;experience en <lb></lb>démontrevoit la fausseté, puisque les plantes que l&#039;on plonge dans l&#039;eau, ou <pb xlink:href="020/01/1652.jpg" pagenum="527"></pb>que l&#039;on met en terre par leur extrémité superieure ne laissent pas de ve­<lb></lb>gétér ” (pag. </s>

<s>369). </s></p><p type="main">

<s>Questo fatto del vedersi un ramo vegetare anche messo in terra per <lb></lb>l&#039;estremità sua superiore, come quell&#039;altro citato già dal Malpighi dei rami <lb></lb>che piantati mettono tutto attorno radici, dimostrano, prosegue a dire il Bon­<lb></lb>net, che il succo sale e scende indifferentemente per i medesimi vasi. </s>

<s>Anzi <lb></lb>è ciò tanto vero che, se alla bella stagione s&#039;introdurrà un ramoscello vivo <lb></lb>in un tubo di vetro pieno di mercurio, si vedrà questo sollevarsi di giorno <lb></lb>e abbassarsi di notte con tanto maggior varietà di livello, quanto saranno <lb></lb>maggiori gli avvicendamenti del caldo e del freddo. </s>

<s>“ La marche de la seve <lb></lb>dans la belle saison, rassemble donc assez à celle de la liqueur d&#039;un Ther­<lb></lb>mometre: l&#039;une et l&#039;autre dependent également des alternatives du chaud <lb></lb>e du frais ” (ivi, pag. </s>

<s>370). </s></p><p type="main">

<s>Così, a mezzo il secolo XVIII, tornavasi a ripetere in sostanza quel che <lb></lb>era stato detto da Galileo, e ciò insegna al Filosofo orgoglioso essere ineffi­<lb></lb>caci a penetrar negli arcani della vita i lunghi e ripetuti conati del nostro <lb></lb>ingegno. </s>

<s>Ma pur v&#039;ha un&#039;altra fra le funzioni della vita vegetativa, che ha <lb></lb>strettissime relazioni col circolo della linfa, e che, sebbene infino a tutto il <lb></lb>secolo XVIII fosse riuscita misteriosa, ebbe nonostante rimosso il velo dalla <lb></lb>Chimica più moderna. </s>

<s>Noi intendiamo dire della respirazione, la quale si <lb></lb>porta o si potrebbe portare per argomento contro coloro, che di poco animo <lb></lb>e vile disperano de&#039;progressi della scienza dell&#039;uomo. </s>

<s>Intorno a che però <lb></lb>è a considerare che la scienza progredisce infin là dove posson sospingerla <lb></lb>le forze sue naturali, dipendenti dai sensi che ammanniscono all&#039;intelletto. </s>

<s><lb></lb>Or perchè è limitata l&#039;apprensione de&#039;sensi, limitate son perciò le notizie, <lb></lb>che approdan per essi. </s>

<s>Quante cose ci saranno, che non si toccano, non si <lb></lb>gustano, non si odorano, non si odono e non si veggono, e che pur possono <lb></lb>essere organi essenziali della vita vegetativa e dell&#039;animale? </s>

<s>Chi riconosce <lb></lb>ciò, riconosce nello studio della vita il mistero, chi non lo riconosce, è irra­<lb></lb>gionevole, negando l&#039;esistenza a quel che non è disposto a cadergli sotto le <lb></lb>passioni del senso. </s></p><p type="main">

<s>Per tornar dunque alla respirazione, la scienza moderna ha progredito <lb></lb>perchè l&#039;ossigeno è cosa trattabile e visibile ne&#039;suoi effetti, ma s&#039;inganne­<lb></lb>rebbe chi credesse che nella chimica dei corpi aerei fossero rivelate le fun­<lb></lb>zioni della vita. </s>

<s>La storia della scienza moderna raccontando le baldanze <lb></lb>precedute ai dubbi, e i dubbi nuovamente insorti ad attutir le baldanze, po­<lb></lb>trebbe assai bene coi fatti dimostrar quell&#039;inganno, ma a noi non resta a <lb></lb>dir altro, se non quel che della respirazion delle piante si seppe dagli scien­<lb></lb>ziati anteriori alla prima metà del secolo XVIII. </s></p><p type="main">

<s>Il Malpighi, appena ebbe scoperta quella delicatissima testura dei vasi <lb></lb>spirali, non dubitò di qualificarli per polmoni delle piante, e gl&#039;insignì per­<lb></lb>ciò di quel medesimo nome di <emph type="italics"></emph>trachee,<emph.end type="italics"></emph.end> che avevano avuto negli animali, <lb></lb>come quelli che secondo lui erano deputati ai medesimi uffici. </s>

<s>La respira­<lb></lb>zione dall&#039;altra parte gli sembrava una delle principali funzioni della vita, <pb xlink:href="020/01/1653.jpg" pagenum="528"></pb>e nel divisarne gli organi, nella varietà dei viventi, riconosce una provvi­<lb></lb>dentissima legge della Natura. </s>

<s>È questa legge “ ut quae perfectiora nobis <lb></lb>censentur, ea minori pulmonum apparatu gaudeant ” (De cortice, Op. </s>

<s>omn. </s>

<s><lb></lb>cit., pag. </s>

<s>32). Negli animali superiori infatti, come nell&#039;uomo e ne&#039;quadru­<lb></lb>pedi, i polmoni son due soli, ma negli uccelli vi si aggiungono le vescicole <lb></lb>dell&#039;aria, che sono un&#039;appendice agli organi polmonari. </s>

<s>Ne&#039;pesci i polmoni <lb></lb>son tanti quante son le fogliette delle branchie, ma negl&#039;insetti se ne con­<lb></lb>tano otto e talvolta dieci, che si moltiplicano per tutte le membra in innu­<lb></lb>merevoli diramazioni. </s>

<s>“ In plantis vero, quae infimum animalium attingunt <lb></lb>ordinem, tantam trachearum copiam et productionem extare par est, ut his <lb></lb>minimae vegetantium partes, praeter corticem, irrigentur ” (ibid.). </s></p><p type="main">

<s>Benchè sia però tanta la necessità della respirazione, e la Natura vi <lb></lb>provveda con sì laborioso apparato di organi, l&#039;uso di lei, prosegue a dire <lb></lb>il Malpighi, “ adeo tamen obscurus, mihique adhuc ignotus est, ut post <lb></lb>multas meditationes ea tantum mihi repetere liceat, quae alias subindicavi ” <lb></lb>(ibid., pag. </s>

<s>33). Dicemmo altrove quali fossero queste malpighiane medita­<lb></lb>zioni, e qui ripetiam coll&#039;Autore che forse l&#039;uso principale dell&#039;aria, intro­<lb></lb>dottasi nelle parti delle piante e degli animali, è quello di provocar la fer­<lb></lb>mentazione, e di mantener la fluidità nella linfa e nel sangue. </s>

<s>L&#039;aria poi <lb></lb>produce que&#039;benefici effetti per via de&#039;sali, specialmente nitrosi, volitanti <lb></lb>continuamente in mezzo a lei, e questa è forse, soggiunge, la ragione per­<lb></lb>chè “ in arborum plantatione altae excitantur per longum ante tempus fo­<lb></lb>veae ” (ibid.). </s></p><p type="main">

<s>Le irose divergenze fra il Malpighi e il Borelli, a proposito della respi­<lb></lb>razione animale, ritornarono pertinaci anche nell&#039;applicar la teorica di quella <lb></lb>funzione alle piante; ond&#039;è che, escludendo il Borelli stesso ogni azione chi­<lb></lb>mica, e tutto riducendo alla meccanica, disse non esser l&#039;aria per altro ne­<lb></lb>cessaria alla vita dei vegetanti, che per allieviare la natia gravezza, e così <lb></lb>più facile in alto promovere il succo. </s>

<s>“ Quod postea plantae nutriri et cre­<lb></lb>scere non possent, si omnino aere carerent, probatur quia succi aquei, ob <lb></lb>nativam gravitatem, per se sursum ascendere non possunt e radicibus ver­<lb></lb>sus truncum et ramos ” (De motu anim., P. II cit., pag. </s>

<s>372). </s></p><p type="main">

<s>Queste e altre teorie meccaniche del Borelli furono facilmente dimen­<lb></lb>ticate dagli stessi suoi più immediati successori, ma scopertasi la sensibile <lb></lb>e insensibile traspirazion delle foglie ebbero a subire una modificazione an­<lb></lb>che le sapienti dottrine del Malpighi. </s>

<s>Quel notabilissimo fatto del traspirare <lb></lb>sembrava tanto simile al respirare, e in animali imperfettissimi (che come <lb></lb>tali si riguardavan le piante) ne simulava così bene le veci, che s&#039;inclinò <lb></lb>molto a credere facessero le foglie stesse, piuttosto che le trachee, l&#039;ufficio <lb></lb>di polmoni. </s>

<s>L&#039;Hales anzi si credè d&#039;aver colle sue statiche esperienze tolto <lb></lb>ogni dubbio, e così sentenziosamente ne concluse: “ Or possiam dunque <lb></lb>con ragione persuadersi di quello, che per tanto tempo si è dubitato, cioè <lb></lb>che le foglie fanno l&#039;ufficio ne&#039;vegetabili, che i polmoni negli animali ” <lb></lb>(Traduz. </s>

<s>cit., pag. </s>

<s>256). </s></p><pb xlink:href="020/01/1654.jpg" pagenum="529"></pb><p type="main">

<s>La sentenziosa conclusione halesiana però era di tanta novità e di tanta <lb></lb>importanza, che non peteva sfuggire all&#039;esame del Bonnet in quella diligen­<lb></lb>tissima fisiologia, ch&#039;egli istituiva dell&#039;uso delle foglie. </s>

<s>Avranno già i nostri <lb></lb>lettori notata nel celebre Naturalista ginevrino una tale inclinazione alle dot­<lb></lb>trine non solo, ma alle ipotesi malpighiane, ch&#039;egli non fa bene spesso altro <lb></lb>che lumeggiarle di nuove idee, e confermarle meglio coll&#039;esperienze. </s>

<s>Il Mal­<lb></lb>pighi aveva, come vedemmo, rassomigliate le foglie alla cute, e il Bonnet, <lb></lb>dop&#039;avere osservato che il giorno il succo nutritizio esala per le aperture <lb></lb>della pagina fogliacea inferiore, e che la notte, chiudendosi quelle aperture <lb></lb>e costringendosi le trachee, fanno rifluire il succo verso la radice; “ on <lb></lb>voit, soggiunge, par cette légere esquisse de la theorie du mouvement de <lb></lb>la seve, que les fevilles ont beaucoup de rapport dans leurs usages avec la <lb></lb>peu du corps humain ” (Recherches cit., pag. </s>

<s>92). </s></p><p type="main">

<s>La persuasione anzi di questa analogia s&#039;era tanto più fermamente sta­<lb></lb>bilita nel Bonnet, che nello stesso Malpighi, in quanto che l&#039;uno avea con­<lb></lb>fessato che ansiosamente cercando “ an in foliis et cortice orificia pro aere <lb></lb>paterent, nec ea unquam deprehendere potui ” (De cortice cit., pag. </s>

<s>32, 33), <lb></lb>e l&#039;altro avea scoperto gli <emph type="italics"></emph>stomi,<emph.end type="italics"></emph.end> ed era di più intervenuto a certe anato­<lb></lb>mie di Gian Lodovico Calandrini, che dimostravano nelle stesse foglie “ une <lb></lb>membrane réticulaire analogue à celle du corps humain ” (Recherches cit., <lb></lb>pag. </s>

<s>93); ossia analoga al <emph type="italics"></emph>Reticolo malpighiano.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Confermatosi dunque il Bonnet per questi nuovi, aggiunti agli argo­<lb></lb>menti antichi, che le foglie fanno le veci della cute, e che perciò l&#039;ufficio <lb></lb>di polmoni rimane alle trachee, senti, in questa persuasione, che si faceva, <lb></lb>e non senza ragionevoli motivi, gran conto della sentenza pronunziata dal­<lb></lb>l&#039;Hales. </s>

<s>Perciò volle istituire alcune nuove esperienze, ch&#039;egli poi descrisse <lb></lb>nella prima delle sue <emph type="italics"></emph>Recherches,<emph.end type="italics"></emph.end> per iscoprir se veramente le foglie siano, <lb></lb>come si diceva, i polmoni delle piante. </s></p><p type="main">

<s>La prima cosa, che in tal proposito gli occorse al pensiero, fu quella <lb></lb>di osservar ciò che accade immergendo i rami con tutte le foglie nell&#039;acqua. </s>

<s><lb></lb>Fece la prima esperienza nell&#039;estate del 1747 sopra un tralcio di vite, ed <lb></lb>ebbe a notarvi questo fatto singolarissimo: “ Dès que la soleil commença <lb></lb>à échauffer l&#039;eau des vases, je vis paroitre sur les fevilles des rameaux beau­<lb></lb>coup de bulles semblabes à de petites perles..... Toutes disparurent après <lb></lb>le coucher du soleil. </s>

<s>Elles reparurent le lendemain matin, lorsque cet astre <lb></lb>vint a darder ses rayons sur les poudriers ” (ivi, pag. </s>

<s>46, 47). Vedeva gal­<lb></lb>lozzolar quell&#039;aria più numerosa e più grossa, via via che, sollevandosi il <lb></lb>sole, dava nel vaso d&#039;acqua più ardente, cosicchè aderendo le bollicelle per <lb></lb>un certo visco lor proprio, più che ad altro, alla superficie inferiore, resi <lb></lb>perciò i pampani assai più leggeri venivano a sollevarsi con tutto il tralcio <lb></lb>a galla. </s></p><p type="main">

<s>Forse fu l&#039;esperienza suggerita al Bonnet da quell&#039;altra simile espe­<lb></lb>rienza instituita, come narrammo nel precedente capitolo, dal Reaumur per <lb></lb>assicurarsi del modo come respirano i bruchi. </s>

<s>Ma comunque sia, il Bonnet <pb xlink:href="020/01/1655.jpg" pagenum="530"></pb>stesso confessa ch&#039;ebbero le remurriane dottrine sulla respirazion degl&#039;in­<lb></lb>setti molta efficacia in farlo andare a credere che anche sulle foglie, come <lb></lb>sopra la cute animale, fossero quelle bollicelle d&#039;aria effetto della respira­<lb></lb>zione. </s>

<s>“ L&#039;apparition de ces bulles à la prèsence du soleil, leur disparition <lb></lb>à l&#039;entrée de la nuit me firent d&#039;abord penser qu&#039;elles êtroient produites par <lb></lb>une sorts de respiration de la plante, par une respiration dont les alterna­<lb></lb>tives dépendoient des alternatives du chaud et du frais; du chaud, pour <lb></lb>l&#039;expiration; du frais pour l&#039;inspiration ” (ivi, pag. </s>

<s>47, 48). </s></p><p type="main">

<s>Ma poi osservando che la superficie inferiore era sempre molto più bol­<lb></lb>licosa dell&#039;altra, e risovvenutosi delle antecedenti esperienze, le quali gli <lb></lb>avevano dimostrato esser quella stessa inferior superfice molto meglio di­<lb></lb>sposta ad assorbire l&#039;umidità, ebbe a mutarsi d&#039;idea, e a dire che quella <lb></lb>non era aria respirata dalle foglie, ma che queste piuttosto, come fanno le <lb></lb>branchie de&#039;pesci, hanno virtù di discriminarla dall&#039;acqua. </s>

<s>Impaziente di ve­<lb></lb>rificare il fatto, ripurgata l&#039;acqua stessa d&#039;ogni aria col tenerla per tre quarti <lb></lb>d&#039;ora a bollire, e nel solito vaso ripieno di essa, messo un ramicello ver­<lb></lb>deggiante agli ardori del sole, “ je ne vis pourtant paroitre aucune bulle ” <lb></lb>(pag. </s>

<s>49). Volle anche fare l&#039;esperienza opposta, insufflando nell&#039;acqua nuova <lb></lb>quantità d&#039;aria, e vide allora ricoprirsi le foglie di bollicelle più numerose, <lb></lb>e più grosse di quelle prima osservate, ciò che pareva confermar la conce­<lb></lb>puta opinione esser l&#039;aria, rimasta così presa in quelle bollicelle, uscita fuori <lb></lb>dal liquido ambiente e non dal verde. </s></p><p type="main">

<s>Questo fluttuare della mente era al Bonnet penoso, e presagio certo che, <lb></lb>non spirando le aure uguali, non avrebbero così facilmente sospinta la na­<lb></lb>vicella del suo ingegno a toccare il porto desiderato. </s>

<s>Ma ecco a un tratto <lb></lb>vede balenare una luce, che gli scopre il suo errore: quelle esperienze riu­<lb></lb>scivano così equivoche, perchè avea trascurata una precauzione importante, <lb></lb>qual era quella di liberar dall&#039;aria, che naturalmente vi aderisce, le foglie, <lb></lb>prima di sommergerle, come faceva, nell&#039;acqua. </s>

<s>Fu questa stessa negligenza <lb></lb>che lo condusse ad ammettere, col Reaumur e contro il Malpighi, essere <lb></lb>espirate dalle trachee quelle bollicelle d&#039;aria, che si vedevano apparir sot­<lb></lb>t&#039;acqua sopra tutta la cute dei bruchi, ma “ lorsque j&#039;ai plongé ces insectes <lb></lb>dans l&#039;eau, apres avoir eu soin de chasser l&#039;air de leur extêrieur, en le frot­<lb></lb>tant à diverses reprises avec un pinceau movillé, je n&#039;ai point vu s&#039;élever <lb></lb>de bulles sur la peau, mais j&#039;en ai vu sortir un grand nombre des stigma­<lb></lb>tes. </s>

<s>On peut voir dans les <emph type="italics"></emph>Transactions philosophiques<emph.end type="italics"></emph.end> n.o 487, le précis <lb></lb>de ces recherches sur la respiration des chenilles ” (pag. </s>

<s>52). Son quivi de­<lb></lb>scritte in gran parte quelle esperienze, che lo Spallanzani prometteva di <lb></lb>pubblicare nel suo <emph type="italics"></emph>Prodromo,<emph.end type="italics"></emph.end> e dalle quali venivasi a confermare contro il <lb></lb>Reaumur quel che del Bombice avea scritto il Malpighi, che cioè per le <lb></lb>stimmate veramente entra ed esce l&#039;aria in quel respirare che fanno i pol­<lb></lb>moni degli insetti. </s></p><p type="main">

<s>Applicatesi dunque dal Bonnet quelle stesse cure in rinettar dall&#039;aria <lb></lb>le foglie, trovò molto maggiori difficoltà che intorno agl&#039;insetti, perhè es-<pb xlink:href="020/01/1656.jpg" pagenum="531"></pb>sendo le foglie naturalmente intonacate di quella loro vernice, l&#039;umidità del <lb></lb>pennello vi s&#039;attacca difficilmente, e mentre si passa a inumidir la parte vi­<lb></lb>cina, quella inumidita già è bell&#039;e rasciutta. </s>

<s>Questo per lo più avviene alle <lb></lb>foglie degli alberi sempre verdi: alcune altre però si riesce a tenerle umide, <lb></lb>e perciò libere da ogni aria aderente, infintantochè non sia il punto d&#039;im­<lb></lb>mergerle nell&#039;acqua. </s>

<s>Or “ toutes les fevilles qui ont pu être humectées a <lb></lb>fond avant que d&#039;être plongées dans l&#039;eau, n&#039;ont donné que peu ou point <lb></lb>de bulles, lorsqu&#039;elles y ont été plongées. </s>

<s>Il en a paru un assez grand nom­<lb></lb>bre sur les fevilles dont je n&#039;ai pu parvenir à chasser éntiérement l&#039;air, mais <lb></lb>ces bulles ont toujours été en moindre quantité que celles qui se sont éle­<lb></lb>vées sur de semblabes fevilles que je n&#039;avois point humectées avant que de <lb></lb>les plonger dans l&#039;eau ” (pag. </s>

<s>54). </s></p><p type="main">

<s>Ecco a qual conclusione andarono finalmante a riuscire le così bene av­<lb></lb>viate esperienze del Bonnet: a negar cioè ogni atto di respirazione alle fo­<lb></lb>glie, perchè quella, che da principio credeva essere aria esalata dall&#039;interno, <lb></lb>trovò invece che aderiva alla esterior superfice, com&#039;aderisce a tutti i corpi <lb></lb>secchi, non eccettuate le stesse foglie inaridite, le quali, tolte da un albero <lb></lb>già tagliato da un anno, trovò che facevano sott&#039;acqua il medesimo effetto <lb></lb>delle verdi. </s>

<s>Ebbe perciò a venire alla final conclusione: “ que les bulles qui <lb></lb>s&#039;élevent sur les fevilles vertes, et qui végetent encore, ne sont pas l&#039;effet de <lb></lb>quelque mouvement vital ” (pag. </s>

<s>56). </s></p><p type="main">

<s>Poniamo che si fosse avventurosamente abbattuto il Bonnet a veder <lb></lb>fatte le sue proprie esperienze dalla Natura nell&#039;acqua di una vasca, dal <lb></lb>fondo della quale ferito da&#039;vivi raggi del sole si vedono sollevarsi le fila di <lb></lb>cert&#039;erbe, che ci vivono dentro, e sulla sera tornare a ricoricarsi nel loro <lb></lb>letto. </s>

<s>L&#039;effetto idrostatico, diligentemente osservando, l&#039;avrebbe senza dubbio <lb></lb>attribuito a quell&#039;aeree bollicelle, che appariscono e spariscono insieme col <lb></lb>sole, e l&#039;origine delle quali, non rimanendo mai le pianticelle in secco, era <lb></lb>forza attribuirla all&#039;esalar che fanno esse pianticelle per una specie di re­<lb></lb>spirazione. </s>

<s>Nè sarebbe stato molto difficile accorgersi che negli sperimen­<lb></lb>tati effetti l&#039;azione era propria della luce e no del calore, vedendosi rima­<lb></lb>nere a giacer le fila erbose in fondo alla vasca, sempre che, essendo l&#039;aria <lb></lb>intorno caldissima, non giunge a penetrarvi dentro raggio vivo di sole. </s>

<s>Così <lb></lb>sarebbe stato direttamente condotto il Bonnet a scoprir che la luce ha una <lb></lb>particolare efficacia sulla respirazion delle piante; scoperta che rimase ai <lb></lb>botanici del secolo appresso, osservando con gli occhi illuminati dalla Chi­<lb></lb>mica i fatti delle stesse esperienze bonnettiane. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi ripensa al gagliardo impulso, che dovette venire alla scienza della <lb></lb>vita vegetativa per fare, in sì breve tempo, i progressi fin qui narrati, lo <lb></lb>riconosce facilmente nella felicissima idea che s&#039;ebbe di riscontrare essa vita <pb xlink:href="020/01/1657.jpg" pagenum="532"></pb>vegetativa con gli organi, e con le funzioni della vita animale. </s>

<s>L&#039;esempio <lb></lb>del Cesalpino, da cui quella scienza ha gl&#039;inizi, fu con fedeltà seguito dal <lb></lb>Malpighi, che la ridusse ai più alti fastigi, e che non dubitò, come poco fa <lb></lb>udimmo, di riguardar le piante quali animalità degl&#039;infimi gradi. </s>

<s>Una cosa <lb></lb>però in queste considerazioni assai notabile è che, concedendosi al Cesalpino <lb></lb>stesso senza tante difficoltà, anzi con quasi universale approvazione, la so­<lb></lb>miglianza fra i semi e le uova, si combattesse poi tanto, e tanto s&#039;aberrasse <lb></lb>in riconoscer ch&#039;essendo, negli animali e nelle piante, le due geniture si­<lb></lb>mili, simili ne dovevan esser pure gli organi e le funzioni. </s>

<s>Deve anzi il fatto <lb></lb>sembrare anche più notabile a coloro, i quali ripensano che i nomi di <emph type="italics"></emph>ma­<lb></lb>schi<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>femmine<emph.end type="italics"></emph.end> furono introdotti, e divennero d&#039;uso comune fra gli an­<lb></lb>tichissimi cultori dei fichi e delle palme. </s>

<s>Dal popolo accettarono quel lin­<lb></lb>guaggio gli scrittori, e dagli scrittori passò, per l&#039;aristotelico magistero, fra <lb></lb>gli studiosi della Storia naturale. </s>

<s>Nel primo libro infatti <emph type="italics"></emph>De plantis,<emph.end type="italics"></emph.end> com­<lb></lb>preso fra quelli di Aristotile, così nel cap. </s>

<s>III si legge: “ In palmis quoque, <lb></lb>si folia vel foliorum pulvis vel palmae masculinae cortex foliis foemellae pal­<lb></lb>mae apponantur, ut cohaereant, cito maturescent eius fructus, casusque co­<lb></lb>rum prohibebitur. </s>

<s>Discerniturque masculus a foemella, quia prius pullulant <lb></lb>eius folia, suntque minora quam illius: itidem e fragrantia discernnntur. </s>

<s><lb></lb>Quod si forte ex odore masculi abduxerit quippiam ventus ad foemellam, <lb></lb>sic quoque maturescent ipsius fructus, quemadmodum cum folia masculi ex <lb></lb>illa fuerit suspensa. </s>

<s>Ficus quoque sylvestres per terram expansae ficubus <lb></lb>hortensibus conferunt ” (Arist., Operum T. VI cit., fol. </s>

<s>77). </s></p><p type="main">

<s>Chi però, fra quelli poco sopra notati, avesse dalla lettura di questo testo <lb></lb>presa occasione di maravigliarsi come mai, avendo avuto la sessualità delle <lb></lb>piante così favorevoli auspici, e così antichi e autorevoli principii, s&#039;indu­<lb></lb>giasse nonostante tanti secoli a professarla come una delle più faticose con­<lb></lb>quiste della scienza moderna; si sentirebbe cessare ogni maraviglia in saper <lb></lb>che quei nomi di maschi e di femmine, dati alle palme, non son sulla lin­<lb></lb>gua dell&#039;Autore aristotelico altro che per una metafora, o per secondare i <lb></lb>predominanti usi del volgo, dalle idee del quale però fa il Filosofo sdegno­<lb></lb>samente divorzio. </s></p><p type="main">

<s>Il primo e dichiarato atto di questo divorzio apparisce in uno de&#039;più <lb></lb>illustri discepoli di Aristotile, Teofrasto, il quale nel cap. </s>

<s>XXIII del III libro <lb></lb><emph type="italics"></emph>De causis plantarum,<emph.end type="italics"></emph.end> si rivolge con filosofico sopracciglio contro coloro, che <lb></lb>dichiaravano le palme femmine insufficienti per sè medesime a condurre il <lb></lb>loro parto, perchè dicevano che avean bisogno d&#039;essere asperse delle pol­<lb></lb>veri del maschio. </s>

<s>Che se fosse veramente così, argomenta il Filosofo, do­<lb></lb>vrebb&#039;essere per una legge universale della Natura, a stabilir la quale non <lb></lb>basta un semplice fatto osservato in una sola specie di piante. </s>

<s>Vero è che <lb></lb>soggiungono costoro avvenir qualche cosa di simile nel fico, ma del capri­<lb></lb>ficio io comprendo, presegue a dir Teofrasto, la ragione, perchè il frutto do­<lb></lb>mestico non giungerebbe a maturità, se gl&#039;insetti, usciti fuor dal silvestre, <lb></lb>non gli aprissero, entrando a pascervisi, la coroncina, d&#039;onde s&#039;apre l&#039;adito <pb xlink:href="020/01/1658.jpg" pagenum="533"></pb>a ricevere i benefici influssi dell&#039;aria e del sole: della necessità però delle <lb></lb>polveri maschili, ad avvalorare le deboli virtù delle femminee palme, non <lb></lb>si sa che alcuno n&#039;abbia resa qualche ragione. </s>

<s>“ Fructum autem perdurare <lb></lb>in palma foemina nunquam posse, nisi florem maris cum pulvere super eam <lb></lb>concusserint, ita enim quidam confirmant, peculiare profecto est, sed simile <lb></lb>caprificationi ficorum qua fructus perficitur. </s>

<s>Ergo foeminam minus ad per­<lb></lb>ficiendum sibi sufficere aliquis potissimo dicet. </s>

<s>Sed hoc non in uno genere <lb></lb>aut duobus, sed vel in omnibus, vel in pluribus constare deberet: naturam <lb></lb>etenim generis ita diiudicamus. </s>

<s>Et in his tamen ipsis paucis generibus mi­<lb></lb>rum quod palmae nulla ratio dari possit cum caprificationis causa conspi­<lb></lb>cua esse putetur ” (Theodoro Gaza interpetre, Luteciae 1529, pag. </s>

<s>167, 68). <lb></lb>In conformità di queste opinioni, per le quali veniva a ripudiarsi la distin­<lb></lb>zion di maschi e di femmine, nel vero e proprio significato che hanno que­<lb></lb>sti nomi applicati agli animali, Teofrasto, ammesso che molte fra quelle <lb></lb>piante sieno per loro propria natura sterili, attribuisce, nel cap. </s>

<s>VIII del <lb></lb>II libro <emph type="italics"></emph>De historia plantarum,<emph.end type="italics"></emph.end> la fecondità indifferentemente ad ambedue <lb></lb>i sessi. </s></p><p type="main">

<s>Nel risorgimento delle lettere, e in quel primo risveglio che n&#039;ebbero <lb></lb>a risentire anche le scienze, Pier Andrea Mattioli è dopo tanti secoli il primo, <lb></lb>che per industria propria, con le modeste intenzioni di tradurre e di com­<lb></lb>mentar Dioscoride, coltivi la storia delle piante. </s>

<s>Trattando, nel cap. </s>

<s>CXXVII <lb></lb>del I libro, <emph type="italics"></emph>Della corteccia dei frutti della palma,<emph.end type="italics"></emph.end> riferisce il detto di Pli­<lb></lb>nio, che cioè non fruttifica la femmina, se non ha il maschio da presso. </s>

<s>Ma <lb></lb>quasi sollecito di spiegarsi in che modo s&#039;abbia a intendere lo strano lin­<lb></lb>guaggio, soggiunge tosto, sull&#039;autorità di Teofrasto, che tanto i maschi quanto <lb></lb>le femmine portano i loro frutti allo stesso modo. </s>

<s>“ E secondo che si legge <lb></lb>al IV del XIII di Plinio, le palme femmine non producono il frutto loro, se <lb></lb>non hanno il maschio appresso, il quale, se per sorte lor vien tagliato o si <lb></lb>secca, non fanno più frutto. </s>

<s>Ma non è però da credere che i maschi non <lb></lb>portino ancora loro il frutto, imperocchè, scrive Teofrasto, che tra le frut­<lb></lb>tifere, perciocchè assai son le sterili, tanto portano i frutti i maschi quanto <lb></lb>le femmine ” (Venezia 1555, pag. </s>

<s>134). </s></p><p type="main">

<s>Per l&#039;autorevole magistero del Mattioli trovavan dunque le scienze spe­<lb></lb>rimentali, nel loro istituirsi e ne&#039;loro primi progressi, ingerita già l&#039;opinione <lb></lb>ch&#039;essendo le femmine delle palme e i maschi ugualmente fruttiferi non <lb></lb>fossero i loro amori altro che un poetico idillio gentile. </s>

<s>Francesco Redi però, <lb></lb>che sapeva esser bene spesso la poesia il fiore della sapienza, in mezzo a <lb></lb>que&#039;giovanili ardori che lo trasportavano a coltivar la storia della Natura, <lb></lb>per ciò che specialmente concerne la generazione degli animali, rivolgeva di <lb></lb>quando in quando il pensiero anche sopra le piante. </s>

<s>Che queste, alle quali <lb></lb>attribuiva una vita sensitiva, non si generassero a caso, ma con certa legge <lb></lb>di organi e di funzioni, analoghe a quelle ch&#039;ei ritrovò proprie infino dei <lb></lb>vilissimi insetti, gli pareva tanto probabile, quanto però difficile a dimostrare. </s>

<s><lb></lb>Non aveva a rimeditare sopr&#039;altro esempio che sopra le Palme, intorno alle <pb xlink:href="020/01/1659.jpg" pagenum="534"></pb>quali, non essendogli possibile d&#039;istituire esperienze, conveniva starsene alle <lb></lb>relazioni degli scrittori, che o antichi o recenti sagacemente riconosceva te­<lb></lb>ner rimescolato insieme il vero col falso. </s>

<s>Volle la sua buona ventura che <lb></lb>capitasse in Firenze uno schiavo affricano, redento dal Granduca, di nome <lb></lb>Abulgaith Ben Farag, che cominciò a interrogarlo con gran curiosità, spe­<lb></lb>rando di raccoglier qualche cosa di più certo da lui, ch&#039;era nato in mezzo <lb></lb>ai palmeti. </s>

<s>Quell&#039;uomo, educato nelle scuole di Fessa, e poi statovi per quin­<lb></lb>dici anni maestro di legge, era, per maomettano, assai dotto, ond&#039;è che, per <lb></lb>le avutene relazioni, potè il senno del Redi sceverare dal vero quel che di <lb></lb>immaginario o di superstizioso aveva letto nei libri. </s>

<s>Egli si certificò così di <lb></lb>un fatto importantissimo, il quale, se fosse stato com&#039;avevalo riferito il Mat­<lb></lb>tioli sull&#039;autorità di Teofrasto, bastava a dichiarare addirittura per una fol­<lb></lb>lia l&#039;assunto di concluder, dall&#039;esempio delle palme, la sessualità di tutte le <lb></lb>piante. </s>

<s>Si certificò dunque il Redi che solamente le femmine, fra quegli al­<lb></lb>beri, menano frutti. </s>

<s>Si certificò inoltre che, per fecondare esse femmine, ba­<lb></lb>stava aspergerle delle polveri del maschio, nelle quali polveri conoscendo una <lb></lb>virtù analoga a quella dell&#039;umor seminale, e argomentando, contrariamente <lb></lb>alla logica di Teofrasto che, per esser la Natura in tutto e sempre simile <lb></lb>a sè medesima, un esempio solo poteva farsi rivelatore di una legge uni­<lb></lb>versale; stabilì seco medesimo che, s&#039;è vera, la sessuale generazion delle <lb></lb>palme, <emph type="italics"></emph>l&#039;erbe tutte e gli alberi hanno il maschio e la femmina.<emph.end type="italics"></emph.end> Nel venir <lb></lb>però a significare, in una Lettera che ha la data del primo Maggio 1666, <lb></lb>questi pensieri suoi propri, per non inimicarsi i ritrosi d&#039;ogni novità, gli <lb></lb>attribuisce a&#039;suoi antecessori, che avevane scritto delle virtù delle piante. </s>

<s>E <lb></lb>perchè nell&#039;eleganza dei modi raccolgon le parole del Redi quell&#039;erudizione <lb></lb>storica, lasciata indietro da noi, crediamo di supplire con larga usura al di­<lb></lb>fetto trascrivendole ai nostri lettori. </s></p><p type="main">

<s>“ Ma siccome, secondo che scrivono coloro, i quali le virtù delle piante, <lb></lb>ovvero la lor natura investigarono, l&#039;erbe tutte e gli alberi hanno il maschio <lb></lb>e la femmina; così in nessuna pianta è più manifesto che nella Palma, im­<lb></lb>perocchè vanno raccontando che la femmina senza maschio non genera e <lb></lb>non mena i frutti, e che all&#039;intorno del maschio molte femmine distendono <lb></lb>i loro rami, e pare che lo allettino e lo lusinghino, ed egli, ruvido ed aspro, <lb></lb>col fiato, col vedere, colla polvere la ingravida. </s>

<s>E se il maschio, o si secca <lb></lb>o venga tagliato, le femmine che gli verdeggiano intorno, fatte per così dir <lb></lb>vedove, diventano sterili. </s>

<s>” </s></p><p type="main">

<s>“ Achille Tazio, nel primo libro degli Amori di Leucippe e di Clito­<lb></lb>fonte, descrive teneramente questi amori della Palma, e con non minor ga­<lb></lb>lanteria ne fanno menzione Teofilatto Simocatta nell&#039;Epistole, Michele Glica <lb></lb>negli Annali, Ammiano Marcellino e Claudiano, che nelle Nozze di Onorio <lb></lb>disse: <emph type="italics"></emph>Vivunt in Venerem frondeis omnisque vicissim felix arbor amat, <lb></lb>nutant ad mutua Palmae foedera. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Invilupparono però tutti costoro la verità con mille poetiche fole, con­<lb></lb>ciossiachè egli è menzogna, per quanto Abulgaith mi dice, che sia neces-<pb xlink:href="020/01/1660.jpg" pagenum="535"></pb>sario che il maschio si pianti vicino alla femmina, e che dalla femmina sia <lb></lb>veduto o ne sia da lei sentito l&#039;odore, imperocchè vi sono de&#039;giardini e <lb></lb>de&#039;palmeti, ne&#039;quali non vi ha maschi, eppure le femmine vi sono feconde, <lb></lb>e là dove sono i maschi, se dal suolo sien recisi, non pertanto quelle desi­<lb></lb>stono ogni anno dal fruttificare. </s>

<s>Egli è con tutto ciò vero che i maschi con­<lb></lb>tribuiscono un non so che per fecondar le femmine, ed io ne scriverò qui <lb></lb>a V. S. quanto ne ho potuto comprendere. </s>

<s>” </s></p><p type="main">

<s>“ Ciò è che la Palma, dall&#039;età sua di tre o di quattro o di cinque anni, <lb></lb>infino al trentesimo, produce al primo apparir della novella primavera, dalle <lb></lb>congiunture di molti de&#039;più bassi rami, un certo verde invoglio, che cresce <lb></lb>alla grandezza d&#039;un mezzo braccio in circa, il qual poi, nel mese di Aprile, <lb></lb>quando è il tempo di fiorire, da sè medesimo screpola e si apre, e vedesi <lb></lb>pieno di moltissimi bianchi ramoscelli, su de&#039;quali in abbondanza spuntano <lb></lb>fiori simili a quelli del gelsomino, bianchi lattati, con un poco di giallo nel <lb></lb>mezzo. </s>

<s>Questo invoglio e questi fiori tanto son prodotti dal maschio che dalla <lb></lb>femmina, ma i fiori del maschio hanno un soave odore, e ne cade una certa <lb></lb>polvere bianca, somigliante alla farina di castagno, dolce al gusto e delicata, <lb></lb>e se ne vanno tutti in rigoglio, e mai non producono i dattili, ancorchè di <lb></lb>diverso parere fosse Teofrasto. </s>

<s>” </s></p><p type="main">

<s>“ Pel contrario i fiori della femmina, che non hanno così buono odore, <lb></lb>e non ispolverano quella farina, fanno i dattili in gran copia, ma bisogna <lb></lb>usarci alcuna diligenza, imperocchè, quando incominciano a sbocciar dall&#039;in­<lb></lb>voglio, o dal mallo che dir lo vogliamo, si taglia tutto intorno tutto l&#039;invo­<lb></lb>glio, e nudi si lasciano i rami de&#039;fiori, tra&#039;quali s&#039;intessono due o tre ra­<lb></lb>muscelli, pur di fiori colti dal maschio. </s>

<s>Quindi tutti uniti si legano insieme <lb></lb>in un mazzo, e così legati si tengono sino a tanto che quegli inseriti ramu­<lb></lb>scelli del maschio sieno secchi, ed allora si tolgono via i legami, e così ven­<lb></lb>gono fecondate le femmine con quest&#039;opera, senza la quale non condurreb­<lb></lb>bono i dattili alla perfezione e alla buona maturezza. </s>

<s>” </s></p><p type="main">

<s>“ Se poi questa sia una superstizione, oppure un consueto modo di <lb></lb>fare, forse ed inutile, io per me non saprei che credermene. </s>

<s>So bene che il <lb></lb>costume è antichissimo, e su questo fondamento andò favoleggiando Achille <lb></lb>Tazio, quando disse che, se il maschio della Palma sia piantato gran tratto <lb></lb>lontano dalla sua femmina, tutto appassito infralisce e quasi vien meno, e <lb></lb>ben tosto diverrebbe arido tronco, se il sagace agricoltore, conosciuto il di <lb></lb>lui male, non istrappasse una vermena dalla desiderata femmina, e non l&#039;in­<lb></lb>nestasse nel cuore di esso maschio, cioè nella più interna midolla, da alcuni <lb></lb>chiamata il cuore della Palma. </s>

<s>” </s></p><p type="main">

<s>“ Io non posso però tacere che da alcuni altri mi è stato affermato che <lb></lb>non è necessario, per render feconda la femmina, l&#039;inserire que&#039;due o tre <lb></lb>ramoscelli de&#039;fiori del maschio tra&#039;fiori di essa femmina, ma che basta so­<lb></lb>lamente spolverizzare sopra un poco di quella bianca farina, che cade da&#039;fiori <lb></lb>del maschio, e se ciò fosse il vero, potremmo dar fede a Plinio che, scri­<lb></lb>vendo delle Palme, ebbe a dire: <emph type="italics"></emph>Adeoque est Veneris intellectus, ut coitus<emph.end type="italics"></emph.end><pb xlink:href="020/01/1661.jpg" pagenum="536"></pb><emph type="italics"></emph>etiam excogitatus sit ab homine ex mariti flore ac lanugine, interim vero <lb></lb>tantum pulvere insperso foeminis ”<emph.end type="italics"></emph.end> (Della nat. </s>

<s>delle Palme, Opere, T. VI, <lb></lb>Napoli 1740, pag. </s>

<s>154-56). </s></p><p type="main">

<s>L&#039;ipotesi in ogni modo, che la femmina delle palme rimanga fecondata <lb></lb>dalla polvere maschile, si riduceva per il Redi a una certezza di fatto, die­<lb></lb>tro le relazioni avute da Abulgaith, che tanto si conformavano co&#039;suoi prin­<lb></lb>cipii fisiologici intorno alla generazion dei viventi. </s>

<s>Attendeva perciò con sol­<lb></lb>lecito studio a investigare gli organi di così fatte generazioni, ch&#039;ei sperava <lb></lb>di trovar simili in tutti gli alberi e in tutte le erbe, ma le difficoltà incon­<lb></lb>trate lo sbigottirono, e gli fecero poi deporre ogni pensiero, quando usci <lb></lb>fuori il Malpighi a descrivere la struttura e gli uffici de&#039;fiori in modo, che <lb></lb>coloro, i quali v&#039;avean riconosciuta qualche immagine dei sessi, ci vedes­<lb></lb>sero specchiato il proprio inganno. </s></p><p type="main">

<s>Nella grande opera malpighiana <emph type="italics"></emph>De anatome plantarum<emph.end type="italics"></emph.end> il trattato <emph type="italics"></emph>De <lb></lb>floribus<emph.end type="italics"></emph.end> è uno de&#039;più insigni, ed è l&#039;Autore tanto diligente in descriver non <lb></lb>solo, ma in disegnar le foglie, gli stami e i pistilli, che il Boherave, per no­<lb></lb>tarne i generi, citò spesso gl&#039;iconismi di lui. </s>

<s>Il frutto poi di queste dili­<lb></lb>genze, ordinate a scoprir le varie proprietà e la natura de&#039;fiori, si può ve­<lb></lb>der concluso ne&#039;paragrafi ultimi di questo stesso trattato. </s></p><p type="main">

<s>De&#039;fiori, vi si legge, alcuni sono sterili, altri fecondi. </s>

<s>Son fecondi tutti <lb></lb>quelli, che son forniti di calice, di foglie, di stami e di stilo, e sono sterili <lb></lb>tutti i rimanenti che dello stesso stilo son privi. </s>

<s>È il fiore come il compen­<lb></lb>dio di tutta intera la pianta: dalla buccia nasce il calice, e dalla sostanza del <lb></lb>legno, composta di fistole e di trachee, hanno origine le foglie. </s>

<s>“ Non longe <lb></lb>a foliis stamina a lignea portione attolluntur, peculiarem succum in propriis <lb></lb>loculis (nelle antere) cribrantia et servantia: hunc patenti hiatu, data via, <lb></lb>sub globulorum forma (così descrive i granellini del polline) effundunt et <lb></lb>dispergunt. </s>

<s>In horum medio stylus fovetur, cuius concavitate colliquamenti <lb></lb>vesicula, vel seminis inchoamentum, conditur, et in ipso augetur, unde plan­<lb></lb>tarum uterum esse automo ” (Opera omnia, T. </s>

<s>I cit., pag. </s>

<s>69). </s></p><p type="main">

<s>Da quest&#039;utero sorge lo stilo, che l&#039;Autore disse più avanti esser parte <lb></lb>del fiore <emph type="italics"></emph>uterinis tubis analogam<emph.end type="italics"></emph.end> (pag. </s>

<s>64), ma perchè l&#039;analogia de&#039;nomi <lb></lb>non si lusingasse alcuno che importasse qualche reale somiglianza nelle fun­<lb></lb>zioni, è sollecito il Malpighi di dire che coteste trombe uterine non sono <lb></lb>aperte, come negli animali, a dar libero passaggio al seme maschile, ma sì <lb></lb>all&#039;aria esterna, perchè il germe più copiosamente ne possa respirare. </s>

<s>Nè <lb></lb>il viscido umore, segreto da que&#039;peli che sono in cima allo stilo, è, come <lb></lb>negli animali, il mucco vaginale, ordinato a deglutir più facilmente la virtù <lb></lb>fecondatrice, ma “ ut reliquum alimenti depuretur, et ne insecta intus ir­<lb></lb>ruant ” (ibid., pag. </s>

<s>70). </s></p><p type="main">

<s>Dubitai talvolta, prosegue a dire il Malpighi, se sien le foglie del fiore, <lb></lb>come del resto conclusi rispetto alle altre foglie, ordinate a concuocere nei <lb></lb>loro utricoli l&#039;alimento, per farlo refluire all&#039;utero tenerello; ma poi pen­<lb></lb>sai meglio che fosse quello di depurare gli umori il loro natural ministero. <pb xlink:href="020/01/1662.jpg" pagenum="537"></pb>Servono inoltre a questa depurazione gli stami, attraendo i corrotti umori <lb></lb>dentro i loro otricelli papillari “ unde fas est dubitare naturam plurimum <lb></lb>humoris, huncque diversae substantiae, seminum generationi incongruum, <lb></lb>per haec quasi emunctoria eliminare ” (ibid.). </s></p><p type="main">

<s>Ma per non finirla in congetture, soggiunge lo stesso Malpighi, ricor­<lb></lb>riamo alle esperienze. </s>

<s>Spesso, svelte le foglie prima che aprisse il fiore, aspet­<lb></lb>tai se lo stilo così denudato crescesse, e trovai a quel suo incremento un <lb></lb>notabile indugio. </s>

<s>Ma qualche altra volta i semi, senza riceverne offesa, giun­<lb></lb>sero alla loro perfetta maturità e grandezza “ unde adhuc dubius sum an <lb></lb>floris folia a solis et externi aeris irruentibns conatibus tenellum uterum <lb></lb>tutentur, an ulterius etiam depurando praeparent auctivam seminis mate­<lb></lb>riam ” (ibid.). </s></p><p type="main">

<s>Tali essendo le dottrine, diffuse dall&#039;autorevolissimo magistero del Mal­<lb></lb>pighi intorno all&#039;uso de&#039;fiori, è da veder quali fossero gl&#039;insegnamenti, che <lb></lb>venivano con autorità non molto minore dal Grew intorno a quel medesimo <lb></lb>soggetto. </s>

<s>Il capitolo V dei <emph type="italics"></emph>Primordii<emph.end type="italics"></emph.end> s&#039;intitola giusto <emph type="italics"></emph>De flore,<emph.end type="italics"></emph.end> e vi s&#039;in­<lb></lb>comincia a dir ch&#039;è il fiore a tutela e ad incremento, perchè le foglie di <lb></lb>lui promovono il succo. </s>

<s>Le antere, alle quali dà il nome di <emph type="italics"></emph>Chioma<emph.end type="italics"></emph.end> (attire), <lb></lb>crederebbe che fossero date a semplice ornamento, se non che non com­<lb></lb>prende perchè sien cave, con quella sottilissima polvere dentro, e perchè <lb></lb>ell&#039;abbiano a rompersi, infelicemente perdendo la loro prima bellezza. </s>

<s>“ Usus <lb></lb>ergo praeterea alius nobis cognoscendus est et observandus, isque est pro <lb></lb>victu animalium..... Cur enim alias hic adeo frequenter reperiuntur? </s>

<s>Or­<lb></lb>dine florem a flore considera, a maioribus ad minimos nullum offendes ab <lb></lb>his hospitibus non obsessum..... Cogitandum haud est Deum Omnipoten­<lb></lb>tem reliquisse quampiam e tota creaturarum familia cuius necessitatibus non <lb></lb>providerit, sed velut Maximum Promocondum hinc et inde pro omnibus <lb></lb>distribuisse cibum, isque pro ingenti turbac huius exiguae copia ut suffice­<lb></lb>ret penum ipsi extruxisse in <emph type="italics"></emph>Florum comis,<emph.end type="italics"></emph.end> ut ita flos quivis fiat diverso­<lb></lb>rium et caenaculum, dum in quovis utrumque reperiunt ” (Acta Curios. </s>

<s><lb></lb>Naturae, Dec. </s>

<s>I, An. </s>

<s>VIII, appendix; Norimbergae 1672, pag. </s>

<s>359). </s></p><p type="main">

<s>Cinque anni dopo, tornando il Grew a scriver de&#039;fiori uno special trat­<lb></lb>tato, che doveva col titolo <emph type="italics"></emph>The anatomy of flowers<emph.end type="italics"></emph.end> far parte del IV libro, <lb></lb>aveva da queste prime sostanzialmente riformate le idee, concorrendo a una <lb></lb>tal riforma in vario modo la lettura del Malpighi e i familiari colloqui con <lb></lb>l&#039;amico suo Tommaso Millington, professor Saviliano. </s>

<s>“ In discourse hereof <lb></lb>with vur learned Savilian professor, sir Thomas Millington, he told me he <lb></lb>conceived: that the Attire doth serve as the male, for the generation of the <lb></lb>seed ” (The anatomy of Plants, London 1682, pag. </s>

<s>171). </s></p><p type="main">

<s>S&#039;era il Millington, come il nostro Redi, formato questo concetto sul­<lb></lb>l&#039;esempio delle Palme, ed era felicemente passato a riconoscer le polveri <lb></lb>maschili di esse simili a quelle, che si diffondono dalle antere, ne&#039;fiori a noi <lb></lb>più familiari. </s>

<s>Piacque al Grew molto il pensiero del Saviliano, ma perchè <lb></lb>il maschio ha necessaria relazione con l&#039;altro sesso, sottilmente investigava <pb xlink:href="020/01/1663.jpg" pagenum="538"></pb>qual potess&#039;esser nel fiore il corrispendente organo femmineo. </s>

<s>Non era in <lb></lb>questa investigazione difficile incontrarsi nell&#039;ovario, e riconoscerlo analogo <lb></lb>all&#039;utero, ma perchè non si dava altro che un&#039;importanza secondaria allo <lb></lb>stilo, e le filamenta staminee, insidenti sull&#039;ovario stesso, si credevan muo­<lb></lb>vere e far parte di lui, accadde al Grew di confondere con quello degli stami <lb></lb>l&#039;uso proprio e distinto de&#039;pistilli. </s>

<s>Lo stame dunque è “ <foreign lang="grc">αρρεν<gap></gap>θηλυς</foreign>, or male <lb></lb>and female ” (ivi). Compie certamente le funzioni di maschio, quando getta <lb></lb>le polveri, e quelle di femmina?.... Qui si sovvenne il Grew di aver poco <lb></lb>fa letto nel trattato <emph type="italics"></emph>De floribus<emph.end type="italics"></emph.end> del Malpighi: “ Huic muneri subserviunt <lb></lb>stamina, unde fas est dubitare Naturam plurimum humoris, huncque diver­<lb></lb>sae substantiae seminum generationi incongruum, per haec, quasi emuncto­<lb></lb>ria, eliminare. </s>

<s>Hinc fortasse non incongrue derivato nomine <emph type="italics"></emph>menstruae pur­<lb></lb>gationis,<emph.end type="italics"></emph.end> quae, in mulieribus, conceptionis tempora proxime antecedunt, veluti <lb></lb>florum eruptiones succedunt.... Et quoniam in menstruorum eruptione ma­<lb></lb>turitas quaedam temporis requiritur ut prorumpant riteque celebrentur, et <lb></lb>his suppressis generatio tollitur et vitiatur; ita florum pariter productio in <lb></lb>plantis non illico succedit, sed post determinatum tempus, nec perpetuo foe­<lb></lb>cunda sunt semina ” (Operum, T. </s>

<s>I cit., pag. </s>

<s>70). Dunque compie lo stame, <lb></lb>concluse di qui il Grew, l&#039;ufficio di femmina, quando attrae dall&#039;ovario e <lb></lb>ripurga il seme dai soverchianti umori, come fa l&#039;utero ne&#039;suoi flussi men­<lb></lb>sili. </s>

<s>“ And as the young and early attire before it opens, answers tho the <lb></lb>menses in the femal; so is it probable theat afterward when it opens or <lb></lb>cracks, it performs the office of the male ” (The anat. </s>

<s>of Plants cit. </s>

<s>pag. </s>

<s>172). </s></p><p type="main">

<s>Essendo così, conveniva risolversi intorno al modo come le polveri ma­<lb></lb>schili esercitano sul soggiacente utero la loro virtù fecondatrice. </s>

<s>Non entrano <lb></lb>materialmente addentro, perchè il Malpighi, micrografo espertissimo e a cui <lb></lb>bisognava credere, avea detto che per le tube non può entrare altro che <lb></lb>l&#039;aria. </s>

<s>Ma facile trovò a tutto il Grew risoluzione, invocando le dottrine ar­<lb></lb>veiane, rimaste fra gli Embriologi, anche a que&#039;tempi, in Inghilterra tenaci. </s>

<s><lb></lb>Come dice l&#039;Harvey, nell&#039;esercitazione XLVIII <emph type="italics"></emph>De generatione animalium,<emph.end type="italics"></emph.end><lb></lb>“ semen illud spiritali substantia et irradiatione quadam in ovum usque pe­<lb></lb>netrare, eiusque chalazas foecundare atque inde pullum effingere ” (Lugd. </s>

<s><lb></lb>Batav. </s>

<s>1737, pag. </s>

<s>177); così diceva il Grew, cadendo il polline sull&#039;esterior <lb></lb>superfice dell&#039;ovario, fecondarne i semi ivi dentro rinchiusi, per una certa <lb></lb>spiritale irradiazione, senz&#039;alcun materiale contagio. </s>

<s>“ Which so soon as <lb></lb>the penis is exerted, or the testicles come to break, falls dawn upon the <lb></lb>seed-case or womb and so touches it with a prolifick virtuc..... And that <lb></lb>these particles only by falling ont the uterus, should comunicate to it or to <lb></lb>the sap therein a prolifick virtue, it may scem the more credible from the <lb></lb>manner wherein coition is made by some animals ” e cita, come l&#039;Harvey, <lb></lb>l&#039;esempio degli uccelli e dei pesci (ivi, pag. </s>

<s>172, 73). </s></p><p type="main">

<s>A ripensar ora che al Malpighi e al Grew, com&#039;a due splendidi soli <lb></lb>appariti contemperanei sull&#039;orizzonte, si rivolgevano i cupidi occhi di tutti <lb></lb>coloro, che attendevano allo studio delle piante, si comprenderà come, in-<pb xlink:href="020/01/1664.jpg" pagenum="539"></pb>formate da principii diversi, anche a diversi termini, rispetto alla feconda­<lb></lb>zion de&#039;fiori, dovessero per lo più riuscire le seguenti opinioni. </s>

<s>Gl&#039;inspirati <lb></lb>alla scuola del Malpighi ripudiarono l&#039;ipotesi dei sessi delle piante, reputan­<lb></lb>dola un ludibrio indegno della Natura e repugnante all&#039;anatomia; gl&#039;inspi­<lb></lb>rati alla scuola del Grew ammirarono invece l&#039;uniforme sapienza de&#039;natu­<lb></lb>rali ordinamenti in propagar così le vite vegetative come le animali. </s>

<s>Quanto <lb></lb>all&#039;anatomia, ritrovaron che s&#039;erano i due grandi Maestri ingannati intorno <lb></lb>alla struttura e agli uffici de&#039;pistilli, ne&#039;quali, rimosse le mostruose <emph type="italics"></emph>arre­<lb></lb>notelie,<emph.end type="italics"></emph.end> scoprirono distintamente gli organi femminei. </s>

<s>Concorsero efficace­<lb></lb>mente alla scoperta le nuove dottrine embriologiche, diffuse dai libri dello <lb></lb>Swammerdam e del Graaf, i quali, svelando i paradossi arveiani, col dimo­<lb></lb>strare l&#039;impossibilità delle fecondazioni <emph type="italics"></emph>spirituali,<emph.end type="italics"></emph.end> e la reale azione dello <lb></lb>sperma sugli ovi; aprirono gli occhi ai Botanici novelli per veder chiara­<lb></lb>mente, negli stimmi e negli stili, aperte al polline le vie di giungere a toc­<lb></lb>car fisicamente i semi, e colla sua virtù prolifica a fecondarli. </s></p><p type="main">

<s>A tal punto, verso la fine del secolo XVII, erano state promosse le <lb></lb>deformi idee del Grew intorno al sessualismo de&#039;fiori, ma nessuno s&#039;atten­<lb></lb>tava ancora di pronunziarle al pubblico, il quale, se inorridì a sentir gli <lb></lb>Anatomici dire che l&#039;uomo nasce come le galline dall&#039;uovo, pensiamo che <lb></lb>farebbe in tornargli i Botanici sfacciatamente a soggiungere che anche le <lb></lb>piante hanno come l&#039;uomo intelletto di amore. </s></p><p type="main">

<s>Primo a rompere il ghiaccio fu Rodolf&#039;Iacopo Camerarius, che nel 1694 <lb></lb>pubblicava in Tubinga una Epistola di quattro pagine in 8°, indirizzata a <lb></lb>Michel Bernardo Valentin col titolo <emph type="italics"></emph>De sexu plantarum;<emph.end type="italics"></emph.end> Epistola che, pre­<lb></lb>sentitane già l&#039;importanza, perchè, affidata com&#039;era a pochi fogli leggeri, <lb></lb>non fosse ai progressi della scienza dannosamente involata, fu raccolta fra <lb></lb>l&#039;Effemeridi dei <emph type="italics"></emph>Curiosi della Natura<emph.end type="italics"></emph.end> in appendice all&#039;anno III della III De­<lb></lb>curia impressa nel 1696 in Norimberga. </s></p><p type="main">

<s>Nell&#039;ardita mossa nonostante, sentita il Camerarius una certa trepida­<lb></lb>zione, quasi ad esempio del nostro Redi, espone i pensieri non come parto <lb></lb>della mente sua propria, ma di quella di uno fra botanici nobilissimo Au­<lb></lb>tore, in mano del quale, dietro ciò che aveva osservato il Grew, si espoliva <lb></lb>la storia della generazion delle piante, come, dietro le osservazioni dell&#039;Har­<lb></lb>veio, dello Stenone e dello Swammerdam, era stata già per altri espolita la <lb></lb>storia della generazione degli animali. </s>

<s>“ Hinc et utraque generationis histo­<lb></lb>ria idem fere fatus experta, et a modernis successive et pedetentim expo­<lb></lb>lita fuit, cum qnod Harvaeus, Steno, Svammerdamius in animalibus, Grevius <lb></lb>et alii in plantis simul observarint ” (Ephem. </s>

<s>Appendix. </s>

<s>Dec. </s>

<s>et anno cit., <lb></lb>pag. </s>

<s>35). </s></p><p type="main">

<s>Quel nobilissimo Botanico dunque, incomincia a dire nella sua Epistola <lb></lb>il Camerarius, non giudica punto secondo il volgo le fioriture dallo specioso <lb></lb>colore de&#039;petali, ma, consideratele come ordinate al frutto, dà tutta l&#039;impor­<lb></lb>tanza agli apici, che con la loro minutissima polvere caduta sopra gli stili <lb></lb>impregnano il seme, e son perciò essi apici che costituiscono il vero e pro-<pb xlink:href="020/01/1665.jpg" pagenum="540"></pb>prio fiore. </s>

<s>“ Apices ergo vere et proprie flores dicendos esse, non tantum <lb></lb>criticis celebrioribus placere, sed et texturae et naturae illorum convenire <lb></lb>putat, cum nihil aliud sint quam vascula quaedam et capsulae, petiolis pro­<lb></lb>priis insidentes, et pulvere quodam minutissimo, tamquam seminio specifico, <lb></lb>repletae, quo vasculum seminale impregnandum erat ” (ibid., pag. </s>

<s>33). </s></p><p type="main">

<s>Son questi apici talvolta in un medesimo fiore congiunti agli stili, e son <lb></lb>tal&#039;altra disgiunti o sull&#039;individuo stesso o in individui diversi, d&#039;onde ven­<lb></lb>gono, secondo questo rispetto, le piante a distribuirsi dal nobilissimo Autore <lb></lb>in tre classi: “ Prima illis distinguitur floribus, in quibus apices seminalis <lb></lb>vasculi stylum seu appendicem immediate circumstant, ut in Tulipa, Vale­<lb></lb>riana, etc..... Secunda classis plantas continet apetalas, quae alia in parte <lb></lb>flores, alia vero semina et fructus, adeoque divulsos a stylis apices habet ut <lb></lb>in Frumento turcico, Ricino, etc..... Tertia classis illarum est plantarum <lb></lb>apetalarum, in quibus individua quaedam semen, alia vero florem gerunt, ut <lb></lb>in Mercuriali, Cannabi, Junipero, etc. (ibid., pag. </s>

<s>33, 34). </s></p><p type="main">

<s>Premesse queste cose, confronta il nobilissimo Botanico la generazione <lb></lb>degli animali con quella delle piante, e la trova mirabilmente riscontrare in <lb></lb>tutte le parti che si possono ridurre alle principali otto seguenti: “ Quod <lb></lb>enim primo in animalibus sunt testes, semine prolifico gaudentes, hoc in <lb></lb>plantis apices pulvere suo turgescentes; et quod in foemellis uterus cum <lb></lb>ovario, hoc in plantis foemininis stylus et vasculum seminale a priore im­<lb></lb>praegnandum, quae utrobique a petalis, tanquam partibus continentibus <lb></lb>externis, ab externa quavis iniuria vindicantur ” (ibid., pag. </s>

<s>34, 35). In se­<lb></lb>condo luogo, prosegue il Camerarius la sua relazione, come giungono nel <lb></lb>medesimo tempo alla pubertà i due sessi negli animali, così giungono anche <lb></lb>ne&#039;fiori. </s>

<s>In terzo e in quarto luogo, son qua e là uguali esempi di erma­<lb></lb>froditi, e i rudimenti del nascituro appariscono in simil modo nell&#039;uovo fe­<lb></lb>condato, e nella fecondata pianticella seminale. </s>

<s>S&#039;ha per quinto riscontro il <lb></lb>polline globuloso, che feconda il fiore come feconda la donna il seme virile; <lb></lb>e come le uova de&#039;pesci, se non sono irrorate dal maschio, sono inutili alla <lb></lb>generazione; così può in sesto luogo notarsi che, senz&#039;essere irrorati dalle <lb></lb>polveri maschili degli apici, non maturano i frutti. </s>

<s>In settimo luogo, come <lb></lb>si distinguono in gallate e in suvventanee le ova de&#039;polli, così si distinguono, <lb></lb>secondo la medesima ragione, i semi dei vegetanti; e all&#039;ultimo, ma che è <lb></lb>il principale e più ponderoso argomento di tutti, “ certum est ad anima­<lb></lb>lium generationem copulam utriusque sexus exigi, quam in plantis (Author), <lb></lb>adeo quoque necessariam ostendit, ut si vel maris apices vel faeminarum <lb></lb>styli, vel utraque deficiunt, nulla proles sequi possit, ut in Frumento tur­<lb></lb>cico, cui iuba praemature resecatur, et Mercuriali mare a foemina separata <lb></lb>constat ” (ibid., pag. </s>

<s>35). </s></p><p type="main">

<s>Crederebbe, dietrò queste considerazioni e dietro queste esperienze quel­<lb></lb>l&#039;illustre Botanico di poter concludere la generazion sessuale delle piante <lb></lb>come cosa certa, se non lo tenessero in dubbio alcuni fatti osservati, come <lb></lb>per esempio che ci son talvolta maschi senza femmine, e femmine senza <pb xlink:href="020/01/1666.jpg" pagenum="541"></pb>maschi. </s>

<s>Ma ciò che gli dà maggior pena è il vedere, in alcune della terza <lb></lb>classe, come per esempio nella Canapa, che senza vicinanza di maschi le <lb></lb>femmine bene spesso rimangon feconde. </s>

<s>Nonostante, così il Camerarius con­<lb></lb>clude la breve esposizione del suo sistema fingendo di riferire pensieri al­<lb></lb>trui, “ ulterioribus experimentis institutis, Naturam se magis explicaturam <lb></lb>fore confidat ” (ibid, pag. </s>

<s>36). </s></p><p type="main">

<s>Il qual costrutto ripreso dal Valentin nella sua <emph type="italics"></emph>Epistola responsoria,<emph.end type="italics"></emph.end><lb></lb>mentre questi ringraziava l&#039;Autore, <emph type="italics"></emph>qui glaciem fregit,<emph.end type="italics"></emph.end> e gli dava, dopo il <lb></lb>Malpighi e il Grew, per aver distinti e dimostrati i sessi delle piante, nella <lb></lb>scienza botanica, i terzi onori; diceva che per poche apparenti difficoltà non <lb></lb>era da mettere in dubbio un sistema, che da tante parti consonava col vero. </s>

<s><lb></lb>Che del resto può il polline seminale invisibilmente ricircolare dentro le fibre <lb></lb>delle femmine cannabine, le quali non son poi tanto lontane dai loro ma­<lb></lb>riti “ quin a proportionatis horum particulis seminalibus, per ventos, apici­<lb></lb>bus excussis et in aere volitantibus, impraegnari possint, cum te neutiquam <lb></lb>lateat quanta saepe locorum, imo regionum intercapedine, actiones fiant <lb></lb>magneticae per effluviorum eiusmodi contactum unice explicandae ” (ibid., <lb></lb>pag. </s>

<s>40). </s></p><p type="main">

<s>La fiducia del Camerarius in ogni modo che, nonostante le prime in­<lb></lb>contrate difficoltà, sarebbero venuti a confermar le sue ipotesi i futuri espe­<lb></lb>rimenti, conseguì non molti anni dopo il suo effetto, per la studiosa opera, <lb></lb>che vi posero attorno Botanici valorosissimi, fra&#039;quali son da commemorar <lb></lb>de&#039;primi Sebastiano Vaillant, e Riccardo Bradley. </s>

<s>Il Francese, disertando dalla <lb></lb>scuola del Tournefurt, lesse nel 1717 innanzi all&#039;Accademia parigina un suo <lb></lb>Discorso, che fu l&#039;anno dopo, insiem con altre operette botaniche dell&#039;Au­<lb></lb>tore, pubblicato in Leyda col titolo di <emph type="italics"></emph>Sermo de structura florum.<emph.end type="italics"></emph.end> Pren­<lb></lb>dendo principalmente le Parietarie per soggetto delle osservazioni, descrive <lb></lb>l&#039;esplosion del polline che va dagli stami ai pistilli, e ne feconda l&#039;utero, <lb></lb>non per materiale contagio, ma in virtù dello spirito seminale. </s></p><p type="main">

<s>Il Bradley pubblicò in Londra nel 1724 il suo libro <emph type="italics"></emph>New experiments <lb></lb>and observations relative to the generation of plants.<emph.end type="italics"></emph.end> I più conclusivi espe­<lb></lb>rimenti del Botanico inglese consistono nell&#039;avere estesa a un gran numero <lb></lb>di piante quella mutilazione operata dal Camerarius sopra il Granturco, e <lb></lb>nell&#039;avere in tutti i casi trovato ch&#039;evirati de&#039;loro apici gli stami sempre <lb></lb>gli ovarii sotto i pistilli rimanevano sterili de&#039;loro frutti. </s>

<s>Le bradleiane os­<lb></lb>servazioni si riducevano principalmente a notar che quasi sempre lo stimma <lb></lb>soggiace all&#039;antera, e che ne&#039;fiori penduli va lo stilo più lungo delle stami­<lb></lb>gne, per rimaner così più facilmente asperso della seminale polvere cadente. </s></p><p type="main">

<s>Prima insomma di Carlo Linneo, benchè rimanessero tuttavia alcune di <lb></lb>quelle difficoltà, che avean fatto andar così timido il Camerarius, il sistema <lb></lb>sessuale delle piante si teneva per cosa già sperimentalmente dimostrata, e <lb></lb>assai confacevole al consueto modo tenuto nell&#039;operare dalla Natura; intanto <lb></lb>che Efraimo Chambers lo ripose qual moneta legittima nel tesoro univer­<lb></lb>sale della scienza, come può vedersi sotto le denominazioni di <emph type="italics"></emph>Stami<emph.end type="italics"></emph.end> e di <pb xlink:href="020/01/1667.jpg" pagenum="542"></pb><emph type="italics"></emph>Pistilli<emph.end type="italics"></emph.end> nel suo <emph type="italics"></emph>Dizionario,<emph.end type="italics"></emph.end> e particolarmente sotto quello di <emph type="italics"></emph>Piante,<emph.end type="italics"></emph.end> dove <lb></lb>tratta della loro generazione. </s></p><p type="main">

<s>Abbiamo fin qui veduto a qual punto fosse stata promossa la scienza <lb></lb>della generazion delle piante, nel primo trentennio del secolo XVIII, per gli <lb></lb>impulsi avuti dal Grew: or è da riconoscere la penosa immobilità, in cui <lb></lb>quella medesima scienza rimase specialmente in Italia, dove bene a ragione <lb></lb>qual solenne maestro di lei si venerava il Malpighi. </s></p><p type="main">

<s>Francese di origine e di magistero il Tournefort, s&#039;era per suoi prin­<lb></lb>cipali Autori eletto tre italiani: il Cesalpino, il Colonna e il Malpighi stesso, <lb></lb>da cui confessava aver la Botanica avuto i massimi incrementi. </s>

<s>In trattar <lb></lb>dei fiori ei si volle, anche nelle minime cose (se pur fra le minime cose è <lb></lb>da riporre la scientifica, proprietà delle parole), mostrar fedele ai maestri, <lb></lb>chiamando sempre <emph type="italics"></emph>petali,<emph.end type="italics"></emph.end> sull&#039;esempio del Colonna, le foglie colorite intorno <lb></lb>al calice fiorale, per distinguerle dalle foglie propriamente dette verdeggianti <lb></lb>sui rami: “ Partes florum dicuntur petala, calyx, stamina, apices, pistillum. </s>

<s><lb></lb>Fabius Columna, vir praeclari ingenii, primus, omnium, quod sciam, <emph type="italics"></emph>petali<emph.end type="italics"></emph.end><lb></lb>vocem proprie usurpavit, ut folia florum a foliis proprie dictis distingueret ” <lb></lb>(Instit. </s>

<s>herbariae, Parisiis 1719, pag. </s>

<s>70). </s></p><p type="main">

<s>Dalle parole passando alle idee, non crede punto il Tournefort quel <lb></lb>ch&#039;era arditamente venuto a proporre il Camerarius, che cioè sien quegli <lb></lb>splendidi petali le seriche cortine, sotto le quali, gelosamente tirate all&#039;in­<lb></lb>torno, celebrano i fiori pudibondi le nozze; ma fedele al suo Malpighi crede <lb></lb>che servano ad apprestar, come le mammelle il latte al bambino, al tenero <lb></lb>seme appropriato alimento, il superfluo del quale sia deposto negli apici “ ve­<lb></lb>lut in cloacas. </s>

<s>Floris igitur proprium munus est nutriendi tenerum fructum, <lb></lb>ipsaque nutricatio paucarum horarum vel dierum est. </s>

<s>Lactis enim, ut <lb></lb>ita dicam fructus tantum indiget in prima partium explicatione ” (ibid., <lb></lb>pag. </s>

<s>68). </s></p><p type="main">

<s>S&#039;aggiunse a questa del Tournefort contro i Sessualisti un&#039;altra grande <lb></lb>botanica potenza in Giulio Pontedera, il quale consacrò a trattar de&#039;fiori un <lb></lb>libro, che perciò intitolava <emph type="italics"></emph>Anthologia.<emph.end type="italics"></emph.end> Il Malpighi, com&#039;udimmo, non si di­<lb></lb>chiarò intorno all&#039;uso proprio degli stami, lasciando in dubbio i lettori se <lb></lb>fossero, come i petali, da dir organi nutritizii, o piuttosto escrementizi. </s>

<s>Il <lb></lb>Tournefort, com&#039;abbiamo ora letto, attribuì a loro questo secondo uso, ma <lb></lb>il Pontedera disse “ nulla ratione efficere possumus ut haec Auctoris opi­<lb></lb>nio cum ratione congruere censeamus ” (Anthol., Patavii 1720, pag. </s>

<s>111), <lb></lb>e parendagli più ragionevole attenersi all&#039;altra malpighiana sentenza, con­<lb></lb>cluse che le antere secernono un succo, il quale poi “ per filamenta ad re­<lb></lb>ceptaculum transmittunt, a quo embryoni subministratur ” (ibid.). Quanto <lb></lb>ai pistilli segue con fedeltà le dottrine espressamente insegnate dallo stesso <lb></lb>Malpighi, concludendo, nel cap. </s>

<s>XXV del I libro della citata Antologia, dal <lb></lb>non aver mai veduto senza tuba allegar frutto essere essa tuba la prima e <lb></lb>principal parte del fiore. </s>

<s>Ricercando poi nel capitolo appresso di quel par­<lb></lb>ticolare organo gli usi, dice esser quelli di tradur l&#039;aria esterna nell&#039;interno <pb xlink:href="020/01/1668.jpg" pagenum="543"></pb>del seme “ quod nihil aliud nisi aer in fructus cavitatem per tubas potest <lb></lb>admitti ” (ibid., pag. </s>

<s>62). </s></p><p type="main">

<s>Stabiliti così fatti principii dottrinali, passa nel suo II libro il Ponte­<lb></lb>dera a esaminare la gran questione dei sessi, e alle prime incontrate diffi­<lb></lb>coltà naturali sa l&#039;arguto ingegno trovarne altre nuove, ch&#039;ebbero gran <lb></lb>momento nel giudizio degli studiosi. </s>

<s>Uno de&#039;primi argomenti a così fatte <lb></lb>difficoltà lo desume il Botanico padovano dall&#039;esame de&#039;fiori petaloidi, nella <lb></lb>maggior parte dei quali egli dice “ apices et tubas ita disponi, ut apicum <lb></lb>corpora ad tubarum oscula aut fistulas posse transferri perdifficile videtur ” <lb></lb>(ibid., pag. </s>

<s>118). Altro simile argomento glielo porge la popolosa famiglia <lb></lb>delle Umbellate, sul calice delle quali, quando son gli stami già adulti, le <lb></lb>tube, che han per lui le prime parti nel fiore, non son ancora cresciute. </s></p><p type="main">

<s>Ma son due fruttescenze in particolare sopra le quali il Pontedera s&#039;in­<lb></lb>trattiene a lungo, per concluderne nel cap. </s>

<s>XVII del citato II libro “ nul­<lb></lb>lam dari in plantis foecundationem ” (pag. </s>

<s>140). Son le fruttescenze, di che <lb></lb>si tratta, quella delle Palme e dei Fichi, a cui pur s&#039;associano, a dar valore <lb></lb>all&#039;argomento contro i sessi, la Canapa, il Luppolo e altre simili piante com­<lb></lb>prese dal Camerarius in quella terza classe, che oggidì si denomina delle <lb></lb><emph type="italics"></emph>Diecie.<emph.end type="italics"></emph.end> Domandava l&#039;Autore dell&#039;Antologia come mai, avendo queste piante <lb></lb>i talami così disgiunti, potessero nonostante celebrare insieme i coniugi. </s>

<s>E <lb></lb>perchè Prospero Alpino, e il Valentin fra&#039;più recenti, avevano invocato in <lb></lb>proposito l&#039;azione del vento, gli sembrava impossibile che il fiato del Lup­<lb></lb>polo maschio potesse, attraverso a monti e a mari, giungere a fecondar le <lb></lb>femmine negli orti di Parigi. </s>

<s>“ Deinde, cum adhuc in eo quaestionis statu <lb></lb>res versaretur, ut scilicet qua ratione et quibus viis quae non haberent a <lb></lb>cognatis acciperent esset explanandum, cum nulla alia ratio suppeteret, ad <lb></lb>ventorum providentiam conversi sunt, iisque mirificum faecunditatis opus <lb></lb>attribuerunt. </s>

<s>Quare faecundari tradunt ex. </s>

<s>gr. </s>

<s>Lupulum marem in Horto <lb></lb>regio parisiensi a Lupolo faemina, quae in insulis Sequanae et Matronae <lb></lb>longe distantibus nascitur, ventorum vi, qui apicum corpuscula ad tubas <lb></lb>usque ferunt ” (ibid., pag. </s>

<s>131). </s></p><p type="main">

<s>Ma il Fico presentava, nella storia sua naturale, tali note, da bastare <lb></lb>esse sole per il più dimostrativo argomento contro l&#039;esistenza dei sessi. </s>

<s><lb></lb>Unico fra gli alberi fruttiferi appariva senza fiore, eppur, così senza fiore, <lb></lb>vedevasi maturare i suoi frutti, o a questo effetto concorrere tutt&#039;altre cause <lb></lb>dalle florali, conosciute sotto il nome di <emph type="italics"></emph>caprificazione<emph.end type="italics"></emph.end> infino dai tempi più <lb></lb>antichi. </s>

<s>Era <emph type="italics"></emph>caprifico<emph.end type="italics"></emph.end> chiamata la pianta silvestre, la quale, sebben non ma­<lb></lb>turi i suoi frutti, dà nonostante la virtù che non ha alla pianta domestica, <lb></lb>generando in sè e dalla sua corruzione il maraviglioso e provvido istinto di <lb></lb>alcuni insetti. </s>

<s>“ Ficos, disse Teofrasto de&#039;cultori di queste piante, caprifi­<lb></lb>cant, quod ea de causa faciunt ut culices parvi, qui ex caprificubus appen­<lb></lb>sis nascuntur, poma fici aperiant ” (De causis plant. </s>

<s>cit., pag. </s>

<s>90). Aperto <lb></lb>il fico, v&#039;entran dentro l&#039;aria e il calor del sole, che concocendo la natural <lb></lb>crudezza lo fanno maturare. </s></p><pb xlink:href="020/01/1669.jpg" pagenum="544"></pb><p type="main">

<s>Non si poteva però la causa della maturazion de&#039;fichi tanto attribuir <lb></lb>dagli Antichi all&#039;opera degl&#039;insetti, che non vi riconoscessero altresì il con­<lb></lb>corso delle polveri, l&#039;effetto delle quali volevano che consistesse nel risec­<lb></lb>care i soverchi umori, e così impedire al frutto la corruzione. </s>

<s>Era in quelle <lb></lb>polveri, che si confondevano facilmente con le sollevate per le vie maestre, <lb></lb>qualche presentimento del vero, e Teofrasto stesso osservando che, anche le <lb></lb>palme, in qualche modo si caprificano, attribuì alle asperse polveri maschili <lb></lb>i medesimi effetti essiccativi. </s>

<s>Ma da un&#039;altra parte gli era balenato alla <lb></lb>mente il luminoso pensiero di rassomigliar la negata fecondazion sessuale <lb></lb>delle Palme alla reale fecondazion sessuale delle uova dei pesci. </s>

<s>“ Quapro­<lb></lb>pter caprificari Palmas quoque fari consuevere. </s>

<s>Flore enim a masculo, et <lb></lb>pulvere et lanugine cum fructus insperguntur, siccitatem ex caliditate ac re­<lb></lb>liqua potestate concipiunt, atque spirantiores redduntur, quibus causis vis <lb></lb>perdurandi acquiritur. </s>

<s>Huic quodammodo simile in piscium quoque genere <lb></lb>evenit, cum mas, editis ovis, vitale suum virus aspergit ” (ibid., pag. </s>

<s>95). </s></p><p type="main">

<s>Plinio, nel cap. </s>

<s>XIX del XV libro della Storia naturale, descrisse e in­<lb></lb>terpetrò la caprificazione allo stesso modo che abbiamo inteso da Teofrasto, <lb></lb>e anzi, a mezzo il secolo XVII, furono nel Tomo I dell&#039;<emph type="italics"></emph>Historia plantarum <lb></lb>universalis<emph.end type="italics"></emph.end> ripetute da Giovanni Bahuin, rispetto al modo dell&#039;operar sulla <lb></lb>pianta domestica il caprifico, le tradizionali storie de&#039;Naturalisti antichi (Ebro­<lb></lb>duni 1650, pag. </s>

<s>135). Pochi anni insomma prima del Malpighi e del Grew, <lb></lb>porgeva il Fico, contro chi avesse pensato alla sessualità delle piante, due <lb></lb>validissimi argementi: l&#039;uno col maturar senza fiore, l&#039;altro col mostrare <lb></lb>o di ritrovare in sè la sua propria fecondità, o di riceverla da individui di <lb></lb>natura tanto diversa, da parer follia il vederci pur l&#039;immagine di un connubio. </s></p><p type="main">

<s>La forza di quel primo argomento però rimase affievolita, quando il Mal­<lb></lb>pighi mostrò ai Botanici anche nel Fico il fiore desiderato. </s>

<s>“ In ficu, cuius <lb></lb>flos apud Botanicos desideratur, inversa et opposita via videtur procedere <lb></lb>Natura, nam, sicut in exaratis floribus pericarpii moles ita assurgit et attol­<lb></lb>litur, ut conicum vel piricale fiat corpus, quod postea flosculis seu stylis te­<lb></lb>gitur et cooperitur; ita in ficu, etevato exteriori ungue, fit concameratio sty­<lb></lb>los et flosculos continens. </s>

<s>Floris vero foliola parum-rubescentia, quae in <lb></lb>Heliotropio et reliquis extremam floralis areae oram ambiunt, in Ficu, in <lb></lb>angustum compressa circulum, exiguum ornant hiatum, et anteriora versus <lb></lb>expansa videntur inversum producere florem ” (De floribus, Op. </s>

<s>omnia, <lb></lb>T. </s>

<s>I cit., pag. </s>

<s>60). </s></p><p type="main">

<s>Verissima è la nuova struttura e la nuova inflorescenza così descritta <lb></lb>nel Fico, il quale, perciocchè ha nel suo ricettacolo per flosculi i soli stili, <lb></lb>sarebbe dunque seconde i Sessualisti un individuo femmineo. </s>

<s>Eppure ben­<lb></lb>chè vergine solitaria concepisce secondo il Malpighi, ed espone il suo parto. <lb></lb></s>

<s>“ Ab interiori concavitate pericarpii styli seu flosculi minimi erumpunt cum <lb></lb>seminum loculis: hi sensim augentur, donec crescente pericarpio tota re­<lb></lb>pleatur concameratio ” (ibid.). Questa era quella <emph type="italics"></emph>partenogenesi<emph.end type="italics"></emph.end> delle piante, <lb></lb>che il Pontedera opponeva ai seguaci del Camerarius, i quali, notabile cosa, <pb xlink:href="020/01/1670.jpg" pagenum="545"></pb>non dubitarono di tenere, infino a questi ultimi giorni, per bene accetta <lb></lb>l&#039;eterodossa opinione, rispetto alla generazion delle Api. </s></p><p type="main">

<s>In chi, sull&#039;autorità del Malpighi, credeva essere il vero pericarpio il <lb></lb>frutto maturato de&#039;Fichi, e aver le tube la parte principale ne&#039;fiori, gli ar­<lb></lb>gomenti, che dagli stessi Fichi e dalle Umbellate il Pontedera adduceva con­<lb></lb>tro i Sessualisti, erano di tal valore, da non ammetter dubbi. </s>

<s>La feconda­<lb></lb>zione a distanza, nelle Palme e nelle altre Diecie, conferiva dall&#039;altra parte <lb></lb>a rendere sempre più ritrose le menti, presentando difficoltà meglio intese, <lb></lb>e più sentite da tutti, cosicchè non è maraviglia se in Italia, sotto la disci­<lb></lb>plina di tali e tanti maestri, quali erano il Malpighi, il Tournefort e il Pon­<lb></lb>tedera, si lasciassero agli immaginosi oltramontani le romantiche storie sulle <lb></lb>nozze dei fiori. </s>

<s>Tanto anzi, soggiogati dall&#039;autorità e per un certo natìo pu­<lb></lb>dore del senno, erano gl&#039;Italiani, nel primo quarto del secolo XVII, alieni <lb></lb>da così fatti pensieri, che gli annotatori del Redi rintuzzarono con gli acu­<lb></lb>lei del Pontedera i lieti germogli spuntati dalla <emph type="italics"></emph>Lettera intorno alle Palme,<emph.end type="italics"></emph.end><lb></lb>ridendosi de&#039;Pistacchi belli e freschi, ma vani per esser rimasti vedovi del <lb></lb>compagno, come diceva il balì Girolami nel presentarli all&#039;ab. </s>

<s>Salvini (T. VI <lb></lb>dell&#039;Op. </s>

<s>cit., nota a pag. </s>

<s>156), e a Pieranton Micheli, che così attentamente <lb></lb>osservò e per il primo descrisse le passioni della Vallisniera palustre (Nova <lb></lb>plantarum genera, Florentiae 1729, pag. </s>

<s>12, 13), non passò nemmen per la <lb></lb>mente che la vicina Vallisnieroide le fosse amorevolmente congiunta co&#039;più <lb></lb>stretti vincoli maritali. </s></p><p type="main">

<s>Si direbbe che avesse risentiti questi influssi in parte anche l&#039;Hales, il <lb></lb>quale, tirandosi fuori dalla questione dei sessi, stette contento a speculare <lb></lb>intorno al modo com&#039;agisse il polline, entrato per il pistillo, in dar vita alla <lb></lb>pianta seminale. </s>

<s>Le fragranze del fiore s&#039;attribuivano principalmente alle <lb></lb>esalazioni sulfuree “ nam sulphur, scrisse il Dygby, est magnus ille uni­<lb></lb>versalis pictor et odorum excitator huius mundi ” (De veget. </s>

<s>plant., Amste­<lb></lb>lodami 1669, pag. </s>

<s>31). Secondando la comune opinione anche il Grew, che <lb></lb>avea notato esser sempre le antere o bianche o gialle, disse che il color di <lb></lb>queste dipendeva dal predominarvi lo zolfo. </s>

<s>“ Hence also it is that the co­<lb></lb>lour of the parts of the attire is usually withe or yellow, never red: the <lb></lb>former depending upon a greater participation of aer, the latter of sulphur ” <lb></lb>(The anatomy of plants cit., pag. </s>

<s>172). </s></p><p type="main">

<s>Non ebbe dietro ciò difficoltà l&#039;Hales di tener che fossero le particelle <lb></lb>del polline addirittura altrettanti granellini di zolfo. </s>

<s>Era venuto il tempo che <lb></lb>il Newton, dop&#039;Ottone di Guerike, avea richiamata l&#039;attenzione dei dotti e dei <lb></lb>curiosi sopra le virtù elettriche di questo elemento, attraente e se i solidi <lb></lb>corpiccioli non solo, ma l&#039;aria e la fiamma. </s>

<s>Di qui è che l&#039;Autore della Sta­<lb></lb>tica dei vegetabili vedeva in quei granellini pollinici penetranti gli ovari una <lb></lb>miscela attivissima di zolfo, d&#039;aria e di luce, dal tocco della qual miscela <lb></lb>credeva che venisse a infondersi nel seme il principio della vita. </s>

<s>“ E se noi, <lb></lb>fondati sulle esperienze del signor Newton, il quale ha ritrovato che il zolfo <lb></lb>attrae il lume, supponiamo che a queste particelle di zolfo e di aria mi-<pb xlink:href="020/01/1671.jpg" pagenum="546"></pb>schiate ed unite insieme si aggiungano alcune particelle di lume, non pos­<lb></lb>siamo dire che il resultato di questi tre principii, i più attivi della Natura, <lb></lb>formi quello che chiamano <emph type="italics"></emph>punctum saliens,<emph.end type="italics"></emph.end> ossia il principio di vita, che <lb></lb>dee comunicarla a tutta la pianta seminale? </s>

<s>” (Traduz. </s>

<s>cit., pag. </s>

<s>278, 79). </s></p><p type="main">

<s>Mentre che l&#039;Hales così penosamente tergiversava, e assottigliava l&#039;in­<lb></lb>gegno, Carlo Linneo era, dalle osservazioni e dagli esperimenti de&#039;suoi tanti <lb></lb>e valorosi predecessori, così ben persuaso essere alla generazion delle piante <lb></lb>e degli animali prescritta dalla Natura una somiglianza di leggi, da non bi­<lb></lb>sognarvi altro che la potenza logica del ragionamento a persuadere i ritrosi. </s>

<s><lb></lb>Nel 1735 perciò pubblicava in Amsterdam un libro col titolo di <emph type="italics"></emph>Philosophia <lb></lb>botanica,<emph.end type="italics"></emph.end> dove si esplicavano i <emph type="italics"></emph>Fondamenti<emph.end type="italics"></emph.end> della scienza per via di osser­<lb></lb>vazioni, di dimostrazioni sperimentali e di esempi. </s>

<s>L&#039;aridità della forma afo­<lb></lb>ristica è largamente compensata dal lucido ordine, e da una sintesi maravi­<lb></lb>gliosa, cosicchè tanta scienza in poche pagine condensata produsse l&#039;effetto <lb></lb>desiderato, simile a quel che suol fare un cibo essenzialmente nutritivo in­<lb></lb>gesto in uno stomaco flatulento. </s></p><p type="main">

<s>Il capitolo V s&#039;intitola <emph type="italics"></emph>Sexus,<emph.end type="italics"></emph.end> e il filosofico ragionamento così, da prin­<lb></lb>cipii o ammessi per certi o dimostrati, procede con rigoroso ordine alla sua <lb></lb>conclusione: Se è vero l&#039;assioma <emph type="italics"></emph>omne vivum ex ovo,<emph.end type="italics"></emph.end> dunque ciò vale an­<lb></lb>che per i vegetabili, i semi de&#039;quali esser uova, oltre alla ragione, ci è di­<lb></lb>mostrato dall&#039;esperienza, per l&#039;analogia che ha l&#039;<emph type="italics"></emph>hilo<emph.end type="italics"></emph.end> col vitello, e i cotile­<lb></lb>doni colla placenta degli animali. </s>

<s>E come in questi la prole non deriva <lb></lb>dall&#039;ovo solo o dalla sola genitura, ma d&#039;ambedue insieme; così è ragio­<lb></lb>nevole che avvenga delle piante, nelle quali la genitura è il polline eiacu­<lb></lb>lato dalle antere sopra gli stimmi, che sono i veri e proprii genitali femmi­<lb></lb>nei. </s>

<s>Ambedue questi organi infatti giungono nel medesimo tempo alla pu­<lb></lb>bertà, e l&#039;uno evirato l&#039;altro si rimane irreparabilmente sterile come negli <lb></lb>stessi animali. </s>

<s>“ Calyx ergo, conclude il Linneo, est thalamus, corolla au­<lb></lb>leum, filamenta vasa spermatica, antherae testes, pollen genitura, stigma <lb></lb>vulva, stylus vagina, germen ovarium, pericarpium ovarium foecundum, se­<lb></lb>men ovum ” (Philos. </s>

<s>bot. </s>

<s>editio altera, Viennae 1753, pag. </s>

<s>96). </s></p><p type="main">

<s>Ogni orazione però non solo dimostra la tesi, ma scioglie le difficoltà, <lb></lb>intorno a che lasciò il Linneo s&#039;esercitassero i suoi discepoli. </s>

<s>Era uno dei <lb></lb>primi fra costoro Giovan Gustavo Wahlbom, il quale, a&#039;di 11 Giugno 1746, <lb></lb>lesse nell&#039;Accademia di Upsalia, innanzi allo stesso Linneo preside, una dis­<lb></lb>sertazione intitolata <emph type="italics"></emph>Sponsalia plantarum,<emph.end type="italics"></emph.end> che fu poi raccolta fra le Acca­<lb></lb>demiche amenità upsaliensi. </s>

<s>Gli articoli del cap. </s>

<s>V della Filosofia linneiana <lb></lb>son qui dall&#039;Autore in altrettanti articoli, con facile e spiegato discorso, com­<lb></lb>mentati, ora per gli esempi stessi addotti nel testo, ora per altri nuovi, e le <lb></lb>obiezioni contro il sistema sessuale, così strenuamente propugnato, trovano <lb></lb>qua e là all&#039;occasione le più appropriate risposte. </s></p><p type="main">

<s>L&#039;obiezione prima del Pontedera, che cioè son gli apici così disposti, <lb></lb>da giunger difficilmente il polline a toccare gli stimmi, se non per tutti i <lb></lb>Petaloidi, come l&#039;obiciente voleva, aveva certo un gran valore rispetto a certi <pb xlink:href="020/01/1672.jpg" pagenum="547"></pb>fiori, come quelli per esempio delle Passiflore e delle Nigelle, ne&#039;quali i pi­<lb></lb>stilli sopravanzano di gran lunga gli stami. </s>

<s>Rispondeva il Wahlbom da <lb></lb>null&#039;altro dipendere la difficoltà, che da difetto di osservazione, la quale, di­<lb></lb>ligentemente instituita, riesce anzi uno de&#039;tratti più eloquenti nella storia <lb></lb>amorosa de&#039;fiori. </s>

<s>Imperocchè nella Nigella arvense “ cum flos primum expan­<lb></lb>ditur, quinque pistilla erecta staminibus longiora sunt. </s>

<s>Flore autem bene <lb></lb>explicato, retorquentur styli ut circumpositos pistillis maritos attingant. </s>

<s>Ac­<lb></lb>cepto vero polline, iterum elevantur, semperque manent erecti. </s>

<s>In Tama­<lb></lb>rindo, Passiflora et Cassiis eodem fere modo reflectuntur styli versus anthe­<lb></lb>ras ” (Amoenitates acad. </s>

<s>upsal., Holmiae 1749, pag. </s>

<s>360). </s></p><p type="main">

<s>Quanto alle Umbellate, l&#039;argomento del Pontedera, osserva il Vahlbom, <lb></lb>si fonda sopra una fallacia, che consiste nell&#039;aver col Malpighi creduto che <lb></lb>sien le tube o i pistilli organi essenziali del fiore, mentre in verità non son <lb></lb>che gli stimmi. </s>

<s>“ Ast stigma est pars illa generationi inserviens, minime <lb></lb>vero stylus. </s>

<s>Hic enim in multis abesse potest, quippe essentiam floris non <lb></lb>constituit. </s>

<s>Sufficiat itaque quod stigmata in Umbellatis eodem cum antheris <lb></lb>tempore vigeant, stylus vero Umbellatarum post conceptionem elongetur, <lb></lb>quemadmodum et in Acere cernitur ” (ibid., pag. </s>

<s>359). </s></p><p type="main">

<s>La fecondazione delle Diecie presentava difficoltà di più grave momento, <lb></lb>e furon quelle massimamente, che fecero arretrare il Camerarius. </s>

<s>Notava <lb></lb>nulladimeno il Wahlbom avvenir talvolta che la Canapa seminifera porti an­<lb></lb>che insieme qualche fiore stamineo “ quo nonnullae feminae impraegnari <lb></lb>possint, quod Rudolphum Camerarium lusit ” (ibid., pag. </s>

<s>369). Rimaneva <lb></lb>però ancora in tutto il suo pieno vigore la difficoltà delle fecondazioni in <lb></lb>distanza, non crollatasi nè per gli effluvi magnetici del Valentin, nè per le <lb></lb>correnti ventose dell&#039;Alpino. </s>

<s>Non pretendeva il Wahlbom di avere in tutto <lb></lb>rivelato il mistero, ma osservò che concorrevano in gran parte a celebrarlo, <lb></lb>attratti dalla dolcezza del nettare, gl&#039;insetti, e specialmente le Api, le quali <lb></lb>“ sub indefessis laboribus pollinem spargunt ut pistillum attingat, quippe <lb></lb>nondum constat quid humor hic nectareus in physiologia floris certo prae­<lb></lb>stet ” (ibid., pag. </s>

<s>372). </s></p><p type="main">

<s>Di rispondere all&#039;altra, che sembrava non punto più lieve difficoltà, ri­<lb></lb>cavata dalla fruttescenza del Fico, non si curò il Wahlbom, avendolo già <lb></lb>fatto il collega suo Cornelio Hegardt, il quale, nella medesima sopra com­<lb></lb>memorata upsaliense Accademia, innanzi al Preside illustre, lesse, il di 15 di <lb></lb>Settembre dell&#039;anno 1744, una dissertazione intitolata <emph type="italics"></emph>Ficus,<emph.end type="italics"></emph.end> ch&#039;entrò pure <lb></lb>a far parte delle <emph type="italics"></emph>Amenità<emph.end type="italics"></emph.end> dianzi citate. </s>

<s>L&#039;enimma della caprificazione vi si <lb></lb>trova finalmente, nella promulgata legge matrimoniale, spiegato: il Caprifico <lb></lb>è il maschio, e la pianta domestica la femmina, i fiori della quale, rimanen­<lb></lb>dosi dentro il ricettacolo rinchiusi e stipati, sarebbe stato impossibile che <lb></lb>venissero dalla polvere fecondatrice aspersi, se la previdente Natura non <lb></lb>avesse all&#039;opera chiamate ministre le Tentredini. </s>

<s>Questi insetti, che udimmo <lb></lb>poco fa dal traduttore di Teofrasto chiamar col nome di <emph type="italics"></emph>Culici,<emph.end type="italics"></emph.end> nascono <lb></lb>dalle uova già deposte nel Caprifico dalle madri pregnanti, e al tempo, che <pb xlink:href="020/01/1673.jpg" pagenum="548"></pb>la Natura ha stabilito alle sue provvide intenzioni opportuno, di bruchi, come <lb></lb>tutti gli altri, diventano alati. </s>

<s>“ Tenthredinibus iam mutatis, alisque instruc­<lb></lb>tis, tempus adest quo Caprificus, seu Ficus mas, florescit, hoc est farinam <lb></lb>edit antherarum. </s>

<s>Tunc Tenthredines e Caprifici cavitatibus farina, molitoris <lb></lb>instar e mola sua prodeuntis, obducti, evolant et coniugibus acquisitis de <lb></lb>ovis pariendis solliciti sunt. </s>

<s>Hinc, ad singulos grossos transvolantes, cavita­<lb></lb>tes Ficus feminae, dolii instar clavis ferreis vel spiculis seu pistillis ab omni­<lb></lb>bus lateribus intus completas, intrando, non possunt non farinam illam, qua <lb></lb>contecti sunt, excutere. </s>

<s>Patet igitur hoc modo Ficum hanc feminam facil­<lb></lb>lime impraegnari ” (ibid., pag. </s>

<s>42). </s></p><p type="main">

<s>Sia pure, instavano ancora i seguaci del Pontedera, ma ne&#039;nostri do­<lb></lb>mestici orti, anche senz&#039;artificio di caprificazione, ci maturano i Fichi, e ciò <lb></lb>vuol dire che riescono le femmine feconde, anche senza gli amplessi virili. </s>

<s><lb></lb>Per rispondere a questa difficoltà, l&#039;Hegardt soggiunge che possono i Fichi <lb></lb>domestici maturare, benchè non sieno stati prima fecondati, perchè il loro <lb></lb>frutto non è propriamente il pericarpio, ma il ricettacolo o il clinanto, come <lb></lb>nelle Fravole e nelle More, che pur maturano allo stesso modo. </s>

<s>Rimase dun­<lb></lb>que il Pontedera ingannato dal Malpighi, il quale qualificò per ovario quello <lb></lb>che in verità niente altro era che il calice del Fico. </s>

<s>“ Botanici quidam, qui­<lb></lb>bus hoc non satis fuit perspectum, arbores hasce sine praevia fecundatione <lb></lb>edere fructus videntes, argumentum contra generationem plantarum satis <lb></lb>validum se hinc invenisse crediderunt, at fructus Ficuum non pericarpium <lb></lb>sed receptaculum commune esse minime perpenderunt ” (ibid., pag. </s>

<s>42). </s></p><p type="main">

<s>Così, per opera del Linneo e de&#039;Linneidi suoi upsaliensi, veniva stabi­<lb></lb>lito e difeso dai contradittori il sistema sessuale delle piante, che s&#039;applicò <lb></lb>largamente come nota specifica in quella classificazione, i fondamenti alla <lb></lb>quale erano stati già posti dal Camerarius. </s>

<s>Dopo un mezzo secolo di com­<lb></lb>battimenti, capitanati da una parte dal Malpighi e dall&#039;altra dal Grew, i se­<lb></lb>guaci di questo ebbero stabile vittoria, a proclamar la quale fra i ritrosi ita­<lb></lb>liani fu uno de&#039;primi e più faccendieri Filippo Arena. </s>

<s>Nel 1768 egli pub­<lb></lb>blicò in Palermo, a nome di suo nipote Ignazio, un trattato diviso in due <lb></lb>parti, col titolo <emph type="italics"></emph>Della natura e cultura de&#039;fiori;<emph.end type="italics"></emph.end> trattato che fu impresso <lb></lb>la seconda volta nel 1771 col nome proprio dell&#039;Autore, ma colla data di <lb></lb><emph type="italics"></emph>Cosmopoli.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Descrive con vivacità l&#039;Autore le Passiflore colte in fallo negli amorosi <lb></lb>congressi, e ne fa argomento da rispondere alle obiezioni del Pontedera, ma <lb></lb>par non sappia o non si ricordi che quelle osservazioni erano state fatte, e <lb></lb>che quelle risposte erano state pubblicamente date dal Wahlbom ventidue <lb></lb>anni avanti: come pur non sospetta che al capitolo suo XXXII, dove spiega <lb></lb>la ragione del caprificio, sia stata da ventiquattr&#039;anni preletta, nell&#039;upsa­<lb></lb>liense accademia, la dissertazion dell&#039;Hegardt sullo stesso argomento. </s></p><p type="main">

<s>Nulla di nuovo è pure nell&#039;Arena rispetto al ministero degl&#039;insetti nelle <lb></lb>fecondazioni a distanza, ma una certa diligenza nelle descrizioni, e un co­<lb></lb>lorirle in modo, che vengan le cose a ricever maggiore importanza, lo ren-<pb xlink:href="020/01/1674.jpg" pagenum="549"></pb>don da questa parte superiore al Wahlbom, e agli altri commentatori della <lb></lb>Filosofia linneana. </s>

<s>Ei non crede per nulla all&#039;azione del vento. </s>

<s>“ Chi vede <lb></lb>e osserva, scrive nel cap. </s>

<s>XXVIII, conosce chiaro che il vento non è mica <lb></lb>un mezzo abile ad altro, che a disperder le polveri. </s>

<s>Posso io attestare che, <lb></lb>in tant&#039;anni di cultura di fiori, non mi son potuto accorgere mai che il <lb></lb>vento abbia trasferite polveri da un fiore all&#039;altro, ancorchè sopra l&#039;istessa <lb></lb>pianta, fuorchè quando sono stati fra sè contig<gap></gap>i o si vicini, che agitati dal <lb></lb>vento insieme fregando con gli apici si loccassero. </s>

<s>” </s></p><p type="main">

<s>“ Queste e simili difficoltà, che io incontrava insuperabili nella comune <lb></lb>opinione, m&#039;impegnarono alla ricerca del vero modo come posson le polveri <lb></lb>di una pianta passare all&#039;altra. </s>

<s>L&#039;ho io detto allegoricamente che il vero <lb></lb>proprio ed universal mezzo sieno certe artifiziosissime macchinette, dalla <lb></lb>provvida Natura preparate e tenute pronte in ogni luogo, per lo trasporto <lb></lb>delle polveri. </s>

<s>Ma ora è tempo di svelarle apertamente, sebbene voi già ve <lb></lb>ne sarete accorti quali sieno, per quel tanto che se n&#039;è parlato. </s>

<s>Son mac­<lb></lb>chine, alle quali la Natura diede occhi perspicaci per vedere, ancor di lon­<lb></lb>tano, onde pigliare e dove lasciar le polveri; diede piedi per moversi, op­<lb></lb>pur diede lor le ali per facilitarne fino a molta distanza il trasporto. </s>

<s>Già vi <lb></lb>accorgete che son gl&#039;insetti di ogni genere, massimamente volatili, e che <lb></lb>sien dessi che portan le polveri lo anderò mostrando in tutto il seguente <lb></lb>capo, sebbene, per accertarsene ad evidenza, la miglior prova sarà che cia­<lb></lb>scun da sè, per sua maggior sicurezza, in un prato o giardino fiorito vada ciò <lb></lb>osservando co&#039;proprii occhi, e così spero che molto meglio ne resterà indu­<lb></lb>bitabilmente convinto ” (Della natura de&#039;fiori, Cosmopoli 1771, pag. </s>

<s>256, 57). </s></p><p type="main">

<s>Forse nel diffondere anche in Italia le nuove dottrine il libro dell&#039;Arena <lb></lb>non ebbe grande efficacia, ma egli è in ogni modo primo fra gl&#039;Italiani a <lb></lb>dar colore di verità alle lontane previsioni del Redi. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Comunque siasi, al sol meridiano ripurgato d&#039;ogni macchia, e scoperto <lb></lb>di ogni nube all&#039;intorno, chi aveva occhi in fronte non poteva oramai più <lb></lb>negare la luce del vero, e s&#039;ammirò da tutti la sapiente Natura, che a man­<lb></lb>tener le specie facesse anche alle insensibili piante gustare il gaudio del­<lb></lb>l&#039;amore. </s>

<s>Ma sarebbe quel gaudio rimasto una infeconda lascivia, se a dif­<lb></lb>fondere i lieti conceputi germi non si fossero aperti gli uteri materni. </s></p><p type="main">

<s>Gl&#039;insetti, divenuti ne&#039;maritali amplessi fecondi, perchè non si trovan, <lb></lb>come gli animali perfetti, mammelle da allattare i loro teneri parti, e per­<lb></lb>chè non hanno il natural calore sul petto e sotto le ali da incubar le loro <lb></lb>uova, come gli uccelli; costretti a mendicare una cuna l&#039;eleggono sagace­<lb></lb>mente ora in mezzo a un calice fiorito, ora dentro l&#039;incisa scorza di un al-<pb xlink:href="020/01/1675.jpg" pagenum="550"></pb>bero, ora anche nel limo, purchè il materno amor ne assicuri che non sarà <lb></lb>ai dolci pegni deposti tradita la fedeltà dell&#039;ospizio, o crudelmente negata <lb></lb>la carità del nutrimento. </s></p><p type="main">

<s>Le piante non han bisogno di tante sollecitudini in eleggere quel più <lb></lb>appropriato ospizio o quel più convenevole nutrimento: dovunque si trovi <lb></lb>terra all&#039;intorno, che sia scoperta alle pioggie e alle rugiade, all&#039;aria e al <lb></lb>sole, ivi trovan le disperse uova chi le fomenti nella loro tenera infanzia, e <lb></lb>le nutrisca. </s>

<s>Giacchè dunque il fine de&#039;patiti amori è unicamente conseguito <lb></lb>per via della dispersione, mirabile è l&#039;industria, che pongono intorno a ciò <lb></lb>gli alberi e l&#039;erbe. </s>

<s>Per lo più involgono le loro uova, come in morbide fa­<lb></lb>sce, nella polpa del pericarpo, il quale serve mirabilmente all&#039;intento. </s>

<s>Ro­<lb></lb>tondo, ruzzola più facilmente per il declivio, e son più pronte le acque a <lb></lb>travolgerlo nelle loro rapine: gustoso, lo divoran le fiere, e vanno qua e là <lb></lb>ad affidare i riposti semi alla terra, con le deposizioni del ventre: corrotto, <lb></lb>il passeggero nauseato lo gitta con la mano, e lo disperde colla punta in­<lb></lb>sultatrice del piede. </s>

<s>Le ruinose cadute, le corse precipitose, i divoramenti <lb></lb>laceratori, le dispettose iatture, tutto che insomma han di più pericoloso a <lb></lb>temere per la vita de&#039;loro parti le madri, sono altrettanti benefizii, di che <lb></lb>lieta la madre pianta ringrazia. </s></p><p type="main">

<s>Vi sono arboscelli, che provvedono alla dispersione delle loro uova in <lb></lb>modo assai più diretto. </s>

<s>Ora le forniscono di ami, con che attaccandosi ai <lb></lb>peli degli animali viaggiano insieme con essi: ora le muniscono di pinne, <lb></lb>perchè volino velocissime trasportate sulle ali de&#039;venti. </s>

<s>Non infrequente è <lb></lb>poi il caso che, facendo per elaterio di molla scattar dalle silique i granel­<lb></lb>lini risecchi, imiti la stessa pianta l&#039;industre opera, che fa la mano dei se­<lb></lb>minatori. </s>

<s>“ Mirabile quoddam elateris genus, scriveva nel 1682 Tommaso <lb></lb>Cornelio in quel suo Proginnasma postumo <emph type="italics"></emph>De sensibus,<emph.end type="italics"></emph.end> percipimus in fructi­<lb></lb>bus cucumeris sylvestris, qui maturescentes vix ita leniter contrectari pos­<lb></lb>sunt, quin statim dissiliant, succumque et semina magno impetu eiaculen­<lb></lb>tur. </s>

<s>Nec dissimilis, licet aliquanto obscurior, vis est in fructibus Momordicae, <lb></lb>seu Balsaminae, aliisque compluribus, qui ad maturitatem perducti sponte <lb></lb>dissiliunt, mirisque motibus agitantur ” (Thomae Cornelii, Op. </s>

<s>posth., Nea­<lb></lb>poli 1688, pag. </s>

<s>14). </s></p><p type="main">

<s>Ma degno di maggior considerazione è, prosegue a dire il Cornelio, quel <lb></lb>che in un certo genere di Trifoglio ebbi più volte, con mia grandissima com­<lb></lb>piacenza, a notare. </s>

<s>È un&#039;erba volgarissima che ha il nome di <emph type="italics"></emph>Trifolium <lb></lb>acetosum<emph.end type="italics"></emph.end> nel linguaggio degli scienziati, e di <emph type="italics"></emph>Alleluia<emph.end type="italics"></emph.end> in quello del popolo, <lb></lb>e benchè il Mattioli descriva e rappresenti anche in disegno la pianticella, <lb></lb>non fa però motto della meravigliosa proprietà, ch&#039;io v&#039;ho scoperto. </s>

<s>“ Fol­<lb></lb>liculos profert in metae formam quodammodo figuratos. </s>

<s>In his semina in­<lb></lb>cluduntur, quae maturescentia minimarum lentium, striato cortice, speciem <lb></lb>exhibere videntur. </s>

<s>Unumquodque autem seminis granulum, dum infra fol­<lb></lb>liculum adhuc latet, alba tenuique tunica circumtegitur, at maturo iam se­<lb></lb>mine alba illa membranula, sponte, magnaque vi exilit, pericarpii corticem <pb xlink:href="020/01/1676.jpg" pagenum="551"></pb>disrumpit, et adnexum seminis granulum ad trium vel quatuor pedum lon­<lb></lb>gitudinem mirabili celeritate provehit. </s>

<s>Atque interea alba illa tunica a se­<lb></lb>mine secreta et in maiorem molem expansa, vermiculi instar cieri contor­<lb></lb>querique videtur. </s>

<s>Quod si semina ad maturitatem proxima nondum sponte <lb></lb>sua exsilierint, tunc ad minimam pericarpii contrectationem statim impetu <lb></lb>facto prosiliunt. </s>

<s>Id autem, quod de Trifolio recitavimus, posse aliis quibus­<lb></lb>dam plantis contingere non diffitemur ” (ibid., pag. </s>

<s>14, 15). </s></p><p type="main">

<s>Disseminati per questi, e per i tanti altri provvidi modi, gli ovoli delle <lb></lb>piante, trovan dentro all&#039;utero della terra quell&#039;umido tiepore, necessario a <lb></lb>potere svolgersi dai loro involucri, e venire a poco a poco a rappresentar <lb></lb>le sembianze, e a rinnovellar la vita stessa della madre. </s>

<s>A investigar quali <lb></lb>sieno di questa novella vita i principii e le fasi, attesero, com&#039;a principa­<lb></lb>lissima parte della loro scienza, i Botanici, e a noi resta ora a narrar l&#039;or­<lb></lb>dine e il frutto che raccolsero dai loro studi. </s></p><p type="main">

<s>Passò per la mente di Empedecle, filosofo antico, la felice idea di ras­<lb></lb>somigliare i semi alle uova e fu dopo tanti secoli quella stessa idea nuova­<lb></lb>mente espressa dal Cesalpino, che scrisse nel suo trattato <emph type="italics"></emph>De plantis:<emph.end type="italics"></emph.end> “ Se­<lb></lb>men enim tanquam ovum est, in quo est principium vitale ” (Florentiae 1583, <lb></lb>pag. </s>

<s>11). Se non che, mentre l&#039;antico Autore non vedeva tra i semi delle <lb></lb>piante e le uova degli animali altro punto di somiglianza, che nel poter dagli <lb></lb>uni e dagli altri ugualmente svolgersi due vite simili a quelle dei generanti; <lb></lb>il Cesalpino, scrutando addentro l&#039;intima composizione, trovò da farne il più <lb></lb>esatto riscontro fra le parti. </s>

<s>Come nell&#039;interno dell&#039;uovo, egli dice, è delineato <lb></lb>tutto il futuro animale, e l&#039;albume che lo circonda serve alla nutrizione del <lb></lb>feto; così nell&#039;interno dei semi si contien la radichetta e la gemma, in che <lb></lb>compendiasi tutta intera la pianticella, al crescer della quale la rimanente <lb></lb>materia che la circonda somministra il necessario alimento. </s>

<s>“ Quemadmo­<lb></lb>dum enim in ovo quaedam particula continetur, in qua est animalis futuri <lb></lb>veluti delineatio, reliquum autem corpulentiae pro alimento est; sic in plan­<lb></lb>tarum seminibus pars illa principatum continet unde radix erumpit et ger­<lb></lb>men; est enim quasi corculum quoddam, reliqua parte seminis alimentum <lb></lb>illi primum subministrante ” (ibid., pag. </s>

<s>12). </s></p><p type="main">

<s>Una condizione essenzialissima perchè il seme inducasi a germogliare <lb></lb>è, prosegue a dire il Cesalpino, l&#039;umidità, la quale mette in calorosa fer­<lb></lb>mentazione la corpulenta materia dell&#039;uovo stesso, a quel modo che fa l&#039;acqua <lb></lb>versata sopra la calce viva. </s>

<s>Così, preparato il domestico nutrimento, crescono <lb></lb>le gracili membra alla rinchiusa pianticella, la quale, mettendo la radichetta <lb></lb>al di sotto e la gemmula al di sopra, esce finalmente da&#039;suoi involucri, come <lb></lb>il pulcino esce dal guscio. </s>

<s>“ Deinde excitato ignis principio in ipsis latente, <lb></lb>ut calei contingit, in humoris occursu, idem humor cum lactea seminis sub­<lb></lb>stantia permixtus et concoctus, tanquam familiare alimentum auget con­<lb></lb>ceptum ante incoatum. </s>

<s>Tunc autem radix primo emergit peciolo quodam ex <lb></lb>corde seminis prodeunte, qua corticem dehiscere et egressum semini con­<lb></lb>cedere necesse est. </s>

<s>Postquam autem radicem in terram egerit, reliqua se-<pb xlink:href="020/01/1677.jpg" pagenum="552"></pb>minis corpulentia in plurimis ex suo cortice, tamquam ex ovo, in lucem <lb></lb>prodit ” (ibid., pag. </s>

<s>12, 13). </s></p><p type="main">

<s>Sebben sia l&#039;albume dell&#039;uovo in alcuni semi rappresentato da una so­<lb></lb>stanza, che circonda l&#039;imbrional pianticella, non facendo però parte inte­<lb></lb>grale di lei, osserva il Cesalpino che, nella maggior parte di quegli stessi <lb></lb>semi, l&#039;alimento è somministrato da due organi, tanto simili alle altre fo­<lb></lb>glie nella struttura e nella inserzione, quanto differenti negli usi, non es­<lb></lb>sendo queste foglie stesse sui rami fatte per altro che per difender dalle <lb></lb>intemperie i frutti. </s>

<s>“ Quae enim heec duo folia exortum ducunt cor est, <lb></lb>quippe radicis caput et germinis principium. </s>

<s>Sunt autem haec alterius ge­<lb></lb>neris folia, quam quae in germinatione exoriuntur: illa enim tantum ad tu­<lb></lb>telam data sunt, tenuia, ex solo cortice orta; haec partes sunt seminis ad <lb></lb>alimentum primum cordi ministrandum, ideo crassa sunt ” (ibid., pag. </s>

<s>13). </s></p><p type="main">

<s>Tali essendo intorno alla generazion delle piante dal seme i documenti <lb></lb>del Cesalpino, convien dire che troppo presto fossero nella stessa nostra Ita­<lb></lb>lia dimenticati, se Giuseppe degli Aromatari venendo, quasi un mezzo se­<lb></lb>colo dopo, a ripetere quelle medesime cose, scriveva in una lettera a Barto­<lb></lb>lommeo Nati essere andato con lento passo a profferirle, perchè potrebbero <lb></lb><emph type="italics"></emph>nimium prorsus nova videri multis, et ab humano conceptu aliena.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La novità de&#039;peregrini concetti fu grandemente ammirata dagli stra­<lb></lb>nieri, e quella Lettera al Nanti, che l&#039;Autore premetteva al suo trattato me­<lb></lb>dico <emph type="italics"></emph>De rabie contagiosa,<emph.end type="italics"></emph.end> pubblicato nel 1625 in Venezia, fu nuovamente <lb></lb>impressa <emph type="italics"></emph>ob dignitatem materiae<emph.end type="italics"></emph.end> in Francfort l&#039;anno dopo, e poi, come pre­<lb></lb>ziosa gemma, raccolta nelle Filosoficali transazioni di Londra. </s>

<s>All&#039;ultimo Gio­<lb></lb>vacchino Joung la trascrisse in appendice a&#039;suoi <emph type="italics"></emph>Opuscoli botanico fisici<emph.end type="italics"></emph.end><lb></lb>stampati nel 1747 in Coburgo, celebrando nella prefazione l&#039;Autore con an­<lb></lb>noverarlo fra&#039;primi “ qui observarunt et docuerunt maximam inter semina <lb></lb>vegetabilium et ova animalium intercedere analogiam. </s>

<s>” </s></p><p type="main">

<s>Un&#039;altra ragion del merito è riconosciuta dall&#039;Joung nelle dottrine del­<lb></lb>l&#039;Aromatari, per aver questi scritto in fine alla sua lettera che, rispetto alle <lb></lb>uova delle galline “ existimamus equidem pullum in ovo delineatum esse, <lb></lb>antequam foveatur ” (Joung, in opusc. </s>

<s>cit., Appendix, pag. </s>

<s>183), non ripen­<lb></lb>sando esser questa una ripetizione, non del concetto solo, ma delle parole <lb></lb>stesse del Cesalpino, le quali suonano, come poco fa udimmo, rappresentarsi <lb></lb>la pianticella nel seme <emph type="italics"></emph>quemadmodum in ovo quaedam particula contine­<lb></lb>tur, in qua est animalis futuri veluti delincatio.<emph.end type="italics"></emph.end> Ond&#039;è che precursore e <lb></lb>inspiratore all&#039;Harvey, anche intorno a ciò, è probabilissimo fosse il Cesal­<lb></lb>pino, piuttosto che, come parve ad alcuni, l&#039;Aromatari, il quale lasciò il li­<lb></lb>bero studio a&#039;suoi ammiratori di riscontrar con le nuove cose da altrui <lb></lb>scoperte “ quae in libro <emph type="italics"></emph>De generatione animalium,<emph.end type="italics"></emph.end> Deo dante, enarrabi­<lb></lb>mus ” (ibid.). </s></p><p type="main">

<s>Forse è vero che l&#039;autore della lettera al Nanti fu più preciso del­<lb></lb>l&#039;autor <emph type="italics"></emph>De plantis<emph.end type="italics"></emph.end> in osservare le varie forme, e gli svolgimenti vari delle <lb></lb>foglie seminali, ma ci esprimiamo così in forma di dubbio, perchè gli afo-<pb xlink:href="020/01/1678.jpg" pagenum="553"></pb>rismi IV-VII non ci sembrano molto chiari. </s>

<s>Certo è in ogni modo non es­<lb></lb>sere sfuggito all&#039;attenzione dell&#039;Aromatari quel fascetto di fibre, che tiene <lb></lb>il fusticino congiunto alle stesse foglie seminali, e ch&#039;egli acutamente ras­<lb></lb>somigliò al cordone umbilicale. </s>

<s>“ Plurimae harum plantarum, dice nell&#039;afo­<lb></lb>rismo IX, quousque extant in vocatis seminibus latentes, nutriuntur per <lb></lb>adnatas quasdam, ut ita dicam, umbilicales vias ” (ibid., pag. </s>

<s>182). E della <lb></lb>pianticella, che ha messe già le radici, nell&#039;aforismo XVII e ultimo, sog­<lb></lb>giunge: “ Nec amplius per adnatas vias nisi ut diximus parum, sed per ra­<lb></lb>dicem sugit, non aliter ac animal quod primo per umbilicales venas creditur <lb></lb>nutrimentum capere, exortum vero per os assumit ” (ibid., pag. </s>

<s>183). </s></p><p type="main">

<s>Secondo l&#039;Aromatari dunque la pianticella già nata attinge la massima <lb></lb>parte del nutrimento dalla terra, per via delle radici, non così però che sia <lb></lb>cessato affatto l&#039;ufficio delle foglie seminali, da cui dura tuttavia la pianti­<lb></lb>cella stessa ad attrarre qualche poco di umore. </s>

<s>Benchè avessero però que­<lb></lb>ste aforistiche asserzioni molta probabilità, sentivasi nonostante il bisogno di <lb></lb>metterle al cimento dell&#039;esperienza, di che dette i primi esempi il Malpi­<lb></lb>ghi, diligentemente osservando che effetto facessero i germogli, tagliate ai <lb></lb>semi le foglie o i cotiledoni, com&#039;egli fu primo a chiamarle. </s>

<s>L&#039;effetto dun­<lb></lb>que fu questo: “ Pluries seminales Fabarum plantulas, detractis omnino <lb></lb>cotyledonibus, plantavi, quorum nullae penitus vegetarunt. </s>

<s>Idem expertus <lb></lb>sum in plantulis Cucurbitae, Peponum, Lupinorum et Phaseolorum, qui in­<lb></lb>signi pollent trunco et gemma ” (De seminum veget., Op. </s>

<s>omnia, T. </s>

<s>I cit., <lb></lb>pag. </s>

<s>199). </s></p><p type="main">

<s>Di qui è lecito congetturare, prosegue a dire lo stesso Malpighi, che <lb></lb>all&#039;uova delle piante manchi qualche cosa di più che all&#039;uova degli animali, <lb></lb>e che sia la madre Terra colei, che largamente supplisce: “ Plantulae enim <lb></lb>seminali haerent quidem gemina, ut plurimum, crassa folia, quae albumini <lb></lb>ovi analoga, uterinae placentae vel cotyledonum vices explent. </s>

<s>Haec humo­<lb></lb>rem exposcunt a terreno utero emanantem quo soluti fermentativi et sper­<lb></lb>matici succi, per propria umbilicalia vascula, plantulae quotidianam suppe­<lb></lb>ditant alimoniam, et auctivam materiam. </s>

<s>Unde plantulae foetus ex fermen­<lb></lb>tatis, et in motum actis particulis in placentis, scilicet in seminalibus foliis, <lb></lb>iam concretis, non solum laxatis meatulis augetur, sed ad vegetandum exci­<lb></lb>tatur ” (ibid., pag. </s>

<s>110). </s></p><p type="main">

<s>Parve al Borelli però che troppo scarsa fosse la materia contenuta nei <lb></lb>cotiledoni per servire a nutrire la pianticella, alla quale sosteneva contro il <lb></lb>Malpighi esser sufficientissima l&#039;acqua, per cui l&#039;umidità di lei è condizione <lb></lb>essenziale al risvegliarsi ne&#039;semi gli spiriti latenti della vita. </s>

<s>Che l&#039;incre­<lb></lb>mento poi, il quale diceva incominciare ad apparir nella radichetta, provenga <lb></lb>dall&#039;intrusione di materie esterne, piuttosto che dall&#039;interior sostanza de&#039;co­<lb></lb>tiledoni, credeva di poter dimostrarlo coll&#039;esperienza delle bacche del lauro <lb></lb>poste in luogo umido a germogliare. </s>

<s>“ Hae quidem exporrigebant per ter­<lb></lb>ram praelongas radices nigricantes et fere ligneas similes funiculis, quarum <lb></lb>aliquae semipedis longitudinem aequabant, et tunc baccarum cortices inte-<pb xlink:href="020/01/1679.jpg" pagenum="554"></pb>gri et aridi erant, atque interna substantia seminis adhuc candida, dura, <lb></lb>eiusdem saporis eiusdemque figurae et magnitudinis erat, quam reliquae <lb></lb>baccae radice carentes habebant ” (De motu anim., P. II cit., pag. </s>

<s>364). </s></p><p type="main">

<s>Conseguiva da ciò che l&#039;uso de&#039;cotiledoni non poteva esser quello as­<lb></lb>segnato dal Malpighi, e perciò il Borelli ne pensò un altro, che gli sembrò <lb></lb>non affatto improbabile, e che dice di aver ritrovato nella scienza fisica “ fa­<lb></lb>cie praeferente eximio Benedicto Castello praeceptore ” (ibid., pag. </s>

<s>362). <lb></lb>Sulla germogliazion de&#039;semi deve esso Castelli aver fatte quelle osservazioni <lb></lb>e quelle esperienze, dalle quali concluse le savie regole economiche inse­<lb></lb>gnate nel discorso <emph type="italics"></emph>Del modo di conservare i grani<emph.end type="italics"></emph.end> (Opusculi filos., Bolo­<lb></lb>gna 1669, pag. </s>

<s>40-45). Di tali esperienze, non pubblicate e forse nemmeno <lb></lb>scritte, il Borelli ebbe notizia nella scuola dalla viva voce del Maestro, e poi <lb></lb>le ridusse ingegnosamente al suo proposito nella proposizione CLXXVII della <lb></lb>II parte <emph type="italics"></emph>Dei moti animali.<emph.end type="italics"></emph.end> Ivi disse che i cotiledoni facevano le veci di due <lb></lb>Termometri santoriani, attraendo la notte gli umori acquosi, e al sopravve­<lb></lb>nire del calor diurno respingendoli in ogni parte della tenera pianticella, che <lb></lb>riceve così al vegetare l&#039;impulso e l&#039;incremento. </s>

<s>“ Postquam vero plantula <lb></lb>adoleverit, ut per se officium folliculorum supplere possit, tunc auxiliarii illi <lb></lb>Thermometri, ut inutiles, sensim arescunt ” (ibid.). </s></p><p type="main">

<s>Benchè dicesse il Borelli di professar queste dottrine come tradizionali <lb></lb>nella scuola italiana, il Malpighi nonostante sospettò fosse per il mal&#039;animo <lb></lb>che lo eccitava a contradirgli, e di ciò sfogavasene nell&#039;Autobiografia là dove <lb></lb>racconta l&#039;origine e la causa delle fiere inimicizie. </s>

<s>Ivi dice che, preso a ri­<lb></lb>scontrar l&#039;esperienze delle bacche del lauro, trovò che mirabilmente confer­<lb></lb>mavano le sue dottrine, d&#039;avversar le quali non ancora contento, “ prosequi­<lb></lb>tur doctissimus Borellus impugnare usum foliarium seminalium, ut successive <lb></lb>concludat aqueum succum in planta non transformari a virtute fermenta­<lb></lb>tiva ” (Opera posth. </s>

<s>cit., Pars II, pag. </s>

<s>75). </s></p><p type="main">

<s>Le contradizioni però del Borelli circa l&#039;uso delle foglie seminali, po­<lb></lb>niamo pure che ci fosse il mal&#039;animo di mezzo, venivano avvalorate da un <lb></lb>fatto, che tenne lungamente in pena i Botanici. </s>

<s>È quel fatto che la polpa <lb></lb>carnosa dei cotiledoni o il perisperma non son solubili nell&#039;acqua, ciò che <lb></lb>pareva sufficiente a concludere control il Malpighi esser l&#039;acqua stessa per <lb></lb>sè sola, e non intorbidata dalla sostanza farinosa del seme, che si dispensa <lb></lb>ad alimentare la tenera pianticella. </s>

<s>Oltre alle esperienze del Van-Helmont <lb></lb>“ qui vidit virgam salicis librarum quinque adeo excrevisse in quinque <lb></lb>annis, ut 169 librarum penderet et tale incrementum superaddidit sola aqua <lb></lb>irrigata ” (De motu anim., P. cit., pag. </s>

<s>364), s&#039;aggiungevano a confermar <lb></lb>l&#039;ipotesi del Borelli i nuovi fatti sperimentati dal Du-Hamel, il quale pre­<lb></lb>sentò nel 1748, innanzi agli Accademici parigini, pianticelle nate sopra le <lb></lb>spugne e sui muschi, non imbevuti d&#039;altro che d&#039;acqua. </s>

<s>Parve perciò che <lb></lb>anche l&#039;Hales concorresse in quella ipotesi borelliana, quando, dalla sua <lb></lb>CXXIV statica esperienza, concluse esser probabilissimo “ che quelle fronde <lb></lb>seminali rendano al germe gli stessi uffici, che le fronde, che sono intorno <pb xlink:href="020/01/1680.jpg" pagenum="555"></pb>ai pomi, ai cotogni ed altri frutti rendono a questi frutti medesimi, cioè di <lb></lb>sollevare l&#039;umor nutritivo e di condurlo fin dentro alla loro sfera di attra­<lb></lb>zione ” (Traduz. </s>

<s>cit., pag. </s>

<s>274). </s></p><p type="main">

<s>Da un&#039;altra parte che l&#039;acqua per una certa virtù fermentativa sciolga <lb></lb>i cotiledoni in nutrimento era dimostrato chiaro al Malpighi per l&#039;esperienze <lb></lb>sue p<gap></gap>oprie sopra tante varietà di semi, non eccettuate le bacche del lauro, <lb></lb>e per l&#039;esperienze del volgo sui bulbi delle cipolle o de&#039;vari pomi riposti <lb></lb>nelle domestiche dispense, i quali, quando per l&#039;umidità dell&#039;aria e per i <lb></lb>tiepori della stagione cominciano a mettere, si sentono tanto alterati di sa­<lb></lb>pore. </s>

<s>S&#039;aggiungevano alle volgari esperienze le autorità degli scienziati, e <lb></lb>massimamente dell&#039;Harvey, il quale giudicando impossibile che l&#039;acqua sola, <lb></lb>o venga dall&#039;aria o dalla terra, si trasformi in tanta varietà di organi, disse <lb></lb>che per i fermenti alteravasi, dentro la sostanza del seme, in diversi modi, <lb></lb>e così veniva a far le veci de&#039;liquori negli ovi. </s>

<s>“ Nam ut plantae omnes <lb></lb>ex eodem communi nutrimento, sive rore seu terrae humore, diversimode <lb></lb>alterato coctoque oriuntur, nutriuntur atque augentur; ita pariter ex iisdem <lb></lb>ovi liquoribus, albuminibus nempe et vitello, totus pullus, singulaeque eius <lb></lb>partes procreantur et crescunt ” (De generat. </s>

<s>anim. </s>

<s>cit., pag. </s>

<s>165). </s></p><p type="main">

<s>Ma le verità professate dal Malpighi, e che s&#039;additavano già prefulgere <lb></lb>in queste citate parole dell&#039;Harvey, rimasero vittoriose sopra gl&#039;ingegnosi <lb></lb>commenti del Borelli, quando più attentamente si studiò la natura delle fo­<lb></lb>glie seminali. </s>

<s>Risultò da tale studio ch&#039;esse foglie non erano strumenti ac­<lb></lb>cessori, come due fistule di termometri santoriani apposte per la nutrizione <lb></lb>dei germi, ma che erano anzi parti del seme tanto essenziali, che il Bohe­<lb></lb>rave le costituì per note da distinguere ne&#039;due grandi ordini delle Dicotile­<lb></lb>doni e delle Monocotiledoni l&#039;immenso e svariato popolo delle piante. </s>

<s>Il Linneo <lb></lb>poi e i Linneidi revocarono alla mente e posero in maggiore evidenza le dot­<lb></lb>trine dell&#039;Harvey trasfuse nelle malpighiane, quando con tant&#039;assidua dili­<lb></lb>genza riscontrarono la generazion delle piante con quella degli animali. </s>

<s>“ Haec <lb></lb>folia seminalia antea totum constituerunt semen, excepto hilo, atque alimen­<lb></lb>tum tenerrimae plantae praeparant, donec firmiores in terra egerit radices, <lb></lb>non secus ac vitellus in ovo, placenta uterina factus, nutrimentum per fu­<lb></lb>niculum umbilicalem porrigit pullo ” (Sponsalia plant. </s>

<s>cit., pag. </s>

<s>345). </s></p><p type="main">

<s>Per tali autorità, e per tante ragioni, si decideva a mezzo il secolo XVIII <lb></lb>la controversia fra il Malpighi e il Borelli, i quali essendo pienamente con­<lb></lb>cordi in riconoscer le foglie seminali necessarie alla vegetazione e all&#039;incre­<lb></lb>mento del germe, discordavano solo intorno al modo del porgersi quegli or­<lb></lb>gani a due tali prestantissimi uffici. </s>

<s>Nonostante, il Bonnet si credè lecito di <lb></lb>scriver così in capo alla sua LXXXIX ricerca sull&#039;uso delle foglie: “ L&#039;usage <lb></lb>des lobes et des fevilles seminales n&#039;est pas encore bien connu. </s>

<s>On sait en <lb></lb>général qu&#039;ils fournisent à la jeune plante une noutriture appropriée à son <lb></lb>état: mais on ne sait pas assez combien ils sont utiles a son accroisse­<lb></lb>ment. </s>

<s>Une expérience que je vais rapporter le fera connoitre ” (Ediz. </s>

<s>cit., <lb></lb>pag. </s>

<s>310, 11). </s></p><pb xlink:href="020/01/1681.jpg" pagenum="556"></pb><p type="main">

<s>L&#039;esperienze che l&#039;Autore passa immediatamente a descrivere, fatte <lb></lb>nello stesso modo, ebbero il medesimo resultato di quelle del Malpighi, se <lb></lb>non che, mentre questi s&#039;esercitò solo intorno alle Dicotiledoni, il Bonnet <lb></lb>non lasciò indietro, per farne il confronto, le Monocotiledoni. </s>

<s>Scelse perciò <lb></lb>i semi de&#039;Fagioli da una parte, e quelli della Saggina dall&#039;altra, e ai primi <lb></lb>tagliati i lobi, ai secondi la foglia seminale, trovò che “ le retranc<gap></gap>ement <lb></lb>des fevilles seminales a eu de beaucoup plus grandes suites dans le Sar­<lb></lb>rasin que n&#039;en a eu celui des lobes dans le Haricot. </s>

<s>Presque toutes les plan­<lb></lb>tes de Sarrasin, qui ont subi cette opération, ont péri. </s>

<s>Celles qui l&#039;ont sou­<lb></lb>tenue sont demeurées si chétives, qu&#039;elles ont toujours été à l&#039;égard des <lb></lb>autres ee qu&#039;est la plus petit nain a l&#039;egard du plus grand géant ” (ivi, <lb></lb>pag. </s>

<s>312). </s></p><p type="main">

<s>Dietro queste esperienze, che parevano dimostrare esser più dell&#039;altre <lb></lb>gelose di ricevere offesa le piante a un cotiledone solo, quasi come son più <lb></lb>gelosi della vista i monoculi di quelli che hanno in fronte due occhi, venne <lb></lb>desiderio al Bonnet d&#039;instituirne altre, per determinare anche meglio l&#039;im­<lb></lb>portanza e l&#039;uso delle foglie seminali. </s></p><p type="main">

<s>Il Malpighi aveva lasciato scritto in proposito: “ Primo itaque vere Fa­<lb></lb>barum plurimas plantulas sevi, detractis prius cotyledonibus seu farinaceo <lb></lb>pericarpio: ex his binae tantum plantulae, reliquis corruptis, parum vege­<lb></lb>tarunt ” (De sem. </s>

<s>veget. </s>

<s>cit., pag. </s>

<s>100). E più sotto: “ Mense quoque Maii <lb></lb>alias seminales plantulas Fabarum et Phaseolorum, ablatis pariter binis se­<lb></lb>minalibus foliis, seu cotyledonibus, incubandas posui, e quibus unica Fabae <lb></lb>plantula vegetavit ” (ibid.). Parevano i resultati di queste esperienze un <lb></lb>po&#039;incerti, e l&#039;incertezza poteva forse dipendere da ciò, che nel detrarre i <lb></lb>cotiledoni venisse a riceverne finalmente offesa anche l&#039;ilo. </s></p><p type="main">

<s>S&#039;accorse in ogni modo il Bonnet che, fatta l&#039;operazione colla punta di <lb></lb>uno scarpello, riusciva sui semi secchi assai pericolosa, ma poi trovò facile <lb></lb>e sicura la riuscita tenendo per qualche giorno gli stessi semi in una spu­<lb></lb>gna imbevuta d&#039;acqua. </s>

<s>L&#039;umidità gli fa rigonfiare “ et il est alors plus fa­<lb></lb>cile de diviser les lobes, et d&#039;en separer le germe sans l&#039;offenser ” (Recher­<lb></lb>ches cit., pag. </s>

<s>314). Ottenuti con tal arte ili nudi e interi di alquanti fagioli, <lb></lb>gli seminò, e gli vide tutti nascere contro la sua aspettazione. </s>

<s>Ma sarebbe <lb></lb>stato molto difficile il riconoscerli nel vero esser loro, tanto erano rimpic­<lb></lb>coliti: “ un botaniste los auroit pris pour une nouvelle espece de <emph type="italics"></emph>Harricot <lb></lb>nain ”<emph.end type="italics"></emph.end> pag. </s>

<s>315). Seminati il di 10 d&#039;Agosto, il di 19 d&#039;Ottobre incomin­<lb></lb>ciarono a fiorire, ma i fiori furono scarsi, e piccoli a proporzione. </s>

<s>Lasciati <lb></lb>allo scoperto, caddero ai primi freddi, e caddero con essi insieme le spe­<lb></lb>ranze di vederli probabilmente allegare ne&#039;piccoli frutti. </s>

<s>Da ciò se ne con­<lb></lb>cluse, lasciando addietro le curiosità, che le foglie seminali son, più che alla <lb></lb>vegetazion delle piante, necessarie al loro incremento. </s></p><p type="main">

<s>Nella Contemplazione della Natura il Bonnet stesso formulò questa con­<lb></lb>clusione, dicendo che le foglie seminali <emph type="italics"></emph>servono principalmente a purificare <lb></lb>il succo nutritizio,<emph.end type="italics"></emph.end> e lo Spallanzani, in tradur dal francese queste parole, <pb xlink:href="020/01/1682.jpg" pagenum="557"></pb>dop&#039;aver riferite in nota le narrate bonnettiane esperienze, soggiunge che <lb></lb>“ sarebbe bene il promoverle coll&#039;applicare il taglio a tante altre piante, ora <lb></lb>levando interamente le due foglie seminali e i due lobi, ora levandone una <lb></lb>sola o un solo ” (T. </s>

<s>I cit., pag. </s>

<s>198, 99). Ciò confermerebbe il dubbio che <lb></lb>s&#039;affacciava alla mente di chi legge il principio della citata Ricerca LXXXIX <lb></lb>sull&#039;uso delle foglie, che cioè, tanto l&#039;autor della Contemplazione della Na­<lb></lb>tura, quanto l&#039;illustre italiano traduttore, avessero dimenticate le numerose <lb></lb>e, per esser le prime, diligentissime esperienze del Malpighi, il quale non <lb></lb>trascurò nemmeno di far quella qui desiderata e proposta dallo Spallanzani. </s>

<s><lb></lb>Chi svolge infatti il trattato <emph type="italics"></emph>De seminum vegetatione<emph.end type="italics"></emph.end> vi legge fra le altre <lb></lb>anco queste parole: “ Plantulis vero a primordiis vegetantibus, unico de­<lb></lb>tracto folio, altero autem superstite, germinatio producebatur, non tanta ta­<lb></lb>men felicitate qualis in non mutilatis observabatur ” (pag. </s>

<s>109). E poniamo <lb></lb>pure che anche queste malpighiane esperienze avessero bisogno d&#039;esser pro­<lb></lb>mosse, era dovere di un Italiano in ogni modo il commemorarle, all&#039;occa­<lb></lb>sione specie che uno straniero veniva quasi un secolo dopo a proporle in <lb></lb>forma, che paressero sue primizie. </s></p><p type="main">

<s>Comunque sia, dobbiamo esser grati al Bonnet che promosse, e allo Spal­<lb></lb>lanzani che intese di promuovere l&#039;esperienze del Malpighi, dalle quali in­<lb></lb>somma veniva a intendersi perchè fosse necessaria l&#039;umidità alla germoglia­<lb></lb>zione. </s>

<s>Se poi questa necessità sia l&#039;unica, o se vi si richieda anche insieme <lb></lb>il concorso dell&#039;aria, benchè le volgari esperienze de&#039;semi rimasti nelle chiuse <lb></lb>profondità sepolti ne paressero una prova certa, non eran però ancora le <lb></lb>menti disposte a bene intenderla. </s>

<s>Secondavano molto queste disposizioni, da <lb></lb>poi che si fece notare la somiglianza che passa fra i semi delle piante e gli <lb></lb>ovi degli animali, le dottrine insegnate dall&#039;Harvey, il quale, escludendo dal­<lb></lb>l&#039;utero nell&#039;atto ch&#039;è reso fecondo ogni minima cosa che venga di fuori, <lb></lb><emph type="italics"></emph>aeris puta aut seminis,<emph.end type="italics"></emph.end> dava argomento a concluderne che, non essendo <lb></lb>l&#039;aria necessaria per concepire, non fosse perciò necessaria nemmeno per <lb></lb>germinare. </s></p><p type="main">

<s>Parve questa logica conclusione esser confortata dalle esperienze, quando <lb></lb>il Boyle tentò di produrre creature viventi nel vuoto. </s>

<s>Essendosi l&#039;illustre Fi­<lb></lb>sico proposto di confutar l&#039;ipotesi della fiamma vitale sentiva che sarebbe <lb></lb>un grande argomento in favore di lei “ si comperiatur quod vitae princi­<lb></lb>pium in seminalibus rudimentis indigeat, non secus ac caeterae flammae, <lb></lb>aeris concursum ut in actum revocetur ” (Op. </s>

<s>omnia cit., T. III, P. II, <lb></lb>pag. </s>

<s>173). Provò a quest&#039;intento di far nascere sotto la campana della mac­<lb></lb>china pneumatica alcune uova di bombici e di altri insetti e furon forse le <lb></lb>difficoltà dello sperimentare e l&#039;incertezza dei resultati, che non gli dettero <lb></lb>animo di proseguire i tentativi ne&#039;semi, dai quali nonostante sperava che <lb></lb>verrebbe dimostrato non esser necessario il concorso dell&#039;aria, per ridestar <lb></lb>negli stessi semi e negli ovi, come nelle fiamme, gli spiriti della vita. </s></p><p type="main">

<s>Sentite le difficoltà dello sperimentare al modo boyleiano, il Malpighi <lb></lb>scelse una via più facile, benchè non fosse così diretta: pensò di sottrarre <pb xlink:href="020/01/1683.jpg" pagenum="558"></pb>i semi dall&#039;azione dell&#039;aria, tenendoli immersi nell&#039;acqua di un vaso, alla <lb></lb>quale soprannotava uno straterello di olio. </s>

<s>I semi, ch&#039;eran di vario genere, <lb></lb>si videro presto cominciare a risolversi in bolle, e a render torbida l&#039;acqua: <lb></lb>dopo venti giorni erano affatto corrotti, senza dar segno di vegetazione. </s>

<s>“ Vi­<lb></lb>gesima transacta die, aqua foetentissima erat, conclusaque semina corrupta <lb></lb>absque vegetatione ” (De sem. </s>

<s>veget. </s>

<s>cit, pag. </s>

<s>108). </s></p><p type="main">

<s>Pareva si dimostrasse da questa esperienza la necessità dell&#039;aria per <lb></lb>vegetare, ma tante difficoltà si potevano contrapporre a una tal conclusione, <lb></lb>che il Malpighi stesso avendole presentite lasciò la questione indecisa. </s>

<s>L&#039;aveva <lb></lb>però il Borelli risoluta con gran confidenza, e già posta per fondamento alla <lb></lb>sua teoria, essendo chiaro che i termometri cotiledonari non avrebbero po­<lb></lb>tuto, senza l&#039;intervento dell&#039;aria, esercitare sul germe i loro uffici, più sot­<lb></lb>tilmente spiegati nella propos. </s>

<s>CLXXXI, che il Borelli stesso formulava: <lb></lb>“ praecipuam causam vegetationis plantarum esse aerem ” (De motu anim, <lb></lb>P. II cit., pag. </s>

<s>371). </s></p><p type="main">

<s>Dietro una tanta autorità nella scienza si durò a credere che l&#039;aria con­<lb></lb>corresse nella germogliazione colla sua elasticità, messa in gioco dalle al­<lb></lb>ternative del caldo e del freddo, infintanto che Guglielmo Homberg non <lb></lb>tornò a tentare quei pneumatici esperimenti, innanzi alle difficoltà de&#039;quali <lb></lb>erasi arretrato il Boyle. </s>

<s>Più fortunato dell&#039;Inglese, o più destro, il nuovo <lb></lb>sperimentatore francese riuscì a far germogliare i semi di varie piante nel <lb></lb>vuoto, dietro il qual fatto pose contro il Borelli queste due conclusioni: <lb></lb>“ I. </s>

<s>Que ni le ressort de l&#039;air, ni sa pesanteur ne sont point la cause prin­<lb></lb>cipale de la germination des plantes, puisque les graines germent dans le <lb></lb>vuide. </s>

<s>II. </s>

<s>Que l&#039;air est cependant au moins une cause accidentelle de cette <lb></lb>germination, quisque d&#039;une mème quantite de graines de la mème espèce, <lb></lb>il en avoit germé un bien plus grand nombre dans l&#039;air que dans le vuide ” <lb></lb>(Collection acad., T. </s>

<s>I cit., pag. </s>

<s>184, 85). </s></p><p type="main">

<s>Sulla fine del secolo XVIII si trovò ch&#039;eran false queste conclusioni <lb></lb>dell&#039;Homberg, e ch&#039;era invece vera la proposizion del Borelli, modificata <lb></lb>però col sostituire ai giochi elastici dell&#039;aria, imparati dall&#039;arte santoriana, <lb></lb>un&#039;azione più sottile e più intima, rivelata da una scienza che apparve nuova. </s>

<s><lb></lb>Ma come al tornar del giorno pieno precede un incerto albore crepuscolino, <lb></lb>così avvenne allo splendido sole di quella scienza. </s></p><p type="main">

<s>Chenelmo Dygby lesse nel collegio di Gresham, il dì 23 Gennaio 1660, <lb></lb>una dissertazione, che fu dal patrio idioma tradotta in latino col titolo <emph type="italics"></emph>De <lb></lb>vegetatione plantarum.<emph.end type="italics"></emph.end> Ivi narra com&#039;aves<gap></gap>e reso fertilissimo un campo, <lb></lb>spargendovi sopra sostanze terree mescolate con nitro. </s>

<s>Si dirà forse, poi sog­<lb></lb>giunge, ch&#039;è lo stesso nitro, attratto dalle radici, quello che ha prodotto <lb></lb>l&#039;ubertà della messe? </s>

<s>Niente affatto, perchè sarebbe presto esaurito, nè po­<lb></lb>trebbe somministrar materia a tanta progenie. </s>

<s>“ Salis nitrum est ibi instar <lb></lb>magnetis quod attrahit similem salem, quo aer redditur faecundus. </s>

<s>Et hinc <lb></lb>Cosmopolita ansam arripiebat dicendi quod <emph type="italics"></emph>in aere occultum quoddam vi­<lb></lb>tae alimentum sit.<emph.end type="italics"></emph.end> In tali aere, qui hoc <emph type="italics"></emph>benigno igne<emph.end type="italics"></emph.end> maxime impraegna-<pb xlink:href="020/01/1684.jpg" pagenum="559"></pb>tus est, salubrem producimus vitam..... Hic sal est alimentum pulmonum <lb></lb>et nutrimentum spirituum..... Hic igitur spiritus qui est in aere attrahi­<lb></lb>tur, veluti per quendam magnetem, per salinum liquorem, quem semen <lb></lb>imbibit et cuius plenum est..... Huic sali <emph type="italics"></emph>omnium rerum seminales vir­<lb></lb>tutes<emph.end type="italics"></emph.end> inclusae sunt..... ” (Amstelodami 1669, pag. </s>

<s>54-57): enimmi alllora, <lb></lb>e lungo tempo da poi, ma che la Chimica moderna ha felicemente inter­<lb></lb>pretati. </s></p><pb xlink:href="020/01/1685.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOTO XIV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dei Minerali<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della sede nettunica del regno minerale. </s>

<s>— II. </s>

<s>Della sede plutonica del regno minerale. </s>

<s>— III. </s>

<s>Della <lb></lb>generazion dei cristalli, e di ciò che intorno alle forme cristalline fu osservato e speculato dagli <lb></lb>Accademici del Cimento. </s>

<s>— IV. Dell&#039;origine e de&#039;progressi della Cristallografia fuori dell&#039;Ac­<lb></lb>cademia del Cimento. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>A quei, che ingannati da fallaci esperienze, ammettevano potersi le piante <lb></lb>nutrir di sola acqua pura, rimaneva il dovere di rispondere a chi gli avesse <lb></lb>interrogati come mai l&#039;acqua stessa riesca a trasformarsi nelle solide fibre <lb></lb>delle foglie, della corteccia e del legno; e come mai valga una sostanza in­<lb></lb>sipida e inodora a infondere tanta soavità ne&#039;frutti, e tant&#039;olezzo ne&#039;fiori. </s>

<s><lb></lb>Si rispondeva nonostante, perchè di parole fu sempre gran dovizia, con ar­<lb></lb>gomenti, che ritraevano tutt&#039;insieme de&#039;difetti provenienti dalle difficoltà <lb></lb>della cosa, e dalla ignoranza della Chimica: alcuni però, come il Bonnet per <lb></lb>esempio, negarono esser l&#039;acqua unico alimento alla vita vegetativa, e se al­<lb></lb>cuni semi furono a spettacolo offerti dal Du-Hamel lietamente germogliati <lb></lb>e cresciuti nel muschio inumidito, nella segatura del legno o nella bamba­<lb></lb>gia, ciò avvien, diceva l&#039;Autore della <emph type="italics"></emph>Contemplazion della Natura,<emph.end type="italics"></emph.end> “ perchè <lb></lb>molte di tali materie o trasmutansi insensibilmente in terra, o contengono <lb></lb>attualmente parti terree, o perchè l&#039;acqua, da cui vengono innaffiate, è pre­<lb></lb>gna di tali particole, che gli organi delle piante estraggono, preparano o si <lb></lb>assimilano ” (Traduz. </s>

<s>cit., T. I, pag. </s>

<s>185). </s></p><p type="main">

<s>Così venivasi nelle piante a riconoscere quella intima relazione, che le <lb></lb>stringe col regno minerale; relazione messa già in grande evidenza dalle <pb xlink:href="020/01/1686.jpg" pagenum="561"></pb>combustioni de&#039;tronchi, de&#039;rami e delle stesse foglie nelle ceneri delle quali, <lb></lb>lisciviate, s&#039;ammirarono l&#039;eleganti varietà delle forme cristalline. </s>

<s>L&#039;esperienze <lb></lb>intorno a questi, che si chiamarono <emph type="italics"></emph>Sali fattizi,<emph.end type="italics"></emph.end> incominciate nel periodo <lb></lb>primo dall&#039;Accademia del Cimento, si perfezionarono nel periodo ultimo per <lb></lb>opera di Franceso Redi, il quale raccolse in XX aforismi il resultato de&#039;suoi <lb></lb>diligentissimi studi. </s></p><p type="main">

<s>Si vedevano dunque così manifestamente ritornare al regno minerale i <lb></lb>cadaveri delle piante, come vi ritornavano in egual modo i cadaveri degli <lb></lb>animali. </s>

<s>Un&#039;assai ovvia osservazione dall&#039;altra parte, che cioè gli animali <lb></lb>stessi nutronsi delle sostanze già preparate ne&#039;vegetanti, mentre che i ve­<lb></lb>getanti si nutrono immediatamente dalla terra, scopriva facile alle menti dei <lb></lb>Filosofi e dei volgari quell&#039;ingradarsi sempre a maggiore altezza e a dignità, <lb></lb>che fanno i tre grandi regni della Natura. </s></p><p type="main">

<s>Rimasero però di così fatti passaggi dalla materia bruta alla organiz­<lb></lb>zata affatto occulte le ragioni e i modi, infin tanto che il benefico Micro­<lb></lb>scopio non venne a diradare alquanto il velo di que&#039;misteri. </s>

<s>Apparvero <lb></lb>allora molte delle particelle minerali informi, perchè forse non riuscì a raf­<lb></lb>figurarle la vista naturale, nemmeno avvalorata dall&#039;arte, ma in alcune al­<lb></lb>tre di quelle particelle si riconobbero figure superficiali ben definite, e con­<lb></lb>terminanti lo spazio in angoli e in lati condotti a regola di squisitissima <lb></lb>geometria. </s>

<s>Negli stami però, di che s&#039;intessono gli organi alle piante e agli <lb></lb>animali, si videro quelle angolosità sparire per ridursi a prendere costante­<lb></lb>mente una figura otricellare o sferoidea. </s></p><p type="main">

<s>Or perchè i solidi, in prendere le loro angolosità, si vedono ritornare <lb></lb>alla sfera, convien dire che questa sia il subietto generale di tutte le figure <lb></lb>poliedriche, cosicchè il definito per esempio nel triangolo e nel quadrato, <lb></lb>nella piramide e nel cubo, si trovi indefinitamente contenuto nella sfera e <lb></lb>nel cerchio. </s>

<s>Di qui vedesi esser mirabilmente l&#039;Istiologia illustrata dalla Geo­<lb></lb>metria, perciocchè nella cellula si comprendono indeterminate le particolari <lb></lb>virtù del cristallo. </s>

<s>La determinata figura perciò di questo non permette altro <lb></lb>incremento che per apposizione di parti ugualmente determinate, mentre <lb></lb>dalla indefinita forma della cellula possono uscire le indefinite varietà di <lb></lb>tutte le altre forme, che si trovano in lei virtualmente comprese. </s></p><p type="main">

<s>La scienza dei minerali non è dunque, come potrebbe sembrare, aliena <lb></lb>dalla scienza dei viventi, perchè lo studio del cristallo conduce o può facil­<lb></lb>mente condurre allo studio della cellula, e poniamo che si trovino, in am­<lb></lb>bedue i casi, difficoltà insuperabili all&#039;ingegno e all&#039;industria dell&#039;uomo, è <lb></lb>un fatto oramai sperimentato in Filosofia che sono i paragoni di scoperte <lb></lb>nuove sempre fecondi. </s></p><p type="main">

<s>Vien forse da queste considerazioni, le quali non si possono da noi ac­<lb></lb>cennare che in fretta, qualche lume d&#039;idee per rispondere a chi volesse sa­<lb></lb>pere se giovi nello studio della Storia naturale incominciar dagli animali o <lb></lb>dai minerali, dall&#039;alto gradatamente scendendo in basso, o facendo a ritroso <lb></lb>il viaggio. </s>

<s>Il proposto quesito è simile a quell&#039;altro: se giovi nello studio <pb xlink:href="020/01/1687.jpg" pagenum="562"></pb>della geometria incominciar dal circolo o dal triangolo, tenendo via sintetica <lb></lb>o analitica: questione di metodo irresolubile in logica, ma che facilmente si <lb></lb>risolve nel pratico insegnamento. </s></p><p type="main">

<s>Comunque sia, s&#039;è da noi tenuto il primo di questi metodi: si è in­<lb></lb>cominciato cioè dal narrar le faticose conquiste dell&#039;ingegno nello studio <lb></lb>della vita animale, perchè sono in essa eminentemente comprese le vite dei <lb></lb>sottoposti ordini naturali, come son le figure poliedriche eminentemente tutte <lb></lb>comprese nella sfera, o come son, nelle virtù della cellula, a sì grande al­<lb></lb>tezza sublimate le virtù dei cristalli. </s></p><p type="main">

<s>Nella storia delle osservazioni e delle esperienze, fatte dalla scienza in­<lb></lb>torno a questi stessi cristalli, s&#039;assolve il presente argomento secondo i limiti <lb></lb>e l&#039;ordine che ci siamo prescritti. </s>

<s>Il rimanente, che può concernere i mi­<lb></lb>nerali, si riduce alle loro origini in seno e sulla superficie della gran madre <lb></lb>Terra, la quale venne per le subite vicende a deporveli in due vari modi. </s>

<s><lb></lb>Costituiscono perciò questi due modi al regno come due cospicue e distinte <lb></lb>sedi, in riconoscer le quali essendosi lungamente e faticosamente studiata la <lb></lb>scienza, non rimane a noi, prima di trattar de&#039;cristalli, che a narrar colla <lb></lb>solita brevità il lento e faticoso progredire di quelli studi. </s></p><p type="main">

<s>Incominciano così fatti studi col propor che si fece il problema dell&#039;ori­<lb></lb>gine dei corpi marini, i quali si ritrovan dispersi per i continenti, o depo­<lb></lb>sti sulle alte cime dei monti, e dal vario modo come fu risoluto quel pro­<lb></lb>blema dipendono, delle nuove scienze che siam per narrare, gli arretramenti <lb></lb>e i progressi. </s>

<s>Dalle tradizioni antiche s&#039;introdusse con Teofrasto l&#039;opinione <lb></lb>che fosse nella terra una virtù plastica, simile a quella del mare, e fu, nei <lb></lb>primi restauramenti scientifici, il Falloppio che accolse, e nel suo trattato <lb></lb><emph type="italics"></emph>De metallis seu fossilibus<emph.end type="italics"></emph.end> dette autorità e diffuse una tale falsa opinione. </s>

<s><lb></lb>Giorgio Agricola, che non molto dopo venne fuori a trattare dello stesso <lb></lb>argomento, ammetteva nel VII libro <emph type="italics"></emph>De natura fossilium<emph.end type="italics"></emph.end> l&#039;esistenza di un <lb></lb>succo lapidescente, il quale, entrando per tutti i pori, gli riempie di tutto <lb></lb>sè, e ne modella gl&#039;incavi. </s>

<s>“ Cum Natura, poi soggiunge, lapides arborum <lb></lb>similes procreet, diligenter videndum est an corticem et medullam aliaque <lb></lb>habeant, quae si absunt non stipites in lapides conversi sunt, sed Na­<lb></lb>tura fecit lapides stirpium simillimos ” (De natura fossilium, Basileae 1546, <lb></lb>pag. </s>

<s>327, 28). </s></p><p type="main">

<s>Ebbero il Falloppio e l&#039;Agricola alle loro ipotesi molti seguaci, i quali <lb></lb>non sentirono a professarle gran repugnanza, in tempi che s&#039;ammetteva dai <lb></lb>più ne&#039;vermi, e in alcune piante, la generazione spontanea. </s>

<s>Argomentavano <lb></lb>infatti costoro che la materia, la quale dà vita a un insetto, può men dif­<lb></lb>ficilmente plasmarsi a comporre il nicchio a una Conchiglia, o a un Echino. </s>

<s><lb></lb>Parve nonostante ad alcuni quella ipotesi dissennata, e il Fracastoro fu primo <lb></lb>a profferire il suo giudizio in privato, e il Cesalpino in pubblico, scrivendo <lb></lb>nel I libro <emph type="italics"></emph>De metallicis<emph.end type="italics"></emph.end> che le conchiglie e altri avanzi marini furono ivi <lb></lb>deposte dalle acque, le quali poi si ritirarono lasciando arido il continente. <lb></lb></s>

<s>“ Hoc enim modo censere, poi ne conclude, magis consonum est rationi, <pb xlink:href="020/01/1688.jpg" pagenum="563"></pb>quam putare vim animalem, intra lapides, rudimenta animalium ac planta­<lb></lb>rum gignere, ut quidam putant ” (Romae 1596, pag. </s>

<s>5). </s></p><p type="main">

<s>Veniva pochi anni dopo a dar maggior forza al ragionamento del Ce­<lb></lb>salpino Fabio Colonna, il quale, invocando il filosofico assioma che la Na­<lb></lb>tura nulla fa a caso, dimostrava la falsità dell&#039;opinione di Teofrasto. </s>

<s>Inutili <lb></lb>infatti sarebbero i denti senza le mascelle, e i nicchi, che non han da co­<lb></lb>prire, e le ossa, che non hanno da sostentar nessun membro animale. </s>

<s>“ Den­<lb></lb>tes sine maxilla, testacea sine animali, ossa unica (nonnisi omnia coniuncta <lb></lb>cum ipso animali) in proprio elemento Natura nunquam fecit: quomodo in <lb></lb>alieno nunc potuisset fecisse est credendum? </s>

<s>Ossa enim ex eodem seminali <lb></lb>excremento ortum habere simul cum animali ipsa experientia et Natura do­<lb></lb>cuit, tam in homine, quam in animalibus sanguine praeditis, et ex semine <lb></lb>initium habentibus, ac etiam quibusdam aliis: quomodo in subterraneis ter­<lb></lb>restribus semen hoc inveniri asseritur? </s>

<s>qua experientia? </s>

<s>Hoc si daretur et <lb></lb>hominem sponte oriri esset observatum vel animalia, ut bos, equus et si­<lb></lb>milia ” (Dissertatio De glossopetris, appendix ad tract. <emph type="italics"></emph>De purpura,<emph.end type="italics"></emph.end> Ro­<lb></lb>mae 1616, pag. </s>

<s>32). </s></p><p type="main">

<s>Comparve nel 1622 alla luce la descrizione del Museo Calzolari, lasciata <lb></lb>a mezzo per causa di morte da Benedetto Ceruti, e condotta a termine da <lb></lb>Andrea Chiocchi, il quale, trattando <emph type="italics"></emph>De lapideis rebus a Natura effigie do­<lb></lb>natis,<emph.end type="italics"></emph.end> divulgò sulla proposta questione quella, ch&#039;egli chiama <emph type="italics"></emph>Magni Fra­<lb></lb>castori sententiam.<emph.end type="italics"></emph.end> Racconta come Torello Sarayna, giureconsulto e archeo­<lb></lb>logo veronese, scavando il patrio monte da quella parte, d&#039;onde sgorga la <lb></lb>fontana così detta del <emph type="italics"></emph>Ferro,<emph.end type="italics"></emph.end> vi trovasse con sua grande maraviglia sepolte <lb></lb>conchiglie, ostriche, con molte altre spoglie di marini animali. </s>

<s>Non sapendo <lb></lb>come spiegare il fatto interrogò il celebre concittadino suo Girolamo Fraca­<lb></lb>storo, il quale rispose aversi della proposta questione tre diverse sentenze. </s>

<s><lb></lb>La prima di coloro, che dicevano essere quegli animali stati trasportati colà <lb></lb>dal Diluvio; sentenza però ch&#039;egli giudicava poco probabile, perchè la uni­<lb></lb>versale inondazione non fu d&#039;acque venute di sotto dal mare, ma di sopra <lb></lb>dal cielo, e poi perchè si potrebbe a quel modo spiegar l&#039;esistenza dei corpi <lb></lb>marini sulle vette, ma no alle falde dei monti. </s></p><p type="main">

<s>Era la seconda sentenza quella di coloro, che tenevano con Teofrasto, <lb></lb>ai quali rispondeva il Fracastoro così argomentando: O le sostanze lapidee, <lb></lb>formate dal succo plastico a imitazione delle parti animali, furono un giorno <lb></lb>viventi o no: Se furono viventi, allora perchè non si vedono tuttavia rivi­<lb></lb>vere simili produzioni? </s>

<s>Dir poi che non furono mai viventi, e che solo imi­<lb></lb>tarono l&#039;esteriori forme animali, è in aperta contradizione col senso, veden­<lb></lb>dosi che le conchiglie fossili, per esempio, hanno tutte le parti delle con­<lb></lb>chiglie vive e vere, con questa sola differenza ch&#039;essendosi corrotte mancano <lb></lb>le parti molli. </s></p><p type="main">

<s>“ Cum hactenus, prosegue a dire il Chiocchi, magni Fracastori senten­<lb></lb>tiam recitasset Sarayna, qua aliorum Phylosophorum sibi hac in re non <lb></lb>probari placita docebat, subiecit. </s>

<s>Ergo se dicebat existimare haec olim vera <pb xlink:href="020/01/1689.jpg" pagenum="564"></pb>animantia fuisse illuc iactata a mari et in mari enata. </s>

<s>” Questa poi con­<lb></lb>clude è la dottrina dell&#039;eccellentissimo Fracastoro, che raccoglie in sè il va­<lb></lb>lore di molte e classiche testimonianze, rappresentando egli medico, filosofo, <lb></lb>poeta e astronomo le persone e il divino ingegno d&#039;Ippocrate, di Aristotile, <lb></lb>di Platone, di Virgilio e di Tolomeo. (Descriptio Musaei Calceolari, Vero­<lb></lb>nae 1622, pag. </s>

<s>409). </s></p><p type="main">

<s>Comunque sia, erano i progressi della scienza mal fondati sopra l&#039;au­<lb></lb>torità di un grand&#039;uomo, quando a confortar le ragioni mancavano l&#039;espe­<lb></lb>rienze dei fatti. </s>

<s>Coteste esperienze, alle quali non si prevedevano da nessuno <lb></lb>ancora possibili i modi, ebbero nella gloriosa Accademia fiorentina i prin­<lb></lb>cipii, com&#039;ora accenneremo, e come meglio vedremo di poi. </s></p><p type="main">

<s>Fu, qualche miglio in distanza da Livorno, nell&#039;anno 1666, pescato un <lb></lb>gran pesce del genere dei Cani, il capo del quale, fatto per ordine del Gran­<lb></lb>duca venire a Firenze, fu consegnato a Niccolò Stenone, nuovo accademico <lb></lb>del Cimento, perchè lo sezionasse. </s>

<s>Carlo Dati, concorso fra gli altri allo spet­<lb></lb>tacolo, vi riconobbe una gran somiglianza con quella testa di Lamia, fatta <lb></lb>incidere in rame e descritta dal Mercati nella Metalloteca sua Vaticana: di <lb></lb>che fece consapevole lo Stenone, a cui, perchè se ne potesse giovare a&#039;suoi <lb></lb>studii, prestò il rame stesso inciso insieme col manoscritto. </s>

<s>L&#039;Autore di que­<lb></lb>sto, come si sa dalle passate storie, riponeva fra i metalli <emph type="italics"></emph>idiomorfi<emph.end type="italics"></emph.end> anche <lb></lb>le Glossopietre, le quali, perciocchè troppo somigliavano ai denti delle La­<lb></lb>mie, così, perchè non l&#039;avessero gl&#039;inesperti a confondere insieme, ne fa­<lb></lb>ceva notare le differenze: “ Video namque Glossopetras magnas et Lamiae <lb></lb>piscis dentes confundi etiam a curiosis. </s>

<s>Similitudo errorem subornavit, quae <lb></lb>tanta est ut, qui utrorumque ortum non noverit, nihil suspicetur; qui utrin­<lb></lb>que notas non contulerit, non dignoscat..... Quod inter dentes et Glosso­<lb></lb>petras illas discriminis est, exiguum sane. </s>

<s>Crassiores plerumque Glossopetrae, <lb></lb>tenuiores dentes, et mollius nitent, ut inter osseam et lapideam Glossopetra­<lb></lb>rum materiam ex aspectu iudicium capiamus. </s>

<s>Unus quoque et perpetuus <lb></lb>dentium color candidus, vel aetate flavescens, Glossopetrae variant ” (Metal­<lb></lb>lotheca vatic. </s>

<s>cit., pag. </s>

<s>333, 34). </s></p><p type="main">

<s>Leggendo lo Stenone nel manoscritto queste parole, s&#039;accorse dell&#039;in­<lb></lb>ganno, che s&#039;era fatto il Mercati, in creder che le notate accidentali varietà <lb></lb>fra i denti delle Lamie e le Glossopietre importassero fra loro qualche sostan­<lb></lb>zial differenza, e fu da ciò condotto a entrare nella questione, così lungamente <lb></lb>agitata, fra chi diceva esser le stesse Glossepietre prodotte dalla terra, e chi <lb></lb>sosteneva invece essere avanzi di antichi animali. </s>

<s>Da varie osservazionì, fra le <lb></lb>quali la più importante si è che i fossili e i viventi si ritrovan simili in tutte le <lb></lb>loro più minime parti, trae il prudente uomo, non bene in tutto rassicurato <lb></lb>dalle troppo scarse esperienze, le seguenti sei conclusioni, alle quali dà il <lb></lb>modesto titolo di <emph type="italics"></emph>congetture.<emph.end type="italics"></emph.end> Nella I e nella II si argomenta non poter es­<lb></lb>sere i fossili prodotti dalla terra, perchè non si vede nelle parti intorno, ri­<lb></lb>mosse se molli, o nella deformata figura dei creduti vegetanti se quelle stesse <lb></lb>parti son dure, nessun evidente segno di accrescimento, come osservasi per <pb xlink:href="020/01/1690.jpg" pagenum="565"></pb>esempio nelle radici degli alberi “ quae in terra duriori mille modis intor­<lb></lb>tae et compressae a figura recedunt ” (Canis carchariae dissectum caput, <lb></lb>Myologiae sperimen. </s>

<s>cit., pag. </s>

<s>94). Nella III, nella IV e nella V congettura <lb></lb>s&#039;ammettono le stratificazioni alluvionali, in che s&#039;affalda la superficie ter­<lb></lb>restre, e nella VI finalmente concludesi: “ Nihil obstare videtur quominus <lb></lb>animalium partibus similia corpora, quae e terris eruuntur, pro animalium <lb></lb>partibus habeantur ” (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Poco tempo dopo che lo Stenone così con gran prudenza fiosofava, <lb></lb>un Pittor sicìliano usciva calorosamente fuori a decidere la controversia, <lb></lb>prendendo per sua più sicura scorta la Filosofia del senso comune. </s>

<s>Agostino <lb></lb>Scilla pubblicava in Napoli, nel 1670, un libretto intitolato <emph type="italics"></emph>Vana specula­<lb></lb>zione disingannata dal senso,<emph.end type="italics"></emph.end> dove si proponeva principalmente di dimo­<lb></lb>strare il vero essere delle Glossopietre, di che trovasi largamente seminata <lb></lb>l&#039;isola di Malta. </s>

<s>“ Rimetto la causa, egli scrive, e la decisione di essa fran­<lb></lb>camente a cotest&#039;Isola candidissima, che non vuole mica addossati miracoli <lb></lb>finti, essendo bene provveduta de&#039;veri e sodi, che la Natura abbondante­<lb></lb>mente in essa ha depositato, come mostrerò nel luogo della dichiarazione <lb></lb>d&#039;alcune sue bellissime medaglie, se piacerà al Signore. </s>

<s>Udiamola in cor­<lb></lb>tesia e incolpiamo noi medesimi se ingannare ci vogliamo. </s>

<s>Essa agli occhi <lb></lb>nostri fedelmente parla, affermandoci che la Natura non ha avuto parte di <lb></lb>generazione, nella sua marga, di denti, di echini, d&#039;ossa, di vertebre, come <lb></lb>pur ora dalle stesse cose l&#039;osserveremo ” (pag. </s>

<s>111). Le osservazioni pro­<lb></lb>cedono con senno non solo, ma con rettitudine di metodo sperimentale, in­<lb></lb>fiorata di antica e di moderna erudizione. </s>

<s>Parevano perciò dover riuscir con­<lb></lb>cludenti ai Filosofi, e tutt&#039;insieme persuasive alle genti volgari, ma in effetto <lb></lb>seguitò ancora la vana speculazione a prevalere sul senso. </s></p><p type="main">

<s>Ai Peripatetici, tuttavia ostinati in credere alle generazioni spontanee <lb></lb>degl&#039;infimi esseri viventi, arridevano meglio delle nuove dottrine le antiche, <lb></lb>che il Gassendo riferiva così nel II Tomo del suo Syntagma filosofico: “ Cae­<lb></lb>teri fere haec referunt aut ad mundi animam, aut universi ad naturam, <lb></lb>quae cum eadem ubique sit, et rerum omnium quos ubique contineat lapi­<lb></lb>des efformat ex succo idoneo in mediis continentibus referentes externa spe­<lb></lb>cie conchas et pisces, quos procreare eadem solet in medio ac dissito mari ” <lb></lb>(editio cit., pag. </s>

<s>104). </s></p><p type="main">

<s>Fra&#039;nostri uno de&#039;più fervorosi seguaci di questa opinione è da anno­<lb></lb>verare Filippo Bonanni, che le altrui autorità confortava con osservazioni sue <lb></lb>proprie, e con ragioni, che dovevano allora essere seducenti. </s>

<s>Diceva parere <lb></lb>impossibile che sieno reliquie di animali le così dette ossa dei giganti, non <lb></lb>essendoci memoria che abbiano mai vissuto al mondo creature così smisu­<lb></lb>rate, e fuori de&#039;consueti ordini naturali. </s>

<s>Che se convien di qui persuadersi <lb></lb>non poter quelle gigantesche ossa esser altro che un gioco della Natura, <lb></lb>perchè non potrà l&#039;argomento applicarsi ai testacei e alle innumereroli altre <lb></lb>reliquie de&#039;corpi marini, che si trovano qua e là disperse ne&#039;continenti? <lb></lb></s>

<s>“ Onde mi restringo a credere, così conclude, generarsi gran parte de&#039;te-<pb xlink:href="020/01/1691.jpg" pagenum="566"></pb>stacei dalla Terra, con l&#039;anima vegetativa, che perfezioni loro la forma, e <lb></lb>distribuisca l&#039;alimento: animati dal Supremo Signore, quando ne vede la <lb></lb>materia disposta, quasi <emph type="italics"></emph>ludens in orbe tarrarum,<emph.end type="italics"></emph.end> ma con gioco non inde­<lb></lb>gno della dignità di lui, poichè tutto è operare di perfettissima Sapienza, e <lb></lb>di Provvidenza infinita ” (Ricreazione dell&#039;occhio cit., pag. </s>

<s>82). </s></p><p type="main">

<s>In Francia rinnovellò, sui principii del secolo XVIII, le idee riferite dal <lb></lb>Gassendo un anonimo Autore di un libro intitolato <emph type="italics"></emph>Nouveau voyage d&#039;Ita­<lb></lb>lie,<emph.end type="italics"></emph.end> dove, nelle lettere XXVI e XXX, si tratta delle origini de&#039;corpi marini <lb></lb>ritrovati scavando sulle cime dei monti. </s>

<s>Il Vallisnieri se ne scandalizzò, e <lb></lb>offeso nell&#039;onor nazionale scriveva così, ardente di zelo: “ Mi credeva, se <lb></lb>Dio mio aiuti, che in Francia più alcuno non si trovasse, che opinioni sì <lb></lb>rancide e sì abominevoli sostenesse, o che altre ne desse continuamente in <lb></lb>luce, sì mal fondate, che a un solo crollo trabocchino e a terra cadano, per­<lb></lb>chè tanto di noi si burlano, e parlano della Filosofia d&#039;Italia come si par­<lb></lb>lerebbe di quella de&#039;Lapponi e degl&#039;Irochesi, se incominciassero a filosofare, <lb></lb>come il nostro insigne letterato, signor abate Conti, udì con le sue proprie <lb></lb>orecchie nella loro reale Accademia, quando fecero l&#039;elogio al morto Mar­<lb></lb>tino Poli, speziale romano, e membro illustre della detta reale Accademia ” <lb></lb>(De&#039;corpi marini che su&#039;monti si trovano, Venezia 1727, pag. </s>

<s>16). </s></p><p type="main">

<s>Aveva ragione di esclamar così il Vallisnieri, e di rinfacciare a quei <lb></lb>Francesi, dispregiatori dell&#039;Italiana filosofia, che quel loro modo di filoso­<lb></lb>fare era un rinnovellar le antiche vanità delle forze plastiche, e delle gene­<lb></lb>razioni spontanee, dal Redi e dal Malpighi, italiani, a cui aggiungeva sè me­<lb></lb>desimo per terzo, cacciate via dalla scienza con tante dimostrative esperienze, <lb></lb>e con tanto solidi ragionamenti. </s>

<s>Cosicchè può giustamente dirsi essere stato <lb></lb>precipuo merito della scienza italiana se, a mezzo il secolo XVIII, s&#039;accettò <lb></lb>senza controversie da tutti la sentenza pronunziata da quel Giovanni Bian­<lb></lb>chi, meglio conosciuto sotto il nome di Jano Planco, il quale, nel catalogo <lb></lb>de&#039;Lincei premesso al <emph type="italics"></emph>Fitobasanos<emph.end type="italics"></emph.end> del Colonna, scrisse a proposito delle <lb></lb>piante fossili escavate in alcuni nostri terreni: “ certissimum est ipsum esse <lb></lb>vere lignum, quaemadmodum sunt verae marinae testae cornua illa Ham­<lb></lb>monis, et omnia marina fossilia, quae in montibus reperiuntur ” (Floren­<lb></lb>tiae 1744, pag. </s>

<s>XXXIII). </s></p><p type="main">

<s>Conquistatasi faticosamente questa prima parte del vero, rimaneva a ri­<lb></lb>solvere l&#039;altra ben più difficìle questione: come mai le conchiglie e gli altri <lb></lb>fossili fossero potuti risalire ai monti dalle basse giaciture dei mari. </s>

<s>Quando <lb></lb>ai problemi naturali si cercavano prima di tutto le soluzioni ne&#039;libri dei Fi­<lb></lb>losofi, si rispondeva al proposto problema de&#039;corpi marini sui monti in due <lb></lb>vari modi, secondo che di Platone o di Aristotile erano i libri via via con­<lb></lb>sultati. </s>

<s>Il primo de&#039;due solenni Maestri, ammettendo essere i monti alla <lb></lb>Terra congeniti, non lasciava a rispondere se non che o la Natura imita fra <lb></lb>terra le produzioni proprie dell&#039;acqua, o che sien quelle marine produzioni <lb></lb>state deposte ne&#039;continenti dalle acque diluviali. </s></p><p type="main">

<s>Le tradizioni bibliche, miste colle platoniche, conciliarono molti seguaci <pb xlink:href="020/01/1692.jpg" pagenum="567"></pb>a questa seconda opinione, ma trovarono altri più spedito il dire che la Na­<lb></lb>tura o il caso danno talvolta alle pietre quelle così bizzarre forme, che le <lb></lb>rendon tanto simili agli animali. </s>

<s>Primeggia fra costoro il Falloppio, il quale, <lb></lb>nel cap. </s>

<s>IV del suo trattato <emph type="italics"></emph>De metallis seu fossilibus,<emph.end type="italics"></emph.end> proponendosi la que­<lb></lb>stione <emph type="italics"></emph>Terra quomodo generetur,<emph.end type="italics"></emph.end> risponde sull&#039;autorità di Platone ch&#039;è ge­<lb></lb>nerata la Terra dalle fumose esalazioni calde e secche, come gli par di po­<lb></lb>terlo persuadere ai lettori con una così fatta esperienza: “ Accipiatis terram <lb></lb>ponetisque eam ipsam in vase aliquo vitreo, quod habeat orificium angu­<lb></lb>stum, et latum sit in fundo, mediaque sui parte. </s>

<s>Postea ponatis portionem <lb></lb>terrae in ipso, et operculo superaddito ponatis vas ad ignem, et sinite ut <lb></lb>calor exagitet terram illam, et videbitis quod ascendet vapor terrestris, et <lb></lb>post aliquod tempus cernetis concrescere aliquid terraei circa osculum va­<lb></lb>sis, quod non aliunde oritur quam ex fumoso illo vapore. </s>

<s>” Come altrimenti, <lb></lb>poi soggiunge, s&#039;intenderebbe la generazione dei monti sulla Terra, nati in­<lb></lb>sieme con lei? (Opera omnia, Francofurti 1584, pag. </s>

<s>327). </s></p><p type="main">

<s>Aristotile, questa volta più che dal proprio ingegno lasciatosi consigliare <lb></lb>alle osservazioni dei fatti, ne conclude una dottrina assai più sana della pla­<lb></lb>tonica, e della quale solamente oggidì si comprende la verità e l&#039;importanza. </s>

<s><lb></lb>Il secondo capitolo del I libro Dei meteorologici comincia con queste parole, <lb></lb>nelle quali il Filosofo raccoglie il frutto delle osservazioni, che si potevano <lb></lb>fare allora sulla superfice terrestre, comparate con quelle, che si ricavavano <lb></lb>dalle relazioni degli scrittori più antichi, o dai naturali rimasti monumenti. <lb></lb></s>

<s>“ Non semper autem eadem loca terrae neque aquosa sunt, neque arida, <lb></lb>sed permutantur secundum fluviorum generationes et defectus. </s>

<s>Quapropter <lb></lb>et quae sunt circa continentem permutantur, et quae circa mare, et non <lb></lb>semper haec quidem terra, haec autem mare perseverant omni tempore, sed <lb></lb>fit mare quidem ubi arida, ubi autem nunc mare hic iterum terra ” (Ope­<lb></lb>rum, T. VI cit., fol. </s>

<s>21). </s></p><p type="main">

<s>Veniva da queste dottrine naturale la soluzione del tanto agitato pro­<lb></lb>blema, e fu il Cesalpino uno de&#039;primi a proporla ai desiderosi, e a divul­<lb></lb>garla nel suo libro II <emph type="italics"></emph>De metallicis,<emph.end type="italics"></emph.end> dove, trattando delle Conchiglie, delle <lb></lb>Belenniti e delle Glossopietre, “ neque mirandum, dice, in mediterraneis et <lb></lb>montibus altissimis reperiri animalia maritima in lapides conversa: non enim <lb></lb>absurdum est ubique mare extitisse, imo necessarium, ut tradit Aristotiles ” <lb></lb>(pag. </s>

<s>133). </s></p><p type="main">

<s>Derivò dalle medesime fonti aristoteliche in sostanza la sua ipotesi an­<lb></lb>che il Fracastoro, il quale diceva essere i monti un agglomerato di arene <lb></lb>gettate dalle onde, rimaste in secco ritirandosi il mare. </s>

<s>Il Chiocchi infatti, <lb></lb>nella citata descrizione del Museo Calzolari, dop&#039;aver detto come, secondo il <lb></lb>Sarayna, esso Fracastoro credeva che i corpi fossili fossero stati un giorno <lb></lb>veri viventi, e che le acque marine gli avessero così deposti fra terra, nel <lb></lb>ridursi ne&#039;loro bacini; “ sed haec dependere aiebat, poi soggiunge il De­<lb></lb>scrittore, ex maiori cognitione: Montes onim omnes a mari factos fuisse <lb></lb>asseverabat, primum iactata arena in cumulos, fuisseque olim mare ubi nunc <pb xlink:href="020/01/1693.jpg" pagenum="568"></pb>montes extant. </s>

<s>Mox, eodem recedente, detectos fuisse montes et insulas, quod <lb></lb>et in dies videtur fieri, quando et Aegyptus tota mari olim obruta fuerit, et <lb></lb>in littoribus etiam Italiae, ut circa Ravennam apparet, ubi longe abest ab <lb></lb>eo quod olim fuerit passuum centum ” (pag. </s>

<s>409). </s></p><p type="main">

<s>A queste del Falloppio, del Cesalpino e del Fracastoro si riducevano <lb></lb>principalmente le ipotesi immaginate, fra la prima metà del secolo XVI e <lb></lb>la seconda metà del secolo appresso, a spiegar l&#039;origine dei continenti, e la <lb></lb>loro distinzione in monti ed in valli, ma s&#039;aggiungevano a queste stesse, <lb></lb>derivate da Platone e da Aristotile, altre ipotesi, ora suggerite dalla fanta­<lb></lb>sia, e ora più consigliatamente dall&#039;osservazione dei fatti. </s>

<s>Parve a Ferrante <lb></lb>Imperato che si venisse da tutte queste a proporre altrettante cause con­<lb></lb>correnti ciascuna, secondo il suo proprio modo di operare, a far mutar fac­<lb></lb>cia alla terra, ed espresse la sua opinione in un <emph type="italics"></emph>Discorso sopra le muta­<lb></lb>zioni dei paesi,<emph.end type="italics"></emph.end> che forma il cap. </s>

<s>IV del VII libro della sua Storia naturale. <lb></lb></s>

<s>“ E prima, ivi egli dice, della commutazion di terra e mare di molte e molte <lb></lb>miglia in Paesi petrosi ne abbiamo ampissima testimonianza nella Puglia. </s>

<s>Il <lb></lb>trasmutarsi il paese piano in montuoso è cosa che facilmente avviene alle <lb></lb>piane, che alte sieno, mentre dal corso dei torrenti si fanno profondità grandi <lb></lb>e valli. </s>

<s>L&#039;alzarsi la terra in alto, nel modo che fanno le posteme nel corpo <lb></lb>degli animali e delle piante, e il dar vegetazione alle pietre, onde possano <lb></lb>li monti alzarsi, non è cosa fuori di sperienza e di ragione: manifestamente <lb></lb>in molte pietre si vede la virtù vegetale. </s>

<s>Veggonsi inoltre monti da incendii <lb></lb>sotterranei avvenuti, come ai nostri tempi nella Campania, nel tenimento di <lb></lb>Pozzuoli, abbiam visto di un monte fatto dalle ceneri di fuoco sotterraneo ” <lb></lb>e soggiunge l&#039;azione dei terremoti, del flusso marino, che solleva le arene <lb></lb>in monti, come si vede nel Belgio. (Venezia 1672, pag. </s>

<s>175-77). </s></p><p type="main">

<s>Aveva insomma la scienza progredito infino a mezzo il secolo XVII, e <lb></lb>del problema geologico in discorso eran le soluzioni che se ne sapevano <lb></lb>dare quelle raccolte e riferite, com&#039;abbiamo udito, da Ferrante Imperato. </s>

<s><lb></lb>Mancava a quelle dottrine il fondamento delle osservazioni, che si paravan <lb></lb>così difficili a farsi per la smisurata ampiezza, e per le varie accidentalità <lb></lb>presentate dalla superfice terrestre, l&#039;edifizio della quale trovasi tanto spesso <lb></lb>circondato o ricoperto da manifeste rovine. </s>

<s>Non aveva nessuno ancora, per <lb></lb>comprendere in uno sguardo e per comparar fra loro le diverse regioni geo­<lb></lb>logiche, istituito nessun viaggio, e de&#039;varii fatti, sui quali principalmente si <lb></lb>fondavano alcune delle ipotesi più sicure, se ne stavano tutti allora alle no­<lb></lb>tizie lasciate ne&#039;loro libri dagli scrittori più antichi. </s></p><p type="main">

<s>Lo Stenone fu il primo a sentire il bisogno di questi scientifici viaggi, <lb></lb>e a manifestarne in pubblico il desiderio, quando, nel descriver l&#039;anatomia <lb></lb>del capo della Carcaria, toccò la questione delle Glossopietre dell&#039;isola di <lb></lb>Malta, sopra l&#039;osservazion delle quali avanzò quelle sei congetture, che con­<lb></lb>tenevano il fecondo germe di una scienza novella. </s>

<s>Fu una gran ventura che <lb></lb>fosse cotesto germe deposto in seno all&#039;Accademia del Cimento, la quale, <lb></lb>educatasi per lungo tempo all&#039;arte dell&#039;esperienze fisiche e delle naturali <pb xlink:href="020/01/1694.jpg" pagenum="569"></pb>osservazioni intorno a tante cose, che appariscono o che si producono sopra <lb></lb>la terra; ora stendeva con generoso ardimento il pensiero a far soggetto dei <lb></lb>suoi nuovi studii la Terra stessa, nelle sue prime origini, e nella sua pre­<lb></lb>sente struttura. </s>

<s>Cooperava a quell&#039;istituto, nella stessa fiorentina Accademia, <lb></lb>il Borelli, quando, ad istanza del cardinale Leopoldo, descriveva la <emph type="italics"></emph>Historia <lb></lb>et meteorologia incendii aetnaei,<emph.end type="italics"></emph.end> e vi cooperava altresì il Viviani, quando <lb></lb>dimostrava al Granduca le utilità grandi, che verrebbero allo Stato dall&#039;ap­<lb></lb>plicare quegli stessi studii scientifici all&#039;economia. </s>

<s>Ci permettano perciò i <lb></lb>Lettori che poniamo sotto i loro occhi la seguente scrittura, nella quale, <lb></lb>portando il Viviani l&#039;esempio delle cave del vetriolo, voleva estendere i suoi <lb></lb>avvedimenti economici a tutti gli altri minerali della Toscana, sulle incerte <lb></lb>giaciture de&#039;quali sarebbe per venir tanta luce da quella nuova scienza, che <lb></lb>pur allora in Firenze s&#039;instituiva: </s></p><p type="main">

<s>“ Il serenissimo Granduca potrebbe, con suo grandissimo utile ed onore, <lb></lb>benefizio universale di tutto lo Stato, ed impiego di gran quantità de&#039;suoi <lb></lb>sudditi, e con pochissima spesa, rendere lo Stato abbondante d&#039;ogni sorta <lb></lb>metalli, minerali e mezzi minerali, senz&#039;aver bisogno di cercarli in paesi <lb></lb>stranieri, con l&#039;estrazione dei denari dello Stato, anzi, con l&#039;estrazione di <lb></lb>detta roba introdurre il danaro di fuori. </s>

<s>Il modo sarebbe tale: ” </s></p><p type="main">

<s>“ Ci sono in molti luoghi dello Stato di S. A. S. miniere d&#039;ogni sorte, <lb></lb>e miniere abbondanti, quali se ne giacciono neglette ed infruttuose. </s>

<s>Però <lb></lb>potrebbe il serenissimo Granduca eleggere un Sopraintendente generale di <lb></lb>tutte le miniere dello Stato, ma che fosse persona intelligente in tale affare, <lb></lb>con assegnarli <emph type="italics"></emph>cavatto<emph.end type="italics"></emph.end> nel negozio, a fine che, volendo utilizzare sè mede­<lb></lb>simo, per necessità, apporterebbe utile maggiore a Sua Altezza. </s>

<s>” </s></p><p type="main">

<s>“ Per rimettere in piedi le fabbriche per ogni sorta miniere, con poca <lb></lb>spesa ed in breve tempo, si potrebbe fare in questo modo: Si ritrovano due <lb></lb>miniere di vitriolo, una a Stazzema, che è la migliore e più abbondante, <lb></lb>l&#039;altra alla Striscia. </s>

<s>Basterebbe mettere andanti ed incamminare questi due <lb></lb>edifizi, che con il solo ritratto di questi, in pochi anni, si pianterebbero le <lb></lb>fabbriche necessarie per tutte le altre miniere. </s>

<s>Perchè il vitriolo si potrebbe <lb></lb>fare di esquisitezza tale, che sarebbe stimato per tutto il mondo migliore di <lb></lb>ogni altro, e con pochissima spesa, o di gran lunga minore di quella face­<lb></lb>vano per il passato, quando facevano il vitriolo ordinario, con risparmio di <lb></lb>legne, di vasi, con più facilità, ed in quella quantità che si volesse. </s>

<s>” </s></p><p type="main">

<s>“ Nello Stato di S. A. S., compresa Lucca, Massa, Carrara e la Luni­<lb></lb>giana, si esiterà in circa migliaia 200 di vitriolo l&#039;anno. </s>

<s>Il prezzo corrente <lb></lb>è di scudi 30 il migliaio; onde migliaia 200 vitriolo farebbero la somma di <lb></lb>scudi 600, e questi si guadagnerebbero nello Stato. </s>

<s>Per Francia poi e per <lb></lb>Alessandria ci sarebbe l&#039;esito di altre tre in quattrocento migliaia. </s>

<s>Ma sup­<lb></lb>poniamo che fuori si esitasse sol tanto vitriolo, che bastasse per pagare <lb></lb>tutte le spese, resterebbero in ogni modo li scudi 600 annui netti e liberi <lb></lb>di spese. </s>

<s>” </s></p><p type="main">

<s>“ Per mettere in piedi gli edifizi detti di vitriolo, con poca spesa si può <pb xlink:href="020/01/1695.jpg" pagenum="570"></pb>fare, perchè l&#039;edifizio di Stazzema, qual&#039;è delli signori Carnesecchi inven­<lb></lb>tori della miniera, si potrebbe mettere andante con facilità, mentre le mu­<lb></lb>raglie sono ancora in essere, ed in parte coperte; sicchè basterebbe coprire <lb></lb>quella parte che manca, fare una caldaia di piombo con il suo fornello, e <lb></lb>due vasche di legno e una fornace per calcinare la vena, che così l&#039;edifizio <lb></lb>sarebbe aggiustato. </s>

<s>” </s></p><p type="main">

<s>“ L&#039;edifizio poi della Striscia si potrebbe rimettere in ordine, mentre <lb></lb>si lavorasse quello di Stazzema, a causa che il vitriolo della Striscia si cava <lb></lb>da una terra, quale avanti sia stagionata vuole stare riposata sotto un ca­<lb></lb>pannone, quasi due anni, ma la vena, che si cava a Stazzema, in pochi giorni <lb></lb>si calcina, e si può mettere in opera, e la vena è in tanta copia, che si può <lb></lb>fare tutta quella quantità del vitriolo che si vuole. </s>

<s>” </s></p><p type="main">

<s>“ Alla Striscia ci è abbondanza grandissima di legna; a Stazzema an­<lb></lb>cora ci sono legne forti in quantità, che senza pregiudizio delli edifizi del <lb></lb>ferro, che sono in quel paese, si potrebbero adoperare, stante che le fabbri­<lb></lb>che del ferro non si possono servire se non di carbon dolce, e per fare il <lb></lb>vitriolo sono necessarie le legne forti, perchè le dolci, come faggio e casta­<lb></lb>gno de&#039;quali si serve la maggioranza, non son buone per fare il vitriolo. </s>

<s>” </s></p><p type="main">

<s>“ Li boschi si possono eternare con il modo di tagliarli, onde sarebbe <lb></lb>necessario che quello, che fosse eletto Sopraintendente generale di tutte le <lb></lb>miniere, avesse anche la sopraintendenza di tutte le boscaglie appartenenti <lb></lb>a dette miniere, che con li boschi si manterrebbero, s&#039;aprirebbero molte <lb></lb>fabbriche di miniere d&#039;ogni sorte, con utile considerabile del serenissimo <lb></lb>Granduca, benefizio pubblico, comodo del privato, e senza danno di alcuno. </s>

<s>” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CXXXVI, c. </s>

<s>89, 90). </s></p><p type="main">

<s>S&#039;accennava di sopra che a riconoscere questi pubblici benefizi e que­<lb></lb>sti comodi privati, i quali dai più attivi esercizi della metallurgia sareb­<lb></lb>bero per provenire alla Toscana, avea dato eccezionale eccitamento la nuova <lb></lb>scienza, che s&#039;istituiva allora nell&#039;Accademia di lei; scienza, che propone­<lb></lb>vasi d&#039;investigar la particolare struttura della superficie terrestre, in seno <lb></lb>alla quale scavando, si trovano qua e là dispersi i vari generi di minerali. </s>

<s><lb></lb>S&#039;accennava inoltre che, fra gli Accademici fiorentini, colui che, presa oc­<lb></lb>casione dai denti delle Carcarie, riconosciuti fossili nelle glossopietre di Malta, <lb></lb>dette inizio ai nuovi studii, era stato lo Stenone, a cui perciò il Granduca <lb></lb>e il cardinale Leopoldo commisero il primo ufficio di esaminare, e di de­<lb></lb>scrivere la struttura geologica del suolo toscano. </s></p><p type="main">

<s>Ebbe per prima cosa lo Stenone a notar questo fatto singolare, che <lb></lb>cioè, dovunque, apparisce la superficie terrestre composta di strati, gli uni <lb></lb>soprapposti agli altri, e benissimo discernibili fra loro per una quasi inter­<lb></lb>ruzione di continuità, e talvolta per una diversa struttura, nella quale in <lb></lb>ogni modo riconoscendo le chiare note di un sedimento, ebbe perciò a con­<lb></lb>cluderne, in conferma delle dottrine aristoteliche, tante volte sull&#039;arida essersi <lb></lb>disteso e poi ritirato il mare, quanti di quegli strati era dato d&#039;annoverare. </s>

<s><lb></lb>Presa la stratigrafia dunque per principal fondamento alle sue congetture, <pb xlink:href="020/01/1696.jpg" pagenum="571"></pb>pensò che ne&#039;primi loro stati naturali ciascuno di quei sedimenti giacesse <lb></lb>in sito orizzontale, e che il trovarli inclinati, e in altri modi sconvolti, fosse <lb></lb>per effetto di cause perturbatrici, alle quali attribuiva tutte le ineguaglianze <lb></lb>e le accidentalità di figura, che si osservano qua e là sulla faccia della Terra. </s>

<s><lb></lb>Risaputo, per relazioni avutene dagli amici, tale esser pure la struttura di <lb></lb>tutte le altre più lontane regioni terrestri, stabilì sui sedimenti alluvionali <lb></lb>una generale scienza geologica, che particolarmente applicata alla Toscana <lb></lb>dette per conclusione essere il suolo di lei passato per sei distinte vicende: <lb></lb>due volte fluido, due volte piano e secco, due volte aspro. </s></p><p type="main">

<s>Il soggetto delle nuove scoperte e delle nuove speculazioni voleva avere <lb></lb>una forma, per presentarsi innanzi all&#039;illustre Accademia, e lo Stenone <lb></lb>avrebbe desiderato di dargliela italiana, ma intanto che, maturandosi la no­<lb></lb>tizia delle cose, sarebbe egli di nazione straniera venuto nell&#039;uso della no­<lb></lb>stra lingua a maggior perfezione, per non indugiar di troppo, distese del <lb></lb>Trattato un <emph type="italics"></emph>prodromo<emph.end type="italics"></emph.end> in latino col titolo <emph type="italics"></emph>De solido intra solidum natura­<lb></lb>liter contento.<emph.end type="italics"></emph.end> Ivi così scriveva in principio, rivolgendo il discorso al Gran­<lb></lb>duca: “ Et haec quidem italico idiomate extendere coeperam, tum quod tibi <lb></lb>ita placere intelligerem, tum quo pateret illustri Academiae, quae suorum <lb></lb>me numero adscripsit, me ut minime dignum tali honore ita maxime avi­<lb></lb>dum esse testandi conatus, quibus in alìquam etruscae linguae cognitionem <lb></lb>pervenire allaboro. </s>

<s>Nec aegre fero impositam mihi necessitatem differendi <lb></lb>eamdem scriptionem. </s>

<s>Ut enim instans iter mihi promittit cumulatiorem no­<lb></lb>titiam rerum quaestioni illustrandae inserventium; sic temporis mora feli­<lb></lb>ciores in linguae studio progressus mihi pollicetur. </s>

<s>” Il manoscritto, fatto <lb></lb>diligentemente copiare, fu consegnato in mano del Viviani, che faceva allora <lb></lb>da segretario dell&#039;Accademia, e che di proprio pugno scrisse alla copia l&#039;in­<lb></lb>titolazione, dopo la quale aggiunse: “ Questo fu stampato sotto la mia cura <lb></lb>in Firenze nel 1669 ” (MSS. Cim., T. XXXII, c. </s>

<s>1). </s></p><p type="main">

<s>Il promesso trattato in lingua italiana non ebbe sventuratamente l&#039;ese­<lb></lb>cuzione, disanimato forse l&#039;Autore dalla poca accoglienza, che si fece a que­<lb></lb>sto Prodromo. </s>

<s>Vedremo gli esempi e le ragioni di ciò nel progresso di <lb></lb>questa storia, ma intanto esaminiamo la nuova scienza geologica, che quasi <lb></lb>vaticinio incompreso vi s&#039;annunziava. </s></p><p type="main">

<s>Dicemmo che aveva quella nuova scienza per lo Stenone il fondamento <lb></lb>nella stratigrafia, e perchè l&#039;ordine de&#039;soprapposti strati alluvionali vede­<lb></lb>vasi qua e là perturbato, per trovare il filo, da non smarrirsi in tanta con­<lb></lb>fusione, ricorse argutamente l&#039;Autore all&#039;esame delle materie fossili. </s>

<s>Gli <lb></lb>suggerì un tale esame alcune note distintive, e gli fornì gli opportuni ar­<lb></lb>gomenti per concluder dell&#039;età di uno strato, e se concorressero a formarlo, <lb></lb>insieme con le marine, altre acque di fiume. </s></p><p type="main">

<s>Trovato anche insieme il modo da riconoscer per queste note paleon­<lb></lb>tologiche che un medesimo strato, deposto originalmente in sito orizzontale, <lb></lb>qua rimaneva depresso o inclinato, là spostato o sconvolto, incominciò lo <lb></lb>Stenone a pensare da quali agenti potess&#039;esser naturalmente prodotto un <pb xlink:href="020/01/1697.jpg" pagenum="572"></pb>tale effetto, nè seppe riconoscervene altri più efficacemente operativi del <lb></lb>fuoco e dell&#039;acqua. </s>

<s>“ Primus modus est stratorum violenta in altum excus­<lb></lb>sio, sive eam producat praeceps incendium halituum subterraneorum, sive <lb></lb>idem efficiat violenta aeris elisio propter ingentes alias in vicinia ruinas.... <lb></lb>Posterior modus est spontaneus stratorum superiorum delapsus, seu ruina, <lb></lb>quando, subducta materia inferiori seu fundamento, superiora rimas agere <lb></lb>coeperint, unde pro cavitatum et rimarum varietate varius diffractorum stra­<lb></lb>torum situs sequitur, dum quaedam horizonti parallela manent, alia ad il­<lb></lb>lum perpendicularia fiunt, pleraque obliquos angulos cum ea constituunt, <lb></lb>nonnulla in arcus inflectuntur, materia eorum tenaci existente ” (pag. </s>

<s>31, 32). <lb></lb>Questa sudduzion di materia, per cui, rimasti gli strati orizzontali senza fon­<lb></lb>damento, rovinano, è, dice lo Stenone, principalmente operata dall&#039;acque, che <lb></lb>sciolgono e portan via le materie terrose, ma può talvolta produrla anche <lb></lb>il fuoco, il quale, liquefacendo le materie solide, le fa scorrere altrove. </s>

<s>Così <lb></lb>i due potentissimi agenti trasformatori della superfice terrestre, di nature <lb></lb>discordi e di modi, si riscontrano negli effetti. </s></p><p type="main">

<s>Proposti così fatti principii, si passa dall&#039;Autore a risolvere il problema <lb></lb>tanto controverso dell&#039;origine de&#039;monti, la quale origine egli naturalmente ri­<lb></lb>conosce dal mutato ordine degli strati. </s>

<s>“ Quod mutatus stratorum situs praeci­<lb></lb>pua montium origo sit inde patet, quod in qualibet congerie montium conspi­<lb></lb>ciantur: I. </s>

<s>Ingentia plana in quorumdam vertice. </s>

<s>II. </s>

<s>Multa strata horizonti <lb></lb>parallela. </s>

<s>III. </s>

<s>Ab eorumdem lateribus strata varia varie ad horizontem incli­<lb></lb>nata. </s>

<s>IV. </s>

<s>In oppositis collium lateribus ruptorum stratorum facies, mate­<lb></lb>riae et figurae omnimodam convenientiam demonstrantes. </s>

<s>V. </s>

<s>Nudì stratorum <lb></lb>limbi. </s>

<s>VI. </s>

<s>Ad radices eiusdem congeriei disruptorum stratorum fragmenta, <lb></lb>partim in colles congesta, partim per vicinos agros dispersa ” (pag. </s>

<s>32). </s></p><p type="main">

<s>Quest&#039;aspetto generale, che presentano all&#039;osservatore geologo i monti, <lb></lb>vien dallo Stenone esemplificato nella Toscana, le sei distinte età geologiche <lb></lb>della quale son per l&#039;Autore stesso illustrate dalle sei seguenti Figure: <lb></lb>“ Esibet autem figura XI planum perpendiculare Etruriae, quo tempore <lb></lb>strata lapidea etiam num integra et horizonti parallela erant. </s>

<s>Figura XII <lb></lb>ingentes cavitates, sive ignium sive aquarum vi exesas, intactis superioribus <lb></lb>stratis. </s>

<s>Figura XIII a disruptis stratis superioribus ortos montes et valles. </s>

<s><lb></lb>Figura XIV a mare facta nova strata in dictis vallibus. </s>

<s>Figura XV ex novis <lb></lb>stratis consumptam partem inferiorum stratorum, intactis superioribus. </s>

<s>Fi­<lb></lb>gura XVI, disruptis superioribus stratis arenaceis, productos ibi colles et <lb></lb>valles ” (ibi, Explicatio figurarum). <lb></lb><figure id="id.020.01.1697.1.jpg" xlink:href="020/01/1697/1.jpg"></figure></s></p><p type="caption">

<s>Figura 11.<pb xlink:href="020/01/1698.jpg" pagenum="573"></pb><figure id="id.020.01.1698.1.jpg" xlink:href="020/01/1698/1.jpg"></figure></s></p><p type="caption">

<s>Figura 12.<lb></lb><figure id="id.020.01.1698.2.jpg" xlink:href="020/01/1698/2.jpg"></figure></s></p><p type="caption">

<s>Figura 13.<lb></lb><figure id="id.020.01.1698.3.jpg" xlink:href="020/01/1698/3.jpg"></figure></s></p><p type="caption">

<s>Figura 14.<lb></lb><figure id="id.020.01.1698.4.jpg" xlink:href="020/01/1698/4.jpg"></figure></s></p><p type="caption">

<s>Figura 15.<lb></lb><figure id="id.020.01.1698.5.jpg" xlink:href="020/01/1698/5.jpg"></figure></s></p><p type="caption">

<s>Figura 16.</s></p><p type="main">

<s>Ora, quella nuova scienza, che dicevasi instituita dagli Accademici del <lb></lb>Cimento, si vede per queste immagini rappresentata ai nostri occhi in tutta <lb></lb>la sua verità, e in tutta la sua vita, ma allora, e per lungo tempo di poi, <lb></lb>parvero quelle sei figure come tanti geroglifici egiziani. </s>

<s>Il Prodromo dello <lb></lb>Stenone rimase da tutti dimenticato, e di quella illustre Accademia, nella <lb></lb>quale fu letto, principe il cardinale Leopoldo, fu negata perfin l&#039;esistenza. </s></p><p type="main">

<s>Questo dall&#039;altra parte era un frutto precoce, maturato sopr&#039;un albero <lb></lb>esotico ne&#039;frequentatissimi orti accademici, all&#039;ombra de&#039;quali mollemente <lb></lb>seduto insegnava il Cartesio a fabbricar con la fantasia non la Terra sola, <lb></lb>ma l&#039;Universo. </s>

<s>Tommaso Burnet non ardì di stendere tanto al largo l&#039;ali <lb></lb>dell&#039;immaginoso suo ingegno, ma della formazion della Terra in particolare <pb xlink:href="020/01/1699.jpg" pagenum="574"></pb>si compiacque di aver immaginato un più bel sistema di quello dell&#039;applau­<lb></lb>dito Maestro. </s>

<s>Legga, chi vuole in tutta la sua integrità veder rappresentarsi <lb></lb>innanzi la nuova architettura cosmica comparata con la cartesiana, il cap. </s>

<s>IV <lb></lb>del II libro <emph type="italics"></emph>Telluris theoria sacra,<emph.end type="italics"></emph.end> dove infin dal titolo si promette che sarà <lb></lb>dall&#039;Autore notato “ discrimen hypothesi nostrae ab illa Cartesii, et in ipsius <lb></lb>defectus animadvertitur ” (Londini 1681, pag. </s>

<s>181) </s></p><p type="main">

<s>È la teoria della terra dall&#039;Autore inglese appellata <emph type="italics"></emph>sacra,<emph.end type="italics"></emph.end> perchè non <lb></lb>ha nelle naturali osservazioni il fondamento, ma nella lettura dei Libri santi, <lb></lb>dai quali apertamente raccogliesi aver nel suo più interno seno la Terra <lb></lb>un&#039;immensa accolta di acque, sotto il nome di <emph type="italics"></emph>abisso,<emph.end type="italics"></emph.end> dalle rotte fonti del <lb></lb>quale si produsse il noetico diluvio. </s>

<s>Or il Burnet, tutto intento a dimostrar <lb></lb>che cotesto fatto tenuto per miracoloso non era punto fuori degli ordini na­<lb></lb>turali, immaginò che l&#039;antidiluviana superfice terrestre fosse solida, polita e <lb></lb>liscia, girata tutto intorno e sopraincombente all&#039;abisso. </s>

<s>Al sole poi si spaccò <lb></lb>cotest&#039;arida crosta, come la belletta delle paludi, e facendo gli ardenti raggi, <lb></lb>penetrati addentro per le fessure, evaporare il liquido sottoposto, venne tutto <lb></lb>a ridursi in frantumi, che rimasero così sommersi nell&#039;acque diluviali. </s>

<s>“ Ex <lb></lb>altera parte etiam notandum est hanc terram, exteriorem solis ardoribus con­<lb></lb>tinuo expositam, progressu temporis et saeculorum magis exsiccam aridam­<lb></lb>que devenisse, et deglutinatis partibus, prae nimia siccitate, et se contrahen­<lb></lb>tibus in plurimis locis secessisse, unde tandem factum est ex una parte com­<lb></lb>page telluris hoc modo labefactata, ex altera vaporibus auctis infra terram <lb></lb>et maiori vi et vehementia se dilatantibus, Tellus decreto tempore et conspi­<lb></lb>rantibus causis, per quandam speciem terraemotus rupta, dissiluerit, moli­<lb></lb>bus illis sive fragmentis, in quae distracta erat in subiectam abyssum, vario <lb></lb>modo et situ delabentibus ” (ibid., pag. </s>

<s>52). </s></p><p type="main">

<s>Di qui concluse facilmente il Burnet l&#039;origine naturale dei monti, e <lb></lb>come venisse la Terra a distinguersi in oceani e in continenti, con super­<lb></lb>ficie aspre da per tutto e ineguali. </s>

<s>“ Nempe cum fatiscebat et in plura <lb></lb>fragmenta disrupta in abyssum delapsa est ea compages, uti partes fragmen­<lb></lb>torum quae aquis quomodocumque eminebant, rationem habuerunt aridae <lb></lb>atque terrae habitabilis; ita istius aridae partes, quocumque modo eminen­<lb></lb>tiores caeteris, montium et collium rationem generalem subierunt ” (ibid., <lb></lb>pag. </s>

<s>94). Questa è però l&#039;origine dei monti, che si possono secondo il Bur­<lb></lb>net chiamare primarii: gli altri secondarii crede che sien l&#039;effetto di più <lb></lb>minuti stritolamenti prodotti dalle concussioni, nel rovinar giù negli abissi. <lb></lb></s>

<s>“ Nempe cum primum inferiores partes fragmenti descendendo contingebant <lb></lb>fundum abyssi, vel forsan etiam superficiem, ex subita illa motus obstruc­<lb></lb>tione orta est magna concussio et vibratio per totum fragmentum, atque inde <lb></lb>denuo dissiliunt et varie disrumpuntur ipsius partes. </s>

<s>Atque ab hac concus­<lb></lb>sione et secunda disruptione ortas esse existimo innumeras illas inaequali­<lb></lb>tates superficiei terrarum: colles, declives agros, planities multiformes, val­<lb></lb>les ” (ibid., pag. </s>

<s>95). </s></p><p type="main">

<s>Il favorevole incontro, che trovarono così fatte fantasie, comparato col-<pb xlink:href="020/01/1700.jpg" pagenum="575"></pb>l&#039;abbandono, in che furono lasciate le sapienti dottrine stenoniane, è cosa <lb></lb>che fa stupire, ma Bernardino Ramazzini fra&#039;nostri, nel cap. </s>

<s>IV del suo <lb></lb>trattato <emph type="italics"></emph>De fontium mutinensium admiranda scaturigine,<emph.end type="italics"></emph.end> tutto in pensiero <lb></lb>di ritrovar l&#039;antica costituzione e la forma del suolo, da cui vedeva scaturir <lb></lb>quelle sue maravigliose fonti modanesi, dop&#039;aver accennato alle rivoluzioni <lb></lb>geologiche, le notizie delle quali attingevano gli eruditi dai libri platonici e <lb></lb>dalle bibliche tradizioni, fa menzione delle teorie del Burnet, e poi così to­<lb></lb>sto soggiunge: “ Huiusmodi excogitatum, utut pro novo accipiatur, non no­<lb></lb>strorum sed antiquiorum temporum constat esse figmentum. </s>

<s>Franciscus Pa­<lb></lb>tritius, vir eruditione sat clarus, in quodam libello suo <emph type="italics"></emph>De antiquorum <lb></lb>rethorica,<emph.end type="italics"></emph.end> italico idiomate conscripto, ac Venetiis impresso per Franciscum <lb></lb>Sanensem anno 1562, dialogo primo, satis lepidam narrationem habet, quam <lb></lb>refert Julium Strozzam a comite Ballhassare Castilioneo audivisse, illum <lb></lb>vero a philosopho quodam abyssino in Hispania accepisse ” (Patavii 1713, <lb></lb>pag. </s>

<s>59, 60). E seguita il Ramazzini a riassumere in poche parole la storia <lb></lb>del filosofico romanzo, la quale poi, perchè crede che debba molto ricreare <lb></lb>i lettori, trascrive a verbo dall&#039;originale citato dialogo del Patrizio. </s></p><p type="main">

<s>I ciechi ammiratori del Burnet, scoperti essere invece gli ammiratori di <lb></lb>un Abissino studioso degli antichissimi etiopici annali, rimasero delusi e <lb></lb>svergognati, e molti fra&#039;nostri e fra gli stranieri si compiacquero, dopo il <lb></lb>Ramazzini, per attizzar sempre più il fuoco ai rossori della vergogna, di <lb></lb>comparare con quello elegantemente riferito dal Patrizio il filosofico romanzo <lb></lb>burneziano. </s>

<s>Il Vallisnieri, ch&#039;è uno de&#039;più zelanti in sostituir le osservazioni <lb></lb>sensate alle vane speculazioni, scrive di certi che troppo si confidavano di <lb></lb>così fatte vanità, per spiegar le origini e le vicende subite dalla superfice <lb></lb>terrestre: “ Cadono in certo modo costoro, senza avvedersene, quasi nel so­<lb></lb>gno galante o nel romanzo bizzarro (almeno così a me pare) dello stato del <lb></lb>mondo avanti il diluvio del famoso Burnet, o di quel sapiente Abissino rap­<lb></lb>portato per dire più cose belle che vere dal dottissimo Francesco Patrizio <lb></lb>nel suo dialogo fra Giulio Strozza e il conte Baldassarre da Castiglione. </s>

<s>Si <lb></lb>contenti di sentirlo, perciocchè le servirà almeno di un onesto e gentile di­<lb></lb>vertimento. </s>

<s>Voleva che la Terra fosse già senza monti, e nel centro tutta <lb></lb>vota e cavernosa, nella cui superfice fossero scavate spelonche e ripostigli, <lb></lb>dagli uomini abitati e dagli animali, per gli cui usi erano le acque e l&#039;aria <lb></lb>sparse per le medesime. </s>

<s>Ma insuperbiti gli uomini e fattisi intollerabili, <lb></lb>Giove al di sopra co&#039;fulmini e Plutone al di sotto co&#039;terremoti, cominciò a <lb></lb>scuotere e crollare orribilmente le sue radici, col quale orrendo fulmina­<lb></lb>mento e crollamento, aprendo in molti luoghi la Terra e rompendola, ella <lb></lb>cadde tutta nelle proprie caverne di sotto, e sè medesima assorse e riempì, <lb></lb>dal che avvenne ch&#039;ella e minor divenne, e si allontanò dal cielo..... (De <lb></lb>corpi marini ecc. </s>

<s>cit., pag. </s>

<s>63). </s></p><p type="main">

<s>Essendosi così, dal Vallisnieri e da parecchi altri eloquenti oratori, pro­<lb></lb>nunziato il giudizio, riconosciuto dai più savi giustissimo, intorno al sistema <lb></lb>del Burnet, che veniva a qualificarsi a parole e a dimostrarsi in fatti per <pb xlink:href="020/01/1701.jpg" pagenum="576"></pb>un romanzo; si potrebbe credere che rinsaviti i cultori della scienza tor­<lb></lb>nassero indietro a rivolgere almeno sul dimenticato Stenone uno sguardo. </s>

<s><lb></lb>Ma è singolare che gl&#039;illusi occhi loro si compiacessero piuttosto in vagheg­<lb></lb>giare una nuova ipotesi, la quale veniva a infondere una certa apparente <lb></lb>solidità nelle vane fantasie del Burnet, per l&#039;osservazioni di alcuni fatti, al­<lb></lb>trimenti però rappresentati da quel vero esser loro, in che gli avea colti, e <lb></lb>dichiarati innanzi agli Accademici fiorentini, la sagacia dello stesso Stenone. </s></p><p type="main">

<s>Giovanni Woodward, connazionale al Burnet, pubblicava in Londra <lb></lb>nel 1695 un libro intitolato <emph type="italics"></emph>An essay towards the natural history of the <lb></lb>Earth.<emph.end type="italics"></emph.end> Credeva l&#039;Autore di poter dare il titolo di Storia naturale al suo si­<lb></lb>stema, perchè muove dall&#039;osservazion degli strati, in che trovò affaldarsi do­<lb></lb>vunque la superfice terrestre. </s>

<s>Ma poi, ripensando a ciò che potesse esser <lb></lb>causa di cotesta singolare stratificazione, non gli occorse nulla di meglio alla <lb></lb>fantasia dell&#039;universale Diluvio, il quale, erompendo dagli abissi, disciolse le <lb></lb>materie terree, e poi le depose a quel modo che l&#039;escavazioni oggidì ce lo <lb></lb>fanno vedere. </s>

<s>A chi gli opponeva come potessero le acque avere una tale <lb></lb>virtù solvente, anche delle materie lapidefatte o metalliche, rispondeva che <lb></lb>per divino decreto fu sospesa la legge della coesione molecolare, e soggiun­<lb></lb>geva essere pure in quel breve tempo sospesa la legge di gravità a chi do­<lb></lb>mandava come mai sostanze, di tanto più gran peso specifico dell&#039;acqua, <lb></lb>potessero esser così venute a sollevarsi in alto dai loro bassi fondi marini. </s></p><p type="main">

<s>Ma come si conciliavano le storie naturali con questi fatti miracolosi? </s>

<s><lb></lb>Quale scientifica dimostrazione si dava dell&#039;esistenza dell&#039;abisso a coloro, i <lb></lb>quali sapevano che ai tempi biblici si credeva esser la Terra una falda, o <lb></lb>una piana isola galleggiante sul mare, e che l&#039;idea delle sotterranee acque <lb></lb>diluviali erompenti era nata dal fatto di quelle scavate fontane, simili ai no­<lb></lb>stri pozzi così detti artesiani? </s>

<s>Era facile a riconoscer, dietro queste consi­<lb></lb>derazioni, come il sistema del Woodward non avea veramente nulla, che gli <lb></lb>meritasse il titolo di Storia naturale, e nonostante quelle così leggere osser­<lb></lb>vazioni stratigrafiche e paleontologiche, credute nuove, riuscirono così se­<lb></lb>ducenti, da rendere accettevole in parte le nuove fantasie, e da indurre gli <lb></lb>stessi più severi ingegni a perdonare all&#039;immaginoso Inglese i manifesti pa­<lb></lb>ralogismi. </s>

<s>Anche fra&#039;nostri Italiani Jano Planco per esempio si professa se­<lb></lb>guace di lui, e lo stesso Vallisnieri, benchè ne repudi risolutamente la vana <lb></lb>speculazione, e nelle sensate osservazioni riconosca l&#039;imperfezione e l&#039;errore, <lb></lb>incerto in che modo risolvere il gran problema geologico, così desiderosa­<lb></lb>mente allora dalla scienza richiesto, non vede, in mezzo a tante tenebre, <lb></lb>venir altra, benchè languida luce, che dalle pagine wowardiane. </s>

<s>Non par che <lb></lb>nemmen egli si accorga esser cotesta luce un incerto riflesso della splendida <lb></lb>face accesa nel Prodromo dello Stenone, in cui è la stratigrafia rappresen­<lb></lb>tata nel suo esser vero, e non come l&#039;effetto di un unico Diluvio, secondo <lb></lb>quel che diceva il Woodward in manifesta contradizione coi fatti nataturali; <lb></lb>ma come il deposto da successive alluvioni, che fecero più volte mutar fac­<lb></lb>cia alla Terra. </s></p><pb xlink:href="020/01/1702.jpg" pagenum="577"></pb><p type="main">

<s>L&#039;unico merito dunque, ch&#039;ebbe il libro del Woodward, fu quello di <lb></lb>rendere accettabile ai negligenti delle scientifiche tradizioni o ai ritrosi quella <lb></lb>parte di scienza stenoniana, che riconosceva per uno de&#039;massimi efficienti <lb></lb>geologici le acque diluviali, d&#039;onde venne a costituirsi al regno mineralo­<lb></lb>gico la sua prima e principale nettunica sede. </s>

<s>Ora è a narrar da chi, e in <lb></lb>che modo si mettesse in evidenza sperimentale la seconda parte di quella <lb></lb>medesima scienza stenoniana, che l&#039;altro massimo efficiente geologico rico­<lb></lb>nobbe nel fuoco, e come d&#039;ambedue le parti, riunite da&#039;moderni insieme e <lb></lb>coltivate con assiduo studio amoroso, venisse ad erigersi in mezzo alla Sto­<lb></lb>ria naturale quel nuovo maraviglioso edifizio, sulle pareti del quale e nel­<lb></lb>l&#039;interno, come in bene appropriati loculi, depose la Natura stessa di sua <lb></lb>propria mano le varie specie dei minerali. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Giova, nell&#039;introdursi a trattare questa seconda importantissima parte <lb></lb>della presente storia, far più diligente attenzione a quella particolare effi­<lb></lb>cienza, che s&#039;attribuisce al fuoco nella Geologia stenoniana. </s>

<s>Nella descrizione <lb></lb>anatomica del capo della Carcaria era già l&#039;Autore ricorso col pensiero a <lb></lb>quell&#039;isole, che raccontavano gli Storici essersi vedute emergere dal mare, <lb></lb>per impeto di sotterranei incendi, perchè, applicando una simile origine plu­<lb></lb>tonica a Malta, venisse ad aversi qualche buona ragion naturale dell&#039;esi­<lb></lb>stenza dei tanti avanzi marini, che si trovan dispersi qua e là sull&#039;arida su­<lb></lb>perfice di lei “ Si credimus historiis e medio mari novae subsiluere insulae, <lb></lb>et quis Melitae prima incunabula novit? </s>

<s>Forsan mari olim supposita ea terra <lb></lb>canum marinorum latibulum fuit, quorum dentes, coenoso fundo olim inse­<lb></lb>pulti, mutato fundi situ per subterraneorum halituum praeceps incendium, <lb></lb>modo in media insula reperiuntur ” (pag. </s>

<s>109, 10). </s></p><p type="main">

<s>Vedemmo già come nel <emph type="italics"></emph>Prodromo<emph.end type="italics"></emph.end> s&#039;attribuisse la rottura degli strati <lb></lb>lapidei a due forze: una naturale o di gravità, e l&#039;altra violenta, consi­<lb></lb>stente nelle scosse prodotte dai fuochi sotterranei, per cui vennero a solle­<lb></lb>varsi in alto gli stessi strati scommossi. </s>

<s>Di que&#039;fuochi, soggiunge poi lo <lb></lb>Stenone, se ne vedono presso i monti sassosi gl&#039;indizi manifesti. </s>

<s>“ Vel in <lb></lb>ipsis montibus saxeis, vel in eorumdem vicinia evidentissima ignis subter­<lb></lb>ranei indicia reperiuntur ” (pag. </s>

<s>33). Nè per la sola spinta di basso in alto <lb></lb>concorrono potentemente cotesti fuochi a sollevar la terra sulle alture dei <lb></lb>monti, ma anche altrimenti, accumulandone talvolta le materie per egestione. <lb></lb></s>

<s>“ Possunt et aliter montes produci ut egestione ignium, cineres et saxa cum <lb></lb>sulphure atque bitumine eructantium, nec non pluviarum et torrentium im­<lb></lb>petu, quo strata saxea, caloris et frigoris vicissitudinibus, iam tum fixa in <lb></lb>praeceps devolvuntur; strata vero terrea, magnis ardoribus, rimas agentia <lb></lb>in varias partes resolvuntur. </s>

<s>Unde patet duo esse summa genera montium <pb xlink:href="020/01/1703.jpg" pagenum="578"></pb>colliumque; primum eorum quod e stratis componitur, quorum binae spe­<lb></lb>cies sunt, dum in quibusdam strata saxea, in aliis terrea strata abundant; <lb></lb>alterum genus eorum est, qui ex stratorum fragmentis et abrasis partibus <lb></lb>confuse et nullo ordine exsurgunt ” (ibid.). </s></p><p type="main">

<s>Benchè la teoria plutonica de&#039;sollevamenti sia così dallo Stenone chia­<lb></lb>ramente espressa, nonostante, in quel descriver ch&#039;ei fa, per una pratica <lb></lb>applicazione de&#039;più generali principii, la carta geologica della Toscana, tra­<lb></lb>scura affatto le forze endogene, per attribuire alla sola forza di gravità la <lb></lb>rottura degli strati lapidescenti e terrosi, sotto i quali <emph type="italics"></emph>ingentes cavitates <lb></lb>formatae erant.<emph.end type="italics"></emph.end> Di queste cavità, sebben sieno talvolta gli efficienti i sot­<lb></lb>terranei fuochi liquefattori, per lo più lo Stenone ne attribuisce l&#039;opera al­<lb></lb>l&#039;azione dissolutiva delle acque, cosicchè, nella nuova istituzione geologica <lb></lb>del nostro Accademico del Cimento, il Nettunismo pareva avere una preva­<lb></lb>lenza. </s>

<s>Nè è a fare di ciò le maraviglie, perchè, quanto evidenti nell&#039;esser <lb></lb>loro e nel prepotente modo di operare gli si mostravano le acque superfi­<lb></lb>ciali, altrettanto incerta apparivagli l&#039;esistenza di quel fuoco centrale, di cui <lb></lb>da sole le relazioni di alcuni fatti storici era dato di argomentare gli effetti. </s>

<s><lb></lb>Simone Maioli, ne&#039;suoi <emph type="italics"></emph>Dies caniculares<emph.end type="italics"></emph.end> pubblicati in Roma nel 1597, ri­<lb></lb>serbò il colloquio XVI a trattare dei monti, e ne descrive verso la fine al­<lb></lb>cuni, nati per forza d&#039;ignee sotterranee esplosioni e di terremoti, secondo <lb></lb>che gli descrivon nelle loro storie Teofrasto, Tacito, Plinio e altri antichi <lb></lb>scrittori. </s>

<s>Ma voleva lo Stenone fondar la sua scienza sulle naturali osserva­<lb></lb>zioni de&#039;fatti, e non sull&#039;autorità degli uomini, e perciò s&#039;indusse con gran <lb></lb>riserbo, e come per semplice congettura, ad ammettere il sollevamento del­<lb></lb>l&#039;isola di Malta, per impulso di sotterraneo incendio su dalle acque del mare. </s></p><p type="main">

<s>Erano dall&#039;altra parte tuttavia vive in Toscana alcune tradizioni, rima­<lb></lb>ste in non troppo onorata fama appresso i fervorosi innovatori delle scienze <lb></lb>sperimentali, perchè quel Ferdinando granduca, a cui ora lo Stenone inti­<lb></lb>tola il suo Prodromo, era quello stesso, a cui ventott&#039;anni prima Giovanni <lb></lb>Nardi aveva dedicata la sua fisica Prolusione <emph type="italics"></emph>De igne subterraneo.<emph.end type="italics"></emph.end> E perchè <lb></lb>la ipotesi di lui, dopo un secolo preciso rinnovellata da un altro Italiano, è <lb></lb>da tutti oramai risonosciuta meritevole di onoranze nelle pagine della Sto­<lb></lb>ria, non rincresca ai Lettori di trattenersi qui brevemente con noi a esami­<lb></lb>nare le principali idee espresse intorno a così nuovo, e tanto lubrico sog­<lb></lb>getto, dal Fisico fiorentino. </s></p><p type="main">

<s>Incomincia l&#039;Autore a dimostrar la sua tesi dai fatti, o com&#039;egli si <lb></lb>esprime, dagli esperimenti: “ Dari ignem subterraneum experimentis con­<lb></lb>firmatur ” (Florentiae 1641, pag. </s>

<s>2), e si riducon questi esperimenti a no­<lb></lb>tare che non ci è regione continentale o insulare sulla superfice terrestre, <lb></lb>in cui non si veggano incendi attuali, o non si trovino scritte memorie, o <lb></lb>non si osservino manifesti indizi d&#039;incendi passati. </s>

<s>Cita di queste scritte me­<lb></lb>morie storiche gli Autori, ai quali aggiunge il suffragio de&#039;sacri testi, dei <lb></lb>Mitologi e dei Poeti. </s>

<s>Passando quindi a farla da fisico, investiga di que&#039;fuo­<lb></lb>chi sotterranei l&#039;indole e la natura, ch&#039;ei riconosce non punto dissimile dal <pb xlink:href="020/01/1704.jpg" pagenum="579"></pb>fuoco elementare, e a cui egli assegna per sua natural sede le cavernosità <lb></lb>della terra, delle quali si trattiene a dimostrar l&#039;esistenza. </s></p><p type="main">

<s>Erano però così fatte opinioni tutte di secondaria importanza, rispetto <lb></lb>a un&#039;altra, la soluzion della quale massimamente si desiderava, e ch&#039;era <lb></lb>intorno a riconoscer la causa efficiente e l&#039;origine di ciò che, per i monti <lb></lb>ignivomi e per altre scaturigini di fuoco, si teneva per manifesto. </s>

<s>E qui il <lb></lb>Nardi, prima di profferir l&#039;opinione sua propria, si trattiene a confutar quella <lb></lb>di coloro, i quali alla compressione degli spiriti aerei e delle acque discor­<lb></lb>renti per le segrete viscere della terra attribuivan la causa degli incendi in <lb></lb>essa latenti. </s>

<s>Credeva di aver tanto da dimostrare la falsità di una tale ipo­<lb></lb>tesi, per l&#039;esempio delle trombe idrauliche e degli schioppi pneumatici, nei <lb></lb>quali due strumenti, alla forte pressione prodotta nel cacciar dell&#039;embolo, <lb></lb>nè l&#039;acqua però nè l&#039;aria concepiscono aumento di calore. </s>

<s>“ Non minus <lb></lb>falsum praeterea, est quod illa maris vel spiritus <emph type="italics"></emph>arctatio<emph.end type="italics"></emph.end> ignem generet, <lb></lb>contrarium nam experimur in hydraulicis, nec non in bellicis tormentis, <lb></lb>flatu solo artificiose compresso pyrii pulveris vicem supplente, quae neque <lb></lb>ignem, neque calorem inde concipiunt ” (ibid., pag. </s>

<s>26). </s></p><p type="main">

<s>Se gli avesse alcuno mostrata sotto gli occhi l&#039;esperienza del fuoco, <lb></lb>che di fatto s&#039;apprende all&#039;esca, per la forte compressione dell&#039;aria, nel così <lb></lb>detto <emph type="italics"></emph>Acciarino pneumatico,<emph.end type="italics"></emph.end> forse il Nardi sarebbesi ricreduto, ed egli pe­<lb></lb>ripatetico scomunicato avrebbe dato l&#039;esempio a tanti ortodossi più recenti, <lb></lb>i quali, non avendo saputo riconoscer la naturale origine del calor centrale <lb></lb>nella compressione della materia attrattavi d&#039;ogni parte, andarono a fanta­<lb></lb>sticar che la Terra fosse un giorno un tizzone acceso, spentosi alla super­<lb></lb>fice a poco a poco. </s>

<s>È da scusarsi dunque esso Nardi se al vero naturale <lb></lb>intraveduto dagli altri sostituì quella sua fantastica opinione, invocatrice della <lb></lb>superna benefica mano dell&#039;Onnipotente, la quale, affinchè non ne avesse <lb></lb>il mondo a ricevere nocumento, relegò come in una carcere il fuoco giu <lb></lb>nelle tartaree caverne. </s></p><p type="main">

<s>Il difetto, che contenevano in sè tanto l&#039;ipotesi del Peripatetico antico, <lb></lb>quanto quelle de&#039;Novatori moderni, dava luogo a promovere un&#039;altra que­<lb></lb>stione intorno al mantenersi i sotterranei fuochi perenni. </s>

<s>Chi riconosce la <lb></lb>vera causa di loro nel premersi, che necessariamente fa la materia in con­<lb></lb>seguenza dell&#039;attrazion centrale, dà la nuova questione implicitamente per <lb></lb>già risoluta, essendo chiaro dover quegli stessi sotterranei incendi durare <lb></lb>quanto durerà la presente costituzion della Terra. </s>

<s>Tutte le Geogonie però, <lb></lb>che professan l&#039;ipotesi di un primitivo globo infocato, son per rispondere <lb></lb>al quesito costrette di ricorrere alle coibenze degli strati superficiali. </s>

<s>Ma que­<lb></lb>sta risposta, se non c&#039;inganniamo, sembra a noi non punto meno meschina <lb></lb>di quella data dal Nardi, il quale, ricercando ai tartarei fuochi il pascolo che <lb></lb>gli mantenga, come il combustibile mantiene gli altri fuochi elementari, si <lb></lb>lusingò di averlo trovato in quel che, secondo l&#039;espressione biblica, è detto <lb></lb><emph type="italics"></emph>pinguedine della terra.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Credeva questa stessa pinguedine il Nardi sufficiente a produrre per sè <pb xlink:href="020/01/1705.jpg" pagenum="580"></pb>sola l&#039;effetto desiderato, anche senza ricorrere, com&#039;altri facevano, alle pin­<lb></lb>guedini dell&#039;acqua, ossia ai bitumi, e ciò argomentava dall&#039;osservar che tal­<lb></lb>volta son più attivi di quegli a mare i vulcani fra terra. </s>

<s>Non vo&#039;nonostante <lb></lb>negar, poi soggiunge, “ et mari inesse pinguedinem, et uberem hinc quan­<lb></lb>doque accessisse fomitem flagrantibus ignibus, verum neque individua fuit <lb></lb>illa comes fidaque sodalis. </s>

<s>Nam et Vesevi atque Aetnae fatiscunt quando­<lb></lb>que incendia, adeo ut impune licuerit curiosis vel craterum intima scrutari <lb></lb>viscera. </s>

<s>Quod si mons uterque maris vicinia nunquam destituitur, neque <lb></lb>tamen perpetuo flagrat, quas ministrabit opes maris pinguedo distantissimis <lb></lb>ignibus? </s>

<s>” (ibid, pag. </s>

<s>49). </s></p><p type="main">

<s>I moderni Geologi che, dall&#039;avere osservato essere i vulcani attivi per <lb></lb>lo più disposti lungo i lidi marini, attribuirono all&#039;acque per sotterranee vie <lb></lb>comunicanti col mare un&#039;azione simile a quella non in tutto osata negare <lb></lb>dal Nardi: per questa e per altre non poche verità che vi si trovano adom­<lb></lb>brate, e quali fecondabili germi disperse, tengono la fisica prolusione <emph type="italics"></emph>De <lb></lb>igne subterraneo,<emph.end type="italics"></emph.end> come una prima e antica reliqua della loro scienza, in <lb></lb>onore. </s>

<s>Ma i contemporanei e i successivi seguaci degl&#039;istituti sperimentali <lb></lb>derisero da principio, e poi facilmente dimenticarono, quasi fossero tutte <lb></lb>allo stesso modo eterodosse, le dottrine di chi chiamava il moto della terra <lb></lb><emph type="italics"></emph>damnata impostura<emph.end type="italics"></emph.end> (pag. </s>

<s>68) e diceva i vitrei organi applicati ad uso di <lb></lb>termometro <emph type="italics"></emph>malo omine a Sanctorio Sanctorio olim fabrefacta<emph.end type="italics"></emph.end> (pag. </s>

<s>62). </s></p><p type="main">

<s>È notabilissimo nonostante che, facendosi Galileo ammiratore delle nuove <lb></lb>speculazioni del Nardi, ne raccomandasse ai discepoli e agli amici, fra&#039;quali <lb></lb>Francesco Rinuccini, la lettura, specialmente dei <emph type="italics"></emph>problemata centum<emph.end type="italics"></emph.end> inve­<lb></lb>stigati nel cap. </s>

<s>L dal proprio ingegno dell&#039;Autore, e gli promette che “ in <lb></lb>una lettura di poco più di un&#039;ora vedrà la soluzione di tanti ammirabili ef­<lb></lb>fetti della Natura, che un solo mi ha messo in disperazione d&#039;intenderlo, <lb></lb>con la contemplazione del tempo di tutta mia vita ” (Alb. </s>

<s>VII, 363). Tanto <lb></lb>sono anzi in Galileo notabili queste espressioni, che le hanno alcuni credute <lb></lb>un&#039;ironia. </s>

<s>Ma che sieno invece la significazione di un sentimento vero vien <lb></lb>confermato dal vedere esso Galileo esprimersi al medesimo modo con altri <lb></lb>amici e scolari suoi, raccomandando a loro la rara eccellenza del libro del <lb></lb>Nardi, ond&#039;è che Fulgenzio Micanzio rispondeva, dietro queste raccomanda­<lb></lb>zioni: “ Cosa commendata da V. S. non può essere che rara ed eccellente, <lb></lb>onde ne ho curiosità suprema ” (Campori, Carteggio galil., Modena 1881, <lb></lb>pag. </s>

<s>574) </s></p><p type="main">

<s>Con la medesima sincerità e persuasione aveva pure Galileo raccoman­<lb></lb>dato il libro <emph type="italics"></emph>De igne subterraneo<emph.end type="italics"></emph.end> a Vincenzio Renieri, il quale però, giu­<lb></lb>dicandone in modo tutto diverso, rimproverava dolcemente il Maestro di <lb></lb>avergli fatto perdere il tempo a rileggere i cento problemi “ ne&#039;quali, così <lb></lb>esprimesi in una lettera indirizzata allo stesso Galileo da Pisa, per la de­<lb></lb>bolezza del mio ingegno non ho saputo trovare quelle maraviglie, che ella <lb></lb>mi accenna. </s>

<s>Può essere che ciò derivi dall&#039;avermi io già presupposto che <lb></lb>il credere la Terra essere piena di fuoco sia un paradosso, e che però io <pb xlink:href="020/01/1706.jpg" pagenum="581"></pb>non arrivi alle altre belle sottigliezze ne&#039;problemi racchiuse. </s>

<s>Ma io sono di <lb></lb>un ingegno così tardo, che stimo non essere differenza tra chi per vedere <lb></lb>quaranta o cinquanta monti gettar fiamme crede esserne piena tutta la Terra, <lb></lb>e tra chi, per veder fumare cinque o sei cammini di Pisa, credesse che le <lb></lb>case di dentro abbruciassero tutte ” (Alb. </s>

<s>X, 410). </s></p><p type="main">

<s>Se fossero tali difficoltà del Renieri giunte alle orecchie dello Stenone, <lb></lb>non sarebbero forse state quelle, che lo fecero andare in ammetter l&#039;esi­<lb></lb>stenza del fuoco sotterraneo così cauto, essendo, come la sentì molto giudi­<lb></lb>ziosamente Galileo, non improbabile congettura di un incendio interno alla <lb></lb>terra il vederlo per tante bocche vomitato al di fuori. </s>

<s>Non era dunque il <lb></lb>fatto in sè, che teneva la mente dell&#039;Autor del Prodromo agitata dal dub­<lb></lb>bio: erano i modi e le ragioni del fatto, intorno a che sentiva, o avrebbe <lb></lb>potuto sentire la debolezza degli argomenti addotti dal peripatetico Nardi, <lb></lb>seppure, negli ultimi tempi dell&#039;Accademia del Cimento, non era la Fisica <lb></lb>prolusione di lui già defunta, e nella granducale biblioteca sepolta. </s></p><p type="main">

<s>Da che può avere origine quel calore si intenso, che liquefà le lapidee <lb></lb>materie e sublima gli stessi metalli? </s>

<s>Qual&#039;è quel pascolo, che nelle riposte <lb></lb>viscere della Terra lo rende perenne? </s>

<s>Opera egli in aprirsi al di fuori le <lb></lb>vie, e in ridurre gli strati alluvionali in frantumi immediatamente per la sua <lb></lb>propria virtù dilatatrice, o mediatamente per l&#039;aria, o per vapore che tona <lb></lb>orribilmente ed esplode? </s>

<s>Eran tutti questi problemi, che si proponevano <lb></lb>alla mente dello Stenone, e giacchè le vie sperimentali da risolverli erano <lb></lb>chiuse, non rimaneva a far altro che attenersi giudizionsamente alle conget­<lb></lb>ture, il momento delle quali nel presente proposito sentì più debole che in <lb></lb>altre sue geologiche speculazioni. </s>

<s>Ma il Plutonismo in ogni modo è per il <lb></lb>nostro Accademico fiorentino la seconda attivissima efficienza delle trasfor­<lb></lb>mazioni superficiali del Globo; efficienza sopra la predicata verità della quale <lb></lb>ci bisognarono ancora settant&#039;anni, prima che uscisse fuori qualcuno a ri­<lb></lb>volgervi l&#039;attenzione. </s></p><p type="main">

<s>Vedemmo come in questo lasso di tempo, dannosamente neglette le <lb></lb>teorie stenoniane, non rimanesse altro vestigio di scienza, che nel libro del <lb></lb>Woodward, qualche languido riflesso del quale eccitava più vivo il deside­<lb></lb>rio di scoprir comecchessia la luce del vero. </s>

<s>Grandissime difficoltà però si <lb></lb>presentavano a tutti coloro, che volevano non fabbricar romanzi ma istituire <lb></lb>una scienza nuova, nella quale dall&#039;altra parte si salvassero le bibliche tra­<lb></lb>dizioni di un unico diluvio di quaranta giorni: per cui anzi le difficoltà ri­<lb></lb>ducendo nell&#039;impossibilità di giungere all&#039;intento desiderato, i più savi si <lb></lb>attennero al partito di preparar le fondamenta e il materiale, intanto che, <lb></lb>col progredir degli studi, sarebbe venuto il tempo di fabbricar l&#039;edifizio. </s></p><p type="main">

<s>Due illustri uomini abbiamo da annoverar fra costoro in Italia: Luigi <lb></lb>Ferdinando Marsili e Anton Maria Vallisnieri. </s>

<s>Il primo, uomo di armi, si <lb></lb>tratteneva nelle militari escursioni ad osservare ciò che di più notabile gli <lb></lb>presentasse, in distanti regioni, la superfice terrestre, con intenzione d&#039;in­<lb></lb>vestigarne l&#039;<emph type="italics"></emph>organica struttura.<emph.end type="italics"></emph.end> Si proponeva poi di raccogliore il frutto di <pb xlink:href="020/01/1707.jpg" pagenum="582"></pb>tali investigazioni in un trattato “ in cui spero, così egli stesso si esprime, <lb></lb>di non avanzar cosa non fondata sul fatto, senza lasciarmi trasportare dal <lb></lb>genio o dal capriccio di vane ipotesi, contento di riferire il veduto, perchè <lb></lb>altri, dediti e avvezzi a queste precise determinazioni, vi lavorino sopra e vi <lb></lb>fabbrichino a loro talento ” (Lettera in appendice al tratt. </s>

<s>del Vallisnieri <lb></lb><emph type="italics"></emph>De&#039;corpi marini ecc.,<emph.end type="italics"></emph.end> ediz. </s>

<s>cit., pag. </s>

<s>144). </s></p><p type="main">

<s>Di questa struttura organica della Terra, che voleva ridurre il Marsili <lb></lb>a trattazione compiuta, avea già ricavato uno splendido saggio da quella co­<lb></lb>stante disposizione di strati sopra strati, in che trovò che da per tutto si <lb></lb>ammassicciano i monti. </s>

<s>Era stato però in queste stratigrafiche osservazioni, <lb></lb>lasciamo andar lo Stenone, prevenuto dal Woodward, e v&#039;attendevano con­<lb></lb>temporaneamente Giovanni Scheuchzer e il Vallisnieri. </s>

<s>Ma seppe bene aprirsi <lb></lb>il Marsili, attiguo a questo, un altro campo che tutti, sbigottiti dalle diffi­<lb></lb>coltà e giudicandolo una temeraria audacia dell&#039;ingegno, lasciarono inesplo­<lb></lb>rato. </s>

<s>Il Boyle, è vero, avea scritta e pubblicata una dissertazione <emph type="italics"></emph>De fundo <lb></lb>maris,<emph.end type="italics"></emph.end> ma non erano in essa altro che i primi tentativi, somiglianti a quelli <lb></lb>di un notatore inesperto, che non sa perdere di vista la linea fiduciosa <lb></lb>del lido. </s></p><p type="main">

<s>Il nostro Bolognese dunque fu il primo, che osò esplorare la struttura <lb></lb>geologica dell&#039;ampio e velato seno del mare, incitato dal desiderio di verifi­<lb></lb>care una sua congettura, se cioè fossero anche que&#039;bassi fondi, come le al­<lb></lb>ture montane, costruiti di strati sopra strati. </s>

<s>Ebbe di qui origine l&#039;<emph type="italics"></emph>Histoire <lb></lb>physique de la mer,<emph.end type="italics"></emph.end> della quale opera, intanto che per mancanza di osser­<lb></lb>vazioni indugiavasi la pubblicazione, eseguita poi in Amsterdam nel 1725; <lb></lb>fece l&#039;Autore stesso nella patria lingua un <emph type="italics"></emph>Ristretto,<emph.end type="italics"></emph.end> in forma di lettera in­<lb></lb>dirizzata a Cristino Martinelli. </s>

<s>In essa, accennando in principio a&#039;suoi nuovi <lb></lb>intrapresi tentativi, così si esprimeva: “ Il motivo, che stimolommi a tali <lb></lb>tentativi, fu quello di volere indagare dentro la struttura dell&#039;alveo marit­<lb></lb>timo se vi fosse un&#039;organica disposizione corrispondente a quella da me ri­<lb></lb>trovata nella parte consistente sassosa, per cui formasi il continente della <lb></lb>Terra, giacchè, avendo io avuto ne&#039;tanti miei viaggi ed impieghi il comodo <lb></lb>di poter misurare, e per così dire anatomizzare in buon numero le parti <lb></lb>della medesima, formai non così piccola idea di voler dimostrare l&#039;organica <lb></lb>struttura di questo globo terrestre, mediante una serie assai numerosa di <lb></lb>osservazioni, massimamente nella parte montuosa che, nel suo corso inter­<lb></lb>rotto entro lo spazio d&#039;Europa, ho in gran parte ocularmente osservato ” <lb></lb>(Venezia 1711, pag. </s>

<s>2, 3). </s></p><p type="main">

<s>Delle cinque parti in fatti, in ch&#039;è distinto questo <emph type="italics"></emph>Saggio fisico della <lb></lb>storia naturale del mare,<emph.end type="italics"></emph.end> riserbandosi la prima a descriver la natura del <lb></lb>fondo, dice l&#039;Autore d&#039;aver verificato in essa la struttura che sospettava, <lb></lb>cioè “ di strati sopra strati, corrispondenti a quei che ho già riscontrati nei <lb></lb>monti dei continenti, ed una tale corrispondenza giovami assai per avanzare <lb></lb>con più fondamento il mio sistema circa la dimostrazione dell&#039;organica strut­<lb></lb>tura del globo terreno ” (ivi, pag. </s>

<s>23). Anche nell&#039;esteriore aspetto, e nel-<pb xlink:href="020/01/1708.jpg" pagenum="583"></pb>l&#039;andamento, si rassomigliano, prosegue a dire il Marsili, coi continenti i <lb></lb>bassi fondi marini, che pur “ variano or piani, ora inarcati, ora irregolari, <lb></lb>ora con alvei, che conducono dal continente fiumi perenni sotterranei d&#039;acque <lb></lb>dolci, ora con monti isolati, che rimangono alcune volte coperti da diverse <lb></lb>altezze d&#039;acque, ed altre volte spuntano appena fuori della medesima, oppure <lb></lb>s&#039;inalzano formando isole visibili ” (ivi, pag. </s>

<s>24). </s></p><p type="main">

<s>Il sistema però <emph type="italics"></emph>circa la dimostrazione dell&#039;organica struttura del globo <lb></lb>terreno,<emph.end type="italics"></emph.end> a stabilire il quale dovevano, come di sopra udimmo, servir questi <lb></lb>studi intorno alla struttura geologica de&#039;bassi fondi marini, non fu dal Mar­<lb></lb>sili, che si sappia, condotto alla sua perfezione. </s>

<s>Ciò forse avvenne perchè, <lb></lb>nel 1726, il Vallisnieri pubblicando la sua lezione accademica <emph type="italics"></emph>Dell&#039;origine <lb></lb>delle fonti,<emph.end type="italics"></emph.end> l&#039;avea corredata di dottissime annotazioni, per giunta alle quali <lb></lb>descrisse la nuova scoperta, ch&#039;egli e lo Scheuchzer avevano fatta, di quella <lb></lb>ch&#039;eran soliti chiamare <emph type="italics"></emph>anatomica composizione dei monti e delle valli.<emph.end type="italics"></emph.end><lb></lb>“ Quantunque i moderni naturali Filosofi, scrive esso Vallisnieri in princi­<lb></lb>pio della detta <emph type="italics"></emph>Giunta,<emph.end type="italics"></emph.end> facilmente intender possano ciò che, intorno la strut­<lb></lb>tura nuovamente scoperta de&#039;monti, tutti a strati sopra strati mirabilmente <lb></lb>composti, mi sono preso la briga di raccontare; nulladimeno per rendere più <lb></lb>agevole l&#039;intendimento, anche a quelli che non gli hanno osservati .... ho <lb></lb>determinato di porre le figure di molti tolte dal naturale, giacchè mi si pre­<lb></lb>senta la sorte di averle elegantissime dal signor Giovanni Scheuchzero, <lb></lb>grande istorico della Natura, delle quali ora, in passando per Padova, con <lb></lb>un discorso <emph type="italics"></emph>Dell&#039;origine dei monti<emph.end type="italics"></emph.end> me ne fa un pregiatissimo dono ” (Ve­<lb></lb>nezia 1726, pag. </s>

<s>100). </s></p><p type="main">

<s>Le figure orografiche sono in una medesima tavola rappresentate in sei <lb></lb>distinti quadretti, che il Vallisnieri illustra nella sua <emph type="italics"></emph>Giunta<emph.end type="italics"></emph.end> con assai brevi <lb></lb>parole descrittive, e contento in rappresentare agli occhi e alla mente dei <lb></lb>suoi lettori l&#039;<emph type="italics"></emph>anatomia,<emph.end type="italics"></emph.end> non si cura punto di quella, che si potrebbe chia­<lb></lb>mare <emph type="italics"></emph>fisi<gap></gap>logia<emph.end type="italics"></emph.end> della Terra. </s>

<s>“ Se il globo terrestre, così egli stesso dichiara <lb></lb>la sua intenzione, avanti l&#039;universale diluvio fosse formato di strati o di <lb></lb>varie cortecce, com&#039;è al presente; se tutti fossero orizzontali, o ci fosse l&#039;al­<lb></lb>tezza e la struttura de&#039;monti che ora veggiamo; se tutti sieno seguiti nel <lb></lb>precipitarsi le parti terrestri, conforme le leggi di gravità, nel fine del di­<lb></lb>luvio; come di poi si sieno rotti, altri inalzati, altri abbassati, altri in mille <lb></lb>guise rivoltati, piegati e sconvolti; o se sieno stati formati da più inonda­<lb></lb>zioni, o da più rovine e terremoti dislogati e disguisati; non è questo il <lb></lb>luogo di ricercarlo, contentandomi di avere solamente esposto ciò che m&#039;aspet­<lb></lb>tava per lo stabilimento del mio problema dell&#039;origine delle fontane ” (ivi, <lb></lb>pag. </s>

<s>108). </s></p><p type="main">

<s>De&#039;proposti problemi geologici dunque si protesta il Vallisnieri di non <lb></lb>aver voluto risolver che questo solo, lasciando all&#039;altrui industria l&#039;eserci­<lb></lb>tarsi intorno ai rimanenti. </s>

<s>N&#039;era fra questi uno però, stato fin allora assai <lb></lb>dibattuto, ma che trovava facile e concludentissima risoluzione a solo volger <lb></lb>lo sguardo sopra queste tavole ori<gap></gap>ognostiche. </s>

<s>Anche il Guglielmini, per ci-<pb xlink:href="020/01/1709.jpg" pagenum="584"></pb>tare uno de&#039;più prossimi e autorevoli esempi, era stato sedotto dall&#039;error <lb></lb>comune, così pensando e scrivendo dell&#039;origine de&#039;monti e delle valli. </s>

<s>“ Se <lb></lb>si considera la parte più alta della Terra, cioè quella che noi chiamiamo <lb></lb>montuosa, si può ben facilmente comprendere che le spaccature, le quali in <lb></lb>essa da per tutto si trovano, per lo fondo delle quali scorrono i rivi, i tor­<lb></lb>renti ed i fiumi, e che sono come termini divisorii d&#039;una montagna dal­<lb></lb>l&#039;altra; è facile, dico, comprendere ch&#039;esse sono state fatte dalla forza delle <lb></lb>acque, che le ha scavate col corso ” (Della natura de&#039;fiumi, Vol. </s>

<s>I, Mi­<lb></lb>lano 1821, pag, 348). Ma il Vallisnieri, confermando le dimenticate dottrine <lb></lb>dello Stenone, argomentava sicuramente dalla stratigrafia de&#039;monti, e sen­<lb></lb>tenziosamente ne concludeva: “ le valli, particolarmente ne&#039;luoghi montuosi, <lb></lb>non sono formate da altro, se non da interrompimento o divisione degli <lb></lb>strati, o dalla rottura o piegatura de&#039;medesimi ” (Giunta cit., pag. </s>

<s>108). </s></p><p type="main">

<s>Qual si fosse però la causa di una tale rottura o piegatura, il Valli­<lb></lb>snieri, come dianzi da lui stesso udimmo, lo lasciava alla investigazione dei <lb></lb>sagaci Naturalisti, fra&#039;quali sorse, non molti anni dopo, Anton Lazzero Moro. </s>

<s><lb></lb>Tutto in istudio di ricercar l&#039;origine de&#039;crostacei, e de&#039;corpi marini, che si <lb></lb>ritrovan sui monti (nel qual problema si rinchiudeva in germe la moderna <lb></lb>Geologia) comprese il Moro che non avrebbero avuto i travagli della mente <lb></lb>nessun conforto, infintanto che dell&#039;origine di quegli stessi monti si ragio­<lb></lb>nasse dai gran Maestri a quel modo che faceva il Guglielmini. </s>

<s>E perchè la <lb></lb>voce dello Stenone era sventuratamente rimasta fra le chiuse pareti dell&#039;Ac­<lb></lb>cademia del Cimento, non rimaneva altro che i disegni stratigrafici aggiunti <lb></lb>alla lezione accademica del Vallisnieri, da cui potessero pigliare eccitamento <lb></lb>e scorta gl&#039;ingegni meditativi. </s></p><p type="main">

<s>Considerando dunque attentamente il Moro cotesti disegni, e suppo­<lb></lb>nendo che gli strati pietrosi rappresentati dovessero essere, nella prima loro <lb></lb>e natural disposizione, tutti livellati all&#039;orizzonte, intravide sagacemente la <lb></lb>ragione di quelle loro curvosità, di quelle loro contorsioni e rotture, ammet­<lb></lb>tendo l&#039;esistenza di una forza, che pingesse con variata gagliardia di mo­<lb></lb>mento dall&#039;interno del terrestre globo all&#039;esterno. </s>

<s>Or, in qual cosa potrebbe <lb></lb>meglio risedere cotesta forza endogena, che nel fuoco sotterraneo, di cui ave­<lb></lb>vano ammessa l&#039;esistenza, e riconosciuta altresì l&#039;efficacia, tanti scrittori, <lb></lb>dall&#039;antico Platone al moderno francese autore del <emph type="italics"></emph>Voyage d&#039;Italie,<emph.end type="italics"></emph.end> citato <lb></lb>dal Vallisnieri? </s></p><p type="main">

<s>Ebbe da queste idee origine quel trattato in folio, che vide la luce in <lb></lb>Venezia nel 1740 col titolo <emph type="italics"></emph>De&#039;crostacei, e degli altri marini corpi, che si <lb></lb>trovano sui monti,<emph.end type="italics"></emph.end> distinto in due libri, nel primo de&#039;quali si confuta il <lb></lb>Nettunismo del Burnet e del Woodward, e nel secondo si stabilisce la teo­<lb></lb>ria vulcanica nuova, per applicarla, così formulata, alla soluzione del prin­<lb></lb>cipale problema: “ Gli animali e i vegetabili marini, le cui spoglie o reli­<lb></lb>quie in oggi o sopra o sotto certi monti si trovano, nati, nutriti e cresciuti <lb></lb>nelle marine acque, innanzi che que&#039;monti sopra la superfice del mare si <lb></lb>alzassero; allora là furono spinti, dove ora esistono per lo più impietriti, <pb xlink:href="020/01/1710.jpg" pagenum="585"></pb>quando que&#039;monti, uscendo dal seno della Terra coperta d&#039;acqua; s&#039;alza­<lb></lb>rono a quelle altezze, in cui ora si veggono ” (pag. </s>

<s>231). </s></p><p type="main">

<s>Sollecito di fare apparire al mondo in questa formulata proposizione <lb></lb>una scoperta originale, il Moro commemora l&#039;anonimo Autor francese del <lb></lb>Viaggio nuovo d&#039;Italia, e l&#039;opinione di quei citati dal Woodward, i quali <lb></lb>dicevano essersi formate tutte l&#039;isole, e le altre terre abitabili a quel modo, <lb></lb>che si formaron Rodi, e Tera, e Terasia, per impeto di terremoti e di sot­<lb></lb>terranee sollevazioni. </s>

<s>Dello Stenone non fa nessun motto: eppure queste <lb></lb>dugent&#039;undici pagine in folio, in che si squaderna il secondo libro del Moro. </s>

<s><lb></lb>non contengono altro insomma che un commentario prolisso, o una verbo­<lb></lb>sissima esplicazione del concetto stenoniano, di cui giova qui ripetere le for­<lb></lb>mali espressioni: <emph type="italics"></emph>Forsitan mari olim supposita ea terra canum marino­<lb></lb>rum latibulum fuit, quorum dentes coenoso fundo olim insepulti, mutato <lb></lb>fundi situ per subterraneorum halituum praeceps incendium, modo in <lb></lb>media insula reperiuntur.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Quel che lo Stenone pensava così in particolare dell&#039;isola di Malta, il <lb></lb>Moro l&#039;applicò a tutte le isole, e ai continenti, e l&#039;ipotesi delle Glossopietre <lb></lb>estese in forma di tesi a tutti i corpi marini. </s>

<s>La nuova teoria plutonica in­<lb></lb>fatti si fonda dal più recente Autore sopra le osservazioni dell&#039;Isola nuova, <lb></lb>nata nell&#039;arcipelago nel 1707; sopra il Monte nuovo, nato nel 1538 presso <lb></lb>Pozzuolo; sopra il Vesuvio e sopra l&#039;Etna, che danno argomento alle de­<lb></lb>scrizioni storiche de&#039;primi capitoli del secondo libro. </s></p><p type="main">

<s>Uno de&#039;principali meriti, ch&#039;ebbe il Moro nel promovere la nuova <lb></lb>scienza, consiste nell&#039;aver richiamata l&#039;attenzione de&#039;Geologi sopra gli ef­<lb></lb>fetti delle forze endogene, l&#039;attività delle quali troppo debolmente si faceva <lb></lb>concorrere nella Dinamica terrestre dello Stenone. </s>

<s>Vedemmo come, nel de­<lb></lb>scrivere la Geologia della Toscana, attribuisse l&#039;insigne uomo la rottura degli <lb></lb>strati al loro proprio peso, che per le avvenute escavazioni si sentiva sotto <lb></lb>mancare il sostegno, e poniamo che si spiegassero bene a cotesto modo le <lb></lb>varie inclinazioni prese da quegli stessi strati, e i patiti dislocamenti, era <lb></lb>però difficile a intendere come si fossero potuti così contorcere violente­<lb></lb>mente e incurvare, a quel modo che gli avea veduti e descritti il Vallisnieri. <lb></lb></s>

<s>“ Se alcuno (esce perciò così il Moro a dar perfezione alle teorie stenoniane) <lb></lb>sia che chiegga come abbiano potuto in tante guise incurvarsi questi pie­<lb></lb>trosi strati, io rispondo che, a somiglianza di ciò che tante volte è stato ve­<lb></lb>duto farsi dal Mongibello e dal Vesuvio, la materia di quegli strati lique­<lb></lb>fatta, fu prima da&#039;monti superiori vomitata, e nelle vicine valli, e fors&#039;anco <lb></lb>nelle acque, che di prima quelle regioni coprivano, distesa. </s>

<s>Fu dipoi o in­<lb></lb>nanzi che indurasse o dopo indurata, ma di nuovo da&#039;sotterranei fuochi <lb></lb>ammollita, fu dico da questi all&#039;insuso qua e là inegualmente sospinta, e <lb></lb>dove le forze del fuoco impellente furono maggiori e più continuate, là più <lb></lb>alta, dove minori furon le forze e non continuate, là più bassa venne quella <lb></lb>materia a trovarsi ” (ivi, pag. </s>

<s>280). </s></p><p type="main">

<s>Difficilmente si sarebbe potuta spiegare, per solo avvallarsi del soggia-<pb xlink:href="020/01/1711.jpg" pagenum="586"></pb>cente terreno, l&#039;origine di quelle immense volte di pietra, indicate con la <lb></lb>lettera B nel primo disegno del Vallisnieri, e con le lettere A e C nel se­<lb></lb>condo, per cui così facile il Moro trovò nelle forze endogene la causa na­<lb></lb>turale del fatto: “ Questi strati, egli dice, furono all&#039;insù spinti dalla forza <lb></lb>del fuoco, in guisa che nelle parti di mezzo delle concavità l&#039;urto fu mag­<lb></lb>giore, che nelle altre parti, ma non tale però, che il fuoco sbucato sia fino <lb></lb>a diromperli ” (ivi, pag. </s>

<s>281). </s></p><p type="main">

<s>Com&#039;aveva il Woodward conferito a mantener viva la prima grande <lb></lb>efficienza geologica, riconosciuta dallo Stenone nell&#039;acqua; così il Moro, per <lb></lb>questo sue divulgate dottrine, s&#039;acquistò il merito, come si diceva, di aver, <lb></lb>non solo resuscitata dall&#039;oblio, ma resa più evidente altresì quella seconda <lb></lb>efficienza, che lo Stenone stesso riconosceva nel fuoco. </s>

<s>Il danno era però che <lb></lb>non si facevano quelle due stesse efficienze, secondo che il Maestro della <lb></lb>nuova scienza insegnava, concorrere insieme, ma come il Woodward a sole <lb></lb>le acque diluviali attribuiva sulla superfice terrestre le subite trasformazioni; <lb></lb>così il Moro le attribuiva a soli gl&#039;incendi sotterranei. </s></p><p type="main">

<s>Il Vallisnieri, benchè non volesse andar tanto innanzi, s&#039;era pur fatto <lb></lb>intendere che gli strati pietrosi fossero un impostime delle acque, e il Moro <lb></lb>voleva invece che fossero materie allo stesso modo deposte, ma vomitate dai <lb></lb>fuochi. </s>

<s>“ Ben dice dunque, così scrive esso Moro, il signor Vallisnieri che <lb></lb>i monti fatti a strati, cioè i monti secondarii, paion tutti fatti in più volte, <lb></lb>e che paion simili a que&#039;tavolati e bellette, che da&#039;torbidi fiumi ne&#039;luoghi <lb></lb>bassi depongonsi. </s>

<s>Avvertasi però che quando il Vallisnieri dice che <emph type="italics"></emph>appari­<lb></lb>scono i monti formati, come d&#039;una crosta sopra un&#039;altra crosta, ognuna <lb></lb>delle quali sia stata lasciata in forma di posatura da varie inondazioni <lb></lb>in tempi a noi ignoti seguite;<emph.end type="italics"></emph.end> intendersi non debbe che quelle inondazioni <lb></lb>sieno state di acqua, ma solamente di quelle materie, benchè non così pensò <lb></lb>il Vallisnieri, di cui ognuna di quelle croste è composta. </s>

<s>Imperciocchè na­<lb></lb>cquero a principio delle cose, cacciati da sotterranei fuochi fuor del seno <lb></lb>della Terra, i monti primarii, ed alzatisi sopra la superfice dell&#039;acqua, che <lb></lb>dianzi il tutto copriva, dalle aperte loro bocche e caverne vomitarono varie <lb></lb>sorte di materie, le quali o a guisa di fiumi scorrendo, o a guisa di pioggia <lb></lb>dall&#039;alto cadendo, si avvallarono e distesero, una dopo l&#039;altra e una sopra <lb></lb>l&#039;altra, alle falde di que&#039;monti, giusta il modo che veggiamo tenersi tavolta <lb></lb>dal Vesuvio, dall&#039;Etna e da altri somiglianti monti fiammiferi, e così ven­<lb></lb>nero a formare in que&#039;bassi luoghi moltissimi tavolati e posature composte <lb></lb>qual d&#039;una sorta, qual d&#039;un&#039;altra, e qual di varie sorte di materia. </s>

<s>Da nuovi <lb></lb>fuochi poi accesi sotterra furono que&#039;tavolati e posature all&#039;insù cacciati, e <lb></lb>indi si formarono que&#039;monti, che secondarii per me si appellano, e che os­<lb></lb>servò il Vallisnieri essere tutti fatti a strati ” (ivi, pag. </s>

<s>271, 72). </s></p><p type="main">

<s>I progressi della Geologia dunque non si potevano altrimenti sperare, <lb></lb>che dall&#039;attemperamento di questa esagerata teoria plutonica colla nettunica, <lb></lb>ma non era venuto ancora il tempo del fecondo connubio. </s>

<s>Quattro anni dopo <lb></lb>che il Moro avea, sulle osservazioni e sull&#039;esperienze, stabilito e reso pub-<pb xlink:href="020/01/1712.jpg" pagenum="587"></pb>blico il suo sistema, l&#039;alito cartesiano che, spinto fuori sulle duttili onde del <lb></lb>Burnet e del Woodward, le avea enfiate nelle variopinte bolle dei loro si­<lb></lb>stemi, tornò in Francia a spirar sul Buffon, che quelle aeree bolle trasformò <lb></lb>in una bomba lanciata nello spazio dagl&#039;incendi del sole. </s>

<s>Raffreddandosi ivi <lb></lb>a poco a poco “ i vapori che prima si erano distesi, come veggiamo disten­<lb></lb>dersi le code delle comete, si condensarono a poco a poco, e deposero al <lb></lb>tempo stesso un loto misto di materie sulfuree e saline, una parte delle <lb></lb>quali pel moto delle acque s&#039;insinuò nelle fenditure perpendicolari, dove <lb></lb>formò i metalli e i minerali, il resto rimase nella superfice della Terra. </s>

<s><lb></lb>Adunque nello stato primiero della Terra era l&#039;interno del globo composto <lb></lb>d&#039;una materia vetrificata, come l&#039;arena, che non è altro che un tritume di <lb></lb>vetro, e al di sopra di questa arena galleggiarono le parti più leggere. </s>

<s>Ogni <lb></lb>cosa era coperta da uno strato di acqua, nata da&#039;vapori condensati, che de­<lb></lb>pose da per tutto una belletta mista di tutte quelle materie, che possono <lb></lb>sublimarsi e svaporare per la violenza del fuoco, e l&#039;aria si formò coi va­<lb></lb>pori più sottili che, per la leggerezza loro, si svilupparono dalle acque e le <lb></lb>sormontarono. </s>

<s>Tale era lo stato del globo, quando l&#039;azione del flusso e ri­<lb></lb>flusso, e quella de&#039;venti e del calore del sole cominciarono ad alterare la <lb></lb>superfice della Terra. </s>

<s>Il moto diurno e quello del flusso e riflusso primie­<lb></lb>ramente sollevarono le acque sotto i climi meridionali, e queste rapirono e <lb></lb>portarono seco verso l&#039;equatore il loto, le crete, le arene, ed elevando le <lb></lb>parti dell&#039;equatore abbassarono per avventura a poco a poco quelle dei poli, <lb></lb>perciocchè le acque disfecero bentosto e ridussero in polvere le pomici e <lb></lb>le altre parti spugnose della materia vetrificata, ch&#039;erano nella superfice; <lb></lb>scavarono delle valli, ed alzarono delle eminenze, che in decorso diventarono <lb></lb>continenti, e cagionarono tutte l&#039;inuguaglianze, che osservansi alla superfice <lb></lb>della Terra ” (Teoria della Terra, Opere, Vol. </s>

<s>I, Venezia 1820, pag. </s>

<s>313, 14). </s></p><p type="main">

<s>Così, dopo lo Stenone, il Marsili, il Vallisnieri e il Moro, seguitavasi a <lb></lb>delirare in Francia, benchè altrove non mancassero provvidamente alcuni, <lb></lb>che s&#039;inspiravan piuttosto al senno italiano. </s>

<s>In Germania furono tradotti i <lb></lb>due libri <emph type="italics"></emph>De&#039;crostacei,<emph.end type="italics"></emph.end> e nel 1751 pubblicati in Lipsia. </s>

<s>In Inghilterra Odoardo <lb></lb>King proponeva nel 1767 innanzi alla Società regia una soluzione del famoso <lb></lb>problema dell&#039;esistenza de&#039;corpi marini sui monti, che si notò riscontrar <lb></lb>con quella data del Geologo nostro veneziano. </s>

<s>Vien perciò da alcuni Italiani <lb></lb>accusato l&#039;Inglese di plagio: ma senz&#039;avere ancora veduta l&#039;opera di Laz­<lb></lb>zero Moro non poteva il King essersi sentito fecondare l&#039;ingegno da quelle <lb></lb>parole con le quali termina lo Stenone di descriver l&#039;anatomia del capo della <lb></lb>Carcaria? </s>

<s>Non era egli naturalissimo che venisse fatto a quel di Londra, <lb></lb>come a quel di Venezia, di passare dall&#039;isola di Malta a tutte l&#039;isole della <lb></lb>Terra, e dalle Glossopietre a tutte le altre spoglie de&#039;viventi nell&#039;acqua ri­<lb></lb>trovate poi sotterra? </s>

<s>È da un&#039;altra parte a riflettere che sui principii del <lb></lb>secolo XVIII tutti i grandi Anatomici, specialmente trattando degli organi <lb></lb>de&#039;sensi, additavano continuamente queste pagine stenoniane, dove son tante <lb></lb>le sentenze quante son le parole, e in ogni sentenza ritrovasi, o esplicita-<pb xlink:href="020/01/1713.jpg" pagenum="588"></pb>mente annunziata, o in germe, qualche grande scoperta. </s>

<s>Consultavano al­<lb></lb>tresì quelle pagine gli antiquarii, i quali ritrovavano in esse investigate le <lb></lb>origini delle antichità o naturali o manufatte, che si scavan di sottoterra. </s>

<s><lb></lb>Or chi potrebbe negare che l&#039;antiquario King non avesse piuttosto derivata <lb></lb>di qui, che ricopiata dal Moro la geologica soluzione del suo problema? </s></p><p type="main">

<s>Comunque sia, poco presso a chiudersi il secolo, che felicemente si <lb></lb>apriva col Marsili, col Vallisnieri e col Moro, la nuova scienza delle super­<lb></lb>ficiali trasformazioni del globo veniva con proprio nome salutata, e a grande <lb></lb>onore accolta fra le maggiori sorelle a partecipare dello storico regno della <lb></lb>Natura. </s>

<s>Par che la Geologia sia nata adulta in paese straniero, ma chi at­<lb></lb>tentamente l&#039;osserva vi riconosce le infantili fattezze, con le quali nella fio­<lb></lb>rentina Accademia fu esposta. </s>

<s>Si effigiava ivi dallo Stenone la Terra, se­<lb></lb>condo che le osservazioni fatte sul suolo toscano gli avevano dimostrato, <lb></lb>come composta di strati sopra strati deposti dalle torbide acque diluviali. </s>

<s><lb></lb>Furono quelle inondazioni tante, ritirandosi il mare e poi tornando a rico­<lb></lb>prir l&#039;arida e a imporvi nuova materia, quanti di quegli strati se ne pos­<lb></lb>sono annoverare affaldati intorno al nucleo del Globo. </s>

<s>Tale pure è la stra­<lb></lb>tigrafia, nel suo essere e nella sua natura, che ci vien descritta dai Geologi <lb></lb>moderni, i quali riconobbero il vero prenunziato già dallo Stenone, in mezzo <lb></lb>alle seduttrici aberrazioni del Woodward e dello stesso Lazzero Moro. </s>

<s>È no­<lb></lb>tabile come il nostro Accademico fiorentino, nel difficile cimento di conci­<lb></lb>liare le tradizioni bibliche con le osservazioni naturali, uscisse destramente <lb></lb>salvo di là, dove l&#039;inesperto Inglese, costretto ad ammettere un unico di­<lb></lb>luvio di pochi giorni, e perciò un&#039;unica deposizione delle materie, avea mi­<lb></lb>seramente fatto naufragio. </s>

<s>Lo Stenone, anche in ciò seguito da molti mo­<lb></lb>derni, ritrovò la causa semplicissima e naturale di quelle molteplici e ripetute <lb></lb>alluvioni, che venivano all&#039;occhio dell&#039;osservatore dimostrate dai fatti. </s>

<s>“ Quod <lb></lb>si quis dixerit in terra centrum gravitatis non semper idem esse cum cen­<lb></lb>tro figurae, sed modo ab una, modo ab altera eius parte recedere, prout ca­<lb></lb>vitates subterraneae variis locis creverint; facilem rationem afferre licet cur <lb></lb>fluidum, initio rerum omnia tegens, certa loca arida reliquerit, iterumque <lb></lb>redierit ad illa occupanda ” (Prodromus cit., pag. </s>

<s>72). </s></p><p type="main">

<s>Lo Stenone insegnò che i monti e le valli niente altro son che l&#039;effetto <lb></lb>della rottura degli strati, e benchè il Buffon, a mezzo il secolo XVIII, so­<lb></lb>gnasse intorno a ciò non meno stranamente de&#039;buoni uomini antichi, i Geo­<lb></lb>logi oggidì confermano essere la dottrina stenoniana la vera. </s>

<s>Hanno solo <lb></lb>riconosciuto in lei il bisogno di venire in parte emendata, sostituendo alla <lb></lb>forza di gravita le forze endogene, messe in tanta evidenza da Lazzero Moro. </s></p><p type="main">

<s>Coloro che dissero maravigliati esser nata e cresciuta la Geologia tra <lb></lb>la fine del secolo XVIII e il principio del secolo appresso, dovrebbero con­<lb></lb>siderare che se crebbe in quel tempo, era già da molto tempo nata in To­<lb></lb>scana, e che apparve il maraviglioso incremento dal congiunger felicemente <lb></lb>insieme, o per dir meglio, dall&#039;infondere in quella dello Stenone la scienza <lb></lb>del Moro. </s>

<s>Agli stranieri, e specialmente ai Francesi, si dà da molti il me-<pb xlink:href="020/01/1714.jpg" pagenum="589"></pb>rito di aver questa stessa scienza abbellita coi sistemi, dai quali si astennero <lb></lb>i Nostri o si mostrarono sempre assennatamente più sobrii. </s>

<s>Sorse dopo il <lb></lb>Buffon la splendida fantasia del La-Place, che lungamente e universalmente <lb></lb>sedusse gl&#039;ingegni, ma che ora si dissipa anch&#039;essa al tocco dell&#039;esperienza, <lb></lb>come le altre bolle enfiate dagli spiriti cartesiani. </s></p><p type="main">

<s>Le ipotesi de&#039;due Francesi ora commemorati avevano principalmente in <lb></lb>mira di accomodarsi e di spiegare due fatti: il calor centrale e la figura <lb></lb>ellissoidea della Terra, e perciò immaginarono un globo tutto internamente <lb></lb>compreso dal fuoco, e da lui reso molle e pastoso. </s>

<s>L&#039;esperienza e il cal­<lb></lb>colo dimostrano invece che dovette il globo terrestre esser solido in prin­<lb></lb>cipio, com&#039;è al presente. </s>

<s>Nacque l&#039;inganno dal credere che una sfera di <lb></lb>solido vetro, per esempio, o di metallo, girata velocemente intorno al suo <lb></lb>asse, e per lunghissimo tempo, non dovesse, anche senza esser molle, ri­<lb></lb>gonfiare nell&#039;equatore in modo simile, e proporzionale a quello, che ha de­<lb></lb>formata la Terra. </s>

<s>È da un&#039;altra parte simile un tale inganno a quello, che <lb></lb>facevasi il Moro e i geologi dopo lui, i quali crederono che non potessero <lb></lb>essere state le stratificazioni pietrose così contorte e incurvate, se non che <lb></lb>quando si trovavan tuttavia plastiche e molli, per l&#039;azione liquefattrice dei <lb></lb>fochi. </s>

<s>Eppure si vedono tutti i giorni gli architravi di pietra incurvarsi nei <lb></lb>nostri edifizi sotto il peso delle muraglia. </s>

<s>Gl&#039;insensibili momenti delle forze <lb></lb>continuamente operanti, accumulati dal tempo, producono questi e moltis­<lb></lb>simi altri fatti naturali, che alcuni invece attribuiscono a cause immaginarie. </s></p><p type="main">

<s>Dicemmo che da questo vizio d&#039;immaginar ciò, che non si arriva a co­<lb></lb>noscer di fatto, si astennero i nostri Italiani, e perchè vogliono gli stranieri <lb></lb>attribuirlo piuttosto a difetto d&#039;ingegno, venga anche quest&#039;altro esempio a <lb></lb>dimostrare i buoni effetti del prudente consiglio. </s>

<s>In fin da quando il Bo­<lb></lb>relli, per gli eccitamenti avuti dal cardinale Leopoldo de&#039;Medici, apriva in <lb></lb>Sicilia, ma sempre come Accademico del Cimento, un nuovo campo alla Pa­<lb></lb>leontologia, si proponeva a sciogliere il problema delle così dette <emph type="italics"></emph>ossa de&#039;gi­<lb></lb>ganti,<emph.end type="italics"></emph.end> le quali più abbondantemente che altrove si ritrovarono sparse in <lb></lb>Toscana per la valle superiore dell&#039;Arno, e per i colli volterrani. </s>

<s>Lo Ste­<lb></lb>none riconosciuto il fatto che coteste erano ossa di animali vissuti sotto altro <lb></lb>cielo, disse che, venuti qua in servizio dell&#039;esercito di Annibale, morti o <lb></lb>naturalmente o in guerra, vi restaron sepolti. </s>

<s>“ Certum est transiisse illac <lb></lb>Annibalem, antequam ad lacum Trasimenum cum Romanis confligeret; cer­<lb></lb>tum est extitisse in ipsius exercitu iumenta africana, et immensae magni­<lb></lb>tudinis elephantes turrigenos; certum est, dum a montibus fesulanis descen­<lb></lb>deret nimia aquarum alluvie, periisse in locis paludosis magnam partem <lb></lb>animalium oneribus vehendis destinatorum ” (ibid., pag. </s>

<s>64). </s></p><p type="main">

<s>Queste ragioni dello Stenone furono poi ripetute da molti, ma il pro­<lb></lb>blema incontrò bene altre difficoltà, quando si ritrovarono elefanti e mam­<lb></lb>mouth fossili in Russia e in Siberia. </s>

<s>Incredibile è l&#039;affaccendamento di co­<lb></lb>loro, che volevano spiegar come mai dalle regioni equatoriali fossero emigrati <lb></lb>colà presso il polo quadrupedi così ponderosi e inerti; indicibile è l&#039;attività <pb xlink:href="020/01/1715.jpg" pagenum="590"></pb>de&#039;Filosofi in assottigliar l&#039;ingegno per ritrovar la ragione di tanta avve­<lb></lb>nuta varietà di climi. </s>

<s>Mentre uno perciò si profonda negli abissi della terra, <lb></lb>e un altro si sublima agli spazii celesti, un nostro Italiano trova da risol­<lb></lb>vere il problema in questa semplice e naturalissima osservazione, che cioè <lb></lb>“ la temperatura de&#039;luoghi situati fuori dei tropici non dipende esclusiva­<lb></lb>mente dalla maggiore o minore distanza dall&#039;equatore, ma è variamente mo­<lb></lb>dificata da cause meteoriche, la massima delle quali è lo spirare di certi <lb></lb>venti ” (Brocchi, Conchiologia fossile, Vol. </s>

<s>I, Milano 1843, pag. </s>

<s>386). Or <lb></lb>perchè queste cause meteoriche dipendono dall&#039;ampiezza de&#039;mari, rispetto <lb></lb>ai continenti, e dalle relative posizioni dei gioghi montani, il solo variato <lb></lb>aspetto della superfice terrestre induce necessariamente una variazione del <lb></lb><gap></gap>lima, il quale poteva porciò esser tale un giorno in Siberia e in Russia, <lb></lb>qual&#039;è oggidì, o non molto differente, nelle regioni affricane. </s></p><p type="main">

<s>La causa tanto agitata del così detto <emph type="italics"></emph>periodo glaciale,<emph.end type="italics"></emph.end> e intorno a che <lb></lb>gli stranieri fantasticarono in sì strani modi, vien naturalmente risoluta da <lb></lb>questa proposizione del Brocchi, a cui dobbiamo altresì la dottrina degli spon­<lb></lb>tanei abbassamenti e sollevamenti del livello del mare con che venivansi a <lb></lb>spiegare le vicende delle allagazioni e dei ritiramenti di lui meglio che con <lb></lb>l&#039;ipotesi dello Stenone. </s>

<s>Vero è che il Brocchi non s&#039;era in tutto ancora de­<lb></lb>liberata la mente dal supposto del violento operare dei cataclismi pensando <lb></lb>che “ essendosi <emph type="italics"></emph>subitaneamente<emph.end type="italics"></emph.end> abbassato il livello del mare si riducesse <lb></lb>nell&#039;odierno suo letto ” (ivi, pag. </s>

<s>383) ma furon queste idee per inevitabile <lb></lb>conseguenza logica portate nella scienza dallo Stenone, ridotto fra l&#039;angustie <lb></lb>della cronologia biblica, e dal Moro a cui fu principalmente inspirata la teo­<lb></lb>ria plutonica dal subitaneo apparirgli sotto gli occhi le nuove Isole greche. </s></p><p type="main">

<s>In qualunque modo si conferma sempre meglio per questi esempi il <lb></lb>proposito nostro, ch&#039;era quello di dimostrare com&#039;avessero gl&#039;Italiani le prime <lb></lb>parti, così nell&#039;istituire, come nel coltivare la Geologia, le due massime effi­<lb></lb>cienze della quale, riconosciute da Niccolò Stenone e da Lazzero Moro, fu­<lb></lb>rono in tutte le loro particolarità messe in evidenza dagli studiosi dei nostri <lb></lb>giorni. </s>

<s>Ci siamo intrattenuti in questa seconda parte del presente capitolo a <lb></lb>trattare della seconda efficienza plutonica, riguardandola come sede del regno <lb></lb>minerale nelle vene metalliche e nei cristalli. </s>

<s>Furono infatti i due Autori <lb></lb>ora commemorati i primi che, alle immaginarie e favolose origini degli stessi <lb></lb>metalli, specialmente preziosi, e delle gemme, sostituirono le investigate cause <lb></lb>naturali. </s>

<s>Fu per essi altresì messa finalmente in chiaro la così dubbia ori­<lb></lb>gine de&#039;cristalli, e s&#039;incominciò allora a filosofare più sanamente intorno <lb></lb>alle ragioni delle loro forme geometriche, ciò ch&#039;essendo di principale im­<lb></lb>portanza nella Mineralogia, ci consiglia a trattenerci più di proposito, nel <lb></lb>seguente articolo, sopra un tale argomento. </s></p><pb xlink:href="020/01/1716.jpg" pagenum="591"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Come spesso avviene che l&#039;abito non trasformato seguiti a far mante­<lb></lb>nere, nelle domestiche e nelle civili consuetudini, i trasformati titoli della <lb></lb>persona; così non di rado avviene de&#039;vocaboli, rispetto alle idee. </s>

<s>Abbiamo <lb></lb>di ciò un notabile esempio nel vocabolo stesso <emph type="italics"></emph>cristallo,<emph.end type="italics"></emph.end> il quale, perchè <lb></lb>vale ai Greci quanto <emph type="italics"></emph>ghiaccio indurito,<emph.end type="italics"></emph.end> si seguitò a credere che tal si fosse <lb></lb>davvero la natura propria del minerale. </s>

<s>Il fatto, che sembra incredibile a chi <lb></lb>non ha ben misurata la forza dell&#039;abitudine, o non ha ben riconosciuta la <lb></lb>tirannia, che sul pensiero esercitano le parole, fu sanzionato dall&#039;antico padre <lb></lb>de&#039;Naturalisti, Cecilio Plinio, il quale, nel cap. </s>

<s>Il del libro XXXVII delle <lb></lb>sue Storie, avendo fatto prima motto di alcuni effetti del calore “ contraria, <lb></lb>soggiunge, huic causa crystallum facit, gelu vehementiori concreto. </s>

<s>Non alicubi <lb></lb>certe reperitur, quam ubi maxime hybernae nives rigent, glaciemque esse <lb></lb>certum est, unde et nomen Gracei dedere ” (Hagenoae 1518, fol. </s>

<s>CCLXXIX <lb></lb>ad terg.). </s></p><p type="main">

<s>In ogni modo avendo la cosa, per chi dava luogo al senno, apparenza <lb></lb>di paradosso, quegli altri che davan luogo piuttosto all&#039;autorità de&#039;maggiori, <lb></lb>si studiavano di salvarla col ricorrere a certe mendicate lusinghiere espe­<lb></lb>rienze. </s>

<s>Volevano che a mettere un cristallo sulla lingua ne sentisse il si­<lb></lb>ziente il medesimo refrigerio, che a mettervi sopra un pezzetto di gelo, e <lb></lb>dall&#039;aver forse osservato per caso che qualche untuosa lamina cristallina, <lb></lb>per effetto di capillarità, galleggia sull&#039;acqua, ne vollero inferire esser que­<lb></lb>sta una proprietà generale, che i cristalli tutti hanno comune col ghiaccio. </s></p><p type="main">

<s>Quando cominciarono ad apparire sull&#039;orizzonte d&#039;Italia gli albori cre­<lb></lb>puscolari della Scienza sperimentale, quel buon senese Vannoccio Biringucci, <lb></lb>che fu primo a richiamar l&#039;attenzione sui minerali del ricco suolo toscano, <lb></lb>e ad accennare alle utilità, che se ne ricaverebbero, per l&#039;esercizio delle <lb></lb>arti, per l&#039;economia dello Stato, e per gli usi della guerra; metteva, così <lb></lb>scrivendo, un poco di senno in quelle scapestrate idee, che s&#039;avevano dagli <lb></lb>studiosi di Plinio intorno all&#039;origine dei cristalli. </s>

<s>“ Cominciandomi a dirvi <lb></lb>del cristallo, vi dico che è una pietra trasparente, lucida e chiara, compo­<lb></lb>sta dalla Natura con predominio acqueo, talchè da molti, contr&#039;all&#039;ordine <lb></lb>delle cose naturali, è stato creduto che la Natura l&#039;abbi generato di pura <lb></lb>acqua per forza d&#039;una potente e perpetua frigidità, ch&#039;è continuamente in <lb></lb>que&#039;monti e luoghi dov&#039;el si trova, ne&#039;quali mai le acque e le nevi, per <lb></lb>li grandissimi freddi, disghiacciar non si possono. </s>

<s>E questa tal loro opinione <lb></lb>han cerca di provar con dire che il cristallo ancor ritiene la natura del­<lb></lb>l&#039;acqua ghiacciata, qual&#039;è, oltre a quel che dimostra nell&#039;aspetto, che s&#039;el <lb></lb>si mette nell&#039;acqua, come ancor fa il ghiaccio, vi galleggia sopra, senza an­<lb></lb>dare a fondo. </s>

<s>Ed anco dicono di più che si usa metterne sotto la lingua <pb xlink:href="020/01/1717.jpg" pagenum="592"></pb>de&#039;sizienti per la sua frigidità ed umidità che rende, e ch&#039;ello spegne la <lb></lb>siccità della sete. </s>

<s>Ma queste cose, ancor che fosser tutte, che non sono, con­<lb></lb>siderando non concludono che sia acqua, perchè il medesimo ancora sarebbe <lb></lb>del diamante e del berillo, e però non mi par da credere ch&#039;el sia acqua <lb></lb>pura gelata, e fatta indissolubile come dicono, perch&#039;è pietra così dalla na­<lb></lb>tura generata. </s>

<s>E di poi, se questo fosse, in que&#039;luoghi dove spesso piove, <lb></lb>e tante nevi che mettono per freddo tutte ghiacciassero e non disghiaccias­<lb></lb>sero mai, e sempre si convertissero in cristallo, vi sarebbero maggiori le <lb></lb>montagne del cristallo, che quelle delle pietre ” (De la Pirotecnia, libri X, <lb></lb>Venezia 1540, fol. </s>

<s>37, 38). </s></p><p type="main">

<s>Faceva eco al nostro Senese dalla lontana Germania, pochi anni dopo, <lb></lb>Giorgio Agricola, il quale, nel libro VI <emph type="italics"></emph>De natura fossilium,<emph.end type="italics"></emph.end> trattando del­<lb></lb>l&#039;origine de&#039;cristalli, dimostra con le ragioni e con l&#039;esperienza esser falsa <lb></lb>l&#039;opinione de&#039;seguaci di Plinio, che dicevano essere essi cristalli generati <lb></lb>sotto terra dalle acque indurite nel gelo, perchè se ciò fosse “ in frigidis­<lb></lb>simis quibusque regionibus, in quibus non rivi modo, sed etiam maximi <lb></lb>amnes usque ad vada glaciantur, plurima fierent ac solis calore liquescerent <lb></lb>rursus, quorum neutrum fieri videmus ” (Basileae 1546, pag. </s>

<s>282). È falso <lb></lb>altresì, soggiunge l&#039;Agricola, che il ghiaccio indurito per anni e per secoli <lb></lb>sui monti si trasformi finalmente in cristallo, perchè, sebbene in cadendo <lb></lb>mostri di essere così duro come la stessa pietra, “ etiam ipsa tandem solis <lb></lb>liquescit calore. </s>

<s>Igitur crystallus est succus, quem, sicut in libris <emph type="italics"></emph>De ortu <lb></lb>et causis subterrancorum<emph.end type="italics"></emph.end> scripsi, frigus intra terram conglutinavit ” (ibid.). </s></p><p type="main">

<s>In Italia, prima della instaurazione del metodo sperimentale, furono man­<lb></lb>tenute vive queste tradizioni della scienza dal Cesalpino, il quale ripudiava <lb></lb>l&#039;opinion di coloro, che dicevano essere i cristalli ghiaccio impietrito per la <lb></lb>semplicissima ragione che i luoghi, dove nascono quegli stessi metalli, come <lb></lb>il diamante per esempio e simili altri, “ non in Septemtrione sunt, sed in <lb></lb>India, Arabia et calidioribus regionibus ” (De metallicis cit., pag. </s>

<s>36). Dopo <lb></lb>la detta instaurazione uno de&#039;più autorevoli nella scienza, che trattassero <lb></lb>dell&#039;origine dei cristalli, fu Tommaso Bartholin nel suo libro <emph type="italics"></emph>De nivis usu <lb></lb>medico,<emph.end type="italics"></emph.end> dove, proponendosi nel cap. </s>

<s>XV di spiegare il detto di Plutarco, che <lb></lb>cioè non sieno altro le pietre se non che terra indurita dal freddo, “ an <lb></lb>hinc, soggiunge, patrocinium invenient qui crystallos ex glacie derivant? </s>

<s>” <lb></lb>(Hafniae 1661, pag. </s>

<s>102). E seguita a riferir le contrarie opinioni degli Au­<lb></lb>tori, da Plinio a&#039;suoi tempi, così all&#039;ultimo concludendo il discorso: “ Nos <lb></lb>chrystallum ita generari credimus sicut, in cryptis et locis subterraneis, ex <lb></lb>stillicidio aquarum lapides frigore concrescunt ” (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Le incrostazioni pietrose del carbonato calcare le credeva dunque il <lb></lb>Bartholin una trasformazione, subìta per via del freddo così intenso dal­<lb></lb>l&#039;acque, e allo stesso modo credeva che si generassero i cristalli. </s>

<s>Il valen­<lb></lb>t&#039;uomo, in tempi ne&#039;quali non aveva ancora la Chimica rivelato il mistero <lb></lb>degli stillicidi pietrificanti, toglieva all&#039;ipotesi pliniana quella sua prima ap­<lb></lb>parente stranezza col richiamar l&#039;attenzione su questo fatto, dal quale forse <pb xlink:href="020/01/1718.jpg" pagenum="593"></pb>rimasero pur sedotti gli Accademici fiorentini, come pare che si rilevi dalle <lb></lb>seguenti parole da loro scritte nella prefazione all&#039;<emph type="italics"></emph>Esperienze intorno agli <lb></lb>artificiali agghiacciamenti.<emph.end type="italics"></emph.end> “ Sul fondamento adunque, essi dicono, dello <lb></lb>strano passaggio, che fanno l&#039;acque e i più di tutti gli altri liquori nel con­<lb></lb>gelare, non è mancato chi creda che, dove il freddo lavora colà nelle sue <lb></lb>miniere co&#039;materiali più proprii, arrivi a condizionare le acque purissime a <lb></lb>ricever così fatta tempera, che e&#039;le formi eziandio in rocche durissime di <lb></lb>cristalli, ed in gioie di varii colori, secondo la varia tintura che possono dar <lb></lb>loro i fumi de&#039;minerali vicini, e sino arrivino all&#039;invincibil saldezza dello <lb></lb>stesso diamante. </s>

<s>E Platone fu di questo parere, che da&#039;rimasugli delle acque, <lb></lb>ond&#039;ei credeva nel segreto della Terra crearsi l&#039;oro, il diamante s&#039;ingene­<lb></lb>rasse, che perciò nel Timeo ramo dell&#039;oro vien nominato il diamante da <lb></lb>quel divino Filosofo ” (Saggi di nat. </s>

<s>esp. </s>

<s>cit., pag. </s>

<s>78). </s></p><p type="main">

<s>In un libro, in cui sempre severamente s&#039;osserva il precetto di non <lb></lb>riferir se non ciò che resulta manifesto per l&#039;esperienza, fa gran maraviglia <lb></lb>quest&#039;ossequioso trattenimento intorno a un platonico concetto, che doveva <lb></lb>allo squisito senso de&#039;nostri Accademici scoprirsi alieno dal vero sperimen­<lb></lb>tale. </s>

<s>La maraviglia però scema per una parte, e cresce per l&#039;altra a chi <lb></lb>senta annunziarsi all&#039;orecchio che la Cristallografia, allora quasi sconosciuta, <lb></lb>ebbe nell&#039;ultimo periodo di quella stessa Accademia, nella quale erano state <lb></lb>già scritte le sopra riferite parole, la sua principale e più intensa cultura. </s>

<s><lb></lb>Lo Stenone infatti rivoltosi, in mezzo allo studio de&#039;cristalli, di cui più qua <lb></lb>narreremo i progressi, a ricercar la loro origine rimasta lungamente così <lb></lb>controversa, fu primo a riconoscerla simile a quella de&#039;sali, formulando così <lb></lb>in questa proposizione la sua sentenza: “ fluidum, in quo crystallus con­<lb></lb>crescit, eodem modo se habet ad crystallum, quomodo aqua comunis se habet <lb></lb>ad salia ” (Prodromus cit, pag. </s>

<s>45). </s></p><p type="main">

<s>Si può facilmente provar questa proposizione, dice l&#039;Autore, da ciò che <lb></lb>nelle concrezioni i cristalli e i sali hanno di comune, ma per non divagar <lb></lb>da que&#039;termini prescritti a un Prodromo, pensa di ridur tutte le prove nella <lb></lb>descrizione della seguente, che a lui par bellissima osservazione sperimen­<lb></lb>tale; “ experimentum recitabo, quod mihi perpulchrum visum est: In eo­<lb></lb>dem lapide variis in locis recedentes ab invicem lamellae eius crystallis ple­<lb></lb>nae erant, quarum nonnullae aqueae, aliae lucidissimae, quaedam albae, <lb></lb>multae amethistinae erant, sibi invicem immixtae sine ulla colorum cenfu­<lb></lb>sione, eodem omnino modo quo vitriolum et alumen in eadem aqua disso­<lb></lb>luta, post consumptam aquae partem, seorsim c<gap></gap>ncrevisse singula, absque <lb></lb>ulla partium miscela, hic facta salium experimenta demonstrant ” (ibid.). </s></p><p type="main">

<s>Dimostravano cioè, secondo lo Stenone, questi esperimenti che l&#039;acqua <lb></lb>non è la genitrice immediata dei cristalli, quasi ch&#039;ella presti a loro della <lb></lb>sua propria costanza, ma è solo il mestruo del succo lapideo, che si depone <lb></lb>in forme regolari, come, sciolti prima nell&#039;acqua stessa, vi si vedono deporre <lb></lb>allo stesso modo i varii sali. </s>

<s>Così con questa generosa rivendicazione del <lb></lb>vero un Accademico del Cimento emendava i falli de&#039;suoi predecessori, ma <pb xlink:href="020/01/1719.jpg" pagenum="594"></pb>infelicemente sparsa la sua voce al vento rimase intera, specialmente negli <lb></lb>stranieri, la ragion delle accuse, che il Boerhaave avventò contro i Nostri <lb></lb>sanguinosissime, mettendoli alla pari con Paracelso. </s></p><p type="main">

<s>Agli stillicidii pietrificanti del Bartholin i seguaci dell&#039;antica ipotesi pli­<lb></lb>niana erano venuti via via, per salvarla, ad aggiungere nuovi argomenti, <lb></lb>opportunamente suggeriti a loro dall&#039;esperienze dei salci e delle zucche nu­<lb></lb>trite di sola acqua, secondo le descrizioni dell&#039;Helmont e del Boyle. </s>

<s>Nè a <lb></lb>ciò solo contenti, entrarono nel campo della Chimica ad additare agl&#039;incre­<lb></lb>duli, nelle acque mescolate alle distillazioni, il principio generatore degli olii. </s>

<s><lb></lb>Fu ciò che dette occasione al Boerhaave d&#039;inveire contro l&#039;ignoranza di co­<lb></lb>storo e di tutti gli altri, che dicevano trar da sola l&#039;acqua tutti i corpi sen­<lb></lb>sibili la necessaria materia ai loro nascimenti. </s>

<s>“ Attamen etiam cavendi hic <lb></lb>errores sunt, quoniam praememorata iam et alia quaedam suscitaverunt opi­<lb></lb>nionem inter Chemicos ac si aqua sola materies foret unde corpora sensi­<lb></lb>bilia cuncta nascerentur. </s>

<s>Fuerunt enim qui scripsere inter principes Chemi­<lb></lb>cos quod aqua, gelu primo defaecatissima reddita, per longum tempus, deinde <lb></lb>autem nunquam regelascens, sed semper sensim increscente frigore constricta, <lb></lb>densata, ponderosior reddita, tandem in veram crystallum montanam transi­<lb></lb>ret. </s>

<s>Quin id narrant audacter in montibus Helvetiorum glacialibus, ad pla­<lb></lb>gas horum boreales, ubi regelascens nunquam per saecula glacies ita tran­<lb></lb>sformari dicitur: de quibus Paracelsus atque Academia Cimentina videantur ” <lb></lb>(Elementa Chemiae, T. I, Lugd. </s>

<s>Batav. </s>

<s>1732, pag. </s>

<s>593). </s></p><p type="main">

<s>La scoperta poi fattasi che il ghiaccio non è capace di ricevere ulte­<lb></lb>rior grado di freddo, ma inalterabilmente si rimane, per qualunque tempo <lb></lb>e in qualunque ambiente, sempre nel medesimo stato, finì per toglier via <lb></lb>dalle menti l&#039;errore. </s>

<s>Martin Kaehler, uno de&#039;Linneidi upsaliensi, lesse in­<lb></lb>nanzi all&#039;illustre Preside, il dì 22 Dicembre 1747, una dissertazione intito­<lb></lb>lata <emph type="italics"></emph>Crystallorum generatio,<emph.end type="italics"></emph.end> la quale valse con la Chimica del Boerhaave <lb></lb>a diffondere nella scienza la verità delle dottrine stenoniane, concludendo, <lb></lb>anche il Medico linneano, la generazione de&#039;cristalli lapidei da questi due <lb></lb>prestabiliti principii: “ I. </s>

<s>Quod crystallissatio salibus competit, nullique cor­<lb></lb>pori quantum novimus alii. </s>

<s>II. </s>

<s>Quod omnis crystallissatio fit in aqua ” (Amoe­<lb></lb>nitates acad. </s>

<s>cit., pag. </s>

<s>438). </s></p><p type="main">

<s>La dottrina dello Stenone però che cioè ogni cristallizzazione si faccia <lb></lb>nell&#039;acqua, o per <emph type="italics"></emph>via umida,<emph.end type="italics"></emph.end> era una conseguenza di quel predominio che <lb></lb>egli dava all&#039;efficienza nettunica. </s>

<s>Lazzero Moro invece, il quale non ricono­<lb></lb>sceva altra efficienza geologica, che la vulcanica, fu primo ad ammettere la <lb></lb>generazion naturale dei cristalli per quella, che si suol dire <emph type="italics"></emph>via secca,<emph.end type="italics"></emph.end> ap­<lb></lb>poggiandosi alle proprie teorie e a certe esperienze intorno ai cristalli arti­<lb></lb>ficialmente ottenuti per via di fusione, che aveva allora lette nell&#039;ottavo <lb></lb>tomo del Giornale dei Letterati d&#039;Italia. </s>

<s>Nel cap. </s>

<s>XII del II libro <emph type="italics"></emph>De&#039;cro­<lb></lb>stacei<emph.end type="italics"></emph.end> il fatto osservato e descritto dal Vallisnieri, che cioè negli strati lapi­<lb></lb>pei dei monti si ammirano cristalli e cristalloidi, è così dallo stesso Lazzero <lb></lb>Moro spiegato, applicandovi il suo sistema: “ Si sa che un cocentissimo fuoco <pb xlink:href="020/01/1720.jpg" pagenum="595"></pb>ha forza di molte materie convertire in cristallo, il perchè, sendo veemen­<lb></lb>tissimo il fuoco che nelle viscere della terra si nutre, non è fuor di ragione <lb></lb>attribuire al medesimo la formazione di quei cristalli, che negli accennati <lb></lb>strati si ammirano “ (pag. </s>

<s>277, 78). </s></p><p type="main">

<s>Così la verace dottrina della generazion de&#039;cristalli, sia per soluzione, <lb></lb>sia per fusione, trionfò all&#039;ultimo sopra l&#039;errore, che avea lungamente sog­<lb></lb>giogati gl&#039;ingegni, ai quali proponevasi nulladimeno a risolvere un altro <lb></lb>problema concernente la ragione di quelle forme geometriche, secondo le <lb></lb>quali si vede sempre assettarsi la cristallizzabile materia, o stemperata in un <lb></lb>liquido o risoluta dal fuoco. </s>

<s>I lunghi e faticosi studi, intrapresi per riuscire <lb></lb>al difficile intento, forniscono il soggetto a un importantissima storia, a cui <lb></lb>servire essendo i documenti di qualità diversa siam costretti a distinguerli <lb></lb>in acroamatici e in esoterici. </s>

<s>Riponiamo fra&#039;primi non quelli soli, che rima­<lb></lb>sero manoscritti, ma quegli altri eziandio, che manoscritti andarono prima <lb></lb>attorno, e poi furono dati alle stampe, come la Storia naturale dell&#039;Impe­<lb></lb>rato, e la Metalloteca del Mercati; e riponiamo pure in quell&#039;ordine quei <lb></lb>documenti storici, ch&#039;essendo usciti in pubblico infino dalle loro origini, <lb></lb>qual sarebbe il Prodromo dello Stenone, rimasero come luce riverberata in <lb></lb>sè stessa dalle opache pareti della chiusa lanterna. </s>

<s>Toccheremo con brevità <lb></lb>questa prima storia, che appartien tutta all&#039;Italia, e più propriamente alla <lb></lb>Toscana, per passar poi ad accennare a quell&#039;altra, che si diffonde in più <lb></lb>ampio teatro, e che rende visibile il suo progresso, come raggio di luce che <lb></lb>si veda per gli aperti spazii rifletter da specchio a specchio. </s></p><p type="main">

<s>Quel Torricelli, che instituiva in Firenze nelle sale medicee la Fisica <lb></lb>sperimentale, trovando ne&#039;varii soggetti naturali fecondo campo, ed eserci­<lb></lb>zio degno a&#039;suoi studii, non lasciò indietro di considerare i cristalli. </s>

<s>Geome­<lb></lb>tra eccellentissimo e discepolo di Galileo, ch&#039;era solito dire aver la Natura <lb></lb>scritto il suo libro con caratteri geometrici, non vide meglio che nelle figure <lb></lb>cristalline questi stessi caratteri espressi, ond&#039;è che, sentitosi potentemente <lb></lb>allettare verso quelli l&#039;ingegno, si volse ad interpetrarli con gli esercizi del­<lb></lb>l&#039;arte. </s>

<s>I minerali, che più di frequente gli erano occorsi ad esaminare col <lb></lb>Microscopio della perlina, di cui, come si sa, egli fu l&#039;inventore e l&#039;arte­<lb></lb>fice; ridotti in minime particelle, trovò configurati in cubi, in ottaedri e in <lb></lb>dodecaedri. </s>

<s>E perchè nella successione di queste forme gli parve un passar <lb></lb>dal semplice al composto, volle nell&#039;arte sua geometrica ritrovar le ragioni <lb></lb>e gli ordini di un tal passaggio. </s>

<s>Così gli vennero facilmente dimostrate va­<lb></lb>rie proposizioni intorno ai solidi poliedri inscritti e circoscritti, lusingato da <lb></lb>una dolce speranza, e da un geloso desiderio che fossero nuove. </s>

<s>Non assi­<lb></lb>curandosene però, volle trepidamente interrogar del fatto Michelangiolo Ricci, <lb></lb>a cui inviava da Firenze le dette geometriche dimostrazioni, insieme con la <lb></lb>notizia di ciò, che aveva nuovamente osservato intorno alle forme cristalline <lb></lb>di alcuni minerali, come del sale ridotto in parallelepipedi, e della marche­<lb></lb>sita in dodecaedri. </s>

<s>Il Ricci così, il dì 13 Agosto del 1645, rispondeva da <lb></lb>Roma al riverito maestro, e al carissimo amico: </s></p><pb xlink:href="020/01/1721.jpg" pagenum="596"></pb><p type="main">

<s>“ Sono piaciute assaissimo le proposizioni degl&#039;inscritti e circoscritti, <lb></lb>ottaedri, dodecaedri, cubi, ecc., e poichè ella pare che nella sua mi accenni <lb></lb>che le fosse grato di sapere se altri abbia preoccupato il luogo di primo in­<lb></lb>ventor di quelle, rispondo che l&#039;abate Maurolico ha considerate le medesime <lb></lb>cose in tutti i casi possibili, con particolar brevità. </s>

<s>E per darne a V. S. <lb></lb>qualche saggio, dell&#039;iscrizione dell&#039;ottaedro nel cubo, così dice: <emph type="italics"></emph>coniunge <lb></lb>sex basium cubi centra per duodecim rectas, quae quidem inclusum octae­<lb></lb>drum configurabimus.<emph.end type="italics"></emph.end> E volendo iscrivere il cubo nell&#039;ottaedro, così dice: <lb></lb><emph type="italics"></emph>octo triangulorum centra continua per duodecim lineas, quippe quae et <lb></lb>latera inclusi cubi erunt.<emph.end type="italics"></emph.end> Quanto alle osservazioni poi del sale ridotto in <lb></lb>parallelepipedi, e alle marchesite in dodecaedri per opera di natura, delle <lb></lb>prime mi ricordo averne fatta osservazione molti anni sono. </s>

<s>Mi dice il signor <lb></lb>Antonio che nell&#039;Istoria naturale di Ferrante Imperato vi si contengono rare <lb></lb>forme e stravaganti di varie pietre e minerali, dove trovansi ancora soggetti <lb></lb>per altre bellissime considerazioni ” (MSS. Gal. </s>

<s>Disc., T. XLII, c. </s>

<s>146, 47). </s></p><p type="main">

<s>Quel signor Antonio, a cui il Ricci qui accenna, è l&#039;aretino Nardi, au­<lb></lb>tore delle <emph type="italics"></emph>Scene accademiche,<emph.end type="italics"></emph.end> in una delle quali fa delle Storie naturali <lb></lb>dell&#039;Imperato, vedute da lui manoscritte, quell&#039;elogio che i nostri lettori al­<lb></lb>trove hanno inteso. </s>

<s>La notizia data da Antonio Nardi relativa alle descrizioni <lb></lb>de&#039;cristalli, che si potevano leggere nell&#039;opera manoscritta, faceva risalire a <lb></lb>un mezzo secolo innanzi quelle osservazioni, alle quali come nuovo si cre­<lb></lb>deva d&#039;essere entrato il Torricelli, e il giudizio dello stesso Nardi, dianzi ri­<lb></lb>ferito dal Ricci, era giustamente fondato sopra ciò, che aveva letto nel li­<lb></lb>bro XXIV delle dette Storie naturali, ai capitoli II, III e IV, dove intorno <lb></lb>alle cristallizzazioni, o agl&#039;<emph type="italics"></emph>ingemmamenti,<emph.end type="italics"></emph.end> come gli chiama l&#039;Autore, si leg­<lb></lb>gono cose nuove per que&#039;tempi, e tuttavia notabili per i nostri. </s></p><p type="main">

<s>Nel secondo di que&#039;capitoli ora detti intitolato <emph type="italics"></emph>Varietà di figure negli <lb></lb>ingemmamenti,<emph.end type="italics"></emph.end> “ dunque nelle dette spezie, si legge, come anco in altre <lb></lb>differenze di pietre si veggono determinate maniere di consistenza e di figura, <lb></lb>e altre sono in figura di dado, come una spezie di marchesita, e il topazio <lb></lb>d&#039;Alemagna, che se ne veggono molti ingemmamenti accostati insieme, per­<lb></lb>ciocchè ciascun di essi è in forma di cubo, di cui un angolo affonda nella <lb></lb>madre, come radice nella terra. </s>

<s>Altre sono in forma dodecaedra, che è il <lb></lb>corpo composto di superfice cinquangole, qual&#039;è l&#039;ingemmamento dello sta­<lb></lb>gno, ed una spezie di marchesita. </s>

<s>Altre sono in forma di colonnetta, che nel <lb></lb>suo fine s&#039;appunta, come alcune spezie di cristalli; altri in forme pirami­<lb></lb>dali ” (Venezia 1672, pag. </s>

<s>558, 59). </s></p><p type="main">

<s>Nel capitolo III, intitolato <emph type="italics"></emph>Cristallo e figure diverse cristalline,<emph.end type="italics"></emph.end> il no­<lb></lb>stro Autore, in mezzo alla predominante ipotesi pliniana, così scrive della <lb></lb>natura e dell&#039;origine dei cristalli: “ Il cristallo è spezie d&#039;ingemmamento <lb></lb>duro, di chiarezza e trasparenza perfetta, simile nell&#039;effigie ad acqua agghiac­<lb></lb>ciata, limpida. </s>

<s>Si apprende in gemme nell&#039;umor petrigno, non altrimenti che <lb></lb>gli zuccheri e sali negli umori della lor sostanza partecipi: s&#039;ingemma e <lb></lb>vegeta in figura seangola ” (ivi, pag. </s>

<s>559). </s></p><pb xlink:href="020/01/1722.jpg" pagenum="597"></pb><p type="main">

<s>Se in questo capitolo dice l&#039;Imperato cose, che porgerebbero secondo <lb></lb>il Nardi <emph type="italics"></emph>soggetto per altre bellissime considerazioni,<emph.end type="italics"></emph.end> nel seguente cap. </s>

<s>IV <lb></lb>descrive quelle <emph type="italics"></emph>Forme cristalline diverse,<emph.end type="italics"></emph.end> che al Nardi stesso parvero <emph type="italics"></emph>rare <lb></lb>e stravaganti.<emph.end type="italics"></emph.end> “ Sono altre spezie cristalline tra le quali l&#039;una è che, con <lb></lb>la fattezza e progresso delle punte, rassembra un riccio marino, di cui cia­<lb></lb>scun raggio è in forma di colonnetta seangola, che nel suo fine s&#039;appunta: <lb></lb>nasce nelli sassi delle vene piombine. </s>

<s>Simili alli raggi detti si ritrovano altri <lb></lb>ingemmamenti di lunghezza e grossezza, che giungono al dito umano, in <lb></lb>figura seangola, che nello stremo s&#039;appunta, ed avviene che ad una colon­<lb></lb>netta maggiore s&#039;attacchino alle volte d&#039;intorno molte colonnette minori. </s>

<s><lb></lb>Sono dette colonnette di trasparenza e chiarezza notabili ... Oltre delle dette <lb></lb>sono le forme olivari, con numero di sei facce e grossezza delle colonnette <lb></lb>dette, ma diverse nell&#039;essere dall&#039;una e l&#039;altra parte appuntate nel modo di <lb></lb>nocciolo.... Vi sono altre forme cristalline, tra le quali è l&#039;ingemmamento <lb></lb>in forma di pigna, perciocchè, siccome nel frutto pineo nascono dal torso <lb></lb>di mezzo le squame ristrette insieme nelli piccoli, ed ingrossan di mano in <lb></lb>mano sinchè vengano nelli nodi apparenti; nell&#039;istesso modo li rai di questa <lb></lb>spezie cristallina si partono da principii ristretti, ingrossandosi fino alla prima <lb></lb>parte apparente, ove si distingue la loro forma seangola, ed indi finalmente si <lb></lb>appuntano in forma piramidata nell&#039;istesso numero di facce ” (ivi, pag. </s>

<s>560). </s></p><p type="main">

<s>Quando nel 1668 lo Stenone, in appendice alla descrizione anatomica <lb></lb>del capo della Carcaria, avea avanzate quelle sue prime congetture geologi­<lb></lb>che, per le quali veniva ad iniziarsi nell&#039;Accademia fiorentina una nuova <lb></lb>scienza intorno alla struttura superficiale della terra, e alle produzioni mi­<lb></lb>neralogiche di lei, nè ancora erano alla pubblica notizia queste cose scritte <lb></lb>dall&#039;Imperato intorno alla natura e alle forme de&#039;cristalli; il cardinale Leo­<lb></lb>poldo, che aveva di così fatte carte manoscritte procurato diligente raccolta, <lb></lb>rileggendo un giorno la sopra citata lettera del Ricci mostrò alla presenza <lb></lb>del Viviani, dello Stenone e del Dati, una vivissima curiosità di sapere quel <lb></lb>che nelle sue Storie avesse scritto, in quel soggetto così lodato dal Nardi, <lb></lb>lo sconosciuto Naturalista napoletano. </s>

<s>Allora il Dati, ch&#039;era stato generoso <lb></lb>d&#039;offerire allo Stenone, accademico collega suo, inciso in rame il capo della <lb></lb>Lamia, disse che, fra gl&#039;iconismi illustrativi della medesima Metalloteca va­<lb></lb>ticana, n&#039;erano parecchi altri rappresentanti variatissime figure di minerali, <lb></lb>benchè avesse l&#039;Autore lasciato di descriverle, forse perchè non ebbe tempo <lb></lb>di dar perfezione all&#039;ultimo Armario, a cui si dovevano riferir senza dub­<lb></lb>bio quegli stessi iconismi. </s>

<s>Entrati a questa notizia col cardinale Leopoldo, <lb></lb>lo Stenone e il Viviani in gran desiderio di vederli, il Dati stesso presentò <lb></lb>nell&#039;Accademia que&#039;cinque bellissimi rami incisi, e le impressioni de&#039;quali <lb></lb>posson ora tutti vedere eseguite da pag. </s>

<s>372-77 dell&#039;ediziòne dell&#039;opera del <lb></lb>Mercati, con tanto amore e con tanta scienza curata dal Lancisi. </s></p><p type="main">

<s>A pagina 372 è rappresentata una figura cristallina ottaedrica, la quale <lb></lb>grandeggia scolpita in mezzo ad altre più piccole isomorfe, incise nel me­<lb></lb>desimo rame, a illustrare la qual figura il Lancisi stesso così scrive in nota: <pb xlink:href="020/01/1723.jpg" pagenum="598"></pb>“ Figura haec adamussim exprimit formam aluminis octaedricam, quam <lb></lb>Auctor fortasse, postquam librum hunc conscripsisset, oblata occasione obser­<lb></lb>vavit, atque proinde incidendam curavit, ideo nihil mirum si in capite <emph type="italics"></emph>De <lb></lb>alumine<emph.end type="italics"></emph.end> huic iconi spatium non reliquerit. </s>

<s>” A pag. </s>

<s>374, nel rame su cui <lb></lb>furono incise varie forme cristalline appartenenti a varie specie di minerali, <lb></lb>tutti però di un medesimo tipo, è sotto scolpita l&#039;iscrizione <emph type="italics"></emph>Lapis multan­<lb></lb>gulus<emph.end type="italics"></emph.end> e <emph type="italics"></emph>Lapis crystallinus <foreign lang="grc">πολυεξαγο<gap></gap>ω</foreign>;<emph.end type="italics"></emph.end> son le parole che si leggono scolpite <lb></lb>sotto l&#039;altro rame impresso a pag. </s>

<s>376 rappresentante un bellissimo gruppo <lb></lb>di cristalli simili a quel topazio di Alemagna, di cui diceva l&#039;Imperato <emph type="italics"></emph>ve­<lb></lb>dersi molti ingemmamenti accostati insieme, perciocchè ciascuno di essi è <lb></lb>in forma di cubo, di cui un angolo affonda nella madre, come radice <lb></lb>nella terra.<emph.end type="italics"></emph.end> A pag. </s>

<s>377 un altro rame rappresenta varie modificazioni delle <lb></lb>figure di quel cristallo “ qui componitur, secondo ch&#039;esprimesi lo Stencne, <lb></lb>ex duabus pyramidibus hexagonis, et columna intermedia itidem hesagona ” <lb></lb>(Prodromus cit., pag. </s>

<s>37). Il Mercati lo chiama <emph type="italics"></emph>Lapis diconus,<emph.end type="italics"></emph.end> e il Lancisi <lb></lb>appone in nota: “ Qui hic lapis diconus a Mercato inscribitur extat apud <lb></lb>Imperatum nomine <emph type="italics"></emph>Ingemmamenti cristallini olivari ed appuntati in ambo <lb></lb>le parti. </s>

<s>”<emph.end type="italics"></emph.end> L&#039;ultimo iconismo cristallografico Vaticano ricorre nella medesima <lb></lb>pagina sotto il precedente, e nello stesso rame è fatta incidere l&#039;iscrizione: <lb></lb><emph type="italics"></emph>Adamantes sponte Naturae formati.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>A tal vista e a tali presentissimi esempi della geometrizzante Natura il <lb></lb>Viviani e lo Stenone si sentirono nascere un desiderio vivissimo di quelli <lb></lb>studii, a cui le parole del cardinale Leopoldo venivano ad aggiungere sti­<lb></lb>moli potentissimi. </s>

<s>Degli esercizi cristallografici del primo non abbiamo altro <lb></lb>documento che in qualche notarella manoscritta, come per esempio sarebbe <lb></lb>questa: “ I diamanti rozzi, che si trovano in alcuni monti d&#039;Armenia ed <lb></lb>altrove, hanno tutti figura di ottaedro ” (MSS. Gal. </s>

<s>Disc., T. CXXXV, c. </s>

<s>5). <lb></lb>Ma le speculazioni del Viviani uscirono associate con quelle dello Stenone, <lb></lb>il quale, nel Prodromo <emph type="italics"></emph>De solido intra solidum naturaliter contento,<emph.end type="italics"></emph.end> sta­<lb></lb>bilì i nuovi fondamentali principii alla Cristallografia. </s></p><p type="main">

<s>Muovono le speculazioni stenoniane dal fatto che in un medesimo li­<lb></lb>quido posson formarsi cristalli di figure diverse, d&#039;onde ne conseguiva che <lb></lb>il moto della cristallizzabile materia “ quo versus iam formatae crystalli plana <lb></lb>determinantur, non oritur a communi quadam causa motus in fluido am­<lb></lb>biente, sed in qualibet crystallo mutatur ” (pag. </s>

<s>42). Le figure dunque per <lb></lb>ciascun cristallo sono prestabilite dalla Natura, e non resta a investigare alla <lb></lb>scienza se non che le ragioni e i modi, come la materia si dispone in quelle <lb></lb>date inclinazioni di linee e di piani, e s&#039;aggiunge via via allo stesso prefor­<lb></lb>mato cristallo per ridurlo al suo ordinario incremento. </s>

<s>Si riconoscono dallo <lb></lb>Stenone quelle ragioni e que&#039;modi in due speciali virtù, una delle quali dia <lb></lb>regola, e l&#039;altra impulso meccanico al moto. </s>

<s>Crede che la prima dipenda da <lb></lb>un fluido sottile, esalante dallo stesso nucleo cristallino, come quello che <lb></lb>esala dal magnete; la seconda poi da null&#039;altro pensa provenire, che dal <lb></lb>turbato equilibrio idrostatico del liquido ambiente. </s>

<s>“ In crystalli incremento <pb xlink:href="020/01/1724.jpg" pagenum="599"></pb>geminus motus considerandus est: unus quo efficitur ut certis crystalli locis <lb></lb>et non aliis apponatur materia crystallina, quem ego motum permeanti fluido <lb></lb>subtili adscribendum suspicor, et allato magnetis exemplo illustrandum; alter <lb></lb>quo apposita crystallo nova materia crystallina in planum extenditur, qui a <lb></lb>fluido ambiente determinandus est. </s>

<s>Sic ubi super magnetem exsurrexerint <lb></lb>fila ferrca, aeris motu quod ab uno decutitur alteri accedit ” (pag. </s>

<s>43, 44). </s></p><p type="main">

<s>Di qual natura sia il fluido sottile rassomigliato al magnetico, dalla po­<lb></lb>larità del quale dipendono le regolate e invariabili inclinazioni delle linee <lb></lb>e de&#039;piani cristallini, lo Stenone espressamente non dice, ma s&#039;intende esser <lb></lb>l&#039;etere, da cui faceva anche il Newton nascere l&#039;attrazione molecolare. </s>

<s>Co­<lb></lb>munque sia, crede il Nostro che per opera di quel fluido etereo si facciano <lb></lb>le rifrazioni, benchè lasci decidere la questione a ingegni più sottili. </s>

<s>“ An <lb></lb>dictum fluidum illud sit cuius ope refractio peragitur, an vero fluidum ali­<lb></lb>quod sit inde diversum, ingeniosioribus examinandum relinquo ” (pag. </s>

<s>42). </s></p><p type="main">

<s>Trasparisce di qui, come da un rado velo, la figura del Viviani, a cui <lb></lb>sempre era solito di rimettersi lo Stenone, quando troppo addentro entra­<lb></lb>vasi nelle sottigliezze geometriche. </s>

<s>Di questa causa delle rifrazioni, dipen­<lb></lb>denti da un fluido etereo, che s&#039;impola nei cristalli, ne scrisse poco dopo <lb></lb>lo stesso Viviani a Erasmo Bartholin, quando questi gli annunziò la sco­<lb></lb>perta della duplice refrazione, che subisce il raggio incidente attraverso allo <lb></lb>spato d&#039;Islanda. </s>

<s>Il Bartholin ben conobbe che nelle diottriche speculazioni <lb></lb>del Geometra fiorentino si troverebbe non difficilmente la ragione del nuovo <lb></lb>fatto spettacoloso, ond&#039;è che, a sollecitar l&#039;amico a studiar meglio la cosa, <lb></lb>dietro le più precise osservazioni riscontrate con l&#039;esperienza, gli mandava <lb></lb>a Firenze, il dì 23 Aprile del 1672, l&#039;opuscolo sull&#039;inusitata refrazione, con <lb></lb>un frustolo del cristallo che la produce. </s>

<s>“ Mitto opusculum de crystallo quo­<lb></lb>dam islandico, figurae et refractionis inusitatae, una cum frustulo eiusdem <lb></lb>crystalli, cuius phaenomena nemo te magis mirabitur, qui naturam refrac­<lb></lb>tionum optime calles ” (MSS. Gal., T. CXLV, c. </s>

<s>222). Da questo lampeg­<lb></lb>giar d&#039;idee intorno alle proprietà diottriche dei cristalli s&#039;intravede quell&#039;am­<lb></lb>pia e intensa cultura, che sarebbesi data nell&#039;Accademia del Cimento alla <lb></lb>Cristallografia, se avesse per avventura avuto effetto la divisata Dissertazione <lb></lb>stenoniana, della quale sola ci è rimasto il Prodromo. </s></p><p type="main">

<s>Proceduti fin qui, non possiamo non soffermarci a indagare i segreti <lb></lb>sentimenti, che avranno suscitato queste storie nell&#039;animo de&#039;nostri Lettori, <lb></lb>ne&#039;quali, anche Italiani, è oramai ingerita la persuasione che, fatto il prin­<lb></lb>cipe Leopoldo cardinale, si chiudessero le porte alla gloriosa Accademia. </s>

<s>In <lb></lb>ogni modo, specialmente gli stranieri, attribuiranno a uno de&#039;soliti vanti <lb></lb>esagerati il dire che la Geologia e la Cristallografia, fra gli autori delle quali <lb></lb>è un miracolo a sentire oggidì pronunziare un nome italiano, furono due <lb></lb>scienze istituite nella nostra Accademia del Cimento. </s>

<s>Ma perchè son le no­<lb></lb>stre asserzioni fondate sempre sopra documenti certissimi, non resta agli <lb></lb>oppositori a far altro, se non che a dimostrare come quegli stessi documenti <lb></lb>sono stati da noi o male intesi, o male applicati. </s></p><pb xlink:href="020/01/1725.jpg" pagenum="600"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>In tanto che la Critica (se pure la non ha da pensare ad altro che a <lb></lb>queste cose) attenderà a trovare argomenti da negare o da riformare la sto­<lb></lb>ria qui addietro da noi narrata, procedendo addiritto per le nostre vie, pas­<lb></lb>seremo a dir dell&#039;origine e dei progressi, che fece la Cristallografia fuori <lb></lb>dell&#039;Accademia del Cimento. </s>

<s>E quanto all&#039;origine, a noi par che non prima <lb></lb>distintamente apparisca che nelle pagine del Cesalpino, il quale osserva che, <lb></lb>nello scindere i corpi duri, alcune particelle escono naturalmente ordinate, <lb></lb>come in quelli che si risolvono in scaglie, altre irregolari, come avvien per <lb></lb>esempio quando si rompe un sasso a furia di colpi da una mazza di ferro. <lb></lb></s>

<s>“ Potest vero, poi soggiunge, et divisio fieri in coagulatione, dum humida <lb></lb>adhuc sunt corpora. </s>

<s>Si enim in coagulatione partes in diversa tendant, di­<lb></lb>visionem fieri necesse est, et pro divisione figuras determinatas, perinde ac <lb></lb>in exsiccatione soli palustris, scinditur enim in multas rimas, unde figurae <lb></lb>diversae contingunt. </s>

<s>Simile quid contingere putandum est in crystalli coa­<lb></lb>gulatione. </s>

<s>Succus enim lapidescens cum totum spacium impleat loci in quo <lb></lb>est, in coagulatione discedentibus in diversa partibus terrenis, et ad latera <lb></lb>saxi continentis attractis agglutinatisque, figuram quoque faciet in concretis <lb></lb>lapillis, quae apta nata sit spacium replere. </s>

<s>Si igitur non uniformiter, sed <lb></lb>vario modo divisiones contingunt, etiam varietate figurarum implebitur spa­<lb></lb>cium. </s>

<s>Si autem uniformiter, quod ob puritatem succi contingit, necesse est <lb></lb>unum genus figurae oriri in omnibus, quae apta nata sit spacium implere ” <lb></lb>(De metallicis cit., pag. </s>

<s>97, 98). </s></p><p type="main">

<s>Le figure geometriche atte nate a riempire senza vuoto intermedio uno <lb></lb>spazio, prosegue a dire il Cesalpino, son tre: il triangolo, il quadrato e l&#039;esa­<lb></lb>gono. </s>

<s>Ma perchè la concrezione di quel succo lapideo, che si suppone esser <lb></lb>purissimo, si fa per una occulta tendenza verso il centro, egli è questo stesso <lb></lb>centro troppo remoto dagli angoli di un quadrato composto di quattro altri <lb></lb>quadrati accostati insieme. </s>

<s>Dall&#039;altra parte ad accostare insieme tanti trian­<lb></lb>goli equilateri, che s&#039;appuntino essi pure in un centro comune, non viene <lb></lb>a comporsi un nuovo triangolo, ma un esagono, “ relinquitur igitur ut sola <lb></lb>hexagona fiat ” (ibid., pag. </s>

<s>98). </s></p><p type="main">

<s>Citava in proposito il nostro Peripatetico l&#039;autorità del Maestro, che <lb></lb>nel III <emph type="italics"></emph>De coelo<emph.end type="italics"></emph.end> avea così scritto: “ In planis tres figurae videntur implere <lb></lb>locum, triangulus, quadratus et sexangulus ” (Arist., Op., T. V, Venetiis 1560, <lb></lb>fol. </s>

<s>229). Ma trattandosi di una questione geometrica, si sovvennero i lettori <lb></lb>di quel che, intorno alle proprietà degl&#039;isoperimetri, aveva dimostrato, nel <lb></lb>V libro delle <emph type="italics"></emph>Collezioni matematiche,<emph.end type="italics"></emph.end> Pappo Alessandrino. </s>

<s>Nella prefazione <lb></lb>al libro, che Federigo Commandino urbinate avea divulgato in lingua latina, <lb></lb>il Matematico antico richiamava l&#039;attenzione di suo figlio Ermodoro e dei let-<pb xlink:href="020/01/1726.jpg" pagenum="601"></pb>tori sul maraviglioso artificio geometrico dei favi. </s>

<s>Crede che, avendo Dio sa­<lb></lb>pientissimo infusa l&#039;intelligenza nelle api, esse scegliessero quella struttura <lb></lb>esagonale per riuscire a due principali intenti, quali erano di riporre il miele <lb></lb>in celle della più capace figura e tale, che permettesse di accostarsi alle altre <lb></lb>simili celle, senza lasciarvi alcuno spazio vuoto intermedio, dove s&#039;avessero <lb></lb>a introdurre esseri o elementi nocivi. </s>

<s>Benchè dunque tra le figure isoperi­<lb></lb>metre la nostra scienza geometrica, dice Pappo, dimostri essere il circolo la <lb></lb>più capace di tutte, le api nulladimeno, le quali non hanno in mente altro <lb></lb>che l&#039;utilità e la fuga dai pericoli, si condussero a eseguire per matematica <lb></lb>necessità la figura esagonale. </s>

<s>“ Cum igitur tres figurae sint, quae per seipsas <lb></lb>locum circa idem punctum consistentem replere possunt, triangulum scilicet, <lb></lb>quadratum et hexagonum, apes illam quae ex pluribus angulis constat, ad <lb></lb>structuram sapienter delegerunt, utpote suspicantes eam plus mellis capere <lb></lb>quam utramque reliquarum. </s>

<s>Et apes quidem illud tantum, quod ipsis utile <lb></lb>est cognoscunt, videlicet hexagonum quadrato et triangulo esse maius, et <lb></lb>plus mellis capere posse, nimirum aequali materia in constructionem uniu­<lb></lb>scuiusque consumpta. </s>

<s>Nos vero, qui plus sapientiae quam apes hebere pro­<lb></lb>fitemur, aliquid etiam magis insigne investigabimus. </s>

<s>Figurarum enim plana­<lb></lb>rum, quae cum aequilaterae et aequiangulae sint ambitum aequalem habent, <lb></lb>ea semper maior est, quae ex pluribus angulis constat, circulus vero omnium <lb></lb>est maximus, si modo aequali ipsis ambitu comprehendatur ” (Bononiae 1660, <lb></lb>pag. </s>

<s>114). </s></p><p type="main">

<s>Queste idee applicate all&#039;ipotesi cristallogenica del Cesalpino ingerirono <lb></lb>facilmente l&#039;opinione che, infusa la Divina Sapienza come nelle api così nel <lb></lb>succo lapideo, questo nel coagularsi in cristalli, per non lasciare gli spazii <lb></lb>vuoti e per adattarsi in luogo della maggior possibile capacità, fosse neces­<lb></lb>sariamente condotto a prendere struttura esagonale. </s></p><p type="main">

<s>Eran tali le meno irragionevoli dottrine professate intorno alla Cristal­<lb></lb>lografia, sui principii del secolo XVII, quando il Keplero scoprì quella me­<lb></lb>desima struttura esagonale ne&#039;fiocchi della neve. </s>

<s>La cosa apparve nuova e <lb></lb>inaspettata, perchè lo stesso Cesalpino aveva giusto negato essere i cristalli <lb></lb>acqua congelata, fra le altre, principalmente per questa ragione, perchè il <lb></lb>ghiaccio non piglia mai figura sessangolare “ sed figuram conservat vel con­<lb></lb>tinentis corporis vel rotundam, aut fortuitam, qualis est in gutta cum in <lb></lb>grandinem congelatur ” (De met. </s>

<s>cit., pag. </s>

<s>96). </s></p><p type="main">

<s>È notabile, ci permettano i lettori la breve digressione, che ottantun&#039;anno <lb></lb>dopo il Keplero Gian Domenico Cassini si credesse di essere stato il primo <lb></lb>ad osservare un&#039;altra cosa nuova e inaspettata nelle figure della neve, ma <lb></lb>è ben assai più notabile che fosse la novità accolta, e come tale divulgata <lb></lb>dall&#039;Accademia parigina. </s>

<s>“ Il y a long-tems que l&#039;on sçait que la neige est <lb></lb>exagone: mais on n&#039;avoit peut être point encore observé que les six rayons <lb></lb>dont chaque floccon est composé, sont souvent comme autant de petites <lb></lb>branches garnies de fevilles, et que quelques floccons forment comme une <lb></lb>espece de fleur. </s>

<s>Ce que M. </s>

<s>Cassini a remarqué en considerant avec un mi-<pb xlink:href="020/01/1727.jpg" pagenum="602"></pb>croscope la neige, qui tomba le premier jour de ce mois (Fevrier 1692). Il <lb></lb>ne se trouve pas ici assez de place pour en faire la description, mais les <lb></lb>deux figures, que l&#039;on en donne, feront comprendre tout d&#039;un coup ce qu&#039;un <lb></lb>long discours ne pourroit peut-ètre pas si bien expliquer ” (Collection academ., <lb></lb>T. I, a Djion 1754, pag. </s>

<s>261, 62). Le due accademiche figure però non giun­<lb></lb>sero per nulla nuove a chi, infin dal 1661, ne avea vedute elegantemente <lb></lb>impresse ben sei di quelle medesime stelle piumate o di quelle rosette fio­<lb></lb>rite nella tavola che precede al trattato <emph type="italics"></emph>De figura nivis<emph.end type="italics"></emph.end> di Erasmo Bartho­<lb></lb>lin. </s>

<s>Ma più s&#039;ebbero a maravigliare della nuova proposta coloro, che nello <lb></lb>schematismo VIII della Micrografia dell&#039;Hook, pubblicata nel 1665, s&#039;erano <lb></lb>trattenuti a contemplare il maraviglioso spettacolo di quelle ventotto e più <lb></lb>figure, rappresentanti in vario modo la neve nelle sue stelle cristalline e <lb></lb>ne&#039;fiori. </s></p><p type="main">

<s>Il Keplero, che non aveva allora i necessarii diottrici strumenti, non <lb></lb>giunse a penetrare una così sottile e complicata struttura, tutto intento dal­<lb></lb>l&#039;altra parte ad usar le sottigliezze del suo ingegno geometrico in ricercar <lb></lb>l&#039;origine nella neve di que&#039;sei perfettissimi raggi di stella, sufficienti per sè <lb></lb>soli ad eccitare ne&#039;contemplanti la maraviglia. </s>

<s>Le correnti opinioni, che si <lb></lb>diceva di sopra, gli fecero prima rivolgere il pensiero agli apiarii, ma la ra­<lb></lb>gione che s&#039;adduceva dalla geometria di Pappo non sembravagli concludente, <lb></lb>perchè diceva che, se gl&#039;industriosi insetti avessero voluto veramente eleg­<lb></lb>gere le celle più capaci, sarebbero dovuti andare a formarle circolari, senza <lb></lb>badar tanto all&#039;economia dello spazio, quasi che in tutto l&#039;alveare non ne <lb></lb>rimanesse altro che quello. </s>

<s>“ Sed non sufficit haec ratio, nam si capacita­<lb></lb>tem quaerunt, cur non quaelibet sibi rotumdum fingit nidum? </s>

<s>quid opus <lb></lb>est minutias loci consectari, quasi nullum in toto alveari restet spacium? </s>

<s>” <lb></lb>(De nive sexangula, Francofurti 1611, pag. </s>

<s>11). </s></p><p type="main">

<s>Si presentavano, insieme con questo delle api, a considerare al Keplero <lb></lb>altri simili esempi, come quello de&#039;grani chiusi nelle mele granate che tutti <lb></lb>si trovano anch&#039;essi in figura di poliedri regolari. </s>

<s>Parendo inconveniente <lb></lb>agli alberi un&#039;anima, come una intelligenza alle api, fu anzi questo secondo <lb></lb>fatto, riconosciuto aver la sua causa nella compressione, che crescendo si <lb></lb>fanno gli stessi grani, rinchiusi nella mela, a vicenda; fu questo fatto di­<lb></lb>ciamo che indusse esso Keplero ad attribuire a una simile compressione la <lb></lb>figura esagonale, che vengono a prendere le celle ceree de&#039;favi, sostituendo <lb></lb>nell&#039;un caso e nell&#039;altro alla elezion della mente un ceca necessità della ma­<lb></lb>teria. </s>

<s>“ Has igitur rationes materialem necessitatem respicientes puto suffi­<lb></lb>cere ut hoc loco non existimem philosophandum de perfectione et pulchri­<lb></lb>tudine, vel nobilitate figurae rhombicae, neque satagendum ut esseutia ani­<lb></lb>mulae, quae est in ape, ex contemplatione figurae quam fabricatur, eliciatur. </s>

<s><lb></lb>Idem de malo punico intelligendum. </s>

<s>Apparet necessitas materialis, quae <lb></lb>acinos producit ad rhombicum succedente incremento. </s>

<s>Itaque vanum est de <lb></lb>essentia animae in hac arbore cogitare, quae rhombicum potissimum effi­<lb></lb>ciat ” (ibid.). </s></p><pb xlink:href="020/01/1728.jpg" pagenum="603"></pb><p type="main">

<s>Dagli alveari e dai pomi granati passando al propostosi soggetto, do­<lb></lb>mandava a sè medesimo il Keplero se a una simile necessità materiale si <lb></lb>dovessero attribuir le figure impresse nella neve. </s>

<s>Si risovvenne, in mezzo a <lb></lb>queste dubbiose ricerche, di quel che aveva sentito dire ad alcuni gioiellieri, <lb></lb>che cioè si trovano i diamanti naturalmente lavorati in forma di perfettis­<lb></lb>simo ottaedro. </s>

<s>Se ciò fosse vero, così ragionava, non sarebbe improbabile il <lb></lb>credere che fosse impressa nel vapore salito dalla terra una figura regolare, <lb></lb>simile a quella che impresse sottoterra al diamante, ricavandola dal suo fe­<lb></lb>condissimo seno, la formatrice Natura. </s>

<s>“ Aiunt gemmarii naturalia in ada­<lb></lb>mantibus inveniri octaedra perfectissimae et limatissimae formae. </s>

<s>Id si est, <lb></lb>multum nos confirmat. </s>

<s>Nam facultas animalis, quae in terra indidit adamanti <lb></lb>formam octaedri, ex penitissimo sinu suae naturae depromptam, eadem cum <lb></lb>vapore progressa de terra figuram eamdem indidit, et nivi ex vapore illo <lb></lb>consistenti ” (ibid., pag. </s>

<s>20). </s></p><p type="main">

<s>Parendogli più ragionevole questa seconda ipotesi, volle il Keplero pa­<lb></lb>ragonarla più diligentemente con quella prima, e riconoscendo la debolezza <lb></lb>degli argomenti dedotti dalle figure geometriche, atte a riempire uno spazio, <lb></lb>per non rendersi chiara la ragione del doversi al triangolo e al quadrato <lb></lb>preferire l&#039;esagono; e non potendosi persuadere perchè s&#039;avesse dagli iso­<lb></lb>perimetri a escludere in ogni modo il circolo, inclinò a credere che la figura <lb></lb>stellata della neve, come quella de&#039;cristalli, non dipendesse da necessità della <lb></lb>materia, ma che piuttosto risultasse tale e non altra perchè “ ipsa huius <lb></lb>formatricis natura in intimo sinu suae essentiae particeps est sexanguli ” <lb></lb>(ibid., pag. </s>

<s>22), </s></p><p type="main">

<s>Quella stessa Natura però, che è così esperta ed esercitata della Geo­<lb></lb>metria, non si restringe a una forma sola, com&#039;è la sessangolare impressa <lb></lb>nella neve e l&#039;ottaedrica nel diamante, ma varia il suo lavoro passando ad <lb></lb>altre forme, come alla dodecaedra e alla icosaedra, in ch&#039;io vidi, dice il <lb></lb>Keplero, configurati alcuni esempi di minerali, visitando il Museo di Dresda. <lb></lb></s>

<s>“ Itaque verisimile est hanc facultatem formatricem pro diverso humore di­<lb></lb>versam fieri ” (ibid., pag. </s>

<s>24). Concludendo poi il discorso per quel che <lb></lb>più particolarmente concerne la neve, si rivolge ai Chimici, per proporre a <lb></lb>loro il quesito se forse anche in essa neve ritrovisi qualche sale, che la in­<lb></lb>formi e la renda partecipe della sua propria figura. </s>

<s>“ Dicant igitur Chymici <lb></lb>an in nive sit aliquid salis, et quodnam salis genus, et quam illud alias in­<lb></lb>duat figuram ” (ibid.). </s></p><p type="main">

<s>Così, intorno all&#039;origine delle figure cristalline, proponeva il Keplero <lb></lb>due ipotesi: una che riconosceva quella stessa origine dalla necessità della <lb></lb>materia, e l&#039;altra che attribuiva il fatto all&#039;essere le particelle materiali già <lb></lb>preformate in tale o tale altro modo dalle stesse mani geometrizzanti della <lb></lb>Natura. </s>

<s>Inclinava il Keplero stesso, com&#039;abbiamo udito, a questa seconda <lb></lb>ipotesi, ma lasciava la decisione ai dotti, ch&#039;ei comprendeva tutti nella per­<lb></lb>sona di quel Giovan Matteo Wacker, a cui particolarmente, in trattar <emph type="italics"></emph>De <lb></lb>nive sexangula,<emph.end type="italics"></emph.end> rivolgeva il discorso. </s></p><pb xlink:href="020/01/1729.jpg" pagenum="604"></pb><p type="main">

<s>Uno de&#039;principali fra que&#039;dotti, che tornarono sull&#039;argomento, fu nel <lb></lb>suo libro delle Meteore il Cartesio, il quale si sentì dal proprio genio por­<lb></lb>tato a scegliere la prima ipotesi, perchè la seconda non lasciava gran campo <lb></lb>aperto ai giochi e alle arguzie dell&#039;ingegno. </s>

<s>Dop&#039;aver trovata e detta la ra­<lb></lb>gione del mutare apparenza, che fanno i sei denti o le appuntate fila, delle <lb></lb>quali ogni globulo di neve s&#039;irraggia, “ aegre tantummodo, poi soggiunge, <lb></lb>poteram coniiciere quidnam in aere libero turbantibus ventis adeo accurate <lb></lb>hos sex dentes formare, et circa singula grana disponere potuisset, donec <lb></lb>tandem in mentem venit facillime fieri potuisse ut ventos nonnulla ex iis <lb></lb>granis versus aliquam nubem expulerit, eaque infra illam vel ultra suspensa <lb></lb>aliquandiu detinuerit, atque ibi procul dubio ita disponi debuisse, ut sin­<lb></lb>gula sex aliis in eodem plano sitis cingerentur, quia talis est ordo naturae ” <lb></lb>(Dissertatio De methodo, Francofurti ad M. 1692, pag. </s>

<s>159). </s></p><p type="main">

<s>Che tale veramente sia l&#039;ordine della Natura, che cioè intorno a ogni <lb></lb>granello ghiacciato se ne dispongano altri sei simili, d&#039;onde venga a risul­<lb></lb>tarne la desiderata figura esagonale, il Cartesio lo vede chiaro così, da non <lb></lb>aver bisogno di alcuna dimostrazione. </s>

<s>Ma Erasmo Bartholin attese appunto <lb></lb>a scrivere il suo Discorso <emph type="italics"></emph>De figura nivis<emph.end type="italics"></emph.end> per spiegar con geometriche de­<lb></lb>scrizioni questo passo delle dottrine cartesiane. </s>

<s>Prese per esempio i favi del <lb></lb>miele e, supposte a principio le cellule circolari, dimostrò come intorno a <lb></lb>ciascuna cellula disponendosene altre sei compresse continuamente dall&#039;ape, <lb></lb>ch&#039;entra ed esce, per la duttilità della cera, come per una necessità della <lb></lb>materia, vengano esse cellule a stringersi l&#039;una contro l&#039;altra, riempiendo <lb></lb>gl&#039;interstizi rimasti fra circoli e circoli, i quali perciò si trasformano in po­<lb></lb>ligoni esagonali. </s></p><p type="main">

<s>Questa dimostrazione de&#039;favi l&#039;applicò il Bartholin, ciò che dall&#039;altra <lb></lb>parte era il suo principale intento, alla neve, la quale egli col Cartesio cre­<lb></lb>deva fosse conformata a principio in granuli o in glomi di ghiaccio, che, <lb></lb>premuti insieme dalla forza dei venti a contrasto della nube, venissero a <lb></lb>trasformare in esagono quel che intorno ad essi era prima un perfettissimo <lb></lb>cerchio. </s>

<s>“ Id enim in globulo cereo fieri animadvertimus. </s>

<s>Legibus hisce na­<lb></lb>turae ratis per totum ambitum observans sex cuspides optime ordinari pos­<lb></lb>sunt forma hexagona, qualem stellula refert. </s>

<s>Idque quod patitur unus glo­<lb></lb>morum intelligimus de omnibus eadem ratione nubem constituentibus ” (De <lb></lb>figura nivis, Hafniae 1661, pag. </s>

<s>37). </s></p><p type="main">

<s>Non dubita il Filosofo e Matematico cartesiano di estendere questa me­<lb></lb>desima generazion materiale alle figure, che prendono nel congelarsi i me­<lb></lb>talli liquefatti, non però gettati alla rinfusa, ma ne&#039;debiti modi. </s>

<s>Soggiunge <lb></lb>anzi esser questa stessa la causa meccanica, che produce le figure geome­<lb></lb>triche ne&#039;cristalli, la materia lapidea de&#039;quali, agitata da forze intestine, vien <lb></lb>compressa nelle varie sue parti. </s>

<s>“ Certe si plumbum liquefactum, ceram <lb></lb>aut quamcunque materiam mollem humidamque incertis legibus proijcias, <lb></lb>infinita genera figurarum irregularium describentur, sed si modulum adhi­<lb></lb><gap></gap>ris accomodabunt sese ad datam formam, tepore languescentes partes, <pb xlink:href="020/01/1730.jpg" pagenum="605"></pb>obstante vel cogente duritie materiae. </s>

<s>Non secus evenit crystallis, salibus, <lb></lb>aliisque, ubi vis interna motum partibus addit, partes quoque singulae pres­<lb></lb>sae invicem figuram ordinant ” (ibid., pag. </s>

<s>26, 27). </s></p><p type="main">

<s>Sarebbero forse prevalse queste cartesiane fantasie nella scienza, se una <lb></lb>maggiore autorità di quella di Erasmo Bartholin non avesse richiamata l&#039;at­<lb></lb>tenzione de&#039;Mineralogisti sopra quelle particole primigenie della materia, <lb></lb>uscite dal fecondo seno della formatrice Natura, e ad ammetter le quali tanto <lb></lb>inclinava il matematico ingegno di Giovanni Keplero. </s>

<s>Tommaso Willis, da <lb></lb>ciò che aveva letto in fine alla dissertazione <emph type="italics"></emph>De nive sexangula,<emph.end type="italics"></emph.end> che cioè le <lb></lb>figure della neve sieno forse dovute a un sale rimescolato fra gli elementi <lb></lb>dell&#039;acqua, si condusse di speculazione in speculazione ad ammettere che si <lb></lb>debbano agli stessi sali, <emph type="italics"></emph>qui constanti ritu efformantur<emph.end type="italics"></emph.end> come gli avevano <lb></lb>dimostrato le varie esperienze, attribuire i principii formativi di tutti quanti <lb></lb>i corpi. </s>

<s>Ma perchè in alcuni di questi, come ne&#039;vegetabili e negli animali, <lb></lb>son le figure assai più varie e più complicate, s&#039;aggiunge la informatrice <lb></lb>virtù dello spirito, ch&#039;è rispetto al sale quel ch&#039;è il compasso rispetto alla <lb></lb>riga nel descriver che fa il Geometra artificiosamente le sue figure. </s>

<s>“ Ete­<lb></lb>nim, in corporum naturalium figuris determinandis, <emph type="italics"></emph>spiritus<emph.end type="italics"></emph.end> ac <emph type="italics"></emph>sal<emph.end type="italics"></emph.end> habent <lb></lb>se uti <emph type="italics"></emph>circinus<emph.end type="italics"></emph.end> ac <emph type="italics"></emph>regula<emph.end type="italics"></emph.end> in describendis figuris mathematicis ” (De fermen­<lb></lb>tis, Op. </s>

<s>omnia, T. I, Lugduni 1681, pag. </s>

<s>60). Son dunque i sali, original­<lb></lb>mente configurati dalla stessa Natura, dopo lo spirito, il secondo elemento <lb></lb>informativo della materia. </s>

<s>“ Sunt enim sales isti elementa velut secunda et <lb></lb>ab eorum in corporibus insitione propriae et nativae rerum figurae pluri­<lb></lb>mum dependent, quare et ipsi configuratione quadam elementari primitus <lb></lb>a Natura imbuuntur ” (ibid.). </s></p><p type="main">

<s>Avevano le dottrine del Willis, come tutti i sistemi, assai dell&#039;imma­<lb></lb>ginario, ma da quella parte che insegnavano essere i sali originalmente pre­<lb></lb>figurati, e non venuti a circoscriversi regolarmente a quel modo per neces­<lb></lb>sità materiale, eran vere, e conferirono a dimostrarle come tali gli Anatomici <lb></lb>nostri italiani scopritori dell&#039;organo del gusto. </s>

<s>I sali artificialmente ricavati <lb></lb>dalle ceneri delle piante e dell&#039;erbe, per lo più comestibili agli uomini e <lb></lb>agli animali, lisciviate nella prima Accademia medicea, fecero balenare alla <lb></lb>mente di Lorenzo Bellini il pensiero, che le varietà degli angoli ora acuti, <lb></lb>ora ottusi, e delle superfice ora aspre, ora levigate, producessero la varietà <lb></lb>de&#039;sapori, variamente titillando le papille nervee, ch&#039;egli avea nuovamente <lb></lb>scoperte nella muccosa linguale. </s>

<s>Concorreva l&#039;immaginazione a rendergli lo <lb></lb>spettacolo più giocondo, lusingandolo di aver ritrovato, anche negli altri ge­<lb></lb>neri di sali che si sentono al gusto dolci, amari, acri, salsi, acidi “ deter­<lb></lb>minatam asperitatem aut levitatem, obtusulos angulos, acutulosve, plures <lb></lb>paucioresve cuspidulas easque breviores aut longiores ” (Gustus organum, <lb></lb>Bononiae 1665, pag. </s>

<s>67). </s></p><p type="main">

<s>Se riuscirono però queste osservazioni immaginarie, e inutili a stabilir <lb></lb>la teoria fisiologica del senso, giovarono non poco ai progressi della Cristal­<lb></lb>lografia, essendo stato il Bellini condotto a concluder da quelle stesse osser-<pb xlink:href="020/01/1731.jpg" pagenum="606"></pb>vazioni “ unumquemque salem certo quodam modo conformatum esse, et <lb></lb>talem hanc extimam habitudinem adeo sibi esse propriam et connaturalem, <lb></lb>ut nunquam eamdem posse exuere et sua sponte dum insensiles particulae <lb></lb>coagmentantur, invicem in eius figurae crassiuscusculam massam confluere ” <lb></lb>(ibid., pag. </s>

<s>66). </s></p><p type="main">

<s>A confermare questa importantissima conclusione soccorre opportuno, <lb></lb>prosegue a dire esso Bellini, il Microscopio, o come a lui piace meglio chia­<lb></lb>marlo l&#039;<emph type="italics"></emph>Engiscopio,<emph.end type="italics"></emph.end> il quale rivela in ogni frustolo di sale la figura impressa <lb></lb>a tutta intera la mole. </s>

<s>Non adducendo però il Nostro della fatta esperienza <lb></lb>nessun esempio particolare, lasciava il campo aperto al Leeuwenhoeck, il <lb></lb>quale sperò a principio di coglier le figure distinte nelle minime particelle <lb></lb>saline, nell&#039;atto stesso che vanno a deporsi giu dal liquido solvente. </s>

<s>Ma per­<lb></lb>chè non era da assicurarsi di aver veduto il vero, per le illusioni che la luce <lb></lb>attraversando il liquido poteva fare all&#039;occhio; sul sal comune superficial­<lb></lb>mente osservato, sul nitro, e con più curioso spettacolo sopra lo zucchero <lb></lb>verificò l&#039;esperienze microscopiche accennate dal Bellini. </s>

<s>“ Tum et istud cre­<lb></lb>dendum est exigua salia, licet millies exiliora sint quam ut ope Microscopii <lb></lb>conspiciatur, figura tamen convenire cum salibus in molem capaciorem con­<lb></lb>cretis, haud secum quam in sale communi, in nitro et in permultis salibus <lb></lb>evenire videmus. </s>

<s>Quin idem observatur in saccharo, quod vulgo candiense <lb></lb>vel creticum appellatur. </s>

<s>Cum enim saccarum illud, aeri prius humidiori <lb></lb>expositum, iterum in suppedaneo siccaretur, nonnunquam mulierculas de <lb></lb>obfuscato sacchari splendore conquerentes audivi. </s>

<s>Cum in obfuscationis istius <lb></lb>rationem inquirerem, animadverti sacchari superficiem ab aere humidiore <lb></lb>nonnihil resolutam vel liquefactam fuisse. </s>

<s>Dum autem per calorem ignis ite­<lb></lb>rum duresceret, incredibilem exiguarum particularum copiam, quarum per­<lb></lb>multae cum maioribus sacchari partibus figura conveniebant, spisseseendo <lb></lb>coivisse. </s>

<s>Haec vero exiguarum particularum imagines sacchari splendorem <lb></lb>obscurabat ” (Epistolae physiol., Epist. </s>

<s>XXII, Delphis 1719, pag. </s>

<s>200, 1). </s></p><p type="main">

<s>Carlo Fracassati è un altro degli anatomici, collega al Bellini nella sco­<lb></lb>perta dell&#039;organo del gusto, e con lui concorso a riconoscerne l&#039;eccitamento <lb></lb>dalle particelle saline, di che si compongono i corpi saporosi. </s>

<s>Dalla fisiolo­<lb></lb>gia trasportato anch&#039;egli nel campo della cristallografia, non gli parve ra­<lb></lb>gionevole ammettere l&#039;ipotesi del Bartholin, per non veder come si possa a <lb></lb>molte figure cristalline applicare il meccanismo della struttura dei favi. </s>

<s>Non <lb></lb>si può, secondo lui, la questione risolvere altrimenti che per via delle os­<lb></lb>servazioni microscopiche, e delle esperienze sopra la cristallizzazione, le quali <lb></lb>anche diligentemente instituite poco insegnerebbero, egli dice, “ ni creda­<lb></lb>mus initio constitutum ut in rebus ipsis quaedam figura confletur, ac prae­<lb></lb>sertim in salibus, quae perpetuo retineatur. </s>

<s>Haecque cum minima sit in pri­<lb></lb>mis particulis ac moleculis, sensum eatenus deinde non fugiat, quatenus <lb></lb>mutua adaptatione in eadem semper conspiratione partium coordinatione <lb></lb>sensibilis ac eadem figura ex pluribus minimis emergat, adeo ut cubus <lb></lb>evidens minimis cubis originem debeat, et figura aliqua regularis a mi-<pb xlink:href="020/01/1732.jpg" pagenum="607"></pb>nimis eiusdem rationis resultet ” (De lingua, cum Malpighi, Op. </s>

<s>T. II cit., <lb></lb>pag. </s>

<s>184). </s></p><p type="main">

<s>Conferma il Fracassati il fatto di questa molecolare struttura ne&#039;cri­<lb></lb>stalli con più ragioni, la prima e principale delle quali si desume dai corpi <lb></lb>organici, che si vedono essere anch&#039;essi composti di molte altre più piccole <lb></lb>membra simili, come per esempio le fibre muscolari e i lobi polmonari ri­<lb></lb>sultanti dalla testura di moltissime altre più piccole fibre, e di più piccoli <lb></lb>lobi, secondo che poco fa ha dimostrato, egli dice, l&#039;anatomia del Malpighi. </s>

<s><lb></lb>Questi dall&#039;altra parte sono i modi tenuti dalla Natura, che dalle piccole cose <lb></lb>assorge alle grandi. </s>

<s>“ Igitur valde probabile videtur in multis, conciliante <lb></lb>assensum experimento, obviam rerum figuram, saliumque praecipue, simili <lb></lb>ac minime interius latitanti respondere ” (ibid.). </s></p><p type="main">

<s>Agli esperimenti, che conciliano assenso a queste cose, aggiunge il Fra­<lb></lb>cassati quello del fuoco, il quale, essendo per la sua virtù dissolvente così <lb></lb>efficace analista della materia, non è nulladimeno capace di distruggere le <lb></lb>latitanti particelle saline informatrici de&#039;varii corpi. </s>

<s>Conchiude perciò da que­<lb></lb>sto fatto, come da chiarissimo argomento, “ esse quasdam texturas primi­<lb></lb>genias, quibus entia differant, quae alias convenirent, quarum coordinatio <lb></lb>debeat manere. </s>

<s>Inde sales forte in cineribus suis, licet passi sint ab igne, <lb></lb>ubi in aqua fluxerint, ad suam redeunt figuram. </s>

<s>Ipsa vegetabilia et mordi­<lb></lb>cus se tueri videbis, ac factam ab igne divisionem umbratili parere coaliti <lb></lb>nemo, qui Vulcano mereat, redivivam e pulvere suo Quercetani rosam igno­<lb></lb>rat, ut hoc portento e cineribus veram quilibet palingenesim possit suspi­<lb></lb>cari. </s>

<s>Ipse Davissonus resinam abietinam distillaturus ad collum cucurbitae <lb></lb>imagines abictis affabre effietas notabat ” (ibid., pag. </s>

<s>185) </s></p><p type="main">

<s>Qui, dall&#039;officina sperimentale del Fisico ci par essere trasportati nelle <lb></lb>sotterranee grotte del mago, alle incantazioni del quale non farà maraviglia <lb></lb>che rimanessero allucinati i peripatetici, se vi rimase così indegnamente preso <lb></lb>anche il Fracassati. </s>

<s>Filippo Bonanni, che fu de&#039;peripatetici più reputati a&#039;suoi <lb></lb>tempi, ammettendo col Willis che si debbano alle insite particelle saline at­<lb></lb>tribuir le figure varie de&#039;corpi, non sapeva provar meglio l&#039;assunta propo­<lb></lb>sizione che con questi argomenti, i quali riferiremo qui con le stesse parole <lb></lb>dell&#039;Autore, perchè servano di qualche ricreazione ai nostri affaticati lettori. <lb></lb></s>

<s>“ E per non porre qui quel tutto (dice nelle <emph type="italics"></emph>Osservazioni delle chiocciole,<emph.end type="italics"></emph.end><lb></lb>dop&#039;aver testualmente riferita la sentenza del Willis) che lungamente vi sa­<lb></lb>rebbe da scriverne in prova, basterà ricordare alcune sperienze, dalle quali <lb></lb>si ha che siccome estratto da qualche sostanza per via del fuoco il sale fisso <lb></lb>nelle ceneri, così il volatile ne&#039;vapori forma la figura medesima in cui era. </s>

<s><lb></lb>E quanto al volatile, verissimo è che nelle fredde notti del verno fa una <lb></lb>foglia di ghiaccio su&#039;vetri delle finestre coll&#039;umido accidentale, che seco esce <lb></lb>da&#039;rami verdi che si ardono, e stampa con essa l&#039;immagine dell&#039;albero onde <lb></lb>è tratto. </s>

<s>Quanto poi al fisso, vero è che abbruciandosi erbe o rami di al­<lb></lb>bero e fattane acqua imbevuta del sale delle lor ceneri, se queste con quella <lb></lb>si porranno in un vaso aperto al sereno del verno che le aggeli, si vedrà <pb xlink:href="020/01/1733.jpg" pagenum="608"></pb>nella crosta del ghiaccio la figura dell&#039;albero di cui è quella cenere. </s>

<s>Giovan <lb></lb>Daniello Horstio dal sale dell&#039;assenzio vide nata l&#039;immagine della sua pianta. </s>

<s><lb></lb>Olao Borricchio dal proprio sale trasse e diè a vedere ottimamente espressa <lb></lb>la figura d&#039;una quasi selvetta di cipressi. </s>

<s>E lasciando quante altre riferir si <lb></lb>potrebbono tutte degne a sapersi, vaglia per tutte quella celebre, che và per <lb></lb>bocca di molti col nome di <emph type="italics"></emph>Rosa polonica,<emph.end type="italics"></emph.end> mostrata al famoso Quercetano <lb></lb>da un Medico pollacco, il quale sapeva sì perfettamente estrarre i sali e con­<lb></lb>servare gli spiriti delle piante in ampolle di vetro ben chiuse che, ricercato <lb></lb>di far germogliare una rosa, preso il vaso ove teneva chiuso il sale di questo <lb></lb>fiore, vi accostò la fiamma di una lucerna per intiepidirlo alquanto. </s>

<s>Allora <lb></lb>quella impalpabile cenere, mettendosi in moto, si vedeva sorgere e aprirsi in <lb></lb>una specie di rosa, che a poco a poco crescesse, rappresentando in sè tutte <lb></lb>le parti del fiore. </s>

<s>Quella ombratile figura però, ricadendo la cenere in fondo, <lb></lb>si disfece, rimossa che fu dal vaso la fiamma ” (Roma 1681, pag. </s>

<s>303, 4). </s></p><p type="main">

<s>Il Bellini, giova dirlo per onor della scienza, sentì con il Fracassati che <lb></lb>sarebbe questa rinascenza dalle ceneri dimostrativa della indistruttibile figura <lb></lb>de&#039;sali, <emph type="italics"></emph>si a veritate non recederet,<emph.end type="italics"></emph.end> così questo che si racconta della Rosa <lb></lb>polonica, con altri simili fatti, come l&#039;olivo risorto nelle foglie e ne&#039;rami <lb></lb>dall&#039;olic rinchiuso in quella boccetta miracolosa data in dono a Ferdinando <lb></lb>Gonzaga. </s>

<s>“ Sed quidquid isthaec sint, seu vera seu falsa narrentur, ” con­<lb></lb>clude esso Bellini (Gustus org. </s>

<s>cit, pag. </s>

<s>59), per dimostrar la primigenia e <lb></lb>indistruttibile figura de&#039;sali non occorre andare a cercare altre prove, quando <lb></lb>il microscopio rivela quella stessa figura così evidente agli occhi di tutti. </s>

<s>Il <lb></lb>Leeuwenhoeck fece, come dicemmo, di questa evidenza di fatto promessa <lb></lb>dal Bellini pubblica e solenne testimonianza, ond&#039;è che il Boerhaave defi­<lb></lb>niva non molti anni dopo come cosa accertata oramai, e fuori di ogni con­<lb></lb>troversia “ crystallisationem salium esse collectionem elementorum salino­<lb></lb>rum eiusdem speciei in glebas unitas, et semper stabilis figurae, propriae <lb></lb>uni singulari sali ” (Elem. </s>

<s>Chemiae cit., T. II, pag. </s>

<s>334). </s></p><p type="main">

<s>Ci si permetta, a questo punto della nostra Storia, una breve sosta, per <lb></lb>considerare i fatti ora esposti, dai quali riconoscesi l&#039;efficacia che, in pre­<lb></lb>parar la certezza di questa boeraviana definizione, ebbe, contro le prevalenti <lb></lb>fantasie del Cartesio, la teoria fisiologica del gusto speculata dagli Anatomici <lb></lb>nostri italiani. </s>

<s>L&#039;ipotesi però del Bellini e del Fracassati, che cioè le varie <lb></lb>saporose affezioni si dovessero unicamente ai sali variamente configurati nei <lb></lb>cibi; ipotesi, che parve nata all&#039;occasione della scoperta delle papille nervee <lb></lb>sopra la lingua, era fra noi alquanto più antica, e risale forse alle prime <lb></lb>prove sperimenteli instituite in Firenze sui così detti sali faltizi. </s></p><p type="main">

<s>Comunque sia, di quell&#039;immaginata causa delle varie figure saline in <lb></lb>produr sulla lingua le affezioni varie del gusto, ne discorreva, come di cosa <lb></lb>già convenuta, il Magalotti in una sua lettera scritta il dì 8 Gennaio 1660 <lb></lb>da Roma al priore Orazio Ricasoli Rucellai. </s>

<s>E perchè nelle eleganti parole <lb></lb>del Segretario della fiorentina Accademia si trovano accennate le principali <lb></lb>dottrine che, in mezzo al trionfante cartesianismo, si professavano allora dai <pb xlink:href="020/01/1734.jpg" pagenum="609"></pb>Nostri intorno alla natura de&#039;sali, alle loro liquazioni e ad altri particolari ef­<lb></lb>fetti; non dispiacerà di veder quelle stesse parole trascritte qui ai nostri Let­<lb></lb>tori, i quali sentiranno gusto dell&#039;ingegnose arguzie dell&#039;Autore in risolvere <lb></lb>un problema curioso, in tempi, in cui la Fisiologia medica pur allora nasceva. </s></p><p type="main">

<s>Passato dunque da Firenze a soggiornare alquanto in Roma il nostro <lb></lb>conte Lorenzo, si trovò mal&#039;affetto da una eruzione cutanea, che con i mo­<lb></lb>lesti e dolorosi pruriti gli tolse affatto per più notti la dolce quiete del sonno. </s>

<s><lb></lb>I medici l&#039;attribuivano a un ribollimento di sangue, occasionato dal mutare <lb></lb>aria e cibi, e specialmente i vini, così gravi in Roma rispetto a quei così deli­<lb></lb>cati di Firenze. </s>

<s>In una di quelle moleste notti perciò, tutta intera passata in­<lb></lb>sonne, il Magalotti, riconoscendo essere il suo malore principalmente occasio­<lb></lb>nato dai vini, ne speculò così il modo, come poi scrisse all&#039;amico suo Rucellai: </s></p><p type="main">

<s>“ Noi vegghiamo per esperienze, diceva, non vi esser sostanza alcuna in <lb></lb>natura, da cui non si estragga il suo sale, e questo in ciascuna ritener co­<lb></lb>stantemente una determinata figura. </s>

<s>Cosi riconosciamo non solo nei puri <lb></lb>sali, cioè a dire nel comune, nell&#039;ammoniaco, nel nitro e nell&#039;allume, ma <lb></lb>universalmente nell&#039;erbe tutte e nelle piante, e talora nelle pietre, ne&#039;mi­<lb></lb>nerali, e finalmente nelle stesse gioie. </s>

<s>Siccome dunque di ciascheduna so­<lb></lb>stanza è una sola determinata figura nelle particelle del suo sale, non sarà <lb></lb>lontano dalla probabilità il credere che diverse viti possano avere diversità <lb></lb>di figure ne&#039;loro sali, perciocchè, se vorremo rifondere la differenza de&#039;loro <lb></lb>sapori in quella di dette figure, bisognerà che queste sieno diversissime, e <lb></lb>niente meno differiranno fra loro le figure de&#039;sali delle viti e dell&#039;uve, di <lb></lb>ciò si differiscano da quelle d&#039;alcun altro frutto, avvengachè assai minor di­<lb></lb>vario sia tra i sapori del moscadello e d&#039;un granato dolce, di quel che si <lb></lb>corra tra la nostra uva di messer Alemanno, ed un abrostino forte. </s>

<s>Ma <lb></lb>quand&#039;anco V. S. Ill.ma volesse controvertermi questo ragionamento, della <lb></lb>verità o falsità del quale pur l&#039;esperienza potrebbe chiarirci con l&#039;estrazione <lb></lb>de&#039;sali di varie viti o uve, e tuttavia volesse credere analoghe le figure dei <lb></lb>sali di tutte le uve di Europa e del mondo; non potrà V. S. Ill.ma negarmi <lb></lb>che diversi sieno i minerali, di cui son pregni i terreni sotto diversi climi. </s>

<s><lb></lb>Così la Tolfa ha miniere di allume, e senza estendere un minerale per tutto un <lb></lb>clima, che saria cosa ridicola, gli metto avanti tutti quei paesi, dove vi hanno <lb></lb>acque termali, e ritroverà che in un circuito di poche miglia, nella nostra <lb></lb>Toscana, ne abbiamo sopra quaranta vene tutte gravide di diverse miniere. </s>

<s><lb></lb>Sarà vero dunque che nell&#039;uve d&#039;un paese, e in quelle di un altro, si ritrovi <lb></lb>diversità di sali, se non per loro natura, almeno per lo finissimo permischia­<lb></lb>mento di quelli, che sono proprii de&#039;minerali portati da questi terreni. </s>

<s>” </s></p><p type="main">

<s>“ Considerata questa verità, io considero ancora il vino, che è il liquore <lb></lb>che da quell&#039;uva si spreme, gravido anch&#039;egli de&#039;medesimi sali. </s>

<s>E se un <lb></lb>vino si concede essere sparso di differenti sali da quei di un altro, se non <lb></lb>per loro natura, come dicemmo, almeno per l&#039;infusione de&#039;minerali suc­<lb></lb>chiati dalla diversità de&#039;terreni; bisognerà dunque che, bevendosi una tal <lb></lb>sorte di vino, nel chilo ancora molto del suo sale si stemperi, e con esso <pb xlink:href="020/01/1735.jpg" pagenum="610"></pb>trapassi per le vene lattee e pe&#039;vasi toracici, e finalmente entri anch&#039;esso <lb></lb>in carriera con la massa del sangue a fare il suo corso. </s>

<s>” </s></p><p type="main">

<s>“ E consideri V. S. che, liquandosi un sale, e&#039;non si fonde mica in <lb></lb>acqua o in altro umore più tenue, ma e&#039;si rimane nel primo esser suo uno, <lb></lb>incorruttibile ed eterno, cioè a dire in un atomo di una tal figura. </s>

<s>E perciò <lb></lb>quand&#039;e&#039;pare che un sale nell&#039;acqua o in altro liquore si stemperi, non sono <lb></lb>gli atomi minimi figurati del sale quei che si struggono, ma si è la massa <lb></lb>del sale, che si fonde: cioè molti di quegli atomi minimi, che insieme uniti <lb></lb>e legati, nel lapillarsi, erano ricresciuti in corpicelli di figure similari, mol­<lb></lb>lificandosi per via dell&#039;umore quel glutine che in sì fatta guisa strignevali, <lb></lb>gli uni dagli altri si sciolgono, e mischiandosi fra atomo e atomo dell&#039;acqua, <lb></lb>ossivvero ficcandosi tra&#039;vacuetti e interstizii di quelli, per modo che poco o <lb></lb>nulla chiuggano il passaggio alla luce, che pur per quei vani passando facea <lb></lb>parer limpida e trasparente l&#039;acqua; alla nostra vista s&#039;occultano. </s>

<s>” </s></p><p type="main">

<s>“ Così per l&#039;appunto, poichè e&#039;sono mischiati col sangue, non altri­<lb></lb>menti si liquano, ma ritengono tuttavia la loro figura, al modello della quale <lb></lb>vanno stampando il cavo per quei meati più angusti, di dove e&#039;passano <lb></lb>nel fare il corso della circolazione. </s>

<s>Venga ora un altro vino di differente <lb></lb>paese, colore e sapore, e perciò imbevuto e pregno di sali diversi Egli è <lb></lb>certo che ogni volta che questi non s&#039;adattino con la loro figura al cavo o <lb></lb>alla stampa impressa da&#039;sali di un altro vino in quelle venuzze sottilissime <lb></lb>capillari, incalzata con impeto la massa del sangue dove galleggiano dal moto <lb></lb>della sistole, dovranno in quelle violenti schizzature di sangue penetrare ad­<lb></lb>dentro, e sì sforzare gli orifizi angustissimi ed i canali di quelle fila di vene, <lb></lb>incavandole d&#039;altra forma per rendersele permeabili nel loro corso. </s>

<s>E suc­<lb></lb>cedendo ciò no nei vasi più grandi ma solo nelle vene finissime, sottilissime, <lb></lb>capillari ed esterne, quindi avviene che quivi si sentano le punture di que­<lb></lb>gli aculei di sale, i quali moltissimi di essi, anzi che stamparle della loro <lb></lb>forma e figura, squarciandole si estrinsecano, e rimanendo fuori della vena <lb></lb>e del corso dell&#039;altro sangue, restano sotto il velo sottilissimo dell&#039;epider­<lb></lb>mide con qualche stilla di sangue, derivata dal piccolo squarcio di quelle <lb></lb>fibre, s&#039;infiammano e pungono, onde poi, col grattare rompendosi il sud­<lb></lb>detto velo, si cava, dirò così, con quell&#039;atometto di sale, quella spina che <lb></lb>punge ” (MSS. Cim., T. XXIV, c. </s>

<s>62, 63). </s></p><p type="main">

<s>Apparisce chiaro da questo documento come, infin da mezzo il se­<lb></lb>colo XVII, si professasse con sicurezza in Firenze quella verità dei nativi e <lb></lb>inalterabili elementi salini che, combattuta dai cartesiani e dai peripatetici, <lb></lb>si ridusse appena in salvo fra gl&#039;insegnamenti del Boerhaave, alquanti anni <lb></lb>dopo il cominciar del secolo appresso. </s>

<s>Rimaneva in ogni modo a sapere <lb></lb>come si potessero comporre insieme gli stabili elementi salini a rappresen­<lb></lb>tare la sempre stabile figura della gleba. </s>

<s>Il problema apparteneva alle ra­<lb></lb>gioni della pura Geometria, e fu il primo a risolverlo geometricamente Gian <lb></lb>Domenico Guglielmini. </s>

<s>Ei riconobbe che le tante e sì varie figure dei sali <lb></lb>si potevano tutte ridurre a prismi e ad ottaedri, ossia a piramidi, essendo <pb xlink:href="020/01/1736.jpg" pagenum="611"></pb>chiaro ch&#039;esso ottaedro risulta di due simili figure piramidali congiunte in­<lb></lb>sieme per la superfice quadrata delle loro basi. </s>

<s>Mettersi a dimostrar che un <lb></lb>prisma si riduce in altri più piccoli prismi sarebbe, dice il Guglielmini, “ un <lb></lb>accendere fiaccole al sole, posciachè ognun sa che i parallelepipedi, colle di­<lb></lb>visioni eguali de&#039;lati, delle basi e delle altezze, si dividono in altri simili ed <lb></lb>eguali fra di sè, onde di otto cubi piccoli se ne fa un grande di lato dop­<lb></lb>pio ad uno de&#039;primi; con ventisette se ne forma un altro triplicato pari­<lb></lb>mente di lato, e così degli altri, il che s&#039;adatta a spiegare la composizione <lb></lb>del Sal comune, del Sal gemma, di tutte le spezie di vitriolo e del tartaro. </s>

<s><lb></lb>E i prismi, come quello del Salnitro, sono composti d&#039;altri più piccoli di <lb></lb>base, o esagona o triangolare equilatera, posciachè in questa figura l&#039;esa­<lb></lb>gona si risolve, dai quali ordinatamente disposti, tanto nella base quanto nel­<lb></lb>l&#039;altezza, ne nascono i prismi esagoni osservati nel Nitro ” (Riflessioni filos. </s>

<s><lb></lb>delle figure dei sali, Bologna 1688, pag. </s>

<s>32). </s></p><p type="main">

<s>Più difficile poteva sembrare la composizione piramidale della gleba, ri­<lb></lb>sultante da più piccole figure piramidali degli elementi salini, ed è perciò <lb></lb>che il Guglielmini si trattien più di proposito in questo particolare, illu­<lb></lb>strando in un&#039;appendice geometrica questo suo, per sè dall&#039;altra parte assai <lb></lb>spiegato discorso: “ Egli è chiaro, ei dice, che dividendo i lati d&#039;un qua­<lb></lb>drato secondo la stessa misura, e connettendo i punti corrispondenti de&#039;lati <lb></lb>opposti con linee rette, resta esso spartito in piccoli quadretti tanti di nu­<lb></lb>mero, quanto importa il quadrato delle misure di uno de&#039;lati. </s>

<s>Quindi è che <lb></lb>dalla divisione in parti eguali resta divisa l&#039;area del primo in quattro mi­<lb></lb>nori quadretti, che ponno essere basi delle piramidi, che fra poco dirovvi. </s>

<s><lb></lb>Egli è altresì manifesto che dividendo i lati d&#039;una piramide quadrata nel <lb></lb>mezzo, e facendo passare per li punti della divisione un piano, si lascia al <lb></lb>di sopra una piramide simile all&#039;intera, ed eguale ad una di quelle, che <lb></lb>terminando colle loro cime ne&#039;punti predetti, hanno per base uno de&#039;pic­<lb></lb>cioli quadrati che di sopra vi mentovava. </s>

<s>Queste co&#039;loro vertici lasciano al <lb></lb>di sopra uno spazio simile ed eguale alla base di una di esse, dentro del <lb></lb>quale colla punta all&#039;ingiu può situarsi un&#039;altra piramide, di cui sulla base <lb></lb>rovesciata posa l&#039;altra piramide eguale, che poco fa vi dissi essere tagliata <lb></lb>dal piano al di sopra. </s>

<s>Ecco adunque come di sei piramidi, quattro delle quali <lb></lb>restano situate colla sua base in un medesimo piano, un&#039;altra rivoltata al­<lb></lb>l&#039;ingiu riempie parte dello spazio, che fra le quattro prime rimane, e l&#039;ul­<lb></lb>tima si posa sopra la base di questa; può formarsi una piramide maggiore <lb></lb>simile in tutto e per tutto a ciascuna delle componenti ” (ivi, pag. </s>

<s>22, 23). </s></p><p type="main">

<s>Così, congiunta alle fisiche osservazioni del Bellini e del Fracassati la <lb></lb>geometria del Guglielmini, venivano a stabilirsi, fuori dell&#039;Accademia del <lb></lb>Cimento, le fondamenta alla scienza dei cristalli, per quel che particolar­<lb></lb>mente concerne il materiale adattamento della loro figura. </s>

<s>Rimaneva a saper <lb></lb>ciò che, pur fuori dell&#039;Accademia del Cimento, si pensasse intorno alla causa, <lb></lb>che dispone a configurarsi in tale e in tale altro modo le disperse parti­<lb></lb>celle della materia. </s>

<s>Il Willis non par che attribuisse quella causa se non al <pb xlink:href="020/01/1737.jpg" pagenum="612"></pb>restringersi i pori del liquido di soluzione, per cui vengono gli elementi sa­<lb></lb>lini ad accostarsi sempre più strettamente fra loro, infin tanto che, per la <lb></lb>sopravvenuta azione del freddo prodottosi dallo stesso liquido evaporante, <lb></lb>non si riduce quel primo legger contatto a farsi più stabilmente tenace. <lb></lb></s>

<s>“ Postea, si liquor iste aliquatenus evaporetur ut meatibus et poris eius <lb></lb>nonnihil constrictis salis corpuscula sibi invicem approximentur, se mutuo <lb></lb>prehendunt et externo frigore constipante una coeunt, et mediis in undis in <lb></lb>crystallos suae naturae proprias figurantur ” (De ferment. </s>

<s>cit., pag. </s>

<s>59, 60). </s></p><p type="main">

<s>Dell&#039;esistenza di questi pori nel liquido, e della loro azione come ricet­<lb></lb>tacoli del sale risoluto, avevano fatto soggetto alle loro prove sperimentali <lb></lb>gli Accademici fiorentini (Targioni, Notizie cit., T. II, P. II, pag. </s>

<s>639), i <lb></lb>quali, com&#039;apparisce dai loro Diarii manoscritti, e specialmente da quello <lb></lb>raccolto nella Parte I del Tomo II, s&#039;occuparono altresì d&#039;investigar <emph type="italics"></emph>l&#039;au­<lb></lb>mento di peso specifico delle soluzioni.<emph.end type="italics"></emph.end> Ond&#039;è che quel si riteneva dall&#039;In­<lb></lb>glese, e da tutti insieme con lui, per semplice ipotesi, i Nostri s&#039;erano, infin <lb></lb>dal 1657, studiati di confermarlo coll&#039;esperienze. </s></p><p type="main">

<s>Lo Stenone, come vedemmo, al vago nome di <emph type="italics"></emph>spirito<emph.end type="italics"></emph.end> immaginato dal <lb></lb>Willis sostituì la più probabile esistenza di un fluido etereo, e l&#039;opera del <lb></lb>compasso, nel descriver le figure saline, più propriamente la riconobbe nelle <lb></lb>polarità magnetiche di quello stesso fluido, esalato dalla materia cristalliz­<lb></lb>zante. </s>

<s>Neglettesi queste idee stenoniane, il Guglielmini se le rivide balenare <lb></lb>alla mente, quando pensò che le particelle figurate “ ponno ricevere il moto <lb></lb>o dal sole o dal lume, ne&#039;corpi che sono senz&#039;anima, o da questa in quelli <lb></lb>che ne sono dotati ” (ivi, pag. </s>

<s>32, 33). Se non fossero rimaste le tradizioni <lb></lb>della scienza italiana dannosamente chiuse fra le pareti dell&#039;Accademia fio­<lb></lb>rentina, il nostro Fisico di Bologna, che vedemmo in altre occasioni aver <lb></lb>idee a quelle del Newton così conformi, preveniva senza dubbio l&#039;Inglese <lb></lb>nel dimostrare i principii dell&#039;attrazione molecolare. </s>

<s>A questa egli invece, <lb></lb>prevalendo in Italia la dottrina galileiana della forza del vacuo, sostituì la <lb></lb>pressione dell&#039;aria, che attragga e tenga le molecole cristalline, come le cop­<lb></lb>pette attraggon la carne o come si tengono insieme due lamine di vetro <lb></lb>lisce e talmente adattate, che non vi resti aria di mezzo. </s>

<s>“ Se adunque, egli <lb></lb>dice, vi proverò essere i pori del sale cotanto piccoli che neghino l&#039;ingresso <lb></lb>all&#039;aria, sarà la pressione di questa, esercitata egualmente per ogni verso, <lb></lb>la cagione dell&#039;adesione delle di lui parti, benchè queste in sole linee una <lb></lb>coll&#039;altra si tocchino ” (ivi, pag. </s>

<s>30). </s></p><p type="main">

<s>Venne poco dopo il Newton il quale, sperimentando che due lamine di <lb></lb>vetro lisce si tengono unite insieme anche nel vuoto, bandì dalla Fisica l&#039;ipotesi <lb></lb>galileiana, per mettere in più chiara evidenza quella dello Stenone, le magne­<lb></lb>tiche azioni speculate dal quale comparvero sotto la nuova forma delle attra­<lb></lb>zioni e delle repulsioni molecolari. </s>

<s>L&#039;applicazione di una tale dottrina neu­<lb></lb>toniana alla Cristallografia consiste nel supporre che le particelle saline, <lb></lb>prima di associarsi, si trovassero notanti in mezzo al liquido, dispostevi l&#039;una <lb></lb>rispe<emph type="italics"></emph>i<emph.end type="italics"></emph.end>to all&#039;altra secondo misurati intervalli, e secondo ordini certi; cosicchè <pb xlink:href="020/01/1738.jpg" pagenum="613"></pb>agissero a vicenda con forze uguali o disuguali fra loro, secondo che si tro­<lb></lb>vassero poste a uguale o a disuguale distanza. </s>

<s>Così intendesi come sempre <lb></lb>vengano a comporsi le particelle in ordini simili, e come, senza queste forze <lb></lb>attrattive, o elle debbano concorrere a caso o andarsene confusamente di­<lb></lb>sperse. </s>

<s>“ Quum liquor sale quovis imbutus, evaporatus est, quod aiunt, ad <lb></lb>cuticulam et deinde refrixit, sal continuo concrescit in figuras aliquas regu­<lb></lb>lares. </s>

<s>Ex quo apparet salis particulas, antequam concrescerent, iam in li­<lb></lb>quore illo aequis interiectis intervallis, certisque ordinibus dispositas, inna­<lb></lb>tasse, et consequenter eas in se invicem egisse vi aliqua, quae aequalis sit <lb></lb>in intervallis aequalibus in iuaequalibus inaequalis. </s>

<s>Nam tali quidem vi illae <lb></lb>se in consimiles ordines usquequaque disponent, sine ea autem circumnata­<lb></lb>bunt dispersim quaquaversus; itemque sine ullo ordine, ut forte ceciderit, <lb></lb>concurrent ” (Opera omnia optica, Patavii 1773, pag. </s>

<s>158). </s></p><p type="main">

<s>Venivano queste neutoniane dottrine a confermare e a rendere tutt&#039;in­<lb></lb>sieme la ragione di quel che diceva il Willis del ristringimento de&#039;pori nel <lb></lb>liquido evaporante, per cui quasi spremute, e costrette d&#039;uscir fuori da&#039;loro <lb></lb>loculi troppo angusti, son costrette a deporsi le risolute particelle del sale. </s>

<s><lb></lb>Il Newton insegnava invece che, restringendosi i pori al liquido raffreddato, <lb></lb>le particelle che prima gli riempivano vengono ad accostarsi così da ridursi <lb></lb>nella loro sfera di attrazione, e perciò tornano a ricomporsi in quel mede­<lb></lb>simo ordine, che avevano prima di essere sciolte. </s>

<s>Applicando poi il Boer­<lb></lb>haave queste dottrine alle soluzioni, fece rilevar l&#039;importanza grande, che ha <lb></lb>il calore nel governo delle loro leggi, e come male si confidassero i Chi­<lb></lb>mici, trascurando quell&#039;elemento, di poter definire la quantità del sale re­<lb></lb>solubile in una data misura di acqua. </s>

<s>“ Inde igitur rursum liquet faculta­<lb></lb>tem aquae qua solvit sales pendere partim ex sale et aqua partim vero ex <lb></lb>copia ignis, qui se adiungit tam sali quam aquae. </s>

<s>Quare etiam colligo defi­<lb></lb>niri haud posse, ut omnes fere Chemici voluerunt, quantum salis in aqua <lb></lb>queat dissolvi, nisi quam accuratissime simul definiatur quantus calor simul <lb></lb>fuerit adhibitus inter dissolvendum ” (Elementa Chemiae, T. </s>

<s>I cit., pag. </s>

<s>575). </s></p><p type="main">

<s>Dovendosi a questo punto, secondo i limiti che ci siamo prescritti, ar­<lb></lb>restare la presente Storia, coloro che si compiacciono de&#039;progressi fatti dalla <lb></lb>moderna Cristallografia confesseranno facilmente a non altro poi ridursi que­<lb></lb>sti stessi ammirati progressi, che allo svolgimento delle dottrine, storica­<lb></lb>mente da noi fin qui esposte, e il più pieno e compendioso esempio delle <lb></lb>quali ci è offerto dallo Stenone. </s>

<s>A chi va oggidì orgoglioso del suo gran sa­<lb></lb>pere in fatto di scienze sperimentali, compassionando la bonaria semplicità <lb></lb>e l&#039;ignoranza degli avi, potrebbero forse qualche poco giovare questa e le <lb></lb>altre Storie passate; felici chiamandoci noi e sodisfatti dei nostri studi, se <lb></lb>valessero a persuadere gl&#039;illusi che i frondosi rami lussureggianti sotto <lb></lb>questo nostro sole attinsero già il nutrimento da quelle antiche radici, le <lb></lb>quali, specialmente sotto il suolo d&#039;Italia, si vanno a ricongiungere nell&#039;al­<lb></lb>bero della scienza, invisibili, ma pur così sempre efficacemente operanti. <pb xlink:href="020/01/1739.jpg"></pb></s></p><pb xlink:href="020/01/1740.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICI<emph.end type="center"></emph.end><pb xlink:href="020/01/1741.jpg"></pb></s></p><pb xlink:href="020/01/1742.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE DEI CAPITOLI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dell&#039;Anatomia nello studio della vita animale.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle istituzioni anatomiche di Galeno, e delle prime instaurazionì dell&#039;arte, per opera <lb></lb>del Berengario e del Vesalio <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 7 </s></p><p type="main">

<s>II Dell&#039;anatomia descrittiva instituita dal Falloppio, e proseguita dall&#039;Eustacbio, dal­<lb></lb>l&#039;Acquapendente e dal Casserio ” 13 </s></p><p type="main">

<s>III Delle vivisezioni praticate da Realdo Colombo e come s&#039;incominciassero ad applicare le <lb></lb>leggi della Fisica a spiegar le funzioni della vita. </s>

<s>” 22 </s></p><p type="main">

<s>IV Dell&#039;Anatomia della Scuola iatromeccanica ” 30 </s></p><p type="main">

<s>V Della Scuola iatromeccanica italiana, e dei limiti naturalmente imposti ai progressi del­<lb></lb>l&#039;Anatomia ” 35 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dei moti muscolari.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle prime ipotesi proposte a rendere la ragione dei moti muscolari, e particolar­<lb></lb>mente dell&#039;ipotesi del Cartesio <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 43 </s></p><p type="main">

<s>II Di altre varie ipotesi principalmente speculate dai nostri Italiani ” 50 </s></p><p type="main">

<s>III Dei moti volontarii, e dei naturali ” 63 </s></p><p type="main">

<s>IV Della meccanica dei moti muscolari ” 73 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dei moti del cuore.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della struttura muscolare del cuore; dei moti di sistole e di diastole <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 84 </s></p><p type="main">

<s>II Delle forze motive del cuore, e della loro misura; del moto del sangue per le arterie <lb></lb>e per le vene ” 96 </s></p><p type="main">

<s>III Delle leggi idrauliche applicate ai moti del sangue ” 111 </s></p><pb xlink:href="020/01/1743.jpg" pagenum="618"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del circolo del sangue.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Del circolo polmonare <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 124 </s></p><p type="main">

<s>II Del circolo universale ” 136 </s></p><p type="main">

<s>III Delle esperienze e delle osservazioni, che dimostrano la verità del circolo universale ” 143 </s></p><p type="main">

<s>IV Del sistema arveiano in Italia, e della trasfusione del sangue ” 152 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Della respirazione.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle cause motive, degli organi e dei modi della respirazione <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 164 </s></p><p type="main">

<s>II Dell&#039;azione dell&#039;aria inspirata sul sangue dei polmoni ” 174 </s></p><p type="main">

<s>III Della respirazione dei neonati; del problema arveiano ” 186 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Della nutrizione.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle varie dottrine professate dai Fisiologi intorno alla digestione, e delle esperienze <lb></lb>in proposito di Lazzero Spallanzani <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 199 </s></p><p type="main">

<s>II Della scoperta delle vie del chilo per le vene lattee del Mesenterio ” 209 </s></p><p type="main">

<s>III Della scoperta del Ricettacolo del chilo, e del Canale toracico ” 217 </s></p><p type="main">

<s>IV Della scoperta dei vasi linfatici; delle esequie al Fegato defunto ” 229 </s></p><p type="main">

<s>V Dell&#039;opera data particolarmente dai nostri Italiani allo studio dei vasi bianchi ” 238 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dei sensi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Del tatto, del gusto e dell&#039;odorato <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 251 </s></p><p type="main">

<s>II Dell organo dell&#039;udito; dell&#039;orecchio medio, ossia della Cassa del timpano ” 264 </s></p><p type="main">

<s>III Dell&#039;orecchio interno, ossia del Labirinto ” 276 </s></p><p type="main">

<s>IV Del senso dell&#039;udito ” 285 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Ancòra Dei sensi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Dell&#039;organo della vista; delle membrane dell&#039;occhio <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 300 </s></p><p type="main">

<s>II Degli umori di rifrangenza nell&#039;occhio ” 321 </s></p><p type="main">

<s>III Del senso della vista ” 334 </s></p><pb xlink:href="020/01/1744.jpg" pagenum="619"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Degli ordinamenti naturali.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Degli ordinamenti degli animali <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 351 </s></p><p type="main">

<s>II Dell&#039;ordinamento delle piante ” 360 </s></p><p type="main">

<s>III Dell&#039;ordinamento dei minerali ” 369 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO X.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>De&#039;Mammiferi e degli uccelli.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della generazione dag&#039;i svolgimenti embrionali dell&#039;uovo <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 378 </s></p><p type="main">

<s>II De&#039;moti locali: del passo e del volo ” 395 </s></p><p type="main">

<s>III Di alcune questioni concernenti le funzioni digestive ne&#039;quadrupedi ruminanti, e negli <lb></lb>uccelli gallinacci; delle vescicole pneumatiche negli uccelli ” 406 </s></p><p type="main">

<s>IV Di cerle piu notabili differenze negli organi dei sensi: degli strumenti della voce e del <lb></lb>canto ” 418 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO XI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dei pesci.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Degli organi, e degli esercizi del nuoto <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 430 </s></p><p type="main">

<s>II Della respirazione branchiale, e del circolo del sangue ” 439 </s></p><p type="main">

<s>III. </s>

<s>Degli organi dei sensi ” 452 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO XII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Degl&#039;Insetti.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della generazione spontanea, e delle varie esperienze istituite per dimostrarla falsa <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 465 </s></p><p type="main">

<s>II Della Micrografia, e delle particolari applicazioni di lei alla scoperta degli organi della <lb></lb>respirazione ” 478 </s></p><p type="main">

<s>III Degli organi de&#039;sensi, e particolarmente degli occhi ” 487 </s></p><p type="main">

<s>IV De&#039;fenomeni di fosforescenza, segnatamente nelle lucciole marine, e nelle terrestri ” 495 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO XIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Delle piante.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle principali funzioni nutritive: delle forze concorrenti a produr l&#039;ascesa dei succhi; <lb></lb>dell&#039;azione, e delle proprietà delle foglie. <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 508 </s></p><p type="main">

<s>II Del circolo della linfa, e della respirazione ” 523 </s></p><p type="main">

<s>III Dell&#039;ufficio dei fiori, della distinzione dei sessi, e della fecondazione dei semi ” 531 </s></p><p type="main">

<s>IV Della germinazione: dell&#039;uso dei lobi e delle foglie seminali: dell&#039;azione dell&#039;aria, e <lb></lb>dei semi posti a germogliare nel vuoto ” 549 </s></p><pb xlink:href="020/01/1745.jpg" pagenum="620"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO XIV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dei Minerali.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della sede nettunica del regno minerale <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 560 </s></p><p type="main">

<s>II Della sede plutonica del regno minerale ” 577 </s></p><p type="main">

<s>III Della generazion dei cristalli, e di ciò che intorno alle forme cristalline fu osservato e <lb></lb>speculato dagli Accademici del Cimento ” 591 </s></p><p type="main">

<s>IV Dell&#039;origine e dei progressi della Cristallografia, fuori dell&#039;Accademia del Cimento ” 600 </s></p><pb xlink:href="020/01/1746.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE ALFABETICO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEGLI AUTORI E DELLE COSE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Co&#039;numeri s&#039;accenna alle pagine.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Achilli<gap></gap>i Alessandro<emph.end type="bold"></emph.end> annoverato fra&#039;primi osservatori dei moti pupillari 315. </s></p><p type="main">

<s><emph type="bold"></emph>Acipensero,<emph.end type="bold"></emph.end> pesce, organo dell&#039;odorato di lui descritto dal Morgagni 461. </s></p><p type="main">

<s><emph type="bold"></emph>Acquapendente (d&#039;) Girolamo Fabrizi<emph.end type="bold"></emph.end> anatomico 19, suoi errori di meccanica muscolare 74, scopre <lb></lb>le valvole delle vene 146, sue idee retrograde intorno al circolo del sangue 143, sue osservazioni <lb></lb>importanti intorno alla figura, e alla disposizione della membrana del Timpano 256, quale uso <lb></lb>egli assegni agli organi interni dell&#039;udito 288, primo cultore dell&#039;Anatomia comparata 357, a <lb></lb>quali organi attribuisca la direzione del volo negli uccelli 404, come non scoprisse nulla di nuovo <lb></lb>negli organi della ruminazione 408, propone i tre problemi, ne&#039;quali concludesi la meccanica del <lb></lb>nuoto de&#039;pesci 431, ammette la generazione spontanea 496. </s></p><p type="main">

<s><emph type="bold"></emph>Acquedutto<emph.end type="bold"></emph.end> scoperto dal Falloppio nell&#039;interno dell&#039;orecchio 379. </s></p><p type="main">

<s><emph type="bold"></emph>Acqueo,<emph.end type="bold"></emph.end> umore dell&#039;occhio: esperienze intorno alla sua generazione 330, sua quantità relativa a <lb></lb>quella degli altri umori 332. </s></p><p type="main">

<s><emph type="bold"></emph>Acustico,<emph.end type="bold"></emph.end> nervo degli uccelli, descritto dallo Scarpa 422. </s></p><p type="main">

<s><emph type="bold"></emph>Aggiunti Niccolò,<emph.end type="bold"></emph.end> come spieghi il modo del salir la linfa ne&#039;vasi delle piante 512. </s></p><p type="main">

<s><emph type="bold"></emph>Aldovrandi Ulisse,<emph.end type="bold"></emph.end> come ordini la sua storia degli uccelli 354, osserva non esser vero che la coda <lb></lb>negli uccelli faccia l&#039;ufficio del timone nelle navi 403. </s></p><p type="main">

<s><emph type="bold"></emph>Ali,<emph.end type="bold"></emph.end> nell&#039;esercizio del volo, rassomigliate da Aristotile ai remi 4<gap></gap>0. </s></p><p type="main">

<s><emph type="bold"></emph>Anastomosi<emph.end type="bold"></emph.end> fra le estremità venose e le arteriose, perchè messe in dubbio dall&#039;Harvey e dal <lb></lb>Pecquet 148. </s></p><p type="main">

<s><emph type="bold"></emph>Angeli Stefano,<emph.end type="bold"></emph.end> suo giudizio intorno alla Miologia stenoniana 37. </s></p><p type="main">

<s><emph type="bold"></emph>Antenne,<emph.end type="bold"></emph.end> intorno alla bocca degli insetti, credute da alcuni organi di sensi speciali 487. </s></p><p type="main">

<s><emph type="bold"></emph>Antiperipatias,<emph.end type="bold"></emph.end> libro nel quale Marc&#039;Aurelio Severino dimostra che i pesci hanno le trachee e i <lb></lb>polmoni 443. </s></p><p type="main">

<s><emph type="bold"></emph>Aorta<emph.end type="bold"></emph.end> ascendente e discendente ne&#039;pesci a quali vasi corrisponda nei polmonati 450. </s></p><p type="main">

<s><emph type="bold"></emph>Api<emph.end type="bold"></emph.end> costruiscono i favi esagonali 601, non gli costruiscono per lume d&#039;intelligenza, ma secondo il <lb></lb>Keplero per necessità materiale 602. </s></p><p type="main">

<s><emph type="bold"></emph>Aranzio Giulio Cesare<emph.end type="bold"></emph.end> descrive i particolari organi inservienti alla circolazione del sangue nel feto, <lb></lb>ed emenda Galeno 190. </s></p><p type="main">

<s><emph type="bold"></emph>Arena Filippo<emph.end type="bold"></emph.end> primo a professsare in Italia il sistema sessuale delle piante 549. </s></p><p type="main">

<s><emph type="bold"></emph>Aria,<emph.end type="bold"></emph.end> primi riconosciuti effetti di lei nella respirazione 166, refrigera, secondo il Cesalpino, il calor <lb></lb>naturale del sangue 166, perchè, secondo il Borelli e il Fracassati, sia necessaria alla vita dei <lb></lb>pesci 446, se sia necessaria alla germogliazione dei semi 558. </s></p><p type="main">

<s><emph type="bold"></emph>Aristotile,<emph.end type="bold"></emph.end> come dia definitiva sentenza del primato tra il cuore e il fegato, giudicando dalla loro <lb></lb>sede 126 </s></p><p type="main">

<s><emph type="bold"></emph>Aromatari Giuseppe,<emph.end type="bold"></emph.end> suoi pensieri intorno alla germogliazione dei semi 552, primo a riconoscers <lb></lb>l&#039;uso delle foglie seminali 553. </s></p><p type="main">

<s><emph type="bold"></emph>Arte della pittura<emph.end type="bold"></emph.end> in servizio della Storia naturale 3<gap></gap>3. </s></p><p type="main">

<s><emph type="bold"></emph>Arterie,<emph.end type="bold"></emph.end> la loro virtù pulsante vien partecipata dal sangue 99. </s></p><p type="main">

<s><emph type="bold"></emph>Asellio Gaspero,<emph.end type="bold"></emph.end> suoi dubbi intorno al circolo polmonare 136, racconta in che modo riusci a sco­<lb></lb>prire le vene lattee 213. </s></p><p type="main">

<s><emph type="bold"></emph>Aura seminale,<emph.end type="bold"></emph.end> sola, secondo il Graaf, fecondatrice 389. </s></p><pb xlink:href="020/01/1747.jpg" pagenum="622"></pb><p type="main">

<s><emph type="bold"></emph>Baglivi Giorgio,<emph.end type="bold"></emph.end> sua teoria dei moti muscolari 59, insegna il modo dl osservare il circolo del sangue <lb></lb>nelle rane 140, suoi errori intorno alla causa, per cui l&#039;aria introducesì ne&#039;polmoni 174, e intorno <lb></lb>all&#039;azione dell&#039;aria sul sangue 186. </s></p><p type="main">

<s><emph type="bold"></emph>Baliani Giovan Batista,<emph.end type="bold"></emph.end> come spieghi in che modo l&#039;animale si muova 50, preferisce le sue fanta­<lb></lb>tasie alle verità scoperte dall&#039;Harvey 157. </s></p><p type="main">

<s><emph type="bold"></emph>Bartholin Tommaso<emph.end type="bold"></emph.end> dimostra il Canal toracico in due cadaveri umani 226, sua nuova storia dei <lb></lb>Vasi linfatici 232. </s></p><p type="main">

<s><emph type="bold"></emph>Basilio Magno,<emph.end type="bold"></emph.end> fa menzione di un&#039;esperienza concernente la respirazion degl&#039;insetti 482. </s></p><p type="main">

<s><emph type="bold"></emph>Beccaria Giovan Batista,<emph.end type="bold"></emph.end> attribuisce la fosforescenza marina a un&#039;azione elettrica 502, riconosce <lb></lb>nell&#039;elettricità il principio visibile della vita 506. </s></p><p type="main">

<s><emph type="bold"></emph>Bellini Lorenzo,<emph.end type="bold"></emph.end> sue teorie de&#039;moti muscolari 57, come spieghi l&#039;alternarsi dei moti del cuore 95, <lb></lb>applica al sangue, fluente dalla aperta vena, gli effetti delle acque de&#039;fiumi nel rompersi degli <lb></lb>argini 115, rassomiglia l&#039;azion dell&#039;aria sul sangue dei polmoni all&#039;azione dell&#039;aria stessa sul­<lb></lb>l&#039;uovo 185, racconta come gli occorresse di scoprir sulla lingua le papille nervee del gusto 257. </s></p><p type="main">

<s><emph type="bold"></emph>Benedetti Giovan Batists,<emph.end type="bold"></emph.end> primo ad applicare le lenti cristalline al foro della Camera oscura, per <lb></lb>meglio rassomigliar lo strumento artificiale all&#039;occhio 339, suo problema meccanico intorno al <lb></lb>girar delle trottole 399. </s></p><p type="main">

<s><emph type="bold"></emph>Berengario Jacopo da Carpi,<emph.end type="bold"></emph.end> suoi commentarii all&#039;Anatomia del Mondino 10, sua Isagoge 11, sua <lb></lb>teoria de&#039;moti muscolari 45, come conge<gap></gap>turasse dover esser costrutto il cuore 87, come sosti­<lb></lb>tuisse le sue proprie immaginazioni alla dimostrata verità del circolo polmonare 129, ammette <lb></lb>con Galeno il setto medio perforato 130, primo inventore de&#039;due primi ossicini dell&#039;udito 270, <lb></lb>descrive le membrane dell&#039;occhio 302. </s></p><p type="main">

<s><emph type="bold"></emph>Bernoulli Giovanni<emph.end type="bold"></emph.end> censura un teorema di Meccanica muscolare dimostrato dallo Stenone 57, av­<lb></lb>verte un error del Borelli 76. </s></p><p type="main">

<s><emph type="bold"></emph>Bils Lodovico,<emph.end type="bold"></emph.end> suo Dutto rorifero 228. </s></p><p type="main">

<s><emph type="bold"></emph>Boheraave Ermanno<emph.end type="bold"></emph.end> confuta l&#039;opinione di chi dic<gap></gap>va tutte le sostanze generarsi dall&#039;acqua 594, come <lb></lb>definisca i sali 608, primo a far notare l&#039;efficacia del calore nelle soluzioni 613, sua teoria della <lb></lb>digestione 205. </s></p><p type="main">

<s><emph type="bold"></emph>Bonanni Filippo<emph.end type="bold"></emph.end> crede che le reliquie fossili animali siano un gioco della Natura 565. </s></p><p type="main">

<s><emph type="bold"></emph>Bonnet Carlo,<emph.end type="bold"></emph.end> sue esperienze sopra la respirazione delle foglie 530, sull&#039;uso proprio delle foglie se­<lb></lb>minali 556, nega che le piante si nutriscano di sola acqua 560. </s></p><p type="main">

<s><emph type="bold"></emph>Borelli Gian Alfonso<emph.end type="bold"></emph.end> promette due libri preparatorii alla teoria de&#039;moti animali 31, sua teorica dei <lb></lb>moti muscolari 55, risponde alle obiezioni dello Stenone 56, si riscontra colla celebre esperienza <lb></lb>del Galvani 61, è primo a dimostrare da che resulti la macchina dei moti muscolari 76, dimo­<lb></lb>stra che l&#039;aria entra nel petto dilatandosi il torace 173, sua controversia col Malpighi intorno <lb></lb>all&#039;uso dei polmoni 183, sua teoria meccanica della respirazione 18<gap></gap>, come sciogliesse il pro­<lb></lb>blema harveiano 195, conferma le osservazioni harveiane intorno alla digestione meccanica degli <lb></lb>uccelli 202, suo giudizio intorno al trattato del Glisson <emph type="italics"></emph>Anatome Hepatis<emph.end type="italics"></emph.end> 244. </s></p><p type="main">

<s><emph type="bold"></emph>Bot<gap></gap>llo Leonardo<emph.end type="bold"></emph.end> crede avere scoperta nel cuore una via nuova al sangue 191, perchè fosse ma­<lb></lb>giudicato dal Flourens 192. </s></p><p type="main">

<s><emph type="bold"></emph>Boyle Reberto<emph.end type="bold"></emph.end> dimostra sperimentalmente che l&#039;aria irrompe spontanea nel dilatato torace 172, primo <lb></lb>a tentar la soluzione del problema harveiano 194, sua esperienza a dimostrar che l&#039;aria è nel <lb></lb>cessaria alla vita dei pesci 444. </s></p><p type="main">

<s><emph type="bold"></emph>Branchie de&#039;pesci,<emph.end type="bold"></emph.end> loro uso secondo il Rondelezio 442, descritte dal Perrault 450. </s></p><p type="main">

<s><emph type="bold"></emph>Brocchi Giovan Batista,<emph.end type="bold"></emph.end> come risolva due celebri problemi geologici 590. </s></p><p type="main">

<s><emph type="bold"></emph>Buffen,<emph.end type="bold"></emph.end> qual falso criterio si proponga in ordinar la Natura 360, sua Teoria della Terra 587. </s></p><p type="main">

<s><emph type="bold"></emph>Burnet Tommaso,<emph.end type="bold"></emph.end> sua Teoria sacra della Terra 574. </s></p><p type="main">

<s><emph type="bold"></emph>Camerarius Bodolf&#039;Jacopo,<emph.end type="bold"></emph.end> primo a proporre in pubblico il sistema sessuale delle piante 539, con­<lb></lb>fronta la generazion delle piante con quella degli animali 540. </s></p><p type="main">

<s><emph type="bold"></emph>Camper Pietro<emph.end type="bold"></emph.end> dimostra che Galeno non sezionò mai cadaveri umani 380. </s></p><p type="main">

<s><emph type="bold"></emph>Canale,<emph.end type="bold"></emph.end> come dal Petit scoperto nell&#039;occhio 326. </s></p><p type="main">

<s><emph type="bold"></emph>Canali<emph.end type="bold"></emph.end> semicircolari dell&#039;orecchio descritti dal Falloppio 283. </s></p><p type="main">

<s><emph type="bold"></emph>Canalicmlo<emph.end type="bold"></emph.end> della vescica natatoria non in tutti i pesci ha origine dallo stomaco 435. </s></p><p type="main">

<s><emph type="bold"></emph>Canani Giovan Batista,<emph.end type="bold"></emph.end> primo a scoprire le valvole delle vene 144. </s></p><p type="main">

<s><emph type="bold"></emph>Capillari,<emph.end type="bold"></emph.end> fenomeni applicati dal Borelli a spiegare il moto del sangue nelle vene 107. </s></p><p type="main">

<s><emph type="bold"></emph>Caprifico,<emph.end type="bold"></emph.end> fico silvestre 543. </s></p><p type="main">

<s><emph type="bold"></emph>Caraffella,<emph.end type="bold"></emph.end> in cui il liquido sale e scende al variare della temperatura, applicata da Galileo e dal <lb></lb>Castelli alla fisiologia vegetabile e animale 27. </s></p><p type="main">

<s><emph type="bold"></emph>Cartes<gap></gap>o <gap></gap>enato<emph.end type="bold"></emph.end> introduce i suoi vizii filosofici anche nell&#039;Anatomia 34, sua teoria dei moti musco-<pb xlink:href="020/01/1748.jpg" pagenum="623"></pb>lari 47, contradice all&#039;Harveio intorno alla regola dei moti del cuore 92, argomenti di questa sua <lb></lb>contradizione 93, è prevenuto dal Cesalpino 94, sua ipotesi intorno all&#039;effetto dell&#039;aria sui pol­<lb></lb>moni 167, sua teoria della digestione 200, ammette l&#039;esistenza di un muscolo sfintere intorno <lb></lb>alla pupilla 316, propone il modo d<gap></gap> osservare le immagini rovesciate nell&#039;occhio 344. </s></p><p type="main">

<s><emph type="bold"></emph>Casserio Giulio,<emph.end type="bold"></emph.end> anatomico 21 </s></p><p type="main">

<s><emph type="bold"></emph>Cassini Gian Domenico<emph.end type="bold"></emph.end> osserva le galle della quercie 470. </s></p><p type="main">

<s><emph type="bold"></emph>Celso Cornelio<emph.end type="bold"></emph.end> descrive le membrane dell&#039;occhio 301. </s></p><p type="main">

<s><emph type="bold"></emph>Cesalpino Andrea<emph.end type="bold"></emph.end> conferma il circolo polmonare del sangue 133, è il primo ad asserire che tutti i <lb></lb>vasi hanno origine dal cuore 141, non conobbe il ritorno del sangue arterioso per le vene 142, <lb></lb>quale ei credesse esser l&#039;uso dell&#039;aria ne&#039;polmoni 166, crede che le meseraiche conducano il chilo <lb></lb>mescolato col sangue 212, non può, secondo il Borelli, attribuirsegli la scoperta dell&#039;Harvey 242, <lb></lb>propone in Botanica il primo sistema razionale 362, come ordini i Minerali 371, riconosce nelle <lb></lb>piante organi simili a quelli degli animali 509, rassomiglia l&#039;ascender della linfa ne&#039;vasi delle <lb></lb>piante all&#039;ascender dell&#039;olio nelle lucerne 510, primo a riconoscere le somiglianze, che passano <lb></lb>fra i semi delle piante, e le uova degli animali 551. </s></p><p type="main">

<s><emph type="bold"></emph>Chiocciola dell&#039;orecchio,<emph.end type="bold"></emph.end> invenzione di lei attribuita ad Empedocle e ad Aristotile 382, descritta dal­<lb></lb>l&#039;Eustachio 382, organo delle particolari percezioni de&#039;suoni, secondo il Cotunnio 299. </s></p><p type="main">

<s><emph type="bold"></emph>Cicale,<emph.end type="bold"></emph.end> organo con cui producono il suono descritto dal Casserio 488. </s></p><p type="main">

<s><emph type="bold"></emph>Cigno,<emph.end type="bold"></emph.end> organi del canto scoperti dall&#039;Aldovrandi in questo uccello 427. </s></p><p type="main">

<s><emph type="bold"></emph>Cigoli Lodovico,<emph.end type="bold"></emph.end> sua teoria della vista 342. </s></p><p type="main">

<s><emph type="bold"></emph>Ciliari,<emph.end type="bold"></emph.end> corpi dell&#039;occhio 309, loro struttura 311. </s></p><p type="main">

<s><emph type="bold"></emph>Cimento Accademici (del),<emph.end type="bold"></emph.end> loro esperienze intorno alla digestione delle galline e delle anatre 202. </s></p><p type="main">

<s><emph type="bold"></emph>Circolazione<emph.end type="bold"></emph.end> dei pianeti paragonata a quella del sangue 125, della linfa ne&#039;vasi delle piante 524. </s></p><p type="main">

<s><emph type="bold"></emph>Circolo cartesiano<emph.end type="bold"></emph.end> concernente l&#039;aria inspirata 170. </s></p><p type="main">

<s><emph type="bold"></emph>Civetta,<emph.end type="bold"></emph.end> occhio di lei scelto dal Briggs per osservare l&#039;inversione delle immagini 344. </s></p><p type="main">

<s><emph type="bold"></emph>Coda<emph.end type="bold"></emph.end> degli uccelli serve secondo Aristotile a dirigere il volo, come il timone dirige il corso alle <lb></lb>navi 403, dei pesci, organo essenziale del nuoto 439. </s></p><p type="main">

<s><emph type="bold"></emph>Cole Guglielmo,<emph.end type="bold"></emph.end> suo teorema idraulico applicato al moto del sangue 119. </s></p><p type="main">

<s><emph type="bold"></emph>Colombo Realdo,<emph.end type="bold"></emph.end> suo trattato <emph type="italics"></emph>De re anatomica<emph.end type="italics"></emph.end> 17, dimostra l&#039;utilità della vivisezione 23, scopre <lb></lb>negli animali vivi che i moti del cuore si fanno diversamente da quel che avea detto il Vesa­<lb></lb>lio 91, come scoprisse che l&#039;arteria vibra quando il ventricolo è in quiete 96, dimostra il circolo <lb></lb>polmonare 132, come enumeri le membrane dell&#039;occhio 303. </s></p><p type="main">

<s><emph type="bold"></emph>Colonna Fabio<emph.end type="bold"></emph.end> ordina le piante secondo il fiore e il frutto 364, come argomenti contro chi ammet­<lb></lb>teva le reliquie fossili marine essere generate dalla terra 563. </s></p><p type="main">

<s><emph type="bold"></emph>Conchiglie<emph.end type="bold"></emph.end> credute generarsi dal limo della terra 476. </s></p><p type="main">

<s><emph type="bold"></emph>Cornelio Tommaso<emph.end type="bold"></emph.end> dimostra esser falso, contro il Cartesio, che il calor del sangue produca i moti <lb></lb>del cuore 94, eseguisce l&#039;esperienza galenica creduta impossibile dall&#039;Harveio 99, primo a me­<lb></lb>ditare e a sperimentare intorno agli usi dell&#039;aria nella respirazione 175, è il primo a fare espe­<lb></lb>rienza che il forame ovale nei neonati si obliterà dopo qualche tempo 197, sua teorica della di­<lb></lb>gestione 203, rivendica le funzioni del Fegato 247, suoi paradossi intorno alla generazione 386. </s></p><p type="main">

<s><emph type="bold"></emph>Coroide,<emph.end type="bold"></emph.end> da che argomentasse il Mariotte esser ella, e non la retina, organo precipuo della visione 345. </s></p><p type="main">

<s><emph type="bold"></emph>Cotunnio Domenico,<emph.end type="bold"></emph.end> sua teorica dell&#039;udito 298. </s></p><p type="main">

<s><emph type="bold"></emph>Cristalli,<emph.end type="bold"></emph.end> secondo Plinio, originati dal ghiaccio 591, come fosse ripudiata questa opinione da Van­<lb></lb>noccio Biringucci 591, e come da Giorgio Agricola 592, come si figurano secondo il Cesalpino 600, <lb></lb>hanno, secondo il Keplero, figure prestabilite dalla Natura 603, si formano, secondo Erasmo Bar­<lb></lb>tholin, come i favi delle api, dalla necessità della materia 604. </s></p><p type="main">

<s><emph type="bold"></emph>Cristallino dell&#039;occhio,<emph.end type="bold"></emph.end> sua figura desunta dalle osservazioni 328, desunta dai principii diottrici 329, <lb></lb>creduto da alcuni Antichi organo essenziale della visione 335, fa, secondo il Plater, da occhiale <lb></lb>alla retina 339, ragione della sua particolar figura nell&#039;occhio dei pesci 453. </s></p><p type="main">

<s><emph type="bold"></emph>Cristallografia,<emph.end type="bold"></emph.end> sua prima cultura nell&#039;Accademia del Cimento 593, suoi principii stabiliti dallo <lb></lb>Stenone 598. </s></p><p type="main">

<s><emph type="bold"></emph>Croone Guglielmo,<emph.end type="bold"></emph.end> sua trattato dei moti muscolari 38, in che secondo lui consista la causa di quei <lb></lb>moti 55, primo a misurare la potenza dei muscoli 75. </s></p><p type="main">

<s><emph type="bold"></emph>Cuore,<emph.end type="bold"></emph.end> suoi moti involontarii 64, come si spieghino dal Borelli 65, è per Ippocrate un muscolo molto <lb></lb>forte 84, con quali argomenti provasse Galeno che non è altrimenti un muscolo 85, il Vesalio è <lb></lb>incerto della sua struttura, e il Colombo nega che sia muscolare 86, suo maraviglioso artificio <lb></lb>descritto dal Borelli 88, è composto di fibre aggomitola&#039;o 89, è tessuto, secondo il Vesalio, come <lb></lb>i vimini di un canestro 90, come si possano dal colore, secondo l&#039;Harveio, riconoscere le fasi <lb></lb>de&#039;suoi moti 92, ritmo de&#039;suoi moti 95, suoi moti dimostrati dall&#039;Harveio farsi contrariamente <lb></lb>a quelli delle arterie 97, misura delle sue forze secondo il Borelli 101, è il sole del Microcosmo 125. </s></p><pb xlink:href="020/01/1749.jpg" pagenum="624"></pb><p type="main">

<s><emph type="bold"></emph>Dati Carlo<emph.end type="bold"></emph.end> invia a Tommaso Bartholin l&#039;epistole malpighiane <emph type="italics"></emph>De pulmonibus<emph.end type="italics"></emph.end> 2<gap></gap>8, descrive la sto­<lb></lb>ria del manoscritto della Metalloteca vaticana 373. </s></p><p type="main">

<s><emph type="bold"></emph>Digby Chenelmo<emph.end type="bold"></emph.end> presente l&#039;azione chimica dell&#039;essigeno dell&#039;aria nella germogliazione dei semi 558. </s></p><p type="main">

<s><emph type="bold"></emph>Digestione degli animali,<emph.end type="bold"></emph.end> esperienze di Lazzero Spallanzani 206, esperienze particolari del medesimo <lb></lb>fatto sull&#039;uomo 208. </s></p><p type="main">

<s><emph type="bold"></emph>Disseminazione delle piante,<emph.end type="bold"></emph.end> suo meccanismo 550. </s></p><p type="main">

<s><emph type="bold"></emph>Dodart Dionirio,<emph.end type="bold"></emph.end> sua teoria della voce e della modulazione dei tuoni 425. </s></p><p type="main">

<s><emph type="bold"></emph>Drebbelio Cornelio,<emph.end type="bold"></emph.end> sua nave sottomarina 178. </s></p><p type="main">

<s><emph type="bold"></emph>Du-Verny Giuseppe<emph.end type="bold"></emph.end> riconosce la vera natura dei vasi sanguigni nei pesci 451. </s></p><p type="main">

<s><emph type="bold"></emph>Ecphrasis,<emph.end type="bold"></emph.end> titolo dato a un libre, dove Fabio Colonna descrive molte piante nuove 363. </s></p><p type="main">

<s><emph type="bold"></emph>Elettricltà,<emph.end type="bold"></emph.end> invocata a spiegare la fosforescenza marina 497. </s></p><p type="main">

<s><emph type="bold"></emph>Engiscopio,<emph.end type="bold"></emph.end> strumento diottrico, usato da Lorenzo Bellini per osservar le figure dei sali 606. </s></p><p type="main">

<s><emph type="bold"></emph>Epatico-acquosi (dutti),<emph.end type="bold"></emph.end> prima scoperti con questa denominazione da Olao Rudbeck 230. </s></p><p type="main">

<s><emph type="bold"></emph>Esperienza galenica<emph.end type="bold"></emph.end> creduta dall&#039;Harveio impossibile a praticarsi 98, del Vesalio intorno al riattivar <lb></lb>l&#039;uso de&#039;polmoni 168. </s></p><p type="main">

<s><emph type="bold"></emph>Etere elettrico<emph.end type="bold"></emph.end> applicato dal Newten a spiegar la causa dei moti muscolari 60. </s></p><p type="main">

<s><emph type="bold"></emph>Eustachio Bartolommeo,<emph.end type="bold"></emph.end> sue Tavole anatomiche 18, sostiene che Galeno descrisse il corpo dell&#039;uomo, <lb></lb>e non delle scimmie 280, se si possa attribuirgli il merito di avere scoperto il Canale toracico 241. </s></p><p type="main">

<s><emph type="bold"></emph>Faber Giovanni<emph.end type="bold"></emph.end> scopre gli organi della ruminazione 408. </s></p><p type="main">

<s><emph type="bold"></emph>Fabry Gnorato,<emph.end type="bold"></emph.end> suoi giudizi intorno alla prima scoperia del Canale toracico 223, sua smania d&#039;ap­<lb></lb>propriarsi le altrui scoperte 224 </s></p><p type="main">

<s><emph type="bold"></emph>Fagioli,<emph.end type="bold"></emph.end> esperienze fatte dal Bonnet intorno alla loro germogliazione 556. </s></p><p type="main">

<s><emph type="bold"></emph>Falloppio Gabbriello,<emph.end type="bold"></emph.end> come si risolvesse a scrivere le sue Osservazioni anatomiche 14, suoi precetti <lb></lb>di Anatemia 16, dimostra, dall&#039;esame degli ossi, che Galeno descrisse lo scheletro delle scimmie 279. </s></p><p type="main">

<s><emph type="bold"></emph>Farfalle,<emph.end type="bold"></emph.end> fosforescenza scoperta ne&#039;loro occhi 566. </s></p><p type="main">

<s><emph type="bold"></emph>Fegato,<emph.end type="bold"></emph.end> epigrafe di Tommaso Bartholin da porsi sul suo tumulo 232, rivendicato nella sua dignità <lb></lb>dal Van-Horne 234. </s></p><p type="main">

<s><emph type="bold"></emph>Fernelio Giovanni<emph.end type="bold"></emph.end> argomenta dalla ragione, e non dal senso, che le meseraiche portano il chilo al <lb></lb>Fegato 210. </s></p><p type="main">

<s><emph type="bold"></emph>Ferrein Antonio,<emph.end type="bold"></emph.end> sua teorica della voce 427. </s></p><p type="main">

<s><emph type="bold"></emph>Fiamma,<emph.end type="bold"></emph.end> che arde in mezzo all&#039;aria, paragonata<gap></gap>al polmone che respira 176. </s></p><p type="main">

<s><emph type="bold"></emph>Fico<emph.end type="bold"></emph.end> addotto per un<gap></gap> de&#039;più validi argomenti contro la sessualità delle piante 544, sua vera inf<gap></gap>re­<lb></lb>scenza da chi prima scoperta 544. </s></p><p type="main">

<s><emph type="bold"></emph>Finck Giovanni<emph.end type="bold"></emph.end> è creduto da Claudio Beriguardo primo dimostratore del Canale toracico 239. </s></p><p type="main">

<s><emph type="bold"></emph>Finextra rotonda,<emph.end type="bold"></emph.end> nell&#039;interno dell&#039;or<gap></gap>hio, sua vera figura 277, non è aperta ma chiusa da una <lb></lb>apposita membrana 278, usi di lei secondo l&#039;Ingrassia 291, secondo il Valsalva 297, nell&#039;or<gap></gap>chio <lb></lb>degli uccelli descritta dallo Scarpa 420. </s></p><p type="main">

<s><emph type="bold"></emph>Fiore delle piante,<emph.end type="bold"></emph.end> ufficio di lui secondo il Malpighi 536, secondo il Grew 537. </s></p><p type="main">

<s><emph type="bold"></emph>Fisiologia del cuore<emph.end type="bold"></emph.end> ebbe origine dalle vivisezioni del Colombo, proseguite dall&#039;Harveio 24. </s></p><p type="main">

<s><emph type="bold"></emph>Fitobasano,<emph.end type="bold"></emph.end> libro dove si descrivono le nuove piante scoperte da Fabio Colonna 363. </s></p><p type="main">

<s><emph type="bold"></emph>Foglie nelle piante<emph.end type="bold"></emph.end> servono, secondo il Malpighi, a concuocere gli alimenti 520, s&#039;imlevono del­<lb></lb>l&#039;umidità dell&#039;aria 521, servono alla traspiraziene 522, aiuta<gap></gap>e l&#039;ascesa dei succo nutritizi<gap></gap> 523. <lb></lb>foglie seminali, loro usi sperimentati dal Malpighi 553, loro ufficii nella germagliazione, secondo <lb></lb>il Borelli 554, sono organi non accessorii, ma necessarii 555. </s></p><p type="main">

<s><emph type="bold"></emph>Folli Francesco<emph.end type="bold"></emph.end> <gap></gap>arra come gli sovvenisse il pensiero di trasfondere il sangue da un animale in <lb></lb>un altro 158. </s></p><p type="main">

<s><emph type="bold"></emph>Forame ovale<emph.end type="bold"></emph.end> nel feto si richiude dopo qualche tempo 196. </s></p><p type="main">

<s><emph type="bold"></emph>Forami,<emph.end type="bold"></emph.end> aperti sulla superfice dei pesci <gap></gap>63. </s></p><p type="main">

<s><emph type="bold"></emph>Fosforescenza marina,<emph.end type="bold"></emph.end> come spiegata dal Cartesio 496, come dal Borelli 497, delle carni dei pesci <lb></lb>sperimentata dal Boyle, e confermata nell&#039;Accademia del Cimento 503. </s></p><p type="main">

<s><emph type="bold"></emph>Fracassati Carlo,<emph.end type="bold"></emph.end> anatomico, allevato dal Borelli 31, propone la sua nu<gap></gap>va Medicina infusoria 160. </s></p><p type="main">

<s><emph type="bold"></emph>Fracastoro Girolamo,<emph.end type="bold"></emph.end> opinioni varie riferite da lui intorno all&#039;origine dei corpi marini, che si tro­<lb></lb>vano fossili dispersi nei continenti 563. </s></p><p type="main">

<s><emph type="bold"></emph>Fuoco<emph.end type="bold"></emph.end> centrale della Terra ammesso da Galileo e negato dal Reni<gap></gap>ri 580. </s></p><p type="main">

<s><emph type="bold"></emph>Galeno,<emph.end type="bold"></emph.end> grande Maestro di Anatomia 9, primo a conoscer gli ufficii de&#039;muscoli 44, come dimostri <lb></lb>il circolo polmenare del sangue 127, sue osservazioni intorno a certi organi inservienti alla cir­<lb></lb>colazione del sangue nel feto 188, idee attribuitegli intorno alla respirazione dei pesci 441. </s></p><pb xlink:href="020/01/1750.jpg" pagenum="625"></pb><p type="main">

<s><emph type="bold"></emph>Galileo<emph.end type="bold"></emph.end> derivò dall&#039;Acquapendente e dal Santorio un certo amore per l&#039;Anatomia, e per la Medi­<lb></lb>cina 25, dimostra il teorema fondamentale della Meccanica animale 77, spiega da che nasca la <lb></lb>stanchezza, che sentesi nelle nostre membra 79, sua teoria meccanica delle funi applicate al <lb></lb>meccanismo del cuore 89, sua faliace instituzione intorno alla vista 341, sue osservazioni intorno <lb></lb>alle piante 511, come spieghi il maturarsi dei frutti 512. </s></p><p type="main">

<s><emph type="bold"></emph>Galle della querce,<emph.end type="bold"></emph.end> loro generazione descritta 475. </s></p><p type="main">

<s><emph type="bold"></emph>Galvani Luigi,<emph.end type="bold"></emph.end> sua teoria elettrica dei moti muscolari 61, come invochi l&#039;azione del fluido elettrico <lb></lb>a spiegare i moti necessarii dei muscoli, e i volontarii 70. </s></p><p type="main">

<s><emph type="bold"></emph>Gangli dei nervi<emph.end type="bold"></emph.end> descritti dal Lancisi 68. </s></p><p type="main">

<s><emph type="bold"></emph>Gassendo Pietro<emph.end type="bold"></emph.end> crede che il passo de&#039;quadrupedi si faccia commutando diagonalmente i piedi 397, <lb></lb>per quali ragioni negasse l&#039;udito ai pesci 459, sue dottrine intorno alla generazion degl&#039;insetti 472. </s></p><p type="main">

<s><emph type="bold"></emph>Geologia moderna<emph.end type="bold"></emph.end> è una esplicazione de&#039;concetti esposti nell&#039;Accademia del Cimento da Niecolò <lb></lb>Stenone 588. </s></p><p type="main">

<s><emph type="bold"></emph>Gesner Currado,<emph.end type="bold"></emph.end> primo a ordinar le piante secondo il fiore e il frutto 362. </s></p><p type="main">

<s><emph type="bold"></emph>Ghiandole sierose,<emph.end type="bold"></emph.end> prima scoperte da Olao Rudbeck 239, conglobate, studiate prima e descritte dal <lb></lb>Malpighi 249. </s></p><p type="main">

<s><emph type="bold"></emph>Glisson Francesco,<emph.end type="bold"></emph.end> usi assegnati da lui alla linfa 237, ammette nell&#039;animale un quinto genere di <lb></lb>vasi 238. </s></p><p type="main">

<s><emph type="bold"></emph>Glottide,<emph.end type="bold"></emph.end> precipuo strumento della voce, secondo Galeno e il Berengario 422. </s></p><p type="main">

<s><emph type="bold"></emph>Graaf Begnero,<emph.end type="bold"></emph.end> suo trattato <emph type="italics"></emph>De mulierum organis<emph.end type="italics"></emph.end> 388. </s></p><p type="main">

<s><emph type="bold"></emph>Grew Neemia<emph.end type="bold"></emph.end> presenta alla R. </s>

<s>Società di Londra la sua Anatomia delle piante 514, esamina e giu­<lb></lb>dica l&#039;Anatomia fitologica del Malpighi 515 e 517. </s></p><p type="main">

<s><emph type="bold"></emph>Grilli,<emph.end type="bold"></emph.end> organi e meccanismo, con cui producono il suono, descritti dal Casserio 488. </s></p><p type="main">

<s><emph type="bold"></emph>Guglielmini Domenico<emph.end type="bold"></emph.end> dimostra co&#039;principii idraulici le leggi del moto del sangue per le arterie 105, <lb></lb>e per le vene 110, conferma un teorema di Guglielmo Colo 120, confuta l&#039;opinione della fiamma <lb></lb>vitale 156, primo ad applicar la Geometria alle figure cristalline 610. </s></p><p type="main">

<s><emph type="bold"></emph>Gusto,<emph.end type="bold"></emph.end> propria sede dell&#039;organo ritrovata dal Bellini 257, e dal Fracassati 258. </s></p><p type="main">

<s><emph type="bold"></emph>Hales Stefano<emph.end type="bold"></emph.end> intraprende esperienze, per trovar la ragione dei moti muscolari 59, misura la forza <lb></lb>impulsiva del cuore 103, sperimenta sulle perdite di velocita del sangue, nel passare dal tronco <lb></lb>ai rami 121. </s></p><p type="main">

<s><emph type="bold"></emph>Haller Alberto<emph.end type="bold"></emph.end> compie la teoria dell&#039;irritabilità dei muscoli proposta dal Bellini 58, come spiegi i <lb></lb>moti muscolari, indipendenti dalla volontà 70, sperimenta la verità del Teorema belliniano, re­<lb></lb>lativo all&#039;emissione del sangue 118. </s></p><p type="main">

<s><emph type="bold"></emph>Harvey Guglielmo,<emph.end type="bold"></emph.end> se la scoperta del circolo del sangue gli possa essere stata ispirata da Galeno 137, <lb></lb>sua opiniono intorno all&#039;uso dell&#039;aria ne&#039;polmoni 167, primo a descrivere il circolo sanguigno <lb></lb>nel feto 194, sue opinioni intorno alla digestione degli uccelli 201, nega le vene lattee 216, come <lb></lb>professasse anch&#039;egli il falso principio della generazione spontanea 497, sue esperienze sopra la <lb></lb>respirazione degl&#039;insetti 482. </s></p><p type="main">

<s><emph type="bold"></emph>Hegardt Cornelio,<emph.end type="bold"></emph.end> primo a spiegar, nel sistema sessuale, la frutescenza del fico 548. </s></p><p type="main">

<s><emph type="bold"></emph>Hire (de la) Filippo<emph.end type="bold"></emph.end> scopre i tre occhi in fronte alle mosche 491. </s></p><p type="main">

<s><emph type="bold"></emph>Hodierna Giovan Batista,<emph.end type="bold"></emph.end> primo a descrivere l&#039;occhio delle mosche 489. </s></p><p type="main">

<s><emph type="bold"></emph>Homberg Guglielmo<emph.end type="bold"></emph.end> trova germogliare i semi anche nel vuoto 558. </s></p><p type="main">

<s><emph type="bold"></emph>Idrauliche,<emph.end type="bold"></emph.end> leggi del moto de&#039;liquidi nelle trombe, applicate dal Borelli ai moti del cuore 112, e del <lb></lb>sangue 113. </s></p><p type="main">

<s><emph type="bold"></emph>I<gap></gap>hmor Natana<gap></gap>le<emph.end type="bold"></emph.end> dimostra i moti della respirazione d<gap></gap>pendere dal torace 169. </s></p><p type="main">

<s><emph type="bold"></emph>Immagini rovesciate<emph.end type="bold"></emph.end> sulla retina, da chi primo sperimentate 343. </s></p><p type="main">

<s><emph type="bold"></emph>Imperato Ferrante,<emph.end type="bold"></emph.end> sue Storie naturali 355, cause da lui assegnate alle variazioni della superfice <lb></lb>terrestre 568, sue osservazioni e descrizioni di varie forme cristalline 596. </s></p><p type="main">

<s><emph type="bold"></emph>Incudine,<emph.end type="bold"></emph.end> origine di questo nome dato a uno degli assicini dell&#039;udito 268. </s></p><p type="main">

<s><emph type="bold"></emph>Insetti fastidiosi,<emph.end type="bold"></emph.end> loro generazione dall&#039;uovo 478, loro occhi riscontrano per ogni parte con quelli <lb></lb>degli animali superiori 493, esperienze otticbe fatte con la cornea dei loro occhi dal Puget, e <lb></lb>descritte dal Reaumur 494. </s></p><p type="main">

<s><emph type="bold"></emph>Insetto,<emph.end type="bold"></emph.end> perchè cosi denominato 495. </s></p><p type="main">

<s><emph type="bold"></emph>Iride dell&#039;occhio,<emph.end type="bold"></emph.end> origine del nome 311, ragione del suo vario colore 312, non ha rigirato intorno al <lb></lb>foro pupillare nessun muscolo sfintere 317, sua struttura striata 318, qual sia lo stato suo natu­<lb></lb>rale, se quando è contratta, o quando è dilatata <emph type="italics"></emph>ivi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Jatromatematica,<emph.end type="bold"></emph.end> scuola instituita in Italia, suoi pregi e sua insufficienza riconosciuta, 40. </s></p><pb xlink:href="020/01/1751.jpg" pagenum="626"></pb><p type="main">

<s><emph type="bold"></emph>Keill Iacopo,<emph.end type="bold"></emph.end> come misuri la forza muscolare del cuore 102, calcola in qual proporzione stia la somma <lb></lb>delle luci de&#039;rami sanguigni, rispetto a quella del tronco 121. </s></p><p type="main">

<s><emph type="bold"></emph>Keplero Giovanni,<emph.end type="bold"></emph.end> come emendasse la teorica della visione data dal Porta 340. </s></p><p type="main">

<s><emph type="bold"></emph>King Oloardo,<emph.end type="bold"></emph.end> probabilmente attinse dallo Stenone le sue teorie geologiche 387, </s></p><p type="main">

<s><emph type="bold"></emph>Klein Iacopo Teodoro<emph.end type="bold"></emph.end> crede di aver ritrovate tutte le parti dell&#039;organo uditorio dei pesci 464. </s></p><p type="main">

<s><emph type="bold"></emph>Lamia,<emph.end type="bold"></emph.end> pesce anatomizzato dallo Stenone 373. </s></p><p type="main">

<s><emph type="bold"></emph>Lamina spirale<emph.end type="bold"></emph.end> dell&#039;orecchio, organo precipuo, secondo il Duverney, dell&#039;udito 295. </s></p><p type="main">

<s><emph type="bold"></emph>Lancisi Giovan Maria,<emph.end type="bold"></emph.end> sua teorica dei moti muscolari 67, applica al cuore la meccanica galileiana <lb></lb>delle funi 90. </s></p><p type="main">

<s><emph type="bold"></emph>Lapilli<emph.end type="bold"></emph.end> nell&#039;orecchio dei pesci 463. </s></p><p type="main">

<s><emph type="bold"></emph>Laringe inferiore<emph.end type="bold"></emph.end> negli uccelli scoperta dall&#039;Aldovrandi 427, confermata dalle esperienze del Perrault 428. </s></p><p type="main">

<s><emph type="bold"></emph>Lattee vene,<emph.end type="bold"></emph.end> da chi prima scoperte nell&#039;uomo 215. </s></p><p type="main">

<s><emph type="bold"></emph>Lauro,<emph.end type="bold"></emph.end> germogliazione delle bacche di lui sperimentata dal Borelli 553. </s></p><p type="main">

<s><emph type="bold"></emph>Leeuwenoeck Antonio<emph.end type="bold"></emph.end> osserva la circolazione del sangue nella coda delle anguille 150. </s></p><p type="main">

<s><emph type="bold"></emph>Lenticolare,<emph.end type="bold"></emph.end> ossicino dell&#039;udito, storia della sua scoperta 273. </s></p><p type="main">

<s><emph type="bold"></emph>Linfa,<emph.end type="bold"></emph.end> sua ascesa nelle piante, come spiegata dal Mariotte e dal Perrault 519, viaggio di lei nelle <lb></lb>piante descritto dal Malpighi 525. </s></p><p type="main">

<s><emph type="bold"></emph>Lingua<emph.end type="bold"></emph.end> dei pesci 454, è in questi animali organo del gusto, secondo il Rondelezio 454, non ha le <lb></lb>papille nervee del gusto, secondo il Fracassati 455. </s></p><p type="main">

<s><emph type="bold"></emph>Linneo Carlo,<emph.end type="bold"></emph.end> suo metodo di ordinare le piante 368, confessa di non aver saputo scoprir la causa <lb></lb>della fosforescenza marina, prima del Vianelli 501, sua filosofia botanica dei s<gap></gap>ssi 546. </s></p><p type="main">

<s><emph type="bold"></emph>Lower Riccardo<emph.end type="bold"></emph.end> fa esperienze sulla trasfusione del sangue 160. </s></p><p type="main">

<s><emph type="bold"></emph>Lucciole,<emph.end type="bold"></emph.end> come perdano il lume nel vuoto, secondo le esperienze degli Accademici del Cimento 503, <lb></lb>organi della loro fosforescenza descritti dal Malpighi 505. </s></p><p type="main">

<s><emph type="bold"></emph>Lusitano Amato,<emph.end type="bold"></emph.end> sua mendace esperienza per dimostrar le valvole delle vene 144. </s></p><p type="main">

<s><emph type="bold"></emph>Magalotti Lorenzo,<emph.end type="bold"></emph.end> suo discorso intorno ai vasi linfatici, e al circolo glissoniano 244-47, ammette la <lb></lb>generazione dei vermi dalla vita delle piante 471. </s></p><p type="main">

<s><emph type="bold"></emph>Magiotti Raffaello<emph.end type="bold"></emph.end> inizia la Jatromatematica insieme con Galileo e col Castelli 28, suggerisce al <lb></lb>Borelli un principio fisico, per spiegare i moti animali 53 e 55, primo a diffondere in Italia la <lb></lb>scoperta del circolo del sangue 155, esorta Galileo a trattar dell&#039;incesso degli animali 397. </s></p><p type="main">

<s><emph type="bold"></emph>Magnol Pietro,<emph.end type="bold"></emph.end> suoi criterii seguiti nell&#039;ordinare le piante 365. </s></p><p type="main">

<s><emph type="bold"></emph>Malpighi Marcello,<emph.end type="bold"></emph.end> chiamato dal Borelli allo studio dell&#039;anatomia 33, come dimostri che i nervi <lb></lb>son tubolari 54, rivendica a se la scoperta delle fibre spirali del cuore 89, fa primo uso delle <lb></lb>iniezioni, per dimostrar le anastomosi de&#039;vasi arteriosi coi venosi 149, osserva il circolo del sangue <lb></lb>nelle vene 149, sua teorica intorno all&#039;uso dei polmoni 181, intravede le vere funzioni dell&#039;aria <lb></lb>inspirata sul sangue 184, conferma l&#039;esistenza delle uova nelle femmine dei quadrupedi 389, <lb></lb>dimostra esser dall&#039;uovo anche la generazione dei vermi delle galle 474, scopre le trachee nelle <lb></lb>piante 513, presenta la sua prima idea dell&#039;Anatomia delle piante alla R. </s>

<s>Società di Londra 514, <lb></lb>scrive altri trattati sull&#039;Anatomia delle piante 515, causa del disordine tenuto nella pubblicazione <lb></lb>di questi trattati, e quale altro ordine avrebbe probabilmente dato a loro l&#039;Autore 516, sue espe­<lb></lb>rienze sopra l&#039;uso delle foglie seminali 556. </s></p><p type="main">

<s><emph type="bold"></emph>Mantice,<emph.end type="bold"></emph.end> rassomigliato, prima da Aristotile e poi dal Cartesio, al polmone 168. </s></p><p type="main">

<s><emph type="bold"></emph>Marini,<emph.end type="bold"></emph.end> corpi ritrovati nei continenti, loro origine secondo il Falleppio, l&#039;Agricola e il Cesalpino 562. </s></p><p type="main">

<s><emph type="bold"></emph>Mariotte Edmondo<emph.end type="bold"></emph.end> descrive una sua nuova esperienza intorno alla vista 344. </s></p><p type="main">

<s><emph type="bold"></emph>Marsili Luigi Ferdinando,<emph.end type="bold"></emph.end> suo saggio fisico della Storia naturale del mare 582. </s></p><p type="main">

<s><emph type="bold"></emph>Martello,<emph.end type="bold"></emph.end> origine di questo nome imposto a uno degli ossicini dell&#039;udito 268. </s></p><p type="main">

<s><emph type="bold"></emph>Mascagni Paolo,<emph.end type="bold"></emph.end> a che attribuisce il moto della linfa 250. </s></p><p type="main">

<s><emph type="bold"></emph>Mattioli Pier Andrea<emph.end type="bold"></emph.end> nega la sessualità dalle piante 535. </s></p><p type="main">

<s><emph type="bold"></emph>Mayow Giovanni<emph.end type="bold"></emph.end> dice che l&#039;aria inspirata, operante sul sangue, è di natura nitro salina 180. </s></p><p type="main">

<s><emph type="bold"></emph>Membrana<emph.end type="bold"></emph.end> tesa nell&#039;interna cavità dell&#039;orecchio da chi prima scoperta 265, del timpano, da chi prima <lb></lb>fosse così denominato <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> come e chi lo trovasse compaginato di più pellicole soprapposte, 266 </s></p><p type="main">

<s><emph type="bold"></emph>Mercati Michele,<emph.end type="bold"></emph.end> come ordini i minirali 376, varie forme cristalline esibite dagli iconismi di lui. </s>

<s>598. </s></p><p type="main">

<s><emph type="bold"></emph>Mercuriale Girolamo,<emph.end type="bold"></emph.end> sue nuove osservazioni anatomiche nel ventricolo dei ruminanti 407. </s></p><p type="main">

<s><emph type="bold"></emph>Mersenne Marino<emph.end type="bold"></emph.end> divulga l&#039;invenzione drebbelliana delle navi sottomarine 178. </s></p><p type="main">

<s><emph type="bold"></emph>Meseraiche vene,<emph.end type="bold"></emph.end> valvole scoperte in esse dal Colombo 211. </s></p><p type="main">

<s><emph type="bold"></emph>Metalloteca vaticana<emph.end type="bold"></emph.end> di Michele Mercati 375. </s></p><p type="main">

<s><emph type="bold"></emph>Michelini Famiano,<emph.end type="bold"></emph.end> suo sistema di Medicina 30, annunzia a Galileo e al Baliani la scoperta del oir­<lb></lb>colo del sangue 156. </s></p><pb xlink:href="020/01/1752.jpg" pagenum="627"></pb><p type="main">

<s><emph type="bold"></emph>Michelotti Pierantonio,<emph.end type="bold"></emph.end> difficoltà da lui promosse contro il calcolo delle forze del cuore fatto dal <lb></lb>Keil 104, è primo a diffidar dell&#039;applicazione delle leggi idrauliche al moto del sangue 117. </s></p><p type="main">

<s><emph type="bold"></emph>Micrografia,<emph.end type="bold"></emph.end> suoi progressi nelle applicazioni allo studio degl&#039;insetti 479, opera di R. </s>

<s>Hoohe 481, <lb></lb>dove vi si trovano descritti gli occhi delle mosche 490. </s></p><p type="main">

<s><emph type="bold"></emph>Minerali,<emph.end type="bold"></emph.end> come Aristotile gli distingua per le loro diverse origini 369. </s></p><p type="main">

<s><emph type="bold"></emph>Molinetti Antonio,<emph.end type="bold"></emph.end> come spieghi l&#039;adattamento dell&#039;occhio a veder distintintamente nelle varie di­<lb></lb>stanze 349. </s></p><p type="main">

<s><emph type="bold"></emph>Montanari Ceminiano<emph.end type="bold"></emph.end> descrive la trasfusione del sangue da un agnello in un cane decrepito 161. </s></p><p type="main">

<s><emph type="bold"></emph>Morgagni Giovan Batista,<emph.end type="bold"></emph.end> qual uso egli assegni ai gangli nervosi 249, scopre esser la membrana <lb></lb>del timpano composta di più pellicole soprapposte 266. dimostra contro il Mariotte che l&#039;organo <lb></lb>precipuo della visione è la retina, e non la cor<gap></gap>dea 347. </s></p><p type="main">

<s><emph type="bold"></emph>Mero Lazzaro,<emph.end type="bold"></emph.end> suo trattato dei crostacei marini <gap></gap>84, suo sistema geologico è uno svolgimento delle <lb></lb>idee dello Stenone 585. </s></p><p type="main">

<s><emph type="bold"></emph>Muscoli,<emph.end type="bold"></emph.end> non possono nel contrarsi rassomigliarsi alle funi inumidite 52. </s></p><p type="main">

<s><emph type="bold"></emph>Muscolo minimo,<emph.end type="bold"></emph.end> trovato dall&#039;Eustachio nell&#039;osso pietrose 274, casseriano, scoperto anche dall&#039;Acqua­<lb></lb>pendente nell&#039;interno dell&#039;orecchio 275. </s></p><p type="main">

<s><emph type="bold"></emph>Nardi Antonio,<emph.end type="bold"></emph.end> de&#039;primi in Italia ad accogliere la scoperta del circolo del sangue 155, crede collo <lb></lb>Harvey che gl&#039;insetti respirino dagli anelli del ventre e se ne assicura coll&#039;esperienza 483. </s></p><p type="main">

<s><emph type="bold"></emph>Nardi Giovanni,<emph.end type="bold"></emph.end> suo trattato <emph type="italics"></emph>De igne subterraneo<emph.end type="italics"></emph.end> 578, lettura di questo trattato raccomandata ai <lb></lb>suoi discepoli da Galileo 580. </s></p><p type="main">

<s><emph type="bold"></emph>Nervi,<emph.end type="bold"></emph.end> non sono, secondo T. Bartholini, canali, 49, ottici, se siano perforati 320, loro inserzione ec­<lb></lb>centrica 334. </s></p><p type="main">

<s><emph type="bold"></emph>Neve,<emph.end type="bold"></emph.end> le figure cristalline di lei fu creduto essere stato il primo a osservarle G. D. </s>

<s>Cassini 601, loro <lb></lb>origine come spiegata dal Cartesio 6<gap></gap>4. </s></p><p type="main">

<s><emph type="bold"></emph>Newton Isacco<emph.end type="bold"></emph.end> applica il principio delle attrazioni e delle repulsioni molecolari alla formazione dei <lb></lb>cristalli 613. </s></p><p type="main">

<s><emph type="bold"></emph>Nitro,<emph.end type="bold"></emph.end> sale, ristoratore, secondo il Digby, dell&#039;aria viziata nella respirazione 179. </s></p><p type="main">

<s><emph type="bold"></emph>Nollet<emph.end type="bold"></emph.end> confessa di avere scoperte le lucciole marine dopo il Vianelli 591. </s></p><p type="main">

<s><emph type="bold"></emph>Notatoio<emph.end type="bold"></emph.end> dei pesci, da chi prima scoperto 433. </s></p><p type="main">

<s><emph type="bold"></emph>Occhio,<emph.end type="bold"></emph.end> sua iconografia 333, suo adattamento a vedere in varie distanze, come spiegato 349. </s></p><p type="main">

<s><emph type="bold"></emph>Ocelli<emph.end type="bold"></emph.end> e occhi del bombice, descritti dal Malpighi 490. </s></p><p type="main">

<s><emph type="bold"></emph>Odorato,<emph.end type="bold"></emph.end> qual credessero che ne fosse lo strumento gli antichi 259, come, secondo il Molinetti, si <lb></lb>moltiplichi nei canaliculi dell&#039;osso cribroso 251, dei pesci, loro organo descritto 460. </s></p><p type="main">

<s><emph type="bold"></emph>Odori,<emph.end type="bold"></emph.end> loro natura descritta da A. </s>

<s>Nardi 260, osservazioni intorno ad essi fatte dal Magalotti 262. </s></p><p type="main">

<s><emph type="bold"></emph>Olivari<emph.end type="bold"></emph.end> corpi, nome dato dal Falloppio ai gangli dei nervi 67. </s></p><p type="main">

<s><emph type="bold"></emph>Olmi,<emph.end type="bold"></emph.end> vermi annidati nelle loro foglie 469. </s></p><p type="main">

<s><emph type="bold"></emph>Ordinamenti<emph.end type="bold"></emph.end> animali secondo Aristotile 352. </s></p><p type="main">

<s><emph type="bold"></emph>Orecchio<emph.end type="bold"></emph.end> dei pesci, cosi volgarmente dette, sono i loro polmoni 447. </s></p><p type="main">

<s><emph type="bold"></emph>Orecchio<emph.end type="bold"></emph.end> esterno variamente configurato nei varii animali 419. </s></p><p type="main">

<s><emph type="bold"></emph>Ossiciui<emph.end type="bold"></emph.end> dell&#039;udito prima commemorati dal Berengario 267, da chi prima veramente scoperti 269, <lb></lb>dell&#039;udito ne&#039;pesci, descritti dal Severino 458. </s></p><p type="main">

<s><emph type="bold"></emph>Ossicino<emph.end type="bold"></emph.end> dell&#039;udito negli uccelli, descritto dallo Scarpa 420. </s></p><p type="main">

<s><emph type="bold"></emph>Palme,<emph.end type="bold"></emph.end> loro sessualità 534. </s></p><p type="main">

<s><emph type="bold"></emph>Papille<emph.end type="bold"></emph.end> nervee ritrovate dal Malpighi sopra la lingua 254, qual sia il loro uso 255, sopra la cute in <lb></lb>che modo le scoprisse il Malpighi <emph type="italics"></emph>ivi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Paracelso<emph.end type="bold"></emph.end> riconosce nell&#039;aria l&#039;elixir della vita 177. </s></p><p type="main">

<s><emph type="bold"></emph>Passo<emph.end type="bold"></emph.end> dei quadrupedi, come si faccia secondo Aristotile e secondo l&#039;Acquapendente 396, come secondo <lb></lb>Galileo e secondo il Borelli 398. </s></p><p type="main">

<s><emph type="bold"></emph>Pecquet Giovanni,<emph.end type="bold"></emph.end> a quali momenti riduca le forze motrici del sangue ne&#039;vasi 100, conferma il moto <lb></lb>circ<gap></gap>lare del sangue supposto dall&#039;Harvey 147, narra come scoprisse il ricettacolo del chilo 219-21. </s></p><p type="main">

<s><emph type="bold"></emph>Peli<emph.end type="bold"></emph.end> negli occhi degl&#039;insetti, scoperti dal Vallisnieri 492. </s></p><p type="main">

<s><emph type="bold"></emph>Perrault Claudio<emph.end type="bold"></emph.end> crede che tutti gli organi dei sensi negl&#039;insetti si riducano a quello del tatto 492. </s></p><p type="main">

<s><emph type="bold"></emph>Pesci artificiall<emph.end type="bold"></emph.end> costruiti dal Magiotti, per dimostrar la meccanica dei loro moti 432; naturali, loro <lb></lb>respirazione negata da Aristotile 440, affermata da Galeno <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> circolo del loro sangue, secondo <lb></lb>il Perrault 449, papille nervee del gusto dove risiedano in essi 455, loro organi che servono <lb></lb>all&#039;udito e all&#039;<gap></gap>fatto, secondo il Casserio 457, alcuni di essi nascono spontaneamente, secondo il <lb></lb>Rondelezio 496. </s></p><pb xlink:href="020/01/1753.jpg" pagenum="628"></pb><p type="main">

<s><emph type="bold"></emph>Petali,<emph.end type="bold"></emph.end> nome imposto da Fabio Colonna alle foglie colorite dei fiori 542. </s></p><p type="main">

<s><emph type="bold"></emph>Pettine,<emph.end type="bold"></emph.end> nell&#039;occhio degli uccelli 419. </s></p><p type="main">

<s><emph type="bold"></emph>Peyer Giovan Currado,<emph.end type="bold"></emph.end> sua Mericologia 409, obiezioni fatte contro lei e risposte 411. </s></p><p type="main">

<s><emph type="bold"></emph>Piante,<emph.end type="bold"></emph.end> come siano ordinate in un libro attribuito ad Aristotile 361. </s></p><p type="main">

<s><emph type="bold"></emph>Pietruzze<emph.end type="bold"></emph.end> nel ventricolo degli uccelli, loro uso secondo l&#039;Harvey 412, secondo il Borelli 413. </s></p><p type="main">

<s><emph type="bold"></emph>Pigmento<emph.end type="bold"></emph.end> delle tuniche dell&#039;occhio 312. </s></p><p type="main">

<s><emph type="bold"></emph>Pinne,<emph.end type="bold"></emph.end> come siano ne&#039;pesci precipuo organo del nuoto 438. </s></p><p type="main">

<s><emph type="bold"></emph>Piater Felice<emph.end type="bold"></emph.end> enumera le membrane dell&#039;occhio 303. </s></p><p type="main">

<s><emph type="bold"></emph>Plinio,<emph.end type="bold"></emph.end> sua storia naturale 353. </s></p><p type="main">

<s><emph type="bold"></emph>Polline,<emph.end type="bold"></emph.end> creduto pieno di granellini di zolfo 545. </s></p><p type="main">

<s><emph type="bold"></emph>Polmoni,<emph.end type="bold"></emph.end> se i loro moti siano spontanei o necessarii 167. </s></p><p type="main">

<s><emph type="bold"></emph>Pontedera Gi<gap></gap>lie,<emph.end type="bold"></emph.end> suoi argomenti contro il sistema sessuale delle piante 543. </s></p><p type="main">

<s><emph type="bold"></emph>Problema<emph.end type="bold"></emph.end> curioso di Meccanica animale risoluto prima dall&#039;Acquapendente e poi dal Borelli 78, <lb></lb>arveiano, come proposto e risoluto 187. </s></p><p type="main">

<s><emph type="bold"></emph>Problemi<emph.end type="bold"></emph.end> varii di Meccanica animale risoluti dal Borelli 81. </s></p><p type="main">

<s><emph type="bold"></emph>Punctum saliens,<emph.end type="bold"></emph.end> da che rappresentato, secondo l&#039;Hales, nel seme delle piante 546. </s></p><p type="main">

<s><emph type="bold"></emph>Punto<emph.end type="bold"></emph.end> cieco nell&#039;occhio, da che dipenda 345. </s></p><p type="main">

<s><emph type="bold"></emph>Pupilla,<emph.end type="bold"></emph.end> sua mobilità 513, il Porta e poi l&#039;Acquapendente, avutane la notizia dal Sarpi, la divulgano <lb></lb>nei loro libri 314. </s></p><p type="main">

<s><emph type="bold"></emph>Ramazzini Bernardino<emph.end type="bold"></emph.end> nota che il sistema geogonico del Burnet riscontra con un romanzo filosofico <lb></lb>narrato da Francesco Patrizio 575. </s></p><p type="main">

<s><emph type="bold"></emph>Rane,<emph.end type="bold"></emph.end> loro generazione spontanea affermata dai Gesuiti, e negata dagli Accademici fiorentini 498. </s></p><p type="main">

<s><emph type="bold"></emph>Ray Giovanni<emph.end type="bold"></emph.end> attende ad ordinare le piante secondo i soli frutti 365. </s></p><p type="main">

<s><emph type="bold"></emph>Reaumur (de) Renato Antonio Ferchaud<emph.end type="bold"></emph.end> conferma le dottrine del Malpighi intorno alla generazione <lb></lb>dei vermi nelle galle 475, contradice al Malpighi in alcune cose relative alla respirazione degli <lb></lb>insetti 485. </s></p><p type="main">

<s><emph type="bold"></emph>Recchi Nard&#039;Antonio,<emph.end type="bold"></emph.end> sue storie naturali del Messico 364. </s></p><p type="main">

<s><emph type="bold"></emph>Redi Francesco<emph.end type="bold"></emph.end> approva, intorno alla digestione, le dottrine di Tommaso Cornelio 205, suo sistema <lb></lb>della generazione ovarica 390, sue esperienze per dimostrar che le pietruzze nel ventricolo degli <lb></lb>uccelli non si r<gap></gap>solvono in chilo 414, crede che i vermi sulle piante siano generati dalla vita <lb></lb>vegetativa 473, pensa che tutti gli alberi e l&#039;erbe abbiano il maschio e la femmina 534. </s></p><p type="main">

<s><emph type="bold"></emph>Respirazione<emph.end type="bold"></emph.end> animale, singolari idee di Stefano Lorenzini intorno ad essa 448, delle piante 528. </s></p><p type="main">

<s><emph type="bold"></emph>Reticolo<emph.end type="bold"></emph.end> sulla cute delle foglie, simile al malpighiano sulla pelle degli animali 529. </s></p><p type="main">

<s><emph type="bold"></emph>Retina<emph.end type="bold"></emph.end> dell&#039;occhio, sua struttura secondo il Valsalva 319. </s></p><p type="main">

<s><emph type="bold"></emph>Reversivo, nerve,<emph.end type="bold"></emph.end> suo uso nella formazion della voce dimostrato da R. </s>

<s>Colombo 422. </s></p><p type="main">

<s><emph type="bold"></emph>Rombo,<emph.end type="bold"></emph.end> come non sia veramente questa la figura degli elementi muscolari 77. </s></p><p type="main">

<s><emph type="bold"></emph>Rondelezio Guglielmo,<emph.end type="bold"></emph.end> come ordini la storia naturale dei pesci 354, canone sperimentale formulato <lb></lb>da lui 441. </s></p><p type="main">

<s><emph type="bold"></emph>Rosa polonica<emph.end type="bold"></emph.end> del Quercetano 608. </s></p><p type="main">

<s><emph type="bold"></emph>Rudbeck Olao,<emph.end type="bold"></emph.end> come fosse uno degli scopritori del Canale toracico 227. </s></p><p type="main">

<s><emph type="bold"></emph>Ruschi Giovan Batista,<emph.end type="bold"></emph.end> come preparasse al Petit la scoperta del Canal <emph type="italics"></emph>godronné<emph.end type="italics"></emph.end> nell&#039;occhio 325. </s></p><p type="main">

<s><emph type="bold"></emph>Ruysch Federigo<emph.end type="bold"></emph.end> dimostra al Bils, che le negava, le valvole ne&#039;linfatici 236, scopre nell&#039;occhio la <lb></lb>membrana detta ruischiana dal nome di lui 308. </s></p><p type="main">

<s><emph type="bold"></emph>Sacculo embrionale,<emph.end type="bold"></emph.end> qualificato dall&#039;Harvey per un uovo 385. </s></p><p type="main">

<s><emph type="bold"></emph>Sagredo Gian Francesco,<emph.end type="bold"></emph.end> sua teoria della vista 341. </s></p><p type="main">

<s><emph type="bold"></emph>Sali,<emph.end type="bold"></emph.end> Sono secondo il Willis i principii formativi di tutti i corpi 605, son gli strumenti eccitatori del <lb></lb>gusto <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> hanno secondo il Bellini figure primigenie 606, è in essi, come nelle altre cose, insita <lb></lb>una loro propria e distinta figura, secondo il Fracassati 607, fissi nelle ceneri e volatili ne&#039;vapori, <lb></lb>formano secondo Filippo Bonanni le figure de&#039;corpi ai quali erano appartenuti 608, come a loro, <lb></lb>residenti nei vini, attribuisca il Magalotti la causa di una sua mala affezione cutanea 609, come <lb></lb>si spiegasse in vari modi l&#039;adesione delle loro particelle nella composizione del tutto 612. </s></p><p type="main">

<s><emph type="bold"></emph>Salto,<emph.end type="bold"></emph.end> negli animali, sua teoria meccanica 82. </s></p><p type="main">

<s><emph type="bold"></emph>Sangue<emph.end type="bold"></emph.end> non può far enfiare i muscoli per moverli 52. </s></p><p type="main">

<s><emph type="bold"></emph>Santorio Sant<gap></gap>rre<emph.end type="bold"></emph.end> dimostra che la retina, per ritener le immagini, dee essere opaca 342. </s></p><p type="main">

<s><emph type="bold"></emph>Sarpi Paolo<emph.end type="bold"></emph.end> se gli si possa attribuir la scoperta delle valvole delle vene 146, non conobbe il circolo <lb></lb>del sangue 153, osserva la variabile grandezza della pupilla 313. </s></p><p type="main">

<s><emph type="bold"></emph>Schelhammer Cristoforo,<emph.end type="bold"></emph.end> sua teoria dell&#039;udito 294. </s></p><p type="main">

<s><emph type="bold"></emph>Scilla Agostino,<emph.end type="bold"></emph.end> suoi retti giudizi intorno all&#039;origine delle glossopietre di Malta 565. </s></p><pb xlink:href="020/01/1754.jpg" pagenum="629"></pb><p type="main">

<s><emph type="bold"></emph>Sclerotica<emph.end type="bold"></emph.end> dell&#039;occhio, sua composizione anatomica 304, da che sia resa trasparente nella parte an­<lb></lb>teriore della cornea 306. </s></p><p type="main">

<s><emph type="bold"></emph>Semicircolari<emph.end type="bold"></emph.end> canali nell&#039;organo auditorio dei pesci 462. </s></p><p type="main">

<s><emph type="bold"></emph>Servet Michele,<emph.end type="bold"></emph.end> suo libro <emph type="italics"></emph>Christianismi restitutio<emph.end type="italics"></emph.end> 134, come descrive il circolo polmonare 135, <lb></lb>confrontato col Colombo 139, di cui ripete le dottrine apprese nella sua scuola 140. </s></p><p type="main">

<s><emph type="bold"></emph>Sessualità<emph.end type="bold"></emph.end> delle piante professata dal Valentin, dal Vaillant, dal Bradley e da altri anteriori al Linneo 541. </s></p><p type="main">

<s><emph type="bold"></emph>Setto<emph.end type="bold"></emph.end> medio del cuore dimostrato dal Colombo essere imperforato 138, membranoso del vestibolo, <lb></lb>organo precipuo dell&#039;udito, secondo il Cotunnio 298. </s></p><p type="main">

<s><emph type="bold"></emph>Sifone idrostatico<emph.end type="bold"></emph.end> applicato al moto del sangue per le vene 106. </s></p><p type="main">

<s><emph type="bold"></emph>Spallanzani Lazzero<emph.end type="bold"></emph.end> verifica che il moto del sangue ora si conferma ora no alle leggi idrauliche 122, <lb></lb>conclusione importantissima di lui, relativa all&#039;applicazione di queste leggi 123, primo a osservare <lb></lb>il circolo del sangue negli animali caldi 151, primo o scoprire il circolo coronario 152, sue espe­<lb></lb>rienze sopra la digestione 207, sue esperienze per dimostrar che le pietruzze ne&#039;ventricoli degli <lb></lb>uccelli non fanno, in triturare i cibi, l&#039;ufficio dei denti 414, propone alcune esperienze intorno <lb></lb>alla germogliazione dei semi, fatte già dal Malpighi 557. </s></p><p type="main">

<s><emph type="bold"></emph>Spermazzoi,<emph.end type="bold"></emph.end> loro scoperta e loro usi nell&#039;opera della generazione 392, negati da molti, n&#039;è confermata <lb></lb>l&#039;esistenza dal Vailisnieri 394. </s></p><p type="main">

<s><emph type="bold"></emph>Spiriti vitali,<emph.end type="bold"></emph.end> loro origine e natura 51. </s></p><p type="main">

<s><emph type="bold"></emph>Staffa,<emph.end type="bold"></emph.end> ossicino dell&#039;udito, questioni intorno alla sua prima invenzione 271, quali si creda esser<gap></gap>e <lb></lb>stati i veri inventori 272. </s></p><p type="main">

<s><emph type="bold"></emph>Stami,<emph.end type="bold"></emph.end> fanno, secondo il Grew, ne&#039;fiori, l&#039;ufficio tutt&#039;insieme di maschi e di femmine 538. </s></p><p type="main">

<s><emph type="bold"></emph>Stenone Niccolò,<emph.end type="bold"></emph.end> suo <emph type="italics"></emph>Specimen Myologiae<emph.end type="italics"></emph.end> 36, difficoltà opposte da lui alla teorica del Borelli intorno <lb></lb>ai moti muscolari 56, primo a descrivere l&#039;anatomia del cuore 86, primo a professare l&#039;ovologia 386, <lb></lb>concetto ch&#039;egli ebbe della respirazione 447, sue congetture intorno all&#039;origine dei corpi marini <lb></lb>sui monti 564, suo Prodromo geologico perchè scritto in latino 571. </s></p><p type="main">

<s><emph type="bold"></emph>Stimmate<emph.end type="bold"></emph.end> negl&#039;insetti scoperte dal Malpighi 484. </s></p><p type="main">

<s><emph type="bold"></emph>Strumenti,<emph.end type="bold"></emph.end> per mezzo dei quali muovesi il corpo animale, 72. </s></p><p type="main">

<s><emph type="bold"></emph>Strumento<emph.end type="bold"></emph.end> del gran vacuo inventato dal Borelli 504. </s></p><p type="main">

<s><emph type="bold"></emph>Swammerdam Giovanni,<emph.end type="bold"></emph.end> sua esperienza per dimostrar la propulsione dell&#039;aria nel respirare 171, <lb></lb>come si lusingasse di avere egli il primo sciolto il problema arveiano 295, dimostra le valvole <lb></lb>dei linfatici 236. </s></p><p type="main">

<s><emph type="bold"></emph>Tatto,<emph.end type="bold"></emph.end> suo strumento secondo gli antichi 253. </s></p><p type="main">

<s><emph type="bold"></emph>Teofrasfo<emph.end type="bold"></emph.end> nega la sessualità delle piante 533. </s></p><p type="main">

<s><emph type="bold"></emph>Termometro Santoriano<emph.end type="bold"></emph.end> applicato dal Borelli all&#039;ascesa del succo nelle piante 519. </s></p><p type="main">

<s><emph type="bold"></emph>Terre<emph.end type="bold"></emph.end> continentali e mari, loro avvicendamento secondo Aristotile 567. </s></p><p type="main">

<s><emph type="bold"></emph>Testicoli femminei,<emph.end type="bold"></emph.end> e loro usi secondo il Berengario 383. </s></p><p type="main">

<s><emph type="bold"></emph>Timone<emph.end type="bold"></emph.end> delle navi, suo uso applicato dal Borelli al volo degli uccelli 405. </s></p><p type="main">

<s><emph type="bold"></emph>Timpano<emph.end type="bold"></emph.end> secondario, nome imposto dallo Scarpa alla finestra rotonda dell&#039;orecchio 299. </s></p><p type="main">

<s><emph type="bold"></emph>Torace,<emph.end type="bold"></emph.end> moti di lui studiati dall&#039;Acquapendente sopra gli uccelli 415. </s></p><p type="main">

<s><emph type="bold"></emph>Torricelli Evangelista,<emph.end type="bold"></emph.end> come precorresse alla istituzione iatromeccanica 28, strumenti per uso me­<lb></lb>dico inventati da lui 29, sue osservazioni intorno alle figure dei cristalli 595. </s></p><p type="main">

<s><emph type="bold"></emph>Toscana,<emph.end type="bold"></emph.end> sue varie età geologiche rappresentate dallo Stenone 572. </s></p><p type="main">

<s><emph type="bold"></emph>Tournefort Giuseppe,<emph.end type="bold"></emph.end> suo metodo di ordinare le piante 367. </s></p><p type="main">

<s><emph type="bold"></emph>Trachee<emph.end type="bold"></emph.end> polmonari scoperte dal Malpighi negl&#039;insetti 484, nelle piante, e loro usi 518. </s></p><p type="main">

<s><emph type="bold"></emph>Tuba eustachiana,<emph.end type="bold"></emph.end> nome imposto dal Valsalva a un acquedotto scoperto dall&#039;Eustachio 280, sua in­<lb></lb>venzione attribuita ad Aristotile 281, com&#039;ella sovvenga apportuna al senso nei sordi 289, fal­<lb></lb>loppiana, descritta dal suo proprio inventore 383. </s></p><p type="main">

<s><emph type="bold"></emph>Tuoni<emph.end type="bold"></emph.end> della voce, come variamente modulati secondo l&#039;Acquapendente 424. </s></p><p type="main">

<s><emph type="bold"></emph>Udito,<emph.end type="bold"></emph.end> suo più intimo organo come funzioni secondo l&#039;Eustachio 287, come creduto volontario dal­<lb></lb>l&#039;Acquapendente 290, esiste anche ne&#039;pesci, secondo il Rondelezio 456, organi da lui descritti <emph type="italics"></emph>ivi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Ulmo Antonio<emph.end type="bold"></emph.end> seziona le galline in servizio dell&#039;Aldovrandi 381. </s></p><p type="main">

<s><emph type="bold"></emph>Umore,<emph.end type="bold"></emph.end> che inonda l&#039;orecchio interno, scoperto dal Valsalva 284, che riempie tutto il Labirinto, sco­<lb></lb>perto dal Cotunnio <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> acqueo dell&#039;occhio trovato dai primi anatomici scarso 322, suo poter re­<lb></lb>frangente 338, vitreo, sua tunica propria 324, suoi usi, secondo l&#039;Acquapendente 338, cristallino, <lb></lb>sua struttura lamellare 327, del Morgagni 327, vaginale e ghiandole che lo secernono 391. </s></p><p type="main">

<s><emph type="bold"></emph>Untuesità,<emph.end type="bold"></emph.end> a che fine sullata dalla superficie dei pesci 452. </s></p><p type="main">

<s><emph type="bold"></emph>Uovo<emph.end type="bold"></emph.end> gallinaceo, perchè scelto dall&#039;Harvey a soggetto de&#039;suoi studi embriologici 382. </s></p><p type="main">

<s><emph type="bold"></emph>Utere<emph.end type="bold"></emph.end> delle galline 381, nelle cerve trovato chiuso dall&#039;Harvey 384. </s></p><pb xlink:href="020/01/1755.jpg" pagenum="630"></pb><p type="main">

<s><emph type="bold"></emph>Valli<emph.end type="bold"></emph.end> sulla superficie terrestre, come formate 584. </s></p><p type="main">

<s><emph type="bold"></emph>Vallianieri Antonio<emph.end type="bold"></emph.end> si meraviglia degli errori rinnovellati in Francia intorno all&#039;origine dei corpi <lb></lb>marini sui monti 566, compendia elegantemente il romanzo geologico raccontato da Francesco <lb></lb>Patrizio 575. </s></p><p type="main">

<s><emph type="bold"></emph>Valsalva Anton Maria<emph.end type="bold"></emph.end> esamina e descrive più diligentemente la Tuba eustachiana 280, sue esperienze <lb></lb>per dimostrar come la luce operi sopra la retina 348. </s></p><p type="main">

<s><emph type="bold"></emph>Valvele<emph.end type="bold"></emph.end> delle vene, loro efficacia in promovere il corso del sangue, dimostrata dal Borelli 108, loro <lb></lb>esistenza perchè negata dal Vesalio 144, perchè dal Falloppio 145, dei vasi linfatici, da chi prima <lb></lb>scoperti 235. </s></p><p type="main">

<s><emph type="bold"></emph>Van-Horne Giovanni<emph.end type="bold"></emph.end> racconta come riuscisse a scoprire il canale toracico 221, medita sul sistema <lb></lb>della generaziono dell&#039;uomo e dei quadrupedi dall&#039;uovo 337, suo Prodromo al trattato della ge­<lb></lb>nerazione 338. </s></p><p type="main">

<s><emph type="bold"></emph>Ventricoli<emph.end type="bold"></emph.end> della laringe, loro usi nel modulare i tuoni, secondo il Morgagni 427, dei ruminanti, nomi <lb></lb>a loro imposti da Aristotile 406. </s></p><p type="main">

<s><emph type="bold"></emph>Verle Giovan Batista,<emph.end type="bold"></emph.end> sua anatomia artifiziale dell&#039;occhio 310. </s></p><p type="main">

<s><emph type="bold"></emph>Vesalio Andrea,<emph.end type="bold"></emph.end> suoi sette libri di anatomia contro Galeno 12, suo esame alle osservazioni anatomiche <lb></lb>del Falloppio 18, sua teoria dei moti muscolari 45, come descriva la struttura del cuore 88, come <lb></lb>si approprii certe idee di Galeno 130, e del Berengario 131, primo a designaro il forame ovale <lb></lb>nel feto 189, si appropria la scoperta degli ossicini dell&#039;udito, poi subito rivendicato dagl&#039;Italiani <lb></lb>all&#039;Achillini e al Berengario 268, a quante ei riduca le parti componenti l&#039;occhio 302, confessa <lb></lb>di avere errato nel detorminare, rispetto agli umori, la quantità dell&#039;acqueo nell&#039;occhio 323. </s></p><p type="main">

<s><emph type="bold"></emph>Vescica notatoria<emph.end type="bold"></emph.end> de&#039;pesci, usi di lei accennati prima dal Rondelezio 431, poi da Galileo 432, è in­<lb></lb>nata in lei l&#039;ar<gap></gap>a secondo il Cornelio <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> meato d&#039;onde esce da lei l&#039;aria contenutavi, scoperto <lb></lb>dagli Accademici del Cimento 433, canaliculo che la mette in comunicazione coll&#039;esterno, scoperto <lb></lb>dal Fracassati <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> creduta servire alla respirazione dall&#039;Harvey e dal Mersenno 434, sfintere di <lb></lb>lei, che secondo il Borelli la comprime e la dilata 435, mancante in alcuni pesci, da che venga <lb></lb>supplita 436. </s></p><p type="main">

<s><emph type="bold"></emph>Vescicole pn<gap></gap>nmatiche<emph.end type="bold"></emph.end> nel ventre degli uccelli osservate dall&#039;Acquapendente 416, dimostrate dal­<lb></lb>l&#039;Harvey 417, loro usi nella respirazione 418. </s></p><p type="main">

<s><emph type="bold"></emph>Vespucci A<gap></gap>erigo<emph.end type="bold"></emph.end> accenna alla Storia naturale del Nuovo Mondo 353. </s></p><p type="main">

<s><emph type="bold"></emph>Vianelli Giuseppe<emph.end type="bold"></emph.end> racconta come scoprisse nelle lucciole la causa della fosforescenza marina 498. </s></p><p type="main">

<s><emph type="bold"></emph>Vidio Guido<emph.end type="bold"></emph.end> ammette il circolo polmonare 136, designa i mescoli ordinati ai moti del torace 173. </s></p><p type="main">

<s><emph type="bold"></emph>Vista,<emph.end type="bold"></emph.end> come si faccia, dimostrato sperimentalmente, prima da Leonardo da Vinci 336, e poi dal <lb></lb>Porta 337. </s></p><p type="main">

<s><emph type="bold"></emph>Viviani Vi<gap></gap>io,<emph.end type="bold"></emph.end> qual parte egli avesse nella Miologia dello Stenone 36, suo discorso intorno ai <lb></lb>minerali della Toscana 569, è sollecitato da Erasmo Bartholin a studiare il fatto della duplice <lb></lb>rifrazione 599. </s></p><p type="main">

<s><emph type="bold"></emph>Vocali, nervi,<emph.end type="bold"></emph.end> dimostrati dalle vivisazioni di R. </s>

<s>Colombo 423. </s></p><p type="main">

<s><emph type="bold"></emph>Velo<emph.end type="bold"></emph.end> degli uccellì, sua meccanica secondo l&#039;Acquapendente 401, secondo il Borelli 402, uso delle penne <lb></lb>nell&#039;esercizio di lui <emph type="italics"></emph>ivi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Volontaril,<emph.end type="bold"></emph.end> moti de&#039;muscoli, applicati al cuore, come il Cartesio gli spieghi 63. </s></p><p type="main">

<s><emph type="bold"></emph>Volta Alessandro<emph.end type="bold"></emph.end> dimostra essere l&#039;elcttricità galvanica insufficiente causa dei moti muscolari 71. </s></p><p type="main">

<s><emph type="bold"></emph>Vuote,<emph.end type="bold"></emph.end> esperienze del Boyle, per concluder se nascano in esso nuovi viventi 557. </s></p><p type="main">

<s><emph type="bold"></emph>Wahibom Gustavo<emph.end type="bold"></emph.end> risponde alle difficoltà promosse dal Pontedera, e da altri, contro il sistema ses­<lb></lb>suale delle piante 547. </s></p><p type="main">

<s><emph type="bold"></emph>Willis Tommase<emph.end type="bold"></emph.end> dice che l&#039;aria inspirata riaccende il sangue 180, nega esister nei pesci un nervo <lb></lb>che presieda all&#039;udito 462. </s></p><p type="main">

<s><emph type="bold"></emph>Woodward Giovanni,<emph.end type="bold"></emph.end> sua storia naturale della Terra 576. </s></p><p type="main">

<s><emph type="bold"></emph>Zona<emph.end type="bold"></emph.end> scoperta nell&#039;occhio da Gotofredo Zinn 326. </s></p><p type="main">

<s><emph type="bold"></emph>Zone<emph.end type="bold"></emph.end> dei canali semicircolari, quale uso abbiano nell&#039;orecchio a produrre, secondo il Valsaiva, il <lb></lb>senso dell&#039;udito 296. </s></p><p type="main">

<s><emph type="bold"></emph>Zucchere,<emph.end type="bold"></emph.end> figure cristalline osservate sulla superficie di lui col Microscopio 606. <pb xlink:href="020/01/1756.jpg"></pb><pb xlink:href="020/01/1757.jpg"></pb></s></p><pb xlink:href="020/01/1758.jpg"></pb><p type="main">

<s>Finito di stampare in Bologna presso la <lb></lb>Libreria Editrice Forni nel Giugno 1970 </s></p><pb xlink:href="020/01/1759.jpg"></pb></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Editor-in-Chief: Harry Woolf<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Willis K. </s>

<s>Shepard Professor of the History of <lb></lb>Science, The Johns Hopkins University<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/1760.jpg"></pb><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph><emph type="italics"></emph>Storia del Metodo<emph.end type="italics"></emph.end><emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph><emph type="italics"></emph>Sperimentale in Italia<emph.end type="italics"></emph.end><emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>by RAFFAELLO CAVERNI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>in Six Volumes<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Volume IV<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE, NO. 134<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>NEW YORK LONDON 1972<emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/1761.jpg"></pb><p type="main">

<s><emph type="center"></emph>Reproduced here is the Florence edition of 1891-1900.<emph.end type="center"></emph.end></s></p><figure id="id.020.01.1761.1.jpg" xlink:href="020/01/1761/1.jpg"></figure><p type="main">

<s><emph type="center"></emph>Copyright © 1972 by Johnson Reprint Corporation All rights reserved<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>111 Fifth Avenue, New York, N.Y. 10003, U.S.A.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Shipton Group House, 24/28 Oval Road, London, NW1 7DD, England<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Printed in Italy<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/1762.jpg"></pb><p type="main">

<s><emph type="center"></emph>DEL METODO SPERIMENTALE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>APPLICATO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>ALLA SCIENZA DEL MOTO DEI GRAVI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>PARTE PRIMA<emph.end type="center"></emph.end><pb xlink:href="020/01/1763.jpg"></pb></s></p><pb xlink:href="020/01/1764.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della Scienza del moto nel secolo XVI<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle prime istituzioni statiche nella Scuola peripatetica, e nella alessandrina — II. </s>

<s>Dei principii <lb></lb>statici di Giordano Nemorario: de&#039;manoscritti di Leonardo da Vinci, e delle fonti, dalle quali <lb></lb>derivò in essi la Scienza del moto. </s>

<s>— III. </s>

<s>Delle dottrine statiche degli Antichi promosse nello <lb></lb>Note manoscritte di Leonardo da Vinci. </s>

<s>— IV. </s>

<s>Di alcuni più notabili teoremi e problemi di <lb></lb>Meccanica dimostrati, e risoluti da Leonardo da Vinci. </s>

<s>— V. </s>

<s>Dei principii dinamici professati <lb></lb>da Leonardo da Vinci intorno alle leggi della caduta dei gravi, e della teoria de&#039;proietti. </s>

<s>— <lb></lb>VI. </s>

<s>Degli altri principali Autori, che promossero la Meccanica dopo la prima metà del se­<lb></lb>colo XVI. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Gli studi del Filosofo intorno ai tre grandi regni della Natura, per dare <lb></lb>un&#039;idea de&#039;quali abbiamo scritto il III Tomo della nostra Storia, si ridu­<lb></lb>cono insomma, in una sentenza sola concludendo il lungo discorso, a inve­<lb></lb>stigare le leggi del moto, da cui risulta ai varii corpi l&#039;essere, e in cui ma­<lb></lb>nifestasi, a noi che non ne sappiamo altro, la vita. </s>

<s>Che se le stesse fisiche <lb></lb>discipline hanno per loro particolar soggetto il moto, che atteggia in varie <lb></lb>guise la materia, e si trasforma in elettricità, in luce e in calore, bene è a <lb></lb>dir che avessero i Peripatetici gran ragione di sentenziar col loro Maestro, <lb></lb>che ignorato il moto veniva necessariamente a ignorarsi la Natura. </s>

<s>Ond&#039;è <lb></lb>facile dietro ciò a congetturare, anche prima di averne avuto dai documenti <lb></lb>storici la certezza, che dovette aver la Meccanica una delle prime e più di­<lb></lb>ligenti culture nella naturale Filosofia degli antichi. </s></p><p type="main">

<s>Si fece anche della Meccanica, come di tutte le discipline applicabili <lb></lb>agli usi della vita, una distinzione in pratica e in razionale, e quella per <pb xlink:href="020/01/1765.jpg" pagenum="8"></pb>logica necessità, come in altri simili esempi s&#039;osserva, dovette precedere a <lb></lb>questa. </s>

<s>Come gli uomini, ne&#039;loro primi esercizi delle arti manuali, incomin­<lb></lb>ciassero a servirsi della leva per inalzare più facilmente i pesi, o del cuneo <lb></lb>per spezzarli e renderli più maneggevoli, o del martello per ficcare adden­<lb></lb>tro lo stesso cuneo, e per via della penetrazione congiungere stabilmente <lb></lb>insieme più corpi; non è facile a dire, ma s&#039;ingannerebbe grandemente co­<lb></lb>lui, che credesse doversi attribuir l&#039;invenzione di questa e di altre simili <lb></lb>macchine all&#039;industria, e all&#039;ingegno della tale o tale altra particolare per­<lb></lb>sona. </s>

<s>Investigar dunque l&#039;origine di così fatti meccanici ritrovati non si <lb></lb>rende per questo solo difficile, perchè, di tempi così lontani, ci mancano gli <lb></lb>storici documenti, ma perchè le prime origini delle cose, come vedesi per <lb></lb>l&#039;esempio delle piante e degli animali, si trovano nelle virtù de&#039;loro semi <lb></lb>latenti, cosicchè, non esplicate ancora in sè medesime, si rendono perciò <lb></lb>inesplicabili a noi. </s>

<s>Di qui viene ch&#039;essendo noi stessi ciechi a quella impe­<lb></lb>netrabile vista, siamo soliti di lusingarci col dire che la pratica è cieca. </s></p><p type="main">

<s>La razionale cultura dell&#039;ingegno, nell&#039;esercizio delle arti meccaniche, <lb></lb>si rassomiglia insomma alla cultura delle piante, la quale incomincia allora <lb></lb>che, sviluppatosi il seme da&#039;suoi invogli, si rende nella definita forma delle <lb></lb>sue parti riconoscibile allo stesso cultore, che non sa, nè si cura d&#039;investi­<lb></lb>gare il mistero della nuova mirabile apparizione. </s>

<s>I Filosofi pure ebbero a <lb></lb>incominciare allora a coltivar la scienza dei pesi, che furono dalle arti ma­<lb></lb>nuali esercitati que&#039;primi e più semplici strumenti, da rendere applicabili o <lb></lb>da moltiplicare le forze, che l&#039;uomo stesso ritrovava in sè, o che studiavasi <lb></lb>di ricavare dai moti degli animali e dai mondani elementi. </s></p><p type="main">

<s>A voler dire chi fossero que&#039;primi antichi Filosofi s&#039;incontrano le me­<lb></lb>desime difficoltà, che a voler mettersi a designare delle cose i primi prin­<lb></lb>cipii, i quali poniamo pure che ne&#039;civili antichissimi consorzii, rispetto a <lb></lb>quella particolare scienza di che si tratta, fossero svolti; la distinta e più <lb></lb>chiara notizia nulladimeno ci s&#039;adombra dalla lontananza dei tempi, o ci ri­<lb></lb>mane affatto ignorata per mancanza di documenti. </s>

<s>Talete Milesio, Pitagora, <lb></lb>Aristeo, Ippocrate di Chio e Archita non sono altro per noi che apparizioni <lb></lb>d&#039;ombre senza persona, o, per più vera e meglio appropriata immagine, <lb></lb>invisibili rivi, delle sotterranee acque menate dai quali ci possiamo solamente <lb></lb>accorgere dall&#039;ingrossare della corrente. </s>

<s>Presso a quattrocento anni prima <lb></lb>dell&#039;era volgare si divise quella corrente in due grandi fiumi, i quali, mi­<lb></lb>rabile a dire, in tanto correre in lungo si sono scavati gli alvei così profondi <lb></lb>che, attraversati e rimescolati con innumerevoli altre ubertose sorgenti in­<lb></lb>contrate per via, serbano ancora in mezzo le loro proprie vestigia distinte <lb></lb>a chi d&#039;alto gli rimira dai colli alle foci. </s></p><p type="main">

<s>Platone e Aristotile sono i due grandi fiumi, che da XXIII secoli ri­<lb></lb>corrono a irrigare tutte intere alla scienza le membra, e avendo le due onde <lb></lb>fluenti qualità varia e moto quasi contrario par che sieno provvidamente <lb></lb>ordinate a mantenere, in quelle stesse membra, perenne il circolo della vita. </s>

<s><lb></lb>Quel di Stagira, più giovane e discepolo dell&#039;Ateniese, fa nella storia della <pb xlink:href="020/01/1766.jpg" pagenum="9"></pb>Meccanica la prima comparsa, perch&#039;egli uscì fuori a insegnarla in un trat­<lb></lb>tatello, che porta scritto in fronte il nome di lui, e dell&#039;autenticità del quale <lb></lb>non lasciano dall&#039;altra parte a dubitare le distintive note del filosofico in­<lb></lb>gegno. </s>

<s>A leggere infatti le prime parole, nelle quali Aristotile definisce le <lb></lb>facoltà dell&#039;arte meccanica, si rivelano aperti i principii professati da lui <lb></lb>intorno all&#039;arte e all&#039;ingegno dell&#039;uomo che, non arrestato dalle difficoltà, <lb></lb>trionfa vittorioso sopra la stessa reluttante Natura. </s>

<s>La Meccanica perciò defi­<lb></lb>niscesi dal Filosofo, di questa vittoria dell&#039;ingegno dell&#039;uomo, come il più <lb></lb>proprio e più splendido esempio. </s>

<s>“ Quando igitur quippiam praeter natu­<lb></lb>ram oportuerit facere, difficultate sua haesitationem praestat, arteque indi­<lb></lb>get, quam ob rem eam artis partem, quae huiusmodi succurrit difficulta­<lb></lb>tibus, Mechanicam appellamus ” (Arist., Quaest. </s>

<s>mech. </s>

<s>Operum, T. XI, <lb></lb>Venetiis 1560, fol. </s>

<s>27). </s></p><p type="main">

<s>I Meccanici, che poi più saviamente seguitarono altri instituti, riconob­<lb></lb>bero anche in queste idee i viziosi peripatetici principii, e Galileo primo fra <lb></lb>gli altri dimostrò non essere nelle macchine punto vero che vi trionfino <lb></lb>l&#039;ingegno e l&#039;arte dell&#039;uomo, quasi ingannando la Natura “ istinto della <lb></lb>quale, anzi fermissima constituzione, è che niuna resistenza possa esser su­<lb></lb>perata da forza, che di quella non sia più potente ” (Alb. </s>

<s>XI, 85). </s></p><p type="main">

<s>Da un tal vizioso fermento compresa la Meccanica aristotelica, sembre­<lb></lb>rebbe che ne fosse per riuscire tutta intera la massa corrotta, nè fa perciò <lb></lb>maraviglia che Galileo stesso se lo credesse, e che lo facesse credere a tutta <lb></lb>la sua scuola. </s>

<s>S&#039;ingannava però, così giudicando, quell&#039;autorevolissimo Mae­<lb></lb>stro della nuova scienza del moto, e appariranno dal processo della nostra <lb></lb>Storia manifesti ai lettori i dannosissimi effetti di quell&#039;inganno. </s>

<s>Ma giova <lb></lb>intanto accennare alla ragione perchè la massima parte delle Questioni ari­<lb></lb>stoteliche, con gran maraviglia di chi sa meditarle, risolute dall&#039;Autore con­<lb></lb>forme al vero, si rimanessero provvidamente immuni dal contagio peripate­<lb></lb>tico. </s>

<s>Quella ragione poi da null&#039;altro dipende che dalla natura propria delle <lb></lb>trattate questioni, le quali partecipano tutto insieme, come lo stesso Aristo­<lb></lb>tile avverte, della scienza matematica e della naturale. </s>

<s>“ Sunt autem haec <lb></lb>neque naturalibus omnino quaestionibus eadem, neque seiungata valde; ve­<lb></lb>rum mathematicarum contemplationum, naturaliumque communia ” (Quaest. </s>

<s><lb></lb>cit., fol. </s>

<s>27). Ma perchè la matematica è prevalente, ecco ciò che salva la <lb></lb>più gran parte di quelle stesse meccaniche questioni dal temuto contagio, e <lb></lb>che le imprime delle indelebili note del vero. </s></p><p type="main">

<s>Tutto il fondamento infatti della nuova istituzione meccanica è, secondo <lb></lb>Aristotile, riposto nelle ammirande dignità, e nelle proprietà geometriche del <lb></lb>circolo, che si rappresentano alla viva mente di lui nel primo mettersi a <lb></lb>penetrare i misteriosi effetti del vette. </s>

<s>Come mai, si domanda, un gran peso, <lb></lb>impossibile a sollevar con la mano, si rende così facilmente trattabile, usan­<lb></lb>dovi quello strumento? </s>

<s>E risponde il Filosofo: “ Omnium autem huiusmodi <lb></lb>causae principium habet circulus ” (ibid., fol. </s>

<s>28). Circolare infatti è il moto <lb></lb>della Libbra, alla quale riducesi il Vette, e perchè nel Vette stesso risol-<pb xlink:href="020/01/1767.jpg" pagenum="10"></pb>vonsi finalmente i moti di quasi tutti gli altri meccanici strumenti, è perciò <lb></lb>che tutta quanta la scienza, di che si tratta, è misteriosamente compresa <lb></lb>nelle proprietà del cerchio. </s>

<s>“ Ea igitur, quae circa Libram fiunt, ad circu­<lb></lb>lum referuntur, quae vero circa Vectem ad ipsam Libram: alia autem fere <lb></lb>omnia, quae circa mechanicas motiones fiunt, ad Vectem ” (ibid.). </s></p><p type="main">

<s>Penetriamo dunque, prosegue a ragionare Aristotile, se vogliamo inten­<lb></lb>dere le ragioni del moto, il meccanismo dello stesso circolo, il quale intanto <lb></lb>ci si presenta come generato dalla composizione di due moti. </s>

<s>E perchè qui <lb></lb>massimamente s&#039;asconde quel mistero, che vuol rivelare alla nostra mente <lb></lb>il Filosofo, incomincia dal far notare che, della detta composizione, l&#039;effetto <lb></lb>resultante è diverso, secondo che le parti componenti hanno o no una de­<lb></lb>finita proporzione fra loro. </s>

<s>Se quella proporzione esiste, la resultante del <lb></lb>moto è una linea retta, altrimenti è una curva. </s>

<s>La prima conclusione è di <lb></lb>tanta importanza nella storia della Meccanica, che vogliamo invitar l&#039;Autore <lb></lb>stesso a dimostrarcela, tanto più che il processo geometrico di lui ha tutta <lb></lb>la facilità e la chiarezza desiderabile in un Antico. </s></p><p type="main">

<s>“ Sit enim proportio, dice Aristotile, secundum quam latum fertur, <lb></lb>quam habet AB ad AC (fig. </s>

<s>1), et A quidem feratur versus B, AB vero <lb></lb><figure id="id.020.01.1767.1.jpg" xlink:href="020/01/1767/1.jpg"></figure></s></p><p type="caption">

<s>Figura 1.<lb></lb>subter feratur versus MC: latum autem sit A <lb></lb>quidem ad D, ubi autem est AB versus E. </s>

<s><lb></lb>Quoniam igitur lationis erat proportio quam <lb></lb>AB habet ad AC necesse est et ad AE hanc <lb></lb>habere proportionem. </s>

<s>Simile igitur est propor­<lb></lb>tione parvum quadrilaterum maiori. </s>

<s>Quamo­<lb></lb>brem et eadem illorum est diameter, et A erit <lb></lb>ad F. </s>

<s>Eodem etiam ostendetur modo ubicum­<lb></lb>que latio deprehendatur, semper enim supra diametrum erit. </s>

<s>Manifestum <lb></lb>igitur quod id, quod secundum diametrum duabus fertur lationibus, acces­<lb></lb>satio secundum laterum proportionem fertur ” (ibid., ad t.). Il quadrilatero <lb></lb>è in questo caso figurato rettangolo, ma il Teorema aristotelico è generale, <lb></lb>e si applica indifferentemente dall&#039;Autore anche al parallelogrammo, per <lb></lb>la diagonale di cui si fa, pur come dianzi, la resultante del moto, secondo <lb></lb><figure id="id.020.01.1767.2.jpg" xlink:href="020/01/1767/2.jpg"></figure></s></p><p type="caption">

<s>Figura 2.<lb></lb>la proporzione de&#039;lati che rappresentano le <lb></lb>componenti. </s>

<s>Disegnatosi infatti il parallelo­<lb></lb>grammo BEC (fig. </s>

<s>2), come vedesi al fol. </s>

<s>29 <lb></lb>delle citate Questioni meccaniche, son tali le <lb></lb>chiarissime parole ivi da Aristotile scritte per <lb></lb>illustrarlo: “ Si quidem igitur in proportione <lb></lb>feratur quam habet BE, EC, fertur utique <lb></lb>secundum diametrum ubi BC. ” </s></p><p type="main">

<s>Chi ha letto quel che continuamente si ripete oramai da tutti, dopo il <lb></lb>Lagrange, che cioè fu Galileo il primo a comporre e a decomporre le forze <lb></lb>nel rettangolo, e il Varignon a far più generalmente lo stesso nel paralle­<lb></lb>logrammo, dee provar necessariamente gran maraviglia de&#039;sopra allegati due <pb xlink:href="020/01/1768.jpg" pagenum="11"></pb>chiarissimi testi, ma per non precorrere alla storia de&#039;fatti importantissimi, <lb></lb>che dipendono da questo ora accennato, seguitiamo Aristotile, il quale va <lb></lb>dimostrandoci il fondamento suo meccanico stabilito nell&#039;ammirande pro­<lb></lb>prietà del cerchio. </s>

<s>Ha principio il moto, di cui servesi la Geometria per de­<lb></lb>scrivere la mistica figura, dal centro, il quale, essendo in sè consistente in <lb></lb>un semplice punto, si espande al di fuori, quasi per una violenta esplosione, <lb></lb>che via via rallenta la sua prima foga a proporzione della distanza. </s>

<s>Quella <lb></lb>forza esplosiva poi, mentre tende a rifuggire per linea retta dal centro, ferma <lb></lb>stando questa linea in uno de&#039;suoi estremi, rigira con l&#039;altro tutt&#039;intorno <lb></lb>allo stesso centro, e così da due moti, uno naturale per la circonferenza e <lb></lb>l&#039;altro violento per il diametro, e non aventi fra loro nessuna proporzione <lb></lb>definita, vien secondo Aristotile a descriversi quella linea curva, indefinita­<lb></lb>mente ritornante in sè stessa, ch&#039;è il cerchio. </s></p><p type="main">

<s>La meccanica della Libbra, come udimmo dianzi dire dal Nostro, ha la <lb></lb>sua causa in questa dignità del circolo, e perchè a quello strumento ridu­<lb></lb>cesi il Vette, ch&#039;è una Libbra di braccia ineguali, qual&#039;è dunque la ragione <lb></lb>della sua potenza, se non che la maggior velocità del braccio più lungo com­<lb></lb>pensa la maggior gravità del peso applicato al braccio più corto? </s>

<s>“ Ipse <lb></lb>vectis est in causa librae existens, spartum inferne habens in inaequalia di­<lb></lb>visa. </s>

<s>Hypomochlion enim est spartum, ambo namque stant ut centrum. </s>

<s>Quo­<lb></lb>niam autem ab aequali pondere celerius movetur maior earum, quae a cen­<lb></lb>tro sunt, duo vero pondera quod movet et quod movetur; quod igitur motum <lb></lb>pondus ad movens, longitudo patitur ad longitudinem. </s>

<s>Semper autem quanto <lb></lb>ab hypomochlio distabit magis, tanto facilius movebit. </s>

<s>Causa autem est quo­<lb></lb>niam quae plus a centro distat, maiorem describit circulum, quare ab eadem <lb></lb>potentia plus separabitur movens illud, quod plus ab hypomochlion dista­<lb></lb>bit ” (ibid., fol. </s>

<s>30 ad t.). </s></p><p type="main">

<s>Riducendo il detto aristotelico in forme più precise, se ne raccoglie <lb></lb>ch&#039;essendo le velocità proporzionali agli spazii, o alle distanze dal centro, <lb></lb>la potenza e la resistenza, applicate alle due estreme parti dello strumento, <lb></lb>stanno reciprocamente come quelle stesse distanze. </s>

<s>Ma questa, che dall&#039;al­<lb></lb>tra parte è facile conclusione geometrica, non era il principale intento del <lb></lb>nostro Filosofo, all&#039;arguto ingegno del quale riserbavasi a investigar la causa, <lb></lb>perchè il braccio più corto della leva sia in ogni modo sempre il più tardo. </s>

<s><lb></lb>La speculata genesi meccanica del circolo è quella appunto che preparavasi <lb></lb>per la risposta. </s>

<s>Imperocchè il raggio più corto, essendo più vicino al cen­<lb></lb>tro, e venendo perciò più fortemente attratto da esso, è men libero ne&#039;suoi <lb></lb>moti di quel che non sia il più lungo; ond&#039;è ragionevole che, essendo meno <lb></lb>spedito, anche a proporzione riesca sempre più tardo. </s>

<s>“ Si autem duobus <lb></lb>ab eadem potentia latis hoc quidem plus repellatur, illud vero minus, ra­<lb></lb>tioni consentaneum est tardius moveri quod plus repellitur eo, quod repel­<lb></lb>litur minus. </s>

<s>Quod videtur accidere maiori et minori illarum, quae ex cen­<lb></lb>tro circulos describunt. </s>

<s>Quoniam enim propius est manentis eius quae minor <lb></lb>est extremum quam id quod est maioris, veluti retractum in contrarium ad <pb xlink:href="020/01/1769.jpg" pagenum="12"></pb>medium, tardius fertur minoris extremum. </s>

<s>Omni quidem igitur circulum <lb></lb>describenti istuc accidit, ferturque eam, quae secundum naturam est latio­<lb></lb>nem, secundum circumferentiam: illam vero praeter naturam in transver­<lb></lb>sum et secundum centrum. </s>

<s>Maiorem autem semper eam, quae praeter na­<lb></lb>turam est, ipsa minor fertur, quia enim centro est vicinior quod retrahit, <lb></lb>vincitur magis ” (ibid., fol. </s>

<s>29). </s></p><p type="main">

<s>Prestabiliti questi generalissimi e fecondi principii di statica razionale, <lb></lb>passa Aristotile a dimostrare quel che aveva prima accennato, che cioè tutti <lb></lb>i moti, i quali si fanno intorno alle Macchine, si riducono in fine alla leva. </s>

<s><lb></lb>Sono, oltre essa leva e la libbra, gli strumenti meccanici informati della <lb></lb>nuova scienza, la Troclea e il Polispasto, l&#039;Asse nel peritrochio e il Cuneo. </s>

<s><lb></lb>La potenza meccanica dell&#039;Asse, la quale si governa secondo le lunghezze <lb></lb>delle scitale o dei bracci della Leva, a cui viene immediatamente applicata <lb></lb>la forza; gli fu occasione d&#039;inganno intorno agli usi della Troclea, credendo <lb></lb>che tanto avesse questo strumento maggior virtù di sollevare i pesi, quanto <lb></lb>fosse maggiore il suo raggio. </s>

<s>In questo falso supposto si propone a risol­<lb></lb>vere la così formulata IX Questione: “ Cur ea, quae per maiores circulos <lb></lb>tolluntur et trahuntur, facilius et citius moveri contingit, veluti maioribus <lb></lb>Trochleis quam minoribus, et scytalis similiter? </s>

<s>” (ibid., fol. </s>

<s>32 ad t). È que­<lb></lb>sto stesso errore quello altresì, che vizia la risoluta Questione XVIII, intorno <lb></lb>al determinar le ragioni che passano tra la potenza e il peso nel Polispasto. </s></p><p type="main">

<s>È certamente un tale errore in Aristotile notabilissimo, rivelandosi chia­<lb></lb>ramente alla mente di ognuno che la Troclea è una Libbra di braccia <lb></lb>eguali. </s>

<s>Ma è da avvertir che l&#039;inganno ha giusto nella stessa Libbra la sua <lb></lb>prima radice. </s>

<s>S&#039;incominciano infatti le meccaniche Questioni dal domandar <lb></lb>come mai le Bilance di braccia più lunghe sieno più diligenti. </s>

<s>Si conferma <lb></lb>il supposto qui dall&#039;Autore per vero, osservando che i moti negli strumenti <lb></lb>più grandi sono assai meglio visibili, perchè le braccia più lunghe fanno <lb></lb>maggiore la declinazione. </s>

<s>Un altro fatto però sembrava confermare tutto il <lb></lb>contrario, cioè che si scelgono i piccoli <emph type="italics"></emph>Saggiatori<emph.end type="italics"></emph.end> dagli orefici come più <lb></lb>squisiti delle grandi Bilance usate dai rivenditori delle merci più vili. </s>

<s>L&#039;os­<lb></lb>servazione fu fatta contro il Filosofo nel VII libro dei Quesiti da Niccolò <lb></lb>Tartaglia, il quale concluse da&#039;suoi nuovi statici principii che ogni sorta di <lb></lb>peso farà il medesimo effetto in ogni sorta di Libbra (Venezia 1546, fol. </s>

<s>77). <lb></lb>L&#039;errore insomma di Aristotile è manifesto, ma giova, a quietar l&#039;animo di <lb></lb>coloro i quali n&#039;hanno fatto così gran caso, osservare che, pur dall&#039;analisi <lb></lb>dei Moderni, resulta esser tanto più mobile la Bilancia, quanto sono più <lb></lb>lunghe le sue braccia. </s></p><p type="main">

<s>Comunque sia, l&#039;Asse nel peritrochio è ben da Aristotile nella Que­<lb></lb>stione XIII ridotto alla Leva, il maggior braccio della quale è costituito nelle <lb></lb>scitale o nei manubrii, tanto più potenti a sollevare il peso, quanto sono <lb></lb>più lunghi, perciocchè riescono in moversi altrettanto più veloci. </s>

<s>E benchè <lb></lb>tantì sieno stati fra i Meccanici i dissidii, hanno i più nulladimeno dato ra­<lb></lb>gione al Maestro antico in ridurre anche il Cuneo alle ragioni del Vette. </s></p><pb xlink:href="020/01/1770.jpg" pagenum="13"></pb><p type="main">

<s>Le arti manuali, accomodando ai loro particolari esercizi gli strumenti, <lb></lb>riuscirono a modificarli così, da non esser facile a riconoscerli nella sempli­<lb></lb>cità dei loro principii, ma Aristotile, che ha professato di riguardare come <lb></lb>principalissimo degli strumenti la Leva, non s&#039;inganna, e nell&#039;uso delle Ta­<lb></lb>naglie, per esempio, secondo che si legge nella XXI Questione, dimostra che <lb></lb>tutta l&#039;efficacia dipende dall&#039;essere le Tanaglie stesse composte di due Vetti, <lb></lb>nell&#039;articolazion de&#039;quali consista l&#039;ipomoclio. </s>

<s>Del resto, per tacere di altri <lb></lb>non meno rilevanti argomenti, le forze centrifughe e le resistenze dei solidi <lb></lb>allo spezzarsi, che per Galileo si svolsero in una scienza nuova, se son Que­<lb></lb>stioni in Aristotile o non bene o non completamente risolute, giovarono nul­<lb></lb>ladimeno a richiamare a sè, infino dalle prime istituzioni della scienza, l&#039;at­<lb></lb>tenzione degli studiosi. </s></p><p type="main">

<s>Tale era insomma la nuova scienza meccanica insegnata ai Peripatetici <lb></lb>dal loro Maestro, il quale occorre primo a commemorar nella storia, più <lb></lb>per dignità, che per tempo. </s>

<s>Gli Accademici, di questi argomenti, che pare­<lb></lb>vano aggirarsi nel trivio delle arti manuali, non udirono trattarne mai alla <lb></lb>divina eloquenza di Platone. </s>

<s>Ma quando nella scuola di Alessandria quelle <lb></lb>matematiche contemplazioni, dallo stesso Platone tanto raccomandate, ebbero <lb></lb>così larga e così intensa cultura, si giudicò non indegno del Filosofo il trat­<lb></lb>tenersi sull&#039;ali dell&#039;ingegno a specular dall&#039;alto secondo qual ragione la <lb></lb>Geometria governi il moto dei corpi. </s></p><p type="main">

<s>Primo e solenne Maestro di Matematiche in cotesta scuola sedeva Eu­<lb></lb>clide, fra&#039;molti libri scritti dal quale se ne annovera uno trattante <emph type="italics"></emph>De pon­<lb></lb>deribus.<emph.end type="italics"></emph.end> Quali siano precisamente i principii meccanici ivi professati non è <lb></lb>possibile averne certezza, essendo anche questa, insieme con la maggior <lb></lb>parte delle opere dell&#039;Autore, andata smarrita, ma un teorema, che da al­<lb></lb>cuni s&#039;attribuisce a lui, ne farebbe ragionevolmente congetturare che la <lb></lb>Meccanica dell&#039;Alessandrino fosse informata a quegli stessi principii, che <lb></lb>furono poi svolti dal nostro Siracusano. </s>

<s>Il teorema infatti, che dicesi Eucli­<lb></lb>deo, tanto ritrae della scienza meccanica di Archimede, che alcuni compila­<lb></lb>tori delle opere di lui, come per esempio il Rivault, lo inserirono, così for­<lb></lb>mulato, in appendice al libro I Degli equiponderanti: “ Si fuerint duae <lb></lb>quantitates in aequilibrio, quae ambae vel ambarum una radiis adhaeserint: <lb></lb>a centris autem gravitatum carumdem in radios quibus appenduntur per­<lb></lb>pendiculares agantur; incident haec in radiorum puncta, a quibus si appen­<lb></lb>sae fuerint eaedem quantitates, ita ut iam radiis non toto corpore adhae­<lb></lb>reant, sed tantum ab illis punctis appendeant; manebunt in aequilibrio ” <lb></lb>(Archimedis Opera per D. Rivaltum, Parisiis 1615, pag. </s>

<s>186). </s></p><p type="main">

<s>L&#039;Autore delle XIII proposizioni <emph type="italics"></emph>De ponderibus,<emph.end type="italics"></emph.end> conosciuto sotto il <lb></lb>nome di Giordano Nemorario, fece del teorema ora formulato la proposi­<lb></lb>zione sua IX, conclusa da tutt&#039;altri principii, e il commentator di Giordano, <lb></lb>dimostrando anch&#039;egli in un altro modo la cosa, terminava la dimostrazione <lb></lb>con le parole: “ Hic explicit secundum aliquos liber Euclidis <emph type="italics"></emph>De ponderi­<lb></lb>bus ”<emph.end type="italics"></emph.end> (De ponderibus cit., pag. </s>

<s>24). </s></p><pb xlink:href="020/01/1771.jpg" pagenum="14"></pb><p type="main">

<s>Se fosse dunque del citato teorema statico Euclide veramente l&#039;autore, <lb></lb>parrebbe si dovesse a lui la prima applicazione dei centri di gravità agli <lb></lb>equiponderanti. </s>

<s>Ma qualunque sia la ragion del primato, intorno a che poco <lb></lb>gioverebbe a noi il disputare, giacchè la nuova istituzione non ci è altri­<lb></lb>menti nota che per le tradizioni archimedee, nel nostro Siracusano perciò <lb></lb>conviene investigarne l&#039;indole e la natura. </s></p><p type="main">

<s>E quanto all&#039;indole è facile avvedersi che si conforma al Platonismo <lb></lb>alessandrino, così autorevolmente introdotto nelle Matematiche da Euclide, <lb></lb>la Meccanica del quale, come quella del Nostro, è schiva d&#039;implicarsi vil­<lb></lb>mente nelle passioni della materia. </s>

<s>Nei corpi infatti, astraendo da tutto il <lb></lb>resto, non si considera da quegli Autori altro che il peso, non come qua­<lb></lb>lità degli stessi corpi, ma come quantità matematicamente, secondo tutte le <lb></lb>altre quantità, computabile in numeri o in linee. </s>

<s>La ponderosità perciò, così <lb></lb>in astratto considerata, fa indipendente la Meccanica alessandrina dalla mole <lb></lb>universale dei corpi materiali, ossia dalla Terra, al mezzo della quale essi <lb></lb>corpi non tendono, per rivolgersi piuttosto là dove potente gli chiama un <lb></lb>loro proprio e particolar centro, in cui si raccolgono, e da cui par che vir­<lb></lb>tualmente si dispensino i pesi. </s></p><p type="main">

<s>L&#039;indole di questa Scuola si par dunque diversa dalla Peripatetica, al <lb></lb>Maestro della quale udimmo poco fa dire che le Questioni meccaniche par­<lb></lb>tecipano della scienza matematica e della naturale. </s>

<s>Ma perchè la naturale i <lb></lb>Platonici l&#039;avevano a schifo, reputandone indegno a un Filosofo lo studio, <lb></lb>si guardavano dalle dottrine peripatetiche come da un contagio, per conferma <lb></lb>e per prova di che è notabile che non si trovi citato quasi mai il nome di <lb></lb>Aristotile dagli Scrittori alessandrini. </s>

<s>Durarono infino a tutto il secolo XVII, <lb></lb>in così fatte questioni, gli esempii della divisione fra le due scuole, ma per­<lb></lb>chè lo Stagirita s&#039;era meglio apposto al vero, si può dir che la scienza mec­<lb></lb>canica, com&#039;ebbe da lui i principii, così avesse anche secondo lui le per­<lb></lb>fezioni. </s></p><p type="main">

<s>L&#039;asserita sentenza ha bisogno in ogni modo di prove, perchè, mentre <lb></lb>da una parte non vien suffragata dalle antiche tradizioni, specialmente pla­<lb></lb>toniche, le due grandi autorità di Galileo e del Cartesio dall&#039;altra, si det­<lb></lb>tero il più sollecito studio di contradirla. </s>

<s>Ma benchè non appariscano di <lb></lb>quelle prove espresse le vestigia, si desumono nulladimeno con sufficiente <lb></lb>certezza dalle leggi, che governano il logico progredir del pensiero, dalle <lb></lb>quali si conclude non dovere in altro consistere le meccaniche istituzioni <lb></lb>archimedee che in una esplicazione de&#039;concetti del Filosofo Stagirita. </s>

<s>Nè ciò <lb></lb>si creda perchè s&#039;inducesse il Siracusano a contradire all&#039;indole della sua <lb></lb>scuola, ma perchè Aristotile stesso pose per fondamento della sua scienza <lb></lb>meccanica una delle più ammirabili dignità della Geometria. </s></p><p type="main">

<s>Questa dignità infatti vedemmo essere costituita nel cerchio, la descri­<lb></lb>zione del quale resulta, secondo il Filosofo, dalla composizione di due moti, <lb></lb>uno diretto secondo il raggio, e che muove dal centro, e l&#039;altro applicato <lb></lb>all&#039;estremità del raggio stesso. </s>

<s>La forza, che produce quel primo moto, <pb xlink:href="020/01/1772.jpg" pagenum="15"></pb>l&#039;aveva Aristotile qualificata per violenta, quasi che il cerchio fosse gene­<lb></lb>rato per esplosione del centro. </s>

<s>Ma intorno alla causa del secondo moto, di <lb></lb>quello cioè che naturalmente conduce in giro l&#039;estremità del raggio, l&#039;Au­<lb></lb>tore delle Meccaniche questioni non s&#039;era bene spiegato. </s>

<s>Ora incominciano <lb></lb>di qui le laboriose speculazioni della Scuola alessandrina, rappresentata per <lb></lb>noi in Archimede, di cui solo alcuni libri salvati e gli scrittori antichi ci <lb></lb>hanno trasmesso qualche notizia. </s></p><p type="main">

<s>Da che dunque potrebbe esser meglio resa evidente la forza applicata <lb></lb>all&#039;estremità del raggio, ragionava Archimede, che da un peso posto nel suo <lb></lb>estremo? </s>

<s>Siasi, per esempio, esso raggio esplicato in fino in A (fig. </s>

<s>3), dove <lb></lb><figure id="id.020.01.1772.1.jpg" xlink:href="020/01/1772/1.jpg"></figure></s></p><p type="caption">

<s>Figura 3.<lb></lb>giunto, il peso P lo devii dalla sua dirittura, <lb></lb>per condurlo in giro. </s>

<s>S&#039;esplichi ancora il rag­<lb></lb>gio infino in B per altrettanto spazio, e ivi <lb></lb>pure s&#039;applichi un peso Q, che faccia forza <lb></lb>di deviarlo e di menarlo in volta come quel <lb></lb>primo. </s>

<s>Perchè B, ritrovandosi a una distanza <lb></lb>doppia di A, è secondo Aristotile attratto al <lb></lb>centro O con la metà della violenza, sembra <lb></lb>dunque ragionevole che quello abbia bisogno <lb></lb>della metà della forza necessaria a questo, per <lb></lb>venir deviato dal suo retto cammino: e in­<lb></lb>somma P conviene essere il doppio più pe­<lb></lb>sante di <expan abbr="q.">que</expan> </s></p><p type="main">

<s>Proseguendo il ragionamento, scendeva <lb></lb>come corollario da questa proposizione che, <lb></lb>applicando in C un peso R eguale a P, e in D un peso S eguale a Q, le <lb></lb>estremità de&#039;due diametri, pareggiate ne&#039;loro contrarii moti, dovessero per­<lb></lb>manere in equilibrio. </s>

<s>Tale appunto è il fondamento statico della Libbra, <lb></lb>d&#039;onde venne immediatamente condotto Archimede a quello della Leva, per­<lb></lb>chè considerando i due cerchi saldati insieme, e BD come una linea sola, <lb></lb>perciocchè P, per esempio, è tanto bene equilibrato dal peso R in C, quanto <lb></lb>dal peso S in D, ne conseguiva dunque, essendo applicabile il caso, non <lb></lb>alla doppia sola, ma a qualunque proporzione; che dovessero avere i pesi <lb></lb>fra loro la reciproca ragione delle distanze. </s></p><p type="main">

<s>Questo fondamentale teorema dava il modo a sciogliere il problema, <lb></lb>tanto dai Meccanici desiderato, <emph type="italics"></emph>Datum pondus data potentia movere;<emph.end type="italics"></emph.end> pro­<lb></lb>blema che, così in sesto luogo formulato da Pappo nell&#039;VIII libro delle sue <lb></lb><emph type="italics"></emph>Collezioni,<emph.end type="italics"></emph.end> gli suggeriva le seguenti parole, premesse alla soluzione come <lb></lb>per nota: “ Hoc enim est quadragesimum inventum mechanicum Archime­<lb></lb>dis, in quo fertur dixisse: <emph type="italics"></emph>Da mihi ubi consistam et Terram commovebo ”<emph.end type="italics"></emph.end><lb></lb>(Pappi Alexandrini Collect., Bononiae 1660, pag. </s>

<s>460). E rispetto a&#039;due cer­<lb></lb>chi saldati insieme, che poi in pratica venivano a trasformarsi in quell&#039;or­<lb></lb>gano meccanico così detto il <emph type="italics"></emph>Timpano,<emph.end type="italics"></emph.end> Pappo stesso, che ne aveva fatta <lb></lb>l&#039;applicazione moltiplicandone secondo la lunghezza dei raggi la potenza al <pb xlink:href="020/01/1773.jpg" pagenum="16"></pb>saepissime imputat Galeno, dum ipsum suis delusum simiis multa afferre et <lb></lb>comminisci ait quae, si humana cadavera secuisset, aliter protulisset ” (ibi, <lb></lb>pag. </s>

<s>510). </s></p><p type="main">

<s>Così veniva chiaramente dimostrato dai fatti che tanto Galeno quanto <lb></lb>il Vesalio erano due uomini, come tutti gli altri, soggetti ad errori; onde <lb></lb>avendosi per cosa certa essere stata l&#039;Anatomia fino a quel tempo coltivata <lb></lb>da uomini e non da Dei, nell&#039;imperfezione umana, in ch&#039;era rimasta, dava <lb></lb>certissima speranza a tutti e prometteva il merito debito a chiunque ne fa­<lb></lb>vorisse i progressi, per cui il Falloppio stesso, ad avvivar la speranza di con­<lb></lb>seguir più facilmente un tal merito, dettava a chi si volesse dare agli eser­<lb></lb>cizii dell&#039;arte i precetti seguenti: </s></p><p type="main">

<s>“ I. </s>

<s>Quae non connata sunt facile ac leviter dividi. </s>

<s>II. </s>

<s>Quae connata <lb></lb>sunt difficillime, nisi maxima adhibita diligentia, dividenda esse. </s>

<s>III. </s>

<s>Nihil <lb></lb>lacerandum. </s>

<s>IV. </s>

<s>Quod summe est necessarium et difficile ut sciamus quae <lb></lb>sit una pars, quae vero plures: ne plures partes simul iunctas constituamus <lb></lb>unam esse, nec ex una plures faciamus. </s>

<s>V. </s>

<s>Quis sit ordo in dissectione obser­<lb></lb>vandus: possumus enim vario modo incipere et mutare ordinem. </s>

<s>Aut enim <lb></lb>habemus rationem dignitatis, et tunc incipimus a dignioribus ut a corde, a <lb></lb>cerebro; aut dirigimus ordinem ad duiturnitatem materiae, et incipimus ab <lb></lb>iis partibus quae citius pereunt et putrescunt, aut respicimus collocationem <lb></lb>et situm partium, ut quando extimas prius secamus servato ordine usque <lb></lb>ad intimas, aut spectamus usum toti corpori exhibitum, et tunc a duriori­<lb></lb>bus incipit ars, utpote ac quae totum corpus fulciunt. </s>

<s>VI. </s>

<s>Ut cognoscamus <lb></lb>quibus instrumentis nunc haec particula nunc illa sit dividenda, cui adhi­<lb></lb>bendi opera ministri, cui minime. </s>

<s>VII. </s>

<s>Ut cognoscamus quae particulae sint <lb></lb>dividendae et inspiciendae in vivis animalibus, quae vero in mortuis et qua <lb></lb>ratione; quaedam enim partes etiam mortuae omnia integra reservant, quae­<lb></lb>dam vero vel nihil vel parum admodum retinent illius quod sensu est per­<lb></lb>cipiendum “ (Institutiones anatom. </s>

<s>inter Op. </s>

<s>omnia cit., pag. </s>

<s>521). </s></p><p type="main">

<s>Nella duplice opera delle <emph type="italics"></emph>Osservazioni<emph.end type="italics"></emph.end> anatomiche e delle <emph type="italics"></emph>Istituzioni,<emph.end type="italics"></emph.end><lb></lb>si rendeva dunque per due conti il Falloppio benemerito de&#039;progressi del­<lb></lb>l&#039;Anatomia: prima, per aver salvato dagli attentati del Vesalio, che voleva <lb></lb>reciderle, le più antiche tradizioni galeniche della scienza; poi, per aver mo­<lb></lb>strato che alla via gloriosamente corsa dallo stesso Vesalio non era posto il <lb></lb>termine nelle scoperte di lui, ma che restava molto ancora a scoprire a chi <lb></lb>vi si fosse rivolto con studio amoroso, com&#039;egli ne&#039;suoi due libri anatomici <lb></lb>insegnava coi fatti e coi precetti. </s></p><p type="main">

<s>Ma i precetti a dir vero accennano all&#039;arte già progredita, la quale si <lb></lb>studia di giungere alla sua perfezione per quella via già segnata dai primi <lb></lb>maestri, senza cercare o saper trovar modo da renderla più diritta e più <lb></lb>aperta. </s>

<s>Vedremo di ciò l&#039;esempio ne&#039;principali Anatomisti, che successero <lb></lb>al Falloppio, mettendo in pratica i precetti di lui, mentre che Realdo Co­<lb></lb>lombo, il quale porgeva nuovi argomenti all&#039;Anatomia per progredire, ri­<lb></lb>maneva incompreso e per lungo tempo dimenticato. <pb xlink:href="020/01/1774.jpg" pagenum="17"></pb>cipio meccanico rimangon deluse, non riducendosi la tanto desiderata dimo­<lb></lb>strazione, alle mani di Archimede, che a un ingegnosissimo gioco della <emph type="italics"></emph>Com­<lb></lb>posizion delle forze parallele.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Come Aristotile dette alla Meccanica la prima ala nella composizione <lb></lb>delle forze angolari, così Archimede la fornì di questa seconda, l&#039;invenzione <lb></lb>della quale gli occorse nelle prime speculazioni <emph type="italics"></emph>De libra.<emph.end type="italics"></emph.end> I pesi infatti, che <lb></lb>s&#039;equilibrano distribuiti nel Timpano, secondo la precedente figura terza, <lb></lb>sono una scomposizione dell&#039;unico peso, che grava nel centro. </s>

<s>E dall&#039;altra <lb></lb>parte, essendo chiaro che, anche tolti i pesi Q, R, rimane tuttavia il sistema <lb></lb>equilibrato, può perciò il peso totale venire altresì decomposto ne&#039;due P <lb></lb>ed S. </s>

<s>Ma qual&#039;è il fondamento, e la regola di questa operazione? </s>

<s>non altra <lb></lb>che il primo postulato dell&#039;Autore: <emph type="italics"></emph>Petimus aequalia pondera ab aequa­<lb></lb>libus distantiis aequiponderare.<emph.end type="italics"></emph.end> Archimede insomma lasciò la scienza in <lb></lb>quella medesima sete, in che l&#039;aveva lasciata Aristotile, e così per l&#039;uno <lb></lb>come per l&#039;altro Maestro il fondamento statico riducesi a un fatto, che bi­<lb></lb>sogna ammettere per evidenza sperimentale, ma che la Geometria confessa <lb></lb>di non avere argomenti da poterlo dimostrare. </s>

<s>Era quel fatto sperimentale, <lb></lb>per Aristotile, che i cerchi di più gran raggio son più veloci, e per Archi­<lb></lb>mede che, posti ad uguali distanze nella Libbra, s&#039;equiponderano insieme <lb></lb>due pesi eguali. </s></p><p type="main">

<s>L&#039;arguto Siracusano avrà ripensato che il Filosofo studiavasi di rendere <lb></lb>la ragione della maggior velocità nel circolo di raggio maggiore, col consi­<lb></lb>derar ch&#039;egli è meno violentemente attratto e avvinto nel centro, ma il fe­<lb></lb>condo principio era, specialmente a que&#039;tempi, più difficile a dimostrare <lb></lb>della sua conseguenza, per cui, a ciò che potevasi così facilmente mettere <lb></lb>in dubbio, parve più prudente consiglio all&#039;Autore Degli equiponderanti so­<lb></lb>stituire la certezza di un fatto. </s></p><p type="main">

<s>Notabile cosa è in questo particolare che quel di Siracusa sì mostri <lb></lb>meno platonico dell&#039;altro di Stagira, il quale aveva fatta meccanica la stessa <lb></lb>Geometria. </s>

<s>Le aristoteliche speculazioni perciò intorno ai moti generatori del <lb></lb>cerchio erano conformissime al genio di Archimede, e, se ne fu sviato dal <lb></lb>nuovo processo che i centri di gravità venivano a introdur nel trattato degli <lb></lb>equilibrii, vi tornò poi più di proposito, per raccoglierne quel pregevolis­<lb></lb>simo frutto, che egli espose nel libro Delle spirali. </s>

<s>L&#039;accennata origine rende <lb></lb>meno inaspettato il nuovo abito, sotto cui si presenta la geometrica tratta­<lb></lb>zione, che è per noi il terzo libro meccanico scritto dal nostro Siracusano. </s></p><p type="main">

<s>Aristotile erasi contentato di accennare così alle leggi dei moti equa­<lb></lb>bili: “ Citius enim bifariam dicitur, sive enim in minori tempore aequalem <lb></lb>pertrausit locum, citius fecisse dicimus; seu, in aequali, maiorem ” (Quaest. </s>

<s><lb></lb>cit., fol. </s>

<s>28 ad t.). Ma Archimede ne fa, nelle due prime proposizioni, sog­<lb></lb>getto a matematica dimostrazione, riferendo la prima che, se sieno le velo­<lb></lb>cità eguali, gli spazii percorsi saranno proporzionali ai tempi, e la seconda <lb></lb>che, se sieno i tempi eguali, le velocità torneranno proporzionali agli spazii. </s></p><p type="main">

<s>L&#039;applicazione di queste leggi de&#039;moti equabili si fa alla generazione <pb xlink:href="020/01/1775.jpg" pagenum="18"></pb>meccanica della spirale, la quale ci vuol poco a intendere come fosse sug­<lb></lb>gerita ad Archimede dalla generazione meccanica del cerchio aristotelico, <lb></lb>che, lasciando impresse le vestigia del punto portato dai due moti equabil­<lb></lb>mente fatti e nello stesso tempo per la circonferenza e per il raggio, ver­<lb></lb>rebbe evidentemente a disegnare la spirale archimedea. </s>

<s>La mirabile gene­<lb></lb>razione meccanica di questa curva, che insomma contenevasi latente nelle <lb></lb>Questioni meccaniche, fu, insieme col principio della composizione delle forze <lb></lb>angolari attinto alle medesime aristoteliche Questioni, conclusa da Archi­<lb></lb>mede in que&#039;suoi teoremi, che riuscirono alla intelligenza dei Matematici <lb></lb>tanto astrusi. </s>

<s>La concisione dello scrittore parve che fosse causa di ciò, ben­<lb></lb>chè unica e vera causa fosse piuttosto la Scuola alessandrina, la quale, sde­<lb></lb>gnosa di partecipar con la Peripatetica, tenne ascosa la chiave di quel mi­<lb></lb>stero, infintantochè in un novello Archimede non venne, dopo tanti secoli, <lb></lb>a ritrovarla il Torricelli. </s></p><p type="main">

<s>Ha l&#039;illustre Discepolo di Galileo una scrittura intitolata <emph type="italics"></emph>Dimostrazione <lb></lb>della XVIII proposizione di Archimede delle Linee spirali colla dottrina <lb></lb>del moto di Galileo,<emph.end type="italics"></emph.end> dove, dopo di aver col principio della composizione <lb></lb>delle forze ortogonali dimostrata la promessa proposizione archimedea, sog­<lb></lb>giunge: “ Nell&#039;istesso modo per appunto si dimostra la verità delle due se­<lb></lb>guenti proposizioni nel maraviglioso libro Delle spirali. </s>

<s>A noi basterà di avere <lb></lb>accennato per qual via Archimede possa esser venuto in cognizione d&#039;una <lb></lb>verità tanto astrusa, e per così dire inopinabile, come la addotta. </s>

<s>Credo certo <lb></lb>che l&#039;Autore a bello studio volesse occultare ed inviluppare la dimostrazione <lb></lb>del Teorema, a segno tale che non si potesse conoscere da che origine <lb></lb>glien&#039;era derivata la cognizione. </s>

<s>Però nel corso di tanti secoli non fu mai <lb></lb>capita evidentemente questa passione della spirale, non per altro che per la <lb></lb>mancanza della dottrina del moto, nota benissimo fino a&#039;suoi tempi all&#039;Ar­<lb></lb>chimede antico, ma pubblicata solamente nei nostri dal Moderno ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. XXVIII, c. </s>

<s>113). </s></p><p type="main">

<s>Credeva dunque il Torricelli, come poi il Lagrangia e altri, che la re­<lb></lb>gola di comporre i moti fosse un mistero riserbatosi in petto da Archimede, <lb></lb>e poi rivelato da Galileo nella proposizione II del IV Dialogo delle due Nuove <lb></lb>Scienze, ma il fatto è che Aristotile aveva insegnata già quella medesima <lb></lb>regola più di venti secoli prima, e che Archimede la presupponeva nelle <lb></lb>sue dimostrazioni come nota oramai a tutti, benchè non da tutti intesa, e <lb></lb>perciò nè approvata, ond&#039;è che non intesa pure e non approvata tornò per <lb></lb>tanti secoli la scienza meccanica, che s&#039;annunziava nel libro Delle spirali. </s>

<s><lb></lb>Maestro dunque di questa scienza non si rendeva Archimede che nel trat­<lb></lb>tato Degli equiponderanti, e, per quegli antichi che lo poterono studiare, nel <lb></lb>trattato <emph type="italics"></emph>De libra.<emph.end type="italics"></emph.end> La determinazione del centro dei gravi, che là si dava per <lb></lb>unico fondamento meccanico, essendo principio troppo astratto, si porgeva <lb></lb>male applicabile a far giusto giudizio fra la proporzione dello strumento e <lb></lb>la potenza motrice. </s>

<s>E se la Statica n&#039;ebbe a risentire vantaggio, fu quando <lb></lb>il Torricelli rivestì l&#039;astratta ponderosità archimedea delle qualità generali <pb xlink:href="020/01/1776.jpg" pagenum="19"></pb>di tutti i corpi, considerando i loro centri in relazione col centro della <lb></lb>Terra. </s></p><p type="main">

<s>Di qui si comprende come non dovesse venire alla Statica, dal trattato <lb></lb>Degli equipondenti, grande impulso a progredire. </s>

<s>Prese la Scuola alessan­<lb></lb>drina, conoscendo che l&#039;impedimento veniva dalla troppo rigorosa osser­<lb></lb>vanza dei precetti platonici, seco medesima consiglio di temperar quel ri­<lb></lb>gore, condescendendo in qualche cosa lo spirito alla materia, ond&#039;è che <lb></lb>Herone fu, secondo Pappo, di sentimento che la Meccanica razionale dovesse <lb></lb>consistere, no nella Geometria sola e nell&#039;Aritmetica, ma eziandio nelle fisi­<lb></lb>che ragioni. </s>

<s>“ Sentit Hero mechanicus, et rationalem quidem partem ex <lb></lb>geometria et arithmetica et ex phisicis rationibus constare ” (Collectiones <lb></lb>mathem. </s>

<s>cit, pag. </s>

<s>442). Nonostante, se ben si considerano gli effetti di que­<lb></lb>sta generosa deliberazione presa dal Meccanico alessandrino, si trovano tanto <lb></lb>sterili, da non aggiungere in sostanza nulla di più all&#039;opera fatta da Archi­<lb></lb>mede intorno alla Libbra. </s></p><p type="main">

<s>Alle considerazioni, dalle quali dipende la verità così conclusa e asse­<lb></lb>rita, porgono argomento le stesse Collezioni matematiche di Pappo, l&#039;ottavo <lb></lb>libro delle quali è un nitidissimo specchio dei progressi, che fece la Mec­<lb></lb>canica nella Scuola alessandrina dai tempi di Filone e di Herone infino a <lb></lb>quelli dell&#039;Autore, che corona l&#039;opera degli antichi con le sue proprie in­<lb></lb>venzioni. </s>

<s>Al trattatello delle Macchine premette poche parole, dove dice che <lb></lb>essendogli i libri antichi capitati alle mani tutti guasti, mancanti del prin­<lb></lb>cipio o del termine, ha creduto bene in servigio degli studiosi di reinte­<lb></lb>grarli, esponendo in un breve discorso le figure, gli usi e i nomi di quelle <lb></lb>meccaniche facoltà, per le quali un dato peso vien mosso da una data po­<lb></lb>tenza. </s>

<s>“ Traditum autem est ab Herone et Philone qua de causa praedictae <lb></lb>facultates in unam reducantur naturam, quamquam figuris multum inter se <lb></lb>distantes. </s>

<s>Nomina igitur haec sunt: Axis in peritrochio, Vectis, Polyspaston, <lb></lb>Cuneus, et praeter haec quae appellatur infinita Cochlea ” (ibid., pag. </s>

<s>482). </s></p><p type="main">

<s>S&#039;aspetterebbe a tali espressioni il Lettore di vedere in che modo s&#039;in­<lb></lb>formino, le cinque macchine annoverate, a un principio solo che le riduca <lb></lb>tutte a un&#039;unica natura, perchè nell&#039;invenzione di quel tale principio con­<lb></lb>sistono insomma i progressi della Statica. </s>

<s>Ma l&#039;aspettazione in singolar modo <lb></lb>è delusa, terminandosi da Pappo la breve descrizione di ciascuno strumento <lb></lb>ora col dire che qual sia la ragione tra la potenza e la resistenza <emph type="italics"></emph>deinceps <lb></lb>ostendemus,<emph.end type="italics"></emph.end> ora affermando esser la tale o tale altra quella ragione, <emph type="italics"></emph>ut osten­<lb></lb>demus,<emph.end type="italics"></emph.end> e intanto, senza poi dimostrar nulla, si chiude il libro. </s></p><p type="main">

<s>Potrebb&#039;essere in ogni modo, tanti pericoli hanno corso nell&#039;approdare <lb></lb>infino a noi queste carte, che, come si sono avute le Collezioni matemati­<lb></lb>che mancanti dei due primi libri, così qualcun altro ne fosse venuto a man­<lb></lb>care oltre all&#039;ottavo, ma tutto dà indizio che là dove la trattazione mecca­<lb></lb>nica ci è rimasta fosse il termine naturale. </s>

<s>Da un&#039;altra parte non mantenne <lb></lb>Pappo le sue promesse, perchè le gli vennero a mancare in Filone e in <lb></lb>Herone, non per essere i loro libri mutilati, ma per l&#039;insufficienza de&#039;prin-<pb xlink:href="020/01/1777.jpg" pagenum="20"></pb>cipii scienziali a progredire tant&#039;oltre. </s>

<s>Si torna perciò a quel che si diceva <lb></lb>più sopra ridursi la Statica degli Alessandrini ai principii archimedci della <lb></lb>Libbra, ciò che dalle stesse Collezioni di Pappo ha la conferma. </s></p><p type="main">

<s>Il Timpano infatti e le Ruote dentate son l&#039;uniche macchine, nelle quali <lb></lb>matematicamente si dimostri la ragion che passa fra la potenza e la resi­<lb></lb>stenza. </s>

<s>“ Hero autem Alexandrinus, constructionem eius in libro qui insci­<lb></lb>bitur <foreign lang="grc">Bαρουλχον</foreign> manifestissime explicavit, sumpto lemmate quod demonstra­<lb></lb>vit in Mechanicis, ubi etiam de quinque facultatibus disserit, videlicet de <lb></lb>Cuneo, Vecte, Cochlea, Polyspasto et Axe ” (ibid., pag. </s>

<s>460). E dop&#039;avere <lb></lb>applicata la detta macchina a produrre un effetto particolare, che consisteva <lb></lb>nel potersi per mezzo di lei movere un peso di mille seicento talenti, con <lb></lb>la sola potenza di ottocento, perchè il diametro del Timpano era doppio di <lb></lb>quello del suo proprio asse; “ hoc enim problema, immediatamente sog­<lb></lb>giunge, demonstratum est ab Herone in Mechanicis, et alia quam plurima <lb></lb>problemata utilissima et vitae nostrae rationibus conducentia conscripta sunt ” <lb></lb>(ibid.). Ma il problema, se vero è quel che Pappo stesso più sotto afferma, <lb></lb>era stato risoluto prima da Archimede nel suo trattato <emph type="italics"></emph>De libra.<emph.end type="italics"></emph.end> E perchè <lb></lb>da questo immediatamente dipendeva l&#039;altro problema delle ruote dentate, <lb></lb>il Collettore alessandrino aggiunge di sua propria mano al troppo scarso cor­<lb></lb>redo della Meccanica il seguente teorema: “ Ponatur Tympanum quidem A <lb></lb>dentium sexaginta, Tympanum vero B dentium quadraginta: dico, ut velo­<lb></lb>citas Tympani A ad velocitatem Tympani B, ita esse dentium B multitudi­<lb></lb>nem ad multutudinem dentium A ” (ibid., pag. </s>

<s>478). </s></p><p type="main">

<s>L&#039;infelice tentativo, del resto, fatto da Pappo stesso intorno al piano in­<lb></lb>clinato, e l&#039;avere alle quattro macchine aristoteliche aggiunta la Coclea, che <lb></lb>malamente riducevasi al Cuneo, sono anzi argomenti, che aggiungono valore <lb></lb>al nostro discorso, da cui volevasi concludere che la Scuola alessandrina non <lb></lb>promosse punto più la Statica da quel grado, in cui l&#039;aveva lasciata Ari­<lb></lb>stotile nelle sue Questioni. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Al Liceo di Alessandria succede nel VII secolo la Scuola araba, il sen­<lb></lb>sualismo della quale fa le più vigorose contrapposizioni con lo spiritualismo <lb></lb>filosofico di Platone. </s>

<s>E perchè le umane discipline erano strette oramai a <lb></lb>tal partito o da rinunziare affatto a ogni magistero di scienza, o da scegliere <lb></lb>fra l&#039;Accademia e il Peripato, si comprende facilmente come all&#039;indole e ai <lb></lb>costumi degli Arabi s&#039;affacessero meglio gl&#039;istituti di questo, che poneva <lb></lb>all&#039;intelletto la precedenza del senso. </s>

<s>Quando perciò la gente nuova avesse <lb></lb>coltivato più la sapienza, che l&#039;utile e il piacere, ci si potrebbe aspettare <lb></lb>che, riprese le aristoteliche tradizioni, dovesse la Meccanica venir per loro <lb></lb>promossa da quella quasi immobilità, in che l&#039;avevano trattenuta gli anti-<pb xlink:href="020/01/1778.jpg" pagenum="21"></pb>chi. </s>

<s>Nonostante, benchè non sia pervenuto alla nostra notizia nessuno arabo <lb></lb>autore, che scrivesse intorno all&#039;arte e alla scienza dei pesi, non si può per <lb></lb>questo affermar da noi che ne fosse a quel tempo negletto lo studio. </s>

<s>Anzi <lb></lb>il vedere i manifesti profitti di lui nell&#039;applicazione di quella scienza a di­<lb></lb>scipline affini, che dal fecondo connubio vengono a ricevere il loro incre­<lb></lb>mento, sarebbe prova certa di non scarsa cultura. </s>

<s>S&#039;intende da noi dire di <lb></lb>Alhazen, autore di un trattato di Ottica, dove la luce si considera come un <lb></lb>corpo, che velocissimo si muove nello spazio, e che percotendo negli altri <lb></lb>corpi si riflette e si rifrange con certe leggi meccaniche, per dimostrar le <lb></lb>quali fa sapiente e libero uso della regola aristotelica, che insegna a decom­<lb></lb>porre una sola in due forze angolari. </s>

<s>Chi poi pensa a quel che verrà coi <lb></lb>fatti a dimostrarci la storia, che cioè dall&#039;uso di quella regola riconosce <lb></lb>massimamente la Meccanica i suoi progressi, vedrà come sia forse da dire <lb></lb>addirittura abbondante quella cultura di lei appresso gli Arabi, che dianzi ci <lb></lb>contentammo di giudicar non iscarsa. </s></p><p type="main">

<s>Le ricercate utilità e i comodi sensuali della vita, il predominante prin­<lb></lb>cipio peripatetico, che dovesse cioè la Natura sottostare e quasi pigliar legge <lb></lb>dal filosofico ingegno, non ci permettono di pensare che gli Arabi trascu­<lb></lb>rassero lo studio e l&#039;esercizio di quelle macchine, ch&#039;erano il trionfo della <lb></lb>potenza dell&#039;uomo sulle ritrosie della materia, e a geometrizzare intorno alle <lb></lb>quali s&#039;erano volti gli Alessandrini per una singolare combattuta condiscen­<lb></lb>denza. </s>

<s>Quelle Questioni aristoteliche dall&#039;altra parte, senza divagare in spe­<lb></lb>culazioni, che apparivano inutili a chi non sapeva apprenderle come belle; <lb></lb>trovavano esplicatissimo il principio statico universale applicabile a trovar <lb></lb>la più giusta proporzione tra la potenza delle varie maniere di strumenti <lb></lb>motori, e la resistenza del peso mosso: ond&#039;è che ragionevolmente può cre­<lb></lb>dersi essere la scienza dei pesi coltivata in quella Scuola un commento più <lb></lb>o meno dotto del maraviglioso segreto usato dalla Natura in moltiplicare le <lb></lb>forze per la loro applicazione immediata ai moti circolari. </s></p><p type="main">

<s>La Scuola latina, che poi successe, fra le tradizioni universali della <lb></lb>scienza attinta dagli Arabi accolse anche quella parte, che concerne le isti­<lb></lb>tuzioni meccaniche, i canoni selettissimi delle quali noi li riconosciamo for­<lb></lb>mulati in quelle XIII proposizioni <emph type="italics"></emph>De ponderibus,<emph.end type="italics"></emph.end> che vanno sotto il nome <lb></lb>di Giordano Nemorario, e che, dopo aver servito per tre secoli di testo ma­<lb></lb>noscritto, sopra cui, passando da Aristotile, si faceva uno studio superiore <lb></lb>della scienza; furono nel 1523, da Pietro Appiano matematico tedesco, di­<lb></lb>vulgate a gran benefizio per le pubbliche stampe. </s></p><p type="main">

<s>Che sia Giordano peripatetico si rivela infino dalle prime parole, nelle <lb></lb>quali professa di voler trattare de&#039;pesi come di una scienza, che da una <lb></lb>parte è soggetta alla Geometria, e dall&#039;altra alla Filosofia naturale. </s>

<s>Incomin­<lb></lb>ciano perciò le investigazioni di lui, come quelle di Aristotile, dal moto cir­<lb></lb>colare della Libbra, e il fatto misterioso del pesar più i gravi, quanto più <lb></lb>si dilungano dal centro, gli si presentava a considerare sotto l&#039;aspetto più <lb></lb>semplice, benchè poi infine torni al medesimo, dell&#039;alleggerirsi che fanno <pb xlink:href="020/01/1779.jpg" pagenum="22"></pb>gli stessi gravi quanto più discendono nel semicerchio. </s>

<s>Perchè nel braccio <lb></lb>della Bilancia AB (fig. </s>

<s>4) il grave A pesa più, come l&#039;esperienza dimostra, <lb></lb><figure id="id.020.01.1779.1.jpg" xlink:href="020/01/1779/1.jpg"></figure></s></p><p type="caption">

<s>Figura 4.<lb></lb>che quando sia sceso in C? — La causa ef­<lb></lb>ficiente di ciò, ragionava argutamente Giordano, <lb></lb>non può consistere in altro che nel particolar <lb></lb>modo della discesa, la quale da una parte si fa <lb></lb>in giù, e dall&#039;altra per traverso. </s>

<s>Ecco i due <lb></lb>moti di Aristotile presentarsi sotto le loro vere <lb></lb>sembianze; ecco una grande rivelazione: la di­<lb></lb>scesa del grave nel circolo resulta dalla composi­<lb></lb>zione di due forze, una naturale diretta al centro <lb></lb>della Terra, e l&#039;altra violenta e diretta al centro <lb></lb>dello strumento. </s>

<s>“ Iste descensus est mixtus ex <lb></lb>descensu naturali et violento ” (De ponderibus cit., pag. </s>

<s>4). E poichè il <lb></lb>moto naturale è tanto più impedito, quanto ha in sè misto più del violento; <lb></lb>in C il corpo è più leggero che in A, e in D più leggero che in C, per­<lb></lb>chè, nella discesa pel maggiore arco, è maggior parte di violenza che nella <lb></lb>discesa per l&#039;arco minore. </s>

<s>“ Potest ex hoc ostendi quod pondus in Libra <lb></lb>tanto fit levius quanto plus descendit in semicirculo. </s>

<s>Incipiat igitur mobile <lb></lb>descendere a termino semicirculi et descendat continue: dico tunc quod <lb></lb>maior arcus circuli plus contrariatur rectae lineae quam minor, et casus <lb></lb>gravis per arcum maiorem plus contrariatur casui gravis, qui per rectam <lb></lb>fieri debet, quam casus per arcum minorem; patet: ergo maior est violen­<lb></lb>tia in motu secundum arcum maiorem, quam secundum minorem ” (ibid.). </s></p><p type="main">

<s>Da questo medesimo principio dipende la soluzione del medesimo pro­<lb></lb>blema sotto l&#039;altra forma, in che piacque di presentarlo ad Aristotile, per­<lb></lb>chè cioè il corpo sia più grave e più velocemente discenda nel circolo più <lb></lb>grande, che nel minore? </s>

<s>Perchè, risponde Giordano, essendo nel maggior <lb></lb>circolo minore l&#039;obliquità, vi è meno di violenza, e la discesa perciò è più <lb></lb>naturale. </s>

<s>“ Eodem syllogismo necesse est pondus gravius esse quodammodo <lb></lb>et velocius descendere quod movetur in circulo maiori, quia, ut prius pro­<lb></lb>batur, minus obliquatur quam in circulo minori, et per consequens minus <lb></lb>habet violentiae: quia igitur minus distat descensus in circulo maiori a <lb></lb>descensu naturali, qui fit per lineam rectam, quam qui est in circulo mi­<lb></lb>nori, dicatur descensus rectior, idest plus tendens ad rectitudinem, atque <lb></lb>in circulo minori, ob rationem oppositam, obliquior descensus ” (ibid., <lb></lb>pag. </s>

<s>5). </s></p><p type="main">

<s>Così veniva Giordano a ritrovar nelle cause naturali quella ragione, che <lb></lb>Aristotile ricavava dalle arguzie del proprio ingegno, e che da Archimede <lb></lb>si faceva tutta consistere nel fatto sperimentale degli equilibrii. </s>

<s>E perchè <lb></lb>anco il Matematico tedesco sentiva che si sarebbero potute fare a lui le dif­<lb></lb>ficoltà, che poi si fecero a Galileo, è sollecito di prevenirle con dire che si <lb></lb>può del grave in quiete ragionare come se si movesse, essendo che nell&#039;uno <lb></lb>e nell&#039;altro stato patisce le medesime contrarietà e la quiete stessa può ri-<pb xlink:href="020/01/1780.jpg" pagenum="23"></pb>guardarsi come il termine del moto. </s>

<s>“ Grave igitur in parte inferiori, sive <lb></lb>moveatur sive quiescat, levius est secundum situm ” (ibid.). </s></p><p type="main">

<s>Quel che Giordano diceva dell&#039;essere un corpo più leggero o più grave <lb></lb><emph type="italics"></emph>secondo il sito<emph.end type="italics"></emph.end> si traduce ora, nel linguaggio più accetto ai moderni, nella <lb></lb>parola <emph type="italics"></emph>momento,<emph.end type="italics"></emph.end> la quantità del quale è varia secondo la varia distanza del <lb></lb>corpo dal punto di sospensione, o secondo il progresso che scendendo fa <lb></lb>nella perpendicolare. </s>

<s>Da così nuovi e fecondi principii trae l&#039;Autore sette <lb></lb>importantissime conclusioni, che per le cose da dimostrare servono di <emph type="italics"></emph>po­<lb></lb>stulati.<emph.end type="italics"></emph.end> “ Prima est: omnis ponderosi motum ad medium esse ” (ibid.), <lb></lb>ossia al centro terrestre, e ciò veniva a ridurre nel vero esser loro le astratte <lb></lb>ponderosità di Archimede. </s>

<s>Il secondo postulato che dice: “ quanto gravius <lb></lb>tanto velocius descendere ” (ibid.) si può giudicare più lubrico che falso, <lb></lb>intendendosi non della libera discesa, che si fa con moto accelerato, ma di <lb></lb>quella, che si fa nelle Macchine equabilmente. </s></p><p type="main">

<s>I postulati però che seguitano contengono in sè il germe di una scienza <lb></lb>nuova intorno ai momenti dei gravi scendenti sopra varie inclinazioni dei <lb></lb>piani. </s>

<s>“ Tertia, gravius esse in descendendo, quanto eiusdem motus ad me­<lb></lb>dium est rectior. </s>

<s>Quarta, secundum situm gravius esse, quanto in eodem <lb></lb>situ minus obliquus est descensus. </s>

<s>Quinta, obliquiorem autem descensum <lb></lb>minus capere de directo in eadem quantitate ” (ibid.). Da questa conclu­<lb></lb>sione e dalla seconda s&#039;argomenta che la gravità <emph type="italics"></emph>secundum situm,<emph.end type="italics"></emph.end> o come <lb></lb>altrimenti si dice il <emph type="italics"></emph>momento,<emph.end type="italics"></emph.end> è il prodotto del peso moltiplicato per la quan­<lb></lb>tità della discesa naturale, d&#039;ond&#039;è facile confermare quello che poco fa si <lb></lb>diceva, che cioè si contengono in questi principii statici di Giordano i ger­<lb></lb>mogli di una scienza nuova. </s>

<s>E infatti, immaginando un corpo scendere ora <lb></lb>sopra l&#039;inclinazione AB (fig. </s>

<s>5), ora sopra la AC, ora sopra la AD, percioc­<lb></lb><figure id="id.020.01.1780.1.jpg" xlink:href="020/01/1780/1.jpg"></figure></s></p><p type="caption">

<s>Figura 5.<lb></lb>chè, pervenuto al sito della ugualità, che il VII postu­<lb></lb>lato dice <emph type="italics"></emph>esse acquidistantiam superficiei orizontis,<emph.end type="italics"></emph.end> ha <lb></lb>raggiunta la medesima quantità del discenso naturale <lb></lb>AE; avrà perciò in ogni caso eguale momento. </s>

<s>Ora es­<lb></lb>sendo questo il principio fondamentale, a cui s&#039;in­<lb></lb>forma e da cui quasi totalmente dipende la Meccanica <lb></lb>galileiana, basterebbe l&#039;aver fatto osservar ciò senz&#039;al­<lb></lb>tro a provar che dallo stesso Giordano muovono le <lb></lb>lontane e occulte radici a quella che, dopo quattro <lb></lb>secoli, pubblicamente s&#039;intitolava <emph type="italics"></emph>Scienza Nuova.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma perchè meglio si confermi fin d&#039;ora un fatto <lb></lb>che, nel primo annunziarsi in questa Storia, trova il conflitto della comune <lb></lb>opinione, vedasi come da questi statici principii del Nemorario concludasi <lb></lb>direttamente la verità di un teorema dimostrato in varii modi dai Meccanici <lb></lb>del secolo XVI, e che Galileo nonostante si lusingò di aver dato per nuovo. </s></p><p type="main">

<s>Sieno sopra i due piani inclinati MO, MR (fig. </s>

<s>6) aventi la medesima <lb></lb>altezza MN posti due gravi P e Q, e si cerchi qual relazione debba passar <lb></lb>fra loro e gli stessi piani, perchè possano scendere con eguali momenti. <pb xlink:href="020/01/1781.jpg" pagenum="24"></pb>Prese AS, CF, nelle due oblique eguali, quel che <emph type="italics"></emph>capiunt de directo in ea­<lb></lb>dem quantitate<emph.end type="italics"></emph.end> saranno le due perpendicolari AB, CD, per cui saranno <lb></lb><figure id="id.020.01.1781.1.jpg" xlink:href="020/01/1781/1.jpg"></figure></s></p><p type="caption">

<s>Figura 6.<lb></lb>espressi i momenti da <lb></lb>P.AB, e da q.CD. </s>

<s>E <lb></lb>perchè si vuole che tali <lb></lb>due momenti tornino e­<lb></lb>guali, avremo dunque <lb></lb>P:Q=CD:AB. </s>

<s>Si com­<lb></lb>pongano i due triangoli <lb></lb>ABS, CDF, dai quali ri­<lb></lb>caveremo le due seguenti <lb></lb>equazioni: CD:CF= <lb></lb>MN:MR; AB:AS=MN:MO, d&#039;onde CD:AB=MO:MR e perciò P:Q <lb></lb>=MO:MR. </s></p><p type="main">

<s>Ma perchè il principale intento del Nemorario era quello di dimostrare <lb></lb>il principio statico, ossia il fondamento a tutte le macchine, da Aristotile ri­<lb></lb>posto nella Leva, a quest&#039;unico strumento fa, nella proposizione VIII, l&#039;ap­<lb></lb>plicazione immediata delle sue dottrine. </s>

<s>Erano state preparate già queste <lb></lb>dottrine, per servire più appropriatamente alla detta VIII proposizione, nella <lb></lb>proposizione I, nella quale si considerano piuttosto le velocità, che gli spazii <lb></lb>percorsi nella naturale discesa: “ Inter quaelibet duo gravia (così quella <lb></lb>I proposizione è formulata) est velocitas descendendo proprie et ponderum <lb></lb>eodem ordine sumpta proportio, descensus autem, et contrarii motus, pro­<lb></lb>partio eadem, sed permutata ” (ibid., pag. </s>

<s>6). </s></p><p type="main">

<s>Sia la Leva DE (fig. </s>

<s>7) sostenuta in A come centro. </s>

<s>La potenza da D <lb></lb>discendendo in M, fa risalire da E in F la resistenza, ma la proporzione in <lb></lb><figure id="id.020.01.1781.2.jpg" xlink:href="020/01/1781/2.jpg"></figure></s></p><p type="caption">

<s>Figura 7.<lb></lb>ogni modo è la medesima, ben­<lb></lb>chè permutata. </s>

<s>Or supposto che <lb></lb>la discesa della prima sia DM, e <lb></lb>l&#039;ascesa della seconda EF, rap­<lb></lb>presentati coi pesi P e Q il mo­<lb></lb>tore e il mosso, sarà dunque il <lb></lb>momento di quello P.DM e di <lb></lb>questo q.EF, che nel caso dell&#039;e­<lb></lb>quilibrio. </s>

<s>daranno la proporzione <lb></lb>P:Q=EF:DM. </s>

<s>Ma perchè i <lb></lb>triangoli ADM, AEF son simili P:Q=AE:AD, che vuol dire la resistenza <lb></lb>s&#039;equilibra con la potenza, quando son reciprocamente proporzionali alle <lb></lb>due braccia della leva, o alle due distanze dal punto d&#039;appoggio o alla velo­<lb></lb>cità virtuale dell&#039;ascesa da una parte e della discesa dall&#039;altra. </s></p><p type="main">

<s>È facile ora scoprire che il principio statico del Cartesio è un imme­<lb></lb>diato e legittimo corollario di questa dimostrazione. </s>

<s>Supponiamo infatti che <lb></lb>AM sia più lunga il doppio di AF, DM sarà pure il doppio di EF, e P sarà <lb></lb>metà del peso di <expan abbr="q.">que</expan> Di qui è che, considerando la potenza ora collocata in <pb xlink:href="020/01/1782.jpg" pagenum="25"></pb>M, ora in F, tanto ci vuole a sollevare Q in F, quanto P in D; ossia la <lb></lb>metà del peso ad un&#039;altezza doppia. </s></p><p type="main">

<s>Per poi far vedere il Nemorario che il suo principio statico generale <lb></lb>s&#039;applica alla soluzione di altri varii problemi, non contento di far soggetto <lb></lb>alla sua IX proposizione il teorema <emph type="italics"></emph>De ponderibus<emph.end type="italics"></emph.end> di Euclide, lo promove <lb></lb>così nella seguente sua X proposizione: “ Si canonium fuerit symmetrum <lb></lb>magnitudine et substantiae eiusdem, dividaturque in duas partes inaequales, <lb></lb>et suspendatur in termino minoris portionis pondus quod faciat canonium <lb></lb>parallelum epipedo orizontis, proportio ponderis illius, ad superabundantiam <lb></lb>ponderis maioris portionis canonii ad minorem, est sicut proportio totius ca­<lb></lb>nonii ad duplum longitudinis minoris portionis ” (ibid., pag. </s>

<s>24). </s></p><p type="main">

<s>Sia AB (fig. </s>

<s>8) il cannone omogeneo e uniforme, diviso in due parti <lb></lb>disuguali nel punto C, da cui si tenga sospeso. </s>

<s>Appendasi dall&#039;estremità A <lb></lb><figure id="id.020.01.1782.1.jpg" xlink:href="020/01/1782/1.jpg"></figure></s></p><p type="caption">

<s>Figura 8.<lb></lb>un pezzo di cannone omogeneo <lb></lb>e uniforme al primo, e di tal <lb></lb>peso che valga a ridurre il can­<lb></lb>none AB orizzontale. </s>

<s>Presa dal <lb></lb>centro una distanza CD=AC <lb></lb>in modo che DB sia la diffe­<lb></lb>renza che passa fra la maggiore e la minor parte della divisione <lb></lb>fatta nel cannon livellato, e considerando il peso di questa diffe­<lb></lb>renza concentrato in E, come quello del cannone pendulo concen­<lb></lb>trato in F, dimostra il Nemorario, che le condizioni del richiesto <lb></lb>equilibrio sono espresse dall&#039;equazione F:E=AB:2AC. </s></p><p type="main">

<s>La concisione del trattatello di Giordano, e lo stretto ordine matema­<lb></lb>tico, con cui procede, ci fanno ragionevolmente supporre che fosse scritto <lb></lb>per servire di testo alle lezioni di Statica, alle quali precedevano le Que­<lb></lb>stioni di Aristotile. </s>

<s>La condensata scienza e la fecondità dei concetti lascia­<lb></lb>vano dall&#039;altra parte ampio e libero campo ai lettori di svolgere le propo­<lb></lb>ste dottrine in teoremi nuovi, o di servirsene per argomento a risolvere <lb></lb>nuovi problemi. </s>

<s>Nei secoli XIV e XV fu creduto che mancassero così fatti <lb></lb>lettori, e che si riducessero le lezioni di Meccanica razionale alle Questioni <lb></lb>aristoteliche, all&#039;oracolo delle quali sarebbe stato un sacrilegio aggiunger <lb></lb>nulla o detrarre. </s>

<s>S&#039;ingerì una così fatta opinione per non s&#039;aver notizia di <lb></lb>nessuno autore di Meccanica in que&#039;tempi, e per essersi fatto concetto che <lb></lb>fosse quella un&#039;epoca d&#039;ignoranza universale. </s>

<s>Ma chi ha penetrato mai nelle <lb></lb>scuole di quell&#039;antica gente? </s>

<s>Chi ha esaminate le loro scritture, quelle par­<lb></lb>ticolarmente che servivano per le lezioni, e nelle quali i Maestri esplicavano <lb></lb>a sè medesimi i loro pensieri? </s>

<s>Chi potesse veder le carte di tanti Filosofi <lb></lb>solitarii di que&#039;tempi, e saper quello che il vigoroso ingegno rivelò a loro <lb></lb>degli effetti naturali, si confesserebbe forse che sono almeno in gran parte <lb></lb>temerarii i correnti giudizi. </s></p><p type="main">

<s>Il secolo nostro ne ha avuto un singolarissimo esempio in Leonardo da <lb></lb>Vinci, sui manoscritti scientifici del quale, dopo tre secoli, il mondo lette-<pb xlink:href="020/01/1783.jpg" pagenum="26"></pb>rato ha da poco fa aperti gli occhi. </s>

<s>È il soggetto per la nostra Storia tanto <lb></lb>importante, che non si può trascurar di dire per quali avventurose vicende <lb></lb>quell&#039;uomo tanto ammirato per l&#039;eccellenza delle sue pitture e sculture, e <lb></lb>per le stupende opere d&#039;ingegneria pratica, si sia ora venuti a riconoscerlo <lb></lb>per un solenne maestro di teorie. </s>

<s>L&#039;importanza poi dell&#039;argomento tanto <lb></lb>per noi più cresce, in quanto che, di quelle teorie, le concernenti la Mec­<lb></lb>canica son più ammirabili di tutte; ond&#039;è che Leonardo, riappiccando il filo <lb></lb>delle tradizioni agli ultimi studiosi di Giordano, lo protrae non solo infino <lb></lb>al secolo XVI, ma par che con valido braccio lo lanci anche al di là di <lb></lb>Galileo. </s></p><p type="main">

<s>La storia avventurosa de&#039;manoscritti vinciani, infino al 1784, si può <lb></lb>leggere così compilata dall&#039;Autore del ragionamento premesso ai Disegni di <lb></lb>Leonardo da Vinci, incisi e pubblicati in quell&#039;anno stesso in Milano da Carlo <lb></lb>Giuseppe Gerli: “ De&#039;codici della Biblioteca ambrosiana ecco ciò che ne <lb></lb>scrive il signor mariette in una nota alla sua Lettera al signor conte di Cay­<lb></lb>lus, che è la LXXXIV fra le Lettere pittoriche (Tomo II, pag. </s>

<s>171), e con <lb></lb>cui concorda il Bosca, nella Storia della Biblioteca ambrosiana: ” </s></p><p type="main">

<s>“ Lasciò Leonardo i suoi disegni a Francesco Melzi, dopo la cui morte <lb></lb>furono così trascurati, che Lelio Gavardi d&#039;Asola, parente stretto di Aldo <lb></lb>Manuzio, maestro in quella casa, ebbe tutto l&#039;agio di prenderseli. </s>

<s>S&#039;impadronì <lb></lb>di tredici volumi, parte in folio e parte in 4°, e portolli a Firenze con spe­<lb></lb>ranza di venderli cari al granduca Francesco de&#039;Medici, ma essendo questi <lb></lb>inaspettatamente morto, Lelio si vide deluso, e compreso dal rimorso pensò <lb></lb>a farne la restituzione, pregando a tale oggetto Gio. </s>

<s>Ambrogio Mazzenta, <lb></lb>gentiluomo milanese, ch&#039;ei ritrovò in Pisa, a volere riportare quei libri ai <lb></lb>signori Melzi. </s>

<s>Così fu fatto, ma tenendone questi poco conto, abbenchè av­<lb></lb>visati del pregio da Pompeo Leoni celebre scultore, sei ne lasciarono in dono <lb></lb>al Mazzenta. </s>

<s>Di questi, uno ne fu donato a Carlo Emanuele duca di Savoia, <lb></lb>un altro n&#039;ebbe il pittore Ambrogio Figini, i cui disegni furono poi ven­<lb></lb>duti al signor Giuseppe Smith, ed uno ne ottenne il cardinale Federigo Bor­<lb></lb>romeo, che ne arricchì la Biblioteca ambrosiana da lui instituita. </s>

<s>È questo <lb></lb>un tomo in folio coperto di velluto rosso, che vi si vede tuttora. </s>

<s>Leonardo <lb></lb>vi tratta de&#039;lumi e delle ombre, da matematico e da pittore. </s>

<s>I tre altri vo­<lb></lb>lumi, che erano in mano del Mazzenta, passarono a Pompeo Leoni sum­<lb></lb>mentovato, il quale ne compose un sol volume ben grosso, che conteneva, <lb></lb>per quel che si dice, 1750 disegni. </s>

<s>Di questo pregevole volume fece acqui­<lb></lb>sto il conte Galeazzo Arconati, che nel 1637 ne fe dono alla mentovata Bi­<lb></lb>blioteca ambrosiana, con tutto quello che aveva potuto raccogliere dal me­<lb></lb>desimo maestro, consistente in dodici volumi, mostrando il più generoso <lb></lb>disinteresse, poichè ricusò di venderli per tremila doppie al re d&#039;Inghilterra, <lb></lb>siccome apparisce dalla marmorea epigrafe, a lui posta in un salone della <lb></lb>Biblioteca medesima. </s>

<s>Quanto ai sette volumi, che si riserbarono i Melzi, si <lb></lb>crede che fossero mandati in Spagna a Filippo II, che si piccava d&#039;esserne <lb></lb>intendente. </s>

<s>” </s></p><pb xlink:href="020/01/1784.jpg" pagenum="27"></pb><p type="main">

<s>“ A quanto dice il Mariette noi non abbiamo che aggiungere, se non <lb></lb>che, oltre i mentovati codici dati alla Biblioteca dall&#039;Arconati e dal Mazzenta, <lb></lb>uno ve n&#039;è in 16° donatole dal conte Orazio Archinto, nel 1674. ” (pag. </s>

<s>8). </s></p><p type="main">

<s>Il documento pubblicato a pag. </s>

<s>131, 32 da Carlo Amoretti (Memorie <lb></lb>storiche ecc., Milano 1804) racconta con qualche varietà la parte ch&#039;ebbe <lb></lb>in questo fatto il Mazzenta, ma perchè non è cosa per noi di grande im­<lb></lb>portanza basti il sapere che, infino dal 1637, si trovarono nella Biblioteca <lb></lb>ambrosiana raccolti di Leonardo quattordici volumi manoscritti. </s>

<s>A quel più <lb></lb>grosso di tutti, messo insieme dal Leoni, fu dato, per la mole e per la con­<lb></lb>gerie dei disegni e delle descrizioni, il nome di <emph type="italics"></emph>Atlantico:<emph.end type="italics"></emph.end> gli altri, non <lb></lb>avendo, per la confusione delle materie comune a tutti, nessun titolo pro­<lb></lb>prio, si distinsero in capriccioso ordine con le lettere dell&#039;alfabeto. </s>

<s>Si fece <lb></lb>forse questa designazione ai codici, quand&#039;ebbero a mutar domicilio e pa­<lb></lb>drone: forse, attesa la diligenza dei bibliotecari ambrosiani, la cosa è più <lb></lb>antica, ma in ogni modo il Venturi, che sentì primo il dovere di citare con <lb></lb>fedeltà le fonti, alle quali aveva attinto i suoi <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> dee aver trovata quel­<lb></lb>l&#039;alfabetica designazione già fatta. </s></p><p type="main">

<s>Comunque sia di ciò, a noi solo importa sapere quali siano le tradi­<lb></lb>zioni dell&#039;antica scienza, che si trovano disperse per coteste carte avventu­<lb></lb>rosamente così raccolte. </s>

<s>Che scienza naturale veramente dentro ci fosse, era <lb></lb>una voce vaga, echeggiante insomma quella messa fuori già dal Vasari, ma <lb></lb>da qualche po&#039;d&#039;Ottica in fuori, che traspariva dal pubblico trattato Della <lb></lb>pittura in servigio dell&#039;arte, nessun aveva notati di altro, in soggetto scien­<lb></lb>tifico, o trascritto gli autentici documenti. </s></p><p type="main">

<s>Dalle carte vinciane, per varie parti d&#039;Europa disperse, s&#039;incominciò, <lb></lb>nel secolo XVIII, a pubblicare disegni o da artisti o da signori dilettanti <lb></lb>dell&#039;arte, e il Caylus, il Grozart, il Mariette, l&#039;Harundel e l&#039;Hollar ne ri­<lb></lb>portarono di grandissime lodi. </s>

<s>Si riscossero a quegli applausi gl&#039;Italiani, che <lb></lb>si ricordarono essere la loro Biblioteca ambrosiana doviziosissima di così fatti <lb></lb>lavori, usciti dalla penna o dalla matita di un tanto Autore, e Baldassarre <lb></lb>Oltrocchi, bibliotecario, sollecitò e fu largo de&#039;suoi consigli al pittor mila­<lb></lb>nese Giuseppe Gerli, che scelse da varii codici le più belle e, per la loro <lb></lb>curiosità, le più notabili figure. </s></p><p type="main">

<s>Fu alla pubblicazione, che avvenne come si disse in Milano nel 1784, <lb></lb>premesso un Ragionamento molto erudito, e da cui forse vennero le prime <lb></lb>e più precise e più particolari notizie di Leonardo come inventore di stru­<lb></lb>menti della scienza e dell&#039;arte, o come cultore delle matematiche applicate. </s>

<s><lb></lb>Si diceva aver trovato, squadernando que&#039;sapienti volumi, nuove proposte <lb></lb>di fontane e di varie trombe, per tirar acqua or co&#039;soffietti, or co&#039;vapori, <lb></lb>or colle secchie attaccate a una fune perpetua: vi si vedevano immaginate <lb></lb>navicelle a ruota, da andare a ritroso della corrente, e vi s&#039;accennava a <lb></lb>quella barca, che apparì poi disegnata nella Tavola XLVII illustrativa del <lb></lb>trattato Del moto e della misura dell&#039;acqua (Bologna 1828), nella quale i <lb></lb>galeotti dovevano, invece dei remi, menare un manubrio applicato a una <pb xlink:href="020/01/1785.jpg" pagenum="28"></pb>ruota dentata, che per via di rocchetti e di altre ruote dentate faceva vol­<lb></lb>gere un&#039;<emph type="italics"></emph>elice,<emph.end type="italics"></emph.end> come ne&#039;piroscafi della nuova invenzione. </s>

<s>S&#039;ammirava la <lb></lb>grande arte meccanica di Leonardo applicata alla ballistica e alla tattica <lb></lb>“ siccome scorgesi nelle moltissime macchine per tirare e alzar pesi, per <lb></lb>gittar sassi, formare e stender ponti, e nelle armi che ha immaginate sì per <lb></lb>offendere che per difendersi, fra le prime delle quali sono da annoverarsi i <lb></lb>carri falcati ” (pag. </s>

<s>3). </s></p><p type="main">

<s>“ Non solo però attese, poi si soggiunge, alle arti distruggitrici, ma <lb></lb>pensò anche alle utili, e veggonsi suoi disegni d&#039;un telaro da far nastri, <lb></lb>d&#039;una gran cesoia, d&#039;un congegno da torcer fili, d&#039;un girarrosto a fumo, <lb></lb>d&#039;una macchina da purgar porti e da formar lime, e d&#039;altri utili ritrovati. </s>

<s><lb></lb>Vedonsi pure alcune figure, che sembrano destinate a spiegare l&#039;acustica, i <lb></lb>fenomeni dell&#039;eco e l&#039;Ottica, intorno alla quale moltissimo ha disegnato e <lb></lb>scritto, e un disegno pur v&#039;è, che direbbesi un Canocchiale ” (ivi, pag. </s>

<s>4). </s></p><p type="main">

<s>Ai curiosi, che s&#039;intrattenevano piacevolmente a squadernare il volume <lb></lb>in folio del Gerli, per ridere sgangheratamente di quelle caricature, e per <lb></lb>ammirar quegli uomini il dorso, le braccia e i piedi de&#039;quali aveva strana­<lb></lb>mente Leonardo impennati di ali, rimaneva largo campo d&#039;immaginar la <lb></lb>scienza acustica e ottica e il Canocchiale e tante altre cose, che dicevasi <lb></lb>avere inventate quel fecondo e mirabilissimo ingegno. </s>

<s>Or chi può mai pre­<lb></lb>scrivere le vie per l&#039;aria ai voli infaticabili della immaginazione? </s></p><p type="main">

<s>Furono in queste esaltazioni di mente trovati dai Francesi i Lombardi <lb></lb>a tempo della conquista, e perchè ogni patria gloria dei conquistati doveva <lb></lb>esser mancipio dei conquistatori, fu così decretato dei manoscritti di Leo­<lb></lb>nardo da Vinci. </s>

<s>Fossero stati intorno a ciò gl&#039;Italiani più silenziosamente <lb></lb>operosi, e meno loquaci, non sarebbero stati forse provocati i vincitori, che <lb></lb>avevano le mani al ferro e non ai libri, ad entrare nell&#039;Ambrosiana per con­<lb></lb>culcar la cresta che di là rizzavano i vinti. </s>

<s>Che poi non fosse quello vera­<lb></lb>mente amore ai libri e alla scienza si conferma dal fatto che, svolti appena <lb></lb>i codici da chi gli ebbe in consegna, e rifiutatone uno perchè pareva appar­<lb></lb>tener piuttosto a Luca Pacioli che a Leonardo, da nessun Francese furono <lb></lb>per lungo tempo mai più aperti. </s>

<s>E messi sulla bilancia i dodici da una parte, <lb></lb>e il Codice atlantico dall&#039;altra, perchè nella mole e nel peso non era molto <lb></lb>grande la differenza, furono ripartite le spoglie fra l&#039;Istituto e la nazionale <lb></lb>Biblioteca di Parigi. </s></p><p type="main">

<s>Gli spogliati insorgevano con parole irosamente impotenti contro l&#039;inde­<lb></lb>gna usurpazione, ma alcuni de&#039;più savi, tornando alla coscenza, si consi­<lb></lb>gliarono di ristorare il danno, e di riparare al patrio onore coi fatti. </s>

<s>Giovan <lb></lb>Batista Venturi corre da Bologna a Parigi dietro i predatori, e là, dove nel­<lb></lb>l&#039;Istituto nazionale avevano allora allora posata una parte della preda, si <lb></lb>mette con diligente studio a ricercarla, perchè di un tesoro egualmente in­<lb></lb>fruttuoso, o sepolto a Milano o a Parigi, potesse usufruirne la scienza uni­<lb></lb>versale. </s>

<s>Così, intanto che meditava di far opera più lunga e più compiuta, <lb></lb>per sodisfare al sollecito desiderio di quei generosi, che nell&#039;amor degli stu-<pb xlink:href="020/01/1786.jpg" pagenum="29"></pb>dii comuni a tutti volevano veder sopita la imparità delle gare municipali, <lb></lb>s&#039;affrettò di dar fuori in Parigi, nel 1797, il suo <emph type="italics"></emph>Essai sur les ouvrages <lb></lb>physico-matematiques de Leonard de Vinci.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ha il Venturi, come gli altri suoi connazionali, preoccupato il giudizio <lb></lb>intorno alla straordinaria eccellenza scientifica di Leonardo, fondata insomma <lb></lb>sopra la rumorosa fama che ne correva, ma non bene accertata ancora coi <lb></lb>fatti. </s>

<s>Traspariscono gl&#039;indizi di quella mente preoccupata infino dalle prime <lb></lb>pagine, nelle quali si vuol Leonardo fare precursor del Copernico, mentre <lb></lb>egli in verità non professa che la semplice rotazione diurna della Terra, im­<lb></lb>mobile nel suo centro, conforme a quell&#039;opinione, comune a molti allora e <lb></lb>ne&#039;secoli precedenti, che si distinse col nome di semicopernicismo. </s>

<s>Al va­<lb></lb>loroso Fisico e Matematico di Bologna mancavano di più i criterii storici ne­<lb></lb>cessari a dare il giusto merito alle speculazioni di Leonardo, comparandole <lb></lb>con le tradizioni più antiche e con la scienza moderna, d&#039;onde avvenne che <lb></lb>alcune cose rimasero incerte nel <emph type="italics"></emph>Saggio,<emph.end type="italics"></emph.end> e alcune altre a parer nostro fu­<lb></lb>rono male intese. </s>

<s>Per scegliere qualche esempio, che si riferisca al nostro <lb></lb>particolare argomento, in quella prima nota tradotta dal Venturi al § VII <lb></lb>non sembra a noi che s&#039;abbia per nulla a intendere della Leva angolare, <lb></lb>non trattandosi in verità d&#039;altro che di una bellissima applicazione delle <lb></lb>forze composte, per cui la Leva si dice da Leonardo <emph type="italics"></emph>reale,<emph.end type="italics"></emph.end> essendo la forza, <lb></lb>attualmente a lei applicata, risoluta nelle due, che si chiamano con molta <lb></lb>proprietà le <emph type="italics"></emph>Leve potenziali.<emph.end type="italics"></emph.end> Fa veramente gran maraviglia che non rico­<lb></lb>noscesse lo stesso Venturi il principio statico della Leva angolare nella nota <lb></lb>seguente, nella quale si dimostra che il momento del peso pendulo appli­<lb></lb>cato all&#039;estremità di un filo o di una verga, la quale un contrappeso va sol­<lb></lb>levando con più o meno forza, è proporzionale al seno dell&#039;angolo dell&#039;in­<lb></lb>clinazione fatto dalla stessa verga con la linea verticale. </s></p><p type="main">

<s>La traduzione francese e la parafrasi delle Note manoscritte che ai sem­<lb></lb>plici e rozzi modi del popolano da Vinci sostituiva l&#039;artificioso linguaggio degli <lb></lb>scienziati moderni, conferiva efficacemente a confermar sempre più l&#039;opinione <lb></lb>che si trovasse in que&#039;solitarii manoscritti da quel miracolo d&#039;ingegno divi­<lb></lb>nata la scienza fisica matematica dei nostri tempi. </s>

<s>L&#039;andar così a genio del <lb></lb>pubblico fece al <emph type="italics"></emph>Saggio<emph.end type="italics"></emph.end> del Venturi riscotere applausi universali, ch&#039;eccitarono <lb></lb>altri in Italia ad imitarne, quant&#039;era a loro possibile, gli esempi. </s>

<s>Nella Va­<lb></lb>ticana trovavasi una copia manoscritta del trattato Della pittura, di cui il Du­<lb></lb>fresne non aveva pubblicato che un saggio, e Guglielmo Manzi, nel 1817, <lb></lb>s&#039;affrettò di darlo alle stampe nuovamente corretto e intero. </s>

<s>Possedeva, pure <lb></lb>in Roma, la Barberiniana il libro <emph type="italics"></emph>Del moto e misura dell&#039;acqua,<emph.end type="italics"></emph.end> che il <lb></lb>p. </s>

<s>Luigi Maria Arconati domenicano aveva, infino dal 1643, finito di tra­<lb></lb>scrivere e di ordinare sulle note sparse di Leonardo, e Francesco Cardinali <lb></lb>lo pubblicò in Bologna nel 1828, raccogliendolo nel Tomo X de&#039;più scelti <lb></lb>Idraulici d&#039;Italia. </s></p><p type="main">

<s>S&#039;aspettava intanto con gran desiderio che il Venturi mantenesse la <lb></lb>promessa di dar compieta l&#039;opera, della quale il pubblico aveva con tanta <pb xlink:href="020/01/1787.jpg" pagenum="30"></pb>avidità accolto il Saggio, ma perchè le speranze oramai venivano meno, Gu­<lb></lb>glielmo Libri, infino dal 1630, pensò di supplire all&#039;importantissimo ufficio. </s>

<s><lb></lb>Erano già quindici anni che il Codice atlantico aveva fatto ritorno in patria, <lb></lb>rimanendo tuttavia gli altri dodici suoi minori fratelli in perpetuo esilio nel­<lb></lb>l&#039;Istituto parigino; e in Milano, dove si ritrovava nella primavera del detto <lb></lb>anno 1630, attendeva il futuro nostro Storico delle Matematiche, con grande <lb></lb>alacrità, a trascrivere dallo stesso Atlantico quel che sembravagli più impor­<lb></lb>tante, e a dilucidarne, come sapeva meglio, i disegni. </s>

<s>Si recò poi nella se­<lb></lb>guente estate a Parigi, per scotere ai dodici Manoscritti dell&#039;Istituto la pol­<lb></lb>vere lasciatavi cader sopra per più di trent&#039;anni. </s></p><p type="main">

<s>La scienza universale, che di fatto ritrovò sparsa per quelle neglette <lb></lb>carte, parve allo stesso Libri superar quella, che andavasi diffondendo dalla <lb></lb>fama, e scrivendo a Gino Capponi gli diceva avervi trovato di tutto: fisica, <lb></lb>matematica, astronomia, storia, filosofia, novelle, meccanica, da parergli un <lb></lb>vero prodigio; ch&#039;era quello insomma un divino ingegno, creatore della Fi­<lb></lb>losofia sperimentale in Italia (Lettere di G. Capponi, Vol. </s>

<s>I, Firenze 1882, <lb></lb>pag. </s>

<s>299, 308). Di qui i ferventi propositi di dar, sotto migliori forme, ese­<lb></lb>cuzione al primo progetto del Venturi; propositi che si sfogarono, come nu­<lb></lb>voloni di estate in poche stille di pioggia, in quella prolissa enumerazione <lb></lb>delle tante cose pensate e fatte da Leonardo, e in quella spruzzagliatella di <lb></lb>note, trascritte e apposte al II libro della Storia delle Matematiche in Italia. </s></p><p type="main">

<s>La fama di Leonardo enciclopedico così cresceva, sempre più andando, <lb></lb>che d&#039;ogni parte scrittori venivano con più risonanti parole a ripetere le <lb></lb>maraviglie scritte dal Libri. </s>

<s>Alla fine di queste declamazioni però voci più <lb></lb>sommesse e assennate parevano domandare e dire ai declamatori: ma fa­<lb></lb>teci un po&#039;leggere e veder co&#039;nostri occhi quel che il grand&#039;uomo ha scritto <lb></lb>e disegnato nella sua integrità originale, giacchè le poche stille sparse dal <lb></lb>Venturi e dal Libri n&#039;accendono più che mai viva la sete. </s></p><p type="main">

<s>Ebbero buona volontà di rispondere a questi onestissimi desiderii al­<lb></lb>cuni Italiani, mettendo mano nel 1872 a pubblicare il Codice atlantico, che <lb></lb>da vent&#039;anni in que è rimasto nel suo primo principio, mentre in Parigi <lb></lb>Carlo Ravaisson-Mollien ha già compiuta la trascrizione e il commento ai <lb></lb>dodici manoscritti dell&#039;Istituto, e Gianpaolo Richter ha dato, da dieci anni, <lb></lb>al pubblico in Londra raccolte e ordinate le note del Nostro, le quali, ben­<lb></lb>chè insomma trattino di tutto, escludendovisi le cose d&#039;argomento fisico­<lb></lb>matematico, s&#039;intitolarono <emph type="italics"></emph>Scritti letterarii.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Se non tutto dunque è ormai sotto gli occhi del pubblico studioso tanta <lb></lb>parte degli scritti di Leonardo, da poter farne il più giusto giudizio, che con­<lb></lb>fermi o rettifichi quello corso già per la fama infino dai tempi del Vasari. <lb></lb></s>

<s>È per prima cosa, in tal proposito, da osservare che la varietà e la molti­<lb></lb>plicità degli argomenti scientifici è il carattere proprio di quasi tutti gli scrit­<lb></lb>tori di quella età, permettendo la ristretta economia della scienza di allora <lb></lb>a un uomo solo di potere attendere a coltivarla in ogni sua parte. </s>

<s>Nei libri <lb></lb><emph type="italics"></emph>De rerum varietate,<emph.end type="italics"></emph.end> per esempio, di Girolamo Cardano è una enciclopedia <pb xlink:href="020/01/1788.jpg" pagenum="31"></pb>ben più larga, e qua e là più profonda di quel che non sia nelle Note di <lb></lb>Leonardo, le proposte di macchinamenti e di capricciosi ingegni, che si leg­<lb></lb>gono nelle quali, non sono molto più maravigliose di quell&#039;altre, che si <lb></lb>leggono scritte nelle due Magie del Porta. </s>

<s>Egli è un fatto insomma che se <lb></lb>quegli scritti, i quali sono usciti oggidi fuori tanto accarezzati, e in così ni­<lb></lb>tide vesti, fossero stati impressi in volumoni in folio, a mezzo il secolo XVI, <lb></lb>avrebbe il loro Autore incontrata la medesima sorte de&#039;suoi contemporanei, <lb></lb>de&#039;quali nessuno apprezza le perle, mentre di Leonardo si fa gran conto <lb></lb>anco delle quisquiglie. </s></p><p type="main">

<s>Chi trova il gusto del vero in queste considerazioni facilmente si ac­<lb></lb>corge che la naturale grandezza della figura viene alquanto esagerata dalle <lb></lb>fumose esalazioni, che s&#039;interpongono fra lei e l&#039;occhio di chi la rimira <lb></lb>ond&#039;è nostro principal dovere il rimovere quelle caligini, perchè la vista ci <lb></lb>si renda sincera. </s>

<s>Dir Leonardo creatore della scienza sperimentale è una tale <lb></lb>iperbole, da non si perdonar così facilmente a uno Storico delle Matemati­<lb></lb>che, perchè la creazione sarebbe nell&#039;uomo un&#039;assurdità, piuttosto che un <lb></lb>vero e proprio prodigio, ed è ufficio della storia quello di dimostrare come <lb></lb>i creduti prodigi si riducono all&#039;ordine naturale svelando l&#039;occulta causa <lb></lb>che gli ha prodotti. </s></p><p type="main">

<s>Nelle tradizioni scientifiche dei secoli precedenti al XVI si scoprirebbero <lb></lb>le fonti naturali, da cui derivò la varietà enciclopedica delle dottrine pro­<lb></lb>fessate da un Artista di que&#039;tempi, ma per non divagar di troppo dal no­<lb></lb>stro argomento, ci contenteremo di dire che, nella Scuola peripatetica e nella <lb></lb>Alessandrina, riassunte da Giordano Nemorario, si trovan naturalmente com­<lb></lb>presi i fecondi principii, da cui concluse i suoi maravigliosi teoremi di Mec­<lb></lb>canica razionale Leonardo da Vinci. </s>

<s>La composizione infatti delle forze pa­<lb></lb>rallele e delle angolari, le velocità virtuali, i momenti de&#039;gravi lungo i piani <lb></lb>inclinati erano cose insegnate da quelle antiche scuole: tutte insomma, verso <lb></lb>la fine del XV secolo, venivano ai Matematici apparecchiate le vie, da con­<lb></lb>dur la scienza del moto a suoi più liberi e più spediti progressi. </s></p><p type="main">

<s>Chi però seguitasse a leggere il seguente nostro § III tornerebbe in­<lb></lb>dietro a farci questa osservazione: non eran pervenute le tradizioni scien­<lb></lb>tifiche, che voi dite, anche al Cardano, al Tartaglia, al Maurolico, al Com­<lb></lb>mandino e a tanti altri illustri Matematici di quel secolo? </s>

<s>Or come mai <lb></lb>Leonardo, nelle Meccaniche, sorvola in molte cose a tutti costoro, e in al­<lb></lb>cune altre, ciò che pare incredibile, allo stesso Galileo, e va a raggiungere <lb></lb>il Torricellì, il Viviani e il Borelli? </s>

<s>Anche ammessa dunque l&#039;efficacia delle <lb></lb>tradizioni par rimanga sempre e in ogni modo un prodigio che un semplice <lb></lb>Artista siasi così potuto avvantaggiare sopra tanti valorosi filosofici ingegni. </s></p><p type="main">

<s>L&#039;osservazione giustissima costringendoci a confessare che la cultura di <lb></lb>quei tempi non era alla scienza, a cui giunse Leonardo, magistero sufficiente, <lb></lb>fa rivolgere il nostro pensiero a cercare e a riconoscere altrove quel che ne <lb></lb>supplisca al difetto, nel magistero stesso dell&#039;esperienza. <emph type="italics"></emph>La isperientia,<emph.end type="italics"></emph.end> dice <lb></lb>il nostro popolano di Vinci, <emph type="italics"></emph>non falla mai, ma sol fallano,<emph.end type="italics"></emph.end> dice audace-<pb xlink:href="020/01/1789.jpg" pagenum="32"></pb>mente rivolgendosi ai Filosofi, <emph type="italics"></emph>i vostri giuditii<emph.end type="italics"></emph.end> (Libri, Histoire des Mathem., <lb></lb>T. III, Paris 1840, pag. </s>

<s>235). </s></p><p type="main">

<s>Non è l&#039;esperienza, che l&#039;Autore qui professa di seguitare, il metodo <lb></lb>artificioso dei moderni, ma è quell&#039;ardore di voler tutto mettere a cimento, <lb></lb>e di tutto certificarsi con le prove di fatto, che la Natura stessa infonde <lb></lb>nell&#039;animo dei fanciulli, e a cui poi le scuole insegnano a sostituire le ar­<lb></lb>guzie dell&#039;ingegno. </s>

<s>Ecco ciò che rende singolare nella storia letteraria del <lb></lb>secolo XVI Leonardo da Vinci; ecco a che principalmente riducesi la feli­<lb></lb>cità di quell&#039;ingegno: all&#039;esser cioè rimasto franco dalla tirannia delle sco­<lb></lb>lastiche discipline. </s>

<s>Mentre gli altri generalmente andavano tronfii di ripetere <lb></lb>quel che avevano letto ne&#039;libri dei Filosofi, per cui argutamente gli chiama <lb></lb><emph type="italics"></emph>recitatori<emph.end type="italics"></emph.end> e <emph type="italics"></emph>trombetti,<emph.end type="italics"></emph.end> egli interpetra la Natura medesima con l&#039;esperienza, <lb></lb>maestra a loro stessi che in Filosofia si facevano maestri. </s>

<s>E ci si mette, <lb></lb>come si diceva, con quell&#039;ardore instancabile che è innato ai fanciulli, dei <lb></lb>quali par che serbi, aggiunta alla vigoria delle membra e alla tenacità del <lb></lb>volere, la squisitezza dei sensi. </s>

<s>Le accidentali varietà per esempio della di­<lb></lb>scesa dei gravi, prodotte dalla resistenza dell&#039;aria secondo la figura del corpo <lb></lb>cadente e il modo com&#039;è rivolta e diretta al centro quella stessa figura, con <lb></lb>tante altre minuzie, che occorrono ad osservare in quello sperimento, sem­<lb></lb>brano cose a nessun altro possibili che alla pazienza infinita di Leonardo. </s></p><p type="main">

<s>Coloro però, che proclamano il grand&#039;uomo non discepolo d&#039;altri che <lb></lb>della sua propria esperienza, profferiscono sentenza non vera, avendosi per <lb></lb>certo ch&#039;egli aveva studiato con Aristotile, Archimede e Euclide, sotto la di­<lb></lb>sciplina del grande amico suo Luca Pacioli. </s>

<s>Non la sola Natura dunque, ma <lb></lb>l&#039;arte altresì concorse a educare nel popolano di Vinci l&#039;ingegno, e special­<lb></lb>mente l&#039;arte del calcolo algebrico, intorno al quale è notabile essere stato <lb></lb>egli de&#039;primi a far uso delle lettere minuscule dell&#039;alfebeto. </s>

<s>Quel che però <lb></lb>potrebbesi affermare per vero è che l&#039;uso di rappresentare in pittura gli <lb></lb>atti più naturali della persona condusse Leonardo a inventare quei segni, <lb></lb>che si praticano anche oggidì per distinguere le quantità positive e le ne­<lb></lb>gative. </s>

<s>Il <emph type="italics"></emph>no<emph.end type="italics"></emph.end> infatti esprimesi naturalmente con la rotazione orizzontale del <lb></lb>capo, nel quale atto si fa più cospicua la linea descritta dalla bocca chiusa. </s>

<s><lb></lb>La linea orizzontale perciò, a indicar le quantità negative, è il taglio della <lb></lb>bocca stessa, che silenziosamente nega. </s>

<s>Il <emph type="italics"></emph>si<emph.end type="italics"></emph.end> invece si suole esprimere ro­<lb></lb>tando il capo verticalmente, e in quell&#039;atto la linea più cospicua è quella <lb></lb>disegnata dal profilo del naso. </s>

<s>Dalla linea verticale perciò veniva suggerita <lb></lb>naturalmente la distinzione delle quantità positive. </s>

<s>Ma perchè potevasi fa­<lb></lb>cilmente confonder quel segno con altri segni comuni, come quello per esem­<lb></lb>pio dell&#039;unità e dell&#039;<emph type="italics"></emph>i,<emph.end type="italics"></emph.end> per evitar la confusione, aggiunse Leonardo al profilo <lb></lb>del naso i due occhi, ossia due punti, che ricongiunti insieme, nella fretta <lb></lb>dello scrivere, dal continuato tratto della penna, vennero a compor la nota <lb></lb>crocellina. </s></p><p type="main">

<s>Le tradizioni dunque scientifiche, apprese a scelti libri, congiunte con <lb></lb>la discrezione del senno popolare, e dalle naturali esperienze illustrate e <pb xlink:href="020/01/1790.jpg" pagenum="33"></pb>promosse formano quel più vero e più compiuto magistero, da cui fu per <lb></lb>le vie della scienza guidato l&#039;elettissimo ingegno di Leonardo da Vinci. </s>

<s>E <lb></lb>che tale sia veramente la qualità e la natura di quel magistero, come po­<lb></lb>trebbesi dimostrare in tutti gli altri scientifici argomenti, così è facile a ve­<lb></lb>rificarsi particolarmente nel nostro, dietro le cose da noi sopra discorse, dalle <lb></lb>quali insomma resulta che, nei principii statici divulgati dalle scuole a quei <lb></lb>tempi, era come in germe rinchiusa la nuova scienza di Galileo. </s>

<s>Meditando <lb></lb>Leonardo e illustrando coll&#039;esperienza cotesti fecondissimi principii, non fa <lb></lb>dunque maraviglia che s&#039;incontrasse in alcuni di quei teoremi, concernenti <lb></lb>le leggi dei momenti, delle velocità e dei tempi de&#039;corpi gravi, disposti a <lb></lb>scendere per i piani inclinati e per gli archi dei cerchi, che poi fecero pub­<lb></lb>blica e solenne mostra al mondo nelle proposizioni del III Dialogo delle due <lb></lb>Nuove scienze. </s></p><p type="main">

<s>Che poi in questo incontro dei due grandi ingegni Toscani non ci sia <lb></lb>nulla di miracoloso e di straordinario, si prova per altri esempi, ne&#039;quali <lb></lb>il medesimo fatto avvenne per manifesta via naturale, come nel Tartaglia <lb></lb>per esempio, da cui il teorema che i pesi di due corpi gravi su due piani <lb></lb>egualmente alti ma variamente inclinati sieno proporzionali alle lunghezze <lb></lb>degli stessi piani è immediatamente concluso, nella Questione X del suo trat­<lb></lb>tatello <emph type="italics"></emph>De ponderositate,<emph.end type="italics"></emph.end> dai principii statici del Nemorario. </s>

<s>Claudio Beri­<lb></lb>guardi nel VI de&#039;suoi Circoli pisani, Parte III, pone i teoremi fondamentali <lb></lb>della Meccanica galileiana, dicendo di essersi incontrato in quelle dimostra­<lb></lb>zioni, “ XX annis antequam illi (Galileo e il Torricelli) de re quidquam <lb></lb>vulgassent ” (Patavii 1660, pag. </s>

<s>307). E noi gli prestiamo pienissima fede, <lb></lb>avendo potuto ritrovare anch&#039;egli, il Beriguardo, venti anni prima della pub­<lb></lb>blicazione dei Dialoghi dei Due massimi sistemi, come Leonardo e il Tar­<lb></lb>taglia e altri, nella scienza anteriore al secolo XVI, i principii a quelle na­<lb></lb>turalissime conclusioni. </s></p><p type="main">

<s>Dell&#039;altro che fu magistero a Leonardo però, consistente nell&#039;esperienza, <lb></lb>e da cui si disse doversi principalmente riconoscere la superiorità, che egli <lb></lb>ottenne fra&#039;contemporanei e i discendenti; si possono nel presente soggetto <lb></lb>i molti esempii ridurre a uno solo. </s>

<s>Quella superiorità infatti, chi ben con­<lb></lb>sidera, ha la sua occulta causa motiva nel principio della composizion delle <lb></lb>forze, che il popolano da Vinci riconosce nel suo senno sperimentale esser <lb></lb>vera contro le cavillose dubitazioni degli scienziati. </s>

<s>Il Cardano per esempio, <lb></lb>nel cap. </s>

<s>X <emph type="italics"></emph>De motibus mirabilibus,<emph.end type="italics"></emph.end> che è parte del IX libro Dei paralipo­<lb></lb>meni, fa un chiarissimo commento del teorema di Aristotile concernente i <lb></lb>due moti, che risultano dalla diagonale del rettangolo, ma poi, nella propo­<lb></lb>sizione LIX dell&#039;<emph type="italics"></emph>Opus novum,<emph.end type="italics"></emph.end> passando a farne l&#039;applicazione ai proietti, <lb></lb>si rimane incerto se le forze, che distraggono il mobile in due diverse parti, <lb></lb>serbino la loro propria natura componendosi in un unico moto. </s>

<s>Il Tarta­<lb></lb>glia ripudiò risolutamente il teorema aristotelico, e benchè il Benedetti si <lb></lb>sforzasse di ritener la scienza sul retto sentiero, Galileo non l&#039;ammise che <lb></lb>nel caso delle direzioni ortogonali, e pure anche in questo particolare non <pb xlink:href="020/01/1791.jpg" pagenum="34"></pb>ne seppe far uso, come sventuratamente non ne sepper far uso il Torri­<lb></lb>celli, il Viviani e il Borelli, se non in qualche caso straordinario e, come <lb></lb>cavalli che adombrino, condotti a mano dalla Geometria per vie trasversali. </s></p><p type="main">

<s>Sarà questo notabilissimo punto di storia da noi trattato nelle sue par­<lb></lb>ticolarità a suo tempo, e vedremo allora le ragioni per cui diffidarono quei <lb></lb>grandi ingegni di por mano al filo, che gli avrebbe potuti sicuramente gui­<lb></lb>dare nei più intricati meccanici labirinti. </s>

<s>Ma perchè insomma quelle ragioni <lb></lb>si riducono a filosofici cavilli, il Popolano di Vinci, non curandoli, s&#039;attiene <lb></lb>all&#039;esperienza, la quale, in vario modo ripetuta, gli confermò la verità an­<lb></lb>tica, che cioè qualunque moto, che si rappresenti per la diagonale, si com­<lb></lb>pone di due altri proporzionali ai lati del rettangolo o del parallelogrammo. </s></p><p type="main">

<s>Ecco scoperta l&#039;occulta causa naturale di quel che, leggendo per le pre­<lb></lb>ziose Note manoscritte, faceva prima stupire come di un miracolo nuovo; <lb></lb>ed ecco in che modo dalle tradizioni, comuni a tutti, e dalla esperienza, pro­<lb></lb>pria e singolare a Leonardo, derivasse naturalmente quella maravigliosa <lb></lb>scienza del moto, della quale, scegliendo qua e là, poniamo innanzi ai no­<lb></lb>stri Lettori in ordine questo seguente Saggio. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Giova prima di tutto sapere qual concetto, da metafisico e tutt&#039;insieme <lb></lb>da immaginoso artista, si fosse della forza e degli effetti di lei formato Leo­<lb></lb>nardo: “ Forza dico essere una virtù spirituale, una potenza invisibile, la <lb></lb>quale, per accidentale esterna violenza, è causata dal moto e collocata e in­<lb></lb>fusa nei corpi, i quali sono dal loro naturale uso ritratti e piegati, dando a <lb></lb>questi vita attiva di maravigliosa potenza, che costringe tutte le create cose <lb></lb>a mutazione di forma e di sito. </s>

<s>Corre con furia alla sua desiderata morte, <lb></lb>e vassi diversificando mediante le cagioni. </s>

<s>Tardità la fa grande, e prestezza <lb></lb>la fa debole; nasce per violenza, e muore per libertà. </s>

<s>E quanto è maggiore <lb></lb>più presto muore e si consuma. </s>

<s>Scaccia con furia ciò che si oppone a sua <lb></lb>disfazione; desidera vincere, occidere la sua cagione, il suo contrasto e muore <lb></lb>vincendo. </s>

<s>Sè stessa occide, fassi più potente dove trova maggiore contrasto, <lb></lb>e caccia con furia ciò che si oppone alla sua morte. </s>

<s>Ogni cosa volentieri <lb></lb>fugge la sua morte. </s>

<s>Essendo costretta, ogni cosa costringe, nessuna cosa <lb></lb>senza lei si muove. </s>

<s>Il corpo, dov&#039;essa giunge, nasce. </s>

<s>Non cresce nè in peso <lb></lb>nè in forma: nessuno moto fatto da lei fia durabile. </s>

<s>Cresce nelle fatiche, e <lb></lb>manca per riposo. </s>

<s>Il corpo dov&#039;è costretta è fuori di libertà, e spesso ge­<lb></lb>nera, mediante il moto, nuova forza. </s>

<s>” </s></p><p type="main">

<s>“ La forza è causata dal moto e infusa nel peso, e similmente il corpo <lb></lb>è causato dal moto e infuso nel peso. </s>

<s>” </s></p><p type="main">

<s>“ La forza è causa del moto, e il moto è causa della forza, e il moto <lb></lb>infonde la forza e il colpo nel peso, mediante l&#039;obietto. </s>

<s>” </s></p><pb xlink:href="020/01/1792.jpg" pagenum="35"></pb><p type="main">

<s>“ La forza in alcuno effetto, quando si disfà, si trasferisce in questo <lb></lb>corpo, che fugge dinanzi, e genera mediante il movimento il colpo di mag­<lb></lb>giore efficacia, e dopo sè fa ruina, com&#039;appare nel moto della pallotta, ch&#039;è <lb></lb>cacciata dalla forza della bombarda. </s>

<s>” </s></p><p type="main">

<s>“ La forza non si estende se non in tre effetti, i quali ne contengono <lb></lb>infiniti, i quali effetti sono tirare, spingere e fermare. </s>

<s>E detta forza può na­<lb></lb>scere in due diversi modi: il primo si è per lo subito accrescimento d&#039;un <lb></lb>corpo raro a un denso, come la moltiplicazione del fuoco nella bombarda, <lb></lb>il quale, non si trovando in vacuo recipiente loco al suo accrescimento, corre <lb></lb>con furia a più ampio sito, scacciando ogni ostacolo che si oppone al suo <lb></lb>desiderio, e questo medesimo fa il corso dell&#039;acqua e del vento, che scac­<lb></lb>cia ogni ostacolo che si oppone. </s>

<s>Secondo, è quello che si crea ne&#039;corpi pie­<lb></lb>gati e storti fuori di loro natura, come il balestro e altre simili macchine. </s>

<s>” <lb></lb>(Ravaisson-Mollien, Les Munuscr. </s>

<s>de Leonard ecc., MSS. A., Paris 1871, <lb></lb>fol. </s>

<s>34 a tergo). </s></p><p type="main">

<s>In queste parole ci sembra che sien comprese tutte quelle varietà di <lb></lb>effetti e di modi, ne&#039;quali può esplicarsi la forza o per gl&#039;impulsi naturali <lb></lb>della gravità, o per quei preternaturali, come Galileo direbbe, della elasti­<lb></lb>cità dei solidi e de&#039;liquidi: effetti e modi che furono soggetti di specula­<lb></lb>zioni e di esperienze al nostro Leonardo. </s></p><p type="main">

<s>Il primo e più ovvio aspetto, secondo il quale s&#039;appresenti a conside­<lb></lb>rare la forza, è quello del peso dei corpi gravitanti verso il centro terrestre, <lb></lb>la quale gravitazione è nel concetto del Vinci un&#039;appetenza, un desiderio, <lb></lb>che hanno tutti i gravi di scendere a ritrovar la loro quiete. </s>

<s>“ Ogni peso <lb></lb>desidera di scendere al centro per la via più breve, e dov&#039;è maggiore pon­<lb></lb>derosità ivi è maggiore desiderio, e quella cosa che più pesa, essendo li­<lb></lb>bera, più presto cade ” (ivi, fol. </s>

<s>35). </s></p><p type="main">

<s>Si sente queste parole render per eco la proposizione I del Nemora­<lb></lb>rio, il quale dicemmo essere stato il primo a riguardare i pesi, non in <lb></lb>astratto secondo Archimede, ma nella loro realtà, e come attratti e diretti <lb></lb>al centro terrestre. </s>

<s>Leonardo mirabilmente illustra questo concetto. </s>

<s>Egli im­<lb></lb>magina che la Terra, per qualsivoglia cagione, venga a essere ridotta in <lb></lb>frantumi confusamente dispersi per lo spazio, e dice che ciascuno di questi <lb></lb>frantumi scenderebbe verso il centro e lo trapasserebbe di altrettanto spa­<lb></lb>zio, reciprocando le sue vibrazioni sempre e sempre minori, infintanto che <lb></lb>non avesse trovato presso a quel centro il conveniente suo collocamento, a <lb></lb>quel modo medesimo che noi vediamo per esperienza avvenire nel pendolo. <lb></lb>(Venturi, <emph type="italics"></emph>Essai<emph.end type="italics"></emph.end> cit., pag. </s>

<s>9). </s></p><p type="main">

<s>Piuttosto che trattenerci qui in estatica ammirazione intorno alla legge <lb></lb>dell&#039;inerzia dei movimenti, e intorno all&#039;oscillazione de&#039;Pianeti dall&#039;uno al­<lb></lb>l&#039;altro apside delle loro orbite come sognò di aver letto in queste espres­<lb></lb>sioni di Leonardo il Venturi, richiameremo l&#039;attenzione de&#039;nostri Lettori <lb></lb>sopra la questione famosa <emph type="italics"></emph>De lapsu lapidis circa centrum mundi,<emph.end type="italics"></emph.end> che do­<lb></lb>vette incominciare ad agitarsi fra gli scienziati infino dal terminar del se-<pb xlink:href="020/01/1793.jpg" pagenum="36"></pb>colo XV. </s>

<s>Il Nostro la risolve a quel modo, che pochi anni dopo la risolvettero <lb></lb>il Tartaglia e il Maurolico, de&#039;quali così scriveva il Benedetti per risposta a <lb></lb>un amico che, in mezzo alle peripatetiche controversie, lo aveva interrogato <lb></lb>intorno a quella stessa questione. </s>

<s>“ De illo, de quo me interrogas, dico Ni­<lb></lb>colaum Tartaleam nec non Franciscum Maurolicum recte sensisse, male vero <lb></lb>Alexandrum Piccolomineum, et exemplum Maurolici optimum esse quod ta­<lb></lb>men, si capere non potes, crede saltem authoritatibus talium virorum, qui <lb></lb>tantum in iis scientiis superant ipsum Alexandrum Piccolomineum, quan­<lb></lb>tum a Sole caetera superantur astra. </s>

<s>Lapis igitur ille transiret centrum re­<lb></lb>diretque cum diminutione tamen motus impressi, eo ferme modo ut scri­<lb></lb>bunt iudiciosissimi illi viri, donec post multas reditiones sursum deorsumque <lb></lb>quiesceret circa centrum mundi ” (Liber spec., Venetiis 1599, pag. </s>

<s>368). </s></p><p type="main">

<s>Si sarebbe senza dubbio dal Benedetti, se avesse potuto veder mano­<lb></lb>scritte quelle Note, che ora ci son sotto gli occhi, annoverato primo Leo­<lb></lb>nardo fra quegli <emph type="italics"></emph>iudiciosissimi viri,<emph.end type="italics"></emph.end> e Galileo affermando “ di poter credere <lb></lb>che, quando il globo terrestre fosse perforato per il centro, una palla d&#039;ar­<lb></lb>tiglieria scendendo per tal pozzo acquisterebbe sino al centro tal impeto di <lb></lb>velocità, che trapassato il centro la spingerebbe in su per altrettanto spa­<lb></lb>zio, quanto fosse stato quello della caduta, diminuendo sempre la velocità <lb></lb>oltre al centro con decrementi simili agli incrementi acquistati nello scen­<lb></lb>dere ” (Alb. </s>

<s>I, 250); mentre coglieva dal Benedetti stesso il frutto già ma­<lb></lb>turo avrebbe dovuto fra sè pensare ch&#039;egli era stato allegato sull&#039;albero di <lb></lb>una scienza più antica. </s></p><p type="main">

<s>In quella stessa scienza, ch&#039;è da noi così poco conosciuta, e perciò di­<lb></lb>sprezzata, il desiderio di confermare le tradizioni sacre de&#039;rivolgimenti, che <lb></lb>sarebbero per avvenire sulla superfice terrestre, introduceva un&#039;altra que­<lb></lb>stione intorno alla variabilità del punto, a cui s&#039;ammetteva oramai che d&#039;ogni <lb></lb>parte tendessero i gravi. </s>

<s>Leonardo, il quale non poteva rimanersi indiffe­<lb></lb>rente innanzi a un problema così strettamente connesso co&#039;principii mec­<lb></lb>canici ch&#039;ei professava, considerando che il centro di gravità di un corpo <lb></lb>dipende dalla sua figura ne concludeva perciò che la Terra, così per conti­<lb></lb>nue vicende trasformabile, doveva necessariamente variare il punto della sua <lb></lb>attrazione. </s>

<s>“ Ogni grave, egli dice, tende al basso, e le cose alte non re­<lb></lb>steranno in loro altezza, ma col tempo tutte discenderanno e così col tempo <lb></lb>il Mondo resterà sferico, e per conseguenza fia tutto coperto dall&#039;acqua ” <lb></lb>(Del moto dell&#039;acqua, Bologna 1828, pag. </s>

<s>282). In questo caso il centro della <lb></lb>gravità della Terra tornerà a un medesimo col centro della figura, ma in­<lb></lb>tanto che si dispone il Mondo a questo suo finale assettamento, quello stesso <lb></lb>centro cangerà sensibilmente di sito, “ e ciò principalmente, dice Leonardo, <lb></lb>per due mutazioni alla sua superfice: l&#039;una si varia ogni sei ore, e l&#039;altra <lb></lb>è fatta in molte migliaia di anni, e quella di sei ore nasce dal flusso e ri­<lb></lb>flusso del mare, l&#039;altra deriva dalla consumazione delle montagne, per li <lb></lb>moti dell&#039;acqua, nati dalle pioggie e dal continuo corso de&#039;fiumi. </s>

<s>Mutasi <lb></lb>adunque il sito al centro del Mondo e non il centro al sito, perchè tal cen-<pb xlink:href="020/01/1794.jpg" pagenum="37"></pb>tro è immobile, e il sito di continuo si muove di moto rettilineo, e non sarà <lb></lb>mai curvilineo ” (ivi, pag. </s>

<s>285). </s></p><p type="main">

<s>Se avesse il Venturi potuto consultar questo passo, sarebbesi facilmente <lb></lb>accorto che, nella Nota infrancesata al § I del suo <emph type="italics"></emph>Essai,<emph.end type="italics"></emph.end> Leonardo ammet­<lb></lb>tave, come tanti altri che lo avevano preceduto, la rotazione della Terra in <lb></lb>sè stessa, ma non intorno a un centro posto fuori di lei. </s>

<s>Sarebbe stato piut­<lb></lb>tosto utile osservare, a quel proposito della linea descritta dai gravi cadenti <lb></lb>in relazione con la vertigine terrestre, come, facendo Leonardo una felicis­<lb></lb>sima applicazione della Spirale archimedea, avesse poi dato agli stessi scien­<lb></lb>ziati moderni maggior sodisfazione di Galileo. </s>

<s>E perchè, dal comparare in­<lb></lb>sieme la scienza di questi due grandi uomini, risulta gran parte della Storia, <lb></lb>e de&#039;frutti che si possono raccogliere dalla Storia; è bene esaminar più da <lb></lb>presso come, ambedue partendo dai medesimi principii, s&#039;incontrassero perciò <lb></lb>necessariamente nelle medesime conclusioni. </s></p><p type="main">

<s>Quasi fosse vero quel ch&#039;esso Galileo si studiò d&#039;insinuare, e riuscì a <lb></lb>persuadere che cioè, ne&#039;dieci e più secoli precedenti a lui, la scienza del <lb></lb>moto non avesse fatto progressi, si lusingò d&#039;essere egli venuto il primo a <lb></lb>riappiccare le tradizioni a quel filo, lungamente rimasto nella Scuola ales­<lb></lb>sandrina interciso, o per dir meglio avviluppato in un nodo, precipua causa <lb></lb>fra quelle che arrestarono il suo svolgimento. </s>

<s>Consisteva quel nodo nella <lb></lb>proposizione IX dell&#039;VIII libro di Pappo, e Galileo si compiacque di averlo <lb></lb>egli finalmente sciolto, dimostrando che, per condurre un grave sopra un <lb></lb>piano perfettamente orizzontale, non ci era bisogno di nessuna potenza, e <lb></lb>che tutta la gran mole della sua Scienza nuova aveva potuto progredire <lb></lb>tant&#039;oltre, principalmente per aver tolto quell&#039;impedimento alla ruota. </s></p><p type="main">

<s>Che fosse questa davvero, come si diceva, una dolce lusinga fattasi dal <lb></lb>gran Maestro se n&#039;ebbero ad accorgere i discepoli stessi, quelli almeno che <lb></lb>non rimasero abbarbagliati agl&#039;improvvisi fulgori, fra&#039;quali altrove citammo <lb></lb>Michelangiolo Ricci, al giudizio del quale ci piace ora aggiungere l&#039;altro di <lb></lb>Antonio Nardi. </s>

<s>Nella veduta I della V scena intitolata <emph type="italics"></emph>Giudizi sopra alcuni <lb></lb>Filosofi,<emph.end type="italics"></emph.end> così esso Nardi scriveva al proposito nostro: “ Il Galileo è stato <lb></lb>de&#039;primi, che ha praticato il modo di accoppiare le fisiche e le matemati­<lb></lb>che discipline: fugli scorta il Benedetti ” (MSS. Gal., T. XX, pag. </s>

<s>633), di <lb></lb>che appunto l&#039;argomento in discorso può servire di presentissimo esempio. <lb></lb><figure id="id.020.01.1794.1.jpg" xlink:href="020/01/1794/1.jpg"></figure></s></p><p type="caption">

<s>Figura 9.</s></p><p type="main">

<s>Nel cap. </s>

<s>XIV infatti del Libro delle specu­<lb></lb>lazioni il Benedetti dimostra che una sfera, la <lb></lb>quale tocchi il piano orizzontale in un punto, può <lb></lb>esser qua e là per quello stesso piano condotta, <lb></lb>senz&#039;alcuna difficoltà o resistenza. </s>

<s>“ Rei exem­<lb></lb>plum, così dice l&#039;Autore, in carta describere pos­<lb></lb>sumus, mediante figura circulari 9 hic subscripta <lb></lb>ANEU, contigua lineae rectae BD in puncto A, <lb></lb>unde EOA perpendicularis erit ipsi BD, et tan­<lb></lb>tum ponderis habebimus a parte AUE, quantum <pb xlink:href="020/01/1795.jpg" pagenum="38"></pb>ab ipsa ANE. </s>

<s>Nunc igitur, si imaginabimur ductum esse centrum versus N, <lb></lb>per lineam ON parallelam ipsi AB, clarus nobis erit quod, absque ulla diffi­<lb></lb>cultate aut resistentia, idem ducemus, quia huiusmodi centrum ab inferiori <lb></lb>parte ad superiorem nunquam mutabit situm respectu distantiae seu inter­<lb></lb>valli, quae inter ipsum lineamque AB intercedit ” (editio cit., pag. </s>

<s>155). </s></p><p type="main">

<s>Ma le tradizioni di questa parte scienziale, raccolte nel suo libro e così <lb></lb>chiaramente esposte dal Benedetti, erano anche più antiche, come appari­<lb></lb>sce dalla proposizione XL dell&#039;<emph type="italics"></emph>Opus Novum<emph.end type="italics"></emph.end> del Cardano così formulata: <lb></lb>“ Omne corpus sphaericum tangens planum in puncto movetur ad latus <lb></lb>per quamcumque vim, quae medium dividere potest ” (Operum, T. IV cit., <lb></lb>pag. </s>

<s>480). Ed è la ragione di ciò secondo l&#039;Autore, come secondo il Bene­<lb></lb>detti, che il centro di gravità della sfera in moversi non sale nè scende, <lb></lb>ond&#039;è ch&#039;essa sfera non ha da superare altra resistenza da quella infuori <lb></lb>contrappostale dal mezzo dell&#039;aria. </s>

<s>Quanto all&#039;attrito poi, che potrebbe na­<lb></lb>scer dal contatto col piano, è anco questo impedimento cessato dal suppo­<lb></lb>sto che lo stesso contatto si faccia matematicamente in un punto, ond&#039;è <lb></lb>che, per aversi maggior possibile corrispondenza fra la Geometria e la Fi­<lb></lb>sica, richiedesi dal Cardano “ planum esse ex durissima materia, quae nullo <lb></lb>modo cedat ” (ibid.). Ma perchè difficile era troppo trovar materia sì dura, <lb></lb>e più difficile che mai girare attorno un corpo in perfettissima sfera, sov­<lb></lb>venne al Cardano stesso il felicissimo pensiero di dimostrar fisicamente il <lb></lb>teorema meccanico per via di quella esperienza de&#039;corpi penduli, descritta <lb></lb>già nel libro <emph type="italics"></emph>De subtilitate.<emph.end type="italics"></emph.end> Coll&#039;allungare il filo diviene il pendolo, benchè <lb></lb>gravissimo, sempre più mobile, e giunge a un punto da venir mosso per <lb></lb>qualunque leggerissimo soffio, intantochè <emph type="italics"></emph>praecantatione moveri videtur<emph.end type="italics"></emph.end><lb></lb>(Lugduni 1580, pag. </s>

<s>97). La ragione di ciò la riconosce l&#039;Autore nell&#039;esser <lb></lb>l&#039;arco simile del maggior cerchio più in rettitudine orizzontale di quel che <lb></lb>non sia il minore, e di qui la gran facilità a venir mosso il pendolo grave <lb></lb>con tanto poca forza, da parer che quasi ubbidisca per incanto al soffio <lb></lb>della parola. </s></p><p type="main">

<s>Son questi principii fondamentali espressi dai sopra citati Autori con <lb></lb>tanta precisione, e con tanta evidenza, da persuader facilmente ognuno che <lb></lb>dovesser essere già prestabiliti nella scienza del moto, come legittimo frutto <lb></lb>dei teoremi archimedei e delle proposizioni del Nemorario. </s>

<s>Un corpo infatti, <lb></lb>secondo quelle dottrine, permane in equilibrio, infintanto che il centro della <lb></lb>gravità non perda il suo sostegno, rimovendosi dal sito della uguaglianza, <lb></lb>che dallo stesso Nemorario ponesi <emph type="italics"></emph>esse aequidistantiam superficiei orizon­<lb></lb>tis.<emph.end type="italics"></emph.end> In piena conformità delle quali dottrine il nostro Leonardo, nel trattato <lb></lb>Della pittura pubblicato dal Manzi, così scriveva: “ Il moto è creato dalla <lb></lb>distruzione del bilico, cioè dalla inegualità, imperocchè nessuna cosa per sè <lb></lb>si muove che non esca del suo bilico, e quella si fa più veloce, che più si <lb></lb>muove dal detto bilico ” (Roma 1817, pag. </s>

<s>169). </s></p><p type="main">

<s>Scendeva direttamente da questi principii quella conclusione, che Gali­<lb></lb>leo pose contro Pappo, ma che il Cardano e il Benedetti avevano, come ve-<pb xlink:href="020/01/1796.jpg" pagenum="39"></pb>demmo, posta assai prima di lui, e prima di tutti loro Leonardo, il quale, <lb></lb>con quasi le medesime parole che si leggono nell&#039;<emph type="italics"></emph>Opus novum<emph.end type="italics"></emph.end> e nel <emph type="italics"></emph>Li­<lb></lb>ber speculationum,<emph.end type="italics"></emph.end> aveva lasciato scritto così nelle sue Note: “ Qualunque <lb></lb>cosa si trova in piano suolo e perfetto, che il suo polo non si trova in fra <lb></lb>parti uguali di pesi, mai si fermerà: lo esempio si vede in quelli che sdruc­<lb></lb>ciolano per lo diaccio, che mai si fermano se le parti non tornano equidi­<lb></lb>stanti al loro centro. </s>

<s>Al contrario, il corpo sferico perfetto posto sul piano <lb></lb>perfetto non avrà alcun movimento, se già non glielo darai, e la ragione si <lb></lb>è che tutte le sue parti sono di pari distanza al centro, onde sempre rimane <lb></lb>in bilancia, e la bilancia, che ha le sue braccia uguali di peso e di lun­<lb></lb>ghezza, sta senza moto. </s>

<s>Essendo, in detto corpo sferico, eguale l&#039;uno suo <lb></lb>mezzo all&#039;altro, ancora lui fia senza moto ” (MSS. A. cit., fol. </s>

<s>21, 22). </s></p><p type="main">

<s>Dietro questo principio, così nello schietto linguaggio del Popolano da <lb></lb>Vinci formulato, il gran Maestro della scienza del moto passò a concludere <lb></lb>la legge dei momenti dei gravi lungo i piani inclinati, con più felice aggres­<lb></lb>sione di Pappo, e a dimostrar le proprietà generali dei movimenti dei corpi, <lb></lb>d&#039;onde immediatamente scendeva la verità dei nuovi teoremi. </s>

<s>Leonardo <lb></lb>muove dai medesimi principii e giunge alle medesime conclusioni. </s>

<s>E perchè <lb></lb>insomma i pensieri di lui procedono dalle proposizioni del Nemorario, non <lb></lb>è maraviglia se si svolgono in simile ordine a quello del Tartaglia, il quale <lb></lb>anch&#039;egli, con più felici auspici di Pappo, s&#039;apparecchiava a dimostrar la <lb></lb>varietà de&#039;momenti ne&#039;pesi per varie obliquità di linee scendenti, sul fon­<lb></lb>damento della seguente Questione, ch&#039;è la nona del suo opuscolo <emph type="italics"></emph>De pon-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.1796.1.jpg" xlink:href="020/01/1796/1.jpg"></figure></s></p><p type="caption">

<s>Figura 10.<lb></lb><emph type="italics"></emph>derositate:<emph.end type="italics"></emph.end> “ Aequalitas declinationis identitas ponde­<lb></lb>ris. </s>

<s>” (Editio cit., fol. </s>

<s>6 ad t.). </s></p><p type="main">

<s>Similmente Leonardo, disegnando questa che con <lb></lb>molta proprietà chiama <emph type="italics"></emph>Bilancia<emph.end type="italics"></emph.end> (fig. </s>

<s>10), così con tali <lb></lb>parole sottoscrittevi la dichiara: “ Se li pesi e le braccia <lb></lb>e li moti (ossia le velocità virtuali) sono uguali in obli­<lb></lb>quità, essi pesi non moveranno l&#039;uno l&#039;altro. </s>

<s>— Li pesi <lb></lb>eguali mantengono la gravità eguale nella obliquità egua­<lb></lb>le ” (Les Manuscr. </s>

<s>E., Paris 1888, fol. </s>

<s>58 ad t.). </s></p><p type="main">

<s>Or se la obliquità è disuguale, con qual proporzione varierà il peso? </s>

<s><lb></lb>Ecco il problema più importante e più difficile del primo, che nuovamente <lb></lb>voleva essere risoluto. </s>

<s>Il Tartaglia lo sciolse con la Geometria, e con la Geo­<lb></lb>metria pure, benchè in vario modo, lo sciolse come presto vedremo anche <lb></lb>Leonardo, ma volle per assicurarsi meglio del vero far precedere alla ma­<lb></lb>tematica l&#039;esperienza, nella quale riuscì più felicemente dello Stevino, del <lb></lb>Beriguardo e di altri, che si vollero quasi un secolo dopo metter per la me­<lb></lb>desima via. </s>

<s>I primi tentativi dee averli fatti con la Bilancia sopra descritta, <lb></lb>variando obliquità e lunghezza ad uno de&#039;bracci di lei, ma perchè difficile <lb></lb>troppo riusciva l&#039;aggiustare i pesi, e senza errore computarne i momenti, <lb></lb>gli sovvenne il felice pensiero di ricorrere alla Bilancia idrostatica, nella <lb></lb>quale il peso dell&#039;acqua è giustissimamente compartito nell&#039;uno e nell&#039;al-<pb xlink:href="020/01/1797.jpg" pagenum="40"></pb>tro braccio dalla stessa Natura. </s>

<s>“ L&#039;acqua ABS (fig. </s>

<s>11) non avrà movi­<lb></lb>mento, perchè intanto pesa l&#039;acqua AB, quanto l&#039;acqua AS, e la linea BS <lb></lb><figure id="id.020.01.1797.1.jpg" xlink:href="020/01/1797/1.jpg"></figure></s></p><p type="caption">

<s>Figura 11.<lb></lb>è piana, e l&#039;acqua piana par sè non si <lb></lb>muove ” (Del moto dell&#039;acqua cit., pag. </s>

<s>436). <lb></lb>Ora il peso <emph type="italics"></emph>p<emph.end type="italics"></emph.end> dell&#039;acqua AS, chiamata *s la <lb></lb>sezione nel punto A comune ai due tubi, <lb></lb>è *s. </s>

<s>AS; e il peso P dell&#039;acqua AB è *s. </s>

<s>AB. </s>

<s><lb></lb>Essendo perciò i due pesi eguali, s&#039;avrà <lb></lb>la proporzione P:<emph type="italics"></emph>p<emph.end type="italics"></emph.end>=AB:AS com&#039;espres­<lb></lb>siva, nel moderno nostro linguaggio, del <lb></lb>resultato medesimo, a cui per così facile e sicura via fu condotto Leonardo. </s></p><p type="main">

<s>Ebbe esso Leonardo altresì dalla medesima Bilancia idrostatica la dimo­<lb></lb>strazione sperimentale di un altro teorema, che gli servì per rispondere al <lb></lb>seguente propostosi quesito: Se l&#039;acqua, che cala uno dito per miglio, cam­<lb></lb>mina uno miglio per ora, quanto camminerà ella calando due dita? </s>

<s>” (Les <lb></lb>Manuscr. </s>

<s>A. cit., fol. </s>

<s>27 ad t.). Galileo, non avendo trovato modo a dimo­<lb></lb>strarlo, ciò che poi fece il Torricelli, suppose quel teorema, da cui si diceva <lb></lb>dipendere la risposta al quesito di Leonardo, come vero, per cui procedeva <lb></lb>nel suo trattato Della scienza meccanica così asseverantemente, ma senza <lb></lb>alcuna dimostrazione, nel suo discorso: “ Se avremo i piani elevati AC, <lb></lb><figure id="id.020.01.1797.2.jpg" xlink:href="020/01/1797/2.jpg"></figure></s></p><p type="caption">

<s>Figura 12.<lb></lb>AD, AE (fig. </s>

<s>12) sopra di essi non sarà spinto un <lb></lb>dato corpo grave, se non con violenza, la quale mag­<lb></lb>giore si richiederà per moverlo sopra la linea AD, <lb></lb>che sopra la AC, e maggiore ancora sopra la AE <lb></lb>che sopra l&#039;AD, il che procede per avere egli mag­<lb></lb>gior impeto di andare al basso per la linea AE che <lb></lb>per l&#039;AD, e per la AD che per l&#039;AC; sicchè po­<lb></lb>tremo concludere i corpi gravi aver maggior resi­<lb></lb>stenza ad esser mossi sopra piani elevati diversa­<lb></lb>mente, secondo che l&#039;uno sarà più o meno elevato <lb></lb>dell&#039;altro ” (Alb. </s>

<s>XI, 114). </s></p><p type="main">

<s>Per Leonardo si trasforma il piano AE in un tubo comunicante col <lb></lb>tubo AB, e perchè piegandosi esso tubo AE in AD, in AC, ecc., le pres­<lb></lb>sioni misurate dall&#039;altezza del livello del liquido nel tubo verticale diminui­<lb></lb>scono via via come le perpendicolari EF, DC, CH, n&#039;ebbe perciò a con­<lb></lb>cludere sperimentalmente, dall&#039;idrostatica facendo legittimo passagggio alla <lb></lb>statica, che gl&#039;impeti di scendere o le velocità di un medesimo grave sopra <lb></lb>un piano variamente inclinato stanno come le altezze perpendicolari, o come <lb></lb>i seni delle elevazioni. </s>

<s>Applicando poi il teorema al sopra propostosi que­<lb></lb>sito ne concludeva la seguente verissima risposta: “ Quell&#039;acqua, la quale <lb></lb>calerà un&#039;oncia per miglio, avrà di movimento un quarto di braccio per un <lb></lb>tempo (cioè per un tempo di musica): quella, che avrà due once per miglio, <lb></lb>avrà di movimento mezzo braccio per tempo, e così quella che cala quat­<lb></lb>tr&#039;once si moverà un braccio per tempo ” (Moto dell&#039;acqua cit., pag. </s>

<s>432). </s></p><pb xlink:href="020/01/1798.jpg" pagenum="41"></pb><p type="main">

<s>Tanto vide Leonardo farsi in questi giochi idrostatici la Natura da sè <lb></lb>medesima rivelatrice delle leggi del moto, che ritornando alla Bilancia, rap­<lb></lb>presentata nella nostra figura XI, vi ritrovò la più chiara conferma delle <lb></lb>supposte verità del Nemorario. </s>

<s>“ L&#039;acqua ricevuta nell&#039;angolo supino occu­<lb></lb>perà tanto più dell&#039;una faccia che dell&#039;altra, quanto l&#039;una faccia fia più <lb></lb>obliqua dell&#039;altra ” (Manuscr. </s>

<s>A. cit, fol. </s>

<s>22). E ciò parve al Nostro la più <lb></lb>bella dimostrazione sperimentale di ciò, che in quarto luogo supponevasi dallo <lb></lb>stesso Nemorario: “ Secundum situm gravius esse, quanto in eodem situ <lb></lb>minus obliquus est descensus ” (De pond. </s>

<s>cit., praefatio). </s></p><p type="main">

<s>Se si fanno in A, seguitava a ragionare Leonardo degli effetti della Bi­<lb></lb>lancia, i due pesi equilibrio, dunque l&#039;impeto di discendere che ha l&#039;acqua <lb></lb>AS è in quel punto eguale all&#039;impeto discensivo dell&#039;acqua AB, come di <lb></lb>qualunque altr&#039;acqua avesse anche maggiore e maggiore obliquità, purchè <lb></lb>attingesse superiormente al livello della orizzontale SB prolungata, nel qual <lb></lb>fatto riconosceva lo stesso Leonardo una dimostrazione sperimentale più fa­<lb></lb>cile e più conclusiva di quella, che immaginò Galileo, perchè gli fosse con <lb></lb>minore difficoltà concesso per teoricamente vero quel suo principio mecca­<lb></lb>nico fondamentale, che cioè “ i gradi di velocità di un mobile, discendente <lb></lb>con moto naturale dalla medesima sublimità per piani in qualsivoglia modo <lb></lb>inclinati, all&#039;arrivo all&#039;orizzonte son sempre eguali, rimossi gl&#039;impedimenti ” <lb></lb>(Alb. </s>

<s>XIII, 177). </s></p><p type="main">

<s>Apparve questa verità alla mente di Leonardo in tanta evidenza, da <lb></lb>fargli pronunziar sotto forma del più certo teorema quello, che sarebbe po­<lb></lb>tuto sembrare un paradosso, che cioè, scendendo un corpo in varii modi, <lb></lb>deviato per obliquità di linee e di rimbalzi, giunge al suo termine orizzon­<lb></lb>tale, come se fosse senz&#039;altro impedimento sempre andato a diritto a ritro­<lb></lb>var quello, che è il sito dell&#039;egualità, secondo l&#039;espressione del Nemorario. <lb></lb></s>

<s>“ Ogni movimento fatto dalla forza conviene che faccia tal corso, quanto è <lb></lb>la proporzione della cosa mossa con quella che muove, e se ella troverà <lb></lb>resistente opposizione finirà la lunghezza del suo debito viaggio per circolar <lb></lb>moto o per altri varii risaltamenti e balzi, i quali computato il tempo e il <lb></lb><figure id="id.020.01.1798.1.jpg" xlink:href="020/01/1798/1.jpg"></figure></s></p><p type="caption">

<s>Figura 13.<lb></lb>viaggio fia come se il corso fosse stato senz&#039;alcuna <lb></lb>contradizione ” (ivi, fol. </s>

<s>60 ad t.). </s></p><p type="main">

<s>Dall&#039;applicazione di questi veri principii riu­<lb></lb>sciva dimostrato uno dei teoremi più fondamentali <lb></lb>della Meccanica, relativo alla proporzione dei tempi <lb></lb>che passa a scendere un grave o per l&#039;obliqua o <lb></lb>per la perpendicolare. </s>

<s>Sia AB (fig. </s>

<s>13) questa per­<lb></lb>pendicolare, lungo la quale abbia a cadere il grave L, <lb></lb>e AC l&#039;obliqua, per la quale abbia pure a scendere <lb></lb>il grave M, che si suppone essere il medesimo o di <lb></lb>pari peso con L. </s>

<s>Non solo, per i posti principii, i <lb></lb>due corpi hanno eguale velocità ne&#039;punti L, M, ma ne&#039;punti O, P; Q, R, e <lb></lb>in tutti gli altri infiniti che si potrebbero determinare con condur linee <pb xlink:href="020/01/1799.jpg" pagenum="42"></pb>infinite parallele alla orizzontale, cosicchè può dirsi essere AB, AC due rette <lb></lb>che si compongono d&#039;infiniti momenti velocitativi fra sè tutti eguali. </s>

<s>Ma <lb></lb>per la definizione di Aristotile nelle Questioni meccaniche, e per i teoremi <lb></lb>di Archimede <emph type="italics"></emph>De spiralibus,<emph.end type="italics"></emph.end> dove le velocità sono eguali i tempi convien <lb></lb>che sieno proporzionati agli spazii, dunque il tempo della discesa del grave <lb></lb>L, al tempo della discesa del grave M starà come la AB alla AC; teorema <lb></lb>che Leonardo stesso formulava con queste parole: “ Tanto caderà più pre­<lb></lb>sto il peso L che il peso M, quanto la linea AB entra nella linea AC ” (ivi <lb></lb>fol. </s>

<s>33). </s></p><p type="main">

<s>Benchè fosse questo, insieme con gli altri teoremi sopra narrati, una <lb></lb>nuova rivelazione che Leonardo veniva a fare alla scienza, non era ancora <lb></lb>esaurita la fecondità di quella Bilancia, che per la facilità de&#039;liquidi ad ub­<lb></lb>bidir docilmente a tutti i minimi impulsi, e per quella loro destrezza, di­<lb></lb>ciam così, a sottrarsi agl&#039;impedimenti, si rendeva leggibilissimo esemplare <lb></lb>del moto degli altri gravi. </s>

<s>L&#039;esattissimo livellamento, che in ogni caso si <lb></lb>osserva nei due tubi comunicanti, era un fatto particolare, il quale general­<lb></lb>mente applicato a tutti i corpi si poteva tradurre in quell&#039;altro fondamentale <lb></lb>principio meccanico, che cioè, secondo l&#039;espressioni stesse di Galileo, “ l&#039;im­<lb></lb>peto acquistato da un grave in qualsivoglia luogo del suo moto sia tanto <lb></lb>che basterebbe a ricondurlo a quell&#039;altezza, d&#039;onde si parti ” (Alb. </s>

<s>I, 27, 28). <lb></lb>E Leonardo, in eguale e più piena sentenza: “ Il corpo che scende per AB <lb></lb>(nella posta addietro figura XI) risalirà in S alla medesima linea orizzontale, <lb></lb>come nel tubo pieno di acqua ” (Manuscr. </s>

<s>A. cit, fol 22). </s></p><p type="main">

<s>Si fece opposizione a Galileo, mettendo in conto le perdite di velocità <lb></lb>subite dal grave per via dell&#039;urto violento e degli attriti; ingiusta e inutile <lb></lb>opposizione, perchè quello stesso teorema galileiano si dava solamente per <lb></lb>vero nel caso che venissero rimossi tutti gl&#039;impedimenti, di che la Bilan­<lb></lb>cia idrostatica, per la fluidità dell&#039;acqua, ne porgeva il più bello e più di­<lb></lb>mostrativo esempio. </s>

<s>Leonardo in ogni modo par che neghi a qualunque <lb></lb>causa accidentale il potere in nulla minorare quella virtù, che vale a riso­<lb></lb>spingere tanto in su il grave, quant&#039;era in giù prima disceso. </s>

<s>“ Oh mira­<lb></lb>bile giustizia di te Primo Motore! Tu non hai voluto mancare a nessuna <lb></lb>potenzia: loro ordini egualità de&#039;suoi necessarii effetti, conciossiachè se una <lb></lb>potenzia debba cacciare cento braccia una cosa vinta da lei, e questa nel <lb></lb>suo ubbidire trovi intoppo, hai ordinato che la potenza del colpo ricausi <lb></lb>nuovo movimento, il quale per diversi balzi ricuperi la intera somma del <lb></lb>suo debito viaggio. </s>

<s>E se tu misurerai la linea fatta dai detti balzi, tu tro­<lb></lb>verai essere di tale lunghezza, qual sarebbe a trarre colla medesima forza <lb></lb>una simile cosa libera per l&#039;aria. </s>

<s>Questa esperienza farai con una piccola <lb></lb>ballotta di vetro battuta sopra un suolo di pietra viva e piana, e abbi una <lb></lb>lancia lunga segnata di diversi colori, e quando hai spettatori fa&#039;tenere l&#039;asta <lb></lb>a uno, e pon mente da alquanto lontano ne&#039;balzi a che colori ella s&#039;alza di <lb></lb>mano in mano a ogni balzo nell&#039;altezza dell&#039;asta, e notali. </s>

<s>E se saranno i <lb></lb>notatori quanti i balzi, più facilmente ognuno terrà a mente il suo. </s>

<s>Ma <pb xlink:href="020/01/1800.jpg" pagenum="43"></pb>fa&#039;che l&#039;asta sia piuttosto ferma da capo o in un buso da piè, perchè chi <lb></lb>la tenesse in mano occuperebbe la veduta ai giudicatori, e fa&#039;che il primo <lb></lb>balzo si facci in mezzo a due angoli retti, acciò la palla caggi sempre in un <lb></lb>medesimo loco, perchè meglio fieno notate l&#039;altezze de&#039;balzi nell&#039;asta. </s>

<s>Poi <lb></lb>fa&#039;trarre da quella medesima potenzia questa ballotta per libero tratto, e <lb></lb>nota il luogo dove percote, e misura, e troverai il secondo viaggio essere <lb></lb>compagno al primo ” (ivi, fol. </s>

<s>24). </s></p><p type="main">

<s>Ne&#039;pendoli, secondo Leonardo, ne&#039;quali l&#039;impeto dell&#039;ascesa non è re­<lb></lb><figure id="id.020.01.1800.1.jpg" xlink:href="020/01/1800/1.jpg"></figure></s></p><p type="caption">

<s>Figura 14.<lb></lb>stituito dall&#039;elasticità dell&#039;urto, ma <lb></lb>dagl&#039;impeti precedenti via via ac­<lb></lb>cumulati nella discesa, deve il fatto <lb></lb>sopra notato verificarsi anche con <lb></lb>maggiore esattezza, intanto che, se <lb></lb>il pendolo casca da A (fig. </s>

<s>14) giun­<lb></lb>gerà in E con tale acquisto di forza, <lb></lb>da poter risalire per essa infino in D <lb></lb>a ritrovare l&#039;orizzontale AD, dalla <lb></lb>quale s&#039;era partito. </s>

<s>Nel medesimo <lb></lb>modo sarà vero che risalirà lo stesso pendolo in B o in F, dop&#039;esser caduto <lb></lb>dai punti G, C nelle orizzontali GB, CF. </s></p><p type="main">

<s>Nella totale escursione per l&#039;emiciclo il grave pendulo ha dunque in G <lb></lb>e in B velocità uguali, ciò che si concludeva da Leonardo, considerando che <lb></lb>sono uguali le condizioni del moto tanto nell&#039;ascesa, quanto nella discesa, <lb></lb>non essendo, secondo il Nemorario la quiete altro che il termine dello stesso <lb></lb>moto, cosicchè, incomincino le reciprocazioni o da A o da D, le mosse di <lb></lb>discendere in ogni modo sono state precedute dagli atti del salire. </s>

<s>“ Il moto <lb></lb>naturale fu prima accidentale, cioè la pietra che cade fu prima portata e <lb></lb>gettata in alto ” (ivi, fol. </s>

<s>31 ad t.); alle quali parole di Leonardo così fanno <lb></lb>quest&#039;altre di Galileo da commento: “ Quando voi reggete in mano una <lb></lb>pietra non altro fate che imprimerli tanta virtù impellente all&#039;insù, quanta <lb></lb>è la facoltà della sua gravità traente in giù ” (Alb. </s>

<s>XIII, 160). </s></p><p type="main">

<s>Essendo dunque in N e in B nell&#039;arco descritto dal pendolo le due ve­<lb></lb>locità eguali, considerò Leonardo che eguali pure sarebbero state quelle ve­<lb></lb>locità, quando il peso A fosse caduto per la perpendicolare AG, o per l&#039;obli­<lb></lb>qua AB, d&#039;onde n&#039;ebbe a formulare la seguente Nota a modo di teorema: <lb></lb>“ Il peso A, dopo esser disceso per C, E risalirà in B con quella velocità <lb></lb>che avrebbe una palla uguale, che fosse scesa da A in B per la linea di­<lb></lb>ritta AB ” (Manuscr. </s>

<s>A. cit., fol. </s>

<s>26). </s></p><p type="main">

<s>Appartiene al medesimo ordine di speculazioni anche quest&#039;altra con­<lb></lb>clusione così espressa in una delle solite Note vinciane, che il Venturi tra­<lb></lb>scrisse dall&#039;appendice al manoscritto B: “ Il corpo grave A scende più veloce <lb></lb>per l&#039;arco ACE che per la corda AE, perchè in AC comincia la sua discesa, <lb></lb>come per la perpendicolare ” (<emph type="italics"></emph>Essai<emph.end type="italics"></emph.end> cit., pag. </s>

<s>18). Devesi senza dubbio Leo­<lb></lb>nardo essersi certificato di questa notizia, sperimentando intorno alla discesa <pb xlink:href="020/01/1801.jpg" pagenum="44"></pb>di qualche pallottola dentro alla cassa di un vaglio, come pure si legge che <lb></lb>facevano Guidubaldo del Monte e Galileo, ma le espressioni <emph type="italics"></emph>in AC comin­<lb></lb>cia la sua discesa come per la perpendicolare<emph.end type="italics"></emph.end> contengono un germe di <lb></lb>dimostrazione, ch&#039;è poi quella, della quale s&#039;ebbe per qualche tempo a con­<lb></lb>tentare lo stesso Galileo. </s>

<s>Divisi infatti da Leonardo l&#039;arco e la corda in due <lb></lb>parti eguali ne&#039;punti C e H di mezzo, considerò che la scesa per AC, ben­<lb></lb>chè più lunga, è nonostante più precipitosa che per AH, e ne concluse per­<lb></lb>ciò, come nella Lettera galileiana allo Staccoli, che la velocità già concepita <lb></lb>pel vantaggio di AC è più potente per conservare l&#039;acquisto fatto che non <lb></lb>è la declività della rimanente parte HE della corda a ristorare il danno della <lb></lb>perdita già fatta (Alb. </s>

<s>VI, 369, 70). </s></p><p type="main">

<s>I saggi, che abbiamo dati fin qui, sembrano a noi sufficienti per di­<lb></lb>mostrare la fecondità di quei principii statici, che si professavano ai tempi, <lb></lb>ne&#039;quali Leonardo attendeva a&#039;suoi studii, e confermano tutto insieme quel <lb></lb>che si diceva che cioè potevasi derivare da quelli stessi principii la miglior <lb></lb>parte della Meccanica galileiana. </s>

<s>Le proposizioni del Nemorario però avevano <lb></lb>un intendimento assai più modesto, ed era quello di stabilire una legge sta­<lb></lb>tica generale, da poter applicarsi alle macchine, per saper secondo qual&#039;or­<lb></lb>dine si corrisponda in esse la resistenza del mobile con la potenza del mo­<lb></lb>tore. </s>

<s>Leonardo architetto non poteva negligere quello studio, per fondamento <lb></lb>al quale pose le velocità virtuali di Aristotile e del Nemorario, mentre dal­<lb></lb>l&#039;altra parte cereava di trarre quel maggior profitto possibile dai teoremi <lb></lb>archimedei Degli equiponderanti. </s>

<s>Fu il Libri il primo a notar che venivano <lb></lb>per i manoscritti vinciani que&#039;teoremi promossi, infino a ricercar co&#039;me­<lb></lb>todi de&#039;moderni il centro della gravità della piramide (Histoire des mathem., <lb></lb>T. III, Paris 1840, pag. </s>

<s>44), ma perchè non sono in tale argomento le dif­<lb></lb>ficoltà della Fisica punto minori di quelle della Geometria, scegliamo, come <lb></lb>più proprii di questi Saggi, alcuni fatti, che sembravano al volgo e agli <lb></lb>stessi dotti miracolosi, ma che Leonardo naturalmente spiegava, applican­<lb></lb>dovi il principio che un corpo, o più corpi congiunti insieme nella più strana <lb></lb>posizione e figura, permangono in stabile equilibrio, quando il centro di gra­<lb></lb>vità del tutto vada a cader giusto sul punto che gli fa da sostegno. </s>

<s>“ Quel <lb></lb>peso unito, che fia sostenuto in mezzo, e il rimanente stia sospeso, di qua­<lb></lb><figure id="id.020.01.1801.1.jpg" xlink:href="020/01/1801/1.jpg"></figure></s></p><p type="caption">

<s>Figura 15.<lb></lb>lunque strana forma si vuole, che sem­<lb></lb>pre si stabilirà sopra il suo sostentacolo <lb></lb>in equilibrio, e qualche volta le estremità <lb></lb>non fieno uguali al centro del peso. </s>

<s>Ver­<lb></lb>bigratia: sia AB (fig. </s>

<s>15) uno pezzo di <lb></lb>riga, il quale posi solamente la estremità <lb></lb>A, e il resto stia sospeso. </s>

<s>Questo fia im­<lb></lb>possibile a fare, se prima tu non unisci <lb></lb>e congiungi con esso il peso CB, il quale <lb></lb>faccia tal contrapposto, che resti in mezzo <lb></lb>fra C, B, e verrà questo peso a fermarsi in sul polo A, e lo strumento di <pb xlink:href="020/01/1802.jpg" pagenum="45"></pb>sotto (fig. </s>

<s>16) è sottoposto a simile ragione ” (Manuscr. </s>

<s>A. cit., fol. </s>

<s>33 ad t.). <lb></lb>Questi semplici e naturali esempi dell&#039;equilibrio stabile dei corpi furono poi <lb></lb><figure id="id.020.01.1802.1.jpg" xlink:href="020/01/1802/1.jpg"></figure></s></p><p type="caption">

<s>Figura 16.<lb></lb>da Leonardo informati di artistica eleganza <lb></lb>in quelle figurine ondeggianti, che torna­<lb></lb>rono un secolo dopo nella mente del Vi­<lb></lb>viani a dar di sè pubblico e curioso spet­<lb></lb>tacolo nel teatro della scienza meccanica: <lb></lb>delle quali figurine e di altre forme più <lb></lb>bizzarre di corpi gravi sospesi Leonardo <lb></lb>stesso così in una breve nota svelava il <lb></lb>mistero agli attoniti ammiratori. </s>

<s>“ Il cen­<lb></lb>tro di ciascuno peso sospeso si stabilisce sotto il suo sostentacolo ” (Ra­<lb></lb>vaisson-Mollien, Manuscr. </s>

<s>B., Paris 1883, fol. </s>

<s>18). </s></p><p type="main">

<s>Ma passiamo a vedere come facesse il Nostro l&#039;applicazione di questi e <lb></lb>degli altri sopra accennati principii statici al moto delle macchine. </s>

<s>L&#039;alte­<lb></lb>razione, che subisce un peso nel dilungarsi più o meno il punto della sua <lb></lb>sospensione dal centro, e che comunemente chiamasi <emph type="italics"></emph>momento,<emph.end type="italics"></emph.end> da Leonardo <lb></lb>è distinto col nome di <emph type="italics"></emph>peso accidentale.<emph.end type="italics"></emph.end> “ Il peso accidentale, egli dice, se <lb></lb>posto in bilancia contro al peso naturale vale quanto esso peso naturale, e <lb></lb>questo si prova mediante il peso, che di loro riceve il polo della Bilancia, <lb></lb>il quale si carica tanto più del peso accidentale che del naturale, quanto il <lb></lb>braccio maggiore di tal bilancia eccede il braccio minore ” (Mollien, Manus. </s>

<s>E., <lb></lb>Paris 1888, fol. </s>

<s>59). </s></p><p type="main">

<s>Da questo principio generale conclude Leonardo i varii teoremi, e rac­<lb></lb>coglie i dati necessarii a risolvere alcuni problemi concernenti la Libbra, <lb></lb><figure id="id.020.01.1802.2.jpg" xlink:href="020/01/1802/2.jpg"></figure></s></p><p type="caption">

<s>Figura 17.<lb></lb>degli uni e degli altri de&#039;quali propo­<lb></lb>niamo ai Lettori i seguenti Saggi: “ I <lb></lb>pesi eguali, mutati per eguale distan­<lb></lb>zia dal centro ovvero polo della Bilan­<lb></lb>cia, terranno gli estremi della Bilancia <lb></lb>equidistanti al sostentacolo della Bilan­<lb></lb>cia: cioè se i pesi M, N (fig. </s>

<s>17), ap­<lb></lb>piccati in C, A, e&#039;siano d&#039;egual peso <lb></lb>ed egual distanza al polo della Bilan­<lb></lb>cia S, e che tu li scosti da esso polo infino in D, B, se le fieno <lb></lb>uguali distanzie, rimarran gli estremi della Bilancia in equilibrio ” <lb></lb><figure id="id.020.01.1802.3.jpg" xlink:href="020/01/1802/3.jpg"></figure></s></p><p type="caption">

<s>Figura 18.<lb></lb>(Manuscr. </s>

<s>A. cit., fol. </s>

<s>52 ad t). — <lb></lb>“ Domando se le due braccia della <lb></lb>Bilancia saranno compartite in parti <lb></lb>eguali e in A, B, C, D, E (fig. </s>

<s>18) <lb></lb>fia posto per ciascheduno una lib­<lb></lb>bra, quante libbre li farà resistenzia <lb></lb>in F? </s>

<s>Farai così: a fare resistenzia a una libbra posta in F, B <lb></lb>fa resistenzia a due, C a tre, D a quattro, ed E a cinque, che <pb xlink:href="020/01/1803.jpg" pagenum="46"></pb>tutta la somma fa resistenzia a quindici libbre poste in F ” (ivi, fol. </s>

<s>5). — <lb></lb>“ Se una Bilancia avrà un peso, il quale sia per lunghezza a similitudine <lb></lb><figure id="id.020.01.1803.1.jpg" xlink:href="020/01/1803/1.jpg"></figure></s></p><p type="caption">

<s>Figura 19.<lb></lb>d&#039;uno de&#039;suoi bracci, cioè MN (fig. </s>

<s>19), <lb></lb>che sia di sei libbre, quante libbre poste <lb></lb>in F li faranno resistenza? </s>

<s>Dico che tre <lb></lb>libbre fiano a sufficienza, imperocchè se <lb></lb>il peso MN sarà lungo quanto uno dei <lb></lb>bracci, potrai stimare che sia collocato <lb></lb>in mezzo al braccio della Bilancia nel <lb></lb>punto A: adunque, se in A fia sei lib­<lb></lb>bre, altre sei libbre poste in R li farebbero resistenza, e se si tirerà al­<lb></lb>trettanto innanzi insino allo estremo della Bilancia, nel punto R, tre libbre <lb></lb>li faranno resistenza ” (ivi). </s></p><p type="main">

<s>Quest&#039;ultimo problema appartiene all&#039;ordine di quelli, di cui si dice che <lb></lb>Euclide abbia dato il primo esempio, promosso dal Nemorario nelle sue ul­<lb></lb>time proposizioni, come altrove accennammo. </s>

<s>E perchè la data soluzione è <lb></lb>vera, sia applicato il bastone MN a contatto del braccio della Libbra, sia so­<lb></lb>speso a fila più o meno lunghe, eguali o diseguali, si credè il Nemorario <lb></lb>stesso di dover con la seguente proposizione III assicurare intorno a ciò i <lb></lb>dubitanti: “ Cum fuerint appensorum pondera aequalia, non motum faciet, <lb></lb>in aequilibri, appendiculorum inaequalitas ” (De pond. </s>

<s>cit., pag. </s>

<s>11). Leo­<lb></lb>nardo dimostrò la medesima proposizione in una Nota, che dice: “ Ogni <lb></lb>corpo di lunga figura, d&#039;eguale grossezza e peso, sospeso ne&#039;suo estremi da <lb></lb>due corde attaccate nelli estremi d&#039;egual braccia della Bilancia, benchè esse <lb></lb>corde siano di varie lunghezze, nientedimeno sempre le Bilance staranno <lb></lb>nella linea della egualità. </s>

<s>La ragione si è che se tiri perpendicolare una li­<lb></lb>nea, che passa sotto il centro della Bilancia, essa linea ancora passerà per <lb></lb>lo centro del sostenuto peso ” (Manuscr. </s>

<s>C. cit., fol. </s>

<s>7). </s></p><p type="main">

<s>Fu il Nemorario quello altresì che messe primo in campo la questione <lb></lb>lasciata indietro da Aristotile intorno alla bilancia di braccia eguali, che, ri­<lb></lb>mossa per violenza dalla posizione orizzontale, per sè naturalmente vi ri­<lb></lb>torna; questione, che fu forse delle più agitate fra&#039;Meccanici infino al ter­<lb></lb>minar del secolo XVII, e così da Leonardo anch&#039;essa risoluta: “ La Bilan­<lb></lb>cia di braccia e pesi eguali, rimossa dal sito della egualità, farà braccia e <lb></lb>pesi ineguali, onde necessità la costringe a racquistare la perduta egualità <lb></lb>di braccia e di pesi. </s>

<s>Provasi per la IIa di questo, e si prova perchè il peso <lb></lb>più alto è più rimoto dal centro del circonvolubile, che il peso più basso, <lb></lb>e pertanto ha più debole sostentacolo, onde più facilmente discende e lieva <lb></lb>in alto la opposita parte del peso congiunto allo estremo del braccio mi­<lb></lb>nore ” (Manuscr. </s>

<s>E. cit., fol. </s>

<s>59). Chi volesse avere la più chiara dimostra­<lb></lb>zione di fatto che la scienza del moto di Leonardo da Vinci è lo svolgi­<lb></lb>mento di una scienza anteriore collazioni il senso di questa Nota con le <lb></lb>proposizioni II e VII dell&#039;antico Giordano, e alla proposizione X di lui ag­<lb></lb>giunga questa Nota vinciana per corollario: “ Per saggiare un uomo e ve-<pb xlink:href="020/01/1804.jpg" pagenum="47"></pb>der se elli ha giudizio vero della natura dei pesi, domandali in che luogo <lb></lb>si debba tagliare uno dei bracci eguali della Bilancia, e fare che il tagliato <lb></lb>appiccato allo estremo del suo rimanente facci contrappeso al braccio suo <lb></lb>opposito con precisione, la qual cosa mai è possibile, e se elli ti divide il <lb></lb>sito, lui è tristo matematico ” (Manuscr. </s>

<s>M., fol. </s>

<s>68 ad t.). </s></p><p type="main">

<s>Le proposizioni statiche intorno alla Bilancia, che abbiamo fin qui dai <lb></lb>manoscritti vinciani raccolte e ordinate, son tutte dipendenti dal principio <lb></lb>che la Bilancia stessa si carica tanto più del peso accidentale, che del na­<lb></lb>turale, quanto il braccio maggiore eccede il braccio minore. </s>

<s>Questo prin­<lb></lb>cipio però si poneva come un semplice fatto sperimentale, senz&#039;altra mate­<lb></lb>matica dimostrazione, la quale non fu poi da Leonardo trascurata, quando <lb></lb>passò a trattare del Vette, ch&#039;è pure una Bilancia a braccia disuguali, e nel <lb></lb>quale distingue col nome proprio di <emph type="italics"></emph>leva<emph.end type="italics"></emph.end> il braccio, che rimane dalla parte <lb></lb>della potenza, e col nome di <emph type="italics"></emph>contralleva<emph.end type="italics"></emph.end> quell&#039;altro, a cui viene applicata <lb></lb>la resistenza. </s>

<s>“ Tanto sarà maggiore, così dice, il moto del motore nello <lb></lb>estremo della leva, che il moto del mobile nella contralleva, quanto il mo­<lb></lb>bile fia di maggior peso naturale. </s>

<s>— Tanto s&#039;aggiunge di peso accidentale <lb></lb><figure id="id.020.01.1804.1.jpg" xlink:href="020/01/1804/1.jpg"></figure></s></p><p type="caption">

<s>Figura 20.<lb></lb>al motore, posto nello estremo <lb></lb>della leva, quanto il mobile, po­<lb></lb>sto nello estremo della contral­<lb></lb>leva, lo eccede di peso naturale. </s>

<s><lb></lb>Provasi, e diremo che il moto <lb></lb>del motore si ha dal D ad M <lb></lb>(fig. </s>

<s>20), e quel del mobile dal­<lb></lb>l&#039;E all&#039;F. </s>

<s>Dico che tanto sarà <lb></lb>maggiore il moto DM che il mo­<lb></lb>to EF, quanto il peso accidentale <lb></lb>di Q eccede il peso P, il quale lo eccede per uno ” (ivi, fol. </s>

<s>58). </s></p><p type="main">

<s>Suppone l&#039;Autore, in questo caso particolare, che DA sia il doppio di <lb></lb>AE, e che perciò per l&#039;equilibrio il peso Q debba stare al peso P come due <lb></lb>sta ad uno, ma la legge medesima è così generalmente formulata in que­<lb></lb>st&#039;altra Nota: “ Quella proporzione, che avrà in sè la lunghezza della leva <lb></lb>colla sua contralleva, tale proporzione troverai nella qualità de&#039;loro pesi, e <lb></lb>simile nella tardità del moto, e nella qualità del cammino fatto da ciascuna <lb></lb>loro estremità, quando fieno pervenute alla permanente altezza del loro polo ” <lb></lb>(Manuscr. </s>

<s>A. cit., fol. </s>

<s>45). — “ Il peso applicato nella stremità della lieva, <lb></lb>fatta di qualunque materia si sia, leverà tanto più peso nel fine della contro <lb></lb>lieva, che il peso di sè, quanto la controlieva entra nella lieva ” (ivi, fol. </s>

<s>47). </s></p><p type="main">

<s>Dal principio della Leva dipende, secondo Aristotile, la legge statica di <lb></lb>tutte le altre macchine, ciò che nel Timpano, nell&#039;Asse in peritrochio, e <lb></lb>nella stessa Troclea semplice rendevasi evidente, benchè il Filosofo non si <lb></lb>accorgesse ch&#039;essendo essa Troclea semplice una Bilancia di braccia eguali <lb></lb>non può la potenza in essa avere nessun vantaggio sopra la resistenza. </s>

<s>Del <lb></lb>facile errore accortisi gli Alessandrini lo emendarono, e Pappo, descrivendo <pb xlink:href="020/01/1805.jpg" pagenum="48"></pb>il Polispasto, dice per evidente prova sperimentale che tanto più facilmente <lb></lb>si sollevano con tale strumento i pesi “ quanto plura membra funis inflecte­<lb></lb>tur ” (Coll. </s>

<s>mat. </s>

<s>cit., pag. </s>

<s>484), benchè non renda ivi di ciò nessuna ra­<lb></lb>gione, lusingando al solito i suoi lettori con le sole promesse. </s></p><p type="main">

<s>Leonardo s&#039;esercitò molto nelle sue Note in descrivere varie composi­<lb></lb>zioni di Polispasti, e in determinare le richieste proporzioni tra i pesi da <lb></lb>sollevarsi e le potenze motrici, di che può aversi un&#039;idea da queste nostre <lb></lb>spigolature. </s>

<s>Incomincia dal porre per fondamento quella verità, che da molti <lb></lb>Peripatetici si negava, e perciò così risolutamente sentenzia: “ Nessuno <lb></lb>corpo ponderoso leverà in Bilancia circolare, con forza del suo semplice peso, <lb></lb>più peso di sè medesimo. </s>

<s>Bilancia circolare chiamo la rotella, ovver carru­<lb></lb>cola, colla quale si trae l&#039;acqua de&#039;pozzi, colla quale non si leverà mai più <lb></lb>peso che si pesi quello che attigne l&#039;acqua. </s>

<s>— Ogni peso levato col mezzo <lb></lb>della Bilancia circolare si raddoppia nel sostentacolo d&#039;essa Bilancia. </s>

<s>Questa <lb></lb><figure id="id.020.01.1805.1.jpg" xlink:href="020/01/1805/1.jpg"></figure></s></p><p type="caption">

<s>Figura 21.<lb></lb>proposizione chiaramente si comprende <lb></lb>ancora nelle carrucole dei pozzi, imperoc­<lb></lb>chè, se uno v&#039;attinghi una secchia di <lb></lb>peso di cento libbre, bisogna che l&#039;attigni­<lb></lb>tore ve ne metti all&#039;opposita parte cento <lb></lb>una libbra, e tutto esso peso rimane a <lb></lb>sostentacolo d&#039;essa carrucola. </s>

<s>— Se rad­<lb></lb>doppi la corda che sostiene le venti lib­<lb></lb>bre (fig. </s>

<s>21), F ne sosterrà 10, e così D <lb></lb>altre 10. Se tu vuoli che C tiri le 10 lib­<lb></lb>bre, che si caricheranno in D, dai a C <lb></lb>libbre undici, e leverà le dieci di D. </s>

<s>Adun­<lb></lb>que il sostentacolo FD sostiene libbre 21. <lb></lb>— Se tu vuoli incordare le taglie in quattro doppii, le quali taglie abbino <lb></lb>a levare 20 libbre di peso, dico che la girella Z (fig. </s>

<s>22) sosterrà 10 lib­<lb></lb>bre, e 10 ne sosterrà la girella K, le quali si trasferiscono a&#039;sua superiori <lb></lb><figure id="id.020.01.1805.2.jpg" xlink:href="020/01/1805/2.jpg"></figure></s></p><p type="caption">

<s>Figura 22.<lb></lb>sostentacoli, cioè Q piglia da Z 5 <lb></lb>libbre, e cinque ne piglia ancora <lb></lb>F da Z, e 5 da K, e questo me­<lb></lb>desimo K ne dà 5 a Q, e chi vo­<lb></lb>lessi vincere le 5 di Q ne metta <lb></lb>6 nel contrappeso X, e mettendo <lb></lb>in nell&#039;ultimo loco 6 contra 5, e <lb></lb>ciascuna delle quattro corde, che <lb></lb>sostengono le 20 libbre, non sen­<lb></lb>tendo per sè se non 5 libbre, quella <lb></lb>libbra di più ch&#039;io metto nella <lb></lb>corda QX, non trovando in nessuna delle apposite corde pari peso a sè, <lb></lb>tutte le vince e tutte le muove ” (Manuscr. </s>

<s>A. cit., fol. </s>

<s>62). Di qui conclude <lb></lb>lo stesso Leonardo che “ il peso applicato alle taglie con quattro girelle starà <pb xlink:href="020/01/1806.jpg" pagenum="49"></pb>in equilibrio col quarto del peso applicato alla corda del primo moto ” <lb></lb>(Manus. </s>

<s>C. cit, fol. </s>

<s>7 ad t.), ciò che traducesi nel linguaggio dei Meccanici <lb></lb>moderni: la resistenza sta alla potenza, come quattro, ossia come il numero <lb></lb>de&#039;tratti di fune, sta ad uno. </s></p><p type="main">

<s>Rispetto al Cuneo, forse più saviamente di alcuni moderni, pensò Leo­<lb></lb>nardo non esservi buone ragioni da contradire Aristotile, che lo strumento <lb></lb>ridusse alla Leva, ond&#039;è che, nella Scienza meccanica degli antichi, le mag­<lb></lb>giori incertezze versano intorno alla Vite. </s>

<s>Pappo la rassomigliò a un Cuneo <lb></lb><emph type="italics"></emph>expers percussionis,<emph.end type="italics"></emph.end> e Galileo, come si lusingò di essere stato il primo a <lb></lb>notar l&#039;errore del Matematico alessandrino, rispetto alla potenza necessaria <lb></lb>a sollevare un peso sopra un piano inclinato; così pure si lusingò di aver <lb></lb>egli ridotto il primo la ragion della vite a quella dei piani più o meno obli­<lb></lb>qui. </s>

<s>Quel primato però è bene più antico, e infintantochè non produca al­<lb></lb><figure id="id.020.01.1806.1.jpg" xlink:href="020/01/1806/1.jpg"></figure></s></p><p type="caption">

<s>Figura 23.<lb></lb>cuno la fede di documenti anteriori, par che <lb></lb>giustamente sia dovuto a Leonardo. </s>

<s>Una sua <lb></lb>Nota infatti s&#039;intitola <emph type="italics"></emph>Della ragion della vite,<emph.end type="italics"></emph.end><lb></lb>e sotto un disegno (fig. </s>

<s>23) rappresentante <lb></lb>un peso posato sulla orizzontale in faccia a <lb></lb>varie obliquità di piani, si legge scritto: <lb></lb>“ Tanto quanto il peso è più presso al primo grado di facilità, che all&#039;ul­<lb></lb>timo, tanto fia più agevole a montare ” (Manuscr. </s>

<s>A. cit., fol. </s>

<s>42 ad t.). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>A misurare i progressi fatti da Leonardo nella scienza del moto, per <lb></lb>quel fecondo svolgersi dei principii, che si trovavano professati nella Statica <lb></lb>degli Autori più antichi, si resta senza dubbio maravigliati, e coloro, i quali <lb></lb>andavano ripetendo esser la Meccanica in que&#039;secoli rimasta immobile nei <lb></lb>libri di Archimede, si trovano oramai costretti di confessare, che la comune <lb></lb>opinione gli aveva ingannati. </s>

<s>Ma i confessati inganni e le maraviglie prese, <lb></lb>per le cose fin qui discorse, tanto dovrebbero più crescere nella mente e <lb></lb>nell&#039;animo dei nostri Lettori, tuttavia ripensando alle nuove cose, che siamo <lb></lb>per riferire, dalle quali apparirà che quell&#039;Uomo, il quale confessava di es­<lb></lb>sere <emph type="italics"></emph>senza lettere,<emph.end type="italics"></emph.end> non emula solamente il gran Galileo, ma lo vince, e quel <lb></lb>ch&#039;è più mirabile vince altresì gli stessi valorosissimi matematici della <lb></lb>scuola di lui. </s></p><p type="main">

<s>Non fa perciò maraviglia che molti dei teoremi, i quali si trovano nelle <lb></lb>Note vinciane conclusi, apparissero una miracolosa rivelazione di un inge­<lb></lb>gno quasi divino. </s>

<s>E l&#039;essere, come si diceva, quei teoremi conclusi e assai <lb></lb>raramente dimostrati, o per dir meglio, il non vedere espressamente formu­<lb></lb>lati quei principii, dai quali si conducono con logico ordine dall&#039;Autore le <pb xlink:href="020/01/1807.jpg" pagenum="50"></pb>dimostrazioni, fu potissima causa che s&#039;ingerisse quella così fatta opinione <lb></lb>in tutti rimasti alla superficiale lettura istupiditi. </s></p><p type="main">

<s>D&#039;investigare cotesti così spesso taciuti principii e di scoprire quel lo­<lb></lb>gico ordine, con che deve Leonardo averli condotti alle conclusioni, è stato <lb></lb>lo studio nostro principale, da cui ci è felicemente venuto l&#039;intendere la <lb></lb>natural ragione di quello, che sarebbe altrimenti rimasto un mistero. </s>

<s>Erano <lb></lb>dall&#039;altra parte così fatti principii, che per noi si riducono principalmente <lb></lb>alla composizion delle forze nel rettangolo e nel parallelogrammo, assai an­<lb></lb>tichi e, per essere stati insegnati da Aristotile, largamente diffusi. </s>

<s>Ma i pe­<lb></lb>ripatetici, inetti, e gli altri diffidenti fecer sì che con danno gravissimo della <lb></lb>scienza si rimanessero nelle Questioni meccaniche sterili o con frutti scarsi <lb></lb>ed agresti. </s></p><p type="main">

<s>Fra i non inetti, e i non diffidenti a quei tempi, Leonardo non fu cer­<lb></lb>tamente il solo, ma il principale e il meglio conosciuto da noi, che abbiamo <lb></lb>finalmente avuto la ventura di poter, come cosa pubblica, leggere i suoi <lb></lb>manoscritti. </s>

<s>E perchè Galileo e i discepoli di lui, tutt&#039;altro che inetti, fu­<lb></lb>rono però diffidenti, ecco naturalmente scoperta la recondita ragione del <lb></lb>perchè Filosofi così valorosi si trovino bene spesso senza vantaggio sopra <lb></lb>l&#039;illetterato artista di Vinci, e talora rimangan anzi da lui superati e vinti. </s>

<s><lb></lb>Ma è bene lasciar le parole e venire ai fatti. </s></p><p type="main">

<s>Ecco il primo saggio, che ci si offre, della fruttuosa applicazione fatta <lb></lb>da Leonardo del principio delle forze composte alla dimostrazion del se­<lb></lb>guente teorema: “ Sia la leva AT (fig. </s>

<s>24) il suo punto d&#039;appoggio in A, <lb></lb><figure id="id.020.01.1807.1.jpg" xlink:href="020/01/1807/1.jpg"></figure></s></p><p type="caption">

<s>Figura 24.<lb></lb>un peso O attaccato in T, e la forza <lb></lb>N, che ha da tenere il peso O in <lb></lb>equilibrio. </s>

<s>Tira AB perpendicolare <lb></lb>a BO e AC perpendicolare a CT: <lb></lb>quella proporzione avrà N ad O che <lb></lb>la linea AB alla linea AC ” (Ma­<lb></lb>nuscr. </s>

<s>E cit., fol. </s>

<s>65). I termini qui <lb></lb>di mezzo fra la conclusione e il <lb></lb>principio non è difficile ritrovarli in <lb></lb>ciò: che considerando Leonardo la <lb></lb>linea AT come la diagonale del ret­<lb></lb>tangolo rappresentatrice di tutta la <lb></lb>forza, che distrae dal suo punto d&#039;appoggio la leva, decompone quella stessa <lb></lb>forza unica in due: AB orizzontale misuratrice della forza traente N, e AC <lb></lb>verticale misuratrice della forza gravitante O per cui son veramente le con­<lb></lb>dizioni dell&#039;equilibrio date dall&#039;equazione N:O=AB:AC, conforme a quel <lb></lb>che dalle Note dell&#039;Autore s&#039;è di sopra trascritto. </s></p><p type="main">

<s>Si faceva da ciò Leonardo via a proporre un altro teorema, i corollarii <lb></lb>del quale s&#039;applicavano utilmente alla desiderata dimostrazion matematica <lb></lb>di alcune verità, già prima conosciute per sola esperienza. </s>

<s>“ Sia un peso <lb></lb>sostenuto da una corda attaccata in A (fig. </s>

<s>25). Dalla posizione perpendi-<pb xlink:href="020/01/1808.jpg" pagenum="51"></pb>colare AB sia ritirato esso peso in AM, per mezzo di una forza F, la dire­<lb></lb><figure id="id.020.01.1808.1.jpg" xlink:href="020/01/1808/1.jpg"></figure></s></p><p type="caption">

<s>Figura 25.<lb></lb>zion della quale formi un angolo retto con AM: <lb></lb>tanto sarà minore la forza F del peso M, quanto <lb></lb>AC è minore di AM ” (Venturi, <emph type="italics"></emph>Essai<emph.end type="italics"></emph.end> cit., pag. </s>

<s>17). </s></p><p type="main">

<s>I mezzi termini di questa dimostrazione, ta­<lb></lb>ciuti al solito da Leonardo, si ritrovano nella pro­<lb></lb>prietà del parallelogrammo delle forze, di cui dee <lb></lb>così l&#039;Autore aver fatto libero uso e sicuro. </s>

<s>Pro­<lb></lb>lunghisi nella stessa XXV figura AM di una quan­<lb></lb>tità MD a piacere, e si rappresenti per essa il peso <lb></lb>del grave M che, per la costruzione del paralle­<lb></lb>logrammo EF, si decompone in due: uno secondo <lb></lb>la natural direzione dei gravi ME, e l&#039;altro MF, <lb></lb>diretto al punto, a cui trae il peso F. </s>

<s>Le con­<lb></lb>dizioni dell&#039;equilibrio tra il grave pendulo M, e <lb></lb>la potenza F che lo travia dalla verticale, sono evi­<lb></lb>dentemente date dall&#039;equazione F:M=MF:ME. </s>

<s><lb></lb>Conducasi ora la orizzontale AC, la quale sia in C incontrata dal prolunga­<lb></lb>mento di EM. </s>

<s>I due triangoli simili AMC, MED danno la proporzione <lb></lb>ED:ME=AC:AM. </s>

<s>E perchè ED=MF è perciò, in piena conformità con <lb></lb>la proposizione di Leonardo, F:M=AC:AM. </s></p><p type="main">

<s>Da ciò concludevasi che, per tener sollevato il grave pendulo nella si­<lb></lb>tuazione orizzontale, nel qual caso AC e AM sono uguali; dee essere F di <lb></lb>pari forza col peso M che, rappresentato dall&#039;intero raggio del cerchio, <lb></lb>quando scende per l&#039;arco e giunge per esempio ne&#039;punti N, M, diminuisce <lb></lb>il momento suo totale a proporzione delle linee AH, AC, che sono i seni <lb></lb>degli angoli dell&#039;inclinazione fatta dal filo, o dal braccio di leva inginoc­<lb></lb>chiata in A, con la linea verticale. </s></p><p type="main">

<s>Fu a dare in pubblico queste conclusioni primo fra i Matematici il Be­<lb></lb>nedetti, nel cap. </s>

<s>II del suo trattato <emph type="italics"></emph>De mechanicis,<emph.end type="italics"></emph.end> e Galileo l&#039;applicò util­<lb></lb>mente come lemma, senza darne dimostrazione. </s>

<s>Come lemma pure, ancora <lb></lb>supposto vero, ne fece il medesimo uso il Torricelli, il quale abbreviò e in­<lb></lb>formò della sua solita eleganza il teorema galileiano. </s>

<s>Prolunghisi nella me­<lb></lb>desima figura XXV la tangente MF in P, e conducasi la orizzontale PR. </s>

<s>I <lb></lb>triangoli simili ACM, FPR danno la proporzione AC:AM=FR:FP e <lb></lb>perciò F:M=FR:FP. </s>

<s>Ora permanendo il grave M ugualmente bene in <lb></lb>equilibrio o sia, come dianzi, sospeso al filo AM, o posato sul piano FP; <lb></lb>dunque ne conclude il Torricelli: “ Momentum totale gravis, ad momen­<lb></lb>tum quod habet in plano inclinato, est ut longitudo ipsius plani inclinati ad <lb></lb>perpendiculum ” (De motu gravium, Florentiae 1644, pag. </s>

<s>101). </s></p><p type="main">

<s>Il processo di Leonardo è facile persuadersi che dovesse esser simile <lb></lb>a questo, con tal differenza però che, mentre il Torricelli ammetteva per <lb></lb>lemma supposto vero che “ quando grave circumfertur a semidiametro <lb></lb>AG=AM, manente puncto A, tunc momentum totale eius, hoc est mo-<pb xlink:href="020/01/1809.jpg" pagenum="52"></pb>mentum, quod habet in situ G, ad momentum quod habet in situ M, est <lb></lb>ut AG=AM:AC ” (ibid.), Leonardo invece ammetteva questo medesimo <lb></lb>come corollario di una sua proposizione già dimostrata, facendo, come s&#039;é <lb></lb>veduto, uso del parallelogrammo delle forze stimato una falsa regola dal Tor­<lb></lb>ricelli stesso e da Galileo. </s>

<s>Ond&#039;è che l&#039;Uomo del popolo, a cui l&#039;ordine del <lb></lb>variare i gravi i loro momenti secondo l&#039;obliquità de&#039;piani era stato rive­<lb></lb>lato dal fatto fisico della Bilancia idrostatica, ora è il primo a darne mate­<lb></lb>matica dimostrazione, non meno elegante di quella dello stesso Torricelli e <lb></lb>più compiuta. </s></p><p type="main">

<s>Che fossero veramente i processi di Leonardo in proposito simili ai tor­<lb></lb>ricelliani si conferma dal vedere che l&#039;uno e l&#039;altro Autore deducono, dalla <lb></lb><figure id="id.020.01.1809.1.jpg" xlink:href="020/01/1809/1.jpg"></figure></s></p><p type="caption">

<s>Figura 26.<lb></lb>medesima proposizione, i medesimi <lb></lb>corollari. </s>

<s>È il primo di questi il se­<lb></lb>guente, illustrato dalla figura 26 rap­<lb></lb>presentante una sfera, all&#039;estremo <lb></lb>diametro della quale è tangente, e <lb></lb>perciò perpendicolare, CP piano in­<lb></lb>clinato. </s>

<s>Prolungata la orizzontale PF <lb></lb>in D, e condotta ED, i triangoli si­<lb></lb>mili EDP, CPF danno la proporzione <lb></lb>PC:CF=EP:DP. “ Hinc colligi­<lb></lb>tur, dice il Torricelli, momentum <lb></lb>sphaerae gravis super diversas pla­<lb></lb>norum elevationes semper esse ut li­<lb></lb>nea illa horizzontalis, quae a contactu <lb></lb>in ipsa sphaera ducitur, posita sem­<lb></lb>per diametro pro momento maximo, sive totali ” (ibid., pag. </s>

<s>102-3). </s></p><p type="main">

<s>Leonardo, invece della corda intera, prende la metà, e prende il raggio <lb></lb>invece del diametro, formulando così, nella sua solita schietta semplicità, il <lb></lb>corollario torricelliano: “ Se P sia il polo, dove la palla tocca il suo piano; <lb></lb>quanto fia maggiore spazio da N a P, tanto fia più veloce il suo corso ” <lb></lb>(Manuscr. </s>

<s>A cit., fol. </s>

<s>52). Ciò fa l&#039;Autore di questa Nota, perchè non aveva <lb></lb>come il Torricelli di mira quest&#039;altro elegantissimo teorema, che si conclu­<lb></lb>deva dal moltiplicar per la circonferenza EDP i due termini EP, DP del­<lb></lb>l&#039;ultima proporzione; teorema che, nel trattato <emph type="italics"></emph>De motu ac momentis<emph.end type="italics"></emph.end> in­<lb></lb>cominciato a compilar dal Viviani, come vedremo a suo luogo, è proposto <lb></lb>sotto questa forma: “ Momentum totale sphaerae gravis EDP, ad momen­<lb></lb>tum partiale in hoc situ, est ut tota sphaerae superficies ad armillam, aut <lb></lb>ad zonam sphaericam descriptam ab arcu inferiori DP, quem subtendet corda <lb></lb>orizontalis DP ducta ex puncto P, in quo sphaera planum tangit, si sphaera <lb></lb>revolvatur circa diametrum horizontali DP parallelam ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XXXVII, c. </s>

<s>91). </s></p><p type="main">

<s>La poco diversa via tenuta da Leonardo fu però anch&#039;essa all&#039;Autore <lb></lb>occasione feconda di rappresentare il principale teorema sotto una forma <pb xlink:href="020/01/1810.jpg" pagenum="53"></pb>nuova, la quale non sarebbe stata indegna dello stesso Torricelli, anche per <lb></lb>la sua sola geometrica eleganza. </s>

<s>Condotta la PS parallela ad AN, e l&#039;AS <lb></lb>parallela alla PN, gli apparve chiaro che l&#039;intero momento della sfera o <lb></lb>ruota posata sul piano orizzontale stava al momento della stessa ruota sul <lb></lb>piano obliquo CP come la linea AP, ad AS, la quale AS misura la distanza <lb></lb>del centro A dal punto del sostegno suo naturale sul prolungamento di AN. </s>

<s><lb></lb>Che se fosse la via anche di più inclinata, e la ruota la toccasse per esem­<lb></lb>pio in Q, quanto viene a crescere AR sopra AS, altrettanto si fa lo scen­<lb></lb>dere più precipitoso. </s>

<s>Il nuovo processo insomma che, sgombrate le vie dagli <lb></lb>errori di Pappo, è il più diretto, conduce a riguardar la sfera come sospesa <lb></lb>dal punto A, quando posa in perfetto piano, e come sospesa dai punti S, R, <lb></lb>quando con minore o maggior impeto tende a scendere in basso. </s>

<s>Ma per­<lb></lb>chè parole anco più ornate delle nostre non è possibile che riescano a quella <lb></lb>stupenda chiarezza, che resulta dallo schietto linguaggio dell&#039;Autore, ecco <lb></lb>come i nuovi, e a que&#039;tempi sublimi concetti, sieno resi in questa breve e <lb></lb>semplice Nota: “ Se il peso fia in A, la sua vera e retta resistenza sarebbe <lb></lb>AB, e in qualunque parte la ruota tocca terra li fia suo polo, e quella parte, <lb></lb>che resta maggiore e fuori d&#039;esso polo, quella cade. </s>

<s>Essendo SP il polo, <lb></lb>chiaro appare pesare più ST che SM, onde conviene che la parte ST cag­<lb></lb>gia in basso, e vinca e levi SM, e movasi alla china con furia. </s>

<s>E se esso <lb></lb>polo fussi in Q, tanto quanto AR è maggiore di AS, tanto correrebbe per <lb></lb>sè la ruota più forte alla china, che facesse il polo in Q che in P ” (Ma­<lb></lb>nuscr. </s>

<s>A cit., fol. </s>

<s>21 ad t.). </s></p><p type="main">

<s>Chi volesse veramente persuadersi dell&#039;efficacia di questa mirabile con­<lb></lb>cisione sopra le prolisse e ornate dimostrazioni de&#039;Meccanici, venuti in tempi <lb></lb>a noi tanto meno lontani, collazioni di grazia la Nota vinciana con quel che <lb></lb>scrive nelle sue <emph type="italics"></emph>Dimostrazioni fisico-matematiche delle sette proposizioni<emph.end type="italics"></emph.end><lb></lb>Donato Rossetti. </s>

<s>Egli, con l&#039;intenzione d&#039;illustrare le dottrine galileiane, <lb></lb>dalle condizioni dell&#039;equilibrio di una sfera, posata sopra un piano perfet­<lb></lb>tamente orizzontale, passa a determinare i momenti sopra varie inclinazioni <lb></lb>di piani, e gli trova proporzionali ai seni degli angoli, fatti con la verticale <lb></lb>dal raggio della ruota o della sfera al punto della sua tangenza col piano; <lb></lb>ossia, secondo l&#039;espression dell&#039;Autore, “ come la distanza alla distanza del <lb></lb>centro di gravità dall&#039;impedimento ” (Firenze 1668, pag. </s>

<s>14), da Leonardo <lb></lb>chiamato col nome di <emph type="italics"></emph>polo.<emph.end type="italics"></emph.end> Ma benchè sieno i processi dimostrativi ne&#039;due <lb></lb>Autori uguali, e simili le stesse loro figure illustrative, chi, volendo aver <lb></lb>chiara e piena intelligenza di quelle cose, non preferirebbe d&#039;impararle piut­<lb></lb>tosto dalla rozza Nota del Pittore da Vinci, che dall&#039;elaborato libro del Ma­<lb></lb>tematico di Livorno? </s></p><p type="main">

<s>Le belle teorie meccaniche, relative al momento dei gravi sopra i piani <lb></lb>inclinati, furon dunque uno de&#039;più preziosi frutti, che raccolse Leonardo <lb></lb>dall&#039;uso di decomporre le forze. </s>

<s>Ma perchè, ritrovata una volta la via, a chi <lb></lb>per essa si mette i recapiti sono inaspettatamente frequenti; così avvenne <lb></lb>felicemente anche al Nostro, che riuscì a dimostrare altri teoremi, ignorati <pb xlink:href="020/01/1811.jpg" pagenum="54"></pb>per l&#039;avanti e per lungo tempo di poi. </s>

<s>È uno de&#039;più importanti e de&#039;più <lb></lb>desiderati fra i detti teoremi quello della ragion varia della percossa, secondo <lb></lb>che viene il colpo obliquamente o a diritto. </s>

<s>Il Cardano proponendosi di di­<lb></lb>chiarare nell&#039;<emph type="italics"></emph>Opus novum<emph.end type="italics"></emph.end> “ quanta proportione decedat ictus in obliquum <lb></lb>parietem, ab eo qui est ad perpendiculum ” (Operum, T. IV cit., pag. </s>

<s>520), <lb></lb>ne conclude essere quella proporzione secondo gli angoli dell&#039;incidenza, e <lb></lb>tanto aveva la cosa lusinghìero aspetto di verità, che fu la medesima carda­<lb></lb>nica conclusione ammessa senz&#039;alcun dubbio anche da Galileo. </s>

<s>Nella re­<lb></lb>staurata scienza fu primo a riconoscer l&#039;errore il Torricelli, fatto accorto <lb></lb>tutto insieme dalla Fisica e dalla Geometria: dietro lui poi il Borelli mosse <lb></lb>più sicuro i suoi passi. </s>

<s>E perchè la via lunga, segnata da Galileo al Bo­<lb></lb>relli, fu compendiosamente, a partir dal medesimo principio e giungere al <lb></lb>medesimo termine, percorsa dal solo Leonardo; giova accennar di volo ai <lb></lb>progressi fatti dalla scuola galileiana, perchè più efficace riesca, colla scienza <lb></lb>sparsa per le solitarie Note vinciane, l&#039;invidioso confronto. </s></p><p type="main">

<s>Rimeditava un giorno il Torricelli queste parole scritte nella I Gior­<lb></lb>nata de&#039;<emph type="italics"></emph>Due massimi sistemi:<emph.end type="italics"></emph.end> “ Fate conto che tutte le linee parallele, che <lb></lb>voi vedete partirsi dai termini A, B (fig. </s>

<s>27) sieno i raggi, che sopra la <lb></lb>linea CD vengono ad angoli retti: inclinate ora la medesima CD, sicchè <lb></lb><figure id="id.020.01.1811.1.jpg" xlink:href="020/01/1811/1.jpg"></figure></s></p><p type="caption">

<s>Figura 27.<lb></lb>penda come DO: non vedete voi che buona <lb></lb>parte di quei raggi, che ferivano la CD, pas­<lb></lb>sano senza toccar la DO? Adunque, se la DO <lb></lb>è illuminata da manco raggi, è ben ragionevole <lb></lb>che il lume ricevuto da lei sia più debole ” <lb></lb>(Alb. </s>

<s>I, 92). L&#039;argomento fisico, nella mente <lb></lb>matematica del Lettore, si trasformava facil­<lb></lb>mente in geometrico, e giacchè l&#039;obliquità DO <lb></lb>riceve tanta parte de&#039;raggi, quanti ne cadono <lb></lb>sulla perpendicolare DM; dunque, n&#039;ebbe a <lb></lb>concludere, la quantità del lume ricevuto sulla <lb></lb>parete eretta sta alla quantità del lume sul­<lb></lb>l&#039;inclinata, come l&#039;intero seno sta al seno dell&#039;angolo dell&#039;incidenza. </s>

<s>Riguar­<lb></lb>dando poi quei raggi come composti d&#039;innumerevoli corpuscoli in moto, <lb></lb>applicò quella legge fotometrica all&#039;analoga legge meccanica della percossa. </s></p><p type="main">

<s>Pubblicatisi appresso i Dialoghi delle Due nuove scienze, altre rimedi­<lb></lb>tate parole ivi lette suggerirono alla Geometria del Torricelli, intorno a ciò, <lb></lb>idee più precise. </s>

<s>Diceva così nel IV di que&#039;Dialoghi Galileo: “ Se la posi­<lb></lb>tura del corpo, che riceve la percossa, sarà tale che il moto del percuziente <lb></lb>la vada a investire ad angoli retti, l&#039;impeto del colpo sarà il massimo. </s>

<s>Ma <lb></lb>se il moto verrà obliquamente, e come diciam noi a scancio, il colpo sarà <lb></lb>più debole, e più e più secondo la maggiore obliquità, perchè in oggetto <lb></lb>in tal modo situato, ancorchè di materia sodissima, non si spenge e ferma <lb></lb>tutto l&#039;impeto e moto del percuziente, il quale sfuggendo passa oltre, con­<lb></lb>tinuando almeno in qualche parte a moversi sopra la superficie del resi-<pb xlink:href="020/01/1812.jpg" pagenum="55"></pb>stente opposto ” (Alb, XIII, 246). La qual considerazione, introdotta da Ga­<lb></lb>lileo nella yolgare notizia della percossa, aprì nel Torricelli la mente a <lb></lb>geometrizzare in questa guisa. </s>

<s>Sia DB la percossa diretta sulla parete resi­<lb></lb>stente BF (fig. </s>

<s>28) e AB l&#039;obliqua. </s>

<s>“ Tanto adunque, dice il Torricelli, sarà <lb></lb><figure id="id.020.01.1812.1.jpg" xlink:href="020/01/1812/1.jpg"></figure></s></p><p type="caption">

<s>Figura 28.<lb></lb>di moto parallelo nella linea AB rispetto alla BF, <lb></lb>quanto è la linea CB. </s>

<s>Ma di questo non facciamo <lb></lb>stima, perchè moltiplicato non aiuta, e diminuito non <lb></lb>debilita il momento, mentre l&#039;altro impeto non al­<lb></lb>terato resti il medesimo. </s>

<s>Di perpendicolare poi nella <lb></lb>stessa sarà quanto la linea AC, e la linea del colpo <lb></lb>sarà maggiore o minore, secondo che nello stesso <lb></lb>tempo sarà la linea AC maggiore o minore.... Si <lb></lb>cava di qui per corollario che la incidenza perpen­<lb></lb>dicolare ha la maggior forza, essendo come il seno <lb></lb>totale;... la proiezione parallela non ha niente, es­<lb></lb>sendo la forza sua come seno nullo; l&#039;incidenza di trenta gradi ha la metà <lb></lb>della forza totale, essendo il seno suo la metà del semidiametro ” (De motu <lb></lb>grav., Florentiae 1644, pag. </s>

<s>241, 42). </s></p><p type="main">

<s>Fu il Borelli però il primo che, nella proposizione XLV del suo trat­<lb></lb>tato <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> applicò direttamente al teorema il principio della <lb></lb>composizione delle forze ortogonali, riguardando AB come la diagonale del <lb></lb>rettangolo risoluta nelle due potenze AE, AC, la seconda delle quali, per <lb></lb>essere perpendicolare alla superfice che ha da ricevere il colpo, è la sola <lb></lb>efficace. </s>

<s>Dall&#039;avere usato questo processo dimostrativo s&#039;ingerì forse nello <lb></lb>stesso Borelli la persuasione d&#039;essere egli stato il primo a dimostrar “ la <lb></lb>misura precisa del momento delle percosse fatte in diverse inclinazioni, le <lb></lb>quali non son misurate dagli angoli dell&#039;incidenza, come taluno mostra di <lb></lb>credere, ma dai loro seni retti ” (Risposta alle considerazioni fatte sopra il <lb></lb>libro della percossa, Messina 1667, pag. </s>

<s>11). </s></p><p type="main">

<s>Mentre dunque nel 1667, quando si scrivevano queste parole, matema­<lb></lb>tici così valorosi, quali erano il Riccioli e l&#039;Angeli, partecipavano agli er­<lb></lb>rori del Cardano e di Galileo; Leonardo da Vinci aveva già da un secolo <lb></lb>e mezzo prima dimostrato matematicamente il vero, servendosi dell&#039;argo­<lb></lb>mento medesimo del celebrato Autore <emph type="italics"></emph>De vi percussionis.<emph.end type="italics"></emph.end> E perchè le ve­<lb></lb>rità non comuni agli uomini son per tutti di faticosa inquisizione, avendo­<lb></lb>sene per le Note vinciane visibili le vestigia, giova ricercar le vie, per le <lb></lb>quali si condusse felicemente l&#039;Autore alla riuscita. </s></p><p type="main">

<s>Fu anch&#039;egli a principio lusingato dall&#039;apparente verità, e ritenne per <lb></lb>certo che l&#039;effetto del colpo sempre riuscisse proporzionale al semplice an­<lb></lb>golo dell&#039;incidenza, come apparisce dalla seguente Nota: “ Se la ballotta C <lb></lb>(fig. </s>

<s>29) correrà per la linea CB, percoterà la linea AG, e farà, colla linea <lb></lb>del suo corso che passa al suo centro e con la linea del loco percosso, lo <lb></lb>angolo CAG, e quante volte questo angolo acuto entra nell&#039;angolo retto, <lb></lb>tanto fia il colpo più debole che non si conviene alla sua fuga, imperocchè <pb xlink:href="020/01/1813.jpg" pagenum="56"></pb>il primo grado del colpo si è infra angoli eguali, che lo fa nel percotere <lb></lb><figure id="id.020.01.1813.1.jpg" xlink:href="020/01/1813/1.jpg"></figure></s></p><p type="caption">

<s>Figura 29.<lb></lb>della linea AE, l&#039;ultimo grado si è nella linea <lb></lb>AC, e il mezzano è nella linea AF ” (Manuscr. </s>

<s><lb></lb>A cit., fol. </s>

<s>22). </s></p><p type="main">

<s>Quelle delicate poi e precise esperienze <lb></lb>dinamiche proprie, alla sola arte pazientissima <lb></lb>di Leonardo, lo fecero entrare in sospetto che <lb></lb>la percossa seguitasse tutt&#039;altra legge da que­<lb></lb>sta, avvertendo che, nella inclinazione di 45 <lb></lb>gradi, serba ancora il colpo tanta virtù, da <lb></lb>non parer dimidiata. </s>

<s>Quel più giusto mezzo <lb></lb>fu dal sagace sperimentatore trovato, quando la linea dell&#039;incidenza s&#039;avvi­<lb></lb>cina ai trenta gradi; ciò che gli fu scorta a scoprire la legge geometrica <lb></lb>dei seni. </s></p><p type="main">

<s>Prima però di trascrivere ai nostri Lettori la Nota, dove quella legge <lb></lb>meccanica è formulata, per confortare di qualche prova ciò che può cre­<lb></lb>dersi essere stato asserito da noi per dubitabile congettura, giova dar un sag­<lb></lb>gio di altre esperienze di Leonardo, che si riferiscono al presente soggetto. <lb></lb></s>

<s>“ I pesi d&#039;eguale materia ed eguale altezza e di varii pesi, posati sopra il <lb></lb>tenero fango, faranno in fra loro eguale profondità d&#039;impressione ” (Manuscr. </s>

<s><lb></lb>C cit., fol. </s>

<s>7 ad t.). </s></p><p type="main">

<s>Che tornino le pressioni e le percosse indipendenti dalla base, e sola­<lb></lb>mente proporzionali alle altezze, è un fatto che non fu bene avvertito nem­<lb></lb>men dai Meccanici del secolo XVII. </s>

<s>Aveva Galileo confusamente accennato <lb></lb>a ciò, quando avvertì che il minor colpo fatto dalle frecce torte dipendeva <lb></lb>da ciò, che “ il centro della loro gravità, non rispondendo alla cuspide per <lb></lb>la linea del moto, non cessa di proseguire alquanto, torcendosi d&#039;avvantag­<lb></lb>gio l&#039;asta lanciata ” (Alb. </s>

<s>XIV, 321), ma pure Isacco Vossio, nel 1663, a <lb></lb>una sua meccanica conclusione già dimostrata ebbe a soggiungere questo <lb></lb>corollario. </s>

<s>“ Quare autem pondus premens in longum, non vero in latum, <lb></lb>extendi debeat, huius rei ratio est manifesta, quia nempe omnis pressio fit <lb></lb>a perpendiculari pondere. </s>

<s>Sola perpendicularis designat corporis prementis <lb></lb>mensuram. </s>

<s>Plurimum itaque falluntur, qui putant quomodocunque dupli­<lb></lb>cato mallei pondere duplicari quoque percussionem. </s>

<s>Nisi duplicetur ferri <lb></lb>longitudo non potest duplicari percussio ” (De motu marium, Appendix <lb></lb>Hagae Comitis 1663, pag. </s>

<s>163, 64). </s></p><p type="main">

<s>Fra gl&#039;ingannati, qui voluti ammonire dal Vossio, era da fare una par­<lb></lb>ticolare eccezione rispetto a Leonardo, il quale aveva così in un&#039;altra sua <lb></lb>Nota lasciato scritto: “ Se lascerai cadere uno martello di una libbra cento <lb></lb>volte l&#039;altezza di uno braccio sopra una verga di piombo, e poi tolli uno <lb></lb>martello d&#039;altro peso che sia della grossezza del martello, e sia tanto lungo <lb></lb>che pesi cento libbre, e fallo medesimamente cadere l&#039;altezza d&#039;uno braccio <lb></lb>sopra una verga di piombo simile alla prima; e vedrai quanto la verga del <lb></lb>colpo unito fia più trafitta che la prima ” (Manuscr. </s>

<s>A cit., fol. </s>

<s>4). </s></p><pb xlink:href="020/01/1814.jpg" pagenum="57"></pb><p type="main">

<s>Soggiungeva il Vossio nel corollario citato una curiosa osservazione <lb></lb>teorica, in piena conformità con la pratica, che cioè volendo aggiungere al <lb></lb>ferro percuziente un manico, come si fa nel martello, perchè più valido ne <lb></lb>riesca e più sicuro il colpo, convien che il ferro stesso sia leggermente in­<lb></lb>curvato. </s>

<s>“ Observandum tamen si scapum ligneum inserere velis, incurvan­<lb></lb>dum esse leniter ferrum. </s>

<s>Quando enim manus ducit malleum in circulum, <lb></lb>pars superior mallei aliquantum a manu recedit, et pressionem facit extra <lb></lb>circulum quem describit. </s>

<s>Ut vero tota pressio et totum pondus premat in <lb></lb>loco debito, necessario ita incurvandum est ferrum, ut nulla eius portio ver­<lb></lb>setur extra circulum, per quem ducendus sit malleus ” (Appendix, sit., <lb></lb>pag. </s>

<s>164). </s></p><p type="main">

<s>Nel trattar di così fatto strumento, cioè del martello, Galileo nella <lb></lb><emph type="italics"></emph>Scienza meccanica<emph.end type="italics"></emph.end> si passa assai leggermente di questa argutissima osser­<lb></lb>vazione vossiana, per trattenersi a redarguire Aristotile, il quale voleva “ la <lb></lb>ragion del mirabile effetto della percossa ridurre alla lunghezza del manu­<lb></lb>brio o manico del martello ” (Alb. </s>

<s>XI, 124). Leonardo invece, dottamente <lb></lb>commenta le dottrine aristoteliche, e in alcuni suoi teoremi enuncia e di­<lb></lb>mostra come sia vero, e secondo qual proporzione la maggiore o minore <lb></lb>lunghezza del manico del martello cooperi efficacemente a rendere o mag­<lb></lb>giore e minore la percossa. </s>

<s>“ Se darai un colpo coll&#039;asta MS (fig. </s>

<s>30) nel <lb></lb><figure id="id.020.01.1814.1.jpg" xlink:href="020/01/1814/1.jpg"></figure></s></p><p type="caption">

<s>Figura 30.<lb></lb>loco N, tenendo M in mano, <lb></lb>tanto quanto MN entra in MS, <lb></lb>tante volte il colpo fia minore <lb></lb>che se lo dessi colla lunghezza <lb></lb>di MS, imperocchè MS fa tanta <lb></lb>lieva dopo N, che il colpo non <lb></lb>è di troppa valetudine ” (Ma­<lb></lb>nuscr. </s>

<s>A cit., fol. </s>

<s>4) ad t.). La <lb></lb>valetudine dunque del colpo, <lb></lb>fatto dal menar della verga MS, tenuta in mano in M come si farebbe del <lb></lb>manico di un martello, è secondo Leonardo e secondo Aristotile proporzio­<lb></lb>nale alla lunghezza del manico stesso. </s>

<s>Il colpo infatti è maggiore o minore <lb></lb>secondo la maggiore o minore velocità del perenziente, la quale ne&#039;punti N, <lb></lb>P, S della verga è manifestamente proporzionale alle lunghezze MN, MP, <lb></lb>MS. Ond&#039;è che se, per esempio, MN è un terzo di tutta la lunghezza della <lb></lb>verga e MP la metà, il colpo fatto ne&#039;due punti P, N starà a quello fatto <lb></lb>in S, come la metà e come un terzo. </s>

<s>“ Il movimento fatto nel terzo di <lb></lb>qualunque asta entrerà tre volte nel moto da capo, e il moto fatto dal mezzo <lb></lb>dell&#039;asta entrerà due volte nel moto ultimo ” (ivi, fol. </s>

<s>7). </s></p><p type="main">

<s>Tali sono i teoremi dimostrati intorno alla forza della percossa da Leo­<lb></lb>nardo, i quali noi abbiamo voluto preporre al principale, perchè agli stu­<lb></lb>pefatti della tanta scienza di un tale uomo ne sia manifesta l&#039;origine e la <lb></lb>preparazione. </s>

<s>Fu dunque quel fondamentale teorema così, un secolo prima <lb></lb>del Torricelli, formulato: “ Due pesi d&#039;eguale qualità caduti da eguale al-<pb xlink:href="020/01/1815.jpg" pagenum="58"></pb>tezza daranno tanto minore colpo l&#039;uno dell&#039;altro, quanto la linea della ca­<lb></lb>duta lia più obliqua all&#039;uno che all&#039;altro: cioè quanto la linea AC (nella <lb></lb>precedente figura XXVIII) entra nella linea AB, tanto il peso B darà mi­<lb></lb>nore colpo che il peso C ” (ivi, fol. </s>

<s>4 ad t.): ciò che nel più proprio lin­<lb></lb>guaggio matematico riesce alla forma, sotto alla quale fu così esposto dal <lb></lb>Borelli quello stesso teorema: “ Si corpus aliquod moveatur inclinato motu <lb></lb>ad superficiem alterius corporis omnino quiescentis, vis et energia percus­<lb></lb>sionis obliquae, ad absolutam percussionem perpendicularem, eamdem pro­<lb></lb>portionem habet quam sinus anguli incidentiae, ad sinum totum ” (De vi <lb></lb>percuss., Bononiae 1667, pag. </s>

<s>89). </s></p><p type="main">

<s>Il felice e maraviglioso incontro fra il Matematico di Messina e il Pit­<lb></lb>tor<gap></gap> da Vinci consegue naturalmente dall&#039;avere i due Autori professati i <lb></lb>medesimi principii. </s>

<s>Il secondo però, che fidatosi non della sola autorità di <lb></lb>Aristotile, ma della propria esperienza, aveva que&#039;medesimi principii estesi <lb></lb>alla composizion delle forze, con qualunque angolo s&#039;incontrassero insieme <lb></lb>nel parallelogrammo; ebbe il vantaggio sul primo, e su tutti gli altri della <lb></lb>Scuola galileiana che, troppo ossequiosi al Maestro, reputarono non valer <lb></lb>quella regola meccanica altro che per le forze composte ad angolo retto, <lb></lb>nelle quali veramente la potenza dell&#039;ipotenusa equivale alla somma delle <lb></lb>potenze de&#039;due cateti. </s>

<s>Quando poi il Varignon e il Newton vinsero così fatti <lb></lb>galileiani pregiudizii, si trovò la Scienza in mano la chiave da aprir certe <lb></lb>vie rimaste fin allora inaccesse, intanto che s&#039;ebbe a poter gloriare del titolo <lb></lb>di <emph type="italics"></emph>Meccanica nuova.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il Torricelli e il Viviani particolarmente s&#039;erano tanto confidati nelle <lb></lb>forze del loro ingegno, rese gagliarde dalla scienza di Galileo, che un se­<lb></lb>colo prima degli stranieri tentarono quelle novità meccaniche, delle quali <lb></lb>così il Torricelli stesso scriveva in una sua lettera al Ricci: “ Questa set­<lb></lb>timana (la prima dell&#039;anno 1643) ho trovato una cosa di Meccanica che è <lb></lb>totalmente nuova ” (Lettere, per Giovanni Ghinassi, Faenza 1864, pag. </s>

<s>16). <lb></lb>Il Viviani imitatore ed emulo del Torricelli tentò pure, oltre questa cosa <lb></lb>nuova in Meccanica che consisteva nel determinar le pressioni esercitate da <lb></lb>una trave appoggiata a un muro, altre simili meccaniche novità, e fu il primo <lb></lb>che si proponesse a risolvere il problema della tension delle funi gravate <lb></lb>di pesi. </s>

<s>Ma perchè non erano così fatti problemi risolubili per altro, che <lb></lb>per l&#039;uso del parallelogrammo, rimasero alle mani del Torricelli e del Vi­<lb></lb>viani o una delusione o una violenza fatta all&#039;ingegno, intanto che la Mec­<lb></lb>canica nuova in Italia risale propriamente ai tempi di Leonardo. </s>

<s>Si trovano <lb></lb>per quelle sue mirabili Note apertissimi di ciò gli esempii, e perchè si veda <lb></lb>chiara la somiglianza che passa fra l&#039;antica scienza italiana e la nuova ri­<lb></lb>sorta, ci tratterremo, come sufficienti per questo Saggio, intorno ai due sopra <lb></lb>citati problemi, comparando i modi, tenuti nel risolverli da Leonardo, con <lb></lb>quegli altri, che tennero i due ora commemorati valorosi discepoli di Galileo. </s></p><p type="main">

<s>Il problema delle funi caricate di pesi propostosi dal Viviani si trova <lb></lb>da lui stesso scritto in una sua Nota in questa forma: “ I fili CFA (fig. </s>

<s>31) <pb xlink:href="020/01/1816.jpg" pagenum="59"></pb>BA cavalchino i chiodi C, B, e sieno date le lunghezze CA, AB, ed al punto A <lb></lb>legato un peso G. </s>

<s>Si cerca che pesi deano attaccarsi alle estremità M, N, <lb></lb><figure id="id.020.01.1816.1.jpg" xlink:href="020/01/1816/1.jpg"></figure></s></p><p type="caption">

<s>Figura 31.<lb></lb>acciocchè il peso G non iscorra <lb></lb>da parte alcuna, e che i fili CA, <lb></lb>AB non allunghino o accorcino, <lb></lb>e che proporzione abbiano tra <lb></lb>di loro i pesi G, M, N ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXIII, fol. </s>

<s>26). </s></p><p type="main">

<s>La soluzione del problema, <lb></lb>che non si ritrova data qui dal­<lb></lb>l&#039;Autore, dipende da una pro­<lb></lb>posizione più generale, che può <lb></lb>essere così formulata: Concor­<lb></lb>rano le due funi CA, AB nel <lb></lb>nodo A, da cui penda il grave G. </s>

<s><lb></lb>Si domanda con quale sforzo siano tese esse funi dai punti C e B, a cui sono <lb></lb>stabilmente fisse per i loro due capi? </s>

<s>— Facendo uso del parallelogrammo <lb></lb>delle forze, la Meccanica nuova insegna a procedere così: Sul prolungamento <lb></lb>delle due linee CA, AB costruiscasi il parallelogrammo HO, di cui la dia­<lb></lb>gonale AG rappresenti il peso G e i lati AH, AO le tensioni delle due funi. </s>

<s><lb></lb>Chiamate T, T′ queste tensioni, avremo T:T′=sen GAO:sen GAH. </s>

<s>Con­<lb></lb>dotta dal punto B l&#039;orizzontale BF, e prolungata la verticale AG infino in D, <lb></lb>avremo sen GAO=sen DAF sta ad FD; come sen GAH=sen DAB sta a DB, <lb></lb>e perciò T:T′=FD:DB. </s>

<s>Moltiplicando ambedue i termini di questa se­<lb></lb>conda ragione per AD/2, avremo che le tensioni delle due corde AB, FA stanno <lb></lb>reciprocamente come i triangoli FAD, DAB. </s></p><p type="main">

<s>Questa della Nuova meccanica è la conclusione medesima, a cui giunse <lb></lb>per le medesime vie, con la meccanica sua antica, Leonardo, il quale, chia­<lb></lb>mando i due ora detti triangoli <emph type="italics"></emph>angoli chiusi,<emph.end type="italics"></emph.end> così propriamente si esprime <lb></lb>in una sua Nota: “ Il grave sospeso nell&#039;angolo delle corde divide il peso <lb></lb>a esse corde in tal proporzione, qual&#039;è la proporzione delli angoli inclusi <lb></lb>infra le dette corde, e la linea centrale di tal peso. </s>

<s>Provasi, e sia l&#039;angolo <lb></lb>della detta corda BAC, nel quale è sospeso il grave alla corda AG. </s>

<s>Sia dun­<lb></lb>que tagliato esso angolo nel sito della egualità dalla linea FB. </s>

<s>Di poi tira <lb></lb>la perpendicolare DA all&#039;angolo A, che sia in continuo diretto colla corda <lb></lb>AG, e quella proporzione che ha lo spazio DF col DB, avrà il peso che <lb></lb>sente la corda BA col peso che sente la corda FA ” (Manuscr. </s>

<s>B cit., fol. </s>

<s>66 <lb></lb>ad t.). Di qui venivasi facilmente alla final conclusione enunciata, perchè <lb></lb>DF e DB son le basi di due triangoli, che hanno la medesima altezza AD e <lb></lb>“ nei triangoli d&#039;eguale altezza, dice Leonardo stesso nella sua Geometria, <lb></lb>fia la medesima proporzione qual&#039;è quella della loro base ” (Ravaisson­<lb></lb>Mollien Man. </s>

<s>K., Paris 1888, fol. </s>

<s>86 ad t.). </s></p><p type="main">

<s>Chiamato per brevità <foreign lang="grc">α</foreign> l&#039;angolo FAD, <foreign lang="grc">α</foreign>′ l&#039;altro angolo adiacente DAB, <pb xlink:href="020/01/1817.jpg" pagenum="60"></pb>il parallelogrammo misuratore della tensione delle due funi, in relazione col <lb></lb>peso G che le aggrava, dà G:T=sen (<foreign lang="grc">α</foreign>+<foreign lang="grc">α</foreign>′):sen <foreign lang="grc">α</foreign>; G:T′=sen <lb></lb>(<foreign lang="grc">α</foreign>+<foreign lang="grc">α</foreign>′):sen <foreign lang="grc">α</foreign>′. </s>

<s>Ond&#039;è che, se sen <foreign lang="grc">α</foreign>′=<emph type="italics"></emph>o<emph.end type="italics"></emph.end> la Ia di queste due equazioni <lb></lb>dà G=T e la IIa dà T′=<emph type="italics"></emph>o<emph.end type="italics"></emph.end>:ciò vuol dire che se dei due tratti di corda <lb></lb>l&#039;uno si mantiene obliquo, e l&#039;altro si riduce in direzion verticale, a que­<lb></lb>sto solo, nulla cooperandovi l&#039;altro, è affidato tutto il peso: corollario im­<lb></lb>portante, non lasciato indietro da Leonardo. </s>

<s>“ Quando la linea intercentrica <lb></lb>(ha così in una sua Nota) non taglia l&#039;angolo fatto dal concorso delle due <lb></lb>corde, che sostengono il grave; allora, sola una di esse corde è sostenitrice <lb></lb>di tutto il grave. </s>

<s>Provasi, e sia prima che la linea intersecatrice DG tagli <lb></lb>l&#039;angolo A fatto dal concorso delle due corde AB, AF, che sostengono il <lb></lb>grave, per la qual linea l&#039;angolo BAF è diviso in due triangoli BAD, DAF. </s>

<s><lb></lb>Noi abbiamo provato come tal proporzione hanno li pesi sostenuti dalle due <lb></lb>corde, nelle quali si divide il peso G, quale è la proporzione che hanno li <lb></lb>detti due triangoli fra loro. </s>

<s>Ma nella figura FDAG la linea intercentrica non <lb></lb>taglia l&#039;angolo del concorso delle due corde che sostengono il peso, ma passa <lb></lb>per l&#039;una delle dette corde, e per questo resta un sol triangolo col quale <lb></lb>non si può dar proporzione, perchè in una cosa sola non si dà proporzione. </s>

<s><lb></lb>Egli è dunque necessario confessare che tutto il peso sia in tutta la corda, <lb></lb>d&#039;onde passa la detta linea intercentrica ” (Manuscr. </s>

<s>E cit., fol. </s>

<s>68). O in <lb></lb>altre parole, come lo stesso Autore nostro altrove si esprime: “ Se due <lb></lb>corde concorreranno alla sospensione di un grave, e che l&#039;una sia diritta e <lb></lb>l&#039;altra obliqua; essa obliqua non sostiene parte alcuna d&#039;esso peso ” (ivi, <lb></lb>fol. </s>

<s>70). </s></p><p type="main">

<s>Se i due angoli <foreign lang="grc">α</foreign>, <foreign lang="grc">α</foreign>′ sono uguali, resulta da quelle due medesime equa­<lb></lb>zioni, dateci di sopra dalla risoluzione del parallelogrammo, T=T′=G/2; <lb></lb>altro corollario così espresso da Leonardo: “ Le due corde eguali, che da <lb></lb>eguale altezza alla sospensione d&#039;un medesimo grave concorrano, sempre <lb></lb>fieno in fra loro d&#039;obliquità eguale, ed egualmente cariche di quel peso che <lb></lb>per loro si sostiene ” (ivi, fol. </s>

<s>67 ad t.). </s></p><p type="main">

<s>Per la semplice inspezione della figura XXXI, che abbiamo seguitato <lb></lb>fin qui ad avere sott&#039;occhio, facilmente si mostra, anche senza ricorrere alle <lb></lb>vie analitiche, che facendosi l&#039;angolo FAB sempre più ottusso vanno via via <lb></lb>le tensioni delle funi a farsi maggiori, rispetto al peso rappresentato dalla <lb></lb>diagonale AG del parallelogrammo, nè può quell&#039;angolo sparire, e ridursi <lb></lb>i due distinti tratti di corda in dirittura, se non a condizione che la diago­<lb></lb>nale stessa svanisca, e che perciò il peso G riducasi a nulla: nuovo e più <lb></lb>che mai importante corollario formulato così da Leonardo: “ Mai la corda, <lb></lb>di qualunque grossezza o potenza, posta nel sito della egualità, colli suoi <lb></lb>opposti estremi si potrà dirizzare, avendo alcuno peso in mezzo alla sua lun­<lb></lb>ghezza ” (ivi, fol. </s>

<s>60 ad t.). E perchè la nuova e inaspettata rivelazione della <lb></lb>Matematica poteva ai volgari ingegni apparire strana, si studiò perciò Leo­<lb></lb>nardo di persuaderli così del vero, applicando il teorema già formulato in <pb xlink:href="020/01/1818.jpg" pagenum="61"></pb>generale a un esempio particolare. </s>

<s>“ Impossibile fia, egli dice, a dirizzare <lb></lb>una corda che la lunghezza sua fia 100 braccia, e sia sospesa in fra due <lb></lb>carrucole di 100 braccia d&#039;intervallo, e a ciascuna testa sia appiccato uno <lb></lb>peso di 1000 libbre. </s>

<s>Dico che se tu appiccherai uno peso in mezzo a detta <lb></lb>corda, che pesi cento libbre, che la corda si romperà prima ch&#039;ell&#039;alzi, di­<lb></lb>rizzandosi, il suo peso nel sito della ugualità. </s>

<s>E&#039;pare quasi impossibile a <lb></lb>dire che duemila libbre di peso, che è attaccato in nelli estremi della corda, <lb></lb>non debba elevare dugento libbre, cioè il peso della corda e quello che è <lb></lb>posto in mezzo alla corda ” (Manuscr. </s>

<s>A cit., fol. </s>

<s>51 ad t.). </s></p><p type="main">

<s>A persuadere la verità di un tale apparente paradosso si sceglie da Leo­<lb></lb>nardo una via indiretta, per la quale, poste quelle e certe altre particolari <lb></lb>condizioni, si viene a concludere che, per tender la corda, non mille libbre <lb></lb>di peso ci bisognerebbero, ma ventimila, intantochè la corda stessa, prima <lb></lb>che tesa, dovrebbe necessariamente essere a tanto sforzo strappata. </s>

<s>I mezzi <lb></lb>termini della conclusione si trovano dal Nostro ne&#039;principii statici del vette, <lb></lb>in un modo simile a quel del Borelli, nella proposizione sua LXV della <lb></lb>I Parte <emph type="italics"></emph>De motu animalium.<emph.end type="italics"></emph.end> È questa proposizione così dall&#039;Autore suo <lb></lb>formulata: “ Nulla potentia finita poterit sublevare aut retinere quamlibet <lb></lb>exiguam resistentiam, usque ad situm horizontalem ” (Romae 1680, pag. </s>

<s>124). <lb></lb>Sia R (fig. </s>

<s>32) una potenza, la quale, tirando obliquamente per la dire­<lb></lb><figure id="id.020.01.1818.1.jpg" xlink:href="020/01/1818/1.jpg"></figure></s></p><p type="caption">

<s>Figura 32.<lb></lb>zione AC, costringe il peso T a salire sempre rasente <lb></lb>il regolo CD. </s>

<s>Dice ch&#039;essendo AH proporzionale alla <lb></lb>potenza, e HD proporzionale al peso stesso non potrà <lb></lb>essere sollevato più su del punto H, e li giunto si <lb></lb>farà l&#039;equilibrio. </s>

<s>Potrebbe la dimostrazione rendersi <lb></lb>più speditamente sicura, applicandovi il principio <lb></lb>della composizion delle forze, imperocchè la potenza <lb></lb>AH può decomporsi nelle due DH, ZH, della seconda <lb></lb>delle quali è rintuzzata l&#039;azione dalla resistenza del <lb></lb>regolo. </s>

<s>Di qui si vede che potrebbe essere un peso <lb></lb>anche sollevato in O, purchè interceda fra lui e la <lb></lb>potenza la relazione di OD ad OA, e si vede inoltre <lb></lb>che la direzione della potenza stessa, qualunque ella <lb></lb>si sia, non potrà mai essere quella di AD, se non a condizione che il peso <lb></lb>da sollevarsi sia nullo. </s></p><p type="main">

<s>Il Borelli però tiene nel dimostrare quest&#039;altra via, quale dalle sue se­<lb></lb>guenti parole vien disegnata. </s>

<s>“ Quod vero absoiute resistentia T perduci aut <lb></lb>retineri non possit in horizontali DA, patet, quia T in D solummodo mo­<lb></lb>veri potest per DC tangentem circulum radio AD descriptum, et sic linea <lb></lb>tractionis AD per vectis DA fulcumentum A transiret, ed ideo potentia R <lb></lb>sustinere non posset exiguam resistentiam T ” (ibid., pag. </s>

<s>125). Considera <lb></lb>insomma il Borelli che AD sia un vette, e che la direzione della potenza <lb></lb>passi per il suo punto d&#039;appoggio, nel qual caso non può veramente il vette <lb></lb>stesso venir sollevato e ridotto in positura orizzontale, se non che da una <pb xlink:href="020/01/1819.jpg" pagenum="62"></pb>potenza infinita. </s>

<s>Abbiamo infatti, riguardando uno de&#039;bracci della leva come <lb></lb>contratto nel punto A, T:R=<emph type="italics"></emph>o<emph.end type="italics"></emph.end>:AD d&#039;onde R=T.AD/<emph type="italics"></emph>o<emph.end type="italics"></emph.end>=∞. </s></p><p type="main">

<s>Leonardo procede nella sua dimostrazione in un modo simile a questo, <lb></lb>se non che suppone che l&#039;altro braccio del vette sia ridotto, non a un punto <lb></lb>matematico, ma a una piccolissima estensione, la quale determinata, benchè <lb></lb>non conduca alla necessità di una potenza infinita, la richiede nulladimeno <lb></lb>talmente grande, da vincere di gran lunga qualunque natural resistenza, che <lb></lb>le possa fare una fune. </s></p><p type="main">

<s>Sia la metà di questa fune rappresentata da AR (fig. </s>

<s>33), e sia OD il <lb></lb>diametro della girella, ch&#039;essa fune cavalca, per esser tenuta tesa dal grave <lb></lb><figure id="id.020.01.1819.1.jpg" xlink:href="020/01/1819/1.jpg"></figure></s></p><p type="caption">

<s>Figura 33.<lb></lb>pendulo Q, mentr&#039;è gravata <lb></lb>in A da un più piccolo peso <lb></lb>P. Leonardo, come il Bo­<lb></lb>relli, deduce le relazioni, che <lb></lb>debbon passare fra i due <lb></lb>detti pesi per l&#039;equilibrio, <lb></lb>dalle leggi del vette, uno <lb></lb>de&#039;bracci del quale sia po­<lb></lb>sto nella lunghezza della fu­<lb></lb>ne, e l&#039;altro nel raggio della <lb></lb>rotella, il centro della quale <lb></lb>fa da fulcro alla stessa leva. </s>

<s>Dà dunque quella legge statica P:Q=DO:AR, <lb></lb>ossia Q=AR/DO.P, e per tutta intera la fune, con i due pesi eguali che la <lb></lb>tirano da&#039;suoi capi, 2Q=2.AR/DO.P. </s>

<s>Passando ora a fare di questa for­<lb></lb>mula l&#039;applicazione numerica; perchè ponesi da Leonardo P=100, AR <lb></lb>=200, DO=1; sarà dunque 2Q=400X100=40,000, d&#039;onde Q= <lb></lb>20,000. </s></p><p type="main">

<s>Tal&#039;è appunto il discorso di Leonardo nella seguente forma da lui pro­<lb></lb>priamente espresso, dop&#039;avere affermato essere impossibile a far tendere una <lb></lb>corda da due pesi di mille libbre, che la tirino fortemente da una parte e <lb></lb>dall&#039;altra: “ La ragione di questo si è, che il peso, posto in mezzo alla <lb></lb>corda, fa quello medesimo offizio al contrappeso delle mille libbre, che fa­<lb></lb>rebbe altrettanto peso appiccato nella estremità di una leva, che fosse lunga <lb></lb>50 braccia. </s>

<s>Adunque, per sapere la verità di questo effetto, cioè se gli è <lb></lb>possibile che il peso delle 2000 libbre può dirizzare la corda, misura il dia­<lb></lb>metro del sodo della girella, che sostiene il peso delle mille libbre, e guarda <lb></lb>quante volte la metà d&#039;esso diametro entra dal mezzo della girella al mezzo <lb></lb>del peso delle cento libbre, sopra la linea RA. </s>

<s>E quanto detta parte del <lb></lb>diametro, cioè OR, entra dugento volte insino al di sopra del mezzo della <lb></lb>corda; altrettanto fa l&#039;altro mezzo, che dice 400. Adunque dì: 400 via 100 <lb></lb>fa quarantamila, e poi v&#039;è il peso della corda, che la regola del suo peso <pb xlink:href="020/01/1820.jpg" pagenum="63"></pb>di sotto. </s>

<s>In effetto la corda, in molta lunghezza, non si dirizzerà, se non si <lb></lb>rompe ” (Manuscr. </s>

<s>A cit., fol. </s>

<s>51 ad t.). </s></p><p type="main">

<s>S&#039;esercitò anche Galileo intorno a questo meccanico problema, ma l&#039;im­<lb></lb>possibilità di dirizzare una corda in linea orizzontale, da qualunque immensa <lb></lb>forza sia tirata, non sapendo come Leonardo far uso del parallelogrammo, <lb></lb>che rende per sè medesimo l&#039;apparente stranezza evidente, si lusingò di poter <lb></lb>concluderla dal principio statico generale de&#039;momenti uguali alle velocità <lb></lb>moltiplicate per i pesi. </s>

<s>“ Intendete per ora, così scrive nella IV giornata <lb></lb>delle Due nuove scienze, questa linea AB (fig. </s>

<s>34) passando sopra i due <lb></lb>punti fissi e stabili A, B, aver nelle estremità sue pendenti come vedete <lb></lb><figure id="id.020.01.1820.1.jpg" xlink:href="020/01/1820/1.jpg"></figure></s></p><p type="caption">

<s>Figura 34.<lb></lb>due immensi pesi eguali C, <lb></lb>D, li quali, tirandola con <lb></lb>grandissima forza, la fac­<lb></lb>ciano star veramente tesa <lb></lb>direttamente, essendo essa <lb></lb>una semplice linea senza <lb></lb>veruna gravità. </s>

<s>Or qui vi <lb></lb>soggiungo e dico che, se <lb></lb>dal mezzo di quella, che <lb></lb>sia il punto E, voi sospenderete qualsivoglia piccolo peso, quale sia que­<lb></lb>sto H; la linea AB cederà, ed inclinandosi verso il punto F, ed in conse­<lb></lb>guenza allungandosi, costringerà i due gravissimi pesi C, D a salire in alto, <lb></lb>il che in tal guisa vi dimostro ” (Alb. </s>

<s>XIII, 264). Descrive, per la dimo­<lb></lb>strazione, Galileo, co&#039;due raggi AE, BE, fissi ne&#039;loro centri A, B, le due por­<lb></lb>zioni di cerchio EG, EM, e per provar possibile che il piccolo peso II ha <lb></lb>virtù di scendere, come per esempio sarebbe in F, e perciò di far risalire <lb></lb>i due grandissimi pesi C e D, per tratti uguali a FL, FI; ricorre al prin­<lb></lb>cipio statico de&#039;momenti, il quale dovrebbe, nel caso dell&#039;equilibrio, dare <lb></lb>l&#039;equazione C:H=EF:FI. </s>

<s>Ma perchè EF ha maggior proporzione a FI <lb></lb>di quel che non ha C ad H, il che Galileo si studia di dimostrare, resta che <lb></lb>il piccolissimo peso abbia tanta viriù di moto in basso, da sollevare i due <lb></lb>grandissimi in alto: “ resta manifesto cioè, dice lo stesso Galileo, che la <lb></lb>linea AB partirà dalla rettitudine orizzontale. </s>

<s>E quel che avviene alla retta <lb></lb>AB priva di gravità, mentre si attacchi in E qualsivoglia minimo peso H, <lb></lb>avviene alla stessa corda AB, intesa di materia pesante, senza l&#039;aggiunta di <lb></lb>alcun altro grave, poichè vi si sospende il peso stesso della materia compo­<lb></lb>nente essa corda ” (ivi, 265). </s></p><p type="main">

<s>Al Viviani, come vedremo più di proposito altrove, entrò poi qualche <lb></lb>scrupolo di questa galileiana dimostrazione, nè gli parve che la tangente e <lb></lb>la secante si movessero in tale ordine fra loro, da rendere le velocità com­<lb></lb>parabili. </s>

<s>Il dubbio dall&#039;altra parte non era senza giusto motivo, reso anche <lb></lb>più manifesto per l&#039;uso del parallelogrammo, da cui resulta che la ragion <lb></lb>del peso C al peso II non è quella delle linee EF:FI, posta da Galileo, ma <lb></lb>sì veramente quell&#039;altra delle linee EF:AE. </s></p><pb xlink:href="020/01/1821.jpg" pagenum="64"></pb><p type="main">

<s>Notabile che Leonardo, il quale si servì di questa medesima costruzione <lb></lb>galileiana, col diretto e immediato intento di dimostrare che, in qualunque <lb></lb>sorta di movimento, allora si stabilisce il sistema in equilibrio, che gli spa­<lb></lb>zii tornano reciprocamente proporzionali ai pesi; rimanesse, come Galileo, <lb></lb>ingannato, reputando che gli allungamenti delle secanti e della tangente, co­<lb></lb>mune ai due archi de&#039;cerchi, potessero servire per la più giusta misura delle <lb></lb>velocità, con le quali i due ponderosi gravi C, D risalgono, e il corpicciolo H <lb></lb>discende. </s>

<s>“ Se la corda AB, egli dice, sia tesa da due forze uguali C, D, <lb></lb>poni nel mezzo della corda in E un piccolo peso H. </s>

<s>Egli scenderà infino <lb></lb>in F, e farà salire nel medesimo tempo i due pesi C, D. </s>

<s>Col raggio AE tira <lb></lb>l&#039;arco EG, il moto del peso C sarà IF. </s>

<s>Il peso H scenderà infintanto che non <lb></lb>si riduca alla proporzione H:C=IF:EF ” (Venturi, <emph type="italics"></emph>Essai<emph.end type="italics"></emph.end> cit., pag. </s>

<s>17). </s></p><p type="main">

<s>Se avesse preso per filo, da non smarrirsi per la intricata via, il paral­<lb></lb>lelogrammo, si sarebbe Leonardo, come negli altri casi, felicemente incon­<lb></lb>trato nel vero, ma benchè riconoscesse quella regola per certa, ebbe nono­<lb></lb>stante questa volta a trovare qualche difficoltà nel bene applicarla. </s>

<s>Di simili <lb></lb>difficoltà, dall&#039;altra parte s&#039;incontrarono bene spesso anche i moderni a dover <lb></lb>fare esperienza, di che il problema della trave appoggiata al muro, accen­<lb></lb>nato di sopra, offre in proposito un singolarissimo esempio. </s>

<s>Dopo l&#039;instau­<lb></lb>razione della Scienza meccanica fu, come si disse, il Torricelli il primo a <lb></lb>fare una tal nuova e pericolosa prova, e benchè debba essere altrove que­<lb></lb>sto per noi argomento a più lungo discorso, basti qui il dir tanto intorno <lb></lb>al modo tenuto in risolver quel meccanico problema dal discepolo di Galileo, <lb></lb>quanto giovi a paragonarlo con quell&#039;altro modo proseguito da Leonardo. </s></p><p type="main">

<s>Così dunque esso Torricelli, presa un giorno la penna in mano, col­<lb></lb>l&#039;intenzione di mettere in bella forma il suo pensiero; ne lasciava in una <lb></lb>notarella manoscritta interrotto il costrutto, dop&#039;avere appena accennato al <lb></lb>suo assunto: “ Fra gli effetti della Meccanica, degni di essere osservati, uno <lb></lb><figure id="id.020.01.1821.1.jpg" xlink:href="020/01/1821/1.jpg"></figure></s></p><p type="caption">

<s>Figura 35.<lb></lb>se ne trova, non avvertito ancora da alcuno che io sappia, ep­<lb></lb>pur da esso possono derivar cognizioni di qualche momento e <lb></lb>di molta curiosità. </s>

<s>Sia AB (fig. </s>

<s>35) un muro eretto al piano del­<lb></lb>l&#039;orizzonte BC, e sia AC una trave appoggiata al muro. </s>

<s>Chiara <lb></lb>cosa è che, mentre ella starà assai eretta, come AC, pochissima <lb></lb>forza che, posta in C, spinga verso B basterà per reggerla, il <lb></lb>che non accaderà, quando la trave sia più in­<lb></lb>clinata, come la DE. Ora, per contemplar ciò, <lb></lb>supponghiamo per ora che AC sia una linea, e <lb></lb>che in A e in C siano due potenze eguali, e <lb></lb>che la A prema perpendicolarmente in giù verso <lb></lb>B, ma la C spinga orizzontalmente verso E. </s>

<s><lb></lb>Cercasi la proporzione del momento, che averanno queste due forze, e dico <lb></lb>che la forza A alla C sarà come la linea CB alla BA, permutatamente prese. </s>

<s><lb></lb>Per provar questo bisognerà discorrere più a lungo .... Ora in cambio delle <lb></lb>due potenze si potrà, come nelle macchine della Meccanica, ed in particolare <pb xlink:href="020/01/1822.jpg" pagenum="65"></pb>nella lieva, considerare in A un peso, ed in C la potenza come sopra..... <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XXXVII, c. </s>

<s>87). </s></p><p type="main">

<s>Nell&#039;attendere a compilare il trattato torricelliano <emph type="italics"></emph>De motu ac momen­<lb></lb>tis<emph.end type="italics"></emph.end> voleva il Viviani raccogliere anche questo fra gli altri teoremi, rendendo <lb></lb>intelligibile il pensiero dell&#039;Autore coll&#039;osservar ch&#039;è la conclusione di lui <lb></lb>dedotta dalla Meccanica galileiana, considerando l&#039;angolo retto B così dispo­<lb></lb>sto, che l&#039;ipotenusa riesca parallela all&#039;orizzonte. </s>

<s>Di qui è che venendo, in <lb></lb>tal disposizione della segnata figura, ed aver le due linee oblique AB, BC <lb></lb>la medesima altezza, un grave che per essa scenda ha gl&#039;impeti reciproca­<lb></lb>mente proporzionali alle loro lunghezze. </s></p><p type="main">

<s>Ecco come pensava il Viviani di spiegare e rendere in forma i concetti <lb></lb>del Torricelli: “ In angulo recto ABC, e perpendiculari AB et horizzontali <lb></lb>BC constituto, concipiatur quaecumque subtensa AC, vel quaedam hasta so­<lb></lb>lida, omni tamen gravitate carens et inflexibilis. </s>

<s>In A, et in C, sint duae <lb></lb>acquales potentiae, quam altera deorsum premat iuxta directionem perpen­<lb></lb>diculi AB, altera autem impellat iuxta directionem horizontalem CB, contra <lb></lb>angulum B. </s>

<s>Dico momentum patentiae in A, ad momentum potentiae in C, <lb></lb>esse in ratione latorum permutatim sumptorum, nempe ut CB ad BA. ” </s></p><p type="main">

<s>“ Ad hoc probandum ponatur, non amplius latus BC, sed hypothenusa, <lb></lb>sive AC, esse horizontaliter constituta, ita ut planum trianguli ABC cum <lb></lb>aliquo verticalium congruat, angulo B deorsum spectante, productisque BA, <lb></lb>BC, in angulis A, C concipiantur aequalia pondera A, C. </s>

<s>Per ea, quae de­<lb></lb>monstravit magnus Galilaeus in suo Mechanicae tractatu, aliisque aggressio­<lb></lb>nibus, et hic Auctor ad initium sui libelli <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> confirmavit, momentum <lb></lb>gravis A directive per planum AB, ad momentum aequalis gravis C directive <lb></lb>per planum CB, est reciproce ut CB ad BA ” (ivi, c. </s>

<s>104 ad t.). </s></p><p type="main">

<s>Non era possibile però che a quel sottile giudizio del Viviani non sem­<lb></lb>brasse questa una troppo gran violenza fatta ai principii statici galileiani, <lb></lb>per accomodarli in qualche modo alla soluzion del problema; nonostante, <lb></lb>proponendosi un caso simile, non par che sapesse trovar, di questa, via <lb></lb>molto migliore. </s></p><p type="main">

<s>“ Sia il muro a piombo AB (scrive esso Viviani in una sua Nota au­<lb></lb>tografa) ed il pavimento BC, ed un corrente DE si vadi appoggiando come <lb></lb>si vede in varie positure e inclinazioni. </s>

<s>Si cerca con che proporzione vadia <lb></lb>questo grave violentando i detti piani sopra i quali si appoggia. </s>

<s>— Credo <lb></lb>che il peso, che sente il piano AB, al peso che sente il pavimento, stia omo­<lb></lb>logamente come l&#039;altezza del muro del toccamento del corrente fino a terra, <lb></lb>nel luogo B, alla lunghezza del pavimento, dal detto B fino all&#039;altro tocca­<lb></lb>mento sopra di esso ” (MSS. Gal. </s>

<s>Disc., T. CXIII, c. </s>

<s>30). </s></p><p type="main">

<s>L&#039;opinione così espressa non si trova qui confortata da nessuna dimo­<lb></lb>strazione, ma che fosse fondata, come si disse, sulla statica galileiana, può <lb></lb>confermarsi da un&#039;altra Nota, nella quale il Viviani stesso conclude le pro­<lb></lb>porzioni delle varie spinte del corrente contro il muro, nelle sue varie in­<lb></lb>clinazioni, dagl&#039;impeti che farebbe un grave supposto scendervi sopra, come <pb xlink:href="020/01/1823.jpg" pagenum="66"></pb>su due varie obliquità di un medesimo piano. </s>

<s>Or perchè i gravi uguali A, D <lb></lb>posti sopra le oblique eguali AC, DE hanno impeti proporzionali alle altezze <lb></lb>AB, DB, applica il Viviani questa ragion meccanica dei momenti a qualun­<lb></lb>que altra potenza, e perciò anche alla spinta data al muro dal corrente, che <lb></lb>in varia giacitura gli si appoggia. </s>

<s>“ Quod vero de momentis aequalium gra­<lb></lb>vium super codem aequali plano AC, DE, intelligatur quoque de momentis <lb></lb>aequalium potentiarum quarumlibet, per directiones AC, DE ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XXXVII, c. </s>

<s>105). </s></p><p type="main">

<s>Se il trapasso, dai momenti sopra i piani inclinati a qualunque potenza <lb></lb>operi in quelle direzioni, sia da concedersi al Viviani, ne dubitarono ragio­<lb></lb>nevolmente i Matematici venuti di poi, i quali, divulgatasi la notizia del pro­<lb></lb>blema proposto dal Torricelli, vi applicarono a risolverlo la regola del pa­<lb></lb>rallelogrammo delle forze. </s>

<s>Il modo più conveniente però di quella applicazione <lb></lb>gli pose in impaccio, ond&#039;è che ne dettero soluzioni varie, e forse non meno <lb></lb>incerte di quelle date dai due commemorati discepoli di Galileo, concluden­<lb></lb>dole dalle dottrine statiche del loro Maestro. </s></p><p type="main">

<s>Può, comunque sia, per facilitar la questione, osservarsi che, se ne&#039;due <lb></lb>punti di appoggio A e C, rappresentati da noi nella solita figura XXXV, <lb></lb>s&#039;intendano applicate due forze orizzontali, eguali e contrarie alle due spinte, <lb></lb>il corrente rimarrà tuttavia in equilibrio, cosicchè è il punto C del pavi­<lb></lb>mento, che ne sostien soprà sè tutto il peso. </s>

<s>L&#039;una o l&#039;altra poi di quelle <lb></lb>spinte eguali può facilmente determinarsi, decomponendole ne&#039;lati del paral­<lb></lb>lelogrammo, da che, chiamata S la detta spinta, P il peso del corrente inteso <lb></lb>raccolto nel suo centro di gravità, <foreign lang="grc">φ</foreign> l&#039;angolo ch&#039;egli fa col muro di appoggio, <lb></lb><emph type="italics"></emph>a<emph.end type="italics"></emph.end> la sua lunghezza, <emph type="italics"></emph>b<emph.end type="italics"></emph.end> la parte di lui che resta dal centro di gravità al punto <lb></lb>di contatto col pavimento; s&#039;ottiene la relazione S:P=(<emph type="italics"></emph>a—b<emph.end type="italics"></emph.end>) tang.<foreign lang="grc">φ</foreign>:<emph type="italics"></emph>a.<emph.end type="italics"></emph.end><lb></lb>Che se il corrente stesso è omogeneo e uniforme, e <emph type="italics"></emph>b<emph.end type="italics"></emph.end> perciò è uguale alla <lb></lb>metà di <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> il valore della spinta è dato da P.(tang.<foreign lang="grc">φ</foreign>)/2=P.(BC)/2; ossia essa <lb></lb>spinta è uguale al peso del grave che si appoggia, moltiplicato per la metà <lb></lb>della sua proiezione ortogonale. </s></p><p type="main">

<s>Ora è da vedere in che modo fosse questo medesimo problema risoluto <lb></lb>da Leonardo, che fu primo a proporlo ai Meccanici, un secolo prima del <lb></lb>Torricelli. </s>

<s>Non avendo nemmen egli, come i moderni, trovato conveniente <lb></lb>modo di applicarvi il principio della composizion delle forze, si lasciò, fin <lb></lb>dove seppero, condurre all&#039;Aritmetica e alla Geometria, e poi, abbandonato <lb></lb>da loro, riposò l&#039;affaticata mente nell&#039;esperienza. </s>

<s>“ Quello corpo, del quale <lb></lb>la continua larghezza è superata dalla lunghezza, conviene che dia di sè <lb></lb>eguale carico ai due sua estremi contatti, quando fieno equidistanti al cen­<lb></lb>tro come F, E (fig. </s>

<s>36), ma quando il corpo starà per linea perpendicolare <lb></lb>dico il contatto della inferiore stremità ricevere sopra sè tutto il di sopra <lb></lb>posto carico, e la superiore niente pesa al suo apposito contatto, come ap­<lb></lb>pare in GE. </s>

<s>Ma se detto corpo fia colle due estremità di discordante distanza <lb></lb>a detto centro, sarà di discordante peso, imperocchè la parte, che più se li <pb xlink:href="020/01/1824.jpg" pagenum="67"></pb>avvicina, più carica, e la più lontana si fa più lieve, come appare in A, C. <lb></lb><figure id="id.020.01.1824.1.jpg" xlink:href="020/01/1824/1.jpg"></figure></s></p><p type="caption">

<s>Figura 36.<lb></lb>Adunque, se nella prima proposizione si di­<lb></lb>mostra il detto peso compartirsi ne&#039;due estre­<lb></lb>mi contatti, e così nella seconda il basso E <lb></lb>riceverà tutto, e il G niente; adunque è ne­<lb></lb>cessario confessare, per ragione geometrica e <lb></lb>arismetrica, che quel peso, che si trova tra <lb></lb>l&#039;uno e l&#039;altro modo, partecipi de&#039;due estremi, <lb></lb>come A, C. </s>

<s>Se il peso AE fia 4 braccia e 8 <lb></lb>libbre, e che tu lo penda in modo, che non <lb></lb>sia tutto nel punto E, e nè compartito per <lb></lb>metà in FE, anzi si trovi in mezzo alla linea <lb></lb>FE, cioè sopra il punto C; dico per ragion di <lb></lb>Arismetrica che se il peso, stando per lo ritto, <lb></lb>dà 8 libbre di carico al punto E, e stando intieramente a diacere glie ne <lb></lb>dà 4; or piglia il mezzo che è infra 4 e 8, che è 6: adunque il punto sia <lb></lb>B e CA sia due fra forza e peso, e per ragion geometrica si trova che, <lb></lb>tolta la base del triangolo ACE, e quella partita per metà nel punto D, dico <lb></lb>sempre DE darsi a A, e così DF darsi in E. DE è simile a AB, e così DF <lb></lb>è simile a BE ” (Manuscr. </s>

<s>B cit., fol 63). </s></p><p type="main">

<s>Non in tutti i casi però vale questa ragione geometrica, perchè DF non <lb></lb>è <emph type="italics"></emph>simile,<emph.end type="italics"></emph.end> ossia uguale a BE, se non che quando il triangolo AEF è equila­<lb></lb>tero, e il corrente è perciò inclinato di 60 gradi sul pavimento. </s>

<s>Nonostante <lb></lb>vuol Leonardo che questa sia regola generale, e che sia da seguirsi per qua­<lb></lb>lunque inclinazione, com&#039;egli dice di aver trovato coll&#039;esperienza. </s>

<s>“ Io trovo <lb></lb>per esperienza che il legno AE darà tanto di sè men carico nel punto E, <lb></lb>quanto è la metà della basa del triangolo AEC: cioè se la mazza sarà 6 brac­<lb></lb>cia e pesi 6 libbre, e la metà della sua base ED sia uno braccio, dico che <lb></lb>il bastone darà di sè peso al punto E cinque, e una libbra ne va in forza <lb></lb>nel loco, dove s&#039;appoggia A ” (ivi, fol. </s>

<s>14 ad t.). </s></p><p type="main">

<s>È chiaro dunque che Leonardo, confondendo le spinte orizzontali con <lb></lb>l&#039;unica verticale, fa quelle variar fra loro secondo l&#039;inclinazione dell&#039;asta <lb></lb>appoggiata al sostegno, ond&#039;è che, chiamando S la spinta data dall&#039;asta <lb></lb>stessa in A, S′ l&#039;altra data in E, e ritenute le solite denominazioni <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> <foreign lang="grc">φ</foreign> poste <lb></lb>di sopra, le relazioni fra S, S′ sarebbero secondo Leonardo espresse dal­<lb></lb>l&#039;equazione S:S′=tang.<foreign lang="grc">φ</foreign>:2<emph type="italics"></emph>a<emph.end type="italics"></emph.end>—tang.<foreign lang="grc">φ. </foreign></s></p><p type="main">

<s>Notabile è a questo proposito l&#039;ingegnoso modo, con che spesso il No­<lb></lb>stro sa tradurre in formule matematiche i resultati delle esperienze. </s>

<s>Le re­<lb></lb>gole, ch&#039;egli dà in varie Note del manoscritto C, per determinar l&#039;altezza <lb></lb>di un liquido, in un vaso chiuso, dall&#039;ampiezza e dalla forma del getto, ce <lb></lb>ne offrirebbero un esempio singolarissimo. </s>

<s>Ma perchè questo appartiene a <lb></lb>un soggetto alquanto diverso dal presente, termineremo il nostro Saggio col <lb></lb>proporre ai lettori un altro problema di Meccanica che, essendo stato prima <lb></lb>secondo noi risoluto dallo stesso Leonardo per esperienza, fu da lui poi ri-<pb xlink:href="020/01/1825.jpg" pagenum="68"></pb>dotto a regola generale geometrica. </s>

<s>“ La infima bassezza dell&#039;arco, che fa <lb></lb><figure id="id.020.01.1825.1.jpg" xlink:href="020/01/1825/1.jpg"></figure></s></p><p type="caption">

<s>Figura 37.<lb></lb>la corda più lunga che lo spazio che è infra <lb></lb>i sua sostentacoli, sostenuta ne&#039;sua stremi da <lb></lb>due varie altezze, toccherà terra tanto più <lb></lb>presso al minore sostentacolo, che al maggiore, <lb></lb>quanto il maggiore riceve dentro a sè l&#039;altezza <lb></lb>del minore. </s>

<s>Verbigrazia, se il sostentacolo AB <lb></lb>(fig. </s>

<s>37) entra due volte in nel maggiore so­<lb></lb>stentacolo ED, lo spazio, che resta infra CB, <lb></lb>entra ancora due volte in DC ” (Manuscr. </s>

<s>A <lb></lb>cit., fol. </s>

<s>48). </s></p><p type="main">

<s>Benchè però, considerato il consueto or­<lb></lb>dine del procedere di Leonardo, siasi da noi <lb></lb>affermato che probabilmente questo teorema <lb></lb>meccanico fu per lui prima il frutto dell&#039;esperienza, le speculate teorie dei <lb></lb>pesi attaccati alle funi dovettero nulladimeno venire a dargliene la conferma. </s>

<s><lb></lb>Negli esempii da noi sopra recati il peso G della figura XXXI si supponeva <lb></lb>così fisso in A, che le funi CA, AB rimanessero sempre di lunghezza inva­<lb></lb>riabile. </s>

<s>Ora volle Leonardo, proseguendo l&#039;amato esercizio, veder come pro­<lb></lb>cedesse il fatto, quando lo stesso peso fosse libero di scorrere per la fune, <lb></lb>infintantochè non si fosse adagiato al suo naturale equilibrio, come sarebbe <lb></lb>per esempio a infilarvi un anello di ferro. </s></p><p type="main">

<s>Dir, come ne concludono analiticamente i Moderni, che dal dover es­<lb></lb>sere la direzione della gravità dell&#039;anello perpendicolare all&#039;ellise da lui de­<lb></lb>scritta nello sorrere per la fune, ne concludesse anche Leonardo che la linea <lb></lb>intercentrica dee divider l&#039;angolo fatto dalla stessa fune in due parti uguali; <lb></lb>sarebbe forse un esagerar di troppo le naturali virtù di quell&#039;ingegno, ma <lb></lb>in ogni modo, o per esperienza, come crediamo noi, o per altre vie, egli <lb></lb>riuscì benissimo a conoscere quella verità, o vogliam dire geometrica, o di <lb></lb>semplice fatto. </s></p><p type="main">

<s>Sieno dunque A e B (fig. </s>

<s>38) i due punti variamente alti, e a cui <lb></lb>stanno fissi i capi della fune AEB, nella quale è stato infilato il pesante <lb></lb><figure id="id.020.01.1825.2.jpg" xlink:href="020/01/1825/2.jpg"></figure></s></p><p type="caption">

<s>Figura 38.<lb></lb>anello E. </s>

<s>Per risolvere il problema conduce <lb></lb>Leonardo per E la orizzontale DC, sopra la <lb></lb>quale abbassa le due perpendicolari AC, BD. </s>

<s><lb></lb>Dovendo la linea intercentrica EF, per le ri­<lb></lb>conosciute condizioni dell&#039;equilibrio, dividere <lb></lb>l&#039;angolo AEB in due parti uguali, cioè in AEF <lb></lb>=EAC, e in FEB=EBD, i due triangoli <lb></lb>simili, o <emph type="italics"></emph>angoli chiusi uguali,<emph.end type="italics"></emph.end> come il Nostro <lb></lb>gli chiama, ACE, BED daranno AC:BD= <lb></lb>CE:ED; proporzione sopra la quale, anche <lb></lb>graficamente, si potrà risolvere il problema <lb></lb>in un modo forse più facile e più spedito di quello stesso suggeritoci dal <pb xlink:href="020/01/1826.jpg" pagenum="69"></pb>Bossut, o da altri Matematici moderni. </s>

<s>“ Quel corpo ponderoso, così pro­<lb></lb>priamente esprimesi Leonardo, che fia sospeso infra la corda, della quale i <lb></lb>sua estremi fieno attaccati a due sostentacoli di diversa altezza, giacerà infra <lb></lb>eguali angoli, de&#039;quali le loro base fieno tanto più larghe l&#039;una che l&#039;altra, <lb></lb>quanto gli estremi della corda fieno fermi più alti l&#039;uno che l&#039;altro ” (ivi, <lb></lb>fol. </s>

<s>48). </s></p><p type="main">

<s>Or è facile vedere che, riguardando la fune come aggravata dal suo <lb></lb>proprio peso, si possa facilmente ridurre alle condizioni dell&#039;antecedente <lb></lb>questo secondo esempio, in cui la fune stessa è aggravata da un peso stra­<lb></lb>niero. </s>

<s>E di quì è a concludere all&#039;ultimo quanto nella Geometria e nella <lb></lb>esperienza, sapientemente contemperate insieme, sapesse ritrovar valido ar­<lb></lb>gomento di progredire la scienza meccanica di Leonardo da Vinci, speculata <lb></lb>dalle naturali virtù del proprio ingegno, e diretta da tutta quella scienza, che <lb></lb>si poteva avere al suo tempo. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Ai magnificatori del divino ingegno, ai troppo creduli della miracolosa <lb></lb>potenza dell&#039;uomo, che crea da sè medesimo nuove scienze, senza prece­<lb></lb>denti tradizioni, e senza un primo maestro; si rivolge in particolare l&#039;ar­<lb></lb>gomento di questa storia, la quale ci sovviene opportuna a confermare il <lb></lb>fatto, che là dove venivano a mancar le anteriori istituzioni e i principii, da <lb></lb>attingervi il vero in essi concluso, andava anche il divino ingegno di Leo­<lb></lb>nardo da Vinci brancolando, insieme con gli altri, fra le tenebre dell&#039;igno­<lb></lb>ranza e dell&#039;errore. </s>

<s>Per la Statica erano date quelle istituzioni e posti quei <lb></lb>principii da Aristotile, da Archimede, e da Giordano Nemorario, che segnano, <lb></lb>secondo noi, nella storia della scienza tre distinte epoche progressive, e fu <lb></lb>mostrato di sopra come, giovandosi di quegli utilissimi documenti, sapesse <lb></lb>ingegnosamente Leonardo applicarli alla teoria delle macchine, e a&#039;momenti <lb></lb>dei gravi sopra i piani inclinati; e come fedelmente, proseguendo la regola <lb></lb>di decomporre le forze, insegnata da Aristotile e messa già in uso in certi <lb></lb>problemi ottici da Alazeno e da Vitellione; riuscisse mirabilmente ad assog­<lb></lb>gettar la più ritrosa parte della Meccanica alle docili discipline della Geo­<lb></lb>metria. </s></p><p type="main">

<s>Alla Dinamica però corse la sorte alquanto diversa. </s>

<s>Benchè avesse le <lb></lb>prime mosse da Archimede, furono però così deboli e così lontane, da non <lb></lb>risentirne l&#039;impulso, se non che tra il finir del secolo XVI, e il principiar <lb></lb>del seguente, per opera precipua del Benedetti e di Galileo. </s>

<s>È perciò che <lb></lb>Leonardo, studioso delle archimedee tradizioni, seppe sgombrarsi la mente <lb></lb>dagli errori aristotelici intorno alìe qualità e alle cause, che rendono i corpi <lb></lb>o gravi o leggeri, riconoscendole facilmente dal vario impulso dei mezzi; ma <lb></lb>da&#039;moti equabili in fuori, non riuscì con l&#039;aiuto delle matematiche a saper <pb xlink:href="020/01/1827.jpg" pagenum="70"></pb>nulla di più de&#039;contemporanei intorno alle leggi dei corpi gravi natural­<lb></lb>mente cadenti e dei proietti. </s>

<s>La stessa mirabile pazientissima diligenza delle <lb></lb>esperienze, se potè farlo accorto di qualche peripatetico errore, non valse <lb></lb>nulladimeno a rivelargli il vero, lungo tempo dopo riserbato alle scoperte <lb></lb>del Cavalieri e di Galileo. </s>

<s>A confermar le quali cose, e a provar l&#039;assunto <lb></lb>propostoci contro chi temerariamente asseriva esser la Scienza meccanica <lb></lb>una creazione della mente di Leonardo da Vinci, convien ricorrere ai docu­<lb></lb>menti, dimostrativi da una parte dell&#039;efficacia, e dall&#039;altra del difetto delle <lb></lb>tradizioni. </s></p><p type="main">

<s>Notabilissimo esempio di così fatta efficacia ci si porge in quel che <lb></lb>s&#039;accennava della naturale gravità e leggerezza, intorno a che aveva Aristo­<lb></lb>tile insegnato moltissimi errori, qual sarebbe per esempio quello che ogni <lb></lb>corpo, nel suo proprio luogo, è grave come l&#039;aria nell&#039;aria, e l&#039;acqua nel­<lb></lb>l&#039;acqua, e che a ciascun corpo l&#039;esser grave e leggero è per una assoluta <lb></lb>proprietà della Natura. </s>

<s>Dimostrò invece Archimede non essere, nella gra­<lb></lb>vità e nella leggerezza de&#039;corpi, nulla di assoluto, ma tutto aver relazione <lb></lb>e dipendenza dalla qualità del mezzo, la circumpulsion del quale lascia ca­<lb></lb>dere il grave s&#039;è vinta dal peso di lui, e lo fa al contrario salire se, sopra <lb></lb>quello stesso peso, riman vincitrice. </s>

<s>In sentenza de&#039;quali savi documenti, <lb></lb>appresi dalla lettura dei Libri archimedei, andava così ripetendo anche il <lb></lb>nostro Leonardo: “ Li moti degli elementi gravi non sono al centro, per <lb></lb>andare ad esso centro, ma perchè il mezzo ove essi sono non li può resi­<lb></lb>stere, e quando l&#039;elemento trova resistenza nel suo elemento, il suo corpo <lb></lb>più non pesa, nè cerca più di andare al centro ” (Del moto dell&#039;acqua cit., <lb></lb>pag. </s>

<s>281). E più sotto ripete, anche più spiegatamente, così lo stesso con­<lb></lb>cetto: “ La terra è grave nella sua sfera, ma tanto più quanto essa sarà <lb></lb>in elemento più lieve. </s>

<s>Il fuoco è lieve nella sua sfera, e tanto più, quanto <lb></lb>esso sarà in elemento più grave. </s>

<s>L&#039;acqua è grave e lieve, e tanto più grave <lb></lb>quanto essa sarà in elemento più lieve, e tanto più lieve quanto essa sarà <lb></lb>in elemento più grave. </s>

<s>Sicchè nessuno elemento semplice ha la sua gravità <lb></lb>o levità nella sua propria sfera. </s>

<s>E se la vessica piena d&#039;aria pesa più nelle <lb></lb>bilance, ch&#039;essendo vuota, questo è perchè tale aria è condensata, e con­<lb></lb>densar si potrebbe il fuoco, che sarebbe più grave che l&#039;aria o eguale all&#039;aria, <lb></lb>e forse più grave che l&#039;acqua, e forse eguale alla terra ” (ivi, pag. </s>

<s>282). </s></p><p type="main">

<s>A mostrar che, da una medesima fonte, salirono queste acque vive, <lb></lb>giova comparar le dottrine del Nostro con quelle, che ha in certe sue abboz­<lb></lb>zate scritture Galileo. </s>

<s>Ma perchè queste stesse galileiane scritture, date ora <lb></lb>alla luce, non sono altro che una giovanile esercitazion dell&#039;Autore sopra le <lb></lb><emph type="italics"></emph>Speculazioni<emph.end type="italics"></emph.end> del Benedetti, pensiamo di trascriver qui le parole del Mate­<lb></lb>matico di Venezia, che sembrano a noi copiate da un più antico esemplare <lb></lb>caduto quasi un secolo prima sotto gli occhi del popolano di Vinci. </s>

<s>Nel trat­<lb></lb>tatello <emph type="italics"></emph>Disputationes de quibusdam placitis Aristotelis,<emph.end type="italics"></emph.end> al cap. </s>

<s>XXVI, così <lb></lb>si legge: “ Omne corpus esse in loco proprio grave, ut Aristoteli placuit, <lb></lb>non est admittendum..... Exemplum, quod ipse de utre inflato proponit, <pb xlink:href="020/01/1828.jpg" pagenum="71"></pb>debuisset saltem ei oculos ad veritatem, quae clarissime fulget, inspiciendam, <lb></lb>aperire. </s>

<s>Verissimum est utrem inflatum plus ponderis habere quam vacuum, <lb></lb>aut quando aer in eo non est per vim inclusus. </s>

<s>Ratio autem huius rei est <lb></lb>quia, quando inflatus est, ea quantitas aeris, in eum per vim iniecti, mino­<lb></lb>rem occupat locum, quam si eidem libere vagari permitteretur, unde vio­<lb></lb>lenter quodammodo condensata est, et quia corpus densum in minus denso <lb></lb>semper descendit, et minus densum in magis denso ascendit. </s>

<s>Hanc ob cau­<lb></lb>sam uter inflatus plenus corpore magis denso, quam est medium quod eum <lb></lb>circumdat, descendit, non quia aer in aere, aut aqua in aqua sit gravis ” <lb></lb>(Editio cit., pag. </s>

<s>85). </s></p><p type="main">

<s>Come le fonti, da cui s&#039;attinsero queste dottrine nel secolo del Bene­<lb></lb>detti, ossia della instaurazion della scienza, e in quello di Leonardo che la <lb></lb>preparava, erano le archimedee; così di là s&#039;appresero nel medesimo tempo <lb></lb>le facili ragioni matematiche dei moti equabili. </s>

<s>“ Se una potenzia (ha così <lb></lb>una delle solite Note vinciane) moverà un corpo in alquanto tempo un al­<lb></lb>quanto spazio, la medesima potenzia moverà la metà di quel corpo nel me­<lb></lb>desimo tempo due volte quello spazio, ovvero la medesima virtù moverà la <lb></lb>metà di quel corpo per tutto quello spazio nella metà di quel tempo ” (Ra­<lb></lb>vaisson-Mollien, Manuscr. </s>

<s>F, Paris 1889, fol. </s>

<s>26). </s></p><p type="main">

<s>Le difficoltà maggiori frugavano più vivamente il desiderio di sapere <lb></lb>il vero intorno ai moti accelerati, principalmente da poi che alcuni, imbe­<lb></lb>vuti delle dottrine archimedee, dall&#039;aver colto Aristotile in fallo circa ai gravi <lb></lb>e ai leggeri, entrarono in gran sospetto che si fosse il Filosofo parimente <lb></lb>ingannato, quando sentenziò che le velocità dei gravi cadenti son propor­<lb></lb>zionali alla potenza dei loro pesi. </s>

<s>Sembrava che l&#039;esperienze da farsi in mezzo <lb></lb>all&#039;aria, per chiarir così fatti dubbii, non fossero molto più difficili di quel­<lb></lb>l&#039;altre fatte già in mezzo all&#039;acqua, ma s&#039;ebbe presto a riconoscere l&#039;illu­<lb></lb>sione, quando, lasciando andare da qualche altura varie sorte di corpi, se ne <lb></lb>volle con gli occhi, o con poco opportuni strumenti, misurar, per compa­<lb></lb>rarle fra loro, le varie velocità delle cadute. </s>

<s>Il vero si nascondeva agli spe­<lb></lb>rimentatori, or qua or là rifuggendo ai due eccessi, intanto che, tutti allo <lb></lb>stesso modo ingannati in osservar le misure degli spazii e dei tempi, par­<lb></lb>vero ad alcuni quelle misure così grandi da venire in conferma della legge <lb></lb>peripatetica, mentre altri credettero di trovarle fra loro così poco differenti. </s>

<s><lb></lb>da pronunziar la sentenza contraria, che cioè due gravi, diversamente pe­<lb></lb>santi, giungono in cadute eguali a toccar nel medesimo istante la terra. </s></p><p type="main">

<s>Leonardo volle entrare di mezzo nella questione che, movendo al trion­<lb></lb>fante Peripaticismo così nuovo e valido assalto, doveva a que&#039;tempi agitarsi <lb></lb>tra&#039;Filosofi e i Matematici con gran fervore. </s>

<s>Si facevano i Matematici forti <lb></lb>dell&#039;autorità di Archimede e anche il Nostro, benchè non dubitasse di poter <lb></lb>logicamente fare il trapasso dalla Statica alla Dinamica, consentendo con Ari­<lb></lb>stotile che, così nelle Macchine come nelle libere cadute, fossero le velocità <lb></lb>proporzionali ai momenti dei pesi, si persuase nulladimeno che il discordar <lb></lb>così come facevano l&#039;esperienze da questa legge, dipendesse tutto acciden-<pb xlink:href="020/01/1829.jpg" pagenum="72"></pb>talmente dalle varie resistenze del mezzo, il quale se può, essendo acqua, o <lb></lb>impedire affatto la velocità del galleggiante o ridurla in verso contrario; potrà <lb></lb>similmente, essendo aria, colla sua resistenza varia, alterare in vario modo <lb></lb>la velocità del grave che discende per essa. </s>

<s>“ Sempre la potenzia del motore, <lb></lb>egli dice, debba essere proporzionata al peso del suo mobile, e alla resistenza <lb></lb>del mezzo per il quale il peso si muove. </s>

<s>Ma di tale azione non si può dare <lb></lb>scienza, se prima non si dà la quantità della condensazione dell&#039;aria percossa <lb></lb>da qualunque mobile, la quale condensazione sarà di maggiore o minor <lb></lb>densità secondo la maggiore o minor velocità, che ha in sè il mobile che la <lb></lb>preme, come ci mostra il volar degli uccelli, li quali, col suono delle loro <lb></lb>alie battendo l&#039;aria, fanno il suono più grave o più acuto, secondo il più <lb></lb>tardo o veloce moto delle loro alie ” (Manuscr. </s>

<s>E cit., fol. </s>

<s>23 ad t.). </s></p><p type="main">

<s>Per giunger dunque ad avere e a dare la desiderata scienza dell&#039;azione <lb></lb>dell&#039;aria sulle libere cadute dei corpi, attese il nostro Leonardo con solle­<lb></lb>cito studio alle fisiche proprietà di lei, e ne conseguì in parte quella noti­<lb></lb>zia, che s&#039;annunziò un secolo e più dopo da Galileo e dal Torricelli per una <lb></lb>nuova grande scoperta. </s>

<s>L&#039;elasticità dell&#039;aereo elemento intorno alla quale <lb></lb>si seguitò a dubitare da molti infino a mezzo il secolo XVII, veniva dimo­<lb></lb>strata con l&#039;esperienze medesime de&#039;moderni negli Spiritali del Porta, e il <lb></lb>Cardano l&#039;applicava, come si vedrà meglio in seguito, alla caduta dei gravi, <lb></lb>illustrando il sopra esposto concetto di Leonardo. </s>

<s>Quanto al peso, l&#039;aveva <lb></lb>benissimo esso Leonardo riconosciuto nell&#039;esperienza aristotelica dell&#039;aria <lb></lb>condensata nel pallone di vetro, ma non si arrestò il progresso di una tale <lb></lb>notizia per lui, che attendeva a scoprir le fisiche proprietà di quello ele­<lb></lb>mento, in mezzo a cui naturalmente discendono tutti i gravi. </s>

<s>L&#039;artificiale <lb></lb>condensazione dell&#039;aria stessa dentro il pallone chiuso, e la misura di lei <lb></lb>rivelatagli da una squisita bilancia, lo condussero, in mezzo a questi suoi prin­<lb></lb>cipali intenti meccanici, a scoprir la naturale condensazione dell&#039;aria per <lb></lb>certe sottilissime vie, delle quali, divagando un poco dal diritto nostro cam­<lb></lb>mino, segneremo qui ai Lettori la traccia. </s></p><p type="main">

<s>Trovò dunque che un corpo intero pesa più di quando sia ridotto in <lb></lb>frantumi, e che una fune avvolta in matassa è alquanto più leggera che se <lb></lb>venga distesa. </s>

<s>Il fatto in sè curioso ritrovò per Leonardo una facile ragion <lb></lb>naturale nelle varie resistenze dell&#039;aria, le quali si fanno o maggiori o mi­<lb></lb>nori, secondo che maggiore o minore è il volume del corpo, o è più o men <lb></lb>lata la superficie dell&#039;immersione. </s>

<s>Quando per esempio la fune è avvolta, <lb></lb>la resistenza s&#039;estende a tutta la superficie della matassa, mentre, quando <lb></lb>è distesa, non trova altra resistenza che nel suo infimo capo, a quel modo <lb></lb>che resiste l&#039;acqua solamente contro la piccola base inferiore di un lungo <lb></lb>e sottil cilindro, che s&#039;immerga nel vaso. </s>

<s>“ Molti piccoli corpi ponderosi, <lb></lb>così scrive il Nostro, giunti insieme uniti fieno di maggior peso che a essere <lb></lb>separati: cioè, se torrai raspatura di piombo o vetro pesto e pesali, e poi <lb></lb>li fondi insieme, troverai questi essere cresciuti ” (Manuscr. </s>

<s>A cit., fol. </s>

<s>4). <lb></lb>E in un&#039;altra Nota: “ se peserai una corda distesa, e poi la pesi avvolta, tro-<pb xlink:href="020/01/1830.jpg" pagenum="73"></pb>verai di maggior peso la distesa che l&#039;avvolta, perchè l&#039;avvolta trova mag­<lb></lb>gior resistenza ” (ivi, fol. </s>

<s>34). </s></p><p type="main">

<s>Ora in queste così delicate e minuziose esperienze, ripetute da Leo­<lb></lb>nardo in tanti modi e tante volte, ebbe a trovare con sua grande sorpresa <lb></lb>che, da un giorno a un altro, e da una stagione a un&#039;altra, il peso sulla <lb></lb>Bilancia variava, ciò che, essendo i corpi medesimi, e medesimi i modi del <lb></lb>trattarli, non poteva attribuirsi ad altro, che a qualche variazione subita nella <lb></lb>densità dell&#039;aria, e perciò nel peso dell&#039;atmosfera. </s>

<s>E perchè osservò che suc­<lb></lb>cedevano così fatte variazioni spesso al variarsi lo stato del cielo, da sereno <lb></lb>per esempio a piovoso, gli si ebbe facilmente a trasformare quella delica­<lb></lb>tissima bilancia delle esperienze in un vero e proprio <emph type="italics"></emph>Barometro.<emph.end type="italics"></emph.end> Tale è <lb></lb>per noi quello strumento <emph type="italics"></emph>da conoscere la costituzione e la densità dell&#039;aria, <lb></lb>e quand&#039;è che il tempo si dispone alla pioggia,<emph.end type="italics"></emph.end> pubblicato dal Venturi <lb></lb>nel § XIII del suo <emph type="italics"></emph>Essai<emph.end type="italics"></emph.end> (pag. </s>

<s>28), e da lui, perchè forse credeva non poter <lb></lb>Leonardo giungere a tanto, giudicato, come quello dell&#039;Alberti o di altri più <lb></lb>antichi, un Igrometro. </s></p><p type="main">

<s>Le vie dall&#039;altra parte, che condussero il Nostro a partecipare alla <lb></lb>grande invenzione del Torricelli, come noi le abbiamo investigate; son na­<lb></lb>turali, nè mancherebbero altre simili esperienze a confermar questa fede <lb></lb>nei dubitanti. </s>

<s>Candido Del Buono scoprì nell&#039;Accademia del Cimento come <lb></lb>un corpo caldo ha sulla bilancia maggior leggerezza ch&#039;essendo freddo. </s>

<s>Il <lb></lb>fatto era stato scoperto lungo tempo prima, e sperimentato dal Nostro, il <lb></lb>quale notò così nelle pagine di un suo manoscritto: “ Sperimento come <lb></lb>il caldo fa lieve i corpi ponderosi. </s>

<s>— L&#039;una delle due cose di pari peso <lb></lb>posta sopra la bilancia, quella che fia infocata fia più lieve che l&#039;altra fredda. </s>

<s><lb></lb>Questa prova farai con due pallotte di rame appiccate a due fili di ferro <lb></lb>colle bilance. </s>

<s>L&#039;una delle due metti in foco, e fa&#039;rovente, e quando dal <lb></lb>foco è fatta rossa tirala fuori dal foco, acciocchè il vapore del calore che si <lb></lb>leva non ispingessi in alto il peso, e vederai che quella pallotta, che prima <lb></lb>essendo fredda era di pari peso coll&#039;altra, esser per lo calore fatta leggera ” <lb></lb>(Manuscr. </s>

<s>A cit., fol. </s>

<s>57). </s></p><p type="main">

<s>Il Borelli ridusse questa medesima esperienza, rimasta una semplice <lb></lb>curiosità nel Del Buono, a farsi dimostrativa del peso dell&#039;aria, alterato dal­<lb></lb>l&#039;azion del calore, nella proposizione LXI <emph type="italics"></emph>De motionibus naturalibus,<emph.end type="italics"></emph.end> dal­<lb></lb>l&#039;Autore stesso così formulata: “ Trutinae aequilibratae una lanx excalefacta, <lb></lb>sursum elevatur, extrusa a pondere aeris, reliquam lanceam ambientis. </s>

<s>” Ora <lb></lb>era naturalissimo che Leonardo, tutto intento a studiare gli effetti della den­<lb></lb>sità dell&#039;aria ne&#039;moti naturali, attribuisse il fatto della leggerezza de&#039;corpi <lb></lb>caldi alle cause medesime, alle quali gli veniva attribuendo il Borelli, e che <lb></lb>perciò gli conferisse anco questa notizia per l&#039;invenzione dello strumento, <lb></lb>da conoscer le varie costituzioni dell&#039;atmosfera. </s></p><p type="main">

<s>Comunque sia di ciò, ritornando al proposito nostro, vedremo quel che <lb></lb>decidesse Leonardo, in ordine alla fervorosa questione insorta a&#039;suoi tempi <lb></lb>delle velocità, con cui scendono i corpi di vario peso e d&#039;ugual materia la-<pb xlink:href="020/01/1831.jpg" pagenum="74"></pb>sciati andare da una medesima altezza. </s>

<s>La sentenza si trova così decisamente <lb></lb>scritta dall&#039;Autore in questa sua Nota: “ Se due palle di una medesima <lb></lb>materia, che l&#039;una sia il doppio peso dell&#039;altra, cadendo in un tempo da <lb></lb>una medesima altezza, non caderà prima altrettanto tempo la maggiore che <lb></lb>la minore ” (Manuscr. </s>

<s>A cit., fol. </s>

<s>34). </s></p><p type="main">

<s>La matematica scienza del moto non poteva però contentarsi di una <lb></lb>sentenza la quale, benchè sia così pronunziata in forma assoluta, si riteneva <lb></lb>nonostante dalla sola parte negativa; ond&#039;è che volendo il coscienzioso scien­<lb></lb>ziato adempire al debito suo, formulò dietro l&#039;esperienze, e dietro i calcoli <lb></lb>della resistenza opposta dall&#039;aria al velocitarsi dei gravi cadenti, una nuova <lb></lb>legge, la quale stava di mezzo fra quella insegnata da Aristotile, e l&#039;altra <lb></lb>riformata dai Matematici novelli. </s>

<s>Dicevano questi che se caderanno da una <lb></lb>medesima altezza due corpi sferici d&#039;ugual materia, ma l&#039;un de&#039;quali abbia <lb></lb>doppio diametro dell&#039;altro, le velocità della loro discesa in ogni modo sa­<lb></lb>ranno uguali. </s>

<s>I Peripatetici invece, volendo mantenere per assolutamente <lb></lb>vera la sentenza del loro Maestro, affermavano che, dovendo essere le velo­<lb></lb>cità proporzionali ai pesi, i quali stanno nei corpi sferici come i cubi dei <lb></lb>raggi, dee dunque la maggiore e più ponderosa sfera scendere otto volte <lb></lb>più veloce della minore. </s>

<s>Leonardo ne conclude che le disputate differenze <lb></lb>delle velocità, negli esempii citati, non sono nè così piccole da reputarsi per <lb></lb>nulle, nè son così grandi, che stieno come i cubi, ma come i semplici raggi <lb></lb>delle sfere, o come i loro diametri. </s>

<s>“ Se caderà dall&#039;alto in basso due di­<lb></lb>seguali corpi sferici, e ponderosi d&#039;egual materia e caduta, tanto caderà più <lb></lb>presto l&#039;uno che l&#039;altro, quanto il diametro dell&#039;uno entra nell&#039;altro ” (ivi, <lb></lb>fol. </s>

<s>32). </s></p><p type="main">

<s>Ecco data così scienza dell&#039;azion dell&#039;aria sulle cadute de&#039;corpi: frutto <lb></lb>di lunghi calcoli e di pazientissime esperienze. </s>

<s>Riman però tuttavia fermo <lb></lb>nella mente di Leonardo l&#039;assoluto principio aristotelico, che cioè <emph type="italics"></emph>sempre <lb></lb>la potenzia del motore debba essere proporzionata al peso del suo mobile.<emph.end type="italics"></emph.end><lb></lb>Cerca perciò nuove esperienze, che gli confermino la creduta verità di così <lb></lb>fatto principio, e facilmente le trova ne&#039;doviziosi ripostigli del suo ingegno <lb></lb>inventivo. </s>

<s>Se si scelgano tali figure di corpi, così fra sè ragionava, nelle <lb></lb>quali, aumentandosi il peso, la resistenza fatta a loro dall&#039;aria rimanga sem­<lb></lb>pre la stessa, dovrà in tal caso verificarsi esattamente quella legge, che ve­<lb></lb>niva dianzi alterata nelle forme sferiche, per non potersi in esse moltiplicar <lb></lb>così la quantità di materia, che non si venga anche insieme ad aumentare <lb></lb>la superfice del resistente. </s>

<s>I cilindri e i prismi si possono quanto si vuole <lb></lb>crescer di peso, allungandoli sulla medesima base, e saranno perciò così fatte <lb></lb>figure opportunissime per l&#039;esperienze, perchè, presa per esempio un&#039;asta <lb></lb>lunga tre braccia, e segata in due pezzi, l&#039;uno d&#039;un braccio e l&#039;altro di due, <lb></lb>se si lasceranno questi due pezzi cadere da una medesima altezza, e per lo <lb></lb>lungo, cosicchè avendo le basi eguali trovino nel fender l&#039;aria le resistenze <lb></lb>pure eguali; quel di due braccia andrà doppiamente veloce di quell&#039;altro. </s>

<s><lb></lb>La teoria, pensa Leonardo stesso, che debba esattamente riscontrare con <pb xlink:href="020/01/1832.jpg" pagenum="75"></pb>l&#039;esperienza. </s>

<s>“ Se dividerai, egli dice, uno pezzo d&#039;asta di tre braccia d&#039;eguale <lb></lb>grossezza e peso in due parti, e l&#039;un de&#039;pezzi sia due braccia e l&#039;altro uno <lb></lb>braccio, e lascieraigli cadere per ritto in un medesimo tempo da una me­<lb></lb>desima altezza, caderà altrettanto più presto l&#039;uno che l&#039;altro ” (ivi, fol. </s>

<s>34). </s></p><p type="main">

<s>Ma perchè nessun creda ch&#039;egli siasi in così pensare ingannato, descrive <lb></lb>altrove i modi più particolari dell&#039;esperienza, e par che inviti scongiurando <lb></lb>i lettori a ripeterla, perchè si persuadano co&#039;loro proprii occhi che così, <lb></lb>com&#039;ei la trova di fatto e la descrive, sta propriamente la cosa. </s>

<s>“ Se vuoi <lb></lb>provare quanto cade più presto uno peso d&#039;una oncia che uno di due once, <lb></lb>cadendo da una medesima altezza, farai così: Piglia due pezzi di sughero <lb></lb>d&#039;una medesima grossezza e di duplicata lunghezza, cioè che quello che pesa <lb></lb>due once sia più lungo altrettanto che l&#039;altro, e falli gittare a uno dall&#039;al­<lb></lb>tezza di un campanile, in un medesimo tempo, e poni l&#039;occhio a quello mi­<lb></lb>nore che rimane indietro, notando con l&#039;occhio i segni del muro, ovver delle <lb></lb>pietre d&#039;onde passa, e quando sentirai dare il botto in terra delle due once, <lb></lb>nota in qual pietra del campanile il peso d&#039;un oncia s&#039;incontrava, e poi mi­<lb></lb>sura quanta via aveva fatta l&#039;oncia, quando le due once dettono il botto in <lb></lb>terra ” (ivi, fol. </s>

<s>30 ad t.). </s></p><p type="main">

<s>Raccogliesi da tali autentici documenti che i progressi fatti da Leo­<lb></lb>nardo, in questa parte della scienza del moto, consistono unicamente nel­<lb></lb>l&#039;aver considerata e calcolata l&#039;azione dell&#039;aria, che accidentalmente perturba <lb></lb>la legge peripatetica, da lui stesso ritenuta per certa, delle velocità propor­<lb></lb>zionali alle quantità della materia. </s>

<s>Per quelle considerazioni però, se potè <lb></lb>vantaggiarsene la Fisica o la Meteorologia, la Dinamica si rimase immobile <lb></lb>nell&#039;errore antico, come si rimase pure immobile in esso, per Leonardo, <lb></lb>quand&#039;ei si propose di passare a sciogliere quest&#039;altro quesito: “ Se uno <lb></lb>peso cade dugento braccia, quanto caderà elli più presto le seconde cento <lb></lb>braccia, che le prime? </s>

<s>” (ivi, fol. </s>

<s>32 ad t.). </s></p><p type="main">

<s>La soluzione, che se ne dava allora da tutti, e che durò a darsi da tutti <lb></lb>fino ai tempi di Galileo, aveva il suo fondamento sopra l&#039;esperienza della <lb></lb>percossa, tanto in sè lusinghiera che nessuno ancora sospettava della falla­<lb></lb>cia. </s>

<s>Si teneva dunque per certissimo che la maggiore o minor trafitta di­<lb></lb>pendesse dalla maggiore o minor velocità del percuziente, o dalla maggiore <lb></lb>o minore altezza della discesa, la quale, essendo per esempio doppia, ren­<lb></lb>desse precisamente sul percosso doppio il suo effetto. </s>

<s>Così venivano lusin­<lb></lb>gandosi i Matematici di avere sperimentalmente conclusa la legge, che le <lb></lb>velocità, nelle naturali cadute dei gravi, son semplicemente proporzionali agli <lb></lb>spazii. </s></p><p type="main">

<s>Non seppe dal numero dei lusingati sottrarsi nemmeno il nostro Leo­<lb></lb>nardo, il quale, in una sua Nota, lasciavaci così scritto: “ Per definire il <lb></lb>discenso o inegualità degl&#039;intervalli delle ballotte dico in prima, per la IX di <lb></lb>questo, che il discenso di ciascuna ballotta, dividendolo a gradi eguali per <lb></lb>altezza, che in ogni grado di esso moto essa ballotta acquista un grado di <lb></lb>velocità, onde questa tale proporzione di gradi di velocità fia proporzione <pb xlink:href="020/01/1833.jpg" pagenum="76"></pb>continua arismetrica, perchè si proporziona insieme li eccessi ovver differen­<lb></lb>zie delle velocità. </s>

<s>Onde concludo che tali spazii saranno eguali, perchè sem­<lb></lb>pre eccedono ovver superano l&#039;uno l&#039;altro con eguale accrescimento ” (Libri, <lb></lb>Histoire cit., T. III, pag. </s>

<s>212). </s></p><p type="main">

<s>Persuaso che l&#039;assegnata proporzione aritmetica fra gli spazii e i tempi <lb></lb>fosse la vera, pensava Leonardo stesso a renderla con qualche ingegno evi­<lb></lb>dente, ciò ch&#039;ei pensava potersi fare nella seguente maniera: “ Caccia ven­<lb></lb>ticinque pallotte d&#039;egual peso in un cannone, in modo che stiano una sopra <lb></lb>l&#039;altra perpendicolari, e mettile in un luogo alto, e distoppa con un filo, e <lb></lb>sta&#039;da piè, ma el moto non ti lascerà conoscere gli spazii puri. </s>

<s>E così se <lb></lb>AB (fig. </s>

<s>39) ha fatto in un grado di tempo un grado di discenso, BC, per <lb></lb>essere più veloce, avrà fatto un grado di più di moto, e così CD, per essere <lb></lb>più veloce, e và seguitando ” (Del moto delle acque cit., pag. </s>

<s>363). </s></p><p type="main">

<s>La proposta era bella, quando non fosse però venuto a guastarla quella <lb></lb>massima difficoltà, confessata dallo stesso Proponente, che cioè il moto troppo <lb></lb><figure id="id.020.01.1833.1.jpg" xlink:href="020/01/1833/1.jpg"></figure></s></p><p type="caption">

<s>Fig.39.<lb></lb><figure id="id.020.01.1833.2.jpg" xlink:href="020/01/1833/2.jpg"></figure></s></p><p type="caption">

<s>Figura 40.<lb></lb>veloce non lasciava all&#039;osservatore co­<lb></lb>noscere gli spazii puri. </s>

<s>Si dette dunque <lb></lb>Leonardo a pensare a un modo come si <lb></lb>potesse arrestare il moto delle pallotte, <lb></lb>nell&#039;atto stesso che ritenevano una certa <lb></lb>natural proporzione gl&#039;intervalli del loro <lb></lb>discenso, cosicchè, colte in tale stato di <lb></lb>quiete, se ne potesse a bell&#039;agio, e pre­<lb></lb>cisamente come stavano in natura, ritro­<lb></lb>var le misure. </s>

<s>L&#039;invenzione, che ha per <lb></lb>verità più del capriccio che dell&#039;ingegno, <lb></lb>è descritta dall&#039;Autore in questo modo: <lb></lb>“ Sia posta in piedi per linea perpen­<lb></lb>dicolare l&#039;asse MN (fig. </s>

<s>40), e sia, con <lb></lb>terra mista con cimatura, bene interrata, <lb></lb>alla quale sia congiunto, ad uso di libro, <lb></lb>l&#039;asse OP, e si possa serrare subito con <lb></lb>due corde come vedi, ed all&#039;estremo di <lb></lb>essa asse interrata sia messo il piè d&#039;una <lb></lb>cerbottana, stoppata da piè e piena di pallotte <lb></lb>di egual peso e figura. </s>

<s>Poi, ferma bene la cer­<lb></lb>bottana e l&#039;asse interrata, subito lascia andare il contrappeso, e le due asse <lb></lb>si serreranno, e le pallotte che cadevano tutte si ficcheranno in essa terra, <lb></lb>e potrai poi misurare la proporzione della varietà delli loro intervalli ” (ivi, <lb></lb>pag. </s>

<s>364). </s></p><p type="main">

<s>Se fosse stata questa esperienza messa dall&#039;Inventore in pratica, e avesse <lb></lb>ottenuto l&#039;effetto che s&#039;immaginava, si sarebbe dovuto senza dubbio togliere <lb></lb>da quell&#039;inganno, in cui persisteva, perchè gl&#039;intervalli delle pallotte, rima­<lb></lb>ste murate nell&#039;assicella, gli avrebbero facilmente mostrato di serbar fra loro <pb xlink:href="020/01/1834.jpg" pagenum="77"></pb>una proporzione assai diversa dall&#039;aritmetica. </s>

<s>Ma i principii, da concluderne <lb></lb>la vera legge della caduta dei gravi, non erano nella Scienza dinamica an­<lb></lb>cora posti, e l&#039;error della mente affascinava anche a Leonardo lo stesso <lb></lb>chiaro lume degli occhi. </s>

<s>Il fatto mirabilmente conferma la legge logica del <lb></lb>pensiero, alla quale doveva naturalmente soggiacere anche il Nostro, che <lb></lb>cioè non si dà progresso, dove mancano le tradizioni, come non si dà svol­<lb></lb>gimento organico della vita vegetativa o della animale, dove manchino i <lb></lb>germi. </s>

<s>L&#039;esperienza stessa, e sia pur diligente e destra, non vale, come non <lb></lb>vale a un campo non seminato qualunque più sottile arte della cultura. </s>

<s>Dove <lb></lb>però un germoglio si giace abbandonato e latente, in qualche più remota <lb></lb>parte del suolo, chi n&#039;ha l&#039;industria l&#039;educa, e pare ai meno esperti o ai <lb></lb>negligenti che abbia nelle sterili zolle, quella mano educatrice, miracolosa­<lb></lb>mente infusa la vita. </s>

<s>Nel soggetto, che è della caduta dei gravi, ci offre Leo­<lb></lb>nardo stesso di ciò che si dice per allegoria il più proprio e più notabile <lb></lb>esempio, in cui pur si verifica che, se al venirgli meno la scienza dei mag­<lb></lb>giori và brancolando anch&#039;egli per le tenebre insieme con gli altri; là dove, <lb></lb>di quella scienza prefulgevali un raggio, ebbe più acuta vista di Calileo. </s></p><p type="main">

<s>Ritorniamo indietro a ripensare al nostro sperimentatore, che ora sale <lb></lb>sull&#039;alta cima di un campanile, per lasciar di lì cadere a terra le variamente <lb></lb>ponderose sfere di piombo, e i prismi di sughero; ora, affidato ad altri il <lb></lb>manuale ufficio, scende a piè della torre, per osservar colla più grande at­<lb></lb>tenzione quanto l&#039;uno de&#039;cadenti scenda più veloce dell&#039;altro. </s>

<s>Un fatto sin­<lb></lb>golarissimo ebbe a notare in queste esperienze, ed era che si vedeva il grave <lb></lb>andare a battere un po&#039;in distanza dalla base della torre, cosicchè sempre <lb></lb>dava in terra quel che pareva piuttosto dover dare a dirittura nel muro. </s>

<s><lb></lb>S&#039;aggiungeva costantemente al fatto che la divergenza del punto della ca­<lb></lb>duta dal perpendicolo rimaneva dalla plaga orientale, ciò che facilmente fece <lb></lb>nascere nell&#039;arguto Osservatore il sospetto, che s&#039;avesse la causa del suo <lb></lb>stupore a riconoscer nel moto circonvolubile della Terra. </s></p><p type="main">

<s>S&#039;applicò pertanto Leonardo con tutto il suo studio a ritrovare una con­<lb></lb>ferma e una dimostrazione delle sue congetture nella Meccanica, e in simili <lb></lb>altri fatti rappresentabili per esperienze. </s>

<s>Le fila della pioggia, che mostrano <lb></lb>scendere obliquamente dall&#039;alto a chi di rincontro a loro cammina, furono <lb></lb>forse il principio alle idee, che si svolsero in quell&#039;acuto meditativo pen­<lb></lb>siero. </s>

<s>Ei volle ad arte sottoporsi quelle piovose fila alla più comoda contem­<lb></lb>plazione, facendo fluir l&#039;acqua dal sottil foro di un vaso, ora equabilmente <lb></lb>mosso, ora tenuto fermo, e mosso invece il soggiacente piano, che ha da <lb></lb>ricever l&#039;artificiosa pioggia cadente. </s>

<s>In una Nota, che s&#039;intitola <emph type="italics"></emph>Del moto <lb></lb>dell&#039;immobile, che versa con moto continuo sopra sito mobile; ovvero es­<lb></lb>sendo mobile quel che versa;<emph.end type="italics"></emph.end> così si legge: “ Il moto del liquido il qual <lb></lb>versa per il fondo del vaso mobile sarà per linea retta situata per obliquo, <lb></lb>la quale obliquità fia di tanto maggiore o minore declinazione, quanto il <lb></lb>moto del vaso che la genera sarà di maggiore o minore velocità ” (Ravais­<lb></lb>son-Mollien, Manuscr. </s>

<s>G, Paris 1890, fol. </s>

<s>54). </s></p><pb xlink:href="020/01/1835.jpg" pagenum="78"></pb><p type="main">

<s>Si vede a illustrar questa Nota disegnato in margine il vaso che, stando <lb></lb>quieto verserebbe verticalmente il filo liquido AB (fig. </s>

<s>41), mentre mosso <lb></lb><figure id="id.020.01.1835.1.jpg" xlink:href="020/01/1835/1.jpg"></figure></s></p><p type="caption">

<s>Figura 41.<lb></lb>in direzion parallela al piano orizzontale BC fa risultarne, <lb></lb>da&#039;due composti insieme, il moto obliquo AC, ch&#039;è la dia­<lb></lb>gonale del rettangolo costruito. </s>

<s>Passando a farne poi la me­<lb></lb>ditata applicazione, vedeva Leonardo in quel vaso la Terra <lb></lb>ch&#039;è il recipiente di tutti i gravi cadenti; la sublimità del <lb></lb>foro di efflusso gli rappresentava l&#039;altezza della Torre, che si <lb></lb>muove in oriente sul suo piano terrestre, e la linea BC gli <lb></lb>misurava la distanza orientale che fa dal perpendicolo il punto, <lb></lb>dove và a battere il grave caduto dalla sommità dell&#039;edifizio. </s></p><p type="main">

<s>Supponiamo, così di speculazione in speculazione si con­<lb></lb>duceva l&#039;alta mente di Leonardo, che il grave non trovi in <lb></lb>C impedimento, nè in altro piano più profondo, ma libero <lb></lb>prosegua la sua discesa; qual sarà il termine e la linea del suo viaggio? </s>

<s>A <lb></lb>risolvere il nuovo arduo problema, che illuse il gran Galileo al ritentarne <lb></lb>che fece un secolo dopo la prova, il Nostro si chiarì bene della verità di un <lb></lb>principio meccanico, illustrato verso la metà del secolo XVII dal Gassendo, <lb></lb>sotto il nome <emph type="italics"></emph>Del moto impresso dal motore traslato.<emph.end type="italics"></emph.end> Propostosi questo <lb></lb>principio da cui n&#039;ebbe a concludere che, rivolgendosi attorno la Terra con <lb></lb>gli elementi, la linea della libera caduta è sempre retta, riuscì il nostro Mate­<lb></lb>matico a dimostrare che la risultante di questo moto diretto e del circonvo­<lb></lb>lubile, a cui soggiace nello scendere il grave, è un&#039;elica, che parte dal prin­<lb></lb>cipio del moto stesso per ritornar continua al centro del mondo. </s></p><p type="main">

<s>Tanta parte di scienza pellegrina, e che si direbbe davvero una crea­<lb></lb>zione da chi non considera in Leonardo il discepolo di Archimede, è come <lb></lb>lampo di viva luce riflessa da questa Nota: <emph type="italics"></emph>“ Del moto della freccia so-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.1835.2.jpg" xlink:href="020/01/1835/2.jpg"></figure></s></p><p type="caption">

<s>Figura 42.<lb></lb><emph type="italics"></emph>spinta dall&#039;arco.<emph.end type="italics"></emph.end> La freccia tratta dal centro <lb></lb>del mondo alla suprema parte degli elementi <lb></lb>s&#039;alzerà e discenderà per una medesima linea <lb></lb>retta, ancorchè li elementi sieno in moto circon­<lb></lb>volubile intorno al centro degli elementi. </s>

<s>— La <lb></lb>gravità, che per li circonvolubili elementi di­<lb></lb>scende, sempre ha il suo moto per la rettitudine <lb></lb>di quella linea, che dal principio del moto al <lb></lb>centro del mondo si estende. </s>

<s>— Le otto linee <lb></lb>(fig. </s>

<s>42) colle otto divisioni, nelle quali esse son <lb></lb>compartite, hanno a dimostrare una sola linea, <lb></lb>e quella è retta, per la quale il peso, che per <lb></lb>li circonvolubili elementi dicende, passa per cia­<lb></lb>scuna delle otto sue partizioni, la qual linea al fine ritorna al medesimo sito <lb></lb>d&#039;onde ella si divise. </s>

<s>Il moto del grave ha dupla denominazione, cioè cur­<lb></lb>vità, elica rettilinea ” (Manuscr. </s>

<s>G cit., fol. </s>

<s>54). </s></p><p type="main">

<s>In un&#039;altra Nota descrive, più particolarmente così, il moto del grave, <pb xlink:href="020/01/1836.jpg" pagenum="79"></pb>a dimostrar che la linea passata da lui è veramente l&#039;elica sopraddetta: <lb></lb>“ Il mobile discendente dalla suprema parte della sfera del fuoco farà moto <lb></lb>retto infino alla Terra, ancora che li elementi fussero in continuo moto cir­<lb></lb>convolubile intorno al centro del mondo. </s>

<s>Provasi, e sia che il grave che <lb></lb>discende per li elementi sia B, (nella precedente figura XLII) che si mova <lb></lb>dall&#039;A, per discendere al centro del mondo M. </s>

<s>Dico che tal grave, ancora <lb></lb>che facci discenso curvo a modo di linea elica, che mai si svierà dal suo <lb></lb>discenso rettilineo, il quale è in continuo processo infra il loco, d&#039;onde si <lb></lb>divise, al centro del mondo, perchè se si partì dal punto A e discese al B, <lb></lb>nel tempo che discese in B e fu portato in D, il sito della A è scivolato <lb></lb>in C, e così D mobile si trova nella rettitudine che s&#039;estende infra C e il <lb></lb>centro del mondo M. </s>

<s>Se il mobile discende dal D all&#039;F, C principio del <lb></lb>moto, in nel medesimo tempo, si move dal C all&#039;E; e se F discende in H, <lb></lb>e&#039;si volta in G, e così in ventiquattr&#039;ore il mobile discende alla Terra sotto <lb></lb>il loco d&#039;onde prima si divise, e tal moto è composto. </s>

<s>Se il mobile discende <lb></lb>dalla suprema all&#039;infima parte degli elementi in ventiquattr&#039;ore, il moto suo <lb></lb>fia composto di retto e curvo.. Retto dico, perchè mai non si svierà dalla <lb></lb>linea brevissima, che s&#039;estende dal loco d&#039;onde si divise al centro degli ele­<lb></lb>menti, e si fermerà nello stremo infimo di tal rettitudine, la qual sempre <lb></lb>sta per zenit sotto il loco, d&#039;onde tal mobile si divise. </s>

<s>E tal moto in sè è <lb></lb>curvo con tutte quante le parti della linea, e per conseguenza è al fine curvo <lb></lb>con tutta la linea. </s>

<s>E di qui nasce che il sasso gettato dalla Torre non per­<lb></lb>cota nel lato d&#039;essa Torre, prima che in terra ” (ivi, fol. </s>

<s>55). </s></p><p type="main">

<s>Accennammo di sopra che nelle nuove Istituzioni della Scienza mecca­<lb></lb>nica Galileo concluse dal principio della composizione dei moti la natura <lb></lb>della curva, che descriverebbe il mobile menato in volta dalla rotazion della <lb></lb>Terra, mentre egli tende a scendere al centro con velocità accelerata, e disse <lb></lb>che probabilmente doveva quella tal curva essere un mezzo cerchio. </s>

<s>L&#039;er­<lb></lb>rore incredibile in tale e tanto Maestro levò un grande scandolo nel mondo <lb></lb>della scienza, a rimediare al quale non giovarono nè le scuse dello stesso <lb></lb>Galileo, nè lo zelo de&#039;suoi discepoli, che fecero per verità peggio che mai a <lb></lb>dire essere quelle cose, nel II dialogo dei Due massimi sistemi, state scritte <lb></lb>dall&#039;Autore per celia. </s>

<s>Dovevano invece confessare che l&#039;origine di un tale er­<lb></lb>rore proveniva dall&#039;inesperienza del risolvere e del comporre insieme due moti, <lb></lb>per cui non potè Galileo stesso accorgersi della fallacia ascosta nell&#039;ammetter <lb></lb>che resultasse in mezzo cerchio un moto misto del circolare e del retto. </s></p><p type="main">

<s>Se dunque l&#039;Autore delle sopra recate Note manoscritte potè, in un se­<lb></lb>colo in cui si disse che la Meccanica non era nata, restar di tanto superiore <lb></lb>al gran Galileo nel rappresentar per un elice la linea descritta dai corpi <lb></lb>gravi cadenti, va principalmente di tutto ciò debitore a quella perizia, che <lb></lb>egli ebbe nel trattar la regola della diagonale ne&#039;rettangoli, e nei paralle­<lb></lb>logrammi. </s>

<s>Nasce altresì dall&#039;uso di questa regola la superiorità che ottenne <lb></lb>il Matematico di Vinci sopra quello di Arcetri, non solo per rispetto alla <lb></lb>proposizion principale di che si tratta, ma agli stessi corollarii di lei. </s></p><pb xlink:href="020/01/1837.jpg" pagenum="80"></pb><p type="main">

<s>Galileo, dal moversi realmente in circolo il grave che scende, ne con­<lb></lb>cluse il paradosso che l&#039;accelerazione, veduta farsi da lui in linea retta, non <lb></lb>era che un&#039;illusione, mentre Leonardo, con grande maraviglia di chi vi pensa, <lb></lb>argomentò da quel moto la ragione di un fatto, che veniva inaspettatamente <lb></lb>a confermar le ragionevoli congetture della rotazione terrestre. </s>

<s>Tanto poi <lb></lb>più cresce una tal maraviglia in chi rammemora i lunghi e faticosi progressi <lb></lb>fatti dalla scienza, prima di giungere a scoprir quella deviazione orientale <lb></lb>nella caduta dei gravi, che s&#039;era già rivelata da due secoli e mezzo alle teo­<lb></lb>rie e alle esperienze di Leonardo da Vinci. </s></p><p type="main">

<s>Andate quelle esperienze e quelle teorie in dimenticanza, con la mag­<lb></lb>gior parte delle tradizioni scientifiche del secolo XVI, s&#039;incominciarono sotto <lb></lb>false apparenze a rivelar di nuovo, poco prima che giungesse alla sua metà <lb></lb>il secolo appresso, alle osservazioni, che sul cader dei gravi dalla sommità <lb></lb>del campanile di Pisa, instituì nel 1641 Vincenzio Renieri. </s>

<s>Accortosi che, <lb></lb>accelerandosi il moto, le sfere gravi incominciavano a non scender più a <lb></lb>perpendicolo, attribuì l&#039;effetto alla resistenza del mezzo (Alb. </s>

<s>X, 410, 11), <lb></lb>di che apertosene con Galileo gli fu da lui risposto osservasse meglio, perchè <lb></lb>forse quel deviar del grave dal suo cadente era una illusione (ivi, pag. </s>

<s>144). <lb></lb>Nel 1679 in Inghilterra si verificò che il Renieri non s&#039;era punto illuso, ma <lb></lb>l&#039;Hook attribuì il fatto a una causa molto diversa. </s>

<s>Un secolo appresso il <lb></lb>D&#039;Alembert in Francia dimostrò che, rivolgendosi la Terra attorno, un corpo <lb></lb>lanciato verso il zenit non dovrebbe, tornando in giù, dare esattamente nel <lb></lb>punto da cui s&#039;era partito. </s>

<s>Fu la congettura confermata da G. B. </s>

<s>Gugliel­<lb></lb>mini nel 1791, facendo in Bologna cadere i gravi dalla cima della Garisenda, <lb></lb>ond&#039;ei raccolse dalle sue esperienze una tale celebrità, da non si potere egua­<lb></lb>gliare a quella, che l&#039;antico Leonardo sarebbesi meritata. </s></p><p type="main">

<s>Ha questo tratto di storia in sè tanto del maraviglioso, da dare, in cosa <lb></lb>sì remota dai sensi, giusto motivo a coloro, che attribuirono al precursore <lb></lb>dell&#039;Hook, del D&#039;Alembert e del Guglielmini il titolo di divino, ma noi di <lb></lb>tale esagerata eccellenza scoprimmo le cause naturali nelle antoriori prepa­<lb></lb>razioni, ch&#039;ebbe la scienza dell&#039;uomo ammirato, al mancar delle quali ci <lb></lb>hanno provato i fatti esser venuta meno ogni adorata divinità dell&#039;ingegno. </s>

<s><lb></lb>Que&#039;fatti, che ci hanno fin qui servito di prova all&#039;intento, concernevano la <lb></lb>legge della caduta dei gravi, dalla quale dipendendo la legge dei proietti <lb></lb>siam sicuri di trovare in ordine ad essa Leonardo non sorvolar coll&#039;ingegno <lb></lb>agli errori, che si commettevano dai Matematici de&#039;suoi tempi. </s></p><p type="main">

<s>Era il primo di quegli errori che la traiettoria andasse, per qualche <lb></lb>tratto dal suo principio, in linea retta, cosicchè, ne&#039;tiri di punto in bianco, <lb></lb>procedesse il proietto, appena uscito dall&#039;obice, per esattissima linea oriz­<lb></lb>zontale. </s>

<s>Conseguiva da ciò che dovesse il proietto stesso, per qualche tempo, <lb></lb>sottrarsi alla sua gravità naturale, e Leonardo, insieme con gli altri, non <lb></lb>dubitò di ammetter per vera una tale falsissima conclusione. </s>

<s>“ Ogni grave, <lb></lb>egli dice, che si muove per il sito della egualità, non pesa se non per la <lb></lb>linea del suo moto. </s>

<s>Provasi nella prima parte che fa il moto della pallotta <pb xlink:href="020/01/1838.jpg" pagenum="81"></pb>della bombarda, il quale moto è nel sito della egualità ” (Manuscr. </s>

<s>G cit., <lb></lb>fol. </s>

<s>77). Rallentandosi poi la prima concepita foga, il proietto comincia a <lb></lb>declinare per una linea curva, creduta anche dal Nostro simile a un&#039;arco <lb></lb>di cerchio, per ridursi finalmente alla linea verticale, come tutti i gravi na­<lb></lb>turalmente cadenti. </s>

<s>Volendo infatti insegnare a conoscere quanto sia tratto <lb></lb>il vino più alto o più basso dal rinchiuso vasello, dice che si riceva il vino <lb></lb>stesso “ quando è caduto fuori del vasello, e dopo che la sua curvazione <lb></lb>s&#039;è ridotta alquanto perpendicolare linea ” (Manuscr. </s>

<s>C cit., fol. </s>

<s>6 ad t.). </s></p><p type="main">

<s>La traiettoria dunque sarebbe per Leonardo una curva, che comincia e <lb></lb>termina per linea retta, ma la questione così, secondo le idee di que&#039;tempi, <lb></lb>dall&#039;Autor risoluta, riguardava piuttosto la teoria che la pratica, alla quale <lb></lb>principalmente importava di saper qual&#039;è, in essa traiettoria, il punto a cui <lb></lb>corrisponde la massima percossa. </s>

<s>Il Nostro determina giusto quel punto nel <lb></lb>mezzo del cammin retto, fatto per l&#039;aria dal corpo ponderoso. </s>

<s>“ Il mezzo <lb></lb>del retto cammino fatto da&#039;ponderosi corpi, che per violento moto discor­<lb></lb>rono per l&#039;aria, fia di maggiore potenza e di maggiore percussione nel suo <lb></lb>opposito contrasto, che nessun altra parte d&#039;esso corso ” (Manuscr. </s>

<s>A cit., <lb></lb>fol. </s>

<s>43 ad t.). </s></p><p type="main">

<s>La ragione di questo teorema è conclusa dai predominanti principii pe­<lb></lb>ripatetici, secondo i quali è l&#039;aria che ora seconda, ora impedisce il moto <lb></lb>al proietto: principii, che sostituiti alla virtù impressa e alla forza d&#039;iner­<lb></lb>zia, non però cessano di esser falsi, benchè Leonardo gl&#039;illustri con inge­<lb></lb>gnosi commenti. </s>

<s>Sia A (fig. </s>

<s>43) l&#039;obice, ABC il sito della egualità, o la per­<lb></lb>fetta linea orizzontale. </s>

<s>S&#039;ammette da Leonardo che il proietto prosegua in <lb></lb><figure id="id.020.01.1838.1.jpg" xlink:href="020/01/1838/1.jpg"></figure></s></p><p type="caption">

<s>Figura 43.<lb></lb>quella linea per un certo tratto <lb></lb>il suo viaggio, come sarebbe <lb></lb>infino in C, di dove poi inco­<lb></lb>mincia a declinare. </s>

<s>Il punto <lb></lb>B di mezzo del cammin retto <lb></lb>AC sarebbe quello della massima velocità, ciò che dall&#039;Autore così si dimo­<lb></lb>stra: “ La ragione di questo si è che, quando il peso si parte dalla forza <lb></lb>del suo motore, benchè essa dipartita sia in primo grado di sua potenza, <lb></lb>nientedimeno, trovando l&#039;aria senza moto, egli si trova in primo grado di <lb></lb>sua resistenza. </s>

<s>E benchè essa aria sia di maggiore somma di resistenza, che <lb></lb>non è la potenza del peso sospinto da lei, nondimeno, percotendone piccola <lb></lb>parte, viene in rimanente vincitore, onde la caccia dal suo sito, e nel cac­<lb></lb>ciarla impedisce alquanto la sua velocità Essendo adunque quest&#039;aria so­<lb></lb>spinta, ella ne sospinge e caccia dell&#039;altra, e genera dopo sè circolari mo­<lb></lb>vimenti, de&#039;quali il peso mosso in essa è sempre centro, a similitudine <lb></lb>de&#039;circoli fatti nell&#039;acqua, che si fanno centro del loco percosso dalla pie­<lb></lb>tra. </s>

<s>E così, cacciando l&#039;uno circolo l&#039;altro, l&#039;aria, ch&#039;è dinanzi al suo mo­<lb></lb>tore tutta per quella linea, è preparata al movimento, il quale tanto più cre­<lb></lb>sce, quanto più s&#039;appressa il peso che la caccia. </s>

<s>Onde, trovando esso peso <lb></lb>men resistenzia d&#039;aria, con più velocità raddoppia il suo corso, a similitudine <pb xlink:href="020/01/1839.jpg" pagenum="82"></pb>della barca tirata per l&#039;acqua, la quale si muove con difficoltà nel primo <lb></lb>moto, benchè il suo motore sia nella più potente forza. </s>

<s>E quando essa acqua <lb></lb>con arcate onde comincia a pigliare moto, la barca seguitando esso moto <lb></lb>trova poca resistenza, onde si move con più facilità. </s>

<s>Similmente, la ballotta <lb></lb>trovando poca resistenzia, seguita il principiato corso, infino a tanto che, <lb></lb>abbandonata alquanto dalla prima forza, comincia a debolire e declinare, <lb></lb>onde, mutando corso, la preparata fuga fattali dinanzi dalla fuggente aria, <lb></lb>non li servono più, e quanto più declina, più trova varia resistenzia d&#039;aria, <lb></lb>e più si tarda, insino a tanto che, ripigliando il moto naturale, si rifà di <lb></lb>più velocità. </s>

<s>La barca torcendosi ritarda ancora lei suo corso. </s>

<s>Ora io con­<lb></lb>chiuggo, per la ragione della VIII proposizione, che quella parte del moto, <lb></lb>che si trova tra la prima resistenzia dell&#039;aria, e il principio della sua de­<lb></lb>clinazione; sia di maggiore potenzia, e che questo è il mezzo del cammino, <lb></lb>il quale è fatto per l&#039;aria con retta e diritta linea ” (ivi, fol. </s>

<s>43 ad t.) </s></p><p type="main">

<s>Di qui, e dalle cose sopra esposte, raccogliesi che Leonardo, nel trattar <lb></lb>de&#039;proietti e della caduta naturale dei gravi, non ne seppe troppo più avanti <lb></lb>de&#039;suoi contemporanei, i quali lasciarono la scienza a quel punto, a cui <lb></lb>l&#039;aveva ridotta Aristotile ne&#039;suoi insegnamenti. </s>

<s>Questo avvenne dall&#039;altra <lb></lb>parte per logica necessità, non potendosi concluder nulla dal falso, com&#039;è <lb></lb>impossibile il progredire colà dove manchi fermezza al piè mosso. </s>

<s>Nella Mec­<lb></lb>canica peripatetica però, misto al falso, si conteneva molta parte del vero, <lb></lb>da cui seppe il Nostro levarsi sublime con l&#039;ala del matematico ingegno. </s>

<s>A <lb></lb>confermare il qual fatto, così importante alla storia scientifica del secolo XVI, <lb></lb>giova aggiungere agli esempii sopra recati alcuni altri concernenti la resi­<lb></lb>stenza dei corpi solidi allo spezzarsi. </s></p><p type="main">

<s>Galileo si vantò di avere, intorno a questo soggetto, istituita una scienza <lb></lb>nuova, la quale non è però altro che una più larga, e più corretta esplica­<lb></lb>zione di ciò che si propose di risolvere Aristotile qua e là nelle sue varie <lb></lb>Questioni. </s>

<s>Nella XXV, applicandosi dal Filosofo la teoria del vette, si rende <lb></lb>la ragione del perchè tanto più facilmente si tribbi un legno, appoggiandovi <lb></lb>il ginocchio nel mezzo, quanto le mani, che lo tengono per le due estremità, <lb></lb>son più remote dallo stesso ginocchio, e Leonardo, passando dalla volgare <lb></lb>curiosità dell&#039;esempio a cercar l&#039;utile che se ne potrebbe ricavar per le co­<lb></lb>struzioni, “ trovo, egli dice, che uno peso posto sopra una asse, sospesa <lb></lb>infra due pilastri, fȧ calare in mezzo detta asse uno braccio: l&#039;asse è quattro <lb></lb>braccia, e il peso è lontano da uno pilastro braccia due. </s>

<s>Se tu fai che detto <lb></lb>peso non sia distante più d&#039;uno braccio, quanto calerà detta asse sotto il <lb></lb>soprapposto peso? </s>

<s>“ (Manuscr. </s>

<s>A ci., fol. </s>

<s>48). E sullo stesso argomento, in <lb></lb>un&#039;altra Nota, si legge: “ Fa esperienza: se uno legno sottile, sospeso per <lb></lb>traverso sopra due sostentacoli ne&#039;sua estremi, regge dieci libbre; che reg­<lb></lb>gerà una trave di medesima proporzione? </s>

<s>e guarda se la regola delle tre <lb></lb>cose ti serve, perchè la sperienza fa buona regola ” (ivi, fol. </s>

<s>33). </s></p><p type="main">

<s>L&#039;aristotelica Questione XXVI intende a rispondere al perchè tanto son <lb></lb>più fragili i legni, quanto sono più lunghi, e anche la ragion di ciò, così <pb xlink:href="020/01/1840.jpg" pagenum="83"></pb>dal Filosofo come da Galileo, concludesi dalla teoria della leva, sull&#039;estre­<lb></lb>mità della quale tanto più s&#039;aggrava il peso, quant&#039;ella va sempre più lunga. </s>

<s><lb></lb>Dietro i quali statici principii Leonardo pure formula i suoi teoremi, e ri­<lb></lb>sponde ai proposti quesiti. </s>

<s>“ Se una lancia di venti braccia regge dieci lib­<lb></lb>bre, uno braccio d&#039;essa, della medesima grossezza, ne reggerà dugento, im­<lb></lb>perocchè tanto quanto l&#039;asta corta entra nella lunga, tante volte sostiene più <lb></lb>peso che la lunga ” (ivi, fol. </s>

<s>49 ad t). — “ Se una lancia lunga cento sue <lb></lb>grossezze regge venti libbre, che reggerà una di cinque grossezze della me­<lb></lb>desima asta? </s>

<s>Tanto quanto cinque entra in cento, tanto l&#039;asta di cento gros­<lb></lb>sezze reggerà men peso, che l&#039;asta di cinque grossezze ” (ivi, fol. </s>

<s>48 ad t.). </s></p><p type="main">

<s>Nel trattato meccanico delle resistenze de&#039;solidi allo spezzarsi una que­<lb></lb>stione manca in Aristotile, ed è quella che riguarda le funi, intorno a che <lb></lb>fu veramente Leonardo il primo a darne una scienza nuova, che in molte <lb></lb>parti si riscontra col vero, lungo tempo dopo insegnato da Galileo. </s>

<s>Nel I dia­<lb></lb>logo delle Due nuove scienze si dimostra che la tegnenza dei canapi dipende <lb></lb>dallo strignimento delle tortuosità, per cui si collegano le separate fila tanto <lb></lb>tenacemente “ che di non molti giunchi, neanco molto lunghi, sicchè poche <lb></lb>sono le spire, con le quali tra di loro s&#039;intrecciano; si compongono robu­<lb></lb>stissime funi ” (Alb. </s>

<s>XIII, 14). Dagli effetti medesimi della quale artificiosa <lb></lb>struttura stabilisce Leonardo la seguente legge sperimentale: “ Trovo che <lb></lb>tanto quanto elleno (le funi) scemano nell&#039;avvoltarsi, tanto sono più potenti <lb></lb>che prima ” (Manuscr. </s>

<s>A cit., fol. </s>

<s>49). </s></p><p type="main">

<s>Un inganno in questo proposito si reputava da Galileo che fosse prima <lb></lb>di lui stato a tutti comune, e consisteva nel credere che tanto fossero più <lb></lb>resistenti le funi, quanto sono più corte. </s>

<s>Fu anche Leonardo un tempo di <lb></lb>questa falsa opinione, come da alcune sue Note chiaramente apparisce. </s>

<s>In <lb></lb>una di esse così domanda: “ Se una corda d&#039;uno braccio regge cento lib­<lb></lb>bre, quante libbre reggerà una corda della medesima grossezza, che sia lunga <lb></lb>cento braccia? </s>

<s>” (ivi, fol. </s>

<s>5). La risposta al quesito è data così dall&#039;Autore <lb></lb>in un&#039;altra Nota: “ Tanto quanto la minor lunghezza della corda entra nella <lb></lb>maggiore, tanto è più forte ch&#039;essa maggiore ” (ivi, fol. </s>

<s>49). Il galileiano <lb></lb>Salviati dimostrò a Simplicio che questa proposizione era <emph type="italics"></emph>falsa non che <lb></lb>impossibile<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 121), ma Leonardo s&#039;avvide poi da sè medesimo del­<lb></lb>l&#039;inganno, senz&#039;altro maestro che la propria ragione e la propria esperienza, <lb></lb>dalle quali ebbe poi a concluderne, come Galileo e come l&#039;Aggiunti, che <lb></lb>“ ogni gravità sospesa è tutta per tutta la lunghezza della corda, che la so­<lb></lb>stiene, ed è tutta in ogni parte di quella ” (Manuscr. </s>

<s>E cit., fol 32 ad t.). </s></p><p type="main">

<s>Un&#039;altra questione relativa alle resistenze, trascurata da Aristotile e da <lb></lb>Galileo, fu trattata da Leonardo, il quale solo potè conoscerne l&#039;importanza, <lb></lb>da giungere alle conclusioni medesime de&#039;Meccanici moderni. </s>

<s>La questione <lb></lb>riguarda quella specie di resistenza, oppostà al libero moto dagli attriti, che <lb></lb>nascono tra la superfice del mobile, e quella del piano che lo sostiene, così <lb></lb>raccogliendo in Nota il frutto delle diligenti esperienze: “ Sia A (fig. </s>

<s>44) <lb></lb>il corpo confregato, ovvero strascinato dal Motore B; CD sia il piano pulito, <pb xlink:href="020/01/1841.jpg" pagenum="84"></pb>dove esso corpo è confregato. </s>

<s>Sono le confregazioni de&#039;corpi di quattro sorte, <lb></lb>delle quali la prima si è, quando due corpi sono puliti e piani, come qui è <lb></lb><figure id="id.020.01.1841.1.jpg" xlink:href="020/01/1841/1.jpg"></figure></s></p><p type="caption">

<s>Figura 44.<lb></lb>proposto. </s>

<s>La seconda è, quando il corpo <lb></lb>strascinato è pulito, e il piano dove si <lb></lb>muove è aspro. </s>

<s>La terza è, quando il <lb></lb>corpo strascinato è aspro, e il piano dove <lb></lb>si muove è pulito. </s>

<s>Il quarto modo è quando <lb></lb>il corpo strascinato, e il piano dove si strascina, è aspro. </s>

<s>Dà l&#039;esperienza <lb></lb>che la cosa pulita, strascinata per pulito piano, resiste nel moto al suo mo­<lb></lb>tore con potenza eguale alla quarta parte della sua gravezza, e delle altre <lb></lb>seguenti due sorte tanto è a movere la cosa aspra sopra piano pulito, quanto <lb></lb>la cosa pulita sopra piano aspro. </s>

<s>La confregazione de&#039;corpi puliti mancherà <lb></lb>tanto più di resistenza e di peso, quanto il sito dove si muove è meno obli­<lb></lb>quo, essendo il motore sopra o sotto il suo mobile ” (Saggio del Codice atlan­<lb></lb>tico, Milano 1872, fol. </s>

<s>195). <lb></lb><figure id="id.020.01.1841.2.jpg" xlink:href="020/01/1841/2.jpg"></figure></s></p><p type="caption">

<s>Figura 45.</s></p><p type="main">

<s>Per determinar più particolarmente questa legge, <lb></lb>segnate in una quarta di cerchio varie obliquità di piani, <lb></lb>così delle resistenze varie incontrate da un corpo, che <lb></lb>lunghessi scenda, ne assegna Leonardo in numeri i gradi <lb></lb>proporzionali: “ N (fig. </s>

<s>45) dà di sè resistenza eguale <lb></lb>al quarto della sua gravità naturale; M resiste per l&#039;ot­<lb></lb>tavo della sua gravità; O resiste per un sedicesimo; P <lb></lb>non resiste, perchè in lui l&#039;O ha consumato la sua con­<lb></lb>fregazione. </s>

<s>Ma a dire meglio N resiste per un quarto del <lb></lb>suo peso naturale; M resiste per un mezzo quarto; O resiste per un quarto <lb></lb>del sopraddetto quarto; P non resiste nulla, perchè il quarto del quarto <lb></lb>sì consuma nel moto fatto dall&#039;O al P ” (Manuscr. </s>

<s>E cit., fol. </s>

<s>78 ad t.). </s></p><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il promesso Saggio dei varii trattati meccanici, gli elementi dei quali <lb></lb>si ritrovan senz&#039;ordine dispersi, e in frettolose Note accennati ne&#039;Manoscritti <lb></lb>di Leonardo da Vinci; è, secondo la nostra possibilità, e l&#039;intento della nostra <lb></lb>Storia, a questo punto compiuto. </s>

<s>I meditativi Lettori penseranno fra sè me­<lb></lb>desimi che, seguitando la Scienza del moto ad esser promossa dagli altri <lb></lb>Autori, che si dettero a coltivarla in quel tempo, con tal valido impulso <lb></lb>quale abbiamo fin qui veduto; avrebbe il primo instaurato edifizio vinto in <lb></lb>grandezza e in decoro quel nuovo, che disegnò la mente di Galileo. </s></p><p type="main">

<s>Il fatto è però che non furono que&#039;successivi progressi punto propor­<lb></lb>zionati all&#039;impulso, che pareva dover ricevere la scienza dall&#039;opera di Leo­<lb></lb>nardo, la quale opera ebbe veramente in sè qualche cosa di straordinario. </s>

<s><lb></lb>Le ragioni di ciò le abbiamo di sopra esposte nel nostro lungo discorso, e <pb xlink:href="020/01/1842.jpg" pagenum="85"></pb>si riducono in somma all&#039;aver saputo felicemente congiungere il singolaris­<lb></lb>simo uomo la scienza della scuola coll&#039;esperienza e col senno popolare. </s>

<s>Nei <lb></lb>contemporanei e nei successori si rivelò varia l&#039;indole dell&#039;ingegno, secondo <lb></lb>che varia era la mistura de&#039;due elementi educativi. </s>

<s>V&#039;erano da una parte <lb></lb>i soli addetti alla scuola, i quali giurando nelle parole del Maestro si ren­<lb></lb>devano perciò inabili a qualunque progresso, e v&#039;erano dall&#039;altra i disce­<lb></lb>poli della propria esperienza e del proprio senno, i quali essendo privi di <lb></lb>lettere mancavano del necessario strumento da comunicare alla scienza qua­<lb></lb>lunque progresso. </s>

<s>Partecipava anche Leonardo alle condizioni di questi tali, <lb></lb>e di quì avvenne che tanti documenti, i quali avrebbe potuto dare util­<lb></lb>mente agli studiosi, riuscirono in gran parte inefficaci. </s>

<s>Diciamo in gran parte, <lb></lb>perchè ci sembra inverosimile che tante speculazioni e tante scoperte si vo­<lb></lb>lessero tutte rimaner chiuse nella mente di chi le pensò, e ne&#039;volumi di chi <lb></lb>le scrisse. </s>

<s>Tanta fiamma non v&#039;era cenere che bastasse a tenerla sotto sè <lb></lb>d&#039;ogni canto sopita. </s></p><p type="main">

<s>Si diffondevano quelle speculazioni nelle stesse controversie, che l&#039;uomo <lb></lb>del senno popolare e delle proprie esperienze aveva così spesso co&#039;Filosofi <lb></lb>in libris, contro i quali scriveva: “ Me inventore disprezzano; quanto mag­<lb></lb>giormente loro, non inventori ma trombetti e recitatori delle altrui opere, <lb></lb>dovranno essere biasimati? </s>

<s>” (Libri, Histoire cit., T. III, pag. </s>

<s>238). Si dif­<lb></lb>fondevano quelle scoperte in quelli stessi, che n&#039;erano pubblici testimoni <lb></lb>di veduta, e che ne facevan uso ora nell&#039;esercizio delle arti, ora a spetta­<lb></lb>colo de&#039;curiosi, com&#039;altrove dicemmo essere avvenuto dell&#039;invenzione della <lb></lb>Camera oscura. </s>

<s>Nè all&#039;esperienza per esempio della caduta dei gravi dalle <lb></lb>sommità degli edifizii, eretti in mezzo a popolose città, potevano mancare <lb></lb>pubblici testimonii, oltre a quelli che davan mano allo sperimentatore, e <lb></lb>che, partecipando con lui alla scoperta del vero, si facevan gloria nel di­<lb></lb>vulgarlo. </s></p><p type="main">

<s>Essendo tali i precipui e più attivi, e si può dire i soli organi della <lb></lb>diffusione, molte parti di scienza speculata, e non intesa dai comunali inge­<lb></lb>gni, si dovette necessariamente arrestare ne&#039;manoscritti informi dell&#039;Autore, <lb></lb>cosicchè rimaneva l&#039;opera promotrice affidata tutta a que&#039;pochi, ch&#039;essendo <lb></lb>pure educati nelle scuole avevano dai libri imparato a pensar da sè, e sa­<lb></lb>pevan con l&#039;arte della parola significare agli altri i loro pensieri. </s>

<s>Delle scuole, <lb></lb>nelle quali insegnavansi le discipline, che formano il principale argomento <lb></lb>di questa storia, n&#039;erano come vedemmo due separate e distinte coi nomi <lb></lb>di Peripatetica e di Alessandrina, dell&#039;una delle quali sedeva autorevole e <lb></lb>solenne maestro Archimede, e dell&#039;altra un più prossimo promotore, Gio­<lb></lb>dano Nemorario. </s>

<s>Nella educazion popolare di Leonardo non si conosceva <lb></lb>distinzion di partito, saggiamente imbevendo, da qualunque fonte gli deri­<lb></lb>vasse, il vero, ma nelle menti educate sotto le più regolari discipline dei <lb></lb>Maestri era impossibile che facessero insieme consorzio Aristotile e Platone. </s>

<s><lb></lb>Come in tutti gli altri rami di scienza, così avvenne anche in questa del <lb></lb>moto che alcuni attesero a professarla coi metodi platonici, sull&#039;esempio di <pb xlink:href="020/01/1843.jpg" pagenum="86"></pb>Archimede, altri invece seguitando i prevalenti metodi peripatetici sull&#039;esem­<lb></lb>pio del Nemorario. </s>

<s>Fu il prevaler di questi una buona ventura ai progressi <lb></lb>della Statica in particolare, perchè i principii archimedei erano assai più ri­<lb></lb>stretti nella cerchia de&#039;loro impulsi, come il nostro discorso lo dimostrava <lb></lb>di sopra con le ragioni, e come ora si vedrà confermato dai fatti. </s></p><p type="main">

<s>Nella prima metà del secolo XVI ebbe la Statica due cultori insigni, e <lb></lb>che rappresentano in sè scolpitamente impressa la varia indole delle due <lb></lb>Scuole. </s>

<s>Francesco Maurolico proponeva nel trattato <emph type="italics"></emph>De momentis aequali­<lb></lb>bus<emph.end type="italics"></emph.end> i suoi teoremi, concludendoli dai principii archimedei, e Niccolò Tarta­<lb></lb>glia, nell&#039;VIII libro de&#039;suoi <emph type="italics"></emph>Quesiti,<emph.end type="italics"></emph.end> dimostrava sui principii del Nemorario <lb></lb>le generali proposizioni concernenti quella, ch&#039;egli chiama <emph type="italics"></emph>Scienzia dei pe­<lb></lb>sci.<emph.end type="italics"></emph.end> Vuole ora l&#039;ordine della nostra Storia, e l&#039;importanza del negletto ar­<lb></lb>gomento, che ci tratteniam brevemente in esaminar la varia opera data a <lb></lb>questi matematici studii dai due Promotori. </s></p><p type="main">

<s>De&#039;quattro libri di che si compone il maurolicano trattato <emph type="italics"></emph>De momentis <lb></lb>aequalibus,<emph.end type="italics"></emph.end> la dimostrazione de&#039;principii statici ricorre propriamente nel <lb></lb>primo. </s>

<s>È da notar che cominciò il nostro Autore a introdur nella scienza <lb></lb>la parola <emph type="italics"></emph>momento,<emph.end type="italics"></emph.end> consacrata poi dall&#039;uso generale nel significato così dal <lb></lb>Maurolico stesso definito: “ Momentum est vis ponderis a spatio quopiam <lb></lb>contra pendentis, unde ponderum aequalium momenta possunt esse inaequa­<lb></lb>lia, et e contra continget momentorum aequalium pondera esse inaequalia ” <lb></lb>(Archimedis monum. </s>

<s>ex traditione Maurolici, Panormi 1685, pag. </s>

<s>86). Ri­<lb></lb>corre altresì in questo trattato la prima dimostrazion matematica del prin­<lb></lb>cipio statico generale, che cioè i momenti stanno in ragion composta degli <lb></lb>spazii e dei pesi. </s></p><p type="main">

<s>La proposizione è conclusa con assai spedito processo dal principio ar­<lb></lb>chimedeo: “ Si gravia reciproca sint distantiis, quibus absunt centra ipso­<lb></lb>rum a puncto quodam in recta linea coniungente centra posito, punctum <lb></lb>illud est commune centrum gravium ” (ibid., 99), d&#039;onde per corollario de­<lb></lb>riva: “ gravia aeque ponderantia reciproca sunt spatiis, e quibus pendent ” <lb></lb>(ibid., 100). Da questi premessi teoremi, e dalla definizion de&#039;momenti, si <lb></lb>fa via l&#039;Autore a dimostrare che “ quam multiplex est pondus ponderis ad <lb></lb>idem spatium, tam multiplex est momentum momenti ” (102), da che imme­<lb></lb>diatamente concludonsi le due proposizioni, “ Gravia ab aequis spatiis pen­<lb></lb>dentia sunt momentis proportionalia; Gravium aequalium, ab inaequalibus <lb></lb>spatiis ponderantium, momenta sunt ad invicem sicut spatia ” (ibid., 103); <lb></lb>proposizioni, che compongonsi nell&#039;altra fondamentale, così formulata: “ Mo­<lb></lb>mentorum ratio componitur ex ratione ponderum, et ex ratione spatiorum, <lb></lb>a quibus gravia pendent ” (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Il manoscritto di quel primo libro, in cui s&#039;espongono ordinatamente <lb></lb>dall&#039;Autore le matematiche dimostrazioni di questi teoremi, è sottoscritto da <lb></lb>Castelbuono nel dì 6 di Dicembre, martedì, dell&#039;anno 1547, come parte in­<lb></lb>tegrante di un&#039;opera, che attendeva a raccogliere e ad illustrare i patrii mo­<lb></lb>numenti di scienza lasciati dall&#039;antico Archimede. </s>

<s>Rimase una tale opera <pb xlink:href="020/01/1844.jpg" pagenum="87"></pb>lungo tempo sconosciuta, fuor che agli eredi del defunto Autore, ultimo dei <lb></lb>quali fu il marchese di Campotondo. </s>

<s>Colto egli stesso e la sua famiglia da <lb></lb>lunghe infermità, gli sovveniva di cure mediche e di medicinali uno Spe­<lb></lb>ziale messinese, di nome Lorenzo di Tommaso, che, venuto finalmente a far <lb></lb>col marchese il conto del suo avere, n&#039;ebbe a ricevere volentieri in paga­<lb></lb>mento, amante della letteratura com&#039;egli era, i libri e i manoscritti del ce­<lb></lb>lebre Antenato. </s>

<s>Gli parvero fra questi da pregiare principalmente i <emph type="italics"></emph>Monu­<lb></lb>menti archimedei,<emph.end type="italics"></emph.end> e sovvenuto dal Senato messinese, a cui voleva dedicarli, <lb></lb>di moneta, e da Gian Alfonso Borelli, professore in quello studio, di consi­<lb></lb>gli, per quel che riguarda la scienza; dette mano nel 1670 a pubblicarli, <lb></lb>per le stampe di Paolo Bonacota. </s>

<s>Era nel 1672 giunta quasi a termine l&#039;im­<lb></lb>pressione, quando per i tumulti civili, costretti ad esular Lorenzo di Tom­<lb></lb>maso e il Borelli, s&#039;impossessò di quelle abbandonate carte il Regio Fisco, <lb></lb>che fece di Messina trasportarle a Palermo. </s>

<s>Quietati poi nel 1681 i tumulti, <lb></lb>e tornata la città sotto il giogo spagnuolo, un signor messinese, zelante delle <lb></lb>patrie lettere, sotto il nome di Cillenio Esperio, riscattò da Palermo le con­<lb></lb>fiscate carte de&#039;suoi concittadini, fra le quali ebbe a trovar, senza principio <lb></lb>e senza fine, i fogli gia stati impressi dal Bonacota. </s>

<s>Non sapendo ancora <lb></lb>nulla delle subite vicende, si rivolse a due padri gesuiti, dai quali ebbe in <lb></lb>risposta le notizie per noi riferite. </s>

<s>Premesse le lettere dei detti gesuiti al­<lb></lb>l&#039;Opera, ei la volle far reimprimere a sue spese, e reintegrare in Palermo, <lb></lb>di dove uscì nel 1685 col titolo di <emph type="italics"></emph>Archimedis siracusani monumenta omnia <lb></lb>mathematica, quae extant, ex traditione Francisci Maurolici.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Si raccoglie da queste notizie ch&#039;essendo venute le tradizioni mauroli­<lb></lb>cane alla luce, quand&#039;era giunta alla sua piena maturità la fiorente Scuola <lb></lb>galileiana, tornarono affatto inutili ai progressi della scienza, ond&#039;è che ri­<lb></lb>mase l&#039;opera promotrice tutta affidata ai pubblici documenti, che s&#039;ebbero <lb></lb>dal Tartaglia. </s>

<s>L&#039;opuscolo postumo <emph type="italics"></emph>De ponderositate,<emph.end type="italics"></emph.end> pubblicato nel 1565 in <lb></lb>Venezia da Curzio Troiano, è importante per la storia, perchè si rivela in <lb></lb>esso come l&#039;Autore tenesse dietro a commentare il Nemorario, con quel fer­<lb></lb>vente amor di discepolo, che il Maurolico stesso faceva intorno al suo grande <lb></lb>Siracusano, ma è superfluo come documento di scienza, perchè tutte le pro­<lb></lb>posizioni meccaniche quivi dimostrate trovano ne&#039;<emph type="italics"></emph>Quesiti e invenzioni,<emph.end type="italics"></emph.end> pub­<lb></lb>blicati dallo stesso Tartaglia nel 1546, amplissimo svolgimento. </s></p><p type="main">

<s>Nell&#039;ottavo di que&#039;libri s&#039;insegna, come si disse, la Scienza dei pesi, <lb></lb>e non è altro insomma che un trattatello di Statica generale, ordinatamente <lb></lb>condotto di proposizione in proposizione sui postulati del Nemorario, ai quali, <lb></lb>segnando nell&#039;antica scienza peripatetica un notabile progresso, s&#039;aggiunge <lb></lb>domandando “ ne sia concesso niun corpo esser grave in sè medesimo, cioè <lb></lb>l&#039;acqua nell&#039;acqua, il vino nel vino, l&#039;olio nell&#039;olio, l&#039;aere nell&#039;aere non <lb></lb>essere di alcuna gravità ” (Quesiti e invenzioni, Venezia 1546, fol. </s>

<s>85 t.). </s></p><p type="main">

<s>Che intenda veramente l&#039;Autore di mettersi egli a ordinare la scienza, <lb></lb>della quale i precedenti scrittori non avevano fatto altro che porre i prin­<lb></lb>cipii, lo dichiara così a don Diego Hurtado di Mendoza, interlocutore del dia-<pb xlink:href="020/01/1845.jpg" pagenum="88"></pb>logo, che aveva domandato qual costrutto si potrebbe cavare da tale scienza. <lb></lb></s>

<s>“ Li costrutti, risponde Niccolò, che di tale scienza si potriano cavare, saria <lb></lb>quasi impossibile a poterli a Vostra Signoria esprimere, ovver connumerare: <lb></lb>nondimeno io vi riferirò quelli, che per al presente a me sono manifesti. </s>

<s><lb></lb>E pertanto dico che, per vigore di tale scienza, egli è possibile a conoscere <lb></lb>e misurare con ragione la virtù e potenza di tutti quelli strumenti mecca­<lb></lb>nici, che dai nostri antichi sono stati ritrovati per augumentare la forza <lb></lb>dell&#039;uomo nell&#039;elevare, condurre, ovver spingere avanti ogni gran peso ” <lb></lb>(ivi, fol. </s>

<s>81). </s></p><p type="main">

<s>Or perchè la virtù e la potenza di tutti gli strumenti meccanici trova, <lb></lb>secondo Aristotile e il Nemorario, la ragion della sua misura nelle leggi del <lb></lb>Vette e della Libbra, il Tartaglia, fedel seguace delle dottrine di quegli Au­<lb></lb>tori, attende a stabilire i fondamenti alla Statica, dimostrando che s&#039;equili­<lb></lb>brano allora insieme la potenza e la resistenza quando son le forze recipro­<lb></lb>camente proporzionali alle distanze. </s>

<s>Incomincia perciò anch&#039;egli, come il <lb></lb>Maurolico, a stabilir la legge principalissima dei momenti, concludendola da <lb></lb>due proposizioni simili a quelle date dal Matematico siciliano. </s>

<s>L&#039;una dice: <lb></lb>“ La proporzione della grandezza dei corpi di un medesimo genere, e quella <lb></lb>della lor potenzia è una medesima ” (ivi, fol. </s>

<s>86); l&#039;altra: “ Se saranno <lb></lb>due corpi semplicemente eguali di gravità, ma ineguali per vigor del sito, <lb></lb>ovver posizione, la proporzione della loro potenzia e quella della lor velo­<lb></lb>cità necessariamente sarà una medesima ” (ivi, fol. </s>

<s>87). Di qui immediata­<lb></lb>mente ne conseguiva esser le potenze stesse in ragion composta delle velo­<lb></lb>cità e delle moli. </s>

<s>Ma perchè le velocità son proporzionali agli spazii, ossia <lb></lb>agli archi descritti dagli estremi bracci della Leva e della Bilancia, e gli archi <lb></lb>hanno la ragion medesima dei raggi, ossia delle distanze dal centro al punto <lb></lb>della sospensione dei pesi; ne conclude perciò il Tartaglia che le potenze <lb></lb>o le forze stanno in ragion composta dei pesi, e delle distanze delle loro <lb></lb>sospensioni dal centro dei movimenti. </s>

<s>Di qui è che, avendosi pesi eguali, i <lb></lb>loro momenti nella Bilancia sono come le lunghezze dei bracci da cui stanno <lb></lb>pendenti, ciò che vien dal Tartaglia stesso formulato nel modo seguente: <lb></lb>“ La proporzione della potenza de&#039;corpi semplici, eguali in gravità, ma ine­<lb></lb>guali per vigor del sito, ovver posizione, e quella della loro distanza dal <lb></lb>sparto, ovver centro della Libra, s&#039;approvano essere eguali ” (ivi, fol. </s>

<s>88). </s></p><p type="main">

<s>Se mantengonsi i pesi tuttavia eguali, e sopra più le braccia della Bi­<lb></lb>lancia sono eguali, concludesi da quel generale principio che i momenti o <lb></lb>le potenze son parimente per riuscire fra loro eguali, ciò che viene dimo­<lb></lb>strato dal Nostro nella V proposizione: “ Quando che la posizione di una <lb></lb>Libbra di braccia eguali sia nel sito della egualità, e nella estremità del­<lb></lb>l&#039;uno e l&#039;altro braccio vi sieno appesi corpi semplicemente eguali in gra­<lb></lb>vità, tal Libbra non si separerà dal sito della egualità, e se per caso la sia <lb></lb>da qualche altro peso, nell&#039;uno dei detti bracci imposto, separata dal sito <lb></lb>della egualità, ovvero con la mano; remosso quel tal peso ovver mano la <lb></lb>Libbra di necessità ritornerà al detto sito della egualità ” (ivi ad t.). </s></p><pb xlink:href="020/01/1846.jpg" pagenum="89"></pb><p type="main">

<s>Se mantenendosi tuttavia le distanze eguali i pesi son però differenti, <lb></lb>il maggiore avrà necessariamente maggior momento, e verrà perciò turbato <lb></lb>alla Libbra l&#039;equilibrio, come procede a dimostrare il Tartaglia nella sua <lb></lb>VI proposizione: “ Quando che la posizione di una Libbra di braccia eguali <lb></lb>sia nel sito della egualità, e che nella estremità dell&#039;uno e dell&#039;altro brac­<lb></lb>cio vi sieno appesi corpi semplicemente ineguali di gravità; dalla parte dove <lb></lb>sarà il più grave sarà forzata a declinare perfino alla linea della direzione ” <lb></lb>(ivi, fol. </s>

<s>90). Se al contrario i pesi sono eguali, ma le distanze dal centro <lb></lb>son differenti, la Bilancia traboccherà dalla parte del braccio maggiore. </s>

<s>“ Se <lb></lb>li bracci della Libbra saranno ineguali, e che nella estremità di cadauno di <lb></lb>quelli vi sieno appesi corpi semplicemente eguali in gravità, dalla parte del <lb></lb>più lungo braccio tal Libbra farà declinazione ” (ivi, fol. </s>

<s>92). </s></p><p type="main">

<s>Son tutte queste proposizioni dall&#039;Autore ordinate alla maggior con­<lb></lb>clusione finale, ed è: che essendo varie le distanze, e tutt&#039;insieme anche i <lb></lb>pesi, quelle stanno in reciproca proporzione di questi. </s>

<s>“ Se li bracci della <lb></lb>Libbra, così propriamente si esprime nella sua VIII proposizione il Tarta­<lb></lb>glia, saranno proporzionali alli pesi in quella imposti, talmente che nel brac­<lb></lb>cio più corto sia appeso il corpo più grave; quelli tai corpi ovver pesi sa­<lb></lb>ranno egualmente gravi, secondo tal posizione ovver sito ” (ivi ad t.): ciò <lb></lb>che dall&#039;altra parte è la version letterale della VIII del Nemorario: “ Si <lb></lb>fuerint brachia Librae proportionalia ponderibus appensorum, ita ut in bre­<lb></lb>viori gravius appendatur, aeque gravia erunt secundum situm ” (De pond. </s>

<s><lb></lb>cit., fol. </s>

<s>21). </s></p><p type="main">

<s>Risedendo in questa proposizione il principio fondamentale a tutta la <lb></lb>Statica, si sentiva perciò ragionevolmente il bisogno di dimostrarla con tutto <lb></lb>il rigor matematico, ciò che fu primo a fare come si disse Archimede nei <lb></lb>suoi Equiponderanti. </s>

<s>E qui giova osservare, a dichiarar meglio le parole, che <lb></lb>soggiungerà il Tartaglia dopo la sua dimostrazione, come nell&#039;Archimede <lb></lb>del Rivault e di altri le due proposizioni, dove si dimostra che, o commen­<lb></lb>surabili o incommensurabili che sieno le grandezze, si equilibrano allora che <lb></lb>stanno in ragion reciproca delle distanze; ricorrono in ordine numerate per <lb></lb>la VI e per la VII. </s>

<s>Altri compilatori però, escludendo da una tal dignità <lb></lb>negli Equiponderanti le due prime proposizioni, perchè non son veramente <lb></lb>altro che la petizione I e II; incominciavano piuttosto a numerarle da quella <lb></lb>che, secondo il Rivault, è la III, cosicchè la VI e la VII tornavano, in que­<lb></lb>sto più ragionevole ordinamento, la IV e la V. </s></p><p type="main">

<s>Ordinava così i teoremi al suo Archimede anche il Tartaglia, e perciò <lb></lb>nel compiacersi di aver data dimostrazione della legge, che governa il moto <lb></lb>delle Macchine, concludendola da principii diversi, ma non però punto men <lb></lb>matematicamente precisi di quelli del Siracusano; fa dir così a Don Diego <lb></lb>Mendoza che, dietro l&#039;enunciata proposizione VIII, era stato con gran pia­<lb></lb>cere ad ascoltarne il ragionamento: “ Questa è una assai bella proposizione, <lb></lb>ma el mi pare, se ben mi ricordo, che Archimede Siracusano ne ponga una <lb></lb>simile, ma el non mi pare che lui la dimostri per questo vostro modo. <pb xlink:href="020/01/1847.jpg" pagenum="90"></pb><emph type="italics"></emph>Niccolò.<emph.end type="italics"></emph.end> Vostra Signoria dice la verità, anzi di tal proposizione lui ne fa due <lb></lb>proposizioni, e queste sono la quarta e la quinta di quel Libro, dove tratta <lb></lb>delli centri delle cose gravi, e in effetto tai due proposizioni lui le dimostra <lb></lb>succintamente per li suoi principii da lui per avanti posti e dimostrati. </s>

<s>E <lb></lb>perchè tali suoi principii ovver argomenti non si convegneriano in questo <lb></lb>trattato, per esser materia alquanto diversa da quella, n&#039;è parso in questo <lb></lb>luoco di dimostrare tal proposizione con altri principii ovver argomenti, più <lb></lb>convenienti in questo loco ” (Quesiti e inv. </s>

<s>cit., fol. </s>

<s>93). </s></p><p type="main">

<s>Il Tartaglia, divulgando col suo commento la dimostrazione de&#039;princi­<lb></lb>pii statici co&#039;nuovi argomenti del Nemorario, apriva un più largo campo <lb></lb>alla scienza, e pareva perciò che dovessero gli studiosi mostrargliene la de­<lb></lb>bita riconoscenza. </s>

<s>Ma invece lo abbandonarono, entrati in sospetto della so­<lb></lb>lidità matematica di quel modo di argomentare, comparato con quello più <lb></lb>risoluto dell&#039;antico Archimede. </s>

<s>Concorreva a confermare il sospetto la nausea, <lb></lb>che s&#039;incominciava a sentire oramai delle dottrine peripatetiche, specialmente <lb></lb>da poi che il Benedetti era con la sua grande autorità venuto ad appor la <lb></lb>nota di falso al principio, da cui il Nemorario stesso e il Tartaglia avevano <lb></lb>conclusa la legge dei momenti. </s>

<s>Nel cap. </s>

<s>I delle <emph type="italics"></emph>Disputationes de quibusdam <lb></lb>placitis Aristotelis,<emph.end type="italics"></emph.end> dop&#039;aver confutato quel che nelle varie sue Opere il Fi­<lb></lb>losofo insegna relativamente ai corpi della medesima specie e figura, che <lb></lb>scendono con velocità proporzionali alle grandezze; così il Matematico vene­<lb></lb>ziano soggiunge: “ Alii quoque permulti eamdem opinionem retinuerunt, <lb></lb>et omnium postremus Nicolaus Tartalea, secunda propositione vigesimi noni <lb></lb>Quaesiti octavi libri, ubi profitetur se demonstratione probare hanc propo­<lb></lb>sitionem veram existere, neque videt quam magna resistentiarum sit diffe­<lb></lb>rentia, quae, tam ex diversitate figurarum quam ex magnitudinum varie­<lb></lb>tati, oriri potest, quas quidem diversitates non consideravit quidem ” (Liber <lb></lb>specul. </s>

<s>cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Il giudizio però, con buona pace del Benedetti, è inconsiderato, non fa­<lb></lb>cendo distinzione fra la libera caduta de&#039;corpi in mezzo all&#039;aria, e la loro <lb></lb>pressione sugli organi delle Macchine, nè avvertendo che, se la legge ari­<lb></lb>stotelica è falsa nei moti, è però verissima nei momenti. </s>

<s>Cosicchè la II pro­<lb></lb>posizione dell&#039;ottavo libro de&#039;<emph type="italics"></emph>Quesiti<emph.end type="italics"></emph.end> corrisponde perfettamente alla XXXVIII <lb></lb>del I libro <emph type="italics"></emph>De momentis aequilibus,<emph.end type="italics"></emph.end> che dice: “ Gravium aequalium ab <lb></lb>inaequalibus spatiis pendentium momenta sunt ad invicem sicut spatia ” <lb></lb>(editio cit., pag. </s>

<s>103): tanto essendo il dire col Tartaglia che le potenze son <lb></lb>proporzionali alle velocità, quanto dir col Maurolico che i momenti son pro­<lb></lb>porzionali agli spazii. </s>

<s>Che se si tien per verissimo questo, non si vede la <lb></lb>ragione perchè quello, come il Benedetti vuole, s&#039;abbia a imputare di falso. </s></p><p type="main">

<s>Comunque sia, fu della Dinamica il Tartaglia alquanto più benemerito <lb></lb>che della Statica, non avendo insomma intorno a questa fatt&#039;altro, che espli­<lb></lb>care e illustrare le proposizioni del Nemorario. </s>

<s>La teoria de&#039;proietti prin­<lb></lb>cipalmente si può dire che ha i principii da lui, perchè gli studii di Leo­<lb></lb>nardo da Vinci non si riducono a più, che a poche regole sperimentali. <pb xlink:href="020/01/1848.jpg" pagenum="91"></pb>L&#039;occasione, ch&#039;ebbe il nostro Bresciano di far della Ballistica una scienza <lb></lb>nuova, fu propriamente quella di rispondere al desiderio de&#039;principi de&#039;suoi <lb></lb>tempi e de&#039;capitani, per sola pratica conduttori in campo di quelle arti­<lb></lb>glierie, con che dovevano miseramente offendersi insieme, e desolarsi le città <lb></lb>italiane. </s></p><p type="main">

<s>Che fosse veramente tale quella detta occasione, ce lo attesta con le <lb></lb>sue proprie parole il Tartaglia, nell&#039;atto di dedicare a Francesco Maria <lb></lb>della Rovere, duca di Urbino, il libro, in cui distese ordinatamente il primo, <lb></lb>e affatto nuovo trattato della Scienza del moto. </s>

<s>In quella Lettera infatti, <lb></lb><emph type="italics"></emph>data in Venetia in le case nuove di S. Salvatore, alli XX di Dicem­<lb></lb>bre M. D. XXXVIII,<emph.end type="italics"></emph.end> così appunto scrive: “ Habitando in Verona l&#039;anno <lb></lb>M. D. XXXI, illustrissimo signor Duca, mi fu adimandato da un mio intimo <lb></lb>e cordiale amico, peritissimo bombardiere in Castel vecchio, uomo attem­<lb></lb>pato e copioso di molte virtù, il modo di mettere a segno uno pezzo di ar­<lb></lb>tiglieria al più che può tirare. </s>

<s>E abbenchè in tale arte io non avessi pratica <lb></lb>alcuna, perchè in vero, eccellentissimo Duca, giammai discargheti (scaricai) <lb></lb>artiglieria, archibuso, bombarda nè schioppo, nientedimeno, desideroso di <lb></lb>servir l&#039;amico, gli promisi di dargli in breve risoluta risposta. </s>

<s>E di poi che <lb></lb>ebbi ben masticata e ruminata tal materia, gli conclusi e dimostrai con ra­<lb></lb>gioni naturali e geometrice qualmente bisognava che la bocca del pezzo <lb></lb>stesse elevata talmente, che guardasse rettamente a 45 gradi sopra l&#039;oriz­<lb></lb>zonte ” e dice che si serviva per far ciò di una squadra, o come più pro­<lb></lb>priamente si direbbe da noi di un archipenzolo, colla quarta del cerchio <lb></lb>divisa in dodici gradi, insegnando che l&#039;obice tornerà giusto eretto a 45 gradi, <lb></lb>quando, posto il lato più lungo di essa squadra in dirittura con l&#039;asse del <lb></lb>cannone, il filo a piombo batterà sul mezzo del quadrante, ossia nel sesto <lb></lb>grado. </s>

<s>Poi prosegue così la narrazione: “ La qual conclusione a esso parve <lb></lb>aver qualche consonantia, pur circa ciò dubitava alquanto, parendo a lui che <lb></lb>tal pezzo guardasse troppo alto. </s>

<s>Il che procedeva per non esser capace delle <lb></lb>nostre ragioni, nè in le matematiche ben corroborato, nientedimeno con al­<lb></lb>cuni esperimenti particolari infine si verificò totalmente così essere. </s>

<s>” </s></p><p type="main">

<s>Prosegue poi con lo stesso tenore il Tartaglia a raccontare che questo <lb></lb>suo intimo amico, a cui egli aveva così insegnato a fare il tiro della mag­<lb></lb>gior volata, inclinando l&#039;asse dell&#039;obice a mezza squadra, ebbe una scom­<lb></lb>messa con un suo compagno d&#039;arme, il quale sosteneva che, a voler raggiun­<lb></lb>ger quella maggior volata, conveniva inclinare il pezzo due punti più basso. </s></p><p type="main">

<s>“ E sopra di questo, poi soggiunge il Tartaglia, fu deposta una certa <lb></lb>quantità di danari, e finalmente venneno alla sperienzia, e fu condotta una <lb></lb>colubrina da 20 a Santa Lucia in campagna, e cadauno di loro tirò secondo <lb></lb>la proposta, senza alcuno avvantaggio di polvere nè di palla, onde quello, <lb></lb>che tirò secondo la nostra determinazione, tirò di lontano, secondo che ne <lb></lb>fu referto, pertiche 1972 da piedi sei per pertica alla veronese; l&#039;altro, che <lb></lb>tirò li due punti più basso, tirò di lontano solamente pertiche 1872. Per la <lb></lb>qual cosa tutti li Bombardieri ed altri si verificarono della nostra determi-<pb xlink:href="020/01/1849.jpg" pagenum="92"></pb>nazione, che avanti di questa esperienzia stasevano (stavano) ambigui, imo, <lb></lb>la maggior parte avevano contraria opinione, parendoli che tal pezzo guar­<lb></lb>dasse troppo alto. </s>

<s>” </s></p><p type="main">

<s>Incoraggiato fervorosamente il Tartaglia in veder che alle sue divina­<lb></lb>zioni di matematica astratta rispondevano così bene i fatti sperimentati, volle <lb></lb>penetrare più addentro in questa materia, nella quale ebbe a scoprir nuove <lb></lb>altre cose non più pensate prima di lui. </s>

<s>“ Et incominciai (son sue proprie <lb></lb>parole) a raziocinare la specie dei moti, che in un corpo grave potesse acca­<lb></lb>dere, onde trovai quelle esser due: videlicet naturale et violento.... Da poi <lb></lb>investigai con ragion geometrica dimostrativa la qualità de&#039;transiti, ovver <lb></lb>moti violenti dei detti corpi gravi, secondo li varii modi che possono essere <lb></lb>eietti, ovver tirati violentemente per aere. </s>

<s>Oltra di questo mi certificai, con <lb></lb>ragioni geometrice dimostrative, qualmente tutti i tiri di ogni sorte di ar­<lb></lb>tiglierie erano fra loro simili, e conseguentemente proporzionali, e simil­<lb></lb>mente le distanzie loro.... Oltra di questo, con ragioni evidentissime, co­<lb></lb>nobbi qualmente un pezzo di artiglieria posseva per due diverse vie, ovvero <lb></lb>elevazioni, percotere in un medesimo luogo. </s>

<s>” </s></p><p type="main">

<s>Esamineremo più particolarmente a suo luogo ciò che trovasse la scienza <lb></lb>de&#039;proietti di vantaggiarsi in queste raziocinazioni e in queste esperienze <lb></lb>del Tartaglia, ma perchè fin d&#039;ora apparisca non tutte essere state una va­<lb></lb>nità della mente, e una illusione degli occhi, giova osservare come fu il <lb></lb>Nostro, il quale presentì la fallacia che s&#039;ascondeva ne&#039;giudizii comuni ai <lb></lb>suoi tempi, secondo i quali si riteneva potersi così furiosamente cacciare un <lb></lb>proietto, da farlo per qualche tratto del suo cammino procedere in linea <lb></lb>retta. </s>

<s>Udimmo di sopra Leonardo partecipare con tutti gli altri a questo <lb></lb>gravissimo errore, quando disse che, ne&#039;tiri di punto in bianco, il moto <lb></lb>della palla della bombarda è <emph type="italics"></emph>nel sito della egualità,<emph.end type="italics"></emph.end> ma il Tartaglia, giu­<lb></lb>stamente considerando che qualunque sia la furia del moto violento, non <lb></lb>può la cacciata palla mai sottrarsi agli stimoli del moto naturale, consentì <lb></lb>che si dicesse impropriamente retta quella, che, sebbene insensibilmente, <lb></lb>conveniva che in ogni modo procedesse per linea curva. </s></p><p type="main">

<s>Partendosi l&#039;Autore della <emph type="italics"></emph>Scientia nuova<emph.end type="italics"></emph.end> da questo verissimo princi­<lb></lb>pio, si sarebbe con buoni auspicii incamminato verso la scoperta delle traiet­<lb></lb>torie, ma le ignorate leggi dei moti naturali ebbero infelicemente ad arre­<lb></lb>star que&#039;progressi. </s>

<s>Ammise anch&#039;egli, come tutti gli altri, che il velocitarsi <lb></lb>dei gravi cadenti fosse dovuto alle attrazioni, e alle impulsioni del mezzo, e <lb></lb>come tutti gli altri pure, argomentando dagli effetti della percossa, ne con­<lb></lb>cluse che le velocità delle cadute son proporzionali agli spazii. </s></p><p type="main">

<s>I progressi insomma, che fece per opera del Tartaglia la Dinamica, si <lb></lb>riducono principalmente ai proietti, intorno ai quali iniziò veramente il no­<lb></lb>stro Bresciano una Scienza nuova. </s>

<s>Le altre parti della Meccanica non eb­<lb></lb>bero da lui che assai scarsa cultura, e da non si pararagonar certamente <lb></lb>con quella di Leonardo da Vinci, mostratasi al nostro esame così larga ed <lb></lb>intensa Non fu una tal larghezza imitata forse a que&#039;tempi meglio che dal <pb xlink:href="020/01/1850.jpg" pagenum="93"></pb>Cardano, per i varii trattati meccanici del quale è notabile che si trovin ri­<lb></lb>dotte nel filo delle correnti tradizioni molte dottrine, rimaste sorrenate ne&#039;Ma­<lb></lb>noscritti vinciani. </s>

<s>E perchè il fatto è importante a persuader coloro, i quali <lb></lb>si credono che il grande Artista si ritrovasse in mezzo al fiume della scienza <lb></lb>senza nulla ricever dall&#039;onda che viene, e senza dar nulla all&#039;onda che và, <lb></lb>è bene che si confermi con qualche esempio. </s></p><p type="main">

<s>Per primo de&#039;quali ci piace addur quello della elasticità dell&#039;aria, e <lb></lb>della sua efficacia sulla caduta dei gravi. </s>

<s>Nella scarsa nostra erudizione sto­<lb></lb>rica non abbiam saputo, di quel fatto fisico che tanto dette a dubitare ai <lb></lb>Saggi, trovar altro documento anteriore a quello portoci da una delle sopra <lb></lb>trascritte Note di Leonardo, nella quale si diceva non si poter dare scienza <lb></lb>del moto dei gravi, <emph type="italics"></emph>se prima non si dà la quantità della condensazione <lb></lb>dell&#039;aria, percossa da qualunque mobile, la qual condensazione sarà di <lb></lb>maggiore o minore densità, secondo la maggiore o minore velocità, che <lb></lb>ha in sè il mobile che la preme.<emph.end type="italics"></emph.end> Or vien da un tal chiarissimo documento <lb></lb>provocata la domanda, se veramente fu Leonardo il primo a scoprire il fatto <lb></lb>del condensamento dell&#039;aria, o s&#039;ei la ricevè piuttosto dalle tradizioni scien­<lb></lb>tifiche de&#039;suoi tempi. </s>

<s>Per risposta di che può opportunamente osservarsi <lb></lb>come il Cardano, a cui si può credere che non fossero mai venuti sott&#039;oc­<lb></lb>chio i manoscritti vinciani, applica, nella proposizione CX del suo <emph type="italics"></emph>Opus no­<lb></lb>vum,<emph.end type="italics"></emph.end> il fatto del condensarsi l&#039;aria a proporzion che il corpo, con più o <lb></lb>men grayezza cadendo, sotto di sè la preme, per conciliare il falso princi­<lb></lb>pio aristotelico con gli apparenti resultati dell&#039;esperienza. </s></p><p type="main">

<s>Nel II libro <emph type="italics"></emph>De subtilitate,<emph.end type="italics"></emph.end> entrando l&#039;Autore, a proposito degli elementi, <lb></lb>a trattare dell&#039;aria, riferisce il detto di coloro che, reputandola lieve in sè <lb></lb>stessa, ne concludevano perciò che vien mossa dalla sua propria forma, per <lb></lb>cui, usciti dalla man del motore, si vede conservarsi tuttavia il moto im­<lb></lb>presso ai proietti. </s>

<s>Intorno a che soggiunge esser quattro le opinioni “ quas <lb></lb>nullus expositor intellexit, et maxime Aristotelis, quem adeo iactant opinio­<lb></lb>nem ” (Lugduni 1580, pag. </s>

<s>90). La quale opinione aristotelica, passando il <lb></lb>Cardano in quarto luogo ad esporre, dice che consisteva nell&#039;ammetter la <lb></lb>comunicazione e la partecipazion del moto al proietto, dall&#039;ondoso moto aereo <lb></lb>concentrico al proiciente, il qual moto, estinguendosi a poco a poco nel diffon­<lb></lb>dersi sempre più al largo, abbandona finalmente il mobile nella sua quiete. </s>

<s><lb></lb>Dopo che torna a ripetere non aver nessuno prima di lui saputo intendere <lb></lb>il testo aristotelico, inteso già benissimo, come vedemmo, ed esposto in que­<lb></lb>sta medesima cardanica sentenza da Leonardo. </s></p><p type="main">

<s>Un altro esempio del consentimento che passa fra le idee dei due ce­<lb></lb>lebri uomini, da che ragionevolmente per noi se ne conclude dover avere <lb></lb>avute in qualche modo comuni le tradizioni, ci si porge dal moto dei corpi <lb></lb>pendoli, intorno ai quali udimmo dianzi ragionar l&#039;Autore delle Note ma­<lb></lb>noscritte così, come fa l&#039;Autore del II libro <emph type="italics"></emph>De subtilitate:<emph.end type="italics"></emph.end> “ At vero, cum <lb></lb>impellitur, tanta ferme vi redit ad medium, quanta ab illo depulsum est. </s>

<s><lb></lb>Igitur cum ea vi iam depulsum sit a medio, gratia exempli, per cubiti spa-<pb xlink:href="020/01/1851.jpg" pagenum="94"></pb>tium, tantumdem descendere in contrariam partem necessarium erit, atque <lb></lb>ita continuo ac alternato reditu tardissime conquiescere ” (ibid., pag. </s>

<s>97). </s></p><p type="main">

<s>Chi poi volesse facilmente persuadersi che il Cardano non lasciò forse <lb></lb>inesplorata nessuna parte di quell&#039;ampio soggetto, che la Meccanica presen­<lb></lb>tava alle speculazioni di Leonardo, non ha a far altro che svolgere le pagine <lb></lb>dell&#039;<emph type="italics"></emph>Opus novum,<emph.end type="italics"></emph.end> dove della Statica e della Dinamica si trovano proposti e <lb></lb>dimostrati i più importanti teoremi. </s>

<s>Il Filosofo non procede in tutti sicuro, <lb></lb>come l&#039;Artista, per le ragioni, altre volte accennate, dell&#039;aver diffidato o del <lb></lb>non essersi ben chiarita in mente la regola di risolvere i moti, a che ag­<lb></lb>giungevasi il prevaler nella mente di lui le speculate teorie ai fatti speri­<lb></lb>mentati. </s>

<s>I principali esempii di quelle incertezze, che poi condussero anche <lb></lb>il Cardano nell&#039;errore comune, si possono desumere dalle proposizioni LXXII <lb></lb>e CXVIII, dove, attendendo l&#039;Autore a ricercare in qual proporzione stanno <lb></lb>i pesi scendenti sopra varie declività di piani, e le percosse sopra varie obli­<lb></lb>quità di pareti, riduce quelle stesse proporzioni agli angoli, piuttosto che ai <lb></lb>seni. </s>

<s>La fallacia del ragionamento di lui consisteva nel concluder ch&#039;essendo <lb></lb>per l&#039;orizzontale il peso e la percossa nulli, e per il perpendicolo quello to­<lb></lb>tale, e questa del massimo effetto; si compartissero giustamente secondo le <lb></lb>varie declività i gradi di mezzo. </s></p><p type="main">

<s>Il Cardano aveva, insieme con gli altri usciti dalle pubbliche scuole, <lb></lb>più fiducia nelle filosofiche virtù del ragionamento, che nell&#039;esperienza, ma <lb></lb>Leonardo, il quale la pensava altrimenti, ritrovò nell&#039;esperienza stessa, come <lb></lb>vedemmo, la sua salvezza. </s>

<s>Forse non ebbe nè anch&#039;esso Cardano, in propo­<lb></lb>sito delle percosse, a trascurar di ricorrere ai fatti, i quali non valsero nulla­<lb></lb>dimeno a farglisi benefici rivelatori del vero, per un inganno che nascon­<lb></lb>devasi sotto. </s>

<s>Consisteva quell&#039;inganno nel deviar che fa il mobile dalla sua <lb></lb>giusta dirittura l&#039;aria, dalla foga di lui innanzi innanzi compressa; sottilissimo <lb></lb>inganno possibile solo a scoprirsi dalla sagacia sperimentale di Vincenzio <lb></lb>lìenieri, e un secolo prima da quella di Leonardo da Vinci. </s>

<s>“ La percussione, <lb></lb>egli dice, d&#039;ogni grave sferico non farà cicatrice che abbian proporzione in <lb></lb>fra loro, qual&#039;è quella dell&#039;obliquità de&#039;siti dov&#039;essi percotono. </s>

<s>— Quel che <lb></lb>si propone non mancherebbe merito che non fussi integralmente confermo <lb></lb>dall&#039;esperienza, se non fosse la fissa condensazione dell&#039;aria sospinta dal fu­<lb></lb>rore della pallotta, la quale, non sendo in sè veloce come il moto fatto da tal <lb></lb>motore che la caccia, si viene a condensare, e tanto più si condensa, quanto <lb></lb>è più cacciata, e per questo accade che percote poi tale pallotta con linea, <lb></lb>che non sia centrale ” (Ravaisson-Mollien, Manuscr. </s>

<s>L, Paris 1890, fol. </s>

<s>44). </s></p><p type="main">

<s>La inferiorità nell&#039;arte sperimentale, a paragone di quella che appari­<lb></lb>sce così sottile in questa Nota di Leonardo, si rivela forse più manifesta nel <lb></lb>fatto della libera caduta dei gravi, intorno a che il Cardano, nella proposi­<lb></lb>zione XIII, non sa far altro che commentare le più volgari dottrine, dimo­<lb></lb>strando che le parti anteriori del mezzo resistono, mentre invece le poste­<lb></lb>riori, entrando a riempire il vacuo, aiutano alla velocità del mobile il moto. </s>

<s><lb></lb>Da ciò poi conclude, nella XXXI, la ragione del perchè, verso la fine, vada <pb xlink:href="020/01/1852.jpg" pagenum="95"></pb>il grave cadente sempre più accelerandosi, che in altra parte del tempo. </s>

<s><lb></lb>Nella scienza poi dei moti violenti si solleva mirabilmente il Cardano sopra <lb></lb>la volgare schiera, principalmente per aver notato che la parte di mezzo <lb></lb>della traiettoria non è circolare, come dicevano Leonardo stesso e il Tarta­<lb></lb>glia “ sed quasi linea, quae parabolae ferme imitatur ” (De subtil. </s>

<s>cit., <lb></lb>pag. </s>

<s>96), e poi per aver combattuto l&#039;antico errore del mezzo, che conserva <lb></lb>anche fuor del motore al mobile l&#039;impulso del moto, sostituendogli franca­<lb></lb>mente l&#039;altra vera sentenza, che cioè “ illud quod movet est impetus acqui­<lb></lb>situs ” (ibid., pag. </s>

<s>93). </s></p><p type="main">

<s>La forza d&#039;inereia trasparisce di qui, nel lungo decorrere della storia <lb></lb>da Aristotile in poi, per la prima volta, benchè ne&#039;moti dei pendoli l&#039;avesse <lb></lb>Leonardo in qualche modo avvertita, e l&#039;avesse posta il Cardano stesso, come <lb></lb>dianzi s&#039;è inteso, in più espressa forma. </s>

<s>Notabile è come una tal notizia, <lb></lb>senza la quale era affatto impossibile che si spedisse alla Dinamica il passo, <lb></lb>si chiarisse così alle menti nel breve tratto di tempo interceduto fra le prime <lb></lb>speculazioni del Cardano e le ultime del Benedetti; che bisognasse a questi <lb></lb>aguzzare l&#039;ingegno per rispondere a chi domandava come mai, date le prime <lb></lb>mosse a un pendolo, per esempio, o a una ruota, non perseverino perpetui <lb></lb>nel moto, come pur dovrebbero fare per necessaria legge della loro inerzia. </s></p><p type="main">

<s>Di qui si vede che gl&#039;incerti albori crepuscolari son già passati, e che <lb></lb>il sole incomincia a vibrare oramai sull&#039;orizzonte scoperti i suoi primi raggi, <lb></lb>prima di rivolgersi a contemplare i quali nelle speculazioni del Benedetti, <lb></lb>giova fissare in Guidubaldo del Monte quell&#039;indivisibile punto, che distin­<lb></lb>gue i più vivi e intensi riflessi dell&#039;aurora dalla luce diretta del giorno. </s></p><p type="main">

<s>Il maraviglioso impulso, che vennero a dare ai progressi delle Matema­<lb></lb>tiche nel secolo XVI le resuscitate tradizioni archimedee, sollecitò le infa­<lb></lb>ticabili cure di Federigo Comandino a cercar dovunque, a tradurre e a com­<lb></lb>mentare i libri di tanti altri Matematici antichi, cosicchè deplorava Guidubaldo <lb></lb>nella morte di lui la perdita di que&#039;medesimi celeberrimi uomini Archita, <lb></lb>Euclide, Apollonio e Archimede stesso, i quali parve essere a un tratto tor­<lb></lb>nati a rivivere nell&#039;Urbinate. </s>

<s>“ Ille autem, poi soggiunge nella prefazione <lb></lb>al <emph type="italics"></emph>Mechanicorum liber<emph.end type="italics"></emph.end> (Pisauri 1577), perpetuo in aliarum mathematicarum <lb></lb>explicationem versans, mechanicam facultatem aut penitus praetermisit, aut <lb></lb>modice attigit. </s>

<s>Quapropter in hoc studium ardentius ego incumbere coepi. </s>

<s>” </s></p><p type="main">

<s>La parola <emph type="italics"></emph>Meccanica<emph.end type="italics"></emph.end> non ha però per Guidubaldo quella estensione di <lb></lb>significato, che ha ora per noi, e ch&#039;ebbe in effetto per Leonardo da Vinci, <lb></lb>per il Cardano e per il Tartaglia, ma si restringeva a significare il trattato <lb></lb>delle Macchine, alla descrizion delle quali insomma riducevasi tutta la scienza. </s>

<s><lb></lb>Lo studio delle facoltà meccaniche, a cui dice di essersi ardentemente rivolto <lb></lb>il Nostro, è dunque assai limitato, ma pur era, più che altri mai, bisognoso <lb></lb>di speciale attenzione sulla fine del secolo XVI, perchè, nel vastissimo campo <lb></lb>aperto dai tre grandi uomini sopra commemorati, rimanevasi unico quasi <lb></lb>negletto. </s></p><p type="main">

<s>Pappo infatti e Vitruvio si erano contentati a descriver le Macchine, e <pb xlink:href="020/01/1853.jpg" pagenum="96"></pb>ad insegnare il modo di disporne così gli organi, che valessero a produrre <lb></lb>il massimo effetto: dalla Scuola alessandrina e dalla Peripatetica s&#039;era già <lb></lb>conclusa, e con matematiche dimostrazioni confermata la legge statica ge­<lb></lb>nerale, ma come poi si applicasse una tal legge, eminentemente rappresen­<lb></lb>tata nella Leva, a tutte le altre Macchine, era un desiderio che Guidubaldo, <lb></lb>col suo ardente studio, si dette a sodisfare, specialmente in coloro “ qui ex <lb></lb>Pappo, ex Vitruvio et aliis didicerint quid sit Vectis, quid Trochlea, quid <lb></lb>Axis in peritrochio, quid Cuneus, quid Cochlea, quomodoque, ut pondera <lb></lb>moveri possint, aptari debeant; adhuc tamen accidentia permulta, quae <lb></lb>inter potentiam et pondus vectis virtute illis insint instrumentis, perdiscere <lb></lb>cupiunt. </s>

<s>” </s></p><p type="main">

<s>L&#039;intenzion dell&#039;Autore, corrispondente ai bisogni reclamati allora dagli <lb></lb>studiosi, era dunque quella di dimostrare come alla virtù del Vette si ridu­<lb></lb>cano le accidentali relazioni, che passano tra la potenza e il peso negli altri <lb></lb>strumenti, e infatti si coronan le proposizioni di ciascun trattato col dire e <lb></lb>col ripetere: “ Ex his manifestum est ita esse pondus ad potentiam, ipsum <lb></lb>pondus sustinentem, sicut spatium potentiae moventis ad spatium ponderis <lb></lb>moti ” (Mechan. </s>

<s>lib. </s>

<s>cit., fol. </s>

<s>82 t.). E perchè gli spazii sono in ogni caso <lb></lb>proporzionali ai tempi, un altro importantissimo corollario si deduce dai di­<lb></lb>mostrati teoremi, ed è: “ quo pondus facilius movetur, eo quoque tem­<lb></lb>pus maius esse; quo vero difficilius, eo minor esse, et e converso ” (ibid., <lb></lb>fol. </s>

<s>105 t.): proprietà generale di tutte le Macchine, che l&#039;Autore stesso ap­<lb></lb>plica così alla Coclea in particolare: “ Ex his manifestum est quo plures <lb></lb>sunt helices, et quo longiores sunt scytalae, sive manubria, pondus ipsum, <lb></lb>facilius quidem, tardius autem moveri ” (ibid., fol. </s>

<s>123). A torto dunque <lb></lb>rimproverava Galileo l&#039;<emph type="italics"></emph>inganno universale<emph.end type="italics"></emph.end> dei Meccanici, ch&#039;ei pretendeva <lb></lb>di esser <expan abbr="veñuto">vennuto</expan> egli primo a scoprire al mondo ignorante, col dimostrargli <lb></lb>come quel che si acquista nella forza si scapita nel tempo (Alb. </s>

<s>XI, 85, 87). <lb></lb>Il trattato galileiano Delle macchine non differisce sostanzialmente da quello <lb></lb>di Guidubaldo, in qualche parte emendato dietro il progredir, che in un <lb></lb>mezzo secolo aveva fatto la scienza. </s></p><p type="main">

<s>Concernono principalmente quegli emendamenti la teoria del piano in­<lb></lb>clinato, intorno alla quale l&#039;Autor del Libro delle meccaniche ripete l&#039;er­<lb></lb>rore antico di Pappo salutato da lui, insieme con Archimede, per suo rive­<lb></lb>rito maestro. </s>

<s>“ Ego enim, in hac praesertim facultate, Archimedis vestigiis <lb></lb>haerere semper volui. </s>

<s>” Maestro poi sopra tutti i maestri riconosce osse­<lb></lb>quioso il grande Aristotile, di cui non fece Archimede stesso ch&#039;esplicar le <lb></lb>dottrine, e applicarle ad esempii particolari. </s>

<s>“ Archimedi saepius fuit mecha­<lb></lb>nicae disciplinae rudimenta explanare, propterea ad magis particularia enu­<lb></lb>cleanda descendere voluit ” (In duos Archim. </s>

<s>libros paraphrasis, Pisauri 1588, <lb></lb>pag. </s>

<s>4). In Guidubaldo insomma non è da aspettarsi nessuna novità della <lb></lb>scienza, ch&#039;egli crede esser benissimo dagli antichi trattata. </s>

<s>E se alcuno si <lb></lb>sentisse intorno a ciò movere qualche dubbio, riducasi solo alla memoria <lb></lb>que&#039;grandi nomi di Aristotile e di Archimede, e se lo vedrà a un tratto <pb xlink:href="020/01/1854.jpg" pagenum="97"></pb>dissipar dalla mente. </s>

<s>“ Ambiget fortasse quispiam numquid haec principia <lb></lb>recte ab illis fuerint pertractata, sed statim omnis cessat dubitandi occasio, <lb></lb>si tantorum virorum praestantia ad memoriam revocetur ” (ibid., pag. </s>

<s>5). </s></p><p type="main">

<s>In Giovan Batista Benedetti però, da cui propriamente s&#039;instaura una <lb></lb>scienza nuova, hanno le parole un tuono molto diverso. </s>

<s>Confessa anch&#039;egli <lb></lb>in Aristotile ammirabile la sapienza, ma benche senta il gran pericolo, che <lb></lb>si correva a&#039;suoi tempi in contraddire ai placiti venerati, “ in medium, egli <lb></lb>francamente dice nella prefazioncella alle <emph type="italics"></emph>Disputazioni,<emph.end type="italics"></emph.end> quaedam proferre <lb></lb>non dubitavi, in quibus me inconcussa Mathematicae philosophiae basis, cui <lb></lb>semper insisto, ab eo dissentire coegit ” (Specul. </s>

<s>liber cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Versano principalmente i dissensi intorno a ciò che il Filosofo aveva <lb></lb>ne&#039;suoi varii libri insegnato degli accidenti, che accompagnano il moto, e <lb></lb>delle cause, che velocitano i gravi. </s>

<s>Avverte sapientemente la fallacia delle <lb></lb>dottrine peripatetiche, in sentenziare che le velocità son proporzionali ai pesi, <lb></lb>consistere nel non avere abbastanza considerato la gran differenza della re­<lb></lb>sistenza opposta dal mezzo alla caduta de&#039;gravi di figura varia, e di varii <lb></lb>volumi: e dop&#039;avere, in una bene ordinata serie di capitoli, dimostrato se­<lb></lb>condo qual proporzione i mezzi stessi variati alterino la legge dei moti; ne <lb></lb>conclude, con gran maraviglia di chi sente annunziarsi una cosa tanto <lb></lb>nuova, “ quod, in vacuo, corpora eiusdem materiae aequali velocitate mo­<lb></lb>verentur ” (ibid., pag. </s>

<s>174). </s></p><p type="main">

<s>Le porte della verità, rimaste dai peripatetici insegnamenti per sì lun­<lb></lb>ghi secoli imprunate, una volta rese così felicemente sgombre dovevano con­<lb></lb>durre il Benedetti a consegnare di propria mano allo stesso Galileo la chiave, <lb></lb>da entrare addirittura ne&#039;più riposti vestiboli del tempio. </s>

<s>Il Cardano e lo <lb></lb>Scaligero avevano fatto fare alla Dinamica il primo passo, dando, fra le varie <lb></lb>opinioni degli antichi, la preferenza a quella, che ammetteva moversi, anche <lb></lb>fuor del motore, il mobile per intrinseca virtù rimastagli impressa, e non <lb></lb>per estrinseca impulsione del mezzo, ma ne&#039;moti naturali non avevano sa­<lb></lb>puto ancora vedere come si potesse convenientemente applicare questa legge <lb></lb>dell&#039;inerzia. </s>

<s>Il Benedetli però, nel cap. </s>

<s>XXIV delle sopra citate Disputazioni, <lb></lb>rimeditava quel sì fecondo principio professato dal Nemorario, non essere <lb></lb>altro cioè la quiete se non che il termine del moto, e poi mirabilmente com­<lb></lb>mentato da Leonardo con dire, che <emph type="italics"></emph>la pietra che cade fu prima portata <lb></lb>e gettata in alto,<emph.end type="italics"></emph.end> e non facendo perciò alcuna distinzione fra moto violento <lb></lb>e naturale, n&#039;ebbe logicamente a concluder che nasceva anche questo da <lb></lb>una certa impressione “ ex impetuositate recepta a dicto mobili, quae im­<lb></lb>pressio et impetuositas, in motibus rectis naturalibus, continuo crescit ” (ibid., <lb></lb>pag. </s>

<s>184). E ciò, in altre parole e in altra forma, voleva appunto dire che <lb></lb>le velocità sono proporzionali ai tempi. </s>

<s>La qual nuova forma introdotta nei <lb></lb>semplicissimi teoremi archimedei, dai quali per facile corollario scendeva <lb></lb>stare gli spazii in ragion composta delle velocità e dei tempi, veniva mira­<lb></lb>bilmente a scoprirsi in quella gran verità, conclusa e al mondo attonito an­<lb></lb>nunziata da Galileo, che cioè gli spazii non vanno altrimenti, come dicevasi <pb xlink:href="020/01/1855.jpg" pagenum="98"></pb>da tutti, secondo i semplici tempi, ma secondo i quadrati di quegli stessi <lb></lb>tempi. </s></p><p type="main">

<s>A questi poi, che sono i principali, s&#039;aggiungono altri meriti dovuti <lb></lb>nell&#039;instaurare la scienza all&#039;insigne Matematico veneziano, quali sarebbero <lb></lb>quello di avere illustrate molte delle Questioni aristoteliche, dimostrando per <lb></lb>esempio come il Cuneo e le Taglie si rìducono propriamente alle ragioni <lb></lb>del Vette; quello di aver prefinita la misura giusta alla lunghezza del brac­<lb></lb>cio, nella Leva angolare, e nelle direzioni oblique di avere insegnato a com­<lb></lb>putarne il momento rotatario; quello di aver posto il principio matematico <lb></lb>alle forze centrifughe, argutamente osservando, <emph type="italics"></emph>id quod a nemine adhuc, <lb></lb>quod sciam est observatum<emph.end type="italics"></emph.end> (pag. </s>

<s>286), che cioè, benchè sia il mobile pre­<lb></lb>potentemente menato in giro dal motore, tende nonostante a rifuggire in <lb></lb>linea retta, non verso il centro del mondo, ma in direzione della tangente. </s>

<s><lb></lb>Da molte altre parti di questo trattatello <emph type="italics"></emph>De mechanicis<emph.end type="italics"></emph.end> scaturiscono vivi <lb></lb>raggi di luce, a illuminare alla scienza gl&#039;incerti sentieri. </s></p><p type="main">

<s>È a questo punto terminato il Prologo del nostro Dramma, ne&#039;perso­<lb></lb>naggi del quale, e specialmente degli ultimi compariti in scena, fissando gli <lb></lb>spettatori lo sguardo, gli riconosceranno quasi tutti, d&#039;abito e di nazione, <lb></lb>italiani. </s>

<s>Simeone Stevino, unico forse fra gli stranieri che vi si fosse intruso, <lb></lb>ha dovuto modestamente ritirarsi in disparte, riconoscendo d&#039;essere stato <lb></lb>prevenuto nell&#039;azion principale dal Cardeno e dal Tartaglia, l&#039;un de&#039;quali <lb></lb>aveva già, per matematiche ragioni, concluso che s&#039;equilibran due pesi sopra <lb></lb>due varie obliquità di piani, le lunghezze de&#039;quali stien come gli stessi pesi; <lb></lb>e l&#039;altro era venuto a dimostrare ai Meccanici il vero principio della com­<lb></lb>posizion delle forze, benchè mostrasse di non sapere in nessun caso come <lb></lb>applicarlo agli esempii. </s></p><p type="main">

<s>Così stando i fatti, fin qui da noi lungamente discorsi, non può non <lb></lb>recarci gran maraviglia quel che leggesi appresso a un celebrato Storico <lb></lb>delle Matematiche, non ridursi cioè l&#039;opera, data allo studio della Mecca­<lb></lb>nica dagli scienziati del secolo XVI, che a certi prolissi commentarii sulle <lb></lb>Questioni aristoteliche. </s>

<s>“ Les travaux des savans du seizieme siècle, sur la <lb></lb>Mecanique, dice Stefano Montucla, ne consistent presque qu&#039;en de prolixes <lb></lb>commentaires sur les Questions mecaniques d&#039;Aristote ” (Tome I, An. </s>

<s>VII, <lb></lb>pag. </s>

<s>689). E altrove avea già il medesimo Autore mostrato un gran disprezzo <lb></lb>per il Filosofo, dicendo che la maggior parte delle spiegazioni meccaniche <lb></lb>di lui son false, e che la prima e fondamentale, dedotta dalle dignità del <lb></lb>circolo, “ est tout-a-fait ridicule ” (ivi, pag. </s>

<s>187). </s></p><p type="main">

<s>Nel secolo XVIII eran pur troppo tali i correnti giudizii dei Matema­<lb></lb>tici; giudizii, a formulare e a confermar ne&#039;quali le menti, avevano avuto <lb></lb>gran parte Galileo e il Cartesio, ambiziosi di tenere il principato della scienza, <lb></lb>e gelosi di dividerne con qualsivoglia altri il potere. </s>

<s>Ma pure al primo esce <lb></lb>più qua e più là ingenuamente di bocca la confessione di aver trovato in <lb></lb>Aristotile il principio a certe sue meccaniche speculazioni, che sarebbero al­<lb></lb>trimenti rimaste forse senza progressi. </s>

<s>Così la nuova scienza delle resistenze <pb xlink:href="020/01/1856.jpg" pagenum="99"></pb>dei solidi confessa aver avuto in lui il motivo dalle Questioni meccaniche <lb></lb>del Filosofo “ mentre vuol render la ragione onde avvenga che i legni, <lb></lb>quanto son più lunghi, tanto son più deboli ” (Alb. </s>

<s>XIII, 125), e mentre <lb></lb>in altra Questione risponde al perchè “ manco fatica si ricerchi a rompere <lb></lb>un legno, tenendo le mani nell&#039;estremità, cioè remote assai dal ginocchio, <lb></lb>che se le tenessimo vicine ” (ivi, pog. </s>

<s>134), riducendo, come Galileo nella <lb></lb>II Giornata delle Due nuove scienze, la causa di questi fatti a quella ge­<lb></lb>neralissima delle Leve, il principio statico che governa le quali, e che con­<lb></lb>siste nel compensarsi la tardità del resistente dalla velocità del movente, <lb></lb>confessa Galileo stesso essere stato Aristotile il primo a proporlo e a dimo­<lb></lb>strarlo (ivi, pag. </s>

<s>264). Nè gli parve quella dimostrazione punto ridicola, come <lb></lb>nou parve tale a Leonardo da Vinci, il quale anzi, in tempi che prevalevano <lb></lb>le dottrine del Nemorario, elesse di tornar così all&#039;antico modo di ragionar <lb></lb>del Filosofo: “ Quella cosa, che fia più lontana al suo firmamento, manco <lb></lb>da essa fia sostenuta. </s>

<s>Essendo manco sostenuta, più fia partecipevole di sua <lb></lb>libertà, e perchè il peso libero sempre discende, adunque quella estremità <lb></lb>dell&#039;asta d&#039;essa Bilancia, che fia più distante al suo firmamento, perchè è <lb></lb>ponderosa, più presto che alcuna parte di sè discenderà ” (Manuscr. </s>

<s>N.o 2038, <lb></lb>Paris 1891, fol. </s>

<s>2 t.). </s></p><p type="main">

<s>In ogni modo a nessuno mai parve ridicola la Questione XXIV “ quam <lb></lb>ob causam maior circulus aequalem minori circumvolvitur lineam, quando <lb></lb>circa idem centrum fuerint positi ” (Arist., operum T. XI cit., fol. </s>

<s>35 t.). <lb></lb>Il Benedetti, che fu forse il primo a torturar nel curioso quesito l&#039;ingegno, <lb></lb>disse nel cap. </s>

<s>XXII del suo trattatello <emph type="italics"></emph>De mechanicis<emph.end type="italics"></emph.end> che il moto del mi­<lb></lb>nor circolo della ruota non è tutto progressivo, ma in parte anche regres­<lb></lb>sivo, e Galileo, che fra tutti disse ammirabile questo problema, rifiutata la <lb></lb>prima spiegazione affacciataglisi alla mente, ripetuta poi da alcuni Francesi, <lb></lb>che cioè fossero i punti della circonferenza minore, tirati dalla maggiore, <lb></lb>strascicati per qualche tratto (Alb. </s>

<s>XIII, 27); andò a immaginare un gioco <lb></lb>de&#039;vacui interposti, quasi la maggiore circonferenza fosse, rispetto aìla mi­<lb></lb>nore, una corda elastica stirata. </s></p><p type="main">

<s>È un fatto però, notabilissimo per la nostra Storia, che volle Galileo a <lb></lb>grande studio tenere occulte le più prossime e più ubertose fonti, dalle <lb></lb>quali derivavagli, specialmente in Italia, a que&#039;suoi tempi la scienza. </s>

<s>Le ve­<lb></lb>locità virtuali e la ragion de&#039;pesi alle lunghezze dei piani inclinati, che po­<lb></lb>nevano da una parte il principio, e dall&#039;altra venivano a dare alla Statica <lb></lb>l&#039;incremento; la regola della composizione dei moti, e le forze d&#039;inerzia, <lb></lb>applicate prima ai proietti e poi alle naturali cadute dei gravi, per cui si <lb></lb>aprivano così facili le vie alla Dinamica; volle l&#039;ambizioso Autore dei Dia­<lb></lb>loghi fare apparire al mondo come dottrine nuove, gelosamente tacendo il <lb></lb>nome del Benedetti, e dispettosamente protestandosi di non saper quel che <lb></lb>s&#039;avessero detto il Cardano e il Tartaglia nei loro libri. </s></p><p type="main">

<s>In tempi, che il Peripato regnava quasi universale e assoluto nelle <lb></lb>scuole, e che non riducevansi le scienze naturali ad altro, che a prolissi e <pb xlink:href="020/01/1857.jpg" pagenum="100"></pb>nebulosi commentarii intorno ai placiti del Filosofo; non riuscì difficile a <lb></lb>Galileo far apparire agli occhi degli spettatori d&#039;un abito e d&#039;un colore quei <lb></lb>tre o quattro, che si sarebbero da viste più sincere facilmente scorti in mezzo <lb></lb>alla turba volgare. </s>

<s>Fu poi tanto destro l&#039;ingegno e tanto fortunata l&#039;opera <lb></lb>di quell&#039;uomo in produrre una così fatta illusione, che dura tuttavia dopo <lb></lb>tre secoli, e durerà chi sa quanto, a far velo ai giudizii degli uomini. </s></p><p type="main">

<s>Comunque sia, è debito principale della nostra Storia lo scoprire l&#039;in­<lb></lb>ganno, e seguendo il filo delle tradizioni dimostrare come per legge natu­<lb></lb>rale si sia svolto il pensiero. </s>

<s>Le creazioni, così facilmente attribuite agl&#039;in­<lb></lb>gegni, si possono ammettere per una iperbole, il qual modo però di dire, <lb></lb>che piace a tanti, non essendo consentito alla scientifica precisione, ci sug­<lb></lb>gerisce il prudente consiglio d&#039;andar a ricercar la scintilla, che sempre per <lb></lb>necessità seconda qualche gran fiamma. </s>

<s>E perchè si saranno accorti i Let­<lb></lb>tori che il proposito nostro s&#039;è in questo primo discorso incominciato già a <lb></lb>mandare ad effetto, proseguiremo in egual modo nelle singole trattazioni di <lb></lb>questa prima parte della Storia della Meccanica, per nostra gloria quasi tutta <lb></lb>italiana, soffermando il passo ne&#039;Dialoghi delle Due nuove scienze, dai quali, <lb></lb>come da editto pubblicamente affisso, si promulgano al mondo le leggi <lb></lb>del moto. </s></p><pb xlink:href="020/01/1858.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dei Baricentri<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della invenzione del centro di gravità nei solidi. </s>

<s>— II. </s>

<s>Dei quattro libri centrobrarict di Paolo <lb></lb>Guldino, e della Geometria degl&#039;indivisibili di Bonaventura Cavalieri. </s>

<s>— III. </s>

<s>Delle risposte del <lb></lb>Cavalieri alle opposizioni fattegli dal Guldino, e come la Regola centrobrarica avesse dal Me­<lb></lb>todo degl&#039;indivisibili la sua prima matematica dimostrazione. </s>

<s>— IV. </s>

<s>Delle nuove dimostrazioni <lb></lb>della Regola centrobrarica che, primi, vennero a dare alle scienze matematiche in Italia Anto­<lb></lb>nio Nardi e Vincenzio Viviani. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le leggi del moto, che dicemmo essere state solennemente promulgate <lb></lb>dai primi Dialoghi di Galileo, segnano un&#039;epoca novella nella storia della <lb></lb>Meccanica. </s>

<s>Ma l&#039;epoca che la precede incomincia anch&#039;essa dal medesimo <lb></lb>fatto delle cadute dei gravi, considerate sotto quel più semplice aspetto, che <lb></lb>ci si presentano tutti i giorni nell&#039;esperienze comuni. </s>

<s>Si vede ogni corpo <lb></lb>sempre per naturale necessità cadere, quando gli venga meno il sostegno, <lb></lb>e o cada liberamente o sia sostenuto, è un sottilissimo filo quello che segna <lb></lb>la libera via, o che impedisce la tendenza del moto. </s>

<s>L&#039;osservazione ovvia al <lb></lb>volgo e insignificante fu principio fecondo di scienza al Filosofo che, consi­<lb></lb>derando come si poteva di qualunque peso impedir la caduta, col sostenerlo <lb></lb>per via di un semplicissimo filo; ebbe a concluderne che nella direzione <lb></lb>verticale di lui si raccoglieva dunque, alla caduta stessa, d&#039;ogni parte il <lb></lb>conato. </s>

<s>Altre esperienze poi fecero questa prima importante notizia progre­<lb></lb>dire più oltre, imperocchè, vedendo rimanersi ugualmente bene nella sua <lb></lb>quiete il grave, da qualunque punto della sua superficie si tenesse sospeso, <lb></lb>non fu difficile, con l&#039;aiuto della Geometria, concluderne che il conato del <pb xlink:href="020/01/1859.jpg" pagenum="102"></pb>cadente raccoglievasi tutto, non in una sottil linea, come dianzi pareva, ma <lb></lb>in un indivisibile punto, qual si viene a determinare dall&#039;intersecamento delle <lb></lb>due verticali, che penetrano dentro il peso pendulo, or in una ora in un&#039;altra <lb></lb>delle variate sue positure. </s>

<s>Dette perciò a quel punto l&#039;artificioso linguaggio <lb></lb>dei Matematici il nome di <emph type="italics"></emph>Baricentro,<emph.end type="italics"></emph.end> o di Centro di gravità, e dal consi­<lb></lb>derarne le varie proprietà e gli effetti ebbe principio quella, che ai nostri <lb></lb>Italiani, i quali si dettero, primi nel secolo XVI, a coltivarla, piacque chia­<lb></lb>mar col nome di Scienza dei pesi. </s></p><p type="main">

<s>Secondo l&#039;uso volgare il permanere qualunque corpo sospeso in equi­<lb></lb>librio si significa col dire ch&#039;egli sta in bilancia, ciò che, mentre da una <lb></lb>parte rivela aver avuto l&#039;artificioso strumento la sua prima origine da un <lb></lb>fatto naturale, dimostra dall&#039;altra come dai centri di gravità si pigliassero i <lb></lb>principii fondamentali alla Statica. </s>

<s>I pesi infatti, che s&#039;impongono di qua e <lb></lb>di là ne&#039;bacini, si raccolgono come in centro nel fulcro della Libbra, e vi <lb></lb>rimangon sospesi in quiete infin tanto che non venga a mancare esso ful­<lb></lb>cro. </s>

<s>Il trattato archimedeo perciò degli Equiponderanti non è, nella sua prima <lb></lb>parte, che l&#039;esplicazione di questo stesso concetto, benchè la prevalente Geo­<lb></lb>metria soggioghi e par che abbia quasi licenziata l&#039;esperienza da&#039;suoi an­<lb></lb>tichi servigi. </s></p><p type="main">

<s>Il soggetto dall&#039;altra parte veniva per sè stesso a vestire schietto abito <lb></lb>geometrico, dipendendo la giusta posizione del centro dalla forma propria <lb></lb>del corpo, nè portando le nuove inquisizioni altra differenza che del consi­<lb></lb>derare come pesanti quelle particelle, che si riguardavano solo come per <lb></lb>ogni verso distese a occupare lo spazio. </s>

<s>Così confermasi l&#039;idea di quello <lb></lb>stretto connubio, che passa fra la Meccanica e le Matematiche; idea che già <lb></lb>ci si rappresentava alla mente chiarissima, infin da quando udimmo Aristo­<lb></lb>tile porre per fondamento alla scienza i moti generatori del cerchio. </s>

<s>Sarebbe <lb></lb>stato anzi giovevole il commemorar queste cose a coloro, a cui giunsero, a <lb></lb>mezzo il secolo XVII, inaspettati i servigi che, nel Metodo centrobrarico, ve­<lb></lb>niva a rendere la Meccanica stessa alla Geometria. </s></p><p type="main">

<s>Ma per procedere ordinatamente nel nostro discorso è da tornare a <lb></lb>quel trattato Degli equiponderanti, in cui dimostrava Archimede essere una <lb></lb>medesima cosa il centro naturale dei gravi, e il centro artificiale della Lib­<lb></lb>bra, matematicamente concludendo le leggi statiche dal principio dei Bari­<lb></lb>centri. </s>

<s>La nuova istituzione archimedea però non giovava allo studio della <lb></lb>Statica sola, ma conferiva mirabilmente ai progressi di tutta intera la Scienza <lb></lb>del moto, la quale veniva a rendersi così tanto più semplice nelle sue la­<lb></lb>boriose dimostrazioni, considerando le disperse virtù come tutte insieme <lb></lb>raccolte in un punto. </s>

<s>Se ci fosse la comparazione permessa, diremmo perciò <lb></lb>che la Baricentrica è, nella Scienza del moto, quel ch&#039;è il cuore nella vita <lb></lb>dell&#039;animale, ond&#039;ei si può intendere com&#039;ella debba nella storia apparire <lb></lb>la prima, quasi <emph type="italics"></emph>punctum saliens<emph.end type="italics"></emph.end> in mezzo alle altre non discernibili parti <lb></lb>dell&#039;embrione. </s></p><p type="main">

<s>Così essendo, si riduceva tutto lo studio a cercare, e a segnar le vie di <pb xlink:href="020/01/1860.jpg" pagenum="103"></pb>giungere in quegli intimi penetrali, dove risiede il cuore impulsivo del moto <lb></lb>in tutti i gravi. </s>

<s>È perciò che Archimede, dop&#039;avere nel I libro dimostrata <lb></lb>la natura e le proprietà del punto, intorno a cui d&#039;ogni parte si radunano <lb></lb>i pesi; passa immediatamente a cercare e a segnar quelle più riposte vie <lb></lb>geometriche, che possono condurre a trovar quel punto preciso, benchè il <lb></lb>primo instituito insegnamento del grande Maestro lasci in vivo desiderio gli <lb></lb>studiosi di vederlo compiuto. </s></p><p type="main">

<s>I teoremi infatti, che ricorrono nella seconda metà del I libro, via via <lb></lb>dimostrati, concernono le sole figure piane circoscritte da linee rette, e il <lb></lb>II libro si consacra tutto alla ricerca del centro di gravità ne&#039;piani curvi­<lb></lb>linei o, come saremmo tentati di chiamarli, triangoloidi parabolici. </s>

<s>Con <lb></lb>ciò, qual dopo tanti secoli e dopo tante vicende pervenne alle mani dei Ma­<lb></lb>tematici, si chiude dall&#039;Autore il trattato Degli equiponderanti. </s></p><p type="main">

<s>Gli studiosi lettori, fra&#039;quali abbiamo noi Italiani da annoverarne, in­<lb></lb>fino a mezzo il secolo XVI, distintamente tre de&#039;più insigni, si trovavano da <lb></lb>quella fida scorta abbandonati colà, dove speravano che sarebbero venuti a <lb></lb>riuscire gli ultimi passi. </s>

<s>Imperocchè quale importanza potevano per sè stesse <lb></lb>avere le superfice, se non in ordine ai solidi, i quali soli son propriamente <lb></lb>ponderosi? </s>

<s>Alla invenzione perciò del centro di gravità de&#039;triangoli si po­<lb></lb>teva attendere com&#039;a studio, ordinato a facilitar la ricerca del centro di gra­<lb></lb>vità nella piramide, e i baricentri ne&#039;trapezii e nelle sezioni del cono si po­<lb></lb>tevano desiderare per venir più facilmente introdotti alle più complicate <lb></lb>risoluzioni dei centri di gravità ne&#039;prismi e nelle conoidi. </s>

<s>Or a veder che <lb></lb>in quelle superfice piane, per sè medesime imponderanti, s&#039;assolve tutta <lb></lb>quanta l&#039;intenzion dell&#039;Autore, se ne dovettero fare due congetture: o che <lb></lb>fosse venuto a mancare il III libro, dove avrebbe Archimede dato il suo <lb></lb>trattato Degli equiponderanti compiuto; o che, contento ad averne posti i <lb></lb>principii, lasciasse alla esercitazione degli studiosi le non difficili desiderate <lb></lb>conclusioni. </s></p><p type="main">

<s>Quanto ai solidi infattì, che si dicono di rivoluzione, era ovviamente <lb></lb>dimostrabile che nella sfera e nel cilindro i centri di gravità corrispondono <lb></lb>ai centri delle grandezze. </s>

<s>Maggiore difficoltà è vero incontravasi rispetto al <lb></lb>cono, le quali difficoltà venivano nonostante ad appianarsi, riguardando quel <lb></lb>solido come una piramide a base poligonare di un numero infinito di lati: <lb></lb>ond&#039;è che riducevasi così la questione alla ricerca del centro nella piramide <lb></lb>stessa, la quale, in qual si voglia modo si presenti composta, è risolubile <lb></lb>sempre in altre minori piramidi a base triangolare. </s>

<s>Ma la baricentrica in­<lb></lb>quis̀izion del triangolo pareva a questo principale intento presa a far dall&#039;Au­<lb></lb>tore in que&#039;teoremi del I libro Dagli equiponderanti, perchè, proseguendo <lb></lb>simili vie, si potessero più facilmente condurre gli studiosì al baricentrico di <lb></lb>ogni solido piramidale. </s></p><p type="main">

<s>Comunque siasi raggiunsero veramente gl&#039;istituti archimedei, nella <lb></lb>Scuola matematica di Luca Pacioli, questo intento, come si dimostra per <lb></lb>l&#039;esempio insigne di Leonardo da Vinci, di cui solo ci rimangono i docu-<pb xlink:href="020/01/1861.jpg" pagenum="104"></pb>menti. </s>

<s>“ Il centro di ogni gravità piramidale, così leggesi in una delle so­<lb></lb>lite Note, è nel quarto del suo assi, verso la base, e se dividerai l&#039;assis per <lb></lb>quattro eguali, e intersegherai due degli assi di tal piramide, tale interse­<lb></lb>gamento verrà nel predetto quarto ” (Manuscr. </s>

<s>F cit., fol. </s>

<s>51). </s></p><p type="main">

<s>Guglielmo Libri che fu, come si disse, il primo a fermar l&#039;attenzione <lb></lb>su queste Note, e a fissare gli occhi sopra le due figure appostevi per illu­<lb></lb>strarle, si credè di poter raccogliere da que&#039;segni che Leonardo “ decom­<lb></lb>posait les pyramides en plans paralleles a la base, comme on le fait a pre­<lb></lb>sent ” (Histoire des Matem., T. III cit., pag. </s>

<s>41 in nota). La conclusione <lb></lb>però sembra a noi temeraria, perchè ne&#039;detti iconismi, e specialmente nel <lb></lb>secondo, niente altro fa l&#039;Autore che rappresentare all&#039;occhio quell&#039;interse­<lb></lb>camento de&#039;due assi, condotti sulle respettive basi da due vertici opposti, <lb></lb>da cui diceva determinarsi alla piramide il preciso punto del centro. </s>

<s>È ciò <lb></lb>dall&#039;altra parte pienamente conforme con gli istituti archimedei, là dove <lb></lb>s&#039;insegna a trovare il centro di gravità ne&#039;triangoli; istituti, ch&#039;ebbe a se­<lb></lb>guir fedelmente anche il nostro Leonàrdo, a cui, ripetiamo, parerci teme­<lb></lb>rario l&#039;attribuire il metodo degl&#039;indivisibili, che s&#039;ebbe necessariamente a <lb></lb>introdur nella scienza, dopo la Geometria nuova del Cavalieri. </s>

<s>E perchè la <lb></lb>questione, a cui ha dato motivo il Libri, è di troppo grande importanza nella <lb></lb>Storia, non increscerà d&#039;intrattenervi attorno brevemente il discorso. </s></p><p type="main">

<s>Il processo dimostrativo, che nel I libro Degli equiponderanti si pro­<lb></lb>poneva, per le ricerche ulteriori, ad esempio, incomincia dalla proposi­<lb></lb>zione XIII, nella quale dimostra Archimede che il centro della gravità del <lb></lb>triangolo si trova nella bissettrice condotta dall&#039;angolo opposto sopra la base. </s>

<s><lb></lb>Poi si passa, per facile via, alla proposizione XIV, che insegna a determi­<lb></lb>nare il punto preciso del centro ricercato nell&#039;intersezione di due delle dette <lb></lb>bissettrici, da due diversi angoli condotte nello stesso triangolo sopra cia­<lb></lb>scuna delle due contrapposte basi. </s>

<s>D&#039;onde con facile dimostrazione geome­<lb></lb>trica si viene a concluderne, nel secondo lemma che segue, essere prefinito <lb></lb>il centro di gravità nel triangolo dalla prima delle tre parti, in che s&#039;in­<lb></lb>tenda, a movere dalla base, essere stata divisa una bissettrice. </s></p><p type="main">

<s>Per procedere alla ricerca del centro della gravità nella piramide il fa­<lb></lb>cile ordine dunque, che si suggeriva dagl&#039;insegnamenti di Archimede, era <lb></lb>questo: trovato il centro di due delle facce triangolari del solido, condurre <lb></lb>dai vertici opposti due linee, nell&#039;intersezion delle quali dovendosi ritrovar <lb></lb>tutta insieme raccolta la gravità piramidale, si dimostrava per Geometria, in <lb></lb>un modo simile a quello del citato lemma archimedeo, che la detta interse­<lb></lb>zione facevasi ne&#039;tre quarti della linea, che movendo dal vertice, va a ter­<lb></lb>minar nel centro della opposta base triangolare. </s></p><p type="main">

<s>Or chi attende a così fatti processi dimostrativi facilmente ritrova che <lb></lb>dipendono ambedue dalla proposizione XIII del I Degli equiponderanti, posta <lb></lb>la quale, se ne concludono tutte le altre come facilissimi corollarii. </s>

<s>Diceva <lb></lb>quella proposizione: “ Cuiuscumque trianguli centrum gravitatis est in recta <lb></lb>linea, quae ab angulo in mediam basim ducitur ” (Archim. </s>

<s>op. </s>

<s>cit., pag. </s>

<s>177), <pb xlink:href="020/01/1862.jpg" pagenum="105"></pb>alla quale, nell&#039;omologo processo inquisitivo del centro della gravità nella <lb></lb>piramide, corrisponde l&#039;altra proposizione dai promotori di Archimede, come <lb></lb>per esempio dal Maurolico, così formulata: “ Recta, quae a vertice pyrami­<lb></lb>dis in eius centrum agitur, producta, cadit in centrum basis triangulae ” <lb></lb>(De mom. </s>

<s>aequal. </s>

<s>cit., pag. </s>

<s>169). </s></p><p type="main">

<s>Il modo però di dimostrare le due proposizioni è molto diverso appresso <lb></lb>agli Autori antichi, e ai moderni. </s>

<s>Si confrontino di grazia le due varie di­<lb></lb>mostrazioni faticosamente condotte, e ambedue, per indiretta via, degli as­<lb></lb>surdi concluse nel trattato di Archimede, con la facile, e non men matema­<lb></lb>tica dimostrazione, che per via degl&#039;indivisibili oggidì se ne dà dai Matematici, <lb></lb>i quali, considerando un triangolo come composto d&#039;infinite linee ponderose, <lb></lb>tutte parallele alla base; da uno de&#039;più elementari teoremi di Geometria, e <lb></lb>dal postulato primo Degli equiponderanti, immediatamente ne concludono <lb></lb>dovere al triangolo essere il centro di gravità nella linea, ch&#039;essendo bisset­<lb></lb>trice alla base, è tutt&#039;insieme bissettrice delle altre infinite condotte a lei <lb></lb>parallele. </s>

<s>Si confronti dall&#039;altra parte il lungo ordine delle proposizioni, che <lb></lb>precedono alla XIV citata nel IV libro maurolicano <emph type="italics"></emph>De momentis aequali­<lb></lb>bus,<emph.end type="italics"></emph.end> con lo spedito processo dei Moderni, i quali, ritrovato il centro di gra­<lb></lb>vità del triangolo, dal riguardar la piramide come composta d&#039;infiniti triangoli <lb></lb>paralleli alla base (dalla quale movendo s&#039;assottigliano sempre più infintan­<lb></lb>tochè non vanno a morir nel vertice) immediatamente ne concludono dover <lb></lb>la gravità del solido raccogliersi tutta intorno alla linea condotta dal vertice <lb></lb>stesso sopra il centro della contrapposta base triangolare. </s></p><p type="main">

<s>Or pretendeva il Libri che tale, qual&#039;è in uso appresso ai Matematici <lb></lb>moderni, fosse il processo inquisitivo del centro della gravità nella piramide <lb></lb>praticato da Leonardo da Vinci. </s>

<s>Ma perchè l&#039;asserzione dello Storico delle <lb></lb>Matematiche in Italia non è in sostanza fondata che sopra un inganno del­<lb></lb>l&#039;occhio frettolosamente da lui gettato sulla citata pagina del manoscritto <lb></lb>vinciano, vuol la ragion critica, e vuole il senso comune che si facciano i <lb></lb>Matematici del secolo XV e XVI discepoli di Archimede, e seguaci de&#039;suoi <lb></lb>metodi antichi, piuttosto che discepoli e seguaci de&#039;metodi nuovi del Cava­<lb></lb>lieri. </s>

<s>Nè vale a rimoverci da questa nostra opinione l&#039;autorità del Torri­<lb></lb>celli, il quale, proponendosi di trovar la quadratura della parabola col me­<lb></lb>todo degl&#039;indivisibili, così scriveva in quella sua breve prefazione al trattato: <lb></lb>“ Quod autem haec Indivisibilium Geometria novum penitus inventum sit, <lb></lb>non ausim affirmare. </s>

<s>Crediderim potius veteres Geometras hac methodo usos <lb></lb>in inventione theorematum difficillimorum, quamquam in demonstrationibus <lb></lb>aliam viam magis probaverint, sive hoc ad occultandum artis arcanum, sive <lb></lb>ne ulla invidis detractoribus proferretur occasio contradicendi ” (Opera <lb></lb>geom., P. II, Florentiae 1644, pag. </s>

<s>56). </s></p><p type="main">

<s>Questi occulti arcani dell&#039;arte antica però, che ben si può intendere <lb></lb>corn&#039;entrassero negl&#039;insegnamenti della morale, della politica e della religione, <lb></lb>non si vede per qual motivo s&#039;avessero da&#039;sapienti a osservare nelle mate­<lb></lb>matiche discipline. </s>

<s>Anche a proposito della composizione dei moti vedemmo <pb xlink:href="020/01/1863.jpg" pagenum="106"></pb>come il Torricelli stesso credesse aver voluto Archimede tener occulta la <lb></lb>regola ai profani, mentr&#039;è un fatto che s&#039;insegnava pubblicamente da Ari­<lb></lb>stotile, e, da chi l&#039;avesse saputa intendere, si praticava senza misteri. </s>

<s>Tro­<lb></lb>vandosene in quelle medesime aristoteliche Questioni i germi, là dove si <lb></lb>dice essere il cerchio generato dall&#039;esplosione del centro, non negheremmo <lb></lb>che potessero gli Antichi avere avuto qualche idea del metodo degli indivi­<lb></lb>sibili: non così chiara però, da applicarla, anche ne&#039;più semplici casi, a. </s>

<s>quel <lb></lb>modo che si fa dai moderni; ond&#039;è che ci confermiamo, con riverenza del <lb></lb>Torricelli e del Libri, nel nostro sentimento, che cioè Leonardo proseguisse <lb></lb>ne&#039;suoi studii baricentrici i metodi antichi, com&#039;è certo che gli prosegui­<lb></lb>rono altri matematici di que&#039;tempi, fra&#039;quali è il Maurolico uno de&#039;più <lb></lb>insigni. </s></p><p type="main">

<s>Al IV libro <emph type="italics"></emph>De momentis aequalibus,<emph.end type="italics"></emph.end> scritto per supplire al difetto o <lb></lb>alla iattura del III archimedeo Degli equiponderanti, premette il Matematico <lb></lb>messinese una prefazioncella, nella quale, per avvertire il lettore della sua <lb></lb>intenzione, ch&#039;era quella di passare alla ricerca dei centri di gravità nei so­<lb></lb>lidi, dice di esser rimasto sorpreso da gran maraviglia, in trovar che ne&#039;li­<lb></lb>bri di Archimede non si lasciava luogo all&#039;importante argomento. </s>

<s>“ Nam, <lb></lb>poi soggiunge, quamvis memorati centri inventio facilis sit in sphaera, faci­<lb></lb>lis in solidis, quae vulgo regularia dicuntur, et centrum omnis prismatis sit <lb></lb>centrum ipsum rectilinei quod basibus medium et parallelum interiacet; <lb></lb>tamen centrum pyramidis non minori industria quam centrum plani trian­<lb></lb>gularis, ne dicam maiori, exquiri poterat ” (Archim. </s>

<s>monum. </s>

<s>cit., pag. </s>

<s>156). </s></p><p type="main">

<s>Si rivela da queste espressioni del Maurolico il processo della sua mente, <lb></lb>il quale come in Leonardo consiste nell&#039;applicare i teoremi archimedei, con­<lb></lb>cernenti i triangoli, alle piramidi. </s>

<s>Ma l&#039;arte matematica dell&#039;Autore supera <lb></lb>di gran lunga quella de&#039;contemporanei, nonchè degli antichi, come può ve­<lb></lb>dersi dall&#039;ordine delle proposizioni, e dal nuovo aspetto, sotto cui le pre­<lb></lb>senta. </s>

<s>S&#039;accennava di sopra due essere le diverse vie che, in ricercare il <lb></lb>centro della gravità ne&#039;piani triangolari e ne&#039;solidi piramidali, tennero i Ma­<lb></lb>tematici, secondo il modo antico o il moderno. </s>

<s>Il Maurolico procede o addita <lb></lb>agli studiosi una via di mezzo, tutta nuova, speditissima, e di mirabile riu­<lb></lb>scita. </s>

<s>Dato un triangolo, come per esempio ABC (fig. </s>

<s>46), ne considera la <lb></lb><figure id="id.020.01.1863.1.jpg" xlink:href="020/01/1863/1.jpg"></figure></s></p><p type="caption">

<s>Figura 46.<lb></lb>gravità divisa in tre parti eguali, e raccòlte in <lb></lb>tre cerchi o dischi, concentrati ciascuno negli <lb></lb>angoli. </s>

<s>S&#039;ha dai più elementari teoremi Degli <lb></lb>equiponderanti che il centro de&#039;due gravi A e <lb></lb>B riesce in G, punto di mezzo della linea AB, <lb></lb>ond&#039;è che, condotta la GC, perciocchè gravano <lb></lb>in uno degli estremi di lei due dischi, e nell&#039;al­<lb></lb>tro estremo C il terzo, avremo il comun centro <lb></lb>de&#039;tre gravi, ch&#039;è il centro medesimo del trian­<lb></lb>golo, stabilito in H per modo, che stia CH ad HG, come due sta ad uno. </s>

<s>A <lb></lb>così facile conclusione elegante conduce per diritta via la proposizione XXXVI <pb xlink:href="020/01/1864.jpg" pagenum="107"></pb>del II libro <emph type="italics"></emph>De momentis aequalibus,<emph.end type="italics"></emph.end> così formulata: “ Si fuerint tria gravia <lb></lb>aequalia, quorum gravitatis centra iungantur per tres rectas, centrum com­<lb></lb>mune illorum erit centrum facti trianguli ” (Archim. </s>

<s>monum. </s>

<s>cit., pag. </s>

<s>132). </s></p><p type="main">

<s>Conduce per analoghe vie, con pari facilità ed eleganza, a ritrovare il <lb></lb>centro d&#039;ogni gravità piramidale la proposizione XVI che, nel IV libro mau­<lb></lb>rolicano, si pone dall&#039;Autore in questa forma: “ Si fuerint quatuor gravia <lb></lb><figure id="id.020.01.1864.1.jpg" xlink:href="020/01/1864/1.jpg"></figure></s></p><p type="caption">

<s>Figura 47.<lb></lb>aequalia, quorum centra, non in uno <lb></lb>plano posita, per sex rectas conficiant <lb></lb>pyramidem trilateram; centrum factae <lb></lb>pyramidis erit commune centrum qua­<lb></lb>tuor gravium ” (ibid., pag. </s>

<s>169). Se <lb></lb>s&#039;intenda infatti la gravità della pira­<lb></lb>mide ABCD (fig. </s>

<s>47) divisa in quat­<lb></lb>tro parti eguali raccolte in quattro <lb></lb>sfere, concentrate in ciascuno dei <lb></lb>quattro angoli solidi; il centro di gra­<lb></lb>vità delle tre A, B, C sarà in M, da <lb></lb>cui condotta la MD gravata in uno <lb></lb>estremo dall&#039;unico peso D, e dall&#039;al­<lb></lb>tro da tre simili pesi, verrà a dare <lb></lb>in T il comun centro, che è il centro <lb></lb>stesso della piramide, cosicchè per <lb></lb>legge statica interceda la relazione TD:MT=3:1; ciò che significa es­<lb></lb>sere la MT, di tutta intera la MD, una quarta parte. </s></p><p type="main">

<s>I Matematici precedenti erano, come si mostrò per l&#039;esempio di Leo­<lb></lb>nardo, riusciti alla medesima facile conclusione, ma il Maurolico, essendosi <lb></lb>per precipuo intento prefisso di promovere Archimede, prosegue oltre a com­<lb></lb>pier l&#039;opera lasciata a mezzo dal suo autore e maestro. </s>

<s>Il secondo libro Degli <lb></lb>equiponderanti è ordinato alla ricerca del centro di gravità nelle sezioni dei <lb></lb>conoidi parabolici; ricerca che s&#039;assolve tutta nella proposizione VIII, per <lb></lb>la quale si dimostra concentrarsi in detta sezione il peso tutto intorno al <lb></lb>diametro, “ ita ut pars ipsius, quae est ad verticem, sit sesquialtera partis, <lb></lb>quae est versus basim ” (Archim., Opera cit., pag. </s>

<s>207). Ma il Maurolico, <lb></lb>dal piano passando al solido rotondo, com&#039;era dianzi passato alla piramide <lb></lb>dal semplice triangolo, primo fra&#039;Matematici di cui ci sieno rimasti i docu­<lb></lb>menti, dimostrò, nell&#039;ultimo libro del suo trattato, la seguente proposizione, <lb></lb>quasi volesse coronar di lei tutta l&#039;opera sua: “ Centrum gravitatis para­<lb></lb>bolici conoidis axem ita dividit, ut pars, quae ad verticem, reliquae ad basim <lb></lb>sit dupla ” (Archim. </s>

<s>monum. </s>

<s>cit, pag. </s>

<s>177). </s></p><p type="main">

<s>Veniva così alla Meccanica dai nostri Matematici italiani, fioriti tra il <lb></lb>finir del XV secolo e il cominciar del secolo appresso, aperto un nuovo <lb></lb>eampo, che forse ebbe qualche cultura dagli antichi, ma che poi, per quel <lb></lb>così lungo abbandono, ebbesi sventuratamente a tornar sodo. </s>

<s>Di quelle eser­<lb></lb>citazioni però o fu affatto perduta la memoria, o se ne trovarono solo assai <pb xlink:href="020/01/1865.jpg" pagenum="108"></pb>più tardi i documenti. </s>

<s>Benchè il Maurolico per esempio fosse de&#039;primi ad <lb></lb>esser conosciuto e, raccogliendosene nel 1575 in Venezia gli Opuscoli ma­<lb></lb>tematici, s&#039;annunziasse in fine all&#039;opera, fra le altre lucubrazioni proprie <lb></lb>all&#039;Autore, anche i quattro libri <emph type="italics"></emph>De momentis aequalibus,<emph.end type="italics"></emph.end> “ in quorum po­<lb></lb>stremo, vi si diceva, de centris solidorum ab Archimede omissis agitur, et <lb></lb>de centro solidi parabolici ”; vedemmo nonostante come se ne indugiasse <lb></lb>infino al 1685 la pubblicazione. </s></p><p type="main">

<s>Anche passata dunque di qualche anno la prima metà del secolo XVI, <lb></lb>seguitava Archimede a far dir di sè i Matematici, fra&#039;quali Federigo Com­<lb></lb>mandino, che avrebbe voluto vedere applicarsi il gran Maestro siracusano <lb></lb>alla desiderata ricerca dei centri di gravità ne&#039;solidi. </s>

<s>Si sentiva inclinato <lb></lb>piuttosto ad accusar l&#039;Autore Degli equiponderanti di negligenza, per aver <lb></lb>lasciata l&#039;opera incompiuta, che a lamentarne, attraverso al fluttuare de&#039;se­<lb></lb>coli, la iattura, quando quel cardinale Cervini, che fu poi papa Marcello II, <lb></lb>gli regalò un esemplare Delle galleggianti pubblicate nel 1549 per cura di <lb></lb>Niccolò Tartaglia, dall&#039;antico testo greco novamente tradotte in latino. </s></p><p type="main">

<s>Mentre studiosamente attendeva a rimeditare il Trattato archimedeo, per <lb></lb>emendarlo degli errori e per commentarlo a comun benefizio degli studiosi, <lb></lb>s&#039;abbattè, passando al II libro, a leggere la dimostrazione del teorema II. </s>

<s><lb></lb>Proponendosi ivi l&#039;Autore di determinar le condizioni dell&#039;equilibrio idro­<lb></lb>statico in una porzione di conoide parabolico immerso, fra gli altri principii <lb></lb>premessi alla conclusione v&#039;ebbe, con sua gran sorpresa, a leggere anche <lb></lb>questo: “ Sumatur autem centrum gravitatis portionis totius, quod nimirum <lb></lb>sit in puncto R diametrum ita dividente, ut totus diameter sit sesquialter <lb></lb>partis, quae est ad verticem, vel haec pars sit dupla eius, quae ad basim ” <lb></lb>(Archim., Opera cit., pag. </s>

<s>506). </s></p><p type="main">

<s>Dunque, cominciò allora a riformare, così ragionando, i suoi primi giu­<lb></lb>dizii il Commandino, non dee esser vero che trascurasse Archimede lo stu­<lb></lb>dio del centro di gravità ne&#039;solidi, trovandosene qui geometricamente defi­<lb></lb>nita la misura nel conoide parabolico. </s>

<s>In ogni modo, o dee averne trattato <lb></lb>egli stesso, il Matematico sicuracusano, o qualcun altro prima di lui, non <lb></lb>essendo possibile dar così confidentemente l&#039;enunciato teorema, senz&#039;averne <lb></lb>prima avuto certezza di dimostrazione. </s>

<s>Ma perchè insomma la dimostrazione, <lb></lb>che pur s&#039;argomentava dover esservi di fatto, nella Geometria antica non <lb></lb>si trovava, pensò il matematico urbinate di supplir secondo le sue forze al <lb></lb>difetto. </s>

<s>“ Cum autem ad hoc scribendum aggressus essem (così prosegue <lb></lb>con le sue proprie parole esso Commandino il racconto) allatus est ad me <lb></lb>liber Francisci Maurolici messanensis, in quo Vir ille doctissimus, et in iis <lb></lb>disciplinis exercitatissimus, affirmabat se de centro gravitatis corporum so­<lb></lb>lidorum conscripsisse. </s>

<s>Cum hoc intellexissem, sustinui me paulisper taci­<lb></lb>tusque expectavi dum opus clarissimi Viri, quem semper honoris caussa <lb></lb>nomino, in lucem proferretur. </s>

<s>Mihi enim exploratissimum erat F. </s>

<s>Mauroli­<lb></lb>cum multo doctius et exquisitius hoc disciplinarum genus scriptis suis tra­<lb></lb>diturum ” (De centro grav. </s>

<s>Praef., pag. </s>

<s>III-IV). Ma perchè l&#039;opera a com-<pb xlink:href="020/01/1866.jpg" pagenum="109"></pb>parire indugiava, e quasi presago che, se gli si fosse di cent&#039;anni prolungata <lb></lb>ancora la vita, non sarebbe stato pure a tempo a vederla; dette risoluta <lb></lb>mano a scrivere quel trattato <emph type="italics"></emph>De centro gravitatis solidorum,<emph.end type="italics"></emph.end> che venne <lb></lb>alla prima pubblica notizia dei Matematici nel 1565 in Bologna. </s></p><p type="main">

<s>Ivi, in XXX ordinate proposizioni, s&#039;investigano dall&#039;Autore i centri <lb></lb>della gravità ne&#039;solidi terminati da superficie piane, specialmente nella pi­<lb></lb>ramide e ne&#039;suoi frusti: poi si passa alla medesima inquisizione ne&#039;tre re­<lb></lb>golari corpi rotondi, nella sfera cioè, nel cilindro e nel cono. </s>

<s>Quanto agli <lb></lb>altri corpi terminati da superfice miste, in parte piane cioè e in parte ro­<lb></lb>tonde, lasciò il Commandino in gran desiderio la scienza, contento a solo il <lb></lb>conoide parabolico, in cui pareva avergli Archimede assegnata alle nuove <lb></lb>speculazioni la meta. </s></p><p type="main">

<s>Aveva il Matematico urbinate insomma, con lo spengerla solamente in <lb></lb>parte, accesa più vivamente che mai la sete del sapere. </s>

<s>Aggiungevasi poi, <lb></lb>al difetto del trattato nell&#039;estensione, qualche difetto qua e là nella condotta <lb></lb>de&#039;particolari teoremi, e Guidubaldo del Monte, per esempio, benchè così <lb></lb>affezionato e riverente al Maestro, pur francamente confessava al p. </s>

<s>Clavio <lb></lb>che l&#039;ultima <emph type="italics"></emph>De centro gravitatis solidorum<emph.end type="italics"></emph.end> “ non era buona, per non <lb></lb>essere universale ” (Alb. </s>

<s>VIII, 2). La pròposizione, a cui qui si accenna, è <lb></lb>la XXX del trattato, e ha per soggetto la ricerca del centro di gravità, no <lb></lb>nelle conoidi intere, ma nelle loro porzioni. </s></p><p type="main">

<s>Soggiungeva Guidubaldo, nelle sopra citate parole indirizzate in una <lb></lb>lettera a Galileo, dop&#039;avere commemorato il Clavio: “ il qual padre mi <lb></lb>mandò poi la sua dimostrazione assai diversa da questa di V. S. ” (ivi). <lb></lb>Ne&#039;principii dell&#039;anno 1588, in cui si scrivevano queste parole, era esso Ga­<lb></lb>lileo dunque, benchè giovanissimo, uno dei Matematici che attendevano alla <lb></lb>baricentrica de&#039;solidi, iniziata dal Commandino. </s>

<s>La mano stessa dell&#039;Autore <lb></lb>già vecchio volle di questi sparsi teoremi intessere una corona, per appen­<lb></lb>derla all&#039;estrema parete del grande edifizio delle Due nuove scienze. </s>

<s>Ivi, <lb></lb>quasi in lapide monumentale, fece al suo Salviati scolpire così fatte parole, <lb></lb>a perpetua memoria: “ Queste sono alcune proposizioni attenenti al centro <lb></lb>di gravità dei solidi, le quali in sua gioventù andò ritrovando il nostro Acca­<lb></lb>demico, parendogli che quello, che in tal materia aveva scritto Federigo <lb></lb>Commandino, non mancasse di qualche imperfezione. </s>

<s>Credette dunque con <lb></lb>queste proposizioni, che qui vedete scritte, poter supplire a quello, che si <lb></lb>desiderava nel libro del Commandino,.... con pensiero di andar seguitando <lb></lb>cotal materia, anco negli altri solidi non tocchi dal Commandino, ma incon­<lb></lb>tratosi dopo alcun tempo nel libro del signor Luca Valerio, sommo geome­<lb></lb>tra, e veduto com&#039;egli risolve tutta questa materia, senza niente lasciare in­<lb></lb>dietro, non seguitò più avanti, benchè le aggressioni sue sieno per istrade <lb></lb>molto diverse da quelle del signor Valerio ” (Alb. </s>

<s>XIII, 266). </s></p><p type="main">

<s>Il libro dell&#039;Autore onorificamente qui commemorato uscì in Roma <lb></lb>nel 1604, col titolo <emph type="italics"></emph>De centro gravitatis solidorum, libri tres.<emph.end type="italics"></emph.end> Scrive nella <lb></lb>prefazione il Valerio come, vivamente dolendosi che dovesse la Geometria <pb xlink:href="020/01/1867.jpg" pagenum="110"></pb>stare in desiderio di conseguire una notizia così degna, qual&#039;era quella dei <lb></lb>centri di gravità nei solidi, lasciati indietro dal Commandino; incorasse una <lb></lb>viva speranza, non atterrito dai lassi di lui, di poter supplire al difetto. </s>

<s>E <lb></lb>perciò “ cum ante exercitationis causa omnium quae proposui solidorum, <lb></lb>excepto conoide parabolico, centra gravitatis aliis viis indagassem; postea <lb></lb>non solum parabolici, sed ante me tentata nemini hyperbolici conoidis et <lb></lb>frusti utriusque et portionis utriusque conoidis, et portionis frusti et hemi­<lb></lb>sphaerii et hemisphaeroidis, et cuiuslibet portionis sphaerae, et sphaeroidis <lb></lb>uno et duobus planis parallelis abscissae centra gravitatis adinveni, multa <lb></lb>autem ex his duplici, quaedam triplici via ” (Praefatio libri cit, pag. </s>

<s>2). </s></p><p type="main">

<s>Dopo XXXIV anni che il campo baricentrico dei solidi era, per ogni <lb></lb>sua più remota parte, stato percorso dal Valerio, per cui quietava senz&#039;altri <lb></lb>desiderii la Geometria nel nuovo riconquistato possesso; Galileo credè me­<lb></lb>ritevoli di essere risaputi dal pubblico i suoi studii giovanili. </s>

<s>E perchè ri­<lb></lb>conosceva egli stesso consistere tutta la ragion di quel merito nel solo essere <lb></lb>le sue aggressioni per istrade molto diverse da quelle del Professor di ma­<lb></lb>tematiche nel ginnasio romano, la curiosità c&#039;invita a cercar quel che, per <lb></lb>la gloria di un tant&#039;uomo, si ritrovasse nel metodo galileiano veramente <lb></lb>di nuovo. </s></p><p type="main">

<s>Anche al primo sguardo nessuna novità si vede apparire nella sostanza, <lb></lb>procedendosi col metodo degl&#039;inscritti e dei circoscritti sulle orme, che al <lb></lb>Maurolico, al Commandino e al Valerio aveva già segnate Archimede ne&#039;suoi <lb></lb>più antichi teoremi. </s>

<s>Tutto il merito dunque, che attribuiscesi Galileo, non <lb></lb>può consistere in altro, che in qualche accidentalità introdotta ne&#039;più triti <lb></lb>processi dimostrativi, i quali perchè insomma, nell&#039;Appendice al quarto dia­<lb></lb>logo delle Due nuove scienze, s&#039;informano al I Lemma e alla proposizione I, <lb></lb>basterà esaminar questa, per dar retto giudizio di tutto il resto. </s></p><p type="main">

<s>Incominciarono le difficoltà da certi Fiorentini amici dell&#039;Autore, i quali, <lb></lb>dop&#039;avere attentamente letta la dimostrazione del Lemma, dissero “ di non <lb></lb>ci aver l&#039;intera satisfazione, non tollerando volentieri quel doppio modo di <lb></lb>considerare le medesime grandezze in diverse bilance ” (Alb. </s>

<s>VI, 2). Gali­<lb></lb>leo non era forse infin d&#039;allora tale, da metter in dubbio il valore del suo <lb></lb>proprio ingegno, ma più per farsi conoscere da loro, che per consultarne <lb></lb>l&#039;oracolo, si rivolse a due de&#039;più famosi Matematici che si conoscessero al­<lb></lb>lora; al padre Clavio e. </s>

<s>a Guidubaldo Del Monte. </s>

<s>Questi insomma approvò <lb></lb>con plauso, ma il Clavio rispondeva “ non gli dar fastidio quel doppio modo <lb></lb>di considerare le medesime grandezze in diverse bilance, perchè Archimede <lb></lb>fa quasi il medesimo nella propos. </s>

<s>VI del libro I Degli equiponderanti ” <lb></lb>(Alb. </s>

<s>VIII, 3), diceva però doversi, per non incorrère in un circolo vizioso, <lb></lb>dimostrare, e non semplicemente supporre, essere uno medesimo il centro <lb></lb>di gravità nelle due bilance. </s></p><p type="main">

<s>In cinquant&#039;anni, quanti intercessero fra queste controversie e la pub­<lb></lb>blicazione degli ultimi Dialoghi, Galileo non trovò nelle sue prime giova­<lb></lb>nili dimostrazioni nulla che fosse da correggere, e perciò, in quella forma <pb xlink:href="020/01/1868.jpg" pagenum="111"></pb>ch&#039;ebbero da principio, solennemente le espose al pubblico giudizio. </s>

<s>Le cri­<lb></lb>tiche del Clavio e de&#039;Fiorentini amici della gioventù dell&#039;Autore tornarono <lb></lb>in campo più vigorose che mai, ond&#039;è che il Viviani, così geloso della glo­<lb></lb>ria del suo Maestro, ben conoscendo che le promosse difficoltà non erano <lb></lb>affatto prive di fondamento, proponeva di dimostrare il medesimo lemma <lb></lb>galileiano in quest&#039;altra maniera. </s></p><p type="main">

<s>“ Si magnitudines quotcumque sese aequaliter excedentes, quarum <lb></lb>excessus minimae eorum sit aequalis, ln eadem linea secta ex distantiis <lb></lb>aequalibus suspensae fuerint; omnium ita suspensarum eentrum gravitatis <lb></lb>ita dividet libram, ut pars versus minores magnitudines, ad partem versus <lb></lb>maiores sit dupla. </s>

<s>” </s></p><p type="main">

<s>“ Ex distantiis aequalibus magnitudines, quales dictae sunt, suspendan­<lb></lb>tur 1, 2, 3, 4, 5, 6, sitque FI (fig. </s>

<s>48) dupla ipsius IE, et eidem aequales <lb></lb><figure id="id.020.01.1868.1.jpg" xlink:href="020/01/1868/1.jpg"></figure></s></p><p type="caption">

<s>Figura 48.<lb></lb>ponantur IN, ND, DM, MO. </s>

<s><lb></lb>Quia itaque magnitudo 2 <lb></lb>dupla est magnitudinis 1, <lb></lb>estque FI ipsius EI simi­<lb></lb>liter dupla; erit I centrum gravitatis compositae ex istis magnitudinibus <lb></lb>1+2. Suspensa est itaque magnitudo 3 in puncto I; suspensa est autem <lb></lb>in D magnitudo 3: ex punctis ergo D, I aequales pendent magnitudines. </s>

<s>Est <lb></lb>autem DN, ipsi NI distantiae, aequalis: equiponderant ergo ex puncto N <lb></lb>magnitudines 1+2+3. Est autem FN dupla ipsius DN, suntque magni­<lb></lb>tudines 1, 2, 3 in puncto N suspensae. </s>

<s>In puncto autem C suspenditur ma­<lb></lb>gnitudo 4, suntque dictae magnitudines ad magnitudinem 4 in sesquialtera <lb></lb>ratione. </s>

<s>Item et CD ipsius DN est sesquialtera: suspensis itaque magnitudi­<lb></lb>nibus 3, 2, 1 in N, et magnitudiues 4 in C, erit omnium centrum gravitatis <lb></lb>in D. </s>

<s>Et est FD ipsius DC dupla: suspensae sunt igitur in D magnitudines <lb></lb>4, 3, 2, 1, in B autem maguitudo 5, quae illarum est dimidium. </s>

<s>Estque BM <lb></lb>ipsius MD dupla: ergo magnitudinum 5, 4, 3, 2, 1, ita suspensarum, cen­<lb></lb>trum gravitatis erit M. </s>

<s>Est autem FM dupla MB: pendent ergo ex M ma­<lb></lb>gnitudines 5, 4, 3, 2, 1, ex A autem 6. Suntque hae magnitudines in ra­<lb></lb>tione 5 ad 2, et rursus AO ad OM est ut 5 ad 2, est enim BO aequalis OM, <lb></lb>et AB sesquialtera BO. </s>

<s>Aequiponderabunt igitur magnitudines omnes sic di­<lb></lb>spositae in puncto O, et est FO dupla ad AO, nam OD dupla est OB, et DF <lb></lb>dupla BA. </s>

<s>Quare patet propositum ” (MSS. Gal. </s>

<s>Disc., T. LXIV, c. </s>

<s>98). </s></p><p type="main">

<s>Condotta così la dimostrazione, come il Viviani la proponeva, sarebbe <lb></lb>da una parte riuscita assai più semplice e più chiara di quella di Galileo, <lb></lb>mentre si veniva dall&#039;altra a cessare ogni difficoltà, e a rimovere ogni ac­<lb></lb>cusa di petizion di principio, e di soverchio abuso de&#039;metodi archimedei. </s>

<s><lb></lb>Confermava dunque, così, il Discepolo sviscerato quelle difficoltà e quelle <lb></lb>accuse, che si davano al suo Maestro, il quale tornava perciò giudicato non <lb></lb>giusto estimatore de&#039;proprii meriti, per comun sentenza de&#039;benevoli e degli <lb></lb>avversarii. </s></p><p type="main">

<s>Da queste considerazioni s&#039;accende in noi più viva la curiosità di pe-<pb xlink:href="020/01/1869.jpg" pagenum="112"></pb>netrare addentro nell&#039;animo di Galileo, per vedervi ciò che lo movesse a <lb></lb>pubblicar, così fuori di proposito, quell&#039;appendice al IV de&#039;Dialoghi trat­<lb></lb>tanti unicamente del moto. </s>

<s>Scrisse nel 1686 in una lettera a Elia Diodati <lb></lb>che le dette conclusioni <emph type="italics"></emph>De centro gravitatis solidorum<emph.end type="italics"></emph.end> erano state ritro­<lb></lb>vate da lui “ essendo d&#039;età di ventun&#039;anno, e di due di studi di geome­<lb></lb>tria ” (MSS. Gal., P. V, T. VI, c. </s>

<s>73). Per questa età, senza dubbio, quelle <lb></lb>matematiche conclusioni son molto: si direbbe anzi che son troppo e tali <lb></lb>che, se si dovesse dai fiori di primavera argomentare ai frutti dell&#039;autunno, <lb></lb>si direbbe che quel giovane in Geometria fosse per riuscir davvero un Ar­<lb></lb>chimede novello. </s>

<s>Le lusinghiere speranze però andarono fallite, perchè ai <lb></lb>giusti giudici s&#039;appresentano i volumi di Galileo, ricchi di tante altre belle <lb></lb>cose, alquanto poveri però di Geometria. </s>

<s>Ora, a ripensare ai lassi nella curva <lb></lb>descritta dai gravi cadenti e nella corda tesa; alla insufficienza in trovar la <lb></lb>matematica dimostrazione delle leggi dei pendoli; a quelle stesse stentate e <lb></lb>avvolte dimostrazioni date negli ultimi due Dialoghi del moto dall&#039;Autore <lb></lb>già vecchio di settant&#039;anni; quelle fatte a ventuno potevano, non solo reg­<lb></lb>gère, ma rimaner superiori al confronto. </s></p><p type="main">

<s>Altri motivi, ch&#039;ebbe l&#039;Autore di dar quell&#039;appendice ai dialoghi delle <lb></lb>Due nuove scienze, si diranno in altro proposito, concludendo intanto che <lb></lb>per quelle galileiane dimostrazioni non fu la Baricentrica punto oltre pro­<lb></lb>mossa dall&#039;opera del Commandino, cosicchè tutto il merito ne rimane a <lb></lb>Luca Valerio. </s>

<s>Dopo il Valerio, il Torricelli ne coltivò lo studio da pari suo, <lb></lb>e il Cavalieri col suo metodo nuovo additava in cielo la stella, a segno della <lb></lb>quale potrebbero i Matematici correr sicuri quel mare, in tutta la sua smi­<lb></lb>surata ampiezza, nei più temuti seni riposti. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Mancavano dieci anni, per raggiungere la sua metà, al secolo XVI, e <lb></lb>in Vienna d&#039;Austria erano già appariti due grossi volumi in folio, l&#039;Autor <lb></lb>deì quali, straniero all&#039;Italia, presumeva baldanzosamente di aver costruita <lb></lb>una nuova nave, che per sè sola bastasse a correre l&#039;ampio mare che si <lb></lb>diceva. </s>

<s>Era imposto a quella nave il nome di <emph type="italics"></emph>Centrobrarica,<emph.end type="italics"></emph.end> e il nocchiero <lb></lb>di lei Paolo Guldin affidavasi al meccanico impulso delle sue vele, per appro­<lb></lb>dar facile e sicuro ai più lontani e infrequentati lidi della Geometria. </s></p><p type="main">

<s>Se si potesse, in argomento così serio, dar qualche parte alla poesia, <lb></lb>si direbbe che restarono a quel fatto i Matematici maravigliati, come le Ninfe <lb></lb>e Nettuno stesso, quando primo Giason dal Pelio spinse nel mar gli abeti. </s>

<s><lb></lb>Ma era una maraviglia, che s&#039;ebbe presto a spengere nei più meditativi, i <lb></lb>quali ripensarono che il fatto era bene più antico, avendone dato il primo <lb></lb>esempio Aristotile nella genesi meccanica del circolo, e poi Archimede nella <lb></lb>genesi meccanica della Spirale. </s>

<s>Il connubio stretto dall&#039;altra parte fra la <pb xlink:href="020/01/1870.jpg" pagenum="113"></pb>scienza del moto e la scienza dello spazio non poteva giunger nuovo a nes­<lb></lb>suno, che riflettesse come giusto il moto non si rende commensurabile e <lb></lb>parvente, che per via dello spazio, e l&#039;avventuroso incontro fra la Mecca­<lb></lb>nica e la Geometria nella Centrobrarica era prestabilito dall&#039;eterna legge <lb></lb>della natura, che le gravità son proporzionate alle moli. </s></p><p type="main">

<s>Abbiamo voluto far balenare alla mente de&#039;nostri lettori queste idee, <lb></lb>perchè intanto si persuadano quanto la Centrobrarica abbia bisogno, e sia <lb></lb>meritevole di storia. </s>

<s>Si narrerà da questa, con quella brevità che le è pre­<lb></lb>scritta, i principii e i progressi della invenzione ammirata, e si mostrerà <lb></lb>come s&#039;ingannasse il Guldino in pretendere che la sua Regola per sè sola <lb></lb>bastasse, e che potesse anzi col suo pratico meccanismo supplir non solo, <lb></lb>ma sopravvincere le alte speculazioni matematiche del Cavalieri. </s></p><p type="main">

<s>E prima di tutto, quanto ai principii, si volle da alcuno riconoscerli <lb></lb>lontanissimi in Pappo, il quale aveva assai bene illustrato il concetto dei <lb></lb>centri gravitativi, e ne avea data un&#039;assai chiara e precisa definizione che, <lb></lb>senza nulla aggiungere o levare, il Commandino e Guidubaldo tradussero <lb></lb>ne&#039;loro libri. </s>

<s>Nella prefazione al libro VII delle Matematiche collezioni il <lb></lb>valoroso Geometra d&#039;Alessandria pone innanzi a contemplare in uno sguardo <lb></lb>le principali opere di Euclide e di Apollonio, e ammirando la fecondità dei <lb></lb>ritrovati, e la bellezza delle speculazioni, vien comparandole con le misere <lb></lb>frivolezze de&#039;suoi tempi. </s>

<s>Io poi, prosegue a dire l&#039;Autore inspirato ai pla­<lb></lb>tonici precetti alessandrini, essendomi dato infin da giovane allo studio delle <lb></lb>Matematiche, e avendo trovati avviliti gl&#039;ingegni nelle questioni naturali, ne <lb></lb>presi gran vergogna, e sentii in me che avrei potuto metter fuori qualche <lb></lb>cosa di meglio. </s>

<s>E per mostrare, o mio figlio Ermodoro, ch&#039;io non sia ve­<lb></lb>nuto a mani vuote innanzi a te e ai lettori, v&#039;annunzierò intanto un teo­<lb></lb>rema, che contiene in sè molti altri bellissimi teoremi concernenti le linee, <lb></lb>le superfice e i solidi: teorema che nessuno ancora ha dimostrato, ma che <lb></lb>io con ragioni geometriche proverò nel XII libro di questi Elementi. </s>

<s>Il teo­<lb></lb>rema dunque è tale: “ Perfectorum utrorumque ordinum proportio com­<lb></lb>posita est ex proportione amphismatum, et rectarum linearum similiter ad <lb></lb>axes ductarum a punctis, quae in ipsis gravitatis centra sunt: imperfecto­<lb></lb>rum autem proportio composita est ex proportione amphismatum, et circum­<lb></lb>ferentiarum a punctis, quae in ipsis sunt centra gravitatis, factarum. </s>

<s>Harum <lb></lb>circumferentiarum proportio dividitur in proportionem ductarum linearum <lb></lb>et earum quas continent ipsarum extrema ad axes ” (Mathem. </s>

<s>collect. </s>

<s>cit., <lb></lb>pag. </s>

<s>252). </s></p><p type="main">

<s>I progressi fatti poi dalla Centrobrarica suggeriscono di queste parole <lb></lb>dell&#039;antico Pappo, lungamente rimaste enimmatiche, una tale interpetrazione, <lb></lb>che l&#039;enunciato alessandrino teorema viene a fare esatto riscontro con quel­<lb></lb>l&#039;altro dimostrato in tempi assai più recenti da Giann&#039;Antonio Rocca e dal <lb></lb>Torricelli, e dal quale scende, per corollario immediato, la Regola del Gul­<lb></lb>dino. </s>

<s>Per perfetti infatti dell&#039;uno e dell&#039;altro ordine si può intendere i so­<lb></lb>lidi di rivoluzione generati da superfice regolari circoscritte da linee rette, <pb xlink:href="020/01/1871.jpg" pagenum="114"></pb>come i triangoli e i quadrati, o da linee curve come i cerchi e le ellissi. </s>

<s><lb></lb>Così fatti solidi dunque, dice Pappo, star fra loro in ragion composta delle <lb></lb>superfice genitrici e delle linee condotte dal centro di gravità all&#039;asse di ro­<lb></lb>tazione, o delle circonferenze da esse linee come raggi descritte. </s>

<s>La mede­<lb></lb>sima regola poi, soggiunge il Collettore alessandrino, vale anche per le su­<lb></lb>perfice imperfette o irregolari, e per evitare intorno a ciò ogni causa di <lb></lb>errore, avverte che il raggio della circonferenza si compone della linea con­<lb></lb>dotta all&#039;asse dal centro di gravità sulla superfice circonvolubile, la qual <lb></lb>linea vuol essere dalla sua estrema parte prolungata infino a toccar l&#039;asse <lb></lb>di rotazione. </s>

<s>Si direbbe, in più brevi parole, essere il raggio della circon­<lb></lb>ferenza, ch&#039;entra nella detta ragione, la perpendicolare condotta dal centro <lb></lb>di gravità sopra l&#039;asse. </s>

<s>Tale è, secondo noi, uno dei significati che si pos­<lb></lb><figure id="id.020.01.1871.1.jpg" xlink:href="020/01/1871/1.jpg"></figure></s></p><p type="caption">

<s>Figura 49.<lb></lb>son dare alle parole <emph type="italics"></emph>Harum circumferentiarum <lb></lb>proportio dividitur in proportionem ductarum <lb></lb>linearum, et earum quas continent ipsarum <lb></lb>extrema ad axes;<emph.end type="italics"></emph.end> significato che s&#039;illustra dalla <lb></lb>figura 49, per la quale si mostra com&#039;essendo <lb></lb>in D il centro di gravità della superfice ABC <lb></lb>circonvolubile all&#039;asse EF, la lunghezza del rag­<lb></lb>gio della circonferenza si compone <emph type="italics"></emph>ductae lineae<emph.end type="italics"></emph.end><lb></lb>DH, e della estremità di lei verso l&#039;asse, HG. </s></p><p type="main">

<s>Dicemmo che il significato delle parole di Pappo ebbe solo nella più <lb></lb>recente scienza una interpetrazione, perchè veramente, prima che si descri­<lb></lb>vesse la Regola guldiniana, pareva impossibile a indovinarsi, e ciò tanto più, <lb></lb>per esser venuto a mancare il XII libro di quegli Elementi, ne&#039;quali pro­<lb></lb>metteva il Matematico alessandrino che avrebbe dato del proposto teorema <lb></lb>la desiderata dimostrazione. </s>

<s>Noi siam dunque persuasi che si trovi in Pappo <lb></lb>promossa la Regola centrobrarica, o che vi si trovi almeno annunziato il <lb></lb>teorema, da cui potere immediatamente concluderlo, e siamo persuasi al­<lb></lb>tresì che non fosse stato difficile ad esso Pappo dimostrar quel teorema, se <lb></lb>non con il metodo del Rocca e del Torricelli, con quell&#039;altro almeno che, <lb></lb>secondo gli ordini antichi, vedremo essere stato tenuto da Antonio Nardi. </s></p><p type="main">

<s>Non possiamo però consentir con coloro, i quali vollero dire che avesse <lb></lb>il Guldino tolta la sua Regola dal citato passo del Matematico greco, sì perchè <lb></lb>quel passo non si porge di facile intelligenza, se non a cui fosse la detta <lb></lb>Regola nota, sì perchè più prossima e più scoperta, nel libro di un suo <lb></lb>contemporaneo e connazionale, era la fonte, a cui attinse il Gesuita tedesco <lb></lb>le acque da riempirne il suo fiume. </s></p><p type="main">

<s>Giovanni Keplero, aiutandosi della Fisica, promosse in modo nuovo, <lb></lb>sopra quella degli antichi la moderna Geometria. </s>

<s>Crediamo in dir così di <lb></lb>aver bene qualificata, se non c&#039;inganniamo, l&#039;indole geometrica di quell&#039;in­<lb></lb>gegno, in cui sempre le immaginose apprensioni del sensibile precorrevano <lb></lb>e preparavano, come fiore il frutto, le sublimi concezioni dell&#039;intelletto. </s>

<s>Il <lb></lb>libro di lui, pubblicato in Lintz nel 1615, s&#039;intitola <emph type="italics"></emph>Nova Stereometria do-<emph.end type="italics"></emph.end><pb xlink:href="020/01/1872.jpg" pagenum="115"></pb><emph type="italics"></emph>liorum,<emph.end type="italics"></emph.end> e la seconda parte, <emph type="italics"></emph>Stereometriae archimedeae supplementum,<emph.end type="italics"></emph.end> co­<lb></lb>mincia con queste parole, nelle quali dichiara l&#039;Autore com&#039;avessero avuto <lb></lb>origine le novità da sè introdotte nella scienza stereometrica degli antichi. <lb></lb></s>

<s>“ Hucusque Archimedes et Geometrae veteres progressi sunt, inquirentes <lb></lb>naturam et dimensiones figurarum ordinatarum rectilinearum et curvilinea­<lb></lb>rum, quaeque ab iis solida proximo gradu gignuntur. </s>

<s>Caeterum, quia figura <lb></lb>Dolii longius a regularibus excurrit, operae praetium me facturum putavi, <lb></lb>si genesim illius et cognatarum, gradusque cognationis earum cum regula­<lb></lb>ribus, eadem quasi Tabella comprehensa, ob oculos exhiberem ” (Nova Ste­<lb></lb>reometria, Lincii 1615, fol. </s>

<s>16 t.). </s></p><p type="main">

<s>Si contengono in questa Tavola descritte molte figure di corpi rotondi <lb></lb>che non avendo avuto ancora un nome proprio dalla scienza, lo derivano <lb></lb>per similitudine o dalle arti fabbrili o dalla stessa natura, come quel per <lb></lb>esempio di anello, di fascia, di fuso; di oliva, di pera e di mela. </s>

<s>Non è in <lb></lb>così fatti corpi nulla che tutt&#039;insieme possa rassomigliarsi alla perfezion <lb></lb>della sfera, del cilindro o del cono, ma il Keplero ingegnosamente pensò di <lb></lb>ridurre a queste forme regolari le parti, se non potevasi il tutto. </s>

<s>Così apriva <lb></lb>alle Matematiche una via che, passando per gl&#039;indivisibili del Cavalieri, do­<lb></lb>veva gloriosamente condurre al calcolo infinitesimale. </s></p><p type="main">

<s>Sia per esempio ABCE (fig. </s>

<s>50) la curva che, rivolgendosi intorno al­<lb></lb><figure id="id.020.01.1872.1.jpg" xlink:href="020/01/1872/1.jpg"></figure></s></p><p type="caption">

<s>Figura 50.<lb></lb>l&#039;asse AE, abbia generato un solido, a cui, per la somi­<lb></lb>glianza col frutto naturale, dà il Keplero il nome di Pera. </s>

<s><lb></lb>Condotte le linee DF, CG, BH perpendicolari all&#039;asse, divi­<lb></lb>deranno queste la curva genitrice in porzioni di curve re­<lb></lb>golari e di linee rette, in modo tale che si potrà tutto il <lb></lb>solido riguardar composto di una callotta sferica, poi di <lb></lb>un tronco di cono, con la base minore in basso, poi di un <lb></lb>altro simile tronco, con la base minore in alto, e così di <lb></lb>seguito, infintantochè dalle risolute parti, regolarmente mi­<lb></lb>surabili, non resulti nella composizione la misura del tutto. </s></p><p type="main">

<s>Fu questo metodo resolutivo applicato altresì dal Kep­<lb></lb>lero a una nuova misura stereometrica, dalla quale doveva immediatamente <lb></lb>conseguire la regola del Guldino. </s>

<s>S&#039;immagini un cilindro di materia duttile, <lb></lb>del quale sia fatta una ciambella. </s>

<s>La misura del nuovo solido di rivoluzione <lb></lb><figure id="id.020.01.1872.2.jpg" xlink:href="020/01/1872/2.jpg"></figure></s></p><p type="caption">

<s>Figura 51.<lb></lb>è senza dubbio quella stessa del cilindro, ma <lb></lb>è però da pensar che, mentre si mantien certa <lb></lb>nella trasformazione e inalterata la base, ha <lb></lb>dovuto dagli opposti lati, per ragion meccanica, <lb></lb>variare l&#039;altezza. </s>

<s>Sia infatti in GCD (fig. </s>

<s>51) <lb></lb>rappresentata una sezione della detta ciambella <lb></lb>composta d&#039;infiniti minimi dischi come EFD. </s>

<s><lb></lb>Nel piegamento, così violentemente subìto, tutti i dischi dalla parte di D <lb></lb>si sono dilatati, e dalla parte di E compressi, cosicchè la prima naturale <lb></lb>altezza del cilindro, nel trasformarsi in ciambella, dall&#039;esterno è cresciuta, <pb xlink:href="020/01/1873.jpg" pagenum="116"></pb>e dall&#039;interno è diminuita. </s>

<s>Di qui è che, per non fare errore in così lubrica <lb></lb>materia, prenderemo, dice il Keplero, quella misura nelle parti di mezzo, e <lb></lb>potrà così riguardarsi la ciambella stessa come generata dalla rivoluzione <lb></lb>del disco EFD, intorno al punto A come a suo centro. </s>

<s>Per la più esatta <lb></lb>misura poi della solidità, prenderemo, come nel cilindro, la base moltipli­<lb></lb>cata per l&#039;altezza, ma non sarà questa altezza la raddirizzata circonferenza <lb></lb>descritta dal raggio AD, perchè eccessiva; nè sarà l&#039;altra più interna circon­<lb></lb>ferenza descritta dal raggio AE, perchè difettiva, ma sì propriamente quella <lb></lb>descritta dal raggio AF, supposto che sia in F il centro del disco, e di tutti <lb></lb>gli altri infiniti che compongono il cilindro. </s>

<s>Ciò è dal Keplero stesso messo <lb></lb>così in forma di proposizione, che è la XVIII della citata sua Stereometria <lb></lb>nuova: “ Omnis annulus sectionis circularis, vel ellipticae, est aequalis <lb></lb>cylindro, cuius altitudo aequat longitudinem circumferentiae, quam centrum <lb></lb>figurae circumductae descripsit; basis vero eadem est cum sectione annuli ” <lb></lb>(ibid., fol. </s>

<s>20 t.). </s></p><p type="main">

<s>La proposizione così esposta non voleva dall&#039;Autore lasciarsi indimo­<lb></lb>strata, ma il modo è affatto fisico o meccanico, e non punto geometrico, e <lb></lb>consiste insomma nel far considerare quel che dall&#039;altra parte è ovvio alla <lb></lb>più volgare esperienza, che cioè, incurvandosi una verga diritta, tanto ven­<lb></lb>gon le parti di lei a rimaner più compresse, quanto son più vicine al cen­<lb></lb>tro di curvatura. </s>

<s>“ Annulo enim GCD sed integro (così propriamente dice <lb></lb>il Keplero) ex centro spacii A secto in orbiculos infinitos ED, cosque mini­<lb></lb>mos, quilibet eorum tanto erit tenuior versus centrum A, quanto pars eius <lb></lb>ut E fuerit propior centro A quam est F, et recta per F ipsi ED perpen­<lb></lb>dicularis in plano secante: tanto etiam crassior versus exteriora D. </s>

<s>Extre­<lb></lb>mis vero dictis, scilicet D, E, simul sumptis, duplum sumitur eius crassitiei, <lb></lb>quae est in orbiculorum medio ” (ibid.). </s></p><p type="main">

<s>Poi soggiungesi un corollario, in cui fa l&#039;Autore osservare che vale la <lb></lb>medesima regola per la misura di altre simili ciambelle, qualunque sieno <lb></lb>le figure della loro sezione, “ dummodo in plano per AD ad annulum recto <lb></lb>sectionis partes, eis et ultra F, fuerint aequales, aequaliterque sitae hinc et <lb></lb>inde, quod explorabimus in figura sectionis quadrata ” (ibid.). </s></p><p type="main">

<s>Era dunque la Regola kepleriana limitata alle figure perfette, nelle quali <lb></lb>sole è possibile a determinarsi con precisione il centro della grandezza. </s>

<s>Sov­<lb></lb>venne in questo al Guldino una felicissima idea, che gli fece senza limiti <lb></lb>approvar quel concetto, e fu di sostituire il centro di gravità al centro di <lb></lb>figura. </s>

<s>Si trattava infatti di ridurre la quantità di materia, variamente di­<lb></lb>stribuita, in un punto solo di mezzo, per cui argutamente pensò dover me­<lb></lb>glio servire all&#039;uopo la Meccanica, con le sue leggi degli equiponderanti, <lb></lb>che non la Geometria con la regola delle sue ci<gap></gap>coscrizioni. </s></p><p type="main">

<s>Nel 1635 aveva il Guldino pubblicato il suo primo libro della Centro­<lb></lb>brarica, che trattava della semplice invenzione del centro di gravità nelle <lb></lb>superfice e ne&#039;solidi. </s>

<s>L&#039;opera, benchè più estesa, è pure nel valor mate­<lb></lb>matico assai inferiore a quella, non del Valerio solo, ma e dello stesso Com-<pb xlink:href="020/01/1874.jpg" pagenum="117"></pb>mandino primo conosciuto iniziator della scienza. </s>

<s>Nel 1640 comparve, pure <lb></lb>in Vienna d&#039;Austria, il secondo libro della stessa Centrobrarica, in cui l&#039;Au­<lb></lb>tore esplicava in questa nuova forma il concetto, che si diceva essergli fe­<lb></lb>licemente sovvenuto in rimeditare il teorema XVIII della Stereometria nuova <lb></lb>del Keplero: “ Partes rotundae quantitatis, quo longius distant a centro seu <lb></lb>axe rotationis, eo plus etiam quantitatis seu potestatis describunt, cum maio­<lb></lb>rem faciant circuitum: et contra quo magis partes ad axem rotationis acce­<lb></lb>dunt, hoc minorem faciunt ambitum, minusque quantitatis efficiunt. </s>

<s>Inve­<lb></lb>nire ergo oportet aliquod medium, ita ut partes hinc inde, hoc est extrorsum <lb></lb>et introrsum, sive ultra et eis descriptae, aliquo modo aequentur. </s>

<s>Hoc au­<lb></lb>tem fiet si linea illa circularis, quae in quantitatem rotundam ducenda erit, <lb></lb>accipiatur ea quam in rotatione describit centrum gravitatis magnitudinis <lb></lb>rotundae, quae est sola et unica. </s>

<s>Hoc enim centrum, cum magnitudinis cuius <lb></lb>centrum dicitur circa se contineat partes aequalium momentorum in motu <lb></lb>recto quidem ac perpendiculari; describet undique atque efficiet rursus par­<lb></lb>tes quantitatis, seu potestatis inde genitae, similiter aequalium momentorum, <lb></lb>ita ut centrum gravitatis effectae potestatis denuo sit in linea, quam in hoc <lb></lb>motu recto descripsit recta ex centro gravitatis magnitudinis motae, ad eam <lb></lb>perpendiculariter educta ” (Centrobraryca, Viennae 1640, pag. </s>

<s>146). </s></p><p type="main">

<s>Ecco dunque in che consiste il progresso della invenzione del Guldino: <lb></lb>il Keplero aveva detto che la misura del solido di rivoluzione GCD, nel <lb></lb>passato nostro LI iconismo, è data dal prodotto della superfice EFD, che si <lb></lb>vuol di perfetta figura come il cerchio o il quadrato, per la circonferenza <lb></lb>descritta dalla linea AF, supposto essere in F il centro della superfice stessa, <lb></lb>dalla quale ha da generarsi il solido rotondo. </s>

<s>Il Guldino viene ora a dare <lb></lb>una regola simile, che vale generalmente qualunque forma abbia la super­<lb></lb>ficie rotante, e annunzia che il corpo generatosi da così fatta rotazione è <lb></lb>misurato dal prodotto della detta superfice per la circonferenza descritta <lb></lb>dalla linea AF, supposto però che segni F il centro della gravità, e non <lb></lb>della figura. </s></p><p type="main">

<s>Il passo guldiniano, da cui questa nuova Regola resulta, lo abbiamo <lb></lb>trascritto dal capitolo VIII del detto libro II; capitolo, che è in forma di <lb></lb>proposizione, alla quale seguitano quattro corollarii Conclude in questi l&#039;Au­<lb></lb>tore le varie regole particolari, che scendono dalla generalissima ne&#039;casi, <lb></lb>che si vogliano paragonare fra loro le misure di due solidi rotondi R, R′ ge­<lb></lb>nerati da due figure diverse. </s>

<s>Chiamate F, F′ queste figure e C, C′ le cir­<lb></lb>conferenze descritte da&#039;loro centri di gravità nell&#039;andare attorno, la regola <lb></lb>centrobrarica si conclude nell&#039;equazione R:R=FC:F′C′, che il Gul­<lb></lb>dino, nel suo corollario terzo, formula con queste parole: “ Si tam quan­<lb></lb>titates rotundae quam viae sive radii rotationis sint inaequales, sequitur ul­<lb></lb>terius potestatum proportionem esse compositam ex ratione quantitatis rotatae <lb></lb>unius ad quantitatem rotatam alterius, et ex ratione viae vel radii illius unius, <lb></lb>ad viam vel radium huius alterius (ibid., pag. </s>

<s>148). </s></p><p type="main">

<s>Se di questa nuova ragione stereometrica non hanno ancora i Matema-<pb xlink:href="020/01/1875.jpg" pagenum="118"></pb>tici finito di ammirare la semplicità e la bellezza, s&#039;immagini qual dovesse <lb></lb>essere l&#039;animo dell&#039;inventore, disposto, per l&#039;indole propria e del suo soda­<lb></lb>lizio, a magnificare e a vantar sopra gli altri ogni minima cosa. </s>

<s>Che è mai <lb></lb>la Stereometria nuova del Keplero, appetto alla sua Baricentrica? </s>

<s>L&#039;Autore <lb></lb>della stereometria delle botti aveva ben tentata la misura di quelli, e di tanti <lb></lb>altri solidi di rivoluzione, ma perchè non seppe riconoscer l&#039;uso, che po­<lb></lb>teva farsi dei centri di gravità, <emph type="italics"></emph>cursum non tenuit, tentatisque excidit ausis.<emph.end type="italics"></emph.end><lb></lb>Così appunto scriveva il Guldino, a pag. </s>

<s>297 del II tomo, nella prefazione <lb></lb>al suo III libro centrobrarico pubblicato nel 1641. </s></p><p type="main">

<s>In quel medesimo anno, congiunto al III, pubblicava pure esso Gul­<lb></lb>dino il IV e ultimo libro, alla fin del quale soggiungeva un capitolo inti­<lb></lb>tolato: <emph type="italics"></emph>Perpenduntur quaedam ex Nova geometria Bonaventurae Cava­<lb></lb>lieri desumpta.<emph.end type="italics"></emph.end> In cinque proposizioni, alcune delle quali corredate di scolii, <lb></lb>si censurano ivi dall&#039;Autore altrettante proposizioni dimostrate nella Geo­<lb></lb>metria degl&#039;indivisibili dal Cavalieri. </s>

<s>Ma già le sollecitudini del Gesuita te­<lb></lb>desco, in vantar l&#039;eccellenza dell&#039;opera sua sopra quella del nostro Italiano, <lb></lb>erano incominciate infin dalla prima pubblicazione del libro II, dove il proe­<lb></lb>mio è principalmente ordinato dall&#039;Autore a glorificar sè e ad opprimere <lb></lb>il suo rivale. </s>

<s>Lo accusava di plagio, per non aver fatto altro che imitare, e <lb></lb>appropriarsi il metodo del Keplero e di Bartolommeo Sovero, e compassio­<lb></lb>nava que&#039;tanto sudati studii che, per non esservisi saputa riconoscer la di­<lb></lb>gnità de&#039;baricentri, non erano riusciti ad altro, che a dar qualche forma <lb></lb>geometrica ai più astrusi paralogismi. </s></p><p type="main">

<s>Il Cavalieri, combattuto da tante altre parti, prese nuovo coraggio al <lb></lb>poderoso assalto, già presago che i posteri, più retti giudici, avrebbero sulla <lb></lb>sua Geometria posata la corona della gloria. </s>

<s>Mentre perciò il Guldino si sfo­<lb></lb>gava in esaltar tutto sè e il suo istituto, sentiva il Cavalieri in coscienza il <lb></lb>dovere di difendere il vero, e s&#039;apparecchiava a farlo con tante ragioni, che <lb></lb>gli tenevano la mente e l&#039;animo in gran tumulto. </s>

<s>Avrebbe voluto rispon­<lb></lb>dere all&#039;Autore della Centrobrarica, appena levati gli occhi dal libro, che <lb></lb>lui piuttosto non aveva fatto altro che proseguire i metodi del Keplero, e <lb></lb>che l&#039;accusa data al Maestro col dire “ analogiis et coniecturis multum tri­<lb></lb>buisse, non scientifice semper conclusisse et insuper sua omnia obscura pro­<lb></lb>posuisse ” (Centrobr. </s>

<s>cit., T. II, pag. </s>

<s>322) si dovevano più giustamente ri­<lb></lb>versar sul discepolo ingrato. </s>

<s>Dove sono infatti, domandava fra sè il Cavalieri, <lb></lb>in questa opera del Guldino i fondamenti matematici? </s>

<s>Si procede anche qui <lb></lb>per analogie e per congetture, che son quelle medesime del Keplero, perchè, <lb></lb>sebbene vi si sia sostituito il centro di gravità al centro della figura, la ra­<lb></lb>gione ultima insomma si riduce al fatto della verga diritta trasformata in <lb></lb>ciambella. </s>

<s>Vero è che non si dà matematica dimostrazione della Stereome­<lb></lb>tria nuova, ma qual matematica dimostrazione conforta le conclusioni della <lb></lb>Centrobrarica? </s>

<s>Tutto si fa consistere in dare a vedere ai lettori come i re­<lb></lb>sultati della Regola nuova riscontrano esattamente con i teoremi di Euclide <lb></lb>e di Archimede. </s>

<s>S&#039;accusano gl&#039;indivisibili di nessuna riuscita, eppur potreb-<pb xlink:href="020/01/1876.jpg" pagenum="119"></pb>besi facilmente dimostrare che si trova in essi uno de&#039;più solidi fondamenti <lb></lb>a quell&#039;edifizio centrobrarico, che il suo Autore ha lasciato per aria. </s></p><p type="main">

<s>Se il Keplero propone tutte le sue cose oscure, seguitava a ragionare <lb></lb>fra sè il Cavalieri, non si lusinghi però della semplicità della sua Regola il <lb></lb>Guldino. </s>

<s>È molto facile a dire: dato il centro di gravità di qualunque su­<lb></lb>perfice irregolare si ha, per sicura e spedita via, la misura del solido ro­<lb></lb>tondo. </s>

<s>Come può ritrovarsi quel centro? </s>

<s>se in modo geometrico, risolvendo <lb></lb>la proposta superfice in tanti triangoli, e componendo in uno i centri par­<lb></lb>ziali; mentre non sarebbe a confidar da una parte che riuscisse quella via <lb></lb>veramente sicura, dovrebbesi confessare dall&#039;altra che non tornerebbe punto <lb></lb>spedita. </s>

<s>Facile senza dubbio s&#039;avrebbe il centro di gravità, in qualunque <lb></lb>superfice più irregolare, dalla intersezione di due perpendicoli; ma pure il <lb></lb>modo sarebbe affatto meccanico, benchè assai confacevole col metodo, che <lb></lb>regola tutta la Centrobrarica del Guldino. </s></p><p type="main">

<s>Dovevano questi tumultuosi ragionamenti uscire in forma di pubblica <lb></lb>scrittura dalla mente del Cavalieri, e a dir come e quando ciò avvenisse ha <lb></lb>da attender ora la nostra Storia. </s>

<s>E perchè dalla Geometria degli indivisibili <lb></lb>piglia la narrazione il suo principio e la sua maggiore importanza, non in­<lb></lb>crescerà ai Lettori l&#039;esser tenuti brevemente in discorso di quell&#039;Opera, ch&#039;è <lb></lb>pure uno de&#039;monumenti più insigni della Scienza italiana. </s></p><p type="main">

<s>Muovono dal Keplero anche le nuove speculazioni del Cavalieri. </s>

<s>Tor­<lb></lb>niamo con lo sguardo indietro sulla nostra L figura. </s>

<s>Può la linea DE fisi­<lb></lb>camente riguardarsi come un arco di cerchio, e le CD, CB come linee rette; <lb></lb>ma se poteva ciò facilmente concedersi al Keplero, per la pratica misura <lb></lb>delle botti, non reggeva però il postulato al più rigoroso istituto geometrico. </s>

<s><lb></lb>Perchè si potessero quelle linee geometricamente riguardar come rette, non <lb></lb>conveniva prenderle in quantità definita, come l&#039;Autore della Stereometria <lb></lb>nuova faceva, ma sì ridurle alla loro ultima divisione, o renderle <emph type="italics"></emph>indivisi­<lb></lb>bili,<emph.end type="italics"></emph.end> come piaceva dire al Cavalieri. </s></p><p type="main">

<s>Della matematica precisione di questo metodo s&#039;erano dall&#039;altra parte <lb></lb>confidati anche i geometri antichi, allora che intendevano studiosi ad aver <lb></lb>tanto più prossima al vero la quadratura del circolo, quanto fossero mag­<lb></lb>giori i lati de&#039;poligoni inscritti e dei circoscritti, d&#039;onde per legittimo ragio­<lb></lb>namento scendeva poter riguardarsi matematicamente come retta la indivisi­<lb></lb>bile porzioncella di un arco. </s>

<s>Il Cavalieri insomma divideva la linea flessuosa <lb></lb>ABCDE in un numero infinito di tratti, infinitamente moltiplicando le pa­<lb></lb>rallele, condotte perpendicolari all&#039;asse dal Keplero; cosicchè di tutte in­<lb></lb>sieme queste parallele venisse quasi a intessersi la proposta superfice, come <lb></lb>di tutti insieme i piani paralleli descritti, veniva per simil modo il solido di <lb></lb>rotazione a compaginarsi. </s>

<s>“ Hinc manifestum est figuras planas nobis ad <lb></lb>instar telae parallelis fiilis contextae concipiendas esse: solida vero, ad instar <lb></lb>librorum, qui parallelis foliis coacervantur ” (Exercit. </s>

<s>geom., Bononiae 1647, <lb></lb>pag. </s>

<s>3). </s></p><p type="main">

<s>Il nuovo metodo dall&#039;altra parte prometteva assai bene di sè, col dif-<pb xlink:href="020/01/1877.jpg" pagenum="120"></pb>fondere sugli antichi teoremi euclidei una maravigliosa chiarezza. </s>

<s>La misura <lb></lb>della superfice di un rettangolo, per esempio, e della solidità di un cilindro, <lb></lb>si rendeva ora assai facile a intendere come fossero date dal prodotto delle <lb></lb>basi per le altezze, perchè quelle basi rappresentano il primo filo e la prima <lb></lb>pagina, da cui, per la soprapposizione di altrettanti simili fili e pagine quanti <lb></lb>son punti indivisibili nell&#039;altezza, viene ad aversi tutto insieme il tessuto <lb></lb>della superfice, e tutta intiera la coacervazion del volume. </s>

<s>Prometteva altresì <lb></lb>quel metodo, che procede per via della division delle parti, di alleggerir <lb></lb>molte di quelle difficoltà, che l&#039;antica geometria ritrovava in considerare il <lb></lb>tutto, quasi come si esperimenta di un gran sasso che, malagevole ad esser <lb></lb>mosso dalla forza di un gigante, ridotto in minutissima polvere, è sollevato <lb></lb>dalla più leggera aura di vento. </s></p><p type="main">

<s>Incoraggiato dunque da così belle promesse, dietro la regola generale <lb></lb>che “ figurae tam planae quam solidae sunt in ratione omnium suorum <lb></lb>indivisibilium collective ” (ibid., pag. </s>

<s>6), messe il Cavalieri in ordine, tra il <lb></lb>finir dell&#039;anno 1621 e il cominciar del seguente, una serie di proposizioni, <lb></lb>e ne compose un trattatello, che il di 22 Marzo del 1622 spediva da Milano <lb></lb>a Firenze a Galileo. </s>

<s>Accompagnava il plico una lettera, nella quale, dopo <lb></lb>alcune avvertenze fatte intorno al principio e al modo di dimostrar per via <lb></lb>degli indivisibili quelle varie proposizioni, si finiva con queste parole: “ Di <lb></lb>grazia mi favorisca di dirmene il suo parere, che lo sto aspettando con gran <lb></lb>desiderio ” (Campori, Carteggio galil., Modena 1881, pag. </s>

<s>191). </s></p><p type="main">

<s>Galileo, che tutto allora era dietro a rimeditare sopra quegli infiniti <lb></lb>istanti di tempo, secondo i quali crescono le velocità nei moti accelerati, <lb></lb>vide in quelle infinite linee, di che il Cavalieri intesseva le superfice, ma­<lb></lb>ravigliosamente specchiati in immagine viva i suoi pensieri, e facendosi agli <lb></lb>indivisibili punti di una linea verticale, presa per l&#039;altezza di un triangolo, <lb></lb>rappresentare gl&#039;infiniti istanti di tempo decorsi, e alla orizzontale, presa <lb></lb>per base, l&#039;ultimo grado della velocità acquistatasi dal mobile nella caduta; <lb></lb>tirata dalle estremità di tal base e di tale altezza un&#039;obliqua, dal triangolo <lb></lb>ch&#039;indi nasceva vedevasi sotto gli occhi rappresentati i tre efficienti del moto. </s>

<s><lb></lb>Lo spazio infatti rappresentato dalla superfice triangolare riusciva proporzio­<lb></lb>nale al prodotto dell&#039;altezza per la base, ossia della velocità per il tempo, se­<lb></lb>condo le leggi per altra via già scoperte, e il corollario fondamentale, che cioè, <lb></lb>movendo un grave dalla quiete e proseguendo poi equabilmente il suo libero <lb></lb>moto naturale, secondo il grado della velocità ultimamente acquistata, pas­<lb></lb>serebbe in tempo eguale uno spazio doppio; appariva visibile nel rettangolo, <lb></lb>che costruito sopra la medesima base triangolare, in eguale altezza, esso <lb></lb>pure in superfice riesce doppio. </s></p><p type="main">

<s>Allettato dalla bellezza di questi nuovi processi dimostrativi, mentre atten­<lb></lb>deva Galileo a metterli in forma, nei primi libri che abbozzava allora <emph type="italics"></emph>De <lb></lb>motu,<emph.end type="italics"></emph.end> s&#039;era voluto dimenticar dell&#039;Inventore, entrato in gran desiderio che <lb></lb>quel trattato degli indivisibili si potesse dir suo. </s>

<s>Chi avrebbe osato mai di <lb></lb>negarglielo, se fosse uscito a dire che quegli stessi pensieri erano prima <pb xlink:href="020/01/1878.jpg" pagenum="121"></pb>passati per la sua mente? </s>

<s>Deliberava intanto di starsene in silenzio, e il <lb></lb>Cavalieri che, in cinque mesi, non aveva avuta la desiderata risposta, tor­<lb></lb>nava, con lettera del dì 11 di Agosto, a manifestar l&#039;ardentissima sete, che <lb></lb>gli era convenuto di sopportare, sperando, diceva, che “ finalmente io sii di <lb></lb>questo da lei graziato. </s>

<s>” Nel Dicembre appresso la grazia ancora non era <lb></lb>ricevuta, e gli era solo, per mezzo del padre Castelli, fatto sapere che chi <lb></lb>aveva a darla non poteva <emph type="italics"></emph>per le sue grandissime occupazioni ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>198). <lb></lb>Passò tutto l&#039;inverno in silenzio, e la primavera seguente tornava il Cava­<lb></lb>lieri con accorata preghiera, a scrivere queste parole: “ Spero dunque dalla <lb></lb>benignità sua che, dal tempo che li togliono i suoi alti pensieri d&#039;altre sue <lb></lb>più necessarie occupazioni, sceglierà alcuna parte per dare un&#039;occhiata a <lb></lb>questo mio trattatello ” (ivi, pag. </s>

<s>201). </s></p><p type="main">

<s>Ma chi poteva persuadersi che in più di un anno non avesse trovato <lb></lb>Galileo qualche ora di tempo, per dare una scorsa al trattato, o pochi mi­<lb></lb>nuti almeno per scriver da sè, senz&#039;altro mediatore, che l&#039;aveva ricevuto? </s>

<s><lb></lb>La semplicità del Cavalieri non doveva essere poi tanta, da non sospettar <lb></lb>che qualche cosa ci doveva esser sotto, e dopo tre anni e più di pena final­<lb></lb>mente ebbe il segreto: Galileo attendeva a scrivere egli stesso un trattato <lb></lb>Degli indivisibili, e non voleva esser prevenuto da un suo discepolo. </s></p><p type="main">

<s>Il Cavalieri, contento che fosse il soggetto reputato di tanta importanza, <lb></lb>aspettava che venisse in luce l&#039;opera del Maestro, a cui il dì 29 Febbraio 1626 <lb></lb>scriveva da Roma: “ Si ricordi dell&#039;opera sua Degli indivisibili, che già de­<lb></lb>terminò di comporre ” (Alb. </s>

<s>IX, 100). Non tralasciava però il primo intra­<lb></lb>preso studio, e dalle superfice era passato a trattar de&#039;solidi, scrivendo il <lb></lb>libro in lingua italiana, “ acciò, diceva a Galileo, se le pare bene, ancora <lb></lb>lei così faccia del suo Degli indivisibili ” (Campori, Cart. </s>

<s>cit., pag. </s>

<s>243). </s></p><p type="main">

<s>Tanto s&#039;esercitò il Cavalieri intorno a scrivere quel suo libro, che il <lb></lb>dì 17 Dicembre 1627 dava di Parma a Galileo la nuova “ come già un mese <lb></lb>fa inviai l&#039;opera, che già componevo, qual V. S. sa, a monsignor Ciampoli, <lb></lb>avendola terminata nel miglior modo che ho saputo e potuto ” (Alb. </s>

<s>IX, 121). <lb></lb>Un anno e pochi mesi dopo, già eletto pubblico professore di Matematiche <lb></lb>nello studio di Bologna, mandava a quei Signori come saggio di sè i VII li­<lb></lb>bri della sua nuova Geometria, per cui, a rispondere alle imputazioni del <lb></lb>Guldino, dichiarava la precedenza del libro suo manoscritto sopra quello <emph type="italics"></emph>De <lb></lb>curvi et recti proportione promota<emph.end type="italics"></emph.end> del Sovero, invocando testimonii di ciò <lb></lb>gl&#039;illustrissimi Senatori dell&#039;inclita città di Bologna, ai quali, dice nella III <lb></lb>delle citate esercitazioni geometriche, “ misi, eodem anno 1629, dictae Geo­<lb></lb>metriae VII libros, etsi manuscriptos, attamen absolutos ” (pag. </s>

<s>183). </s></p><p type="main">

<s>S&#039;aspettava tuttavia con desiderio l&#039;opera, che Galileo aveva determi­<lb></lb>nato di comporre sopra questo medesimo argomento, ma, giunti all&#039;anno 1632, <lb></lb>non s&#039;era altro veduto di lui che l&#039;applicaziene fatta degli indivisibili a di­<lb></lb>mostrar, nella II Giornata dei Due massimi sistemi, il teorema del moto equa­<lb></lb>bile, che in tempo eguale all&#039;accelerato passa uno spazio doppio (Alb. </s>

<s>I, 252). <lb></lb>Nelle passioni, a cui fu soggetto l&#039;animo dell&#039;Autore per questa pubblica-<pb xlink:href="020/01/1879.jpg" pagenum="122"></pb>zione, s&#039;attuti lo spirito che traboccando voleva invadere gli altrui dominii, <lb></lb>nè, dedicandosi poi tutto alle speculazioni del moto, seppe veder come si <lb></lb>raccoglierebbe di lì tanto frutto, da compensare in coscienza i rimorsi del­<lb></lb>l&#039;usurpato. </s>

<s>Rimasto dunque il metodo dagl&#039;indivisibili in libertà del suo le­<lb></lb>gittimo inventore, s&#039;apparecchiava questi, senza più lungamente indugiare, <lb></lb>a pubblicarlo. </s>

<s>E giacchè andava Galileo per ogni parte annunziando la pros­<lb></lb>sima stampa della dottrina del moto, tanto desiderata, il Cavalieri scrive­<lb></lb>vagli così il dì 10 di Gennaio del 1634 da Bologna: “ La vorrei ben pre­<lb></lb>gare, se le venisse a taglio, che si compiacesse toccare qualche cosa ancora <lb></lb>della dottrina degli indivisibili, come già alcuni anni sono aveva pensiero, <lb></lb>in grazia della mia Geometria, che glie ne resterei obbligatissimo: credo che <lb></lb>dal dialogizzare potrà far nascere l&#039;occasione, perciò spererò di esserne fa­<lb></lb>vorito ” (Alb. </s>

<s>X, 4). </s></p><p type="main">

<s>Il Cavalieri andava con ragione rammemorando gli anni passati, ne&#039;quali <lb></lb>la bellezza del nuovo metodo aveva così sedotta la mente di Galileo, nè sa­<lb></lb>rebbesi aspettato mai che il primo fervente amore si fosse convertito in al­<lb></lb>trettanta freddezza di odio. </s>

<s>Nel Luglio del 1634 erano già finiti di stampare <lb></lb>in Bologna i primi cinque libri della Geometria degl&#039;indivisibili, e man­<lb></lb>datigli a Galileo perchè, avendone agio, <emph type="italics"></emph>gliene desse un poco d&#039;occhiata<emph.end type="italics"></emph.end><lb></lb>(Alb. </s>

<s>X, 48), n&#039;ebbe a gustar l&#039;Autore dalla risposta il primo amaro sag­<lb></lb>gio di quella inaspettata mutazione. </s>

<s>Dicevasi in tal risposta, fatta sulla fine <lb></lb>del Settembre del 1634, non sembrargli il nuovo metodo del tutto impro­<lb></lb>babile, ma che ci avevano però molte difficoltà, la prima e più forte delle <lb></lb>quali consisteva in questa, che noi ora diremo come fosse nata nella mal <lb></lb>disposta mente dell&#039;oppositore. </s></p><p type="main">

<s>Intendasi il mezzo cerchio AFB (fig. </s>

<s>52), il cui centro C, ed intorno ad <lb></lb>esso il parallelogrammo rettangolo ADEB, e dal centro ai punti D, E siano <lb></lb>le linee rette CD, CE. </s>

<s>Figurandoci poi il semidiametro CF perpendicolare a <lb></lb><figure id="id.020.01.1879.1.jpg" xlink:href="020/01/1879/1.jpg"></figure></s></p><p type="caption">

<s>Figura 52.<lb></lb>una delle due AB, DE immobile, intendiamo <lb></lb>intorno a quello girarsi tutta questa figura. <lb></lb></s>

<s>È manifesto che dal triangolo CDF sarà ge­<lb></lb>nerato un cono, e dal triangoloide ADF un <lb></lb>cilindro scavato da un emisferio, a cui si <lb></lb>può, per la somiglianza, dare il nome di <lb></lb>cratere o di scodella. </s>

<s>Luca Valerio aveva, per <lb></lb>servirsene come lemma alla proposizione XII <lb></lb>del II libro <emph type="italics"></emph>De centro gravitatis,<emph.end type="italics"></emph.end> dimostrato che, non solo la solidità di tutto <lb></lb>il cratere e quella di tutto il cono sono eguali, ma che, condotto a qualsi­<lb></lb>voglia punto un piano secante parallelo alla base DE, sono altresì eguali fra <lb></lb>loro le due porzioni. </s>

<s>Anzi, non le porzioni sole generate per esempio dalla <lb></lb>figura GAI, e dal triangolo CHP, ma lo stesso circolo descritto dal raggio HP <lb></lb>e l&#039;armilla o nastro descritto dalla linea GI, relative basi delle due sezioni, <lb></lb>si serbano costantemente fra loro eguali. </s></p><p type="main">

<s>La dimostrazione del Valerio consisteva nel condurre moltissime linee <pb xlink:href="020/01/1880.jpg" pagenum="123"></pb>come la GN, le quali nel cono e nel cratere segassero piccolissime porzioni, <lb></lb>ch&#039;ei dimostrava essere eguali, per concluder poi l&#039;eguaglianza del tutto dal­<lb></lb>l&#039;eguaglianza delle singole parti. </s>

<s>Aveva il processo di quella dimostrazione, <lb></lb>col metodo degl&#039;indivisibili, una somiglianza, che volle Galileo irragionevol­<lb></lb>mente ridurre a un&#039;assoluta identità, argomentando allo stesso modo dover <lb></lb>esser fra loro eguali le due ultime porzioni nelle divisioni del Valerio, e le <lb></lb>due esaustioni, secondo il metodo del Cavalieri. </s>

<s>Ma perchè sono evidente­<lb></lb>mente quelle due esaustioni l&#039;orlo della scodella e l&#039;apice del cono, condur­<lb></lb>rebbe dunque il metodo degl&#039;indivisibili, diceva Galileo, all&#039;assurda conse­<lb></lb>guenza che fossero insieme eguali una linea lunghissima e un punto. </s></p><p type="main">

<s>Rispondeva il Cavalieri, scoprendo nel sillogismo di Galileo una fallacia, <lb></lb>la quale consisteva nel voler dedurre la medesima illazione dalle variate pre­<lb></lb>messe. </s>

<s>Nell&#039;ultima divisione infatti le due quantità comparate dal Valerio <lb></lb>mantengono sempre la loro prima natura di solidi, e perciò vale la conclu­<lb></lb>sione dell&#039;eguaglianza: non vale però, quando de&#039;due solidi uno sia trasfor­<lb></lb>mato in un punto, e l&#039;altro in una linea. </s>

<s>Che se conducasi l&#039;argomento a <lb></lb>rigor di logica, l&#039;applicazione degl&#039;indivisibili al Lemma del Valerio conduce <lb></lb>alla verità, e non all&#039;assurdo. </s>

<s>“ Nel suo esempio infatti (per citar le parole <lb></lb>proprie che il Cavalieri usò nel risponderè a Galileo) gl&#039;indivisibili sono piani, <lb></lb>e di questi rimangono sempre parti eguali, detraendo parti eguali dal cono <lb></lb>e dalla scodella; e perchè per arrivare all&#039;ultima esinanizione di questi, cioè <lb></lb>all&#039;annullare i piani, basta levarvi una dimensione; perciò parmi che con <lb></lb>ragione si dica che queste ultime esinanizioni sono eguali, essendo noi ar­<lb></lb>rivati al nullo piano, tanto nel cono, quanto nella scodella ” (Alb. </s>

<s>X, 56). </s></p><p type="main">

<s>Diceva insomma il Cavalieri esser tanto vera la eguaglianza fra zero e <lb></lb>zero, a cui conducono gl&#039;indivisibili, quanto è vera l&#039;eguaglianza fra quan­<lb></lb>tità e quantità, a cui conduceva il metodo del Valerio, e confortava il suo <lb></lb>retto modo di ragionare con quest&#039;altro geometrico esempio. </s>

<s>Nel semicer­<lb></lb>chio AFB (fig. </s>

<s>52 prec.) l&#039;eguaglianza fra ARXRB e QR2 è la medesima <lb></lb>per tutte le altre infinite linee, che si volessero, al di qua e al di là, con­<lb></lb>durre a RQ parallele, nè una tale costante eguaglianza per questo cessa, <lb></lb>perchè uno de&#039;segmenti riesca il massimo, e l&#039;altro, insieme con la perpen­<lb></lb>dicolare, riducasi a nulla, facendo ABX0 e 0X0 insieme equazione ve­<lb></lb>rissima. </s></p><p type="main">

<s>Dopo questa risposta, fatta in una lettera del dì 2 Ottobre 1634, ne sov­<lb></lb>vennero al Cavalieri altre, non meno persuasive, che tornò a scrivere a Ga­<lb></lb>lileo in una seconda lettera del dì 19 Dicembre. </s>

<s>Diceva che, intessendosi <lb></lb>secondo il suo metodo le superfice dal moto delle basi, non si possono attri­<lb></lb>buire a queste le proprietà di quelle, come non si possono alla spola in quiete <lb></lb>attribuire le medesime proprietà della spola che si muove, “ perchè il prin­<lb></lb>cipio e termine del moto non è moto ” (Campori, Carteggio cit., pag. </s>

<s>423). <lb></lb>Nè perchè s&#039;intessano le superfice di linee e i solidi s&#039;affaldino di piani, vien <lb></lb>per questo che debbano essere necessariamente eguali le superfice involgenti <lb></lb>e le moli. </s>

<s>Prendiamo per esempio il parallelepipedo, fatto da tre linee pro-<pb xlink:href="020/01/1881.jpg" pagenum="124"></pb>porzionali, come 1, 2, 4, e il cubo, fatto dalla media. </s>

<s>Saranno ambedue le <lb></lb>solidità date da 8, essendo a questo numero eguali tanto la potenza 23 quanto <lb></lb>il prodotto 1X2X4. Ma mentre la superfice del cubo è data da 4X6=24; <lb></lb>la superfice del parallelepipedo è data invece da 2+2+2X4+2X8=28. <lb></lb>“ Siccome dunque, ne conclude il Cavalieri, sta l&#039;eguaglianza delle solidità <lb></lb>con le diseguaglianze delle superfice ambienti; così sta l&#039;egualità di tutti i <lb></lb>piani di due solidi con la disegualità di tutte le linee che giaccione nelle <lb></lb>superfice ambienti, senza alcun pregiudizio, essendo ciò conforme alle mie <lb></lb>definizioni ” (ivi). </s></p><p type="main">

<s>Questi argomenti però non valsero a persuader Galileo, incocciato oramai <lb></lb>con quegli indivisibili, ai quali aveva fatto in principio così lieta accoglienza. </s>

<s><lb></lb>Nè sapendo in che modo ricoprire innanzi al Cavalieri quella sua cocciutag­<lb></lb>gine, gli veniva scrivendo che la vecchiaia non gli permetteva d&#039;intender <lb></lb>cose tanto difficili, a che rispondeva il buon Frate non doversi attribuir ciò <lb></lb>alla vecchiaia di chi leggeva, ma sì piuttosto alla debolezza dell&#039;ingegno di <lb></lb>chi aveva scritto (ivi, p. </s>

<s>429). In ogni modo, s&#039;annunziava il dì 12 Marzo 1635 <lb></lb>che di quello scritto da parecchi anni sarebbe finita la stampa fra due o <lb></lb>tre settimane (ivi, pag. </s>

<s>432). E fu davvero felicemente finita in Bologna, di <lb></lb>dove si divulgò col titolo <emph type="italics"></emph>Geometria indivisibilibus continuorum nova qua­<lb></lb>dam ratione promota.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Tre anni dopo gli Elzeviri in Leida pubblicavano i quattro dialoghi <lb></lb>Delle due nuove scienze. </s>

<s>Il Cavalieri non s&#039;aspettava forse che la preghiera, <lb></lb>fatta quattro anni prima all&#039;Autore di dir cioè qualche cosa degl&#039;indivisi­<lb></lb>bili in grazia della sua Geometria; fosse esaudita, ma non avrebbe pensato <lb></lb>mai che quella sua povera Geometria avesse dovuto ricevere il tradimento <lb></lb>di sentirsi chiamata complice nella dimostrazion di un assurdo. </s></p><p type="main">

<s>Nel primo di que&#039;dialoghi galileiani si risolve la questione della <emph type="italics"></emph>Ruota <lb></lb>di Aristotile,<emph.end type="italics"></emph.end> dicendo che la circonferenza, svolta dalla ruota stessa nel mo­<lb></lb>versi, era l&#039;espansione o la distrazione del suo centro. </s>

<s>L&#039;assurdità perciò, <lb></lb>che conseguiva da una tal soluzione, del dover esser cioè un punto e una <lb></lb>linea eguali, ammettendo la dottrina dell&#039;interpozion de&#039;vacui, si sarebbe <lb></lb>potuta sciogliere da Galileo con l&#039;esempio di una minuta gocciola d&#039;acqua <lb></lb>saponata, che insufflata diventa un gran pallone. </s>

<s>Ma lasciando gli argomenti <lb></lb>fisici, per attenersi ai matematici, chiama, invece della bolla del sapone, a <lb></lb>rendergli il servigio di mostrar probabile il paradosso, la Geometria del <lb></lb>Cavalieri. </s>

<s>“ Vedendo di non ci poter fare altro per ora, proverò di quie­<lb></lb>tare, egli dice, o almeno temperare una improbabilità con un&#039;altra simile <lb></lb>o maggiore, come talvolta una maraviglia s&#039;attutisce con un miracolo ” <lb></lb>(Alb. </s>

<s>XIII, 30). E passa a descrivere la generazione della scodella e del <lb></lb>cono, per poi concluderne, dall&#039;applicarvi il metodo degl&#039;indivisibili, che la <lb></lb>circonferenza, ossia punti infiniti, sono uguali a un punto solo. </s></p><p type="main">

<s>Avevagli il Cavalieri dimostrato, con argomenti matematici da persua­<lb></lb>dere il più indocile ostinato intelletto, che l&#039;equazione, chiamata C per bre­<lb></lb>vità la circonferenza, non è C=0, come se ne voleva concluder paralogiz-<pb xlink:href="020/01/1882.jpg" pagenum="125"></pb>zando, ma CX0=0; verissima e non assurda, anco quando C rappre­<lb></lb>sentasse qualcuno degl&#039;immensi orbi celesti. </s>

<s>Or come mai Galileo ostinarsi <lb></lb>così contro la verità conosciuta? </s>

<s>Che ci fosse in quel giudizio passione, ce <lb></lb>l&#039;hanno fatto sospettar facilmente le cose addietro narrate, ma non è facile <lb></lb>scoprir l&#039;occulta origine di quella passione, se non forse applicandovi la nota <lb></lb>favola della volpe che, non potendo giunger di terra al bel grappolo del­<lb></lb>l&#039;uva si vendicava con dire che la non era matura. </s></p><p type="main">

<s>Sembrerà l&#039;applicazione ingiuriosa, ma è ben assai più ingiurioso il <lb></lb>modo pensato dagli sviscerati amici di Galileo, per salvare il venerato nome <lb></lb>di lui dall&#039;ingiuria. </s>

<s>Fra&#039;dotti familiari colloqui, che tenevano insieme in Roma <lb></lb>Stefano Gradi, bibliotecario della Vaticana, il fiorentino abate Ottavio Fal­<lb></lb>conieri e il conte Giulio Montevecchi, cadde un giorno il ragionamento sopra <lb></lb>questo discorso, che fa degl&#039;infiniti il Salviati galileiano. </s>

<s>Di ciò che fu al­<lb></lb>lora dagli amici disputato il Gradi stesso scrisse una dissertazione episto­<lb></lb>lare latina, che il Viviani accolse con grande amorevolezza e, di sua propria <lb></lb>mano copiata, la inserì gelosamente fra le sue carte. </s></p><p type="main">

<s>Ebbero prima di tutto a convenire i tre dotti uomini nella sentenza che <lb></lb>la dimostrazione del punto eguale a una linea era addirittura un paradosso. <lb></lb></s>

<s>“ Alioquin eadem opera, dicevano, lineam aequalem superficici, et superfi­<lb></lb>ciem corpori, ac proinde punctum ipsum, hoc est rem nullius mensurae, <lb></lb>quantitati trinae dimensae statuemus aequalem. </s>

<s>Quod, queso, quid aliud est <lb></lb>quam omni philosophiae, omnique rectae rationi manifestam inferre vim, et <lb></lb>ipsam rerum universitatem ad chaos, imo ad nihilum antiquum, redigere? </s>

<s>” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CXXXVII, c. </s>

<s>32 t.). </s></p><p type="main">

<s>Soggiungevano poi, pure d&#039;unanime consenso, i tre Filosofi amici che <lb></lb>il ragionamento del Salviati era un paralogismo, e adducendo altri matema­<lb></lb>tici esempii riuscivano insomma, benchè inconsapevoli, a confermar con si­<lb></lb>mili argomenti la fallacia scoperta nel discorso di Galileo dal Cavalieri. </s>

<s>Pas­<lb></lb>savano oltre ad esaminar le ragioni di coloro, che intendevano di salvar la <lb></lb>logica galileiana con l&#039;esempio autorevolissimo del Valerio. </s>

<s>“ Verum nihil <lb></lb>alteri cum altero commune: ibi enim (in prop. </s>

<s>XII lìbri II <emph type="italics"></emph>De centro gra­<lb></lb>vitatis<emph.end type="italics"></emph.end>) Author ille gravissimus aequalitatem inter craterem et conum de­<lb></lb>ducit ex eo, quod per quaedam plana, basi cylindri aequidistantia, dividitur <lb></lb>conus quidem in plures cylindros, crater vero in totidem orbes cylindricos <lb></lb>(voco orbes cylindricos solidum illud, quod restat ex maiore cylindro, si mi­<lb></lb>nor cylindrus eiusdem axis ab eo auferatur) ita ut unicuique cylindro com­<lb></lb>ponenti conum respondeat orbis cylindricus eiusdem magnitudinis. </s>

<s>Recte <lb></lb>autem ex aequalitate singularum partium aequalitas consurgit universarum, <lb></lb>et sic, ex aequalitate cylindrorum et orbium cylindricorum, aequalitas cra­<lb></lb>teris et coni, prout in Elementis..... ” </s></p><p type="main">

<s>“ In casu autem, quo de agimus, ad nullam recte institutam argumen­<lb></lb>tandi rationem Salviati collectio reduci potest. </s>

<s>Vel enim punctum et circum­<lb></lb>ferentia, de quorum aequalitate ille pronunciat, concurrunt tanquam partes <lb></lb>ad componendum integraliter craterem et conum, et tunc argumentum non <pb xlink:href="020/01/1883.jpg" pagenum="126"></pb>procedit, quia cum sine illis hae duae quantitates aequales inter se sint, ex <lb></lb>eorum quae inaequalia sunt additione inaequalia fiunt, vel saltem, cum ae­<lb></lb>qualitas huiusmodi dubia et in quaestione sit, dubia quoque fiat necesse est <lb></lb>compositarum ex illis quantitatum aequalitas, et ita nihil inde potest inferri <lb></lb>ad conclusionis quaesitae resolutionem. </s>

<s>” </s></p><p type="main">

<s>“ Multo minus argumentum procederet si, ut res est, nec punctum ad <lb></lb>conum, nec circumferentia ad craterem, tanquam partes integrales, concur­<lb></lb>runt. </s>

<s>Tunc enim non bene resultat aequalitas residui duorum aequalium ex <lb></lb>utrinque ablatorum aequalitate: nam ad verificandum axioma de veritate <lb></lb>residui ex aequalitate ablatorum a totis aequalibus, necesse est ut illa tota <lb></lb>aequalia, quae invicem comparantur, a suo quoque ablato et residuo, tan­<lb></lb>quam a partibus integralibus, componantur; alioquin si quis auferat ex ali­<lb></lb>qua triremi modium frumenti, eandemque quantitatem ex aliquo parvo lin­<lb></lb>tre, concludere poterit lintrem esse triremi aequalem. </s>

<s>Ex quibus apparet <lb></lb>sine dubio mens Galilei, in illo Dialogo, nequaquam sic affecta exactam ad <lb></lb>severas geometricas leges doctrinam tradere intendat ” (fol. </s>

<s>33 t. </s>

<s>et 34). </s></p><p type="main">

<s>Or quale altra dunque potrebb&#039;essere l&#039;intenzion di un Geometra, che <lb></lb>tratta di Geometria? </s>

<s>E rispondono in strana sentenza i tre galileiani romani: <lb></lb>quella di parlar da Poeta, l&#039;industria del quale “ in hoc omnis posita est <lb></lb>ut delectet intelligentem. </s>

<s>Quapropter non video quamobrem ingenuae Gali­<lb></lb>laei nostri urbanitati non licuerit, in hoc suo paradoxo aequalitatis inter li­<lb></lb>neam et punctum, eumdum ludum ludere, quem olim in suis <emph type="italics"></emph>De agricul­<lb></lb>tura<emph.end type="italics"></emph.end> lusit Hesiodus, ubi ait: <emph type="italics"></emph>Stulti, nesciunt enim quam maius sit dimidium <lb></lb>toto ”<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>34 t.). </s></p><p type="main">

<s>Il ripiego di questi non è però meno strano di quello usato da altri ga­<lb></lb>lileiani, quando asserirono essere stato scritto ne&#039;Dialoghi Del mondo per <lb></lb>celia che i cadenti si muovono in un mezzo cerchio, per andar dalla super­<lb></lb>fice al centro della Terra mossa. </s>

<s>Quasi che il dire aver Galileo trattata la <lb></lb>scienza da poeta e da burla non sia oltraggio maggiore che a confessare i <lb></lb>passionati errori di lui, ch&#039;era pur un uomo come tutti gli altri. </s></p><p type="main">

<s>Da un tal giusto criterio guidati, e scorti dai fatti svelatici dal sopra <lb></lb>allegato commercio epistolare, ignoto ai disputanti romani; noi crediamo che <lb></lb>il ragionamento intorno all&#039;eguaglianza della linea e del punto fosse posto <lb></lb>da Galileo per far onta alla nuova Geometria del Cavalieri, della quale e <lb></lb>del Calcolo infinitesimale, con la pronunziata sentenza che degli infiniti “ non <lb></lb>si può dire uno esser maggiore o minore o eguale all&#039;altro ” (Alb. </s>

<s>XIII, 35), <lb></lb>si venivano a recidere i teneri stami vitali. </s></p><p type="main">

<s>Che fosse veramente ceco l&#039;odio di Galileo, in menar così attorno la <lb></lb>falce, lo prova il non aver pensato e salvar l&#039;onor suo da una manifesta <lb></lb>contradizione. </s>

<s>Egli aveva, come si disse, prediletti gl&#039;Indivisibili, e ne&#039;dialo­<lb></lb>loghi dei Due massimi sistemi gli aveva assunti alla gloria di dimostrare in <lb></lb>Meccanica uno dei principali teoremi. </s>

<s>Se avesse poi avuto qualche ragione <lb></lb>di repudiarli conveniva dirlo in tutt&#039;altra maniera che da Poeta didattico o <lb></lb>satirico, o almeno per prudenza tacere. </s>

<s>Eppure, mentre nel I dialogo si sen-<pb xlink:href="020/01/1884.jpg" pagenum="127"></pb>tenzia, come ora udimmo, non si poter dare un infinito maggiore di un altro, <lb></lb>nel III, trascrivendosi le cose scritte nel 1622, vi si legge conclusa una delle <lb></lb>prime e principali verità meccaniche dall&#039;essere le infinite linee di un trian­<lb></lb>golo la metà delle infinite linee di un parallelogrammo della medesima base <lb></lb>e della medesima altezza. </s>

<s>“ Hoc enim motu ex quiete accelerato iuxta pa­<lb></lb>rallelas trianguli conficitur; illud vero iuxta parallelas parallelogrammi quae, <lb></lb>dum fuerint infinitae, duplae sunt ad parallelas infinitas trianguli ” (ivi, <lb></lb>pag. </s>

<s>200). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quando il Cavalieri attendeva a dar più compiuta che fosse possibile <lb></lb>la prima edizione della sua Geometria, perchè <expan abbr="dīceva">dinceva</expan>: “ non so se più stam­<lb></lb>però di simili materie, che sono da molti aborrite, da pochi viste, e da po­<lb></lb>chissimi apprezzate ” (Campori, Carteggio cit., pag. </s>

<s>429), era forse ancora <lb></lb>lontano dal sospettar che tra que&#039;pochi sarebbe da annoverar lo stesso Ga­<lb></lb>lileo, a cui scriveva quelle parole. </s>

<s>Ma correvano da tre anni oramai per le <lb></lb>mani di tutti i dialoghi Delle due nuove scienze, in cui il discorso degli infi­<lb></lb>niti e del loro uso da farsi nelle Matematiche vi pareva inserito apposta, per­<lb></lb>chè fosse universalmente aborrita e disprezzata quella povera nuova Geo­<lb></lb>metria. </s>

<s>Il Guldino se ne prevalse, e fra gli argomenti, nella prefazione al <lb></lb>II libro centrobrarico raccolti per dimostrar falso il metodo degl&#039;indivisibili, <lb></lb>l&#039;autorevole giudizio di Galileo, trattandosi di un tanto maestro contro il suo <lb></lb>discepolo, fu nelle destre mani dell&#039;avversario uno de&#039;più potenti. </s>

<s>“ Gali­<lb></lb>leus profecto in eodem dialogo <emph type="italics"></emph>De motu locali,<emph.end type="italics"></emph.end> disputans de infinito, de pro­<lb></lb>prietatibus finitorum, quas infinitis applicare minime liceat; contra ipsum <lb></lb>concludit ” (Centrobr., T. II cit., pag. </s>

<s>3). </s></p><p type="main">

<s><emph type="italics"></emph>Amicus Plato,<emph.end type="italics"></emph.end> rispondeva fra sè medesimo il Cavalieri, sette anni prima <lb></lb>di dirlo in pubblico, <emph type="italics"></emph>sed magis amica veritas<emph.end type="italics"></emph.end> (Exerc. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>181), <lb></lb>per la sacrosanta difesa della quale verità, piuttosto che di sè stesso, revo­<lb></lb>cava tutte a sè le virtù del proprio ingegno. </s>

<s>Voleva rispondere al Guldino <lb></lb>l&#039;ammirata celebrità del quale più noceva alla sua causa che non le addotte <lb></lb>ragioni, e perchè non s&#039;avesse, come per lo più nelle controversie accade, <lb></lb>a perdere inutilmente il tempo in parole, attendeva a dimostrar la bontà del <lb></lb>suo metodo dai frutti dati, e dai tanti più che avrebbe potuto dare. </s></p><p type="main">

<s>Erano in gran fama di matematici valorosi a quei tempi, oltre al Tor­<lb></lb>ricelli, l&#039;aretino Antonio Nardi, e il reggiano Giann&#039;Antonio Rocca, i quali <lb></lb>voleva il Cavalieri chiamar commiliti alla difesa del vero, pregandoli a dar <lb></lb>fuori qualche saggio de&#039;loro studii, e confortandoli a proseguirli, perchè <lb></lb>dell&#039;applicazione del nuovo metodo vedessero il Guldino e il mondo gli <lb></lb>effetti. </s></p><p type="main">

<s>Il Nardi attendeva a raccogliere i suoi sparsi teoremi in un libro, che <pb xlink:href="020/01/1885.jpg" pagenum="128"></pb>avrebbe voluto intitolare <emph type="italics"></emph>Ricercate geometriche,<emph.end type="italics"></emph.end> e il Rocca, stato già in Pia­<lb></lb>cenza discepolo dell&#039;Autor degl&#039;indivisibili, aveva con quel metodo sciolto il <lb></lb>problema della relazione stereometrica, che passa tra il fuso parabolico e il <lb></lb>cilindro circoscritto. </s>

<s>Ma il Torricelli era tutto allora in sollecito studio di <lb></lb>raccogliere, per darle alle stampe, le sue varie opere geometriche, fra le <lb></lb>quali sapeva il Cavalieri esserne molte trattate col metodo nuovo: ond&#039;è che, <lb></lb>cogliendo l&#039;occasione di rispondere allo stesso Torricelli, che gli avea man­<lb></lb>date certe sue nuove dimostrazioni del centro di gravità in un segmento di <lb></lb>sferoide, rendendo facilissimi e spediti i lunghi e faticosi processi del Vale­<lb></lb>rio; così in una lettera del dì 3 Gennaio 1643 scriveva da Bologna, dichia­<lb></lb>rando le sue intenzioni di rispondere al Guldino, e chiedendo all&#039;opera, dal <lb></lb>valoroso amico, aiuto e consiglio. </s></p><p type="main">

<s>“ Se mi è parsa maravigliosa la prima sua speculazione, questa seconda <lb></lb>del modo di ritrovare i centri di gravità, mi è parsa pur sommamente bella. </s>

<s><lb></lb>Ma infatti il padre. </s>

<s>Guldini battezza tutte queste cose, trovate per gl&#039;indivi­<lb></lb>sibili, come provate solo per modo meccanico, e non veramente dimostra­<lb></lb>tivo. </s>

<s>Ho di già visto il suo secondo tomo della Centrobrarica, nel quale, ben­<lb></lb>chè sia assai grosso, non consuma però più che nove ovvero dieci carte per <lb></lb>la contradizione alla mia Geometria, della quale dice non aver visto se non <lb></lb>queste poche cose, che egli prende a impugnare, riserbandosi a miglior tempo <lb></lb>il confutare il resto. </s>

<s>” </s></p><p type="main">

<s>“ Incominciando dunque dalla prima proposizione del I libro, che è di <lb></lb>trovare il vertice di una figura, il che eseguisco io con far movere equidi­<lb></lb>stantemente una retta o piano, sino che tocchi la figura, oppone esser modo <lb></lb>meccanico, ma vedrei un poco volentieri che, in cosa così universale, mi <lb></lb>somministrasse egli miglior modo, quale, se io non m&#039;inganno, stimo esser <lb></lb>difficilissimo, mentre non si discenda alle specie delle figure. </s>

<s>Passa poi, senza <lb></lb>vedere altro del primo, al secondo libro, ed ivi a bocca aperta biasima le <lb></lb>differenti petizioni, e la I e III proposizione, pronunziandole per false asso­<lb></lb>lutamente: il tutto perchè gl&#039;infiniti indivisibili non si danno <emph type="italics"></emph>actu,<emph.end type="italics"></emph.end> ma solo <lb></lb><emph type="italics"></emph>potentia<emph.end type="italics"></emph.end> nel continuo, e poi perchè sono infiniti, e però incomparabili. </s>

<s>” </s></p><p type="main">

<s>“ Tralasciato poi il resto, passa ai nuovi fondamenti del VII libro, oppo­<lb></lb>nendo a quella supposizione delle figure egualmente analoghe come a cosa <lb></lb>meccanica, e che non finirebbe mai. </s>

<s>E sebbene, per levare ogni ombra a <lb></lb>chi avesse dubbio per questo non finir mai, soggiungo un&#039;altra dimostra­<lb></lb>zione dell&#039;istesso, quanto alle figure piane, conforme allo stile di Archimede; <lb></lb>finalmente cavilla pure anche contro di questa, mostrando che io non posso <lb></lb>spezzare le figure tanto diverse e stravaganti in più pezzi, che fanno a mio <lb></lb>proposito; onde conclude la mia Geometria non aver sussistenza alcuna. </s>

<s>” </s></p><p type="main">

<s>“ Ora io son risoluto, con la occasione dell&#039;Opusculo di Trigonometria <lb></lb>con le tavole de&#039;seni e logaritmi, che io stampo in grazia di questi scolari; <lb></lb>di aggiungervi un poco di risposta. </s>

<s>E perchè egli stima questa mia maniera <lb></lb>infruttuosa, mi saria molto caro se io potessi o accennare o mostrare quei <lb></lb>trovati maravigliosi, ai quali è arrivata Lei, con l&#039;aggiunta della sottigliezza <pb xlink:href="020/01/1886.jpg" pagenum="129"></pb>del suo ingegno. </s>

<s>Questo però che io dico intendo sia per non detto, quando <lb></lb>a lei paresse altrimenti. </s>

<s>” </s></p><p type="main">

<s>“ Ma volendosi compiacere di farmi questo favore, parmi che in due <lb></lb>modi ciò potesse farsi; cioè, o essendo Lei per stampare le sue speculazioni <lb></lb>in breve, che ella v&#039;inserisse ancora le cose trovate per gl&#039;indivisibili, in <lb></lb>grazia mia; ovvero che ella le diffondesse ed inviasse a me, in forma di let­<lb></lb>tera, e che si contentasse che io le inserissi nella mia risposta, precisamente <lb></lb>come me le mandasse, e come cose sue, e sotto il suo nome, e non in altro <lb></lb>modo; cioè nel modo stesso che le farebbe stampar Lei, acciò il Padre nel <lb></lb>medesimo tempo vedesse il frutto di quelli, conoscesse il mondo il valore <lb></lb>di V. S., e che gl&#039;indivisibili sono accetti ai Geometri d&#039;incomparabile va­<lb></lb>lore; bench&#039;egli dica non essere approvati dai Geometri. </s>

<s>Però sia questo <lb></lb>per non detto, quando ella non ci abbia gusto o comodità di farlo, nè nel­<lb></lb>l&#039;uno nè nell&#039;altro modo. </s>

<s>” </s></p><p type="main">

<s>“ Se il signor Antonio Nardi avesse stampato le sue <emph type="italics"></emph>Ricercate geome­<lb></lb>triche,<emph.end type="italics"></emph.end> mi saria stato molto caro e molto a proposito; ma, non avendo io <lb></lb>con lui corrispondenza di lettere, non ho campo di pregarnelo, come volen­<lb></lb>tieri farei. </s>

<s>E se mai ella avesse occasione di scrivergli, riceverei a sommo <lb></lb>favore che ella glie ne desse qualche motivo. </s>

<s>Spero ancora che il signor <lb></lb>Giovanni Antonio Rocca mi farà grazia di due o tre proposizioni, ritrovate <lb></lb>pur da lui per gl&#039;indivisibili, e che sono veramente molto singolari, e molto <lb></lb>a proposito per rispondere al detto Padre, siccome ora intenderà: intendo <lb></lb>pure di pubblicarle, com&#039;è il dovere, sotto il nome suo. </s>

<s>” </s></p><p type="main">

<s>“ Imperocchè deve sapere che il detto Padre ha ritrovato una bellis­<lb></lb>sima cosa, poichè è universale per tutte le figure solide, che nascono per <lb></lb>rivoluzione intorno all&#039;asse, e per le superfice curve descritte pure dalle linee <lb></lb>o rette o curve, che s&#039;intendano pure generarsi per rivoluzione intorno l&#039;asse, <lb></lb>alle quali non sono ancora arrivati gl&#039;indivisibili, e quello che importa è as­<lb></lb>sai più facile da intendersi, che lo spezzamento degl&#039;indivisibili, e questo <lb></lb>consiste tutto in questa proposizione: <emph type="italics"></emph>“ Se sarà trovato il centro di gra­<lb></lb>vità della figura, piano o linea che si sia da rivolgersi, moltiplicando la <lb></lb>circonferenza, descritta nella intera rivoluzione dal centro di gravità, nella <lb></lb>figura piana o linea revoluta, si produrrà la solidità del corpo o la su­<lb></lb>perfice descritta. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Questo gran principio è lasciato dal Padre senza alcuna dimostrazione, <lb></lb>e dice di volerlo solo provare <emph type="italics"></emph>ab indutione,<emph.end type="italics"></emph.end> cioè che le conclusioni cavate <lb></lb>da esso son vere, concorrendo con quelle di Euclide e di Archimede. </s>

<s>Il che <lb></lb>parmi, quand&#039;io non avessi altra cosa in mia difesa, che mi somministri la <lb></lb>risposta adeguata per il detto Padre, poichè ancor le mie proposizioni con­<lb></lb>cordano, e però dovranno per lui stimarsi veri anco i miei principii. </s>

<s>” </s></p><p type="main">

<s>“ E poichè anco al signor Rocca sovvenne due anni sono una simil <lb></lb>cosa, poichè dimostrò che il momento della parabola librata intorno la base, <lb></lb>con un parallelogrammo applicato all&#039;istessa base, al momento del paralle­<lb></lb>logrammo è come il solido descritto dalla parabola, cioè il fuso parabolico <pb xlink:href="020/01/1887.jpg" pagenum="130"></pb>al cilindro fatto dal parallelogrammo; perciò ne cavò di qua che il fuso al <lb></lb>cilindro ha la proporzione composta, come si dimostra essere il momento al <lb></lb>momento di due pesi, della proporzione della parabola al parallelogrammo, <lb></lb>e della distanza del centro di gravità della parabola dall&#039;asse della rivolu­<lb></lb>zione alla distanza del centro di gravità del parallelogrammo dal detto asse. </s>

<s><lb></lb>La quale, quando il parallelogrammo si supponga dell&#039;istessa altezza con la <lb></lb>parabola, sarà come 4 a 5, siccome la parabola al parallelogrammo è come <lb></lb>2 a 3, quali compongono la proporzione di 8 a 15, cioè del fuso al cilindro, <lb></lb>siccome appunto trova anco il detto Padre. </s>

<s>” </s></p><p type="main">

<s>“ E perchè le distanze dei centri dall&#039;asse della rivoluzione sono come <lb></lb>le circonferenze da loro descritte, e la dimostrazione, dal signor Rocca <lb></lb>fatta per gl&#039;indivisibili, s&#039;adatta ad ogni altra figura piana; perciò è mani­<lb></lb>festo che il signor Rocca viene virtualmente ad aver dimostrato che questi <lb></lb>corpi rotondi, come generalmente anch&#039;esso Padre gli chiama, hanno la pro­<lb></lb>porzion composta della proporzione delle figure geometriche, e delle circon­<lb></lb>ferenze descritte dai centri, d&#039;onde finalmente si prova facilmente che la so­<lb></lb>lidità di un qualunque corpo rotondo è il prodotto della circonferenza fatta <lb></lb>dal centro, moltiplicata nella figura genitrice. </s>

<s>Cosa che il Padre lascia senza <lb></lb>dimostrazione, e perciò calzerà bene che gl&#039;indivisibili facciano questo ser­<lb></lb>vigio, almeno quanto ai solidi, sebbene stimo l&#039;istesso potersi anco provare <lb></lb>per la circoscrizione ed inscrizione. </s>

<s>” </s></p><p type="main">

<s>“ Quanto poi alle superfice, descritte da linee rette, si cava detto prin­<lb></lb>cipio per la misura del circolo, superfice, e frusto di superfice datoci da Ar­<lb></lb>chimede, e da questi si trasferisce alla superfice della sfera ed altre super­<lb></lb>fice curve per l&#039;inscrizione e circoscrizione delle rette. </s>

<s>Sicchè ella intende <lb></lb>quanto sia bello questo principio, e quanto a me torni a proposito il pro­<lb></lb>varlo con la invenzione del signor Rocca, per gl&#039;indivisibili, come diceva <lb></lb>di sopra. </s>

<s>” </s></p><p type="main">

<s>“ Ora perchè il Padre, avendo incontrata questa maniera veramente <lb></lb>bella, par che voglia sbandire, non solo dalla persona propria, ma da ogni <lb></lb>altra, gl&#039;indivisibili, è necessario che io gli mostri che, se questa maniera <lb></lb>avanza gl&#039;indivisibili in qualche cosa, ancor questi avanzano quelli in qual­<lb></lb>che altra. </s>

<s>E per tralasciare l&#039;infinità dei solidi, ai quali essi continuamente <lb></lb>s&#039;estendono, mi vado indovinando che il modo di trovare il centro di gra­<lb></lb>vità dei solidi, e massime da lei accennatomi, sia uno degli avanzi. </s>

<s>Simil­<lb></lb>mente non mi pare da sprezzare la misura del fuso iperbolico, supposta la <lb></lb>quadratura dell&#039;iperbola, da esso Padre non ritrovata, ed insomma in molte <lb></lb>altre, per non parlare anco delle cose fisiche, parmi che gl&#039;indivisibili pos­<lb></lb>sano avvantaggiar quel modo, com&#039;ella sa meglio di me, i quali, se in qualche <lb></lb>modo si adattassero alle superfice curve, non vi saria che desiderarvi. </s>

<s>” </s></p><p type="main">

<s>“ Se ella dunque si disponesse a farmi questo favore, ella farebbe un <lb></lb>segnalato servigio agl&#039;indivisibili, ed a me ancora. </s>

<s>E perchè la somma delle <lb></lb>difficoltà fattemi dal Padre si riduce all&#039;incomprensibilità degl&#039;infiniti, ed <lb></lb>alla superposizione da farsi di una figura spezzata sopra un&#039;altra eguale <pb xlink:href="020/01/1888.jpg" pagenum="131"></pb>innumerabili volte, che pare pure impossibile; la vorrei pregare, benchè abbi <lb></lb>diverse cose da dire in risposta, se gli sovvenisse qualche cosa, che potesse <lb></lb>maggiormente mettere in chiaro la risposta a queste due cose, la quale non <lb></lb>sovvenisse a me, mi vogli onorare di darmene un poco di motivo, poichè e <lb></lb>la mia continua infermità m&#039;impedisce la totale applicazione, <emph type="italics"></emph>et plura vi­<lb></lb>dent oculi plures, quam solus ocellus,<emph.end type="italics"></emph.end> e chi è sopra il gioco pare che veda <lb></lb>meglio i colpi che chi gioca, oltre la sua incomparabile sottigliezza d&#039;inge­<lb></lb>gno, che può giungere dove la mia debolezza di corpo e di mente non pos­<lb></lb>sono arrivare, e con pregarla a scusarmi le bacio affettuosamente le mani. </s>

<s>” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XLI, c. </s>

<s>144-52). </s></p><p type="main">

<s>Non sembra che si curasse il Torricelli di assottigliar l&#039;ingegno per sug­<lb></lb>gerire al Cavalieri la risposta alle due dette obiezioni del Guldino, non si <lb></lb>offendendo sostanzialmente per esse i principii della Matematica, ma insti­<lb></lb>gava l&#039;amico ad attutire l&#039;arroganza del Gesuita, col dimostrargli la falsità <lb></lb>di parecchie proposizioni, che si trovavano nel suo libro. </s>

<s>Argomentò <emph type="italics"></emph>ab in­<lb></lb>dutione<emph.end type="italics"></emph.end> l&#039;Autore della Centrobrarica, dal veder che il centro, nella super­<lb></lb>fice conica e nel frusto di cono, è il medesimo che nella figura piana gene­<lb></lb>ratrice; doversi ciò verificare anche ne&#039;frusti di sfera, di sferoide e di conoide <lb></lb>parabolico. </s>

<s>L&#039;analogia aveva tanto del verisimile, che fu creduta esser quella <lb></lb>la verità, anche dal Cavalieri, ma entrato poi in sospetto di ciò, dietro il <lb></lb>teorema torricelliano del centro di gravità della superfice di un frusto sfe­<lb></lb>rico, ritrovò false le proposizioni guldiniane, e ne dette al Torricelli stesso <lb></lb>avviso, per lettera del dì 23 Aprile 1643, mandandogliene la dimostrazione, <lb></lb>che fu poi pubblicata da pag. </s>

<s>236-38 della II Esercitazione geometrica. </s>

<s>Do­<lb></lb>veva questa accusa di falsità essere uno degli argomenti da inserirsi nella <lb></lb>Risposta, intorno alla quale scriveva così il Cavalieri da Bologna il dì 22 Set­<lb></lb>tembre di quel medesimo anno 1643, per sodisfare alla curiosità, che di sa­<lb></lb>perne qualche cosa gli aveva il Torricelli mostrata pochi giorni prima. </s></p><p type="main">

<s>“ Cammino assai lentamente nella risposta al Guldini, non essendo an­<lb></lb>cora al fine del I dialogo, poichè mi son risoluto, ad imitazione del Galileo, <lb></lb>di rispondergli in dialogo, avendolo onorato con introdurvi per interlocutori <lb></lb>il padre don Benedetto, un signor Cesare Marsili, gentiluomo bolognese, <lb></lb>morto un pezzo fa, che fu amico mio e si dilettava della Matematica, ed un <lb></lb><emph type="italics"></emph>Gesulpa Geniuldus,<emph.end type="italics"></emph.end> anagramma di <emph type="italics"></emph>Paulus Guldinus.<emph.end type="italics"></emph.end> In questo però si con­<lb></lb>tiene la parte difensiva, siccome in altro sarà, non dirò l&#039;offensiva, ma l&#039;esame <lb></lb>del fondamento del Guldino da lui non provato, la dimostrazione di quello <lb></lb>per gl&#039;indivisibili e senza, ed altre cose, che mostreranno il frutto, che si <lb></lb>cava dagl&#039;indivisibili. </s>

<s>In un altro poi, che sarà il terzo Dialogo, metterò <lb></lb>quelle poche cose, che mi è accaduto di trovare in diverse materie, eziandio <lb></lb>senza gl&#039;indivisibili, acciò non periscano ” (ivi, c. </s>

<s>182, 83). </s></p><p type="main">

<s>Dopo un mese, quel I dialogo era già finito, e l&#039;Autore significava per <lb></lb>lettera al Torricelli il desiderio che aveva di mandarglielo, perchè gli desse <lb></lb>un&#039;occhiata, e gliene dicesse il suo senso (ivi, c. </s>

<s>185). Benchè fosse tutto <lb></lb>allora in studio di curar le sue opere geometriche, delle quali era quasi a <pb xlink:href="020/01/1889.jpg" pagenum="132"></pb>mezzo la stampa, il Torricelli rispose che volentieri avrebbe veduto quel dia­<lb></lb>logo in difesa degl&#039;indivisibili, e il dì 8 Gennaio 1644, con una lettera, nella <lb></lb>quale si dicevano queste cose, il Cavalieri accompagnavagli il manoscritto: </s></p><p type="main">

<s>“ In conformità di quello, che io gliene scrissi, confidato nella sua amo­<lb></lb>revoleza, gl&#039;invio questo primo dialogo, per contenersi in esso materia prin­<lb></lb>cipalmente di controversia in cosa, della quale ella è benissimo, per non dire <lb></lb>più di me, informata. </s>

<s>So che ella vi troverà di molte imperfezioni, ma spero <lb></lb>che mi avrà in parte per iscusato, sapendo di quanto pregiudizio mi sia allo <lb></lb>speculare la continua mia infermità corporale..... So che le dimostrazioni <lb></lb>o lemmi, che quivi dimostro, potevano forse apportarsi in miglior modo, e <lb></lb>con più chiarezza; tuttavia, dovendo esser vista principalmente da queìli, che <lb></lb>hanno intesa la mia Geometria, ai quali le indirizzo, spero che supereranno <lb></lb>facilmente le difficoltà che incontreranno. </s>

<s>Vi ho inserito alcuni discorsi fatti <lb></lb>dal Marsigli, con un poca di libertà filosofica, acciò anche i puri Filosofi vi <lb></lb>abbiano qualche cosa per il gusto loro, sebbene di poco momento. </s>

<s>Anzi so <lb></lb>che a molte cose daranno del naso, come alla composizione del continuo <lb></lb>d&#039;indivisibili, alle immagini e lumi, che si riducono a un punto, il che da <lb></lb>me è stato messo per un certo ghiribizzo, e come cosa ammirabile: o che <lb></lb>si riducano o no ad un punto, è degno di considerazione ” (ivi, 186, 87). </s></p><p type="main">

<s>Rispose il Torricelli di aver letto con piacere il Dialogo e di approvare <lb></lb>le risposte fattevi al Guldino, e avendo intanto già riveduti e licenziati per <lb></lb>la stampa i foglietti della prima parte delle Opere geometriche, come pri­<lb></lb>maticcio anticipato frutto, gl&#039;inviava a Bologna all&#039;amico. </s>

<s>Si comprendevano <lb></lb>in que&#039;foglietti i due libri <emph type="italics"></emph>De solidis sphaeralibus,<emph.end type="italics"></emph.end> e il Cavalieri in leggerli <lb></lb>ci vedeva mirabilmente promossa la Geometria antica, piuttosto che la nuova. </s>

<s><lb></lb>Incominciò a dubitare allora che le belle speranze concepute, ed espresse <lb></lb>nella prima lettera del dì 3 Gennaio 1643, volessero rimanersi deluse, e che <lb></lb>s&#039;avesse a rinnovare l&#039;esempio di Galileo, tanto più che il Torricelli gli aveva <lb></lb>scritte certe difficoltà contro il metodo degl&#039;indivisibili, venute, ei diceva, <lb></lb>da un gran Matematico di Francia. </s>

<s>Con paterna sollecitudine, non delle spe­<lb></lb>culazioni sue proprie, ma della matematica verità, che vedeva così chiara <lb></lb>risplendergli nella mente, l&#039;Autore della Geometria nuova trovò a quella diffi­<lb></lb>coltà dell&#039;Anonimo francese facile la risposta. </s>

<s>Ebbe anzi a maravigliarsi che <lb></lb>a nessuno de&#039;suoi oppositori, nemmeno al Guldino stesso, non fosse sov­<lb></lb>venuta un&#039;altra difficoltà, che, in antivedere le offese, era sovvenuta spon­<lb></lb>tanea allo stesso difensore; difficoltà ch&#039;era di grande apparenza, e che il <lb></lb>Cavalieri volle mettere innanzi al Torricelli insieme con la risposta, per mo­<lb></lb>strar quanto fosse, in mezzo al fiero combattimento, sicuro della vittoria: </s></p><p type="main">

<s>“ La difficoltà dunque (così dicevasi dallo stesso Cavalieri, in una let­<lb></lb>tera del dì 5 Aprile 1644, che poi, voltata in latino, fu inserita da pag. </s>

<s>238-40 <lb></lb>della III Esercitazione) consiste in questo. </s>

<s>Sia HD (fig. </s>

<s>53) perpendicolare <lb></lb>ad AG, ed AD minore, e DG maggiore di essa DH. </s>

<s>Giunte poi le HG, HA, <lb></lb>sia regola HD, e di tutte le linee del triangolo HAD se ne prendano quante <lb></lb>si voglia KB, IC.... e per K, I tirinsi le KM, IL parallele ad AG, e le <pb xlink:href="020/01/1890.jpg" pagenum="133"></pb>LE, MF parallele ad HD. È dunque manifesto che la KB è eguale ad MF, <lb></lb><figure id="id.020.01.1890.1.jpg" xlink:href="020/01/1890/1.jpg"></figure></s></p><p type="caption">

<s>Figura 53.<lb></lb>ed IC ad LE, e in conseguenza che <lb></lb>a quante si voglia si estenderanno in <lb></lb>tal modo nel triangolo HAD: cioè, <lb></lb>dirà alcuno, a tutte le linee del trian­<lb></lb>golo HAD troveremo eguali tutte le <lb></lb>linee del triangolo HDG, onde questi <lb></lb>triangoli saranno eguali, eppure son <lb></lb>diseguali, dunque.... ” </s></p><p type="main">

<s>“ Ora a questo dubbio direi che, <lb></lb>intendendo noi prese nel triangolo HAD tutte le di lui linee di retto tran­<lb></lb>sito, che sono tante quanti sono i punti di retto transito della AD; altret­<lb></lb>tanti punti, ma di obliquo transito, prendiamo nella AH, ed altrettante pa­<lb></lb>rallele ad AG, ed in conseguenza altrettante nel triangolo HDG parallele ad <lb></lb>HD, le quali in conseguenza non sono tante, quanti sono i punti di retto <lb></lb>transito della maggiore di DA, DG, cioè quante sono tutte le linee del trian­<lb></lb>golo HDG, cioè non sono tante infinità di linee queste, come quelle, e però, <lb></lb>non si prendendo in ambedue questi triangoli per questa via tutte le loro <lb></lb>linee di retto transito, non si conclude bene l&#039;egualità di detti triangoli. </s>

<s>” </s></p><p type="main">

<s>“ Parmi che ciò, per una certa analogia, si possi dare ad intendere con <lb></lb>la tela, poichè intendendo HAG essere pur di tela, AG regola dell&#039;ordito, <lb></lb>ed HD del tessuto, essendo nel triangolo HAD cento fili di tessuto, saranno <lb></lb>cento ancora i punti segnati in HA, da&#039;quali per l&#039;ordito stesi cento fili <lb></lb>noteranno cento punti in HG, e cento parallele ad HD nel tessuto del trian­<lb></lb>golo HDG. </s>

<s>Ma il tessuto di esso HDG porta molti più fili, cioè per esempio <lb></lb>trecento, essendo DG tripla di DA; dunque di questi trecento fili non ne <lb></lb>prendiamo se non cento, e così allo stesso modo negl&#039;infiniti ” (ivi, c. </s>

<s>198-200). </s></p><p type="main">

<s>Due mesi, dop&#039;aver ricevuta questa difficoltà con la sua soluzione, che <lb></lb>aiutandosi così de&#039;fisici esempii si rendeva anche ai meno acuti d&#039;ingegno <lb></lb>assai intelligibile; il Torricelli spediva da Firenze al Cavalieri i foglietti già <lb></lb>stampati della II parte delle Opere geometriche, contenenti la risoluzione <lb></lb>de&#039;due problemi della misura della parabola, e del Solido acuto iperbolico. </s>

<s><lb></lb>Quanto alla parabola, si proponevano dal fecondo ingegno geometrico del­<lb></lb>l&#039;Autore venti varii modi di trovarne la quadratura, i primi dieci secondo <lb></lb>i metodi antichi, e gli altri per la nuova Geometria degl&#039;indivisibili. </s>

<s>Nella <lb></lb>prefazione a questa II parte del trattato <emph type="italics"></emph>De dimensione parabolae<emph.end type="italics"></emph.end> il Tor­<lb></lb>ricelli esaltava il metodo nuovo, da cui breve, diretto e affermativo scendeva <lb></lb>il modo di dimostrare moltissimi teoremi, imperscrutabili agli antichi, con­<lb></lb>cludendo con queste parole: “ Haec enim est in mathematicis spinetis via <lb></lb>vere regia, quam primus omnium aperuit, et ad publicum bonum com­<lb></lb>planavit mirabilium inventorum macbinator Cavalerius ” (Florentiae 1644, <lb></lb>pag. </s>

<s>56). </s></p><p type="main">

<s>Il Cavalieri respirò in leggere così fatte parole, e prese subito la penna <lb></lb>in mano per ringraziare il Torricelli dell&#039;aver così onorata la sua persona. <pb xlink:href="020/01/1891.jpg" pagenum="134"></pb>Poi soggiungeva, in questa medesima lettera, che è del dì 15 Giugno, dopo <lb></lb>aver dimostrata la sua compiacenza in veder de&#039;suoi metodi esposto così <lb></lb>bel frutto sotto gli occhi de&#039;suoi tanti contradittori: “ Confesso che il ve­<lb></lb>derla astenersene nell&#039;opera De&#039;solidi sferali mi generò qualche timore di <lb></lb>restar privo di così gloriosa testimonianza, ma ora veggo che ella ha fatto <lb></lb>davvantaggio ” (MSS. Gal., T. cit., fol. </s>

<s>209 a t.). </s></p><p type="main">

<s>La compiacenza era nel Cavalieri tanto più giustamente sentita, in quanto <lb></lb>che vedeva rimediarsi dal Torricelli il grave danno, che era derivato alla <lb></lb>sua Geometria dai nuovi dialoghi di Galileo. </s>

<s>E in vero, senza una tale e <lb></lb>tanta autorità del Discepolo, che in Geometria reputavasi meritamente su­<lb></lb>periore a quella del Maestro, forse la italiana Geometria degl&#039;indivisibili ri­<lb></lb>maneva soggiogata per chi sa quanto tempo dalla Centrobrarica del Guldino. <lb></lb></s>

<s>È perciò ch&#039;esso Cavalieri, benchè di continuo tormentato dalla podagra, <lb></lb>prendeva da quelle torricelliane proposizioni animo di proseguire a com­<lb></lb>battere per l&#039;amore del vero, e per le glorie scientifiche dell&#039;Italia, e dopo <lb></lb>avere, il dì 13 marzo 1644, annunziato al Torricelli di aver dato principio a <lb></lb>stampare il I Dialogo, in risposta alle soverchierie del Guldino (ivi, fol. </s>

<s>197), <lb></lb>dopo sei mesi, in mezzo a quegli spasimi atroci, che lo rendevano affranto <lb></lb>ma non vinto, tornava in altra lettera, tra accorato e lieto, a dargli questa <lb></lb>nuova: “ È stampato il I dialogo, ma il II e il III, non solo non è stam­<lb></lb>pato, ma neanche composto: insomma io sono in stato di far poco ” (ivi, <lb></lb>fol. </s>

<s>211). </s></p><p type="main">

<s>La morte del Guldino, avvenuta in Gratz sulla fine dell&#039;anno 1643, ma <lb></lb>della quale non ebbe il Cavalieri notizia, se non che nella primavera se­<lb></lb>guente, fecero all&#039;intrapresa opera mutar proposito e forma, volendo il pio <lb></lb>e gentile animo dell&#039;Autore osservare il precetto naturale del <emph type="italics"></emph>parce sepulto.<emph.end type="italics"></emph.end><lb></lb>E giacchè la forma del dialogo lo conduceva ad affogare in una superfluità <lb></lb>di parole le idee, scelse, anche per risparmiar tempo e fatica, di espor le <lb></lb>medesime cose in discorso disteso, ond&#039;è che, negletti i primi fogli stam­<lb></lb>pati e dismessa la cura di proseguir sull&#039;andamento di quelli, si trasforma­<lb></lb>rono i tre meditati dialoghi in quelle sei geometriche Esercitazioni, che vi­<lb></lb>dero nel 1647 la prima luce in Bologna. </s>

<s>Il trasformato stile non detrasse <lb></lb>però nulla alla efficacia della prima intenzione, che era quella di rispon­<lb></lb>dere al Guldino, e di attutirne la filosofica baldanza. </s>

<s>E perchè il tornar sopra <lb></lb>cose scritte dodici anni fa poteva riuscire oscuro a chi le avesse dimenti­<lb></lb>cate, tanto più che della Geometria degl&#039;indivisibili, nel 1647, a testimo­<lb></lb>nianza dell&#039;Autore, <emph type="italics"></emph>nulla amplius inveniebantur penes bibliopolas exem­<lb></lb>plaria,<emph.end type="italics"></emph.end> pensò il Cavalieri di premettere alla esercitazione apologetica due <lb></lb>altre esercitazioni, nelle quali s&#039;esponesse compendiosamente l&#039;uno e l&#039;al­<lb></lb>tro metodo: quello cioè che trattava gl&#039;indivisibili collettivamente presi, e <lb></lb>in che ponevansi le fondamenta al Calcolo integrale, e l&#039;altro, che quegli <lb></lb>stessi indivisibili riguardava distributivamente presi, insegnando a calcolar, <lb></lb>come oggidì si direbbe, le quantità nei loro differenziali. </s></p><p type="main">

<s>Segue immediatamente la III Esercitazione, nella quale si propone l&#039;Au-<pb xlink:href="020/01/1892.jpg" pagenum="135"></pb>tore di volere esaminar le difficoltà fatte contro gli esposti metodi dal Gul­<lb></lb>dino, e nelle prime parole premesse al trattato si compendia così dal Ca­<lb></lb>valieri stesso la importante storia letteraria, da noi precedentemente ne&#039;suoi <lb></lb>particolari narrata: “ Dum eas omnes, quas in hucusque declaratam indivi­<lb></lb>sibilium doctrinam difficultates evulgarat Guldinus, mente obvolvebam, ac <lb></lb>pleniori rationum volumine, quae responsionis loco afferre posse videbantur, <lb></lb>retexere aggrediebar, quinimo et iam ipsius Operis aliquot folia praelo com­<lb></lb>mississem; repente cum fama tum litteris amicorum nunciatum est ipsum, <lb></lb>de Geometria quidem benemeritum, fato concessisse. </s>

<s>Indolui vehementer, <lb></lb>cum ob publicum Reipublicae litterariae damnum, tum ob mihi praereptam <lb></lb>laboris pene confecti materiam, quam viventi conseveram. </s>

<s>Mors enim ipsa, <lb></lb>ingrato me silentio damnans, multa vetuit prodere, quae disserendi campus <lb></lb>opportunior, si vixisset, aperuerat ” (Exercit. </s>

<s>cit., pag. </s>

<s>177). </s></p><p type="main">

<s>Quel largo campo infatti, che si voleva alle disputazioni aprire il Cava­<lb></lb>lieri, ne&#039;tre dialoghi divisati nelle lettere da noi sopra alligate al Torricelli; <lb></lb>si restrinse, morto il Guldino, in que&#039;XV compendiosi capitoli della III geo­<lb></lb>metrica Esercitazione. </s>

<s>Lasceremo addietro l&#039;esame di ciò che in tali capi­<lb></lb>toli ordinatamente discorre il Cavalieri a confutar gli argomenti, dall&#039;Autor <lb></lb>della Centrobrarica accampati contro la nuova Geometria, e ci tratterremo <lb></lb>piuttosto intorno all&#039;ultimo, ch&#039;è il più importante per la nostra Storia, e in <lb></lb>cui si dimostra quale utilità avrebbe potuto ricavar dagl&#039;indivisibili l&#039;Au­<lb></lb>tore stesso della Centrobrarica, che pubblicamente gli avea repudiati. </s>

<s>Per <lb></lb>concluder poi che questa utilità era la maggiormente desiderabile, dop&#039;aver <lb></lb>notato che il Guldino lasciava la sua Regola senza il conforto di nessuna <lb></lb>matematica ragione, volle il Cavalieri mostrar come a tanta necessità sov­<lb></lb>venissero i suoi principii opportuni. </s>

<s>E qui, per aggiungere alle sue proprie <lb></lb>speculazioni il suffragio e l&#039;opera di Matematici valorosi, adduceva in propo­<lb></lb>sito un lemma di Giann&#039;Antonio Rocca, da cui facilmente scendeva dimo­<lb></lb>strata la Regola guldiniana. </s>

<s>L&#039;importanza del corollario conferisce tanta <lb></lb>dignità alla proposizion principale, che giova risalire alle origini di essa <lb></lb>proposizione, in questo breve cenno di storia. </s></p><p type="main">

<s>Un Gesuita fiammingo, mosso dalla fama, che del valore del Cavalieri <lb></lb>in cose geometriche s&#039;era fino oltre monte diffusa, gli scrisse una volta, pro­<lb></lb>ponendogli a risolvere questo problema: Essendo un parallelogrammo cir­<lb></lb>coscritto ad una parabola, e rivolgendosi questa e quello intorno alla base, <lb></lb>come ad asse comune, si domanda la ragione che avranno insieme le mi­<lb></lb>sure dei due solidi così generati, del cilindro cioè e del fuso. </s>

<s>Poi soggiun­<lb></lb>geva di aver egli stesso, il Matematico fiammingo, già risoluto il problema, <lb></lb>e di aver trovato essere il fuso la metà del cilindro circoscritto. </s></p><p type="main">

<s>Essendo il Cavalieri alquanti anni dopo tutto intento a raccogliere pro­<lb></lb>blemi geometrici per la sua Centuria, gli occorse, in mezzo a quella eletta <lb></lb>varietà, di tornar sul problema già propostogli da quel Fiammingo, e appli­<lb></lb>candovi il metodo degl&#039;indivisibili trovò che, delle quindici parti del cilin­<lb></lb>dro, il fuso non ne conteneva che otto. </s>

<s>Dava di ciò avviso a Galileo, per <pb xlink:href="020/01/1893.jpg" pagenum="136"></pb>lettera del dì 25 Gennaio 1636, dop&#039;avergli accennato al modo di quadrare <lb></lb>la volta a crociera: “ Mi è anche venuto trovato che essendo un parallelo­<lb></lb>grammo circoscritto ad una parabola, e rivolgendosi quella intorno alla base, <lb></lb>il cilindro generato dal parallelogrammo è come 15 a 8, benchè un padre <lb></lb>Gesuita fiammingo mi scrivesse di aver ritrovato essere tra quelli propor­<lb></lb>zione doppia. </s>

<s>L&#039;uno e l&#039;altro poi di questi problemi è da me dimostrato <lb></lb>per i principii della mia Geometria ” (Alb. </s>

<s>X, 325). </s></p><p type="main">

<s>Cinque anni dopo, cioè sulla fine dell&#039;anno 1640, essendosi Giann&#039;An­<lb></lb>tonio Rocca, sotto le discipline del Cavalieri, dato con grande applicazione <lb></lb>allo studio della Geometria, volle provarsi a risolvere quel medesimo pro­<lb></lb>blema, proposto già al suo Maestro dal Gesuita fiammingo, e vi riuscì per <lb></lb>una via facilissima, e in tutto nuova. </s>

<s>Si preparò a quell&#039;intento un bellis­<lb></lb>simo Lemma, che dal Torricelli, avutone notizia dal Cavalieri nella prima <lb></lb>lettera da noi dianzi trascritta, fu, per servirsene a uno de&#039;venti modi da <lb></lb>ritrovar la quadratura della Parabola, reso per la prima volta pubblicamente <lb></lb>noto sotto questa forma: “ Si figura plana super aliqua sui recta linea figu­<lb></lb>ram ipsam secante libretur, erunt momenta segmentorum figurae ut sunt <lb></lb>solida rotunda ab ipsis segmentis, circa secantem lineam revolutis, descri­<lb></lb>pta ” (Operum geom., P. II cit., pag. </s>

<s>76). <lb></lb><figure id="id.020.01.1893.1.jpg" xlink:href="020/01/1893/1.jpg"></figure></s></p><p type="caption">

<s>Figura 54.</s></p><p type="main">

<s>Sieno le figure piane qualun­<lb></lb>que ACDB, AEFB (fig. </s>

<s>54) revo­<lb></lb>lubili intorno all&#039;asse AB, a cui si <lb></lb>conducano a piacere le CIE, DHF <lb></lb>perpendicolari. </s>

<s>Considerate queste <lb></lb>linee come ponderose, e come aventi <lb></lb>ne&#039;respettivi centri L, N i lòro pesi <lb></lb>raccolti, si avrà, chiamando con M, <lb></lb>M′ i momenti delle dette grandezze <lb></lb>librate intorno ai punti H, I, M:M′= <lb></lb>DHXLH:HFXHM=DH2:HF2, <lb></lb>che è altresì eguale a CoDH:CoHF, <lb></lb>stando, per gli Elementi, i circoli <lb></lb>come i quadrati dei raggi. </s></p><p type="main">

<s>Essendo poi queste così trovate <lb></lb>relazioni vere, non solo per la linea <lb></lb>CIE, ma per le infinite altre, che si potessero condurre alla DHF parallele, ne <lb></lb>conseguirà che la somma dei momenti M sta alla somma dei momenti M′, <lb></lb>come stanno le somme de&#039;circoli descritti dalle infinite linee condotte per­<lb></lb>pendicolari all&#039;asse AB nell&#039;una e nell&#039;altra delle due volubili rappresen­<lb></lb>tate figure. </s>

<s>Perciochè ora di queste somme di circoli infiniti si compaginano <lb></lb>i solidi rotondi dalle dette figure piane generati, accennando con R, R′ que­<lb></lb>sti solidi, e colla cifra Ŗ, che ci rammemori l&#039;origine del calcolo integrale, <lb></lb>la somma di tutti i detti momenti. </s>

<s>avremo R:R′=ŖM:ŖM′; equazione <lb></lb>che rende appunto dimostrato il proposto lemma del Rocca. </s></p><pb xlink:href="020/01/1894.jpg" pagenum="137"></pb><p type="main">

<s>Si passava di qui a un corollario che, a risolvere il problema stereome­<lb></lb>trico del fuso parabolico e del cilindro circoscritto, serviva di più prossima <lb></lb>preparazione immediata. </s>

<s>Sia infatti O il comun centro di N e di L, e si <lb></lb>conduca OP perpendicolare all&#039;asse: si ha per facile dimostrazione che la <lb></lb>somma dei momenti N, L è eguale alla somma delle grandezze CI, DH mol­<lb></lb>tiplicata per OP. </s>

<s>Se si assommino ora, invece di due soli, tutti gl&#039;infiniti <lb></lb>momenti della superfice ACDB, la somma di tutte le infinite grandezze si <lb></lb>raccoglierà in un punto per esempio in O, che sarà il centro di gravità di <lb></lb>essa superfice, la quale chiameremo S. </s>

<s>Procedendo allo stesso modo per <lb></lb>l&#039;altra superfice S′, sia il centro di gravità di lei in Q e sia PQ la più breve <lb></lb>distanza di questo stesso centro dall&#039;asse: avremo dunque ŖM=SXOP, <lb></lb>ŖM′=S′XPq. </s>

<s>I quali due valori, sostituiti nel precedente Lemma, <lb></lb>davano al Rocca, per quel corollario importante che si diceva, R:R′= <lb></lb>SXOP:S′XPQ, ciò che significa avere i due solidi rotondi la ragion <lb></lb>composta delle due figure genitrici, e della distanza del centro di gravità <lb></lb>di ciascuna dall&#039;asse di rotazione. </s></p><p type="main">

<s>Preparatosi così l&#039;argomento, s&#039;usava in tal maniera dal Rocca a risol­<lb></lb>vere il propostosi problema. </s>

<s>Sieno il rettangolo AS, che chiameremo R, e <lb></lb>la parabola ATB, che chiameremo P, le due figure genitrici del cilindro C <lb></lb>e del fuso F. </s>

<s>Se in O, Q rispondono i due centri delle dette figure, e son <lb></lb>perciò OP, PQ le respettive distanze dall&#039;asse di rotazione, avremo dunque, <lb></lb>per le cose ultimamente dimostrate, C:F=RXOP:PXPq. </s>

<s>Ma la <lb></lb>ottava archimedea del II <emph type="italics"></emph>De aequiponderantibus<emph.end type="italics"></emph.end> (Opera cit., pag. </s>

<s>207) dà <lb></lb>OP:PQ=5:4, e la XXIV <emph type="italics"></emph>De quadratura paraboles<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>441) <lb></lb>dà R:P=3:2, perciò se ne conclude C:F=15:8. </s></p><p type="main">

<s>“ His demonstratis (così nel cap. </s>

<s>XIV della III Esercitazione ripigliò il <lb></lb>costrutto il Cavalieri) remanet ostendendum quomodo ex his inferatur re­<lb></lb>gula Guldini, quo ad figuras planas, earumque potestates, quod nunc pate­<lb></lb>fiet ” (pag. </s>

<s>232). Sieno nella precedente figura il rettangolo AS e la figura <lb></lb>qualunque AEFB le due seperfice genitrici. </s>

<s>Avremo, per le cose già dimo­<lb></lb>strate dal Rocca, che i due solidi rotondi generati hanno la ragion composta <lb></lb>del rettangolo e dell&#039;altra superfice irregolare nelle distanze OP, PQ de&#039;loro <lb></lb>centri dall&#039;asse. </s>

<s>E perchè i raggi stanno come le circonferenze, avremo <lb></lb>dunque R:R′=ASXCaOP:AEFBXCa<expan abbr="Pq.">Pque</expan> Rappresentando R un <lb></lb>cilindro sarà perciò eguale ad ABXCoBS=ABXBS/2XCaBS= <lb></lb>ABXBSXCaOP, perchè il rettangolo dà BS=2 OP.Ma ABXBS= <lb></lb>AS, dunque sarà R=ASXCaOP, e perciò anche R′=AEFBXCa<expan abbr="Pq.">Pque</expan> <lb></lb>“ Hoc autem, conclude il Cavalieri, est conforme regulae Guldini ” (ibid., <lb></lb>pag. </s>

<s>233). </s></p><pb xlink:href="020/01/1895.jpg" pagenum="138"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il Rocca, col dimostrato Lemma, e il Torricelli, con la seconda parte <lb></lb>delle Opere geometriche, avevano dunque assai generosamente corrisposto <lb></lb>ai desiderii del Cavalieri, e cooperato efficacemente con lui in difendere la <lb></lb>Geometria degl&#039;indivisibili dagl&#039;insulti del Guldino. </s>

<s>Rimaneva, de&#039;tre chia­<lb></lb>mati alla difesa, il Nardi, il quale però sembra che diffidasse dell&#039;assoluta <lb></lb>bontà dei metodi nuovi. </s>

<s>Trasparisce una tal diffidenza da certe parole scritte <lb></lb>nella Veduta XLII della Scena VI, le quali crediam bene di sottoporre alla <lb></lb>considerazione degli studiosi. </s></p><p type="main">

<s>“ In grazia dei Matematici, egli ivi dice, ho posto accademicamente che <lb></lb>le linee, i punti e le superfice siano in atto ne&#039;corpi, come parti veraci e <lb></lb>componenti, da che ne seguirebbe l&#039;aver quei termini propria esistenza, e <lb></lb>nulla vieterebbe potersi da qualche forza separar dal soggetto, e da qualche <lb></lb>suprema potersi separar tutti. </s>

<s>Quindi si darebbe uno spazio ed un numero <lb></lb>infinito, il che repugna alle cose poste. </s>

<s>Diciamo dunque che i punti, le linee <lb></lb>e le superfice, in tanto sono cosa reale, in quanto sono modi o termini dei <lb></lb>corpi. </s>

<s>Onde, come cosa reale, si riferiscono alle qualità, e si dividono alcuni <lb></lb>di loro per accidente, come il giallo alla divisione dell&#039;oro, e dirassi un corpo <lb></lb>comporsi e misurarsi d&#039;infinite superfice, come quasi l&#039;oro dalle infinite su­<lb></lb>perfice in atto o in potenza che, per accidente, agguagliano tutta la super­<lb></lb>fice di quello. </s>

<s>” </s></p><p type="main">

<s>“ E così anche per esempio una superfice dividesi alla divisione d&#039;un <lb></lb>corpo, come lungo e largo, ma la stessa, come mancante di profondità, è un <lb></lb>nulla, e dal nulla non si può comporre cosa alcuna, benchè si moltiplichi <lb></lb>per qualsivoglia numero finito e anche infinito, se dar si potesse: è ben <lb></lb>vero poi che il giallo non riducesi alla ragione del quanto, come riduconsi <lb></lb>la linea e la superfice al corpo. </s>

<s>Ora il Galilei, benchè parli molto ambiguo <lb></lb>degli infiniti di atto e di potenza, di numero e di mole, come anche del con­<lb></lb>tinuo e del congiunto, e di altri somiglianti principii, contuttociò si lascia <lb></lb>intendere essere i corpi composti d&#039;infiniti indivisibili attuali, e nello stesso <lb></lb>modo contenersi, ed esser distinti l&#039;uno dall&#039;altro i punti in una periferia, <lb></lb>come i lati nel perimetro di un poligono, ma questi principii, con altre con­<lb></lb>seguenze, hanno bisogno di ridursi a buon senso. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. XX, <lb></lb>pag. </s>

<s>970, 71). </s></p><p type="main">

<s>Questo ragionamento del sì valoroso matematico amico suo, se dette <lb></lb>occasione al Torricelli di scrivere <emph type="italics"></emph>De doctrina indivisibilium non temere <lb></lb>usurpanda<emph.end type="italics"></emph.end> (Fabroni, Vitae Ital., Vol. </s>

<s>I, Pisis 1778, pag. </s>

<s>375), non valse <lb></lb>però a persuadergli che, per mancare le superfice di profondità, come si <lb></lb>diceva, non se ne potessero comporre i solidi, e per protestare contro que­<lb></lb>sta opinione, nella II parte <emph type="italics"></emph>De dimensione parabolae,<emph.end type="italics"></emph.end> entrava francamente <pb xlink:href="020/01/1896.jpg" pagenum="139"></pb>per quella via regia apertagli innanzi dal Cavalieri. </s>

<s>Questa pubblica prova <lb></lb>però è posteriore all&#039;altra, che si desume dai privati commerci epistolari, <lb></lb>ne&#039;quali si lesse come, non avendo familiarità col Nardi, esso Cavalieri pre­<lb></lb>gasse il Torricelli a voler dar motivo all&#039;amico d&#039;entrare a pigliar le difese <lb></lb>della nuova Geometria contro la presunzion del Guldino. </s></p><p type="main">

<s>Non mancò il Torricelli di far l&#039;impostogli ufficio, e fu per questa oc­<lb></lb>casione ch&#039;ebbe il Nardi la prima notizia della Centrobrarica, come il Tor­<lb></lb>ricelli stesso l&#039;avea poco fa avuta da quella lettera da Bologna del dì 3 Gen­<lb></lb>naio 1643 da noi trascritta di sopra, essendo un fatto in tal proposito assai <lb></lb>notabile, che tanto s&#039;esercitassero i nostri Matematici intorno a dar ragio­<lb></lb>nevole fondamento a quella Regola meccanica universale, senz&#039;aver mai po­<lb></lb>tuto, per la sua rarità, leggere l&#039;opera del Gesuita tedesco. </s></p><p type="main">

<s>Il Nardi dunque informato della questione, contento di aver avuto di li <lb></lb>l&#039;impulso a&#039;suoi studii geometrici, si tenne, quanto fosse possibile, in di­<lb></lb>sparte dai litiganti. </s>

<s>Concorse nonostante a confermare quelle accuse di fal­<lb></lb>sità, che l&#039;Autor della Geometria nuova volea ritorcere contro alcune pro­<lb></lb>posizioni della Centrobrarica. </s>

<s>Era una di queste proposizioni quella del centro <lb></lb>di gravità di un segmento sferico, o di un emisferio, che il Torricelli, ad <lb></lb>istanza del Cavalieri, determinò in un punto assai diverso da quello, che <lb></lb>una geometrica fallacia avea suggerito al Guldino. </s>

<s>Propostosi questo mede­<lb></lb>simo problema baricentrico al Nardi, s&#039;incontrò per altra via nella conclu­<lb></lb>sione torricelliana, così lasciando scritto in quel suo ampio Teatro accade­<lb></lb>mico, nell&#039;ultima Scena, che s&#039;intitola <emph type="italics"></emph>Più vedute in una:<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Essere il centro di gravità d&#039;una superfice emisferica nel mezzo del­<lb></lb>l&#039;asse, in che sbagliossi il Guldino, provasi da me facilmente con dividere <lb></lb>detto asse in particelle eguali, e ciascuna minore della distanza che l&#039;avver­<lb></lb>sario vuole dal mezzo. </s>

<s>Quindi, tirati piani paralleli alla base, per dette <lb></lb>divisioni si tagliano parti eguali di superfice, quali, per essere uniforme­<lb></lb>mente gravi, peseranno egualmente, ed averà ciascuna il centro dentro i <lb></lb>termini della sua particella di asse, e quindi dedurrassi facilmente l&#039;assurdo. </s>

<s><lb></lb>Trovasi anche facilmente il centro delle superfice coniche e cilindriche, come <lb></lb>anche col Teorema generale meccanico, quello della mezza periferia, ed in <lb></lb>questo osservasi la medesima analogia, da chi ben l&#039;intende, che nella su­<lb></lb>perfice emisferica. </s>

<s>Con l&#039;aiuto poi di queste invenzioni si discende alle più <lb></lb>particolari proposte intorno alla stessa materia ” (MSS. Gal. </s>

<s>Disc., T. XX, <lb></lb>pag. </s>

<s>1360). </s></p><p type="main">

<s>Si rivela ai sagaci lettori da queste parole il genio geometrico del Nardi, <lb></lb>il quale, avuta la notizia della Regola guldiniana, rimasta per l&#039;inventore <lb></lb>una cosa puramente meccanica; provò una viva compiacenza in trovar che <lb></lb>la ragion matematica così da tutti desiderata scendeva chiarissima dalle sue <lb></lb>proprie invenzioni. </s>

<s>Erano quelle invenzioni novelli frutti menati dall&#039;albero <lb></lb>antico, a piè del quale rampollava un gran principio, che il Nardi stesso <lb></lb>chiama <emph type="italics"></emph>Della trasformazion delle figure.<emph.end type="italics"></emph.end> Questa trasformazione dunque, che <lb></lb>ne&#039;libri del Keplero e del Guldino apparve a tutti i Geometri nuova, la vide <pb xlink:href="020/01/1897.jpg" pagenum="140"></pb>il Nostro, in sè e nelle sue mirabili conseguenze, espressa da quel I teo­<lb></lb>rema archimedeo, in cui il circolo s&#039;insegna a trasformare in un triangolo. </s>

<s><lb></lb>Così parevagli che si venisse quel teorema a svolgere in tutte le proprietà <lb></lb>de&#039;triangoli, dimostrate da Euclide nel VI libro Degli elementi, e perciò escla­<lb></lb>mava, in fine alla XXV veduta della II Scena, dop&#039;averne dimostrate le <lb></lb>feconde applicazioni: “ Ora questo gran principio, cioè la I Della misura <lb></lb>del cerchio e la sua proporzionale, che altro sono in effetto, se non la <lb></lb>I del VI e la sua proporzionale? </s>

<s>” (MSS. cit., pag. </s>

<s>329). </s></p><p type="main">

<s>La Centrobrarica insomma, che i loro Autori avevano derivata da stra­<lb></lb>niere sorgenti, veniva il Nardi a dimostrare com&#039;ella scaturisse dalle stesse <lb></lb>più sincere fonti della Geometria, sì per le linee, sì per le superfice comun­<lb></lb>que poste, e di qualunque figura, revolubili intorno all&#039;asse. </s>

<s>A che altro <lb></lb>accennano gli antichi teoremi euclidei della superfice piana del circolo, e <lb></lb>della convessa del cilindro, se non alla manifesta trasformazione di quelle <lb></lb>stesse superfice rotonde in due rettangoli, l&#039;uno de&#039;quali sia costruito sulla <lb></lb>circonferenza e sulla metà del raggio, e l&#039;altro sulla circonferenza descritta <lb></lb>dalla base, e sull&#039;altezza della linea che, menata in giro alla sua parallela <lb></lb>immobile, descrive quella cilindrica superfice? </s></p><p type="main">

<s>Nè una tale trasformabilità delle superfice curve in rette si verifica solo <lb></lb>nelle due citate proposizioni, ma in quell&#039;altre eziandio, dice il Nardi, con­<lb></lb>cernenti le superfice coniche, o de&#039;frusti di coni. </s>

<s>Sia la linea AB (fig. </s>

<s>55) <lb></lb>revolubile intorno all&#039;asse CD. </s>

<s>Se si prende in E il mezzo della linea AB, <lb></lb><figure id="id.020.01.1897.1.jpg" xlink:href="020/01/1897/1.jpg"></figure></s></p><p type="caption">

<s>Figura 55.<lb></lb>e si conduce EF perpendicolare a CD, la superfice così <lb></lb>descritta sarà eguale a quella del cilindro. </s>

<s>Per la XVI <lb></lb>archimedea infatti <emph type="italics"></emph>De sphaera et cylindro<emph.end type="italics"></emph.end> (Opera cit., <lb></lb>pag. </s>

<s>38), si ha <foreign lang="grc">π</foreign>.AB(AC+BD)=<foreign lang="grc">π</foreign>.2 EFXAB <lb></lb>=CaEFXAB. </s>

<s>Se poi la linea s&#039;inclina fino a <lb></lb>toccare in H l&#039;asse di rotazione, la superfice rotata <lb></lb>riuscirà conica, e avrà per misura, secondo la Geome­<lb></lb>tria antica, CaBDXBH/2=CaEF′XBH, che esat­<lb></lb>tamente risponde con la Regola nuova. </s>

<s>Ma ascoltiamo <lb></lb>le parole proprie del Nardi che, nella citata Veduta <lb></lb>XXV del suo scientifico Panorama, ci distese in po­<lb></lb>che parole, e sotto il titolo di <emph type="italics"></emph>Teorema generale mec­<lb></lb>canico,<emph.end type="italics"></emph.end> il primo trattato compiuto di Geometria centrobrarica. </s></p><p type="main">

<s>“ Tal Teorema, egli dice, fu proposto, per quanto intendo, senza dimo­<lb></lb>strazione, dal padre Guldino, e deducesi da certa regola del Keplero. </s>

<s>E ben­<lb></lb>chè io non abbia veduta l&#039;Opera sua, mi vien detto nondimeno essere in <lb></lb>sostanza questo: <emph type="italics"></emph>Se sarà trovato il centro di gravità della linea, o figura <lb></lb>piana da rivolgersi, moltiplicando la circonferenza, descritta secondo la <lb></lb>intera rivoluzione dal centro di gravità, nella linea revoluta o figura piana, <lb></lb>si produrrà la superfice descritta o la solidità del corpo. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Questo teorema ha molti casi, quali tutti dal Metodo della trasforma-<pb xlink:href="020/01/1898.jpg" pagenum="141"></pb>zione delle figure facilmente si mostrano. </s>

<s>E facendomi dalle linee, saranno <lb></lb>o rette o curve: se rette, o semplici o composte: se semplici, o perpendico­<lb></lb>lari o parallele o inclinate all&#039;asse della rivoluzione. </s>

<s>Le perpendicolari o toc­<lb></lb>cheranno o segheranno o saranno disgiunte dall&#039;asse. </s>

<s>” </s></p><p type="main">

<s>“ Se la linea perpendicolare tocchi l&#039;asse, descriverà un cerchio, e in <lb></lb>questo si verifica, per le cose da noi dimostrate, la proposizione. </s>

<s>Se lo se­<lb></lb>ghi, avverrà lo stesso, benchè la parte minore resti oziosa. </s>

<s>Se sia disgiunta, <lb></lb>descriverà una fascia circolare, in cui anche si trova, per le cose da noi <lb></lb>dette, la verità della proposta, ma la retta parallela all&#039;asse descriverà una <lb></lb>superfice cilindrica, qual&#039;è manifesto che eguaglia ad un rettangolo sotto <lb></lb>essa linea, e sotto la periferia descritta dalla distanza dell&#039;asse. </s>

<s>” </s></p><p type="main">

<s>“ Che se la stessa retta s&#039;inclini, mantenendo il suo centro la stessa <lb></lb>distanza dall&#039;asse, descriverà una porzione di conica superfice eguale alla <lb></lb>cilindrica, il che raccogliesi dalle nostre invenzioni, e dalla XV ancora del <lb></lb>I Della sfera e cilindro. </s>

<s>E se inclinandosi tocchi l&#039;asse, descriverà una su­<lb></lb>perfice conica eguale, per le cose insegnate, ad un triangolo rettangolo, di <lb></lb>cui l&#039;altezza s&#039;agguagli alla linea revoluta, e la base alla periferia descritta <lb></lb>dalla perpendicolare dall&#039;altro estremo della linea nell&#039;asse. </s>

<s>Adunque il ret­<lb></lb>tangolo, sotto la medesima linea e sotto la metà della periferia suddetta, sarà <lb></lb>eguale alla conica superfice. </s>

<s>Ma questa metà vien descritta dalla perpendi­<lb></lb>colare, che congiunge l&#039;asse al centro di gravità di essa linea, com&#039;è pa­<lb></lb>lese. </s>

<s>Se poi la medesima linea inclinandosi seghi l&#039;asse, farannosi due su­<lb></lb>perfice coniche, ove ha luogo la ragione me­<lb></lb>desima. </s>

<s>” </s></p><p type="main">

<s>“ Di qui passeremo alla teoria dei casi <lb></lb>composti. </s>

<s>Siano le tre linee rette GD, DC, CF <lb></lb>(fig. </s>

<s>56) revolute intorno all&#039;asse HB: dico <lb></lb><figure id="id.020.01.1898.1.jpg" xlink:href="020/01/1898/1.jpg"></figure></s></p><p type="caption">

<s>Figura 56.<lb></lb>che la superfice descritta da esse è eguale ad <lb></lb>un rettangolo contenuto sotto di esse linee, <lb></lb>come una, e sotto la periferia descritta dalla <lb></lb>perpendicolare, che congiunge l&#039;asse e il cen­<lb></lb>tro della loro gravità. </s>

<s>” </s></p><p type="main">

<s>“ Poniamo, per dare esempio di tutti i casi possibili, che la linea DG <lb></lb>sia inclinata all&#039;asse, e che <lb></lb>DC sia parallela, e che CF <lb></lb>sia perpendicolare al mede­<lb></lb>simo asse. </s>

<s>Divisa DC egual­<lb></lb>mente in A, tirisi all&#039;asse la <lb></lb>perpendicolare AB, e trovisi <lb></lb>il rettangolo MS (fig. </s>

<s>57) <lb></lb><figure id="id.020.01.1898.2.jpg" xlink:href="020/01/1898/2.jpg"></figure></s></p><p type="caption">

<s>Figura 57.<lb></lb>eguale alla superfice cilindrica <lb></lb>descritta da DC, qual rettan­<lb></lb>golo abbia il lato MN eguale <lb></lb>a DC. </s>

<s>Adunque l&#039;altro lato <pb xlink:href="020/01/1899.jpg" pagenum="142"></pb>MT sarà eguale alla periferia descritta da AB. Parimente, divisa DG egual­<lb></lb>mente in E (fig. </s>

<s>56 prec.), tirisi EH perpendicolare all&#039;asse, e trovisi il ret­<lb></lb>tangolo NP eguale alla porzione di superfice conica descritta da DG. </s>

<s>Dun­<lb></lb>que se il lato NO, posto a dirittura con MN, s&#039;agguagli a DG, anche OP <lb></lb>s&#039;agguaglierà alla periferia descritta da HE. </s>

<s>Sia SY l&#039;eccesso di NS sopra <lb></lb>OP, e dividasi SY in R, sicchè RY ad RS si trovi come MN ad NO, e <lb></lb>compiscasi il rettangolo MQ, con prodursi OP, e tirarsi RQ parallela ad <lb></lb>MO. </s>

<s>Adunque il rettangolo MQ s&#039;agguaglierà ai due MS, NP, poichè eguali <lb></lb>sono i rettangoli TR, RP. ” </s></p><p type="main">

<s>“ Cada ora in AB perpendicolare EV e congiungansi i punti E, A, e <lb></lb>trovato il centro comune della gravità delle rette GD, DC, sia L, da cui per­<lb></lb>pendicolare in AB cade LZ. </s>

<s>Sarà dunque come AL ed LE, ovvero come GD <lb></lb>a DC, così AZ a YV; ovvero RS ad RY, e però la periferia descritta da BZ, <lb></lb>cioè da IL, sarà eguale alla retta NR, onde, moltiplicata per GD e DC come <lb></lb>una, cioè per MO, formerà il rettangolo MQ eguale a due rettangoli MS, <lb></lb>NP, il che bisognava dimostrare. </s>

<s>” </s></p><p type="main">

<s>“ Nello stesso modo si proverà che, trovato il centro di gravità delle <lb></lb>due GC, DC come una, e di CF, il rettangolo contenuto sotto tutte tre come <lb></lb>una, e sotto la periferia descritta dalla perpendicolare da esso centro nel­<lb></lb>l&#039;asse, s&#039;agguaglia alla superfice nata dalla rivoluzione di dette due linee. </s>

<s><lb></lb>E quello che in tre, in tutte le altre linee in infinito, con lo stesso metodo, <lb></lb>si proverà. </s>

<s>” </s></p><p type="main">

<s>“ Passiamo alle linee curve, le quali o sono curve uniformi o difformi. </s>

<s><lb></lb>Chiamo uniformi quelle, che sono curve verso la stessa parte; difformi <lb></lb>quelle, che verso le contrarie parti. </s>

<s>Ora le difformi si riducono, come com­<lb></lb>poste, alle uniformi, onde, provata la mede­<lb></lb>sima verità in queste, anche in quelle si pro­<lb></lb>verà. </s>

<s>” </s></p><p type="main">

<s>“ Sia dunque la curva GAC (fig. </s>

<s>58) da <lb></lb>rivolgersi intorno all&#039;asse HB, e di essa curva <lb></lb>sia centro di gravità L. </s>

<s>Dico che la superfice <lb></lb>descritta dalla sua rivoluzione s&#039;agguaglia al <lb></lb>rettangolo sotto una eguale a GAC, e sotto <lb></lb>la periferia descritta da LB perpendicolare in <lb></lb>HB. </s>

<s>Intendansi sottese al concavo di essa curva <lb></lb><figure id="id.020.01.1899.1.jpg" xlink:href="020/01/1899/1.jpg"></figure></s></p><p type="caption">

<s>Figura 58.<lb></lb>molte rette, che abbiano i medesimi termini colla curva, ed anche al con­<lb></lb>vesso, nello stesso modo, altre rette si circoscrivano. </s>

<s>E nulla importa qual <lb></lb>posizione abbia la linea curva verso HB. ” </s></p><p type="main">

<s>“ Ora perchè, nella figura da noi posta, accade che il concavo suo ri­<lb></lb>miri l&#039;asse, avverrà che il centro delle inscritte linee, V, sia più verso al­<lb></lb>l&#039;asse, che il centro Z delle circoscritte, restando di mezzo il centro L della <lb></lb>curva. </s>

<s>E s&#039;avverta che tutti questi centri si sono posti in una retta, perchè <lb></lb>nulla importa il considerare l&#039;esser sotto o sopra di essa, ma solo attendesi <lb></lb>la distanza dell&#039;asse. </s>

<s>” </s></p><pb xlink:href="020/01/1900.jpg" pagenum="143"></pb><p type="main">

<s>“ Ciò avvertito, dico apparir la verità della proposta, perchè se dices­<lb></lb>simo che la superfice descritta dalla curva non s&#039;agguagliasse al rettangolo <lb></lb>sotto di essa e della periferia descritta da LB, avverria che o fosse mag­<lb></lb>giore o minore. </s>

<s>Se maggiore, ne sia determinato l&#039;eccesso. </s>

<s>E perchè le cir­<lb></lb>coscritte rette GD, DC...., avendo i medesimi termini con la curva verso <lb></lb>la stessa parte, sono maggiori della curva; avverrà che, moltiplicandosi le <lb></lb>circoscrizioni delle linee rette, eccedano queste la curva di meno, che la su­<lb></lb>perfice descritta da queste eccede il rettangolo sopraddetto, e così poi av­<lb></lb>verrà che il rettangolo contenuto sotto queste circoscritte, e sotto la perife­<lb></lb>ria descritta da LB, fosse minore dell&#039;altro sotto la curva, e sotto la medesima <lb></lb>periferia, il che è assurdo, trovandosi le circoscritte più lontane dall&#039;asse, <lb></lb>che non è la curva, quale anche è minore di quelle. </s>

<s>” </s></p><p type="main">

<s>“ La stessa maniera serve per provare che non può esser minore, e <lb></lb>più brevemente, per le cose da noi dimostrate altrove. </s>

<s>Concluderassi che, <lb></lb>per mantenersi la stessa analogia delle inscritte e circoscritte rette alla curva, <lb></lb>in ogni moltiplicazione intorno a trasformarsi in punti, anche in tal caso la <lb></lb>proporzionale conclusione avrà luogo. </s>

<s>” (MSS. cit., pag. </s>

<s>314-21). </s></p><p type="main">

<s>La premeditata elezione del metodo antico degl&#039;inscritti e dei circoscritti <lb></lb>condusse il Nardi a dimostrare quest&#039;ultimo teorema all&#039;assurdo, mentre, <lb></lb>proseguendo il metodo nuovo, avrebbe potuto dare un&#039;assai facile dimostra­<lb></lb>zione diretta, considerando la curva, qualunque ella si fosse, come compo­<lb></lb>sta d&#039;indivisibili particelle che, essendo rette, riducevano questo al caso pre­<lb></lb>cedente. </s>

<s>Le linee infatti DG, DC, CF della passata figura LVI, indivisibilmente <lb></lb>moltiplicate, purchè sempre si rimangano nel medesimo piano giacenti, sono <lb></lb>atte a rappresentar l&#039;andamento di qualunque specie di curva. </s></p><p type="main">

<s>Ma pure, moltiplicandosi più e più le linee inscritte e circoscritte, in­<lb></lb>torno a ridurle in punti, il metodo antico, come nella quadratura del cir­<lb></lb>colo, viene a riscontrarsi col nuovo, e il Nardi, nelle parole ultimamente ci­<lb></lb>tate, par che giusto voglia accennare a questo incontro. </s>

<s>È perciò forse che, <lb></lb>passando, dai rotondi generati da linee, a trattar de&#039;rotondi generati da su­<lb></lb>perfice, non si sentirebbe punto ritroso di prendere a fondamento e a prin­<lb></lb>cipio delle sue speculazioni quel Lemma del Rocca, di cui gli avea il Torri­<lb></lb>celli dato notizia, ammirandone la bellezza. </s>

<s>Ma pur non men bello sembrava <lb></lb>al Nardi il Metodo della trasformazion delle figure, e tra per l&#039;amore alle <lb></lb>proprie invenzioni, e per rendere il processo dimostrativo uniforme, seguitò <lb></lb>a far vedere com&#039;anche per i solidi rotondi derivi dalla Geometria antica la <lb></lb>Centrobrarica nuova. </s></p><p type="main">

<s>Quel Metodo, che condusse il Nostro a tante nuove conclusioni, quali <lb></lb>invano si desidera di veder distese nel libro delle <emph type="italics"></emph>Ricercate geometriche,<emph.end type="italics"></emph.end> ha, <lb></lb>nelle particolari applicazioni alla Centrobrarica, come accennammo, il suo <lb></lb>fondamento in questo teorema, che da Archimede si pone per principio alla <lb></lb>dimensione del circolo: “ Omnis circulus aequalis est triangulo rectangulo, <lb></lb>cuius radius est par uni eorum, quae sunt circa rectum angulum, circum­<lb></lb>ferentia vero basi ” (Opera cit., pag. </s>

<s>128). </s></p><pb xlink:href="020/01/1901.jpg" pagenum="144"></pb><p type="main">

<s>Ora è davvero, come parve al Nardi, maravigliosamente bello il modo, <lb></lb>che offre questo archimedeo teorema, di trasformar le figure, le quali si ri­<lb></lb>ducono ne&#039;più semplici casi o a rettangoli, che generano <lb></lb>cilindri, o a triangoli, che rotati descrivono coni. </s>

<s>Rap­<lb></lb>presenti AB (fig. </s>

<s>59) uno di questi rettangoli revolubile <lb></lb>intorno al lato CB: il rotondo cilindrico nato da così fatta <lb></lb>rivoluzione è noto aver per misura CoEBXBC eguale, <lb></lb>per il citato teorema archimedeo, ad EB/2XCaEBXBC <lb></lb>=EBXBCXCaEB/2. Se ora sia G il centro di gra­<lb></lb>vità del rettangolo, da cui si conduca GD perpendicolare <lb></lb>all&#039;asse, CaEB/2 sarà eguale a CaGD, ond&#039;è che per tal <lb></lb>metodo geometrico viene il solido cilindrico a trasfor­<lb></lb><figure id="id.020.01.1901.1.jpg" xlink:href="020/01/1901/1.jpg"></figure></s></p><p type="caption">

<s>Figura 59.<lb></lb>marsi nel parallelepipedo EBXBCXCaGD, il quale perciò ha per base <lb></lb>il rettangolo genitore AB, e per altezza la circonferenza descritta dal centro <lb></lb>di gravità, come pel metodo centrobrarico. </s></p><p type="main">

<s>Sia poi revolubile intorno al medesimo asse CB il triangolo CEB: il <lb></lb>cono così descritto ha per misura CoEBXCB/3 che, per il citato <lb></lb>principio <lb></lb>archimedeo, è eguale ad EB/2XCaEBXCB/3=EBXCaGDXCB/3, man­<lb></lb>tenuta la costruzion precedente. </s>

<s>Abbassata ora la bissettrice CP, suppongasi <lb></lb>in N il centro di gravità del triangolo, da cui si conduca la perpendicolare <lb></lb>NO. </s>

<s>I triangoli simili e la posizion di quel centro, danno 3:2=GD:NO= <lb></lb>CaGD:CaNO, d&#039;onde CaGD=3 CaNO/2; valore che, sostituito nella supe­<lb></lb>riore misura geometrica ultimamente trovata, dà il cono trasformato nel <lb></lb>prisma triangolare EBXCB/2XCaNO, conforme alla Regola centrobrarica. </s>

<s><lb></lb>Ma perchè le parole proprie del Nardi, nella loro original concisione, sono <lb></lb>assai più efficaci, seguitiamo a trascriverle fedelmente ai nostri Lettori: </s></p><p type="main">

<s>“ Passiamo alle superfice rivoltate intorno ad un asse. </s>

<s>E qui avverti­<lb></lb>sco primieramente essere stato dimostrato dal sottilissimo G. </s>

<s>Antonio Rocca <lb></lb>che i solidi rotondi hanno la proporzione delle figure genitrici, e delle cir­<lb></lb>conferenze descritte dai centri, da che ci riscontriamo con la proposta di <lb></lb>sopra fatta. </s>

<s>Ma per far noi uniforme il metodo di dimostrare i prodotti delle <lb></lb>superfice, e quelli delle linee, prenderemo il principio dai più semplici casi, <lb></lb>proponendo un rettangolo AEBC (fig. </s>

<s>prec.), il quale si può intendere ri­<lb></lb>volgersi intorno ad un lato o intorno ad altro asse disgiunto. </s>

<s>Se intorno ad <lb></lb>un lato, descrive un cilindro, ed a questo s&#039;agguaglia, com&#039;è facile a in­<lb></lb>tendersi dalle cose da noi dimostrate, un prisma contenuto da tre rettan­<lb></lb>goli e da due triangoli laterali, anch&#039;essi rettangoli. </s>

<s>Ciascuno di questi trian-<pb xlink:href="020/01/1902.jpg" pagenum="145"></pb>goli s&#039;agguaglia al cerchio base del cilindro, e il rettangolo, che fa angolo <lb></lb>retto con l&#039;altra base del prisma, è lo stesso che AEBC, ma l&#039;altro sud­<lb></lb>detto rettangolo si contiene sotto la retta CB, e sotto la periferia descritta <lb></lb>dal doppio di GD, posto esser GD la retta, che dal centro del rettangolo <lb></lb>cade perpendicolare in CB. ” </s></p><p type="main">

<s>“ Adunque è manifesto, per gli Elementi, che il solido, sotto AEBC e <lb></lb>sotto la periferia descritta da GD, s&#039;agguaglia al prisma. </s>

<s>E lo stesso è vero <lb></lb>nei parallelogrammi non rettangoli revoluti, poichè l&#039;eccesso di uno estremo <lb></lb>compensa il difetto dell&#039;altro nei solidi prodotti. </s>

<s>” </s></p><p type="main">

<s>“ Che se tirato sia nel rettangolo AEBC il diametro CE, e si rivolga <lb></lb>il triangolo CEB intorno all&#039;asse CB, descriverà un cono, che al cilindro del <lb></lb>rettangolo ha la ragione di uno a tre. </s>

<s>Adunque un solido sotto detto trian­<lb></lb>golo, e sotto la periferia descritta da GD, averà al cono la ragione di tre a <lb></lb>due, quale è la medesima che quella della linea GD alla linea, che perpen­<lb></lb>dicolare cade dal centro del triangolo in CB. </s>

<s>E così le comuni regole dei <lb></lb>solidi, nati dalla rivoluzione dei piani, avranno luogo anche in questo caso. </s>

<s>” </s></p><p type="main">

<s>“ Ora se il rettangolo s&#039;intende rivolgersi disgiunto, ma parallelo con <lb></lb>un suo lato all&#039;asse, descriverà un anello cilindrico, e se inclinato descrive­<lb></lb>rallo conico: e qui le proporzionali cose avvengono che nelle linee revolute. </s>

<s><lb></lb>Onde, supponendo di scrivere a persone perite, non m&#039;intertengo più, e pas­<lb></lb>sandomene alle superfice contenute da rette più irregolarmente poste, od a <lb></lb>curve linee, dico che, mediante la circoscrizione di rettangoli o parallelo­<lb></lb>grammi, s&#039;otterrà l&#039;intento. </s>

<s>” </s></p><p type="main">

<s>“ E prendiamo in esempio la parabola, a cui sia circoscritto il paral­<lb></lb>lelogrammo, com&#039;anche alla usanza archimedea altri minori parallelogrammi <lb></lb>siano inscritti e circoscritti, perchè, rivoltate tutte queste figure intorno alla <lb></lb>base parabolica, si descriverà dal parallelogrammo un cilindro, dalla parabola <lb></lb>un fuso, e dalle figure inscritte e circoscritte descriverannosi due solidi com­<lb></lb>posti di cilindri e di anelli cilindrici. </s>

<s>” </s></p><p type="main">

<s>“ La proporzione poi del cilindro, descritto dal parallelogrammo, al so­<lb></lb>lido descritto dalla figura circoscritta alla parabola, o a quello descritto dalle <lb></lb>inscritte, si troverà col metodo sopra usato esser composta della proporzione <lb></lb>del parallelogrammo alla figura, e della linea, che dal centro va, a quella <lb></lb>del centro di quelle, e ciò insino all&#039;ultimo. </s>

<s>Adunque anche il cilindro al <lb></lb>fuso sarà nella stessa proporzione. </s>

<s>Ora il parallelogrammo alla parabola è <lb></lb>come 6 a 4, per le cose da noi dimostrate. </s>

<s>E la linea dal centro suo, a <lb></lb>quella del centro di questa, è come 5 a 4, come da Archimede si dimostra. </s>

<s><lb></lb>Adunque il cilindro al fuso sarà come 30 a 16 o come 15 a 8. ” </s></p><p type="main">

<s>“ Che se la parabola e il rettangolo si rivolgano per la cima di essa, <lb></lb>vedrassi in un tratto essere il cilindro al solido come 5 a 4. Finalmente, se <lb></lb>la mezza parabola si rivolge insieme col parallelogrammo, che quella com­<lb></lb>prenda intorno ad una parallela all&#039;asse e segante la acuta parabolica; sarà <lb></lb>nello stesso modo la proporzione dei solidi nota. </s>

<s>Ma sono quasi impossibili <lb></lb>le investigazioni a priori di cotali materie per il metodo antico, e bisogna <pb xlink:href="020/01/1903.jpg" pagenum="146"></pb>ridursi al nuovo, col quale anche a priori dimostrasi questa universalissima <lb></lb>proposta meccanica. </s>

<s>” (MSS. cit., pag. </s>

<s>321-26). </s></p><p type="main">

<s>In queste ultime espressioni del Nardi si dà la dovuta importanza alla <lb></lb>Regola centrobrarica, della quale si dice poter aversi prova a priori, ossia <lb></lb>matematica, e non solamente fisica, com&#039;erasi avuta dal Keplero e dal Gul­<lb></lb>dino, in que&#039;loro impropriamente chiamati teoremi. </s>

<s>Il metodo della trasfor­<lb></lb>mazion delle figure aveva all&#039;Autore offerti di quelle matematiche dimostra­<lb></lb>zioni gli esempi sopra recati, ma i centri di gravità introdottivi partecipavano <lb></lb>ancora qualche cosa del meccanico ai nuovi processi dimostrativi, ond&#039;è che <lb></lb>il Nardi, il quale voleva assolutamente renderli geometrici, pensò di sostituire <lb></lb>a quelli stessi centri di gravità il <emph type="italics"></emph>centro della potenza.<emph.end type="italics"></emph.end> Intendeva per que­<lb></lb>sto nome significato quel che&#039;è oggidì nel comun linguaggio dei Matema­<lb></lb>tici, estendendolo a qualunque prodotto di quantità numeriche o lineari, da <lb></lb>cui giusto vien la potenza di produr da linee superfice, e da superfice so­<lb></lb>lidità di corpi. </s>

<s>Così tornava la Meccanica centrobrarica del Guldino, per <lb></lb>opera del Nostro, non solo, diciam così, trasposta negli orti, ma qual novello <lb></lb>ramo inoculata nel grande albero antico della Geometria. </s></p><p type="main">

<s>“ Veramente maravigliosa (così proseguesi nel manoscritto l&#039;interrotto <lb></lb>ragionamento) sembra la suddetta Regola generalissima con la sua prova <lb></lb>intorno alla potenza delle linee e superfice rivoltate in giro. </s>

<s>Mancagli non­<lb></lb>dimeno il riducimento dal meccanico al geometrico, con ridurre il centro <lb></lb>della gravità al centro della potenza. </s>

<s>Dico centro della gravità d&#039;una super­<lb></lb>fice il definito altre volte, ma centro della potenza dico il punto dentro alla <lb></lb>sua superfice o suo concavo, da cui, tirata una retta perpendicolare all&#039;asse <lb></lb>di qualsivoglia rivoluzione descrive essa retta, con un suo estremo, una pe­<lb></lb>riferia eguale all&#039;altezza di un solido, che per base abbia la superfice di <lb></lb>un solido voltata poi in giro, ed al solido da quella superfice descritto sia <lb></lb>eguale. </s>

<s>” </s></p><p type="main">

<s>“ Il centro dunque della potenza sarà in effetto lo stesso che quello <lb></lb>della gravità, ma sarà dato per termini geometrici. </s>

<s>Il centro poi della figura <lb></lb>sarà talvolta diverso da quello della potenza, poichè per esempio dirassi: nel <lb></lb>mezzo cerchio il centro della figura è nel mezzo della sua base; nel cerchio <lb></lb>poi e nel parallelogrammo conviene in uno l&#039;un centro e l&#039;altro. </s>

<s>” </s></p><p type="main">

<s>“ Se finalmente vogliamo definire nelle linee il centro della potenza, <lb></lb>diremo esser quel punto, dentro alla linea o suo concavo, da cui tirata una <lb></lb>retta perpendicolare all&#039;asse di qualsivoglia rivoluzione descriva essa retta <lb></lb>con un suo estremo una periferia eguale al lato di un rettangolo, il qual <lb></lb>rettangolo sia eguale alla superfice descritta dalla linea voltata in giro, ed <lb></lb>abbia l&#039;altro suo lato eguale ad essa linea. </s>

<s>” </s></p><p type="main">

<s>“ Ora, quanto alla generale dimostrazione in tutti i suoi casi da noi <lb></lb>apportata, non lasceremo d&#039;avvertire com&#039;ella è tutta fondata nella prima <lb></lb>proposta della misura del cerchio, ond&#039;è quasi un corollario suo e della sua <lb></lb>proporzionale. </s>

<s>Dico dunque che le line rette voltate in giro non possono <lb></lb>descrivere se non cerchi e sue fasce, superfice coniche e cilindriche, poichè <pb xlink:href="020/01/1904.jpg" pagenum="147"></pb>non possono aver se non tre situazioni rispetto all&#039;asse della rivoluzione. </s>

<s><lb></lb>Agguagliato dunque ad un triangolo noto o rettangolo il cerchio in quello <lb></lb>trasformato, agguaglieremo anco la sua fascia e settore, come parimente la <lb></lb>superfice conica e sua parte, e la cilindrica, che è un rettangolo. </s>

<s>Saputa poi <lb></lb>la potenza d&#039;una retta, si sa quella di due e quante vogliamo, poichè que­<lb></lb>sto non si riduce ad altro, se non che i rettangoli uguali hanno reciproche <lb></lb>le basi e le altezze. </s>

<s>Dall&#039;applicar poi, di fuori e di dentro alle curve, rette, <lb></lb>si prova della potenza delle curvo quella che delle rette. </s>

<s>” </s></p><p type="main">

<s>“ E passando alla potenza delle superfice, noi sappiamo, con la analo­<lb></lb>gia della I suddetta della misura del cerchio, che un rettangolo, voltato in­<lb></lb>torno alla base o ad una parallela alla base, descrive un cilindro o un anello <lb></lb>cilindrico, e questi s&#039;agguagliano, trasformati, ad un prisma o parallelepi­<lb></lb>pedo retto. </s>

<s>Saputo la potenza di un rettangolo, sapremo quella di due o <lb></lb>più, poichè ciò non si riduce ad altro, se non che i parallelepipedi uguali <lb></lb>hanno reciproche le basi e le altezze. </s>

<s>Quindi, passando alle inscrizioni e <lb></lb>circoscrizioni di rettangoli o parallelogrammi alle piane figure, s&#039;otterrà pro­<lb></lb>porzionalmente lo stesso che nelle stesse linee. </s>

<s>Tanto importa un principio <lb></lb>grande, mentre bene applicar si sappia. </s>

<s>Ora, questo gran principio, cioè la <lb></lb>I della misura dal cerchio e la sua proporzionale, che altro sono in effetto, <lb></lb>se non la I del VI e le sue proporzionali? </s>

<s>” (MSS. cit., pag. </s>

<s>326-29). </s></p><p type="main">

<s>A ripensar che le conseguenze di questo gran principio archimedeo, con <lb></lb>le bellissime applicazioni di lui al modo di trasformar le figure, si dimo­<lb></lb>strarono dal Nardi nel libro delle Ricercate geometriche, e in quello delle <lb></lb>Scene accademiche, l&#039;uno rimasto tuttavia manoscritto e l&#039;altro a quel che <lb></lb>sembra perduto; si può facilmente intendere quale documento importante <lb></lb>sia venuto a mancare alla storia della Scienza italiana. </s>

<s>Quanto al presente <lb></lb>proposito poi si comprenderà qual grave danno dovesse venire a risentirne <lb></lb>la Centrobrarica, la quale seguitava a rimanere nei quattro libri del Gul­<lb></lb>dino senz&#039;alcun fandamento di Geometria. </s>

<s>Vero è bene che il Cavalieri vi <lb></lb>avea sufficientemente supplito, ma è pure un fatto notabilissimo che quel <lb></lb>XIV capitolo, con tutta la III geometrica Esercitazione, furono parole in Ita­<lb></lb>lia gettate al vento. </s>

<s>Gl&#039;indivisibili avevano avuto un colpo mortale dai Dia­<lb></lb>loghi di Galileo, e perciò i seguaci del potentissimo uomo, benchè si sentis­<lb></lb>sero allettati allo splendore e alla bellezza del vero, o s&#039;astennero nonostante, <lb></lb>come il Nardi, dal professarli, o gli professarono con riserbo, come il Tor­<lb></lb>ricelli e il Viviani. </s>

<s>Nelle opere matematiche di questo si legge un tal sen­<lb></lb>timento non meno espresso, che nelle opere di quello, imperocchè, nella <lb></lb>IX proposizione <emph type="italics"></emph>De maximis et minimis,<emph.end type="italics"></emph.end> dop&#039;avere in una prima maniera <lb></lb>dimostrato che la parabola è sesquialtera al triangolo della medesima base <lb></lb>e della medesima altezza, così il Viviani stesso soggiunge per monito al let­<lb></lb>tore: “ Ut hoc loco ex adverso indirectae antiquorum viae per duplicem <lb></lb>positionem luce clarius pateat quantum facilitatis, brevitatis atque evidentiae <lb></lb>nanciscatur a nova directaque methodo, <emph type="italics"></emph>recte tamen cauteque usurpata,<emph.end type="italics"></emph.end><lb></lb>acutissimi geometrae Cavalerii, per indivisibilium doctrinam, nobis amicis-<pb xlink:href="020/01/1905.jpg" pagenum="148"></pb>simam; ex hac alteram accipe eiusdem theorematis demonstrationem ” (Flo­<lb></lb>rentiae 1659, pag. </s>

<s>35). </s></p><p type="main">

<s>L&#039;applicazione però degl&#039;indivisibili è fatta qui, come ne&#039;teoremi tor­<lb></lb>ricelliani, rispetto ai più semplici casi elementari del metodo, ma le proposi­<lb></lb>zioni, in che quello stesso metodo via via si svolge, e sempre più altamente <lb></lb>s&#039;ingrada, sembravano ai Galileiani audacie temerarie dell&#039;ingegno. </s>

<s>Ad imi­<lb></lb>tazione perciò del Maestro come non vollero entrar nell&#039;alto della Geometria <lb></lb>in VII libri, così non si curarono di leggerne il compendio nelle due prime <lb></lb>Esercitazioni, insiem con le quali ebbe a trovarsi esclusa dalla lettura an­<lb></lb>che la III contro il Guldino. </s></p><p type="main">

<s>Di qui è dato intendere come, morti il Cavalieri, il Torricelli e il Nardi, <lb></lb>venisse della Centrobrarica, nella Scuola galileiana, a perdersi quasi ogni me­<lb></lb>moria. </s>

<s>Ebbero gran parte in quell&#039;oblio le difficoltà, che trovarono a penetrar <lb></lb>fra noi i due Tomi in folio stampati a Vienna. </s>

<s>Vedemmo come il Cavalieri <lb></lb>stesso ne avesse avuto notizia solamente due anni da poi, che furono pub­<lb></lb>blicati, e rispondeva così al Torricelli, che con grande istanza gli avea ri­<lb></lb>chiesti: “ Circa il libro del Guldini non posso dirle altro, se non che qua <lb></lb>in Bologna non se ne trovano, essendo venuto solo quello che ho io, ed un <lb></lb>altro, che fu comprato da un altro. </s>

<s>Ma credo che a Venezia se ne trove­<lb></lb>ranno, poichè di là vennero questi due. </s>

<s>È stampato in Vienna dell&#039;Austria <lb></lb>nel 1640 ” (MSS. Gal. </s>

<s>Disc., XLI, fol. </s>

<s>161). Ma non sembra fosse rimasto <lb></lb>in Venezia altro esemplare del libro desiderato, cosicchè forse il Torricelli <lb></lb>non lo vide se non che assai tardi, com&#039;è certo che non lo aveva ancora <lb></lb>veduto il Nardi, quando scrisse le vedute della II Scena. </s>

<s>Ventisei anni dopo <lb></lb>par che seguitasse tuttavia fra noi la penuria, giacchè il Viviani, avendone <lb></lb>data la commissione in Roma a Matteo Campani, questi gli rispondeva il <lb></lb>dì 18 Gennaio 1670: “ Il libro del Guldino da monsù Biagio non si trova, <lb></lb>nè io ho potuto ancora far diligenza altrove, per la mia indisposizione ” (ivi, <lb></lb>Disc., T. CXLV, fol. </s>

<s>127). </s></p><p type="main">

<s>Della Centrobrarica insomma, oltrepassata di alcuni anni la metà del <lb></lb>secolo XVII, non si sapeva nulla di più da&#039;Nostri di quel che avessero per <lb></lb>caso sentito dire dagli altri, ond&#039;è che giova a noi raccontare dai discorsi <lb></lb>di chi e come si venisse a riaccendere nell&#039;ingegno de&#039;Matematici italiani <lb></lb>la fiamma, rimasta spenta o sopita nelle Esercitazioni del Cavalieri, e nelle <lb></lb>Scene del Nardi. </s></p><p type="main">

<s>Ne&#039;primi giorni di Aprile del 1656 Erasmo Bartholin, venuto a viag­<lb></lb>giare in Italia, capitò in Padova, dov&#039;era poco prima da Firenze giunto an­<lb></lb>che il Viviani. </s>

<s>Incontratisi insieme i due Matematici amici, e caduto com&#039;è <lb></lb>naturale il discorso intorno agli amati studii, disse il Bartholin che il padre <lb></lb>Guldin gesuita aveva, nella II parte della sua Centrobrarica, proposto senza <lb></lb>però dimostrarlo un gran teorema universale, e soggiungeva che l&#039;avea ri­<lb></lb>cavato da un manoscritto greco di Pappo alessandrino. </s></p><p type="main">

<s>La medesima notizia era venuta in quel tempo anche alle orecchie del <lb></lb>Borelli, il quale, forse due mesi prima di diventargli così fiero e ostinato <pb xlink:href="020/01/1906.jpg" pagenum="149"></pb>nemico, ne dette amichevole avviso al Viviani, soggiungendo in che egli cre­<lb></lb>desse consistere quel teorema guldiniano, e formulandogli ne&#039;suoi veri e <lb></lb>precisi termini la Regola centrobrarica. </s></p><p type="main">

<s>Parve al Viviani l&#039;annunziata verità bellissima, e tutto allora in ammi­<lb></lb>razione de&#039;sublimi concetti di Apollonio e di Aristeo, i perduti libri de&#039;quali <lb></lb>si disponeva a divinare, sentì nascersi vivissimo il desiderio di ricercar quella <lb></lb>Regola centrobrarica nelle carte greche del Matematico antico. </s>

<s>La cosa però <lb></lb>si rendeva assai difficile, trattandosi di un manoscritto. </s>

<s>Poi seppe che il Bar­<lb></lb>tholin era stato male informato, e che il libro, da cui si diceva aver rica­<lb></lb>vata la sua invenzione il Gesuita tedesco, correva oramai per le mani di <lb></lb>tutti tradotto in lingua latina, e commentato dal Commandino. </s></p><p type="main">

<s>Il curioso riscontro del nuovo nell&#039;antico passò per alquanti anni inos­<lb></lb>servato, nè sapremmo noi dire chi fosse il primo, a cui occorresse di farlo. </s>

<s><lb></lb>Non fu certamente il Cavalieri, in man del quale avrebbe quella nota po­<lb></lb>tuto fare un bellissimo gioco, perchè, nel ritorcer le accuse contro il Gul­<lb></lb>dino, lo avrebbe potuto tacciare qual plagiario di Pappo, con più acuta <lb></lb>ferita, che dicendolo imitator del Keplero. </s>

<s>Benchè dunque il Bartholin fran­<lb></lb>tendesse, dee aver pure attinta a&#039;suoi connazionali o ai vicini quella noti­<lb></lb>zia, che, alteratasi di discorso in discorso e già penetrata in Italia, venne <lb></lb>finalmente a scoprirsi al Viviani sotto l&#039;aspetto del vero. </s></p><p type="main">

<s>Le matematiche Collezioni erano state tradotte, come dicemmo, dal Com­<lb></lb>mandino, il quale, sopraggiunto dalla morte, avendo lasciata inedita e in <lb></lb>alcune parti imperfetta la sua versione, non si risolverono perciò gli eredi <lb></lb>di pubblicarla, infin tanto che il duca Francesco Maria Della Rovere non <lb></lb>venne a interporvi l&#039;autorevole sua mediazione, ordinandone in Urbino la <lb></lb>stampa a sue proprie spese. </s>

<s>Il Viviani dunque si dette con gran diligenza <lb></lb>a cercare il Volume, e nelle parole, con le quali si chiude al VII libro quella <lb></lb>lunga erudita prefazione, parvegli aver trovato quel che cercava, riducendo <lb></lb>all&#039;espressa formula del Borelli l&#039;enimmatico senso. </s></p><p type="main">

<s>C&#039;è fra le carte dello stesso Viviani (MSS. cit. </s>

<s>Disc., T. XCVIII, fol. </s>

<s>161) <lb></lb>tuttavia rimasta la copia, che di sua propria mano fece del passo di Pappo, <lb></lb>e com&#039;ei par che se lo volesse per più comoda meditazione sottoporre in <lb></lb>quel foglio sott&#039;occhio, così noi pensiamo di trascriver qui, nella sua inte­<lb></lb>gra fedeltà, il testo, perchè possano i nostri lettori aver più comoda e più <lb></lb>facile intelligenza dell&#039;arguto commento: “ Perfectorum utrorumque ordi­<lb></lb>num proportio composita est ex proportione amphismatum, et rectarum li­<lb></lb>nearum similiter ad axes ductarum a punctis, quae in ipsis gravitatis centra <lb></lb>sunt: imperfectorum autem proportio composita est ex proportione amphi­<lb></lb>smatum, et circumferentiarum a punctis, quae in ipsis sunt centra gravita­<lb></lb>tis, factorum. </s>

<s>Harum circumferentiarum proportio dividitur in proportionem <lb></lb>ductarum linearum, et earum quas continent ipsarum extrema ad axes .... <lb></lb>angulorum .... ” (Collectiones cit., pag. </s>

<s>252). </s></p><p type="main">

<s>Quest&#039;ultimo periodo, che per la corruzione del testo è di più difficile <lb></lb>intelligenza, servì al Viviani di chiave per aprire il chiuso degli altri, inter-<pb xlink:href="020/01/1907.jpg" pagenum="150"></pb>petrandolo nella seguente guisa, e illustrando l&#039;interpetrazione con l&#039;appo­<lb></lb>sta figura, per noi in ordine LXa, nella quale MN, RS rappresentano due <lb></lb>superfice qualunque, i centri di gravità delle quali A, C sien revolubili at­<lb></lb><figure id="id.020.01.1907.1.jpg" xlink:href="020/01/1907/1.jpg"></figure></s></p><p type="caption">

<s>Figura 60.<lb></lb>torno all&#039;asse BD, in distanze varie e per vario <lb></lb>angolo di rotazione: “ Harum circumferentiarum <lb></lb>proportio dividitur in proportionem ductarum li­<lb></lb>nearum AB, GD et in proportionem angulorum <lb></lb>ABE, GDF earumdem linearum a centro gravitatis <lb></lb>extremorum amphismatum ad axem rotationis <lb></lb>ductarum ” (MSS. T. cit., fol. </s>

<s>163). </s></p><p type="main">

<s>L&#039;interpretazione dall&#039;altra parte risponde <lb></lb>conformissima con la Regola centrobrarica, perchè, <lb></lb>rimanendo le due superfice sempre per la mede­<lb></lb>sima base ai due solidi cilindrici, o ai due pri­<lb></lb>smatici, in cui vengono trasformati; le circonferenze, che ne misuran le re­<lb></lb>lative altezze, tornan maggiori o minori, secondo che sono i centri di <lb></lb>gravità A, G più o meno distanti, o per maggiore o minore angolo intorno <lb></lb>all&#039;asse rotati. </s>

<s>La distinzione perciò di <emph type="italics"></emph>perfetti<emph.end type="italics"></emph.end> e d&#039;<emph type="italics"></emph>imperfetti<emph.end type="italics"></emph.end> appella, se­<lb></lb>condo il Viviani, al grado della rotazione, la quale, se sia fatta per tutto il <lb></lb>circolo intera, genera il rotondo perfetto, e lo genera imperfetto se, prima <lb></lb>di ritornare in sè, il moto rotatorio si arresta. </s>

<s>A questi poi si accomodano, <lb></lb>secondo l&#039;interpetre, gli altri sensi, così in questa nota autografa dichiarati: </s></p><p type="main">

<s><emph type="italics"></emph>“ Amphisma, amphismatis.<emph.end type="italics"></emph.end> Pro hac voce amphisma intelligit fortasse <lb></lb>Pappus omne id quod circa manentem axem circumfertur, vel circumver­<lb></lb>titur, vel circumducitur, aut circum rotatur, vel illud sit linea in plano, in <lb></lb>quo est axis manens, vel superficies plana figurata in plano, in quo idem <lb></lb>axis repertur. </s>

<s>Si linea, in ipsa circumrotatione describit superficiem rotun­<lb></lb>dam, quam voco annularem. </s>

<s>Si superficies plana, hoc est figura plana, so­<lb></lb>lidum rotundum vel clausum vel apertum ad instar annuli describet. </s>

<s>” </s></p><p type="main">

<s>“ Pro illa voce <emph type="italics"></emph>ordo<emph.end type="italics"></emph.end> intelligit forsan unumquodque horum producto­<lb></lb>rum a rotantibus, nempe vel rotundum superficie annulari, vel rotundum <lb></lb>solidum annulare clausum vel apertum. <emph type="italics"></emph>Perfectus ordo<emph.end type="italics"></emph.end> forsan est id quod <lb></lb>amphismate in integra ac perfecta rotatione describitur. </s>

<s>Nos autem dicimus <lb></lb>superficiem annularem vel annulum. </s>

<s>Imperfectus vero ordo, quod ab im­<lb></lb>perfecta, non integra, sed partiali, fit rotatione, et quod voco sectorem, vel <lb></lb>superficiem annularem, vel annulum ” (ibid., fol. </s>

<s>162). </s></p><p type="main">

<s>Sarebbero così le cose per ogni verso assai bene accomodate, quando <lb></lb>nell&#039;ultimo trascritto periodo avesse veramente voluto esprimer Pappo quel <lb></lb>che il Viviani v&#039;intende, e quando, in corrispondenza alle voci greche del <lb></lb>testo, fossero dal Commandino rese le latine <emph type="italics"></emph>imperfectum<emph.end type="italics"></emph.end> e <emph type="italics"></emph>perfectum,<emph.end type="italics"></emph.end> le <lb></lb>quali, avendo il radicale nel verbo <emph type="italics"></emph>perficio,<emph.end type="italics"></emph.end> sono atte nate a significare o <lb></lb>la cosa manca o ridotta alla sua perfezione. </s>

<s>In qualunque modo, è il com­<lb></lb>mento non indegno del divinator di Apollonio e di Aristeo, il qual divina­<lb></lb>tore, nella estrema vecchiezza ritornando indietro su queste cose con la lunga <pb xlink:href="020/01/1908.jpg" pagenum="151"></pb>memoria, si compiacque di essere stato egli il primo a togliere agli strani <lb></lb>versi il velame. </s>

<s>Un giovane studente di Firenze gli venne un giorno a pro­<lb></lb>por la stereometria del pinnacolo delle due piramidi erette sulla piazza di <lb></lb>S. </s>

<s>Maria Novella, che parendogli assai bello e nuovo problema, si dette vo­<lb></lb>lentieri a scioglierlo, servendosi della Regola centrobrarica, da lui stesso <lb></lb>chiamata “ quell&#039;ammirando universale teorema, che assai oscuramente ac­<lb></lb>cennò Pappo Alessandrino, senza già dimostrarlo, ma però interpetrato da <lb></lb>me, 50 e più anni sono corsi, ed allora anche da me provato in più modi ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XCII, fol. </s>

<s>29). </s></p><p type="main">

<s>Al buon vecchio quasi ottuagenario dee però, nello scrivere quel nu­<lb></lb>mero 50, aver fatto fallo o la memoria o la penna, perchè da lui stesso <lb></lb>altrove è stato scritto il giorno, in ch&#039;ebbe della Centrobrarica dal Barto­<lb></lb>lino la prima notizia, e il mese, in ch&#039;egli attese a esercitarsi in trovar quelle <lb></lb>dimostrazioni, ch&#039;eran venute a mancare in Pappo e nel Guldino, e che <lb></lb>formavano dianzi, nella scrittura del Nostro intorno al pinnacolo delle Pi­<lb></lb>ramidi fiorentine, il secondo oggetto della sua compiacenza. </s></p><p type="main">

<s>Cotali importanti documenti, per cui viene a precisarsi questa crono­<lb></lb>logia, e a confermarsi la storia da noi sopra accennata, si ricavano dal se­<lb></lb>guente poscritto a una lettera autografa dello stesso Viviani, e da lui diretta <lb></lb>a Erasmo Bartholin da Padova, il di 3 Giugno del 1656: “ Non voglio man­<lb></lb>care, ivi si legge, di dar parte a V. S. come, nello speculare alcune mate­<lb></lb>rie geometriche meccaniche, mi è sortito ritrovare la dimostrazione, ed an­<lb></lb>che in più modi, di un gran teorema universale, del quale tre mesi sono <lb></lb>con V. S. mi diede notizia il signor Giovanni Alfonso Borelli, già matema­<lb></lb>tico di Pisa, come proposto, ma non dimostrato dal padre Guldini gesuita <lb></lb>nella II parte della sua Centrobrarica, e pensò che sia quel medesimo, del <lb></lb>quale V. S. mi accennò che detto Padre aveva cavato da un manoscritto <lb></lb>greco di Pappo, perchè, ricercando detto signor Borelli qual potess&#039;essere <lb></lb>quel principio del Guldini o teorema, del quale V. S. mi aveva discorso <lb></lb>quando lei fu qua, mi rispose che credeva potess&#039;esser questo, cioè: che <lb></lb>rivoltandosi qualunque figura piana regolare intorno una retta linea, come <lb></lb>asse della rivoluzione, proponeva il Guldini che il solido rotondo o annulare <lb></lb>descritto da detta figura fosse uguale ad un cilindro, che ha per base la <lb></lb>detta figura, e per altezza una linea uguale alla periferia descritta nella ri­<lb></lb>voluzione dal centro di gravità della detta figura, soggiungendo però che non <lb></lb>lo dimostrava, e non sapeva che fosse stato provato nemmeno da altri. </s>

<s>Io <lb></lb>dunque su questo e su quel principio, del quale intenderà V. S.; lo dimo­<lb></lb>stro in più modi assai belli, e più genericamente proposti, cioè di qualun­<lb></lb>que figura piana, benchè irregolare, e per ottener questo mi è convenuto <lb></lb>trovare una mano di lemmi nuovi, e ne ho poi dedotto una quantità di altri <lb></lb>teoremi bellissimi, oltre all&#039;avere ancora con tale occasione speculato sopra <lb></lb>la misura delle superfice curve con qualche acquisto, e certamente vi saria <lb></lb>da fare un trattato molto curioso ” (MSS. Gal. </s>

<s>Disc., T. CXLII, fol. </s>

<s>11, 12). </s></p><p type="main">

<s>L&#039;avere inteso dal Borelli, ignaro delle Scene del Nardi e dimentico <pb xlink:href="020/01/1909.jpg" pagenum="152"></pb>delle Esercitazioni del Cavalieri, che il teorema guidiniano da nessuno an­<lb></lb>cora era stato dimostrato, fece nascere nel Viviani il desiderio di mettersi <lb></lb>egli, che si credeva il primo, alla prova, e riuscitagli felicemente feconda <lb></lb>ne dava sollecito avviso al Bartholin, perchè quel Borelli, divenutogli in que­<lb></lb>sto mezzo tempo acerbissimo nemico, non avesse a vantarsi di averlo pre­<lb></lb>venuto. </s>

<s>Il principio, su cui la dimostrazion si fondava, e che accennavasi <lb></lb>nell&#039;allegato poscritto, par che sia rivelato dal seguente titolo, scritto in <lb></lb>fronte a una delle tre centrobrariche proposizioni, occorse all&#039;Autore le prime <lb></lb>nell&#039;esercitarsi intorno alla ricerca dei Massimi e dei minimi elementi: <lb></lb>“ Elementum maximum, pro dimensione rotundarum superficierum et so­<lb></lb>lidorum ” (MSS. Gal. </s>

<s>Disc., T. LXXXIII, fol. </s>

<s>112). </s></p><p type="main">

<s>Informe, e a gran fatica leggibile è il citato manoscritto: i fogli son <lb></lb>nella cucitura del volume slocati, e ne mancano alcuni, in cui dee avere il <lb></lb>Viviani lasciata scritta la dimostrazione del primo teorema controbrarico fon­<lb></lb>damentale, concernente le superfice descritte dalla rotazione delle semplici <lb></lb>linee. </s>

<s>Benchè nel metodo proseguito dal Nostro si ponesse così fatto teorema <lb></lb>per principale, come si è detto, gli dovea pure riuscir di assai facile dimo­<lb></lb>strazione, tanto più che bastava alla somma delle cose il considerar quelle <lb></lb>linee come rette, e in qualunque modo rivolte verso l&#039;asse. </s>

<s>Se perpendico­<lb></lb>lari, la figura descritta è un circolo o un nastro tondo, se parallele, è una <lb></lb>superfice cilindrica, ed è finalmente conica, se la retta revolubile è comun­<lb></lb>que inclinata. </s>

<s>Per tutti questi tre casi la trasformazion del rotondo geome­<lb></lb>trico nel retto centrobrarico è data immediatamente dagli Elementi, e se ne <lb></lb>sarà in poche parole spedito il Viviani come, richiamandosi agli antichi teo­<lb></lb>remi di Euclide e di Archimede, se n&#039;era già molto prima spedito il Nardi. </s></p><p type="main">

<s>Faceva a questa prima proposizione centrobrarica seguito l&#039;altra, la quale, <lb></lb>dal caso delle linee semplici passandosi alle linee composte, veniva dall&#039;Au­<lb></lb>tore stesso così formulata: “ Si in eodem plano, in quo axis rotationis re­<lb></lb>peritur, ad alteram axis partem fuerint quotvis rectae lineae terminatae, <lb></lb>utcumque positae, ac circa axem fiat rotatio plani, in quo assumptae rectae <lb></lb>insunt: erit aggregatum superficierum omnium, ab ipsis rectis in rotatione <lb></lb>descriptarum, aequale aggregato totidem rectangulorum, quorum bases sint <lb></lb>ipsae rectae datae, altitudines vero singulae sint aequales illi peripheriae, <lb></lb>quae a datarum rectarum communi cen­<lb></lb>tro gravitatis, in eadem rotatione, descri­<lb></lb>bitur ” (ibid.). </s></p><p type="main">

<s>Si abbiano a principio, per proceder <lb></lb>con più facile ordine, due sole linee CD, <lb></lb>PF (fig. </s>

<s>61), comunque poste rispetto al­<lb></lb>l&#039;asse AB, e, divise ambedue in mezzo nei <lb></lb>punti M, N, sia trovato in O il loro cen­<lb></lb>tro, con la nota legge degli Equiponde­<lb></lb>ranti, che dà ON stare ad OM, reciproca­<lb></lb>mente come CD sta a PF. Condotte, dai <lb></lb><figure id="id.020.01.1909.1.jpg" xlink:href="020/01/1909/1.jpg"></figure></s></p><p type="caption">

<s>Figura 61.<pb xlink:href="020/01/1910.jpg" pagenum="153"></pb>tre notati punti centrali, perpendicolari all&#039;asse le tre linee MR, OS,NT, e <lb></lb>da M e da N abbassate le MZ, NV sopra OS, “ iam, prosegue così propria­<lb></lb>mente il Viviani il suo ragionamento, cum ex hypothesi sit ut CD ad PF, <lb></lb>ita reciproce NO ad OM, vel, in similibus triangulis NOV, MOZ, ut VO ad OZ; <lb></lb>erit rectangulum sub PF, VO aequale rectangulo sub CD, ZO. ” </s></p><p type="main">

<s>“ Et quoniam rectangulum sub CD in OS aequale est rectangulis sub <lb></lb>CD in ZS vel in MR, et sub eadem CD in OZ, hoc est sub PF in ON, quod <lb></lb>ipsi sub CD in OZ aequale modo ostendimus; addito communi rectangulo <lb></lb>sub PF in OS, erunt duo simul rectangula sub CD in OS, et sub PF in OS <lb></lb>aequalia tribus simul rectangulis sub CD in MR, sub PF in OV, et sub <lb></lb>PF in OS. ” </s></p><p type="main">

<s>“ Sed hae duo postrema rectangula conficiunt unum tantum sub PF <lb></lb>in VS; ergo illa duo rectangula simul, sub CD in OS et sub PF in OS, <lb></lb>aequantur duobus simul sub CD in MR, et sub PF in VS, vel in NT. ” </s></p><p type="main">

<s>“ Sed ut sunt horum omnium rectangulorum latera OS, MR, NT, ita <lb></lb>sunt circulares peripheriae ab ipsis lateribus tanquam radiis in rotatione <lb></lb>descriptae; ergo et duo rectangula simul, hoc est sub CD in peripheriam a <lb></lb>radio SO, et sub PF in eamdem peripheriam, aequalia sunt duobus simul <lb></lb>rectangulis sub CD in peripheriam a radio RM, et sub PF in peripheriam <lb></lb>a radio TN. ” </s></p><p type="main">

<s>“ Sed rectangulum sub CD in peripheriam a radio RM aequale osten­<lb></lb>dimus (theor. </s>

<s>I) superficiei descriptae a recta CD in sua rotatione, et simi­<lb></lb>liter rectangulum sub PF in peripheriam a radio NT aequale esse superfi­<lb></lb>ciei descriptae in rotatione a recta PF; ergo eadem simul rectangula, nempe <lb></lb>sub CD et sub PF in totidem peripherias aequales ei quae puncto O primo <lb></lb>invento describitur, aequantur praedictis superficiebus, ab eisdem rectis CD, <lb></lb>PF in rotatione descriptis circa axem AB, quod memento ” (ibid., fol. </s>

<s>112, <lb></lb>et 115). </s></p><p type="main">

<s>Sian ora, così soggiunge il Viviani per la sua dimostrazione, oltre a CD <lb></lb>e a PF, altre simili linee, come GH, IL, comunque poste esse pure rispetto <lb></lb>all&#039;asse, purchè giacenti nel medesimo piano, e rispondenti dalla medesima <lb></lb>parte. </s>

<s>Divisa anche GH in mezzo, e congiunto questo punto con O, sia Q <lb></lb>il comun centro delle due grandezze CD, EF da una parte, e di GH dal­<lb></lb>l&#039;altra. </s>

<s>Costruite le parti come dianzi, si giungerà per una simile via a una <lb></lb>simile conclusione, a dimostrar cioè che l&#039;aggregato delle superfice, descritte <lb></lb>dalle dette tre linee nella loro simultanea rotazione, eguaglia altrettanti ret­<lb></lb>tangoli aventi ciascuno una di queste linee per base, e per altezza tutti la <lb></lb>medesima circonferenza descritta dal raggio, che dal punto Q vada, per la <lb></lb>via più breve, a ritrovar l&#039;asse. </s></p><p type="main">

<s>Divisa similmente IL nel mezzo, e congiunto questo punto con Q, sia <lb></lb>Y il centro di gravità, intorno a cui si equilibrano le tre grandezze da una <lb></lb>parte con questa quarta dall&#039;altra. </s>

<s>Sarà facile, con lo stesso processo, il di­<lb></lb>mostrare che le superfice descritte insieme dalle quattro dette linee sono <lb></lb>eguali ad altrettanti rettangoli, eretti su ciascuna di esse, a una altezza che, <pb xlink:href="020/01/1911.jpg" pagenum="154"></pb>per tutte, s&#039;agguagli alla circonferenza descritta da quel raggio, che va dal <lb></lb>punto Y a raggiunger l&#039;asse. </s></p><p type="main">

<s>Sien pure proposte quante altre linee si voglia, sarà sempre vera per <lb></lb>tutte quella conclusione, che per le quattro date è dal Viviani così formu­<lb></lb>lata: “ Aggregatum igitur superficierum a rectis CD, EF, GH, IL in rota­<lb></lb>tione factarum, quaecumque illae sint, vel armillares, vel cilindricae vel co­<lb></lb>nicae, aequale est aggregato totidem rectangulorum super easdem bases CD, <lb></lb>EF, GH, IL, et quorum singulae altitudines sint aequales peripheriae a com­<lb></lb>muni earumdem rectarum centro gravitatis Y in ipsa rotatione descriptae. </s>

<s><lb></lb>Quod erat demonstrandnm ” (ibid., fol. </s>

<s>113). </s></p><p type="main">

<s>Da questa seconda proposizione, applicandovi il metodo degl&#039;indivisibili, <lb></lb>fa, quasi da corollario, scendere il Viviani la terza: “ Rotundum solidum, <lb></lb>a quacumque figura plana circa axem rotante genitum, aequale est cylin­<lb></lb>drico, cuius basis sit ipsa plana figura, altitudo vero aequalis sit peripheriae <lb></lb>ab illius gravitatis centro descriptae ” (ibid., fol. </s>

<s>114). </s></p><p type="main">

<s>Sia ABC (fig. </s>

<s>62) quella qualunque figura piana revolubile intorno al­<lb></lb>l&#039;asse EF, e s&#039;immagini che siano sopr&#039;essa disegnate, a piacer nostro, e <lb></lb><figure id="id.020.01.1911.1.jpg" xlink:href="020/01/1911/1.jpg"></figure></s></p><p type="caption">

<s>Figura 62.<lb></lb>quali tutte insieme concentrate in D, innume­<lb></lb>revoli grandezze lineari, parallele, È chiaro che <lb></lb>verrà dal loro aggregato nella rotazione descritto <lb></lb>l&#039;aggregato di altrettante superfice, le quali <lb></lb>riusciranno o cilindriche o coniche, secondo la <lb></lb>direzione scelta e data da noi a quelle stesse <lb></lb>linee, che l&#039;hanno generata. </s>

<s>“ Sed aggregatum <lb></lb>omnium simul figurarum aequidistantium ab <lb></lb>his omnibus rectis, in rotatione descriptum, <lb></lb>aequalem esse demonstravimus aggregato totidem rectangulorum, quorum <lb></lb>bases sint ipsae rectae, altitudines vero singulae sint aequales peripheriae <lb></lb>a centro D descriptae; et primum aggregatum rotundum solidum constituit, <lb></lb>secundum vero cylindricum facit super basi ABC in altitudine circumfe­<lb></lb>rentiae a puncto D; ergo ipsum solidum solido ipsi cylindrico aequale est, <lb></lb>quod erat demonstrandum ” (ibid.). </s></p><p type="main">

<s>Altre proposizioni centrobrariche si trovano qua e là dal Viviani dimo­<lb></lb>strate ne&#039;suoi manoscritti, come nel tomo XCV della collezione citata, nei <lb></lb>primi fogli del quale la dimostrazione della Regola guldiniana conducesi in <lb></lb>altro modo da quello ora esposto, e vi si trova notato il corollario, dall&#039;al­<lb></lb>tra parte a concludersi facilissimo, che se cioè le superfice MN, RS (nella <lb></lb>passata figura LX) son proporzionali alle distanze AB, DC “ rotundae ma­<lb></lb>gnitudines, quae ab ipsis fient, erunt inter se ut quadrata distantiarum ea­<lb></lb>rum ” (fol. </s>

<s>3 t.). </s></p><p type="main">

<s>Di tutte queste proposizioni poi messe in ordine compose il Viviani un <lb></lb>trattatello di Centrobrarica, ch&#039;egli intendeva di preparar per le stampe. </s>

<s>Sa­<lb></lb>rebbe quel trattatello, per esser venuto il primo a sottoporre all&#039;edifizio gul­<lb></lb>diniano il suo matematico fondamento, riuscito utilissimo all&#039;universale, e <pb xlink:href="020/01/1912.jpg" pagenum="155"></pb>di particolar gloria per la scienza italiana. </s>

<s>Ma meditando l&#039;Autore cose forse <lb></lb>maggiori, erasi oramai condotto all&#039;estrema vecchiezza, senza dar nè di que­<lb></lb>ste nè di quelle alcuna pubblica sodisfazione, quando un Cardinale, che aveva <lb></lb>a sue proprie spese fatta erigere una nuova Tipografia, gli mostrò il desi­<lb></lb>derio di stampar qualche cosa delle tante scritture di lui sconosciute. </s>

<s>Per <lb></lb>rispondere al quale invito prese un giorno il Viviani la penna in mano, con <lb></lb>l&#039;intenzione di far recapitare all&#039;Eminentissimo innominato questa lettera <lb></lb>scritta: </s></p><p type="main">

<s>“ Son già molti anni che io mi trovo distese tre mie antiche operette <lb></lb>di Geometria, l&#039;una intitolata <emph type="italics"></emph>De tetragonismicis,<emph.end type="italics"></emph.end> l&#039;altra <emph type="italics"></emph>De centrobraricis,<emph.end type="italics"></emph.end><lb></lb>divisa ciascuna in due libri, e la terza <emph type="italics"></emph>De terebratione solidorum,<emph.end type="italics"></emph.end> e di tutte <lb></lb>è già gran tempo che sono intagliate le figure in bossolo già ben fatte. </s>

<s>E <lb></lb>perchè in questa età mia cadente di LXXIV anni e in continuo moto per <lb></lb>le campagne, in servizio di questa serenissima Altezza, quand&#039;io non mi <lb></lb>trovi in letto malato, io dispero oramai di poter perfezionare molte altre di <lb></lb>quelle, che sono abbozzate, e perciò io desidero di veder fuori almeno que­<lb></lb>ste tre insieme, ma specialmente sotto il benigno patrocinio dell&#039;Eminenza <lb></lb>V. R.ma, mentre però si compiacesse di farmi degna di tanto onore. </s>

<s>Queste <lb></lb>dunque farei prontamente copiare assai ben corrette, e quando me ne desse <lb></lb>la permissione, le invierei una per volta, insieme con le figure, affinchè <lb></lb>V. Emin. </s>

<s>si contentasse ancora di far qualche pregio a tali opere con i no­<lb></lb>bilissimi caratteri della sua nuova Stamperia ” (MSS. cit., T. CI, fol. </s>

<s>124). </s></p><p type="main">

<s>È scritta in fronte a questa bozza, pure autografa, la nota: <emph type="italics"></emph>Questa let­<lb></lb>tera non la mandai e non....<emph.end type="italics"></emph.end> cosicchè il trattatello centrobrarico del Vi­<lb></lb>viani riman tuttavia un desiderio di tutti coloro, che avrebbero voluto ve­<lb></lb>der qualche pubblico documento dell&#039;importantissima opera data, prima degli <lb></lb>stranieri, dai Matematici nostri intorno alle ammirate novità del Guldino. </s></p><pb xlink:href="020/01/1913.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Degli Equiponderanti<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della legge delle equiponderanze dimostrata col principio delle velocità virtuali. </s>

<s>— II. </s>

<s>Della legge <lb></lb>delle equiponderanze dimostrata coi principii archimedei. </s>

<s>— III. </s>

<s>Della teoria de&#039;momenti ap­<lb></lb>plicata a dimostrar la legge degli equiponderanti. </s>

<s>— IV. </s>

<s>Delle Bilancie di braccia eguali e delle <lb></lb>condizioni del loro equilibrio, nel caso delle forze o parallele o convergenti al centro terrestre. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nella scienza de&#039;centri di gravità fu detto, e si conferma dalla storia <lb></lb>del capitolo precedente, che si compendia tutta intera la scienza meccanica, <lb></lb>ond&#039;è che di questa è riconosciuto solenne maestro al mondo Archimede. </s>

<s><lb></lb>Come nel trattato del nostro Siracusano s&#039;applicassero i baricentrici, a di­<lb></lb>mostrar la legge dell&#039;equilibrio fra&#039;pesi, s&#039;è già scritto da noi nell&#039;intro­<lb></lb>durre il discorso intorno alla presente parte storica, e fu mostrato allora <lb></lb>quanto, per i matematici specialmente italiani del secolo XVI, venissero l&#039;ar­<lb></lb>chimedee dottrine ad essere largamente promosse. </s>

<s>S&#039;accennò anco insieme <lb></lb>ad un&#039;altra fonte più antica, dalla quale si derivò in quel secolo non men <lb></lb>larga vena di scienza, e come, in mezzo agli aperti dissidii, si sapessero con­<lb></lb>giungere insieme, in tacito e più fecondo connubio, gl&#039;insegnamenti del <lb></lb>Matematico di Siracusa con quelli del Filosofo di Stagira. </s></p><p type="main">

<s>Di queste attrazioni, diciam così, e di queste repulsioni, dalle quali par <lb></lb>che resulti la vita dell&#039;intelletto, com&#039;è certo che resulta la vita della ma­<lb></lb>teria, ci offre in proposito un notabilissimo esempio quel Leonardo da Vinci, <lb></lb>i manoscritti del quale, che unici per avventura ci son rimasti, specchiano <lb></lb>la mente dell&#039;Autore e quella tutto insieme de&#039;Matematici de&#039;suoi tempi. <pb xlink:href="020/01/1914.jpg" pagenum="157"></pb>Si ripeteva da questi il principio statico del Nemorario, riducendolo a dire <lb></lb>che il peso, applicato all&#039;estremità di un raggio più lungo, ha maggior mo­<lb></lb>mento, perchè il maggior circolo volge più da presso al retto discenso; prin­<lb></lb>cipio non voluto approvare da Leonardo per concludente, perché, attaccato <lb></lb>il peso a un filo avvolto all&#039;estremità del raggio per l&#039;altro capo, benchè <lb></lb>non faccia il suo viaggio circolare ma retto, pur si vede scendere allo stesso <lb></lb>modo, e vincere un egual peso, che stia similmente pendulo dal raggio più <lb></lb>corto. </s>

<s>“ Dice il Pelacane che il maggior braccio di questa bilancia (appel­<lb></lb>lando alla figura disegnata in margine del foglio) cadrà più presto che il <lb></lb>minore, perchè il suo descenso descrive il suo quarto circolo più diritto che <lb></lb>non fa il minore, e perchè i pesi desiderano cadere perpendicolare linea. </s>

<s><lb></lb>Quanto esso circolo più si torcerà, più si ritarderà il moto. </s>

<s>La figura getta <lb></lb>per terra questa ragione perchè il discenso de&#039;suoi pesi non vanno per cir­<lb></lb>colo; eppure cala il peso del maggiore braccio ” (Ravaisson-Mollien, Manus. </s>

<s><lb></lb>N.0 2038 italien de la Bibliot. </s>

<s>nationale, Paris 1891, fol. </s>

<s>2 t.). </s></p><p type="main">

<s>L&#039;obiezione a dir vero avrebbe trovata una assai facile risposta nel Pe­<lb></lb>lacane, e in tutti gli altri, che avevano imparato dal Nemorario a misurare <lb></lb>la quantità della discesa, no nell&#039;obliqua o circolare o retta, ma nella per­<lb></lb>pendicolare, alla quale dovevasi, per gl&#039;insegnamento dello stesso Giordano, <lb></lb>ridurre una tal discesa, o fosse il grave affisso al raggio o libero vi pen­<lb></lb>desse da un filo. </s>

<s>Ma fu in ogni modo la proposta difficoltà giudicata da Leo­<lb></lb>nardo di tanta forza, da farlo andare in cerca di un altro principio, da cui <lb></lb>concluder la legge statica fondamentale tanto desiderata. </s>

<s>Di questo principio <lb></lb>dall&#039;altra parte non si sarebbe potuto negar la verità da nessuno, che non <lb></lb>patisse difetto o di ragione o di esperienza, consistendo insomma nell&#039;affer­<lb></lb>mar che un peso tanto è men sostenuto, quanto è più lontano dal suo so­<lb></lb>stegno. </s>

<s>Era da ciò facile concluder la ragione perchè il peso stesso quanto <lb></lb>è applicato al braccio della Bilancia più lungo, altrettanto abbia a moversi <lb></lb>più veloce. </s>

<s>“ Quella cosa che fia più lontana al suo firmamento, manco da <lb></lb>esso fia sostenuta. </s>

<s>Essendo manco sostenuta, più fia partecipevole di sua li­<lb></lb>bertà. </s>

<s>E perchè il peso libero sempre discende, adunque quella estremità <lb></lb>dell&#039;asta d&#039;essa Bilancia, che fia più distante al suo firmamento, perchè è <lb></lb>ponderosa, più presto che alcuna parte di sè discenderà ” (ivi). </s></p><p type="main">

<s>La teoria vinciana prende dunque il principio da Archimede, dalle dot­<lb></lb>trine di cui si deduce che un peso è tanto men sostenuto, quanto il suo <lb></lb>centro di gravità è più distante dal suo sostegno, ma nel passar poi a con­<lb></lb>cluderne la legge della equiponderanza bisognava dire che due gravi si fa­<lb></lb>rebbero allora insieme equilibrio, quando l&#039;uno e l&#039;altro fossero disposti a <lb></lb>scendere nel medesimo tempo. </s>

<s>Così venivano da varie parti a riscontrarsi <lb></lb>Archimede e Aristotile; il principio baricentrico e quello delle velocità vir­<lb></lb>tuali, celebrandosi fra le due scuole discordi quel clandestino connubio, il <lb></lb>portato del quale ebbe, sul cominciar del secolo XVII, ostetrici che lo espo­<lb></lb>sero al mondo maravigliato. </s></p><p type="main">

<s>Che tali, cioè ostetrici della scienza statica e non veri genitori, si fos-<pb xlink:href="020/01/1915.jpg" pagenum="158"></pb>sero lo Stevino, il Galileo e il Cartesio manifesto apparisce dalla storia del <lb></lb>capitolo I di questo tomo, ond&#039;è che, lasciando oramai di tornare indietro <lb></lb>sopra la legittimità della origine, ci tratterremo ad esaminare il parto, ri­<lb></lb>volgendoci prima di tutto colà, dove nelle sue pagine celebrate ci fu espo­<lb></lb>sto da Galileo. </s></p><p type="main">

<s>Il libro, in cui il principio statico professato da Galileo fece, non la <lb></lb>prima, ma la più solenne sua pubblica mostra fu quello dei Massimi sistemi, <lb></lb>dove disputandosi nella Giornata seconda intorno alle resistenze, che oppon­<lb></lb>gono i gravi all&#039;essere sollevati, si conclude per l&#039;esempio della Stadera do­<lb></lb>vere ivi i pesi resister con forza diversa da quella della semplice gravità. </s>

<s><lb></lb>Or da che altro mai può scaturire questa forza ristoratrice, se non dal moto, <lb></lb>cosicchè “ la velocità del mobile meno grave compensi la gravità del mo­<lb></lb>bile più grave e meno veloce? </s>

<s>” (Alb. </s>

<s>I, 237). </s></p><p type="main">

<s>S&#039;immagini infatti di avere a pesare una balla di lana o di seta: “ il <lb></lb>moversi lo spazio di cento dita il romano, nel tempo che la balla si muove <lb></lb>per un sol dito, è l&#039;istesso che il dire esser la velocità del moto del romano <lb></lb>cento volte maggiore della velocità del moto della balla. </s>

<s>Ora, prosegue a <lb></lb>dire il Salviati galileiano, fermatevi bene nella fantasia come principio vero <lb></lb>e notorio che la resistenza, che viene dalla velocità del moto, compensa <lb></lb>quello che dipende dalla gravità di un altro mobile, sicchè in conseguenza <lb></lb>tanto resiste all&#039;esser frenato un mobile d&#039;una libbra, che si muova con <lb></lb>cento gradi di velocità, quanto un altro mobile di cento libbre, la cui velo­<lb></lb>cità sia d&#039;un grado solo ” (ivi). </s></p><p type="main">

<s>Le resistenze dunque non sono in semplice ragion de&#039;pesi, ma in ra­<lb></lb>gion composta delle velocità e de&#039;pesi, ond&#039;è che, nel caso degli equipon­<lb></lb>deranti, essendo quelle resistenze eguali, dovranno le velocità stare in reci­<lb></lb>proca proporzione degli stessi pesi. </s>

<s>È qui dunque formulato da Galileo quel <lb></lb>principio statico, che si disse <emph type="italics"></emph>delle velocità virtuali,<emph.end type="italics"></emph.end> di che trattando il La­<lb></lb>grange, nell&#039;introduzione alla sua celebre <emph type="italics"></emph>Mecanique analitique,<emph.end type="italics"></emph.end> scriveva: <lb></lb>“ il ne paroit pas que les Geometres, qui ont précèd<gap></gap> Galilèe, en aient eu <lb></lb>connoissance, et je crois pourvoit en attribuer la dècouverte a cet Auteur ” <lb></lb>(Paris 1788, pag. </s>

<s>8). </s></p><p type="main">

<s>Pare incredibile che uno Scrittore tanto grave possa aver sentenziato <lb></lb>essere il detto principio statico rimasto ignoto ai precursori di Galileo, quando <lb></lb>Galileo stesso lo dichiara come cosa <emph type="italics"></emph>notissima e dimostrata da Aristotile <lb></lb>nelle sue Questioni meccaniche<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 265). Chi poi rammemora le <lb></lb>cose, da noi scritte nel cap. </s>

<s>I di questo tomo, sa come di fatto il principio <lb></lb>delle velocità virtuali, appresso ai matematici de&#039;secoli anteriori al XVII, <lb></lb>fosse veramente notissimo e dimostrato. </s></p><p type="main">

<s>In ogni modo, professandosi tale dottrina in quel libro galileiano tanto <lb></lb>famoso, veniva, come face, a risplendere sul moggio e a farsi perciò più <lb></lb>scoperto segno agli applausi e alle contradizioni. </s>

<s>Il Cartesio, fra tanti con­<lb></lb>tradittori il più valido e il più infervorato di tutti, non sapendo trovar ra­<lb></lb>gione di accusar come assolutamente falso il principio professato da Galileo, <pb xlink:href="020/01/1916.jpg" pagenum="159"></pb>lo accusava come difettoso ed incerto, proponendone un altro che riusciva, <lb></lb>secondo lui, nella generale applicazione alle condizioni dell&#039;equilibrio in tutte <lb></lb>le macchine, più semplice e più sicuro. </s>

<s>Consisteva in sostanza il principio <lb></lb>cartesiano nel sostituire gli spazii alle velocità, rappresentandosi sotto que­<lb></lb>sta forma assai seducente, che cioè tanta forza ci vuole a sollevare un peso <lb></lb>di cento libbre all&#039;altezza di due piedi, quanto a sollevare un peso di du­<lb></lb>gento libbre all&#039;altezza di un piede solo. </s>

<s>A così fatta legge volle poi dimo­<lb></lb>strar l&#039;Autore che s&#039;informavano tutte le macchine, nello spiegar le quali, <lb></lb>in quel trattatello <emph type="italics"></emph>De mechanica<emph.end type="italics"></emph.end> pubblicato postumo, incominciava con que­<lb></lb>ste parole: “ Machinarum harum omnium inventio unico tantum principio <lb></lb>innititur, quod nimirum iisdem viribus quibus pondus v. </s>

<s>g. </s>

<s>100 librarum <lb></lb>in duorum pedum altitudinem attolli potest, iisdem inquam aliud quoque <lb></lb>200 librarum in unius pedis altitudinem possit elevari ” (Amstelodami 1704, <lb></lb>pag. </s>

<s>13). </s></p><p type="main">

<s>Essendo il moto delle macchine uniforme, e sempre nei moti uniformi <lb></lb>rispondendo in egual tempo le velocità agli spazii, il principio del Cartesio <lb></lb>non differiva adunque dal galileiano che per una semplice accidentalità della <lb></lb>forma, e noi vedemmo come fosse una tale trasformazione fatta già, nella <lb></lb>Meccanica aristotelica, dal Nemorario. </s>

<s>Nonostante, per quella smania che <lb></lb>aveva il Filosofo francese di soverchiare il nostro Italiano, si studiava di <lb></lb>persuadere agli amici che, col mettere in conto le velocità piuttosto che gli <lb></lb>spazii, mentre si veniva da una parte a rendere più difficile la Scienza mec­<lb></lb>canica, le si poneva dall&#039;altra per fondamento un principio o non affatto <lb></lb>vero o dubbioso. </s></p><p type="main">

<s>Quanto alle difficoltà si compiaceva, in una Epistola al Mersenno, di <lb></lb>averle cessate in gran parte, mettendo in considerazione due sole, invece di <lb></lb>tre dimensioni, e faceva in ciò principalmente consistere la fina arte usata <lb></lb>in distendere il suo statico trattatello. </s>

<s>“ Quod si celeritatis considerationem <lb></lb>cum spatii consideratione iungere voluissem, habuissem necesse tres dimen­<lb></lb>siones virtuti isti tribuere: ut vero illam excluderem duas tantum illi tri­<lb></lb>bui. </s>

<s>Et si quid artis in ulla exigui huius <emph type="italics"></emph>De statica<emph.end type="italics"></emph.end> scripti parte ostendi, <lb></lb>velim sciant me nusquam plus quam in hoc ostendisse ” (Epistolae Pars I, <lb></lb>Francof. </s>

<s>ad Moenum 1692, pag. </s>

<s>229). </s></p><p type="main">

<s>Il principio statico di Galileo, poi soggiunge il Cartesio stesso in un&#039;al­<lb></lb>tra sua lettera al Mersenno, non solo viene a rendere la Statica più com­<lb></lb>plicata, ma che è peggio sta fondato sul falso: falso essendo che a raddop­<lb></lb>piare una data velocità si richieda sempre una forza precisamente doppia. <lb></lb></s>

<s>“ Quantum vero ad id quod Galileus de Bilance et Vecte scripsit, optime <lb></lb>quidem explicat quod ita sit, sed non cur ita sit, sicut per principium meum <lb></lb>explico. </s>

<s>Qui vero dicunt debuisse me cum Galileo celeritatem considerare, <lb></lb>non vero spatium, ut machinarum rationem redderem, inter nos puto eos <lb></lb>id temere dicere, nec quicquam in hac materia intelligere. </s>

<s>Et quamvis cla­<lb></lb>rissimum sit opus esse maiore vi ad corpus aliquod celerrime, quam lente <lb></lb>attollendum, nihilominus falsum est vim debere exacte duplam ad duplican-<pb xlink:href="020/01/1917.jpg" pagenum="160"></pb>dam celeritatem, et facillimum est contrarium probare ” (Epistolae Pars II, <lb></lb>ibid., pag. </s>

<s>255) </s></p><p type="main">

<s>Tace qui il Cartesio la facile prova, ma in un&#039;altra epistola, indirizzata <lb></lb>essa pure al Mersenno, dice che può dedursi dal fatto della Bilancia in equi­<lb></lb>librio, sul piattello della quale chi getta una piccola moneta vede moversi <lb></lb>il braccio in basso assai lentamente, ma a gettarvi una moneta doppia si <lb></lb>osserva farsi allora la declinazione più che doppiamente sollecita. </s>

<s>“ Si bi­<lb></lb>lanci in aequilibrio constitutue imposueris nummum aliquod, quod illi mo­<lb></lb>mentum dare possit, tum enim admodum lente deprimetur, cum contra si <lb></lb>eiusdem istius ponderis duplum imposueris, decidet plus quam duplo citius ” <lb></lb>(ibid., pag. </s>

<s>320). </s></p><p type="main">

<s>Le varie proporzioni di moto nella Bilancia si concludevan dunque per <lb></lb>il Cartesio da un semplice fatto sperimentale, ond&#039;è che venivasi male a <lb></lb>proposito invocando la Fisica a decidere una questione di Matematica pura. </s>

<s><lb></lb>Era una tal questione risoluta già da Galileo, quand&#039;egli dimostrò “ che il <lb></lb>cadente, partendosi dalla quiete passa per tutti gl&#039;infiniti gradi di tardità ” <lb></lb>(Alb. </s>

<s>I, 34). La teoria così formulata doveva esser quella che venisse a in­<lb></lb>formare il fatto sperimentale invocato dal Cartesio, correggendo i facili in­<lb></lb>ganni che, rispetto ai moti della Bilancla, si poteva far l&#039;occhio, ma ripu­<lb></lb>diando una certezza matematica per attenersi a una fisica fallacia, s&#039;ostinò <lb></lb>il Cartesio stesso a negar quel che delle velocità iniziali aveva sapientemente <lb></lb>concluso Galiteo. </s>

<s>“ Sciendum enim est, quidquid in contrarium dicant Ga­<lb></lb>lileus et alii nonnulli, corpora quae descendere, vel quocumque modo mo­<lb></lb>veri incipiunt, non transire per omnes tarditatis gradus, sed a primo instanti <lb></lb>aliquantam velocitatem obtinere, quae postea multum augetur ” (Epistol., <lb></lb>P. II cit., pag. </s>

<s>115). </s></p><p type="main">

<s>Il Mersenno, a cui si dirigevano queste parole, domandava la prova di <lb></lb>così fatta sentenza, ma perchè il Cartesio non l&#039;aveva pronta, e conosceva <lb></lb>forse che non sarebbe riuscito mai a trovarla, si scusava rispondendo non <lb></lb>aver inteso di negare assolutamente che il mobile passi per tutti gl&#039;infiniti <lb></lb>gradi di tardità ” sed vero dixi non posse id, nisi praecognita gravitatis na­<lb></lb>tura, determinari ” (ibid., pag. </s>

<s>122). Non si capiva però come mai non si <lb></lb>potesse determinare il moto iniziale di un grave, senza preconoscere la na­<lb></lb><figure id="id.020.01.1917.1.jpg" xlink:href="020/01/1917/1.jpg"></figure></s></p><p type="caption">

<s>Figura 63.<lb></lb>tura della gravità, ond&#039;è perciò che il Mersenno citava la <lb></lb>dimostrazione di Galileo, la quale concludevasi, senz&#039;altre <lb></lb>prenozioni, dai principii certissimi della Geometria. </s>

<s>Così in <lb></lb>fatti, rappresentandosi con i lati di un triangolo gli ele­<lb></lb>menti del moto, procede nella Giornata II dei Due massimi <lb></lb>sistemi quella galileiana dimostrazione: “ Essendo posto il <lb></lb>termine A (fig. </s>

<s>63) come momento minimo di velocità, <lb></lb>cioè come stato di quiete, e come primo instante del tempo <lb></lb>susseguente AD, ě manifesto che, avanti l&#039;acquisto del <lb></lb>grado di velocità DH fatto nel tempo AD, si è passato <lb></lb>per altri infiniti gradi minori e minori guadagnati negli <pb xlink:href="020/01/1918.jpg" pagenum="161"></pb>infiniti instanti, che sono nel tempo DA, corrispondenti agli infiniti punti, <lb></lb>che sono nella linea DA. </s>

<s>Però per rappresentare la infinità dei gradi di <lb></lb>velocità, che precedono al grado DH, bisogna intendere infinite linee sempre <lb></lb>minori e minori, che s&#039;intendano tirate dagli infiniti punti della linea DA <lb></lb>parallele alla DH, la quale infinità di linee ci rappresenta in ultimo la su­<lb></lb>perfice del triangolo AHD. </s>

<s>E così intenderemo qualsivoglia spazio passato <lb></lb>dal mobile con moto che, cominciando dalla quiete, si vadia uniformemente <lb></lb>accelerando, aver consumato ed essersi servito di infiniti gradi di velocità <lb></lb>crescenti conforme alle infinite linee che, cominciando dal punto A, s&#039;in­<lb></lb>tendono tirate parallele alla linea HD ” (Alb. </s>

<s>I, 252). Il Cartesio, che anche <lb></lb>la Matematica voleva soggiacesse alle finzioni del suo cervello, così rispon­<lb></lb>deva al Mersenno per infirmare la conclusione di Galileo: “ Non possum <lb></lb>definire qua velocitate unumquodque grave descendere incipiat: quaestio <lb></lb>enim est tantum de facto, quae pendet ex celeritate materiae subtilis. </s>

<s>Haec <lb></lb>autem celeritas in initio tantumdem aufert de proportione celeritatis qua <lb></lb>corpora descendunt, quantum exiguum triangulum AHD de triangulo ABC, <lb></lb>si supponatur linea HD repraesentare primum velocitatis momentum et BC <lb></lb>ultimum ” (Epistol., P. II cit, pag. </s>

<s>127). </s></p><p type="main">

<s>Ma intanto che l&#039;invidioso rivale si schermiva così d&#039;ogni parte, per <lb></lb>riparare ed eludere i colpi dell&#039;avversario, non si avvedeva che alcuni altri <lb></lb>attendevano tacitamente ad aguzzare un&#039;arme, da cui riceverebbero, senza <lb></lb>presente rimedio, eguale offesa i due combattenti. </s>

<s>Sia infatti che s&#039;equi­<lb></lb>ponderino due gravi quando sono reciprocamente proporzionali alle velocità <lb></lb>o agli spazii, di un effetto in atto s&#039;adduceva, così da Galileo come dal Car­<lb></lb>tesio, una cagione in potenza. </s>

<s>Non era questa volta un rivale, che faceva <lb></lb>l&#039;obiezione contro le professate dottrine dell&#039;avversario, ma era un disce­<lb></lb>polo affezionato che, persuaso di difendere il vero, contradiceva al suo pro­<lb></lb>prio maestro. </s>

<s>Antonio Nardi, dop&#039;avere in una delle sue scene dimostrate <lb></lb>alcune verità generali appartenenti alla Statica, così soggiungeva: <lb></lb><figure id="id.020.01.1918.1.jpg" xlink:href="020/01/1918/1.jpg"></figure></s></p><p type="caption">

<s>Figura 64.</s></p><p type="main">

<s>“ Si raccorrà che male si persuadono i Mecca­<lb></lb>nici comunemente compensarsi, in una Bilancia di <lb></lb>disuguali braccia, le velocità del moto con la gran­<lb></lb>dezza del momento, onde cercano di render ragione <lb></lb>perchè questi pesi disuguali da distanze reciproca­<lb></lb>mente disuguali pesino ugualmente. </s>

<s>Ma ciò non è <lb></lb>in vero cagione dell&#039;equilibrio, perchè così discor­<lb></lb>rendo s&#039;adduce di un effetto in atto una cagione in <lb></lb>potenza. </s>

<s>Il Galilei nel libro Delle galleggianti dice <lb></lb>così: <emph type="italics"></emph>Sia al vaso larghissimo EIDF<emph.end type="italics"></emph.end> (fig. </s>

<s>64) <emph type="italics"></emph>con­<lb></lb>tinuata l&#039;angustissima canna ICAB, ed intendasi <lb></lb>in essi infusa l&#039;acqua sino al livello LGH, la quale <lb></lb>in questo stato si quieterà, non senza maraviglia di <lb></lb>alcuno, che non capirà così subito come esser possa<emph.end type="italics"></emph.end><pb xlink:href="020/01/1919.jpg" pagenum="162"></pb><emph type="italics"></emph>che il grave carico della gran mole d&#039;acqua GD, premendo abbasso, non <lb></lb>sollevi e scacci la piccola quantità dell&#039;altra contenuta dentro alla canna CL, <lb></lb>dalla quale gli vien contesa e impedita la scesa. </s>

<s>Ma tal maraviglia ces­<lb></lb>serà, se noi cominceremo a fingere l&#039;acqua GD essersi abbassata solamente <lb></lb>sino a Q, e considereremo poi ciò che averà fatto l&#039;acqua CL, la quale <lb></lb>per dare luogo all&#039;altra, che si è scemata dal livello GH sino al livello Q, <lb></lb>doverà per necessità essersi nell&#039;istesso tempo alzata dal livello L sino <lb></lb>in AB, e essser la salita LB tanto maggiore della scesa GQ, quant&#039;è <lb></lb>l&#039;ampiezza del vaso GD maggiore della larghezza della canna LC, che <lb></lb>insomma è quanto l&#039;acqua GD è più della LC. </s>

<s>Ma essendo che il mo­<lb></lb>mento della velocità del moto in un mobile compensa quello della gravità <lb></lb>di un altro, qual maraviglia sarà se la velocissima salita della poca <lb></lb>acqua CL resisterà alla tardissima scesa della molta GD?<emph.end type="italics"></emph.end> Sino a qui il <lb></lb>mio Maestro ” (MSS. Gal. </s>

<s>Dis., T. XX, pag. </s>

<s>861, 62). </s></p><p type="main">

<s>Avendo fin qui il Nardi repudiato il principio delle velocità virtuali, se­<lb></lb>guita nel suo discorso ad assegnar dell&#039;equilibrio idrostatico una causa di­<lb></lb>versa, come ad una causa diversa attribuiva l&#039;equiponderanza dei pesi nella <lb></lb>Stadera. </s>

<s>Abbiamo inteso già qual si fosse di questo repudio il motivo, ma <lb></lb>ora ci rimane ad esaminar se egli fosse ragionevole e giusto. </s></p><p type="main">

<s>L&#039;obiezione non era punto nuova, come nuova non era la dottrina, e <lb></lb>perciò il Nemorario, a cui primo fu fatta, rispondeva argutamente col dire <lb></lb>ch&#039;essendo la quiete il termine del moto si potevano attribuire a quella le <lb></lb>passioni di questo. </s>

<s>Si noti come Leonardo da Vinci esplicasse questo con­<lb></lb>cetto, affermando che la pietra che cade fu prima portata in alto, e perchè <lb></lb>accennavasi infin d&#039;allora che i pensieri medesimi di Giordano e di Leo­<lb></lb>nardo si riscontravano in Galileo, vediamo come la scienza antica avesse <lb></lb>dalla nuova il suo più chiaro commento. </s></p><p type="main">

<s>Svolgiamo le pagine, nelle quali è scritta la III Giornata, per soffermar <lb></lb>l&#039;attenzione colà dove il Sagredo considera che la virtù impressa al proietto, <lb></lb>contrastando continuamente con la gravità, quando questa riman vincitrice <lb></lb>su quella intercede la quiete, che è il termine dell&#039;ascesa e il principio della <lb></lb>discesa, e vuol da questo dedurne la causa dell&#039;accelerazione del moto. </s>

<s>Op­<lb></lb>pone Simplicio che l&#039;arguto pensiero non è concludente e non sodisfa, se <lb></lb>non a que&#039;moti naturali che son preceduti da un moto violento, per cui il <lb></lb>Sagredo medesimo domanda se può nel proietto imprimersi una virtù che <lb></lb>sia molta o sia poca, sicchè possa essere scagliato in alto cento braccia, ed <lb></lb>anche venti o quattro o uno: ciò che avendo Simplicio affermato gli vien <lb></lb>su quel fondamento fatta una tale risposta: </s></p><p type="main">

<s>“ E non meno potrà cotal virtù impressa di così poco superar la re­<lb></lb>sistenza della gravità, che non l&#039;alzi più di un dito, e finalmente può la <lb></lb>virtù del proiciente esser solamente tanta che pareggi per l&#039;appunto la re­<lb></lb>sistenza della gravità, sicchè il mobile sia non cacciato in alto, ma solamente <lb></lb>sostenuto. </s>

<s>Quando dunque voi reggete in mano una pietra che altro fate <lb></lb>voi che l&#039;imprimerli tanta virtù impellente all&#039;insù quanta è la facoltà della <pb xlink:href="020/01/1920.jpg" pagenum="163"></pb>sua gravità traente in giù? </s>

<s>E questa vostra virtù non continuate voi di con­<lb></lb>servargliela impressa, per tutto il tempo che voi la sostenete in mano? </s>

<s>Si <lb></lb>diminuisce ella forse per la lunga dimora, che voi la reggete? </s>

<s>E questo <lb></lb>sostentamento, che vieta la scesa al sasso, che importa che sia fatto più dalla <lb></lb>vostra mano che da una tavola, o da una corda, dalla quale ei sia sospeso? </s>

<s><lb></lb>Certo niente. </s>

<s>Concludete pertanto, signor Simplicio, che il precedere alla ca­<lb></lb>duta del sasso una quiete lunga o breve o momentanea non fa differenza <lb></lb>alcuna, sicchè il sasso non parta sempre affetto da tanta virtù contraria alla <lb></lb>sua gravità, quanto appunto bastava a tenerlo in quiete ” (Alb. </s>

<s>XIII, 160). </s></p><p type="main">

<s>Aveva Galileo applicato alla Statica questi suoi principii là dove, nel <lb></lb>trattato della Scienza meccanica, volle confermare le conclusioni archimedee <lb></lb>concernenti l&#039;equilibrio della leva con l&#039;invocare il principio delle velocità <lb></lb>virtuali. </s>

<s>“ Avendo noi mostrato, egli ivi dice, come i momenti di pesi dise­<lb></lb>guali vengono pareggiati dall&#039;essere contrariamente in distanze che abbiano <lb></lb>la medesima proporzione di essi, non mi pare da doversi passar con silen­<lb></lb>zio un&#039;altra congruenza di probabilità, dalla quale può essere ragionevolmente <lb></lb>confermata la medesima verità. </s>

<s>Perciocchè considerisi la libbra DE (fig. </s>

<s>65) <lb></lb>divisa in parti diseguali nel punto A, e i pesi della medesima proporzione <lb></lb>che hanno le distanze AD, AE, alternamente sospesi dai punti D, E. È già <lb></lb><figure id="id.020.01.1920.1.jpg" xlink:href="020/01/1920/1.jpg"></figure></s></p><p type="caption">

<s>Figura 65.<lb></lb>manifesto come l&#039;uno contrappo­<lb></lb>serà l&#039;altro e, conseguentemente, <lb></lb>come, se a uno di essi fosse ag­<lb></lb>giunto un minimo momento di <lb></lb>gravità, si moverebbe al basso inal­<lb></lb>zando l&#039;altro. </s>

<s>Sicchè aggiunto in­<lb></lb>sensibil peso al grave P si moverà <lb></lb>la Libbra, discendendo dal punto D <lb></lb>verso M, e ascendendo l&#039;altra estre­<lb></lb>mità E in F. </s>

<s>E perchè, per fare abbassare il P, ogni minima gravità accre­<lb></lb>sciutali è bastante, però, non tenendo noi conto di questo insensibile, non <lb></lb>faremo differenza dal potere un peso sostenere un altro al poterlo muovere ” <lb></lb>(Alb. </s>

<s>XI, 95). </s></p><p type="main">

<s>Entrando dunque bene addentro ai pensieri di Galileo, i quali eran poi <lb></lb>quelli di Giordano, di Leonardo e di tutti gli altri, che avevano accolte e <lb></lb>illustrate le più antiche dottrine di Aristotile, si vede bene come per essi <lb></lb>non è altro la quiete se non un moto iniziale, cosicchè venivano insomma a <lb></lb>dar delle velocità virtuali una definizione identica a quella dei moderni, i quali <lb></lb>dicon giusto velocità virtuale esser “ celle qu&#039;un corps en équilibre est <lb></lb>dispose à recevoir, en cas que l&#039;équilibre vienne à ètre rompu; c&#039;est a dire <lb></lb>la vitesse que ce corps prendroit reelllement dans le premier instant de son <lb></lb>mouvement ” (Lagrange, Mechan. </s>

<s>anal. </s>

<s>cit, pag. </s>

<s>8). </s></p><p type="main">

<s>Or come mai si domanderà, essendo una tal definizione del Lagrange <lb></lb>universalmente approvata, per avere il suo fondamento ne&#039;più certi princi­<lb></lb>pii matematici, potè il Nardi, ch&#039;era pure così studioso discepolo di Gali-<pb xlink:href="020/01/1921.jpg" pagenum="164"></pb>leo, metterla in dubbio, e bandir le velocità virtuali dall&#039;ingerirsi delle sta­<lb></lb>tiche dimostrazioni? </s>

<s>Soccorre facile e pronta la risposta a una tale domanda <lb></lb>sulle labbra di coloro, che ripensano come i principii, a cui s&#039;informa la <lb></lb><emph type="italics"></emph>Mechanique analitique<emph.end type="italics"></emph.end> del Matematico torinese erano ai tempi del Nardi, <lb></lb>negl&#039;insegnamenti dello stesso Galileo, o ambigui o apertamente ripudiati <lb></lb>per falsi. </s>

<s>Vedemmo di questa ambiguità, nel capitolo precedente, gli esem­<lb></lb>pii, e insegnandosi dal Maestro non si poter trattare degl&#039;indivisibili allo <lb></lb>stesso modo che delle quantità finite, com&#039;era possibile che allignasse nella <lb></lb>sua scuola il Calcolo infinitesimale o qualcuna delle sue più feconde appli­<lb></lb>cazioni? </s>

<s>Se i moti iniziali infatti, o i primi istanti di tempo in un grave <lb></lb>sostenuto a un braccio di leva o più lungo o più corto, son, come si con­<lb></lb>clude per la dottrina di Galileo, tutti egualmente disposti, per non ci essere <lb></lb>un infinito o un infinitesimo maggiore o minore di un altro; com&#039;era pos­<lb></lb>sibile confermare le leggi statiche col principio delle velocità virtuali? </s>

<s>Ne <lb></lb>sarebbe conseguito l&#039;assurdo che un peso nella Libbra, a qualunque distanza <lb></lb>dal sostegno serbasse sempre eguale momento. </s></p><p type="main">

<s>Questi ragionamenti incominciati nella mente del Nardi s&#039;ebbero poi a <lb></lb>fare anche dal Torricelli e dal Viviani, i quali presero risoluzione di ban­<lb></lb>dire addirittura dalla Statica il principio delle velocità virtuali. </s>

<s>Il primo dei <lb></lb>due commemorati Geometri infatti, proponendosi di dimostrar che due gravi <lb></lb>posati sopra due varie obliquità di piani della medesima altezza, se sono <lb></lb>omologamente proporzionali alle lunghezze di quegli stessi piani, hanno i <lb></lb>momenti eguali, causò d&#039;imitar Galileo (il quale in occasione di dimostrare <lb></lb>un suo principio supposto aveva allora allora trovata la proporzione mede­<lb></lb>sima di que&#039;momenti col principio delle velocità virtuali) per attenersi più <lb></lb>sicuramente a un principio affatto diverso, concludendo l&#039;equilibrio fra i <lb></lb>detti corpi costituiti sopra varie declività dal dimostrar che nuovamente fa­<lb></lb>ceva “ centrum commune gravitatis eorum descendere non posse, sed in <lb></lb>eadem semper horizontali linea, quantumlibet gravia moveantur, reperiri ” <lb></lb>(Oper. </s>

<s>geom., Pars I cit., pag. </s>

<s>100). </s></p><p type="main">

<s>Il Viviani poi dà del notabile fatto esempii più positivi. </s>

<s>Nel tomo IV, <lb></lb>parte V de&#039;manoscritti di Galileo, son raccolte insieme e cucite alla rinfusa <lb></lb>fettucce e frustuli di carte, nelle quali riconoscono facilmente gli esperti il <lb></lb>carattere calligrafico, giovanile, dello stesso Viviani. </s>

<s>Vi son notati pensieri <lb></lb>di vario soggetto scientifico, che il diligente discepolo scriveva in fretta, come <lb></lb>gli venivano alla memoria, e secondo ch&#039;egli stesso diceva <emph type="italics"></emph>ad mentem Ga­<lb></lb>lilei.<emph.end type="italics"></emph.end> Nella prima faccia del foglio 26, in mezzo ad altre notarelle del più <lb></lb>svariato argomento, alcune delle quali assai curiose, si legge: “ L&#039;impeto <lb></lb>che ha un grave nel voler discendere è tanto, quanto è forza che basti per <lb></lb>sostenerlo. </s>

<s>” Ma passando poi di qui al foglio 39 la nostra attenzione è ri­<lb></lb>volta a leggere con qualche maraviglia quest&#039;altra nota: “ Pensare se è vero <lb></lb>che per ritenere un peso serva tanta forza, quanta ne fa quello per scen­<lb></lb>dere: come si farà per rimanerne sicuri? </s>

<s>” </s></p><p type="main">

<s>La prima importante notizia che di qui ricava il lettore sarebbe che Ga-<pb xlink:href="020/01/1922.jpg" pagenum="165"></pb>lileo stesso fosse entrato in sospetto della verità del principio statico da lui <lb></lb>professato, Anzi, quando s&#039;avesse a credere che fossero tutte queste note <lb></lb>veramente scritte dal Viviani <emph type="italics"></emph>ad mentem Galilei,<emph.end type="italics"></emph.end> verrebbe quella prima <lb></lb>irresoluta notizia a confermarsi nella certezza, giacchè quivi stesso, a tergo <lb></lb>del foglio 41, leggesi un frammento di Dialogo dove, mettendosi dal Sagredo <lb></lb>in dubbio il principio delle velocità virtuali, per esser duro ad apprendere <lb></lb>come una cosa che non è ancora possa produrre un effetto presente, il Sal­<lb></lb>viati, ossia Galileo così risponde: “ V. S. ha molto ben ragione di dubitare <lb></lb>ed io ancora, non restando ben sodisfatto di simile discorso, trovai di quie­<lb></lb>tarmi per un altro verso molto semplice e speditivo. </s>

<s>” </s></p><p type="main">

<s>Questo modo più semplice e speditivo, che il Salviati passa a proporre, <lb></lb>in sostituzion di quello delle velocità virtuali, sembra essere stato suggerito <lb></lb>da ciò che, nella Parafrasi ai due libri archimedei <emph type="italics"></emph>De aequiponderantibus,<emph.end type="italics"></emph.end><lb></lb>dice così proemiando Guidubaldo del Monte: “ Sint duo pondera A, B in <lb></lb>aliquo vecte, A maius, B minus quorum simul ita in vecte dispositorum sit <lb></lb>centrum gravitatis C. </s>

<s>Sit autem sub vecte inter C, A fulcimentum in D, et <lb></lb>quoniam pondera A, B penes C gravitatis centrum inclinantur, tunc C deor­<lb></lb>sum naturaliter movebitur ac per consequens pondus quoque B movebi­<lb></lb>tur ” (Pisauri 1588, pag. </s>

<s>2). La dimostrazione fatta nel frammento di dia­<lb></lb>logo dal Salviati è fondata sui fatti statici descritti in queste parole di Gui­<lb></lb>dubaldo. </s></p><p type="main">

<s>Ma è egli veramente quel frammento di dialogo fra il Sagredo e il <lb></lb>Salviati scritto secondo l&#039;intenzione di Galileo? </s>

<s>La nota autografa apposta <lb></lb>in margine dal Viviani <emph type="italics"></emph>di questo ho l&#039;originale<emph.end type="italics"></emph.end> farebbe anzi credere che <lb></lb>Galileo stesso avesse di sua propria mano distesa l&#039;interlocuzione, e che il <lb></lb>Viviani non avesse fatto altro che copiarla. </s>

<s>Anche noi, avendo creduto da <lb></lb>principio che le cose stessero propriamente così, come ci si rappresentavano, <lb></lb>asserimmo nel Discorso preliminare a questa Storia che Galileo aveva inten­<lb></lb>zione di riformare il dialogo delle Due nuove scienze, per sostituirvi un altro <lb></lb>principio statico diverso da quello delle velocità virtuali, ma poi, svolgendo <lb></lb>le carte propriamente appartenenti allo zelante discepolo, scoprimmo che <lb></lb>quella sostituzione aveva inteso di farla egli di suo proprio moto, e non per <lb></lb>copia avutane o per desiderio espressogli dal Maestro. </s>

<s>Il seguente documento, <lb></lb>che noi trascriviamo qui nella sua integrità, mette in chiaro le cose nei loro <lb></lb>più minuti particolari. </s></p><p type="main">

<s>“ Trovandomi un giorno, scrive di sua propria mano il Viviani, a ra­<lb></lb><figure id="id.020.01.1922.1.jpg" xlink:href="020/01/1922/1.jpg"></figure></s></p><p type="caption">

<s>Figura 66.<lb></lb>gionamento di varie materie con un tal <lb></lb>Simplicio patrizio anconitano, passò que­<lb></lb>sti ad interrogarmi sopra il seguente <lb></lb>dubbio meccanico, il quale per meglio <lb></lb>esplicare rappresenterò con alquanto di <lb></lb>figura nel modo appresso: Sia sostenuta <lb></lb>nel punto C (fig. </s>

<s>66) la Libbra di brac­<lb></lb>cia disuguali, AC maggiore, CB minore: <pb xlink:href="020/01/1923.jpg" pagenum="166"></pb>cercasi la cagione onde avvenga che, posti nell&#039;estremità due pesi eguali <lb></lb>A, B, la Libbra non resti in quiete o in equilibrio, ma inclini dalla parte <lb></lb>del braccio maggiore trasferendosi come in EF. ” </s></p><p type="main">

<s>“ La ragione, che comunemente se ne assegna, è perchè la velocità del <lb></lb>peso A nello scendere sarebbe maggiore della velocità del peso B, per esser <lb></lb>la distanza CA maggiore della distanza CB, onde il mobile A, eguale quanto <lb></lb>al peso al B, lo supera quanto al momento della velocità, e però gli pre­<lb></lb>vale e scende sollevando l&#039;altro. </s>

<s>” </s></p><p type="main">

<s>“ Qui dubitasi circa il valore di tal ragione, la quale par che non ab­<lb></lb>bia forza di concludere, perchè è ben vero che il momento di un grave <lb></lb>s&#039;accresce congiunto con velocità sopra il momento d&#039;un grave eguale, che <lb></lb>sia costituito in quiete, ma che, posti ambedue in quiete, cioè dove non sia <lb></lb>neppur moto, non che velocità maggiore di un&#039;altra, quella maggioranza, <lb></lb>che ancora non è ma ancora ha da essere, possa produrre un effetto pre­<lb></lb>sente, ha qualche durezza nel potersi apprendere, sentendovisi veramente <lb></lb>difficoltà notabile. </s>

<s>” </s></p><p type="main">

<s>“ A così fatta istanza sovvennemi di subito rispondere, alla presenza <lb></lb>ancora di amico caro, che fu il signor Cosimo Galilei, il quale io adduco in <lb></lb>testimonio, in ogni caso che il Signor patrizio, scordandosi aver ricevuto da <lb></lb>me tal risposta e credendosela propria, in qualche occasione se ne vestisse; <lb></lb>che con molto apparente ragione S. S. Ecc.ma dubitava, non restando ancor <lb></lb>io ben sodisfatto di tal discorso, ma che io credevo ben di poter quietarlo, <lb></lb>con una ragione potissima, semplicissima e spedita, senza supporre altro che <lb></lb>la prima e comunissima notizia meccanica, cioè che tutte le cose gravi vanno <lb></lb>all&#039;ingiù in tutte le maniere che gli vien permesso, e che quando possono <lb></lb>scendere, benchè per minimo spazio, sempre se ne ingegnano. </s>

<s>Per esempio, <lb></lb>quando nella suddetta libbra AB si pongono due pesi eguali, se questa si <lb></lb>lascerà andare liberamente, fin che non trovi intoppo, se ne calerà al cen­<lb></lb>tro comune delle cose gravi, mantenendo sempre il centro della sua gra­<lb></lb>vità, che è il punto di mezzo D, nella retta che da esso và al centro uni­<lb></lb>versale, poichè un grave in tanto si muove e scende naturalmente, in quanto <lb></lb>il suo centro di gravità può acquistare e scendere verso il centro comune. </s>

<s><lb></lb>Ma se in questo moto della Libbra si opporrà un intoppo sotto il centro D, <lb></lb>il moto si fermerà, restando la Libbra co&#039;suoi pesi in equilibrio, non po­<lb></lb>tendo il loro centro di gravità comune D calare a basso. </s>

<s>Ma se l&#039;intoppo <lb></lb>si metterà fuori del centro D, come sarebbe in C, tale intoppo non fermerà <lb></lb>la Bilancia, ma il centro D devierà dalla perpendicolare, per la quale cam­<lb></lb>minava, e così scenderà come gli è permesso dal sostegno C, cioè per <lb></lb>l&#039;arco DO. ” </s></p><p type="main">

<s>“ Insomma questa Libbra con i due pesi eguali nell&#039;estremità è un <lb></lb>corpo solo, ed un grave solo, il cui centro di gravità è il punto D, e que­<lb></lb>sto solo corpo grave scenderà sempre quando e quanto potrà, e la sua scesa <lb></lb>sarà regolata dal centro di gravità suo proprio, e quando se gli sottopone <lb></lb>il sostegno C, il centro D cala in O, seguitando anche di moversi fino al <pb xlink:href="020/01/1924.jpg" pagenum="167"></pb>perpendicolo, sicchè quello che scende è tutto il corpo aggregato e compo­<lb></lb>sto della Libbra e suoi pesi. </s>

<s>” </s></p><p type="main">

<s>“ La risposta adunque propria ed adeguata all&#039;interrogazione perchè <lb></lb>inclini la Libbra sospesa fuori del centro, è perchè, come quella che è una <lb></lb>sola macchina, trovandosi qualche poco in libertà, scende e si avvicina quanto <lb></lb>più può al centro comune di tutti i gravi, essendo massima indubitabile che, <lb></lb>qualunque volta una macchina di uno o più gravi abbia il suo comun cen­<lb></lb>tro di gravità costituito in luogo, che possa per qualche parte, benchè mi­<lb></lb>nimo, far qualche acquisto verso il comun centro dei gravi, cioè della Terra; <lb></lb>sempre si muova e discenda. </s>

<s>E quando tal centro col muoversi non possa <lb></lb>subito far qualche acquisto <emph type="italics"></emph>deorsum,<emph.end type="italics"></emph.end> se ne stia infallibilmente in una per­<lb></lb>petua quiete. </s>

<s>” (MSS, Gal. </s>

<s>Dis., T. CXXXV, fol. </s>

<s>8, 9). </s></p><p type="main">

<s>Ora, nel citato volume manoscritto di Galileo, trovandosi messo in forma <lb></lb>di dialogo questo medesimo discorso, illustrato da eguale figura e con le <lb></lb>stesse stessissime lettere di richiamo, s&#039;ha scoperto l&#039;inganno da quella <lb></lb>mano propria che l&#039;aveva tessuto. </s>

<s>Quel giocar poi con la finzione e addi­<lb></lb>mesticarsi con la menzogna, che non troverebbe in giudici severi così fa­<lb></lb>cile scusa, è la più giusta misura da estimar quanto fosse nel Viviani lo <lb></lb>zelo di salvar l&#039;onore e la gloria del suo adorato Maestro. </s>

<s>Avrebbe voluto <lb></lb>che fosse sotto il solo nome di lui raccolta tutta intera la scienza, la quale, <lb></lb>per esser senza mende, fosse andata esente da qualunque censura. </s>

<s>I mano­<lb></lb>scritti rivelano nello sviscerato Discepolo queste intenzioni, delle quali si farà <lb></lb>a suo tempo disamina più diligente contentandoci per ora di quel frammento <lb></lb>di dialogo, in cui poco fa c&#039;incontrammo. </s></p><p type="main">

<s>Conosceva il Viviani che qualunque dottrina avesse avuto per fonda­<lb></lb>mento il principio delle quantità infinitamente piccole era in Galileo una <lb></lb>contradizione, la quale più che altrove appariva manifesta colà, dove ne&#039;dia­<lb></lb>loghi delle Due nuove scienze trattavasi di applicare agli equiponderanti il <lb></lb>principio delle velocità virtuali. </s>

<s>Finse perciò il Viviani che l&#039;Autore avesse <lb></lb>per sè medesimo pensato di riformare il dialogo, a quel modo ch&#039;esibivasi <lb></lb>dalla supposta copia, coll&#039;intenzion d&#039;inserirla a suo luogo nella prima ri­<lb></lb>stampa. </s>

<s>L&#039;essersi messo intorno a ciò con tanto ardore, da non curare il <lb></lb>pericolo certissimo di trovarsi convinto di menzogna, sarebbe fra gli altri <lb></lb>uno de&#039;più chiari segni che il Viviani partecipava con le idee del Nardi e <lb></lb>del Torricelli, che fossero cioè da repudiar nella Statica le velocità virtuali, <lb></lb>essendo il principio matematico infinitesimale, in ch&#039;elle trovavano sicurezza, <lb></lb>a que&#039;tempi, immaturi a comprendere l&#039;importanza della Geometria del Ca­<lb></lb>valieri; ambiguamente esposto da chi non l&#039;avesse, come Galileo, aperta­<lb></lb>mente negato. </s></p><p type="main">

<s>E qui, presso a chiudere questo cenno di storia, la quale risale al Tar­<lb></lb>taglia, al Nemorario, e anzi molto più su, non possiamo non rammemorare <lb></lb>ai Lettori, perchè riconoscano quanto sia alieno dal vero, il giudizio che, <lb></lb>per essere pronunziato da un celebre Autore, fu ripetuto e tuttavia si ri­<lb></lb>pete da molti. </s>

<s>Il Lagrange dunque, dop&#039;avere accennato a quelle velocità, <pb xlink:href="020/01/1925.jpg" pagenum="168"></pb>che danno virtù di moto, e sul principio delle quali si stabilì quel suo in­<lb></lb>signe analitico Libro, immediatamente soggiunge: “ Pour peu qu&#039;on exa­<lb></lb>mine les conditions de l&#039;equilibre dans le levier et dans les autres machi­<lb></lb>nes, il est facile de reconnoître la verité de ce principe: cependan<emph type="italics"></emph>t<emph.end type="italics"></emph.end> il ne <lb></lb>paroît pas que les Geometres qui ont précédé Galilee, en aient eu connois­<lb></lb>sance, et je crois pouvoir en attribuer la decouverte à cet Auteur ” (Mechan. </s>

<s><lb></lb>analit. </s>

<s>cit., pag. </s>

<s>8). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Galileo per verità non fece mai cenno di credersi o di volersi far credere <lb></lb>Autore della scoperta, la quale egli anzi francamente, come vedemmo, attri­<lb></lb>buisce ad Aristotile. </s>

<s>In ogni modo però tanto <emph type="italics"></emph>dans son traite<emph.end type="italics"></emph.end> Della scienza <lb></lb>meccanica, quanto <emph type="italics"></emph>dans ses dialogues sur le mouvement,<emph.end type="italics"></emph.end> citati dallo stesso <lb></lb>Lagrange, le velocità virtuali non hanno se non che una parte secondaria, <lb></lb>e s&#039;adducono per una certa <emph type="italics"></emph>congruenza e probabilità, dalla quale può es­<lb></lb>sere ragionevolmente confermata<emph.end type="italics"></emph.end> (Alb. </s>

<s>XI, 95) la legge delle equiponde­<lb></lb>ranze, già dall&#039;Autore ivi dimostrata secondo il metodo di Archimede. </s>

<s>Ga­<lb></lb>lileo dunque, così in principio della <emph type="italics"></emph>Scienza meccanica,<emph.end type="italics"></emph.end> come nel II dialogo <lb></lb>Delle due nuove scienze, pone per principale fondamento alla statica il teo­<lb></lb>rema VI <emph type="italics"></emph>De acquiponderantibus:<emph.end type="italics"></emph.end> “ Commensurabiles magnitudines ex di­<lb></lb>stantiis reciprocis, eamdem rationem habentibus quam pondera, aequiponde­<lb></lb>rant ” (Opera cit., pag. </s>

<s>165). Gli si dovrebbe intorno a ciò confermare il <lb></lb>merito di aver resa più semplice e più generale la dimostrazione archime­<lb></lb>dea, se non fosse stato prevenuto dallo Stevino, di cui quella dello stesso <lb></lb>Galileo è una imitazione perfetta. </s></p><p type="main">

<s>Il Matematico di Bruges, nel suo libro <emph type="italics"></emph>Des elemens de Statique,<emph.end type="italics"></emph.end> pub­<lb></lb>blicato verso la fine del secolo XVI, dimostra in due varii modi, corrispon­<lb></lb>denti ai teoremi VI e VII di Archimede, questa sua prima e fondamentale <lb></lb>proposizione: “ De deux pesanteurs equilibres la plus pesante a telle raison <lb></lb>a la plus legere, comme le long rayon au cort ” (Ouvres mathematique, <lb></lb>Leyde 1634, pag. </s>

<s>436). </s></p><p type="main">

<s>Incomincia dal primo modo, che suppone i due gravi commensurabili, <lb></lb>e invece di suppor, come fa Archimede, una linea imponderabile uniforme­<lb></lb>mente gravata di pesi eguali, immagina che sia da equilibrare un solido pon­<lb></lb><figure id="id.020.01.1925.1.jpg" xlink:href="020/01/1925/1.jpg"></figure></s></p><p type="caption">

<s>Figura 67.<lb></lb>deroso omogeneo e uniforme, come un <lb></lb>prisma per esempio o un cilindro. </s>

<s>Sia <lb></lb>dunque ABCD (fig. </s>

<s>67) questo cilindro, <lb></lb>che si suppone essere di sei libbre, uni­<lb></lb>formemente compartite per i piani EF, <lb></lb>GH, IK, LM, NO condotti paralleli alla <lb></lb>base, e secanti l&#039;asse PQ ne&#039;punti R, <pb xlink:href="020/01/1926.jpg" pagenum="169"></pb>S, T, V, X. </s>

<s>Si prenda AM per il peso maggiore, che ha da equiponderare <lb></lb>all&#039;altro minore LC. È chiaro ch&#039;essendo X il centro di gravità di questo, <lb></lb>e S il centro di gravità di quello, si potranno i due pesi riguardar come <lb></lb>bilanciati agli estremi della linea SX sostenuta in T, centro di gravità di <lb></lb>tutto il solido, cosicchè sia TX il maggior braccio di tal Bilancia, e TS il <lb></lb>minore. </s></p><p type="main">

<s>Ora, prosegue a dir lo Stevino, “ il faut demonstrer que la pesanteur <lb></lb>majeure LD est a la moindre LC comme le long rayon TX au plus court TS ” <lb></lb>ciò che si fa dall&#039;Autore in assai facile modo, perchè i due cilindri LD, LC, <lb></lb>avendo basi eguali, stanno come le altezze PV, VQ, le quali stanno come 4:2. <lb></lb>Ma anche TX sta a ST come due sta ad uno, ossia come 4:2, dunque <lb></lb>LD:LC=TX:ST. </s></p><p type="main">

<s>Se poi si vuol dividere il cilindro equilibrato in due parti incommen­<lb></lb>surate e incommensurabili, la conclusione è la medesima, come passa a di­<lb></lb>mostrar lo Stevino nel suo secondo esempio, supponendo ch&#039;esso cilindro, <lb></lb><figure id="id.020.01.1926.1.jpg" xlink:href="020/01/1926/1.jpg"></figure></s></p><p type="caption">

<s>Figura 68.<lb></lb>rappresentato in AC (fig. </s>

<s>68), sia dal <lb></lb>piano EF, parallelo alla base AD, se­<lb></lb>gato in due porzioni qualunque AF, <lb></lb>EC. </s>

<s>Sia poi condotto l&#039;asse GH: nei <lb></lb>punti M, metà dello stesso GH, K <lb></lb>metà di GI, L metà di IH saranno co­<lb></lb>stituiti i centri di gravità del solido <lb></lb>intero e della maggiore e della minor <lb></lb>parte di lui. </s>

<s>Poste le quali cose “ il faut demonstrer que comme le corps <lb></lb>ou pesanteur (les quels sont icy de mesme à cause de leur proportion, car <lb></lb>comme le corps EFDA au corps EFCB ainsi la pesanteur de celuy-la a ce­<lb></lb>luy-cy, d&#039;autant que la colomne est de tout costé de pesanteur uniforme) de <lb></lb>EFDA a EFCB, ainsi le long rayon ML au plus court MK ” (ivi, pag. </s>

<s>437): <lb></lb>e ciò fa l&#039;Autore in tre articoli, che si possono compilare nel modo seguente. </s></p><p type="main">

<s>Avendo i due cilindri le basi eguali saranno proporzionali alle altezze <lb></lb>o alle loro metà, per cui avremo AF:EC=KI:IL. </s>

<s>Se ora a MH e a MG <lb></lb>eguali s&#039;aggiunga KM otterremo una nuova eguaglianza HK=MG+KM, <lb></lb>dal primo termine della quale tolto GK, e dall&#039;altro KI, essendo le quantità <lb></lb>tolte eguali, eguali pure saranno le rimanenti, le quali facilmente si ridu­<lb></lb>cono a IH/2=IL=KM: all&#039;una e all&#039;altra delle quali due ultime quan­<lb></lb>tità eguali aggiungendo IM s&#039;avrà ML=KI. </s>

<s>Così preparate le cose, un <lb></lb>passo solo conduce all&#039;ultima conclusione, perchè l&#039;eguaglianza AF:EC= <lb></lb>KI:IL, sostituitovi ML a KI, e KM ad IL, si trasforma nell&#039;altra AF:EC= <lb></lb>ML:KM, come dovevasi dimostrare. </s></p><p type="main">

<s>“ On pourroit encor, soggiunge lo Stevino, repliquer que cesta demon­<lb></lb>stration tient lieu entre les corps de matiere uniforme, et qui font ensemble <lb></lb>una colomne, pour a quoy subvenir s&#039;ensuit la regle generale .... ” (ivi) e <lb></lb>passa a dimostrar che vale la medesima regola anco se i corpi son disformi, <pb xlink:href="020/01/1927.jpg" pagenum="170"></pb>sempre equilibrandosi anch&#039;essi allora, che i loro pesi stanno reciprocamente <lb></lb>alle lunghezze dei raggi. </s></p><p type="main">

<s>Chi ora da questi elementi di Statica dello Stevino passa a leggere di­<lb></lb>mostrato, nella Scienza meccanica di Galileo “ come pesi diseguali pesino <lb></lb>egualmente sospesi da distanze diseguali, le quali abbiano contraria propor­<lb></lb>zione di quella, che essi pesi si ritrovano avere ” (Alb. </s>

<s>XI, 92) trova i me­<lb></lb>desimi modi, variati di sì leggere accidentalità, ch&#039;è pur forza di confessare <lb></lb>esser questa galileiana dimostrazione, come si diceva, perfettamente imitata <lb></lb>da quella del Matematico olandese. </s></p><p type="main">

<s>Nella seconda Giornata Delle due nuove scienze si pone per fondamento <lb></lb>alle dimostrazioni delle resistenze dei solidi, e come principio noto “ quello <lb></lb>che nelle Meccaniche si dimostra tra le passioni del Vette, che noi chia­<lb></lb>miamo Leva, cioè che nell&#039;uso della Leva la forza alla resistenza ha la pro­<lb></lb>porzion contraria di quella, che hanno le distanze tra il sostegno e le me­<lb></lb>desime forza e resistenza ” (Alb. </s>

<s>XIII, 112). Alla qual proposta del Salviati <lb></lb>soggiungendo Simplicio essere stato dimostrato ciò da Aristotile, il Salviati <lb></lb>stesso risponde: “ Voglio che gli concediamo il primato nel tempo, ma nella <lb></lb>fermezza della dimostrazione parmi che se gli debba per grand&#039;intervallo <lb></lb>anteporre Archimede, da una sola proposizione del quale, dimostrata da esso <lb></lb>negli Equiponderanti, dipendono le ragioni, non solamente della Leva, ma <lb></lb>della maggior parte degli altri strumenti meccanici. </s></p><p type="main">

<s>Si conferma di qui quel che altrove si disse che cioè il principio ari­<lb></lb>stotelico delle velocità virtuali era creduto da Galileo aver minore fermezza <lb></lb>di quell&#039;altro posto da Archimede negli Equiponderanti, e perciò, volendo <lb></lb>quasi lemma ai suoi nuovi teoremi ridurre alla memoria la dimostrazione <lb></lb>di quel principio archimedeo, lo fa, Galileo, in modo tanto simile a quello <lb></lb>prima tenuto nella Scienza meccanica, che, nelle Opere, i Fiorentini editori <lb></lb>di queste, rimandano i lettori ai principii della sopra detta Giornata seconda <lb></lb>Del moto. </s></p><p type="main">

<s>La fama acquistata dall&#039;Autore fece credere a tutti essere stato egli il <lb></lb>primo a metter mano nella dimostrazione degli Equiponderanti, rendendola <lb></lb>assai più semplice, e comprendendo in una le due proposizioni archimedee. </s>

<s><lb></lb>Ma l&#039;intento principale di Galileo era quello di cessar certe difficoltà, che <lb></lb>egli ebbe a sentir promosse contro a sè stesso, infin da quando s&#039;esercitava <lb></lb>da giovane intorno ai Baricentri, da coloro i quali “ non tolleravano volen­<lb></lb>tieri quel doppio modo di considerare le medesime grandezze in diverse Bi­<lb></lb>lance ” (Alb. </s>

<s>VI, 2). </s></p><p type="main">

<s>Rappresentandoci infatti nuovamente sott&#039;occhio la figura LXVII e ri­<lb></lb>guardando le linee AD, EF, GH, ecc., come pesanti, e ordinatamente disposte <lb></lb>sulla lunghezza della linea PQ, la Bilancia sospesa in I si risolve da Archi­<lb></lb>mede in altre due Bilance, l&#039;una sospesa in G e l&#039;altra in N, ed era ciò <lb></lb>che mal si tollerava dai Fiorentini oppositori di Galileo. </s></p><p type="main">

<s>Nelle nuove dimostrazioni il difetto si rendeva meno sensibile, ma pur <lb></lb>rimaneva sempre, ond&#039;è che non valsero le sollecitudini dello stesso Galileo <pb xlink:href="020/01/1928.jpg" pagenum="171"></pb>e dello Stevino a quietar lo spirito degl&#039;intolleranti. </s>

<s>Il Mariotte, per citarne <lb></lb>uno de&#039;più celebri, nella seconda parte del suo <emph type="italics"></emph>Moto delle acque,<emph.end type="italics"></emph.end> propone <lb></lb>un principio statico generale da applicarsi al moto de&#039;fluidi; principio che <lb></lb>egli insomma riduce a quello delle velocità virtuali, dicendo che allora si <lb></lb>equilibrano due corpi quando o urtandosi o movendosi l&#039;uno in modo da <lb></lb>far necessariamente movere anche l&#039;altro le velocità stanno reciprocamente <lb></lb>alle moli. </s>

<s>“ De-la, egli dice, on prouve facilement le principe de Mechani­<lb></lb>que qui a eté mal prouvé par Archimede, par Galilee et par plusieurs Au­<lb></lb>teurs, scavoir que lorsqu&#039;en une Balance les poids sont reciproques à leurs <lb></lb>distances du centre de la Balance, ils font equilibre ” (Oeuvres, T. II, a la <lb></lb>Haye 1740, pag. </s>

<s>357). </s></p><p type="main">

<s>L&#039;Huyghens più moderatamente si contentò di dire che, nella proposi­<lb></lb>zione fondamentale della Meccanica, Archimede “ tacite ponit quid de quo <lb></lb>iure aliquo possumus dubitare ” (Opera varia, Vol. </s>

<s>I, Lugd. </s>

<s>Batav., pag. </s>

<s>282), <lb></lb>e giacchè anche a lui sembrava che nè lo Stevino nè Galileo non avessero <lb></lb>tolto affatto il difetto, s&#039;ingegnò di salvare il principato al teorema archi­<lb></lb>medeo, tenendo nel dimostrarlo altro modo. </s>

<s>Chiede perciò ne sia concesso <lb></lb>a lui, come all&#039;Autore antico, due cose; la prima: che due pesi eguali, attac­<lb></lb>cati alle estremità di due braccia di leva eguali, si fanno equilibrio, e la se­<lb></lb>conda che la Bilancia di braccia diseguali cariche d&#039;egual peso inclina dalla <lb></lb>parte del braccio più lungo. </s>

<s>A questi aggiunge l&#039;Huyghens un terzo postu­<lb></lb>lato ed è che, come fu concesso ad Archimede essere imponderabile la linea, <lb></lb>così concedasi a lui essere imponderabile il piano, che fa il medesimo offi­<lb></lb>cio di sostenere i pesi per l&#039;equilibrio. </s></p><p type="main">

<s>Poi prepara l&#039;Huyghens due lemmi di tanto facile dimostrazione, che <lb></lb>il primo si riduce a un fatto, e il secondo non si potrebbe altrimenti dimo­<lb></lb>strare che dagli assurdi, che ne conseguono. </s>

<s>È quella prima lemmatica pro­<lb></lb>posizione dall&#039;Autore così formulata: “ Si super planum horizontale, quod <lb></lb>imponitur lineae rectae quae id dividit in duas partes, applicetur pondus, <lb></lb>vis quam illud pondus habebit ad deflectendum planum partem versus ad <lb></lb>quam applicatur, erit maior quam si positum sit prope dictam lineam ” (ibid., <lb></lb>pag. </s>

<s>283). Il secondo poi di que&#039;lemmi si pone dall&#039;Autore stesso sotto la <lb></lb>seguente forma: “ Si planum horizontale oneratum plurimis ponderibus ma­<lb></lb>neat in aequilibrio impositum lineae rectae quae id secat in duas partes, cen­<lb></lb>trum gravitatis plani sic onerati erit in ipsa linea recta ” (ibid., pag. </s>

<s>283, 84). </s></p><p type="main">

<s>Di questo e dell&#039;altro Lemma si serve l&#039;Huyghens per dimostrar la <lb></lb>proposizione sua principale, così formulata: “ Duo gravia commensurabilia <lb></lb>appensa ad extremitates brachiorum Librae erunt in aequilibrio, si brachia <lb></lb>sint in ratione reciproca gravium ” (ibid., pag. </s>

<s>284). </s></p><p type="main">

<s>Sieno i due detti gravi conmmensurabili A e B (fig. </s>

<s>69), e sia con essi <lb></lb>la Libbra CE talmente disposta, che il minor braccio CD abbia al suo mag­<lb></lb>giore DE quella proporzione medesima, che ha reciprocamente il maggior <lb></lb>peso A a B suo minore: “ dico Libram esse in aequilibrio appenso A ad <lb></lb>extremum C, et B ad extremum E, si CE sustineatur in D. ” </s></p><pb xlink:href="020/01/1929.jpg" pagenum="172"></pb><p type="main">

<s>Nel piano orizzontale, per cui passa CE, si conducano ad essa CE, per­<lb></lb>pendicolari in C e in E, le due linee KM, LG, e presa EF=CD si con­<lb></lb>ducano per i punti F, D le linee GK, ML che, facendo con la Libbra CE <lb></lb>una mezza squadra, s&#039;intersechino in N ad angolo retto. </s></p><p type="main">

<s>Così fatto, se il peso A sta a B come per esempio 9 sta a 4, si distri­<lb></lb>buiscano ad ordinati intervalli le nove parti di A sulla linea KM, e le quat­<lb></lb><figure id="id.020.01.1929.1.jpg" xlink:href="020/01/1929/1.jpg"></figure></s></p><p type="caption">

<s>Figura 69.<lb></lb>tro parti di B sulla linea LG, e da <lb></lb>ciascuna porzion de&#039;pesi così distri­<lb></lb>buiti si conducano sulla LM altret­<lb></lb>tante linee perpendicolari. </s>

<s>Si dimostra <lb></lb>facilmente che i pesi dell&#039;una parte <lb></lb>si equilibrano con quelli dell&#039;altra <lb></lb>intorno alla linea LM, sopra la quale <lb></lb>si dee trovar pure il comun centro <lb></lb>di gravità per le cose già dimostrate <lb></lb>nel II lemma. </s>

<s>“ Sed centrum gravi­<lb></lb>tatis etiam est in linea CE, quoniam <lb></lb>evidens est planum etiam futurum <lb></lb>in aequilibrio si in hac linea susti­<lb></lb>neatur. </s>

<s>Erit ergo centrum gravitatis <lb></lb>punctum commune illis duabus lineis <lb></lb>LM, et CE, scilicet punctum D, in quo, si planum sustineatur, manet in <lb></lb>aequilibrio. </s>

<s>Patet ergo veritas theorematis ” (ibid., pag. </s>

<s>286). </s></p><p type="main">

<s>La dimostrazione ugeniana, benchè così elaborata, è nonostante meno <lb></lb>comprensiva di quella dello Stevino, non essendo applicabile se non che alle <lb></lb>quantità commensurabili, e pur qui come là è qualche cosa che gli schifil­<lb></lb>tosi non saprebbero tollerare. </s>

<s>Un altro Matematico non men valoroso del­<lb></lb>l&#039;Huyghens si volle perciò provare se forse gli riusciva di contentarli, affi­<lb></lb>dandosi alla maravigliosa efficacia, allora allora incominciatasi a sperimentare, <lb></lb>del principio della composizion delle forze. </s>

<s>Il Newton dunque nel I libro <lb></lb>Dei principii matematici propose della legge degli Equiponderanti una nuova <lb></lb>dimostrazione che, ridotta alla sua maggiore semplicità, procede nel modo <lb></lb>seguente. <lb></lb><figure id="id.020.01.1929.2.jpg" xlink:href="020/01/1929/2.jpg"></figure></s></p><p type="caption">

<s>Figura 70.</s></p><p type="main">

<s>Sìa OK (fig. </s>

<s>70) il minore, o <lb></lb>OL il maggior braccio della Bilan­<lb></lb>cia KL, dagli estremi L, K della <lb></lb>quale pendano i pesi P ed A. </s>

<s><lb></lb>Fatto centro in O, e con un rag­<lb></lb>gio eguale ad OL, si descriva un <lb></lb>cerchio, che tagli il filo KA nel <lb></lb>punto D, da cui conducasi a DO <lb></lb>la linea DC perpendicolare. </s>

<s>Presa <lb></lb>per misura del peso A la lunghezza <lb></lb>della linea DC, si decomponga con <pb xlink:href="020/01/1930.jpg" pagenum="173"></pb>la regola del parallelogrammo la forza rappresentata da essa DC nelle due forze <lb></lb>DM, DC, quella rintuzzata dalla resistenza del centro O, e questa unica ri­<lb></lb>masta nella sua libera azione. </s>

<s>I triangoli simili DAC, OKD danno AD:DC= <lb></lb>OD:OK, e perciò DC=ADXOK/OD. </s>

<s>Ma considerando che DC trae in di­<lb></lb>rezione perpendicolare al braccio di leva OD, eguale per costruzione al brac­<lb></lb>cio OL, è certo che fa forza come se fosse un peso applicato in L nella <lb></lb>direzione del filo LP, e non potrà perciò stabilirsi la macchina in equilibrio, <lb></lb>se non a patto che sia P=DC. </s>

<s>Ponendo perciò nel valore di essa DC <lb></lb>superiormente determinato, A invece di AD e OL invece di OD, avremo <lb></lb>P=AXOK/OL ossia A:P=OL:OK. “ Pondera igitur A et P, ne con­<lb></lb>clude il Newton, quae sunt reciproce ut radii in directum positi OK et OL, <lb></lb>idem pollebunt, et sic consistent in aequilibrio, quae est proprietas notis­<lb></lb>sima Librae, Vectis et Axis in peritrochio ” (Princ. </s>

<s>mathem., T. I, Gene­<lb></lb>vae 1739, pag. </s>

<s>28). </s></p><p type="main">

<s>Si oppose anche a questa neutoniana proposizione che il dimostrar <lb></lb>l&#039;equilibrio nella leva diritta, col ridurla a torta ed incurva, non sembrava <lb></lb>modo da doversi con faciltà tollerare. </s>

<s>Ma il Newton insomma usciva, così, <lb></lb>in pubblico uno de&#039;primi e il più autorevole di tutti nell&#039;applicare alla Sta­<lb></lb>tica i principii della <emph type="italics"></emph>Meccanica nuova,<emph.end type="italics"></emph.end> de&#039;quali facendo quell&#039;uso, che poi <lb></lb>videsi così largamente fare al Varignon, si poteva per essi dimostrar la ra­<lb></lb>gion delle equiponderanze in modo, che anche gl&#039;intolleranti vi s&#039;avessero <lb></lb>finalmente a quietare. </s></p><p type="main">

<s>Riducendosi infatti sull&#039;esempio del Newton i pesi a forze rappresen­<lb></lb>tate da linee, abbiasi la Bilancia AB (fig. </s>

<s>71), nella quale sia AG il brac­<lb></lb>cio minore, e GB il maggiore, tirato questo in giù dalla forza BQ, come <lb></lb><figure id="id.020.01.1930.1.jpg" xlink:href="020/01/1930/1.jpg"></figure></s></p><p type="caption">

<s>Figura 70.<lb></lb>quello è tirato dalla forza AP, ambedue <lb></lb>fra sè parallele, come son parallele fra <lb></lb>loro le direzioni dei liberi pesi archimedei. </s>

<s><lb></lb>Applicate ai punti A, B, nella direzione di<lb></lb>AB, due forze AM, BN eguali e contrarie&#039; <lb></lb>e nei parallelogrammi MP, NQ, già co­<lb></lb>struiti, condotte le diagonali XA, YB, che <lb></lb>prolungate s&#039;incontrino in S, da cui si<lb></lb>conduca SG parallela ad AP, dimostra­<lb></lb>rono assai facilmente i novelli Meccanici <lb></lb>successeri del Newton che questa stessa <lb></lb>linea SG rappresenta una forza equipol­<lb></lb>lente alle due AP, BQ in reciproca ragion delle quali stanno le braccia BG, <lb></lb>GA della Bilancia AB, nel punto G intersegata. </s>

<s>Se dunque SG tira in dire­<lb></lb>zione contraria alle due BQ, AP il sistema permarrà in equilibrio, e perciò <lb></lb>essendo P, Q, due pesi pendoli dai fili AP, BQ, secondo il metodo archi­<lb></lb>medeo, la Bilancia stessa rimarrà per le medesime ragioni equilib<gap></gap>ta, se <pb xlink:href="020/01/1931.jpg" pagenum="174"></pb>nel punto G, distante da A e da B reciprocamente come i pesi ivi appli­<lb></lb>cati, consiste il suo proprio sostegno. </s></p><p type="main">

<s>Nella composizione dunque e nella risoluzione delle forze parallele si <lb></lb>giudicò che avesse finalmente la teoria degli Equiponderanti ritrovata la sua <lb></lb>più precisa dimostrazione, e le antiche difficoltà sommosse contro i seguaci <lb></lb>di Archimede ebbero a risiedere, come risiede colui che furiosamente era <lb></lb>insorto contro una persona al primo riconoscerla ch&#039;ei fa sott&#039;abito trasfor­<lb></lb>mato. </s>

<s>Si voleva dire cioè che il teorema VI <emph type="italics"></emph>De aequiponderantibus<emph.end type="italics"></emph.end> è di­<lb></lb>mostrato da Archimede col principio della composizione e della risoluzione <lb></lb>delle forze parallele, ond&#039;è che i Matematici fiorentini oppositori di Galileo <lb></lb>durarono nelle opposizioni infin tanto che, sotto il seducente abito nuovo, <lb></lb>non riconobbero ascondersi la persona stessa del venerando Siracusano. </s>

<s>I <lb></lb>pesi infatti per lui son qualità astratte dalla più vile materia; sono in­<lb></lb>somma forze geometricamente commensurabili, che agiscono insieme paral­<lb></lb>lele. </s>

<s>La linea dunque GH, alla quale consideriamo ridotto il solido AC nella <lb></lb>figura LXVIII, è sollecitata da tante forze eguali e parallele quanti sono in <lb></lb>essa punti materiali, e saranno perciò dette forze in numero proporzionale <lb></lb>alla lunghezza di lei. </s>

<s>La resultante poi c&#039;insegnano i Meccanici novelli <lb></lb>essere equipollente alla somma di tutte le componenti (alle quali riesce pa­<lb></lb>rallela) applicata in M giusto mezzo della linea GH. </s>

<s>Se sia dunque essa GH <lb></lb>sospesa in M per un filo rimarrà in equilibrio, e in così fatto discorso, chi <lb></lb>ben considera, si trasforma la prima petizion di Archimede: <emph type="italics"></emph>aequalia pon­<lb></lb>dera ab aequalibus distantiis aequiponderare.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Avrebbero preteso alcuni che il postulato s&#039;avesse a dimostrare, ma <lb></lb>qual dimostrazione, di grazia, ne hanno fatta i moderni? </s>

<s>Supponiamo che <lb></lb>nella rappresentata figura LXXI, AP e AQ siano eguali, e che il punto G <lb></lb>torni nel giusto mezzo della Bilancia AB equilibrata dalla forza SG eguale <lb></lb>e contraria alle dette altre due: qual ragione rendono i moderni dell&#039;equi­<lb></lb>librio? </s>

<s>Null&#039;altra da quella in fuori suggerita a tutti dal senso comune, <lb></lb>che cioè due forze eguali e contrarie si elidono a vicenda. </s>

<s>Ora questo, che <lb></lb>è il postulato della Meccanica moderna, è il postulato altresì della Mec­<lb></lb>canica antica, perchè, dando alla Bilancia forma di una carrucola, per la <lb></lb>gola della quale passi una fune con due pesi eguali penduli ai capi; è ma­<lb></lb>nifesto che <emph type="italics"></emph>aequalia pondera ab aequalibus distantiis aequiponderare<emph.end type="italics"></emph.end> val <lb></lb>precisamente quanto a dire che si fanno insieme equilibrio due forze eguali <lb></lb>e contrarie. </s></p><p type="main">

<s>Passando ora al teorema VI Degli equiponderanti, soggetto a tante e <lb></lb>così lunghe contradizioni, sieno trasformati i pesi in forze parallele, e si ve­<lb></lb>drà facilmente, come si diceva, che il metodo di Archimede è quel mede­<lb></lb>simo tenuto da&#039;Moderni nel risolvere e ricomporre insieme più forze paral­<lb></lb>lele. </s>

<s>Ritorniamo indietro anche un&#039;altra volta sulla figura LXVIII, e la linea <lb></lb>GH equilibrata in M suppongasi divisa in due differenti parti ponderose <lb></lb>GI, IH sollecitate da tante forze parallele quanti punti materiali si compren­<lb></lb>dono in ciascuna di esse. </s>

<s>La resultante della forza GI, eguale alla loro <pb xlink:href="020/01/1932.jpg" pagenum="175"></pb>somma e ad esse parallela, è applicata in K, com&#039;è applicata in L la resul­<lb></lb>tante delle forze IH. </s>

<s>Se poi anche tali due forze così resultate si compon­<lb></lb>gano con la medesima regola, tutte le potenze sollecitatrici si riducono a <lb></lb>una sola applicata in M, punto distante da K e da L reciprocamente alle <lb></lb>forze applicate in L e in K. </s>

<s>Questo processo dunque è identico a quello <lb></lb>dello Stevino e di Galileo, e come senza difetto s&#039;approva ora dai moderni, <lb></lb>così dovevasi allora passare agli antichi senza difetto. </s></p><p type="main">

<s>Anche la Baricentrica tutta è stabilita da Archimede sul principio della <lb></lb>composizion delle forze parallele, com&#039;è per sè manifesto nel circolo, nel <lb></lb>rettangolo e in tutte le altre figure, nelle quali il centro della gravità è quel <lb></lb>medesimo del centro della grandezza, e com&#039;è facile altresì riscontrar nel <lb></lb>trangolo e nelle varie superficie, che ne dipendono. </s>

<s>Nel triangolo ABC per <lb></lb>esempio (figura LXIII addietro) le infinite linee ponderose parallele alla base <lb></lb>possono rappresentarsi da altrettante forze applicate al mezzo di ciascuna <lb></lb>linea, e proporzionali alla lunghezza di lei, cosicchè la composizion di tutte <lb></lb>queste forze, dalle quali nasce la gravità del triangolo, ci darà una resul­<lb></lb>tante unica applicata a un punto della bissettrice, che sia dal vertice A di­<lb></lb>stante per due terzi. </s>

<s>È apertissimo dunque che si riducono allo stesso la <lb></lb>invenzion del baricentrico nella superfice triangolare, e la invenzion del cen­<lb></lb>tro delle forze parallele, che la sollecitano tutte insieme per farla o ponde­<lb></lb>rar sul sostegno o libera cadere. </s></p><p type="main">

<s>L&#039;identità de&#039;due metodi, come si riscontra nelle superficie, così è fa­<lb></lb>cile riscontrarla ne&#039;solidi da quelle stesse superfice compaginati, ond&#039;è che <lb></lb>la Meccanica antica troverebbe nella moderna la sua più stabile conferma <lb></lb>e la sua più sicura difesa, quando fosse vero però che venissero i pesi ben <lb></lb>rappresentati da forze tutte in direzioni fra loro parallele. </s>

<s>Le platoniche <lb></lb>astrattezze archimedee furono da tutti i Matematici concordemente appro­<lb></lb>vate e imitate nelle loro meccaniche dimostrazioni, infintantochè, incomin­<lb></lb>ciatasi sulla fine del secolo XVI a instaurare la nuova scienza, non si pensò <lb></lb>che non eran da tenere oramai più lungamente chiuse le orecchie alle voci <lb></lb>di colui, che si sentiva per amor del vero doversi riconoscere di quella stessa <lb></lb>scienza primo Autore, il quale aveva sentenziato nelle sue <emph type="italics"></emph>Questioni<emph.end type="italics"></emph.end> essere <lb></lb>da educar la Meccanica con matematiche contemplazioni, non disgiunte dalle <lb></lb>questioni naturali. </s>

<s>Volendosi perciò da&#039;Meccanici moderni celebrar tra la <lb></lb>Fisica e la Geometria il connubio secondo il prescritto antichissimo rito, co­<lb></lb>nobbero che, tendendo i gravi al centro della Terra a cui sono uniti, non <lb></lb>potevano le loro direzioni esser parallele ma convergenti. </s></p><p type="main">

<s>Così essendo, i presidii, che si diceva aver ritrovati nella moderna l&#039;an­<lb></lb>tica scienza archimedea, vennero improvvisamente a mancarle, e s&#039;ebbe essa <lb></lb>stessa a veder trasformata in altra ne&#039;suoi fondamentali teoremi e ne&#039;suoi <lb></lb>corollarii immediati. </s>

<s>Come fosse tentata e divisata una tale trasformazione <lb></lb>è ciò che noi vogliamo brevemente narrare ai lettori sui documenti, che son <lb></lb>potuti venire alla nostra notizia. </s></p><p type="main">

<s>Ne&#039;primi giorni del Novembre dell&#039;anno 1635, Giovanni di Beaugrand, <pb xlink:href="020/01/1933.jpg" pagenum="176"></pb>gentiluomo francese e studiosissimo delle Matematiche, viaggiando in Italia <lb></lb>si diresse a Firenze con la principale intenzione di conoscere di persona il <lb></lb>famosissimo Galileo, e di trattenersi qualche ora in ragionamento con lui. </s>

<s><lb></lb>Salito infatti ad Arcetri disse, per dar qualche saggio de&#039;suoi studii, eh&#039;egli <lb></lb>avea tempo fa dimostrata una proposizione affatto nuova, che cioè i gravi <lb></lb>mutan peso, scemandolo quanto più si avvicinano al centro della Terra. </s>

<s>Ri­<lb></lb>mase Galileo sorpreso da questa notizia e mostrò vivissimo desiderio di ve­<lb></lb>der come si potesse dimostrare una proposizione tanto straordinaria. </s>

<s>Il Beau­<lb></lb>grand, sceso in Firenze, scrisse di città una lettera, in data del dì 3 Novembre <lb></lb>sopraddetto, la quale terminava con queste parole: “ Le mando il compen­<lb></lb>dio della dimostrazione, ch&#039;io ho fatta qualche tempo fa delle proporzioni <lb></lb>delle varie gravità d&#039;un corpo grave secondo i suoi varii intervalli dal cen­<lb></lb>tro della Terra, di che parlassimo insieme nella mia ultima visita, e che <lb></lb>mi mostrò aggradire di vederla. </s>

<s>Sarò contentissimo che passi per il suo <lb></lb>esame, al quale la sottometto ” (Alb. </s>

<s>X, 120). </s></p><p type="main">

<s>Non ci è rimasto documento nè dell&#039;esposto processo dimostrativo nè <lb></lb>del giudizio, che ne fu dato: questo solo si sa che, passando il Beaugrand <lb></lb>a Roma, Galileo scrisse raccomandandolo con gran lodi al padre Benedetto <lb></lb>Castelli. </s>

<s>Rimase il Castelli innamorato degli amabilissimi modi del Genti­<lb></lb>luomo, e quanto ai discorsi, con lui tenuti in soggetto matematico, così ne <lb></lb>scriveva il dì 30 dello stesso mese in una lettera a Galileo: “ Ieri poi il <lb></lb>congresso secondo fu lunghissimo, ed avessimo ragionamento di diverse ma­<lb></lb>terie. </s>

<s>Mi raccontò diversi titoli di trattati che ha fra le mani, e in partico­<lb></lb>lare mi disse che trattava delle meccaniche e de&#039;centri di gravità, e che, <lb></lb>dove da&#039;passati scrittori erano considerati i pesi come discendenti paralleli, <lb></lb>che lui li maneggiava come concorrenti nel centro della Terra, come real­<lb></lb>mente sono ” (ivi, pag. </s>

<s>124). </s></p><p type="main">

<s>Prosegue a dire il Castelli a Galileo essergli sembrata quella una sot­<lb></lb>tilissima speculazione, e come ripensandoci sopra fosse rimasto confuso dalla <lb></lb>conseguenza che sarebbe scesa necessariamente da quei principii. </s>

<s>Tanto si <lb></lb>sentì la mente ripiena delle nuove idee che, poco essendo una lettera scritta, <lb></lb>se ne sfogò con l&#039;amico e discepolo suo Antonio Nardi, ne&#039;ragionamenti col <lb></lb>quale espose il teorema del Beaugrand e i corollari ch&#039;egli stesso vedeva ne <lb></lb>sarebbero conseguiti. </s>

<s>Ben conobbe il Nardi che, ammettendosi le direzioni <lb></lb>dei pesi non parallele ma convergenti, mentre s&#039;allargava il campo alla Mec­<lb></lb>canica nuova, veniva ad esser l&#039;antica ne&#039;suoi fondamentali principii modi­<lb></lb>ficata, e pensava come potesse ciò farsi, distendendo così, come si leggono <lb></lb>nella VI Scena accademica, i suoi pensieri. </s></p><p type="main">

<s>“ Nel principio dei superficiali equilibrii suppone Archimede che pesi <lb></lb>eguali da distanze eguali pesino egualmente, ma non così da diseguali. </s>

<s>Di­<lb></lb>mandasi tal principio concedere senz&#039;altra prova, come che il comun giu­<lb></lb>dizio e l&#039;esperienza lo manifesti, almeno nell&#039;equidistanza della Libbra dal <lb></lb>piano orizzontale. </s>

<s>Ma chiunque sapesse che la dimostrazione sua pende im­<lb></lb>mediatamente da un altro più universale principio, che cioè i gravi tendono <pb xlink:href="020/01/1934.jpg" pagenum="177"></pb>al centro loro, saprebbe anco più chiaramente le conclusioni, che da quello <lb></lb>rampollano. </s>

<s>” </s></p><p type="main">

<s>“ I gravi dunque tendere al centro è principio indubitabile per il senso, <lb></lb>ed anco per la ragione, poichè a comporre una naturale sfera o un mon­<lb></lb>dano corpo, qual&#039;è la Terra, par necessario che ad un punto le parti sue <lb></lb>cospirino, e per il contrario vediamo che, mentre disciorre una tal compo­<lb></lb>sizione si deva, tutte le parti del composto dal comun centro di essa com­<lb></lb>posizione si allontanano, come nel fuoco, cioè nelle materie quali perfetta­<lb></lb>mente risolvonsi, appare. </s>

<s>Quando dunque un particolar corpo arda e disciol­<lb></lb>gasi avviene che le parti sue, dal comune loro centro allargandosi, acquistino, <lb></lb>insieme con la rarità, leggerezza, e per trovarsi in un mezzo più di loro <lb></lb><figure id="id.020.01.1934.1.jpg" xlink:href="020/01/1934/1.jpg"></figure></s></p><p type="caption">

<s>Figura 72.<lb></lb>denso sono premute all&#039;insù, onde proprietà del fuoco <lb></lb>giudicasi l&#039;andare in alto, benchè ciò da straniera ca­<lb></lb>gione gli avvenga, poichè il proprio suo è dì disten­<lb></lb>dersi per ogni banda. </s>

<s>Ma forse anco da straniera, oltre <lb></lb>alla propria cagione, avviene il tendere ad un comun cen­<lb></lb>tro le cose gravi, di che per ora non occorre trattare. </s>

<s>” </s></p><p type="main">

<s>“ In quel cambio suppongasi il globo ABC (fig. </s>

<s>72) <lb></lb>rappresentare il Globo terrestre, il cui centro D, e il <lb></lb>diametro AC. </s>

<s>Prendasi fuori del globo qualsivoglia <lb></lb>punto H, onde scenda la perpendicolare HD in AC, e <lb></lb>parallela ad AC intendasi EGI, che in G tagli DH. </s>

<s>Di <lb></lb>nuovo siano EGI le braccia eguali di una Bilancia: il <lb></lb>sostegno sia H, sicchè G sia il centro dei momenti delle braccia, onde in H <lb></lb>si rifletta il peso composto della Bilancia. </s>

<s>” </s></p><p type="main">

<s>“ Basti ora sapere al Meccanico risedere nel punto D o là almeno ten­<lb></lb>dere una virtù, che a sè rapisca la linea EGI, naturale o matematica che <lb></lb>quella fingiamo, di maniera che, se ritenuta ella non fosse, s&#039;unirebbe il <lb></lb>punto suo G col punto D. </s>

<s>E se li punti, che compongono al modo loro EGI, <lb></lb>non fossero fortemente congiunti, ne seguirebbe che ciascuno di loro a di­<lb></lb>rittura si tirasse al centro, di maniera che al punto G toccherebbe il luogo <lb></lb>D, e di mano in mano i più prossimi a G otterrebbero i luoghi più pros­<lb></lb>simi a D intorno a cui s&#039;unirebbero. </s>

<s>” </s></p><p type="main">

<s>“ Immaginiamoci dunque dal punto D partirsi le linee DE, DI, e così <lb></lb>altre di mezzò, infinite, in EG, GI, e saranno eguali e similmente ritire­<lb></lb>ranno i punti E, I verso il centro D, e lo stesso s&#039;intenderà delle altre tutte <lb></lb>in EG, GI, sicchè niuna di esse braccia prevaleria all&#039;altra, poichè scambie­<lb></lb>volmente si rintuzzano i loro momenti. </s>

<s>” </s></p><p type="main">

<s>“ Ma se da EG si tagli la EF, eguale ad FG, avverrà che, essendo FG <lb></lb>minore il doppio di GI e così similmente minori le linee, che dal centro in <lb></lb>lei terminano; cioè essendo il triangolo GDF la metà del triangolo GDI, sarà <lb></lb>ancora il momento di quello minore il doppio del momento di questo, e <lb></lb>perciò l&#039;estremità I sarà tirata nel punto, in sè mobile, G verso il centro, <lb></lb>sino a che arrivi alla linea della direzione HGD, ov&#039;è il più vicin luogo che <pb xlink:href="020/01/1935.jpg" pagenum="178"></pb>possa il punto I ottener verso D, e così per il contrario verrà in alto re­<lb></lb>spinta la FE. ” </s></p><p type="main">

<s>“ Immaginiamoci dunque che la EG sia composta di diseguale spes­<lb></lb>sezza di punti, di maniera che per esempio FG, la quale si pone la metà <lb></lb>di EG, sia il doppio più densa di FE. </s>

<s>Adunque nel caso nostro il doppio <lb></lb>più linee o atti lineari al centro ritireranno FG, che non ritireranno GK, <lb></lb>eguale e contrapposta a FG. </s>

<s>Adunque di nuovo tutto il momento composto <lb></lb>di EDG sarà sesquialtero del momento di GDI, e quindi il punto E si abbas­<lb></lb>serà, e l&#039;altro si alzerà. </s>

<s>Ma perchè il triangolo EDF è eguale all&#039;altro, si­<lb></lb>mile e similmente in GI, qual sia KDI, avverrà che, se tagliamo la parte FE <lb></lb>e resti FG, si compensino i momenti, perchè EF pesa una parte di quelle <lb></lb>di che GI o EG è due. </s>

<s>Perciò, quando sia come la distanza GI alla distanza <lb></lb>GF, così il momento GE al momento GI, si farà l&#039;equilibrio. </s>

<s>E perchè, come <lb></lb>la distanza GI alla distanza GF, così puossi fare in infinito una distanza GI <lb></lb>ad un&#039;altra in GF; quindi, se dalle suddette distanze pendano come da fon­<lb></lb>damento simili pesi, o se in esse si sospendano similmente gli stessi trian­<lb></lb>goli FDE, IDG resteranno come prima compensati i momenti, poichè i <lb></lb>pesi reciprochi informano le distanze proporzionalmente. </s>

<s>” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XX, pag. </s>

<s>853-56). </s></p><p type="main">

<s>Come tutte le sue speculazioni così anche questa il Nardi comunicò al <lb></lb>Torricelli, il quale ebbe a concluderne che “ quando noi ammettiamo che <lb></lb>i pesi nella Libbra abbiano inclinazione verso il centro della Terra, siccome <lb></lb>naturalmente l&#039;hanno, e non che le linee di detta inclinazione ne&#039;pesi siano <lb></lb>parallele fra loro, secondo che comunemente si suppone; ne seguirà che non <lb></lb>ci sia Libbra orizzontale con braccia disuguali, e con pesi con reciproca pro­<lb></lb>porzione della lunghezza delle braccia, sicchè detti pesi facciano equilibrio ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XL, c. </s>

<s>112 a t.) </s></p><p type="main">

<s>Dimostra il Torricelli questa sua proposizione in due maniere, la prima <lb></lb>delle quali consiste nel provare l&#039;impossibilità del supposto che la Libbra <lb></lb><figure id="id.020.01.1935.1.jpg" xlink:href="020/01/1935/1.jpg"></figure></s></p><p type="caption">

<s>Figura 73.<lb></lb>stia orizzontale, “ imperocchè sia, egli dice, pri­<lb></lb>mieramente la Libbra AB (fig. </s>

<s>73) ed in essa i <lb></lb>punti A e B siano egualmente distanti dal centro <lb></lb>della Terra E, al quale inclinano secondo le rette <lb></lb>AE, BE. </s>

<s>Facciasi BC a CA reciprocamente come <lb></lb>il peso A al peso B, i quali pesi come ancora le <lb></lb>braccia della Libbra si suppongono disuguali fra <lb></lb>di loro ed il centro della Libbra sarà C. Dopo, si <lb></lb>congiunga la ECD, la quale non può essere per­<lb></lb>pendicolare alla Libbra AB, perchè il triangolo <lb></lb>isoscele AEB, sega la base AB in parti disuguali. </s>

<s><lb></lb>Adunque posto che CD rappresenti la trutina, con <lb></lb>la quale si sospende la Libbra dal suo centro, detta trutina deve direttamente <lb></lb>guardare il centro della Terra E e non sarà la trutina perpendicolare alla <lb></lb>Libbra, e in conseguenza la Libbra non è orizzontale. </s>

<s>Il che ecc. </s>

<s>” (ivi, c. </s>

<s>113). </s></p><pb xlink:href="020/01/1936.jpg" pagenum="179"></pb><p type="main">

<s>Passando alla seconda maniera abbiasi la medesima Libbra AB (fig. </s>

<s>74) <lb></lb>con pesi di differente gravità reciprocamente proporzionali alle braccia AC, <lb></lb><figure id="id.020.01.1936.1.jpg" xlink:href="020/01/1936/1.jpg"></figure></s></p><p type="caption">

<s>Figura 74.<lb></lb>BC, e l&#039;uno posto a una distanza BE dal cen­<lb></lb>tro della Terra e l&#039;altro a una distanza AE <lb></lb>minore. </s></p><p type="main">

<s>“ Dal centro C della Libbra si tirino, <lb></lb>dice il Torricelli, le perpendicolari CF, CG alle <lb></lb>linee delle inclinazioni dei pesi al centro della <lb></lb>Terra, e si tagli BH eguale ad AE, e si giun­<lb></lb>gano le CE, CH. </s>

<s>Averà il triangolo CEB al <lb></lb>triangolo CEA, cioè la base BC alla base CA, <lb></lb>maggior proporzione che il triangolo CHB al medesimo triangolo CEA, cioè <lb></lb>l&#039;altezza CG all&#039;altezza FG. ” </s></p><p type="main">

<s>“ Si supponga inoltre un peso in B eguale al peso in A, e sarà il mo­<lb></lb>mento del peso maggiore in B al momento del peso minore, pure in B, <lb></lb>come la mole alla mole, cioè come la mole del peso in A alla mole del peso <lb></lb>minore in B, ovvero come BC a CA, per la costruzione. </s>

<s>Ma il momento del <lb></lb>medesimo peso maggiore in B al momento del suo eguale in A è come la <lb></lb>perpendicolare CG alla perpendicolare CF, per le cose dichiarate da Giovan <lb></lb>Batista de&#039;Benedetti nelle sue <emph type="italics"></emph>Speculazioni matematiche,<emph.end type="italics"></emph.end> al trattato della <lb></lb>Meccanica al Cap. </s>

<s>III, ovvero IV; adunque ha maggior proporzione il mo­<lb></lb>mento del peso maggiore in B al momento del peso minore in B, che il <lb></lb>medesimo momento del peso maggiore in B al momento del peso in A, e <lb></lb>per conseguenza il momento del peso minore in B e il momento del peso <lb></lb>in A non sono eguali e non fanno equilibrio, ma è maggiore il momento <lb></lb>del peso in A e però si muterà la Libbra, il che si doveva provare. </s>

<s>Onde <lb></lb>resta provato che non ci sia Libbra di braccia ineguali, la quale stia oriz­<lb></lb>zontalmente in equilibrio con i pesi, che abbiano reciproca proporzione con <lb></lb>le braccia della medesima Libbra ” (ivi, c. </s>

<s>113 a t.). </s></p><p type="main">

<s>Queste meccaniche proposizioni son parti di un trattatello, che il Tor­<lb></lb>ricelli stesso preparava per risolvere finalmente un problema antico, e in­<lb></lb>torno a cui gli Autori, nel secolo XVI, avevano così lungamente e senza <lb></lb>nulla concluderne disputato: il problema delle condizioni dell&#039;equilibrio nelle <lb></lb>Bilance o nella Libbra di braccia eguali. </s>

<s>Alla questione, promossa già da <lb></lb>Aristotile, presero fervorosa parte il Cardano, il Tartaglia e il Del Monte, <lb></lb>che le parteciparono perciò la celebrità del loro nome, ond&#039;è che, tra per <lb></lb>questo e tra per la pratica importanza dello strumento così spesso invocato <lb></lb>a geloso giudice del valor delle merci più preziose, non si vuol passar in <lb></lb>silenzio nella Storia degli equiponderanti. </s>

<s>Ma perchè la matematica soluzion <lb></lb>del problema dipende in gran parte dalla teoria de&#039;momenti, e dal più giu­<lb></lb>sto modo di computarli, faremo di una tal teoria e delle applicazioni di lei <lb></lb>a dimostrar la legge delle equiponderanze primo soggetto alla seguente parte <lb></lb>del nostro discorso. </s></p><pb xlink:href="020/01/1937.jpg" pagenum="180"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Fu notato altrove da noi che la parola <emph type="italics"></emph>momento<emph.end type="italics"></emph.end> s&#039;introdusse nel lin­<lb></lb>guaggio meccanico dal Maurolico, consacrandola a significar propriamente <lb></lb>lo sforzo di un peso <emph type="italics"></emph>a spatio quopiam contra pendentis.<emph.end type="italics"></emph.end> Si dee al Mate­<lb></lb>matico messinese altresì la prima dimostrazione, condotta sui principii archi­<lb></lb>medei, che cioè stanno i momenti in ragion composta delle distanze e dei <lb></lb>pesi. </s>

<s>Se la ragion del primato però vuol concedersi quanto al linguaggio, <lb></lb>non sarebbe da far lo stesso quanto all&#039;assoluta sostanza della cosa signi­<lb></lb>ficata, perchè il Nemorario, illustrando la Meccanica aristotelica, aveva già <lb></lb>insegnato a computar quelli che si chiamaron momenti nei gravi posati so­<lb></lb>pra i loro sostegni, contro i quali fanno, secondo il sito, maggiore o mi­<lb></lb>nore lo sforzo computabile dal prodotto della mole per la quantità del <lb></lb>discenso. </s></p><p type="main">

<s>Nell&#039;uno e nell&#039;altro metodo il computo in conclusione torna allo stesso, <lb></lb>ma in quello proseguito dal Nemorario si venivano a cansar certi difficili <lb></lb>incontri, i quali dal Maurolico o non preveduti o non affrontati, condussero <lb></lb>a naufragar tanti, che s&#039;erano volentieri voluti imbarcar con lui. </s>

<s>Volendo <lb></lb>il diligente Raccoglitore de&#039;Monumenti archimedei definir com&#039;abbiasi a in­<lb></lb>tendere l&#039;equiponderar de&#039;pesi dai loro sostegni nel compararne insieme i <lb></lb>momenti; “ gravia vero, egli dice, aeque pendere, sive aeque ponderare, <lb></lb>dicuntur cum ab aliquo puncto appensa ita pendent, ut recta, quae gravi­<lb></lb>tatum centra vel appensionum puncta coniungit, horizonti aequidistet. </s>

<s>” <lb></lb>(Monum. </s>

<s>archim. </s>

<s>cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Qui però si riguarda la leva nel caso più comune e particolare, in cui <lb></lb>le due braccia di lei sieno disposte in linea retta, e le direzioni de&#039;pesi o <lb></lb>delle forze sieno ad esse braccia perpendicolari. </s>

<s>Ma poniamo che le dette <lb></lb>braccia sian curve o che facciano angolo fra loro: poniamo che, pur essendo <lb></lb>rette, non sia alla loro rettitudine la direzione delle forze ortogonale: come <lb></lb>si deve computare il momento in questi casi possibili e naturali, e in cui <lb></lb>viene a mancar la regola insegnata dell&#039;equidistanza dall&#039;orizzonte della li­<lb></lb>nea, che congiunge i centri di gravità de&#039;pesi o i punti delle loro sospen­<lb></lb>sioni? </s>

<s>Il Maurolico non sa risolvere dalla mente i dubbi penosi, e perciò <lb></lb>giova narrar da chi e come si diffondesse la benefica luce sopra questi incerti <lb></lb>segnati sentieri. </s></p><p type="main">

<s>Facendo per maggior chiarezza distinto questo passo storico in due parti, <lb></lb>secondo che l&#039;anomalia si riguarda nella leva o nella direzione della forza <lb></lb>applicata, e incominciando dalla prima, diciamo che al difetto del Maurolico <lb></lb>avrebbero ben saputo supplire i contemporanei o i predecessori che s&#039;eser­<lb></lb>citarono in quel medesimo studio. </s>

<s>Leonardo da Vinci, che oramai è uno dei <lb></lb>più conoscìutì, sì propone a risolvere l&#039;importante qucsito nel vario sforzo <pb xlink:href="020/01/1938.jpg" pagenum="181"></pb>che fa, per mover la ruota, un medesimo peso attaccato in varii punti della <lb></lb>circonferenza, e dice ch&#039;essendo il detto peso ora attaccato per esempio <lb></lb><figure id="id.020.01.1938.1.jpg" xlink:href="020/01/1938/1.jpg"></figure></s></p><p type="caption">

<s>Figura 75.<lb></lb>in A (fig. </s>

<s>75), ora in B, condotte le perpendicolari <lb></lb>AC, BD sopra la orizzontale ZQ, lo sforzo o il mo­<lb></lb>mento del peso in A sta allo sforzo o al momento <lb></lb>del medesimo peso in B, come OC sta ad OD, ciò <lb></lb>che nel potente linguaggio popolare del Nostro è <lb></lb>così espresso: “ La ruota essendo co&#039;sua estremi <lb></lb>egualmente distante al suo centro, tutti i pesi posti <lb></lb>nella sua circonferenza faranno tale forza in essa, <lb></lb>quale farebbero simili pesi posti sotto loro perpendi­<lb></lb>colare sopra la linea della egualità QZ ” (Ravaisson-Mollien, Manuscr. </s>

<s>N.02038 <lb></lb>ital., Paris 1891, fol. </s>

<s>2 t.). </s></p><p type="main">

<s>Che il bel teorema non si rimanesse nella scienza di Leonardo chiuso <lb></lb>e infecondo, ma che ne&#039;contemporanei e ne&#039;successori immediati fosse dif­<lb></lb>fuso, ce lo attesta il Cardano, il quale nel suo I libro <emph type="italics"></emph>De subtilitate<emph.end type="italics"></emph.end> segue <lb></lb>la medesima regola per computar, ne&#039;varii punti della circonferenza, il mo­<lb></lb><figure id="id.020.01.1938.2.jpg" xlink:href="020/01/1938/2.jpg"></figure></s></p><p type="caption">

<s>Figura 76.<lb></lb>mento vario di un peso, che si supponga at­<lb></lb>taccato a un raggio circonvolubile al centro. </s>

<s><lb></lb>Sia questo centro B (fig. </s>

<s>76) e si supponga il <lb></lb>peso ora collocato in C, ora in F, dai quali due <lb></lb>punti sien condotte le CB, FP perpendicolari <lb></lb>alla linea della direzione, ossia alla verticale <lb></lb><expan abbr="Aq.">Aque</expan> Ne conclude il Cardano che il momento <lb></lb>del peso in C è tanto maggiore del momento <lb></lb>del medesimo peso in F, quanto CB è mag­<lb></lb>giore distanza di FP. “ Manifestum est in sta­<lb></lb>teris, et in his qui pondera elevant, quod <lb></lb>quanto magis pondus a trutina eo magis grave <lb></lb>videtur. </s>

<s>Sed pondus in C distat a trutina quan­<lb></lb>titate BC lineae, et in F quantitate FP. </s>

<s>Sed CB est maior FP ex XVa tertii <lb></lb>Elementorum Euclidis, igitur, lance posita in C, gravius pondus videbitur <lb></lb>quam in F ” (Operum T. III, Lugduni 1663, pag. </s>

<s>370). </s></p><p type="main">

<s>È questo il metodo, che si tiene ancora per computare i momenti, de­<lb></lb>rivato da Aristotile secondo gli ordini archimedei. </s>

<s>Ma il Cardano v&#039;aggiunse <lb></lb>l&#039;altra dimostrazione secondo il metodo del Nemorario, concludendo essere <lb></lb>in C il corpo più pesante che in F, perchè in egual tempo quello si muove <lb></lb>al centro per maggiore spazio di questo. </s>

<s>“ Ut autem cognoscamus quod C <lb></lb>sit gravius in eo situ quam in F, necessarium est ut in aequali tempore <lb></lb>moveatur per maius spatium versus centrum ” (ibid.). </s></p><p type="main">

<s>Prende per la dimostrazione il Cardano due archi FG, CE eguali, e con­<lb></lb>dotte le GO, EM perpendicolari ad AQ, e le FL, CS perpondicolari a GO, <lb></lb>SM, per gli Elementi geometrici ne conclude essere, CS ossia BM, mag­<lb></lb>giore di FL, ossia di OP. “ Dum igitur Libra movetur ex C in E pondus <pb xlink:href="020/01/1939.jpg" pagenum="182"></pb>descendit per BM lineam, seu proprinquus centro redditur quam esset in C. </s>

<s><lb></lb>Et dum movetur per spatium arcus FG descenditque per OP et BM maior <lb></lb>est OP. Igitur, supposito etiam quod in aequali tempore transiret ex C in <lb></lb>E et ex F in G, adhuc velocius descendit ex C quam ex F. </s>

<s>Igitur gravius <lb></lb>est in C quam in F ” (ibid.). </s></p><p type="main">

<s>Furono questi teoremi, così dal Cardano come e dal Tartaglia, dimo­<lb></lb>strati per servirsene a risolvere la questione delle Bilance, e in proposito <lb></lb>pure di tal questione si presero ad esaminar da Guidubaldo Del Monte, il <lb></lb>quale ebbe a notarli di errore. </s>

<s>Non mi posso persuadere, diceva, che la ra­<lb></lb>gion vera dell&#039;essere il grave in C (nella sopra apposta figura LXXVI) più <lb></lb>peso che in F, consista nell&#039;esser CB maggiore di FP “ cum potius signum, <lb></lb>quam vera causa esse videatur ” (Mechanicorum liber, Pisauri 1577, fol. </s>

<s>9 t.). <lb></lb>Gli faceva anche ombra quel leggere nel Cardano la dimostrazione condotta <lb></lb>col principio de&#039;<emph type="italics"></emph>momenti virtuali,<emph.end type="italics"></emph.end> considerandovisi il peso che fa il suo <lb></lb>sforzo in C, e in F “ non quatenus est in C, et in F, sed quatenus a <lb></lb>punctis C, F recedit ” (ibid.). Negava assolutamente poi che il massimo <lb></lb>peso s&#039;acquisti dal corpo quand&#039;è attaccato sulla circonferenza all&#039;estremità <lb></lb>del semidiametro orizzontale: “ ostendam falsum esse pondus in C gravius <lb></lb>esse quam in alio situ ” (ibid.). </s></p><p type="main">

<s>Dimostrava Guidubaldo non essere quel punto C, ma un altro che fosse <lb></lb>al centro B più vicino, d&#039;onde veniva a concluderne la falsità della regola <lb></lb>del Cardano. </s>

<s>Si faceva tutta l&#039;efficacia della dimostrazione dipendere dal ri­<lb></lb>guardar le direzioni de&#039;pesi come convergenti al centro della Terra, e non <lb></lb>come parallele: perchè in fatti se sia in T il detto centro, da cui si con­<lb></lb>duca CT, questa come obliqua tirerà meno della perpendicolare TV e per­<lb></lb>ciò in V, avrà il grave maggior momento che in C, benchè la distanza da <lb></lb>AQ sia minore a quel punto che a questo. </s></p><p type="main">

<s>Conseguiva di qui non essere nel secondo de&#039;due sopra commemorati <lb></lb>teoremi del Cardano le due linee FL, CS alle PO, BM parallele, per cui, <lb></lb>ciò negando, veniva a rovinare tutta quella cardanica dimostrazione, alle <lb></lb>mani di coloro che la tenevan per vera “ nisi fortasse dixerint haec, omnia, <lb></lb>propter maximam a centro mundi usque ad nos distantiam, adeo insensi­<lb></lb>bilem esse, ut propter insensibilitatem tanquam vera supponi possint ” (ibid., <lb></lb>fol. </s>

<s>15 t.). </s></p><p type="main">

<s>La diritta logica del ragionamento avrebbe dovuto dunque condurre <lb></lb>alla conclusione che i teoremi del Cardano son solamente veri nel suppo­<lb></lb>sto che le direzioni dei pesi, per la gran lontananza dal centro della Terra, <lb></lb>sieno sensibilmente parallele, ma Guidubaldo vuol pronunziarne della fal­<lb></lb>sità sentenza assoluta, non rimovendosi dal suo giudizio, nemmen quando <lb></lb>egli si vede scorto da quegli stessi reputati falsi principii alla desiderata <lb></lb>conquista del vero. </s>

<s>“ Ex ipsorum quin etiam rationibus ac falsis supposi­<lb></lb>tionibus iam declaratos Librae effectus ac motus deducere ac manifestare <lb></lb>libet, ut quanta sit veritatis efficacia appareat, quippe ex falsis etiam elu­<lb></lb>cescere contendit ” (ibid., fol. </s>

<s>25 t.). Che nella Bilancia di braccia eguali <pb xlink:href="020/01/1940.jpg" pagenum="183"></pb>e col punto di sospensione al di sopra, rimossa dall&#039;orizzonte, il lato più <lb></lb>alto abbia maggior momento lo prova anche Guidubaldo, applicandovi i teo­<lb></lb>remi del Cardano, dall&#039;esser maggiore la distanza del centro, e maggiore <lb></lb>la quantità del discenso, ma invece di argomentar di qui, secondo la buona <lb></lb>Logica che non potevano non esser veri que&#039;repudiati teoremi, dice esser <lb></lb>tanta della verità l&#039;efficacia ch&#039;ella risplende anche in mezzo all&#039;errore. </s></p><p type="main">

<s>Quella logica, che nel libro <emph type="italics"></emph>Mechanicorum,<emph.end type="italics"></emph.end> così ragionando l&#039;Autore, <lb></lb>a giudizio di tutti i savii faceva difetto, s&#039;instaurò nella scienza dal Bene­<lb></lb>detti, il quale dette autorità ai teoremi del Cardano e di Leonardo da Vinci, <lb></lb>dimostrando nel capitolo I della sua Meccanira, dal supposto comunemente <lb></lb>approvato delle forze parallele, che “ omne pondus positum in extremitate <lb></lb>alicuius braehii Librae maiorem aut minorem gravitatem habet, pro diversa <lb></lb>ratione situs ipsius brachii ” (Speculationum lib. </s>

<s>cit., pag. </s>

<s>111); cosicchè, <lb></lb>come passa a dimostrar nel capitolo II, la proporzione del peso, in Q (nella <lb></lb>precedente figura LXXV) al medesimo peso in B “ erit quemadmodum to­<lb></lb>tius brachii OQ ad partem OD ” (ibid., pag. </s>

<s>142). Di qui ne conclude la <lb></lb>regola, che conferma la già insegnata da Leonardo, esser cioè la perpendi­<lb></lb>colare, condotta dal centro sulla direzione del peso, quella “ quae nos du­<lb></lb>cit in cognitionem quantitatis virtutis illius ” (ibid., pag. </s>

<s>143). </s></p><p type="main">

<s>La regola di computare i momenti, quando i centri di gravità dei pesi <lb></lb>o i loro punti di sospensione non si ritrovano sopra la medesima linea oriz­<lb></lb>zontale, veniva così insegnata dal Benedetti con matematica certezza, e po­<lb></lb>niamo che non fosse in verità l&#039;insegnamento affatto nuovo, conferì nono­<lb></lb>stante a confermar quello, che avevano detto alcuni suoi predecessori. </s>

<s>Nessuno <lb></lb>però, che si sappia, aveva risposto ancora a quell&#039;altro quesito: come sia, <lb></lb><figure id="id.020.01.1940.1.jpg" xlink:href="020/01/1940/1.jpg"></figure></s></p><p type="caption">

<s>Figura 77.<lb></lb>cioè, da computare il momento, <lb></lb>quando le forze non agiscono <lb></lb>in direzione perpendicolare ma <lb></lb>obliqua, come per esempio AC <lb></lb>(fig. </s>

<s>77), che s&#039;intenda applicata <lb></lb>all&#039;estremo braccio OA di una <lb></lb>Libbra. </s>

<s>Ricorrendo al principio <lb></lb>dei moti composti riesce facilis­<lb></lb>sima la risoluzione del propo­<lb></lb>sto problema, perchè, presa la <lb></lb>linea AC per la misura di tutta intera la detta forza, e costruito sopr&#039;essa <lb></lb>linea il rettangolo AECD, il lato AE sta per la più giusta misura della virtù <lb></lb>che rimane. </s></p><p type="main">

<s>Quando però quel modo di risolvere un moto in due non era fra&#039;Mec­<lb></lb>canici in uso, il determinar con matematica certezza quanto, dal tirare obli­<lb></lb>quo, rimetta del suo intero valore una forza, era problema superiore all&#039;arte <lb></lb>di un comunale geometra, e nonostante quel Benedetti, che aveva insegnato <lb></lb>a computar le distanze, qualunque fosse il punto della sospensione, insegna <lb></lb>ora a conputar, dovunque ella sia diretta, la intensità che rimane alla forza, <pb xlink:href="020/01/1941.jpg" pagenum="184"></pb>e dice “ debere deprehendi a perpendicularibus, quae a centro Librae ad <lb></lb>lineas inclinationis exiliunt ” (ibid.). </s></p><p type="main">

<s>Secondo una tal regola dunque, prolungata la AC, e da O condotta al <lb></lb>OH perpendicolare sopra questo prolungamento, se con AO si rappresenta <lb></lb>tutto il valor della forza, OH è la misura giusta di quel che in lei rimane <lb></lb>di attivo, ciò che fa esatto riscontro con la regola desunta dalla risoluzione <lb></lb>del moto, essendo che i triangoli simili AEC, OHA danno AC:AE=OA:OH. </s></p><p type="main">

<s>Nella instaurazion della scienza, felicemente avvenuta sui principii del <lb></lb>secolo XVII, si trovarono dunque fra gl&#039;insegnamenti del Benedetti le re­<lb></lb>gole più sicure per computare i momenti, e veniva, così, a rendersi possi­<lb></lb>bile il promovere o il correggere i falli de&#039;teoremi più antichi. </s>

<s>Il Cartesio <lb></lb>per verità, preferendo di misurar gli spazii nella quantità delle discese ver­<lb></lb>ticali, a modo del Nemorario e del Tartaglia, piuttosto che considerare i <lb></lb>moti più o men veloci negli archi dei cerchi; non sentì nè il bisogno nè <lb></lb>l&#039;utilità delle regole insegnate dal Matematico nostro veneziano, ma Gali­<lb></lb>leo ne ricavò gran profitto, e deve alla loro sapiente applicazione se la sua <lb></lb>Scienza meccanica s&#039;avvantaggia da molte parti sopra quella di Guidubaldo. </s></p><p type="main">

<s>Il fondamento a quella Scienza meccanica, com&#039;apparisce da ciò che se <lb></lb>n&#039;è detto addietro a varie occasioni, è posto da Galileo nella teoria dei mo­<lb></lb>menti, ch&#039;egli, quasi con le medesime parole del Maurolico, definisce “ quel­<lb></lb>l&#039;impeto di andare al basso, composto di gravità, posizione o altro, dal che <lb></lb>possa essere tal propensione cagionata ” (Alb. </s>

<s>XI, 90). Mentre però il Mau­<lb></lb>rolico non aveva considerato quella posizione, se non che nel caso più co­<lb></lb>mune e particolare de&#039;centri di gravità o delle sospensioni in una medesima <lb></lb>linea orizzontale, Galileo contempla anche il caso che quegli stessi centri si <lb></lb>trovino a varie altezze, per essere le braccia della Bilancia o incurve o an­<lb></lb>golari, e rammemora perciò la Regola del Benedetti ai lettori, avvertendoli <lb></lb>“ come le distanze si devono misurare con linee perpendicolari, le quali dal <lb></lb>punto della sospensione caschino sopra le rette, che dai centri della gravità <lb></lb>de&#039;pesi si tirano al centro comune delle cose gravi ” (ivi, pag. </s>

<s>91). </s></p><p type="main">

<s>Il fondamento statico scelto da Galileo era senza dubbio d&#039;assai più ge­<lb></lb>nerale applicazione di quell&#039;altro, volutosi preferir dal Cartesio, ma riusciva <lb></lb>all&#039;intelligenza alquanto più duro, essendo più facilmente disposta a conce­<lb></lb>der che un corpo tanto maggior momento acquisti quanto più scende, di <lb></lb>quel che non sia a conceder che un simile corpo, tanto acquisti maggior gra­<lb></lb>vità quanto più si dilunga dal centro della sua sospensione. </s>

<s>Vedemmo gli <lb></lb>sforzi che, incominciando da Aristotile, fecero per rivelare il mistero i Ma­<lb></lb>tematici antichi, e i Moderni pure avrebbero desiderato che Galileo avesse <lb></lb>fatto lo stesso. </s>

<s>La questione è vero era più filosofica che matematica, ma <lb></lb>perchè sentivasi che, se non utile, adornare la scienza di così fatte specu­<lb></lb>lazioni sarebbe stato almen bello; qualcuno della Scuola galileiana si provò, <lb></lb>non diciam di supplire al difetto, ma di esplicare in altra forma e di ri­<lb></lb>durre più direttamente alla Statica alcuni concetti del Maestro. </s></p><p type="main">

<s>Noi vogliamo rammemorare ai Lettori in tal proposito i pensieri di An-<pb xlink:href="020/01/1942.jpg" pagenum="185"></pb>tonio Nardi, il quale, dopo aver, nel passo poco addietro, addotto, insegnato <lb></lb>a computare i momenti dal composto di tutte insieme le linee radiose di <lb></lb>forza appuntate da una parte nel centro terrestre, e dall&#039;altra in tutte le <lb></lb>particelle materiali della Bilancia; e dop&#039;avere osservato che, inclinandosi <lb></lb>essa Bilancia, vanno i momenti di lei dall&#039;infinito a terminare nel zero, sog­<lb></lb>giunge quanto appresso: </s></p><p type="main">

<s>“ Poichè, sebbene il peso è lo stesso, la forza nondimeno è divisa, onde <lb></lb>stanno insieme il pesar più e il forzar meno, e per il contrario ancora. </s>

<s>Di <lb></lb>più, se alcuno prenda qualche bacchetta, e in un ginocchio piegar la voglia, <lb></lb>proverà diverso effetto se verso il mezzo o se verso un estremo la forzi, <lb></lb>poichè in questo caso meno piegherà con egual virtù la più corta, che la <lb></lb>più lunga parte di essa bacchetta. </s>

<s>Quindi raccor devesi che, facendosi la <lb></lb>forza secondo la profondità di essa bacchetta, più resiste la stessa profon­<lb></lb>dità all&#039;impeto, quale informa la minore, che a quello che informa la mag­<lb></lb>gior lunghezza, poichè maggiore ragione ha a quella che a questa. </s>

<s>Quindi <lb></lb>è palese che l&#039;atto e l&#039;impeto, siccome corpo non è, così occupa senza te­<lb></lb>ner luogo tutto un corpo, e si moltiplica in esso così, che maggiore è nel <lb></lb>maggiore che nel minor soggetto, quando però uguale la sua cagione si <lb></lb>fosse. </s>

<s>E se un soggetto fosse privo d&#039;ogni momento ed atto più si move­<lb></lb>rebbe da uguale impeto, mentre grande, che mentre piccolo il soggetto fosse, <lb></lb>il che un paradosso parrebbe, se l&#039;esperienza non l&#039;approvasse, anco nelle <lb></lb>cose che straniero momento ottengono. </s>

<s>” </s></p><p type="main">

<s>“ Di già è noto che con la stessa forza più lontano lanciamo una me­<lb></lb>diocre palla di sasso, che una galla o un grano di arena. </s>

<s>Dicono alcuni che <lb></lb>la galla e il grano di arena non ponno romper l&#039;aria, ma questa è sempli­<lb></lb>cità, poichè per il solo romper l&#039;aria si deve attendere la solidità del corpo, <lb></lb>qual&#039;è la galla o il grano di arena, e se questi corpi non romponla, viene, <lb></lb>non per difetto della solidità loro, ma per incapacità di ricever l&#039;impeto, <lb></lb>nata o per la piccolezza o per la rarità, che alla piccolezza riducesi, del sog­<lb></lb>getto, a che concorre l&#039;aria, per quella parte che risguarda il più o meno <lb></lb>veloce rompersi, e massime dai minimi leggeri e cadenti corpi. </s>

<s>” </s></p><p type="main">

<s>“ Quest&#039;altra esperienza anco mirabilmente conferma il parer nostro, <lb></lb>poichè di due travi disuguali di lunghezza, ma uguali in grossezza, mentre <lb></lb>galleggiano placidamente nell&#039;acqua, si spingerà e si tirerà più validamente <lb></lb>la più lunga da forze eguali e parallele al piano dell&#039;orizzonte, che non si <lb></lb>farà la più corta. </s>

<s>Ma in aria, non così sempre avverrà, poichè il momento <lb></lb>dalle cose intorno al centro impressoli non è più pareggiato dall&#039;ambiente, <lb></lb>onde talvolta accaderà che la forza straniera impressali sia molto minore <lb></lb>della gravità sua. </s>

<s>Ma se due forze eccedano due diseguali solidi, e non <lb></lb>affetti da altro sensibil momento, farassi proporzionalmente maggiore effetto <lb></lb>nel maggiore, il che vedesi nelle bombarde e negli schioppi. </s>

<s>” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XX, pag. </s>

<s>857, 58). </s></p><p type="main">

<s>Illustrare, così come faceva il Nardi, la teoria de&#039;momenti nell&#039;astruso <lb></lb>concetto delle forze incorporee, che misteriosamente si moltiplicano a pro-<pb xlink:href="020/01/1943.jpg" pagenum="186"></pb>porzione della quantità della materia, era non bello solo, ma necessario, spe­<lb></lb>cialmente a que&#039;tempi, ne&#039;quali si voleva stabilir la scienza sopra più fermi <lb></lb>principii, e infonderle un vigor nuovo di vita. </s>

<s>Il fondamonto naturale però <lb></lb>era da ritrovar nella Matematica, ma benchè avesso Galileo trattato co&#039;mo­<lb></lb>menti molta parte della Scienza meccanica, misurandoli dal prodotto del peso <lb></lb>per la distanza, la matematica dimostrazione nulladimeno di questo fonda­<lb></lb>mental teorema, fecondissimo di tanti corollarii, era quella che, ne&#039;primi <lb></lb>decennii del secolo XVII, quando ancora non era nemmen conosciuto il trat­<lb></lb>tato del Maurolico, più vivamente da tutti si desiderava. </s></p><p type="main">

<s>Alla fine del terzo di quei decennii quel che di Meccanica aveva pub­<lb></lb>blicamente insegnato Galileo si riduceva ne&#039;dialoghi Dei due massimi Si­<lb></lb>stemi, nel secondo dei quali, avendo asserito il Salviati che due momenti <lb></lb>si eguagliano allora insieme quando si eguagliano i prodotti delle velocità <lb></lb>per i pesi, il Sagredo così gli domanda: “ Ma credete voi che la velocità <lb></lb>ristori per l&#039;appunto la gravità? </s>

<s>cioè che tanto sia il momento e la forza <lb></lb>di un mobile v. </s>

<s>g. </s>

<s>di quattro libbre di peso, quanto quella di un di cento, <lb></lb>qualunque volte quello avesse cento gradi di velocità, e questo quattro gradi <lb></lb>solamente? </s>

<s>” (Alb. </s>

<s>I, 237). Il che voleva dire in altre parole: credete voi <lb></lb>che i momenti stiano veramente in ragion composta delle velocità e dei pesi? </s>

<s><lb></lb>A che risponde il Salviati: “ Certo sì, come io vi potrei con molte espe­<lb></lb>rienze provare ” (ivi), fra le quali molte esperienze sceglie quella notissima <lb></lb>della stadera, nella quale veramente si vede che la maggior velocità del pic­<lb></lb>colo romano compensa il legger moto della gravissima balla. </s></p><p type="main">

<s>Ma questo era insomma un rendere più ardente la sete, che già ne <lb></lb>aveva accesa Archimede, a cui, domandandosi perchè due pesi eguali equi­<lb></lb>ponderino da due eguali distanze, rispondeva con più ragione di Galilao, ri­<lb></lb>mandando i curiosi alla disciplina delle esperienze volgari. </s>

<s>Il progresso di <lb></lb>tanti secoli esigeva con più diritto matematiche dimostrazioni, e giacchè lo <lb></lb>stesso Galileo non aveva corrisposto al comun desiderio, pensò di supplirvi <lb></lb>opportunamente uno de&#039;suoi primi discepoli, Niccolò Aggiunti. </s>

<s>Egli, precor­<lb></lb>rendo di quasi un mezzo secolo al Mariotte ed altri Matematici, avea tentato <lb></lb>una più generale dimostrazione delle leggi dei momenti, riducendoli così a <lb></lb>quella che, in qualunque condizion del mobile, o stabilmente sospeso o libe­<lb></lb>ramente mosso, ebbe proprio nome di <emph type="italics"></emph>quantità di moto.<emph.end type="italics"></emph.end> Abbiamo detto che <lb></lb>tentò di fare quel che certamente avrebbe messo ad effetto, se così giovane non <lb></lb>l&#039;avesse alla scienza rapito la morte. </s>

<s>Ma quel che in ogni modo può respi­<lb></lb>golarsi dalle informi carte lasciate da lui, in quella parte che fu senza dubbio <lb></lb>scritta fra l&#039;anno 1632 e il 1635, basta per farci argomentare a qual maggior <lb></lb>grado di perfezione sarebbe giunta la scienza del moto infino da&#039;suoi principii, <lb></lb>se la Fisica di Galileo avesse avuto il conforto della Geometria dell&#039;Aggiunti. </s></p><p type="main">

<s>Il valoroso giovane precursore del Mariotte e del Borelli, nelle sparse <lb></lb>pagine del suo trattato, primaticcio frutto di quella, che poi si chiamò da <lb></lb>Galileo Scienza nuova, incominciò dal definire i modi e le sperimentate leggi, <lb></lb>secondo le quali i corpi in moto operano la percossa. </s></p><pb xlink:href="020/01/1944.jpg" pagenum="187"></pb><p type="main">

<s>“ La percossa del grave, egli dice, che discendendo percote l&#039;addiman­<lb></lb>deremo <emph type="italics"></emph>percossa naturale. </s>

<s>Percossa violenta<emph.end type="italics"></emph.end> intenderemo quella del grave, <lb></lb>che ascendendo percote. <emph type="italics"></emph>Percossa media<emph.end type="italics"></emph.end> diremo quella del grave, che mo­<lb></lb>vendosi orizzontalmente percote. <emph type="italics"></emph>Percossa composta<emph.end type="italics"></emph.end> diremo quella di quel <lb></lb>grave, il cui moto naturale è accelerato da motore estrinseco, e con tal moto <lb></lb>accelerato percota. </s>

<s>” </s></p><p type="main">

<s>“ La percossa opera con la velocità e con la copia della materia, in <lb></lb>cui s&#039;imprime detta velocità, e però se caderanno dalla medesima altezza <lb></lb>due gravi disuguali dell&#039;istessa materia, come due palle di ferro disuguali, <lb></lb>le loro percosse saranno disuguali, e maggiore sarà la percossa della mag­<lb></lb>gior palla, benchè ambedue discendano con la medesima velocità ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>95). </s></p><p type="main">

<s>Ora questo, che sembrava essere approvato dall&#039;esperienza, si voleva <lb></lb>dall&#039;Aggiunti confermare con la teoria, dimostrando che i momenti, o più <lb></lb>in generale le quantità di moto, son matematicamente proporzionali al pro­<lb></lb>dotto delle velocità per le quantità della materia. </s>

<s>La proposizione era quella <lb></lb>stessa XXVII dimostrata quarant&#039;anni dopo nel trattato <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end><lb></lb>e come ivi il Borelli la conclude dalle due proposizioni precedenti, così <lb></lb>avrebbe voluto fare l&#039;Aggiunti, proponendosi di dimostrar come, essendo le <lb></lb>moli eguali, i momenti stanno in ragione delle velocità, ed essendo le ve­<lb></lb>locità uguali stanno essi momenti in diretta ragion delle moli. </s></p><p type="main">

<s>La prima di queste proposizioni non si trova a suo luogo, e invece se <lb></lb>ne legge nel manoscritto un&#039;altra, che potrebbesi dire un corollario di <lb></lb>lei, se non fosse una falsità manifesta o una di quelle arguzie delle quali <lb></lb>si trova nelle speculazioni dell&#039;Aggiunti più di un esempio. </s>

<s>La detta pro­<lb></lb>posizione, che tiene nel citato manoscritto il luogo della prima, è così for­<lb></lb>mulata: “ Anco la sola velocità senza il peso opera ed ha momento ” (ivi <lb></lb>a tergo). Aveva Aristotile sentenziato “ che senza l&#039;inerenza del suo sog­<lb></lb>getto non può nè essere nè anco immaginarsi alcun movimento ” sentenza <lb></lb>che, ripetuta da Simplio nel II dialogo Dei due massimi sistemi, è dal Sa­<lb></lb>gredo ivi approvata per vera. </s>

<s>Volle nonostante l&#039;Aggiunti, così argutamente <lb></lb>discorrendo, contradire al giudizio di Aristotile e di Galileo, ciò che avrebbe <lb></lb>avuto il diritto di fare, quando non avesse contradetto insieme alla ragion <lb></lb>matematica, perchè se una delle quantità componenti il momento è zero, dee <lb></lb>necessariamente il momento stessa ridursi a zero: </s></p><p type="main">

<s>“ Che la velocità, senza il peso, operi ed abbia forza, è manifesto nei <lb></lb>venti, i quali, non essendo altro che aria mossa nell&#039;aria (perchè un grave <lb></lb>in un mezzo ugualmente grave in specie ad esso, come dimostra Archimede, <lb></lb>non ha peso alcuno in detto mezzo) adunque tutta la forza del vento na­<lb></lb>sce dalla sola velocità, con la quale si muove l&#039;aria. </s>

<s>È ancora manifesto <lb></lb>nelle percosse violente perchè, facendosi la percossa violenta dal grave al­<lb></lb>l&#039;insù, ed essendo l&#039;inclinazione del grave all&#039;ingiù, l&#039;effetto dunque della <lb></lb>percossa non può nascere dal peso, cioè dalla propensione all&#039;ingiù, ma sì <lb></lb>bene dalla velocità impressagli all&#039;insù. </s>

<s>È finalmente questo stesso manife-<pb xlink:href="020/01/1945.jpg" pagenum="188"></pb>sto nella percossa media, ovvero orizzontale, nella quale, movendosi il grave <lb></lb>parallelo all&#039;orizzonte, l&#039;effetto che resulta da tal movimento non verrà dal <lb></lb>suo peso, cioè dalla sua inclinazione al centro, ma dall&#039;impulso laterale ov­<lb></lb>vero orizzontale, al quale il peso ovver moto all&#039;ingiù non osta, ma neanco <lb></lb>opera nè coopera ” (ivi). </s></p><p type="main">

<s>La proposizione II, che immediatamente segue, è così formulata: “ La <lb></lb>medesima volocità, nelle maggiori e minori quantità di materia, opera più <lb></lb>o meno potentemente, secondo la proporzione della materia ” (ivi a tergo). <lb></lb>Vi si doveva intendere premessa la dimostrazione di un lemma, che si legge <lb></lb>altrove nel manoscritto, e che risponde alla proposizione XXXVII del I libro <lb></lb>maurolicano <emph type="italics"></emph>De momentis:<emph.end type="italics"></emph.end> “ Gravia ab aequis spatiis pendentia sunt mo­<lb></lb>mentis proportionalia ” (Monum. </s>

<s>archim. </s>

<s>cit., pag. </s>

<s>103); proposizione da­<lb></lb>taci dall&#039;Aggiunti sotto quest&#039;altra forma: “ Due gravi della medesima ma­<lb></lb>teria omogenea, attaccati nell&#039;istesso punto della Bilancia, hanno i loro <lb></lb>momenti proporzionali alle moli ” (MSS. cit., fol. </s>

<s>100). </s></p><p type="main">

<s>Supponesi, per le cose da dimostrare, essersi già previamente dimostrato <lb></lb>ch&#039;essendo le distanze reciproche alle moli i momenti sono eguali, ciò che <lb></lb>in via analitica conduce ora noi in due passi alla conclusione, perchè, chia­<lb></lb>mate D <emph type="italics"></emph>d<emph.end type="italics"></emph.end> le distanze, M <emph type="italics"></emph>m<emph.end type="italics"></emph.end> le moli, Q <emph type="italics"></emph>q<emph.end type="italics"></emph.end> i momenti, essere DM=<emph type="italics"></emph>dm<emph.end type="italics"></emph.end> val <lb></lb>quanto dire Q=<emph type="italics"></emph>q,<emph.end type="italics"></emph.end> e dall&#039;equazione Q:<emph type="italics"></emph>q<emph.end type="italics"></emph.end>=DM:<emph type="italics"></emph>dm,<emph.end type="italics"></emph.end> se D=<emph type="italics"></emph>d,<emph.end type="italics"></emph.end> si con­<lb></lb>clude immediatamente l&#039;annunziato teorema. </s>

<s>Ma l&#039;Aggiunti per le antiche <lb></lb>vie lunghe così procede: </s></p><p type="main">

<s>“ Nella Bilancia AB (fig. </s>

<s>78), il cui centro sia C, pendano dal mede­<lb></lb>simo punto M li due gravi I, G, dico ecc. </s>

<s>Come sta la mole G alla mole I, <lb></lb><figure id="id.020.01.1945.1.jpg" xlink:href="020/01/1945/1.jpg"></figure></s></p><p type="caption">

<s>Figura 78.<lb></lb>così stia la distanza CB alla distanza <lb></lb>CM, e la distanza DC facciasi eguale <lb></lb>a CM. </s>

<s>Poi attacchisi in B il peso K, <lb></lb>eguale ad I, ed in D il peso F eguale <lb></lb>a G. </s>

<s>Perchè le distanze son recipro­<lb></lb>che alle moli, il momento di K è <lb></lb>uguale al momento di F, cioè al mo­<lb></lb>mento di G, essendo G ed F pesi <lb></lb>eguali in distanze eguali. </s>

<s>Ma il mo­<lb></lb>mento di K al momento di I ha la proporzione della distanza BC alla di­<lb></lb>stanza CM, cioè della mole G alla mole I: adunque ancora il momento di G <lb></lb>al momento di I ha la proporzione della mole C alla mole I, il che dove­<lb></lb><figure id="id.020.01.1945.2.jpg" xlink:href="020/01/1945/2.jpg"></figure></s></p><p type="caption">

<s>Figura 79.<lb></lb>vamo dimostrare ” (ivi a tergo). </s></p><p type="main">

<s>Ciò premesso, passa l&#039;Ag­<lb></lb>giunti a dimostrare che, se sa <lb></lb>ranno due solidi B, A (fig. </s>

<s>79) <lb></lb>mobili di uguali velocità nel­<lb></lb>l&#039;orizzonte CD, fatti della stessa <lb></lb>materia ma disuguale, il mo­<lb></lb>mento dell&#039;uno al momento del-<pb xlink:href="020/01/1946.jpg" pagenum="189"></pb>l&#039;altro sta come la quantità della materia dell&#039;uno alla quantità della materia <lb></lb>dell&#039;altro. </s>

<s>“ Imperocchè, egli dice, alzisi nel punto D la linea DE perpendico­<lb></lb>lare all&#039;orizzonte, e detta linea intendasi come una leva convertibile intorno <lb></lb>al punto fisso F, preso nel mezzo di essa. </s>

<s>Di poi alzisi dal punto E la linea <lb></lb>EH, la quale, passando per la girella volubile intorno al punto K, discenda <lb></lb>perpendicolarmente in I. Dopo, intendansi attaccati alla linea HI due gravi <lb></lb>N, M dell&#039;istessa materia, i quali siano di figura simile ed eguali alli so­<lb></lb>lidi A, B, l&#039;uno all&#039;uno e l&#039;altro all&#039;altro, e la loro velocità nella perpen­<lb></lb>dicolare HI sia uguale alla velocità delli A, B nella linea CD. Adunque, per <lb></lb>l&#039;assioma, la forza e momento dell&#039;uno sarà uguale al momento e forza <lb></lb>dell&#039;altro a sè uguale. </s>

<s>Posto dunque che N sia uguale ad A, se il mobile A <lb></lb>farà forza in D, perchè la linea EH vien tirata dalla forza del grave N è <lb></lb>come se N fosse attaccato in E, e facesse la medesima forza per la linea <lb></lb>EH, ch&#039;egli fa per la linea CI. </s>

<s>Ma le distanze FE, FD sono eguali, e la ve­<lb></lb>locità e quantità della materia è uguale nell&#039;uno e nell&#039;altro mobile, dun­<lb></lb>que il momento del grave N pendente nella linea HI appunto sarà uguale <lb></lb>al momento del mobile A posto in D, e per l&#039;istessa ragione la forza o mo­<lb></lb>mento del grave M pendente dalla linea. </s>

<s>HI sarà uguale al momento del <lb></lb>mobile B, che faccia forza in D. </s>

<s>E perciò come stanno fra loro i momenti <lb></lb>de&#039;gravi M, N, così tra di loro stanno i momenti de&#039;mobili B, A. </s>

<s>Ma per­<lb></lb>chè li gravi M, N son dell&#039;istessa materia, e pendenti dal medesimo punto, <lb></lb>sarà il momento di M al momento di N come la mole M alla mole N. </s>

<s>Adun­<lb></lb>que anco il momento di B al momento di A starà come la mole M alla <lb></lb>mole N, cioè come la mole di B alla mole di A, essendo l&#039;una eguale al­<lb></lb>l&#039;una e l&#039;altra all&#039;altra ” (ivi, fol. </s>

<s>96). </s></p><p type="main">

<s>Sopra questa dimostrazione troverà forse da ridir qualche cosa chi ha <lb></lb>fatto l&#039;abito oramai ai metodi nuovi, ma era pure conforme al nostro isti­<lb></lb>tuto il dimostrare per qualche esempio qual si fosse l&#039;incerto e faticoso eser­<lb></lb>cizio dell&#039;ali, prima che potesse il pensiero spiegar, come ora noi lo vediamo, <lb></lb>per l&#039;aria il suo libero volo. </s>

<s>In ogni modo concludendo l&#039;Aggiunti dalle sue <lb></lb>proposizioni che le quantità di moto stanno in ragion composta delle velo­<lb></lb>cità e delle moli, e che perciò, stando queste velocità e queste moli in re­<lb></lb>ciproca ragione fra loro, esse quantità sono eguali, veniva a sostituire un <lb></lb>principio universale di Meccanica a quello che il Mariotte diceva essere stato <lb></lb>mal provato da Archimede e da Galileo. </s></p><p type="main">

<s>Giovanni Wallis, sopra questo principio universale dell&#039;ugualità dei mo­<lb></lb>menti, fondò nel 1670 l&#039;edifizio della sua Statica, applicando alle macchine <lb></lb>principali le leggi della Libbra. </s>

<s>Scrisse intorno a questa, nella I parte del <lb></lb>suo trattato <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> un libro particolare, la XII proposizion del quale si <lb></lb>espone così in sè e ne&#039;suoi corollarii: “ Si idem sit Librae centrum atque <lb></lb>centrum motus, quae ex illa libera pendent gravia, aut etiam alias directe <lb></lb>vel subsunt vel incumbunt, in ea ratione ponderant, seu gravant sua re­<lb></lb>spectiva brachia, caeteris paribus, quae ex rationibus ponderum et distan­<lb></lb>tiarum punctorum applicationis a communi Librae et motus centre compo-<pb xlink:href="020/01/1947.jpg" pagenum="190"></pb>nitur. </s>

<s>Adeoque, si distantiae sint aequales, in ratione ponderum; si pondera <lb></lb>sint aequalia, in ratione distantiarum; si vel utraque sint aequalia vel sint <lb></lb>reciproce proportionalia, aequiponderant. </s>

<s>” </s></p><p type="main">

<s>“ Idem intellige de viribus aliis, nempe in ea ratione movendo pollent <lb></lb>quae componitur ex rationibus virium et distantiarum a communi centro <lb></lb>motus et Librae, sive quod huius instar est, quibus directe applicantur vi­<lb></lb>res ” (Londini 1670, pag. </s>

<s>82). </s></p><p type="main">

<s>Così fatti principii s&#039;applicavano ugualmente bene, qualunque relazione <lb></lb>avessero fra loro le braccia della Libbra, propostasi innanzi alla mente come <lb></lb>oggetto di matematica contemplazione. </s>

<s>Ma quando questa Libbra mentale <lb></lb>veniva a scendere a&#039;suoi pratici esercizii, e a farsi perciò materiata, s&#039;ebbe <lb></lb>a riconoscere un intestino conflitto fra la teoria e l&#039;esperienza, specialmente <lb></lb>in quella Bilancia di braccia eguali intorno agli effetti della quale tenevano <lb></lb>aperti gli occhi i compratori delle merci preziose, sollecitando la scienza a <lb></lb>suggerir la ragione e il modo di assicurarsi dal pericolo delle frodi. </s>

<s>Le sol­<lb></lb>lecite cure, ch&#039;essa scienza volentieri si prese, perchè si regolassero con <lb></lb>equa lance i contratti, sono antichissime e meritevoli di una pagina propria <lb></lb>nella storia delle Equiponderanze; pagina che noi ora vogliamo spiegar sotto <lb></lb>gli occhi dei nostri Lettori, dop&#039;aver detto della regola de&#039;momenti dal­<lb></lb>l&#039;ignorar la quale o dal professarla dipendono in gran parte. </s>

<s>come si di­<lb></lb>ceva sulla fine dell&#039;altra parte di questo discorso, alle speculazioni che pas­<lb></lb>siamo a narrare o i corti voli o i provvidi avvedimenti. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Aristotile incomincia dalle Bilance le sue Meccaniche questioni, a ri­<lb></lb>solver le quali accenna essere stato consigliato dal dovere dl scoprir le frodi, <lb></lb>che andavano macchinando i venditori di porpora, ora col non mettere nel <lb></lb>giusto mezzo lo sparto, ora coll&#039;aggiungere all uno o all&#039;altro bacino pez­<lb></lb>zetti di piombo o barbe e nodi di legno: “ ligni enim gravior illa est pars <lb></lb>in qua est radix: nodus vero radix quaedam est ” (Operum, T. XI cit., <lb></lb>fol. </s>

<s>30). La ragione del quanto e del come così facendo defraudavano i detti <lb></lb>e simili altri venditori si notò che non seppe il Filosofo dedurla da&#039;suoi veri <lb></lb>principii, cosicchè da capo cominciando le censure, i baldanzosi avversarii, <lb></lb>senza voler risparmiar nulla, le condussero fino in fondo. </s>

<s>Diremo di queste <lb></lb>censure poi per trattenerci ora intorno alla seconda meccanica questione, <lb></lb>che non si potè nè anch&#039;essa liberar da censure nuove e più forti. </s></p><p type="main">

<s>“ Cur, domanda Aristotile sempre in proposito delle Bilance di braccia <lb></lb>eguali, siquidem sursum fuerit spartum, quando deorsum lato pondere quis­<lb></lb>piam id amovet rursum ascendit Libra:-si autem deorsum constitutum fue­<lb></lb>rit non ascendit sed manet? </s>

<s>” (ibid.). Sia la Bilancia BC (fig. </s>

<s>80) per il <lb></lb>suo mezzo D superiormente sospesa in A: perchè abbassata a forza da C <pb xlink:href="020/01/1948.jpg" pagenum="191"></pb>in E, rimossa appena la mano, torna da questa forzata nella prima sua po­<lb></lb><figure id="id.020.01.1948.1.jpg" xlink:href="020/01/1948/1.jpg"></figure></s></p><p type="caption">

<s>Figura 80.<lb></lb>sizion naturale? </s>

<s>E risponde Ari­<lb></lb>stotile, supposto che sia ADM il <lb></lb>perpendicolo: “ quia DH maior <lb></lb>est dimidio ” (ibid.) e perciò dal <lb></lb>suo stesso maggior peso è quella <lb></lb>maggior parte costretta a scendere <lb></lb>nuovamente in basso. </s></p><p type="main">

<s>Tutt&#039;altrimenti avviene, pro­<lb></lb>segue a dire il Filosofo, quando <lb></lb>il punto di sospensione sia sotto <lb></lb>alla Bilancia CN come per esem­<lb></lb>pio in M (fig. </s>

<s>81) perchè rimo­<lb></lb>vendo essa Bilancia in OR, se sia <lb></lb>MD il perpendicolo, “ plus dimidio fit Librae quae deorsum est pars DO, <lb></lb><figure id="id.020.01.1948.2.jpg" xlink:href="020/01/1948/2.jpg"></figure></s></p><p type="caption">

<s>Figura 81.<lb></lb>quam quod perpendiculum secet: qua­<lb></lb>propter non ascendit; elevata enim <lb></lb>pars levior est: ablato igitur onere, <lb></lb>necesse est manere ” (ibid. </s>

<s>ad tergum). </s></p><p type="main">

<s>Fra&#039;primi e più conosciuti pro­<lb></lb>motori di Aristotile, nel secolo XVI, <lb></lb>Niccolò Tartaglia illustrò, nell&#039;una e <lb></lb>nell&#039;altra parte della Questione i con­<lb></lb>cetti del Filosofo, e solo si compiacque <lb></lb>di aver dato della prima “ ragione al­<lb></lb>quanto più chiara et miglior figura ” <lb></lb>(Quesiti e invenzioni cit., fol. </s>

<s>79 a t.). <lb></lb>La seconda parte della proposta aristo­<lb></lb>telica ha da queste precise parole la <lb></lb>più piena conferma e il più spiegato commento: “ Per essere adunque la <lb></lb>elevata parte DR di menor quantità della inclinata OD, viene a esser più <lb></lb>debole, ovver men potente di lei, e però non è atta nè sofficiente a poterla <lb></lb>urtare e sforzare a farla ascendere al suo primo loco in C, come fece nella <lb></lb>passata, anzi quella resterà così inclinata al basso e la retenerà lei così in <lb></lb>aere elevata ” (ivi, fol. </s>

<s>80). </s></p><p type="main">

<s>Così Aristotile però come il Tartaglia peccano nel risolvere la Que­<lb></lb>stione, commettendo nella prima parte improprietà, e nella seconda un pa­<lb></lb>tentissimo errore. </s>

<s>Guidubaldo del Monte si potè salvare dall&#039;uno e dall&#039;altro <lb></lb>fallo, dimostrando la sua II e III proposizione <emph type="italics"></emph>De libra<emph.end type="italics"></emph.end> col principio de&#039;cen­<lb></lb>tri di gravità, i quali, secondo che riescon sotto o sopra al punto della so­<lb></lb>spensione, rendono alla macchina e al corpo o stabile o no l&#039;equilibrio. </s></p><p type="main">

<s>Nella detta proposizione II, che corrisponde al primo caso della Que­<lb></lb>stione aristotelica, considera Guidubaldo che, rimossa la Libbra, il centro di <lb></lb>gravità D nella precedente figura LXXX s&#039;è dovuto trasferire in G fuori <pb xlink:href="020/01/1949.jpg" pagenum="192"></pb>del perpendicolo, “ et quoniam AG horizzonti non est perpendicularis, ma­<lb></lb>gnitudo ex ponderibus E, H composita in hoc situ minime persistet, sed <lb></lb>deorsum, secundum eius centrum gravitatis G, per circumferentiam GD mo­<lb></lb>vebitur, donec AG horizonti fiat perpendicularis, scilicet donec AG in AD <lb></lb>redeat ” (Mechanic. </s>

<s>lib., Pisauri 1677, fol. </s>

<s>4). La nuova dimostrazione, mo­<lb></lb>vendo da principii più sicuri, è più propria di quella di Aristotile e più pre­<lb></lb>cisa, perchè, mentre la ragion del Filosofo si faceva principalmente dipen­<lb></lb>dere dal peso delle braccia della Bilancia, quella di Guidubaldo astrae da <lb></lb>questa material condizione, ed è perciò applicabile al caso, in cui secondo <lb></lb>gl&#039;istituti archimedei si considerino i pesi sostenuti da leve imponderabili. </s></p><p type="main">

<s>Quanto al secondo caso della detta Question meccanica lo stesso Gui­<lb></lb>dubaldo, nella proposizione sua III, sempre scorto da quella fida regola ba­<lb></lb>ricentrica, corregge il gravissimo errore di Aristotile, inconsideratamente ri­<lb></lb>petuto, come udimmo, dal Tartaglia: e perciocchè, rimossa la Bilancia in OR, <lb></lb>nell&#039;antecedente figura LXXXI, il centro di gravità s&#039;è dovuto trasferire in <lb></lb>G, e GM perciò non più riesce perpendicolare all&#039;orizzonte “ magnitudo, <lb></lb>dunque di qui ne conclude, ex O, R ponderibus composita, in hoc situ <emph type="italics"></emph>mi­<lb></lb>nime manebit,<emph.end type="italics"></emph.end> sed secundum eius gravitatis centrum G deorsum per cir­<lb></lb>cumferentiam GH movebitur ” (ibid., fol. </s>

<s>5). </s></p><p type="main">

<s>È ora una così fatta conclusione manifestamente contraria a quella di <lb></lb>Aristotile, il quale aveva detto nel sopra allegato testo che, rimossa la Bi­<lb></lb>lancia dal sito suo orizzontale, ivi <emph type="italics"></emph>necesse est manere.<emph.end type="italics"></emph.end> Notabile è a questo <lb></lb>proposito che Guidubaldo, invece di reclamare contro l&#039;errore scoperto, si <lb></lb>lusinghi di ridurre i falsi sensi del Filosofo alle più chiare espressioni del <lb></lb>vero. </s>

<s>“ Aristotelis quoque ratio hic perspicua erit: si enim punctum D (nella <lb></lb>preposta figura LXXXI) ubi OR, DM se invicem secant; erit DO maior DR, <lb></lb>et quoniam DM perpendiculum, secundum ipsum Aristotilem, Libram OR <lb></lb>in partes inaequales dividit, et maior pars est versus O, hoc est DO: Libra <lb></lb>OR ex parte O deorsum movebitur, cum id quod plus est deorsum fera­<lb></lb>tur ” (ibid., fol. </s>

<s>25 ad t.). </s></p><p type="main">

<s>Si può facilmente concedere, supposto che la ponderosità della Bilancia <lb></lb>resulti non da&#039;pesi soli ma e dalle braccia, che la ragion di Aristotile sia <lb></lb>da questo commento resa fin qui perspicua: ma quel che segue benchè <lb></lb>Guidubaldo non faccia vista, e non sospetti che se n&#039;abbiano ad avvedere i <lb></lb>sagaci lettori, la rende apertamente contradittoria, perchè mentre là nelle <lb></lb>Questioni meccaniche si diceva che, rimosso in O (nella passata fig. </s>

<s>LXXXI) <lb></lb>lo strumento, <emph type="italics"></emph>necesse est ibi manere,<emph.end type="italics"></emph.end> qui, nel libro <emph type="italics"></emph>Mechanicorum,<emph.end type="italics"></emph.end> si sog­<lb></lb>giunge così, descrivendo con tutta la più desiderabile precisione le condi­<lb></lb>zioni e gli effetti degl&#039;instabili equilibrii: “ Similiter ex dictis quoque eli­<lb></lb>ciemus Libram OR, centrum habens infra libram, quo magis a situ CN <lb></lb>distabit velocius moveri. </s>

<s>Centrum enim gravitatis G, quo magis a puncto D <lb></lb>distat, eo velocius pondus ex O, R ponderibus Libraque OR compositum <lb></lb>movebitur, donec angulus CGO rectus evadat: adhuc insuper velocius mo­<lb></lb>vebitur quo Libram a centro D magis distabit ” (ibid.). </s></p><pb xlink:href="020/01/1950.jpg" pagenum="193"></pb><p type="main">

<s>La riverenza, o forse più veramente il timore di non avere a scanda­<lb></lb>lizzare o provocarsi l&#039;odio degli adoratori del Nume, consigliò a Guidubaldo <lb></lb>la prudenza di questa logica, ma il Benedetti, senza tante paure e senza <lb></lb>tanti riguardi, disse a chi lo voleva sapere che Aristotile, nella seconda parte <lb></lb>della sua seconda meccanica Questione, “ toto coelo aberrat, quia necessa­<lb></lb>rium est ut Libra omnino cadat ” (Specul. </s>

<s>liber cit., pag. </s>

<s>154). </s></p><p type="main">

<s>Procedendo con la medesima libertà in esaminar la prima parte della <lb></lb>Questione, tutt&#039;altro che commentare ossequiosamente il testo, come fa Gui­<lb></lb>dubaldo, argutamente il Benedetti notava che, non deducendola dalla gene­<lb></lb>ralità de&#039;principii, non poteva risolvere Aristotile la sua stessa propostasi <lb></lb>questione, che con certe sue difettose ragioni. </s>

<s>Causa, diceva, del tornare <lb></lb>dalla posizion violenta alla naturale la Libbra, “ non solum est maior quan­<lb></lb>titas ponderis brachiorum, quae iam praetergressa est ultra verticalem li­<lb></lb>neam, sed etiam est longitudo brachii elevati, quae ultra verticalem lineam <lb></lb>reperitur, unde eius extremi pondus redditur gravius in proportione ” (ibid.): <lb></lb>ciò che mostrasi dal Benedetti stesso anche più evidente, abbassando dal <lb></lb>punto H, nella figura LXXX, la verticale HQ, e da E conducendo la oriz­<lb></lb>zontale EQ, per esser dalla differenza delle due linee EM, MQ esattamente <lb></lb>misurata la differenza dei due momenti. </s></p><p type="main">

<s>Voleva così confermare il Matematico veneziano l&#039;utilità della Regola <lb></lb>delle distanze dal perpendicolo, per risolvere con precisione sicura questa e <lb></lb>altre simili statiche questioni, e perchè vedemmo non essere, a mezzo il se­<lb></lb>colo XVI, quella Regola nuova, si potrebbe congetturare che, in ridurre a <lb></lb>maggior precisione e in correggere i primi aristotelici quesiti dall&#039;errore, <lb></lb>non fossero stati nè Guidubaldo nè il Benedetti stesso dei primi. </s>

<s>Vengono <lb></lb>ora le congetture a ridursi a certezza di fatti, per le Note di Leonardo da <lb></lb>Vinci, in una delle quali si legge: “ La Bilancia di braccia e pesi eguali, <lb></lb>rimossa dal sito della egualità, farà braccia e pesi ineguali, onde necessità <lb></lb>la costringe a racquistare la perduta egualità di braccia e di pesi. </s>

<s>Provasi <lb></lb>per la II di questo, e si prova, perchè il peso più alto è più remoto dal <lb></lb>centro del circonvolubile, che il peso più basso, e pertanto ha più debole <lb></lb>sostentamento, onde più facilmente discende e leva in alto la opposta parte <lb></lb>del peso congiunto allo estremo del braccio minore ” (Manuscr. </s>

<s>E cit., <lb></lb>fol. </s>

<s>59). Ora, perchè la distanza del peso H, nella solita figura LXXX, dal <lb></lb>circonvolubile, ossia da qualunque punto della linea verticale, è MQ, e la <lb></lb>distanza del peso E è manifestamente EM, veniva dunque la prima parte <lb></lb>della Questione seconda di Aristotile risoluta da Leonardo, prima che dal <lb></lb>Benedetti, con la maggior possibile precisione, applicandovi la Regola dei <lb></lb>momenti. </s></p><p type="main">

<s>Nè la seconda parte della medesima Questione, che si proponeva dal <lb></lb>gran Maestro della Meccanica a tutti gli studiosi di allora, poteva passare <lb></lb>alla scienza di Leonardo inosservata. </s>

<s>Così infatti si legge in quest&#039;altra sua <lb></lb>Nota, tenendo, nel computar la varietà dei momenti la stessa regola seguita <lb></lb>di sopra: “ Quanto lo estremo della superiore parte della Bilancia s&#039;avvi-<pb xlink:href="020/01/1951.jpg" pagenum="194"></pb>cina più alla linea perpendicolare, che non fa lo estremo della parte infe­<lb></lb>riore, tanto più lungo e ponderoso si troverà il braccio inferiore che il su­<lb></lb>periore, essendo l&#039;asse d&#039;egual qualità ” (Manuscr. </s>

<s>Ash. </s>

<s>N.02038, Paris 1891, <lb></lb>fol. </s>

<s>3). Tornando dunque indietro alla figura LXXXI, prolungata la perpen­<lb></lb>dicolare da una parte e dall&#039;altra, e da essa, con le linee RP, OQ, misurate <lb></lb>le distanze di R, e di O, dice Leonardo, esser di tanto maggior momento <lb></lb>O, di R, quanto è più lunga la distanza OQ della distanza PR, com&#039;era per <lb></lb>ripeter poi, sulla costruzione medesima, il Benedetti. </s></p><p type="main">

<s>Nella ora letta Nota il manoscritto vinciano non si spiega più avanti, <lb></lb>nè noi ci siamo abbattuti a leggere altrove qual si fosse l&#039;opinione di Leo­<lb></lb>nardo intorno allo stato o al moto della Bilancia OR, se cioè la si rimanga <lb></lb>a quel modo inclinata, come, con Aristotile, diceva il Tartaglia, o s&#039;ella se­<lb></lb>guiti a scendere infino a capovolgersi perpendicolare, come dalle teorie dei <lb></lb>centri di gravità ebbe a concluderne Guidubaldo. </s>

<s>Noi siamo certi che anche <lb></lb>Leonardo, leggendo il testo, deve aver come il Benedetti esclamato che il <lb></lb>Filosofo <emph type="italics"></emph>toto coelo aberrat,<emph.end type="italics"></emph.end> ed è la nostra certezza fondata nel saper che lo <lb></lb>stesso Leonardo aveva benissimo divisate le condizioni del vario equilibrio, <lb></lb>il quale può allora solamente, diceva, essere stabile “ quando il centro di <lb></lb>gravità di ciascuno peso sospeso si stabilisca sotto il suo sostentacolo ” (Ma­<lb></lb>nuscr. </s>

<s>B cit., fol. </s>

<s>18 a tergo). Quando dunque il centro di gravità riman <lb></lb>sopra al sostentacolo stesso, come in quel secondo caso della Bilancia, non <lb></lb>può essere in essa alcuna stabilità, e perciò tutt&#039;altro che rimanere segui­<lb></lb>terà, sempre più precipitando, la sua discesa. </s></p><p type="main">

<s>Fra le Questioni, promosse da Aristotile intorno all&#039;equilibrio delle Bi­<lb></lb>lance di braccia eguali, se n&#039;agitava, infino dagli stessi tempi di Leonardo <lb></lb>da Vinci, un&#039;altra, lasciata dal Filosofo addietro, e in proposito della quale <lb></lb>finge Niccolò Tartaglia di avere avuto col signore ambasciator di Mendoza <lb></lb>il seguente colloquio: <emph type="italics"></emph>“ Signor ambasciator.<emph.end type="italics"></emph.end> Ma se ben me aricordo voi <lb></lb>dicesti anchora, nel principio del nostro ragionamento, che Aristotile pre­<lb></lb>termette over tace una questione sopra delle dette Libre, di non puoca im­<lb></lb>portantia, over speculatione: hor ditime che question è questa. <emph type="italics"></emph>Nicolò.<emph.end type="italics"></emph.end> Se <lb></lb>vostra Signoria ben se aricorda della sua seconda questione, in questa ivi in­<lb></lb>terrogatamente adimanda et consequentemente dimostra perchè causa, quando <lb></lb>chel sparto sera di sopra della Libra, et che luno di brazzi di quella da qual­<lb></lb>che peso sìa portato over spinto a basso, remosso che sia over levato via <lb></lb>quel tal peso, la detta Libra di nuovo reascende e ritorna al suo primo luoco. </s>

<s><lb></lb>Et sel detto sparto è di sotto della detta Libra, et che medesimamente luno <lb></lb>di suoi brazzi sia da qualche peso pur portato over spinto a basso, remosso, <lb></lb>over levado che sia via quel tal peso, la detta Libra non riascende nè ri­<lb></lb>torna al suo primo luoco, come che fu nellaltra positione, ma rimane di <lb></lb>sotto cioè a basso. </s>

<s>Hor dico che lui pretermette over tace unaltra questione, <lb></lb>che in questo luoco se convegnaria, di molta maggior speculatione di ca­<lb></lb>dauna delle sopradette, la qual question è questa: Perchè causa, quando <lb></lb>chel sparto è precisamente in essa Libra, e che lun di brazzi di quella sia <pb xlink:href="020/01/1952.jpg" pagenum="195"></pb>da qualche peso portato, over urtado a basso, remosso, over levado che sia <lb></lb>via quel tal peso, la detta Libra di nuovo reascende al suo primo luoco, <lb></lb>si come che fa anchora quella che ha il sparto di sopra da lei ” (Quesiti et <lb></lb>inventioni cit., fol. </s>

<s>79). </s></p><p type="main">

<s>La questione, che qui Niccolò proponeva all&#039;Ambasciator come nuova, <lb></lb>era stata messa in campo tre secoli avanti da Giordano Nemorario, il quale <lb></lb>formulava così la seconda delle sue XIII proposizioni <emph type="italics"></emph>De ponderibus:<emph.end type="italics"></emph.end> “ Cum <lb></lb>fuerit aequilibris aequalis, aequis ponderibus appensis, ab aequalitate non <lb></lb>recedet: et si ab aequidistantia separetur, ad aequalitatis situm revertetur ” <lb></lb>(Editio cit., pag. </s>

<s>9). </s></p><p type="main">

<s>Dimostrava il Matematico tedesco questa sua proposizione con la va­<lb></lb>rietà dei momenti, computati nella quantità del discenso verticale, secondo <lb></lb>il suo proprio instituto, cecamente seguito, come accennavano le sopra ci­<lb></lb>tate parole, dal Tartaglia, il quale non seppe avvedersi che, sebben fosse <lb></lb>quella istituita regola giusta, veniva nonostante al caso male applicata. </s>

<s>In­<lb></lb>torno a ciò i Matematici precedenti dovevano avere avuto qualche contro­<lb></lb>versia, come apparisce dalle Note di Leonardo, il quale non si poteva per­<lb></lb>suadere della verità della proposizion di Giordano, a quel modo che facevano <lb></lb>tanti altri a&#039;suoi tempi, sull&#039;autorità del Maestro. </s>

<s>Il popolano di Vinci, edu­<lb></lb>catosi l&#039;ingegno fuor della Scuola, seguitava piuttosto l&#039;infallibile autorità <lb></lb>della Geometria, ta quale gli ragionava che, se la Libbra è di braccia e di <lb></lb><figure id="id.020.01.1952.1.jpg" xlink:href="020/01/1952/1.jpg"></figure></s></p><p type="caption">

<s>Figura 82.<lb></lb>pesi eguali, sospesa nel suo centro di gravità, deve <lb></lb>in qualunque posizione rimanere equilibrata, sem­<lb></lb>pre serbando, i pesi, eguali i loro momenti. </s></p><p type="main">

<s>La dimostrazione era chiara, computando con <lb></lb>la regola delle distanze orizzontali dal circonvolubile <lb></lb>quegli stessi momenti, perchè rimossa la Libbra ZQ <lb></lb>(fig. </s>

<s>82) in BM, per esempio, o in AN, essendo i <lb></lb>momenti BXOD con MXOR, e AXOC con <lb></lb>NXOP esattamente eguali, dee lì dove fu lasciata <lb></lb>rimanere in perfetto equilibrio. </s>

<s>La teoria dall&#039;altra parte veniva a Leonardo <lb></lb>confermata dall&#039;esperienza della ruota o del cerchio girato intorno al suo polo. </s></p><p type="main">

<s>Per dimostrare poi più chiaramente la cosa, in un tempo solo, con le <lb></lb>ragioni e coi fatti, immaginava Leonardo di avere una tavoletta di basi ret­<lb></lb>tangolari, esattamente impolata nel suo centro di gravità e di figura, e così <lb></lb>sotto, il titolo <emph type="italics"></emph>Sperientia della Bilancia,<emph.end type="italics"></emph.end> scriveva: “ Questa Bilancia resterà <lb></lb>dove tu la lasci, come fa il cerchio intorno al suo polo. </s>

<s>Per tutte le ragioni <lb></lb>dette questa Bilancia non si moverà dal suo sito, avendo rispetto al centro <lb></lb>del mondo ” (Manuscr. </s>

<s>G cit., fol. </s>

<s>78 a tergo). Poi, per dichiarar meglio il <lb></lb>suo pensiero, ch&#039;egli accenna di aver notato anche altrove; sotto l&#039;ultima <lb></lb>di queste righe soggiunge: </s></p><p type="main">

<s>“ Se la ponderazione della Bilancia sarà fatta in polo vicino al punto <lb></lb>matematico, che si fa centro della gravità della Bilancia; allora le braccia <lb></lb>eguali della Bilancia resteranno in quella obliquità, che la mano dell&#039;uomo <pb xlink:href="020/01/1953.jpg" pagenum="196"></pb>la lascerà. </s>

<s>Provasi, perchè la linee BD (fig. </s>

<s>83), nel mezzo della quale è <lb></lb><figure id="id.020.01.1953.1.jpg" xlink:href="020/01/1953/1.jpg"></figure></s></p><p type="caption">

<s>Figura 83.<lb></lb>situato il centro matematico della Bilancia, divide la <lb></lb>quantità della Bilancia nelli due triangoli BCD, DBE, <lb></lb>li quali sono infra loro simili e eguali in figura e <lb></lb>in peso, sol si variano nella situazione. </s>

<s>Ma per tal <lb></lb>variazione non si variano li pesi dalla linea centrale <lb></lb>del polo BD, perchè l&#039;angolo superiore C del trian­<lb></lb>golo BCD è tanto remoto dalla linea centrale BD, <lb></lb>quanto si sia l&#039;angolo E, come mostra la linea EP, <lb></lb>e perchè è provato non dare noia da essere più alto <lb></lb>l&#039;un peso che l&#039;altro, cioè l&#039;angolo C che l&#039;an­<lb></lb>golo E ” (ivi). </s></p><p type="main">

<s>Ma per far la dimostrazione anche più precisa <lb></lb>riduceva Leonardo tutto il peso de&#039;due triangoli <lb></lb>eguali ne&#039;loro centri di gravità N, E, d&#039;onde condotte le NM, EF perpen­<lb></lb>dicolari alla linea centrale BD, si rende manifesto che, rimanendo fra loro <lb></lb>in qualunque posizione l&#039;egualità dei due triangoli rettangoli BMN, EFD, <lb></lb>anche le distanze EF, MN si serbano in qualunque modo fra loro eguali. </s>

<s><lb></lb>Ciò che laconicamente disse Leonardo in queste parole sottoscritte alle pre­<lb></lb>cedenti: “ Noi abbiamo concluso che tal Bilancia non avrà moto, essendo <lb></lb>il suo centro matematico in mezzo a tutti li oppositi pesi fra loro eguali ” (ivi). </s></p><p type="main">

<s>Questo riguardar le cose sotto vario aspetto, come ci rivelano le addotte <lb></lb>Note, per meglio certificarsi di aver veduto il vero, è indizio manifeste delle <lb></lb>contradizioni che dovette patire Leonardo dai seguaci del Nemorario, i quali <lb></lb>uscirono poi dalle private disputazioni in pubblico nelle Opere del Tarta­<lb></lb>glia e del Cardano. </s>

<s>Nell&#039;ottavo libro dei Quesiti il primo de&#039;due detti Ma­<lb></lb><figure id="id.020.01.1953.2.jpg" xlink:href="020/01/1953/2.jpg"></figure></s></p><p type="caption">

<s>Figura 84.<lb></lb>tematici dimostra la proposizione II di Giordano <lb></lb>concludendola, come Giordano stesso, dalla inegua­<lb></lb>lità dei momenti virtuali che, rimossa la Bilancia <lb></lb>dalla orizzontale, sollecitano la caduta de&#039;due pesi. </s></p><p type="main">

<s>Sia la Bilancia orizzontale AB (fig. </s>

<s>84) ri­<lb></lb>mossa in DC: vuol dimostrare il Tartaglia che ivi <lb></lb>non rimarrà, perchè il peso D avendo maggior mo­<lb></lb>mento di C, viene a ridurla in basso. </s>

<s>Che il mo­<lb></lb>mento di D sia veramente maggiore di C lo prova, <lb></lb>perchè avendo a scendere per eguale spazio, come <lb></lb>per esempio D in E, e C in F, D acquista maggiore quantità del descenso <lb></lb>essendo IH maggiore di GF. </s></p><p type="main">

<s>“ Dico che il corpo B, scrive il Tartaglia, stante quel nel punto D viene <lb></lb>a esser più grave, secondo il sito, del corpo A, stante quello in ponto C, <lb></lb>perchè il decenso del detto corpo B dal ponto D nel ponto E è più rettto <lb></lb>del decenso del corpo A dal ponto C nel ponto F, per la seconda parte <lb></lb>della quarta petitione, perchè capisse più della linea della diretione, cioè che <lb></lb>nel discendere il detto corpo B dal ponto D nel ponto E, lui capisse over <pb xlink:href="020/01/1954.jpg" pagenum="197"></pb>piglia della linea della diretione la parte IH, ed il corpo A, nel discendere <lb></lb>dal ponto C nel ponto F, lui caperia della detta linea della diretione la parte <lb></lb>GF. </s>

<s>E perchè la parte IH è maggiore della linea over parte CF, per la <lb></lb>17a diffinizione, più obliquo sarà il decenso dal ponto C al ponto F di quello <lb></lb>dal ponto D al ponto E. Onde, per la seconda parte della quarta petitione, <lb></lb>il corpo B in tal positione sarà più grave secondo il sito del corpo A..... <lb></lb>E però al detto corpo B farà reascendere il detto corpo A al ponto A, suo <lb></lb>primo et condecente luoco, et lui medesimamente discendarà nel ponto B, <lb></lb>pur suo primo et condecente luoco, cioè nel sito della egualità. </s>

<s>nel qual <lb></lb>sito li detti dui corpi se trovarano egualmente gravi secondo el sito, et per­<lb></lb>chè sono anchora simplicemente egualmente gravi se conservarano nel detto <lb></lb>luoco ” (fol. </s>

<s>89 a tergo). </s></p><p type="main">

<s>Fu detto da alcuni, e ripetuto da molti, che il Cardano sentì anch&#039;egli, <lb></lb><figure id="id.020.01.1954.1.jpg" xlink:href="020/01/1954/1.jpg"></figure></s></p><p type="caption">

<s>Figura 85.<lb></lb>degli effetti della Bilancia rimossa dalla oriz­<lb></lb>zontale, come il Nemorario commentato da que­<lb></lb>ste parole del Tartaglia. </s>

<s>Ma nel libro I <emph type="italics"></emph>De <lb></lb>subtilitate,<emph.end type="italics"></emph.end> che è il luogo propriamente citato <lb></lb>da costoro, si conclude intorno alla seconda <lb></lb>Question meccanica di Aristotile con dire che <lb></lb>non è ciò dimostrato da Giordano, nè inteso. </s>

<s><lb></lb>Consisteva quel discorso nel provare che in F <lb></lb>(fig. </s>

<s>85) il peso della Bilancia CD è men grave <lb></lb>che in C, per la giusta ragione della inegua­<lb></lb>lità dei momenti, così misurati dalle distanze <lb></lb>FP, CB, come dai discensi OP, BM, e dopo <lb></lb>questo soggiunge: “ Ex hoc autem demon­<lb></lb>stratur quod dicit Philosophus quod, si aequalia sint pondera in F et C, <lb></lb>Libra tamen sponte redit ad situm CD, ubi trutina sit AB. </s>

<s>Nec hoc de­<lb></lb>monstrat Jordanus nec intellexit ” (Op. </s>

<s>T. III cit., pag. </s>

<s>369). </s></p><p type="main">

<s>È chiaro dunque di qui che il discorso del Cardano tendeva a ritrovar <lb></lb>la vera ragion matematica della prima parte della seconda Questione aristo­<lb></lb>telica, relativa alle condizioni dell&#039;equilibrio nella Bilancia sospesa dalla parte <lb></lb>di sopra. </s>

<s>Passa poi a trattare dell&#039;altro caso, quando cioè il sostegno ri­<lb></lb>manga al disotto, e dice che, abbassatosi il peso in R, “ non solum non re­<lb></lb>vertitur ad situm CD, imo magis R descendit versus Q, et F ascendit ver­<lb></lb>sus A, ut experimento patet. </s>

<s>Hoc etiam Jordanus non demonstravit ” (ibid.). </s></p><p type="main">

<s>Ed è vero che Giordano non lo dimostrò, perchè non era il suo intento, <lb></lb>ma è curioso che si dica essere stato ciò dimostrato da Aristotile, il quale, <lb></lb>come udimmo dalla lettura del testo, avea asserito tutto il contrario da quel <lb></lb>che il Cardano stesso diceva essere per esperienza manifesto. </s>

<s>Non si sa poi <lb></lb>dove si legga il nuovo principio statico attribuito al Filosofo che cioè il mag­<lb></lb>giore angolo, fatto dalla trutina con le braccia, renda maggiore da quella <lb></lb>parte il peso della Bilancia. </s>

<s>“ Aristotiles dicit hoc contingere quum trutina <lb></lb>est supra Libram, quia angulus QBF metae maior est angulo QBR. </s>

<s>Et si-<pb xlink:href="020/01/1955.jpg" pagenum="198"></pb>militer, quum trutina fuerit QB, erit meta AB, et tunc angulus BBA maior <lb></lb>erit angulo FBA. </s>

<s>Sed maior angulus reddit gravius pondus, igitur, dum tru­<lb></lb>tina superius est, F erit gravius R, ideo F trahet Libram versus C; et, dum <lb></lb>fuerit inferius, R erit gravius quam F, ideo trahet Libram versus Q ” (ibid.). </s></p><p type="main">

<s>Aristotile aveva detto invece che R <emph type="italics"></emph>necesse est manere,<emph.end type="italics"></emph.end> e avea detto <lb></lb>contro la ragion matematica e contro l&#039;esperienza. </s>

<s>Ma se fa bene il Car­<lb></lb>dano a gettare un velo sulle vergogne del Padre, non era però necessario <lb></lb>il far mendace vista al mondo che quel velo posticcio fosse l&#039;abito proprio <lb></lb>e naturale. </s>

<s>Avrebbe in qualunque modo fatto assai meglio a difendere la <lb></lb>verità, senza accettazion di persona; ciò che l&#039;avrebbe fatto meno ligio ad <lb></lb>Aristotile, e più giusto con Giordano, la seconda proposizion del quale fu <lb></lb>lui che non la dimostrò e non la intese. </s>

<s>Fra quelle cardaniche speculazioni <lb></lb>infatti non si trova nemmeno un cenno dell&#039;equilibrio della Bilancia, non <lb></lb>sospesa nè sopra nè sotto, ma nel suo proprio centro. </s></p><p type="main">

<s>Il Cardano insomma e il Tartaglia, l&#039;uno fedel seguace del Nemorario <lb></lb>e l&#039;altro capriccioso interpetre di Aristotile, sono gli esemplari de&#039;matema­<lb></lb>tici di poco anteriori, co&#039;quali ebbe Leonardo le sue controversie, decise <lb></lb>oramai, sopra le riferite cose, nel giudizio de&#039;nostri matematici Lettori. </s>

<s>Ma <lb></lb>la risoluzion finale dipende da considerazioni un poco più sottili, per dir <lb></lb>delle quali, a complemento di questa storia, ci convien ritornare indietro ai <lb></lb>colloqui, ch&#039;ebbe Giovanni di Beugrand in Roma con Benedetto Castelli. </s></p><p type="main">

<s>Dop&#039;avere inteso dal Matematico francese che i corpi, avvicinandosi al <lb></lb>centro della Terra, diventano sempre men gravi, maravigliato il Nostro di <lb></lb>quella novità incominciò a pensare fra sè alle strane conseguenze, una delle <lb></lb>quali, scriveva a Galileo pochi giorni di poi, è questa: “ che io non so più <lb></lb>dove sia il centro di gravità di una sfera, poichè, intesa segata la sfera in <lb></lb>due parti eguali da un piano orizzontale, essendo la parte che è verso il <lb></lb>centro più vicina al centro della Terra, che non è l&#039;altro emisfero; sarà <lb></lb>ancora meno grave, e dovendo il centro di gravità del composto di tutti e <lb></lb>due gli emisferi essere nella linea che congiunge il loro centro di gravità, <lb></lb>e in quel punto di essa, che la divide in modo che la parte che tocca al <lb></lb>minor peso, alla parte che tocca al maggior peso abbia la proporzione re­<lb></lb>ciproca che ha il maggior peso al minore; è manifesto che il centro di gra­<lb></lb>vità di tutta la sfera non può essere nel centro di magnitudine, come si <lb></lb>pensa che sia. </s>

<s>” </s></p><p type="main">

<s>“ Ma quello che accresce in me la maraviglia è che, portando la me­<lb></lb>desima sfera più verso il centro della Terra, si van continuamente mutando <lb></lb>le proporzioni delle distanze dei due emisferi, e così il centro della gravità <lb></lb>del composto dei due emisferi si anderà sempre mutando, nè mai si potrà <lb></lb>determinare il centro di gravità di una sfera, senza la relazione della lon­<lb></lb>tananza dei centri di gravità dei due emisferi dal centro della Terra. </s>

<s>” <lb></lb>(Alb. </s>

<s>X, 121, 22). </s></p><p type="main">

<s>Avendo comunicato poi il Castelli così fatti pensieri, che gli passavano <lb></lb>per la mente, al Nardi, questi, dop&#039;aver riformata la Statica archimedea, <pb xlink:href="020/01/1956.jpg" pagenum="199"></pb>come si vide, raccolse dal suo discorso alcuni quesiti e corollari importanti, <lb></lb>dai quali dovea dipendere quella final risoluzione del problema della Bilan­<lb></lb>cia, che poco fa si diceva. </s>

<s>Se i pesi variano, ragionava fra sè esso Nardi, <lb></lb>secondo le distanze dal centro terrestre, non è dunque il primo postulato <lb></lb>di Archimede. <emph type="italics"></emph>Petimus aequalia pondera ab aequalibus distantiis aequi­<lb></lb>ponderare,<emph.end type="italics"></emph.end> vero assolutamente, ma nel solo caso che la Bilancia stia oriz­<lb></lb>zontale. </s>

<s>E qui gli si riduceva alla memoria la seconda proposizion di Gior­<lb></lb>dano, l&#039;enunciato della quale aveva fin allora, come Leonardo, creduto falso, <lb></lb>ma che ora vedeva esser salvo, non già dalle ragioni addotte dallo stesso <lb></lb>Giordano, ma perchè il peso sollevato, essendo più distante dal centro della <lb></lb>Terra, è più grave, e dee far perciò tornare la Bilancia alla prima sua po­<lb></lb>sizione orizzontale, benchè l&#039;eccessiva distanza da noi a quell&#039;infimo centro <lb></lb>ne impedisca di vederne con gli occhi l&#039;effetto. </s>

<s>Che poi i corpi pesino tanto <lb></lb>più, quanto da quello stesso centro del mondo son più distanti, come il <lb></lb>Beaugrand aveva detto al Castelli, sembrava al Nardi molto probabile: sem­<lb></lb>brava probabile cioè che intorno al centro della Terra, mantenessero i corpi <lb></lb>la ragion medesima di egualità, che intorno al centro della Bilancia, nella <lb></lb>quale pure si osserva che tanto son più pesi quanto son più lontani. </s></p><p type="main">

<s>Di questi pensieri ci lasciò il Nardi stesso scritta la memoria dopo il <lb></lb>discorso, altrove da noi disteso, e nel quale, riguardando le forze conver­<lb></lb>genti, presentava sotto un nuovo punto di vista gli antichi teoremi archi­<lb></lb>medei. </s>

<s>“ Molti e importanti quesiti e corollari, egli dice, dal presente di­<lb></lb>scorso si potrebbero fare e raccorre, onde per esempio cercherassi se pesi <lb></lb>eguali, disegualmente rimossi dal centro, pesin disegualmente, e se più pe­<lb></lb>sino i più lontani. </s>

<s>Quando ciò sia vero, non sarà assolutamente vera la prima <lb></lb>domanda di Archimede. </s>

<s>Pare certamente probabile che, se il punto G (fig. </s>

<s>86) <lb></lb><figure id="id.020.01.1956.1.jpg" xlink:href="020/01/1956/1.jpg"></figure></s></p><p type="caption">

<s>Figura 86.<lb></lb>s&#039;intenda trasportato nel centro D, mantenghino i pesi <lb></lb>in E e in I le stesse ragioni di egualità in detto centro <lb></lb>che fuori, e così il piccolo lontano contrappeserà al <lb></lb>grande vicino, là dove nel centro D mancheranno in <lb></lb>tutto di momento i gravi, che ivi si quietano. </s>

<s>Scorgesi <lb></lb>di qui che vera saria l&#039;opinione di quelli, i quali vole­<lb></lb>vano che la linea EI, non parallela ad AC per qualche <lb></lb>violenza, dovesse, tolta tal violenza, ritornar parallela, <lb></lb>ma la ragione di ciò essi ad altro non molto felicemente <lb></lb>riferivano. </s>

<s>È ben vero che ad essi conveniva asserire, <lb></lb>concordemente con tutti quelli i quali la stessa opinione <lb></lb>approvavano, che la lontananza dal centro così ecces­<lb></lb>siva impedisce tal effetto, non altrimenti che impedisce all&#039;occhio il veder <lb></lb>l&#039;inclinazione delle due linee, che dagli estremi della Bilancia concorrono <lb></lb>prodotte nel centro. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>873). </s></p><p type="main">

<s>Apparisce da questo documento che i pensieri del Beaugrand e del Ca­<lb></lb>stelli vennero a ridestare le controversie intorno all&#039;equilibrio della Bilancia, <lb></lb>nella quale sieno collocati i centri delle grandezze; pensieri e controversie <pb xlink:href="020/01/1957.jpg" pagenum="200"></pb>che il Nardi comunicò al Torricelli, in sul punto ch&#039;era questi per dimo­<lb></lb>strare i venti modi varii di quadrar la Parabola. </s>

<s>Le rumorose novità veni­<lb></lb>vano a mettere qualche scrupolo in que&#039;torricelliani teoremi, che l&#039;Autore <lb></lb>avea condotti secondo gl&#039;instituti archimedei, seguiti anche da Galileo, ma <lb></lb>non curando così fatte sottigliezze, reputate inutili e inefficaci, mantenne, per <lb></lb>le medesime ragioni di Leonardo che, o fossero i pesi più alti o più bassi <lb></lb>nella Libbra, o fosse essa Libbra orizzontale o inclinata, s&#039;equiponderino le <lb></lb>gravità, quand&#039;hanno reciproca ragione alle distanze, o quand&#039;esse gravità <lb></lb>sono eguali e sono appese a distanze parimente eguali. </s>

<s>Fra i supposti infatti <lb></lb>premessi al trattato <emph type="italics"></emph>De dimensione parabolae<emph.end type="italics"></emph.end> pose in VI luogo anche que­<lb></lb>sto: “ Aequalia gravia ex aequalibus distantiis aequiponderant, sive Libra <lb></lb>ad horizontem parallela fuerit sive inclinata; et gravia eandem reciproce ra­<lb></lb>tionem habentia quam distantiae aequiponderant, sive Libra sit ad horizon­<lb></lb>tem parallela sive inclinata ” (Opera geom. </s>

<s>cit., P. II, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Benchè dunque, poco prima del 1644, avesse il Torricelli deliberato di <lb></lb>badare a sè e non si divagar la mente nelle sottilità propostegli dal Nardi, <lb></lb>e nelle altrui controversie (maluimus rei nostrae servire quam aliorum con­<lb></lb>troversiae demonstrationem accommodare), venne però presto il tempo che <lb></lb>s&#039;ebbe a trovar messo su quelle stesse vie, a grande industria scansate, e <lb></lb>a compiacer del buon termine a cui si vide condotto. </s>

<s>La più efficace occa­<lb></lb>sione di quel ravviarsi colà, dove le speculazioni dello stesso Nardi gli aveano <lb></lb>accennato, fu questa che ora diremo. </s></p><p type="main">

<s>Il Cartesio, per applicare alle macchine quello ch&#039;egli chiamava suo <lb></lb>nuovo principio statico, aveva, in poche parole francesi, disteso un tratta­<lb></lb>tello, che andò lungamente attorno manoscritto, pubblicato postumo nell&#039;ori­<lb></lb>ginale, e poi dal Poisson, insieme con altre operette del medesimo Autore, <lb></lb>nel 1704 in Amterdam tradotto in latino. </s>

<s>Il Mersenno mandò cotesto ma­<lb></lb>noscritto meccanico al Torricelli, il quale non intendendo il francese se ne <lb></lb>faceva tradur qualche cosa al Viviani, che ne prese in tale occasione copia, <lb></lb>inserita poi ne&#039;primi fogli del Tomo CXI dei Discepoli di Galileo. </s>

<s>Il titolo <lb></lb>è <emph type="italics"></emph>Les Mechaniques,<emph.end type="italics"></emph.end> poco sotto al quale si legge: <emph type="italics"></emph>“ Mechanice prima prin­<lb></lb>cipia explicat<emph.end type="italics"></emph.end> des engins, par l&#039;aide des quels on peut, avec petite force, <lb></lb>lever un tardeau fort pesant ” (fol. </s>

<s>1). </s></p><p type="main">

<s>Nell&#039;ultimo capitoletto, ch&#039;è il VI, <emph type="italics"></emph>Du Levier,<emph.end type="italics"></emph.end> dop&#039;aver dimostrate le <lb></lb>condizioni dell&#039;equilibrio nello strumento, riguardando le forze naturali che <lb></lb>lo sollecitano come convergenti al centro del mondo, l&#039;Autore così conclude: <lb></lb>“ De quoy on peut resondre toutes les difficultes de la Balance nestre, qu&#039;n <lb></lb>point indivisibile, ainsy que iay suppose pour le Levier, si les bras sont pen­<lb></lb>dues de part et d&#039;autre, celuy qui sera le plus bas se doit tousiours tro­<lb></lb>vuer le plus pesant, en sorte que le centre de la gravitè n&#039;est pas.... et <lb></lb>immoble en casque corps, ainsy que l&#039;avoient supposè les ancines, ce que <lb></lb>personne encore, que ie sathe, n&#039;a remarquè (ivi, fol. </s>

<s>5 a tergo). </s></p><p type="main">

<s>Ora al significato di queste parole s&#039;ebbe facilmente a risovvenire il <lb></lb>Torricelli delle speculazioni del Nardi, con le quali e co&#039;pensieri medesimi <pb xlink:href="020/01/1958.jpg" pagenum="201"></pb>del Castelli si riscontravano queste vantate novità cartesiane. </s>

<s>Incominciò a <lb></lb>dubitare allora se a introdur così fatte novità nella scienza fosse stato primo <lb></lb>il Beaugrand o il Cartesio, quando un giorno gli occorse di tornare a svol­<lb></lb>gere il libro <emph type="italics"></emph>Mecanicorum<emph.end type="italics"></emph.end> di Guidubaldo del Monte. </s>

<s>Si levò dalla medita­<lb></lb>zione di quelle pagine maravigliato che i suoi maestri Galileo, e il padre <lb></lb>don Benedetto, avessero potuto credere al Beaugrand, che si vantava di es­<lb></lb>sere stato il primo, dopo tutti i passati scrittori (Alb. </s>

<s>X, 121) a maneggiare <lb></lb>i pesi, non come paralleli ma come converganti, mentre Guidubaldo, cin­<lb></lb>quant&#039;ott&#039;anni prima che venisse a insegnarla un Francese, aveva dato ag&#039;Ita­<lb></lb>liani, e a chiunque fosse piaciuto di ascoltarla, questa lezione: </s></p><p type="main">

<s>“ In quocunque enim situ pondus aliquod constituatur, si naturalem <lb></lb>eius ad propium locum motionem spectemus, cum recta ad eum suapte na­<lb></lb>tura moveatur, supposita totius universi figura eiusmodi erit: ut semper <lb></lb>spatium, per quod naturaliter movetur, rationem habere videatur lineae a <lb></lb>circumferentia ad centrum productae. </s>

<s>Non igitur naturales descensus recti <lb></lb>cuiuslibet soluti ponderis per lineas fieri possunt inter se parallelas. </s>

<s>cum <lb></lb>omnes in centrum mundi conveniant ” (Editio cit., fol. </s>

<s>15 a t.). E come <lb></lb>così convenienti avea riguardate quelle direzioni de&#039;pesi nel trattare ivi <emph type="italics"></emph>De <lb></lb>libra,<emph.end type="italics"></emph.end> mettendosi in mezzo a quelle controversie, dalle quali s&#039;era fin allora <lb></lb>astenuto il Torricelli, ma che ora tornavano ad allettarlo, perchè avea sco­<lb></lb>perto in Italia il maestro a quel Cartesio e a quel Beugrand, ch&#039;eran ve­<lb></lb>nuti a farsi maestri di novità agl&#039;Italiani e al mondo. </s></p><p type="main">

<s>Guidubaldo dunque propugnava, come Leonardo da Vinci, l&#039;opinione <lb></lb>dell&#039;equilibrio indifferente della Bilancia, contro la proposizione di Gior­<lb></lb>dano e contro il quesito del Tartaglia, scoprendo la fallacia, che s&#039;ascon­<lb></lb>deva nel loro discorso; fallacia, che egli diceva consistere nel riguardar, per <lb></lb>le premesse, i pesi come liberi, e nel riguardarli poi come congiunti, ve­<lb></lb>nendo alla conclusione. </s>

<s>Con la loro stessa regola di computare i momenti, <lb></lb>soggiungeva l&#039;arguto censore, si dimostra che l&#039;equilibrio non è nella Bi­<lb></lb>lancia di Giordano stabile ma indifferente, perchè, mentre il peso D (nella <lb></lb>retro apposta figura LXXXIV) discende per l&#039;arco DE, il peso C riascende <lb></lb>per un arco eguale CL, e son pure eguali MG, HI, quantità dell&#039;ascesa e <lb></lb>del descenso. </s>

<s>“ Qualis ergo erit propensio unius ad motum deorsum, talis <lb></lb>etiam erit resistentia alterius ad motum sursum; resistentia scilicet violen­<lb></lb>tiae ponderis in C in ascensu naturali potentiae ponderis in D in descensu <lb></lb>contra nitendo opponitur, cum sit ipsi aequalis, quo enim pondus in D na­<lb></lb>turali potentia deorsum velocius descendit, eo tardius in C violenter ascendit, <lb></lb>quare neutrum ipsorum alteri praeponderabit, cum ab aequali non proveniat <lb></lb>actio. </s>

<s>Non igitur pondus in D pondus in C sursum movebit ” (ibid., fol. </s>

<s>18 a t.). </s></p><p type="main">

<s>Così veniva bene confutato, co&#039;suoi proprii argomenti, il Tartaglia, il <lb></lb>quale aveva dimostrato dover esser maggiore il momento del peso più alto, <lb></lb>e che perciò era necessario tornasse la Bilancia a stabilirsi nel suo primo <lb></lb>equilibrio, mentre sanamente applicando quella regola ne conseguiva dover <lb></lb>essa Bilancia anzi rimanere, serbando, in qualunque posizione i pesi eguali <pb xlink:href="020/01/1959.jpg" pagenum="202"></pb>i momenti. </s>

<s>Avrebbe così Guidubaldo raggiunto, per le medesime vie di Leo­<lb></lb>nardo l&#039;intento, ma perchè non stimava, come vedemmo, quella regola di <lb></lb>computare i momenti per buona, cercò altro modo alle sue dimostrazioni. </s>

<s><lb></lb>Mentre così cercava, conformando il discorso agli effetti della Natura, che fa <lb></lb>convergere i pesi al centro del mondo, s&#039;abbattè a dover concluderne una <lb></lb>verità inaspettata, ehe cioè nello scendere la Bilancia s&#039;aggrava. </s></p><p type="main">

<s>Siano D, E (fig. </s>

<s>87) i due pesi in<gap></gap>orno al centro C, e posto in S il <lb></lb>centro della Terra siano DS, ES le loro direzioni: “ quare, si ut rei veri­<lb></lb><figure id="id.020.01.1959.1.jpg" xlink:href="020/01/1959/1.jpg"></figure></s></p><p type="caption">

<s>Figura 87.<lb></lb>tas est, ponderis descensus magis <lb></lb>minusve obliquus dicetur secun­<lb></lb>dum recessum et accessum ad <lb></lb>spatia per lineas DS, ES designata, <lb></lb>iuxta naturales ipsorum ad pro­<lb></lb>pria loca lationes, conspicuum est <lb></lb>minus obliquum esse descensum <lb></lb>ipsius E per EG, quam ipsius D, <lb></lb>per DA.... quare in E pondus <lb></lb>magis gravitabit quam in D, quod est penitus op­<lb></lb>positum eius, quod ipsi ostendere conati sunt ” (ibi, <lb></lb>fol. </s>

<s>19 a t.). </s></p><p type="main">

<s>La conclusione contradiceva a Giordano e al <lb></lb>Tartaglia, i quali avevano voluto dimostrare che, in­<lb></lb>vece il peso in E è meno grave, ma contradiceva <lb></lb>altresì alle intenzioni stesse dell&#039;Autore, le quali <lb></lb>erano quelle di provar che i due pesi, comunque <lb></lb>volti, serbano eguali i momenti. </s>

<s>Guidubaldo perciò <lb></lb>ebbe a rifiutar quella sua conclusione, e perchè in­<lb></lb>somma non era possibile salvar nella Bilancia l&#039;in­<lb></lb>differenza dell&#039;equilibrio, se non a patto che fos­<lb></lb>sero le forze parallele, si trovò costretto ad ammet­<lb></lb>tere il supposto antico di Archimede e di Leonardo. </s>

<s><lb></lb>Disse che, quando i pesi D, E son liberi di se­<lb></lb>condar gli effetti della Natura, le direzioni son convergenti, ma che son pa­<lb></lb>rallele, quando si trovano nello strumento artificiosamente congiunti. </s>

<s>“ In­<lb></lb>surgent autem fortasse contra nos: si igitur, dicent, pondus in E gravius est <lb></lb>pondere in D, Libra DE in hoc situ minime persistet, quod equidem tueri <lb></lb>proposuimus, sed in EG movebitur. </s>

<s>Quibus respondemus plurimum referre <lb></lb>sive consideremus pondera quatenus sunt invicem disiuncta, sive quatenus <lb></lb>sunt sibi invicem connexa: alia est enim ratio ponderis in E sine connexione <lb></lb>ponderis in D, alia vero eiusdem alteri ponderi connexa, ita ut alterum sine <lb></lb>altero moveri non possit, nam ponderis in E, quatenus est sine alterius pon­<lb></lb>deris connexione, rectus naturalis descensus est per lineam ES; quatenus <lb></lb>vero connexum est ponderi in D, eius naturalis descensus non erit amplius <lb></lb>per lineam ES, sed per lineam CS parallelam ” (ibid.). </s></p><pb xlink:href="020/01/1960.jpg" pagenum="203"></pb><p type="main">

<s>Ebbe facilmente il Torricelli a scoprire il paralogismo di questo discorso, <lb></lb>perchè anche stando i due pesi connessi dovevano essere le loro forze con­<lb></lb>correnti, e perciò il peso in E doveva, per le ragioni di Guidubaldo, cioè <lb></lb>per la varietà della discesa, essere in qualunque modo il più grave. </s>

<s>Se non <lb></lb>che mancava a determinarsi la quantità, e nell&#039;uno e nell&#039;altro peso, la pro­<lb></lb>porzione di quella discesa, ciò che sarebbesi potuto fare, conducendo ne&#039;punti <lb></lb>E, D al cerchio due tangenti, come fu da questa stessa figura del Nostro, <lb></lb>suggerito al Cartesio, ma il Torricelli, ricordandosi del Benedetti, seguì la <lb></lb>più spedita via segnatagli da lui. </s></p><p type="main">

<s>In un luogo delle sue Meccaniche, da noi citato di sopra, dop&#039;avere inse­<lb></lb>gnato il Matematico veneziano che la regola per determinar la quantità di <lb></lb>una forza obliquamente diretta, rispetto alla ortogonale, era quella di con­<lb></lb>dur dal centro una perpendicolare alla direzione, soggiunge: “ Hinc quoque <lb></lb>corollarium quoque sequetur quod, quanto propinqius erit centrum Librae <lb></lb>centro regionis elementaris, tantum quoque minus erit grave ” (Specul. </s>

<s><lb></lb>lib. </s>

<s>cit., pag. </s>

<s>143). </s></p><p type="main">

<s>Dal caso della Bilancia orizzontale, qui contemplato dal Benedetti, passa <lb></lb>il Torricelli ad applicare il teorema al caso della Bilancia inclinata, e non <lb></lb><figure id="id.020.01.1960.1.jpg" xlink:href="020/01/1960/1.jpg"></figure></s></p><p type="caption">

<s>Figura 88.<lb></lb>solamente conferma la conclusione di Guidu­<lb></lb>baldo, che cioè il peso in E è più grave che <lb></lb>in D, ma dimostra in qual proporzione sia <lb></lb>l&#039;un peso minore dell&#039;altro, preparandosi a <lb></lb>ciò fare le vie con questo Lemma: Abbiasi il <lb></lb>triangolo ABC (fig. </s>

<s>88), in cui sia il lato AB <lb></lb>minore del lato BC, e sia BD bissettrice. </s>

<s>Con­<lb></lb>ducansi dal punto D, ai detti lati, DF e DE perpendicolari; sarà ABXDF <lb></lb>=BCXED; ossia AB:BC=ED:DF. </s></p><p type="main">

<s>“ Ora posto, dice il Torricelli, che B figuri il centro, ed AC una Lib­<lb></lb>bra di braccia eguali, con due pesi eguali nelle estremità A, C, i cui mo­<lb></lb>menti o gravità son misurate dalle perpendicolari DF, DE, siccome dichiara <lb></lb>Giov. </s>

<s>Battista de&#039;Benedetti nel suo libro Delle speculazioni matematiche, <lb></lb>capitolo III ovvero IV; ne segue che il momento del peso in A, al momento <lb></lb>del peso in C, sia reciprocamente come la retta BC alla retta AB, cioè re­<lb></lb>ciprocamente come la distanza dei pesi dal centro della Terra. </s>

<s>E di qui ab­<lb></lb>biamo, non solamente che il peso più vicino al centro, mentre è nella Lib­<lb></lb>bra, pesa più del meno vicino, ma sappiamo ancora in qual proporzione più <lb></lb>pesa ” (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>112). </s></p><p type="main">

<s>Abbiamo voluto citar piuttosto il passo manoscritto, che quello pubbli­<lb></lb>cato dal Grandi nelle note a Galileo (Alb. </s>

<s>XIV, 121), non solo perchè la <lb></lb>pubblicazione di lui, in alcune parti infedele, nuoce alla chiarezza, ma per­<lb></lb>chè, seguitando a leggere nello stesso manoscritto, trovasi dal Torricelli, con <lb></lb>la considerazione delle forze centrali, risoluto più sottilmente che possa de­<lb></lb>siderarsi il problema meccanico da Aristotile proposto nella sua prima Que­<lb></lb>stione. </s>

<s>Il Tartaglia ne discorse a lungo nel VII libro de&#039;suoi Quesiti, accu-<pb xlink:href="020/01/1961.jpg" pagenum="204"></pb>sando di falso il detto del Filosofo, che cioè le Bilanee di braccia più lunghe <lb></lb>siano più diligenti, e fa ivi notare che, per quella maggior diligenza, si eleg­<lb></lb>gono anzi dagli orefici i piccoli Saggiatori. </s>

<s>Conclude il suo lungo discorso <lb></lb>con dire che, essendo le Bilance più piccole più esenti dalle passioni della <lb></lb>materia, rispondono perciò meglio alle intenzioni del Geometra, secondo le <lb></lb>quali hanno eguale mobilità così le lunghe braccia come le corte “ perchè <lb></lb>ogni sorte di peso, posto in qualsivoglia sorte di Libra, farà inclinar quella <lb></lb>de continuo, per fino a tanto che quella sia gionta all&#039;ultimo over più basso <lb></lb>luoco, che quella inclinar si possa ” (fol. </s>

<s>77 a tergo). </s></p><p type="main">

<s>Ma questo si verifica nel caso della Bilancia <emph type="italics"></emph>folle,<emph.end type="italics"></emph.end> ch&#039;è il più temuto <lb></lb>vizio dello strumento, e i Saggiatori non per questo son agili, <emph type="italics"></emph>perchè più <lb></lb>se accostano over approprinquano alle parti della Libra ideale,<emph.end type="italics"></emph.end> ma per­<lb></lb>chè la loro leggerezza conferisce a fare avvicinar più che sia possibile il <lb></lb>centro di gravità al punto di appoggio, cosicchè, senz&#039;andar ne&#039;difetti del­<lb></lb>l&#039;equilibrio indifferente, ne partecipano de&#039;vantaggi. </s></p><p type="main">

<s>Il Benedetti perciò correggeva Aristotile con altre ragioni dedotte dalla <lb></lb>natura del Vette, perchè, in due Bilance solamente differenti per la lun­<lb></lb>ghezza delle braccia, il peso è nel braccio più lungo più ponderoso, “ et <lb></lb>hac de causa movebit ad partem inferiorem maiori cum agilitate brachium: <lb></lb>multo magis etiam illud ipsum deprimet, idest maiorem etiam angulum fa­<lb></lb>ciet ” (Specul. </s>

<s>lib. </s>

<s>cit., pag. </s>

<s>153). </s></p><p type="main">

<s>Il Torricelli poi dimostrò, come necesaria conseguenza delle forze con­<lb></lb>vergenti, che appena inclinata la Bilancia dal suo preponderante questo ac­<lb></lb>cresce il momento con proporzion maggiore nel braccio più lungo, che nel <lb></lb>più corto, e di qui la ragion vera dei vantaggi da Aristotile predicati. </s>

<s>“ Inol­<lb></lb>tre (così ripigliasi nel manoscritto torricelliano il costrutto che si lasciò di <lb></lb>sopra interrotto) possiamo dedurne un&#039;altra verità, che non si cammina con <lb></lb><figure id="id.020.01.1961.1.jpg" xlink:href="020/01/1961/1.jpg"></figure></s></p><p type="caption">

<s>Figura 89.<lb></lb>la medesima proporzione nella Libbra grande <lb></lb>e nella piccola sempre. </s>

<s>” </s></p><p type="main">

<s>“ Sia una Libbra AB (fig. </s>

<s>89) ed una <lb></lb>minore CD, il cui centro comune sia in E, <lb></lb>ambedue con braccia eguali e con pesi eguali, <lb></lb>e l&#039;estremità F rappresenti il centro della <lb></lb>Terra, al quale tendono naturalmente i pesi <lb></lb>per linee non parallele, ma convergenti in F. </s>

<s><lb></lb>E perchè il peso A al peso B ha, secondo il <lb></lb>suo momento, la proporzione reciproca di BF <lb></lb>ad FA, ed il momento del peso C al momento <lb></lb>del peso D è come la DF alla CF, e la BF <lb></lb>alla CF ha maggior ragione che la DF alla <lb></lb>medesima FC (suppongo che la Libbra sia totalmente obliqua, che il punto <lb></lb>A sia il più vicino al centro F e poi il punto C, e poi E e poi D e B sia il <lb></lb>più lontano) ed essendo FC maggiore di FA, sarà per conseguenza molto <lb></lb>maggiore la ragione di BF ad FA, che di DF a FC; cioè maggiore ragione <pb xlink:href="020/01/1962.jpg" pagenum="205"></pb>del momento di A rispetto al momento del peso B, che del peso C al <lb></lb>peso D. ” </s></p><p type="main">

<s>“ E questa speculazione ci fa intendere un segreto vantaggio, che ha <lb></lb>la Libbra grande sopra la piccola, nel mostrare la inegualità di due pesi, <lb></lb>che stiano appesi alle estremità di quella Libbra. </s>

<s>Imperocchè, sebbene stando <lb></lb>in equilibrio, o diciamo in sito orizzontale, le due Libbre, la maggiore e la <lb></lb>minore, non cammina la proporzione della maggior proporzione de&#039;momenti <lb></lb>nella Libbra maggiore che nella minore; tuttavia, ponendosi che un peso <lb></lb>sia maggiore dell&#039;altro, il maggiore rimove la Libbra dal sito orizzontale, <lb></lb>ed indi acquista il maggior peso molto maggior momento nella Libbra grande <lb></lb>che nella piccola, siccome si è dimostrato di sopra, ed in conseguenza ci mo­<lb></lb>stra più apertamente l&#039;inegualità. </s>

<s>Nelle Libbre però materiali nel punto del­<lb></lb>l&#039;equilibrio nasce un certo ritardamento dal tocco che si fa, il quale impe­<lb></lb>disce più la Libbra maggiore che la minore ” (fol. </s>

<s>112). </s></p><p type="main">

<s>Avendo più sopra mostrato qual si fosse l&#039;origine di queste specula­<lb></lb>zioni del Torricelli, giova soggiunger che un&#039;origine simile dovettero aver <lb></lb>le speculazioni del Cartesio, a cui aveva riferito il Mersenno le conclusioni <lb></lb>dello stesso Torricelli, e il modo da lui tenuto in computare i momenti nella <lb></lb><figure id="id.020.01.1962.1.jpg" xlink:href="020/01/1962/1.jpg"></figure></s></p><p type="caption">

<s>Figura 90.<lb></lb>Bilancia considerate le forze co­<lb></lb>me dirette al centro della Terra. <lb></lb></s>

<s>“ Quantum ad id quod de Bilance <lb></lb>scribis, rispondeva Renato all&#039;ami­<lb></lb>co, in eorum sum sententia qui <lb></lb>dicunt pondera esse in aequilibrio, <lb></lb>quando sunt in ratione reciproca <lb></lb>linearum perpendicularium, quae <lb></lb>ducuntur a centro Librae in lineas <lb></lb>rectas, quae extremitates brachiorum centro Terrae <lb></lb>connectunt ” (Epist., T. II cit., pag. </s>

<s>93). E fu in <lb></lb>questa sentenza condotto e in essa confermato da <lb></lb>un ragionamento, simile a quello, a cui il Torricelli <lb></lb>aveva nel <emph type="italics"></emph>Mechanicorum liber<emph.end type="italics"></emph.end> ritrovato, come si <lb></lb>disse, il principio. </s>

<s>Riduciamoci perciò alla memoria <lb></lb>il discorso, in cui dianzi dimostravasi da Guidubaldo <lb></lb>che il più basso peso nella Bilancia prepondera al <lb></lb>più alto, e rappresentiamoci nuovamente sott&#039;occhio <lb></lb>l&#039;iconismo illustrativo (fig. </s>

<s>90). Diceva che il peso in <lb></lb>E ha la discesa più retta del peso D, perchè l&#039;an­<lb></lb>golo SEG è più acuto di SDA e ciò dee naturalmente <lb></lb>aver suggerito al Cartesio l&#039;uso delle due tangenti, <lb></lb>che venivano così a rappresentargli i due pesi come <lb></lb>posati sopra due piani, in cui le Meccaniche avevano <lb></lb>insegnato già a computar, fra la gravezza assoluta e la relativa, la propor­<lb></lb>zion del momento. </s></p><pb xlink:href="020/01/1963.jpg" pagenum="206"></pb><p type="main">

<s>Non altrimenti infatti da questo primo avvio procede, nell&#039;epist. </s>

<s>LXXVIII <lb></lb>della I parte, quella cartesiana dimostrazione, nella quale si dice essere la <lb></lb>gravità relativa del peso D all&#039;assoluta come il perpendicolo DI sta al piano <lb></lb>inclinato DH, e allo stesso modo essere le due gravità di E come EF sta <lb></lb>ad EL. </s>

<s>Ma perchè CM è stata condotta perpendicolare a MS, i triangoli si­<lb></lb>mili ELF, CEM daranno EF:EL=CM:CE. </s>

<s>Simili parimente essendo i <lb></lb>due triangoli DHI, DIC si avrà per essi DI:DH=IC:DC. Ond&#039;è che, se <lb></lb>siano i pesi assolutamente eguali, ossia se EL=DH, avendo la Bilancia le <lb></lb>due braccia CE, DC uguali, le due dette ragioni si ridurranno in quest&#039;una <lb></lb>EF:DI=CM:IC. </s>

<s>Ora prosegue a dimostrare il Cartesio, in modo simile <lb></lb>a quello del Torricelli, che CM:IC=DS:ES. “ Pondus autem, quod est <lb></lb>in E, se habet ad pondus, quod est in D, ut CM:IC, ergo ut DS:ES. </s>

<s>Unde <lb></lb>liquet centrum gravitatis duorum ponderum D, E, simul iunctorum per li­<lb></lb>neam DE, non esse in puncto C, sed inter C et E, ex. </s>

<s>gr. </s>

<s>in puncto R, in <lb></lb>quod suppono cadere lineam illam, quae dividit angulum DSE in duas ae­<lb></lb>quales partes. </s>

<s>Hoc enim posito, notum est in Geometria lineam DR esse <lb></lb>ad RE ut DS ad ES, ita ut debeant pondera in D et E sustineri a puncto R, <lb></lb>ut in aequilibrio maneant in eo in quo sunt loco. </s>

<s>Verum, si supponatur <lb></lb>linea DE aliquanto magis aut minus inclinata super horizontem, aut si suppo­<lb></lb>nantur pondera haec in alia a Terra distantia, oportebit illa ab alio puncto <lb></lb>sustineri ut sint in aequilibrio, et sic illorum centrum gravitatis non est sem­<lb></lb>per in eodem puncto ” (Fancof. </s>

<s>1692, pag. </s>

<s>226, 27). E così quel che asse­<lb></lb>riva l&#039;Autore in fine alle sue <emph type="italics"></emph>Mechaniques<emph.end type="italics"></emph.end> è matematicamente qui dimo­<lb></lb>strato. </s></p><p type="main">

<s>Veniva dunque dal Cartesio e dal Torricelli, per queste loro matematiche <lb></lb>dimostrazioni, confermato quel che contro Giordano e il Tartaglia aveva da <lb></lb>quella sua meccanica speculazione concluso già Guidubaldo, ond&#039;è che sem­<lb></lb>brava aversi finalmente decisa, da tre così grandi autorità nella scienza, la <lb></lb>causa della II proposizion <emph type="italics"></emph>De ponderibus,<emph.end type="italics"></emph.end> rimasta accusata di falsità nel suo <lb></lb>enunciato e nelle sue ragioni. </s>

<s>La Bilancia di braccia e di pesi eguali, ri­<lb></lb>mossa dalla natural sua posizione orizzontale, non rimane, come diceva Leo­<lb></lb>nardo, nè ritorna, come voleva Giordano: non indifferente anzi nè stabile, <lb></lb>ma folle, seguita a scender giù infin tanto che non si posi nel perpendicolo, <lb></lb>tirata e vinta dalla maggior gravità che, avvicinandosi al centro della Terra, <lb></lb>acquista il peso più basso. </s></p><p type="main">

<s>La questione però non era semplicemente matematica, e pur come ma­<lb></lb>tematica pareva che si potesse risolvere in diversa maniera, perchè, rima­<lb></lb>nendo i pesi orizzontali, scemano com&#039;avea concluso il Benedetti, tanto più <lb></lb>di momento, quanto il centro della Bilancia s&#039;avvicina più al centro del <lb></lb>mondo: mentre, rimanendo immobile essa Bilancia e sol variandosi intorno <lb></lb>a lei la posizione de&#039;pesi, questi, quanto son men lontani dal comun cen­<lb></lb>tro dei gravi, tanto più crescono, come dalla regola del Benedetti stesso re­<lb></lb>sulta, i loro momenti. </s></p><p type="main">

<s>Sembrerebbe dunque che si dovesse ricavar la legge dal primo fatto, <pb xlink:href="020/01/1964.jpg" pagenum="207"></pb>in cui tutta la macchina si muove, o non dal secondo, in cui si move sola <lb></lb>una parte, e che ne sia perciò da concludere aver la gravità diretta, e non <lb></lb>reciproca ragione delle distanze. </s>

<s>Si volle nonostante il Torricelli tener fermo <lb></lb>a questa seconda, perchè s&#039;accomodava con una sua certa idea singolare, <lb></lb>che cioè fosse natura propria dei gravi quella, non di tendere, ma di rifug­<lb></lb>gire dal centro. </s>

<s>Sarebbe perciò quella comunemente chiamata gravità da dir <lb></lb>piuttosto leggerezza, intorno alla quale scrisse due eloquenti lezioni, coll&#039;in­<lb></lb>tendimento di dimostrare agli Accademici fiorentini “ non esser possibile <lb></lb>che gli elementi vadano al centro, primieramente perchè non possono arri­<lb></lb>varvi, e secondariamente perchè arrivandovi sarebbe un distruggere sè me­<lb></lb>desimi ” (Lezioni accad., Milano 1823, pag. </s>

<s>148). Quanto più dunque si di­<lb></lb>lungano i corpi dal centro della Terra tanto più, secondo il Torricelli, en­<lb></lb>trando nella loro propria region naturale, divengono leggeri, ossia scemano <lb></lb>di quel momento che violentemente trattenevali in basso. </s></p><p type="main">

<s>Il Cartesio, incerto intorno al modo di definir le cose secondo il suo <lb></lb>proprio sistema, giacchè Guidubaldo l&#039;avea condotto a concluder che le gra­<lb></lb>vità stanno in reciproca ragione delle distanze, si studiava di confortare le <lb></lb>matematiche dimostrazioni con l&#039;esperienze, osservando i grossi uccelli “ ut <lb></lb>grues, ciconias etc. </s>

<s>multo facilius volare in altiore aere quam inferius ” <lb></lb>(Epist. </s>

<s>LXXIII cit., pag. </s>

<s>215), non per altro, diceva, che per ritrovarsi co­<lb></lb>lassù più leggerì, e lo stesso notava de&#039;così detti aquiloni o cervi volanti. </s>

<s><lb></lb>Nulla ha però maggiore efficacia a confermarlo in quella sua opinione di <lb></lb>un&#039;esperienza eseguita dal suo amico Mersenno, il quale, avendo fatto tirar <lb></lb>verso il zenit palle da gran cannoni, e non vedendole tornare a basso, do­<lb></lb>mandava maravigliato dove fassero andate, e a lui rispondeva il Cartesio che <lb></lb>dovevano esser lassù divenute tanto leggere, da andar disperse com&#039;al vento <lb></lb>le foglie. </s>

<s>“ Denique, si experimentum illud quod a teipso factum fuisse mihi <lb></lb>significasti, et de quo alii etiam nonnulli scripserunt, verum sit, nempe glo­<lb></lb>bos maiorum tormentorum versus zenith recta explosorum non recidere, col­<lb></lb>ligere licet ictus eos in tantam altitudinem ferri, atque a Terrae centro adeo <lb></lb>elongari, ut omnem suam gravitatem inde deperdant ” (ibid.). </s></p><p type="main">

<s>Queste, francamente parlando, son puerili semplicità, come quegli del <lb></lb>Torricelli, trattenendosi sulla superfice e nell&#039;interno della Terra, si direb­<lb></lb>bero filosofi capricci se, pigliando dalla luce, dal calore e dal suono gli <lb></lb>esempii (Lez. </s>

<s>cit., pag. </s>

<s>147), non avessero le leggi della loro diffusione po­<lb></lb>tuto portare a concluder, per gli spazii celesti, direttamente la legge neuto­<lb></lb>niana della gravitazion de&#039;pianeti in reciproca ragion de&#039;quadrati delle di­<lb></lb>stanze dai loro centri attrattivi. </s>

<s>Questionandosi però de&#039;corpi componenti <lb></lb>questa bassa regione elementare, sembrava a molti, che più sanamente ra­<lb></lb>gionavano sull&#039;andare di Antonio Nardi, assai ragionevole che intorno al <lb></lb>centro della Terra serbassero i pesi proporzioni simili a quelle, che si ve­<lb></lb>dono osservare intorno al centro della Bilancia. </s></p><p type="main">

<s>Il concetto delle forze attrattive, che venivasi a chiarir sempre meglio, <lb></lb>pigliava ardore dagli inavvertiti spiriti aristotelici, i quali avevano pronun-<pb xlink:href="020/01/1965.jpg" pagenum="208"></pb>ziato essere nel centro della Libbra un&#039;attrazion simile a quella, che si di­<lb></lb>ceva avere il centro della Terra. </s>

<s>E perciò, come ammetteva il Filosofo essere <lb></lb>a proporzione delle distanze men sostenuto il peso nell&#039;artificiale strumento; <lb></lb>così sembrava ragionevole che dovesse avvenir nella macchina naturale, ossia <lb></lb>nella Terra, in cui pure si avveri che, tanto più crescano i pesi di momento, <lb></lb>quanto più si dilungano dal centro. </s>

<s>Il Castelli e il Viviani fra&#039;nostri furono <lb></lb>di questo sentimento, e ne dettero dimostrazione, il primo in appendice a <lb></lb>una lettera a Galileo (Alb. </s>

<s>X, 125-27), e il secondo in un suo foglio ma­<lb></lb>noscritto pubblicato dal padre Grandi (Alb. </s>

<s>XIV, 120). Sostenne questa opi­<lb></lb>nione in Francia il Fermat, contro validi oppositori, e la professarono molti <lb></lb>altri, fra&#039;quali più autorevole di tutti fu il Newton, che formulava così, <lb></lb>ne&#039;<emph type="italics"></emph>Principii matematici,<emph.end type="italics"></emph.end> la proposizione IX del III libro: “ Gravitatem, <lb></lb>pergendo a superficiebus planetarum, deorsum decrescere in ratione distan­<lb></lb>tiarum a centro quam proxime ” (Genevae 1742, pag. </s>

<s>53); proposizione, <lb></lb>che viene ad essere dimostrata dalla LXXIII del I libro, supposto che serbi <lb></lb>in sè da per tutto uguale densità la materia componente il pianeta. </s></p><p type="main">

<s>Se così è, dopo tante vicende fortunose, la proposizion di Giordano è <lb></lb>salva, almeno nel suo pronunziato. </s>

<s>La Bilancia violentemente rimossa si ri­<lb></lb>stabilisce nel suo primo equilibrio orizzontale, perchè il peso che riman sopra <lb></lb>acquista maggior momento, non già dalla maggior rettitudine della discesa <lb></lb>nel cerchio, ma dalla maggior distanza che, rispetto al peso di sotto, lo se­<lb></lb>para dal centro della regione elementare. </s></p><p type="main">

<s>Se tutte le acque scendessero ai fiumi, la loro ubertà sarebbe propor­<lb></lb>zionale alle piogge, e così avverrebbe del fiume della scienza, se tutte le <lb></lb>speculazioni entrassero nell&#039;aperto alveo, che mena e regola la corrente. </s>

<s>Ma <lb></lb>come molte acque rimangono stagnanti o vanno per sotterranei rigagnoli <lb></lb>disperse, così avvien delle idee, di che ci porgono un singolare esempio le <lb></lb>cose fin qui discorse, essendo che tanto lavorio di mente, fatto da quegli <lb></lb>insigni matematici intorno alle proprietà della Bilancia, o si rimanesse nei <lb></lb>manoscritti o si riducesse in libri, non per tempo venuti alla luce. </s>

<s>Di qui <lb></lb>è che questa parte della scienza degli equilibrii, verso l&#039;anno 1667, era si <lb></lb>può dire a quel punto, in cui l&#039;avea lasciata, quasi un secolo prima, Gui­<lb></lb>dubaldo del Monte. </s></p><p type="main">

<s>Geminiano Montanari infatti, professore nello studio di Bologna, dettava <lb></lb>in quell&#039;anno a&#039;suoi scolari una lezione intorno agli effetti delle Bilance, <lb></lb>dimostrati in sette matematiche proposizioni, nelle quali si concludeva dover <lb></lb>essere una Libbra, che abbia il punto di sospensione nel centro, in condi­<lb></lb>zione di equilibrio indifferente. </s>

<s>E benchè fosse questa, come si sa, l&#039;opi­<lb></lb>nione di Guidubaldo, teneva nonostante il Montanari in approvarla altro <lb></lb>modo, ch&#039;era quello di far vedere com&#039;avendo in qualunque posizione l&#039;un <lb></lb>peso e l&#039;altro egual distanza dalla verticale, condotta per il punto del cir­<lb></lb>convolubile, hanno perciò eguali i momenti, secondo il ragionamento stesso <lb></lb>che avea fatto due secoli prima Leonardo da Vinci. </s></p><p type="main">

<s>L&#039;anno dopo che fu dettata questa lezione, l&#039;autografo della quale è <pb xlink:href="020/01/1966.jpg" pagenum="209"></pb>inserito dal foglio 128-31 del tomo XIX de&#039;Manoscritti del Cimento, Donato <lb></lb>Rossetti pubblicava in Firenze le sue <emph type="italics"></emph>Dimostrazioni fisico-matematiche delle <lb></lb>VII proposizioni,<emph.end type="italics"></emph.end> nella II delle quali, con principii statici che avevano l&#039;ap­<lb></lb>parenza di nuovi, si tornava a discorrere degli effetti delle Bilance, propo­<lb></lb>nendosi a risolvere il problema sotto questa forma: “ Si pigli una Bilancia, <lb></lb>che abbla uguali le braccia, all&#039;estremità delle quali si appendino i pesi <lb></lb>uguali, e si costituisca inclinata all&#039;orizzonte: si fermi, e dopo si lassi in <lb></lb>sua libertà. </s>

<s>L&#039;esperienza insegna che in tal sito non si fermi, ma che si <lb></lb>porti con le braccia parallele all&#039;orizzonte. </s>

<s>Cercasi la causa di tal movi­<lb></lb>mento ” (pag. </s>

<s>9). </s></p><p type="main">

<s>Se bastasse la sola considerazione dei centri di gravità, dovrebbe la Bi­<lb></lb>lancia, dice il Rossetti, rimanere, ma perchè il fatto dimostra che ritorna, <lb></lb>è da ricercar di ciò la ragione in qualche altra cosa diversa, dipendènte da <lb></lb>questo, ch&#039;egli vuole gli sia concesso, che cioè “ un corpo prema e graviti <lb></lb>sopra un altro, non solo per il proprio momento, ma ancora per tutto il <lb></lb>momento degli altri corpi, che uno sopra l&#039;altro l&#039;aggravano ” (ivi, pag. </s>

<s>4). <lb></lb>Ammesso questo, poi soggiunge, “ se ne deduce, levati gl&#039;impedimenti, che <lb></lb>ogni settore di globo sarà sem­<lb></lb>pre in peso assoluto eguale ad <lb></lb>un altro settore a sè medesi­<lb></lb>mamente eguale ” (ivi). </s></p><p type="main">

<s>Se ora siano GD, ND, LD <lb></lb>(fig. </s>

<s>91) tre linee, che s&#039;appun­<lb></lb>tano nel centro della Terra D, <lb></lb>facendo gli angoli GDN, NDL <lb></lb>eguali, e sia la Bilancia EF so­<lb></lb>spesa nel suo centro di gravità <lb></lb>in C, supposte le due braccia <lb></lb>CE, CF eguali e i pesi in E e <lb></lb>in F eguali, rimarrà EF nella <lb></lb>perfetta linea orizzontale, per­<lb></lb>chè il settore GDN, avendo ca­<lb></lb><figure id="id.020.01.1966.1.jpg" xlink:href="020/01/1966/1.jpg"></figure></s></p><p type="caption">

<s>Figura 91.<lb></lb>pacità uguale a quella del settore NDL, vengono EC, e CF ugualmente pre­<lb></lb>mute dall&#039;una parte e dall&#039;altra. </s></p><p type="main">

<s>Ma s&#039;inclini la Bilancia, e si lasci nella posizione AB: il peso A serba <lb></lb>tuttavia il momento medesimo del peso B, ma i settori HDN, NDM sono <lb></lb>disuguali e perciò, aggiungendo quegli uguali momenti a questi disuguali <lb></lb>settori, si farebbe contro la causa degli equilibrii. </s>

<s>“ Adunque non può la <lb></lb>Bilancia stessa, ne conclude il Rossetti, fermarsi in questa inclinazion di set­<lb></lb>tori, uno maggiore dell&#039;altro, ed è necessario che si riduca all&#039;orizzontale <lb></lb>EF, nel qual posto solo aggiunge i suoi momenti uguali ai momenti uguali <lb></lb>degli uguali settori NDL, NDG ” (ivi, pag. </s>

<s>16). </s></p><p type="main">

<s>Entrato il Rossetti, per via specialmente della spiegazione de&#039;fenomeni <lb></lb>di capillarità, in gare letterarie col Montanari, questi pubblicò in Bologna <pb xlink:href="020/01/1967.jpg" pagenum="210"></pb>nel 1669, sotto il nome del suo discepolo Ottavio Finetti, un libro apologe­<lb></lb>tico col titolo di <emph type="italics"></emph>Prostasi fisico-matematica,<emph.end type="italics"></emph.end> dove, dopo la stampa della sopra <lb></lb>commemorata Lezione <emph type="italics"></emph>Degli effetti delle bilance,<emph.end type="italics"></emph.end> si facevano alcune consi­<lb></lb>derazioni intorno a ciò che degli equilibrii aveva nella II delle sue propo­<lb></lb>sizioni dimostrato lo stesso Rossetti. </s>

<s>Si diceva che se CB ha maggior mo­<lb></lb>mento di AC dee necessariamente seguitare a scendere, e non a risalire <lb></lb>all&#039;orizzonte, e quanto all&#039;efficacia de&#039;centri di gravità e all&#039;esperienza, da <lb></lb>cui la speculazione pigliava il fondamento, così si diceva: </s></p><p type="main">

<s>“ È manifesto che il signor Rossetti s&#039;inganna in credere che, quando <lb></lb>un corpo è sospeso per il centro di gravità sua, non resti in ogni sito equi­<lb></lb>librato, il che nel suo caso succederebbe sempre, purchè li tre punti del­<lb></lb>l&#039;asse e degli estremi fossero in una linea retta a capello. </s>

<s>Ma il fatto sta <lb></lb>che niuna Bilancia buona ha questi tre punti in linea retta, ma bensì quello <lb></lb>di mezzo è d&#039;alquanto superiore agli altri due, onde da ciò nascono gli ef­<lb></lb>fetti considerati. </s>

<s>E se il signor Rossetti, nel fare l&#039;esperienze sue, avesse <lb></lb>bene avvertito alla vera struttura delle Bilance, non avrebbe ricercato infino <lb></lb>al ccntro della Terra la cagione di quegli effetti ” (pag. </s>

<s>42). </s></p><p type="main">

<s>Erano il Montanari e il Rossetti stati ascritti all&#039;Accademia del Cimento, <lb></lb>in quell&#039;ultimo periodo che seguitava a presiederla, già fatto cardinale, il <lb></lb>principe Leopoldo, il quale volle sentire intorno a quelle controversie delle <lb></lb>Bilance il giudizio del Viviani. </s>

<s>Rispose questi che il Montanari, come fisico <lb></lb>matematico, ragionava bene, perchè, attendendo alla smisurata distanza che <lb></lb>è dalla superfice al centro della Terra, si possono le direzioni dei pesi ri­<lb></lb>guardar come parallele, e perciò, se il punto di sospensione è nel centro o <lb></lb>vicinissimo al centro, la Bilancia è in condizione di equilibrio indifferente, <lb></lb>com&#039;è confermato dalla più facile esperienza. </s>

<s>Ma l&#039;esperienza del Rossetti <lb></lb>diceva liberamente essere una fallacia, perche, se rimosso uno de&#039;pesi la <lb></lb>vedeva tornare all&#039;orizzonte, non poteva esser per altro, se non che per <lb></lb>aversi il punto di sospensione costituito più in alto del centro. </s>

<s>Notava inol­<lb></lb>tre che s&#039;introducevano da lui le direzioni convergenti fuor di proposito, <lb></lb>perch&#039;essendo il più basso peso il più grave ne doveva seguire un effetto <lb></lb>contrario. </s></p><p type="main">

<s>Restava così confermata l&#039;accusa del Montanari, che cioè il Rossetti non <lb></lb>aveva bene avvertito alla vera struttura delle Bilance, e il Viviani stesso <lb></lb>ebbe in questa occasione a fare esperienza del difetto che, di queste cogni­<lb></lb>zioni intorno al principio delle equiponderanze, era in parecchi altri a quei <lb></lb>tempi, come si mostrerà dal seguente fatto, col quale siam per chiudere <lb></lb>nella nostra Storia questo episodio. </s></p><p type="main">

<s>Aveva posto più volte mente il Viviani a quell&#039;ondeggiare, che fanno <lb></lb>le Bilance prima di ristabilirsi in equilibrio, e il lungo ago gli si rappre­<lb></lb>sentava nella viva immaginazione qual persona folle e ubriaca. </s>

<s>Gli venne di <lb></lb>qui il pensiero di quella macchinetta spettacolosa che, senza conoscerne l&#039;in­<lb></lb>ventore, si descrive in quasi tutti i trattati di Fisica, per dar l&#039;esempio e <lb></lb>mostrar la ragione dell&#039;equilibrio stabile ne&#039;corpi sospesi; esempio rappre-<pb xlink:href="020/01/1968.jpg" pagenum="211"></pb>sentato in un fantoccio, con due contrappesi in una mano e nell&#039;altra, che <lb></lb>posato sulla punta di un piè, su qualunque sostegno, va balenando qua e là <lb></lb>nè casca mai. </s>

<s>Di contro all&#039;abbozzato disegno scriveva il Viviani stesso di <lb></lb>sua propria mano in un foglio: “ Tutto il segreto dentro la figuretta ondeg­<lb></lb>giante sul bilico senza mai cadere, bench&#039;ella non sia collegata col soste­<lb></lb>gno, ma solamente vi posi colla punta, sta che il centro di gravità del compo­<lb></lb>sto si trova sempre sotto il punto del sostegno ” (MSS. Gal. </s>

<s>Disc., T. CXLIII, <lb></lb>fol. </s>

<s>64). Era il segreto stesso tanto tempo prima scoperto da Leonardo da <lb></lb>Vinci: <emph type="italics"></emph>il centro di ciascuno peso sospeso ci stabilisce sotto il suo sosten­<lb></lb>tacolo,<emph.end type="italics"></emph.end> eppure Giuseppe Ferroni, valoroso fisico e matematico, discepolo del <lb></lb>Viviani, veduta con sua gran maraviglia in Bologna, dov&#039;era allora profes­<lb></lb>sore nel collegio dei gesuiti, una di quelle figurine ondeggianti in casa Co­<lb></lb>spi, non seppe, con tutta la sua scienza nè con quella de&#039;suoi colleghi, ren­<lb></lb>dersi la ragione di quel fatto spettacoloso. </s></p><p type="main">

<s>“ Ho visto in casa del marchese Cospi, perciò scriveva al Viviani, una <lb></lb>statuetta di legno di un Maestro, la quale, tenendo in mano un&#039;asta rigida <lb></lb>con due contrappesi, ed avendo nel piede una punta ferrata di trottola, posta <lb></lb>su un candeliere di legno, su quello si gira, facendo molti ondeggiamenti, <lb></lb>come se volesse cadere, ma però sempre si mantiene in piedi. </s>

<s>Io pensai <lb></lb>che questo equilibrio nascesse dal centro della gravità, qual fosse nella punta <lb></lb>di ferro, che le serve dì polo per raggirarsi, ma conobbi di aver fallito, per­<lb></lb>chè, avendo provato a sospendere la statuetta da detta punta di ferro, non <lb></lb>stava equilibrata, ma prevalevano i contrappesi. </s>

<s>Onde mi sono immaginato <lb></lb>vi sia dentro qualche artifizio di argento vivo, quale scorra in que&#039;tanti on­<lb></lb>deggiamenti per l&#039;asta de&#039;contrappesi. </s>

<s>So questa invenzione esser venuta <lb></lb>di Firenza, onde la stimo parto dell&#039;ingegno di V. S. illustrissima. </s>

<s>Sono som­<lb></lb>mamente bramoso di saperne l&#039;arcano, onde fo ricorso alla sua gentilezza, <lb></lb>pregandola si compiaccia di spiegarmelo. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. CXLVI, <lb></lb>fol. </s>

<s>281). </s></p><p type="main">

<s>Il Viviani compiacque al discepolo e all&#039;amico, ma è notabile che si <lb></lb>servisse per la spiegazione di un esempio men naturale di quello delle Bi­<lb></lb>lance, e che volesse sostituire alla dottrina de&#039;centri di gravità, di così fa­<lb></lb>cile applicazione ne&#039;comuni strumenti da pesare, le più complicate teorie <lb></lb>de&#039;centri di oscillazione dei pendoli. </s>

<s>Il Ferroni in ogni modo vedeva come <lb></lb>si potesse far dipendere il segreto da più alti principii de&#039;vulgari, e così <lb></lb>rispondeva, per significare la sua gratitudine alla liberalità del Maestro: </s></p><p type="main">

<s>“ Mi è stata graditissima la sua spiegazione, la quale ho notificata ad <lb></lb>alcuni di questi lettori di Filosofia, e perchè mi domandano la sua lettera, <lb></lb>io per sodisfare a tutti in un colpo ho risoluto di far venire in collegio, di <lb></lb>casa del bali Cospi, il fantoccio barcollante, e farlo vedere a tutta questa <lb></lb>nostra numerosa scolaresca, che pochissimi di loro l&#039;hanno veduto, e con <lb></lb>quella occasione farvi sopra l&#039;eruditissima spiegazione della sua lettera. </s>

<s>Ser­<lb></lb>virommi della sua similitudine molto calzante del vaso cupo dondolante sulla <lb></lb>punta di un coltello, sulla schiena superiore del qual vaso s&#039;inchiodasse un <pb xlink:href="020/01/1969.jpg" pagenum="212"></pb>fantoccio. </s>

<s>Conforme i suoi insegnamenti <lb></lb>ridurrò la macchina al pendolo, ma per <lb></lb>più facile intelligenza degli scolari, la ri­<lb></lb>durrò al pendolo composto di asta rigida <lb></lb>ABC (fig. </s>

<s>92), la di cui asta BC, di sotto <lb></lb>al B centro del moto, se si divaricasse in <lb></lb>due aste de&#039;contrappesi del fantoccio bar­<lb></lb>collante, farebbe sulla punta B la supe­<lb></lb>riore asta BA quegli ondeggiamenti, che <lb></lb>fa la macchinetta ammirata ” (ivi, fol. </s>

<s>282). <lb></lb><figure id="id.020.01.1969.1.jpg" xlink:href="020/01/1969/1.jpg"></figure></s></p><p type="caption">

<s>Figura 92.</s></p><pb xlink:href="020/01/1970.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle Macchine<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della natura delle Macchine e del modo di operar del Vette, dell&#039;Asse nella ruota, e delle Taglie; <lb></lb>del Cuneo e della Vite. </s>

<s>— II. </s>

<s>Delle proporzioni tra la resistenza, e la potenza necessaria a sol­<lb></lb>levare i gravi, per via dei piani inclinati. </s>

<s>— III. </s>

<s>Delle censure di Alessandro Marchetti sopra <lb></lb>i teoremi di Galileo e del Torricelli del momento dei gravi su i piani inclinati: della etero­<lb></lb>dossia meccanica di Giovan Francesco Vanni, e delle difficoltà, che trovarono in confutarla i <lb></lb>Galileiani. </s>

<s>— IV. </s>

<s>Delle confutazioni speculate dai Matematici stranieri, e della questione in­<lb></lb>torno alla composizion dei momenti, proposta in Roma per rispondere ai sofismi del Vanni: <lb></lb>degli errori di Luc&#039;Antonio Porzio confutati dal Grandi. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>A definir l&#039;essere e le proprietà naturali di quegli ingegni ritrovati dal­<lb></lb>l&#039;arte e dall&#039;industria dell&#039;uomo ora per isgravarsi, ora per esercitar più <lb></lb>facilmente le forze nel maneggio dei pesi, giova ripensare a quegli atti, che <lb></lb>comunemente si fanno, e che, sebben passino inavvertiti dal volgo, il Filo­<lb></lb>sofo nonostante piglia per fondamento alle sue speculazioni. </s>

<s>Chiunque vuol <lb></lb>dalle sue spalle deporre qualche cosa, che gliele aveva aggravate con fati­<lb></lb>cosa molestia, o la getta a posar per terra o l&#039;attacca a qualche mensola. </s>

<s><lb></lb>Il piano suolo dunque direttamente, e gli oggetti fermati in esso e sopr&#039;esso <lb></lb>elevati son le macchine più naturali, che i primi uomini ebbero a trovar <lb></lb>negli aperti campi, e ne&#039;rami degli alberi sporgenti. </s>

<s>L&#039;essenza poi di co­<lb></lb>teste macchine, che la Natura spontanea offeriva agli affaticati, si vede non <lb></lb>in altro insomma consistere che nell&#039;uso dei sostegni. </s></p><p type="main">

<s>I corpi però, così ben sostenuti, si rimanevano tuttavia immobili, e a <lb></lb>colui, che, per suo desiderio o per suo bisogno, gli avesse voluti traslocare, <pb xlink:href="020/01/1971.jpg" pagenum="214"></pb>conveniva riprenderseli nuovamente di là, dove aveagli o posati o sospesi, <lb></lb>riaggravandosi di tutta quella prima deposta fatica le braccia e gli omeri. </s>

<s><lb></lb>Il non poter sempre durare una tal fatica, e il desiderio innato di allegge­<lb></lb>rirla affinò l&#039;industria, e suggerì i primi esercizi dell&#039;arte. </s>

<s>Dovett&#039;essere il <lb></lb>più ovvio di questi suggerimenti quello di traslocare il pesante corpo posato <lb></lb>in piano col rotolarlo, ciò che serviva bene, quando si voleva mettere da una <lb></lb>parte piuttosto che da un&#039;altra, ma non già, quando fosse stato bisogno di <lb></lb>sollevarlo più in alto. </s>

<s>S&#039;ebbe a sperimentare anzi che, dove là bastava una <lb></lb>piccolissima forza, qui era invece necessità di mettercela tutta. </s>

<s>Doveva es­<lb></lb>servi dunque, tra questo massimo e quel minimo, una via di mezzo, ed era <lb></lb>ciò appunto che si cercava, perchè ben riconoscendo non esser possibile a <lb></lb>sollevare un peso senza fatica, nè potendo per natura scansarla, si cercava <lb></lb>l&#039;arte di alleggerirla o di ridurla almen tale, che si potesse durare. </s></p><p type="main">

<s>S&#039;aprì da questi desiderii la mente, la quale intese che, a rotolare il <lb></lb>grave sul piano, ci voleva piccolissima forza, perchè rimaneva tutto sul suo <lb></lb>sostegno, e che a sollevarlo ce ne bisognava grandissima, perchè nulla oramai <lb></lb>più gli serviva di appoggio. </s>

<s>Bene essendosi di qui compresa la ragion della <lb></lb>maggiore e della minore difficoltà del moto, suggerì l&#039;arte che quello si cer­<lb></lb>cava si sarebbe facilmente potuto ritrovare <lb></lb>col far sì che il grave, se non tutto, fosse <lb></lb>almeno sostenuto dalla macchina in parte, <lb></lb>e si lasciasse il resto alle forze del motore. </s></p><p type="main">

<s>S&#039;otteneva l&#039;intento con l&#039;inclinare più <lb></lb>o meno il piano sull&#039;orizzonte, e secondo <lb></lb>quella maggiore o minore inclinazione si <lb></lb>compartivano, fra la potenza e la resistenza, <lb></lb>le virtù a talento dell&#039;arte. </s>

<s>Sia AB (fig. </s>

<s>93) <lb></lb>il piano e AD il perpendicolo: a rotolare <lb></lb>un grave sopra AB richiedesi piccolissima, <lb></lb>anzi nessuna forza, se fosse possibile ri­<lb></lb>movere ogni sorta d&#039;impedimenti, perchè <lb></lb>la macchina resiste per sè a tutto il peso. </s>

<s><lb></lb>Ma a sollevar quello stesso grave per AD, <lb></lb><figure id="id.020.01.1971.1.jpg" xlink:href="020/01/1971/1.jpg"></figure></s></p><p type="caption">

<s>Figura 93.<lb></lb>si richiede tutta intera la forza necessaria, <lb></lb>perchè la macchina nulla ne sostenta. </s>

<s>Fra B e D son segnate infinite le vie <lb></lb>di mezzo, e quanto più si sale, tanto <lb></lb>meno resiste la macchina al peso, e più <lb></lb>perciò ne rilascia alle forze del motore. </s></p><p type="main">

<s>Dal piano passando alla mensola, o <lb></lb>di qualunque sia forma e comunque sia <lb></lb>posto, al fulcro, ebbe l&#039;arte a essere <lb></lb>scorta da esperienze simili e da simili <lb></lb><figure id="id.020.01.1971.2.jpg" xlink:href="020/01/1971/2.jpg"></figure></s></p><p type="caption">

<s>Figura 94.<lb></lb>ragionamenti, quando volle provarsi a sollevare i pesi, esercitandovi at­<lb></lb>torno la Leva. </s>

<s>Sia in C (fig. </s>

<s>94) ad essa Leva il fulcro, e sia in B col-<pb xlink:href="020/01/1972.jpg" pagenum="215"></pb>locato il peso: facilissime esperienze dimostrarono che, facendosi forza in A <lb></lb>a una distanza da C eguale a quella di B, si durava fatica quanto a tenere <lb></lb>il peso in mano, o quanto a riprenderlo dalla mensola, dove s&#039;era attac­<lb></lb>cato, e rimetterselo sulle braccia. </s>

<s>Ritirando però B verso C si sentiva alle­<lb></lb>viare via via la fatica, infin tanto che, giunto in C, non ci voleva forza di <lb></lb>nulla. </s>

<s>S&#039;ebbe anche di qui perciò a riconoscere che fra il tutto e il nulla <lb></lb>v&#039;erano le vie di mezzo, la ragion delle quali dipendeva dalla maggiore o <lb></lb>minor distanza dal sostegno, secondo la qual distanza si potevano a piacer <lb></lb>dell&#039;arte compartire, fra la potenza e la resistenza, i respettivi momenti. </s>

<s><lb></lb>Quanto più debole si sentiva il motore, tanto più studiavasi di caricarsi di <lb></lb>men peso per sè, e di lasciarlo piuttosto sul sostegno, pigliando giusta re­<lb></lb>gola dalle distanze, giacchè l&#039;esperienza gli avea insegnato che tanto più resi­<lb></lb>ste la macchina, quanto ha il peso più vicino al centro del moto, e tanto <lb></lb>men fatica si dura, quanto gli si resiste di più lontano. </s></p><p type="main">

<s>La Leva e il Piano inclinato sono i due esemplari, a cui s&#039;informano, <lb></lb>e da cui dipendono le altre macchine conosciute e descritte dalla scienza <lb></lb>ne&#039;suoi trattati, giacchè derivano dalla prima l&#039;Asse in peritrochio e il Po­<lb></lb>lispasto, e dalla seconda il Cuneo e la Coclea. </s>

<s>Que&#039;Filosofi perciò, che al <lb></lb>sopra detto modo ragionavano, investigarono l&#039;intima costituzione di tutt&#039;e <lb></lb>sei le potenze meccaniche, e facilmente ne riconobbero le proprietà nelle <lb></lb>ragioni e negli usi. </s></p><p type="main">

<s>Fruga i nostri Lettori la curiosità di sapere se fossero que&#039;Filosofi, o <lb></lb>gli antichi del tempo di Archimede, o i moderni del tempo di Galileo, per <lb></lb>dar sodisfazione alla qual curiosità rispondiamo essere stati coloro, che più <lb></lb>espressamente riducevano le virtù delle macchine al sostegno, Filosofi sco­<lb></lb>nosciuti di que&#039;tempi di mezzo, ne&#039;quali speculava Leonardo da Vinci. </s>

<s>Il <lb></lb>fondamento statico di Lui, come si riferì nella prima parte del precedente <lb></lb>discorso, è riposto nel principio notissimo che <emph type="italics"></emph>quella cosa, che fia più lon­<lb></lb>tana dal suo firmamento, manco da esso fia sostenuta,<emph.end type="italics"></emph.end> d&#039;onde se ne con­<lb></lb>cludono le leggi dell&#039;equilibrio tra la potenza e la resistenza dei gravi so­<lb></lb>spesi. </s>

<s>Quanto ai gravi posati sui piani, vedemmo nel capitolo primo di que­<lb></lb>sto Tomo come Leonardo, immaginando di aver la ruota di un carro, che <lb></lb>si muova su per un&#039;erta, determinasse con geometrica precisione quel che <lb></lb>va del peso al sostegno, e quel che rimane a tirare alle forze dell&#039;uomo o <lb></lb>del cavallo. </s></p><p type="main">

<s>Investigata così la natura delle macchine nelle sue ragioni, era facile <lb></lb>secondo la verità a comprenderne gli usi, imperocchè s&#039;immagini di aver, <lb></lb>nella passata figura XCIII, qualche corpo pesante A, il quale si voglia, ser­<lb></lb>vendosi del piano inclinato, sollevare a un&#039;altezza possibile alle nostre forze. </s>

<s><lb></lb>Sia quello scelto piano AM, e sopr&#039;esso tirisi il grave, per mezzo della fune <lb></lb>AE, che passi in E, per la gola della puleggia ivi affissa. </s>

<s>Giunto A in M è <lb></lb>scorsa tanto di fune EH, quanto è la lunghezza AM, e s&#039;è così conseguito <lb></lb>l&#039;intento. </s>

<s>Volendosene ora esaminare il modo, si troverà che, se avessimo <lb></lb>avuto forza pari alla resistenza, e nè perciò bisogno alcuno di macchina, sa-<pb xlink:href="020/01/1973.jpg" pagenum="216"></pb>rebbesi il peso A potuto sollevare in quel medesimo atto e tempo all&#039;al­<lb></lb>tezza AD, com&#039;è facile a intendere immaginando che A, invece di posar sul <lb></lb>piano pendesse libero in F della puleggia. </s>

<s>Ma intanto, benchè siasi fatt&#039;uso <lb></lb>della macchina, è tanto piccola l&#039;altezza CM, a cui siamo giunti, quanto pic­<lb></lb>cola era la forza applicata. </s></p><p type="main">

<s>Le medesime proporzioni si osservano nella Leva, perchè, posto per <lb></lb>esempio il peso in D (nella figura XCIV poco addietro rappresentata) e a <lb></lb>una maggior distanza dal fulcro applicata in A la potenza, se avessimo avuto <lb></lb>forze sufficienti si sarebbe, senza altr&#039;uso di macchina, nel medesimo atto <lb></lb>e nel medesimo tempo, sollevato il peso infino in E, mentre non siam riu­<lb></lb>sciti a portarlo più su che in F, a un&#039;altezza tanto minore di E, quanto le <lb></lb>nostre facoltà si trovarono inferiori al bisogno. </s>

<s>Non è dunque vero, s&#039;ebbe <lb></lb>a concluderne di qui, che per gli strumenti meccanici s&#039;avvalorin le forze, <lb></lb>e che se ne moltiplichi l&#039;effetto, vedendosi secondo i meriti, nè più nè meno, <lb></lb>retribuita la più giusta mercede. </s>

<s>Sicchè insomma, bene esaminate le cose, <lb></lb>si trovò non ci prestar le macchine altro servizio, che di render, quantun­<lb></lb>que piccole, efficaci le nostre forze e, non avendo a dispor del tutto, potere <lb></lb>almeno renderne fruttuosa una parte. </s></p><p type="main">

<s>Tale è il luminoso concetto che investe le Meccaniche di Leonardo, ma <lb></lb>che negli Autori succeduti a lui apparisce alquanto meno sincero. </s>

<s>Aveva <lb></lb>Guidubaldo fatto notare che “ quo pondus facilius movetur, eo quoque tem­<lb></lb>pus maius esse; quo vero difficilius, eo minus esse ” (Mechanic. </s>

<s>lib. </s>

<s>cit., <lb></lb>fol. </s>

<s>105 a t.), e Galileo faceva da questo fatto dipendere la natura degli stru­<lb></lb>menti meccanici, e la ragione de&#039;loro effetti, “ perchè, avendo noi scarsità <lb></lb>di forza e non di tempo ” (Alb. </s>

<s>XI, 36), supplisce con l&#039;abbondanza di que­<lb></lb>sto la macchina al difetto di quella. </s>

<s>S&#039;ebbe di qui a formulare il meccanico <lb></lb>aforismo: <emph type="italics"></emph>quel che s&#039;acquista in forza si perde in tempo,<emph.end type="italics"></emph.end> ciò che dai ra­<lb></lb>gionamenti riferiti di sopra non appare assolutamente vero, essendosene tut­<lb></lb>t&#039;altrimenti concluso che nulla s&#039;acquista di forza e nulla si perde di tempo. </s>

<s><lb></lb>Quell&#039;aforismo, che certamente non s&#039;avvera nè nel Piano inclinato nè nella <lb></lb>Leva, Guidubaldo lo applicò alla Troclea, all&#039;Asse nella ruota e alla Vite, <lb></lb>d&#039;onde è facile a comprendersi che la considerazione del tempo, non sov­<lb></lb>vien dall&#039;essenza della macchina, ma dal particolar modo com&#039;è disposta, <lb></lb>che, senza nulla variar degli organi, permette di ripetere e di continuare i <lb></lb>primi intrapresi esercizi. </s>

<s>Il Peritrochio infatti è una Leva continua, com&#039;è un <lb></lb>piano continuo la Coclea: e la Taglia stessa è una fune continuamente tesa. </s></p><p type="main">

<s>La natura delle Macchine sembra dunque essere stata assai meglio de­<lb></lb>finita da Leonardo, che non da Guidubaldo o da Galileo, ond&#039;è facile aspet­<lb></lb>tarsi che dovesse avere il primo qualche vantaggio sugli altri due, anche <lb></lb>nell&#039;investigarne la ragion degli effetti. </s>

<s>Quanto al Piano che, secondo il con­<lb></lb>cetto dello stesso Leonardo, è la Macchina essenziale, e a cui si riduce infine <lb></lb>la stessa Leva; quel vantaggio apparisce dalle cose dette nel capitolo I di <lb></lb>questo Tomo assai manifesto, e si farebbe manifesto altresì per le altre mac­<lb></lb>chine secondarie, se fosse qui o altrove, nella nostra Storia, luogo a trattar <pb xlink:href="020/01/1974.jpg" pagenum="217"></pb>di proposito della Scienza meccanica di Leonardo da Vinci. </s>

<s>Si vedrà non­<lb></lb>stante nel seguente compendioso discorso ricorrerne più di un esempio. </s></p><p type="main">

<s>Richiederebbe l&#039;ordine logico che si facesse primo il piano, e le due <lb></lb>Macchine che ne dipendono, naturale soggetto a quel discorso, e che si <lb></lb>venisse poi a dir della Leva e delle altre due Macchine, che pur da essa de­<lb></lb>rivano. </s>

<s>Ma non può la storia degli svolgimenti del pensiero adattarsi all&#039;or­<lb></lb>dine di un trattato, che suppone il pensiero stesso già svolto. </s>

<s>Ciò necessa­<lb></lb>riamente conduce a far ultimo quel ch&#039;era primo, e ci consiglia a cominciar <lb></lb>dal Vette, e dagli strumenti che hanno forma di lui. </s></p><p type="main">

<s>Quando il punto di sospensione è nel mezzo, si applicano immediata­<lb></lb>mente al Vette le leggi delle equiponderanze, delle quali Aristotile pose i <lb></lb>principii, e Archimede poi ne dettò al mondo geometrica dimostrazione. </s>

<s>Si <lb></lb>poteva però disporre lo strumento in altri due modi, o ponendo il peso tra <lb></lb>la potenza e il sostegno, o la potenza fra il sostegno e il peso. </s>

<s>Di questi due <lb></lb>nuovi generi di Leva non si trova fatta chiara distinzione appresso agli An­<lb></lb>tichi, benchè la XXIX Questione aristotelica proponga a considerare un esem­<lb></lb>pio, che imitasi così spesso ne&#039;manuali esercizi. </s>

<s>Perchè, domanda il Filo­<lb></lb>sofo, trasportandosi un peso pendente da un legno, posato coll&#039;estremità <lb></lb>sulle spalle a due uomini, si senton questi egualmente aggravati, se il peso <lb></lb>è nel mezzo, ma, se riman da una parte, se ne sente più addosso il più vi­<lb></lb>cino? </s>

<s>Forse perchè, risponde, il legno è un Vette, il peso è il fuìcro, e un <lb></lb>degli uomini fa da potenza e l&#039;altro da resistenza? </s>

<s>“ An quoniam Vectis <lb></lb>quidem lignum efficitur, pondus vero hypomochlion, qui autem proprior est <lb></lb>ponderi ex iis qui illud gestant, id quod movetur, alter vero portantium <lb></lb>quod movet ” (Operum, T. XI cit., fol. </s>

<s>38). </s></p><p type="main">

<s>La questione in sostanza era ben risoluta, se non che, per non trasfi­<lb></lb>gurar di troppo la natura delle cose, giovava lasciare al peso rappresentar <lb></lb>la propria qualità di resistenza; a uno degli uomini il fulcro, e all&#039;altro il <lb></lb>motore. </s>

<s>Così veniva ben distinto il secondo genere di Leva, che poi, come <lb></lb>Aristotile insomma fa, si riduce alle medesime leggi del primo. </s>

<s>La distinzion <lb></lb>chiara però della nuova forma e le ragioni della trasformazione s&#039;incomin­<lb></lb>ciarono a dimostrar dai Meccanici del secolo XV, ma non apparvero forse <lb></lb>prima alla luce, che ne&#039;libri del Benedetti e di Guidubaldo del Monte. </s>

<s>Que­<lb></lb>sti, come lemma preparatorio al suo trattatello <emph type="italics"></emph>De trochlea,<emph.end type="italics"></emph.end> considerò, nelle <lb></lb>proposizioni II e III <emph type="italics"></emph>De vecte,<emph.end type="italics"></emph.end> gli altri due modi di usar lo strumento, di­<lb></lb>versi dall&#039;ordinario descritto da Archimede, e, nel caso che sia il peso nel <lb></lb>mezzo, dimostrò in due maniere che la potenza e la resistenza hanno ragion <lb></lb>reciproca delle distanze dal fulcro. </s>

<s>Galileo imitò Guidubaldo, alla seconda <lb></lb>maniera del quale s&#039;accosta la dimostrazione che, nella <emph type="italics"></emph>Scienza meccanica,<emph.end type="italics"></emph.end><lb></lb>vien proposta per lemma al capitolo <emph type="italics"></emph>Delle taglie<emph.end type="italics"></emph.end> (Alb. </s>

<s>XI, 104, 5). </s></p><p type="main">

<s>Tengono i due Autori il medesimo modo, tenuto già da Leonardo, ma <lb></lb>egli è più agile e, in quella sua naturale <lb></lb>semplicità, più elegante di loro. </s>

<s>Sia AD <lb></lb>(fig. </s>

<s>95) una Leva di primo genere col ful­<lb></lb><figure id="id.020.01.1974.1.jpg" xlink:href="020/01/1974/1.jpg"></figure></s></p><p type="caption">

<s>Figura 95.<pb xlink:href="020/01/1975.jpg" pagenum="218"></pb>cre in C, e co&#039;pesi A, D in equilibrio, secondo la nota proporzione D:A= <lb></lb>AC:CD. </s>

<s>Si trasporti A in B, in distanza eguale dal centro: non verrà per <lb></lb>questo alterata in nulla quella prima equiponderanza, la ragion della quale, <lb></lb>posta BC invece di CA, e B invece di A, sarà espressa in quest&#039;altra forma <lb></lb>D:B=BC:CD. </s>

<s>Nella seconda maniera di Guidubaldo, e in quella che <lb></lb>imitò da lui Galileo, si riducono le lunghe parole a questo breve discorso, <lb></lb>che si legge scritto così in una Nota di Leonardo: </s></p><p type="main">

<s>“ Se la lieva è doppia della contrallieva, tanto fa al motore avere il <lb></lb>peso in mezzo alla lieva, quanto nel termine della contrallieva. </s>

<s>Provasi, e <lb></lb>sia CD la lieva, CA la contrallieva, la quale è per la metà d&#039;essa lieva. </s>

<s>E <lb></lb>se il peso sarà applicato nel mezzo della lieva in B, allora tanto ne sentirà <lb></lb>il sito C, quanto ne sente D, perchè le distanze CB, e DB, ch&#039;el sostengono, <lb></lb>sono uguali, e per la nona di questo libro tal fia la proporzione de&#039;pesi, che <lb></lb>sente li sostentacoli del peso da lor sostenuto, qual&#039;è quella delle distanze, <lb></lb>che hanno li centri de&#039;sostentacoli dal centro del grave sospeso. </s>

<s>Adunque <lb></lb>è concluso che C, D sostentacoli si caricano ugualmente di B peso. </s>

<s>Oltre a <lb></lb>di questo, se il peso B fia trasmutato tanto al di là del fine della lieva, <lb></lb>quanto era di qua, il motore D sentirà tanto peso del grave trasmutato, <lb></lb>quanto esso si sentissi di prima. </s>

<s>Provasi: CD lieva del motore D è doppia <lb></lb>alla contrallieva del mobile A, adunque D motore sente la metà del mobile, <lb></lb>come sentire solea, quando esso mobile era in B, e così è concluso il nostro <lb></lb>intento ” (Manuscr. </s>

<s>G cit., fol. </s>

<s>63). </s></p><p type="main">

<s>Riman qui Leonardo nel solo modo di dimostrare superiore a Guidu­<lb></lb>baldo, ma altrove, ciò che più importa, lo vince, quando sia per inusitati <lb></lb>sentieri da giungere alla scoperta del vero. </s>

<s>Le proposizioni VIII e IX <emph type="italics"></emph>De <lb></lb>vecte<emph.end type="italics"></emph.end> son manifestamente false, e farebbe gran maraviglia che non avessero <lb></lb>l&#039;esperienze fatto ravveder de&#039;suoi errori l&#039;Autore, se avesse saputo il modo <lb></lb>di applicare all&#039;estremo braccio della leva inclinata la giusta direzione della <lb></lb>potenza. </s>

<s>“ Sit vectis AB (fig. </s>

<s>96), <lb></lb><figure id="id.020.01.1975.1.jpg" xlink:href="020/01/1975/1.jpg"></figure></s></p><p type="caption">

<s>Figura 96.<lb></lb>egli dice, horizonti aequidistans, cu­<lb></lb>ius fulcimentum C, pondus autem <lb></lb>BD, eiusdem vero gravitatis centrum <lb></lb>sit supra vectem uhi H, sitque po­<lb></lb>tentia sustinens in A. </s>

<s>Moveatur dein­<lb></lb>de Vectis AB in EF, sitque pondus <lb></lb>motum in FG: dico primum mino­<lb></lb>rem potentiam E sustinere pondus <lb></lb>FG, vecte EF, quam potentia in A <lb></lb>pondus BD, vecte AB.... Sit deinde <lb></lb>vectis in QR, et pondus in QS, cuius centrum gravitatis sit O: dico maio­<lb></lb>rem requiri potentiam in R ad sustinendum pondus QS, quam in A, ad <lb></lb>pondus BD ” (Mechanic., lib. </s>

<s>cit., fol. </s>

<s>44, 45). </s></p><p type="main">

<s>La ragione di questi asserti la fa Guidubaldo dipendere dalle interse­<lb></lb>zioni delle perpendicolari condotte sulle Leve dai centri di gravità dei pesi, <pb xlink:href="020/01/1976.jpg" pagenum="219"></pb>le quali perpendicolari, nel peso orizzontale BD, precidono il braccio di leva <lb></lb>in I, ma nel peso sollevato in FG lo precidono in M più vicino, e nel peso <lb></lb>abbassato in QI lo precidono in T, più lontano dal fulcro di quel che non <lb></lb>sia I. </s>

<s>Da questa varietà di distanze, così misurate, conclude Guidubaldo la <lb></lb>varietà dei momenti, ma Leonardo, seguendo in ciò la regola vera, ch&#039;era <lb></lb>quella di porre i pesi <emph type="italics"></emph>sotto la loro perpendicolare sopra la linea della ugua­<lb></lb>lità,<emph.end type="italics"></emph.end> se questa linea della ugualità è AB, abbassate sopr&#039;essa, dai due cen­<lb></lb>tri K, O, le perpendicolari KY, TX, avrebbe sicuramente detto essere CY <lb></lb>e CX, e non CM e CT le distanze dal centro, per le quali s&#039;ha, rispetto a <lb></lb>CI, da misurare la varietà del momento che subisce il peso o più alto o più <lb></lb>basso. </s>

<s>Si sarebbe di qui facilmente scoperta la fallacia, che s&#039;ascondeva nel <lb></lb>discorso, per cui concludevasi da Guidubaldo dover essere in QI il grave <lb></lb>più ponderoso, quando non gli fosse in più diritto e sicuro modo rivelato <lb></lb>il vero dall&#039;esperienza, come doveva essergli occorso nel trattar dell&#039;Asse <lb></lb>nel peritrochio. </s></p><p type="main">

<s>Di questa macchina non lasciarono gli Antichi altro documento, da quel <lb></lb>che si legge nell&#039;ottavo libro delle Collezioni di Pappo, dove il Matematico <lb></lb>alessandrino si limita a descrivere brevemente gli organi, chiamando asse <lb></lb>il cilindro, intorno a cui s&#039;avvolge la fune che ha da tirare il peso, timpano <lb></lb>la ruota attraversata nel suo centro dall&#039;asse, e scitale dall&#039;ufficio le leve <lb></lb>confitte sulla circonferenza della stessa ruota, le quali valgono per noi quanto <lb></lb>a dire manubrii. </s>

<s>Rimase perciò ai moderni l&#039;ufficio di dare scienza dell&#039;arte, <lb></lb>e Guidubaldo del Monte, fra&#039;primi e più conosciuti, dimostrò questa facile <lb></lb>proposizione: “ Potentia pondus sustinens Axe in peritrochio ad pondus, <lb></lb>eamdem habet proportionem, quam semidiameter Axis ad semidiametrum <lb></lb>tympani, una cum scytala ” (Mechan., lib. </s>

<s>cit., fol. </s>

<s>107). </s></p><p type="main">

<s>Le difficoltà cominciarono quando, costituendosi la potenza in un altro <lb></lb>peso, la scitala usciva fuori della sua prima posizione orizzontale. </s>

<s>Vennero <lb></lb>allora l&#039;esperienze a far veder chiaramente che quella stessa potenza va­<lb></lb>riava il momento, e Guidubaldo, applicandovi la regola de&#039;centri di gravità, <lb></lb>riuscì a dimostrare il fatto e la causa, ma non le giuste proporzioni di una <lb></lb>tal variazione. </s>

<s>Quelle esperienze però, più giudiziosamente consultate che <lb></lb>nelle proposizioni VIII e IX <emph type="italics"></emph>De vecte,<emph.end type="italics"></emph.end> rivelarono all&#039;Autore il vero, almeno <lb></lb>in una sua parte più rilevante, ponendo mente alla differenza che passa, <lb></lb>quando si fa l&#039;equilibrio della macchina vincere a un peso morto, o a una <lb></lb>potenza animata, come son le mani e le braccia dell&#039;uomo. </s>

<s>In questo caso, <lb></lb>o tirando l&#039;un manubrio o l&#039;altro, la fatica è sempre la stessa, perchè la <lb></lb>forza non è diretta secondo il perpendicolo, ma secondo la circonferenza. <lb></lb></s>

<s>“ Tunc eademmedet potentia, vel in F vel in T constituta, idem pondus <lb></lb>sustinere poterit, cum semper, in cuiuscumque extremitate scytalae ponatur, <lb></lb>ab eodem centro aequidistans fuerit, ac secundum eamdem circumferentiam <lb></lb>ab eodem centro aequaliter semper distantem propensionem habeat. </s>

<s>Neque <lb></lb>enim, sicuti pondus, proprio nutu magis in centrum ferri exoptat quam cir­<lb></lb>culariter moveri, cum utrumque seu quemlibet alium motum nullo prorsus <pb xlink:href="020/01/1977.jpg" pagenum="220"></pb>respiciat discrimine. </s>

<s>Propterea non eodem modo res se habet, sive pondera, <lb></lb>sive animatae potentiae iisdem locis, eodem munere obeundo, fuerint consti­<lb></lb>tutae ” (ibid., fol. </s>

<s>109). </s></p><p type="main">

<s>Galileo, dietro i documenti che s&#039;avevano oramai studiando nelle Mec­<lb></lb>caniche del Benedetti, illustrò e ridusse a matematica precisione il concetto <lb></lb>di Guidubaldo, che cioè “ se nella medesima circonferenza fosse applicata <lb></lb>forza animata, la quale avesse momento di far impeto per tutti i versi, po­<lb></lb>tria far l&#039;effetio, costituita in qualsivoglia luogo di detta circonferenza, ti­<lb></lb>rando non al basso, ma in traverso secondo la contingente ” (Alb. </s>

<s>XI, 101), <lb></lb>perch&#039;essendo la tangente perpendicolare al raggio serba, per le cose dimo­<lb></lb>strate dal Benedetti, tutta intera la sua potenza. </s>

<s>Si riduce in conclusione a <lb></lb>queste e a poche altre semplici considerazioni quel che, esplicando e di più <lb></lb>facili parole ornando il trattato di Guidubaldo, trovò da aggiungere Galileo <lb></lb>nella scienza meccanica dell&#039;Asse nella ruota. </s>

<s>Ma passando alle Taglie non <lb></lb>promove proprio di nulla la scienza del suo predecessore, fedelmente e in <lb></lb>tutto seguitata da lui, benchè fosse facile a riconoscerla in sè così difettosa. </s></p><p type="main">

<s>La seconda proposizione <emph type="italics"></emph>De trochlea,<emph.end type="italics"></emph.end> nel libro di Guidubaldo, è così <lb></lb>formulata: “ Si funis orbiculo trochleae ponderi alligatae circumducatur, al­<lb></lb>tero eius extremo alicubi religato, al­<lb></lb>tero vero a potentia pondus susti­<lb></lb>nente apprehenso, erit potentia pon­<lb></lb>deris subdupla ” (fol. </s>

<s>64 t.). Figurata <lb></lb>in BCD (fig. </s>

<s>97) la rotella, dall&#039;asse <lb></lb>E dalla quale penda il peso A, soste­<lb></lb>nuto dalle funi FB, GD, una delle <lb></lb>quali sia fissa in F e sia all&#039;altra ap­<lb></lb>plicata la potenza, dimostra Guidu­<lb></lb>baldo quella sua proposizione, condu­<lb></lb>cendo il diametro DB, in cui vede rap­<lb></lb>presentarsi una Leva di secondo genere <lb></lb>col sostegno in B, colla resistenza po­<lb></lb>sta nel mezzo E, e con la potenza ap­<lb></lb>plicata in D, la quale, per le cose di­<lb></lb><figure id="id.020.01.1977.1.jpg" xlink:href="020/01/1977/1.jpg"></figure></s></p><p type="caption">

<s>Figura 97.<lb></lb>mostrate <emph type="italics"></emph>De vecte,<emph.end type="italics"></emph.end> dee stare al peso come BE a BD o come uno sta a due. </s></p><p type="main">

<s>Galileo, avendo anch&#039;egli premessa per servir di lemma, come dicemmo, <lb></lb>la dimostrazione delle condizioni dell&#039;equilibrio nella Leva di secondo ge­<lb></lb>nere, l&#039;applica, ad imitazione di Guidubaldo, alla girella sostenuta da due <lb></lb>funi, e poi soggiunge: “ Abbiamo fin qui esplicato come, col mezzo della <lb></lb>Taglia, si possa duplicar la forza. </s>

<s>Resta che, con maggior brevità che sia <lb></lb>possibile, dimostriamo il modo di crescerla secondo qual si voglia moltipli­<lb></lb>cità, e prima parleremo della moltiplicità secondo i numeri pari, e poi <lb></lb>impari, e per dimostrar come si possa aumentare la forza in proporzione <lb></lb>quadrupla, proporremo la seguente speculazione, come lemma delle cose se­<lb></lb>guenti ” (Alb. </s>

<s>XI, 108, 9). </s></p><pb xlink:href="020/01/1978.jpg" pagenum="221"></pb><p type="main">

<s>Il lemma, che passa a dimostrar Galileo, è la proposizione VI formu­<lb></lb>lata così da Guidubaldo: “ Sint duo vectes AB, CD (fig. </s>

<s>98) bifariam divisi <lb></lb>in E, F, quorum fulcimenta sint in B, D; sitque pondus G in E, F utrique <lb></lb><figure id="id.020.01.1978.1.jpg" xlink:href="020/01/1978/1.jpg"></figure></s></p><p type="caption">

<s>Figura 98.<lb></lb>vecti appensum, ita ut ex utroque <lb></lb>aequaliter ponderet, duaeque sint po­<lb></lb>tentiae in A, C aequales pondus su­<lb></lb>stinentes; dico unamquamque poten­<lb></lb>tiam in A, C subquadruplam esse pon­<lb></lb>deris G ” (Mechan., lib. </s>

<s>cit., fol. </s>

<s>70). <lb></lb>La facile dimostrazione è uguale nel­<lb></lb>l&#039;uno e nell&#039;altro Autore, com&#039;è ugua­<lb></lb>le l&#039;applicazione che da ambedue se <lb></lb>ne fa, quando una girella di sopra <lb></lb>sostiene altre due girelle di sotto, i diametri delle quali fanno l&#039;ufficio, e <lb></lb>seguon perciò le leggi statiche de&#039;due vetti proposti. </s>

<s>Provasi con analogo <lb></lb>discorso che, se i vetti son tre, la potenza è un sesto, se son quattro, è <lb></lb>un ottavo del peso, “ atque ita deinceps in infinitum ” (ibid.). </s></p><p type="main">

<s>“ Passando ora, dice Galileo, alla dichiarazione del modo di moltipli­<lb></lb>care la forza secondo i numeri dispari, e facendo principio dalla proporzione <lb></lb>tripla, prima metteremo avanti la presente speculazione, come che dalla sua <lb></lb>intelligenza dipenda tutto il presente negozio ” (Alb. </s>

<s>XI, 111). La specula­<lb></lb>zione consiste nella proposizione IV da Guidubaldo così formulata: “ Sit <lb></lb>vectis AB (nella precedente figura) cuius fulcimentum sit B, qui bifariam <lb></lb>dividatur in E, sitque pondus G in E appensum, duaeque sint potentiae ae­<lb></lb>quales in E, A pondus G sustinentes: dico unamquamque potentiam in E, A <lb></lb>ponderis G subtriplam esse (Mechan., lib. </s>

<s>cit., fol. </s>

<s>67 a t.). </s></p><p type="main">

<s>Serve anche questa proposizione ad ambedue gli Autori di lemma a <lb></lb>dimostrar che la potenza è un terzo della resistenza, quando alla girella in­<lb></lb>feriore, da cui pende il peso, ne sovrasti una superiore congiuntale per una <lb></lb>corda, un capo della quale sia fermato alla stessa girella inferiore, e sia al­<lb></lb>l&#039;altro applicata la virtù motrice. </s>

<s>Con ragioni analoghe a queste si dimo­<lb></lb>stra da Guidubaldo il modo e la ragione di ridurre a un quinto, a un set­<lb></lb>timo, a un nono, e cosi di seguito la forza applicata alla fune, rispetto a <lb></lb>quella, che assolutamente bisognerebbe per sollevare senz&#039;altra macchina il <lb></lb>peso. </s>

<s>È poi sollecito di far notare in corollarii che si deducono via via dalle <lb></lb>dimostrate proposizioni, come al diminuir della forza corrisponde sempre una <lb></lb>lunghezza maggiore nel viaggio; cosicchè non si riduce essa forza per esem­<lb></lb>pio alla metà, o a un terzo, senza ch&#039;ella non abbia contrariamente a per­<lb></lb>correre il doppio o il triplo dello spazio. </s>

<s>In conformità di che Galileo, dopo <lb></lb>aver dimostrato il modo e le ragioni di ridur per le Taglie a metà la fatica <lb></lb>soggiunge: “ E qui, come negli altri strumenti s&#039;è fatto e ne&#039;seguenti si <lb></lb>farà, non passeremo senza considerazione come il viaggio, che fa la forza, <lb></lb>venga ad essere doppio del movimento del peso ” (Alb. </s>

<s>XI, 107). </s></p><p type="main">

<s>Il Cartesio, descrivendo nelle sue Meccaniche le proprietà della Troclea, <pb xlink:href="020/01/1979.jpg" pagenum="222"></pb>faceva notar, come cosa nuova e importante, che le virtù della macchina <lb></lb>non nascono dalla Troclea in sè stessa, ma dalla fune, la quale, avvolta so­<lb></lb>lamente di sotto, se la potenza tira in su, o di sotto e di sopra, se si vuol <lb></lb>farla tirare in giù, percorre uno spazio doppio di quello, che nello stesso <lb></lb>tempo si percorre dal peso. </s>

<s>“ Observandum quoque est vires illas non a <lb></lb>Trochlea proficisci, sed tantummodo a funis motu illius, qui ponderi est <lb></lb>motus duplo ” (Editio cit., pag. </s>

<s>15). In una delle sue Epistole poi diceva <lb></lb>essere una sciocchezza quella di Guidubaldo, che riduceva la Troclea alla <lb></lb>natura del Vette. </s>

<s>“ In Trochea autem ineptum mihi videtur Vectem quae­<lb></lb>rere, quod, si bene memini, Guidonis Ubaldi figmentum est ” (Epist., P. II <lb></lb>cit., pag. </s>

<s>93). </s></p><p type="main">

<s>L&#039;accusa insolente è stata oramai giudicata dai Matematici moderni, i <lb></lb>quali, benchè considerino più volentieri le tensioni delle funi, non credon <lb></lb>però che sia ridicolo il riconoscere nella Troclea le virtù stesse del Vette. </s>

<s><lb></lb>Più giudiziosa dunque di quella del Cartesio sembrerà a tutti la delibera­<lb></lb>zione presa da un nostro Italiano, se non precursore certamente contempo­<lb></lb>raneo al Filosofo francese, il qual nostro Autore, intendendo che sia la po­<lb></lb>tenza applicata alle funi, pensava di avere a dimostrar le proposizioni delle <lb></lb>Taglie meglio di Guidubaldo. </s></p><p type="main">

<s>Niccolò Aggiunti sanamente ragionava non poter essere le virtù, dove <lb></lb>manchi la natura del Vette, la quale par che essenzialmente sia posta nel <lb></lb>sostegno. </s>

<s>“ Se il peso G, egli dice (nella precedente figura XCVIII), sarà <lb></lb>sostenuto dalle forze A, C, il sostegno in B sosterrà quel che avanza a dette <lb></lb>forze, perchè il sostegno B non fa forza in su ma solo ritien che la leva, <lb></lb>dalla parte B, non si muova in giù. </s>

<s>Sicchè, quando le sole forze A, C fos­<lb></lb>sero bastanti a sostenere il peso G (come sempre avvien nelle Taglie) il so­<lb></lb>stegno non opera cosa alcuna ” (MSS. Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>91). </s></p><p type="main">

<s>Persuaso dunque che debba esser così, come la mente gli ragionava, <lb></lb>che cioè nelle taglie operino solamente le forze applicate alle funi, a dimo­<lb></lb>strare il particolar modo di così fatta operazione s&#039;apparecchiava l&#039;Aggiunti <lb></lb>il seguente teorema: “ Sia la <lb></lb>superfice parallelogramma o ret­<lb></lb>tangola AB (fig. </s>

<s>99) orizzontale, <lb></lb>ed in essa sia la linea ED, che <lb></lb>divida nel mezzo FB, AI, ed essa <lb></lb>ancora sia divisa in mezzo col <lb></lb>punto C, dal quale ereggasi la <lb></lb>CH perpendicolare al piano AB. </s>

<s><lb></lb>Intendasi la detta linea ED mo­<lb></lb>bile intorno al punto C, come <lb></lb>una bilancia di braccia uguali, <lb></lb>ed al moto di essa intendasi con­<lb></lb>seguentemente mobile la super­<lb></lb>fice AB. </s>

<s>Intendansi poi distese <lb></lb><figure id="id.020.01.1979.1.jpg" xlink:href="020/01/1979/1.jpg"></figure></s></p><p type="caption">

<s>Figura 99.<pb xlink:href="020/01/1980.jpg" pagenum="223"></pb>secondo le linee equidistanti AF, ED, IB, le corde NAFM, XEDK, QIBR, e <lb></lb>dalla parte AI penda attaccato il cilindro grave NQ, il quale sia sospeso da <lb></lb>tutt&#039;e tre le corde in sito orizzontale e parallelo alla AI. Dall&#039;altra parte <lb></lb>della FB pendano, dai tre capi delle corde, i tre gravi U, S, T eguali in <lb></lb>mole e in peso ciascuno a ciascuno, e tra tutti e tre di egual peso che il <lb></lb>cilindro <expan abbr="Nq.">Nque</expan> ” </s></p><p type="main">

<s>“ Essendo dunque i tre gravi pendenti, come se fossero attaccati co&#039;loro <lb></lb>centri di gravità ugualmente distanti l&#039;un dall&#039;altro, dunque, per la V di <lb></lb>Archimede, il centro della gravezza composta di tutti e tre sarà nel punto <lb></lb>D, sicchè tutto il peso di tutti e tre gravita massimamente in D, esercitando <lb></lb>l&#039;istessa gravità, attaccati ne&#039;punti F, D, B, come se tutti e tre fossero at­<lb></lb>taccati in D, e così il cilindro NQ è come se fosse attaccato solamente in <lb></lb>E, e l&#039;istesso peso sente la libbra ED, quando il cilindro pende dai punti <lb></lb>A, E, I, come quando pende da E solamente. </s>

<s>” </s></p><p type="main">

<s>“ Essendo dunque in questo modo pesi uguali attaccati in distanze uguali <lb></lb>dalla libbra ED, si farà l&#039;equilibrio, e la colonna equipondererà alli tre pesi. </s>

<s><lb></lb>Ma i tre pesi attaccati in F, D, B gravitano a parte, come appesi tutti in­<lb></lb>sieme al punto D, e la colonna sospesa come prima in A, E, I gravita come <lb></lb>sospesa solamente dal punto E; dunque anco in questo stato il peso S non <lb></lb>può se non sostenere del peso NQ, attaccato in egual distanza a quella <lb></lb>d&#039;onde egli stesso è sospeso; non può dico sostenere se non quella parte, <lb></lb>che sarà uguale a lui medesimo. </s>

<s>Ma il peso di esso è una terza parte del <lb></lb>cilindro NQ, per il supposto, ponendo tutti e tre eguali a tutto NQ, adun­<lb></lb>que il peso S sostiene la terza parte del peso <expan abbr="Nq.">Nque</expan> Adunque le rimanenti <lb></lb>due terze parti son sostenute dalli pesi U, T. </s>

<s>Ma questi sono tra loro uguali, <lb></lb>e costituiti nel medesimo modo rispetto alla libbra ED, dunque sostengono <lb></lb>ugualmente, e però anch&#039;essi sostengono una terza parte del cilindro ” (ivi). </s></p><p type="main">

<s>Seguita a questa proposizione un corollario, in cui dichiara l&#039;Autore la <lb></lb>sua intenzione di applicare i dimostrati principii alle Taglie. </s>

<s>“ Dal che rac­<lb></lb>cogliesi, egli dice, che se, invece delli tre pesi pendenti ed eguali, s&#039;inten­<lb></lb>deranno applicate tre forze eguali, una per una alle corde NA, XE, QI, che <lb></lb>per appunto sostenessero il grave NQ orizzontalmente; ciascuna di queste <lb></lb>forze è uguale alla terza parte del peso sostenuto. </s>

<s>Di qui, s&#039;io non erro, <lb></lb>dimostrerò meglio del signor marchese Guidubaldo le proposizioni delle Ta­<lb></lb>glie, considerando nelle corde che sostengono il peso essere applicate forze <lb></lb>eguali tra di loro. </s>

<s>La qual considerazione sarà verissima, perchè finalmente <lb></lb>la sola forza, ch&#039;è posta nel capo della corda che s&#039;avvolge alle girelle, è <lb></lb>quella che tien per tutto tirata la corda, e che si va per tutto insinuando <lb></lb>in essa, come a suo luogo dichiareremo, e dimostreremo le proposizioni delle <lb></lb>Taglie, senza considerare in esse i sostegni, come fa Guidubaldo, i quali non <lb></lb>pare che vi abbiano luogo ” (ivi, fol. </s>

<s>90). </s></p><p type="main">

<s>La meccanica delle Taglie veniva, per così fatte considerazioni, ridotta <lb></lb>alla sua perfezione, raggiuntasi assai presto in Italia por opera di Guidu­<lb></lb>baldo e dell&#039;Aggiunti. </s>

<s>Ma sulla fine del secolo XV si comprendevano insieme <pb xlink:href="020/01/1981.jpg" pagenum="224"></pb>le specuìazioni dei due Autori dai Matematici di quei tempi, che gli avevano <lb></lb>preceduti, com&#039;apparisce dai documenti rimastici ne&#039;manoscritti di Leonardo <lb></lb>da Vinci. </s>

<s>Riconoscendo anche nelle Taglie la natura propria a tutte le mac­<lb></lb>chine, facevano consistere la loro essenzial virtù nel sostegno, il quale in <lb></lb>questo caso è la mensola che sostenta il peso, non immediatamente, ma me­<lb></lb>diante un filo o una fune a cui si attacca. </s>

<s>Riprendendosi in mano cotesto <lb></lb>filo, si veniva a riprendere anche tutta insieme la prima deposta fatica, ma, <lb></lb>sperimentando e ragionando a quel modo che facevasi dianzi intorno al Piano <lb></lb>e alla Leva, s&#039;ebbe a riconoscere facilmente che si poteva esercitar, non <lb></lb>avendola tutta, una forza parziale coll&#039;incaricarsi di una parte del peso, ri­<lb></lb>lasciandone a sostenere alla mensola il resto. </s>

<s>Così, supposto che sia GF nella <lb></lb>precedente figura 97, una mensola, alla quale sieno attaccati i due capi G, F <lb></lb>della corda GCF, che infilata in una puleggia o in un anello sostenga il peso A <lb></lb>di sotto, lasciando fermo il capo F e solo prendendo l&#039;altro capo G in mano, <lb></lb>si sentirà questa alleggerita della metà dello sforzo. </s></p><p type="main">

<s>Facilissimo era poi trovar modo di far sostenere alla mensola qualun­<lb></lb>que altra parte del peso maggiore della metà, col moltiplicar, per mezzo di <lb></lb>una traversa ferma di sopra, alle corde i punti di appoggio, e per mezzo di <lb></lb>un&#039;altra traversa di sotto i punti di attacco. </s>

<s>S&#039;immagini infatti di aver fer­<lb></lb>mata in ACB (fig. </s>

<s>100) la traversa AB, la quale possa nella sua lunghezza <lb></lb>dar luogo a più punti di appoggio, e da quel di mezzo C penda la corda <lb></lb><figure id="id.020.01.1981.1.jpg" xlink:href="020/01/1981/1.jpg"></figure></s></p><p type="caption">

<s>Figura 100.<lb></lb>CD, alla quale sia in D legata la tra­<lb></lb>versa EF, che sostiene il peso G nel <lb></lb>suo mezzo. </s>

<s>Presi i quattro punti di <lb></lb>appoggio O, M, N, I e P, H, L, K re­<lb></lb>spettivi punti di attacco delle corde <lb></lb>OP, MH, NL, IK, è facile intendere <lb></lb>come sciolta la CD le quattro che la <lb></lb>suppliscono sostengano ciascuna la <lb></lb>quarta parte di tutto il peso, cosic­<lb></lb>chè se il capo della fune O sia so­<lb></lb>stenuto dal braccio di un uomo, que­<lb></lb>sto, per sostenere il grave pendente, non ha da far che sola una quarta parte <lb></lb>dello sforzo. </s>

<s>E perchè si può a piacere moltiplicare il numero delle corde, <lb></lb>s&#039;intende come si può a piacere incaricarsi di qualunque piccolo peso, la­<lb></lb>sciandone tutto il resto al sostegno. </s></p><p type="main">

<s>Andava però così bene il discorso, quando si trattava di sostenere, ma <lb></lb>trattandosi di movere, non era questo lo strumento adattato al bisogno. </s>

<s>Vo­<lb></lb>levano essere le funi, non fisse, ma scorrevoli, e comunicantisi la forza l&#039;una <lb></lb>all&#039;altra, ciò che facilmente s&#039;otteneva, fissando ne&#039;punti R, S, T, U altret­<lb></lb>tante girelle, sulle quali scorrendo, si continuasse una fune dall&#039;uno all&#039;al­<lb></lb>tro suo estremo. </s></p><p type="main">

<s>Era questa la natura delle Taglie, che rappresentavasi nelle specula­<lb></lb>zioni di Leonardo, il quale, ritraendo nel suo modo di dimostrare il modo <pb xlink:href="020/01/1982.jpg" pagenum="225"></pb>stesso come gli s&#039;eran venuti a svolgere nella mente i pensieri, quasi sem­<lb></lb>pre disegna disposte come nella figura C le carrucole, che hanno a servir <lb></lb>d&#039;esempio alle sue proposizioni. </s>

<s>Veniva così benissimo a riconoscersi lo stru­<lb></lb>mento in ciò che ha di comune con le altre macchine, che pigliano la loro <lb></lb>virtù dai sostegni, e in ciò che gli è proprio, e lo rende una macchina par­<lb></lb>ticolare, per l&#039;uso che vi si fa delle funi, le quali, avendo ugual tensione <lb></lb>nell&#039;equilibrio, una piccola forza, che sopraggiungasi alla potenza, <emph type="italics"></emph>tutte le <lb></lb>vince,<emph.end type="italics"></emph.end> dice Leonardo stesso nel suo potente linguaggio, <emph type="italics"></emph>e tutte le muove.<emph.end type="italics"></emph.end><lb></lb>L&#039;espressione è resa dall&#039;Aggiunti in quelle parole, poco dianzi citate, nelle <lb></lb>quali diceva che <emph type="italics"></emph>la sola forza, posta nel capo della corda che s&#039;avvolge <lb></lb>alle girelle, è quella che tien per tutto tirata la corda, e che si va per <lb></lb>tutto insinuando in essa.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Era dunque bisogno venisse dimostrato che la forza s&#039;insinua in tutta <lb></lb>la lunghezza della fune? </s>

<s>Senza dubbio: e se Galileo ne trattò in modo fisico, <lb></lb>fu l&#039;Aggiunti il primo a darne matematica dimostrazione, com&#039;apparisce da <lb></lb>ciò che si legge nel capitolo V del nostro II Tomo a pag. </s>

<s>215. Sembra che <lb></lb>rimanesse intorno a ciò ingannato, a principio, anche Leonardo, ma poi si <lb></lb>persuase del vero così espresso in una Nota, da noi anche altrove trascritta: <lb></lb><emph type="italics"></emph>Ogni gravità sospesa è tutta per tutta la lunghezza della corda, che la <lb></lb>sostiene, ed è tutta in ogni parte di quella.<emph.end type="italics"></emph.end> D&#039;ond&#039;è facile intendere come, <lb></lb>seguitando a correre l&#039;errore, che cioè non per tutta la lunghezza si diffonda <lb></lb>nella fune la forza uguale, non poteva Guidubaldo professare il principio <lb></lb>così semplice delle tensioni, a cui supplì con la ragion certissima del Vette. </s>

<s><lb></lb>Non era questo dunque un commettere errore, e tanto meno, come impu­<lb></lb>dentemente volle dire il Cartesio, uno scorrere in ridicolezze, ma piuttosto <lb></lb>era un difetto inevitabile a una scienza, alla quale era rotto il filo delle più <lb></lb>prossime tradizioni, e che, rimasta alle forze di un uomo solo, rendeva ine­<lb></lb>vitabili altri e maggiori difetti. </s>

<s>Nel <emph type="italics"></emph>Liber mechanicorum<emph.end type="italics"></emph.end> del nostro Urbi­<lb></lb>nate si suppon sempre, in qualunque disposizione di Taglie, che le funi ti­<lb></lb>rino fra loro parallele, ciò che non sempre nella pratica si avvera, e benchè <lb></lb>fosse facile sperimentare che quella perpendicolar direzion delle forze tor­<lb></lb>nava più vantaggiosa, la necessità nonostante portava a dover tirare spesso <lb></lb>in direzione obliqua. </s></p><p type="main">

<s>In questo caso l&#039;esperienza stessa mostrava che le relazioni fra la re­<lb></lb>sistenza e la potenza variavano, al variarsi l&#039;angolo dell&#039;obliquità, ma con <lb></lb>qual ordine si facesse una tal variazione non era facile a Guidubaldo il di­<lb></lb>mostrarlo, nè a Galileo, i quali perciò non vollero nemmen tentare l&#039;arduo <lb></lb>problema. </s>

<s>Al difetto, in cui lasciarono i due Matematici la scienza, aveva <lb></lb>come vedemmo largamente supplito Leonardo, il quale, con la regola della <lb></lb>composizion delle forze, facendo rappresentare il peso alla diagonale, deter­<lb></lb>minava la tension delle funi a proporzione de&#039;due lati opposti nel paralle­<lb></lb>logrammo. </s>

<s>Veniva così, un secolo e mezzo prima del Varignon, ridotta alla <lb></lb>sua più desiderabile perfezione la teoria delle Taglie, e nella fune gravata <lb></lb>da pesi, ridotta alle più certe leggi della Statica, s&#039;incominciò a riconoscere <pb xlink:href="020/01/1983.jpg" pagenum="226"></pb>una delle più usate e più importanti macchine elementari, sconosciuta a <lb></lb>Pappo e agli altri matematici antichi. </s>

<s>Quella Meccanica dunque che, sui <lb></lb>principii del secolo XVIII, si volle dire novella, era nel XVI già bene adulta, <lb></lb>e con proprio nome fra le sorelle scienze distinta. </s></p><p type="main">

<s>Simeone Stevìno, raccogliendo e sponendo al pubblico le tradizioni, fino <lb></lb>allora rimaste nelle private scuole e nei manoscritti, dette a quella scienza <lb></lb>il nome di <emph type="italics"></emph>Spartostatica, ou de l&#039;Art ponderaire par Cordages.<emph.end type="italics"></emph.end> La mac­<lb></lb>china funicolare ha secondo l&#039;Autore, come tutti gli altri meccanici stru­<lb></lb>menti, le sue statiche e certissime leggi, le quali dipendono da un principio, <lb></lb>che si suppone verissimo e noto, e che, non avendo perciò altro bisogno <lb></lb>che di essere spiegato, si risolve in tanti distinti corollarii. </s>

<s>Nel III si sup­<lb></lb>pone di avere un peso colonnare AB (fig. </s>

<s>101) sostenuto, per il suo centro <lb></lb>di gravità C, da due forze, una diretta secondo CD, e l&#039;altra secondo CE. <lb></lb><figure id="id.020.01.1983.1.jpg" xlink:href="020/01/1983/1.jpg"></figure></s></p><p type="caption">

<s>Figura 101.<lb></lb>Dato il peso della colonna, il quale agisce <lb></lb>secondo la perpendicolare CI, e dati gli an­<lb></lb>goli DCI, ECI, si vuol determinare il grado <lb></lb>della forza, che s&#039;ha da fare in D e in E, <lb></lb>per sostenere il grave sospeso. </s>

<s>A far ciò, <lb></lb>rappresentando la lunghezza della linea CI <lb></lb>la gravezza totale, si conduca dal punto I <lb></lb>la IH parallela a CE, “ comme CI a CH, <lb></lb>dice lo Stevino, ainsi le poids de la colomne <lb></lb>entiere au poids qui avient en D. </s>

<s>Et de <lb></lb>mesme maniere trouvera-on le poids, qui advient in E, en menant de I jus­<lb></lb>ques a CE la ligne IK parallele a DC, et disant: comme l&#039;elevation droite <lb></lb>CI a l&#039;elevation oblique CK, ainsi lo poids de la colomne au poids qui advient <lb></lb>sur E ” (Oeuvres mathem. </s>

<s>cit., pag. </s>

<s>505). </s></p><p type="main">

<s>Qui poi osserva l&#039;Autore ch&#039;essendo sempre CK=HI non è necessa­<lb></lb>rio descrivere tutto intero il parallelogrammo, avendosi gli elementi che <lb></lb>bisognano a risolvere il problema dal triangolo IHC, “ avec le quel on dira: <lb></lb>comme CI a CH, ainsi le poids de la colomne au poids qui advient sur D. <lb></lb>D&#039;avantage CI a IH ainsi le poids de la colomne au poids, qui advient sur E. </s>

<s><lb></lb>Derechef comme CH a HI, ainsi le poids, qui advient sur D. au poids qui <lb></lb>advient sur E ” (ivi). Nel corollario V s&#039;applicano i medesimi principii, e <lb></lb>la medesima regola che ne deriva, al caso che AB riducasi in un peso sfe­<lb></lb>roideo infilato e pendolo da una fune, ai due capi della quale gli sforzi ne­<lb></lb>cessarii per far la debita resistenza son tuttavia proporzionali ai lati del <lb></lb>triangolo, che insiste sulla perpendicolare, presa per misura dello stesso peso <lb></lb>assoluto. </s></p><p type="main">

<s>Precede la Spartostatica nelle Meccaniche dello Stevino a un altro trat­<lb></lb>tato, che ha pure un distinto nome di <emph type="italics"></emph>Trocheologia,<emph.end type="italics"></emph.end> nella prefazioncella <lb></lb>alla quale il Matematico del conte Maurizio di Naussau così dice: “ Apres <lb></lb>que Son Excellence eust leu un livre intitulé <emph type="italics"></emph>Delle fortificazioni di Bo­<lb></lb>naiuto Lorini,<emph.end type="italics"></emph.end> et illec veu un traite touchant les poulies, et ce seulement <pb xlink:href="020/01/1984.jpg" pagenum="227"></pb>par elevations perpendiculaires a l&#039;horizon, par le moyen des forces atti­<lb></lb>rantes du haut en bas directement, ce quì n&#039;arrive pas tousiours en la <lb></lb>practique, il a esté quant et quant desidereux de scavoir la propriete d&#039;icel­<lb></lb>les, qui est necessaire pour scavoir quelle force est requise, pour elever <lb></lb>quelque pesanteur ” (ivi, pag. </s>

<s>509). Per soddisfare al qual desiderio dice lo <lb></lb>Stevino di aver dato mano a scrivere la sua Trocheologia, la quale avrebbe <lb></lb>potuto risparmiare al Varignon un secolo dopo quella sua <emph type="italics"></emph>Memoire sur les <lb></lb>poulies,<emph.end type="italics"></emph.end> ch&#039;ebbe qual cosa nuova chi l&#039;ammirò e chi la contraddisse. </s></p><p type="main">

<s>Applicando dunque il vecchio Matematico di Bruges alle tensioni delle <lb></lb>funi oblique nella Troclea la regola del parallelogrammo delle forze, inse­<lb></lb>gnata già nella Spartostatica al V corollario, immagina che siano CN, MC <lb></lb>(fig. </s>

<s>97 a pag. </s>

<s>220) le direzioni delle forze, che sostengono il grave A pen­<lb></lb>dente dalla puleggia, e dice che, prolungate quelle direzioni, si debbono in­<lb></lb>contrare in C in un medesimo punto della perpendicolare KC, sopra la quale <lb></lb>determinato un punto K, e da esso condotta la KI parallela a NC, il desi­<lb></lb>derato quesito delle relazioni che passano fra le potenze M, N e la resi­<lb></lb>stenza A è sciolto dalle seguenti equazioni: KC:KI:IC=A:N:M. <lb></lb>“ Comme ces 3 lignes l&#039;une a l&#039;autre KC, KI, IG, ainsi les pesanteurs de A, <lb></lb>qui eschoit sur CN, qui eschoit en M ” (ivi, pag. </s>

<s>510). </s></p><p type="main">

<s>Si disse chc in questa Spartostatica steviniana si raccoglievano le er­<lb></lb>ranti tradizioni di una scienza anteriore, e della quale non ci è noto altro <lb></lb>documento dai manoscritti di Leonardo, che la coltivò, non per consolar­<lb></lb>sene semplicemente l&#039;ingegno meditativo, ma per consultarla utilmente nelle <lb></lb>pratiche applicazioni, di che ci offron le Taglie un importantissimo esem­<lb></lb>pio. </s>

<s>Essendo la potenza, che ha da vincere e da movere tutte le funi, le <lb></lb>braccia degli operai, che ne tirano a stratte il capo, si dubitava se in quelle <lb></lb>stratte si venisse a fare troppo gran violenza al sostegno, intorno a che ri­<lb></lb>pensando Leonardo si propose a sciogliere il seguente <emph type="italics"></emph>“ Quesito delli pesi <lb></lb>che discendono.<emph.end type="italics"></emph.end> Domandasi se delli pesi, che discendono in fra le carru­<lb></lb>cole, se dan di sè più o men peso alli poli delle Taglie nel discendere, che <lb></lb>nello stare fermi ” (Manuscr. </s>

<s>G cit, fol. </s>

<s>17 a tergo). </s></p><p type="main">

<s>Per dar di ciò la desiderata risolu­<lb></lb>zione, s&#039;applicò Leonardo stesso a fare <lb></lb>una esperienza bellissima, più semplice, <lb></lb>e meglio accomodata alle speculazioni di <lb></lb>alcuni matematici moderni, di quel che <lb></lb>non fossero le due secchie nella bilancia <lb></lb>descritta da Galileo (Alb. </s>

<s>XIII, 309) per <lb></lb>misurare la forza della percossa. </s>

<s>“ Il peso <lb></lb>grave che libero discende, così Leonardo <lb></lb>formula la sua proposizione, non dà di sè <lb></lb>peso ad alcuno sostentacolo. </s>

<s>Provasi: A <lb></lb>(fig. </s>

<s>102) è uno, e B due; seguita che M <lb></lb>sostiene solamente due, perchè l&#039;eccesso <lb></lb><figure id="id.020.01.1984.1.jpg" xlink:href="020/01/1984/1.jpg"></figure></s></p><p type="caption">

<s>Figura 102.<pb xlink:href="020/01/1985.jpg" pagenum="228"></pb>che ha 2B sopra uno, è uno, il quale uno, non avendo chi il sostenga in A, <lb></lb>discende libero. </s>

<s>Adunque non ha sostantacolo, e non avendo sostentacolo, <lb></lb>non li è proibito il moto. </s>

<s>Adunque M stremo della Bilancia non sente tale <lb></lb>eccesso, perchè chi cade non è sostenuto ” (ivi, fol. </s>

<s>13 a t.). </s></p><p type="main">

<s>Confermavano sempre più questi fatti sperimentali Leonardo nell&#039;opi­<lb></lb>nione che pigliassero le Taglie virtù di movere dalle funi, e che non si ri­<lb></lb>ducessero perciò se non che dalla lontana alla natura del Vette, della quale <lb></lb>cosi strettamente partecipa l&#039;Asse nella rota. </s>

<s>Appartengono, comunque sia, <lb></lb>ambedue i detti strumenti all&#039;ordine di quelle macchine, che sostengono per <lb></lb>sospensione dentro un&#039;area assai circoscritta del piano, a cui si riducono <lb></lb>insomma esse Macchine tutte, come a elemento primario, e le varie accli­<lb></lb>vità del quale son che danno ora maggiore, ora minore virtù di movere al <lb></lb>Cuneo e alla Vite. </s>

<s>Le leggi statiche di questi principali organi motori fu­<lb></lb>rono, com&#039;apparisce dall&#039;ottavo libro di Pappo, dagli antichi poco ben co­<lb></lb>nosciute, e dovendosi ora narrar da noi come e quando venissero i moderni <lb></lb>ad averne la desiderata notizia, si dovrebbe incominciare dal Piano inclinato. </s>

<s><lb></lb>Da lui anzi, come da principal fondamento meccanico, avrebbe dovuto mo­<lb></lb>vere il nostro discorso, ma le ragioni che ce ne sviarono allora ci consi­<lb></lb>gliano a non ridurci in via, se non che dopo aver detto di quel poco, che <lb></lb>dallo stesso piano inclinato distingue nell&#039;operare il Cuneo e la Vite. </s></p><p type="main">

<s>Aristotile, nella sua XVII Questione <lb></lb>meccanica ridusse le virtù del Cuneo a <lb></lb>quelle del Vette, così dicendo: “ Sit <lb></lb>Cuneus ubi ABC (fig. </s>

<s>103), quod vero <lb></lb>cuneo scinditur DEFG: Vectis igitur fit <lb></lb>ipsa AB, pondus vero ipsius B inferior <lb></lb>pars, hypomochlion autem DG, huic au­<lb></lb>tem contrarius vectis BC. </s>

<s>Percussa igi­<lb></lb>tur AC, utroque illorum utitur vecte: <lb></lb>scindit enim ipsum B ” (Operum, T. XI <lb></lb>cit., fol. </s>

<s>33 a tergo). Nè altro par che <lb></lb>s&#039;aggiungesse dagli Antichi a dichiarar <lb></lb><figure id="id.020.01.1985.1.jpg" xlink:href="020/01/1985/1.jpg"></figure></s></p><p type="caption">

<s>Figura 103.<lb></lb>meglio la natura, e a spiegar gli effetti dello strumento, giacchè Pappo, li­<lb></lb>mitandosi a darne al solito una brevissima descrizione, fa notar solamente <lb></lb>così in generale che “ quanto Cunei angulus minor est, tanto facilius agit ” <lb></lb>(Collectiones mathem. </s>

<s>cit., pag. </s>

<s>486). </s></p><p type="main">

<s>Guidubaldo fra&#039;moderni è de&#039;primi, che siasi studiato di cogliere da <lb></lb>varii aspetti la versatile natura del Cuneo, e dop&#039;avere accennato all&#039;opi­<lb></lb>nion di Aristotile soggiunge sembrargli assai più conveniente il ridurre il <lb></lb>modo dell&#039;operare dello strumento a quello di una Leva di secondo genere, <lb></lb>cosicchè, se sia ABC il Cuneo, come nella precedente figura, e GDEF il <lb></lb>corpo da scindersi verso le duo opposte parti IG, RD. “ IG movebitur a <lb></lb>puncto I vecte AB, cuius fulcimentum B. </s>

<s>Punctum enim I tangit pondus, <lb></lb>et instrumenta movent per contactum. </s>

<s>Similiter RD movebitur ab R vecte <pb xlink:href="020/01/1986.jpg" pagenum="229"></pb>CB, cuius fulcimentum B, et uterque vectis utrique resistit in B, ita ut po­<lb></lb>tius fulcimenti vice fungalur, quam movendi ponderis, qnod ipsum hoc quo­<lb></lb>que modo manifestum erit ” (Mechanic. </s>

<s>lib. </s>

<s>cit., fol. </s>

<s>113). </s></p><p type="main">

<s>Parve anche al Benedetti, acutamente esaminando la Questione aristo­<lb></lb>telica, che i due lati del Cuneo operassero a modo di una Leva, non di <lb></lb>primo genere, com&#039;avea detto il Filosofo, ma di secondo, se non che dispo­<lb></lb>neva al motore al mobile e all&#039;ipomoclio, diversamente da Guidubaldo, i <lb></lb>luoghi e gli ufficii, sembrando in verità poco probabile il costituire in B il <lb></lb>fulcro che, aprendosigli innanzi il corpo scindibile, rimane per lo più libero <lb></lb>da qualunque contatto. </s>

<s>Considerando poi l&#039;acuto Matematico veneziano che <lb></lb>la forza dalla testa del Cuneo si diffonde ne&#039;punti I, R, applicò quivi la po­<lb></lb>tenza, in M, termine della parte scissa, costituì la resistenza, e nelle parti <lb></lb>scindibili, che immediatamente succedono, suppose l&#039;ipomoclio. </s>

<s>“ Oportet <lb></lb>nunc imaginari duos Vectes in hunc modum ut puncta I, R ligni sint loco <lb></lb>extremi ipsius Vectis, et T, X loco virtutis applicatae, et resistentia circa <lb></lb>punctum M, et pars K, quasi immediata post M versus extremitatem FE <lb></lb>ligni, sit loco hypomochlii. </s>

<s>Hinc fiet ut quanto longiores erunt lineae IMK, <lb></lb>et RMK tanto quoque facilius virtutes T, X impellent I, R ” (Specul., <lb></lb>lib. </s>

<s>cit., pag. </s>

<s>162). </s></p><p type="main">

<s>Guidubaldo però fu forse il primo, che riguardasse il Cuneo sotto un <lb></lb>altro aspetto, in quanto cioè le parti del corpo scindibile strisciano sopra i <lb></lb>lati insinuantisi come sopra due piani inclinati. </s>

<s>“ Quoniam autem totus Cu­<lb></lb>neus scindendo movetur, possumus idcirco eumdem alio quoque modo consi­<lb></lb>derare, videlicet dum ingreditur id quod scinditur nihil aliud esse nisi pondus <lb></lb>supra planum horizonti inclinatum movere ” (Mechan., lib. </s>

<s>cit., fol. </s>

<s>113, 14). <lb></lb>Condotta da B ad AC la BH perpendicolare, osserva che il moto del Cuneo <lb></lb>si fa nella direzione BH, e il moto delle parti scindibili nella direzione GD, <lb></lb>cosicchè, quando esso Cuneo sia entrato tutto, s&#039;è la potenza mossa quanto <lb></lb>BH, e la resistenza quanto AC, d&#039;onde immediatamente ne conclude: “ quo <lb></lb>minor est angulus eo facilius movet ac scindit ” (ibid., fol. </s>

<s>115 a t.). </s></p><p type="main">

<s>Il Cartesio poi considerò il Cuneo propriamente cosi, com&#039;è rappresen­<lb></lb>tato nelle relazioni fra il motore e il mobile da quel Guidone Ubaldo, sulla <lb></lb>scienza del quale volle versare il ridicolo: “ Facultas Cunei ABC, dice nel <lb></lb>cap. </s>

<s>III Delle meccaniche, per se nunc facile intelligitur ex illis, quae de <lb></lb>Plano inclinato iamiam dicta sunt. </s>

<s>Vis enim, qua deorsum pellitur, ita se <lb></lb>movet, ut, cum propellat secundum lineam BH (nell&#039;ultima nostra figura) <lb></lb>et lignum aliudve corpus scindendum non hiscit, vel quoque sarcina quam <lb></lb>attollit non elevatur, nisi iuxta lineam AC, ita ut vis qua Cuneus pellitur <lb></lb>seu deprimitur eamdem habere debeat rationem ad ligni huius vel sarcinae <lb></lb>resistentiam, quam habet linea AC ad lineam BH ” (editio cit., pag. </s>

<s>17). </s></p><p type="main">

<s>La meccanica del Cuneo così, come dal Cartesio, dopo Guidubaldo, vien <lb></lb>divisata, riuscirebbe semplicissima, ma i Matematici posteriori, meglio esa­<lb></lb>minando il fatto, v&#039;ebbero a ritrovare un tal complicato concorso di cause, <lb></lb>da disperar di venirne a capo, e, anche invocando quella taumaturga ope-<pb xlink:href="020/01/1987.jpg" pagenum="230"></pb>razione della composizion delle forze, quel che insomma seppero dirne ri­<lb></lb>ducesi a questo: Incominciatasi a far la scissione per <lb></lb>esempio di un legno dai punti, dove le parti scisse <lb></lb>contrastano con i lati del Cuneo, si alzino sopr&#039;essi <lb></lb>lati due perpendicolari, le quali, supponendosi il trian­<lb></lb>gono VV′T (fig. </s>

<s>104) isoscele, s&#039;incontreranno in un <lb></lb>medesimo punto H della bissettrice TT′. </s>

<s>Presa poi sopra <lb></lb>questa una lunghezza PH a rappresentare la forza insi­<lb></lb>nuatrice, si prolunghino le due dette perpendicolari in <lb></lb>R′, R, e costruiscasi il parallelogrammo, in cui anche <lb></lb><figure id="id.020.01.1987.1.jpg" xlink:href="020/01/1987/1.jpg"></figure></s></p><p type="caption">

<s>Figura 104.<lb></lb>si tiri la diagonale R′R, che intersechi in I l&#039;altra dia­<lb></lb>gonale PH. </s>

<s>Dai triangoli simili RIH, TT′V, R′IP si avranno queste due <lb></lb>equazioni HI=HR T′V/TV, IP=HR′V′T′/TV, le quali sommate insieme, e, per <lb></lb>essere come s&#039;è detto il Cuneo isoscele, posto HR=HR′, e T′V+T′V′=VV′, <lb></lb>saranno HI+IP=HR VV′/TV. </s>

<s>E perchè HI+IP=HP, che s&#039;è detto rap­<lb></lb>presentar la potenza, se ne conclude dunque di qui dover esser questa stessa <lb></lb>potenza, alla resistenza HR, come VV′, che è la testa del Cuneo, a TV, che <lb></lb>è uno de&#039;suoi lati. </s></p><p type="main">

<s>Al Cuneo ridusse Pappo la Vite, la quale niente altro è per lui “ quam <lb></lb>assumptus Cuneus expers percussionis ” (Collect. </s>

<s>cit., pag. </s>

<s>486). Guidubaldo <lb></lb>ripetè la sentenza medesima fra&#039;moderni, ma perchè il Cuneo si riduce per <lb></lb>lui al Piano inclinato, così dunque riducesi anche la Vite, com&#039;egli stesso <lb></lb>dimostra nella II <emph type="italics"></emph>De Cochlea<emph.end type="italics"></emph.end> così proposta: “ Si fuerit Cochlea helices <lb></lb>habens aequales, dico has nihil aliud esse praeter planum horizonti inclina­<lb></lb>tum circa cylindrum revolutum ” (Mechan., lib. </s>

<s>cit., fol. </s>

<s>124). </s></p><p type="main">

<s>Le leggi statiche però del piano elicale, essendo quelle medesime del <lb></lb>piano svolto, se ne rimette intorno a ciò il Nostro a quello, che nelle Ma­<lb></lb>tematiche collezioni era stato insegnato da Pappo. </s>

<s>“ Quomodo autem hoc <lb></lb>ad Libram reducatur manifestum est ex nona octavi libri eiusdem Pappi ” <lb></lb>(ibid., fol. </s>

<s>124 a tergo). Da questa IX proposizione del Matematico alessan­<lb></lb>drino incomincia la storia del Piano inclinato, che è poi la storia stessa della <lb></lb>Coclea, a narrar la quale distintamente si riserba, per quella prima dignità <lb></lb>meccanica, la seguente seconda parte del nostro discorso. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>È quella nona proposizione, alla quale rimanda Guidubaldo i lettori de­<lb></lb>siderosi d&#039;intendere in che modo si riducano le ragioni del Piano inclinato <lb></lb>a quelle della Libbra, così, nell&#039;ottavo libro delle Collezioni matematiche, <lb></lb>formulata: “ Dato pondere a data potentia ducto in plano horizonti paral-<pb xlink:href="020/01/1988.jpg" pagenum="231"></pb>lelo, et altero plano inclinato, quod ad subiectum planum datum angulum <lb></lb>efficiat, invenire potentiam, a qua pondus in plano inclinato ducatur ” (Edi­<lb></lb>tio cit., pag. </s>

<s>458). Nel testo greco, e nella versione del Commandino che <lb></lb>abbiamo sott&#039;occhio, si costruisce dall&#039;Autore il problcma e si risolve, ma <lb></lb>non dispiacerà ai nostri Lettori che si sostituisca al discorso di lui quello <lb></lb>di un suo studioso, più chiaro e più spedito, e che piglia accidentalmente <lb></lb>importanza, per essere stato fatto da uno sconosciuto fiorentino discepolo di <lb></lb>Galileo. </s></p><p type="main">

<s>Cosimo Noferi lasciò fra&#039;suoi manoscritti un compendio e un commento <lb></lb>alle Meccaniche di Pappo, alle quali si pone per principio e per fondamento <lb></lb>la proposizione nona sopra accennata, ridotta a quest&#039;altra semplice e chia­<lb></lb>rissima forma: <emph type="italics"></emph>“ Pappi<emph.end type="italics"></emph.end> De Mechanica <emph type="italics"></emph>propositio I.<emph.end type="italics"></emph.end> Potentia C (fig. </s>

<s>105) <lb></lb><figure id="id.020.01.1988.1.jpg" xlink:href="020/01/1988/1.jpg"></figure></s></p><p type="caption">

<s>Figura 105.<lb></lb>moveat pondus A in <lb></lb>plano horizontali NM: <lb></lb>quaeritur quae poten­<lb></lb>tia movebit idem pon­<lb></lb>dus A in plano incli­<lb></lb>nato secundum an­<lb></lb>gulum HMN. </s>

<s>Tangat <lb></lb>planum HM circulus <lb></lb>GLX ad ipsum ere­<lb></lb>ctus, et iuncta EL, <lb></lb>quae erit perpendicu­<lb></lb>laris, ducatur EH parallela plani NM, et ab L mittatur perpendicularis LF, <lb></lb>et fiat ut GF ad FE, ita pondus A ad pondus B, et potentia C ad poten­<lb></lb>tiam D. </s>

<s>Dico potentias ambas D, C movere pondus A per planum HM. ” </s></p><p type="main">

<s>“ Quia ergo ut GF ad FE, ita A ad B, ergo, suspensis his ponderibus <lb></lb>in E, A, et in G, B, aequiponderabunt fulcimento F, tamquam nixo plano <lb></lb>horizontali. </s>

<s>Sed pondus A movebatur a potentia C in plano NM, ergo in <lb></lb>plano HM movebitur ab utrisque potentiis D, C ” (MSS. Gal. </s>

<s>Disc., T. VII, <lb></lb>fol. </s>

<s>39 a tergo). </s></p><p type="main">

<s>Il trovare uno de&#039;più immediati discepoli, e uno de&#039;più prossimi pre­<lb></lb>cursori di Galileo a trattenersi tuttavia intorno ai paralogismi di Pappo, ci <lb></lb>fa ripensare alla sterilità della Scuola alessandrina, in comparazione con la <lb></lb>Pitagorica rinvigorita di novella gioventù da Giordano Nemorario, e da&#039;se­<lb></lb>guaci di lui così validamente promossa. </s>

<s>Appartiene al numero di questi se­<lb></lb>guaci Leonardo da Vinci, ne&#039;manoscritti del quale la statica del Piano in­<lb></lb>clinato vien ridotta a quella maggior perfezione, che si possa desiderare dai <lb></lb>Matematici odierni. </s>

<s>Così fatte dimostrate verità, che nel lontano e riposto <lb></lb>campo, dove noi le vediam rifiorire, par che riposino in pace solitaria, si <lb></lb>educarono sotto l&#039;aperto cielo contrastate da coloro, che preferivano le lu­<lb></lb>cerne e le serre alla luce e ai tiepori del sole. </s>

<s>Pochi uscirono vittoriosi dalla <lb></lb>lotta, ceme Leonardo, e son cotesti pochi a noi sconosciuti, ma quegli altri <lb></lb>che, verso la metà del secolo XVI, lasciarono nelle pubbliche carte impressa <pb xlink:href="020/01/1989.jpg" pagenum="232"></pb>della loro mente l&#039;effige, si vedono uscir fuori dal combattimento con l&#039;abito <lb></lb>lacerato, o rimasto sozzo nel cader nella polvere e nello strisciar per il fango. </s>

<s><lb></lb>Il Cardano e il Tartaglia sono i due più famosi fra costoro, e il campo, dove <lb></lb>ebbero a combattere, a risorgere e a ricadere, è smisurato, ma noi ci pro­<lb></lb>poniamo qui di restringer quella misura a un punto, che è quel segnato, <lb></lb>dove si diceva dianzi, nelle Collezioni di Pappo. </s></p><p type="main">

<s>Difficile, prima del Commandino, la lettura del testo greeo, il Matema­<lb></lb>tico d&#039;Alessandria non era saputo. </s>

<s>E dall&#039;altra parte le XIII Proposizioni <lb></lb>del Nemorario, dove si dimostravan le leggi delle discese rette e oblique dei <lb></lb>gravi, incoravano una dolce speranza nei promotori d&#039;aver facile a risolvere <lb></lb>il famoso problema della proporzion del peso di una sfera pendula al discen­<lb></lb>dente per un piano acclive. </s>

<s>Il Cardano nell&#039;<emph type="italics"></emph>Opus novum<emph.end type="italics"></emph.end> proponeva giusto <lb></lb>in tal forma la questione: “ Proportionem ponderis sphaerae pendentis ad <lb></lb>descendentem per acclive planum invenire ” (Operum, T. IV cit., pag. </s>

<s>496). <lb></lb>E si credeva di avere a ritrovar la desiderata verità con un discorso di que­<lb></lb>sta fatta: Per mover la sfera nel piano orizzontale non ci vuol forza di nulla, <lb></lb>ma per sollevarla nel perpendicolo ci bisogna una forza, che sia uguale a <lb></lb>tutto il peso. </s>

<s>Fra il tutto e il nulla sono le vie di mezzo, per comparar le <lb></lb>quali si doveva cercare un termine di confronto. </s>

<s>Il Cardano, che s&#039;era così <lb></lb>avviato bene, a questo punto incespica, e invece di pigliar per termine di <lb></lb>confronto la discesa verticale, fatta in un dato tempo dalla sfera libera ca­<lb></lb>dente, come pareva che suggerissero gl&#039;insegnamenti del Nemorario, prese <lb></lb>la rettitudine dell&#039;angolo, che la discesa fa con l&#039;orizzontale, cosicchè in­<lb></lb>somma, nel risolvere il problema, gli vennero scambiati gli angoli con i seni. </s>

<s><lb></lb>Ecco qual&#039;è la forma propria e la conclusione del suo ragionamento: </s></p><p type="main">

<s>“ Sit sphaera aequalis ponderi G (fig. </s>

<s>106) in puncto B, quae debeat <lb></lb>trahi super BE acclive planum BO ad perpendiculum plani BF. </s>

<s>Quia ergo <lb></lb>in BO movetur a quantitate modica, ut per <lb></lb><figure id="id.020.01.1989.1.jpg" xlink:href="020/01/1989/1.jpg"></figure></s></p><p type="caption">

<s>Figura 106.<lb></lb>dicta superuis, erit per communem animi sen­<lb></lb>tentiam, vis quae movebit G per BO nulla; per <lb></lb>dieta vero G movebitur ad F semper a costanti <lb></lb>vi aequali G, et per BE a costanti vi aequali K, <lb></lb>sicut per BD a costanti vi aequali H. Ergo, <lb></lb>per ultimam petitionem, cum termini servent <lb></lb>quoad partem eamdem rationem singuli per se, <lb></lb>et motum per BO sit a nulla vi, erit proportio <lb></lb>G ad K velut proportio vis, quae movet per BF, <lb></lb>ad vim quae movet per BE, et velut anguli per <lb></lb>EBO facti ad angulum EBO. </s>

<s>Et ita vis, quae <lb></lb>movet sphaeram per BF, et est, ut dictum est, G, ad vim, quae movet per <lb></lb>BD, et est K, est ex supposito, ut FBO ad DBO. </s>

<s>Igitur proportio difficul­<lb></lb>tatis motus per BD, ad idem per BO, est veluti H ad K, quod erat demon­<lb></lb>strandum ” (ibid.). </s></p><p type="main">

<s>Questo cardanico teorema, che cioè la gravità assoluta sta alla relativa <pb xlink:href="020/01/1990.jpg" pagenum="233"></pb>nel piano inclinato come l&#039;angolo retto sta all&#039;angolo fatto con l&#039;orizzonte <lb></lb>dallo stesso piano, doveva esser quello comunemente dimostrato dai Mate­<lb></lb>matici contemporanei, e dai predecessori, male deducendolo dai principii sta­<lb></lb>tici del Nemorario. </s>

<s>Imperocchè si dovevano, secondo que&#039;principii, compu­<lb></lb>tare i momenti per la discesa virtuale del grave nel diretto, ossia per i seni <lb></lb>e non per gli angoli delle inclinazioni. </s>

<s>S&#039;era Leonardo ben saputo delibe­<lb></lb>rare da questo errore, a cui poi, insieme con la volgar turba dei Matema­<lb></lb>tici, rimase preso anco il Cardano, ma il Tartaglia, esercitandosi intorno alle <lb></lb>XIII proposizioni <emph type="italics"></emph>De ponderibus,<emph.end type="italics"></emph.end> e ragionando intorno ad esse a dovere, fu <lb></lb>condotto alla conclusion vera, che si desiderava, e fu il primo a dar pub­<lb></lb>blica dimostrazione delle leggi dell&#039;equilibrio de&#039;gravi, in atto di scendere <lb></lb>lungo i piani inclinati. </s>

<s>Di quelle giovanili esercitazioni lasciò il Matematico <lb></lb>bresciano memoria in un opuscolo, intitolato <emph type="italics"></emph>Jordani opusculum<emph.end type="italics"></emph.end> De pon­<lb></lb>derositate <emph type="italics"></emph>Nicolai Tartaleae studio correctum,<emph.end type="italics"></emph.end> pubblicato postumo, com&#039;al­<lb></lb>trove si disse, nel 1565 in Venezia. </s>

<s>In cotesto opuscolo la questione X è <lb></lb>così proposta: “ Si per diversarum obliquitatum vias duo pondera descen­<lb></lb>dant, fiantque declinationum et ponderum una proportio, eodem ordine <lb></lb>sumpta, una erit utriusque virtus in declinando ” (fol. </s>

<s>7). E nel risolverla <lb></lb>ch&#039;e&#039;fa è sollecito di avvertire i Lettori, ch&#039;egli è venuto a salvare dal co­<lb></lb>mune naufragio, come, trattando di declinazioni, non intende di quelle degli <lb></lb>angoli, ma delle linee o de&#039;seni: “ dico non angulorum, sed linearum usque <lb></lb>ad aequidistantem resecationem, in qua aequaliter sumunt de directo ” (ibid.). </s></p><p type="main">

<s>Le giovanili esercitazioni <emph type="italics"></emph>De ponderositate<emph.end type="italics"></emph.end> furono poi dal medesimo <lb></lb>Tartaglia più ampiamente svolte, e in più piacevole forma ridotte fra&#039;<emph type="italics"></emph>Que­<lb></lb>siti,<emph.end type="italics"></emph.end> nel IX libro de&#039;quali la XV proposizione così procede in dialogo, fra <lb></lb>Nicolò e il signor don Diego ambasciator cesareo in Venezia. <emph type="italics"></emph>“ Nicolò.<emph.end type="italics"></emph.end> Se <lb></lb>dui corpi gravi descendano per vie de diverse obliquità, et che la propor­<lb></lb>tione delle declinationi delle due vie e della gravità de detti corpi sia fatta <lb></lb>una medesima, tolta per el medesimo ordine; anchora la virtù de luno e <lb></lb>laltro de detti dui corpi gravi, in el descendere, sarà una medesima. <emph type="italics"></emph>Am­<lb></lb>basciator.<emph.end type="italics"></emph.end> Questa propositione mi par bella e <lb></lb>però datime anchora un essempio chiaro, acciò <lb></lb>che meglio mi piaccia. <emph type="italics"></emph>Nicolò.<emph.end type="italics"></emph.end> Sia la linea ABC <lb></lb>(fig. </s>

<s>107) equidistante al horizonte et sopra di <lb></lb>quella sia perpendicolarmente eretta la linea BD, <lb></lb>et dal ponto D descendano de qua et de la le <lb></lb>due vie over linee DA et DC et sia la DC di <lb></lb>maggior obliquità. </s>

<s>Per la proportione adunque <lb></lb>delle lor declinationi, non dico delli lor angoli <lb></lb>ma delle linee per fin alla equidistante reseca­<lb></lb>tione, in la quale equalmente summono del di­<lb></lb>retto. </s>

<s>Sia adunque la lettera F supposta per un <lb></lb>corpo grave, posto sopra la linea DC, et un al­<lb></lb>tro la lettera H sopra la linea DA, et sia la <lb></lb><figure id="id.020.01.1990.1.jpg" xlink:href="020/01/1990/1.jpg"></figure></s></p><p type="caption">

<s>Figura 107.<pb xlink:href="020/01/1991.jpg" pagenum="234"></pb>proporzione della semplice gravità del corpo F alla semplice gravità del corpo <lb></lb>H sì come quella della DC alla DA: dico li detti dui corpi gravi essere in <lb></lb>tai siti over luochi di una medesima virtù over potentia ” (Ediz. </s>

<s>cit., fol. </s>

<s>97). </s></p><p type="main">

<s>La promessa dimostrazione si conclude dalla proposizion precedente così <lb></lb>annunziata: “ La equalità della declinatione è una medesima equalità de <lb></lb>peso ” (ivi, fol. </s>

<s>96 a tergo), e da Leonardo, come si riferì altrove: “ li pesi <lb></lb>eguali mantengono le gravità eguali nelle obliquità eguali ” (MSS. E, fol. </s>

<s>58). <lb></lb>Il Tartaglia lo dimostra assai facilmente dai professati principii perchè, posto <lb></lb>il medesimo peso ora in E ora F, sul medesimo declivio DC, scendendo per <lb></lb>tratti uguali EC, FG, si accosta ugualmente al comun centro dei gravi, es­<lb></lb>sendo i due diretti FM, EN eguali, e perciò serbano sempre eguali i mo­<lb></lb>menti. </s>

<s>“ Adunque il detto corpo ponderoso si essendo nel ponto F come <lb></lb>nel ponto E in quantità over decensi equali capirà equalmente del diretto, <lb></lb>sarà di una medesima gravità in qual si voglia di quelli ” (Quesiti cit., <lb></lb>fol. </s>

<s>97). Di qui scende immediatamante che le due obliquità DC, DA, pren­<lb></lb>dendo ugualmente del diretto DB, debbono le gravità E, H, star come le <lb></lb>quantità delle respettive discese, ossia come DC ad AD, ed è tanto la con­<lb></lb>clusione, come si diceva, immediata e diretta, che, volendosi provare il Tar­<lb></lb>taglia a dimostrarla, non sa trovare altri termini, che quelli della riduzione <lb></lb>agli assurdi. </s>

<s>Nonostante, dop&#039;essere stato pazientemente don Diego ad ascol­<lb></lb>tare, ebbe a dire verso Nicolò, che aveva appena allora finito il suo di­<lb></lb>scorso: “ Questa è stata una bella speculatione et me e piaciuta assai ” <lb></lb>(ivi, fol. </s>

<s>97 a tergo). </s></p><p type="main">

<s>Piacque poi il teorema anche a Simeone Stevino, il quale, dato mano <lb></lb>a costruire quella nuova Bilancia, trovò che veramente i fatti rispondevano <lb></lb>alle speculazioni, perchè legate le due sfere H, F a un filo, scorrevole sulla <lb></lb>puleggia P, se le gravità di esse sfere son proporzionali <emph type="italics"></emph>per il medesimo <lb></lb>ordine,<emph.end type="italics"></emph.end> come diceva il Tartaglia, ai lati del triangolo DC, DA, si fanno in­<lb></lb>sieme equilibrio. </s>

<s>Allettato il Matematico di Bruges da un&#039;invenzione, che <lb></lb>nella sua semplicità ebbe a ritrovar tanto bella, si mise dietro amorosa­<lb></lb>mente ad accarezzarla, e gli riuscì di aggiungerle nuova bellezza, ch&#039;egli <lb></lb>stesso poi descrisse così nel teorema XI della sua Statica: </s></p><p type="main">

<s>“ Soit accomodè a l&#039;entour <lb></lb>du triangle ABC (fig. </s>

<s>108) un <lb></lb>entour de 14 globes egaux en <lb></lb>pesanteur, en grandeur, et equi­<lb></lb>distans comme D, E, F, G, H, I, <lb></lb>K, L, M, N, O, P, Q, R, enfilez <lb></lb>d&#039;une ligne passant par leurs <lb></lb>centres, ainsi qu&#039;ils puissent tour­<lb></lb>ner sur leurs subdits centres, et <lb></lb>qu&#039;il y puisse avoir 2 globes sur <lb></lb>le coste BC, et 4 sur BA: alors, <lb></lb>comme ligne a ligne, ainsi le <lb></lb><figure id="id.020.01.1991.1.jpg" xlink:href="020/01/1991/1.jpg"></figure></s></p><p type="caption">

<s>Figura 108.<pb xlink:href="020/01/1992.jpg" pagenum="235"></pb>nombre des glohes au nombre des globes. </s>

<s>Qui aussi en S, T, V soyent trois <lb></lb>poincts fermes, dessus lesquels la ligne ou le filet puisse couler, et que les <lb></lb>deux parties au dessus dei triangle soyent paralleles aux costez d&#039;iceluy AB, <lb></lb>BC, tellement que le tout puisse torner librement, et dans accrochement, <lb></lb>sur les dists costez AB, BC. ” </s></p><p type="main">

<s>“ Si la pouvoir des poids D, R, Q, P n&#039;estoit egal au pouvoir des deux <lb></lb>globes E, F, l&#039;un coste sera plus pesant que l&#039;autre, donc, s&#039;il est possible, <lb></lb>que les 4 D, R, Q, P soyent plus pesans que les deux, E, F. </s>

<s>Mais les 4 O, <lb></lb>N, M, L sont egaux aux 4 G, H, I, K, parquoy le coste des 8 globes D, R, <lb></lb>Q, P, O, N, M, L sera plus pesant selon leur disposition, que non pas <lb></lb>les 6 E, F, G, H, I, K. </s>

<s>Et puisque la partie plus pesante emporte la plus <lb></lb>legere, les 8 globes descenderont, et les autres 6 monteront. </s>

<s>” </s></p><p type="main">

<s>“ Qui il soit ainsi donc et que D vienne ou O est presentement, et <lb></lb>ainsi des autres. </s>

<s>Voire que E, F, G, H viennent ou sont maintenant P, Q, <lb></lb>R, D, aussi I, K ou sont maintenant E, F. </s>

<s>Ce neont moins l&#039;entour des <lb></lb>globes aura la mesma disposition qu&#039;auparavant, et par mesme raison les <lb></lb>8 globes aurent le dessus en pesanteur, et en tombant feront revenir 8 au­<lb></lb>tres en leurs places, et ainsi ce mouvement n&#039;auroit aucunne fin, ce qui est <lb></lb>absurde. </s>

<s>” </s></p><p type="main">

<s>“ Et de mesme sera la demonstration de l&#039;autre costé. </s>

<s>La partie donc <lb></lb>de l&#039;entour D, R, Q, P, O, N, M, L sera en equilibre avec la partie E, F, <lb></lb>G, H, I, K. </s>

<s>Qui si on oste des deux costez les pesanteurs egales, et qui <lb></lb>ont mesme desposition, comme sont les 4 globes O, N, M, L d&#039;une part, et <lb></lb>les 4 G, H, I, K d&#039;autre part; les 4 restans D, R, Q, P seront et demeu­<lb></lb>reront en equilibre avec le 2 E, F, parquoy E aura un pouvoir duble au <lb></lb>pouvoir de D. </s>

<s>Comme donc le costé BA 2 au costé BC 1, ainsi le pouvoir <lb></lb>de E au pouvoir de D. ” (Oeuvres mathem. </s>

<s>cit., pag. </s>

<s>448). </s></p><p type="main">

<s>Tanto in questa dimostrazione sperimentale dello Stevino, quanto nel <lb></lb>teorema del Tartaglia, la conclusione si verifica, anche quando uno de&#039;lati <lb></lb>del triangolo è verticale, essendo anzi questo stesso lato verticale la misura <lb></lb>immediata e diretta della discesa. </s>

<s>Ma lo Stevino stesso credè bene di do­<lb></lb>verne avvertire i Lettori con questo corollario: “ Soit mantenant l&#039;un des <lb></lb>costez du triangle comme BD, qui est moitie du l&#039;autre AB, perpendicu­<lb></lb>laire a AC come cy joignant, le globe D, qui est double a G sera encor <lb></lb>en equilibre avec E, car, comme le coste AB a BC, ainsi le globe D au <lb></lb>globe E ” (ivi). </s></p><p type="main">

<s>Il Lagrange, nell&#039;introduzione alla sua Meccanica analitica, volle in par­<lb></lb>ticolar modo rammemorare ai matematici de&#039;suoi tempi questa dimostra­<lb></lb>zion dello Stevino “ parce qu&#039;elle, ei dice, est tres-ingenieuse, et qu&#039;elte est <lb></lb>d&#039;ailleurs peu connue ” (Editio cit., pag. </s>

<s>5). Sarebbe stata nonostante que­<lb></lb>sta meritevole commemorazione del Matematico italiano assai più efficace, <lb></lb>se non avesse lasciato di avvertir che l&#039;olandese Autor <emph type="italics"></emph>Des elemens de Sta­<lb></lb>tique<emph.end type="italics"></emph.end> suppone già noto il teorema del Tartaglia, senza il quale tutte le in­<lb></lb>gegnose eleganze sarebbero rimaste una veste senza persona, o per più pro-<pb xlink:href="020/01/1993.jpg" pagenum="236"></pb>prio dire una fisica fuor di luogo in quel libro di matematica. </s>

<s>Cosicchè <lb></lb>insomma non intende lo Stevino di dimostrare, ma di confermare con una <lb></lb>bella esperienza la bellissima <emph type="italics"></emph>speculatione<emph.end type="italics"></emph.end> del nostro Matematico di Brescia. </s></p><p type="main">

<s>Pietro Herigon, per rendere quella intenzione più sincera e più mani­<lb></lb>festa, fece alla dimostrazione fisica precedere la matematica, componendo <lb></lb>insieme e riducendo a più compendiosa semplicità il teorema del Tartaglia e <lb></lb>l&#039;esperienza dello Stevino. </s>

<s>Nel trattatello di Meccanica, compreso nel III Tomo <lb></lb>del <emph type="italics"></emph>Corso matematico,<emph.end type="italics"></emph.end> la proposizione VIII è così formulata: “ Si recta, a <lb></lb>vertice trianguli ad basim ducta, sit perpendicularis horizonti, pondera su­<lb></lb>per lateribus trianguli, habentia eamdem proportionem quam latera, aequi­<lb></lb>ponderant ” (Paris 1644, pag. </s>

<s>300). </s></p><p type="main">

<s>Sia D (fig. </s>

<s>109) il grave sul piano AC equilibrato dall&#039;altro grave G, <lb></lb>che libero scende lungo CB. </s>

<s>Presa AE=CB, l&#039;ascesa virtuale del primo <lb></lb>sarà EF, e la discesa del secondo nel me­<lb></lb>desimo tempo sarà CB, e deve, per i prin­<lb></lb>cipii statici professati dal Tartaglia, aversi <lb></lb>D:G=CB:EF=AC:AE, ossia CB, per <lb></lb>costruzione. </s>

<s>“ Hinc perspicuum est, dice <lb></lb>propriamente l&#039;Herigonio, pondus D ad <lb></lb>pondus, quo in lineam CB gravitat, habere <lb></lb>eamdem proportionem quam AC ad CB ” <lb></lb>(ibid.). <lb></lb><figure id="id.020.01.1993.1.jpg" xlink:href="020/01/1993/1.jpg"></figure></s></p><p type="caption">

<s>Figura 109.</s></p><p type="main">

<s>A confermar coi fatti, e a render di più facile intelligenza la mecca­<lb></lb>nica proposizion con gli esempii, il parigino Compilator della scienza mate­<lb></lb>matica universale di allora, così soggiunge: “ Si pondera habentia eamdem <lb></lb>proportionem, quam habent trianguli, non essent situ aequilibra, sequere­<lb></lb>tur fieri posse motum continuum circa triangulum. </s>

<s>Atqui hoc est absurdum, <lb></lb>cum Natura nihil suscipiat quod non exequatur, igitur, pondera, habentia <lb></lb>eamdem proportionem quam latera trianguli, sunt situ aequilibra ” (ibid., <lb></lb>pag. </s>

<s>303). Il moto continuo che ne seguiredbe lo dimostra l&#039;Herigonio a <lb></lb>modo dello Stevino, se non che trasforma i globi infilati in un tubo pieno <lb></lb>d&#039;acqua, disposto come si rappresentavan dianzi quegli stessi quattordici globi <lb></lb>nella figura steviniana. </s>

<s>Il liquido dunque, per non incorrere nell&#039;assurdità <lb></lb>del moto perpetuo, dee essere in A e in C in equilibrio, ossia debbono es­<lb></lb>sere ivi le due pressioni uguali. </s>

<s>“ Cum igitur aqua tubi non perpetuo mo­<lb></lb>veatur, necesse est potentiam descensus aquae tubi AB esse aequalem po­<lb></lb>tentiae descensus tubi BC, quod erat demonstrandum ” (ibid., pag. </s>

<s>305). </s></p><p type="main">

<s>Queste tradizioni della scienza non fu solo l&#039;Herigonio a raccoglierle, <lb></lb>ma lo imitarono anche altri di que&#039;tempi, fra quali si gloria di essere stato <lb></lb>il primo Claudio Beriguardi. </s>

<s>Nella terza parte de&#039;suoi <emph type="italics"></emph>Circoli pisani,<emph.end type="italics"></emph.end> cir­<lb></lb>colo VI, confessa che della discesa dei gravi trattarono accuratamente Ga­<lb></lb>lileo e il Torricelli, ma soggiunge ch&#039;egli stesso aveva concluso quelle me­<lb></lb>desime verità da altri principii “ XX annis antequam illi de ea re quidquam <lb></lb>vulgassent ” (Patavii 1660, pag. </s>

<s>307). Non dice però, come sarebbe stato <pb xlink:href="020/01/1994.jpg" pagenum="237"></pb>giusto dovere, che quei principii erano stati posti, e pubblicamente profes­<lb></lb>sati più di altri vent&#039;anni avanti, e descrive quale speculazione sua propria <lb></lb>l&#039;esperienza dello Stevino, che cioè sei globi uguali infilati son necessarii <lb></lb>per fare equilibrio a due altri simili globi, se i lati del triangolo su cui ri­<lb></lb>posano stanno come tre a uno. </s>

<s>Soggiunge, cosa dall&#039;altra parte assai ovvia <lb></lb>a sovvenire in mente a ciascuno, e notata già come si vide da Leonardo, e <lb></lb>un secolo dopo dall&#039;Herigonio, che si dimostrerebbe lo stesso, quando fosse <lb></lb>il triangolo un tubo pieno di acqua o d&#039;argento vivo. </s></p><p type="main">

<s>Così fatte esperienze variabili in tante guise erano tutte una bella con­<lb></lb>ferma del teorema del Tartaglia che, sebben sotto altra forma, compariva <lb></lb>in sostanza un secolo dopo nella statica del Cartesio. </s>

<s>Il famoso principio in­<lb></lb>fatti che tanta forza ci vuole a sollevare un peso di due libbre all&#039;altezza <lb></lb>di un braccio, quanto un peso di una libbra sola all&#039;altezza di due brac­<lb></lb>cia, si riduce, come altrove avvertimmo, a dire che sono i momenti uguali, <lb></lb>quando s&#039;uguagliano i prodotti dei descensi retti per le loro respettive moli, <lb></lb>d&#039;ond&#039;ebbe il Tartaglia a concluder la sua bella speculazione, a quel modo <lb></lb>che poi fece il Cartesio, perchè, rivolgendo lo sguardo sulla figura CIX, è <lb></lb>facile vedere che la scesa verticale del peso G è uguale ad AC, e l&#039;ascesa <lb></lb>di D è uguale a BC, e perciò dall&#039;essere DXCD=GXAC ne viene <lb></lb>D:G=AC:CB, cioè, dice lo stesso Cartesio, “ minor vis requiritur ad <lb></lb>pondus D, iuxta lineam AC trahendum, quam secundum lineam CB; hoc est, <lb></lb>si AC sit dupla lineae CB, vis tantum dimidia requiritur ” (Epist., Pars. </s>

<s>I <lb></lb>cit., pag. </s>

<s>212). </s></p><p type="main">

<s>La riduzione del principio cartesiano a quello, che ne concluse il Tar­<lb></lb>taglia dai principii del Nemorario, fu efficacemente espressa da Giovanni <lb></lb>Wallis nella sua VIII proposizione <emph type="italics"></emph>De motuum declivivitate,<emph.end type="italics"></emph.end> dove dimostra <lb></lb>che i momenti si compongono della ragion delle altezze e delle moli. </s>

<s>“ Cum <lb></lb>enim ea ratione plus ponderant gravia, caeteris paribus, qua sunt maioris <lb></lb>ponderis, quoque plus descenditur; ea ratione ponderabunt utriusque ratione <lb></lb>habita qua pollent eorum, secundum utramque considerationem, descensus <lb></lb>ascensusve, hoc est ea quae ex ponderum et altitudinum rationibus compo­<lb></lb>nitur ” (De motu cit., pag. </s>

<s>39). E lo prova con l&#039;esempio della Leva e del <lb></lb>Piano inclinato, dove si vede che i due gravi D e G, nella solita figura ul­<lb></lb>timamente rappresentata, si equiponderano, quando stanno i loro pesi reci­<lb></lb>procamente come le quantità dell&#039;ascesa e della discesa virtuale. </s>

<s>Conclude <lb></lb>poi di qui la XXI proposizione, che dice: “ Grave ponderat, pro varia ascen­<lb></lb>suum descensuumve obliquitate, in ratione rectorum sinuum inclinationis ad <lb></lb>horizontem, sive complementi obliquitatis ” (ibid., pag. </s>

<s>54). </s></p><p type="main">

<s>Tale essendo l&#039;ubertà del frutto raccolto dai seguaci della Scuola peri­<lb></lb>patetica, sterili sembreranno al confronto gli studii di chi, in grazia del Com­<lb></lb>mandino, potè tutti vedere in Pappo misurati i progressi della Scuola ales­<lb></lb>sandrina. </s>

<s>Dopo le Meccaniche di Guidubaldo il primo pubblico documento <lb></lb>in proposito s&#039;ha dalla Filosofia magnetica di Niccolò Cabeo, il quale invoca <lb></lb>le leggi statiche della discesa dei gravi ne&#039;piani inclinati a risolvere un que-<pb xlink:href="020/01/1995.jpg" pagenum="238"></pb>sito, che gli si propone intorno alla perpetuità del moto, possibile ad otte­<lb></lb>nersi dalle virtù perpetuamente attrattive del magnete. </s>

<s>S&#039;applica perciò ad <lb></lb>esaminar diligentemente la proposizione IX dell&#039;ottavo libro delle matema­<lb></lb>tiche Collezioni, e facilmente si avvede che l&#039;assunto preso dall&#039;Autore, per <lb></lb>concluder la sua proposizione, era falso, perchè, per movere il peso nel­<lb></lb>l&#039;orizzonte, tutt&#039;altro che bisognarvi maggior forza che a moverlo su per <lb></lb>l&#039;acclivio, non ci vuol anzi forza di nulla, come, per i teoremi del Cardano <lb></lb>e del Benedetti, era a tutti oramai notissimo. </s>

<s>Fa notare di più il Cabeo l&#039;as­<lb></lb>surdo, che conseguirebbe manifestissimo dalle posizioni di Pappo, perchè, se <lb></lb>nella figura CV, la potenza P deve stare al peso E come EF ad FG, “ si <lb></lb>HM accedat ad perpendicularem, requireretur potentia maxima, et, si sit <lb></lb>omnino perpendicularis, infinita, quod est impossibile ” (Coloniae 1629, <lb></lb>pag. </s>

<s>342). Se nell&#039;equazione infatti P=EXEF/FG, FG riducesi a zero, do­<lb></lb>vrebbe tornar P uguale all&#039;infinito. </s></p><p type="main">

<s>Perchè dunque da un principio falso non poteva conseguirne il vero, <lb></lb>propone il Cabeo una soluzion del problema diversa da quella di Pappo, e <lb></lb>perchè insomma non si trattava d&#039;altro, che di trovar la forza necessaria a <lb></lb>far risalire il grave sopra l&#039;acclività del piano HM, considera questa forza <lb></lb>applicata in I all&#039;estremità di una leva di secondo genere, che abbia in F <lb></lb>o in L il fulcro, e in E la resistenza. </s>

<s>Le note leggi del Vette, applicate al <lb></lb>piano inclinato, davano dunque risoluto il problema col far come FI ad FE, <lb></lb>così il peso alla potenza, che ha da sollevarlo. </s>

<s>Che se questa ragione non <lb></lb>piace “ quia vere etiam ipsa suas habet difficultates, donec exactius exami­<lb></lb>netur, hanc aliam habeto ” (ibid., pag. </s>

<s>343), ma la nuova, che si propone, <lb></lb>sembra andare anche più lontana dal vero, per raggiungere il quale sarebbe <lb></lb>allo stesso Cabeo stato meglio deliberarsi affatto dalla costruzione, e dalla <lb></lb>geometrica dimostrazione di Pappo. </s></p><p type="main">

<s>Così giudiziosamente avea fatto Galileo, a cui sorti perciò di dare il <lb></lb>primo la ragion del piano inclinato, derivandola dai principii della Scuola <lb></lb>alessandrina che, reputata da lui unica legittima, gli fece ingiustamente dire, <lb></lb>nell&#039;accingersi a trattar delle proporzioni dei moti di un medesimo mobile <lb></lb>sopra diversi piani inclinati, che quella era questione “ a Philosophis nul­<lb></lb>lis, quod sciam, pertractata ” (Alb. </s>

<s>XI, 56). Consiste la nuova dimostrazione <lb></lb>nel trapassar, dai gravi sostenuti dal braccio di <lb></lb>una Libbra, a considerarli come sostenuti dalla re­<lb></lb>sistenza di un piano, appropriando a questo le note <lb></lb>condizioni dell&#039;equilibrio di quella. </s>

<s>Se dal braccio <lb></lb>AB di una Leva (fig. </s>

<s>110) penda in B un peso, que­<lb></lb>sto eserciterà il suo momento totale, mentre esso <lb></lb>braccio rimanga in AB livellato. </s>

<s>Ma se inclinisi in <lb></lb>AC, il momento parziale di C, rispetto al totale in B, <lb></lb>sarà, secondo il noto teorema del Benedetti, come <lb></lb>la porzione AD, precisa dalla perpendicola CD, a <lb></lb><figure id="id.020.01.1995.1.jpg" xlink:href="020/01/1995/1.jpg"></figure></s></p><p type="caption">

<s>Figura 110.<pb xlink:href="020/01/1996.jpg" pagenum="239"></pb>tutta intera la AB. </s>

<s>Se s&#039;immagini ora nel punto C essere applicato un piano <lb></lb>EF, perpendicolare ad AC, tanto fa al grave a pendere dal braccio della <lb></lb>Leva, quanto a riposare sul piano, per scendere lungo il quale esercita ugual <lb></lb>momento che lungo l&#039;arco del cerchio. </s>

<s>Dunque anche il momento parziale di <lb></lb>C, posato sul piano EF, sarà al momento totale come AD ad AC, ossia AB, <lb></lb>e come EG sta ad EF, per la similitudine dei triangoli. </s>

<s>“ Però concluderemo, <lb></lb>scrive Galileo, questa universal proposizione col dire: sopra il piano la forza <lb></lb>al peso avere la medesima proporzione che la perpendicolare, dal termine <lb></lb>del piano tirata all&#039;orizzonte, alla lunghezza di esso piano ” (ivi, pag. </s>

<s>118). </s></p><p type="main">

<s>Correva attorno questa galileiana dimostrazione manoscritta, prima del­<lb></lb>l&#039;anno 1615, sotto il nome del Vieta, cosa creduta da molti, come dal Ba­<lb></lb>liani (Alb. </s>

<s>XVI, 105) anche in Italia, ma benchè più seducente era nondi­<lb></lb>meno più lubrica di quella del Tartaglia. </s>

<s>Attribuisce Alessandro Marchetti <lb></lb>a questa lubricità, delìa quale vedremo nella seguente parte del nostro di­<lb></lb>scorso gli esempii, l&#039;aver Galileo tenuto altro modo nell&#039;aggiunta postuma <lb></lb>al terzo dialogo Delle due nuove scienze. </s>

<s>Ivi, come lo stesso Tartaglia, sug­<lb></lb>geritogli forse dall&#039;Herigonio, di cui siam certi aver esso Galileo fra&#039;suoi <lb></lb>libri il Corso matematico (Alb. </s>

<s>X, 211, 28); dimostra esser due gravi con­<lb></lb>giunti insieme in equilibrio, quando le ascese e le discese virtuali nel per­<lb></lb>pendicolo stanno reciprocamente fra loro come i pesi. </s>

<s>“ Mentrechè dunque <lb></lb>il grave D (nella passata figura CIX) movendosi da A in C, resiste solo nel <lb></lb>salire lo spazio perpendicolare CB, ma che l&#039;altro G scende a perpendicolo, <lb></lb>necessariamente quanto tutto lo spazio AC, e che tal proporzione di salita <lb></lb>e scesa si mantiene sempre l&#039;istessa, poco o molto che sia il moto dei detti <lb></lb>mobili, per esser collegati insieme; possiamo assertivamente affermare che, <lb></lb>quando debba seguire l&#039;equilibrio, cioè la quiete tra essi mobili, i momenti, <lb></lb>le velocità o le lor propensioni al moto, cioè gli spazii che da loro si pas­<lb></lb>serebbero nel medesimo tempo, devon rispondere reciprocamente alle loro <lb></lb>gravità ” (Alb. </s>

<s>XIII, 176). Posto il qual principio, professato dal Tartaglia, <lb></lb>la conclusione era necessariamente la medesima, cosicchè il teorema del Ma­<lb></lb>tematico di Brescia aveva un secolo dopo dal Fiorentino la sua più solenne <lb></lb>conferma. </s></p><p type="main">

<s>Era venuto però in quel tempo il Nardi a mettere scrupolo intorno alle <lb></lb>discese, e alle velocità virtuali, invocando il logicale assioma che <emph type="italics"></emph>a posse ad <lb></lb>esse non valet illatio,<emph.end type="italics"></emph.end> nè parendo ragionevole il trattar di una cosa da farsi, <lb></lb>come se fosse già fatta. </s>

<s>Persuaso anche il Torricelli che dalle propensioni <lb></lb>al moto non si potesse ragionevolmente argomentare al moto, ebbe a cer­<lb></lb>care altro principio così formulato: “ Duo gravia simul coniuncta ex se <lb></lb>moveri non posse, nisi centrum commune gravitatis ipsorum descendat ” <lb></lb>(Op. </s>

<s>geom., P. </s>

<s>I cit., pag. </s>

<s>99); principio che si trovò opportuno a dimo­<lb></lb>strare il teorema del Tartaglia, e fecondo di altre bellissime conseguenze. </s></p><p type="main">

<s>Se sopra i due piani CM, CN (fig. </s>

<s>111) diversamente inclinati, e insi­<lb></lb>stenti sulla medesima orizzontale MN, sien posati due corpi tali, che i loro <lb></lb>pesi stiano come le linee CM, CN, bilanciati insieme poseranno in equilibrio, <pb xlink:href="020/01/1997.jpg" pagenum="240"></pb>ossia non avranno motivo d&#039;andar nè in su nè in giù. </s>

<s>“ Ostendemus enim <lb></lb>centrum commune gravitatis eorum descendere non posse, sed in eadem <lb></lb><figure id="id.020.01.1997.1.jpg" xlink:href="020/01/1997/1.jpg"></figure></s></p><p type="caption">

<s>Figura 111.<lb></lb>semper horizontali linea, quantumlibet gra­<lb></lb>via moveantur, reperiri ” (ivi, pag. </s>

<s>100). <lb></lb>Suppongasi infatti che non rimangano i <lb></lb>due corpi bilanciati, ma che l&#039;uno risalga <lb></lb>da A in E, mentre l&#039;altro scende da B in <lb></lb>D, per egual tratto. </s>

<s>Si farebbe ciò mani­<lb></lb>festamente senza motivo, perchè il centro <lb></lb>di gravità ch&#039;essendo in A e in B costituiti i due corpi si trova sopra la linea <lb></lb>orizzontale AB, nella nuova posizione E, D in essa linea orizzontale rimane, <lb></lb>ciò che si dimostra dal Torricelli così con la sua solita facilità elegante. </s>

<s>Si <lb></lb>ha per supposizione E:D=AC:CB. </s>

<s>E da E condotta EF parallela a CB, <lb></lb>AC:CB=AE:EF=BD:EF=GD:EG. </s>

<s>Ma se E e D stanno recipro­<lb></lb>camente come GD a EG il loro comun centro di gravità è in G, ch&#039;è pure <lb></lb>un punto della orizzontale AB niente più alto o più basso del primo, e per­<lb></lb>ciò la Bilancia, nelle condizioni supposte, è in stato d&#039;equilibrio indifferente. </s></p><p type="main">

<s>Se fosse il lato CB a perpendicolo, il peso B graviterebbe lungh&#039;esso <lb></lb>col suo momento totale, e dal general teorema ora dimostrato ne consegui­<lb></lb>rebbe immediatamente che “ momentum totale gravis ad momentum, quod <lb></lb>habet in plano inclinato, est ut longitudo ipsius plani inclinati ad perpen­<lb></lb>diculum (ibid., pag. </s>

<s>101). Il Torricelli però ne fa una dimostrazione distinta, <lb></lb>per condur la quale, entrato oramai in diffidanza del principio delle velo­<lb></lb>cità virtuali, è costretto di tornare agl&#039;istituti meccanici di Galileo, conclu­<lb></lb>dendo dalla statica della Libbra quella del piano inclinato, col processo me­<lb></lb>desimo, che s&#039;illustrava dianzi dalla CX figura. </s></p><p type="main">

<s>Fu l&#039;esempio del Torricelli efficacissimo sopra la Scuola galileiana, dalla <lb></lb>quale, banditisi i moti potenziali, non rimaneva altro modo per comparare <lb></lb>i momenti da quello in fuori di misurarli dalle <lb></lb>gravità attuali, esercitate sul braccio orizzontale <lb></lb>e inclinato della Leva. </s>

<s>Il Borelli volle dare alla <lb></lb>dimostrazione una forma nuova, costruendola <lb></lb>nella seguente maniera. </s>

<s>Sia TFR (fig. </s>

<s>112) una <lb></lb>Leva angolare col braccio TF parallelo all&#039;oriz­<lb></lb>zonte, e con l&#039;altro eguale FR comunque sol­<lb></lb>levato, e abbia in F essa Leva il suo fulcro. </s>

<s><lb></lb>Sopra T e sopra R si alzino in ciascun de&#039;due <lb></lb>bracci le perpendicolari, che prolungate s&#039;in­<lb></lb><figure id="id.020.01.1997.2.jpg" xlink:href="020/01/1997/2.jpg"></figure></s></p><p type="caption">

<s>Figura 112.<lb></lb>contreranno in D, come pure s&#039;incontreranno <lb></lb>in E i prolungamenti di TF e di DR, venendosi così a disegnare il triangolo <lb></lb>rettangolo DTE, dal funicolo TDR teso lungo il qual triangolo, sian congiunti <lb></lb>due pesi, uno pendulo in T, e l&#039;altro posato in R sul declivio del piano DE, <lb></lb>e si vogliano determinare le condizioni del loro equilibrio. </s></p><p type="main">

<s>Tanto essendo al grave R il venir sostenuto dal piano DE, quanto dal <pb xlink:href="020/01/1998.jpg" pagenum="241"></pb>braccio FR, e al grave T il pendere dal funicolo DT o dal braccio FT, le <lb></lb>richieste condizioni dell&#039;equilibrio saranno, nell&#039;uno e nell&#039;altro caso, le <lb></lb>stesse. </s>

<s>Ma per le note leggi della Leva, abbassata la perpendicolare RH, si <lb></lb>ha che R sta a T come TF, ossia FR, sta ad FH. “ Et quia, per conclu­<lb></lb>der con le parole medesime del Borelli, similia sunt duo triangula FRH et <lb></lb>DTE, latera sunt proportionalia, nempe FR ad FH erit ut ED ad DT, et <lb></lb>proinde pondus R ad T erit ut ED ad DT ” (De motu anim., P. I, Ro­<lb></lb>mae 1688, pag. </s>

<s>121). </s></p><p type="main">

<s>Anche il Viviani, in uno de&#039;suoi primi esercizii, aguzzò l&#039;ingegno per <lb></lb>concluder dalla statica della Leva, in qualche altro modo, la proposizione da <lb></lb>lui stesso così formulata: “ Il momento totale del grave al momento ch&#039;egli <lb></lb>ha, essendo posato sopra un piano obliquo, ha quella proporzione che la <lb></lb>lunghezza del detto piano inclinato al suo perpendicolo. </s>

<s>” </s></p><p type="main">

<s>“ Sia la lunghezza CI (fig. </s>

<s>113) parallela al piano dell&#039;orizzonte, dal <lb></lb>cui estremo C penda obliquamente, se­<lb></lb><figure id="id.020.01.1998.1.jpg" xlink:href="020/01/1998/1.jpg"></figure></s></p><p type="caption">

<s>Figura 113.<lb></lb>condo qualunque inclinazione, il piano <lb></lb>CB, il cui perpendicolo BL, e sopra qual­<lb></lb>sivoglia parte D del detto piano CB si <lb></lb>posi il grave A, ritenuto dal piano DM <lb></lb>attaccato al piano CB: dico il momento <lb></lb>totale del grave A, al momento ch&#039;egli ha <lb></lb>posato sopra il piano inclinato CB, avere <lb></lb>quella proporzione che ha la lunghezza <lb></lb>del piano CB al suo perpendicolo BL. ” </s></p><p type="main">

<s>“ Cada dall&#039;estremo C la perpendicolare CE, uguale a CD, e giungasi <lb></lb>ED, e si prolunghi. </s>

<s>E perchè l&#039;angolo CED è uguale all&#039;angolo CDE, sarà <lb></lb>CED minore d&#039;un retto, e perciò la ED prodotta concorrerà con CI. </s>

<s>Con­<lb></lb>corra per esempio in H, e sia H centro della Libbra, il cui braccio HC. È <lb></lb>manifesto che il grave A, posato sopra MD, farà forza per scendere obli­<lb></lb>quamente verso DM, e però farà forza allo ingiù contro il braccio della Lib­<lb></lb>bra CH. </s>

<s>Tanto dunque sarà il momento, con che il grave A spinge l&#039;osta­<lb></lb>colo CD, quanto è il momento, con cui sforza ad abbassarsi il braccio della <lb></lb>Libbra CH. </s>

<s>Ma rispetto alla Libbra il momento del grave A posato in C al <lb></lb>momento del medesimo posato in D ha quella proporzione che la distanza <lb></lb>CH alla distanza FH, dunque il momento del grave A, posato in C, cioè il <lb></lb>momento totale, a quello ch&#039;egli ha pesato in D verso DM, è come la CH <lb></lb>alla FH, e perciò come la CE alla DF, cioè come la CD alla DF, e perciò <lb></lb>come la CB alla BL, il che dovevasi dimostrare ” (MSS. Cim., T. XXXIV, <lb></lb>fol. </s>

<s>207, 8). </s></p><p type="main">

<s>Dicemmo che questo trapassar dalle leggi dell&#039;equilibrio nella leva alle <lb></lb>proporzioni del moto sui piani inclinati, di che dette forse Galileo i primi <lb></lb>esempii, benchè seducente era lubrico, com&#039;ebbe il Viviani stesso a sperimen­<lb></lb>tar nell&#039;eleggere a questa sua dimostrazione i mezzi termini, i quali manife­<lb></lb>stamente contengono una fallacia. </s>

<s>Perchè se il grave A fa forza di abbassare <pb xlink:href="020/01/1999.jpg" pagenum="242"></pb>la Libbra nella direzione CD, il suo momento comparato con quello, che egli <lb></lb>ha nella direzione CE, non sta come CH ad HF, ma ad HN condotta da H <lb></lb>perpendicolare sopra CB, secondo la regola insegnata dal Benedetti. </s>

<s>Di una <lb></lb>tal costruzione fa gran maraviglia che non si servissero, e che non ne co­<lb></lb>noscessero l&#039;importanza que&#039;sagaci galileiani, perchè riducendosi a quella, <lb></lb>che si usa per decompor le forze, avrebbe potuto condur per una via di­<lb></lb>retta e sicura a concluder l&#039;intento. </s>

<s>Dalla similitudine infatti de&#039;triangoli <lb></lb>HNC, CLB si sarebbe immediatamente dedotto che HC sta ad HN, ossia la <lb></lb>forza diretta alla obliqua, o com&#039;altrimenti vuol dirsi il momento totale nel <lb></lb>perpendicolo al parziale sul piano inclinato, come BC sta a BL. </s></p><p type="main">

<s>Dev&#039;essersi però il Viviani facilmente accorto di quella sua fallacia, <lb></lb>quand&#039;egli, primo nella Scuola galileiana imparò a decomporre il momento <lb></lb>totale ne&#039;due parziali, l&#039;un de&#039;quali s&#039;esercita contro, e l&#039;altro lungo il piano <lb></lb>inclinato; ciò che, passatosi fin allora senza considerazione, costituiva quella <lb></lb>lubricità, che si diceva essere per tornare pericolosa a chi, argomentando <lb></lb>dalla Libbra, avesse voluto imitare gli esempii di Galileo. </s></p><p type="main">

<s>Nell&#039;aggiunta postuma alla terza giornata Delle due nuove scienze si <lb></lb>accennava al fecondo principio, di cui disse bene il Lagrange: “ il paruit <lb></lb>que Galilee n&#039;a pas connu toute l&#039;importance ” (Mechan. </s>

<s>anal. </s>

<s>cit., pag. </s>

<s>8), <lb></lb>considerando nel triangolo BEF (fig. </s>

<s>114) “ il moto del mobile, per esem­<lb></lb>pio all&#039;insù da B in E, esser composto del trasversale orizzontale BF, e del <lb></lb><figure id="id.020.01.1999.1.jpg" xlink:href="020/01/1999/1.jpg"></figure></s></p><p type="caption">

<s>Figura 114.<lb></lb>perpendicolare FE, ed essendo che, quanto <lb></lb>all&#039;orizzontale, nessuna è la resistenza del <lb></lb>medesimo all&#039;esser mosso, non facendo con <lb></lb>tal moto perdita alcuna, nemmeno acquisto, <lb></lb>in riguardo della propria distanza dal comun <lb></lb>centro delle cose gravi, che nell&#039;orizzonte <lb></lb>si conserva sempre l&#039;istessa; resta la resi­<lb></lb>stenza esser solamente rispetto al dover sa­<lb></lb>lire la perpendicolare FE ” (Alb. </s>

<s>XIII, 176). Ma il Torricelli, nel corollario <lb></lb>alla proposizione II <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> proponendosi di risolvere il problema <lb></lb>di Pappo, che per i falli di Guidubaldo e del Cabeo dice esser divenuto a <lb></lb>quei tempi famoso, faceva una costruzione e un ragionamento, da cui pote­<lb></lb>vasi facilmente concludere la quantità, in che il momento totale di un grave <lb></lb>si comparte sul piano ne&#039;suoi momenti parziali. </s>

<s>Rappresenti, egli dice, la <lb></lb>verticale BC quello stesso momento totale, e dalla sua estremità C si ab­<lb></lb>bassi la CD perpendicolare all&#039;obliqua BE: il segmento BD misura la po­<lb></lb>tenza necessaria a ritenere il grave sopra il declivio, ed è così manifesta­<lb></lb>mente ne&#039;suoi veri termini risoluto il problema famoso. </s></p><p type="main">

<s>Ne&#039;lati BC, BD del triangolo CBD s&#039;hanno dunque prefigurati il mo­<lb></lb>mento totale nel perpendicolo, e il momento della discesa lungo il declivio: <lb></lb>or che altro può essere il terzo lato CD, che retto insiste sopr&#039;esso decli­<lb></lb>vio, se non che la misura, con cui il grave scendendo preme sul suo soste­<lb></lb>gno? </s>

<s>Le proporzioni dunque de&#039;moti, in che si risolve la gravità totale, son <pb xlink:href="020/01/2000.jpg" pagenum="243"></pb>date dalla similitudine de&#039;due triangoli BCD, EBF, dalla quale concludesi <lb></lb>immediatamente che, rappresentando, l&#039;ipotenusa BE essa gravità totale, i <lb></lb>due cateti danno la misura giusta delle due gravità parziali, la verticale EF <lb></lb>rappresentando l&#039;impeto dello scendere, e la orizzontale la pressione eser­<lb></lb>citata dal grave sul piano che gli soggiace. </s></p><p type="main">

<s>Sarebbe la similitudine de&#039;due detti triangoli potuta valer di matema­<lb></lb>tica dimostrazione, per chi avesse avuto dimestichezza con la regola di de­<lb></lb>comporre i momenti, come ve l&#039;aveva Leonardo da Vinci, nelle Note del <lb></lb>quale si trovano con sicurezza proposti tutti que&#039;teoremi che, negletti da <lb></lb>Galileo e dal Torricelli, si diceva, e or ora lo vedremo, essere stato il primo <lb></lb>a dimostrarli laboriosamente il Viviani. </s>

<s>“ Il grave uniforme, così annunzia <lb></lb>Leonardo la sua proposizione, che discende per obliquo divide il suo peso <lb></lb>in due varii aspetti. </s>

<s>Provasi, e sia AB (fig. </s>

<s>115) mobile situato per la obli­<lb></lb>quità ABC: dico che il peso del grave AB comparte la sua gravità per due <lb></lb>aspetti: cioè per la linea BC e per la linea <lb></lb><figure id="id.020.01.2000.1.jpg" xlink:href="020/01/2000/1.jpg"></figure></s></p><p type="caption">

<s>Figura 115.<lb></lb>BM (perpendicolare a BC) ” (Manuscr. </s>

<s>G cit., <lb></lb>fol. </s>

<s>75). La dimostrazione, per la quale rimanda <lb></lb>Leonardo al suo trattato di Statica, a cui era <lb></lb>ormai dal Nemorario consacrato il titolo di <emph type="italics"></emph>Li­<lb></lb>bro dei pesi,<emph.end type="italics"></emph.end> si doveva concludere immediata­<lb></lb>mente dalla costruzion del triangolo delle forze, <lb></lb>di cui rivelasi in quest&#039;altra Nota tutta l&#039;arte e la scienza: “ Il grave, che <lb></lb>non pesa inverso il centro del mondo, sempre pesa in due o più lochi. </s>

<s>Pro­<lb></lb>vasi, e sia il grave AB, il quale non pesa per la linea centrale BE, adunque <lb></lb>pesa alli due sostentacoli BC, BM ” (ivi, fol. </s>

<s>76 a tergo), i quali due so­<lb></lb>stentacoli fanno equilibrio all&#039;impeto discensivo del grave e al gravitativo <lb></lb>di lui sul piano inclinato, secondo la proporzionale misura delle loro lun­<lb></lb>ghezze lineari BE, EC, presa la BC per misura dell&#039;impeto totale. </s></p><p type="main">

<s>Se l&#039;angolo BCM è semiretto le due linee BE, EC tornano uguali, ciò <lb></lb>che vuol dir compartirsi in quel caso il momento totale ugualmente ne&#039;due <lb></lb>parziali; corollario che Leonardo stesso prometteva avrebbe concluso dalla <lb></lb>proposizion principale in quel Libro, dove egli aveva intenzione di dimo <lb></lb>strarla. </s>

<s>“ Il perchè e&#039;l quanto è maggiore il peso più all&#039;uno che all&#039;altro <lb></lb>aspetto, e che obliquità fia quella che comparte due pesi per egual parte, <lb></lb>sarà detto nel libro <emph type="italics"></emph>Delli pesi ”<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>75). </s></p><p type="main">

<s>Il Viviani, in maneggiar queste regole poco esperto, nè fidandosi d&#039;al­<lb></lb>tra scorta che di quella di Galileo, riuscì alle medesime conclusioni di Leo­<lb></lb>nardo, ma quanto più laboriosamente si giudichera dai nostri Lettori, alla <lb></lb>pubblica notizia dei quali rendiamo la seguente scrittura, viva immagine di <lb></lb>una pupilla, che al primo trasparir di mezzo alle nuvole un raggio chiaro <lb></lb>di luce, si volge a lui per accoglierlo con letizia desiderosa. </s>

<s>In un angolo <lb></lb>del foglio 16 del Tomo CXIII dei Discepoli di Galileo leggesi così scritto <lb></lb>dal Viviani di propria mano: “ Questa corrisponde a quella del Galileo, che <lb></lb>prova che l&#039;impeto composto di due moti equabili, perpendicolare ed oriz-<pb xlink:href="020/01/2001.jpg" pagenum="244"></pb>zontale, è uguale in potenza a tutt&#039;e due: Credo che il momento totale sia <lb></lb>uguale in potenza al momento gravitativo, e al momento discensivo insieme <lb></lb>presi. </s>

<s>Così è veramente, e lo provo qui sotto, dopo la quarta di queste mie <lb></lb>seguenti proposizioni. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Proposizione I.<emph.end type="italics"></emph.end> Il momento totale di un grave, al momento discen­<lb></lb>sivo sopra un piano, sta come il piano inclinato alla elevazione del mede­<lb></lb>simo piano. </s>

<s>” </s></p><p type="main">

<s>“ Poichè, quando il peso A al C (fig. </s>

<s>116) sta come l&#039;inclinata BA alla <lb></lb>BC perpendicolare, i pesi hanno momento uguale di discendere. </s>

<s>Ma C eser­<lb></lb><figure id="id.020.01.2001.1.jpg" xlink:href="020/01/2001/1.jpg"></figure></s></p><p type="caption">

<s>Figura 116.<lb></lb>cita il suo momento totale, dunque C è la <lb></lb>misura del momento discensivo di A per BA. </s>

<s><lb></lb>Ma il totale di A al totale di C sta come A <lb></lb>a C, e si è dimostrato che il totale di C è il <lb></lb>medesimo che il discensivo di A; dunque il <lb></lb>totale di A al discensivo del medesimo sopra <lb></lb>BA sta come la AB, piano inclinato, alla BC <lb></lb>perpendicolare, che è la sua elevazione. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Proposizione II.<emph.end type="italics"></emph.end> Il momento discensivo di un grave per un piano, <lb></lb>al discensivo del medesimo sopra altro piano, sta in proporzione reciproca­<lb></lb>mente de&#039;medesimi piani. </s>

<s>” </s></p><p type="main">

<s>“ Sia altro piano BD, e sia un grave D uguale all&#039;A. </s>

<s>Sarà il discen­<lb></lb>sivo di A per BA, al totale di A, cioè di D, come CB a BA, per l&#039;antece­<lb></lb>dente, ed il totale di D, al discensivo di D per BD, come DB a BC, per la <lb></lb>medesima antecedente. </s>

<s>Adunque <emph type="italics"></emph>ex aequo,<emph.end type="italics"></emph.end> per la perturbata, il discensivo <lb></lb>di A per BA, al discensivo di D cioè del medesimo A per BD, starà come <lb></lb>BD a BA. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Proposizione III.<emph.end type="italics"></emph.end> Il momento discensivo di un grave per un piano <lb></lb>inclinato, al gravitativo sopra il medesimo piano, sta come la elevazione del <lb></lb>piano alla orizzontale. </s>

<s>” </s></p><p type="main">

<s>“ Se i due piani BA, AF (fig. </s>

<s>117) fanno angolo retto in A, è chiaro <lb></lb>che il momento discensivo di un grave, posto in A, che tocchi tutt&#039;e due <lb></lb><figure id="id.020.01.2001.2.jpg" xlink:href="020/01/2001/2.jpg"></figure></s></p><p type="caption">

<s>Figura 117.<lb></lb>i piani, cioè che il discensivo per BA è il me­<lb></lb>desimo del gravitativo sulla FA, ed il discensivo <lb></lb>della FA è il medesimo del gravitativo sulla BA. </s>

<s><lb></lb>Stante questo, e quanto di là, cioè posto che <lb></lb>il grave A al C stia come il piano AB al per­<lb></lb>pendicolare BC, tirata per B la BE perpendico­<lb></lb>lare a BA, cioè parallela ad AF, è chiaro che il momento discensivo di un <lb></lb>grave E, uguale allo A, per BE, è uguale al discensivo dello A per FA, es­<lb></lb>sendo ugualmente inclinato l&#039;uno che l&#039;altro, cioè il gravitativo di A sopra <lb></lb>FA, per la precedente riflessione, ossia il discensivo di A per BA, al di­<lb></lb>scensivo di E per BE, sta come la BE alla BA, per la II. </s>

<s>Adunque il discen­<lb></lb>sivo di A per BA al gravitativo di A sopra BA, starà come la EB alla BA, <lb></lb>cioè come la BC, perpendicolare all&#039;orizzonte, alla CA orizzontale. </s>

<s>” </s></p><pb xlink:href="020/01/2002.jpg" pagenum="245"></pb><p type="main">

<s><emph type="italics"></emph>“ Corollario.<emph.end type="italics"></emph.end> Quando l&#039;angolo dell&#039;inclinazione sarà mezzo retto, allora <lb></lb>il discensivo di un grave sarà uguale al gravitativo, perchè la perpendico­<lb></lb>lare torna uguale alla orizzontale. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Proposizione IV.<emph.end type="italics"></emph.end> Il momento totale di un grave, al momento gravi­<lb></lb>tativo del medesimo sopra un piano inclinato, sta come il piano inclinato <lb></lb>alla orizzontale. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Positis iisdem,<emph.end type="italics"></emph.end> il totale di A al discensivo di A per BA, sta come la <lb></lb>AB alla BC, per la I, e il discensivo di A per BA, al gravitativo di A so­<lb></lb>pra BA, sta come la BC alla CA per la III. </s>

<s>Adunque <emph type="italics"></emph>ex aequo<emph.end type="italics"></emph.end> il totale <lb></lb>di A al gravitativo del medesimo sopra BA stanno come BA ad AC. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario.<emph.end type="italics"></emph.end> Onde se il momento totale di un grave come A si porrà <lb></lb>che sia misurato per esempio dal piano inclinato AB, il momento descen­<lb></lb>sivo del medesimo per detto piano sarà misurato dalla BC, ed il gravitativo <lb></lb>dalla AC, per la I e per la III di questo foglio. </s>

<s>Ma la AB, è in potenza <lb></lb>uguale alle BC, AC, adunque il momento totale di un grave è sempre uguale <lb></lb>al momento gravitativo, di esso sopra un piano col momento discensivo per <lb></lb>il medesimo piano. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Proposizione V.<emph.end type="italics"></emph.end> Che i momenti discensivi di un grave per diverse <lb></lb>inclinazioni di piani stiano come i seni retti delle elevazioni de&#039;medesimi <lb></lb>piani, si dimostra da Galileo e dal Torricelli nel corollario della III <emph type="italics"></emph>De motu <lb></lb>gravium.<emph.end type="italics"></emph.end> Ma che i momenti gravitativi di un grave, sopra diverse inclina­<lb></lb>zioni di piani, siano come i seni retti degli angoli de&#039;complementi delle ele­<lb></lb>vazioni de&#039;medesimi piani, così dalla nostra precedente si deduce; ” </s></p><p type="main">

<s>“ Poichè il momento gravitativo di A sopra AC, (fig. </s>

<s>118) al suo to­<lb></lb>tale momento, sta come la DC alla CA, per la precedente, ed il totale di <lb></lb>A, cioè di B, che è uguale ad A, al gravitativo di B <lb></lb><figure id="id.020.01.2002.1.jpg" xlink:href="020/01/2002/1.jpg"></figure></s></p><p type="caption">

<s>Figura 118.<lb></lb>sopra BC, sta come la CA, cioè come la CB alla CE, <lb></lb>per la medesima; adunque <emph type="italics"></emph>ex aequo<emph.end type="italics"></emph.end> il gravitativo di <lb></lb>A sopra AC, al gravitativo del medesimo A sopra BC, <lb></lb>starà come CD a CE, che sono i seni retti de&#039;compi­<lb></lb>menti degli angoli delle elevazioni ACE, BCE. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario.<emph.end type="italics"></emph.end> Di qui si ricava che nelle inclina­<lb></lb>zioni, che <emph type="italics"></emph>aequaliter distant a semicirculo,<emph.end type="italics"></emph.end> sempre <lb></lb>il gravitativo sopra un piano è uguale al discensivo <lb></lb>per l&#039;altro, e il discensivo al gravitativo, perchè il <lb></lb>seno retto dell&#039;uno è uguale al seno del complemento dell&#039;altro ” (ivi, <lb></lb>fol. </s>

<s>16, 17). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Con le cinque proposizioni dal Viviani, al modo ora esposto dimostrate, <lb></lb>veniva la Statica del piano inclinato, nella scuola galileiana, a ridursi alla <lb></lb>sua perfezione, e perchè doveva sopr&#039;essa posarsi il fondamento a tutto l&#039;edi-<pb xlink:href="020/01/2003.jpg" pagenum="246"></pb>fizio meccanico, giovarono provvidamente a confermarla da una parte le sot­<lb></lb>tili disamine, e le temerarie contradizioni dall&#039;altra. </s>

<s>Alessandro Marchetti <lb></lb>mandava fuori in Firenze nel 1669 un trattato <emph type="italics"></emph>De resistentia solidorum,<emph.end type="italics"></emph.end> a <lb></lb>cui poneva per fondamento un principio “ quo nullum aliud fortasse fir­<lb></lb>mius in mechanicis reperias unquam ” (pag. </s>

<s>XI) e che solo, senz&#039;altra mac­<lb></lb>china, dice essergli stato sufficiente a sollevar la mole, ch&#039;egli veniva a met­<lb></lb>tere in pubblica mostra. </s>

<s>Quel fondamento, al dir del macchinatore, frutto <lb></lb>di meditazioni alte e profonde, consisteva nella proposizione <emph type="italics"></emph>Momenta gra­<lb></lb>vium proportionem habent compositam ex proportionibus ponderum et <lb></lb>longitudinum<emph.end type="italics"></emph.end> (ivi) che, felicemente occorsagli a dimostrare, ebbe a fargli <lb></lb>menare il vanto di una grande scoperta. </s>

<s>Comunicata a Lorenzo Bellini, amico <lb></lb>suo e collega nello studio pisano, la novità preziosa, “ suscipit ipse hilari <lb></lb>vultu, favet utrique nostrum fortuna, ostendimus ambo, diversa tamen ra­<lb></lb>tiocinatione, quam deinde nobis invicem exibemus ” (ivi). </s></p><p type="main">

<s>La iattanza desta in noi una gran maraviglia, la quale di poco si dimi­<lb></lb>nuisce, anche ripensando alle condizioni di quei tempi, perchè, sebbene sia <lb></lb>vero che non erano ancora nel 1669 pubblicate le proposizioni del Mauro­<lb></lb>lico nè quelle dell&#039;Aggiunti, e che i trattati, in cui il Barrow e il Wallis <lb></lb>applicavano alla statica le teoria de&#039;momenti non potessero essere al Mar­<lb></lb>chetti e al Bellini ancora noti; nota era al mondo scientifico la borelliana <lb></lb>proposizione XXVII <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> e più noto che mai, nella proposi­<lb></lb>zione XVIII <emph type="italics"></emph>De dimensione Parabolae<emph.end type="italics"></emph.end> il Lemma geometrico del Rocca in­<lb></lb>vocato dal Torricelli. </s>

<s>In ogni modo la vantata scoperta del nuovo fondamento <lb></lb>meccanico sembra a noi una puerilità, perchè la proposizion che i momenti <lb></lb>si compongono delle distanze e delle moli si conclude immediatamente dal <lb></lb>supposto che due pesi uguali e ugualmente distanti dal sostegno si fanno <lb></lb>insieme equilibrio o, come si vuol dire, hanno uguale il momento, il quale <lb></lb>chiamato M è espresso dalla formula M=PXD, intendendosi per P il <lb></lb>peso, e per D la distanza. </s>

<s>Per un altro peso <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> e per un&#039;altra distanza <emph type="italics"></emph>d,<emph.end type="italics"></emph.end><lb></lb>il momento <emph type="italics"></emph>m<emph.end type="italics"></emph.end> è parimenti espresso da <emph type="italics"></emph>m<emph.end type="italics"></emph.end>=<emph type="italics"></emph>p<emph.end type="italics"></emph.end>X<emph type="italics"></emph>d<emph.end type="italics"></emph.end> e queste due equazioni <lb></lb>contengono in sè dimostrata la proposizion del Marchetti, con i suoi corol­<lb></lb>larii che essendo uguali le distanze i momenti stanno come i pesi, e che, se <lb></lb>essi pesi stanno reciprocamente come le distanze, i momenti sono uguali: <lb></lb>corollarii supposti per veri dallo stesso Marchetti, e sopra i quali ei conduce <lb></lb>nel seguente modo la sua dimostrazione. </s></p><p type="main">

<s>Se dagli estremi della Libbra AC <lb></lb><figure id="id.020.01.2003.1.jpg" xlink:href="020/01/2003/1.jpg"></figure></s></p><p type="caption">

<s>Figura 119.<lb></lb>(fig. </s>

<s>119) sostenuta in B, pendano in equi­<lb></lb>librio le moli E, F, si avrà per i principii <lb></lb>archimedei F:E=AB:BC. </s>

<s>Intendasi <lb></lb>appesa all&#039;estremo A una terza mole D: <lb></lb>sarà per la ragione identica D:F=D:F, <lb></lb>DXF:FXE=ABXD:BCXF. </s>

<s>Ma i <lb></lb>momenti M.oD, M.oE, supposti i pesi D, E <lb></lb>attaccati ai medesimi punti della Libbra, <pb xlink:href="020/01/2004.jpg" pagenum="247"></pb>stanno come le moli D, E, e il momento di E è uguale al momento di F, dunque <lb></lb>MoD:MoF=ABXD:BCXF, “ momentum scilicet D ad E, hoc est F in <lb></lb>composita est proportione ex rationibus D ad F et AB ad BC ” (ibid., pag. </s>

<s>2). </s></p><p type="main">

<s>Il Bellini usò un artificio simile per dimostrare la sua proposizione, <lb></lb>“ Momenta inaequalium facultatum, ab inaequalibus longitudinibus penden­<lb></lb>tium, sunt in ratione composita ponderum et longitudinum ” (Opera omnia, <lb></lb>P. II, Venetiis 1703, pag. </s>

<s>88), e fu perciò chiamato dal Marchetti a parte­<lb></lb>cipare al merito di aver gettato quelle <emph type="italics"></emph>Fondamenta universae scientiae de <lb></lb>motu,<emph.end type="italics"></emph.end> con le quali si pretendeva di dar fermezza all&#039;edifizio meccanico del <lb></lb>Torricelli e di Galileo. </s>

<s>Nel 1674 usciva in Pisa, col detto titolo prosuntuoso, <lb></lb>un libricciolo di poche paginette in 24°, nella prefazione al quale così diceva <lb></lb>il Marchetti rivolgendosi al suo lettore: “ Causam huius inscriptionis sta­<lb></lb>tim intelliges, agnosces enim hisce inniti, non ea solum quae primus omnium <lb></lb>circa eiusmodi subiectum excogitavit maximus, admirabilis ac toto orbe ce­<lb></lb>leberrimus Galileus, sed et quae rursus illis addidit eximius vir Evangeli­<lb></lb>sta Torricellius, aliique insignes huius saeculi Mathematici, immo et innu­<lb></lb>mera propemodum, quae in diem alii etiam moliri possunt. </s>

<s>Fecit haec <lb></lb>memoratus Galileus, et, dicam libere id quod sentio, non satis firme, quod <lb></lb>vel ex eo evinci potest quia, in posthuma editione suorum operum, ipse no­<lb></lb>vis ratiociniis ea fulcire conatus est. </s>

<s>Idipsum fecerat Torricellius, aliique <lb></lb>etiam tentarunt, sed quorum nullus, nisi mea me opinio fallat, exacte prae­<lb></lb>stitit, omnes namque satis quidem probabiliter ratiocinati sunt, sed neces­<lb></lb>sarias, et quales decuit vere geometricas, demonstrationes nemo exhibuit. </s>

<s><lb></lb>An tales itaque ego exhibuerim tu ipse iudica ” (pag. </s>

<s>6). </s></p><p type="main">

<s>Galileo e il Torricelli, in queste parole rimproverati, avrebbero potuto <lb></lb>rispondere al petulante discepolo che avevano molto bene considerate le cose, <lb></lb>dette quali egli si vanta di essere stato il primo; e noi in altra occasione <lb></lb>trascriveremo a giustificarli i teoremi, che lasciarono ambedue manoscritti, <lb></lb>per dimostrar che i momenti stanno in ragion composta delle distanze e dei <lb></lb>pesi, non con intenzione di applicarli ai piani inclinati, ma alle resistenze <lb></lb>dei solidi allo spezzarsi. </s></p><p type="main">

<s>La prima vera geometrica dimostrazione che, secondo il Marchetti, non <lb></lb>fu, tale quale si conveniva, esibita dal Torricelli, è questa: che pesi uguali, <lb></lb>sopra uguali piani variamente inclinati, hanno i momenti proporzionali ai <lb></lb>perpendicoli. </s>

<s>La proposta, ch&#039;è la III torricelllana <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> dovrebbe a ri­<lb></lb>gore di geometria essere dimostrata così, come il Marchetti stesso voleva <lb></lb>insegnare a fare ai due celeberrimi esi­<lb></lb>mii maestri, nella prefazione al suo li­<lb></lb>bricciolo commemorati. </s>

<s>Sia il grave sfe­<lb></lb>rico G, col centro in H, posato ora sul <lb></lb>piano AC (fig. </s>

<s>120) e ora sul medede­<lb></lb>simo piano, ma abbassatosi da CE in DF. </s>

<s><lb></lb>Tirate in ciascuna figura da H le ver­<lb></lb>ticali HN, e dai punti di contatto I, K <lb></lb><figure id="id.020.01.2004.1.jpg" xlink:href="020/01/2004/1.jpg"></figure></s></p><p type="caption">

<s>Figura 120.<pb xlink:href="020/01/2005.jpg" pagenum="248"></pb>le orizzontali IL, KM, le due coppie di triangoli simili IHL, CAE, e KMH, <lb></lb>DEF danno le due proporzioni LI:IH=EC:CA, KH:KM=ED:DF, <lb></lb>e perciò LI:KM=EC:DF. </s>

<s>Ma perchè LI sta ad MK come il momento <lb></lb>di G sepra AC sta al momento del medesimo peso sopra ED, “ ergo mo­<lb></lb>mentum ponderis G supra CA, ad momentum eiusdem ponderis supra DE, <lb></lb>in eadem est proportione, in qua CE est ad DF ” (ibid., pag. </s>

<s>11, 12). </s></p><p type="main">

<s>La solita macchina, operatrice dei primi maravigliosi effetti in sollevar <lb></lb>la mole <emph type="italics"></emph>De resistentia solidorum,<emph.end type="italics"></emph.end> è che gioca qui nelle mani dell&#039;Autore, <lb></lb>per raddirizzare e confermare il teorema torricelliano de&#039;momenti dei gravi <lb></lb>sopra i piani inclinati, la dimostrazion del quale è, come apertamente si <lb></lb>vede, conclusa dal principio già dimostrato che stanno essi momenti in ra­<lb></lb>gion composta delle distanze e dei pesi. </s>

<s>Galileo e il Torricelli, tutto attri­<lb></lb>buendo l&#039;impeto del discendere ai pesi, non badarono alle distanze, e non <lb></lb>fecero perciò distinzione fra l&#039;essere il centro di gravità nel piano o sopra <lb></lb>il piano, nel primo dei quali due casi il grave come, se pendesse dal cen­<lb></lb>tro della Libbra, non esercita momento propriamente detto, mentre nel se­<lb></lb>condo caso è come se pendesse da un braccio della stessa Libbra. </s>

<s>Così, nei <lb></lb>due sopra addotti esempii, altro è avere la sfera G il centro di gravità in <lb></lb>I o in K nel piano, altro è averlo in H sopra il piano, non sentendo nel <lb></lb>primo caso altr&#039;impeto che quello della discesa naturale obliqua, ed eser­<lb></lb>citando nel secondo un vero e proprio momento, misurabile dal prodotto del <lb></lb>peso G per la distanza IL o MK. </s></p><p type="main">

<s>Il Marchetti però non sta a richiamar l&#039;attenzione sopra questo esame <lb></lb>particolare, lasciandone la cura a un giovane suo discepolo, Giuseppe Vanni, <lb></lb>che nel 1688 pubblicava in Firenze sua patria una esercitazione meccanica <lb></lb><emph type="italics"></emph>De&#039;momenti de&#039;gravi sopra a&#039;piani.<emph.end type="italics"></emph.end> Ivi “ mi maraviglio bene, egli dice, <lb></lb>e non so per qual destino, che ancor quel grand&#039;uomo d&#039;Evangelista Tor­<lb></lb>ricelli, nella seconda proposizione del primo libro Dei moti, per altro certa, <lb></lb>parlando dei gravi similmente posti si servisse d&#039;una dimostrazione, nella <lb></lb>quale due cose egli afferma che non mi paiono vere. </s>

<s>Dice in primo luogo <lb></lb>che, se il peso A (fig. </s>

<s>121) al peso D sta come AB a BC, il momento del <lb></lb>peso A è uguale al momento del peso D, ciò che nè è vero, nè si deduce <lb></lb><figure id="id.020.01.2005.1.jpg" xlink:href="020/01/2005/1.jpg"></figure></s></p><p type="caption">

<s>Figura 121.<lb></lb>com&#039;egli afferma dalla sua prece­<lb></lb>dente. </s>

<s>Perciocchè nella prima consi­<lb></lb>dera i pesi co&#039;centri delle lor gravità <lb></lb>nel piano, cioè posti, come s&#039;è defi­<lb></lb>nito, nel piano, e nella seconda gli <lb></lb>pone sopra il piano, cosa che varia <lb></lb>di gran lunga i momenti: anzi nel <lb></lb>primo caso i gravi, come noi dimostreremo, non hanno momento alcuno, e <lb></lb>nel secondo il più delle volte l&#039;esercitano. </s>

<s>Secondariamente pronunzia che il <lb></lb>momento del grave C, al momento del grave D, sta come la mole alla mole, <lb></lb>essendosi dimostrato, nella seconda di questo, aver proporzion composta della <lb></lb>mole alla mole, e della distanza alla distanza ” (pag. </s>

<s>37, 38). </s></p><pb xlink:href="020/01/2006.jpg" pagenum="249"></pb><p type="main">

<s>Queste non son però altro che sottigliezze di effetti, dipendenti dalla <lb></lb>particolar figura del corpo disposto a scendere ora strisciando, ora rivolgen­<lb></lb>dosi in sè stesso o ruzzolando, e Galileo e il Torricelli non sempre usano <lb></lb>la parola momento in senso proprio, come lo definì il Maurolico, ma lo fanno <lb></lb>più spesso sinonimo d&#039;impeto o di, qualunque egli sia, conato al moto, il <lb></lb>quale impeto o conato totale, non variandosi in un medesimo mobile per <lb></lb>variar di posizione o di figura, anche gl&#039;impeti parziali rimangon gli stessi, <lb></lb>e perciò la questione è lasciata a decidere al principio della composizion <lb></lb>delle forze, di bene altra efficacia della macchina dei momenti costruita dal <lb></lb>Marchetti e dal Vanni. </s></p><p type="main">

<s>Se di quella sicurissima regola di decomporre le forze avesse saputo <lb></lb>far uso Vitale Giordano, si sarebbe facilmente ravveduto della insussistenza <lb></lb>delle sue obiezioni contro il lemma della proposizione II del Torricelli, e le <lb></lb>sue nubi “ quae videntur obscuritatis nescio quid ac dubii praecedentis theo­<lb></lb>rematis conclusioni offundere ” (Fundam. </s>

<s>doctrinae motus, Romae 1688, <lb></lb>pag. </s>

<s>1) gli si sarebbero d&#039;un tratto dissipate dalla mente, perchè il mo­<lb></lb>mento totale del peso sostenuto orizzontalmente dal braccio della Libbra si <lb></lb>decompone sul piano in due, uno, che solo rimane attivo, e l&#039;altro che si <lb></lb>rintuzza dalla resistenza del piano. </s>

<s>Ma il Giordano che non sapeva vedere <lb></lb>in che modo e in qual precisa quantità le parti rispondessero al tutto, per­<lb></lb>ciò oppose che non può il momento del peso, sostenuto dal solo vette, es­<lb></lb>sere il medesimo di quello sostenuto tutt&#039;insieme dal vette e dal declivio, <lb></lb>sopra il quale egli scende. </s></p><p type="main">

<s>Dall&#039;aver dunque trascurata la regola dei moti composti, e non quella <lb></lb>dei momenti, dipendeva la lubricità della prima galileiana dimostrazione, fe­<lb></lb>delmente imitata dal Torricelli, il quale, se non si fosse contentato di dir <lb></lb>così in generale che il grave è in parte abbandonato al proprio impeto, e <lb></lb>in parte è sostenuto dal piano obliquo; non avrebbe dato al Giordano, mes­<lb></lb>sosi su per quel lubrico, occasione di cader così tante volte com&#039;egli fece. </s>

<s><lb></lb>Maravigliosa perciò apparirà, anco da questa parte, la scienza di Leonardo <lb></lb>da Vinci, che fra tanti insidiosi agguati procede sicura, e che ora dà sodi­<lb></lb>sfazione al Marchetti, dimostrando come lui la proposizione del grave sfe­<lb></lb>rico ruzzolante con la regola dei momenti; ora dà sodisfazione al Vanni, <lb></lb>considerando il grave che non ruzzola, ma che striscia suì piano, e pure, <lb></lb>in mezzo alte variate cause accidentali, mostra essere una medesima la ve­<lb></lb>rità dell&#039;effetto. </s>

<s>Cotesta sua sicurezza vedemmo nascere dall&#039;aver saputo com­<lb></lb>partire la gravità per due aspetti, ciò che, non essendosi saputo fare nè da <lb></lb>Galileo nè dal Torricelli, provocò prima i restauri del Marchetti inutili e <lb></lb>inefficaci, e poi la famosa demolizione della Statica antica, tentata dal ge­<lb></lb>suita lucchese Giovan Francesco Vanni. </s></p><p type="main">

<s>Antonio Magliabecchi, bibliotecario del granduca di Firenze, mandò un <lb></lb>giorno del 1684 a cotesto Gesuita lucchese, che allora insegnava in Roma, <lb></lb>il libricciolo del Marchetti Dei fondamenti della scienza universale del moto, <lb></lb>dove leggendo il Vanni che Galileo e il Torricelli avevano dimostrata la <pb xlink:href="020/01/2007.jpg" pagenum="250"></pb>proposizion dei momenti sopra i piani inclinati, <emph type="italics"></emph>non satis firme,<emph.end type="italics"></emph.end> prese ardir <lb></lb>di soggiungere ch&#039;era affatto impossibile dar fermezza a ciò che non sussi­<lb></lb>ste. </s>

<s>Pochi giorni dopo andava attorno per Roma un foglietto in 24° di quat­<lb></lb>tro sole paginette stampate, la prima delle quali portava scritto in fronte: <lb></lb>“ Specimen libri De momentis gravium, Auctore I. F. V. lucensi, ad illu­<lb></lb>strissimum et eruditissimum D. </s>

<s>Antonium Magliabechium Sereniss. </s>

<s>M. D. </s>

<s><lb></lb>Etruriae Bibliothecarium. </s>

<s>” Poi subito sotto si rivolgeva l&#039;Autore allo stesso <lb></lb>Magliabecchi, per annunziargli che la intenzion della sua breve scrittura era <lb></lb>quella di dimostrar come la proposizione che il momento totale sta al par­<lb></lb>ziale sul piano, reciprocamente come il piano stesso sta al perpendicolo, cre­<lb></lb>duta da Galileo, dal Torricelli e da tanti altri esimi Matematici vera, era una <lb></lb>falsità manifesta. </s>

<s>Il ragionamento procedeva così, come noi compendiosa­<lb></lb>mente lo ridurremo da ciò che leggesi nel citato foglietto volante. </s></p><p type="main">

<s>Sia il piano inclinato XNC (fig. </s>

<s>122) di cui si prolunghi la base oriz­<lb></lb>zontale NC della quantità CO, uguale ad XN, e sopra O eretto il perpendi­<lb></lb>colo ZO, uguale a NC, s&#039;appoggi l&#039;altro piano ZC, che farà per la costru­<lb></lb><figure id="id.020.01.2007.1.jpg" xlink:href="020/01/2007/1.jpg"></figure></s></p><p type="caption">

<s>Figura 122.<lb></lb>zione l&#039;angolo XCZ retto, dentro il quale s&#039;im­<lb></lb>magini posato il grave sferico IFH. </s>

<s>Il peso totale <lb></lb>si compartirà ugualmente nelle due direzioni <lb></lb>FI, IH, condotte dal centro I ai punti di con­<lb></lb>tatto, e perciò perpendicolari ai due piani tan­<lb></lb>genti. </s>

<s>Chiamati ora M. </s>

<s>T il momento totale, <lb></lb>M. XC, M.ZC i momenti parziali sopra i piani <lb></lb>XC, ZC, si dovrebbe, secondo il teorema dimo­<lb></lb>strato da Galileo e dal Torricelli, avere le due <lb></lb>proporzioni M.T:M.XC=XC:XN, M.T:M.ZC <lb></lb>=XC:NC, le quali composte darebbero M.T:M.XC+M.ZC=XC:XN+NC; <lb></lb>cioè, dice il Vanni, “ momentum totale ad momenta partialia, simul sumpta, <lb></lb>est ut hypothenuse XC ad latera XN, et NC, in directum posita eiusdem trian­<lb></lb>guli XNC. </s>

<s>Atqui hypothenusa XC non est aequalis lateribus XN, NC, sed <lb></lb>est illis minor, ergo, si totale momentum ad partialia sit ut XC ad XN et <lb></lb>NC, momentum totale non aequatur, sed est minus momentis partialibus <lb></lb>simul sumptis. </s>

<s>Ergo momentum totale, ad momentum super plano declivi XC, <lb></lb>non est ut longitudo plani XC ad perpendiculum XN ” (Romae 1684, pag. </s>

<s>3). </s></p><p type="main">

<s>È indicibile la confusione che venne a mettere in tutto il mondo ma­<lb></lb>tematico questo argomento del Vanni, in cui ora, a noi che abbiamo dime­<lb></lb>stichezza col parallelogrammo delle forze, è tanto facile scoprire il paralo­<lb></lb>gismo. </s>

<s>Ma non era allora così: l&#039;arguto oppositore concludeva contro la <lb></lb>proposizione di Galileo da un principìo insegnato dallo stesso Galileo, che <lb></lb>cioè “ si aliquod mobile duplici motu aequabili moveatur, nempe horizon­<lb></lb>tali et perpendiculari, impetus, seu momentum lationis ex utroque motu <lb></lb>compositae, erit potentia aequalis ambobus momentis priorum motum ” <lb></lb>(Alb. </s>

<s>XIII, 234). Questa galileiana risponde alla XLI <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end><lb></lb>dove il Borelli avverte che il moto resultante per XC (nella precedente <pb xlink:href="020/01/2008.jpg" pagenum="251"></pb>figura CXXII) è uguale alla somma dei due componenti, fatti per la oriz­<lb></lb>zontale NC e per la verticale XN, non in lunghezza, ma solamente in po­<lb></lb>tenza. </s>

<s>“ Hic vero XC non est aequalis longitudine, set potentia tantum, mo­<lb></lb>tibus XN et NC, propter angulum rectum ” (Bononiae 1667, pag. </s>

<s>85). </s></p><p type="main">

<s>Il Borelli, dietro gl&#039;insegnamenti di Galileo, s&#039;illudeva con le potenze <lb></lb>che producono i quadrati <emph type="italics"></emph>propter angulum rectum:<emph.end type="italics"></emph.end> era chiaro però che si <lb></lb>trattava di forze, la potenza delle quali non può consistere in altro che nello <lb></lb>spingere un grave in un dato tempo per uno spazio determinato, ond&#039;è che, <lb></lb>secondo esso Borelli, si misura quella stessa potenza dal prodotto della ve­<lb></lb>locità motrice per la quantità di materia mossa. </s>

<s>Siano al peso, rappresen­<lb></lb>tato in C nell&#039;ultima figura, applicate due forze, una delle quali abbia virtù <lb></lb>di trasportarlo equabilmente in un minuto secondo da C in N, per la oriz­<lb></lb>zontale, e l&#039;altra di sollevarlo da N in X, nello stesso tempo, per la verti­<lb></lb>cale: saranno quelle due potenze come le velocità, o come gli spazii pas­<lb></lb>sati, ossia come le lunghezze NC, XN, e sarà pure come la lunghezza XC <lb></lb>la resultante de&#039;due moti composti, o il tutto rispetto alle sue parti. </s>

<s>Se dun­<lb></lb>que queste, sommate insieme, debbono uguagliarsi a quella, come dimostra­<lb></lb>vano Galileo e il Borelli, essere la potenza XC uguale alla somma delle due <lb></lb>potenze NC e XN non voleva altro dire, fuor di ogni altra ambage, se non <lb></lb>ch&#039;essere l&#039;ipotenusa uguale alla somma de&#039;due cateti. </s>

<s>Ma perchè questo <lb></lb>è manifestamente falso, e a un tal passo inevitabilmente conduce il suppo­<lb></lb>sto che il momento totale stia al parziale come il piano sta al perpendicolo, <lb></lb>dunque concludeva il Vanni quel supposto teorema non può esser vero. </s></p><p type="main">

<s>Sembrava glì si dovesse da tutti rispondere esser piuttosto falso che il <lb></lb>momento totale debba equivalere alla somma dei due parziali, ma illudeva <lb></lb>così il male applicato assioma che il tutto è uguale alle parti, e sopra i più <lb></lb>prevaleva così grande l&#039;autorità di Galileo, che non si vollero in generale <lb></lb>ascoltar le ragioni, con le quali il Mersenno si studiava di ridurre al vero <lb></lb>le menti. </s>

<s>Com&#039;è possibile, diceva nella prefazione alla sua Meccanica, che <lb></lb>un martello, sceso con la velocità XC, faccia ugual percossa su C a quella <lb></lb>di un altro, che scenda con la velocità XN+NC, tanto più grande, se è <lb></lb>vero che sia tanto maggior l&#039;impeto di un corpo, quanto va più veloce? </s>

<s><lb></lb>Che dunque il moto per XC sia uguale alla somma dei moti per XN e NC <lb></lb>“ est ex mente Galilei pag. </s>

<s>250 Dialogorum, quod tamen minime verum <lb></lb>esse videtur ” (Parisiis 1644). </s></p><p type="main">

<s>Aveva il Vanni insomma proposto a sciogliere ai Matematici sbigottiti <lb></lb>questo dilemma: o è falso il teorema del moto per l&#039;ipotenusa composto <lb></lb>dei due per i cateti, come si dimostra da Galileo nella IV giornata Delle due <lb></lb>nuove scienze, o è falso l&#039;altro teorema della proporzion dei momenti di un <lb></lb>medesimo grave nel declivio e nel perpendicolo, com&#039;è da Galileo stesso ivi <lb></lb>dimostrato nell&#039;aggiunta postuma alla III Giornata. </s>

<s>L&#039;audace oppositore, ap­<lb></lb>provando quello per vero, ripudiò questo come falso e, ritornando indietro <lb></lb>un secolo e mezzo a intromettersi nella questione fra il Tartaglia e il Car­<lb></lb>dano, ripetè con costui che il peso nel perpendicolo sta al peso nel piano <pb xlink:href="020/01/2009.jpg" pagenum="252"></pb>inclinato come l&#039;angolo dell&#039;elevazione sta all&#039;angolo retto. </s>

<s>In un libricciolo <lb></lb>di poche pagine uscito fuori anonimo in Roma nel settembre del 1686 col <lb></lb>titolo <emph type="italics"></emph>Exegeses physico mathematicae de momentis gravium, de Vecte ac <lb></lb>de motu aequabiliter accelerato,<emph.end type="italics"></emph.end> si studiò di dare apparenza di vero a quel <lb></lb>ripudiato cardanico teorema, confermandolo poi nel 1693 con nuovi paralo­<lb></lb>gismi in un altro libretto di maggior mole, <lb></lb>uscito pure in Roma a nome dell&#039;Autore, <lb></lb>col titolo <emph type="italics"></emph>Investigatio momentorum,<emph.end type="italics"></emph.end> e in <lb></lb>cui la XXVI proposizione così viene annun­<lb></lb>ziata: “ Si globi G et D (fig. </s>

<s>123) deti­<lb></lb>neantur immoti a potentia Q, per filum <lb></lb>DQG, cuius una pars sit normalis horizonti, <lb></lb>altera sit parallela plano declivi AC, ac sup­<lb></lb>ponamus conatum quam adhibet potentia Q <lb></lb><figure id="id.020.01.2009.1.jpg" xlink:href="020/01/2009/1.jpg"></figure></s></p><p type="caption">

<s>Figura 123.<lb></lb>nullatenus differre a conatibus simul sumptis quos adhibent potentiae D, G, <lb></lb>globus G ad globum D est ut angulus elevationis A ad rectum B ” (pag. </s>

<s>65). </s></p><p type="main">

<s>Lo <emph type="italics"></emph>Specimen<emph.end type="italics"></emph.end> del Vanni era come il lampo precursore alla folgore del­<lb></lb>l&#039;<emph type="italics"></emph>Esegesi,<emph.end type="italics"></emph.end> avventata, per distruggerlo dalle fondamenta, contro l&#039;antico edi­<lb></lb>fizio meccanico condotto da Galileo al più alto fastigio; ond&#039;è che tutti co­<lb></lb>loro, i quali vi si riparavano sotto, o che uscivano di quando in quando fuori <lb></lb>per ammirarlo, furiosi insorsero contro il mago, che aveva con le malefiche <lb></lb>arti condensato nel sereno aere la inaspettata procella. </s>

<s>E qui, come sempre <lb></lb>suole avvenire in simili casi, l&#039;insurrezione si sfogava, secondo l&#039;indole della <lb></lb>persona o la qualità dell&#039;ingegno in varia maniera. </s>

<s>I più, per assicurarsi <lb></lb>del pericolo, si stavano contenti a ricercare e a mettere a nuova prova la <lb></lb>stabilità del fondamento, mentre alcuni altri volevano anche più avanti en­<lb></lb>trare addentro all&#039;officina del mago, per spezzar quelle filosofiche ampolle, <lb></lb>dalle quali si faceva esalare il malefico fiato. </s>

<s>Del primo modo d&#039;insorgere, <lb></lb>specialmente in Italia, s&#039;ebbero molti esempii, ma pochi del secondo, per­<lb></lb>chè, sebben fosse facile a riconoscer quella per una vipera, difficile riusciva <lb></lb>a scoprir la borsa e i canali, d&#039;onde stilla il veleno, come apparirà dai fatti <lb></lb>che ora riferiremo. </s></p><p type="main">

<s>Vedemmo come il lampo minaccioso del Vanni, prima che a nessun al­<lb></lb>tro, si scoprisse agli occhi del Magliabechi, il quale, rimasto a un tratto così <lb></lb>abbarbagliato, volle interpellare il giudizio di varii suoi dotti amici, fra&#039;quali <lb></lb>Antonio Monfort, che così gli rispondeva il di 10 Settembre 1685 da Na­<lb></lb>poli: “ Le rendo infinite grazie dell&#039;opuscolo del signor Vanni, il quale non <lb></lb>l&#039;ho veduto prima di oggi. </s>

<s>In quanto al mio giudizio so che sarà molto de­<lb></lb>bole, ma perchè V. S. illustrissima comanda così, non posso se non ob­<lb></lb>bedire. </s>

<s>” </s></p><p type="main">

<s>“ Il Galileo ed anco Renato, nella II parte delle Lettere, epist. </s>

<s>LXXII, <lb></lb>vogliono che il momento del grave D per l&#039;inclinata AC (nella precedente <lb></lb>figura) sia al momento medesimo per la perpendicolare CB, come la CB alla <lb></lb>AC, e per conseguenza, quando si uniranno i due triangoli come vuole il <pb xlink:href="020/01/2010.jpg" pagenum="253"></pb>p. </s>

<s>Vanni, non si compartiscono i due momenti sopra le loro ipotenuse in <lb></lb>modo, che uniti si eguaglino al momento totale, ma sempre saranno mag­<lb></lb>giori di quello, siccome li due lati del triangolo rettangolo avanzano l&#039;ipo­<lb></lb>tenusa. </s>

<s>Ora il Padre doveva dimostrare che li due suddetti momenti non <lb></lb>possono esser maggiori del momento totale, per aver poi luogo la sua con­<lb></lb>seguenza. </s>

<s>Dirà il Padre che questo è noto <emph type="italics"></emph>lumine naturae,<emph.end type="italics"></emph.end> ma con sua li­<lb></lb>cenza non par così, quando tanti grandi uomini, non solo non l&#039;hanno co­<lb></lb>nosciuto per tale, ma ne hanno dimostrato il contrario, che nell&#039;unione dei <lb></lb>triangoli, per lo scambievole impedimento, cessano li momenti per l&#039;incli­<lb></lb>nata, e totalmente il peso si riduce sopra le basi NC, CO della figura del <lb></lb>Padre. </s>

<s>” </s></p><p type="main">

<s>“ Prego V. S. Ill.ma a restar servito che questo giudizio, qualunque egli <lb></lb>sia, resti fra noi, perchè non vorrei briga con costoro, i quali, benchè siano <lb></lb>amici infruttuosi, son però nemici efficaci ” (MSS. Gal. </s>

<s>Disc., T. CXXXII, <lb></lb>fol. </s>

<s>77). </s></p><p type="main">

<s>Se fosse, senza alcuna paura delle gesuitesche inimicizie, proceduto il <lb></lb>Monfort avanti, forse avrebbe risoluta la questione ne&#039;suoi veri termini, ma <lb></lb>mettendo dubbii intorno al II teorema del IV Dialogo del moto, sarebbe ve­<lb></lb>nuto ad attaccar briga tutt&#039;insieme co&#039;gesuiti e coi galileiani, i quali, messi <lb></lb>in grande imbarazzo dal dilemma del Vanni, non potevan far altro che con­<lb></lb>fermare il vero, senza saper scoprire la fallacia nei ragionamenti, che vo­<lb></lb>levano dargli apparenza di falso. </s></p><p type="main">

<s>La mattina del dì 28 Aprile 1685 il Viviani riceveva da Roma una let­<lb></lb>tera, dove un tal Girolamo Pollini gli scriveva, fra le altre, queste parole: <lb></lb>“ Coll&#039;occasione che ieri l&#039;altro mi fu dato un foglietto da un mio amico <lb></lb>stampato, che io gli mando copiato, di un certo Francesco Spoleti di Luci­<lb></lb>gnano, dottore di medicina, quale adesso si ritrova in Venezia, ho volsuto <lb></lb>cercare l&#039;origine per il quale fu stampato, ed ieri appunto trovai il p. </s>

<s>Gio­<lb></lb>van Francesco Vanni lucchese, gesuita nel Collegio romano, che mi donò <lb></lb>il presente foglietto stampato da lui, che io gl&#039;invio (lo <emph type="italics"></emph>Specimen,<emph.end type="italics"></emph.end> che tien <lb></lb>luogo de&#039;fogli 69, 70 nel Tomo CXLVII de&#039;<emph type="italics"></emph>Discepoli<emph.end type="italics"></emph.end> fra i manoscritti del <lb></lb>Viviani) il quale padre mi disse di vantaggio che il dottissimo Galileo e il <lb></lb>Torricelli si sono molto ingannati nel dimostrare le sue proposizioni, par­<lb></lb>ticolarmente <emph type="italics"></emph>De vecte,<emph.end type="italics"></emph.end> e che esso ha una dottrina contraria ad essi, quale <lb></lb>mi mostrò manoscritta, quale per il tempo così breve, diss&#039;egli, non volse <lb></lb>che si leggesse, ma solo qualche proposizione, dicendo che fra poco l&#039;avrebbe <lb></lb>stampata, avendo la licenza di poterla stampare. </s>

<s>” </s></p><p type="main">

<s>“ Prego la bontà di V. S. Ecc.ma di riflettere alla proposta del padre <lb></lb>Gesuito, ed alla risposta dello Spoleti, dicendo esso Gesuito che lo Spoleti <lb></lb>non abbia arrivato al fondo della proposizione di detto Padre, ma che esso <lb></lb>prova bene, ma non conclude alcuna cosa contro la propria proposizione ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CXLVI, fol. </s>

<s>276). </s></p><p type="main">

<s>Il foglietto dello Spoleti, che noi leggiamo fra i manoscritti del Viviani <lb></lb>copiato dal Pollini, s&#039;intitolava <emph type="italics"></emph>De momento gravis in plano inclinato, di-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2011.jpg" pagenum="254"></pb><emph type="italics"></emph>cato Christinae Succorum Reginae a Francisco Spoleti lucignanensi.<emph.end type="italics"></emph.end> In <lb></lb>una prefazioncella prometteva l&#039;Autore ai lettori avrebbe a loro provato, con <lb></lb>metodo nuovo, che il momento del grave sul piano obliquo sta al suo mo­<lb></lb>mento totale come il perpendicolo all&#039;ipotenusa “ non solum ad hanc fir­<lb></lb>mandam doctrinam, verum etiam ut falsitatis arguam propositionem nuper <lb></lb>editam Romae a Mathematico lucensi, qui hac in re hallucinatos ait excel­<lb></lb>lentissimos Magistros, censetque momenta gravis in duobus planis inclina­<lb></lb>tis, simul sumpta, esse aequalia suo momento totali, quod falsum ostendam ” <lb></lb>(MSS. Gal., T. CXLVI, foI. 277). </s></p><p type="main">

<s>Applicando infatti le formule generali ai <lb></lb>numeri, suppone lo Spoleti essere NCO (fig. </s>

<s>124) <lb></lb>sette ulne, delle quali NC=ZO ne contenga <lb></lb>tre, e CO=NX ne contenga quattro. </s>

<s>Calcolati <lb></lb>poi convenientemente co&#039;logaritmi gli elementi <lb></lb>trigonometrici in questione, conclude: “ Hinc <lb></lb>patet momenta sphaerae I in planis inclinatis <lb></lb>XC, ZC simul sumpta ad suum momentum to­<lb></lb>tale non esse ut 1 ad 1, sicut Mathematicus <lb></lb>lucensis volebat, sed ut 7 ad 5, nempe ut ver­<lb></lb><figure id="id.020.01.2011.1.jpg" xlink:href="020/01/2011/1.jpg"></figure></s></p><p type="caption">

<s>Figura 124.<lb></lb>ticalis XN et verticalis ZO (eguale alla orizzontale NC) ad hypothenusam XC, <lb></lb>quod erat ostendendum ” (ivi, fol. </s>

<s>279). </s></p><p type="main">

<s>Questo numerico esempio dello Spoleti confermava senza dubbio il teo­<lb></lb>rema di Galileo e del Tartaglia, ma aveva ragione il Vanni a dire che non <lb></lb>concludeva alcuna cosa contro il suo argomento, perchè, per far ciò, sarebbe <lb></lb>convenuto provare come mai il tutto non debba essere eguale alle parti, con­<lb></lb>tro l&#039;assioma, e contro il teorema II dimostrato da Galileo nella sua IV gior­<lb></lb>nata Del moto. </s>

<s>Un Galileiano perciò non poteva far altro che ostinarsi a <lb></lb>mantenere il vero contro i liberi sofismi, come presso a poco fa colui che <lb></lb>la mente combattuta riposa nell&#039;evidenza dei fatti. </s>

<s>S&#039;attenne a questo par­<lb></lb>tito un altro Gesuita, ch&#039;ebbe educato l&#039;ingegno a una scuola diversa da <lb></lb>quella del Vanni, il fiorentino Giuseppe Ferroni, il quale scriveva così da <lb></lb>Siena il dì 9 Luglio 1687 al suo amato maestro Vincenzio Viviani: </s></p><p type="main">

<s>“ Il mio scolare, dottor Pier Antonio Morozzi, com&#039;Ella avrà potuto co­<lb></lb>noscere, è un angelo d&#039;ingegno e di costumi, ed io ho pensato di fargli <lb></lb>onore con fargli stampare a suo nome, senza mentovarmi, un problema. </s>

<s>Ri­<lb></lb>pensando qual problema dar gli potessi, mi è sovvenuto il foglio volante del <lb></lb>p. </s>

<s>Domenico (così) Vanni lucchese Del momento dei gravi discendenti sopra <lb></lb>i piani inclinati, e della sua Esegesi, ove, con discorsi filosofici che non hanno <lb></lb>alcuno odore di Geometria, pretende di gettare a terra la dottrina <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end><lb></lb>del nostro gran maestro Galileo, e di stampare un foglio volante in rispo­<lb></lb>sta. </s>

<s>Egli mena troppa galloria, vedendo che niun risponde alla sua obie­<lb></lb>zione. </s>

<s>Penso rispondere, e con sua buona licenzia valermi dei moti equipol­<lb></lb>lenti, come V. S. Ill.ma m&#039;insegnò in Firenze, e soggiungere per i momenti <lb></lb>dei gravi una dimostrazione, presa in parte da alcuni manoscritti del p. </s>

<s>Egi-<pb xlink:href="020/01/2012.jpg" pagenum="255"></pb>dio Gottignes, ma da me variata in gran parte, e accomodata al mio intento. </s>

<s><lb></lb>Ma perchè in Geometria non mi fido di me, la mando qui a V. S. Ill.ma, <lb></lb>acciò mi faccia grazia di esaminarla, e vedere se sta a martello, e quando <lb></lb>pur vi stia mi faccia grazia di motterla in più chiarezza, ed in miglior lume. </s>

<s><lb></lb>Non ardirei incomodarla di tanto, se non sapessi che l&#039;amore di V. S. Ill.ma<lb></lb>verso il nostro riverito maestro Galileo gli fosse per addolcire la noia ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CXLVII, fol. </s>

<s>19). </s></p><p type="main">

<s>La proposizione meccanica inclusa in questa lettera del Ferroni veniva <lb></lb>così formulata: “ Potentia, pondus sustinens in plano inclnato AC (fig. </s>

<s>125), <lb></lb><figure id="id.020.01.2012.1.jpg" xlink:href="020/01/2012/1.jpg"></figure></s></p><p type="caption">

<s>Figura 125.<lb></lb>ad potentiam idem pondus sustinendum <lb></lb>in perpendiculari CE, seu momentum <lb></lb>gravis in plano inclinato, ad momantum <lb></lb>absolutum, est reciproce ut perpendicu­<lb></lb>laris CE ad inclinatam AC ” (ivi, fol. </s>

<s>20). <lb></lb>La dimostrazione si allunga e si raggira <lb></lb>per i più elementari teoremi euclidei, <lb></lb>ma si spedisce in sostanza in poche pa­<lb></lb>role, considerando HIL come una leva angolare col fulcro in I, con la po­<lb></lb>tenza applicata in H, in direzione parallela ad AC, e con la resistenza in <lb></lb>L, cosicchè si avrà, per le notissime leggi archimedee, che sta la detta po­<lb></lb>tenza alla sua respettiva resistenza come IL sta ad IH, o, per la similitu­<lb></lb>dine de&#039;triangoli, come CE sta ad AC. </s></p><p type="main">

<s>Il proposito manifestato dal Ferroni di valersi dei moti equipollenti, in­<lb></lb>segnatigli dal Viviani nelle cinque sopra riferite proposizioni, sarebbe riu­<lb></lb>scito efficacissimo per soggiunger, dopo la verità conclusa dalla leva ango­<lb></lb>lare, al Vanni una risposta, quando si fosse però quella equipollenza intesa <lb></lb>a dovere. </s>

<s>Ma perchè vi si manteneva salva la falsa dottrina galileiana, che <lb></lb>il momento per l&#039;ipotenusa fosse uguale in potenza alla somma de&#039;momenti <lb></lb>per i cateti, era impossibile al Ferroni e al Viviani, e a qualunque altro di <lb></lb>quella setta, il rispondere in modo che non ripetesse il Vanni stesso a loro <lb></lb>quel che avea detto allo Spoleti, che cioè ragionavano bene, ma che contro <lb></lb>il suo argomento non concludevano niente. </s>

<s>Di qui è che lo zelo del Viviani, <lb></lb>rinfocolato da tanti, se ce ne fosse stato bisogno, che si rivolgevano a lui, <lb></lb>s&#039;ebbe a rimanere inerte in difender da que­<lb></lb>sta parte l&#039;onor del suo Nume, e sopportare <lb></lb>in pace i sacrileghi insulti, e lasciar menar <lb></lb>galloria a chi vedeva fuggirglisi innanzi i pau­<lb></lb>rosi. </s>

<s>Anche lo zelante Discepolo, ritirato in di­<lb></lb>sparte, mentre si faceva attorno così grande <lb></lb>schiamazzo, meditava fra sè, e poi scriveva così <lb></lb>di rincontro a una figura, che rammentava <lb></lb>quella del Vanni: “ Il grave A (fig. </s>

<s>126) po­<lb></lb>sato su due piani inclinati BC, BD violenta sul­<lb></lb>l&#039;uno e sull&#039;altro, e compartisce il suo peso <lb></lb><figure id="id.020.01.2012.2.jpg" xlink:href="020/01/2012/2.jpg"></figure></s></p><p type="caption">

<s>Figura 126.<pb xlink:href="020/01/2013.jpg" pagenum="256"></pb>o momento parte sul piano BC, e parte sul BD. </s>

<s>Cerca con che proporzione <lb></lb>sian divisi questi momenti in differenti inclinazioni di piano, e variandosi <lb></lb>l&#039;angolo DBC da acuto a retto e da retto a ottuso ” (MSS. Gal. </s>

<s>Disc., T. <lb></lb>CXIII, fol. </s>

<s>30 a tergo). </s></p><p type="main">

<s>Non molto tempo dopo lasciava così in un altro foglio il Viviani stesso <lb></lb>abbozzato quel che cercando aveva trovato: “ Sia la sfera A, nella mede­<lb></lb>sima figura, che posi nell&#039;angolo de&#039;due piani DB, BC. e sia DC orizzon­<lb></lb>tale, BE perpendicolare, e DG parallela ad EB, ed EF a CB. </s>

<s>Dico il mo­<lb></lb>mento gravitativo di A sopra CB, al gravitativo sopra DB, stare come DB <lb></lb>ad EF, <emph type="italics"></emph>vel ad BG, vel ut EII ad EI parallelae ipsis planis, vel ut EL <lb></lb>ad EM perpendiculares iisdem planis,<emph.end type="italics"></emph.end> cioè come i seni retti de&#039;comple­<lb></lb>menti delle inclinazioni de&#039;piani. </s>

<s>” </s></p><p type="main">

<s>“ Poichè il gravitativo sopra BC al totale sta come EC a CB, ovvero <lb></lb>come DE ad EF, ed il totale, al gravitativo sopra DB, sta come BD a DE; <lb></lb>così <emph type="italics"></emph>ex aequo in ratione perturbata,<emph.end type="italics"></emph.end> come il gravitativo sopra BC, al gra­<lb></lb>vitativo sopra DB, così la DB alla EF. </s>

<s>Ma EF è uguale a GB, però il gravi­<lb></lb>tativo al gravitativo sta come DB a BG, ovvero EH ad HB <emph type="italics"></emph>vel ad EI. </s>

<s>Sed <lb></lb>duetis perpendicularibus EL, EM, triangula EHL, EIM fiunt similia, et <lb></lb>propterea, ut EH ad EI, ita EL ad EM, quae sunt sinus recti comple­<lb></lb>mentarum angulorum ECB, EDB elevationum ”<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>18). </s></p><p type="main">

<s>Ecco messa così dallo stesso Viviani a partito la dottrina dei moti equi­<lb></lb>pollenti, ma quale argomento somministrava per rispondere al Vanni? </s>

<s>Nuovo <lb></lb>era senza dubbio e bello il meccanico teorema che le pressioni si compar­<lb></lb>tono sui due piani proporzionalmente ai coseni degli angoli delle elevazioni, <lb></lb>ma qual&#039;è la terza linea che rappresenta la pressione totale, proporzional­<lb></lb>mente comparabile con le due trovate pressioni parziali? </s>

<s>Noi sappiamo es­<lb></lb>sere quella terza linea la EB, diagonale del parallelogrammo EIBH, ma il <lb></lb>Viviani avversava questa dottrina, reputandola falsa, perchè, non essendo <lb></lb>l&#039;angolo EIB retto, non potevano i moti per EI e per IB essere eguali a <lb></lb>quello fatto per EB, che non è ipotenusa, come EI e IB non sono cateti; <lb></lb>nè perciò alla potenza di quella si può dire uguale la somma delle potenze <lb></lb>di questi. </s>

<s>Essendo però così, come Galileo insegnava nel teorema II Dei <lb></lb>proietti, ben comprendeva il Viviani che, tutt&#039;altro che confutare, anzi si <lb></lb>confermava l&#039;obiezione del Vanni, per cui a risolverla, tentando altra via, <lb></lb>disputavasi intanto in Roma intorno al modo di computare i momenti. </s>

<s>Non <lb></lb>vuol di quelle dispute passarsi la nostra Storia, ma prima di dir di loro <lb></lb>giova veder quel che se ne pensasse in proposito dai Matematici stranieri. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Aveva il Vanni stesso mandato il suo <emph type="italics"></emph>Specimen<emph.end type="italics"></emph.end> agli eruditi di Lipsia, <lb></lb>che lo inserirono ne&#039;loro atti di Novembre dell&#039;anno 1684, con la ri­<lb></lb>sposta, nella quale, benchè si affermasse non essere assurdo che i momenti <pb xlink:href="020/01/2014.jpg" pagenum="257"></pb>parziali sommati insieme eccedano il momento totale del globo posato sui <lb></lb>due piani, la dimostrazione nonostante che se ne dava non era quella pro­<lb></lb>prio che faceva al caso; ond&#039;è che parve a molti si confermasse, invece di <lb></lb>rispondere all&#039;obiezione. </s>

<s>Furono di questo parere due grandi uomini Goti­<lb></lb>fredo Leibniz e Iacopo Bernoulli, che cercavan perciò di dar sodisfazione ai <lb></lb>curiosi, e di rassicurare la scienza in altri modi. </s>

<s>Come però vi riuscissero, <lb></lb>si vedrà da quel che ora diremo. </s></p><p type="main">

<s>Nel 1685 gli eruditi di Lipsia accoglievano nei loro atti una scrittura <lb></lb>del Leibniz, che s&#039;intitolava: <emph type="italics"></emph>Demonstratio geometrica Regulae, apud sta­<lb></lb>ticos receptae, de momentis gravium in planis inclinatis, nuper in dubium <lb></lb>vocatae, et solutio casus elegantis, in Actis nov. </s>

<s>1684, pag. </s>

<s>512, propositi, <lb></lb>De globo duobus planis angulum rectum facientibus simul incumbente, <lb></lb>quantum unumquodque planorum prematur determinans.<emph.end type="italics"></emph.end> (Opera omnia, <lb></lb>T. III, Genevae 1768, pag. </s>

<s>176). Incomincia ivi l&#039;Autore dal confermar la <lb></lb>verità contradetta dal Vanni, dimostrando che due corpi son allora insieme <lb></lb>in perfetto equilibrio, quando le loro gravità son proporzionali alle lunghezze <lb></lb>dei piani, e lo fa servendosi del medesimo principio, e ragionando allo stesso <lb></lb>modo, che aveva fatto, nella proposizione sua I. <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> il Tor­<lb></lb>ricelli. </s>

<s>Il non farsi motto di un uomo, e di un trattato, nella Scienza mec­<lb></lb>canica tanto celebre, dette occasione di maraviglia a molti, i quali s&#039;avranno <lb></lb>tanto più a maravigliare di ciò che ora diremo. </s></p><p type="main">

<s>Speditosi di quella torricelliana dimostrazione, il Leibniz passa a risol­<lb></lb>vere il caso proposto dal Vanni, prendendo per suo primo e principale ar­<lb></lb>gomento il principio che due sono i momenti esercitati dal grave sul piano <lb></lb>inclinato. </s>

<s>“ Statim autem patet (quod etiam ab admodum R. P. Kochanskio, <lb></lb>in actis Junii 1685, recte notatum video) globum in plano aliquo inclinato <lb></lb>duplex exercere momentum; unum quod decliviter descendere tendit, alte­<lb></lb>rum quo planum declive premit, quae duo simul obsolutum, seu totale gra­<lb></lb>vis momentum constituunt ” (ibid.). Cotesti due momenti erano stati, come <lb></lb>vedemmo, designati coi nomi di <emph type="italics"></emph>momento discensivo<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>momento gravi­<lb></lb>tativo<emph.end type="italics"></emph.end> sul piano dal Viviani, il quale aveva altresì dimostrato, nelle sue Cin­<lb></lb>que proposizioni, il primo stare al totale come XN ad XC (nella fig. </s>

<s>127), <lb></lb><figure id="id.020.01.2014.1.jpg" xlink:href="020/01/2014/1.jpg"></figure></s></p><p type="caption">

<s>Figura 127.<lb></lb>ed il secondo, al medesimo momento totale, star <lb></lb>come NC alla stessa XC. </s>

<s>Il Leibniz invece, per­<lb></lb>suaso che questo momento gravitativo sia la dif­<lb></lb>ferenza che passa fra il totale e il discensivo, lo <lb></lb>fa proporzionale a XC-XN. “ Itaque, in nostro <lb></lb>casu, ob duas causas, planum alterutrum, ut <lb></lb>XFC, a globo I premi intelligitur: prima est <lb></lb>quod globus I, descendere tendens in plani XFC, <lb></lb>linea FC, momento quod sit ad totale ut XN <lb></lb>ad XC, quemadmodum demonstravimus, aget re­<lb></lb>liquo, quod erit ad totale ut XC-XN ad XC, in ipsum planum declive XFC, <lb></lb>a quo sustentatur ” (ibid., pag. </s>

<s>176, 77). </s></p><pb xlink:href="020/01/2015.jpg" pagenum="258"></pb><p type="main">

<s>L&#039;errore, di cui pare incredibile non si dovesse avvedere un tale e tanto <lb></lb>Matematico, era stato, com&#039;abbiamo letto, insegnato già negli Atti lipsiensi <lb></lb>dal padre Kochanski, che anzi il Leibniz altamente loda, e affettuosamente <lb></lb>ringrazia come colui “ qui viam iam tum designavit, cui recte insistendo, <lb></lb>ad determinationem pressionis cuiuscumque plani perveniri poterat ” (ibid., <lb></lb>pag. </s>

<s>178). Ma perchè il Kochanski era discepolo, e promotore degl&#039;insegna­<lb></lb>menti del nostro piacentino Paolo Casati, par che il Leibniz abbia voluto <lb></lb>eleggere i due Gesuiti a maestri. </s></p><p type="main">

<s>In quel medesimo anno 1684, in cui il padre Vanni spacciava in Roma <lb></lb>il suo foglietto volante, uscivano in Lione gli otto libri della Meccanica del <lb></lb>Casati. </s>

<s>Nel cap. </s>

<s>XV del I libro, proponendosi l&#039;Autore di trattar dell&#039;equi­<lb></lb>librio de&#039;corpi sospesi da una o più funi, offriva il primo esempio di così <lb></lb>fatti problemi che, risoluti già francamente da Leonardo e dallo Stevino, <lb></lb>crano dalla nuova scuola, per la troppa facilità, reputati fallaci. </s>

<s>Penda il <lb></lb>grave A (fig. </s>

<s>128) dalle due funi AB, AC, fisse ne&#039;punti B e C. </s>

<s>Considera <lb></lb>il Casati separatamente i due sforzi, e prima, nel funicolo AC, risolve il mo­<lb></lb>mento totale in due, uno libero e l&#039;altro impedito. </s>

<s>Per il teorema galileiano <lb></lb><figure id="id.020.01.2015.1.jpg" xlink:href="020/01/2015/1.jpg"></figure></s></p><p type="caption">

<s>Figura 128.<lb></lb>secondo De&#039;proietti, dice che, se il momento <lb></lb>totale è AC, il libero è AE, ma l&#039;impedito <lb></lb>non può essere altro che la differenza tra <lb></lb>questi due, la quale essendo PC, dunque il <lb></lb>grave A sforza da questa parte la fune con <lb></lb>due momenti uguali ad AP+PC. Simil­<lb></lb>mente, dall&#039;altra parte, essendo AD=AQ <lb></lb>il momento libero, e QB l&#039;impedito, il grave <lb></lb>farà forza sulla fune con momento uguale <lb></lb>ad AQ+BQ, intantochè, se fossero i due <lb></lb>funicoli di ugual lunghezza, la somma dei <lb></lb>quattro momenti riuscirebbe doppia a quella <lb></lb>di tutto il peso. </s>

<s>Conobbe a questo punto il Casati che il suo ragionamento lo <lb></lb>avea condotto a un assurdo, e benchè non avesse saputo scoprire ascondersi <lb></lb>la fallacia in ciò principalmente che i due momenti impediti non son pro­<lb></lb>porzionali alle differenze PC, QB, ma sì veramente alle perpendicolari CE, <lb></lb>DB; una inspirazione venutagli dalle tradizioni, rimaste nell&#039;Herigonio in­<lb></lb>tercise, gli fece provvidamente corregger l&#039;errore, costruendo su&#039;due lati <lb></lb>AR=AD, e AG=AE il parallelogrammo RG, e dicendo che a questi due <lb></lb>momenti parziali s&#039;attempera il totale rappresentato dalla diagonale AN dello <lb></lb>stesso parallelogrammo. </s></p><p type="main">

<s>S&#039;accorgono i Lettori che questa, aperta anche più largamente dal Ca­<lb></lb>sati, come or ora vedremo, era la vera via regia, da condursi a risolvere il <lb></lb>paralogismo del Vanni, ma a correr per essa il Leibniz non s&#039;era bene an­<lb></lb>cora accomodato i calzari. </s>

<s>Come il Kochaski aveva imparato di qui a mi­<lb></lb>surare il momento gravitativo sul piano inclinato; così il Leibniz stesso tra­<lb></lb>sformò facilmente questa costruzione in modo, che BA, AC rappresentassero, <pb xlink:href="020/01/2016.jpg" pagenum="259"></pb>non due funi, ma due piani, e la sfera A, dianzi pendula, s&#039;immaginò rin­<lb></lb>chiusa dentro l&#039;angolo BAC, come ritenutavi fra due sponde. </s></p><p type="main">

<s>Procedendo il Matematico tedesco con un ragionamento similissimo a <lb></lb>quello del nostro Piacentino, s&#039;ebbe a incontrar nel medesimo assurdo, che <lb></lb>cioè i quattro momenti parziali tornavan doppi al totale, a che, come trovò <lb></lb>il Nostro rimedio applicandovi la Regola del parallelogrammo delle forze, <lb></lb>sostituì lo Straniero, che di quella diffidava, un&#039;altra Regola, da lui detta <lb></lb><emph type="italics"></emph>Degli alternativi,<emph.end type="italics"></emph.end> che consisteva insomma nel ridurre un caso di Meccanica <lb></lb>alle condizioni di un gioco d&#039;azzardo. </s>

<s>“ Verum, cum quatuor premendi cau­<lb></lb>sis simul sumptis bis integretur momentum totale; patet illas, sic absolute <lb></lb>sumptas, non esse compatibiles, nec <emph type="italics"></emph>cumulative<emph.end type="italics"></emph.end> sed, ut post dicam, tantum <lb></lb><emph type="italics"></emph>elective,<emph.end type="italics"></emph.end> sive <emph type="italics"></emph>alternative<emph.end type="italics"></emph.end> componendas, alioqui effectus globi in plano maior <lb></lb>esset momento globi totalis absoluti. </s>

<s>Cum vero manifestum sit duas semper <lb></lb>causas in quolibet plano, aequali ratione, in considerationem venire debere, <lb></lb>nec tamen integras retineri posse; adhibenda est <emph type="italics"></emph>Regula alternativorum,<emph.end type="italics"></emph.end><lb></lb>quae in iure accrescendi, in aestimatione aleae ludentium, eiusque casibus <lb></lb>locum habet, hoc est utriusque momenti sumendum est dimidium, seu, quod <lb></lb>eodem redit, medium inter ipsa aritmeticum, sive dimidium summae ex am­<lb></lb>bobus ” (ibid., pag. </s>

<s>178). Così, conclude il Leibniz, è tolta quella difficoltà, <lb></lb>che avea fatto arretrare e rivolgere altrove il Casati (di cui però, come del <lb></lb>Torricelli, non si fa il minimo cenno) perchè la metà della somma, presa <lb></lb>secondo la proposta regola metafisica, riduce uguali al totale i quattro de­<lb></lb>signati momenti parziali. </s></p><p type="main">

<s>Non erano, sull&#039;esempio del Leibniz, disposti gli altri Matematici ad ap­<lb></lb>provare la Regola del parallelogrammo, ch&#039;era quasi la pietra del paragone, <lb></lb>per scoprir che quello del Vanni era peltro; ma è pur notabile come Ja­<lb></lb>copo Bernoulli vi si riducesse molto d&#039;appresso, e giungesse perciò il primo <lb></lb>a dar, con qualche matematica ragionevolezza, alla famosa difficoltà la ri­<lb></lb>sposta desiderata, la quale, sotto il mese di Febbraio del 1686, s&#039;inserì con <lb></lb>questo titolo a pag. </s>

<s>96 negli Atti degli eruditi di Lipsia: “ Jacobi Bernoulli <lb></lb>solutio difficultatis contra propositionem quamdam me­<lb></lb>chanicam aut. </s>

<s>J. F. V. lucensi proposita 1685. ” </s></p><p type="main">

<s>Si raccolse poi questa scrittura fra le opere dell&#039;Au­<lb></lb>tore, pubblicate nel 1744 in Ginevra, dove, da pag. </s>

<s>245-47 <lb></lb>del I Tomo, si trascrive lo <emph type="italics"></emph>Specimen<emph.end type="italics"></emph.end> del Vanni, insieme <lb></lb>con la breve censura fatta da un Matematico, a nome del­<lb></lb>l&#039;Accademia, in tal modo però che parve al Bernoulli non <lb></lb>risolvere l&#039;obiezione. </s>

<s>Diceva quel matematico Censore es­<lb></lb>ser possibile che i momenti sui piani si compongano in­<lb></lb>sieme, da eccedere il momento del grave assoluto, e lo <lb></lb>provava supponendo che uno di essi piani, per esempio AC <lb></lb>(fig. </s>

<s>129) fosse verticale, nel qual caso “ utique momenta <lb></lb>in ambobus planis in unum addita non possunt aequari <lb></lb>uni ex ipsimet, totum parli, quod tamen, secundum obiicientis sontentiam, <lb></lb><figure id="id.020.01.2016.1.jpg" xlink:href="020/01/2016/1.jpg"></figure></s></p><p type="caption">

<s>Figura 129.<pb xlink:href="020/01/2017.jpg" pagenum="260"></pb>fieri deberet: momentum enim in plano verticali utique est ipsum momen­<lb></lb>tum gravis absolutum ” (pag. </s>

<s>247). </s></p><p type="main">

<s>Il Bernoulli giustamente negava che il momento nel piano verticale <lb></lb>AC fosse assoluto, perchè la direzione IH gli riesce obliqua, come riesce <lb></lb>obliqua la direzione IF all&#039;altro piano XC, cosicchè, nè in questo nè in <lb></lb>quello, il momento è propriamente tutto, ma è diminuito, e potrebbe dire <lb></lb>alcuno perciò che, sebben nel tutto i due momenti eccedano il momento <lb></lb>del grave assoluto, diminuiti nonostante lo possono eguagliare “ quod Au­<lb></lb>thorem obiectionis in sua potius opinione confirmaret ” (ivi, pag. </s>

<s>249). </s></p><p type="main">

<s>Dovendosi dunque cercare altrove, nell&#039;argomento del Vanni, la frode, <lb></lb>crede il Bernoulli di averla scoperta in ciò che si confondono insieme dal­<lb></lb>l&#039;oppositore il peso e il momento del peso. </s>

<s>Son queste due cose ben assai <lb></lb>differenti, come si vede, egli dice, per esempio nel Vette, in cui, benchè il <lb></lb>peso rimanga il medesimo, cresce o scema nonostante il momento, secondo <lb></lb>che maggiore o minore è la lunghezza del braccio. </s>

<s>Così pure, secondo le <lb></lb>varie inclinazioni, cresce o scema il peso, con cui preme un grave il piano <lb></lb>sottoposto, nè difficile è, soggiunge lo stesso Bernoulli, a determinarne il <lb></lb>momento, attendendo a ciò che <lb></lb>accade, quando scendono, il cor­<lb></lb>po, e il piano tutt&#039;a un tempo <lb></lb>che lo sostiene. </s></p><p type="main">

<s>Se il sostegno è orizzon­<lb></lb>tale comeK (fig.130), e la scesa <lb></lb>è per un tratto verticale, come <lb></lb>KL, a voler che il grave non <lb></lb>sia abbandonato dal suo soste­<lb></lb>gno, bisogna che corrano am­<lb></lb>bedue ugualmente veloci. </s>

<s>Al­<lb></lb>trimenti però avviene se il corpo <lb></lb>è sostenuto da due piani, come <lb></lb><figure id="id.020.01.2017.1.jpg" xlink:href="020/01/2017/1.jpg"></figure></s></p><p type="caption">

<s>Figura 130.<lb></lb>XC, ZC (fig. </s>

<s>131) perchè, mentre il globo I per <lb></lb>esempio scende equabilmente da I in L, per lo <lb></lb><figure id="id.020.01.2017.2.jpg" xlink:href="020/01/2017/2.jpg"></figure></s></p><p type="caption">

<s>Figura 131.<lb></lb>spazio IL=CP, il piano XC è sceso in QP per uno spazio, misurato dalla <lb></lb>linea brevissima CQ, ond&#039;è che, stando i momenti come le velocità, e come <lb></lb>gli spazii, il momento sopra XC, che significheremo con M.XC, è alla metà <lb></lb>del peso P del globo come CP a <expan abbr="Cq.">Cque</expan> In pari modo M.ZC:P/2=CP:CR. </s>

<s><lb></lb>E di qui, essendo CR=CQ, P=(M.XC+M.ZC)/CP CQ, ossia M.XC+ <lb></lb>M.ZC:P=CP:Cq. </s>

<s>“ Adeoque momentum globi super utroque plano, <lb></lb>simul sumptum, est ad totum ipsius ponderis, seu ad momentum absolu­<lb></lb>tum, ut CP ad <expan abbr="Cq.">Cque</expan> Est vero CP maior CQ, igitur momentum ec. </s>

<s>quod erat <lb></lb>demonstrandum ” (ibid., pag. </s>

<s>249). </s></p><p type="main">

<s>Il Viviani trascrisse di sua propria mano questa scrittura del Bernoulli, <pb xlink:href="020/01/2018.jpg" pagenum="261"></pb>che si trova inserita ne&#039;fogli 77, 78 del tomo CXXXII de&#039;Discepoli di Ga­<lb></lb>lileo, dove alla figura sono apposte in lapis le linee da noi punteggiate, e <lb></lb>in margine, con una crocellina per segno di richiamo, all&#039;ultima ragione <lb></lb>scritta CP:AQ è soggiunto: “ vel ut IC ad IF, vel ut FC ad CO ” e ciò <lb></lb>vorrebbe dire che la somma dei momenti parziali di tanto eccede il totale, <lb></lb>di quanto il totale stesso eccede il solo momento gravitativo. </s></p><p type="main">

<s>A rispondere alla nostra curiosità di saper qual giudizio facesse di que­<lb></lb>sta bernulliana soluzione il Viviani, non abbiamo altro argomento che la tra­<lb></lb>scritta postilla, ma possiamo congetturare che non gli sodisfacesse, come <lb></lb>quella che portava a concludere contro i principii di Galileo, ai quali non <lb></lb>era possibile in ogni modo ridurre l&#039;osservazione che così faceva il Ber­<lb></lb>noulli stesso in un suo corollario: “ Concludimus, quo acutiorem angulum <lb></lb>ambo plana constituunt, eo magis, et quo obtusiorem eo minus momenta <lb></lb>partialia excessura esse momentum totale, ratione rectae CP ad <expan abbr="Cq;">Cque</expan> illo <lb></lb>casu existente maiore, hoc minore, donec tandem apertura anguli tanta fiat, <lb></lb>ut ambo plana coalescant in unum horizontalem, quo facto, coincident quo­<lb></lb>que CQ et CR cum CP, sustinebitque planum non nisi ipsum momentum <lb></lb>globi absolutum ” (ibid., pag. </s>

<s>250). </s></p><p type="main">

<s>Nella meccanica del Casati avrebbero potuto, questo teorema e questo <lb></lb>corollario del Bernoulli, trovare il loro pieno e più chiaro commento, inten­<lb></lb>dendo che la sopra allegata figura CXXVIII rappresenti in AB e in AC due <lb></lb>piani inclinati, nell&#039;angolo fatto dai quali, posato il globo A, vien questo <lb></lb>sollecitato da due momenti, l&#039;uno per AG e l&#039;altro per AR, che si com­<lb></lb>pongono insieme nella diagonale AN del parallelogrammo. </s>

<s>Nè sarebbe da così <lb></lb>fatta costruzione immediatamente resultato che la somma dei momenti, nei <lb></lb>due piani, sta al momento totale come AG+AR, ossia AG+GN, sta ad <lb></lb>AN, qualunque poi si fosse l&#039;angolo BAC. </s></p><p type="main">

<s>Aveva il Casati, come accennammo, presentita in questa conclusione la <lb></lb>difficoltà stessa del Vanni, la quale egli risolse, unico e primo, un anno <lb></lb>avanti che fosse fatta, con le sue vere e proprie ragioni. </s>

<s>Com&#039;è possibile, <lb></lb>così gli passò per la mente la prima ombra del dubbio, che, dovendo es­<lb></lb>sere il tutto eguale alle parti, sia una così fatta e necessaria uguaglianza <lb></lb>rappresentata dalle linee AG+GN, e dalla AN, se questa evidentemente è <lb></lb>minore di queìle? </s>

<s>Poi trovò che doveva di necessità esser così, perchè i due <lb></lb>moti si elidono, o, come s&#039;era espresso Giovan Marco Marci, matematico di <lb></lb>Praga, nel suo libro <emph type="italics"></emph>De proportione motus,<emph.end type="italics"></emph.end> si contrariano, ed elidendosi e <lb></lb>contrariandosi diminuiscono il loro effetto: or come potrebbero, diminuendo, <lb></lb>ragguagliarsi, se non fossero originariamente maggiori? </s></p><p type="main">

<s>Che poi la terribile difficoltà trovi, in questa semplicissima ragion delle <lb></lb>collisioni, la sua risposta, lo spiega il Casati stesso richiamando l&#039;attenzione <lb></lb>sul parallelogrammo delle forze, in cui si vede, egli dice, che la resultante <lb></lb>è maggiore, quanto minore è l&#039;angolo, e al contrario, avvicinandosi in quel <lb></lb>caso le componenti alla concorrenza, e in questo all&#039;apposizione. </s>

<s>“ Qua in <lb></lb>re plurimum interest quam invicem habeant inclinationem directiones mo-<pb xlink:href="020/01/2019.jpg" pagenum="262"></pb>tuum in diversa abeuntium: quo enim acutiorem angulum constituunt, eo <lb></lb>longius provehitur mobile, ut, AB, <lb></lb>AC (fig. </s>

<s>132) in acutum angulum <lb></lb>coeuntibus, mobile ex A in D ve­<lb></lb>nit, quo vero obtusior fuerit angu­<lb></lb>lus, eo etiam brevius est iter ipsius <lb></lb>mobilis .... ut ipsa motuum natura <lb></lb><figure id="id.020.01.2019.1.jpg" xlink:href="020/01/2019/1.jpg"></figure></s></p><p type="caption">

<s>Figura 132.<lb></lb>postulat, qui nimirum sibi invicem magis adversantur, magisque in diversa <lb></lb>abeunt, se magis elidunt ” (Mechanic., libri cit., pag. </s>

<s>103, 4). </s></p><p type="main">

<s>Se il Bernoulli dunque costrinse il Vanni a ricredersi in forza di una <lb></lb>matematica dimostrazione, non facile ad arrivarsi da tutti, e non sfuggevole <lb></lb>a tutte le cavillazioni; lo avea il Casati già convinto con ragioni tanto sem­<lb></lb>plici e chiare, da non riluttarvi, se non chi patisse difetto di senso comune, <lb></lb>o avesse la mente stravolta da pregiudizii, com&#039;avvenne a que&#039;Matematici <lb></lb>romani, i quali s&#039;accennava dianzi essere entrati in disputa intorno al modo <lb></lb>di computare i momenti. </s></p><p type="main">

<s>Vitale Giordano, pubblicando in Roma nel 1687 una sua dissertazione <lb></lb>sopra questo argomento, dop&#039;aver nell&#039;avvertenza detto al Lettore essere il <lb></lb>fine del suo discorso quello di rispondere all&#039;Autor dell&#039;Esegesi fisico ma­<lb></lb>tematica <emph type="italics"></emph>De momentis gravium,<emph.end type="italics"></emph.end> soggiunge: “ Existimavit quidam non modo <lb></lb>subtilem Anonymi doctrinam hoc sophismate laborare, quod in ea compo­<lb></lb>nantur momenta gravium per additionem, cum sint revera componenda per <lb></lb>multiplicationem, verum etiam Isaacum Barrow ac R. P. </s>

<s>Casatum sibi adsti­<lb></lb>pulari. </s>

<s>” Aveva il Casati, nel sopra citato capitolo della sua Meccanica, scritto <lb></lb>queste precise parole: “ Re autem ipsa quod ex iis componitur momentum, <lb></lb>non ex ipsorum momentorum additione conflatur, sed ex ipsis temperatur ” <lb></lb>(pag. </s>

<s>103). Se dunque non per addizione, vollero concluderne i disputanti, <lb></lb>per moltiplicazione si compongono i momenti, non badando a quel che di <lb></lb>più importante era negli insegnamenti del Matematico piacentino, il quale, <lb></lb>dopo avere affermato che il momento della resultante non è uguale alla <lb></lb>somma delle componenti, soggiunge <emph type="italics"></emph>sed ex ipsis temperatur,<emph.end type="italics"></emph.end> andando nella <lb></lb>diagonale del parallelogrammo. </s></p><p type="main">

<s>Il Giordano, pregato da&#039;suoi scolari, <emph type="italics"></emph>tota ferme Europa longe dissitis,<emph.end type="italics"></emph.end><lb></lb>a volere, in grazia loro e per utilità della Repubblica letteraria, pronun­<lb></lb>ziare la sua sentenza, dimostrò, benchè con falsi teoremi, che non si pote­<lb></lb>vano per moltiplicazione comporre i momenti, e che in tale assurdo non in­<lb></lb>corse il Casati, per le opere del quale attentamente leggendo, “ nusquam <lb></lb>inveni verbum quod eo spectet, ut momenta gravium componantur per mul­<lb></lb>tiplicationem ” (Dissert. </s>

<s>cit., pag. </s>

<s>4): quel che però più importava non seppe <lb></lb>nemmen egli, il Giordano, come gli altri, intendere il significato del tempe­<lb></lb>rarsi i momenti nella diagonale del parallelogrammo, nè prevalersi perciò <lb></lb>di quella dottrina, unica efficace a rispondere ai paralogismi del Vanni, che <lb></lb>era il fine del discorso, scritto dal professore nell&#039;Archiginnasio romano. </s></p><p type="main">

<s>Ebbe ancora a indugiare questa risposta infin verso alla fine del secolo, <pb xlink:href="020/01/2020.jpg" pagenum="263"></pb>quando l&#039;autorità del Newton, e le insistenze del Varignon riuscirono final­<lb></lb>mente a persuadere i Matematici di ciò, che avevano praticato Leonardo, lo <lb></lb>Stevino e altri pochi, in così eletto modo però che il Casati stimò essere a <lb></lb>tutti notissima la Regola del parallelogrammo. </s>

<s>“ Notum omnibus est mo­<lb></lb>tum, qui ex AB et AC (nella precedente figura) componitur, non fieri ex <lb></lb>earum additione, sed temperari ad lineam AD, quae dimetiens est paralle­<lb></lb>logrammi, quod ex earumdem linearum AB, AC longitudine, ac mutua in­<lb></lb>clinatione, formam desumit ” (Mech., pag. </s>

<s>103). </s></p><p type="main">

<s>Veniva di qui, contro la seconda proposizione meccanica del IV dialogo <lb></lb>di Galileo, solennemente confermata quella sentenza di condanna, pronun­<lb></lb>ziata già dal Mersenno, e il dilemma famoso del Vanni, intorno a cui suda­<lb></lb>rono inutilmente un Leibniz e un Viviani, si sapeva sciogliere oramai da <lb></lb>chiunque avesse nelle scuole matematiche appresi i primi elementi. </s></p><p type="main">

<s>Mentre che i Matematici si travagliavano così affannosamente, come ap­<lb></lb>parisce dai fatti narrati, per salvar la verità del teorema, dimostrato già dal <lb></lb>Tartaglia, contro chi veniva nella Meccanica a rinnovellare gli errori del Car­<lb></lb>dano; s&#039;insorgeva con altri sofismi a turbar la pace della scienza, preso ar­<lb></lb>dire dall&#039;esempio del Vanni. </s>

<s>Il Cartesianismo, dominante nella Scuola fisico­<lb></lb>matematica napoletana, suggerì a Luc&#039;Antonio Porzio una nuova costruzione <lb></lb>meccanica, riguardando i perpendicoli non <lb></lb>paralleli, come comunemente si fa, ma quali <lb></lb>sono in realtà convergenti al centro ter­<lb></lb>restre, secondo che il Cartesio stesso sem­<lb></lb>pre scrupolosamente osserva nel descriver <lb></lb>gli effetti delle Macchine. </s>

<s>Essendo così, non <lb></lb>è vero, diceva il Porzio, ciò che insegna il <lb></lb>Maestro che, se cioè CA (fig. </s>

<s>133) è dop­<lb></lb>pia di CB, per far salire il peso sul piano <lb></lb><figure id="id.020.01.2020.1.jpg" xlink:href="020/01/2020/1.jpg"></figure></s></p><p type="caption">

<s>Figura 133.<lb></lb>ci voglia la metà della forza, necessaria a <lb></lb>ritirarlo in su per il perpendicolo, perchè, <lb></lb>sottilmente ragionando, quella proporzion <lb></lb>tra la forza e il peso trovasi alquanto di­<lb></lb>versa da quella, che nelle sue Meccaniche <lb></lb>assegna il Cartesio. </s>

<s>Il ragionamento era <lb></lb>tale qual si può argomentare dalla seguente <lb></lb>nota dell&#039;Autore: </s></p><p type="main">

<s>“ Nel piano, secante o tangente la Terra <lb></lb>DCE (fig. </s>

<s>134), sia AB secante o tangente <lb></lb>un cerchio massimo, alla quale, dal centro <lb></lb>C, si tiri la perpendicolare CD. </s>

<s>Egli è ma­<lb></lb>nifesto che, se altra sfera I sia collocata <lb></lb>sopra varii punti del piano già detto, e in <lb></lb>modo che sempre AB sia tangente di un <lb></lb>certo cerchio massimo IH, quando questa <lb></lb><figure id="id.020.01.2020.2.jpg" xlink:href="020/01/2020/2.jpg"></figure></s></p><p type="caption">

<s>Figura 134.<pb xlink:href="020/01/2021.jpg" pagenum="264"></pb>sfera sarà collocata sopra il punto D, la linea CD prolungata dividerà il <lb></lb>cerchio massimo IH in due parti uguali, e se il cerchio avesse gravità si do­<lb></lb>vrebbe fare equilibrio tra i segmenti eguali. </s>

<s>Quando ella sarà sopra il punto <lb></lb>F, la linea CF prolungata segherà il cerchio massimo IH in parti diseguali, <lb></lb>e se i segmenti diseguali fossero gravi non si potrebbero tra loro fare equi­<lb></lb>librio, lo che agevolmente si dimostra. </s>

<s>E da ciò facilmente ancora si può <lb></lb>provare che, se per un piano caggia una sfera grave, sempre in dato punto <lb></lb>una sua porzione contrasterà e ripugnerà alla caduta, ma non sarà ella ba­<lb></lb>stevole a far l&#039;equilibrio in quel punto. </s>

<s>Qual porzione, mentre scende la <lb></lb>sfera, sempre si fa vie più e più grande, finchè, giunta la sfera al punto <lb></lb>D, cesserà per la linea AB l&#039;impeto di gravità, imperocchè in D la metà <lb></lb>della sfera appunto contrasterà, e ripugnerà ad ogni moto, che di qua e di <lb></lb>là dal punto D potesse fare la sfera, cioè in D si fa l&#039;equilibrio sulla linea <lb></lb>AB ” (Opera omnia, T. II, Neapoli 1736, pag. </s>

<s>233, 34). </s></p><p type="main">

<s>Da queste considerazioni ebbe il Porzio a concluderne che la sfera IHF, <lb></lb>posata sul piano inclinato AB, venendo a esser segata dal perpendicolo CFH <lb></lb>nelle parti disuguali HIL, HLF, avrà tant&#039;impeto di scendere quant&#039;è l&#039;ec­<lb></lb>cesso dell&#039;una parte sull&#039;altra, perchè il menisco HLFH riman sostenuto dal <lb></lb>perpendicolo stesso, che lo attraversa per il centro, lasciando alla sua libera <lb></lb>caduta il resto. </s>

<s>Di qui il teorema del Tartaglia, per più di un secolo appro­<lb></lb>vatosi da tanti insigni Matematici di tutto il mondo, veniva dal Porzio, nella <lb></lb>sua proposizione XIII <emph type="italics"></emph>De motu corporum,<emph.end type="italics"></emph.end> così riformato: “ Pondus abso­<lb></lb>lutum datae sphaerae uniformis insistentis dato puncto plani, quod appellant <lb></lb>inclinatum, ad eiusdem gravitatem relativam, quam dicunt, sive partialem; <lb></lb>minorem habet rationem ea, quam longitudo dati plani habet ad perpendi­<lb></lb>culum ” (Op., T. cit., pag. </s>

<s>137). </s></p><p type="main">

<s>Aveva anche l&#039;obiezione del Porzio senza dubbio qualche cosa di se­<lb></lb>ducente, perchè pareva non si potesse negare essere il solo menisco HLFH <lb></lb>la parte sostenuta del peso. </s>

<s>Per scoprire però la frode conveniva dimostrare <lb></lb>la vera direzione del fulcro, ciò che riusciva assai difficile a chi non avesse <lb></lb>uso del parallelogrammo. </s>

<s>Di qui è che inutilmente, in una sua Epistola di­<lb></lb>vulgata in Roma, vi si provò Vitale Giordano, il quale a quello del Porzio <lb></lb>sostituì un altro più grave errore, volutosi matematicamente dimostrar da <lb></lb>lui nel <emph type="italics"></emph>Fondamentum doctrinae motus gravium,<emph.end type="italics"></emph.end> dove, dopo di aver nella <lb></lb>VII proposizione asserito. </s>

<s>“ Pondus totale gravis, ad momentum quod ha­<lb></lb>bet in plano declivi, est ut longitudo ipsius plani declivis ad perpendicu­<lb></lb>lum ” (Romae 1688, pag. </s>

<s>38), passa a provar, nelle proposizioni seguenti, <lb></lb>che può il peso totale, al momento nel piano, ora aver maggiore, e ora mi­<lb></lb>nor proporzione del declivio al perpendicolo. </s></p><p type="main">

<s>Non mancarono alcuni della scuola del Marchetti, i quali ebbero a no­<lb></lb>tare che il vizio, nei ragionamenti del Giordano, consisteva nel paragonare <lb></lb>il peso, espresso da una linea, col momento, espresso da un rettangolo; ma <lb></lb>infatti tanta poca sicurtà dagli errori e tanta incertezza nel rispondere alle <lb></lb>obiezioni da null&#039;altro dipendeva, che dal non si saper risolvere i quesiti, <pb xlink:href="020/01/2022.jpg" pagenum="265"></pb>applicandovi il principio della composizion delle forze. </s>

<s>Nei primi anni del <lb></lb>secolo XVIII incominciò quel principio a divulgarsi nei Matematici, e Guido <lb></lb>Grandi potè, con la sua Epistola mathematica <emph type="italics"></emph>De momentis gravium in <lb></lb>planis inclinatis,<emph.end type="italics"></emph.end> ravviar la scienza ne&#039;suoi retti sentieri. </s></p><p type="main">

<s>Bisognava dimostrar contro il Porzio che la direzione del fulcro, da cui <lb></lb>è sostenuto il grave sul piano inclinato, si dee prender secondo il perpen­<lb></lb>dicolo condotto dal centro di gravità sul piano, e non al centro terrestre. </s>

<s><lb></lb>Per far ciò premette il Grandi per lemma alla sua dimostrazione il princi­<lb></lb>pio della compòsizion delle forze, le quali essendo due, come AB, AC (nella <lb></lb>passata figura CXXXII) sollecitanti il punto A in quelle due direzioni, dice, <lb></lb><emph type="italics"></emph>id quod, notissimum est,<emph.end type="italics"></emph.end> essere allora quel punto in equilibrio, quando una <lb></lb>terza forza AH, uguale alla diagonale AD del parallelogrammo, tiri in verso <lb></lb>contrario. </s></p><p type="main">

<s>Ciò premesso, abbiasi la sfera grave K (fig. </s>

<s>135) sollecitata da due forze, <lb></lb>l&#039;una KQ nella direzion della gravità naturale, e l&#039;altra KR diretta secondo <lb></lb>la fune PK, che fa forza alla stessa sfera, affinchè la <lb></lb>non debba cadere. </s>

<s>Perchè dunque ella potesse ivi rima­<lb></lb>nere in equilibrio, bisognerebbe applicare in K una terza <lb></lb>forza, uguale e contraria alla diagonale KM del paralle­<lb></lb>logrammo. </s>

<s>Ma questa forza è sostituita dalla resistenza <lb></lb>del piano AB, dunque il piano è premuto nella direzione, <lb></lb>e con forza proporzionale alla linea KM, la quale gli è <lb></lb>perpendicolare. </s>

<s>“ Quare, così propriamente il Grandi con­<lb></lb>clude, cum haec sit plano perpendicularis ad contactum, <lb></lb>demonstratum erit actionem sustinentis plani iuxta dic­<lb></lb>tam perpendicularem exerceri ” (Lucae 1711, pag. </s>

<s>25). <lb></lb><figure id="id.020.01.2022.1.jpg" xlink:href="020/01/2022/1.jpg"></figure></s></p><p type="caption">

<s>Figura 135.</s></p><p type="main">

<s>Ma co&#039;Matematici del secolo XVIII fece la scienza <lb></lb>tali progressi, da non temere oramai più di così fatte <lb></lb>contradizioni, ond&#039;è che sopra questo statico fondamento <lb></lb>venne a confermarsi sempre più la Dinamica, della quale è tempo che si <lb></lb>cominci la storia. </s></p><pb xlink:href="020/01/2023.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle libere cadute dei gravi<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della legge di Aristotile che le velocità dei cadenti son proporzionali ai pesi, e come prima si tro­<lb></lb>vasse quella legge contraria alle esperienze, e poi si dimostrasse contraria alla ragione, e si <lb></lb>verificasso finalmente che tutti i corpi nel vuoto scendono ugualmente veloci. </s>

<s>— II. </s>

<s>Delle cause <lb></lb>acceleratrici del moto, e come Galileo fosse il primo a concluder la legge matematica dì un <lb></lb>tale acceleramento dai principii del Benedetti. </s>

<s>— III. </s>

<s>Della forza d&#039;inerzia applicata ai moti na­<lb></lb>turali, e delle leggi dei moti accelerati geometricamente dimostrate da Galileo e dal Baliani. </s>

<s>— <lb></lb>IV. </s>

<s>Dei pretendenti o dei contradittori di Galileo, e come si confermassero, per l&#039;esperienze del <lb></lb>Riccioli e per i teoremi dell&#039;Huyghens, le leggi galileiane dei gravi cadenti. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dagl&#039;insegnamenti aristotelici ebbero le due parti, in che distinguesi <lb></lb>la Scienza del moto, variamente efficaci gl&#039;impulsi, perchè, mentre la Sta­<lb></lb>tica era giunta per questi alla sua quasi total perfezione, la Dinamica, dopo <lb></lb>pochi passi fatti a gran pena, rimanevasi tuttavia implicata in gravissimi er­<lb></lb>rori. </s>

<s>Le varietà della fortuna si parteciparono dalle prime speculazioni del <lb></lb>Maestro a quelle de&#039;lontani e numerosi suoi discendenti, un poco senza dub­<lb></lb>bio per vizioso contagio, e un poco perchè così portava il naturale anda­<lb></lb>mento delle cose. </s>

<s>Del quale andamento chi volesse mettersi a ricercare i <lb></lb>principii gli troverebbe facilmente in ciò, che Aristotile poneva per fonda­<lb></lb>mento alla Statica la Geometria, e alla Dinamica invece dava nuove leggi, <lb></lb>non ricavate dai fatti naturali, ma dalle più infelici arguzie del filosofico <lb></lb>ingegno. </s></p><p type="main">

<s>I libri, che s&#039;intitolano <emph type="italics"></emph>Physicorum,<emph.end type="italics"></emph.end> son quelli principalmente, in cui <lb></lb>il Filosofo lascia alle sue arguzie più libero il freno, e proponendosi, nel <pb xlink:href="020/01/2024.jpg" pagenum="267"></pb>quarto dei detti fisici libri, di contradire agli Autori, che lo avevano prece­<lb></lb>duto e che ammettevano l&#039;esistenza del vacuo, come quello ch&#039;è necessario <lb></lb>a intendere le osservate passioni del moto; impone capricciosamente alla Na­<lb></lb>tura sì fatte leggi, da ridurla in ogni modo a concludere i suoi proprii ar­<lb></lb>gomenti. </s>

<s>Consisteva uno de&#039;così fatti argomenti nel provar che, dandosi il <lb></lb>vacuo, non sarebbe possibile il moto locale, perchè dovrebbe la traslazione <lb></lb>farsi in un istante, mentre il moto stesso non è che una successione cau­<lb></lb>sata dall&#039;impulso, e regolata dalla maggiore o minore resistenza del mezzo. </s>

<s><lb></lb>La ragione poi di una tal resistenza è, secondo il Filosofo, che và un corpo <lb></lb>tanto più o meno veloce quanto è più raro o più denso il mezzo, dentro al <lb></lb>quale si muove. </s>

<s>“ Sit enim B, egli dice nel 70° testo del IV libro, quidem <lb></lb>aqua, D vero aer: quanto ergo subtilior est aer aqua, et incorporalior, tanto <lb></lb>citius A per D movebitur quam per B. </s>

<s>Habet ergo eandem rationem secun­<lb></lb>dum quam distat aer ab aqua, velocitas ad velocitatem ” (Operum, T. IV, <lb></lb>Venetiis 1560, fol. </s>

<s>129 ad t.). Ma nel vuoto la rarità è infinita, dunque an­<lb></lb>che la velocità ivi dentro è infinita. </s></p><p type="main">

<s>Da quest&#039;altra argomentazione si rivela anche meglio la temerità del­<lb></lb>l&#039;ingegno, che vuol ridurre le leggi della Natura alle sue proprie ragioni. </s>

<s><lb></lb>Dall&#039;ammettere il vacuo, diceva, ne conseguirebbe in ogni modo che le ve­<lb></lb>locità di qualunque peso fossero uguali, ma questo è impossibile, dunque <lb></lb>il vacuo non può darsi. </s>

<s>Le prove di una tale impossibilità poi le desumeva <lb></lb>il Filosofo dai fatti, per i quali non ha dubbio di affermar che manifesta­<lb></lb>mente si vede essere le velocità sempre proporzionali ai pesi. </s>

<s>“ Videmus <lb></lb>corpora, quae sunt magis ponderosa, sive gravia sive levia, cum fuerint in <lb></lb>aliis dispositionibus in capitulo figurae, eodem modo moveri in aequali loco <lb></lb>velocius secundum proportiones eorum ad invicem. </s>

<s>Ergo sequitur ut talis <lb></lb>sit dispositio eorum in vacuo etiam. </s>

<s>Sed hoc est impossibile, quoniam non <lb></lb>potest aliquis dicere qua de causa expellitur in eo velocius, quoniam hoc in <lb></lb>plano est necessarium. </s>

<s>Quod enim est fortius velocius dividit illud: illud <lb></lb>enim quod movetur aut illud quod cedit, aut per suam figuram dividit, aut <lb></lb>per suum pondus. </s>

<s>A quo sequitur ut motus omnium corporum sit aequalis <lb></lb>in velocitate, quod est impossibile ” (ibid., fol. </s>

<s>135 ad t.). </s></p><p type="main">

<s>Stabilite così dal Filosofo le due leggi della caduta dei gravi, quali sono: <lb></lb>che vanno per varii mezzi le velocità alle rarezze proporzionali, e che, in <lb></lb>un medesimo mezzo, hanno esse velocità la proporzion diretta dei pesi, si <lb></lb>approvarono cecamente da tutti infintanto che, risorto nel secolo XV Archi­<lb></lb>mede, i fatti che, conforme alle verità naturali, si dimostrano da lui nel <lb></lb>trattato Delle galleggianti, non vennero provvidamente a fare almeno in parte <lb></lb>ravvedere gl&#039;illusi. </s>

<s>S&#039;ebbe allora con gran maraviglia a notare un manife­<lb></lb>sto errore nella fondamentale dottrina del Filosofo, il quale insegnava essere <lb></lb>ne&#039;corpi una leggerezza positiva, e che ciascuno pesava nel suo proprio ele­<lb></lb>mento. </s>

<s>Resultava invece dai teoremi archimedei niente altro essere la leg­<lb></lb>gerezza che una certa diminuzione della gravità assoluta, la quale fa risa­<lb></lb>lire un corpo, non per naturale attività, ma per la patita circumpulsione del <pb xlink:href="020/01/2025.jpg" pagenum="268"></pb>mezzo. </s>

<s>Galileo, in alcune sue esercitazioni preparatorie ai trattati Del moto, <lb></lb>applicava direttamente a illustrar questi effetti della gravità positiva i teo­<lb></lb>remi archimedei (Opere, ediz. </s>

<s>naz., T. I, Firenze 1890, pag. </s>

<s>346-52, 363-66) <lb></lb>e più di un mezzo secolo dopo istituivano gli Accademici del Cimento due <lb></lb>belle esperienze, <emph type="italics"></emph>per provar che non v&#039;è leggerezza positiva<emph.end type="italics"></emph.end> (Saggi di na­<lb></lb>turali esper., Firenze 1841, pag. </s>

<s>131-35). Ma erano gli ostinati. </s>

<s>Peripatetici <lb></lb>a que&#039;tempi oramai ridotti a sì pochi, che sembrano quelle descrizioni quasi <lb></lb>lussureggiare nel libro de&#039;nostri Fisici fiorentini. </s>

<s>L&#039;opera di costoro era in­<lb></lb>cominciata già infino da Leonardo, e la proseguirono valorosamente il Car­<lb></lb>dano, il Tartaglia, il Benedetti, dai quali tutti ammettevasi, contro il Filo­<lb></lb>sofo, quasi senza contradizione, che l&#039;aria nell&#039;aria, come l&#039;acqua nell&#039;acqua, <lb></lb>non pesi. </s></p><p type="main">

<s>Le medesime benefiche istituzioni archimedee avevano altresì fatti de­<lb></lb>stri gl&#039;ingegni a scoprir, nel primo de&#039;riferiti argomenti di Aristotile, le <lb></lb>fallacie, delle quali ebbe non difficilmente a persuadersi quello stesso Sim­<lb></lb>plicio galileiano, a cui diceva il Salviati “ che quando fosse vero che l&#039;istesso <lb></lb>mobile in mezzi di differente sottilità e rarità, ed insomma di diversa ce­<lb></lb>denza, quali per esempio son l&#039;acqua e l&#039;aria, si movesse con velocità nel­<lb></lb>l&#039;aria maggiore che nell&#039;acqua, secondo la proporzione della rarità dell&#039;aria <lb></lb>a quella dell&#039;acqua; ne seguirebbe che ogni mobile, che scendesse per aria, <lb></lb>scenderebbe anco nell&#039;acqua. </s>

<s>Il che è tanto falso, quanto che moltissimi corpi <lb></lb>scendono nell&#039;aria che nell&#039;acqua, non pur non discendono, ma sormontano <lb></lb>all&#039;insù ” (Alb. </s>

<s>XIII, 68). </s></p><p type="main">

<s>Del secondo aristotelico argomento si dimostra pure da Galileo la fal­<lb></lb>sità in più luoghi delle sue Opere, con lunghi ragionamenti, che si com­<lb></lb>pendiano in questa breve nota, ritrovata da noi manoscritta: “ Contempletur <lb></lb>quod quemadmodum gravia omnia supra horizonte quiescunt, licet maxima <lb></lb>vel minima; ita in linaeis inclinatis eadem velocitate moventur, quemadmo­<lb></lb>dum et in ipso quoque perpendiculo, quod bonum erit demonstrare dicendo <lb></lb>quod, si gravius velocius, sequeretur quod gravius tardius, iunctis gravibus <lb></lb>inaequalibus. </s>

<s>” </s></p><p type="main">

<s>“ Movebuntur autem eadem celeritate, non solum gravia inaequalia et <lb></lb>homogenea sed et eterogenea, ut lignum et plumbum. </s>

<s>Cum enim antea <lb></lb>ostensum fuerit magna et parva homogenea aequaliter moveri, dicas: sit B <lb></lb>sphaera lignea, et A plumbea, adeo magna, ut cum in medio habeat cavi­<lb></lb>tatem pro B, sit tamen gravior quam sphaera solida lignea ipsi A aequalis, <lb></lb>ita ut per adversarium velocius moveatur quam B. Ergo, si in cavitate illa <lb></lb>ponatur B, tardius movebitur A, quam cum erat levior, quod est absurdum. </s>

<s>” <lb></lb>(MSS. Gal., P. V, T. II, fol. </s>

<s>147). </s></p><p type="main">

<s>Ma forse, meglio di qualunque più sottil ragionamento, veniva la fal­<lb></lb>lacia del Filosofo scoperta dalle giornaliere esperienze dei domestici più <lb></lb>abietti, quando gettano dalle finestre la spazzatura, le varietà degli oggetti <lb></lb>raccolti nella quale si vedono quasi a un tempo cadere a terra, se non gli <lb></lb>turbi o non gli dissipi il vento. </s>

<s>All&#039;aristotelica sentenza nonostante, che cioè <pb xlink:href="020/01/2026.jpg" pagenum="269"></pb>siano le velocità proporzionali alle grandezze, dava grande apparenza di ve­<lb></lb>rità la Statica, confondendosi facilmente i pesi con i momenti, i quali son <lb></lb>senza dubbio, nelle macchine, proporzionali alle velocità o alle distanze. </s></p><p type="main">

<s>Benchè per tutto il secolo XVI, come vedremo, si persistesse dannosa­<lb></lb>mente dai Matematici in questo errore, nonostante i primi nuovi seguaci di <lb></lb>Archimede incominciarono a dubitar, nel secolo avanti, che, come s&#039;era in <lb></lb>altre parti manifestamente scoperto l&#039;errore, così fosse almen qualche cosa <lb></lb>d&#039;improprio in quest&#039;altra sentenza del Filosofo, nella quale francamente si <lb></lb>pronunziava essere le velocità proporzionali alle grandezze. </s>

<s>Le più triviali <lb></lb>esperienze, come si faceva dianzi osservare, contradicevano a quel <emph type="italics"></emph>videmus<emph.end type="italics"></emph.end><lb></lb>del Maestro, perchè invece gli occhi facevan vedere a tutti molto diversa­<lb></lb>mente. </s>

<s>Si vollero perciò istituire in proposito esperienze più diligenti, e noi <lb></lb>narrammo quelle fatte da Leonardo da Vinci, il quale n&#039;ebbe sentenziosa­<lb></lb>mente a concludere il fatto che <emph type="italics"></emph>due palle di una medesima materia, che <lb></lb>una sia il doppio peso dell&#039;altra, cadendo in un tempo da una medesima <lb></lb>altezza, non cadrà prima altrettanto tempo la maggiore che la minore.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>A chi prima udi pronunziare una tal sicura sentenza, tanto aliena dalle <lb></lb>prevalenti opinioni, parve quasi vedere un lampo abbagliante sotto un cielo <lb></lb>nuvoloso, ma erano i nuvoli già dissipati dal rinascente Sole archimedeo, <lb></lb>verso cui non fu Leonardo solo a rivolgere gli occhi. </s>

<s>Hanno molti creduto <lb></lb>così, ma sarebbe da dire improvvido il benefizio della Natura, se al soprav­<lb></lb>venire i tiepori di una nuova primavera facesse, anche in remota selva ed <lb></lb>incolta, aprire un fiore solo e allegare un sol frutto. </s>

<s>Non mancarono eru­<lb></lb>diti, i quali accennarono a un Bellaso, a un Michele Varrone o a qualcun <lb></lb>altro, ma il Libri notò e trascrisse un documento, dal quale apparisce es­<lb></lb>sersi, intorno al fatto della caduta dei gravi, scoperto l&#039;errore aristotelico <lb></lb>anche da altri Filosofi contemporanei a Leonardo. </s></p><p type="main">

<s>È quel documento ricavato da certe <emph type="italics"></emph>Questioni sull&#039;Alchimia<emph.end type="italics"></emph.end> scritte, <lb></lb>infino dal 1544, da Benedetto Varchi, ma che videro solamente nel 1827 in <lb></lb>Firenze la luce, per solo fine di condir forse con questo tanti altri insipidi <lb></lb>testi di lingua. </s>

<s>Il Libri pone il Varchi nel numero di Giovanni Rucellai, <lb></lb>poeta naturalista delle api, di Bernardino Baldi, cronista dei Matematici an­<lb></lb>tichi, e di Bernardo Bontalenti, architettore di macchine maravigliose, di­<lb></lb>cendo dello Storico fiorentino “ qui etudie avec soin la chute des graves ” <lb></lb>(Histoire des Mathem., T. III cit., pag. </s>

<s>199) e accennando a un passo delle <lb></lb>Lezioni di lui, stampate in Firenze da Filippo Giunti nel 1590, per mostrar <lb></lb>che l&#039;Autore ben conobbe “ l&#039;influence de le couleur des surfaces sur <lb></lb>l&#039;absorption des rayons calorifiques ” (ivi). Dee essere il passo, a cui il Li­<lb></lb>bri accenna, senza dubbio quello che è così scritto nella lezion <emph type="italics"></emph>Dei colori,<emph.end type="italics"></emph.end><lb></lb>unica di fisico argomento: “ E chi non l&#039;ha veduto non crederebbe o ma­<lb></lb>lagevolmente che un pezzo di cristallo ardesse tutti gli altri colori, dal bianco <lb></lb>in fuori ” (pag. </s>

<s>259). </s></p><p type="main">

<s>Il giudizio però, che dette intorno al Varchi come scienziato il Libri, <lb></lb>è assai diverso da quello di Galileo, dalla bocca del quale lo raccolse, e così <pb xlink:href="020/01/2027.jpg" pagenum="270"></pb>ne serbò memoria in una Nota il Viviani: “ Il Varchi dice quel che non <lb></lb>intende, e però non intende quel che dice ” (MSS. Gal., P. V, T. IV, fol. </s>

<s>26). <lb></lb>Sembra a noi che ambedue i giudici vadano negli eccessi, perchè, sebbene <lb></lb>sia vero che il Varchi non abbia nè qualità nè meriti di scienziato, sentì <lb></lb>nonostante gusto della scienza, che desideroso raccolse da coloro, i quali po­<lb></lb>tevano insegnargliela o ne&#039;libri o a viva voce, e seppe scegliere con libertà <lb></lb>quelle opinioni, che gli parvero più vere, come dimostrò nel fatto della ca­<lb></lb>duta dei gravi, intorno a che non studiò con senno, come dice il Libri, ma <lb></lb>con senno approvò i resultati delle esperienze altrui, e il giudizio di quei <lb></lb>pochi, i quali dicevano esser quella, come tutte le altre verità naturali, da <lb></lb>apprender, non dai libri di Aristotile, ma dalla osservazione dei fatti. </s>

<s>“ E <lb></lb>sebbene, egli scrive, il costume dei Filosofi moderni è di creder sempre e <lb></lb>non provar mai tutto quello che si trova scritto ne&#039;buoni Autori, e massi­<lb></lb>mamente in Aristotile, non è però che non fosse e più sicuro e più dilet­<lb></lb>tevole fare altrimenti, e discendere qualche volta alle sperienze in alcune <lb></lb>cose, come v. </s>

<s>g. </s>

<s>nel movimento delle cose gravi, nella qual cosa e Aristo­<lb></lb>tile e tutti li altri Filosofi, senza mai dubitarne, hanno creduto e affermato <lb></lb>che, quanto una cosa sia più grave, tanto più tosto discende, il che la prova <lb></lb>dimostra non esser vero. </s>

<s>E se io non temessi d&#039;allontanarmi troppo dalla <lb></lb>proposta materia mi distenderei più lungamente in provare questa opinione, <lb></lb>della quale ho trovato alcuni altri, e massimamente il reverendo padre (non <lb></lb>men detto Filosofo che buon Teologo) fra Francesco Beato, metafisico di <lb></lb>Pisa, e messer Luca Ghini, medico e semplicista singolarissimo, oltre la <lb></lb>grande, non solamente cognizione, ma pratica dei Minerali tutti quanti, se­<lb></lb>condo che a me parve, quando gli udii da lui pubblicamente nello Studio <lb></lb>di Bologna ” (<emph type="italics"></emph>Alchimia<emph.end type="italics"></emph.end> cit., pag. </s>

<s>54). </s></p><p type="main">

<s>Se dunque il Ghini e il Beato erano già convinti della falsità che, quanto <lb></lb>una cosa è più grave, tanto più tosto discenda, per prove fatte quand&#039;era <lb></lb>il Varchi ancora giovane studente; convien dir che fossero le loro esperienze <lb></lb>o contemporanee o di poco posteriori a quelle di Leonardo, il quale aveva <lb></lb>insomma concluso esser l&#039;errore aristotelico solamente accidentale, e nò nella <lb></lb>sostanza, perchè se due gravi omogenei e uniformi, benchè di vario peso, <lb></lb>dispongansi così che trovino cadendo resistenza uguale nel mezzo, si ve­<lb></lb>dranno, diceva, andar con velocità proporzionali alle potenze, cosicchè <emph type="italics"></emph>quella <lb></lb>cosa che più pesa, essendo libera, più presto cade.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Correva dunque, sui principii del secolo XVI, l&#039;opinione fra i più li­<lb></lb>beri ingegni che fossero solo da attribuire alle resistenze del mezzo le ano­<lb></lb>malie osservate nella legge aristotelica, ond&#039;è che, sperimentando i più da <lb></lb>piccole altezze, e osservando che fra due corpi cadenti di vario peso, ma <lb></lb>uniformi e omogenei, le differenze del tempo sono insensibili, argutamente <lb></lb>introducendo gli effetti dell&#039;elasticità dell&#039;aria, pensarono di conciliar la se­<lb></lb>ducente dottrina del Filosofo coi fatti sperimentali apertamente contarii, di­<lb></lb>cendo che le resistenze opposte ai cadenti dal mezzo son direttamente pro­<lb></lb>porzionali ai pesi. </s>

<s>Il Cardano dette forma scientifica a questo pensiero nella <pb xlink:href="020/01/2028.jpg" pagenum="271"></pb>proposizione CX del suo <emph type="italics"></emph>Opus novum,<emph.end type="italics"></emph.end> che così formulava: “ Si duae sphae­<lb></lb>rae ex eadem materia descendant in aere, eodem temporis momento ad pla­<lb></lb>num veniunt ” (Operum, T. IV cit., pag. </s>

<s>515). </s></p><p type="main">

<s>Piacque l&#039;ingegnosa cardanica dimostrazione, e s&#039;introdusse nella scienza <lb></lb>di coloro, i quali professavano, in sul finir del secolo, i più liberi e i più <lb></lb>creduti sani principii di Filosofia naturale. </s>

<s>Son fra questi più insigni pro­<lb></lb>fessori da annoverare il Moleto e il Benedetti, il primo dei quali dettava <lb></lb>dalla cattedra padovana, a cui sarebbe per succedere Galileo, alcune lezioni <lb></lb>di Meccanica, che avevan per uno de&#039;principali argomenti a trattar della <lb></lb>caduta dei gravi, secondo le più accurate osservazioni dei fatti. </s>

<s>Per poi me­<lb></lb>glio divulgar le nuove dottrine pensò il Moleto stesso di dare a loro forma <lb></lb>di dialogo, e finse, per salvarsi dall&#039;ira peripatetica, che uscissero così fatte <lb></lb>novità di bocca a un gran personaggio, a un Principe reale, che sta l&#039;Au­<lb></lb>tore ascoltando ossequioso, benchè non punto stupidamente ne approvi ogni <lb></lb>detto. </s>

<s>Son dunque gl&#039;interlocutori <emph type="italics"></emph>P,<emph.end type="italics"></emph.end> che vuol dire il Principe, e <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> ossia <lb></lb>l Autore: e perchè crediamo che sia un tale importantissimo documento alla <lb></lb>maggior parte dei nostri Lettori ignoto, pensiamo di trascrivere intanto, dal­<lb></lb>l&#039;Appendice ai Manoscritti galileiani, questo primo passo, che concerne le <lb></lb>velocità, secondo le quali si muovono, attraverso a qualche resistenza del <lb></lb>mezzo, i varii gravi: </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — Or il grave, movendosi naturalmente, può muoversi con mag­<lb></lb>giore e con minore velocità rispetto al mezzo, poichè per un mezzo più sot­<lb></lb>tile si muove con maggior velocità, e per un mezzo più crasso con meno. </s>

<s><lb></lb>Il che tutto può V. S. intenderlo benissimo con le cose che si muovono al­<lb></lb>l&#039;ingiù per l&#039;acqua, e con quelle per l&#039;aria. </s>

<s>Laddove, se V. S. piglierà una <lb></lb>profondità d&#039;acqua di cento passi, e vi lascerà andare un grave, ed osser­<lb></lb>verà il tempo che consumerà a toccare il fondo, e noteralla da parte, e di <lb></lb>nuovo piglierà un&#039;altezza di cento passi parimente e vi lascerà andare un <lb></lb>grave del peso, sostanza e figura dell&#039;altro, e terrà conto del tempo, che <lb></lb>consumerà nel venire a basso; troverà questo tempo essere molto minore <lb></lb>dell&#039;altro. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — Perchè vuole V. A. che il grave sia della stessa sostanza, peso <lb></lb>e figura dell&#039;altro? </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — Per levar le cagioni da dubitare. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — E che dubbio può esserci intorno a questo? </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — Grandissimo, perciocchè Aristotile ha dato cagione da dubi­<lb></lb>tare, dicendo che per uno stesso mezzo la velocità delle cose, che si muo­<lb></lb>vono per movimento naturale, essendo della stessa natura e figura, è sic­<lb></lb>come le potenze loro. </s>

<s>Cioè, se dalla cima di un&#039;alta torre nòi lasceremo <lb></lb>venir giù due palle, l&#039;una di piombo di venti libbre, e l&#039;altra parimenti di <lb></lb>piombo d&#039;una libbra, che il movimento della maggiore sarà venti volte più <lb></lb>veloce di quello della minore. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — Questo mi pare assai ragionevole, anzi, quando mi fosse do­<lb></lb>mandato per principio, lo concederei. </s>

<s>” </s></p><pb xlink:href="020/01/2029.jpg" pagenum="272"></pb><p type="main">

<s><emph type="italics"></emph>P.<emph.end type="italics"></emph.end> — Vossignoria s&#039;ingannerebbe: anzi vengono tutti in uno stesso <lb></lb>lempo, e di ciò se n&#039;è fatta la prova, non una volta, ma molte. </s>

<s>E v&#039;è di <lb></lb>più che una palla di legno, o più o men grande d&#039;una di piombo, lasciata <lb></lb>venir giù d&#039;una stessa altezza, nello stesso tempo con quella di piombo, di­<lb></lb>scendono e trovano la terra o il suolo nello stesso momento di tempo. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — Se l&#039;A. V. non mi dicesse di averne fatta la prova io nol cre­<lb></lb>derei; e come si può salvare Aristotile? </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — Molti si sono sforzati di salvarlo diversamente, ma infatti mal <lb></lb>si può salvare. </s>

<s>Anzi, per dire a V. S. il tutto, io credei un giorno di aver <lb></lb>trovato il modo di salvarlo, ma poi, pensando meglio al fatto, così non fu. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — Tuttavia non può essere che non sia ingegnoso ed arguto, e <lb></lb>perciò l&#039;A. V. sia servita a dirlo. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — Per compiacerla lo dirò, ma prima dichiarerò alcuni principii <lb></lb>che mi bisognano. </s>

<s>È chiara cosa appresso che quanto più un grave si muove <lb></lb>per proprio movimento, come il sasso col discendere, tanto più venghi ve­<lb></lb>locitandosi; laddove chi presupponesse uno spazio infinito, infinita sarebbe <lb></lb>per quello la velocità del grave. </s>

<s>Se dunque presupponessimo che nel con­<lb></lb>cavo della Luna fosse un grandissimo sasso, prima che fosse nella superfice <lb></lb>della terra si sarebbe fatto di movimento molto veloce. </s>

<s>Può di questa ve­<lb></lb>locità V. S. certificarsene, oltre l&#039;autorità dei Filosofi, in questo modo. </s>

<s>Potrà <lb></lb>pigliare una palla o di sasso o di piombo o di ferro o d&#039;altra materia grave, <lb></lb>e lasciar venir giù questa palla da due diverse altezze, la quale percota in <lb></lb>due resistenti d&#039;egual natura, e vedrà che quella, che verrà dal luogo più <lb></lb>alto, farà maggiore effetto nel resistente, che quella che verrà dalla minore <lb></lb>altezza: e non essendo la stessa cosa cresciuta di peso, adunque converrà <lb></lb>dire il maggiore effetto venir dalla maggiore velocità. </s>

<s>Appresso stante a que­<lb></lb>sto principio, se noi faremo d&#039;una stessa altezza venire due palle di disu­<lb></lb>guale grandezza, e siano della stessa materia, è manifesto che la maggiore <lb></lb>nello stesso resistente farà maggiore effetto che la minore. </s>

<s>Adunque sarà <lb></lb>venuta con maggiore velocità che la minore: adunque non si muovono con <lb></lb>egual velocità, che è quello che si vuole. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — Ho inteso la ragione di V. A. ed in vero par che possa sal­<lb></lb>vare Aristotile, nè saprei per ora trovarvi l&#039;inganno, se non vi pensassi su. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — L&#039;inganno è facile da scoprire, poichè la maggior percossa della <lb></lb>maggior palla non nasce dalla velocità del movimento, essendo che il senso <lb></lb>osserva essere il movimento eguale, ma nasce dal peso, il che si può pro­<lb></lb>vare così. </s>

<s>Lasciamo venir da alto, e da due diverse distanze due palle della <lb></lb>medesima materia, ma di disugual peso, e venga la minore dalla maggiore <lb></lb>altezza, la quale ecceda la minore nel triplo o nel quadruplo, e facciamo <lb></lb>che la minore di due once venghi da un&#039;altezza di cento passi, e la mag­<lb></lb>giore di due o tre libbre venghi non più da alto, che da quattro o cinque <lb></lb>passi: qual crede V. S. che nello stesso resistente farà maggiore effetto e <lb></lb>percossa? </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — E chi dubita che la maggiore, e così dimostra l&#039;esperienza? </s>

<s>” </s></p><pb xlink:href="020/01/2030.jpg" pagenum="273"></pb><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — E ciò di dove è se non dal maggior peso? </s>

<s>e con tutto ciò con <lb></lb>maggior velocità discende la minore, poichè da maggiore altezza viene. </s>

<s>Essi <lb></lb>poi sforzato Girolomo Cardano, nel libro suo <emph type="italics"></emph>Delle proporzioni,<emph.end type="italics"></emph.end> di mostrare <lb></lb>che due palle di disegual grandezza, messe in pari altezza, sieno per venir <lb></lb>giù nello stesso tempo. </s>

<s>Ma, perchè la dimostrazione sua non mi piace in­<lb></lb>teramente, io lascio di dirla a V. S. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — Anzi voglio supplicare V. A. che me la dica, per vedere l&#039;er­<lb></lb>rore d&#039;un uomo così famoso. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — Io non voglio dire che sia errore, ma ho solo detto che non <lb></lb>mi piace, e dirolla per sodisfare a V. S. </s>

<s>Egli dice: sieno due palle, A mag­<lb></lb>giore, e B minore (fig 136) ed il diametro di A sia di tre palmi v. </s>

<s>g. </s>

<s>o <lb></lb>qual altra misura si voglia, e quello di B uno della stessa misura, e sieno <lb></lb><figure id="id.020.01.2030.1.jpg" xlink:href="020/01/2030/1.jpg"></figure></s></p><p type="caption">

<s>Figura 136.<lb></lb>della medesima materia, e sieno mosse con egual <lb></lb>distanza da CD, il quale sia il piano dove sieno per <lb></lb>dare. </s>

<s>Dico che, lasciate andare nello stesso tempo, <lb></lb>che parimente nello stesso tempo daranno nel piano <lb></lb>CD, poichè il diametro del corpo A è triplo al dia­<lb></lb>metro del corpo B. </s>

<s>Adunque il corpo A al corpo B <lb></lb>sarà come 27 a uno, poichè le sfere hanno la pro­<lb></lb>porzione fra di loro che i cubi de&#039;loro diametri, per <lb></lb>l&#039;ultima del XII di Euclide. </s>

<s>Adunque la gravità di A <lb></lb>alla gravità di B è come di 27 a uno. </s>

<s>Ma perchè <lb></lb>ogni peso, nel discender suo, condensa l&#039;aria in quel <lb></lb>grado, ch&#039;egli pesa, come l&#039;aria sotto A è 27 volte più densa che l&#039;aria <lb></lb>sotto B, però il peso A, avendo da passare aria più densa, forza è che più <lb></lb>peni nel discender suo. </s>

<s>Adunque, essendo la proporzione di A a B come <lb></lb>27 a uno, e tale essendo la potenza di A a B, seguirebbe che, quando non <lb></lb>avesse impedimento, che si dovesse movere nella velocità di 27 a uno. </s>

<s>Ora, <lb></lb>l&#039;impedimento di A all&#039;impedimento di B è come 27 a uno; adunque uguale <lb></lb>è l&#039;impedimento alla potenza, e però seguirà che il movimento loro debba <lb></lb>essere in egual tempo. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — Se il Cardano la mette così facile e chiara, come V. A. l&#039;ha <lb></lb>detto, a me pare una bella dimostrazione, nè saprei, per quel ch&#039;io me ne <lb></lb>intenda, dire se non che fosse interamente e per ogni parte bella. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — A me piace più, adesso che l&#039;ho detta a V. S., che quando la <lb></lb>lessi appresso dell&#039;Autore. </s>

<s>E quel che a me non piaceva era quella densità, <lb></lb>perchè non son ben capace che l&#039;aria si condensi secondo il peso. </s>

<s>Che si <lb></lb>condensi ancora si potrebbe dubitare. </s>

<s>Ma concedendo che l&#039;aria si condensi, <lb></lb>e si condensi secondo il peso, la dimostrazione corre benissimo, ed è bella <lb></lb>e ingegnosa. </s>

<s>Quanto al condensarsi dell&#039;aria molti par che lo concedano, e <lb></lb>particolarmente nelle cose de&#039;movimenti, perchè, quando non si concedesse <lb></lb>tal condensazione, saremmo sforzati a concedere il vacuo, cosa tanto odiosa <lb></lb>alla Natura; la quale più presto comporta che le cose gravi ascendano, che <lb></lb>ammettere quello. </s>

<s>” </s></p><pb xlink:href="020/01/2031.jpg" pagenum="274"></pb><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — E come potrà V. A. mostrare che la Natura ammette piutto­<lb></lb>sto che le cose gravi ascendano, che il vacuo? </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — In molti modi potrei mostrarlo a V. S., ma poichè questo non <lb></lb>è il suo luogo, però sarà bene soprassedere alquanto. </s>

<s>” (Opusc. </s>

<s>scientifici, <lb></lb>T. II, fol. </s>

<s>3-6). </s></p><p type="main">

<s>Della bella proposizion del Cardano, così chiaramente espostaci da Sua <lb></lb>Altezza in questo dialogo del Moleto, dette il Benedetti dimostrazione non <lb></lb>meno bella, nel cap. </s>

<s>XI delle sue <emph type="italics"></emph>Disputazioni.<emph.end type="italics"></emph.end> Per provar ivi che “ cor­<lb></lb>pora, licet inaequalia, eiusdem materiae et figurae, si resistentias habuerint <lb></lb>ponderibus proportionales, aequaliter movebuntur ” (Specul. </s>

<s>cit., pag. </s>

<s>175); <lb></lb>immagina di avere un corpo sferico omogeneo, la gravità del quale raccolta <lb></lb>nel suo centro gli partecipi nel cadere un certo grado d&#039;impulso, uguale <lb></lb>a quello che risentirebbe una Bilancia nel suo centro, a distanze eguali dal <lb></lb>quale fossero sospesi due altri corpi sferici, che pesassero ciascuno la metà <lb></lb>del maggiore. </s>

<s>La cosa è chiara per sè, dice il Benedetti, perchè i corpi <lb></lb>tanto pesano separati, quanto congiunti, ed essendosi supposto che le resi­<lb></lb>stenze tornino ad essi pesi proporzionali, è dunque vero quel che si diceva, <lb></lb>che cioè i due corpi “ tam separata quam coniuncta candem velocitatem <lb></lb>retinerent ” (ibid.). </s></p><p type="main">

<s>Non si comprende però come si possa questa conciliare con la propo­<lb></lb>sizion precedente “ quod in vacuo corpora eiusdem materiae aequali velo­<lb></lb>citate moverentur ” (ibid., pag. </s>

<s>174), che si dimostra dal Benedetti in modo <lb></lb>simile a quello di dianzi, osservando che nel vuoto tanto il centro di gra­<lb></lb>vità del peso congiunto, quanto il centro della Bilancia nelle due metà se­<lb></lb>parate, sentendo uguale impulso, e non avendo nulla che impedisca a loro <lb></lb>il moto, debbono andare ugualmente veloci; perchè da ciò che dimostra l&#039;Au­<lb></lb>tore stesso nel cap. </s>

<s>XI ne sarebbe stato da concluder piuttosto che si do­<lb></lb>vrebbe nel vuoto la legge aristotelica esattamente verificare; vi si dovrebbe <lb></lb>cioè vedere le velocità tanto varie, quanto varie ai cadenti son le grandezze. </s></p><p type="main">

<s>La mente del Matematico veneziano non sembra a noi che serbi, in­<lb></lb>torno a questo punto, la sua ordinaria serenità: si direbbe anzi addirittura <lb></lb>ch&#039;ella sta affannosamente fluttuante fra l&#039;errore antico e la verità nuova, <lb></lb>perchè, mentre nel libro <emph type="italics"></emph>De resolutione omnium Euclidis problematum<emph.end type="italics"></emph.end> par <lb></lb>che vi si trovi per la prima volta, come fece osservare il Libri in una Nota <lb></lb>al III Tomo della sua Storia, “ la consideration de la gravitè proportionnelle <lb></lb>a la masse ” (pag. </s>

<s>122), ciò che confermerebbe la conclusione delle velo­<lb></lb>cità uguali nel vuoto; i due primi capitoli delle <emph type="italics"></emph>Disputazioni<emph.end type="italics"></emph.end> non lasciano <lb></lb>luogo a dubitare che il Benedetti tornò a considerare le velocità proporzio­<lb></lb>nali ai pesi, come legge naturale verissima in sè, benchè alterabile per la <lb></lb>varia resistenza, e per l&#039;attitudine varia, che hanno le varie figure de&#039;corpi <lb></lb>a penetrare la crassizie dei mezzi. </s>

<s>Accennando infatti, nel cap. </s>

<s>I, gli errori <lb></lb>di Aristotile, ch&#039;egli si disponeva a confutare, soggiunge che anche altri, <lb></lb>fra&#039;quali il Tartaglia, tennero quella opinione che cioè due corpi della me­<lb></lb>desima specie e della medesima figura serbino esatta proporzione con le ve-<pb xlink:href="020/01/2032.jpg" pagenum="275"></pb>locità nei loro moti: opinione non per altro falsa, dice il Benedetti, se non <lb></lb>perchè non considerarono costoro “ quam magna resistentiarum sit diffe­<lb></lb>rentia quae, tam ex diversitate figurarum, quam ex magnitudinum varietate <lb></lb>exoriri potest ” (Specul. </s>

<s>cit., pag. </s>

<s>168). Nel seguente capitolo poi si spiega <lb></lb>meglio il concetto dell&#039;Autore, il quale vuol concluder dal suo ragionamento <lb></lb>che, se le velocità non sono, come dovrebbero essere per ragion naturale, <lb></lb>proporzionali ai pesi, ciò da null&#039;altro dipende, se non perchè quella pro­<lb></lb>porzione è alterata dalla inegualità della figura, alla quale non ugualmente <lb></lb>resiste il mezzo, o da una qualche varia direzione del moto rispetto alla linea <lb></lb>perpendicolare. </s>

<s>“ Quotiescumque igitur duo corpora unam eandemque re­<lb></lb>sistentiam ipsorum superficiebus aut habebunt aut recipient, eorum motus <lb></lb>inter seipsos eodem plane modo proportionati consurgent, quo erunt ipso­<lb></lb>rum virtutes moventes ” (ibid, pag. </s>

<s>169). </s></p><p type="main">

<s>Non veniva dunque il Benedetti in tal proposito nulla insegnando di <lb></lb>meglio di quel che si potesse legger da tutti, ne&#039;libri del Cardano, e tali <lb></lb>insegnamenti erano quelli insomma, che autorevolmente si davano, sul finir <lb></lb>del secolo XVI, agli studiosi della scienza del moto. </s>

<s>Era fra questi studiosi <lb></lb>Jacopo Mazzoni, il quale, venuto a professare Filosofia nello Studio pisano, <lb></lb>richiamava l&#039;attenzione de&#039;suoi discepoli sopra il libro del Matematico di <lb></lb>Venezia, di cui compendiava, nel cap. </s>

<s>XVIII del suo <emph type="italics"></emph>Preludio,<emph.end type="italics"></emph.end> le confuta­<lb></lb>zioni de&#039;molti errori, detti in Fisica e in Matematica da Aristotile, ramme­<lb></lb>morando in particolare gli argomenti, per cui dimostravasi non esser vero <lb></lb>“ corpora, eadem specie et figura praedita, per idem medium mota, eamdem <lb></lb>plane proportionem in suorum motuum velocitatibus, quam in suis magni­<lb></lb>tudinibus habent, retinere ” (In universam Plat. </s>

<s>et Arist. </s>

<s>philosophiam prae­<lb></lb>ludia, Venetiis 1597, pag. </s>

<s>192). </s></p><p type="main">

<s>Era fra i giovani, uditori in Pisa a que&#039;tempi, anche Galileo, in cui ri­<lb></lb>conoscendo il Mazzoni una singolare attitudine dell&#039;ingegno a penetrare la <lb></lb>scienza del moto, raccomandavagli il libro del Benedetti, e glie ne spiegava <lb></lb>in privato le speculazioni. </s>

<s>Sentì il giovane alunno, da quelle vive parole del <lb></lb>Maestro e dalla lettura che gli suggeriva, instillarglisi il primo ineffabile gu­<lb></lb>sto della libertà nel pensare, e perchè i fervorosi consigli e gli esempii effi­<lb></lb>caci gli avean fatto deliberar nell&#039;animo non doversi credere oramai più al­<lb></lb>l&#039;autorità di Aristotile, dunque, ne concludeva, nemmeno a quella di nessun <lb></lb>altro Filosofo, non eccettuato lo stesso Benedetti, quando si riconosca an­<lb></lb>ch&#039;egli traviar dalla rettitudine delle verità naturali. </s></p><p type="main">

<s>Studiando Galileo, con questa libera libertà propostasi, i varii capitoli <lb></lb>delle <emph type="italics"></emph>Disputazioni,<emph.end type="italics"></emph.end> ebbe a notar che il X e l&#039;XI, se non si contradicevano, <lb></lb>per lo meno non erano conseguenti, perchè, ammessa pure l&#039;ipotesi delle <lb></lb>resistenze a proporzione dei pesi, non era possibile che, così nel vuoto come <lb></lb>nel pieno, le velocità, come cercavasi di dimostrare, tornassero uguali. </s>

<s>Ri­<lb></lb>meditava perciò fra sè quale delle due proposìzioni potess&#039;esser la vera, e <lb></lb>giacchè anche il Benedetti, lasciandosi andare ad ammettere per ipotesi le <lb></lb>resistenze proporzionali ai pesi, pareva averci qualche gran dubbio; e giac-<pb xlink:href="020/01/2033.jpg" pagenum="276"></pb>chè il principio della condensazione e della elasticità dell&#039;aria, come dal Mo­<lb></lb>leto, a quel che faceva dire a Sua Altezza, così anche da Galileo malvolen­<lb></lb>tieri si concedevano al Cardano; e perciò tratteneva esso Galileo il meditativo <lb></lb>pensiero sopra quel che leggeva proposto, e poi dimostrato <emph type="italics"></emph>Quod in vacuo <lb></lb>corpora eiusdem materiae aequali velocitate moverentur,<emph.end type="italics"></emph.end> ciò ch&#039;essendo <lb></lb>vero condannerebbe la legge aristotelica per falsa, non accidentalmente. </s>

<s>come <lb></lb>da tutti s&#039;era fin&#039;allora insegnato, non escluso lo stesso Benedetti, ma per <lb></lb>falsa nella sostanza. </s>

<s>Le speculazioni però, in argomento tanto sottile, vole­<lb></lb>vano essere aiutate dall&#039;esperienza, e il discepolo del Mazzoni, divenutogli <lb></lb>in Pisa già collega, stava, tutto baldanzoso della nuova Filosofia, intorno alla <lb></lb>base del Campanile, per osservar quando due sfere dello stesso metallo, ma <lb></lb>di varia grandezza, lasciate da scolari o da amici andar dall&#039;alto della torre <lb></lb>a un tempo, giungessero in terra. </s></p><p type="main">

<s>Intorno a questo passo della vita scientifica di Galileo son corse, e cor­<lb></lb>rono tuttavia, certe opinioni, della falsità o della improprietà delle quali è <lb></lb>debito nostro avvertire i Lettori. </s>

<s>E prima di tutto si crede fossero queste <lb></lb>fatte in Pisa le prime esperienze, che invece s&#039;è veduto essere state inco­<lb></lb>minciate un secolo prima, intantochè sopr&#039;esse il Cardano ritrovò e condusse <lb></lb>quella sua celebre proposizione, riscontrata pubblicamente in Padova, per <lb></lb>tacere altri esempii, dal Moleto coi fatti. </s>

<s>Dette il Riccioli inoltre autorità a <lb></lb>quell&#039;altra opinione, largamente diffusa dal Wolf, che cioè Galileo, speri­<lb></lb>mentando da troppo piccole altezze, nè potendo perciò accorgersi di nessuna <lb></lb>sensibile differenza, dicesse giunger due palle di piombo, una piccola e l&#039;al­<lb></lb>tra grande, a toccar nel medesimo istante il piano sottoposto. </s>

<s>È da osser­<lb></lb>var però contro i detti di costoro, come apparirà meglio dal progresso del <lb></lb>nostro discorso, che, sebben Galileo ritenesse come vero quel sincronismo, <lb></lb>fu condotto però a pronunziare una tal sentenza da tutt&#039;altre ragioni, che <lb></lb>da quelle delle esperienze, alla diligenza delle quali, benchè fossero l&#039;altezze <lb></lb>piccole, non era sfuggita l&#039;osservazione che la minore sfera rimanevasi an­<lb></lb>cora indietro di qualche palmo, quando già la maggiore avea dato sul pa­<lb></lb>vimento. </s>

<s>A persuadersi poi che dovesser essere quelle galileiane esperienze <lb></lb>delle più diligenti, dopo le diligentissime istituite da Leonardo da Vinci, <lb></lb>giova leggere quel capitolo <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> dove, proponendosi lo stesso Galileo <lb></lb>di scoprir l&#039;errore dei Filosofi, i quali dicevano esser l&#039;aria inclusa la causa <lb></lb>per cui i lievi si muovono in principio più velocemente dei gravi, così in <lb></lb>terzo luogo, fra gli altri modi, argomenta: “ Si multum aeris, quod in ligno <lb></lb>est, illud velocius facit, ergo semper velocius. </s>

<s>dum fuerit in aere movebi­<lb></lb>tur. </s>

<s>Experientia tamen contrarium ostendit: verum enim est lignum in prin­<lb></lb>cipio sui motus ocius ferri plumbo; attamen paulo post adeo acceleratur <lb></lb>motus plumbi, ut lignum post se relinquat, et, si ex alta turri demittantur, <lb></lb>per magnum spatium praecedat: et de hoc saepe periculum feci ” (Le Opere <lb></lb>di Galileo, ediz. </s>

<s>naz., T. </s>

<s>I cit., pag. </s>

<s>334). </s></p><p type="main">

<s>Riconoscendo benissimo Galileo doversi così fatte differenze di moto at­<lb></lb>tribuire alle varie resistenze del mezzo, che si rendon sensibili anche quando, <pb xlink:href="020/01/2034.jpg" pagenum="277"></pb>essendo omogenei e uniformi i cadenti, son però di grandezze diverse; con­<lb></lb>fermavasi in quel che, per semplice speculazione, avea già concluso col Be­<lb></lb>nedetti, che cioè nel vuoto, dove quelle stesse resistenze son nulle, così la <lb></lb>grande e la piccola sfera di piombo, come quella di piombo e l&#039;altra simile <lb></lb>di legno, passerebbero in tempi uguali sempre uguale uno spazio. </s>

<s>Essendo <lb></lb>il fatto ritrovato così, per ragioni e per esperienze, certissimo, cercava Ga­<lb></lb>lileo la causa di un effetto tanto singolare, e intorno a cui tutti prima di <lb></lb>lui avevano fatto naufragio. </s>

<s>Dopo lunghe meditazioni gli parve di non poter <lb></lb>risolvere altrimenti il problema, se non con ammettere “ che di ciaschedun <lb></lb>corpo grave cadente sia una da Natura determinata velocità, sicchè l&#039;ac­<lb></lb>crescergliela o diminuirgliela non si possa, se non con usargli violenza ” <lb></lb>(Alb. </s>

<s>XIII, 65). </s></p><p type="main">

<s>Ecco rivelato alla scienza per la prima volta un gran vero, ed ecco <lb></lb>tolto ai progressi di lei un grande impedimento: i pesi non son proporzio­<lb></lb>nali alla semplice gravità, ma sì alla gravità moltiplicata per la <emph type="italics"></emph>massa,<emph.end type="italics"></emph.end> per <lb></lb>cui, in qualunque ponderoso, la forza che ne velocita la caduta si mantiene <lb></lb>invariabile. </s>

<s>Così la legge aristotelica veniva da Galileo a dimostrarsi falsa, <lb></lb>non accidentalmente, ma nella sua causa, e scoprivasi finalmente l&#039;insidiosa <lb></lb>fallacia; intanto che, mentre appariva da una parte chiarissimo, come mai <lb></lb>una sfera di piombo e un frustulo di lei dovessero andare ugualmente ve­<lb></lb>locitati, cadendo, si scoprivan facilmente dall&#039;altra i paralogismi dell&#039;antica <lb></lb>Filosofia. </s></p><p type="main">

<s>Qui consiste il vero merito di Galileo, non saputo riconoscere, nè per­<lb></lb>ciò degnamente apprezzare da tanti ciechi ammiratori di lui, contenti a farlo, <lb></lb>dopo un secolo, ripetitore dal campanile di Pisa delle esperienze di Leonardo <lb></lb>e di Luca Ghini. </s>

<s>E perchè l&#039;origine e il progresso della nuova galileiana <lb></lb>rivelazione non manchino del loro debito documento, ridurremo alla memo­<lb></lb>ria dei nostri Lettori queste parole, estratte dal Discorso scritto in risposta <lb></lb>a un libro peripatetico di Antonio Rocco. </s></p><p type="main">

<s>“ Incontratomi, dice Galileo, nel testo di Aristotile, nel quale egli per <lb></lb>manifesta suppone la sua proposizione, subito sentii gran repugnanza nel­<lb></lb>l&#039;intelletto come potesse essere che un corpo, dieci o venti volte più grave <lb></lb>dell&#039;altro, dovesse cadere a basso con decupla o vigecupla velocità, e mi <lb></lb>sovvenne aver veduto nelle tempeste mescolatamente cadere piccoli grani di <lb></lb>grandine con mezzani e con grandi dieci e più volte, e non questi antici­<lb></lb>pare il loro arrivo in terra; nè meno esser credibile che i piccoli si fosser <lb></lb>mossi un pezzo avanti ai grandissimi. </s>

<s>” </s></p><p type="main">

<s>“ Di qui, passando col discorso più oltre, mi formai un&#039;assioma, da <lb></lb>non essere revocato in dubbio da nessuno, e supposi qualsivoglia corpo grave <lb></lb>discendente aver nel suo moto un grado di velocità, da natura limitato ed <lb></lb>in maniera prefisso, che il volerglielo alterare col crescergli la velocità o <lb></lb>diminuirgliela non si potesse fare, senza usargli violenza, per ritardargli o <lb></lb>concitargli il detto suo limitato corso naturale. </s>

<s>Fermato questo discorso, mi <lb></lb>figurai colla mente due corpi eguali in mole e in peso, quali fossero per <pb xlink:href="020/01/2035.jpg" pagenum="278"></pb>esempio due mattoni, li quali da una medesima altezza in un medesimo <lb></lb>istante si partissero. </s>

<s>Questi non si può dubitare che scenderanno con pari <lb></lb>velocità, cioè coll&#039;assegnata loro dalla Natura, la quale, se da qualche altro <lb></lb>mobile dee loro essere accresciuta, è necessario che esso con maggior velo­<lb></lb>cità si muova. </s>

<s>Ma se si figureranno i mattoni nello scendere unirsi ed at­<lb></lb>taccarsi insieme, quale di loro sarà quello che, aggiungendo impeto all&#039;altro, <lb></lb>gli raddoppi la velocità, stante che ella non può essere accresciuta da un <lb></lb>sopravveniente mobile, se con maggior velocità non si muove? </s>

<s>Convien dun­<lb></lb>que concedere che il composto di due mattoni non alteri la loro prima ve­<lb></lb>locità ” (Alb. </s>

<s>II, 315, 16). </s></p><p type="main">

<s>Sentesi di qui echeggiare, quasi nelle medesime parole, il concetto del <lb></lb>Benedetti, ma Galileo recide con la sua solita arte, o a dir meglio nasconde <lb></lb>anche questo filo delle più prossime tradizioni, benchè non riuscisse ad arre­<lb></lb>stare il corso alla logica della Natura, la quale con pari liberalità porgeva <lb></lb>quello stesso filo per guida anche ad altri ingegni speculativi. </s>

<s>Abbiam fra <lb></lb>questi da annoverare Giovan Marco, matematico di Praga, e Giovan Ba­<lb></lb>tista Baliani, il quale, pubblicando per la prima volta in Genova nel 1638 un <lb></lb>suo trattatello <emph type="italics"></emph>De motu gravium<emph.end type="italics"></emph.end> raccontava nella prefazione come nel 1611, <lb></lb>essendo per patria legge prefetto alla Rocca di Savona, la comodità di quel­<lb></lb>l&#039;altura e l&#039;avere a mano le palle dei cannoni militari lo invogliassero a far <lb></lb>esperienze della caduta dei gravi. </s>

<s>Ebbe da così fatte esperienze ripetute più <lb></lb>volte che due de&#039;suddetti globi, uno di una libbra e l&#039;altro di cinquanta, <lb></lb>giungevano a toccare il suolo <emph type="italics"></emph>in indivisibili temporis momento.<emph.end type="italics"></emph.end> (De motu <lb></lb>natur., editio 2a, Genuae 1646, pag. </s>

<s>5). </s></p><p type="main">

<s>Incominciò allora a pensare che i fatti non concordavano con le dot­<lb></lb>trine della maggior parte dei Filosofi, ond&#039;è che volle veder se la legge da <lb></lb>loro approvata si verificasse, almeno ne&#039;corpi di differente gravità in spe­<lb></lb>cie. </s>

<s>Ma fatti andar giù dall&#039;alto della Rocca due globi, uno di piombo e <lb></lb>l&#039;altro di cera, trovò che questo rimaneva sì all&#039;altro indietro, di un tale <lb></lb>spazio però da non serbar proporzione alcuna con le differenti gravezze. <lb></lb></s>

<s>“ Porro, cum ex experimentis satis superque liqueret in naturali motu gra­<lb></lb>vium proportionem gravitatum communiter creditam non servari, in eam <lb></lb>descendi sententiam ut arbitrarer fortasse gravitatem se habere ut agens, <lb></lb>materiam vero, seu mavis materiale corpus, ut passum, et proinde gravia <lb></lb>moveri iuxta proportionem gravitatis ad materiam, et ubi sine impedimento <lb></lb>naturaliter perpendiculari motu ferantur moveri aequaliter, quia ubi plus <lb></lb>est gravitatis plus pariter sit materiae, seu materialis gravitatis ” (ibid., <lb></lb>pag. </s>

<s>6, 7). </s></p><p type="main">

<s>Penetrando bene addentro al significato di queste parole, ben si com­<lb></lb>prende come, dicendo il Baliani che le due sfere omogenee si vedevan ca­<lb></lb>dere <emph type="italics"></emph>in indivisibili temporis momento,<emph.end type="italics"></emph.end> non intendeva escludere qualche pic­<lb></lb>cola real differenza di moto, la quale accidentalmente nascesse dall&#039;impedi­<lb></lb>mento del mezzo, in conformità della quale intenzione gli abbiamo sentito <lb></lb>espressamente dire che allora due corpi, comunque tra loro differenti, si <pb xlink:href="020/01/2036.jpg" pagenum="279"></pb>moverebbero di moto uguale, <emph type="italics"></emph>ubi sine impedimento<emph.end type="italics"></emph.end> (ciò che solo può av­<lb></lb>venire nel vuoto) <emph type="italics"></emph>naturaliter perpendiculari motu ferantur.<emph.end type="italics"></emph.end> In questo stato <lb></lb>di assoluta libertà da tutti gl&#039;impedimenti considerava anche Giovan Marco <lb></lb>le cadute de&#039;corpi, quando asseriva: “ motum, quatenus a gravitate proce­<lb></lb>dit, eiusdem speciei seu gradus, eadem celeritate fieri in omnibus, quan­<lb></lb>tumvis mole, figura, pondere a se differant ” (De proportione motus, Pra­<lb></lb>gae 1639, P.). </s></p><p type="main">

<s>Non ebbe questa considerazione il gesuita Niccolò Cabeo, il quale, tro­<lb></lb>vandosi nella quaresima del 1636 a predicare in Genova, strinse amicizia <lb></lb>col Baliani che, discorrendo degli amati suoi studi, si era più volte espresso <lb></lb>(per formular la legge naturale nella sua essenza, consistente nell&#039;aver cia­<lb></lb>ciascuna divisa particella materiale il medesimo impulso discensivo di tutta <lb></lb>insieme la mole) dicendo che qualunque corpo dovrebbe cader dall&#039;alto <lb></lb>ugualmente veloce. </s>

<s>Intese il Cabeo quel discorso senza alcuna discrezione, <lb></lb>e perchè forse ridusse le sue esperienze a lasciarseli cadere dall&#039;una e dal­<lb></lb>l&#039;altra mano, scrisse di avere sperimentato che un pezzo di piombo e <emph type="italics"></emph>fru­<lb></lb>stum panis<emph.end type="italics"></emph.end> cadevano nel medesimo tempo. </s></p><p type="main">

<s>Incontrò un caso simile a Galileo che, secondo le intenzioni medesime <lb></lb>del Baliani, si esprimeva nei medesimi modi in privato coi discepoli e con <lb></lb>gli amici, e poi, lusingandosi di dover essere inteso dai giudiziosi, così pub­<lb></lb>blicamente scriveva nella II Giornata dei Due massimi sistemi: “ Palle di <lb></lb>una, di dieci, di cento, di mille libbre tutte misureranno le medesime cento <lb></lb>braccia nello stesso tempo ” (Alb. </s>

<s>I, 245). Era fra quegli scolari, che aveva <lb></lb>prima ascoltato e poi letto Galileo, Vincenzio Renieri, il quale si trovava a <lb></lb>professare le Matematiche in Pisa, quando nel 1641 gli giunse notizia del­<lb></lb>l&#039;esperienze del Cabeo. </s>

<s>E perchè queste, com&#039;è facile indovinare, si tene­<lb></lb>vano per incredibili, come per dubbiose s&#039;avevano quelle di Galileo; per <lb></lb>certificarsi della verità dei fatti s&#039;istituirono, ne&#039;primi giorni di Marzo di <lb></lb>quell&#039;anno 1641, dal campanile di Pisa opportune esperienze, delle quali il <lb></lb>Renieri, dopo pochi giorni, scriveva allo stesso Galileo così per lettera il re­<lb></lb>sultato: </s></p><p type="main">

<s>“ Abbiamo qui avuto occasione di fare una esperienza di due gravi ca­<lb></lb>denti dall&#039;alto di diversa materia, cioè uno di legno e uno di piombo, ma <lb></lb>della stessa grandezza; perchè un tal Gesuita scrive che scendono nello stesso <lb></lb>tempo, e con pari velocità arrivano a terra, ed un tale Inglese affermava che <lb></lb>il Liceti componeva di ciò un problema, e ne rendeva la ragione. </s>

<s>Ma final­<lb></lb>mente abbiamo trovato il fatto in contrario, perchè dalla cima del campa­<lb></lb>nile del. </s>

<s>Duomo tra la palla di piombo e quella di legno vi corrono tre brac­<lb></lb>cia almeno di differenza. </s>

<s>Si fecero anche esperienze di due palle di piombo, <lb></lb>una della grandezza eguale a una ordinaria di artiglieria, e l&#039;altra da mo­<lb></lb>schetto, e si vedeva tra la più grossa e la più piccola, dall&#039;altezza dello <lb></lb>stesso campanile, esservi un buon palmo di differenza, del quale la più <lb></lb>grossa anticipava la più piccola ” (Alb. </s>

<s>X, 410). </s></p><p type="main">

<s>Galileo si compiacque di queste esperienze, che diceva sovvenire a con-<pb xlink:href="020/01/2037.jpg" pagenum="280"></pb>ferma delle sue dottrine, ciò che giunse nuovo, e contrario a quel che si <lb></lb>aspettava il Renieri, il quale credeva di aver anzi trovato che i fatti contra­<lb></lb>dicevano a quel che aveva udito dire al suo Maestro o letto nel sopra ci­<lb></lb>tato luogo dei dialoghi Del mondo. </s>

<s>Galileo allora dichiarò meglio in qual <lb></lb>senso si dovesse interpetrare quel luogo, in cui intendevasi formular la legge <lb></lb>assolutamente, astraendo dalle accidentalità prodotte dall&#039;impedimento del <lb></lb>mezzo, gli effetti del quale, da che solo potevano dipendere le differenze <lb></lb>nelle varie cadute sperimentate, diceva di aver minutamente considerati e <lb></lb>discorsi nel primo dialogo Dei moti, alla lettura del quale, se voleva avere <lb></lb>intera scienza di quelle cose, rimandava il Renieri. </s></p><p type="main">

<s>Il Renieri però rispondeva ingenuamente di non avere avuto ancora <lb></lb>tempo in due anni di leggere il libro con quell&#039;attenzione, che richiedevan <lb></lb>le proposizioni ivi matematicamente dimostrate. </s>

<s>“ L&#039;ultimo Dialogo di V. S. E. <lb></lb>non è stato da me letto, se non in qua e in là, perchè l&#039;estate passata, che <lb></lb>avrei potuto attendervi con diligenza, ella sa come io stetti, e di poi non ho <lb></lb>avuto tempo di poterlo vedere con quella applicazione, che ricercano le di­<lb></lb>mostrazioni che sono in esso. </s>

<s>So che è verissimo che due gravi differenti in <lb></lb>specie, benchè uguali di mole, non serbano proporzione alcuna di gravità <lb></lb>nello scendere, anzi che per esempio nell&#039;acqua il legno si moverà al con­<lb></lb>trario del piombo, e però fino da principio mi risi della esperienza del Ge­<lb></lb>suita, che affermava che il piombo <emph type="italics"></emph>et frustum panis,<emph.end type="italics"></emph.end> per dire com&#039;egli <lb></lb>scrive, si movevano con egual velocità al centro. </s>

<s>Ma che due gravi ineguali <lb></lb>di peso, ma della stessa materia, cadendo dalla stessa altezza a perpendi­<lb></lb>colo, abbiano ad arrivare con diversa velocità e in diverso tempo al cen­<lb></lb>tro, mi pareva d&#039;aver da lei udito o letto, che ora non mi ricordo, non poter <lb></lb>essere ” (ivi, pag. </s>

<s>414). </s></p><p type="main">

<s>Soggiungeva il Renieri a queste parole, scritte il dì 20 di Marzo, che <lb></lb>nelle prossime vacanze di Pasqua avrebbe atteso finalmente alla lettura del <lb></lb>libro, e mandando, secondo le altrui promesse e i desiderii proprii, la cosa <lb></lb>ad effetto, avrà trovato quel che Galileo discorre a lungo delle difficoltà in­<lb></lb>contrate dai cadenti al loro libero velocitarsi, nel mezzo, e si sarà persuaso <lb></lb>di aver franteso, quando gli parve aver udito dire al Maestro non essere <lb></lb>assolutamente possibile che due gravi della stessa materia, cadendo dalla <lb></lb>stessa altezza per l&#039;aria, in diverso tempo arrivino al centro. </s></p><p type="main">

<s>Non così però, a dispetto della ragione e dei fatti, se ne volle persua­<lb></lb>dere il Cabeo, il quale pubblicando in due volumoni in folio, nel 1646, i <lb></lb>suoi Commentarii sui quattro libri meteorologici di Aristotile, torna nel primo <lb></lb>libro sulla questione se di tutti i cadenti le velocità siano uguali, e come <lb></lb>avesse a dimostrare il teorema più certo di Geometria così scrive: “ Sint <lb></lb>primo duo gravia eiusdem rationis, ut duo plumbea, sive omnino similem <lb></lb>habeant figuram, ut quod ambo sint sphaerica, sive non, quae simul ex edito <lb></lb>loco decidant: dico simul physice ex quacumque altitudine ad terram per­<lb></lb>venire. </s>

<s>Hoc multis experimentis et ego ipse sum expertus et alii etiam <lb></lb>experti sunt, et semper omnino aequali tempore descendere deprehendi, <pb xlink:href="020/01/2038.jpg" pagenum="281"></pb>etiamsi unum esset unius unciae, alterum quinquaginta, nec quolibet po­<lb></lb>sito magno discrimine in pondere potest notari sensibile discrimen in casu ” <lb></lb>(In libros meteor. </s>

<s>Arist., T. I, Romae 1646, pag. </s>

<s>97). </s></p><p type="main">

<s>Non contento di ciò, il Cabeo, con la sua solita temeraria franchezza <lb></lb>poco appresso asserisce non due soli globi di piombo grandemente diversi <lb></lb>di mole, “ Sed etiam globos valde impares in materia, ut plumbeum et li­<lb></lb>gneum, et dispares in figura, ut quadratum seu piramidale et rotundum, si <lb></lb>simul ex edito loco, tranquillo coelo, cadant, ambo simul ad terram perve­<lb></lb>nire, ita ut quantumcumque sit discrimen ponderis non possit notari sensi­<lb></lb>bile discrimen temporis quo ad terram allidunt ” (ibid.). Non ignora quel <lb></lb>che andavano dicendo alcuni doversi tener conto, in così fatti esperimenti, <lb></lb>della resistenza dell&#039;aria, ma, guardate, rispondeva il Cabeo, quanto son varii <lb></lb>i cervelli degli uomini! chi vuol che l&#039;aria acceleri il moto, e chi vuole che <lb></lb>lo ritardi. </s>

<s>Ma lasciamo i discorsi e atteniamoci ai fatti, tante volte da me <lb></lb>sperimentati, i quali ci persuadono “ aerem nihil efficere in isto motu nec <lb></lb>pro nec contra velocitatem ” (ibid., pag. </s>

<s>68). </s></p><p type="main">

<s>Non potè, in leggere queste cose, Giovan Batista Riccioli tenersi dal <lb></lb>rimproverare il suo confratello, per essersi così ostinatamente messo a im­<lb></lb>pugnare la verità conosciuta, e nel II Tomo dell&#039;Almagesto nuovo pubbli­<lb></lb>camente confessa che, per quanto si studiasse di persuadere il Cabeo con <lb></lb>addurre i certissimi fatti in contrario “ nunquam ex ea opinione per me <lb></lb>divelli potuit ” (Bononiae 1651, pag. </s>

<s>382). Prosegue poi a dire che quella <lb></lb>opinione, così asseveranteinente professata nel libro Delle meteore, era af­<lb></lb>fatto temeraria, perchè ivi non si dice da che altura furon fatti gli esperi­<lb></lb>menti, sebben giurasse d&#039;esser certo, il Riccioli, che da quelli fatti insieme <lb></lb>nel 1634 in Ferrara dal Campanile della chiesa del Gesù, non bene alta <lb></lb>24 metri “ nunquam adduci potuit ut eam vel ullam inaequalitatem admit­<lb></lb>teret, aut discrimen in lapsis ” (ibid.). </s></p><p type="main">

<s>A concluder qualche cosa di certo ci bisognavano altezze maggiori, ond&#039;è <lb></lb>che, venuto il Riccioli a insegnare nel Collegio della sua Compagnia di Gesù <lb></lb>in Bologna, rivolse lieto lo sguardo alla torre degli Asinelli, che poi ritrovò <lb></lb>tanto comoda a esperimentar le cadute dei gravi <emph type="italics"></emph>perinde ac si ad hunc <lb></lb>finem esset constituta.<emph.end type="italics"></emph.end> Di lassù, fra gli altri, tuttavia memorabili nella sto­<lb></lb>ria per la loro straordinaria diligenza, istituì quella IV classe di esperimenti <lb></lb><emph type="italics"></emph>pro duorum gravium diversi ponderis descensu inaequali,<emph.end type="italics"></emph.end> che andavano <lb></lb><emph type="italics"></emph>ad hominem<emph.end type="italics"></emph.end> contro il Cabeo, e contro tutti coloro ch&#039;ei credeva tenesser <lb></lb>con lui. </s></p><p type="main">

<s>Molto fallace, incomincia a dire il Riccioli, è questo modo di sperimen­<lb></lb>tare, se non vi si usi una grande circospezione, la quale si fa principal­<lb></lb>mente consister da lui nello sceglier due corpi che, avendo differente peso, <lb></lb>incontrino nonostante nell&#039;aria una medesima resistenza. </s>

<s>Eragli a principio, <lb></lb>come a Leonardo, venuto in mente di usar cilindri o prismi della medesima <lb></lb>base e di differente altezza, ma, rotando questi intorno al loro centro di gra­<lb></lb>vità, rendevano troppo incerto il tempo della caduta, e perciò scelse piut-<pb xlink:href="020/01/2039.jpg" pagenum="282"></pb>tosto due globi di argilla fresca, i quali, avendo ambedue uguale diametro, <lb></lb>scavandone uno intorno al centro, riducevasi sotto pari volume la metà più <lb></lb>leggero dell&#039;altro, che pesava esattamente vent&#039;once. </s></p><p type="main">

<s>Così preparati, si lasciavano nello stesso tempo cadere i due globi dalla <lb></lb>maggiore altura della torre degli Asinelli, lungo le pareti della quale de­<lb></lb><figure id="id.020.01.2039.1.jpg" xlink:href="020/01/2039/1.jpg"></figure></s></p><p type="caption">

<s>Figura 137.<lb></lb>scrivan le due linee GI, OD (fig. </s>

<s>137), in cui i due punti I, D <lb></lb>designano il pavimento, e G, O i merli della torre. </s>

<s>Furono l&#039;espe­<lb></lb>rienze ripetute più volte: nel Maggio del 1640, nell&#039;Agosto del 1645, <lb></lb>nell&#039;Ottobre del 1648, e ultimamente nel 1650, sempre alla pre­<lb></lb>senza di molti testimoni, che il Riccioli cita per nome, i più ge­<lb></lb>suiti, fra&#039;quali due destinati ad ottenere una meritata celebrità nella <lb></lb>scienza; Francesco Maria Grimaldi, assiduo sempre e diligentissimo <lb></lb>cooperatore, e Paolo Casati. </s>

<s>“ Siquidem, così descriveva il Riccioli <lb></lb>stesso il resultato di queste esperienze, globus argillaceus levior <lb></lb>seu 10 unciarum, eodem momento quo argillaceus alter eiusdem <lb></lb>molis sed unciarum 20 demissus fuit ex O, apparuit adhuc in F <lb></lb>distans a pavimento I pedes saltem 15, eo momento quo gravior <lb></lb>pavimentum idem percusserat in D, et iam in sexcenta fragmina <lb></lb>dissiluerat ” (ibid., pag. </s>

<s>387). </s></p><p type="main">

<s>Fra i testimoni invocati, e i curiosamente concorsi a spettacolo di que­<lb></lb>ste esperienze “ aderant, dice il Riccioli stesso, tres aut quatuor Philoso­<lb></lb>phiae aut Theologiae magistri, qui cum Galilaeo aut Cabeo et Arriaga exi­<lb></lb>stimaverant duo quaelibet gravia, dimissa simul ex eadem altitudine quan­<lb></lb>tacumque, descendere ad terram eodem physico temporis momento. </s>

<s>At statim <lb></lb>opinionem hanc deposuerunt ” (ibid.). </s></p><p type="main">

<s>Era dunque anche il Riccioli dell&#039;opinion del Renieri, e, argomentando <lb></lb>da quel che aveva trovato scritto ne&#039;dialoghi Dei due massimi sistemi, po­<lb></lb>neva senza eccezione Galileo nel novero del Cabeo e dell&#039;Arriaga. </s>

<s>I dialo­<lb></lb>ghi Del moto o non furono dall&#039;illustre Sperimentator bolognese mai letti <lb></lb>o secondando gl&#039;istituti della sua setta si serbò ritroso a quelle dottrine, <lb></lb>giacchè dalle XIII classi di esperimenti descritti intorno alla caduta dei gravi, <lb></lb>ne deduce alcuni teoremi, nell&#039;ultimo de&#039;quali, trovandosi costretto a pro­<lb></lb>fessar contro lo stesso Aristotile, non sa più dove andare a ritrovare il vero <lb></lb>smarrito. </s>

<s>“ Quoniam vero difficile reddi potest ratio a priori cur effectus <lb></lb>velocitatis ad velocitatem non servet proportionem, quam habet causa ad <lb></lb>causam, nempe gravitas ad gravitatem; hinc factum ut non pauci ex iam <lb></lb>nominatis putarint per se duo quaelibet gravia, quantumvis differentia in <lb></lb>pondere, aequaliter descendere, si removeantur quae per accidens unum <lb></lb>eorum retardant ” (ibid., pag. </s>

<s>396). Ciò reputasi dal Riccioli impossibile, <lb></lb>perchè supponeva nel suo discorso che si volesser rimovere tutti gl&#039;impe­<lb></lb>dimenti esterni, considerando i gravi sempre moversi in mezzo all&#039;aria, ma <lb></lb>Galileo e i <emph type="italics"></emph>pauci ex iam nominatis<emph.end type="italics"></emph.end> intendevano che il principale, anzi l&#039;unico <lb></lb>impedimento al moto dei gravi, fosse l&#039;aria stessa, per rimover la quale sup­<lb></lb>ponevano il vuoto. </s></p><pb xlink:href="020/01/2040.jpg" pagenum="283"></pb><p type="main">

<s>Accennammo già alla dimostrazione geometrica del Benedetti, e ora sog­<lb></lb>giungeremo quell&#039;altra fisica, che dettero contemporaneamente i due grandi <lb></lb>Maestri del moto in Alemagna e in Italia. </s>

<s>Giovan Marco scriveva così nel <lb></lb>suo capitolo <emph type="italics"></emph>De inaequalium ponderum lapsu:<emph.end type="italics"></emph.end> “ Quia ergo retardatio mo­<lb></lb>tus est a medio, quo medium magis resistit divisioni eo minor velocitas <lb></lb>motus, maior autem excessus tarditatis in minori, propterea quod aucta re­<lb></lb>sistentia eadem differentia in minori intervallo. </s>

<s>E contra minuitur excessus <lb></lb>in medio magis raro. </s>

<s>Itaque si detur corpus infinitae raritatis, cuiusmodi <lb></lb>vacuum, quia nulla resistentia, nulla quoque erit inaequalitas motus ” (De <lb></lb>propor. </s>

<s>motus, Pragae 1639, P3). </s></p><p type="main">

<s>Nella medesima forma argomentava il Salviati nella giornata prima Delle <lb></lb>due nuove scienze (Alb. </s>

<s>XIII, 75) e nel Discorso contro il peripatetico Rocco, <lb></lb>così dicendo: “ Tuttavolta che noi vediamo che con l&#039;attenuare e allegge­<lb></lb>rire il mezzo, anco nel mezzo dell&#039;aria, che pure è corporeo e perciò resi­<lb></lb>stente, arriviamo a vedere due mobili, sommamente differenti di peso, per <lb></lb>un breve spazio moversi di velocità niente o pochissimo differenti, le quali <lb></lb>poi siamo certi farsi diverse, non per le gravità che sempre son le stesse, <lb></lb>ma per gl&#039;impedimenti e ostacoli del mezzo, che sempre s&#039;augumentano; <lb></lb>perchè non dobbiamo tener per fermo che, rimossa del tutto la gravità, la <lb></lb>crassizie e tutti gli altri impedimenti del mezzo pieno, nel vacuo, i metalli <lb></lb>tutti, le pietre, i legni ed insomma tutti i gravi si movesser colla stessa ve­<lb></lb>locità? </s>

<s>” (Alb. </s>

<s>II, 328). </s></p><p type="main">

<s>Con tale intenzione s&#039;asseriva pure ne&#039;dialoghi Del mondo, e nel primo <lb></lb>Del moto che non solo una lacrima di piombo avrebbe a moversi veloce, <lb></lb>come una palla di artiglieria, ma un grano di rena, come una macina di <lb></lb>guado (Alb. </s>

<s>XIII, 67). Venendo però a farne esperienza non si trova se­<lb></lb>guirne così puntualmente l&#039;effetto, per gl&#039;impedimenti dell&#039;aria, i quali son <lb></lb>poi dallo stesso Galileo ridotti alle loro più giuste ragioni. </s>

<s>“ L&#039;esperienza, <lb></lb>egli dice, fatta con due mobili quanto più si possa differenti di peso, col <lb></lb>farli scendere da un&#039;altezza, per osservare se la velocità loro sia uguale, <lb></lb>patisce qualche difficoltà, imperocchè se l&#039;altezza sarà grande, il mezzo che <lb></lb>dall&#039;impeto del cadente dee essere aperto e lateralmente spinto, di molto <lb></lb>maggior pregiudizio sarà al piccol momento del mobile leggerissimo, che alla <lb></lb>violenza del gravissimo, per lo che per lungo spazio il leggero rimarrà in­<lb></lb>dietro, e nell&#039;altezza piccola si potrebbe dubitare se veramente non vi fusse <lb></lb>differenza, o pur se ve ne fosse, ma inosservabile ” (ivi, pag. </s>

<s>86, 87). </s></p><p type="main">

<s>Per scansar le quali difficoltà, non vedendo ancora possibile il modo di <lb></lb>levar affatto l&#039;aria di mezzo, fu condotto Galileo all&#039;ingegnosissimo partito <lb></lb>di renderne poco sensibili gl&#039;impedimenti “ col fare scendere i mobili sopra <lb></lb>un piano declive, non molto elevato sopra l&#039;orizzontale, che sopra questo, <lb></lb>non meno che nel perpendicolo, potrà scorgersi quello che facciano i gravi <lb></lb>differenti di peso. </s>

<s>E passando più avanti ho anco voluto liberarmi da qual­<lb></lb>che impedimento, che potesse nascer dal contatto di essi mobili sul detto <lb></lb>piano declive, e finalmente ho preso due palle, una di piombo e una di su-<pb xlink:href="020/01/2041.jpg" pagenum="284"></pb>ghero; quella ben più cento volte più grave di questa, o ciascuna di loro <lb></lb>attaccate a due sottili spaghetti eguali, lunghi quattro o cinque braccia, le­<lb></lb>gati ad alto. </s>

<s>Allontanata poi l&#039;una e l&#039;altra palla dallo stato perpendicolare, <lb></lb>gli ho dato l&#039;andare nell&#039;istesso momento, ed esse scendendo per le circon­<lb></lb>ferenze dei cerchi descritti dagli spaghi, eguali loro semidiametri, e passate <lb></lb>oltre al perpendicolo, son poi per le medesime strade ritornate indietro. </s>

<s>E <lb></lb>reiterando ben cento volte per lor medesime le andate e le tornate, hanno <lb></lb>sensatamente mostrato come la grave va talmente sotto il tempo della leg­<lb></lb>gera, che nè in ben cento vibrazioni nè in mille anticipa il tempo di un <lb></lb>minimo momento, ma camminano con passo ugualissimo ” (ivi, pag. </s>

<s>87). </s></p><p type="main">

<s>Dice di essere anche il Baliani ricorso al medesimo efficacissimo espe­<lb></lb>rimento dimostrativo delle velocità sempre uguali, in corpi delle più diffe­<lb></lb>renti gravità specifiche, fatti vibrare ne&#039;pendoli. </s>

<s>“ Globos in gravitate et in <lb></lb>materia inaequales appendi funiculis aequalibus, et agitatos animadverti mo­<lb></lb>veri tempore aequali, et hoc servare adeo fideliter ut globus plumbeus dua­<lb></lb>rum unciarum, alter librarum duarum; ferreus librarum 34 et lapideus <lb></lb>40 circiter, nec non et lapis informis, quorum funiculi, comprehensis ipso­<lb></lb>rum semidiametris, aequales essent, uno et eodem temporis spatio moveren­<lb></lb>tur, et vibrationes easdem numero darent hinc inde sive motus unius globi <lb></lb>fieret per aequale spatium, sive per inaequale ” (De motu natur. </s>

<s>cit., pag. </s>

<s>6). </s></p><p type="main">

<s>Notava però Galileo, e l&#039;avrà pure dovuto notare il Baliani, scorgersi <lb></lb>anche in quelle esperienze l&#039;operazione del mezzo dal diminuire assai più <lb></lb>presto “ le vibrazioni del sughero che quelle del piombo ” (Alb. </s>

<s>XIII, 87) <lb></lb>per toglier la quale inesattezza, che avrebbe potuto forse mettere qualche <lb></lb>scrupolo nella conclusione, il Newton fece tornire due scatolette sferiche di <lb></lb>legno uguale, e di uguale diametro, e l&#039;una empì di trucioli pur di legno <lb></lb>e l&#039;altra del medesimo peso di oro diligentemente curando di situarlo nel <lb></lb>centro dell&#039;oscillazione. </s>

<s>“ Pyxides ab aequalibus pedum undecim filis pen­<lb></lb>dentes constituebant pendula, quoad pondus, figuram et aeris resistentiam, <lb></lb>omnino paria; et paribus oscillationibus iuxta positae, ibant una et redibant <lb></lb>diutissime ” (Principia mathem., T. III, Genevae 1742, pag. </s>

<s>33). Sperimentò <lb></lb>poi con altri corpi della più varia natura, e n&#039;ebbe sempre i medesimi re­<lb></lb>sultati. </s>

<s>“ Rem tentavi in auro, argento, plumbo, vitro, arena, sale communi, <lb></lb>ligno, aqua, tritico ” (ibid.). </s></p><p type="main">

<s>Sembra che dovessero quelle prime esperienze di Galileo e del Baliani <lb></lb>coi pendoli, rese dal Newton poi sì perfette, essere sufficienti a dimostrar <lb></lb>che una medesima è la velocità nel composto e nella materia divisa, e che <lb></lb>dipendon le differenze dalla sola resistenza del mezzo. </s>

<s>Ma Galileo non si <lb></lb>contentò di questo, e prevenendo il male inteso pensiero del Riccioli e del <lb></lb>Renieri si trattenne con assai lungo e spiegato discorso, nel Io dialogo Delle <lb></lb>due nuove scienze, a mostrar come ogni differenza di moto, da lui benis­<lb></lb>simo ne&#039;varii casi osservata prima de&#039;suoi contradittori, dipendeva dai varii <lb></lb>impedimenti dell&#039;aria. </s></p><p type="main">

<s>E quanto alle esperienze del Riccioli coi cadenti di ugual natura e vo-<pb xlink:href="020/01/2042.jpg" pagenum="285"></pb>lume, ma differenti di peso, dalle quali esperienze costantemente resultava <lb></lb>andar sempre il più grave alquanto più veloce dell&#039;altro, aveva già Galileo <lb></lb>resa la ragione di questa anomalia, osservando che, se l&#039;altezza sarà grande, <lb></lb>il mezzo, che dall&#039;impeto del cadente dee essere aperto e lateralmente spinto, <lb></lb>di molto maggior pregiudizio sarà al più piccolo momento del mobile più <lb></lb>leggero, che alla maggior violenza del più grave (Alb. </s>

<s>XIII, 86). </s></p><p type="main">

<s>Quanto poi all&#039;esperienza del Renieri, con le sfere cadenti omogenee e <lb></lb>varie, non solo di peso, ma di volume, aveva pure Galileo matematica­<lb></lb>mente dimostrato come dall&#039;impedimento minore, che viene a ricever dal­<lb></lb>l&#039;aria la maggior palla, dipendesse l&#039;anticipare sopra la minore di quel <emph type="italics"></emph>buon <lb></lb>palmo.<emph.end type="italics"></emph.end> Ammesso che le resistenze sien proporzionali alle superfice, riduce­<lb></lb>vasi la dimostrazione ai principii della Geometria ” la quale c&#039;insegna che <lb></lb>molto maggior proporzione è tra la mole e la mole, nei solidi simili, che tra <lb></lb>le loro superfice ” (ivi, pag. </s>

<s>92). E però il più piccol corpo, avendo mag­<lb></lb>gior superfice del grande, a proporzion del peso diminuito, è disposto per­<lb></lb>ciò a ricevere anche maggiore impedimento. </s></p><p type="main">

<s>Nel Discorso altre volte citato si spiega intorno a ciò Galileo col Rocco <lb></lb>non men chiaramente di quel che facesse il Salviati con Simplicio. </s>

<s>“ Nei <lb></lb>corpi della medesima materia, e simili di figura, cotal impedimento non ri­<lb></lb>ceverebbe augumento nè diminuzione, per crescimento o diminuzione di <lb></lb>grandezza, tuttavolta che le lor superfice crescessero e calassero colla me­<lb></lb>desima proporzione. </s>

<s>Ma perchè le superfice dei solidi simili, no nell&#039;istessa <lb></lb>proporzione, ma in minore, cioè in subsesquialtera di quella di essi solidi, <lb></lb>crescono e calano; però, diminuendo assai più la grandezza e peso del so­<lb></lb>lido, che non dimuisce la superfice, l&#039;impedimento vien tuttavia crescendo <lb></lb>a proporzione della virtù, cioè della gravità del solido, dalla quale l&#039;impe­<lb></lb>dimento dell&#039;aderenza della superfice dee essere superato..... E così, se <lb></lb>noi anderemo suddividendo e scemando sempre con proporzion maggiore la <lb></lb>mole corporea che la superficiale, cioè diminuendo quella in sesquialtera <lb></lb>proporzione di questa, ci ridurremo ad una polverizzazione di particole così <lb></lb>minime, che la mole e gravità loro diverrà piccolissima, in comparazione <lb></lb>delle loro superfice, le quali potranno esser mille volte maggiori di quello <lb></lb>che converrebbe, acciò fusse l&#039;impedimento dell&#039;aderenza colla medesima <lb></lb>proporzione superato dalla gravità de&#039;loro corpuscoli, e queste saranno quei <lb></lb>minimi atomini della sottilissima arena, che intorbida l&#039;acqua, e non calano <lb></lb>se non in molte ore quello spazio, che un sassetto quanto una noce passa <lb></lb>in una battuta di polso ” (Alb. </s>

<s>II, 324, 25). </s></p><p type="main">

<s>Ritornando Galileo, dop&#039;avere scritto questo Discorso e dop&#039;aver già <lb></lb>pubblicati i IV dialoghi Del moto, sopra questo argomento, s&#039;incontrò in un <lb></lb>assai facile, ma elegante teorema formulato così in una sua Nota: “ D&#039;una <lb></lb>palla grande ne fo palline: la superfice delle palline tutte è tanto maggiore <lb></lb>della superfice della grande, quanto il diametro della grande supera il dia­<lb></lb>metro della piccola ” (MSS. Gal., P. V, T. IV, fol. </s>

<s>29). </s></p><p type="main">

<s>Trovasi la dimostrazione di ciò scritta in un altro foglio, applicandola <pb xlink:href="020/01/2043.jpg" pagenum="286"></pb>per più facile esempio ai cubi, piuttosto che alle sfere, e così ragionando, <lb></lb>dietro i più elementari principii della Stereometria: “ Il numero de&#039;cubi, <lb></lb>ne&#039;quali uno si risolve, è il numero delle parti, che son nel lato del cubo <lb></lb>che si risolve, come, per esempio, diviso il lato del cubo in tre o quattro <lb></lb>parti, i cubi, che da esse parti si faranno, saranno 27 o 64, ed avendo ogni <lb></lb>cubo sei quadrati in superfice, moltiplicando 27 per 6, e 64 pur per 6, <lb></lb>averemo i numeri dei quadrati, che son superfice dei detti cubi. </s>

<s>Tutte le <lb></lb>superfice dei piccoli cubi risoluti prese insieme, alla superfice del cubo grande <lb></lb>risoluto, hanno la medesima proporzione che il numero delle parti del lato <lb></lb>che si sega, all&#039;uno, e così tutte le superfice dei 27 cubi, alla superfice del <lb></lb>primo massimo cubo, saranno triple, e tutte le superfice delli 64 cubetti, <lb></lb>prese insieme, saranno quadruple della superfice dell&#039;intero gran cubo, es­<lb></lb>sendo che il lato di questo fu diviso in tre parti, per cavarne li 27 cubi, <lb></lb>ed in 4, per cavarne li cubi 64 ” (ivi, fol. </s>

<s>19). </s></p><p type="main">

<s>Doveva il teorema, nel riordinamento che meditava di dar Galileo ai <lb></lb>dialoghi Delle due nuove scienze, inserirsi nel Io stampato, là dove si trat­<lb></lb>tava dì questo soggetto, per meglio dichiarar la legge della resistenza dei <lb></lb>mezzi nelle cadute dei gravi, e già avevalo reso generale, considerando il <lb></lb>maggior cubo diviso in qualunque numero di parti, e aveva già distesa la <lb></lb>bozza del frammento dialogizzato, dove, dopo la dimostrazion del Salviati, <lb></lb>così, lodato avendo la bellezza e l&#039;utilità del teorema, dovea soggiungersi <lb></lb>dal Sagredo: “ Mi par di notare un altro modo di potere, in una sola e <lb></lb>semplice operazione, ritrovare l&#039;eccesso delle superfice di molti solidi, tra <lb></lb>di loro simili ed uguali, sopra la superfice di un solo, pur simile, ma uguale <lb></lb>a tutti quelli. </s>

<s>Questo mi par che ci venga dato dalla radice cuba del nu­<lb></lb>mero de&#039;piccoli solidi, come per esempio: la superfice di mille palline quanto <lb></lb>è maggiore della palla sola, eguale e simile a tutte quelle eguali e simili <lb></lb>tra di loro? </s>

<s>diremo esser maggiore dieci volte, per esser dieci la radice cuba <lb></lb>di mille, e dieci volte il diametro della grande conterrà il diametro della <lb></lb>piccola ” (ivi, fol. </s>

<s>38). </s></p><p type="main">

<s>Ma già nei Dialoghi stampati, anche senza queste aggiunte, si contene­<lb></lb>vano ampiamente svolte le dottrine della resistenza dell&#039;aria nei cadenti di <lb></lb>varia specie e di varia mole, che, divulgatesi nel mondo della scienza, si <lb></lb>vollero riscontrar con nuove e più diligenti esperienze. </s>

<s>Il Mersenno scriveva, <lb></lb>in proposito di queste sperimentate dottrine galileiane, al Cartesio, il quale <lb></lb>così rispondeva: “ Supponis pondus quod ex gravi materia constat, et cui <lb></lb>proinde aer minus obstat, sed omissis experimentis de turre Argentinensi, <lb></lb>illic enim neminem notum habeo, ausim asserere pondus ex gravi materia <lb></lb>constans citius descensurum quam aliud ex leviori. </s>

<s>Atque ex duobus eius­<lb></lb>dem materiae et figurae ponderibus illud celerius descensurum, quod est <lb></lb>crassius ” (Epist., P. II cit., pag. </s>

<s>301). </s></p><p type="main">

<s>Nella teoria delle resistenze, del resto, come abbiamo ora letto, appro­<lb></lb>vata, ritrovò però il Cartesio in Galileo falsa questa proposizione: “ non es­<lb></lb>sere sfera sì grande, nè di materia sì grave, che la renitenza del mezzo, <pb xlink:href="020/01/2044.jpg" pagenum="287"></pb>ancorchè tenuissimo, non raffreni la sua accelerazione, e che, nella conti­<lb></lb>nuazion del moto, non la riduca alla equabilità ” (Alb. </s>

<s>XIII, 95). Perciò, in <lb></lb>quella medesima lettera sopra citata in risposta al Mersenno, dop&#039;aver con­<lb></lb>sentito che possa dopo qualche spazio l&#039;accelerazione ridursi insensibile, di­<lb></lb>mostra il Cartesio l&#039;impossibilità di un&#039;assoluta uguaglianza matematica fra <lb></lb>gl&#039;impulsi accelerativi e le resistenze sempre crescenti, “ et proinde, così <lb></lb>conclude il discorso, celeritas semper augebitur, neque tamen unquam, ut <lb></lb>dixi, ccloritas tantum minuetur a resistentia aeris quantum accipit a gravi­<lb></lb>tate incrementi, unde liquet ex sana Malhesi falaam esse propositionem <emph type="italics"></emph>Ga­<lb></lb>lilei ”<emph.end type="italics"></emph.end> (Epist. </s>

<s>cit., pag. </s>

<s>300). </s></p><p type="main">

<s>Falsa pure fu dimostrata la proposizione di Galileo dall&#039;Huyghens e dal <lb></lb>Newton, da cui nonostante ebbero le dottrine della caduta dei gravi la loro <lb></lb>più autorevole conferma. </s>

<s>Nello scolio alla proposizione XL del III libro <emph type="italics"></emph>Dei <lb></lb>principii<emph.end type="italics"></emph.end> s&#039;hanno descritte le più diligenti esperienze intorno ai gravi, di <lb></lb>vario peso e di vario volume, lasciati andar dal comignolo della chiesa di <lb></lb>San Paolo di Londra, e nel mese di Giugno del 1710 dall&#039;Autore stesso os­<lb></lb>servati. </s></p><p type="main">

<s>I precedenti sperimentatori non avevano operato mai soli, ma sempre <lb></lb>con l&#039;aiuto di uno almeno o di più compagni, i quali non sempre erano <lb></lb>così destri, come, con quasi militar disciplina aveva il Riccioli ridotti i suoi <lb></lb>frati, che s&#039;esercitavan da lui a pronunziare in dialetto bolognese i numeri <lb></lb><emph type="italics"></emph>un, du, tri....<emph.end type="italics"></emph.end> con suono tanto veloce, da tener dietro al moto dei velo­<lb></lb>cissimi pendoli oscillanti. </s>

<s>Erano per tale esercizio divenuti sì esperti che, <lb></lb>venendosi a fare il riscontro tra le vibrazioni contate da quelli di sopra la <lb></lb>torre, e le contate in terra dallo stesso Riccioli, si trovò sempre, nei ripe­<lb></lb>tuti esperimenti “ nunquam discrimen inter nos fuisse unius integrae vi­<lb></lb>bratiunculae, quod scio vix creditum iri a quibusdam, et tamen verissime <lb></lb>ita fuisse testor ” (Almag., T. II cit., pag. </s>

<s>385). </s></p><p type="main">

<s>Non tutti potendo istituire una così disciplinata milizia, il Newton trovò <lb></lb>ingegnosamente il modo di far da sè solo, col posare i gravi, consistenti in <lb></lb>due palloni di vetro, uno pien di mercurio e l&#039;altro d&#039;aria, su un&#039;assicella <lb></lb>che, rovesciata, facevali ambedue cader nel medesimo tempo. </s>

<s>Il sostegno che, <lb></lb>venendo meno all&#039;assicella, doveva farla così traboccare, si levava di terra, <lb></lb>per mezzo di un fil di ferro, il quale, nell&#039;atto stesso che si tirava, dava <lb></lb>l&#039;andare al pendolo. </s>

<s>“ Tabula lignea ad unum eius terminum polis ferreis <lb></lb>suspendebatur, ad alterum pessulo ligneo incumbebat, et globi duo, huic ta­<lb></lb>bulae impositi, simul demittebantur, subtrahendo pessulum ope fili ferrei ad <lb></lb>terram usque demissi, et eodem temporis momento pendulum ad minuta <lb></lb>secunda oscillans, per filum illud ferreum tractum, demitteretur et oscillare <lb></lb>inciperet ” (T. III cit., pag. </s>

<s>332). </s></p><p type="main">

<s>Ripetè gli esperimenti, dal medesimo luogo, il solertissimo Hauksbec, <lb></lb>e il dì 25 Aprile del 1719 il Desaguliers glì riprese, ripetendogli il dì 14 di <lb></lb>Luglio di quel medesimo anno, secondo che apparisce dal N.o 362 delle <emph type="italics"></emph>Fi­<lb></lb>losofiche transazioni,<emph.end type="italics"></emph.end> e secondo riferisce nel sopra citato scolio il Newton, <pb xlink:href="020/01/2045.jpg" pagenum="288"></pb>il quale racconta come, per aver globi della maggior leggerezza possibile, <lb></lb>che più degli altri risentissero nel cadere gl&#039;impedimenti dell&#039;aria, s&#039;accon­<lb></lb>ciasse esso Desaguliers di propria mano vessiche suine. </s>

<s>“ Tempora autem <lb></lb>mensurabantur pendulis, ad dimidia minuta secunda oscillantibus. </s>

<s>Et eorum, <lb></lb>qui in terra stabant, unus habebat horologium cum elatere ad singula mi­<lb></lb>nuta secunda, quater vibrante. </s>

<s>Alius habebat machinam aliam affabre con­<lb></lb>structam, cum pendulo etiam ad singula minuta secunda quater vibrante. </s>

<s><lb></lb>Et similem machinam habebat unus eorum, qui stabant in summitate Tem­<lb></lb>pli. </s>

<s>Et haee instrumenta ita formabantur, ut motus eorum pro lubitu vel <lb></lb>inciperet, vel sisteretur ” (ibid., pag. </s>

<s>335). </s></p><p type="main">

<s>Veniva da tali esperienze, più precise di tutte le precedenti, che abbia <lb></lb>in tal proposito a raccontare la storia, e insuperabili forse ai futuri speri­<lb></lb>mentatori; a confermarsi direttamente il teorema del Newton, che cioè in <lb></lb>qualunque fluido <emph type="italics"></emph>caeteris paribus<emph.end type="italics"></emph.end> le resistenze son proporzionali alla den­<lb></lb>sità, e indirettamente, e per necessaria conseguenza, veniva anche insieme <lb></lb>a confermarsi il teorema di Galileo. </s></p><p type="main">

<s>Ma il teorema galileiano della caduta dei gravi si concludeva in somma <lb></lb>nella proposizione che, levato ogni impedimento, ossia nel vuoto, i corpi, di <lb></lb>qualunque mole e di qualunque specie, si vedrebbero ivi andare ugualmente <lb></lb>veloci. </s>

<s>Non era questa però altro che un&#039;induzione dall&#039;esperienze fatte in <lb></lb>mezzi via via sempre più rari, giacchè l&#039;esperienza diretta “ è forse, diceva <lb></lb>Galileo, impossibile a farsi ” (Alb. </s>

<s>II, 327): </s></p><p type="main">

<s>Occorse finalmente l&#039;invenzione della Macchina pneumatica, presentita <lb></lb>in quel <emph type="italics"></emph>forse,<emph.end type="italics"></emph.end> e il Boyle, percorrendo quasi tutto il campo della Fisica, non <lb></lb>avrebbe lasciata questa parte indietro, se avesse potuto procurarsi tubi di <lb></lb>vetro della necessaria lunghezza. </s>

<s>Il Newton in ogni modo volle, come gli <lb></lb>era possibile, fare il primo esperimento, il quale però non riuscì decisivo, <lb></lb>perchè, in altezze inferiori a un metro, si vedono anche in mezzo all&#039;aria <lb></lb>cadere in un tempo i corpi gravi e i leggeri. </s>

<s>Il Desaguliers allora attese a <lb></lb>costruire una colonna di tubi congiunti insieme con mastice, e sostenuti <lb></lb>su su da traverse di legno, fissate da una parte e dall&#039;altra, come i gradi <lb></lb>di una scala, a due staggi eretti sulla base della macchina, cosicchè potè <lb></lb>comporne un tubo andante di vetro lungo presso a quattro metri. </s>

<s>Fattosi <lb></lb>in cotesto tubo il vuoto, nel Settembre del 1717, si dette pubblico spetta­<lb></lb>colo, essendovi presente il Re, e il principe di Walles, i quali videro ma­<lb></lb>ravigliati cader nello stesso tempo una ghinea e un bocconcello di carta. </s></p><p type="main">

<s>Il Gravesande descrisse poi, con la sua solita minuziosa diligenza, una <lb></lb>macchina “ qua duo corpora in vacuo eodem momento demittuntur ” (Phy­<lb></lb>sices elem., T. II, Leidae 1748, pag. </s>

<s>618-24) perchè veramente la maggior <lb></lb>difficoltà, e la cura più necessaria per la precisione dell&#039;esperienza, consiste <lb></lb>nel lasciare i due corpi a un tempo: ciò che in questa macchina s&#039;otteneva <lb></lb>per mezzo di una morsetta, un labbro della quale essendo elastico, s&#039;allon­<lb></lb>tanava dall&#039;altro immobile, per mezzo di un filo di ferro. </s>

<s>Erano anzi que­<lb></lb>ste morsette sei, disposte intorno al centro di un esagono, per cui, fatto <pb xlink:href="020/01/2046.jpg" pagenum="289"></pb>addentare a ciascuna di esse o la medesima coppia o differenti coppie com­<lb></lb>poste di un grave e di un leggero, introdotte tutte insieme, così saldate sulla <lb></lb>lamina esagonale, nella sommità del tubo, che veniva per ciò esattamente <lb></lb>chiuso; si poteva sei volte, col non far altro che girare una vite, la quale <lb></lb>riducesse a basso ora una morsa ora un&#039;altra, ripetere sei volte lo spetta­<lb></lb>coloso esperimento. </s>

<s>Era il tubo del resto costruito di pezzi saldati insieme <lb></lb>con cera, e montato come quello del Desaguliers, benchè l&#039;altezza della <lb></lb>colonna non aggiungesse bene a due metri. </s></p><p type="main">

<s>Anche il Wolf, nel cap. </s>

<s>I del II tomo della Fisica sperimentale, dove <lb></lb>tratta <emph type="italics"></emph>De lapsu corporum gravium,<emph.end type="italics"></emph.end> descrisse un apparecchio per lasciare <lb></lb>andare a un tempo i due cadenti nel tubo vuoto; apparecchio, che consi­<lb></lb>steva in una specie di staffa, formata dalla congiunzione di due lamine ela­<lb></lb>stiche, che si potevano separare e così lasciavano in abbandono i corpi ivi <lb></lb>sopra posati, tutte le volte che, per mezzo di un filo, da potersi tirar di <lb></lb>fuori, si venivano ad allontanare gli elastri ” (Versio latina, Venetiis 1756, <lb></lb>pag. </s>

<s>15-18). </s></p><p type="main">

<s>Si tolgono ora gli sperimentatori d&#039;ogni sollecitudine col capovolgere il <lb></lb>tubo, in cui sieno stati posti gli oggettì, prima di fare il vuoto, e col chiu­<lb></lb>dere, per mezzo di una chiavetta, l&#039;ingresso all&#039;aria, la quale, riammessa a <lb></lb>poco per volta, fa notar sempre maggiore la differenza fra la caduta del corpo <lb></lb>grave e del leggero. </s>

<s>Così, dopo due secoli, la speculazione del Benedetti <lb></lb><emph type="italics"></emph>quod in vacuo corpora aequali velocitate moverentur,<emph.end type="italics"></emph.end> si riduceva al più <lb></lb>certo fatto sperimentale. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La semplice osservazione, ovvia a tutti, senz&#039;altro artificio di macchi­<lb></lb>namenti, dava certezza di questo fatto: che anche in mezzo all&#039;aria i corpi <lb></lb>gravi resi, con l&#039;andare, a vincere ogni impedimento sempre più validi, <lb></lb>tanto si vanno più affrettando nel loro moto, quanto più si dilungano dal <lb></lb>loro principio. </s>

<s>Rimaneva al Filosofo però l&#039;ufficio d&#039;investigar le cause di <lb></lb>così fatto acceleramento, intorno a che ebbero gli Antichi tanto poco ragio­<lb></lb>nevoli, e così strane opinioni, che dal troppo debole impulso ricevuto non <lb></lb>molto ebbe a progredire la scienza, quando vennesi a restaurare in tempi <lb></lb>a noi meno lontani. </s></p><p type="main">

<s>Leonardo da Vinci, com&#039;attribuiva al mezzo la causa del ritardarsi il <lb></lb>moto nei liberi cadenti, così attribuiva alla medesima causa il velocitarsi, <lb></lb>perchè il grave, diceva, mette nel cadere in circolar moto ondoso l&#039;aria, <lb></lb>attraverso alla quale egli passa “ e così, cacciando l&#039;un circolo l&#039;altro, <lb></lb>l&#039;aria, che è dinanzi al suo motore, tutta per quella linea è preparata al <lb></lb>movimento, il quale tanto più cresce, quanto se le appressa il peso che la <lb></lb>caccia. </s>

<s>Onde, trovando esso peso men resistenza d&#039;aria, con più velocità rad-<pb xlink:href="020/01/2047.jpg" pagenum="290"></pb>doppia suo corso, a similitudine della barca tirata per l&#039;acqua ” (Manuscr. </s>

<s>A <lb></lb>cit., fol. </s>

<s>43 ad t.). </s></p><p type="main">

<s>Il Tartaglia trovava quelle medesime tradizioni, ch&#039;erano venute prima <lb></lb>a inspirare la scienza di Leonardo, col quale anch&#039;egli dimostra che, messa <lb></lb>l&#039;aria sotto il cadente in moto, questa muove innanzi a sè l&#039;altr&#039;aria con­<lb></lb>tigua, “ ita ut illa mota gravitatem descendentem impediat minus, unde gra­<lb></lb>vius efficitur et cadentia amplius impelli, ita ut iam non impellantur, sed <lb></lb>etiam trahant. </s>

<s>Sicque fit ut illius gravitas tractu illorum adiuvatur, et mo­<lb></lb>tus eorum gravitate ipsius augetur, unde et velocitatem illius continue mul­<lb></lb>tiplicare constat ” (Opusc. <emph type="italics"></emph>De ponderositate<emph.end type="italics"></emph.end> cit., fol. </s>

<s>14). </s></p><p type="main">

<s>Ripete anche il Cardano, nella proposizione XIII dell&#039;<emph type="italics"></emph>Opus novum,<emph.end type="italics"></emph.end> le <lb></lb>medesime cose, dimostrando che “ in omni corpore mobili in medio partes <lb></lb>medii resistunt obviae, aliae impellunt ” (Op. </s>

<s>omnia, T. IV cit, pag. </s>

<s>477), <lb></lb>ma nella XXX e XXXI proposizione della medesima Opera comincia ad ap­<lb></lb>parire un raggio incerto di luce che consola, come dopo una notte lunga <lb></lb>l&#039;albeggiare del giorno. </s>

<s>L&#039;acceleramento non dipende solo dalla causa estrin­<lb></lb>seca del mezzo, ma dalla intrinseca della gravità, la qual causa motiva “ cum <lb></lb>sit perpetua, et a principio aeterno, quod per dicta aequaliter movet, igitur <lb></lb>motus ille fiet velocior in fine, quam in alia parte temporis ” (ibid.). Secondo <lb></lb>questo cardanico concetto il moto accelerato non sarebbe altro dunque che <lb></lb>l&#039;equabile, a cui sopraggiungon via via sempre nuovi impulsi equabilmente <lb></lb>crescenti; concetto sottilissimo e, come si diceva, albore di un nuovo sole, <lb></lb>che a quegli occhi sonnolenti però non si discerneva ancora ben dalle te­<lb></lb>nebre. </s>

<s>Di qui è che i seguaci del Cardano non seppero accoglier, delle dot­<lb></lb>trine di lui, se non quelle sole, che si confacevano meglio con le correnti <lb></lb>opinioni, come accadde a quel Principe nel dialogo del Moleto, che noi ri­<lb></lb>prendiamo in mano per seguitare a trascriverlo ai nostri Lettori: </s></p><p type="main">

<s>“ Vorrei intendere, dice l&#039;Autore a Sua Altezza, se fosse possibile di­<lb></lb>mostrare perchè il grave, quanto più discende, tanto più viene velocitandosi, <lb></lb>perchè mi pare di avere sentito dire non so che di luogo..... ” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — Dirò a V. S. intorno a ciò molte sono state le opinioni, ma le <lb></lb>famose sono l&#039;una del luogo, l&#039;altra del movimento, la terza rispetto al <lb></lb>modo, e questa par che abbia del dimostrativo. </s>

<s>Quanto al luogo, molti hanno <lb></lb>detto che il luogo è cagione della velocità del grave, e così del lieve, di­<lb></lb>cendo che il grave appetisce l&#039;andare al luogo suo, e però quanto a quello <lb></lb>più si appressa, tanto più si velocita, per arrivar più presto a quello. </s>

<s>Il che <lb></lb>non pare che possa essere vero, essendo che, quando così fosse, nel grave <lb></lb>verrebbe ad essere una virtù conoscente, cosa fuori del ragionevole. </s>

<s>L&#039;altra <lb></lb>è del movimento, perciocchè, essendo il movimento l&#039;atto del mobile, e l&#039;atto <lb></lb>essendo la perfezion della cosa, adunque, quando il grave si muove è nella <lb></lb>sua perfezione. </s>

<s>Ma chi è già in atto segue l&#039;operazione, che da quell&#039;atto <lb></lb>viene, con più facilità nell&#039;ultimo, che nel principio e nel mezzo; adunque, <lb></lb>cominciando il grave a moversi, non si muove con quella facilità, che fa dopo <lb></lb>che si sarà mosso per alquanto di spazio, essendo che viene alterandosi di <pb xlink:href="020/01/2048.jpg" pagenum="291"></pb>mano in mano, e però, quanto più si moverà, con tanto più facilità verrà <lb></lb>a moversi, e per consequente con tanto più velocità. </s>

<s>Da dove è che con più <lb></lb>velocità si move nel fine, che nel principio e nel mezzo. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ A.<emph.end type="italics"></emph.end> — Questa mi pare dimostrazione, e nella quale non è cosa al­<lb></lb>cuna da negare, e parmi simile alle ragioni, che si dicono nelle morali, che, <lb></lb>come l&#039;uomo ha acquistato l&#039;abito delle virtù, le fa senza fatica, e quanto <lb></lb>più opera, tanto più apprende. </s>

<s>È simile ancora a quello che diciamo del­<lb></lb>l&#039;intendere, che l&#039;intelletto non s&#039;affatica nell&#039;intendere, e son certo che, se <lb></lb>Franceschino che suona l&#039;organo di S. Barbera, non sentisse il travaglio del <lb></lb>corpo, che quanto più sonasse, tanto più sonerebbe: ma è forza che all&#039;ul­<lb></lb>timo le membra s&#039;affatichino. </s>

<s>Ciò non può avvenire al grave, poichè le parti <lb></lb>sue non s&#039;affaticano nel discendere, per esser cosa inanimata, e però, come <lb></lb>V. A. ha detto, e bene, più e più si velocita dall&#039;attivarsi più e più col <lb></lb>discendere, ed io quanto a me mi contenterei di questa sola ragione. </s>

<s>Ma se <lb></lb>V. A., per suo contento, vuol dire l&#039;altra, io l&#039;udirò volentieri. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ P.<emph.end type="italics"></emph.end> — Poichè si è nominata, è bene dirla, perchè acquieta non meno <lb></lb>della pur ora detta, ed è messa dal Cardano. </s>

<s>S&#039;ha da provare che il grave <lb></lb>discendendo, quanto più discende, tanto più si farà veloce nel movimento <lb></lb>suo, essendo tale il movimento suo naturale. </s>

<s>Si presuppone con verità che <lb></lb>l&#039;aria sia l&#039;impedimento al movimento del grave, poichè, come prova Ari­<lb></lb>stotile, quando dal concavo della Luna infino al centro dell&#039;universo non <lb></lb>fosse corpo di sorta alcuna, o fosse il luogo vacuo, il movimento si farebbe <lb></lb>in istante. </s>

<s>Ma quanto più l&#039;aria è presso, tanto più si condensa, e quanto <lb></lb>più è condensata, tanto più resiste al movimento del grave. </s>

<s>Adunque, men­<lb></lb>tre il grave si muove, quanto più è lontano dal luogo, dove ha da andare, <lb></lb>tanto più ha d&#039;impedimento, poichè tanto più aria ha da passare, e per con­<lb></lb>sequente condensata dal peso del grave, e però più tardi sarà il movimento. </s>

<s><lb></lb>Ma quanto più discenderà, tanto meno averà d&#039;impedimento, e però più ve­<lb></lb>loce sarà. </s>

<s>Giugniamo a questo che se noi intenderemo il grave A (fig. </s>

<s>138) <lb></lb><figure id="id.020.01.2048.1.jpg" xlink:href="020/01/2048/1.jpg"></figure></s></p><p type="caption">

<s>Figura 138.<lb></lb>nel concavo della Luna, inteso per DE, nel <lb></lb>dispiccarsi da quel luogo, intendendo il piano <lb></lb>della Terra essere FG, averà il cilindro ABH <lb></lb>d&#039;aria densa da passare, e dopo lui non <lb></lb>sarà aria che le succeda. </s>

<s>Ma quando il corpo <lb></lb>A sarà venuto nel B, oltre che averà solo <lb></lb>il cilindro BH da passare, che resisterà meno <lb></lb>di quel che faceva ABH; averà l&#039;aria AB <lb></lb>che, succedendogli per ragione del vacuo, <lb></lb>verrà con l&#039;impulso suo a velocitare il mo­<lb></lb>mento del grave. </s>

<s>E per consequente, quanto <lb></lb>più discenderà, tanto maggiore impulso <lb></lb>averà, e minore resistenza, e però maggiore sarà sempre la sua velocità. </s>

<s><lb></lb>Laddove, quando sarà in H, sarà di maggior velocità, che quandò sarà <lb></lb>in B, per le allegate ragioni. </s>

<s>E così è vero che, quanto più il grave di-<pb xlink:href="020/01/2049.jpg" pagenum="292"></pb>scenderà, con tanto maggior velocità si moverà. </s>

<s>” (MSS. Gal. </s>

<s>Appendice cit., <lb></lb>fol. </s>

<s>6-8). </s></p><p type="main">

<s>Non si decide bene dalla forma del dialogo se preferiscasi quest&#039;ultima <lb></lb>ragione del luogo, a quella precedentemente detta <emph type="italics"></emph>del modo<emph.end type="italics"></emph.end> giudicandosi <lb></lb>forse l&#039;una e l&#039;altra ugualmente dimostrativa: questa per l&#039;autorità del Car­<lb></lb>dano, ma quella per una certa ragione, che acquietava la mente, perchè ve­<lb></lb>devasi sotto una veste simbolica trasparir qualche effigie del vero. </s>

<s>Notabile <lb></lb>che, in alcuni pensieri di Galileo copiati dal Viviani, si trovi quasi il me­<lb></lb>desimo concetto espresso in forme simili a quelle del Moleto. </s></p><p type="main">

<s>“ La forza del vento, diceva, non subito imprime la massima velocità <lb></lb>alla nave, ma successivamente e con tempo, avvegnachè nel principio la <lb></lb>trovi immota, e di mano in mano opera sopra il mobile continuamente ef­<lb></lb>fetto di maggiore velocità. </s>

<s>Nè dobbiamo porre alcuna differenza tra gl&#039;im­<lb></lb>pulsi dati per intervalli, e quello che vien conferito con forza continuata, <lb></lb>perchè siccome tra gl&#039;impulsi interrotti nessuna varietà si deve considerare, <lb></lb>se talvolta in dieci minuti di tempo si dieno venti scosse o trenta, o cento <lb></lb>o mille; così neanche può cadere alcuna alterazione tra quelli e l&#039;impulso <lb></lb>continuato, non essendo questo altro che una frequentissima moltitudine di <lb></lb>spinte, cioè infinite, dentro allo stesso tempo. </s>

<s>Non basta dunque che il mo­<lb></lb>bile, il mezzo e la facoltà sieno sempre le stesse a fare l&#039;introduzione di una <lb></lb>tanta celerità, ma vi vuole, partendosi il mobile dalla quiete, una succes­<lb></lb>sione di tempo. </s>

<s>” </s></p><p type="main">

<s>“ In simil guisa penso io che proceda il negozio nei mobili naturali, <lb></lb>partendosi dalla quiete, dove da qualche impedimento erano ritenuti, purchè <lb></lb>il mezzo sia sempre lo stesso, lo stesso il mobile, e la stessa la gravità mo­<lb></lb>vente. </s>

<s>Tuttavia essa gravità sul principio opera sopra un mobile non abi­<lb></lb>tuato di moto alcuno, ma poi successivamente va operando sopra mobile <lb></lb>affetto di velocità, onde, operando essa virtù nel modo stesso, muove pìù, <lb></lb>perchè accresce moto sopra mobile, ch&#039;ella ritrova in moto. </s>

<s>” (MSS. Gal., <lb></lb>P. V, T. IV, fol. </s>

<s>14 a tergo). </s></p><p type="main">

<s>Se non era questo il formato concetto del vero, n&#039;era però il germe <lb></lb>fecondo, che ora diremo come si venisse a svolgere e ad apparire. </s>

<s>All&#039;aria, <lb></lb>infino a mezzo il secolo XVI, s&#039;attribuiva dai più il mantenersi tuttavia in <lb></lb>moto il proietto, anche uscito fuori e abbandonato dal proiiciente, ma il Car­<lb></lb>dano, esaminando nel libro <emph type="italics"></emph>De subtilitate<emph.end type="italics"></emph.end> intorno a ciò le varie opinioni, <lb></lb>per prima egli annovera quella della virtù rimasta impressa nel mobile, come <lb></lb>il calore nell&#039;acqua; “ sed nos (poi all&#039;ultimo conclude, dop&#039;avere esposte <lb></lb>altre tre varie opinioni) indigemus prima, quae est simplicissima, et etiam <lb></lb>non tantas difficultates patitur, et cum supponitur quod omne quod mo­<lb></lb>vetur ab aliquo movetur, verissimum est, sed illud quod movet est im­<lb></lb>petus acquisitus, sicut calor in aqua, qui est ibi praeter naturam ab igne in­<lb></lb>ductus, et tamen, igne sublato, manum tangentibus exurit ” (Lugduni 1580, <lb></lb>pag. </s>

<s>93). </s></p><p type="main">

<s>La divisione che si faceva tra il moto naturale e il violento, creduti <pb xlink:href="020/01/2050.jpg" pagenum="293"></pb>sull&#039;autorità di Aristotile di natura diversa, non lasciava al Cardano appli­<lb></lb>care ai cadenti il verissimo principio della forza, che rimane impressa nei <lb></lb>proietti, e benchè ne avesse pur qualche sentore, come apparisce dalla <lb></lb>XXXI proposizione, da noi poco addietro citata, pure il passo, che dovea <lb></lb>ridur la scienza alle mani di Galileo, non fu fatto da altri, prima che dal <lb></lb>Benedetti. </s>

<s>Nel cap. </s>

<s>XXIV Delle disputazioni, dop&#039;aver confutato Aristotile <lb></lb>con dir che l&#039;aria, tutt&#039;altrimenti che mantenere il moto nel proiiciente, anzi <lb></lb>glielo impedisce, “ huiusmodi, soggiunge, corporis separatim a primo mo­<lb></lb>vente velocitas oritur a quadam naturali impressione, ex impetuositate re­<lb></lb>cepta a dicto mobili, quae impressio et impetuositas, in motibus rectis na­<lb></lb>turalibus, continuo crescit, cum perpetuo in se causam moventem, idest <lb></lb>propensionem eundi ad locum, et a natura assignatum habeat ” (Specul. </s>

<s><lb></lb>lib. </s>

<s>cit., pag. </s>

<s>184). </s></p><p type="main">

<s>Ecco finalmente scoperta, e rivelata la vera causa fisica dell&#039;accelerarsi <lb></lb>i cadenti, ne&#039;quali riman la virtù della gravità impressa, dopo il principio <lb></lb>del moto, come riman la virtù del proiiciente impressa tuttavia nel proietto. </s>

<s><lb></lb>Aristotile dunque, così prosegue il Benedetti a spiegare il suo pensiero, non <lb></lb>doveva dire che, quanto più s&#039;avvicina il corpo al termine <emph type="italics"></emph>ad quem,<emph.end type="italics"></emph.end> ma <lb></lb>piuttosto che, quanto più si dilunga dal termine <emph type="italics"></emph>a quo,<emph.end type="italics"></emph.end> tanto più cadendo <lb></lb>si fa veloce, “ quia tanto maior fit semper impressio, quanto magis move­<lb></lb>tur naturaliter corpus, et continuo novum impetum recipit, cum in se mo­<lb></lb>tus causam contineat, quae est inclinatio ad locum suum eundi, extra quem <lb></lb>per vim consistit ” (ibid.). </s></p><p type="main">

<s>Chi dubitasse ancora se quei primi scritti galileiani <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> siano ve­<lb></lb>ramente, come noi gli qualificammo, esercitazioni sopra i libri del Benedetti, <lb></lb>può con facilità persuadersene, rileggendo quel capitolo. </s>

<s>“ In quo causa ac­<lb></lb>celerationis motus naturalis in fine, in medio affertur ” (Opere, ediz. </s>

<s>naz. </s>

<s><lb></lb>cit., pag. </s>

<s>315-23) che è un lungo e luminoso commento delle parole ulti­<lb></lb>mamente citate dal libro <emph type="italics"></emph>Delle disputazioni.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La quiete del grave fuori del centro è una violenza, secondo il Bene­<lb></lb>nedetti, simile a quella fatta allo stesso grave, che la mano o la fionda git­<lb></lb>tano in su, dilungandolo dal suo centro, cosicchè i due moti di scesa e di <lb></lb>salita, benchè in apparenza contrarii, dipendono dalla medesima causa, e <lb></lb>nell&#039;uno e nell&#039;altro è della naturalità e della violenza la medesima pro­<lb></lb>porzione. </s>

<s>In piena conformità con le quali speculazioni scriveva Galileo: <lb></lb>“ Io non credo che voi fuste renitenti a concedermi che l&#039;acquisto dei gradi <lb></lb>di velocità del sasso, cadente dallo stato di quiete, possa farsi col medesimo <lb></lb>ordine, che la diminuzione e perdita dei medesimi gradi, mentre da virtù <lb></lb>impellente fusse ricacciato in su alla medesima altezza ” (Alb. </s>

<s>XIII, 158). <lb></lb>Conseguiva di qui che un tal grave “ non persista per verun tempo quanto <lb></lb>in alcun medesimo grado di velocità ” (ivi) e che l&#039;accelerazione dipenda <lb></lb>dall&#039;essere la virtù impressa superata e vinta dalla gravità prevalente: che <lb></lb>sono i principii da Galileo premessi alla dimostrazion della legge, secondo <lb></lb>la quale si fa la detta accelerazione rispetto agli spazii e ai tempi. </s>

<s>La grande <pb xlink:href="020/01/2051.jpg" pagenum="294"></pb>scoperta scaturiva dalle medesime fonti, come vedremo, dop&#039;averne ricer­<lb></lb>cati e brevemente corsi i sotterranei diverticoli. </s></p><p type="main">

<s>I più Antichi, per l&#039;insufficienza dei sensi a giudicare la proporzion <lb></lb>degli spazii, in moti tanto veloci, e per la mancanza dei necessari strumenti, <lb></lb>non ebbero forse speranza di ritrovar la legge dell&#039;acceleramento dei gravi. </s>

<s><lb></lb>I naturali effetti della percossa incominciaron poi a ingerir nell&#039;animo qual­<lb></lb>che lusinga perchè, vedendosi per esperienza che quanto un grave cade più <lb></lb>d&#039;alto, produce tanto più valido colpo, e sembrando assai verosimile che, <lb></lb>rimanendosi la gravità la stessa, si dovesse alla sola velocità la maggior forza <lb></lb>acquistata; fu pensato che questa potess&#039;essere di quella stessa velocità la <lb></lb>più giusta misura. </s>

<s>S&#039;informano a così fatti pensieri in ogni modo quelle <lb></lb>proposizioni intorno ai moti accelerati, che primo venne in pubblico a di­<lb></lb>mostrar nella sua <emph type="italics"></emph>Nuova scientia<emph.end type="italics"></emph.end> il Tartaglia. </s></p><p type="main">

<s>“ El si suppone, egli dice, che il corpo ugualmente grave vada più ve­<lb></lb>loce, dove fa, ovvero faria, per comun sentimento, maggiore effetto in un <lb></lb>resistente. </s>

<s>— Quanto più un grave, egualmente grave, verrà da grande altezza <lb></lb>di moto naturale, tanto maggiore effetto farà in un resistente ” (In Vene­<lb></lb>tia 1537, fol. </s>

<s>11 a tergo). </s></p><p type="main">

<s>Date queste definizioni e fatte queste ipotesi, passa l&#039;Autore a dimo­<lb></lb>strar le due seguenti proposizioni, nelle quali si conclude insomma tutta la <lb></lb>nuova scienza dei moti accelerati. </s>

<s>È la prima proposizione così formulata: <lb></lb>“ Ogni corpo ugualmente grave nel moto naturale, quanto più el se anderà <lb></lb>aluntanando dal suo principio, ovvero approprinquando al suo fine, tanto <lb></lb>più anderà veloce ” (ivi, fol. </s>

<s>12), e la seconda: “ Tutti li corpi egual­<lb></lb>mente gravi, simili ed eguali, dal principio delli loro movimenti naturali si <lb></lb>partiranno da egual velocità, ma giongendo al fine di tali lor movimenti, <lb></lb>quello, che avrà transito per più lungo spazio, anderà più veloce ” (ivi, <lb></lb>fol. </s>

<s>13 a t.). </s></p><p type="main">

<s>Che siano le velocità proporzionali agli spazii fu creduto, come vedemmo, <lb></lb>anche da Leonardo da Vinci, il quale propose quella sua esperienza della <lb></lb>tavoletta lutata, da ritenere in sè impressi i globi cadenti nelle loro varie <lb></lb>stazioni. </s>

<s>Benchè si comprenda come non si potesse un tale strumento far a <lb></lb>nessun più esperto sperimentatore rivelator fedele de&#039;ricercati effetti natu­<lb></lb>rali, non si sa però se si volgesse Leonardo a fare esperienze della percossa, <lb></lb>che all&#039;ingegno fecondamente inventivo di lui si sarebbero presentate a fare <lb></lb>in varie maniere, come per esempio deducendo la proporzion della forza <lb></lb>dall&#039;intensità del suono, dallo stritolamento, dalle ripercussioni e da simili <lb></lb>altri effetti, che si sogliono variamente produrre dai varii corpi percossi. </s>

<s>Ma <lb></lb>com&#039;era possibile a ritrovar le misure proporzionali tra il fragore prodotto <lb></lb>o il numero de&#039;frantumi, in che riducesi per esempio un piatto di porcel­<lb></lb>lana, sotto i colpi di una palla di piombo lasciata ora cader da un&#039;altezza, <lb></lb>ora da un&#039;altra doppia o tripla? </s>

<s>S&#039;intende come la difficoltà dovess&#039;essere, <lb></lb>a qualunque arte sperimentale, specialmente a que&#039;tempi, insuperabile, ben­<lb></lb>chè non si creda da noi fosse stato per sfuggire alla diligenza di Leonardo <pb xlink:href="020/01/2052.jpg" pagenum="295"></pb>l&#039;osservazione del fatto, che cioè i frantumi di una sfera di argilla secca, <lb></lb>per esempio, o di un vuoto globo di vetro, venuti dall&#039;altezza di venti metri, <lb></lb>fanno segno d&#039;esser l&#039;effetto di un colpo qualche cosa più del doppio di <lb></lb>quello, dai medesimi corpi risentito nel cader dall&#039;altezza di soli dieci metri. </s></p><p type="main">

<s>Tanto in qualunque modo lusingava la semplicità della serie dei numeri <lb></lb>naturali, assegnata per legge agl&#039;incrementi degli spazii, e tanto verosimile <lb></lb>appariva essere gli effetti delle percosse proporzionali alle altezze, che nei <lb></lb>primi anni del secolo XVII si trovò sedotto da una tal fallacia anche Gali­<lb></lb>leo, il quale pubblicamente confessò essergli da principio sembrata cosa da <lb></lb>non si mettere in dubbio “ che quel grave, che viene dall&#039;altezza di sei <lb></lb>braccia, non abbia e percota con impeto doppio di quello, che ebbe, sceso <lb></lb>che fu tre braccia, e triplo di quello che ebbe alle due, e sescuplo dell&#039;avuto <lb></lb>nello spazio di uno ” (Alb. </s>

<s>XIII, 161). Cosicchè, dietro questi fatti speri­<lb></lb>mentali creduti verissimi, ebbe anch&#039;egli, insieme con tutti gli altri, a de­<lb></lb>finire: “ Moto uniformemente accelerato esser quello, nel quale la velocità <lb></lb>andasse crescendo, secondo che cresce lo spazio che si va passando ” (ivi). </s></p><p type="main">

<s>Ora è da veder come Galileo riuscisse felicemente il primo a scoprir <lb></lb>la fallacia, che si conteneva in questa definizione, argomentando dalle pro­<lb></lb>prietà de&#039;moti uniformi, benissimo conosciute anco agli Antichi, e dimo­<lb></lb>strate da Archimede nel libro Delle spirali. </s>

<s>Resultando da cosi fatte propo­<lb></lb>sizioni com&#039;avendosi le velocità proporzionali agli spazii i tempi sono uguali, <lb></lb>si scopriva l&#039;addotta definizione falsa e impossibile, quanto che il moto si <lb></lb>faccia in un istante, come Galileo stesso dimostrava col seguente evidentis­<lb></lb>simo ragionamento: “ Quando le velocità hanno la medesima proporzione <lb></lb>che gli spazii passati o da passarsi, tali spazii vengono passati in tempi eguali. </s>

<s><lb></lb>Se dunque le velocità, con le quali il cadente passò lo spazio di quattro brac­<lb></lb>cia, furon doppie delle velocità, con le quali passò le due prime braccia (sic­<lb></lb>come lo spazio è doppio dello spazio) adunque i tempi di tali passaggi sono <lb></lb>uguali. </s>

<s>Ma passare il medesimo mobile le quattro braccia e le due nell&#039;istesso <lb></lb>tempo non può aver luogo, fuor che nel moto istantaneo, e noi vediamo che <lb></lb>il grave cadente fa suo moto in tempo, ed in minore passa le due braccia, <lb></lb>che le quattro; adunque è falso che la velocità sua cresca come lo spazio ” <lb></lb>(ivi, pag. </s>

<s>161, 62). </s></p><p type="main">

<s>Scopertasi così la fallacia, e l&#039;impossibilità della proposizion del Tarta­<lb></lb>glia e di tutti coloro, che tenevano insiem con lui essere ne&#039;cadenti le ve­<lb></lb>locità proporzionali agli spazii, è ammirabile la facilità e la prontezza, con la <lb></lb>quale, applicando Galileo ai teoremi dei moti equabili le dottrine del Bene­<lb></lb>detti, si trovò in mano la vera legge dei moti accelerati. </s>

<s>Se i tempi sono <lb></lb>eguali, le velocità stanno come gli spazi, e se le velocità sono uguali, gli <lb></lb>spazi stanno come i tempi. </s>

<s>Se sono gli spazi uguali, le velocità son recipro­<lb></lb>che dei tempi: essendo poi gli spazi diversi, hanno questi la ragion compo­<lb></lb>sta delle velocità, e dei tempi passati. </s></p><p type="main">

<s>Queste quattro proposizioni, dimostrate da Galileo nel I libro Dei mo­<lb></lb>vimenti locali con gli antichi processi archimedei, si deducono a colpo d&#039;oc-<pb xlink:href="020/01/2053.jpg" pagenum="296"></pb>chio, facendo uso dei simboli algebrici, dalle due equazioni V=S/T, <emph type="italics"></emph>v=s/t,<emph.end type="italics"></emph.end><lb></lb>intendendovi per V, <emph type="italics"></emph>v<emph.end type="italics"></emph.end> due diverse velocità, come per S, <emph type="italics"></emph>s,<emph.end type="italics"></emph.end> e per T, <emph type="italics"></emph>t<emph.end type="italics"></emph.end> due <lb></lb>spazi, e due tempi diversi. </s>

<s>D&#039;immediata conclusione di qui è pure la pro­<lb></lb>porzione S:<emph type="italics"></emph>s<emph.end type="italics"></emph.end>=V.T:<emph type="italics"></emph>v.t,<emph.end type="italics"></emph.end> che rende dimostrato il teorema IV Dei moti <lb></lb>equabili, intorno al quale Galileo così meditava: Secondo la dottrina del Be­<lb></lb>nedetti il moto accelerato non è altro che lo stesso moto equabile, <emph type="italics"></emph>qui con­<lb></lb>tinuo novum impetum recipit.<emph.end type="italics"></emph.end> Or se fosse vero questo supposto, che cioè <lb></lb>gl&#039;impeti o le velocità crescono come i tempi, ne conseguirebbe che gli spazi <lb></lb>sarebbero proporzionali ai quadrati dei tempi. </s></p><p type="main">

<s>Facendo uso de&#039;simboli algebrici, noi vediamo di una tal conseguenza <lb></lb>la dimostrazione immediata, sostituendo la ragione di T:<emph type="italics"></emph>t<emph.end type="italics"></emph.end> a quella di V:<emph type="italics"></emph>v<emph.end type="italics"></emph.end><lb></lb>nella proporzione ultimamente scritta, la quale vien perciò a trasformarsi in <lb></lb>quest&#039;altra S:<emph type="italics"></emph>s<emph.end type="italics"></emph.end>=T2:<emph type="italics"></emph>t<emph.end type="italics"></emph.end>2. </s>

<s>Ma Galileo, senza simboli, ragionava allo stesso <lb></lb>modo in quest&#039;altra forma, che il Viviani, nella sua nativa semplicità, ci <lb></lb>conservò trascritta: “ Quando la velocità è l&#039;istessa ed uniforme, gli spazi <lb></lb>passati hanno fra loro la medesima proporzione dei tempi, e quando il tempo <lb></lb>è lo stesso, e le velocità differenti, gli spazi passati son fra di loro come esse <lb></lb>velocità. </s>

<s>Quando dunque la velocità crescesse secondo la proporzione del­<lb></lb>l&#039;allungamento del tempo, gli spazi passati crescerebbero con doppia pro­<lb></lb>porzione di quella che cresce il tempo ” (Alb. </s>

<s>XIV, 322). Ebbe poi lo stesso <lb></lb>argomento più nobile forma nel III dialogo Delle due nuove scienze, dove <lb></lb>così concludesi la proposizione II: “ Verum, in quarta propositione primi <lb></lb>libri, demonstratum est mobilium, aequabili motu latorum, spatia peracta <lb></lb>habere inter se rationem compositam ex ratione velocitatum, et ex ratione <lb></lb>temporum. </s>

<s>Hic autem ratio velocltatum est eadem cum ratione temporum; <lb></lb>ergo ratio spatiorum peractorum dupla est ratione temporum, quod erat de­<lb></lb>monstrandum ” (Alb. </s>

<s>XIII, 168, 69). </s></p><p type="main">

<s>Intorno al nuovo teorema, così con inaspettata facilità dimostrato, non <lb></lb>sarebbe da metter dubbio, quando fosse stato vero il supposto del Bene­<lb></lb>detti, il qual supposto sembrava dall&#039;altra parte a Galileo assai conforme <lb></lb>con gl&#039;istituti della Natura, in tutte le altre sue ammirabili operazioni, “ in <lb></lb>quibus exarandis uti consuevit mediis primis, simplicissimis, facillimis ” (ivi, <lb></lb>pag. </s>

<s>154). Volle nonostante averne il parere del Sarpi, a cui così scriveva di <lb></lb>Padova, il dì 16 Ottobre del 1604: “ Ripensando circa le cose del moto, nelle <lb></lb>quali, per dimostrare gli accidenti da me osservati, mi mancava principio <lb></lb>totalmente indubitabile, da poter porlo per assioma, mi son ridotto ad una <lb></lb>proposizione, la quale ha molto del naturale e dell&#039;evidente, e questa sup­<lb></lb>posta dimostrò poi il resto: cioè gli spazi passati dal moto naturale essere <lb></lb>in proporzione doppia dei tempi, e per conseguenza gli spazi passati in tempi <lb></lb>eguali essere come i numeri impari ab unitate, e le altre cose. </s>

<s>Il principio <lb></lb>è questo: che il mobile naturale vada crescendo di velocità con quella pro­<lb></lb>porzione, che si discosta dal principio del suo moto..... Averò caro che <lb></lb>V. S. M. R. lo consideri un poco, e me ne dica il suo parere ” (Alb. </s>

<s>VI, 24, 25). </s></p><pb xlink:href="020/01/2054.jpg" pagenum="297"></pb><p type="main">

<s>Qualunque si fosse il parere del Sarpi, il più autorevole giudice nono­<lb></lb>stante, trattandosi di un fatto, era l&#039;esperienza, alla quale non mancò di ri­<lb></lb>correre Galileo, sperando di ritrovare a&#039;suoi dubbi definitiva risoluzione. </s>

<s>La <lb></lb>via più diretta sarebbe stata quella di osservare, nella successione dei tempi, <lb></lb>gli spazi passatì, mentre un grave liberamente scende lungo le mura di qual­<lb></lb>che alta torre, ma la prospettiva facilmente inganna l&#039;osservatore, se non <lb></lb>essendo l&#039;altezza tale, da poter la virtù del mobile vincere le resistenze, non <lb></lb>è l&#039;occhio così disposto “ ut angulorum disparitate minime decipiatur ” <lb></lb>(Alb. </s>

<s>XI, 53). E perchè trovava Galileo difficile il sodisfare a così fatte co­<lb></lb>modità, pensò di attendere ad altre esperienze, le quali, benchè per una via <lb></lb>meno diretta, lo conducessero al fine desiderato. </s>

<s>E per prima cosa gli oc­<lb></lb>corse di rivolgersi ad esaminare gli effetti della percossa, ma l&#039;ebbe a tro­<lb></lb>vare implicata in insuperabili difficoltà e aver gli effetti di lei piuttosto pro­<lb></lb>porzione con l&#039;infinito. </s></p><p type="main">

<s>Tornò allora col pensiero a que&#039;piani inclinati, che aveva dianzi trovati <lb></lb>così comodi, quando trattavasi di dimostrare che corpi di qualunque mole e <lb></lb>di qualunque specie vanno ugualmente veloci, perchè, mentre da una parte <lb></lb>essi gravi così lentamente scendendo ricevono dall&#039;aria minore impedimento, <lb></lb>danno dall&#039;altra tutto l&#039;agio all&#039;osservatore di esaminare, in tempi tanto più <lb></lb>lunghi, le proporzioni degli spazi passati. </s>

<s>Disposto perciò un regolo lungo <lb></lb>dodici braccia, con una delle sue estremità elevata un braccio o due sul <lb></lb>piano dell&#039;orizzonte, e per diminuire l&#039;attrito incollatavi sopra una carta pe­<lb></lb>cora bene stirata, vi lasciava scendere una perfetta sfera di bronzo, e per <lb></lb>via di una clessidra a acqua “ esaminando il tempo di tutta la lunghezza <lb></lb>col tempo della metà, e con quello di due terzi o dei tre quarti, o in con­<lb></lb>clusione con qualunque altra divisione, per esperienze ben cento volte re­<lb></lb>plicate (afferma così Galileo) sempre s&#039;incontrava gli spazi passati esser tra <lb></lb>di loro come i quadrati dei tempi ” (Alb. </s>

<s>XIII, 172). </s></p><p type="main">

<s>Chiudesi la descrizione dell&#039;esperienza col dire che “ tali operazioni <lb></lb>molte e molte volte replicate giammai non differivano di un notabile mo­<lb></lb>mento ” (ivi, pag. </s>

<s>173), ciò che noi c&#039;induciamo a credere difficilmente, <lb></lb>con buona pace di Galileo, sì rispetto alla misura degli spazi, passati sul <lb></lb>regolo con resistenze sempre difformi, sì rispetto alla misura dei tempi, presa <lb></lb>con strumenti tanto imperfetti, e quando ancora s&#039;ignoravan le leggi del­<lb></lb>l&#039;efflusso dei liquidi dai fori dei vasi. </s>

<s>Vero è bene che, secondo osserva il <lb></lb>Wolf, essendosi scelta <emph type="italics"></emph>una gran secchia,<emph.end type="italics"></emph.end> “ tempus a corpore labento in­<lb></lb>sumptum, admodum parvum, aqua ad modicam altitudinem interea fidit, <lb></lb>proindeque res perinde se habuit, ac si in vase ad eamdem semper altitu­<lb></lb>dinem aqua mansisset, et invariata celeritate iugiter effluxisset ” (Physica <lb></lb>experim., Vol. </s>

<s>II, Venetiis 1756, pag. </s>

<s>2): vero è bene che, secondo udiremo <lb></lb>dire tra poco allo stesso Galileo, si pesava l&#039;acqua <emph type="italics"></emph>con una bilancia così <lb></lb>esatta, che tirava ad un sessantesimo di grano,<emph.end type="italics"></emph.end> ma come computare le <lb></lb>perdite per evaporazione, per aderenza alle pareti dei vasi, e per tanti altri <lb></lb>accidenti dovuti al visco del liquido, e alle cause capillari? </s>

<s>Eppure dovevano <pb xlink:href="020/01/2055.jpg" pagenum="298"></pb>tali minime cause concorrere efficacemente in alterar la misura di que&#039;mi­<lb></lb>nimi tempi, ciò che ben riconosciuto da que&#039;due valorosi sperimentatori che <lb></lb>furono il Ricci e il Torricelli, gli fece restar muti innanzi al Mersenno, il <lb></lb>quale diceva “ esser difficilissimo il certificarsi dell&#039;esattezza dell&#039;esperienza <lb></lb>fatta da Galileo, e riferita a c. </s>

<s>175 del suo libro Del moto ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XLII, fol. </s>

<s>116). </s></p><p type="main">

<s>Si poteva il pericolo manifesto d&#039;incorrere in simili inesattezze dir con <lb></lb>dolce lusinga di averlo superato a parole, come fa in questo dialogo il Sal­<lb></lb>viati, il quale s&#039;era nonostante, nell&#039;altro Dialogo, già tradito, quando si <lb></lb>volle cimentare coi fatti. </s>

<s>Ivi, per confondere i Peripatetici, si proponeva di <lb></lb>trovare il preciso tempo della caduta di una palla di artiglieria dall&#039;orbe <lb></lb>lunare; tempo che, conosciutasi la distanza dalla Luna a noi, e trovato per <lb></lb>esperienza il tempo, che impiegò il mobile a passare uno spazio dato, si de­<lb></lb>terminava facilmente in numeri, supposta, come da Galileo si credeva, la <lb></lb>gravità costante, applicandovi la nuova legge scoperta dei moti accelerati. </s>

<s><lb></lb>Ora l&#039;esperienza, dice il Salviati stesso nel II dialogo Dei due massimi si­<lb></lb>stemi, di averla fatta, e, avendola anche più volte replicata, di aver sempre <lb></lb>trovato che una palla di cento libbre “ scende dall&#039;altezza di cento braccia <lb></lb>in cinque minuti secondi d&#039;ora ” (Alb. </s>

<s>I, 246). </s></p><p type="main">

<s>Non dicendosi però il modo come l&#039;operazione fu fatta, si credè da <lb></lb>tutti, specialmente prima di aver letta l&#039;esperienza descritta nel III dialogo <lb></lb>Delle due nuove scienze, che avesse Galileo adoperato il pendolo, per la mi­<lb></lb>sura dei tempi, e che avesse direttamente osservati gli spazi nelle libere ca­<lb></lb>dute verticali. </s>

<s>Fu tra coloro, che ingerirono una tale opinione, il Riccioli, <lb></lb>il quale, attendendo nel 1634 in Ferrara a fare insieme col Cabeo espe­<lb></lb>rienze intorno alle cadute dei gravi, credè di averne ricavata la legge na­<lb></lb>turale che vadano gl&#039;incrementi degli spazi in serie continuamente tripla, <lb></lb>cioè come i numeri 1, 3, 9, 27, ecc. </s>

<s>Non aveva però letti ancora i dialoghi <lb></lb>Dei due massimi sistemi, proibiti dalla sacra Congregazione dell&#039;Indice, ma, <lb></lb>avutane poi nel 1640 licenza, vi trovò, per quegl&#039;incrementi degli spazi, <lb></lb>formulata una legge alquanto diversa, da lui creduta semplicemente speri­<lb></lb>mentale, e ch&#039;era quella della serie de&#039;numeri impari <emph type="italics"></emph>ab unitate.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Stava incerto in quale dei due resultati sperimentali consistesse l&#039;er­<lb></lb>rore, quando s&#039;abbattè a leggere di quella palla di artiglieria di cento lib­<lb></lb>bre, che passa le cento braccia in cinque minuti secondi. </s>

<s>Si risovvenne al­<lb></lb>lora che uno de&#039;suoi globi di argilla era sceso dai merli della torre degli <lb></lb>Asinelli, cioè per braccia 187, in quattro minuti secondi e venti terzi, “ cer­<lb></lb>tusque eram in mei temporis numeratione nullum sensibilem errorem fuisse ” <lb></lb>(Almag. </s>

<s>novum, T. II cit., pag. </s>

<s>386), per cui concluse dover esser senza <lb></lb>dubbio l&#039;errore nelle esperienze di Galileo. </s>

<s>Avrà egli, incominciò allora a <lb></lb>ripensare fra sè il Riccioli, sbagliato Galileo nell&#039;osservare gli spazi o nel <lb></lb>misurare i tempi? </s>

<s>Gli pareva per verità difficile che si dovesse una palla <lb></lb>di cento libbre portare così per gusto sulla cima di un&#039;alta torre, e che si <lb></lb>potesse di lassù maneggiare con la destrezza necessaria, per la precisione <pb xlink:href="020/01/2056.jpg" pagenum="299"></pb>dell&#039;esperienza, ed essendo, anche per le grandi città, così fatte torri assai <lb></lb>rare, avrebbe dovuto Galileo nominar quella, ch&#039;ei trovò meglio accomodata <lb></lb>al bisogno. </s>

<s>Pure, non passando per la mente al Riccioli il possibile uso dei <lb></lb>piani inclinati, non seppe rimoversi dal suo primo supposto, che cioè fossero <lb></lb>quelle galileiane osservazioni fatte nelle cadute perpendicolari, le quali, per­<lb></lb>ciocchè sembravano men difficili a contrassegnar lungo il muro della torre <lb></lb>secondo i vari intervalli, di quel che non fosse difficile aggiustar le lun­<lb></lb>ghezze ai pendoli; al tempo di questi, “ non exacto ad primi mobilis tem­<lb></lb>pus, et fixarum transitum per medinm coeli ” (ibid.), volle esso Riccioli at­<lb></lb>tribuir piuttosto gli sbagli nelle esperienze di Galileo. </s></p><p type="main">

<s>I dialoghi Delle due nuove scienze, attentamente considerati, avrebbero <lb></lb>potuto servire all&#039;Autore dell&#039;Almagesto nuovo di commento, per fargli in­<lb></lb>tendere perchè Galileo non nominasse la torre, che non era necessaria, e <lb></lb>come si potesse con facilità, e senza punto pregiudicare alla precisione delle <lb></lb>esperienze, far uso di una palla di cento libbre. </s>

<s>Avrebbe congetturato in­<lb></lb>somma che quella palla di ferro si faceva, in una comoda stanza a pian ter­<lb></lb>reno, su un lungo regolo leggermente inclinato, risalir, per poi lasciarla <lb></lb>scendere, con tal debole impulso, da non eccedere, benchè così grave di cento <lb></lb>libbre, le forze muscolari di un Filosofo. </s></p><p type="main">

<s>Dal tempo delle scese del grave lungo il piano inclinato si poteva ar­<lb></lb>gomentare il tempo della scesa nel perpendicolo, o per via del teorema terzo <lb></lb>del terzo dialogo Delle due nuove scienze (Alb. </s>

<s>XIII, 179) o anche meglio, <lb></lb>per via di un altro teorema, che, sebben non si trovi fra gli altri dimo­<lb></lb>strato nel dialogo ora detto, formulavasi così dallo stesso Galileo nel suo <lb></lb>primo trattato manoscritto: “ Si ex eodem puncto horizontis ducatur per­<lb></lb>pendiculus et planum inclinatum, et in plano inclinato sumatur quodlibet <lb></lb>punctum, a quo in plano perpendicularis linea usque ad perpendiculum pro­<lb></lb>trahatur; lationes in parte perpendiculi, inter horizontem <lb></lb>et occursum perpendicularis intercepta, et in parte plani <lb></lb>inclinati inter eamdem perpendicularem et horizontalem <lb></lb>intercepta, eodem tempore absolvuntur ” (MSS. Gal., P. V, <lb></lb>T. II, fol. </s>

<s>180). </s></p><p type="main">

<s>S&#039;immagini essere AC (fig. </s>

<s>139) la lunghezza del de­<lb></lb>clivio sul quale sia stato trovato scendere un grave in un <lb></lb><figure id="id.020.01.2056.1.jpg" xlink:href="020/01/2056/1.jpg"></figure></s></p><p type="caption">

<s>Figura 139.<lb></lb>tempo già misurato: per sapere a qual punto, pur par­<lb></lb>tendosi da C, sarebbe lo stesso grave sceso nel perpendi­<lb></lb>colo in quel medesimo tempo, “ tirate, insegna così a fare <lb></lb>il Salviati al Sagredo, da A la perpendicolare sopra la CA, <lb></lb>prolungando essa e la CB fino al concorso in D: quello <lb></lb>sarà il punto cercato ” (Alb. </s>

<s>I, 32). </s></p><p type="main">

<s>Questo solo senz&#039;altro sarebbe stato sufficiente per computare il tempo, <lb></lb>che spenderebbe una palla di artiglieria a scendere infino a noi dal mondo <lb></lb>della Luna, ma Galileo, per pigliare a fondamento della sua costruzione un <lb></lb>dato sperimentale più specioso, volle ridurre la distanza DC alle cento brac-<pb xlink:href="020/01/2057.jpg" pagenum="300"></pb>cia, o sia per far credere di essere veramente salito a quell&#039;altezza, o sia <lb></lb>per frugar più vivamente l&#039;animo di coloro, che dovevano esser curiosi di <lb></lb>saper com&#039;avesse fatto a indovinare con tanta precisione in quanto tempo <lb></lb>un grave scende giù da un campanile, senz&#039;esserne mai salito in cima a <lb></lb>farne le prove. </s>

<s>Comunque sia, trovatosi T, tempo della discesa per la lun­<lb></lb>ghezza perpendicolare CD; il tempo incognito X della discesa per le cento <lb></lb>braccia, essendo gli spazi come i quadrati dei tempi, veniva dato dall&#039;equa­<lb></lb>zione DC:T2=100:X2=T2.100/DC, ossia X=T.√100/DC, che Galileo, <lb></lb>come udimmo, trovò uguale a cinque minuti secondi. </s></p><p type="main">

<s>Il Riccioli, persuaso che la scoperta della legge dell&#039;incremento degli <lb></lb>spazi, secondo la serie dei numeri impari, fosse il frutto dell&#039;esperienza; era <lb></lb>alieno dall&#039;indovinar che per tali vie indirette si fosse condotto Galileo a <lb></lb>sciogliere il suo dinamico problema, com&#039;era alieno dal creder che, per mi­<lb></lb>surare i tempi, seguitasse a far uso della Clessidra, all&#039;imperfezion della <lb></lb>quale, e non ai male aggiustati pendoli, progettati da Galileo stesso, ma non <lb></lb>saputi ridurre alla pratica, si dee principalmente l&#039;esorbitante errore del­<lb></lb>l&#039;aver egli fatto penar cinque interi secondi un grave a scender per sole <lb></lb>cento braccia. </s>

<s>E perchè alieni dal creder così son pur anche coloro, i quali <lb></lb>fanno Galileo inventor del pendolo misuratore del tempo, lasceremo, a per­<lb></lb>suadergli meglio del loro inganno, le congetture, per venire alla certezza <lb></lb>dei fatti. </s></p><p type="main">

<s>Leggendo il Baliani il II dialogo Dei due massimi sistemi, era entrato <lb></lb>in gran curiosità di sapere com&#039;avesse fatto Galileo a trovar quelle cento <lb></lb>braccia in cinque secondi. </s>

<s>Credè anch&#039;egli, come il Riccioli, che avesse os­<lb></lb>servate la cadute dirette, e che ne avesse misurato il tempo col pendolo, ma <lb></lb>non essendone certo, interrogò Galileo stesso, il quale indugio a rispondere, <lb></lb>come vedremo in altra occasione, sette anni, e finalmente, nel dì primo di <lb></lb>Agosto del 1639, rispondeva alle richieste dell&#039;amico, le quali si riducevano <lb></lb>a due: al tempo della discesa per le cento braccia, e al saper qual parte <lb></lb>sia questo tempo di un giorno sidereo. </s>

<s>“ Quanto alla prima operazione, dice <lb></lb>Galileo, la scesa di quella palla, che io fo scendere per quel canale, ad ar­<lb></lb>bitrio nostro inclinato, ci darà tutti i tempi, non solo delle cento braccia, <lb></lb>ma di qualsivoglia altra quantità di caduta perpendicolare, atteso che, co­<lb></lb>m&#039;ella medesima sa e dimostra, la lunghezza del detto canale, o vogliamo <lb></lb>dire piano inclinato, è media proporzionale tra la perpendicolare elevazione <lb></lb>di detto piano, e la lunghezza di tutto lo spazio perpendicolare, che nel <lb></lb>medesimo tempo si passerebbe dal mobile cadente ” (Lettere, Pisa 1864, <lb></lb>pag. </s>

<s>41). </s></p><p type="main">

<s>Alla seconda richiesta rispondeva Galileo proponendo l&#039;uso dei pendoli, <lb></lb>difficile a ridursi in pratica, perchè supponeva fosse ritrovato il numero <lb></lb>delle vibrazioni, fatte da un pendolo di qualunque lunghezza in 24 ore si­<lb></lb>deree, ond&#039;è che soggiungeva così Galileo stesso, riconoscendo non esser <lb></lb>quello altro che un bel progetto: “ Vero è che noi pofremo passare a più <pb xlink:href="020/01/2058.jpg" pagenum="301"></pb>esatte misure con avere veduto ed osservato qual sia il flusso dell&#039;acqua per <lb></lb>un sottile cannello, perchè, raccogliendo ed avendo pesata quanta ne passa <lb></lb>v. </s>

<s>g. </s>

<s>in un minuto, potremo poi, col pesare la passata nel tempo della scesa <lb></lb>per il canale, trovare l&#039;esattissima misura e quantità di esso tempo, serven­<lb></lb>doci massime di una Bilancia così esatta, che tira ad un sessantesimo di <lb></lb>grano ” (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Resi oramai certi che i congetturati processi di Galileo sono i veri, si <lb></lb>vede da qual radice dovessero inevitabilmente provenire gli errori, ma si <lb></lb>aggiungeva di più, contro la desiderata precisione dell&#039;esperienza, l&#039;uso dei <lb></lb>piani inclinati. </s>

<s>Il Riccioli non volle lasciare indietro nemmeno questa classe <lb></lb>di esperimenti, e ai gradi di una scala di pietra, AD (fig. </s>

<s>140) alto sul pa­<lb></lb>vimento undici once e mezzo di piede romano antico, AE, alto un piede, <lb></lb>dieci once e mezzo, AF, alto due piedi e 50 once, appoggiava ora un ca­<lb></lb><figure id="id.020.01.2058.1.jpg" xlink:href="020/01/2058/1.jpg"></figure></s></p><p type="caption">

<s>Figura 140.<lb></lb>nale, ora un regolo lungo 35 piedi, e per quello <lb></lb>faceva scendere l&#039;acqua, e per questo corpi di <lb></lb>varia specie, come globi di legno e di argilla. </s>

<s><lb></lb>L&#039;acqua, nelle tre varie disposizioni del regolo <lb></lb>in DC, EC, FC, lo passava in 15″, 40tʹ; 9, 10; <lb></lb>6, 40: il globo di legno, nelle tre simili di­<lb></lb>sposizioni, passava il regolo in 18″, 0tʹ; 11, <lb></lb>0; 8, 10, e il globo di argilla in 19″, 0tʹ; <lb></lb>12, 0; 8, 59. Ora è facile argomentare di qui <lb></lb>al notabile indugio prodotto dagli attriti, vedendosi l&#039;acqua, che ne risente <lb></lb>meno, scendere assai più veloce. </s>

<s>Che se il globo di argilla, benchè più <lb></lb>grave, procedeva nonostante men frettoloso, dipendeva, dice il Riccioli, uni­<lb></lb>camente da ciò, “ quia fricatione magis continua descendebat per canalem, <lb></lb>et ligneus saltitando sua levitate ulterius promovebatur ” (Almag. </s>

<s>novum, <lb></lb>T. II cit., pag. </s>

<s>393). </s></p><p type="main">

<s>Se dunque Galileo trovò che una palla di artiglieria scende cento brac­<lb></lb>cia in cinque secondi, mentre si sa che ella la scenderebbe in qualche cosa <lb></lb>meno di tre secondi e mezzo, s&#039;intende da che dovesse dipender l&#039;errore, <lb></lb>che, in computo così sottile, è da dire esorbitante. </s>

<s>E perchè l&#039;esorbitanza, <lb></lb>concorrendovi le medesime cause, doveva pure ritrovarsi ne&#039;risultati del­<lb></lb>l&#039;esperienza descritta nel III dialogo Delle due nuove scienze, dicano dun­<lb></lb>que i nostri Lettori qual fede sia da dare allo stesso Galileo, quando volle <lb></lb>asserir, là, che gli spazi passati dalla palla di bronzo rispondevano esatta­<lb></lb>mente ai quadrati dei tempi. </s>

<s>Di non esser creduto se l&#039;aspettava egli stesso, <lb></lb>e che facendone altri esperienze più diligenti avrebbero trovato falso il suo <lb></lb>detto. </s>

<s>Si contentava perciò di aver proposto innanzi a chi avesse saputo bene <lb></lb>usarlo un bello artificio, “ il quale, scriveva al Baliani, penso che ella sti­<lb></lb>merà squisitissimo, ancorchè poi, volendo sperimentare se quello che io <lb></lb>scrissi delle cento braccia in cinque secondi sia vero, lo trovasse falso, per­<lb></lb>chè, per manifestare la estrema gofferia di quegli, che scriveva ed assegnava <lb></lb>il tempo della caduta della palla d&#039;artiglieria dall&#039;orbe lunare, poco importa <pb xlink:href="020/01/2059.jpg" pagenum="302"></pb>che i cinque minuti delle cento braccia siano o no giusti ” (Lettere cit., <lb></lb>pag. </s>

<s>43). </s></p><p type="main">

<s>Ecco, dal loro proprio Autore, qualificata l&#039;indole delle esperienze ga­<lb></lb>lileiane, nel descriver le quali si può dir veramente, come disse in altro <lb></lb>proposito Stefano Gradi, ch&#039;egli parlò da poeta. </s>

<s>Il fondamento della verità <lb></lb>era per Galileo nella Matematica, e per sempre meglio confermarla invo­<lb></lb>cava la Geometria, dalla quale, dopo quelle prime rivelazioni che s&#039;è detto <lb></lb>di sopra, incominciano a pigliar forma i nuovi teoremi. </s>

<s>Il moto però, come <lb></lb>ha leggi sue proprie, così ha proprii i principii, dal congiungere i quali con <lb></lb>quelli della Geometria riuscì Galileo, come da fecondo connubio, a far na­<lb></lb>scere una Scienza nuova. </s>

<s>È uno de&#039;più fondamentali, tra que&#039;meccanici prin­<lb></lb>cipii, e de&#039;più necessarii a condurre le nuove dimostrazioni, quello così detto <lb></lb>dell&#039;inerzia, intorno a che, prima di proseguire più oltre, ha da fare una <lb></lb>breve sosta il passo frettoloso della nostra Storia. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il Newton poneva per terza definizione al primo libro De&#039;principii ma­<lb></lb>tematici di Filosofia naturale che fosse nella materia insita una virtù di re­<lb></lb>sistere, per la quale ciascun corpo, quanto è in sè, persevera nel suo primo <lb></lb>stato o di quiete o di moto uniformemente diretto. </s>

<s>“ Unde etiam vis insita <lb></lb>nomine significantissimo <emph type="italics"></emph>Vis inertiae<emph.end type="italics"></emph.end> dici possit ” (Editio cit., pag. </s>

<s>4). Il <lb></lb>corpo dunque non esercita questa forza, che per resistere alle mutazioni di <lb></lb>stato, a cui tenterebbe di ridurlo qualche forza straniera, ond&#039;è un tale <lb></lb>esercizio tutt&#039;insieme resistenza e impeto. </s></p><p type="main">

<s>L&#039;aver trovato il nome da dare alla cosa, valse al Newton per una sco­<lb></lb>perta, che gli si attribuì facilmente, quando, dietro una tanta autorità, di­<lb></lb>venne fra&#039;Matematici quella frase di un uso comune. </s>

<s>Accennarono poi alcuni <lb></lb>eruditi che l&#039;invenzione risaliva al Cartesio, e avrebbero più giustamente <lb></lb>dovuto avvertire che su un tal principio d&#039;inerzia era fondata la dimostra­<lb></lb>zione data da Galileo della legge dei moti accelerati. </s>

<s>Chiunque però ha senno <lb></lb>s&#039;avvedrà facilmente come, trattandosi non di un fatto fisico, ma di un con­<lb></lb>cetto, che trovò nel Newton una definizione appropriata agli instituti mate­<lb></lb>matici della sua Filosofia, non poteva non essere quel concetto più antico <lb></lb>del Cartesio e di Galileo. </s>

<s>La prima indole sua metafisica vale a confermar­<lb></lb>gli una tale nota di antichità, perchè dal desiderio, innato in ogni creatura, <lb></lb>di conservarsi nella sua propria esistenza, presero i Filosofi uno de&#039;princi­<lb></lb>pali argomenti a dimostrare l&#039;immortalità dell&#039;anima umana. </s>

<s>Vollero dire <lb></lb>alcuni che fosse questo sentimento della nostra immortalità, e gli sperimen­<lb></lb>tati istinti della conservazione della propria vita negli animali, che fecero <lb></lb>anche alla materia bruta attribuire un sentimento simile e un simile istinto, <lb></lb>ma risolverono altri sapientemente la questione, risalendo alla Causa prima, <pb xlink:href="020/01/2060.jpg" pagenum="303"></pb>la quale a ogni creato effetto, insieme con l&#039;essere, partecipa anche le virtù <lb></lb>necessarie per conservarsi nell&#039;esistenza. </s></p><p type="main">

<s>Imbevute le menti di così fatti principii di Filosofia universale, si ap­<lb></lb>plicarono dai Matematici, per tacito consenso, alla particolare scienza del <lb></lb>moto, intantochè, a mezzo il secolo XVI, era così ben chiaro e così ben per­<lb></lb>suaso dover un corpo messo in moto perseverare in esso, che si proponeva <lb></lb>al Benedetti a risolvere il seguente quesito: “ An motus circularis alicuius <lb></lb>molae molendinariae, si super aliquod punctum quasi mathematicum quie­<lb></lb>sceret, posset esse perpetuus, cum aliquando esset mota, supponendo ettam <lb></lb>eandem esse perfecte rotundam et levigatam ” (Specul, lib. </s>

<s>cit., pag. </s>

<s>285). <lb></lb>Si rispondeva non poter essere un tal moto perpetuo, e neanco lungamente <lb></lb>duraturo, perchè, oltre alla resistenza dell&#039;aria ci è la violenza fatta alle <lb></lb>parlicelle materiali, che compongono il corpo, alle quali particelle repugna <lb></lb>il moto circolare e vertiginoso, essendo loro naturale inclinazione l&#039;andar <lb></lb>per linea retta. </s>

<s>“ Unde tanto magis contra suammet naturam volvuntur, ita <lb></lb>ut secundum naturam quiescant, quia cum eis proprium sit, quando sunt <lb></lb>motae, eundi recta, quanto violentius volvuntur, tanto magis una resistit <lb></lb>alteri, et quasi retro revocat eam quam antea reperitur habere ” (ibid.). </s></p><p type="main">

<s>In un&#039;altra Lettera al medesimo Paolo Capra, che gli avea proposto <lb></lb>questo primo quesito, torna il Benedetti sullo stessso argomento, applicando <lb></lb>la forza d&#039;inerzia, non a soli i moti violenti ma altresi ai naturali, d&#039;onde <lb></lb>venne Galileo scorto a ritrovare la prima dimostrazione geometrica dei moti <lb></lb>accelerati, come vedremo or ora, dop&#039;avere in uno sguardo comprese quelle <lb></lb>vie, che conducono a diritto sulle soglie della Filosofia neutoniana. </s></p><p type="main">

<s>Galileo dunque, secondo l&#039;opinione oramai invalsa a&#039;suoi tempi, ripe­<lb></lb>teva, a proposito delle vibrazioni di un pendolo, che potrebbero perpetuarsi <lb></lb>“ e crederò, egli dice, che lo farebbero, se si potesse levare l&#039;impedimento <lb></lb>dell&#039;aria ” (Alb. </s>

<s>I, 250). Ma nella II lettera intorno alle macchie solari, ren­<lb></lb>deva anche più esplicito, e nella sua massima precisione, il concetto, così <lb></lb>scrivendo: “ Rimossi tutti gl&#039;impedimenti esterni, un grave, nella super­<lb></lb>fice sferica e concentrica della Terra, sarà indifferente alla quiete ed ai mo­<lb></lb>vimenti verso qualunque parte dell&#039;orizzonte, ed in quello stato si conser­<lb></lb>verà, nel quale una volta sarà posto, cioè, se sarà stato messo in istato di <lb></lb>quiete, quello conserverà, e se sarà posto in movimento, v. </s>

<s>g. </s>

<s>verso occi­<lb></lb>dente, nell&#039;istesso si manterrà ” (Alb. </s>

<s>III, 418): cosicchè, rimeditando esso <lb></lb>Galileo sopra la nuova legge scoperta <emph type="italics"></emph>spatia ut quadrata temporum,<emph.end type="italics"></emph.end> ne con­<lb></lb>cludeva quel che leggesi in questa nota: “ L&#039;impeto contribuito ad un mobile <lb></lb>è probabile che sia eterno, e che eternamente si moverebbe, quando il mobile <lb></lb>non avesse propensione verso alcuna parte ” (MSS. Gal., P. V, T. 4, fol. </s>

<s>29). </s></p><p type="main">

<s>In un&#039;altra nota autografa, apposta alla dimostrazion del teorema, che <lb></lb>lo spazio, passato equabilmente dal mobile con l&#039;ultimo grado di velocità <lb></lb>acquistata, è doppio del primo spazio passato dallo stesso mobile accelera­<lb></lb>tamente, partendosi dalla quiete; “ Huic demonstrationi, scrive, necessarium <lb></lb>mihi videtur ostendisse antea motum horizontalem progredi in infinitum ” <pb xlink:href="020/01/2061.jpg" pagenum="304"></pb>(MSS. Gal., P. V, T. II, fol. </s>

<s>181). Ma la dimostrazione era difficile a de­<lb></lb>dursi dai principii naturali, secondo i quali non si poteva ragionare altri­<lb></lb>menti da quel che poi fece Galileo stesso nel III dialogo Delle due nuove <lb></lb>scienze, dove tutta la dimostrazione dell&#039;eternità del moto equabile si ridu­<lb></lb>ceva a questa ragion semplicissima: “ si enim est aequabilis, non debilita­<lb></lb>tur, aut remittitur, et multo minus tollitur ” (Alb. </s>

<s>XIII, 201). </s></p><p type="main">

<s>L&#039;Aggiunti, fra le sue sollecitudini di confermare dimostrativamente le <lb></lb>dottrine galileiane, dop&#039;aver detto che ogni minima forza vale a movere un <lb></lb>sfera grave in un perfettissimo piano orizzontale, così ragionando conclude <lb></lb>un suo lemma, premesso alla soluzione di un problema, di cui a suo tempo <lb></lb>i Lettori ammireranno la novità curiosa: “ Se la forza movente sarà estrin­<lb></lb>seca, e dopo l&#039;impulso abbandona il mobile, detto mobile si moverà, rimosso <lb></lb>l&#039;impedimento del mezzo, sempre con la medesima velocità, perchè, a voler <lb></lb>che si movesse più tardi, bisognerebbe crescere la resistenza, e a voler che <lb></lb>si movesse più presto, bisognerebbe crescere l&#039;inclinazione a quel moto. </s>

<s>Ma <lb></lb>nè l&#039;una nè l&#039;altra si cresce, mentre il motore è estrinseco, e il mezzo senza <lb></lb>impedimento; adunque durerà sempre a moversi di velocità uniforme ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. 18, fol. </s>

<s>97). </s></p><p type="main">

<s>Anche il Cartesio, in una delle sue lettere al Mersenno, dop&#039;avergli <lb></lb>detto che, per dimostrar la legge dei moti accelerati, supponeva che il mo­<lb></lb>bile una volta mosso perseverasse nel suo moto, soggiungeva: “ idque in <lb></lb>Physica mea demonstraturum me spero ” (Epist., P. III cit., pag. </s>

<s>298, 99). <lb></lb>Ma poi ebbe nell<gap></gap> Metafisica invece a ricercare i principii alla sua dimo­<lb></lb>strazione, e gli ritrovò nella immutabilità di Dio e delle leggi della Natura. <lb></lb></s>

<s>“ Harum prima est unamquamque rem, quatenus est simplex et indivisa, <lb></lb>manere quantum in se est in eodem semper statu, nec unquam mutari, nisi <lb></lb>a causis externis. </s>

<s>Ita, si pars aliqua materiae sit quadrata, facile nobis per­<lb></lb>suademus illam perpetuo mansuram esse quadratam, nisi quid aliunde adve­<lb></lb>niat, quod eius figuram mutet. </s>

<s>Si quiescat, non credimus illam unquam in­<lb></lb>cepturam moveri, nisi ab aliqua causa ad id impellatur. </s>

<s>Nec ulla maior ratio <lb></lb>est, si moveatur, cur putemus ipsam unquam sua sponte, et a nullo alio <lb></lb>impeditam motum illum suum intermissuram. </s>

<s>Atque ideo concludendum est <lb></lb>id quod movetur, quantum in se est, semper moveri ” (Principia Philos., <lb></lb>Amstelodami 1650, pag. </s>

<s>51, 52). </s></p><p type="main">

<s>Chi pensi ora alla diffusione, ch&#039;ebbero questi principii di Filosofia car­<lb></lb>tesiana, concludenti in sè le tradizioni del secolo precedente, si persuaderà <lb></lb>facile di quel che si diceva, non aver cioè fatto altro il Newton che attri­<lb></lb>buire alla materia una virtù di resistere alle cause esterne, che venissero <lb></lb>à perturbarla dal suo primo stato, e dare a quella virtù il nome significan­<lb></lb>tissimo di Forza d&#039;inerzia. </s>

<s>Ond&#039;è ch&#039;essendosi dimostrato come, anche senza <lb></lb>nome distinto, era benissimo conosciuta e insegnata nel secolo XVI questa <lb></lb>proprietà della materia, è tempo che si veda quanto si giovasse Galileo di <lb></lb>così fatto insegnamento, per condur la sua prima dimostrazione geometrica, <lb></lb>e concluderne di lì le principali proprietà dei moti accelerati. </s></p><pb xlink:href="020/01/2062.jpg" pagenum="305"></pb><p type="main">

<s>Aveva il Benedetti messo innanzi così agli studiosi del suo libro Delle <lb></lb>speculazioni: “ Omne corpus grave, aut sui natura, aut vi motum, in se <lb></lb>recipit impressionem aut impetum motus, ita ut, separatum a virtute mo­<lb></lb>vente, per aliquod temporis spatium ex seipso moveatur ” (Editio cit., <lb></lb>pag. </s>

<s>286, 87), e in quest&#039;impeto rimasto nel mobile impresso riconosceva <lb></lb>la causa acceleratrice del moto. </s>

<s>Suppongasi, ragionava dietro ciò Galileo, che <lb></lb>abbia il mobile, partendosi dalla quiete in A (fig. </s>

<s>141), percorso lo spazio <lb></lb><figure id="id.020.01.2062.1.jpg" xlink:href="020/01/2062/1.jpg"></figure></s></p><p type="caption">

<s>Figura 141.<lb></lb>AB in.un primo tempo, e che, giunto in B, sia sottratto agl&#039;im­<lb></lb>pulsi continui della gravità in qualunque modo, come per esem­<lb></lb>pio rivolgendo in direzione orizzontale il suo corso. </s>

<s>Proseguirà, <lb></lb>secondo gl&#039;insegnamenti del Benedetti, il conceputo moto spon­<lb></lb>taneamente, passando uno spazio che, aggiuntovi poi quello, per <lb></lb>cui sarebbe spinto dalla propria gravità, se gli fosse rimasta im­<lb></lb>pressa, ossia se non avesse deviato dalla prima direzion perpen­<lb></lb>dicolare, dee esser nel secondo tempo necessariamente maggior che <lb></lb>nel primo. </s>

<s>Il secondo viaggio BE insomma, fatto in parte spon­<lb></lb>taneamente dal mobile, e in parte per impulso della propria gra­<lb></lb>vità, si vede dover esser necessariamente maggiore del primo AB, <lb></lb>ma Galileo voleva saper di più qual ne fosse precisamente l&#039;ec­<lb></lb>cesso. </s></p><p type="main">

<s>Il progresso fatto per solo impulso di gravità, e che vien rap­<lb></lb>presentato dalla linea continua DE, si comprende come dovess&#039;es­<lb></lb>sere uguale nel primo e nel secondo tempo, che pur si suppongono <lb></lb>uguali, ond&#039;è che tutto si riduceva a sapere la quantità dello spa­<lb></lb>zio, passato dal mobile con la spontaneità del suo moto, e che si <lb></lb>distingue con la linea BD punteggiata. </s>

<s>Per saper dunque qual <lb></lb>parte dello spazio AB sia lo spazio BD, Galileo così ragionava: <lb></lb>Partendosi dalla quiete A rappresentata da zero, suppongasi che, <lb></lb>giunto in B, abbia il mobile acquistato nel primo tempo 5 gradi <lb></lb>di velocità, cosicchè, divisa la linea AB in cinque parti, la prima <lb></lb>contenga uno spazio, la seconda due, e così di seguito in fino alla <lb></lb>quinta, che ne conterrà cinque, e saranno perciò tutti insieme gli <lb></lb>spazi 0+1+2+3+4+5=15. Ora, giunto il mobile in B, <lb></lb>si suppone che con moto uniforme prosegua spontaneamente, nel <lb></lb>secondo tempo uguale al primo, con la velocità iniziale ulterior­<lb></lb>mente acquistata uguale a 5: cosicchè i termini da sommarsi, che <lb></lb>dianzi erano sei, da zero a cinque, ora son pur sei, ma tutti eguali a 5, e <lb></lb>perciò la somma degli spazii contenuti nella linea BD sarà uguale a 30. ” E <lb></lb>perciò, così Galileo conclude il suo ragionamento, movendosi il mobile per <lb></lb>altrettanto spazio, ma con velocità equabile, e qual&#039;è quella del sommo <lb></lb>grado 5, doverà passare spazio doppio di quello, che passò nel tempo acce­<lb></lb>lerato, che cominciò dallo stato di quiete ” (Alb. </s>

<s>I, 251). </s></p><p type="main">

<s>Se dunque BD è il doppio di AB, e se DE gli è uguale, lo spazio BE, <lb></lb>passato dal mobile nel secondo tempo, sarà tre volte più grande dello spa-<pb xlink:href="020/01/2063.jpg" pagenum="306"></pb>zio AB passato nel primo. </s>

<s>Con un ragionamento simile seguitava a dimo­<lb></lb>strar Galileo che EK, KR, spazi passati dal mobile nel IIIo e nel IVo tempo, <lb></lb>erano cinque e sette volte più grandi dello spazio AB, cosicchè ne conclu­<lb></lb>deva che i ricercati eccessi stavano come la serie de&#039;numeri impari 3, 5, 7.... <lb></lb>E giacchè numerati, nella linea della caduta AR, gli spazi ordinatamente ai <lb></lb>tempi, si vede che, se alla fine del Io lo spazio è 1, alla fine del IIo è 4, <lb></lb>del IIIo è 9, del IVo è sedici; si confermava per la nuova dimostrazione quel <lb></lb>ch&#039;era riuscito Galileo a dimostrare per altre vie, che cioè crescono gli <lb></lb>spazi come i quadrati dei tempi. </s></p><p type="main">

<s>Nel 1622 il Cavalieri propose, come altrove vedemmo, il suo metodo <lb></lb>degl&#039;indivisibili a Galileo, il quale lo trovò opportunissimo a rendere anche <lb></lb>più perfette queste dimostrazioni per via geometrica, facendo rappresentare <lb></lb>gl&#039;infiniti istanti, contenuti in un tempo quanto, agl&#039;infiniti punti contenuti <lb></lb>in una linea, e gli spazi alle infinite linee di che si contenesse, secondo il Ca­<lb></lb>valieri, una superfice. </s>

<s>Perciò al Sagredo che, servendosi di numeri deter­<lb></lb>minati, avea concluso il sopra riferito ragionamento, il Salviati soggiungeva: <lb></lb>“ Voi mi avete fatto venire in mente di aggiungere qualche cosa di più, <lb></lb>imperocchè, essendo nel moto accelerato l&#039;agumento continuo, non si pos­<lb></lb>sono compartire i gradi della velocità, la quale sempre cresce, in numero <lb></lb>alcuno determinato, perchè mutandosi di momento in momento son sempre <lb></lb>infiniti: però meglio potremo esemplificare la nostra intenzione, figurandoci <lb></lb>un triangolo ” (Alb. </s>

<s>I, 251, 52). </s></p><p type="main">

<s>La dimostrazione delle proprietà dei moti accelerati riusciva, per que­<lb></lb>sta nuova via geometrica, di una facilità e di un&#039;evidenza maravigliosa, im­<lb></lb><figure id="id.020.01.2063.1.jpg" xlink:href="020/01/2063/1.jpg"></figure></s></p><p type="caption">

<s>Figura 142.<lb></lb>perocchè, figurandoci essere quel triangolo AFH (fig. </s>

<s>142) <lb></lb>si può immaginare che le parti uguali AC, CD, DE, EF, <lb></lb>prese sopra il lato AF perpendicolare, rappresentino i tempi, <lb></lb>e che le linee CG, DK, EI, FH, orizzontalmente condotte <lb></lb>parallele alla base FH, rappresentino le velocità via via <lb></lb>crescenti, per le proprietà dei triangoli simili, a propor­<lb></lb>zione dei tempi. </s>

<s>Gli spazi perciò, che si sa avere la ragion <lb></lb>composta delle velocità e dei tempi, saranno rappresentati <lb></lb>dai triangoli ACG, ADK, AEI, AFH, aventi AC, AD, AE, <lb></lb>AF per altezze, e CG, DK, EI, FH per loro respettive basi; <lb></lb>per cui, chiamandosi per brevità S, S′, S″ quegli stessi spazi, <lb></lb>o i triangoli a cui sono proporzionali, sarà S:S′:S″= <lb></lb>ACXCG:ADXDK:AEXEI, e perchè AC:AD:AE= <lb></lb>CG:DK:EI, dunque S:S′:S″=AC2:AD2:AE2, ossia gli spazi stanno <lb></lb>come i quadrati dei tempi. </s>

<s>Dai trapezi inoltre CK, DI, EH, che si potranno <lb></lb>significare per brevità con T, T′, T″, verranno rappresentati gl&#039;incrementi <lb></lb>degli spazi via via decorsi, e perchè T=3CGXCD/2, T′=5CGXDE/2, <lb></lb>T″=7CGXEF/2, e perciò T:T′:T″....=3:5:7.... </s></p><pb xlink:href="020/01/2064.jpg" pagenum="307"></pb><p type="main">

<s>Ma ascoltiamo lo stesso Galileo, il quale, prima di esporsi in pubblico, <lb></lb>s&#039;esercitava così, verso il 1622, a distendere i suoi pensieri: </s></p><p type="main">

<s>“ Io suppongo, e forse potrò dimostrarlo, che il grave cadente natu­<lb></lb>ralmente vada continuamente accrescendo la sua velocità, secondo che ac­<lb></lb>cresce la distanza dal termine onde si parti, come v. </s>

<s>g., partendosi il grave <lb></lb>dal punto A (nella precedente figura) e cadendo per la linea AB, suppongo <lb></lb>che il grado di velocità nel punto D sia tanto maggiore che il grado di ve­<lb></lb>locità in C, quanto la distanza DA è maggiore della CA, e così il grado di <lb></lb>velocità in E essere al grado di velocità in D, come EA a DA:e così in <lb></lb>ogni punto della linea AB trovarsi con gradi di velocità proporzionali alle <lb></lb>distanze dei medesimi punti dal termine A. </s>

<s>Questo principio mi par molto <lb></lb>naturale, e che risponda a tutte le esperienze, che veggiamo negli strumenti <lb></lb>e macchine, che operano percotendo, dove il percuziente fa tanto maggiore <lb></lb>effetto, quanto da più grande altezza casca, e supposto questo principio dimo­<lb></lb>strerò il resto. </s>

<s>” </s></p><p type="main">

<s>“ Faccia la linea AH qualunque angolo con la AF e per li punti, C, D, <lb></lb>E, F sieno tirate le parallele CG, DK, EI, FH:e perchè le linee FH, EI, <lb></lb>DK, CG sono tra di loro come le FA, EA, DA, CA; adunque le velocità <lb></lb>nei punti F, E, D, C sono come le linee FH, EI, DK, CG; vanno dunque <lb></lb>continuamente crescendo i gradi di velocità in tutti i punti della linea AF, <lb></lb>secondo l&#039;incremento delle parallele tirate da tutti i medesimi punti. </s>

<s>” </s></p><p type="main">

<s>“ Inoltre, perchè la velocità, con la quale il mobile è venuto da A in D, <lb></lb>è composta di tutti i gradi di velocità avuti in tutti i punti della linea AD, <lb></lb>e la velocità, con che ha passata la linea AC, è composta di tutti i gradi <lb></lb>di velocità, che ha avuto in tutti i punti della linea AC; adunque la velo­<lb></lb>cità, con che ha passata la linea AD, alla velocità, con che ha passata la <lb></lb>linea AC, ha quella proporzione che hanno tutte le linee parallele, tirate da <lb></lb>tutti i punti della linea AD, sino alla AK, a tutte le parallele tirate da tutti <lb></lb>i punti della linea AC sino alla AG, e questa proporzione è quella che ha <lb></lb>il triangolo ADK al triangolo ACG, cioè il quadrato AD al quadrato AC. ” </s></p><p type="main">

<s>“ Adunque la velocità, con che si è passata la linea AD, alla velocità <lb></lb>con che è passata la linea AC, ha doppia proporzione di quella, che ha DA <lb></lb>a CA. </s>

<s>E perchè la velocità alla velocità ha contraria proporzione di quella, <lb></lb>che ha il tempo al tempo, imperocchè il medesimo è crescere la velocità <lb></lb>che scemare il tempo;; adunque il tempo del moto in AD al tempo del moto <lb></lb>in AC ha sudduplicata proporzione di quella, che ha la distanza AD alla di­<lb></lb>stanza AC. </s>

<s>Le distanze dunque dal principio del moto sono come i quadrati <lb></lb>dei tempi, e dividendo gli spazi passati in tempi uguali, sono come i nu­<lb></lb>meri impari ab unitate, che risponde a quello che ho sempre detto, e con <lb></lb>esperienze osservato, e così tutti i veri si rispondono. </s>

<s>” </s></p><p type="main">

<s>“ E se queste cose son vere, io dimostro che la velocità nel moto vio­<lb></lb>lento va decrescendo con la medesima proporzione, con la quale, nella me­<lb></lb>desima linea retta, cresce nel moto naturale. </s>

<s>Imperocchè sia il principio del <lb></lb>moto violento il punto B ed il fine il termine A. </s>

<s>E perchè il proietto non <pb xlink:href="020/01/2065.jpg" pagenum="308"></pb>passa il termine A, adunque l&#039;impeto, che ha avuto in B, fu tanto, quanto <lb></lb>poteva cacciarlo fino al termine A, e l&#039;impeto, che il medesimo proietto ha <lb></lb>in F, è tanto, quanto può cacciarlo al medesimo termine A, essendo il me­<lb></lb>desimo proietto in E, D, C si trova congiunto con impeto potente a spin­<lb></lb>gerlo al medesimo termine A, nè più nè meno. </s>

<s>Dunque l&#039;impeto va giu­<lb></lb>stamente calando, secondo che scema la distanza del mobile dal termine A. </s>

<s><lb></lb>Ma secondo la medesima delle distanze dal termine A va crescendo la ve­<lb></lb>locità, quando il medesimo grave caderà dal punto A, come di sopra si è <lb></lb>supposto, e confrontato con le altre prime nostre osservazioni e dimostra­<lb></lb>zioni; adunque è manifesto quello che volevamo provare. </s>

<s>” (MSS. Gal., P. V, <lb></lb>T. II, fol. </s>

<s>128). </s></p><p type="main">

<s>Un altro confronto, fra le prime dimostrazioni date in numeri determi­<lb></lb>nati, e queste nuove condotte col metodo degli indivisibili, non fu lasciato <lb></lb>indietro da Galileo, ne&#039;<emph type="italics"></emph>Massimi sistemi,<emph.end type="italics"></emph.end> dove, dopo di aver costituito il trian­<lb></lb>golo per la scala delle velocità, suppone che il mobile, invece di partir dalla <lb></lb>quiete, movesse da A (nella solita ultima figura) con una velocità iniziale <lb></lb>AM, eguale a FH, e con quella medesima seguitasse per tutto il tempo AF. <lb></lb>È manifesto che il triangolo AFH s&#039;è raddoppiato, trasformandosi nel ret­<lb></lb>tangolo AFHN, e però “ se il mobile che cadendo si è servito dei gradi di <lb></lb>velocità accelerata, conforme al triangolo AFH, ha passato in tanto tempo <lb></lb>un tale spazio, è ben ragionevole e probabile che, servendosi delle velocità <lb></lb>uniformi, e rispondenti al parallelogrammo, passi con moto equabile, nel me­<lb></lb>desimo tempo, spazio doppio al passato dal moto accelerato ” (Alb. </s>

<s>I, 553). </s></p><p type="main">

<s>In questi dialoghi Dei due massimi sistemi la nuova Scienza galileiana <lb></lb>del moto appariva sull&#039;orizzonte, come aurora, che precedeva agli altri Dia­<lb></lb>loghi, e intanto servì quell&#039;insolito albore di scorta ai vigili e d&#039;impulso <lb></lb>agl&#039;irresoluti. </s>

<s>Fra questi è da annoverare de&#039;primi lo stesso Cavalieri, il <lb></lb>quale dalla fecondità del suo metodo ricavò un&#039;altra dimostrazione dei moti <lb></lb>accelerati, più bella di quella stessa, che avea suggerita allo stesso Galileo, <lb></lb>considerando i gradi delle velocità, piuttosto che nel triangolo, in un cir­<lb></lb>colo, il centro del quale rappresenti la quiete, e le onde concentriche, in <lb></lb>che si diffonde al largo, le varie velocità, le quali sono infinite. </s>

<s>“ Ora per­<lb></lb>chè pare impossibile, dice l&#039;Autore dello <emph type="italics"></emph>Specchio ustorio,<emph.end type="italics"></emph.end> il sommare infi­<lb></lb>nite circonferenze, io mi prevaglio dell&#039;area dello stesso cerchio, e ne cavo <lb></lb>le proporzioni delle aggregate velocità, incominciando dal centro o dalla <lb></lb>quiete, e procedendo fino alla circonferenza estrema, cioè fino al massimo, <lb></lb>avendo dimostrato io nella mia Geometria che qual proporzione hanno i cer­<lb></lb>chi fra loro, tale anco l&#039;hanno tutte le circonferenze descrittibili sopra il <lb></lb>centro dell&#039;uno, a tutte le circonferenze descrittibili sopra il centro dell&#039;al­<lb></lb>tro. </s>

<s>Perciò, se nel nostro cerchio, nel quale voglio misurare le aggregate <lb></lb>velocità con la distanza di un terzo del semidiametro, per esempio, descri­<lb></lb>verò un cerchio, la cui circonferenza mi rappresenti un tal grado di velo­<lb></lb>cità, saprò che qual proporzione ha il cerchio grande al piccolo, tale ancora <lb></lb>l&#039;averanno tutte le circonferenze concentriche del cerchio grande, a tutte le <pb xlink:href="020/01/2066.jpg" pagenum="309"></pb>circonferenze concentriche del piccolo; cioè tutti i gradi di velocità, acqui­<lb></lb>stati nel trapassare dalla quiete al grado massimo, a tutti i gradi acquistati <lb></lb>passando dall&#039;istessa quiete al grado intermedio, che abbiamo preso. </s>

<s>Ma i <lb></lb>cerchi sono tra loro come i quadrati de&#039;semidiametri, dunque anche dette <lb></lb>velocità cresceranno secondo l&#039;incremento de&#039;quadrati de&#039;semidiametri. </s>

<s>Ma <lb></lb>con qual proporzione cresce la velocità nel mobile, crescono anche li spazi <lb></lb>decorsi dall&#039;istesso mobile, com&#039;è ragionevole chi acquista altrettanta velo­<lb></lb>cità, quanta si trovava avere, guadagna ancora forza di trapassare altret­<lb></lb>tanto spazio, quanto faceva, e così nelle altre proporzioni; adunque gli spazi <lb></lb>decorsi dal mobile, nel quale si vanno aggregando le velocità, saranno come <lb></lb>i quadrati de&#039;semidiametri de&#039;cerchi, ne&#039;quali si possono considerare dette <lb></lb>velocità, cioè come i quadrati dei tempi, quali intenderemo nel semidiame­<lb></lb>tro del dato cerchio. </s>

<s>Se quello dunque si supponesse diviso in cinque parti <lb></lb>uguali, posto che il quadrato dell&#039;una di queste parti fosse uno, il quadrato <lb></lb>di due sarebbe quattro, di tre nove, di quattro sedici, e tal proporzione <lb></lb>avrebbero i cinque cerchi descritti sopra questi semidiametri, e perciò, sot­<lb></lb>traendo ciascun antecedente dal suo conseguente, resterebbono questi nu­<lb></lb>meri 1, 3, 5, 7, che mostrerebbono la progressione del minimo cerchio e <lb></lb>delli seguenti residui o armille, che ci rappresentano i gradi acquistati dal <lb></lb>mobile continuamente ne&#039;suddetti tempi eguali ” (Bologna 1650, ediz. 2

a, <lb></lb>pag. 

95-97). </s></p><p type="main">

<s>Ma non era il proposito del Cavalieri quello di trattare del moto, di cui <lb></lb>tocca incidentemente, per confermare l&#039;utilità, che potrebbe venire alla Mec­<lb></lb>canica dall&#039;applicarvi i metodi della nuova Geometria. </s>

<s>Due trattati di quella <lb></lb>Scienza, della quale s&#039;eran già ne&#039;dialoghi Dei due massimi sistemi posti i <lb></lb>principii, apparvero contemporanei a quello pubblicato da Galileo in Leyda <lb></lb>nel 1638, e son gli Autori di que&#039;trattati Del moto il nostro Giovan Batti­<lb></lb>sta Baliani, e l&#039;alemanno Giovan Marco Marci. </s>

<s>Ebbero tutt&#039;e tre i valentuo­<lb></lb>mini meriti proprii, che i giusti estimatori riconosceranno meglio dal pro­<lb></lb>gresso della nostra Storia, la quale intanto si limita qui a dire quel che <lb></lb>avessero ciascuno di proprio o di comune intorno al modo di dimostrar la <lb></lb>legge dei moti accelerati. </s></p><p type="main">

<s>Galileo, nelle due prime proposizioni del III dialogo, e nello scolio alla <lb></lb>proposizione XXIII, non segue altro metodo, che quello degl&#039;indivisibili, e <lb></lb>perciò, repudiata la prima maniera da lui tenuta avanti al 1623, cioè quando <lb></lb>ancora non aveva avuto notizia della Geometria nuova del Cavalieri, s&#039;at­<lb></lb>tenne a questa seconda, come quella, che, sostituendo il nuovo calcolo dif­<lb></lb>ferenziale, rendeva essa sola trattabile con precisione una parte della Mate­<lb></lb>matica, nella quale s&#039;introducevano gl&#039;infiniti. </s></p><p type="main">

<s>E qui non si vorrebbe da noi tornare sull&#039;odioso argomento del rim­<lb></lb>proverare l&#039;ingratitudine, con la quale Galileo rimeritò la Geometria nuova <lb></lb>dei prestati servigi, ma non si può lasciare inavvertita una cosa, necessaria <lb></lb>a intendere quel che non intesero que&#039;dotti uomini romani, presieduti da <lb></lb>Stefano Gradi, i quali, per levar di mezzo ogni occasione di accusa, e per <pb xlink:href="020/01/2067.jpg" pagenum="310"></pb>fare sparire le contradizioni, manifeste ne&#039;dialoghi Delle due nuove scienze, <lb></lb>non videro con la mente affascinata que&#039;teoremi, e que&#039;problemi, che pro­<lb></lb>cedono ivi dimostrati e risoluti con gli schietti metodi del Cavalieri. </s></p><p type="main">

<s>Sembrerebbe la cosa incredibile, se non avessimo, oltre ai recati nel <lb></lb>capitolo II, nuovi documenti di ciò, in una scrittura dello stesso Gradi, con­<lb></lb>servataci dal Viviani, l&#039;intenzione della quale scrittura rivelasi dalle prime <lb></lb>parole, con le quali incomincia: “ Videtur assignari posse non insufficiens <lb></lb>causa etiam a priori eius aequalitatis. </s>

<s>quam in motu naturaliter accelerato <lb></lb>crescentis per singula momenta velocitatis clarissimus Galieus, in egregio <lb></lb>suo de hac materia tractatu, supponit, nec alia probatione firmare videtur, <lb></lb>quam quae a convenentia quadam ac Naturae in similibus operibus consue­<lb></lb>tudine duci potest ” (MSS. Gal. </s>

<s>Disc., T. CXXXII, fol. </s>

<s>92). </s></p><p type="main">

<s>Per assegnare la causa sufficiente di quelle egualità di moto accelerato <lb></lb>prende il Gradi la linea AB (fig. </s>

<s>143), divisa in parti uguali determinate, <lb></lb><figure id="id.020.01.2067.1.jpg" xlink:href="020/01/2067/1.jpg"></figure></s></p><p type="caption">

<s>Figura 143.<lb></lb>per la scala dei tempi, secondo i quadrati de&#039;quali <lb></lb>crescon gli spazi, “ ita ut toto tempore AB spatium <lb></lb>loci confectum a dato corpore sit aequale rectangulis <lb></lb>ACD, ECF, GEH, BGI contentis a figura denticulata <lb></lb>ABL. </s>

<s>Ita sine dubio eveniret, si dicta motus velocitas, <lb></lb>in dato corpore perseverans, nonnisi per assignata in­<lb></lb>tervalla sua caperet incrementa. </s>

<s>Quod si talia intervalla <lb></lb>in eodem tempore duplo minora essent, et consequen­<lb></lb>ter prima velocitas AD duplo maior poneretur eadem <lb></lb>figura ABL, minutioribus sine dubio denticulis incisa <lb></lb>esset, et ad trianguli ABL naturam propius accederet, <lb></lb>idque semper magis ac magis ita eveniret, quo minor prima velocitas esset, <lb></lb>et quo plura adeoque breviora intervalla idem illud temporis spatium se­<lb></lb>carent ” (ivi, fol. </s>

<s>95). </s></p><p type="main">

<s>Ora, fa certo gran maraviglia che il Gradi, galileiano sì dotto, amico <lb></lb>al Viviani e a Michelangiolo Ricci estimatissimo, si mettesse a discorrere <lb></lb>così, per supplire al difetto di Galileo, il quale aveva, nella giornata II Dei <lb></lb>massimi sistemi, fatto fra il Sagredo e il Salviati discorrere in quel mede­<lb></lb>simo modo, per assegnar quella medesima causa dell&#039;equalità del moto ac­<lb></lb>celerato, che il Gradi si proponeva di assegnare a priori. </s>

<s>Anche il Sagredo <lb></lb>infatti, che determinava co&#039;numeri conseguenti dall&#039;uno al cinque le cre­<lb></lb>scenti velocità, se fosse dall&#039;aritmetica passato alla geometria, avrebbe rap­<lb></lb>presentati gli spazi col triangolo denticulato, ma il Salviati soggiungeva a <lb></lb>quel discorso che l&#039;addentellatura si viene a ridurre all&#039;uguaglianza della <lb></lb>linea AL del triangolo, non facendo crescere le velocità secondo numeri de­<lb></lb>terminati, ma secondo le infinite linee, che contessono la superfice del trian­<lb></lb>golo stesso, come insegnava a fare il Cavalieri, le nuove dottrine del quale <lb></lb>son, con sottil arte da Galileo velate di sì strano mistero, da rintuzzar l&#039;acume <lb></lb>del Gradi e de&#039;suoi amici e colleghi. </s></p><p type="main">

<s>Quale efficacia avessero propriamente le tradizioni della scienza italiana <pb xlink:href="020/01/2068.jpg" pagenum="311"></pb>sulla mente di Giovan Marco, è difficile a indovinare in scrittore, che par <lb></lb>simile a una di quelle montagne, mal discernibile ad occhio nudo nella pro­<lb></lb>spettiva aerea del lontano orizzonte. </s>

<s>Comunque sia però, dal principio che <lb></lb>la virtù locomotiva cresce in quel modo, che cresce il triangolo <emph type="italics"></emph>sibi simile <lb></lb>manens,<emph.end type="italics"></emph.end> dimostra la sua XII proposizione: “ Incrementa velocitatis ratio­<lb></lb>nem habent quam temporum quadrata ” (De proport. </s>

<s>motus cit., fol. </s>

<s>19 <lb></lb>a tergo), e pur col modesimo principio dimostra l&#039;altra proposizione XVIII: <lb></lb>“ Velocitas in fine motus, aequabili tempore, per spatium movet duplum <lb></lb>velocitatis eodem motu collectae ” (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>Ma il Baliani, seguendo altra via, che in una lettera al Castelli chiama <lb></lb>egli stesso <emph type="italics"></emph>molto stravagante,<emph.end type="italics"></emph.end> riuscì a dimostrare la medesima proposizione, <lb></lb>concludendola dalle proprietà dei pendoli di varia lunghezza. </s>

<s>“ Iam ante <lb></lb>plures annos, così ci racconta l&#039;Autore la storia di queste sue meccaniche <lb></lb>speculazioni, mihi visus sum assequi causam accelerationis motus, dum adhuc <lb></lb>mobile a motore impellitur; quia nimirum mobili moto imprimatur impetus <lb></lb>causa motus subsequentis, ex quo in secundo tempore adsunt duo motores, <lb></lb>unde est velocior, et impetus maior. </s>

<s>In tertio tempore sunt duo itidem mo­<lb></lb>tores, et alter, puta impetus maioris virtutis, unde motus adhuc celerior, et <lb></lb>ita deinceps. </s>

<s>Non vero ex hoc constabat qua proportione talis acceleratio <lb></lb>fieret. </s>

<s>Interdum, dum pendulorum motus perquirerem, praeter expectatio­<lb></lb>nem se se mihi obtulit eorum longitudines diuturnitatibus in duplicata re­<lb></lb>spondere ratione, de quo in prioris libri praefatione, ex quo demum nihil <lb></lb>minus cogitanti mihi in sexta propositione eiusdem deducere contigit mo­<lb></lb>tum tali pacto accelerari, ut in secundo tempore sit prioris triplum, in ter­<lb></lb>tio quintuplum, et deinceps iuxta numerorum imparum progressionem ” (De <lb></lb>motu natur. </s>

<s>cit., pag. </s>

<s>99). </s></p><p type="main">

<s>Per dimostrare la VI proposizione citata, e che si formula <emph type="italics"></emph>Lineae de­<lb></lb>scensus gravium, dum naturali motu perpendiculariter feruntur, sunt in <lb></lb>duplicata ratione diuturnitatum,<emph.end type="italics"></emph.end> l&#039;Autore suppone come cosa vera di fatto <lb></lb>l&#039;isacronismo dei pendoli, rimossi per qualunque ampiezza nella quarta del <lb></lb>cerchio, e principalmente ritien come certo per esperienza che “ Pendulo­<lb></lb>rum inaequalium longitudines sunt ut <lb></lb>quadrata vibrationum ” (ibid., pag. </s>

<s>15). </s></p><p type="main">

<s>S&#039;aggiungono ai supposti quattro <lb></lb>petizioni, la prima delle quali è che le <lb></lb>porzioni delle vibrazioni, fatte da due <lb></lb>pendoli di varia lunghezza, sieno in cia­<lb></lb>scuno proporzionali alle stesse vibrazioni <lb></lb>intere, a quelle cioè che farebbero per <lb></lb>tutta intera la quarta del cerchio, come <lb></lb>per esempio, se sieno due pendoli, uno <lb></lb>di lunghezza AB (fig. </s>

<s>144), l&#039;altro di <lb></lb><figure id="id.020.01.2068.1.jpg" xlink:href="020/01/2068/1.jpg"></figure></s></p><p type="caption">

<s>Figura 144.<lb></lb>lunghezza AE, chiede gli sia concesso <lb></lb>che il tempo della intera vibrazione BII <pb xlink:href="020/01/2069.jpg" pagenum="312"></pb>stia al tempo della intera vibrazione EI, come il tempo della parzial vibra­<lb></lb>zione BC sta al tempo di EF. </s>

<s>Nelle petizioni II e III vuole il Baliani che la <lb></lb>circonferenza si riguardi come un poligono di moltissimi lati, e crede non <lb></lb>doverglisi negare che, data una linea di qualunque lunghezza, non si possa <lb></lb>descrivere una circonferenza tanto ampia, che quella stessa linea non trovi <lb></lb>da rettificarsi in una qualche porzione della detta circonferenza. </s>

<s>Che se <lb></lb>questo non gli si neghi, gli verrà ultimamente concesso che i cadenti ser­<lb></lb>bino nel moto retto e nel circolare la medesima proporzione. </s>

<s>Dietro ciò, <lb></lb>ecco come facilmente il Baliani dimostra il suo teorema. </s></p><p type="main">

<s>Sieno KM, LN, nella detta figura, due spazi verticali passati da due <lb></lb>gravi ne&#039;tempi O, P: convien dimostrare essere KM:LN=O2:P2. </s>

<s>Si de­<lb></lb>scrivano le due quarte di cerchio HCB, IFE con raggi di tal lunghezza, che <lb></lb>gli archi BC, EF si possano riguardare come due linee rette uguali a KM, <lb></lb>LN, e s&#039;immagini che i gravi cadenti per queste linee siano le sfere pen­<lb></lb>dole H, I, sollevate in B, E Il tempo per BC dunque sarà O, e per EF <lb></lb>sarà P, ond&#039;è che, per la IIIa supposizione, avremo AB:AE=O2:P2. </s>

<s>Ma <lb></lb>per la somiglianza de&#039;triangoli ABC, AEF abbiamo AB:AE=BC:EF, e <lb></lb>BC=KM, EF=LN, dunque KM:LN=O2:P2, come volevasi dimo­<lb></lb>strare. </s></p><p type="main">

<s>L&#039;altra proposizione, corollario di questa, che è formulata: “ Gravia na­<lb></lb>turali motu descendunt semper velocius, ea ratione ut temporibus aequalibus <lb></lb>descendant per spatia semper maiora, iuxta proportionem quam habent im­<lb></lb>pares numeri ab unitate inter se ” (ibid., pag. </s>

<s>25); si dimostra dal Baliani <lb></lb>in modo grafico, ma evidentissimo, in questa maniera: “ Sieno le linee <lb></lb>uguali AB, BC, CD (fig. </s>

<s>145) a rappresentare i tempi uguali, e i quadrati <lb></lb><figure id="id.020.01.2069.1.jpg" xlink:href="020/01/2069/1.jpg"></figure></s></p><p type="caption">

<s>Figura 145.<lb></lb>AE, AF, AG rappresentino gli spazi. </s>

<s>Si vede <lb></lb>che al primo tempo AB corrisponde il solo qua­<lb></lb>drato AE; al secondo tempo AC corrisponde il <lb></lb>quadrato AF, composto d&#039;altri quattro più pic­<lb></lb>coli quadrati tutti uguali ad AE, e al terzo tempo <lb></lb>AD corrisponde il quadrato AG, che de&#039;quadrati <lb></lb>piccoli uguali ad AE ne comprende evidente­<lb></lb>mente nove. </s>

<s>Cosicchè, essendo 1, 2, 3.... i <lb></lb>tempi, gli spazi respettivamente passati son co­<lb></lb>me 1, 4, 9...., e perciò gli incrementi come <lb></lb>1, 3, 5...., secondo la serie de&#039;numeri impari <lb></lb>ab unitate. </s></p><p type="main">

<s>Si compiaceva seco stesso il Baliani della facilità, con la quale era riu­<lb></lb>scito a dimostrar quel medesimo di Galileo, senza farsi imitator di nessuno, <lb></lb>ma, venendo a istituire fra&#039;due Autori il confronto, troppo bene se ne ri­<lb></lb>conosceva la differenza, e quanto rimanesse indietro la fisica sperimentale <lb></lb>dell&#039;uno alla matematica rigorosa dell&#039;altro. </s>

<s>Galileo stesso, tanto più viva­<lb></lb>mente eccitato dall&#039;emulazione, ne faceva rilevare queste differenze, e ardi­<lb></lb>menti chiamava i supposti del Baliani, e le petizioni errori. </s>

<s>Di ciò scriveva <pb xlink:href="020/01/2070.jpg" pagenum="313"></pb>in una lettera al Renìeri (Campori, Carteggio eit., pag. </s>

<s>539) la quale non è <lb></lb>pervenuta alla nostra notizia, ma vi supplisce una scrittura, che il Viviani <lb></lb>fece in Arcetri, essendo ospite in casa il Maestro, che glie la dettava, e che <lb></lb>perciò si dice essere stata scritta <emph type="italics"></emph>ad mentem Galilaei.<emph.end type="italics"></emph.end> È intitolata <emph type="italics"></emph>Sopra i <lb></lb>principii del Baliani,<emph.end type="italics"></emph.end> a cui dal Censore si rivolge così il discorso: </s></p><p type="main">

<s>“ È la nostra intenzione investigare e dimostrare geometricamente ac­<lb></lb>cidenti e passioni, che accaggiono ai mobili gravi naturalmente e libera­<lb></lb>mente discendenti sopra spazi retti differenti, o di lunghezza o d&#039;inclinazione, <lb></lb>o d&#039;ambedue insieme. </s>

<s>Nel venir poi alla elezione dei principii, sopra i quali <lb></lb>deve esser fondata la scienza, prendete come chiara notizia accidenti, i quali <lb></lb>niuna connessione hanno con moti fatti sopra linee non rette, non di asse­<lb></lb>gnabile inclinazione, nè che in esse le diverse lunghezze operino quello, che <lb></lb>operano nelle linee rette, ma in tutto e per tutto cose differentissime, lo che <lb></lb>mi par grave errore, e tanto maggiore, quanto che e&#039;se ne tira dietro un <lb></lb>altro non minore. </s>

<s>Mi dichiaro: voi pigliate come principio noto e indubi­<lb></lb>tato le vibrazioni del medesimo pendolo farsi tutte sotto tempi uguali, siano <lb></lb>elle di qualsivoglia grandezza. <emph type="italics"></emph>Item<emph.end type="italics"></emph.end> supponete i tempi delle vibrazioni di <lb></lb>pendoli diseguali esser tra di loro in suddupla proporzione delle lunghezze <lb></lb>dei loro fili, assunto veramente ardito. </s>

<s>E da questo, che supponete accadere <lb></lb>nei mobili discendenti per circonferenze di cerchi, volete raccorre quello che <lb></lb>occorre nei moti retti. </s>

<s>Ma se io non erro, assai meno obliquamente si po­<lb></lb>teva ottener l&#039;intento, discorrendo così: ” </s></p><p type="main">

<s>“ La linea AB (fig. </s>

<s>146) intendasi rappresentare il filo pendente, e, <lb></lb>stando fermo il termine supremo A, intendasi il mobile posto in B dise­<lb></lb>gnare l&#039;arco del quadrante BC. Similmente, preso A<emph type="italics"></emph>b<emph.end type="italics"></emph.end> come pendolo minore, <lb></lb><figure id="id.020.01.2070.1.jpg" xlink:href="020/01/2070/1.jpg"></figure></s></p><p type="caption">

<s>Figura 146.<lb></lb>sia l&#039;arco del quadrante <emph type="italics"></emph>bc<emph.end type="italics"></emph.end> quello, che descri­<lb></lb>verebbe il mobile posto in <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> e d&#039;essi qua­<lb></lb>dranti siano le corde suttese BC, <emph type="italics"></emph>bc,<emph.end type="italics"></emph.end> ed in­<lb></lb>tendansi le tangenti orizzontali BD, <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> alle <lb></lb>perpendicolari CD, <emph type="italics"></emph>cd.<emph.end type="italics"></emph.end> Ora, essendo le due <lb></lb>declinazioni in tutto e per tutto simili, molto <lb></lb>ragionevolmente si può prendere, e come prin­<lb></lb>cipio noto supporre, che le proporzioni dei <lb></lb>moti, che accadessero farsi sopra le rette AB, <lb></lb>BC, per l&#039;arco CB, fossero le medesime, che <lb></lb>nella minor figura per le linee analoghe A<emph type="italics"></emph>b, <lb></lb>bc,<emph.end type="italics"></emph.end> onde, permutando, il moto per l&#039;arco <emph type="italics"></emph>cb,<emph.end type="italics"></emph.end><lb></lb>al moto per l&#039;arco CB abbia la medesima proporzione, che il moto per la <lb></lb>perpendicolare <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> al moto per la perpendicolare AB, onde, pigliando per <lb></lb>supposto che i tempi per gli archi siano in suddupla proporzione delle <lb></lb>lunghezze dei fili, già è manifesto che con altrettanta verità si può supporre <lb></lb>che i tempi per le perpendicolari A<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> AB siano in suddupla proporzione <lb></lb>delle lunghezze A<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> AB. </s>

<s>E così si viene a schivare la supposizione assai <lb></lb>dura, come appresso diremo, che i moti per le parti minime delli archi siano <pb xlink:href="020/01/2071.jpg" pagenum="314"></pb>come se fosser fatti per linee rette, assunto come dico assai duro, imperoc­<lb></lb>chè con gran ragione può il lettore domandare che gli sia assegnata la quan­<lb></lb>tità dell&#039;arco, che V. S. chiama minima, sicchè, per esempio, ella intenda <lb></lb>l&#039;arco esser minimo fino che non giunga alla metà di un grado. </s>

<s>Inoltre, <lb></lb>sarebbe stato necessario dichiararsi quale delle stesse linee rette si deva <lb></lb>prendere per gli archi minimi, cioè se quella, che, partendosi dal medesimo <lb></lb>punto dell&#039;arco, tocca la circonferenza, oppure la sega come corda di esso <lb></lb>arco minimo, oppure è una delle altre molte, che dal medesimo punto primo <lb></lb>possono tirarsi. </s>

<s>” </s></p><p type="main">

<s>“ Da queste molte linee pare che venga esclusa la tangente necessa­<lb></lb>riamente, imperocchè, considerando nella figura passata la tangente dell&#039;arco <lb></lb>BC nel punto B; che viene ad essere la orizzontale BD, manifesta cosa è <lb></lb>che il mobilo, posto sopra di essa, in nessuna parte si moverà, ma bene, <lb></lb>posto in qualsivoglia punto dell&#039;arco BC remoto dal B, discenderà egli in B. </s>

<s><lb></lb>Essendo dunque la discrepanza tra la tangente e l&#039;arco tanto grande, per <lb></lb>quanto appartiene al moto, quanto è differente la quiete dal moto; con poca <lb></lb>o niuna probabilità si potrà supporre che il moversi dal punto C, per la <lb></lb>tangente o per l&#039;arco, siano l&#039;istessa cosa. </s>

<s>” </s></p><p type="main">

<s>“ Ma vegghiamo un&#039;altra disparità massima. </s>

<s>Niuno negherà i moti del <lb></lb>medesimo mobile, fatti sopra piani di diversa inclinazione, esser tra di loro <lb></lb>differenti, e che in conseguenza un moto, il quale, cominciato sopra una tale <lb></lb>inclinazione debba di parte in parte trapassar sopra altrettante altre diverse <lb></lb>inclinazioni, sarà sommamente differente da quello, che sopra una stessa in­<lb></lb>clinazione deve andarsi continuando. </s>

<s>Ora, nella circonferenza del quadrante <lb></lb>CB, tante sono le diverse inclinazioni, quante le tangenti, e queste sono <lb></lb>quante i punti, cioè infinite, per lo che anco in qualsivoglia piccola parte <lb></lb>della circonferenza, siccome vi sono infiniti punti, vi sono anche infinite in­<lb></lb>clinazioni, per la mutazione delle quali non si può dire che il moto per <lb></lb>l&#039;arco possa esser simile, non che l&#039;istesso, che per una medesima inclina­<lb></lb>zione sola. </s>

<s>” (MSS. Gal., P. V, T. IV, fol. </s>

<s>36-38). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il Discorso di Galileo non sembra che fosse mandato al Baliani, a cui <lb></lb>era indirizzato, ma egli ebbe sentore di quelle censure, divulgatesi in Ge­<lb></lb>nova fra gli amici di Daniele Spinola, il quale così scriveva a Galileo stesso <lb></lb>in una sua del di 25 Marzo 1639: “ Ho da pregiarmi poi grandemente che <lb></lb>qualche pensiero, venutomi circa il libro del signor Baliani, sia stato da <lb></lb>V. S. autenticato nella lettera scritta ultimamente al p. </s>

<s>d. </s>

<s>Vincenzo, impe­<lb></lb>rocchè, tacendo del rimanente, quelle sue supposizioni mi son sempre parse <lb></lb>alquanto difficili da concedere ” (Campori, Carteggio cit., pag. </s>

<s>539). Di qui <lb></lb>si passava a fare il confronto fra i due emuli Autori della Scienza del moto, <pb xlink:href="020/01/2072.jpg" pagenum="315"></pb>e si avviliva l&#039;uno, spesso con passionato giudizio, per secondare le gloriose <lb></lb>inclinazioni dell&#039;altro. </s>

<s>Lo stesso Spinola scriveva nel seguente Agosto al me­<lb></lb>desimo Galileo: “ Veramente i supposti del signor Giovan Batista appresso <lb></lb>di ognuno han mestieri di gagliarda dimostrazione..... Or considerisi qual <lb></lb>piacere si può cavare dalle proposizioni fondate sopra di essi, le quali molti <lb></lb>stimano che non sian del tutto sue, perchè si vede di dove ponno esser <lb></lb>tolte. </s>

<s>Ma nel libro di V. S. son congiunte la chiarezza, la facilità, la novità, <lb></lb>il diletto, il profitto e la maraviglia in ogni cosa ” (ivi, pag. </s>

<s>546). </s></p><p type="main">

<s>Tale era il giudizio che sentiva di sè il Baliani fare a&#039;suoi concittadini, <lb></lb>e dovette sentir rammarico, più che delle lodi esagerate del suo rivale, delle <lb></lb>odiosità calunniose, in chi sembrava dover piuttosto inclinare alla benevo­<lb></lb>lenza. </s>

<s>Poteva consolarsi de&#039;più assennati giudizi di coloro, i quali dicevano <lb></lb>aver tenuto i due Autori due vie diverse, e ora rimanere indietro l&#039;uno, <lb></lb>ora precedere all&#039;altro; ma, vinto da un sentimento d&#039;ira vendicatrice, volle <lb></lb>con le calunnie rispondere ai calunniosi, e dire che anzi Galileo aveva preso <lb></lb>da lui, nè mancarono animi disposti ad accogliere quelle suggestioni. </s></p><p type="main">

<s>Fu tra costoro de&#039;primi il Cabeo, il quale nel suo libro primo sulla <lb></lb>Meteorologia di Aristotile si maravigliò come Galileo si fosse pubblicamente <lb></lb>vantato di essere egli venuto il primo ad annunziare al mondo la ritrovata <lb></lb>misura nell&#039;impeto dei cadenti. </s>

<s>“ Melius dixisset se nusquam legisse aut <lb></lb>scivisse ab aliquo mensuratum, nam et ego et ali mecum mensuraverant, <lb></lb>et fateor me ab ipso hoc non didicisse ” (T. </s>

<s>I cit., pag. </s>

<s>92). Intende per <lb></lb>quegli altri, ch&#039;ebbe soci nelle operazioni, il Baliani, il quale alcuni anni <lb></lb>più tardi citava questo passo del Cabeo al Mersenno, per testimoniare le sue <lb></lb>pretensioni di aver prevenuto Galileo. </s>

<s>Al quale annunzio esso Mersenno ri­<lb></lb>spondeva così con lettera del dì 25 Ottobre 1647, da Parigi: “ Ho gran <lb></lb>gusto che V. S. m&#039;abbia imparato per l&#039;ultima sua che Galileo non sia il <lb></lb>primo, che ha osservato la proporzione del moto dei corpi gravi, che ca­<lb></lb>scano giù, perchè io pubblicherò a tutti quanti che in ciò siete stato il primo <lb></lb>osservatore, come l&#039;ha confermato il P. </s>

<s>Cabeo nel luogo citato da voi nelle <lb></lb>sue <emph type="italics"></emph>Meteore ”<emph.end type="italics"></emph.end> (Baliani, Opere diverse, Genova 1666, pag. </s>

<s>10). </s></p><p type="main">

<s>Dovevano esser passati pochi anni, da che il medesimo Mersenno aveva <lb></lb>ricevuto lettere di un altro, che nella scoperta legge dei moti accelerati pre­<lb></lb>tendeva il primato su Galileo. </s>

<s>Il Cartesio infatti gli scriveva, un lunedì mat­<lb></lb>tina, che un tal D. B. era venuto a riprendersi i dialoghi Dei due massimi <lb></lb>sistemi, che gli aveva portato a leggere il sabato sera, cosicchè non potette <lb></lb>avere che per sole trent&#039;ore il libro fra le mani. </s>

<s>“ Integrum tamen evolvi.... <lb></lb>Cogitationum mearum nonnullas hic illic sparsas animadverti, atque inter <lb></lb>alias duae sunt, quas ad te scripsisse me opinor, nempe spatia, quae cor­<lb></lb>pora gravia desc<gap></gap>ndendo percurrunt, esse ad se invicem ut quadrata tem­<lb></lb>porum, quae descendendo impendunt.... altera est vibrationes eiusdem fu­<lb></lb>nis pari fere temporis spatio fieri, quamvis aliae aliis longe maiores esse <lb></lb>possint ” (Epist., P. II cit., pag. </s>

<s>219). In un&#039;altra Epistola, indirizzata pure <lb></lb>al Mersenno, accenna il Cartesio stesso a un Innominato che, se non è Ga-<pb xlink:href="020/01/2073.jpg" pagenum="316"></pb>lileo, è in ogni modo oratoriamente rivestito di un abito, che non si diffe­<lb></lb>renzia in nulla da quello di Galileo, di cui dice che “ supponit mecum id <lb></lb>quod semel moveri coepit sponte sua pergere in motu, etiam absque novo <lb></lb>impulsu, donec ab aliqua causa exteriori impediatur, et proinde corpus ali­<lb></lb>quod, semel motum in vacuo, motum iri in aeternum, sed in aere aliter se <lb></lb>res habet, propterea quod aeris resistentia eius motum paulatim minuit. </s>

<s><lb></lb>Praeterea supponit corpus aliquod gravitate sua singulis momentis deorsum <lb></lb>impelli, atque ita in vacuo celeritatem motus perpetuo augeri, secundum <lb></lb>proportionem a me antea observatam, quam illi plus decem retro annos <lb></lb>explicui, hoc enim ab eo tempore in adversariis meis notatum reperio ” <lb></lb>(ibid., pag. </s>

<s>299). </s></p><p type="main">

<s>Mancando a questa oratoria esercitazione in forma epistolare la data, <lb></lb>non è possibile assegnar l&#039;anno preciso, in cui il Cartesio notò fra&#039;suoi ri­<lb></lb>cordi l&#039;anno della scoperta, che nel libro de&#039;ricordi di Galileo, per certis­<lb></lb>simo documento, è il 1604, quando il Filosofo francese, nato nel 1596, era <lb></lb>ancora fanciullo. </s>

<s>Quelle nuove scoperte verità intorno alle leggi dei moti <lb></lb>accelerati ora le chiama il Cartesio sue <emph type="italics"></emph>cogitazioni,<emph.end type="italics"></emph.end> ora sue <emph type="italics"></emph>osservazioni,<emph.end type="italics"></emph.end><lb></lb>lasciando noi che leggiamo incerti se si tratti di matematiche speculazioni <lb></lb>o d&#039;esperienze. </s>

<s>Ma perchè a sperimentare il fatto mancava anche a lui l&#039;arte, <lb></lb>e mancavano gli strumenti, non potevano essere quelle sue altro che cogi­<lb></lb>tazioni, fondate come quelle di Galileo sul principio dell&#039;inerzia della mate­<lb></lb>ria, e sul supposto che le velocità, via via sopraggiunte al mobile, siano pro­<lb></lb>porzionali ai tempi. </s>

<s>Nella seconda infatti delle Epistole sopra commemorate <lb></lb>il ragionamento dell&#039;Autore è tale: “ Supponatur molem plumheam gravi­<lb></lb>tatis suae vi cadere, et statim, post primum quo coepit descendere momen­<lb></lb>tum, Deus totam eius gravitatem adimat, ita ut moles ista gravior non sit <lb></lb>aere aut pluma: nihilominus perget descendere in vacuo, quandoquidem <lb></lb>incoepit moveri, neque porro ratio reddi potest cur deberet quiescere..... <lb></lb>Verum non amplius augebitur eius celeritas, et si postmodum Deus ad mo­<lb></lb>mentum reddit huic moli plumbeae totam, quam ante habuerat, gravitatem, <lb></lb>et momento post eam illi iterum adimat, annon liquet secundo hoc momento <lb></lb>molem hanc plumbeam, haud minus quam primo, impulsum iri ab eadem <lb></lb>illa vi gravitatis, et proinde motus eius dupla velocitate auctus erit, idemque <lb></lb>fiet in tertio, quarto et quinto momentis? </s>

<s>” (ibid., pag. </s>

<s>298, 99). </s></p><p type="main">

<s>È questo, come dicemmo, il ragionamento medesimo, che faceva anche <lb></lb>Galileo, cosicchè ambedue i Filosofi, dai principii già posti dal Benedetti, e <lb></lb>divenuti oramai nella scientifica istituzione universali, giungevano alle me­<lb></lb>desime conclusioni: ciò che, mentre toglie da una parte ogni maraviglia <lb></lb>nata dal pensare a un fortuito incontro, fa comprender dall&#039;altra quanto <lb></lb>irragionevolmente chiamasse il Cartesio sue cogitazioni le cose lette in Ga­<lb></lb>lileo, non ripensando che, portati i semi sulle libere ali dei venti, possono <lb></lb>cader qui come là, un poco prima o un poco dopo, e benchè d&#039;una origine, <lb></lb>germogliar solitari, crescere separati e vivere sconosciuti. </s>

<s>Ma il Cartesio, che <lb></lb>presumeva di esser nato spontaneo, senza seme, e che perciò credeva di non <pb xlink:href="020/01/2074.jpg" pagenum="317"></pb>avere nessun simile a sè, chiamava sue certe virtù, ch&#039;egli stesso, e gli altri <lb></lb>ne&#039;quali s&#039;abbatteva a ritrovarle, avevano partecipate dai generanti. </s></p><p type="main">

<s>Queste frettolose considerazioni che, in universale applicate, togliereb­<lb></lb>bero via le contese del mio e del tuo, nella storia delle scoperte così fre­<lb></lb>quenti; si dovrebbero applicare, se fosse il caso, anche al Baliani. </s>

<s>Diciamo <lb></lb>se fosse il caso, perchè lo sdegnato Genovese si servì, a persuadere più fa­<lb></lb>cilmente nel Cabeo, nel Mersenno e negli altri così fatti, le sue ragioni, del­<lb></lb>l&#039;equivoco, che nasceva dal non distinguere nella caduta dei gravi le sem­<lb></lb>plici velocità osservate dalla legge delle loro proporzioni, potendo intorno a <lb></lb>quelle citar testimoni i Savonesi, i quali avevano veramente veduto cader <lb></lb>dall&#039;alto della loro rocca a scientifico esercizio, le palle dei cannoni parec­<lb></lb>chi anni prima, che si leggessero i dialoghi Dei due massimi sistemi. </s></p><p type="main">

<s>Prima però di essere entrato in queste gare, incitatovi dagli odiosi pa­<lb></lb>ragoni, e principalmente dagl&#039;ingiusti giudizi de&#039;suoi concittadini, aveva il <lb></lb>Baliani stesso confessato il vero al Castelli, raccontandogli così in una let­<lb></lb>tera da Savona, del dì 20 Febbraio 1627, com&#039;avuta da Galileo la notizia <lb></lb>che l&#039;incremento degli spazi nelle cadute naturali dei gravi è secondo la <lb></lb>serie de&#039;numeri impari, gli occorresse senz&#039;altro, per una via nuova e ina­<lb></lb>spettata, di ritrovar ora la dimostrazione: “ Facendo il trattato dei solidi, <lb></lb>così propriamente egli dice, avvenne che senza cercarla mi riuscì a parer <lb></lb>mio ben dimostrata una proposizione, per una via molto stravagante, la <lb></lb>quale il signor Galileo m&#039;avea detta per vera, senza però addurmene la di­<lb></lb>mostrazione, ed è che i corpi di moto naturale vanno aumentando la velo­<lb></lb>cità loro con la proporzione 1, 3, 5, e così in infinito ” (Alb. </s>

<s>IX, 142). </s></p><p type="main">

<s>La question del primato fra i pretendenti è così dunque definitivamente <lb></lb>decisa a favore di Galileo, alla compiuta gloria del quale rimane ancora a <lb></lb>veder come venisse finalmente a confermarsi la verità di quella legge dei <lb></lb>moti accelerati, ch&#039;egli ebbe il primo scoperta e dimostrata. </s>

<s>Non manca­<lb></lb>rono, com&#039;è da credere, nemmeno intorno a questa novità i dubbi e le con­<lb></lb>tradizioni, di alcune delle quali, come di quelle del Cabeo, ci vorremmo <lb></lb>volentieri passare, per non essere provocate che dal mal animo o dalla igno­<lb></lb>ranza. </s>

<s>Nel I libro de&#039;commentari sulla Meteorologia aristotelica fa dir l&#039;Au­<lb></lb>tore a Galileo “ velocitatem temporibus aequalibus crescere iuxta numeros <lb></lb>impares ” (T. </s>

<s>I cit., pag. </s>

<s>94) e costruendo il triangolo dimostra che invece <lb></lb>crescono come la serie de&#039;numeri naturali, non avvedendosi esser questa <lb></lb>la supposizione, che lo stesso Galileo fa, e che di lì ne conseguiva non star <lb></lb>le velocità, ma gl&#039;incrementi degli spazi come la serie de&#039;numeri impari. </s>

<s><lb></lb>A suggello poi di questa sua interpetrazione o maliziosa o ignorante, avendo <lb></lb>sotto gli occhi il triangolo, che gli rappresentava crescere ordinatamente le <lb></lb>velocità da zero a un grado determinato, dice di non sapere quanta è la <lb></lb>velocità “ qua quodlibet grave motum incipit ” e finisce col rimanere incerto <lb></lb>“ utrum possim facere triangulum velocitatis ” (ibid.). </s></p><p type="main">

<s>I dubbi, d&#039;onde aspettava la verità la sua conferma, volevan movere da <lb></lb>animi ben più retti, e da ingegni più meditativi, ai quali non potevano man-<pb xlink:href="020/01/2075.jpg" pagenum="318"></pb>car di ciò le occasioni, principalmente perchè le difficoltà di eseguirle non <lb></lb>lasciavano aver quella piena fede che bisognava nell&#039;esperienze, cosicchè <lb></lb>ai fatti della Natura s&#039;andava a ricercar la certezza nelle speculazioni della <lb></lb>Geometria. </s>

<s>Ma perchè questa stessa Geometria, benchè costituita di numeri <lb></lb>e di linee, s&#039;implicava nelle passioni della materia, non poteva perciò por­<lb></lb>gere nessun sicuro asilo alla mente, che si studiava di pellegrinare dal senso. </s>

<s><lb></lb>De&#039;penosi travagli di lei in vedersi scoperto falso quel che così confidente­<lb></lb>mente riteneva per vero, giova qui recar qualcuno de&#039;più notabili esempi, <lb></lb>il primo de&#039;quali ci si presenta nella storia, poco dopo che le nuove leggi <lb></lb>dinamiche furono annunziate nei dialoghi Dei due massimi sistemi. </s></p><p type="main">

<s>Pietro Carcavil, di Parigi, mandava a Galileo, nel Maggio dell&#039;anno 1637, <lb></lb>alcune carte di un suo amico, che non nomina, ma che sappiamo essere il <lb></lb>Fermat, il quale così, dop&#039;aver dimostrato essere un&#039;elice, e non un semi­<lb></lb>cerchio, la linea descritta dai cadenti, incominciava le censure sopra gli altri <lb></lb>teoremi galileiani: “ De linea seu helice, quam describit grave naturaliter <lb></lb>descendens secundum proportionem motus a Galilaeo assignatam, a nobis <lb></lb>multa probata sunt, sed quia accuratius perpendenti haec proportio gravium <lb></lb>naturaliter descendentium non satis patet, imo geometricis demonstrationi­<lb></lb>bus repugnare videtur, aliquam in experiendo fallaciam irrepsisse facile cre­<lb></lb>diderim. </s>

<s>Quis autem rationem sensibus non praetulerit? </s>

<s>Propositionem geo­<lb></lb>metricam huic experientiae repugnantem, praemisso postulatu, conspicemus. </s>

<s><lb></lb>Postulatum hoc sit: Nullum motum fieri absque celeritate corporis moti ” <lb></lb>(MSS. Gal., P. V, T. VII, fol. </s>

<s>98). </s></p><p type="main">

<s>Vuol da questo postulato il Fermat dimostrare esser falso quel che Ga­<lb></lb>lileo dice del mobile che, partendosi dalla quiete, acquista via via velocità, <lb></lb>mentre si muove, perchè, egli così argomenta, o si fa quell&#039;acquisto nel <lb></lb>primo istante o in tempo determinato. </s>

<s>Se nel primo istante, come dunque <lb></lb>si parte dalla quiete? </s>

<s>Se in qualche tempo determinato, perchè così e non <lb></lb>prima nè dopo? </s>

<s>E perchè da questo principio, che cioè, partendosi dalla <lb></lb>quiete per giungere a un moto determinato, passa il mobile per tutti gl&#039;in­<lb></lb>finiti gradi delle velocità intermedie, si dimostra da Galileo la proporzione <lb></lb>dei moti accelerati, ne conclude il Fermat “ non potest igitur constare Ga­<lb></lb>lilaei propositio ” (ibid.). </s></p><p type="main">

<s>Galileo rispose a queste e a simili altre difficoltà, promosse dal mede­<lb></lb>simo Censore, in una lettera, indirizzata al Carcavil stesso il dì 5 Giugno <lb></lb>di quell&#039;anno 1637, da Arcetri, e son le risposte di lui, mirabil cosa, com­<lb></lb>pendiate così in questo discorso che faceva il Cartesio in una delle sue epi­<lb></lb>stole al Mersenno: “ Quod ait Galileus corpora descendentia transire per <lb></lb>omnes tarditatis gradus, haud puto vulgo fieri, sed non esse impessibile quin <lb></lb>id fiat aliquando. </s>

<s>Aberrat vero D. </s>

<s>Fermat in argumento quo utitur ad illum <lb></lb>refellendum, cum dicit <emph type="italics"></emph>acquiritur velocitas, vel in primo instanti, vel in <lb></lb>tempore aliquo determinato,<emph.end type="italics"></emph.end> neutrum enim verum est, et utendo terminos <lb></lb>scholae dici potest quod <emph type="italics"></emph>acquiritur in tempore inadacquate sumpto.<emph.end type="italics"></emph.end> Deni­<lb></lb>que, quidquid ille dicit de gradibus celeritatis motus potest, eodem modo, <pb xlink:href="020/01/2076.jpg" pagenum="319"></pb>dici de gradibus latitudinis trianguli ABC (fig. </s>

<s>147), et tamen haud credo <lb></lb>negaturum il um quin inter punctum A et lineam BC reperiuntur latitudi­<lb></lb><figure id="id.020.01.2076.1.jpg" xlink:href="020/01/2076/1.jpg"></figure></s></p><p type="caption">

<s>Figura 147.<lb></lb>nes omnes ipsa BC minores ” (Epistol., P. II cit., pag. </s>

<s>249). </s></p><p type="main">

<s>Le censure del Fermat sulla legge galileiana de&#039;moti <lb></lb>accelerati, e le risposte di Galileo stesso e del Cartesio ri­<lb></lb>masero per qualche tempo ne&#039;privati commerci scientifici <lb></lb>di quegli Autori, cosicchè le prime delle dette censure, <lb></lb>pubblicamente note, vennero da quel Baliani, il quale ve­<lb></lb>demmo quanto si fosse compiaciuto di aver ritrovato della <lb></lb>detta legge galileiana una nuova dimostrazione. </s>

<s>Notabile <lb></lb>che poi confessasse di essersi messo a dimostrar quel teo­<lb></lb>rema, non perchè lo credesse vero, ma per emulare o per prevenire, in <lb></lb>una esercitazione geometrica, Galileo rimasto ingannato, diceva, da fallaci <lb></lb>esperienze, alle quali, chi saviamente supplisca con la ragione, troverebbe <lb></lb>non crescer veramente gli spazi secondo la serie dei numeri impari, ma se­<lb></lb>condo quella piuttosto dei numeri naturali. </s>

<s>Il discorso, che faceva il Mate­<lb></lb>matico genovese, per provare il suo assunto, si riduce al seguente. </s></p><p type="main">

<s>Sia da A (fig. </s>

<s>148) passato un mobile in E, indipendentemente dall&#039;im­<lb></lb>peto acquistato per la forza d&#039;inerzia, la quale incominci ad agire in E. È <lb></lb><figure id="id.020.01.2076.2.jpg" xlink:href="020/01/2076/2.jpg"></figure></s></p><p type="caption">

<s>Figura 148.<lb></lb>chiaro che tanto maggiori sa­<lb></lb>ranno le parti, in che s&#039;intende <lb></lb>esser diviso lo spazio AE, quanto <lb></lb>saranno più piccole. </s>

<s>Suppongasi <lb></lb>che siano dieci, e che il mobile abbia in tre tempi uguali successivamente <lb></lb>passati gli spazi AB, BC, CD. Quante, in questi spazi, si troveranno ad AE <lb></lb>particelle uguali? </s>

<s>Sarà facile a dar di ciò la risposta, sommando la serie <lb></lb>de&#039;numeri naturali da uno infino a dieci; da 11 infino a 20, e da 21 infino <lb></lb>a 30. E perchè la prima somma dà 55, la seconda 155, e la terza 255, delle <lb></lb>particelle uguali ad AE se ne conteranno in AB 55, in BC 155, in CD 255. <lb></lb>Gl&#039;incrementi dunque degli spazi AB, BC, CD staranno come 55; 155; 255, <lb></lb>ossia come 11; 31; 51, con qualche notabile differenza dalla serie de&#039;numeri <lb></lb>impari. </s>

<s>Ora, se non in dieci, ma in cento parti, dividasi lo spazio AE, si <lb></lb>troverà, come dianzi operando, contenersene in AB, di quelle centesime <lb></lb>5050; in BC 15050; in CD 25050, procedenti nella serie de&#039;numeri 101, <lb></lb>301, 501, pochissimo differente da quella de&#039;numeri impari ab unitate. </s></p><p type="main">

<s>Da un tal discorso poi il Baliani stesso trae questa conclusione: “ Au­<lb></lb>getur igitur, ni fallor, motus iuxta progressionem arithmeticam, non nume­<lb></lb>rorum imparium ab unitate hucusque creditam, sed naturalem. </s>

<s>At nihilo­<lb></lb>minus cum fere idem effectus subsequatur, ob insensibilem discrepantiam, <lb></lb>mirandum non est creditum fuisse spatia esse in duplicata ratione tempo­<lb></lb>rum, quando quidem, etiamsi verum praecise fortasse non sit, est attamen <lb></lb>adeo veritati proximum, ut veritatem in adhibitis experimentis sensus per­<lb></lb>cipere nequiverit: quamobrem excusandi sunt quicumque ita censuerunt. </s>

<s><lb></lb>Ego autem modo veritatem delitescentem detexisse spero, causam nimirum, <pb xlink:href="020/01/2077.jpg" pagenum="320"></pb>qua huiusmodi proportio emanat aperuisse, et insuper quales errores fue­<lb></lb>rint in suppositionibus et experimentis hucusque habitis, quod an re vera <lb></lb>consecutus fuerim aliorum sit iudicium ” (De motu natur. </s>

<s>cit., pag. </s>

<s>113). </s></p><p type="main">

<s>De&#039;chiamati a dare il loro giudizio alcuni, come Onorato Fabry, rispo­<lb></lb>sero stranamente che, tanto poteva esser vera l&#039;ipotesi galileiana, quanto <lb></lb>un&#039;altra diversa, ch&#039;egli stesso, il Fabry, proponeva, e secondo la quale sa­<lb></lb>rebbero gl&#039;incrementi degli spazi come la serie de&#039;numeri 4, 8, 16, 32, 64...: <lb></lb>quella, cioè l&#039;ipotesi galileiana, “ ad usum omnino adhibenda est, ” ma vo­<lb></lb>lendo ridurre il fatto alla vera causa dell&#039;accelerazione, “ mea certe, non <lb></lb>modo praeferenda est, verum etiam necessario tenenda ” (Dial. </s>

<s>physici De <lb></lb>motu Terrae, Lugduni 1665, pag. </s>

<s>68). </s></p><p type="main">

<s>Altri però di più senno, come il Mariotte, traevano dal discorso del Ba­<lb></lb>liani verissimo una conclusione affatto diversa, riducendola a confermare la <lb></lb>legge galileiana, la quale, perciocchè è solo allora esattamente dimostrabile <lb></lb>quando il tempo e lo spazio son per via degl&#039;indivisibili rappresentati dagli <lb></lb>infiniti punti di una linea, e dalle infinite linee di un triangolo; par che <lb></lb>dunque sia da tener per la più vera la serie de&#039;numeri impari, alla quale <lb></lb>tanto più ci si avvicinava, quanto più lo spazio AE, nel sopra riferito esem­<lb></lb>pio dello stesso Baliani, riducevasi in minime parti. </s></p><p type="main">

<s>Nel terzo Discorso sul moto delle acque, parte seconda, per far inten­<lb></lb>dere in che modo abbiasi a concepire l&#039;acceleramento, immagina il Mariotte <lb></lb>un leggerissimo corpo veloce, che a furia di ripetuti urti commove un pe­<lb></lb>santissimo corpo dalla sua quiete, e dice che, se al primo urto passa una <lb></lb>linea, al secondo ne passerà due, al terzo tre, e così di seguito secondo la <lb></lb>serie de&#039;numeri naturali. </s>

<s>“ Or si l&#039;on prend plusieurs nombres de suite, <lb></lb>commençant à l&#039;unité, comme 1, 2, 3, 4, etc., iusques a 20, et q&#039;on compte <lb></lb>20 momens; la somme de cette progression sera 210; et si on compte 40 mo­<lb></lb>mens, selon la meme progression iusques a 40, la somme de ces derniers <lb></lb>nombres sera 820, qui est quadruple au peu pres de 210, somme des 20 pre­<lb></lb>miers nombres, mais a l&#039;infini cette derniere somme sera quadruple de la <lb></lb>premiere precisement, parce que la proportion du defaut diminue touiurs: <lb></lb>ce que Galileo a aussi conclu dans son Traite de l&#039;acceleration du mouve­<lb></lb>ment des corps qui tombent ” (Oeuvres, T. II a l&#039;Haye 1740, pag. </s>

<s>393). </s></p><p type="main">

<s>Doveva esser questa pure la conclusione del discorso del Baliani, e se <lb></lb>fu irragionevolmente diversa, è da attribuire in gran parte al bisogno sen­<lb></lb>titosi in que&#039;tempi, in cui mancavano esperienze sicure, di addimesticare <lb></lb>con la verità i ritrosi ad ammetterla, perchè gl&#039;incrementi degli spazi, fa­<lb></lb>cendoli come la serie de&#039;numeri impari, sembravano eccessivi. </s>

<s>Fu da ragioni <lb></lb>simili mosso a dubitare degl&#039;insegnamenti di Galileo uno de&#039;discepoli di lui <lb></lb>più valorosi, Antonio Nardi, il quale proponeva perciò di sostituire al trian­<lb></lb>golo la parabola, facendo crescere le velocità come le radici dei tempi, co­<lb></lb>sicchè la ragione per esempio di due a uno si riducesse a quella di √8 a <lb></lb>√4, ch&#039;esso Nardi scrive R. </s>

<s>Q 8 a R. </s>

<s>Q 4, non essendosi ancora quel segno del <lb></lb>radicale introdotto nell&#039;uso. </s>

<s>Sostituita dunque, secondo questa nuova ipotesi, <pb xlink:href="020/01/2078.jpg" pagenum="321"></pb>√T:√<emph type="italics"></emph>t<emph.end type="italics"></emph.end> alla ragione di V:<emph type="italics"></emph>v,<emph.end type="italics"></emph.end> l&#039;equazione S:<emph type="italics"></emph>s<emph.end type="italics"></emph.end>=V.T:<emph type="italics"></emph>v.t<emph.end type="italics"></emph.end> si trasforma <lb></lb>nell&#039;altra S:<emph type="italics"></emph>s<emph.end type="italics"></emph.end>=T√T:<emph type="italics"></emph>t<emph.end type="italics"></emph.end> √<emph type="italics"></emph>t<emph.end type="italics"></emph.end>=√T3:√<emph type="italics"></emph>t<emph.end type="italics"></emph.end>3, che conclude essere gli spazi <lb></lb>come le radici dei cubi de&#039;tempi. </s></p><p type="main">

<s>“ La nuova scienza del Galileo intorno al moto dei cadenti e dei pro­<lb></lb>ietti, leggesi nella veduta XLII della seconda Scena, s&#039;appoggia tutta a due <lb></lb>principii: l&#039;uno che il moto orizzontale sia uguale, l&#039;altro che il moto dei <lb></lb>cadenti riceva nuova aggiunta di velocità, secondo la ragione dei tempi. </s>

<s>Du­<lb></lb>bito nondimeno che questo secondo principio non bene con l&#039;esperienza con­<lb></lb>cordi, sicchè non tanto si velociti un cadente, quanto da esso principio se­<lb></lb>gue. </s>

<s>Nè l&#039;esperienza della palla sdrucciolante per un canale si reputa da me <lb></lb>sicura, oltrechè il moto di essa è composto di due, mentre, scendendo, si <lb></lb>ruzzola per il sostegno e, per l&#039;aderenza al <gap></gap>nale, in sè stessa. </s>

<s>E siccome, <lb></lb>per l&#039;aderenza e sostegno, quella riesce più tarda di un&#039;altra, che per l&#039;aria <lb></lb>discenda; così, mediante la complicazione de&#039;due moti, e per premere obli­<lb></lb>quamente sopra il canale, può da principio rendersi meno veloce dell&#039;altra <lb></lb>suddetta. </s>

<s>Dunque in tale esperienza qualche cosa desidero, e massime che il <lb></lb>sostegno e l&#039;aderenza al canale non solo può ritardar la palla, ma anco di fatto <lb></lb>la rattiene dallo scorrere, mentre sia il canale poco all&#039;orizzonte inclinato. </s>

<s>” </s></p><p type="main">

<s>“ Alcuno dunque pensar potrebbe che nel III dialogo Del moto, a c. </s>

<s>170 <lb></lb>(<emph type="italics"></emph>nella prima edizione di Leyda<emph.end type="italics"></emph.end>) la velocità EB (fig. </s>

<s>149) alla velocità I non <lb></lb><figure id="id.020.01.2078.1.jpg" xlink:href="020/01/2078/1.jpg"></figure></s></p><p type="caption">

<s>Figura 149.<lb></lb>fosse come la retta EB alla retta I, o come due ad uno, ma <lb></lb>come R. </s>

<s>Q 8 a R. </s>

<s>Q 4. Sicchè, in cambio di prendere un <lb></lb>triangolo AEB, si prendesse una semiparabola, di cui la cima <lb></lb>A, la semibase EB, e l&#039;asse AB. </s>

<s>Ma ricevendosi che i gravi <lb></lb>s&#039;affrettino come vuole il Galileo, ne segue che lo spazio <lb></lb>trascorso in un dato tempo, il che sopra accennammo, al <lb></lb>trascorso nella prima metà di esso tempo, sia come quattro <lb></lb>a uno, e successivamente come i quadrati dei tempi. </s>

<s>Anche <lb></lb>ne segue che i tempi del moto uguale e dell&#039;affrettato siano <lb></lb>uguali, quando il massimo grado di velocità dell&#039;affrettato <lb></lb>sia doppio di qualsivoglia grado dell&#039;uguale. </s>

<s>Ma dalla nuova <lb></lb>ipotesi segue che i tempi del moto uguale e dell&#039;affrettato <lb></lb>siano uguali, quando il massimo grado di velocità dell&#039;af­<lb></lb>frettato sia sesquialtero di qualsivoglia grado dell&#039;uguale. </s>

<s><lb></lb>Inoltre segue che lo spazio trascorso in un dato tempo, al <lb></lb>trascorso nella prima metà di esso tempo, sia come 8 a <lb></lb>R. </s>

<s>Q 8, onde avrebbe minor ragione che tre ad uno, e gli <lb></lb>spazi trascorsi dal cadente in tempi uguali saranno come i cubi delle R. </s>

<s>Q <lb></lb>di essi tempi, cioè come R. </s>

<s>O 1, R. </s>

<s>Q 8, R. </s>

<s>Q 27, R. </s>

<s>Q 64. ” </s></p><p type="main">

<s>“ Considerisi la discrepanza tra le conclusioni dell&#039;una e dell&#039;altra ipo­<lb></lb>tesi, e non è dubbio che coloro, i quali ascrivevano a cattive osservazioni <lb></lb>il credere che i gravi s&#039;affrettino cadendo, si sottoscriverebbero più all&#039;ul­<lb></lb>tima che all&#039;altra ipotesi, per parere almeno di non avere essi errato così <lb></lb>all&#039;ingrosso nelle loro osservazioni. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>973, 74). </s></p><pb xlink:href="020/01/2079.jpg" pagenum="322"></pb><p type="main">

<s>Negli stessi discepoli dunque di Galileo quella che, annunziata prima <lb></lb>nei dialoghi Del mondo, e poi dimostrata negli altri dialoghi Del moto, si <lb></lb>chiama ora per noi col nome di <emph type="italics"></emph>legge,<emph.end type="italics"></emph.end> non aveva più valore che di una <lb></lb>semplice <emph type="italics"></emph>ipotesi,<emph.end type="italics"></emph.end> più dipendente da un supposto principio, che da un fatto <lb></lb>sperimentato. </s>

<s>Si conferma insomma da ciò quel che si diceva, che cioè le <lb></lb>incertezze e i dubbi, in <expan abbr="ammetterẽ">ammetterem</expan> nell&#039;accelerazione dei gravi quella nuova <lb></lb>proporzione degli incrementi, dipendevano principalmente dal non esser riu­<lb></lb>scito ancora nessuno a farne osservazioni dirette, per le quali si potessero <lb></lb>persuadere di fatto i ritrosi essere una falsità quel che si teneva per assai <lb></lb>ragionevole, e che sembrava essere così ben confermato dagli effetti delle <lb></lb>percosse. </s>

<s>Le esperienze infatti proposte, e poeticamente descritte nel III dia­<lb></lb>logo Delle due nuove scienze, vedemmo quanto, mettendosi a praticarle, do­<lb></lb>vessero andar soggette a fallacie: opinione autorevolmente confermata dalle <lb></lb>sopra riferite parole del Nardi. </s>

<s>Il Baliani pure, benchè ne fosse dallo stesso <lb></lb>Galileo messo in sospetto, non si curò di verificare se quella palla di ferro <lb></lb>metteva a scendere per lo spazio di cento braccia precisamente cinque mi­<lb></lb>nuti secondi di tempo. </s>

<s>Argomentasi ciò da una lettera di lui, scritta da Ge­<lb></lb>nova il 16 di Settembre del 1639, e indirizzata ad Arcetri, dove, riferendo <lb></lb>l&#039;esperienza di una palla di moschetto, che, lasciata cader dall&#039;alto albero <lb></lb>di una nave fatta vogar dalla ciurma velocissimamente, si vedeva con gran <lb></lb>maraviglia di tutti battere, senza punto rimanerne in dietro, a piè dell&#039;al­<lb></lb>bero stesso; soggiunge: “ eppure, essendo l&#039;albero alto più di sessanta brac­<lb></lb>cia, massime che la galea è grossa, cioè la nostra Capitana, per ragione la <lb></lb>palla dovea star per aria più di tre minuti secondi ” (Alb. </s>

<s>X, 370). </s></p><p type="main">

<s>Anche il Fermat e il Cartesio, come per le loro proprie testimonianze <lb></lb>più sopra udimmo, fecero dell&#039;accelerarsi dei gravi <emph type="italics"></emph>prove<emph.end type="italics"></emph.end> e <emph type="italics"></emph>osservazioni,<emph.end type="italics"></emph.end><lb></lb>che si trovarono riscontrar con la legge formulata da Galileo, ma non di­<lb></lb>cendoci il particolar modo che, in provare e in osservare, fu da loro tenuto, <lb></lb>è da creder che di poco differisse, nella struttura e nell&#039;efficacia, da ciò che <lb></lb>nello stesso proposito suggerì l&#039;industria al Gassendo. </s>

<s>Fu il celebre Filo­<lb></lb>sofo parigino uno de&#039;difensori più strenui della legge galileiana contro i pa­<lb></lb>ralogismi del gesuita Pietro Casrée, a cui indirizzava tre eruditissime epi­<lb></lb>stole, che videro la pubblica luce sotto il titolo <emph type="italics"></emph>De proportione, qua gravia <lb></lb>accelerantur.<emph.end type="italics"></emph.end> Risponde ivi agli argomenti dell&#039;avversario con matematiche <lb></lb>ragioni, ma per quel che s&#039;appartiene alle esperienze in particolare, “ obser­<lb></lb>vationes, egli dice, a Galilaeo recitatas praetereo: ad meas quod spectat, <lb></lb>quotquot mihi licuit et quantum licuit peragere, illam proportionem semper <lb></lb>exhibuerunt ” (De proportione etc., Parisiis 1646, pag. </s>

<s>230). </s></p><p type="main">

<s>Quali poi si fossero queste esperienze, e come fossero particolarmente <lb></lb>condotte, l&#039;aveva scritto già il Gassendo nell&#039;epistola I, dove si leggon tre <lb></lb>vari modi proposti dall&#039;Autore per confermare sperimentalmente che gli <lb></lb>spazi passati dai gravi liberamente cedenti son proporzionali ai quadrati delle <lb></lb>velocità o dei tempi. </s>

<s>Il primo modo incominciava allora a rendersi famoso <lb></lb>per le controversie, alle quali sarebbe tra gl&#039;Idrometri andato soggetto: con-<pb xlink:href="020/01/2080.jpg" pagenum="323"></pb>troversie, che non temute dal Gassendo, lo lasciaron sicuro nell&#039;approvare <lb></lb>il fatto, che le velocità del flusso di un liquido dal foro aperto in un vaso <lb></lb>son proporzionali alle radici delle altezze. </s>

<s>Prendi, egli perciò dice, uno dei <lb></lb>così fatti vasi cilindrici, e infusavi acqua infino a una certa altezza, mante­<lb></lb>nutavi costante, supponiamo che aperto il foro tu ne abbi attinto un fiasco <lb></lb>in un minuto. </s>

<s>“ Ut deinde tempore eodem, et per idem foramen, exsiliant <lb></lb>duo congii, et aqua proinde sit duplo compressior, ad quamnam usque al­<lb></lb>titudinem adaugendus erit, complendusve cylindrus? </s>

<s>Ad duplam ne solum? </s>

<s><lb></lb>Non sane sed omnino ad quadruplam. </s>

<s>Et ut exsiliant tres, ad triplam ne? </s>

<s><lb></lb>Haudquaquam profecto, sed ad nonuplam. </s>

<s>Et ut exsiliant quatuor, ad qua­<lb></lb>druplam ne? </s>

<s>Minime gentium, sed ad sexdecuplam ” (ibid., pag. </s>

<s>36). </s></p><p type="main">

<s>Il secondo modo, o non è da noi bene inteso, o contiene in sè una fal­<lb></lb>lacia, consistendo nel proporre un peso pendolo, in cui s&#039;esperimenta, dice <lb></lb><figure id="id.020.01.2080.1.jpg" xlink:href="020/01/2080/1.jpg"></figure></s></p><p type="caption">

<s>Figura 150.<lb></lb>il Gassendo, che, rimanendosi la fune <lb></lb>ugualmente lunga, le velocità delle oscil­<lb></lb>lazioni crescono come i quadrati dei pesi <lb></lb>uguali, che devono aggiungersi al primo, <lb></lb>perchè se ne solleciti il moto. </s>

<s>Passando <lb></lb>perciò al terzo modo, immagina l&#039;Autore <lb></lb>di avere più pendoli disposti lungo la <lb></lb>medesima linea verticale AQ (fig. </s>

<s>150) <lb></lb>crescenti in lunghezza via via come i <lb></lb>quadrati de&#039;numeri naturali, cosicchè, <lb></lb>essendo AM uno, sia AO quattro, AQ <lb></lb>nove, ecc. </s>

<s>Rimossi tutti insieme per un <lb></lb>angolo uguale dal perpendicolo, in modo <lb></lb>che si trovino in diritta linea, come per <lb></lb>esempio sull&#039;obliqua AG, “ observa­<lb></lb>mus, dice il Gassendo, tempus quo glo­<lb></lb>bus secundus pervenit ad O esse duplum <lb></lb>temporis, quo primus pervenit ad M, et <lb></lb>tempus, quo tertius ad Q, triplum ” <lb></lb>(ibid., pag. </s>

<s>40). Ma per costruzione lo spazio circolare GQ, o il retto PQ <lb></lb>che gli corrisponde, è nonuplo, e lo spazio EO o NO è quadruplo dello spa­<lb></lb>zio CM o LM passato dal pendolo nel primo tempo. </s></p><p type="main">

<s>Che sia veramente così, cioè che gli spazi stanno come i quadrati dei <lb></lb>tempi, è confermato, soggiunge quivi il Gassendo stesso, da un altro fatto, <lb></lb>che a me sperimentando “ observare licuit, constitutam pilam supra planum <lb></lb>libellatum oppositumque ad M, ad O, ad Q, dum percuteretur propellere­<lb></lb>turque o globis incurrentibus, assequi velocitatem excurrereque, non iuxta <lb></lb>numeros quadratos, quales sunt CM, EO, GQ, sed iuxta radices ipsorum, <lb></lb>qualia sunt et tempora unum, duo, tria ” (ibid., pag. </s>

<s>41). </s></p><p type="main">

<s>Chiunque ora chiuda, lette queste belle proposizioni, il libro, e pene­<lb></lb>tri con l&#039;immaginazione dentro il segreto gabinetto sperimentale del Gas-<pb xlink:href="020/01/2081.jpg" pagenum="324"></pb>sendo, scoprirà facilmente che il Filosofo faceva conto di aver veduto con gli <lb></lb>occhi del corpo quel che avea chiaramente speculato con la luce dell&#039;intel­<lb></lb>letto. </s>

<s>Quali strumenti usava l&#039;Autore, o suggeriva a chi avesse voluto imi­<lb></lb>tarlo, per la più esatta misura di così minimi tempi? </s>

<s>Non si fa menzione <lb></lb>d&#039;altro misuratore, che delle arterie pulsanti, ond&#039;è che l&#039;esperienza vera, <lb></lb>da dimostrar che quella del Gassendo non poteva essere altro che immagi­<lb></lb>naria, consisterebbe nel mettere un ignorante degli elementi della Meccanica, <lb></lb>per veder ciò che riuscisse a sapere delle differenze de&#039;tempi, impiegati dai <lb></lb>pendoli a passar per gli archi CM, EO, GQ, con gran diligenza toccandosi <lb></lb>e attentamente ascoltandosi i polsi. </s></p><p type="main">

<s>Così fatti generi d&#039;esperienze si lusingarono tanti altri, da Galileo al <lb></lb>Gassendo, di averle eseguite, ma quand&#039;anco avessero avuto per caso una <lb></lb>buona riuscita, non era da riposare in esse con fede, come non credè di <lb></lb>avervi a riposare il Fermat, conscio che a lui mancavano gli strumenti ne­<lb></lb>cessari per osservare così sfuggevoli, e pur necessariamente concludenti mi­<lb></lb>nuzie de&#039;tempi. </s>

<s>Non si ridusse il prezioso cronometro praticabile, con indi­<lb></lb><figure id="id.020.01.2081.1.jpg" xlink:href="020/01/2081/1.jpg"></figure></s></p><p type="caption">

<s>F. 151.<lb></lb>cibile pertinacia e solerzia, che per l&#039;industria di Giovan Batista Ric­<lb></lb>cioli, a cui primo si deve l&#039;aver, con esattezza maravigliosa, confer­<lb></lb>mata la teoria galileiana con i fatti sperimentati. </s></p><p type="main">

<s>Ritorniamo alla storia, da noi lasciata altrove interrotta nel II tomo <lb></lb>dell&#039;Almagesto nuovo, per le pagine del quale si leggeva come fosse <lb></lb>l&#039;Autore entrato in sospetto che, nel prescrivere le proporzioni de&#039;moti <lb></lb>accelerati, fosse incorso Galileo in qualche fallacia. </s>

<s>Vedemmo quali <lb></lb>fossero di quel sospetto i ragioneveli motivi, e com&#039;avesse speranza il <lb></lb>Riccioli, più diligentemente sperimentando, di ritrovare per gl&#039;incre­<lb></lb>menti degli spazi una serie aritmetica, diversa da quella de&#039;numeri <lb></lb>impari. </s>

<s>A conseguir poi una tal maggior diligenza sperimentale si con­<lb></lb>fidava principalmente l&#039;Autore nell&#039;uso dei pendoli, da lui stesso, <lb></lb>com&#039;altrove diremo, con laboriosissima industria ritrovati aggiustatis­<lb></lb>simi, e volendo studiare il moto nel suo libero esercizio, e non vio­<lb></lb>lentemente costretto ne&#039;piani inclinati o nei pendoli a rispondere alle <lb></lb>intenzioni, e a secondare le comodità dell&#039;arte; ritornava con desiderio, <lb></lb>come a strumento di nessun altro atto meglio a rappresentare gli effetti <lb></lb>della Natura, alla torre degli Asinelli. </s></p><p type="main">

<s>Disegnata dunque nell&#039;altezza della gran Torre una linea NH <lb></lb>(fig. </s>

<s>151) e preparato un pendolo così lungo, che ad ogni vibrazione <lb></lb>batteva dieci terzi di minuto, cercò il Riccioli, col suo fido compagno <lb></lb>Francesco Maria Grimaldi, qual si fosse l&#039;altezza, da cui un globo di <lb></lb>argilla cadeva in cinque delle dette vibrazioni, e trovò con ripetute <lb></lb>prove essere quella precisa altezza BH di dieci piedi romani antichi. </s>

<s><lb></lb>Passarono poi i due sperimentatori a cercar l&#039;altra altezza, necessaria <lb></lb>perchè il medesimo globo dovesse giù da essa cadere in tempo doppio, <lb></lb>e trovarono essere 40 piedi, l&#039;intervallo dei quali è segnato dalla linea <lb></lb>KH. </s>

<s>Di lì, via via ascendendo più in alto, trovarono passare il cadente le <pb xlink:href="020/01/2082.jpg" pagenum="325"></pb>linee LH, MH, NH, di 90, di 160 e di 250 piedi, in quindici, in venti, in <lb></lb>venticinque vibrazioni, ossia in tempo triplo, quadruplo e quintuplo di quel <lb></lb>primo. </s></p><p type="main">

<s>Venendo dopo ciò il Riccioli, con trepido desiderio, a fare il conto de­<lb></lb>gl&#039;incrementi subiti, per decider se procedevano secondo la serie da Galileo <lb></lb>proposta, o secondo quell&#039;altra, ch&#039;egli aveva sospettata più vera, al vedersi <lb></lb>tornar sotto la punta della penna 10—40=30, 90—40=50, 160—90= <lb></lb>70, 250—160=90, precisamente insomma secondo la serie de&#039;numeri im­<lb></lb>pari; ebbe a rimanerne stupito. </s>

<s>E tuttavia fermo in credere che fosse riu­<lb></lb>scito Galileo alla sua scoperta, per diritta via sperimentale, non si poteva <lb></lb>dar pace come, da esperienze così imperfette e necessariamente fallaci, avesse <lb></lb>potuto quell&#039;uomo così puntualmente coglier nel vero. </s></p><p type="main">

<s>Gli passò per la mente il sospetto che qualche errore fosse scorso, o <lb></lb>nelle osservazioni sue proprie o in quelle del Grimaldi, e perciò volle ripe­<lb></lb>tere l&#039;esperienza, servendosi di un altro pendolo, che batteva un minuto <lb></lb>secondo preciso di tempo sidereo. </s>

<s>Nè contento ancora, provò in altri modi, <lb></lb>e sempre costantemente riducevasi il conto a dire che gli spazi crescono se­<lb></lb>condo la serie de&#039;numeri impari, e che perciò vanno veramente come i qua­<lb></lb>drati dei tempi. </s>

<s>“ Ergo ad p. </s>

<s>Bonaventuram Cavalerium, in bononiensi uni­<lb></lb>versate primarium Matheseos professorem, et quondam Galilaei alumnum, <lb></lb>me contuli, cum p. </s>

<s>Grimaldo, ipsique narravi consensum meorum experi­<lb></lb>mentorum cum experimentis Galilaei, quoad hanc quidem proportionem, <lb></lb>neque enim ille, chiragra simul et podagra lectulo aut sellulae affixus, in­<lb></lb>teresse ipsis poterat. </s>

<s>Incredibile autem dictu est quantopere ex nostra hac <lb></lb>contextatione fuerit exhilaratus ” (Almag. </s>

<s>novum, T. II cit., pag. </s>

<s>386). </s></p><p type="main">

<s>Il Cavalieri, così devotamente affezionato al suo Maestro, ripensava, in <lb></lb>mezzo ai dolori atroci della podagra, alla consolazione che avrebbe dovuto <lb></lb>provare a una tal notizia il buon vecchio, il quale avrebbe potuto dire di <lb></lb>morir contento, dop&#039;essere stato fatto finalmente certo che la sua Nuova <lb></lb>scienza non era una semplice ipotesi, ma un fatto reale, e che le sue pro­<lb></lb>posizioni Del moto non erano da rassomigliare alle conclusioni dimostrate <lb></lb>da Archimede circa la spirale, vere solamente in astratto “ per non ri­<lb></lb>trovarsi in natura mobile, che in quella maniera spiralmente si muova ” <lb></lb>(Alb. </s>

<s>VII, 157). </s></p><p type="main">

<s>Nel 1651 si divulgarono l&#039;esperienze del Riccioli, rimaste fin&#039;allora so­<lb></lb>lamente note ai familiari e agli amici, e per quelle varie descrizioni, che si <lb></lb>leggevano nel II tomo dell&#039;Almagesto nuovo, si mostrava la verità presa da <lb></lb>così sottil arte, e avvinta da così stretti legami, che nessuno osò poi più di <lb></lb>mettere in dubbio se l&#039;accelerazione dei gravi, qual consegue dal supporre <lb></lb>crescenti le velocità come i tempi, fosse un fatto fisico o una matematica <lb></lb>esercitazione. </s>

<s>Sotto questo duplice abito, fisico matematico, fece la Scienza <lb></lb>del moto la sua prima e solenne comparsa nell&#039;<emph type="italics"></emph>Orologio oscillatorio<emph.end type="italics"></emph.end> del­<lb></lb>l&#039;Huyghens, la seconda parte del quale, a stabilir le leggi della discesa dei <lb></lb>gravi, incomincia dal dimostrare i teoremi di Gelileo. </s>

<s>Consistendo i princi-<pb xlink:href="020/01/2083.jpg" pagenum="326"></pb>pii, da&#039;quali si concludono quelle leggi o si dimostrano que&#039;teoremi, nella <lb></lb>forza di gravità, e nella forza d&#039;inerzia, riguardò ingegnosamente l&#039;Huyghens <lb></lb>gli spazi acceleratamente passati come la resultante unica di due moti. </s></p><p type="main">

<s>Sia spinto il mobile A (fig. </s>

<s>152), da qualsivoglia forza, nella direzione <lb></lb>AB: se fingasi un tal mobile senza peso, o se gli effetti della gravità di lui <lb></lb>siano dal sostentamento di qualche piano impediti, procederà esso mobile <lb></lb><figure id="id.020.01.2083.1.jpg" xlink:href="020/01/2083/1.jpg"></figure></s></p><p type="caption">

<s>Figura 152.<lb></lb>per tutta la linea AB equabilmente. </s>

<s>Ma suppongasi <lb></lb>che la gravità liberamente eserciti il suo impulso <lb></lb>discensivo, come quando un corpo vien gettato per <lb></lb>aria: allora, se nel mentre che con equabile moto <lb></lb>il proietto è passato in B, la gravità sua naturale <lb></lb>l&#039;ha fatto scendere infino in C, non è la linea del <lb></lb>moto la somma delle due AB, BC, ma una linea <lb></lb>di mezzo, che s&#039;intravede facilmente dover essere <lb></lb>una curva, benchè non importi ora a noi di sapere <lb></lb>a quale specie appartenga. </s>

<s>Se non è però la tra­<lb></lb>sversale descritta dal moto del proietto la somma <lb></lb>delle due componenti, s&#039;avvicina ad esser tale, via <lb></lb>via che la linea AB tende a dirigersi nel perpendicolo, come per esempio, <lb></lb>immaginando che ella declini sempre più in basso, volgendosi intorno al <lb></lb>punto A come a suo centro. </s>

<s>Quando infatti essa AB è orizzontale, la re­<lb></lb>sultante del moto è AC, ma è AC′, quando B siasi abbassato in B′, e, ri­<lb></lb>dottosi finalmente in B″, sopra un punto della verticale; la resultante allora <lb></lb>del moto è AC″=AB″+B″C″, ossia è uguale alla somma per l&#039;appunto <lb></lb><figure id="id.020.01.2083.2.jpg" xlink:href="020/01/2083/2.jpg"></figure></s></p><p type="caption">

<s>Figura 153.<lb></lb>delle due componenti. </s>

<s>Se ora nella naturale discesa <lb></lb>dei gravi, così conclude l&#039;Huyghens il ragionamento, <lb></lb>“ scorsim, uti diximus, duos motus consideremus, <lb></lb>alterumque ab altero nullo modo impediri cogitemus, <lb></lb>hinc iam accelerationis gravium cadentium causam <lb></lb>legesque reperire licebit ” (Opera varia, Vol. </s>

<s>I, <lb></lb>Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>52). </s></p><p type="main">

<s>Sia infatti lo spazio verticale, percorso dal mo­<lb></lb>bile nel primo tempo, uguale ad AB (fig. </s>

<s>153) il <lb></lb>quale “ dimidium est eius spatii, quod pari tempore <lb></lb>transiret motu aequabili cum velocitate, quam acqui­<lb></lb>sivit ultimo casus momento ” come dimostra l&#039;Huy­<lb></lb>ghens nella II proposizione (ibid., pag. </s>

<s>54). Dunque <lb></lb>nel secondo tempo il moto è composto dell&#039;orizzon­<lb></lb>tale BC, doppio ad AB, e del verticale CD=AB, <lb></lb>cosicchè, dovendo nella perpendicolare la resultante <lb></lb>essere uguale alla somma delle componenti, sarà <lb></lb>BE=3AB. </s>

<s>Nel punto E, da cui comincia a decor­<lb></lb>rere il terzo tempo, il moto equabile, in quel medesimo tempo assoluto, <lb></lb>sarà, per la detta II proposizione, EF=4AB. Ora, componendosi questo con <pb xlink:href="020/01/2084.jpg" pagenum="327"></pb>quèllo della gravità costante FG, ch&#039;è perciò uguale ad AB, farà resultarne <lb></lb>il terzo moto EH=5AB: ond&#039;è che, proseguendosi per il quarto, per il <lb></lb>quinto, e per tutti gli altri tempi, il medesimo ragionamento, se ne con­<lb></lb>clude essere gl&#039;incrementi degli spazi come la serie de&#039;numeri impari, e gli <lb></lb>spazi stessi perciò come i quadrati de&#039;tempi decorsi. </s></p><p type="main">

<s>I cinque libri dell&#039;<emph type="italics"></emph>Orologio oscillatorio<emph.end type="italics"></emph.end> ebbero, specialmente appresso <lb></lb>agli stranieri, maggior diffusione de&#039;quattro dialoghi Delle due nuove scienze, <lb></lb>sì perchè la lingua latina, in cui furono originalmente scritti quelli, era d&#039;in­<lb></lb>telligenza universale, sì perchè, avendo l&#039;Olandese derivata nella sua la <lb></lb>scienza dell&#039;Italiano, s&#039;attingeva di là, con pari utile e con comodità mag­<lb></lb>giore, che a risalire alle prime faticose sorgenti. </s>

<s>S&#039;ingerì da ciò l&#039;opinione <lb></lb>che avesse Galileo conclusa la legge dei cadenti dai medesimi principii uge­<lb></lb>niani, per cui il Newton, stabilite nella forza d&#039;inerzia le <emph type="italics"></emph>Leggi<emph.end type="italics"></emph.end> del moto, <lb></lb>e nel principio della composizione delle forze conclusi i <emph type="italics"></emph>Corollari<emph.end type="italics"></emph.end> “ per le­<lb></lb>ges duas primas, soggiungeva, et corollaria duo prima Galilaeus invenit de­<lb></lb>scensum gravium esse in duplicata ratione temporum ” (Principia mathem., <lb></lb>T. </s>

<s>I cit., pag. </s>

<s>45, 46). Ora si sa dai nostri Lettori quanto fossero i processi <lb></lb>galileiani alieni dal far uso de&#039;moti composti, per cui il fatto del Newton, <lb></lb>se mostra da una parte quanto poco si leggessero i libri di Galileo nel loro <lb></lb>originale, conferma dall&#039;altra come a lui solo, di unanime consenso, in mezzo <lb></lb>alle pretensioni del Cartesio, s&#039;attribuisse la scoperta, ond&#039;è che nessun&#039;al­<lb></lb>tra espressione si conforma col vero storico forse meglio di quella, che chiama <lb></lb><emph type="italics"></emph>galileiane<emph.end type="italics"></emph.end> le leggi dei gravi cadenti. </s></p><pb xlink:href="020/01/2085.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle scese dei gravi lungo i piani inclinati<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Dei principii fondamentali, da cui si dimostra la scienza dei moti inclinati, e di una supposizione <lb></lb>fatta in proposito da Galileo. </s>

<s>— II. </s>

<s>Ordinamento e pubblicazione del primo Libro galileiano <lb></lb><emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> contenente i teoremi dimostrati infino all&#039;anno 1602. — III. </s>

<s>Ordinamento e pubbli­<lb></lb>cazione del secondo Libro galileiano <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> incominciato nel 1604, e nel 1609 rimasto inter­<lb></lb>rotto, per le ragioni che qui si diranno. </s>

<s>— IV. </s>

<s>Ordinamento delle proposizioni lasciate mano­<lb></lb>scritte da Galileo, per condurre in una terza maniera il suo trattato <emph type="italics"></emph>De motu.<emph.end type="italics"></emph.end> — V. </s>

<s>Dei teoremi <lb></lb>concernenti i Moti locali, ordinati da Galileo per la stampa, e delle critiche fatte dal Cartesio <lb></lb>contro essi. </s>

<s>— VI. </s>

<s>Di ciò che può dirsi nuovo nel trattato di Galileo, che qui paragonasi con <lb></lb>quello del Baliani, e dell&#039;opera data da altri Autori stranieri, come dal Mariotte e dall&#039;Huy­<lb></lb>ghens, intorno al medesimo soggetto del moto dei gravi per i piani inclinati. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;attributo, che si dà alle scoperte dei Fisici o alle speculazioni dei <lb></lb>Filosofi, desumendolo dal particolar nome di un uomo, è, a volere esser <lb></lb>giusti, una improprietà, che si può solo salvare nella convenzion del linguag­<lb></lb>gio, e che viene a ridursi, in più rigorosi termini, a una falsità, nel tribu­<lb></lb>nale della giustizia, ogni volta che si vogliono quelle attribuzioni fare esclu­<lb></lb>sive, come Galileo e il Cartesio pretendevano nelle loro speculazioni e nelle <lb></lb>loro scoperte. </s>

<s>Perchè, nell&#039;ordine intellettuale, è un consorzio non meno <lb></lb>stretto, nè men necessario di quel che sia negli ordini civili, e perciò da <lb></lb>uno e da un altro autore piglia nome questa o quella parte della scienza, <lb></lb>come piglia nome dal gerarca o dal padre una società religiosa o una fa­<lb></lb>miglia. </s></p><p type="main">

<s>Dir dunque galileiane le leggi della caduta dei gravi non si deve in­<lb></lb>tendere a quel modo che tanti fanno, quasi fossero uscite spontanee quelle <pb xlink:href="020/01/2086.jpg" pagenum="329"></pb>verità naturali dalla solitaria mente di Galileo, il quale è padre nella scienza, <lb></lb>come fu padre nella famiglia, e non potrebbe esser tale nell&#039;una e nell&#039;al­<lb></lb>tra, senza esser disceso dagli avi, e senz&#039;aver celebrato un connubio. </s>

<s>Ha la <lb></lb>precedente storia narrato chi fossero quegli avi, e qual si fosse il rito di <lb></lb>quel connubio per ciò, che particolarmente concerne i primi fondamenti posti <lb></lb>alla Dinamica, e perchè il medesimo Architettore sopra una sì ben fondata <lb></lb>base dette mano a costruir l&#039;edifizio, ha la nostra storia a narrare con quali <lb></lb>strumenti, e con quale industria fosse condotto. </s>

<s>L&#039;essersi mostrato alla pub­<lb></lb>blica vista quel monumento della scienza in abito, in corporatura o in ti­<lb></lb>tolo di nuovo, lusingava l&#039;Autore, e seduceva gli spettatori, ma lo spetta­<lb></lb>colo era simile a quello di colui che, non avendo saputo dianzi distinguere <lb></lb>il calice dall&#039;altro verde, vede ora, a ripassar pel medesimo giardino, la so­<lb></lb>litaria fronda scoppiata nelle fragranze del fiore. </s></p><p type="main">

<s>Tornando dall&#039;immagine specchiata indietro all&#039;oggetto reale, s&#039;incon­<lb></lb>tra questo, secondo la nostra intenzione, nel III dialogo Delle due nuove <lb></lb>scienze; fiore aperto, a cui, perchè non si creda una incantevole apparizione, <lb></lb>giova riconoscer la boccia e la pianticella madre che l&#039;ha generato. </s></p><p type="main">

<s>In quel III Dialogo, che si diceva, legge il Protagonista agli altri inter­<lb></lb>locutori una serie di teoremi, scritti in altra lingua, e posti sotto altra forma, <lb></lb>nei quali teoremi, dalle proporzioni del moto per la verticale, si passa a <lb></lb>dimostrar geometricamente le proporzioni del moto nelle direzioni oblique. </s>

<s><lb></lb>E perchè una tale obliquità di direzione non può il mobile prenderla, se <lb></lb>non per qualche violenza, che lo costringa a moversi contro l&#039;inclinazione <lb></lb>sua naturale, è perciò che la nuova scienza attende a dimostrar le leggi, se­<lb></lb>condo le quali i gravi scendono lungo i piani inclinati. </s>

<s>Se si considerino <lb></lb>però in queste scese i semplici impeti, o s&#039;attenda solamente a ritrovare la <lb></lb>proporzion dei momenti, la Scienza nuova si riduce all&#039;antica, e la pianti­<lb></lb>cella madre, di che simboleggiando si diceva, scopresi ne&#039;principii statici di <lb></lb>Giordano Nemorario, e la boccia del fiore tanto ammirato nei negletti <emph type="italics"></emph>Que­<lb></lb>siti<emph.end type="italics"></emph.end> del Tartaglia. </s></p><p type="main">

<s>Esplicatesi infatti le medesime questioni, e dimostrato con la sola no­<lb></lb>vità del processo, diverso un poco da quello del Tartaglia, che gl&#039;impeti nel <lb></lb>perpendicolo e nell&#039;obliqua hanno ragion reciproca delle lunghezze, Galileo, <lb></lb>introducendosi alle sue nuove speculazioni, così scriveva: “ Ex his facile <lb></lb>erit aliquorum problematum solutionem assequi, qualia haec sunt: primo, <lb></lb>datis duobus planis inclinatis, quorum rectus descensus idem sit, invenire <lb></lb>proportionem celeritatum eiusdem mobilis ” (Alb. </s>

<s>XI, 61). </s></p><p type="main">

<s>Il linguaggio stesso, come sentono echeggiarsi nelle orecchie i Lettori, <lb></lb>è quello del Nemorario, che primo aprì le vie al Tartaglia di ritrovar la <lb></lb>proporzione tra l&#039;impeto nell&#039;obliquo e nel retto descenso; impeto che, ri­<lb></lb>guardato come causa efficiente della celerità, trasformava il teorema dello <lb></lb>stesso Tartaglia in quest&#039;altro concluso ivi così da Galileo: “ Constat ergo <lb></lb>eiusdem mobilis, in diversis inclinationibus, celeritates esse inter se, permu­<lb></lb>tatim, sicut obliquorum descensuum, aequales rectos descensus comprehen-<pb xlink:href="020/01/2087.jpg" pagenum="330"></pb>dentium, longitudines ” (ibid., pag. </s>

<s>62). E perchè le celerità hanno ragion <lb></lb>contraria alle tardità, ossia ai tempi, rimanendo gli spazi i medesimi, dun­<lb></lb>que i tempi, nell&#039;obliquo e nel retto descenso, stanno come le lunghezze <lb></lb>non permutate: “ erit ergo sicut tarditas ad tarditatem, ita linea ad li­<lb></lb>neam ” (ibid.). </s></p><p type="main">

<s>Chi si risovviene delle cose lette nel capitolo I di questo Tomo, sa che <lb></lb>a una tal conclusione era, dai medesimi principii, giunto anche Leonardo <lb></lb>da Vinci, e perchè di là, cioè dall&#039;essere i tempi, nel perpendicolo e nel­<lb></lb>l&#039;obliqua di uguali altezze, come gli spazi, si svolge quasi tutta intera la <lb></lb>serie dei teoremi galileiani, i quali dipenderebbero perciò unicamente dalla <lb></lb>Statica del Nemorario e del Tartaglia; scarsi e limitati alle sole cadute di­<lb></lb>rette apparirebbero i frutti della Dinamica nuova. </s>

<s>Eppure, al primo entrare <lb></lb>allo studio del Trattato galileiano, si rivela esser l&#039;intenzion dell&#039;Autore <lb></lb>tutta diversa, perchè i primi teoremi, che s&#039;incontrano dimostrati, e da cui <lb></lb>dipendono gli altri, son puramente dinamici, e progredendo oltre nella let­<lb></lb>tura non è possibile non accorgersi della sollecitudine di chi scrive, in non <lb></lb>derivar mai <emph type="italics"></emph>ex mechanicis,<emph.end type="italics"></emph.end> ossia dalla statica, quant&#039;è possibile, i principii <lb></lb>alle sue dimostrazioni. </s></p><p type="main">

<s>Di questo notabilissimo fatto, e delle sue ragioni, le cose che siamo per <lb></lb>dire ci renderanno certi, ma intanto non si può non ripensare al modo, come <lb></lb>potesse Galileo rendere indipendente la sua Dinamica dai principii già sta­<lb></lb>biliti in una scienza anteriore, perchè ciò sembrerebbe evidentemente un <lb></lb>voler raccogliere i frutti dai novelli rami recisi dal tronco. </s>

<s>Essendo però <lb></lb>questa intenzione dell&#039;audace cultore contraria affatto alle leggi della Na­<lb></lb>tura, non sarebbe stata in nessun modo riuscibile se, mettendosi a recidere <lb></lb>alla rigogliosa pianta lo stelo, non avesse salvata la più profonda radice, dalla <lb></lb>quale s&#039;argomentò di fare scoppiare le nuove fronde. </s></p><p type="main">

<s>Galileo infatti, nel bandire dalla sua Scienza nuova il teorema del Tar­<lb></lb>taglia, non potè fare a meno di ridursi a professar quel principio, da cui, <lb></lb>come da radice, era germogliato esso teorema; principio, il quale noi sap­<lb></lb>piamo consistere nell&#039;ammetter che, per le varie obliquità, i momenti dei gravi <lb></lb>siano allora uguali, quando <emph type="italics"></emph>aequaliter capiunt de directo.<emph.end type="italics"></emph.end> E perchè i mo­<lb></lb>menti o gl&#039;impeti, quali cause efficienti, supponeva ragionevolmente Galileo <lb></lb>che fossero proporzionali alle velocità, come a loro effetti immediati; e perciò <lb></lb>il principio statico del Nemorario si trasforma, nelle semplici parole e non <lb></lb>punto nella sostanza, in quest&#039;altro, da cui si fa dipendere tutta la nuova <lb></lb>scienza galileiana: “ Accipio gradus velocitatis eiusdem mobilis, super di­<lb></lb>versas planorum inclinationes acquisitos, tunc esse aequales, cum eorumdem <lb></lb>planorum elevationes aequales sint ” (Alb. </s>

<s>XIII, 163). </s></p><p type="main">

<s>Da ciò, senz&#039;avere altrimenti bisogno d&#039;invocare il teorema del Tarta­<lb></lb>glia, si concludeva la dimostrazione dei tempi proporzionali agli spazi, per­<lb></lb>chè, supponendo un medesimo mobile o due mobili uguali movere dalla <lb></lb>quiete in A (fig. </s>

<s>154), e l&#039;uno scendere per la diritta AB e l&#039;altro per la <lb></lb>obliqua AC, perciocchè nei puntì D, E; F, G; H, I ecc., resecati dalle re-<pb xlink:href="020/01/2088.jpg" pagenum="331"></pb>spettive linee condotte parallele alla orizzontale BC, gl&#039;impeti o le velocità <lb></lb>sono uguali, in quanto che le scese AD, AE; AF, AG; AH, AI ecc., tutte <lb></lb><figure id="id.020.01.2088.1.jpg" xlink:href="020/01/2088/1.jpg"></figure></s></p><p type="caption">

<s>Figura 154.<lb></lb><emph type="italics"></emph>capiunt aequaliter de directo;<emph.end type="italics"></emph.end> dunque, nei moti <lb></lb>per tutta l&#039;AB, e per tutta l&#039;AC, son le velocità <lb></lb>uguali. </s>

<s>Ma dove sono le velocità uguali, gli spazi <lb></lb>son proporzionali ai tempi, e perciò il tempo per <lb></lb>AB, al tempo per AC, sta come la linea AB alla <lb></lb>linea AC. </s></p><p type="main">

<s>Tale essendo il processo di Galileo tradisce <lb></lb>le sue intenzioni di rendere la scienza nuova in­<lb></lb>dipendente dall&#039;antica, alla quale, non solamente <lb></lb>appartiene il supposto delle velocità uguali nel­<lb></lb>l&#039;egual rettitudine del descenso, ma i teoremi al­<lb></lb>tresì, che concernono i moti equabili, dai quali <lb></lb>accidentalmente derivano gli accelerati. </s>

<s>La Dina­<lb></lb>mica nuova insomma si fondava sopra questi tre massimi principii: che le <lb></lb>velocità siano in ragion diretta degli spazi e reciproca dei tempi; che sian <lb></lb>proporzionali agl&#039;impeti, e che si trovino sempre uguali in qualunque obli­<lb></lb>quità, quando le scese rette siano uguali. </s>

<s>Il primo principio, che non ne <lb></lb>avrebbe avuto bisogno, è in sè e nelle sue conseguenze dimostrato da Ga­<lb></lb>lileo in quelle sei proposizioni dei moti equabili, che precedono al trattato <lb></lb>dei moti accelerati; il secondo tiene in sè impressa la nota dell&#039;evidenza, <lb></lb>ma il terzo non ha d&#039;altronde il suffragio che dall&#039;aver condotto Leonardo <lb></lb>da Vinci e il Tartaglia a conseguenze vere. </s>

<s>Poteva, per questo e per la sua <lb></lb>propria ragionevolezza, quel supposto approvarsi, ma a Galileo, che sopra <lb></lb>lui solo erigeva la gran mole, sembrava conveniente saggiarne meglio la <lb></lb>solidità, perchè, vacillando quello, ne vacillava tutto intero l&#039;edifizio costruito, <lb></lb>come su regola, sul supposto che le medesime leggi governino il moto nel <lb></lb>perpendicolo e nei piani inclinati. </s>

<s>“ Id autem, quod demonstratum est in <lb></lb>lationibus peractis in perpendiculis, intelligatur etiam itidem contingere in <lb></lb>planis utcumque inclinatis, in iisdem enim assumptum est accelerationis <lb></lb>gradus eadem ratione augeri ” (Alb. </s>

<s>XIII, 173, 74). </s></p><p type="main">

<s>Le cure però, poste dall&#039;Istitutore in confermare quel suo fondamento, <lb></lb>non appariscono proporzionate al bisogno, perchè non si limitano ad altro, <lb></lb>che a descrivere un&#039;esperienza, per la quale alle già probabili ragioni si <lb></lb>viene a crescere tanto la probabilità, “ che poco gli manchi all&#039;agguagliarsi <lb></lb>ad una ben necessaria dimostrazione ” (ivi, pag. </s>

<s>164). È quella esperienza <lb></lb>desunta dalle vibrazioni del pendolo, in cui si osserva che sormonta quasi <lb></lb>a quella medesima altezza, d&#039;onde fu sceso, ed è da credere che vi arrive­<lb></lb>rebbe precisamente, quando si togliessero gl&#039;impedimenti dell&#039;aria e del filo. <lb></lb></s>

<s>“ Dal che possiamo veracemente concludere, dice Galileo, che l&#039;impeto acqui­<lb></lb>stato nel punto B (fig. </s>

<s>155) dalla palla, nello scendere per l&#039;arco CB, fu <lb></lb>tanto, che bastò a risospingersi per un simile arco BD alla medesima al­<lb></lb>tezza ” (ivi). </s></p><pb xlink:href="020/01/2089.jpg" pagenum="332"></pb><p type="main">

<s>Per rendere poi questa dimostrazione sperimentale anche più conclu­<lb></lb>dente, immagina l&#039;Autore che, rimosso il filo in AC, e di lì lasciato andare, <lb></lb><figure id="id.020.01.2089.1.jpg" xlink:href="020/01/2089/1.jpg"></figure></s></p><p type="caption">

<s>Figura 155.<lb></lb>incontri in E un chiodo, co­<lb></lb>sicchè sia costretto di risa­<lb></lb>lir dall&#039;opposta parte, de­<lb></lb>scrivendo un arco di cer­<lb></lb>chio con un raggio EB più <lb></lb>corto del primo, e vuol che <lb></lb>poi si abbassi anche di più <lb></lb>quell&#039;ostacolo, come in F, da <lb></lb>far risalire il grave pendulo <lb></lb>per un arco appartenente a <lb></lb>un circolo descritto anche <lb></lb>da minor raggio, e nono­<lb></lb>stante si osserva che l&#039;im­<lb></lb>peto, conceputo in B per la <lb></lb>discesa dal medesimo pun­<lb></lb>to C, fa in tutt&#039;e tre i casi <lb></lb>risalire il pendolo stesso nei <lb></lb>punti D, G, I, situati con C sulla medesima linea orizzontale. </s>

<s>Sarebbe il <lb></lb>fatto riuscito meglio dimostrativo coi sifoni pieni di acqua, che servirono così <lb></lb>bene al medesimo intento a Leonardo da Vinci, come vedemmo, nè a Ga­<lb></lb>lileo sfuggì l&#039;appropriatissimo esempio, quando nel I dialogo Dei due mas­<lb></lb>simi sistemi, a confermare la verità della sentenza che l&#039;impeto acquistato <lb></lb>dal mobile in qualsivoglia luogo del suo moto è tanto, che basterebbe a ri­<lb></lb>condurlo all&#039;altezza d&#039;onde si partì; dop&#039;avere invocata l&#039;esperienza del pen­<lb></lb>dolo, soggiunge: “ Mostrami l&#039;istesso l&#039;acqua, che, scendendo per un sifone, <lb></lb>rimonta altrettanto, quanto fu la sua scesa ” (Alb. </s>

<s>I, 28). </s></p><p type="main">

<s>Anzi è a notare che in questo primo Dialogo, dove si pongono i prin­<lb></lb>cipii a uno special trattato di Meccanica, concernente il moto della Terra <lb></lb>in particolare, Galileo s&#039;intrattiene a dimostrare il supposto delle velocità <lb></lb>uguali, dopo cadute uguali, più a lungo e con maggior varietà e valore di <lb></lb>argomenti di quel che non faccia nel III dialogo Delle due nuove scienze, <lb></lb>dove quello stesso principio è supposto a trattare in tutta la sua generalità <lb></lb>la scienza del moto. </s>

<s>Forse la ragione, per cui parve che Galileo stesso se <lb></lb>ne passasse qui con troppa leggerezza, è perchè credeva di averne detto al­<lb></lb>trove abbastanza: e infatti gli attori dei <emph type="italics"></emph>Due massimi sistemi<emph.end type="italics"></emph.end> s&#039;intratten­<lb></lb>gono nelle loro prime interlocuzioni a confermare i principii della Mecca­<lb></lb>nica, dipendenti da quel discorso, che si fa da pag. </s>

<s>29-32 dell&#039;edizione, da <lb></lb>noi tenuta sott&#039;occhio. </s>

<s>Chi volesse poi di un tal discorso avere in poche pa­<lb></lb>role condensata la sostanza, legga la seguente nota manoscritta: <emph type="italics"></emph>“ Miran­<lb></lb>dum:<emph.end type="italics"></emph.end> numquid motus per perpendiculum AD (fig. </s>

<s>156) velocior sit quam <lb></lb>per inclinationem AB? </s>

<s>Videtur esse, nam aequalia spacia citius conficiun­<lb></lb>tur per AD, quam AB; attamen videtur et non esse, nam, ducta horizon-<pb xlink:href="020/01/2090.jpg" pagenum="333"></pb>tali BC, tempus per AB, ad tempus per AC, est ut AB ad AC. </s>

<s>Ergo eadem <lb></lb><figure id="id.020.01.2090.1.jpg" xlink:href="020/01/2090/1.jpg"></figure></s></p><p type="caption">

<s>Figura 156.<lb></lb>momenta velocitatis per AB et per AC: est enim una ca­<lb></lb>demque velocitas illa, quae, temporibus inaequalibus, spa­<lb></lb>cia transit inaequalia eamdem quam tempora rationem ha­<lb></lb>bentia ” (MSS. Gal., P. V, T. II, fol. </s>

<s>164 a tergo). </s></p><p type="main">

<s>Il teorema fondamentale dei tempi proporzionali agli <lb></lb>spazi nella verticale e nell&#039;obliqua ugualmente elevate, è qui <lb></lb>come là concluso dallo stesso supposto principio, ma ne&#039;dia­<lb></lb>loghi Del mondo è la supposizione, messa per fondamento ai <lb></lb>dialoghi Del moto, fatta dipendere da un&#039;altra supposizione, <lb></lb>tolta la quale, rovinerebbe necessariamente ogni scienza dei <lb></lb>moti naturali e dei proietti. </s>

<s>Abbiamo poco fa udito consi­<lb></lb>stere una tal supposizione nell&#039;ammetter che l&#039;impeto della <lb></lb>scesa sia bastante a far risalire il mobile alla medesima al­<lb></lb>tezza, di che dà Galileo, a varie occasioni, nelle varie sue <lb></lb>Opere, tal dimostrazione, da non si mettere in dubbio per <lb></lb><figure id="id.020.01.2090.2.jpg" xlink:href="020/01/2090/2.jpg"></figure></s></p><p type="caption">

<s>Figura 157.<lb></lb>nessuno, che specialmente gli abbia concesso esser nei <lb></lb>moti accelerati le velocità proporzionali ai tempi. </s>

<s>In quel <lb></lb>discorso infatti, trascritto a pag. </s>

<s>307 nel capitolo addietro, <lb></lb>si sovverranno i Lettori come, dal suppor <emph type="italics"></emph>che il grave <lb></lb>cadente naturalmente vada continuamente accrescendo <lb></lb>la sua velocità, secondo che accresce la distanza dal <lb></lb>termine onde si partì,<emph.end type="italics"></emph.end> se ne concludesse che il mobile <lb></lb>in C, in D, in E (fig. </s>

<s>157) e negli altri infiniti punti <lb></lb>della linea AB, ha per la caduta acquistato tale impeto, <lb></lb>da ricondursi in A al suo primo principio. </s></p><p type="main">

<s>Sperava Galileo di poter forse dimostrare quel suo <lb></lb>supposto, da cui diceva conseguir questo effetto, ma la <lb></lb>sua dimostrazione, che cioè si velocitino i gravi proporzio­<lb></lb>natamente ai tempi, rimase per l&#039;Autore e per noi un desiderio, non so­<lb></lb>disfatto che in parte e indirettamente dagli Accademici del Cimento, i quali <lb></lb>narrano di aver fatto una tale esperienza: “ Una pallina di vetro piena, <lb></lb>lasciata dall&#039;altezza di 50 parti, arrivò con la riflessione maggiore a gradi <lb></lb>48, mancandoli, per arrivare d&#039;ond&#039;ella partissi dalla quiete, due gradi soli, <lb></lb>che potevano importare un soldo in circa del nostro braccio a panno fio­<lb></lb>rentino. </s>

<s>Da questa esperienza vien quasi confermata la conclusione del Ga­<lb></lb>lileo, che un grave, nell&#039;infimo termine della sua scesa, abbia acquistato tan­<lb></lb>t&#039;impeto, che basti a ricondurlo alla medesima orizzontale, dove egli principiò <lb></lb>suo moto, potendo probabilmente dirsi che l&#039;impedimento del mezzo, come <lb></lb>il medesimo Galileo dice seguire nei pendoli, ed il cedere, benchè pochissimo, <lb></lb>del grave cadente e del piano, ov&#039;egli venne a riflettersi; abbian dato mo­<lb></lb>tivo alla detta palla, e sieno stati causa che ella non si riduca con la rifles­<lb></lb>sione precisamente alla medesima altezza di parti 50. ” (Targioni, Notizie <lb></lb>delle scienze fisiche in Toscana, T. II, P. II, Firenze 1780, pag. </s>

<s>667, 68). </s></p><pb xlink:href="020/01/2091.jpg" pagenum="334"></pb><p type="main">

<s>Nelle esperienze degli Accademici fiorentini, e nel ragionamento di Ga­<lb></lb>lileo, le proiezioni e i rimbalzi si consideravano fatti nella linea verticale, <lb></lb>ma ciò a poco giovava senza dimostrar che lo stesso avviene e si verifica <lb></lb>nelle linee oblique, e nei piani inclinati. </s>

<s>Contemplandosi, in mezzo a que­<lb></lb>ste galileiane speculazioni, un tal caso, si sarebbe molto più per tempo giunti <lb></lb>a far l&#039;importantissima osservazione dell&#039;isocronismo del ramo ascendente <lb></lb>col discendente nella traiettoria, e sarebbero le due scienze dei moti natu­<lb></lb>rali e dei proietti nate a un parto, mentre invece, per passare a concluder <lb></lb>la potenza degl&#039;impeti a far risalire il mobile per il medesimo tratto di via <lb></lb>comunque obliqua, fu costretto Galileo a far indietro anche un&#039;altra volta <lb></lb>ritorno alla statica antica, computando gl&#039;impeti secondo la quantità del di­<lb></lb>scenso retto, e ciò per l&#039;unica ragione che un grave, in tanto solo acquista <lb></lb>momento, in quanto che movendosi s&#039;avvicina al suo centro. </s>

<s>Ond&#039;è che <lb></lb>l&#039;impeto dello scendente per il piano AII, nella precedente figura, giunto <lb></lb>che sia al termine H, è uguale all&#039;impeto acquistato dal medesimo mobile, <lb></lb>dopo la scesa perpendicolare AF “ perchè in effetto ambedue si sono avvi­<lb></lb>cinati al centro ugualmente ” (Alb. </s>

<s>I, 28, 29). </s></p><p type="main">

<s>La ragione ultima del supposto galileiano riducesi in somma a questa, <lb></lb>pubblicamente esposta con sì gran solennità in quel libro, che annunziava <lb></lb>la nuova Scienza del moto, la quale sembrava al suo Autore potersi fon­<lb></lb>dare con sicurezza sopra un tal ragionevolissimo assunto, come quello, da <lb></lb>cui s&#039;eran dedotte le approvatissime leggi dei momenti dei gravi sopra i <lb></lb>piani inclinati. </s>

<s>Nonostante, ai dimentichi o ai non curanti delle preparazioni <lb></lb>fatte nei dialoghi Del mondo al libro Dei moti locati, parvero quelle espe­<lb></lb>rienze del pendolo, sulle quali sole si tratteneva, e per le quali sole si vo­<lb></lb>leva conquistar l&#039;assenso dei Lettori, principio non conveniente a una trat­<lb></lb>tazione, che procedeva del resto con tutto il rigore della Geometria, ond&#039;è <lb></lb>che, al primo apparire in Leyda del volume famoso, si levò contro lui una <lb></lb>voce universale, che diceva esser la nuova scienza un&#039;illusione o in difetto, <lb></lb>perchè posata sopra non vero o poco stabile fondamento. </s></p><p type="main">

<s>Quella voce poi si diffuse dai varii Scrittori con tenor vario, secondo <lb></lb>che movevano le opposizioni o dall&#039;amore o dall&#039;odio alla Scienza nuova. </s>

<s><lb></lb>Il Cabeo, pronto sempre a dimostrar falsa una sentenza, purchè Galileo <lb></lb>l&#039;avesse pronunziata, non rimase, nemmeno in questa occasione, indietro nel <lb></lb>suo poco lodevole ufficio, e formulato l&#039;assunto che, in una medesima oriz­<lb></lb>zontale, gl&#039;impeti acquistati dal cadente, per l&#039;obliqua o per il perpendi­<lb></lb>colo, sono uguali. </s>

<s>“ puto, soggiunge, ego hoc falsum, et ex principiis eiusdem <lb></lb>Auctoris evidenter confutari ” (Comment. </s>

<s>in Meteor. </s>

<s>Arist., T. </s>

<s>I cit., pag. </s>

<s>92). <lb></lb>Gli argomenti però son tali, da mostrar che il Censore non aveva le prime <lb></lb>notizie elementa<gap></gap>i della Meccanica, consistendo nel dir che l&#039;impeto, vale­<lb></lb>vole a far risalir da B (nella fig. </s>

<s>155 poco addietro) il pendolo in I, dev&#039;es­<lb></lb>ser maggiore dell&#039;altr&#039;impeto, che basta a farlo risalire in D, perchè il viag­<lb></lb>gio BI è più erto del viaggio BD, e si fa con più celere moto. </s></p><p type="main">

<s>Queste del Cabeo eran pure le ragioni del Cazr, secondo che riferisce, <pb xlink:href="020/01/2092.jpg" pagenum="335"></pb>per confutarle, il Gassendo. </s>

<s>“ Inquis, cum neque ex terminis notum sit, neque <lb></lb>ulla sufficiente experientia confirmatum, imo cum rationes etiam non de­<lb></lb>sint, quibus oppositum probabilius reddatur, nempe gradus velocitatis per <lb></lb>longius planum acquisitos gradibus per brevius planum acquisitos esse mi­<lb></lb>nores; id a Galilaeo non peti, sed debuerat demonstrari, cum praesertim <lb></lb>maxima pars subsequentium theorematum hoc unico postulato nitantur. </s>

<s>Quid <lb></lb>enim certi ex incertis concludi potest aut ex principio, ut ipsemet Galilaeus <lb></lb>agnoscit, verisimili tantum ac probabili, demonstrari? </s>

<s>” (De proportione qua <lb></lb>gravia accelerantur, Epist. </s>

<s>I cit., pag. </s>

<s>21). Il Mersenno era pure di questo <lb></lb>sentimento, e diceva in Roma a Michelangiolo Ricci “ che l&#039;assunto primo <lb></lb>fatto dal Galileo era bisognoso di prove, e perciò o probabile o improbabile, <lb></lb>ed in conseguenza le proposizioni sei seguenti osserva esser tanto lontane <lb></lb>dall&#039;evidenza geometrica, quant&#039;è impossibile aver certezza di una conclu­<lb></lb>sione dedotta da verosimile assunto ” (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>116). <lb></lb>Ripeteva così dicendo il Censore quel che gli aveva pochi anni prima scritto <lb></lb>il Cartesio in una sua Epistola, nella quale, fra le parecchie altre cose no­<lb></lb>tate contro a quello che novamente aveva letto nel Galileo, era anche que­<lb></lb>sta: “ Supponit etiam velocitatis gradus eiusdem corporis in diversis planis <lb></lb>esse aequales, quando aequales sunt istorum planorum elevationes. </s>

<s>Hoc vero <lb></lb>ille non probat, neque exacte verum est. </s>

<s>Et quia sequentia omnia ex dua­<lb></lb>bus hisce hypothesibus dependent, dici potest illum in aere aedificasse ” <lb></lb>(Epist., P. II cit., pag. </s>

<s>243, 44). </s></p><p type="main">

<s>Nel Mersenno e nel Cartesio, come nel Cabeo e nel Cazr, non erano <lb></lb>scevri da passione così fatti giudizi, ma che fossero comuni, lo conferma <lb></lb>l&#039;esservi anche i più amorevoli a Galileo, benchè per diverso motivo, con­<lb></lb>corsi. </s>

<s>Il Viviani così scriveva a proposito de&#039;suoi studii giovanili: “ Appena <lb></lb>ebbi scorsi i primi Elementi, che, impaziente di vederne l&#039;applicazione, pas­<lb></lb>sai alla scienza dei moti naturali, nuovamente promossa dal Galileo, e che <lb></lb>allora appunto era uscita alla luce, ed arrivato a quel principio supposto <lb></lb>che le velocità dei mobili naturalmente per piani di una medesima eleva­<lb></lb>zione siano uguali fra loro, dubitai, non già della verità dell&#039;assunto, ma <lb></lb>della evidenza di poterlo suppor come noto ” (Scienza universale delle pro­<lb></lb>porzioni, Firenze 1674, pag. </s>

<s>99). </s></p><p type="main">

<s>Nel medesimo tempo che il Viviani, attendeva allo studio delle Matema­<lb></lb>tiche il giovane principe Leopoldo dei Medici, sotto la direzione di Famiano <lb></lb>Michelini, il quale scriveva a Galileo che S. A. aveva difficoltà in ammet­<lb></lb>tere per certo l&#039;assunto, che si supponeva nel bellissimo libro Del moto, e <lb></lb>lo pregava perciò a volergliene mandar la dimostrazione, perchè senz&#039;essa <lb></lb>pareva al suo regio alunno “ di andare al buio, ancorchè quelle esperienze, <lb></lb>che Ella pone nel libro, siano poco meno che dimostrazione ” (MSS. Gal., <lb></lb>P. VI, T. XIII, fol. </s>

<s>112). </s></p><p type="main">

<s>Fu il supposto meccanico dimostrato da Galileo, come narreremo in <lb></lb>quest&#039;altra parte della nostra Storia, e n&#039;ebbero il Viviani, il principe Leo­<lb></lb>poldo e tutti gli altri a rimaner sodisfatti, ma perchè intanto s&#039;aspettava che <pb xlink:href="020/01/2093.jpg" pagenum="336"></pb>occorresse di fare una seconda edizione dei dialoghi Delle due nuove scienze, <lb></lb>per inserirvi la dimostrazione tanto desiderata, il Torricelli, che nel 1644 <lb></lb>dava alla luce il suo celebre libro <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> scriveva così nel proe­<lb></lb>mio, dop&#039;aver formulato quello stesso supposto galileiano. </s>

<s>“ Ex hac peti­<lb></lb>tione dependet quasi universa illius doctrina de motu, tum accelerato, tum <lb></lb>proiectorum. </s>

<s>Si quis de principio dubitet, de iis, quae inde consequntur, cer­<lb></lb>tam omnino scientiam non habebit ” (Opera geom., P. </s>

<s>I cit., pag. </s>

<s>98). So <lb></lb>bene, prosegue il Torricelli a dire, che Galileo ritrovò negli ultimi anni della <lb></lb>sua vita di quel supposto la dimostrazion matematica, ma perchè rimane <lb></lb>tuttavia inedita, vi suppliremo noi nel presente trattato “ ut appareat quod <lb></lb>Galilei suppositio demonstrari potest, et quidem immediate, ex illo theore­<lb></lb>mate, quod pro demonstrato ex mechanicis ipse desumit in se, in secunda <lb></lb>parte sextae propositionis De motu accelerato. </s>

<s>” </s></p><p type="main">

<s>Il teorema, a cui qui si accenna, è il seguente: Siano AB, AD (fig. </s>

<s>158) <lb></lb>due piani di lunghezza uguale, l&#039;uno elevato secondo DF, l&#039;altro secondo <lb></lb><figure id="id.020.01.2093.1.jpg" xlink:href="020/01/2093/1.jpg"></figure></s></p><p type="caption">

<s>Figura 158.<lb></lb>BE. “ Supponit Galileus, dice il Torricelli, <lb></lb>pro demonstrato, momentum in plano AB, <lb></lb>ad momentum in plano AD, esse ut BE ad <lb></lb>DF ” (ibid.). Ora è cosa veramente singo­<lb></lb>lare che il Torricelli non si avvedesse es­<lb></lb>sere il teorema, in quella stessa VI propo­<lb></lb>sizione da lui citata, non già supposto, ma <lb></lb>benissimo dimostrato in questo modo: <lb></lb>“ Constat ex meis Elementis mechanicis <lb></lb>momentum ponderis super plano secundum <lb></lb>lineam ABC (nella medesima figura) elevato, ad momentum suum totale, esse <lb></lb>ut BE ad BA, vel ad DA; eiusdemque ponderis momentum super elevatione <lb></lb>AD, ad totale suum momentum, esse ut DF ad DA, vel BA. </s>

<s>Ergo eiusdem pon­<lb></lb>deris momentum super plano secundum DA inclinato, ad momentum super <lb></lb>inclinatione secundum ABC, est ut linea DF ad lineam BE ” (Alb. </s>

<s>XIII, 182). </s></p><p type="main">

<s>La dimostrazione, come ognun vede, è legittima, perchè, chiamato M.o il <lb></lb>momento, dalle due equazioni M.oAB:M.oBE=BE:AB; M.oAD:M.oDF= <lb></lb><figure id="id.020.01.2093.2.jpg" xlink:href="020/01/2093/2.jpg"></figure></s></p><p type="caption">

<s>Figura 159.<lb></lb>DF:AD, si conclude il teorema, come allo stesso <lb></lb>modo lo concluse il Viviani nella seguente sua <lb></lb>Nota: “ Sint gravia A, D (fig. </s>

<s>159) aequalia et <lb></lb>plana AC, DE aequalia. </s>

<s>Jam momentum A per <lb></lb>AC, ad momentum A per AB, est ut AB ad <lb></lb>AC, vel ad DE: et momentum A, vel D, per <lb></lb>DB, ad momentum D per DE, est ut DE ad <lb></lb>DB. </s>

<s>Ergo ex aequo momentum absolutum pon­<lb></lb>deris A per AC, ad momentum absolutum pon­<lb></lb>deris D per DE, est ut AB ad DB, vel ut altitu­<lb></lb>dinem planorum ” (MSS. Gal. </s>

<s>Disc., T. XXXVII, <lb></lb>fol. </s>

<s>105). </s></p><pb xlink:href="020/01/2094.jpg" pagenum="337"></pb><p type="main">

<s>Or essendo così, fa, ripetiamo, gran maraviglia che il Torricelli dicesse <lb></lb>di non essersi mai incontrato in un simile teorema: <emph type="italics"></emph>nos in huiusmodi theo­<lb></lb>rema non incidimus,<emph.end type="italics"></emph.end> e ch&#039;egli credesse perciò di essere stato il primo a <lb></lb>dimostrarlo, come fece nella sua III proposizione, in modo però men sem­<lb></lb>plice di quello di Galileo, e meno diretto. </s>

<s>Che i momenti insomma sui piani <lb></lb>di lunghezza uguale, ma variamente inclinati, stiano come i seni degli an­<lb></lb>goli delle elevazioni, si suppone è vero da Galileo nel trattato Delle mac­<lb></lb>chine, ma no nel secondo processo dimostrativo della proposizione VI Dei <lb></lb>moti accelerati, dove anzi ne dà una bella dimostrazione, che passò, non si <lb></lb>sa come, di vista al Torricelli, e che, per servirsene a risolvere il problema <lb></lb>delle pressioni fatte dalla trave appoggiata al muro, fu raccolto nelle sue <lb></lb>cose meccaniche dal Viviani. </s></p><p type="main">

<s>Avvertito ciò, che fa accorti i saggi poter cecuzzire talvolta anche le <lb></lb>linci, proseguiamo oltre a leggere nel libro <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> per trattener <lb></lb>particolarmente la nostra attenzione intorno a ciò, che riguarda gli usi e le <lb></lb>necessità dell&#039;invocato supposto galileiano. </s>

<s>Dop&#039;avere, nella IV proposizione, <lb></lb>dimostrato dalla precedente che i tempi, nelle varie inclinazioni ugualmente <lb></lb>alte, son come gli spazi, sovvenne al Torricelli un&#039;altra dimostrazione, alla <lb></lb>quale premette queste parole: “ Praecedens theorema poterat demonstrari <lb></lb>sine ulla suppositione. </s>

<s>Demonstrat enim Galileus, in propos. </s>

<s>VI De motu <lb></lb>accelerato, tempora lationum per chordas omnes in circulo aequalia esse. </s>

<s><lb></lb>Idque tribus modis probat. </s>

<s>In primo et tertio subest principium suum non <lb></lb>satis evidens; in secundo vero nihil supponitur, praeter iam dictum theorema <lb></lb>mechanicum. </s>

<s>Quod si, ipso teste, demonstratum antea fuerat, ex ipso imme­<lb></lb>diate, tamquam corollarium, necessaria illatio suae tertiae propositionis, imo <lb></lb>et suae petitionis demonstrari poterat ” (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>107). </s></p><p type="main">

<s>Accenna insomma il Torricelli a un partito che, se avesse saputo Ga­<lb></lb>lileo destramente afferrarlo, lo avrebbe condotto a dimostrare il suo terzo <lb></lb>fondamental teorema, che cioè i tempi per l&#039;inclinata e per la perpendico­<lb></lb>lare stanno come le lunghezze, senza alcuna supposizione. </s>

<s>Consisterebbe <lb></lb>quel partito nel movere dal teorema meccanico, e per esso dimostrare, come <lb></lb>lo stesso Galileo fa nel secondo modo della sua VI proposizione, che le corde <lb></lb>al diametro nel cerchio sono equidiuturne. </s>

<s>Dimostrato ciò, la proposizione <lb></lb>terza, per la quale bisognò invocare il supposto, nella teoria dei moti ac­<lb></lb>celerati ne scendeva per legittimo corollario immediato. </s></p><p type="main">

<s>A far che dunque tutto nel terzo dialogo Delle due nuove scienze pro­<lb></lb>cedesse per legittima dimostrazione, bastava, secondo il Torricelli, dare ai <lb></lb>teoremi galileiani un ordine alquanto diverso, qual sarebbe il seguente. </s>

<s>Ai due <lb></lb>primi teoremi dimostrativi della legge dei moti accelerati, e ai loro corol­<lb></lb>lari, specialmente al II del II teorema, che dice essere i tempi impiegati a <lb></lb>percorrere due spazi qualunque proporzionali all&#039;uno dei detti spazi, e alla <lb></lb>media fra ambedue; dovrebbe seguitare il teorema meccanico, da cui si di­<lb></lb>mostrerebbe quella, che ricorre in ordine la VI nel trattato di Galileo. </s>

<s>A <lb></lb>questa succederebbe l&#039;altra proposizione che, nello stesso trattato galileiano, <pb xlink:href="020/01/2095.jpg" pagenum="338"></pb>le viene anteposta, e che concerne i tempi proporzionali alle lunghezze delle <lb></lb>scese oblique, sopra la qual proposizione erigendosi tutto il meccanico edi­<lb></lb>fizio, verrebbe questo, senza che nessuno avesse ragione di dubitarne, a ri­<lb></lb>posar sul più solido fondamento. </s></p><p type="main">

<s>Il Torricelli mostra, nell&#039;<emph type="italics"></emph>aliter<emph.end type="italics"></emph.end> alla proposizione sua IV, in che modo, <lb></lb>così disponendosi le cose, si verrebbe a concluder la desiderata verità fon­<lb></lb>damentale alla nuova Scienza galileiana, tutto dimostrando, senza nulla sup­<lb></lb>porre, ma si può l&#039;esempio di lui rendere anche più spedito nella forma <lb></lb>che segue: Sia ADB (fig. </s>

<s>160) il piano inclinato, e sia la lunghezza perpen­<lb></lb><figure id="id.020.01.2095.1.jpg" xlink:href="020/01/2095/1.jpg"></figure></s></p><p type="caption">

<s>Figura 160.<lb></lb>dicolare AC media proporzionale fra AB e AD. Avremo, <lb></lb>per il II sopra citato corollario alla proposizione II Dei <lb></lb>moti accelerati (Alb. </s>

<s>XIII, 173), T.oAB:T.oAD= <lb></lb>AB:AC. </s>

<s>Congiunti i punti D, C ne resulta il triangolo <lb></lb>rettangolo ADC, in cui, circoscrittogli il mezzo cerchio, <lb></lb>il lato AD si dimostra dal teorema meccanico essere ad <lb></lb>AC equidiuturno. </s>

<s>Ond&#039;è che a T.oAD sostituito il suo <lb></lb>uguale T.oAC nella sopra scritta ragione, si verrà sen­<lb></lb>z&#039;altro ad avere T.oAB:T.oAC=AB:AC, ossia che i tempi nella per­<lb></lb>pendicolare e nell&#039;obliqua stanno come le loro rispettive lunghezze. </s></p><p type="main">

<s>Ripensando a queste cose, direbbesi da tutti insieme col Torricelli es­<lb></lb>sere stata una mala ventura di Galileo quella di non aver conosciuto, e di <lb></lb>non aver messo in esecuzione un così bello espediente. </s>

<s>Che se parve acco­<lb></lb>starvisi, quando dettava al Viviani il teorema inserito postumo nel III dia­<lb></lb>logo Del moto, troppo tardi direbbero venne l&#039;inspirazione al buon vecchio. </s></p><p type="main">

<s>In così fatti sentimenti eravamo anche noi, quando, svolgendo il se­<lb></lb>condo Tomo della Parte quinta dei Manoscitti galileiani, ci abbattemmo a <lb></lb>leggere una proposizione, che ritraeva in sè l&#039;ordine propriamente divisato <lb></lb>dal Torricelli: si dimostrava cioè in essa che i tempi son proporzionali alle <lb></lb>lunghezze dei piani ugualmente elevati dop&#039;aver dal teorema meccanico con­<lb></lb>cluso l&#039;isocronismo per le corde dei cerchi. </s>

<s>Fummo a un tratto soprappresi <lb></lb>da tanta maraviglia, che non sapendo allora come attutirla, s&#039;andò a pen­<lb></lb>sare fra noi che fossero quelle cose dettate da Galileo a qualcuno de&#039;suoi <lb></lb>più familiari, come l&#039;ultimo progressivo svolgimento de&#039;suoi pensieri. </s>

<s>Ma ci <lb></lb>dovemmo poi persuadere che quello scritto era autografo, da mostrar che <lb></lb>non impigrita punto dalla vecchiezza fosse la mano, la quale, guidata an­<lb></lb>cora dalla libera vista, faceva correre la penna sicura. </s></p><p type="main">

<s>Seguitando avanti e indietro a squadernare il volume, tutti sopra pen­<lb></lb>siero di queste cose, ebbe quella prima nostra maraviglia a crescere anche <lb></lb>di più all&#039;incontrarci in un&#039;altra proposizione autografa, nella quale, col me­<lb></lb>desimo processo ma in modo alquanto diverso, dimostravasi, dal Teorema <lb></lb>meccanico, e dalla proprietà delle corde isocrone, che le tardità di due gravi <lb></lb>scendenti per due varie obliquità di piani ugualmente elevati erano propor­<lb></lb>zionali alle lunghezze delle discese. </s>

<s>In quel contrapporre le tardità alle ce­<lb></lb>lerità, causate dai momenti, ci parve riconoscere l&#039;esercizio delle ali giova-<pb xlink:href="020/01/2096.jpg" pagenum="339"></pb>nette, prima di spiegare i liberi voli, e il frammento, pubblicato nel Tomo XI <lb></lb>a pag. </s>

<s>56-62 dall&#039;Albèri, ci confermava nell&#039;opinione, che i ritrovati processi <lb></lb>dimostrativi, creduti degli ultimi, erano invece dei primi tempi. </s></p><p type="main">

<s>Allora, a uno de&#039;quesiti, che ci avevano tante volte tenuto in angustia, <lb></lb>cominciò ad apparire la speranza di una risposta. </s>

<s>Avendo letto quel che <lb></lb>scriveva Galileo, nel 1602, a Guidubaldo del Monte, delle leggi dei moti dei <lb></lb>gravi scendenti per la quarta di un cerchio, e ripensando che quella era <lb></lb>una delle ultime proposizioni, che suppone le parecchie altre dimostrate nel <lb></lb>libro Dei moti locali; si domandava a noi stessi: forse che la serie dei teo­<lb></lb>remi, i quali nel III dialogo Delle due nuove scienze si recitano dal Sal­<lb></lb>viati, fu dall&#039;Accademico ordinata infino dal 1602? Ma come è possibile ciò, <lb></lb>se non era ancora dimostrata la legge dei moti accelerati, la quale non occorse <lb></lb>prima del 1604, come si sa per certissimi documenti? </s>

<s>Eppure è un fatto <lb></lb>che aveva due anni prima Galileo dimostrato esser nelle scese dei gravi per <lb></lb>i cerchi l&#039;arco brachistocrono della corda sottesa; proposizione che doveva <lb></lb>necessariamente conseguire da altre proposizioni, fra le quali, non potendo <lb></lb>essere le due prime del secondo libro inserito nel Dialogolo terzo, sembrava <lb></lb>che la conclusion meccanica scritta a Guidubaldo non potess&#039;esser condotta <lb></lb>al modo, che si legge nel Dialogo ora detto, dove supponesi dimostrata la <lb></lb>proporzion dei tempi impiegati a percorrere acceleratamente in una mede­<lb></lb>sima direzione due spazi. </s>

<s>Ma perchè da questo in fuori non ha quella <lb></lb>XXXVI proposizione stampata nient&#039;altro di dinamico, si pensava che, di­<lb></lb>mostrato in altro modo e da tutt&#039;altri principii concluso il corollario secondo <lb></lb>della II proposizione Dei moti accelerati, poteva la detta proposizione XXXVI, <lb></lb>anche dalla statica sola, senza difficoltà, derivarsi. </s>

<s>Ritrovato perciò che s&#039;ebbe, <lb></lb>fra quelle confuse carte galileiane, il Teorema, dove dall&#039;isocronismo di due <lb></lb>corde, variamente inclinate al diametro perpendicolare di un cerchio, si con­<lb></lb>cludeva essere i tempi della discesa per le due varie altezze, come una di <lb></lb>esse altezze alla media fra tutt&#039;e due; non ci parve mancar altro per dire <lb></lb>di aver ritrovata la serie e il processo dimostrativo di quei teoremi, che, <lb></lb>pieno di compiacente maraviglia per la inaspettata verità dimostrata, Galileo, <lb></lb>per lettera del dì 29 del Novembre 1602, annunziava a Guidubaldo del Monte. </s></p><p type="main">

<s>Preso animo di qui a proseguire le nostre investigazioni, per rispon­<lb></lb>dere ai varii quesiti, che gli uni dagli altri ci rampollavano nella mente fe­<lb></lb>condi, si volle sapere qual relazione avesse con le annunziate a Guidubaldo <lb></lb>quella proposizione, nella quale dicemmo d&#039;esserci prima abbattuti, e che <lb></lb>per dimostrar come i tempi, nella perpendicolare e nell&#039;obliqua alte ugual­<lb></lb>mente son proporzionali alle lunghezze, procedeva propriamente a quel modo, <lb></lb>che suggerivasi dal Torricelli, per evitar qualunque supposto. </s>

<s>Si pensò da <lb></lb>principio che fosse una tal proposizione dimostrata, per sostituirsi a quella <lb></lb>delle <emph type="italics"></emph>tardità,<emph.end type="italics"></emph.end> fra i teoremi nel Settembre del 1602 già prima ordinati, ma <lb></lb>poi ci accorgemmo che quella stessa proposizione faceva parte di altre ri­<lb></lb>trovate da noi manoscritte, le quali accennavano a un trattato assai più <lb></lb>compiuto, e mostravano un andamento diverso dal primo: ci accorgemmo <pb xlink:href="020/01/2097.jpg" pagenum="340"></pb>insomma che Galileo riformava, e riordinava il primo libro dopo le scoperte <lb></lb>leggi dei moti accelerati. </s></p><p type="main">

<s>La curiosità però, sodisfatta così da una parte, accresceva piuttosto che <lb></lb>diminuire quella prima presa maraviglia dall&#039;altra, perchè, certificati ora­<lb></lb>mai due essere stati i varii modi di procedere senza nulla supporre, non si <lb></lb>sapeva intendere come, nel render solennemente pubblico il suo trattato <lb></lb>Dei movimenti locali, Galileo ripudiasse que&#039;due primi rigorosi processi per <lb></lb>eleggerne un terzo, che moveva da una supposizione, e che doveva metter <lb></lb>perciò negli animi tanto scandolo, e nelle menti tanto scompiglio. </s></p><p type="main">

<s>Desiderosi dunque d&#039;intendere la ragione di così strano ripudio, si tor­<lb></lb>nava, con più diligenza che mai, a quel manoscritto meccanico laberinto, <lb></lb>tenendo in mano, per filo da non ismarrirci, la proposizione fondamentale <lb></lb>dei tempi lungo i piani ugualmente elevati, dalla qual proposizione dipen­<lb></lb>dono tutte le altre appartenenti a quel secondo libro, che dopo la teoria dei <lb></lb>moti accelerati era, come dicemmo, la riforma e il riordinamento del primo <lb></lb>annunziato già nella sopra citata lettera a Guidubaldo. </s>

<s>Da un teorema, tor­<lb></lb>nando per quelle zibaldate carte innanzi e indietro, correndo e ricorrendo <lb></lb>faticosamente per le difformi facce di que&#039;fogli, a cercar l&#039;altro, che ne sa­<lb></lb>rebbe dovuto seguitare, secondo l&#039;intrapreso ordine dimostrativo, si trova­<lb></lb>vano i principii statici conserti coi dinamici a dar giusta misura, e quasi <lb></lb>bellezza di moto all&#039;andamento delle proposizioni. </s>

<s>A un tratto ci troviamo <lb></lb>dalla statica abbandonati, e ci accorgiamo che l&#039;Autore la scansa, come per­<lb></lb>sona a cui si creda esser sotto la veste ascosta un&#039;arme insidiosa. </s>

<s>Ma per­<lb></lb>chè non ce ne rimanga alcun dubbio, ce l&#039;ha Galileo stesso di mano pro­<lb></lb>pria lasciato scritto. </s>

<s>Dimostrato un teorema <emph type="italics"></emph>ex mechanicis,<emph.end type="italics"></emph.end> secondo il solito <lb></lb>modo, lo assale un dubbio molesto se quel ch&#039;è proprio dei moti equabili <lb></lb>possa convenire agli accelerati, e senz&#039;altro risolve e imperiosamente dice <lb></lb>a sè stesso: <emph type="italics"></emph>Demonstra aliter sic,<emph.end type="italics"></emph.end> e da lì innanzi rimane a condur le pro­<lb></lb>posizioni la Dinamica sola. </s></p><p type="main">

<s>Sodisfatti, per avere scoperto il motivo di ciò che ci aveva prima de­<lb></lb>stato così gran maraviglia, teniam dietro all&#039;Autore nella presa risoluzione, <lb></lb>e riconosciamo in quei manoscritti il teorema fondamentale concluso dal <lb></lb>nuovo supposto; teorema che doveva indegnamente supplantare i bei teo­<lb></lb>remi, derivati dalla teoria meccanica dei momenti. </s>

<s>Di qui dunque comincia <lb></lb>una nuova riforma, e si dà ordine a un trattato nuovo, che è il terzo ma­<lb></lb>noscritto, e che solo rimane a Galileo per preparazione immediata a quello, <lb></lb>che vedrà finalmente in Leyda la pubblica luce. </s>

<s>La stampa risponde talvolta <lb></lb>con leggere varietà al manoscritto, ma più spesso se ne dilunga con varietà <lb></lb>notabilissima, e utile di essere collazionata, perchè sovente, con l&#039;intenzione <lb></lb>di spiegar meglio il concetto, s&#039;avvolge ne&#039;ricorsi, e si smembra negl&#039;in­<lb></lb>cisi. </s>

<s>Cosicchè lo stampato, che è il quarto, non ci dispensa che solo in parte <lb></lb>dal far conoscere ai nostri lettori anche quel terzo libro, o terzo modo di <lb></lb>trattare dei movimenti locali, rimasto fin qui, insieme con gli altri due, non <lb></lb>visto fra gli studiati manoscritti di Galileo. </s></p><pb xlink:href="020/01/2098.jpg" pagenum="341"></pb><p type="main">

<s>Dir que&#039;libri non visti, o meglio non visti i materiali e i disegni la­<lb></lb>sciatici per costruirli, non parrà forse credibile a chi sa essere stati man­<lb></lb>dati, pochi anni addietro, per tutto il mondo trombetti a convocare mano­<lb></lb>scritti galileiani, e non potrà persuadersi costui che siasi atteso con tanta <lb></lb>industria a raccoglier <emph type="italics"></emph>Lettere<emph.end type="italics"></emph.end> di fuori, non curando in casa i teoremi, e a <lb></lb>mettere in pubblica mostra gli <emph type="italics"></emph>Scampoli,<emph.end type="italics"></emph.end> lasciando chiuse le stoffe negli <lb></lb>armadi. </s>

<s>Eppur, ne&#039;primi volumi dell&#039;<emph type="italics"></emph>Edizion nazionale,<emph.end type="italics"></emph.end> ne&#039;quali le opere <lb></lb>di Galileo ricorrono in ordine cronologico, avrebbero dovuto trovar luogo il <lb></lb>primo Libro, anteriore al 1602, e il secondo riformato tra il 1604 e il 1609, <lb></lb>nè ritrovandoveli, e ripensando che dovevano aver gl&#039;Italiani eletto all&#039;opera <lb></lb>alcuni de&#039;più valorosi in questa specialità di studii, s&#039;incominciava a dubi­<lb></lb>tare di esserci noi stessi ingannati, quando, meglio esaminando i fastosi <lb></lb>volumi nazionali, ci parve che non fosse l&#039;edizione diretta da quella propria <lb></lb>e particolare scienza richiesta al bisogno, e che fossero principalmente <lb></lb>rivolte le cure degli egregi editori a mettere i punti e le virgole al loro <lb></lb>posto, a restituir le dieresi e altri segni esquisiti, come farebbe un acca­<lb></lb>demico della Crusca, a cui fosse dato a curare qualche prezioso testo di <lb></lb>lingua. </s></p><p type="main">

<s>Ritrovatici dunque a correr soli questo mar periglioso, raddoppiammo <lb></lb>le nostre industrie in cercar d&#039;ogni parte argomenti, e in accomodarli al <lb></lb>nostro bisogno, perchè valessero tutti insieme a ridurci la fragile barca in <lb></lb>porto. </s>

<s>Daremo il nome di formali ad alcuni di quegli argomenti, e di ma­<lb></lb>teriali agli altri, intendendo per i primi quelli, che consistono nel concetto, <lb></lb>a cui s&#039;informano le varie proposizioni. </s>

<s>Dal progressivo concettuale svolgi­<lb></lb>mento si desume con certezza logica il relativo ordine cronologico e nume­<lb></lb>rico della serie de&#039;teoremi, ma gli altri argomenti, che si dissero materiali, <lb></lb>mentre da una parte servono di riscontro per l&#039;ordine relativo, sovvengono <lb></lb>dall&#039;altra necessari a determinare il tempo assoluto, rivelatoci massimamente <lb></lb>dalla data certissima dei commerci epistolari. </s></p><p type="main">

<s>A far materiale riscontro alla cronologia presunta dalla logica, ci han <lb></lb>servito non poco le forme calligrafiche, e le stesse varie tinte dell&#039;inchio­<lb></lb>stro. </s>

<s>È a tutti noto come la mano che scrive risenta varietà dagli anni, a <lb></lb>quel modo che la risentono i moti di tutte le altre membra, e come può <lb></lb>ciascuno fare esperienza in sè stesso, confrontando con quelle scritte a <lb></lb>trent&#039;anni le carte scritte a cinquanta. </s>

<s>Sarebbe la differenza senza dubbio <lb></lb>assai più notabile, se si facesse il confronto fra la calligrafia della prima <lb></lb>gioventù, con quella dell&#039;ultima vecchiezza, ma ci siam tenuti ai vent&#039;anni, <lb></lb>che son lo spazio intercesso fra queste scritture, lasciate nel 1610, e non <lb></lb>riprese di proposito fino al 1630, come si parrà a suo luogo da certissimi <lb></lb>documenti. </s>

<s>I teoremi dimostrati tra il 1602 e il 1610 sono scritti con in­<lb></lb>chiostro più chiaro, e con agili forme rotonde. </s>

<s>Nel 1630, la vista affievolita <lb></lb>così, che sarebbesi tra pochi anni affatto spenta, aveva bisogno di segni me­<lb></lb>glio scolpiti: l&#039;inchiostro perciò è nero, le linee grosse, le forme quadrate. </s>

<s><lb></lb>A noi quasi pareva di veder viva la mano, che in tante carte del detto <pb xlink:href="020/01/2099.jpg" pagenum="342"></pb>Tomo II torna, dopo vent&#039;anni, a scrivere sotto un teorema l&#039;enunciazione, <lb></lb>in quella forma propria che l&#039;originale serberà per la prossima stampa. </s></p><p type="main">

<s>D&#039;altre particolarità non terremo in discorso i Lettori, i quali le in­<lb></lb>tenderanno assai meglio, vedendole in atto nella pubblicazione, e nella sto­<lb></lb>ria di quei primi teoremi, intorno ai quali, per istituire una delle sue nuove <lb></lb>scienze, esercitò Galileo le sue matematiche speculazioni. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nella Lettera, scritta da Padova il dì 29 di Novembre del 1602, e che <lb></lb>s&#039;è più volte commemorata, dava Galileo a Guidubaldo del Monte notizia di <lb></lb>alcune esperienze di moti, che avendo apparenza di straordinari, e giudican­<lb></lb>dosi perciò dalla volgare opinione incredibili, diceva essergli stati confermati <lb></lb>dalla Geometria, la quale eragli nello stesso tempo venuta a rivelare que­<lb></lb><figure id="id.020.01.2099.1.jpg" xlink:href="020/01/2099/1.jpg"></figure></s></p><p type="caption">

<s>Figura 161.<lb></lb>st&#039;altre, non meno inopinabili conclusioni. <lb></lb></s>

<s>“ Sia dal cerchio BDA (fig. </s>

<s>161) il diame­<lb></lb>tro BA eretto all&#039;orizzonte, e dal punto A <lb></lb>fino alla circonferenza tirate linee <emph type="italics"></emph>utcum­<lb></lb>que<emph.end type="italics"></emph.end> AF, AE, AD, AC. Dimostro, dice Gali­<lb></lb>leo, mobili uguali cadere in tempi uguali, <lb></lb>e per la perpendicolare BA, e per gli piani <lb></lb>inclinati, secondo le linee CA, DA, EA, FA, <lb></lb>sicchè, partendosi nell&#039;istesso momento dalli <lb></lb>punti B, C, D, E, F arriveranno nell&#039;istesso <lb></lb>momento al termine A, e sia la linea FA <lb></lb>piccola quanto esser si voglia. </s>

<s>E forse anco <lb></lb>più inopinabile parerà questo pur da me <lb></lb>dimostrato, che, essendo la linea SA non <lb></lb>maggiore della corda di una quarta, e le linee SI, IA <emph type="italics"></emph>utcumque,<emph.end type="italics"></emph.end> più presto <lb></lb>fa il modesimo mobile il viaggio SIA, partendosi da S, che il viaggio solo <lb></lb>IA, partendosi da I ” (Alb. </s>

<s>VI, 23). </s></p><p type="main">

<s>Le annunziate proposizioni dipendevano da principii già noti, e da ve­<lb></lb>rità legittimamente di lì concluse con sottili matematici ragionamenti, che <lb></lb>s&#039;andarono, come rigagnoli in un fiume, a disperdere fra i teoremi inseriti <lb></lb>nel III dialogo Delle due nuove scienze. </s>

<s>E perchè la scienza universale della <lb></lb>Natura è irrigata da quest&#039;acque vive, non può chi cammina lungo le sponde <lb></lb>ad ammirare, e a cogliere i frutti dell&#039;ubertosa campagna, non tener desi­<lb></lb>deroso dietro i passi di colui, che viene ora a mostrar d&#039;onde salga la be­<lb></lb>nefica fonte, e a segnar quali sieno del primo formatosi ruscelletto i lontani <lb></lb>smarriti sentieri. </s></p><p type="main">

<s>PROPOSITIO I. — “ Momenta gravitatis eiusdem mobilis supra plano in-<pb xlink:href="020/01/2100.jpg" pagenum="343"></pb>clinato, et in perpendiculo, permutatim respondent longitudini et elevationi <lb></lb>eiusdem plani. </s>

<s>” </s></p><p type="main">

<s>“ Sit ad horizontem AB (fig. </s>

<s>162) planum inclinatum CA, in quo su­<lb></lb><figure id="id.020.01.2100.1.jpg" xlink:href="020/01/2100/1.jpg"></figure></s></p><p type="caption">

<s>Figura 162.<lb></lb>matur quodcumquo punctum C, et, dimissa perpendi­<lb></lb>culari ad horizontem CB, sit plani CA altitudo seu ele­<lb></lb>vatio. </s>

<s>Dico momentum gravitatis mobilis D, super plano <lb></lb>CA, ad totale suum momentum in perpendiculo CB, <lb></lb>esse ut altitudo CB ad eiusdem plani longitudinem CA ” <lb></lb>(MSS. Gal., P. V, T. II, fol. </s>

<s>179). Per la dimostrazione <lb></lb>di ciò rimanda Galileo al suo trattato Della scienza mec­<lb></lb>canica, che doveva dunque nel 1602 esser noto, benchè <lb></lb>andasse attorno anonimo e manoscritto. </s>

<s>“ Id autem ex Mechanicis probatum <lb></lb>est ” (ibid.). </s></p><p type="main">

<s>PROPOSITIO II. — “ Momenta gravitatis eiusdem mobilis, super diver­<lb></lb>sas planorum inclinationes, habent inter se permutatim eamdem rationem, <lb></lb><figure id="id.020.01.2100.2.jpg" xlink:href="020/01/2100/2.jpg"></figure></s></p><p type="caption">

<s>Figura 163.<lb></lb>quam eorumdem planorum longitudines, dum eidem <lb></lb>elevationi respondeant. </s>

<s>” </s></p><p type="main">

<s>“ Sint diversae planorum inclinationes AB, AC <lb></lb>(fig. </s>

<s>163) quae eidem elevationi AD respondeant. </s>

<s><lb></lb>Dico momentum gravitatis eiusdem mobilis super <lb></lb>AB, ad momentum gravitatis super AC, eamdem <lb></lb>habere rationem quam longitudo AC habet ad lon­<lb></lb>gitudinem AB. </s>

<s>Ex antecedenti enim momenta gra­<lb></lb>vitatis super AB, ad totale momentum in perpen­<lb></lb>diculo AD, est ut AD ad AB. </s>

<s>Totale vero momen­<lb></lb>tum per AD, ad momentum per AC, est ut CA <lb></lb>ad AD. Ergo, ex aequali, in analogia perturbata, momentum per AB, ad <lb></lb>momentum per AC, erit ut longitudo AC ad longitudinem AB. </s>

<s>Quod erat <lb></lb>demonstrandum ” (ibid.). </s></p><p type="main">

<s>PROPOSITIO III. — “ Sit ad horizontalem AH (fig. </s>

<s>164) perpendicula­<lb></lb><figure id="id.020.01.2100.3.jpg" xlink:href="020/01/2100/3.jpg"></figure></s></p><p type="caption">

<s>Figura 164.<lb></lb>ris BC, et inclinata BD, in qua sumatur <lb></lb>BE, et ex E, ad BD, perpendicularis aga­<lb></lb>tur EF, ipsi BC occurrens in F. </s>

<s>Demon­<lb></lb>strandum sit tempus per BE aequari <lb></lb>tempori per BF. ” </s></p><p type="main">

<s>“ Ducatur ex E perpendicularis ad <lb></lb>AB, quae sit EG, et quia impetus per <lb></lb>BE, ad impetum per EG, est ut EG ad <lb></lb>BE, ut supra demonstratur, ut autem <lb></lb>EG ad BE, ita BE ad BF, ob similitudi­<lb></lb>nem triangulorum GEB, BEF; ergo, ut <lb></lb>BF spacium, ad spacium BE, ita impetus <lb></lb>per BF ad impetum per BE. </s>

<s>Ergo eodem tempore fiet motus per BF et <lb></lb>per BE ” (ibid., fol. </s>

<s>147 ad terg.). </s></p><pb xlink:href="020/01/2101.jpg" pagenum="344"></pb><p type="main">

<s>La dimostrazione, che Galileo sarà per mettere in miglior forma in <lb></lb>quest&#039;altro Libro, dandocela più distesa, va qui succinta, come quella che <lb></lb>doveva solo servire per memoria all&#039;Autore, e che poteva anche così ba­<lb></lb>stare agli esperti di queste materie, i quali non occorreva fare avvertiti che <lb></lb>l&#039;impeto per EG è uguale all&#039;impeto per BF, essendo ambedue quelle linee <lb></lb>dirette nel perpendicolo. </s>

<s>Nè si richiama, per questi stessi motivi, il teorema <lb></lb>che nel libro Dei moti equabili si suppone essere stato già dimostrato, e da <lb></lb>cui dipende quella final conclusione, che cioè, essendo per BE e per BF <lb></lb>gl&#039;impeti o le velocità proporzionali agli spazi, i tempi necessariamente deb­<lb></lb>bono essere uguali. </s></p><p type="main">

<s>Era l&#039;attenzione di Galileo dalla dimostrata similitudine dei triangoli <lb></lb>GBE, EBF richiamata piuttosto ad avvertire un fatto, che non poteva esser <lb></lb>senza ragioni, e ci lasciava di una tale singolar avvertenza il documento <lb></lb>scritto in questa Nota. </s>

<s>“ Advertas cur cadentia ex B (nella preallegata figura) <lb></lb>sint semper una in locis sibi respondentibus, ut EF, ita ut angulus BEF <lb></lb>sit aequalis angulo FBH ” (ibid., fol. </s>

<s>57 ad terg.). Il costrutto, lasciato nel <lb></lb>manoscritto a questo punto interrotto, si compieva facilmente coll&#039;osservare <lb></lb>che, come l&#039;angolo BEF è uguale all&#039;angolo FBH, così l&#039;angolo EFB è <lb></lb>uguale all&#039;angolo GBE, intanto che se, data la lunghezza BE si voglia sa­<lb></lb>pere come dirigere la EF, che, incontrando la verticale BC prefinisca in essa <lb></lb>lo spazio BF sincrono alla data BE, si dee per quella direzione prender l&#039;an­<lb></lb>golo BEF uguale a FBH, che è l&#039;angolo fatto dalla linea BC con la oriz­<lb></lb>zontale. </s>

<s>Se sia data invece BF e si voglia da F dirigere sopra EB una linea, <lb></lb>che tagli nella BD una porzione EB sincrona alla BF, l&#039;angolo BFE della <lb></lb>direzione dev&#039;essere uguale a GBE, ch&#039;è pur l&#039;angolo fatto dalla stessa EB <lb></lb>con la orizzontale. </s>

<s>Son dunque date le direzioni, in ambedue i casi, dagli <lb></lb>angoli permutatamente fatti dalle linee EB, BF colla orizzontale: nuova av­<lb></lb><figure id="id.020.01.2101.1.jpg" xlink:href="020/01/2101/1.jpg"></figure></s></p><p type="caption">

<s>Figura 165.<lb></lb>vertita conclusione elegante, che si <lb></lb>verifica anche quando BC, a simili­<lb></lb>tudine di BD, sia obliqua, come Ga­<lb></lb>lileo passa così a dimostrare. </s></p><p type="main">

<s>PROPOSITIO IV. — Infra horizon­<lb></lb>tem AB (fig. </s>

<s>165), ex eodem puncto C, <lb></lb>sint duae rectae aequales utcumque <lb></lb>inclinatae CD, CE, et ex terminis D, E, <lb></lb>ad horizontem perpendiculares, agantur DA, EB, et lineae CD a puncto D <lb></lb>costituatur angulus CDF angulo BCE aequalis. </s>

<s>Dico ut DA ad BE ita esse <lb></lb>DC ad CF. ” </s></p><p type="main">

<s>“ Ducatur perpendicularis CG: et quia CDF aequatur angulo BCE, et <lb></lb>rectus G recto B, erit ut DC ad CG, ita CE ad EB. </s>

<s>Est autem CD ipsi CE <lb></lb>aequalis; ergo CG aequatur BE. </s>

<s>Et cum angulus CDF angulo BCE sit ae­<lb></lb>qualis, et angulus FCD communis, reliquus ad duos rectos DFC reliquo DCA <lb></lb>aequabitur, et anguli ad A, et G sunt recti. </s>

<s>Ergo triangulus ADC triangulo <lb></lb>CGF est similis, quare, ut AD ad DC, ita GC ad CF, et permutando, ut AD <pb xlink:href="020/01/2102.jpg" pagenum="345"></pb>ad CG, hoc est ad BE, ita DC ad CF, quod erat probandum ” (idid., fol. </s>

<s>148 <lb></lb>ad terg.). </s></p><p type="main">

<s>Il semplice Lemma geometrico s&#039;applica alla Meccanica con questo, che <lb></lb>immediatamente da Galileo si soggiunge, quasi in forma di corollario. </s>

<s>“ Cum <lb></lb>autem impetus per CD, ad impetum per CF, sit ut perpendiculus AD ad <lb></lb>perpendiculum BE; constat motus per CD et CF eodem tempore absolvi. </s>

<s><lb></lb>Itaque distantiae, quae in diversis inclinationibus eodem tempore conficiun­<lb></lb>tur, determinantur per lineam, quae, ut facit DF, lineis inclinatis occurrit <lb></lb>secundum angulos aequales illis, quos inclinatae ad horizontem constituunt, <lb></lb>permutatim sumptos ” (ibid.). </s></p><p type="main">

<s>Nemmen qui Galileo, a cui dovevano rimanere queste scritture per suo <lb></lb>uso privato, è sollecito di sminuzzar così il pane della Scienza, come quando <lb></lb>sarà per metterlo innanzi ai Simplicii sopra il pubblico desco, certissimo che <lb></lb>i Sagredi, ai quali soli intendeva allora di rivolgere il discorso, avrebbero <lb></lb>da sè medesimi, per la prima Proposizione facilmente compreso ch&#039;essendo <lb></lb>M.oCD:M.oAD=AD:DC, e M.oCE:M.oBE=BE:CE, da queste due <lb></lb>equazioni, nelle quali M.oAD=M.oBE, DC=CE, e M.oCE=M.oCF si <lb></lb>concludeva legittimamente essere i momenti stessi o gl&#039;impeti per CD o <lb></lb>per CF proporzionali alle due perpendicolari AD, BE, come ivi, senza trat­<lb></lb>tenersi a dimostrarlo, si ammette. </s>

<s>Questa concisione, che sarebbe ai buoni <lb></lb>intenditori tanto meglio piaciuta delle molte parole, è serbata pure nella <lb></lb><figure id="id.020.01.2102.1.jpg" xlink:href="020/01/2102/1.jpg"></figure></s></p><p type="caption">

<s>Figura 166.<lb></lb>seguente bellissima proposizione, feconda <lb></lb>di altre nuove bellissime conseguenze. </s></p><p type="main">

<s>PROPOSITIO V. — “ Sit GD (fig. </s>

<s>166) <lb></lb>erecta ad horizontem, DF vero inclinata; <lb></lb>dico eodem tempore fieri motum ex G in <lb></lb>D, et ex F in D. ” </s></p><p type="main">

<s>“ Momentum enim super FD est idem <lb></lb>ac super tangentem in E, quae ipsi FD sit <lb></lb>parallela. </s>

<s>Ergo momentum super FD, ad <lb></lb>totale momentum, erit ut CA ad AB, idest <lb></lb>AE. </s>

<s>Verum ut CA ad AE, ita ID ad DA, <lb></lb>et dupla FD ad duplum DG; ergo momen­<lb></lb>tum super FD, ad totale momentum super <lb></lb>GD, est ut FD ad GD. </s>

<s>Ergo eodem tempore <lb></lb>fiet motus per FD, et GD ” (ibid., fol. </s>

<s>152). </s></p><p type="main">

<s>I nostri Lettori riconoscono facilmente in questa una di quelle costru­<lb></lb>zioni, con le quali i Matematici, da Leonardo da Vinci al Torricelli, s&#039;ar­<lb></lb>gomentarono di concludere dalla Libbra le leggi statiche dei momenti sopra <lb></lb>i piani inclinati. </s>

<s>Costituito infatti il piano dalla tangente LN, elevata di NM <lb></lb>sopra la orizzontale LM, i triangoli simili LMN, AEC conducono per la via <lb></lb>piana a quel punto, a cui di slancio saltò Galileo, il quale pure ivi sottin­<lb></lb>dende un corollario, d&#039;altra parte di facilissima derivazione, dop&#039;avere osser­<lb></lb>vato che le dimostrate proprietà della corda DF convengono altresì a DO, <pb xlink:href="020/01/2103.jpg" pagenum="346"></pb>e a un&#039;altra corda qualunque. </s>

<s>Ora se GP, GQ sono uguali, e similmente <lb></lb>inclinate alle DF, DO, i moti per queste è evidente dover essere i mede­<lb></lb>simi dei moti per quelle, cosicchè insomma si riduce l&#039;accennato Corollario <lb></lb>a dire che in qualunque corda si conduca dall&#039;estremità D o dalla sommità <lb></lb>C del diametro a un punto della circonferenza, si spedisce il moto nel me­<lb></lb>desimo tempo come se cadesse il mobile per tutta la lunghezza verticale del <lb></lb>diametro stesso. </s>

<s>Le quali cose così ben predisposte conducono Galileo a di­<lb></lb>mostrar la seguente proposizione fondamentale. </s></p><p type="main">

<s>PROPOSITIO VI. — “ Sit planum horizontis secundum lineam ABC (fig. </s>

<s>167) <lb></lb>ad quam sint duo plana inclinata secundum lineas DB, DA. </s>

<s>Dico idem mo­<lb></lb><figure id="id.020.01.2103.1.jpg" xlink:href="020/01/2103/1.jpg"></figure></s></p><p type="caption">

<s>Figura 167.<lb></lb>bile tardius moveri per DA, quam per <lb></lb>DB, secundum rationem longitudinis <lb></lb>DA ad longitudinem DB. ” </s></p><p type="main">

<s>“ Erigatur enim ex B perpendicu­<lb></lb>laris ad horizontem, quae sit BE: ex D <lb></lb>vero, ipsi BD perpendicularis, DE oc­<lb></lb>curcens BE in E, et circa BDE trian­<lb></lb>gulum circulus describatur, qui tanget <lb></lb>AC in puncto B, ex quo, ipsi AD pa­<lb></lb>rallela, ducatur BF, et connectatur FD. </s>

<s><lb></lb>Patet tarditatem per FB esse consimilem tarditati per DA. </s>

<s>Quia vero tempore <lb></lb>eodem movetur mobile per DB et FB, patet velocitates per BD, ad velocita­<lb></lb>tes per BF, esse ut DB ad FB, ita ut semper iisdem temporibus duo mo­<lb></lb>bilia, ex punctis D, F venientia, linearum DB, FB partes, integris lineis DB, <lb></lb>FB proportione respondentes, peregerint. </s>

<s>” </s></p><p type="main">

<s>“ Cum vero angulus BFD, in portione, angulo DBA ad tangentem sit <lb></lb>aequalis, angulus vero DBF alterno BDA; aequiangula erunt triangula BFD, <lb></lb>ABD, et, ut BD ad BF, ita AD ad DB. </s>

<s>Ergo ut AD ad DB, ita velocitas <lb></lb>per DB ad velocitatem per DA, et ex opposito tarditas per DA, ad tardita­<lb></lb>tem per BD. ” </s></p><p type="main">

<s>“ Si hoc ponatur, reliqua demonstrari possunt. </s>

<s>Ponatur igitur augeri <lb></lb>et imminui motus velocitatem secundum proportionem, qua augentur et <lb></lb>minuuntur gravitatis momenta, et cum constet eiusdem mobilis momenta <lb></lb>gravitatis super plano DB, ad momenta super plano DA, esse ut longitudo <lb></lb>DA ad longitudinem DB; idcirco velocitatem per DB, ad velocitatem per DA, <lb></lb>esse ut AD ad DB ” (ibid., fol. </s>

<s>34). </s></p><p type="main">

<s>Il linguaggio stesso accenna, come si disse, essere stata delle prime a <lb></lb>dimostrarsi questa proposizione, nella quale <emph type="italics"></emph>tardità,<emph.end type="italics"></emph.end> o <emph type="italics"></emph>diuturnità,<emph.end type="italics"></emph.end> come ad <lb></lb>altri piacque dir meglio, si chiama quello, che poi Galileo, nel perfezionato <lb></lb>esercizio della sua scienza, chiamerà sempre col nome di <emph type="italics"></emph>tempo.<emph.end type="italics"></emph.end> A questo <lb></lb>ultimamente trascritto. </s>

<s>come a teorema antecedentemente dimostrato, accenna <lb></lb>il discorso pubblicatosi dall&#039;Albèri (Tomo XI, pag. </s>

<s>61, 62), da cui si con­<lb></lb>ferma che, posto essere i tempi come le lunghezze delle oblique ugualmente <lb></lb>elevate, <emph type="italics"></emph>reliqua demonstrari possunt.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2104.jpg" pagenum="347"></pb><p type="main">

<s>La prima cosa, che occorreva a dimostrare, per servirsene nel progresso <lb></lb>delle altre dimostrazioni, era che i tempi, per due spazi ugualmente diretti, <lb></lb>son proporzionali a uno dei detti spazi e alla media fra ambedue. </s>

<s>Ciò po­<lb></lb>tevasi immediatamente dedurre dalla legge dei moti accelerati, ma non es­<lb></lb>sendo questa ancora a Galileo nota, fu costretto a far del facile corollario <lb></lb>un elaborato teorema, a cui convenne di più chiamare in aiuto un lemma <lb></lb>geometrico, che ritrovasi manoscritto a tergo del folio 172 nel citato codice, <lb></lb>e che corrisponde al primo lemma premesso alla XXXVI proposizione stam­<lb></lb>pata (Alb. </s>

<s>XIII, 214). Noi potremmo rimandar là i Lettori, se in due parole <lb></lb><figure id="id.020.01.2104.1.jpg" xlink:href="020/01/2104/1.jpg"></figure></s></p><p type="caption">

<s>Figura 168.<lb></lb>non si riducesse qui alla loro memoria. </s>

<s>Per ritrovare <lb></lb>infatti le relazioni, che passano fra le tre linee AS, <lb></lb>AB, AC nella figura 168, basta congiungere insieme i <lb></lb>due punti B, C, d&#039;onde nascono i due triangoli SBC, <lb></lb>BCA che, riconosciuti simili, danno AB:AC=AC:AS, <lb></lb>in che consiste il Lemma geometrico, che s&#039;invoca per <lb></lb>condur la seguente proposizione. </s></p><p type="main">

<s>PROPOSITIO VII. — “ Posteaquam (in antecedenti <lb></lb>propos. </s>

<s>V et eius corollario) ostensum fuerit tempora <lb></lb>per AB, AC esse aequalia, demonstrabitur tempus per <lb></lb>AD, ad tempus per AE, esse ut DA ad mediam inter DA, AE. ” </s></p><p type="main">

<s>“ Nam tempus per DA, ad tempus per AC, est ut DA ad AC lineam: <lb></lb>Tempus autem per AC, idest per AB ad tempus AE, est ut lina AB ad AE, <lb></lb>hoc est AS ad AD. </s>

<s>Ergo ex aequali, in analogia perturbata, tempus per AD, <lb></lb>ad tempus AE, est ut linea AS ad lineam AC. </s>

<s>Cumque AC, ex demonstra­<lb></lb>tis, sit media inter SA, AB, et ut SA ad AB, ita DA ad AE; ergo tempus <lb></lb>per AD, ad tempus per AE, est ut DA ad mediam inter DA, AE, quod erat <lb></lb>probandum ” (ibid., fol. </s>

<s>147). </s></p><p type="main">

<s>Si sottintende da Galileo, anche dopo questa, un facile corollario, in <lb></lb>cui si dimostra che, non solo nelle direzioni verticali, ma e nelle oblique <lb></lb>corre la medesima proporzione dei tempi. </s>

<s>Avendosi infatti le oblique AC, AD <lb></lb>(fig. </s>

<s>169) se AR è media fra AB, AG, condotte dai punti G, R le due oriz­<lb></lb>zontali GE, RN, è facile vedere che, in virtù dei triangoli simili, venutisi a <lb></lb>descrivere dalle dette orizzontali parallele, AT e AN son medie proporzio­<lb></lb>nali fra AC, AF, e AD, AE. </s>

<s>Ed essendo pure, in virtù dei triangoli simili, <lb></lb><figure id="id.020.01.2104.2.jpg" xlink:href="020/01/2104/2.jpg"></figure></s></p><p type="caption">

<s>Figura 169.<lb></lb>fra AR e AG, AB, nella verticale, come fra <lb></lb>AT e AC, AF, nell&#039;obliqua, la medesima pro­<lb></lb>porzion degli spazi; è chiaro che la medesima <lb></lb>proporzione si serberà pure dei tempi. </s>

<s>In <lb></lb>ogni modo si suppongon da Galileo facil­<lb></lb>mente note queste meccaniche proprietà, nella <lb></lb>proposizione, che così passa a dimostrare. </s></p><p type="main">

<s>PROPOSITIO VIII. — “ Sint ad horizon­<lb></lb>tem DB (in eadem figura 169) quotcumque <lb></lb>lineae ab eadem altitudine A demissae AB, <pb xlink:href="020/01/2105.jpg" pagenum="348"></pb>AC, AD, et sumpto quolibet puncto G, per ipsum horizonti parallela sit GFE, <lb></lb>sitque media inter GA, AB ipsa AR, et per R altera parallela RTN. </s>

<s>Constat <lb></lb>lineas AT, AN esse medias inter CA, AF, et DA, AE. </s>

<s>Dico quod si absuma­<lb></lb>tur AB esse tempus, quo mobile cadit ex A io B, tempus RB esse illud, <lb></lb>quo conficitur GB; TC vero esse tempus ipsius CF, et ND ipsius ED. ” </s></p><p type="main">

<s>“ Id autem constat, nam, cum AR sit media inter BA, AG, sitque BA <lb></lb>tempus casus totius AB; tempus AR erit tempus casus per AG. </s>

<s>Ergo reli­<lb></lb>quum temporis RB erit tempus casus per GB, post AG, et idem dicetur de <lb></lb>aliis temporibus TC, ND, et lineae FC, ED. ” </s></p><p type="main">

<s>“ Patet insuper tempora casuum per GB, FC, ED esse ut lineas GB, <lb></lb>FC, ED. </s>

<s>Non tamen a magnitudinibus linearum GB, FC, ED esse determi­<lb></lb>nandas eorumdem temporum quantitates si temporis mensura ponatur AB, <lb></lb>in quo tempore conficiatur linea AB, sed desumendas esse a lineis RB, <lb></lb>TC, ND ” (ibid., fol. </s>

<s>178). </s></p><p type="main">

<s>L&#039;avvertimento è importante, e sembra che Galileo l&#039;abbia fatto a sè <lb></lb>stesso, dop&#039;averne sperimentata la fallacia, nella quale essendo egli prima <lb></lb>incorso, si trovò impedita la via di giungere alla sua final conclusione. </s>

<s>Que­<lb></lb>sta conclusione si sa dalla Lettera a Guidubaldo esser quella che, per le <lb></lb>corde spezzate, il tempo speso da un mobile per giungere da un punto della <lb></lb>circonferenza all&#039;infimo contatto di lei col piano orizzontale, sopra cui sup­<lb></lb>ponesi eretta, è più breve che per la corda intera. </s>

<s>Per giunger felicemente <lb></lb>a concluder ciò le otto sopra dimostrate proposizioni servivano quasi tutte <lb></lb>di principii necessari e di mezzi: una però mancavane ancora, per la quale <lb></lb><figure id="id.020.01.2105.1.jpg" xlink:href="020/01/2105/1.jpg"></figure></s></p><p type="caption">

<s>Figura 170.<lb></lb>si dimostrasse che, partendosi un mobile per esempio <lb></lb>in D (fig. </s>

<s>170) dalla quiete, giunto in B, deve avere <lb></lb>acquistata la velocità medesima, come se fosse venuto <lb></lb>per l&#039;obliqua AE, o per qualunque altra che, movendo <lb></lb>pure da A, risalisse a toccare un punto della orizzon­<lb></lb>tale DE prolungata. </s>

<s>La dimostrazione sarebbe per dare <lb></lb>in seguito a Galileo gran faccenda, ma egli intanto se <lb></lb>n&#039;espediva, supponendola inclusa, e facilmente deri­<lb></lb>vabile per corollario da quest&#039;altro teorema, che si <lb></lb>propone così e si dimostra. </s></p><p type="main">

<s>PROPOSITIO IX. — “ Tempora casuum in planis, <lb></lb>quorum eadem sit altitudo, eamdem inter se servant <lb></lb>rationem, sive illis idem impetus praecedat, sive ex quiete incipiant. </s>

<s>” </s></p><p type="main">

<s>“ Sint plana AB, AC (in supra signata figura) quorum eadem altitudo. </s>

<s><lb></lb>Extenso autem BA utcumque in D, fiat casus ex D per ambo AC, AB. </s>

<s>Dico <lb></lb>tempus per AC, ad tempus per AB, esse in eadem ratione, ac si principium <lb></lb>casus foret in A. </s>

<s>Sit enim ipsarum BD, DA media DF, et ducta parallela <lb></lb>ex F erit GE media inter CE, AE. </s>

<s>Facto igitur principio lationis ex D, tem­<lb></lb>pora casuum per AC, AB erunt inter se ut AG, AF. </s>

<s>Quod si casus inci­<lb></lb>piat ex A, erunt tempora per AC, AB inter se ut AC, AB lineae. </s>

<s>Ergo pa­<lb></lb>tet proposituum ” (ibid., fol. </s>

<s>38). </s></p><pb xlink:href="020/01/2106.jpg" pagenum="349"></pb><p type="main">

<s>Così tutto, con matematica legge preordinato a dimostrare l&#039;ultima <lb></lb>proposizione annunziata nella lettera a Guidubaldo, nient&#039;altro rimaneva a <lb></lb>fare a Galileo, che premetter due lemmi geometrici, che sono il II e il III <lb></lb>premessi alla XXXIX proposizione stampata, e che si leggono manoscritti <lb></lb>l&#039;uno al foglio 163, e l&#039;altro al foglio 172 del citato volume. </s>

<s>È il primo dei <lb></lb>detti lemmi stampati quello già premesso alla VII proposizione, da noi pub­<lb></lb>blicatasi nelle pagine poco addietro, cosicchè, tutte insomma ricomposte le <lb></lb>membra, danno quasi abito di persona e atteggiamento di vita alla verità <lb></lb>così ultimamente annunziata. </s></p><p type="main">

<s>PROPOSITIO X. — “ Sit circuli circumferentia AIS (fig. </s>

<s>171), et diame­<lb></lb><figure id="id.020.01.2106.1.jpg" xlink:href="020/01/2106/1.jpg"></figure></s></p><p type="caption">

<s>Figura 171.<lb></lb>ter AB ad horizontem erectum, et ducatur <lb></lb>SA, non maior subtendente quadrante, et a <lb></lb>terminis S, A aliae duae ad quodcumque <lb></lb>punctum I: dico mobile ex termino S ferri <lb></lb>per duas SI, IA lineas tempore breviori, <lb></lb>quam per SA, ex eodem termino S, vel per <lb></lb>solam AI, ex termino I. ” </s></p><p type="main">

<s>“ Ducta sit per S ipsi AB perpendi­<lb></lb>cularis .... ” (ibid., fol. </s>

<s>163) e seguita come <lb></lb>nello stampato (Alb. </s>

<s>XIII, 216, 17) con <lb></lb>qualche leggerissima differenza nelle pa­<lb></lb>role. </s>

<s>Ed ecco per quali vie, rimaste in mezzo <lb></lb>a tanto fervore di studii galileiani, nella <lb></lb>storia della Scienza fin qui non segnate, si <lb></lb>condusse Galileo, <emph type="italics"></emph>senza trasgredire i termini meccanici,<emph.end type="italics"></emph.end> a dimostrare le sue <lb></lb>inopinabili conclusioni. </s>

<s>Erano que&#039;termini meccanici ridotti alla Statica, e <lb></lb>l&#039;Autore, nelle dieci proposizioni che compongono quel suo primo trattato <lb></lb><emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> non si serve nè poteva servirsi d&#039;altro argomento. </s>

<s>Ma, istituitasi <lb></lb>nel 1604 la Dinamica nuova, s&#039;aprirono alla Scienza altre più late vie, e si <lb></lb>potè giungere per più diretti e piani sentieri al medesimo intento deside­<lb></lb>rato, ch&#039;era quello di dimostrare il brachistocronismo dei gravi scendenti <lb></lb>per le molteplici corde inflesse e sottese a una quarta di cerchio. </s>

<s>Essendo <lb></lb>questo dunque il termine fisso, rimaneva nel teorema meccanico tuttavia <lb></lb>fermo il principio, cosicchè venivasi la trasformazione a subire dal solo mezzo, <lb></lb>e da ciò dipendon principalmente le note distintive di quel secondo Libro <lb></lb>che, raccolto dai Manoscritti galileiani e ordinato, si porge ora alla notizia <lb></lb>e all&#039;esame dei nostri meditativi Lettori. </s></p><pb xlink:href="020/01/2107.jpg" pagenum="350"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chi, dalle nuove aure menato, s&#039;asside nella mirabile navicella a cor­<lb></lb>rere questo lucido mare aperto da Galileo, s&#039;accorge che una vela, benchè <lb></lb>rimanga alquanto più sotto alla maestra, è nondimeno la più frequente nel­<lb></lb>l&#039;opera, e in render agile il corso forse la più efficace di tutte le altre. </s>

<s>È <lb></lb>facile agli studiosi della Scienza meccanica, vogliam dire passando al senso <lb></lb>proprio dal figurato, accorgersi che, nella massima parte dei teoremi gali­<lb></lb>leiani, chi conduce innanzi le dimostrazioni, e più efficacemente le volge alla <lb></lb>loro final conclusione, è la legge dei tempi, che si passano dal mobile in <lb></lb>percorrer due spazi ugualmente diretti. </s>

<s>Abbiamo veduto per quali vie lun­<lb></lb>ghe e tortuose fosse dovuto passar Galileo, prima di giungere, nella sopra <lb></lb>trascritta proposizione VII, a quella conclusione, che ora invece vedeva scen­<lb></lb>dere per corollario immediato dal principio dinamico, sentenziosamente da <lb></lb>lui stesso formulato in queste parole: “ Momenta velocitatum cadentis ex <lb></lb>sublimi sunt inter se ut radices distantiarum peractarum, nempe in subdu­<lb></lb>pla ratione illarum ” (MSS. Gal., P. V, T. II, fol. </s>

<s>164 a tergo). </s></p><p type="main">

<s>Di qui è che, avendo le velocità la medesima proporzione dei tempi, se <lb></lb>cada il mobile da A in B (fig. </s>

<s>172) o da A in C, per due spazi diversi, ma se­<lb></lb>condo la medesima linea AL diretti, avremo T.oAB:T.oAC=√AB:√AC= <lb></lb>AB:√AB.AC, che è quel che appunto proponevasi di dimostrar Galileo <lb></lb><figure id="id.020.01.2107.1.jpg" xlink:href="020/01/2107/1.jpg"></figure></s></p><p type="caption">

<s>Figura 172.<lb></lb>stesso, co&#039;principii statici, nella detta sua VII pro­<lb></lb>posizione. </s></p><p type="main">

<s>Incomincia perciò questo secondo Libro, dietro <lb></lb>i principii dinamici riformato, dal dimostrare le pro­<lb></lb>prietà generali dei moti accelerati, per derivarne di <lb></lb>lì gli opportuni corollari. </s>

<s>Ma non abbiamo trovate <lb></lb>scritte le proposizioni preparate a questo particolare <lb></lb>intento di servir come d&#039;introduzione al nuovo trat­<lb></lb>tato. </s>

<s>Forse, tutto in sollecitudine di ridurre intanto <lb></lb>alle forme più convenienti il teorema fondamentale <lb></lb>dei tempi, nelle oblique ugualmente elevate, propor­<lb></lb>zionali agli spazi; non attese Galileo a distendere <lb></lb>quelle prime dimostrazioni relative alle libere ca­<lb></lb>dute dei gravi, riserbandosi a farlo dopo che, dallo stesso ora detto fonda­<lb></lb>mentale, si sarebbe svolta la serie di tutti gli altri teoremi. </s>

<s>Quando poi, per <lb></lb>ridursi sotto gli occhi compiuto il disegno del suo trattato, prese risoluzione <lb></lb>di porre a questa serie i primi termini tralasciati, era già venuto il Cava­<lb></lb>lieri a proporgli il suo Metodo degli indivisibili, secondo il quale condusse <lb></lb>Galileo stesso le proposizioni, che si ricopian dal Manoscritto, per ridurle <lb></lb>qui ne&#039;primi ordini di questo secondo Libro, resa la ragione ai Lettori del <lb></lb>commesso anacronismo. </s></p><pb xlink:href="020/01/2108.jpg" pagenum="351"></pb><p type="main">

<s>PROPOSITIO I. — “ Absumo eam esse cadentis mobilis per lineam AL <lb></lb>(nella precedente figura 172) accelerationem, ut, pro ratione spatii peracti, <lb></lb>crescat velocitas, ita ut velocitas in C, ad velocitatem in B, sit ut spacium <lb></lb>CA ad spacium BA. ” </s></p><p type="main">

<s>“ Cum autem haec ita se habeant, ponatur AX, cum AL angulum con­<lb></lb>tinens, sumptisque partibus AB, BC, CD, DE .... aequalibus, protrahantur <lb></lb>BM, CN, DO, EP.... Si itaque cadentis per AL velocitates, in B, C, D, E <lb></lb>locis, se habent ut distantiae AB, AC, AD, AE; ergo se quoque habent ut <lb></lb>lineae BM, CN, DO, EP. ” </s></p><p type="main">

<s>“ Quia vero velocitas augetur consequenter in omnibus punctis lineae <lb></lb>AE, et non tantum in adnotatis B, C, D, ergo velocitates illae omnes sese <lb></lb>respiciunt ut lineae, quae, ab omnibus dictis punctis lineae AE, ipsis BM, <lb></lb>CN, DO aequidistanter producuntur. </s>

<s>Ipsae autem infinitae sunt et consti­<lb></lb>tuunt triangulum AEP: ergo velocitates, in omnibus punctis lineae AB, ad <lb></lb>velocitates in omnibus punctis lineae AC, ita se habent ut triangulus ABM <lb></lb>ad triangulum ACN, et sic de reliquis, hoc est in duplicata proportione li­<lb></lb>nearum AB, AC ” (MSS. Gal., P. V, T. II, fol. </s>

<s>35 a tergo). </s></p><p type="main">

<s>Si vede bene che questa proposizione è compendiata da quell&#039;altra scrit­<lb></lb>tura italiana, che si pubblicò nel capitolo precedente, per adattarla alle forme <lb></lb>proprie, e al succinto andamento dei nuovi teoremi. </s>

<s>Ma che Galileo vera­<lb></lb>mente la scrivesse con la particolare intenzione di premetterla al secondo <lb></lb>libro Dei movimenti locali, si conferma dal soggiungersi immediatamente il <lb></lb>seguente corollario, che ricorre, per questo e per gli altri simili trattati, con <lb></lb>assidua vicenda, quasi moto di spola a tesser le fila della lunga tela. </s></p><p type="main">

<s>COROLLARIUM. — “ Quia vero, pro ratione incrementi accelerationis, <lb></lb>tempora, quibus motus ipsi fiunt, debent imminui; ergo tempus, quo mo­<lb></lb>bile permeat AB, ad tempus, quo permeat AC, est ut AB linea ad eam, <lb></lb>quae inter AB, AC media proportionalis existit ” (ibid.). </s></p><p type="main">

<s>Il metodo degl&#039;Indivisibili, applicato a dimostrar la legge fondamentale <lb></lb>dei moti accelerati, si porgeva altresì opportuno a dimostrarne le conseguenze <lb></lb>più rilevanti, compendiate in questa, che qui si soggiunge </s></p><p type="main">

<s>PROPOSITIO II. — “ Factus sit motus, ex A (fig. </s>

<s>173) usque B, natu­<lb></lb><figure id="id.020.01.2108.1.jpg" xlink:href="020/01/2108/1.jpg"></figure></s></p><p type="caption">

<s>Figura 173.<lb></lb>raliter acceleratus: Dico quod, si velocitas, in omnibus <lb></lb>punctis AB, fuisset eadem ac reperitur in puncto B, du­<lb></lb>plo citius fuisset peractum spacium AB, quia velocitates <lb></lb>omnes, in singulis punctis AB lineae, ad totidem velocita­<lb></lb>tes, quarum unaquaeque esset aequalis velocitati BC, eam­<lb></lb>dem haberent rationem, quam triangulus ABC ad rectan­<lb></lb>gulum ABCD. ” </s></p><p type="main">

<s>COROLLARIUM I. — “ Sequitur ex hoc, quod, si ad <lb></lb>horizontem CB fuerit planum BA elevatum, sitque BC <lb></lb>dupla ad BA, mobile, ex A in B, et successive, ex B in C, temporibus aequa­<lb></lb>libus esse perventurum, nam, postquam est in B, per reliqua BC, uniformi <lb></lb>velocitate et eadem movetur, qua in ipsomet termino B, post casum AB. ” </s></p><pb xlink:href="020/01/2109.jpg" pagenum="352"></pb><p type="main">

<s>COROLLARIUM II. — “ Patet rursus totum tempus per ABC, ad tempus <lb></lb>per AB, esse sesquialterum ” (ibid., fol. </s>

<s>181). </s></p><p type="main">

<s>Le proposizioni III e IV, che contengono in sè dimostrato il principio <lb></lb>meccanico, son le medesime della I e II, scritte nel primo Libro, e si pre­<lb></lb>mettono qui come necessarie a concluderne la proposizione V, che è la V <lb></lb>di quello stesso primo Libro, corredata però di un elegante corollario. </s>

<s>Fu <lb></lb>un tal corollario suggerito a Galileo dall&#039;essersi, in cercare i mezzi termini <lb></lb>della detta V proposizione, incontrato nel seguente teorema: Sia CDA (fig. </s>

<s>174) <lb></lb><figure id="id.020.01.2109.1.jpg" xlink:href="020/01/2109/1.jpg"></figure></s></p><p type="caption">

<s>Figura 174.<lb></lb>un circolo, a cui giunga nel punto A la AF tan­<lb></lb>gente. </s>

<s>Se si conducano dal punto di contatto le due <lb></lb>corde AC, AD, e presa AB=AD, si abbassino da <lb></lb>B, D alla AF due perpendicolari, s&#039;avrà la propor­<lb></lb>zione DF:EB=AD:AC. </s></p><p type="main">

<s>Facendo ora il trapasso dalla Geometria alla <lb></lb>Meccanica, considerando la AF orizzontalmente di­<lb></lb>retta, e AD, AC quali due piani inclinati, il dimo­<lb></lb>strato teorema geometrico, insieme con la detta pro­<lb></lb>posizione V, davan facile modo a Galileo di risolver <lb></lb>questo meccanico teorema: Sopra il piano AC trovare il punto, da cui par­<lb></lb>tendosi un mobile, giunga in A nel medesimo tempo, che vi giungerebbe <lb></lb>quel medesimo mobile, partendosi da D sull&#039;altro piano; imperocchè la cer­<lb></lb>cata lunghezza AC s&#039;è trovato esser quarta proporzionale dopo DF, EB, AD, <lb></lb>ed essere di più una corda che, partendosi dal medesimo infimo punto del <lb></lb>diametro a un punto della medesima circonferenza, si sa, per la dimostrata <lb></lb>proposizione V, dover essere alla corda AD tautocrona, per cui soggiungesi <lb></lb>da Galileo così a quella stessa V proposizione, per modo di corollario: </s></p><p type="main">

<s>“ Collige, existentibus planis inaequaliter inclinatis AD, AC, atque data <lb></lb>longitudine AD, inveniri posse, in plano AC, portionem, quae eodem tem­<lb></lb>pore cum DA peragatur. </s>

<s>Ducto enim perpendiculo DF, et, posita AB ae­<lb></lb>quali AD, ducto perpendiculo BE, fiat, ut DF ad EB, ita DA ad AC, erit­<lb></lb>que tempus per CA aequalc tempori per DA ” (ibid., fol. </s>

<s>47). </s></p><p type="main">

<s>Così nuovamente preparate le cose, nel corollario della prima proposi­<lb></lb>zione, nel teorema meccanico, e in questo ultimo del tautocronismo delle <lb></lb>corde nel cerchio; passava felicemente Galileo, senza nulla supporre, a di­<lb></lb>mostrar questa, che è in ordine la VI proposizione del Libro, e che può <lb></lb>considerarsi rispetto all&#039;altre come la canocchia, dalla quale si dovrà trarre <lb></lb>e compilare il lungo filo. </s></p><p type="main">

<s>PROPOSITIO VI. — “ Tempus casus per planum inclinatum, ad tempus <lb></lb>sasus per lineam suae altitudinis, est ut eiusdem plani longitudo ad longi­<lb></lb>tudinem suae altitudinis. </s>

<s>” </s></p><p type="main">

<s>“ Sit planum inclinatum BA (fig. </s>

<s>175) ad lineam horizontis AC, sitque <lb></lb>linea altitudinis perpendicularis BC: Dico tempus casus, quo mobile move­<lb></lb>tur per BA, ad tempus, in quo cadit per BC, esse ut BA ad BC. ” </s></p><p type="main">

<s>“ Erigatur perpendicularis ad horizontem ex A, quae sit AD, cui oc-<pb xlink:href="020/01/2110.jpg" pagenum="353"></pb>currat in D perpendicularis ad AB ducta ex B, quae sit BD, et circa trian­<lb></lb><figure id="id.020.01.2110.1.jpg" xlink:href="020/01/2110/1.jpg"></figure></s></p><p type="caption">

<s>Figura 175.<lb></lb>gulum ABD circulus describatur. </s>

<s>Et quia DA, <lb></lb>BC ambae sunt ad horizontem perpendiculares, <lb></lb>constat tempus casus per DA, ad tempus casus <lb></lb>per BC, esse ut media inter DA, BC ad ipsam <lb></lb>BC. </s>

<s>Tempus autem casus per DA aequatur <lb></lb>tempori casus per BA: media vero inter DA <lb></lb>et BC, est ipsa AB; ergo patet propositum. </s>

<s>” </s></p><p type="main">

<s>COROLLARIUM. — “ Ex hoc sequitur ca­<lb></lb>suum tempora per plana inclinata, quorum <lb></lb>eadem sit altitudo, esse inter se ut eorumdem <lb></lb>planorum longitudines. </s>

<s>Si enim fuerit aliud planum inclinatum BE, tempus <lb></lb>casus per BA, ad tempus casus per BC est ut BA linea ad BC. </s>

<s>Tempus vero <lb></lb>per BE, ad tempus per BC, est ut BE ad BC; ergo, ex aequali, patet pro­<lb></lb>positum ” (ibid., fol. </s>

<s>60). </s></p><p type="main">

<s>Preordinato, in queste proposizioni, e specialmente nella bellissima ul­<lb></lb>tima, l&#039;andamento di tutto il resto, procedeva Galileo innanzi per raggiun­<lb></lb>gere il suo finale intento, lieto nella propria coscienza di non aver trasgre­<lb></lb>dito i termini meccanici, in conformità de&#039;quali soggiungeva la seguente <lb></lb>proposizione, dando miglior forma a quella in terzo luogo, nel I Libro, già <lb></lb>dimostrata: </s></p><p type="main">

<s>PROPOSITIO VII. — “ Si ex eodem puncto horizontis ducatur perpendicu­<lb></lb>lus et planum inclinatum, et in plano inclinato sumatur quodlibet punctum, <lb></lb>a quo in plano perpendicularis linea usque ad perpendiculum protrahatur; <lb></lb>lationes, in parte perpendiculi inter horizontem et occursum perpendicula­<lb></lb>ris intercepta, et in parte plani inclinati inter eamdem perpendicularem et <lb></lb>horizontalem intercepta, eodem tempore absolvuntur. </s>

<s>” </s></p><p type="main">

<s>“ Sint, ex eodem puncto B horizontalis AH (fig. </s>

<s>176), perpendicularis <lb></lb>BC, et planum inclinatum BD. </s>

<s>Sumpto quolibet puncto E, ex eo, ad EB, <lb></lb><figure id="id.020.01.2110.2.jpg" xlink:href="020/01/2110/2.jpg"></figure></s></p><p type="caption">

<s>Figura 176.<lb></lb>perpendicularis agatur EF, occurrens <lb></lb>perpendiculo in puncto F: Dieo lationes <lb></lb>per BF, et per EB, eodem tempore con­<lb></lb>fici. </s>

<s>” </s></p><p type="main">

<s>“ Demittatur, ex eodem puncto E, <lb></lb>perpendicularis ad horizontem, EG, quae <lb></lb>erit perpendiculo BF parallela, et angu­<lb></lb>lus GEB coalterno EBF aequalis, et rec­<lb></lb>tus BGE recto BEF: quare aequiangula <lb></lb>erunt triangula GEB, BEF, et, ut GE ad <lb></lb>EB, ita EB ad BF. </s>

<s>Ut autem GE ad EB, <lb></lb>ita momentum gravitatis mobilis in plano <lb></lb>BD, ad totale suum momentum in perpendiculo BC. </s>

<s>Habet igitur distantia <lb></lb>EB, ad distantiam BF, eamdem rationem, quam gravitatis momentum super <lb></lb>planum EB, ad totale momentum super perpendiculum BF: quare eodem <pb xlink:href="020/01/2111.jpg" pagenum="354"></pb>tempore conficiuntur lationes per EB et BF ” (MSS. Gal., P. V, T. II, <lb></lb>fol. </s>

<s>180). </s></p><p type="main">

<s>Il lieto e libero progresso delle proposizioni, a questo punto, si arresta, <lb></lb>perchè, ripensando Galileo intorno al principio meccanico invocato nell&#039;ul­<lb></lb>tima parte di questa dimostrazione, per concluderne efficacemente l&#039;intento, <lb></lb>dubita se, essendo il moto del grave lungo il piano e nel perpendicolo acce­<lb></lb>lerato, possa legittimamente applicarsi in questo caso il teorema dei moti <lb></lb>equabili, che cioè, avendosi le velocità uguali, i tempi sono proporzionali agli <lb></lb>spazi. </s>

<s>Perciò, dopo la proposizione VII, ora ultimamente trascritta, rivela <lb></lb>così la penosa tenzione dei suoi nuovi dubbi, e la subitanea presa risolu­<lb></lb>zione di dare altro indirizzo ai suoi pensieri: </s></p><p type="main">

<s>“ Necessariam hanc propositionem ad praecedentem existimo. </s>

<s>Velocita­<lb></lb>tes mobilium, quae in aequali momento incipiunt motum, sunt semper inter <lb></lb>se in eadem proportione, ac si aequabili motu progrederent, ut verbi gra­<lb></lb>tia mobile per AC (fig. </s>

<s>177) incipit motum cum momento, ad momentum <lb></lb><figure id="id.020.01.2111.1.jpg" xlink:href="020/01/2111/1.jpg"></figure></s></p><p type="caption">

<s>Figura 177.<lb></lb>per CB, ut CB ad AC. </s>

<s>Si aequabili motu progredere­<lb></lb>tur, tempus per AC, ad tempus per CB, esset ut AC <lb></lb>ad CB, quod in accelerato dubito quidem, et ideo de­<lb></lb>monstra aliter sic: ” </s></p><p type="main">

<s>PROPOSITIO VIII. — “ Tempus per AC (in eadem <lb></lb>figura) ad tempus per CB, ex praecedentibus, est ut <lb></lb>linea AC, ad lineam CB. </s>

<s>Sed etiam ad tempus CD habet <lb></lb>eamdem rationem, cum CB sit media inter AC, DC; ergo <lb></lb>tempora CD, CB erunt aequalia ” (ibid., fol. </s>

<s>177). </s></p><p type="main">

<s>Qui dunque si rimane questo secondo Libro, mosso con sì lieti auspici, <lb></lb>interrotto, e le belle meccaniche dimostrazioni, che lo componevano, son la­<lb></lb>sciate dall&#039;Autore in abbandono, come farebbe l&#039;Artefice degli elaborati or­<lb></lb>gani di una macchina in costruzione, la quale vuol essere riformata sopra <lb></lb>altro modello. </s>

<s>E perchè il fulcro, diciamo così di una tal macchina consi­<lb></lb>steva nella VII sopra scritta proposizione, soggetta ai dubbi nati intorno alla <lb></lb>proposizione seguente, e per le medesime ragioni; doveva la riforma inco­<lb></lb>minciare di lì, e in altri modi fuor dei meccanici, e con principii diversi da <lb></lb>quelli, che son proprii dei moti equabili, conveniva dimostrar che, in piani <lb></lb>ugualmente alti ma variamente inclinati, i tempi delle cadute son propor­<lb></lb>zionali agli spazi. </s></p><p type="main">

<s>La prima difficoltà, che doveva pararsi innanzi alla mente di Galileo, <lb></lb>in ridur le cose alle sue intenzioni, consisteva nell&#039;aver riconosciuto impos­<lb></lb>sibile a rendere i moti accelerati indipendenti dagli equabili, cosicchè non <lb></lb>rimaneva a far altro, per quietare i dubbi e per rendere legittime le con­<lb></lb>clusioni, che dimostrar come l&#039;una qualità di moto ritorni nell&#039;altra. </s>

<s>Per <lb></lb>far ciò, non essendo istituita ancora la Geometria degl&#039;Indivisibili, bisognava <lb></lb>contentarsi alle approssimazioni, attribuendo alle piccole particelle quante <lb></lb>quel che non è proprio a rigore che delle infinitesime. </s></p><p type="main">

<s>Siano AB (fig. </s>

<s>178) perpendicolare e AC inclinata comprese fra le oriz-<pb xlink:href="020/01/2112.jpg" pagenum="355"></pb>zontali AM, BC, e dividasi tutta la detta AB nelle porzioncelle AE, EG, GI, <lb></lb>IL .... conducendo da ogni punto di divisione altrettante orizzontali, come <lb></lb>DE, FG, HI.... Credeva Galileo di poter leggittimamente riguardar come <lb></lb><figure id="id.020.01.2112.1.jpg" xlink:href="020/01/2112/1.jpg"></figure></s></p><p type="caption">

<s>Figura 178.<lb></lb>equabile il moto fatto per i brevi tratti AE, AD; <lb></lb>EG, DF; GI, FH; ... cosicchè, quando fosse vero <lb></lb>che in E e in D le velocità sono uguali, se ne <lb></lb>concluderebbe che il tempo per AE sta al tempo <lb></lb>per AD come lo spazio AE sta allo spazio AD, <lb></lb>d&#039;onde, dal semplice passando al composto, tor­<lb></lb>nerebbe altresì dimostrato, scansando i modi mec­<lb></lb>canici e i repentini passaggi dai moti equabili agli <lb></lb>accelerati, che il tempo per tutta la AB sta al <lb></lb>tempo per tutta la AC, come la lunghezza AB <lb></lb>perpendicolare sta alla lunghezza AC obliqua. </s></p><p type="main">

<s>Il modo di toglier dunque ogni dubbio, che <lb></lb>potesse nascere intorno ai processi dimostrativi <lb></lb>delle prime proposizioni, credeva Galileo che fosse così ritrovato, quando <lb></lb>gli si concedesse da tutti per vero che in D e in E, in F e in G, in H e <lb></lb>in I, e in somma, in tutti i punti ugualmente distanti dall&#039;orizzonte, le <lb></lb>velocità nel perpendicolo e nell&#039;obliqua fossero uguali. </s>

<s>Ma questo dall&#039;al­<lb></lb>tra parte era il principio, da cui s&#039;era fatta dipendere la Statica antica, la <lb></lb>verità della quale nessuno avrebbe osato negare, come nessuno aveva messo <lb></lb>ancora dubbio intorno al modo di computare i momenti, secondo l&#039;uso del <lb></lb>Nemorario, del Cardano e del Tartaglia, moltiplicando per le discese rette <lb></lb>le quantità della materia. </s>

<s>Supponevasi di più è vero da Galileo che le ve­<lb></lb>locità fossero proporzionali ai momenti, ma nemmeno intorno a ciò pareva <lb></lb>che potesse nascer dubbio, dovendo esser necessariamente le cause propor­<lb></lb>zionali agli effetti. </s>

<s>Non fidandosi nonostante di sè medesimo, ed essendo <lb></lb>la cosa di tanta importanza, volle Galileo stesso averne il parere da uno <lb></lb>dei più grandi Matematici, che si conoscessero allora in Italia, e il dì 5 di <lb></lb>Giugno del 1609 scriveva da Padova a Roma una lettera a Luca Valerio, <lb></lb>comunicandogli i due supposti, e interrogandolo se credeva che, senz&#039;altra <lb></lb>prova, si potessero ammetter per veri. </s>

<s>Indugiò il Valerio infino al dì 18 del <lb></lb>seguente mese di Luglio, per farvi più riposata considerazione, <lb></lb><figure id="id.020.01.2112.2.jpg" xlink:href="020/01/2112/2.jpg"></figure></s></p><p type="caption">

<s>Figura 179.<lb></lb>e finalmente rispose che, per principii di una scienza di mezzo, <lb></lb>non gli sembravano i due proposti punto oscuri, ma gli si ren­<lb></lb>devano anzi chiarissimi a quel lume di metafisica “ che, mol­<lb></lb>tiplicandosi la virtù della causa sufficiente, è necessario si <lb></lb>moltiplichi la quantità dell&#039;effetto, secondo la medesima pro­<lb></lb>porzione ” (Alb. </s>

<s>VII, 46). </s></p><p type="main">

<s>“ Dunque (soggiungeva poco appresso lo stesso Valerio, <lb></lb>riducendo ai casi particolari le generalità del suo discorso) se <lb></lb>l&#039;impeto e l&#039;inclinazione della gravità del corpo A (fig. </s>

<s>179), <lb></lb>sopra il piano inclinato all&#039;orizzonte secondo l&#039;angolo B, si <pb xlink:href="020/01/2113.jpg" pagenum="356"></pb>supponga esser doppio dell&#039;impeto della gravità del medesimo A sopra il <lb></lb>piano inclinato all&#039;orizzonte secondo l&#039;angolo C, maggiore dell&#039;angolo B, e <lb></lb>tali due diversi impeti nascano dalla gravità di A, limitata verso la produ­<lb></lb>zione dell&#039;impeto diversamente, per le diverse inclinazioni dei detti piani; <lb></lb>si vede per immediata conseguenza che la velocità del moto naturale di A, <lb></lb>sopra il piano meno inclinato, sarà doppia della velocità del moto della me­<lb></lb>desima A sopra quell&#039;altro piano più inclinato. </s>

<s>Dunque il vigore della causa <lb></lb>immediata della doppia velocità, che è l&#039;impeto o l&#039;inclinazione alla doppia <lb></lb>velocità, doveva esser doppia dell&#039;inclinazione alla mezza velocità, secondo <lb></lb>la maggiore inclinazione dell&#039;altro piano ” (ivi, pag. </s>

<s>47). </s></p><p type="main">

<s>A confermare la ragionevelezza di questo discorso, interrompendo per <lb></lb>un poco il filo alla storia, giova osservare come inconsapevolmente si ri­<lb></lb>scontrasse con quell&#039;altro discorso, che faceva il Torricelli, quando venne <lb></lb>il Mersenno a promovere di fatto le difficoltà sospettate da Galileo. </s>

<s>Nello <lb></lb>scolio alla proposizione II <emph type="italics"></emph>De motu gravium<emph.end type="italics"></emph.end> aveva scritto l&#039;Autore: “ Sup­<lb></lb>ponimus hic, cum ipso Galileo, velocitates in diversis planorum inclinatio­<lb></lb>nibus ita esse, ut sunt momenta, quando eadem fuerit moles ” (Op. </s>

<s>geom. </s>

<s><lb></lb>cit, P. I, pag. </s>

<s>104). Ora, avendo il Mersenno letto il trattato torricelliano, <lb></lb>scriveva da Parigi all&#039;Autore stesso, fra le parecchie altre cose che non gli <lb></lb>erano piaciute, anche queste: “ Supponis cum Galileo velocitates in diver­<lb></lb>sis planorum inclinationibus ita esse, ut sunt momenta, quando fuerit eadem <lb></lb>moles. </s>

<s>Si quis negaverit hanc hypothesim, ob paralogismum et confusionem <lb></lb>momentorum, seu gravitationum, cum ipsis motibus; quomodo suppositum <lb></lb>probare possit, ne forte corruant quaecumque Galileus se probaturum exi­<lb></lb>stimavit, aut tu ipse in illius gratiam addideris? </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. XLI, <lb></lb>fol. </s>

<s>68 ad t.). </s></p><p type="main">

<s>A queste difficoltà e a queste accuse rispondeva così, per sè e per Galileo, <lb></lb>il Torricelli con i medesimi argomenti, che il comun senso aveva suggeriti al <lb></lb>Valerio: “ Quod ego suppono pag. </s>

<s>104, cum Galileo, adeo manifestum mihi vi­<lb></lb>detur, ut sine ulla dubitatione loco principii admitti et concedi posse videatur. </s>

<s><lb></lb>Ratio physica est. </s>

<s>Si fuerint a diversis planis duae sphaerae, exempli gratia, <lb></lb>vitreae et aequales, postquam ostendero momentum unius ad momentum al­<lb></lb>terius esse duplum, quis non concedat et velocitatem ad velocitatem esse du­<lb></lb>plam? </s>

<s>Dupla enim causa duplum effectum parere debet in eodem subìecto. </s>

<s><lb></lb>Moles supponuntur aequeles, eiusdemque materiae, virtus vero, quae im­<lb></lb>pellit alteram molem, dupla demonstratur virtutis alterius. </s>

<s>Ergo, si dupla <lb></lb>virtus est, duplam proculdubio velocitatem efficiet ” (ivi, T. LX, fol. </s>

<s>76). </s></p><p type="main">

<s>Bello è quel che il Torricelli soggiunge, per prevenire le difficoltà e <lb></lb>per confermare la dottrina galileiana che le velocità, nelle scese naturali dei <lb></lb>gravi, sono indipendenti dai loro pesi, concludendo in queste parole la sua <lb></lb>lunga dimostrazione: “ Virtus minor, ad minus pondus a se movendum, <lb></lb>eamdem habet rationem, quam virtus maior ad maius pondus a se moven­<lb></lb>dum ” (ibid., fol. </s>

<s>76 ad t.). Ma è da tornare al Valerio, per veder quel che <lb></lb>egli sentisse di quell&#039;altro importante supposto comunicatogli da Galileo. </s></p><pb xlink:href="020/01/2114.jpg" pagenum="357"></pb><p type="main">

<s>Egli dava, nel riconoscerne la naturale evidenza, la più decisa e più <lb></lb>concludente dimostrazione fra le molte che, dai Matematici posteriori, a in­<lb></lb>cominciare dallo stesso Galileo infino all&#039;Huyghens, furono speculate, e pro­<lb></lb>poste a verificare le prime fatte supposizioni. </s>

<s>Si desumeva per esso Valerio <lb></lb>la detta dimostrazione dal principio della composizione dei moti, considerando <lb></lb>l&#039;impeto della scesa per l&#039;obliqua AC (fig. </s>

<s>180) come prodotto dalla forza <lb></lb><figure id="id.020.01.2114.1.jpg" xlink:href="020/01/2114/1.jpg"></figure></s></p><p type="caption">

<s>Figura 180.<lb></lb>AC, la quale venga decomposta nella verticale BC e nella <lb></lb>orizzontale AB. </s>

<s>E perciocchè per questa la forza impel­<lb></lb>lente è nulla, non riman dunque attivo altro che l&#039;im­<lb></lb>peto per BC, e perciò essendo le cadute o per AC o <lb></lb>per BC del medesimo effetto, si vede come debbano <lb></lb>essere in B e in A le velocità uguali. </s>

<s>E perchè son <lb></lb>documento assai importante alla storia dei moti com­<lb></lb>posti e a quella del famoso supposto meccanico, rife­<lb></lb>riamo le parole proprie, che soggiungeva alle sopra trascritte il valoroso pro­<lb></lb>fessore nell&#039;Arciginnasio romano. </s></p><p type="main">

<s>“ Per quanto poi si riferisce alla seconda supposizione, scriveva a Ga­<lb></lb>lileo, questa non mi si rende men chiara della prima, perciocchè essendo il <lb></lb>moto del corpo grave D, nella figura precedente, mosso per l&#039;AC all&#039;oriz­<lb></lb>zonte AB, mobile verso l&#039;AB, e l&#039;altro per una perpendicolare all&#039;orizzonte, <lb></lb>essa ancor mobile; cosa chiara è che, quando D sarà in A, avrà acquistato <lb></lb>tanto impeto o inclinazione a velocemente muoversi, che è la quantità del­<lb></lb>l&#039;effetto (in quanto effetto, dico, di quella parte del moto composto, che si <lb></lb>fa per la perpendicolare mobile eguale alla stabile CB) quanto avrebbe acqui­<lb></lb>stato, se D si fosse mosso per la sola perpendicolare CB, e ciò dico in vi­<lb></lb>gore del sopra detto principio ” (Alb. </s>

<s>VIII, 47, 48). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Rassicurato dunque così Galileo che, supponendosi noti i due principii <lb></lb>sottoposti all&#039;autorevole giudizio di Luca Valerio, si poteva sopr&#039;essi, sen­<lb></lb>z&#039;altro bisogno di ricorrere al Teorema meccanico, stabilire con sicurezza il <lb></lb>nuovo architettato edifizio; nell&#039;estate del 1609 dette mano a condurlo se­<lb></lb>condo quest&#039;altro meditato disegno, lusingandosi che sarebbe senz&#039;alcuna <lb></lb>contradizione approvato. </s>

<s>Le due prime proposizioni perciò del II Libro ri­<lb></lb>manevano ferme, come il primo anello, da cui doveva dipendere la lunga <lb></lb>catena, senz&#039;altro intermedio delle due seguenti proposizioni meccaniche, le <lb></lb>quali venivano perciò repudiate come sospette di fallacia in concludere da <lb></lb>esse le ragioni dei moti accelerati. </s>

<s>Dovevano in loro luogo supplire i due <lb></lb>principii supposti, dai quali si verrebbe a dimostrare il Teorema fondamen­<lb></lb>tale, che cioè i tempi nel perpendicolo e nell&#039;obliqua hanno la proporzione <lb></lb>delle loro lunghezze lineari. </s></p><pb xlink:href="020/01/2115.jpg" pagenum="358"></pb><p type="main">

<s>Premesso dunque il trattato Dei moti equabili, e le dette proposizioni <lb></lb>Ia e IIa Dei moti accelerati, la IIIa, che doveva immediatamente seguitare in <lb></lb>questo terzo libro galileiano <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> era così formulata, e dalla fatta <lb></lb>supposizione delle velocità uguali, dopo cadute uguali, nel seguente modo <lb></lb>condotta: </s></p><p type="main">

<s>PROPOSITIO III. — “ Si in perpendiculo et in plano inclinato, quorum <lb></lb>eadem sit altitudo, feratur idem mobile, tempora lationum erunt inter se ut <lb></lb>plani inclinati, et perpendiculi longitudines. </s>

<s>” </s></p><p type="main">

<s>“ Sint ad planum horizontis CB (fig. </s>

<s>181) perpendicularis AB, et pla­<lb></lb>num inclinatum AC, quorum eadem sit altitudo, nempe ipsa perpendicula­<lb></lb><figure id="id.020.01.2115.1.jpg" xlink:href="020/01/2115/1.jpg"></figure></s></p><p type="caption">

<s>Figura 181.<lb></lb>ris AB, et per ipsam descendat idem mobile. </s>

<s>Dico <lb></lb>tempus lationis per AB, ad tempus lationis per <lb></lb>AC, esse ut longitudo AB, ad longitudinem AC. ” </s></p><p type="main">

<s>“ Cum enim assumptum sit, in inclinato de­<lb></lb>scensu, volocitatis momenta eadem semper repe­<lb></lb>riri in punctis aequaliter ab horizonte distanti­<lb></lb>bus, iuxta perpendiculares distantias continue <lb></lb>augeri secundum rationem elongationis perpen­<lb></lb>dicularis a linea horizontali, in qua fuit lationis <lb></lb>initium; constat quod, producta linea horizontali <lb></lb>AM, quae ipsi BC erit parallela, sumptisque in <lb></lb>perpendiculari AB quotcumque punctis E, G, I, <lb></lb>L, et per ipsis ductis parallelis horizonti ED, GF, <lb></lb>IH, LK, erit mobilis per AB momentum, seu gradus velocitatis in puncto E <lb></lb>idem cum gradu velocitatis lati per AC in puncto D, cum punctorum E, D <lb></lb>eadem sit distantia perpendicularis ab horizonte AM, et similiter concludatur <lb></lb>in punctis F, G idem esse velocitatis momentum, et rursus in punctis H, I, <lb></lb>et K, L, et C, B. </s>

<s>Et quia velocitas semper intenditur pro ratione elongationis <lb></lb>a termino A, constat in latione AB tot esse velocitatis gradus, seu momenta <lb></lb>diversa, quot sunt in eadem linea AB puncta magis a termino A distantia, <lb></lb>quibus totidem in linea AC respondent, et per parallelas lineas determinantur, <lb></lb>in quibus iidem sunt gradus velocitatis. </s>

<s>” </s></p><p type="main">

<s>“ Sunt igitur in linea AB quasi innumerabilia quaedam spaciola, qui­<lb></lb>bus multitudine quidem aequalia, et bina sumpta, in eamdem rationem re­<lb></lb>spondentia, alia signant in AC, per lineas innumeras parallelas, ex punctis <lb></lb>lineae AB ad lineam AC extensas. </s>

<s>Intercepta nam AD, DF, EH ad spacia <lb></lb>AE, EG, GI respondent singula singulis ad rationem AC ad AB, suntque <lb></lb>in singulis binis sibi respondentibus iidem velocitatis gradus. </s>

<s>Ergo, ex prae­<lb></lb>cedentibus, tempora omnia simul sumpta lationum omnium per AB, ad tem­<lb></lb>pora omnia similiter accepta lationum omnium per AC, eamdem hubebunt <lb></lb>rationem quam spacia omnia lineae AB, ad spacia omnia lineae AC. </s>

<s>Hoc <lb></lb>autem idem esse ac tempus casus per AB ad tempus casus per AC; idest <lb></lb>ut linea AB ad AC, quod erat demonstrandum ” (MSS. Gal., P. V, T. II, <lb></lb>fol. </s>

<s>179). </s></p><pb xlink:href="020/01/2116.jpg" pagenum="359"></pb><p type="main">

<s>Di quel che si dava nel II Libro per corollario ne fa in questo l&#039;Au­<lb></lb>tore una proposizione distinta, che immediatamente succede alla sopra scritta, <lb></lb>in quarto luogo, e in tal forma: </s></p><p type="main">

<s>PROPOSITIO IV. — “ Tempora lationum per diversas lineas inclinatas, <lb></lb>quarum eadem sit altitudo perpendicularis, sunt inter se ut earumdem li­<lb></lb>nearum longitudines. </s>

<s>” </s></p><p type="main">

<s>“ Sint ad horizontem BD (fig. </s>

<s>182) diversa plana inclinata AB, AC, <lb></lb><figure id="id.020.01.2116.1.jpg" xlink:href="020/01/2116/1.jpg"></figure></s></p><p type="caption">

<s>Figura 182.<lb></lb>quorum eadem sit altitudo AD perpendicularis. </s>

<s>Dico <lb></lb>tempus casus per AB, ad tempus casus per AC, esse <lb></lb>ut AB longitudo, ad longitudinem AC. ” </s></p><p type="main">

<s>“ Ex antecedenti enim tempus casus per AB, <lb></lb>ad tempus casus per perpendicularem AD, est ut AB <lb></lb>linea ad lineam AD, et, per eamdem, ut AC linea <lb></lb>ad ipsam AD, ita tempus casus per AC, ad tempus <lb></lb>casus per AD. Ergo, ex aequali, ut longitudo AB <lb></lb>ad longitudinem AC, ita tempus casus per AB. ad <lb></lb>tempus casus per AC ” (ibid., fol. </s>

<s>179 ad t.). </s></p><p type="main">

<s>L&#039;altra proposizione fondamentale concernente <lb></lb>il tautocronismo delle corde nei cerchi, che nel primo e nel secondo Libro <lb></lb>si concludeva direttamente dal Teorema meccanico, escluso ora questo Teo­<lb></lb>rema, conveniva dimostrarla in altro modo, che la VIII proposizione del II <lb></lb>Libro avrebbe offerto in sè pronto e spedito. </s>

<s>Imperocchè se nel triangolo <lb></lb>ADC (fig. </s>

<s>183), rettangolo in D, il tempo per AD è uguale al tempo per <lb></lb><figure id="id.020.01.2116.2.jpg" xlink:href="020/01/2116/2.jpg"></figure></s></p><p type="caption">

<s>Figura 183.<lb></lb>AC, bastava circoscrivere il mezzo cerchio ADC al detto <lb></lb>triangolo rettangolo, perchè fosse all&#039;occhio insieme e <lb></lb>alla mente manifesto che la caduta per la corda AD, e <lb></lb>per il diametro AC si spediscono nel medesimo tempo. </s>

<s><lb></lb>Volle Galileo nonostante dar così altra macchina a una <lb></lb>proposizione, che doveva al suo intento essere della <lb></lb>massima importanza. </s></p><p type="main">

<s>PROPOSITIO V. — “ Si in circulo, ad horizontem <lb></lb>erecto, a puncto sublimi quocumque ducantur lineae rectae, usque ad circum­<lb></lb>ferentiam, per quas cadant gravia quotcumque, omnia tem­<lb></lb><figure id="id.020.01.2116.3.jpg" xlink:href="020/01/2116/3.jpg"></figure></s></p><p type="caption">

<s>Figura 184.<lb></lb>poribus aequalibus ad terminos suos pervenient. </s>

<s>” </s></p><p type="main">

<s>“ Sit enim circumferentia ad horizontem erecta ABEC <lb></lb>(fig. </s>

<s>184), punctum sublime A, a quo lineae quotcumque, <lb></lb>ad circumferentiam usque, protrahantur AE, AB, et per <lb></lb>ipsas cadant mobilia: Dico, temporibus aequalibus, illa <lb></lb>perventura esse ad terminos E, B. ” </s></p><p type="main">

<s>“ Sit enim AC per centrum ducta, cui ex B per­<lb></lb>pendiculasis sit BD. </s>

<s>Patet AB mediam esse proportiona­<lb></lb>lem inter CA, AD, quare, ex demonstratis, tempus, quo <lb></lb>mobile ex A cadit in C, ad tempus casus ex A in D, est <lb></lb>ut linea BA, ad lineam AD. ” </s></p><pb xlink:href="020/01/2117.jpg" pagenum="360"></pb><p type="main">

<s>“ Verum, similiter, ex demonstratis, tempus casus ex A in B, ad tem­<lb></lb>pus casus ex A in D, est ut BA ad AD. </s>

<s>Ergo tempora casuum AB, AC <lb></lb>erunt aequalia, cum eamdem, ad idem tempus casus, habeant rationem. </s>

<s>Et <lb></lb>similiter de reliquis omnibus demonstratur. </s>

<s>Ergo patet propositum ” (ibid., <lb></lb>fol. </s>

<s>48). </s></p><p type="main">

<s>È soggiunto a questa proposizione un Corollario, a cui non avrebbe <lb></lb>pensato di supplire nel trattato a stampa il Viviani, se l&#039;avesse qui trovato <lb></lb>nel Manoscritto. </s>

<s>Vedremo tra poco come si sian bene incontrati, benchè <lb></lb>inconsapevolmente, il Discepolo col Maestro. </s></p><p type="main">

<s>COROLLARIUM. — “ Ex his colligitur gravia eodem tempore pertransire <lb></lb>plana inaequalia, et inaequaliter inclinata, dum, quam proportionem habet <lb></lb>longitudo maioris plani, ad longitudinem alterius, eamdem duplicatam habeat <lb></lb>perpendicularis maioris plani, ad perpendicularem minoris. </s>

<s>Cum enim qua­<lb></lb>dratum AE sit aequale rectangulo CAF, quadratum vero BA rectangulo <lb></lb>CAD; rectangulum vero CAF, ad rectangulum CAD, est ut FA ad AD; ergo <lb></lb>FA ad AD est ut quadratum EA, ad quadratum BA. </s>

<s>Ratio igitur perpendicu­<lb></lb>laris FA, ad perpendicularem DA, dupla est rationis EA ad AB. etc. </s>

<s>” (ibid.). </s></p><p type="main">

<s>Non mancava che aggiungere a questa V la proposizione IX del I Li­<lb></lb>bro, con i tre Lemmi geometrici ivi già preparati, per concludere il princi­<lb></lb>pale intento, qual era quello di dimostrare il brachistocronismo dell&#039;arco <lb></lb>rispetto alle corde inflesse e sottese, a quel modo che fu mantenuto in tutte <lb></lb>le varie forme di trattati, dal primo, composto nel 1604, infino all&#039;ultimo <lb></lb>mandato nel 1638 alle stampe. </s>

<s>La somma dunque dei principali teoremi, che <lb></lb>qualificarono questo III Libro, e che lo distinguono nella mossa e nell&#039;an­<lb></lb>damento dai precedenti, si riduceva alle cinque proposizioni, in parte sopra <lb></lb>accennate, e in parte trascritte, dalle quali s&#039;è detto come un passo solo <lb></lb>condurrebbe Galileo alla sua finale intenzione. </s>

<s>Ma si conteneva in quei teo­<lb></lb>remi un rigoglio giovanile di vita, che voleva scoppiare in numerosi ram­<lb></lb>polli, i nodi germinativi de&#039;quali s&#039;ascondevano latenti nella ultima trascritta <lb></lb>proposizione V, nel corollario di lei, e nella proposizione IX del I Libro. </s>

<s><lb></lb>Basta rivolger l&#039;occhio sulla figura 184, qui poco addietro impressa, e ri­<lb></lb>chiamarsi alla mente le nozioni, ch&#039;ella doveva illustrare, per vedervi sotto <lb></lb>annidati due varii germi, da ciascun de&#039;quali si svolgerebbe un proprio e <lb></lb>distinto ordine di teoremi. </s>

<s>Le inclinate AB, AE infatti, per le quali s&#039;im­<lb></lb>magina da Galileo avere le loro scese i gravi, ora si considerano in quanto <lb></lb>sono corde di un cerchio, come si fa nella proposizione, ora in quanto son <lb></lb>piani, adattati comunque all&#039;uso di sostentare i corpi cadenti, come si fa <lb></lb>nell&#039;immediato corollario ivi soggiunto. </s>

<s>Dal riguardar le cose sotto quel <lb></lb>primo aspetto, si rappresentavano alla mente, come raggio di luce in varie <lb></lb>parti riflesso e diffratto, i teoremi e i problemi concernenti i varii casi dei <lb></lb>piani, da un mobile passati in tempi o più lunghi o più brevi; mentre, dal <lb></lb>riguardar le cose sotto quell&#039;altro aspetto, nasceva la curiosità di saper le <lb></lb>leggi, a cui vanno soggette le scese, secondo che i piani variamente incli­<lb></lb>nati son di uguale o differente lunghezza. </s>

<s>La IX proposizione poi, che bi-<pb xlink:href="020/01/2118.jpg" pagenum="361"></pb>sognò a Galileo aggiungere, nel primo e negli altri trattati, per ritrovare in <lb></lb>qual proporzione stia il tempo, che impiega un mobile a scendere per due <lb></lb>piani inflessi, era la più feconda di tutte, come quella che rendevasi trasfor­<lb></lb>mabile in una numerosa elegante varietà di casi. </s></p><p type="main">

<s>In quelle cinque proposizioni dunque, che s&#039;è detto di sopra, e nelle <lb></lb>altre due, l&#039;una delle quali preparava immediatamente, e l&#039;altra concludeva <lb></lb>la finale intenzion dell&#039;Autore, ch&#039;era quella di dimostrar come la scesa per <lb></lb>l&#039;arco è più breve che per le corde; si rappresentava, per dir così, il nudo <lb></lb>tronco, che, dai tre detti nodi scoppiando, si dovea rivestire via via di no­<lb></lb>velli rami e di fronde. </s>

<s>L&#039;opera dedita ad aggiungere all&#039;albero della Nuova <lb></lb>scienza questo decoro, fu per Galileo lunga, perchè distratta dalle maravi­<lb></lb>gliose scoperte celesti, e interrotta dai casi fortunosi della vita. </s>

<s>Posto nel <lb></lb>1609 il nuovo fondamento, sulle due ipotesi comunicate a Luca Valerio, e <lb></lb>riformate le due proposizioni fondamentali concernenti il tempo della scesa <lb></lb>per le oblique di uguale altezza, e il tautocronismo delle corde, con che rap­<lb></lb>presentavasi della Nuova scienza, come dicevasi, il nudo tronco; non fece <lb></lb>altro Galileo, infino al 1630, che derivar qualche ramo ora dall&#039;uno, ora <lb></lb>dall&#039;altro centro germinativo. </s>

<s>Son di una tale opera rimaste segnate, nei <lb></lb>Manoscritti galileiani, le disperse vestigia, le quali noi intendiamo di rasse­<lb></lb>gnare nei tre detti ordini distinti, secondo che le cose via via dimostrate <lb></lb>dipendono, come da loro principio, o dalla V proposizione e dal corollario <lb></lb>di lei in questo III libro, o dalla IX proposizione del primo. </s></p><p type="main">

<s>Incominciando dal dar ordine in questo terzo Trattato ai teoremi, con­<lb></lb>cernenti il tempo nelle corde dei cerchi, e che si derivano dalla V propo­<lb></lb>sizione fondamentale come corollarii, si deve alla detta ultima proposizione <lb></lb>trascritta far succedere immediatamente le due seguenti: </s></p><p type="main">

<s>PROPOSITIO VI. — “ Si in circulo, cuius diameter sit ad perpendicnlum, <lb></lb>ducatur linea, quae ad diametrum non pertingat, motus per ipsam citius <lb></lb>absolvetur, quam per diametrum perpendicularem. </s>

<s>” </s></p><p type="main">

<s>“ Circuli ad horizontem erecti esto diameter perpendicularis AB (fig. </s>

<s>185): <lb></lb><figure id="id.020.01.2118.1.jpg" xlink:href="020/01/2118/1.jpg"></figure></s></p><p type="caption">

<s>Figura 185.<lb></lb>De plano DF, ad diametrum non pertingente, <lb></lb>quod tempus descensus in eo sit brevius, demon­<lb></lb>stratur ducto plano DB, quod et longius erit, et <lb></lb>minus declive, quam DF: ergo tempus per DF <lb></lb>brevius, quam per DB, hoc est, per AB ” (MSS. <lb></lb>Gal., P. V, T. II, fol. </s>

<s>164). </s></p><p type="main">

<s>PROPOSITIO VII. — “ Si in circulo, cuius <lb></lb>diameter sit ad perpendiculum, ducatur linea, <lb></lb>quae a diametro secetur, motus per ipsam tardius <lb></lb>absolvetur, quam per diametrum perpendicula­<lb></lb>rem. </s>

<s>” </s></p><p type="main">

<s>“ In praecedenti enim figura sit linea qua­<lb></lb>libet DE, et quia ipsa erit longior quam DB, et magis inclinata, propositum <lb></lb>fit manifestum ” (ibid.). </s></p><pb xlink:href="020/01/2119.jpg" pagenum="362"></pb><p type="main">

<s>Dipendenti dalla V proposizione fondamentale, e conseguenze immediate <lb></lb>di lei, son queste altre due proposizioni, che ordiniamo qui sotto, e che i <lb></lb>Lettori, nella materia e nella forma troveranno eleganti. </s></p><p type="main">

<s>PROPOSITIO VIII. — Motuum, qui a dato puncto, usque ad datam li­<lb></lb>neam, per lineas rectas conficiuntur, ille brevissimo tempore absolvitur, qui <lb></lb>in recta fit abscindens de data linea partem aequalem ei parti lineae hori­<lb></lb>zontalis, quae per datum punctum usque ad datam lineam producitur, quae <lb></lb>inter datum punctum et occursum intercipitur. </s>

<s>” </s></p><p type="main">

<s>“ Sit datum punctum A (fig. </s>

<s>186), et linea quaecumque BDC, et per A <lb></lb>horizonti aequidistans AB, quae lineae BD in B occurrat, et interceptae AB <lb></lb><figure id="id.020.01.2119.1.jpg" xlink:href="020/01/2119/1.jpg"></figure></s></p><p type="caption">

<s>Figura 186.<lb></lb>ponatur aequalis BD. </s>

<s>Dico motum per AD <lb></lb>absolvi tempore breviori, quam per quam­<lb></lb>cumque aliam lineam, ex puncto A, ad <lb></lb>quodcumque punctum lineae BDC, pro­<lb></lb>ductam. </s>

<s>” </s></p><p type="main">

<s>“ Ducatur ad BA perpendicularis AC, <lb></lb>et ex D, ad ipsam BC perpendicularis DE, <lb></lb>occurrens AC in E. </s>

<s>Et quia, in triangulo <lb></lb>aequicruri ABD, anguli BAD, BDA sunt <lb></lb>aequales, ergo reliqua ad rectos, nempe EAD, EDA aequales pariter erunt, <lb></lb>et linea EA, aequalis ipsi ED. ” </s></p><p type="main">

<s>“ Si itaque, centro E, intervallo EA, circulus describatur, transibit per <lb></lb>D, ubi lineam BDC tanget. </s>

<s>Quare lineae omnes, quae supra et infra AD, <lb></lb>usque ad lineam BC, producuntur, ultra circumferentiam circuli extendun­<lb></lb>tur, ex quo patet propositum ” (ibid., fol. </s>

<s>127, ad t.). </s></p><p type="main">

<s>PROPOSITIO IX. — “ Sit linea horizontalis AC (fig. </s>

<s>187), perpendiculus <lb></lb>vero BG, et in AC accipiatur quodcumque C: Dico quod, si mobile debet <lb></lb><figure id="id.020.01.2119.2.jpg" xlink:href="020/01/2119/2.jpg"></figure></s></p><p type="caption">

<s>Figura 187.<lb></lb>ex C ad lineam perpendiculi, per unicam lineam <lb></lb>moveri, ad eam perveniet tempore brevissimo, si <lb></lb>veniat per CE, quae lineam BE, ipsi BC aequa­<lb></lb>lem, adsumit. </s>

<s>” </s></p><p type="main">

<s>“ Centro enim B, intervallo BE, circulus de­<lb></lb>scribatur, ductisque CF, et CG utcumque, patebit <lb></lb>motum per CE citius absolvi quam per CF, aut <lb></lb>CG. </s>

<s>Si enim ducatur tangens circulum ICH, et <lb></lb>ipsi CF parallela ELH, erit LE brevior quam CF. </s>

<s><lb></lb>Sed tempus per CE aequatur tempori per LE, <lb></lb>ergo .... ” </s></p><p type="main">

<s>“ Similiter, ducta EHI ipsi CG parallela et <lb></lb>aequali, constat CG longiorem esse HE. </s>

<s>At tem­<lb></lb>pus per CE aequater tempori per HE, ergo patet <lb></lb>propositum ” (ibid., fol. </s>

<s>140). </s></p><p type="main">

<s>Queste quattro, con alcun&#039;altra che forse <lb></lb>ci è passata d&#039;occhio, sono le proposizioni dimo-<pb xlink:href="020/01/2120.jpg" pagenum="363"></pb>strate da Galileo, per svolgere il concetto principale, espresso nella quinta <lb></lb>proposizione di questo Libro. </s>

<s>Il corollario di lei dette luogo pure a espli­<lb></lb>carsi in altri, non men curiosi e importanti quesiti, com&#039;è quello di trovare <lb></lb>in qual proporzione stiano i tempi dei cadenti su due piani variamente incli­<lb></lb><figure id="id.020.01.2120.1.jpg" xlink:href="020/01/2120/1.jpg"></figure></s></p><p type="caption">

<s>Figura 188.<lb></lb>nati, e ora uguali in lunghezza, ora differenti. </s>

<s>Appar­<lb></lb>tiene al primo caso un teorema, dimostrato in due varie <lb></lb>maniere, all&#039;una delle quali è premesso il seguente <lb></lb>Lemma: </s></p><p type="main">

<s>“ Sint tres lineae utcumque A, D, E (fig. </s>

<s>188) et <lb></lb>inter A, D media proportionalis sit B; inter A, E me­<lb></lb>dia proportionalis sit C; inter E, D tandem media sit G: <lb></lb>Dico, ut C ad B, ita esse G ad D. ” </s></p><p type="main">

<s>“ Quia enim B est media inter A, D, erit quadratum <lb></lb>B aequale rectangulo A.D. </s>

<s>Similiter quadratum C ae­<lb></lb>quale rectangulo A.E. Igitur, ut rectangulus A.E, ad <lb></lb>rectangulum A.D, ita quadratum C, ad quadratum B. </s>

<s><lb></lb>Ut autem rectangulus A.E, ad rectangulum A.D, ita <lb></lb>linea E, ad D. </s>

<s>Ut vero linea E, ad lineam D, ita qua­<lb></lb>dratum G, ad quadratum D: urgo, ut quadratum C, ad <lb></lb><figure id="id.020.01.2120.2.jpg" xlink:href="020/01/2120/2.jpg"></figure></s></p><p type="caption">

<s>Figura 189.<lb></lb>quadratum B, ita quadratum G, ad quadratum D, et, ut <lb></lb>C ad B, ita G ad D ” (ibid., fol. </s>

<s>37). </s></p><p type="main">

<s>Dietro il qual Lemma, ecco in che modo Galileo di­<lb></lb>mostra in qual proporzione stieno i tempi delle cadute di <lb></lb>un medesimo grave sopra due piani ugualmente lunghi, <lb></lb>ma variamente inclinati. </s></p><p type="main">

<s>PROPOSITIO X. — “ Sint plana aequalia AB, CB (fig. </s>

<s>189) <lb></lb>inaequaliter inclinata, et altitudo inclinationis plani AB sit <lb></lb>BE; ipsius vero BC sit BD. </s>

<s>Dico tempus casus super BA, <lb></lb>ad tempus casus per BC, esse ut media proportionalis in­<lb></lb>ter DB, BE, ad ipsam BE. ” </s></p><p type="main">

<s>“ Accipiatur FB ipsis CB, AB aequalis, et ipsarum <lb></lb>FB, BD media sit BS: ipsarum vero FB, BE media sit BR. </s>

<s><lb></lb>Et quia tempus casus FB, ad tempus casus BD, est ut SB ad BD; tempus <lb></lb>vero casus BD, ad tempus casus BC, ut BD ad BC; ergo, ex aequali, tem­<lb></lb>pus casus BF, ad tempus casus BE, ut SB ad BE. </s>

<s>Et convertendo, tempus <lb></lb>casus BE, ad tempus casus BF, ut BE ad BS. ” </s></p><p type="main">

<s>“ Similiter autem demonstrabitur, ut tempus casus BF, ad tempus ca­<lb></lb>sus BA, ita linea RB ad BA, aut BC: ergo, ex aequali, in analogia pertur­<lb></lb>bata, ut tempus casus BC, ad tempus casus BA, ita RB ad SB. </s>

<s>Et conver­<lb></lb>sim, ut tempus casus BA, ad tempus casus BC, ita SB ad BR. </s>

<s>Ex Lemmate <lb></lb>vero antecedenti, ut SB ad BR, ita media inter DB, BE ad ipsam BE; quare <lb></lb>patet propositum. </s>

<s>” </s></p><p type="main">

<s>“ Aliter absque Lemmate. </s>

<s>” </s></p><p type="main">

<s>“ Sit BI (fig. </s>

<s>190) media inter BD, BE, et IS parallela ed DC: et quia, <pb xlink:href="020/01/2121.jpg" pagenum="364"></pb>ut tempus per BA, ad tempus per BE, ita linea BA, ad lineam BE: ut au­<lb></lb><figure id="id.020.01.2121.1.jpg" xlink:href="020/01/2121/1.jpg"></figure></s></p><p type="caption">

<s>Figura 190.<lb></lb>tem tempus BE, ad tempus BD, ita linea BE ad BI; ut <lb></lb>autem tempus BD, ad tempus BC, ita linea BD ad BC, hoc <lb></lb>est BI ad BS; ergo, ex aequali, ut tempus per BA ad <lb></lb>tempus per BC, ita linea AB, seu BC, ad BS, hoc est <lb></lb><figure id="id.020.01.2121.2.jpg" xlink:href="020/01/2121/2.jpg"></figure></s></p><p type="caption">

<s>Figura 191.<lb></lb>DB ad BI, seu IB ad BE, quod erat pro­<lb></lb>bandum ” (ibid., fol. </s>

<s>37). </s></p><p type="main">

<s>Dai piani di lunghezze uguali, pas­<lb></lb>sando a quelli di lunghezze differenti, di­<lb></lb>mostrava Galileo quest&#039;altra proposizione: </s></p><p type="main">

<s>PROPOSITIO XI. — “ Sint plana quaecumque inclinata <lb></lb>AB, AC (fig. </s>

<s>191) et perpendiculus AE, cui, ad rectos an­<lb></lb>gulos, BG, et sit inter CA, AD media AF: Dico tempus per <lb></lb>AB, ad tempus per AC, esse ut BA ad AF. ” </s></p><p type="main">

<s>“ Nam, tempus per AB, ad tempus per AD, est ut AB <lb></lb>ad AD: tempus vero per AD, ad tempus per AC, est ut AD <lb></lb>ad AF: ergo, ex aequali, tempus per AB, ad tempus per AC, est ut AB ad <lb></lb>AF, quod erat ostendendum ” (ibid., fol. </s>

<s>58). </s></p><p type="main">

<s>Di qui, cioè dall&#039;essere T.oAB:T.oAC=AB:AF, avendosi AF= <lb></lb>√AC.AD, viene T.oAB:T.oAC=AB√AC:AC√AD.E perchè AC:AD= <lb></lb>AE:AG, resterebbe di qui dimostrata, a quel modo che leggesi nel trattato <lb></lb>a stampa, la proposizione V, la formula della quale trovasi autografa a tergo <lb></lb>del foglio 35, dove si fa del teorema l&#039;applicazione a un caso numerico, posto <lb></lb>AB uguale a 8, AC uguale a 20, e AG, AE, altezze perpendicolari, uguali a <lb></lb>4 e a 16. Galileo calcola la formula T.oAC:T.oAB=√AC2.AG:√AB2.AE, <lb></lb>ponendo per AC, AG, AB, AE i respettivi valori numerici, e trova T.oAC: <lb></lb>T.oAB=√1600:√1024=10:8; conclusione scritta in testa al citato fo­<lb></lb>glio, che dice: “ Tempo per AC, al tempo per AB, è come 10 a 8. ” </s></p><p type="main">

<s>Venne in altro modo confermata a Galileo la proposta verità, suppo­<lb></lb>nendo che i piani AB, AC sian corde di cerchi, perchè si sa, in questo caso, <lb></lb>doverne, per le cose già dimostrate, resultare l&#039;uguaglianza dei tempi. </s>

<s>Tale <lb></lb>sembra infatti fosse l&#039;intenzione, ch&#039;egli ebbe, nel soggiungere così, per <lb></lb>modo di corollario, alla sopra riferita XI proposizione: </s></p><p type="main">

<s>“ Ratio temporis AC, ad tempus AB (in semicirculo ABC) componitur <lb></lb>ex ratione AC ad AB, et altitudinis AG, ad mediam inter altitudines AG, <lb></lb>AE, quae ratio est eadem cum ratione BA ad AC. </s>

<s>Quadratum enim AB, ad <lb></lb>quadratum AC, est ut AG ad AE, nempe, ut rectangulus HAG, ad rectan­<lb></lb>gulum HAE. </s>

<s>Sed ratio composita ex CA ad AB, et ex AB ad CA, est ratio <lb></lb>aequalitatis, ergo fit propositum ” (ibid., fol. </s>

<s>35). </s></p><p type="main">

<s>Di più fecondo svolgimento dicemmo essere la proposizione IX del I li­<lb></lb>bro, concernente i tempi delle scese per due varie inflessioni di piani; pro­<lb></lb>posizione, che Galileo dimostra qui in altro modo, e pone sotto un altro <lb></lb>aspetto, forse per prepararsi più facile la via a dimostrar, ne&#039;varii casi da <lb></lb>contemplarsi, le varie proporzioni del moto. </s></p><pb xlink:href="020/01/2122.jpg" pagenum="365"></pb><p type="main">

<s>PROPOSITIO XII. — “ Sit AC (fig. </s>

<s>192) perpendicularis ad horizontem <lb></lb>CD, ponaturque inclinata BD, fiatque motus ex A per ABD: Dico tempus per <lb></lb><figure id="id.020.01.2122.1.jpg" xlink:href="020/01/2122/1.jpg"></figure></s></p><p type="caption">

<s>Figura 192.<lb></lb>BC, post casum AB, ad tempus per BD, post <lb></lb>eumdem casum AB, esse ut linea BC ad BD. ” </s></p><p type="main">

<s>“ Ducatur AF parallela DC, et protrahatur <lb></lb>DB ad F. </s>

<s>Erit iam tempus casus per FBD, ad <lb></lb>tempus casus per ABC, ut FD linea, ad lineam <lb></lb>AC. </s>

<s>Est autem tempus casus per FB, ad tempus <lb></lb>casus per AB, ut linea FB ad lineam AB, ergo <lb></lb>tempus casus reliquae BC, post AB, ad tempus <lb></lb>casus reliquae BD, post FB, erit ut reliqua BC, <lb></lb>ad reliquam BD. </s>

<s>Sed tempus casus per BD, post <lb></lb>FB, est idem cum tempore per BD, post AB, <lb></lb>cum AF sit horizonti aequidistans; ergo patet <lb></lb>propositum. </s>

<s>” </s></p><p type="main">

<s>COROLLARIUM. — “ Colligitur autem ex hoc, quod tempora casuum per <lb></lb>BC, et per BD, sive fiat principium motus ex termino B, sive praecedat <lb></lb>motus ex eadem tamen altitudine, eamdem inter se servant rationem, nempe <lb></lb>eam, quae est lineae BC ad BD ” (ibid., fol. </s>

<s>68). </s></p><p type="main">

<s>Uno dei primi, e più curiosi quesiti, relativi a questa dimostrata pro­<lb></lb>posizione, era tale: Poniamo che un grave partendosi dalla quiete A (nella <lb></lb>precedente figura) scenda perpendicolare infino in B, dove giunto, ora se­<lb></lb>guiti per la sua prima dirittura BC, ora s&#039;infletta secondo BD, terminando <lb></lb>in ambedue i casi il viaggio nella medesima orizzontale DC: si vuol sapere <lb></lb>in qual proporzione stiano i tempi delle due scese. </s>

<s>Rispondesi a ciò con la <lb></lb>seguente, così da Galileo proposta e dimostrata: </s></p><p type="main">

<s>PROPOSITIO XIII. — “ Fiat motus per ABC, et per duas AB, BD: sit <lb></lb>RA media inter CA, AB, et ipsi DC parallela ducatur RS: Dico iam tem­<lb></lb>pus per ABC, ad tempus per ABD, esse ut linea AC, ad lineam AR cum SD. ” </s></p><p type="main">

<s>“ Si enim protrahatur BD usque ad occursum cum AF, horizonti DC <lb></lb>parallela, erit FS media inter DF, FB. Et, ut CA ad AR, ita tempus per <lb></lb>CA, ad tempus per AB: ita ut, si ponatur AC tempus per AC, erit AR <lb></lb>tempus per AB, et RC tempus per BC. ” (In fatti CA:AR=T.oAC:T.oAB. </s>

<s><lb></lb>Ma tempo AC uguale AC, dunque AR=T.oAB. </s>

<s>Di più AR=AC—RC= <lb></lb>T.oAC—RC:dunqueT.oAC—T.oAB=RC. </s>

<s>Or perchè T.oAC—T.oAB= <lb></lb>T.oBC, sarà dunque, come Galileo ha concluso, T.oBC=RC). “ Et sinili­<lb></lb>ter SD demonstrabitur esse tempus per BD, post casum ex F, vel ex A, <lb></lb>ex quo patet tempus per totam AC, ad tempus per duas ABD, esse ut AR <lb></lb>cum RC, ad AR cum SD ” (ibid., fol. </s>

<s>56). </s></p><p type="main">

<s>Altro caso, più semplice di quello ora proposto, ma più conducevole al <lb></lb>finale intendimento di questo trattato, era la proporzione dei tempi passati <lb></lb>dai gravi nello scendere per la flessura di due piani distinti, come per esem­<lb></lb>pio, prima per AB (fig. </s>

<s>193) e poi per BC, ciò che Galileo fa in due varii <lb></lb>modi, dopo il primo dei quali si trova notato così nel Manoscritto: “ Huic <pb xlink:href="020/01/2123.jpg" pagenum="366"></pb>praemittenda videtur sequens propositio: Si linea, in qua fiat latio ex quiete, <lb></lb><figure id="id.020.01.2123.1.jpg" xlink:href="020/01/2123/1.jpg"></figure></s></p><p type="caption">

<s>Figura 193.<lb></lb>dividatur utcumque, tempus lationis prioris par­<lb></lb>tis, ad tempus lationis secundae partis, est ut <lb></lb>ipsamet prima pars, ad excessum, quo eadem <lb></lb>pars superatur a media inter totam, et ipsam <lb></lb>primam partem ” (ibid., fol. </s>

<s>49). Questa, come <lb></lb>si sovverranno facilmente i nostri Lettori, è la <lb></lb>proposizione XI del trattato a stampa, di assai <lb></lb>facile conclusione dalla nota legge dei moti ac­<lb></lb>celerati, che cioè i tempi stanno come le radici <lb></lb>degli spazi. </s>

<s>Abbiamo infatti nel presente caso <lb></lb>T.oEB:T.oBC=EB:√EB.BC=EB:√(EB(CE—EB)), ch&#039;esprime in <lb></lb>cifra quel che intendeva Galileo di dire col suo discorso. </s>

<s>Questa proposizione <lb></lb>poi, che è come si è detto l&#039;XI del trattato a stampa, non fu solamente pre­<lb></lb>messa, ma sostituita alla seguente manoscritta: </s></p><p type="main">

<s>PROPOSITIO XIV. — “ Fiat latio per plana inflexa AB, BC (in praece­<lb></lb>denti figura) et invenienda sit ratio temporis casus per AB, ad tempus ca­<lb></lb>sus per BC, post casum AB. ” </s></p><p type="main">

<s>“ Ducatur horizontalis AE, cui CB producta occurrat in E, et ipsarum <lb></lb>CE, EB media sit ED. </s>

<s>Dico tempus per AB, ad tempus per BC, esse ut AB <lb></lb>ad BD. ” </s></p><p type="main">

<s>“ Tempus enim per AB, ad tempus per EB, est ut AB ad EB: tem­<lb></lb>pus vero per EB, ad tempus per BC, est ut EB ad BD: ergo tempus per <lb></lb>AB, ad tempus per BC, est ut AB ad BD, quod erat demonstrandum ” <lb></lb>(ibid., fol. </s>

<s>49). </s></p><p type="main">

<s>La medesima proposizione si trova così altrimenti dimostrata, ed è, tra <lb></lb><figure id="id.020.01.2123.2.jpg" xlink:href="020/01/2123/2.jpg"></figure></s></p><p type="caption">

<s>Figura 194.<lb></lb>le notabili differenze, da osservar la forma teo­<lb></lb>rematica, sostituita alla problematica. </s></p><p type="main">

<s>“ Sit FG (fig. </s>

<s>194) horizontalis, et ex su­<lb></lb>blimi A fiat motus per ABF, et, protracta AB <lb></lb>usque ad D, sit media inter DA, AB ipsa AC, <lb></lb>et horizonti aequidistans sit CE: Dico tempus <lb></lb>per AB, ad tempus per BF, esse ut AB, ad BE. ” </s></p><p type="main">

<s>“ Nam tempus per AB, ad tempus per BD, <lb></lb>est ut AB ad BC. </s>

<s>Tempus vero per BD, post AB, <lb></lb>ad tempus per BF, post AB, est ut BD ad BF, <lb></lb>idest BC ad BE. Ergo, ex aequali, tempus per AB, ad tempus per BF, est <lb></lb>ut AB ad BE ” (ibid., fol. </s>

<s>126). </s></p><p type="main">

<s>Sarebbe stato il soggetto, senza dubbio, di altre simili esplicazioni fe­<lb></lb>condo, le quali però, se conferivano ad aggiungere una lussuriosa ricchezza <lb></lb>alla Scienza del moto, avrebbero divagato l&#039;Autore dal suo principale intento, <lb></lb>e perciò, coi Lemmi geometrici preparatorii, e con la proposizione X del <lb></lb>primo, si chiudeva da Galileo anche questo terzo Trattato manoscritto. </s></p><pb xlink:href="020/01/2124.jpg" pagenum="367"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dicemmo come fossero le proposizioni, da noi sopra ordinate in forma <lb></lb>di trattato, dimostrate interrottamente da Galileo, in certe ore di quiete dai <lb></lb>travagli dell&#039;animo, e di riposo dallo studio delle cose celesti, quando nel 1630, <lb></lb>ritiratosi in pace solitaria nell&#039;amena suburbana villa di Bellosguardo, an­<lb></lb>nunziava agli amici, come a Niccolò Aggiunti “ l&#039;acquisto conseguito nella <lb></lb>Scienza del moto ” (Alb. </s>

<s>IX, 215). Abbiamo di un tale acquisto, che si do­<lb></lb>veva essere steso a vario, e più largo soggetto, un documento curioso nelle <lb></lb>stesse carte galileiane, e particolarmente nella 78a e nella 93a del citato vo­<lb></lb>lume, sulla prima delle quali leggesi, a quel modo che fu data alle stampe, <lb></lb>la proposizione XXIX manoscritta sul tergo di una lettera, indirizzata all&#039;Au­<lb></lb>tore il dì 10 di Gennaio di quell&#039;anno 1630, da un amico, per invitarlo a <lb></lb>pranzo nella sua prossima villa delle Rose; e la proposizione XXXIV, scritta <lb></lb>pure dalla propria mano di Galileo, sul rovescio di quell&#039;altra carta citata, <lb></lb>che è una lettera indirizzatagli di que&#039;giorni da un signore della famiglia <lb></lb>Galletti. </s></p><p type="main">

<s>Mentre così attendeva all&#039;opera di esplicar meglio il trattato, e dai primi <lb></lb>e principali teoremi dedurre le conseguenze o più curiose o più importanti, <lb></lb>era venuto il tempo di raccogliere finalmente i materiali dispersi, e nel corso <lb></lb>di quasi trent&#039;anni già preparati, per dar mano a costruire il nuovo pre­<lb></lb>meditato edifizio. </s>

<s>Tre abbiamo veduto essere stati i disegni, che vuol ora <lb></lb>Galileo prendere in esame, per elegger quello, che sarà giudicato meritevole <lb></lb>di essere esposto alla pubblica vista. </s>

<s>Procedevano i primi due in perfetta <lb></lb>regola, senz&#039;altre supposizioni, da quelle in fuori che il comun senso appro­<lb></lb>verebbe come verità per sè chiare e naturali, e si poneva al terzo per fon­<lb></lb>damento un supposto, che l&#039;Autore stesso credeva, se non necessario, al­<lb></lb>meno utile il dimostrarlo. </s>

<s>Il motivo di questo, che fu per comune giudizio <lb></lb>un progredire in peggio, si disse essere stato il dubbio se, dalle proprietà <lb></lb>dei moti equabili si potessero legittimamente concludere quelle dei moti ac­<lb></lb>celerati; dubbio che fece lasciare a Galileo la diritta via regia, come cavallo <lb></lb>che subito adombra. </s></p><p type="main">

<s>Poi s&#039;ebbe a persuader del suo inganno, specialmente quando rivolse <lb></lb>l&#039;attenzione sopra quel teorema, che lasciò nel foglio 163 manoscritto, e che <lb></lb><figure id="id.020.01.2124.1.jpg" xlink:href="020/01/2124/1.jpg"></figure></s></p><p type="caption">

<s>Figura 195.<lb></lb>fu collocato in ordine il XXV nella serie delle <lb></lb>proposizioni, che compongono il trattato a stampa. </s>

<s><lb></lb>Succedendo il moto equabile per la orizzontale CF <lb></lb>(fig. </s>

<s>195) al moto accelerato per l&#039;obliqua AB, e <lb></lb>per la perpendicolare AC, se BE sia la metà di <lb></lb>AB, e DC la metà di AC, si ha per quella XXV <lb></lb>proposizione T.oAB:T.oEB=AB:EB; T.oAC:T.oDC=AC:DC. </s></p><pb xlink:href="020/01/2125.jpg" pagenum="368"></pb><p type="main">

<s>Se si supponga ora che in B e in C le velocità siano uguali, i tempi <lb></lb>dei moti per la orizzontale CF staranno come gli spazi, e perciò dall&#039;essere <lb></lb>essi tempi equabilmente passati per le EB, DC come le linee stesse EB, DC, <lb></lb>vedeva Galileo venir legittimamente conclusa, dalle due soprascritte propor­<lb></lb>zioni, la proposizione fondamentale, che cioè, come le linee AB, AC stanno <lb></lb>pure i tempi dei moti, per quelle stesse linee accelerati. </s></p><p type="main">

<s>Che fossero veramente tali i pensieri, passati per la mente di Galileo, <lb></lb>e in virtù dei quali ebbesi a ravveder del suo inganno, oltre a quel che si <lb></lb>legge nel III Dialogo, dopo la III proposizione, si conferma dalla seguente <lb></lb>Nota rimastaci manoscritta: </s></p><p type="main">

<s>“ Spatia motus accelerati ex quiete, et spatia motuum aequabilium, ad <lb></lb>motus acceleratos consequentia, et temporibus iisdem confecta, eamdem inter <lb></lb>se retinent rationem. </s>

<s>Sunt enim haec spatia dupla illorum. </s>

<s>” </s></p><p type="main">

<s>“ Tempora vero et gradus velocitatum acquisitarum eamdem inter se <lb></lb>habent rationem. </s>

<s>Haec enim ratio subdupla est rationis spatiorum dictorum. </s>

<s>” </s></p><p type="main">

<s>“ Spatia motus accelerati AB, AC (fig. </s>

<s>196), motuum aequabilium con­<lb></lb>sequentium BE, CD, eamdem cum illis habent rationem: sunt enim dupla <lb></lb><figure id="id.020.01.2125.1.jpg" xlink:href="020/01/2125/1.jpg"></figure></s></p><p type="caption">

<s>Figura 196.<lb></lb>illorum. </s>

<s>Tempora per AB, AC sunt inter se ut gradus <lb></lb>velocitatis in B et in C. </s>

<s>Ratio vero haec subdupla est <lb></lb>rationis BA ad AC, vel BE ad CD ” (ibid., fol. </s>

<s>79 ad t.). </s></p><p type="main">

<s>A confermare anche in altro modo le corrispondenze <lb></lb>tra i moti equabili e gli accelerati, sembra che fosse preso <lb></lb>a dimostrare da Galileo quest&#039;altro teorema, diligente­<lb></lb>mente copiatoci dal Viviani, e di cui s&#039;ha l&#039;auttentica <lb></lb>copia nel Volume che citeremo. </s>

<s>Leggesi ivi così: “ Dei <lb></lb>moti fatti in tempi eguali, gli spazi stanno come le velocità; Dei fatti con <lb></lb>velocità uguale, gli spazi stanno come i tempi; Dei fatti in spazi eguali, le <lb></lb>velocità risponderanno contrariamente ai tempi ” (MSS. Gal., P. V, T. IV, <lb></lb>fol. </s>

<s>5). </s></p><p type="main">

<s>Son queste, così annunziate proposizioni, le prime da Galileo stesso di­<lb></lb>mostrate nel primo libro Dei moti locali, di facile conseguenza dal principio, <lb></lb>per sè evidente, che cioè un moto si dice essere tanto più veloce, quanto <lb></lb>è più corto il tempo, e lo spazio è più lungo. </s>

<s>Chiamate perciò V, S, T; <lb></lb><emph type="italics"></emph>v, s, t<emph.end type="italics"></emph.end> due diverse velocità, due diversi spazi, e due tempi diversi, vien quello <lb></lb>stesso principio espresso dalle formule V=S:T; <emph type="italics"></emph>v=s:t<emph.end type="italics"></emph.end>, dalle quali, se <lb></lb>S=<emph type="italics"></emph>s,<emph.end type="italics"></emph.end> immediatamente si conclude la terza delle proposizioni sopra enun­<lb></lb><figure id="id.020.01.2125.2.jpg" xlink:href="020/01/2125/2.jpg"></figure></s></p><p type="caption">

<s>Figura 197.<lb></lb>ciate, che cioè, essendo gli spazi uguali, le velocità ri­<lb></lb>spondono contrariamente ai tempi. </s></p><p type="main">

<s>Ma Galileo trovò che potevansi così le medesime <lb></lb>cose dimostrare dal principio dei moti accelerati nel <lb></lb>perpendicolo AB (fig. </s>

<s>197), e nell&#039;inclinata AC, sopra <lb></lb>la quale si prenda una lunghezza AE uguale ad AB. </s>

<s><lb></lb>Chiamata M la media tra AC, AE, s&#039;hanno, per le note <lb></lb>leggi dei moti accelerati, le due proporzioni T.′AB:T.oAE=AE:M; <pb xlink:href="020/01/2126.jpg" pagenum="369"></pb>V.aAE:V.aAC=AE:M. Ond&#039;e che, supposto V.aAC=V.aAB, immediata­<lb></lb>mente se ne conclude di qui T.oAB:T.oAE=V.aAE:V.aAB, come in­<lb></lb>tendeva Galileo stesso di dimostrare con questo suo più lungo discorso. </s></p><p type="main">

<s>“ Posta la parte AE eguale alla AB, il tempo per AB, al tempo per AC, <lb></lb>sta come AB ad AC, cioè AE ad AC. </s>

<s>Ma come il tempo per AE, al tempo <lb></lb>per AC, così la media tra le AE, AC alla AC; dunque, come il tempo per <lb></lb>AB, al tempo per AE, così la AB, cioè la AE, alla detta media. </s>

<s>Ma, come <lb></lb>la velocità per AC, alla velocità per AE, così la medesima media alla AE; <lb></lb>adunque, la velocità per AB, che è la medesima che la velocità per AC, alla <lb></lb>velocità per AE, sta come la AE a quella medesima. </s>

<s>Adunque è manifesto <lb></lb>che i tempi per le uguali AB, AE rispondono contrariamente alle velocità <lb></lb>per le medesime, il che bisognava dimostrare ” (ivi). </s></p><p type="main">

<s>Restavano di qui confermate le verità, da Galileo espresse nel ragiona­<lb></lb>mento illustrato dianzi dalla figura 195, che cioè i moti equabili e gli acce­<lb></lb>lerati serbano la medesima proporzione fra gli spazi e i tempi, ond&#039;è che <lb></lb>veniva tolta di qui ogni ombra a quel dubbio, che lo aveva fatto arretrare, <lb></lb>e che lo avea consigliato, ai dimostrati teoremi, di sostituire un supposto <lb></lb>bisognoso di dimostrazione. </s></p><p type="main">

<s>Nel metter dunque in ordine le proposizioni, che dovevano comporre il <lb></lb>trattato da inserirsi nel III Dialogo, per dar finalmente alla luce la nuova <lb></lb>Scienza del moto, si crederebbe che, ripresa la fiducia antica del Teorema <lb></lb>meccanico, volesse Galileo ritornar sulla dirittura della prima via abbando­<lb></lb>nata, dimostrativamente concludendo da quello stesso Teorema la proposi­<lb></lb>zione fondamentale delle proporzionalità fra i tempi e gli spazi, nei declivi <lb></lb>ugualmente elevati, a quel modo che aveva fatto nel II Libro, immeritata­<lb></lb>mente repudiato, e dove tutto, in bel geometrico modo, si dimostrava senza <lb></lb>alcuna temeraria supposizione. </s></p><p type="main">

<s>Eppure i primi, ch&#039;ebbero fra mano il volume stampato in Leyda, tro­<lb></lb>varono la proposizione III, dimostrata col principio supposto, quale fu co­<lb></lb>municato a Luca Valerio, condotta in sostanza a quel modo, che la III del <lb></lb>III Libro, se non che nel metodo degl&#039;Indivisibili si rendeva più ferma, e <lb></lb>si riduceva più esatta. </s>

<s>Per segno poi della fatta riconciliazione col Teorema <lb></lb>meccanico non rimaneva altro che la VI proposizione, nella quale, fra i varii <lb></lb>modi di dimostrare il tautocronismo delle scese per le corde dei cerchi, si met­<lb></lb>teva in secondo luogo anche quello derivato <emph type="italics"></emph>ex mechanicis.<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 182). </s></p><p type="main">

<s>L&#039;elezione insomma, fra i tre tentati disegni del trattato Dei moti lo­<lb></lb>cali, cadde per Galileo sul III, a cui pose per fondamenti, come vedemmo, <lb></lb>i teoremi dimostrativi delle leggi dei moti accelerati, e il supposto che, in <lb></lb>uguali discese rette, le velocità dei cadenti, per qualunque declivio, sono <lb></lb>uguali. </s>

<s>Riconobbe pur troppo anche da sè stesso Galileo l&#039;imprudenza dello <lb></lb>stabilire il fondamento alla sua Scienza nuova sopra un principio non certo, <lb></lb>e in margine alla proposizione III del III Libro, nella quale faceva la prima <lb></lb>applicazione del detto supposto, scrisse, appellando alla relativa figura, che <lb></lb>per noi è la 181, “ credo esse utile, si non necessarium, demonstrasse mo-<pb xlink:href="020/01/2127.jpg" pagenum="370"></pb>bile in D esse eiusdem momenti, quod in E ” (MSS. Gal., P. V, T. II, fol. </s>

<s>88). <lb></lb>Ma si ridusse tutta quella dimostrazione nel fatto sperimentale dei pendoli, <lb></lb>che risalgono alla medesima altezza orizzontale, da cui furono scesi. (Alb. </s>

<s><lb></lb>XIII, 164, 65). </s></p><p type="main">

<s>Delle proposizioni, che compongono il terzo trattato manoscritto, non ne <lb></lb>fu nello stampato lasciata addietro nessuna nella sostanza, ma furono quasi <lb></lb>tutte rifuse. </s>

<s>Talvolta un teorema si umilia al grado di corollario, e tal altra <lb></lb>un corollario si esalta alla dignità di teorema. </s>

<s>Non sempre però, in così fare, <lb></lb>si riducono le cose in meglio, giudice il Viviani, il quale avrebbe voluto ve­<lb></lb>der trattata, per esempio, la proposizione VI, stampata, in altro modo, e non <lb></lb>sapendo nulla del corollario alla V proposizione del III libro manoscritto, e <lb></lb>credendo che avesse Galileo per inavvertenza così lasciate le cose in difetto, <lb></lb>vi supplì di suo in una Nota, che l&#039;Albèri pubblicò a pag. </s>

<s>184 del citato <lb></lb>Tomo XIII. </s></p><p type="main">

<s>Anche la proposizione VIII del II Libro, benchè solennemente promessa <lb></lb>nel I dialogo Dei due massimi sistemi (Alb. </s>

<s>I, 32), non apparisce esplicita <lb></lb>nel III dialogo Delle scienze nuove, benchè si derivi per facile corollario <lb></lb>dalla IX, stampata in quel Dialogo stesso. </s></p><p type="main">

<s>Le proposizioni principali hanno, anco in questo stampato, quei tre cen­<lb></lb>tri evolutivi da noi notati nel III Libro, e dai quali sembrava si dovesse far <lb></lb>dipendere la bene ordinata serie dei teoremi, ma Galileo non sempre osserva <lb></lb>quest&#039;ordine. </s>

<s>Si direbbe anzi che non osserva ordine alcuno, nel distribuire <lb></lb>le parti accessorie e le mediane del suo trattato, e quel lasciare un soggetto, <lb></lb>per passare a un altro, e poi tornare ancora indietro sopra quel primo, fu <lb></lb>una delle precipue ragioni, per cui parvero le dimostrate cose, specialmente <lb></lb>ad alcuni poco benevoli, oscure e prolissamente noiose. </s></p><p type="main">

<s>Prese giusto da questa prolissità motivo il Cartesio di dire che non ebbe <lb></lb>la pazienza di leggere le galileiane dimostrazioni, benchè, pur così come <lb></lb>stavano, avesse fiducia che fossero vere. </s>

<s>“ De geometricis demonstrationi­<lb></lb>bus, quibus liber eius refertus est, scriveva così del libro di Galileo in una <lb></lb>delle sue Epistole al Mersenno, nihil dico; non enim potui a me impetrare ut <lb></lb>illas legerem, et quidem crediderim veras esse omnes ” (Pars. </s>

<s>II cit., pag. </s>

<s>244). <lb></lb>In semplicemente legger però l&#039;enunciato dei varii proposti teoremi disse di <lb></lb>avervi questo notato come certo, che non era cioè punto necessario essere <lb></lb>un gran Geometra per ritrovarli, e che non s&#039;andava, nel condurre il ra­<lb></lb>gionamento, per le vie più spedite. </s>

<s>“ Hoc enim observavi, propositiones inspi­<lb></lb>ciendo, non esse opus ut quisquam sit magnus Geometra ad illas invenien­<lb></lb>das ” (ibid.). </s></p><p type="main">

<s>Il giudizio è forse uno dei più giusti, che uscissero dalla mente del <lb></lb>Cartesio, perchè, appetto alla Geometria, così largamente promossa da lui, <lb></lb>questa di Galileo doveva sembrare una esercitazione da scolaretti. </s>

<s>Ma è a <lb></lb>pensar che il Trattato galileiano, uscito alla pubblica luce nel 1638, e dal <lb></lb>Cartesio stesso letto qualche anno dopo, s&#039;era incominciato a comporre nei <lb></lb>princiqii del secolo, quando la Geometria non conosceva altri promotori che <pb xlink:href="020/01/2128.jpg" pagenum="371"></pb>il Commandino, il Valerio, e Guidubaldo. </s>

<s>Si dovrebbero dunque i teoremi, <lb></lb>scritti nel III dialogo delle due Nuove scienze, paragonare con quelli dimo­<lb></lb>strati da così fatti Autori, e non con gli altri, che poterono, quarant&#039;anni <lb></lb>dopo, venir sublimati sulle ali della nuova analisi cartesiana. </s>

<s>Istituito da que­<lb></lb>sta parte il confronto, non par che Galileo rimanga di gran lunga inferiore <lb></lb>ai Matematici, che lo avevano preceduto. </s>

<s>Si direbbe anzi che gli avanza per <lb></lb>una certa elegante facilità, come si può argomentare da alcuni esempi di <lb></lb>teoremi puramente geometrici, nei quali s&#039;incontrò più volte l&#039;Autore, cer­<lb></lb>cando i mezzi alle sue meccaniche dimostrazioni. </s></p><p type="main">

<s>Ripensando alle proprietà geometriche delle linee, tessenti la figura, <lb></lb>sopra la quale erasi dimostrato il corollario alla XI del III libro, vide sca­<lb></lb>turirne questo teorema: che cioè la corda esterna, dalla estremità della quale <lb></lb>sia condotta una perpendicolare al diametro, è media proporzionale fra la <lb></lb><figure id="id.020.01.2128.1.jpg" xlink:href="020/01/2128/1.jpg"></figure></s></p><p type="caption">

<s>Figura 198.<lb></lb>corda interna tutta intera, e il segmento di lei rimasto tra <lb></lb>la sommità del cerchio, e la perpendicolare stessa interse­<lb></lb>cante. </s>

<s>Così, come aveva riconosciuto una tale geometrica <lb></lb>proprietà, con le ragioni di lei, Galileo notava, in mezzo ai <lb></lb>Teoremi di Meccanica, nel suo manoscritto: “ AB (fig. </s>

<s>198) <lb></lb>est media inter CA, AD, nam rectangulus CAD aequatur <lb></lb>rectangulo HAG. </s>

<s>Si enim ducatur HC, erit triangulus ACH <lb></lb>simile triangulo ADG ” (MSS. Gal., P. V, T. II, fol. </s>

<s>35). </s></p><p type="main">

<s>Quest&#039;altre geometriche relazioni deve averle ricono­<lb></lb>sciute Galileo, in mezzo alle proposizioni di Meccanica, di­<lb></lb>mostrative dei tempi delle scese per le corde dei cerchi, e <lb></lb>dop&#039;avere, in testa al foglio 58 del citato volume, notato <emph type="italics"></emph>haec non est motus <lb></lb>materia,<emph.end type="italics"></emph.end> così soggiunge: “ Sit IC (fig. </s>

<s>199) perpendicularis ad diametrum <lb></lb>circuli AB, ductaque a puncto A quaecumque linea circumferentiae et per­<lb></lb><figure id="id.020.01.2128.2.jpg" xlink:href="020/01/2128/2.jpg"></figure></s></p><p type="caption">

<s>Figura 199.<lb></lb>pendiculari CI occurrens, ut AID, <lb></lb>AD, ADI, dico rectangulum DAI rec­<lb></lb>tangulo BAC esse aequale. </s>

<s>” </s></p><p type="main">

<s>“ Si enim iungatur recta DB, <lb></lb>erit angulus in semicirculo, ad pun­<lb></lb>ctum D, rectus, estque angulus C <lb></lb>quoque rectus, communis autem an­<lb></lb>gulus ad A. </s>

<s>Ergo triangulorum ae­<lb></lb>quiangulorum DAB, CAI latera erunt <lb></lb>proportionalia, utque BA ad AD, ita <lb></lb>IA ad AC. </s>

<s>Ergo patet propositum. </s>

<s>” </s></p><p type="main">

<s>Si riferisce probabilmente alla <lb></lb>medesima origine quest&#039;altro teo­<lb></lb>rema di Geometria, così proposto <lb></lb>da Galileo e così dimostrato: “ Sit circulus, cuius diameter AB (fig. </s>

<s>200) <lb></lb>et ipsi parallela tangens CE, et ex termino B quaelibet linea BO in circulo <lb></lb>applicetur. </s>

<s>Dico perpendiculares, quae a termino B et O, ipsi BO, accomo-<pb xlink:href="020/01/2129.jpg" pagenum="372"></pb>dantur, protractas, de linea CE partem, diametro circuli aequalem, semper <lb></lb><figure id="id.020.01.2129.1.jpg" xlink:href="020/01/2129/1.jpg"></figure></s></p><p type="caption">

<s>Figura 200.<lb></lb>intercipere. </s>

<s>” </s></p><p type="main">

<s>“ Jungantur enim A, O, et extendatur ad <lb></lb>tangentem in F, quae ad BO erit perpendicularis, <lb></lb>cui ex B parallela sit BE: demonstrandum FE <lb></lb>diametro circuli esse aequalem. </s>

<s>Id autem constat, <lb></lb>quia in parallelogrammo ABEF latera AB, FE <lb></lb>opposita aequalia sunt, ex Elementis. </s>

<s>” </s></p><p type="main">

<s>“ Vel dicas quod ducta, ex O, OG parallela <lb></lb>ipsi AB, et BG perpendiculari ad BO, abscindet <lb></lb>semper OG aequalis diametro circuli, quod patet <lb></lb>ex triangulis AOB, OBG similibus, et aequali­<lb></lb>bus ” (ibid., fol. </s>

<s>68). </s></p><p type="main">

<s>Ritornando al Cartesio, e ai giudizi di lui <lb></lb>scritti in confidenza al Mersenno, è da osservare <lb></lb>di più che, nei teoremi galileiani, non si tratta <lb></lb>di semplice Geometria pura, ma di Geometria <lb></lb>applicata alla Scienza del moto, ciò che impor­<lb></lb>tava un assai maggiore difficoltà, per esser cose, <lb></lb>delle quali i predecessori o non ne avevano dati <lb></lb>alcuni o pochissimi esempi. </s>

<s>Di qui è che spesso, <lb></lb>per assicurarsi meglio delle verità di quelle nuove conclusioni, riduceva Ga­<lb></lb>lileo le astratte generalità ai casi concreti, e invocava l&#039;Aritmetica a far ri­<lb></lb>scontro colla Geometria. </s>

<s>Così fatte applicazioni ricorrono nel citato mano­<lb></lb>scritto galileiano frequenti, ond&#039;è che più volte occorse all&#039;Autore, anche <lb></lb>in mezzo a così fatti aritmetici esercizi, di ritrovare alcuni teoremi nuovi, <lb></lb>e nella loro semplicità eleganti. </s>

<s>Tale sarebbe per esempio il seguente, così <lb></lb>formulato al foglio 35: “ In numeris, ab unitate consequentibus, summa <lb></lb>cuiuslibet multitudinis, ad aliam summam alterius multitudinis, si ab utra­<lb></lb>que dimidium maximi numeri auferatur, est ut quadratum multitudinis unius <lb></lb>ad quadratum alterius multitudinis. </s>

<s>” </s></p><p type="main">

<s>Per la dimostrazione però non si fa dell&#039;Algebra altr&#039;uso, che in appa­<lb></lb>renza, chiamando <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> la somma dei numeri in serie naturale, da 1 a 8, e <lb></lb><emph type="italics"></emph>ac<emph.end type="italics"></emph.end> la somma di un&#039;altra simile serie, da 1 a 6, e notando che il Teorema <lb></lb>generale formulato si verifica esattamente nelle particolarità del preso esem­<lb></lb>pio numerico. </s>

<s>“ Summa enim <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> est 36: ablato dimidio 8, remanet 32. <lb></lb>Summa <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> est 21: ablato dimidio 6, remanet 18. Et 32 ad 18 est ut qua­<lb></lb>dratum multitudinis <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> nempe 64, ad quadratum multitudinis <emph type="italics"></emph>ac,<emph.end type="italics"></emph.end> quod <lb></lb>est 36 ” (ibid.). </s></p><p type="main">

<s>Sia pure che, per ritrovare così fatti Teoremi di Geometria e di Aritme­<lb></lb>tica, non ci fosse bisogno di essere gran Matematici, ma non poteva il Car­<lb></lb>tesio negare che non fosse Galileo stato il primo ad applicare la Geometria <lb></lb>e l&#039;Aritmetica a quel modo, per dimostrare le nuove proprietà e i varii e <lb></lb>complicati effetti del moto. </s></p><pb xlink:href="020/01/2130.jpg" pagenum="373"></pb><p type="main">

<s>Un&#039;altra delle ragioni, per cui non piaceva al Cartesio stesso quel trat­<lb></lb>tato galileiano, era perchè, nel dimostrar quei tanti teoremi, non teneva le <lb></lb>vie più compendiose. </s>

<s>“ Observavi eum maxime compendiosas vias non <lb></lb>sectari ” (Epist. </s>

<s>cit., pag. </s>

<s>244). E anche questo giudizio cartesiano è vero, <lb></lb>suffragato da quello degli stessi nostri Lettori, i quali avranno già fatto in <lb></lb>sè medesimi il confronto fra la elegante snellezza delle dimostrazioni, stese <lb></lb>nei tre libri manoscritti, con quelle date a stampa uggiosamente pesanti. </s></p><p type="main">

<s>Il Salviati, così nell&#039;attuale occasione del ragionare, come nel riferire <lb></lb>le cose già prima ragionate, aveva da una parte riguardo ai Sagredi, i quali <lb></lb>si sarebbero potuti facilmente condurre per le vie compendiose, ma ripen­<lb></lb>sava dall&#039;altra ai Simplicii, che avendo le gambe deboli e corte conveniva <lb></lb>condur per le vie piane, e perciò inevitabilmente più lunghe. </s>

<s>E perciocchè, <lb></lb>non al Cartesio solo, ma a tutti i Matematici rappresentati in Gian Fran­<lb></lb>cesco Sagredo, si vede che sarebbero piaciute meglio le dimostrazioni, quali <lb></lb>uscirono di primo getto, che non le rifatte per la stampa (inutili del resto <lb></lb>ai Simplicii, ai quali, per quanto fosse sminuzzato, rimarrebbe sempre quel <lb></lb>solido cibo indigesto) crediamo di aver fatto cosa grata ai sopraddetti Mate­<lb></lb>matici, e di avere anche in parte provveduto alla gloria di Galileo, nel dare <lb></lb>alla luce i tre libri <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> nelle loro forme originali. </s></p><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il trattato Dei moti locali, intorno a cui ha avuto occasione d&#039;intrat­<lb></lb>tenersi fin qui lungamente la nostra Storia, contiene in sè, e rappresenta <lb></lb>una di quelle due scienze, che Galileo era solito chiamare col titolo di nuove. </s>

<s><lb></lb>Molti, che questo titolo gli concessero cecamente, crederono, e l&#039;Autore stesso <lb></lb>si studiò con arte di confermarli in quella loro opinione, che cioè s&#039;avessero <lb></lb>tali novità a intendere in senso assoluto, quasi che si fossero alle insegnate <lb></lb>dottrine posti i principii, oltre all&#039;averne svolte le conseguenze. </s>

<s>Dicemmo <lb></lb>altrove come fosse questa una vana lusinga, e una incredibile presunzione, <lb></lb>confortando il nostro detto coi fatti, dai quali ci venne dimostrato aver avuto <lb></lb>la scienza del moto, nel secolo XVI, certezza di principii, e speranza lieta <lb></lb>di futuri progressi. </s></p><p type="main">

<s>Il seme, da cui germinò la scienza di Galileo, vedemmo essere stato il <lb></lb>Teorema meccanico del Tartaglia: e perciocchè s&#039;era a comun benefizio, per <lb></lb>mezzo del libro dei <emph type="italics"></emph>Quesiti e inventioni,<emph.end type="italics"></emph.end> un tal fecondo seme largamente <lb></lb>disperso, non pareva credibile ne dovesse nascere un filo solo. </s>

<s>Vero è che, <lb></lb>come spesso avviene ai seminatori del campo, un granello va a cader sulla <lb></lb>pietra, e se lo beccano gli uccelli dell&#039;aria: un&#039;altro cade in terra mal fon­<lb></lb>data, e germoglia, ma poi presto, per mancanza di umore, si secca, cosic­<lb></lb>chè quello solo, che va a cadere in ben disposto terreno, nasce e cresce e <lb></lb>matura nella spiga. </s></p><pb xlink:href="020/01/2131.jpg" pagenum="374"></pb><p type="main">

<s>Così fatte buone disposizioni, dal figurato passando al senso proprio, <lb></lb>non si debbono tanto intender dipendere dalle qualità della mente, quanto <lb></lb>dal fine accidentale, che s&#039;erano proposti di conseguire gli Autori, per al­<lb></lb>cuni dei quali riducevasi tutto quel fine in promovere in qualche modo il <lb></lb>teorema del Tartaglia, mentre Galileo, essendosi prefisso per termine il bra­<lb></lb>chistocronismo degli archi rispetto alle corde, dovette necessariamente pas­<lb></lb>sare per la lunga e ordinata serie delle proposizioni intermedie. </s></p><p type="main">

<s>Di qui avvenne ch&#039;essendo, nelle poche menti disposte a riceverlo e a <lb></lb>fecondarlo, medesimo il seme, uno dei grani spuntò appena: o come si vuol <lb></lb>dire in senso proprio non fu da qualche Autore promosso il Teorema mec­<lb></lb>canico oltre alle sue prime conseguenze, mentre ebbe per qualche altro uno <lb></lb>svolgimento assai più largo, benchè lontano dal raggiunger l&#039;estensione, a <lb></lb>cui fu ridotto da Galileo, il quale è perciò, nell&#039;istituire la nuova scienza, <lb></lb>il maggiore, ma non il solo. </s>

<s>I concorrenti si riducono per noi a questi due <lb></lb>principali: a Claudio Beriguardi cioè, e a Giovan Batista Baliani, che, giu­<lb></lb>dicati dai più imitatori o emuli non solo, ma plagiari di Galileo, appariscono <lb></lb>ora innanzi alla Storia nella verità del loro aspetto, in quanto rappresen­<lb></lb>tano le varie disposizioni delle menti aperte a ricevere il seme della scienza, <lb></lb>che la provvida Mano superna sparge largamente, e diffonde per tutto l&#039;aperto <lb></lb>campo sottoposto, e non in qualche chiuso e privilegiato orticello. </s></p><p type="main">

<s>Quando, nel VI della III parte dei <emph type="italics"></emph>Circoli pisani,<emph.end type="italics"></emph.end> si lesse che l&#039;Autore <lb></lb>asseriva di aver dimostrato le proprietà del moto, nelle rette e nelle obli­<lb></lb>que discese dei gravi, vent&#039;anni prima che Galileo e il Torricelli avessero <lb></lb>pubblicato nulla intorno a quello argomento; molti se ne risero, avendo per <lb></lb>cosa impossibile che il losco Peripatetico fosse penetrato a veder tanto ad­<lb></lb>dentro, quanto l&#039;acuto Linceo. </s>

<s>Quando apparve in Genova il trattato <emph type="italics"></emph>De <lb></lb>motu naturali,<emph.end type="italics"></emph.end> in quel tempo medesimo, che in Leida si pubblicarono i <lb></lb>dialoghi Delle due nuove Scienze, sempre fermi costoro nel medesimo pen­<lb></lb>siero, che cioè, a ricever le arcane rivelazioni della Scienza del moto, non <lb></lb>ci fosse altro cervello capace, che quello di Galileo, dissero che il Baliani <lb></lb>lo avea ricopiato. </s>

<s>E perchè non aveva ciò alcuna apparente verosimiglianza, <lb></lb>essendo le due pubblicazioni contemporanee, tennero per cosa certa che il <lb></lb>Genovese avesse avuto fra mano il trattato galileiano manoscritto, nonostante <lb></lb>che, del gratuito asserto, sia dimostrata la falsità dalla storia narrata qui <lb></lb>addietro. </s>

<s>Se fosse mai stato a loro noto, avrebbero, del libro di Giovan Marco <lb></lb>Tedesco, fatto il medesimo commento, non avvedendosi che, così, male si <lb></lb>spiegava il fatto dipendente piuttosto da quella causa naturale, da noi sopra <lb></lb>proposta, che cioè, partendo Autori d&#039;indole, di studii e di patria diversi dai <lb></lb>medesimi principii, dovevano necessariamente riuscire alle medesime conse­<lb></lb>guenze, almeno più prossime e più immediate. </s>

<s>Ciò che si induce dalla ra­<lb></lb>gione, vien confermato dal fatto che, consistendo quel principio, come più <lb></lb>volte s&#039;è detto, nel Teorema meccanico, e le immediate conseguenze di lui <lb></lb>riducendosi nel passar dai momenti alle velocità, e da queste ai tempi; si <lb></lb>videro riscontrarsi inconsapevoli insieme, in tal processo dimostrativo, gli <pb xlink:href="020/01/2132.jpg" pagenum="375"></pb>Autori, come sconosciuti pellegrini che, tendendo a un medesimo luogo, si <lb></lb>incontrano per la medesima via. </s></p><p type="main">

<s>Il Beriguardi infatti, dop&#039;aver dimostrato che il medesimo grave tanto <lb></lb><figure id="id.020.01.2132.1.jpg" xlink:href="020/01/2132/1.jpg"></figure></s></p><p type="caption">

<s>Figura 201.<lb></lb>è più ponderoso nel perpendicolo BC (fig. </s>

<s>201) che nel <lb></lb>declivio AC, quanto la linea AC è maggiore di BC, con­<lb></lb>sidera molto ragionevolmente che questo ponderar di­<lb></lb>verso del medesimo globo, per la sola ragione del venir <lb></lb>collocato su due piani diversi, “ non videtur provenire <lb></lb>posse, nisi a virtute, qua celerius movetur per BC, <lb></lb>quam per AC, secundum permutatam laterum propor­<lb></lb>tionem ” (Circuli pisani, editio 2a, Patavii 1660, pag. </s>

<s>310). <lb></lb>Di qui perciò ne conclude che, supposto esser AC tripla di BC, la velocità <lb></lb>nella perpendicolare deve contrariamente esser tripla dell&#039;altra nell&#039;inclinata. </s></p><p type="main">

<s>Vede l&#039;Autore, da una tal conclusione, derivarsi un corollario di tanta <lb></lb>importanza, che stabilisce il primo passo, da progredire oltre liberamente <lb></lb>per la scienza galileiana. </s>

<s>Se, come s&#039;è supposto dianzi essere AC tripla di <lb></lb>BC, così suppongasi ora essere la stessa BC tripla di CD, partendosi il mo­<lb></lb>bile dal punto C, dov&#039;era in quiete, passerà i due spazi CB, CD nel mede­<lb></lb>simo tempo. </s>

<s>Che se volesse, poi soggiunge, alcuno determinare graficamente <lb></lb>il punto D, non dovrebbe far altro che condurre da B, estremità della perpen­<lb></lb>dicolare, la normale DB all&#039;inclinata, dalla qual normale si verrebbe a descri­<lb></lb>vere il triangolo BCD, ch&#039;essendo simile ad ABC darebbe AC:BC=BC:CD. </s></p><p type="main">

<s>Questa dimostrazione, condotta su particolari dati numerici, si ridur­<lb></lb>rebbe assai facilmente alla sua generalità, ragionando in un modo simile a <lb></lb>quello dell&#039;Autore. </s>

<s>Imperocchè, chiamata V la velocità per la perpendico­<lb></lb>lare, <emph type="italics"></emph>v<emph.end type="italics"></emph.end> la velocità per la inclinata, abbiamo V:<emph type="italics"></emph>v<emph.end type="italics"></emph.end>=AC:BC. </s>

<s>Per trovar <lb></lb>poi il punto D, dove sarà giunto il grave sull&#039;obliqua, nel tempo che il me­<lb></lb>desimo grave avrebbe passata la diretta BC, diremo ch&#039;essendo i tempi <lb></lb>uguali debbon essere le velocità proporzionali agli spazi, per cui, chiamata X <lb></lb>la lunghezza CD incognita, avremo V:<emph type="italics"></emph>v<emph.end type="italics"></emph.end>=BC:X, e perciò AC:BC= <lb></lb>BC:X. Ora, tirata da B la BD, perpendicolare ad AC, i triangoli simili ABC, <lb></lb>BCD danno AC:BC=BC:CD; dunque X=CD. </s></p><p type="main">

<s>Le meccaniche proprietà del circolo, che apparvero, come veramente <lb></lb>sono, maravigliose, scendevano dimostrate di qui per corollario immediato, <lb></lb>perchè, circoscritto al triangolo rettangolo DCB un mezzo cerchio, il tauto­<lb></lb>cronismo, concluso per la precedente proposizione, veniva a riferirsi a CD, <lb></lb>come corda, e a CB come a diametro di quel medesimo cerchio. </s>

<s>Il Beri­<lb></lb>guardi non accenna per verità a questo progresso, che conduceva molto ad­<lb></lb>dentro alla scienza galileiana Giovan Marco, il quale, dalla XIII sua propo­<lb></lb>sizione dimostrativa dell&#039;equidiuturnità per la verticale e per l&#039;inclinata, <lb></lb>ambedue prefinite dalla perpendicolare, che da quella giunge a questa; passa <lb></lb>a concluder, nella XV: “ Motus, ex eodem puncto, per lineas subtensas, <lb></lb>sunt aequales motus per diametrum eiusdem circuli ” (De prop. </s>

<s>motus cit., <lb></lb>fol. </s>

<s>23 ad t.). </s></p><pb xlink:href="020/01/2133.jpg" pagenum="376"></pb><p type="main">

<s>Vedemmo come fossero questi memorabili teoremi, nel primo Libro di <lb></lb>Galileo, ordinati a servire di Lemmi, per dimostrare il fondamento alla nuova <lb></lb>Dinamica, che cioè i tempi, nelle scese da uguali altezze, stanno come gli <lb></lb>spazi. </s>

<s>Ora, nè il Beriguardi nè Giovan Marco progredirono tant&#039;oltre nelle <lb></lb>loro meccaniche speculazioni, rimanendosi di gran lunga indietro, non a Ga­<lb></lb>lileo solo, ma al Baliani, il trattatello del quale procede nelle sue dimostra­<lb></lb>zioni in un modo tanto simile a quello, che si osserva nel primo Manoscritto <lb></lb>galileiano, da dar qualche apparenza di verità a quel che si diceva dianzi <lb></lb>calunnioso commento. </s>

<s>Se non che, farebbesi forse meglio a rassomigliare i <lb></lb>processi del Baliani a quelli del Torricelli, così nella eleganza dei modi, come <lb></lb>nell&#039;elezione degli ordini dimostrativi. </s>

<s>Che se allo stesso Torricelli, in voler <lb></lb>render la scienza indipendente da qualunque ipotesi, occorse di ritornar sulle <lb></lb>tracce, e quasi indovinare i primi modi tenuti da Galileo, senz&#039;averne ve­<lb></lb>duti i Manoscritti, ma condottovi dalla logica dei pensieri; diciamo che que­<lb></lb>sto stesso incontrò nello speculare al Baliani, cosicchè l&#039;identità dei profes­<lb></lb>sati principii, e il comune studio di proseguire in Geometria le vie più <lb></lb>compendiose, conducessero i due Autori alle conseguenze medesime nella <lb></lb>sostanza e nelle forme. </s></p><p type="main">

<s>Apriamo, per passar dalle parole ai fatti, il citato trattatello <emph type="italics"></emph>De motu <lb></lb>naturali,<emph.end type="italics"></emph.end> pubblicato la prima volta, nel 1638, dal Matematico genovese, e <lb></lb>troveremo, come principal cosa da notare, che mentre Galileo in principio <lb></lb>si fa Autore del Teorema meccanico, e poi lo repudia come sospetto; il Ba­<lb></lb>liani lo riguarda come un vero matematico, o per dimostrazione o per na­<lb></lb>turale evidenza, così chiaro, da scriversi in quarto luogo fra i postulati sotto <lb></lb>una tal forma: “ Momentum gravis super plano inclinato est ad ipsius gra­<lb></lb>vitatem ut perpendicularis ad inclinatam, si ab eodem puncto ducta sint ad <lb></lb>idem planum orizontale dicta perpendicularis et dictum planum inclinatum, <lb></lb>et proinde tali casu proportio gravitatis ad momentum est reciproca propor­<lb></lb>tione linearum super quibus grave movetur ” (De motu natur., edizio 2a, <lb></lb>Genuae 1646, pag. </s>

<s>15, 16). Da questo, e dall&#039;altro postulato già premesso, <lb></lb>che cioè il momento sta al momento del solido grave, come la velocità sta <lb></lb>alla velocità, ne conclude il Baliani che le velocità stesse, nel perpendicolo <lb></lb>e nell&#039;obliqua, stanno reciprocamente come le lunghezze. </s></p><p type="main">

<s>Questa proposizione, che è l&#039;XI del I libro, è ordinata dall&#039;Autore al­<lb></lb>l&#039;altra fondamental proposizione dei tempi proporzionali alle lunghezze del­<lb></lb>l&#039;obliqua e della perpendicolare, al qual uso è premessa altresì in XVII luogo, <lb></lb>la soluzione del seguente, per altre vie oramai ben noto Problema: “ Data <lb></lb>linea perpendiculari, per quam grave descendat, cui annectatur linea, seu <lb></lb>planum declinans; in declinante reperire punctum, quo grave perveniat eo <lb></lb>tempore, quo pertransiverit perpendiculum ” (ibid., pag. </s>

<s>34). </s></p><p type="main">

<s>Sia il piano inclinato AC, nell&#039;ultima rappresentata figura 201, elevato <lb></lb>all&#039;altezza BC sopra il piano orizzontale AB, e si voglia sapere a qual punto <lb></lb>si troverà un grave scendente per AC, mentre un altro simile grave, par­<lb></lb>titosi dal medesimo punto C, abbia percorso tutto intero il perpendicolo CB. <pb xlink:href="020/01/2134.jpg" pagenum="377"></pb>Condotta la BD perpendicolare ad AC, sarà D il punto cercato, imperocchè <lb></lb>abbiamo, dice il Baliani, per le cose già dimostrate, che la velocità, lungo <lb></lb>AC, sta alla velocità, lungo CB, come CB sta ad AC. </s>

<s>Ma perchè, essendo CD <lb></lb>terza proporzionale dopo AC, CB, si ha CB:AC=CD:CB, dunque le ve­<lb></lb>locità, nel piano inclinato e nel perpendicolo, stanno come CD a CB, ossia, <lb></lb>come gli spazi passati. </s>

<s>Ma quando le velocità stanno come gli spazi, i tempi <lb></lb>sono uguali, dunque è vero quel che si diceva, che cioè i tempi per CD e <lb></lb>per CB sono uguali. </s></p><p type="main">

<s>Da questa proposizione ne deduce, per facile corollario, l&#039;Autore, come <lb></lb>Giovan Marco e come il Torricelli, il tautocronismo fra le corde e il diame­<lb></lb>tro, circoscrivendo al triangolo rettangolo CDB un semicerchio, d&#039;onde s&#039;apre <lb></lb>la via a dimostrar quest&#039;altra proposizione, ch&#039;è il fondamento, su cui posa <lb></lb>la nuova Scienza del moto: “ Si duo gravia descendunt, alterum quidem <lb></lb>perpendiculariter, alterum vero super plano declinante, pervenient ad idem <lb></lb>planum orizontale, tali ratione, ut sit eadem proportio inter diuturnitates <lb></lb>eorum, quae inter perpendicularem et declinantem ” (ibid., pag. </s>

<s>36). </s></p><p type="main">

<s>Propostasi innanzi la medesima figura 201, a dimostrar che il tempo <lb></lb>per AC sta al tempo per CB, come AC linea sta a CB, procede spedita­<lb></lb>mente sicuro il Baliani in questa maniera: Perciocchè abbiamo, per le già <lb></lb>dimostrate leggi dei moti accelerati, che CD:AC=T.oCD2:T.oAC2 e per <lb></lb>una delle proposizioni antecedenti, che T.oCD=T.oCB, ne conseguiranno <lb></lb>dunque le relazioni CD:AC=T.oCB2:T.oAC2=CDXAC:AC2. </s>

<s>Ma <lb></lb>perchè i triangoli simili ABC, BCD danno CB2=CDXAC, sarà T.oCB2: <lb></lb>T.oAC2=CB2:AC2, e perciò anche i semplici tempi per CB e per AC sta­<lb></lb>ranno come le semplici linee CB, AC. </s></p><p type="main">

<s>Il fondamento alla Scienza nuova era dunque posto anche dal Baliani, <lb></lb>con questa proposizione, la quale è conclusa, come si vede, da principii di­<lb></lb>versi, ed è condotta in diverso modo da quella di Galileo. </s>

<s>Ma perchè s&#039;as­<lb></lb>solvevano, in stabilire un tal fondamento, le intenzioni del Matematico ge­<lb></lb>novese, ei non dà alla sua scienza tutta l&#039;estensione della scienza galileiana, <lb></lb>a confronto della quale, se rimane inferiore rispetto alla materia, vince però <lb></lb>l&#039;esaltato emulo suo rispetto alla elegante semplicità della forma. </s>

<s>Dicemmo, <lb></lb>e lo ripetiamo, che in ciò il Baliani, meglio che a Galileo, si rassomiglia al <lb></lb>Torricelli, col trattato del quale, che si compone, secondo la stessa modesta <lb></lb>espression dell&#039;Autore, delle respigolature fatte nel dovizioso campo gali­<lb></lb>leiano, si riduceva al suo perfezionamento in Italia la nuova istituita Scienza <lb></lb>del moto. </s></p><p type="main">

<s>Oltremonti però avveniva quel che suole avvenire, la mattina, agli abi­<lb></lb>tanti delle valli occidentali, che si trovano innanzi rischiarata la via, e cam­<lb></lb>minano in mezzo al chiaro giorno, senza pensar che anche quella, benchè <lb></lb>giunga ai loro occhi diffusa, è la luce viva del sole. </s>

<s>Edmondo Mariotte leg­<lb></lb>geva un giorno, innanzi all&#039;accademica Assemblea parigina, una certa sua <lb></lb>dissertazioncella, con la quale s&#039;argomentava di rendere la ragione del perchè <lb></lb>una corda di liuto, mossa, faccia spontaneamente risonare le altre corde tese <pb xlink:href="020/01/2135.jpg" pagenum="378"></pb>all&#039;unisono o all&#039;ottava. </s>

<s>Fra i molti dotti, ivi convenuti, il solo Cristiano Huy­<lb></lb>ghens sentì che quella era la ragione medesima data da Galileo, e lo disse <lb></lb>all&#039;Autore, il quale si scusò asseverando che il libro di Galileo non l&#039;aveva <lb></lb>mai letto. </s>

<s>Poi, messosi per curiosità, dopo qualche tempo, a leggere, “ J&#039;ai <lb></lb>trouvé en effet que ses pensées étoient tellement conformes aux miennes, <lb></lb>sur ce suiet, que vous pouviez croire, avec beaucoup de raison, que j&#039;avois <lb></lb>emprunté de lui ce que j&#039;en avois écrit ” (Oeuvres, T. II, a l&#039;Haye 1740, <lb></lb>pag. </s>

<s>558). </s></p><p type="main">

<s>Rivolgeva queste precise parole il Mariotte all&#039;Huyghens stesso, in una <lb></lb>lettera, scritta da Dijon il dì primo del Febbraio 1668, per dedicare al fu­<lb></lb>turo Autore dell&#039;<emph type="italics"></emph>Orologio oscillatorio<emph.end type="italics"></emph.end> alcune sue proposizioni sul moto dei <lb></lb>pendoli e dei corpi gravi, le quali, benchè confessi essere in sostanza quelle <lb></lb>medesime già dimostrate da Galileo, “ il y a pourtant una difference toute <lb></lb>entière entre les façons de démontrer, et l&#039;ordre et suite des propositions, <lb></lb>comme vous le pourrez juger facilement, s&#039;il vous plaìt de lire l&#039;ecrit ci­<lb></lb>joint. </s>

<s>Car vous verrez que dans ma première proposition je donne, ou crois <lb></lb>donner, la vraie cause de l&#039;acceleration du mouvement, au lieu que Galilee <lb></lb>se contente de la supposer et d&#039;enfaire une définition; que dans ma V je <lb></lb>prouve ce qu&#039;il prend pour principe, et qu&#039;il demande lui ètre accordé au <lb></lb>commencement de son Traité; et que dans ma VIII je donne la proportion <lb></lb>du tems par le còté du quarré, avec le tems par les 2 còtez de l&#039;octogone, et <lb></lb>par celui des 3 còtez du dodecagone, ce qu&#039;il n&#039;a pas fait ” (ivi, pag. </s>

<s>558, 59). </s></p><p type="main">

<s>Se abbia propriamente il Mariotte, com&#039;ei vorrebbe far credere, data in <lb></lb>quella sua I proposizione la vera causa dell&#039;accelerazione del moto, lo la­<lb></lb>sciamo giudicare ai nostri Lettori, perché a noi sembra non aver fatto altro <lb></lb>il Matematico francese che mettere in altra forma i concetti stessi di Gali­<lb></lb>leo, i quali rimangono, così per l&#039;uno come per l&#039;altro Autore, indipenden­<lb></lb>temente dalle parole usate a significarli, non più che una semplice defini­<lb></lb>zione. </s>

<s>Quanto al vantarsi poi di aver dato dimostrazione di quel che, nel <lb></lb>Trattato galileiano, si chiede ne sia concesso come noto, non si vede troppo <lb></lb>giusta ragion di tal vanto, essendo stato fatto ciò, tanti anni prima, con <lb></lb>pubblica solennità, dal Baliani e dal Torricelli, e avendo anzi il Gassendo <lb></lb>divulgata in Francia la notizia che quella tanto desiderata dimostrazione era <lb></lb>stata fatta dallo stesso Galileo, per inserirsi, occorrendo di ristamparlo, nel <lb></lb>suo III dialogo Del moto. </s></p><p type="main">

<s>Qualche cosa nonostante di nuovo e di singolare è nella VII proposi­<lb></lb>zione, nella quale s&#039;insegna dal Mariotte a calcolare la proporzion del tempo, <lb></lb>scendendo il grave per la sottesa a una quarta di cerchio, per i due lati <lb></lb>dell&#039;ottagono, e per i tre del dodecagono, a fin di concluderne il brachisto­<lb></lb>cronismo degli archi rispetto alle corde. </s>

<s>Ostentava, in ordine a ciò, l&#039;eccel­<lb></lb>lenza del suo proprio trattato, in confronto di quello di Galileo, il quale, se <lb></lb><emph type="italics"></emph>il n&#039;a pas fait,<emph.end type="italics"></emph.end> non è da apporglielo a difetto, avendo egli tenuto altre vie <lb></lb>più generali, e diciamolo francamente, più matematiche di quelle proseguite <lb></lb>dall&#039;Accademico parigino. </s>

<s>Si può aggiungere anzi che la VIII proposizione del <pb xlink:href="020/01/2136.jpg" pagenum="379"></pb>francese Autore <emph type="italics"></emph>Du mouvement des pendules<emph.end type="italics"></emph.end> dipende dalla precedente, che <lb></lb><figure id="id.020.01.2136.1.jpg" xlink:href="020/01/2136/1.jpg"></figure></s></p><p type="caption">

<s>Figura 202.<lb></lb>si deriva per corollario dalla XIV, ordinata da <lb></lb>noi di sopra, nel pubblicare il III libro galileiano. </s></p><p type="main">

<s>La detta VII proposizione infatti, nel trattato del <lb></lb>Mariotte, è così formulata: “ Soit AB (fig. </s>

<s>202) per­<lb></lb>pendiculaire à l&#039;horison; AC, BD perpendiculaires à <lb></lb>AB, et AE le quart de la ligne; et soit FED quelcon­<lb></lb>que ligne entre les deux paralleles AC, BD: je dis que <lb></lb>le tems par FE, EB sera égal au tems par AE, ED. </s>

<s><lb></lb>Mais si AE est moindre que le quart de AB, le tems <lb></lb>par AE, ED, sera plus grand que par FE, EB. </s>

<s>Mais <lb></lb>si AE est plus que le quart, le tems par FE, EB sera <lb></lb>le plus grand ” (Ouvres, T. II cit., pag. </s>

<s>564, 65). </s></p><p type="main">

<s>La dimostrazione si deriva per legittimo e immediato discorso, come <lb></lb>s&#039;è detto, dalla XIV del III libro manoscritto di Galileo, dalla quale, prese <lb></lb>FG, AH medie proporzionali fra FD, FE, e AB, AE, si hanno l&#039;equazioni <lb></lb>T.oAE:T.oED=AE:EG; T.oFE:T.oEB=FE:EH, che danno per com­<lb></lb>posizione T.oAE+T.oED:T.oED=AE+FG:EG; T.oFE+T.oEB: <lb></lb>T.oEB=FE+EH:EH. </s>

<s>Ma perchè T.oFD=EG, e T.oEB=EH, sarà <lb></lb>T.oAE+T.oED:T.oFE+T.oEB=AE+EG:FE+EH. </s></p><p type="main">

<s>Vien di qui dimostrato il teorema del Mariotte, ne&#039;suoi tre casi di­<lb></lb>stinti, imperocchè, quanto al primo, se AE, e perciò anche EF, son la quarta <lb></lb>parte precisa delle AB, GD, sono altresì respettivamente uguali alle EH, EG, <lb></lb>e perciò T.oAE+T.oED=T.oEF+T.oEB. </s>

<s>Essendo nel secondo caso as­<lb></lb>sai facile dimostrare che AE+EG&gt;FE+EH,
e nel terzo che AE+EG &lt;<lb></lb>FE+EH, se ne conclude, rispetto all&#039;uno e all&#039;altro propostosi caso, dalla <lb></lb>formulata equazione, l&#039;intento. </s></p><p type="main">

<s>Soggiunge a ciò poi il Mariotte il seguente Scolio, che serve efficace­<lb></lb>mente di Lemma alla VIII proposizione: “ On prouvera le meme, si les <lb></lb>deux lignes AEB, FED sont toutes deux inclinées: et l&#039;on peut conclure, <lb></lb>par ce qui est dit au troisieme cas, qu&#039;un poids commençant sa descent par <lb></lb>une ligne perpendiculaire, ou peu inclinée, et la finissan par une beaucoup <lb></lb>inclinée, fait le tems plus court que s&#039;il commençoit et finissoit au contraire, <lb></lb><figure id="id.020.01.2136.2.jpg" xlink:href="020/01/2136/2.jpg"></figure></s></p><p type="caption">

<s>Figura 203.<lb></lb>si la perpendiculaire et l&#039;inclinèe sont égales, et <lb></lb>meme, quand la perpendiculaire et l&#039;inclinée se­<lb></lb>roient un peu plus grandes que l&#039;inclinée et la <lb></lb>perpendisulaire ” (ivi, pag. </s>

<s>565). </s></p><p type="main">

<s>Dietro le quali cose, ecco in che modo con­<lb></lb>duce il Mariotte la sua VIII proposizione, corri­<lb></lb>spondente alla XXXVI di Galileo. </s>

<s>Siano alla me­<lb></lb>desima quarta di cerchio BDEC (fig. </s>

<s>203) inscritti <lb></lb>il lato BC del quadrato, i due lati BF, FC del­<lb></lb>l&#039;ottagono, e i tre lati BD, DE, EC del dodeca­<lb></lb>gono, e s&#039;immagini che scenda per essi da B un <pb xlink:href="020/01/2137.jpg" pagenum="380"></pb>grave per giungere all&#039;infimo punto C dello stesso quadrante, eretto sul piano <lb></lb>dell&#039;orizzonte, in modo che AC gli riesca perpendicolare. </s>

<s>S&#039;argomenta dal­<lb></lb>l&#039;ultima fatta considerazione, e osservando che la scesa per BFC è meno <lb></lb>inclinata in principio, e più inclinata nel termine di quel che non sia BC; <lb></lb>come pure che l&#039;altra scesa per BDEC è meno inclinata in principio e <lb></lb>più inclinata nel suo termine di quel che non sia la scesa per BFC; s&#039;ar­<lb></lb>gomenta, diciamo, che più breve per BFC che non per BC, e più breve <lb></lb>ancora per BDEC che non per BFC sarà il tempo della scesa di quel mede­<lb></lb>simo grave. </s>

<s>Cosicchè, venendo ai calcoli numerici, si troverebbe, dice il Ma­<lb></lb>riotte, che, essendo il tempo per BC centomila, quello per BFC sarà 93,758, <lb></lb>e quello per BDEC 93,072, presso a poco. </s>

<s>“ D&#039;ou l&#039;on peut conclure, così <lb></lb>termina l&#039;Autore la sua dimostrazione, que le tems par quatre soutendantes <lb></lb>de suite sera encore plus court, et enfin que par la circonference BC il <lb></lb>sera le plus court de tous, et pourroit etre au tems par BC comme 93 a 100, <lb></lb>ou 13 a 14 a peu pres ” (ivi, pag. </s>

<s>565). </s></p><p type="main">

<s>Questo trattatello <emph type="italics"></emph>Du mouvement,<emph.end type="italics"></emph.end> in VIII proposizioni, con una con­<lb></lb>clusione relativa all&#039;isocronismo dei pendoli, fu nel 1668 dedicato, come di­<lb></lb>cemmo, all&#039;Huyghens, il quale, pubblicando cinque anni dopo il suo <emph type="italics"></emph>Orolo­<lb></lb>gio oscillatorio,<emph.end type="italics"></emph.end> veniva con tanto più valide forze del Mariotte a promovere <lb></lb>la Scienza del moto. </s>

<s>Doveva anch&#039;egli partire dai medesimi principii, dei <lb></lb>quali riconobbe con imparziale giudizio primo autore Galileo, se non che <lb></lb>dei modi da lui tenuti in dimostrarli non è sodisfatto. </s>

<s>Era a quel tempo <lb></lb>già venuta alla luce l&#039;aggiunta postuma al III dialogo delle Due nuove <lb></lb>scienze, dove si dimostrava quel che s&#039;era prima supposto, che cioè sono <lb></lb>uguali le velocità sopra piani diversamente inclinati, ma della medesima al­<lb></lb>tezza, e questa galileiana dimostrazione all&#039;Huyghens <emph type="italics"></emph>parum firma videtur,<emph.end type="italics"></emph.end><lb></lb>per cui crede di dovergliene sostituire un&#039;altra. (Horol. </s>

<s>oscill., Lib. </s>

<s>II, pro­<lb></lb>posizione VI, Opera varia, T. </s>

<s>I cit., pag. </s>

<s>62, 63). </s></p><p type="main">

<s>Parve inoltre anche all&#039;Autore dell&#039;<emph type="italics"></emph>Horologio,<emph.end type="italics"></emph.end> come al Cartesio, che non <lb></lb>tenesse l&#039;Accademico nostro fiorentino le vie più compendiose, specialmente <lb></lb>in dimostrare quel teorema “ cui reliqua omnia, quae de descensu super <lb></lb>planis inclinatis tradidit, superstruuntur ” (ibid., pag. </s>

<s>63). È quel galileiano <lb></lb>teorema, a cui qui si accenna, il III, che nel pubblico trattato Dei moti lo­<lb></lb>cali riman tuttavia concluso dal principio supposto. </s>

<s>Ma l&#039;Huyghens, avendo <lb></lb>già prima dato dimostrazione di quello stesso supposto, osservava che, dalle <lb></lb><figure id="id.020.01.2137.1.jpg" xlink:href="020/01/2137/1.jpg"></figure></s></p><p type="caption">

<s>Figura 204.<lb></lb>proprietà dei moti equabili succedentisi agli accelerati, <lb></lb>s&#039;aveva una dimostrazione assai più semplice e più spe­<lb></lb>dita di quella stessa data da Galileo, benchè con l&#039;aiuto <lb></lb>degli Indivisibili. </s></p><p type="main">

<s>Scenda infatti il grave per AB (fig. </s>

<s>204) e per AC. <lb></lb>S&#039;ha, per le proprietà del moto equabile dopo l&#039;ac­<lb></lb>celerato, dimostrate nella I proposizione di Galileo, che <lb></lb>la velocità in B è uguale a 2.AB/T.oAB, e che la velocità in C è uguale a 2.AC/T.oAC. <pb xlink:href="020/01/2138.jpg" pagenum="381"></pb>Ma, secondo che suppone esso Galileo o secondo che volle l&#039;Huyghens di­<lb></lb>mostrare, le velocità in B e in C sono uguali, dunque T.oAB:T.oAC= <lb></lb>AB:AC, che è il fondamento alla nuova scienza del moto, sostituito nella VII <lb></lb>del II libro dell&#039;<emph type="italics"></emph>Orologio oscillatorio<emph.end type="italics"></emph.end> alla III del III dialogo delle Due nuove <lb></lb>scienze. </s></p><p type="main">

<s>Così fatte sostituzioni però, concernenti la forma piuttosto che la so­<lb></lb>stanza, non detraggono che in assai piccola parte a Galileo il merito di es­<lb></lb>sere egli stato il primo a mettere in ordine di trattato que&#039;teoremi, che <lb></lb>l&#039;Huyghens e il Mariotte, per tacere di altri, resero con le loro speculazioni <lb></lb>d&#039;altre nuove mirabili conseguenze fecondi. </s></p><pb xlink:href="020/01/2139.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle scese dei gravi per gli archi dei cerchi<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle varie esperienze e delle teorie, che persuasero essere i tempi delle scorse dei gravi, nelle <lb></lb>concavità dei cerchi e nei pendoli, per qualunque ampiezza di arco, uguali. </s>

<s>— II. </s>

<s>Delle nuove <lb></lb>esperienze e delle teorie, che dimostrarono non essere i tempi dello corse e delle ricorse dei <lb></lb>cadonti, per le concavità dei cerchi e nei pendoli, esattamente uguali. </s>

<s>— III. </s>

<s>Delle leggi delle <lb></lb>cadute dei gravi per archi di cerehi simili, e delle loro applicazioni al problema del pendolo a <lb></lb>secondi. </s>

<s>— IV. </s>

<s>Di ciò che operarono i Discepoli di Galileo, e s<gap></gap>guatamente il Viviani. </s>

<s>per dare <lb></lb>scienza delle supposte proprietà dei pendoli disugnali. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;argomento storico del capitolo precedente ha in sè un&#039;importanza, <lb></lb>ch&#039;è sfuggita forse all&#039;attenzione dei nostri Lettori, ma che a noi preme di <lb></lb>far osservare. </s>

<s>Si riferisce una tale importanza al sodisfar che le narrate sto­<lb></lb>rie fanno alla curiosità di coloro, i quali, essendo passati per la lunga serie <lb></lb>delle proposizioni, di che si compila il trattato galileiano Dei moti locali, in­<lb></lb>serito nel III dialogo Delle due nuove scienze, domandano, appena usciti <lb></lb>fuori dalla faticosa lettura, qual potesse essere stata l&#039;intenzion dell&#039;Autore <lb></lb>in raggirarsi prolissamente intorno a così fatte speculazioni, che, ridotte a <lb></lb>quelle sole, dalle quali verrebbe propriamente promossa la Scienza, si pote­<lb></lb>vano tanto più efficacemente concludere in un piccol numero di teoremi. </s></p><p type="main">

<s>La curiosità, che dee senza dubbio aver frugato tutti i Lettori del trat­<lb></lb>tato a stampa, vien ora ad essere sodisfatta in chi rammemora i primi ma­<lb></lb>noscritti sul medesimo argomento, ne&#039;quali s&#039;incominciava dallo stabilire le <lb></lb>leggi dei moti accelerati, per concluderne brevemente, previi i necessarii <lb></lb>Lemmi, il brachistocronismo degli archi rispetto alle sottese dei cerchi. </s>

<s>Quel <pb xlink:href="020/01/2140.jpg" pagenum="383"></pb>che sta di mezzo vedemmo non esser altro che una soprabbondanza di or­<lb></lb>dito, messo in mezzo alle rare fila dal tessitore, quando impose altro nome, <lb></lb>e volle riserbare ad altr&#039;uso l&#039;inaspettatamente riuscita eccellenza della tela. </s>

<s><lb></lb>Per servirsi d&#039;altra immagine a significare il medesimo concetto, si direbbe <lb></lb>che avvenne a Galileo come a colui, che, correndo la ruota, vede uscire un&#039;an­<lb></lb>fora dall&#039;argilla posta in sul tornio, per ridurla alle semplici forme di un <lb></lb>orciolo. </s>

<s>La curiosa trasformazione apparisce evidente a chi paragona il primo <lb></lb>trattatello manoscritto, l&#039;intenzion del quale era quella di concluder che il <lb></lb>tempo per gli archi è più breve che per le corde inflesse, con l&#039;ultimo trat­<lb></lb>tato a stampa, in cui proponevasi l&#039;Autore di dimostrare le proprietà dei <lb></lb>moti locali, a fine d&#039;instaurarne una Scienza nuova. </s></p><p type="main">

<s>È dunque manifesta di qui l&#039;origine storica di quel III dialogo Del moto, <lb></lb>che formò l&#039;ammirazione del mondo: è manifesto cioè che, dall&#039;esercitarsi <lb></lb>Galileo intorno alle proprietà meccaniche dei cerchi, fu condotto a ritrovare <lb></lb>i principii e le conseguenze nuove della Scienza universale dei moti. </s>

<s>Ora è <lb></lb>notabile che questa universalità si riduca infine e torni alle particolarità delle <lb></lb>prime intenzioni, giacchè si vede che anche il trattato, a cui s&#039;impose il <lb></lb>titolo Dei moti locali, si corona con la proposizione XXXVI, nella quale si <lb></lb>dimostra che la via più breve di giungere da un punto all&#039;altro, non è per <lb></lb>la rettitudine della corda, ma per l&#039;arco sotteso. </s>

<s>Quella XXXVI proposizione <lb></lb>dunque, che non è più la finale intenzion del trattato, vi riman nulladimeno <lb></lb>una delle principali; ond&#039;è che la sua propria dignità c&#039;invita a ricercarne <lb></lb>l&#039;origine, e a indagarne il fine, che nel libro di Galileo, come il nostro di­<lb></lb>scorso confermerà, non apparisce. </s>

<s>Anche il Cartesio perciò dettesi a indo­<lb></lb>vinare, e si credè che il fine della detta proposizione, e di tutto anzi il trat­<lb></lb>tato, che ne preparava le conclusioni; fosse quello di dimostrare l&#039;isocronismo <lb></lb>dei pendoli. </s>

<s>“ Caeterum, così scriveva al Mersenno, nel far la critica al libro <lb></lb>di Galileo, tertium suum Dialogum non alio consilio scripsisse mihi videtur, <lb></lb>quam ut rationem redderet cur eiusdem chordae vibrationes sint inter se <lb></lb>aequales, quod tamen non praestat, sed solum concludit pondera citius de­<lb></lb>scendere secundum arcum circuli, quam secundum eiusdem arcus chordam ” <lb></lb>(Epist., P. II cit., pag. </s>

<s>244). </s></p><p type="main">

<s>Nessun&#039;altra divinazione dette mai me­<lb></lb>glio di questa nella cruna del vero, essendo <lb></lb>che Galileo stesso, rivelando i segreti suoi <lb></lb>pensieri a Guidubaldo Del Monte, dica esser <lb></lb>passate per la sua mente le cose proprie a <lb></lb>quel modo, che avea scritto il Cartesio. </s>

<s>Nella <lb></lb>lettera infatti del dì 20 di Novembre del <lb></lb>1602, dop&#039;aver dato allo stesso Guidubaldo <lb></lb>notizia delle dimostrate proposizioni concer­<lb></lb>nentì il tempo della scesa per l&#039;arco, e per <lb></lb><figure id="id.020.01.2140.1.jpg" xlink:href="020/01/2140/1.jpg"></figure></s></p><p type="caption">

<s>Figura 205.<lb></lb>le inflesse corde sottese; il medesimo Gali­<lb></lb>leo immediatamente soggiunge: “ Sin qui ho dimostrato senza trasgredire <pb xlink:href="020/01/2141.jpg" pagenum="384"></pb>i termini meccanici, ma non posso spuntare a dimostrare come gli archi <lb></lb>SIA (fig. </s>

<s>205), IA sieno passati in tempi uguali, che è quello che cerco ” <lb></lb>(Alb. </s>

<s>VI, 23). </s></p><p type="main">

<s>Essendoci così dunque certificati che l&#039;occasione d&#039;istituire la Scienza <lb></lb>nuova del moto venne veramente a Galileo dall&#039;essersi voluto mettere a di­<lb></lb>mostrare l&#039;isocronismo dei pendoli, si può dir che la storia della Dinamica <lb></lb>incominci dalla storia di una tale scoperta. </s>

<s>Una tradizione volgare, avva­<lb></lb>lorata dall&#039;autorità del Viviani, narra che ciò avvenne nel Duomo di Pisa, <lb></lb>attendendo ivi al dondolar lungo e lento di una lampada sospesa. </s></p><p type="main">

<s>“ Trovavasi il Galileo, scrive esso Viviani nella sua <emph type="italics"></emph>Storia dell&#039;appli­<lb></lb>cazione del pendolo all&#039;Orologio,<emph.end type="italics"></emph.end> in età di vent&#039;anni in circa, intorno al­<lb></lb>l&#039;anno 1583, nella città di Pisa, dove per consiglio del padre s&#039;era applicato <lb></lb>agli studii della Filosofia e della Medicina, ed essendo un giorno nel Duomo <lb></lb>di quella città, come curioso ed accortissimo ch&#039;egli era, caddegli in mente <lb></lb>di osservare, dal moto di una lampana che era stata allontanata dal perpen­<lb></lb>dicolo, se per avventura i tempi delle andate e tornate di quelle, tanto per <lb></lb>gli archi grandi, che per i mediocri e per i minimi, fossero uguali, paren­<lb></lb>dogli che il tempo per la maggior lunghezza dell&#039;arco grande potesse forse <lb></lb>restar contraccambiato dalla maggior velocità, con che per esso vedeva mo­<lb></lb>vere la lampana, come per linea nelle parti superiori più declive. </s>

<s>Sovven­<lb></lb>negli dunque, mentre questa andava quietamente movendosi, di far di quelle <lb></lb>andate e tornate un esamine, come suol dirsi, alla grossa, per mezzo delle <lb></lb>battute del proprio polso, e con l&#039;aiuto ancora del tempo della Musica, nella <lb></lb>quale egli già con gran profitto erasi esercitato, e per allora con questi tali <lb></lb>riscontri parvegli non aver falsamente creduto della egualità di quei tempi ” <lb></lb>(Alb. </s>

<s>XIV, 342). </s></p><p type="main">

<s>Nella <emph type="italics"></emph>Vita di Galileo,<emph.end type="italics"></emph.end> e in varie scritture inedite, come in quella <emph type="italics"></emph>Del <lb></lb>votamento dei vasi<emph.end type="italics"></emph.end> o <emph type="italics"></emph>Delle clessidre<emph.end type="italics"></emph.end> (MSS. Gal., T. CXVIII, fol. </s>

<s>6), e in <lb></lb>quell&#039;altra da noi in parte pubblicata a pag. </s>

<s>303, 4 del I Tomo di questa <lb></lb>nostra Storia, ripete il Viviani il medesimo commento, che tale e non altro <lb></lb>è per noi propriamente il nome, che si meritan così fatte narrazioni. </s>

<s>In que­<lb></lb>st&#039;ultima citata scrittura inedita però soggiunge esso Viviani le seguenti pa­<lb></lb>role, con la storica verità forse meglio conformi: “ Nella medesima età sua <lb></lb>giovanile, quando Galileo studiava Filosofia, che fu pure intorno al 1580, si <lb></lb>chiarì, con l&#039;aiuto di questo suo Pendolo, della falsità di que&#039;due pronun­<lb></lb>ziati di Aristotile, con l&#039;un dei quali egli afferma vedersi che due mobili di <lb></lb>gravità diverse discendono per l&#039;istesso mezzo con velocità proporzionali alle <lb></lb>medesime gravità loro: con l&#039;altro che l&#039;istesso mobile si muove per di­<lb></lb>versi mezzi con velocità continuamente proporzionali alle lor densità o gra­<lb></lb>vezze, facendone. </s>

<s>per chiarirsi della verità del primo, varie esperienze nel­<lb></lb>l&#039;aria con diversi gravi lasciati cader nell&#039;istesso tempo dall&#039;altezza del <lb></lb>campanile di Pisa, e per riscontro del secondo varie altre prove nell&#039;aria e <lb></lb>nell&#039;acqua, indagata prima industriosamente la proporzione delle densità o <lb></lb>gravità in specie di tali fluidi ” (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>62). </s></p><pb xlink:href="020/01/2142.jpg" pagenum="385"></pb><p type="main">

<s>Ora, sembra a noi che questa di confutare gli errori aristotelici fosse <lb></lb>la più naturale e la più ragionevole occasione a Galileo di scoprire l&#039;iso­<lb></lb>cronismo dei pendoli. </s>

<s>Come, a sperimentare che i gravi, di qualunque ma­<lb></lb>teria e di qualunque mole, scendono ugualmente veloci, Galileo stesso, non <lb></lb>sodisfatto de&#039;piani inclinati, per evitare ogni attrito, ricorresse ai pendoli, <lb></lb>fu da noi fatto avvertire altrove, citandone gli opportuni documenti. </s>

<s>Era <lb></lb>perciò naturalissimo che in così fatte esperienze, nelle quali si trattava di <lb></lb>comparare le velocità di due pendoli diversi, si accorgesse il sagace Speri­<lb></lb>mentatore della equidiuturnità delle loro vibrazioni, come ingenuamente narra <lb></lb>di essersi, a una simile occasione, abbattuto il Baliani a fare la medesima <lb></lb>scoperta. </s>

<s>Dop&#039;avere, nella prefazione al primo libro <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> detto in che <lb></lb>modo gli occorresse di sperimentare che i gravi, comunque fossero ponde­<lb></lb>rosi, lasciati cader per un eguale spazio perpendicolare, lo passavano tutti <lb></lb>nel medesimo tempo, “ institi adhuc, soggiunge il Matematico genovese, et <lb></lb>globos, in gravitate et in materia inaequales, appendi funiculis aequalibus, <lb></lb>et agitatos animadverti moveri tempore aequali, et hoc servare adeo fideli­<lb></lb>ter, ut globus plumbeus duarum unciarum, alter librarum duarum, fèrreus <lb></lb>librarum 34, et lapideus quadraginta circiter, nec non et lapis informis, quo­<lb></lb>rum funiculi, comprehensis ipsorum semidiametris, aequales essent; uno et <lb></lb>eodem temporis spatio moverentur, et vibrationes easdem numero darent <lb></lb>hinc inde, sive motus unius globi fieret per aequale spatium, sive per inae­<lb></lb>quale, ita ut qui maiori impetu iactabatur, et sic maius spatium percurre­<lb></lb>bat, illud tanto velocius pertransiret ” (Editio secunda cit., pag. </s>

<s>6). </s></p><p type="main">

<s>Dice il Baliani essergli felicemente occorsa una tale scoperta nel 1611, <lb></lb>quando l&#039;esperienze proprie, per determinar la legge dei gravi cadenti, l&#039;eb­<lb></lb>bero fatto accorto degli altrui inveterati errori. </s>

<s>Ma Galileo, come, allo stesso <lb></lb>modo sperimentando, aveva parecchi anni prima scoperto quei medesimi er­<lb></lb>rori; così, parecchi anni prima del Baliani, ebbe occasione di avvertir che <lb></lb>le varie ampiezze dei corpi oscillanti eran passate da loro nei medesimi tempi. </s>

<s><lb></lb>Vuol giustizia perciò che debbasi a lui, a Galileo, la precedenza nel merito <lb></lb>della scoperta, la quale non avvenne per quelle quasi romantiche avventure <lb></lb>giovanili, alle quali ci fa ripensare il Viviani, ma per i meditati esercizi del­<lb></lb>l&#039;uomo più maturo, e della mente aperta a ricevere, o a risentire almeno, <lb></lb>gl&#039;influssi delle scientifiche tradizioni. </s></p><p type="main">

<s>Alcune delle più singolari proprietà del moto dei gravi, costretti a scen­<lb></lb>der per un arco di cerchio, appesi a una fune fissa nella sua sommità, e <lb></lb>libera alla sua estremità inferiore; erano state sagacemente avvertite dai <lb></lb>nostri Matematici del secolo XVI, e vedremo tra poco come da così fatte <lb></lb>esperienze delicatissime avesse principio e impulso a progredire la Scienza <lb></lb>meccanica di Leonardo da Vinci. </s>

<s>Il Cardano poi iniziava nel suo libro <emph type="italics"></emph>De <lb></lb>subtilitate<emph.end type="italics"></emph.end> questa nuova Scienza da un&#039;occasione sovvenutagli simile a quella <lb></lb>di Galileo e del Baliani perchè, ripensando anch&#039;egli alla difficoltà di mo­<lb></lb>vere un grave posat in piano orizzontale, si volse a paragonare il fatto con <lb></lb>quella grandissima facilità, con la quale si può imprimere un tal simile moto <pb xlink:href="020/01/2143.jpg" pagenum="386"></pb>al medesimo grave, tenendolo sospeso, ed ebbe di qui motivo a sciogliere <lb></lb>un problema, che fu poi posto per fondamento alla Meccanica galileiana. <lb></lb></s>

<s>“ Cum per aequidistantem finitori lineam tam difficulter gravia moveantur, <lb></lb>cur est quod, suspensa, facile adeo impelluntur, ut annulus filo suspensus <lb></lb>sponte videatur moveri? </s>

<s>” (Lugduni 1580, pag. </s>

<s>97). </s></p><p type="main">

<s>La causa di ciò, dice il Cardano, è perchè, quando il grave è posato, <lb></lb>la forza dee sostenerlo e moverlo, mentre, quando è sospeso, non dee far <lb></lb>che moverlo solo. </s>

<s>E pur così movendolo, “ tanta ferme vi redit ad medium, <lb></lb>quanta ab illo depulsum est: igitur, cum ea vi iam depulsum sit a medio, <lb></lb>gratia exempli, per cubiti spatium, tantumdem descendere in contrariam par­<lb></lb>tem necessarium erit, atque ita continuo ac atternato reditu tardissime con­<lb></lb>quiescere ” (ibid.). </s></p><p type="main">

<s>Si trovano in queste parole, come i nostri Lettori s&#039;accorgono facil­<lb></lb>mente, incluse le fondamentali dottrine dei pendoli, i quali ondeggiando <lb></lb>risalgon <emph type="italics"></emph>ferme<emph.end type="italics"></emph.end> alla medesima altezza, d&#039;onde furono scesi, e vi risalireb­<lb></lb>bero puntualmente, quando non ricevessero impedimento dal mezzo, cosicchè <lb></lb>nel vuoto quegli ondeggiamenti, che nell&#039;aria vanno a morir tardissimi, con­<lb></lb>tinuerebbero ivi perpetui. </s>

<s>Cotali pensieri, che fanno esatto riscontro con <lb></lb>quelli di Galileo (Alb. </s>

<s>I, 250), non sono qui dal Cardano espressi, ma s&#039;ar­<lb></lb>gomentano facilmente da ciò che il medesimo Autore insegna nella XL pro­<lb></lb>posizione dell&#039;<emph type="italics"></emph>Opus novum,<emph.end type="italics"></emph.end> dove dice che una perfetta sfera, per moversi <lb></lb>in piano perfettamente orizzontale, non ha bisogno d&#039;altra forza da quella <lb></lb>in fuori “ quae potest scindere aerem ” (Operum. </s>

<s>T. IV cit., pag. </s>

<s>480). </s></p><p type="main">

<s>Soggiunge il Cardano, nel citato libro <emph type="italics"></emph>De subtilitate,<emph.end type="italics"></emph.end> al medesimo pro­<lb></lb>posito, un&#039;altra osservazione importante, ed è che l&#039;anello grave sospeso a <lb></lb>un filo si move tanto più facilmente, quanto il filo stesso è più lungo. </s>

<s>La <lb></lb>ragione di ciò, illustrata dall&#039;Autore con apposita figura, e confortata dagli <lb></lb>invocati teoremi della sua Geometria, si conclude insomma col dire ch&#039;es­<lb></lb>sendo il filo più lungo riesce a proporzione più ampio l&#039;arco descritto, e <lb></lb>perciò il grave, in ugual tratto, men si discosta dalla tangente orizzontale, <lb></lb>d&#039;onde la facilità del suo moto maggior che nell&#039;altro appeso a un filo più <lb></lb>corto, il quale è necessario che “ a centro Terrae magis ascendat ” (pag. </s>

<s>97). </s></p><p type="main">

<s>Ravviandoci ora al nostro primo ragionamento, diciamo che le consi­<lb></lb>derazioni dei pendoli, in mezzo alle meccaniche speculazioni, potevano na­<lb></lb>turalmente sovvenire a Galileo dagli esempi degli anteriori Maestri della <lb></lb>Scienza, anche senza l&#039;avventuroso incontro nel Duomo di Pisa, immagi­<lb></lb>nato forse da chi si dette a credere che nessun altro avesse pensato mai di <lb></lb>ritrovare scienza di così fatti moti per gli archi dei cerchi, ond&#039;ebbe a fa­<lb></lb>voleggiarne l&#039;origine prima dalle lampade ondeggianti. </s>

<s>Non sembra che Ga­<lb></lb>lileo avesse parte in ingerire una tale opinione, perchè, anche là dove sa­<lb></lb>rebbe caduto opportuno di accennare a ciò, che dette prossima occasione <lb></lb>alla scoperta, ne tace, e dice anzi per bocca del Sagredo che “ avendo ben <lb></lb>mille volte posto cura alle vibrazioni in particolare delle lampade pendenti <lb></lb>in alcune chiese da lunghissime corde, inavvertentemente mosse da alcuno, <pb xlink:href="020/01/2144.jpg" pagenum="387"></pb>il più che io cavassi da tale osservazione fu l&#039;improbabilità dell&#039;opinione di <lb></lb>quelli, che vogliono che simili moti vengano mantenuti, e continuati dal <lb></lb>mezzo, cioè dall&#039;aria ” (Alb. </s>

<s>XIII, 100). </s></p><p type="main">

<s>Se la storia dunque ha da fondarsi sui documenti, si dovrebbe dire che <lb></lb>Galileo stesso nega di avere imparato l&#039;isocronismo dalle lampade oscillanti, <lb></lb>dalle quali solo prese occasione di riconoscer l&#039;impossibilità dell&#039;opinione <lb></lb>aristotelica intorno all&#039;aria, che produce e mantiene il moto ai proietti. </s>

<s>Quanto <lb></lb>al moto dei gravi naturalmente cadenti, come i corpi appesi a un filo, piut­<lb></lb>tosto che striscianti lungo un piano, gli servissero a sperimentar le leggi <lb></lb>delle cadute, e a scoprire le altre non meno inverosimili opinioni del Filo­<lb></lb>sofo, lo dice in questo stesso Dialogo poco avanti, quasi volesse da sè me­<lb></lb>desimo Galileo confermar che fu dall&#039;usare i pendoli in così fatte esperienze, <lb></lb>che gli occorse di avvertire l&#039;ugual tempo delle loro maggiori o minori <lb></lb>oscillazioni. </s></p><p type="main">

<s>Comunque sia, il primo autentico documento, in cui facciasi menzione <lb></lb>dello scoperto isocronismo, è una lettera del 1602 indirizzata a Guidubaldo <lb></lb>del Monte, quando Galileo non era semplice scolare, ma professore in Pa­<lb></lb>dova, dove non s&#039;esercitava per suo giovanile diletto intorno alla Musica, <lb></lb>ma insegnava alla gioventù, d&#039;ogni parte del mondo convenutavi, la Mate­<lb></lb>matica. </s>

<s>Appartengono a cotesti tempi alcune scritture del professor pado­<lb></lb>vano, dalle quali giusto apparisce ch&#039;egli studiava allora intorno alle pro­<lb></lb>prietà del moto, sgombrandosi innanzi le vie dagli aristotelici errori. </s>

<s>Starebbe <lb></lb>perciò anche questo a confermar l&#039;opinione che fosse la scoperta fatta in <lb></lb>quel tempo, o poco prima che ne desse lo Scopritore avviso a Guidubaldo, <lb></lb>a cui parve impossibile che per pochi gradi e per l&#039;intero quadrante pas­<lb></lb>sasse un mobile tanto differente lunghezza di via nel medesimo tempo. </s>

<s>Volle <lb></lb>nonostante ricorrere alle esperienze, facendo scendere alcune pallottoline den­<lb></lb>tro uno scatolone, e confermando dal fatto quella prima impossibilità giu­<lb></lb>dicata col semplice discorso. </s></p><p type="main">

<s>Galileo importunamente insisteva per persuadere al celebre Matematico <lb></lb>che la cosa non era impossibile, e, invece di servirsi dello scatolone, fallace <lb></lb>o per non essere ben pulito, <lb></lb>o per non essere esattamen­<lb></lb>te girato in cerchio; lo con­<lb></lb>sigliava a tener quel mede­<lb></lb>simo modo, col quale diceva <lb></lb>di essersi egli stesso con tan­<lb></lb>ta certezza chiarito del ve­<lb></lb>ro. </s>

<s>“ Piglio, scriveva nella ci­<lb></lb>tata Lettera, data da Padova <lb></lb>il dì 20 Novembre 1602, due <lb></lb><figure id="id.020.01.2144.1.jpg" xlink:href="020/01/2144/1.jpg"></figure></s></p><p type="caption">

<s>Figura 206.<lb></lb>fili sottili, lunghi ugualmente due o tre braccia l&#039;uno, e <lb></lb>sieno AB (fig. </s>

<s>206), EF (fig. </s>

<s>207), e gli appicco a due <lb></lb><figure id="id.020.01.2144.2.jpg" xlink:href="020/01/2144/2.jpg"></figure></s></p><p type="caption">

<s>Figura 207.<lb></lb>chiodetti A, E, e nell&#039;altre estremità B, F lego due palle di piombo uguali, <pb xlink:href="020/01/2145.jpg" pagenum="388"></pb>sebben niente importa se fossero disuguali, rimovendo poi ciascuno dei detti <lb></lb>fili dal suo perpendicolo, ma uno assai, come saria per l&#039;arco CB, e l&#039;altro <lb></lb>pochissimo, come saria per l&#039;arco IF. </s>

<s>Gli lasciò poi nell&#039;istesso tempo andare <lb></lb>liberamente, e l&#039;uno comincia a descrivere archi grandi simili al BCD, e <lb></lb>l&#039;altro ne descrive de&#039;piccoli, simili al FIG, ma non però consuma più <lb></lb>tempo il mobile B a passare tutto l&#039;arco BCD, che si faccia l&#039;altro mobile <lb></lb>F a passare l&#039;arco FIG ” (Alb. </s>

<s>VI, 20, 21). </s></p><p type="main">

<s>Il modo di assicurarsi della verità di questo fatto Galileo lo riduce prin­<lb></lb>cipalmente a numerare le vibrazioni grandi e le piccole, ma poi ne soggiunge <lb></lb>un altro, in cui si chiama giudice il senso della vista. </s>

<s>Questo secondo modo, <lb></lb>oltre ad essere meno tedioso, si rendeva assai più concludente, e fu grande <lb></lb>sventura dello Sperimentatore il non dargli che un&#039;importanza secondaria, <lb></lb>per cui non usò forse in praticarlo la debita diligenza. </s>

<s>Ciò che i fatti da <lb></lb>narrare confermeranno trasparisce intanto dalle seguenti parole che Galileo <lb></lb>prosegue a scrivere a Guidubaldo: </s></p><p type="main">

<s>“ Il mobile B passa per lo grand&#039;arco BCD, e ritorna per lo mede­<lb></lb>simo BCB, e poi ritorna verso D, e va per 500 e 1000 volte reiterando le <lb></lb>sue reciprocazioni. </s>

<s>L&#039;altro parimente va da E in G, e di poi torna in F, e <lb></lb>parimente farà molte reciprocazioni, e nel tempo ch&#039;io numero <emph type="italics"></emph>v, g,<emph.end type="italics"></emph.end> le prime <lb></lb>cento grandi reciprocazioni BCD, DCB, ecc., un altro osservatore numera <lb></lb>cento altre reciprocazioni per FIG piccolissime, e non ne numera pure una <lb></lb>sola di più; segno evidentissimo che ciascheduna particolare di esse gran­<lb></lb>dissime BCD consuma tanto tempo, quanto ognuna delle minime particolari <lb></lb>FIG. </s>

<s>Or se tutta la BCD vien passata in tanto tempo, in quanto la FIG, <lb></lb>ancora le loro metà, che sono le cadute per gli archi disuguali della mede­<lb></lb>sima quarta, saranno fatte in tempi uguali. </s>

<s>Ma anco, senza stare a nume­<lb></lb>rar altro, V. S. Ill.ma vedrà che il mobile F non farà le sue piccolissime <lb></lb>reciprocazioni più frequenti, che il mobile B le sue grandissime, ma sempre <lb></lb>anderanno insieme ” (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>Lusingandosi ora Galileo che fossero queste sue esperienze tanto esatte, <lb></lb>da non si mettere in dubbio la verità del nuovo fatto scoperto, erasi dato <lb></lb>con grande studio a ricercarne la matematica dimostrazione, persuaso doversi <lb></lb>corrispondere amichevolmente insieme la Fisica e la Geometria. </s>

<s>E giunto, <lb></lb>per quelle vie che sono ai nostri Lettori oramai ben note, a dimostrar le <lb></lb>ammirabili proprietà delle corde, sperava che un breve passo lo dovesse fe­<lb></lb>licemente condurre alla desiderata dimostrazione dell&#039;isocronismo per gli ar­<lb></lb>chi, ciò che a far dianzi l&#039;udimmo accoratamente dire a Guidubaldo <emph type="italics"></emph>non <lb></lb>esser potuto spuntare.<emph.end type="italics"></emph.end> L&#039;espressione, nella proprietà del linguaggio toscano, <lb></lb>era efficacissima a significar la mente e l&#039;animo di Galileo, il quale tanto <lb></lb>era certo del fatto, da non sospettar nemmeno dalla lontana che non si po­<lb></lb>tesse, senza trasgredire i termini meccanici, dimostrarlo, perchè non era esat­<lb></lb>tamente vero; ma ne dava tutta la colpa alla sua propria insufficienza, co­<lb></lb>sicchè, invocando altri principii, tenendo altre vie, facendo insomma nuovi <lb></lb>sforzi, sperava di riuscire a dimostrar con meccaniche ragioni che le corse <pb xlink:href="020/01/2146.jpg" pagenum="389"></pb>e le ricorse per gli archi di qualunque ampiezza si spediscono dai pendoli <lb></lb>tutte nei medesimi tempi. </s></p><p type="main">

<s>Trent&#039;anni dopo quegli sforzi fatti, e i progrediti esercizi intorno alla <lb></lb>Scienza del moto, erano riusciti a niente, cosicchè, volendo alla fin dei dia­<lb></lb>loghi Dei due massimi sistemi render solennemente noto al mondo il pro­<lb></lb>gramma delle sue meccaniche scoperte, intanto che meditava di raccoglierle <lb></lb>insieme in un Libro a parte, annunziava tra le altre maravigliose proprietà <lb></lb>del pendolo, “ che fa le sue vibrazioni con l&#039;istessa frequenza, o pochissimo <lb></lb>o quasi insensibilmente differente, sien elleno fatte per archi grandissimi o <lb></lb>per piccolissimi dell&#039;istessa circonferenza ” soggiungendo di essersi per ri­<lb></lb>petute esperienze assicurato che “ se noi rimoveremo il pendolo dal perpen­<lb></lb>dicolo uno, due, o tre gradi solamente, oppure lo rimoveremo 79, 80, o an­<lb></lb>che sino a una quarta intera, lasciato in sua libertà, farà nell&#039;uno e nell&#039;altro <lb></lb>caso le sue vibrazioni con la medesima frequenza ” (Alb. </s>

<s>I, 487). </s></p><p type="main">

<s>Dop&#039;avere ripetuto così, senz&#039;altre nuove osservazioni, quel che tren­<lb></lb>t&#039;anni prima avea scritto a Guidubaldo del Monte, Galileo, come corollario <lb></lb>dipendente dall&#039;isocronismo dei pendoli, annunziava la bellissima conclusione <lb></lb>che, fatto un arco con una tavola ben pulita e liscia, come sarebbe la cassa <lb></lb>di un vaglio, e posta una palla in qual si voglia punto della sua concavità, <lb></lb>arriva al termine infimo, sempre, di dovunque movesse, in tempi uguali: <lb></lb>soggiungeva poi a questi pur per simili corollarii delle proprietà del pen­<lb></lb>dolo, il tautocronismo per le corde, e il brachistocronismo per gli archi (ivi, <lb></lb>pag. </s>

<s>488). </s></p><p type="main">

<s>Sembrerebbe di qui che, per ragione meccanica della sua scoperta, non <lb></lb>essendo dopo tanto tempo e dopo tante fatiche potuto spuntar Galileo a tro­<lb></lb>vare una dimostrazione diretta, s&#039;acquetasse finalmente a far valere per gli <lb></lb>archi il tautocronismo ritrovato verissimo per le corde. </s>

<s>La congettura è ve­<lb></lb>rificata da chiarissimi documenti posteriori, come dalle celebri Lettere al <lb></lb>Carcaville (Alb. </s>

<s>VII, 158) e a Lorenzo Realio (ivi, pag. </s>

<s>168) ma più solen­<lb></lb>nemente dal primo dialogo Delle due nuove scienze, dove così espressamente <lb></lb>si legge: “ E quanto al primo dubbio che è se veramente e puntualissi­<lb></lb>mamente l&#039;istesso pendolo fa tutte le sue vibrazioni massime, mediocri e mi­<lb></lb>nime, sotto tempi precisamente eguali, io mi rimetto a quello, che intesi già <lb></lb>dal nostro Accademico, il quale dimostra bene che il mobile, che discen­<lb></lb>desse per le corde suttese a qual si voglia arco, le passerebbe necessaria­<lb></lb>mente tutte in tempi eguali, tanto le suttese sotto cent&#039;ottanta gradi, cioè <lb></lb>tutto il diametro, quanto le suttese di cento, di sessanta, di due, di mezzo <lb></lb>e di quattro mìnuti, intendendo che tutte vadano a terminar nell&#039;infimo <lb></lb>punto toccante il piano orizzontale ” (Alb. </s>

<s>XIII, 98). </s></p><p type="main">

<s>Quel giovane, così scrupoloso di trasgredire i termini meccanici, ora <lb></lb>dunque da vecchio s&#039;è fatto di più rilasciata coscienza, la quale non avreb­<lb></lb>begli dovuto consentire così facile il trapasso dalle proprietà meccaniche <lb></lb>delle corde alle analoghe proprietà meccaniche per gli archi sottesi. </s>

<s>Che se <lb></lb>avesse dovuto ridurlo ai termini del dovere, conveniva piuttosto suggerirgli <pb xlink:href="020/01/2147.jpg" pagenum="390"></pb>questa per la più sicura via da tenere: ammetter cioè che, in tanto si po­<lb></lb>tessero dire isocroni gli archi, in quanto si confondono con le corde, le quali <lb></lb>solo s&#039;è riuscito a dimostrare isocrone: e insomma non asserire così con­<lb></lb>fidentemente che, per tutta la quarta del cerchio, vanno le vibrazioni eguali, <lb></lb>ma quelle sole fatte per un piccolo numero di gradi. </s>

<s>Che se non tenne Ga­<lb></lb>lileo dietro alla severa logica di questo discorso, si deve alla persuasione che <lb></lb>fossero puntualissime le sue esperienze, le quali non avendo potuto altri­<lb></lb>menti dimostrare, e non convenendogli di confessar al pubblico la sua in­<lb></lb>sufficienza, com&#039;avea fatto da giovane e in privato con Guidubaldo; s&#039;attenne <lb></lb>al partito di far dell&#039;isocronismo dei pendoli un corollario alla VI proposi­<lb></lb>zione del II libro Dei moti locali. </s></p><p type="main">

<s>Nella fallacia di così fatte delicatissime esperienze incorsero altresì il <lb></lb>Baliani e Giovan Marco, il primo dei quali non professò l&#039;isocronismo, che <lb></lb>quale un semplice supposto sperimentale, ponendolo così formulato per uno <lb></lb>dei fondamenti alle sue meccaniche proposizioni: “ Aequipendulorum eorum­<lb></lb>dem vibrationes sunt aequidiuturnae etiamsi inaequales ” (De motu cit., <lb></lb>pag. </s>

<s>15). Ma il Matematico tedesco volle provarsi a darne diretta dimostra­<lb></lb>zione matematica, con l&#039;apparato di quattro lemmi, premessi in servigio al <lb></lb>suo XXIV teorema <emph type="italics"></emph>De proportione motus,<emph.end type="italics"></emph.end> proposto in tal forma: “ Perpen­<lb></lb>diculum, ex quolibet puncto eiusdem circuli, <lb></lb>aequali tempore recurrit in suam stationem. <lb></lb></s>

<s>” Nel circolo TUXB (fig. </s>

<s>208), col centro in <lb></lb>A, sollevato il perpendicolo AT o in AB, o in <lb></lb>AD, o in AF, o in qual si voglia altra minore <lb></lb>altezza, dimostra l&#039;Autore che tanto da B, <lb></lb>quanto da D o da F, ricorre in T esso perpen­<lb></lb>dicolo alla sua prima stazione, sempre nel <lb></lb>medesimo tempo. </s>

<s>Il ragionamento muove in <lb></lb>parte da principii dimostrati, e in parte da <lb></lb>principii supposti, ma la conclusione non è, e <lb></lb>non poteva esser altro che uno sforzo dell&#039;inge­<lb></lb><figure id="id.020.01.2147.1.jpg" xlink:href="020/01/2147/1.jpg"></figure></s></p><p type="caption">

<s>Figura 208<lb></lb>gno. </s>

<s>Le velocità in B, in D e in F son proporzionali ai seni AB, CD, EF, <lb></lb>che in uguali archi intercetti vanno via via scemando di lunghezza, ma cre­<lb></lb>scono le proporzioni fra loro, avendo CD a EF maggior ragione che AB a <lb></lb>CD, cosicchè l&#039;incremento da una parte e il decremento dall&#039;altra riducono <lb></lb>all&#039;egualità costante la fine del moto. </s>

<s>“ At vero quia ad singula puncta, <lb></lb>mutata sinuum ratione, mutatur quoque ratio velocitatis; maior enim propor­<lb></lb>tio CD ad EF, quam AB ad CD, erit quoque maior proportio arcus D F ad <lb></lb>ad FH quam arcus BD ad DF. </s>

<s>Quia ergo, cum hoc sinuum et arcuum decre­<lb></lb>mento, continuo augetur illorum proportio, minuitur vero distantia termi­<lb></lb>norum motus; necesse est demum absumi et deficere, illoque deficiente, mo­<lb></lb>tum coaequari ” (fol. </s>

<s>I, 2). </s></p><p type="main">

<s>Lusingavasi Giovan Marco di aver dato così buona dimostrazion mate­<lb></lb>matica dell&#039;isocronismo dei pendoli, ingannato dalle osservazioni dei fatti, <pb xlink:href="020/01/2148.jpg" pagenum="391"></pb>intorno ai quali abbiamo dianzi veduto come fossero similmente tratti in <lb></lb>inganno Galileo e il Baliani. </s>

<s>Che fosse da un&#039;altra parte una tale osserva­<lb></lb>zione veramente ingannatrice, lo conferma l&#039;esempio del più diligente spe­<lb></lb>rimentatore, che si conoscesse a quei tempi, il quale pubblicò solennemente <lb></lb>di aver per ripetuti sperimenti scoperto che, oscillando i pesi penduli a un <lb></lb>filo, passano i maggiori e i minori archi descritti in tempi sempre fra loro <lb></lb>uguali. </s></p><p type="main">

<s>Giovan Batista Riccioli era nel 1629 professore in Parma, nel collegio <lb></lb>dei gesuiti, quando un giorno gli scrisse il Cabeo da Ferrara, pregandolo a <lb></lb>fare esperienza se due pendoli, del medesimo peso e della medesima altezzza, <lb></lb>ritirati a ugual distanza dal perpendicolo, e poi di lì lasciati ambedue a un <lb></lb>tempo, andavano e ritornavano sempre di pari passo. </s>

<s>Ebbe esecuzion la ri­<lb></lb>chiesta in compagnia di Daniello Bartoli e di Alfonso Iseo, i quali ritrova­<lb></lb>rono essere propriamente così, come il Cabeo aveva a loro annunziato. </s></p><p type="main">

<s>Stava allora il Riccioli tutto in sollecito studio di ritrovare le propor­<lb></lb>zioni delle cadute dei gravi, ma a condur la difficile impresa vivamente <lb></lb>sentiva il bisogno di uno strumento, da misurare esatte le minuzie del <lb></lb>tempo. </s>

<s>Le pulsazioni delle arterie, i flussi dell&#039;acqua o della polvere nelle <lb></lb>clessidre, e simili altri cronometri allora in uso, gli reputava tanto fallaci, <lb></lb>da non si confidar che le proporzioni così misurate, nemmen prossimamente, <lb></lb>rispondessero alle vere. </s>

<s>Occorsogli poi per avventura di fare, agl&#039;inviti del <lb></lb>Cabeo, le sopra dette esperienze, “ tunc suspicari coepi, scrive lo stesso Ric­<lb></lb>cioli, oscillationes eiusdem perpendiculi quaslibet aequales esse quibuslibet <lb></lb>in tempore, quod postea (ciò che a pag. </s>

<s>386 del II tomo dello stesso <emph type="italics"></emph>Alma­<lb></lb>gesto nuovo,<emph.end type="italics"></emph.end> dice essere avvenuto in Ferrara nel 1634) iteratis accuratius <lb></lb>experimentis, perdidici. </s>

<s>Necdum enim tum ad manus meas pervenerant dia­<lb></lb>logi Galilaei <emph type="italics"></emph>De mundi systemate,<emph.end type="italics"></emph.end> ubi, dialogo II, idem affirmatur, nec <lb></lb>D. </s>

<s>Joannis Baptistae Baliani opusculum <emph type="italics"></emph>De motu naturali solidorum:<emph.end type="italics"></emph.end> illos <lb></lb>enim biennio, hoc decennio post tantummodo legi ” (Almag. </s>

<s>novi, T. I, Bo­<lb></lb>noniae 1651, pag. </s>

<s>84). </s></p><p type="main">

<s>Gli esperimenti, dai quali dice il Riccioli di avere appresso il fatto an­<lb></lb>nunziato, son descritti nell&#039;appresso proposizione I del cap. </s>

<s>XX del II libro, <lb></lb>la quale, richiamando i Lettori addietro alla figura 207 per rammemorare <lb></lb>a loro che <emph type="italics"></emph>vibrazione semplice<emph.end type="italics"></emph.end> chiama l&#039;Autore la semplice andata da F <lb></lb>in G, e <emph type="italics"></emph>vibrazione composta<emph.end type="italics"></emph.end> la detta andata col ritorno da G in H, un poco <lb></lb>più sotto ad F; è così formulata: “ Perpendiculi eiusdem quaelibet vibratio <lb></lb>simplex cuilibet vibrationi simplici, et quaelibet composita cuilibet compo­<lb></lb>sitae ad sensum aequalis est in tempore sui motus, per se, seu est aequi­<lb></lb>diuturna, seu, graece, <emph type="italics"></emph>isochrona ”<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>85). </s></p><p type="main">

<s>Numerammo, poi si legge per la dimostrazione, nelle notti del 19 e <lb></lb>20 Maggio, e del 2 Giugno, il numero delle vibrazioni fatte da un pendolo <lb></lb>dal punto del passaggio della Spiga, al punto del passaggio di Arturo al <lb></lb>medesimo meridiano, e trovammo due volte vibrazioni semplici 3212, e una <lb></lb>volta 3214. “ At si vibrationes eiusdem perpendiculi inaequali tempore sen-<pb xlink:href="020/01/2149.jpg" pagenum="392"></pb>sibiliter fierent, non posset non esse magna differentia in numero illarum, <lb></lb>post multas saltem vibrationes se prodiens. </s>

<s>Nusquam autem se prodit, ergo <lb></lb>ad sensum sunt aequales in tempore ” (ibid.). </s></p><p type="main">

<s>Soggiunge immediatamente il Riccioli a queste parole ch&#039;egli intende <lb></lb>dire dell&#039;uguaglianza assoluta, escluse le cause accidentali. </s>

<s>È notabile poi che <lb></lb>riduca queste cause accidentali al vento, “ qui ex adverso flaret, aut aliud <lb></lb>quidpiam extraordinarium perpendiculum incitaret, aut retardaret ” (ibid.). <lb></lb>Dicemmo esser ciò notabile, perchè la temuta causa perturbatrice in verità <lb></lb>non esiste, essendo, come Galileo aveva già pubblicamente insegnato, del <lb></lb>tutto impossibile il far fare a un pendolo le vibrazioni sotto altri tempi, da <lb></lb>quelli per naturale necessità determinati “ salvo che con allungargli o ab­<lb></lb>breviargli la corda ” (Alb. </s>

<s>I, 487). </s></p><p type="main">

<s>Dal non aver riconosciuta la natura meccanica dello strumento dipende <lb></lb>pure l&#039;altra inutile scrupolosaggine dal Riccioli osservata nelle sue espe­<lb></lb>rienze, qual è quella di tenere esattissimo conto del peso del pendolo e delle <lb></lb>sue sospensure. </s>

<s>Può essere il peso accidentalmente notato nelle esperienze <lb></lb>di colui che sa ridurre il pendolo composto al semplice, e che è ben per­<lb></lb>suaso essere le vibrazioni maggiori più diuturne, essendo che un maggior <lb></lb>peso conferisce alla maggior duratura delle vibrazioni ampie: ma nella mente <lb></lb>del Riccioli che professava l&#039;isocronismo assoluto, e che tanto era ancora <lb></lb>lontano dal presentir la teoria de&#039;centri di oscillazione, quel notare il peso <lb></lb>del grave ondeggiante, e della sua catena, era senza alcuna ragione, e un <lb></lb>impaccio di più, volontariamente frappostosi alla facilità, e talvolta anco al­<lb></lb>l&#039;esattezza delle esperienze. </s>

<s>Non l&#039;arte insomma, ma la scienza fu che fece <lb></lb>difetto in ciò al solertissimo Sperimentatore. </s></p><p type="main">

<s>Galileo aveva dell&#039;assoluta uguaglianza dei pendoli assegnata un&#039;altra <lb></lb>causa perturbatrice, la quale, perciocchè non appariva avversa alle approvate <lb></lb>verità della scienza, riuscì molto più seducente di quella falsa assegnata dal <lb></lb>Riccioli. </s>

<s>Si riduce quell&#039;accennata causa perturbatrice al mezzo dell&#039;aria “ la <lb></lb>quale resistendo all&#039;essere aperta, ritarda qualche poco, e impedisce il moto <lb></lb>del pendolo, ma l&#039;impedimento è ben poco, di che è argomento il numero <lb></lb>grande delle vibrazioni, che si fanno avanti che il mobile si fermi del tutto ” <lb></lb>(Alb. </s>

<s>I, 250). Or essendo da tutti quest&#039;impedimento riconosciuto reale, e <lb></lb>dal fatto qui notato da Galileo argomentandosi alla sua piccolezza, questa <lb></lb>era tale da lusingar che a lei sola si dovessero attribuir quelle piccole ine­<lb></lb>guaglianze, notabili all&#039;esperienze più diligenti e più delicate. </s>

<s>Di qui s&#039;in­<lb></lb>tende perchè, nella prima metà del secolo XVI, la maggior parte e i più au­<lb></lb>torevoli fra i Fisici e i Matematici professassero, astraendo dalle piccole cause <lb></lb>perturbatrici, dipendenti dalle resistenze del mezzo, con Galìleo, col Baliani <lb></lb>e con Giovan Marco, l&#039;isocronismo assoluto. </s></p><p type="main">

<s>Per citare di quei Fisici, e di quei Matematici qualche esempio, il Mer­<lb></lb>senno, in un libro, in cui ordinava e dava solenne pubblicità a molte dot­<lb></lb>trine per la massima parte da lui attinte ai libri, o nei familiari colloqui con <lb></lb>gli Scienziati italiani, così scriveva: “ Recursus fili AB (fig. </s>

<s>209), a quovis <pb xlink:href="020/01/2150.jpg" pagenum="393"></pb>puncto quadrantis BD, vel BC, redeuntes, sunt proxime isocroni, hoc est <lb></lb>fiunt aequali tempore, nam, sive globulum <lb></lb>ex B ad G, vel ad E, vel ad D traxeris, <lb></lb>tempus, quo descendit a G ad B, prope­<lb></lb>modum aequale est tempori, quo descendit <lb></lb>a G ad B. </s>

<s>Dixi <emph type="italics"></emph>propemodum<emph.end type="italics"></emph.end> et <emph type="italics"></emph>prox ime,<emph.end type="italics"></emph.end><lb></lb>quod aer, a D ad B interiectus, magis <lb></lb>impediat globum B ex D, quam aer, inter <lb></lb>E et B interpositus, globum ex E rede­<lb></lb><figure id="id.020.01.2150.1.jpg" xlink:href="020/01/2150/1.jpg"></figure></s></p><p type="caption">

<s>Figura 209<lb></lb>untem ” (Cogitata physico mat., Parisiis 1644, pag. </s>

<s>10). Così fatto impe­<lb></lb>dimento avvertiva il Mariotte essere altresì maggiore o minore, secondo la <lb></lb>maggiore o minor virtù del peso specifico del pendolo in superarlo, cosic­<lb></lb>chè da certi calcoli, istituiti nella proposizione VIII del suo trattato <emph type="italics"></emph>Du mou­<lb></lb>vement,<emph.end type="italics"></emph.end> conclude che se il pendolo stesso è d&#039;oro “ et que la resistance <lb></lb>de l&#039;air n&#039;augmente le tems de sa chûte par 90 degrez que de 1/13, les gran­<lb></lb>des et les petites vibrations seront egales. </s>

<s>Mais soit que le poids soit de bois <lb></lb>ou de plumb, les vibrations par un arc de 30 degrez et au-dessous seront <lb></lb>sensiblement egales ” (Oeuvres, T. II cit., pag. </s>

<s>566). </s></p><p type="main">

<s>Le teorie però del Mariotte erano per sè medesime insufficienti a de­<lb></lb>cidere la questione dell&#039;isocronismo dei pendoli circolari, la qual questione, <lb></lb>prima che pubblicasse l&#039;Huyghens il suo <emph type="italics"></emph>Orologio oscillatorio,<emph.end type="italics"></emph.end> veniva ri­<lb></lb>messa al giudizio unico delle esperienze. </s>

<s>Queste, non molti anni dopo pas­<lb></lb>sata la prima metà del secolo XVII, riuscirono finalmente a confermare i <lb></lb>dubbi di quei pochi, che contradissero a Galileo, o ai primi seguaci di lui, <lb></lb>concludendo, come si narrerà in quest&#039;altra parte del nostro discorso, che <lb></lb>l&#039;isocronismo assoluto, nelle scese per gli archi dei cerchi, repugna alla <lb></lb>verità dei fatti, con maggior diligenza che non si fosse fatto fin allora, os­<lb></lb>servati. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Guidubaldo del Monte, a cui primo Galileo annunziava la sua scoperta, <lb></lb>fu anche il primo a contradirla, parendogli irragionevole che, “ pigliandosi <lb></lb>una quarta di cerchio lunga cento miglia, due mobili uguali possano pas­<lb></lb>sarla uno tutta, e l&#039;altro un palmo solo in tempi uguali ” (Alb. </s>

<s>VI, 22). <lb></lb>Soggiungeva, a conferma della sua contradizione, un&#039;esperienza, che Gali­<lb></lb>leo stesso, per le già accennate ragioni, reputava fallace. </s>

<s>Nonostante, nel <lb></lb>dialogo ultimo Dei due massimi sistemi, descriveva l&#039;Autore l&#039;esperienza <lb></lb>medesima di Guidubaldo, suggerendo di farla, con una palla ben rotonda e <lb></lb>tersa, dentro la cassa di un vaglio, e affermando, com&#039;avrebbe fatto della <lb></lb>proposizion matematica più certamente dimostrata, che “ posta la palla in <lb></lb>qualsivoglia luogo, o vicino o lontano dall&#039;infimo termine B (immaginando <lb></lb>che DEGB, nella precedente figura, rappresenti la quarta della concavità cir­<lb></lb>colare), come mettendola nel punto G, ovvero in E o in D, e lasciata in li-<pb xlink:href="020/01/2151.jpg" pagenum="394"></pb>bertà, in tempi uguali o insensibilmente differenti arriverà al termine B, par­<lb></lb>tendosi dal G o dall&#039;E o dal D, o da qualsivoglia altro luogo ” (Alb. </s>

<s>I, 488). </s></p><p type="main">

<s>Se una tal formulata proposizione fosse puramente teorica o sperimen­<lb></lb>tale, non è difficil decidere a chi ripensa che mancavano, così a Galileo come <lb></lb>a Guidubaldo, gli strumenti necessari a misurar, nella scesa del grave o dal <lb></lb>punto G o dal punto D, l&#039;uguaglianza o la differenza dei tempi; e dall&#039;al­<lb></lb>tra parte potevasi avere ugualmente dubbio della perfetta forma circolare, <lb></lb>così nello scatolone, come nella cassa del vaglio. </s>

<s>Fu la sola teoria dunque <lb></lb>che resistè alle contradizioni, alle quali non si sarebbe potuto dare per ve­<lb></lb>rità risposta definitiva nemmeno dalle esperienze più accurate, come dovet­<lb></lb>tero senza dubbio esser quelle istituite dagli Accademici del Cimento, a cui <lb></lb>parve in principio che avesse avuto ragion Guidubaldo, e poi confermarono <lb></lb>l&#039;assoluta proposizione annunziata di sopra da Galileo. </s>

<s>Sperimentando infatti <lb></lb>la prima volta il dì 29 Dicembre 1661, trovarono che “ le corse e ricorse <lb></lb>d&#039;una palla d&#039;avorio, fatte per un canal circolare, non sono equitemporanee, <lb></lb>ma le maggiori sono più veloci, e le minori più tarde ” (Targioni, Noti­<lb></lb>zie ecc. </s>

<s>cit., T. II, P. II, pag. </s>

<s>669, 70). Il dì 7 del Gennaio appresso, tor­<lb></lb>nando a ripetere la medesima esperienza, scrissero gli Accademici, nel loro <lb></lb>solito Diario, di avere invece trovato che “ le corse e ricorse d&#039;una palla <lb></lb>nel canale circolare, sia quella di metallo o di avorio, maggiore o minore, <lb></lb>sono equitemporanee ” e che “ sia la palla di metallo o d&#039;avorio, grande o <lb></lb>piccola, fa ugual numero di vibrazioni in tempi uguali ” (ivi, pag. </s>

<s>670). </s></p><p type="main">

<s>Ben s&#039;accorsero que&#039;solertissimi Sperimentatori che l&#039;eleggere questo <lb></lb>modo era un voler andar, senza vantaggio, ad affrontare le incertezze ine­<lb></lb>vitabili prodotte dagli attriti, e dalla imperfetta rotondità del canale, e tor­<lb></lb>naron perciò con savio consiglio ai funependoli. </s>

<s>Ma perchè pareva a loro <lb></lb>che di questi avesse dato certezza di scienza Galileo, e non si potevano in­<lb></lb>durre a sottoporre al cimento le dottrine del venerato Maestro, se non che <lb></lb>quando altri avesse sollevato intorno a quelle qualche temibile dubbio, giova <lb></lb>a noi accennare ad alcuni di quei primi e più autorevoli, che, avendo con <lb></lb>diligenza osservate le corse e le ricorse dei pendoli, trovarono che non tutte <lb></lb>erano equidiuturne, e che le dottrine di Galileo perciò non rispondevano <lb></lb>esattamente alla verità dei fatti sperimentati. </s></p><p type="main">

<s>Citeremo fra que&#039;liberi censori di Galileo, o fra quegli spregiudicati os­<lb></lb>servatori dei fatti naturali, Gotifredo Wendelin, e Niccolò Cabeo, l&#039;efficacia <lb></lb>dei quali in diffondere la notizia delle loro esperienze si dee forse, piutto­<lb></lb>sto che a loro stessi, all&#039;opera del Riccioli. </s>

<s>Nell&#039;Almagesto nuovo infatti, <lb></lb>più facilmente che ne&#039;libri del Matematico straniero, a noi rari, o nelle di­<lb></lb>sperse epistole e nelle erudite dissertazioni di lui, lessero gl&#039;Italiani che alle <lb></lb>cause dell&#039;inuguaglianza dei pendoli “ addit Vendelinus, si pendulum attol­<lb></lb>latur ultra gradus 40, aut 45 vibrationes eius, esse longioris temporis ” <lb></lb>(T. </s>

<s>I cit., pag. </s>

<s>85). </s></p><p type="main">

<s>Poco più avanti, in questo medesimo cap. </s>

<s>XX del libro II, si cita dal <lb></lb>Riccioli il trattato del Wendelin <emph type="italics"></emph>De ecclipsibus, et idea Tabularum atlan-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2152.jpg" pagenum="395"></pb><emph type="italics"></emph>ticarum,<emph.end type="italics"></emph.end> per mostrar come ivi, in prefinir la misura alla lunghezza del pen­<lb></lb>dolo che batte i secondi, non fosse stato esso Wendelin col Langreno e con <lb></lb>altri molto esatto, e richiamando all&#039;esame altre sentenze, in tal proposito <lb></lb>soggiunte, il Riccioli stesso così scrive: “ Non ostendit autem quomodo vera <lb></lb>sint quae subnectit: <emph type="italics"></emph>Etsi autem verum non est aeque diuturnas esse omnes <lb></lb>eiusdem suspensurae oscillationes, verum autem est hyeme, hoc est sole <lb></lb>perigeo, plures una hora fieri, quam estate, seu sole apogeo<emph.end type="italics"></emph.end> Et nisi forte <lb></lb>putet ob Terrae motum eas incitari, concitato motu diurno ob accessum ad <lb></lb>Solem, retardari autem in recessu, quod etiam Keplero, Longomontano et <lb></lb>Bullialdo placuisse docebimus; concedit tamen Vendelinus: <emph type="italics"></emph>Si utrinque pen­<lb></lb>dulum extra lineam perpendiculi sui extrahatur ad gradus 10, conficere <lb></lb>oscillationes plurimas, et in longissimum tempus isochronas, seu aeque <lb></lb>diuturnas, et ad omnem sensum aequales ”<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>88). </s></p><p type="main">

<s>Il Riccioli non crede all&#039;esperienza del Wendelin, che cioè nell&#039;in­<lb></lb>verno faccia più frequenti il pendolo le sue vibrazioni che nell&#039;estate, per­<lb></lb>chè, non essendosi ancora scoperto che la causa del misterioso effetto era <lb></lb>dovuta alla dilatazion del calore, per cui le sospensure metalliche s&#039;allun­<lb></lb>gano e s&#039;accorciano al variare delle stagioni, s&#039;attribuiva il fatto al moto <lb></lb>della Terra, con tanta ostinazione negato dal Riccioli stesso, il quale però <lb></lb>non sembra ritroso a concedere al Wendelin l&#039;altra osservazione, di non <lb></lb>minore importanza, perchè riduceva alle precision del vero le dottrine di <lb></lb>Galileo; che cioè il moto dei pendoli non è uguale per tutta l&#039;ampiezza del <lb></lb>quadrante, ma quando solo si riduce alle vibrazioni piccole, come dentro a <lb></lb>una diecina di gradi. </s></p><p type="main">

<s>Quanto al Cabeo, egli instituiva nel I libro de&#039;suoi Commenti meteo­<lb></lb>rologici una questione sui pendoli, revocando a uno a uno a sottile e rigo­<lb></lb>roso esame i documenti galileiani, ma più di proposito trattenendosi sopra <lb></lb>quello, in cui si asserisce essere uguali in tempo le vibrazioni di due pen­<lb></lb>doli di ugual lunghezza, benchè uno sia grave e l&#039;altro leggero. </s>

<s>Nel primo <lb></lb>dialogo infatti Delle due nuove scienze aveva, più chiaramente che altrove, <lb></lb>espressa così questa sua dottrina, comparando insieme due pendoli sospesi <lb></lb>a ugual lunghezza di filo, ma uno di sughero e l&#039;altro di piombo: </s></p><p type="main">

<s>“ Slargato il pendolo del piombo v. </s>

<s>g. </s>

<s>cinquanta gradi dal perpendi­<lb></lb>colo, e di lì lasciato in libertà, scorre, e passando oltre al perpendicolo quasi <lb></lb>altri cinquanta, descrive l&#039;arco di quasi cento gradi, e ritornando per sè <lb></lb>stesso indietro, descrive un altro minore arco, e continuando le sue vibra­<lb></lb>zioni, dopo gran numero di quelle, si riduce finalmente alla quiete. </s>

<s>Cia­<lb></lb>scheduna di tali vibrazioni si fa sotto tempi uguali, tanto quella di novanta <lb></lb>gradi, quanto quella di cinquanta o di venti, di dieci, di quattro; sicchè in <lb></lb>conseguenza la velocità del mobile vien sempre languendo, poichè, sotto <lb></lb>tempi eguali, va passando successivamente archi sempre minori a minori. </s>

<s><lb></lb>Un simile, anzi l&#039;istesso effetto, fa il sughero pendente da un filo altret­<lb></lb>tanto lungo, salvo che in minor numero di vibrazioni si conduce alla quiete, <lb></lb>come meno atto, mediante la sua leggerezza, a superar l&#039;ostacolo dell&#039;aria. <pb xlink:href="020/01/2153.jpg" pagenum="396"></pb>Con tutto ciò tutte le vibrazioni grandi e piccole si fanno sotto tempi <lb></lb>eguali tra di loro, ed eguali ancora ai tempi delle vibrazioni del piombo ” <lb></lb>(Alb. </s>

<s>XIII, 88). </s></p><p type="main">

<s>Ora, osserva il Cabeo che questo, così francamente asserito da Galileo, <lb></lb>può ammettersi <emph type="italics"></emph>si rudi minerva et crassiori mensura examinetur,<emph.end type="italics"></emph.end> ma, se <lb></lb>si vuol discutere con più esatti e pazienti esperimenti, si troverà manifesta­<lb></lb>mente falso. </s>

<s>“ Si enim, ex aequali filo, duo valde inaequalia pondera suspen­<lb></lb>dantur, et remotis illis a perpendiculo utrumque omnino eodem temporis <lb></lb>puncto liberetur, post primas undationes statim incipiunt dissentire, nec so­<lb></lb>lum aequales, quoad magnitudinem, undationes non faciunt, sed nec aequa­<lb></lb>les quoad tempus, et sicut gravius longiora spatia metitur, ita etiam longiori <lb></lb>mora producitur ” (Editio cit., pag. </s>

<s>99). E soggiunge di aver fatto di ciò, <lb></lb>per sè stesso e per altri, esperienza con due palle di piombo, ambedue so­<lb></lb>spese a ugual lunghezza di filo, ma l&#039;una pesa 60 scrupoli, e l&#039;altra 15, e <lb></lb>di aver trovato che, mentre questa faceva 115 vibrazioni, quell&#039;altra più pe­<lb></lb>sante ne faceva appena cento nel medesimo tempo. </s></p><p type="main">

<s>S&#039;interrompe a questo punto dal Cabeo il ragionamento, per significare <lb></lb>ai Lettori un suo dubbio intorno al modo di misurar la lunghezza del filo, <lb></lb>d&#039;onde potrebbe in parte dipendere la differenza fra l&#039;esperienze di Galileo <lb></lb>e le sue proprie. </s>

<s>Avendo la palla di piombo, di 60 scrupoli, assai maggior <lb></lb>diametro dell&#039;altra, di soli scrupoli 12, <emph type="italics"></emph>si dee prender la lunghezza del filo <lb></lb>insino a tutto il corpo grave pendente, o insino al centro di esso?<emph.end type="italics"></emph.end> Questo <lb></lb>medesimo quesito, in questa medesima forma, fu proposto da Giovanni Pie­<lb></lb>roni a Galileo (Alb. </s>

<s>X, 68), il quale non seppe che si rispondere con cer­<lb></lb>tezza di scienza, essendo troppo ancora lontana la soluzion del problema dei <lb></lb>centri di oscillazione. </s>

<s>Nonostante, udimmo poco fa dire al Baliani doversi <lb></lb>misurare i fili nella loro lunghezza <emph type="italics"></emph>comprehensis semidiametris<emph.end type="italics"></emph.end> dei corpi <lb></lb>di varia mole da essi fili pendenti, ciò che anche al Cabeo parve esser <emph type="italics"></emph>magis <lb></lb>secundum naturam rerum,<emph.end type="italics"></emph.end> e ne seguiron gli esempi gli stessi Accademici <lb></lb>del Cimento, i quali usarono di sospender palline di oro a tenuissimi fili di <lb></lb>seta, per avere il centro dell&#039;oscillazione costituito nel centro della figura. </s></p><p type="main">

<s>Ma Galileo, intorno a ciò incerto, per fare esperienza dell&#039;isocronismo <lb></lb>di due pendoli di vario peso, sceglieva corpi di differente gravità specifica, <lb></lb>quali erano il sughero e il piombo, riducendoli sotto ugual forma e volume, <lb></lb>e così rendevasi sicuro della ugual lunghezza delle loro sospensure, o sì <lb></lb>avessero a computar fino alla superficie o insino al centro del corpo grave <lb></lb>pendente. </s></p><p type="main">

<s>Comunque sia, questo, dice il Cabeo, m&#039;hanno costantemente dimostrato <lb></lb>le mie esperienze, al contrario di quelle descritte da Galileo, “ pondus sci­<lb></lb>licet minus leve plures exhibuisse, eodem tempore, vibrationes ” (Comment. </s>

<s><lb></lb>meteor., T. </s>

<s>I cit., pag. </s>

<s>100). Il Riccioli confermò poi solennemente i risul­<lb></lb>tati sperimentali del suo Collega, nelle proposizioni V, VI e VII del cap. </s>

<s>XX <lb></lb>del II libro dell&#039;Almagesto nuovo, dove piuttosto che Galileo si prende di <lb></lb>mira il Baliani, il quale, come vedemmo, concluse l&#039;uguaglianza dei pendoli <pb xlink:href="020/01/2154.jpg" pagenum="397"></pb>dall&#039;essere tutte uguali le ondulazioni dei corpi di vario peso, come di globi <lb></lb>di piombo di due once o di due libbre, e di un pezzo di pietra informe, <lb></lb>purchè tutti pendenti da uguali lunghezze. </s></p><p type="main">

<s>La detta V proposizione, che contiene in sè le altre due, è così formu­<lb></lb>lata: “ Duorum perpendiculorum, in omnibus aequalium praeter quam in <lb></lb>gravitate, illud quod gravius est diutius in motu perseverat, et intra aequale <lb></lb>tempus plures numero vibrationes peragit ” (T. </s>

<s>I cit., pag. </s>

<s>85). Questa, in­<lb></lb>sieme con le altre due, “ est, dice il Riccioli, contra Balianum, qui, si al­<lb></lb>titudo perpendiculorum sit aequalis, vibrationes eorum aequidiuturnas pu­<lb></lb>tat. </s>

<s>Sed ergo non possum ocuìis meis non credere ” (ibid., pag. </s>

<s>85, 86). </s></p><p type="main">

<s>Il senso della vista, a cui non si poteva non credere, aveva al Riccioli <lb></lb>e al Cabeo testimoniato del vero, ma, dimostrando la falsità dell&#039;isocroni­<lb></lb>smo in due pendoli di differente peso, veniva anche insieme a farne argo­<lb></lb>mentare la falsità dell&#039;isocronismo assoluto, in pendoli di peso uguale, o nel <lb></lb>medesimo pendolo, per via di un ragionamento, ch&#039;era riserbato a farsi a <lb></lb>un collega dei due commemorati sperimentatori, come or ora vedremo. </s>

<s>Fa <lb></lb>perciò gran maraviglia che rimanesse intorno a ciò allucinato il Riccioli, il <lb></lb>quale non avrebbe affermato quell&#039;assoluto isocronismo, se, piuttosto che <lb></lb>servirsi delle osservazioni astronomiche, si fosse rivolto a farne esperienze <lb></lb>dirette, sull&#039;andare di quelle che gli avean messo sotto gli occhi la verità <lb></lb>dei fatti formulati nelle tre sopra dette proposizioni. </s></p><p type="main">

<s>Il Cabeo però, proseguendo nella citata Questione a discutere intorno <lb></lb>ai professati insegnamenti di Galileo, affermò rimanergli in dubbio se del <lb></lb>medesimo pendolo le vibrazioni maggiori e le minori si spediscano precisa­<lb></lb>mente nel medesimo tempo, perchè da certe esperienze istituite in proposito <lb></lb>appariva in que&#039;moti ondulatorii una, piccola sì, ma pur sensibile diffe­<lb></lb>renza. </s>

<s>“ Ego, si rem mathematice definire vellem, adhuc, ut verum fatear, <lb></lb>fere sto in ancipiti; nam, si duo aequalia pondera pendeant ex aequali filo, <lb></lb>et alterum illorum moveatur per arcus decem graduum, et alterum per ar­<lb></lb>cus triginta quinque graduum, etiam si in initio simul incedant, tamen, post <lb></lb>mulias undationes, patebit dissentire ” (Comment. </s>

<s>meteor., lib. </s>

<s>I cit., pag. </s>

<s>100). <lb></lb>Soggiunge esser vero che il dissenso è assai piccolo, non trovandosi la diffe­<lb></lb>renza di una vibrazione, se non che dopo un lunghissimo tempo, ma chi <lb></lb>avesse preso Galileo alla parola, rimovendo l&#039;un dei pendoli per dieci gradi <lb></lb>e l&#039;altro, non per trentacinque soli, ma per settanta o ottanta; avrebbe le <lb></lb>disegualità in tali moti veduto apparirgli innanzi molto più presto. </s>

<s>E per­<lb></lb>ciocchè questo modo di sperimentare, di cui Galileo, nelle sue relazioni con <lb></lb>Guidubaldo, non seppe riconoscere l&#039;efficacia, non potevan mancar altri che <lb></lb>lo eleggessero come il più facile di tutti, e il più risolutivo; è perciò che <lb></lb>sarebbero bastate le osservazioni del Wendelin, del Cabeo e del Riccioli, <lb></lb>anche senz&#039;altro, per mettere in trepida sollecitudine gli Accademici del <lb></lb>Cimento. </s></p><p type="main">

<s>Trattandosi dell&#039;onore dell&#039;adorato Maestro, è facile indovinare che il <lb></lb>più affaccendato di tutti gli Accademici fosse il Viviani, del quale facemmo, <pb xlink:href="020/01/2155.jpg" pagenum="398"></pb>a pag. </s>

<s>319 del I tomo della nostra Storia, note alcune esperienze di due pen­<lb></lb>doli dì uguale lunghezza, e sospesi dal medesimo sostegno, che fatto vibrare <lb></lb>l&#039;uno si vede spontaneamente incominciare a moversi anche l&#039;altro. </s>

<s>Rife­<lb></lb>rimmo allora così fatte esperienze come istituite a fine di confermare il <lb></lb>fatto di quella maravigliosa simpatia dei pendoli scoperta dall&#039;Huyghens, e <lb></lb>ora soggiungiamo che forse il Viviani prese occasione da Galileo di osservar <lb></lb>le medesime cose, e di scoprirne l&#039;occulte e più probabili ragioni. </s></p><p type="main">

<s>Nel primo dialogo infatti Delle due nuove scienze s&#039;istituisce la dot­<lb></lb>trina dei pendoli per applicarla alla soluzione di alcuni problemi di Musica, <lb></lb>e principalmente a quello delle due corde tese all&#039;unisono, delle quali vi­<lb></lb>brando una, per esempio in un cembalo, fa questa tremar l&#039;aria che le è <lb></lb>appresso, i cui tremori si distendono per grande spazio, e vanno a urtare <lb></lb>tutte le altre corde del medesimo strumento. </s>

<s>“ Ma la corda, che è tesa al­<lb></lb>l&#039;unisono con la tocca, essendo disposta a far le sue vibrazioni sotto il <lb></lb>medesimo tempo, comincia al primo impulso a muoversi un poco, e so­<lb></lb>praggiungendogli il secondo, il terzo, il ventesimo e più altri, e tutti negli <lb></lb>aggiustati e periodici tempi, riceve finalmente il medesimo tremore, che la <lb></lb>prima tocca, e si vede chiarissimamente andar dilatando le sue vibrazioni <lb></lb>giusto allo spazio della sua motrice ” (Alb. </s>

<s>XIII, 101). </s></p><p type="main">

<s>Or perchè Galileo rassomigliava il vibrar delle corde sonore al vibrar <lb></lb>di due pendoli muti, di ugual lunghezza di filo, era naturale sovvenisse in <lb></lb>mente al meditativo Viviani che, a quel modo che l&#039;aria comunica il suo <lb></lb>moto alla corda quieta, e disposta a vibrare nei medesimi tempi; così avve­<lb></lb>nisse dell&#039;aria commossa dall&#039;un pendolo, che comunica il suo proprio moto <lb></lb>all&#039;altro pendolo quieto, ma disposto pure a vibrar sotto i medesimi tempi <lb></lb>anch&#039;esso, perchè sospeso a lunghezza uguale di filo. </s></p><p type="main">

<s>Il simpatico mistero si trovava dunque, nel fatto e nelle sue più pro­<lb></lb>babili ragioni, involuto nelle parole di Galileo, e il Viviani, forse alla noti­<lb></lb>zia della osservazione ugeniana comunicatagli dal principe Leopoldo, lo sciolse <lb></lb>da que&#039;suoi involucri, e se lo pose a contemplare innanzi agli occhi svelato, <lb></lb>nelle descritte danze dei due pendoli uguali. </s>

<s>Diceva intanto a sè stesso, in <lb></lb>mezzo a così belle scientifiche contemplazioni: “ Anche questo darà modo <lb></lb>di conoscere se i pendoli sono equidiuturni ” (MSS. Cim., T. X, fol. </s>

<s>47). </s></p><p type="main">

<s>Questa espressione, lasciamo andare tutte le altre questioni, che si po­<lb></lb>trebbero movere intorno al curioso fatto osservato dall&#039;Huyghes, e alla parte <lb></lb>che v&#039;ebbero i Nostri nello spiegarlo; ci rivela che nell&#039;Accademia fioren­<lb></lb>tina, specialmente per opera del Viviani, si discuteva intorno all&#039;isocronismo <lb></lb>dei pendoli, e si pensava ai modi più accomodati per risolverne i dubbi. </s>

<s>Si <lb></lb>fu uno di questi modi, e forse dei primi, quello di far correre e ricorrere <lb></lb>le palline gravi dentro canali semicircolari, e non avendone avuta sodisfa­<lb></lb>zione, come si vide, si volsero gli Accademici a sperimentare i libramenti <lb></lb>di varii liquidi dentro i rami dei loro sifoni, giacchè ritenevasi allora da tutti <lb></lb>quel che avea così lasciato scritto il Mersenno, in un luogo delle sue <emph type="italics"></emph>Nuove <lb></lb>osservazioni:<emph.end type="italics"></emph.end> “ Quod autem de funependulis audisti .... possis etiam referre <pb xlink:href="020/01/2156.jpg" pagenum="399"></pb>ad vibrationes hydrargirii a tubo quopiam descendentis ” (T. III, Parisiis 1647, <lb></lb>pag. </s>

<s>159). E benchè queste vibrazioni, o libramenti, fatti per discese rette <lb></lb>e non circolari, fossero propriamente isocroni, come ne concluse il Newton <lb></lb>nel corollario I della proposizione XLIV dimostrata nel II libro dei suoi <lb></lb><emph type="italics"></emph>Principii<emph.end type="italics"></emph.end> (edizione cit., pag. </s>

<s>357); ebbero nonostante i nostri Accademici a <lb></lb>raccogliere anche di qui poco di certo, come apparisce dalle seguenti re­<lb></lb>lazioni: </s></p><p type="main">

<s>“ A&#039;dì 23 Novembre 1661, leggesi in uno dei Diarii, osservati i libra­<lb></lb>menti, che fa l&#039;acqua infusa in un sifone di vetro, con gli suoi rami per­<lb></lb>pendicolari al fondo; si trovarono equitemporanei tanto quelli che avevano <lb></lb>origine da maggiore altezza, che gli altri di minore.... A&#039;dì 24 detto, i li­<lb></lb>bramenti dell&#039;argento vivo, nel sifone di braccia perpendicolari, sono equi­<lb></lb>temporanei fra di loro, e con quelli dell&#039;acqua infusa alla medesima altezza <lb></lb>dell&#039;argento vivo ” (Targioni, Notizie ecc., T. II cit., pag. </s>

<s>647). </s></p><p type="main">

<s>Corrisponderebbero queste esperienze, come si vede, a quelle dei fu­<lb></lb>nependoli di vario peso o specifico, o assoluto, e parevano confermare le <lb></lb>osservazioni di Galileo e del Baliani, ritrovate false dal Cabeo e dal Riccioli. </s>

<s><lb></lb>Di qui dunque avranno dovuto a principio argomentar gli Accademici la ve­<lb></lb>rità dell&#039;isocronismo galileiano, nel medesimo pendolo o in pendoli uguali, <lb></lb>ma poi vennero a infirmar la logica dell&#039;argomento altre esperienze, dalle <lb></lb>quali ebbero gli Accademici stessi a ricavar che i libramenti dell&#039;argento <lb></lb>vivo, in sifoni della medesima altezza “ non sono equitemporanei, anzi li <lb></lb>massimi son più tardi dei mezzani, e questi ancor più tardi dei minimi ” <lb></lb>(ivi, pag. </s>

<s>651). </s></p><p type="main">

<s>Veniva questo fatto a confermare l&#039;esperienze del Wendelin divulgate <lb></lb>dall&#039;opera del Riccioli, per cui stavano gli Accademici in gran trepidazione <lb></lb>d&#039;aver a confessar finalmente i falli di Galileo. </s>

<s>Lasciati addietro perciò gli <lb></lb>altri modi, i quali avevano ritrovati tanto incerti, vennero nella final deci­<lb></lb>sione di sperimentare direttamente, com&#039;esso Wendelin aveva fatto, sui pesi <lb></lb>ondeggianti dai fili. </s>

<s>Ma come assicurarsi che anche questi secondano i moti <lb></lb>dei pendoli con l&#039;argento vivo, facendo più tarde delle mezzane e delle mi­<lb></lb>nime le loro massime vibrazioni? </s>

<s>Venne allora in mente al Viviani di co­<lb></lb>struir quel Cronometro, rappresentato in disegno nel libro dei <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> e coi <lb></lb>moti di lui, i quali per forza della molla, fra gli ugualmente scompartiti <lb></lb>denti della ruota, erano obbligati a farsi sempre uguali; comparare i moti <lb></lb>osservati nei pendoli liberamente oscillanti. </s>

<s>L&#039;esperienze corrisposero esat­<lb></lb>tamente con quelle dei libramenti dell&#039;argento vivo sopra descritti, come, <lb></lb>sotto i dì 29 Novembre 1661, si registrò nel Diario con queste precise pa­<lb></lb>role: “ Esaminato ugual numero di vibrazioni dell&#039;istesso pendolo grandi <lb></lb>e piccole, si trova che in tempi uguali, dati dalle vibrazioni di un altro pen­<lb></lb>dolo, lasciato andare sempre dalla medesima altezza, ne vanno più delle mi­<lb></lb>nime che delle maggiori, e di queste più che delle massime. </s></p><p type="main">

<s>Rimase l&#039;importantissima Nota al foglio 156 del II tomo dei Manoscritti <lb></lb>del Cimento, infino al 1780, anno in cui il Targioni la pubblicò a pag. </s>

<s>390 <pb xlink:href="020/01/2157.jpg" pagenum="400"></pb>del II tomo, parte II, delle citate <emph type="italics"></emph>Notizie degli aggrandimenti delle scienze <lb></lb>fisiche, avvenuti in Toscana.<emph.end type="italics"></emph.end> Cosicchè non era, prima del Targioni, pubbli­<lb></lb>camente noto, di questo sperimental lavorio degli Accademici fiorentini, se <lb></lb>non che quel cenno, che se ne faceva così nel libro dei <emph type="italics"></emph>Saggi di naturali <lb></lb>esperienze:<emph.end type="italics"></emph.end> “ Qui par luogo di dire che l&#039;esperienza ci avea mostrato (come <lb></lb>fu anche avvertito dal Galileo, dopo l&#039;osservazione che, prima d&#039;ogni altro, <lb></lb>ei fece, intorno all&#039;anno 1583, della loro prossima ugualità) non tutte le vi­<lb></lb>brazioni del pendolo correre in tempi precisamente tra loro uguali, ma quelle, <lb></lb>che di mano in mano si accostano alla quiete, spedirsi in più breve tempo, <lb></lb>che non fanno le prime, come si dirà a suo luogo ” (Firenze 1841, pag. </s>

<s>21). </s></p><p type="main">

<s>La promessa però non fu mantenuta, non facendosi del pendolo, in <lb></lb>tutto il Libro, altra parola. </s>

<s>Sconsigliò dal proposito il Principe dell&#039;Accade­<lb></lb>mia e i Colleghi il Viviani, trepido per l&#039;onore dell&#039;adorato Maestro, il qual <lb></lb>Viviani, costretto a passare al Segretario quel cenno sopra trascritto, gli sug­<lb></lb>gerì le parole incluse fra parentesi, nelle quali, per salvar Galileo, non per­<lb></lb>donò al pudore di fornicar pubblicamente con la menzogna. </s>

<s>Fra tanti timidi <lb></lb>e ciechi adoratori del Nume è da lodare massimamente Paolo Frisi, il quale, <lb></lb>con la molta scienza che aveva di quelle cose, giudicando secondo, che ri­<lb></lb>chiedeva il dovere, il Soggetto elogiato, e lasciando di ripetere inutilmente, <lb></lb>anzi dannosamente le solite declamazioni; scriveva con filosofica libertà in <lb></lb>questo proposito: “ Non può ammettersi quanto si legge negli attì dell&#039;Ac­<lb></lb>cademia del Cimento che il Galileo erasi accorto di qualche disuguaglianza dei <lb></lb>tempi delle maggiori e minori vibrazioni ” (Elogio di Galileo, Livorno 1775, <lb></lb>pag. </s>

<s>96, in nota). </s></p><p type="main">

<s>Non era il Frisi di quelli che magnifican Galileo, senz&#039;averlo mai letto, <lb></lb>ma cercando per le opere maggiori e minori di lui i tanti luoghi, dove si <lb></lb>parla delle proprietà dei pendoli, trovò, come troverebbero tutti i diligenti <lb></lb>lettori, che sempre vi si professa il più assoluto isocronismo. </s>

<s>Poteva il Vi­<lb></lb>viani attaccarsi a quel che si legge nel II dialogo Dei massimi sistemi, al <lb></lb>luogo da noi sopra citato, dove si accenna all&#039;impedimento dell&#039;aria, che <lb></lb><emph type="italics"></emph>ritarda qualche poco<emph.end type="italics"></emph.end> il moto del pendolo: e, perchè nelle vibrazioni più <lb></lb>ampie quell&#039;impedimento è maggiore, argomentarne che dunque le mag­<lb></lb>giori fra quelle stesse vibrazioni sono, almeno insensibilmente, secondo Ga­<lb></lb>lileo, più tarde delle minori. </s>

<s>Ma che l&#039;argomento, così artificiosamente con­<lb></lb>dotto, non fosse secondo le finali espresse intenzioni di chi avea scritto quel <lb></lb>Dialogo, poteva riconoscerlo il Viviani dalla collazione con le seguenti pa­<lb></lb>role, nelle quali alla dottrina dell&#039;isocronismo dei pendoli si poneva da Ga­<lb></lb>lileo stesso l&#039;ultimo e più solenne suggello: </s></p><p type="main">

<s>“ Sospendansi, egli dice nel IV dialogo Delle nuove scienze, due fili, <lb></lb>egualmente unghi e di lunghezza di quattro o cinque braccia, due palle di <lb></lb>piombo eguali, e, attaccati i detti fili in alto, si rimuovano ambedue le palle <lb></lb>dallo stato perpendicolare, ma l&#039;una si allontani per ottanta o più gradi, e <lb></lb>l&#039;altra non più che quattro o cinque; sicchè, lasciata in libertà l&#039;una, scenda, <lb></lb>e trapassando il perpendicolo descriva archi grandissimi di 160, 150, 140 <pb xlink:href="020/01/2158.jpg" pagenum="401"></pb>gradi ecc. </s>

<s>diminuendoli a poco a poco; ma l&#039;altra, scorrendo liberamente, <lb></lb>passi archi piccoli di 10, 8, 6 ecc. </s>

<s>diminuendoli essa pure a poco a poco. </s>

<s><lb></lb>Qui primieramente dico che, in tanto tempo passerà la prima li suoì gradi <lb></lb>180, 160 ecc., in quanto l&#039;altra li suoi 10, 8 ecc. </s>

<s>Dal che si fa manifesto <lb></lb>che la velocità della prima palla sarà 16 e 18 volte maggiore della velocità <lb></lb>della seconda, sicchè, quando la velocità maggiore più dovesse essere im­<lb></lb>pedita dall&#039;aria che la minore, più rade dovriano esser le vibrazioni negli <lb></lb>archi grandissimi di 180 o 160, che nei piccolissimi di 10, 8, 4, ed anche <lb></lb>di 2, e di 1. Ma a questo repugna l&#039;esperienza. </s>

<s>Imperocchè, se due com­<lb></lb>pagni si metteranno a numerare le vibrazioni, l&#039;uno le grandissime e l&#039;altro <lb></lb>le piccolissime, vedranno che ne numereranno, non pur le diecine, ma le <lb></lb>centinaia ancora, senza discordar di una, anzi di un sol punto. </s>

<s>E questa os­<lb></lb>servazione ci assicura congiuntamente delle due proposizioni, cioè che le <lb></lb>massime e le minime vibrazioni si fanno tutte, a una a una, sotto tempi <lb></lb>eguali, e che l&#039;impedimento e ritardamento dell&#039;aria non opera più nei moti <lb></lb>velocissimi, che nei tardissimi ” (Alb. </s>

<s>XIII, 231). </s></p><p type="main">

<s>Si persuaderanno anche i più ritrosi, dietro la lettura di questo certis­<lb></lb>simo documento, che l&#039;esperienze degli Accademici fiorentini non confer­<lb></lb>mavano, come avrebbe voluto far credere il Viviani, ma riformavano le dot­<lb></lb>trine di Galileo, e del benefizio di una tale riforma va debitrice la scienza <lb></lb>galileiana, come si disse, al Riccioli. </s>

<s>Se non fossero le parole di lui venute <lb></lb>a mettere il sospetto nei Nostri, stimolandogli a ritornare ai fatti, perchè <lb></lb>fossero meglio esaminati, non si sarebbe forse all&#039;infallibile Nume, dai ge­<lb></lb>losi custodi del tempio, turbata così la pace dei venerandi riposi. </s></p><p type="main">

<s>Una tale efficacia del Riccioli era naturale che si dovesse far sentire <lb></lb>anche più valida ai liberi ingegni, come per esempio al padre Francesco <lb></lb>Lana, il quale incominciò giusto a sospettar della verità dell&#039;assoluto isocro­<lb></lb>nismo professato da Galileo, ripensando a quelle tre proposizioni intorno ai <lb></lb>pendoli di ugual lunghezza, ma di peso diverso, formulate, come si disse, <lb></lb>dallo stesso Riccioli nel citato luogo dell&#039;Almagesto. </s>

<s>Perchè, domandava a <lb></lb>sè medesimo, il pendolo più grave fa in ugual tempo minor numero di vi­<lb></lb>brazioni dell&#039;altro pendolo più leggero? </s>

<s>E veniva al Lana la risposta, non <lb></lb>data ancora da nessuno, dal ripensar che forse, più lungamente durando il <lb></lb>pendolo più grave nelle vibrazioni sue più larghe, eran queste più diuturne <lb></lb>di quelle, fatte dall&#039;altro pendolo più leggero, che si riduce più presto a <lb></lb>languir nelle vibrazioni più strette. </s>

<s>Pareva il felice pensiero essergli confer­<lb></lb>mato dalle esperienze, quando nel 1668 s&#039;abbattè a leggere, nel libro degli <lb></lb>Accademici fiorentini, il passo che poco sopra abbiamo trascritto. </s>

<s>Non tro­<lb></lb>vandovi espresso nulla, entrò in gran curiosità di sapere come i celebri Spe­<lb></lb>rimentatori si fossero assicurati di quelle disuguaglianze, e dal cenno, che ivi <lb></lb>se ne fa, dicendosi che, per ridurlo alla desiderata uguaglianza di moto, <emph type="italics"></emph>fu <lb></lb>stimato bene applicare il pendolo all&#039;orivolo,<emph.end type="italics"></emph.end> congetturò, com&#039;era il vero, <lb></lb>che avessero gli Accademici comparate le varietà delle libere oscillazioni con <lb></lb>quelle costrette a farsi nello strumento sempre per archi uguali. </s></p><pb xlink:href="020/01/2159.jpg" pagenum="402"></pb><p type="main">

<s>Or perchè, così essendo, giudicava il Lana il suo metodo sperimentale <lb></lb>assai più sicuro, lo descriveva perciò in una lettera del dì 9 Maggio 1668, <lb></lb>diretta da Brescia a quegli Accademici, che dunque non credeva a quel tempo <lb></lb>già morti, come temerariamente fu detto e ripetuto da tanti, ma ch&#039;ei sa­<lb></lb>peva proseguir anzi, benchè dispersi, più largamente che mai gli studi spe­<lb></lb>rimentali sotto la presidenza del cardinale Leopoldo dei Medici. </s>

<s>“ L&#039;espe­<lb></lb>rienze poi, scriveva il Lana dop&#039;avere ossequiosamente introdotto il discorso, <lb></lb>che mi hanno mostrato non compirsi le vibrazioni in tempi uguali, sono le <lb></lb>seguenti: ” </s></p><p type="main">

<s>“ Servendomi di due pendoli, uno de&#039;quali corrispondeva nelle sue sem­<lb></lb>plici vibrazioni ad un minuto secondo, l&#039;altro ad un mezzo secondo, li alzai <lb></lb>ad un medesimo grado del suo arco, minore di 45 gradi. </s>

<s>Mentre il primo <lb></lb>compì 64 vibrazioni semplici, il secondo ne compì 129, e perchè ne doveva <lb></lb>compire solo 128, la diversità stimai provenirne perchè il pendolo più alto <lb></lb>era molto più pesante, onde continuava a scorrere archi grandi, quando l&#039;altro <lb></lb>più leggero aveva notabilmente diminuito li suoi archi. </s>

<s>Ciò mi fu confer­<lb></lb>mato dalla seguente esperienza: Lasciai cadere il pendolo più lungo dall&#039;al­<lb></lb>tezza di gradi 60, e l&#039;altro dall&#039;altezza di gradi 30: mentre quello compiè <lb></lb>20 vibrazioni, questo ne compiè 41. ” </s></p><p type="main">

<s>“ Più chiara mi parve l&#039;esperienza seguente: Lasciai cadere il maggior <lb></lb>pendolo dall&#039;altezza di gradi 20, ed il minore da quella di gradi 30. Quindi <lb></lb>accadeva che gli archi di questo pendolo, come quello che era più leggero, <lb></lb>ed era anche caduto da maggiore altezza; si andavano impiccolendo più no­<lb></lb>tabilmente, che non facevano gli archi dell&#039;altro pendolo più pesante, e ca­<lb></lb>duto da minore altezza, e che, dopo 100 vibrazioni, incominciarono a descri­<lb></lb>vere archi uguali. </s>

<s>In tutto questo tempo le vibrazioni dell&#039;uno e dell&#039;altro <lb></lb>andavano di concerto, compiendosi nel medesimo tempo una semplice del­<lb></lb>l&#039;uno, mentre si compiva una composta dell&#039;altro, ma poi tosto gli archi <lb></lb>del minor pendolo incominciarono a farsi minori di quelli, ch&#039;erano scorsi <lb></lb>dal maggiore, e nel medesimo tempo parimente incominciarono ad essere <lb></lb>più veloci, sicchè, dopo altre 100 vibrazioni del maggiore, il minore ne com­<lb></lb>pìva 201. ” </s></p><p type="main">

<s>“ Rimanevami alcun sospetto che la predetta disuguaglianza potesse <lb></lb>provenire dal maggior peso, ovvero altezza di un pendolo, in riguardo del­<lb></lb>l&#039;altro, perchè, sospesi due pendoli dalla medesima altezza, l&#039;uno di legno <lb></lb>pesante scrupoli 16 1/2, l&#039;altro di metallo, scrupoli 22 1/2, e lasciati cadere <lb></lb>l&#039;uno e l&#039;altro da una medesima altezza, avveniva che il primo, per essere <lb></lb>meno pesante e di maggior mole, incominciò subito a scorrer gli archi molto <lb></lb>minori dell&#039;altro, e medesimamente in più breve tempo compivali, e per <lb></lb>certificarmi che ciò non provenisse da qualche disuguaglianza nella lunghezza <lb></lb>del filo, che in misurarlo avesse ingannato l&#039;occhio, lasciai cadere li mede­<lb></lb>simi pendoli da inuguali altezze, cioè quello di legno da una minore, e l&#039;altro <lb></lb>di metallo da una maggiore. </s>

<s>E perchè gli archi maggiori si vanno dimi­<lb></lb>uendo più notabilmente di quello, che facciano li minori, quindi accadeva <pb xlink:href="020/01/2160.jpg" pagenum="403"></pb>che il pendolo di metallo, caduto da maggiore altezza, andava più notabil­<lb></lb>mente diminuendo i suoi archi, e, con la sua proporzione, anche i tempi <lb></lb>delle ondazioni erano più brevi. </s>

<s>” </s></p><p type="main">

<s>“ In queste e in altre simili esperienze ho sempre osservato che un <lb></lb>pendolo precorre all&#039;altro, solo allorquando le ondazioni si fanno in archi <lb></lb>minori, checchessia del maggior peso, e della maggior mole, purchè i fili <lb></lb>siano uguali. </s>

<s>” (MSS. Cim., T. XXV, fol. </s>

<s>11, 12). </s></p><p type="main">

<s>Si conclude in queste ultime parole il fatto, non bene osservato da Ga­<lb></lb>lileo nelle sue prime esperienze descritte a Guidubaldo del Monte, che cioè, <lb></lb>lasciati andare due pendoli, benchè di diverso peso, purchè di lunghezze <lb></lb>uguali, nello stesso tempo e dalla stessa parte, si vedono andar di pari passo <lb></lb>infin tanto che fanno le vibrazioni di uguale, o di poco differente ampiezza <lb></lb>di arco, ma al diminuirsi quest&#039;ampiezza notabilmente più nell&#039;uno che nel­<lb></lb>l&#039;altro, si vede sempre preceder quello, che va per archi minori. </s>

<s>La costanza <lb></lb>di questo fatto osservato fece proporre al Lana, nel suo tomo secondo <emph type="italics"></emph>Ma­<lb></lb>gisterii Naturae et Artis,<emph.end type="italics"></emph.end> il seguente esperimento, che è in ordine il XIX, <lb></lb>nel cap. </s>

<s>I del V libro: “ Unius eiusdemque penduli singulae vibrationes <lb></lb>non sunt omnino aequidiuturnae, sed successive minori ac minori temporis <lb></lb>spatio absolvuntur ” (Brixiae 1686, pag. </s>

<s>342). ” </s></p><p type="main">

<s>La certezza, che aveva il Lana del fatto, avrebbe desiderato si parte­<lb></lb>cipasse altresì alla ragione del fatto, ma non seppe, come tantì altri, in che <lb></lb>meglio riconoscerla che negli impedimenti dell&#039;aria, per cui credeva che il <lb></lb>perfetto isocronismo s&#039;avesse a osservare nel vuoto. </s>

<s>“ Mi sarebbe cosa gra­<lb></lb>tissima, scriveva nei principii della citata lettera agli Accademici fiorentini, <lb></lb>il sapere con quale artificio si sono assicurati che l&#039;ondazioni del pendolo <lb></lb>siano inuguali di tempo, poichè se fosse con l&#039;applicazione del pendolo al­<lb></lb>l&#039;oriolo, averei qualche dubbio che ciò fosse bastante a provare l&#039;intento, <lb></lb>e stimerei piuttosto che ne potesse certificare l&#039;esperienza fatta nel vuoto, <lb></lb>in cui parmi che tutte le vibrazioni dovrebbero compirsi in tempi uguali, e <lb></lb>di ciò volentieri ne riceverei alcuna prova da lor altri Signori, la quale an­<lb></lb>che servirebbe a fine di conoscere quanta sia la resistenza dell&#039;aria, in pa­<lb></lb>ragone della mole e peso del pendolo, che a me, in un pendolo di piombo <lb></lb>pesante scrupoli 8, gr. </s>

<s>39, le cui vibrazioni composte si facevano in un <lb></lb>minuto secondo; è stata in proporzione di 10,638 ad 1. Ed in un altro, di <lb></lb>mistura poco più grave dell&#039;acqua, cioè 16 volte in circa più leggera del <lb></lb>piombo, e 4 volte maggiore nella sua superfice di quello fosse la superfice <lb></lb>del precedente pendolo di piombo, fu come 156 a 1 ” (MSS. cit., fol. </s>

<s>11). </s></p><p type="main">

<s>Le prove nel vuoto, richieste agli Accademici fiorentini dal Lana, erano <lb></lb>state parecchi anni prima tentate in varii modi coi libramenti de&#039;liquidi nei <lb></lb>sifoni, e direttamente coi funependoli, ma i resultati delle esperienze riu­<lb></lb>scirono sempre incerti. </s>

<s>“ I libramenti dell&#039;acqua in un sifone ritorto, leg­<lb></lb>gesi in uno dei Diarii sotto il dì 2 Gennaio 1662, dopo fatto il vuoto, pare <lb></lb>che durino più che quando vi è l&#039;aria ” (Targioni, Notizie cit., T. II, <lb></lb>pag. </s>

<s>651). </s></p><pb xlink:href="020/01/2161.jpg" pagenum="404"></pb><p type="main">

<s>Al fol. </s>

<s>78 del tomo X dei Manoscritti del Cimento vedesi, di mano del <lb></lb>Viviani, disegnata la camera del vuoto, dalla vôlta della <lb></lb>quale pende un filo con una pallina (fig. </s>

<s>210), e benchè <lb></lb>non sianvi scritte altre dichiarazioni, s&#039;argomenta pure <lb></lb>da quei semplici segni, per sè stessi eloquenti, la non <lb></lb>riuscita intenzione degli Sperimentatori. </s>

<s>Il Boyle ripetè <lb></lb>poi con la massima diligenza lo stesso esperimento, per <lb></lb>mezzo della sua Macchina pneumatica, sotto la campana <lb></lb>della quale, dop&#039;averne aspirata l&#039;aria, facendo oscillar <lb></lb>un pendolo, ne comparava le oscillazioni con quelle fatte <lb></lb>da un altro pendolo in mezzo all&#039;aria aperta. </s>

<s>“ Verum, <lb></lb>n&#039;ebbe però a concluder l&#039;Autore, ex facto hoc esperi­<lb></lb>mento parum didicimus, nisi quod discrimen inter mo­<lb></lb>tum penduli istiusmodi in communi aere, atque in aere <lb></lb><figure id="id.020.01.2161.1.jpg" xlink:href="020/01/2161/1.jpg"></figure></s></p><p type="caption">

<s>Figura 210<lb></lb>valde rarefacto in vasis, vix sensibile sit ” (Nova Experim. </s>

<s>Op. </s>

<s>omnia, T. <lb></lb>I, Venetiis 1697, pag. </s>

<s>61). </s></p><p type="main">

<s>Non essendosi dunque potuto decidere con l&#039;esperienza se le disugua­<lb></lb>glianze osservate nei pendoli nascevano, come probabilmente si sospettava, <lb></lb>dall&#039;impedimento dell&#039;aria, presentivasi del fatto una causa più riposta, la <lb></lb>quale s&#039;ebbe finalmente scoperta, invocatosi dai Fisici il valido aiuto della <lb></lb>Geometria. </s>

<s>Fu il fortunato discopritore Cristiano Huyghens, il quale, mes­<lb></lb>sosi addentro alla questione infino dal 1656, la dette nel 1673, con mirabile <lb></lb>opera matematica, risoluta. </s>

<s>Ei non ebbe a dubitar punto se le massime oscil­<lb></lb>lazioni son più tarde delle minime, essendosene bene assicurato con questo, <lb></lb>ch&#039;egli dice facile esperimento: “ Nam si pendula duo, pondere et longitu­<lb></lb>dine aequalia, alterum procul a perpendiculo, alterum parumper dimovea­<lb></lb>tur, simul dimissa, non diu in partes easdem una ferri cernentur, sed prae­<lb></lb>vertet illud, cuius exiliores erunt recursus ” (Horologium, Opera varia, Vol. </s>

<s>I, <lb></lb>Lugduni Batav. </s>

<s>1724, pag. </s>

<s>12). L&#039;esperienza ugeniana è, come si ramme­<lb></lb>moreranno i nostri Lettori, quella proposta in secondo luogo da Galileo a <lb></lb>Guidubaldo del Monte, e poi ripetuta dal Cabeo. </s>

<s>Che se questo ne rimase <lb></lb>in dubbio, e quell&#039;altro disse di non essersi accorto, in pendoli così oscil­<lb></lb>lanti, di nessuna disuguaglianza di moto, non è da attribuire ad altro, che <lb></lb>alla poca perizia, o alla poca diligenza nell&#039;osservare, e, per le preconcette <lb></lb>idee della mente, al non aver voluto credere alla testimonianza degli occhi. </s></p><p type="main">

<s>Fu quella certissima sperimentata disuguaglianza, che indusse l&#039;Huy­<lb></lb>ghens ad applicare il pendolo alle ruote degli orologi, come v&#039;avea indotto <lb></lb>in quel medesimo tempo il Viviani per quelle stesse ragioni, ma il Mate­<lb></lb>matico olandese, più libero nel pensare del Nostro, persuaso dall&#039;esperienze <lb></lb>del Boyle e dalle poco sodisfacenti teorie del Mariotte non si potere attri­<lb></lb>buire all&#039;aria, nè a nessun altra estrinseca causa gli effetti sperimentati, pe­<lb></lb>netrò addentro alla natura delle cose, e sagacemente scoprì che Galileo fu, <lb></lb>prima che dai fatti, ingannato dalle speculazioni. </s>

<s>“ Mensura enim temporis <lb></lb>certa atque aequalis pendulo semplici natura non inerat, cum latiores excur-<pb xlink:href="020/01/2162.jpg" pagenum="405"></pb>sus angustioribus tardiores observentur, sed Geometria duce diversam ab ea, <lb></lb>ignotamque antea penduli suspensionem reperimus, animadversa lineae cuius­<lb></lb>dam curvatura, quae ad optatam aequalitatem illi conciliandam, mirabili plane <lb></lb>ratione, comparata est ” (Horol. </s>

<s>oscill., Op. </s>

<s>varia cit., T. I, pag. </s>

<s>30). </s></p><p type="main">

<s>La curva tautocrona insomma scoprì l&#039;Huyghens che non era il cir­<lb></lb>colo, come credevasi da Galileo, e da tutti gli altri dietro lui, ma la Cicloide, <lb></lb>per la quale, oscillando il pendolo, serba l&#039;isocronismo assoluto. </s>

<s>Che se, <lb></lb>infino dai tempi del Wendelin, si osservò l&#039;uguaglianza del moto verificarsi <lb></lb>nelle piccole digressioni, e fisicamente poi si spiegò il fatto col dire che i <lb></lb>piccoli archi pochissimo differiscono dalle corde suttese; ora, per i teoremi <lb></lb>ugeniani, si riduceva la fisica alla precision matematica, dicendosi esatta­<lb></lb>mente isocroni i pendoli semplici, le vibrazioni dei quali si fanno per un <lb></lb>circolo osculatore alla cicloide. </s>

<s>E così venne finalmente la Geometria a to­<lb></lb>gliere d&#039;ogni sollecitudine Galileo, rivelandogli, dopo settantun anno, che <lb></lb>se non era spuntato, senza trasgredire i termini meccanici, a dimostrar che <lb></lb>i gravi, per qualunque punto della quarta di un cerchio cadendo, giungono <lb></lb>al basso nel medesimo tempo; era perchè il falso, per qualunque argomento <lb></lb>della retta ragione, non si poteva ridurre al vero. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Annunziando l&#039;Huyghens a Lodovico XIV le nuove scoperte proprietà <lb></lb>meccaniche della Cicloide, si compiaceva di aver dato finalmente alla Nau­<lb></lb>tica e all&#039;Astronomia il tanto desiderato esatto misuratore del tempo. </s>

<s>Il Vi­<lb></lb>viani meditava pochi anni prima di comparire innanzi alla medesima regia <lb></lb>Maestà, per rivendicar que&#039;meriti al suo Galileo, ripetendo al re di Francia <lb></lb>quel ch&#039;avea nel 1654 scritto al principe Leopoldo di Toscana, che cioè Ga­<lb></lb>lileo, nella sua gioventù “ con la sagacità del suo ingegno inventò quella <lb></lb>semplicissima e regolata misura del tempo, per mezzo del pendolo .... della <lb></lb>quale invenzione si valse poi in varie esperienze, e misure di tempi e moti, <lb></lb>e fu il primo che le applicasse alle osservazioni celesti, con incredibile acqui­<lb></lb>sto della Astronomia e Geografia ” (Alb. </s>

<s>XV, 331, 32). </s></p><p type="main">

<s>I vanti del Viviani furono ripetuti, e si ripetono tuttavia da tutti, fuor <lb></lb>che da noi, fatti accorti dalla passata storia che, chiunque avesse inteso far <lb></lb>del pendolo galileiano un misuratore del tempo, si sarebbe trovato alle mani <lb></lb>uno strumento fallace. </s>

<s>Non s&#039;accorse l&#039;ammirato Inventore della fallacia, <lb></lb>perchè, contro i gratuiti asserti e le correnti opinioni, ei non fece uso mai <lb></lb>di un tale strumento, e solo negli ultimi anni della sua vita lo proponeva, <lb></lb>nei più incomodi e impraticabili esercizi, al Baliani, posponendolo nonostante <lb></lb>alle volgari clessidre. </s></p><p type="main">

<s>Questo, che sarà, così al primo annunzio, dispettosamente ripudiato dai <lb></lb>lettori dell&#039;elogio di Galileo, è quel che ora intende di venire innanzi a nar­<lb></lb>rare la nostra Storia, la quale, avendo già frugato per i giovanili scritti mi-<pb xlink:href="020/01/2163.jpg" pagenum="406"></pb>nori, e cercate le due maggiori opere distese in dialogo, ha trovato sempre <lb></lb>le proprietà del pendolo descritte come una meccanica speculazione, o come <lb></lb>una estatica contemplazione delle maraviglie della Natura, ma non mai come <lb></lb>un artificio dell&#039;uomo, per servirsene alle più giuste misure del tempo. </s></p><p type="main">

<s>Facemmo, a pagine 301, 302 del nostro I tomo, avvertire che, primo a <lb></lb>servirsi del pendolo per uso cronometrico, fu il Santorio, e non avremmo <lb></lb>risospinta indietro la vista così lontano, se non ci premesse di confessare <lb></lb>ai lettori l&#039;errore, in cui allora cademmo, in dar lo strumento santoriano, <lb></lb>da una delle antiche misure denominato <emph type="italics"></emph>Cotyla,<emph.end type="italics"></emph.end> per un automa, mentre <lb></lb>era il dito che, movendo o da una parte o da un&#039;altra l&#039;indice per un certo <lb></lb>numero di gradi, faceva rotare ora a destra ora a sinistra un cilindro, da <lb></lb>cui svolgendosi, o su cui avvolgendosi il filo del pendolo, si poteva a pia­<lb></lb>cere aggiustarlo alla misura corrispondente al numero segnato dalla punta <lb></lb>dell&#039;indice stesso sopra la mostra. </s>

<s>Il Santorio insomma apparisce nella storia <lb></lb>il primo, che applicasse il pendolo agli usi pratici, mentre Galileo si trat­<lb></lb>teneva sterilemente a contemplarne la teoria. </s>

<s>Ma perchè, da chi tutto vuole <lb></lb>attribuire a quell&#039;uomo, adorato come divino, anche questa distinzione è ne­<lb></lb>gata, è ben lasciare i rettorici discorsi a chi se ne diletta, per ridurci alla <lb></lb>severa e schietta conclusione dei fatti. </s></p><p type="main">

<s>Nell&#039;Aprile del 1632 Galileo mandava in dono una copia dei dialoghi <lb></lb>Dei due massimi sistemi al Baliani, il quale, come in altra occasione accen­<lb></lb>nammo, attentamente leggendo, ebbe a rimaner sorpreso della precision della <lb></lb>misura ivi assegnata al tempo di un grave, che sia liberamente sceso per <lb></lb>lo spazio di cento braccia, e gli venne gran curiosità di sapere com&#039;avesse <lb></lb>fatto Galileo a ritrovar che quello spazio era passato nel preciso tempo di <lb></lb>cinque minuti secondi. </s>

<s>Ringraziando perciò del dono, scriveva da Genova, il <lb></lb>dì 23 del detto mese, una lettera, nella quale, dop&#039;essersi professato obbli­<lb></lb>gatissimo per le tante cose nuove bellissime chiaramente spiegate nel libro, <lb></lb>esprimeva così all&#039;Autore il suo desiderio: </s></p><p type="main">

<s>“ Io riceverei a gran favore che V. S. mi desse conto del modo, con <lb></lb>che ha ritrovato che il grave scende per cento braccia in cinque secondi. </s>

<s><lb></lb>Altre volte io tentai l&#039;impresa, per mezzo di una palla attaccata ad una fu­<lb></lb>nicella, tanto lunga che le sue vibrazioni durassero un secondo per appunto, <lb></lb>nè mi è finora riuscito di trovar qual sia la lunghezza precisa della fune.... <lb></lb>Di questo orologio, che misurasse i secondi, io mi do ad intendere che me <lb></lb>ne servirei a più usi; e in misurar le grandi distanze, per mezzo della dif­<lb></lb>ferenza del tempo, che è fra la vista e l&#039;udito, se pure è vero, come credo, <lb></lb>che tal differenza sia proporzionata alle distanze, onde facendo sparar un&#039;ar­<lb></lb>tiglieria lontano circa 30 miglia, purchè io possa vederne il fuoco e sentirne <lb></lb>il tuono, dalla lor differenza verrei in cognizione della distanza precisamente; <lb></lb>e in ritrovare i gradi della longitudine, mediante il moto della Luna, ancor­<lb></lb>chè non vi sia ecclissi, atteso che, con un oriolo così esatto, si ritroverebbe <lb></lb>precisamente la differenza della distanza della Luna a qualche stella, e del­<lb></lb>l&#039;un meridiano all&#039;altro, calcolandovi però le anomalie di essa Luna, e molte <pb xlink:href="020/01/2164.jpg" pagenum="407"></pb>cose simili. </s>

<s>Che perciò io la prego a dirmi il modo di misurare i secondi ” <lb></lb>(Alb. </s>

<s>IX, 266, 67). </s></p><p type="main">

<s>L&#039;orologio così ideato era proprio quello, che si ricercava per la solu­<lb></lb>zione di tanti problemi o curiosi o utili, e in tutti i modi bellissimi e nuovi, <lb></lb>nè poteva il Baliani immaginarsi che non fossero quelle medesime idee pas­<lb></lb>sate per la mente inventiva di Galileo. </s>

<s>Colui, fra sè pensava, il quale ha <lb></lb>prefiniti i tempi al cadere dei gravi, e il periodo al Gioviali, inventore e <lb></lb>magnificatore delle proprietà del pendolo, deve aver sicurissimo il modo di <lb></lb>misurar col pendolo un minuto secondo, ed egli spero me lo dirà, ma il de­<lb></lb>siderio non fu sodisfatto. </s></p><p type="main">

<s>Due anni e mezzo dopo, Giovanni Pieroni, che si trovava in Austria, e <lb></lb>che s&#039;esercitava nell&#039;Astronomia, scrivendo da Vienna il dì 4 Gennaio 1635 <lb></lb>allo stesso Galileo, gli diceva di certe sue osservazioni fatte sopra le stelle <lb></lb>fisse, e poi soggiungeva: “ Io son dietro a farne cento altre, che a suo tempo <lb></lb>le comunicherò, ma mi sarebbe di grandissimo vantaggio in esse sapere da <lb></lb>V. S. quanto vada lungo un pendolo per misurare uno o alquanti secondi <lb></lb>di tempo, o se la lunghezza si prende insino o tutto il corpo grave pen­<lb></lb>dente, o insino al centro di esso. </s>

<s>Però, se piacesse a V. S. darmene noti­<lb></lb>zia, non potrei dirle quanto grato favore mi farebbe, e potrebbe dirmelo alla <lb></lb>misura del braccio di costì, perchè io la ritenga meco esatta ” (Alb. </s>

<s>X, 68). </s></p><p type="main">

<s>Nemmeno il Pieroni ebbe a questa sua istante domanda la desiderata <lb></lb>risposta, e se volesse saper qualcuno chi ci abbia chiarito di una tale no­<lb></lb>tizia, la contraria verità della quale potrebbe risultar forse dai privati com­<lb></lb>merci epistolari rimasti a noi sconosciuti, risponderemo francamente che, <lb></lb>contro l&#039;opinion del Baliani, del Pieroni e di tutti, Galileo non aveva avuto <lb></lb>infin allora il pensiero di applicare il pendolo alle osservazioni celesti, e <lb></lb>tanto meno aveva conceputa la speranza di risolvere il problema della lun­<lb></lb>ghezza da dare al filo, perchè il pendolo stesso batta esattamente un mi­<lb></lb>nuto secondo. </s></p><p type="main">

<s>La più certa soluzione infatti di quel problema dipende, come si sa, <lb></lb>dalla legge delle proporzioni, che passano fra due varie lunghezze di pen­<lb></lb>doli, e la durata o il numero delle vibrazioni fatte da ciascuno nei mede­<lb></lb>simi tempi; legge che voleva prima esser conosciuta in sè stessa, per poi <lb></lb>venire applicata a risolvere la questione proposta. </s>

<s>Or si comprende bene <lb></lb>quanto sia necessario il saper nei presenti dubbi come e quando riuscisse <lb></lb>Galileo a scoprir che i tempi delle vibrazioni dei pendoli stanno come le <lb></lb>radici delle lunghezze dei fili. </s>

<s>Il Baliani dice di essersi abbattuto a caso a <lb></lb>osservare il fatto, istituendo nel 1611 quelle sue esperienze intorno al moto <lb></lb>dei pendoli di vario peso, per concluderne dal loro isocronismo che le ve­<lb></lb>locità non sono proporzionate alle moli. </s>

<s>In mezzo a queste osservazioni dei <lb></lb>pendoli di lunghezze uguali, gli venne voglia di sperimentare in pendoli di <lb></lb>lunghezze differenti, “ in quibus peragendis illud, egli dice, praeter expecta­<lb></lb>tionem sese mihi obtulit, quod, quotiescumque globi penderent ex funicu­<lb></lb>lis inaequalibus, ita inaequali motu ferebantur, ut longitudines funiculorum <pb xlink:href="020/01/2165.jpg" pagenum="408"></pb>durationibus motuum in duplicato ratione responderent ” (De motu natur. </s>

<s><lb></lb>cit., pag. </s>

<s>6). </s></p><p type="main">

<s>Galileo, in nessuno dei libri pubblicati da lui infino al 1632 o a qual­<lb></lb>che anno di poi, fa motto di questa insigne legge, sperimentalmente sco­<lb></lb>perta dal Baliani. </s>

<s>Anzi si conclude da un luogo della giornata quarta Dei <lb></lb>due massimi sistemi che l&#039;Autore credeva allora fossero i tempi delle vi­<lb></lb>brazioni proporzionali alle semplici lunghezze dei pendoli, come, nell&#039;asta <lb></lb>accomodata a temperare il tempo degli orologi, fanno i pesi di piombo a <lb></lb>dilungarli o a ritirarli più verso il centro. </s>

<s>“ Qui la virtù movente è la me­<lb></lb>desima, cioè il contrappeso, i mobili sono i medesimi piombi, e le vibra­<lb></lb>zioni loro son più frequenti, quando son più vicini al centro, cioè quando <lb></lb>si muovono per minori cerchi. </s>

<s>Sospendansi pesi eguali da corde diseguali <lb></lb>e, rimossi dal perpendicolo, lascinsi in libertà. </s>

<s>Vedremo gli appesi a corde <lb></lb>più brevi fare lor vibrazioni sotto più brevi tempi, come quelli, che si muo­<lb></lb>vono per cerchi minori ” (Alb. </s>

<s>I, 487). Ond&#039;è chiaro che i tempi per gli <lb></lb>archi son, secondo questo discorso, non proporzionali alle radici, ma alle <lb></lb>semplici lunghezze dei raggi. </s></p><p type="main">

<s>Si posson di qui tutti facilmente persuadere che colui, il quale versava <lb></lb>in così fatti errori, non era in grado di risolvere i quesiti propostigli dal <lb></lb>Baliani e dal Pieroni. </s>

<s>Troppo erano però quei quesiti importanti, e tali da <lb></lb>meritar che vi esercitasse attorno Galileo la sua scienza, la quale nel 1537 <lb></lb>parve esaurita. </s>

<s>Aveva già riconosciuto allora il suo inganno in paragonare <lb></lb>ai moti equabili dei pesi nell&#039;orologio a ruote i moti accelerati dei pendoli, <lb></lb>i quali non potevano sottrarsi alle leggi universali dei gravi cadenti, di cui <lb></lb>i tempi son anche proporzionati alle radici, e non ai semplici spazi passati. </s>

<s><lb></lb>Notabile è che Galileo, rispetto alle cadute per gli archi dei cerchi, incor­<lb></lb>resse in quei medesimi crrori, che fu egli il primo a scoprire nelle cadute <lb></lb>rette dei gravi: però è più notabile che, spendendo tanta scienza matematica <lb></lb>intorno a queste cadute verticali, si rimettesse per quelle circolari alla sem­<lb></lb>plice esperienza. </s>

<s>Ma l&#039;arte sperimentale aveva troppo corte le ali per sol­<lb></lb>levar l&#039;ingegno a risolvere con precisione matematica il problema della lun­<lb></lb>ghezza, che vuol avere un pendolo per battere i secondi; ond&#039;è che, dovendosi <lb></lb>far d&#039;esso pendolo un misuratore del tempo, confidatosi tutto nella falsa legge <lb></lb>dell&#039;isocronismo, fondò sopr&#039;essa un progetto, in cui, senza poter andare più <lb></lb>avanti per non avere scienza delle proprietà dei pendoli di varia lunghezza, <lb></lb>esaurì, come si disse, Galileo le forze del proprio ingegno. </s>

<s>Non parvero queste <lb></lb>però punto deboli a quell&#039;Uomo, che si lusingava dover lo stesso Orologio <lb></lb>a minuti secondi, quando pure alcuno l&#039;avesse saputo trovare, rimanersi in­<lb></lb>feriore a quel suo squisito <emph type="italics"></emph>Misuratore del tempo,<emph.end type="italics"></emph.end> che gli incorò la speranza <lb></lb>di aver per esso a risolvere con sicurezza il problema delle longitudini. </s></p><p type="main">

<s>Sotto il dì 6 di Giugno di quell&#039;anno 1637 abbiamo infatti scritta a <lb></lb>Lorenzo Realio, ch&#039;era uno dei deputati dagli Olandesi ad esaminar la pro­<lb></lb>posta di Galileo intorno al modo di trovare le longitudini, una lettera, nella <lb></lb>quale è nitidamente specchiata la scienza galileiana dei pendoli nei loro usi <pb xlink:href="020/01/2166.jpg" pagenum="409"></pb>pratici, dedotti dalla teoria, la quale anche qui, con manifesta trasgressione <lb></lb>di ogni termine di Meccanica e di Logica, si riduce a concludere il tauto­<lb></lb>cronismo degìi archi dal tautocronismo delle corde (Alb. </s>

<s>VII, 168). Vi si <lb></lb>professa pure il più assoluto isocronismo delle vibrazioni, invocando per con­<lb></lb>fermarlo quell&#039;esperienza, che fece chiaramente vedere il contrario all&#039;Huy­<lb></lb>ghens, e a tutti coloro che non vogliano negar fede ai loro occhi proprii <lb></lb>(ivi, pag. </s>

<s>169). Sopra questo principio, che nonostante da Galileo si dà per <lb></lb>verissimo e stabile, è fondata la nuova invenzione di misurar i minimi tempi, <lb></lb>“ perchè fatta una volta tanto, con pazienza, la numerazione delle vibrazioni, <lb></lb>che si fanno in un giorno naturale, misurato colla rivoluzione di una stella <lb></lb>fissa; s&#039;averà il numero delle vibrazioni d&#039;un&#039;ora, d&#039;un minuto o d&#039;altra <lb></lb>minor parte. </s>

<s>Potrassi ancora, fatta questa prima esperienza col pendolo di <lb></lb>qualsivoglia lunghezza, crescerlo o diminuirlo, sicchè ciascheduna vibrazione <lb></lb>importi il tempo di un minuto secondo, imperocchè le lunghezze di tali pen­<lb></lb>doli mantengono fra di loro duplicata proporzione di quella dei tempi, come <lb></lb>per esempio: posto che un pendolo di lunghezza di quattro palmi faccia in <lb></lb>un dato tempo mille vibrazioni, quando noi volessimo la lunghezza d&#039;un <lb></lb>altro pendolo, che nell&#039;istesso tempo, facesse duplicato numero di vibrazioni, <lb></lb>bisogna che la lunghezza del pendolo sia la quarta parte della lunghezza <lb></lb>dell&#039;altro. </s>

<s>Ed insomma, come si può vedere coll&#039;esperienza, la moltitudine <lb></lb>delle vibrazioni dei pendoli di lunghezze diseguali è sudduplicata di esse <lb></lb>lunghezze ” (Alb. </s>

<s>VII, 170). </s></p><p type="main">

<s>La legge è dunque formulata qui molto diversamente da quel che, cin­<lb></lb>que anni prima, si fosse fatto nella IV giornata dei Massimi sistemi, ma <lb></lb>come e a qual felice occasione si fosse Galileo ravveduto del suo errore non <lb></lb>si cura di dirlo, non essendo dell&#039;indole di quell&#039;uomo, come in simili altri <lb></lb>casi notammo, il far pur vista di avere sbagliato. </s>

<s>Questo solo ci dice che <lb></lb>fu una tal legge scoperta e verificata per via dell&#039;esperienza: e perchè in <lb></lb>quel tempo, cioè nel 1637, attendeva a metter in ordine, per darlo alle <lb></lb>stampe, il manoscritto del primo dialogo delle Scienze nuove, ivi ebbero so­<lb></lb>lenne pubblicità i fatti osservati, che non avevano, a volere esser giusti, nes­<lb></lb>sun diritto d&#039;essere esposti al mondo come nuovi, essendosi incontrato in <lb></lb>essi, infino dal 1611, il Baliani, e avendoli il Mersenno, in un suo libro <lb></lb>stampato in francese in Roma nel 1636, già divulgati. </s></p><p type="main">

<s>Nuovo sarebbe stato il problema del pendolo a secondi, che pareva aversi <lb></lb>risoluto nelle sopra scritte parole al Realio, per cui fa a prima vista gran <lb></lb>maraviglia il non veder quella soluzione inserita nei dialoghi del Moto, là <lb></lb>dove specialmente sperava d&#039;avercela a trovare il Baliani. </s>

<s>“ Anzi che in <lb></lb>quelli (nei dialoghi del Sistema) V. S. dice qualche cosa, di che io sperava <lb></lb>che ne dovesse dar più distinto conto in questi, cioè di aver osservato che <lb></lb>il grave discende, di moto accelerato, per cento braccia in cinque minuti <lb></lb>secondi di ora; sperava dico che dovesse dir con che ragione si è assicu­<lb></lb>rata che sian cinque secondi, e massime dove dà conto di altre esperienze <lb></lb>fatte in simil materia ” (Alb. </s>

<s>X, 353). </s></p><pb xlink:href="020/01/2167.jpg" pagenum="410"></pb><p type="main">

<s>Chi non si sarebbe infatti aspettato che, stabilitasi la legge dei quadrati <lb></lb>dei tempi proporzionali alle lunghezze dei pendoli, non avesse Galileo appli­<lb></lb>cato il corollario de&#039;quadrati delle vibrazioni, ad esse lunghezze reciproca­<lb></lb>mente proporzionali, a dar regola matematica per trovar la lunghezza del <lb></lb>pendolo, che batte i secondi? </s>

<s>E invece s&#039;applica a risolvere un problema <lb></lb>di pura curiosità, qual&#039;è quello “ di saper la lunghezza di una corda pen­<lb></lb>dente da qualsivoglia grandissima altezza ” (Alb. </s>

<s>XIII, 99). Nè il discorso <lb></lb>in materia de&#039;pendoli s&#039;introduce in questo primo dialogo per applicare ad <lb></lb>essi, nel terzo, le conclusioni intorno ai moti locali, le quali si rimangono <lb></lb>ivi perciò una sterile esercitazione, ma per spiegare il fatto assai trito “ delle <lb></lb>due corde tese all&#039;unisono, che al suono dell&#039;una l&#039;altra si muove ” (ivi, <lb></lb>pag. </s>

<s>98) e per mostrare il modo, col quale l&#039;occhio ancora possa ricrearsi <lb></lb>nel vedere i medesimi scherzi, che sente l&#039;udito nelle varie consonanze mu­<lb></lb>sicali (ivi, pag. </s>

<s>109). </s></p><p type="main">

<s>Certo una tal negligenza, in soggetto tanto importante, e ad una delle <lb></lb>più grandi utilità, che s&#039;aspettavano da Galileo la Dinamica, la Nautica e <lb></lb>l&#039;Astronomia preferire gli scherzi della Musica, fa gran maraviglia, la quale <lb></lb>ci vien tolta dal pensar che non bastava la notizia di un semplice principio <lb></lb>sperimentale, per ricavarne una regola matematica. </s>

<s>Che se fosse quel prin­<lb></lb>cipio per sè bastato, non aveva bisogno di ricorrere a Galileo quel Baliani, <lb></lb>il quale aveva parecchi anni prima scoperto che le lunghezze dei pendoli <lb></lb>stanno come i quadrati dei tempi delle vibrazioni. </s>

<s>Conveniva dunque ridurre <lb></lb>questo fatto a un calcolo, il quale, benchè fosse assai semplice, era nono­<lb></lb>stante così sottile, da sfuggire all&#039;arte dello stesso Galileo. </s>

<s>A chi non lo <lb></lb>crederebbe faremo intanto avvertire una improprietà di linguaggio, scorsa <lb></lb>nella Lettera al Realio, che poi nel Dialogo si ripete, dicendosi là <emph type="italics"></emph>che la <lb></lb>moltitudine delle vibrazioni dei pendoli di lunghezze diseguali è suddu­<lb></lb>pla di esse lunghezze,<emph.end type="italics"></emph.end> e quà, che <emph type="italics"></emph>le lunghezze delle corde hanno fra loro <lb></lb>la proporzione, che hanno i quadrati dei numeri delle vibrazioni, che si <lb></lb>fanno nel medesimo tempo.<emph.end type="italics"></emph.end> La parola <emph type="italics"></emph>reciproca,<emph.end type="italics"></emph.end> che si legge nell&#039;edizione <lb></lb>dell&#039;Albèri, in carattere corsivo, è una correzione introdottavi da una copia <lb></lb>dell&#039;edizione di Leyda postillata dal Viviani. </s></p><p type="main">

<s>L&#039;improprietà del linguaggio, che in due così insigni scritture non si <lb></lb>potrebbe facilmente passare per una semplice inavvertenza, è indizio e causa <lb></lb>di una confusion nelle idee, della quale ci porge Galileo stesso l&#039;esempio, <lb></lb>quando, poco dopo d&#039;aver annunziata la legge, che governa il moto dei pen­<lb></lb>doli di varia lunghezza, si propon di ricavarne la soluzione di questo pro­<lb></lb>blema, per render visibile il gioco delle consonanze musicali: S&#039;abbiano tre <lb></lb>pendoli, e si cerchi quali debban essere le loro lunghezze, perchè, mentre <lb></lb>il più lungo fa due vibrazioni, il mezzano ne faccia tre, e il più corto quat­<lb></lb>tro. </s>

<s>Questo otterremo, dice il Salviati, “ quando il più lungo contenga sedici, <lb></lb>palmi, o altre misure, delle quali il mezzano ne contenga nove, e il minore <lb></lb>quattro ” (Alb. </s>

<s>XIII, 109). Ma qui è un error di calcolo manifesto, perchè, <lb></lb>se i numeri delle vibrazioni son 2, 3, 4, e debbono le lunghezze reciproca-<pb xlink:href="020/01/2168.jpg" pagenum="411"></pb>mente stare come i quadrati di questi numeri, non saranno dunque 16, 9 e 4, <lb></lb>ma 36 16 e 9. Fu il primo il Viviani a notare lo sbaglio, e, a pag. </s>

<s>107 di <lb></lb>una copia dell&#039;edizione di Leyda, scrisse di propria mano in margine, con <lb></lb>insolita libertà, la seguente postilla: </s></p><p type="main">

<s>“ Quando i numeri delle vibrazioni, fatte nel medesimo tempo dai tre <lb></lb>fili pendoli, differenti in lunghezza, sono queste: cioè 2, 3, 4 come gli pone <lb></lb>il signor Galileo, dovendo tali lunghezze stare in proporzione reciproca dei <lb></lb>quadrati di detti numeri, staranno come questi numeri 9, 4 2 1/4, cioè 16, <lb></lb>7 1/9, 4, onde, dove qui al quarto verso dicesi <emph type="italics"></emph>nove,<emph.end type="italics"></emph.end> è errore di calcolo, e <lb></lb>deve dire <emph type="italics"></emph>sette e un nono.<emph.end type="italics"></emph.end> Che se le lunghezze dei fili de&#039;tre pendoli fos­<lb></lb>sero quali le pone sopra il signor Galileo, cioè fossero 16, 9, 4, i tempi delle <lb></lb>loro uniche vibrazioni sarebbero 4, 3, 2: i numeri delle vibrazioni, fatte <lb></lb>nel medesimo tempo, sarebbero 3, 4, 6, onde gl&#039;incontri di esse seguireb­<lb></lb>bero ad ogni 3 vibrazioni del lungo, 4 del mezzano e 6 del corto, e non ad <lb></lb>ogni 2, 3, 4, com&#039;ei dice ” (MSS. Gal., P. V, T. IX). </s></p><p type="main">

<s>L&#039;errore non è, come il Viviani voleva credere, materiale del calcolo, <lb></lb>ma formale della regola, male istituita a ben condurlo, ond&#039;è che Galileo, <lb></lb>veduta la difficoltà di spuntare a risolvere il problema del pendolo, che batte <lb></lb>i secondi, annunziato già nella lettera al Realio, ridusse l&#039;ambita invenzione <lb></lb>del suo nuovo Misuratore del tempo per gli usi nautici quale ei lo descrisse <lb></lb>per gli usi astronomici nelle <emph type="italics"></emph>Operazioni,<emph.end type="italics"></emph.end> che son l&#039;unica prima scrittura, <lb></lb>nella quale si parli di proposito del pendolo, per uso di Cronometro. </s>

<s>E per­<lb></lb>chè una tale scrittura è del 1639, come apparisce da certissimo documento <lb></lb>(Alb. </s>

<s>VII, 193) ecco una dimostrativa conferma di ciò, che abbiamo ad altre <lb></lb>occasioni asserito, che cioè, non prima del 1637, cominciò a pensar Galileo <lb></lb>di far de&#039;pendoli quelle cronometriche applicazioni, delle quali annunziava <lb></lb>nel 1639 il definitivo progetto. </s>

<s>Consisteva un tal progetto nel servirsi di un <lb></lb>pendolo di qualunque lunghezza, e, fallacemente supposto che facesse tutte <lb></lb>le sue vibrazioni uguali, contare il numero delle fatte da lui in 24 ore si­<lb></lb>deree, “ imperocchè da esse, in tutte l&#039;altre osservazioni di tempi, potremo <lb></lb>avere la quantità loro in ore, minuti, secondi, terzi, ecc., operando con la <lb></lb>regola aurea ” (Alb. </s>

<s>V, 374). </s></p><p type="main">

<s>Così essendo, non si trovava ora dunque Galileo chiusa in tutto la bocca, <lb></lb>come nel 1632, e nel 1635, quando il Baliani e il Pieroni erano venuti a <lb></lb>proporgli i loro quesiti. </s>

<s>E perciò al primo commemorato, che nel principio <lb></lb>del Luglio 1639 era venuto a ripetere la dimenticata domanda, fatta con <lb></lb>tanta istanza sette anni avanti all&#039;occasione del vedersi smarrita la speranza <lb></lb>d&#039;avere a ritrovar nei dialoghi Del moto descritto lo strumento, con cui si <lb></lb>potesse ognuno certificare essere il tempo speso da un mobile a passar cento <lb></lb>braccia precisamente cinque secondi; Galileo, ora liberale dell&#039;acquistata <lb></lb>scienza, rispondeva con lettera del dì primo Agosto di quel medesimo anno, <lb></lb>dove, dopo aver detto come, facendo uso de&#039;suoi teoremi, si fosse assicu­<lb></lb>rato del tempo assoluto della scesa del mobile per quello spazio, passa a <lb></lb>propor l&#039;altro modo da tenersi per ritrovare il tempo relativo. </s></p><pb xlink:href="020/01/2169.jpg" pagenum="412"></pb><p type="main">

<s>“ Ciò otterremo, scriveva, dalla ammirabile proprietà del pendolo, che <lb></lb>è di fare tutte le sue vibrazioni, grandi e piccole, sotto tempi eguali. </s>

<s>Si ri­<lb></lb>cerca, <emph type="italics"></emph>pro una vice tantum,<emph.end type="italics"></emph.end> che due, tre o quattro amici, curiosi e pazienti, <lb></lb>avendo appostata una stella fissa, che risponde contro a qualche segno sta­<lb></lb>bile, preso un pendolo di qualsivoglia lunghezza, vadano numerando le sue <lb></lb>vibrazioni per tutto il tempo del ritorno della medesima fissa al primo luogo, <lb></lb>e questo sarà il numero delle vibrazioni di 24 ore. </s>

<s>Dal numero di queste <lb></lb>potremo ritrovare il numero delle vibrazioni di qualsivogliano altri pendoli <lb></lb>minori e minori a nostro piacimento, sicchè, se v. </s>

<s>g. </s>

<s>le numerate da noi <lb></lb>nelle 24 ore fossero state per esempio 234,567, pigliando un altro pendolo <lb></lb>più breve, nel quale uno numeri per esempio 800 vibrazioni, mentre che <lb></lb>l&#039;altro misurasse 156 delle maggiori, già avremo, per la regola aurea, il nu­<lb></lb>mero delle vibrazioni di tutto il tempo delle 24 ore. </s>

<s>E se con queste vi­<lb></lb>brazioni vorremo sapere il tempo della scesa per il canale, potremo, con la <lb></lb>medesima agevolezza, ritrovare non solo i minuti primi, secondi e terzi, ma <lb></lb>quarti e quinti, e quanto più ci piacerà ” (Lettere di Galileo, Pisa 1864, <lb></lb>pag. </s>

<s>42). </s></p><p type="main">

<s>Così fatte minuzie erano più però a lussuria di calcolo, che per servire <lb></lb>alla precisione delle esperienze, per le quali sarebbesi massimamente desi­<lb></lb>derato che fosse giusto il numero delle vibrazioni, contate nel tempo delle <lb></lb>24 ore da que&#039;due o tre o quattro amici. </s>

<s>Ma dove ritrovar tanta resistenza <lb></lb>al disagio, o tanta durazione nella lunga pazienza? </s>

<s>E quando pure si fos­<lb></lb>sero ritrovate così rare virtù, nell&#039;abito corporeo e nelle disposizioni del­<lb></lb>l&#039;animo, chi sarebbesi potuto ripro ne<gap></gap>tere tanta infallibilità del senso, da <lb></lb>assicurarsi che, di quelle tante migliaia di vibrazioni, nemmen una gliene <lb></lb>fosse sfuggita all&#039;attenzion della vista? </s>

<s>Furon quelle riflessioni, che, alle <lb></lb>sopra lasciate interrotte, suggeriron le parole seguenti: “ Vero è che noi <lb></lb>potremo passare a più esatta misura, con avere veduto ed osservato qual sia <lb></lb>il flusso dell&#039;acqua per un sottile cannello, perchè, raccogliendo ed avendo <lb></lb>pesata quanta ne passa v. </s>

<s>g. </s>

<s>in un minuto, potremo poi, col pesare la pas­<lb></lb>sata nel tempo della scesa per il canale, trovare l&#039;esattissima misura e quan­<lb></lb>tità di esso tempo, servendosi massimamente di una bilancia così esatta, che <lb></lb>tira ad un sessantesimo di grano ” (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Ecco dunque dove vanno a finire tutte le declamate eccellenze di quel <lb></lb>Misuratore del tempo, con cui si ritroverebbero infallibilmente, in mezzo al­<lb></lb>l&#039;incerto mare, i naviganti olandesi; ecco dove va a sfumar la gloria del­<lb></lb>l&#039;ambita invenzione! a dir che, rispetto al pendolo, son più esatta misura <lb></lb>le clessidre, e, in tanto fasto di novità, tornare indietro a Proclo e a Cleo­<lb></lb>mede. </s>

<s>Sentiva il Baliani questi rimproveri nella sua propria coscienza po­<lb></lb>tenti, e s&#039;infervorava sempre più in voler aver quel pendolo a secondi, da <lb></lb>cui sperava la felice risoluzione di tanti bei problemi di Ottica, di Acustica, <lb></lb>di Goografia, di Astronomia e di Nautica, i quali tutti Galileo, a scusar sè, <lb></lb>e a giustificarsi di ciò che aveva scritto per verificare la legge delle cadute <lb></lb>dei gravi, sacrificava agl&#039;ignobili vasi sgocciolanti. </s></p><pb xlink:href="020/01/2170.jpg" pagenum="413"></pb><p type="main">

<s>Nei giorni, in cui recapitò questa lettera di Firenze, si trovava di pas­<lb></lb>saggio in Genova il p. </s>

<s>Niccolò Cabeo, a cui si rivolse il Baliani, pregandolo <lb></lb>a voler usar di tutto il suo studio, e di tutta la sua pazienza, per veder di <lb></lb>ricavar da que&#039;documenti galileiani la misura giusta del pendolo oscillante <lb></lb>a ogni minuto secondo. </s>

<s>Tornato il Cabeo a Ferrara, si dette con indicibile <lb></lb>assiduità all&#039;opera, e in poco più di una settimana si lusingò di averla con­<lb></lb>dotta a buon termine, scrivendo a Genova, e mandandone la misura. </s>

<s>Lieto <lb></lb>il Baliani di aver finalmente conseguito lo strumento, che gli potrebbe “ ser­<lb></lb>vire per un Orologio da misurar molte cose, che richiedano tempo breve ” <lb></lb>(Alb. </s>

<s>X, 360) ne dava, per lettera del dì 19 Agosto, avviso a Galileo, dicen­<lb></lb>dogli essere stato il Cabeo, che, reputato atto a ciò, “ e a molto maggior <lb></lb>cosa ” (ivi) l&#039;aveva, pregatone, sodisfatto del suo desiderio. </s></p><p type="main">

<s>Galileo cominciò a quell&#039;avviso a ripensar curiosamente com&#039;avesse fatto <lb></lb>esso Cabeo a ritrovare una tal misura, e il dì primo del seguente Settembre <lb></lb>significava così al Baliani il suo pensiero: “ In risposta alla gratissima del <lb></lb>19 del passato mese, dico che, quanto a misurare il tempo con un pendolo <lb></lb>aggiustato a fare le sue vibrazioni in un minuto secondo, si avanza la fa­<lb></lb>tica del fare il calcolo con la semplice operazione della regola aurea, avendo <lb></lb>una volta tenuto conto del numero delle vibrazioni di qualsivoglia pendolo, <lb></lb>fatte in 24 ore, la quale osservazione è necessario che il p. </s>

<s>Cabeo abbia <lb></lb>fatta con un pendolo di qualsiasi lunghezza, e da esso cavatone, con l&#039;in­<lb></lb>venzione delle medie, la lunghezza del pendolo di un minuto secondo ” (Let­<lb></lb>tere di Gal. </s>

<s>cit., pag. </s>

<s>47). </s></p><p type="main">

<s>Ma che cosa è questa <emph type="italics"></emph>invenzion delle medie,<emph.end type="italics"></emph.end> domandava a sè stesso il <lb></lb>Baliani, a cui era venuta da Ferrara la misura, non però il modo usato in <lb></lb>ritrovarla. </s>

<s>Rispondeva perciò a Galileo non saper dirgli, in proposito di quel <lb></lb>modo, altro che questo: “ Il calcolo del padre Cabeo credo che sia fatto al <lb></lb>modo di V. S., che così io gli suggerii, quando egli era qui, non però tanto <lb></lb>esattamente, da numerare le vibrazioni fatte in 24 ore, ma credo in una o <lb></lb>due ore solamente, in qualunque lunghezza del pendolo, col farci poi il conto <lb></lb>per la regola aurea, come V. S. dice ” (Alb. </s>

<s>X, 365). </s></p><p type="main">

<s>La regola aurea però, così usata intorno a pendoli di qualunque lun­<lb></lb>ghezza, non poteva bastar per sè sola a ritrovar la prefinita misura del pen­<lb></lb>dolo a secondi, altro che per via di ripetuti tentativi, allungando o occor­<lb></lb>ciando il filo, trovato battere una certa misura del tempo, infino a ridurlo <lb></lb>a un secondo preciso; nei quali tentativi consisteva quella, che Galileo chia­<lb></lb>mava <emph type="italics"></emph>invenzion delle medie.<emph.end type="italics"></emph.end> Se dovea dunque il Cabeo seguitar necessa­<lb></lb>riamente questa via di prova, non c&#039;era, secondo lo stesso Galileo, nessun&#039;al­<lb></lb>tra regola matematicamente sicura. </s>

<s>Le parole perciò scritte nella lettera al <lb></lb>Realio non dovettero aver, nella mente dello scrittore, il significato, che <lb></lb>sembrava esservi espresso, che cioè, trovato il numero delle vibrazioni fatte <lb></lb>in un minuto secondo da un pendolo di qualunque lunghezza, si potesse, <lb></lb>dal teorema ivi opportunamente invocato, che cioè <emph type="italics"></emph>la moltitudine delle vi­<lb></lb>brazioni dei pendoli di lunghezze diseguali è<emph.end type="italics"></emph.end> reciprocamente <emph type="italics"></emph>sudduplicata<emph.end type="italics"></emph.end><pb xlink:href="020/01/2171.jpg" pagenum="414"></pb><emph type="italics"></emph>di esse lunghezze;<emph.end type="italics"></emph.end> dedurne la lunghezza del pendolo a secondi: imperocchè <lb></lb>l&#039;operazione fatta con questa regola si riduceva alla certezza di un calcolo <lb></lb>aritmetico, consistente nel moltiplicar la misura del pendolo arbitrario per <lb></lb>il quadrato del numero delle vibrazioni, fatte da lui in un minuto secondo. </s></p><p type="main">

<s>Essendo insomma Galileo persuaso non si poter risolvere il problema <lb></lb>del pendolo, determinatamente lungo, altro che per ripetute esperienze fatte <lb></lb>col pendolo di qualunque lunghezza, ne concludeva che in precisione era <lb></lb>questo suo orologio superiore a quello dell&#039;altro, e che perciò male il Ba­<lb></lb>liani aveva provveduto al suo bisogno, dando la preferenza alla invenzione <lb></lb>del Cabeo, che va inevitabilmente sottoposta a qualche errore, “ il quale, <lb></lb>benchè piccolo, moltiplicato secondo il numero delle molte vibrazioni, può <lb></lb>partorire notabile errore, il che non accade nelle vibrazioni, non obbligate <lb></lb>alla lunghezza del filo, che, molte centinaia di volte replicata, ci deve dare <lb></lb>la misura del tempo; sicchè ogni piccolo errore, preso nella lunghezza del <lb></lb>pendolo, va molte centinaia di volte moltiplicato, mentre nell&#039;altra mia ope­<lb></lb>razione l&#039;errore non può nascere salvo che dal numerare le vibrazioni, delle <lb></lb>quali una sola parte di una sola vibrazione può essere presa più o meno del <lb></lb>giusto ” (Lettere di Gal. </s>

<s>cit., pag. </s>

<s>48). </s></p><p type="main">

<s>Questo, che dice qui Galileo, è come il più distinto suggello a confer­<lb></lb>mar ch&#039;ei non doveva conoscere altro modo, che tentare e ritentare per via <lb></lb>della esperienza, perchè, se avesse saputa la regola del calcolo, istituita die­<lb></lb>tro le ragioni, che serbano insieme i pendoli, tra i tempi del loro vibrare <lb></lb>e le lunghezze dei fili; non avrebbe avuto alcun dubbio che, tanto il pen­<lb></lb>dolo obbligato, quanto quello non obbligato a lunghezza, sarebbero andati <lb></lb>soggetti ai medesimi errori, dipendenti unicamente dagli sbagli nel nume­<lb></lb>rare le vibrazioni fatte in 24 ore, e nel dedurne di lì il numero delle vi­<lb></lb>brazioni fatte in un minuto secondo, potendo esser l&#039;une, e perciò anche <lb></lb>l&#039;altre, prese, come Galileo stesso dianzi diceva, più o meno del giusto. </s>

<s>Se <lb></lb>chiamata L infatti l&#039;arbitraria lunghezza del pendolo, e N2 il quadrato del <lb></lb>numero delle vibrazioni, da lui fatte in un minuto secondo, la cercata lun­<lb></lb>ghezza X dell&#039;orologio a secondi vien rappresentata dalla formula X=LN2; <lb></lb>è chiaro che tutta l&#039;esattezza, così di questa come dell&#039;operazione di Gali­<lb></lb>leo, dipende dal valore di N, non avendo L nessuna difficoltà a dare a chiun­<lb></lb>que la voglia la precisa lunghezza sua lineare. </s></p><p type="main">

<s>Or perchè da nessuna parte dei consultati commerci epistolari resulta <lb></lb>chiaro se il modo tenuto dal Cabeo fosse propriamente quello congetturato <lb></lb>da Galileo, nè il Baliani a lui scrisse quanta fosse la ritrovata misura del <lb></lb>pendolo, rimarremo qui in gran curiosità di saper la parte più importante <lb></lb>di questa storia, se il Cabeo stesso, pubblicando i suoi commentari sulla Me­<lb></lb>teorologia di Aristotile, non fosse venuto a darci la desiderata notizia. </s>

<s>Nella <lb></lb>Questione ultimamente citata, nella quale si richiamavano a sottile esame le <lb></lb>dottrine galileiane intorno ai pendoli di uguale lunghezza, dop&#039;avere il Cabeo <lb></lb>concesso che, per esser piccole le disuguaglianze osservate, si potevano i moti <lb></lb>di quegli stessi pendoli reputare isocroni, così soggiunge: “ Ex hoc habe-<pb xlink:href="020/01/2172.jpg" pagenum="415"></pb>tur utilissimum sane instrumentum, vel potius Horologium, ad mensuran­<lb></lb>dum tempora brevissima, ita ut ex serico filo suspendendo globulum plum­<lb></lb>beum, non solum tibi possis instruere Horologium, quo minuta secunda <lb></lb>metiaris, sed etiam 3, 4, immo et 5 unius secundae poteris metiri. </s>

<s>Ego mihi <lb></lb>comparavi, satis pertinaci labore, mensurando integram horam, longitudinem <lb></lb>fili penduli exactissime, qua unam habeo secundam. </s>

<s>Longitudo fili est un­<lb></lb>ciarum 9 pedis romani antiqui ” (Editio cit., T. I, pag. </s>

<s>100). </s></p><p type="main">

<s>La notizia è importante, perchè sappiamo ora di certo che la quantità <lb></lb>della misura del pendolo a secondi, reputata dal Cabeo e creduta dal Baliani <lb></lb>esattissima, era nove once di piede romano antico, ossia un palmo, che, se­<lb></lb>condo le comuni tavole di riduzione, corrisponderebbe a 0m, 223. L&#039;enorme <lb></lb>sbaglio, che non poteva solo dipendere dalla poco esatta misura dell&#039;ora, <lb></lb>presa forse dagli orologi scioterici o dalle clessidre, farebbe credere che di­<lb></lb>pendesse piuttosto dalla mala corrispondenza di quei tentativi, ai quali era, <lb></lb>secondo Galileo, necessario si riducesse l&#039;osservatore, per conseguire il suo <lb></lb>intento. </s>

<s>Dal sopra trascritto passo però non s&#039;argomenta nulla in proposito, <lb></lb>ma nel II tomo di quelia stessa Opera meteorologica ci toglie intorno a ciò <lb></lb>l&#039;Autore ogni dubbio. </s>

<s>Dice anzi che, nel provarsi ad allungare e ad accor­<lb></lb>ciare il pendolo, per ridurlo alla desiderata misura, si accorse di un fatto <lb></lb>inaspettato, che cioè la frequenza delle vibrazioni non diminuiva a proporzion <lb></lb>dei fili accorciati. </s>

<s>Dop&#039;aver trovato con la regola di Galileo che un pendolo <lb></lb>faceva per esempio quattro vibrazioni in un minuto secondo, credeva che, <lb></lb>per avere una vibrazione sola, bastasse ridurlo quattro volte più lungo, e <lb></lb>trovò invece, con sua gran sorpresa, che si dovea allungare molto di più, <lb></lb>cosicchè, se un palmo avesse dato un secondo preciso, per avere un minuto <lb></lb>primo, tutt&#039;altro che 60 palmi disse di non aver trovato ancora un filo tanto <lb></lb>lungo, che gli fosse bastato al bisogno. </s>

<s>“ Imminuto filo penduli fiunt qui­<lb></lb>dem undationes incitatiores, at non inci&#039;antur ad rationem imminuti fili, ita <lb></lb>ut, si filium fiat dimidio brevius, et undatio duplo fiat incitatior, non hoc <lb></lb>inquam sequitur, nam pendulum, cuius filum sit palmare, unam fere absumit <lb></lb>secundam singulis undationibus, et tamen filum sexaginta palmorum non <lb></lb>unum explet integrum minutum. </s>

<s>Immo nullam hactenus taniam fili longi­<lb></lb>tudinem habere potui, quae integrum daret minutum ” (pag. </s>

<s>289). </s></p><p type="main">

<s>Tale fu la cultura, e tali furono i frutti, che raccolse il Cabeo dal suo <lb></lb>pertinace lavoro, dai consigli del Baliani, e dagli insegnamenti di Galileo. </s>

<s><lb></lb>Non sapendo il pubblico nulla di così fatti consigli, e di così fatti insegna­<lb></lb>menti, rimasti nei privati commerci epistolari, ebbe a far le maraviglie di <lb></lb>tanto errore e di tanta ignoranza, di che al Cabeo solo restò a sopportare <lb></lb>l&#039;accusa. </s>

<s>“ Quae omnia non impediunt, scriveva il Mersenno dopo aver letto, <lb></lb>ne&#039;commentari alla Meteorologia aristotelica, il passo ora copiato, quin fieri <lb></lb>nequeat ut filum palmare secundum minutum fere duret, cum vix secundi <lb></lb>respondeat dimidio, adeo ut ostenderit Cabeus se non satis exacte duratio­<lb></lb>nes funependuli examinasse, neque rationem temporum duplicatam nosse, <lb></lb>ut clarum est ex eodem loco, quod eo magis admiror quod illam rationem <pb xlink:href="020/01/2173.jpg" pagenum="416"></pb>ex Galilaeo didicisse debuerit, quem toties refellere conatus est, quodque ex <lb></lb>nostris <emph type="italics"></emph>Harmonicis,<emph.end type="italics"></emph.end> Romae decennio prostantibus antequam suum in Me­<lb></lb>teora volumen ederet, rationem illam funependulorum discere potuit ” (Re­<lb></lb>flexiones phisico-malhem., Parisiis 1647, pag. </s>

<s>158) </s></p><p type="main">

<s>Forse il Cabeo non aveva letto altro che nell&#039;ultima giornata dei Mas­<lb></lb>simi sistemi, dove s&#039;insinua la falsa dottrina dei tempi proporzionali alle <lb></lb>semplici lunghezze dei pendoli. </s>

<s>Ma poniamo che avesse appreso, dal primo <lb></lb>dialogo delle Nuove scienze o dagli <emph type="italics"></emph>Armonici,<emph.end type="italics"></emph.end> che que&#039;tempi sono invece <lb></lb>proporzionali alle radici delle lunghezze; non gli sarebbe però bastata que­<lb></lb>sta notizia a conseguire una misura del pendolo più giusta, come non bastò <lb></lb>al Baliani e a Galileo, dei quali avrebbe avuto più ragione di maraviglia si <lb></lb>il Mersenno. </s>

<s>Vien tolta ogni occasione di maraviglia però dal ripensar le cause, <lb></lb>che resero così incerti nella dottrina, e così mal sicuri nella pratica quei tre, <lb></lb>che primi in Italia dettero opera insieme a risolvere il problema del pendolo <lb></lb>a secondi; cause che si riducono, come tante volte abbiam detto, al non aver <lb></lb>nessuno di essi penetrate le matematiche ragioni di un fatto, ch&#039;ebbe a ri­<lb></lb>manersi perciò fra la non superabile angusta cerchia delle esperienze. </s></p><p type="main">

<s>In quel medesimo anno 1638, in cui Galileo e il Baliani si confessa­<lb></lb>vano impotenti all&#039;impresa, e vi faceva il Cabeo così infelice riuscita, si stam­<lb></lb>pava in Praga un libro, rivelatore di quella scienza dei pendoli, ch&#039;era <lb></lb>venuta meno ai nostri Italiani. </s>

<s>Giovan Marco, nella XXVIII proposizione <emph type="italics"></emph>De <lb></lb>proportione motus,<emph.end type="italics"></emph.end> era il primo che, da principii matematici, venisse a di­<lb></lb>mostrare <emph type="italics"></emph>Motus circulorum sunt in ratione suorum temporum, quam habent <lb></lb>diametri ad se duplicatam<emph.end type="italics"></emph.end> (fol. </s>

<s>37 ad t.). </s></p><p type="main">

<s>I principii matematici, che servon come di lemmi alla dimostrazione, son <lb></lb>pur essi dall&#039;Autore matematicamente dimostrati in altre proposizioni ante­<lb></lb>cedenti, fra le quali è la XIII del trattato, coll&#039;aggiunta di un corollario, che <lb></lb><figure id="id.020.01.2173.1.jpg" xlink:href="020/01/2173/1.jpg"></figure></s></p><p type="caption">

<s>Figura 211<lb></lb>manca alla proposizione III del primo libro manoscritto di <lb></lb>Galileo. </s>

<s>Essendo AB (fig. </s>

<s>211) verticale e AC obliqua, pre­<lb></lb>cisa in C dalla BC condottale perpendicolare, si dimostra in <lb></lb><figure id="id.020.01.2173.2.jpg" xlink:href="020/01/2173/2.jpg"></figure></s></p><p type="caption">

<s>Figura 212<lb></lb>quel manoscritto galileiano che, a move­<lb></lb>re da A, si passano dal mobile i due spazi <lb></lb>AB, AC nel medesimo tempo, e Giovan <lb></lb>Marco soggiunge che nel medesimo tem­<lb></lb>po anche si passerebbe la BC, essen­<lb></lb>do in C il principio del moto, perchè, <lb></lb>costruito il parallelogrammo AD, la BC, <lb></lb>in virtù del teorema galileiano, è isocro­<lb></lb>na a CD, e perciò anche ad AB, ond&#039;è <lb></lb>che AB, AC, BC sono isocrone insieme. </s>

<s>L&#039;altra proposi­<lb></lb>zione, più prossimo lemma a quella da dimostrare, è la <lb></lb>XXVI, che cioè i tempi per gli archi simili son propor­<lb></lb>zionali ai tempi per i seni corrispondenti. </s></p><p type="main">

<s>Dietro ciò, ecco insomma come Giovan Marco, con eleganza spedita, <pb xlink:href="020/01/2174.jpg" pagenum="417"></pb>dimostra che il tempo per l&#039;arco CD (fig. </s>

<s>212), di cui il seno è CE, sta al <lb></lb>tempo per l&#039;arco BF, di cui il seno è BG, come la radice di AC sta alla <lb></lb>radice di AB. </s>

<s>Abbiamo To.CD:To.BF=To.CE:To.BG, e perchè CE è <lb></lb>isocrona ad AC, e BG isocrona ad AB, To.CD:To.BF=To.AC:To.AB. </s>

<s><lb></lb>Ma il tempo per AC sta al tempo per AB, come la radice di AC sta alla <lb></lb>radice di AB; dunque, secondo queste medesime radici, che son quelle delle <lb></lb>altezze dei pendoli, o delle lunghezze dei raggi, stanno anche i tempi per <lb></lb>gli archi simili da loro descritti. </s></p><p type="main">

<s>Di qui, mentre il Cabeo andava fra le tenebre brancolando a cercar <lb></lb>l&#039;esatto misuratore dei secondi minuti, e Galileo conveniva non si potere <lb></lb>andar altro che brancolando, ricavava Giovan Marco la regola matemati­<lb></lb>camente sicura. </s>

<s>Supponiamo, diceva, di aver trovato che un pendolo, preso <lb></lb>di tal lunghezza che si giudichi alcun poco maggiore della richiesta, fa 1200 <lb></lb>vibrazioni in un&#039;ora, o 20 in un minuto, e si voglia ridurlo a farne preci­<lb></lb>samente 60 in quel medesimo tempo. </s>

<s>È certo che tanto dovrà essere più <lb></lb>frequente questo di quello, quanto 60 è maggior numero di 20, o tre è mag­<lb></lb>giore di uno. </s>

<s>Or perchè le altezze dei pendoli stanno, secondo il dimostrato <lb></lb>teorema, come i quadrati dei tempi, diremo che la maggiore altezza sta nel <lb></lb>presente caso alla minore, come il quadrato di tre sta al quadrato di uno, <lb></lb>e avremo perciò questa stessa minore altezza, ch&#039;è la conveniente a un oro­<lb></lb>logio a secondi, riducendo a un nono la nota altezza maggiore. </s>

<s>“ Sumatur <lb></lb>quaecumque productio fili, aliquanto tamen longior, quo minus cito a motu <lb></lb>conquiescat, numereturque huius escursus per spatium unius horae qua­<lb></lb>drantis, et sint v. </s>

<s>g. </s>

<s>300, eruntque spatio horae unius 1200. Quod si ergo <lb></lb>fiat ut quadratum temporis, nimirum trium secundorum, idest 9 ad 1, ita <lb></lb>longitudo fili ad minorem, erit huius motus aequalis secundo ” (ibid., fol. </s>

<s>63). </s></p><p type="main">

<s>Essendo il libro del Matematico di Praga rimasto in Italia e in Francia <lb></lb>per molti anni sconosciuto, non ebbero gl&#039;insegnamenti di lui quà dai monti <lb></lb>nessuna efficacia, ma pur la soluzion del problema del pendolo a secondi <lb></lb>dipendeva dalle dottrine di Galileo e del Baliani così immediata, che non <lb></lb>trovarono difficoltà i discepoli a conseguirla da quegli stessi principii, posti <lb></lb>così stabilmente dai loro proprii maestri. </s>

<s>Da commemorare fra quei disce­<lb></lb>poli uno dei primi è Benedetto Castelli, il quale, nel secondo libro Della mi­<lb></lb>sura delle acque correnti, dedicato manoscritto infino dal 1642 a Cosimo gran <lb></lb>principe di Toscana, proponeva per gli usi idrometrici il pendolo, di cui di­<lb></lb><figure id="id.020.01.2174.1.jpg" xlink:href="020/01/2174/1.jpg"></figure></s></p><p type="caption">

<s>Figura 213<lb></lb>ceva “ si devono numerare le vibrazioni, <lb></lb>che si fanno mentre dura l&#039;opera, e saran­<lb></lb>no tanti minuti secondi, quando però il <lb></lb>filo sia lungo tre piedi romani ” (Bologna <lb></lb>1660, pag. </s>

<s>80). Il Mersenno poi, pubbli­<lb></lb>cando nel 1644 in Parigi il suo libro <emph type="italics"></emph>Co­<lb></lb>gitata physico-mathematica,<emph.end type="italics"></emph.end> così, a pro­<lb></lb>posito del pendolo misuratore del tempo, <lb></lb>in quella sua general prefazione, scriveva: “ Si enim filum illud AB (fig. </s>

<s>213) <pb xlink:href="020/01/2175.jpg" pagenum="418"></pb>tripedale fuerit, globuli, ad punctum G vel F aut aliud quodvis usque ad C vel <lb></lb>D erecti, recursus per semicircumferentiam DBC, tempus unius secundi <lb></lb>consumit, recursus vero a D ad B, vela C ad B, semisecundum ” (pag. </s>

<s>9). </s></p><p type="main">

<s>Tre piedi romani, ossia 0m, 885, e tre piedi parigini, ossia 0m, 972, son <lb></lb>misure del pendolo a secondi straordinariamente più giuste di quelle date <lb></lb>dal Cabeo pochi anni prima, della quale aggiustatezza è da riconoscere la <lb></lb>ragione nell&#039;avere il Castelli e il Mersenno non operato a caso, ma dietro <lb></lb>quella regola matematicamente certa, che conseguiva, come dicemmo, dai <lb></lb>teoremi di Galileo e dai supposti del Baliani, immediata. </s>

<s>Non bastava però <lb></lb>la semplice regola matematica, sopra la quale proporre la soluzion teorica <lb></lb>del problema, ciò che solo erasi contentato di far Giovan Marco; bisognava <lb></lb>di più venire ai casi pratici, ed avere in effetto misurate le vibrazioni, fatte <lb></lb>da qualunque lunghezza di pendolo in una certa esatta durata di tempo. </s>

<s><lb></lb>Deve ciò necessariamente essere stato operato dal Castelli e dal Mersenno, <lb></lb>ma come non lo sappiamo: non sappiamo cioè se fu quel tempo misurato <lb></lb>dal moto delle stelle, come insegnava Galileo, o dai flussi delle polveri e dei <lb></lb>liquidi, o dagli appulsi delle ombre alle linee gnomoniche, secondo si crede <lb></lb>aver fatto il Cabeo. </s></p><p type="main">

<s>In quel medesimo tempo però del Castelli s&#039;esercitava intorno a ri­<lb></lb>durre alla sua pratica soluzione il problema del pendolo a secondi un no­<lb></lb>stro insigne Sperimentatore, che ne lasciò pubblica e particolare notizia del <lb></lb>modo, e che, sebben avverso per istituto, si professava nulladimeno in quel <lb></lb>caso anch&#039;egli discepolo di Galileo. </s>

<s>Giovan Batista Riccioli, proponendosi nel <lb></lb>II libro del I tomo dell&#039;Almagesto nuovo di trattar delle oscillazioni dei pen­<lb></lb>doli, e delle loro applicazioni alla misura dei tempi, concludeva così le brevi <lb></lb>parole premesse nel cap. </s>

<s>XX al suo trattatello: “ Quae igitur, per meipsum, <lb></lb>et ope sociorum, ad satietatem usque expertus sum, una cum selectis ex <lb></lb>Galileo et Baliano, recensebo ” (Bononiae 1651, pag. </s>

<s>84). </s></p><p type="main">

<s>Da Galileo e dal Baliani dice di aver principalmente appreso, e di aver <lb></lb>poi confermato co&#039;suoi proprii esperimenti che le varie lunghezze di due <lb></lb>pendoli stanno reciprocamente come i quadrati dei numeri delle vibrazioni, <lb></lb>d&#039;onde conseguono <emph type="italics"></emph>duo insignia problemata,<emph.end type="italics"></emph.end> il primo dei quali è che, dato <lb></lb>il numero delle vibrazioni e la lunghezza di un pendolo, si può di lì otte­<lb></lb>nerne la lunghezza dell&#039;altro. </s>

<s>Ricava di qui il Riccioli la regola per la mi­<lb></lb>sura del pendolo a secondi, ma non avrebbe potuto per sè medesima quella <lb></lb>stessa regola condurre all&#039;intento, senza premetter la soluzione di un altro <lb></lb>problema, qual era quello di ritrovare il tempo del primo mobile, o del giorno <lb></lb>solare conveniente a tutto il moto o alle singole vibrazioni di un pendolo <lb></lb>dato. </s>

<s>Conveniva dunque ricorrere a una misura di confronto, la quale si po­<lb></lb>teva ottener da quei modi, che più erano in uso appresso agli antichi, come <lb></lb>dalle pulsazioni delle arterie, dalle Clessidre, e dagli Orologi solari. </s>

<s>Volle il <lb></lb>Riccioli esaminar ciascuno di questi tre modi, che gli si porgevano per la <lb></lb>pratica facili e pronti, ma che poi ebbe a rifiutar, non essendo nessun di <lb></lb>loro trovato esatto. </s></p><pb xlink:href="020/01/2176.jpg" pagenum="419"></pb><p type="main">

<s>Quanto ai polsi, aveva letto nella proposizione LVIII dell&#039;<emph type="italics"></emph>Opus novu<gap></gap><emph.end type="italics"></emph.end><lb></lb>del Cardano che “ in hora sunt pulsus arteriarum quatuor millia ictuum <lb></lb>in homine prope temperamentum: (Operum, T. </s>

<s>V cit, pag. </s>

<s>489); alla qua <lb></lb>sentenza del celebre medico, e del fisico valoroso, parve sottoscrivere anche <lb></lb>il Keplero, quando, nell&#039;Epitome astronomica, per comparar le frazioni del <lb></lb>l&#039;ora equinoziale ai polsi dell&#039;uomo, concludeva, dopo ripetute osservazion <lb></lb>fatte intorno al loro numero in varii individui: “ Breviter, in una hora qua­<lb></lb>tuor millia, plus minus ” (Lentiis 1618, pag. </s>

<s>279). Ma il Riccioli, riducendo <lb></lb>alle vibrazioni di un pendolo, fatte in un minuto, le pulsazioni osservate in <lb></lb>un gran numero di persone, appartenenti al suo proprio sodalizio; trovò che <lb></lb>differivano dalle 50 alle 85. Pensò in tale incertezza di fare esperienza delle <lb></lb>Clessidre, ma, comparate anch&#039;esse con le vibrazioni di un pendolo, fatte in <lb></lb>un quarto d&#039;ora, trovò che ne rispondevano di quelle stesse vibrazioni ora <lb></lb>più ora meno, ond&#039;è che, sperando di conseguire una maggiore esattezza, <lb></lb>si dette, insieme col p. </s>

<s>Francesco Maria Grimaldi, a costruire, con la mag­<lb></lb>gior possibile diligenza, un orologio solare. </s>

<s>“ Sed quia umbrae ad lineas <lb></lb>horarias appulsus non potest discerni adeo axacte, ut non formidemus de <lb></lb>aliquorum secundorum errore, ideo, dimisso hoc modo, ad alios me con­<lb></lb>tuli ” (Almag. </s>

<s>Novi, T. </s>

<s>I cit., pag. </s>

<s>86). </s></p><p type="main">

<s>I modi, a cui s&#039;ebbe finalmente a rivolgere il Riccioli furon quelli che <lb></lb>erano stati proposti da Galileo, e i tre o quattro amici pazienti, ch&#039;egli ri­<lb></lb>chiedeva all&#039;operazione, e che rimasero in vita sua non più che una lusin­<lb></lb>ghiera speranza, gli trovò il Riccioli stesso fra&#039;suoi più giovani confratelli. </s>

<s><lb></lb>Ne scelse fra questi nove, ch&#039;egli addestrò con gesuitica disciplina, e dal <lb></lb>mezzogiorno del dì 2 Aprile 1642 al mezzogiorno del di appresso, gli tenne <lb></lb>vigili in assidua opera diligente a contare il numero delle vibrazioni fatte <lb></lb>nelle 24 ore da un pendolo, lungo 3972 centesime di oncia di piede romano <lb></lb>antico. </s>

<s>Si davano la muta di mezz&#039;ora in mezz&#039;ora, e per evitar la lunga <lb></lb>pronunzia dei numeri più grossi gettavano, a ogni sessanta vibrazioni con­<lb></lb>tate, una fava o altro calcolo in una cestella. </s>

<s>Si trovò dunque, alla fine del­<lb></lb>l&#039;operazione, riducendo il giorno solare al sidereo, che un calcolo, ossia ses­<lb></lb>santa vibrazioni, erano state fatte dal pendolo in 3576 minuti terzi. </s></p><p type="main">

<s>Così fatto, non bisognava altro a risolvere il problema della lunghezza <lb></lb>del pendolo a secondi, che applicare alla regola teorica i numeri trovati. </s>

<s>E <lb></lb>perchè, chiamata L la lunghezza del pendolo arbitrario, ed N il numero delle <lb></lb>vibrazioni da lui fatte in un certo tempo; chiamata L&#039;la cercata lunghezza <lb></lb>del pendolo a secondi, ed N′ il numero delle vibrazioni, che in quel mede­<lb></lb>simo tempo si vorrebbe che fosser fatte da lui; la detta regola è espressa <lb></lb>da L′=LN2/N.2, facendosi dunque L=3867, N=60, N′=3576/60, s&#039;ebbe <lb></lb>L′=3867X36002/35762. </s>

<s>“ Ergo, si quadratum numeri 3600, quod est 12,960,000, <lb></lb>ducatur per altitudinem centesimarum 3867, fiet summa 50,416,320,000, quae <lb></lb>divisa per quadratum tertiorum 3576, qnod est 12,787,776, relinquit cente-<pb xlink:href="020/01/2177.jpg" pagenum="420"></pb>simas unciarum 3927; hoc est pedes 3, uncias 3, et 27/100 ” (ibid., pag. </s>

<s>87). <lb></lb>E tale è, secondo il Riccioli, la precisa lunghezza del pendolo misurator dei <lb></lb>secondi. </s></p><p type="main">

<s>Se il piede romano antico fosse precisamente tale, quale ce lo danno <lb></lb>le comuni Tavole di riduzione, corrispondente cioè a 0m, 295, un dodicesimo <lb></lb>di lui, ossia un&#039;oncia, equivarrebbe a 0m, 025, presso a poco, e un cente­<lb></lb>simo d&#039;oncia a 0m, 00025; cosicchè 3927 centesime, quante ha trovato il <lb></lb>Riccioli dovere andar lungo il pendolo oscillante a ogni secondo, tornereb­<lb></lb>bero prossimamente 0m, 98175. Non siam certi però se quali le Tavole ce <lb></lb>le danno fossero le riduzioni esatte del piede romano antico, secondo il Ric­<lb></lb>cioli, il quale ne trattò particolarmente nel XII libro della Geografia nuova <lb></lb>riformata, designandolo col nome proprio di <emph type="italics"></emph>Piede vespasianeo.<emph.end type="italics"></emph.end> Ma nel mar­<lb></lb>gine inferiore della pag. </s>

<s>58 del I tomo dell&#039;Almagesto esibì, della metà di <lb></lb>lui, la precisa lunghezza lineare, scrivendo: “ Est autem vera longitudo se­<lb></lb>mipedis romani antiqui quantam vides in sequenti schemate R. ” La lun­<lb></lb>ghezza R, quivi rappresentata, è divisa in sei parti equivalenti alle sei once, <lb></lb>sopra le quali riportata, con la maggior diligenza possibile, una riga, ci parve <lb></lb>che corrispondessero ciascuna a 0m, 026 prossimamente. </s>

<s>D&#039;onde parrebbe che <lb></lb>le 3927 centesime si dovessero ridurre a 1m, 02102, ch&#039;è misura alcun poco <lb></lb>maggiore di quell&#039;altra ricavata dalle Tavole di riduzione. </s></p><p type="main">

<s>Consistendo lo strumento, usato all&#039;operazione, in un globo di ferro <lb></lb>sospeso a una catena di ferro, e resultandone perciò un pendolo composto, <lb></lb>non si possono le sopra calcolate misure, in qualunque modo ridotte, rife­<lb></lb>rire a quelle convenienti al pendolo semplice, le quali si sa che, per la lati­<lb></lb>tudine di Bologna, sono 0m, 993. Ma comunque sia aveva ragione il Riccioli <lb></lb>di compiacersi, non solo d&#039;essere stato egli il primo, ma di aver dato, della <lb></lb>lunghezza del pendolo a secondi, la misura più giusta di qualunque altro <lb></lb>s&#039;esercitasse a calcolarla in quel tempo o poco dipoi. </s>

<s>“ Gavisus sum autem <lb></lb>cum, post aliquot annos, audivi perpendiculi oscillationes ab aliis Astrono­<lb></lb>mis adhibitas, nimirum a Michaele Florentio Langreno, ut ex literis ad me <lb></lb>ab ipso datis didici, a Gottefrido Vendelino, a p. </s>

<s>Athanasio Kirchero, a Mer­<lb></lb>senno et aliis, sed non constat omnes aeque accuratos fuisse in mensuris <lb></lb>perpendiculi determinandis. </s>

<s>Nam, ut una vibratio uni secundo temporis ae­<lb></lb>quivaleat, Mersennus requirit funiculum pedum 3, sed parisiensium. </s>

<s>Kir­<lb></lb>cherus autem filum 3 pedum cum dimidio, non adiecto pondere, cui fere <lb></lb>subscribit Vendelinus ” (ibid., pag. </s>

<s>88). Le cause dell&#039;incertezza e dell&#039;er­<lb></lb>rore, dipendenti principalmente dal non saper determinare il centro del­<lb></lb>l&#039;oscillazione, e dal reputar le vibrazioni maggiori isocrone alle minori, erano <lb></lb>a tutti questi sperimentatori comuni, non eccettuato lo stesso Riccioli, il <lb></lb>quale si dilungò nonostante dal vero assai meno degli altri, per la incom­<lb></lb>parabile diligenza da lui usata nelle osservazioni. </s></p><pb xlink:href="020/01/2178.jpg" pagenum="421"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Al Riccioli dunque si debbono, intorno agli usi del pendolo, attribuire <lb></lb>quei meriti, che un opinione universalmente invalsa attribuisce a Galileo, <lb></lb>l&#039;opera del quale in proposito ci ha mostrato la storia essere stata incredi­<lb></lb>bilmente debole e scarsa. </s>

<s>Del difetto, che ritrovavasi negli insegnamenti del <lb></lb>Maestro, n&#039;ebbero a risentire anche i primi Discepoli, i quali è notabilis­<lb></lb>sima cosa che, esercitandosi così valorosamente in svolgere e in confermare <lb></lb>i varii teoremi dei movimenti locali, non promovessero nemmen d&#039;un passo, <lb></lb>rispetto al pendolo, i principii galileiani. </s>

<s>Svolgendo infatti i manoscritti e i <lb></lb>pubblici trattati del Castelli, del Renieri, del Cavalieri, del Nardi e di simili <lb></lb>altri, non ci siamo abbattuti mai a trovare in essi una proposizione mecca­<lb></lb>nica intorno a quello argomento, e il Torricelli stesso, nel suo celebre trat­<lb></lb>tato, non fa del moto dei gravi penduli da fili nemmeno un semplice motto. </s>

<s><lb></lb>Solamente ci è occorso, in consultare i manoscritti di lui, di notare una pro­<lb></lb>posizione, delle feconde conseguenze della quale però non par che si cu­<lb></lb>rasse l&#039;Autore, contento a considerarne alcuna della minore importanza. </s>

<s>È <lb></lb>la detta proposizione così messa in formula, e così dimostrata: </s></p><p type="main">

<s>“ Quod libet pondus a qualibet potentia moveri; vel nullum pondus <lb></lb>pendens tam magnum esse, ut ab omni minima potentia non moveatur. </s>

<s>” <lb></lb><figure id="id.020.01.2178.1.jpg" xlink:href="020/01/2178/1.jpg"></figure></s></p><p type="caption">

<s>Figura 214</s></p><p type="main">

<s>“ Sit pondus A (fig. </s>

<s>214) suspensum filo BA, <lb></lb>intelligaturque pondus esse ut ipsa BA. </s>

<s>Detur <lb></lb>iam potentia BC, et ducatur perpeudiculum CD: <lb></lb>dico pondus A a data potentia moveri usque in <lb></lb>D. </s>

<s>Ducatur tangens FDE, horizontalis FH ubicu­<lb></lb>mque, et perpendicularis EH ubicumque. </s>

<s>Eritq­<lb></lb>ue, ut BD ad BC, ita FE ad EH. </s>

<s>Ergo pondus <lb></lb>sustinetur a potentia in D, puncto plani; quare et­<lb></lb>iam in D, puncto quadrantis, et propterea in <lb></lb>quolibet puncto arcus AD movetur ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XXXVII, fol. </s>

<s>97). </s></p><p type="main">

<s>Sembrava che dovesse di quì concluderne <lb></lb>il Torricelli quel corollario importante, che avea condotto Giovan Marco a <lb></lb>instituire le prime teorie dei pendoli, che cioè, essendo BD a BC come FE <lb></lb>ad EH, il peso pendulo nel perpendicolo A sta allo stesso pendolo, rimos­<lb></lb>so nella posizione D, come il seno totale sta al seno dell&#039;angolo dell&#039;incli­<lb></lb>nazione. </s>

<s>Ma, come dicemmo, non ha di una tal conclusione l&#039;Autore nem­<lb></lb>meno il minimo pensiero. </s></p><p type="main">

<s>Notabile è che Niccolò Aggiunti, in una Nota pubblicata dal Nelli nel <lb></lb>suo <emph type="italics"></emph>Saggio di storia letteraria,<emph.end type="italics"></emph.end> si fosse qualche anno prima proposto di di­<lb></lb>mostrar questo medesimo del Torricelli, e nel medesimo modo, per servir­<lb></lb>sene come lemma a concludere il suo assunto, che “ se un pendolo grave sarà <pb xlink:href="020/01/2179.jpg" pagenum="422"></pb>rimosso dal suo perpendicolo durerà a moversi alternamente in perpetuo ” <lb></lb>(Lucca 1759, pag. </s>

<s>89). L&#039;intenzion dell&#039;Autore era quella di confermar con <lb></lb>matematiche ragioni ciò che aveva semplicemente asserito come probabile <lb></lb>Galileo, nella giornata II Dei massimi sistemi (Alb. </s>

<s>I, 250), ma si poteva <lb></lb>pure utilmente promovere il teorema a dimostrare altre proprietà mecca­<lb></lb>niche del pendolo, ciò che qui trascura di fare anche l&#039;Aggiunti. </s></p><p type="main">

<s>I primi esercizi, intorno a questo così negletto argomento, fatti nella <lb></lb><figure id="id.020.01.2179.1.jpg" xlink:href="020/01/2179/1.jpg"></figure></s></p><p type="caption">

<s>Figura 215<lb></lb>Scuola galileiana, incominciano dal Viviani, il quale ci <lb></lb>lasciava fra i suoi manoscritti questo notabilissimo do­<lb></lb>cumento: “ La violenza che patisce il filo AB (fig. </s>

<s>215), <lb></lb>essendo stirato dal grave A, credo che sia tale, quale <lb></lb>è il momento del medesimo grave, movendosi per il <lb></lb>piano BA, cioè che la forza fatta dal grave al filo nel <lb></lb>luogo AB, alla forza fatta al filo nel luogo BC, che è <lb></lb>la forza totale, sia come il momento del medesimo grave <lb></lb>sopra un piano inclinato quanto BA, al momento totale <lb></lb>per la perpendicolare BC. </s>

<s>Credo ancora che la somma <lb></lb>dei due momenti del grave A, l&#039;uno per la dirittura <lb></lb>del filo BA, l&#039;altro per la tangente AE, sia uguale al <lb></lb>momento totale. </s>

<s>Inventa un modo per esperimentarlo ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CXIII, fol, 30 a tergo). </s></p><p type="main">

<s>Tanto senti il Viviani al bisogno la Matematica inesperta, che volle aver <lb></lb>refugio nell&#039;esperienza. </s>

<s>E che cosa gli doveva l&#039;esperienza dimostrare? </s>

<s>que­<lb></lb>sto nè più, nè meno: che cioè la somma dei momenti parziali è uguale al <lb></lb>momento totale. </s>

<s>Ora, si risovverranno i Lettori delle famose obiezioni del <lb></lb>Vanni, dietro le quali si tirerà la memoria quell&#039;altre analoghe parole, la­<lb></lb>sciateci scritte dallo stesso Viviani, a proposito del momento dei gravi so­<lb></lb>pra i piani inclinati: <emph type="italics"></emph>credo che il momento totale sia uguale in potenza <lb></lb>al momento gravitativo, e al momento discensivo insieme presi.<emph.end type="italics"></emph.end> La falla­<lb></lb>cia, che s&#039;asconde in quella parola <emph type="italics"></emph>potenza,<emph.end type="italics"></emph.end> è nota oramai a chi ha letto <lb></lb>la nostra Storia, e dietro quella fallacia, felicemente dal caso emendata, riu­<lb></lb>scì all&#039;Autore delle <emph type="italics"></emph>Cinque proposizioni<emph.end type="italics"></emph.end> a dimostrar secondo qual propor­<lb></lb>zione, nelle discese oblique, si compartano i momenti dei gravi. </s></p><p type="main">

<s>Nel medesimo modo, e non già per via della esperienza, si sarebbe <lb></lb>forse potuto dar matematica dimostrazione di ciò che il Viviani credeva <lb></lb>esser vero nella proposta questione del pendolo, essendo la forza, che stira <lb></lb>il filo nella direzione AB, comparabile col momento gravitativo sul piano in­<lb></lb>clinato, come l&#039;altra forza, diretta secondo la tangente AE, è pur compara­<lb></lb>bile col momento discensivo. </s>

<s>Questo, nelle dette <emph type="italics"></emph>Cinque proposizioni<emph.end type="italics"></emph.end> si dimo­<lb></lb>stra proporzionale al seno, e quello al coseno dell&#039;angolo dell&#039;inclinazione, <lb></lb>ciò ch&#039;è pur vero, secondo che il Viviani credeva, nel pendolo, come si <lb></lb>dimostrerebbe, facendo uso del principio della composizion delle forze, im­<lb></lb>perocchè, se la perpendicolare AF, qual diagonale del parallelogrammo, rap­<lb></lb>presenta il momento totale, i lati AE, AD, che corrispondono ai momenti <pb xlink:href="020/01/2180.jpg" pagenum="423"></pb>parziali, stanno a quella stessa diagonale come il seno e il coseno dell&#039;an­<lb></lb>golo DAF, uguale all&#039;angolo dell&#039;inclinazione, stanno al seno totale. </s></p><p type="main">

<s>Si diceva che sarebbe il Viviani potuto riuscire a questa medesima con­<lb></lb>clusione importante dietro ciò ch&#039;era stato dimostrato da lui del momento <lb></lb>dei gravi sopra i piani inclinati, ma non siam certi che vi si provasse, e, <lb></lb>se dovessimo dare intorno a ciò il nostro giudizio, sarebbe che quella sua <lb></lb>scienza del pendolo si rimase, almeno per qualche tempo, un semplice <emph type="italics"></emph>credo.<emph.end type="italics"></emph.end><lb></lb>Or una tale incertezza nel Viviani, e negli altri più immediati discepoli di <lb></lb>Galileo, si contrappone, in modo che fa stupire, con la sicurezza della scienza <lb></lb>di Leonardo da Vinci, nei manoscritti del quale si trova, come si riferì a suo <lb></lb>luogo, dimostrato il teorema delle forze sollecitanti il pendolo, per ridurlo <lb></lb>alla sua prima stazione perpendicolare. </s>

<s>Ebbero, come quasi sempre, le spe­<lb></lb>culazioni principio dall&#039;esperienza, la quale, benchè sembri delicatissima, era <lb></lb>nonostante assai meglio dimostrativa di quell&#039;altra impossibile, che si pro­<lb></lb>poneva d&#039;inventare il Viviani. </s></p><p type="main">

<s>La figura disegnata a tergo del foglio 76 del Manoscritto G, e che noi <lb></lb><figure id="id.020.01.2180.1.jpg" xlink:href="020/01/2180/1.jpg"></figure></s></p><p type="caption">

<s>Figura 216<lb></lb>imitiamo nella figura 216, s&#039;illustra <lb></lb>da Leonardo con queste parole: “ Il <lb></lb>peso ventilante da destra a sinistra, <lb></lb>e da sinistra a destra, si fa tanto più <lb></lb>grave al suo appendiculo, d&#039;esso ap­<lb></lb>pendiculo, quanto esso appendiculo è <lb></lb>meno obliquo. </s>

<s>” E a tergo del seguente foglio 79 un&#039;altra Nota, nello stesso <lb></lb>proposito, così dice: “ Il grave ventilante, per qualunque aspetto, avrà tanto <lb></lb>più o men gravezza, intorno alla fronte che ha l&#039;asta della Bilancia, quanto <lb></lb>la congiunzione, che ha l&#039;appendiculo del peso col braccio della bilancìa, <lb></lb>sarà più vicino all&#039;angolo retto. </s>

<s>” Il modo dell&#039;esperienza è assai chiaro, <lb></lb>essendo alle due estremità A, C della Bilancia di braccia uguali, sostenuta <lb></lb>in B, penduli, da due fili di ugual lunghezza, i pesi uguali D, E. </s>

<s>Nella quiete, <lb></lb>o nella posizione verticale di questi pesi, permane l&#039;equilibrio, ma, rimosso <lb></lb>per esempio il peso D in F, l&#039;altro contrappeso E la vince, con tanto però <lb></lb>minor prevalenza, quanto l&#039;angolo FAD, fatto dall&#039;appendicolo FA con la <lb></lb>fronte A della Bilancia, è più vicino all&#039;angolo retto. </s></p><p type="main">

<s>Dimostrava dunque la bella e delicata esperienza che il grave in F pesa <lb></lb>meno sulla Bilancia che in D, ma secondo qual precisa proporzione si di­<lb></lb>minuisce il momento non era l&#039;esperienza per sè stessa atta a rivelarlo con <lb></lb>regola certa; ond&#039;è, che rivolgendosi a trattar la cosa con le leggi matema­<lb></lb>tiche del moto, si condusse Leonardo a specular quel teorema, da noi posto <lb></lb>a pagine 51 di questo tomo. </s>

<s>Deriva da quel teorema per corollario la pro­<lb></lb>porzione del moto di un grave cadente lungo un piano inclinato; propor­<lb></lb>zione conclusa in modo somigliantissimo a quello tenuto da Galileo, il quale <lb></lb>però, considerando il peso sostenuto dal braccio di una leva, piuttosto che <lb></lb>da un filo, si precluse, a dimostrar le proprietà meccaniche del pendolo, quel <lb></lb>trapasso, che felicemente fu fatto da Leonardo. </s></p><pb xlink:href="020/01/2181.jpg" pagenum="424"></pb><p type="main">

<s>Venendo così la scienza galileiana dei pendoli a mancar del suo mec­<lb></lb>canico fondamento, rimase tutta raccomandata alle esperienze, sterili per sè <lb></lb>medesime d&#039;ogni frutto migliore. </s>

<s>I frutti infatti che s&#039;ebbero, e si notò an­<lb></lb>che altrove, furono alcune curiose applicazioni alla Musica, e alla misura <lb></lb>delle altezze, ciò che veniva dannosamente a sedur col diletto, e a traviar <lb></lb>dall&#039;utile, come si può confermare da questo esempio. </s>

<s>A un Matematico di <lb></lb>Roma, allettato da quel modo che s&#039;insegna nel primo dialogo Delle due <lb></lb>nuove scienze, per dedur dalle semplici vibrazioni la lunghezza di una corda <lb></lb>pendente; venne un giorno il capriccio d&#039;inventar qualche altra cosa di si­<lb></lb>mile, per misurar le altezze, servendosi di un filo. </s>

<s>Non riuscitogli però il <lb></lb>desiderio, si rivolse a Michelangiolo Ricci, il quale dava così, del modo come <lb></lb>avea sodisfatto l&#039;amico, la seguente notizia in una lettera, scritta il dì 18 Giu­<lb></lb>gno 1643 al Torricelli: </s></p><p type="main">

<s>“ Li giorni addietro un amico mio voleva misurare certe altezze, con <lb></lb>l&#039;aiuto di un filo, e venne a consultare meco, per trovar qualche mezzo alla <lb></lb><figure id="id.020.01.2181.1.jpg" xlink:href="020/01/2181/1.jpg"></figure></s></p><p type="caption">

<s>Figura 217<lb></lb>consecuzione del suo intento. </s>

<s>Fattavi un poco di ri­<lb></lb>flessione, dimostrai che il filo ABC (fig. </s>

<s>217), essendo <lb></lb>attaccato a due capi, e che per esso scorra qualche <lb></lb>peso, detto peso incurverà il filo in angolo, facendo <lb></lb>gli angoli ABE, CBD uguali sopra la retta EBD, tirata <lb></lb>nel punto B parallela all&#039;orizzonte. </s>

<s>L&#039;avvertenza di <lb></lb>questo fu bastante all&#039;amico per conseguire il suo <lb></lb>pensiero, ed alla sagacità di V. S. l&#039;aver detto questo sarà più che troppo, <lb></lb>per farle intendere dimostrativamente che la cosa vada così ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XLII, fol. </s>

<s>136). </s></p><p type="main">

<s>Il teorema si sovverranno i Lettori essere stato dimostrato da Leonardo, <lb></lb>in quelle Note da noi trascritte a pagine 68 e 69 di questo tomo, ond&#039;è che <lb></lb>molti stupiranno del fortuito incontro fra il semplice Artista di Vinci, e il <lb></lb>valoroso Matematico di Roma. </s>

<s>Bene è però più da stupire che il Discepolo <lb></lb>di Galileo facesse argomento unico e principale, nella dottrina dei pesi pen­<lb></lb>denti da fili, quel che il Discepolo del Nemorario riguardava come cosa se­<lb></lb>condaria, e data quasi per mescere all&#039;utile qualche diletto. </s>

<s>Ma qual utile, <lb></lb>a promover la scienza, ricavasse il Ricci da quel suo teorema, lo lasciamo al <lb></lb>giudizio di chi rimedita i fatti di questa Storia. </s></p><p type="main">

<s>Sarebbe superfluo l&#039;intrattener più lungamente il discorso a dimostrar <lb></lb>che, nella prima metà del secolo XVII, veniva la vera scienza del moto dei <lb></lb>gravi per gli archi dei cerchi a mancar nella Scuola galileiana, nè par si <lb></lb>accorgessero i seguaci di lei del difetto, se non allora che sentiron vivo il <lb></lb>bisogno d&#039;invocare i principii di quella stessa scienza a regolar gli strumenti <lb></lb>misuratori esatti dei minimi tempi. </s>

<s>Ritorniamo con la memoria a Firenze, <lb></lb>quando il principe Leopoldo dei Medici poneva il Viviani e il Borelli quasi <lb></lb>pietre angolari, prima di dar forma all&#039;edifizio della gloriosa sperimentale <lb></lb>Accademia. </s>

<s>Riducendosi principalmente gl&#039;istituti di lei a promovere la Fi­<lb></lb>sica galileiana, si fecero primi soggetti all&#039;esperienze le misure della velo-<pb xlink:href="020/01/2182.jpg" pagenum="425"></pb>cità del suono e della luce. </s>

<s>Ma quali si avevano allora strumenti, che ser­<lb></lb>vissero all&#039;uso? </s>

<s>Erano è vero infin dal 1651 resi pubblicamente noti gli <lb></lb>strumenti, e i metodi del Riccioli, ma riuscivano difficilmente praticabili agli <lb></lb>osservatori o poco attenti o poco esperti, e in conclusione tornavano fallaci. </s></p><p type="main">

<s>Il fatto, di cui s&#039;ebbe finalmente a persuadere lo stesso Viviani, che <lb></lb>cioè non tutte le vibrazioni d&#039;un medesimo pendolo sono esattamente uguali, <lb></lb>ma che le minori si spediscono in tempo sensibilmente più breve delle mag­<lb></lb>giori; gli fece, verso il 1656, immaginare quell&#039;Orologio a ruote, mosse dal­<lb></lb>l&#039;elaterio di una molla, e regolate dal pendolo, di cui, nel secondo capitolo <lb></lb>del nostro primo tomo, fu narrata la storia. </s>

<s>L&#039;Huyghens meditava allora <lb></lb>intorno a una simile invenzione, ch&#039;ebbe pubblicità in quel medesimo <lb></lb>anno 1657, quando si metteva già in uso il Cronometro fiorentino. </s>

<s>La no­<lb></lb>tizia, che è per riuscire delle più importanti nella Storia della Meccanica, e <lb></lb>delle invenzioni italiane, vuol trattener qui, ne&#039;suoi particolari, il nostro <lb></lb>discorso. </s></p><p type="main">

<s>L&#039;esattezza dello strumento, che s&#039;immaginava di costruire il Viviani, <lb></lb>dipendeva dalla misura esatta dei pendoli, che si dovevano adattare, e so­<lb></lb>stituir l&#039;uno all&#039;altro, secondo che si voleva, per esempio un secondo per <lb></lb>ogni vibrazione, o qualche altra parte osservabile di lui. </s>

<s>Con qual regola <lb></lb>dunque si dovrebbero precisare queste misure? </s>

<s>Aveva il Riccioli insegnata <lb></lb>già quella regola, e l&#039;aveva altresi messa in pratica, ma, poniamo che fosse <lb></lb>vera, non aveva altro suffragio che i fatti, dal Riccioli stesso trovati riscon­<lb></lb>trar con l&#039;esperienze di Galileo e del Baliani. </s>

<s>Se fu sentito mai quel difetto <lb></lb>della scienza galileiana, che fu più volte da noi lamentato, si fu questa una <lb></lb>delle più efficaci occasioni per dover riconoscerlo, e per risolversi ad emen­<lb></lb>darlo. </s>

<s>Si trattava dall&#039;altra parte di applicar quella regola a risolvere un <lb></lb>problema di una tal precisione, da non sperar mai di conseguirla, senza il <lb></lb>magistero supremo della Geometria. </s></p><p type="main">

<s>I primi esercizi, fatti dal Viviani a geometrizzare quel che nel I dia­<lb></lb>logo delle Nuove scienze si dice essere stato per esperienza scoperto intorno <lb></lb>ai tempi delle oscillazioni, in relazione con la lunghezza dei pendoli; appa­<lb></lb>riscono da una di quelle postille alla copia dell&#039;edizione di Leyda, che è il <lb></lb>tomo IX della Parte V de&#039;Manoscritti di Galileo. </s>

<s>Ivi, a piè della pag. </s>

<s>97, <lb></lb>così, di mano propria del Viviani, si legge: “ Adunque, di due pendoli dise­<lb></lb>guali, il tempo per l&#039;arco dell&#039;uno, al tempo per l&#039;arco dell&#039;altro, sta come <lb></lb>il tempo pel seno dell&#039;uno, al tempo pel seno di un arco simile dell&#039;altro, <lb></lb>i quali seni formano un sol piano inclinato, e per i quali i mobili natural­<lb></lb>mente discendenti scorrono in tempi, che hanno suddupla proporzione di <lb></lb>essi seni. </s>

<s>Or, perchè questi son proporzionali ai loro raggi, che sono le lun­<lb></lb>ghezze dei pendoli, dunque, ecc. </s>

<s>” </s></p><p type="main">

<s>Supposto ben dimostrato il principio, la conseguenza è matematicamente <lb></lb>vera, e si somiglia molto alla proposizione di Giovan Marco, resa molto più <lb></lb>semplice, e più bella. </s>

<s>Imperocchè, se il tempo per BD (fig. </s>

<s>218) sta al tempo <lb></lb>per BE come il tempo per BF sta al tempo per BG, i quali tempi stanno <pb xlink:href="020/01/2183.jpg" pagenum="426"></pb>come le radici degli spazi; essendo la radice di BF alla radice di BG, come <lb></lb><figure id="id.020.01.2183.1.jpg" xlink:href="020/01/2183/1.jpg"></figure></s></p><p type="caption">

<s>Figura 218<lb></lb>la radice di AB è alla radice di CB, ne vien per legit­<lb></lb>tima conseguenza che, come tali radici, le quali son le <lb></lb>lunghezze dei pendoli; così stieno i tempi delle vibra­<lb></lb>zioni per gli archi simili. </s></p><p type="main">

<s>Ma come i tempi per gli archi simili sieno pro­<lb></lb>porzionali ai tempi per i seni corrispondenti, non si <lb></lb>accenna da qual principio lo concluda il Viviani. </s>

<s>Forse <lb></lb>proponevasi di darne altrove, o in altro tempo, la dimo­<lb></lb>strazione, la quale doveva, come nel trattato di Giovan <lb></lb>Marco, dipendere dal teorema, che il momento totale <lb></lb>del pendolo nel perpendicolo sta al momento parziale <lb></lb>dello stesso pendolo, fuori del perpendicolo, come il seno <lb></lb>totale sta al seno dell&#039;angolo dell&#039;inclinazione. </s>

<s>Ma per­<lb></lb>chè intorno a questo teorema il Viviani stesso versava, come vedemmo, in <lb></lb>qualche incertezza rispetto al compartire giustamente il momento totale nel <lb></lb>discensivo per la tangente all&#039;arco, e nel gravitativo, secondo la direzione <lb></lb>del filo; è assai probabile che la dimostrazione, accennata nella detta postilla, <lb></lb>si rimanesse ivi incompiuta, e che pensasse l&#039;Autore di sostituirle quell&#039;altra <lb></lb>meno matematica e più lunga, nella quale c&#039;incontreremo fra poco. </s></p><p type="main">

<s>Ma intanto la Geometria, nel definir quelle relazioni tra le semplici li­<lb></lb>nee e i quadrati, rivelava alla mente del Viviani l&#039;equazione della parabola, <lb></lb>per la quale si significherebbero, in nuovo modo elegante, le meccaniche <lb></lb>proprietà dei pendoli, facendo alle ordinate rappresentare i tempi delle vi­<lb></lb>brazioni, e alle ascisse le lunghezze dei fili. </s>

<s>Del qual pensiero, appena sov­<lb></lb><figure id="id.020.01.2183.2.jpg" xlink:href="020/01/2183/2.jpg"></figure></s></p><p type="caption">

<s>Figura 219<lb></lb>venutogli, lasciò scritta il Viviani stesso la <lb></lb>seguente memoria: “ Se le linee OA, OC, <lb></lb>OE (fig. </s>

<s>219) rappresentano i tempi delle <lb></lb>vibrazioni di diverse lunghezze, le linee AB, <lb></lb>GD, HF, ecc., del trilineo parabolico ABI, <lb></lb>di cui vertice sia I, rappresentano le lun­<lb></lb>ghezze dei fili: cioè, se la vibrazione di un <lb></lb>tempo AO vuole lunghezza di filo quanto <lb></lb>AB, la vibrazione del tempo CO vorrà lunghezza del filo quanto GD, ed il <lb></lb>tempo EO lunghezza di filo quanto HF, e questo perchè le lunghezze dei fili <lb></lb>sono tra loro come i quadrati dei tempi delle vibrazioni, siccome le linee AB, <lb></lb>GD, HF sono tra loro, <emph type="italics"></emph>ob parabolam,<emph.end type="italics"></emph.end> come i quadrati delle AO, CO, EO, ecc. </s>

<s><lb></lb>Di qui si potrà cavare la fabbrica di uno strumento, che dia le lunghezze <lb></lb>de&#039;fili dei cercati tempi ” (MSS. Cim., T. X, fol. </s>

<s>49). </s></p><p type="main">

<s>L&#039;idea di questo strumento, così sovvenuta, fece nella mente del Vi­<lb></lb>viani definir la forma del Cronometro, per servire all&#039;esperienze della ve­<lb></lb>locità del suono e della luce, il qual Cronometro, come sappiamo, indicava <lb></lb>sopra la medesima mostra variamente i tempi, secondo le lunghezze varie <lb></lb>dei fili applicati. </s>

<s>Quello strumento dunque, da trovar giuste e speditamente <pb xlink:href="020/01/2184.jpg" pagenum="427"></pb>così fatte lunghezze, era parte essenziale dell&#039;invenzione, e fu perciò l&#039;In­<lb></lb>ventore sollecito di mandar l&#039;idea conceputa ad effetto. </s>

<s>Abbiamo il docu­<lb></lb>mento di ciò nella seguente scrittura, nella quale la descrizion del Trilineo <lb></lb>parabolico si fa dipendere dai suoi proprii principii matematici, sostituiti alle <lb></lb>semplici e fuggitive osservazioni di Galileo. </s></p><p type="main">

<s>“ Il Galileo, nel primo dialogo delle due nuove scienze meccaniche, a <lb></lb>faccia 96 dell&#039;edizione di Leida del 1638, dice, in persona del Salviati, così: <lb></lb><emph type="italics"></emph>Quanto poi alla proporzione de&#039;tempi delle uniche vibrazioni di mobili, <lb></lb>pendenti da fila di differente lunghezza, le replicate esperienze, colle quali <lb></lb>ciascuno può sodisfarsi, mi han dimostrato che sono essi tempi in propor­<lb></lb>zione suddupla delle lunghezze delle fila, ovver le lunghezze sono in dupla <lb></lb>proporzione dei tempi, cioè sono come i quadrati di essi tempi.<emph.end type="italics"></emph.end> Tal pro­<lb></lb>prietà non la fortifica l&#039;Autore con alcuna dimostrazione, bastandogli forse <lb></lb>l&#039;esperienza, ch&#039;ei ne doveva aver fatta con diverse proporzioni cognite di <lb></lb>fili, e come di fatti riesce, e ciascuno può con somma facilità assicurarsene. </s>

<s><lb></lb>Nondimeno, per tentar di convalidarla con qualche ragione, almeno proba­<lb></lb>bile, se non chiarissima, io la discorro in tal guisa: ” </s></p><p type="main">

<s>“ TEOREMA I. — Considerinsi AB, AC (fig. </s>

<s>220) essere due differenti <lb></lb><figure id="id.020.01.2184.1.jpg" xlink:href="020/01/2184/1.jpg"></figure></s></p><p type="caption">

<s>Figura 220<lb></lb>fila, in un medesimo perpendicolo, con gravi <lb></lb>eguali appesi alle loro estremità B, C, ed al­<lb></lb>lontanati dal medesimo perpendicolo per ar­<lb></lb>chi simili BD, CE, non maggiori degli archi <lb></lb>BF, CG de&#039;quadranti dei loro cerchi. </s>

<s>La­<lb></lb>scinsi da D e da E in loro libertà: dico <lb></lb>prima che il tempo della vibrazione del pen­<lb></lb>dolo AD, per l&#039;arco DB, al tempo della vi­<lb></lb>brazione del pendolo AE, per l&#039;arco simile <lb></lb>EC, ha suddupla proporzione della lunghezza <lb></lb>del proprio filo AD, alla lunghezza del pro­<lb></lb>prio filo AE. ” </s></p><p type="main">

<s>“ Imperocchè, essendo FB, GC archi simili, e similmente posti, e pro­<lb></lb>porzionali ai loro semidiametri AB, AC, posti nella medesima dirittura; par <lb></lb>ragionevole che il tempo della caduta di un mobile da A in B, al tempo <lb></lb>della scorsa del medesimo per l&#039;arco del proprio quadrante, abbia da avere <lb></lb>in tutto simile proporzione a quella della caduta del mobile, pel raggio mi­<lb></lb>nore da A in C, al tempo della scorsa per l&#039;arco GC del proprio quadrante, <lb></lb>non vi essendo ragione per cui tali proporzioni debbano differire. </s>

<s>” </s></p><p type="main">

<s>“ E similmente par ragionevole che, essendo tanto gli archi FB, GC, <lb></lb>che gli archi DB, EC, simili e similmente posti, il tempo della scorsa del <lb></lb>mobile per l&#039;arco FB del quadrante maggiore, al tempo della scorsa per <lb></lb>l&#039;arco proprio DB, abbia da esser la stessa che quella del tempo della scorsa <lb></lb>per l&#039;arco GC del quadrante minore, al tempo della scorsa pel proprio arco <lb></lb>EC, proporzionale al GC, come il DB all&#039;FB; onde verrebbe per l&#039;ugualità <lb></lb>che il tempo per AB, al tempo per DB, fosse come Il tempo per AC, al <pb xlink:href="020/01/2185.jpg" pagenum="428"></pb>tempo per l&#039;arco EC: e, permutando, che il tempo per AB, al tempo per <lb></lb>AC, stesse come il tempo per l&#039;arco DB, al tempo per l&#039;arco EC. </s>

<s>Ma il <lb></lb>tempo per AB al tempo per AC ha suddupla proporzione di AB ad AC; <lb></lb>adunque anche il tempo per DB, al tempo per EC, avrebbe suddupla pro­<lb></lb>porzione dell&#039;AB all&#039;AC, che son le lunghezze de&#039;fili dei pendoli. </s>

<s>Ma cia­<lb></lb>scuna vibrazione di ciascun di essi pendoli, larghe o strette che sieno, nel <lb></lb>proprio cerchio passa in tempi uguali, come la esperienza il dimostra, adun­<lb></lb>que par manifesto quanto senz&#039;altra prova asserì il Galileo, cioè che i tempi <lb></lb>hanno suddupla proporzione delle lunghezze delle fila, ovvero che le lun­<lb></lb>ghezze hanno dupla proporzione dei tempi, cioè sono come i quadrati dei <lb></lb>tempi. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>63). </s></p><p type="main">

<s>Soggiunge immediatamente il Viviani che questa bella proprietà, così <lb></lb>dimostrata, gli somministrò la fabbrica di quello strumento, di cui gli era <lb></lb>già venuta l&#039;idea, e che qui prosegue a descrivere con quelle stesse parole, <lb></lb>da noi trascritte a pag. </s>

<s>328, 29 del nostro primo Tomo. </s>

<s>A complemento <lb></lb>della qual descrizione aggiungeremo qui quel che suggerisce il Viviani per­<lb></lb>chè, chiunque non si trovasse altro a mano che una semplice riga e una <lb></lb>catenella, potesse, più facilmente e con maggior brevità, conseguire il me­<lb></lb>desimo intento. </s></p><p type="main">

<s>“ Ma con più brevità conseguiremo, egli dice, l&#039;istesso, senza macchina, <lb></lb>mediante una riga CD (fig. </s>

<s>221) la di cui metà CE sia divisa in 60 parti <lb></lb><figure id="id.020.01.2185.1.jpg" xlink:href="020/01/2185/1.jpg"></figure></s></p><p type="caption">

<s>Figura 221<lb></lb>eguali, da E sino in C, e mediante <lb></lb>ancora d&#039;un sol filo di catenuzza <lb></lb>formata di piccolissimi anelli. </s>

<s>Per­<lb></lb>chè, tenuta essa riga CD orizzontal­<lb></lb>mente, e fermato in C uno dei capi <lb></lb>del detto filo di catena, e questo <lb></lb>lasciato far la sacca sua naturale <lb></lb>CMHD, che forma sempre parabola, <lb></lb>fatto passar rasente il punto D, ed <lb></lb>allontanato talmente che di tal sacca <lb></lb>la massima altezza EF, la qual passa <lb></lb>pel punto di mezzo E, dov&#039;è il <lb></lb>numero 60, sia appunto uguale al <lb></lb>filo AB (del pendolo che batte i secondi) quivi presentato, e poi questo <lb></lb>portato or in G, al numero 30, or in L, al numero 20; le intersecazioni <lb></lb>H, M di esso filo colla catenuzza daranno, fuor della sacca, le lunghezze HI, <lb></lb>MN, che dovranno avere i pendoli cercati ” (ivi, fol. </s>

<s>64). </s></p><p type="main">

<s>Lo strumento era così ben preparato agli usi di prefinir le misure dei <lb></lb>pendoli, dietro i principii matematici dimostrati neì I Teorema, in cui è no­<lb></lb>tabile che sentisse il Viviani di aver dato ragione <emph type="italics"></emph>probabile,<emph.end type="italics"></emph.end> ma non chia­<lb></lb>rissima. </s>

<s>Questa confessata insufficienza conferma la nostra congettura, che <lb></lb>cioè quella prima dimostrazione, accennata a piè della pagina 97 dell&#039;edi­<lb></lb>zione di Leyda, rimanesse incompiuta, per non aversi certezza dei momenti, <pb xlink:href="020/01/2186.jpg" pagenum="429"></pb>in cui si comparte l&#039;assoluta gravità del pendolo, rimosso dalla stazion sua <lb></lb>perpendicolare. </s>

<s>Versando in tale incertezza, anche il Borelli non seppe pro­<lb></lb>porre altra dimostrazione, da quella che fu poi scritta in ordine la XCII nel <lb></lb>trattato <emph type="italics"></emph>De vi percussionis<emph.end type="italics"></emph.end> (Bononiae 1667, pag. </s>

<s>212, 13) e nella quale, dal <lb></lb>suppor, come il Viviani fa, ch&#039;essendo le lunghezze de&#039;raggi proporzionali <lb></lb>alle ampiezze degli archi, fossero altresì proporzionali i tempi, si concludeva <lb></lb>che questi per essi archi erano proporzionali alle radici delle altezze dei pen­<lb></lb>doli. </s>

<s>A confermar poi la somiglianza del processo dimostrativo, in ambedue <lb></lb>gli Autori, sovvien la considerazione che ambedue suppongono essere nello <lb></lb>stesso pendolo <emph type="italics"></emph>itus et reditus aequitemporaneos<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>212), e ciò con­<lb></lb>ferma che gli Accademici fiorentini non si persuasero delle disuguaglianze <lb></lb>delle libere vibrazioni, se non da poi che l&#039;ebbero comparate con quelle, <lb></lb>fatte sempre per uguale ampiezza d&#039;arco, nell&#039;Orologio. </s></p><p type="main">

<s>Di questo Orologio dunque era stata, nel Teorema I, speculata dal Vi­<lb></lb>viani la teoria, e non rimaneva altro, per metterlo in uso, che a trovar la <lb></lb>precisa lunghezza del filo AB (nella precedente figura) corrispondente a un <lb></lb>secondo. </s>

<s>Come gli stessi Accademici fiorentini risolvessero l&#039;importante pro­<lb></lb>blema lo vedremo tra poco, per non perder di mira quello stesso Viviani, <lb></lb>a cui preme di seguitare a dar dimostrazione delle conclusioni supposte da <lb></lb>Galileo, e specialmente di quella, che le lunghezze dei pendoli stanno reci­<lb></lb>procamente come i quadrati de&#039;numeri delle vibrazioni fatte nei medesimi <lb></lb>tempi. </s>

<s>Furono a quest&#039;effetto preparati altri due teoremi, ai quali si pre­<lb></lb>mette dall&#039;Autore un discorso, nelle sue prime parti da noi trascritto a <lb></lb>pag. </s>

<s>303, 304 del nostro I Tomo, ma che ora vogliam dar per compiuto, <lb></lb>affinchè possa chi legge paragonare i fiori del rettorico elogio con i frutti <lb></lb>della semplice Storia. </s></p><p type="main">

<s>“ Nella medesima età sua giovanile, prosegue dunque il Viviani a dire <lb></lb>di Galileo, quando studiava Filosofia, che fu intorno al 1580, si chiarì, col­<lb></lb>l&#039;aiuto di questo suo pendolo, della falsità di que&#039;due pronunziati di Ari­<lb></lb>stotile, con l&#039;un de&#039;quali egli afferma vedersi che due mobili di gravità di­<lb></lb>versa discendono per lo stesso mezzo con velocità proporzionali alle medesime <lb></lb>gravità loro; con l&#039;altro, che lo stesso mobile si muove per diversi mezzi <lb></lb>con velocità continuamente proporzionali alle loro densità e gravezze, facen­<lb></lb>done, per chiarirsi della verità del primo, varie esperienze nell&#039;aria, con di­<lb></lb>versi gravi lascìati cader nello stesso tempo dall&#039;altezza del campanile di Pisa, <lb></lb>e, per riscontro del secondo, varie altre prove nell&#039;aria e nell&#039;acqua, inda­<lb></lb>gata prima industriosamente la proporzione delle densità e gravità in specie <lb></lb>di tali fluidi. </s>

<s>” </s></p><p type="main">

<s>“ Da queste, e da mille altre fallacie degli scrittori antichi, scoperte dal <lb></lb>libero ed inventivo ingegno del nostro Accademico, veramente linceo; ebbe <lb></lb>la prima origine, e il natale in Toscana questa libertà di filosofare, ch&#039;egli <lb></lb>usò sempre, e che si propalò poi per Italia, e per tutte le Università del­<lb></lb>l&#039;Europa, dove in oggi tanto fiorisce, e con la quale si son fatti finora sì <lb></lb>gran progressi in ogni parte della Fisica, dell&#039;Astronomia, dell&#039;Anatomia, e <pb xlink:href="020/01/2187.jpg" pagenum="430"></pb>di ogni altra più nobile facoltà. </s>

<s>Ond&#039;è che meritamente l&#039;ingegnoso Gas­<lb></lb>sendo lo riconosce e commenda per padre della vera Filosofia, a confusione <lb></lb>di quegli ingrati Italiani, e di alcuni altri oltre a&#039;monti, i quali, benchè di <lb></lb>professione religiosa, non sapendo occultar la propria passione, gli si dimo­<lb></lb>strarono nemici capitalissimi con gli scritti e co&#039;fatti, stimati da loro a lui <lb></lb>sommamente pregiudicevoli, quantunque poi sien risultati in gloria al me­<lb></lb>mesimo, ed a loro di biasimo, e vituperio appresso i veri sapienti, e senza <lb></lb>passione.... Ma lasciando tale digressione, vengo alla dimostrazione delle <lb></lb>conclusioni supposte dal Galileo, e prima pongo il seguente Lemma: ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Se due grandezze omogenee ed eguali, sono divise in differente nu­<lb></lb>mero di parti eguali, il numero delle parti della prima, al numero delle <lb></lb>parti della seconda, sta reciprocamente come una sola parte della seconda <lb></lb>ad una sola parte della prima. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Siano AB, CD (fig. </s>

<s>222) le due date grandezze omogenee, eguali, <lb></lb><figure id="id.020.01.2187.1.jpg" xlink:href="020/01/2187/1.jpg"></figure></s></p><p type="caption">

<s>Figura 222<lb></lb>e la prima AB sia divisa in qualun­<lb></lb>que numero di parti eguali AE, EF, <lb></lb>FG, GH, HI, IL, LB, e la seconda CD <lb></lb>in altro qualunque numero di parti <lb></lb>uguali CM, MN, ND. </s>

<s>Dico che il nu­<lb></lb>mero delle parti della prima AB, al <lb></lb>numero delle parti della seconda CD, <lb></lb>sta come una sola parte CM della <lb></lb>seconda ad una sola parte AE della <lb></lb>prima. </s>

<s>” </s></p><p type="main">

<s>“ Essendo il numero delle parti in AB differente dal numero delle parti <lb></lb>in CD, pongasi che il numero maggiore sia in AB, ed al numero minore, <lb></lb>che è in BD, prendasi eguale il numero AG, talmente che tante parti eguali <lb></lb>siano in AG, che in CD. </s>

<s>Avrà dunque il numero delle parti in AB, al nu­<lb></lb>mero delle parti in CD, la medesima proporzione che il numero delle parti <lb></lb>in AB al numero delle parti in AG, cioè che la grandezza AB alla AG, cioè <lb></lb>che la grandezza CD, posta uguale alla AB, alla grandezza AG, cioè, che la <lb></lb>summultiplice grandezza CM alla ugualmente summultiplice grandezza AE, <lb></lb>che è quello che si doveva dimostrare ” (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>62). </s></p><p type="main">

<s>Il Lemma stesso, facendo uso dell&#039;analisi, si dimostrerebbe efficacemente <lb></lb>in due parole, perchè, chiamando A, A&#039;le due grandezze omogenee, uguali; <lb></lb>N il numero delle parti, in cui si vuol divisa l&#039;una, N′ il numero delle parti, <lb></lb>in cui s&#039;intende esser divisa l&#039;altra, e P una sola parte di quella, P&#039;una <lb></lb>sola parte di questa; le due equazioni A/N′=P, A′/N′=P′ danno N:N′= <lb></lb>P′:P. </s>

<s>In simile spedito modo si dimostrerebbe che i numeri delle vibra­<lb></lb>zioni stanno rcciprocamente come i tempi, e da questo e dal Teorema I si <lb></lb>concluderebbe, con pari facilità, che le lunghezze dei pendoli stanno reci­<lb></lb>procamente come i quadrati de&#039;numeri delle vibrazioni. </s>

<s>Compia infatti un <lb></lb>numero N di vibrazioni un pendolo, mentre un altro, nel medesimo tempo <foreign lang="grc">θ</foreign>, <pb xlink:href="020/01/2188.jpg" pagenum="431"></pb>ne compie N′. </s>

<s>Il tempo T di una vibrazione del primo sarà T=<foreign lang="grc">θ</foreign>/N e il <lb></lb>tempo T′ d&#039;una vibrazione del secondo sarà T′=<foreign lang="grc">θ</foreign>/N′, d&#039;onde T:T′= <lb></lb>N′:N, e anche T2:T′2=N′2:N2. </s>

<s>Chiamate ora L, L′ le lunghezze dei <lb></lb>pendoli corrispondenti, essendo stato dianzi dimostrato, nel trascritto Teo­<lb></lb>rema I, che L:L′=T2:T′2, immediatamente se ne conclude L:L′= <lb></lb>N′2:N2. </s>

<s>Ma il Viviani, proseguendo i metodi antichi, ha bisogno di quel più <lb></lb>lungo discorso, che ora leggeremo, per dimostrare i due seguenti teoremi, <lb></lb>che sono il II e il III del suo trattatello <emph type="italics"></emph>Dei pendoli di lunghezze disuguali.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ TEOREMA II. — <emph type="italics"></emph>I numeri delle vibrazioni di due pendoli disuguali, <lb></lb>fatte dentro a un medesimo tempo, sono fra loro in proporzione reciproca <lb></lb>dei tempi delle uniche vibrazioni de&#039;medesimi pendoli, ed anche in reci­<lb></lb>proca proporzione della somma dei tempi di eguali numeri di vibrazioni <lb></lb>di essi pendoli.<emph.end type="italics"></emph.end> — Imperocchè, passandosi le singolari vibrazioni di ciascun <lb></lb>pendolo, considerate in sè, in tempi uguali, il numero delle vibrazioni del <lb></lb>primo pendolo, al numero delle vibrazioni del secondo, starà come il nu­<lb></lb>mero de&#039;tempi uguali del numero delle vibrazioni del primo al numero dei <lb></lb>tempi uguali del numero delle vibrazioni del secondo. </s>

<s>Ma, per il supposto, <lb></lb>il tempo del numero delle vibrazioni del primo è uguale al tempo del nu­<lb></lb>mero delle vibrazioni del secondo, poichè quelle del primo si son poste pas­<lb></lb>sate nel medesimo tempo che quelle del secondo; adunque, per l&#039;antece­<lb></lb>dente Lemma, il numero de&#039;tempi uguali delle vibrazioni del primo, al <lb></lb>numero de&#039;tempi uguali delle vibrazioni del secondo, cioè, pel dimostrato <lb></lb>qui a principio, il numero delle vibrazioni del primo, al numero delle vi­<lb></lb>brazioni del secondo, sta come il tempo dell&#039;unica vibrazione del secondo <lb></lb>al tempo dell&#039;unica vibrazione del primo: e, presi di questi tempi gli egual­<lb></lb>mente molteplici, come la somma de&#039;tempi uguali di un numero di vibra­<lb></lb>zioni del primo pendolo alla somma de&#039;tempi uguali d&#039;egual numero di vi­<lb></lb>brazioni del secondo, il che si doveva dimostrare. </s>

<s>” </s></p><p type="main">

<s>“ TEOREMA III. — <emph type="italics"></emph>Le lunghezze delle corde de&#039;pendoli hanno fra loro <lb></lb>la proporzione reciproca, che hanno i quadrati de&#039;numeri delle vibrazioni, <lb></lb>che si fanno nel medesimo tempo da essi pendoli. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Essendosi provato nel passato teorema che il numero delle vibrazioni <lb></lb>del primo dei pendoli, al numero delle vibrazioni del secondo, fatte in un <lb></lb>medesimo tempo, sta reciprocamente come il tempo dell&#039;unica vibrazione <lb></lb>del secondo al tempo dell&#039;unica vibrazione del primo, è manifesto che, an­<lb></lb>che il quadrato del medesimo numero delle vibrazioni del primo, al qua­<lb></lb>drato del medesimo numero delle vibrazioni del secondo, fatte in un me­<lb></lb>desimo tempo, sta reciprocamente come il quadrato del tempo dell&#039;unica <lb></lb>vibrazione del secondo al quadrato del tempo dell&#039;unica vibrazione del primo. </s>

<s><lb></lb>Ma, per il Teorema I, il quadrato del tempo dell&#039;unica vibrazione del se­<lb></lb>condo, al quadrato del tempo dell&#039;unica vibrazione del primo, sta come la <lb></lb>lunghezza del secondo alla lunghezza del primo; adunque anche il quadrato <pb xlink:href="020/01/2189.jpg" pagenum="432"></pb>del suddetto numero delle vibrazioni del primo, al quadrato del suddetto nu­<lb></lb>mero delle vibrazioni del secondo, fatte in quel medesimo tempo, sta come <lb></lb>la lunghezza del filo del secondo alla lunghezza del filo del primo: onde, <lb></lb>permutando queste proporzioni e convertendo i termini, la lunghezza del filo <lb></lb>del primo, alla lunghezza del filo del secondo, sta come il quadrato del nu­<lb></lb>mero delle vibrazioni del secondo al quadrato del numero delle vibrazioni <lb></lb>del primo, il che dovevasi dimostrare ” (ivi). </s></p><p type="main">

<s>Volle il Viviani stesso fare l&#039;applicazioni numeriche di questo dimostrato <lb></lb>Teorema, calcolando le varie lunghezze dei fili, supposto esser cento la lun­<lb></lb>ghezza di quello, che in un dato tempo fa cento vibrazioni. </s>

<s>Perchè ne fa­<lb></lb>cesse 90, in quel medesimo tempo, trovò che il filo doveva esser lungo <lb></lb>123 37/81; perchè ne facesse 80, lungo 156 1/4; perchè ne facesse 70, lungo <lb></lb>204 4/49, e perchè ne facesse 60, lungo 277 7/9. Per aver poi 110 vibrazioni <lb></lb>trovò dover essere la lunghezza del pendolo 82 78/121, e per averne 120 do­<lb></lb>veva essere la lunghezza del filo 69 4/9 di quelle medesime parti. </s>

<s>Si vedono <lb></lb>questi numeri scritti in colonne lungo una linea, che rappresenta il filo di <lb></lb>un pendolo disegnato nel foglio 51 del X tomo dei manoscritti del Cimento. </s>

<s><lb></lb>A sinistra è la colonna dei <emph type="italics"></emph>Numeri di vibrazioni fatte nel medesimo tempo,<emph.end type="italics"></emph.end><lb></lb>e a destra, nei punti corrispondenti, l&#039;altra colonna dei <emph type="italics"></emph>Numeri delle lun­<lb></lb>ghezze dei fili.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Questo trattatello <emph type="italics"></emph>Dei pendoli,<emph.end type="italics"></emph.end> il quale è il primo, che occorra a com­<lb></lb>memorar nella Storia della Meccanica in Italia, aveva nella mente del Vi­<lb></lb>viani una duplice intenzione: quella cioè di supplire ai difetti gravi della <lb></lb>Scienza galileiana, e l&#039;altra di stabilir bene le teorie, da costruirvi sopra il <lb></lb>Cronometro, che doveva nella Corte medicea servire alle esperienze della <lb></lb>velocità del suono e della luce. </s>

<s>Essendosi dunque tutto così bene prestabi­<lb></lb>lito, come siam fin qui venuti narrando, non mancava a far altro, per met­<lb></lb>tere il detto Cronometro in uso, che a trovar la lunghezza del pendolo a <lb></lb>secondi, perchè si potesse ricavar di lì, o col calcolo o per via dello stru­<lb></lb>mento, le lunghezze delle fila convenienti a dar la richiesta misura delle <lb></lb>più sottili minuzie dei tempi. </s>

<s>Era stato l&#039;importante problema risoluto, come <lb></lb>si disse, dal Riccioli, e per risoluto ritenevasi pure nella Scuola galileiana, <lb></lb>come si par dall&#039;esempio del Castelli. </s>

<s>Ma perchè dubitavasi, in così fatte <lb></lb>misure, di quella precisione, che si voleva per le nuove accademiche espe­<lb></lb>rienze, ne diè il principe Leopoldo, sul cominciar dell&#039;anno 1657, commis­<lb></lb>sione al Borelli, già professore nello Studio pisano. </s>

<s>Pensò il peritissimo Astro­<lb></lb>nomo di dedurre il numero delle vibrazioni, fatte in ventiquattr&#039;ore da un <lb></lb>pendolo di qualunque lunghezza, in più squisito e più facile modo di quello <lb></lb>suggerito da Galileo, ed eseguito dai pazientissimi sodali del gesuita Ric­<lb></lb>cioli; dal contar quelle sole vibrazioni fatte in tempo, che il sole scorre suì <lb></lb>circolo equinoziale per tutta la lunghezza del suo diametro apparente, la qual <lb></lb>lunghezza essendo, per le diligentissime osservazioni degli Astronomi, nota, <lb></lb>dava sicuro il calcolo delle vibrazioni, che da quello stesso pendolo si sa­<lb></lb>rebbero dovute fare in tutto il tempo delle ventiquattr&#039;ore sideree. </s>

<s>Dietro <pb xlink:href="020/01/2190.jpg" pagenum="433"></pb>ciò, e dietro la dimostrata legge che le lunghezze dei pendoli stanno reci­<lb></lb>procamente come i quadrati dei numeri delle vibrazioni, era dal Borelli, con <lb></lb>metodi nuovi, risoluto il problema dell&#039;Orologio a secondi. </s></p><p type="main">

<s>Non apparendo, che per noi si sappia, da nessuna parte della Storia, si <lb></lb>comprende di quanta curiosità, e di quanta importanza debba riuscir la no­<lb></lb>tizia del resultato dei calcoli del Borelli, applicati a dar nel Cronometro fio­<lb></lb>rentino le più precise misure dei più minuziosi intervalli dei tempi. </s>

<s>Ci por­<lb></lb>gono i primi cenni di questa così desiderata notizia le seguenti parole, scritte <lb></lb>da Pisa, il di 14 Aprile 1657, dallo stesso Borelli al principe Leopoldo, in <lb></lb>una lettera pubblicata fra le altre, che raccolse Angelo Fabbroni: “ Intanto <lb></lb>invio a V. A. S. le misure squisite delle lunghezze dei pendoli corrispon­<lb></lb>denti a minutissimi tempi orarii, le quali lunghezze le ho aggiustate, con <lb></lb>quanta maggior diligenza ho potuto, il giorno di questo Equinozio passato, <lb></lb>numerando diligentemente più e più volte le vibrazioni di tali pendoli nel <lb></lb>transito del disco solare mandato da uno squisito perfetto Telescopio, il qual <lb></lb>modo è il più squisito e certo, che si possa in tal proposito usare ” (Let­<lb></lb>tere inedite, T. II, Firenze 1775, pag. </s>

<s>60). </s></p><p type="main">

<s>Sembra che il Borelli abbia voluto soprabbondare nel rispondere al que­<lb></lb>sito, ch&#039;era strettamente quello di cercar la misura della lunghezza del pen­<lb></lb>dolo a secondi, perchè se ne sarebbe di lì facilmente, per via del Trilineo <lb></lb>parabolico inventato dal Viviani, ricavata la misura di tutti gli altri pendoli <lb></lb>minori. </s>

<s>Il Borelli invece mandava precise tutt&#039;esse misure, le quali poi <lb></lb>eran quelle, che si dovevano direttamente applicare al Cronometro, rispar­<lb></lb>miando la fatica di calcolarle, o lasciandone solamente la cura di confron­<lb></lb>tarle nello strumento. </s>

<s>Dall&#039;altra parte era assai facile dedur di lì la lun­<lb></lb>ghezza del pendolo a secondi, presa per fondamento ad aggiustar quelle dette <lb></lb>misure. </s></p><p type="main">

<s>Il medesimo modo, che porgevasi al Principe e al Viviani sì certo, ser­<lb></lb>virebbe anche a noi, desiderosi di scoprire un tal fondamento, da cui dedur <lb></lb>la misura del pendolo a secondi, ritrovata per le nuove osservazioni astro­<lb></lb>nomiche del Borelli; se apparisse dalla lettera edita dal Fabbroni la quan­<lb></lb>tità delle varie lunghezze ivi accennate. </s>

<s>Ma non aggiungendosi dall&#039;editore <lb></lb>l&#039;importante notizia, dubitammo che il Borelli stesso avesse mandate quelle <lb></lb>misure, prese sulla lunghezza di qualche filo o di qualche strisciola di carta, <lb></lb>la quale, acclusa nella lettera, fosse andata smarrita. </s>

<s>Ci occorse, in mezzo <lb></lb>a così fatti dubbii, il pensiero che doveva il Principe aver consegnate le ri­<lb></lb>cevute misure al Viviani, il quale aveva a metterle in uso, e ci sembrò per <lb></lb>questo probabile che, ad evitare il pericolo di un tal facile smarrimento, ne <lb></lb>avesse preso e lasciato scritto più stabile ricordo. </s>

<s>La congettura venne pre­<lb></lb>sto e felicemente a verificarsi, cercando, secondo questa nostra intenzione, <lb></lb>per i Manoscritti del Cimento, nel X tomo dei quali ci occorse a leggere, <lb></lb>nel noto carattere del Viviani, così, sulla prima spaziosa faccia del foglio 191: </s></p><p type="main">

<s>“ Lunghezze mandate dal signor Borelli al serenissimo principe Leo­<lb></lb>poldo: ” </s></p><pb xlink:href="020/01/2191.jpg" pagenum="434"></pb><p type="main">

<s>“ AB, lunghezza del pendolo, la cui vibrazione è dieci minuti secondi di <lb></lb>un&#039;ora, sicchè sei vibrazioni di AB fanno un secondo, e 360 fanno un primo. </s>

<s>” </s></p><p type="main">

<s>“ AC, 15tʹ; sicchè 4 AC fanno un secondo, e 240 vibrazioni di AC <lb></lb>fanno un primo. </s>

<s>” </s></p><p type="main">

<s>“ AD, 20tʹ; sicchè 3 AD fanno un secondo, e 180 un primo. </s>

<s>” </s></p><p type="main">

<s>“ AE, 25tʹ; sicchè 2 2/5 AE fanno un secondo, e 140 un primo. </s>

<s>” </s></p><p type="main">

<s>“ AF, 30tʹ; sicchè 2 AF fanno un secondo, e 120 un primo. </s>

<s>” </s></p><p type="main">

<s>“ Notisi che in questi il signor Borelli intende per vibrazione una sola <lb></lb>andata, od un solo ritorno del pendolo. </s>

<s>” </s></p><p type="main">

<s>Ma rimase anche di qui la nostra principale speranza delusa, non ap­<lb></lb>parendo, da nessuna parte del Manoscritto, delle indicate lunghezze vesti­<lb></lb>gio. </s>

<s>Ci venne allora voglia di consultare l&#039;originale, da cui doveva aver tra­<lb></lb>scritta quella lettera il Fabbroni, e lo trovammo facilmente, nella citata <lb></lb>raccolta dei Manoscritti del Cimento, ai fogli 65 e 66 del Tomo XVI. </s>

<s>A tergo <lb></lb>del precedente foglio 64, bianco nella sua prima faccia, si notò tracciata una <lb></lb>linea orizzontale, divisa in parti disugualmente nei punti contrassegnati dalle <lb></lb>lettere A, B, C ... la qual linea ci apparve prima interrotta nella <gap></gap>ucitura, <lb></lb>ma poi trovammo che passava di sotto alla piegatura de&#039;detti fogli 65 e 66, <lb></lb>per andare a continuarsi nella medesima direzione sulla prima faccia del fo­<lb></lb>glio 67, procedendo nelle divisioni segnate con le lettere D, E, e, com&#039;era <lb></lb>cominciata con la lettera A, così terminava con la lettera F. </s></p><p type="main">

<s>La corrispondenza di queste lettere, con quelle indicateci dal Viviani, <lb></lb>sarebbe per sè medesima bastata a farci accorti dover esser ivi quella linea <lb></lb>tracciata per rappresentar le lunghezze dei pendoli, quando non fossero ve­<lb></lb>nute a toglierci d&#039;ogni dubbio le sottoscritte dichiarazioni: “ AB, lunghezza <lb></lb>di pendolo, la cui vibrazione è dieci minuti terzi di ora. </s>

<s>— AC, pendolo, la <lb></lb>vibrazione del quale è quindici minuti terzi. </s>

<s>— AD, di venti minuti terzi; <lb></lb>AE, di venticinque minuti terzi; AF, pendolo, una sola vibrazione del quale <lb></lb>è trenta minuti terzi. </s>

<s>” </s></p><p type="main">

<s>Sulle lunghezze della linea AF, disegnata nel foglio del Borelli, prese <lb></lb>dunque il Viviani, per fare esperienza del suo Cronometro, le misure dei <lb></lb>pendoli, ma non trovò praticabile altro che quella dei mezzi secondi, per­<lb></lb>chè, come poi fece scrivere nel libro dei <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> “ tutti gli altri più corti <lb></lb>riescono così veloci, che gli occhi non gli pòsson seguire ” (Firenze 1841, <lb></lb>pag. </s>

<s>22). Qui per verità non s&#039;intende come mai i pendoli, più corti di <lb></lb>quello dei mezzi secondi, si dicano andar tanto veloci, da non poter esser <lb></lb>seguiti dagli occhi, tanto più che non era necessario osservarne direttamente <lb></lb>i moti, venendo questi comunicati all&#039;indice, moventesi regolarmente più <lb></lb>lento sulla mostra dell&#039;Orologio. </s>

<s>Comunque sia, rigettate per inutili le mi­<lb></lb>sure dei dieci, dei quindici, dei venti e de&#039;venticinque terzi, trovava il Vi­<lb></lb>viani le altre divisioni, comprese fra un secondo intero e la metà di lui, <lb></lb>per mezzo del suo Trilineo parabolico, la massima ordinata del quale, d&#039;onde <lb></lb>prendevano regola tutte le altre, s&#039;aveva, con assai facile calcolo, definita <lb></lb>da una qualunque delle misure descritte dallo stesso Borelli. </s></p><pb xlink:href="020/01/2192.jpg" pagenum="435"></pb><p type="main">

<s>Il modo insomma tenuto dal Viviani è quello stesso, che si porge pa­<lb></lb>rato a noi, se vogliamo sapere quant&#039;egli mettesse lunga, tra la riga e il <lb></lb>vertice della catenuzza, la linea corrispondente alla lunghezza del pendolo a <lb></lb>secondi. </s>

<s>Possiamo anche noi infatti tornare sul foglio del Borelli, che ci è <lb></lb>rimasto, e da una delle misure calcolate da lui riuscire, con pari facilità, <lb></lb>alla medesima conclusione. </s></p><p type="main">

<s>Noi ci siamo provati, e misurando, con la maggior diligenza che ci sia <lb></lb>stata possibile, la lunghezza della linea AF conveniente a un mezzo secondo, <lb></lb>ci è sembrato corrispondesse a 0m, 289; cosicchè la lunghezza di tutto il pen­<lb></lb>dolo di un secondo, quale fu ritrovata dal Borelli, e quale fu dal Viviani ap­<lb></lb>plicata al Cronometro usato alle più delicate esperienze degli Accademici <lb></lb>del Cimento, sarebbe di 1m, 156, come resulta dal moltiplicar 0m, 289, che <lb></lb>è la data altezza del pendolo dei mezzi secondi, per il quadrato del tempo <lb></lb>doppio. </s>

<s>Difficile è vero, per la grossezza delle linee e de&#039;punti segnati dalla <lb></lb>penna del Borelli, e per la difficoltà di mettere in piano il foglio, ritrarre <lb></lb>le misure esatte. </s>

<s>Ma perchè in somma non potrebbe l&#039;errore importar altro <lb></lb>che qualche millimetro, vien questa lunghezza del pendolo a secondi a riu­<lb></lb>scire in ogni modo eccessiva, e più aberrante dal vero di quella stessa da­<lb></lb>taci dal Riccioli. </s>

<s>Non è possibile, massimamente per esserci <gap></gap>imaste ignote <lb></lb>le particolarità dei modi tenuti nelle osservazioni, computare le complicate <lb></lb>cause di questi errori, ma le principali, e che furono ad ambedue i Mate­<lb></lb>matici nostri comuni, si riducono al ritener che fecero per isocrone così le <lb></lb>massime come le minime vibrazioni, e al non aver saputo ridurre al suo <lb></lb>vero centro oscillatorio il pendolo composto. </s></p><p type="main">

<s>Comunque sia, non doveva, così come vollero gli Accademici fiorentini, <lb></lb>rilasciarsi questa loro opera, data intorno alla costruzione dell&#039;Orologio, alle <lb></lb>curiose indagini della Storia, nè par che facesse bene il Viviani a sacrificar <lb></lb>l&#039;invenzione alla gloria del suo Maestro. </s>

<s>Il Cronometro, ch&#039;egli istituiva sulle <lb></lb>dimostrate teorie, e ch&#039;egli costruiva secondo le regole dell&#039;arte, piuttosto <lb></lb>che <emph type="italics"></emph>sull&#039;andare di quello di Galileo,<emph.end type="italics"></emph.end> era sull&#039;andar di quell&#039;altro, che im­<lb></lb>maginava l&#039;Huyghens qualche mese dopo, e che s&#039;eseguì in Olanda nel me­<lb></lb>desimo tempo. </s></p><pb xlink:href="020/01/2193.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle resistenze dei solidi<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle proposizioni dimostrate da Galileo nel secondo dialogo delle due Nuove Scienze. </s>

<s>— II. </s>

<s>Dei <lb></lb>trattati di Francesco Blondel, di Vincenzio Viviani e di Alessandro Marchetti. </s>

<s>— III. </s>

<s>Delle con­<lb></lb>troversie insorte fra Alessandro Marchetti e Guido Grandi. </s>

<s>— IV. Dell&#039;applicazione della teo­<lb></lb>ria dei momenti. </s>

<s>— V. </s>

<s>Delle osservazioni dei fatti, e delle esperienze concorse a promovere <lb></lb>la nuova scienza di Galileo. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;altra Scienza nuova, che si compiaceva di avere istituita Galileo, dopo <lb></lb>quella dei Moti locali, concerne le dimostrazioni delle virtù dei solidi, nel <lb></lb>resistere allo spezzarsi, o gravati dal proprio peso o da pesi stranieri. </s>

<s>Ben­<lb></lb>chè sia però, da questa parte, la novità più apparente, non è che mancas­<lb></lb>sero nemmen qui le tradizioni rimaste salve, a comun benefizio degli stu­<lb></lb>diosi, in quei meccanici <emph type="italics"></emph>Quesiti,<emph.end type="italics"></emph.end> ne&#039;quali raccoglieva Aristotile la preziosa <lb></lb>eredità di una scienza più antica. </s>

<s>Nel XVI si domanda perchè tanto sien più <lb></lb>deboli i legni, quanto sono più lunghi, cosicchè un fuscello, lungo per esem­<lb></lb>pio un cubito, sostenuto a un estremo, si mantiene diritto, e al contrario <lb></lb>una verga, lunga cento cubiti, dall&#039;altro suo estremo liberamente pendente, <lb></lb>piegasi in basso. </s>

<s>“ An quia, risponde il Filosofo, et vectis et onus et hypo­<lb></lb>mochlion, in levando, ipsa fit ligni proceritas? </s>

<s>Prior namque illius pars ceu <lb></lb>hypomochlion fit; quod vero in extremo est, pondus. </s>

<s>Quamobrem quanto <lb></lb>extensius fuerit id quod ab hypomochlio est, tanto inflecti necesse est ma­<lb></lb>gis ” (Operum cit., T. XI, fol. </s>

<s>33). </s></p><p type="main">

<s>Vuol dire insomma Aristotile: Se i due legni AB, CD (fig. </s>

<s>223) son so­<lb></lb><figure id="id.020.01.2193.1.jpg" xlink:href="020/01/2193/1.jpg"></figure></s></p><p type="caption">

<s>Figura 223<lb></lb>stenuti in A, C, rimanendo in B, D liberi, e <lb></lb>se si riguardino i loro pesi concentrati nei <lb></lb>due punti di mezzo E, F, il primo opera con <lb></lb>la leva AE, e l&#039;altro con la leva CF, tanto <lb></lb>più lunga, e perciò s&#039;inflette costretto d&#039;ub­<lb></lb>bedire a una forza maggiore. </s></p><pb xlink:href="020/01/2194.jpg" pagenum="437"></pb><p type="main">

<s>Il solido resistente ha, nel proposto Quesito, da una parte sola l&#039;ap­<lb></lb>poggio, onde, a dar compiuta risoluzione di questa Scienza, par che voglia <lb></lb>Aristotile stesso considerare il caso della resistenza, quando il legno ha l&#039;ap­<lb></lb>poggio in ambedue gli estremi, come avviene allora che, per tribbiarlo, un <lb></lb>lo tiene di qua e di là con le mani, e lo sforza nel mezzo, puntandovi il <lb></lb>piede o il ginocchio “ Cur eiusdem magnitudinis lignum facilius genu fran­<lb></lb>gitur, si quispiam aeque deductis manibus, extrema comprehendens, frege­<lb></lb>rit, quam si iuxta genu? </s>

<s>” (ibid.). Pone qui Aristotile il principio verissimo <lb></lb>che la minima resistenza del solido CD, sostenuto da ambedue gli estremi, <lb></lb>come nella precedente figura, sia nel mezzo, e che fuori da questo mezzo <lb></lb>si faccia quella prima resistenza sempre minore, perchè minore è la leva <lb></lb>della forza. </s>

<s>“ Genu centrum est: quanto autem remotius a centro fuerit, <lb></lb>facilius movetur quodcumque: moveri autem quod frangitur necesse est ” <lb></lb>(ibid.). Tale è la ragione perchè, a sforzarlo in F nel mezzo, più facilmente <lb></lb>il legno si spezzi, che a sforzarlo in II. </s></p><p type="main">

<s>Chi ripensi ora a quei tempi, nei quali i divulgati insegnamenti aristo­<lb></lb>telici venivano dai teoremi di Archimede in gran parte emendati, e valida­<lb></lb>mente promossi, non crederà possibile che i discepoli di Luca Pacioli la­<lb></lb>sciassero questa nuova scienza delle resistenze del tutto incolta. </s>

<s>A conferma <lb></lb>di che basterebbero i teoremi di Leonardo da Vinci, e le disperse specula­<lb></lb>zioni dei contemporanei e degli immediati successori di lui: teoremi e spe­<lb></lb>culazioni che, giusto per essere state disperse o nei pubblici libri non bene <lb></lb>schiarite, resero, come si diceva, le novità di Galileo più apparenti. </s></p><p type="main">

<s>Queste novità, che nel 1638 fecero la loro pubblica e solenne comparsa, <lb></lb>erano già infino dal 1609 uscite dalla mente dell&#039;Autore, il quale ne lasciò <lb></lb>così autentico documento in una scrittura, d&#039;altre simili e contemporanee <lb></lb>verità scoperte, rivelatrice importante: “ E pure ultimamente ho finito di <lb></lb>ritrovare tutte le conclusioni, con le sue dimostrazioni, attenenti alle forze <lb></lb>e resistenze dei legni di diverse lunghezze, grossezze e figure; e quanto sien <lb></lb>più deboli nel mezzo che negli estremi, e quanto maggior peso sosterranno <lb></lb>se quello sarà distribuito per tutto il legno, anzi che in un sol luogo, e qual <lb></lb>figura doveria avere acciò fosse per tutto egualmente gagliardo: la quale <lb></lb>Scienza è molto necessaria nel fabbricare macchine ed ogni sorta di edifi­<lb></lb>zio, nè vi è alcuno che ne abbia trattato ” (Alb. </s>

<s>VI, 69). </s></p><p type="main">

<s>Hanno tutte le conclusioni qui accennate la loro dimostrazione nel <lb></lb>II dialogo delle due Scienze nuove, in forma di trattato, che a rivelar gli <lb></lb>influssi delle tradizioni più antiche si divide in due parti, corrispondenti ai <lb></lb>due detti Quesiti aristotelici, nell&#039;un de&#039;quali si considera il solido appog­<lb></lb>giato a un solo, e nell&#039;altro ai suoi due estremi. </s>

<s>A dare scienza di queste <lb></lb>passioni della materia bisognava definir prima la natura della forza, che re­<lb></lb>siste alla separazione delle particelle materiali; forza che per Galileo si ri­<lb></lb>duce a due capi: “ l&#039;uno dei quali è quella decantata repugnanza, che ha <lb></lb>la Natura all&#039;ammettere il vacuo: per l&#039;altro bisogna, non bastando questo <lb></lb>del vacuo, introdur qualche glutine, visco o colla, che tenacemente colleghi <pb xlink:href="020/01/2195.jpg" pagenum="438"></pb>le particole, delle quali esso corpo è composto ” (Alb. </s>

<s>XIII, 15). La forza <lb></lb>così definita è quella, che oggidì si chiama di <emph type="italics"></emph>coesione,<emph.end type="italics"></emph.end> la quale Galileo ap­<lb></lb>plicò al legno, come al vetro e al marmo, e a simili altri corpi duri, cosic­<lb></lb>chè, distratte appena le particelle, la rottura in tutti, allo stesso modo, ne <lb></lb>segue a un tratto e immediata. </s></p><p type="main">

<s>Per misurar poi i varii gradi della potenza, necessaria a fare una tal <lb></lb>distrazione, Galileo stesso ricorse alla Statica, secondo i principii della quale <lb></lb>si possono avere gli equivalenti di qualunque forza dal prodotto del peso <lb></lb>per l&#039;altezza verticale a cui vien sollevato. </s>

<s>Supponiamo che il solido AB <lb></lb>(fig. </s>

<s>224) sia col suo lato CB aderente ad altra materia, dalla quale si vo­<lb></lb><figure id="id.020.01.2195.1.jpg" xlink:href="020/01/2195/1.jpg"></figure></s></p><p type="caption">

<s>Figura 224<lb></lb>glia staccarlo. </s>

<s>Si può operare in due modi: o <lb></lb>col tirare perpendicolarmente alla linea del con­<lb></lb>tatto, o col sollevare essa linea da una parte, <lb></lb>facendo appoggio dall&#039;altra, cosicchè ci sarebbe <lb></lb>nel primo caso bisogno di una potenza assoluta, <lb></lb>ossia uguale alla resistenza, e nel secondo ba­<lb></lb>sterebbe quella sola potenza, che è respettiva <lb></lb>agli effetti della leva. </s>

<s>La proporzione, che passa <lb></lb>fra l&#039;una e l&#039;altra potenza di rompere un medesimo solido, la conclude Galileo <lb></lb>dal detto fondamento statico in modo, che in sostanza riducesi al seguente: </s></p><p type="main">

<s>Se la linea CB, aderente prima alla EH, si supponga essere stata stac­<lb></lb>cata in tutti i suoi punti per distanze tutte eguali a BH, la forza che ha <lb></lb>prodotto l&#039;effetto è manifestamente quella, che è necessaria a sollevare al­<lb></lb>l&#039;altezza BH tutti i punti materiali contenuti nella linea CB. </s>

<s>E perchè que­<lb></lb>sti punti son tanti, quanto è lunga la linea stessa CB, sarà dunque, per il <lb></lb>detto principio statico misurata la proposta forza dal prodotto CB2XBH. </s></p><p type="main">

<s>Nel caso però che si fosse procurata la medesima rottura, applicando <lb></lb>la forza in B, e facendo rivolgere la linea CB intorno a C come a centro, <lb></lb>il favor della leva diminuisce notabilmente quella prima forza assoluta, e <lb></lb>con qual proporzione, comparata con la respettiva, può facilmente conclu­<lb></lb>dersi, considerando il punto B sollevato in BI, a un&#039;altezza uguale alla BH. </s>

<s><lb></lb>Gli altri punti di mezzo fra B e C saranno sollevati per altezze via via sem­<lb></lb>pre minori, corrispondenti alle ordinate nel triangolo CBI, per cui sarà data <lb></lb>la misura della nuova forza dal prodotto di queste stesse ordinate per il nu­<lb></lb>mero dei punti materìali contenuti in BC, ossia da CB2XBI/2=CB2XBH/2. <lb></lb>La cosa può ridursi alla maggiore esattezza matematica considerando BH, <lb></lb>BI come distanze infinitesime, e sufficienti a produrre la rottura del solido, <lb></lb>cosicchè quella prima forza contemplata sta a questa seconda, come BH sta a <lb></lb>BH/2. E perchè la forza necessaria a separare le particelle materiali è uguale <lb></lb>e contraria alla forza, con cui le particelle stesse resistono all&#039;essere sepa­<lb></lb>rate, dunque la resistenza <emph type="italics"></emph>assoluta<emph.end type="italics"></emph.end> è doppia della <emph type="italics"></emph>respettiva.<emph.end type="italics"></emph.end> “ E questa, <lb></lb>dice Galileo, sia la nostra prima proposizione ” (Alb. </s>

<s>XIII, 117). </s></p><pb xlink:href="020/01/2196.jpg" pagenum="439"></pb><p type="main">

<s>Posto così alla nuova Scienza il suo fondamento “ conviene ora, sog­<lb></lb>giunge lo stesso Galileo, che cominciamo a investigare secondo qual pro­<lb></lb>porzione vada crescendo il momento della propria gravità, in relazione alla <lb></lb><figure id="id.020.01.2196.1.jpg" xlink:href="020/01/2196/1.jpg"></figure></s></p><p type="caption">

<s>Figura 225<lb></lb>propria resistenza all&#039;essere spezzato, in un pri­<lb></lb>sma o cilindro grave, mentre stando parallelo al­<lb></lb>l&#039;orizzonte si va allungando, il qual momento <lb></lb>trovo andar crescendo in duplicata proporzione <lb></lb>dell&#039;allungamento, cioè secondo i quadrati delle <lb></lb>lunghezze ” (ivi, pag. </s>

<s>118). La dimostrazione <lb></lb>riducesi alla seguente, supponendo essere AD <lb></lb>(fig. </s>

<s>225) la sezione di un solido prismatico fisso <lb></lb>nel muro AC con la sua base. </s>

<s>Tutto il peso <lb></lb>della detta sezione, che si può riguardar come <lb></lb>raccolto nel suo centro di gravità H, è dato da <lb></lb>CDXAC, cosicchè, condotta la HI=CD/2 perpendicolare alla base, sarà il <lb></lb>momento, a cui debbon resistere le particelle materiali AC aderenti al muro, <lb></lb>CDXACXCD/2. Se ora la sezione stessa s&#039;immagini prolungata in E, co­<lb></lb>sicchè i pesi delle sue particelle d&#039;ogni parte si raccolgano in M, il nuovo <lb></lb>momento, a cui debbon resistere i punti di attacco al sostegno, si troverà <lb></lb>allo stesso modo di dianzi uguale a CFXACXCF/2. Stanno dunque vera­<lb></lb>mente le due resistenze come CD2 a CF2, secondo che diceva di aver tro­<lb></lb>vato Galileo. </s></p><p type="main">

<s>Procedendo oltre a dimostrare, secondo i posti principii, le ragioni del <lb></lb>resistere allo spezzarsi rasente il muro, a cui siano stati affissi per le loro <lb></lb>basi di varia grandezza, due cilindri di lunghezze uguali, come per esempio <lb></lb>A, B (fig. </s>

<s>226), osserva l&#039;Autore che “ se consideriamo l&#039;assoluta e sem­<lb></lb><figure id="id.020.01.2196.2.jpg" xlink:href="020/01/2196/2.jpg"></figure></s></p><p type="caption">

<s>Figura 226<lb></lb>plice resistenza, che risiede nelle basi, <lb></lb>cioè nei cerchi EF, DC, all&#039;essere strap­<lb></lb>pati, facendogli forza col tirarli per di­<lb></lb>ritto; non è dubbio che la resistenza del <lb></lb>cilindro B è tanto maggiore che quella <lb></lb>del cilindro A, quanto il cerchio EF è <lb></lb>maggiore del CD, perchè tanto più sono <lb></lb>le fibre, i filamenti o le parti tenaci, che <lb></lb>tengono unite le parti dei solidi. </s>

<s>Nel far forza però per traverso ci serviamo <lb></lb>di due leve, delle quali le parti o distanze, dove si applicano le forze, sono <lb></lb>le linee DG, FH; i sostegni sono nei punti D, F, ma le altre parti o di­<lb></lb>stanze, dove son poste le resistenze, sono i semidiametri dei cerchi DC, EF, <lb></lb>perchè i filamenti, sparsi per tutte le superficie dei cerchi, è come se tutti si <lb></lb>riducessero nei centri ” (ivi, pag. </s>

<s>119, 20). </s></p><p type="main">

<s>Così dunque la resistenza respettiva del cilindro B sarà tanto maggiore <pb xlink:href="020/01/2197.jpg" pagenum="440"></pb>della resistenza respettiva del cilindro A, quanto il prodotto della superficie <lb></lb>del circolo di raggio OF per esso raggio, è maggiore del prodotto della su­<lb></lb>perficie del circolo di raggio ID per il medesimo raggio. </s>

<s>Ma le superficie <lb></lb>dei circoli stanno come i quadrati dei raggi, dunque starà la prima resi­<lb></lb>stenza alla seconda come OF3 ad ID3, o come anche EF3 a CD3: ossia, come <lb></lb>Galileo propriamente si esprime, la resistenza all&#039;esser rotti i due cilindri <lb></lb>“ cresce in triplicata proporzione dei diametri delle loro grossezze, cioè delle <lb></lb>loro basi ” (ivi, pag. </s>

<s>119). </s></p><p type="main">

<s>Stabiliti questi fondamentali teoremi della prima parte del suo Trat­<lb></lb>tato, Galileo si trattiene a risolvere alcuni quesiti, e a dedurne alcuni corol­<lb></lb><figure id="id.020.01.2197.1.jpg" xlink:href="020/01/2197/1.jpg"></figure></s></p><p type="caption">

<s>Figura 227<lb></lb><figure id="id.020.01.2197.2.jpg" xlink:href="020/01/2197/2.jpg"></figure></s></p><p type="caption">

<s>Figura 228<lb></lb>larii, o curiosi in sè stessi, o utili per le <lb></lb>loro applicazioni, come sarebbe per esem­<lb></lb>pio: perchè una verga più resista all&#039;esser <lb></lb>rotta, facendo forza secondo la sua lar­<lb></lb>ghezza, che secondo la grossezza? </s>

<s>Abbiasi <lb></lb>la riga BE (fig. </s>

<s>227): chi volesse romperla <lb></lb>così ritta troverebbe molto maggior resi­<lb></lb>stenza che a romperla posta per piatto, <lb></lb>come nella figura 228, di che la ragione <lb></lb>apparisce chiara dai posti principii, per­<lb></lb>chè, mentre in ambedue i casi la resi­<lb></lb>stenza assoluta è la medesima, essendo le <lb></lb>medesime le superficie aderenti, la resi­<lb></lb>stenza respettiva è tanto maggiore nella <lb></lb>prima posizione che nella seseconda, quanto AB, o la sua metà che serve <lb></lb>di contralleva, è maggiore della metà di CD. </s></p><p type="main">

<s>Quest&#039;altra curiosa e importante novità si conclude pure dagli stessi <lb></lb>principii: sia il cilindro vuoto AE ugualmente lungo, e ugualmente peso del <lb></lb>cilindro massiccio IN (fig. </s>

<s>229): chi si volesse provare a stroncar questi due <lb></lb>solidi, facendo forza in E, N contro le basi AB, IL aderenti, troverebbe molto <lb></lb><figure id="id.020.01.2197.3.jpg" xlink:href="020/01/2197/3.jpg"></figure></s></p><p type="caption">

<s>Figura 229<lb></lb>maggior difficoltà nel primo che nel <lb></lb>secondo, e ciò perchè, mentre in am­<lb></lb>bedue la resistenza assoluta è la mede­<lb></lb>sima, la resistenza respettiva nell&#039;uno <lb></lb>però è tanto minore della resistenza <lb></lb>respettiva dell&#039;altro, quanto il diame­<lb></lb>tro IL, o la metà di lui che fa da con­<lb></lb>tralleva, è minore della metà di AB. <lb></lb>Ond&#039;è a concluder di qui con Galileo <lb></lb>che “ le resistenze di due cilindri eguali, ed egualmente lunghi, l&#039;uno dei <lb></lb>quali sia vuoto e l&#039;altro massiccio, hanno tra di loro la medesima propor­<lb></lb>zione che i loro diametri ” (ivi, pag. </s>

<s>145). </s></p><p type="main">

<s>L&#039;utilità di questa conclusione, nelle opere dell&#039;arte, è abbellita per Ga­<lb></lb>lileo dal contemplare il provvido e sapiente magistero della Natura nel fab-<pb xlink:href="020/01/2198.jpg" pagenum="441"></pb>bricar le leggere ossa ai volanti per l&#039;aria, o i gracili calami, sopra i quali <lb></lb>ondeggiano al vento le pingui spighe nei campi. </s>

<s>Considera inoltre l&#039;Autore <lb></lb>di questa nuova Scienza che le resistenze dei solidi non mantengono la pro­<lb></lb>porzione delle grandezze, come nella Geometria, nella quale non si muta <lb></lb>proprietà alle figure simili; cosicchè s&#039;ingannerebbe molto colui, il quale <lb></lb>credesse che, a raddoppiare a un cilindro la base e la lunghezza, dovesse <lb></lb>tuttavia serbare una resistenza uguale alla prima. </s>

<s>La ragione di ciò si vede <lb></lb>nei professati principii chiarissima, perchè sebben nel cilindro doppio sia rad­<lb></lb>doppiate la leva, e siano altresì raddoppiati i filamenti o i punti di attacco, <lb></lb>la contralleva nonostante è cresciuta meno del doppio, e tanto meno quanto <lb></lb>minore di due è la sua propria radice. </s>

<s>Di qui sapientemente conclude Galileo <lb></lb>la ragione del non riuscire secondo i modelli le macchine in grande, e come <lb></lb>sarebbe impossibile all&#039;arte fabbricare edifizii grandissimi, e alla Natura al­<lb></lb>beri o animali di smisurata grandezza, se già non si togliesse materia molto <lb></lb>più dura e resistente della consueta, o non si volessero così deformare le <lb></lb>ordinarie figure, da metterle in vista di orribili mostri (ivi, pag. </s>

<s>128, 29). </s></p><p type="main">

<s>Venivano queste considerazioni ad accennare a un&#039;altra Scienza nuova, <lb></lb>che sarebbe tra non molto per istituire il Borelli, e della quale intanto sem­<lb></lb>bra che volesse il Viviani, con queste parole, preconizzare i natalizii: </s></p><p type="main">

<s>“ Fra le molte ed ammirabili conclusioni, avvertite e dimostrate dal <lb></lb>Galileo, bellissima ed utilissima è quella in materia di resistenza dei corpi <lb></lb>solidi, a caso per così dire conosciuta e messa in opera dall&#039;Arte, ma prima <lb></lb>e più altamente dalla sovrana maestra Natura, la quale, bisognosa in alcuni <lb></lb>suoi macchinamenti di diminuire assai il peso, ma meno assai la gagliardia <lb></lb>di alcuni corpi, di lor natura molto gravi; ha industriosamente trovatane la <lb></lb>maniera e messala ad effetto, e questo ella ha osservato, come acutamente <lb></lb>avvertisce il medesimo Galileo, nelle ossa degli animali, le quali, come di <lb></lb>materia per sè stessa assai grave, era necessario per certo rispetto farle <lb></lb>quanto fosse più possibile leggere negli uccelli, per facilitare il potersi so­<lb></lb>stenere per aria, e che nel medesimo tempo fossero gagliarde e robuste, ed <lb></lb>in particolare quelle delle ali, acciò con forza a volontà potessero battere le <lb></lb>medesime ali, che in larghi spazi s&#039;aprono e si dilatano; dovecchè negli ani­<lb></lb>mali terrestri, non era necessaria tanta leggerezza, ma bene un&#039;altra sorta <lb></lb>di robustezza. </s>

<s>Sono perciò con somma provvidenza fatte da Dio le ossa degli <lb></lb>uccelli con gran cavità e con sottile corteccia, ma non così quelle dei ret­<lb></lb>tili che, rispetto alla grossezza, hanno dentro poco vacuo. </s>

<s>Dico fatto ciò molto <lb></lb>provvidamente, perchè dovendo i terrestri esercitare i movimenti loro tra <lb></lb>sassi e sterpi, dove si corre pericolo di urtare, era necessario l&#039;ossa loro <lb></lb>essere resistenti alle forze, alle quali l&#039;ossa, quanto più cave, tanto meno <lb></lb>sono resistenti. </s>

<s>Ma nei volatili, ch&#039;esercitano il loro velocissimo corso per <lb></lb>il liquido dell&#039;aria, come liberi dal pericolo delli ur<gap></gap>i, la resistenza non era <lb></lb>così necessaria, ma bene la leggerezza ” (MSS. Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>18). </s></p><p type="main">

<s>Le riferite conclusioni che il Viviani, così discorrendo, applicava alla <lb></lb>Meccanica animale, appartengono, come si diceva, alla prima parte del Trat-<pb xlink:href="020/01/2199.jpg" pagenum="442"></pb>tato galileiano, dove si considerano i momenti e le resistenze dei prismi e <lb></lb>cilindri solidi, l&#039;una estremità dei quali sia posta immobile, e solo nell&#039;al­<lb></lb>tra sia applicata la forza di un peso premente. </s>

<s>“ Ora voglio, soggiunge <lb></lb>lo stesso Galileo, che discorriamo alquanto dei medesimi prismi e cilindri, <lb></lb>quando fossero sostenuti da ambedue le estremità ” (Alb. </s>

<s>XIII, 132): e pro­<lb></lb>postasi la questione aristotelica del legno, tenuto per i due capi con le mani <lb></lb>a fin di spezzarlo, puntandovi contro il ginocchio; considerati, come il Fi­<lb></lb>losofo fa, gli effetti della leva, ne riduce i momenti, con questo fondamen­<lb></lb>tale teorema, alle loro più giuste proporzioni: “ Se nella lunghezza di un <lb></lb>cilindro si noteranno due luoghi, sopra i quali si voglia far la frazione di <lb></lb>esso cilindro, le resistenze di detti due luoghi hanno fra di loro la mede­<lb></lb>sima proporzione che i rettangoli fatti dalle distanze di essi luoghi contra­<lb></lb>riamente presi ” (ivi, pag. </s>

<s>135). </s></p><p type="main">

<s>Or perchè quello che dicesi dei cilindri si applica ugualmente ai prismi, <lb></lb>se sarà dunque una trave prismatica DB (fig. </s>

<s>230), sostenuta nelle sue te­<lb></lb>state, com&#039;ai palchi delle stanze; e se le resistenze vanno colle dimostrate <lb></lb><figure id="id.020.01.2199.1.jpg" xlink:href="020/01/2199/1.jpg"></figure></s></p><p type="caption">

<s>Figura 230<lb></lb>proporzioni crescendo dal mezzo di qua <lb></lb>e di là verso i sostegni, si potrebbe dun­<lb></lb>que levar della grossezza di essa trave <lb></lb>non piccola parte, con alleggerimento <lb></lb>del peso, con abbellimento del palco, <lb></lb>e con qualche diminuzione del prezzo. </s>

<s><lb></lb>Provocò un tal pensiero in Galileo la <lb></lb>soluzione di un problema, che si pre­<lb></lb>sentava alla sua speculazione di una no­<lb></lb>vità e di una bellezza maravigliosa, e che consisteva “ nel ritrovar quale <lb></lb>figura dovrebbe aver quel tal solido, che in tutte le sue parti fosse egual­<lb></lb>mente resistente, tal che non più facile fosse ad esser rotto da un peso, che <lb></lb>lo premesse nel mezzo, che in qualsivoglia altro luogo ” (ivi, pag. </s>

<s>136, 37). </s></p><p type="main">

<s>Trovò felicemente la desiderata figura segando la detta trave prisma­<lb></lb>tica BD lungo il filo della parabola FNB, cosicchè il solido parabolico, che <lb></lb>indi ne nasce, sia d&#039;ugual resistenza così nella base AD, come in CO, e in <lb></lb>qualunque altra sezione. </s>

<s>A dimostrar che ciò sia il vero s&#039;apparecchia Galileo <lb></lb>con questo Lemma: “ Se saranno due Libre o Leve divise dai loro sostegni <lb></lb>in modo, che le due distanze, dove si hanno a costituire le potenze, abbiano <lb></lb>tra di loro doppia proporzione delle distanze, dove saranno le resistenze, le <lb></lb><figure id="id.020.01.2199.2.jpg" xlink:href="020/01/2199/2.jpg"></figure></s></p><p type="caption">

<s>Figura 231<lb></lb>quali resistenze stiano fra loro come <lb></lb>le loro distanze; le potenze sostenenti <lb></lb>saranno eguali ” (ivi, pag. </s>

<s>138). </s></p><p type="main">

<s>Si può la dimostrazione galile­<lb></lb>iana ridurre così a maggior brevità <lb></lb>e chiarezza: Siano le due leve AB, <lb></lb>CD (fig. </s>

<s>231), aventi i loro fulcri <lb></lb>in E, F, e si chiamino R, R′ le resi-<pb xlink:href="020/01/2200.jpg" pagenum="443"></pb>stenze applicate in C, A; P, P′ le potenze applicate in D, B: sup; osto che <lb></lb>sia (I) EB:FD=AE2:FC2; (II) AE:FC=R′:R, convien dimostrare <lb></lb>che P=P′. </s>

<s>Si prenda sul braccio della Leva EB la lunghezza GE media <lb></lb>proporzionale fra EB, FD: avremo (III) EG2:FD2=AE2:FC2; e anche <lb></lb>insieme (IV) EB2:EG1=AE2:FC2. </s>

<s>Ma abbiamo per le proprietà del Vette, <lb></lb>e per la IIIa, la Va R:P=DF:FC=GE:AE, e pure, per la proprietà <lb></lb>del Vette (VI) R′:P′=BE:AE, e per la IIIa e la IVa R:R′=GE:BE; <lb></lb>dunque la Va e la VIa daranno P:P′=AE:AE, ossia P=P′ come do­<lb></lb>vevasi dimostrare. </s></p><p type="main">

<s>Inteso ciò, torniamo con Galileo indietro sulla figura CCXXX a consi­<lb></lb>derar la trave prismatica ridotta, col filo della sega, al solido parabolico <lb></lb>DOGBCA, che è quello che si dice esser per tutto di ugual potenza in re­<lb></lb>sistere a un peso che lo prema. </s>

<s>Avendo infatti la resistenza da pareggiare <lb></lb>con la leva BA, alla resistenza da pareggiarsi con la leva BC, la medesima <lb></lb>proporzione che il rettangolo DA al rettangolo OC, la quale proporzione è <lb></lb>la medesima di quella che ha la linea AF alla NC; chiamata dunque come <lb></lb>dianzi R′ la prima resistenza, ed R la seconda, sarà R′:R=AB:BC. </s>

<s>Ma <lb></lb>le proprietà della parabola danno AB:BC=AF2:NC2 e perciò, per le con­<lb></lb>clusioni del precedente Lemma, preparato già per applicarsi al caso presente, <lb></lb>la potenza, che ha di resistere AB, sarà uguale alla potenza di CO, e di qual <lb></lb>si voglia altra sezione condotta nella trave parabolica parallela alla base. </s>

<s>Or <lb></lb>perchè, per le cose dimostrate dai Matematici antichi, il solido parabolico <lb></lb>così rimasto è due terzi di tutto il prisma da cui fu segato, ne conclude <lb></lb>perciò Galileo che nella trave, diminuita di un terzo del suo peso, non è <lb></lb>però menomata per nulla quella prima potenza che aveva essendo intera. </s></p><p type="main">

<s>La conclusione è bellissima, anzi veramente maravigliosa, mentre che <lb></lb>però si rimanga nei libri alla contemplazion dei Filosofi, i quali possono con <lb></lb>la mente astrarre dalla materia. </s>

<s>Ma Galileo si lusingava di esser col suo Teo­<lb></lb>rema venuto a suggerire una utilissima applicazione alle costruzioni, spe­<lb></lb>cialmente navali, vedendosi “ come con diminuzion di peso di più di tren­<lb></lb>tatre per cento si posson fare i travamenti, senza diminuir punto la loro <lb></lb>gagliardia, il che, nei navigli grandi in particolare, per regger le coverte, <lb></lb>può essere di utile non piccolo, attesochè in cotali fabbriche la leggerezza <lb></lb>importa infinitamente ” (ivi, pag. </s>

<s>140). </s></p><p type="main">

<s>Le contradizioni, ch&#039;ebbe per ciò a patir Galileo dai Meccanici poste­<lb></lb>riori, si diranno più qua: per ora non son da passare inosservati i due <lb></lb>modi, ch&#039;egli propone per descrivere una parabola. </s>

<s>Notò il Cartesio che quei <lb></lb>modi son puramente meccanici “ et secundum Geometriam accuratam falsi ” <lb></lb>(Epist. </s>

<s>cit., P. II, pag. </s>

<s>243) ciò che sapevasi benissimo anche da Galileo, ma <lb></lb>tant&#039;era la fiducia che aveva di esser venuto colle sue teorie a recare non <lb></lb>piccola utilità all&#039;arte, che scelse i due detti modi perchè <emph type="italics"></emph>sopra tutti gli <lb></lb>altri speditissimi<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 144), e perchè la sega in mano dell&#039;operaio è <lb></lb>impossibile che vada a filo dell&#039;accurata Geometria. </s>

<s>S&#039;aggiungeva la com­<lb></lb>piacenza della novità non saputa che da quei pochissimi, ai quali fosse per <pb xlink:href="020/01/2201.jpg" pagenum="444"></pb>avventura capitato il Manoscritto di Guidubaldo del Monte, dove dice che la <lb></lb>linea dei proietti si rassomiglia a quella disegnata da una catenuzza, pen­<lb></lb>dula nelle sue estremità da due punti fissi orizzontali, e che l&#039;esperienza di <lb></lb>tal moto proiettizio “ si può far pigliando una palla tinta d&#039;inchiostro, e <lb></lb>tirandola sopra un piano di una tavola, il qual stia quasi perpendicolare al­<lb></lb>l&#039;orizzonte ” (Libri Histoire des Mathem., T. IV, Paris 1841, pag. </s>

<s>397). </s></p><p type="main">

<s>Nè furon queste sole le notizie in tal congiuntura partecipatesi a Gali­<lb></lb>leo: l&#039;applicazione delle proprietà dei pendoli al vibrare delle corde sonore, <lb></lb>e la soluzion del problema famoso relativo alla corda tocca, che fa simpa­<lb></lb>ticamente tremare le altre corde unisone e quiete, son cose che si legge­<lb></lb>vano per le neglette carte scoperte dal Libri, più di trent&#039;anni prima, che <lb></lb>si vedessero trasposte nel terzo dialogo delle due Nuove Scienze. </s>

<s>E qui ca­<lb></lb>drebhe in proposito il dire qual parte avesse Galileo nelle esperienze dei <lb></lb>proietti descritte da Guidubaldo, e qual giudizio facesse delle teorie in pro­<lb></lb>posito o delle opinioni di lui. </s>

<s>Ma perchè dovremo di ciò tenere altrove par­<lb></lb>ticolare discorso, richiameremo l&#039;attenzione dei nostri Lettori intorno a ciò, <lb></lb>che lo stesso Guidubaldo ivi insegna della resistenza delle corde tirate da pesi. </s></p><p type="main">

<s>“ Una corda che sostenta un peso, egli dice, tanto sostiene essendo <lb></lb>corta, quanto lunga. </s>

<s>È ben vero che nella lunga, prima per la sua gravità, <lb></lb>poi perchè nella lunga ci possono esser molte parti deboli, può esser che <lb></lb>ella si tronchi più facilmente e da minor peso, ma se, dove ella si stronca <lb></lb>per la sua distrazione, la corda fosse sostenuta poco di sopra, e poco di sotto <lb></lb>fosse stato il peso, senza dubbio ella medesimamente si sarebbe stroncata, <lb></lb>perchè si sarebbe nel medesimo modo distratta ” (ivi, pag. </s>

<s>398). Chi ora <lb></lb>collazionasse queste parole con quelle che si leggono in Galileo, nella II gior­<lb></lb>nata delle Scienze nuove a pag. </s>

<s>121 della citata edizione, non ci troverebbe <lb></lb>altra differenza che nell&#039;essere dialogizzate. </s></p><p type="main">

<s>L&#039;importanza di queste verità, delle quali ebbe forse a persuadersi Gui­<lb></lb>dubalde dop&#039;avere scritto il suo trattato Delle meccaniche, in mezzo ai pre­<lb></lb>valenti errosi messi in campo dal Simplicio galileiano, consigliò l&#039;Aggiunti <lb></lb>di specular quella sua sottilissima dimostrazione, che si riferi a pag. </s>

<s>215, 16 <lb></lb><figure id="id.020.01.2201.1.jpg" xlink:href="020/01/2201/1.jpg"></figure></s></p><p type="caption">

<s>Figura 232<lb></lb>del nostro II Tomo. </s>

<s>Anche il Tor­<lb></lb>ricelli, benchè vedesse assai chiaro <lb></lb>che la forza di un uomo, applicata <lb></lb>in B (fig. </s>

<s>232) a un capo della corda <lb></lb>di qualunque lunghezza, si propaga uguale di tratto in tratto infino all&#039;altro <lb></lb>capo C, a cui il peso da tirarsi è raccomandato; non credè nonostante inu­<lb></lb>tile spendervi attorno qualche discorso. </s></p><p type="main">

<s>“ Io considero qui primieramente, egli dice, che tutta la corda BC averà <lb></lb>la medesima tensione in ogni sua parte, cioè tanto sarà tirata nel princi­<lb></lb>pio B, quanto nel mezzo D, e quanto verso il fine C. </s>

<s>Questo è assai chiaro, <lb></lb>astraendo però da qualche varietà, che potesse fare il peso della corda, ed <lb></lb>anco astraendo dalla differenza, che potesse nascere dal toccamento della <lb></lb>corda sopra il piano a lei sottoposto, che però la considereremo in aria, e <pb xlink:href="020/01/2202.jpg" pagenum="445"></pb>senza la gravità propria. </s>

<s>Nondimeno si può con qualche discorso dimo­<lb></lb>strare così: ” </s></p><p type="main">

<s>“ L&#039;uomo traente conferisce al punto B tanta forza, quanta ne ha esso <lb></lb>uomo: il punto B tira poi con tanta forza il punto E suo congiunto, quanta <lb></lb>ne ha esso B, cioè quanta è la forza dell&#039;uomo, e il punto E tira il punto <lb></lb>F suo congiunto con quanta ne ha esso E, cioè quanta è la forza dell&#039;uomo, <lb></lb>e così si può andar discorrendo di tutti i punti, cioè di tutta la corda BC, <lb></lb>e concluderemo che l&#039;ultimo punto C, e perciò il gran sasso A, vien tirato <lb></lb>con altrettanta forza per appunto, con quanta vien tirato il punto B, cioè <lb></lb>con la forza dell&#039;uomo traente, non accresciuta nè diminuita. </s>

<s>Concludiamo <lb></lb>dunque questo principio: che qualunque volta averemo una lunghezza, cioè <lb></lb>una estensione di punti continuati, e che il primo di essi punti venga ti­<lb></lb>rato o spinto con una tal forza, anco tutti gli altri successivamente saranno <lb></lb>tirati o spinti con la medesima forza, senza accrescerla nè diminuirla, ma <lb></lb>trasmettendola sino al fine ” (MSS. Gal., T. XXXVII, fol. </s>

<s>123). </s></p><p type="main">

<s>La medesima conclusione scende da un principio dinamico più gene­<lb></lb>rale, ed è che la forza comunicata non varia di grado non variando la ve­<lb></lb>locità nella sezione costante, come si suppone avere la corda BC, che tira <lb></lb>il sasso. </s>

<s>Ma se da D per esempio verso C la corda è più sottile o più grossa, <lb></lb>che da D verso B, allora, essendo le velocità in ragion reciproca delle se­<lb></lb>zioni, la forza non si propaga più eguale, e restando indietro le parti meno <lb></lb>veloci si separano necessariamente dalle altre sempre in punti determinati. </s>

<s><lb></lb>Nascon di qui certi fatti maravigliosi, che in alcuni moderni scrittori ebbero <lb></lb>apparenza di nuovi, ma che furono molto prima osservati dal Viviani, e in <lb></lb>alcune sue Note autografe così descritti: </s></p><p type="main">

<s>“ Il peso A (fig. </s>

<s>233) di cinque libbre stia attac­<lb></lb><figure id="id.020.01.2202.1.jpg" xlink:href="020/01/2202/1.jpg"></figure></s></p><p type="caption">

<s>Figura 233<lb></lb>cato dalla sottilissima fune BC, e al medesimo peso stia <lb></lb>pendente un&#039;altra simil cordicella BF: dico potersi dar <lb></lb>caso che, nel tirar questa a basso con forza, ella si <lb></lb>stianti e rimanga la corda BC salda e illesa col peso A, <lb></lb>e ciò seguirà per mezzo di una stratta, che si dia alla <lb></lb>funicella BF con un colpo. </s>

<s>” </s></p><p type="main">

<s>“ Ma più maraviglia sarà, quando anco la corda BF <lb></lb>sia più forte e più grossa della superiore BC, perchè è <lb></lb>certo che, tirando a basso da F, questa si romperà nella <lb></lb>parte BC. </s>

<s>Nondimeno si potrà fare che si rompa la più forte BF, che in B <lb></lb>vi sia attaccato un peso tale, che appena sia retto dalla sottil corda BC. </s>

<s>Que­<lb></lb>sto si conseguirà per mezzo dell&#039;asta infilata nel muro D, e alla corda nella <lb></lb>estremità F, sulla quale asta o bastone si dia un colpo col maglio ra­<lb></lb>sente F. ” (MSS. Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>29). </s></p><p type="main">

<s>Potrebbero questi fatti passar per semplici giochi, se non avessero una <lb></lb>seria applicazione nelle funi da sostener pesi, o da sollevarli per via delle <lb></lb>Macchine; ciò che saviamente consigliò Galileo di farne argomento nel trat­<lb></lb>tar delle resistenze. </s>

<s>Non poteva egli reputare innocuo l&#039;error di Simplicio <pb xlink:href="020/01/2203.jpg" pagenum="446"></pb>in creder che tanto fossero le corde più valide a sostenere, quanto fossero <lb></lb>state più corte, avendo, insiem con lo stesso Guidubaldo, dovuto riconoscere <lb></lb>che, dal versare intorno a ciò o nell&#039;errore o nel dubbio, nacque l&#039;imper­<lb></lb>fezione, in cui si lasciò la meccanica delle Taglie. </s></p><p type="main">

<s>Il trattato Delle resistenze dei solidi nel II dialogo galileiano è dunque <lb></lb>così, nella novità del suo argomento, compiuto, nè resta a far altro, in mezzo <lb></lb>alle ammirazioni, che a notarne i difetti. </s>

<s>Chi, non frastornato dal lungo cla­<lb></lb>mor degli applausi, esamina tranquillamente, s&#039;accorge prima di tutto di un <lb></lb>disordine nel succedersi delle proposizioni, le ultime delle quali hanno re­<lb></lb>lazione strettissima con le prime. </s>

<s>Il difetto, è vero, scomparisce nella forma <lb></lb>del dialogo, ed è perciò il dialogo stesso che toglie precisione al trattato, <lb></lb>intanto che avvenne in questo quel che nell&#039;altro proposito dei Moti locali, <lb></lb>che cioè, per dare inutile sodisfazione ai Simplicii, n&#039;ebbero i Sagredi a ri­<lb></lb>maner mal contenti. </s></p><p type="main">

<s>Giova ricercar nella Storia di questo mal contento un esempio, che ci <lb></lb>occorre nella prima lettura del Dialogo, dove, propostosi il caso che si vo­<lb></lb>glia sollevare un masso, per via di una Leva, si domanda qual parte sia del <lb></lb>peso totale quella, che vien sostenuta dal soggetto piano, e quale quell&#039;al­<lb></lb>tra, che grava nell&#039;estremità della stessa Leva (Alb. </s>

<s>XIII, 415). Il problema <lb></lb>era per sè di facilissima soluzione e spedita, perchè supposto essere A (fig. </s>

<s>234) <lb></lb>il masso da sollevarsi con l&#039;appoggio in N, è manifesto che la resistenza ap­<lb></lb><figure id="id.020.01.2203.1.jpg" xlink:href="020/01/2203/1.jpg"></figure></s></p><p type="caption">

<s>Figura 234<lb></lb>plicata in C, all&#039;estremità della <lb></lb>Leva di primo genere GNC, è la <lb></lb>stessa potenza della Leva di se­<lb></lb>condo genere CHB, che ha l&#039;ap­<lb></lb>poggio in B sul terreno, e il <lb></lb>peso in H nell&#039;intersezione della <lb></lb>verticale AH fatta scendere dal <lb></lb>centro di gravità del masso. </s>

<s>Cosicchè, abbassata da C perpendicolarmente <lb></lb>la CF sopra la orizzontale BF, e prolungata la AH in O, si rendono, in virtù <lb></lb>dei triangoli CBF, HBO, simili le due Leve CHB, FOB, ond&#039;è che avremo, <lb></lb>chiamata A la potenza, e C la resistenza, A:C=BF:BO. </s>

<s>Questa stessa <lb></lb>resistenza dunque, applicata in C all&#039;estremità della contralleva NC, avrà alla <lb></lb>potenza G della Leva la relazione così espressa: A.BO/BF:G=GN:NC, ossia <lb></lb>A/G=GN.BF/NC.BO, che vuol dire “ il momento di tutto il peso, al momento della <lb></lb>potenza in G, avere la proporzione composta della distanza GN alla distanza <lb></lb>NC, e della FB alla BO ” (ivi, pag. </s>

<s>115, 16) come Galileo si proponeva di <lb></lb>dimostrare. </s></p><p type="main">

<s>Ma vedasi come quella galileiana dimostrazione, illustrata da una figura <lb></lb>poco precisa, e nelle successive edizioni anche più deturpata; s&#039;aggiri per <lb></lb>vie più lunghe e faticose, non per altro fine che di renderla di più facile <lb></lb>intelligenza: e intanto usciva fuori un Matematico gesuita a mostrare quel <pb xlink:href="020/01/2204.jpg" pagenum="447"></pb>mal contento che si diceva. </s>

<s>Volle il Viviani difendere il suo Maestro nella <lb></lb>seguente postilla, inserita fra le pagine 112, 113 della citata edizione di <lb></lb>Leida: </s></p><p type="main">

<s>“ Quando il Galileo dice: <emph type="italics"></emph>la potenza in B alla potenza in C sta come <lb></lb>la FO alla OB,<emph.end type="italics"></emph.end> egli intende di quelle potenze, che resistono alle forze del <lb></lb>sasso, le quali vengono fatte ed esercitate nei punti C, B, sul Vette o sul <lb></lb>terreno, per le direzioni delle perpendicolari all&#039;orizzonte, che passano per <lb></lb>detti punti C, B, nella guisa che tutto il sasso fa la sua forza di discendere <lb></lb>col suo centro di gravità per il perpendicolo AO: ed in tal maniera intesa <lb></lb>la sua dimostrazione cammina benissimo, e non merita di essere incolpata <lb></lb>d&#039;alcuno errore dal reverendo padre G..... Che se poi altri volesse inten­<lb></lb>dere che le forze o potenze, delle quali parla il Galileo nella sua medesima <lb></lb>dimostrazione, e le quali resistono alle forze del sasso, agissero per altre di­<lb></lb>rezioni diverse da quelle dei detti perpendicoli; allora converrebbe discorrere <lb></lb>le cose diversamente, come il Galileo stesso averebbe saputo fare, e far bene, <lb></lb>in seguito di tale nuova e diversa ipotesi, senza che il detto Padre se ne <lb></lb>pigliasse pensiero ” (MSS. Gal., P. V, T. IX). </s></p><p type="main">

<s>Ma in verità non si tratta d&#039;ipotesi: si tratta di principii, che non pos­<lb></lb>sono essere punto diversi da quelli, che Galileo stesso professa e insegna <lb></lb>nelle sue <emph type="italics"></emph>Meccaniche,<emph.end type="italics"></emph.end> dalle cose dimostrate nelle quali si concluderebbe, <lb></lb>checchè se ne dica il Viviani, essere per lo meno una improprietà riguar­<lb></lb>dare come potenza il fulcro della Leva, e non distinguere il genere delle due <lb></lb>macchine nella varietà delle loro applicazioni. </s></p><p type="main">

<s>Così fatte improprietà nel significare i concetti si vedrebbero forse evi­<lb></lb>tate, se potessimo aver sott&#039;occhio i primi getti, che fece Galileo di quelle <lb></lb>sue dimostrazioni, quando non pensava ancora di renderle in così inefficace <lb></lb>modo pepolari. </s>

<s>Ci sarebbe, comunque sia, rimasto di quella prima e più ap­<lb></lb>propriata maniera pubblico documento, quando avesse il Salviati mantenuta <lb></lb>la promessa, fatta sulla sera della prima Giornata, di comparire la mattina <lb></lb>appresso innanzi agli interlocutori, per trattar con essi delle resistenze dei <lb></lb>solidi allo spezzarsi, recando seco <emph type="italics"></emph>alcuni fogli,<emph.end type="italics"></emph.end> dov&#039;aveva per ordine notati <lb></lb>i teoremi e problemi attenenti a quel soggetto (Alb. </s>

<s>XIII, 94). </s></p><p type="main">

<s>A quest&#039;annunzio incorammo la speranza di avere a ritrovar que&#039;fogli <lb></lb>tra i Manoscritti, i quali ci porgerebbero materia a riordinare, e occasione <lb></lb>a render pubblicamente noto ai Lettori il primo trattato galileiano Delle re­<lb></lb>sistenze, come facemmo del primo trattato Dei movimenti locali. </s>

<s>Ma furono <lb></lb>questa volta le nostre ricerche meno felici, perchè non fu possibile di que&#039;fo­<lb></lb>gli ritrovarne altro che pochi, e delle cose dimostrate in altri le semplici <lb></lb>conclusioni. </s></p><p type="main">

<s>Notabile è tra que&#039;fogli uno, in cui fu scritto il teorema delle condi­<lb></lb>zioni generali dell&#039;equilibrio della Leva, quando il grave non è sollevato di <lb></lb>peso, ma da una estremità si appoggia sul suolo; teorema, che appartiene <lb></lb>al trattato <emph type="italics"></emph>Della scienza meccanica,<emph.end type="italics"></emph.end> d&#039;onde lo trasse l&#039;Autore, per metterlo <lb></lb>in dialogo in principio alla seconda giornata delle due Nuove Scienze. </s>

<s>Fa <pb xlink:href="020/01/2205.jpg" pagenum="448"></pb>perciò maraviglia che l&#039;Albèri, il quale fu primo a reintegrare colla dimo­<lb></lb>strazione della Leva archimedea quel trattato galileiano, lasciasse da questa <lb></lb>parte la reintegrazione incompleta, come l&#039;hanno lasciata gli editori novelli, <lb></lb>che troppo spesso seguono, senz&#039;avvedersene, le vestigia di lui. </s>

<s>Quel teo­<lb></lb>rema dunque, ch&#039;è quasi un corollario alla terza proposizione <emph type="italics"></emph>De aequipon­<lb></lb>derantibus,<emph.end type="italics"></emph.end> fu da Galileo dialogizzato sopra questa scrittura, della quale, <lb></lb>come di tutto il trattato delle Meccaniche, non è rimasto se non che la copia: </s></p><p type="main">

<s>“ Se sia un solido sopra l&#039;orizzonte, e questo si deva alzare, è cosa <lb></lb>chiara che, se piglieremo una leva, che abbia il suo sostegno, che, a volerlo <lb></lb>equilibrare, bisognerà, volendo prima sollevarlo, mettere dall&#039;altra parte della <lb></lb>lieva potenza tale, che abbia al peso assoluto di detto solido la medesima <lb></lb>proporzione, che hanno tra loro le parti di detta lieva, ma contrariamente <lb></lb>prese. </s>

<s>Ma se ci contenteremo di alzarne una parte, e che il rimanente si <lb></lb>posi in terra, in questo caso, mentre si comincia ad alzarne una parte, sem­<lb></lb>pre va scemando il peso sopra la lieva, e va crescendo in terra. </s>

<s>Però si di­<lb></lb>mostrerà che detto peso, alla potenza che deve equilibrarlo, in qualsivoglia <lb></lb>sito che sarà detto solido, abbi proporzione composta di quella, che hanno <lb></lb>tra di loro le parti della lieva, cioè quella che è dal fulcro verso il solido, <lb></lb>e di quella, che ha la linea parallela all&#039;orizzonte, compresa tra la perpen­<lb></lb>dicolare che casca dove tocca la lieva nel solido, e dove tocca il solido in <lb></lb>terra, a quella che è compresa tra la perpendicolare che casca a detta linea <lb></lb>dal centro di gravità di detto solido, e dove tocca detto solido la detta linea <lb></lb>orizzontale. </s>

<s>” </s></p><p type="main">

<s>“ Sia il solido A (nella precedente figura) il quale sia equilibrato dalla <lb></lb>lieva GC, sostenuta nel punto N, e che posi in terra nel punto B: dico che <lb></lb>il peso assoluto di detto solido, in qualsivoglia sito, ha alla potenza posta in <lb></lb>G una proporzione composta di quella, che ha la GN alla NC, e di quella <lb></lb>di FB alla BO. ” </s></p><p type="main">

<s>“ Facciasi, come la BF alla BO, così NC ad un&#039;altra che sia H, e ti­<lb></lb>risi AO dal centro della gravità del solido perpendicolare alla BF orizzon­<lb></lb>tale. </s>

<s>Perchè dunque la potenza, che sostiene il solido A nel punto C, alla <lb></lb>potenza che sostiene il medesimo nel punto B, ha la proporzione che ha la <lb></lb>linea BH alla HC, sendo detto solido sostenuto nelli due punti C, B; sarà, <lb></lb>componendo tutt&#039;e due le potenze, cioè il peso assoluto del solido A, che è <lb></lb>l&#039;istesso alla potenza C, come FB alla BO, cioè come CN alla H. </s>

<s>Ma la po­<lb></lb>tenza di C, a quella di G, è come GN alla NC; adunque <emph type="italics"></emph>ex aequali,<emph.end type="italics"></emph.end> in pro­<lb></lb>porzion perturbata, il peso A alla potenza G ha la proporzione di GN alla <lb></lb>H, che è composta di quella, che ha la GN alla NC, e di quella di NC alla H, <lb></lb>cioè di BF alla BO, che è quello etc. </s>

<s>” </s></p><p type="main">

<s>“ Per voler poi trovare la quantità, moltiplichinsi insieme le due ante­<lb></lb>cedenti, cioè la GN per la BF, e la NC per la BO, e così sarà noto che <lb></lb>potenza ci bisogni in qualsivoglia sito. </s>

<s>” (MSS. Gal., P. V, T. II, fol. </s>

<s>27). </s></p><p type="main">

<s>Quali siano, dopo questo, gli altri fogli, da&#039;quali tradusse Galileo nei <lb></lb>Dialoghi i dimostrati teoremi, si vedrà nel processo di questo nostro discorso, <pb xlink:href="020/01/2206.jpg" pagenum="449"></pb>e benchè questi, come si diceva dianzi, sian pochi alle nostre speranze, e al <lb></lb>desiderio degli studiosi, son sufficienti nulladimeno a confermare quello, che <lb></lb>solo congetturando s&#039;annunziava, che cioè si vedrebbero in queste prime <lb></lb>forme dimostrative evitate le improprietà e le tediose lungaggini dei teoremi <lb></lb>dialogizzati. </s>

<s>Ma si vengono altresì, leggendo que&#039;fogli, a scoprir cose bene <lb></lb>assai più importanti: Alla seconda parte del trattato si pone per fondamento, <lb></lb>come altrove avvertimmo, la proposizione che le resistenze in due punti di­<lb></lb>versi del medesimo cilindro “ hanno fra di loro la medesima proporzione <lb></lb>che i rettangoli fatti dalle distanze di essi luoghi contrariamente presi ” (ivi, <lb></lb>pag. </s>

<s>135). Il teorema però apparisce in questa parte del Dialogo galileiano <lb></lb>difettoso per più ragioni: prima di tutto, perchè si suppone, senza dimo­<lb></lb>strarlo, che la proporzion dei momenti sia composta delle distanze e dei pesi; <lb></lb>e poi, perchè non risponde direttamente alla Questione aristotelica che lo <lb></lb>avea provocato, a risolver la quale bisognava piuttosto dimostrare in qual <lb></lb>ragione stia la medesima forza del ginocchio, rispetto alla resistenza opposta <lb></lb>ne&#039;varii punti fuor del mezzo del legno che si vuole spezzato. </s></p><p type="main">

<s>Concorsero zelanti a supplire ai difetti del Maestro Michelangiolo Ricci, <lb></lb>il Torricelli, il Viviani e il Marchetti, quest&#039;ultimo compiacendosi di aver <lb></lb>data dimostrazione della composizion dei momenti, e quegli altri di aver di­<lb></lb>rettamente risoluta la Questione aristotelica, concludendo che, supposto esser <lb></lb>rigido il legno e troncativo secondo l&#039;ipotesi galileiana, gli sforzi fatti nelle <lb></lb>varie parti di lui dal ginocchio, fuori del mezzo, stanno omologamente come <lb></lb>i rettangoli delle distanze dai punti, dove le mani lo tengon preso: d&#039;onde <lb></lb>il bellissimo corollarìo che la scala dei momenti dei detti sforzi è nelle <lb></lb>linee parallele al diametro di una Parabola ordinaria, che abbia per base la <lb></lb>lunghezza dello stesso legno, compresa fra i due estremi punti di appoggio. </s></p><p type="main">

<s>Or si diceva dunque che, leggendo in quei fogli rimasti in mano al <lb></lb>Salviati, si scopre con gran maraviglia avere per sè medesimo Galileo già <lb></lb>pensato di dimostrar tutto quello, che soggiunsero i quattro sopra comme­<lb></lb>morati discepoli di lui, per rendere il teorema delle resistenze del solido ap­<lb></lb>poggiato alle sue due estremità d&#039;ogni parte compiuto: nè, senza attribuirlo <lb></lb>alla forma del dialogo, e al desiderio di rendere quelle matematiche diffi­<lb></lb>coltà di facile intelligenza a tutti, si comprenderebbe perchè Galileo volesse <lb></lb>darci le laboriose scoperte mutilate così nella loro parte migliore. </s></p><p type="main">

<s>Di vederle ora finalmente reintegrate non può non nascere vivo il de­<lb></lb>siderio in chi ama questi nuovi studii galileiani, e noi volentieri sodisfaremo <lb></lb>più qua agli studiosi, quando ce ne porgerà l&#039;occasione il discorso. </s>

<s>Intanto, <lb></lb>quasi per caparra di quello che si promette, daremo fuori uno di quei fogli <lb></lb>manoscritti che, sebben non contenga nulla di più di quel che si legge nel <lb></lb>Dialogo, quanto alla materia; giova nonostante nella sua forma a confermar <lb></lb>ciò che s&#039;è detto più volte, che cioè nella matematica precisione del primo <lb></lb>trattato si vedrebbero sparire in gran parte le improprietà ingannatrici, e <lb></lb>cessare i tedii impazienti della mente, che vorrebbe correre spedita alla con­<lb></lb>clusione, e importunamente si vede trattenuta in parole. </s></p><pb xlink:href="020/01/2207.jpg" pagenum="450"></pb><p type="main">

<s>Manca a quel foglio il Lemma, che Galileo non scrive, perchè non è <lb></lb>suo, ma è, così formulata, la III manifestazione del I dei due Lemmi pre­<lb></lb>messi da Archimede alla proposizione XI Delle spirali: “ Si similes figurae <lb></lb>describantur ab omnibus, quae sese aequali invicem superant, et ab iis quae <lb></lb>sunt illarum maximae aequales; quae sane fiunt ab aequalibus maximae, <lb></lb>eorum quae fiunt ab iis quae sese aequaliter excedunt, minora sunt quam <lb></lb>tripla: sublata vero figura, quae describitur a maxima, reliquarum sunt plus <lb></lb>quam tripla ” (Opera omnia cit., pag. </s>

<s>365). </s></p><p type="main">

<s>Supposto questo che cioè: se quante linee si vogliono si eccederanno <lb></lb>egualmente, e l&#039;eccesso sia eguale alla minima di quelle, ed altrettante siano <lb></lb>ciascheduna eguale alla massima, i quadrati di tutte queste saranno meno <lb></lb>che tripli dei quadrati di quelle che si eccedono, ma i medesimi saranno <lb></lb>più che tripli di quegli altri che restano, trattone il quadrato della massima; <lb></lb>ecco come Galileo aveva, secondo l&#039;espression del Salviati, <emph type="italics"></emph>altra volta di­<lb></lb>mostrata<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>140) la sua proposizione, per applicarla al solido paea­<lb></lb>bolico di ugual resistenza, e così confermare contro i dubitanti l&#039;asserto che <lb></lb>egli sia veramente due terzi del prisma, da cui fu segato: </s></p><p type="main">

<s>“ Sit parabola CBA (fig. </s>

<s>235), parallelogrammo CP inscripta: dico pa­<lb></lb><figure id="id.020.01.2207.1.jpg" xlink:href="020/01/2207/1.jpg"></figure></s></p><p type="caption">

<s>Figura 235<lb></lb>rallelogrammum parabolae esse se­<lb></lb>squialter; hoc est esse triplum reli­<lb></lb>qui spacii ABP extra parabolam. </s>

<s>” </s></p><p type="main">

<s>“ Si enim non sit, aut erit maius <lb></lb>aut minus. </s>

<s>Sit primo maius: exces­<lb></lb>sus autem, quo spacium PC maius <lb></lb>est quam triplum spacii APB, vo­<lb></lb>cetur X, divisoque parallelogrammo <lb></lb>continue in spacia aequalia, per li­<lb></lb>neas ipsis AC, PB parallelas, devenie­<lb></lb>mus ad spacia, quorum unum ipso X <lb></lb>erit minus, quale sit OB, et per puncta, ubi reliquae parallelae lineam para­<lb></lb>bolae secant, ducantur aequidistantes ipsi AP, donec figura quaedam spacio <lb></lb>relicto extra parabolam circumscribatur, constans ex parallelogrammis AG, <lb></lb>KE, LF, MH, NI, OB, quae figura spacium APB extra parabolam minori <lb></lb>quantitate superabit quam sit X, cum superet idem quantitate adhuc minori <lb></lb>parallelogrammo OB. </s>

<s>Ergo idem parallelogrammum CP maius erit quam <lb></lb>triplum dictae figurae circumscriptae, quod est impossibile. </s>

<s>” </s></p><p type="main">

<s>“ Non est ille minus quam triplum: nam cum DA ad AZ sit ut qua­<lb></lb>dratum DE ad quadratum ZG; ut autem DA ad AZ, ita parallelogrammum <lb></lb>DK, seu KE, ad parallelogrammum KZ; ergo, ut quadratum ZG ad quadra­<lb></lb>tum DE (ita quadratum AK ad quadratum AL) ita parallelogrammum AG <lb></lb>ad parallelogrammum KE. ” </s></p><p type="main">

<s>“ Similiter ostendemus reliqua parallelogramma LF, MH, NI, OB esse <lb></lb>inter se ut quadrata linearum AK, AL, AM, AN, AO, AP sese aequaliter <lb></lb>excedentium, et quorum excessus minimae AK est aequalis. </s>

<s>” </s></p><pb xlink:href="020/01/2208.jpg" pagenum="451"></pb><p type="main">

<s>“ Cum itaque sint huiusmodi spacia ut quadrata linearum sese aequa­<lb></lb>liter excedentium, quarum excessus minimae est aequalis; si sint alia toti­<lb></lb>dem numero, magnitudine vero unumquodque maximo OB aequalia, pa­<lb></lb>rallelogrammum nempe CP componentia, constat haec ad spacia, a sese <lb></lb>aequaliter excedentium linearum, minora esse quam tripla. </s>

<s>” </s></p><p type="main">

<s>“ Dico praeterea non esse minus parallelogrammum CP quam triplum, <lb></lb>ad idem spacium APB. </s>

<s>Si enim CP dicatur esse minus, sit defectus X, et <lb></lb>figura similiter inscr batur, constans ex parallelogrammis KQ, LR, MS, NT, <lb></lb>OU, quae sint ut quadrata linearum sese aequaliter excedentium etc., quae <lb></lb>deficiat a dicto spacio minori quantitate quam sit X (cum deficiat per mi­<lb></lb>norem quam sit OB) quae erit adhuc maior quam tertia pars parallelogrammi <lb></lb>CP, quod pariter est falsum, cum sit minor. </s>

<s>” (MSS. Gal., P. V, T. II, <lb></lb>fol. </s>

<s>102 a tergo). </s></p><p type="main">

<s>La conclusione, nel foglio che veniva a mancare, è taciuta, come quella <lb></lb>che occorrerebbe alla mente dei Lettori spontanea, perchè avendo provato <lb></lb>non poter essere il triangolo mistilineo ABP nè maggiore nè minore della <lb></lb>terza parte del parallelogrammo CP scendeva dunque senz&#039;altro che do­<lb></lb>vess&#039;essere eguale. </s>

<s>Si collazioni ora di grazia questa dimostrazione con quella <lb></lb>inserita nel Dialogo, e che comprende quasi mezza la pagina 140, la 141, 42 <lb></lb>e un terzo della 143 dell&#039;edizion dell&#039;Albèri, e si vedrà quanto lo sminuz­<lb></lb>zare le cose per renderle più chiare noccia, in queste matematiche propo­<lb></lb>sizioni, alla chiarezza. </s></p><p type="main">

<s>Che se di questa chiarezza l&#039;ordine è causa principale la libertà del dia­<lb></lb>logo a ogni passo l&#039;infrange, e non è perciò maraviglia se, avendo Galileo <lb></lb>incominciato in margine a numerare le proposizioni, fa dopo l&#039;VIII cessare <lb></lb>anche questa guida al Lettore. </s>

<s>Ne&#039;quei numeri, giusto per far l&#039;ufficio di <lb></lb>guida e d&#039;indice, avrebbero reso piccolo servigio, specialmente in ramme­<lb></lb>morare e in dovere ad altri indicar questo o quello dei dimostrati teoremi. </s>

<s><lb></lb>Un tal bisogno fu che consigliava al Viviani di proseguire a segnar sopra <lb></lb>la copia da lui postillata l&#039;interrotta numerazione infino alla XV, perchè <lb></lb>spesso occorrevagli di citarle nell&#039;esercitarsi che fece intornò a quello stesso <lb></lb>argomento. </s>

<s>E perchè anche noi, nel dover dirne la storia, ci troveremo <lb></lb>nel medesimo caso, abbiam voluto condurre a termine la detta numera­<lb></lb>zione, della quale intendiamo servirci per togliere ogni equivoco, e per <lb></lb>non esser costretti a ripeter sempre le formule, spesso spesso non brevi, <lb></lb>di Galileo. </s></p><p type="main">

<s>L&#039;equivoco, che potrebbe nuocere alla chiarezza delle cose da dire, e <lb></lb>che perciò preme a noi di evitare, può nascer dal credere che si debbano <lb></lb>mettere in ordine tutte le proposizioni dimostrate, mentre Galileo stesso inco­<lb></lb>minciò a numerar quelle sole attenenti alla meccanica delle resistenze, la­<lb></lb>sciando indietro le altre di pura Geometria. </s></p><p type="main">

<s>Seguitando dunque anche noi quegli esempii, raccoglieremo qui ordi­<lb></lb>nate le proposizioni o abbiano forma loro propria, o si trovino involte nel <lb></lb>conversevole discorso del Salviati. </s>

<s>Il primo dei numeri, che apponiamo a <pb xlink:href="020/01/2209.jpg" pagenum="452"></pb>ciascuna, appella alla edizione di Leida, e l&#039;altro, che gli segue appresso, a <lb></lb>quella dell&#039;Albèri. </s></p><p type="main">

<s>PROPOSIZIONE I. — “ Figuriamoci il prisma solido ABCD, fitto in un <lb></lb>muro dalla parte AB, e nell&#039;altra estremità s&#039;intenda la forza del peso E:... <lb></lb>il momento della forza E, posta in C, al momento della resistenza, che ha <lb></lb>nella grossezza del prisma, ha la medesima proporzione che la lunghezza CB <lb></lb>alla metà della BA ” (114, 116). </s></p><p type="main">

<s>PROPOSIZIONE II. — “ Intendasi una riga AD, la cui lunghezza sia AC, <lb></lb>e la grossezza assai minore CB: si cerca perchè, volendola romper per ta­<lb></lb>glio, resisterà al gran peso T, ma posta per piatto non resisterà all&#039;X mi­<lb></lb>nore del T ” (116, 118). </s></p><p type="main">

<s>PROPOSIZIONE III. — “ I momenti delle forze dei prismi o cilindri ugal­<lb></lb>mente grossi, ma disegualmente lunghi, son tra di loro in duplicata pro­<lb></lb>porzione di quella delle loro lunghezze ” (117, 119). </s></p><p type="main">

<s>PROPOSIZIONE IV. — “ Nei prismi e cilindri egualmente lunghi, ma <lb></lb>disegualmente grossi, la resistensa all&#039;esser rotti cresce in triplicata propor­<lb></lb>zione dei diametri delle loro grossezze, cioè delle loro basi ” (118, 119). </s></p><p type="main">

<s>PROPOSIZIONE V. — “ Dei prismi e cilindri, di diversa lunghezza e gros­<lb></lb>sezza, le resistenze all&#039;esser rotti hanno proporzione composta della propor­<lb></lb>zione dei cubi de&#039;diametri delle lor basi, e della proporzione delle loro <lb></lb>lunghezze, permutatamente prese ” (121, 122). </s></p><p type="main">

<s>PROPOSIZIONE VI. — “ Dei cilindri e prismi simili i momenti compo­<lb></lb>sti, cioè resultanti dalle loro gravità e dalle loro lunghezze, che sono come <lb></lb>leve, hanno tra di loro proporzione sesquialtera di quella, che hanno le re­<lb></lb>sistenze delle medesime loro basi ” (122, 123). </s></p><p type="main">

<s>PROPOSIZIONE VII. — “ Dei prismi o cilindri simili gravi un solo e unico <lb></lb>è quello, che si riduce, gravato dal proprio peso, all&#039;ultimo stato tra lo <lb></lb>spezzarsi e il sostenersi intero ” (124, 155). </s></p><p type="main">

<s>PROPOSIZIONE VIII. — “ Dato un cilindro o prisma di massima lun­<lb></lb>ghezza, da non esser dal suo proprio peso spezzato, e data una lunghezza <lb></lb>maggiore, trovar la grossezza d&#039;un altro cilindro o prisma che, sotto la <lb></lb>data lunghezza, sia l&#039;unico e massimo resistente al proprio peso ” (125, <lb></lb>126). </s></p><p type="main">

<s>PROPOSIZIONE IX. — “ Dato il cilindro AC, qualunque si sia il suo mo­<lb></lb>mento verso la sua resistenza, o data qualsiasi lunghezza DE, trovar la gros­<lb></lb>sezza del cilindro, la cui lunghezza sia DE, e il suo momento verso la sua <lb></lb>resistenza ritenga la medesima proporzione, che il momento del cilindro AC <lb></lb>alla sua ” (128, 128). </s></p><p type="main">

<s>PROPOSIZIONE X. — “ Dato un prisma o cilindro col suo peso, ed il <lb></lb>peso massimo sostenuto da esso, trovare la massima lunghezza, oltre alla <lb></lb>quale prolungato, dal solo suo proprio peso si romperebbe ” (131, 131). </s></p><p type="main">

<s>PROPOSIZIONE XI. — “ Il cilindro, che gravato dal proprio peso sarà <lb></lb>ridotto alla massima lunghezza, oltre alla quale più non si sosterrebbe, o <lb></lb>sia retto nel mezzo da un solo sostegno, ovvero da due nelle estremità, po-<pb xlink:href="020/01/2210.jpg" pagenum="453"></pb>trà essere lungo il doppio di quello che sarebbe fitto nel muro, cioè soste­<lb></lb>nuto in un sol termine ” (132, 132). </s></p><p type="main">

<s>PROPOSIZIONE XII. — “ Se nella lunghezza d&#039;un cilindro si noteranno <lb></lb>due luoghi, sopra i quali si voglia far la frazione di esso cilindro, le resi­<lb></lb>stenze dei detti due luoghi hanno fra di loro la medesima proporzione, <lb></lb>che i rettangoli fatti dalle distanze di essi luoghi, contrariamente presi ” <lb></lb>(135, 135). </s></p><p type="main">

<s>PROPOSIZIONE XIII. — “ Dato il peso massimo retto dal mezzo di un ci­<lb></lb>lindro o prisma, dove la resistenza è minima, e dato un peso maggiore di <lb></lb>quello, trovare nel detto cilindro il punto, nel quale il dato peso maggiore <lb></lb>sia retto come massimo ” (136, 136). </s></p><p type="main">

<s>PROPOSIZIONE XIV. — “ Il prisma, segato diagonalmente, ottiene contraria <lb></lb>natura del prisma intero, cioè che meno resiste all&#039;essere spezzato sopra il <lb></lb>termine C, che sopra l&#039;A, dalla forza posta in B, quanto la lunghezza CB <lb></lb>è minore della BA ” (138, 137). </s></p><p type="main">

<s>PROPOSIZIONE XV. — “ Nella faccia di un prisma sia segnata la linea pa­<lb></lb>rabolica, secondo la quale sia segato esso prisma: dico tal solido esser per <lb></lb>tutto egualmente resistente ” (140, 139). </s></p><p type="main">

<s>PROPOSIZIONE XVI. — “ Le resistenze di due cilindri eguali ed egual­<lb></lb>mente lunghi, l&#039;uno dei quali sia vuoto e l&#039;altro massiccio, hanno tra di loro <lb></lb>la medesima proporzione che i loro diametri ” (147, 145). </s></p><p type="main">

<s>PROPOSIZIONE XVII. — “ Data una canna vuota, trovare un cilindro <lb></lb>pieno uguale ad essa ” (148, 146). </s></p><p type="main">

<s>PROPOSIZIONE XVIII. — “ Trovare qual proporzione abbiano le resistenze <lb></lb>di una canna e di un cilindro, qualunque siano, purchè egualmente lun­<lb></lb>ghi ” (148, 146). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Non oziosamente si disse avere il Viviani preso in mano il lapis, a pro­<lb></lb>seguire la numerazione di queste proposizioni, ma per ridursele più facil­<lb></lb>mente alla memoria, e indicarle ne&#039;suoi studiosi esercizii. </s>

<s>Abbiamo docu­<lb></lb>mento certo che cominciarono questi esercizii infino dal 1644, e che vi ritornò <lb></lb>sopra, interrompendo spesso l&#039;opera sua, ma non intiepidendo nel suo primo <lb></lb>fervore. </s>

<s>Quel che via via gli occorreva a notare, si per ridurre le dottrine <lb></lb>del suo Maestro più compiute e più corrette, sì per applicarle a più ampio <lb></lb>soggetto, rendendole di nuove o curiose o utili conseguenze feconde; scri­<lb></lb>veva, secondo il suo solito, sopra foglietti sciolti, che poi alla rinfusa si rac­<lb></lb>coglievano insieme in un inserto. </s>

<s>Erano materiali preziosi e abbondanti, per <lb></lb>comporre delle resistenze dei solidi un trattato perfetto, il quale però, per i <lb></lb>casi della vita distratta in tante altre cure, e per l&#039;indole propria dell&#039;Autore, <lb></lb>si rimase per sempre informe, e se ne potè poco giovare la scienza, e sola­<lb></lb>mente dopo quelle lunghe avventure, che si narreranno in questa Storia. </s></p><pb xlink:href="020/01/2211.jpg" pagenum="454"></pb><p type="main">

<s>Intanto, nel 1661, Francesco Clousier pubblicava in Parigi una lettera <lb></lb>di Francesco Blondel, sottoscritta il di 12 Agosto 1657, e indirizzata a Paolo <lb></lb>Wrz “ in qua, dicevasi nel frontespizio, famosa Galilaei propositio discuti­<lb></lb>tur circa naturam lineae, qua trabes secari debent, ut sint aequalis ubique <lb></lb>resistentiae, et in qua lineam illam, non quidem parabolicam, ut ipse Gali­<lb></lb>laeus arbitratus est, sed ellipticam esse demonstratur. </s>

<s>” </s></p><p type="main">

<s>La scoperta del Blondel era come un saggio, che si dava al pubbico <lb></lb>di studii più ampii, fatti sopra Galileo, intantochè ne aveva l&#039;illustre Ma­<lb></lb>tematico francese composto già, nel 1649, un libro <emph type="italics"></emph>De resistentia solidorum,<emph.end type="italics"></emph.end><lb></lb>ch&#039;egli avrebbe voluto intitolare <emph type="italics"></emph>Galilaeus promotus.<emph.end type="italics"></emph.end> “ Ayant, scriveva in <lb></lb>un suo Discorso apologetico nel 1661, pour ce suiet compos<gap></gap> le livre, que <lb></lb>vous avez veu prest a estre donn<gap></gap> au public. </s>

<s>Il y a plus de douze ans, que <lb></lb>j&#039;appelle <emph type="italics"></emph>Galilaeus promotus, De resistentia solidorum,<emph.end type="italics"></emph.end> et que pouvant quel­<lb></lb>que jour estre mis en <gap></gap> miere ” (Recueil de plusieurs traietez de Mathem., <lb></lb>Paris 1673, pag. </s>

<s>60). Quel giorno però non venne mai, e vedremo perchè <lb></lb>il Blondel revocasse quel suo primo fervoroso pensiero, com&#039;attesta il Leib­<lb></lb>niz in una sua lettera autografa al Grandi: “ Blondellus librum De resisten­<lb></lb>tia solidorum composuerat, sed, re melius comperta, cum ego Parisiis age­<lb></lb>rem, idest paulo post annum 1672, totum revocarat ” (MSS. Cim., T. XXIX, <lb></lb>fol. </s>

<s>287). Cosicchè non ebbe il pubblico degli studii del Blondel intorno alla <lb></lb>resistenza dei solidi altro che le proposizioni, nelle quali si dimostra esser <lb></lb>l&#039;ellittico e no il parabolico il solido atto a resistere ugualmente per tutto <lb></lb>alla pressione di un peso. </s></p><p type="main">

<s>Se fossero, com&#039;asserirono alcuni, queste dimostrazioni approdate per <lb></lb>tempo in Italia a dare impulso agli ingegni, non si potrebbe affermar con <lb></lb>certezza, ma non sembra che avesse il Viviani, per esempio, bisogno di tali <lb></lb>impulsi stranieri: e dall&#039;altra parte, in mezzo a studii così primaticci e ope­<lb></lb>rosi, era naturale gli si rivelasse spontaneo alla mente l&#039;errore del Maestro, <lb></lb>dalle dottrine stesse insegnate dal quale concludevasi facilmente esser da <lb></lb>segar la trave, perchè ugualmente resista, non secondo il filo della parabola, <lb></lb>ma secondo quel dell&#039;ellisse, e anzi di altre curve, e di quella stessa pa­<lb></lb>rabolica, che si mettesse con la superficie terminata da lei in piano, piut­<lb></lb>tosto che eretta. </s></p><p type="main">

<s>Professa di essersi condotto a queste medesime conclusioni Alessandro <lb></lb>Marchetti, non per altro impulso che per quello venutogli direttamente dalla <lb></lb>lettura del Dialogo galileiano, incominciata a farsi da lui con più attenzione <lb></lb>nel 1659. “ Aveva io, egli dice, nello studiare il Galileo intorno alla ugual <lb></lb>resistenza del solido parabolico in ogni sua parte, osservato come da tal pro­<lb></lb>posizione il Salviati, principale tra i personaggi dal medesimo Galileo intro­<lb></lb>dotti a parlare in quel suo dialogo, deduce per corollario che potrebbero <lb></lb>fabbricarsi i travamenti delle navi con diminuzione di peso di più di 33 <lb></lb>per cento, senza diminuire punto la loro gagliardia, al che, facendo io qual­<lb></lb>che attenta e matura riflessione, e considerando che i suddetti travamenti <lb></lb>non si appoggiano a un sostegno solo, come il solido parabolico, del quale <pb xlink:href="020/01/2212.jpg" pagenum="455"></pb>esso Galileo aveva, poco innanzi la suddetta, ammiranda invero e del suo su­<lb></lb>blime ingegno degnissima, proprietà dimostrato, ma vengon retti in ambe­<lb></lb>due le loro estremità, ancorchè io mi persuadessi che potesse esser vero, <lb></lb>che anche questi secondo la linea parabolica fossero in ogni lor parte egual­<lb></lb>mente resistenti, per vederlo affermato con tanta franchezza da un sì gran­<lb></lb>d&#039;Uomo; pur nondimeno volli meglio certificarmene per mezzo di qualche <lb></lb>evidente dimostrazione, alla quale avendo io più volte pensato e ripensato, <lb></lb>e non potendone venire a capo, incolpava da principio il corto mio inten­<lb></lb>dimento, quasi che egli fosse incapace di penetrar colà, ove con una sola <lb></lb>occhiata della sua eccelsa mente aveva, col dedurre dalla detta proposizione <lb></lb>quel corollario, penetrato il divino ingegno del Galileo. </s>

<s>Ma disingannatomi <lb></lb>finalmente, e conosciuto, e con geometrica evidenza provato, che non il so­<lb></lb>lido parabolico, sostenuto in ambedue i suoi estremi termini, non era per <lb></lb>tutto egualmente resistente, ma che di lui neanche verificavasi la suddetta <lb></lb>proprietà, quando viene appoggiato a un sostegno solo, se non in caso che <lb></lb>egli si consideri come nulla pesante (cosa che può ben da noi immaginarsi, <lb></lb>ma non giammai ottenersi, mettendo in opera le dette travi, per essere que­<lb></lb>ste necessariamente materiali, e però sempre congiunte col proprio peso) <lb></lb>presi animo, non solo di speculare o dimostrare alcune altre proposizioni a <lb></lb>tal materia appartenenti, ma di mandarle manoscritte, dalla mia villa di Pon­<lb></lb>tormo, dove io allora mi ritrovava, a Firenze, al non mai lodato abbastanza <lb></lb>mio gran maestro G. A. Borelli, per sentirne da lui il suo dottissimo e sin­<lb></lb>cerissimo parere. </s>

<s>Ed avendomi egli prontamente risposto, e non solo appro­<lb></lb>vato le suddette proposizioni, ma consigliatomi di più a specularne delle <lb></lb>nuove, io di buona voglia mi accinsi all&#039;opera, quale, a dir vero, non senza <lb></lb>molto studio e fatica ridussi al fine desiderato ” (<emph type="italics"></emph>Lettera, nella quale si <lb></lb>ribattono le ingiuste accuse del P. D. G. G., Lucca 1711, pag. </s>

<s>27, 28<emph.end type="italics"></emph.end>). <lb></lb>La fatica però, soggiungeva nella prefazione al libro da darsi alla luce, <lb></lb>essergli stata non poco alleviata dall&#039;invenzione della composizion dei mo­<lb></lb>menti, per la quale, se prima conveniva dare allo stesso libro il titolo di <lb></lb><emph type="italics"></emph>Galileo ampliato,<emph.end type="italics"></emph.end> ora poteva, senz&#039;altro, sostituirglisi quello <emph type="italics"></emph>Della resistenza <lb></lb>dei solidi.<emph.end type="italics"></emph.end> “ Hinc haud immerito ex hoc libello expunctus titulus <emph type="italics"></emph>Galilaeus <lb></lb>ampliatus,<emph.end type="italics"></emph.end> eiusque vice iure substitutus <emph type="italics"></emph>De resistentia solidorum ”<emph.end type="italics"></emph.end> (Flo­<lb></lb>rentiae 1669, pag. </s>

<s>IX). </s></p><p type="main">

<s>Messa dunque così in ordine l&#039;opera laboriosa, si presenta un giorno <lb></lb>il Marchetti innanzi al cardinale Leopoldo, offerendogli il manoscritto, ed <lb></lb>esprimendogli il desiderio di dedicarne la stampa all&#039;Eminenza Sua Sere­<lb></lb>nissima. </s>

<s>Alla nuova l&#039;animo del Viviani entrò in gran tumulto: egli va­<lb></lb>gheggiava da lungo tempo il proposito di raccogliere in un volume tutte le <lb></lb>cose scritte a illustrar le dottrine del suo Maestro, specialmente attinenti <lb></lb>alle resistenze dei solidi, e premessavi la vita di Galileo dedicar tutto a <lb></lb>Luigi XIV di Francia, in riconoscenza dei ricevuti onori e delle munificenze. </s>

<s><lb></lb>L&#039;opera del Marchetti avrebbe resa inutile, o solamente secondaria la mi­<lb></lb>glior parte dell&#039;opera sua, e non vedendo perciò altro rimedio al suo danno <pb xlink:href="020/01/2213.jpg" pagenum="456"></pb>va al Cardinale stesso, supplicandolo a interporre la sua autorità, per otte­<lb></lb>ner dal Marchetti la dilazione della stampa per alquanti mesi. </s>

<s>Il Marchetti, <lb></lb>soggiogato, tacque alla proposta, e s&#039;intese che tacendo volesse acconsen­<lb></lb>tire “ di che, scrisse poi, dal signor Lorenzo Bellini, e particolarmente dal <lb></lb>signor Gio. </s>

<s>Alfonso Borelli fui agramente ripreso ” (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Queste e altre simili espressioni darebbero gran fondamento al sospetto <lb></lb>che soffiasse, con enfiate guance, nella fiamma il Borelli, avido di vendetta <lb></lb>contro il Viviani, ch&#039;egli accusava di avere stimolato, e concorso con lo Ste­<lb></lb>none a prevenire, nella Miologia, la nuova Scienza dei moti animali. </s>

<s>Gli era <lb></lb>forse venuto alle orecchie che il Viviani stesso avesse presa, dalle resistenze <lb></lb>dei corpi duri, occasione d&#039;entrare in argomento delle resistenze delle ossa <lb></lb>e delle membra, ciò che poi era il vero, com&#039;apparisce da certe note, e spe­<lb></lb>cialmente da quella, nella quale si propose: “ Consideretur magna vis in <lb></lb>impellendo, dum crura ad coxas angulos obtusos faciunt ” (MSS. Gal., P. V, <lb></lb>T. VII, fol. </s>

<s>38) rassomigliando la forza delle membra a quella stessa di un <lb></lb>legno, secondo un simile angolo inflesso. </s></p><p type="main">

<s>In qualunque modo, non s&#039;intende a che pro richìedere l&#039;indugio di <lb></lb>alquanti mesi, quando, a dar forma all&#039;opera, non sarebbero al Viviani ba­<lb></lb>stati altrettanti anni: nè, risolvendosi ancora di porvi mano, pregava Carlo <lb></lb>Dati di tornare al principe Leopoldo, per veder di prolungare ancora di più <lb></lb>quell&#039;indugio. </s>

<s>Rispose il Principe sentir gran passione di questo negozio; <lb></lb>avrebbe fatto il possibile, ma che non voleva comandare. </s>

<s>Ciò che inteso il <lb></lb>Viviani depose affatto il pensiero, e, per provvedere in qualche modo alla <lb></lb>iattura, raccolse le sue carte in un fascio, e andò a farle riconoscere, con <lb></lb>la propria firma e con l&#039;impression del sigillo, a Sua Altezza, “ il che, scri­<lb></lb>veva allo stesso Marchetti, riuscirà di mia somma quiete e sodisfazione, per <lb></lb>poter far constar, con aprirlo a chi e quando occorresse, che io non m&#039;era <lb></lb>mosso nè per iattanza, nè per impedire il proseguimento de&#039;suoi intenti ” <lb></lb>(<emph type="italics"></emph>Lettera pubblicata dal Grandi nella Risposta apol., Lucca 1712, pag. </s>

<s>75<emph.end type="italics"></emph.end>). <lb></lb>Avvisava nel tempo stesso Francesco Blondel, ch&#039;era allora in viaggio per <lb></lb>l&#039;Italia, scrivesse al Colbert per quali penose avventure avea dovuto deporre <lb></lb>il pensiero di dedicare il libro su Galileo al Re di Francia. </s></p><p type="main">

<s>Un lampo fuggitivo venne poco dopo a rallegrare al Viviani la faccia <lb></lb>rannuvolata: la luce lusinghiera appariva attraverso alle parole di questa <lb></lb>lettera, che il Marchetti scriveva il dì 14 Febbraio 1668 al cardinale Leo­<lb></lb>poldo: </s></p><p type="main">

<s>“ Tre mesi di proroga, domandatami dal signor Carlo Dati per ordine <lb></lb>di V. A. R. intorno alla pubblicazion del mio libro di resistenze, son già <lb></lb>spirati da molti giorni. </s>

<s>Ne dò parte, com&#039;è mio debito, alla R. A. V. ed in­<lb></lb>sieme la supplico vivamente, e con ogni maggiore ossequio di umiltà, a farlo <lb></lb>sapere al signor Viviani, acciò, se egli è all&#039;ordine, come credo, con la sua <lb></lb>Opera, possiamo, con quelle condizioni e cautele che più parranno conve­<lb></lb>nevoli a V. A. R., dare ambedue principio unitamente alla stampa: se no, <lb></lb>io con buona grazia di V. A. R., e sotto il benigno auspicio del suo nome <pb xlink:href="020/01/2214.jpg" pagenum="457"></pb>gloriosissimo, comincerò ogni volta a stampare la mia, nella quale, per la­<lb></lb>sciare anco libero il campo al signor Viviani di potere con suo comodo ed <lb></lb>a sua voglia ampliare le dottrine di Galileo, ed inserirle nella sua Vita, <lb></lb>com&#039;ei desidera, tacerò il titolo di <emph type="italics"></emph>Galileo ampliato,<emph.end type="italics"></emph.end> nè mi servirò d&#039;al­<lb></lb>cuno principio di quel grand&#039;uomo, come innanzi mi ero proposto, ma solo, <lb></lb>con fondamenti proprii miei, tratterò, senza pur farne alcuna menzione, della <lb></lb>resistenza dei corpi duri ” (MSS. Cim, T. XIX, fol. </s>

<s>144). </s></p><p type="main">

<s>Intese il Cardinale che il Marchetti si dichiarasse di voler trattar nel <lb></lb>suo libro materie non toccate da Galileo, cosicchè, essendo le opere dei due <lb></lb>concorrenti di argomento diverso, si potessero stampare ambedue insieme, <lb></lb>senza che l&#039;una recasse all&#039;altra nessun pregiudizio. </s>

<s>Lieto di veder che final­<lb></lb>mente riusciva a buon termine il geloso negozio, ne diè sollecito avviso al <lb></lb>Viviani, il quale subito, con l&#039;animo ravvivato, revocava così dal Blondel la <lb></lb>datagli commissione: “ Molto opportunamente risolse V. S. illustrissima di <lb></lb>non scrivere all&#039;eccellentissimo signor Colbert intorno a quel suo partico­<lb></lb>lare, se non dopo arrivato a Roma, poichè, con la medesima mia lettera e <lb></lb>sotto quella fede da lei promessami nel rimanente, devo dirle come in que­<lb></lb>sti giorni il serenissimo Cardinale mi ha significato di aver avuto infallibile <lb></lb>certezza che quell&#039;Amico ha variato affatto pensiero, e non tratta punto di <lb></lb>resistenze de&#039;corpi duri, nè fa mai menzione del trattato di Galileo, e nem­<lb></lb>meno lo nomina. </s>

<s>Tanto, e niente più mi ha partecipato S. A., dicendo non <lb></lb>saper altro, onde, essendo così, non vedo che io debba qua far istanza di <lb></lb>sospensione, ma lascerolla uscire fuori, ed io da qui avanti, con l&#039;animo che <lb></lb>V. S. illustrissima per sua bontà me ne ha dato, ripiglierò le fatiche di <lb></lb>quella <emph type="italics"></emph>Vita,<emph.end type="italics"></emph.end> e anderò seguitando ad ordinare e distendere il restante di quella <lb></lb>materia informe, che io le feci vedere ” (<emph type="italics"></emph>Lettera pubblicata dal Grandi <lb></lb>nella Risposta apol. </s>

<s>cit., pag. </s>

<s>83, 84<emph.end type="italics"></emph.end>). </s></p><p type="main">

<s>Un anno, e qualche mese dopo, vede il Viviani stesso comparirsi in­<lb></lb>nanzi un libretto in ottavo, legato in foglio, sopravi scritto: <emph type="italics"></emph>dono dell&#039;Au­<lb></lb>tore,<emph.end type="italics"></emph.end> e, svolta per curiosità la copertina, posa sul frontespizio gli occhi ran­<lb></lb>nuvolati:.... era il trattato del Marchetti <emph type="italics"></emph>De resistentia solidorum,<emph.end type="italics"></emph.end> uscito <lb></lb>allora allora alla luce in Firenze dalla tipografia di Vincenzio Vangelisti. </s>

<s>Le <lb></lb>figure stesse intercalate nel testo gli rivelarono amaramente che il cardinale <lb></lb>Leopoldo aveva frantese l&#039;espressioni del Marchetti, e ch&#039;erano ambedue ri­<lb></lb>masti ugualmente ingannati nel creder che non si trattasse lì nè di Gali­<lb></lb>leo, nè di resistenze dei corpi duri. </s>

<s>Leggendo poi più attentamente, e con <lb></lb>animo oramai rassegnato, ebbe anzi a maravigliarsi del riscontro che notava <lb></lb>fra le principali di quelle proposizioni e le sue proprie, intantochè, come il <lb></lb>Blondel, vedute le cose del Viviani; così il Viviani stesso revocò per sem­<lb></lb>pre le sue, vedute le cose del Marchetti. </s></p><p type="main">

<s>Questa conclusione è tutt&#039;affatto contraria a quella dei partigiani, un <lb></lb>dei quali più infervorato di tutti, ammirava la mortificazione che allora fece <lb></lb>il Viviani stesso “ della curiosità, che naturalmente nascer gli dovette nel <lb></lb>cuore, di leggere il trattato del Marchetti, e riscontrarlo nelle cose più prin-<pb xlink:href="020/01/2215.jpg" pagenum="458"></pb>cipali, per sapere se in parte o in tutto l&#039;avesse prevenuto, ed in qual modo <lb></lb>impugnasse lo sbaglio preso da Galileo ” (Grandi, Risposta apol. </s>

<s>cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Noi invece, vedendo che il Viviani abbandonò per sempre il proposito, con <lb></lb>sì fervorose espressioni ultimamente comunicate al Blondel, teniamo che ciò <lb></lb>non fosse nè per volubilità, nè per ignavia, ma perchè, riscontrando il Mar­<lb></lb>chetti nelle parti principali, conobbe che veramente lo aveva prevenuto, e che <lb></lb>s&#039;era mirabilmente riscontrato seco nell&#039;impugnare lo sbaglio preso da Galileo. </s></p><p type="main">

<s>Nello scolio infatti alla proposizione LXXXIII del I libro, l&#039;Autore <emph type="italics"></emph>De <lb></lb>resistentia solidorum<emph.end type="italics"></emph.end> così scriveva: “ Hic fortasse non abs re erit animad­<lb></lb>vertere quod, licet solidum parabolicum, abstrahendo a momento suae gra­<lb></lb>vitatis, sit ubique aequalis resistentiae, quemadmodum in suis dialogis osten­<lb></lb>dit Galileus, et nos etiam paulo inferius alia via ostensi sumus; si tamen <lb></lb>illius pondus consideretur, magis magisque semper resistit, quam magis ma­<lb></lb>gisque peragendae fractionis locus eius vertici proximior est ” (Floren­<lb></lb>tiae 1669, pag. </s>

<s>60). </s></p><p type="main">

<s>Le vie tenute dal Marchetti, per dimostrar che il solido parabolico, sup­<lb></lb>posto senza peso, è di ugual resistenza, sono speditissime, e là dove Galileo <lb></lb>premette un lemma e faticosamente, come vedemmo, s&#039;aggira, il Marchetti, <lb></lb>col principio della composizion dei momenti già dimostrato, e dietro il di­<lb></lb>mostrato teorema che i momenti delle resistenze delle sezioni, aventi basi <lb></lb>uguali e differenti altezze, stanno come i quadrati di esse altezze, così, in <lb></lb>due parole, conclude la sua proposizione. </s></p><p type="main">

<s>Sia il solido parabolico DB (fig. </s>

<s>236) e OB una sua parte: posto che <lb></lb><figure id="id.020.01.2215.1.jpg" xlink:href="020/01/2215/1.jpg"></figure></s></p><p type="caption">

<s>Figura 236<lb></lb>i pesi F, G equivalgano col loro mo­<lb></lb>mento ai momenti delle resistenze delle <lb></lb>sezioni AD, CO, che chiameremo M.oAD, <lb></lb>M.oCO, abbiamo M.oAD:M.oCO= <lb></lb>F.AB:G.CB. </s>

<s>Ma per le cose dimo­<lb></lb>strate M.oAD:M.oCO=AF2:NG2, e in <lb></lb>virtù della parabola AF2:NC2=AB:CB, <lb></lb>dunque AB:CB=F.AB:G.CB. <lb></lb>“ Ergo F ad G, hoc est resistentia so­<lb></lb>lidi DB, ad resistentiam solidi OB, proportionem habet aequalitatis ” (ibid.). <lb></lb><figure id="id.020.01.2215.2.jpg" xlink:href="020/01/2215/2.jpg"></figure></s></p><p type="caption">

<s>Figura 237</s></p><p type="main">

<s>Il Viviani a principio, non sapendosi distaccare <lb></lb>dalle orme di Galileo, aveva pensato di sostituire un <lb></lb>altro lemma, così intitolato da lui stesso e così scritto: <lb></lb><emph type="italics"></emph>“ Lemma pro propositione XV Galilei, pag. </s>

<s>140, ali­<lb></lb>ter demonstranda, et ope infrascripti lemmatis ge­<lb></lb>neralis:<emph.end type="italics"></emph.end> In parabola ABC (fig. </s>

<s>237), ductis ordina­<lb></lb>tis AC, EF, et inter partes diametri CB, BE sumpta BH <lb></lb>media proportionalis, ductis BG, HI, semper erit ut AC <lb></lb>ad CG ita EF ad IH. </s>

<s>Nam recta CB ad BE, vel qua­<lb></lb>dratum CB ad quadratum BH, est ut quadratum AC <lb></lb>ad quadratum EF. </s>

<s>Est etiam linea AC ad FE ut li-<pb xlink:href="020/01/2216.jpg" pagenum="459"></pb>nea CB ad BH, vel ut CG ad IH, et, permutando, AC ad CG ut EF ad IH, <lb></lb>quod erat etc. </s>

<s>” (MSS. Gal., P. V, T. VII, fol. </s>

<s>54). </s></p><p type="main">

<s>Ma ebbe poi anche il Viviani a ritrovare non difficilmente quell&#039;altra <lb></lb>macchina, della quale non era nessun&#039;altra più valida <emph type="italics"></emph>ad attollendam hanc <lb></lb>molem:<emph.end type="italics"></emph.end> e come il Marchetti, che proemiando così si esprimeva, erasi nelle <lb></lb>due prime proposizioni dell&#039;uno e dell&#039;altro libro accomodata così fatta mac­<lb></lb>china ai bisogni; così avevasela al medesimo intento apparecchiata il Viviani <lb></lb>stesso in questo, ch&#039;egli intitola <emph type="italics"></emph>Lemma generale:<emph.end type="italics"></emph.end> “ Se A (fig. </s>

<s>238) equi­<lb></lb>libri B, e D equilibri C, sempre il peso A al peso D ha la ragion compo­<lb></lb><figure id="id.020.01.2216.1.jpg" xlink:href="020/01/2216/1.jpg"></figure></s></p><p type="caption">

<s>Figura 238<lb></lb>sta della distanza GE alla EH, del <lb></lb>peso B al peso C, o resistenza B <lb></lb>alla C, e della distanza LF alla FI ” <lb></lb>(ivi, fol. </s>

<s>52). Possono vederne i Let­<lb></lb>tori la dimostrazione trascritta nel <lb></lb>trattato del Grandi (Alb. </s>

<s>XIV, 16), ma <lb></lb>l&#039;intralciato ragionamento si com­<lb></lb>pendia e si dichiara per l&#039;applica­<lb></lb>zione delle proprietà generali della <lb></lb>Leva, dalle quali abbiamo A:B= <lb></lb>GE:EH; C:D=FL:FI. </s>

<s>Moltiplicate poi insieme queste due proporzioni, <lb></lb>e con l&#039;identica B:C=B:C, danno A.B.C:B.C.D, ossia A:D= <lb></lb>GE.B.LF:HE.C.FI, com&#039;erasi proposto di dimostrare il Viviani. </s></p><p type="main">

<s>Deduce da questo il Viviani stesso un altro Lemma più particolare, per <lb></lb>servire all&#039;uso di quelle dimostrazioni, da trattarsi specialmente con la teo­<lb></lb><figure id="id.020.01.2216.2.jpg" xlink:href="020/01/2216/2.jpg"></figure></s></p><p type="caption">

<s>Figura 239<lb></lb>ria dei momenti, ed è così formu­<lb></lb>lato: “ Se saranno le due libbre <lb></lb>AB, CD (fig. </s>

<s>239) coi sostegni E, <lb></lb>F, e con le contralleve AE, CF <lb></lb>eguali tra loro, e con i pesi e re­<lb></lb>sistenze G, H, che tra loro stiano <lb></lb>come le leve EB, FD omologa­<lb></lb>mente; dico che, se in B, D si <lb></lb>appenderanno i pesi I, L, che equi­<lb></lb>librino le resistenze G, H; che i <lb></lb>detti pesi I, L saranno uguali ” (ivi, fol. </s>

<s>66). La dimostrazione, che s&#039;ha <lb></lb>trascritta dal Grandi nel luogo citato, pag. </s>

<s>17, si conduce direttamente e <lb></lb>con gran facilità dagli stessi principii della Leva, i quali danno I:G= <lb></lb>AE:EB; L:H=CF:FD. </s>

<s>Ma per supposizione G:H=EB:FD, dun­<lb></lb>que I:L=AE:CF. </s>

<s>E pure è per supposizione AE=CF, dunque I=L. </s></p><p type="main">

<s>Ora, dietro queste dimostrate proprietà generali del momento dei pesi <lb></lb>nella Libbra, e dietro la proposizione III di Galileo, dalla quale avevasi per <lb></lb>facile corollario che i momentì delle sezìoni ugualmente larghe e differen­<lb></lb>temente alte stanno come i quadrati delle altezze; ecco come il Viviani, mo­<lb></lb>vendo dai principii medesimi posti già dal Marchetti, fosse proceduto con <pb xlink:href="020/01/2217.jpg" pagenum="460"></pb>maraviglioso riscontro per le medesime vie di lui, e fosse giunto perciò, ben­<lb></lb>chè con più complicato discorso, alle medesime conclusioni: In un foglio, <lb></lb>inserito poi tra la pag. </s>

<s>140 e 141 della più volte citata edizione di Leida, <lb></lb>postillata dal Viviani, il postillatore così di sua propria mano aveva scritto: <lb></lb><emph type="italics"></emph>Per la faccia 240 della prima edizione di Leida; la proposizione del so­<lb></lb>lido parabolico senza bisogno del Lemma:<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Il momento della resistenza della sezione AD (fig. </s>

<s>240) a quello della <lb></lb>CO, ha la proporzione composta della sezione AD alla CO, ovvero dell&#039;al­<lb></lb>tezza AF all&#039;altezza CN, e della leva della AD, alla leva della CO, ovvero <lb></lb><figure id="id.020.01.2217.1.jpg" xlink:href="020/01/2217/1.jpg"></figure></s></p><p type="caption">

<s>Figura 240<lb></lb>della medesima AF alla CN. </s>

<s>Ma tali due <lb></lb>proporzioni compongono quella del qua­<lb></lb>drato AF al quadrato CN, cioè della <lb></lb>leva BA alla BC; adunque il momento <lb></lb>della resistenza della sezione AD, al mo­<lb></lb>mento della resistenza della sezione CO, <lb></lb>sta come la leva BA alla leva BC, o <lb></lb>come il momento di un grave appeso <lb></lb>in B dalla distanza BA, al momento del <lb></lb>medesimo grave appeso in B dalla distanza BC. E, permutando, il momento <lb></lb>della resistenza della sezione AD, al momento di un grave appeso in B, dalla <lb></lb>distanza BA, sta come il momento della resistenza della sezione CO, al mo­<lb></lb>mento del medesimo grave appeso in B dalla distanza BC. ” </s></p><p type="main">

<s>“ Se dunque sarà appeso in B, dalla distanza BA, un grave, il di cui <lb></lb>momento pareggi appunto il momento della resistenza della sezione AD, an­<lb></lb>che il momento del medesimo grave, appeso in B dalla distanza BC, pareg­<lb></lb>gerà il momento della resistenza della sezione CN. </s>

<s>E perciò questo solido <lb></lb>parabolico, nel considerarlo senza peso, si può dire che sia per tutto ugual­<lb></lb>mente resistente, perchè tanto il momento della resistenza della maggior se­<lb></lb>zione AD, quanto quello di ogni altra minore sezione CO, è pareggiato dal <lb></lb>momento di un medesimo grave assoluto posto in B, or dalla distanza BA, <lb></lb>ed ora dalla distanza BC. Onde, per render vera la proposizione del Galileo <lb></lb>posta a faccia 140, basta considerare che quel suo solido parabolico sia senza <lb></lb>peso, e che i varii momenti della resistenza delle sue varie sezioni sian posti <lb></lb>a cimento dei movimenti di un medesimo grave assoluto appeso alle estre­<lb></lb>mità delle lunghezze, che stanno fuori del muro. </s>

<s>” (MSS. Gal., P. V, T. IX). </s></p><p type="main">

<s>Ecco, come il Viviani avesse <emph type="italics"></emph>impugnato la sbaglio di Galileo:<emph.end type="italics"></emph.end> nel cor­<lb></lb>regger poi questo sbaglio erano pure proceduti ambedue gli Autori, incon­<lb></lb>sapevoli, nello stessissimo modo. </s>

<s>In un altro foglietto infatti, inserito nella <lb></lb>citata copia di Leida, e propriamente applicato alla pag. </s>

<s>141, il Viviani stesso <lb></lb>così aveva scritto: </s></p><p type="main">

<s>“ Pongasi ora che tal solido parabolico AFDOG (nella precedente figura) <lb></lb>sia con peso, ora fuori del muro quanto AB, ora quanto CB. </s>

<s>Il momento <lb></lb>della resistenza della sezione AD, al momento della resistenza della sezione <lb></lb>CO, sta come il quadrato AF al quadrato CN. </s>

<s>Ma il momento del grave so-<pb xlink:href="020/01/2218.jpg" pagenum="461"></pb>lido ADGB, al momento del grave COGB, avendo ragion composta di quella <lb></lb>fra il solido e il solido, cioè del cubo AF al cubo CN, e di quella della leva <lb></lb>AB alla leva BC, cioè di quella del quadrato AF al quadrato CN, le quali <lb></lb>due ragioni compongono quella del quadrato cubo AF al quadrato cubo CN, <lb></lb>e la proporzione del quadrato AF al quadrato CN è suddupla sesquialtera <lb></lb>del quadrato cubo AF al quadrato cubo CN; adunque anche la proporzione <lb></lb>del momento della resistenza della sezione AD, al momento della resistenza <lb></lb>della sezione CO, è suddupla sesquialtera della proporzione del momento del <lb></lb>grave solido FAG, al momento del grave solido NCG ” (ivi). </s></p><p type="main">

<s>La conclusione di questo teorema dipende manifestamente da due prin­<lb></lb>cipii: il primo dei quali, chiamati M.oAD, M.oOC i momenti delle resistenze <lb></lb>delle due sezioni, è espresso dall&#039;equazione M.oAD:M.oOC=AF2:CN2, <lb></lb>che corrisponde precisamente con la LXXXII del Marchetti, benchè si met­<lb></lb>tano le ascisse, ossia le lunghezze in luogo dei quadrati delle ordinate: “ So­<lb></lb>lidi parabolici, et ex eo abscissae portionis momenta resistentiarum sunt inter <lb></lb>se ut longitudines ” (De resistentia solid. </s>

<s>cit., pag. </s>

<s>57). </s></p><p type="main">

<s>L&#039;altro principio premesso dal Viviani è che i momenti del solido pa­<lb></lb>rabolico e della sua parte stanno come le quinte potenze delle basi, o delle <lb></lb>loro altezze, avendo le larghezze uguali, ciò che corrisponde pure esatta­<lb></lb>mente con la LXXXIII dello stesso Marchetti: “ Solidi parabolici, et ex eo <lb></lb>abscissae portionis momenta ponderum sunt in quintupla proportione basis <lb></lb>ad basim ” (ibid., pag. </s>

<s>58): che vuol dire, chiamati M.oS, M.oS′ i momenti <lb></lb>di tutto il solido e della sua porzione, M.oS:M.oS′=AF5:CN5. </s>

<s>Inalzata <lb></lb>ora questa a quadrato, e l&#039;altra dei momenti delle resistenze delle sezioni <lb></lb>alla quinta potenza, si ha M.oAD5:M.oCO5=M.oS2:M.oS2, ossia M.oAD: <lb></lb>M.oCO=M.oS2/5:M.oS′2/5, che è la proporzion <emph type="italics"></emph>suddupla sesquialtera<emph.end type="italics"></emph.end> se­<lb></lb>condo la conclusion del Viviani; o anche M.oS:M.oS′=M.oAD5/2:M.oCO5/2, <lb></lb>che è la ragion <emph type="italics"></emph>dupla sesquialtera,<emph.end type="italics"></emph.end> sotto la qual forma, dalle due citate pro­<lb></lb>posizioni LXXXII e LXXXIII, concludesi così la medesima verità dal Mar­<lb></lb>chetti: “ Ex duabus hisce propositionibus facile elicitur Solidi parabolici, et <lb></lb>ex eo abscissae portionis momenta ponderum esse inter se in dupla sesquial­<lb></lb>tera proportione momentorum resistentiarum ” (ibid., pag. </s>

<s>59). </s></p><p type="main">

<s>Passando a esaminare altre parti di minore curiosità, o di minore im­<lb></lb>portanza, ebbe pure a trovare il Viviani, tra le proposizioni del Marchetti e <lb></lb>le sue, simili riscontri, che lo fecero con tranquillo animo e con sereno giu­<lb></lb>dizio finalmente persuaso essere per riuscire superflua, almeno nella so­<lb></lb>stanza, l&#039;opera sua, dopo quella del suo rivale. </s>

<s>Altre parti del suo ingegno, <lb></lb>non per questo avvilito nè stanco, dedicherebbe, in rendimento di grazie, <lb></lb>al Re di Francia, e dignitosamente ritiratosi così da parte pose fine alla <lb></lb>controversia. </s></p><pb xlink:href="020/01/2219.jpg" pagenum="462"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Sui principii del secolo XVIII, quando già il Viviani dormiva da sette <lb></lb>anni nel sonno della pace, si risvegliò quel fuoco che, non sopito ma spento <lb></lb>oramai, si credeva sotto le ceneri del sepolcro. </s>

<s>Fu Guido Grandi che rinfo­<lb></lb>colò quelle ire, mostrando di aver sotto la cappa del monaco nascosta la <lb></lb>spada per difendere il suo Maestro, come ei diceva, ma veramente per of­<lb></lb>fendere il Marchetti, nell&#039;insegnamento delle Matematiche nello Studio pi­<lb></lb>sano, suo rivaleggiante collega. </s>

<s>Nel 1710 pubblicava esso Grandi per la se­<lb></lb>conda volta un libro intitolato <emph type="italics"></emph>Quadratura circuli et hyperbolae,<emph.end type="italics"></emph.end> nella <lb></lb>prefazione al quale, fra i varii esempii di Matematici illustri, che inconsa­<lb></lb>pevoli s&#039;erano riscontrati nelle medesime conclusioni, cita anche quello del <lb></lb>Marchetti, il quale, nel dimostrare la composizion dei momenti si riscontrò <lb></lb>con Galileo, col Cavalieri e col Torricelli, e nel trattare delle resistenze dei <lb></lb>solidi col Blondel “ qui idem Galilaei sphalma de solido parabclico aequalis <lb></lb>ubique resistentiae, etiam cum utrimque fulcitur, prior detexit ” (ibid., <lb></lb>pag. </s>

<s>XIII). </s></p><p type="main">

<s>L&#039;orlo della coppa, se non esalava le fragranze del buon liquore, non <lb></lb>mandava però il fetor del veleno, che raccoglieva nel fondo, e che dalle <lb></lb>esperte narici del Marchetti fu troppo bene sentito. </s>

<s>Incominciò a lamentar­<lb></lb>sene con gli amici, e fece, perchè circolasse in Corte, innanzi alla quale <lb></lb>massimamente gli doleva di venire accusato, per essere il libro della Qua­<lb></lb>dratura del circolo dedicato al principe Gian Gastone; una scrittura per di­<lb></lb>mostrare che in verità non aveva tolto nulla nè dal Cavalieri nè dal Blon­<lb></lb>dello. </s>

<s>Il Principe e i cortigiani al gran romore che ogni giorno cresceva più <lb></lb>levarono le orecchie, e per intendere il diritto o il torto di questa lite si <lb></lb>rivolsero al Grandi, che ne scrisse perciò la seguente <emph type="italics"></emph>Informatione:<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Il signor dottore Alessandro Marchetti, da due passi dell&#039;Opera del <lb></lb>p. </s>

<s>Grandi, ultimamente stampata e dedicata al serenissimo principe Giovan <lb></lb>Gastone, piglia motivo di lamentarsi e tenersi offeso: L&#039;uno è nella prefa­<lb></lb>zione, pag. </s>

<s>XII, § <emph type="italics"></emph>Nonnulli,<emph.end type="italics"></emph.end> e l&#039;altro è verso il mezzo dell&#039;Opera da pag. </s>

<s>29 <lb></lb>a pag. </s>

<s>34. ” </s></p><p type="main">

<s>“ Pretende nel primo luogo che il p. </s>

<s>Grandi abbia voluto far credere <lb></lb>che l&#039;opera <emph type="italics"></emph>De resistentia solidorum<emph.end type="italics"></emph.end> del suddetto signor Marchetti fosse da <lb></lb>altri rubata. </s>

<s>Al che risponde il p. </s>

<s>Grandi non esser mai stata questa la sua <lb></lb>intenzione, nè potersi ciò dedurre dalle sue parole: anzi apparire il contra­<lb></lb>rio dallo stesso contesto. </s>

<s>Persino nella prima stampa di quest&#039;Opera aveva <lb></lb>il p. </s>

<s>Grandi asserito che, in materie matematiche, <expan abbr="ēra">erra</expan> facilissimo che gli <lb></lb>Autori s&#039;incontrassero nel dire le medesime cose, come confessa essere tal­<lb></lb>volta a lui stesso avvenuto. </s>

<s>” </s></p><p type="main">

<s>“ In questa nuova impressione aveva motivo di mostrare ciò più evi­<lb></lb>dentemente con varii esempii. </s>

<s>Fra questi, dop&#039;aver nominato monsù di Fer-<pb xlink:href="020/01/2220.jpg" pagenum="463"></pb>mat, il signor Viviani, il Guldino e Grogorio di S. Vincenzio, nomina con <lb></lb>lode il signor Marchetti, chiamandolo <emph type="italics"></emph>praeclarum illum Poetam, nostrique <lb></lb>pisani Licei Mathematicum,<emph.end type="italics"></emph.end> ed accennando alla sfuggita il Teorema del <lb></lb>momento dei gravi, che si era attribuito, e che poi il Viviani fece vedere <lb></lb>pubblicamente che prima era stato detto da Galileo, dal Cavalieri, da Anto­<lb></lb>nio Rocca e dal Torricelli; difende che ciò potesse accadere, senza che possa <lb></lb>sospettarsi averlo egli dai suddetti rubato, <emph type="italics"></emph>cum tamen id citra ullam plagii <lb></lb>suspicionem eventus facillime suadeat. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Poi passa al libro <emph type="italics"></emph>De resistentia solidorum<emph.end type="italics"></emph.end> di esso Marchetti, dove <lb></lb>questi cerca di confutare una proposizione di Galileo, e correggerne lo sba­<lb></lb>glio preso in tal materia da quel grand&#039;Uomo, il che dice il p. </s>

<s>Grandi es­<lb></lb>sere stato stampato otto anni prima da monsù Blondel, che lo stesso sba­<lb></lb>glio scoprì, e lo emendò allo stesso modo; e dice che dodici anni avanti <lb></lb>avea per ciò scritto un volume <emph type="italics"></emph>De resistentia solidorum<emph.end type="italics"></emph.end> intitolato <emph type="italics"></emph>Galilaeus <lb></lb>promotus,<emph.end type="italics"></emph.end> che il Marchetti dice nella sua prefazione aver egli prima posto <lb></lb>al suo libro, e sotto il qual nome fu dal Rossetti citato: cose tutte di fatto <lb></lb>indubitabile, e che può mostrarsi co&#039;libri allora stampati. </s>

<s>” </s></p><p type="main">

<s>“ Quindi passa ad altri esempii, da m. </s>

<s>Ischyrnhausen, m. </s>

<s>Wallis, m. </s>

<s>Leib­<lb></lb>niz, m. </s>

<s>De l&#039;Hopital, m. </s>

<s>Parent, al p. </s>

<s>Intieri, e finalmente si dichiara di non <lb></lb>essere stata sua intenzione di pregiudicare perciò in nulla alla gloria di quei <lb></lb>celebratissimi Uomini, con queste parole, che sono a pag. </s>

<s>XV: <emph type="italics"></emph>Cum autem <lb></lb>nihil inventionis gloriae praeiudicet quod quis se ab aliis praeoccupatum <lb></lb>deprehendat, quia semper invenisse acumìnis est, primum invenisse for­<lb></lb>tunae; non erit opinor qui haec a me superius notata fuisse suspicetur, <lb></lb>ut clarissimorum virorum inventis quidquam propterea detraherem, sed <lb></lb>unice ut facilem hunc in rebus geometricis consensum pluribus exemplis <lb></lb>confirmarem.<emph.end type="italics"></emph.end> Dal che è chiarissimo non essere stata intenzione del p. </s>

<s>Grandi <lb></lb>nè di offendere in ciò il Marchetti, nè di pregiudicargli in conto alcuno, nè <lb></lb>di asserire che quel libro fosse da lui rubato: il che non sarebbe stato a <lb></lb>proposito del suo argomento, che era solo dell&#039;incontrarsi casualmente i <lb></lb>Matematici nel dire le medesime cose. </s>

<s>” (MSS. Cim., T. XXIX, fol. </s>

<s>311, 12). </s></p><p type="main">

<s>Accompagnava il Grandi questa Informazione con una sua lettera, scritta <lb></lb>il dì 22 Maggio 1711 da Pisa, nella quale, detto di aver risaputo della scrit­<lb></lb>tura che il Marchetti avea sparsa nella Corte medicea, con intenzione di farla <lb></lb>stampare, soggiungeva riserbarsi però “ di rispondere più individualmente <lb></lb>alle sue querele, quando avrò fortuna di vedere la sopra nominata Scrit­<lb></lb>tura, e di difendere que&#039;passi, ch&#039;egli pretende di accusare di errore ” <lb></lb>(ivi, fol. </s>

<s>303). </s></p><p type="main">

<s>Dopo pochi mesi usciva quella desiderata Scrittura in pubblico da Lucca, <lb></lb>in forma di Lettera dedicata a Bernardo Trevisano, che, procuratore di <lb></lb>S. Marco, era uso con <emph type="italics"></emph>ragione e con dritto a librar l&#039;altrui colpa e il <lb></lb>merto. (Sonetto premesso alla Lettera).<emph.end type="italics"></emph.end> Rispondeva contro le accuse del <lb></lb>Grandi che, quanto alla composizion dei momenti, era verissimo che il Ca­<lb></lb>valieri l&#039;aveva dimostrata prima di lui, “ con altro metodo però diverso, <pb xlink:href="020/01/2221.jpg" pagenum="464"></pb>egli dice, dal mio, e senza che in quel tempo veduto avessi la sua dimo­<lb></lb>strazione ” <emph type="italics"></emph>(Lettera nella quale si ribattono le accuse date dal P. D. G. G., <lb></lb>Lucca 1711, pag. </s>

<s>20).<emph.end type="italics"></emph.end> Per quel poi particolarmente riguarda il Blondel, <lb></lb>reca documenti a provar ch&#039;egli avea già, infino dal 1659, notato lo sbaglio <lb></lb>di Galileo, due anni prima che il Matematico francese pubblicasse la sua <lb></lb>Epistola al Vulzio. </s>

<s>Quanto poi al <emph type="italics"></emph>Galileo promoto<emph.end type="italics"></emph.end> del medesimo Autore, non <lb></lb>essendo stato mai pubblicato “ come poteva io, ne conclude il Marchetti <lb></lb>stesso, averlo veduto, nè pure avutone alcun sentore, ond&#039;io potessi pi­<lb></lb>gliarne, non dirò i pensieri e le dimostrazioni, ma nè anche lo stesso ti­<lb></lb>tolo? </s>

<s>” (ivi, pag. </s>

<s>23). </s></p><p type="main">

<s>A un animo generoso, e non punto pregiudicato, sarebbero dovute que­<lb></lb>ste risposte bastare per buone ragioni, ma il Grandi, lette per le pubbliche <lb></lb>stampe queste cose, mandò ad effetto la promessa di <emph type="italics"></emph>rispondere indivi­<lb></lb>dualmente alle querele,<emph.end type="italics"></emph.end> pubblicando in Lucca nel 1712 un libro intitolato <lb></lb><emph type="italics"></emph>Risposta apologetica alle apposizioni fatte dal signor Alessandro Marchetti, <lb></lb>nella sua Lettera diretta a Bernardo Trevisano.<emph.end type="italics"></emph.end> Fu allora che tirò fuori <lb></lb>l&#039;arme rimasta, nella prefazione al libro <emph type="italics"></emph>Della quadratura del circolo,<emph.end type="italics"></emph.end> ar­<lb></lb>tificiosamente coperta sotto il finto velo delle parole, e non solo confermò <lb></lb>contro il Marchetti le accuse di plagio, ma soggiunse che in quell&#039;avevaci <lb></lb>di suo era tutto pieno di errori. </s>

<s>Il Marchetti uscì a fare le sue difese in <lb></lb>un Discorso, diretto al medesimo Trevisano, e pubblicato in Lucca nel 1714, <lb></lb>dimostrando come gli errori fossero da attribuirsi piuttosto al suo avversario. </s></p><p type="main">

<s>L&#039;importanza dell&#039;argomento non ci dispensa dall&#039;entrar giudici in que­<lb></lb>sta lite, ma prima vogliam dire che, secondo per lo più avviene fra i liti­<lb></lb>ganti, anche fra questi due fu l&#039;ultimo a tacere colui che aveva meno ra­<lb></lb>gione. </s>

<s>E perchè tale all&#039;imparzial nostro giudizio apparisce il Grandi, egli, <lb></lb>non perdonando al sepolcro, riepilogò le irragionevoli accuse quattro anni <lb></lb>dopo la morte del Marchetti, quando nel 1718 compilò le informi note del <lb></lb>Viviani nel trattato <emph type="italics"></emph>Delle resistenze.<emph.end type="italics"></emph.end> Siam perciò dal filo dell&#039;argomento <lb></lb>condotti a dire di una tale compilazione, e prima di tutto dei motivi che <lb></lb>s&#039;ebbe di farla, risalendo così ai principii col nostro discorso. </s></p><p type="main">

<s>Quando il Viviani protestò al Marchetti di aver levato affatto il pen­<lb></lb>siero di concorrere con lui, prima di avere in quella medesima Lettera detto <lb></lb>del deposito delle sue carte nelle mani del principe Leopoldo, che le sot­<lb></lb>toscrisse e le legò, fermandone la legatura col suo sigillo; aveva asserito <lb></lb>che molte di quelle conclusioni le aveva già comunicate a più d&#039;uno, che <lb></lb>pur vive, e che erano ventitre o ventiquattr&#039;anni che aveva cominciato ad <lb></lb>applicar la mente a quelle discipline, quando lui che veniva ora a concor­<lb></lb>rere seco era tuttavia fanciullo. </s></p><p type="main">

<s>Le affermazioni erano sincere, e si può per prima loro testimonianza <lb></lb>citare il Magalotti, il quale si gloriava così dicendo: “ Per tre anni ebbi in <lb></lb>sorte di essere tosoriere de&#039;preziosi concetti del signor Vincenzio Viviani, <lb></lb>onde appresso di lui <emph type="italics"></emph>si trovan molte gioie care e belle,<emph.end type="italics"></emph.end> che nelle opere <lb></lb>stampate del Galileo non si veggono, e che ben presto verranno in luce ” <pb xlink:href="020/01/2222.jpg" pagenum="465"></pb><emph type="italics"></emph>(Lettere scientifiche ed erudite, Firenze 1721, pag. </s>

<s>2).<emph.end type="italics"></emph.end> S&#039;accenna in que­<lb></lb>ste parole, che dovettero essere scritte nel 1668, evidentemente al trattato <lb></lb>Delle resistenze, per conferma di che, e dell&#039;aver veramente veduto un tale <lb></lb>trattato, il Magalotti, in quella sua prima Lettera scientifica, applica alcuni prin­<lb></lb>cipii ivi supposti, e una proposizione ivi pur dimostrata, per risolvere al priore <lb></lb>Orazio Rucellai, che glielo aveva proposto, il problema: perchè in tempo <lb></lb>di neve si fiacchino più facilmente i rami agli ulivi, e a simili altre piante. </s></p><p type="main">

<s>I villici attribuivano il caso, osservato giusto in que&#039;giorni in certe pos­<lb></lb>sessioni del Rucellai, alla neve venuta a piombo, ma il Megalotti, sovvenen­<lb></lb>dosi di aver letto nei fogli manoscritti del Viviani “ che la cedenza della <lb></lb>materia dei solidi altera la proporzione delle loro resistenze, a segno tale <lb></lb>che un medesimo ferro sarà ora più ora meno resistente, secondo la diffe­<lb></lb>renza della tempera ” (MSS. Gal., P. V, T. VII, fol. </s>

<s>29) applicò questo prin­<lb></lb>cipio ai rami degli ulivi con dire che, avendo il freddo altrerata la loro tem­<lb></lb>pera, ne aveva fatto altresì variare i momenti delle resistenze. </s>

<s>Rassomigliava <lb></lb>poi così fatte alterazioni, prodotte dal freddo nel legno, alle alterazioni pro­<lb></lb>dotte dall&#039;argento vivo, che penetra dentro l&#039;oro, e come questo, ridotto per <lb></lb>esempio in forma di cilindro e ficcato nel muro, resisterebbe al proprio peso <lb></lb>alquantò meno di un altro cilindro uguale, ma di oro schietto; così per so­<lb></lb>miglianza affermava che, meno dei naturali, resistono allo spezzarsi i rami <lb></lb>penetrati dal freddo. </s></p><p type="main">

<s>Volendo ora il Magalotti dare ad intendere la proporzion delle varia­<lb></lb>zioni di così fatte resistenze, comparate con quelle dei cilindri dell&#039;oro, ora <lb></lb>puro, ora alterato nella sua naturale gravità in specie, per l&#039;inzuppamento <lb></lb>dell&#039;argento vivo; dice che si potrebbero in ambedue i casi reggere i detti <lb></lb>solidi da sè stessi, purchè “ il quadrato della lunghezza del cilindro del­<lb></lb>l&#039;oro inzuppato, al quadrato della lunghezza del cilindro dell&#039;oro puro, stia <lb></lb>reciprocamente come la gravità in specie dell&#039;oro puro, alla gravità in spe­<lb></lb>cie dell&#039;oro inzuppato, siccome dimostra il signor Vincenzio Viviani ” (Let­<lb></lb>tere cit., pag. </s>

<s>7). </s></p><p type="main">

<s>Il Grandi, ne&#039;manoscritti ch&#039;ebbe a mano, ritrovò sotto questa forma, <lb></lb>del teorema, il semplice enunciato: <emph type="italics"></emph>Allora i cilindri orizzontalmente fitti <lb></lb>nel muro, che sieno d&#039;uguale grossezza, ma di differente gravità in spe­<lb></lb>cie, sono d&#039;egual momento verso le loro resistenze, quando i quadrati <lb></lb>delle loro lunghezze hanno reciproca proporzione delle gravità in specie, <lb></lb>ovvero che le lunghezze hanno reciproca proporzione delle gravità asso­<lb></lb>lute<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIV, 31). Il Compilatore supplì di suo alla dimostrazion che man­<lb></lb>cava, ma che il Magalotti attesta essere stata fatta, e noi, dietro gl&#039;indizii <lb></lb>di lui, crediamo che facilmente procedesse così, in maniera forse più con­<lb></lb>forme col rimanente di quella ivi suggerita dallo stesso Grandi: </s></p><p type="main">

<s>Sia GF (fig. </s>

<s>241) la sezione del cilindro dell&#039;oro puro, HM quella dello <lb></lb>inzuppato, che manterrà nonostante uguale grossezza. </s>

<s>Si vuol sapere qual <lb></lb>proporzione debbano avere le lunghezze massime EF, IM verso i pesi asso­<lb></lb>luti o in specie, a cui que&#039;solidi han da resistere. </s></p><pb xlink:href="020/01/2223.jpg" pagenum="466"></pb><p type="main">

<s>Applicato al centro di gravità B il peso P, la resistenza sarà P.AB, <lb></lb>come pure, applicato al centro D il peso P′, la resistenza sarà P′.CD. Ora, <lb></lb>perchè debbono queste due resistenze respettive essere eguali, avremo P:P′= <lb></lb><figure id="id.020.01.2223.1.jpg" xlink:href="020/01/2223/1.jpg"></figure></s></p><p type="caption">

<s>Figura 241<lb></lb>CD:AB=IM:EF, che vuol dire che le <lb></lb>lunghezze hanno ragion reciproca dei pesi <lb></lb>assoluti. </s>

<s>Chiamati poi V, V′ i volumi dei <lb></lb>due cilindri o delle loro sezioni, e G, G′ le <lb></lb>loro gravità in specie, sarà G.V:G′ V′= <lb></lb>IM:EF, ossia G:G′=V′.IM:V.EF.Ma <lb></lb>perchè V=EF.EG, V′=IM.IH, ed EG= <lb></lb>IH; sarà dunque G:G′=IM2:EF2, ossia <lb></lb>che le gravità in specie stanno reciproca­<lb></lb>mente come i quadrati delle lunghezze, se­<lb></lb>condo avea concluso il Viviani in quel suo <lb></lb>manoscritto Delle resistenze, veduto dal Ma­<lb></lb>galotti. </s></p><p type="main">

<s>Quella Lettera scientifica al Rucellai sarebbe dunque venuta opportuna <lb></lb>ad attestare della reale esistenza di un tal Manoscrito, ma si fece pubbli­<lb></lb>camente nota troppo tardi, perchè se ne potesse persuadere l&#039;animo sospet­<lb></lb>toso del Marchetti, il quale anzi reputò, e poi disse al pubblico essere stata <lb></lb>un&#039;impostura l&#039;andare il Viviani con quell&#039;involto di carte sotto il braccio <lb></lb>al Cardinale dei Medici, e, facendogliele vedere così alla grossa e alla sfug­<lb></lb>gita, dargli ad intendere che conteneva un&#039;opera simile alla sua, ciò che <lb></lb>concludeva non essere altro “ che un mero vanto, o che, confrontando egli <lb></lb>le sue fatiche con le mie, e conoscendole di gran lunga inferiori, amò an­<lb></lb>ch&#039;egli meglio di sopprimerle, che di pubblicarle ” <emph type="italics"></emph>(Lettera in cui si ri­<lb></lb>batton le accuse ecc., pag. </s>

<s>25).<emph.end type="italics"></emph.end> E come fossero queste al glorioso nome del <lb></lb>Viviani leggere ingiurie, soggiungeva che per invidia s&#039;era astutamente messo <lb></lb>a impedirgli per molto tempo la pubblicazion del suo libro, intanto che, con <lb></lb>suo grave danno, avesse il Blondel in Francia a prevenirlo. </s></p><p type="main">

<s>Volarono le calunniose querele largamente attorno a titillare le orec­<lb></lb>chie, e a insinuarsi nell&#039;animo dei Matematici, fra&#039;quali il Leibniz scriveva <lb></lb>così in una lettera al Grandi: “ Clarissimum Marchettum audivi quaeri de <lb></lb>insigni Viro, et mihi olim amico, Vincentio Viviano, quod hic illum multos <lb></lb>ante annos aeditionem libri <emph type="italics"></emph>De resistentia solidorum<emph.end type="italics"></emph.end> diu differre coegerit. </s>

<s><lb></lb>Ego meum iudicium hic non intorpono, neque Vivianum, quamtumvis ami­<lb></lb>cum, excusarem, si quid in ea re humani passus esset ” (MSS. Cim., T. XXIX, <lb></lb>fol. </s>

<s>287). </s></p><p type="main">

<s>Non voleva il Leibniz coscenziosamente farsi giudice, per mancanza di <lb></lb>prove, che il Grandi aveva già in mano infin da quando si dette a scrivere <lb></lb>la sua <emph type="italics"></emph>Risposta apologetica,<emph.end type="italics"></emph.end> a pag. </s>

<s>88, della quale, dop&#039;avere accennato che, <lb></lb>dal silenzio tenuto dal Viviani con gli stessi suoi più familiari, s&#039;incomin­<lb></lb>ciò a dubitare se veramente avesse atteso a trattare delle Resistenze dei so­<lb></lb>lidi; soggiunge che il medesimo signor abate Jacopo Panzanini, nipote ed <pb xlink:href="020/01/2224.jpg" pagenum="467"></pb>erede dello stesso Viviani, non ne era punto informato, ma che poi, fattagli <lb></lb>istanza da chi aveva interessi in questa causa, finalmente ritrovò il Ma­<lb></lb>noscritto in quell&#039;argomento, e con i contrassegni corrispondenti con la de­<lb></lb>scrizione fattane da suo zio al Marchetti, quando lo avvisò per lettera del <lb></lb>deposito di quello stesso suo Manoscritto, e della recognizione impressavi <lb></lb>dalla mano e dal sigillo del cardinale Leopoldo. </s>

<s>La lettera, con cui il Pan­<lb></lb>zanini annunziava al Grandi la scoperta, fu scritta da Firenze il dì 24 No­<lb></lb>vembre 1711; e incomincia con queste parole: </s></p><p type="main">

<s>“ Al mio ritorno di villa scrissi altra lettera a V. P. Rev.ma, ed ora che <lb></lb>ho avuto tempo di ricercar meglio gli scritti del signor Vincenzio Viviani <lb></lb>mio zio, posso aggiungerle che ho trovate alcune sue fatiche in tre fascetti, <lb></lb>che uno intorno le Resistenze dei corpi solidi, altro sopra le Galleggianti, <lb></lb>ed altro di varie speculazioni meccaniche, quali portano nel frontespizio la <lb></lb>firma del fu serenissimo principe cardinale Leopoldo, sotto il dì 2 Marzo 1667 <lb></lb><emph type="italics"></emph>ab Incarnatione,<emph.end type="italics"></emph.end> e sono infilzati in un cordone di seta, annodato e segnato <lb></lb>col sigillo dell&#039;A. S. Rev.ma, che non può revocarsi in dubbio la vera esi­<lb></lb>stenza dei medesimi in quel tempo ” (MSS. Gal. </s>

<s>Disc., T. CXLVIII, fol. </s>

<s>169). </s></p><p type="main">

<s>Venuto il Grandi nelle prossime vacanze del Natale a Firenze, dette a <lb></lb>quelle carte una scorsa in casa del Panzanini, trascrivendone qualche cosa, <lb></lb>che poi pubblicò nella sua <emph type="italics"></emph>Risposta apologetica.<emph.end type="italics"></emph.end> Ma sentito dalla lettera del <lb></lb>Leibniz che s&#039;erano negli animi insinuate le orgogliose querele del Mar­<lb></lb>chetti, e trovandosi oramai così impegnato in difendere la causa del suo <lb></lb>Maestro, giudicò non esserci altro più efficace modo, che di pubblicare il <lb></lb>Manoscritto felicemente ritrovato, dietro il quale giudicherebbero i Matema­<lb></lb>tici se era impostura quel che il Viviani diceva di avere speculato intorno <lb></lb>alle Resistenze dei solidi, e se erano quelle speculazioni spregevoli, e da non <lb></lb>venire in confronto con quelle dello stesso Marchetti. </s>

<s>Fatto al Panzanini <lb></lb>motto di questa sua intenzione, mentre pensava al modo di mandarla ad <lb></lb>effetto, gli si fa innanzi Benedetto Bresciani, che attendeva allora in Firenze <lb></lb>con Tommaso Bonaventuri a fare una nuova edizione delle opere di Galileo, <lb></lb>fra le quali il trattato Delle resistenze si potrebbe inserire come commento. </s>

<s><lb></lb>Acconsentì il Grandi, e fece, per mezzo dello stesso Bresciani, richiedere il <lb></lb>Manoscritto al Panzanini, il quale anzi raccolse, insieme con quello delle <lb></lb>Resistenze, gli altri trattati di suo zio, della consegna dei quali dava così, <lb></lb>per lettera del dì 27 Giugno 1713, avviso allo stesso Grandi: </s></p><p type="main">

<s>“ Ho consegnato, secondo la richiesta fattami dal signor Benedetto Bre­<lb></lb>sciani, gli tre fascetti consaputi di Vincenzio Viviani, avendomi rappresen­<lb></lb>tato che V. Rev.za si sia esibita di distendere quelle proposizioni in essi <lb></lb>enunciate, con ridurle in buona forma. </s>

<s>E potendo queste servir di moto alla <lb></lb>sua fecondissima mente, per crearne infinite altre, ben volentieri io ne sono <lb></lb>contento, e vado fra me stesso considerando la bella sorte toccata a mio <lb></lb>zio di aver, dopo la sua morte, un sostenitore della sua gloria di sì alto va­<lb></lb>lore: ricompensa a mio credere centuplicata del zelo sì premuroso, che aveva <lb></lb>verso il suo Maestro ” (ivi, fol. </s>

<s>171). </s></p><pb xlink:href="020/01/2225.jpg" pagenum="468"></pb><p type="main">

<s>Le carte dunque, ch&#039;ebbe sott&#039;occhio il Grandi a esaminare, e che ci <lb></lb>son tuttavia rimaste raccolte nel Tomo VII della V parte dei Manoscritti di <lb></lb>Galileo, contenevano proposizioni mutilate, informi e senz&#039;ordine, parte scritte <lb></lb>in latino, e parte in italiano: lemmi preparati, ma de&#039;quali non appariva la <lb></lb>diretta intenzione; pensieri sparsi, propositi di tentar cose nuove, espressi <lb></lb>sentenziosamente in parole, o per via di semplici abbozzate figure. </s>

<s>Difficile <lb></lb>cavar di li costrutto a un teorema perfetto, o pensiamo a un intero trat­<lb></lb>tato. </s>

<s>Supplì felicemente il Grandi, col suo valor matematico, alla dimostra­<lb></lb>zione di molti teoremi, nel Manoscritto solamente accennati, ma dove s&#039;in­<lb></lb>voca l&#039;esperienza a conforto della Geometria, non seppe ben comprendere <lb></lb>il suo Autore, nè farne perciò rilevare quel che, sopra Galileo e il Mar­<lb></lb>chetti, aveva di più nuovo e importante. </s></p><p type="main">

<s>Si propone per esempio, fra gli altri, a risolvere questi problemi: “ Cur <lb></lb>lignum horizontale facilius inflectatur quam inclinatum, et de proportione <lb></lb>diversarum inclinationum. </s>

<s>— Cur prisma triangulare facilius inflectatur su­<lb></lb>perficie deorsum spectante, quam angulo. </s>

<s>— Non omne pondus, quod po­<lb></lb>test inflectere lignum, potest quoque frangere: Lignum enim inflexum minus <lb></lb>trahitur, quam horizontaliter distentus, cum <lb></lb>ad angulum obtusum trahatur ” (MSS. Gal., <lb></lb>P. V, T. VII, fol. </s>

<s>38). Di così fatti quesiti <lb></lb>e pensieri compilò il Grandi la sua LXXVIII <lb></lb>proposizione (Alb. </s>

<s>XIV, 67), che illustrò di <lb></lb>considerazioni sue proprie, le quali egli dice <lb></lb>darebbero campo “ a molte particolari spe­<lb></lb>culazioni, alle quali per ora non posso ap­<lb></lb>plicare ” (ivi, pag. </s>

<s>68). Ma il Viviani, me­<lb></lb>glio che alle speculazioni, aveva pensato, <lb></lb>nell&#039;incertezza del caso, d&#039;interpellar l&#039;espe­<lb></lb>rienza, accennata in queste due semplici <lb></lb>figure 242 e 243, la prima delle quali s&#039;il­<lb></lb><figure id="id.020.01.2225.1.jpg" xlink:href="020/01/2225/1.jpg"></figure></s></p><p type="caption">

<s>Figura 242<lb></lb><figure id="id.020.01.2225.2.jpg" xlink:href="020/01/2225/2.jpg"></figure></s></p><p type="caption">

<s>Figura 243<lb></lb>lustra dalla nota seguente: “ Sperimenta <lb></lb>questo: cioè con che proporzione de&#039;pesi <lb></lb>A, B si faccia l&#039;equilibrio della libbra o <lb></lb>leva DE orizzontale ” (MSS. Gal., P. V, T. <lb></lb>VII, a tergo del fol. </s>

<s>24). </s></p><p type="main">

<s>Perchè in questi, e in altri simili se­<lb></lb>gni, di che son piene parecchie facce del <lb></lb>Manoscritto, s&#039;ascondeva come si disse l&#039;ori­<lb></lb>ginalità dei pensieri del Viviani, non sa­<lb></lb>pendoli il Grandi interpetrare, veniva a perdere, nella difesa della sua causa, <lb></lb>l&#039;argomento migliore. </s>

<s>Nè solo si mettevano così alla luce le medesime cose, <lb></lb>ch&#039;erano nel Marchetti, ma si lasciava ben assai più completo del nuovo ap­<lb></lb>parire il libro di lui, che aveva le proposizioni del famoso solido parabolico <lb></lb>mancante nella compilazione del Grandi. </s>

<s>Mancano qui pure altre proposizioni, <pb xlink:href="020/01/2226.jpg" pagenum="469"></pb>per cui vengono a concludersi dietro un supposto alcuni fra i principali <lb></lb>Teoremi. </s>

<s>Tale sarebbe per esempio il LVII, che è del prisma parabolico <lb></lb>d&#039;ugual resistenza, e nella presente causa di massima importanza: Teorema <lb></lb>però che qui non conclude, se non ammesso il non dimostrato che cioè i <lb></lb>momenti de&#039;pesi uguali, gravanti in varie parti fuori del mezzo un cilin­<lb></lb>dro, sostenuto nelle sue estremità; stanno direttamente come i rettangoli <lb></lb>delle distanze. </s></p><p type="main">

<s>Non aveva il Viviani tralasciata questa dimostrazione: l&#039;aveva anzi, come <lb></lb>vedremo a suo luogo, resa generalissima in modo, da applicarsi per fonda­<lb></lb>mento alle molte proposizioni del suo trattato, rimaste in aria nella compi­<lb></lb>lazione del Grandi, la quale vien perciò notata di un difetto gravissimo, da <lb></lb>cui va senza dubbio esente il Marchetti. </s></p><p type="main">

<s>Fu un grande inganno di esso Grandi quel di credere che, nelle sole <lb></lb>carte ritrovate dal Panzanini, consistesse tuttociò che delle Resistenze dei <lb></lb>solidi aveva speculato il Viviani, e quell&#039;inganno recò alla causa che difen­<lb></lb>deva gravissimo danno. </s>

<s>Videro quelle ordinate speculazioni, nel 1718, in Fi­<lb></lb>renze la luce, inserite nel III Tomo delle opere di Galileo, ma qual effetto <lb></lb>ebbe l&#039;intenzione di chi avea condotto il faticoso lavoro? </s>

<s>Si veniva senza <lb></lb>dubbio a purgare il Viviani dalla calunnia che fingesse di avere un trattato <lb></lb>Delle resistenze, e che volesse pubblicarlo per impedire i progressi al Mar­<lb></lb>chetti, ma chi leggeva alla II giornata di Galileo il nuovo commento non <lb></lb>poteva non giudicarlo superfluo, dopo quello dello stesso Marchetti: e perchè <lb></lb>le novità, per le quali si sarebbe potuto distinguer quello stesso commento, <lb></lb>rimanevano nell&#039;opera del Compilatore affogate o spente, inferior nell&#039;am­<lb></lb>piezza del soggetto, nella concisione delle dimostrazioni, e nell&#039;ordine delle <lb></lb>parti. </s>

<s>Ma nell&#039;animo del Grandi prevaleva il pensiero di sè, a quello che <lb></lb>doveva aver del Viviani, e parve perciò che avesse presa principalmente <lb></lb>quella fatica, per scagliar l&#039;ultima pietra sulla tomba del suo nemico. </s>

<s>L&#039;atto <lb></lb>che sa d&#039;empio, era mosso e guidato da quella irragionevolezza, che risul­<lb></lb>terà dall&#039;esame delle controversie insorte fra i due Matematici professori <lb></lb>nello studio di Pisa. </s></p><p type="main">

<s>Fermo in quel pregiudizio, comune a tanti, che fosse Galileo infallibile <lb></lb>oracolo di ogni verità matematica, non poteva patire il Grandi che si dicesse <lb></lb>avere sbagliato il divino Uomo circa all&#039;ugual resistenza del solido parabo­<lb></lb>lico: ciò egli reputava una vera <emph type="italics"></emph>calunnia,<emph.end type="italics"></emph.end> di che volle agramente ripren­<lb></lb>dere il Marchetti e il Blondel (Alb. </s>

<s>XIV, 86), contrapponendo alla loro au­<lb></lb>dacia l&#039;esempio del Viviani, il quale con buona pace dimostrò che tutto il <lb></lb>male si rimediava, ponendo il solido con la superfice parabolica in piano <lb></lb>piuttosto che eretta, come per inavvertenza doveva averla disegnata lo stesso <lb></lb>Galileo. </s></p><p type="main">

<s>I nostri Lettori, i quali hanno oramai i documenti in mano, sanno <lb></lb>come si trovassero mirabilmente il Marchetti e il Blondel col Viviani con­<lb></lb>cordi nel correggere quel trascorso: che se l&#039;Autore <emph type="italics"></emph>De resistentia solido­<lb></lb>rum<emph.end type="italics"></emph.end> scrisse nella sua prefazione <emph type="italics"></emph>Salviatus illic veri specie fuit deceptus<emph.end type="italics"></emph.end><pb xlink:href="020/01/2227.jpg" pagenum="470"></pb>il Postillatore dell&#039;edizione di Leida scrisse in margine, di rincontro alla <lb></lb>proposizìone formulata dallo stesso Salviati, <emph type="italics"></emph>falsa,<emph.end type="italics"></emph.end> dichiarandosi come si <lb></lb>rendesse vera, cosiderata la figura in astratto e qual puramente geometrica, <lb></lb>e conclucendo nel modo medesimo del Marchetti, come si vide, che l&#039;er­<lb></lb>rore di Galileo non in altro consisteva che nel volere applicare le proprietà <lb></lb>di un solido senza peso alla travatura delle navi, per necessità naturale <lb></lb>pesanti. </s></p><p type="main">

<s>Anzi il Viviani, che in riconoscere gli sbagli del suo Maestro non cre­<lb></lb>deva punto di calunniarlo, ebbe a notare parecchie altre proposizioni par­<lb></lb>tecipanti la falsità medesima di quella famosa corretta dal Marchetti, di cui <lb></lb>bene spesso si mostra più sottile e più libero censore. </s>

<s>È notabile, fra gli <lb></lb>altri esempii di così fatte censure, quella che liberamente egli esercitò in­<lb></lb>torno alla proposizione XIV, manifestamente falsa nel suo principio, e per­<lb></lb>ciò nella sua conclusione. </s>

<s>Dice ivi Galileo: “ Questo DB (fig. </s>

<s>244) è un <lb></lb><figure id="id.020.01.2227.1.jpg" xlink:href="020/01/2227/1.jpg"></figure></s></p><p type="caption">

<s>Figura 244<lb></lb>prisma (il Viviani vi aggiunge: <lb></lb><emph type="italics"></emph>senza peso)<emph.end type="italics"></emph.end> la cui resistenza al­<lb></lb>l&#039;essere spezzato nell&#039;estremità <lb></lb>AD, da una forza premente nel <lb></lb>termine B, è tanto minore della <lb></lb>resistenza, che si troverebbe nel <lb></lb>luogo CI, quanto la lunghezza <lb></lb>CB è minore della BA ” (Alb. </s>

<s><lb></lb>XIII, 137): che vuol dire avere <lb></lb>le resistenze reciproca propor­<lb></lb>zione delle lunghezze, con fal­<lb></lb>sità manifesta. </s>

<s>Nè par credibile che Galileo non s&#039;accorgesse dello sbaglio, <lb></lb>perchè, segato dal piano DMB il prisma nel mezzo, dice più sotto che la <lb></lb>resistenza AD sta alla resistenza CO, come il rettangolo AD sta al rettan­<lb></lb>golo CO. </s>

<s>Se ora per questa medesima ragione le resistenze AD, CI debbono <lb></lb>stare come i rettangoli son dunque esse resistenze insieme uguali, e dovreb­<lb></lb>bero esser perciò uguali altresì le lunghezze AB, CB: cosa tanto assurda, <lb></lb>da far avveduto chiunque che sarebbe dovuto il ragionamento procedere in <lb></lb>quest&#039;altra maniera: </s></p><p type="main">

<s>Applicati in B due pesi P.P′ la resistenza della sezione AD è uguale <lb></lb>ad AB.P, ed è per somigliante ragione CB.P′ la resistenza della sezione <lb></lb>CI. </s>

<s>Ma perchè sono le due resistenze uguali, dunque P:P′=CB:AB, e <lb></lb>perciò stanno i pesi e non le resistenze, come Galileo diceva, in proporzione <lb></lb>reciproca delle lunghezze. </s></p><p type="main">

<s>Il Viviani insomma, così rettamente come dovevasi ragionando, notò in <lb></lb>quella sua cartuccia, inserita fra la pag. </s>

<s>138 e 139 della edizione di Leida, <lb></lb>riferendosi alla detta proposizione qual si legge nel testo: “ È falsa così pro­<lb></lb>nunziata: le resistenze del medesimo prisma o cilindro fitti nel muro, con­<lb></lb>siderati senza peso, sono fra loro come i pesi attaccati alle estremità, che <lb></lb>siano bastanti a spezzargli, i quali pesi hanno fra loro la proporzion reci-<pb xlink:href="020/01/2228.jpg" pagenum="471"></pb>proca delle lunghezze fuori del muro. </s>

<s>Vera così: gli equivalenti la mede­<lb></lb>sima resistenza assoluta (ossia i pesi assoluti da noi sopra significati con <lb></lb>P.P′) di un cilindro o prisma senza peso, fitti in un muro da diverse lun­<lb></lb>ghezze, hanno proporzione reciproca delle lunghezze ” (MSS. Gal., P. V, <lb></lb>T. IX). E rendendo la galileiana proposizione anche più generale, avrebbe <lb></lb>volentieri voluto sostituire, a quella falsa messa in bocca al Salviati, que­<lb></lb>st&#039;altra più conforme col vero, così formulata: “ I minimi pesi bastanti a <lb></lb>pareggiar da diverse lunghezze la medesima resistenza della sezion verticale <lb></lb>di un cilindro o prisma o altro qualunque solido, senza peso, fitto in un <lb></lb>muro, sono fra loro in reciproca proporzione delle medesime lunghezze ” (ivi). </s></p><p type="main">

<s>È lecito di qui argomentare quanto fosse il Viviani docile a pigliare stu­<lb></lb>pidamente contro le calunnie del Blondel e del Marchetti le difese di Ga­<lb></lb>lileo, ricorrendo allo strattagemma di riguardare il solido parabolico posato <lb></lb>in piano. </s>

<s>Si poteva la strana idea sopportare nel Grandi, infintanto che il <lb></lb>teorema del Prisma parabolico, sostenuto dalle due parti, gli occorse a no­<lb></lb>tare nel primo frettoloso esame del Manoscritto, separatamente dagli altri: <lb></lb>ma quando attese di proposito e con pace a metter ordine a tutto il trat­<lb></lb>tato, dalle relazioni che aveva quel teorema con altri simili ivi dimostrati <lb></lb>si sarebbe dovuto avveder che il Viviani, tutt&#039;altro che insorgere avverso, <lb></lb>si trovava col Marchetti e col Blondel, per riuscir con loro a un termine, <lb></lb>sulla dirittura del medesimo sentiero. </s></p><p type="main">

<s>Hanno nel primo aspetto gl&#039;incontri dei tre Autori qualche cosa di ma­<lb></lb>raviglioso, ma è il Grandi stesso che ci toglie ogni maraviglìa, avvertendo <lb></lb>nella prefazione al suo libro <emph type="italics"></emph>Della quadratura del circolo,<emph.end type="italics"></emph.end> che in Matema­<lb></lb>tica, a partire dai medesimi principii, chiunque retto ragiona non solo è <lb></lb>facile ma è necessario s&#039;incontri nelle medesime conclusioni. </s>

<s>Ebbero il Blon­<lb></lb>del, il Viviani e il Marchetti comune lo studio sul Galileo, non fatto super­<lb></lb>ficialmente e in fretta, come quel del Cartesio, il quale è curioso che, no­<lb></lb>tando tante altre verità di errore, del solido parabolico di ugual resistenza <lb></lb>convenisse con lo stesso Galileo che <emph type="italics"></emph>verum est vere<emph.end type="italics"></emph.end> (Epist. </s>

<s>cit., P. II, pag. </s>

<s>243) <lb></lb>ad eccezione di tutto il rimanente. </s>

<s>I tre sopra commemorati videro invece, <lb></lb>al medesimo chiaro lume della Geometria, ch&#039;era falso, e, scorti dalla me­<lb></lb>desima infallibile guida a investigare la verità della cosa, non poterono non <lb></lb>incontrarsi nella medesima conclusione, che cioè il solido parabolico pesante, <lb></lb>tanto più resiste, quanto la forza lo preme più presso al vertice, in ragion <lb></lb>dupla sesquialtera dei momenti dei pesi ai momenti delle resistenze. </s></p><p type="main">

<s>Come procedessero d&#039;ugual passo il Viviani e il Marchetti, in questa <lb></lb>investigazione, già di sopra si vide: e si può con certezza argomentare che <lb></lb>fossero queste stesse le vie tenute dal Blondel. </s>

<s>Scopertosi ora non essere pro­<lb></lb>priamente parabolica la figura del solido, che ugualmente resiste, era natura­<lb></lb>lissimo che si proponesse ai tre Autori, nel medesimo tempo, il quesito: qual <lb></lb>altra dunque dovrebb&#039;essere quella vera figura? </s>

<s>E non poteva far altro la <lb></lb>Geometria che rispondere: la ellittica, come di fatti dimostrò il Marchetti nella <lb></lb>proposizione XXXIX del II libro, e il Viviani nella XCVI del suo trattato. </s></p><pb xlink:href="020/01/2229.jpg" pagenum="472"></pb><p type="main">

<s>Ma la dimostrazione di ciò era facile vedere che si applicava a parec­<lb></lb>chi altri solidi “ quae, cum nixa sint super extremitatibus, aequaliter re­<lb></lb>sistunt ponderi, quod intra fulcimentum sit appensum ” (MSS. Gal., P. V, <lb></lb>T. VII, fol. </s>

<s>59), fra&#039;quali solidi annovera lo stesso Viviani, in questo luogo <lb></lb>citato, il Prisma parabolico, il Semicilindrico e base circolare, il Semicilin­<lb></lb>drico a base elittica, e le volte, che abbian per centina un semicerchio e <lb></lb>una semiellisse, o due semiellissi di egual diametro orizzontale, e di diverso <lb></lb>diametro perpendicolare. </s></p><p type="main">

<s>Ecco dunque com&#039;ebbe origine nel Viviani l&#039;invenzion di quel prisma <lb></lb>parabolico, che s&#039;immaginò il Grandi essere stata fatta per servire appunto <lb></lb>“ a confutare la calunnia opposta al Galileo, prima da m. </s>

<s>Blondello in Fran­<lb></lb>cia, e poi dal signor Marchetti in Italia ” (Alb. </s>

<s>XIV, 87): ecco quanto ri­<lb></lb>dicolo apparisca lo stesso Grandi, quando ci descrive il Viviani, che si mette <lb></lb>attorno a duplicare il Cuneo galileiano, e poi lo raddoppia di nuovo, <emph type="italics"></emph>per <lb></lb>maggiore stabilità e vaghezza!<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>86). Ma, mentre il Valentuomo si <lb></lb>trattiene in queste ridicolezze, e per mostrare la maggiore fecondità dell&#039;in­<lb></lb>gegno del Viviani, sopra quel del Marchetti, ordina le varie proposizioni con­<lb></lb>cernenti la varietà delle forme dei solidi di resistenze uguali; non s&#039;avvede <lb></lb>che manca ad esse proposizioni il fondamento, e che quello che vi si sot­<lb></lb>topone non è il loro proprio. </s></p><p type="main">

<s>Le XCV, XCVI infatti, questa degli emi­<lb></lb>cilindri di base circolare o di base ellittica <lb></lb>(Alb. </s>

<s>XIV, 87), quella del Prisma elittico <lb></lb>QM (fig. </s>

<s>245), sostenuto alle sue estremità <lb></lb><figure id="id.020.01.2229.1.jpg" xlink:href="020/01/2229/1.jpg"></figure></s></p><p type="caption">

<s>Figura 245<lb></lb>M, N (ivi, pag. </s>

<s>86), si concludono da tali <lb></lb>due principii: che i pesi uguali pendenti <lb></lb>da I, L stanno come i rettangoli MI.IN, <lb></lb>ML.LN, e che i momenti delle resistenze <lb></lb>delle sezioni AB.CD son proporzionali alle <lb></lb>basi GB, HD. </s>

<s>Come alla conclusione mancasse, negli <lb></lb>ordinamenti del Grandi, quel primo fondamento, già <lb></lb>lo dicemmo: ora è da soggiungere che il secondo ivi <lb></lb>indicato non è il suo proprio. </s>

<s>Per verificare infatti l&#039;as­<lb></lb>serta proporzion dei momenti delle sezioni, s&#039;indica <lb></lb>la proposizione II: <emph type="italics"></emph>I momenti delle resistenze, nelle se­<lb></lb>zioni dei solidi, le di cui basi siano disuguali ed eguali <lb></lb>le altezze, sono come le medesime basi<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>14), <lb></lb>la qual proposizione prende valore dalla prima, che <lb></lb>dice: <emph type="italics"></emph>I momenti di resistenza della medesima sezione, <lb></lb>o di sezioni uguali, sono tra di loro come le distanze <lb></lb>del centro di gravità di esse dal sostegno<emph.end type="italics"></emph.end> (ivi). <lb></lb><figure id="id.020.01.2229.2.jpg" xlink:href="020/01/2229/2.jpg"></figure></s></p><p type="caption">

<s>Figura 246</s></p><p type="main">

<s>Il Grandi, invocando i principii della Leva, dice questa proposizion del <lb></lb>Viviani evidente, e tale senza dubbio sarebbe, mentre che si trattasse delle <lb></lb>resistenze respettive, perchè, avendosi le due sezioni AC, EH (fig. </s>

<s>246) con <pb xlink:href="020/01/2230.jpg" pagenum="473"></pb>le altezze AD, EG uguali, e con i centri di gravità in O, M, le leve fa­<lb></lb>vorevoli ON, MR producono momenti di forza uguali ad AB.AD.NO, <lb></lb>EF.EG.RM; onde, chiamate R.R′ le resistenze delle dette sezioni, se ne <lb></lb>conclude R:R′=AB.AD.NO:EP.EG.RM=AB:EF. </s></p><p type="main">

<s>Ma nelle sezioni AB, CD del Prisma parabolico, rappresentato nella <lb></lb>figura 245, si tratta di resistenze assolute, dove non è perciò favore alcuno <lb></lb>di Leva, e nonostante asserisce il Viviani anche di esse: “ Momenta resi­<lb></lb>stentiarum sectionum solidi, quarum bases sint inaequales, aequales vero <lb></lb>altitudines, sunt inter se ut ipsae bases ”, avvertendo che ciò si avvera “ in <lb></lb>omnibus sectionum figuris, quarum centra gravitatis axes dividant in eadem <lb></lb>ratione ” (MSS. Gal., P. V, T. VII, fol. </s>

<s>56). Anzi la stessa proposizione I, <lb></lb>che s&#039;è riferita dianzi secondo la traduzione del Grandi, nell&#039;originale è <lb></lb>così formulata: “ Momenta resistentiarum eiusdem sectionis, vel aequalium <lb></lb>sectionum, sunt inter se ut distan­<lb></lb>tiae centri gravitatis îpsarum a ful­<lb></lb>cimento ” (ibid.), ed è nel Mano­<lb></lb>scritto illustrata da varie coppie di <lb></lb>figure uguali, come di triangoli o <lb></lb>di ellissi, ora posate sul sostegno <lb></lb>con l&#039;apice, ora con la base. </s>

<s>Così, <lb></lb>il momento della resistenza, nel <lb></lb>triangolo ABC (fig. </s>

<s>247), sta al mo­<lb></lb><figure id="id.020.01.2230.1.jpg" xlink:href="020/01/2230/1.jpg"></figure></s></p><p type="caption">

<s>Figura 247<lb></lb>mento della resistenza, nel mede­<lb></lb>simo triangolo posto secondo DEF, come HG sta ad LF, distanza dei centri <lb></lb>di gravità dal sostegno. </s>

<s>Similmente, ne&#039;rettangoli AC, EH (fig. </s>

<s>248), aventi le <lb></lb><figure id="id.020.01.2230.2.jpg" xlink:href="020/01/2230/2.jpg"></figure></s></p><p type="caption">

<s>Figura 248<lb></lb>basi BC, DH uguali, i momenti stanno <lb></lb>come i quadrati delle altezze AB, ED, <lb></lb>e pure ne&#039;rettangoli o ellissi o al­<lb></lb>tro, aventi le altezze AC, ED uguali <lb></lb>(fig. </s>

<s>249), i momenti delle resistenze <lb></lb>stanno come le basi. </s></p><p type="main">

<s>Queste, che noi col Grandi ab­<lb></lb>biam chiamate proposizioni, il Viviani <lb></lb>le intitola <emph type="italics"></emph>Lemmata universalia pro <lb></lb>resistentiis<emph.end type="italics"></emph.end> in servigio principalmente <lb></lb>delle proposizioni concernenti i solidi di resistenze uguali. </s>

<s>Essendo perciò <lb></lb>di tanta importanza nel Trattato quei Lemmi, pensò bene l&#039;Ordinatore di <lb></lb><figure id="id.020.01.2230.3.jpg" xlink:href="020/01/2230/3.jpg"></figure></s></p><p type="caption">

<s>Figura 249<lb></lb>esso Trattato di supplir̀e alle dimostra­<lb></lb>zioni, che non si trovan nel Manoscritto, <lb></lb>ma non ebbe il pensiero nessun buono <lb></lb>effetto, per le accennate ragioni del ve­<lb></lb>nir meno l&#039;invocato favor della Leva <lb></lb>nelle resistenze assolute delle varie di­<lb></lb>segnate sezioni, i centrì di gravità delle quali battono a perpendicolo sul <pb xlink:href="020/01/2231.jpg" pagenum="474"></pb>sostegno. </s>

<s>Dovette dunque il Viviani, a confortare i suoi Lemmi, avere invo­<lb></lb>cato un diverso principio, che non s&#039;intenderebbe, senza attribuirlo all&#039;animo <lb></lb>preoccupato, come il Grandi non indovinasse esser quello dei momenti delle <lb></lb>forze proporzionali alle velocità moltiplicate per i pesi. </s></p><p type="main">

<s>Così, per esempio, nelle sopra disegnate figure triangolari 247, la re­<lb></lb>sistenza è vinta, quando il centro di gravità è portato da H e da L in G <lb></lb>e in F, fuori del sostegno, a che fare ci bisognan due forze, atte a movere <lb></lb>il medesimo peso triangolare, l&#039;una con la velocità HG, l&#039;altra con la ve­<lb></lb>locità LF; ond&#039;è ch&#039;esse forze saranno, come conclude il Viviani, propor­<lb></lb>zionali a queste due distanze. </s>

<s>Similmente, nelle sezioni rettangolari di ugual <lb></lb>base e di differente altezza, rappresentate dianzi nella figura 248, i momenti <lb></lb>delle forze, che vincono le resitenze assolute, sono AB.BC.MP, ED.DH.OQ, <lb></lb>e perciò, avendosi MP=AB/2, OQ=ED/2, torneranno i detti momenti pro­<lb></lb>porzionali ai quadrati delle respettive altezze, e proporzionali alle basi tor­<lb></lb>neranno nelle sezioni AD, EF, rappresentate nell&#039;ultima figura 249, per es­<lb></lb>sere gli spazi ON, MP, che misuran le velocità uguali, ambedue la metà <lb></lb>delle altezze rettangolari uguali. </s></p><p type="main">

<s>L&#039;universalità di questi Lemmi, dal Viviani applicati ai solidi ugual­<lb></lb>mente resistenti, conduceva a concludere che infinite posson essere le varie <lb></lb>figure di così fatti solidi, non che quelle tre, per le quali il Grandi (Rispo­<lb></lb>sta apol. </s>

<s>cit., pag. </s>

<s>129) mena vanto di superiorità del suo Autore, sopra <lb></lb>l&#039;unico solido ellittico proposto dal Marchetti. </s>

<s>S&#039;annovera tra quelle tre <lb></lb>figure il Cuneo triangolare, di che certo, essendo cosa di si facile conse­<lb></lb>guenza, non avrebbe tenuto conto lo stesso Viviani. </s>

<s>Sono di quella facilità <lb></lb>indizio le due stesse varie maniere di dimostrare la proposizione, alle quali <lb></lb>due maniere dell&#039;Autore ne aggiunge il Grandi una terza, che non è pure <lb></lb>da rassomigliar a quest&#039;altra, quale può aversi per via diretta: </s></p><p type="main">

<s>Sia il Cuneo triangolare AC (fig. </s>

<s>250), sporgente fuori del muro, ora <lb></lb><figure id="id.020.01.2231.1.jpg" xlink:href="020/01/2231/1.jpg"></figure></s></p><p type="caption">

<s>Figura 250<lb></lb>quanto DO, ora quanto QD, e il peso <lb></lb>G pareggi, col suo momento G.DO, <lb></lb>la resistenza R della sezione AB, men­<lb></lb>tre l&#039;altro peso H pareggia, col mo­<lb></lb>mento H.DQ, la resistenza R′ della <lb></lb>sezione FE. </s>

<s>Considerando che, per via <lb></lb>di uno de&#039;Lemmi universali gia di­<lb></lb>mostrati, le resistenze delle sezioni <lb></lb>aventi uguali altezze stanno come le <lb></lb>basi AI, NE, o come le lunghezze OD, <lb></lb>QD, avremo R:R′=G.DO:H.DQ <lb></lb>=DO:DQ e perciò G=H. </s></p><p type="main">

<s>Il discorso lungo, fin qui da noi <lb></lb>intrattenuto sulle controversie insorte fra i due Professori pisani, per deci­<lb></lb>der delle ragioni del primato, e dei modi cen cui si vollere, circa al solido <pb xlink:href="020/01/2232.jpg" pagenum="475"></pb>parabolico di ugual resistenza, riformare e promovere i teoremi di Galileo; <lb></lb>ci ha portato a concludere che fossero d&#039;ogni parte irragionovoli i giudizii <lb></lb>del Grandi. </s>

<s>Ma perchè l&#039;odio divampa al largo con le sue fiamme voraci, <lb></lb>ritroveremo una pari irragionevolezza, quando esso Grandi, non contento di <lb></lb>avere accusato il Marchetti di plagio, passa a fare un sottile esame di altre <lb></lb>varie proposizioni di lui, per voler notarle vergognosamente di errore. </s></p><p type="main">

<s>Nel II capitolo della I parte della <emph type="italics"></emph>Risposta apologetica<emph.end type="italics"></emph.end> l&#039;Autore, per to­<lb></lb>gliere al Marchetti il vanto di aver egli il primo dimostrata la composizion <lb></lb>dei momenti, cita la proposizione VI del dialogo II, e dice che ivi Galileo <lb></lb>“ suppone evidentemente la ragione de&#039;momenti composta di quella dei pesi <lb></lb>e delle lunghezze onde dipendono, e se ne serve al proposito della resi­<lb></lb>stenza dei solidi: sebbene egli ne deduce una conclusione alquanto diversa <lb></lb>da quella del signor Marchetti, il quale, esaminando lo stesso soggetto nella <lb></lb>proposizione XI del I libro Della resistenza dei solidi, mostra che la ragion <lb></lb>de&#039;momenti ne&#039;solidi simili è <emph type="italics"></emph>duplicata<emph.end type="italics"></emph.end> di quella delle resistenze, quando <lb></lb>il Galileo l&#039;ha detta di sopra <emph type="italics"></emph>sesquialtera,<emph.end type="italics"></emph.end> verificandosi però in diverso senso <lb></lb>l&#039;una e l&#039;altra proposizione, come si può supporre, da che in questo par­<lb></lb>ticolare non ha preteso il mio dottissimo Avversario di corregger sbaglio <lb></lb>veruno nel Galileo ” (pag. </s>

<s>37, 38). </s></p><p type="main">

<s>Qui però sembra strano che un&#039;assoluta verità matematica abbia ad <lb></lb>accomodarsi a diverso senso, e giacchè ambedue gli Autori accolgono le me­<lb></lb>desime ipotesi, e muovono dai medesimi principii, si vedeva impossibile che <lb></lb>una proporzione fosse tutto insieme sesquialtera e duplicata. </s>

<s>Certi dunque <lb></lb>che doveva la verità essere o da una parte o dell&#039;altra, e scevri dai pre­<lb></lb>giudizii del Grandi, e di tanti altri insieme con lui, che una conclusione sia <lb></lb>vera perchè Galileo l&#039;ha dimostrata; abbiamo voluto meglio esaminare la <lb></lb>cosa, e ci pare aver trovato che la ragione sia dalla parte del Marchetti, il <lb></lb>quale avrebbe potuto perciò a tutto diritto correggere in Galileo un altro <lb></lb>sbaglio, meno assai perdonabile del primo. </s></p><p type="main">

<s>Siano i due cilindri simili AB, CD (fig. </s>

<s>251): Galileo dice, nella sua <lb></lb>VI proposizione, che i loro momenti “ hanno tra di loro proporzione se­<lb></lb><figure id="id.020.01.2232.1.jpg" xlink:href="020/01/2232/1.jpg"></figure></s></p><p type="caption">

<s>Figura 251<lb></lb>squialtera di quella, che hanno le resistenze <lb></lb>delle loro basi ” (Alb. </s>

<s>XIII, 123) e il Mar­<lb></lb>chetti invece formula la sua XI proposizione: <lb></lb>“ Solidorum inter se similium momenta pon­<lb></lb>derum in duplicata sunt proportione resi­<lb></lb>stentiarum ” (pag. </s>

<s>10). Chiamati C, C′ i due <lb></lb>detti cilindri, e M.o C, M.o C′ i loro mo­<lb></lb>menti, convengono ambedue gli Autori nello <lb></lb>stabilire l&#039;equazione (A) M.o C:M.o C′= <lb></lb>C.AB:C′.CD. </s>

<s>Ma perchè C, C′ stanno come i cubi dei diametri D, D′ delle <lb></lb>basi o delle altezze proporzionali, Galileo ha per prima conclusione (B) M.oC: <lb></lb>M.oC′=D3:D′3, e il Marchetti (C) M.oC:M.oC′=AB1:CD1=D1:D′1, <lb></lb>d&#039;onde nasce la diversità della conclusione finale, perchè chiamate R, R′ le <pb xlink:href="020/01/2233.jpg" pagenum="476"></pb>resistenze, essendo pure per ambedue gli Autori (D) R:R′=D2:D′2, cu­<lb></lb>bando questa, e quadrando la (B), si ottiene M.oC2:M.oC′2=R3:R′3, ossia <lb></lb>M.oC:M.oC′=R3/2:R′3/2, che è la ragione sesquialtera di Galileo: mentre <lb></lb>la (D) quadrata, e la (C) danno M.oC:M.oC′=R2:R′2, che è la ragion <lb></lb>duplicata del Marchetti. </s></p><p type="main">

<s>Or perchè tutta la question si riduce a saper se AB è uguale a CD, <lb></lb>per cui si possano le due quantità eliminare dalla seconda ragione di (A), <lb></lb>o se sono diverse, per cui debbano rimaner nella (C) come fattori, chiun­<lb></lb>que abbia meno scienza del Grandi, ma miglior senso comune, senza mezzi <lb></lb>termini, decide esser vera la proposizion del Marchetti, e falsa addirittura <lb></lb>quella di Galileo. </s>

<s>“ La forza della leva AB, egli dice, è eguale alla forza <lb></lb>della leva CD, e questo perchè la lunghezza AB, al semidiametro della base B, <lb></lb>ha la medesima proporzione, per la similitudine dei cilindri, che la lun­<lb></lb>ghezza CD al semidiametro della base D ” (Alb. </s>

<s>XIII, 123, 24); nè s&#039;av­<lb></lb>vedeva il grand&#039;Uomo che, mentre nelle similitudini de&#039;cilindri la ragione <lb></lb>è diretta, nella forza della leva e inversa, e che AB, e CD nella (A) non <lb></lb>rappresentano le leve, ma le semplici lunghezze delle leve, le quali perciò <lb></lb>non compongono da sè sole i momenti delle forze. </s></p><p type="main">

<s>Erano state già da noi fatte e scritte queste avvertenze, quando, tor­<lb></lb>nando a svolgere, nel T. IX della P. </s>

<s>V dei Manoscritti di Galileo, le po­<lb></lb>stille del Viviani al secondo dialogo delle Nuove scienze, fu trattenuta la <lb></lb>nostra attenzione sopra un foglietto, in testa al quale il Postillatore stesso <lb></lb>scriveva: <emph type="italics"></emph>Propos. </s>

<s>VI del Galileo generalmente e diversamente enunciata, <lb></lb>per esser quella non vera.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il più autorevole giudice che si potesse desiderare aveva dato dunque <lb></lb>sentenza contro Galileo, e aveva già deciso a favor del Marchetti, togliendo <lb></lb>insieme ogni refugio a quei dissennati, i quali non dubitavano di sacrifi­<lb></lb>care all&#039;amore del vero la vana gloria di un uomo. </s>

<s>Dicevano costoro, e si <lb></lb>ripeteva dal Grandi, ch&#039;era possibile salvar la VI proposizione di Galileo da <lb></lb>ogni nota di errore, intendendo delle <emph type="italics"></emph>resistenze assolute<emph.end type="italics"></emph.end> quel che ivi si dice <lb></lb>dei momenti, ma il Viviani soggiunge che non verrebbesi a togliere la fal­<lb></lb>sità, nemmeno così benignamente interpetrando la detta proposizione, la <lb></lb>quale può solo esser vera a quel modo, che dal Marchetti fu poi pronun­<lb></lb>ziata. </s>

<s>“ E per chi dubitasse, dice nella sua postilla il Viviani, che l&#039;enun­<lb></lb>ziazione del Galileo si dovesse intendere così: cioè che i momenti gravanti <lb></lb>dei cilindri simili hanno proporzion sesquialtera di quella, che hanno le re­<lb></lb>sistenze assolute però, e non i momenti loro resistenti; pur si prova che, <lb></lb>volendo paragonare il rispetto dei momenti gravanti con quello delle resi­<lb></lb>stenze assolute, l&#039;enunziazione sia profferita diversamente così, cioè: <emph type="italics"></emph>I mo­<lb></lb>menti gravanti dei solidi simili son fra loro in doppia proporzione delle <lb></lb>resistenze assolute delle basi. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>L&#039;esser proceduto a diritto il Marchetti, senza fare nè queste osserva­<lb></lb>zioni nè questi confronti, rivela nell&#039;animo di lui riverenza molto maggiore <lb></lb>di quella, che non mostrasse di avere in sè il Grandi, che, riprensore così <pb xlink:href="020/01/2234.jpg" pagenum="477"></pb>zelante dei calunniatori del divino Uomo, non ebbe poi scrupolo di mettersi <lb></lb>nel numero di loro, quando vide aver di lì meglio libero il braccio, per av­<lb></lb>ventare al nemico le saette avvelenate. </s>

<s>S&#039;argomenta e si prova ciò dal modo <lb></lb>che tenne in censurare la II proposizione del libro II <emph type="italics"></emph>De resistentia soli­<lb></lb>dorum,<emph.end type="italics"></emph.end> e le molte altre dipendenti da lei, tutte dal Grandi allo stesso modo <lb></lb>notate di false, perchè fondate, egli dice, sul falso supposto, “ cioè che la <lb></lb>resistenza d&#039;un solido prismatico fitto nel muro, alla resistenza nel mezzo <lb></lb>di esso, in caso che retto sia dall&#039;una o dall&#039;altra parte, sia in ragion sud­<lb></lb>dupla, cioè come uno sta a due ” (Risposta apol. </s>

<s>cit., pag. </s>

<s>118). </s></p><p type="main">

<s>Ora è da osservar che il Marchetti divide, come Galileo, dietro le più <lb></lb>antiche tradizioni aristoteliche, il suo trattato in due parti, alla seconda delle <lb></lb>quali, che è de&#039;solidi retti nelle due loro estremità, pone per fondamento <lb></lb>il supposto dal medesimo Galileo, cioè “ che il cilindro che, gravato dal <lb></lb>proprio peso, sarà ridotto alla massima lunghezza, oltre alla quale più non <lb></lb>si sosterrebbe, o sia retto nel mezzo da un solo sostegno, ovvero da due <lb></lb>nelle estremità, potrà essere lungo il doppio di quello, che sarebbe fitto nel <lb></lb>muro, cioè sostenuto in un sol termine ” (Alb. </s>

<s>XIII, 132). </s></p><p type="main">

<s>Parve ai due Autori la cosa per sè tanto manifesta nelle note leggi <lb></lb>degli equiponderanti, che non ci videro nessun bisogno di dimostrarla, e <lb></lb>dall&#039;altra parte non ritrovarono ragione al­<lb></lb>cuna di dubitare che, se per esempio il ci­<lb></lb>lindro AB (fig. </s>

<s>252), confitto con la sua <lb></lb><figure id="id.020.01.2234.1.jpg" xlink:href="020/01/2234/1.jpg"></figure></s></p><p type="caption">

<s>Figura 252<lb></lb>base A nel muro, e il cilindro BC, confit­<lb></lb>tovi con la sua base C, resistono al proprio <lb></lb>peso, non debbano altresì resistere attestati <lb></lb>insieme i due cilindri in B (fig. </s>

<s>253), com­<lb></lb>ponenti un cilindro solo AC doppiamente <lb></lb>lungo, non venendosi per questo avvicina­<lb></lb><figure id="id.020.01.2234.2.jpg" xlink:href="020/01/2234/2.jpg"></figure></s></p><p type="caption">

<s>Figura 253<lb></lb>mento a far altro, che a favorire anzi la <lb></lb>virtù di resistere alla rottura, col contatto <lb></lb>adesivo delle due superficie BE, e col re­<lb></lb>ciproco appoggio delle testate. </s></p><p type="main">

<s>Incominciarono i dubbî a nascere, quan­<lb></lb>do la chiarezza dei fatti venne a intorbidarsi <lb></lb>agitata dalle speculazioni, imperocchè, con­<lb></lb>siderati i cilindri AB, BC della figura 252 <lb></lb>senza peso, e fatti rappresentare i momenti delle resistenze dai pesi uguali <lb></lb>P, Q, operanti col favor delle leve uguali AB, BC; si domandava se attestati <lb></lb>i due cilindri si dovevano i pesi P, Q unire insieme, o se bastava un solo <lb></lb>di essi a rappresentare le parti congiunte: sarebbe lo stesso che domandare <lb></lb>se in B, nella figura 253, le due linee BE, BE si son fuse in una, o se, per <lb></lb>la semplice congiunzione, si mantengan distinte. </s>

<s>E giacchè, considerate le <lb></lb>gravità dei due cilindri AB, BC riunite nei loro centri, i pesi P, Q son la <lb></lb>metà dei pesi di essi cilindri, si riduceva la domanda a sapere se il peso R, <pb xlink:href="020/01/2235.jpg" pagenum="478"></pb>pendente dal mezzo del cilindro doppio a rappresentarne la resistenza, sia <lb></lb>uguale alla somma dei pesi P, Q, o ad uno di essi solo. </s>

<s>Che se sia uguale <lb></lb>alla somma, e la resistenza in B patisca perciò doppia violenza, non potrebbe <lb></lb>esser vero il supposto di Galileo, se non a patto che il cilindro AC sia più <lb></lb>sottile o più corto. </s></p><p type="main">

<s>Fu il dubbio primo a nascere nella mente del Viviani, il quale si pose <lb></lb>perciò innanzi a risolvere così il quesito: “ Se il cilindro AB, nell&#039;ultima <lb></lb>figura 253, fitto nel muro, è bastante a spezzare in B, cioè a superare la <lb></lb>resistenza B, col proprio peso e con la leva AB, aggiungendo dall&#039;altra parte <lb></lb>altrettanto cilindro BC, pare che la medesima resistenza B venga violentata <lb></lb>da doppia forza, e che, per spezzarsi col sostegno in mezzo, voglia essere <lb></lb>la metà più sottile, o di lunghezza media proporzionale tra AB e BD metà <lb></lb>di AB ” (MSS. Gal., P. V, T. VII, fol. </s>

<s>29). </s></p><p type="main">

<s>Rimaste queste cose lungamente sepolte nei manoscritti, è notabile che <lb></lb>entrasse nel medesimo filo delle speculazioni, sulla fine del secolo XVII, un <lb></lb>celebre matematico francese, Filippo De-la-Hire, che nel suo <emph type="italics"></emph>Traité de Me­<lb></lb>canique<emph.end type="italics"></emph.end> risolve con nostra gran meraviglia le questioni della Libbra, avuto <lb></lb>riguardo ai pesi che tendono al centro della Terra, in quel modo che ve­<lb></lb>demmo averle già risolute il Torricelli nei manoscritti suoi sconosciuti. </s>

<s>L&#039;Ac­<lb></lb>cademico parigino dunque, trattando nella sua proposizione CXXVI <emph type="italics"></emph>De la <lb></lb>resistance des solides,<emph.end type="italics"></emph.end> scrive così a proposito della proposizione XI di Ga­<lb></lb>lileo: “ Il dit que ce cylindre doit se rompre de même, soit qu&#039;il soit sou­<lb></lb>tenu par son milieu, ou par ses extremitez: mais il n&#039;a pas fait assez d&#039;at­<lb></lb>tention à ce qu&#039;il a avancé, et s&#039;il s&#039;étoit donné la peine d&#039;en suivre la <lb></lb>démonstration jusqu&#039;à la fin, il auroit trouvé que, dans sa supposition des <lb></lb>liens, ce cylindre ne doit avoir que la moyenne proportionelle entre AB (nel­<lb></lb>l&#039;ultima nostra figura), et sa moitié DB ” (A Paris 1695, pag. </s>

<s>483). </s></p><p type="main">

<s>La dimostrazione si può, per brevità e per maggiore chiarezza, ridurre alla <lb></lb>forma seguente: Sia il cilindro ABC sostenuto nel suo mezzo B, come si rap­<lb></lb>presenta nella figura ora citata: il momento <lb></lb>della sua resistenza, chiamata B la base <lb></lb>dello stesso cilindro, sarà B.AD.DB. </s>

<s>Ab­<lb></lb>biasi poi un altro cilindro di ugual gros­<lb></lb>sezza, e perciò di ugual base, ma talmente <lb></lb><figure id="id.020.01.2235.1.jpg" xlink:href="020/01/2235/1.jpg"></figure></s></p><p type="caption">

<s>Figura 254<lb></lb>lungo che la metà sua EG (fig. </s>

<s>254) sia media proporzionale tra AD, DB: il <lb></lb>momento della resistenza in E sarà uguale a B.EG.EG. </s>

<s>Ma EG.EG, ossia EG2, <lb></lb>è per supposizione uguale ad AD.DB, dunque le due resistenze sono uguali. </s></p><p type="main">

<s>Dir che Galileo non si <emph type="italics"></emph>donné la peine<emph.end type="italics"></emph.end> di condurre alla sua final con­<lb></lb>clusione una dimostrazione così fondamentale, doveva secondo il Grandi pa­<lb></lb>rere un&#039;altra calunnia: eppure, per offendere il Marchetti egli approva le <lb></lb>censure del De-la-Hire, salutato ossequiosamente col nome di <emph type="italics"></emph>profondissimo <lb></lb>Geometra,<emph.end type="italics"></emph.end> e con lui ripete “ che, dall&#039;essere un cilindro retto nel mezzo <lb></lb>equilibrato con la sua resistenza, non doveva il Galileo inferire che il me­<lb></lb>desimo reggere si dovesse appoggiato a due sostegni nelle sue estremità, e <pb xlink:href="020/01/2236.jpg" pagenum="479"></pb>che piuttosto dovea dire che la lunghezza d&#039;un cilindro, da reggersi sopra <lb></lb>due sostegni, esser debba mezzana proporzionale tra quella lunghezza, che <lb></lb>si può reggere pendente da un muro, e la doppia della medesima ” (Ri­<lb></lb>sposta apol. </s>

<s>cit., pag. </s>

<s>122): d&#039;onde, contro il Marchetti, conclude che la re­<lb></lb>sistenza di un solido prismatico fitto nel muro, alla resistenza nel mezzo di <lb></lb>esso, non sta come uno a due, ma come uno a quattro, e che son perciò <lb></lb>da correggere tutte le proposizioni <emph type="italics"></emph>De resistentia solidorum,<emph.end type="italics"></emph.end> dipendenti <lb></lb>dalla seconda del secondo libro, col duplicare il conseguente delle proposi­<lb></lb>zioni, ivi dall&#039;Autore assegnate. </s></p><p type="main">

<s>Rispondeva il Marchetti, per difendere sè dalle accuse e insieme anche <lb></lb>Galileo, dimostrasse il suo Avversario perchè mai il peso B della figura 253 <lb></lb>debba esser la somma dei due pesi P, Q pendenti nella precedente figura, <lb></lb>e non piuttosto uguale a uno di essi solo, essendo che da un tal supposto <lb></lb>non dimostrato pigli tutta la virtù di concludere la proposizion del De-la­<lb></lb>Hire. </s>

<s>E giacchè la dignità di Galileo vedeva essere così avvilita dal suo stesso <lb></lb>Difensore zelante, egli è il Marchetti il primo che, cogliendone di qui l&#039;oc­<lb></lb>casione, pensi a salvarla dalle apparenti contradizioni. </s></p><p type="main">

<s>Sui principii del primo dialogo delle Nuove Scienze leggesi descritto il <lb></lb>fatto di una colonna di marmo che, posata presso la sua estremità sopra <lb></lb>due pezzi di trave, si ruppe a sottoporle un terzo simile sostegno nel mezzo <lb></lb>(Alb. </s>

<s>XIII, 9). “ Or dal successo, da Galileo raccontato, osserva il Marchetti, <lb></lb>e dalla cagione dal medesimo assegnatane, pare che quel grand&#039;Uomo si <lb></lb>desse a credere che la resistenza di un medesimo cilindro, appoggiato nel <lb></lb>mezzo ad un solo sostegno, sia minore della resistenza del medesimo appog­<lb></lb>giato a due ne&#039;suoi punti estremi, il che è poi tutto il contrario di quello <lb></lb>che lo stesso Galileo afferma nella proposizione XI del secondo dialogo ” <lb></lb>(Discorso cit., pag. </s>

<s>59, 60). </s></p><p type="main">

<s>Essendo questo insomma il principo, posto per fondamento alla Scienza <lb></lb>delle resistenze dei solidi appoggiati su due sostegni, premeva troppo al Mar­<lb></lb>chetti di confermarlo, almeno con l&#039;autorità di Galileo, e perciò impiega l&#039;ul­<lb></lb>tima parte del suo <emph type="italics"></emph>Discorso apologetico,<emph.end type="italics"></emph.end> da pag. </s>

<s>58 a pag. </s>

<s>68, a provar che <lb></lb>le teorie professate nel secondo dialogo non contradicono alle esperienze de­<lb></lb>scritte nel primo, sì perchè le due travi, che facevano alla pesante colonna <lb></lb>da sostegni, non essendo punti indivisibili non dovevano segnare le distanze <lb></lb>precise dal mezzo; sì perchè, non essendo la colonna un cilindro perfetto, <lb></lb>ma, come tutte le altre colonne materiali erette per i nostri edifizi, essendo <lb></lb>sensibilmente più grossa da una parte che da un&#039;altra, il centro di gravità <lb></lb>non doveva riuscire appunto nel mezzo della figura, dove si dice esserle stato <lb></lb>sottoposto quel terzo sostegno, per maggior sicurezza. </s></p><p type="main">

<s>Quanto poi al principio, da cui s&#039;informa la proposizion del De-la-Hire, <lb></lb>con tanto ardore proseguita dal Grandi, faceva argutamente osservare esso <lb></lb>Marchetti che il peso del cilindro EGF nella figura 254 “ allora tutto si rac­<lb></lb>coglie ed esercita la sua energia sul proprio centro di gravità, quando pende <lb></lb>in aria liberamente, senza esser retto da alcun sostegno, il che non succede <pb xlink:href="020/01/2237.jpg" pagenum="480"></pb>nel caso, nel quale il cilindro EGF è appoggiato ne&#039;suoi estremi a due so­<lb></lb>stegni, i quali vengono a scemarli la metà del suo peso ” (Discorso cit., <lb></lb>pag. </s>

<s>56). Accusava perciò di falsi i modi di dimostrare del De-la-Hire e del <lb></lb>Grandi, i quali, nel computare il momento della parte EG del cilindro, pren­<lb></lb>dono per leva favorevole EG, mentre dovrebbe esser quella vera leva la di­<lb></lb>stanza del centro di gravità di esso EG dal suo proprio sostegno. </s>

<s>Così se <lb></lb>ne concluderebbe che tutto il cilindro EF, appoggiato dalle sue estremità, <lb></lb>è lungo e grosso quanto AC appoggiato solo nel mezzo, come lo rappresenta <lb></lb>la figura 253, e come fu supposto da Galileo. </s></p><p type="main">

<s>La forza di queste ragioni non poteva non essere presentita dal Grandi, <lb></lb>il quale, trovandosi la mente già tentata dai dubbii, ne volle avere il giudi­<lb></lb>zio del Leibniz. </s>

<s>Rispondeva il celebre Matematico, letto il libro del Mar­<lb></lb>chetti: “ Haerebam in primis in eius demonstratione, quando accedebat ad <lb></lb>solidum utrinque fultum. </s>

<s>Sane, cum tunc ruptura alicubi fit in medio, con­<lb></lb>tingit aliqua veluti extritio, quae non est obvia, cum solidum ex muro proie­<lb></lb>ctum est, et rumpitur prope murum ” (MSS. Cim., T. XXIX, fol. </s>

<s>287). </s></p><p type="main">

<s>Questa osservazione consigliò forse il Grandi a tenere una via di mezzo, <lb></lb>in risolvere la questione, dicendo che la proposizione del De-la-Hire è vera, <lb></lb>quando il solido semplicemente si appoggia con le sue estremità sui soste­<lb></lb>gni. </s>

<s>“ Quando poi, soggiunge, i termini di un solido fossero immobilmente <lb></lb>fitti in due pareti, ed impegnativi dentro, allora cresce il doppio di prima <lb></lb>la resistenza di esso solido, perchè, do­<lb></lb>vendosi spezzare, dovrebbe rompersi an­<lb></lb>cora vicino ai due sostegni, le quali due <lb></lb>frazioni equivalgono appunto alla rottura <lb></lb>del mezzo, come mostra il p. </s>

<s>Hostè, li­<lb></lb>bro II, propos. </s>

<s>LIX e LXII <emph type="italics"></emph>Della costru­<lb></lb>zion dei vascelli,<emph.end type="italics"></emph.end> d&#039;onde in tal caso si <lb></lb>verifica esattamente la proposizione del <lb></lb>Galileo ” (Risposta apol. </s>

<s>cit., pag. </s>

<s>122, 23). </s></p><p type="main">

<s>La proposizione LIX, che quì il <lb></lb>Grandi cita dal II libro della <emph type="italics"></emph>Theorie<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2237.1.jpg" xlink:href="020/01/2237/1.jpg"></figure></s></p><p type="caption">

<s>Figura 255<lb></lb><emph type="italics"></emph>de la costruction des vaisseux<emph.end type="italics"></emph.end> di Paolo Hosté, è così formulata: “ Si le <lb></lb>poids C (fig. </s>

<s>255), en faisant l&#039;ouverture FNG, fait aussi les ouvertures AML, <lb></lb>BHI, ces deus ouvertures prises ensemble <lb></lb>vaudront autant que l&#039;ouverture FNG ” <lb></lb>(A Lyon 1697, pag. </s>

<s>114): di che la dimo­<lb></lb>strazione è ovvia, dietro i primi elementi <lb></lb>della Geometria, essendo l&#039;angolo FNE= <lb></lb>AML, come pure, per simili ragioni, l&#039;an­<lb></lb>golo GNE=IHB. </s></p><p type="main">

<s>Questa LIX proposizione però di­<lb></lb>pende dalla XVII, che poteva forse il <lb></lb><figure id="id.020.01.2237.2.jpg" xlink:href="020/01/2237/2.jpg"></figure></s></p><p type="caption">

<s>Figura 256<lb></lb>Grandi citare più opportunamente, perchè, date due travi, una AC (fig. </s>

<s>256), <pb xlink:href="020/01/2238.jpg" pagenum="481"></pb>appoggiata nel mezzo E, e gravata dai pesi A, C ne&#039;suoi estremi; l&#039;altra <lb></lb>MO, perfettamente uguale alla AC, ma appoggiata dalle due parti M, O, e <lb></lb>caricata nel mezzo dal peso N; dimostra l&#039;Hosté “ que la vitesse de la puis­<lb></lb>sance N est moins grande que la vitesse des poids A, C ” (ivi, pag. </s>

<s>101). <lb></lb>E nel corollario alla seguente proposìzione XVIII, nella quale dimostra che <lb></lb>la velocità del peso N, sta alla velocità dei pesi A, C, come il coseno del­<lb></lb>l&#039;angolo della metà dell&#039;apertura sta al seno totale; osserva che, se l&#039;aper­<lb></lb>tura è infinitesima, o come diremmo volgarmente se la trave è semplice­<lb></lb>mente <emph type="italics"></emph>incrinata,<emph.end type="italics"></emph.end> il peso N sarà uguale alla somma dei pesi A, C. “ Si on <lb></lb>fait l&#039;ouverture de la poutre infinement petite, la vitesse de la puissance N <lb></lb>sera egale à la vitesse des poids A, C; c&#039;est pourquoi la puissance N sera <lb></lb>egale aux poids A, C ” (ivi, pag. </s>

<s>102). </s></p><p type="main">

<s>Così essendo, occorre ora a domandare se citasse opportunamente il <lb></lb>Grandi queste proposizioni dell&#039;Hosté a decider tra il De-la-Hire e il Mar­<lb></lb>chetti la differenza, incominciata da un semplice dubbio del Viviani intorno <lb></lb>alla proposizione XI di Galileo. </s>

<s>È facile a rispondere che non può nel pre­<lb></lb>sente giudizio nulla valere l&#039;autorità dell&#039;Hosté, il quale ammette ipotesi e <lb></lb>professa principii tutt&#039;affatto diversi da quelli di Galileo, e perciò del De­<lb></lb>la-Hire e del Marchetti. </s>

<s>Lo fa avvertire l&#039;Autore stesso nella prefazione a <lb></lb>questo secondo libro, dove, dopo aver detto che il desiderio di fare accorti <lb></lb>gli Stati di tante inutili spese, nel provvedere alla stabilità delle navi da <lb></lb>guerra, gli avea fatto intraprendere la fatica di ricercar la teorica delle loro <lb></lb>costruzioni; soggiunge di non aver ignorato che Galileo l&#039;avea prevenuto, <lb></lb>nel trattar l&#039;argomento, “ quoique les voyes que j&#039;ai tenues soient tout a <lb></lb>fait differentes ” (ivi, pag. </s>

<s>94). La qual differenza apparisce notabile dalla <lb></lb>proposizione XXV, in cui si dimostra che la scala dei momenti dei pesi uguali <lb></lb>attaccati ad una libbra, sostenuta ne&#039;suoi estremi, sta nel triangolo, mentre <lb></lb>per Galileo sta nella parabola. </s></p><p type="main">

<s>Al giudizio dunque del Matematico francese, male a proposito invocato <lb></lb>dal Grandi, potremo sostituire quello del nostro italiano Mariano Fontana, il <lb></lb>quale, avendo nel primo de&#039;suoi tre libri <emph type="italics"></emph>Della dinamica<emph.end type="italics"></emph.end> preso ad esami­<lb></lb>nar sottilmente la proposizione del De-la-Hire, con la quale s&#039;accorda <emph type="italics"></emph>il ce­<lb></lb>lebre geometra Guidone Grandi,<emph.end type="italics"></emph.end> sentenza che <emph type="italics"></emph>questi s&#039;ingannano senza, <lb></lb>dubbio, e che il Galileo ha ragione.<emph.end type="italics"></emph.end> Gli argomenti da provar ciò si ridu­<lb></lb>cono principalmente a quelli, con i quali il Marchetti si studiava di salvare <lb></lb>i principii ch&#039;egli professava dalle fallacie de&#039;due contradittori ora comme­<lb></lb>morati “ l&#039;errore dei quali, dice il Fontana, ha origine dalla supposizione, <lb></lb>la quale essi fanno, che tutto il peso del prisma EF, nella nostra figura 254, <lb></lb>sia riunito nel suo centro di gravità in G.... Ma, da quanto fu dimostrato <lb></lb>di sopra, chiaro apparisce che non è permesso, nel presente caso, di sup­<lb></lb>porre tutto il peso del prisma EF nel suo centro di gravità. </s>

<s>I due segmenti <lb></lb>EG, GF formano due sistemi, e questi sono in una vera opposizione l&#039;uno <lb></lb>contro l&#039;altro. </s>

<s>Quindi si può bene supporre che il peso di ciascun segmento <lb></lb>sia nel suo centro di gravità, ma non già che i pesi dei due segmenti siano <pb xlink:href="020/01/2239.jpg" pagenum="482"></pb>riuniti nel centro di gravità del prisma.... Veramente è singolare che uo­<lb></lb>mini forniti di tanto ingegno, e di così squisita dottrina, non vedessero che <lb></lb>altro effetto dee fare il peso tutto riunito in G, ed il peso stesso distribuito <lb></lb>nella lunghezza del prisma ” (Pavia 1790, pag. </s>

<s>306, 7). Il qual discorso si <lb></lb>può concluder col dire che, riducendo in G il centro, il prisma si considera <lb></lb>come se dovesse rimanere intero, e non disposto alla rottura. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Risulta da tutto il precedente discorso il mal animo, e il perverso giu­<lb></lb>dizio del Grandi verso il Marchetti, ma abbiamo voluto riserbare alla pre­<lb></lb>sente parte del nostro capitolo l&#039;esame di un&#039;altra accusa di plagio, perchè <lb></lb>ci porge occasione a un argomento speciale, e importante in questa storia <lb></lb>Delle resistenze. </s></p><p type="main">

<s>L&#039;Autore dunque <emph type="italics"></emph>De quadratura circuli,<emph.end type="italics"></emph.end> in quel luogo della sua pre­<lb></lb>fazione, da noi altrove citato, incominciò maliziosamente dall&#039;accennare al <lb></lb>teorema meccanico de&#039;momenti composti delle distanze e dei pesi: e perchè <lb></lb>di ciò il Marchetti menava vanto come di una scoperta sua propria, egli al <lb></lb>contrario, per attutirne la baldanza, citava un passo dalla <emph type="italics"></emph>Scienza delle pro­<lb></lb>porzioni,<emph.end type="italics"></emph.end> dove il Viviani dichiara essere stato il detto teorema Dei momenti <lb></lb>insegnato già, e messo in uso da Galileo, dal Cavalieri, dal Rocca e dal Tor­<lb></lb>ricelli. </s>

<s>Poi soggiunge l&#039;Autore di quella Prefazione, facendo vista di volere <lb></lb>scusare il Marchetti: <emph type="italics"></emph>cum tamen id citra ullam plagii suspicionem eventu <lb></lb>facillimum suadeat obvia cuilibet ex primis vulgatisque Mechanicae prin­<lb></lb>cipiis dictae propositionis deductio.<emph.end type="italics"></emph.end> Ma il velo, tolto a queste parole da lui <lb></lb>stesso, che con tant&#039;arte ce lo aveva messo, mentre lo rende colpevole della <lb></lb>più scaltra e più vile ipocrisia, viene a confermar sempre meglio l&#039;irragio­<lb></lb>nevolezza di quelle accuse, che vedemmo non aver provocate altro che l&#039;odio. </s></p><p type="main">

<s>Proponiamoci prima di tutto quel che scrisse il Viviani nella sua <emph type="italics"></emph>Scienza <lb></lb>universale delle proporzioni,<emph.end type="italics"></emph.end> in quel luogo citato dal Grandi, cioè dopo la <lb></lb>conclusione V che dice: <emph type="italics"></emph>Quorumcumque gravium a quibuslibet distantiis <lb></lb>suspensorum momenta sunt in ratione composita ex ratione distantiarum <lb></lb>et ex ratione gravitatum. </s>

<s>”<emph.end type="italics"></emph.end> Questo teorema, ivi si legge, fu dimostrato dal­<lb></lb>l&#039;acutissimo matematico il padre Bonaventura Cavalieri, e da lui stampato <lb></lb>nel 1647, alla proposizione VI della sua quinta <emph type="italics"></emph>Esercitazione geometrica,<emph.end type="italics"></emph.end><lb></lb>benchè di tal conclusione si fosse prima servito un tal Giovanni Antonio <lb></lb>Rocca, insigne Geometra e discepolo di detto Padre, in un suo proprio lemma <lb></lb>meccanico, il quale fu poi riferito dal Torricelli, in piè della proposizione XVIII <lb></lb>delle sue <emph type="italics"></emph>Quadrature della parabola.....<emph.end type="italics"></emph.end> Ma però questa medesima con­<lb></lb>clusione molto prima era nota al nostro Galileo, come apparisce da quel suo <lb></lb>teorema meccanico, nel trattato <emph type="italics"></emph>Delle resistenze,<emph.end type="italics"></emph.end> premesso come lemma al <lb></lb>problema che propone: <emph type="italics"></emph>Dato il peso massimo retto dal mezzo d&#039;un ci-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2240.jpg" pagenum="483"></pb><emph type="italics"></emph>lindro o prisma, dove la resistenza è minima, e dato un peso maggiore di <lb></lb>quello, trovare nel detto cilindro il punto, nel quale il dato peso maggiore <lb></lb>sia retto come peso massimo:<emph.end type="italics"></emph.end> dove manifestamente si riconosce tal quinta <lb></lb>conclusione, ed ancora il mezzo per dimostrarla ” (Firenze 1674, pag. </s>

<s>8, 9). </s></p><p type="main">

<s>Potrebb&#039;essere che il Viviani s&#039;inducesse a fare questi cenni storici del <lb></lb>Teorema meccanico dei momenti, per levare ogni vana presunzione dall&#039;animo <lb></lb>del Marchetti: non apparisce da nessuna parte del suo discorso però che fosse <lb></lb>propriamente questa la sua intenzìone, della quale nonostante si fa interpetre <lb></lb>il Grandi, per aver, nell&#039;offendere il comune nemico, un ausiliario così potente. </s>

<s><lb></lb>Il Marchetti, che sotto la pelle dell&#039;agnello, della quale s&#039;era coperto l&#039;Autore <lb></lb>della Quadratura del circolo, sapeva bene nascondersi l&#039;arti insidiose del lupo, <lb></lb>intese che Galileo, il Cavalieri e il Torricelli gli venivano proposti, per rinfac­<lb></lb>ciargli la temerità di essersi appropriata un&#039;invenzione, della quale si ricono­<lb></lb>scevano quelli per primi autori. </s>

<s>E perchè si sentiva, per solo avere ignorata la <lb></lb>storia, la coscienza franca intorno a ciò di ogni colpa volontaria, ne volle far <lb></lb>pubblica confessione in modo, che, se non in ogni incidente, nel merito prin­<lb></lb>cipale della causa però noi giudici imparziali abbiam dovuto riconoscerne l&#039;in­<lb></lb>nocenza. </s>

<s>Affinchè poi la promessa imparzialità del giudizio apparisca sincera, <lb></lb>e venga ad aver perciò sull&#039;animo e nella mente dei nostri Lettori maggiore <lb></lb>efficacia, vogliamo che le difese, prima di sentirle uscire dalla bocca dell&#039;im­<lb></lb>putato, resultino in favore a lui dal diligente esame dei fatti. </s></p><p type="main">

<s>E per cominciare da Galileo, la proposizione, nella quale da lui dice <lb></lb>il Viviani essere invocato il Teorema dei momenti, è la XII, così formulata: <lb></lb>“ Se nella lunghezza d&#039;un cilindro si noteranno due luoghì, sopra i quali <lb></lb>si voglia far la frazione di esso cilindro, le resistenze di detti due luoghi <lb></lb>hanno tra di loro la medesima proporzione, che i rettangoli fatti dalle di­<lb></lb>stanze di essi luoghi, contrariamente presi ” (Alb. </s>

<s>XIII, 135). </s></p><p type="main">

<s>Proponiàmoci la medesima <lb></lb>figura galileiana, per noi la 257, <lb></lb>nella quale A, B rappresentano i <lb></lb>minimi pesi atti a rompere il ci­<lb></lb>lindro AB in C, come E, F rap­<lb></lb>presentan pure i minimi pesi, per <lb></lb>rompere in D: abbiamo, per la <lb></lb>teoria della leva, A:B=BC:AC, <lb></lb>E:F=BD:AD, le quali due <lb></lb><figure id="id.020.01.2240.1.jpg" xlink:href="020/01/2240/1.jpg"></figure></s></p><p type="caption">

<s>Figura 257<lb></lb>equazioni danno per composizione ciascuna A+B:B=BA:AC; E+F:F= <lb></lb>BA:AD; d&#039;onde s&#039;ha, permutando, A+B:E+F=B/F:AC/AD. </s>

<s>Ma per le <lb></lb>supposte cose, e per ragione del Vette “ come la forza B alla F, così, <lb></lb>dice Galileo, sta reciprocamente la linea DB alla BC ” (ivi) e perciò, sosti­<lb></lb>tuendo nell&#039;ultima B/F il suo uguale DB/BC, si viene alla proposta conclusione <lb></lb>A+B:E+F=BD.AD:AC.BC. </s></p><pb xlink:href="020/01/2241.jpg" pagenum="484"></pb><p type="main">

<s>Diceva il Viviani, come dianzi udimmo, che in questo processo dimo­<lb></lb>strativo di Galileo si riconosce la conclusion dei momenti, <emph type="italics"></emph>ed ancora il mezzo <lb></lb>di dimostrarla.<emph.end type="italics"></emph.end> E infatti, se per momento s&#039;intende, com&#039;esso Galileo nella <lb></lb><emph type="italics"></emph>Scienza meccanica<emph.end type="italics"></emph.end> insegna, <emph type="italics"></emph>quell&#039;impeto di andare al basso composto di <lb></lb>gravità e di posizione<emph.end type="italics"></emph.end> (Alb. </s>

<s>XI, 90), i prodotti B.BC, F.BD rappresen­<lb></lb>tano due momenti Mo.B, Mo.F uguali, perchè i due pesi B, F, operando colle <lb></lb>distanze BC, BD, s&#039;è supposto che producano effetti uguali. </s>

<s>Abbiamo dunque <lb></lb>Mo.B:Mo.F=B.BC:F.BD; equazione, che tiene in sè scritta la scoperta <lb></lb>del Marchetti dei momenti proporzionali ai prodotti delle distanze e dei pesi. </s></p><p type="main">

<s>Ma poteva il Marchetti rispondere che in Galileo si riconosce il Teo­<lb></lb>rema ne&#039;suoi principii, non però nella forma della conclusione, in dar la <lb></lb>qual forma poteva tuttavia compiacersi l&#039;Autor <emph type="italics"></emph>De resistentia solidorum<emph.end type="italics"></emph.end> di <lb></lb>essere stato il primo. </s>

<s>Or che avrebbero mai detto e fatto il Grandi e il Vi­<lb></lb>viani, se avessero saputo che Galileo, anche in mettere in espressa forma <lb></lb>la conclusione aveva prevenuto e superato il Marchetti? </s>

<s>Nessuno par che <lb></lb>fin qui abbia avuto notizia dei pochi rimasti fra que&#039;fogli, dove il Salviati <lb></lb>diceva di aver per ordine notati i teoremi e problemi attenenti alle Resi­<lb></lb>stenze, e colui stesso, che gli raccolse nel Volume in cui noi gli abbiamo <lb></lb>trovati, mettendo innanzi il foglietto che doveva venir dopo, poneva e sè, e <lb></lb>chiunque avesse superficialmente svolte le dotte carte in grande difficoltà di <lb></lb>ricavarne il costrutto. </s>

<s>È tempo perciò che diamo ai nostri Lettori la già <lb></lb>promessa sodisfazione, negata al Viviani, al Grandi e ai tanti altri Galile­<lb></lb>iani sviscerati, trascrivendo dall&#039;autografo il Teorema famoso così formulato: </s></p><p type="main">

<s><emph type="italics"></emph>“ Ponderum, in Libra suspensorum, momenta habent rationem com­<lb></lb>positam ex ratione ipsorum ponde­<lb></lb>rum, et ex ratione distantiarum.<emph.end type="italics"></emph.end> — <lb></lb>Pendeant pondera DE et F (fig. </s>

<s>258) <lb></lb>ex dìstantiis AB, BC: dico momen­<lb></lb>tum ponderis DE, ad momentum pon­<lb></lb>deris F, habere rationem compositam <lb></lb>ex rationibus ponderis DE ad pen­<lb></lb><figure id="id.020.01.2241.1.jpg" xlink:href="020/01/2241/1.jpg"></figure></s></p><p type="caption">

<s>Figura 258<lb></lb>dus F, et distantiae AB, ad distantiam BC ” (MSS. Gal., P. V, T. II, fol. </s>

<s>40). </s></p><p type="main">

<s>La dimostrazione muove da due principii: il primo dei quali è quello, <lb></lb>che il Viviani riconobbe nella XII proposizione del II dialogo delle Scienze <lb></lb>nuove, dichiarata da noi più sopra, e l&#039;altro, che immediatamente deriva <lb></lb>dalle proprietà del Vette, gli effetti del quale son proporzionali alle forze ap­<lb></lb>plicate nelle medesime, o in eguali distanze. </s>

<s>Presa perciò del maggior peso <lb></lb>DE tanta parte DO, che, avendosi per l&#039;uno dei proposti principii F:OD= <lb></lb>AB:BC, il momento di F sia uguale a quello di DO, avendosi per l&#039;altro <lb></lb>dei premessi principii M.oOD:M.oDE=OD:DE; se si ponga in questa <lb></lb>equazione M.oOD=M.oF, e OD=F.BC/AB, si giunge alla conclusione <lb></lb>M.oF:M.oDE=F.BC:DE.AB, alla quale pure giunge Galileo, mettendo <lb></lb>in quest&#039;altra forma il suo discorso: </s></p><pb xlink:href="020/01/2242.jpg" pagenum="485"></pb><p type="main">

<s>“ Ut enim AB ad BC, ita fiat pondus F ad pondus DO: cum ergo pon­<lb></lb>dera F et DO habeant rationem distantiarum AB, BC permutatam, erit mo­<lb></lb>mentum ponderis F aequale momento ponderis DE. </s>

<s>Cum igitur sint tria <lb></lb>pondera utcumque ED, F et DO, erit ratio ponderis ED ad DO composita <lb></lb>ex ratione ED ad F, et F ad DO. ” </s></p><p type="main">

<s>“ Ut autem pondus ED ad pondus DO, ita momentum ED ad momen­<lb></lb>tum DO: pendent enim ex eodem puncto. </s>

<s>Igitur, cum momentum DO sit <lb></lb>aequale momento F, ratio momenti ED, ad momentum F, erit composita <lb></lb>ex ratione ponderis ED, ad pondus F, et ponderis F ad pondus DO. ” </s></p><p type="main">

<s>“ Factum est autem pondus F, ad pondus DO, ut distantia AB ad distan­<lb></lb>tiam BC; ergo patet momentum ponderis ED, ad momentum ponderis F <lb></lb>habere rationem compositam ex rationibus ponderum ED, F, et distantiarum <lb></lb>AB, BC ” (ibid.). </s></p><p type="main">

<s>Seguita un corollario, che serve per lemma a un&#039;altra proposizione, nel­<lb></lb>l&#039;intender la quale s&#039;aggiungerà nei nostri Lettori, alla maraviglia dell&#039;aver <lb></lb>Galileo lasciata indietro quella prima proposizione importante, la maraviglia <lb></lb>dell&#039;averne anche insieme lasciata una seconda, per sè, e per le sue appli­<lb></lb>cazioni al trattato delle resistenze, assai bella. </s></p><p type="main">

<s>“ Quod si suspendatur, così dice quel corollario, ex puncto S (nella <lb></lb>medesima fig. </s>

<s>258), facta distantia BS aequali distantiae BC, pondus T ae­<lb></lb>quale ponderi F, erit eius momentum momento F aequale, et similiter pon­<lb></lb>derum ED et T momenta habebunt rationem compositam ex ponderibus <lb></lb>ED, T, et ex distantiis AB, BS. ” </s></p><p type="main">

<s>“ Sit modo cylindrus EGT (fig. </s>

<s>259), respondens Librae ABCD, utcum­<lb></lb><figure id="id.020.01.2242.1.jpg" xlink:href="020/01/2242/1.jpg"></figure></s></p><p type="caption">

<s>Figura 259<lb></lb>que sectum in SG: dico momentum <lb></lb>totius cylindri pendentis ex C, ad mo­<lb></lb>mentum frusti EG pendentis ex B, <lb></lb>esse ut rectangulus DCA, ad rectan­<lb></lb>gulum DBA. ” </s></p><p type="main">

<s>“ Ex demonstratis enim momen­<lb></lb>tum ponderis EGT, ad momentum pon­<lb></lb>deris EG, habet rationem compositam ex pondere EGT ad pondus EG, et <lb></lb>distantiae CD ad distantiam DB. </s>

<s>Pondus autem EGT, ad pondus EG, est <lb></lb>ut linea AC ad AB; ergo momentum ponderis EGT, ad momentum ponde­<lb></lb>ris GE, habet rationem compositam ex CD ad DB, et ex CA ad AB, quae <lb></lb>est rectanguli DCA, ad rectangulum DBA ” (ibid.). </s></p><p type="main">

<s>Rimaste queste cose ne&#039;Manoscritti sconosciute, non si poteva a tutto <lb></lb>diritto negare al Marchetti il vanto di aver egli il primo esplicato, e pre­<lb></lb>messo in form̀a al suo libro Delle resistenze il Teorema meccanico dei mo­<lb></lb>menti: cosicchè o cessa, o viene ad essere infirmata quell&#039;accusa di pla­<lb></lb>gio, mossagli incontro dal Viviani e dal Grandi, per quello che s&#039;appartiene <lb></lb>a Galileo. </s></p><p type="main">

<s>Quanto poi al Torricelli, è verissimo che, alla proposizione XVIII del <lb></lb>secondo libro Delle quadrature della parabola, soggiungeva il Lemma, in cui <pb xlink:href="020/01/2243.jpg" pagenum="486"></pb>il Rocca servivasi per dimostrarlo di questo principio: che cioè, se sia data <lb></lb>una linea retta ponderosa sostenuta in un punto, che la divida in due parti, <lb></lb>il momento dell&#039;una al momento dell&#039;altra “ habebit rationem compositam <lb></lb>ex ratione magnitudinum, et ex ratione distantiarum ” (Opera geom., P. II <lb></lb>cit., pag. </s>

<s>77): ma nè dall&#039;uno, nè dall&#039;altro Autore però si dimostrava per­<lb></lb>chè dovesse aversi quella detta ragione. </s>

<s>Anzi lo stesso Torricelli aveva dato <lb></lb>al Marchetti, e a Giuseppe Vanni suo discepolo, come altrove accennammo, <lb></lb>occasione di esser ripreso intorno alla seconda proposizione <emph type="italics"></emph>De motu gra­<lb></lb>vium,<emph.end type="italics"></emph.end> nella quale si pronunzia che il momento del grave scendente per <lb></lb>l&#039;un piano inclinato sta al momento del discendente per l&#039;altro, <emph type="italics"></emph>ut moles <lb></lb>ad molem<emph.end type="italics"></emph.end> (ibid., P. I, pag. </s>

<s>100), mentre la ragion vera di essi momenti è <lb></lb>composta dei pesi assoluti, e delle distanze. </s></p><p type="main">

<s>Benchè quella seconda torricelliana proposizione sia vera, e si possano <lb></lb>in qualche modo salvare i principii di mezzo, ivi invocati per dimostrarla, <lb></lb>è però un fatto notabilissimo che il Torricelli, in due teoremi lasciatici ma­<lb></lb>noscritti, mostrò di esser davvero scorso in quegli errori, pubblicamente <lb></lb>notati nella meccanica Esercitazione del Vanni. </s></p><p type="main">

<s>È il primo dei due detti Teoremi proposto dall&#039;Autore in questa forma: <lb></lb>“ Se due pesi di diversa gravità in specie, ma di mole eguali, saranno po­<lb></lb>sti a distanze disuguali dal centro, il peso assoluto del primo, al peso as­<lb></lb>soluto del secondo, averà la proporzione composta della proporzione, che ha <lb></lb>la gravità in specie del primo alla gravità in specie del secondo, e della <lb></lb>proporzione, che ha la distanza del primo alla distanza del secondo dal <lb></lb>centro. </s>

<s>” </s></p><p type="main">

<s>“ Siano i due pesi <emph type="italics"></emph>ut ponitur<emph.end type="italics"></emph.end> L, O (fig. </s>

<s>260) il centro C, e le distanze <lb></lb>disuguali OC, CL. Facciasi, come la gravità del primo O, alla gravità del <lb></lb><figure id="id.020.01.2243.1.jpg" xlink:href="020/01/2243/1.jpg"></figure></s></p><p type="caption">

<s>Figura 260<lb></lb>secondo L; così la linea A <lb></lb>alla B; e, come la distanza <lb></lb>del primo, alla distanza del <lb></lb>secondo, così la linea B alla <lb></lb>D: dico che il peso asso­<lb></lb>luto di O, all&#039;assoluto di L, <lb></lb>è come la linea A alla D. ” (MSS. Gal. </s>

<s>Disc., T. XXXVII, fol. </s>

<s>77). </s></p><p type="main">

<s>Per rendere, in poche parole e più chiara, la dimostrazion dell&#039;Autore, <lb></lb>chiaminsi G.O, G.L le gravità dei due pesi, e D.O, D.L le loro distanze: <lb></lb>abbiamo, secondo il supposto, G.O:G.L=A:B; D.O:D.L=B:D. </s>

<s><lb></lb>Moltiplicando termine per termine fra loro queste due proporzioni, o poi eli­<lb></lb>minando la quantità B dalla seconda ragione, se ne conclude immediata­<lb></lb>mente G.OXD.O:G.LXD.L=A:D. </s></p><p type="main">

<s>Ora, è di qui manifesto che, essendo per la fatta supposizione le moli, <lb></lb>ossia i volumi uguali, questa prima scritta ragione rappresenta la composi­<lb></lb>zion dei momenti, e son perciò essi momenti che stanno come A a D, e <lb></lb>non i pesi assoluti, come diceva il Torricelli. </s></p><p type="main">

<s>L&#039;errore, incredibile in tanto Uomo e in tanto facile argomento, fu no-<pb xlink:href="020/01/2244.jpg" pagenum="487"></pb>tato già dal Viviani, quando, nel raccogliere anche queste fra le altre tor­<lb></lb>ricelliane proposizioni, rimaste senz&#039;ordine e senza forma nei manoscritti; <lb></lb>la metteva per la X nel trattato, ch&#039;egli aveva preso a compilare <emph type="italics"></emph>De molu <lb></lb>ac momentis,<emph.end type="italics"></emph.end> avvertendo ch&#039;era stata da lui “ fatta latina, e corretta col <lb></lb>mutare per tutto le parole <emph type="italics"></emph>peso assoluto,<emph.end type="italics"></emph.end> dicendo <emph type="italics"></emph>momento,<emph.end type="italics"></emph.end> ed aggiungendo <lb></lb>alla parola <emph type="italics"></emph>gravità<emph.end type="italics"></emph.end> sempre <emph type="italics"></emph>in specie,<emph.end type="italics"></emph.end> perchè, se in luogo di momento dicesse <lb></lb>peso assoluto, ed in luogo di gravità in specie dicesse solamente gravità, tutta <lb></lb>la proposizione e dimostrazione è falsa ” (ivi, fol. </s>

<s>95). Onde a renderla vera <lb></lb>il Viviani stesso intendeva così di proporla: “ Si duo pondera diversae gra­<lb></lb>vitatis in specie, sed aequalium molium, appensa fuerint in aequalibus a <lb></lb>centro distantiis, momentum primi ponderis, ad momentum secundi, habe­<lb></lb>bit rationem compositam ex ratione gravitatis in specie primi, ad gravita­<lb></lb>tem in specie secundi, et ex proportione distantiae primi, ad distantiam se­<lb></lb>cundi ” (ivi). </s></p><p type="main">

<s>L&#039;altro Teorema, soggiunto nel manoscritto del Torricelli a dimostrare <lb></lb>la ragion dei momenti, da qualunque distanza pendano i gravi, e qualun­<lb></lb>que sia la loro gravità specifica, e il loro volume; vien proposto dall&#039;Autore <lb></lb>in questa forma: “ Se saranno due solidi di gravità diversa in specie, di <lb></lb>mole disuguali, posti in distanze disuguali dal centro, e se si farà come la <lb></lb>gravità del primo, alla gravità del secondo, così l&#039;A al B, e come la mole <lb></lb>del primo, alla mole del secondo, così B al C, e come la distanza del primo, <lb></lb>alla distanza del secondo, così C al D; averà il peso assoluto del primo, al <lb></lb>peso assoluto del secondo, la proporzione che ha l&#039;A al D. ” </s></p><p type="main">

<s>“ Sia il primo A, il secondo B, il centro C; e siano le linee D, E, F, G, <lb></lb>come si suppone: dico che il peso assoluto di A, al peso assoluto di B, è <lb></lb>come D a G ” (ivi, fol. </s>

<s>77). </s></p><p type="main">

<s>È facile scoprire anche in questo un errore simile a quello scoperto <lb></lb>nel Teorema precedente, imperocchè, chiamate G.A, V.A, D.A; G.B, <lb></lb>V.B, D.B, le gravità in specie, le moli o i volumi e le distanze di A e <lb></lb>di B, si hanno le tre equazioni G.A:G.B=D:E; V.A:V.B=E:F; <lb></lb>D.A:D.B=F:G, le quali moltiplicate insieme, ed eliminato il comun <lb></lb>prodotto EXF nella seconda ragione, concludono G.AXV.AXD.A: <lb></lb>G.BXV.BXD.B=D:G. Ora, perchè G.AXV.A, G.BXV.B <lb></lb>sono uguali ai pesi assoluti di A e di B, è manifesta la falsità della propo­<lb></lb>sta torricelliana, e come essi pesi assoluti, non semplicemente, ma molti­<lb></lb>plicati per le distanze, ossia i loro momenti, abbiano come D a G le loro <lb></lb>ragioni. </s></p><p type="main">

<s>Il Viviani perciò, che raccolse anche questa seconda proposizione, per <lb></lb>metterla in ordine la XI nel trattato torricelliano <emph type="italics"></emph>De motu ac momentis,<emph.end type="italics"></emph.end><lb></lb>notava in margine al suo manoscritto di averla “ fatta latina, corretta come <lb></lb>la passata, perchè era falsa al modo scritto dall&#039;Autore ” (ivi, fol. </s>

<s>96), onde <lb></lb>egli avrebbe voluto renderla alla verità, pronunziandola in quest&#039;altra ma­<lb></lb>niera: “ Si fuerint duo solida A, B, diversae gravitatis in specie et inae­<lb></lb>qualium molium, ex inaequalibus a centro C distantiis appensa, et fiat ut <pb xlink:href="020/01/2245.jpg" pagenum="488"></pb>gravitas specifica primi A, ad specificam secundi B, ita linea D ad E, et, ut <lb></lb>distantia primi ad distantiam secundi, ita E ad F, et, ut moles primi A, ad <lb></lb>molem secundi B, ita F ad G; erit momentum primi, ad momentum se­<lb></lb>cundi, ut D ad G ” (ivi). </s></p><p type="main">

<s>Insufficientemente dunque il Rocca, e male a proposito il Torricelli si <lb></lb>citavano quali premostratori del Teorema dei momenti, cosicchè non restava <lb></lb>altro che il Cavalieri a dar valore all&#039;argomento del Grandi. </s>

<s>Nella V Eser­<lb></lb>citazione geometrica si può dir che veramente apparisca, così, nella sua più <lb></lb>espressa e più ordinata forma, il Teorema, che dovea levar tanto romore: <lb></lb>“ Quorumcumque gravium, a quibus libet distantiis suspensorum, momenta <lb></lb>sunt in ratione composita ex ratione distantiarum, et gravitatum ” (Bono­<lb></lb>niae 1647, pag. </s>

<s>336). L&#039;Autore premette, a dimostrar questa, due altre pro­<lb></lb>posizioni, la prima delle quali facilmente conclude, dalle proprietà del Vette, <lb></lb>ch&#039;essendo uguali le distanze, i momenti son proporzionali ai pesi; e la se­<lb></lb>conda, ch&#039;essendo uguali i pesi, i momenti son proporzionali alle distanze. </s></p><p type="main">

<s>Ciò premesso, abbiansi, dice il Cavalieri, due pesi E, D (fig. </s>

<s>261) ap­<lb></lb>plicati nelle estremità della Libbra CB, sostenuta in A. </s>

<s>Prendasi un terzo <lb></lb><figure id="id.020.01.2245.1.jpg" xlink:href="020/01/2245/1.jpg"></figure></s></p><p type="caption">

<s>Figura 261<lb></lb>peso F, uguale ad E, e si sospenda <lb></lb>in G, a una distanza AG uguale ad AB: <lb></lb>avremo per la prima M.oF:M.oD= <lb></lb>F:D, e per la seconda, M.oE:M.oF= <lb></lb>AC:AG. </s>

<s>Moltiplicate queste due equa­<lb></lb>zioni, eliminato M.oF da ciascun ter­<lb></lb>mine della prima ragione, e ad AG <lb></lb>sostituito AB, ad F, E; si giunge in ultimo ad avere M.oE:M.oD= <lb></lb>CA.E:AB.D, nella quale concludesi l&#039;intenzione del Cavalieri, da lui stesso <lb></lb>così espressa: “ Momentum E, ad momentum D, est in ratione composita ex <lb></lb>ratione CA ad AB, et ex ratione gravitatis E, ad gravitatem D ” (ibid.). </s></p><p type="main">

<s>Rispose il Marchetti, in sentirsi indicare questa dimostrazione, pubbli­<lb></lb>cata da un Matematico tanto celebre ventidue anni prima della sua, che il <lb></lb>metodo però era diverso, e che non aveva allora veduto il libro del Cava­<lb></lb>lieri (Lettera cit., pag. </s>

<s>20). Il Grandi gli rinfacciò ch&#039;ei l&#039;aveva <emph type="italics"></emph>esistente <lb></lb>nella sua libreria<emph.end type="italics"></emph.end> (Risposta cit., pag. </s>

<s>31), nè valse il rispondere che non <lb></lb>tutti si leggono i libri, che s&#039;hanno per i palchetti, perch&#039;esso Grandi ne­<lb></lb>gasse fede a quelle buone ragioni. </s></p><p type="main">

<s>Ora, il nostro giudizio è alquanto diverso, e, se il Marchetti confessò <lb></lb>ingenuamente di non aver lette le Esercitazioni geometriche, crediamo di­<lb></lb>cesse la verità, confortata dall&#039;esempio di certi altri fatti, ricorsi indietro <lb></lb>in questa nostra Storia. </s>

<s>Si rammemoreranno i Lettori di ciò, che dicemmo <lb></lb>nel II capitolo baricentrico, a proposito del teorema del Guldino, rimasto <lb></lb>ignoto al Borelli e al Viviani, benchè avesse fatta pubblica e sì battagliera <lb></lb>comparsa nella III Esercitazione del Cavalieri. </s>

<s>Com&#039;è dunque certo che il <lb></lb>Borelli e il Viviani non avevano letto il libro nel 1656; così può credersi <lb></lb>che non l&#039;avesse letto il Marchetti, seguitando l&#039;esempio de&#039;suoi maggiori, <pb xlink:href="020/01/2246.jpg" pagenum="489"></pb>i quali, male insinuati da Galileo, non facevano troppo buon viso all&#039;Au­<lb></lb>tore della Geometria degl&#039;indivisibili. </s></p><p type="main">

<s>Comunque sia, venivano i fatti a decidere la controversia del primato, <lb></lb>e perciò il Marchetti, il quale sentivasi forse, meglio che dal suo Avversa­<lb></lb>rio, rimproverare dalla propria coscienza la vanagloria dell&#039;aver descritta in­<lb></lb>nanzi al suo libro la mirabile invenzione occorsagli del meccanico Teorema; <lb></lb>si volse a dire “ che non del detto Teorema, per sè medesimo considerato <lb></lb>feci io gran caso, nè della sua invenzione e dimostrazione sperai gran lode, <lb></lb>ma bensì dell&#039;avere io avvertito quanto egli a maraviglia giovar potevami <lb></lb>a dimostrar brevemente e facilmente, non solo tante mie nuove proposizioni <lb></lb>intorno alla resistenza dei corpi duri, ma eziandio quelle stesse, le quali con <lb></lb>altro mezzo, e con assai maggior lunghezza e difficoltà, aveva già dimostrate <lb></lb>il gran Galileo ” (Lettera cit., pag. </s>

<s>22). </s></p><p type="main">

<s>Il Grandi, che, a confettar d&#039;aloe sulla lingua del suo avversario anche <lb></lb>quest&#039;ultima compiacenza, non aveva materia, e di quella che poteva avere <lb></lb>non seppe far uso, contrappose insipide ragioni, riducendosi, per confrontar <lb></lb>la lunghezza e la brevità, infino a contar le linee spese nelle dimostrazioni <lb></lb>dai due Autori. </s>

<s>Che se avesse ricercato, o si fosse saputo prevalere degli argo­<lb></lb>menti, avrebbe potuto provar contro il Marchetti che, anche prima di lui, il <lb></lb>Torricelli e il Viviani, e anzi il medesimo Galileo, in certi fogli smarriti, ave­<lb></lb>vano promossa la nuova Scienza istituita nel II dialogo delle Scienze nuove, <lb></lb>applicandovi il Teorema dei momenti. </s>

<s>Noi, per render di così belle, e così im­<lb></lb>portanti notizie rifiorita la nostra Storia, faremo quello che avrebbe dovuto fare <lb></lb>lo stesso Grandi, incominciando dal riferire un Teorema sconosciuto al pub­<lb></lb>blico, dove il Torricelli promoveva le dottrine della proposizione XII galileiana. </s></p><p type="main">

<s>È questa proposizione, come <lb></lb>altre volte s&#039;è detto, il fonda­<lb></lb>mento alla parte seconda del Trat­<lb></lb>tato, che è delle resistenze dei so­<lb></lb>lidi, appoggiati nelle loro estremità <lb></lb>a due sostegni: e benchè nella <lb></lb>figura, che nella nostra 262 ri­<lb></lb>torna sott&#039;occhio, e nella dichia­<lb></lb>razione di Galileo non apparisca <lb></lb><figure id="id.020.01.2246.1.jpg" xlink:href="020/01/2246/1.jpg"></figure></s></p><p type="caption">

<s>Figura 262<lb></lb>tale, è pur assai facile ridurvela, essendo manifesto che rimangono le proposte <lb></lb>condizioni inalterate, mettendo in A, B i sostegni, e facendo da D, C pendere <lb></lb>due pesi uguali alla somma di A, B, e di E, F. </s>

<s>Intese la detta proposi­<lb></lb>zione XII così trasformata il Torri­<lb></lb>celli, quando scrisse: “ Il Galileo mo­<lb></lb>stra che preso il punto A (fig. </s>

<s>263) <lb></lb>nel mezzo, ed il B nò nel mezzo, la <lb></lb>resistenza in A, alla resistenza in B, <lb></lb>sia come reciprocamente il rettan­<lb></lb>golo CBD al rettangolo CAD. ” <lb></lb><figure id="id.020.01.2246.2.jpg" xlink:href="020/01/2246/2.jpg"></figure></s></p><p type="caption">

<s>Figura 263</s></p><pb xlink:href="020/01/2247.jpg" pagenum="490"></pb><p type="main">

<s>“ E stante questo, immediatamente soggiunge, sia attaccato in A il peso <lb></lb>F, e sia tale che basti per romper l&#039;asta, cioè sia uguale alla resistenza, che <lb></lb>essa ha in A. </s>

<s>Sia poi un altro peso H, uguale all&#039;F, ma attaccato in B: dico <lb></lb>che il momento del peso F, al momento di H, sta come il rettangolo CAD <lb></lb>al rettangolo CBD. ” </s></p><p type="main">

<s>“ Intendasi il peso E tale, che sia uguale alla resistenza dell&#039;asta in B: <lb></lb>perciocchè per momento qui intendiamo la proporzione, che ha l&#039;attività o <lb></lb>forza del peso attaccato verso la resistenza dell&#039;asta; averanno dunque li <lb></lb>pesi E ed F, ne&#039;siti loro, egual momento e virtù verso l&#039;asta. </s>

<s>” </s></p><p type="main">

<s>“ Ora, perchè E ed H sono nello stesso sito, sarà il momento E, al <lb></lb>momento H, come la mole E alla mole H; cioè la mole E alla mole F; <lb></lb>cioè la resistenza di B alla resistenza di A; cioè il rettangolo, per Galileo, <lb></lb>CAD al rettangolo GBD. È dunque vero che il momento E, cioè il mo­<lb></lb>mento F uguale, ha la medesima proporzione al momento H, che ha il ret­<lb></lb>tangolo CAD al rettangolo CBD. ” </s></p><p type="main">

<s>“ Intendansi ora due altri pesi uguali fra loro I ed L (fig. </s>

<s>264), e si <lb></lb>attacchino dai punti A, B. È chiaro che il momento F, al momento I, per <lb></lb><figure id="id.020.01.2247.1.jpg" xlink:href="020/01/2247/1.jpg"></figure></s></p><p type="caption">

<s>Figura 264<lb></lb>essere nel medesimo sito, sta come <lb></lb>la mole alla mole, ossia, come il mo­<lb></lb>mento H al momento L. Adunque, <lb></lb>permutando, come il momento F al <lb></lb>momento H, così il momento I al mo­<lb></lb>mento L. <emph type="italics"></emph>Vel sic melius:<emph.end type="italics"></emph.end> momen­<lb></lb>tum I ad F est ut moles ad molem. </s>

<s><lb></lb>Ergo, permutando, momentum I, ad <lb></lb>momentum L, ut momentum F ad <lb></lb>H; nempe ut rectangulus CAD ad rectangulum CBD. ” (MSS. Gal. </s>

<s>Disc, <lb></lb>T. XXXVII, fol. </s>

<s>65). </s></p><p type="main">

<s>Veniva così dunque il Torricelli ad arricchire la Scienza galileiana delle <lb></lb>resistenze di un altro bel Teorema, cioè che i momenti dei pesi uguali, pre­<lb></lb>menti un&#039;asta sostenuta agli estremi in varii punti della sua lunghezza, son <lb></lb>direttamente proporzionali ai rettangoli descritti con le distanze dai due so­<lb></lb>stegni. </s>

<s>Comunicò, come tutte le altre speculazioni, anche questa al suo gio­<lb></lb>vane amico e discepolo in Roma Michelangiolo Ricci, il quale,, eccitato così <lb></lb>dagli esempii del Maestro a speculare su quel medesimo argomento offertogli <lb></lb>dalla proposizione XII di Galileo, s&#039;accorse che il problema proposto nella <lb></lb>seguente XIII, e per risolvere il quale Galileo stesso era ricorso al semicer­<lb></lb>chio, si scioglieva con mirabile facilità e speditezza, applicandovi invece la <lb></lb>parabola, notissima proprietà della quale è che le linee condotte parallele al <lb></lb>diametro segan la base in modo, da riuscir tutte e sempre proporzionali <lb></lb>ai rettangoli costruiti sulle sezioni. </s></p><p type="main">

<s>A dimostrar perciò al Torricelli che non infruttuose erano riuscite le <lb></lb>sue premure, e non inefficaci gli esempii, così scrivevagli il dì 18 Luglio 1643, <lb></lb>lo stesso Ricci, in una lettera da Roma: “ E poichè vedo che V. S. è così <pb xlink:href="020/01/2248.jpg" pagenum="491"></pb>proprizio al mio profitto, non voglia gravarsi di leggere la infrascritta di­<lb></lb>mostrazione, la quale, quando mi venga approvata da V. S., mi renderò si­<lb></lb>curo, non solo della bontà della dimostrazione, ma assieme d&#039;aver ben capita <lb></lb>la materia delle resistenze del Galileo, intorno alla quale versa. </s>

<s>” </s></p><p type="main">

<s>“ Sia dato il prisma o cilindro AB (fig. </s>

<s>265), nel quale, preso ad arbi­<lb></lb><figure id="id.020.01.2248.1.jpg" xlink:href="020/01/2248/1.jpg"></figure></s></p><p type="caption">

<s>Figura 265<lb></lb>trio il punto E, sia quivi sostenuto il peso L <lb></lb>come peso massimo. </s>

<s>Dato poi un altro peso G, <lb></lb>si cerca di trovare nel prisma AB il luogo, <lb></lb>dove il peso G sia retto come peso massimo. </s>

<s>” </s></p><p type="main">

<s>“ Sulla lunghezza AB s&#039;intenda descritta <lb></lb>la parabola ADB, il cui diametro DC, e ad esso <lb></lb>sia parallela la FE. </s>

<s>Si faccia, come il peso G <lb></lb>al peso L, così la retta EF alla parte HC del <lb></lb>diametro DC, e dal punto H si tiri la HI pa­<lb></lb>rallela alla BA, e dal punto I la KI parallela <lb></lb>al diametro DC: dico il punto K essere il punto <lb></lb>cercato, perchè il peso G al peso L si è fatto <lb></lb>come la FE alla HC, ovvero KI, cioè, come il <lb></lb>rettangolo BEA al rettangolo AKB; cioè, come <lb></lb>la resistenza in K, alla resistenza in E. Dunque, permutando, il peso G, <lb></lb>alla resistenza in K, ha la proporzione del peso L alla resistenza in E, che <lb></lb>sono uguali per il supposto, e però il peso G sarà sostenuto in K come peso <lb></lb>massimo. </s>

<s>Il che ecc. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>11, 12). </s></p><p type="main">

<s>Il Torricelli, non solo approvò la proposizione del Ricci, ma ebbe a <lb></lb>ringraziarlo come colui, ch&#039;era venuto con quella sua parabola a rivelargli <lb></lb>un&#039;altra cosa bellissima, da mettersi per corollario al Teorema dianzi rife­<lb></lb>rito, cioè che i momenti dei pesi uguali prementi l&#039;asta, o, come il Viviani <lb></lb>incominciò a dire, la <emph type="italics"></emph>Scala<emph.end type="italics"></emph.end> di essi momenti è in una parabola, che insiste <lb></lb><figure id="id.020.01.2248.2.jpg" xlink:href="020/01/2248/2.jpg"></figure></s></p><p type="caption">

<s>Figura 266<lb></lb>come su base sulla lunghezza stessa dell&#039;asta. </s>

<s>Gli <lb></lb>passò di qui l&#039;agile pensiero a quell&#039;altra para­<lb></lb>bola, che Galileo diceva esser descritta da una ca­<lb></lb>tena che faccia saccaia, e si compiacque di aver <lb></lb>avuto a ritrovare in quel suo Teorema, e nel co­<lb></lb>rollario suggeritogli dal Ricci, la dimostrazione <lb></lb>desiderata. </s></p><p type="main">

<s>Sia la catena ACB (fig. </s>

<s>266): pensò il Tor­<lb></lb>ricelli che ciascuno anello di lei, come per esem­<lb></lb>pio E, F, fossero ivi scesi, trasportativi dai punti <lb></lb>G, H con forze, misurate dai pesi di essi anelli <lb></lb>moltiplicati per le velocità GE, HF: cosicchè, chiamate F, F′ cotali forze, <lb></lb>e P il peso, in ciascuno degli anelli uguale, fosse F=P.GE, F′=P.HF, <lb></lb>ossia F:F′=GE:HF. </s>

<s>Ma perchè sono queste forze evidentemente uguali <lb></lb>ai momenti, ch&#039;eserciterebbero gli stessi anelli, se si considerassero come in­<lb></lb>filati nella linea AB; e stanno, per il dimostrato Teorema, essi momenti come <pb xlink:href="020/01/2249.jpg" pagenum="492"></pb>i rettangoli AGB, AHB; dunque F:F′=AGB:AHB, e perciò AGB:AHB= <lb></lb>GE:HF. </s>

<s>Dunque la linea curva AECFB, in che disponesi la catena, è ve­<lb></lb>ramente, come Galileo diceva, una parabola. </s>

<s>Tale è l&#039;esplicato discorso, che <lb></lb>si condensa dal Torricelli in questa sua Nota: “ Funis, seu catenula ACB <lb></lb>pendens, parabolam format, quia unaquaeque portio pendens descendit pro <lb></lb>ratione sui momenti ” (MSS. Gal. </s>

<s>Disc., T. XXXVII, fol. </s>

<s>81). </s></p><p type="main">

<s>Rimaste queste speculazioni lungo tempo sepolte nella cassetta, dove <lb></lb>gelosamente si deposero i manoscritti del Torricelli, il Viviani, a cui non <lb></lb>era stato consegnato ancora il deposito prezioso, era per sè medesimo (non <lb></lb>punto meno studioso de&#039;dialoghi di Galileo, di quel che si fossero il Tor­<lb></lb>ricelli stesso e il Ricci) entrato in quel medesimo filo di speculazioni, e, cre­<lb></lb>dendosi di essere stato il primo, era per altre vie riuscito a dimostrare i <lb></lb>medesimi teoremi. </s>

<s>Scrisse perciò in fronte a una sua carta questo titolo: <lb></lb><emph type="italics"></emph>Theorema a nullo, quod sciam, demonstratum comprehendens illud quo­<lb></lb>que, quod ostenditur a Galileo, ad fac. </s>

<s>136, secundi dialogi De resisten­<lb></lb>tia corporum solidorum<emph.end type="italics"></emph.end> (MSS, Gal., T. CXVII, fol. </s>

<s>22). Il Teorema poi è <lb></lb>così formulato: </s></p><p type="main">

<s>“ Sia il peso D (fig. </s>

<s>267) appeso al mezzo C della leva AB, sostenuta <lb></lb>negli estremi A, B, ed egual peso E penda dal punto F, fuori del mezzo di AB: <lb></lb><figure id="id.020.01.2249.1.jpg" xlink:href="020/01/2249/1.jpg"></figure></s></p><p type="caption">

<s>Figura 267<lb></lb>dico che il momento di <lb></lb>D in C, al momento di <lb></lb>E in F, sta omologa­<lb></lb>mente come il rettan­<lb></lb>golo ACB al retrangolo <lb></lb>AFB ” (ivi). La dimo­<lb></lb>strazione è molto ela­<lb></lb>borata, coll&#039;intenzione <lb></lb>di renderla comprensiva <lb></lb>della XII di Galileo, della <lb></lb>quale vedemmo come il Torricelli invece avesse fatta la sua un semplice <lb></lb>corollario. </s></p><p type="main">

<s>“ Prolunghisi, prosegue il Viviani, tal linea AB dall&#039;una e dall&#039;altra <lb></lb>parte, cosicchè AG, BH siano uguali fra loro ed alle metà AC, CB, ed in <lb></lb>H penda I metà del peso D, ed in G penda il peso L metà del medesimo <lb></lb>peso D, che il momento di D in C sarà ugual momento de&#039;due L, I posti <lb></lb>in G, H. </s>

<s>Si faccia poi come FA ad AG, così L ad M, che il momento di <lb></lb>M sarà uguale al momento di L. </s>

<s>Si faccia ancora come FB a BH, così <gap></gap><lb></lb>ad N, che il momento di N sarà uguale al momento di I; onde il momento <lb></lb>di ambedue L, I, in G, H, cioè il momento di D in C sarà uguale al mo­<lb></lb>mento di ambedue M, N in F. </s>

<s>Ora il peso M all&#039;L sta come GA ad AF, <lb></lb>ed il peso L cioè l&#039;I al peso N sta come FB a BH, cioè a GA; dunque, <lb></lb>per la ragione perturbata, il peso M all&#039;N sta come BF ad FA, ed i pesi <lb></lb>M, N ad N come BA ad FA ” (ivi). </s></p><p type="main">

<s>Dalle equazioni M:L=GA:AF; I:N=FB:GA composta per mol-<pb xlink:href="020/01/2250.jpg" pagenum="493"></pb>tiplicazione la M:N=FB:FA, e da questa per somma la M+N:N= <lb></lb>FB+FA:FA, ossia M+N:N=AB:FA; ecco come il Viviani procede in <lb></lb>questa sua dimostrazione: Si ha per supposto N:2I=BH:2FB, la quale, <lb></lb>a moltiplicarla con l&#039;ultima ritrovata, dà M+N:2I=AB.BH:2FB.FA. </s>

<s><lb></lb>Ma perchè 2I=E, BH=HC/2=AB/2, sarà M+N:E=AB2:4BF.FA, <lb></lb>ossia M+N:E=(AB/2)2:BF.FA. </s>

<s>E perchè AB=AC=CB, dunque <lb></lb>M+N:E=AC.CB:BF.FA. Ora, essendo che i pesi M+N, E, attac­<lb></lb>cati al medesimo punto F, stanno come i loro momenti, e per le cose già di­<lb></lb>mostrate M.oD=M.o(M+N), dunque in ultima conclusione M.oD:M.oE= <lb></lb>AC.CB:BF.FA. </s></p><p type="main">

<s>A chi poi desiderasse avere la dimostrazione ne&#039;modi, e secondo il lin­<lb></lb>guaggio proprio dell&#039;Autore, sodisfaremo seguitando così a trascrivere di là, <lb></lb>dove sopra lasciammo interrotto il manoscritto: </s></p><p type="main">

<s>“ Ma i pesi M, N al doppio di I, cioè ai pesi L, I, cioè al solo peso E <lb></lb>hanno ragion composta della M, N alla N, cioè, pel dimostrato adesso, di BA <lb></lb>ad AF, e di N al doppio di I, cioè di HB al doppio di BF, cioè di HC ov­<lb></lb>vero BA al quadruplo di BF; e la ragion composta di BA ad AF, e di BA <lb></lb>al quadruplo di BF ha quella del quadrato BA al rettangolo di AF nel qua­<lb></lb>druplo di BF; adunque i pesi M, N al peso E stanno come il quadrato di <lb></lb>BA al rettangolo di AF nel quadruplo di BF: o, presi i suqquadrupli di <lb></lb>tali spazi, come il quadrato di BC, cioè il rettangolo BCA al rettangolo BFA. </s>

<s><lb></lb>Ma il momento dei pesi M, N in F, al momento del peso E in F, sta come <lb></lb>il composto dei pesi M. </s>

<s>N al peso E, cioè, pel provato adesso, come il ret­<lb></lb>tangolo BCA al rettangolo BFA, ed il momento de&#039;pesi M, N in F si provò <lb></lb>uguale al momento del peso D in C; adunque anche il momento del peso <lb></lb>D in C, al momento dell&#039;egual peso E in F, sta come il rettangolo BCA al <lb></lb>rettangolo BFA, il che ecc. </s>

<s>” (ivi). </s></p><p type="main">

<s>Avvertiva nell&#039;intitolazione il Viviani che questa sua era comprensiva <lb></lb>della XII di Galileo, la quale infatti deriva per corollario dalla equazione <lb></lb>M+N:E=AC.CB:AF.FB, postovi E=D; corollario dal Viviani stesso <lb></lb>così formulato: “ Di qui si cava che i pesi M, N ed il peso D, che hanno <lb></lb>momenti uguali, hanno ragion reciproca dei rettangoli ACB, AFB ” (ivi). </s></p><p type="main">

<s>Derivavasi pure dal Viviani di qui un altro corollario, nel quale si ri­<lb></lb>scontrava col Torricelli, come s&#039;era riscontrato nel dimostrare la proposi­<lb></lb>zione principale. </s>

<s>Quel corollario era dall&#039;Autore messo in questa forma: “ La <lb></lb>scala dei momenti de&#039;pesi uguali G, H, nella precedente nostra figura 266, <lb></lb>attaccati ad una Libbra, sostenuta ne&#039;suoi estremi A, B, sta nelle linee EG, <lb></lb>FH della parabola ACB, parallele al diametro, essendo la libbra AB base di <lb></lb>detta parabola ” (MSS. Gal., P. V, T. VII, fol. </s>

<s>61). </s></p><p type="main">

<s>Incontratosi il Grandi in questo corollario, staccato dalla sua proposi­<lb></lb>zione, lo inserì per il teorema LIV nel trattato Delle resistenze, supplendo <lb></lb>così di suo alla dimostrazione, che in quella parte del manoscritto si tro-<pb xlink:href="020/01/2251.jpg" pagenum="494"></pb>vava mancare: “ imperocchè i detti momenti sono come i rettangoli AGB, <lb></lb>AFB fatti dalle parti di essa Libbra, come dimostra il Galileo nella propo­<lb></lb>sizione XIII. </s>

<s>Ma a questi rettangoli sono proporzionali le linee GE, HF, ti­<lb></lb>rate nella parabola parallele al diametro, dunque ecc. </s>

<s>” (Alb. </s>

<s>XIV, pag. </s>

<s>79). </s></p><p type="main">

<s>Per quella che qui il Grandi chiama proposizione XIII s&#039;intende vera­<lb></lb>mente, secondo la segnatura incominciata da Galileo, la XII, nella quale che <lb></lb>non si dimostri essere i momenti come i rettangoli AGB, AFB lo seppero <lb></lb>molto bene il Torricelli e il Viviani, i quali altrimenti non si sarebbero af­<lb></lb>faticati, nè compiaciutisi di avere essi i primi ritrovato il nuovo teorema. </s>

<s>La <lb></lb>compiacenza poi da parte di esso Viviani era troppo giusta, perchè, da quel <lb></lb>ch&#039;ei credeva <emph type="italics"></emph>a nullo demonstratum,<emph.end type="italics"></emph.end> gli venivano felicemente concluse le <lb></lb>proposizioni dei solidi di resistenze uguali, della Scala dei momenti nella pa­<lb></lb>rabola, e di tante altre belle dottrine aggiunte alle galileiane, che nell&#039;opera <lb></lb>del Grandi si rimangono come rivi senza sorgente, non scoprendosi quella <lb></lb>unica da lui indicata, a chi si metta più diligentemente a cercare, così ma­<lb></lb>nifesta. </s></p><p type="main">

<s>Quando Lodovico Serenai consegnò i manoscritti torricelliani al Viviani, <lb></lb>questi, nel mettere all&#039;ordine il trattato <emph type="italics"></emph>De motu ac momentis,<emph.end type="italics"></emph.end> ebbe a di­<lb></lb>singannarsi, ritrovando per que&#039;fogli quel ch&#039;egli credeva non aver nessun <lb></lb>altro dimostrato prima di lui. </s>

<s>Abbattutosi poi in quella Nota, nella quale, <lb></lb>dalla Scala dei momenti de&#039;pesi in una Libbra sostenuta dalle due parti, si <lb></lb>concludeva essere la linea, in che disponesi la catena una parabola; scrisse <lb></lb>in margine: <emph type="italics"></emph>Questa io la tralascio, perch&#039;è di Galileo.<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XXXVII, fol. </s>

<s>81). </s></p><p type="main">

<s>Ma dove ha dimostrato, dai principii meccanici, Galileo, avrebbe potuto <lb></lb>domandare il Torricelli al suo discepolo, amico e collega, che la sacca di una <lb></lb>fune o di una catena è in figura di parabola? </s>

<s>Nel secondo dialogo delle <lb></lb>Scienze nuove, dopo la XV proposizione, null&#039;altro si fa che affermare, die­<lb></lb>tro ciò che apparisce alla vista: “ la catenella si piega in figura parabolica ” <lb></lb>(Alb. </s>

<s>XIII, 144). </s></p><p type="main">

<s>Or chi sa come sarebbero rimasti i due interlocutori, se fosse entrato <lb></lb>qualcuno in mezzo a loro, mostrando una carta autografa, dalla quale ma­<lb></lb>nifestamente apparisse che Galileo aveva già da sè dimostrato il Teorema <lb></lb>da ambedue creduto una loro propria invenzione; che ne avea dedotta per <lb></lb>corollario la scala parabolica de&#039;momenti dei pesi uguali attaccati nella lun­<lb></lb>ghezza di una Libbra, e che ne aveva pure indi concluso dovere in figura <lb></lb>di parabola insenarsi, rilasciata dai due capi fissi, una catena? </s></p><p type="main">

<s>Quella carta autografa, che non videro mai i due Discepoli zelanti, può <lb></lb>essere ora alla notizia di tutti che, andando a squadernare il secondo tomo <lb></lb>della parte quinta dei Manoscritti di Galileo, fermino sul foglio 43 la loro <lb></lb>attenzione. </s>

<s>Ivi apparirà grandeggiare in campo una figura, da noi rappre­<lb></lb>sentata nella 268, sottovi scritte, da una parte del foglio, sentenziosamente <lb></lb>così queste righe: “ Il grave in G preme con manco forza che in S, se­<lb></lb>condo la proporzione del rettangolo FGC al rettangolo FSC ”: ciò ch&#039;esat-<pb xlink:href="020/01/2252.jpg" pagenum="495"></pb>tamente corrisponde col Teorema <emph type="italics"></emph>a nullo quod siam demonstratum,<emph.end type="italics"></emph.end> in cui <lb></lb>il Viviani, come Galileo, ma dopo Galileo non saputo, asserisce che il mo­<lb></lb>mento del peso in G, al momento del medesimo peso in S, sta omologa­<lb></lb>mente come il rettangolo FGC al rettangolo FSC. </s></p><p type="main">

<s>Le linee ST, GD, nella figura galileiana, accennano evidentemente che <lb></lb>i momenti dei pesi in S e in G son proporzionali ad esse linee condotte <lb></lb><figure id="id.020.01.2252.1.jpg" xlink:href="020/01/2252/1.jpg"></figure></s></p><p type="caption">

<s>Figura 268<lb></lb>parallele al diametro AQ della curva FAC, la qual <lb></lb>curva essere intesa per quella, in cui si piega la <lb></lb>catena, e dover essere parabolica, è dichiarato <lb></lb>espressamente dalla Nota scritta in capo al fo­<lb></lb>glio, che così dice: “ Passi la catenella per i <lb></lb>punti F, C, e, dato lo scopo Z, tira tanto la ca­<lb></lb>tena che passi per Z, e troverai la distanza SC, <lb></lb>e l&#039;angolo della elevazione. </s>

<s>Dimostrasi che, sic­<lb></lb>come è impossibile tirar la catena in retto; così <lb></lb>essere impossibile che il proietto vadia mai per <lb></lb>diritto, se non nella perpendicolare in su, come <lb></lb>anco la catena a piombo si stende in retto. </s>

<s>Sic­<lb></lb>come la parabola del proietto è descritta da due <lb></lb>moti, orizzontale e perpendicolare; così la cate­<lb></lb>nella resulta da due sforzi: orizzontale da chi la <lb></lb>tira nella estremità, e perpendicolare <emph type="italics"></emph>deorsum<emph.end type="italics"></emph.end><lb></lb>dal proprio peso. </s>

<s>” </s></p><p type="main">

<s>Queste note furono scritte verso il 1637, che vuol dire un ventisette o <lb></lb>vent&#039;ott&#039;anni dopo essere stati scritti que&#039;fogli, nei quali erano secondo il <lb></lb>Salviati, messi in ordine di trattato i teoremi e problemi delle Resistenze, <lb></lb>fra&#039;quali teoremi doveva essere dimostrato anche quello dei pesi uguali pre­<lb></lb>menti in varii punti la lunghezza di un&#039;asta, con momenti proporzionali <lb></lb>direttamente ai rettangoli delle distanze dagli appoggi; intorno a che Gali­<lb></lb>leo avea prevenuta l&#039;industria del Torricelli e del Viviani, il quale a pag. </s>

<s>105 <lb></lb>della sua <emph type="italics"></emph>Scienza delle proporzioni<emph.end type="italics"></emph.end> (Firenze 1674), facendosi a indovinar <lb></lb>come Galileo deducesse che la sacca naturale delle catenuzze s&#039;adatta sem­<lb></lb>pre alle linee paraboliche, colse così nel vero com&#039;avesse avuto sott&#039;occhio <lb></lb>il manoscritto da noi sopra citato. </s>

<s>Ma la parabola de&#039;proietti, venuta come <lb></lb>vedremo, ad esercitare l&#039;ingegno dello stesso Galileo in su gli ultimi anni <lb></lb>de&#039;suoi studii meccanici, gli fece revocare alla mente le prime antiche spe­<lb></lb>culazioni, sperando che alla Dinamica nuova fosse per recare qualche lume <lb></lb>la statica delle resistenze. </s></p><p type="main">

<s>Era senz̀a dubbio significantissima l&#039;analogia tra la catena e il proietto, <lb></lb>che non si possono tirare in linea retta, per non esser possibile spogliar del <lb></lb>loro peso naturale la palla scagliata, e gli anelli tesi da qualunque forza: <lb></lb>com&#039;era pure assai lusinghiero il pensiero del Torricelli, che fossero cioè i <lb></lb>pesi in T e in D scesi da S e da G, trattivi con forze proporzionali alle <lb></lb>linee ST, GD, condotte parallele al diametro della parabola. </s>

<s>Ma non sem-<pb xlink:href="020/01/2253.jpg" pagenum="496"></pb>bra che l&#039;analogia più regga, quando, dalla Statica trapassando ai più as­<lb></lb>soluti principii della Dinamica, Galileo rassomiglia i moti, che fanno piegar <lb></lb>la catena, ai medesimi moti, da&#039;quali resulta la linea dei proietti. </s>

<s>Che se, <lb></lb>in considerare la scesa degli anelli, gli spazi ST, GD non son passati stati­<lb></lb>camente con moto equabile, ma dinamicamente con moto accelerato, non <lb></lb>sarebbe possibile dimostrar che la curva FAC è una parabola, a quel modo <lb></lb>che, se le cose da lui supposte fossero state esattamente vere, era riuscito <lb></lb>a dimostrare il Torricelli. </s></p><p type="main">

<s>Forse del confidarsi che si potesse con matematica esattezza la catena­<lb></lb>ria rassomigliare alla traiettoria fu sconfortato Galileo dall&#039;esperienza, de­<lb></lb>scrivendo coi metodi geometrici una parabola, e adattandovi sopra pendente <lb></lb>una catenuzza. </s>

<s>Osservò che tali adattamenti si fanno via via più precisi, <lb></lb>che la curva è più tesa, cosicchè, mentre prima aveva assolutamente sen­<lb></lb>tenziato, come udimmo, che la catenella <emph type="italics"></emph>si piega in figura parabolica,<emph.end type="italics"></emph.end> ora, <lb></lb>temperando il discorso, soggiunge che <emph type="italics"></emph>si piega in linee, le quali assai si <lb></lb>avvicinano alle paraboliche<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 163). Fa a questa opinione di Ga­<lb></lb>lileo bel riscontro quella dell&#039;Huyghens, il quale, in descrivere nella sua <lb></lb><emph type="italics"></emph>Astroscopia<emph.end type="italics"></emph.end> l&#039;antenna, che porta in alto la lente, dice del filo che, racco­<lb></lb>mandato da un capo a essa lente per moverla, scende giù con l&#039;altro alle <lb></lb>mani dell&#039;osservatore: “ Quae ad eius flexum attinent, Geometriae ratio­<lb></lb>nibus experimentisque expendi possunt: nempe contentum filum, flexu illo <lb></lb>exiguo, parabolicam lineam tam prope exprimit, ut pro vera absque errore <lb></lb>habeat ” (Opera varia cit., pag. </s>

<s>268). </s></p><p type="main">

<s>Così l&#039;Huyghens dunque come Galileo ritenevano che fosse la catenaria <lb></lb>una parabola, specialmente quand&#039;è piccolo il flesso. </s>

<s>Ciò dall&#039;altra parte è <lb></lb>confermato assai bene dall&#039;analisi, comparando l&#039;equazioni delle due curve, <lb></lb>che per l&#039;una è X:X′=<emph type="italics"></emph>y2:y′2<emph.end type="italics"></emph.end>, e per l&#039;altra X:X′=<emph type="italics"></emph>yc:y′c′<emph.end type="italics"></emph.end>, inten­<lb></lb>dendosi per <emph type="italics"></emph>c, c′<emph.end type="italics"></emph.end> i tratti, che son compresi fra il principio delle ascisse e <lb></lb>il fine delle ordinate, i quali tratti è manifesto che tanto più si accostano <lb></lb>con esse ordinate, quanto il flesso è minore, o la catena è più distesa. </s></p><p type="main">

<s>Ritornando ora colà, d&#039;onde siam deviati col nostro discorso, son tali <lb></lb>i teoremi e tali le conclusioni della teoria dei momenti applicata alle resi­<lb></lb>stenze da Galileo, dal Torricelli e dal Viviani: teoremi e conclusioni, che <lb></lb>si sarebbero dovuti citare dal Grandi, se avesse voluto con argomenti rin­<lb></lb>tuzzare la gloria, che il suo rivale menava d&#039;essere stato, a maneggiar quella <lb></lb>teoria egli il primo fra tutti. </s>

<s>Ma perchè esso Grandi far ciò o non potè o <lb></lb>non seppe, resta a concludersi dunque il nostro lungo ragionamento con <lb></lb>dire, che irragionevoli appariscono da ogni parte le censure di lui contro <lb></lb>quel trattato <emph type="italics"></emph>De resistentia solidorum,<emph.end type="italics"></emph.end> meditato dal Marchetti e scritto in <lb></lb>gran parte ne&#039;tempi delle vacanze autunnali, passate ora nella paterna casa <lb></lb>di Empoli, ora nella prossima villa di Pontormo, ai verdi campi della quale, <lb></lb>e ai pioppi pampinosi, memorie dolcissime della nostra fanciullezza, ci sia <lb></lb>permesso di mandare un saluto. </s></p><pb xlink:href="020/01/2254.jpg" pagenum="497"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le cose, ne&#039;precedenti articoli di questo capitolo esposte intorno alle <lb></lb>Resistenze, non sono state altro che di speculazioni, alle quali si vedeva <lb></lb>d&#039;alto precedere l&#039;infallibile scorta della Geometria. </s>

<s>Tale, dall&#039;altra parte, <lb></lb>è stata sempre la legge storica del pensiero, che concepisce le forme astratte, <lb></lb>prima di considerarle incarnate nella materia, come per un esempio insi­<lb></lb>gne, e appropriatissimo al caso dell&#039;Archimede novello, può vedersi nelle <lb></lb>opere dell&#039;Archimede antico. </s>

<s>Come dunque, alla Statica e alla Idrostatica <lb></lb>archimedea, che considerano la gravità ne&#039;solidi, e la fluidità nei liquidi <lb></lb>astrattamente dalle altre passioni della materia, successero le due nuove <lb></lb>Scienze, che vollero richiamare le matematiche astrazioni a rispondere alla <lb></lb>presente realtà dei fatti; così avvenne della Scienza delle resistenze dei corpi <lb></lb>allo spezzarsi. </s></p><p type="main">

<s>Fu dei primi a dar mano all&#039;opera Paolo Wrz, o Vulzio, come lo chia­<lb></lb>marono i nostri Italiani, se ha da credersi al Leibniz, il quale, dop&#039;avere <lb></lb>accennato al libro delle Resistenze, che il Blondel avea revocato, soggiunge <lb></lb>così, nella citata lettera autografa al Grandi: “ Paulus Wurzius, qui ductor <lb></lb>exercitus apud Batavos, paulo post initium Belli gallici, idest paulo post eum­<lb></lb>dem annum 1672, obiit, idem argumentum tractarat per experimenta, quae <lb></lb>Galilaeo hand consona deprehenderat, sed scheda eius periere ” (MSS. Cim., <lb></lb>T. XXIX, fol. </s>

<s>287). </s></p><p type="main">

<s>Che tra i teoremi galileiani e gli sperimenti non fosse per passare quella <lb></lb>consonanza, si vedeva per necessità conseguente dalla legge sopra accennata, <lb></lb>ma il Viviani ne aveva riconosciute le intime cause speciali, forse prima del <lb></lb>Vulzio, quando scrisse nella seguente nota: “ Pare che in questa Scienza <lb></lb>delle resistenze si deva astrarre la flessibilità dei corpi, che fanno molla, po­<lb></lb>tendo questi alterare le proporzioni investigate, siccome la temperie e varie <lb></lb>crudezze di metalli ” (MSS. Gal., P. V, T. VII, fol. </s>

<s>29). </s></p><p type="main">

<s>Apparisce da altre Note sparse per queste medesime carte manoscritte, <lb></lb>e dal Grandi secondo noi, nelle <emph type="italics"></emph>Definizioni<emph.end type="italics"></emph.end> premesse al Trattato e nelle <lb></lb><emph type="italics"></emph>Supposizioni,<emph.end type="italics"></emph.end> non bene ordinate; che il Viviani aveva già pensato di ritro­<lb></lb>vare, per via di esperimenti opportuni, le relazioni che passano fra la re­<lb></lb>sistenza assoluta e la respettiva in varie qualità di corpi, sperando così di <lb></lb>poter ridurre le verità della Geometria a consentire in qualche modo con <lb></lb>le verità naturali. </s>

<s>“ Si sperimenti, egli scrive, quanto peso ci voglia a strap­<lb></lb>pare i cilindri di vetro per diritto a piombo, attaccando al termine inferiore <lb></lb>tanto peso, che faccia lo strappamento. </s>

<s>— Di qui si cava la <emph type="italics"></emph>tariffa<emph.end type="italics"></emph.end> delle <lb></lb>resistenze assolute di uguali sezioni di metalli, e si può provare se doppia <lb></lb>sezione voglia doppio peso, come la ragione ce ne persuade ” (Alb. </s>

<s>XIV, 5). </s></p><p type="main">

<s>La particolare scelta delle materie, fatta dal Viviani per le sue espe­<lb></lb>rienze, aveva un fine importantissimo nella decisione dell&#039;ipotesi ammessa <pb xlink:href="020/01/2255.jpg" pagenum="498"></pb>da Galileo, perchè i metalli duri, e specialmente il vetro, pareva che si po­<lb></lb>tessero proporre per gli esempii delle rotture, che si fanno istantanee. </s>

<s>Ma <lb></lb>quando il Viviani stesso ebbe a sperimentare, nell&#039;Accademia del Cimento, <lb></lb>che anche il vetro cede alle forze del calore, <emph type="italics"></emph>per lo ficcamento de&#039;volanti <lb></lb>corpiccioli del fuoco nell&#039;esterna porosità<emph.end type="italics"></emph.end> (Saggi cit., pag. </s>

<s>118), entrò in so­<lb></lb>spetto che dovesse similmente cedere alle forze di un peso; sospetto, che <lb></lb>si verificò con quella bella esperienza, descritta poi nel citato libro dei <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end><lb></lb>dove si legge che, adattati due vasi di vetro, uno conico l&#039;altro piramidale, <lb></lb>negl&#039;incastri di una grossa tavola, essendo vuoti, tornando a rimetterveli <lb></lb>pieni di argento vivo, non v&#039;entravano al segno di prima, <emph type="italics"></emph>secondo che la <lb></lb>forza del peso gli distendeva ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>125). </s></p><p type="main">

<s>Lo stesso vetro dunque, n&#039;ebbe di qui a concludere il Viviani, è di <lb></lb>que&#039;corpi, che fanno molla, e si dovrebbe perciò, secondo i propositi scritti, <lb></lb>astrarre anche questo dalla Scienza matematica delle resistenze, cosicchè <lb></lb>non vedeva a qual mai corpo in natura si potessero adattare le ipotesi e i <lb></lb>teoremi di Galileo. </s>

<s>Parrebbero queste conclusioni contradire a uno di quei <lb></lb>supposti, premessi al suo Trattato in tal forma: “ La separazione delle due <lb></lb>superfice del solido, tenuto per traverso, si fa nel medesimo istante, tanto <lb></lb>nei punti remoti dal sostegno, che nei vicini, e che in quelli di mezzo, stante <lb></lb>che tale separazione si fa con moto regolare dell&#039;una superfice, che si muove <lb></lb>dall&#039;altra che sta ferma ” (Alb. </s>

<s>XIV, 9). Ogni contradizione però sparisce, <lb></lb>penetrando addentro alla intenzione del Viviani, il quale, professando l&#039;ipo­<lb></lb>tesi e i teoremi galileiani come formule astratte, si proponeva di ridurle poi <lb></lb>ai casi particolari della tale o tale altra materia resistente, introducendovi <lb></lb>quelle, ch&#039;ei chiamava <emph type="italics"></emph>tariffe,<emph.end type="italics"></emph.end> e i moderni <emph type="italics"></emph>coefficienti sperimentali.<emph.end type="italics"></emph.end> Il sa­<lb></lb>piente istituto, il quale mirabilmente si conforma con quello proseguito og­<lb></lb>gidì, dopo tanti pericoli, dalla Scienza, non ebbe effetto per quelle avven­<lb></lb>ture, che si son già narrate nella nostra Storia. </s></p><p type="main">

<s>Apprese nonostante da&#039;familiari colloqui col Viviani sembrano nel ca­<lb></lb>pitolo XVIII della Meccanica le osservazioni del Mersenno (Parisiis 1644, <lb></lb>pag. </s>

<s>62-68), il quale poi, nel III tomo delle Riflessioni fisiche matematiche, <lb></lb>faceva notar che il ferro e gli altri metalli, anzi tutti i corpi, s&#039;inflettono <lb></lb>prima di rompersi: difficoltà per chi tratta delle resistenze, <emph type="italics"></emph>quam et ipse <lb></lb>Galileus vitavit.<emph.end type="italics"></emph.end> E bench&#039;egli si presumesse di aver proposte le cose con <lb></lb>certezza di dimostrazione, “ examine diligenti egent, quod inibunt, quibus <lb></lb>otium et voluntas adfuerit ” (Parisiis 1647, pag. </s>

<s>151). </s></p><p type="main">

<s>Il primo, a cui venne questa volontà, ed ebbe quest&#039;ozio, sembra es­<lb></lb>sere stato il Mariotte, il quale narra nel trattato <emph type="italics"></emph>Du mouvement des eaux<emph.end type="italics"></emph.end><lb></lb>di aver fatto, insieme col signor Hubin, un&#039;altra bella esperienza, dopo quella <lb></lb>de&#039;nostri Accademici fiorentini, di un filo di vetro grosso un quarto di linea <lb></lb>e lungo quattro piedi, che stirato si allungava, e lasciato ritornava allo stato <lb></lb>di prima. </s>

<s>Ebbe di qui a persuadersi il Mariotte, come il Viviani, non v&#039;es­<lb></lb>ser corpo, per quanto credasi rigido e duro, che si rompa a un tratto, senza <lb></lb>prima cedere o più o meno alla forza del peso. </s>

<s>Ma mentre il Nostro non <pb xlink:href="020/01/2256.jpg" pagenum="499"></pb>si credè per questo di dover bandire l&#039;ipotesi galileiana dal Trattato delle <lb></lb>resistenze, il Francese dettesi a speculare, e a sperimentare per sostituir­<lb></lb>vene un&#039;altra. </s></p><p type="main">

<s>Supposto dunque che siano tutti i corpi duri intessuti di fibre, le quali <lb></lb>cedano alquanto alla forza, che tenterebbe di romperle, pensò il Mariotte <lb></lb>che le resistenze, specialmente respettive, dovevano avere effetti diversi da <lb></lb>quelli ammessi da Galileo, secondo il quale i momenti di esse resistenze non <lb></lb>variano, per variar la potenza dei punti di attacco, che in ciascuno secondo <lb></lb>lui è assoluta, ma per solo variar la distanza dal fulcro nella contralleva: <lb></lb>mentre veramente attendendo alla maggior e minor tensione delle fibre, che <lb></lb>debb<gap></gap>n rompersi tutte insieme, il momento varia, si per la distanza dal ful­<lb></lb>cro, e sì per la potenza, che non può, rispetto alla naturale testura del corpo <lb></lb>resistente, mantenersi assolutamente uguale in ogni parte della stessa con­<lb></lb>tralleva. </s></p><p type="main">

<s>Spiegava il Mariotte assai bene così il suo concetto: Abbiasi la Libbra <lb></lb>ACB (figura 269), col fulcro in C, ed essendo BC a CE come dodici a uno, <lb></lb>sospendansi in E, in D, a una distanza DC doppia di EC, e in A, a una <lb></lb><figure id="id.020.01.2256.1.jpg" xlink:href="020/01/2256/1.jpg"></figure></s></p><p type="caption">

<s>Figura 269<lb></lb>distanza AC doppia di DC, i tre <lb></lb>pesi I, H, G, ciascuno uguale a <lb></lb>dodici libbre, ai quali tutt&#039;e tre <lb></lb>farà perciò equilibrio in B il peso <lb></lb>F, che sia di sette libbre. </s>

<s>Questo <lb></lb>sarebbe conforme con l&#039;ipotesi di <lb></lb>Galileo, secondo la quale le resi­<lb></lb>stenze rappresentate da I, H, G, operanti cìascuna col peso assoluto di do­<lb></lb>dici libbre, non per altro variano i loro momenti, che per variare le distanze <lb></lb>delle contralleve EC, CD, CA dal loro punto di appoggio. </s></p><p type="main">

<s>Succede però la cosa molto diversamente, soggiunge il Mariotte, quando <lb></lb>le resistenze non son rappresentate da pesi, che operino ciascuno con as­<lb></lb>soluta potenza indipendentemente gli uni dagli altri, ma da fibre, che ven­<lb></lb>gano stirate con varia violenza, e l&#039;una delle quali non si rompe, se non <lb></lb>si rompe nello stesso tempo anche l&#039;altra. </s>

<s>Rappresenti ACPQ (fig. </s>

<s>270) un <lb></lb><figure id="id.020.01.2256.2.jpg" xlink:href="020/01/2256/2.jpg"></figure></s></p><p type="caption">

<s>Figura 270<lb></lb>solido, stabilmente congiunto con <lb></lb>la contralleva DC per via delle tre <lb></lb>corde uguali, e di ugual resistenza <lb></lb>DI, GL, HM, in distanze CA, CE, <lb></lb>CB dal fulcro, che stieno fra loro, <lb></lb>e con la leva CF, come i pesi con­<lb></lb>siderati di sopra. </s>

<s>Si supponga che, <lb></lb>a voler rompere ciascuna di esse corde, si debba prima distrarla per due <lb></lb>linee dallo stato attuale. </s>

<s>A che fare, attaccato in F, sia bastante il peso R <lb></lb>di quattro libbre; e si supponga altresi, ciò che è assai verosimile e con­<lb></lb>fermato dalle esperienze, che le tensioni siano proporzionali alle forze ten­<lb></lb>denti: egli è chiaro, dice il Mariotte, che bisogneranno due libbre in R per <pb xlink:href="020/01/2257.jpg" pagenum="500"></pb>distendere due linee la corda GL, essendo sola, e una libbra solamente per <lb></lb>distendere allo stesso modo la corda HM. </s>

<s>Ma perchè, quando la corda DI è <lb></lb>distratta due linee, la corda GL non è distratta che una linea sola, e la <lb></lb>corda HM una mezza linea; ne segue, per la seconda delle fatte supposizioni, <lb></lb>che, quando si tirano tutte insieme, un peso d&#039;una libbra in circa sarà ba­<lb></lb>stante a fare equilibrio con la tensione della corda GL, tesa non più di una <lb></lb>linea, e sole quattr&#039;once basteranno, per fare equilibrio con la tensione HM, <lb></lb>benchè la resistenza assoluta di quest&#039;ultima sia una libbra. </s>

<s>Cosicchè, per <lb></lb>ridurre le tre corde in questo stato, basterà porre in R poco più di cinque <lb></lb>libbre, e non sette, come vorrebbesi per Galileo. </s></p><p type="main">

<s>Per riscontrare la verità di questo ragionamento istituì il Mariotte, alla <lb></lb>presenza del Carcavy, del Roberval e dell&#039;Huyghens, alcune esperienze con <lb></lb>cilindri di legno secco, e con cannelli di vetro, e sempre afferma di aver <lb></lb>trovato che, per la più giusta misura delle loro resistenze respettive, non <lb></lb>bisognava prendere la proporzione della lunghezza alla metà, ma a un terzo <lb></lb>poco più della grossezza. </s>

<s>Cosicchè, trattando nel secondo Discorso della <lb></lb>parte quinta <emph type="italics"></emph>Del moto delle acque,<emph.end type="italics"></emph.end> delle forze di resistenza dei condotti, <lb></lb>avuto riguardo alla materia e alla pressione, renunziò all&#039;ipotesi, e alle con­<lb></lb>seguenze ch&#039;indi ne trasse Galileo, di cui così parla l&#039;Autore, nell&#039;intro­<lb></lb>durre il citato Discorso: </s></p><p type="main">

<s>“ Galilée a fait un Traité de la resistance des solides, ou il explique <lb></lb>à sa manière la force, que doit avoir un poids, lorsqu&#039;il est suspendu à <lb></lb>l&#039;extremité d&#039;un solide fiché dans un mur. </s>

<s>Comme si le mur est AB (fig. </s>

<s>271) <lb></lb><figure id="id.020.01.2257.1.jpg" xlink:href="020/01/2257/1.jpg"></figure></s></p><p type="caption">

<s>Figura 271<lb></lb>et le solide CDEF, et que le poids G soit suspendu <lb></lb>en F par la corde FG, il dit que la longueur FD est <lb></lb>comme le bras d&#039;un levier, et que l&#039;epaisseur CD est <lb></lb>comme le contre-levier, en sorte que, si on vouloit <lb></lb>separer une partie, qui est en C, et que sa resistance <lb></lb>absolue fùt de 10 livres, il faudroit que le poids G <lb></lb>fùt seulement de 2 livres, si la longueur FD etoit 5 <lb></lb>fois plus grande que DC. </s>

<s>Mais en considerant une au­<lb></lb>tre partie comme I, également distante de C et D, il <lb></lb>ne faudroit qu&#039;une livre en G, parce que le levier FD seroit alors 10 fois <lb></lb>plus grand que le contre-levier DI. </s>

<s>Et parce qu&#039;il suppose que la rupture se <lb></lb>fait en mème tems dans toutes les parties de CD, dont les unes sont entre <lb></lb>D et I, et les autres entre I et C, il pretend qu&#039;il faut considérer l&#039;augmen­<lb></lb>tation de la force du poids, selon la raison de FD à la moienne distance DI, <lb></lb>ce qui pourtant repugne a plusieurs experiences, que j&#039;ai faites avec des <lb></lb>solides de bois et de verre, ou j&#039;ai trouvé qu&#039;il faloit prendre la raison de FD <lb></lb>a une ligne moindre que DI, comme le quart de DC, ou le tiers, et non <lb></lb>de FD à la moitié de DC ” (Oeuvres, T. II, A la Haye 1740, pag. </s>

<s>461). </s></p><p type="main">

<s>Il ragionamento e le conclusioni del Mariotte sedussero i Matematici, e <lb></lb>giacchè il Francese aveva tentata una dimostrazione, ma non osò di ridurla <lb></lb>a tutto il rigore della Geometria, se ne assunse l&#039;incarico il Leibniz in una <pb xlink:href="020/01/2258.jpg" pagenum="501"></pb>Dissertazione, inserita, per il mese di Luglio 1684, negli Atti degli Eruditi <lb></lb>di Lipsia. </s>

<s>Incomincia a fare osservare l&#039;Autore che due corpi coerenti non <lb></lb>si staccano a un tratto, come può giudicarsi per l&#039;esempio di un bastone, <lb></lb>che si piega, prima di rompersi, o di una corda, che si distende, prima di <lb></lb>strapparsi. </s>

<s>Anzi che qualunque materiata forma, per quanto rigidissima, s&#039;in­<lb></lb>fletta a ogni legger colpo, si dimostra nel suono, il quale non per altro si pro­<lb></lb>duce, che per le reciprocate vibrazioni, benchè insensibili, del corpo risonante. </s>

<s><lb></lb>Lo stesso vetro è flessibile, a quel che pare da&#039;filamenti di lui, e benchè mas­<lb></lb>siccio si contrae e si dilata al calore, e sotto un peso che non leggermente <lb></lb>lo prema, come si legge nel libro degli Sperimenti fiorentini. </s>

<s>Le parti pure <lb></lb>delle piante e degli animali ci son dall&#039;Anatomia descritte come tessili. </s></p><p type="main">

<s>“ Consideremus ergo, prosegue a dire il Leibniz, velut fibras quasdam, <lb></lb>quae partes corporum connectant, et intelligamus trabem MC (fig. </s>

<s>272) pa­<lb></lb>rieti, vel substentaculo DE plurimis fibrarum plexibus alligari in punctis <lb></lb><figure id="id.020.01.2258.1.jpg" xlink:href="020/01/2258/1.jpg"></figure></s></p><p type="caption">

<s>Figura 272<lb></lb>A, H, B, et aliis intermediis innumeris. </s>

<s>Appenso iam pon­<lb></lb>dere in C, movebitur nonnihil trabs circa fulcrum A, et <lb></lb>punctum trabis B, a pariete discedens, a puncto parietis B <lb></lb>veniet ad punctum a pariete distans M, secumque tra­<lb></lb>hens fibram, quae parieti annectitur, eam tendet instar <lb></lb>chordae, sive ultra naturalem suum statum extendet ” <lb></lb>(Opera omnia, T. III, Genevae 1768, pag. </s>

<s>163). Lo stesso <lb></lb>avverrà di qualunque altro punto H, ma la fibra HK sarà <lb></lb>stirata con tanto minor forza della fibra BM, quanto il <lb></lb>quadrato di AH è minore del quadrato di AB. </s></p><p type="main">

<s>Da questa proposizione, che cioè i momenti delle re­<lb></lb>sistenze fatte dalle varie fibre son proporzionali ai qua­<lb></lb>drati delle distanze dal fulcro, piglia ogni valore la teoria <lb></lb>leibniziana, la quale perciò si dimostra dall&#039;Autore con un <lb></lb>matematico discorso, che noi riduciamo così a poche pa­<lb></lb>role. </s>

<s>Supposto, com&#039;è ragionevole, e com&#039;è, dice il Leib­<lb></lb>niz, dimostrato altrove, che le forze sieno proporzionali <lb></lb>alle tensioni, e che queste siano proporzionali alle lunghezze, a cui son ri­<lb></lb>dotte le fibre, il momento M.oF della forza di resistenza, che fa la fibra BM, <lb></lb>sarà evidentemente AB.BM, come, per ugual ragione, il momento M.oF′ <lb></lb>della forza, che fa la fibra HK, sarà AH.HK. </s>

<s>E perchè la similitudine dei <lb></lb>triangoli dà BM:HK=AB:AH, sarà dunque M.oF:M.oF′=AB2:AH2. </s></p><p type="main">

<s>È questa, come si vede, l&#039;equazione a una parabola, che piacque al <lb></lb>Leibniz di descrivere dentro il quadrato SN, preso a rappresentare, con le <lb></lb>infinite linee tutte uguali a SR delle quali s&#039;intesse, la resistenza assoluta <lb></lb>della trave. </s>

<s>Se si sega il lato RN in F, in modo da avere RN:FN=AB:AH, <lb></lb>e se da F si conduce alla parabola, parallela all&#039;asse delle ascisse, la FQ, <lb></lb>avremo, per le proprietà di essa parabola, RS:FQ=NR2:FN2, ond&#039;è <lb></lb>M.oF:M.oF′=RS:Fq; che vuol dir che, se RS rappresenta la resistenza <lb></lb>in B, FQ rappresenta la resistenza in H. </s></p><pb xlink:href="020/01/2259.jpg" pagenum="502"></pb><p type="main">

<s>Si può la medesima conclusione applicare a tutti gl&#039;infiniti punti, com­<lb></lb>presi fra R ed N, da ciascun de&#039;quali condotte le ordinate alla parabola, si <lb></lb>verrà di tutte insieme a tessere la superficie del trilineo parabolico concavo <lb></lb>NRSQN, il quale servirà perciò a rappresentare la resistenza respettiva della <lb></lb>trave, come il quadrato SN, allo stesso trilineo circoscritto, s&#039;era preso dianzi <lb></lb>a reppresentare la resistenza assoluta. </s>

<s>Ma il trilineo è la terza parte del <lb></lb>quadrato, dunque anche la resistenza respettiva è la terza parte dell&#039;asso­<lb></lb>luta. </s>

<s>“ Generaliter ergo, conclude il Leibniz la sua dimostrazione, pondus, <lb></lb>trabem parallelepipedam directe evellens, erit, ad pondus abrumpens trans­<lb></lb>verse seu per modum vectis, ut longitudo vectis, ad tertiam partem crassi­<lb></lb>tiei trabis ” (ibid., pag. </s>

<s>164). </s></p><p type="main">

<s>Alcuni Autori di Meccanica resero più semplice questa dimostrazion <lb></lb>leibniziana, introducendovi il centro di gravità, ma potevasi invece applicare <lb></lb>il centro delle forze parallele, che conduce alla medesima conclusione per <lb></lb>una via, la quale, essendo la più diretta, è anche perciò la più conveniente <lb></lb>e la più spedita. </s>

<s>Sia infatti P il peso che, applicato all&#039;estremità di una leva <lb></lb>lunga quant&#039;uno de&#039;lati del quadrato MC, opera con momento uguale alla <lb></lb>potenza, che sarà perciò espressa da P.AB. </s>

<s>La resultante di tutte le forze <lb></lb>parallele resistenti è data da BM.AB/2, che è la somma di tutte le fibre, o <lb></lb>infinite linee, di cui si tesse il triangolo ABM, il quale si può per maggior <lb></lb>precisione riguardare come infinitesimo, e il punto di applicazione della detta <lb></lb>resultante sarà in H, a due terzi dalla linea AB, a partire dal fulcro. </s>

<s>Sarà <lb></lb>perciò il momento della resistenza BM.AB/2X2AB/3, che, dovendo per l&#039;equi­<lb></lb>librio essere uguale al momento delle potenza, darà P.AB=BM.AB.AB/3. <lb></lb>e fatto Q=BM.AB, P=Q/3. Ma perchè Q è manifestamente la somma di <lb></lb>tutte le forze uguali, che concorrono a fare la resistenza assoluta, e P dal­<lb></lb>l&#039;altra parte rappresenta la forza della resistenza respettiva; questa è dun­<lb></lb>que la terza parte di quella. </s></p><p type="main">

<s>Suppongasi ora che il peso del quadrato materiale SN sia quel che ci <lb></lb>vuole per strappare direttamente la trave MC dalla parete AB, con la quale <lb></lb>era prima coerente: per aver la quantità del peso, che applicato in C è ne­<lb></lb>cessario a troncar la medesima trave per traverso, ossia col far girare il <lb></lb>lato AM intorno al centro A, bisogna secondo Galileo segare il quadrato lungo <lb></lb>la linea retta NS, e, secondo il Leibniz, lungo il filo della parabola SQN, <lb></lb>e il peso del trilineo concavo NRSQN, secondo l&#039;uno Autore, o il peso del <lb></lb>triangolo RSN, secondo l&#039;altro, daranno quello che si cercava. </s></p><p type="main">

<s>La maggior parte dei Matematici, specialmente stranieri, preferì l&#039;ipo­<lb></lb>tesi leibniziana, della quale il Varignon, in una delle pubbliche adunanze, <lb></lb>tenute nel 1702 dall&#039;Accademia di Parigi, diceva che, sebbene la gli sem­<lb></lb>brasse <emph type="italics"></emph>tres vraisemblables, pourroit n&#039;etre pas encore au grė de tout le<emph.end type="italics"></emph.end><pb xlink:href="020/01/2260.jpg" pagenum="503"></pb><emph type="italics"></emph>monde.<emph.end type="italics"></emph.end> Giacomo Bernoulli infatti dirigeva, sotto il dì 12 Marzo 1705, a quella <lb></lb>medesima Accademia una lettera, nella quale, dopo avere accennato alle <lb></lb>nuove ipotesi, che il Mariotte e il Leibniz volevano sostituire alla galileiana. </s>

<s><lb></lb>soggiuge: “ Mais aucun de ces Auteurs ne considerant les corps comme <lb></lb>sujets à compression, et sur-tout leur hypothese des tensions des fibres, pro­<lb></lb>portionnelles aux forces tendantes, ne s&#039;accordant pas precisement avec la <lb></lb>Nature ” (Opera, T. II, Genevae 1744, pag. </s>

<s>978). </s></p><p type="main">

<s>Sarà pur troppo vero che le tensioni delle fibre, nello strapparsi natu­<lb></lb>ralmente i solidi, non sono proporzionali alle forze tendenti, ma è falso che <lb></lb>nessuno de&#039;due Autori commomerati non consideri i corpi come soggetti a <lb></lb>compressione, leggendosi così espressamente scritto dal Mariotte, in quel suo, <lb></lb>da noi sopra citato Discorso: “ Cela étant suppose, si DCEF (nella prece­<lb></lb>dente nostra figura 271) est un bàton quarré fiché dans un mur, on peut <lb></lb>concevoir que depuis D jusqu&#039;a I, qui est la moitié de l&#039;epaisseur DC, les <lb></lb>parties se pressent par le poids G: celle, qui sont proches de D, davantage <lb></lb>que celles vers I; et que depuis I jusques a C, elles s&#039;etendent ” (Oeu­<lb></lb>vres cit. </s>

<s>pag. </s>

<s>465). </s></p><p type="main">

<s>Tale è l&#039;espresso concetto del Mariotte, benchè pochi sian per conce­<lb></lb>dergli che il punto della distinzion tra le fibre stirate e le compresse sia <lb></lb>nella precisa metà della grossezza DC del bastone; e tanto meno sien di­<lb></lb>sposti a concedere quel che il Mariotte stesso soggiunge e ammette come <lb></lb>verosimile, che cioè “ ces pressemens resistent autant que les extensions, <lb></lb>et qu&#039;il faut un mème poids pour les faire ” (ivi). </s></p><p type="main">

<s>Ora, in correggere specialmente la prima di queste ipotesi, tutt&#039;altro <lb></lb>che verosimile, consiste il merito e la novità della <emph type="italics"></emph>Veritable hypothese de <lb></lb>la resistance des solides,<emph.end type="italics"></emph.end> come al Bernoulli stesso udiremo confessar tra <lb></lb>poco, nel concludere il suo discorso, il quale piglia valore dal suppor che <lb></lb>sia medesimo l&#039;effetto della rottura, e sia uguale la forza necessaria, tanto <lb></lb>a portar la trave BD (fig. </s>

<s>273) con la sua base da AB in AF, facendola gi­<lb></lb>rar sul sostegno A, quanto a farla indietreggiare in GF, strisciandola sullo <lb></lb><figure id="id.020.01.2260.1.jpg" xlink:href="020/01/2260/1.jpg"></figure></s></p><p type="caption">

<s>Figura 273<lb></lb>stesso sostegno, cosicchè, nel triangolo BSF, <lb></lb>sian comprese tutte le fibre stirate, e nel <lb></lb>triangolo GSA tutte le fibre compresse. </s>

<s>Die­<lb></lb>tro la quale ipotesi dimostra il Bernoulli che <lb></lb>la forza di produr tali effetti di compres­<lb></lb>sione e di distrazione è quella medesima, <lb></lb>che potrebbe estendere le fibre tutte in­<lb></lb>sieme comprese nel triangolo BAF, o com­<lb></lb>primere tutte le altre, comprese nel trian­<lb></lb>golo GAF, ciò ch&#039;egli fa nel IV lemma, così propriamente da lui formu­<lb></lb>lato: “ La mème force, qui fait plier une poutre ou perche ABCD de AB <lb></lb>en GF, en etendant une partie de ses fibres de la quantité du triangle <lb></lb>BSF, et comprimant l&#039;autre de la quantité du triangle ASG; seroit capable <lb></lb>d&#039;ètendre l&#039;assemblage de toutes les fibres sur l&#039;apui A de la qnantitè du <pb xlink:href="020/01/2261.jpg" pagenum="504"></pb>triangle ABF, ou bien de comprimer cet assemblage sur l&#039;apui B ou F de <lb></lb>la quantité du triangle BAG, ou FAG ” (Opera cit., pag. </s>

<s>982). </s></p><p type="main">

<s>In virtù di questo Lemma si scioglie dal Bernoulli stesso, con l&#039;aiuto <lb></lb>dell&#039;analisi infinitesimale, il primo dei due problemi da lui promessi in prin­<lb></lb>cipio della sua Lettera, concludendo che la forza, sufficiente a rompere a <lb></lb>diritto la trave, sta a quella, necessaria per romperla a traverso, come la <lb></lb>lunghezza AD sta a una quarta proporzionale, che è sempre minore della <lb></lb>terza parte della grossezza AB. “ Ce qui s&#039;accorde avec les experiences de <lb></lb>mr. </s>

<s>Mariotte, qu&#039;a toujours trouvé cette quantité moindre que le tiers, et <lb></lb>plus grande que le quart de la l auteur AB ” (ivi, pag. </s>

<s>988). </s></p><p type="main">

<s>Sarebbe l&#039;opera del Bernoulli riuscita proficua, quando i fondamenti, <lb></lb>posti a quella sua analisi, fossero andati esenti da tutte le più giudiziose <lb></lb>censure. </s>

<s>Ma insorsero il Bullinger e il Parent, i quali opposero, fra le altre <lb></lb>cose, che sebben sia lo stesso, geometricamente parlando o rispetto alla sem­<lb></lb>plice situazione, il considerar la testata della trave, prima trasferita in AF <lb></lb>e poi in GF, o il considerarla come portata a un tratto in GF; non è però <lb></lb>vero che possa la medesima forza indifferentemente operare o l&#039;uno o l&#039;al­<lb></lb>tro effetto. </s>

<s>Conclusero perciò i due savi e valorosi Censori che la soluzione <lb></lb>del difficile problema era da sperar, non dall&#039;analisi, ma dalla esperienza. </s></p><p type="main">

<s>Fu questa via, tra&#039;Nostri, dop&#039;essersi lungamente intrattenuto in eser­<lb></lb>citaziani geometriche, e in speculazioni loquaci, approvata e proposta agli <lb></lb>studiosi, in fine alle <emph type="italics"></emph>Istituzioni<emph.end type="italics"></emph.end> meccaniche, dal Grandi, quand&#039;una delle <lb></lb>principali questioni, ch&#039;egli ebbe col Marchetti, parve che decisamente ve­<lb></lb>nisse a risolversi dall&#039;esperienze, fatte in Padova dal Poleni. </s>

<s>Si rammemo­<lb></lb>reranno i nostri Lettori che, nella proposizione III del secondo libro <emph type="italics"></emph>De re­<lb></lb>sistentia solidorum,<emph.end type="italics"></emph.end> professava l&#039;Autore essere la resistenza del prisma <lb></lb>appoggiato ai due estremi doppia della resistenza del medesimo prisma af­<lb></lb>fisso a una parete: contro la qual supposizione, fatta prima da Galileo, il <lb></lb>Grandi, animato dal De-la-Hire, prese a dimostrar che, non doppia era la <lb></lb>detta resistenza, ma quadrupla, e secondo alcuni calcoli anche ottupla del­<lb></lb>l&#039;altra. </s>

<s>Or perchè non poteva la mente desiderosa del vero assoluto acquie­<lb></lb>tarsi in tali incertezze, volle il Poleni esaminare i fatti, e sperimentando sopra <lb></lb>un prisma di abete, e sopra varii cilindri di cera e di vetro, raccolse da <lb></lb>queste sue esperienze, come il Grandi stesso riferisce nelle <emph type="italics"></emph>Istituzioni<emph.end type="italics"></emph.end> ci­<lb></lb>tate, che <emph type="italics"></emph>la proporzione dei pesi, ne&#039;casi supposti, è sempre vicina alla <lb></lb>proporzione di uno a quattro<emph.end type="italics"></emph.end> (Firenze 1739, pag. </s>

<s>160). </s></p><p type="main">

<s>Nel medesimo tempo o poco prima Pietro van Musschenbroek istituiva <lb></lb>in Olanda esperienze simili a quelle del nostro Poleni, costruendo perciò <lb></lb>una Macchina particolare. </s>

<s>Anzi, tanto sentì il Professore ultraiettino la ne­<lb></lb>cessità dell&#039;argomento, che tutto volle percorrere il campo della nuova <lb></lb>Scienza galileiana, intorno alla quale scrisse, e pubblicò in Leida nel 1699 <lb></lb>una elaboratissima dissertazione intitolata <emph type="italics"></emph>Introductio ad cohaerentiam cor­<lb></lb>porum firmorum.<emph.end type="italics"></emph.end> Concede che sia una tal coerenza dovuta all&#039;attrazione <lb></lb>molecolare, ma in che consista, e da che dipenda una tal misteriosa forza <pb xlink:href="020/01/2262.jpg" pagenum="505"></pb>attrattiva non trova che sia detto da quella nuova Filosofia, della quale esplica <lb></lb>le dottrine, che specialmente si leggono ne&#039;dialoghi di Galileo, ne&#039;discorsi <lb></lb>idraulici del Mariotte, e nelle scritture accademiche del Leibniz e del Ber­<lb></lb>noulli. </s>

<s>E giacchè egli pur conviene con i tre ultimi Autori commemorati <lb></lb>che tutti i corpi sono più o meno flessibili, “ quaenam proportio aut pro­<lb></lb>portiones, essendo così poi domanda, erunt inter cohaerentiam absolutam <lb></lb>et respectivam? </s>

<s>” (pag. </s>

<s>528). Il Mariotte, soggiunge, ritrovò quella propor­<lb></lb>zione essere di tre o di quattro a uno, nè si può negare che talvolta non <lb></lb>sia così, come ci risultò da varii nostri esperimenti, “ verum plurimas alias <lb></lb>proportiones dari etiam ex illis constabit, et quidem aliquando esse ut 8 <lb></lb>ad 1: immo omnes intermedias inter 3 ad 1, et 18 ad 1 obtinere, quod <lb></lb>probat Mariotti assertum non esse universale ” (ibid). </s></p><p type="main">

<s>Nè si confidi, prosegue a dire il Musschenbroek, di aver nulla di uni­<lb></lb>versale asserito ne&#039;suoi teoremi il Leibniz, perchè, sebben sia vero talvolta <lb></lb>che gli allungamenti delle fibre son proporzionali alle forze traenti, per lo <lb></lb>più si osserva che, moltiplicandosi i pesi non si moltiplicano a proporzion <lb></lb>le estensioni, come si vede per la seguente esperienza. </s>

<s>Presa una corda da <lb></lb>violino, lunga tre piedi, si fece tirar da pesi ora di 2, ora di 4, di 6, e di <lb></lb>otto libbre, e si osservò essere i respettivì allungamenti 9, 17, 23, 27 linee, <lb></lb>mentre dovevano essere 9, 18, 27, 36 linee, se fosse stata vera l&#039;ipotesi <lb></lb>leibniziana delle forze proporzionali alle tensioni (ivi, pag. </s>

<s>530). </s></p><p type="main">

<s>“ Sequitur ex his, ne conclude l&#039;Autore, non dari in Natura unam re­<lb></lb>gulam universalem exponentem proportionem eamdem inter cohaerentiam <lb></lb>respectivam et absolutam, qualem Geometrae dare annisi sunt, cum diver­<lb></lb>sissima esse debeat proportio pro varia corporum flexibilitate, quemadmo­<lb></lb>dum revera experientia evincit. </s>

<s>Si Philosophi, antequam operam huic doctri­<lb></lb>nae navassent, prius plurima tentamina accurata instituissent, multis peper­<lb></lb>cissent laboribus, neque unquam uni universali regulae incubuissent. </s>

<s>Quot <lb></lb>enim fere diversa corpora dantur, totidem diversae proportiones inter cohae­<lb></lb>rentiam absolutam et respectivam deprehenduntur ” (ibid., pag. </s>

<s>534). A <lb></lb>questa diversità di proporzioni corrispondevano quelle, che il Viviani chia­<lb></lb>mava <emph type="italics"></emph>tariffe,<emph.end type="italics"></emph.end> ond&#039;è notabile che, nella sentenza approvata oramai da tutti i <lb></lb>Fisici e da tutti i Matematici, dopo tanti pericoli fatti, si riscontrassero, nel <lb></lb>mezzo e nel principio del faticoso cammino di quasi due secoli, l&#039;olandese <lb></lb>Alunno del Newton, e il fiorentino Discepolo di Galileo. </s></p><pb xlink:href="020/01/2263.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>De&#039;proietti<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Di ciò che specularono il Tariaglia, il Cardano e il Benedetti, e come fossero, sui principii del se­<lb></lb>colo XVII, promosse da Guidubaldo del Monte quelle speculazioni. </s>

<s>— II. </s>

<s>De progressi fatti da <lb></lb>Galileo: com&#039;ei credesse la linea descritta dai proietti esser, nella sua parte curva, circolare. </s>

<s><lb></lb>e come primo il Cavalieri la dimostrasse parabolica. </s>

<s>— III. </s>

<s>Della prima parte del quarto Dia­<lb></lb>logo galileiano; ossia della misura degl&#039;impeti in ciascun punto della parabola. </s>

<s>— IV. </s>

<s>Della <lb></lb>seconda e terza parte del trattato galileiano; ossia della massima ampiezza dei tiri a mezza <lb></lb>squadra, e della costruzione delle Tavole ballistiche. </s>

<s>— V. </s>

<s>Delle difficoltà mosse contro la teo­<lb></lb>ria del moto parabolico, e di alcune esperienze istituite per confrantarle co&#039;teoremi di questa <lb></lb>nuova Scienza. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nel trattato Delle resistenze consisteva l&#039;altra Scienza nuova, che s&#039;isti­<lb></lb>tuiva da Galileo, dopo quella Dei moti locali, e noi ne abbiamo voluto di­<lb></lb>scorrere nella nostra Storia, con ordine diverso da quello che tenne ne&#039;suoi <lb></lb>dialoghi l&#039;Autore, ma che meglio si conforma coi tempi, e con l&#039;origine delle <lb></lb>speculazioni. </s>

<s>Vedemmo infatti come fossero, nel 1604, già posti al trattato <lb></lb><emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> i fondamenti, mentre solamente cinque anni dopo s&#039;incomincia ad <lb></lb>aver le prime notizie delle proposizioni dimostrate intorno al resistere dei <lb></lb>corpi duri. </s></p><p type="main">

<s>Si comprendono nella general denominazione di moti i così detti natu­<lb></lb>rali e i violenti, i quali hanno nei detti dialeghi un discorso distinto sì, ma <lb></lb>nella successione non interrotto, e da Galileo composto con tale artificio, da <lb></lb>parer che la Scienza dei gravi naturalmente cadenti fosse nata a un parto <lb></lb>con quella de&#039;proietti. </s>

<s>Venuti alla luce i tre dialoghi tutti insieme, il pub­<lb></lb>blico, che con tanto applauso gli accolse, non si curò di sapere come si con­<lb></lb>cepisse, o secondo qual ordine si svolgessero gli organi al nuovo parto ma­<lb></lb>raviglioso, e fu perciò facilmente creduto dai Lettori quel che più premeva <lb></lb>all&#039;Autor di far credere, che cioè nei foglietti, recati seco dal Salviati per <lb></lb>leggerli nella terza e nella quarta Giornata agl&#039;interlocutori, fossero scritti <pb xlink:href="020/01/2264.jpg" pagenum="507"></pb>insieme i teoremi dimostrativi delle proprietà dei moti naturali, e dei vio­<lb></lb>lenti: ond&#039;essendo propriamente la scienza di questi incominciata dalla di­<lb></lb>mostrazione delle traiettorie paraboliche, si veniva destramente a insinuare <lb></lb>che anche una tale dimostrazione facesse parte delle dottrine più antiche, <lb></lb>comprese nel trattato Dei moti locali. </s>

<s>Dai fatti diligentemente esaminati però <lb></lb>si scopre che i teoremi, per i quali si veniva a far della manuale arte bal­<lb></lb>listica una terza Scienza nuova, non occorsero al pensiero di Galileo che <lb></lb>in sugli ultimi anni della sua vita scientifica, a appariscono ne&#039;suoi libri <lb></lb>come improvvisi raggi di sol vespertino, che sia rimasto tutto il di nuvoloso. </s>

<s><lb></lb>Ma perchè, per essere un frutto serotino, non vuol dire perciò che sia di­<lb></lb>fettoso, e suole anzi di più acquistare di pregio, rimarrebbe l&#039;industria usata <lb></lb>da Galileo per farlo apparir primaticcio un mistero, se non ci fosse rivelato <lb></lb>dalla storia, che siam per narrare, e che insomma si riduce tutta e procede <lb></lb>dalla scoperta delle Traiettorie paraboliche. </s></p><p type="main">

<s>In qual difetto si rimanesse intorno a ciò la Scienza del moto, la quale <lb></lb>aveva pure tant&#039;oltre progredito, sulla fine del secolo XV, per gl&#039;impulsi <lb></lb>avuti da Ciordano Nemorario; si mostra con l&#039;esempio di Leonardo da Vinci, <lb></lb>le dottrine del quale intorno ai proietti sono oramai note ai nostri Lettori, <lb></lb>cosicchè, nel 1537, ebbe <gap></gap>n secolo prima di Galileo ogni ragione il Tarta­<lb></lb>glia d&#039;intitolare il suo libro <emph type="italics"></emph>Scientia nuova.<emph.end type="italics"></emph.end> Le proposizioni però, che qui <lb></lb>concernono le traiettorie, sono false nella loro radice, concludendosi nella <lb></lb>quinta del primo libro, così formulata: “ Niun corpo egualmente grave può <lb></lb>andare per alcun spacio di tempo, over di luoco, di moto naturale e violente <lb></lb>insieme misto ” (Vinegia 1537, fol. </s>

<s>15 a tergo). Scende questa dalla prima <lb></lb>difettosa, e dalla terza, manifestamente falsa nell&#039;asserire che “ quanto più <lb></lb>un corpo egualmente grave se andara luntanando dal suo principio, over <lb></lb>proprinquando al suo fine nel moto violente, tanto più andarà pigro e tardo ” <lb></lb>(ivi, fol. </s>

<s>13 a tergo). </s></p><p type="main">

<s>S&#039;incontra nonostante al primo aprire del libro, nell&#039;Epistola dedica­<lb></lb>toria a Francesco Maria Della Rovere, duca di Urbino, una vera novità, la <lb></lb>promessa dimostrazione scientifica della quale apparisce meravigliosa, che <lb></lb>cioè, <emph type="italics"></emph>per mettere a segno un pezzo de artiglieria, al più che può tirare, <lb></lb>bisognava che la bocca del pezzo stesse ellevata talmente, che guardasse <lb></lb>rettamente a 45 gradi sopra al orizonte<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>3). </s></p><p type="main">

<s>Narra il Tartaglia come, a lui di queste cose inesperto, fosse proposto <lb></lb>il problema da un cordiale amico suo, <emph type="italics"></emph>peritissimo bombardiere in Castel <lb></lb>vecchio,<emph.end type="italics"></emph.end> e come gli occorresse in tale occasione, per aggiustare l&#039;inclina­<lb></lb>zione del pezzo, d&#039;inventare una Squadra di legno “ over di alcun metallo <lb></lb>(come l&#039;Autore stesso ce la descrive nel suo <emph type="italics"></emph>Primo quesito<emph.end type="italics"></emph.end>) fatta con di­<lb></lb>ligentia, la quale ha interchiuso uno quadrante, cioè una quarta parte dun <lb></lb>cerchio, e tutto quel spacio vol esser diviso prima in 12 parti equali, e que­<lb></lb>ste 12 parti li chiamaremo ponti. </s>

<s>Anchora cadauna di queste tai parti over <lb></lb>ponti vol esser anchora divisa in altre 12 parti equali, le qual parti chia­<lb></lb>maremo menuti, e questi menuti si segnano con lineete alquanto più corte <pb xlink:href="020/01/2265.jpg" pagenum="508"></pb>di quelle delli ponti. </s>

<s>Fatto questo bisogna ficare uno pironcino di ferro, over <lb></lb>di ottone, precisamente nel centro del quadrante, e a quel tal pironcino attac­<lb></lb>carvi uno perpendicolo girabile, cioè uno fil di seta o daltro con un piom­<lb></lb>bino da capo ” (Quesiti et Inventioni, Venetia 1546, fol. </s>

<s>5). </s></p><p type="main">

<s>Di un tale strumento, il quale <emph type="italics"></emph>già più di cent&#039;anni,<emph.end type="italics"></emph.end> scriveva nel 1641 <lb></lb>il Torricelli a pag. </s>

<s>227 della prima parte delle Opere geometriche, <emph type="italics"></emph>è stato <lb></lb>in uso, ed è ancora l&#039;unico regolatore dei Bombardieri,<emph.end type="italics"></emph.end> si servi il Tarta­<lb></lb>glia per eseguir l&#039;esperienza del massimo tiro, che mostrò, contro la comune <lb></lb>opinione, avvenir veramente allora quando, infilata la più lunga delle due <lb></lb>gambe della Squadra nella bocca del cannone, il perpendicolo batteva nel <lb></lb>sesto punto. </s>

<s>Confermavano dunque i fatti quel che, dice il Tartaglia stesso <lb></lb>al Duca d&#039;Urbino, <emph type="italics"></emph>dimostrai con ragioni naturale et geometrice, di poi che <lb></lb>hebbi ben masticata e ruminata tal materia,<emph.end type="italics"></emph.end> le quali ragioni naturali e <lb></lb>geometriche sono esposte nel secondo libro, alla VIII proposizione che dice: <lb></lb>“ Se una medema possansa eiettara, over tirara corpi egualmente gravi si­<lb></lb>mili et eguali in diversi modi violentemente per aere. </s>

<s>Quello che farà il suo <lb></lb>transito elevato a 45 gradi sopra a l&#039;orizonte fara etiam il suo effetto più <lb></lb>lontan dal suo principio sopra il pian dell&#039;orizzonte, che in qualunque altro <lb></lb>modo elevato ” (Scientia n. </s>

<s>cit., fol. </s>

<s>27 a tergo). </s></p><p type="main">

<s>Chiunque s&#039;abbatta a udire una tal proposta, per que&#039;tempi sì nuova, <lb></lb>corre curiosamente trepido a leggerno la dimostrazione, ma rimane com&#039;un <lb></lb>che sogni, e che, mentre stende le braccia all&#039;oggetto desiderato, si desta. </s>

<s><lb></lb>Le ragioni geometriche del Tartaglia consistono nel suppor che le traietto­<lb></lb>rie si compongano di moto violento schietto, in parte retto, e in parte curvo, <lb></lb>e di moto naturale lungo la tangente all&#039;estremo punto della curva: le ra­<lb></lb>gioni naturali poi si riducono a invocar l&#039;assioma che, fra due massima­<lb></lb>mente contrari, è sempre un luogo di mezzo. </s>

<s>Dietro le quali due ragioni, <lb></lb>e dietro il fatto accomodatizio che cioè il termine del moto violento nella <lb></lb>verticale è più al di sopra, e nella orizzontale più al di sotto dell&#039;orizzonte, <lb></lb>che in tutte le altre inclinazioni intermedie; così procede il Tartaglia e con­<lb></lb>clude il suo proprio discorso: </s></p><p type="main">

<s>“ Perchè evidentemente sapemo che, se un corpo egualmente grave <lb></lb>sarà eietto, over tirato violentemente per il pian de l&#039;orizzonte, quel andara <lb></lb>a terminare il suo moto violento più sotto a l&#039;orizonte, che in qualunque <lb></lb>modo elevato, ma se lo andaremo allevando pian piano sopra a l&#039;orizonte <lb></lb>per un tempo andara terminando il detto suo moto violente pur sotto a l&#039;ori­<lb></lb>zonte, ma continuando tal elevatione evidentemente sapemo che a tempo <lb></lb>terminara di sopra al detto orizonte, et poi, quanto più se andara elevando <lb></lb>tanto più andara a terminare più in alto, e finalmente, giongendo alla per­<lb></lb>pendicolare sopra al orizonte, quel terminara più in alto over più lontano <lb></lb>di sopra al detto piano del orizonte, che in qualunque modo ellevato: onde <lb></lb>seguiria, per le antecedenti propositioni over argumentationi, che gli sia una <lb></lb>ellevatione così conditionata, chel debbia far terminare precisamente in el <lb></lb>proprio piano del orizonte, la qual argumentatione essendo vera se verifi-<pb xlink:href="020/01/2266.jpg" pagenum="509"></pb>cara realmente al senso, etiam al intelletto, in quella ellevatione, che è media <lb></lb>fra quelle due massimamente contrarie in terminatione et questa ellevatione <lb></lb>media è quando il detto transito, over moto violente dun corpo egualmente <lb></lb>grave, è allevato alli 45 gradi sopra al orizonte ” (ivi, fol. </s>

<s>29). </s></p><p type="main">

<s>Nessuno si crederebbe che, a determinare l&#039;inclinazione del pezzo, per <lb></lb>avere il tiro della massima volata, fosse condotto il Tartaglia da così fatto <lb></lb>strano discorso, ond&#039;è più ragionevole il pensare che indovinasse il vero, <lb></lb>argomentando piuttosto dall&#039;attenta osservazione dei fatti. </s>

<s>Basta guardare, <lb></lb>quando fanno tra loro alle sassate per le strade i monelli, che sempre get­<lb></lb>tano il sasso <emph type="italics"></emph>a mezz&#039;aria,<emph.end type="italics"></emph.end> e i più esperti così puntualmente, com&#039;avessero <lb></lb>in mano la Squadra. </s></p><p type="main">

<s>Più difficile però sembrava a indovinare dai fatti un&#039;altra verità, di­<lb></lb>pendente dalla prima scoperta, e benchè Galileo, promettendo di dimostrare <lb></lb>che sono uguali fra loro i tiri, quando le elevazioni superano o mancano <lb></lb>dalla semiretta per angoli uguali, dicesse ciò <emph type="italics"></emph>forse per l&#039;esperienza non è <lb></lb>stato osservato<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 251), il Tartaglia, non per osservazioni sperimen­<lb></lb>tali, ma per ragioni evidentissime asserisce, innanzi al Duca di Urbino, di <lb></lb>aver concluso questo medesimo, cent&#039;anni prima che venisse a concluderlo <lb></lb>Galileo col suo discorso dimostrativo. </s>

<s>“ Oltre di questo, Signor generosis­<lb></lb>simo, con ragioni evidentissime conobbi qualmente un pezzo de artiglieria <lb></lb>posseva, per due diverse vie, over ellevationi percottere in un medemo lnoco: <lb></lb>etiam trovai il modo di mandar tal cosa accadendo a essecutione: cose non <lb></lb>più audite, Signor Preclarissimo, ne d&#039;alcun altro antico ne moderno cogi­<lb></lb>tate ” (ivi, fol. </s>

<s>5 a tergo). </s></p><p type="main">

<s>Comunque sia, benchè s&#039;abbiano qui due felici divinazioni del vero, le <lb></lb>quali, in qualunque modo si vogliano interpetrare, lasciano l&#039;animo nostro <lb></lb>pieno di maraviglia; non conferivano certo a sollevare l&#039;arte del Bombar­<lb></lb>diere alla dignità di scienza: e nonostante non abbiamo in tutto il hbro del <lb></lb>Tartaglia altro che questo, che potesse poi dalla Scienza venire assunto per <lb></lb>suo soggetto. </s>

<s>Le altre parti più principali, che consistono nel definire la <lb></lb>qualità della linea descritta dal proietto, e la quantità dell&#039;impeto, non hanno <lb></lb>altro valore che di semplici supposizioni, le quali derivano la loro falsità <lb></lb>dalla viziata radice della proposizione quinta del primo libro. </s>

<s>Si suppone in­<lb></lb>fatti in secondo luogo, a scientifico fondamento del libro secondo, che “ ogni <lb></lb>transito, over moto violente de corpi egualmente gravi, che sia fuora della <lb></lb>perpendicolare de l&#039;orizonte, sempre sara in parte retto e in parte curvo, e la <lb></lb>parte curva sara parte d&#039;una circonferentia di cerchio ” (ivi, fol. </s>

<s>19 a tergo). <lb></lb>E in suppor ciò consiste tutta la scienza del Tartaglia intorno alle traiettorie. </s>

<s><lb></lb>Per quel poi riguarda le quantità degl&#039;impeti si riduce ogni scienza alla già <lb></lb>citata proposizione terza del primo libro, nella quale s&#039;insegna tanto esser <lb></lb>più debole il moto del proietto, quanto più si dilunga dal suo principio. </s></p><p type="main">

<s>Se non che manifestamente contradiceva a questa proposizione l&#039;arte <lb></lb>ballistica, principal virtù della quale è anzi quella di allungare la linea del <lb></lb>tiro, perchè faccia la palla maggior passata. </s>

<s>Si studiò per questo il Tarta-<pb xlink:href="020/01/2267.jpg" pagenum="510"></pb>glia stesso di togliere la contradizione nel secondo dialogo del primo libro, <lb></lb>dove, proponendosi dal Duca di Urbino, interlocutore, il caso di avere a <lb></lb>battere una fortezza o con un cannone, che posto in monte tiri da vicino <lb></lb>di punto in bianco, o con un altro cannone, che tiri in direzione inclinata, <lb></lb>posto in pianura e alla stessa Fortezza più di lontano; si domanda quale <lb></lb>de&#039;due strumenti sia per fare maggiore effetto. </s></p><p type="main">

<s>Il Duca, secondo i supposti principii, e secondo ciò che appariva per <lb></lb>ragion naturale, non penava a credere ch&#039;essendo l&#039;artiglieria sul monte più <lb></lb>vicina alla fortezza <emph type="italics"></emph>la balla doveria far maggiore effetto in lei<emph.end type="italics"></emph.end> ma Niccolò <lb></lb><figure id="id.020.01.2267.1.jpg" xlink:href="020/01/2267/1.jpg"></figure></s></p><p type="caption">

<s>Figura 274<lb></lb>risponde esser tutto il contrario, come <lb></lb>troppo ben sanno gli stessi Bombar­<lb></lb>dieri: sembrava però strano a credere <lb></lb>al Duca che una medesima palla sia, <lb></lb>con la medesima carica, spinta più vi­<lb></lb>gorosamente in alto e lontano, che in <lb></lb>piano e vicino, per cui Niccolò cerca di <lb></lb>soddisfarlo, ricorrendo alla Scienza dei <lb></lb>pesi, per la quale si vede che, stando <lb></lb>una Libbra a livello, si abbassa molto <lb></lb>più in ugual declinazione ch&#039;essendo <lb></lb>elevata. </s>

<s>Così per esempio, declinando <lb></lb>la libbra AB (fig. </s>

<s>274) dalla posizione <lb></lb>orizzontale AB per l&#039;angolo AOC, si <lb></lb>abbassa della quantità OE, mentre declinando dalla posizione verticale FI, <lb></lb>per un angolo FOG, uguale ad AOC, si abbassa solo quanto FH, molto <lb></lb>minore di OE. </s></p><p type="main">

<s>“ Voglio inferir per questo (risponde Niccolò al Duca, che non vedeva <lb></lb>dove fosse per riuscire il discorso) che ogni artegliaria essendo alivellata, la <lb></lb>se intende esser nel sito della equalità, e la balla, tirata da quella in tal <lb></lb>sito, usce del pezzo più grave, che in qualunque altro modo ellevata, over <lb></lb>separata da quel sito della equalità, per le ragioni di sopra adutte, e però <lb></lb>in tal sito la balla va con più difficoltà, e molto più presto comincia a de­<lb></lb>clinar al basso, cioè verso terra, et in maggior quantità lei va declinando, <lb></lb>che in qualunque modo ellevata, cioè che lei va, come fra bombardieri si <lb></lb>dice, molto manco per linea retta, che in qualunque altro modo ellevata, e <lb></lb>però li effetti di tiri fatti in tal sito saranno men vigorosi, over di meno ef­<lb></lb>fetto che in qualunque altro verso ” (Quesiti et inventioni cit., fol. </s>

<s>9 a tergo). </s></p><p type="main">

<s>Si puo dalle cose fin qui esposte argomentar che poco o nulla promosse <lb></lb>il Tartaglia la Scienza dei proietti, lasciata quasi intatta ai suoi successori, <lb></lb>alle speculazioni dei quali egli propriamente il primo veniva a proporre una <lb></lb><emph type="italics"></emph>Scientia nuova.<emph.end type="italics"></emph.end> Ma per investigare con la speranza di qualche buona riu­<lb></lb>scita le proprietà del moto violento si comprendeva come bisognasse prima <lb></lb>definirne la natura, intorno a che esso Tartaglia, non avendo insegnato nulla <lb></lb>di nuovo, lasciava con gli errori di Aristotile a combatter gl&#039;ingegni. </s></p><pb xlink:href="020/01/2268.jpg" pagenum="511"></pb><p type="main">

<s>Fu de&#039;primi il Cardano a mostrar con ragioni, che non superavano la <lb></lb>capacità del senso comune, quanto fosse falso quel che insegna il Filosofo <lb></lb>della freccia che o lungi o presso alla corda si move al moto dell&#039;aria che <lb></lb>la circonda, e approvando per verissimo detto che <emph type="italics"></emph>omne quod movetur ab <lb></lb>aliquo movetur,<emph.end type="italics"></emph.end> soggiunge: “ sed illud quod movet est impetus acquisi­<lb></lb>tus, sicut calor in aqua, qui est ibi praeter naturam ab igne inductus, et <lb></lb>tamen, igne sublato, manum tangentis exurit, et ideo et accidens violenter <lb></lb>adhaerens vim suam retinet ” (De subtilitate, Lugduni 1580, pag. </s>

<s>93). </s></p><p type="main">

<s>Giulio Cesare Scaligero, entrato col Cardano in gara di sottilizzare d&#039;in­<lb></lb>gegno, diceva che, a mostrar la futilità delle ragioni di Aristotile, non era <lb></lb>argomento migliore di un&#039;esperienza da lui stesso così descritta: Abbiasi <lb></lb><figure id="id.020.01.2268.1.jpg" xlink:href="020/01/2268/1.jpg"></figure></s></p><p type="caption">

<s>Figura 275<lb></lb>una levigatissima tavola, nella quale <lb></lb>s&#039;incida col tornio una ruzzola, a cui <lb></lb>si dian le mosse per via di un ma­<lb></lb>nubrio che, sostenuto esso stesso da <lb></lb>due forcelle, la sostenga: vedrai ma­<lb></lb>nifestamente essa ruzzola seguitare a <lb></lb>moversi in giro, benchè non mossa <lb></lb>dall&#039;aria. </s>

<s>“ A tabula (fig. </s>

<s>275) B or­<lb></lb>bis, C, C vectis, D manubrium, F, F <lb></lb>furcellae. </s>

<s>Non enim tunc in motu cir­<lb></lb>culari locus erit aeri impellenti. </s>

<s>Jam <lb></lb>ipse aer inter orbem ac tabulam adeo exiguus, ut nullas vires ad fictum <lb></lb>illum motum sit habiturus. </s>

<s>Et ipsius orbis politisima levitas neutiquam a <lb></lb>circumstante aere agitationis instigationem recipere poterit ” (Adversus Car­<lb></lb>danum, Exercitationes, Francofurti 1592, pag. </s>

<s>130). </s></p><p type="main">

<s>Ma più efficaci di tutti, a restaurare il vero sopra i demoliti errori ari­<lb></lb>stotelici, furono gl&#039;insegnamenti del Benedetti, sentenziosamente raccolti in <lb></lb>queste parole scritte in una di quelle Epistole, che sulla fine del secolo XVI <lb></lb>erano il più gradito pascolo de&#039;matematici studiosi: “ Omne corpus grave, <lb></lb>aut sui natura aut vi motum, in se recipit impressionem aut impetum mo­<lb></lb>tus, ita ut, separatum a virtute movente per aliquod temporis spatium, ex <lb></lb>seipso moveatur ” (Speculat., lib. </s>

<s>cit., pag. </s>

<s>286, 87). Cosicchè Galileo, che <lb></lb>ne&#039;suoi Dialoghi e negli scritti minori spende, a dimostrare <emph type="italics"></emph>a quo movean­<lb></lb>tur proiecta,<emph.end type="italics"></emph.end> così lunghi discorsi, niente altro fa che confermar le dottrine, <lb></lb>ripetendo bene spesso glì argomenti medesimi de&#039;suoi predecessori. </s></p><p type="main">

<s>Aperta così alla Scienza la prima entrata al vero, col definir la natura <lb></lb>del moto violento, fu possibile al Cardano e al Benedetti farvi anche qual­<lb></lb>che progresso, di cui vanno principalmente debitori i due valent&#039;uomini al­<lb></lb>l&#039;avere scoperta la gran fallacia, che ascondevasi nella proposizione quinta <lb></lb>del primo libro della <emph type="italics"></emph>Scientia nuova,<emph.end type="italics"></emph.end> dove afferma l&#039;Autore non poter al­<lb></lb>cun grave andare per alcun tempo di moto misto tutt&#039;insieme di naturale <lb></lb>e di violento. </s>

<s>Nè per vero dire ad avvedersi della falsità di una tale propo­<lb></lb>sta ci bisognava troppo grande sagacia, contradicendosi manifestamente que-<pb xlink:href="020/01/2269.jpg" pagenum="512"></pb>sta con ciò che supponesi nel secondo libro, dove si dice: “ Niun transito, <lb></lb>over moto violente d&#039;un corpo egualmente grave, che sia fuor della per­<lb></lb>pendicolare del orizonte, mai puol havere alcuna parte, che sia perfetta­<lb></lb>mente retta, per causa della gravità che se ritruova in quel tal corpo, la <lb></lb>quale continuamente lo va stimulando e tirando verso il centro del mondo ” <lb></lb>(fol. </s>

<s>19 a tergo). Se dunque la gravità non abbandona mai il proietto, con­<lb></lb>tinuamente tirandolo verso il centro del mondo, e se in ciò consiste il moto <lb></lb>suo naturale, mal si dichiara dal Tartaglia esser, nel principio della traiet­<lb></lb>toria <emph type="italics"></emph>insensibilmente curva,<emph.end type="italics"></emph.end> quel moto violento puro. </s>

<s>“ Sed si dixisset ipse, <lb></lb>soggiungo il Benedetti, illum motum esse purum naturalem, hoc esset fal­<lb></lb>sum, eo quod purus naturalis motus alicuius corporis non impediti, extra <lb></lb>locum suum, sit per lineam rectam et non per curvam ” (Specul., lib. </s>

<s>cit., <lb></lb>pag. </s>

<s>365). </s></p><p type="main">

<s>Il Cardano si salvò provvidamente dall&#039;errore, professando le dottrine <lb></lb>aristoteliche dei moti misti, dai quali insieme, secondo lui, resulta la parte <lb></lb>curva della traiettoria, che non è circolare, come volle dire il Tartaglia, ma <lb></lb><figure id="id.020.01.2269.1.jpg" xlink:href="020/01/2269/1.jpg"></figure></s></p><p type="caption">

<s>Figura 276<lb></lb>sì piuttosto somigliantissima alla Parabola. </s>

<s>“ Cum <lb></lb>vero pila ad supremam rectam pervenerit, non per <lb></lb>circulum, nec recta rursum illic descendit, sed <lb></lb>media quasi linea, quae Parabolae ferme imitatur <lb></lb>circumambientem lineam, ut BC (fig. </s>

<s>276) est. </s>

<s>De­<lb></lb>mum, ex C in D, motu gravis recti ad unguem. </s>

<s><lb></lb>Quae igitur proiiciuntur tribus ex motibus con­<lb></lb>stant: primo, violento, ultimo exquisite naturali, <lb></lb>et medio ex utroque mixto. </s>

<s>Propter tam multipli­<lb></lb>cem motus rationem metiri ad unguem talia plane est impossibile ” (De su­<lb></lb>btil. </s>

<s>cit., pag. </s>

<s>96). </s></p><p type="main">

<s>E veramente impossibile era la cosa a que&#039;tempi, in cui del moto na­<lb></lb>turale e del violento s&#039;ignoravano le leggi, per cui, nel ravvisare ad occhio <lb></lb>una somiglianza tra la linea descritta dai proietti e la parabola, s&#039;arrestava. </s>

<s><lb></lb>per quanto nuovo e inaspettato apparisse, di queste cardaniche speculazioni <lb></lb>ogni progresso. </s>

<s>Per quella medesima difficoltà di misurare <emph type="italics"></emph>ad unguem<emph.end type="italics"></emph.end> le <lb></lb>traiettorie, riusciva pure impossibile di determinarne nei vari punti le quan­<lb></lb>tità degl&#039;impeti respettivi, ond&#039;è che non seppe il Cardano far altro che <lb></lb>ripetere l&#039;opinion di Aristotile, “ qui dixit motum naturalem in fine, vio­<lb></lb>lentum in principio, proiectorum in medio fieri velociorem ” (De subtil. </s>

<s>cit., <lb></lb>pag. </s>

<s>94). </s></p><p type="main">

<s>Il Benedetti stesso, benchè riconoscesse falsa l&#039;applicazione de&#039;princi­<lb></lb>pii statici della Libbra, fatta dal Tartaglia nel suo secondo Quesito, non <lb></lb>seppe però sostituirvi un&#039;altra dottrina, che sentisse meglio del vero. </s>

<s>Era <lb></lb>facile avvedersi ch&#039;essendo la libbra G, nella nostra figura 274 qui poco <lb></lb>addietro, nelle condizioni della libbra L, ne seguirebbe che ugualmente va­<lb></lb>lido fosse il colpo della bombarda elevata o depressa sotto l&#039;orizzonte per <lb></lb>angoli uguali: <emph type="italics"></emph>id quod non ita se habet.<emph.end type="italics"></emph.end> Ma la vera causa per cui la bom-<pb xlink:href="020/01/2270.jpg" pagenum="513"></pb>barda elevata fa più valido il colpo, soggiunge tosto il Benedetti, si riduce <lb></lb>principalmente a ciò che, con tanto maggior forza si muove un corpo, quanto <lb></lb>più ne raccoglie in sè resistendo per più lungo tempo alla virtù movente. <lb></lb></s>

<s>“ Atque hoc supradictis ictibus elevatis accidit, quia gravitas pilae ea est, <lb></lb>quae resistens virtuti moventi dat ei commoditatem colligendi, dictam vir­<lb></lb>tutem, multo magis quam esset ea, quae ad depressiorem elevationem eam <lb></lb>impelleret ” (Speculat., lib. </s>

<s>cit., pag. </s>

<s>258). </s></p><p type="main">

<s>Non rivolse il Benedetti sopr&#039;altre parti dell&#039;argomento le sue specu­<lb></lb>lazioni, ma pure egli aveva col Cardano recato non piccolo giovamento alla <lb></lb>Scienza, liberandola dai più dannosi errori del Tartaglia. </s>

<s>Ma come per lo <lb></lb>più avviene che i primi abiti si dismettono, almeno in parte, più difficil­<lb></lb>mente; così avvenne degl&#039;insegnamenti di quella, che appariva propriamente <lb></lb>agl&#039;ingegni una <emph type="italics"></emph>Scientia nuova.<emph.end type="italics"></emph.end> Il più notabile esempio di ciò n&#039;è offerto <lb></lb>da Galileo, sul giovanile ingegno del quale non valse l&#039;autorità del Bene­<lb></lb>detti a rimoverlo dall&#039;opinione, che non v&#039;abbia nella traiettoria mistione <lb></lb>alcuna di moto, per cui sia vero che va il proietto sempre più tardo, quanto <lb></lb>più si dilunga dal suo principio. </s>

<s>Una delle cose infatti che proponevasi di <lb></lb>dimostrar nel dialogo <emph type="italics"></emph>De motu gravium<emph.end type="italics"></emph.end> è: “ undenam accidat quod motus <lb></lb>naturalis velocior in fine quam in medio vel in principio; violentus vero ve­<lb></lb>locior in principio quam in medio, et hic quam in fine existat ” (Alb. </s>

<s>XI, 11). </s></p><p type="main">

<s>Professando poi, come il Tartaglia, che la traiettoria si compone di moto <lb></lb>puro violento, di moto circolare e di moto naturale, par che voglia Galileo <lb></lb>rispondere al Benedetti col dire che nel moto circolare non è vero che siano <lb></lb>misti insieme due moti, ma è un moto puro distinto, che non è nè natu­<lb></lb>rale nè violento. </s>

<s>Supposto che la circolazione, come de&#039;proietti avviene, si <lb></lb>faccia intorno al centro della Terra, ch&#039;egli immagina esser centro di una <lb></lb>sfera che gira, così Galileo stesso dimostra non essere nè violento nè natu­<lb></lb>rale il moto di tale sfera: “ Motus itaque naturalis est dum mobilia ince­<lb></lb>dendo ad loca propria accedunt; violentus vero est dum mobilia, quae mo­<lb></lb>ventur, a proprio loco recedunt. </s>

<s>Haec, cum ita se habeant, manifestum est <lb></lb>sphaeram supra centrum mundi circumvolutam neque naturali, neque vio­<lb></lb>lento motu moveri ” (ibid., pag. </s>

<s>65). </s></p><p type="main">

<s>Vedremo come questa giovanile opinione della linea circolare, che de­<lb></lb>scrivono i proietti, venisse per Galileo a trovare una conferma e quasi una <lb></lb>dimostrazione di fatto nel moto circolare della Terra, ma giova intanto sa­<lb></lb>pere come risolvesse l&#039;altro quesito proposto nello stesso luogo del Dialogo <lb></lb>dianzi citato, “ cur tormenta tum muralia tum manualia longius per rectam <lb></lb>lineam plumbeas sphaeras iaciunt, si eas per lineas inclinatas orizonti proii­<lb></lb>ciant, quam si per lineam eidem orizonti parallelam. </s>

<s>” </s></p><p type="main">

<s>La soluzione, dalla quale doveva dipendere ogni scienza dell&#039;arte balli­<lb></lb>stica, si legge nell&#039;altro trattato giovanile <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> e si riduce insomma <lb></lb>in attribuire il fatto a due cause. </s>

<s>La prima è quella, che vedemmo essere <lb></lb>stata assegnata già dal Benedetti, in risolvere il problema del Tartaglia <emph type="italics"></emph>De <lb></lb>ictu bombardae,<emph.end type="italics"></emph.end> e che si conclude anche per Galileo da quel principio che <pb xlink:href="020/01/2271.jpg" pagenum="514"></pb>dice “ virtutem impellentem acrius longe imprimi in eo quod magis resi­<lb></lb>stit ” (Edizion nazionale, T. I, 1890, pag. </s>

<s>337). L&#039;altra causa però è d&#039;in­<lb></lb>venzione propria, e balenandovi dentro un concetto nuovo merita di essere <lb></lb>attentamente considerata. </s></p><p type="main">

<s>Si getti il mobile A (fig. </s>

<s>277) ora per la verticale AB, ora per le obli­<lb></lb>que AC, AD, AE: la causa per cui in AB la rettitudine è maggiore che in <lb></lb>AC, in AC maggiore che in AD, e in AD maggiore che in AE, dice Gali­<lb></lb><figure id="id.020.01.2271.1.jpg" xlink:href="020/01/2271/1.jpg"></figure></s></p><p type="caption">

<s>Figura 277<lb></lb>leo, è questa: che nella direzion verticale il mobile non può <lb></lb>tornare indietro, al termine da cui si partì, che per la me­<lb></lb>desima rettitudine dell&#039;ascesa, per cui è costretto di sfogare <lb></lb>tutto il suo impeto per quella via. </s>

<s>Ma nelle direzioni obli­<lb></lb>que può tornare indietro per una via diversa, deflettendosi <lb></lb>prima di esaurir tutto per linea retta il primo impeto con­<lb></lb>ceputo. </s>

<s>E perchè questa facilità di defletter dal primo corso <lb></lb>è tanto più grande, quanto l&#039;angolo fatto dalla direzione del <lb></lb>tiro con l&#039;orizzonte è più acuto; s&#039;intende perchè, gettato <lb></lb>il mobile ora per AC, ora per AD, ora per AE, vada in <lb></lb>dirittura per tratti via via sempre minori. </s>

<s>“ Verum, si fer­<lb></lb>tur per lineam perpendicularem AB, ab ea nullo modo mobile declinare po­<lb></lb>test, nisi super eadem recedendo, ad terminum a quo recessit, accedat; hoc <lb></lb>autem, dum vivet, nunquam patietur virtus impellens. </s>

<s>Cum autem mobile <lb></lb>per lineam AC fertur, quia adhuc inclinatio, ad terminum a quo, tendit, nisi <lb></lb>valde debilitata, eam non sinet virtus motiva. </s>

<s>Cum autem fertur per AE hori­<lb></lb>zonti fere aequidistantem, potest quantumlibet cito inclinari incipere mobile; <lb></lb>inclinatio enim haec recessum a termino non impedit ” (ibid., pag. </s>

<s>339, 40). </s></p><p type="main">

<s>Si diceva che da queste galileiane speculazioni si vede balenare in volto <lb></lb>alla Scienza de&#039;proietti un concetto nuovo, il quale sarebbe poi per pigliare <lb></lb>essenza di vero, quando l&#039;impeto verticale, che ora s&#039;esaurisce nella retti­<lb></lb>tudine e nella deflessione del moto, s&#039;intenderà compartito fra lo spingere <lb></lb>in alto il mobile, e il mandarlo al largo per l&#039;orizzonte, in quelle che si <lb></lb>chiameranno <emph type="italics"></emph>altezza,<emph.end type="italics"></emph.end> e <emph type="italics"></emph>amplitudine<emph.end type="italics"></emph.end> della Parabola. </s>

<s>Prima però che questo <lb></lb>essenzial vero gli si facesse noto, persistè Galileo per quarant&#039;anni nell&#039;er­<lb></lb>rore, da cui venne non per propria ma per altrui virtù finalmente salvato. </s>

<s><lb></lb>Come questo avvenisse è ciò che ci resta a narrar di più nuovo, e anche <lb></lb>di più curioso, perchè fu Galileo stesso che, scoperte le leggi dei moti na­<lb></lb>turali, dava altrui il modo di dimostrar le leggi dei moti violenti. </s>

<s>Il primo <lb></lb>esempio del non aver saputo adoperar l&#039;argomento colui, che industriosa­<lb></lb>mente l&#039;avea fabbricato, risale a quegli anni, ne&#039;quali, dall&#039;aver supposto <lb></lb>le velocità proporzionali ai tempi riuscì a concluder che gl&#039;incrementi degli <lb></lb>spazi nel moto accelerato stanno come la serie de&#039;numeri impari, e che <emph type="italics"></emph>la <lb></lb>velocità nel moto violento va decrescendo con la medesima proporzione, <lb></lb>con la quale nella medesima linea retta cresce nel moto naturale.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Che occorressero a farsi queste scoperte verso il 1604 si provò altrove, <lb></lb>e si conferma qui da una lettera, scritta il dì 9 d&#039;Ottobre di quell&#039;anno, e <pb xlink:href="020/01/2272.jpg" pagenum="515"></pb>nella quale il Sarpi così comincia, per esporre e avere da Galileo la solu­<lb></lb>zione di un dubbio: “ Già abbiamo concluso che nessun grave può essere <lb></lb>tirato all&#039;istesso termine in su, se non con una forza, e per consequente <lb></lb>con una velocità. </s>

<s>Siamo passati, così V. S. ultimamente affermò ed inventò, <lb></lb>che per li stessi termini tornerà in giù pei quali andò in sù ” (Alb. </s>

<s>VIII, 29). </s></p><p type="main">

<s>Le medesime cose che al Sarpi furono nel tempo stesso partecipate da <lb></lb><figure id="id.020.01.2272.1.jpg" xlink:href="020/01/2272/1.jpg"></figure></s></p><p type="caption">

<s>Figura 278<lb></lb>chi le affermò e inventò a Guidubaldo del Monte, il quale, ri­<lb></lb>meditando il fatto che, spinto il mobile da A in B (fig. </s>

<s>278) <lb></lb>torna da B in A, avendo in C, D, E e in tutti gli altri punti <lb></lb>intermedi acquistata nello scender la medesima velocità, che <lb></lb>ivi ebbe nel risalire; dovette concluderne che, leggermente <lb></lb>inclinata la direzione del tiro tanto da distinguere le due vie, <lb></lb>quella FG per cui cala è simile alla AF per cui il mobile <lb></lb>monta. </s>

<s>Nè si vedeva perchè la medesima conclusione non si <lb></lb>potesse applicare al caso, in cui declinando anche di più la <lb></lb>direzione del tiro, il proietto va, come per ACE (fig. </s>

<s>279), <lb></lb>per una via più aperta. </s></p><p type="main">

<s>Imbevuto Guidubaldo delle più sane dottrine del Benedetti fu da lui <lb></lb>persuaso che, non potendo per il tratto AB la gravità abbandonare il pro­<lb></lb><figure id="id.020.01.2272.2.jpg" xlink:href="020/01/2272/2.jpg"></figure></s></p><p type="caption">

<s>Figura 279<lb></lb>ietto, nè per il tratto DE la gravità stessa essere abban­<lb></lb>donata dal primo impeto impresso, che non può tutto <lb></lb>essersi esaurito; quelle linee son ambedue curve gene­<lb></lb>rate da moto misto: ond&#039;essendo di moto misto resul­<lb></lb>tante tutta intera la traiettoria, ebbe a concluderne, <lb></lb>dietro gli avvertimenti del Cardano, che non per sola la <lb></lb>parte inflessa BCD, ma che per tutta la lunghezza ACE <lb></lb>la linea del moto si compone in modo, da rassembrare <lb></lb>una parabola. </s>

<s>E perchè il mobile per l&#039;aria non lascia di sè vestigio, Gui­<lb></lb>dubaldo stesso ricorse all&#039;ingegnoso partito di tirar sopra un piano una palla <lb></lb>tinta d&#039;inchiostro, la via disegnata dalla quale, arrovesciata e tenuta pen­<lb></lb>dula, gli pareva, con que&#039;punti interrotti pel saltellar che andando faceva la <lb></lb>palla stessa, rassomigliarsi alla sacca di una catena lentamente sospesa. </s>

<s>Gli <lb></lb>venne allora in pensiero che anche la sacca della catena risulti da un moto <lb></lb>naturale consistente nel peso degli anelli, misto al moto violento di chi la <lb></lb>tira ai due capi, è fu il primo a rassomigliare a vista la catenaria e la tra­<lb></lb>iettoria fra loro, e ambedue alla parabola. </s></p><p type="main">

<s>Questi pensieri venutisi, sul principio del secolo XVII, a svolgere dalle <lb></lb>precedenti tradizioni, e dalle nuove dottrine galileiane, segnano nella Scienza <lb></lb>de&#039;proietti un tal progresso, da non restar altro al perfezionamento di lei, <lb></lb>se non che la Geometria v&#039;apponesse il suggello del vero. </s>

<s>Dalla natura e <lb></lb>dalla qualità della curva riconosciuta veniva sicuro il modo di misurare gli <lb></lb>effetti del colpo, e nelle varie elevazioni le ragioni del tiro: ond&#039;è che ve­<lb></lb>ramente i teoremi dimostrati trent&#039;anni dopo nel terzo dialogo delle due <lb></lb>Scienze nuove si contengono, come in germe, in queste parole di Guidu-<pb xlink:href="020/01/2273.jpg" pagenum="516"></pb>baldo, che si leggono sulla fine del manoscritto di lui, pubblicato fra le Note <lb></lb>all&#039;ultimo tomo della <emph type="italics"></emph>Storia<emph.end type="italics"></emph.end> del Libri: </s></p><p type="main">

<s>“ Se si tira una palla o con una balestra o con artiglieria o con la mano <lb></lb>o con altro instrumento sopra la linea del horizonte, il medesimo viaggio <lb></lb>fa nel callar che nel montare, e la figura è quella che, rivoltata sotto la <lb></lb>linea horizontale, fa una corda che non stia tirata, essendo l&#039;un e l&#039;altro <lb></lb>composto di naturale e di violento, et è una linea in vista simile alla pa­<lb></lb>rabola.... La esperienza di questo moto si po far pigliando una palla tinta <lb></lb>d&#039;inchiostro, e tirandola sopra un piano di una tavola, il qual stia quasi <lb></lb>perpendicolare al horizonte: che se ben la palla va saltando, va però fa­<lb></lb>cendo li punti, dalli quali si vede chiaro che, siccome ella ascende, così anco <lb></lb>descende, et è così ragionevole, perchè la violentia, ch&#039;ella ha acquistata <lb></lb>nel andare in su, fa che nel callar vadi medesimamente superando il moto <lb></lb>naturale nel venire in giù: che la violentia, che superò dal B (nell&#039;ultima <lb></lb>figura) al C, conservandosi, fa che dal C al D sia uguale a CB, e descen­<lb></lb>dendo, di mano in mano perdendosi la violentia, fa che dal D al E sia uguale <lb></lb>a BA, essendo che non ci è ragione che dal C verso DE mostri che si perda <lb></lb>a fatto la violentia; che se ben va continuamente perdendo verso E, non­<lb></lb>dimeno sempre se ne resta, che è causa che verso E il peso non va mai <lb></lb>per linea retta ” (A Paris 1844, pag. </s>

<s>397, 98). </s></p><p type="main">

<s>Furono senza dubbio queste speculazioni risapute da Galileo, ma non <lb></lb>ci è riuscito ancora di sapere in che modo. </s>

<s>Disse una volta Muzio Oddi al <lb></lb>Cavalieri che esso Galileo e Guidubaldo avevano con le artiglierie fatto in­<lb></lb>sieme esperienze intorno ai proietti, ciò che deve esser dunque avvenuto <lb></lb>prima del 1607, anno in cui mori Guidubaldo. </s>

<s>Di queste pubbliche espe­<lb></lb>rienze però non abbiamo nè documento certo, nè parole che ne facciano <lb></lb>qualche cenno, e dall&#039;altra parte l&#039;esperienza riferita nella sopra addotta <lb></lb>scrittura era così semplice e così naturale, da non aver bisogno d&#039;altro aiuto <lb></lb>o testimonio. </s>

<s>Noi perciò crediamo che il manoscritto ritrovato dal Libri, o <lb></lb>nell&#039;originale o in copia, fosse, poco dopo il 1607, capitato alle mani di Ga­<lb></lb>lileo, e perchè vi sì ritrovavan dottrine di acustica, di resistenze e di moti, <lb></lb>che egli intendeva appropriarsi, non potendo, per la ragion che ne avreb­<lb></lb>bero potuto richieder coloro, i quali avesser veduto o sentito dire del Ma­<lb></lb>noscritto, tutto defraudare a Guidubaldo; per dir com&#039;egli ci entrasse di <lb></lb>mezzo dette voce che avevano sperimentato, specialmente con le artiglierie, <lb></lb>quelle cose tutt&#039;e due insieme. </s></p><p type="main">

<s>Comunque sia però delle esperienze, che sian propriamente dell&#039;Autore <lb></lb>del manoscritto le speculazioni ammirate, si prova dal fatto, che Galileo ri­<lb></lb>fiutò di esse la parte migliore, rimanendo tuttavia in dubbio intorno alla <lb></lb>qualità della linea descritta dal proietto, e inclinando molto verso la prima <lb></lb>concepita opinione che cioè, così la traiettoria come la catenaria partecipas­<lb></lb>sero la loro curvità non dalla parabola, ma sì piuttosto dal cerchio. </s>

<s>Come <lb></lb>avvenisse la subitanea conversione, e come quel Salviati, già disposto fin <lb></lb>da principio ad accogliere il risoluto problema della corda non tocca che <pb xlink:href="020/01/2274.jpg" pagenum="517"></pb>risona all&#039;unisono di un&#039;altra vibrata, e la ragion della resistenza de&#039;canapi <lb></lb>uguale in tutta la loro lunghezza; si risolvesse all&#039;ultimo di derivare altresì <lb></lb>ne&#039;suoi dialoghi, dal manoscritto di Guidubaldo, il modo di descriver mec­<lb></lb>canicamente la parabola, e di applicare ai proietti quella mistione di moto <lb></lb>naturale e di violento, che ritrovasi nella catena; lo vedremo nella seguente <lb></lb>parte del nostro discorso, dop&#039;esserci trattenuti a veder quali fossero i pro­<lb></lb>gressi, che fece Galileo speculando sopra le più approvate speculazioni dello <lb></lb>stesso Guidubaldo. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dovea fra le approvate speculazioni senza dubbio esser quella dell&#039;ugual <lb></lb>viaggio, che il proietto fa nel salire e nello scendere, e della ugual velocità, <lb></lb>che si trova ne&#039;due punti, ne&#039;quali son dalla medesima orizzontale interse­<lb></lb>cati i due rami della via, essendo tuttociò consequente come avvertimmo, <lb></lb><figure id="id.020.01.2274.1.jpg" xlink:href="020/01/2274/1.jpg"></figure></s></p><p type="caption">

<s>Figura 280<lb></lb>dallo stesso principio galileiano, <lb></lb>“ che il cadente naturale ed il <lb></lb>proietto violento passano per la <lb></lb>medesima proporzione di velo­<lb></lb>cità ” (Alb. </s>

<s>VI, 25). Così non in <lb></lb>sola la traiettoria ABC (fig. </s>

<s>280), <lb></lb>ma in tutte le altre EBF, GBH, <lb></lb>aventi la medesima altezza BO, <lb></lb>si avvererà che il cadente naturale in M e in O dovrà avere la medesima <lb></lb>proporzione di velocità che il proietto violento in N e in P, in C e in H. </s></p><p type="main">

<s>Ma qui occorse alla mente di Galileo un dubbio, che gli ragionava non <lb></lb>parer verosimile che in N e in P abbia il grave la medesima velocità, o <lb></lb>partitosi da B con moto iniziale, o partitosi dalla quiete: per gli stabiliti <lb></lb>principii dinamici infatti il cadente naturale da B, per i piani convessi BN, <lb></lb>BP, ha acquistato i medesimi gradi di velocità, che in M, come si dice avere <lb></lb>acquistato il proietto violento. </s>

<s>Quella velocità però, proseguiva a ragionar <lb></lb>Galileo, non l&#039;ha il grave acquistata, se non col tempo, il quale è propor­<lb></lb>zionato alle lunghezze dei piani BN, BP, ond&#039;ei sarebbe ragionevole il du­<lb></lb>bitar dell&#039;ugualità degl&#039;impeti, quando anche i tempi del proietto fossero <lb></lb>via via tanto più lunghi, quanto son più lunghi i descritti viaggi. </s></p><p type="main">

<s>Veniva così dunque a proporsi una nuova questione importante, che pa­<lb></lb>reva risolversi dal considerar che forse è l&#039;impeto impresso, il quale opera <lb></lb>nel proietto violento quel che nel cadente naturale opera il tempo, cosicchè <lb></lb>mentre qui gl&#039;impeti naturali in M, in N e in P son ragguagliati dai di­<lb></lb>versi tempi spesi nelle cadute, sien là invece ragguagliati dagl&#039;impeti vio­<lb></lb>lenti, che una forza straniera partecipa al mobile, rimanendosi per qualun­<lb></lb>que lunghezza di via i tempi sempre fra loro uguali. </s>

<s>Pareva insomma a <pb xlink:href="020/01/2275.jpg" pagenum="518"></pb>Galileo assai verosimile che, se fosse in B la bocca di un cannone livellato, <lb></lb>i tempi spesi a descrivere i getti BH, BF, BC dovessero essere tutti fra loro <lb></lb>uguali, e al tempo in cui la palla sarebbe giunta dallo stesso punto B in O, <lb></lb>per semplice via naturale. </s></p><p type="main">

<s>Il discorso richiedeva dalla esperienza qualche conforto, e perchè non <lb></lb>poteva una persona privata avere a sua disposizione artiglierie militari, e <lb></lb>dall&#039;altra parte non eran queste sempre nè di pronta nè di comoda osser­<lb></lb>vazione a un Filosofo, pensò di servirsi dei getti d&#039;acqua, il maggiore o <lb></lb>minore impeto dei quali s&#039;attemperava assai facilmente col crescere o col <lb></lb>diminuire l&#039;altezza del liquido nel vaso. </s>

<s>Ebbe per Galileo di qui occasione <lb></lb>una Scienza nuova, gli oscuri natalizi della quale si celebrarono nella pro­<lb></lb>posizione che i getti dell&#039;acqua, essendo il cannone livellato, giungono a terra <lb></lb>nel medesimo tempo delle gocciole naturalmente cadenti, tiratesi sotto dallo <lb></lb>stesso cannone, e che gli zampilli, da qualunque forza sian fatti, purchè <lb></lb>giungano alla medesima altezza, si spediscono tutti in tempi uguali. </s>

<s>E perchè <lb></lb>non erano questi effetti dipendenti che dalla sola gravità, non dubitò Gali­<lb></lb>leo di applicarli ai tiri delle artiglierie, compiacendosi così di avere, tra il <lb></lb>finir del 1608 e il cominciar dell&#039;anno seguente, progredito nell&#039;acquisto <lb></lb>della Scienza de&#039;proietti, e di averne fatta la prima felice applicazione alla <lb></lb>materia delle acque. </s>

<s>Tali erano infatti l&#039;espressioni della sua compiacenza, <lb></lb>quali si leggono in una lettera scritta da Padova a un Principe di casa Me­<lb></lb>dici, il dì 11 Febbraio 1609: </s></p><p type="main">

<s>“ Sono adesso intorno ad alcune questioni che mi restano intorno al <lb></lb>moto dei proietti, tra le quali molte appartengono ai tiri delle artiglierie, e <lb></lb>pure ultimamente ho ritrovata questa: che, ponendo il pezzo sopra qualche <lb></lb>luogo elevato dal piano della campagna, e appuntandolo livellato giusto, la <lb></lb>palla uscita dal pezzo, sia spinta da molta o da pochissima polvere, o anco <lb></lb>da quanto basti solamente a farla uscire dal pezzo, viene sempre declinando <lb></lb>ed abbassandosi verso terra con la medesima velocità, sicchè nello stesso <lb></lb>tempo, in tutti i tiri livellati, la palla arriva in terra e siano i tiri lontanis­<lb></lb>simi o brevissimi, oppure anco esca la palla dal pezzo solamente, e caschi <lb></lb>a piombo nel piano della campagna. </s>

<s>E l&#039;istesso occorre nei tiri elevati, li <lb></lb>quali si spediscono tutti nell&#039;istesso tempo, tuttavolta che si alzino alla me­<lb></lb>desima altezza perpendicolare.... Nella materia delle acque e degli altri <lb></lb>fluidi, parte ancor lei intatta, ho parimente scoperte grandissime proprietà <lb></lb>della Natura ” (Alb. </s>

<s>VI, 69, 70). </s></p><p type="main">

<s>Le grandissime proprietà nella natura de&#039;fluidi scoperte si riducevano <lb></lb>insomma alla sopra riferita proposizione, ma il tema delle Artiglierie si pre­<lb></lb>sentava bene assai più vasto e più importante, derivando una sua tale im­<lb></lb>portanza, non da solo avere avvertito l&#039;isocronismo delle traiettorie, ma dal­<lb></lb>l&#039;avere riconosciuta l&#039;egualità degli impeti ne&#039;due punti del loro viaggio <lb></lb>intersecato dalla medesima orizzontale. </s>

<s>Così veniva l&#039;antica arte ballistica ad <lb></lb>essere radicalmente riformata, perchè, là dove il Tartaglia aveva insegnato <lb></lb>che tanto è più debole il colpo, quanto la palla è più lontana dalla bocca <pb xlink:href="020/01/2276.jpg" pagenum="519"></pb>del cannone, e il Cardano che il maggior impeto del proietto è nel mezzo; <lb></lb>la nuova Scienza, come cosa inaspettata e quasi incredibile, rivelava che il <lb></lb>medesimo effetto fa la palla alla bocca del cannone elevato, e nel luogo più <lb></lb>lontano, dov&#039;ella batte per terra. </s></p><p type="main">

<s>Erano queste verità intravedute come in ombra o indicate per assai <lb></lb>verosimili dall&#039;esperienza, ma non dimostrate dalla Geometria o da discorso, <lb></lb>che potesse servire di fondamento alla Geometria, e nonostante lusingarono <lb></lb>tanto Galileo, da proporsi di stendere delle Artiglierie, con le quali ei pure <lb></lb>confessa di non aver mai fatto esperienza (Alb. </s>

<s>II, 100), un intero trattato, <lb></lb>i sommi capi del quale si trovano così intitolati e ordinatamente scritti di <lb></lb>propria mano di lui, in un foglio che ci è rimasto: </s></p><p type="main">

<s>“ I. </s>

<s>Particolari privilegi dell&#039;Artiglieria sopra gli altri strumenti mec­<lb></lb>canici. </s>

<s>” </s></p><p type="main">

<s>“ II. </s>

<s>Della sua forza, ed onde proceda. </s>

<s>” </s></p><p type="main">

<s>“ III. </s>

<s>Se operi con maggior forza in una certa distanza, o da vicino. </s>

<s>” </s></p><p type="main">

<s>“ IV. </s>

<s>Se la palla vadia per linea retta, non sendo tirata a perpendicolo. </s>

<s>” </s></p><p type="main">

<s>“ V. </s>

<s>Che linea descriva la palla nel suo moto. </s>

<s>” </s></p><p type="main">

<s>“ VI. </s>

<s>La causa ed il tempo dello stornare il pezzo. </s>

<s>” </s></p><p type="main">

<s>“ VII. </s>

<s>Impedimenti che rendono il pezzo difettoso ed il tiro incerto. </s>

<s>” </s></p><p type="main">

<s>“ VIII. </s>

<s>Del metterle a cavallo e scavalcarle. </s>

<s>” </s></p><p type="main">

<s>“ IX. </s>

<s>Della fabbrica del calibro. </s>

<s>” </s></p><p type="main">

<s>“ X. Dell&#039;esamine circa la bontà e giustezza del pezzo. </s>

<s>” </s></p><p type="main">

<s>“ XI. </s>

<s>Se quanto è più lungo il pezzo tiri più lontano, e perchè. </s>

<s>” </s></p><p type="main">

<s>“ XII. </s>

<s>A quale elevazione tiri più lontano, e perchè. </s>

<s>” </s></p><p type="main">

<s>“ XIII Che nel termine la palla in giù, nel perpendicolo, torna con la <lb></lb>medesìma forza e velocità che andando in su. </s>

<s>” </s></p><p type="main">

<s>“ XIV. </s>

<s>Diverse palle artifiziate e lanterne e loro uso. </s>

<s>” (MSS. Gal., <lb></lb>P. V, T. II, fol. </s>

<s>193). </s></p><p type="main">

<s>Molti de&#039;proposti soggetti della trattazione concernono, come si vede, <lb></lb>la parte fisica o tecnica dell&#039;Arte militare, ma quei che principalmente s&#039;ap­<lb></lb>partengono alla Scienza meccanica son fra&#039;primi che s&#039;incontrano in que­<lb></lb>sto elenco il terzo, il quarto e il quinto, i quali ultimi due, insieme col XII, <lb></lb>venivano da Galileo risoluti con le ragioni medesime del Tartaglia. </s>

<s>Rispetto <lb></lb>al quarto infatti l&#039;osservazione scritta nella seconda supposizione del secondo <lb></lb>libro della <emph type="italics"></emph>Scientia nuova<emph.end type="italics"></emph.end> vedesi tradotta in queste parole, con le quali <lb></lb>Simplicio, domandato quanto stia il proietto appena uscito di mano al proi­<lb></lb>ciente a declinare in basso, risponde: “ Credo che cominci subito, perchè, <lb></lb>non avendo chi lo sostenti, non può esser che la propria gravità non operi ” <lb></lb>(Alb. </s>

<s>I, 215). In piena conformità coi quali principii Galileo pure scioglie il <lb></lb>quinto dei proposti quesiti, dicendo che la linea descritta dalla palla nel suo <lb></lb>moto è in parte tale da potersi avere per retta, e in parte manifestamente <lb></lb>curva, e la parte curva <emph type="italics"></emph>sarà parte di una circonferentia di cerchio,<emph.end type="italics"></emph.end> come <lb></lb>si legge nel detto libro della <emph type="italics"></emph>Scientia nuova.<emph.end type="italics"></emph.end> All&#039;altro quesito XII non po­<lb></lb>teva Galileo stesso risponder di meglio di quel che, non con ragioni geome-<pb xlink:href="020/01/2277.jpg" pagenum="520"></pb>triche ma sperimentali, avea già risposto il Tartaglia, che cioè l&#039;elevazione, <lb></lb>alla quale tira l&#039;obice più di lontano, è nel sesto punto della Squadra. </s>

<s>Il <lb></lb>problema poi, scritto nel sopra addotto elenco in undecimo luogo, ritenevasi <lb></lb>come risoluto di fatto per il Cardano, il quale annovera fra le cause che <lb></lb>rendono o più tardo o più veloce il moto violento “ quod per magnum spa­<lb></lb>tium: ideo machinae bellicae quo longiores eo procul magis eiaculantur ” <lb></lb>(De subtil. </s>

<s>cit., pag. </s>

<s>93). E probabilmente al fatto, che si credeva confer­<lb></lb>mato dall&#039;esperienza, si riducevano anche le ragioni di Galileo. </s></p><p type="main">

<s>I galileiani quesiti dunque, da risolversi coi principii nuovi, non si ri­<lb></lb>ducevano che al III e al XIII, ne&#039;quali volevasi dimostrare, contro le co­<lb></lb>muni opinioni, e contro le dottrine a que&#039;tempi insegnate, che la palla può <lb></lb>avere, così da vicino come a distanza, la medesima forza, essendo questa <lb></lb>tanta nel salire quant&#039;è nello scendere, e spedendosi in egual tempo i due <lb></lb>viaggi contrarii. </s>

<s>Furono tali le conclusioni, che principalmente incorarono, <lb></lb>verso il 1609, la speranza di farsi maestro al mondo dell&#039;arte bellica nel­<lb></lb>l&#039;animo di Galileo, ma ripensando poi che queste nuove erano bene assai <lb></lb>piccola parte delle dottrine antiche, e che non trovavano ancora nella Geo­<lb></lb>metria nessun solido fondamento; non solo ei depose il pensiero di trattar <lb></lb>delle Artiglierie, ma non fece per allora altro conto dello scoperto isocro­<lb></lb>nismo dei tiri, fatti con qualunque forza di punto in bianco, aspettando che <lb></lb>gli occorresse, a confermare il vero, discorso più dimostrativo di quello, che <lb></lb>si fondava nel comparare gl&#039;impeti del proietto per le vie aeree, e del ca­<lb></lb>dente naturale lungo i piani convessi. </s></p><p type="main">

<s>Non poteva la desiderata dimostrazione aspettarsi da altro, che dal prin­<lb></lb>cipio dei moti composti, perchè dall&#039;ammetter che il viaggio del proietto <lb></lb>resulti da un moto verticale e da un altro orizzontale, come avvien per esem­<lb></lb>pio nel considerar la palla di artiglieria scender lungo l&#039;albero maestro, <lb></lb>mentre la nave si muove; era manifesto che la perpendicolar caduta natu­<lb></lb>rale e la trasversale violenta, descritta dalla palla stessa, si spediscono nel <lb></lb>medesimo tempo. </s></p><p type="main">

<s>Una tal composizione di forza però, ne&#039;moti violenti, era stata aperta­<lb></lb>mente negata dal Tartaglia, e benchè il Benedetti avesse lasciato scritto che <lb></lb><figure id="id.020.01.2277.1.jpg" xlink:href="020/01/2277/1.jpg"></figure></s></p><p type="caption">

<s>Figura 281<lb></lb>era ciò un grande errore, e avesse il Cardano dimo­<lb></lb>strate le proprietà, che egli chiama ammirande, dei moti <lb></lb>misti, la XLIX proposizion nonostante pareva scritta <lb></lb>apposta da lui nell&#039;<emph type="italics"></emph>Opus novum,<emph.end type="italics"></emph.end> per concluder tut­<lb></lb>t&#039;altrimenti di quel sincronismo, che era nuovamente <lb></lb>venuto a concludersi da Galileo. </s></p><p type="main">

<s>La detta cardanica proposizione è così espressa: <lb></lb>“ Omne mobile motum duobus motibus non ad idem <lb></lb>tendentibus, utrumque seorsum tardius moveretur si­<lb></lb>mili motu ” (Operum, T. IV, Lugduni 1663, pag. </s>

<s>490). <lb></lb>Sia A (fig. </s>

<s>281) il mobile, mosso per ABC, con moto <lb></lb>misto di naturale e di violento, e sia D il termine dell&#039;uno, E il termine <pb xlink:href="020/01/2278.jpg" pagenum="521"></pb>dell&#039;altro: dice il Cardano che più tardi giungerà in C, che in D, e in E. </s>

<s><lb></lb>Quanto ad E, la cosa è chiara: prima, perchè manca ad AE, per aggua­<lb></lb>gliarsi ad AC, la parte AD, e poi, perchè, per la definizione della linea retta, <lb></lb>AC è più lunga di AE “ quare tardius mobile perveniet ad C quam ad E <lb></lb>duplici ratione. </s>

<s>Dico etiam quod tardius ad C quam D. </s>

<s>Quia enim vis, quae <lb></lb>fert ad D, repugnat ei quae fert ad E, et vis quae fert ad E repugnat ei, <lb></lb>quae fert ad D: Igitur tardius perveniet ad C, quam D ” (ibid.). </s></p><p type="main">

<s>Galileo invece aveva scoperto che giunge in C e in E il mobile nel me­<lb></lb>desimo tempo, e fu per questa contradizione che sempre più diffidò di quei <lb></lb>moti misti, introdotti dal Cardano nella Scienza dei proietti. </s>

<s>Ma perchè in <lb></lb>ogni modo non potevasi aver quel ch&#039;esso Galileo cercava di dimostrare, se <lb></lb>non che facendo uso del principio che, imbevuto oramai delle viete dottrine <lb></lb>del Tartaglia, egli avea ripudiato; sarebbe alle speculazioni, così felicemente <lb></lb>incominciate, venuto ad arrestarsi ogni progresso, se non gli fosse avven­<lb></lb>turosamente occorso di scoprire che non in sè, ma nel modo, era fallace <lb></lb>l&#039;argomento, di cui s&#039;era servito il Cardano. </s></p><p type="main">

<s>Venne quell&#039;avventurosa occasione alquanti anni dopo, quando a lui, <lb></lb>dichiaratosi Copernicano, opponevano i Peripatetici che, se la Terra vera­<lb></lb>mente girasse in ventiquattr&#039;ore in sè stessa, i corpi gravi, lasciati andar <lb></lb>dall&#039;alto di una torre, non verrebber a batterle al piede. </s>

<s>Confermavano il <lb></lb>loro discorso con l&#039;esempio di una nave, nella quale se, mentre sta ferma <lb></lb>in porto, si lascia dalla sommità dell&#039;albero cadere liberamente una pietra, <lb></lb>quella batte a piè dell&#039;albero stesso a piombo sotto il luogo, dove si lasciò <lb></lb>cadere; il quale effetto, soggiungevano, non avviene, quando va il naviglio <lb></lb>innanzi con corso veloce, perchè, nel tempo che il grave scende nel per <lb></lb>pendicolo, egli è già trascorso per linea orizzontale, e perciò il termine della <lb></lb>caduta non è più, come dianzi, a piè dell&#039;albero, ma verso la poppa. </s></p><p type="main">

<s>Dicevano così costoro, non perchè avessero osservato i fatti, ma perchè, <lb></lb>secondo il loro vizioso istituto, dovevano i fatti accomodarsi e rispondere <lb></lb>alle ragioni, le quali si leggevano a nome di Aristotile scritte nella detta <lb></lb>proposizion XLIX del Cardano. </s>

<s>Ivi erasi concluso che in C il moto è più <lb></lb>tardo che in E, per cui se AE rappresenta l&#039;albero della nave, e ABC la <lb></lb>linea del viaggio fatto dal cader della pietra, essendo per questa linea, ch&#039;è <lb></lb>della perpendicolare più lunga, il moto più tardo, deve la pietra stessa, cor­<lb></lb>rendo innanzi la nave, necessariamente restare in dietro. </s></p><p type="main">

<s>L&#039;istituto di Galileo era a questo peripatetico tutt&#039;affatto contrario, ond&#039;è <lb></lb>che saviamente secondandolo, giunse per la via regia della esperienza a sco­<lb></lb>prir la fallacia di un tal discorso fattogli allora, insieme con altri anche più <lb></lb>scipiti, da un tal Francesco Ingoli, casuidico di Ravenna. </s>

<s>A lui e a&#039;peripa­<lb></lb>tetici colleghi suoi rispondeva Galileo stesso nella primavera del 1624, ri­<lb></lb>trovandosi a Roma, rimproverandoli del produrre esperienze come fatte e <lb></lb>rispondenti al bisogno, senz&#039;averle mai fatte nè osservate “ ed una di tali <lb></lb>esperienze, poi soggiunge, è appunto questa del sasso cadente dalla som­<lb></lb>mità dell&#039;albero nella nave, al piè della quale va sempre a terminare e fe-<pb xlink:href="020/01/2279.jpg" pagenum="522"></pb>rire, tanto quando la nave è in quiete, quanto mentre ella velocemente cam­<lb></lb>mina, e non va, com&#039;essi credevano, scorrendo via la nave, mentre la pietra <lb></lb>per aria viene a basso, a ferir lontano dal piede verso la poppa. </s>

<s>Nella quale <lb></lb>occasione io sono stato doppiamente miglior filosofo di loro, perchè eglino <lb></lb>al dir quello che è contrario in effetto hanno anco aggiunta la bugia, di­<lb></lb>cendo d&#039;aver ciò veduto dall&#039;esperienza, ed io ne ho fatto l&#039;esperienza, <lb></lb>avanti la quale il natural discorso mi avea molto fermamente persuaso che <lb></lb>l&#039;effetto doveva succedere come appunto succede ” (Alb. </s>

<s>II, 99). </s></p><p type="main">

<s>Ritrovato così che i fatti confermavano il discorso naturale, Galileo <lb></lb>credè che la fallacia dell&#039;argomento del Cardano consistesse nell&#039;ammetter <lb></lb>che l&#039;uno dei moti fosse d&#039;impedimento all&#039;altro. </s>

<s>Ond&#039;essendo il vero che <lb></lb>l&#039;impeto, con cui va la nave, resta indelebilmente impresso nella pietra, <lb></lb>dop&#039;essersi separata dall&#039;albero, e che questo moto non reca impedimento <lb></lb>o ritardamento al moto all&#039;ingiù; in quest&#039;amica composizione di forze, che <lb></lb>egli aveva prima tante volte repudiata, vide chiara Galileo stesso la ragione, <lb></lb>che da tanto tempo cercava, del sincronismo nel perpendicolo e nella tra­<lb></lb>sversale, o sia il grave, mentre cade naturalmente, trasportato dalla nave, <lb></lb>o da altro con cui si muova, o dall&#039;impeto nella medesima direzione impres­<lb></lb>sagli dal proiciente. </s></p><p type="main">

<s>“ Quando sia vero (così nel secondo dialogo dei Massimi Sistemi è messo <lb></lb>in bocca al Sagredo) che l&#039;impeto, col quale si muove la nave resti im­<lb></lb>presso indelebilmente nella pietra, dopo che s&#039;è separata dall&#039;albero, e sia <lb></lb>in oltre vero che questo moto non arrechi impedimento o ritardamento al <lb></lb>moto retto all&#039;ingiù naturale della pietra, è forza che ne segua un effetto <lb></lb>meraviglioso in natura. </s>

<s>Stia la nave ferma e sia il tempo della caduta d&#039;un <lb></lb>sasso dalla cima dell&#039;albero due battute di polso: muovasi poi la nave, e <lb></lb>lascisi andar dal medesimo luogo l&#039;istesso sasso, il quale, per le cose dette, <lb></lb>metterà pure il tempo di due battute ad arrivare a basso, nel qual tempo <lb></lb>la nave avrà v. </s>

<s>g. </s>

<s>scorso venti braccia, talchè il vero moto della pietra sarà <lb></lb>stato una linea trasversale assai più lunga della prima retta e perpendico­<lb></lb>lare, che è la sola lunghezza dell&#039;albero; tuttavia la palla l&#039;avrà passata nel <lb></lb>medesimo tempo. </s>

<s>Intendasi di nuovo il moto della nave accelerato assai più, <lb></lb>sicchè la pietra nel cadere dovrà passare una trasversale ancor più lunga <lb></lb>dell&#039;altra, e insomma, crescendosi la velocità della nave quanto si voglia, il <lb></lb>sasso cadente descriverà le sue trasversali sempre più e più lunghe, e pur <lb></lb>tutte le passerà nelle medesime due battute di polso. </s>

<s>” </s></p><p type="main">

<s>“ A questa similitudine, quando in cima di una torre fosse una colu­<lb></lb>brina livellata, e con essa si tirassero tiri di punto bianco, cioè paralleli al­<lb></lb>l&#039;orizzonte, per poca o molta carica che si desse al pezzo, sicchè la palla <lb></lb>andasse a cadere ora lontana mille braccia, or quattro mila, or sei mila, or <lb></lb>dieci mila ecc. </s>

<s>tutti questi tiri si spedirebbero in tempi uguali tra di loro, <lb></lb>e ciascheduno eguale al tempo, che la palla consumerebbe a venire dalla <lb></lb>bocca del pezzo sino in terra, lasciata senz&#039;altro impulso cadere semplice­<lb></lb>mente giù a perpendicolo. </s>

<s>” (Alb. </s>

<s>I, 171, 72). </s></p><pb xlink:href="020/01/2280.jpg" pagenum="523"></pb><p type="main">

<s>A questa medesima conclusione, quando non s&#039;erano ancora le dispute <lb></lb>co&#039;Peripatetici anticopernicani fatte così fervorose, era, come vedemmo, già <lb></lb>venuto Galileo nel 1609, per discorso però, a cui mancava la fermezza del <lb></lb>fondamento, la quale, ritrovata ora nel principio dei moti misti, fece deli­<lb></lb>berarlo di divulgar la scoperta come cosa nuova fra i discepoli e gli amici <lb></lb>curiosi. </s>

<s>Il Castelli la insegnava pubblicamente, illustrandola con l&#039;esperienza <lb></lb>de&#039;getti di acqua e degli zampilli a&#039;suoi scolari di Pisa, fra&#039;quali sapremo <lb></lb>tra poco con certezza essere ìl Cavalieri. </s>

<s>Mario Guiducci la leggeva nel 1626 <lb></lb>in una solenne adunanza agli Accademici fiorentini, applicandola ad illu­<lb></lb>strare un luogo di Omero. </s>

<s>Nel canto XXI dell&#039;Odissea dice il Poeta che Pe­<lb></lb>nelope, per far cimento del valore dei Proci, presentò a loro innanzi il for­<lb></lb>tissimo arco di Ulisse, offerendo in premio per sposa sè stessa a chi di loro <lb></lb>avesse avuto forza di caricarlo, e di far passar libera la scoccata saetta per <lb></lb>gli anelli di dodici accette, orizzontalmente disposte in fila. </s></p><p type="main">

<s>Vuole il Guiducci far rilevar l&#039;acutezza del concetto omerico, osservando <lb></lb>che quel gioco presupponeva le proprietà delle curve descritte dai proietti, <lb></lb>le quali vanno sempre piegandosi verso terra, ma quel piegamento è tanto <lb></lb>meno sensibile in una breve distanza, quanto il proietto è gettato con mag­<lb></lb>gior forza. </s>

<s>Così, poniamo che sia il primo anello collocato in AB (fig. </s>

<s>282), <lb></lb>e l&#039;ultimo in BC, stando gli altri dieci fra mezzo. </s>

<s>Tirando la freccia in modo, <lb></lb><figure id="id.020.01.2280.1.jpg" xlink:href="020/01/2280/1.jpg"></figure></s></p><p type="caption">

<s>Figura 282<lb></lb>ch&#039;ella imbocchi sotto <lb></lb>il punto A il primo <lb></lb>anello, proseguendo il <lb></lb>suo impeto descriverà <lb></lb>una curva, la quale po­<lb></lb>trebb&#039;essere così AD, <lb></lb>come AE, secondo che <lb></lb>l&#039;arco era più o meno <lb></lb>teso. </s>

<s>Che se ebbe tal tensione, da poter rilasciato sospinger la saetta per <lb></lb>la via AE, gli anelli saranno tutti passati fuor fuori, ma se fosse stata in­<lb></lb>vece AD quella via, per più debole impulso dato alla corda, non sarebbero <lb></lb>stati passati se non che quegli anelli soli, i quali fossero stati fra&#039;punti B <lb></lb>e D collocati nel mezzo. </s></p><p type="main">

<s>Il gioco dunque ingegnosamente proposto da Penelope era bene atto a <lb></lb>misurare la forza della tirata dell&#039;arco, ed era fondato sopra una nozione, <lb></lb>che facilmente s&#039;aveva dalla volgare esperienza. </s>

<s>Ma il Guiducci vuol ridurre <lb></lb>a un principio scientifico quello strattagemma; principio, ch&#039;egli dice essere <lb></lb>stato nuovamente da Galileo così proposto: “ I proietti scacciati con vio­<lb></lb>lenza dal proiciente, il quale non sia elevato nè inclinato, ma parallelo al­<lb></lb>l&#039;orizzonte, arrivano nel tempo medesimo al piano sottopostoli della terra, <lb></lb>come se vi fossero dalla medesima altezza lasciati cadere perpendicolari ” <lb></lb>(Prefazione alle rime di M. A. Bonarroti, Firenze 1863, pag. </s>

<s>CXXXII). E <lb></lb>dop&#039;aver fatto osservare che un uomo, sdrucciolando dall&#039;albero di una barca, <lb></lb>giunge al piede nel medesimo tempo o la barca stessa stia ferma o si muova, <pb xlink:href="020/01/2281.jpg" pagenum="524"></pb>benchè in questo caso descriva una trasversale tanto più lunga; “ nella <lb></lb>stessa guisa, soggiunge, avvien per l&#039;appunto ai proietti, il cui moto, es­<lb></lb>sendo composto di due moti, procedenti da due virtù diversamente motrici, <lb></lb>cioè una naturale per linea tendente al centro, l&#039;altra violenta per linea <lb></lb>orizzontale; non può questa impedire nè ritardare l&#039;altra naturale e al cen­<lb></lb>tro, sicchè il proietto non termini nell&#039;istesso tempo il suo moto, nel quale <lb></lb>lo finirebbe, se progressivamente non si movesse ” (ivi). </s></p><p type="main">

<s>Agli Accademici fiorentini veniva così dunque anticipata da sei anni la <lb></lb>lettura di quella pagina, che vedrebbe il pubblico impressa nel secondo dia­<lb></lb>logo dei Massimi Sistemi, ne&#039;quali il Sagredo, a quel che dianzi udimmo, <lb></lb>discorre nella sostanza e nella forma come il Guiducci. </s>

<s>Se non che questi, <lb></lb>prima di descrivere l&#039;esperienza della nave, avverte esservi di ciò la <emph type="italics"></emph>dimo­<lb></lb>strazione geometrica,<emph.end type="italics"></emph.end> la quale egli però non dice, e non accenna, perchè <lb></lb>forse da Galileo gli era stata solamente promessa. </s>

<s>Ne&#039;citati Dialoghi infatti <lb></lb>la proposizion de&#039;proietti non piglia altro valore dimostrativo che dalla espe­<lb></lb>rienza, se forse nella composizion dei moti, che non s&#039;impediscono, non si <lb></lb>volesse far consistere tutta la promessa Geometria. </s></p><p type="main">

<s>Del non esservi poi, nè in questo nè negli altri più lunghi discorsi, che <lb></lb>ne&#039;Dialoghi si fanno intorno ai proietti, nulla di geometrico; è manifesto <lb></lb>argomento il non decidersi la qualità della linea, che descrive la pietra con <lb></lb>moto naturale misto al moto violento, o della barca, che con lei si muove, <lb></lb>o della forza a lei impressa dal proiciente. </s>

<s>Quella linea è sempre da Gali­<lb></lb>leo vagamente chiamata col nome di <emph type="italics"></emph>trasversale,<emph.end type="italics"></emph.end> nè si decide mai se sia <lb></lb>retta o curva, o essendo curva a quale specie di linee curve appartenga. </s>

<s>A <lb></lb>pag. </s>

<s>169 della prima edizione, fatta nel 1632 in Firenze sotto gli occhi del­<lb></lb>l&#039;Autore, quella trasversale è disegnata come retta, essendo in apparenza <lb></lb>tale, perchè il grande impeto del cannone, che ivi si rappresenta, non rende <lb></lb>in sì breve tratto sensibile l&#039;effetto della gravità in inclinare a basso la palla. </s>

<s><lb></lb>Che sia però quella linea realmente curva, non potendo il proietto essere <lb></lb>abbandonato mai dalla gravità sua naturale, Galileo lo teneva per cosa certa, <lb></lb>come aveva insegnato il Tartaglia, di cui si crederebbe però avesse ripu­<lb></lb>diato l&#039;errore delle curvità circolari nella traiettoria, ora che alla singolar <lb></lb>proprietà de&#039;proietti, scoperta nel 1609, si diceva d&#039;aver ritrovata la geo­<lb></lb>metrica dimostrazione. </s>

<s>È un fatto ch&#039;egli non ha più allo stesso Tartaglia <lb></lb>quella prima fede, che gli fece risolutamente negare le similitudini parabo­<lb></lb>liche, quando Guidubaldo gliele mostrava nelle vestigie lasciate impresse <lb></lb>sulla tavola levigata dalla palla intinta nell&#039;inchiostro, ma vacilla. </s>

<s>Così va­<lb></lb>cillando però inclina tuttavia a credere che la curva del proietto, o appa­<lb></lb>risca come tale o no, sia in ogni modo parte di un cerchio descritto con un <lb></lb>raggio o più lungo o più corto. </s></p><p type="main">

<s>Nella Risposta all&#039;Ingoli sopra citata così concludesi l&#039;esperienza della <lb></lb>pietra, lasciata liberamente cader giù dall&#039;albero della nave: “ Dicovi per­<lb></lb>tanto, signor Ingoli, che, mentre la nave è in corso, con altrettanto impeto <lb></lb>si muove ancor quella pietra, il qual impeto non si perde perchè quello che <pb xlink:href="020/01/2282.jpg" pagenum="525"></pb>la teneva apra la mano e la lasci in libertà; anzi indelebilmente si conserva <lb></lb>in lei, sicchè mediante quello ell&#039;è bastante a seguitar la nave, e per la <lb></lb>propria gravità, non impedita da colui, se ne discende al basso componendo <lb></lb>di ambedue un sol moto <emph type="italics"></emph>e forse anco circolare,<emph.end type="italics"></emph.end> trasversale, e inclinato verso <lb></lb>dove cammina la nave ” (Alb. </s>

<s>II, 100). La sostanza delle dottrine esposte <lb></lb>in questa Lettera copernicana venne poco di poi dialogizzata nei Massimi <lb></lb>Sistemi, dove si dice vedersi il sasso uscito dalla fionda <emph type="italics"></emph>descrivere un arco<emph.end type="italics"></emph.end><lb></lb>(Alb. </s>

<s>I, 212), e distendersi <emph type="italics"></emph>non rettamente ma in arco<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>254) si <lb></lb>dice, vibrando il pendolo, la catena, che, secondo Guidubaldo, s&#039;incurva a <lb></lb>somiglianza di un ramo della parabola. </s></p><p type="main">

<s>Che devasi in questi passi intendere <emph type="italics"></emph>arco di cerchio,<emph.end type="italics"></emph.end> secondo l&#039;opi­<lb></lb>nione rimasta per quarant&#039;anni di studio intorno alle proprietà dei proietti <lb></lb>nella mente di Galileo sempre tenace; si conferma da ciò, che dice in que­<lb></lb>sta stessa Giornata, dove parla della fionda e della catena del pendolo, per <lb></lb>determinar la specie della linea, che descrive una pietra, cadendo da un&#039;alta <lb></lb>torre di moto naturale composto col moto vertiginoso della Terra. </s>

<s>Sia B <lb></lb>(fig. </s>

<s>283) la base, e C la sommità della torre, i quali due punti, rivolgen­<lb></lb><figure id="id.020.01.2282.1.jpg" xlink:href="020/01/2282/1.jpg"></figure></s></p><p type="caption">

<s>Figura 283<lb></lb>dosi intorno ad A centro terrestre, descrivano <lb></lb>i due archi BI, CD: “ divisa poi la linea CA in <lb></lb>mezzo in E, col centro E, intervallo EC, de­<lb></lb>scrivo, dice Galileo, il mezzo cerchio CIA, per <lb></lb>il quale dico ora che assai probabilmente si può <lb></lb>credere che una pietra, cadendo dalla sommità <lb></lb>della torre C, venga, movendosi del moto compo­<lb></lb>sto del comune circolare e del suo proprio retto ” <lb></lb>(Alb. </s>

<s>I, 18<gap></gap>). È manifesto perciò che la cercata <lb></lb>linea, descritta nel cader la pietra dalla sommità <lb></lb>al piè della torre, è la CI, arco del semicer­<lb></lb>chio AIC. </s>

<s>E perchè a questa similitudine va la <lb></lb>cosa, quando si supponga in C un cannone li­<lb></lb>vellato, che avesse potenza di spinger la palla <lb></lb>da C in D, nello stesso tempo che quello spazio percorresi dalla Terra, il <lb></lb>proietto dunque, secondo Galileo, descriverebbe la medesima linea CI; ossia <lb></lb>il medesimo arco di cerchio. </s>

<s>Di qui nella lettera all&#039;Ingoli vien con tutta la <lb></lb>precisione dichiarato il pensiero di chi la scrisse, perchè se BC rappresenta <lb></lb>l&#039;albero della nave, e BI la superfice convessa dell&#039;acqua, movendosi da B <lb></lb>in I essa nave, mentre dalla sommità dell&#039;albero cade al piede la pietra, <lb></lb>questa descriverà la linea CI, che è <emph type="italics"></emph>la trasversale, inclinata verso dove <lb></lb>cammina la nave e forse anche circolare,<emph.end type="italics"></emph.end> di cui, come dianzi vedemmo, <lb></lb>ivi scrive l&#039;Autore. </s></p><p type="main">

<s>Se si debbon dunque intendere le parole come tutti schiettamente le <lb></lb>intendono a significare le idee, nè nei Dialoghi famosi, nè in nessuna delle <lb></lb>precedenti scritture, si dimostra da Galileo la propria specie della curva di­<lb></lb>segnata nell&#039;aria dal proietto, e <emph type="italics"></emph>forse,<emph.end type="italics"></emph.end> e <emph type="italics"></emph>probabilmente<emph.end type="italics"></emph.end> si dice essere un <pb xlink:href="020/01/2283.jpg" pagenum="526"></pb>arco di cerchio. </s>

<s>Anche il Cartesio confessava a que&#039;tempi di non avere an­<lb></lb>cora intorno a ciò fatto nessuno studio. </s>

<s>Credeva che una palla gettata con <lb></lb>più o meno forza descriva due linee omogenee, “ sed cuiusmodi sint istae <lb></lb>lineae nunquam examinavi ” (Epist., P. II cit., pag. </s>

<s>312). Di qualunque spe­<lb></lb>cie però esse linee si fossero in questo si trovavano i Matematici concordi, in <lb></lb>escluderle cioè dal rappresentare curvità circolari. </s>

<s>Quando il movimento retto <lb></lb>verso il centro della Terra fosse uniforme, dice il Salviati galileiano, essendo <lb></lb>anco uniforme il circolare verso oriente, si verrebbe a comporre di ambe­<lb></lb>due un moto per una linea spirale di quelle definite da Archimede. </s>

<s>Ma per­<lb></lb>chè il moto retto del grave cadente è continuamente accelerato, è forza che <lb></lb>la linea del composto dei due movimenti sia un mezzo cerchio (Alb. </s>

<s>I, 182, 83). </s></p><p type="main">

<s>La fallacia di questo discorso, preveduta infino da Leonardo da Vinci, <lb></lb>ebbe facilmente a notarsi dai lettori del Dialogo, concordi nell&#039;ammettere <lb></lb>che non potesse la linea del cadente al centro dall&#039;alto della torre esser di <lb></lb>diverso genere dalla spirale, benchè confessassero assai facilmente dover pro­<lb></lb>cedere con altro passo dall&#039;archimedea. </s>

<s>Di ciò faceva il Fermat in Francia <lb></lb>argomento alle sue censure, e il Cabeo fra&#039;Nostri diceva, più giudiziosamente <lb></lb>delle altre volte, che nell&#039;esempio della pietra cadente dall&#039;albero, mentre <lb></lb>la nave scorre sopra la liquida circolar superfice del globo, la trasversale CI <lb></lb>generata con duplice moto s&#039;incurva in arco no di circolo ma di spirale <lb></lb>“ quae composita est cum consurgat ex duplici motu descensionis et pro­<lb></lb>gressionis, quorum alter rectus est, alter circularis supra centrum Terrae, <lb></lb>sicut ex duplici motu generatur spira ” (Comment. </s>

<s>meteor., T. </s>

<s>I cit., pag. </s>

<s>89). </s></p><p type="main">

<s>Era fra quei lettori del Dialogo di Galileo Bonaventura Cavalieri, il quale, <lb></lb>avuto nel carnevale del 1632 il libro in dono da un suo scolare in Bologna, <lb></lb>scriveva il dì 22 di Marzo all&#039;Autore di averlo, in que&#039;giorni di comune al­<lb></lb>legrezza, allegrissimamente veduto “ anzi divorato con gli occhi, raccogliendo <lb></lb>con somma avidità i fiori di sì vago giardino ” (Alb. </s>

<s>IX, 264). Ma poi, en­<lb></lb>trato più addentro ai riposti orti di Accademo, e ivi quietamente sedutosi <lb></lb>all&#039;ombra per saggiarne i frutti, ebbe a trovarli agresti in alcune parti, e <lb></lb>principalmente in quella che riguarda la linea descritta dai proietti. </s>

<s>Non si <lb></lb>poteva dar pace che dalla composizion di due moti, l&#039;uno equabile orizzon­<lb></lb><figure id="id.020.01.2283.1.jpg" xlink:href="020/01/2283/1.jpg"></figure></s></p><p type="caption">

<s>Figura 284<lb></lb>tale, e l&#039;altro accelerato in modo da crescer <lb></lb>gli spazii, secondo la serie dei numeri im­<lb></lb>pari, come ivi s&#039;insegna, se ne avesse a con­<lb></lb>cludere in quel medesimo libro che la re­<lb></lb>sultante è per un arco di cerchio. </s></p><p type="main">

<s>Sia A (fig. </s>

<s>284), ragionava così presso <lb></lb>a poco il Cavalieri, un proietto spinto da <lb></lb>qualunque forza per la orizzontale AC, sulla <lb></lb>quale seguiterebbe a moversi equabilmente, <lb></lb>se non lo inclinasse a basso la sua propria <lb></lb>gravità, in direzione perpendicolare parallela alla AF. </s>

<s>Supponiamo che, mentre <lb></lb>il moto violento farebbe passare il mobile da A in B, la naturale sua forza <pb xlink:href="020/01/2284.jpg" pagenum="527"></pb>di gravità l&#039;avesse fatto scendere in D per la linea BD, e mentre passerebbe <lb></lb>in C, nel tempo AC, l&#039;abbia quella stessa forza di gravità fatto scendere in E, <lb></lb>per la linea CE. </s>

<s>Si possono riferire i punti D, E agli assi ortogonali AC, AF, <lb></lb>e così vedere a quale speccie di curva appartengano. </s>

<s>Rappresentando infatti, <lb></lb>come s&#039;è detto le AB, AC uguali alle applicate GD, FE i tempi, e le ascisse <lb></lb>AG, AF uguali alle BD, CE gli spazii, i quali per la legge galileiana stanno <lb></lb>come i quadrati di quegli stessi tempi; sarà per conseguenza AG:AF= <lb></lb>GD2:FE2. </s>

<s>I punti D, E dunque e gli altri infiniti, per cui passa il proietto, <lb></lb>son disposti lungo una linea parabolica, ed è questa, pensava il Cavalieri, <lb></lb>conclusione verissima in Geometria, mentre che si rimanga sulla superficie <lb></lb>terrestre, dentro i quai limiti le linee BD, CE son parallele, e verissima <lb></lb>pure sarebbe anche in Natura, se si potesse toglier di mezzo l&#039;impedimento <lb></lb>dell&#039;aria. </s></p><p type="main">

<s>Teneva lo stesso Cavalieri da qualche tempo fra&#039;suoi fogli un tratta­<lb></lb>tello degli specchi parabolici, iperbolici ed ellittici, e ricondotto nel 1632 alla <lb></lb>cattedra di matematiche nello studio di Bologna, con aumento di cento scudi, <lb></lb>fece proposito, come significava in una sua lettera a Galileo (Alb. </s>

<s>IX, 269), <lb></lb>di stampare finalmente il libretto, e di dedicarlo per ringraziamento alla Reg­<lb></lb>genza. </s>

<s>Mentre ivi insegnavasi con metodi nuovi a descriver le sezioni co­<lb></lb>niche, si dimostravano alcuni loro mirabili effetti intorno al suono, al calore <lb></lb>e alla luce, per cui parve convenirsi al libro il titolo di <emph type="italics"></emph>Specchio ustorio.<emph.end type="italics"></emph.end><lb></lb>La legge della diffusione sferica, per cui crescono le superficie ondose lu­<lb></lb>cide, calorifiche e sonore come i quadrati de&#039;raggi, suggerì al Cavalieri, dopo <lb></lb>la lettura del Dialogo galileiano, quella bella dimostrazione delle proporzioni <lb></lb>del moto nei liberi cadenti, attissima a rivelar che gl&#039;imponderabili stessi <lb></lb>non si sottraggono alla legge universale dei gravi, e che tutto cospira quag­<lb></lb>giù in un&#039;armonica unione di forze. </s></p><p type="main">

<s>Dal venir così confermati i principii dottrinali del moto, posti da Gali­<lb></lb>leo, prese occasione il Cavalieri di mostrarne le conseguenze, per ciò che <lb></lb>s&#039;appartiene ai proietti, e l&#039;una e l&#039;altra parte pensò d&#039;inserir nel trattato <lb></lb>delle sezioni coniche, dove si vedrebbe a una nuova e mirabile dignità esal­<lb></lb>tata la Parabola. </s>

<s>Introdottosi perciò ne&#039;capitoli XL e XLI alla <emph type="italics"></emph>Cognizione <lb></lb>del moto,<emph.end type="italics"></emph.end> e dal diffondersi concentrico di un punto in circoli ondosi, con­<lb></lb>fermata, per la Geometria degl&#039;indivisibili, la legge degli spazii proporzio­<lb></lb>nali ai quadrati dei tempi; passa nel XLII a proporsi il quesito <emph type="italics"></emph>Qual sorta <lb></lb>di linea descrivano i gravi nel loro moto, spiccati che siano dal proiciente,<emph.end type="italics"></emph.end><lb></lb>e lo risolve dicendo: “ che i gravi, spinti dal proiciente a qualsivoglia banda <lb></lb>fuorchè per la perpendicolare all&#039;orizzonte, separati che siano da quello, ed <lb></lb>escluso l&#039;impedimento dell&#039;ambiente, descrivono una linea curva insensibil­<lb></lb>mente differente dalla Parabola ” (Specchio Ust., ediz. 2a, Bologna 1650, <lb></lb>pag. </s>

<s>99). </s></p><p type="main">

<s>La dimostrazione è conclusa dal principio dei moti misti, a quel modo <lb></lb>che dicemmo di sopra, ma era appena scritta e ordinata per le stampe che, <lb></lb>rileggendola il Cavalieri, pensava a quel che nel vederla vorrebbe dir Ga-<pb xlink:href="020/01/2285.jpg" pagenum="528"></pb>lileo. </s>

<s>Dubitava non dovesse incontrare a questi proietti terrestri la medesima <lb></lb>sorte che ai celesti: e com&#039;esso Galileo persisteva tuttavia in approvar le <lb></lb>orbite circolari, benchè ellittiche le avesse dimostrate il Keplero; così s&#039;aspet­<lb></lb>tava che volesse mantener circolari le traiettorie anc&#039;ora, che dagli stessi <lb></lb>principii di lui si concludevano paraboliche con facile discorso. </s>

<s>Par che, nel­<lb></lb>l&#039;atto stesso di venire scacciati dall&#039;animo, scappino que&#039;dubbi dalla punta <lb></lb>della penna, mentr&#039;è menata a scrivere così in fine della detta dimostra­<lb></lb>zione: “ Ci contenteremo di questo poco, per intender le varie condizioni e <lb></lb>nobiltà delle Sezioni coniche, avendole anco il Keplero in supremo grado <lb></lb>nobilitate, mentre ci ha fatto vedere con manifeste ragioni, ne&#039;Commentari <lb></lb>di Marte e nell&#039;Epitome copernicana, che le circolazionì de&#039;Pianeti intorno <lb></lb>al Sole non sono altrimenti circolari, ma ellittiche ” (ivì, pag. </s>

<s>101, 2). </s></p><p type="main">

<s>Poi, quasi impaurito il Cavalieri al pensiero di diventare anch&#039;egli og­<lb></lb>getto al disprezzo e all&#039;ira di Galileo, come per somiglianti motivi era di­<lb></lb>ventato il Keplero, cercò le vie di placarlo e di comprimerne i moti del ter­<lb></lb>ribile sdegno. </s>

<s>Rileggendo a questo intento quella infelice opinione messa in <lb></lb>bocca al Salviati, e che illustravasi dalla figura rappresentata da noi nella 283 <lb></lb>qui poco addietro, ebbe a notar che la linea CI, secondo la quale anderebbe <lb></lb>in aria la palla esplosa dal cannone livellato, e posto in C con la bocca; è <lb></lb>una minima particella del grandissimo circolo AIC, che ha nella descrizione <lb></lb>di Galileo per diametro il semidiametro della Terra: onde, avendo nel co­<lb></lb>rollario al cap. </s>

<s>LVI del medesimo Specchio ustorio dimostrato, in prepara­<lb></lb>zione alla teoria de&#039;circoli osculatori, che uno specchio sferico pochissimo <lb></lb>cavo, o una lente sferica pochissimo colma, pochissimo differiscono dalla Pa­<lb></lb>rabola e dall&#039;Iperbola nella curvatura; per salvare in qualche modo l&#039;errore <lb></lb>di Galileo, e per farlo apparire meno strano dal vero, volle soggiungere ivi <lb></lb>queste parole: “ Potrà insieme ancora la dottrina di questo corollario dar <lb></lb>sodisfazione a coloro, che stimassero la strada disegnata dal proietto esser <lb></lb>circolare, poichè, essendo quel cerchio notabilmente grande, ed il viaggio del <lb></lb>grave poca parte dell&#039;intera circonferenza, può esser che talora riesca pure <lb></lb>pochissimo differente dalla Parabola ” (ivi). </s></p><p type="main">

<s>Nell&#039;Agosto del medesimo anno 1632 lo Specchio ustorio era già stam­<lb></lb>pato, e l&#039;Autore nè dava così avviso a Galileo in una lettera scritta l&#039;ul­<lb></lb>timo di quel mese da Bologna: “ Non mancherò di fargli avere uno de&#039;miei <lb></lb>libretti ora stampati, quale ho intitolato <emph type="italics"></emph>Specchio ustorio,<emph.end type="italics"></emph.end> nel quale vedrà <lb></lb>un mio pensiero intorno lo Specchio d&#039;Archimede, dove tratto universal­<lb></lb>mente delle Sezioni coniche, considerando alcuni effetti di natura, ne&#039;quali <lb></lb>hanno che fare. </s>

<s>Ho toccato qualche cosetta del moto de&#039;proietti, mostrando <lb></lb>che dovria essere per una Parabola, escluso l&#039;impedimento dell&#039;ambiente, <lb></lb>supposto il suo principio del movimento dei gravi che si velociti secondo <lb></lb>l&#039;incremento de&#039;numeri dispari continuati dall&#039;unità, attestando però d&#039;aver <lb></lb>imparato in gran parte da lei ciò ch&#039;io tocco in questa materia, adducendo <lb></lb>insieme anch&#039;io una ragione per quel principio ” (Alb. </s>

<s>IX, 286). </s></p><p type="main">

<s>Era nella ragione di quel principio, che definiva gli spazi proporzionali <pb xlink:href="020/01/2286.jpg" pagenum="529"></pb>ai quadrati dei tempi, scolpita così a vivo l&#039;effigie della Parabola, che Ga­<lb></lb>lileo ebbe a stupire di non averla riconosciuta se non ora, che veniva ad <lb></lb>aprirgliene gli occhi la lettera del Cavalieri. </s>

<s>Avrebbe sentito dispetto di sè, <lb></lb>invidia della sorte altrui, se non fossero tali due sentimenti rimasti concul­<lb></lb>cati dal baldanzoso insorgere di quell&#039;ardor di rapina, che spira dalle se­<lb></lb>guenti parole scritte in una lettera al signor Cesare Marsili, cittadino di Bo­<lb></lb>logna, e protettore dello stesso Cavalieri: </s></p><p type="main">

<s>“ Tengo lettera del padre fra Bonaventura con avviso come S. P. ha <lb></lb>nuovamente stampato un trattato dello Specchio ustorio, nel quale, con certa <lb></lb>occasione, dice avervi inserito la proposizione e dimostrazione della linea de­<lb></lb>scritta dai proietti, provando com&#039;è una linea parabolica. </s>

<s>Io non posso na­<lb></lb>scondere a V. S. I. tale avviso essermi stato di poco gusto, nel vedere come, <lb></lb>di un mio studio di più di quarant&#039;anni, conferitone buona parte con larga <lb></lb>confidenza al detto Padre, mi deva ora esser levato la primizia, e sfiorata <lb></lb>quella gloria, che tanto avidamente desideravo, e mi promettevo da sì lun­<lb></lb>ghe mie fatiche: perchè veramente il primo intendimento che mi mosse a <lb></lb>specular sopra il moto, fu il ritrovar tal linea, la quale, se ben ritrovata, è <lb></lb>poi di non molto difficile dimostrazione, tuttavia io che l&#039;ho provata so quanta <lb></lb>fatica ho avuto in ritrovar tal conclusione. </s>

<s>E se il padre fra Bonaventura <lb></lb>mi avesse innanzi la pubblicazione significato il suo pensiero, come forse la <lb></lb>civil creanza richiedea, io l&#039;avrei tanto pregato, che mi avrebbe permesso <lb></lb>che io avessi prima stampato il mio libro, dopo il quale poteva egli poi sog­<lb></lb>giunger quanti trovati gli fosse piaciuto. </s>

<s>Starò attendendo di veder ciò che <lb></lb>ei produce, ma gran cosa certo ci vorrebbe a temperare il mio disgusto, e di <lb></lb>quanti miei amici hanno ciò inteso, dai quali, per mia maggior mortificazione, <lb></lb>mi vien buttato in occhio il mio troppo confidare: porta la mia stella che <lb></lb>io abbia a combattere, e anco con pèrdita, la roba mia ” (Alb. </s>

<s>VII, 5, 6). </s></p><p type="main">

<s>La mattina del 19 Settembre 1632, otto giorni dopo la data di questa <lb></lb>lettera da Firenze, va il Marsili a picchiare alla cella di fra Bonaventura, il <lb></lb>quale ebbe a legger negli occhi di lui l&#039;afflizione, prima che nel foglio aper­<lb></lb>togli innanzi. </s>

<s>S&#039;aspettava piuttosto che, per aver nello Specchio ustorio con­<lb></lb>cluso diversamente da quel ch&#039;era scritto nel Dialogo, se ne volesse risen­<lb></lb>tir Galileo, nè sapeva intendere com&#039;a veder dimostrata la Parabola dei <lb></lb>proietti si dovesse aspettar la stampa di un nuovo libro, quando in quello <lb></lb>dei due Massimi Sistemi, allora allora stampato, s&#039;escludeva la parabola, per <lb></lb>ammettervi il cerchio. </s>

<s>Non avrebbe mai creduto il buon Frate che l&#039;Uomo <lb></lb>tanto riverito e amato, per non confessare di non aver saputo vedere nei <lb></lb>suoi propri principii una conseguenza così manifestamente immediata, si fosse <lb></lb>messo a profferire altrettante menzogne, quante nella lettera al Marsili erano <lb></lb>le sentenze, per cui ingenuamente credendo a quei quarant&#039;anni, a cui leg­<lb></lb>geva risalire un tale studio, e a questa fede associando le notizie avute dal­<lb></lb>l&#039;Oddi, pensò che delle traiettorie paraboliche si trattasse infin da quelle <lb></lb>prime esperienze, che si diceva essere state fatte dallo stesso Galileo insieme <lb></lb>con Guidubaldo Del Monte. </s>

<s>— E dall&#039;altra parte, discorreva fra sè il Ca-<pb xlink:href="020/01/2287.jpg" pagenum="530"></pb>valieri, ho io veduto tutto quel che, da&#039;Dialoghi in fuori, si discorre da quel <lb></lb>grand&#039;Uomo intorno ai moti violenti? </s>

<s>A me pareva per verità, essendo sco­<lb></lb>lare in Pisa, che il padre don Benedetto non pronunziasse mai esser para­<lb></lb>bolici i getti dell&#039;acqua, e che si limitasse a far notar l&#039;ugual tempo, in cui <lb></lb>il liquido cade o naturalmente o per l&#039;impeto ricevuto dall&#039;altezza del suo <lb></lb>livello nel vaso: ma forse io non intesi bene tutta intiera la dottrina di Ga­<lb></lb>lileo, che il Castelli ci dimostrava con sì bella esperienza. </s>

<s>— </s></p><p type="main">

<s>Così discorrendo, si disponeva il buon uomo a lasciarsi docilmente spo­<lb></lb>gliare del suo: e giacchè nessuna naturale estrinseca forza par che possa <lb></lb>usar sull&#039;animo violenza, convien dire che avesse qualche cosa del demo­<lb></lb>niaco o del mago colui, che usò nel rubare tant&#039;arte, da movere il legit­<lb></lb>timo possessore della roba a portargliela infino a casa, confessandosi sincera­<lb></lb>mente convinto d&#039;avergliela rubata, come fece insomma il Cavalierì in questa <lb></lb>lettera a Galileo: </s></p><p type="main">

<s>“ Il cordoglio, ch&#039;ella mostra d&#039;aver sentito, come l&#039;illustrissimo signor <lb></lb>Cesare Marsili mi ha significato, per avere io toccato non so che della linea <lb></lb>parabolica descritta dai proietti nel mio Specchio ustorio, non è al sicuro <lb></lb>stato tale e tanto, quanto il mio, per avere io inteso ch&#039;ella abbia ricevuto <lb></lb>offesa da quello, che io sono trascorso a fare, piuttosto per eccesso di reve­<lb></lb>renza, che per altro. </s>

<s>Quello che ho detto del moto, l&#039;ho detto come suo <lb></lb>discepolo e del padre don Benedetto, avendone visto fare esperienze da lui <lb></lb>con altri scolari, da&#039;quali pure ho sentito l&#039;istessa conclusione, e ch&#039;ella <lb></lb>n&#039;era l&#039;autore, sicchè non può cader dubbio alcuno ch&#039;io me la potessi <lb></lb>arrogare come cosa mia.... Aggiungo di più ch&#039;io veramente pensai che <lb></lb>in qualche luogo ella ne avesse trattato, non avendo io potuto aver fortuna <lb></lb>di vedere tutte le opere sue, e questo molto me l&#039;ha fatto credere il sen­<lb></lb>tirla fatta tanto pubblica, e per tanto tempo, che l&#039;Oddi mi disse, dieci anni <lb></lb>sono, ch&#039;ella ne aveva fatto qualche esperienza col signor Guidubaldo Del <lb></lb>Monte ” (Alb. </s>

<s>IX, 291, 92). </s></p><p type="main">

<s>Un altr&#039;animo franco da quella suggezione avrebbe potuto rispondere <lb></lb>a Galileo: ma se tanto vi stava a cuore la gloria di raccogliere il frutto <lb></lb>delle vostre fatiche di quarant&#039;anni, e tanto trepidaste che non venissero <lb></lb>gli altri a sfiorarvela, perchè, invece di confidare a loro privatamente la cosa, <lb></lb>non ve ne assicuraste la proprietà nella pubblicazione del Dialogo famoso, <lb></lb>come pur faceste di tutte le altre conclusioni da voi ritrovate intorno alla <lb></lb>scienza del moto? </s>

<s>O che strana cosa è mai questa, che voi dite di aver con­<lb></lb>ferito con larga confidenza a fra Bonaventura la proposizione che dal moto <lb></lb>retto del cadente, mescolato con l&#039;equabile per l&#039;orizzonte, resulta una pa­<lb></lb>rabola, e poi, con pubblica solennità, scrivete che probabilmente dalla mi­<lb></lb>stura di que&#039;due moti si compone un arco della circonferenza? </s></p><p type="main">

<s>La domanda nasceva dalle pretensioni di Galileo tanto spontanea, che <lb></lb>egli stesso, sentendone la molestia, aveva pensato di spacciarsene col ri­<lb></lb>spondere che era detto a quel modo per celia, e per parlare, non già da <lb></lb>scienziato, ma da poeta. </s>

<s>“ Nel Dialogo, sebbene vien detto poter essere che, <pb xlink:href="020/01/2288.jpg" pagenum="531"></pb>mescolato il retto del cadente con l&#039;equabile circolare del moto diurno, si <lb></lb>componesse una semicirconferenza, che andasse a terminare nel centro della <lb></lb>Terra; ciò fu detto per scherzo, come assai manifestamente apparisce, men­<lb></lb>tre vien chiamato un capriccio e una bizzarria, cioè <emph type="italics"></emph>iocularis quaedam au­<lb></lb>dacia.<emph.end type="italics"></emph.end> Desidero pertanto in questa parte esser dispensato, e massime tiran­<lb></lb>dosi dietro questa dirò poetica finzione quelle tre inaspettate conseguenze, <lb></lb>cioè che il moto del mobile sarebbe sempre circolare, secondariamente sempre <lb></lb>equabile, terzo, che in questo apparente moto <emph type="italics"></emph>deorsum<emph.end type="italics"></emph.end> niente si mova di <lb></lb>più di quello, che si faceva mentre era in quiete ” (Alb. </s>

<s>VII, 155). </s></p><p type="main">

<s>Il Salviati per verità si mostra persuaso del suo discorso, non meno <lb></lb>qui che là, nella lettera all&#039;Ingoli, e il Sagredo gliel&#039;approva dicendo di non <lb></lb>poter credere che la linea del moto composto, secondo la quale va per aria <lb></lb>il proietto, sia diversa dalla circolare (Alb. </s>

<s>I, 183). — Ma giacchè voi, signor <lb></lb>Galileo, avete voluto mettere la dignità de&#039;vostri attori in commedia, e in­<lb></lb>torno a cosa di tanta importanza, e che tanto premeva di sapere ai Prin­<lb></lb>cipi e ai Capitani conduttori degli eserciti in guerra, vi compiacete di averne <lb></lb>nella massima Opera vostra discorso in burla, diteci in qual altra vostra, o <lb></lb>dissertazione, o lettera, o nota, in quarant&#039;anni di studii fatti intorno ai <lb></lb>proietti, avete scritto delle loro vie paraboliche sul serio. </s>

<s>Nel 1592 vi troviamo <lb></lb>a specular la ragione, per cui il proietto va tanto più lungamente in linea <lb></lb>retta, quanto l&#039;angolo fatto dalla direzione del tiro con l&#039;orizzonte è più <lb></lb>acuto: nel 1604 Guidubaldo Del Monte vi fece ravveduto di questo errore, <lb></lb>ma nel concedergli che la traiettoria non può non esser curva in ogni sua <lb></lb>parte, gli negaste le somiglianze con la Parabola, alla quale preferiste una <lb></lb>linea, che si componesse d&#039;archi di cerchio con vario raggio di curvatura. </s>

<s><lb></lb>Scopriste nel 1609 l&#039;isocronismo dei getti di qualunque ampiezza, purchè <lb></lb>ugualmente alti, per semplice congettura, di che poi nel 1624 diceste di <lb></lb>aver trovato la dimostrazione, non già nella teoria del moto parabolico, ma <lb></lb>nell&#039;esperienza della pietra, che cade dalla sommità a piè dell&#039;albero sem­<lb></lb>pre, o stia ferma la nave o velocemente si muova. </s>

<s>S&#039;arrestarono a questo <lb></lb>punto i vostri progressi, che infino al 1632 rimasero stazionari, intanto che, <lb></lb>se voi non producete documento anteriore al mese di Settembre di quel­<lb></lb>l&#039;anno, noi non vi leveremo l&#039;accusa di avere, in modo indegno di un Fi­<lb></lb>losofo e di un animo onesto, usurpata al Cavalieri la tanto ambita scoperta. </s></p><p type="main">

<s>Galileo presentì pur troppo nella colpevole sua coscienza i terrori di <lb></lb>questa minaccia, i quali ei s&#039;argomentò d&#039;illudere, mettendo in mano al <lb></lb>Salviati certi foglietti, perchè, sopr&#039;essi scritti in latino, leggesse agl&#039;inter­<lb></lb>locutori i teoremi <emph type="italics"></emph>De motu proiectorum,<emph.end type="italics"></emph.end> come seconda parte di quel trat­<lb></lb>tato più antico <emph type="italics"></emph>De motu loculi,<emph.end type="italics"></emph.end> in modo da fare apparir che tutto avesse <lb></lb>l&#039;Accademico dimostrato nel medesimo tempo. </s>

<s>I documenti però attestano <lb></lb>che, mentre le prime proposizioni latine dei moti accelerati risalgono al 1604, <lb></lb>quelle de&#039;proietti son, per la massima parte, scritte nel 1636 e 37. Nel Gen­<lb></lb>naio di quest&#039;anno, come si rileva da una lettera di Dino Peri, l&#039;Elzevirio <lb></lb>in Leida aveva sotto i torchi i Dialoghi delle Resistenze e del Moto, ma no <pb xlink:href="020/01/2289.jpg" pagenum="532"></pb>quello de&#039;proietti, perchè l&#039;Autore v&#039;andava tuttavia lavorando (Alb. </s>

<s>X, 184): <lb></lb>e che vi lavorasse nel Febbraio seguente e nel Marzo, Galileo stesso lo scri­<lb></lb>veva al Micanzio (ivi, pag. </s>

<s>188) e al Magiotti, che rispondeva godere della <lb></lb>notizia in estremo (MSS. Gal., P. VI, T. XIII, fol. </s>

<s>14). De&#039;faticosi calcoli <lb></lb>aritmetici, fatti per costruire la <emph type="italics"></emph>Tabula altitudinum semiparabolarum ad <lb></lb>singulos gradus elevationis,<emph.end type="italics"></emph.end> è tutto pieno il tergo di una lettera di Ales­<lb></lb>sandro Ninci, scritta da Campoli nel Marzo del 1636 (ivi, P. V, T. II, fol. </s>

<s>125). </s></p><p type="main">

<s>Del non essere i foglietti, che il Salviati legge nel terzo Dialogo, con­<lb></lb>temporanei a quelli letti nel quarto, par che possa esser non lieve argomento <lb></lb>il non aver l&#039;Accademico avvertito ch&#039;essendo gli spazi come i quadrati dei <lb></lb>tempi, le relazioni, che passan fra loro, son rappresentate dalle ascisse e dalle <lb></lb>ordinate di una semiparabola, ciò che, dalla contemplazione de&#039;moti natu­<lb></lb>ralmente accelerati, avrebbe per diretta via potuto condurre a riconoscer le <lb></lb>proprietà della parabola ne&#039;proietti; <emph type="italics"></emph>quod non scripsit Galilaeus<emph.end type="italics"></emph.end> osservò il <lb></lb>Torricelli (Op. </s>

<s>geom., P. l cit., pag. </s>

<s>110), il quale fu primo a dimostrare in <lb></lb>pubblico che nella Parabola stessa convengono mirabilmente le due specie <lb></lb>di moti. </s></p><p type="main">

<s>Per confermar poi il nostro discorso che cioè, a rivelar l&#039;ingegno della <lb></lb>Natura <emph type="italics"></emph>circa parabolicam lineam ludentis,<emph.end type="italics"></emph.end> Galileo convertito non attese che <lb></lb>negli ultimi anni della sua vita, si avvertirà che non abbiamo dell&#039;avvenuta <lb></lb>conversione documento anteriore al dì 5 Giugno 1637, in quella lettera scritta <lb></lb>a Pietro Carcavy di Parigi, e nella quale, riducendo gli scherzi del Dialogo <lb></lb>al serio, si legge che “ sebbene dalla composizione del moto equabile col <lb></lb>retto perpendicolarmente discendente, con l&#039;accelerazione fatta nella propor­<lb></lb>zione da me assegnata, si descriverebbe una linea che, andando a terminare <lb></lb>nel centro, sarebbe spirale; nientedimeno, sinche noi ci trattenghiamo sopra <lb></lb>la superfice del globo terrestre, io non mi pento d&#039;assegnare a tale compo­<lb></lb>sizione una linea parabolica ” (Alb. </s>

<s>VII, 155). </s></p><p type="main">

<s>Convien dir che da scherzo intendesse pure di parlare il Salviati anche <lb></lb>colà, dove nel Dialogo copernicano afferma incurvarsi in arco la catena on­<lb></lb>deggiante col grave fatto pender da lei, ond&#039;è che, discorrendone sul serio <lb></lb>la prima volta in quarant&#039;anni nel nuovo Dialogo meccanico, non solo ivi <lb></lb>si dice che quella medesima catena s&#039;incurva in figura di parabola, ma, <lb></lb>dop&#039;avere insegnato il modo di descriverla com&#039;insegna Guidubaldo, acco­<lb></lb>gliendo ora amichevolmente quel che sempre erasi rifiutato; s&#039;aggiunge <lb></lb>l&#039;altra maniera di servirsi, per quella medesima descrizione, direttamente <lb></lb>della catena, <emph type="italics"></emph>punteggiandone sopra un muro la strada<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 144). </s></p><p type="main">

<s>Mentre avrebbe dovuto il Salviati ripensar che il primo modo di de­<lb></lb>scriver con maravigliosa facilità quante parabole uno vuole, col tirare una <lb></lb>palla inumidita sopra la superfice di uno specchio inclinato, non era inven­<lb></lb>zion dell&#039;Amico; piglia occasione di soggiungere che s&#039;ha di li esperienza il <lb></lb>moto de&#039;proietti farsi per linee paraboliche: “ effetto non osservato, prima che <lb></lb>dal nostro Amico, il quale ne arreca anco la dimostrazione ” (Alb. </s>

<s>XIII, 144). <lb></lb>Nella prefazioncella latina alla Giornata terza intorno i movimenti locali, os-<pb xlink:href="020/01/2290.jpg" pagenum="533"></pb>serva lo stesso Amico del Salviati che, gettato un grave per aria, descrive <lb></lb>una certa linea curva, “ verumtamen eam esse Parabolam nemo prodidit ” <lb></lb>(ibid., pag. </s>

<s>148). Se fosse Galileo potuto starsi sicuro che si tenessero per <lb></lb>anticamente scritte nella realtà queste parole, come si volevano fare appa­<lb></lb>rire nella forma, bastava avere ingerita ne&#039;lettori una tale persuasione, per­<lb></lb>chè non dovessero mettersi a ricercar d&#039;altro. </s>

<s>Ma pure compariva quell&#039;an­<lb></lb>nunzio di novità alla luce nel 1638, che vuol dire sei anni dopo che l&#039;aveva <lb></lb>già prodotto l&#039;Autore dello Specchio ustorio, per cui gli avversari o i poco <lb></lb>facili a credere a coloro, che vogliono in ogni cosa apparire i primi, avreb­<lb></lb>bero potuto notar l&#039;Autore della detta prefazioncella o di avere ignorate le <lb></lb>tradizioni della Scienza, o di aver profferito una menzogna manifesta. </s></p><p type="main">

<s>La sagacità di Galileo aveva prevedute anche le punte di questa saetta. </s>

<s><lb></lb>Atterrito dalle parole scritte al Marsili, concludeva il Cavalieri così le sue <lb></lb>difese: “ Insomma, s&#039;ella pur vuole che sia errore, non è di malizia al si­<lb></lb>curo. </s>

<s>Vegga pur quello vuole che io faccia per darle sodisfazione, che io son <lb></lb>prontissimo a farlo. </s>

<s>Ne ho dato fuori solo alcune copie quà in Bologna: <lb></lb>frattanto io non ne lascerò uscire altre, sino a che sia aggiustato il negozio, <lb></lb>se si può, in modo che ella vi abbia sodisfazione. </s>

<s>Perchè o io differirò a <lb></lb>darne fuori più, sinch&#039;ella non abbia stampato il suo libro Del moto, o ch&#039;ella <lb></lb>potrà stamparlo con l&#039;antidata ... o che finalmente abbrucerò tutte le copie, <lb></lb>perchè si distrugga con quelle la ragione d&#039;aver dato disgusto al mio signor <lb></lb>Galileo ” (Alb. </s>

<s>IX, 263). Galileo, benchè facesse altra vista, fu inteso pia­<lb></lb>cergli meglio di aver sodisfazione in quest&#039;ultimo modo, e così, com&#039;era il <lb></lb>suo piacere, fu fatto. </s>

<s>Le copie dello Specchio ustorio nel 1638 erano dive­<lb></lb>nute sì rare, che ne sarebbe andata perduta per sempre ogni memoria, se <lb></lb>Urbano Davisi, discepolo e ascritto al medesimo ordine religioso dell&#039;Autore, <lb></lb>non avesse fatto ristampare il libro nel 1650 in Bologna. </s></p><p type="main">

<s>I tiranni, con esempio non infrequente nelle Storie civili, hanno lavato <lb></lb>le loro colpe col sangue, generosamente versato a pro della patria: Galileo, <lb></lb>che s&#039;è presentato a noi sotto l&#039;aspetto di un tiranno, lavò pure le colpe <lb></lb>co&#039;sudori della sua fronte, sparsi a pro della Scienza, la quale videsi entrare <lb></lb>per lui, da quel varco apertole dal Cavalieri, al possesso di una provincia <lb></lb>nuova. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Posta, nella Giornata quarta, dove si seguita il discorso Dei movimenti <lb></lb>locali, per principio fondamentale la proposizione che il proietto <emph type="italics"></emph>dum fer­<lb></lb>tur motu composito ex horizontali aequabili, et ex naturaliter accelerato <lb></lb>deorsum, lineam semiparabolicam describit in sua latione;<emph.end type="italics"></emph.end> conclude Ga­<lb></lb>lileo da essa ordinatamente le principali proprietà dei moti violenti. </s>

<s>Queste <lb></lb>proprietà erano dall&#039;altra parte oramai note, per le belle esperienze di Gui-<pb xlink:href="020/01/2291.jpg" pagenum="534"></pb>dubaldo Del Monte, e per le ammirabili congetture del Tartaglia, intantochè <lb></lb>si proponeva al Promotor dei due Autori a dimostrare per scienza, e per <lb></lb>ragion conseguente dal moto parabolico, che massima è l&#039;ampiezza del tiro <lb></lb>elevato a mezza sqadra: ed essendo gl&#039;impeti nell&#039;ascesa e nella discesa <lb></lb>uguali, si lasciava a lui il prefinirne la giusta quantità in ciascun punto della <lb></lb>traiettoria. </s></p><p type="main">

<s>Ma non poteva il moto parabolico non ridursi, e non rientrare in quelle <lb></lb>leggi universali, dimostrate da Galileo nella precedente Giornata, rimanendo <lb></lb>in ogni modo gl&#039;impeti proporzionali ai tempi, e variando solo la linea della <lb></lb>caduta, che non è retta ma curva. </s>

<s>Che poi il moto curvo circolare non si <lb></lb>acquisti mai naturalmente, senza il moto retto che lo precede, fu specula­<lb></lb>zione antica dello stesso Galileo, il quale, applicandola alla Cosmografia, im­<lb></lb>maginò che il Creatore, collocato nel Sole immobile il centro, avesse fabbri­<lb></lb>cato tutti i pianeti nel medesimo luogo, “ e di lì datali inclinazione di moversi, <lb></lb>discendendo verso esso centro, sin che acquistassero quei gradi velocità, che <lb></lb>pareva alla Mente Divina: li quali acquistati, fossero volti in giro ciasche­<lb></lb>duno nel suo cerchio, mantenendo la già concepita velocità ” (Alb. </s>

<s>I, 34, 35). <lb></lb><figure id="id.020.01.2291.1.jpg" xlink:href="020/01/2291/1.jpg"></figure></s></p><p type="caption">

<s>Figura 285</s></p><p type="main">

<s>Quale efficacia dovessero avere questi pensieri in confermar, nella <lb></lb>mente di chi gli avea concepiti, l&#039;opinione delle traiettorie, circolari <lb></lb>esse pure, come le orbite celesti; si comprende assai facilmente. </s>

<s><lb></lb>Ma, riformatasi poi quell&#039;opinione, il concetto della genesi del <lb></lb>moto curvo parabolico dal moto retto precedente rimase, e <lb></lb>immaginando che si riducesse quel moto retto d&#039;acce­<lb></lb>lerato in equabile, col rivolgersi per l&#039;orizzontale, si <lb></lb>dispose Galileo a riconoscer per vero che, mentre, <lb></lb>rimanendosi il detto moto equabile, circolerebbe <lb></lb>intorno al centro; mescolato col moto naturale, <lb></lb>che non abbandona il mobile nemmeno per <lb></lb>la scesa curvilinea, compone quella stessa <lb></lb>linea, che sarebbe stata per sè circo­<lb></lb>lare, in parabolica. </s></p><p type="main">

<s>S&#039;immagini essere in C <lb></lb>(fig. </s>

<s>285) un grave spinto con <lb></lb>un dato impeto nella dire­<lb></lb>zione orizzontale CO: <lb></lb>descriverà per l&#039;aria <lb></lb>la semiparabola CD, <lb></lb>conl&#039;impeto retto <lb></lb>precedente, <lb></lb>dovuto alla <lb></lb>caduta, <lb></lb>che sia <lb></lb>per <pb xlink:href="020/01/2292.jpg" pagenum="535"></pb>esempio tale qual&#039;è da A in C, volto a sfogarsi orizzontalmente per la linea CO; <lb></lb>e con l&#039;impeto naturale, che seguita ad accompagnare il mobile in descri­<lb></lb>vere la semiparabola, il quale impeto è tanto, quanto ne acquisterebbe il ca­<lb></lb>dente in G, per la libera scesa CG. </s></p><p type="main">

<s>Sopravvenga in C un impeto doppio, qual si produrrebbe, quando il <lb></lb>moto retto precedente fosse fatto per l&#039;altezza BC, quadrupla di AC: per <lb></lb>quest&#039;impeto così concepito si passerebbe orizzontalmente dal mobile uno <lb></lb>spazio EG, doppio del primo DG, e per una simile ragione si passerebbe lo <lb></lb>spazio FG, doppio di EG, quando il moto retto precedente in C fosse per <lb></lb>un&#039;altezza quadrupla alla BC. </s></p><p type="main">

<s>Dietro un ragionamento, dalle già dimostrate leggi dei moti naturali in <lb></lb>simil guisa iniziato, sperava Galileo di poter determinare in D, in E e in F <lb></lb>le quantità degl&#039;impeti respettivi. </s>

<s>Sia, diceva, in C l&#039;impeto del cadente da A <lb></lb>uguale a 100, e poniamo CG uguale ad AC. </s>

<s>Essendo così dunque in D com­<lb></lb>posti insieme due impeti, ciascun de&#039;quali è come 100, sarà il totale 200. <lb></lb>In B, l&#039;impeto retto precedente, dovuto alla caduta in C dall&#039;altezza BC, è <lb></lb>doppio del cadente da A, e perciò è come 200; onde, aggiuntosi l&#039;impeto <lb></lb>acquistato dal venir per la parabola CE, o per l&#039;altezza CG, ch&#039;è pur 100; <lb></lb>tutto intero l&#039;impeto in E tornerà 300. Per queste medesime ragioni si ve­<lb></lb>drà che in F la somma de&#039;due impeti è 400 più 100, che vuol dir 500. <lb></lb>L&#039;impeto in F, pareva di poter concludere a Galileo, sta dunque all&#039;impeto <lb></lb>in E, come 5 a 3, e l&#039;impeto in E, all&#039;impeto in D, come 3 a 2, cioè, se­<lb></lb>condo dicevasi allora, in sesquialtera proporzione. </s></p><p type="main">

<s>“ Cadens ex A in C, conversus, describit parabolam CD. </s>

<s>Si vero mo­<lb></lb>mentum velocitatis in C duplum foret, describeret parabolam CE, cuius EG <lb></lb>dupla esset ad GD: impetus enim duplus in C permeat in orizontem du­<lb></lb>plicem spacium tempore eodem. </s>

<s>Sed, ut acquiratur in C momentum duplum, <lb></lb>necesse est casum fieri ex quadrupla altitudine, nempe ex CB. Pariter, ex <lb></lb>altitudine quadrupla ad CB, describetur parabola CF, cuius amplitudo GF <lb></lb>dupla est ad GE. ” </s></p><p type="main">

<s>“ Verum mobile in D videtur supra impetum in C addere impetum <lb></lb>acquisitum per parabolam CD, quod respondet altitudini CG. </s>

<s>Mobile vero <lb></lb>in E idem momentum addit supra impetum quam habuit in C, qui erat <lb></lb>duplus ad impetum alterius mobilis; ergo impetus mobilis in E videtur esse <lb></lb>sexquialterus ad impetum mobilis in D. </s>

<s>Similiter invenietur impetum in F, <lb></lb>ad impetum in E, esse ut 5 ad 3. ” </s></p><p type="main">

<s>“ In elevatione igitur EA, si proiectum habuerit impetum sexquialte­<lb></lb>rum ad impetum in D, proiecti secundum elevationem DA proiicientur se­<lb></lb>cundum parabolas EC, DC, intra easdem parallelas, sed distantia EG dupla <lb></lb>erit ad DG. ” (MSS. Gal., P. V, T. II, fol. </s>

<s>90). </s></p><p type="main">

<s>Incominciano di qui ad apparire in queste prime speculazioni galileiane <lb></lb>due supposti, i quali son di non lieve importanza nella Storia dei proietti. </s>

<s><lb></lb>Il primo è che la stessa semiparabola venga a descriversi o dall&#039;esplosione <lb></lb>in C, con tiro di punto in bianco, o dall&#039;esplosione in D, secondo l&#039;eleva-<pb xlink:href="020/01/2293.jpg" pagenum="536"></pb>zione DA. Ora, essendo DA tangente alla parabola in D, si suppone in se­<lb></lb>condo luogo che, cessando il moto parabolico di accelerarsi nel punto D, pro­<lb></lb>seguirebbe indefinitamente il suo moto per la direzione di essa tangente. </s>

<s>Era <lb></lb>anche questa però dottrina antica di Galileo, il quale aveva nella Giornata <lb></lb>seconda dei Massimi Sistemi fatto sentenziare al Salviati “ che il proietto <lb></lb>acquista impeto di moversi per la tangente dell&#039;arco, descritto dal moto del <lb></lb>proiciente nel punto della separazione di esso proietto dal proiciente ” <lb></lb>(Alb. </s>

<s>I, 213). </s></p><p type="main">

<s>Ritenuto dunque per vero che la direzione del tiro in D, per la quale <lb></lb>si ritesse dal mobile la semiparabola DC, sia secondo la tangente DA, es­<lb></lb>sendosi fatto AG uguale a GD, l&#039;angolo ADG tornerà semiretto, e Galileo <lb></lb>preparavasi questa costruzione, col fine di dimostrar ciò che il Tartaglia avea <lb></lb>congetturato sugli avvisi dell&#039;esperienza. </s>

<s>Facciasi GH doppia di AG: essendo <lb></lb>EG pure doppia di DG, ossia di AG, congiunti i punti E, H l&#039;angolo HEG <lb></lb>sarà a mezza squadra, e il medesimo proietto dal medesimo punto E secondo <lb></lb>le direzioni EH, EA, descriverà le due semiparabole EA, EC, le quali avranno <lb></lb>la medesima ampiezza. </s></p><p type="main">

<s>Ora, applicando Galileo i teoremi già dimostrati rispetto agl&#039;impeti pro­<lb></lb>porzionali ai tempi, i quali stanno come le radici degli spazi, calcola le quan­<lb></lb>tità dell&#039;impeto necessario al proietto in E perchè possa descrivere la semi­<lb></lb>parabola EA: quantità che, dovendo resultare dall&#039;impeto del cadente in A <lb></lb>da H, ritrovato 141 (essendo AC sempre cento), e dall&#039;impeto in G da A, <lb></lb>che è pur 141, sarà uguale a 282. Ma l&#039;impeto necessario in E perchè possa <lb></lb>il proietto disegnare la via EC fu ritrovato dianzi 300, dunque, nell&#039;eleva­<lb></lb>zion semiretta, si passa il medesimo spazio che in elevazion minore, con tanto <lb></lb>minor forza, quanto 282 è minor di 300, e perciò con forza d&#039;impeto uguale, <lb></lb>nel tiro a mezza squadra, si passerà secondo tal proporzione uno spazio mag­<lb></lb>giore. </s>

<s>Soggiunge Galileo un altro simile esempio di ciò, duplicando in GX <lb></lb>la GH, e comparando l&#039;impeto necessario a descriver la semiparabola FH, <lb></lb>secondo l&#039;elevazion semiretta FX, con l&#039;impeto necessario a descriver la se­<lb></lb>miparabola FC, e trova quello tanto esser minore di questo, quanto 400 è <lb></lb>minore di 500. </s></p><p type="main">

<s>Restava a comparar l&#039;impeto, nella elevazion semiretta, con l&#039;impeto a <lb></lb>una elevazione maggiore, e dal calcolo resultò ancora a Galileo che l&#039;uno <lb></lb>riusciva sempre maggiore dell&#039;altro. </s>

<s>Presa perciò CG uguale a RG, consi­<lb></lb>derava la semiparabola RC generata dal moto retto antecedente, l&#039;impeto <lb></lb>del quale in C, da S, trovò esser come 50, e dal moto conseguente per CG, <lb></lb>l&#039;impeto del quale in G da C fu posto come 100; cosicchè l&#039;impeto totale <lb></lb>in R, nella elevazione maggiore della semiretta, per la quale si suppone <lb></lb>esser descritta la R C, tornerebbe uguale a 150. Divisa poi la CG in mezzo <lb></lb>in T, passava Galileo a calcolar l&#039;impeto che, dal medesimo punto R, fa­<lb></lb>rebbe descrivere al proietto la via RT, secondo la elevazion semiretta RC, <lb></lb>e trovato al calcolo essere in T l&#039;impeto del veniente da C 70 1/2, ne con­<lb></lb>cluse che l&#039;impeto della elevazion semiretta in R era 141, minore di 150. </s></p><pb xlink:href="020/01/2294.jpg" pagenum="537"></pb><p type="main">

<s>Incollato sotto il foglio, da cui fu trascritto il modo di misurare gl&#039;impeti <lb></lb>ne&#039;punti F, E, D, delle semiparabole aventi la medesima altezza CG, si trova <lb></lb>un pezzetto di carta, in un angolo della quale, dalla medesima mano di Gali­<lb></lb>leo, è scritta in tre linee la tavoletta: “ Impetus in C, cadentis ex A, sit 100; <lb></lb>— cadentis ex B erit 200; — impetus in E erit 300. ” Di contro, e sotto, <lb></lb>seguita questa Nota, nella quale si contempla il caso della elevazion maggiore <lb></lb>della semiretta, che vuol aver maggior forza, per fare la medesima volata: </s></p><p type="main">

<s>“ Cadentis in A ex H impetus in E erit 141: cadentis vero per para­<lb></lb>bolam AE impetus in E erit duplicatus, nempe 282. Constat igitur maiorem <lb></lb>esse impetum venientis per parabolam CE in E, quam venientis per para­<lb></lb>bolam AE. </s>

<s>Et si proiectum ex E, secundum elevationem EH, habet impe­<lb></lb>tum ut 282, conficiet parabolam EA: secundum elevationem vero EA, confi­<lb></lb>ciet proiectum parabolam EC, si habuerit impetum ut 300. Ergo, in elevatione <lb></lb>semirecti EH, ab eadem vi, longius eiaculatur, quam in elevatione ea, quae <lb></lb>minor est semirecti. </s>

<s>” </s></p><p type="main">

<s>“ Cadentis in H ex X impetus in H erit 200: cadentis vero per para­<lb></lb>bolam HF impetus in F erit duplicatus, nempe 400. Impetus in F est 500 <lb></lb>venientis per parabolam CF: venientis vero per parabolam HF impetus in F <lb></lb>est 400. Ex quo patet etiam longius eiaculari ab eadem vi per elevationem <lb></lb>semirecti, quam per minorem “ (ibid.). </s></p><p type="main">

<s>È sotto a questa scritta dalla penna di Galileo l&#039;altra Nota relativa ai <lb></lb>calcoli comparativi fra l&#039;impeto della elevazion semiretta e un&#039;altra che di <lb></lb>lei sia comunque maggiore, e di contro alla tavoletta che dice, scritta in <lb></lb>due linee, “ Impetus in C ex S erit 50; — in R erit 150 ” si leggono que­<lb></lb>ste parole: “ Impetus vero in T ex C est fere 70 1/2; conversi per para­<lb></lb>bolam TR in R erit 141: minor nempe quam venientis ex S per C in R, <lb></lb>qui fuit 150. Unde constat quod in elevatione semirecti RT ab eadem vi <lb></lb>longior fit proiectio, quam per elevationem RC ” (ibid.). </s></p><p type="main">

<s>Queste non erano propriamente dimostrazioni, ma una buona promessa <lb></lb>e una lieta speranza che, dalle generali proprietà dei moti naturali, si sa­<lb></lb>rebbero potute ritrovare, alle proprietà dei moti proiettizi, le mate natiche <lb></lb>dimostrazioni, le quali, svolte da principii proprii e ordinate, aggiungessero <lb></lb>una parte nuova e desideratissima al trattato Dei movimenti locali. </s>

<s>Essendo <lb></lb>que&#039;principii premonstrati nella parabola, dovevano alcuni necessariamente <lb></lb>ridursi alle proprietà geometriche di lei, dipendenti dalla principalissima che <lb></lb>dice essere le ascisse proporzionali ai quadrati delle ordinate, d&#039;onde il Ca­<lb></lb>valieri, e poi Galileo, ne conclusero le fondamentali proprietà meccaniche <lb></lb>della curva, facendo alle ascisse rappresentare gli spazi e alle ordinate i <lb></lb>tempi. </s>

<s>Il supposto, applicato ne&#039;calcoli precedenti, che cioè l&#039;elevazione del <lb></lb>tiro sia designata dalla tangente, faceva alla Meccanica invocare quell&#039;altra <lb></lb>proprietà geometrica della Parabola, che dice essere la suttangente dupla <lb></lb>all&#039;ascissa; proprietà che Galileo, com&#039;Apollonio, dimostra dagli assurdi, dopo <lb></lb>aver premessa l&#039;equazion della curva, che il Torricelli dice “ Apollonii qui­<lb></lb>dem, sed marte proprio a Galileo demonstratam ” (Op. </s>

<s>geom. </s>

<s>cit, pag. </s>

<s>110). </s></p><pb xlink:href="020/01/2295.jpg" pagenum="538"></pb><p type="main">

<s>Ma i principali elementi delle traiettorie dovevano necessariamente co­<lb></lb>stituirsi infino da quelle prime speculazioni galileiane intorno alla misura <lb></lb>degl&#039;impeti, che contenevano in germe la scienza de&#039;proietti, dalle quali <lb></lb>speculazioni apparisce ridursi quegli elementi a tre: alla linea del moto retto <lb></lb>antecedente, alla linea del moto retto conseguente, e alla linea della distesa <lb></lb>orizzontale, i quali tre elementi della Scienza nuova, perchè volevano essere <lb></lb>designati con nomi propri, chiamò Galileo <emph type="italics"></emph>sublimità<emph.end type="italics"></emph.end> la prima delle dette <lb></lb>linee, <emph type="italics"></emph>altezza<emph.end type="italics"></emph.end> la seconda, e <emph type="italics"></emph>amplitudine<emph.end type="italics"></emph.end> la terza. </s>

<s>“ Advertatur semiparabo­<lb></lb>lae CD (nella precedente figura) <emph type="italics"></emph>amplitudinem<emph.end type="italics"></emph.end> a me vocari horizontalem <lb></lb>GD; <emph type="italics"></emph>altitudinem<emph.end type="italics"></emph.end> CG, nempe eiusdem parabolae axem: lineam vero AC, <lb></lb>ex cuius descensu determinatur impetus horizontalis, <emph type="italics"></emph>sublimitatem<emph.end type="italics"></emph.end> appelllo ” <lb></lb>(Alb. </s>

<s>XIII, 237). </s></p><p type="main">

<s>Perchè dalla sublimità dipende il moto proiettizio per l&#039;orizzonte, in <lb></lb>che consiste la violenza del tiro, e il fine per cui si mettono in esercizio le <lb></lb>macchine ballistiche, si comprende com&#039;uno de&#039;primi e de&#039;più importanti <lb></lb>problemi, che si proponesse a risolvere Galileo, fosse quello di trovare il <lb></lb>punto sublime, da cui dovrebbe cader il grave per descrivere una data Pa­<lb></lb>rabola. </s>

<s>Son della soluzione rimaste ne&#039;manoscritti le prime prove, le quali <lb></lb>si vedon movere dalla considerazione del caso più semplice, in cui cioè l&#039;am­<lb></lb>piezza è doppia dell&#039;altezza, perch&#039;è allora la tangente stessa, che decide, <lb></lb>nell&#039;incontrare l&#039;asse prolungato, il punto della sublimità che si cercava. </s>

<s><lb></lb>Passa da questo Galileo al caso, in cui l&#039;ampiezza abbia all&#039;altezza qualun­<lb></lb>que proporzione; e perchè in ogni modo la Parabola è la medesima, e me­<lb></lb>desimo è il punto sublime, dimostra essere un tal punto nel prolungamento <lb></lb>dell&#039;asse, a una distanza dal vertice, che sia terza proporzionale tra l&#039;altezza <lb></lb>e la metà della base. </s></p><p type="main">

<s>“ Sit parabola ABC (fig. </s>

<s>286), cuius amplitudo CD dupla sit altitudi­<lb></lb><figure id="id.020.01.2295.1.jpg" xlink:href="020/01/2295/1.jpg"></figure></s></p><p type="caption">

<s>Figura 286<lb></lb>nis DA, et illa tangat EC in pun­<lb></lb>cto C: erit AE aequalis AD, et cadens <lb></lb>ex E, conversum in A, describit pa­<lb></lb>rabolam ABC. ” </s></p><p type="main">

<s>“ Sumatur in parabola quodli­<lb></lb>bet punctum B: contemplandum est <lb></lb>quomodo, pro describenda parabola <lb></lb>AB, requiratur idem impetus caden­<lb></lb>tis ex E usque ad A. </s>

<s>Ex A reperia­<lb></lb>tur punctum E, ex quo decidat pro­<lb></lb>iectum. </s>

<s>Tangat BGF ipsam in B, et <lb></lb>ducatur horizontalis BH: erit AH ae­<lb></lb>qualis AF. </s>

<s>Dico modo punctum E re­<lb></lb>periri, quia ut AF ad AG, ita est GA <lb></lb>ad AE, quod sic probatur. </s>

<s>Ut DA ad AG, ita dupla DA ad duplam AG, nempe <lb></lb>DC ad HB: et ut quadratus DA ad quadratum AG, ita quadratus DC ad qua­<lb></lb>dratum HB, et ita est linea DA ad AH, seu EA ad AF ” (MSS. Gal. </s>

<s>ibid., fol. </s>

<s>115). </s></p><pb xlink:href="020/01/2296.jpg" pagenum="539"></pb><p type="main">

<s>La conclusione, che nel manoscritto galileiano segue immediata, dipende <lb></lb>dalle cose dimostrate, ed espresse dalla serie di queste equazioni: DA2:AG2= <lb></lb>DE2:HB2=AD:AH=EA:AF, le due estreme ragioni delle quali danno <lb></lb>EA.AF=AG2 ossia AF:AG=AG:EA. “ Constat igitur quod, si datae <lb></lb>parabolae AB inveniendus sit punctus sublimis E, ex quo cadens conficiat <lb></lb>parabolam AB, posita AF aequali AH, et ducta FGB, quae parabolam tan­<lb></lb>gat in B, sumpta tertia proportionalis ipsarum FA, AG, dabit AE, ex qua <lb></lb>cadens etc. </s>

<s>quod erat faciendum ” (ibid.). </s></p><p type="main">

<s>Seguono sotto a queste, nel medesimo foglio, altre linee, in principio <lb></lb>delle quali si legge <emph type="italics"></emph>Melius,<emph.end type="italics"></emph.end> e in margine è notato <emph type="italics"></emph>Scritta,<emph.end type="italics"></emph.end> e vuol dire che <lb></lb>la medesima dimostrazione fatta meglio era stata inserita nel Dialogo, dove <lb></lb>propriamente si legge sotto la proposizione quinta <emph type="italics"></emph>De motu proiectorum.<emph.end type="italics"></emph.end><lb></lb>Nel trascriverla però di qui Galileo fa alcune leggere variazioni, come in <lb></lb>tutte le altre, nelle quali si nota che furono scritte. </s>

<s>E perchè possano di tali <lb></lb>variazioni i Lettori avere un&#039;idea, trascriveremo dal citato foglio il secondo <lb></lb>modo di trovar meglio la sublimità, data che sia la parabola. </s></p><p type="main">

<s>“ Melius: Sit parabola AB (nella passata figura) cuius amplitudo BH, <lb></lb>et axis perpendicularis HE, in quo invenienda sit altitudo, ex qua cadens <lb></lb>parabolam describat. </s>

<s>Ponatur AF aequalis AH, et connectatur FB secans <lb></lb>horizontalem AG in G, et tangentem parabolam in B. </s>

<s>Sitque ipsarum FA, <lb></lb>AG tertia proportionalis AE. </s>

<s>Dico E esse punctum quaesitum. </s>

<s>” </s></p><p type="main">

<s>“ Si enim intelligatur EA esse mensura temporis casus ex E in A, et <lb></lb>impetus acquisiti in A, erit AG (media nempe inter EA, AF) tempus et im­<lb></lb>petus venientis ex F in A, seu ex A in H. </s>

<s>Sed impetus in A cadentis ex E, <lb></lb>tempore E A, cum impetu acquisito in A, conficit in horizontali motu ae­<lb></lb>quabili duplam EA; ergo etiam eodem impetu, in tempore AG, conficiet <lb></lb>duplam GA, nempe BH, et in perpendiculari motu ex quiete, eodem tem­<lb></lb>pore GA, conficit AH. </s>

<s>Ergo eodem tempore conficiuntur amplitudo et alti­<lb></lb>tudo AH. </s>

<s>Describitur ergo Parabola AB ex casu F, quod quaerebatur ” (ibid.). </s></p><p type="main">

<s>Ne deduce di qui Galileo il corollario, che la metà della base è media <lb></lb>proporzionale tra la sublimità e l&#039;altezza della semiparabola, ciò che dava <lb></lb>occasione al Viviani di scioglier così in un modo assai più spedito quel me­<lb></lb>desimo problema: “ Quaeratur sublimitas parabolae AB, cuius axis AH (nella <lb></lb>medesima ultima figura) basis HB. </s>

<s>Ducatur tangens BF, ac tangens AG, et <lb></lb>iuncta HG, ipsi ad G perdendicularis, erigatur GE axi occurrens in E. </s>

<s>Nam <lb></lb>AE erit sublimitas quaesita. </s>

<s>Est enim AG dimidium basis HB, media pro­<lb></lb>portionalis inter altitudinem et sublimitatem, per corollarium huius. </s>

<s>Ergo AE <lb></lb>erit sublimitas quaesita ” (MSS. Cal., P. V, T. IX. <emph type="italics"></emph>Postille del V. all&#039;edi­<lb></lb>zione di Leida<emph.end type="italics"></emph.end>). </s></p><p type="main">

<s>Il quesito dicemmo essere stato uno dei primi, a cui si propose di ri­<lb></lb>spondere Galileo nel dimostrare le meccaniche proprietà dei proietti, il trat­<lb></lb>tato delle quali, nell&#039;intenzione che s&#039;era formata allora, si limitava alla <lb></lb>misura degl&#039;impeti, e alle ragioni dei tiri elevati a mezza squadra. </s>

<s>Diremo <lb></lb>com&#039;egli aggiungesse poi a queste due una terza parte, nella quale appli-<pb xlink:href="020/01/2297.jpg" pagenum="540"></pb>cava agli esercizi militari le teorie, insegnando a calcolare e a disporre in <lb></lb>Tavole digradate i tiri del cannone. </s>

<s>Ma è da vedere intanto quanto sudasse <lb></lb>il grand&#039;Uomo, e quanto s&#039;affannassero dietro lui il Torricelli e il Viviani <lb></lb>per determinar l&#039;impeto in ciascun punto della parabola, ch&#039;è problema di <lb></lb>sì facile soluzione a chiunque non rifiuti di far uso del parallelogrammo o <lb></lb>del rettangolo delle forze. </s>

<s>Per avere infatti le relazioni tra l&#039;impeto totale <lb></lb>e gl&#039;impeti parziali nel punto C della parabola ABC, nella precedente fig. </s>

<s>286, <lb></lb>non occorre far altro che prendere della tangente CE una porzione a pia­<lb></lb>cere qual sarebbe CM, e sopr&#039;essa come diagonale costruire il rettangolo ON, <lb></lb>di cui il lato MN rappresenterà l&#039;impeto perpendicolare, e l&#039;altro CN l&#039;im­<lb></lb>peto orizzontale. </s>

<s>E perchè il triangolo CMN è simile al triangolo CED, s&#039;hanno <lb></lb>le cercate proporzionalità rappresentate dagli stessi elementi della Parabola, <lb></lb>nella quale la tangente CE è tanta parte della suttangente ED e dell&#039;ordi­<lb></lb>nata DC, quanta parte l&#039;impeto totale è del diretto nel perpendicolo, e per <lb></lb>l&#039;orizzonte. </s></p><p type="main">

<s>A un tal termine conducevano insomma le tortuose erte vie, proseguite <lb></lb>da Galileo e dai due sopra commemorati Promotori di lui, nè si crederebbe <lb></lb>che il veder riuscire quelle due vie sì diverse a un termine, non valesse a <lb></lb>persuader così grandi e liberi ingegni che dovevano ambedue essere ugual­<lb></lb>mente buone, e ch&#039;era una follia lasciar, per mettersi agli erti e lunghi, i <lb></lb>più brevi e piani sentieri. </s>

<s>Dev&#039;essere stato dunque motivo a così strano <lb></lb>modo di procedere qualche fallacia, l&#039;origine della quale facilmente si sco­<lb></lb>pre nelle cose poco addietro narrate. </s></p><p type="main">

<s>Si rammemoreranno i Lettori come il Cardano considerando che i due <lb></lb>moti composti AD, AE (fig. </s>

<s>287) s&#039;impediscono a vicenda, ne aveva con­<lb></lb>cluso che il proietto in C arriva più tardi di quel che non avrebbe fatto <lb></lb><figure id="id.020.01.2297.1.jpg" xlink:href="020/01/2297/1.jpg"></figure></s></p><p type="caption">

<s>(Figura 287)<lb></lb>liberamente cadendo per AE: Galileo aveva invece sco­<lb></lb>perto, per ragione e per esperienza, che tanto la linea <lb></lb>trasversale AC, quanto la diretta AE, son passate dal <lb></lb>mobile scendente in A dalla quiete nel medesimo tempo, <lb></lb>ond&#039;è che, trascorrendo in una fallacia simile a quella <lb></lb>del Cardano, dal non essere il moto resultante per AC <lb></lb>indugiato, ne aveva concluso che i due componenti <lb></lb>per AD e per AE non s&#039;impediscono, e che la somma <lb></lb>delle parti doveva esattamente essere uguale all&#039;intero. </s>

<s><lb></lb>Secondo una tal conclusione vedemmo essere stati, nella <lb></lb>figura 284, computati gl&#039;impeti in F, in E e in D re­<lb></lb>sultanti dalla somma esatta del moto retto antecedente, e del conseguente <lb></lb>nella Parabola. </s></p><p type="main">

<s>Se non che dal pensar che il moto retto antecedente volgesi per l&#039;orizzon­<lb></lb>tale GD; che il retto conseguente prosegue per il perpendicolo AG, e che <lb></lb>il composto d&#039;ambedue è diretto secondo la tangente AD, incominciò a na­<lb></lb>scere nella mente di Galileo il dubbio che si venisse una linea retta a fare <lb></lb>uguale alla spezzata: dubbio ch&#039;ei si studiava di quietare dicendo non si <pb xlink:href="020/01/2298.jpg" pagenum="541"></pb>trattar di linee geometriche circoscriventi uno spazio, ma di linee dinami­<lb></lb>che rappresentanti una forza o una potenza, sicch&#039;essendo l&#039;angolo AGD <lb></lb>retto è verissimo che la potenza o il quadrato di AB è uguale alla somma <lb></lb>delle potenze, o dei quadrati di DG e di AG. </s></p><p type="main">

<s>Prende da un tale equivoco tutto il suo valore dimostrativo la propo­<lb></lb>sizione II del quarto Dialogo galileiano, dalla quale dipendendo la teoria degli <lb></lb>impeti riesce questa, nell&#039;intenzion dell&#039;Autore, per tutto falsa, e avventu­<lb></lb>rosamente si corregge e riducesi al vero, con l&#039;intender che gl&#039;impeti non <lb></lb>siano proporzionali alle potenze, ma alle semplici linee, cosicchè la somma <lb></lb>delle componenti di tanto ecceda la resultante del moto, di quanto i due <lb></lb>lati del rettangolo distesi in dirittura eccedono la lunghezza della diagonale. </s>

<s><lb></lb>Si può ora di qui intendere perchè Galileo e i seguaci di lui scegliessero <lb></lb>le vie aspre e tortuose, e come, per essere i due impeti nella Parabola or­<lb></lb>togonali, si rendano avventurosamente veri i loro teoremi, dando altro si­<lb></lb>gnificato alle loro espressioni, che son bene spesso quelle medesime di chi <lb></lb>fa libero uso del parallelogrammo delle forze. </s>

<s>Così non infrequentemente <lb></lb>leggesi nelle dimostrazioni di Galileo comporsi i due moti nella <emph type="italics"></emph>diagonale,<emph.end type="italics"></emph.end><lb></lb>invece di dir nell&#039;<emph type="italics"></emph>ipotenusa,<emph.end type="italics"></emph.end> secondo il linguaggio proprio alle professate <lb></lb>dottrine. </s>

<s>Ma i discorsi s&#039;intenderanno meglio dal passar che faremo all&#039;esame <lb></lb>dei fatti. </s></p><p type="main">

<s>Le proposizioni terza e quarta, nella quarta Giornata delle due Nuove <lb></lb>Scienze, e tutta l&#039;interlocuzione che le commenta, non sono altro per così <lb></lb><figure id="id.020.01.2298.1.jpg" xlink:href="020/01/2298/1.jpg"></figure></s></p><p type="caption">

<s>Figura 288<lb></lb>dire che una soluzione assai lunga, e spesso <lb></lb>spesso noiosa, della seguente Nota mano­<lb></lb>scritta, nella quale la concisione aggiunge <lb></lb>al pensiero mirabile chiarezza: “ In motu <lb></lb>ex quiete eadem ratione intenditur velocita­<lb></lb>tis momentum et tempus ipsius motus. </s>

<s>Fiat <lb></lb>enim motus per AB (fig. </s>

<s>288), ex quiete <lb></lb>in A, et accipiatur quodlibet punctum C, et <lb></lb>ponatur AC esse tempus casus per AC, et <lb></lb>momentum celeritatis in C acquisitum esse <lb></lb>pariter ut AC. </s>

<s>Sumaturque rursus quodlibet punctum B: <emph type="italics"></emph>Dico tempus ca­<lb></lb>sus per AB, ad tempus per AC, esse ut momentum velocitatis in B, ad <lb></lb>momentum in C. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sumatur AS media inter BA, AC, et cum positum sit tempus casus <lb></lb>per AC esse AC, erit AS tempus per AB. </s>

<s>Demonstrandum igitur est mo­<lb></lb>mentum celeritatis in C, ad momentum celeritatis in B, esse ut AC ad AS. ” </s></p><p type="main">

<s>“ Sumantur horizontales CD dupla ad CA, BE vero dupla ad BA. </s>

<s>Con­<lb></lb>stat ex demonstratis cadens per AC, conversum in horizontem CD, confi­<lb></lb>cere CD motu aequabili, aequali tempore atque ipsam AC confecit motu <lb></lb>accelerato naturaliter: et similiter BE confici eodcm tempore atque AB. </s>

<s>Sed <lb></lb>tempus ipsius AB est AS, ergo horizontalis BE conficitur tempore AS. ” </s></p><p type="main">

<s>“ Fiat ut tempus SA ad tempus AC, ita EB ad BL. </s>

<s>Cumque motus <pb xlink:href="020/01/2299.jpg" pagenum="542"></pb>per BE sit aequabilis, erit spacium BL peractum tempore AC, secundum <lb></lb>momentum celeritatis in B. </s>

<s>Sed secundum momentum celeritatis in C, eo­<lb></lb>dem tempore AC, conficitur spacium CD: momenta autem celeritatis sunt <lb></lb>inter se ut spacia, quae iuxta ipsa momenta eodem conficiuntur tempore; <lb></lb>ergo momentum celeritatis in C, ad momentum celeritatis in B, est ut DC <lb></lb>ad BL. ” </s></p><p type="main">

<s>“ Quia vero ut DC ad BE, ita ipsarum dimidia, nempe CA ad AB; ut <lb></lb>aulem EB ad BL, ita BA ad AS, ergo, ex aequali, ut DC ad BL, ita CA <lb></lb>ad AS: hoc est, ut momentum celeritatis in C, ad momentum celeritatis <lb></lb>in B, ita CA ad AS: hoc est, tempus per CA, ad tempus per AB, quod erat <lb></lb>demonstrandum. </s>

<s>” </s></p><p type="main">

<s>“ Determinatur ergo impetus in singulis punctis parabolae ABC (fig. </s>

<s>289) <lb></lb>ex potentia momenti acquisiti per descensum EA, quod semper servatur <lb></lb><figure id="id.020.01.2299.1.jpg" xlink:href="020/01/2299/1.jpg"></figure></s></p><p type="caption">

<s>Figura 289<lb></lb>idem, et determinatur impetum ori­<lb></lb>zontalem BH ex potentia alterius <lb></lb>momenti acquisiti in descensu per­<lb></lb>pendiculari. </s>

<s>Ut v. </s>

<s>g, in B, erit im­<lb></lb>petus determinatus a linea poten­<lb></lb>tiae EA, et mediam inter AD, AH, <lb></lb>quae sit AI. ” (MSS. cit., P. V, T. <lb></lb>H, fol. </s>

<s>91 a tergo). </s></p><p type="main">

<s>Poche parole bastano a espli­<lb></lb>care il concetto, da Galileo esplicato <lb></lb>nel Dialogo con si prolisso discorso, <lb></lb>osservando che s&#039;insegna ivi il modo <lb></lb>di determinar l&#039;impeto, in qualun­<lb></lb>que punto delia Parabola, dall&#039;im­<lb></lb>peto misurato in quel particolar punto di lei, che ci vien riferito dall&#039;ordinata <lb></lb>doppia all&#039;ascissa, e perciò uguale alla suttangente, qual sarebbe il punto C <lb></lb>nella precedente figura. </s>

<s>Essendo in questo caso EA, uguale ad AD, i due im­<lb></lb>peti orizzontale e perpendicolare sono uguali, ond&#039;è che la potenza resultante <lb></lb>dalle due dette potenze componenti s&#039;avrà, secondo Galileo, costruendo un <lb></lb>triangolo co&#039;cateti uguali ad AE, dall&#039;ipotenusa del quale avremo rappre­<lb></lb>sentato l&#039;impeto che si cerca. </s>

<s>Or perchè in questa medesima figura che ab­<lb></lb>biamo sott&#039;occhio AL è uguale ad AE, il triangolo EAL con l&#039;ipotenusa <lb></lb>EL, ci porge la desiderata dinamica costruzione già fatta. </s></p><p type="main">

<s>Di qui passa Galileo, come si diceva, a determinar l&#039;impeto in qualun­<lb></lb>que altro punto della Parabola, come sarebbe in B, in cui l&#039;impeto oriz­<lb></lb>zontale rimanendo il medesimo sarà come dianzi rappresentato da AE. </s>

<s>Non <lb></lb>riman dunque che a determinar la lunghezza dell&#039;altro cateto, rappresen­<lb></lb>tante l&#039;impeto perpendicolare, il qual impeto è tanto, quant&#039;è del cadente <lb></lb>da A in H, ed ha perciò per misura AI, media tra AD, AH, essendo presa <lb></lb>AD qual misura del tempo e del&#039;impeto per AD. Cosicchè, se la orizzon­<lb></lb>tale AL si risega in G in modo, che sia AG uguale ad AI, sarà essa AG il <pb xlink:href="020/01/2300.jpg" pagenum="543"></pb>cateto che mancava a costruire il triangolo dinamico, e l&#039;impeto in C starà <lb></lb>all&#039;impeto in B, nella medesima Parabola, come la potenza dell&#039;ipotenusa EL <lb></lb>sia alla potenza dell&#039;ipotenusa EG. </s></p><p type="main">

<s>È un fatto dunque che il primo modo, insegnato da Galileo per misu­<lb></lb>rare gl&#039;impeti ne&#039;vari punti della traiettoria, anco corretto dalla falsità sua <lb></lb>radicale, è indiretto, e perciò faticoso. </s>

<s>Gl&#039;immediati Promotorì di lui che, <lb></lb>non accettando pure la regola del parallelogrammo, non poterono nemmen <lb></lb>essi mettersi per le vie più dirette, si dovettero contentare di rendere i me­<lb></lb>todi medesìmi del Maestro o più facili o più eleganti. </s>

<s>La Storia non ha fin <lb></lb>qui conosciuto fra que&#039;Promotori che il Torricelli, ma noi ora gli aggiun­<lb></lb>giamo collega il Viviani, il quale, nella postilla manoscritta alla citata copia <lb></lb>di Leida, osservava, nella presignata figura, ch&#039;essendo BF tangente e AG, <lb></lb>uguale ad AI, media tra AD, cioè AE, e AH; congiunta la GH, il triangolo <lb></lb>EGH torna rettangolo in G, ond&#039;è che, circoscrittogli col diametro EH un <lb></lb>mezzo cerchio, la cercata misura dell&#039;impeto in B è data dalla sottesa EG, <lb></lb>che si potrà dunque definir colla semplice riga e col compasso. </s></p><p type="main">

<s>“ Quum, in superiori constructione, sit AI, vel AG, media proportio­<lb></lb>nalis inter AD, AH, vel inter AE, AH, si iungatur GH erit angulus EGH <lb></lb>rectus, ac ideo EG media proportionalis inter EH, AE. </s>

<s>Impetus ergo in B <lb></lb>facilius reperitur describendo semicirculum super EH, cuius circumferentia, <lb></lb>secans AL in G, dabit chordam EG pro mensura impetus in B ” (MSS. Gal., <lb></lb>P. V, T. IX, pag. </s>

<s>256). </s></p><p type="main">

<s>“ Vel sic expeditius: Sumatur AG aequalis dimidio ordinatae HB; nam, <lb></lb>iuncta EG, erit mensura impetus in B. </s>

<s>Vel ducta ex B contingente BF, se­<lb></lb>cante AL in G, erit EG mensura impetus in B, quae est quoque mensura <lb></lb>impetus in H, post casum EH, quod EG sit media proportionalis inter <lb></lb>AE, EH ” (ibid., pag. </s>

<s>257). </s></p><p type="main">

<s>Come corollario al teorema di Galileo, ridotto così alle più semplici con­<lb></lb>clusioni, credeva il Viviani dì poter dire che, essendo in ogni semiparabola, <lb></lb>come per esempio in ABC, nella solita figura, gl&#039;impeti verticali, ne&#039;vari <lb></lb>punti della discesa come in B, C, proporzionali alle AG, AL, e l&#039;impeto oriz­<lb></lb>zontale il medesimo AE; che questo sempre sta a quelli come la linea su­<lb></lb>blime sta alla metà delle semibasi. </s>

<s>“ Essendo AE misura dell&#039;impeto orizzon­<lb></lb>tale, e AG misura del perpendicolare in B, e AL misura del perpendicolare <lb></lb>in C, avrà sempre l&#039;orizzontale al perpendicolare, in qualunque dato punto <lb></lb>della parabola come in C, la medesima proporzione dell&#039;AE, sublimità della <lb></lb>parabola, alla AL, metà della semibase CD ” (ivi, pag. </s>

<s>262). </s></p><p type="main">

<s>Galileo stesso però aveva pensato di far del corollario soggiunto poi <lb></lb>dal Viviani un bel teorema da potersi vantaggiosamente sostituire alla pro­<lb></lb>posizione quarta del Dialogo: teorema, ch&#039;ebbe a rimanersi escluso dal trat­<lb></lb>tato, quando il problema di ritrovar la sublimità della parabola e il corol­<lb></lb>lario di lui, che cioè l&#039;ampiezza è media fra l&#039;altezza e la sublimità, furono <lb></lb>posposti alla detta quarta proposizione, la quale dicemmo dover essere stata <lb></lb>dimostrata e rassegnata in ordine delle prime. </s>

<s>Quel galileiano teorema, in <pb xlink:href="020/01/2301.jpg" pagenum="544"></pb>cui, con sì spedito modo elegante, dimostravasi che, essendo l&#039;impeto oriz­<lb></lb>zontale rappresentato dalla linea sublime, il verticale per ogni punto della <lb></lb>parabola veniva rappresentato dalla metà della semibase, è quale qui noi <lb></lb>dall&#039;autografo lo trascriviamo, e che, se fosse stato noto al Viviani, gli ri­<lb></lb>sparmiava la sollecitudine della riferita postilla: </s></p><p type="main">

<s>“ Parabola BD (fig. </s>

<s>290), describitur ab elevatione AB, cum altitudine <lb></lb>BC. </s>

<s>Ponatur AB esse tempus et impetum casus AB, sitque DE tangens pa­<lb></lb><figure id="id.020.01.2301.1.jpg" xlink:href="020/01/2301/1.jpg"></figure></s></p><p type="caption">

<s>Figura 290<lb></lb>rabolam: erit EB aequalis BC. </s>

<s>Cumque BF sit su­<lb></lb>bdupla amplitudinis CD, erit quoque media inter su­<lb></lb>blimitatem AB, et altitudinem BC, eritque tempus <lb></lb>casus et impetus per BC in C. </s>

<s>Iuncta igitur AF erit <lb></lb>mensura impetus in D cadentis per ABD ” (MSS. <lb></lb>Gal., P. V, T. II, fol. </s>

<s>83). </s></p><p type="main">

<s>Sfuggì però in tal proposito a Galileo stesso e <lb></lb>al Viviani una considerazione importante, per la <lb></lb>quale si sarebbero facilmente condotti a quella tanto <lb></lb>desiderata, e non mai conseguita semplicità di co­<lb></lb>struzione, che ne suggerisce l&#039;uso del parallelo­<lb></lb>grammo delle forze. </s>

<s>Si tiene infatti nel superior <lb></lb>teorema per dimostrato dal corollario alla quinta <lb></lb>proposizione del Dialogo, essere FB2=AB.BE, la <lb></lb>quale equazion duplicata dà 2FB.FB=AB.2BE, ossia DC.FB=AB.EC, <lb></lb>d&#039;onde AB:FB=DC:EC, proporzione, da cui si conclude che, essendo AB <lb></lb>misura dell&#039;impeto orizzontale, e FB del verticale, se DC si farà misura del­<lb></lb>l&#039;orizzontale, sarà EC invece misura del verticale, come del resto s&#039;avrebbe <lb></lb>avuto, applicandovi la semplicissima regola del parallelogrammo. </s></p><p type="main">

<s>È notabile che il Viviani giunse a questa medesima conclusione, a di­<lb></lb>mostrar cioè che l&#039;impeto orizzontale e il verticale son proporzionali alla <lb></lb>semibase e alla suttangente, e che perciò l&#039;impeto totale vien rappresentato <lb></lb>dalla diagonale del rettangolo costruito sopra i due detti elementi della Pa­<lb></lb>rabola. </s>

<s>Ma è bene assai più notabile ch&#039;ei concluda dall&#039;errore una verità, <lb></lb>verso la quale mostravasi tanto ritroso. </s></p><p type="main">

<s>Riduciamoci nuovamente sott&#039;occhio la figura 286. Dice il Viviani di <lb></lb>aver provato che la tangente al punto C passa per L, dove arriva la LE <lb></lb>misura dell&#039;impeto composto in C, e che, essendo AL media fra AD.AH, <lb></lb>ossia fra AE, AF, dalla proporzione AF:AL=AL:AE si conclude che <lb></lb>gl&#039;impeti orizzontale e verticale possono essere così bene rappresentati da <lb></lb>AF, AL, come da AL, AE, ossia da CD semibase e da DE suttangente. </s>

<s>Ma <lb></lb>o fosse causa la fretta dello scrivere, o il lubrico della dottrina galileiana, <lb></lb>sopra la quale credeva nonostante di poter fermare il piede, scivolò in quel­<lb></lb>l&#039;errore che i nostri Lettori avranno di già notato, non essendo altrimenti <lb></lb>AL media fra AD, AH, ma fra AD, AE, le quali due linee, per essersi EC <lb></lb>condotta tangente in C, ed E costituito punto sublime, sono tra loro uguali. </s>

<s><lb></lb>Dall&#039;equazione EA:AL=AL:AD, essendo AB=AE concludesi legitti-<pb xlink:href="020/01/2302.jpg" pagenum="545"></pb>mamente che l&#039;impeto orizzontale e il verticale possono essere così rappre­<lb></lb>sentati da EA, AL, come da AL, AE, ossia dalla semibase CD, e dalla sut­<lb></lb>tangente DE, la quale suttangente è in questa particolar costruzione la somma <lb></lb>dell&#039;altezza, e della sublimità della parabola. </s></p><p type="main">

<s>“ Avendo io provato nella IX precedente (scrive il Viviani in quella sua <lb></lb>postilla al dialogismo, che segue alla quarta proposizione galileiana) che la <lb></lb>tangente in C passa per L, dove arriva la EL misura dell&#039;impeto composto <lb></lb>in C, ed essendo AL media proporzionale fra le AD, AH, sarà AL media <lb></lb>ancora fra le AE, AF; onde AF:AL=AL:AE. </s>

<s>Ma quando AF è misura <lb></lb>dell&#039;impeto orizzontale, la AL è misura dell&#039;impeto perpendicolare; adun­<lb></lb>que, se AL sarà misura dell&#039;orizzontale, sarà AE misura del perpendicolare, <lb></lb>ovvero CD dell&#039;orizzontale e DE del perpendicolare, e così seguirà in ogni <lb></lb>altro punto della parabola fuori di C. ” </s></p><p type="main">

<s>“ Di qui è manifesto che, se il cadente, giunto in C, restasse di più <lb></lb>accelerarsi col moto perpendicelare, conservando poi in sè l&#039;uno o l&#039;altro <lb></lb>impeto, co&#039;quali si trova quivi; continuerebbe a moversi per la tangente EC, <lb></lb>prodotta in infinito sotto C, perchè per quella sola direzione segue che il <lb></lb>mobile passa sempre di perpendicolo e di orizzonte parti proporzionali sem­<lb></lb>pre agl&#039;impeti perpendicolare ed orizzontale già concepiti nel punto C ” (MSS. <lb></lb>Gal., P. V, T. IX, pag. </s>

<s>262). </s></p><p type="main">

<s>Accennammo alla lubricità della dottrina galileiana, nel dar regola di <lb></lb>misurare gl&#039;impeti nella parabola, come a una delle occasioni date all&#039;error <lb></lb>del Viviani, a cui non si può credere che non entrasse di ciò qualche so­<lb></lb>spetto, come siam certi ch&#039;entrò nell&#039;animo dello stesso Galileo, quando, <lb></lb>per accertarsi se veramente l&#039;impeto totale resulta uguale in potenza alle <lb></lb>potenze parziali, ricorse a farne la riprova coi numeri. </s>

<s>Nell&#039;angolo sinistro <lb></lb>e inferiore del foglio, dov&#039;è il Teorema galileiano ultimamente trascritto, <lb></lb>leggesi la seguente Nota illustrata dalla nostra figura 290: “ Attende num­<lb></lb>quid tempus et impetus per AB, cum parabola BD, est idem cum tempore <lb></lb>et impetu per inclinationem AD ” (MSS. Gal., P. V, T. II, fol. </s>

<s>84). La ri­<lb></lb>prova particolare di ciò consegue dalle fatte riprove delle m sure degl&#039;im­<lb></lb>peti, generalmente dimostrate e concluse in quel medesimo Teorema, dando <lb></lb>alle linee, prese a rappresentare il moto retto antecedente e il moto retto <lb></lb>conseguente, particolari valori numerici, e contentandosi dell&#039;approssima­<lb></lb>zione dei resultati, com&#039;apparisce da questa Nota, che si trascrive: </s></p><p type="main">

<s>“ Tutta AC 140; e tanto sia il tempo e l&#039;impeto in C, il quale impeto <lb></lb>è di passare 280 nel tempo 140. ” </s></p><p type="main">

<s>“ AB 80: sarà il suo tempo la media tra AC, AB, cioè tra 140 e 80, <lb></lb>che è 105, e però nell&#039;orizzontale BG la velocità sarà di passare, nel tempo <lb></lb>105 di AB, 160, che è il doppio di AB. </s>

<s>Ma il tempo di BC, dalla quiete <lb></lb>in B, è la media tra AC 140 e BC 60, che è 91; adunque diremo: in que­<lb></lb>sto tempo 91, quanto si passerà di BG, della quale nel tempo di AB, che <lb></lb>è 105, se ne passa 160? — Per la regola se ne passerà 138, e torna bene, <lb></lb>cha tanto è CD. ” </s></p><pb xlink:href="020/01/2303.jpg" pagenum="546"></pb><p type="main">

<s>“ Sia AB 80, tempo ed impeto in B, che nella BG, in tempo 80, pas­<lb></lb>serà 160. Il tempo di BC sarà la media tra BC 60, e AB 80, che sarà 69. <lb></lb>In questo tempo 69, quanto si passerà în BG, dove in 80 di tempo si <lb></lb>passa 160? — Si passa 138 e torna bene. </s>

<s>” </s></p><p type="main">

<s>“ AB 60, tempo et impeto; BC 30. Sarà suo tempo et impeto la media <lb></lb>tra 60 e 30, che è 42 1/3; adunque tutto il tempo di ABD è 102 1/3. L&#039;am­<lb></lb>piezza CD è doppia della media tra AB, BC: è dunque 84 2/3. Ma tutta AC <lb></lb>è 90, e CD 84 2/3; adunque AD sarà 123, ed il tempo di tutta AD sarà <lb></lb>quanto la media tra DA e AG, che torna 100 e più, e mostra star bene ” <lb></lb>(ivi, a tergo del foglio 86). </s></p><p type="main">

<s>Assicurato così da queste riprove, confidò Galileo che fossero vere le <lb></lb>regole da lui dimostrate per la misura degl&#039;impeti. </s>

<s>Abbiamo detto in che <lb></lb>modo si studiasse il Viviani di confermarle, e come, in volerle render più <lb></lb>semplici, s&#039;incontrasse finalmente dopo lunghi raggiri nella regola stessa del <lb></lb>parallelogrammo. </s>

<s>Ora è da vedere come a tal conclusione riuscissero pure le <lb></lb>vie segnate dal Torricelli, benchè siano rifiorite così di eleganza nuova, da <lb></lb>ingannar la fatica e il tedio della lunghezza. </s>

<s>È dall&#039;insigne Promotore con­<lb></lb>seguito un tale effetto principalmente, con introdur la parabola per la scala <lb></lb><figure id="id.020.01.2303.1.jpg" xlink:href="020/01/2303/1.jpg"></figure></s></p><p type="caption">

<s>Figura 291<lb></lb>degl&#039;impeti e dei tempi nelle libere cadute <lb></lb>naturali. </s>

<s>Ridottaci nuovamente sotto gli oc­<lb></lb>chi la figura, sopra la quale vedemmo dianzi <lb></lb>come Galileo condusse la dimostrazion sua <lb></lb>laboriosa, il Torricelli così ragionava: Dati <lb></lb>gli spazi AC, AB (fig. </s>

<s>291), se AC è la <lb></lb>misura del tempo e dell&#039;impeto per AC, la <lb></lb>misura del tempo e dell&#039;impeto per AB <lb></lb>sarà la media fra AC, e AB: che se l&#039;im­<lb></lb>peto in C si rappresenta con la orizzontale <lb></lb>DC, e l&#039;impeto in B con la orizzontale BE, avremo dunque CD:BE= <lb></lb>AC:√AC.AB=√AC:√AB, ossia CE2:DB2=AC:AB; equazione di una <lb></lb>parabola. </s>

<s>“ Hinc manifestum est, ne conclude perciò il Torricelli, impetus <lb></lb>gravium in fine portionum diametri parabolae esse inter se ut lineae, quae <lb></lb>ordinatim applicantur ad extrema ipsarum portionum puncta ” (Op. </s>

<s>geom. </s>

<s><lb></lb>cit., pag. </s>

<s>113). </s></p><p type="main">

<s>Vedendosi di qui aprire un campo nuovo, erasi poco prima compia­<lb></lb>ciuto il Promotore che, di quel che egli veniva ora ad annunziare nel suo <lb></lb>corollario, <emph type="italics"></emph>non scripsit Galilaeus<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>110). Ed è ciò verissimo, giu­<lb></lb>dicando dai Dialoghi e dalle altre opere pubblicamente note, ma fra&#039;Mano­<lb></lb>scritti è rimasta autografa una proposizione, la quale fa mirabile riscontro <lb></lb>con la X torricelliana del primo libro. </s>

<s>La proposizione di Galileo, tirata fuori <lb></lb>da quel prunaio dove l&#039;abbiamo trovata, è dunque tale. </s></p><p type="main">

<s>Siano AB, AC (fig. </s>

<s>292) due spazi, e AD medio fra loro. </s>

<s>Se AB rap­<lb></lb>presenta il tempo per AB, AD rappresenterà <gap></gap>l tempo per AC. </s>

<s>Sia poi BE <lb></lb>la velocità e l&#039;impeto in B, e si faccia BA:AD=BE:CF; sarà CF l&#039;im-<pb xlink:href="020/01/2304.jpg" pagenum="547"></pb>peto in C, presa AC per misura dello spazio. </s>

<s>Ma se, condotta la AE, si <lb></lb>prolunghi infino a che ella non s&#039;incontri con DQ in Q, sarà DQ=FC <lb></lb>misura dell&#039;impeto in D, presa AD per misura del tempo. </s>

<s>Ora, dal dato <lb></lb>AD2=CA.AB avendosi CA:AD=AD:AB=QD:EB=CF:EB, qua­<lb></lb><figure id="id.020.01.2304.1.jpg" xlink:href="020/01/2304/1.jpg"></figure></s></p><p type="caption">

<s>Figura 292<lb></lb>drando, si concluderà CA2:AD2=CF2:EB2. </s>

<s>Dal me­<lb></lb>desimo dato, e dall&#039;identica AC2=AC2 si concluderà <lb></lb>pure AC2:AD2=AC2:AC.AB, onde avremo dalle due <lb></lb>conclusioni AC:AB=CF2:BE2. </s>

<s>Ma trascriviamo le <lb></lb>precise parole di Galileo: </s></p><p type="main">

<s>“ Sit ut BA ad AD, ita DA ad AC, et sit BE gra­<lb></lb>dus velocitatis in B, et ut BA ad AD ita sit BE ad CF: <lb></lb>erit CF gradus velocitatis in C. </s>

<s>Cum itaque sit ut CA <lb></lb>ad AD, ita CF ad BE, erit et ut quadratus CA ad qua­<lb></lb>dratum AD, ita quadratus CF ad quadratum BE. </s>

<s>Ut <lb></lb>autem quadratus CA ad quadratum AD, ita CA ad AB: <lb></lb>ut igitur CA ad AB, ita quadratus CF ad quadratum BE. </s>

<s><lb></lb>Sunt ergo puncta E, F in parabola ” (MSS. Gal., P. V, <lb></lb>T. II, fol. </s>

<s>152). Or perchè, sceso naturalmente il grave <lb></lb>dal vertice A della parabola in B e in C, gli corrispon­<lb></lb>dono gl&#039;impeti EB, FC, che son le ordinate delle por­<lb></lb>zioni del diametro AB, AC; <emph type="italics"></emph>hinc<emph.end type="italics"></emph.end> manifestum est, si può soggiunger per <lb></lb>corollario anche a questa galileiana, <emph type="italics"></emph>impetus gravium, in fine portionum <lb></lb>diametri parabolae, esse inter se ut lineae, quae ordinatim applicantur <lb></lb>ad extrema ipsarum portionum puncta.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Rimase però per Galilèo questa proposizione infruttuosa, ma il Torri­<lb></lb>celli, invocando altre proprietà geometriche della parabola, le applicò a pro­<lb></lb>movere mirabilmente la scienza del moto, e a determinare la misura degli <lb></lb>impeti, per una via tutta nuova. </s>

<s>Fra quelle geometriche proprietà notabile <lb></lb>è questa, che cioè sempre nella parabola terza proporzionale, dopo un&#039;ascissa <lb></lb>qualunque e la corrispondente ordinata, è una linea, alla quale gli antichi <lb></lb>davano il nome di <emph type="italics"></emph>Lato retto,<emph.end type="italics"></emph.end> corrispondente a quel che ora i moderni chia­<lb></lb><figure id="id.020.01.2304.2.jpg" xlink:href="020/01/2304/2.jpg"></figure></s></p><p type="caption">

<s>Figura 293<lb></lb>man <emph type="italics"></emph>Parametro.<emph.end type="italics"></emph.end> Per applicare ai moti parabolici questo <lb></lb>puro elemento geometrico, incomincia il Torricelli a di­<lb></lb>mostrare, così presso a poco, nella VII proposizion del <lb></lb>primo libro, che la sublimità della parabola è la quarta <lb></lb>parte del Lato retto. </s></p><p type="main">

<s>Sia CA (fig. </s>

<s>293) la parabola, AD la sua ampiezza, <lb></lb>e CS la sublimità. </s>

<s>Chiamato P il parametro, abbiamo, <lb></lb>per la data definizione di questo elemento, P=AD2/CD: <lb></lb>ed essendo MD=AD/2, sarà P=4.MD2/CD. </s>

<s>Per il corolla­<lb></lb>rio poi alla V proposizione di Galileo (Alb. </s>

<s>XIII, 248) è MD2=CD.CS, <lb></lb>e perciò P=4.CD.CS/CD=4.CS, ossia CS=P/4. “ Quando (dice il Tor-<pb xlink:href="020/01/2305.jpg" pagenum="548"></pb>ricelli) sumitur in axe parabolae, ut in praecedenti figura, ex vertice linea <lb></lb>CF, quae aequalis sit quartae parti lateris recti, tunc punctum F vocatur <lb></lb><emph type="italics"></emph>focus<emph.end type="italics"></emph.end> parabolae. </s>

<s>Manifestum ergo est punctum sublime S et focum F ae­<lb></lb>qualiter distare a vertice parabolae; nempe tantum utrinque, quanta est <lb></lb>quarta pars Lateris recti ” (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>112). </s></p><p type="main">

<s>Soggiunge poi il Torricelli stesso che l&#039;ordinata condotta dal foco è <lb></lb>doppia della sublimità, o della porzione dell&#039;asse intercetta al vertice, ciò <lb></lb>che si può così, sopra la solita figura, con facilità dimostrare: Sia FG quel­<lb></lb>l&#039;ordinata:avremo CF:CD=GF2:AD2=GF2:4MD2.Ma MD2=CD.CS, <lb></lb>dunque CF:CD=GF2:4.CD.CS; d&#039;onde GF2=4CF.CS=4.CF2, e <lb></lb>perciò GF=2.CF=2CS. </s></p><p type="main">

<s>Ora, passando ad applicare queste proprietà geometriche della parabola <lb></lb>ai moti proiettizi, osserva il Torricelli che GF, misura del tempo equabile <lb></lb>dopo l&#039;accelerato per CF o per SC, è altresi la misura dell&#039;impeto orizzon­<lb></lb>tale in ciascun punto della curva, come per esempio in A, in cui l&#039;impeto <lb></lb>verticale fu dimostrato aver per misura l&#039;ordinata AD. </s>

<s>Dato dunque il foco, <lb></lb>non richiedevasi altro, per potersi determinare le componenti dell&#039;impeto, in <lb></lb>qual si voglia punto della parabola. </s>

<s>La resultante poi sarebbe secondo Ga­<lb></lb>lileo data dall&#039;ipotenusa, costruita nel triangolo rettangolo avente AD, GF <lb></lb>per cateti, e il Torricelli mostra di professare anch&#039;egli, specialmente nel <lb></lb>suo secondo libro, le false dottrine insegnate nella proposizione seconda del <lb></lb>quarto dialogo galileiano. </s>

<s>Ma è notabile ch&#039;egli dimostri, e autorevolmente <lb></lb>sanzioni, la regola del parallelogrammo, dalla quale infatti conclude che <lb></lb>l&#039;impeto composto in A è misurato dalla diagonale del rettangolo costruito <lb></lb>sopra i lati AD, GF, o sopra le linee ED, AD, che sono ad essi lati pro­<lb></lb>porzionali. </s></p><p type="main">

<s>Del modo come, nella XVIII di questo primo libro torricelliano, si di­<lb></lb>mostra quella regola del parallelogrammo, avremo in quest&#039;altra parte della <lb></lb>nostra Storia della Meccanica importantissima occasion di discorso: ora è da <lb></lb>vedere come per il Torricelli stesso sia vero che, condotta la tangente AE, <lb></lb>le linee AD, GF, dalle quali verrebbero immediatamente misurati gli im­<lb></lb>peti in A, sian proporzionali alla suttangente ED, e alla semibase AD della <lb></lb>parabola, d&#039;onde ne risulti l&#039;impeto totale esibito dalla stessa tangente AE, <lb></lb>riguardata come la diagonale del rettangolo, che avesse AD per base, e <lb></lb>DE per altezza. </s>

<s>La dimostrazione del resto è facilissima perchè dalla es­<lb></lb>senza del Parametro, che seguiteremo a chiamar P, abbiamo l&#039;equazione <lb></lb>AD:P=DC:AD, la quale, sostituitovi P=4.CF=2GF, si trasforma <lb></lb>nell&#039;altra AD:2GF=DC:AD; ossia AD:GF=ED:AD. </s></p><p type="main">

<s>Potrebbesi domandare perchè dunque non applicò il Torricelli la re­<lb></lb>gola del parallelogrammo immediata? </s>

<s>Ma essendo la risposta non breve, e <lb></lb>aspettando altro luogo nella nostra Storia, basti ripeter per ora quel che <lb></lb>poco fa s&#039;accennava, che cioè non seppe nemmen egli scotere il prepotente <lb></lb>giogo galileiano, contento d&#039;aver trasformati i rigidi legami, con i quali tutti <lb></lb>gli altri vi si tenevano avvinti, in lentissime trecce di fiori. </s></p><pb xlink:href="020/01/2306.jpg" pagenum="549"></pb><p type="main">

<s>Dei fiori di eleganza matematica, sparsi nel primo libro torricelliano, e <lb></lb>fra&#039;quali s&#039;allega il frutto di quelle proposizioni, ordinate ad illustrare il <lb></lb>modo di misurare gl&#039;impeti, nella semiparabola descritta dai tiri di punto <lb></lb>in bianco; debbono, dai brevi saggi dati, i Lettori averne sentito il gusto: <lb></lb>ora è da dire come il Torricelli stesso illustri l&#039;altro modo, che Galileo pro­<lb></lb>pone per misurare gl&#039;impeti, quando l&#039;obice elevato descrive la parabola <lb></lb>intera. </s></p><p type="main">

<s>Sia l&#039;elevazione seconda AH (fig. </s>

<s>294), e con essa descrivasi la para­<lb></lb>bola ABC: condotta la orizzontale AC, domandava la nuova scienza a Ga­<lb></lb>lileo qual misura d&#039;impeto si dovesse assegnare al proietto in A, perchè si <lb></lb>venisse a disegnare la detta parabola. </s>

<s>Per rispondere a ciò, partiva dalla <lb></lb><figure id="id.020.01.2306.1.jpg" xlink:href="020/01/2306/1.jpg"></figure></s></p><p type="caption">

<s>Figura 294<lb></lb>considerazione del tiro eretto nel perpendicolo, in cui l&#039;impeto necessario a <lb></lb>sollevare il proietto, per esempio in F, è tanto, quanto sarebbe del cadente <lb></lb>naturale da F in A. </s>

<s>Ma nel tiro elevato una parte dell&#039;impeto naturale si <lb></lb>consuma nello spingere il proietto per l&#039;orizzonte, cosicchè non rimane di <lb></lb>lui che la parte BD, ossia EA, la quale corrispondendo all&#039;altezza lascia al­<lb></lb>l&#039;altra EF rappresentare la sublimità della parabola. </s>

<s>Sarebbe dunque ben <lb></lb>dimostrato, argomentava Galileo, che l&#039;impeto in A è uguale a quello del <lb></lb>cadente da F, quando si dimostrasse che la potenza di AF è uguale alle <lb></lb>potenze dell&#039;altezza e della sublimità sommate insieme. </s>

<s>La dimostrazione è <lb></lb>fatta nel VII teorema (Alb. </s>

<s>XIII, 253), dove si dice che la potenza di AE, <lb></lb>ossia dell&#039;altezza, è data dalla media fra AF, e AE, e che la potenza della <lb></lb>sublimità EF è data dalla media fra AF, FE. Ora, che la somma di tali due <lb></lb>potenze o quadrati sia uguale al quadrato di AF, lo deduce Galileo in forza <lb></lb>di un lemma già premesso al teorema, nel qual lemma, costruito sopra AF <lb></lb>il semicerchio AGF, apparisce manifesto, dal triangolo rettangolo AGF, che <lb></lb>essendo le due medie FG, AG, i quadrati di queste sommati insieme sono <lb></lb>uguali al quadrato di AF. </s></p><p type="main">

<s>Il Torricelli ridusse il lemma galileiano a proposizion principale, che è <lb></lb>la XXI del secondo suo libro (pag. </s>

<s>174), e il semicerchio si congiunse mi-<pb xlink:href="020/01/2307.jpg" pagenum="550"></pb>rabilmente per lui con la parabola a mostrar circa il moto l&#039;ingegno e i <lb></lb>lusi della Natura. </s>

<s>“ Sit AE altitudo, et FE sublimitas parabolae: ergo, im­<lb></lb>petus cadentis per FE sublimitatem parabolae erit ut linea FG media pro­<lb></lb>portionalis inter AF, EF. </s>

<s>At iste impetus cadentis ex F in E est ille purus <lb></lb>horizontalis, qui lationi inest in quolibet puncto parabolae, et est invariabi­<lb></lb>lis: Quare in unoquoque puncto parabolae impetus horizontalis erit ut li­<lb></lb>nea FG. ” </s></p><p type="main">

<s>“ Perpendicularis vero impetus, qui est in primo lationis puncto, sic <lb></lb>determinabitur: manente semper unica suppositione, impetum scilicet casus <lb></lb>per FA esse ipsam FA; impetus perpendicularis, in fine parabolae C, est <lb></lb>tamquam naturaliter cadentis ex B in D, vel ex E in A. </s>

<s>Est ergo media <lb></lb>proportionalis AG ” (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>174). Di qui ne conclude esser la <lb></lb>somma delle potenze AG, FG uguale alla potenza AF, come si conclude per <lb></lb>Galileo, alle dottrine del quale dunque ancora il Torricelli ritorna, lasciata <lb></lb>la sicura e semplicissima regola del parallelogrammo. </s>

<s>Eppure era facile av­<lb></lb>vedersi che, avendosi, per la similitudine dei triangoli, AF:AG:FG= <lb></lb>AH:HD:AD, ciò che dimostra corrispondersi la tangente col diametro, e <lb></lb>la semibase e la suttangente della parabola con le due suttese agli archi; la <lb></lb>costruzione del semicerchio non si riduceva a più che a una lussuriosa bel­<lb></lb>lezza della scienza. </s></p><p type="main">

<s>Primo a ritornare, fra&#039;seguaci di Galileo, a quella semplicità di costru­<lb></lb>zione, che non si dilunga dalla regola del parallelogrammo, fu il Borelli <lb></lb>nella proposizione LV <emph type="italics"></emph>De vi percussionis.<emph.end type="italics"></emph.end> Ivi egli osserva che il proietto <lb></lb>esploso in B, nella precedente figura, giunge in A con impeto composto del­<lb></lb>l&#039;orizzontale equabile per AD, e del verticale accelerato per BD, il quale <lb></lb>pure può trasformarsi in equabile, raddoppiandone lo spazio nella suttan­<lb></lb>gente DH. “ Et proinde erit AH tangens parabolam, quae inclinationem in­<lb></lb>cidentiae designabit, atque hypothenusa AH ostendet impetum eiusdem cor­<lb></lb>poris in actu incidentiae ” (Bononiae 1667, pag. </s>

<s>105). </s></p><p type="main">

<s>Non solamente però si riducono in questa stessa proposizione alla de­<lb></lb>siderata semplicità le costruzioni di Galileo, ma se ne promove altresì la <lb></lb>scienza degl&#039;impeti, perchè, mentre, nel quarto Dialogo delle Scienze nuove, <lb></lb>sempre si considera l&#039;impeto quant&#039;è in sè medesimo, cioè rispetto a quel <lb></lb>piano, in cui perpendicolarmente egli percote; il Borelli lo considera quanto <lb></lb>egli è rispetto al piano resistente, variato solamente dalla diversità degl&#039;an­<lb></lb>goli dell&#039;incidenza, a proporzion del seno dei quali dimostra farsi nel per­<lb></lb>pendicolo la percossa. </s>

<s>Cosicchè, nel tiro di punto in bianco da B, la palla <lb></lb>del cannone giunge in A con un impeto verticale misurato da HD, ch&#039;è il <lb></lb>seno dell&#039;angolo dell&#039;incidenza HAD: d&#039;onde ci è dato intendere il para­<lb></lb>dosso come la medesima bomba, che varrebbe a rovesciare il muro di una <lb></lb>saldissima torre, riesca impotente a passare il velo di un&#039;acqua ghiacciata. </s></p><p type="main">

<s>È da notar però che XXIII anni prima era stata, così, promossa la <lb></lb>scienza galileiana dal Torricelli, il quale dice di aver trovato <emph type="italics"></emph>intatto<emph.end type="italics"></emph.end> il pro­<lb></lb>blema a&#039;suoi tempi (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>239), ne&#039;quali erano sconosciuti <pb xlink:href="020/01/2308.jpg" pagenum="551"></pb>i manoscritti di Leonardo da Vinci. </s>

<s>Il Torricelli medesimo, avendo, nel co­<lb></lb>rollario alla proposizion XXI del suo secondo libro, osservato che gl&#039;impeti <lb></lb>perpendicolari non crescono secondo l&#039;altezza della parabola, ma secondo la <lb></lb>corda del semicerchio, “ hinc animadvertere licet, immediatamente sog­<lb></lb>giunge, futurum fore ut idem globus ferreus, eodem tormento explosus, <lb></lb>dum ad horizontem redit, aliquando tecta fornicesque domorum traiiciat, <lb></lb>quandoque vero, neque glaciem alicuius lacunae laedere poasît ” (ibid., <lb></lb>pag. </s>

<s>174). La quarta torricelliana di questo medesimo libro secondo, inse­<lb></lb>gna pure il modo di determinare gl&#039;impeti in ciascuna parte della para­<lb></lb>bola, in un modo assai più semplice, e non meno dimostrativo di quello del <lb></lb>Borelli, prendendo le porzioni delle tangenti “ inter duas parallelas diame­<lb></lb>tro interceptae ” (ibid., pag. </s>

<s>161); e nella quinta seguente dimostra quel <lb></lb>che Galileo parve avere dimenticato dopo tant&#039;anni, da che aveva assistito <lb></lb>all&#039;esperienze di Guidubaldo, che cioè gl&#039;impeti “ in punctis parabolae ae­<lb></lb>qualiter utrinque a vertice distantibus, aequales sunt inter se licet alter ascen­<lb></lb>dat, alter vere descendat ” (ibid., pag. </s>

<s>162). </s></p><p type="main">

<s>Si direbbe che queste torricelliane sottigliezze fossero meglio atte di <lb></lb>tutte le altre a penetrare addentro a ogni parte del profondo soggetto, so­<lb></lb>lamente toccato da Galileo, un sottil pensiero del quale vedesi mirabilmente <lb></lb>illustrato dalla quarta sopra citata proposizione, che mostra come nel ver­<lb></lb>tice della parabola, benchè siavi spento ogn&#039;impeto verticale, non è però la <lb></lb>quiete assoluta. </s>

<s>“ Il mobile (leggesi così espresso in una Nota quel pen­<lb></lb>siero galileiano) nel descrivere la parabola, benchè angustissima, non passa <lb></lb>per la quiete nel termine ultimo, ma sì bene nel moversi per la perpendi­<lb></lb>colare, cioè ritornando per la medesima retta in giù: e se Aristotile avesse <lb></lb>detto che nel moto riflesso si passa per la quiete, avrebbe detto bene ” (MSS. <lb></lb>Gal., P. V, T. IV, fol. </s>

<s>15 a tergo). </s></p><p type="main">

<s>Nella medesima quarta torricelliana immediatamente, e non in alcuno <lb></lb>de&#039;teoremi di Galileo trova pure quest&#039;altra nota del Viviani il suo più <lb></lb>chiaro commento: “ Sia l&#039;AC (fig. </s>

<s>295) parallela all&#039;orizzonte, e la para­<lb></lb>bola ABC, per la quale venga spinto o cacciato il mobile S: è manifesto <lb></lb><figure id="id.020.01.2308.1.jpg" xlink:href="020/01/2308/1.jpg"></figure></s></p><p type="caption">

<s>Figura 295<lb></lb>per Galileo che, fin che dura la salita, <lb></lb>l&#039;impeto del proietto S va diminuen­<lb></lb>dosi, cioè fino al punto B. </s>

<s>Inclinando <lb></lb>poi per la BC al basso, l&#039;impeto si do­<lb></lb>verà augumentare, onde ne segue che <lb></lb>il moto sia tardissimo in B, cioè nel <lb></lb>mezzo del suo viaggio ABC, e ciò si <lb></lb>potrà esperimentare con frecce o bolzoni. </s>

<s>Adunque, domandandosi a uno: <lb></lb>dovendo tu esser ferito da una freccia, tirata secondo la linea ABC, dove <lb></lb>vorresti stare? </s>

<s>Egli direbbe in C, ma la minore offesa sarebbe in B ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>14 a t.). </s></p><pb xlink:href="020/01/2309.jpg" pagenum="552"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Tali, quali sono stati fin qui discorsi, furono i principii e i progressi <lb></lb>delle speculazioni di Galileo, e de&#039;suoi primi Promotori, per determinare, <lb></lb>in ciascun punto della parabola, la forza del colpo, che farebbe il proietto <lb></lb>sopra un piano contrappostogli nel suo libero viaggio. </s>

<s>Dopo questo, dicemmo <lb></lb>essere l&#039;altro argomento, che si proponeva a trattare alla Scienza nuova, <lb></lb>quello di dimostrar dalla teoria del moto parabolico le verità sperimentali <lb></lb>pronunziate già dal Tarlaglia intorno alla maggiore ampiezza del tiro semi­<lb></lb>retto, e alla ugual distanza orizzontale, a cui giungono i proietti con eleva­<lb></lb>zioni, che manchino ugualmente o eccedano da quella stessa semiretta per <lb></lb>angoli uguali. </s>

<s>I primi processi dimostrativi, che ci si rivelarono in quella <lb></lb>Nota manoscritta, illustrata dalla figura 285, furono quelli stessi, che poi <lb></lb>tenne Galileo nelle proposizioni inserite nel Dialogo, e delle quali si com­<lb></lb>pone, come si disse, la seconda parte del suo nuovo trattato. </s></p><p type="main">

<s>Che il tiro dunque, messo l&#039;obice a mezza squadra, dia veramente la <lb></lb>massima volata, anche qui, ciò nel Dialogo IV, come là, nella detta Nota, <lb></lb>si conclude per corollario dalla VII proposizione, che dice: “ In proiectis, <lb></lb>a quibus semiparabolae eiusdem amplitudinis describuntur, minor requiri­<lb></lb>tur impetus in eo, quod describit illam, cuius amphtudo suae altitudinis sit <lb></lb>dupla, quam in quolibet alio ” (Alb. </s>

<s>XIII, 249). </s></p><p type="main">

<s>Sia l&#039;ampiezza DC (fig. </s>

<s>296) della parabola BD doppia all&#039;altezza BC, <lb></lb>e si conduca l&#039;AD tangente in D, secondo la quale sarà dìretto il tiro, con <lb></lb><figure id="id.020.01.2309.1.jpg" xlink:href="020/01/2309/1.jpg"></figure></s></p><p type="caption">

<s>Figura 296<lb></lb>l&#039;inclinazione ADC semiretta. </s>

<s>L&#039;impeto composto in D <lb></lb>è per le cose già dimostrate, dice Galileo, rappresen­<lb></lb>tato dall&#039;ipotenusa AE. </s></p><p type="main">

<s>Con la medesima ampiezza DC, ma con maggiore <lb></lb>altezza CG, abbiasi l&#039;altra parabola GD, a descriver <lb></lb>la quale l&#039;impeto necessario in D, composto del moto <lb></lb>retto antecedente per la sublimità, e del conseguente <lb></lb>per l&#039;altezza CG della parabola, è stato detto come <lb></lb>debbasi misurarlo. </s>

<s>Se GL è terza proporzionale dopo <lb></lb>KG, GH, sappiamo costituirsi in L il punto sublime, <lb></lb>da cui cadendo in G il grave dà la misura dell&#039;im­<lb></lb>peto retto antecedente. </s>

<s>Ora, essendosi dianzi implici­<lb></lb>tamente supposto che sia AB la misura del tempo e <lb></lb>dell&#039;impeto per AB, la misura dell&#039;impeto, dovuto al moto del cadente per <lb></lb>LG, sarà una media fra AB, LG, la quale sia per esempio GM. </s></p><p type="main">

<s>Parimente, essendo NG media fra AB, GC, verrà per lei rappresentato <lb></lb>l&#039;impeto, dovuto al moto retto conseguente per l&#039;altezza GC. </s>

<s>Sarà dunque <lb></lb>l&#039;ipotenusa NM la misura dell&#039;impeto composto, necessario in D a descriver <pb xlink:href="020/01/2310.jpg" pagenum="553"></pb>la semiparabola GD, e si conclude perciò il proposto assunto col dimostrar <lb></lb>che NM è maggiore di AE. </s>

<s>In qual modo poi si faccia la dimostrazione lo <lb></lb>vedremo or ora, per dire intanto che, nella precitata VII proposizione, non <lb></lb>contempla Galileo che il caso, in cui la direzione del tiro eccede la semi­<lb></lb>retta. </s>

<s>L&#039;altra proposizione, in cui supponesi il caso, che l&#039;angolo dell&#039;in­<lb></lb>clinazione manchi dal semiretto, è rimasta ancora fra&#039;manoscritti, e benchè <lb></lb>la somiglianza de&#039;processi dimostrativi possa aver dispensato l&#039;Autore dal­<lb></lb>l&#039;inserirla nel Dialogo, noi crediamo per molte ragioni che sia bene met­<lb></lb>terla alla notizia de&#039;nostri Lettori. </s></p><p type="main">

<s>“ Sit CE (fig. </s>

<s>297) dupla ad EA, et FC tangat parabolam AC. </s>

<s>Sit adhuc <lb></lb>HD aequalis CE, et maior quam dupla ad DG, et HK tangat parabolam GH, <lb></lb><figure id="id.020.01.2310.1.jpg" xlink:href="020/01/2310/1.jpg"></figure></s></p><p type="caption">

<s>Figura 297<lb></lb>et ut KG ad GI, ita sint IG ad GL: <lb></lb>erit L punctum casus per parabo­<lb></lb>lam. </s>

<s>Et sit GX media inter AE, GD; <lb></lb>GS vero media inter IG (eguale ad <lb></lb>AB che è eguale ad AE) GL: de­<lb></lb>monstrandum est SX maiorem esse <lb></lb>quam FB. ” </s></p><p type="main">

<s>“ Quadratus FB aequatur qua­<lb></lb>dratis FA, AB; hoc est duplum qua­<lb></lb>drati GI: et quadratus SX aequatur <lb></lb>quadratis SG, GX: ostende ergo qua­<lb></lb>drata SG, GX, vel quadratum SX, esse plus quam dupla quadrati IG. ” </s></p><p type="main">

<s>“ Quadratum GX aequatur reclangulo IGD: ut DG ad GX, ita GX ad <lb></lb>GI; ergo, ut DG ad GI, ita quadratum DG ad quadratum GX. </s>

<s>Ut autem DG, <lb></lb>seu KG, ad GI, ita IG ad GL. Quia, ut quadratum XG ad quadratum GI, <lb></lb>ita IG ad GL; ut autem IG ad GL, ita quadratum IG, ad quadratum me­<lb></lb>diae inter IG, GL, quae sit GS: ergo ut quadratum XG ad quadratum GI, <lb></lb>ita quadratus GI ad quadratum GS: est autem XG minor quam GI, quia <lb></lb>et DG minor est quam GI; ergo quadratum IG minor est quadrato me­<lb></lb>diae ” (MSS. Gal., P. V, T. II, fol. </s>

<s>111). </s></p><p type="main">

<s>Sin qui tutto va bene, correttosi da noi nel copiare lo sbaglio fatto per <lb></lb>inavvertenza da Galileo, il quale, essendosi proposto di dimostrare che SX <lb></lb>è maggiore di FB, scrisse <emph type="italics"></emph>ostende ergo quadrata LG, GX,<emph.end type="italics"></emph.end> invece di <emph type="italics"></emph>qua­<lb></lb>drata SG, GX, esse plus quam dupla quadrati IG.<emph.end type="italics"></emph.end> Nè accortosi dello sba­<lb></lb>glio alla fine della dimostrazione, dop&#039;aver concluso l&#039;assunto, che cioè la <lb></lb>somma de&#039;quadrati GX, GS è più che doppia del quadrato di GI, soggiunge: <lb></lb><emph type="italics"></emph>ergo multo plus quam dupla erunt quadrata XG, GL,<emph.end type="italics"></emph.end> essendo, nel par­<lb></lb>ticolar caso contemplatosi della direzione del tiro minore della semiretta, GL <lb></lb>maggiore di GS. </s>

<s>La final conclusione dunque, che soggiungesi nel Mano­<lb></lb>scritto galileiano, dop&#039;aver dimostrato che il quadrato di IG è minore del <lb></lb>quadrato della media, è come segue: “ Sed cum tria quadrata XG, GI et <lb></lb>mediae sint proportionalia, erunt extrema plusquam dupla quadrati GI. </s>

<s>Ergo <lb></lb>multo plus quam dupla erunt quadrata XG, GL ” (ibid.). </s></p><pb xlink:href="020/01/2311.jpg" pagenum="554"></pb><p type="main">

<s>Nella VII proposizione del Dialogo, dall&#039;essersi in simil guisa dimo­<lb></lb>strato che i tre quadrati NG2, KG2, GM2 sono in proporzione continua, si <lb></lb>conclude che la somma de&#039;due estremi NG2+GM2=NM2 è maggiore di <lb></lb>2KG2=AE2. </s>

<s>“ Ergo linea MN maior linea EA, quod erat domonstran­<lb></lb>dum ” (Alb. </s>

<s>XIII, 250). Dimostratosi così, in questa stampata, che maggior <lb></lb>impeto si richiede a fare il tiro elevato sopra il semiretto, e nella mano­<lb></lb>scritta che maggior impeto pur si richiede a fare il tiro sotto il semiretto, <lb></lb>posto che debbano i mobili descriver parabole di ampiezza uguale a quella, <lb></lb>che si descriverebbe nella stessa elevazion semiretta; ne deduce Galileo per <lb></lb>corollario che, se dunque si daranno impeti uguali, “ maxima proiectio, seu <lb></lb>amplitudo semiparabolae, sive integrae parabolae, erit ea, quae consequitur <lb></lb>ad elevationem anguli semirecti ” (ibid.). </s></p><p type="main">

<s>Veniva così, per la prima volta, matematicamente dimostrato quel che <lb></lb>il Tartaglia aveva asserito un secolo prima per vero, confermatovi dalle espe­<lb></lb>rienze dei bombardieri di Urbino. </s>

<s>Ma un&#039;altra cosa, anche più pellegrina, <lb></lb>aveva come accennammo prenunziato lo stesso Tartaglia, che cioè <emph type="italics"></emph>un pezzo <lb></lb>de artiglieria posseva, per due diverse vie, over elevationi, percotere in <lb></lb>un medemo loco,<emph.end type="italics"></emph.end> gli angoli delle quali elevazioni fossero quelli, che ecce­<lb></lb>dono e mancano ugualmente dal semiretto. </s>

<s>Anche questo, che pure aveva <lb></lb>aspetto di vero, e sembrava riscontrare con l&#039;esperienze, dovevasi dimostrar <lb></lb>dalla nuova Scienza, concludendolo dai principii del moto parabolico, e Ga­<lb></lb>lileo incominciò a tentare se, così ragionando, gli riusciva di conseguire <lb></lb>l&#039;intento. </s></p><p type="main">

<s>Sia il triangolo rettangolo ABC (fig. </s>

<s>298) semiretto in B, e si facciano <lb></lb>sotto e sopr&#039;esso gli angoli ABE, ABD uguali. </s>

<s>Divisa EC in F nel mezzo, <lb></lb><figure id="id.020.01.2311.1.jpg" xlink:href="020/01/2311/1.jpg"></figure></s></p><p type="caption">

<s>Figura 298<lb></lb>conducasi parallela a BC la GF, la quale sia media <lb></lb>tra EF, FL. </s>

<s>Immaginando che passi per F, B una <lb></lb>semiparabola, sarebbe questa precisamente quella, <lb></lb>che si descriverebbe dal tiro in B, con l&#039;eleva­<lb></lb>zione BE, e che avrebbe per altezza FC=EF, per <lb></lb>sublimità FL, e GF per metà dell&#039;ampiezza. </s>

<s>In si­<lb></lb>mil guisa, sia H il punto di mezzo della DC, e con­<lb></lb>ducasi la HI parallela a BC: le semiparabola, che <lb></lb>s&#039;immagini passar per B, H, sarà quella che ver­<lb></lb>rebbe descritta dal tiro in B, con l&#039;elevazione BD, <lb></lb>e che vorrebbesi dimostrare avere ampiezza uguale <lb></lb>a quella della semiparabola FB, descritta di sotto. </s>

<s><lb></lb>Or perchè si sarebbe felicemente conseguito l&#039;in­<lb></lb>tento, quando si fosse dimostrato che IH è media <lb></lb>fra HD, HL, conferì Galileo intorno a ciò il suo <lb></lb>primo studio, com&#039;apparisce dalla seguente bozza di manoscritto: </s></p><p type="main">

<s>“ Sit triangulum rectangulum ABC (nella medesima figura), latera <lb></lb>habens aequalia AC, CB. </s>

<s>Fiant anguli aequales DBA, ABE, et divisa EC <lb></lb>bifariam in F, et ducta FG, parallela ad BC, fiat ut EF ad FG, ita FG ad <pb xlink:href="020/01/2312.jpg" pagenum="555"></pb>FL: dico quod, si tota DC bifariam secetur in H, ducta HI, parallela BC, <lb></lb>erit ut DH ad HI, ita IH ad HL. ” </s></p><p type="main">

<s>“ Quia enim angulus CAB aequatur angulo CBA, et DBA angulo ABE, <lb></lb>et angulus CEB duobus EAB, ABE est aequalis, ergo CEB ipsi CBD aequa­<lb></lb>bitur, et triangulus ECB triangulo DCB erit similis, et illis quoque et inter <lb></lb>se similes sunt EGF, DIH. </s>

<s>Sed quia est ut EF ad FG, ita GF ad FL, erit <lb></lb>triangulus AGF ipsi EGF similis, et ipsi quoque DIH..... ” (MSS. Gal., <lb></lb>P. V, T. II, fol. </s>

<s>111 a tergo). </s></p><p type="main">

<s>A questo punto rimase la scrittura interrotta, perchè Galileo s&#039;accorse <lb></lb>di avere sbagliato. </s>

<s>Dalla proporzione infatti EF:FG=GF:FL si con­<lb></lb>clude, non già la similitudine fra i triangoli EGF, AGF, ma fra EGF e LGF, <lb></lb>il qual triangolo LGF conveniva dimostrar simile al triangolo ILH che pure <lb></lb>è simile al triangolo IDH, a voler conseguire direttamente l&#039;intento. </s>

<s>Ma per­<lb></lb>chè gli sarebbe la dimostrazione riuscita contorta, non volle proseguire più <lb></lb>oltre, e a tutto quel che aveva scritto dette di frego. </s></p><p type="main">

<s>Rinunziato a questo primo processo, si volse a pensarne un altro, di <lb></lb>cui ci lasciò in una nota manoscritta il disegno. </s>

<s>Supposto non aver bisogno <lb></lb>il Lettore che gli sia detto nè dimostrato com&#039;avendo il triangolo ABC (nella <lb></lb>medesima figura 298) i due cateti BC, AC uguali, se prolungato AC e con­<lb></lb>dotta la BD si farà l&#039;angolo EBC uguale all&#039;angolo BDC, i due angoli DBA, <lb></lb>ABE sono uguali, e i due triangoli DBC, EBC fra loro simili; ecco qual&#039;è <lb></lb>la via che, per condursi alla desiderata conclusione, Galileo preparavasi in <lb></lb>questa Nota, riferendosi sempre alla medesima precedente figura: </s></p><p type="main">

<s>“ In triangulo rectangulo BCD fiat angulo D aequalis CBE, et iunga­<lb></lb>tur BE. </s>

<s>Erunt ergo duo triangula DCB, EBC similia. </s>

<s>Dividatur tota DC bi­<lb></lb>fariam in H, et parallela HI sit ipsi CB. </s>

<s>Dividatur EC bifariam in F, et <lb></lb>ducatur FG parallela BC, et fiat ut DH ad HI, ita IH ad HL, et iungatur <lb></lb>LI. </s>

<s>Erit triangulus LIH simile triangulo DHI, et ob id simile quoque ipsi <lb></lb>EFG. </s>

<s>Sed HI est aequalis GF, utriusque enim dupla est BC, ergo reliqua <lb></lb>latera HL, FE aequalia erunt: quare tertia proportionalis ipsarum LH, HI, <lb></lb>nempe HD, erit aequalis tertiae proportionali ipsarum EF, FG. </s>

<s>Sed HD, ter­<lb></lb>tia proportionalis ipsarum LH, HI, est HC, dimidia nempe totius DC; ergo <lb></lb>tertia proportionalis ipsarum EF, FG aequabitur dimidiae CD, nempe ipsi DH. </s>

<s><lb></lb>Sed CH est aequalis FL, cum EF sit aequalis HL, et EH communis, ergo <lb></lb>tertia proportionalis ipsarum EF, FG erit FL, terminata in puncto L, ubi <lb></lb>terminatur tertia proportionalis ipsarum DH, HI ” (MSS. Gal., P. V, T. II, <lb></lb>fol. </s>

<s>80). </s></p><p type="main">

<s>Soggiunge immediatamente Galileo sotto questa dimostrazione, che do­<lb></lb>veva far l&#039;ufficio di lemma: “ Ex hoc demonstrabitur proiectorum, quorum <lb></lb>elevationes a semirecta, supra et infra per angulos aequales factorum, am­<lb></lb>plitudines parabolarum esse aequales ” (ibid.). Immaginando infatti che per <lb></lb>F, B, e per H, B passino due semiparabole, saranno queste quelle mede­<lb></lb>sime, che verrebbero disegnate in aria dal tiro in B, secondo le direzioni <lb></lb>BE, BD, facenti angoli uguali sopra e sotto all&#039;angolo a mezza squadra. </s>

<s>Che <pb xlink:href="020/01/2313.jpg" pagenum="556"></pb>debbano poi tali due parabole avere uguale ampiezza, consegue immediata­<lb></lb>mente dal sopra scritto Lemma, in cui, poste IH, GF uguali, fu dimostrato <lb></lb>essere da queste due linee misurata la metà dell&#039;ampiezza della semipara­<lb></lb>bola respettiva. </s></p><p type="main">

<s>Dietro il disegno così preparato, eseguì Galileo la proposizione VIII del <lb></lb>Dialogo, la quale prometteva di riuscire, se si fosse mantenuta quella prima <lb></lb>semplicità, più spedita e più chiara. </s>

<s>Rimase anche per un lato in difetto <lb></lb>capitalissimo, non apparendovi la condizione che i proietti sono <emph type="italics"></emph>eodem im­<lb></lb>petu explosi,<emph.end type="italics"></emph.end> ciò che dall&#039;altra parte sarebbe tornato facilissimo dimostrare, <lb></lb>osservando che, per essere FL+FC=AH+HC, hanno ambedue le se­<lb></lb>miparabole per misura dell&#039;impeto quello del cadente per la medesima al­<lb></lb>tezza LC. </s>

<s>La proposizione X però, nella quale Galileo dice che l&#039;impeto in <lb></lb>ciascuna semiparabola “ aequatur momento naturaliter cadentis in perpen­<lb></lb>diculari ad horizontem, quae tanta sit, quanta est composita ex sublimitate <lb></lb>cum altitudine semiparabolae ” (Alb. </s>

<s>XIII, 253), non era stata ancora di­<lb></lb>mostrata, e il Viviani perciò pensò di supplir egli al notato difetto (ivi, <lb></lb>pag. </s>

<s>252) applicandovi il metodo di misurare gl&#039;impeti insegnato da Gali­<lb></lb>leo nella proposizione sua quarta. </s>

<s>Resulta da tali insegnamenti che, essendo <lb></lb>LH, HI le misure dell&#039;impeto orizzontale e del verticale nella semiparabola <lb></lb>HB, nell&#039;altra FB sono invece FG, FE, cosicchè, avendosi per le cose dimo­<lb></lb>strate LH=EF, IH=GF, e le ipotenuse IL, GE altresì uguali, saranno <lb></lb>perciò uguali gl&#039;impeti composti in B, solo permutata la rappresentazion <lb></lb>delle componenti. </s></p><p type="main">

<s>Non lasciò pure il Torricelli di promovere anche questa parte della <lb></lb>Scienza galileiana, a cui dette maggior opera del Viviani, e la ridusse a una <lb></lb>elegante facilità maravigliosa. </s>

<s>Nella IX del libro secondo si propone di scio­<lb></lb>gliere il seguente problema: Dato l&#039;impeto FA (fig. </s>

<s>299), e data la dire­<lb></lb><figure id="id.020.01.2313.1.jpg" xlink:href="020/01/2313/1.jpg"></figure></s></p><p type="caption">

<s>Figura 299<lb></lb>zione AH del tiro, ritrovare l&#039;ampiezza, l&#039;altezza e tutta la parabola di que­<lb></lb>sta proiezione. </s>

<s>Si descriva intorno al diametro FA un semicerchio, a cui sieno <lb></lb>le AD, FL tangenti, e condotta da E una perpendicolare, che incontri in G <pb xlink:href="020/01/2314.jpg" pagenum="557"></pb>il semicerchio, si prolunghi di altrettanto in B, per il qual punto passi la <lb></lb>DL parallela ad AF, e compiasi il rettangolo FD. </s>

<s>La parabola che pass <lb></lb>per A, B, dice il Torricelli, sarà la cercata, ed essendo EG media fra EF <lb></lb>ossia BL, e AE, ossia BD, ne saranno EG, o la sua uguale GB, la semiam­<lb></lb>piezza, BD l&#039;altezza, e BL la sublimità che si voleva. </s></p><p type="main">

<s>È di qui manifesto, soggiunge il Torricelli stesso per corollario, che <lb></lb>avendosi una macchina, la quale esplode con impeti uguali al cadente da <lb></lb>E in A (fig. </s>

<s>300), per la linea EA, diametro di un semicerchio, e con di­<lb></lb><figure id="id.020.01.2314.1.jpg" xlink:href="020/01/2314/1.jpg"></figure></s></p><p type="caption">

<s>Figura 300<lb></lb>rezioni secondo le corde AC, AD, AB; verranno per i <lb></lb>seni FC, HD, GB rappresentate le semiampiezze delle <lb></lb>parabole, via via descritte da questi tiri, ond&#039;è che, se <lb></lb>l&#039;angolo HAD è semiretto, HD sarà il seno totale, e <lb></lb>perciò il massimo di tutti. </s>

<s>Ed essendo gli archi CD, <lb></lb>DB, che misurano gli angoli sottesi uguali, i seni FC, <lb></lb>GB, ossia le semiampiezze delle parabole descritte con <lb></lb>elevazioni dalla semiretta ugualmente distanti, saranno <lb></lb>pure tra loro uguali. </s>

<s>“ Corollarium ergo erit, conclude <lb></lb>tutto compiacente di ciò il Torricelli, quod Galileo theo­<lb></lb>rema satis arduum fuerat ” (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>168). </s></p><p type="main">

<s>Il teorema pur troppo era arduo, come i fatti ce <lb></lb>l&#039;hanno mostrato, in questa nuova Scienza de&#039;proietti ìstituita da Galileo <lb></lb>ma pure eravi riuscito senza trasgredire in nulla i termini meccanici, co­<lb></lb>sicchè si seppero finalmente quelle vere ragioni <emph type="italics"></emph>naturale et geometrice,<emph.end type="italics"></emph.end> che <lb></lb>il Tartaglia si lusingava di aver riconoseiute per sè <emph type="italics"></emph>evidentissime.<emph.end type="italics"></emph.end> Con que­<lb></lb>sta seconda parte pensò Galileo stesso da principio di aver reso il suo nuov<gap></gap><lb></lb>trattato assoluto, ridotto così a quelle sole XII proposizioni, delle quali si legge <lb></lb>nella seguente nota autografa nitidamente scritto il sommario: </s></p><p type="main">

<s>“ Prima proposizione: Che il proietto descrive la Parabola. </s>

<s>— II. </s>

<s>Prova <lb></lb>il moto composto de&#039;due equabili, orizzontale e perpendicolare, essere in <lb></lb>potenza uguale ad ambedue. </s>

<s>— III. </s>

<s>Considera il moto composto di due: <lb></lb>orizzontale equabile, e perpendicolare accelerato. </s>

<s>— IV. </s>

<s>Mostra come si debba <lb></lb>determinare l&#039;impeto del proietto in tutti i punti della Parabola. </s>

<s>— V. </s>

<s>Tro­<lb></lb>vare nell&#039;asse prolungato della data Paradola il punto sublime, dal quale i<gap></gap><lb></lb>cadente descrive la Parabola. </s>

<s>Segue il corollario che la metà dell&#039;ampiezza <lb></lb>è media tra l&#039;altezza e la sublimità della Parabola. </s>

<s>S&#039;aggiunge l&#039;altro co­<lb></lb>rollario, che è: le amplitudini delle Parabole essere uguali, quando le loro <lb></lb>elevazioni e sublimità alternativamente sono uguali. </s>

<s>— VI. </s>

<s>Data la subli­<lb></lb>mità e l&#039;altezza, trovare l&#039;ampiezza della Parabola. </s>

<s>— VII. </s>

<s>Nel descriver <lb></lb>parabole di ampiezze uguali, minor impeto si ricerca in quella, la cui am­<lb></lb>piezza è doppia dell&#039;altezza, che in qualsivoglia altra. </s>

<s>Segue il corollario <lb></lb>Nelle parabole descritte dal medesimo impeto, l&#039;amplitudine massima esse<gap></gap><lb></lb>di quella, che nasce dall&#039;elevazione dell&#039;angolo semiretto. </s>

<s>— VIII. </s>

<s>Le am­<lb></lb>piezze dei tiri, cacciati con l&#039;istesso impeto e per angoli ugualmente man­<lb></lb>canti o escedenti l&#039;angolo semiretto, sono uguali. </s>

<s>— IX. </s>

<s>Le ampieze sono <pb xlink:href="020/01/2315.jpg" pagenum="558"></pb>uguali delle parabole, le altezze e sublimità delle quali si rispondono con­<lb></lb>trariamente. </s>

<s>— X. </s>

<s>I momenti delle parabole d&#039;eguali ampiezze son fra loro <lb></lb>come i momenti delle altezze perpendicolari, dalle quali si generano esse <lb></lb>parabole. </s>

<s>— XI. </s>

<s>Il momento di qualsivoglia semiparabola è uguale al mo­<lb></lb>mento del cadente per la perpendicolare, composta dell&#039;altezza e sublimità <lb></lb>della Parabola. </s>

<s>— XII. </s>

<s>Dato l&#039;impeto e l&#039;ampiezza, trovar l&#039;altezza della <lb></lb>Parabola ” (MSS. Gal., P. V, T. II, fol. </s>

<s>106 a tergo). </s></p><p type="main">

<s>Corrispondono esattamente, nell&#039;ordine e negli argomenti di questo Som­<lb></lb>mario, le proposizioni stampate nel Dialogo quarto, se non che manca il <lb></lb>secondo corollario, annunziato dopo la V, per essere stato fatto soggetto di <lb></lb>dimostrazion propria nella IX, e manca pure la X, la quale, non sembrando <lb></lb>a noi formulata con chiarezza, non si saprebbe perciò nemmeno decidere se <lb></lb>Galileo pensò di lasciarla, per averla trovata inutile o falsa. </s>

<s>Vale in ogni <lb></lb>modo questo Sommario per documento certissimo che veramente, secondo <lb></lb>la prima intenzione di Galileo, si doveva il libro de&#039;proietti comporre di sole <lb></lb>due parti, nelle quali si tratterebbe della misura degl&#039;impeti, e delle ra­<lb></lb>gioni de&#039;teoremi annunziati dal Tartaglia. </s>

<s>Come poi si deliberasse l&#039;Autore <lb></lb>di aggiungere una terza parte, per applicare i teoremi ai militari esercizi, <lb></lb>non è difficile intendere ripensando che i calcoli, dai quali il Tartaglia stesso <lb></lb>diceva di aver ricavato <emph type="italics"></emph>la proportion dil crescer e calar che fa ogni pezzo <lb></lb>de artiglieria, alzandolo aver arbassandolo sopra il pian del orizonte,<emph.end type="italics"></emph.end> non <lb></lb>erano altro che belle promesse: nè è difficile pure accorgersi che non ve­<lb></lb>niva questa terza aggiunta preparata dall&#039;ordine e dal modo puramente teo­<lb></lb>rico della trattazion precedente. </s>

<s>È da tener nonostante per una calunnia <lb></lb>quella del Cartesio, il quale disse che il quarto dialogo delle Nuove scienze <lb></lb>non con altro consiglio sembrava scritto “ quam ut tormentorum bellico­<lb></lb>rum, secundum diversas elevationes explosorum, vim explicaret. </s>

<s>Praeterea <lb></lb>observandum est quod, quum hypotheses has proponeret, quo facilius admit­<lb></lb>terentur, tormenta bellica exceperit, et tamen sub finem conclusiones suas <lb></lb>ad tormenta bellica potissimum applicat: hoc est uno verbo omnia aeri su­<lb></lb>perstruxit ” (Epist., P. II cit., pag. </s>

<s>244). Quel che può essere in Galileo di <lb></lb>aereo apparirà da quest&#039;altra parte del nostro capitolo: ora è da vedere in <lb></lb>che modo egli applicasse ai tiri delle artiglierie le sue conclusioni. </s></p><p type="main">

<s>Posto che sia trovato per esperienza quanto getta un cannone per l&#039;oriz­<lb></lb>zontale la palla, nella elevazione a mezza squadra, Galileo insegna il modo <lb></lb>di calcolare, e calcola in effetto, quanto quel medesimo cannone, con la me­<lb></lb>desima carica, getterebbe la medesima palla in distanza orizzontale, elevato <lb></lb>o depresso, grado per grado, intorno a quella stessa direzion semiretta, la <lb></lb>quale, dando come si sa, la massima volata, si prende perciò per termine <lb></lb>di confronto. </s>

<s>Il problema è annunziato così nella XII proposizione del Dia­<lb></lb>logo, secondo il linguaggio proprio della scienza: “ Semiparabolarum omnium <lb></lb>amplitudines calculo colligere, atque in tabulas exigere, quae a proiectis, <lb></lb>codem impetu explosis, describuntur ” (Alb. </s>

<s>XIII, 255). </s></p><p type="main">

<s>Per condurre i calcoli però bisognava, direbbero i Matematici moderni, <pb xlink:href="020/01/2316.jpg" pagenum="559"></pb>prepararsi la formula, ciò che Galileo fa nella detta proposizione XII, ma <lb></lb>che noi vogliam presentare ai nostri Lettori in quell&#039;amabile semplicità di <lb></lb>abito, con cui ella uscì dalla mente dell&#039;Autore, senza que&#039;posticci belletti, <lb></lb>che le furono messi attorno, per farla comparir fra l&#039;altre sulla pubblica <lb></lb>scena. </s>

<s>Chi ha dimestichezza oramai con queste cose, non ha bisogno gli si <lb></lb>dica che, dovendo le parabole secondo il supposto tutte avere il medesimo <lb></lb>impeto che nella elevazion semiretta, alla somma, che hanno in questa, <lb></lb>debbono in ciascuna di quelle equivaler le somme della sublimità e della <lb></lb>altezza. </s></p><p type="main">

<s>“ Sia l&#039;angolo ADC (fig. </s>

<s>301) gradi 45: è manifesto che dalla subli­<lb></lb>mità AB nascerà la parabola, la cui altezza BC. </s>

<s>Posto l&#039;angolo EDC gradi 55, <lb></lb>si cerca la parabola alla elevazione di gradi 55, la cui sublimità e altezza <lb></lb>siano uguali alla AC. ” <lb></lb><figure id="id.020.01.2316.1.jpg" xlink:href="020/01/2316/1.jpg"></figure></s></p><p type="caption">

<s>Figura 301</s></p><p type="main">

<s>“ Con falsa posizione cerca se di tal parabola <lb></lb>fosse l&#039;asse nella EC, e la tangente ED, e poi, di­<lb></lb>videndo la EC in mezzo in F, fa che l&#039;altezza di tal <lb></lb>parabola sia FC, e la sublimità FA, il che allora <lb></lb>sarebbe, quando la metà dell&#039;ampiezza CD si tro­<lb></lb>vasse esser media proporzionale tra la CF e la FA. </s>

<s><lb></lb>Ma tra EF, cioè FC, ed FA media una minore della <lb></lb>metà di CD, essendo che la metà di CD è media <lb></lb>tra CB e BA; cerca dunque qual&#039;è la sublimità, tra <lb></lb>la quale e la FE sia media la metà dell&#039;ampiezza CD, <lb></lb>cioè la CB, e trovata che sia, pongasegli uguale la <lb></lb>FO, ed averassi la sublimità OF descrivere la para­<lb></lb>bola, la cui altezza sia FC, ed ampiezza CD. ” </s></p><p type="main">

<s>“ È dunque tal parabola maggiore della cercata, secondo che la OC è <lb></lb>maggiore della AC, ma bene gli è simile, sendo toccata dalla ED. </s>

<s>Convien <lb></lb>dunque descriverne altra simile, diminuendo la sua sublimità e ampiezza <lb></lb>secondo la proporzione di CA a CO. </s>

<s>Facciasi dunque come OC a CA, così <lb></lb>CD a DN, ed avremo l&#039;ampiezza cercata, cioè della parabola, la cui subli­<lb></lb>mità e altezza sono uguali alla AC, e per conseguenza nasceranno da im­<lb></lb>peti eguali de&#039;proietti cacciati dal punto D ” (MSS. Gal., P. V, T. II, <lb></lb>fol. </s>

<s>122 a tergo). </s></p><p type="main">

<s>La formula dunque, che resulta da questa dimostrazione, e sopra la <lb></lb>quale si possono calcolare le ampiezze di tutte le parabole, descritte dal me­<lb></lb>desimo cannone, che tiri in D elevato grado per grado, sopra e sotto la <lb></lb>elevazion semiretta AD; è DN=CA.CD/OC, dove DN rappresenta l&#039;ampiezza <lb></lb>che si cerca. </s>

<s>Il prodotto CA.CD è sempre un quadrato, avendosi DC, am­<lb></lb>piezza della parabola con elevazion semiretta, uguale ad AC, tangente del­<lb></lb>l&#039;angolo di 45 gradi, la qual tangente sappiamo essere uguale al raggio del <lb></lb>circolo, che è CD, e che ponesi uguale a diecimila. </s>

<s>“ Eligimus autem, dice <lb></lb>Galileo, numerum 10,000, quia utimur in calculis tabula tangentium, cuius <pb xlink:href="020/01/2317.jpg" pagenum="560"></pb>hic numerus congruit cum tangente gr. </s>

<s>45 ” (Alb. </s>

<s>XIII, 255, 56). Il divi­<lb></lb>dendo della formula è perciò sempre uguale al quadrato di diecimila, ma <lb></lb>il divisore ad ogni calcolo varia, essendo dato in funzione della tangente <lb></lb>dell&#039;angolo della elevazione. </s>

<s>Dato dunque l&#039;angolo EDC, le Tavole daranno <lb></lb>la tangente EC, o la metà di lei FC, alla quale aggiunta la FO, che sap­<lb></lb>piamo esser terza proporzionale dopo la stessa FC, e la metà di DC, e perciò <lb></lb>nota; sarà pur nota la CO della formula, e con essa infine la DN, ch&#039;era <lb></lb>l&#039;incognita del problema. </s>

<s>A questo modo, con moltiplicazioni e con divisioni <lb></lb>numeriche laboriosissime, fu calcolata da Galileo la prima Tavola, che s&#039;in­<lb></lb>titola: “ Amplitudines semiparabolarum ab eodem impetu descriptarum ” <lb></lb>(ibid., pag. </s>

<s>259). </s></p><p type="main">

<s>Per le varie elevazioni del cannone sapere la volata del tiro era, negli <lb></lb>eser<emph type="italics"></emph>c<emph.end type="italics"></emph.end>izi delle artiglierie, la cosa più importante, dopo la quale veniva la no­<lb></lb>tizia dell&#039;altezza perpendicolare, a cui giunge la palla nel descriver le am­<lb></lb>piezze via via calcolate. </s>

<s>Aggiunge perciò Galileo, alla prima Tavola costruita, <lb></lb>una seconda, per calcolar la quale bisognava pure prepararsi la formula op­<lb></lb>portuna. </s>

<s>Come facesse ciò nella XIII proposizione del Dialogo è pubblicamente <lb></lb>noto, ma noi, sempre desiderosi di conoscere addentro l&#039;Uomo famoso, an­<lb></lb>deremo a trovarlo anche questa volta, prima ch&#039;egli esca fuori in toga acca­<lb></lb>demica, nella libera quiete della sua stanza di studio. </s>

<s>Ivi l&#039;udiremo così, <lb></lb>presso a poco, ragionare fra sè, e poi scrivere: </s></p><p type="main">

<s>L&#039;altezza della parabola con elevazion semiretta è nota, essendo ella la <lb></lb>metà della tangente, ossia di diecimila, ond&#039;è che si riduce tutto il presente <lb></lb>problema a trovar quanta sia la distanza del vertice delle altre parabole dal <lb></lb>vertice di quella stessa parabola semiretta. </s>

<s>E perchè posson que&#039;vertici ora <lb></lb>rimaner sotto, ora sopra a questo, secondo che gli angoli della direzion dei <lb></lb>tiri son minori o maggiori di 45 gradi, avrà dunque il problema a contem­<lb></lb>plare due casì. </s></p><p type="main">

<s>S&#039;incominci, par che voglia dir Galileo, a calcolare le altezze al di sotto <lb></lb>della metà del quadrante, e sien gl&#039;impeti, da cui nascon le altre parabole, <lb></lb><figure id="id.020.01.2317.1.jpg" xlink:href="020/01/2317/1.jpg"></figure></s></p><p type="caption">

<s>Figura 302<lb></lb>tutti uguali all&#039;impeto della semiretta, rappresentato dalla <lb></lb>linea BD (fig. </s>

<s>302), cosicchè tornerà il vertice di essa <lb></lb>parabola semiretta in E, dove la DB stessa è tagliata nel <lb></lb>mezzo. </s>

<s>Sia il vertice di un&#039;altra parabola in A: si vuol <lb></lb>costruire la formula, dietro la quale possa calcolarsi <lb></lb>quanto A, che è uno degl&#039;infiniti punti della linea EB, <lb></lb>sia distante da A, termine fisso. </s>

<s>I pensieri di Galileo <lb></lb>sipossono così brevemente significare, con queste equa­<lb></lb>zioni: AB.AD=(BE—AE)(DE+AE)=(BE—AE) <lb></lb>(BE+AE)=BE2—AE2. </s>

<s>E perchè AB.AD è il pro­<lb></lb>dotto dell&#039;altezza per la sublimità della parabola AC, <lb></lb>che sappiamo dover essere uguale al quadrato della <lb></lb>metà dell&#039;ampiezza FB, sarà dunque AE2=BE2—FB2, con la quale equa­<lb></lb>zione, essendo BE costantemente la metà dell&#039;impeto, ossia 5000, ed FB <pb xlink:href="020/01/2318.jpg" pagenum="561"></pb>essendo data dalla Tavola precedente; si potrà avere il valore di AE, che <lb></lb>misura la distanza del vertice della parabola CA dal vertice della parabola <lb></lb>con elevazion semiretta. </s>

<s>Dopo ciò, per mezzo dell&#039;equazione AB=EB—AE, <lb></lb>si verrà ad aver la diretta, e final soluzione del proposto problema. </s></p><p type="main">

<s>Nell&#039;altro caso, che l&#039;angolo della elevazione sia maggiore di 45 gradi, <lb></lb>e che perciò il punto A riesca superiore ad E, si potrà calcolare AE come <lb></lb>sopra: la quantità però, che dal calcolo ne resulta, si dovrebbe ora aggiun­<lb></lb>gere ad EB, mentre dianzi si sottraeva; cosicchè la formula tornerebbe così <lb></lb>leggermente trasformata: AB=EB+AE. </s>

<s>Ma ascoltiamo come Galileo si­<lb></lb>gnifichi questi stessi pensieri, nella sua propria maniera, e quali la prima <lb></lb>volta gli caddero giù dalla penna. </s></p><p type="main">

<s>“ Sit impetus datus semper idem, nempe BD (nella medesima fig. </s>

<s>302), <lb></lb>ex altitudine et sublimitate composita linea DB 10,000. Et quia dimidia am­<lb></lb>plitudo, nempe BF, mediat inter altitudinem et sublimitatem, intelligatur DB <lb></lb>divisa ut rectangulum partium, quae sint v. </s>

<s>g. </s>

<s>DA, AB, sit aequale qua­<lb></lb>drato FB. </s>

<s>Quod si DB divisa sit bifariam in E, erit quadratum BE aequale <lb></lb>rectangulo partium ipsius DB, et quadrato AE. </s>

<s>Si ergo a quadrato BE de­<lb></lb>matur quadratum FB, seu dicas rectangulum illi aequale a partibus con­<lb></lb>tentum, remanebit quadratum AE, cuius radix, dempta ex EB, relinquet BA <lb></lb>altitudinem quaesitam. </s>

<s>Amplitudo autem BC iam calculata est ad singulos <lb></lb>gradus elevationis ” (MSS. Gal., P. V, T. II, fol. </s>

<s>103 a tergo). </s></p><p type="main">

<s>Ne deduce di qui Galileo stesso la seguente regola pratica <emph type="italics"></emph>“ Per tro­<lb></lb>vare l&#039;altezza della parabola.<emph.end type="italics"></emph.end> Dal quadrato della metà dell&#039;impeto, che è <lb></lb>l&#039;altezza colla sublimità della parabola, cava il quadrato della metà dell&#039;am­<lb></lb>piezza della semiparabola, e la radice del rimanente, aggiunta alla metà del­<lb></lb>l&#039;impeto, darà l&#039;altezza cercata, quando l&#039;elevazione è più di gradi 45. Per <lb></lb>la presente tavola, che si fabbrica, la metà dell&#039;impeto è sempre 5000, e il <lb></lb>suo quadrato 25,000,000. Ma se l&#039;elevazione sarà meno di gradi 45, la detta <lb></lb>radice del rimanente si dee sottrarre dalla metà dell&#039;impeto, ed il restante <lb></lb>è l&#039;altezza cercata ” (ivi, fol. </s>

<s>110). Sotto sono scritti alla rinfusa i calcoli, <lb></lb>fatti sempre per via di moltiplicazioni, di divisioni e di somme di numeri, <lb></lb>il primo esempio de&#039;quali, per la costruzion della Tavola, incomincia dalla <lb></lb>elevazione di gradi 50. </s></p><p type="main">

<s>Calcolate così le Tavole delle ampiezze e delle altezze delle parabole, <lb></lb>descritte dal medesimo impeto, rimaneva, secondo le teorie, a considerare <lb></lb>il terzo elemento, che è delle sublimità, per calcolar le quali porgeva faci­<lb></lb>lissima e immediata la formula il corollario della proposizione quinta. </s>

<s>Chia­<lb></lb>mata M infatti la semibase della semiparabola, S la sublimità, e A l&#039;altezza, <lb></lb>abbiamo per il detto corollario M2=S.A, d&#039;onde S=M2/A. Fra&#039;problemi <lb></lb>perciò, che risoluti dovevano servire alla costruzione delle Tavole ballistiche, <lb></lb>Galileo aveva preparato anche questo: </s></p><p type="main">

<s><emph type="italics"></emph>“ Data amplitudine et altitudine semiparabolae, sublimitatem re­<lb></lb>perire. </s>

<s>”<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2319.jpg" pagenum="562"></pb><p type="main">

<s>“ Id statim colligitur ex eo quod dimidia amplitudo mediat inter alti­<lb></lb>tudinem et sublimitatem: ergo, diviso quadrato dimidiae amplitudinis per <lb></lb>altitudinem, habemus sublimitatem quaesitam ” (ibid., fol. </s>

<s>118 a tergo). </s></p><p type="main">

<s>Ma rimase questo problema tra&#039;fogli di Galileo, il quale, dopo qualche <lb></lb>esempio, lasciò di farne l&#039;applicazione a costruir le Tavole delle sublimità, <lb></lb>forse perchè riconosceva che sarebbero tornate inutili agli artiglieri, in ser­<lb></lb>vigio de&#039;quali aveva fabbricato le prime due. </s>

<s>Dall&#039;altra parte erano le pre­<lb></lb>cedenti dottrine di facile guida a chi avesse voluto, per sua propria curio­<lb></lb>sità, sapere da quale altezza dovrebbe naturalmente scender la palla, per <lb></lb>acquistar quella violenza d&#039;impeto orizzontale impressale dalla forza del <lb></lb>cannone. </s></p><p type="main">

<s>Più utile di ciò pensava Galileo che tornerebbe agli artiglieri il sapere <lb></lb>quanta debba esser la carica, perchè, secondo i gradi delle elevazioni via via <lb></lb>crescenti da uno a novanta, possa il cannone sempre cacciar la palla alla <lb></lb>medesima distanza orizzontale. </s>

<s>Misura alla detta carica è quel che, in que­<lb></lb>sta nuova Scienza galileiana, chiamasi impeto, il quale si compone dell&#039;al­<lb></lb>tezza e della sublimità della parabola. </s>

<s>La formula dunque, per questi cal­<lb></lb>coli nuovi, consisteva nella soluzione di quest&#039;altro problema: <emph type="italics"></emph>Trovar l&#039;al­<lb></lb>tezza e la sublimità delle parabole, aventi la medesima ampiezza.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Quanto all&#039;altezza è cosa di facilissima invenzione, perchè, avendosi i <lb></lb>tiri per esempio diretti secondo DM, DA, DE, nella poco addietro fig. </s>

<s>301, <lb></lb>le respettive altezze delle parabole s&#039;avranno misurate dalle linee QC, BC, <lb></lb>FC, metà delle MC, AC. EC, che son le tangenti degli angoli MDC, ADC, <lb></lb>EDC nel circolo descritto col raggio DC, fatto anche per questa terza Ta­<lb></lb>vola da Galileo diecimila: cosicchè cinquemila è l&#039;altezza BC della parabola, <lb></lb>che vien descritta dal tiro diretto a mezza squadra. </s>

<s>Saranno dunque date in <lb></lb>generale, dalle mezze tangenti degli angoli delle elevazioni, le altitudini delle <lb></lb>parabole via via richieste. </s>

<s>Le sublimità poi si possono facilmente calcolar <lb></lb>con la formula S=M2/A, in cui M è data, e A s&#039;è detto ora come trovarla. </s>

<s><lb></lb>Ma il detto è propriamente di Galileo, nella XIV proposizione del Dialogo, <lb></lb>raffazzonata sopra questa semplice Nota manoscritta: </s></p><p type="main">

<s><emph type="italics"></emph>“ Altitudines semiparabolarum, quarum eadem sit amplitudo, re­<lb></lb>perire. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Id autem absolvitur, per dimidiam tangentem arcum elevationis da­<lb></lb>tae semiparabolae. </s>

<s>” </s></p><p type="main">

<s>“ Inventa ex dictis altitudine, sublimitatem singularum semiparabola­<lb></lb>rum, quarum eadem sit amplitudo, facilem reperies. </s>

<s>Nam, cum dimidia am­<lb></lb>plitudo mediet inter altitudinem et sublimitatem, diviso quadrato mediae <lb></lb>amplitudinis per altitudinem, habebimus sublimitatem, quae postea, addita <lb></lb>altitudine, exhibet impetum. </s>

<s>Fabricemus ergo Tabulas sublimitatum, sitque <lb></lb>semper dimidia amplitudo semiparabolae 5000, cuius quadratum semper <lb></lb>idem 25,000,000 ” (ibid., fol. </s>

<s>125 a tergo). </s></p><p type="main">

<s>Sotto è gremito il foglio tutto di numeri, disposti in ordine, com&#039;usava <pb xlink:href="020/01/2320.jpg" pagenum="563"></pb>allora, per estrarne le radici, e per farne le divisioni. </s>

<s>Si disse altrove come <lb></lb>sopra la faccia retta di questo medesimo foglio sia distesa una lettera di <lb></lb>Alessandro Ninci, scritta da Campoli nel Marzo del 1636, dopo il qual tempo <lb></lb>dev&#039;essere stata dunque fabbricata questa Tavola terza, e molto ragionevol­<lb></lb>mente anche le altre due, de&#039;calcoli serviti per le quali è una fitta selva <lb></lb>in parecchi fogli del codice da noi citato. </s>

<s>Non si può da quella pagine le­<lb></lb>vare gli occhi, senza ripensare alla pazienza invitta, e all&#039;improba fatica del <lb></lb>calcolatore, specialmente a quei tempi, in cui la vista indebolita, non invi­<lb></lb>gilandone i moti, poteva facilmente far trascorrere la penna in non colpe­<lb></lb>voli errori. </s>

<s>Cosicchè, verrebbe fatto anche a noi di esclamare col Torricelli: <lb></lb>“ Cuius enim industriae tanta solertia est, ut per innumeras multiplicatio­<lb></lb>num, divisionum et radicum ambages ad eosdem pene numeros appellere <lb></lb>potuerit, quos ex Tabula desumere nobis concessum fuit? </s>

<s>” (Op. </s>

<s>geom. </s>

<s>cit., <lb></lb>pag. </s>

<s>104). </s></p><p type="main">

<s>Se non che si direbbe follia, piuttosto che industriosa solerzia, quella <lb></lb>di Galileo, che potendo, come poi fece il Torricelli stesso per le sue Tavole, <lb></lb>delle quali diremo altrove; trascrivere i calcoli <emph type="italics"></emph>ex ipsa Tabula sinuum, ac <lb></lb>tangentium, facili brevique negatio,<emph.end type="italics"></emph.end> si volesse nulladimeno sottoporre a sì <lb></lb>lunghe e laboriose vigilie. </s>

<s>Ma nè da industria soverchiamente solerte, nè da <lb></lb>follia dipende la stranezza del fatto: diremo piuttosto che dipende dagli <lb></lb>studii, e dall&#039;indole dell&#039;ingegno di Galileo, arretratosi alla vista di quella <lb></lb>mostruosa macchina trigonometrica, dalla gola della quale faceva. </s>

<s>Enrico <lb></lb>Bryggs vomitar le sue Tavole de&#039;seni e delle tangenti. </s>

<s>Più tardi, il Cava­<lb></lb>lieri attendeva in Italia a perfezionare quelle medesime Tavole, con più co­<lb></lb>moda applicazione dei Logarimmi, la materia de&#039;quali sentì ancora Galileo <lb></lb>di difficile intelligenza. </s>

<s>Nè a fargliene, nei calcoli numerici, riconoscer l&#039;uti­<lb></lb>lità dell&#039;uso, valsero le persuasioni dello stesso Cavalieri, il quale scriveva <lb></lb>in una sua lettera non stimare i suoi <emph type="italics"></emph>Logarimmi<emph.end type="italics"></emph.end> materia sì difficile, che <lb></lb>un Galileo, <emph type="italics"></emph>con non molta applicazione, non l&#039;intendesse.<emph.end type="italics"></emph.end> (Campori, Car­<lb></lb>teggio gal., Modena 1881, pag. </s>

<s>330). </s></p><p type="main">

<s>Comunque sia, mancherebbe a queste atlantiche fatiche, durate nel ri­<lb></lb>tessere i calcoli per le tre Tavole ballistiche, ogni ragion di scusa e di me­<lb></lb>rito, se fosse vero ch&#039;elle non fosser altro che castelli in aria, com&#039;andava <lb></lb>dicendo fra gli amici il Cartesio. </s>

<s>L&#039;accusa del Filosofo famoso, per quanto <lb></lb>possa essere stata suggerita o dall&#039;emulazione o dall&#039;invidia, dà indizio del <lb></lb>dover esservi altre difficoltà promosse da uomini d&#039;altro animo e d&#039;altro <lb></lb>ingegno, delle quali difficoltà, e della loro efficacia in confermar sempre me­<lb></lb>glio la Scienza de&#039;proietti, novamente istituita da Galileo, faremo ora sog­<lb></lb>getto questa ultima parte del nostro discorso. </s></p><pb xlink:href="020/01/2321.jpg" pagenum="564"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;istituzione di quella nuova Scienza galileiana essendo tutta fondata <lb></lb>sul moto parabolico, sarebbe stata dunque per i contradittori rovesciata dalle <lb></lb>sue fondamenta, quando fossero state false le ipotesi, dalle quali consegui­<lb></lb>van legittimamente le ragioni di una tal direzione dei moti proiettizi. </s>

<s>“ Fal­<lb></lb>sam aliam hypothesin prioribus adiicit (soggiunge il Cartesio stesso nella <lb></lb>citata Epistzla al Mersenno, dove censura tante altre dottrine di Galileo) <lb></lb>nempe corpora in aerem proiecta aequali velocitate ferri secundum horizon­<lb></lb>tem, descendendo vero illorum velocitatem in ratione spatii duplicata augeri. </s>

<s><lb></lb>Hoc autem posito, facillimum est concludere motum proiectorum sequi li­<lb></lb>neam parabolicam, sed, cum eius hypotheses sint falsae, conclusio etiam a <lb></lb>vero valde remota esse potest ” (pag. </s>

<s>244). </s></p><p type="main">

<s>Perchè falsa debba tenersi l&#039;ipotesi, che il proietto venga equabilmente <lb></lb>promosso per linea orizzontale, discendendo nel perpendicolo con velocità <lb></lb>crescenti in duplicata proporzion degli spazi, il Cartesio non dice, ma lo <lb></lb>dicon bene gli altri, a cui i dubbi facevano nella mente le medesime ten­<lb></lb>zoni. </s>

<s>Dicevan dunque che il moto nell&#039;orizzonte, tutt&#039;altro ch&#039;essere equa­<lb></lb>bile, è più accelerato nel principio, e più tardo verso la fine, e che una <lb></lb>tanta violenza d&#039;impeto impedisce così la libera discesa del grave, che non <lb></lb>può accelerarsi secondo la natural sua proporzione. </s></p><p type="main">

<s>I dubbi cartesiani si vedono passar per la mente degli stessi discepoli <lb></lb>di Galileo, con ombre di sì ugual tinta e figura, da escludere in sollevarle <lb></lb>qualunque mala disposizion dell&#039;animo nel geloso rivale. </s>

<s>Ascoltiamo Anto­<lb></lb>nio Nardi, che così prosegue, nella veduta XLII della scena VI, dop&#039;aver <lb></lb>censurate le dottrine del suo proprio Maestro, circa alla proporzione del­<lb></lb>l&#039;accelerarsi i gravi nei loro liberi moti. </s>

<s>E prima di tutto è a notare un&#039;opi­<lb></lb>nione di lui, dimostrata falsa dalle cose discorse ne&#039;precedenti capitoli di <lb></lb>questa Storia, che cioè dalla scoperta della parabola dei proietti prendesse <lb></lb>Galileo occasione d&#039;assegnare ai cadenti naturali le medesime leggi. </s>

<s>Contro <lb></lb>dunque quel che notò il Torricelli <emph type="italics"></emph>de linea parabolica pro motibus natu­<lb></lb>raliter cadentium, quod non scripsit Galileus,<emph.end type="italics"></emph.end> così il Nardi incomincia la <lb></lb>seconda parte delle sue censure. </s></p><p type="main">

<s>“ Quanto poi all&#039;essere il moto de&#039;proietti apparentemente parabola, <lb></lb>concordo col Galilei, che forse quindi congetturò i gravi affrettarsi con la <lb></lb>medesima ragione, ma osservisi che diverse strade conducono al medesimo <lb></lb>termine. </s>

<s>Dunque è vero che il moto orizzontale è uguale, ma ciò s&#039;intende, <lb></lb>mentre un mobile sia sostenuto e mosso per qualche orizzontal superfice, <lb></lb>sicchè compensato vengane il suo momento. </s>

<s>Ma un proietto per l&#039;aria muo­<lb></lb>vesi, perchè non viene compensato il momento suo, di due moti, quali in­<lb></lb>sieme rimescolati non si mantengono ciascuno di essi sinceri, ma scambie-<pb xlink:href="020/01/2322.jpg" pagenum="565"></pb>volmente si alterano, e par necessario che il violento sia più veloce nell&#039;uscire <lb></lb>dal proiciente, che allontanatone, com&#039;anco nel natural moto avviene, e però <lb></lb>non passerà di sua natura spazi uguali in tempi uguali, come in tal punto <lb></lb>dubitò il Galilei. </s>

<s>Anzi che alcuni Meccanici si persuasero che nell&#039;uscir la <lb></lb>palla dall&#039;artiglieria andasse per qualche spazio rettamente, il che, sebbene <lb></lb>vero non è, perchè non s&#039;annulla l&#039;azione della gravità, con tutto ciò par <lb></lb>vero che il moto orizzontale sostenga da principio il proietto, sicchè non di­<lb></lb>scenda con la ragione, con la quale discenderebbe per la sola gravità, ma <lb></lb>nel progresso è necessario che la gravità vinca l&#039;impeto straniero, acciò si <lb></lb>riconduca il proietto al centro, e così anche appare necessario che la forza, <lb></lb>quale prima mosse un proietto dallo stato di quiete, non così muover lo <lb></lb>possa, dopo l&#039;acquisto e accrescimento di moto verso il centro. </s>

<s>Ora, dal­<lb></lb>l&#039;intrecciamento di questi moti, momenti e tempi, componsi una linea molto <lb></lb>vicino alla parabolica, ma difficilissimo da me si reputa il dimostrarla tale, <lb></lb>per i suoi immediati principii. </s>

<s>E tanto, per modo di semplice dubitazione, <lb></lb>basti aver apportato intorno a varii pensieri del mio Maestro ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XL, pag. </s>

<s>973, 74). </s></p><p type="main">

<s>Andando a ricercar però la profonda radice di questi dubbi, così libe­<lb></lb>ramente esposti dal Nardi, si troverebbe in quel principio della composizione <lb></lb>dei moti, da cui risulta la parabola dei proietti; principio, che quale è espo­<lb></lb>sto nella II proposizione di Galileo, giova ripeterlo ancora dopo tante volte, <lb></lb>è manifestamente falso. </s>

<s>Anche, senza il Mersenno, dovevasi a quel vivo <lb></lb>lampo di luce, riflesso dallo scolio alla proposizione XVIII del primo libro <lb></lb>del Torricelli, riconoscer impossibile, che non si elidano due forze ango­<lb></lb>lari, onde al sentor di falso, che veniva dalla dottrina galileiana, trascorre­<lb></lb>vasi nell&#039;apposto errore insegnato dal Cardano. </s></p><p type="main">

<s>Ci porge un notabile esempio di ciò il Baliani, il quale dice, nel suo <lb></lb>breve proemio al terzo libro <emph type="italics"></emph>De motu naturali,<emph.end type="italics"></emph.end> che sarebbe quello il luogo <lb></lb>di trattar de&#039;proietti, “ ni via, quam eorum motu conficiunt, me adhuc la­<lb></lb>teret, quamvis non ignorem viris oculatissimis visam esse parabolicam ” <lb></lb>(Gennae 1646, pag. </s>

<s>80). Tale però a me non sembra, soggiunge lo stesso <lb></lb>Baliani, perchè, contro ciò che da que&#039;chiarissimi uomini si suppone, “ ap­<lb></lb>paret proiectum descendere minori celeritate, quam si a sola ducatur gra­<lb></lb>vitate, et libere demissum celerius solum attingere, quam horizontaliter la­<lb></lb>tum ” (ibid., pag. </s>

<s>81). La ragione di ciò è, secondo l&#039;Autore, quella medesima <lb></lb>già detta dal Cardano, e ripetuta dal Nardi, come dianzi udimmo, dovendo <lb></lb>la forza, che trasporta il grave per linea orizzontale, repugnare all&#039;altra, che <lb></lb>lo farebbe scendere nel perpendicolo. </s></p><p type="main">

<s>Per altre due ragioni credeva il Baliani di non poter consentire col Ca­<lb></lb>valieri, col Galileo e col Torricelli, che la via de&#039;proietti sia parabolica. </s>

<s><lb></lb>Prima, perchè, se il mobile passa successivamente nella traiettoria spazi sem­<lb></lb>pre più lunghi, “ motus est successive velocior, quippe maius spatium aequo <lb></lb>tempore permeat, unde si, vis proiicientis provenit a maiori velocitate, ic­<lb></lb>tus eo est validior, quo missile longius a proiiciente distat, contra id quod <pb xlink:href="020/01/2323.jpg" pagenum="566"></pb>quotidie experimur ” (idid.). Ma qui evidentemente si confonde il tiro ele­<lb></lb>vato con quello di punto in bianco, nel qual caso concorrono la teoria e <lb></lb>l&#039;esperienza a dimostrare che il colpo è veramente tanto più valido, <emph type="italics"></emph>quo <lb></lb>missile longius a proiiciente distat.<emph.end type="italics"></emph.end> Nè punto più ragionevole di questa è <lb></lb>l&#039;altra difficoltà, ivi in terzo luogo promossa dal medesimo Autore, da cui <lb></lb>si crede che, supponendo essere il proietto abbandonato a un tratto dal­<lb></lb>l&#039;impeto della propria gravità, proseguirebbe secondo la direzion tangen­<lb></lb>ziale, non avvedendosi che piegare il mobile verso il centro dei gravi, e sup­<lb></lb>porlo senza gravità, è una manifesta contradizione. </s></p><p type="main">

<s>I secondi dubbi, esposti così dal Baliani, nascevano dunque da incon­<lb></lb>sideratezza delle teorie galileiane, ma del primo erano queste medesime <lb></lb>teorie che, così in lui come nel Nardi e nel Cartesio, ne avevano data pre­<lb></lb>sentissima occasione. </s>

<s>Gli osservatori zelanti delle dottrine di Galileo avevano <lb></lb>un bel dire che il moto trasversale non impedisce il naturale <emph type="italics"></emph>deorsum,<emph.end type="italics"></emph.end> per <lb></lb>le ragioni e per i fatti accennati nella seguente nota del Viviani: “ Si trans­<lb></lb>versalis motus deorsum naturalem impediret, lapis transversim proiectus <lb></lb>numquam descenderet, nisi assumpto transversali motu, quoniam naturalis <lb></lb>deorsum adeo lente in principio procedit, ut quicumque transversalis motus <lb></lb>ipsum naturalem impediet. </s>

<s>Sed transversalis impetus nunquam cessat, ergo <lb></lb>lapis nunquam descenderet, quod est contra Naturae leges, et contra quo­<lb></lb>tidiana experimenta ” (MSS. Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>19). Ma non pote­<lb></lb>vano aver queste ragioni nessuna efficacia sulla mente dei dubitanti, i quali, <lb></lb>ben riconoscendo non essere le potenze dinamiche, introdotte da Galileo <lb></lb>nella sua proposizione seconda, altro che linee, vedevano concludersi da <lb></lb>quella medesima proposizione l&#039;assurdo che l&#039;ipotenusa sia uguale alla somma <lb></lb>dei cateti. </s>

<s>Non furono i dubbi perciò, da questa parte, soluti, se non che <lb></lb>quando ebbero i Matematici, con universale consentimento, approvata la re­<lb></lb>gola del parallelogrammo, dalla quale apparì chiaro come i moti si elidano <lb></lb>nel compor la parabola, in modo però, che rimangano uguali i tempi im­<lb></lb>piegati a passar ora divisamente i lati, ora compostamente la diagonale. </s></p><p type="main">

<s>Altri dubbi, che potessero passar per la mente ai lettori, erano stati <lb></lb>prevenuti già dal Cavalieri e da Galileo, i quali condussero le loro propo­<lb></lb>sizioni, astraendo dagl&#039;impedimenti del mezzo, de&#039;quali pure essendo sgom­<lb></lb>bri i proietti disse il Cavalieri che descrivono una linea curva <emph type="italics"></emph>insensibil­<lb></lb>mente differente dalla parabola.<emph.end type="italics"></emph.end> Accenna perciò, nella sua precisione, il <lb></lb>Matematico che non sarebbe perfettamente parabolica, nemmen la curva de­<lb></lb>scritta nel vuoto, non essendo propriamente parallele le direzioni delle forze <lb></lb>di gravità, ma concorrenti. </s>

<s>Galileo volle esplicitamente avvertire che la pro­<lb></lb>posizione sua prima era solamente vera nel supposto medesimo fatto da Ar­<lb></lb>chimede, “ il quale, nelle sue Meccaniche, e nella prima quadratura della <lb></lb>parabola, piglia come principio vero l&#039;ago della bilancia o stadera essere <lb></lb>una linea retta in ogni suo punto ugualmente distante dal centro comune <lb></lb>dei gravi, e le corde alle quali sono appesi i gravi esser tra di loro paral­<lb></lb>lele ” (Alb. </s>

<s>XIII, 228): ond&#039;è che parabolica può esser la via de&#039;proietti <pb xlink:href="020/01/2324.jpg" pagenum="567"></pb>nelle sole brevi distanze, a cui posson giungere l&#039;esplosioni dei nostri stru­<lb></lb>menti. </s>

<s>Con ragione dunque dimostrava Domenico Guglielmini nella VI pro­<lb></lb>posizione della sua <emph type="italics"></emph>Epitropeia,<emph.end type="italics"></emph.end> che a 1600 miglia, quanto si suppone da un <lb></lb>suo contradittore farsi un getto, questo esorbiterebbe grandemente dalla pa­<lb></lb>rabola <emph type="italics"></emph>“ etiam in doctrina Galilei ”<emph.end type="italics"></emph.end> (Bononiae 1676, pag. </s>

<s>19). Nella grande <lb></lb>ampiezza infatti della semiparabola BI (fig. </s>

<s>303), le direzioni della gravità <lb></lb>del proietto ne&#039;punti G, F, E essendo GX, FX, EX, se con raggi appun­<lb></lb><figure id="id.020.01.2324.1.jpg" xlink:href="020/01/2324/1.jpg"></figure></s></p><p type="caption">

<s>Figura 303<lb></lb>tati in X si descrivono cerchi, che <lb></lb>seghino la parabola ne&#039;punti D, H, I, <lb></lb>si vedrà manifesto che le linee obli­<lb></lb>que GK, FN, EB son minori delle re­<lb></lb>spettive perpendicolari GD, FH, EI, <lb></lb>ond&#039;è che ne&#039;tempi BG, BF, BE non <lb></lb>sarebbe il proietto sceso in D, H, I, <lb></lb>lungo la parabola, ma sotto i punti <lb></lb>K, N, B, dentro la parabola, “ quare <lb></lb>linea, per ea puncta descensuum de­<lb></lb>scripta, non erit parabola ” (ibid., <lb></lb>pag. </s>

<s>21, 22). </s></p><p type="main">

<s>Il Guglielmini dunque conferma­<lb></lb>va, piuttosto che impugnare le dot­<lb></lb>trine di Galileo, le quali venivano <lb></lb>nonostante assalite da altre parti. </s>

<s>Le <lb></lb>teorie degli impeti e le loro applica­<lb></lb>zioni si fanno, nel quarto dialogo delle <lb></lb>Nuove Scienze, dipendere da due sup­<lb></lb>posti: il primo de&#039;quali è che la direzione del moto si fa secondo la tan­<lb></lb>gente alla curva, nel punto della separazione, e il secondo, che la parabola <lb></lb>CA (fig. </s>

<s>304), descritta dall&#039;esplosione in C con tiro livellato, è la mede­<lb></lb>sima che la parabola AC, descritta dall&#039;esplosione in A con tiro inclinato. <lb></lb><figure id="id.020.01.2324.2.jpg" xlink:href="020/01/2324/2.jpg"></figure></s></p><p type="caption">

<s>Figura 304<lb></lb>Il primo era stato supposto anche dal Tartaglia, nel se­<lb></lb>condo libro della <emph type="italics"></emph>Nova scientia,<emph.end type="italics"></emph.end> ove dice: “ Ogni corpo <lb></lb>egualmente grave in fine de ogni moto violente, che sia <lb></lb>fuora della perpendicolare di l&#039;orizonte, si moverà di <lb></lb>moto naturale il qual sarà contingente con la parte curva <lb></lb>del moto violente ” (fol. </s>

<s>19 a tergo). Ma Galileo aveva, <lb></lb>come dicemmo, esplicato assai minutamente, ne&#039;dialoghi <lb></lb>dei Massimi sistemi, queste dottrine, contro le quali nul­<lb></lb>ladimeno così volle argomentare l&#039;Aggiunti. </s></p><p type="main">

<s>“ Acciocchè un mobile acquisti da virtù estrinseca <lb></lb>impeto di muoversi per una tal direzione, bisogna che <lb></lb>il motore l&#039;abbia movendo accompagnato per qualche <lb></lb>spazio in essa dirittura. </s>

<s>Gli esempi sono di questo la balestra, che, accom­<lb></lb>pagnando poco la palla, la move anche pochissimo. </s>

<s>Il maglio, scorrendo <pb xlink:href="020/01/2325.jpg" pagenum="568"></pb>e non accompagnando, non muove, e piegandosi nel manico, perchè allora <lb></lb>all&#039;accompagnatura del braccio v&#039;aggiunge quella del ritorno del manico pie­<lb></lb>gato, fa maggior colpo. </s>

<s>La racchetta per questo manda più la palla lon­<lb></lb>tana, che la mestola. </s>

<s>” </s></p><p type="main">

<s>“ Quanto insomma minore sarà questa accompagnatura, <emph type="italics"></emph>caeteris pari­<lb></lb>bus,<emph.end type="italics"></emph.end> minore sarà l&#039;acquisto dell&#039;impeto, sicchè, se un motore movesse un <lb></lb>mobile in un poligono di moltissimi lati e brevissimi, onde le accompagna­<lb></lb>ture sarebbero ancor esse brevissime, questo mobile non acquisterebbe nota­<lb></lb>bile impeto di moversi per alcuna di queste linee. </s>

<s>Adunque perchè il mobile, <lb></lb>mosso dai motori in un cerchio, cioè in un poligono d&#039;infiniti lati, e per­<lb></lb>ciò di niuna longitudine, variano ad ogni momento direzione di moto; le <lb></lb>accompagnature in ciascuna direzione sarebbero istantanee, e però di niuno <lb></lb>o minimo momento. </s>

<s>E per questo l&#039;acquisto d&#039;impeto di moversi in alouna <lb></lb>di esse sarebbe nullo o minimo, laonde sarà falso che dalla vertigine di <lb></lb>una ruota si conferisca alla sua parte impeto di moversi per la tangente, <lb></lb>come asserisce l&#039;eccellentissimo signor Galileo ” (MSS. Gal. </s>

<s>Disc., T. XVIII, <lb></lb>fol. </s>

<s>59). </s></p><p type="main">

<s>Non potrebbe dunque nemmeno il proietto aver valido impulso di mo­<lb></lb>versi lungo la tangente della parabola, se fosse vera la conclusion dell&#039;Ag­<lb></lb>giunti, la quale parte dal principio delle accompagnature, male applicato <lb></lb>agli effetti dei citati strumenti, e manifestamente falso in sè stesso, perchè <lb></lb>la forza si comunica in istante, e non con tempo. </s>

<s>D&#039;altro momento è perciò <lb></lb>l&#039;opposizione fatta al secondo supposto, la quale non sfuggi alla censura del <lb></lb>Cartesio. </s>

<s>“ Conversam propositionis suae assumit, egli dice nella citata epi­<lb></lb>stola al Mersenno, neque demonstratam, neque explicatam; nimirum quod, <lb></lb>si globus, secundum horizontem explosus a C (nella precedente figura) ver­<lb></lb>sus O, sequatur parabolam CA, globus etiam, sursum explosus secundum <lb></lb>lineam AO, debeat eamdem parabolam AC sequi, quod quidem ex eius hypo­<lb></lb>thesibus recte sequitur, sed haec explicare non videtur ausus, ne eorum fal­<lb></lb>sitas nimis aperte pareret ” (pag. </s>

<s>244). </s></p><p type="main">

<s>Il Torricelli, che riseppe forse le calunniose cartesiane censure dallo <lb></lb>stesso Mersenno, pensò di ovviarle e di rispondere con quella elaboratissima <lb></lb>proposizione III del secondo suo libro, nella quale dimostra che la linea <lb></lb>curva “ quae describitur a mobili, secundum quamlibet elevationem proiecto, <lb></lb>parabola est, et prorsus eadem, quam describeret mobile, si cum horizon­<lb></lb>tali impetu proiceretur a vertice eiusdem lineae curvae ” (pag. </s>

<s>157). Ma è <lb></lb>notabile che Galileo stesso, appena dimostrate le proposizioni attenenti alle <lb></lb>prime due parti del suo trattato, avesse già presentite quelle medesime dif­<lb></lb>ficoltà, e quasi, per ridursene alla memoria la risposta, da inserirsi poi nel <lb></lb>venire a stendere il Dialogo quarto; ne lesciava scritto di sua propria mano, <lb></lb>sotto il sommario delle proposizioni, questo così compendioso commento: </s></p><p type="main">

<s><emph type="italics"></emph>“ Simplicio.<emph.end type="italics"></emph.end> — Che la palla, ricacciata in su, descriva la medesima SX <lb></lb>(fig. </s>

<s>305) mi par duro. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Sagredo.<emph.end type="italics"></emph.end> — Ma se non vi par duro che, descrivendo la parabola in-<pb xlink:href="020/01/2326.jpg" pagenum="569"></pb>tera YXS, possa ridescrivere la SXY, non vedete che di necessità fa la SX? ” <lb></lb>(MSS. Gal., P. V, T. II, a tergo del fol. </s>

<s>106). </s></p><p type="main">

<s>Poi andò il proposito in dimenticanza, della quale dolendosi Galileo col <lb></lb>Viviani, gli veniva dettando il frammento del Dialogo, da aggiungere dopo <lb></lb>la VII proposizion de&#039;proietti, quando delle Due nuove scienze si fosse per <lb></lb><figure id="id.020.01.2326.1.jpg" xlink:href="020/01/2326/1.jpg"></figure></s></p><p type="caption">

<s>Figura 305<lb></lb>fare una ristampa. </s>

<s>Avremo occasione di tornare so­<lb></lb>pra ciò in discorso in quest&#039;altra parte della nostra <lb></lb>Storia, e per ora vediamo com&#039;esso Viviani, appro­<lb></lb>priandoselo, esplicasse quel pensiero di Galileo: </s></p><p type="main">

<s>“ Nella dottrina de&#039;moti de&#039;proietti, e partico­<lb></lb>larmente alla VII proposizione, a c. </s>

<s>270, si suppone <lb></lb>dal Galileo come indubitato che, venuto il proietto <lb></lb>da alto al basso, con descrivere la semiparabola, cac­<lb></lb>ciato poi per lo contrario da basso ad alto, e&#039;debba <lb></lb>tornare per la medesima linea parabolica, ricalcando precisamente le mede­<lb></lb>sime vestigia. </s>

<s>Ma non avendo per ciò fare il detto proietto altro regolatore <lb></lb>che la direzione della semplice linea retta, toccante la già disegnata semi­<lb></lb>parabola, per la cui declinazione fatta dall&#039;alto al basso l&#039;impeto transver­<lb></lb>sale orizontale ed equabile ci quieta ad ammettere la molta curvazione nella <lb></lb>sommità. </s>

<s>Cercasi d&#039;intendere come l&#039;impulso fatto da basso ad alto, per una <lb></lb>retta tangente, possa restituire un tal impeto trasversale, e che sia atto a re­<lb></lb>golare la medesima curvità nel viaggio di detto proietto. </s>

<s>” </s></p><p type="main">

<s>“ Qui per risposta potrassi dire che, nel nominare la retta tangente, si <lb></lb>lascia una sua condizione, che è l&#039;esser tangente e inclinata, la quale in­<lb></lb>clinazione è bastante a far che il proietto, in tempi eguali, si accosti oriz­<lb></lb>zontalmente per spazi uguali all&#039;asse della parabola. </s>

<s>Inoltre, se la linea de­<lb></lb>scritta da un proietto da basso ad alto, secondo qualche inclinazione, è ve­<lb></lb>ramente una intera linea parabolica, e se niente importa che la proiezione <lb></lb>si faccia da levante verso ponente, o per l&#039;opposito, quando però l&#039;eleva­<lb></lb>zione sia l&#039;istessa, ed istessa la forza proiciente, fatto che si sia il tiro da <lb></lb>qualsivoglia parte; che cosa ha da mettere in dubbio che la semiparabola <lb></lb>da basso ad alto del secondo tiro, che si faccia in contrario del primo, non <lb></lb>sia la medesima che la seconda semiparabola del primo tiro, sicchè il pro­<lb></lb>ietto ritorni per la medesima strada? </s>

<s>Che quando ciò non fosse, manco la <lb></lb>parabola intera del secondo tiro sarebbe uguale a quella del primo ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>16). </s></p><p type="main">

<s>La risposta, che faceva così il Viviani in quella sua <emph type="italics"></emph>Raccolta di espe­<lb></lb>rienze e di pensieri,<emph.end type="italics"></emph.end> che diceva essergli sovvenuti in mente intorno a ma­<lb></lb>terie meccaniche e fisiche, è, come si vede, uno svolgimento del pensiero <lb></lb>medesimo già sovvenuto in mente allo stesso Galileo, a prevenire le cen­<lb></lb>sure fatte poi dal Cartesio intorno a cose puramente speculative. </s>

<s>Ma la spe­<lb></lb>culazione stessa aveva in mano degli oppositori, per via dell&#039;esperienza, un <lb></lb>criterio ben assai più certo, per decidere in proposito del vero e del falso. </s></p><p type="main">

<s>Che si potessero propriamente le galileiane teorie de&#039;proietti illustrare <pb xlink:href="020/01/2327.jpg" pagenum="570"></pb>con l&#039;esperienze, sembra essere stato uno de&#039;primi pensieri sovvenuti agli <lb></lb>Accademici fiorentini, come può congetturarsi dalla seguente Nota, lascia­<lb></lb>taci manoscritta dal Viviani: “ Quod mobile sursum proiectum, per directio­<lb></lb>nem non perpendicularem, in suo descensu numquam per spacium perpen­<lb></lb>diculare moveatur, experiemur si proiectiones fiant sagittis vel virgulis ferro <lb></lb>cuspidatis, quae, dum solum pertingent; ad aequales angulos eum perfora­<lb></lb>bunt, ac omnino pares iis, secundum quos factae sunt proiectiones ” (ibid., <lb></lb>fol. </s>

<s>14). </s></p><p type="main">

<s>La bella esperienza sarà stata forse felicemente eseguita, ma non si trova <lb></lb>fatto di essa, almeno nel libro dei <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> alcuna memoria, perchè dovevasi <lb></lb>lasciar luogo alla descrizione di altre esperienze, credute ben assai più de­<lb></lb>cisive della verità o della falsità delle nuove dottrine galileiane. </s>

<s>Fondamento <lb></lb>a così fatte dottrine apparisce dalla Storia essere stato l&#039;isocronismo delle <lb></lb>curve de&#039;proietti, aventi la medesima altezza, intorno a che i Matematici <lb></lb>sent<gap></gap>rono diversamente. </s>

<s>In Francia tenevasi così per certo spedirsi la ca­<lb></lb>duta perpendicolare e la parabolica nel medesimo tempo, che dalla sensi­<lb></lb>bile differenza osservata si credeva di potere argomentarne quanto fosse l&#039;im­<lb></lb>pedimento dell&#039;aria. </s>

<s>Il Mersenno, nel III tomo delle sue Nuove osservazioni <lb></lb>fisiche matematiche, proponeva a Lodovico principe di Vales di fare espe­<lb></lb>rienze in una fortezza, posta a mare, dalla quale si facesse con vario im­<lb></lb>peto esplodere un cannone, con tiro semiretto. </s>

<s>S&#039;ha dalla teoria, in questo <lb></lb>caso, che il tempo impiegato a descrivere l&#039;intera parabola è doppio di quel <lb></lb>che ci vorrebbe a scender per l&#039;altezza di lei, ossia uguale a quello del <lb></lb>veniente per una linea perpendicolare, quadrupla dell&#039;altezza della parabola, <lb></lb>ond&#039;è che misurando con un pendolo a secondi il tempo speso dalla palla <lb></lb>in passare queste vie diverse, se vi si nota alcuna differenza è da attribuire <lb></lb>all&#039;impedimento dell&#039;aria, che così dunque sapremo quanto egli sia. </s>

<s>“ Porro <lb></lb>Tauroentum eligi potest, a cuius portu nobili iactum semirectum in mari <lb></lb>mediterraneo, ad unum vel alterum milliare situm, dimetientur observato­<lb></lb>res, vel in ipso castello, vel secus illud in statione positi, cum horologiis, <lb></lb>quibus tam verticalis, quam semirecti et horizontalis iactuum durationes <lb></lb>explorent ” (Parisiis 1647, pag. </s>

<s>III). </s></p><p type="main">

<s>Se fossero propriamente fatte, in quella fortezza o altrove, in Francia, <lb></lb>le difficili esperienze, non è certo, com&#039;è certo che furon fatte in Italia, <lb></lb>dove le imbevute dottrine cardaniche avevano dato ai giudizì de&#039;matematici <lb></lb>altra forma. </s>

<s>Vedemmo come il Baliani tenesse esser la scesa per la curva più <lb></lb>diuturna che per il perpendicolo, a cagione dell&#039;impedirsi i due moti com­<lb></lb>ponenti a vicenda, e dall&#039;altra parte troppo aveva seducente apparenza di <lb></lb>vero il dir che pi<gap></gap> tempo bisogna a far la via più lunga, che la più corta. </s>

<s><lb></lb>De&#039;più facilmente sedotti fra costoro fu il Cabeo che, mostrandosi anche <lb></lb>questa volta censore di Galileo assai poco giudizioso, dop&#039;aver riferito le <lb></lb>dottrine di lui circa all&#039;isocronismo tra la scesa retta e la parabolica, sog­<lb></lb>giunge: “ Hoc ego non admitto, donec experimentis credam, quod experi­<lb></lb>mentum hactenus facere non potui. </s>

<s>Fiet autem facile, si in litore supra mare <pb xlink:href="020/01/2328.jpg" pagenum="571"></pb>quietum, aut lacum, constituas bombardam horizontaliter collocatam, et su­<lb></lb>pra bombardam constituas globum, et explodas: dum enim explodis, ex illo <lb></lb>motu decidit globus ” (Metereol. </s>

<s>comm., lib. </s>

<s>I, Romae 1646, pag. </s>

<s>95). </s></p><p type="main">

<s>L&#039;esperienza, che dice il Cabeo di non aver potuta fare, e le contro­<lb></lb>versie insorte fra&#039;Matematici in questo proposito, invogliarono gli Accede­<lb></lb>mici del Cimento, in un Diario manoscritto dei quali leggesi, fra le tante <lb></lb>altre, “ L&#039;esperienza CCLXXXVIII per molti, che dicevano per i loro scritti, <lb></lb><figure id="id.020.01.2328.1.jpg" xlink:href="020/01/2328/1.jpg"></figure></s></p><p type="caption">

<s>Figura 306<lb></lb>ed altri affermavano che, dato un tiro di una ar­<lb></lb>tiglieria sopra una elevazione es. </s>

<s>gr. </s>

<s>A (fig. </s>

<s>306), <lb></lb>ove fosse la bocca del pezzo, con una palla di egual <lb></lb>peso di quella che dentro al pezzo era stata messa, <lb></lb>e quella alla bocca di detto era attaccata con un <lb></lb>filo, calando per l&#039;appunto sotto l&#039;orlo del pezzo; <lb></lb>che, mentre usciva la palla di dentro, faceva ca­<lb></lb>dere ad un tratto quella di fuori: ed affermavano <lb></lb>che sarebbe caduta la palla, che usciva portata dal <lb></lb>fuoco nel punto B, nell&#039;istesso tempo che l&#039;altra, <lb></lb>a perpendicolo cadendo, arrivava nel punto C, piano <lb></lb>stesso di BD, e ciò fu provato a Livorno, facendosi <lb></lb>tirare il pezzo dalla torre della fortezza verso il <lb></lb>mare, con un cannone da quattordici. </s>

<s>” </s></p><p type="main">

<s>“ Parve a molti che cadessero tutte ad un tempo, ma, con uno da venti, <lb></lb>fu osservato prima dare nel piano quella, che cadeva a perpendicolo, che <lb></lb>l&#039;altra che cadeva nella distanza, e tanto tempo dette che, vistola cadere <lb></lb>in C, dette tempo di rivoltare il viso a vedere cadere l&#039;altra in B. ” </s></p><p type="main">

<s>“ Ci fu chi appellò, benchè si riprovasse più volte, che poteva venire <lb></lb>dalla più quantità del solito della polvere, e non di tanta squisitezza; ma <lb></lb>con più meglio (sic) ragione, dicevano ancora che ci era differenza quanto <lb></lb>dalla bocca del pezzo alla fine per di sotto dell&#039;orlo, e perciò cadeva più <lb></lb>presto: di più, che la Torre, non bagnando con il piede per l&#039;appunto nel <lb></lb>mare, ma ci poteva esser differenza di più alto da un braccio; che l&#039;una e <lb></lb>l&#039;altra differenza poteva far che prima quella a perpendicolo nel piano BD <lb></lb>arrivasse, perchè la vera ragione voleva tutt&#039;e due in uno stesso tempo ca­<lb></lb>dessero. </s>

<s>Ma si tennero tutti supposti, per trovare appello ancora a quel che <lb></lb>sensibilmente s&#039;era visto. </s>

<s>Nulladimeno si lasciò la proposizione in pendente, <lb></lb>senza deciderla ” (MSS. Cim., T. III, fol. </s>

<s>66). </s></p><p type="main">

<s>La dicitura, tanto lontana dall&#039;eleganza dei <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> è del Rinaldini, che <lb></lb>faceva allora l&#039;ufficio di segretario dell&#039;Accademia, prima del Magalotti, il <lb></lb>qual Rinaldini tornò, per decidere la questione, a ripetere, nel Genna io <lb></lb>del 1658, da quella medesima fortezza di Livorno, l&#039;esperienze rimaste così <lb></lb>incerte. </s>

<s>“ Inoltre, scriveva il dì primo di Febbraio al Viviani, ho fatto l&#039;espe­<lb></lb>rienza del tiro del pezzo, osservando se la palla, nel medesimo tempo, cade <lb></lb>perpendicolarmente dalla bocca, e la spinta dalla polvere arriva al mede­<lb></lb>simo piano, e dopo molte riprove abbiamo ritrovato che ambe le palle ca-<pb xlink:href="020/01/2329.jpg" pagenum="572"></pb>dono in un tempo stesso, onde in un medesimo tempo l&#039;una e l&#039;altra giunge <lb></lb>al piano dell&#039;orizonte, del che ne ho avuto sommo gusto ” (ivi, T. XXXVII, <lb></lb>fol. </s>

<s>39). </s></p><p type="main">

<s>Tre giorni dopo, nell&#039;occasione di dar conto allo stesso Viviani di altre <lb></lb>esperienze, il Rinaldini gli ripeteva: “ Di già le ho dato avviso dell&#039;espe­<lb></lb>rienza fatta a Livorno del pezzo, come nel medesimo tempo è caduta la palla <lb></lb>dalla bocca, e giunta all&#039;orizonte, che quella spinta dalla polvere, e sebbene, <lb></lb>in un pezzo più grosso, pare abbi fatto qualche poco di differenza, nulladi­<lb></lb>meno credo assolutamente che ciò sia proceduto dal non essere ben livel­<lb></lb>lato il pezzo, sicchè si puol concludere che cadono nel tempo medesimo ” <lb></lb>(ivi, fol. </s>

<s>41). </s></p><p type="main">

<s>La conclusione del Rinaldini era senza dubbio fallace, e meglio si con­<lb></lb>formavano col vero le prime esperienze sopra descritte, perchè, se l&#039;aria, <lb></lb>nel viaggio più lungo, anche impedisce più a proporzione la velocità del <lb></lb>moto; era impossibile vedere esattamente i fatti corrispondere con le teorie, <lb></lb>che astraggono da ogni sorta d&#039;impedimenti. </s>

<s>Ma quegli sperimentatori non <lb></lb>sembra che pensassero punto a queste cose, e le ragioni che, come udimmo, <lb></lb>dissero pro e contro nelle loro dispute, non rivelano degli Accademici del <lb></lb>Cimento il consueto senno ed acume, la misura del quale è data partico­<lb></lb>larmente in questo fatto dalla mente propria del Rinaldini. </s>

<s>Ora, sanno bene <lb></lb>i nostri Lettori chi fosse quell&#039;uomo, il quale vestiva la stola dell&#039;Accade­<lb></lb>mia sopra la toga peripatetica. </s>

<s>Con quale intelligenza poi egli dirigesse le <lb></lb>delicate esperienze si può argomentare dal fatto, ch&#039;ei non s&#039;era ancora <lb></lb>studiato d&#039;intenderne il fine. </s>

<s>Aveva sentito dire essere questo fine quello <lb></lb>di verificare un&#039;opinione di Galileo, ma come e dove fosse una tale opinione <lb></lb>esposta ei non sapeva, per cui, quasi un mese dopo aver fatta l&#039;esperienza <lb></lb>a Livorno, si rivolgeva al Viviani, pregandolo a volerlo avvisare “ dove il <lb></lb>Galileo tratta precisamente del tiro del pezzo, e della palla cadente dalla <lb></lb>bocca. </s>

<s>V. S. ne puol domandare al signor Cosimo (Galilei), il quale mi pro­<lb></lb>mise di avvisarmelo ” (ivi, fol. </s>

<s>43). </s></p><p type="main">

<s>Una tale ignoranza in un Accademico del Cimento non era scusabile, <lb></lb>essendo il luogo ch&#039;ei cercava assai cospicuo nel secondo dialogo dei Mas­<lb></lb>simi Sistemi, dove, a pag. </s>

<s>148, 49 dell&#039;edizione originale, avrebbe potuto <lb></lb>leggere: “ e quando non ci fusse l&#039;impedimento accidentario dell&#039;aria, io <lb></lb>tengo per fermo che se, nell&#039;uscir la palla dal pezzo si lasciasse cadere un&#039;al­<lb></lb>tra dalla medesima altezza giù a piombo, amendue arriverebbero in terra <lb></lb>nel medesimo istante. </s>

<s>” </s></p><p type="main">

<s>Nè sembra che gli altri disputanti col Rinaldini, sotto la fortezza di Li­<lb></lb>vorno, fossero punto più pratici delle materie scritte nel Dialogo famoso, <lb></lb>ciò che prova esservi anc&#039;allora ammiratori fanatici del grand&#039;Uomo, senza <lb></lb>averne mai meditati i libri. </s>

<s>Perchè, se avessero nel citato luogo letto ed in­<lb></lb>teso che si verificherebbe nella caduta delle due palle l&#039;isocronismo, <emph type="italics"></emph>quando <lb></lb>non vi fosse l&#039;impedimento dell&#039;aria,<emph.end type="italics"></emph.end> quella prima esperienza, che mo­<lb></lb>strava come, vista l&#039;una delle dette palle cadere nel perpendicolo, dette <pb xlink:href="020/01/2330.jpg" pagenum="573"></pb>tempo di rivoltare il viso a veder l&#039;altra, che veniva per la parabola, do­<lb></lb>vevasi ritener senz&#039;altro per decisiva. </s></p><p type="main">

<s>Lasciata invece la proposizione in dipendenza, e risoluta poi dal Rinal­<lb></lb>dini in quel modo che s&#039;è veduto; al venire il Viviani a farne, per comando <lb></lb>del principe Leopoldo, esame più diligente, non potè non riconoscerne la <lb></lb>leggerezza. </s>

<s>E dall&#039;altra parte troppo importava sapere e descrivere il fine <lb></lb>della cosa, per l&#039;amore del vero, per l&#039;onore di Galileo e della nobile Ac­<lb></lb>cademia. </s>

<s>Di qui è che il Viviani stesso pensò di andare in persona a diri­<lb></lb>gere l&#039;esperienze a Livorno, le quali si rendevano molto più precise di <lb></lb>quelle dirette dal Rinaldini, col misurare il tempo spesso nel cader della <lb></lb>palla, ora naturalmente dal medesimo punto, ora per la spinta violenta del <lb></lb>cannone. </s>

<s>Il delicato misuratore era il pendolo, con la palla di oro di otto <lb></lb>millimetri e mezzo di raggio, sospesa a un filo di seta, lungo 52 millime­<lb></lb>tri; cosicchè, con pendolo semplice di lunghezza uguale a 0m.0605, si cre­<lb></lb>deva aver le vibrazioni composte, esattamente corrispondenti ai mezzi se­<lb></lb>condi. </s>

<s>L&#039;importante notizia leggesi in una Nota autografa del Viviani, in <lb></lb>margine alla quale è segnata la figura del pendolo, da cui si son ricavate <lb></lb>le riferite misure; Nota, che il Magalotti compendiò nel descriver la prima <lb></lb>delle <emph type="italics"></emph>Esperienze intorno ai proietti,<emph.end type="italics"></emph.end> quali si leggono nel libro dei <emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end><lb></lb>ma che noi vogliamo trascrivere qui ai lettori, nella loro integrità originale: </s></p><p type="main">

<s><emph type="italics"></emph>“ A&#039;di 2 Aprile 1662 in Livorno.<emph.end type="italics"></emph.end> Sulla torre della Fortezza vecchia, <lb></lb>di braccia 50 di altezza, con falconetto da 7 1/3 di palla, lungo bocche 13 1/2, <lb></lb>con tiri di punto in bianco, le palle fasciate arrivarono all&#039;acqua in vibra­<lb></lb>zioni 4 1/2, con libbre quattro di polvere fina. </s>

<s>Con la colubrinetta da 14, <lb></lb>con libbre dieci di polvere, la palla fasciata arrivò in cinque vibrazioni: non <lb></lb>fasciata, in cinque e mezzo, poco più, e tanto più lontano. </s>

<s>La caduta delle <lb></lb>due palle perpendicolarmente fu in vibrazioni quattro, e le vibrazioni erano <lb></lb>intere di andata e tornata, con lunghezza di filo, qual&#039;è segnata in mar­<lb></lb>gine, con la palla di oro, delle quali vibrazioni ne va 120 a minuto primo, <lb></lb>che sono mezzi minuti secondi ” (MSS. Gal. </s>

<s>Disc., T. CXXXIX, fol. </s>

<s>24). </s></p><p type="main">

<s>Così il Viviani, come il Segretario dell&#039;Accademia fiorentina, si stettero <lb></lb>contenti alla semplice descrizione del fatto, da cui resultava non trovarsi in <lb></lb>piena conformità insieme la teoria e la pratica. </s>

<s>È da credere che attribuis­<lb></lb>sero la causa di ciò agl&#039;impedimenti dell&#039;aria, ma i calcoli delle Tavole bal­<lb></lb>listiche, riscontrati ne&#039;militari esercizi, avevano fatto troppo ben conoscere <lb></lb>dover essere assai più complicate le cause, per le quali si vedono l&#039;espe­<lb></lb>rienze aberrare così dai teoremi. </s>

<s>Si volle prendere motivo di qui a infir­<lb></lb>mare la virtù di così fatti teoremi, a che Galileo stesso pensava di rispon­<lb></lb>dere, dettando a Marco Ambrogetti un frammento di Dialogo, da inserirsi <lb></lb>nella ristampa delle <emph type="italics"></emph>Due nuove Scienze.<emph.end type="italics"></emph.end> E perchè avremo altrove occasione di <lb></lb>richiamar quei frammento, per confermare certe indagini storiche, importan­<lb></lb>tissime alla storia della letteratura galileiana, lo trascriveremo allora, per pas­<lb></lb>sare a far qui in ultimo un cenno di alcuni fatti, i quali si credeva che contra­<lb></lb>dicessero, non a sole le dimostrate teorie, ma alle più ovvie ragioni naturali. </s></p><pb xlink:href="020/01/2331.jpg" pagenum="574"></pb><p type="main">

<s>Quando le Tavole ballistiche del Torricelli erano venute a dar tanta <lb></lb>importanza ai calcoli di Galileo, che in quasi tutte le fortezze d&#039;Italia si <lb></lb>facevano dai militari esperienze, con quelle Tavole in mano, limitandosi per <lb></lb>lo più a riscontrare le ampiezze calcolate, con quelle date dal tiro; ai Fio­<lb></lb>rentini, più degli altri operosi, venne in mente di osservare di più come si <lb></lb>corrispondessero gl&#039;impeti, creduti da loro proporzionali al numero dei gra­<lb></lb>nelli tutti uguali della medesima polvere, con la quale si caricava il can­<lb></lb>none. </s>

<s>Dicevano che se, per esempio, con quattro grani di polvere si pas­<lb></lb>savano sei braccia, con cinque grani se ne dovrebbero passare sette e mezzo, <lb></lb>avendo, a tal numero, sei quella proporzione, che cinque ha a quattro. </s>

<s>Tro­<lb></lb>vavano invece, venendo ai fatti, esser non sette braccia e mezzo, ma qual­<lb></lb>che cosa di più di diciannove quella passata. </s></p><p type="main">

<s>Parve il caso aver qualche cosa di straordinario, e di tanto curioso, da <lb></lb>richiamar l&#039;attenzione del granduca Ferdinando, il quale si compiaceva di <lb></lb>sodisfare a quella sua curiosità, interrogando coloro, che avevano promosse <lb></lb>ed eseguite più volte, e in più modi, le nuove esperienze. </s>

<s>Alcuni de&#039;più <lb></lb>leggeri risposero lì per lì cose spropositate: altri di più senno vollero tempo <lb></lb>a pensarvi, e intanto esponevano in scritto i loro pensieri. </s>

<s>Il Granduca però <lb></lb>non sperava, e non confidava di avere da que&#039;signori la vera soluzion del <lb></lb>problema, ma volle metterli alla prova, per veder quel che sapessero dire <lb></lb>appetto al suo gran matematico Vincenzio Viviani, a cui fece proporre il <lb></lb>quesito, coll&#039;ordine di darne la risposta. </s>

<s>Non credeva il Viviani che la cosa <lb></lb>avesse levato tanto romore in palazzo, nè che tanti vi s&#039;affaccendassero in­<lb></lb>torno a stillarvi il cervello, per cui prese la penna, e scrisse così al Segre­<lb></lb>tario del Granduca, sicuro che avrebbe in qualunque modo sodisfatto al <lb></lb>comando, il principal merito del quale sapeva che facevasi per lo più con­<lb></lb>sistere nell&#039;esser pronto: </s></p><p type="main">

<s>“ Il problema, che V. S. mi propone di comandamento del Padron <lb></lb>Serenissimo, è veramente curiosissimo, e a prima faccia tiene in sè dello <lb></lb>stravagante, poichè l&#039;evento si dimostra molto diverso da quello, che si pro­<lb></lb>metterebbe il comun giudizio, pochi essendo quelli, che non credessero che, <lb></lb>mantenuta la medesima elevazione di canna, gli spazi passati orizzontali, che <lb></lb>vengono scorsi con moto equabile, non avessero a mantenere tra di loro la <lb></lb>medesima proporzione delle velocità o delle forze impellenti, in tal maniera <lb></lb>che, se con quattro grani di polvere o con quattro gradi di forza, si passano <lb></lb>braccia sei, con cinque grani o cinque gradi di forza si avessero a passare <lb></lb>solamente braccia sette e mezzo, e non braccia 19, come mi avvisa V. S.; <lb></lb>che tal proporzione ha quattro a cinque, che sei a sette e mezzo: ovvero <lb></lb>dovrebbero dare le lunghezze 6 e 19, che son quelle che V. S. mi dice <lb></lb>esser passate da quattro e da cinque grani di polvere. </s>

<s>E supposto che la <lb></lb>prima sia scorsa dalla palla, cacciata con quattro gradi d&#039;impeto, bisogne­<lb></lb>rebbe che la seconda fosse stata scacciata da gradi dodici e due terzi, poi­<lb></lb>chè tal proporzione ha 6 a 19, che 4 a 12 2/3. ” </s></p><p type="main">

<s>“ Ma se, con la scorta della Geometria e con la dottrina de&#039;moti del <pb xlink:href="020/01/2332.jpg" pagenum="575"></pb>Galileo, c&#039;interneremo oltre alla scorza di questo effetto, vedrassì che, nel <lb></lb>caso di che si tratta, non può mai conservarsi tal proporzione, e che que­<lb></lb>sta, rimossi gl&#039;impedimenti, s&#039;osserva solo dalla Natura in quei moti equa­<lb></lb>bili, che son fatti dentro un medesimo tempo. </s>

<s>Ma perchè qui i moti son <lb></lb>fatti sotto tempi disuguali, è necessario tenerne conto, e ricorrere ad esa­<lb></lb>mine più accurata, per la quale si troverà mitigata alquanto la stravaganza, <lb></lb>poichè si avrà che la seconda proiezione dovrebb&#039;esser, non braccia sette <lb></lb>e mezzo, ma bensì braccia 9 3/8, che tanto si deduce dalla Scienza de&#039;pro­<lb></lb>ietti, dalla quale ancora si ha che, stanti ferme le date lunghezze di brac­<lb></lb>oia 6 e 19, supposto che la prima di sei sia fatta da un impeto di quattro <lb></lb>grani di polvere, o di gradi quattro di forza; la seconda di braccia 19 do­<lb></lb>vrebbe essere scorsa da un impeto di grani 7 1/8 di polvere, e non di grani <lb></lb>cinque, come segue infatto, nemmeno di grani 12 2/3, come vedemmo di <lb></lb>sopra che dava la regola, fatta senz&#039;altro esame. </s>

<s>” </s></p><p type="main">

<s>“ Ma giacchè l&#039;esperienza così dimostra, e le misure delle braccia 6 <lb></lb>e 19 son reali, nè vi può essere equivoco, mentre sì ammettano per veri <lb></lb>i principii supposti dal Galileo nelle dottrine dei moti, applicati ai nostri <lb></lb>gravi, considerati però esenti e liberi da ogni accidentario impedimento; <lb></lb>converrà dire che l&#039;equivoco sia nella considerazione degl&#039;impeti, e che que­<lb></lb>sti della polvere particolarmente non mantenghino la medesima proporzione <lb></lb>delle moli e de&#039;pesi di essa polvere: cioè che, se quattro grani operano e <lb></lb>spingono, per esempio, con forza di quattro gradi; cinque grani poi non <lb></lb>spinghino con forza di cinque gradi, ma operino per più, com&#039;è di 7 1/8. <lb></lb>Qual poi sia la cagione di tal, per così dire, sproporzione di forza sopra la <lb></lb>comune stimativa, io veramente, per esimermi dal pericolo di censure in <lb></lb>addurla, dovrei dire col Galileo che questa ancora è una delle cose che io <lb></lb>non so.... ” (MSS. Gal. </s>

<s>Disc., T. CXLII, fol. </s>

<s>95). </s></p><p type="main">

<s>Mancando a questo punto del citato codice i fogli, sopra i quali si pro­<lb></lb>seguiva, nella presente e in una lettera successiva, a dir, della cosa che si <lb></lb>confessava ignorare, qualche probabile opinione; non sappiamo perciò quale <lb></lb>ella fosse, ma in ogni modo siam certi che il Granduca aspettò a leggerla <lb></lb>perchè voleva sentir prima quel che ne saprebbero dire gli altri interrogati. </s>

<s><lb></lb>Dette il Segretario avviso di questa intenzione al Viviani, il quale intese <lb></lb>anche insieme che il Granduca ci premeva molto, e che molti ci stavano as­<lb></lb>sottigliando l&#039;ingegno. </s>

<s>Allora si pentì di aver fatto sull&#039;argomento poco accu­<lb></lb>rata riflessione, e conobbe che le cose scritte nelle due lettere potevano, a <lb></lb>rigor di scienza, andar soggette a censure. </s>

<s>Secondo quella scienza infatti <lb></lb>non si poteva ragionevolmente decider nulla intorno alla quantità della vo­<lb></lb>lata, a proporzion della carica, senza sapere il grado della elevazion del can­<lb></lb>none. </s>

<s>Aveva imprudentemente sentenziato il Viviani, non curante di que­<lb></lb>ste notizie, che non può mai, nel proposto caso, conservarsi tra gl&#039;impeti e <lb></lb>le ampiezze delle parabole una tal proporzione, la quale anzi osservasi nel <lb></lb>tiro semiretto, essendo allora gl&#039;impeti, uguali al doppio delle altezze delle <lb></lb>semiparabole, proporzionali alle semibasi. </s>

<s>Nelle altre elevazioni, superiori o <pb xlink:href="020/01/2333.jpg" pagenum="576"></pb>inferiori alla semiretta, essendo gl&#039;impeti uguali alla somma della sublimità <lb></lb>con l&#039;altezza, s&#039;intende perciò come non si possano puntualmente determi­<lb></lb>nare, senza conoscer prima il preciso grado della detta elevazione. </s></p><p type="main">

<s>Riconosciutosi ciò dal Viviani, e saputo che le sue lettere non erano <lb></lb>state ancora aperte dal Granduca, pregava il Segretario, s&#039;era permesso, a <lb></lb>volergliele rimandar per correggerle, e a dirgli insieme a qual preciso punto <lb></lb>della squadra corrispondeva nelle varie esperienze la direzione del tiro: pre­<lb></lb>gavalo inoltre a volergli dare altre più particolari notizie, come qui si leg­<lb></lb>gon richieste, in una lettera del dì 27 Febbraio 1664, che da noi si tra­<lb></lb>scrive: </s></p><p type="main">

<s>“ Intendo in che grado è il negozio, e giacchè si vede che S. A. ci <lb></lb>preme, e che altri soggetti maggiori infinitamente di me ci stanno specu­<lb></lb>lando, per scrivere, sarebbe pur bene che io ci facessi ancora io più accu­<lb></lb>rata riflessione, oltre a quella fattavi subito improvvisamente, per mostrar <lb></lb>la prontezza nell&#039;obbedire: e se V. S. mi avesse fatto onore di avvisarmi <lb></lb>prima che S. A. non ha voluto sentire le lettere, col fine di aspettare quel <lb></lb>che altri dica sopra di ciò, io l&#039;avrei pregata a rimandarmele, per aggiu­<lb></lb>starle meno male di quel che stanno. </s>

<s>Pure, io la prego adesso, se ella pensa <lb></lb>che io sia a tempo, a volermi prontamente rimandare indietro tutt&#039;e due <lb></lb>le mie lettere, che parlano di ciò, perchè gli prometto di rimandargliele su­<lb></lb>bito subito, per la prima occasione. </s>

<s>” </s></p><p type="main">

<s>“ Di grazia, non manchi di favorirmi, siccome di dirmi insieme a che <lb></lb>elevazione si trovasse il pezzetto, quando si fecero quelle prove del caso <lb></lb>propostomi di grani quattro di polvere, a braccia sei di distanza, e poi di <lb></lb>grani cinque, a braccia diciannove in venti: cioè, se a mezzo angolo retto, <lb></lb>oppur sopra, oppur sotto il detto angolo. </s>

<s>” </s></p><p type="main">

<s>“ Inoltre, quando la palla è dentro, vorrei sapere quanto resta lontana <lb></lb>dalla bocca del pezzo, e quanto è lunga la camera, che ciò facilmente V. S. <lb></lb>lo può vedere da sè, senza metterla in negozio con nessuno, bastando toc­<lb></lb>car da sè il pezzetto, e con un fuscello misurare quanto è dalla bocca al <lb></lb>fondo della camera, e poi metter la palla, e misurar sul medesimo quanto <lb></lb>è dalla bocca alla palla, e sul medesimo fuscello metter la misura del dia­<lb></lb>metro della medesima palla, e questa misura poi trasportarla sopra un fo­<lb></lb>glio, insieme con la lunghezza della detta camera, perchè quella della canna <lb></lb>la caverò da me dalla palla. </s>

<s>” </s></p><p type="main">

<s>“ Vorrei sapere ancora la storia degli altri tiri, oltre a que&#039;soli due, <lb></lb>che V. S. mi ha scritto, cioè la lunghezza de&#039;tiri fatti con uno, con due, <lb></lb>con tre grani, e poi con sei, con sette, e con quanti se n&#039;è fati e potuti <lb></lb>fare. </s>

<s>Insomma vorrei più di due tiri, oltre a que&#039;fatti con quattro grani, e <lb></lb>con cinque di polvere. </s>

<s>Di più, se è possibile, vorrei sapere se pel focone <lb></lb>svapora gran fiamma, e se ci hanno rimediato che non ne esca, con met­<lb></lb>tere uno stoppino nel focone o in altro modo, e se di questo accidente di <lb></lb>svaporare se ne fa caso; se il pezzetto era fisso, che non potesse rinculare <lb></lb>nè alzarsi di bocca. </s>

<s>Finalmente, più notizie che lei mi darà sopra questo, più <pb xlink:href="020/01/2334.jpg" pagenum="577"></pb>l&#039;avrò caro, acciocchè io me ne possa valere, nel raggiustare le lettere, che lei <lb></lb>mi rimanderà, le quali subito le accomoderò in miglior forma ” (ivi, fol. </s>

<s>97, 98). </s></p><p type="main">

<s>Il fine del ricercar notizie intorno alla elevazione del pezzo è manife­<lb></lb>sto, per le cose già dette, ma perchè i teoremi galileiani, dietro quelle stesse <lb></lb>notizie applicati si vedevan pure in ogni modo così aberrare dai fatti; non <lb></lb>rimaneva altro di certo al Viviani, in mezzo a questi dubbi, che la conclu­<lb></lb>sione scritta nella prima lettera al Segretario del Granduca, che cioè gl&#039;im­<lb></lb>peti della polvere non mantengono la proporzione delle moli e dei pesi. </s>

<s>La <lb></lb>desiderata soluzion del problema perciò usciva fuori del campo della Mate­<lb></lb>matica astratta, per entrare in quello della Fisica, all&#039;esperienze della quale <lb></lb>era necessario ricorrere, per saper quanto, sopra la proporzion della mole <lb></lb>e del peso, cresca, nella polvere accesa, la violenza dell&#039;impeto. </s>

<s>A ciò ten­<lb></lb>devano le domande fatte dal Viviani intorno alla capacità della camera, allo <lb></lb>sfiatar del focone, e al rinculare del pezzo, ma pure erano troppo pochi tutti <lb></lb>questi dati a determinar le incognite del complicato problema. </s></p><p type="main">

<s>La difficoltà del conseguire l&#039;intento non ne spense però nel Viviani, <lb></lb>nemmeno per lunghezza di tempo, il desiderio. </s>

<s>Vent&#039;anni dopo passava per <lb></lb>Firenze, sul finir della primavera, il generale Luigi Ferdinando Marsili, che <lb></lb>volle visitare il celebre Matematico, in cui vedevasi continuare la vita stessa <lb></lb>di Galileo. </s>

<s>I colloqui fra due uomini di quell&#039;indole, e di quella professione, <lb></lb>era naturale che cadessero sopra le Matematiche applicate all&#039;arte militare, <lb></lb>con la quale occasione raccontava il Viviani l&#039;esperienze fatte e gli studii, <lb></lb>per rispondere ai quesiti, che gli erano stati proposti infin da&#039;tempi del <lb></lb>granduca Ferdinando. </s>

<s>Rispose allora il Marsili che l&#039;arte da lui esercitata, <lb></lb>e l&#039;amor alla scienza, lo avevano invogliato di simili studii sperimentali, dei <lb></lb>quali, tornato a Bol<gap></gap>gna, riferiva allo stesso Viviani un saggio in questa <lb></lb>lettera, scritta il di 18 Giugno 1684: </s></p><p type="main">

<s>“ È obbligo di chiunque esercita un&#039;arte l&#039;intendere non solo gli ef­<lb></lb>fetti, ma anco i mezzi, con i quali la medesima s&#039;esercita, e perciò, com&#039;è <lb></lb>noto a V. S. Ill.ma, ho intrapreso d&#039;impiegarmi in quella delle armi, che <lb></lb>ne&#039;tempi d&#039;oggi si rendono strepitose per l&#039;industria animata della forza <lb></lb>della polvere, che esaminandola in più occasioni non ho volsuto tralasciare <lb></lb>di avvertire la di lei forza, con più esperimenti, che, col benefizio dell&#039;ozio <lb></lb>in una pace o in un quartiere d&#039;inverno, non mancherò più fondatamente <lb></lb>digerire, affine di potere tutto in una esatta serie dimostrare a V. S. Ill.ma, <lb></lb>secondo gli ho promesso nel mio passaggio per Firenze, non solo per con­<lb></lb>trassegno di rispetto alla di lei persona, ma anche per poterne ricavare van­<lb></lb>taggio da quei riflessi saranno fatti dalla di lei virtù. </s>

<s>” </s></p><p type="main">

<s>“ Cominciando in ora a dimostrargliene uno circa l&#039;accension della me­<lb></lb>desima, che a me pare possi essere fondamento non solo di conoscere la <lb></lb>forza della stessa, ma anche di bene appropriarla a benefizio della mia arte, <lb></lb>dico che, per conoscere adunque verso qual parte faccia maggior impeto la <lb></lb>polvere di schioppo, nell&#039;accendersi ch&#039;ella fa, ho praticata la seguente <lb></lb>esperienza: ” </s></p><pb xlink:href="020/01/2335.jpg" pagenum="578"></pb><p type="main">

<s>“ Descritto un circoletto piccolo sopra un cartone assai grande, situato <lb></lb>parallelo all&#039;orizzonte, dentro di esso disposi egualmente una certa quan­<lb></lb>tità di polvere, talchè da essa veniva ad essere riempita tutta la area del <lb></lb>detto circolo. </s>

<s>Di poi li posi nella circonferenza, distanti l&#039;una dall&#039;altra no­<lb></lb>vanta gradi, quattro palline di sughero di ugual grossezza, e consequente­<lb></lb>mente di ugual peso, e bene rotonde. </s>

<s>Accesa la polvere in una parte della <lb></lb>circonferenza del circolo, vicino alla pallina A (fig. </s>

<s>307) furono levate dal <lb></lb>suo sito dall&#039;impeto della polvere tutt&#039;e quattro le palline, ma disugual­<lb></lb><figure id="id.020.01.2335.1.jpg" xlink:href="020/01/2335/1.jpg"></figure></s></p><p type="caption">

<s>Figura 307<lb></lb>mente, in maniera che la pallina A, ch&#039;era vi­<lb></lb>cina al luogo dell&#039;accensione, fu spinta all&#039;in­<lb></lb>dietro per tanto spazio, quanto importavano <lb></lb>quattro diametri della stessa pallina, ma la op­<lb></lb>posta B fu cacciata all&#039;innanzi 36 delli stessi <lb></lb>diametri, ma le laterali D, C furono spinte la­<lb></lb>teralmente 12 diametri, in maniera che, se i <lb></lb>spazi percorsi e gl&#039;impeti fossero proporzio­<lb></lb>nali, pare si potesse concludere da questa espe­<lb></lb>rienza che l&#039;impeto della polvere fosse nove <lb></lb>volte maggiore verso la parte opposta al luogo <lb></lb>dell&#039;accensione, e che l&#039;impeto laterale fosse <lb></lb>tre volte maggiore che nel luogo dell&#039;accensione, e parimente tre volte mi­<lb></lb>nore di quello sia nella parte opposta al luogo dell&#039;accensione, supponendo <lb></lb>però che l&#039;esperienza, fatta più volte con quantità maggiore o minore di <lb></lb>polvere, e in altra figura, resti sempre la medesima. </s>

<s>” </s></p><p type="main">

<s>“ Disposta la polvere nell&#039;istesso circolo, nel modo predetto, e datogli <lb></lb>il fuoco nel centro, fece egual impeto per ogni verso, spingendo tutt&#039;e quat­<lb></lb>tro le palline per eguali spazi. </s>

<s>Senza le palline si può, ma non così esat­<lb></lb>tamente, conoscere l&#039;impulso dalle strisce, che lasciano segnate di nero i <lb></lb>grani della polvere nel cartone, le quali sempre sono maggiori dalla parte <lb></lb>opposta al luogo dell&#039;accensione, in maniera che, dall&#039;una e dall&#039;altra espe­<lb></lb>rienza, si viene a concludere lo stesso. </s>

<s>” </s></p><p type="main">

<s>“ Attenderò con somma impazienza le di lei erudite e fondate consi­<lb></lb>derazioni, per poter procedere nell&#039;incominciato studio della polvere, raffer­<lb></lb>mandomi al solito Aff.mo Obbligmo <emph type="italics"></emph>Luigi Ferdinando Marsili. </s>

<s>”<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s><lb></lb>Disc., T. CXLVI, fol. </s>

<s>268). </s></p><p type="main">

<s>I documenti, ricercati con diligenza ne&#039;commerci letterari de&#039;due va­<lb></lb>lorosi uomini, rivelerebbero forse in tale argomento conclusioni ben assai <lb></lb>più curiose e più importanti, che noi però dobbiam lasciare allo studio di <lb></lb>chi scriverà la <emph type="italics"></emph>Storia delle artiglierie in Italia.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2336.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO X.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Conclusione di questa prima Parte<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. De&#039;principali cultori della Meccanica contemporanei di Galileo. </s>

<s>— II. De&#039;Dialoghi de&#039;due Massimi <lb></lb>Sistemi, e come s&#039;incominciassero a diffondere di li i semi della nuova Scienza del moto. </s>

<s>— <lb></lb>III. </s>

<s>Del primo dialogo delle due Nuove Scienze, e della pubblicazione di lui, insieme con gli <lb></lb>altri tre, fatta dagli Elzeviri in Olanda. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dop&#039;essersi fin qui la nostra Storia aggirata per le volte e rivolte del <lb></lb>filo di tante sottili speculazioni, intorno ai principali argomenti della Scienza <lb></lb>del moto, riusciti com&#039;a termine fisso all&#039;anno 1638, in cui per i Dialoghi <lb></lb>galileiani ebbe quella stessa Scienza il suo nuovo istituto; giova trattenere <lb></lb>alquanto il passo, come fa il pellegrino che, riposando per pigliar lena a <lb></lb>proseguire, volge a piè del grand&#039;albero, sotto cui siede, tutt&#039;intorno desi­<lb></lb>deroso lo sguardo. </s>

<s>S&#039;è per molti immaginato e descritto il termine, a cui <lb></lb>siamo giunti, come un campo arido e desolato, in mezzo a cui solo l&#039;al­<lb></lb>bero che s&#039;è detto grandeggia, e rallegra il viandante col verde e coll&#039;om­<lb></lb>bra. </s>

<s>Che sia questo però un immaginar falso, e un falso descriver le cose <lb></lb>lo persuade con facilità l&#039;osservazion naturale, che mai non è quercia soli­<lb></lb>taria in selva, ma la circondano umili virgulti e più elevati arboscelli, o <lb></lb>nati di straniero seme, o dalle stesse ghiande cadute dalla chioma di lei. </s>

<s><lb></lb>Dall&#039;altra parte lo straordinario rigoglio della madre pianta attesta la ben <lb></lb>disposta qualità del terreno, e il benigno volgere della stagion, che favori­<lb></lb>scono, con general provvidenza, il germogliare e il crescere degli altri semi. </s>

<s><lb></lb>E perchè sempre nel mondo fisico vedonsi il morale e l&#039;intellettuale sim­<lb></lb>boleggiati, sorgono intorno al grande Galileo altri minori, nel campo della <lb></lb>Scienza meccanica largamente dispersi, dovunque intelligenze umane aprano <pb xlink:href="020/01/2337.jpg" pagenum="580"></pb>a ricever lo spirito fecondatore del vero. </s>

<s>Giunge l&#039;aura divina attraverso a <lb></lb>mari in Olanda a Simeone Stevino; attraverso a monti, in Germania, a Paolo <lb></lb>Guldino e a Giovan Marco Marci, mentre fra noi Guidubaldo del Monte, <lb></lb>Girolamo Fabricio d&#039;Acquapendente e Giovan Batista Baliani sembra che ne <lb></lb>risentan gl&#039;influssi più prossimi e più efficaci. </s></p><p type="main">

<s>Tutti coloro i quali, contro il senso comune, contro la legge naturale <lb></lb>e contro i fatti, si ostinano in voler riconoscere Galileo nella Scienza mec­<lb></lb>canica primo e unico Maestro al mondo, s&#039;immaginano che da lui abbiano, <lb></lb>in qualunque modo, i commemorati Autori contemporanei imparato tutto <lb></lb>quel che nei loro libri hanno scritto delle ragioni del moto. </s>

<s>L&#039;assunto per <lb></lb>verità è di difficile dimostrazione, la quale anzi si direbbe impossibile, spe­<lb></lb>cialmente riguardo allo Stevino, in cui riconoscemmo già il sapiente e ze­<lb></lb>lante banditore di quella, che due secoli dopo s&#039;intitolò Meccanica nuova. </s>

<s><lb></lb>Che poi le tradizioni osservate dal Matematico olandese fossero tutt&#039;affatto <lb></lb>diverse dalle galileiane lo dimostrano i fatti, narrati in questo stesso Tomo <lb></lb>a varie occasioni, d&#039;ond&#039;è manifesto in quali gravissimi errori e a quali <lb></lb>false conseguenze si trovasse condotto Galileo, sempre che gli occorra a ra­<lb></lb>gionare della composizion delle forze. </s></p><p type="main">

<s>Come dalle più antiche fonti aristoteliche, sapientemente derivate dal <lb></lb>Nemorario, sorgesse l&#039;ubertà della Statica steviniana, fu da noi mostrato a <lb></lb>suo luogo, nè qui importa ripetere il già detto, per sodisfar piuttosto alla <lb></lb>curiosità di coloro, i quali hanno ora sentito annoverar fra i Meccanici <lb></lb>l&#039;Acquapendente. </s>

<s>Medico e anatomico famosissimo si trovò tirato nel campo <lb></lb>della Meccanica quando, nella terza parte della sua Miologia, pubblicata <lb></lb>nel 1614, ebbe a dimostrare secondo qual ragione s&#039;esercitano le forze mu­<lb></lb>scolari. </s>

<s>Amico a Galileo, e collega nel medesimo Studio padovano, chi non <lb></lb>direbbe che l&#039;Anatomico si fosse, in una questione difficilissima, rivolto a <lb></lb>consultare il Matematico, tutto allora in studio di dare alla <emph type="italics"></emph>Scienza mecca­<lb></lb>nica<emph.end type="italics"></emph.end> ordine e perfezion di trattato? </s>

<s>Eppure è tanto certo non avere avuto <lb></lb>l&#039;Acquapendente intorno a ciò alcun consulto che, quand&#039;anco si fosse di­<lb></lb>sposto a richiederlo, non avrebbe Galileo saputo ritrovar nella sua Scienza <lb></lb>meccanica di che sodisfarlo. </s>

<s>La questione miologica infatti risolvevasi essen­<lb></lb>zialmente co&#039;principii statici della Leva, ritrovati già da Aristotile e dal Ne­<lb></lb>morario, co&#039;quali due autorevolissimi Maestri anche il Fabricio, dop&#039;aver <lb></lb>descritti gli effetti della macchina, dice: “ Porro haec omnia ex natura cir­<lb></lb>culi petuntur. </s>

<s>Nimirum, quo longior a centro linea est, eo celerius fertur, <lb></lb>ac proinde facilius attollit breviorem, quae ultra centrum producta est li­<lb></lb>neam ” (Opera omnia, Lugd. </s>

<s>Batav. </s>

<s>1738, pag. </s>

<s>419). </s></p><p type="main">

<s>Non era dunque bisogno consultar la moderna Scienza galileiana, per <lb></lb>saper da quali principii matematici derivino le proprietà generali del Vette. </s>

<s><lb></lb>Quanto poi ai particolari, consistenti nel miglior modo di applicar la potenza, <lb></lb>a che insomma si riduceva la difficoltà della questione; Galileo non poteva <lb></lb>nulla giovare ai progressi della Miologia, per i quali richiedevasi un argo­<lb></lb>mento, sconosciuto affatto in quella sua nuova meccanica officina. </s>

<s>Riduce-<pb xlink:href="020/01/2338.jpg" pagenum="581"></pb>vasi un tale argomento infatti al principio della composizion delle forze, che <lb></lb>l&#039;Acquapendente trovava preparato così nella Scienza antica, da poter facil­<lb></lb>mente con esso risolvere il problema: “ Cur musculi longiores, non solum <lb></lb>longiores, sed etiam robustiores dant motus ” (ibid., pag. </s>

<s>420). </s></p><p type="main">

<s>Si fa la desiderata risoluzione dipendere, come da Lemma, dal seguente <lb></lb>Teorema, che i nostri Lettori conosceranno facilmente informato dalle più <lb></lb>sane dottrine dei moti composti, benchè non s&#039;applichi immediatamente la <lb></lb>descrizione del parallelogrammo: “ Sit vectis AB (fig. </s>

<s>308) et in ipso C <lb></lb>pondus, B fulcimentum; chorda vero perpendicularis DF, aliae vero obli­<lb></lb>quae DG, DE. </s>

<s>Dico facilius attolli pondus chorda DF, quam chorda DE, <lb></lb>vel DG. ” <lb></lb><figure id="id.020.01.2338.1.jpg" xlink:href="020/01/2338/1.jpg"></figure></s></p><p type="caption">

<s>Figura 308</s></p><p type="main">

<s>“ Cum enim vis in E consti­<lb></lb>tuta attrahit secundum lineam ED, <lb></lb>cum vectis AB attrahatur versus <lb></lb>fulcimentum B, pars virium absu­<lb></lb>mitur contra fulcimentum: tractus <lb></lb>enim obliquus ED videtur potius <lb></lb>esse ad impellendum fulcimentum, <lb></lb>quam ad pondus attollendum. </s>

<s>Pa­<lb></lb>riter etiam trahens chorda GD ni­<lb></lb>titur potius ut avellat Vectem ex fulcimento, quam ut pondus attollat: <lb></lb>absumitur ergo vis magna ex parte in fulcimento B expellendo. </s>

<s>Quod si <lb></lb>attrahatur chorda perpendiculo in FD, nulla pars virium suam non exercet <lb></lb>facultatem in pondere elevando: imo tota ad ipsum attollendum converti­<lb></lb>tur ” (ibid.). </s></p><p type="main">

<s>Seguono al Teorema due corollarii: “ Ex quo colligitur, quo punta E, G <lb></lb>elatiora fuerint, eo facilius moveri vectem, et pondus attolli ” (ibid). Non <lb></lb>già che l&#039;Acquapendente creda, come i più credevano allora, che le corde <lb></lb>più lunghe siano a proporzione più forti, ma la maggior lunghezza fa men <lb></lb>rapidamente diminuire l&#039;angolo dell&#039;inclinazione, da cui solo dipende il va­<lb></lb>riar della forza. </s>

<s>L&#039;altro corollario poi, da cui traluce il concetto che l&#039;in­<lb></lb>forma, è così espresso: “ Patet etiam quod, si vectis et chorda in eadem <lb></lb>essent linea constituta, nullo pacto motus fierent, ut patet per lineas DH, DL. </s>

<s><lb></lb>Posita enim vis in H, vel in L, utraque omni ex parte applicabitur ad mo­<lb></lb>vendum fulcimentum B, non autem ad attollendum Vectem ” (ibid.). </s></p><p type="main">

<s>Quanto siano così fatte dottrine aliene dalle tradizioni galileiane pos­<lb></lb>sono giudicarlo da sè i Lettori, cavandone i criterii dalle storie passate; cri­<lb></lb>terii, che valgono altresì per Guidubaldo del Monte, nella Statica maestro a <lb></lb>Galileo, e nell&#039;Acustica e nella Ballistica premostratore. </s>

<s>Il Guldin, amico <lb></lb>dello stesso Galileo ch&#039;ei conobbe in Roma, e a cui mandò per mezzo di <lb></lb>Giovanni Pieroni il libro <emph type="italics"></emph>De centro gravitatis partium circuli,<emph.end type="italics"></emph.end> si faceva con <lb></lb>esso primo cultore di una delle più belle e delle più ammirate parti della <lb></lb>Meccanica, qual è la Centrobrarica, le tradizioni della quale risalgono, come <lb></lb>a suo luogo narrammo, alla Scuola alessandrina. </s>

<s>Or chi sa quanti altri Au-<pb xlink:href="020/01/2339.jpg" pagenum="582"></pb>tori, sconosciuti al pubblico e a noi, avranno promossa, ne&#039;principii del se­<lb></lb>colo XVII, la Scienza, della quale non sapevano ancora ciò che s&#039;era nova­<lb></lb>mente insegnato dalla cattedra di Padova, e dalla solitudine di Arcetrì? </s></p><p type="main">

<s>Si dirà che le notate promozioni appartengono tutte alla Statica, della <lb></lb>quale principalmente Archimede aveva preparati i progressi: ma come si <lb></lb>potrebbe provare che non sia la Dinamica tutt&#039;opera di Galileo, da cui si <lb></lb>ebbero matematicamente dimostrate le leggi, scoperte prima per l&#039;esperienza? </s>

<s><lb></lb>Le prove, rispondiamo, si ritrovano pure nella storia da noi addietro inve­<lb></lb>stigata nei fatti, la somma dei quali si riduce a dire che, contemporanea­<lb></lb>mente con i Dialoghi delle due Nuove Scienze, apparvero alla luce in Italia <lb></lb>e in Germania due altri libri di Dinamica nuova, insigni al giudizio di tutti <lb></lb>gl&#039;imparziali. </s></p><p type="main">

<s>Giovan Marco Marci di Crownland, prima medico e poi gesuita, pub­<lb></lb>blicava in Praga nel 1639, con i tipi di Giovanni Bilina, un libro intitolato <lb></lb><emph type="italics"></emph>De proportione motus,<emph.end type="italics"></emph.end> perchè, dalla legge che gl&#039;incrementi delle velocità <lb></lb><emph type="italics"></emph>rationem habent quam temporum quadrata,<emph.end type="italics"></emph.end> si dimostrano le proprietà dei <lb></lb>cadenti nel perpendicolo, per le linee oblique, e per gli archi dei cerchi. </s>

<s><lb></lb>L&#039;assunto dunque è qui proprio il medesimo, che nel terzo dialogo delle <lb></lb>Nuove Scienze, con l&#039;Autor del quale non si vede che relazione potess e <lb></lb>avere un uomo, così distante di patria, di educazione e di studii, e tale che, <lb></lb>ancora oggidì che tanto e per tutto si fruga, vien passato di vista agli eru­<lb></lb>diti. </s>

<s>Potrebbe forse nascere il sospetto ch&#039;essendo il manoscritto de&#039;Dialo­<lb></lb>ghi galileiani capitato in Praga, alle mani del Pieroni, per farlo ivi stam­<lb></lb>pare, fosse stato veduto o riferito agli studiosi, ma la poca probabilità del <lb></lb>fatto conduce a negarlo poi con certezza chiunque si metta a confrontare <lb></lb>insieme i due diversi trattati. </s></p><p type="main">

<s>Nel Matematico tedesco è manifesto il fine delle dinamiche proposizioni, <lb></lb>che è quello di applicarle alla <emph type="italics"></emph>Regola sfigmica;<emph.end type="italics"></emph.end> intendimento, che fallisce <lb></lb>affatto nel dialogo del Nostro, il quale, essendosi proposto di dimostrare <lb></lb>quella lunga serie di teoremi in grazia delle proprietà de&#039;pendoli, non fa <lb></lb>poi de&#039;pendoli, e fuor di proposito, che un leggerissimo motto. </s>

<s>Le leggi <lb></lb>delle oscillazioni dei gravi, pendenti da varie lunghezze di fili, son per Ga­<lb></lb>lileo semplici fatti sperimentali, che matematicamente Giovan Marco riduce <lb></lb>ai loro propri principii, per applicarli poi alla soluzione dell&#039;importantissimo <lb></lb>problema della lunghezza del pendolo a secondi. </s></p><p type="main">

<s>Se da questa sola parte si volesse considerare, basterebbe per dire che <lb></lb>il trattato stampato in Praga supera notabilmente quello stampato in Leid a, <lb></lb>ma ben altre ragioni ci sono di quella superiorità, per prezzar debitamente <lb></lb>le quali giova ridurci a memoria che, a levare i voli più sublimi, ebbe la <lb></lb>Meccanica per sue ali il Calcolo differenziale e la Regola del parallelogrammo. </s>

<s><lb></lb>Ora è a notare che Galileo, recidendo, come dalla Storia apparisce, i due <lb></lb>strumenti, ne impediva così que&#039;liberi voli, che tutta la Scienza del moto, <lb></lb>com&#039;egli forse avrebbe desiderato, si sarebbe anche a&#039;nostri giorni rima­<lb></lb>sta nella breve cerchia de&#039;suoi teoremi. </s>

<s>Giovan Marco invece preparava al <pb xlink:href="020/01/2340.jpg" pagenum="583"></pb>Newton, da un secolo e mezzo, quella che, dalle mani del Varignon, gli ve­<lb></lb>niva porta come Meccanica nuova, dimostrando che il moto perfettamente <lb></lb>misto “ fit per diametrum parallelogrammi, cuius latera constituit motus <lb></lb>simplex ” (fol. </s>

<s>38 ad t.). E quasi avesse presentiti i gravissimi danni, che <lb></lb>sarebbero per derivare alla Scienza dalla seconda proposizion galileiana Dei <lb></lb>proietti, pronunziava contro la falsità di lei quella gran verità, intesa allora <lb></lb>da pochi: “ Metus mixtus est necessario minor diametro quadrati, aut pa­<lb></lb>rallelogrammi ” (fol. </s>

<s>40). </s></p><p type="main">

<s>Benchè grande sia, senza dubbio, il merito dell&#039;avere imbandita così <lb></lb>la mensa di cibi salutari a gente, che gli credeva veleni: è nonostante in <lb></lb>qualche piccola parte minorato dal non avere le proposizioni dei moti mi­<lb></lb>sti tutta quella originalità, che hanno le altre nel libro di Giovan Marco, <lb></lb>dove ei dimostra le leggi degli urti. </s>

<s>A che si riducano tutti i discorsi, te­<lb></lb>nuti per quarant&#039;anni da Galileo intorno alla forza della percossa, lo ve­<lb></lb>dranno coloro, i quali avranno la pazienza di leggere il cap. </s>

<s>III della seconda <lb></lb>parte di questa Storia della Meccanica. </s></p><p type="main">

<s>La nuova Scienza insomma delle proporzioni del moto, insegnata in <lb></lb>Germania, era per questa parte superiore a quella nel medesimo tempo inse­<lb></lb>gnata in Italia, benchè da un altro lato gli rimanga inferiore, non trattando <lb></lb>Giovan Marco delle resistenze dei solidi allo spezzarsi, e de&#039;proietti ripe­<lb></lb>tendo gli antichi errori. </s>

<s>“ Quae autem motu violento moventur, cuiusmodi <lb></lb>proiecta seu manu, seu machina, a principio quidem velocissime, inde mi­<lb></lb>nus velociter moventur, impulsu veluti senescente ” (fol. </s>

<s>18 ad t.). Or chi <lb></lb>non si persuaderebbe, dietro queste osservazioni, che l&#039;Autore <emph type="italics"></emph>De propor­<lb></lb>tione motus<emph.end type="italics"></emph.end> aveva speculazioni sue proprie, e indipendenti da quelle di Ga­<lb></lb>lileo, che non si poteva dunqne vantare di avere istituita la Dinamica egli <lb></lb>il primo ed il solo? </s></p><p type="main">

<s>Un altro competitore egli ebbe nel Baliani, levatogli di mezzo da molti, <lb></lb>com&#039;una molesta festuca dagli occhi, co&#039;soffi del disprezzo. </s>

<s>Noi abbiamo <lb></lb>avuto occasione più volte di esaminare le speculazioni e le scoperte del Ma­<lb></lb>tematico genovese, e le abbiamo trovate di fatto o precedere, o esser con­<lb></lb>temporanee, e perciò indipendenti da quelle di Galileo, che per verità non <lb></lb>si mostra, come i suoi zelatori, punto maravigliato dell&#039;esser due, che vanno <lb></lb>per la medesima strada, giunti insieme al termine stesso. </s>

<s>“ Il signor Fi­<lb></lb>lippo Salviati, scriveva esso Galileo al Baliani, al quale ho conferito buona <lb></lb>parte delle mie immaginazioni filosofiche, mi scrive aver trovata grande con­<lb></lb>formità tra le sue speculazioni e le mie, di che io non mi sono punto ma­<lb></lb>ravigliato, poichè studiamo sopra il medesimo libro e con i medesimi fon­<lb></lb>damenti ” (Lettere di Galileo, pel suo Trecentesimo, Pisa 1864, pag. </s>

<s>16). </s></p><p type="main">

<s>Quando poi, venute queste speculazioni nel 1638 alla luce, si potè tra <lb></lb>le stampate in Leida e le stampate in Genova istituire il confronto, ecco <lb></lb>come Galileo stesso, più imparziale de&#039;suoi fanatici esaltatori, ne scrisse al <lb></lb>suo proprio rivale il giudizio: “ La gratissima lettera di V. S. Ill.ma mi fu <lb></lb>resa ieri, insieme col suo libro <emph type="italics"></emph>Del moto,<emph.end type="italics"></emph.end> dal molto rev. </s>

<s>padre don Cle-<pb xlink:href="020/01/2341.jpg" pagenum="584"></pb>mente di S. Carlo.... Io ho trattato la medesima materia, ma alquanto più <lb></lb>diffusamente, e con aggressioni diverse, imperocchè io non suppongo cosa <lb></lb>nessuna, se non la definizione del moto, del quale io voglio trattare e di­<lb></lb>mostrare gli effetti, imitando in questo Archimede nelle sue spirali. </s>

<s>Non pre­<lb></lb>mettendo altra cosa nessuna, vengo alla prima dimostrazione, nella quale <lb></lb>provo gli spazi passati da cotal mobile essere in duplicata proporzione dei <lb></lb>tempi, e seguito poi a dimostrare buon numero di altri accidenti, de&#039;quali <lb></lb>ella ne tocca alcuni, ma io molti più ve ne aggiungo, e per avventura più <lb></lb>pellegrini ” (ivi, pag. </s>

<s>35-37). Ed è ciò verissimo, ma l&#039;ordine del trattato <lb></lb>è tanto più matematico, è il processo delle dimostrazioni tanto più semplice <lb></lb>e chiaro, che chi avesse a imparar la Scienza nelle sue fonti preferirebbe <lb></lb>l&#039;opuscolo del Baliani al Dialogo di Galileo. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Se ci è lecito rivolgerci ancora indietro a ripigliar l&#039;immagine, per sim­<lb></lb>bolegniare il nostro concetto, diremmo che gli Autori, fin qui da noi com­<lb></lb>memorati, si rassomigliano, nel campo della Scienza del moto, a quegli al­<lb></lb>beri cresciuti, per l&#039;ubertà del suolo e per la benignità del cielo, d&#039;estraneo <lb></lb>seme, intorno a quel maggior albero, che ci raffigura la scienza di Gelileo. </s>

<s><lb></lb>Ma come vedesi nella selva verdeggiare a preferenza una specie dì piante, <lb></lb>disseminate o fatte scoppiare a piè della maggiore; così avvenne delle dot­<lb></lb>trine galileiane, incominciatesi a disseminar dai Dialoghi dei due Massimi <lb></lb>Sistemi. </s>

<s>Le ali della fama e i venti della discordia furono i principali mi­<lb></lb>nistri di quella disseminazione, che si fece, attraverso a monti e a mari, per <lb></lb>tutte le regioni d&#039;Europa. </s>

<s>Noi facciamo spesso le maraviglie, e confessiamo <lb></lb>la nostra propria ignoranza intorno all&#039;origine di certe pianticelle, nate e <lb></lb>cresciute sotto i nostri occhi d&#039;invisibile seme, ma lo stesso si dovrebbe dir <lb></lb>delle idee, le quali, apparite ne&#039;libri di tanti scrittori stranieri quasi spon­<lb></lb>tanee, derivarono dalla notizia dei Dialoghi famosi il germe latente. </s>

<s>Son per <lb></lb>que&#039;Dialoghi infatti annunziate le conclusioni di tutte le verità meccaniche <lb></lb>scoperte, e dimostrate da Galileo in trent&#039;anni. </s></p><p type="main">

<s>Il fondamento statico, ritrovato nelle velocità virtuali, si dimostra pro­<lb></lb>lissamente dagl&#039;Interlocutori nella seconda Giornata, a proposito della gra­<lb></lb>vità, che nella Leva di braccia disuguali lavora con altra resistenza e con <lb></lb>altra forza. </s>

<s>Cosicchè, propostasi per esempio la stadera, con la quale si vo­<lb></lb>lesse pesare una balla di lana o di seta, concludesi dal Sagredo, che “ il <lb></lb>moversi per lo spazio di cento dita il romano, nel tempo che la balla si <lb></lb>muove per un sol dito, è l&#039;istesso che il dire esser la velocità del moto del <lb></lb>romano cento volte maggiore della velocità del moto della balla ” per cui <lb></lb>fermasi come principio vero e notorio, “ che la resistenza, che viene dalla <pb xlink:href="020/01/2342.jpg" pagenum="585"></pb>velocità del moto, compensa quella, che dipende dalla gravità di un altro <lb></lb>mobile ” (Alb. </s>

<s>I, 237). </s></p><p type="main">

<s>Di maggiore importanza, e di maggior merito, erano i fondamenti della <lb></lb>Dinamica, i problemi appartenenti alla quale credeva Galileo non essere stati <lb></lb>saputi fin allora da Filosofo, nè da Matematico alcuno (ivi, pag. </s>

<s>181). Con­<lb></lb>futato Aristotile, con ragioni così chiare e naturali da persuadere gli stessi <lb></lb>Simplicii, conclude che i corpi cadono dalla medesima altezza a terra, più <lb></lb>o meno pesi, nel medesimo tempo; verità che non era nuova, ma che pur <lb></lb>giovava trattenervi attorno eloquentemente il discorso per confermarla. </s></p><p type="main">

<s>Benchè da tutti però si sapesse per volgare esperienza che, partendosi <lb></lb>i gravi dalla quiete, si vanno continuamente accelerando, la proporzione di <lb></lb>un tale acceleramento nulladimeno, dice il Salviati, “ è stata sino ai tempi <lb></lb>nostri ignota a tutti i filosofi, e primieramente ritrovata e dimostrata dal­<lb></lb>l&#039;Accademico, nostro comune amico, il quale, in alcuni suoi scritti non ancor <lb></lb>pubblicati, ma in confidenza mostrati a me e ad alcuni altri amici suoi, di­<lb></lb>mostra come l&#039;accelerazione del moto retto dei gravi si fa secondo i numeri <lb></lb>impari <emph type="italics"></emph>ab unitate:<emph.end type="italics"></emph.end> cioè che, segnati qualì e quanti si vogliano tempi eguali, <lb></lb>se nel primo tempo, partendosi il mobile dalle quiete, averà passato un tale <lb></lb>spazio, come per esempio una canna, nel secondo tempo passerà tre canne, <lb></lb>nel terzo cinque, nel quarto sette, e così conseguentemente secondo i suc­<lb></lb>cedenti numeri caffi; che insomma è l&#039;istesso che il dire che gli spazi pas­<lb></lb>sati dal mobile, partendosi dalla quiete, hanno tra di loro proporzione du­<lb></lb>plicata di quella, che hanno i tempi, ne&#039;quali tali spazi son misurati; o <lb></lb>vogliam dire che gli spazi passati son tra di loro come i quadrati dei tempi ” <lb></lb>(ivi, pag. </s>

<s>244). </s></p><p type="main">

<s>La dimostrazione promette il Salviati di darla, <emph type="italics"></emph>quando tratteremo la <lb></lb>materia de&#039;moti separatamente,<emph.end type="italics"></emph.end> ossia nei dialoghi delle Nuove Scienze, ma <lb></lb>intanto si porge qui l&#039;argomento principale della dimostrazione nel teorema <lb></lb>che, cessando il grave di accelerarsi, e proseguendo con gli uniformi gradi <lb></lb>della velocità ultimamente acquistata, “ passa con moto equabile, nel me­<lb></lb>desimo tempo, spazio doppio al passato dal moto accelerato ” (ivi, pag. </s>

<s>253). </s></p><p type="main">

<s>La massima proposizion dinamica, che si dimostra per mezzo di que­<lb></lb>sto teorema, si svolge nel terzo dialogo delle Scienze nuove in quella lunga <lb></lb>e varia serie di teoremi, che muove dall&#039;avere il tempo per l&#039;obliqua e per <lb></lb>la perpendicolare, terminate al medesimo orizzonte, la stessa proporzione che <lb></lb>la lunghezza dell&#039;obliqua ha alla lunghezza della perpendicolare; ciò che si <lb></lb>dimostra ne&#039;principii della prima giornata dei Massimi Sistemi col suppo­<lb></lb>sto famoso delle velocità uguali nei punti ugualmente cadenti (ivi, pag. </s>

<s>30-32). <lb></lb>E per dar delle nuove dottrine intera notizia, insiem con ciò, che costitui­<lb></lb>sce il principio del trattato Dei moti locali, s&#039;annunzia l&#039;ultima “ conclu­<lb></lb>sione d&#039;un problema bellissimo, che è: che, data una quarta di cerchio eretta <lb></lb>all&#039;orizzonte, sicchè insista sul piano toccandolo in un punto, e fatto un arco <lb></lb>con una tavola ben pulita e liscia dalla parte concava, piegandola secondo <lb></lb>la curvità della circonferenza, sicchè una palla ben rotonda e tersa vi possa <pb xlink:href="020/01/2343.jpg" pagenum="586"></pb>liberamente scorrer dentro; dico che, posta la palla in qualsivoglia luogo, o <lb></lb>vicino o lontano dall&#039;infimo termine, e lasciata in libertà, in tempi eguali, <lb></lb>o insensibilmente differenti, arriverà al termine, partendosi da qualsivoglia <lb></lb>luogo; accidente veramente maraviglioso. </s>

<s>Aggiungete un altro accidente, non <lb></lb>meno bello di questo, che è che, anco per tutte le corde tirate dal punto <lb></lb>infimo a qualunque punto della circonferenza, il mobile stesso scenderà in <lb></lb>tempi assolutamente uguali. </s>

<s>Aggiungete l&#039;altra maraviglia, qual&#039;è che i moti <lb></lb>dei cadenti, fatti per gli archi della quarta, si fanno in tempi più brevi, che <lb></lb>quelli, che si fanno per le corde dei medesimi archi ” (ivi, pag. </s>

<s>488). </s></p><p type="main">

<s>I Matematici esperti avrebbero avuto in queste notizie i dati necessari <lb></lb>per costruire, sei anni prima della pubblicazione, con le loro proprie mani <lb></lb>l&#039;edifizio dinamico co&#039;materiali già preparati da Galileo, nè mancarono al­<lb></lb>cuni che, frugati dalla curiosità e dall&#039;amor della Scienza, v&#039;esercitarono <lb></lb>l&#039;ingegno. </s>

<s>Possiamo de&#039;nostri annoverar fra costoro principali, lasciando il <lb></lb>Cavalieri, di cui, in dimostrare le proprietà del moto appena pubblicate <lb></lb>nel 1632, son note le promozioni; il Magiotti e il Torricelli, che conveni­<lb></lb>vano in Roma desiderosi ad ascoltare i commenti, fatti a loro sulla lettura <lb></lb>dei dialoghi dei Massimi Sistemi, da Benedetto Castelli, il quale scriveva <lb></lb>allo stesso Galileo queste parole: “ Io godo spesso la conversazione di un <lb></lb>signor Raffaele Magiotti da Montevarchi, e di un signor Evangelista Torri­<lb></lb>ricelli da Imola, ambedue eruditissimi di Geometria ed Astronomia, già messi <lb></lb>da me per la buona strada. </s>

<s>Questi bene spesso mi vengono a ritrovare, e <lb></lb>si leggono i Dialeghi con tanto applauso della dottrina, dei concetti, della <lb></lb>lingua e della spiegazione, che, se bene meritano molto più, so che V. S. <lb></lb>non lo potrebbe desiderar maggiore ” (Alb. </s>

<s>IX, 273). </s></p><p type="main">

<s>Degli studii del Magiotti non potè il pubblico gustare i frutti, soprab­<lb></lb>bondantemente ricompensato dal Torricelli, che ampliò le galileiane dottrine <lb></lb>del moto con aggressioni diverse, e con maravigliosa facilità ed eleganza. </s>

<s><lb></lb>Avrebbe, insieme co&#039;due discepoli del Castelli, dovuto formare il triunvi­<lb></lb>rato glorioso Niccolò Aggiunti, se fosse stato a tempo di veder pubblicate, <lb></lb>per ispirarsi alla loro lettura, le due Nuove Scienze. </s>

<s>Ma egli è pure l&#039;esem­<lb></lb>pio più perfetto di ciò che, a metter gl&#039;ingegni sul diritto sentiero, confe­<lb></lb>rissero i dialoghi de&#039;due Massimi Sistemi. </s>

<s>Di quegli studii nemmen egli <lb></lb>potè dare pubblico saggio, ma pure, a giudicar de&#039;progressi già fatti e a <lb></lb>presagir di quelli, che avrebbe potuto fare, se così giovane non l&#039;avesse <lb></lb>colto la morte; basta quel che fu pietosamente raccolto, e trasmesso in ere­<lb></lb>dità della scienza dalle pagine di lui manoscritte. </s>

<s>Le speculazioni, che ivi <lb></lb>si leggono intorno alla tensione delle corde, meccanicamente e acusticamente <lb></lb>considerata; intorno alla teoria delle taglie, e all&#039;inerzia dei pendoli, insiem <lb></lb>con altri pensieri più o men lucidamente riflettenti il vero, ma pur sem­<lb></lb>pre ingegnosi e nuovi; son per le varie pagine della nostra Storia occorse <lb></lb>già alla notizia dei nostri Lettori. </s>

<s>Ma il generoso desiderio e il giovanile ar­<lb></lb>dimento di tentar cose nuove non apparisce meglio, che dalla dimostrazione <lb></lb>di un fatto, intorno a cui pareva impossibile che si potesse dare scienza. </s></p><pb xlink:href="020/01/2344.jpg" pagenum="587"></pb><p type="main">

<s>Sia posata sul piano, per esempio di un tavolino, una catena di ferro, <lb></lb>e una parte di lei resti pendula: questa, nei casi ordinari, non si strasci­<lb></lb>cherà l&#039;altra che giace, facendola tutta cadere a terra, so non che quando <lb></lb>ia la stessa parte pendula tanto pesa, da vincere l&#039;attrito degli anelli con­<lb></lb>tro la superfice del piano. </s>

<s>Che se facciasi astrazione da questo attrito, e si <lb></lb>supponga quello stesso piano perfettamente livellato, dimostra l&#039;Aggiunti che <lb></lb>un mezzo anello solo non sostenuto sarà bastante a tirarsi dietro tutti gli <lb></lb>altri, e a far tutta cader con sè la catena quant&#039;ella è lunga. </s>

<s>La dimostra­<lb></lb>zione perciò dipende, e come da suo proprio principio si conclude dal se­<lb></lb>guente Lemma: </s></p><p type="main">

<s>“ Quel mobile, che non ha inclinazione a moversi verso alcun termine, <lb></lb>starà fermo, ma sarà indifferente a qualsivoglia moto; e da qualunque mi­<lb></lb>nima forza sarà mosso verso qualsivoglia parte. </s>

<s>Starà fermo, perchè, s&#039;egli <lb></lb>si movesse verso qualche parte, averebbe verso quella qualche inclinazione, <lb></lb>contro il supposto. </s>

<s>Starà ancora fermo un mobile lasciato in un mezzo li­<lb></lb>bero, se arà verso qualsivoglia termine eguale inclinazione al moversi. </s>

<s>Im­<lb></lb>perocchè, essendo le inclinazioni a tutte le parti uguali, saranno ancora le <lb></lb>resistenze alle parti opposte uguali. </s>

<s>Ma queste resistenze si ritrovano in detto <lb></lb>mobile, perchè, essendo egli inclinato ugualmente, si moverà verso qualun­<lb></lb>que parte: adunque sarà ugualmente inclinato a moversi verso i termini <lb></lb>opposti, cioè al moto verso qualsivoglia parte averà altrettanta resistenza. </s>

<s><lb></lb>Ma egli per il supposto inclina ugualmente al moto per tutti i versi; adun­<lb></lb>que egli stesso resiste al moto ugualmente per tutti i versi. </s>

<s>Sicchè tanto è <lb></lb>a dire un mobile inclinato ugualmente a moversi verso qualunque parte, <lb></lb>quanto dire un mobile, che resiste a moversi ugualmente per tutti i versi. </s>

<s><lb></lb>Ma se tale è, dunque non si moverà, lasciato in un mezzo libero, ma sì bene <lb></lb>ogni minima forza lo moverà a qualunque parte, perchè ogni minima forza, <lb></lb>aggiunta all&#039;inclinazione verso qualche parte, fa che la resistenza opposta <lb></lb>resti minore, che di prima era uguale. </s>

<s>Ma quando l&#039;inclinazione è mag­<lb></lb>giore della resistenza il mobile si muove; adunque, con qualsivoglia minima <lb></lb>forza aggiunta, detto mobile si moverà. </s>

<s>” </s></p><p type="main">

<s>“ Di qui si raccoglie che tanto è un mobile che resista o inclini egual­<lb></lb>mente a moversi verso qualunque termine, quanto quel mobile, che non in­<lb></lb>clina a moversi verso parte alcuna; perchè tanto quello come questo da ogni <lb></lb>minima forza è mosso a qualunque parte ” (MSS. Gal. </s>

<s>Disc., T. XVIII, <lb></lb>fol. </s>

<s>97). </s></p><p type="main">

<s>Posti questi principii, si preparava l&#039;Aggiunti alla soluzione del suo <lb></lb>problema, prima considerando il corpo, che s&#039;immagina posato in parte sul <lb></lb>piano e in parte fuori, come rigido, e tutt&#039;insieme connesso. </s>

<s>In questo caso <lb></lb>le condizioni dell&#039;equilibrio si riducono facilmente a quelle della stessa Leva. </s></p><p type="main">

<s>“ Nel piano orizzontale HF (fig. </s>

<s>309) sia posto il solido grave GF, con <lb></lb>la parte DE posata sopra detto piano, e col rimanente DF fuori. </s>

<s>Se il solido <lb></lb>sarà composto di parti fisse, dure e saldamente l&#039;una con l&#039;altra connesse, <lb></lb>non potrà abbassarsi la parte DF senza sollevar l&#039;altra DE. ” </s></p><pb xlink:href="020/01/2345.jpg" pagenum="588"></pb><p type="main">

<s>“ Da&#039;centri di gravità della parte DE, e della DF, siano tirate le per­<lb></lb>pendicolari al piano orizzontale HF, le quali sono tra lor parallele, e però <lb></lb>nel medesimo piano. </s>

<s>Producasi dunque per esse un piano, il quale seghi <lb></lb>l&#039;orizzontale HF, dilatato quanto bisogna, e la comune sezione sia la retta <lb></lb><figure id="id.020.01.2345.1.jpg" xlink:href="020/01/2345/1.jpg"></figure></s></p><p type="caption">

<s>Figura 309<lb></lb>AB, quale seghi la linea LM <lb></lb>nel punto C. </s>

<s>Sarà dunque la <lb></lb>linea AB una bilancia, ovvero <lb></lb>leva, il cui sostegno in C, ed <lb></lb>i pesi DF, DE pendono dalli <lb></lb>punti A, B. </s>

<s>Quando dunque il <lb></lb>peso DF, al peso DE, averà mag­<lb></lb>gior proporzione che la distanza <lb></lb>AC alla distanza CB, allora il <lb></lb>solido DF alzerà il solido DE. ” </s></p><p type="main">

<s>“ Ma se nel medesimo piano HF sia posto, parte in esso e parte fuori, <lb></lb>il solido KNO (fig. </s>

<s>310) composto, non di parti duramente affisse, ma fra <lb></lb>di sè lente e flessibili agevolmente, come una corda, catenella, serpe o an­<lb></lb>guilla etc.; allora dico che, qualunque parte di esso penda fuori del piano <lb></lb>HF, detto solido sdrucciolerà e cascherà dal piano ” (ivi). </s></p><p type="main">

<s>La dimostrazione si conduce dai principii di una Scienza nuova, della <lb></lb>quale Galileo ne&#039;suoi dialoghi Del mondo non fa il minimo cenno, benchè <lb></lb>egli dica di avere infin dal principio del 1609 <emph type="italics"></emph>finito di ritrovarne tutte le <lb></lb>conclusioni<emph.end type="italics"></emph.end> (Alb. </s>

<s>VI, 69). Nel 1633 attendeva a dare a quelle conclusioni <lb></lb><figure id="id.020.01.2345.2.jpg" xlink:href="020/01/2345/2.jpg"></figure></s></p><p type="caption">

<s>Figura 310<lb></lb>ordine di trattato, con <lb></lb>intenzione di pubbli­<lb></lb>carlo nei nuovi dialo­<lb></lb>ghi Del moto, e in tale <lb></lb>occasione com&#039;è certo <lb></lb>che fu eccitatato a stu­<lb></lb>diar le leggi delle re­<lb></lb>sistenze Andrea Arri­<lb></lb>ghetti, di cui son pub­<lb></lb>blicamente noti alcuni <lb></lb>teoremi (Alb. </s>

<s>VII, 34-37) dallo stesso Galileo giudicati nel loro procedere <lb></lb><emph type="italics"></emph>maestosi<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>38); così non ebbe a rimanersi indietro l&#039;Aggiunti, <lb></lb>come può giudicarsi dal modo di dimostrar l&#039;annunziata proposizione, che <lb></lb>è tale: </s></p><p type="main">

<s>“ Sia nell&#039;orizzonte HF (come nella precedente figura) un cilindro di <lb></lb>materia omogenea, uniforme, e perciò in ogni sua parte da egual forza egual­<lb></lb>mente flessibile, e la parte KN sia posata nel piano, NO avanzi fuori. </s>

<s>La re­<lb></lb>sistenza all&#039;essere inflesso detto cilindro sarà una forza posta nella leva NP, <lb></lb>col centro del suo momento posto in N, e il fulcimento in P. </s>

<s>La parte poi <lb></lb>del cilindro NO sarà come un peso attaccato nella leva PZ, il cui sostegno <lb></lb>è in P, e detta leva sarà congiunta con l&#039;altra leva PN in P. </s>

<s>Sia dunque <pb xlink:href="020/01/2346.jpg" pagenum="589"></pb>tale il peso di NO, che superi la resistenza, che hanno le parti del cilin­<lb></lb>dro all&#039;esser distratte: dunque si distrarranno. </s>

<s>” </s></p><p type="main">

<s>“ Distraggansi le parti dunque successivamente, sicchè la parte NO del <lb></lb>cilindro discenda in PX. </s>

<s>Di nuovo sarà nella leva PZ, che ha il fulcimento <lb></lb>in P, attaccato il peso del solido ZX, e nella leva PZ saranno, l&#039;una dopo <lb></lb>l&#039;altra, susseguentemente attaccate, nel punto Z, le potenze; e le resistenze <lb></lb>alla distrazione R, S, T saranno come pendenti dal punto N, perchè la forza, <lb></lb>che fa la parte del cilindro RN per stare attaccata con l&#039;altra RS, vien mas­<lb></lb>simamente e validissimamente fatta per la linea RN, nella quale sono i cen­<lb></lb>tri di esse resistenze alla distrazione. </s>

<s>” </s></p><p type="main">

<s>“ Posto dunque che il peso XZ, pendente dalla leva ZP, sia tale che <lb></lb>possa col suo momento superar la forza, con che resistono le parti del ci­<lb></lb>lindro all&#039;essere distratte; perchè nel torcere un solido maggiore e mag­<lb></lb>gior forza ci vuole di mano in mano a voler far più e più distratte le me­<lb></lb>desime parti del solido, sicchè minima è quella forza, che si richiede per dar <lb></lb>principio alla distrazione; di qui è che il peso XZ, che per i filamenti P <lb></lb>e Z, con la leva PZ, fa forza di tirare il solido KN, piuttosto che maggior­<lb></lb>mente distrarre li detti filamenti o fibre POZ, il che è più difficile, prin­<lb></lb>cipierà piuttosto, sendo questo più facile, a distrarre le susseguenti prossime <lb></lb>parti, e in tal distrazione le minime particole indistraibili componenti il ci­<lb></lb>lindro verranno verso PZ, e maggiormente caricando il solido ZX lo ren­<lb></lb>deranno sempre più potente a distrarre le parti che succedono. </s>

<s>” </s></p><p type="main">

<s>“ Ma perchè il solido XZ, facendo forza di distrarre il solido KN, pigne <lb></lb>a basso, e l&#039;istesso fanno le parti, che distratte cadono sopr&#039;esso; perciò il <lb></lb>solido KN verrà nel medesimo tempo tirato orizzontalmente secondo la linea <lb></lb>ZP, al qual movimento, non avendo alcun grave resistenza alcuna, egli an­<lb></lb>cora obbedirà. </s>

<s>Se dunque porremo che il cilindro sia flessibile in ogni sua <lb></lb>parte da ogni forza, è manifesto che qualunque parte di esso sia fuori del <lb></lb>piano lo farà sdrucciolare, e cader tutto ” (MSS. Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>98). </s></p><p type="main">

<s>Di qui si passa a considerare il corpo, che è posato sul piano, non come <lb></lb>tutto ugualmente rigido, nè come tutto in sè flessibile e lento, ma come <lb></lb><figure id="id.020.01.2346.1.jpg" xlink:href="020/01/2346/1.jpg"></figure></s></p><p type="caption">

<s>Figura 311<lb></lb>partecipante d&#039;ambedue le <lb></lb>qualità insieme, qual sareb­<lb></lb>be, aggiunta con anelli ugua­<lb></lb>li, una catena di ferro. </s>

<s>Sia <lb></lb>questa catena AB (fig. </s>

<s>311) <lb></lb>tirata dall&#039;anello BC pendulo <lb></lb>o da qualunque altro minimo <lb></lb>peso, che la condurrà con sè <lb></lb>irresistibilmente a terra, fa­<lb></lb>cendo passar ciascuno anello <lb></lb>di lei per varie fasi di moto. </s>

<s>Attendiamo all&#039;anello DB, mentr&#039;egli tutto si <lb></lb>giace ancora sul piano: il peso BC diffonde la sua azione per tutta la lun­<lb></lb>ghezza della catena, sopra la quale opera a modo di cuneo, qual sarebbe <pb xlink:href="020/01/2347.jpg" pagenum="590"></pb>per esempio TSX, che, insinuandosi nel mezzo fra le giunture di questo e <lb></lb>di quello anello, sospinge ciascuno innanzi per la dirittura SP. </s>

<s>Verrà così <lb></lb>l&#039;anello DB portato fuori del piano per la porzione FB del suo diame­<lb></lb>tro (fig. </s>

<s>312) e ivi si rimarrà, infintantochè il braccio della sua leva FB, <lb></lb>crescendo, non operi con tale momento, da prevalere sull&#039;altro braccio FD, <lb></lb><figure id="id.020.01.2347.1.jpg" xlink:href="020/01/2347/1.jpg"></figure></s></p><p type="caption">

<s>Figura 312<lb></lb>facendo rivoltar l&#039;asse dell&#039;anello <lb></lb>stesso intorno ad F suo punto <lb></lb>d&#039;appoggio. </s>

<s>L&#039;estremità D della <lb></lb>leva si alzerà, e alzerà con sè <lb></lb>insieme anche l&#039;asse dell&#039;anello <lb></lb>ED (fig. </s>

<s>313) il centro di gra­<lb></lb>vità del quale, tendendo ad ac­<lb></lb>costarsi al piè della perpendi­<lb></lb>colare ID, farà che finalmente l&#039;anello DB cada tutto dal piano, tornando <lb></lb>egli che stavagli dietro a giacervi sopra, come vi giaceva dianzi lo stesso <lb></lb>anello DB, di cui subirà le medesime vicende, come le subiranno tutti gli <lb></lb>altri anelli via via, infin tanto che non sia la catena scorsa giù per tutta <lb></lb>la sua lunghezza. </s>

<s>Il caso è descritto così dall&#039;Aggiunti, con finezza di ma­<lb></lb>tematico, e con bellezza di artista: </s></p><p type="main">

<s>“ Ma se sarà nell&#039;orizonte HO la catena AB, della quale la parte AB <lb></lb>sia distesa nel piano, e il resto BC penda fuori del piano dal punto B, <lb></lb><figure id="id.020.01.2347.2.jpg" xlink:href="020/01/2347/2.jpg"></figure></s></p><p type="caption">

<s>Figura 313<lb></lb>ogni volta che la parte sospesa dal <lb></lb>punto B sarà tale, che il suo peso <lb></lb>possa, mediante la leva DFB, che <lb></lb>ha il suo sostegno in F, alzare <lb></lb>quella parte dell&#039;anello DB, che <lb></lb>è nel piano, e gravita nella parte <lb></lb>DF della leva DFB; dico che al­<lb></lb>lora la catena AB scorrerà verso B, <lb></lb>sin a tanto che ella vada in terra. </s>

<s>” </s></p><p type="main">

<s>“ Perchè, nel sollevarsi l&#039;anello DB, l&#039;altro anello DE, il quale è con­<lb></lb>vertibile intorno alla parrte D dell&#039;anello DB, ed intorno alla parte E del­<lb></lb>l&#039;altro anello EG, non si alzerà in dirittura con l&#039;anello DB, ma solamente <lb></lb>verrà sollevato dalla parte D, e con l&#039;altra parte toccherà il piano. </s>

<s>Perchè <lb></lb>poi se uno anello sarà sostenuto da due forze, poste nell&#039;estremità di un <lb></lb>suo diametro parallelo all&#039;orizonte, allora ciascuna forza sostiene la metà di <lb></lb>tutto il peso dell&#039;anello; perciò solamente, quando l&#039;anello fusse posato <lb></lb>orizontale, la forza, che, posta in uno estremo de&#039;suoi diametri si serve del <lb></lb>diametro per leva, e del punto del toccamento per sostegno, vuole alzarlo; <lb></lb>deve essere sul principio eguale alla metà del peso di detto anello, ma dopo <lb></lb>successivamente può essere sempre minore, perchè sempre si diminuisce <lb></lb>il peso. </s>

<s>” </s></p><p type="main">

<s>“ Ora, nel nostro caso, quando l&#039;anello DE sarà orizontale, e perciò <lb></lb>l&#039;anello DB eretto al piano orizontale, volutandosi l&#039;anello DB nell&#039;orizonte, <pb xlink:href="020/01/2348.jpg" pagenum="591"></pb>il seguente anello ED non viene alzato, non ci essendo chi gli faccia forza <lb></lb>all&#039;insù, ed avendo egli sempre il suo medesimo peso, ma ne vien ben <lb></lb>tirato orizontalmente, perchè, siccome se noi volessimo cacciare il conio STX <lb></lb>(fig. </s>

<s>309 poco addietro) nell&#039;anello SP, col moverlo verso S, secondo la <lb></lb>linea TS, è manifesto che l&#039;anello SP, per dar luogo di mano in mano alle <lb></lb>parti più larghe del conio, sarebbe mosso verso SP; così, nel subentrare <lb></lb>nell&#039;anello ED, le parti dell&#039;anello DB, che son sempre più prossime al <lb></lb>punto B, è necessario che l&#039;anello ED, e in conseguenza tutta la catena, <lb></lb>venga tirata verso B. </s></p><p type="main">

<s>“ Nè a tal movimento, come orizontale, ella non ha resistenza; dun­<lb></lb>que sarà mossa da ogni minimo peso pendente dal primo anello DB. </s>

<s>Dico <lb></lb>da ogni minimo peso, perchè, essendo il primo anello eretto al piano, le <lb></lb>parti anteriori equipondereranno alle posteriori: dunque ogni minimo peso <lb></lb>aggiunto a questa alzerà quella, e tirerà tutte le altre. </s>

<s>” </s></p><p type="main">

<s>“ Sia dunque il primo anello caduto dal piano, dopo la caduta del <lb></lb>quale resterà per primo anello nell&#039;orizonte l&#039;anello, che diremo pure DB, <lb></lb>non più parallelo, ma inclinato all&#039;orizonte. </s>

<s>Se dunque il peso pendente dal <lb></lb>punto B sarà (come s&#039;è rappresentato nella 311 figura) tale che alzi FD, e <lb></lb>di più un peso eguale al predetto anello DE, il qual peso s&#039;intendesse at­<lb></lb>taccato nel punto D della leva DFB; allora tutta la catena scorrerà, per­<lb></lb>chè, alzandosi con la leva DB il punto D dell&#039;anello DB, sarà l&#039;anello DE <lb></lb>come un peso pendulo dal suo centro della gravità nella linea, che si tira <lb></lb>dal punto di sospensione perpendicolare all&#039;orizonte. </s>

<s>Dunque l&#039;anello DE <lb></lb>cercherà di accomodare il suo diametro DE nella linea DI perpendicolare <lb></lb>all&#039;orizonte. </s>

<s>Ma il diametro DB cioè il diametro DE, essendo gli anelli <lb></lb>uguali, è maggiore della linea DI, adunque, alzisi quanto si voglia il punto <lb></lb>D, sempre l&#039;anello DE, con le parti verso E, inciamperà nell&#039;orizonte, men­<lb></lb>tre fa forza di andare in DI. </s>

<s>Perchè poi il punto D nell&#039;alzarsi si accosta <lb></lb>verso B, dunque anche l&#039;altra estremità E del diametro ED si sarà acco­<lb></lb>stata verso B. </s>

<s>Ma all&#039;estremità E vien concatenato l&#039;altro anello EG ori­<lb></lb>zontale, dunque, movendosi detto punto E verso B, anche l&#039;anello EG bi­<lb></lb>sogna che si muova. </s>

<s>Di modo che l&#039;anello DE, nell&#039;andar verso B, tira a <lb></lb>quella volta la catena EA. </s>

<s>Ma a tal tiramento, perch&#039;è orizontale, ella non <lb></lb>resiste; adunque scorrerà verso, fin tanto che DB sia col centro di gravità <lb></lb>fuor del piano, dal qual cadendo divenga pendulo dall&#039;anello che gli suc­<lb></lb>cede. </s>

<s>E così rinnovandosi dal peso pendulo fuori del piano, che tuttavia cre­<lb></lb>sce, i medesimi movimenti come sopra, la catena finalmente cadrà tutta fuori <lb></lb>del piano ” (ivi, fol. </s>

<s>98, 99). </s></p><pb xlink:href="020/01/2349.jpg" pagenum="592"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Benchè l&#039;Aggiunti s&#039;educasse l&#039;ingegno a specular così sottili, e così <lb></lb>nuove ragioni del moto alla lettura dei dialoghi dei due massimi Sistemi <lb></lb>del mondo, egli nonostante, morto tre anni prima che vedessero la pubblica <lb></lb>luce in Leida, attinse, delle dottrine insegnate ne&#039;nuovi dialoghi Del moto, <lb></lb>qualche cosa da&#039;familiari colloqui intrattenuti con l&#039;Autore nelle ville di <lb></lb>Bellosguardo e di Arcetri. </s>

<s>Dello strumento per esempio, immaginato e de­<lb></lb>scritto nel primo dialogo, per misurare la forza del vacuo, vedemmo come <lb></lb>ne facesse l&#039;Aggiunti un&#039;applicazione ingegnosa, per ridurre a teorema quel <lb></lb>che Galileo semplicemente asseriva delle corde e delle verghe ugualmente <lb></lb>resistenti in tutta la loro lunghezza. </s>

<s>Tra il 1632 e il 1635 infatti esso Ga­<lb></lb>lileo attendeva a scrivere il detto dialogo primo, che doveva servir come di <lb></lb>prefazione ai due trattati Delle resistenze dei solidi, e Dei moti locali. </s>

<s>E <lb></lb>benchè nel rileggerlo sempre gli cascassero in mente nuove materie, e la <lb></lb>maniera dello scrivere in dialogo gli porgesse assai conveniente attacco d&#039;in­<lb></lb>serirle (Alb. </s>

<s>VII, 56), si potrebbe asserir nonostante che, quale diceva nel <lb></lb>Marzo del 1635 di averlo ridotto al netto e trascritto l&#039;Autore, tale siaci ri­<lb></lb>masto quello stesso primo dialogo nelle stampe. </s></p><p type="main">

<s>L&#039;asserto da una parte conferma e dall&#039;altra è confermato dal fatto, <lb></lb>che la seconda Scienza nuova, alla quale allora pensava Galileo, versava solo <lb></lb>intorno ai moti equabili e agli accelerati, non essendoglisi mostrata ancora <lb></lb>la proposizione del Cavalieri intorno ai moti parabolici feconda di tutte <lb></lb>quelle dottrine de&#039;proietti, che sarebbero venute ad aggiungere un&#039;altra no­<lb></lb>bilissima parte al trattato Dei moti locali. </s>

<s>L&#039;ordine storico perciò, che per <lb></lb>esser compiuto, dopo l&#039;esame dei tre ultimi dialoghi non vuol che si tra­<lb></lb>scuri il primo, e il desiderio di confermare le conclusioni del capitolo pre­<lb></lb>cedente, in coloro che ne fossero tuttavia rimasti dubitosi, ci consigliano di <lb></lb>trattener qui brevemente il discorso intorno al dialogo sopraddetto, per ve­<lb></lb>der com&#039;egli veramente preluda al trattato Delle resistenze e dei moti na­<lb></lb>turali, senza preparare il pensiero o fare il minimo cenno dei moti violenti. </s></p><p type="main">

<s>A proposito dell&#039;arsenal di Venezia introduce il Salviati il suo discorso <lb></lb>intorno alla costruzione delle macchine navali, annunziando a coloro, che <lb></lb>dalla robustezza delle piccole argomentavano a quella delle grandi, la con­<lb></lb>clusione, che nella prima Scienza nuova si vedrà dimostrata, come cioè nel <lb></lb>crescersi la quantità della materia non si moltiplichino con lo stesso rag­<lb></lb>guaglio la robustezza e la gagliardia (Alb. </s>

<s>XIII, 10). La virtù del resistere <lb></lb>i corpi duri alla rottura dipende dalla tenacità e coerenza delle loro parti, <lb></lb>che si riducono, specialmente ne&#039;legni, a fibre o a filamenti, come nei ca­<lb></lb>napi, intorno ai quali si discorrono le ragioni del loro essere in sostener <lb></lb>così validi. </s></p><pb xlink:href="020/01/2350.jpg" pagenum="593"></pb><p type="main">

<s>Ma considerar la testura sola non basta, dovendo essere nelle stesse <lb></lb>minime fibre qualche cosa, che le colleghi insieme e le tenga; ciò che dal­<lb></lb>l&#039;altra parte è manifesto nelle pietre e nei metalli, la coerenza ne&#039;quali dee <lb></lb>dipender da altro glutine, che da filamenti. </s>

<s>Di qui si passa a cercare qual <lb></lb>sia questo glutine, e dove ei risegga, per risolvere la qual questione s&#039;in­<lb></lb>comincia ad esaminare “ quella decantata repugnanza, che ha la Natura ad <lb></lb>ammettere il vacuo ” (ivi, pag. </s>

<s>15). Le favolose dottrine dei peripatetici si <lb></lb>vedono finalmente cenfutate dai fatti sperimentali, qui per la prima volta <lb></lb>descritti, d&#039;onde resulta esser la virtù attribuita al vacuo assai limitata e <lb></lb>insufficiente all&#039;effetto, essendo ella una sola delle cinque parti di quella <lb></lb>forza, che sarebbe necessaria per vincer l&#039;aderenza delle superficie di due <lb></lb>corpi levigati (ivi, pag. </s>

<s>19). Convien dunque di una tal maggioranza di forza <lb></lb>ritrovar la causa, la quale, dovend&#039;essere una sola potissima e vera, “ men­<lb></lb>tr&#039;io non trovo, dice il Salviati, altro glutine, perchè non debbo tentar di <lb></lb>vedere se questo del vacuo che si trova può bastarci? </s>

<s>” (ivi, pag. </s>

<s>23). </s></p><p type="main">

<s>Come altrove notammo aveva Galileo, nelle sue prime speculazioni, at­<lb></lb>tribuita la coerenza dei corpi a un&#039;attrazione quasi magnetica fra le loro <lb></lb>particelle, prelucendo a quella, che universalmente è approvata oggidì sotto <lb></lb>il nome di <emph type="italics"></emph>attrazione molecolare.<emph.end type="italics"></emph.end> Ma i nuovi fatti osservati, e ne&#039;quali si <lb></lb>lusingava di aver ritrovata la ragione del non si poter sostenere un cilindro <lb></lb>d&#039;acqua, ne&#039;tubi delle trombe aspiranti, più su delle diciotto braccia; lo <lb></lb>consigliarono a bandir dalla sua mente ogni virtù magnetica, per ridur tutto <lb></lb>a quella repugnanza del vacuo, ch&#039;egli aveva a principio derisa, e della <lb></lb>quale le presenti esperienze gli avevano dimostrato l&#039;insufficienza. </s>

<s>L&#039;accusa <lb></lb>non gli è risparmiata dal suo libero Simplicio, per difendersi dalla quale <lb></lb>egli, al gran vacuo insufficiente a produr l&#039;effetto, sostituendo i minimi <lb></lb>spazi fra particelle e particelle innumerevolmente disseminate, risponde “ che, <lb></lb>se bene tali vacui sarebber piccolissimi, ed in conseguenza ciascuno facile <lb></lb>ad esser superato, tuttavia l&#039;innumerabile moltitudine, innumerabilmente, <lb></lb>per così dire, moltiplica le resistenze ” (ivi, pag. </s>

<s>24). </s></p><p type="main">

<s>È da questa innumerabilità che si coglie l&#039;occasione d&#039;entrare a trat­<lb></lb>tar degl&#039;infiniti e degli indivisibili con discorsi, che si sollevan per le ne­<lb></lb>bulose regioni, colla principale intenzione di suscitarvi dagli elementi discordi <lb></lb>una tempesta contro le nuove dottrine del Cavalieri. </s>

<s>Rasserenata poi la <lb></lb>mente nel dire quel ch&#039;ei si compiace altrove (Alb. </s>

<s>VII, 55) di chiamar suo <lb></lb>pensiero <emph type="italics"></emph>ammirando e assai peregrino,<emph.end type="italics"></emph.end> intorno alla rarefazione, alla con­<lb></lb>densazione e alla penetrazione dei corpi; si termina, con una questione geo­<lb></lb>metrica degl&#039;isoperimetri, questa prima parte del dialogo, che prolude al <lb></lb>trattato delle Resistenze. </s></p><p type="main">

<s>L&#039;altro trattato, in cui si doveva presentare al pubblico la seconda <lb></lb>Scienza nuova, era quello dei moti naturali, a discorrer dei quali in forma <lb></lb>di proemio si prende attacco dal vacuo, creduto da Aristotile impossibile, <lb></lb>perchè il moto si dovrebbe in esso far nell&#039;istante. </s>

<s>La conclusion del Fi­<lb></lb>losofo scendeva dal falso principio “ che le velocità del medesimo mobile, <pb xlink:href="020/01/2351.jpg" pagenum="594"></pb>in diversi mezzi, ritengono tra di loro la proporzione contraria di quella, <lb></lb>che hanno le grossezze e densità di essi mezzi ” (pag. </s>

<s>64): falsità che con <lb></lb>facile discorso è scoperta qui dal Salviati, insiem con l&#039;altra, pur dal Filo­<lb></lb>sofo medesimo insegnata, e contro la quale si dimostra per prova “ che <lb></lb>una palla di artiglieria, che pesi cento, dugento ed anco più libbre, non <lb></lb>anticiperà di un palmo solamente l&#039;arrivo in terra della palla di un mo­<lb></lb>schetto, che ne pesi una mezza, venendo anco dall&#039;altezza di dugento brac­<lb></lb>cia ” (ivi). </s></p><p type="main">

<s>La sentenza nuova, contrapposta così all&#039;aristotelica antica, voleva es­<lb></lb>sere ben dichiarata col mettere in considerazione l&#039;operazion dell&#039;aria, che <lb></lb>impedisce la velocità naturale più o meno, secondo che varia la gravità spe­<lb></lb>cifica e l&#039;assoluta dei corpi cadenti. </s>

<s>Si divaga di qui il discorso intorno al <lb></lb>modo di misurar la gravità in specie de&#039;liquidi, per via degli areometri <lb></lb>(pag. </s>

<s>71, 72); intorno alla tenacità dell&#039;acqua, e alla resistenza del mezzo, <lb></lb>che riduce finalmente all&#039;equabilità ogni moto accelerato (pag. </s>

<s>77, 95, 96), <lb></lb>e intorno al peso e alla compressione dell&#039;aria, ritornando all&#039;argomento del <lb></lb>moto colla descrizione dei pendoli che, o gravi o leggeri, vanno oscillando <lb></lb>sotto i medesimi tempi, se non che anch&#039;essi risentono l&#039;operazione del <lb></lb>mezzo (pag. </s>

<s>87). </s></p><p type="main">

<s>Lo strumento non è però solamente dimostrativo delle leggi della ca­<lb></lb>duta dei gravi: altri quesiti ci sono attenenti a questa materia, che <emph type="italics"></emph>a molti <lb></lb>parrebbe assai arida<emph.end type="italics"></emph.end> (pag. </s>

<s>97), ma che il Salviati non vuol disprezzare, fa­<lb></lb>cendone intanto rilevare il pregio col dar sodisfazione ad alcune difficoltà <lb></lb>del Sagredo intorno alle dissonanze musicali, e all&#039;intendere il perchè tese <lb></lb>due corde all&#039;unisono, sonando l&#039;una, anche l&#039;altra si move. </s>

<s>Il fatto, e il <lb></lb>modo di sperimentarlo è antichissimo, e in una Nota di Leonardo da Vinci <lb></lb>si legge così descritto: “ Il colpo dato nella campana risponderà e moverà <lb></lb>alquanto un&#039;altra campana simile a sè, e la corda sonata di un liuto ri­<lb></lb>sponderà e moverà un&#039;altra simile corda di simile boce in un altro liuto, <lb></lb>e questo vedrai col porre una paglia sopra una corda simile alla sonata ” <lb></lb>(Les Manus., Manus A, Paris 1881, fol. </s>

<s>32). </s></p><p type="main">

<s>Guidubaldo del Monte non aveva solo descritto il fatto, ma aveva dato <lb></lb>di più la ragione del fatto delle due corde unisone, e delle loro dissonanze, <lb></lb>così scrivendo: “ Due corde in unisono vanno bene insieme e non si per­<lb></lb>cotono fra loro, mentre sonano; che nasce perchè hanno il medesimo moto <lb></lb>nell&#039;andare e tornare: che se se ne scorda e move una, non sonano bene <lb></lb>insieme, ma si percotono.... Di qui ancora si può render ragione perchè <lb></lb>causa, se saranno due strumenti vicini ed abbiano più corde, e posta una <lb></lb>paglia sopra le corde di uno, e poi con l&#039;altro si tocchi una corda, si sente <lb></lb>che quella corda dell&#039;altro strumento, che sarà unisono a quella che si tocca, <lb></lb>suona ancor lei, e le altre non suonano: e questo potrebbe nascer da que­<lb></lb>sto che l&#039;aere della corda ch&#039;è sonata, per la sua agitazione, muove tutte <lb></lb>le altre corde. </s>

<s>Ma perchè quelle, che non sono in unisono, non possono ri­<lb></lb>cevere il medesimo moto di quella ch&#039;è sonata, e quella che è in unisono <pb xlink:href="020/01/2352.jpg" pagenum="595"></pb>lo può ricevere; però ancor ella suona, e le altre non suonano ” (Libri, <lb></lb><emph type="italics"></emph>Histoire<emph.end type="italics"></emph.end> cit., Note al T. IV, pag. </s>

<s>395, 96). </s></p><p type="main">

<s>Galileo ebbe sott&#039;occhio questa e le altre Note manoscritte di Guidu­<lb></lb>baldo, e rese visibile il vibrar delle corde sonore sotto i medesimi tempi <lb></lb>per via dei pendoli di ugual sospensura, ai quali assegnò per legge l&#039;iso­<lb></lb>cronismo assoluto delle vibrazioni, e per via dei pendoli di sospensure dif­<lb></lb>ferenti, ch&#039;egli aveva osservato come cosa nuova, benchè non riconosciuta <lb></lb>conseguente dalle leggi generali del moto, far le loro vibrazioni in tempi, <lb></lb>che hanno suddupla proporzione delle lunghezze dei fili. </s>

<s>Tanto arida dun­<lb></lb>que sentì Galileo questa materia, che se ne spacciò in poche parole alla fin <lb></lb>del proemio a quel trattato, che doveva, attraverso ai più varii teoremi, con­<lb></lb>durre a concluder le leggi dei cadenti, non per gli archi dei pendoli, ma <lb></lb>per le casse dei vagli. </s></p><p type="main">

<s>Benchè arido insomma, pur si fa di questi moti per gli archi dei cer­<lb></lb>chi qualche cenno di prolusione, ma de&#039;proietti, e del ricorrere il loro trat­<lb></lb>tato nei Dialoghi seguenti, non si fa dall&#039;Autore nemmeno un motto, tanto <lb></lb>gli premeva la gloria, e tanto era vero in lui il desiderio d&#039;assicurarsi il <lb></lb>frutto di uno studio di quarant&#039;anni. </s>

<s>E sì che non gli sarebbe mancata l&#039;oc­<lb></lb>casione d&#039;entrar nel geloso argomento, specialmente là dove, posto per teo­<lb></lb>ria il principio che il proietto in su nel perpendicolo e il cadente natural­<lb></lb>mente in giù fanno il medesimo viaggio, nel dover passare dalle specula­<lb></lb>zioni all&#039;esperienza, credeva il Salviati “ che la velocità, che ha la palla <lb></lb>vicino all&#039;uscita del pezzo, sarebbe di quelle che l&#039;impedimento dell&#039;aria <lb></lb>non gli lascerebbe conseguire giammai, mentre con moto naturale scen­<lb></lb>desse, partendosi dalla quiete da qualsivoglia grande altezza ” (ivi, pag. </s>

<s>97). <lb></lb>Ora, perchè l&#039;impeto della palla alla bocca del cannone si pone nel IV dia­<lb></lb>logo uguale a quello, che la palla stessa acquisterebbe venendo per l&#039;al­<lb></lb>tezza, e per la sublimità della parabola; si comprende quanto fosse questa <lb></lb>osservazione opportuna a prevenire le difficoltà di coloro, i quali sarebbero <lb></lb>per negar fede alle ragioni, non vedendole in tutto esattamente rispondere <lb></lb>ai fatti. </s></p><p type="main">

<s>Il moto naturale, preso per misura del violento, avrebbe potuto sugge­<lb></lb>rire allo stesso Galileo questo pensiero, che sovvenne al Viviani come per <lb></lb>corollario alla X proposizione nel dialogo dei proietti. </s>

<s>“ Di qui è manifesto <lb></lb>che le percosse de&#039;proietti, nei punti della sua parabola, ricevute da piani <lb></lb>che siano perpendicolari alle tangenti i punti di essa parabola, le quali per­<lb></lb>cosse sono le massime; sono necessariamente uguali a quelle, che farebbe <lb></lb>il medesimo grave, quando cadesse per una perpendicolare composta della <lb></lb>sublimità e dell&#039;altezza della parabola. </s>

<s>Dal che si cava che la Natura non <lb></lb>si può per tal via superare, e che il proietto non scapita e non acquista di <lb></lb>forza, ma si conserva sempre con quella, che gli dà il discenso retto per­<lb></lb>pendicolare ” (MSS. Gal., P. V, T. IX, pag. </s>

<s>273). Anche le ballistiche dun­<lb></lb>que seguon la natura di tutte le altre macchine, e il beneficio, che si riceve <lb></lb>particolarmente da quelle, consiste nel potere imprimere immediatamente <pb xlink:href="020/01/2353.jpg" pagenum="596"></pb>nel proietto quella forza, che pure gli s&#039;imprimerebbe sollevandolo con gran <lb></lb>disagio, e con gran perdita di tempo, alla convenevole altezza perpendi­<lb></lb>colare. </s></p><p type="main">

<s>Ritornando ora all&#039;intenzione del nostro discorso, chiaramente ci sem­<lb></lb>bra dimostrato che, quando Galileo scriveva il primo Dialogo di proemio, <lb></lb>le due nuove Scienze, ch&#039;egli intendeva insegnare, si riducevano alle Resi­<lb></lb>stenze dei solidi, e ai Moti naturali. </s>

<s>Sulla fine del 1634 erano già stati messi <lb></lb>in ordine di trattato i teoremi, e quanto ai moti accelerati in particolare an­<lb></lb>nunzia il dì 19 Novembre di quell&#039;anno, con queste parole al Micanzio, la <lb></lb>final risoluzione presa di fondare il nuovo meccanico edifizio sul principio <lb></lb>supposto delle velocità uguali ne&#039;cadenti per varie linee della medesima al­<lb></lb>tezza, dopo quelle lunghe tenzoni, che ci si rivelarono nel cap. </s>

<s>VI, confron­<lb></lb>tando i primi libri manoscritti <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> con quello, che fu poi dato alle <lb></lb>stampe: “ Il trattato del moto, tutto nuovo, sta all&#039;ordine, ma il mio cer­<lb></lb>vello inquieto non può restar d&#039;andar mulinando, e con gran dispendio di <lb></lb>tempo, perchè quel pensiero, che ultimo mi sovvenne circa qualche novità, <lb></lb>mi fa buttare a monte tutti i trovati precedenti ” (Alb. </s>

<s>VII, 56). </s></p><p type="main">

<s>Stabilito dunque l&#039;ordine e il fondamento, da sottoporre a quel trat­<lb></lb>tato del moto, e da parecchi anni preparato già l&#039;altro delle Resistenze, <lb></lb>attendeva Galileo, nella quieta solitudine di Arcetri, a ridurre al netto e a <lb></lb>trascrivere quel primo dialogo di prefazione, com&#039;egli stesso scriveva in una <lb></lb>lettera del di 15 Marzo 1635 a Elia Diodati (ivi). Si diffuse la tanto desi­<lb></lb>derata notizia fra gli amici e i discepoli, a uno de&#039;quali, a Giovanni Pie­<lb></lb>roni, giunse la notizia infino in Vienna, dov&#039;era stato chiamato da Firenze <lb></lb>a servire l&#039;Imperatore in qualità d&#039;ingegnere. </s>

<s>Non bastava però a saziare <lb></lb>i desiderii di costoro il saper che l&#039;opera si scriveva: volevano esser certi <lb></lb>che sarebbe stampata, ma prevedevano certe difficoltà, che ne sfioravano la <lb></lb>bella speranza. </s></p><p type="main">

<s>Sanno oramai troppo bene i nostri Lettori che la causa della condanna <lb></lb>dei dialoghi dei due Massimi Sistemi furono i Gesuiti, gelosi di mantenere <lb></lb>il principato in ogni ordine di scienza: e come allora contesero per rima­<lb></lb>ner primi nell&#039;Astronomia, così era da aspettarsi che volessero contender <lb></lb>ora, per seguitar a primeggiar nella Meccanica. </s>

<s>Pare impossibile che la cri­<lb></lb>tica non abbia col suo senno avuto tanto di autorità, da reprimer le voci <lb></lb>degl&#039;insipienti declamatori, ai quali fu dato ad intendere che si trattasse di <lb></lb>mettere in contradizione un sistema scientifico co&#039;principii religiosi. </s>

<s>Nei <lb></lb>nuovi dialoghi le questioni erano puramente scientifiche, eppure ebbero <lb></lb>anch&#039;essi a patir le medesime contradizioni dei primi. </s>

<s>Tanto son poi leg­<lb></lb>geri i giudizi degli scrittori volgari che anzi, andando a ricercare il vero <lb></lb>della cosa, si trova che coloro, i quali essi incolpano più volentieri, furono <lb></lb>con la mente e con l&#039;animo favorevoli a Galileo, e solo forse colpevoli in <lb></lb>questo: nel non aver saputo prevaler, nè resistere a una potenza, che il <lb></lb>Micanzio chiamava infernale. </s>

<s>Ma perchè alcuno non abbia a mettere fra i <lb></lb>declamatori anche noi, passiamo serenamente a raccontare la storia. </s></p><pb xlink:href="020/01/2354.jpg" pagenum="597"></pb><p type="main">

<s>Il Pieroni dunque, scrivendo d&#039;Austria il di 4 Gennaio 1635, dop&#039;aver <lb></lb>detto a Galileo che tutti erano in gran desiderio di veder palesato al mondo <lb></lb>il libro del moto, soggiungeva: “ E perchè m&#039;è venuto pensiero che V. S. <lb></lb>in pubblicarlo poss&#039;avere qualche difficoltà o rispetto, ho risoluto di signi­<lb></lb>ficarle che, se le paresse bene e a proposito che si stampasse quà in qual­<lb></lb>che città, potrebbe questo venirle fatto molto facilmente, se ella volesse <lb></lb>fidarsi a mandarlo a me, perchè io lo farei stampare in buoni caratteri, con <lb></lb>le figure ch&#039;ella m&#039;imponesse, puntualissimamente ” (ivi, X, 66, 67). </s></p><p type="main">

<s>Galileo, per ragioni facili a intendersi, avrebbe voluto più volentieri <lb></lb>stampare il libro in Italia: nonostante, mandando il primo dialogo mano­<lb></lb>scritto a fra Fulgenzio Micanzio a Venezia, gli annunziava quel mezzo, che <lb></lb>gli veniva proposto di Vienna. </s>

<s>Non spiaceva al Micanzio il partito, ma in­<lb></lb>tanto volle tastar l&#039;animo dell&#039;Inquisitore, mostrandogli il desiderio di far <lb></lb>ristampare il discorso Delle galleggianti. </s>

<s>Rispose di avere espressa commis­<lb></lb>sione da Roma in contrario. </s>

<s>— Forse di non ristampare il Sistema coper­<lb></lb>nicano? </s>

<s>— domandò il Micanzio — e l&#039;altro replicava: — No, no, è di­<lb></lb>vieto generale <emph type="italics"></emph>de editis et edendis.<emph.end type="italics"></emph.end> — Ma se vorrà stampare il <emph type="italics"></emph>Credo<emph.end type="italics"></emph.end> e il <lb></lb><emph type="italics"></emph>Pater noster?<emph.end type="italics"></emph.end> — a cui, per troncare il discorso, concludeva l&#039;Inquisitore <lb></lb>che gli avrebbe fatto avere una copia della commissione in proposito venu­<lb></lb>tagli da Roma. </s></p><p type="main">

<s>Nel riferire a Galileo questo colloquio, lo stesso Micanzio soggiungeva <lb></lb>che, anche facendo stampare i nuovi Dialoghi in Austria, conveniva andar <lb></lb>molto cauti, “ nel che pensiamo, sono sue proprie parole, se possa servire <lb></lb>che io, favorito di questo tesoro per mia curiosità, ne abbia fatto copia, e <lb></lb>voluto cercare e procurare la stampa, che non mi curo che gridi chi vuole. </s>

<s><lb></lb>V. S. E. discorre singolarmente che non conviene ricevere negativa, nè an­<lb></lb>cora io qui la voglio a modo veruno. </s>

<s>Ma se vedrò l&#039;ordine quale di sopra, <lb></lb>o supererò la difficoltà o troverò modo fuori: stampati li voglio di certo ” <lb></lb>(ivi, pag. </s>

<s>76). Egli però che aveva presa così ferma risoluzione contro la <lb></lb>tirannia (pag. </s>

<s>75); che giurava non perirebbero cose tali se ci si mettesse <lb></lb>tutto l&#039;inferno (pag. </s>

<s>77), ritornato all&#039;Inquisitore “ e veduto l&#039;ordine rigo­<lb></lb>rosissimo de&#039;stampati e da stamparsi, a me, diceva a Galileo, non dà fasti­<lb></lb>dio, ma non si deve creare a V. S. persecuzioni. </s>

<s>Ho pensato, se ella lo con­<lb></lb>sente, far fare una bella copia di tutto, e collocarla nella pubblica libreria <lb></lb>di S. </s>

<s>Marco ” (ivi, pag. </s>

<s>81). </s></p><p type="main">

<s>Il Pieroni però sperava che sarebbero in ogni modo stampati, almeno <lb></lb>i dialoghi delle Scienze nuove, in Austria, dove gli recò il principe don Ma­<lb></lb>tias de&#039;Medici, che partiva da Firenze il dì 9 Giugno 1635 ambasciatore in <lb></lb>Alemagna (ivi, VII, 57). Un viaggio in Ungheria fece sì che le carte non <lb></lb>recapitassero alle mani del Pieroni, prima del dì 11 Agosto, ricevute le quali <lb></lb>se ne rallegrò, e pensava a dispor le cose in modo, che non s&#039;avesse Ga­<lb></lb>lileo a pentire di aver finalmente accettato quel partito. </s>

<s>Avrebbe voluto <lb></lb>stampare in Austria, mettendo il libro sotto la protezione dell&#039;Imperatore, <lb></lb>ma poi considerò che i Gesuiti erano ivi onnipotenti, “ e che avrebbero <pb xlink:href="020/01/2355.jpg" pagenum="598"></pb>preso materia di suggerire scrupoli a quella delicatissima coscienza di Sua <lb></lb>Maestà, e derivarne o proibizione, o almeno non gradimento..... Il Re di <lb></lb>Polonia, soggiungeva significando questi pensieri allo stesso Galileo, è di <lb></lb>ottimo gusto, massime di simili cose, e non è soverchiamente nè scrupoloso, <lb></lb>nè ai Gesuiti affetto, ed in riguardo suo solo non sarebbe, credo certo, abor­<lb></lb>rita a Roma nè avuta a male cosa posta sotto la sua protezione ” (ivi). </s></p><p type="main">

<s>Vedendo però del negozio dall&#039;una e dall&#039;altra parte lunghissima la <lb></lb>spedizione, si volse il Pieroni per altre strade, ch&#039;egli giudicava, da&#039;temuti <lb></lb>assalti degl&#039;inimici, assai più sicure. </s>

<s>Il cardinale Dictristain aveva a sue pro­<lb></lb>prie spese in Olmutz fondata una tipografia molto bella, e un&#039;altra pure ne <lb></lb>aveva in propio il cardinale di Harach in Praga. </s>

<s>Ma perchè, più che in Boe­<lb></lb>mia, tornava comodo al Pieroni dirigere la stampa in Moravia, ne dava, per <lb></lb>lettera del 1° Marzo 1636, a Galileo questo avviso: “ Della seguente setti­<lb></lb>mana sarò col divino aiuto in Moravia a dar principio alla stampa del libro <lb></lb>di V. S., non avendo potuto prima distrigare tutti gl&#039;intoppi che ho incon­<lb></lb>trati, e credami V. S. che non ho riposo alla mia mente, in sino che io non <lb></lb>mi veda di adempire quanto devo in servirla. </s>

<s>Le figure sono intagliate quasi <lb></lb>tutte, e le provate riescono, pare a me, ragionevolmente ” (ivi, pag. </s>

<s>141). </s></p><p type="main">

<s>Ma di dar principio alla stampa, già passato tutto il mese di Marzo non <lb></lb>si vedeva risoluzione, perchè tardava ancora di venir la licenza. </s>

<s>S&#039;aggiun­<lb></lb>geva che al cardinale Dictristain, benchè avesse tutte le buone intenzioni, <lb></lb>mancavano le persone, che sapessero maneggiare i tipi della nuova officina: <lb></lb>le cose andavano in lungo, e il Pieroni era sollecitato di ritornare in patria. </s>

<s><lb></lb>In questo mentre si facevano premure per stampare i Dialoghi in Francia, <lb></lb>dove i Gesuiti eran deboli, o in Olanda d&#039;onde erano esclusi, di che Gali­<lb></lb>leo stesso dava questo avviso al Micanzio, curioso di sapere come in Ale­<lb></lb>magna procedesse il negozio: “ In Alemagna s&#039;attraversano vari impedi­<lb></lb>menti, tra i quali uno è che quello, che si aveva preso l&#039;assunto, sta in <lb></lb>procìnto di tornarsene qui alla patria. </s>

<s>Io gli domando che mi rimandi quanto <lb></lb>prima la copia, la quale mi vien domandata per mandarla in luce in Lione, <lb></lb>o in Parigi, o in Olanda ” (ivi, VII, 61). </s></p><p type="main">

<s>Il Micanzio non dubitava di preferire alla Francia l&#039;Olanda, nella quale <lb></lb>sarebbe stata piena libertà di stampare il libro, e gli parve che la fortuna <lb></lb>secondasse l&#039;effetto, facendo capitare in quel tempo a Venezia Lodovico El­<lb></lb>zevirio. </s>

<s>Scrisse, perchè fosse il manoscritto messo in ordine per le stampe, <lb></lb>a Galileo, il quale rispondeva, ne&#039;principii del Luglio di quel medesimo <lb></lb>anno 1636, che aveva fatto già, per mandarle, copiare <emph type="italics"></emph>le due opere Del moto <lb></lb>e Delle resistenze<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>67), e verso la fin del mese prometteva che <lb></lb>avrebbe, fra una quindicina di giorni, mandato de&#039;nuovi dialoghi il resto <lb></lb>(ivi, pag. </s>

<s>71). </s></p><p type="main">

<s>Don Benedetto Castelli era informato di tutto, e dolendogli che s&#039;avesse <lb></lb>il libro a stampare fuori d&#039;Italia, in paese di protestanti, faceva ogni sforzo <lb></lb>per veder di ricorrere alla legittima protestà contro le passionate ingerenze <lb></lb>dei Gesuiti. </s>

<s>Favorito dal conte di Noailles, ambasciatore di Francia, pregava <pb xlink:href="020/01/2356.jpg" pagenum="599"></pb>quel signore a voler trattare della licenza di questa stampa direttamente col <lb></lb>Papa, il quale rispose che avrebbe volentieri proposta la cosa in Congrega­<lb></lb>zione. </s>

<s>Risaputosi ciò dal cardinale Antonio Barberini, tutt&#039;ardente di zelo <lb></lb>per la causa di Galileo, disse al Conte queste parole: <emph type="italics"></emph>Buono, buono ed io <lb></lb>farò ufficio con tutti li cardinali<emph.end type="italics"></emph.end> (ivi, X, 164). La benignità di questi però <lb></lb>non valse a vincere la malignità di quegli altri, i quali, avendo trionfato <lb></lb>della volontà del Papa e dei Cardinali, non pensavano che sarebbe bastato <lb></lb>un semplice operaio di Leida, per mandare all&#039;aria tutti i loro trionfi. </s></p><p type="main">

<s>L&#039;Elzevirio infatti, avuti dal Micanzio i dialoghi manoscritti, gli recava <lb></lb>seco in Olanda per dar principio, con tutta la libertà, alla stampa, ed il dì <lb></lb>16 Marzo 1637 dava avviso allo stesso Micanzio che aveva fatto già inta­<lb></lb>gliar le figure, mandandone intanto quattro per prova (ivi, pag. </s>

<s>202). Nel <lb></lb>Novembre era l&#039;edizione già condotta più che a mezzo, e alla fine del Gen­<lb></lb>naio dell&#039;anno appresso non rimaneva ad aggiungere al volume, che la de­<lb></lb>dica e il frontespizio (ivi, pag. </s>

<s>260). </s></p><p type="main">

<s>Si discusse lungamente, fra Galileo e gli amici più confidenti, se si do­<lb></lb>vesse in quel frontespizio scrivere il nome proprio dell&#039;Autore, e sotto la <lb></lb>protezione di chi metterlo, per riparo dalle ire nemiche. </s>

<s>Fu pensato al conte <lb></lb>di Noailles, nella lettera dedicatoria al quale si fingeva che, essendo andate <lb></lb>attorno più copie manoscritte, capitatane una per caso in Olanda all&#039;Elze­<lb></lb>virio, egli di suo proprio moto ne intraprendesse la stampa. </s>

<s>Nell&#039;Agosto, <lb></lb>avutane commissione dallo stesso Galileo, Elia Diodati presentava al Conte <lb></lb>in Parigi una copia del libro a lui dedicato (ivi. </s>

<s>VII, 217). </s></p><p type="main">

<s>Come l&#039;aria respirando si diffonde tanto più al largo, quanto più era <lb></lb>stata compressa; così avvenne a questo stesso libro, contro l&#039;intenzione e <lb></lb>l&#039;opera de&#039;suoi propri nemici. </s>

<s>I trattati del Baliani e di Giovan Marco, an­<lb></lb>dati in dimenticanza, rimase a questi soli dialoghi di Galileo il più autore­<lb></lb>vole magistero della nuova Scienza del moto. </s>

<s>Di qui comincia per la Mec­<lb></lb>canica un&#039;era novella, i fasti della quale si narreranno in quest&#039;altra parte <lb></lb>della nostra Storia. <pb xlink:href="020/01/2357.jpg"></pb></s></p><pb xlink:href="020/01/2358.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICI<emph.end type="center"></emph.end><pb xlink:href="020/01/2359.jpg"></pb></s></p><pb xlink:href="020/01/2360.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE DEI CAPITOLI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Della Scienza del moto nel secolo XVI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle prime istituzioni statiche, nella Scuola peripatetica, e nella alessandrina <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 7 </s></p><p type="main">

<s>II Dei principii statici di Giordano Nemorario: de&#039;manoscritti di Leonardo da Vinci, e <lb></lb>delle fonti, dalle quali derivò in essi la scienza del moto ” 20 </s></p><p type="main">

<s>III Delle dottrine statiche degli Antichi promosse nelle Note manoscritte di Leonardo da <lb></lb>Vinci ” 34 </s></p><p type="main">

<s>IV Di alcuni più notabili teoremi e problemi di Meccanica dimostrati, e risoluti da Leo­<lb></lb>nardo da Vinci ” 49 </s></p><p type="main">

<s>V Dei principii dinamici professati da Leonardo da Vinci intorno alle leggi della caduta <lb></lb>dei gravi, e della teoria de&#039;proietti ” 69 </s></p><p type="main">

<s>VI Degli altri principali Autori, che promossero la Meccanica, dopo la prima metà del se­<lb></lb>colo XVI ” 84 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dei Baricentri.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della invenzione del centro di gravità nei solidi <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 101 </s></p><p type="main">

<s>II Dei quattro libri centrobrarici di Paolo Guldino, e della Geometria degl&#039;Indivisibili di <lb></lb>Bonaventura Cavalieri ” 112 </s></p><p type="main">

<s>III Delle risposte del Cavalieri alle opposizioni fattegli dal Guldino, e come la Regola cen­<lb></lb>trobrarica avesse dal Metodo degl&#039;indivisibili la sua prima matematica dimostrazione ” 127 </s></p><p type="main">

<s>IV Delle nuove dimostrazioni della Regola centrobrarica, che primi vennero a dare alle <lb></lb>Scienze matematiche in Italia Antonio Nardi, e Vincenzio Viviani ” 138 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Degli Equiponderanti.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della legge delle Equiponderanze dimostrata col principio delle Velocità virtuali <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 156 </s></p><p type="main">

<s>II Della legge delle Equiponderanze dimostrata coi principii archimedei ” 168 </s></p><p type="main">

<s>III Della teoria dei momenti applicata a dimostrar la legge degli Equiponderanti ” 180 </s></p><p type="main">

<s>IV Delle Bilance di braccia uguali, e delle condizioni del loro equilibrio, nel caso delle forze <lb></lb>o parallele o convergenti al centro terrestre ” 190 </s></p><pb xlink:href="020/01/2361.jpg" pagenum="604"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Delle Macchine.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della natura delle Macchine, e del modo di operar del Vette, dell&#039;Asse nella ruota, e <lb></lb>delle Taglie; del Cuneo e della Vite <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 213 </s></p><p type="main">

<s>II Delle proporzioni tra la resistenza e la potenza necessarie a sollevare i gravi per via <lb></lb>dei piani inclinati ” 230 </s></p><p type="main">

<s>III Delle censure di Alessandro Marchetti sopra i teoremi di Galileo e del Torricelli del mo­<lb></lb>mento dei gravi sopra i piani inclinati: della eterodossia meccanica di Giovan Fran­<lb></lb>cesco Vanni, e delle difficoltà che trovarono in confutarla i Galileiani ” 245 </s></p><p type="main">

<s>IV Delle confutazioni speculate dai Matematici stranieri, e della questione intorno alla com­<lb></lb>posizion dei momenti proposta in Boma per rispondere ai sofismi del Vanni: degli <lb></lb>errori di Luc&#039;Antonio Porzio confutati dal Grandi ” 256 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Delle libere cadute dei gravi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della legge di Aristotile che le velocità dei cadenti son proporzionali ai pesi, e come <lb></lb>prima si trovasse quella legge contraria alle esperienze, e poi si dimostrasse contra­<lb></lb>ria alla ragione, e si verificasse finalmente che tutti i corpi nel vuoto scendono ugual­<lb></lb>mente veloci <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 266 </s></p><p type="main">

<s>II Delle cause acceleratrici del moto, e come Galileo fosse il primo a concluder la legge <lb></lb>matematica di un tale acceleramento dai principii del Benedetti ” 289 </s></p><p type="main">

<s>III Della forza d&#039;inerzia applicata ai moti naturali, e delle leggi dei moti accelerati geome­<lb></lb>tricamente dimostrate da Galileo, e dal Baliani ” 302 </s></p><p type="main">

<s>IV Dei pretendenti e dei contradittori di Galileo, e come si confermassero, per l&#039;esperienze <lb></lb>del Riccioli e per i teoremi dell&#039;Huyghens, le leggi galileiane dei gravi cadenti ” 314 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Delle scese dei gravi lungo i piani inclinati.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Dei principii fondamentali, da cui si dimostra la Scienza dei moti inclinati, e di una <lb></lb>supposizione fatta in proposito da Galileo <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 328 </s></p><p type="main">

<s>II Ordinamento e pubblicazione del primo libro galileiano <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> contenente i teoremi <lb></lb>dimostrati infino al 1602 ” 342 </s></p><p type="main">

<s>III Ordinamento e pubblicazione del secondo libro galileiano <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> incominciato nel 1604, <lb></lb>e nel 1609 rimasto interrotto, per le ragioni che qui si diranno ” 350 </s></p><p type="main">

<s>IV Ordinamento delle proposizioni lasciate manoscritte da Galileo, per condurre in una <lb></lb>terza maniera il suo trattato <emph type="italics"></emph>De motu ”<emph.end type="italics"></emph.end> 357 </s></p><p type="main">

<s>V Dei teoremi concernenti i Moti locali ordinati da Galileo per la stampa, e delle critiche <lb></lb>fatte dal Cartesio contr&#039;essi ” 367 </s></p><p type="main">

<s>VI Di ciò che può dirsi nuovo nel trattato di Galileo, che qui paragonasi con quello del <lb></lb>Baliani; e dell&#039;opera data da altri Autori stranieri, come dal Mariotte e dall&#039;Huy­<lb></lb>ghens, intorno al medesimo soggetto del moto dei gravi per i piani inclinati ” 373 </s></p><pb xlink:href="020/01/2362.jpg" pagenum="605"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Delle scese dei gravi per gli archi dei cerchi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle varie esperienze, e delle teorie, che persuasero essere i tempi delle scorse dei <lb></lb>gravi, nelle concavità dei cerchi e nei pendoli, per qualunque ampiezza di arco, <lb></lb>uguali <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 382 </s></p><p type="main">

<s>II Delle nuove esperienze, e delle teorie, che dimostarono non essere i tempi delle corse <lb></lb>e delle ricorse dei cadenti per le concavità dei cerchi, e nei pendoli, esattamente <lb></lb>uguali ” 393 </s></p><p type="main">

<s>III Delle leggi delle cadute dei gravi per archi di cerchio simili, e delle loro applicazioni <lb></lb>al problema del pendolo a secondi ” 405 </s></p><p type="main">

<s>IV Di ciò che operarono i discepoli di Galileo, e segnatamente il Viviani, per dare scienza <lb></lb>delle supposte proprietà dei pendoli disuguali ” 421 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Delle resistenze dei solidi.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Delle proposizioni dimostrate da Galileo nel secondo dialogo delle due Scienze nuove <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 436 </s></p><p type="main">

<s>II Dei trattati di Francesco Blondel, di Vincenzio Viviani e di Alessandro Marchetti ” 453 </s></p><p type="main">

<s>III Delle controversie insorte fra Alessandro Marchetti e Guido Grandi ” 462 </s></p><p type="main">

<s>IV Dell&#039;applicazione della teoria dei momenti ” 482 </s></p><p type="main">

<s>V Delle osservazioni dei fatti, e delle esperienze concorse a promovere la nuova scienza di <lb></lb>Galileo ” 497 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>De&#039;proietti.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Di ciò che specularono il Tartaglia, il Cardano e il Benedetti, e come fossero, sui prin­<lb></lb>cipii del secolo XVII, promosse da Guidubaldo del Monte quelle speculazioni <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 506 </s></p><p type="main">

<s>II De&#039;progressi fatti da Galileo: com&#039;ei credesse la linea descritta dai proietti esser, nella <lb></lb>sua parte curva, circolare e come primo il Cavalieri la dimostrasse parabolica ” 517 </s></p><p type="main">

<s>III Della prima parte del quarto Dialogo galileiano; ossia della misura degl&#039;impeti in cia­<lb></lb>scun punto della Parabola ” 533 </s></p><p type="main">

<s>IV Della seconda e terza parte del Trattato galileiano; ossia della massima ampiezza dei <lb></lb>tiri a mezza squadra, e della costruzione delle Tavole ballistiche ” 552 </s></p><p type="main">

<s>V Delle difficoltà mosse contro la teoria del moto parabolico, e di alcune esperienze isti­<lb></lb>tuite per confrontarle co&#039;teoremi di questa nuova Scienza ” 564 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO X.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Conclusione di questa prima parte.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I De&#039;principali cultori della Meccanica contemporanei di Galileo <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 579 </s></p><p type="main">

<s>II De&#039;dialoghi dei due Massimi Sistemi, e come s&#039;incominciassero a diffondere di <gap></gap> i semi <lb></lb>della nuova Scienza del moto ” 584 </s></p><p type="main">

<s>III Del primo dialogo delle due nuove Scienze e della pubblicazione di lui, insieme con gli <lb></lb>altri tre, fatta dagli Elzeviri in Olanda ” 592 </s></p><pb xlink:href="020/01/2363.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEI DOCUMENTI ESTRATTI DAI MANOSCRITTI GALILEIANI <lb></lb>E NOTATI SECONDO L&#039;ORDINE DEI CAPITOLI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Antonio Nardi riconosce maestro a Galileo il Benedetti, pag. </s>

<s>37. </s></p><p type="main">

<s>Teorema del Torricelli appartenente al trattato <emph type="italics"></emph>De motu ac momentis<emph.end type="italics"></emph.end> 52. </s></p><p type="main">

<s>Teorema delle funi gravate da pesi, propostosi a risolvere dal Viviani 59. </s></p><p type="main">

<s>Il Torricelli proponesi di trovar la ragione di un effetto meccanico, che dice non essere stato ancora <lb></lb>avvertito 64, 65. </s></p><p type="main">

<s>Si studia di trovar quella ragione per simili vie anche il Viviani 65, 66. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo II.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Lemma preniesso da Galileo al suo trattato Dei centri di gravità dimostrato altrimenti dal Vi­<lb></lb>viani, pag. </s>

<s>111. </s></p><p type="main">

<s>Passi estratti da una Epistola di Stefano Gradi intorno a un paradosso di Galileo 125. </s></p><p type="main">

<s>Lettera di Bonaventura Cavalieri al Torricelli, relativa alle difficoltà promosse dal Guldino contro la <lb></lb>Geometria degl&#039;Indivisibili 128-31. </s></p><p type="main">

<s>Frammento di lettera, dove il Cavalieri espone al Torricelli la sua intenzione di rispondere al Gul­<lb></lb>dino in forma di dialogo 131. </s></p><p type="main">

<s>Altro frammento di lettera, con la quale il Cavalieri accompagna il suo primo dialogo manoscritto <lb></lb>in risposta al Guldino 132. </s></p><p type="main">

<s>Una difficoltà <gap></gap>ntro la Geometria degli Indivisibili sciolta dallo stesso Cavalieri 132, 33. </s></p><p type="main">

<s>Pocho parole estratte da una lettera del Cavalieri, il quale ringrazia il Torricelli per aver promosse <lb></lb>il Metodo degl&#039;Indivisibili 134. </s></p><p type="main">

<s>Antonio Nardi par che non approvi il Metodo degl&#039;Indivisibili 138, parole, nelle quali accenna a un <lb></lb>suo metodo di ritrovare il centro di gravità delle superfice curve 139, dimostra un suo Teorema <lb></lb>generale meccanico, che contiene un trattato compiuto di Geometria centrobrarica 140-43, applica <lb></lb>il medesimo teorema alla superflce rivoltata intorno ad un assse 144-46, per rendere geometrico <lb></lb>il Metodo centrobrarico sostituisce al Centro di gravità il Centro della potenza 146, 47. </s></p><p type="main">

<s>Estratto di lettera del Cavalieri al Torricelli, dove si accenna alle difficoltà di trovare venali in Ita­<lb></lb>lia i Libri centrobrarici del Guldino 148. </s></p><p type="main">

<s>Interpetrazione, che dette il Viviani del passo centrobrarico di Pappo Alessandrino 150. </s></p><p type="main">

<s>Poscritto di Vincenzio Viviani a Erasmo Bartholin relativo alla Centrol rarica 151. </s></p><p type="main">

<s>Teoremi centrobrarici dimostrati dal Viviani 153, 54. </s></p><p type="main">

<s>Estratto di una lettera del Viviani, dove l&#039;Autore tratta di alcune sue opere matematiche da stam­<lb></lb>parsi 155. </s></p><pb xlink:href="020/01/2364.jpg" pagenum="607"></pb><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo III.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Passso estratto dalle Scene accademiche, dove il Nardi dichiara irragionevole il principio galileiano <lb></lb>delle velocità virtuali, pag. </s>

<s>161, 62. </s></p><p type="main">

<s>Due noterelle scritte dal Viviani <emph type="italics"></emph>ad mentem Galilei<emph.end type="italics"></emph.end> 164. </s></p><p type="main">

<s>Scrittura, nella quale il Viviani propone, per applicarsi alla Statica, un principio diverso da quello <lb></lb>delle velocità virtuali 165, 66. </s></p><p type="main">

<s>Luogo estratto dalla VI Scena di Antonio Nardi, dove si dimostrano le condizioni dell&#039;equilibrio della <lb></lb>Bilancia considerate le forze sollecitanti come dirette al centro della Terra 176-78. </s></p><p type="main">

<s>Teorema del Torricelli della Libbra di braccia disuguali, e con le direzioni dei pesi convergenti al <lb></lb>centro terrestre 178, 79. </s></p><p type="main">

<s>Pensieri di Antonio Nardi intorno alla natura delle forze, e dei momenti 185. </s></p><p type="main">

<s>Proposizioni relative alle leggi dei momenti dimostrate da Niccolò Aggiunti 187-89. </s></p><p type="main">

<s>Parole, con le quali Antonio Nardi risolve brevemente la famosa questione delle Bilance di braccia <lb></lb>eguali, rimosse dalla loro posizione orizzontale 199. </s></p><p type="main">

<s>Due proposizioni del Torricelli concernenti le leggi dell&#039;equilibrio nelle Bilance di braccia uguali, e <lb></lb>sollecitate da forze convergenti 203-5. </s></p><p type="main">

<s>Nota, nella quale il Viviani spiega il segreto delle figurine ondeggianti 211. </s></p><p type="main">

<s>Da una lettera di Giuseppe Ferroni, il quale domanda al Viviani spiegazione delle figurine ondeg­<lb></lb>gianti 211. </s></p><p type="main">

<s>Da altra lettera dello stesso Ferroni, scritta pure al Viviani per ringraziarlo dello svelato segreto <lb></lb>delle figurine ondeggianti 211, 12. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo IV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Teoremi, nei quali dimostra Niccolò Aggiunti le proposizioni delle Taglie, considerando la tension <lb></lb>delle funi e.no i sostegni, pag. </s>

<s>222, 23. </s></p><p type="main">

<s>Proposizione IX del libro VIII di Pappo compendiata da Cosimo Noferi 231. </s></p><p type="main">

<s>Teorema, con cui il Viviani dimostra, in un modo suo proprio, le proporzioni tra la gravità assoluta <lb></lb>e la relativa nei piani inclinati 241. </s></p><p type="main">

<s>Proposizioni V di Vincenzio Viviani dimostrative delle proporzioni, che passano tra il momento to­<lb></lb>tale di un grave, e il discensivo e il gravitativo di lui sopra un piano inclinato 243-45. </s></p><p type="main">

<s>Lettera al Magliabechi, dove Antonio Monfort dà il suo giudizio intorno all&#039;argomento scritto nello <lb></lb><emph type="italics"></emph>Specimen<emph.end type="italics"></emph.end> di G. </s>

<s>Francesco Vanni 252, 53. </s></p><p type="main">

<s>Lettera, con la quale Girolamo Pollini accompagna al Viviani due foglietti, cioè lo <emph type="italics"></emph>Specimen<emph.end type="italics"></emph.end> del <lb></lb>Vanni, e la risposta di Francesco Spoleti alle opposizioni di lui 253. </s></p><p type="main">

<s>Lettera di Giuseppe Ferroni al Viviani, colla quale si accompagna un teorema, per confermare le <lb></lb>dottrine di Galileo contro i sofismi del Vanni 254, 55. </s></p><p type="main">

<s>Teorema del Viviani, in cui si dimostra come si comportano le pressioni di un grave appoggiato <lb></lb>sopra due piani 255, 56. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo V.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Nota, nella quale brevemente Galileo dimostra contro Aristotile che le velocità dei gravi cadenti non <lb></lb>possono essere proporzionali ai pesi, pag. </s>

<s>268. </s></p><p type="main">

<s>Un giudizio di Galileo intorno alla scienza naturale di Benedetto Varchi 270. </s></p><p type="main">

<s>Frammento di Dialogo di Giuseppe Moleto, in cui si dimostra contro Aristotile che le velocità dei <lb></lb>gravi cadenti non sono proporzionali ai pesi 271-74. </s></p><p type="main">

<s>Teorema di Galileo delle proporzioni che serbano le solidità, rispetto alle superficie, nelle divisioni <lb></lb>dei corpi 285, 86. </s></p><p type="main">

<s>Altro frammento del Dialogo del Moleto relativo alle cause del velocitarsi i gravi cadenti 290-92. </s></p><p type="main">

<s>Nota di Galileo relativa alle cause del velocitarsi i corpi gravi cadenti 292. </s></p><p type="main">

<s>Note di Galileo, che efficacemente illustrano il concetto della forza d&#039;inerzia 303. </s></p><pb xlink:href="020/01/2365.jpg" pagenum="608"></pb><p type="main">

<s>Passo, in cui Niccolò Aggiunti dimostra che un mobile dura a moversi con la prima velocità im­<lb></lb>pressa 304. </s></p><p type="main">

<s>Scrittura, nella quale Galileo, con la Geometria degli indivisibili, dimostra le relazioni, che passano <lb></lb>fra gli spazi e i tempi, nelle libere cadute dei gravi 307, 8. </s></p><p type="main">

<s>Passi estratti da una Scrittura, dove Stefano Gradi si propone di dimostrare <emph type="italics"></emph>a priori<emph.end type="italics"></emph.end> l&#039;egualità del <lb></lb>moto rappresentata per determinati intervalli nel triangolo denticulato 310. </s></p><p type="main">

<s>Discorso dettato da Galileo al Viviani <emph type="italics"></emph>Sopra i principii del Baliani<emph.end type="italics"></emph.end> relativi alle proprietà dei pen­<lb></lb>doli 313, 14. </s></p><p type="main">

<s>Da uno scritto, in cui il Fermat contradice alle proporzioni assegnate da Galileo ai moti naturali 318. </s></p><p type="main">

<s>Dalla veduta XLII della seconda Scena del Nardi, dove, al triangolo preso da Galileo per la scala <lb></lb>delle velocità dei cadenti, si sostituisce la semiparabola 321. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo VI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><gap></gap>na osservazione di Galileo intorno alla velocità del moto nella direzion perpendicolare, e nella in­<lb></lb>clinata, pag. </s>

<s>332. </s></p><p type="main">

<s>Passo di una lettera, nella quale il Mersenno censura il principio fondamentale posto alla sua Mec­<lb></lb>canica da Galileo 335. </s></p><p type="main">

<s>Teorema, in cui il Viviani dimostra che i momenti dei gravi sopra piani di lunghezza eguale, ma <lb></lb>variamento inclinati, stanno come i seni degli angoli delle inclinazioni 336. </s></p><p type="main">

<s>Proposizioni X, delle quali si componeva il primo trattato galileiano <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> raccolte e ordi­<lb></lb>nate 342-49. </s></p><p type="main">

<s>Proposizioni VIII, nelle quali Galileo aveva incominciato, co&#039;principii dinamici, a riformare il su <gap></gap><lb></lb>primo trattato <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> 351-54. </s></p><p type="main">

<s>Contro il principio che, essendo le moli uguali, le velocità son proporzionali ai momenti: obiezioni <lb></lb>del Mersenno e risposte del Torricelli 359. </s></p><p type="main">

<s>Proposizioni XIV preparate da Galileo, per condurre il suo libro <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> sopra il supposto principio <lb></lb>delle velocità uguali nella perpendicolare e nell&#039;obliqua di altezze uguali 358-66. </s></p><p type="main">

<s>Note di Galileo, e Teoremi relativi al trattato <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> 368, 369, 379. </s></p><p type="main">

<s>Teoremi tre di Geometria, occorsi a dimostrare a Galileo in mezzo alle speculazioni dei moti 371, 372. </s></p><p type="main">

<s>Teorema aritmetico di Galileo 372. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo VII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Notizie di V. </s>

<s>Viviani intorno ai primi usi, che Galileo <gap></gap> del pendolo, pag. </s>

<s>384. </s></p><p type="main">

<s>Da una lettera di Francesco Lana agli Accademici del Cimento, dove si descrivono le esperienze isti­<lb></lb>tuite per certificarsi che le vibrazioni maggiori e le minori del pendolo non sono uguali 402, 3. </s></p><p type="main">

<s>Strumento diseguato dal Viviani, per sperimentar se le vibrazioni del pendolo son tutte isocrone nel <lb></lb>vuoto 404. </s></p><p type="main">

<s>Il Viviani nota un errore di calcolo, in cui trascorse Galileo nell&#039;asseg<gap></gap>are il numero delle vibra­<lb></lb>zioni, e i tempi, in pendoli variamente lunghi 411. </s></p><p type="main">

<s>Proposizione del Torricelli applicabile, ma non applicata da lui al moto dei pendeli 421. </s></p><p type="main">

<s>Nota, che contiene i primi tentativi del Viviani intorno alla decomposizione del moto nei pendoli <lb></lb>oscillanti 422. </s></p><p type="main">

<s>Teorema nuovo di M. A. Ricci, che si riscontra con un antico di L. da Vinci 424. </s></p><p type="main">

<s>Il Viviani accenna a un modo di dimostrar le relazioni, che passano fra le varie lunghezze dei pen­<lb></lb>doli, e i tempi delle loro vibrazioni 425: propone l&#039;uso della parabola, per trovar le varie lun­<lb></lb>ghezze dei fili, per i tempi cercati 426. </s></p><p type="main">

<s>Lemmi, Teoremi e descrizioni di Vincenzio Viviani appartenenti al trattatello di lui <emph type="italics"></emph>Dei pendoli di <lb></lb>lunghezze disuguali<emph.end type="italics"></emph.end> 427-32. </s></p><p type="main">

<s>Note del Viviani e del Borelli, nelle quali si descrivono varie lunghezze di pendoli corrispondenti <lb></lb>a minimi tempi 433, 34. </s></p><pb xlink:href="020/01/2366.jpg" pagenum="609"></pb><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo VIII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Discorso, in cui il Viviani applica le proposizioni galileiane delle resistenze dei solidi alle ossa degli <lb></lb>animali, pag. </s>

<s>441. </s></p><p type="main">

<s>Discorso del Torricelli, per dimostrare che una corda tirata soffre ugual tensione in ogni sua <lb></lb>parte 444, 45. </s></p><p type="main">

<s>Alcuni casi curiosi di rottura di corde, descritti dal Viviani 445. </s></p><p type="main">

<s>Postilla del Viviani, nella quale si studia di difendere Galileo accusato di aver mal dimostrata una <lb></lb>proposizione intorno alla leva, applicata a sollevare un masso da terra 447. </s></p><p type="main">

<s>Dimostrazione che Galileo dà della Leva, applicata a sollevare un masso da terra 448. </s></p><p type="main">

<s>Dimostrazione originale data da Galileo della quadratura della parabola 450, 51. </s></p><p type="main">

<s>Estratto da una lettera di Alessandro Marchetti al principe Leopoldo dei Medici, relativa all&#039;argo­<lb></lb>mento delle resistenze dei solidi 456, 57. </s></p><p type="main">

<s>Il Viviani, impugnando lo sbaglio di Galileo, dimostra, in modo simile a quel Marchetti, che il solido <lb></lb>parabolico per avere ugual resistenza in ogni parte, dev&#039;esser considerato come impondera­<lb></lb>bile 458-60. </s></p><p type="main">

<s>Il Viviani, correggendo lo sbaglio di Galileo, dimostra, in modo simile a quel del Marchetti, che nel <lb></lb>solido parabolico, i momenti dei pesi hanno dupla ragion sesquialtera dei momenti delle resi­<lb></lb>stenze 460, 61. </s></p><p type="main">

<s>Informazione del p. </s>

<s>Guido Grandi alla Corte medicea intorno ai dissensi, nati fra lui e il Mar­<lb></lb>chetti 462, 63. </s></p><p type="main">

<s>Passi estratti da una lettera del Leibniz relativi alle controversie insorte fra il Viviani e il Mar­<lb></lb>chetti 466, 480, 497. </s></p><p type="main">

<s>Il Panzanini annunzia al Grandi di aver ritrovato, fra le carte del suo zio V. Viviani, il trattato Delle <lb></lb>resistenzo dei solidi 467. Annunzia allo <gap></gap>tesso di aver consegnato il manoscritto a Benedetto Bre­<lb></lb>sciani, <emph type="italics"></emph>ivi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Teoremi annunziati dal Viviani, e sperimenti disegnati, relativi alle resistenze dei solidi 468. </s></p><p type="main">

<s>Il Viviani coregge la proposizione XIV di Galileo nel trattato delle resistenze 470, 71. </s></p><p type="main">

<s><emph type="italics"></emph>Lemmata universalia pro resistentiis<emph.end type="italics"></emph.end> dimostrati dal Viviani 472-74. </s></p><p type="main">

<s>Il Viviani sentenza che non si può salvare la sesta proposizione galileiana delle resistenze dalla nota <lb></lb>di falsità, nemmeno altrimenti interpetrata 476. </s></p><p type="main">

<s>Nota del Viviani relativa alla resistenza di un cilindro intero e appoggiato nel mezzo, o diviso in <lb></lb>due appoggiati agli estremi 478. </s></p><p type="main">

<s>Dimostrazione fatta da Galileo del famoso teorema che i momenti stanno in ragion composta delle <lb></lb>distanze e dei pesi: soggiunge altre proposizioni per corollarii 484, 85. </s></p><p type="main">

<s>Due teoremi dei momenti, erroneamente dimostrati dal Torricelli, e corretti dal Viviani 486-88. </s></p><p type="main">

<s>Teorema, in cui dal Torricelli si dimostra che i momenti dei pesi uguali prementi un&#039;asta, soste­<lb></lb>nuta agli estremi in vari punti della sua lunghezza, son direttamente proporzionali ai rettangoli <lb></lb>descritti con le distanze dai due sostegni 489, 90. </s></p><p type="main">

<s>Michelangiolo Ricci applica la parabola a sciogliere il problema proposto de Galileo nella XIII delle <lb></lb>resistenze 491. </s></p><p type="main">

<s>Nota, nella quale il Torricelli conclude la dimostrazione che la catenaria è una parabola 492. </s></p><p type="main">

<s>La proposizne XII delle resistenze di Galileo, resa più generale dal Viviani in un Teorema, ch&#039;egli <lb></lb>credeva <emph type="italics"></emph>a nullo demonstratum<emph.end type="italics"></emph.end> 492, 93. </s></p><p type="main">

<s>Note autografe di Galileo, nelle quali si trovano formulati, non solo il Teorema, che il Viviani cre­<lb></lb>deva <emph type="italics"></emph>a nulla demonstratum,<emph.end type="italics"></emph.end> ma l&#039;altro altresi, che dimostra la catenaria essere una para­<lb></lb>bola 494, 95. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo IX.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Sommi capi di un trattato delle Artiglierie, che Galileo si proponeva di scrivere verso il 1609, pag.519. </s></p><p type="main">

<s>Proposizioni, e osservazioni varie di Galileo relative al moto dei proietti 535, 537, 538, 539, 541, 544, <lb></lb>545, 547, 551, 553, 554, 555, 557, 559, 561, 562, 598. </s></p><p type="main">

<s>Nota, nella quale il Viviani, più brevemente di Galileo, risolve il problema: data una parabola, tro­<lb></lb>vare la sublimità, dalla quale cadendo un proietto la descriverebbe 539, e insegna un modo più <lb></lb>facile di quello dello stesso Galileo, per determinar l&#039;impeto nella parabola 543. Si nota però uno <pb xlink:href="020/01/2367.jpg" pagenum="610"></pb>sbaglio del Postillatore di Galileo nel medesimo proposito di determinare gl&#039;impeti 545. Nota <lb></lb>nella quale si propone dallo stesso Viviani un&#039;esperienza, per dimostrare in qual punto della <lb></lb>parabola sia maggiore l&#039;impeto del proietto 551. </s></p><p type="main">

<s>Obiezioni di Antonio Nardi contro il moto parabolico dimostrato da Galileo ne&#039;proietti, 564. </s></p><p type="main">

<s>Osservazioni del Viviani, per dimostrare che il moto trasversale non impedisce il naturale de&#039;pro­<lb></lb>ietti 566. </s></p><p type="main">

<s>Obiezioni di Niccolò Aggiunti contro la dottrina di Galileo che la vertigine di una ruota conferisca <lb></lb>impeto di moversi per la tangente 568. </s></p><p type="main">

<s>Come il Viviani esplichi un pensiero di Galileo, per dimostrar che la medesima parabola è descritta <lb></lb>dal tiro di punto in bianco, e dal tiro elevato 569, e quale esperienza proponga per dimostrar che <lb></lb>il proietto non va mai per spazio perpendicolare 570. </s></p><p type="main">

<s>Esperienze fatte dagli Accademici del Cimento, per verificare l&#039;opinione di Galileo, che il proietto, <lb></lb>nella semiparabola e nella orizzontale, cade nel medesimo tempo 571, 572, 573. </s></p><p type="main">

<s>Come il Viviani si studiasse di conciliar l&#039;esperienze con le teorie, nella misura degl&#039;impeti, parte­<lb></lb>cipati dalla polvere pirica ai proietti 574, 75: come correggesse e perfezionasse quo&#039;suoi primi <lb></lb>studi 576. </s></p><p type="main">

<s>Ferdinando Marsill riferisce al Viviani le sue esperienze, fatte intorno alla polvere pirica, in deter­<lb></lb>minare i vari impeti dei proietti 577. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo X.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Lemmi e proposizioni di Niccolò Aggiunti, per dimostrare le condizioni d&#039;equilibrio e di moto in <lb></lb>una catena, posata sopra un piano, e tirata tutta in terra dal primo anello pendulo, pag. </s>

<s>587-91. </s></p><p type="main">

<s>Corollario, che il Viviani voleva aggiungere alla X proposizione galileiana dei proietti 595. </s></p><pb xlink:href="020/01/2368.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE ALFABETICO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEGLI AUTORI E DELLE COSE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Co&#039;numeri s&#039;accenna alle pagine.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Accademici del Cimento<emph.end type="bold"></emph.end> fanno esperienze del cadente, che risale all&#039;altezza medesima d&#039;onde <lb></lb>scese 333, sperimentano le corse e le nicorse di una palla dentro un canal circolare 394, ritro­<lb></lb>vano che le oscillazioni strette dei pendoli non sono isocrone con le più larghe 399, come ritro­<lb></lb>vassero, e quanta la lunghezza del pendolo a secondi, per applicarla al loro Cronometro 433-35. </s></p><p type="main">

<s><emph type="bold"></emph>Acquapendente (d&#039;) Girolamo Fabricio<emph.end type="bold"></emph.end> applica i teoremi degli antichi alla Meccanica animale 581. </s></p><p type="main">

<s><emph type="bold"></emph>Aggiunti Niccolò<emph.end type="bold"></emph.end> promove una proposizione galileiana intorno al moto dei pendoli 422. </s></p><p type="main">

<s><emph type="bold"></emph>Alessandrina (scuola),<emph.end type="bold"></emph.end> qual sia l&#039;indole sua propria negl&#039;insegnamenti della Meccanica 14. </s></p><p type="main">

<s><emph type="bold"></emph>Arabi,<emph.end type="bold"></emph.end> loro cultura della Scienza meccanica 21. </s></p><p type="main">

<s><emph type="bold"></emph>Archimede,<emph.end type="bold"></emph.end> suoi primi libri meccanici 16, insegna primo la regola di comporre le forze parallele 17, <lb></lb>dimostra la legge dei moti equabili <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> deduce la genesi delle spirali dal principio della com­<lb></lb>posizione dei moti 18. </s></p><p type="main">

<s><emph type="bold"></emph>Aria<emph.end type="bold"></emph.end> nell&#039;aria non è grave 71, impedisce le velocità nei cadenti 283, dà impulso, secondo gli anti­<lb></lb>chi, e occasione di velocitarsi ai cadenti 290. </s></p><p type="main">

<s><emph type="bold"></emph>Aristotile<emph.end type="bold"></emph.end> primo a dimostrar che le forze si compongono nella diagonale del parallelogrammo 10, <lb></lb>riduce tutte le macchine al vette 13, accenna alla legge dei moti equabili 17, due false leggi asse­<lb></lb>gnate da lui alla caduta dei gravi 267, suoi quesiti intorno alle resistenze dei solidi 436, 37. </s></p><p type="main">

<s><emph type="bold"></emph>Attriti,<emph.end type="bold"></emph.end> come indugino le velocità dei cadenti lungo i piani inclinati, secondo l&#039;esperienze del Ric­<lb></lb>cioli 301. </s></p><p type="main">

<s><emph type="bold"></emph>Ballani Giovan Batista<emph.end type="bold"></emph.end> scopre, contemporaneamente con Galileo, la ragione perchè i gravi di qua­<lb></lb>lunqne mole cadendo vanno ugualmente veloci 278, come, contemporaneamente con Galileo, di­<lb></lb>mostri le leggi dei liberi cadenti 311, 12, vuol rivendicare a sè il primato delle scoperte leggi <lb></lb>dei moti accelerati 315, confessa che Galileo l&#039;aveva prevenuto 317, dimostra che gl&#039;incrementi <lb></lb>delle velocità nelle libere cadute dei gravi son come la serie dei numeri naturali 319, si con­<lb></lb>frontano i teoremi di lui con quelli pubblicati nello stesso tempo da Galileo 375-77, chiede a <lb></lb>Galileo quanta debba essere la lunghezza del pendolo, che misura i secondi 407, sue obiezioni <lb></lb>contro il moto parabolico dei proietti 565, giusto giudizio de&#039;meriti di lui nella Scienza, dato <lb></lb>dallo stesso Galileo 583, 84. </s></p><p type="main">

<s><emph type="bold"></emph>Bar<gap></gap>centro,<emph.end type="bold"></emph.end> sua definizione e descrizione 102, come si riscontri la sua teoria con quella della com­<lb></lb>posizione delle forze parallele 175. </s></p><p type="main">

<s><emph type="bold"></emph>Benedetti Giovan Batista<emph.end type="bold"></emph.end> instauratore della Scienza del moto 97, suoi principali teoremi dimostrati <lb></lb>nel libro <emph type="italics"></emph>De mechanicis<emph.end type="italics"></emph.end> 98, conferma la verità della regola osservata da Leonardo e dal Car­<lb></lb>dano, per computare i momenti 183, insegna a misurar quanta parte si elida delle forze nel ti­<lb></lb>rare obliquamente 184, corregge gli errori aristotelici nella questione relativa all&#039;equilibrio delle <lb></lb>bilancie 193, sue proposizioni intorno ai gravi cadenti 274, primo a conoscere la vera causa acce­<lb></lb>leratrice dei moti 293. </s></p><pb xlink:href="020/01/2369.jpg" pagenum="612"></pb><p type="main">

<s><emph type="bold"></emph>Beriguardi Claudio,<emph.end type="bold"></emph.end> suoi teoremi di Meccanica 33, concorre con Galileo nello stabilire i fondamenti <lb></lb>della Dinamica 375. </s></p><p type="main">

<s><emph type="bold"></emph>Bernoulli Giacomo<emph.end type="bold"></emph.end> primo a scoprire il sofisma del Vanni intorno alle pressioni di un grave sopra <lb></lb>due piani inclinati 259, 60, sua ipotesi delle resistenze de&#039;solidi allo spezzarsi 503, 4. </s></p><p type="main">

<s><emph type="bold"></emph>Beugrand Giovanni,<emph.end type="bold"></emph.end> sua dimostrazione del variar peso i gravi, nell&#039;avvicinarsi o nel dilungarsi dal <lb></lb>centro terrestre 176. </s></p><p type="main">

<s><emph type="bold"></emph>Bilancia,<emph.end type="bold"></emph.end> questione intorno all&#039;equilibrio di lei promossa da Aristotile 190, 91, come fosse finalmente <lb></lb>risoluta 208. </s></p><p type="main">

<s><emph type="bold"></emph>Bilancia idrostatica<emph.end type="bold"></emph.end> come servisse a Leonardo da Vinci, per trovar la legge dei momenti dei gravi <lb></lb>sopra i piani inclinati 40. </s></p><p type="main">

<s><emph type="bold"></emph>Borelli Gian Alfonso,<emph.end type="bold"></emph.end> suo teorema concernente la forza necessaria a sollevare un braccio di leva <lb></lb>inclinato in sito orizontale 61. </s></p><p type="main">

<s><emph type="bold"></emph>Blondel Francesco<emph.end type="bold"></emph.end> medita di scrivere un libro <emph type="italics"></emph>De resistentia solidorum<emph.end type="italics"></emph.end> 454. </s></p><p type="main">

<s><emph type="bold"></emph>Cabeo Niccolò,<emph.end type="bold"></emph.end> suoi errori intorno ai gravi cadenti come fossero notati dal Riccioli 281, sue ingiuste <lb></lb>censure delle dottrine galileiane intorno ai gravi cadenti 317, manda al Baliani la misura del <lb></lb>pendolo a secondi 413, conosce falsa la IX proposizione dell&#039;ottavo libro di Pappo, ma non rie­<lb></lb>sce a sostituirvi la vera 238. </s></p><p type="main">

<s><emph type="bold"></emph>Cardano Girolamo,<emph.end type="bold"></emph.end> sua Scienza del moto 94, 95, non risolve propriamente la questione aristotelica <lb></lb>della Bilancia di braccia uguali 197, suo falso teorema del piano mclinato 232, sue osservazioni <lb></lb>intorno al moto dei pendoli 386, suo falso teorema che il moto composto sia più tardo dei com­<lb></lb>ponenti 520. </s></p><p type="main">

<s><emph type="bold"></emph>Cartesio Renato,<emph.end type="bold"></emph.end> suo principio statico riscontra con quello di Giordano Nemorario 24, per quali ra­<lb></lb>gioni lo creda da preferire a quello di Galileo 159, 60, dimostra, a modo del Torricelli, il propor­<lb></lb>zionato variar dei pesi, secondo la loro relativa positura rispetto al centro terrestre 205, esperienze <lb></lb>da lui citate per confermar che i corpi, dilungandosi dal centro della Terra, divengono più leg­<lb></lb>geri 207, accusa Guidubaldo, per aver ridotta la troclea al vette 222, segue, nella meccanica del <lb></lb>cuneo, gl&#039;insegnamenti di Guidubaldo 229, dimostra falsa la proposizione di Galileo che final­<lb></lb>mente i gravi cadenti si riducano all&#039;equabilità del moto 287, dice di aver egli prima scoperte <lb></lb>le leggi dei gravi cadenti 315, 16, indovina l&#039;intenzione, ch&#039;ebbe Galileo nello scrivere il trattato <lb></lb>dei moti locali 383. </s></p><p type="main">

<s><emph type="bold"></emph>Casati Paolo<emph.end type="bold"></emph.end> risolve il problema dei pesi pendenti da funi 258, propone e interpetra la regola del <lb></lb>parallelogrammo delle forze 262. </s></p><p type="main">

<s><emph type="bold"></emph>Cavalieri Bonaventura,<emph.end type="bold"></emph.end> sua Geometria degl&#039;indivisibili com&#039;avesse origine dalla stereometria del <lb></lb>Keplero 119, manda, nel 1622, a Galileo le sue prime proposizioni geometriche dimostrate col <lb></lb>metodo degli indivisibili 120, lungamente ne attende l&#039;autorevole giudizio 121, nel 1627 ha com­<lb></lb>piuto, nella Geometria degl&#039;indivisibili, un intero trattato diviso in sette libri <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> risponde a un <lb></lb>argomento, col quale Galileo pretendeva di dimostrare che il metodo degl&#039;indivisibili conduce <lb></lb>all&#039;assurdo 123, scrive al Torricelli di alcune difficoltà fatte contro la Geometria degl&#039;indivisi­<lb></lb>bili 128, lo invita a rispondere, piuttosto che con le parole, coi fatti 129 e pensa al miglior modo <lb></lb>di rispondere egli stesso 130, quale avesse occasion di scrivere le sue <emph type="italics"></emph>Esercitazioni geometri­<lb></lb>che<emph.end type="italics"></emph.end> 134, avvisa Galileo di aver ritrovate le proporzioni stereometriche tra il fuso parabolico e il <lb></lb>cilindro circoscritto 136, conclude la dimostrazione della regola centrobrarica da un teorema di <lb></lb>Giann&#039;Antonio Rocca 137, dimostra gl&#039;incrementi del moto nei liberi cadenti con gl&#039;incrementi <lb></lb>delle cinconferenze, che si diffondono equabilmente dal centro 308, dà la prima pubblica dimo­<lb></lb>strazione che i momenti nella bilancia stanno in ragion composta dei pesi e delle distanze 488, <lb></lb>come dimostri esser parabolica la linea descritta dai proietti 426, come inserisse nello <emph type="italics"></emph>Specchio <lb></lb>ustorio<emph.end type="italics"></emph.end> la nuova proposizione 527, come si studiasse di scusar Galileo, che diceva essere la linea <lb></lb>de&#039;proietti, non parabolica ma circolare 528, com&#039;essendo usurpato da Galileo, se ne confessasse <lb></lb>egli stesso l&#039;usurpatore 530, e come chieda di far del fallo, a richiesta dell&#039;offensore, la peni­<lb></lb>tenza 533. </s></p><p type="main">

<s><emph type="bold"></emph>Centrobrarica,<emph.end type="bold"></emph.end> in che modo se ne rinfrescasse la notizia in Italia 148. </s></p><p type="main">

<s><emph type="bold"></emph>Centro di gravità,<emph.end type="bold"></emph.end> difficoltà del determinarlo in una sfera, avuto riguardo alla distanza di lei dal <lb></lb>centro terrestre 198. </s></p><p type="main">

<s><emph type="bold"></emph>Circolo,<emph.end type="bold"></emph.end> sua dignità meccanica, secondo Aristotile 9, si genera, secondo il Filosofo, dalla composizione <lb></lb>di due moti 11. </s></p><p type="main">

<s><emph type="bold"></emph>Coesiene (forxa di)<emph.end type="bold"></emph.end> definita da Galileo 438. </s></p><p type="main">

<s><emph type="bold"></emph>Commsadine Federige,<emph.end type="bold"></emph.end> qual fosse l&#039;occasione e il fine del suo trattato <emph type="italics"></emph>De centro gravitatis<emph.end type="italics"></emph.end> 108, sua <lb></lb>vera teorica dei momenti 181. </s></p><p type="main">

<s><emph type="bold"></emph>Corda<emph.end type="bold"></emph.end> impossibile a esser tesa in linea retta orizontale da qualunque peso la tiri, secondo la dimo­<lb></lb>strazione di Galileo 63. </s></p><pb xlink:href="020/01/2370.jpg" pagenum="613"></pb><p type="main">

<s><emph type="bold"></emph>Corpi,<emph.end type="bold"></emph.end> se più pesino avvicinati o dilungati dal centro terrestre 207, varie opinioni dei Matematici <lb></lb>intorno a questo punto 208. </s></p><p type="main">

<s><emph type="bold"></emph>Cuneo,<emph.end type="bold"></emph.end> proposizioni meccaniche di lui come dimostrate da Aristotile, da Guidubaldo e dal Bene­<lb></lb>detti 228, 29. </s></p><p type="main">

<s><emph type="bold"></emph>Dialoghi<emph.end type="bold"></emph.end> delle due Scienze nuove: storia della loro pubblicazione 596. </s></p><p type="main">

<s><emph type="bold"></emph>Dialogo<emph.end type="bold"></emph.end> primo delle Scienze nuove serve come di larga prefazione ai trattati delle resistenze, e dei <lb></lb>moti accelerati 592-96. </s></p><p type="main">

<s><emph type="bold"></emph>Equiponderanze,<emph.end type="bold"></emph.end> loro principio come dimostrato dallo Stevino 168, come, a imitazione di lui, dimo­<lb></lb>strato da Galileo 170, come dall&#039;Huyghens 171, 72, come dal Newton 172, 73, come a quella di­<lb></lb>mostrazione s&#039;applicassero i moti composti 173. </s></p><p type="main">

<s><emph type="bold"></emph>Esperienza,<emph.end type="bold"></emph.end> sentenza di Leonardo da Vinci intorno alle verità rivelate da lei 31. </s></p><p type="main">

<s><emph type="bold"></emph>Euclide,<emph.end type="bold"></emph.end> suo trattato <emph type="italics"></emph>De panderibus<emph.end type="italics"></emph.end> 13. </s></p><p type="main">

<s><emph type="bold"></emph>Fontana Mariano<emph.end type="bold"></emph.end> difende la verità della XI proposizion galileiana delle resistenze contro le accuse <lb></lb>del De-la-Hire e del Grandi 481. </s></p><p type="main">

<s><emph type="bold"></emph>Forze parallele,<emph.end type="bold"></emph.end> loro composizione 17. </s></p><p type="main">

<s><emph type="bold"></emph>Frisi Paolo<emph.end type="bold"></emph.end> dice non esser conforme al vero l&#039;asserto degli Accademici del Cimento che cioè Galileo <lb></lb>avvertisse le vibrazioni maggiori del pendolo essere più diuturne delle minori 400. </s></p><p type="main">

<s><emph type="bold"></emph><gap></gap> Galileo<emph.end type="bold"></emph.end> attende giovanissimo a trattare dei centri di gravità, per supplire ai difetti del Com­<lb></lb>mandino 109, difficoltà trovate dai primi esaminatori di questo trattato 110, si propone di trattare <lb></lb>degli indivisibili 121, oppone difficoltà alle dottrine degli indivisibili del Cavalieri, prendendo ar­<lb></lb>gomento dal teorema così detto della <emph type="italics"></emph>Scodella<emph.end type="italics"></emph.end> 122, diventa nemico degli indivisibili 124, suo teo­<lb></lb>rema de&#039;momenti dei gravi sopra i piani inclinati, concluso dai principii statici della Libbra 238 <lb></lb>osservazioni intorno a ciò che si dice da lui dei gravi cadenti da grandi altezze 276, come scopre <lb></lb>e dimostra la legge che ogni particella materiale ha una velocità propria, determinata dalla Na­<lb></lb>tura 277, prima partecipò de&#039;comuni errori, poi trovò la vera legge dei moti accelerati, appli­<lb></lb>cando ai teoremi di Archimede i principii del Benedetti 295, come dimostrasse matematicamente <lb></lb>la detta legge 305, com&#039;applicasse gl&#039;indivisibili a questa dimostrazione 306, crede a principio <lb></lb>che i tempi delle vibrazioni dei pendoli fossero come le semplici lunghezze dei fili 408, come e <lb></lb>quando scoprisse che i tempi stanno come le radici delle dette lunghezze 409, descrive al Ba­<lb></lb>liani il suo misuratore del tempo 411, sue prime proposizioni delle resistenze dei solidi 438, cu­<lb></lb>riose applicazioni fatte da lui de&#039;teoremi delle resistenze dei solidi 440, come spieghi perchè vanno <lb></lb>tanto più in linea retta i proietti, quanto son meno oblique le direzioni dei tiri 514, scopre, spe­<lb></lb>rimentando coi getti di acqua, che i tiri livellati, con qualunque impeto sian fatti, giungono al <lb></lb>piano dell&#039;orizzonte nel medesimo tempo 518, sperimenta, per farne l&#039;applicazione ai proietti, che <lb></lb>una pietra, lasciata cader lungo l&#039;albero di una nave, gli batte al piede, o la nave stessa si <lb></lb>muova o stiasi in quiete 521, come credesse a principio vera l&#039;opinion dei Tartaglia, che cioè la <lb></lb>parte curva della via dei proietti sia circolare 524, scrive una lettera a Cesare Marsili, per la­<lb></lb>mentarsi che il Cavalieri avesse pubblicata la dimostrazione della linca parabolica descritta dai <lb></lb>proietti 529, si scusa di un suo errore intorno ai proietti, dicendo di aver inteso di parlare da <lb></lb>scherzo 531. </s></p><p type="main">

<s><emph type="bold"></emph>Gassendo Pietro,<emph.end type="bold"></emph.end> sue esperienze istituite per confermare le leggi galileiane dei moti accelerati 323. </s></p><p type="main">

<s><emph type="bold"></emph>Gerli Carlo Giuseppe<emph.end type="bold"></emph.end> pubblica i disegni a tocco in penna di Leonardo da Vinci 27. </s></p><p type="main">

<s><emph type="bold"></emph>Giordano Vitale,<emph.end type="bold"></emph.end> suo principio dei momenti composti 262. </s></p><p type="main">

<s><emph type="bold"></emph>Gradi Stefano<emph.end type="bold"></emph.end> confessa che nel ragionamento fatto da Galileo, per dimostrar che una circonferenza <lb></lb>è uguale a un punto, si conterrebbe un paralogismo, se Galileo stesso non intendesse di parlar <lb></lb>da poeta 126. </s></p><p type="main">

<s><emph type="bold"></emph>Grandi Guido,<emph.end type="bold"></emph.end> dimostra contro L. A. </s>

<s>Porzio che la direzione del fulcro, su cui si appoggia un grave <lb></lb>in un piano inclinato, s&#039;ha da prendere nella direzione del perpendicolo, condotto dal centro di <lb></lb>gravità del peso sopra lo stesso piano 265, accusa il Marchetti di essersi appropriata la dimo­<lb></lb>strazione, che i momenti hanno ragion composta delle distanze e dei pesi 485. </s></p><p type="main">

<s><emph type="bold"></emph>Gravi cadenti,<emph.end type="bold"></emph.end> loro uguali velocità nel vuoto sperimentate dal Desaguliers, dal S&#039;Gravesande e dal <lb></lb>Wolf 288. </s></p><p type="main">

<s><emph type="bold"></emph>Gravità<emph.end type="bold"></emph.end> contrasta ne&#039;proietti con la virtù impressa 162. </s></p><p type="main">

<s><emph type="bold"></emph><gap></gap> Mario<emph.end type="bold"></emph.end> riferisce una proposizione di Galileo relativa ai proietti 523. </s></p><p type="main">

<s><emph type="bold"></emph>G<gap></gap> P<gap></gap>lo,<emph.end type="bold"></emph.end> processo della sua invenzione centrobrarica 117. </s></p><pb xlink:href="020/01/2371.jpg" pagenum="614"></pb><p type="main">

<s><emph type="bold"></emph>Herigonio Pietro,<emph.end type="bold"></emph.end> dimostrando la legge dei momenti dei gravi ne&#039;piani inclinati, vi comprende in­<lb></lb>sieme il teorema del Tartaglia, e la esperienza dello Stevino 236. </s></p><p type="main">

<s><emph type="bold"></emph>Hire (de la) Filippo<emph.end type="bold"></emph.end> censura una proposizione di Galileo, relativa alle resistenze, e il Grandi ne ap­<lb></lb>prova le censure 478. </s></p><p type="main">

<s><emph type="bold"></emph>Hosté Paolo,<emph.end type="bold"></emph.end> sua proposizione della resistenza dei solidi male invocata dal Grandi, per confermare <lb></lb>la falsità della XI galileiana 480. </s></p><p type="main">

<s><emph type="bold"></emph>Huyghens Cristiano<emph.end type="bold"></emph.end> applica i moti composti a dimostrar la legge galileiana dell&#039;acceleramento dei <lb></lb>gravi 326, dimostra, altrimenti da Galileo, i teoremi fondamentali dei moti accelerati <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> dimo­<lb></lb>stra matematicamente che le vibrazioni del pendolo circolare non possono essere isocrone 405, <lb></lb>credeva parabolica la curva catenaria, per ragioni similissime a quelle di Galileo 496. </s></p><p type="main">

<s><emph type="bold"></emph>Inerzia (forza d&#039;),<emph.end type="bold"></emph.end> sua denominazione, e suo concetto definito da Galileo, dall&#039;Aggiunti e dal Carte­<lb></lb>sio 302-4, benchè fosse ben chiaro ai matematici del secolo XVI <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> come ne facessero l&#039;applica­<lb></lb>zione alla Meccanica il Cardano, lo Scaligero e il Benedetti 511. </s></p><p type="main">

<s><emph type="bold"></emph>Isocronismo<emph.end type="bold"></emph.end> dei pendoli dimostrato da Giovan Marco Marci 390, sperimentato dal Riccioli 391, cre­<lb></lb>duto assolutamente tale dai Fisici nella prima metà del XVII secolo 392, scoperto non vero dal <lb></lb>Wendelin e dal Cabeo 395. </s></p><p type="main">

<s><emph type="bold"></emph>Kepler Giovanni,<emph.end type="bold"></emph.end> sua stereometria nuova 115. </s></p><p type="main">

<s><emph type="bold"></emph>Leibniz Gotifredo Guglielmo,<emph.end type="bold"></emph.end> suo errore nel determinar le pressioni di un grave sopra due piani <lb></lb>inclinati 257, sua regola <emph type="italics"></emph>degli alternativi<emph.end type="italics"></emph.end> applicata alla Meccanica 259, dimostra che la resistenza <lb></lb>respettiva dei solidi allo spezzarsi non è la metà, come diceva Galileo, ma la terza parte del­<lb></lb>l&#039;assoluta 501. </s></p><p type="main">

<s><emph type="bold"></emph>Leva,<emph.end type="bold"></emph.end> esemplare, a cui s&#039;informano le altre macchine 215, vari generi di questo strumento 217. </s></p><p type="main">

<s><emph type="bold"></emph>Libbra,<emph.end type="bold"></emph.end> suo fondamento meccanico, secondo Aristotile 11, e secondo Archimede 15. </s></p><p type="main">

<s><emph type="bold"></emph>Libramenti<emph.end type="bold"></emph.end> dei liquidi ne&#039;sifoni sperimentati dagli Accademici del Cimento 399. </s></p><p type="main">

<s><emph type="bold"></emph>Libri Guglielmo<emph.end type="bold"></emph.end> si propone di pubblicare i manoscritti di Leonardo da Vinci 30, dà occasione a una <lb></lb>questione storica relativa al modo di ritrovare il centro della gravità nella piramide 104. </s></p><p type="main">

<s><emph type="bold"></emph>Logaritmi,<emph.end type="bold"></emph.end> come Galileo confessasse al Cavalieri di non intenderli 563. </s></p><p type="main">

<s><emph type="bold"></emph>Macchine,<emph.end type="bold"></emph.end> loro efficacia nel sostegno 213, in che propriamente consista la loro potenza 216. </s></p><p type="main">

<s><emph type="bold"></emph>Magalotti Lorenzo<emph.end type="bold"></emph.end> risolve un problema delle resistenze dei solidi, applicandovi un teorema annun­<lb></lb>ziato dal Viviani 465. </s></p><p type="main">

<s><emph type="bold"></emph>Manoscritti<emph.end type="bold"></emph.end> di Leonardo da Vinci: storia delle loro vicende 26. </s></p><p type="main">

<s><emph type="bold"></emph>Marchetti Alessandro<emph.end type="bold"></emph.end> crede di essere stato il primo a dimostrar che i momenti stanno in ragion <lb></lb>composta delle distanze e dei pesi 246, suo trattato dei Fondamenti della Scienza universale del <lb></lb>moto 247, occasione ch&#039;egli ebbe di scrivere il trattato <emph type="italics"></emph>De reristentia solidorum<emph.end type="italics"></emph.end> 454, è pregato <lb></lb>dal Viviani a dilazionar la pubblicazione del manoscritto dello stesso trattato 456, dimostra l&#039;ugual <lb></lb>resistenza del solido parabolico, considerato senza peso, più speditamente di Galileo 458, risponde <lb></lb>alle accuse mossegli contro da Guido Grandi 464, si decide esser vera la proposizione di lui, e <lb></lb>falsa la VI galileiana delle resistenze 475. </s></p><p type="main">

<s><emph type="bold"></emph>Marci Giovan Marco<emph.end type="bold"></emph.end> dimostra le leggi delle cadute de&#039;gravi contemporaneamente con Galileo 311, <lb></lb>risolve il problema del pendolo a secondi 417, istituisce la scienza del moto nel medesimo tempo, <lb></lb>e indipendentemente da Galileo 582. </s></p><p type="main">

<s><emph type="bold"></emph>Mariotte Edmondo,<emph.end type="bold"></emph.end> suo principio di statica generale sostituito a quello di Archimede e di Galileo 171, <lb></lb>dimostra, altrimenti da Galileo, il brachistocronismo degli archi rispetto alle corde 379, propone, <lb></lb>tra le resistenze assolute e le respettive, una proporzione diversa da quella di Galileo 498. </s></p><p type="main">

<s><emph type="bold"></emph>Martello,<emph.end type="bold"></emph.end> qual&#039;effetto faccia la maggiore o minor lunghezza del manico 57. </s></p><p type="main">

<s><emph type="bold"></emph>Maurolico Francesco,<emph.end type="bold"></emph.end> storia del suo trattato manoscritto intitolato <emph type="italics"></emph>Monumenta Archimedis<emph.end type="italics"></emph.end> 87. </s></p><p type="main">

<s><emph type="bold"></emph>Mazzoni Jacopo<emph.end type="bold"></emph.end> inizia Galileo alla Scienza del moto 275. </s></p><p type="main">

<s><emph type="bold"></emph>Meccanica,<emph.end type="bold"></emph.end> come Aristotile la definisce 9. </s></p><p type="main">

<s><emph type="bold"></emph>Mechaniques (les),<emph.end type="bold"></emph.end> trattatello del Cartesio, che il Viviani ricopiò dall&#039;originale francese 200. </s></p><p type="main">

<s><emph type="bold"></emph>Monte (del) Guidubaldo,<emph.end type="bold"></emph.end> come nel suo <emph type="italics"></emph>Mechanicorum liber<emph.end type="italics"></emph.end> promovesse la scienza 96, come dimo­<lb></lb>stri il modo di computare i momenti contro il Cardano 182, come corregge l&#039;errore aristotelico <lb></lb>rispetto all&#039;equilibrio instabile delle Bilance 291, come dimostri che, nello scendere, il braccio <lb></lb>della Bilancia si aggrava 202, sua fallacia nel determinare le condizioni dell&#039;equilibrio della <lb></lb>leva 218, suoi modi di descrivere le parabole, e altre novità di lui appropriatesi da Galileo 444, <lb></lb>sue esperienze intorno alle traiettorie paraboliche 515, descrive e rende la ragion della corda, <lb></lb>che tocca fa moverne un&#039;altra quieta ma tesa all&#039;unisono 594. </s></p><pb xlink:href="020/01/2372.jpg" pagenum="615"></pb><p type="main">

<s><emph type="bold"></emph>Momenti<emph.end type="bold"></emph.end> stanno, secondo la dimostrazion del Maurolico, in ragion composta dei pesi e degli spazi 86, <lb></lb>loro teorica nel Maurolico difettosa 180, come definiti da Galileo, e da lui stesso applicati alla <lb></lb>Statica 184. </s></p><p type="main">

<s><emph type="bold"></emph>Momento<emph.end type="bold"></emph.end> come definito dal Maurolico 86. </s></p><p type="main">

<s><emph type="bold"></emph>Montanari Gemiuiano,<emph.end type="bold"></emph.end> sua teoria dell&#039;equilibrio delle Bilance di braccia uguali 208, come risponda <lb></lb>in proposito alle contradizioni di Donato Rossetti 210. </s></p><p type="main">

<s><emph type="bold"></emph>Moti misti<emph.end type="bold"></emph.end> non usati da Galileo, nè dai promotori di lui, per determinar gl&#039;impeti nelle parabole dei <lb></lb>proietti 540. </s></p><p type="main">

<s><emph type="bold"></emph>Moto<emph.end type="bold"></emph.end> circolare non è, secondo Galileo, nè naturale nè violento 513. </s></p><p type="main">

<s><emph type="bold"></emph>Musschenbroeck Pietro,<emph.end type="bold"></emph.end> sue esperienze e conclusioni intorno alla proporzione fra le resistenze asso­<lb></lb>lute e respettive dei solidi 504. </s></p><p type="main">

<s><emph type="bold"></emph>Nardi Antonio,<emph.end type="bold"></emph.end> sue Ricercate geometriche 128, suo fecondo principio della trasformazione delle <lb></lb>figure 139. </s></p><p type="main">

<s><emph type="bold"></emph>Nemorario Giordano,<emph.end type="bold"></emph.end> sue XIII proposizioni <emph type="italics"></emph>De ponderibus<emph.end type="italics"></emph.end> 21, suo principio statico 22, suoi postu­<lb></lb>lati 23, come si concluda da essi postulati la legge statica del Vette 24, come promove un teo­<lb></lb>rema statico di Euclide 25, propone, prima del Tartaglia, una questione sulle Bilance, preter­<lb></lb>messa da Aristotile 195 </s></p><p type="main">

<s><emph type="bold"></emph>Newton Isacco,<emph.end type="bold"></emph.end> sue esperienze sulle cadute dei gravi 287. </s></p><p type="main">

<s><emph type="bold"></emph>Pappo Alessandrino,<emph.end type="bold"></emph.end> principio meccanico da lui professato 19, suo teorema annunziato nella prefazione <lb></lb>al libro VII delle <emph type="italics"></emph>Matematiche collezioni<emph.end type="italics"></emph.end> 113, come si possa interpetrare l&#039;oscuro significato 114. </s></p><p type="main">

<s><emph type="bold"></emph>Parabola<emph.end type="bold"></emph.end> descritta dai proietti, secendo il Cardano 512. </s></p><p type="main">

<s><emph type="bold"></emph>Parabolico (solido)<emph.end type="bold"></emph.end> dimostrato da Galileo essere di ugual resistenza in ogni sua parte 442. </s></p><p type="main">

<s><emph type="bold"></emph>Parallele (forze),<emph.end type="bold"></emph.end> invenzione del loro centro applicata a dimostrar la legge delle equiponderanze 174. </s></p><p type="main">

<s><emph type="bold"></emph>Pendoli<emph.end type="bold"></emph.end> usati da Galileo, dal Baliani e dal Newton a dimostrare che le velocità sono uguali in qua­<lb></lb>lunque specie di corpi cadenti 284, obiezioni di Guidubaldo contro il loro isocronismo 387, Gali­<lb></lb>leo applica agli archi l&#039;isocronismo dimostrato per le sole corde 389, di ugual lunghezza e diffe­<lb></lb>rente peso, il più grave fa maggior numero di vibrazioni nel medesimo tempo 396, ragione delle <lb></lb>loro simpatie nel vibrare, data dal Viviani, dietro le dottrine di Galileo 398, misurator dei se­<lb></lb>condi quanto il Cabeo lo trovasse lungo 415, quanto il Castelli e il Mersenno 417, quanto il Ric­<lb></lb>cioli 420. </s></p><p type="main">

<s><emph type="bold"></emph>Percossa,<emph.end type="bold"></emph.end> proporzione degli effetti di lei nelle varie direzioni 54, opera secondo la lunghezza del <lb></lb>percuziente 56. </s></p><p type="main">

<s><emph type="bold"></emph>Peritrochio (asse in),<emph.end type="bold"></emph.end> condizioni dell&#039;equilibrio in questa macchina dimostrate da Guidubaldo e da <lb></lb>Galileo 219. </s></p><p type="main">

<s><emph type="bold"></emph>Plano inclinato<emph.end type="bold"></emph.end> esemplare, a cui s&#039;informano le altre macchine 215, usato da Galileo a sperimentar <lb></lb>l&#039;accelerazione del moto nei gravi cadenti 297. </s></p><p type="main">

<s><emph type="bold"></emph>Piramide,<emph.end type="bold"></emph.end> differenza tra il metodo antico e il moderno in ricercarne il centro di gravità 105, come <lb></lb>insegni il Maurolico a ritrovare esso centro 107. </s></p><p type="main">

<s><emph type="bold"></emph>Poleni Giovanni,<emph.end type="bold"></emph.end> sue esperienze sulla resistenza dei solidi 504. </s></p><p type="main">

<s><emph type="bold"></emph>Porzio Luc&#039;Antonio,<emph.end type="bold"></emph.end> sue opposizioni contro la comune teoria dei piani inclinati 263. </s></p><p type="main">

<s><emph type="bold"></emph>Proietti,<emph.end type="bold"></emph.end> errori detti dal Tartaglia intorno ad essi 507, come il Cardano e lo Scaligero fossero i primi <lb></lb>a insegnar che proseguono il loro moto, per la virtù rimastavi impressa 511, vanno, secondo il Car­<lb></lb>dano, per un moto impresso, che in principio è violento, in fine naturale, e nel mezzo compo­<lb></lb>sto dell&#039;uno e dell&#039;altro 512. </s></p><p type="main">

<s><emph type="bold"></emph>Proposizioni<emph.end type="bold"></emph.end> comprendenti il trattato galileiano delle resistenze ordinatamente disposte e formn­<lb></lb>late 452. </s></p><p type="main">

<s><emph type="bold"></emph>Renieri Vincenzo<emph.end type="bold"></emph.end> scopre, per esperienze fatte sul campanile di Pisa, alcuni errori detti da N. </s>

<s>Cabeo <lb></lb>intorno alle cadute dei gravi 279. </s></p><p type="main">

<s><emph type="bold"></emph>Riccioli Giovan Ratista<emph.end type="bold"></emph.end> sperimenta non esser vero che due corpi, di ugual materia e forma, ma <lb></lb>differenti di peso, scendano da uguali altezze nel medesimo tempo 282, ripensa alle leggi gali­<lb></lb>leiane dei moti accelerati 298, è il primo che confermi sperimentalmente la detta legge 324, suoi <lb></lb>studi per trovar la precisa lunghezza del pendolo a secondi 418. </s></p><p type="main">

<s><emph type="bold"></emph>Rocca Giovann&#039;Antonio,<emph.end type="bold"></emph.end> suo Lemma meccanico pubblicato dal Torricelli 136, dimostra le ragioni <lb></lb>stereometriche del fuso parabolico al cilindro circoscritto, per via degl&#039;indivisibili 137. </s></p><p type="main">

<s><emph type="bold"></emph>Rossetti Donato,<emph.end type="bold"></emph.end> come dimostri le ragioni dell&#039;equilibrio nelle Bilance di braccia uguali 209. </s></p><p type="main">

<s><emph type="bold"></emph>Sfera<emph.end type="bold"></emph.end> si muove nel piano orizontale senza sforzo 38. </s></p><p type="main">

<s><emph type="bold"></emph>Squadra dei bombardieri<emph.end type="bold"></emph.end> descritta dal Tartaglia 507. </s></p><pb xlink:href="020/01/2373.jpg" pagenum="616"></pb><p type="main">

<s><emph type="bold"></emph>Stevino Simeone,<emph.end type="bold"></emph.end> sua <emph type="italics"></emph>Spartostatica<emph.end type="italics"></emph.end> e sua <emph type="italics"></emph>Trocheologia<emph.end type="italics"></emph.end> trattate col principio della composizion delle <lb></lb>forze 226, conferma con una bella esperienza il Teorema del Tartaglia dei momenti dei gravi <lb></lb>sopra i piani inclinati 235. </s></p><p type="main">

<s><emph type="bold"></emph>Supposto<emph.end type="bold"></emph.end> principio, su cui aveva fondata la sua Meccanica Galileo 335. </s></p><p type="main">

<s><emph type="bold"></emph>Tardità,<emph.end type="bold"></emph.end> come il mobile, partendosi dalla quiete, passi per tutti i gradi di lei 160. </s></p><p type="main">

<s><emph type="bold"></emph>Tariffe,<emph.end type="bold"></emph.end> secondo il Viviani, corrispondono coi coefficienti sperimentali da introdursi nelle formule <lb></lb>astratte 498. </s></p><p type="main">

<s><emph type="bold"></emph>Tartaglia Niccolò,<emph.end type="bold"></emph.end> suo opuscolo postumo <emph type="italics"></emph>De pouderositate<emph.end type="italics"></emph.end> 87, principii fondamentali della Statica <lb></lb>da lui dimostrati 88, narra a quali occasioni gli occorresse di applicare i principii della scienza <lb></lb>all&#039;arte dei bombardieri 91, propone un quesito sopra le Bilance, lasciato indietro da Aristo­<lb></lb>tile 194, come risolva un tal quesito coi principii del Nemorario 196, primo a dimostrar che i <lb></lb>pesi, proporzionali alle discese oblique de&#039;lati di un triangolo, si fanno insieme equilibrio 233, <lb></lb>sue proposizioni dimostrative delle cruse e delle leggi, secondo le quali si velocitano i gravi ca­<lb></lb>denti 294, come avesse scoperto, e creduto dimostrare che i tiri a mezza squadra son quelli della <lb></lb>massima volata 507, come scoprisse, prima di Galileo, che due tiri hanno la medesima ampiezza, <lb></lb>quando superano o mancano ugualmente della inelinazion semiretta 509, come spieghi perchè il <lb></lb>tiro faccia maggior colpo in direzione inclinata, che di punto in bianco 510. </s></p><p type="main">

<s><emph type="bold"></emph>Tempo<emph.end type="bold"></emph.end> speso da un grave nello scender per cento braccia perpendicolari, come e quanto ritrovato da <lb></lb>Galileo 299. </s></p><p type="main">

<s><emph type="bold"></emph>Torricelli Evangelista,<emph.end type="bold"></emph.end> come non si curasse a principio d&#039;entrar nella questione della Bilancia di <lb></lb>braccia uguali, rimossa dalla posizione orizzontale 200, a qual proposito entrasse in così fatta <lb></lb>questione <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> come si accorgesse che a trattar le questioni meccaniche, supposte le forze conver­<lb></lb>genti al centro terrestre, fosse primo, non il Beaugrand o il Cartesio, ma Guidubaldo del Monte 201, <lb></lb>come risolvesse la questione della Bilancia di braccia uguali, avuto riguardo che le forze son <lb></lb>convergenti 203, sue singolari idee intorno alla natura dei gravi 207, sostituisce un altro princi­<lb></lb>cipio diverso da quello delle velocità virtuali 240, suo teorema, da cui facile concludevansi le pro­<lb></lb>porzioni, secondo le quali si comparte un peso sopra un piano inclinato 242, come dimostri che, <lb></lb>nella perpendicolare e nell&#039;obliqua, i tempi stanno come le respettive lunghezze 338, suo nuovo <lb></lb>modo di misurare gl&#039;impeti nella semiparabola 548, e nella parabola intera 549, come dimostri <lb></lb>matematicamente, e per più facile via di Galileo, le conclusioni sperimentali del Tartaglia in­<lb></lb>torno ai tiri delle artiglierie 557, risponde a un&#039;obiezione fatta dal Cartesio contro le dottrine ga­<lb></lb>lileiane dei proietti 568. </s></p><p type="main">

<s><emph type="bold"></emph>Tradixio<gap></gap><emph.end type="bold"></emph.end> della Scienza, comuni a Leonardo da Vinci e al Cardano 93. </s></p><p type="main">

<s><emph type="bold"></emph>Triangolo,<emph.end type="bold"></emph.end> suo centro di gravità come dimostrato dal Maurolico 106. </s></p><p type="main">

<s><emph type="bold"></emph>Tro<gap></gap>lea,<emph.end type="bold"></emph.end> errori di Aristotile intorno ad essa 12, condizioni dell&#039;equilibrio in questa macchina dimo­<lb></lb>strate da Guidubaldo del Monte e da Galileo 220. </s></p><p type="main">

<s><emph type="bold"></emph>Valerio Luca,<emph.end type="bold"></emph.end> suo trattato <emph type="italics"></emph>De centro gravitatis solidorum<emph.end type="italics"></emph.end> 109, come risponde, interrogato da Gali­<lb></lb>leo intorno a due supposti principii meccanici 355, 357. </s></p><p type="main">

<s><emph type="bold"></emph>Vanni Gian Francesco,<emph.end type="bold"></emph.end> suo dilemma intorno al teorema del momento dei gravi sopra i piani incli­<lb></lb>nati 250, ne propone la soluzione ai seguaci delle dottrine di Galileo 251. </s></p><p type="main">

<s><emph type="bold"></emph>Vanni Giuseppe<emph.end type="bold"></emph.end> dimostra l&#039;improprietà di un teorema del Torricelli, relativo al momento dei grael <lb></lb>sopra i piani inclinati 248. </s></p><p type="main">

<s><emph type="bold"></emph>Varchi Benedetto,<emph.end type="bold"></emph.end> suo gusto nelle scienze sperimentali 279. </s></p><p type="main">

<s><emph type="bold"></emph>Velocità virtuali,<emph.end type="bold"></emph.end> loro principio applicato da Galileo alle macchine semplici 158, come, dietro il La­<lb></lb>grange, definite dai moderni 163, principio diverso sostituito in luogo di esse dal Torricelli 164. </s></p><p type="main">

<s><emph type="bold"></emph>Venturi Giovan Batista<emph.end type="bold"></emph.end> pubblica un saggio dei manoscritti di Leonardo da Vinci 28, difetti di que­<lb></lb>sta pubblicazione 29. </s></p><p type="main">

<s><emph type="bold"></emph>Vetro<emph.end type="bold"></emph.end> non si rompe a un tratto ma cede prima alla pressione, come dimostrarono gli Accademici <lb></lb>del Cimento 498. </s></p><p type="main">

<s><emph type="bold"></emph>Vinci (da) Leouardo,<emph.end type="bold"></emph.end> meriti scientifici di lui esagerati 31, primo a far uso delle lettere alfabetiche <lb></lb>in algebra, e della linea orizzontale e della crocellina, per significare le quantità negative e vi <lb></lb>positive 32, de&#039;primi a introdur nelle questioni meccaniche il principio della composizion delle <lb></lb>forze 33, prende a sua maestra l&#039;esperienza 34, come descrive il concetto, e definisce la natura <lb></lb>della forza 34, scioglie, prima del Maurolico e del Tartaglia, il problema della pietra, che s&#039;im­<lb></lb>magina giungere al centro della Terra 35, suoi pensieri intorno alle forze centrali, e alle trasfor­<lb></lb>mazioni della superficie terrestre 36, dimostra un teorema meccanico supposto da Galileo 40, <lb></lb>dimostra il teorema del tempo per la perpendicolare e per l&#039;obliqua, in che si riscontra con le <lb></lb>proposizioni di Galileo 41, suo principio della intera restituzione del moto 42, suo teorema in <lb></lb>proposito della scesa di un grave per un arco di cerchio 43, suoi vari esempi d&#039;equilibrio sta-<pb xlink:href="020/01/2374.jpg" pagenum="617"></pb>bile 44, vari casi da lui proposti dell&#039;equilibrio dei pesi nella Bilancia 45, sua dimostrazione della <lb></lb>statica del Vette 47 e delle Taglie 48, applica il principio della composizion delle forze alla Leva <lb></lb>angolare 50, sua dimostrazione dei momenti dei gravi sopra i piani inclinati 52, sperimenta che <lb></lb>nella forza della percossa ha grande efficacia la lunghezza del percuziente 56, dimostra gli effetti <lb></lb>della lunghezza del manico del martello 57, scioglie il problema della tension delle funi 59 e della <lb></lb>corda, impossibile a ridursi in dirittura orizzontale 61, scioglie l&#039;altro problema delle pressioni <lb></lb>fatte da un&#039;asta contro il pavimento e il muro, a cui si appoggia 66, determina il punto, in cui <lb></lb>tocca il piano orizzontale una fune, o liberamente sostenuta ne&#039;due capi a varie altezze, o stirata <lb></lb>da qualche peso che vi s&#039;infili 68, formula le leggi dei moti equabili 71, curiosi effetti della re­<lb></lb>sistenza dell&#039;aria, da lui bene osservati 72, strumento da lui inventato, per conoscer la varia <lb></lb>densità dell&#039;aria atmosferica, e che riducesi a un Baroscopio 73, resultati delle sue esperienze <lb></lb>intorno alle velocità dei gravi cadenti 74, sua falsa legge dei moti accelerati come pensi di di­<lb></lb>mostrarla 76, sua esperienza del moto dell&#039;immobile sopra sito mobile 77, dimostra che la linea <lb></lb>dei cadenti al centro della Terra è un&#039;elice 78, suoi errori intorno alle traiettorie 81, suoi espe­<lb></lb>rimenti e problemi intorno alla resistenza dei solidi a spezzarsi, e delle funi a rompersi 82, sue <lb></lb>leggi sperimentali degli attriti 83, determina il centro di gravità della piramide 104, suoi prin­<lb></lb>cipii statici contro il Pelacane 157, sua vera teorica dei momenti 181, corregge gli errori aristo­<lb></lb>telici, relativi alle questioni delle Bilance 193, sua <emph type="italics"></emph>sperentia delle bilance<emph.end type="italics"></emph.end> 195, dimostra le con­<lb></lb>dizioni dell&#039;equilibrio nella leva di secondo genere 217, sua teoria delle taglie 224, sua bellissima <lb></lb>proposizione sperimentale applicata al trar delle funi nelle Taglie 227, decompone, come il Vi­<lb></lb>viani, il momento totale dei gravi sopra i piani inclinati 243, sua bella esperienza intorno ai pen­<lb></lb>doli 423, sua esperienza per dimostrar che, tocca una corda sonora, ne fa movere un&#039;altra in <lb></lb>quiete, ma tesa all&#039;unisono 594. </s></p><p type="main">

<s><emph type="bold"></emph>Vite,<emph.end type="bold"></emph.end> strumento meccanico ridotto da Guidubaldo al piano inclinato 230. </s></p><p type="main">

<s><emph type="bold"></emph>Viviani Vincenzio<emph.end type="bold"></emph.end> dimostra un teorema, e fa osservazioni importanti intorno al metodo degl&#039;indivi­<lb></lb>sibili 146, chiamato dal cardinale Leopoldo dei Medici a decidere intorno alla questione delle Bi­<lb></lb>lance, insorta fra il Montanari e il Rossetti 210. </s></p><p type="main">

<s><emph type="bold"></emph>Wallis Giovanni,<emph.end type="bold"></emph.end> come stabilisse la statica sulla legge dei momenti 189, conferma il teorema del <lb></lb>Tartaglia della gravità de&#039;pesi nelle varie declività dei piani 237. </s></p><p type="main">

<s><emph type="bold"></emph>Wrz Paolo<emph.end type="bold"></emph.end> primo a riscontrare con l&#039;esperienza i teoremi galileiani della resistenza dei solidi 497. <pb xlink:href="020/01/2375.jpg"></pb></s></p><pb xlink:href="020/01/2376.jpg"></pb><p type="main">

<s>Finito di stampare in Bologna presso la <lb></lb>Libreria Editrice Forni nel Marzo 1970 </s></p><pb xlink:href="020/01/2377.jpg"></pb></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Editor-in-Chief: Harry Woolf<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Willis K. </s>

<s>Shepard Professor of the History of <lb></lb>Science, The Johns Hopkins University<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/2378.jpg"></pb><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph><emph type="italics"></emph>Storia del Metodo <lb></lb>Sperimentale in Italia<emph.end type="italics"></emph.end><emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>by RAFFAELLO CAVERNI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>in Six Volumes<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Volume V<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE, NO. 134<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>NEW YORK LONDON 1972<emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/2379.jpg"></pb><p type="main">

<s><emph type="center"></emph>Reproduced here is the Florence edition of 1891-1900.<emph.end type="center"></emph.end></s></p><figure id="id.020.01.2379.1.jpg" xlink:href="020/01/2379/1.jpg"></figure><p type="main">

<s><emph type="center"></emph>Copyright © 1972 by Johnson Reprint Corporation All rights reserved <lb></lb>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>111 Fifth Avenue, New York, N.Y. 10003, U.S.A.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Shipton Group House, 24/28 Oval Road, London, NW17DD, England<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Printed in Italy<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/2380.jpg"></pb><p type="main">

<s><emph type="center"></emph>DEL METODO SPERIMENTALE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>APPLICATO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>ALLA SCIENZA DEL MOTO DEI GRAVI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>PARTE SECONDA<emph.end type="center"></emph.end><pb xlink:href="020/01/2381.jpg"></pb></s></p><pb xlink:href="020/01/2382.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle correzioni e delle riforme <lb></lb>ne&#039;Dialoghi delle due Scienze nuove<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del supposto principio delle velocità uguali, dopo cadute uguali, e come sortisse a Galileo, al Mi­<lb></lb>chelini e al Baliani finalmento di dimostrarlo. </s>

<s>— II. </s>

<s>Del supposto galileiano confermato per le <lb></lb>dimostrazioni del Torricelli, del Baliani, dell&#039;Huyghens e del Marchetti. </s>

<s>— III. </s>

<s>Di alcune ag­<lb></lb>giunte da farsi ai Dialoghi, dettate da Galileo al Viviani suo ospite in Arcetri. </s>

<s>— IV. Dell&#039;opera <lb></lb>di ampliar le dottrine esposto no&#039;dialoghi Del moto, proseguita dal Viviani, dopo la morte di <lb></lb>Galileo. </s>

<s>— V. </s>

<s>Delle correzioni di aleuni falsi teoremi di Galileo, che fecero finalmente risolvere <lb></lb>il Viviani d&#039;illustrare e di promovere in un&#039;opera a parte le dottrine del suo Maestro. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I quattro dialoghi delle Scienze nuove apparirono in Leyda come in mezzo <lb></lb>all&#039;oceano la luce di un faro, a cui tutti rivolgevano gli occhi o invidi o de­<lb></lb>siderosi degl&#039;insoliti splendori: I desiderii però nei più ardenti non erano pie­<lb></lb>namente sodisfatti, promettendosi sulla fine del libro di trattare certi argo­<lb></lb>menti, e non vedendo all&#039;Autore poi mantenere le solenni promesse. </s>

<s>E perchè <lb></lb>non si vedono pure mantenute oggidì, che dicono gli editori di averci date <lb></lb>le opere galileiane complete, giova esaminare il fatto e scoprirne la ragione. </s></p><p type="main">

<s>Sulla sera di questa quarta Giornata promette il Salviati ai conversevoli <lb></lb>amici che <emph type="italics"></emph>appresso<emph.end type="italics"></emph.end> avrebbe detto a loro delle utilità non piccole, alle quali <lb></lb>servirebbero le catenuzze, oltre a quella di descriver le linee paraboliche; a <lb></lb>mantenere la qual promessa è sollecitato poi da Simplicio, che s&#039;aspettava <lb></lb>inoltre d&#039;intendere le speculazioni fatte dall&#039;Accademico intorno alla forza della <lb></lb>percossa (Alb. </s>

<s>XIII, 266). Ma il Salviati risponde che l&#039;ora era troppo tarda, <lb></lb>e che perciò ad altro tempo più opportuno si differirebbe il congresso (ivi). </s></p><p type="main">

<s>S&#039;avvisavano così dunque gli spettatori che non era finito il dramma, <pb xlink:href="020/01/2383.jpg" pagenum="8"></pb>a cui doveva succedere una quinta scena, la quale Galileo speraya di poter <lb></lb>fare rappresentare in quella medesima veglia, ma per varie difficoltà attra­<lb></lb>versatesi venute meno così belle speranze, si lasciò lo spettacolo senza con­<lb></lb>gedo. </s>

<s>L&#039;Elzevirio infatti, avendo già condotto a termine il dialogo quarto, <lb></lb>aspettava il manoscritto del rimanente, e avuto avviso dall&#039;Autore che non <lb></lb>l&#039;aveva in ordine, e ch&#039;era costretto di lasciar la stampa a quel punto, ri­<lb></lb>spondeva d&#039;Amsterdam, il dì 4 Gennaio 1638: “ In quanto al trattato Della <lb></lb>percossa e Dell&#039;uso della catenella, se V. S. non lo può condurre a perfe­<lb></lb>zione, farò il compimento secondo il suo ordine ” (Alb. </s>

<s>X, 252). Tornava <lb></lb>pochi giorni appresso pur d&#039;Amsterdam a ripetere le medesime cose a Ga­<lb></lb>lileo, soggiungendogli che, dovendosi così lasciar l&#039;opera incompleta, gli man­<lb></lb>dasse a dire in che modo ei dovesse significarlo ai lettori, dopo l&#039;appendice <lb></lb>Dei centri di gravità, “ acciocchè non si commettano errori ” (ivi, pag. </s>

<s>260). <lb></lb>Ma l&#039;Elzevirio non ebbe a ciò risposta, e gli attori taciti, come si diceva, e <lb></lb>senza congedo, si lasciarono sparire dietro la scena. </s></p><p type="main">

<s>Aveva Galileo però la speranza che vi si dovessero ricondur presto, per <lb></lb>cui non curò il mormorio che si farebbe tra gli uditori, curiosi di vedere il <lb></lb>fine dell&#039;opera, così disgustosamente rimasta a mezzo. </s>

<s>Per ridurla infatti a <lb></lb>quel fine desiderato, non bisognando altro all&#039;Autore che d&#039;aggiungervi i di­<lb></lb>scorsi delle catenuzze e della percossa, i materiali già preparati non richie­<lb></lb>devano che il tempo necessario a ricever ordine conveniente, e vaghezza di <lb></lb>forma. </s>

<s>La speranza dunque di tornar presto in scena, e con l&#039;occasione del <lb></lb>compierla correggere e perfezionare quella parte dell&#039;opera già pubblicata, <lb></lb>non sarebbe nell&#039;animo di Galileo stata illusoria, se non fosse venuta a in­<lb></lb>firmarla prima, e poi a dissiparla affatto una grande sventura. </s>

<s>Il di 2 Gen­<lb></lb>naio 1638 faceva, piangendo, scrivere da Arcetri a Elia Diodati: “ Ahimè, <lb></lb>signor mio, il Galileo vostro caro amico e servitore, da un mese in qua è fatto <lb></lb>irreparabilmente del tutto cieco ” (Alb. </s>

<s>VII, 207). </s></p><p type="main">

<s>Il sacerdote fiorentino Marco Ambrogetti, chiamato in casa pochi mesi <lb></lb>prima, perchè traducesse in latino l&#039;opere, che l&#039;Elzevirio aveva promesso di <lb></lb>stampar tutte insieme; serviva al povero cieco di amanuense, ma, non avendo <lb></lb>uso delle Matematiche, non valeva d&#039;alcuno aiuto là dove si trattasse di tor­<lb></lb>nar sopra una dimostrazione, illustrata da qualche figura complessa, e perciò <lb></lb>difficile a ritenersi nell&#039;immaginazione ferma, e come innanzi agli occhi pre­<lb></lb>sente. </s>

<s>Don Clemente Settimii, che spesso, dal collegio di S. Carlo, saliva ad <lb></lb>Arcetri, poco poteva trattenervisi, occupato nel fare scuola, e legato alle disci­<lb></lb>pline dell&#039;ordine religioso; intanto che Galileo si stava nelle tenebre ad incu­<lb></lb>bare lo svolgimento de&#039;suoi luminosi pensieri, aspettando qualche provvida <lb></lb>mano, per mezzo della quale, guidata dall&#039;intelligenza, potesse significarli: <lb></lb>nè la provvidenza indugiò molto a venire. </s></p><p type="main">

<s>Frequentava le scuole di S. Carlo, dove il Settimii era maestro, un gio­<lb></lb>vane sui diciott&#039;anni, a cui era bastato spiegare le prime proposizioni di geo­<lb></lb>metria, perchè si mettesse da sè, senz&#039;altra guida, a dimostrar le rimanenti, <lb></lb>che si leggono nei libri di Euclide. </s>

<s>Quel giovanotto si chiamava Vincenzio <pb xlink:href="020/01/2384.jpg" pagenum="9"></pb>Viviani, che, invaghito ogni giorno più di così nobile studio, impaziente di <lb></lb>vederne l&#039;applicazione alla Scienza dei moti naturali, si dette a leggere i Dia­<lb></lb>loghi, allora allora venuti alla luce. </s>

<s>Desideroso di conoscere un Autore di <lb></lb>tanta fama, il Settimii un giorno lo condusse seco ad Arcetri, dov&#039;ebbe da <lb></lb>Galileo tale accoglienza, che diventarono di lì in poi le visite quasi quoti­<lb></lb>diane. </s>

<s>Proseguendo in tanto l&#039;incominciata lettura; arrivato a quel princi­<lb></lb>pal supposto che le velocità dei mobili, naturalmente discendenti per declivii <lb></lb>d&#039;una medesima elevazione, siano uguali fra loro, dubitò il Viviani, non già <lb></lb>della verità dell&#039;assunto, ma dell&#039;evidenza di poterlo suppor come noto, ond&#039;ei <lb></lb>richiese a voce lo stesso. </s>

<s>Galileo di qualche più chiara confermazione di quel <lb></lb>principio (Scienza universale delle proporz., Firenze 1674, pag. </s>

<s>99). </s></p><p type="main">

<s>La domanda trovò la mente del Vecchio solitario, a cui si rendeva dif­<lb></lb>ficile l&#039;internarsi in più profondi pensieri, tutta occupata nelle tenebre not­<lb></lb>turne, com&#039;egli stesso scrisse un giorno al Baliani, intorno alle prime e più <lb></lb>semplici proposizioni dei moti naturali, riordinandole e disponendole in mi­<lb></lb>glior forma ed evidenza (Lettere per il trecentes, natal., Pisa 1864, pag. </s>

<s>45): <lb></lb>sicchè in queste disposizioni s&#039;abbattè facile Galileo a dimostrar quello, che <lb></lb>il Viviani desiderava. </s>

<s>Di ciò occorrerebbe ora a dire, ma crediam bene di <lb></lb>dover prima risalire alle origini, ed accennar le vicende, che precedettero alla <lb></lb>tanto festeggiata dimostrazione. </s></p><p type="main">

<s>Che l&#039;assunto, posto da Galileo per fondamento alla Dinamica nuova, <lb></lb>fosse quello medesimo, di che si veniva a informare la Statica antica, lo ab­<lb></lb>biamo fatto già notare altra volta: e come il Nemorario e il Tartaglia dice­<lb></lb>vano esser l&#039;impeto uguale nell&#039;ugual rettitudine del discenso; così in egual <lb></lb>forma sentenziava il Salviati che “ due mobili uguali, ancorchè scendenti per <lb></lb>diverse linee, senza veruno impedimento, fanno acquisto d&#039;impeti uguali, tut­<lb></lb>tavolta che l&#039;avvicinamento al centro sia uguale ” (Alb. </s>

<s>I, 28). L&#039;evidenza <lb></lb>dunque del principio era universalmente riconosciuta, e i semplici esempi <lb></lb><figure id="id.020.01.2384.1.jpg" xlink:href="020/01/2384/1.jpg"></figure></s></p><p type="caption">

<s>Figura 1.<lb></lb>de&#039;pendoli, e dei liquidi ne&#039;si­<lb></lb>foni, bastavano per confermarla. </s>

<s><lb></lb>In mezzo a questo pacifico con­<lb></lb>senso dei Matematici sentì piut­<lb></lb>tosto Galileo il bisogno di ri­<lb></lb>spondere ai peripatetici, sottil­<lb></lb>mente scoprendo la fallacia delle <lb></lb>lorp ragioni. </s>

<s>Dicevano essi, co­<lb></lb>me poi il Cabeo e il Cazr, così valorosamente con­<lb></lb>futato dal Gassendo, non esser possibile che, ve­<lb></lb>nendo da C (fig. </s>

<s>1) per la CA lentamente, e per la CB <lb></lb><figure id="id.020.01.2384.2.jpg" xlink:href="020/01/2384/2.jpg"></figure></s></p><p type="caption">

<s>Figura 2.<lb></lb>a precipizio, abbia il mobile <lb></lb>guadagnato in A e in B i me­<lb></lb>desimi gradi di forza. </s>

<s>Quanto <lb></lb>poi al particolare esempio del <lb></lb>pendolo diceva il Cabeo che l&#039;impeto di risalire da B in I (fig. </s>

<s>2) doveva <pb xlink:href="020/01/2385.jpg" pagenum="10"></pb>esser maggiore dell&#039;impeto di risalir dal medesimo punto in G, “ cum acqui­<lb></lb>rat idem mobile impetum ascendendi breviori tempore, et per lineam magis <lb></lb>erectam ” (Comment. </s>

<s>metheor., T. I, Romae 1646, pag. </s>

<s>93). </s></p><p type="main">

<s>Queste sono, nel primo dialogo dei Massimi Sistemi, le medesime diffi­<lb></lb>coltà, che promove Simplicio, a cui il Salviati domanda quand&#039;egli creda di <lb></lb>poter dire che due mobili sono ugualmente veloci. </s>

<s>E rispondendo Simplicio: <lb></lb>quando passano spazi uguali in tempi uguali, gli vien fatto osservare che, a <lb></lb>render la definizione universale, conveniva aggiunger di più che le velocità <lb></lb>sono uguali “ quando gli spazi passati hanno la medesima proporzione dei <lb></lb>tempi, ne&#039;quali son passati ” (Alb. </s>

<s>I, 30). </s></p><p type="main">

<s>In fallacie simili a quelle dell&#039;immaginario Simplicio incorreva in realtà <lb></lb>l&#039;ingegner Bartolotti, ammettendo che in due alvei d&#039;ugual caduta, ma di <lb></lb>varia lunghezza, vadan l&#039;acque nel più lungo con moto molto più lento. </s>

<s>Ga­<lb></lb>lileo affermava invece che i due moti erano uguali, per dichiarar la qual pro­<lb></lb>posizione, che aveva l&#039;apparenza di un paradosso, “ non credo, scriveva a <lb></lb>Raffaello Staccoli, auditore del tribunale delle acque in Toscana, che dall&#039;in­<lb></lb>gegner Bartolotti nè da altri mi sarà negato verissimo essere il pronunziato <lb></lb>di colui, che dirà le velocità di due mobili potersi chiamare eguali, non so­<lb></lb>lamente quando essi mobili passano spazi eguali in tempi eguali, ma quando <lb></lb>ancora li spazi passati in tempi diseguali avessero tra di loro la proporzione <lb></lb>dei tempi de&#039;loro passaggi. </s>

<s>Così per esempio quello, che in quattr&#039;ore an­<lb></lb>dasse da Firenze a Pistoia, non si può chiamare più pigro d&#039;un altro, che <lb></lb>in due ore andassse da Firenze a Prato, tuttavolta che Pistoia fosse lon­<lb></lb>tana venti miglia, e Prato solamente dieci, perchè a ciascheduno tocca sot­<lb></lb>tosopra ad aver fatto cinque miglia per ora, cioè avere in tempi eguali pas­<lb></lb>sati spazi eguali. </s>

<s>E però, qualunque volta due mobili scendano per due canali <lb></lb>disuguali, se passassero in tempi, che avessero la medesima proporzione che <lb></lb>le lunghezze degli stessi canali, si potranno veramente chiamare essere ugual­<lb></lb>mente veloci. </s>

<s>Ora bisogna che quelli, ai quali sin qui è stato ignoto, sap­<lb></lb>piano che due canali, quanto si voglia disuguali in lunghezza, purchè le to­<lb></lb>tali pendenze loro siano uguali, vengono dall&#039;istesso mobile passati in tempi <lb></lb>proporzionali alle loro lunghezze ” (Alb. </s>

<s>VI, 354). </s></p><p type="main">

<s>Si riduce a questa medesima conclusione il discorso nel dialogo dianzi <lb></lb>citato, dove la risoluzion del dubbio si fa dipendere dal teorema, che il tempo <lb></lb>della scesa per CA, nella prima figura qui poco addietro, al tempo della ca­<lb></lb>duta per CB, ha la medesima proporzione che la linea CA alla CB “ ma la di­<lb></lb>mostrazione, dice il Salviati agli amici, aspettatela un&#039;altra volta ” (Alb. </s>

<s>I, 32). </s></p><p type="main">

<s>Di qui traspariscono chiari i pensieri di Galileo, e s&#039;intende perch&#039;egli <lb></lb>allora non si desse nessuna sollecitudine di dimostrar matematicamente un <lb></lb>principio, che scendeva per corollario immediato dalla proposizione VI in cia­<lb></lb>scuno de&#039;due primi trattati manoscritti intorno ai moti locali. </s>

<s>Dimostrato <lb></lb>infatti, come ivi si fa, che i tempi stanno come gli spazi, ne conseguiva ne­<lb></lb>cessariamente che le velocità fossero uguali. </s>

<s>Come unica intenzione perciò <lb></lb>rimaneva quella, che poco fa si diceva, e che si pone in bocca al Salviati, <pb xlink:href="020/01/2386.jpg" pagenum="11"></pb>di rimover cioè l&#039;incredulità dalla mente dei peripatetici (ivi, pag. </s>

<s>32), ar­<lb></lb>gomentandosi di raggiunger l&#039;intento in vari modi. </s>

<s>Uno di questi modi, e dei <lb></lb>non meno efficaci, ha grandissima somiglianza con quello tenuto già con Gui­<lb></lb>dubaldo del Monte, per persuadergli come possa esser vero che una palla <lb></lb>pendula scenda, o per l&#039;arco di un grado o per tutto un quadrante, nel me­<lb></lb>desimo tempo: perchè, come qui le maggiori velocità ragguagliano i tempi, <lb></lb>così là il maggior tempo riduce le velocità ad essere uguali. </s>

<s>Le due propo­<lb></lb>sizioni, soggiungeva lo stesso Galileo “ non hanno seco per avventura più <lb></lb><figure id="id.020.01.2386.1.jpg" xlink:href="020/01/2386/1.jpg"></figure></s></p><p type="caption">

<s>Figura 3.<lb></lb>inverosimilitudine di quello che si abbia <lb></lb>che i triangoli tra le medesime parallele <lb></lb>e le basi uguali sieno sempre uguali, po­<lb></lb>tendone fare un brevissimo, e l&#039;altro <lb></lb>lungo mille miglia ” (Alb. </s>

<s>VI, 22). Come <lb></lb>infatti è verissimo ch&#039;essendo le basi HI, <lb></lb>CH (fig. </s>

<s>3) uguali, i triangoli IAH, HAC <lb></lb>sono uguali; così è vero che in D e in F, <lb></lb>in C e in I le velocità sono uguali, ben­<lb></lb>chè i piani AI, AC siano così differenti, che l&#039;uno possa essere anche mille <lb></lb>miglia più lungo dell&#039;altro. </s></p><p type="main">

<s>Vien confermato insomma, per queste considerazioni, che, ne&#039;primi or­<lb></lb>dinamenti della Dinamica galileiana, si teneva avere i cadenti da uguali al­<lb></lb>tezze uguali velocità come principio tanto secondario, da <lb></lb>sottintendersi <lb></lb>qual ovvia e natural conseguenza della VI proposizione nel primo, e nel secondo <lb></lb>trattato manoscritto dei moti locali. </s>

<s>Come poi fosse quello stesso principio <lb></lb>posto per fondamento all&#039;edifizio dinamico, si disse nel precedente tomo della <lb></lb>nostra Storia, al capitolo VI. </s>

<s>Bandito il Teorema meccanico, da cui si con­<lb></lb>cludeva che nelle scese da uguale altezza i tempi son proporzionali agli spazi, <lb></lb>quel che lasciavasi sottintender per corollario, che cioè, dove sono i tempi <lb></lb>proporzionali agli spazi convien che le velocità vadano uguali, s&#039;esaltò al grado <lb></lb>di proposizion principale, senza pensar di nobilitarla dalla prima sua nativa <lb></lb>umiltà, o di renderla così cospicua, che potesse sostener la nuova dignità, a <lb></lb>cui veniva assunta. </s>

<s>Il proposito era stato già fatto, quando Galileo scrisse in <lb></lb>margine a quel suo foglio 88, raccolto nel secondo tomo della quinta parte <lb></lb>de&#039;suoi Manoscritti: <emph type="italics"></emph>credo utile, si non necessarium, demonstrasse mobile <lb></lb>in B<emph.end type="italics"></emph.end> (nella precedente figura) <emph type="italics"></emph>esse eiusdem momenti quod in C.<emph.end type="italics"></emph.end> Ma o fosse <lb></lb>per dimenticanza, o per qualche difficoltà trovata nella dimostrazione, il prin­<lb></lb>cipio, da cui scende nel terzo dialogo galileiano tutta la scienza del moto, si <lb></lb>rimase nelle umili condizioni di un semplice postulato. </s></p><p type="main">

<s>Quando venne dunque a farsi al solitario Vecchio di Arcetri la domanda <lb></lb>del Viviani, dovè risovvenirsi del proposito scritto, e o sentir pentimento della <lb></lb>dimenticanza, o mortificazione delle difficoltà incontrate nel mandarlo ad ef­<lb></lb>fetto. </s>

<s>In qualunque modo, se l&#039;aveva prima creduta utile, doveva ora parergli <lb></lb>necessaria quella dimostrazione, nella quale felicemente s&#039;incontrò una notte <lb></lb>dell&#039;Ottobre 1638, mentre dolorando vegliava in mezzo a quelle sue tenebre <pb xlink:href="020/01/2387.jpg" pagenum="12"></pb>luminose. </s>

<s>Ritenuto per dimostrato nel suo primo trattato <emph type="italics"></emph>Della scienza mec­<lb></lb>canica<emph.end type="italics"></emph.end> il teorema del Tartaglia, e nelle prime proposizioni del suo dialogo <lb></lb>terzo la legge dei moti accelerati, un semplice triangolo, che si poteva senza <lb></lb>gran difficoltà tenere innanzi rappresentato in immagine, bastò a Galileo per <lb></lb>condurre così il discorso alla desiderata conclusione. </s></p><p type="main">

<s>Sia ABC (fig. </s>

<s>4) quel triangolo, c CB rappresenti il perpendicolo della <lb></lb>caduta, AC la scesa obliqua di un medesimo grave. </s>

<s>Dà il Teorema mecca­<lb></lb><figure id="id.020.01.2387.1.jpg" xlink:href="020/01/2387/1.jpg"></figure></s></p><p type="caption">

<s>Figura 4.<lb></lb>nico che il momento per CB sta al momento per AC re­<lb></lb>ciprocamente, come AC a CB, e omologamente come CB <lb></lb>sta a CD, presa questa linea terza proporzionale dopo AC <lb></lb>e CB. </s>

<s>Ma essere i due momenti omologamente come CB <lb></lb>a CD non vuol dir altro se non che, presa la CB per la <lb></lb>misura dell&#039;impeto in B, la misura dell&#039;impeto in D è <lb></lb>CD: ciò che ci viene signifieato per l&#039;equazione B:D= <lb></lb>BC:CD, chiamati B, D gl&#039;impeti respettivi o i momenti. </s>

<s><lb></lb>Ma essendo per la legge dei cadenti naturali (chiamati A, D gl&#039;impeti in A <lb></lb>e in D) A:D=√AC:√CD=√AC.DC:DC, ed avendosi √AC.DC=BC <lb></lb>per costruzione, sarà dunque A:D=BC:CD, che, confrontata con la pro­<lb></lb>porzion precedente, dà B=A, come dovevasi dimostrare. </s></p><p type="main">

<s>Era la dimostrazione riuscita di così insolita facilità, da rimanerne lo <lb></lb>stesso Galileo compiacentemente stupito, ma ebbero la compiacenza e lo stu­<lb></lb>pore a crescere molto più, quando, in contemplar la nuova luce apparita, la <lb></lb>vide intorno intorno soavemente irradiarsi di quelle verità principali, ch&#039;egli <lb></lb>era andato prima cercando per sì lunghe vie faticose. </s>

<s>Se per CB e CD, rap­<lb></lb>presentandoci sempre innanzi l&#039;ultima figura, gl&#039;impeti stanno come gli spazi, <lb></lb>dunque i tempi sono uguali: e perchè, congiuntisi i punti B, D, la BD scende <lb></lb>sopr&#039;AC perpendicolare, vien così dunque risoluto il problema: trovare nel <lb></lb>perpendicolo e nell&#039;obliqua gli spazi, che sarebbero in tempi uguali passati <lb></lb>da due mobili uguali, nel medesimo punto partitisi dalla quiete. </s>

<s>Potendosi <lb></lb>poi sempre intorno al triangolo rettangolo CBD circoscrivere un semicerchio, <lb></lb>che abbia la metà dell&#039;ipotenusa BC per raggio, dunque la corda DC è iso­<lb></lb>crona al diametro. </s>

<s>Questo mirabile isocronismo, con si inaspettata facilità con­<lb></lb>cluso, veniva di più a farsi ala per condurre agile la proposizione III del <lb></lb>III dialogo, che, portata già come grave pietra fondamentale dell&#039;edifizio, era <lb></lb>costata a Galileo tante ambagi e tanti sudori. </s>

<s>È, per la legge dei moti acce­<lb></lb>lerati, To.AC:To.DC=√AC:√DC=AC:√AC.DC. </s>

<s>Ma √AC.DC= <lb></lb>BC e To.DC=To.BC, resta dunque concluso To.AC:To.BC=AC:BC, <lb></lb>come per legittima conseguenza dell&#039;essere, nel cadente e nell&#039;obliqua, le ve­<lb></lb>locità sempre uguali. </s></p><p type="main">

<s>Se fossero state così riformate tutte le proposizioni, il trattato Dei moti <lb></lb>locali nel terzo dialogo galileiano vinceva di facilità e d&#039;eleganza quel ma­<lb></lb>raviglioso inarrivabile trattato del Torricelli, ma essendo Galileo costretto dalla <lb></lb>vecchiezza e dalla cecità a rimanersi intorno a ciò in sterili desiderii con­<lb></lb>templativi, ebbe a chiamarsi contento di aver finalmente potuto mettere ad <pb xlink:href="020/01/2388.jpg" pagenum="13"></pb>effetto un proposito antico, e di aver sodisfatto al Viviani, e a tutti gli altri, <lb></lb>che fossero studiando venuti ne&#039;medesimi dubbi di lui. </s></p><p type="main">

<s>Un altro giovane era allora in Firenze, che, se cedeva al Viviani nel­<lb></lb>l&#039;acutezza matematica dell&#039;ingegno e nell&#039;ardor degli studii, lo superava di <lb></lb>gran lunga per lo splendor dei natali. </s>

<s>Il principe Leopoldo dei Medici veniva <lb></lb>istruito nelle Matematiche, e in particolare nell&#039;Algebra, secondo che Galileo <lb></lb>diceva quasi scherzando (Alb. </s>

<s>VII, 212), dall&#039;aulico don Famiano Michelini, <lb></lb>il quale, appena sparsasi la nuova della ritrovata dimostrazione, così da Siena <lb></lb>scriveva il di 6 Novembre 1638, in una sua lettera indirizzata ad Arcetri: </s></p><p type="main">

<s>“ Il serenissimo signor principe Leopoldo mio signore mi ha comandato <lb></lb>scrivere a V. S. che S. A. S. desidera la dimostrazione nuovamente da lei <lb></lb>ritrovata, che, dei gravi sopra diversi piani inclinati, mentre abbino la me­<lb></lb>desima elevazione sopra il piano orizontale, le velocità acquistate siano uguali <lb></lb>sopra il detto piano orizontale: poichè S. A. ha difficoltà in ammetter per <lb></lb>noto l&#039;assunto, che ella suppone nel bellissimo suo libro del moto. </s>

<s>Il Sere­<lb></lb>nissimo ha di già visti i sei libri di Euclide, e di presente vede l&#039;undecimo, <lb></lb>e il detto libro Del moto, col pensiero di veder prima le opere di V. S. Ecc.ma, <lb></lb>e poi il resto dei Matematici..... Il latore della presente è un vetturale di <lb></lb>palazzo, al quale S. A. desidera che V. S. dia la dimostrazione suddetta, perchè <lb></lb>senz&#039;essa le pare di andare al buio, ancorchè quelle esperienze ch&#039;ella pone nel <lb></lb>libro sieno poco meno che dimostrazione ” (MSS. Gal., P. VI, T. XIII, fol. </s>

<s>112). </s></p><p type="main">

<s>Ventitre giorni dopo lo stesso Michelini ringraziava Galileo, per essersi <lb></lb>compiaciuto d&#039;inviargli la dimostrazione “ circa l&#039;uguaglianza delle velocità <lb></lb>dei mobili di uguale elevazione, quando siano arrivati per qualunque incli­<lb></lb>nazione al piano orizontale ” (Alb. </s>

<s>X, 316, 17), soggiungendo che si trovava <lb></lb>allora, per un fiero dolor di testa, così ottuso l&#039;ingegno, da disperar di sco­<lb></lb>prire la verità o la falsità delle cose dimostrate. </s>

<s>Forse la difficoltà dipendeva <lb></lb>in gran parte dall&#039;aver dovuto Galileo dettare a qualcuno poco pratico di <lb></lb>quelle materie, e compendiare con qualche scapito della chiarezza quel suo <lb></lb>sottile discorso, che poi disse il Michelini di avere inteso, e di averlo trovato <lb></lb>concludere il vero. </s>

<s>“ La difficoltà, soggiungeva, tornando a scrivere il di 11 di <lb></lb>Dicembre al medesimo Galileo, proveniva dal mio poco giudizio, e dallo stare <lb></lb>più applicato al ritrovamento della mia, che al penetrar la sua bellissima di­<lb></lb>mostrazione ” (ivi, pag. </s>

<s>321). </s></p><p type="main">

<s>Il Michelini dunque attendeva a ritrovar del supposto galileiano una dimo­<lb></lb>strazione sua propria, ingegnandosi, com&#039;egli dice, di persuadere altrui “ che in <lb></lb>tempi uguali li spazi passati dal moto accelerato stiano come gl&#039;impeti ” (ivi). <lb></lb>E bench&#039;egli stesso soggiunga esser questa una bagattella, che ogni bambino <lb></lb>la saprebbe dimostrare, e confessi che il discorso tornava a quel medesimo <lb></lb>di Galileo, poco avendoci del suo; nonostante è notabile la varietà del pro­<lb></lb>cesso. </s>

<s>Anch&#039;egli, il Michelini, poneva il Teorema meccanico per principio, ma <lb></lb>nel servirsi del mezzo differiva dai modi tenuti da Galileo, perchè, mentre <lb></lb>questi direttamente dimostrava che gl&#039;impeti in B e in D, secondo l&#039;ultima <lb></lb>figura, stanno come le linee CB, CD, egli invece s&#039;ingegnava di persuadere <pb xlink:href="020/01/2389.jpg" pagenum="14"></pb>il medesimo dall&#039;esser per quelle stesse linee i tempi uguali. </s>

<s>Quali però si <lb></lb>fossero di una tale persuasion le ragioni non si rileva chiaro dalla citata let­<lb></lb>tera del Michelini. </s>

<s>Ma dicendovi essere unico suo assunto “ che gl&#039;impeti <lb></lb>stieno in reciproca proporzione degli spazi, nei diversi piani inclinati ” (ivi, <lb></lb>pag. </s>

<s>321) si può credere che ragionasse così, come, indipendentemente dai <lb></lb>teoremi dimostrati nelle nuove Scienze, dice di aver fatto già il Beriguardo. </s>

<s><lb></lb>Supposto che nel solito triangolo il lato AC sia triplo di CB, “ quando glo­<lb></lb>bus (si legge nel VI dei <emph type="italics"></emph>Circoli pisani,<emph.end type="italics"></emph.end> parte III) saliens ex C pervenerit <lb></lb>ad D, aut aliud punctum lateris inclinati praedicti utlibet, si quis velit assi­<lb></lb>gnare punctum in latere BC, producto similiter, ad quod aequali tempore <lb></lb>perveniret idem globus, aut alter aequalis, si demittatur simul ex puncto C <lb></lb>per latus CB; si quis inquam hoc velit, sumatur in latere CB punctum tri­<lb></lb>plo magis distans a puncto C, quam punctum D distet ab ipso C, sitque <lb></lb>puntum illud B: nam quando globus ex C pervenerit ad D, idem aut ae­<lb></lb>qualis ex C perveniet ad B aequali tempore ” (Patavii 1660, pag. </s>

<s>310). </s></p><p type="main">

<s>Il modo poi facile di ritrovar il punto B prosegue a dire esser quello <lb></lb>d&#039;alzar sopra AC in D una perpendicolare, la quale venga a descrivere il <lb></lb>triangolo DCB, ch&#039;essendo simile ad ACB darà, per la somiglianza, che BC <lb></lb>è media fra le AC e DC. </s>

<s>Dimostratosi dunque anche dal Michelini, al modo <lb></lb>sopra detto o in altro simile, che i tempi per CB e per CD sono uguali, ne <lb></lb>concludeva che gl&#039;impeti in B e in D stanno come gli spazi, e dietro l&#039;ap­<lb></lb>plicazion della legge dei moti accelerati, e l&#039;invenzione della DC, terza pro­<lb></lb>porzionale dopo AC, CB, riusciva a dimostrar finalmente, con i medesimi <lb></lb>processi di Galileo, che anche gl&#039;impeti in A e in B sono uguali. </s></p><p type="main">

<s>Sembra che la dimostrazione fosse dal padre Settimii letta a Galileo, il <lb></lb>quale la lodò molto (Alb. </s>

<s>X, 327), specialmente per quel suo modo tenuto <lb></lb>in dimostrare che la CD e la CB erano passate dal mobile nel medesimo <lb></lb>tempo. </s>

<s>Salendo pochi giorni dopo quel medesimo Settimii ad Arcetri, portava <lb></lb>seco, da consegnarsi a Galileo, un libro, e una lettera del Baliani. </s>

<s>Era quella <lb></lb>lettera scritta da Genova il di 17 Dicembre 1638, per accompagnare il detto <lb></lb>libro, ch&#039;era quello <emph type="italics"></emph>De motu naturali,<emph.end type="italics"></emph.end> pregando lui, a cui veniva presen­<lb></lb>tato, a leggerlo per favore, e a volergliene dire il suo parere. </s>

<s>Se sarà Galileo <lb></lb>stato ad ascoltare quella lettura, specialmente alla VII proposizione, si sarà <lb></lb>dovuto maravigliare che l&#039;Autor di lei e il Michelini si fossero così incon­<lb></lb>trati nel medesimo modo di dimostrar che la linea, condotto da un punto <lb></lb>della verticale perpendicolarmente sull&#039;inclinata, prefinisce qui come là due <lb></lb>spazii, che son passati dal mobile nei medesimi tempi. </s></p><p type="main">

<s>Comunque sia, Galileo mandava per contraccambio a Genova i suoi dia­<lb></lb>loghi Del moto, accompagnandoli con lettera del di 20 Giugno 1639 al Ba­<lb></lb>liani, il quale rispondeva il dì primo Luglio appresso, dicendo che, sebbene <lb></lb>non avesse avuto per leggere e per intender le cose scritte nel libro nè il <lb></lb>tempo necessario, nè l&#039;ozio, nonostante, mentr&#039;egli in generale ammirava la <lb></lb>bell<gap></gap>zza e la bontà delle dottrine, avrebbe pure avuto a notarvi qualche cosa, <lb></lb>particolarmente quanto ai supposti fatti al fol. </s>

<s>166, i quali, consentendo in <pb xlink:href="020/01/2390.jpg" pagenum="15"></pb>ciò col Viviani e col Michelini, scriveva “ io li tengo verissimi, ma dubito <lb></lb>che vi sia tanta evidenza, quanto par che sia necessario nei principii ” (ivi, <lb></lb>pag. </s>

<s>354). A sodisfare ai quali dubbi vennero presto le seguenti parole, scritte <lb></lb>in una lettera del di primo Agosto da Arcetri: </s></p><p type="main">

<s>“ Che poi il principio che io suppongo, come V. S. nota, a facce 166, <lb></lb>non le paia di quella evidenza che si ricercherebbe nei principii da supporsi <lb></lb>come noti, glielo voglio concedere per ora, ancorchè Ella medesima faccia la <lb></lb>stessa supposizione, cioè che i gradi di velocità, acquistati sopra l&#039;orizzonte <lb></lb>da mobili discendenti per diversi piani della medesima altezza, siano uguali. </s>

<s><lb></lb>Ora sappia V. S. Ill.ma che, dopo aver perso la vista, e per conseguenza la <lb></lb>facoltà di potere andare internando in più profonde proposizioni e dimostra­<lb></lb>zioni, mi sono andato nelle tenebre notturne occupando intorno alle prime <lb></lb>e più semplici proposizioni, riordinandole e disponendole in miglior forma ed <lb></lb>evidenza, tra le quali mi è occorso di dimostrare il sopraddetto principio, nel <lb></lb>modo che a suo tempo Ella vedrà, se mi succederà di avere tanto di forza, <lb></lb>che io possa migliorare ed ampliare lo scritto e pubblicato da me sin qui in­<lb></lb>torno al moto, con aggiungervi altre speculazioncelle, ed in particolare quelle <lb></lb>attinenti alla forza della percossa, nell&#039;investigazion della quale ho consumato <lb></lb>molte centinaia e migliaia di ore, e finalmente ridottala ad assai facile espli­<lb></lb>cazione, sicchè altri, in manco di mezz&#039;ora di tempo, può restarne capace ” <lb></lb>(Lettere pel trecent. </s>

<s>natal. </s>

<s>cit., pag. </s>

<s>45, 46). </s></p><p type="main">

<s>Ricevuta così la notizia della dimostrazion del principio, che Galileo aveva <lb></lb>prima semplicemente supposto come vero, il Baliani, inclinatissimo a specu­<lb></lb>lare intorno alla verità delle cose (Alb. </s>

<s>X, 369), piuttosto che aspettar l&#039;al­<lb></lb>trui, amò meglio di tentare la propria fortuna, la quale pareva arridergli già, <lb></lb>avendolo fatto incontrare in quella settima proposizione, dalla quale Galileo <lb></lb>e il Michelini avevano così facilmente concluse le loro dimostrazioni. </s>

<s>Quella VII <lb></lb><emph type="italics"></emph>De motu naturali<emph.end type="italics"></emph.end> era ivi infatti messa in questa forma, com&#039;a pag. </s>

<s>34 dello <lb></lb>stesso trattato, che più ampiamente l&#039;Autore condusse nel 1646: “ Data linea <lb></lb>perpendiculari, per quam grave descendat, cui annectatur linea, seu planum <lb></lb>declinans; in declinante reperire punctum, quo grave perveniat eo tempore, <lb></lb>quo pertransiverit perpendicularem. </s>

<s>” </s></p><p type="main">

<s>Rappresentando BC quella perpendicolare e AC l&#039;inclinata, come nella <lb></lb>figura ultimamente qui addietro posta, si risolve il problema, conducendo la <lb></lb>BD normale ad AC, d&#039;onde, come da Galileo si conclude che le velocità in B <lb></lb>e in D son proporzionali agli spazi, e, come dal Michelini, che le CB, CD <lb></lb>son passate dal mobile nei medesimi tempi. </s>

<s>Ma aveva il Baliani prevenuto <lb></lb>altresì Galileo in una cosa ben&#039;assai più importante, in servirsi cioè del co­<lb></lb>rollario che le CB, CD sono isocrone insieme per lemma, a dimostrar la pro­<lb></lb>posizione sua XV, ivi a pag. </s>

<s>36 così formulata: “ Si duo gravia descendunt, <lb></lb>alterum quidem perpendiculariter, alterum vero super plano declinante, per­<lb></lb>veniunt ad idem planum orizontale tali ratione, ut sit eadem proportio inter <lb></lb>diuturnitates eorum, quae inter perpendicularem et declinantem. </s>

<s>” Ha la <lb></lb>dimostrazione aria di novità, e tutt&#039;insieme di eleganza, perchè, essendo <pb xlink:href="020/01/2391.jpg" pagenum="16"></pb>per la legge dei moti accelerati, ritenuta la medesima figura, DC:AC= <lb></lb>To.DC2:To.AC2=To.BC2:To.AC2, in virtù del precedente Lemma, e <lb></lb>per la similitudine de&#039;triangoli ABC, CDB essendo CD:AC=CB2:AC2, <lb></lb>immediatamente se ne conclude CB2:AC2=To.CB2:To.AC2, e però an­<lb></lb>che i semplici spazi staranno, secondo il proposito, come i semplici tempi. </s></p><p type="main">

<s>Ripensando Galileo fra sè, in farsi leggere il trattatello del Baliani, a <lb></lb>queste conclusioni, avrà dovuto maravigliarsi di trovar che altri avevan già <lb></lb>penetrato quel che solitario era ito speculando in mezzo alle tenebre. </s>

<s>Non <lb></lb>si vedeva però in quelle dimostrazioni concluso l&#039;intento principale, perchè <lb></lb>il Baliani relegava in settimo luogo tra i postulati anche questo: “ ductis pla­<lb></lb>nis inclinatis et linea perpendiculari inter lineas parallelas orizontales, gravia <lb></lb>super illis mota, ubi perveniunt ad parallelam inferiorem, habent aequales <lb></lb>velocitatis gradus, et proinde, si ab inde infra sortiantur parem inclinationem, <lb></lb>aequivelociter moventur. </s>

<s>” Ei riteneva come Galileo la cosa probabile, sì per <lb></lb>l&#039;esperienza dei pendoli, <emph type="italics"></emph>quae quamtumvis longiora aut breviora, et proinde <lb></lb>circa finem magis aut minus inclinata, pariter ascendunt si pariter de­<lb></lb>scendant;<emph.end type="italics"></emph.end> e sì per l&#039;esempio dell&#039;acqua, la quale, essendo per sifoni retti o <lb></lb>inclinati in qualunque modo condotta, <emph type="italics"></emph>videmus pariter ascendere, si pariter <lb></lb>descendat.<emph.end type="italics"></emph.end> Ma più che in questi fatti fisici s&#039;affidava il Baliani della verità <lb></lb>del suo postulato in veder ch&#039;egli aveva una dipendenza immediata dalla pro­<lb></lb>posizione sua XV, <emph type="italics"></emph>quia, si diuturnitates sunt longitudinibus proportionales, <lb></lb>credibile est motus in fine esse aequales.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Si vede bene insomma che, a raggiunger l&#039;intento principale, mancava <lb></lb>a fare al Baliani un passo solo, tentando, per non avere a invidiare quella <lb></lb>di Galileo, la sua propria fortuna, che felicemente gli riuscì in questo modo. </s>

<s><lb></lb>Riferendosi sempre all&#039;ultima impressa figura, è dimostrato T.oCB:T.oAC= <lb></lb>CB:AC. </s>

<s>Ma per la legge dei moti accelerati gli spazi stanno come i quadrati <lb></lb>dei tempi, o come i rettangoli delle velocità e dei tempi; dunque, significandosi <lb></lb>con V.a la velocità, come con T.o si significa il tempo, sarà T.oCB:T.oAC= <lb></lb>T.oCB.V.aCB:T.oAC.V.aAC, e perciò V.aCB=V.aAC. </s></p><p type="main">

<s>Quel ch&#039;era dunque prima supposto nell&#039;operetta <emph type="italics"></emph>De motu naturali,<emph.end type="italics"></emph.end> o <lb></lb>come sempliccmente probabile ritenuto, ottenne in tal guisa la sua matematica <lb></lb>dimostrazione, la quale il Baliani, occorrendogli di far ristampare un foglio per <lb></lb>un errore trascorso, fece inserir nel volume, revocando quelle poche copie già <lb></lb>uscite, e non approvando che le altre così corrette. </s>

<s>Volle una di queste mandar <lb></lb>subito a Galileo, accompagnandogliela con una lettera del dì 16 Settembre 1639, <lb></lb>nella quale, dop&#039;altre in proposito, soggiungeva queste parole: “ Ho avuto <lb></lb>per bene di mandarle una copia di detta mia operetta così racconcia, pre­<lb></lb>gandola che la faccia degna di star in un canto della sua libreria, con strac­<lb></lb>ciar l&#039;altra che le mandai prima, che non vorrei che ci stesse in alcun modo. </s>

<s><lb></lb>Io credo che sia buona dimostrazione, supposto per principio che la propor­<lb></lb>zione degli spazi si compone della proporzione dei tempi e delle velocità, e ne <lb></lb>ho fatta una giunta alla dimostrazione del settimo postulato ” (Alb. </s>

<s>X, 369). </s></p><p type="main">

<s>Così, infin dal Settembre del 1639, dava il Baliani al pubblico la sua <pb xlink:href="020/01/2392.jpg" pagenum="17"></pb>Dinamica confermata già sul suo più stabile fondamento, mentre Galileo, con <lb></lb>speranza assai più lunga di quel che l&#039;infermità e la vecchiezza gli avreb­<lb></lb>bero dato per misura, aspettava il tempo e l&#039;occasione di una ristampa dei <lb></lb>Dialoghi, ch&#039;egli attendeva a correggere e ampliare. </s>

<s>Intanto, essendogli il <lb></lb>Viviani di frequente visitatore divenuto ospite permanente, volle facesse il <lb></lb>disteso della dimostrazione, che finalmente gli sortì d&#039;incontrare, di che <lb></lb>mandò subito copia al Castelli, accompagnandola con una lettera del dì 3 Di­<lb></lb>cembre 1639, nella quale, dop&#039;essersi compiaciuto dell&#039;invenzione così sog­<lb></lb>giungeva: “ È scritta in dialogo, come sovvenuta al Salviati, acciò si possa, <lb></lb>quando mai si stampassero di nuovo i miei Discorsi e dimostrazioni, inse­<lb></lb>rirla immediatamente dopo lo scolio della seconda proposizione del suddetto <lb></lb>trattato, come teorema essenzialissimo allo stabilimento delle Scienze del moto <lb></lb>da me promosse ” (Alb. </s>

<s>VII, 238, 39). </s></p><p type="main">

<s>I Dialoghi si stamparono insieme con le altre opere in Bologna, dove il <lb></lb>disteso, da diciassett&#039;anni già preparato, apparve postumo, facendosi il Vi­<lb></lb>viani geloso esecutore testamentario delle ultime volontà del suo Maestro. </s>

<s><lb></lb>L&#039;edizion bolognese era diretta da Carlo Rinaldini, e si faceva stampando a <lb></lb>parte via via i trattati, ch&#039;erano prima venuti a mano, e raccogliendoli poi <lb></lb>insieme in due volumi. </s>

<s>Il primo era nel 1655 già pronto, e l&#039;anno dopo si <lb></lb>mandò fuori il secondo, dove in ultimo si raccoglievano i Discorsi e le dimo­<lb></lb>strazioni intorno alle due nuove Scienze del moto. </s>

<s>Il Viviani stesso in pro­<lb></lb>posito di scrivere in una sua lettera al Rinaldini, <emph type="italics"></emph>della nuova impressione <lb></lb>delle dette Opere, promossa ed ultimata per mezzo solo di V. S. E.,<emph.end type="italics"></emph.end> sog­<lb></lb>giungeva: “ Vi è ancora quella dimostrazione del principio supposto, che pone <lb></lb>il signor Galileo avanti alla Scienza del moto accelerato, ed a quella maniera <lb></lb>che fu distesa da me di suo ordine, in tempo ch&#039;io mi trovavo appresso di <lb></lb>lui, che fu poco dopo ch&#039;ei la ritrovò, quando già era composto il suddetto <lb></lb>libro Del moto, ed è l&#039;istessa che si mandò fuori a diversi amici dal mede­<lb></lb>simo signor Galileo ” (MSS. Gal. </s>

<s>Disc., T. CXLII, fol. </s>

<s>3). </s></p><p type="main">

<s>Che veramente dopo il Castelli fosse stata mandata la dimostrazione a <lb></lb>diversi amici in Italia e fuori ci vien confermato dai documenti, ed era il <lb></lb>medesimo Viviani che ricopiava e spediva, sotto gli ordini di Galileo, questa <lb></lb>specie di circolari. </s>

<s>Erano però, per maggior brevità e per essere inutili allo <lb></lb>scopo, tralasciate le parti, che dovevano servir per le attaccature e per le <lb></lb>articolazioni del dialogo, rimanendo la nuda dimostrazione in discorso disteso. </s>

<s><lb></lb>L&#039;original forma di così fatta scrittura circolare s&#039;ha da carte 11-13 del <lb></lb>tomo IV, parte V, dei Manoscritti di Galileo, non con molta proprietà dal Vi­<lb></lb>viani stesso intitolata <emph type="italics"></emph>Dimostrazione trovata dal gran Galileo l&#039;anno 1639,<emph.end type="italics"></emph.end><lb></lb>perchè, sebben fosse messa in forma in quest&#039;anno, l&#039;invenzion nonostante, <lb></lb>com&#039;apparisce dalle cose narrate, risale all&#039;anno precedente. </s>

<s>Sembrerebbe <lb></lb>fosse questo il luogo opportuno di rendere alla notizia dei nostri Lettori nella <lb></lb>sua propria forma questo discorso, ma ei ce la esibirà fra poco in fedel copia <lb></lb>uno di coloro, a cui fu mandato, collega e amico a quel Torricelli, ch&#039;è per <lb></lb>aver gran parte in questo episodio della storia della Meccanica. </s></p><pb xlink:href="020/01/2393.jpg" pagenum="18"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Mentre Galileo, come albero annoso, rimaneva sopra il colle di Arcetri <lb></lb>solitario, un rampollo di lui, Benedetto Castelli, spandeva in Roma i rami <lb></lb>rigogliosi, sotto l&#039;ombra de&#039;quali si raccoglievano a filosofare Evangelista <lb></lb>Torricelli, Raffaello Magiotti, Antonio Nardi e Michelangiolo Ricci. </s>

<s>Prediletto <lb></lb>argomento a quei filosofici discorsi si porgeva dalla lettura dei nuovi dialo­<lb></lb>ghi Del moto, e incontrò specialmente al Torricelli quel ch&#039;era in Firenze <lb></lb>incontrato al Viviani, di mettere cioè dubbio intorno alla evidenza dell&#039;as­<lb></lb>sunto di Galileo. </s>

<s>Entrato più addentro alle dimostrazioni di lui, gli parve che <lb></lb>l&#039;andare i mobili per varie obliquità di scesa ugualmente veloci, dopo cadute <lb></lb>uguali, fosse una verità da non doversi semplicemente supporre, ma da po­<lb></lb>tersi con facilità dimostrare. </s>

<s>Del modo poi volle farne alcun cenno al Ricci, <lb></lb>a cui bastò per condurre una dimostrazione ch&#039;ei conferì col Magiotti, ral­<lb></lb>legrandosi di vederla tale quale specchiata nelle Opere stampate dello stesso <lb></lb>Torricelli, a cui, sulla fin del Settembre 1644, scriveva queste parole: “ Mi <lb></lb>son rallegrato di trovarvi sopra sette o otto proposizioni, con le sue dimo­<lb></lb>strazioni per l&#039;appunto, come le avevo pensate io, ed in particolare la prova <lb></lb>di quella supposizione fatta dal Galileo ne&#039;libri Del moto la conferii al signor <lb></lb>Magiotti due o tre anni sono, avendola rintracciata con quel lume, che ebbi <lb></lb>da V. S. ” (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>52). </s></p><p type="main">

<s>Posto così dunque il fondamento, vi andò il Torricelli sopra edificando, <lb></lb>e riuscì a dimostrare molte proposizioni <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> in diverso modo, più fa­<lb></lb>cile e più elegante di quello stesso tenuto da Galileo, componendone un nuovo <lb></lb>trattato. </s>

<s>Il Castelli in leggerlo n&#039;ebbe a stupire, e scrivendo da Roma il di <lb></lb>2 Marzo 1641 ad Arcetri avvisava il suo vecchio Maestro che, venendo pre­<lb></lb>sto a Firenze per riverirlo, gli avrebbe portato un libro fatto da un suo di­<lb></lb>scepolo, il quale, avendo avuti i primi principii di geometria dieci anni fa <lb></lb>alla sua scuola, aveva poi fatto tal progresso da mostrar quanto fossero fe­<lb></lb>condi i germi, nei nuovi Dialoghi seminati in materia del moto (Alb. </s>

<s>X, 408). <lb></lb>Dopo tredici giorni infatti, salito una mattina il Castelli ad Arcetri, entrava <lb></lb>nella camera, dove giacevasi Galileo, presentandogli un volume manoscritto, <lb></lb>con una lettera che l&#039;accompagnava. </s>

<s>Scusavasi quivi l&#039;Autore di avere scritti <lb></lb>que&#039;fogli <emph type="italics"></emph>De motu gravium naturaliter descendentium et proiectorum<emph.end type="italics"></emph.end> “ non <lb></lb>per bisogno che io giudicassi averne le sue dottrine, ma per necessità che aveva <lb></lb>io di formar questo memoriale di erudizione alla mia poca intelligenza, e pel <lb></lb>desiderio che teneva di mostrare al mio Maestro lontano come, anco in as­<lb></lb>senza, aveva propagato con qualche studio mio la sua disciplina ” (ivi, pag. </s>

<s>412). </s></p><p type="main">

<s>Nell&#039;ascoltare il processo tenuto dal Torricelli nelle prime cinque propo­<lb></lb>posizioni del primo libro, per concluder quello, che due anni fa era andato <lb></lb>fra le tenebre così affannosamente cercando; Galileo non ebbe a stupir meno <pb xlink:href="020/01/2394.jpg" pagenum="19"></pb>degli altri. </s>

<s>Di questi suoi sensi fatte scrivere le espressioni in una letttera <lb></lb>andata smarrita, tornava il dì 27 Settembre di quel medesimo anno 1641 a <lb></lb>dire al Torricelli la grande stima, che faceva de&#039;suoi trovati e delle sue con­<lb></lb>clusioni, riserbandosi a trattarne poi seco a bocca i particolari. </s>

<s>“ Mando que­<lb></lb>sta, così terminava la lettera, sotto una del signor Nardi, dal quale ella la <lb></lb>riceverà, insieme colla dimostrazione di quello che io supponeva nell&#039;ultimo <lb></lb>mio dialogo come principio conceduto. </s>

<s>Vedanla insieme e l&#039;emendino, comu­<lb></lb>nicandola anche al terzo mio riverito padrone il signor Magiotti, ed a tutto <lb></lb>il triumvirato con reverente affetto bacio le mani ” (Alb. </s>

<s>VII, 367). </s></p><p type="main">

<s>Il Nardi ci conservò la scrittura avuta da Galileo, inserendola nella <lb></lb>IX veduta della seconda scena col titolo: <emph type="italics"></emph>D&#039;un principio meccanico del Ga­<lb></lb>lileo,<emph.end type="italics"></emph.end> e con questo motto per semplice introduzione: “ Così scrivevami sopra <lb></lb>tal materia il mio maestro Galilei: ” </s></p><p type="main">

<s>“ I gravi scendenti dalla medesima sublimità sopra l&#039;orizonte avere <lb></lb>acquistati uguali gradi di velocità (proposizione da me sin qui supposta, e <lb></lb>solo con esperienze e probabili discorsi confermata) potremo nel seguente <lb></lb>modo dimostrativamente provare, pigliando com&#039;effetto notissimo le velocità <lb></lb>dello stesso mobile esser diverse sopra diverse inclinazioni, e la massima <lb></lb>essere per la linea perpendicolarmente sopra l&#039;orizonte elevata, e per le altre <lb></lb>inclinate diminuirsi tal velocità, secondo che più dal perpendicolo si disco­<lb></lb>stano, cioè più obliquamente s&#039;inclinano, dal che si scorge che l&#039;impeto, il <lb></lb>momento, l&#039;energia, o vogliam dire il talento del discendere, viene determi­<lb></lb>nato nel mobile dal suggetto piano, sopra il quale s&#039;appoggia e discende. </s>

<s>” <lb></lb><figure id="id.020.01.2394.1.jpg" xlink:href="020/01/2394/1.jpg"></figure></s></p><p type="caption">

<s>Figura 5.</s></p><p type="main">

<s>“ E per meglio dichiararmi, <lb></lb>intendasi AB (fig. </s>

<s>5) perpendicolar­<lb></lb>mente eretta sopra l&#039;orizonte AC: <lb></lb>pongasi poi la medesima in diverse <lb></lb>inclinazioni verso l&#039;orizonte, pie­<lb></lb>gata come in AD, AE, AF, ecc., <lb></lb>dico che l&#039;impeto massimo e totale <lb></lb>del grave per discendere è nella <lb></lb>perpendicolare BA, minore nella <lb></lb>AD, minore ancora nella EA, e <lb></lb>successivamente andarsi diminuendo nella FA, e finalmente esser del tutto <lb></lb>estinto nella orizontale CA, dove il mobile non ha per sè stesso inclinazione <lb></lb>alcuna, nè in conseguenza resistenza all&#039;esservi mosso. </s>

<s>” </s></p><p type="main">

<s>“ Appresa questa mutazione d&#039;impeto, mi fa mestieri ritrovare e dimo­<lb></lb>strare con qual proporzione ella si faccia, come per esempio nel piano incli­<lb></lb>nato AF. </s>

<s>Tirisi la sua elevazione sopra l&#039;orizonte AC, cioè la linea FC, per <lb></lb>la quale l&#039;impeto ed il momento del discendere è il massimo: cercasi qual <lb></lb>proporzione abbia ad esso l&#039;impeto per l&#039;inclinata FA. È manifesto tanto <lb></lb>essere questo impeto e talento del discendere quanta è la resistenza o forza <lb></lb>minima, che basta per proibirlo e fermarlo. </s>

<s>Per tal forza e resistenza e sua <lb></lb>misura mi voglio servire della gravità di un altro mobile grave. </s>

<s>” </s></p><pb xlink:href="020/01/2395.jpg" pagenum="20"></pb><p type="main">

<s>“ Intendasi sopra il piano FA posare il mobile G, il quale venga rite­<lb></lb>nuto col filo che, cavalcando sopra FC, pendendo a perpendicolo, abbia at­<lb></lb>taccato un peso H, il quale, gravando a perpendicolo, proibisca al G lo scen­<lb></lb>dere per la inclinata FA. </s>

<s>Riducendosi a memoria quello che si dimostra in <lb></lb>tutti i casi dei movimenti meccanici, che cioè la velocità del moto d&#039;un mo­<lb></lb>bile men grave compensa con reciproca proporzione della gravità la minor <lb></lb>velocità dell&#039;altro mobile più grave, che è quanto a dire che gli spazi pas­<lb></lb>sati nell&#039;istesso tempo abbiano reciproca proporzione della gravità; conside­<lb></lb>riamo che lo spazio della scesa a perpendicolo del grave H è bene uguale a <lb></lb>tutta la salita del mobile G per l&#039;inclinata AF, ma non già per la salita a <lb></lb>perpendicolo, nella quale esso G esercita la sua resistenza, il che è manife­<lb></lb>sto, imperocchè, considerando nel triangolo AFC il moto da A in F esser <lb></lb>composto del trasversale orizontale AC, e del perpendicolare CF, ed essendo <lb></lb>che, quanto all&#039;orizontale, nessuna è la resistenza del mobile, resta la resi­<lb></lb>stenza esser solamente rispetto alla perpendicolare CF. </s>

<s>Mentre che dunque <lb></lb>il mobile G, movendosi da A in F, resiste solo nel salire lo spazio perpen­<lb></lb>dicolare CF, ma che l&#039;altro grave scende a perpendicolo quanto è tutto lo <lb></lb>spazio FH, possiamo molto ragionevolmente af<gap></gap>ermare le velocità o gli spazi <lb></lb>passati nel medesimo tempo da tali mobili dover rispondere reciprocamente <lb></lb>alle loro gravità, e basterà per impedire la scesa del G che l&#039;H sia tanto <lb></lb>men grave di quello, quanto lo spazio CF è minore della inclinata FA. </s>

<s>E per­<lb></lb>chè siamo convenuti che tanto sia l&#039;impeto, l&#039;energia, il momento ed il ta­<lb></lb>lento del mobile al moto, quanta è la forza e resistenza che basta a fermarlo, <lb></lb>concludiamo dunque, come si è detto, l&#039;impeto per l&#039;inclinata, all&#039;impeto <lb></lb>massimo per la perpendicolare, stare com&#039;essa perpendicolare, cioè l&#039;eleva­<lb></lb>zione della inclinata, alla medesima inclinata. </s>

<s>” </s></p><p type="main">

<s>“ Stabilito ciò, e posto che il mobile grave, partendosi dalla quiete e <lb></lb>naturalmente scendendo, vada con eguali giunte accrescendo la sua velocità, <lb></lb>onde, come quindi dimostro, gli spazi passati sono in duplicata proporzione <lb></lb>dei tempi, ed in conseguenza dei gradi di velocità, la quale, come abbiamo <lb></lb>detto, cresce con la proporzione del tempo; dimostreremo la nostra conclu­<lb></lb>sione, cioè i gradi di velocità nell&#039;orizonte essere eguali: quelli cioè acqui­<lb></lb>stati dal mobile, che dalla quiete si parta da qualsivoglia altezza, e per quali <lb></lb>si siano inclinazioni pervenga all&#039;orizonte. </s>

<s>” </s></p><p type="main">

<s>“ E qui devesi avvertire che, stabilito che in qualsivogliano inclinazioni <lb></lb>il mobile dalla partita dalla quiete vada crescendo la velocità con la propor­<lb></lb><figure id="id.020.01.2395.1.jpg" xlink:href="020/01/2395/1.jpg"></figure></s></p><p type="caption">

<s>Figura 6.<lb></lb>zione del tempo, sia qualsivoglia l&#039;inclinazione e in con­<lb></lb>seguenza la quantità dell&#039;impeto; quali furono gl&#039;impeti <lb></lb>nella prima mossa, tali saranno i gradi della velocità gua­<lb></lb>dagnata nello stesso tempo, poichè e questi e quelli cre­<lb></lb>scono con la medesima proporzione, che cresce il tempo. </s>

<s>” </s></p><p type="main">

<s>“ Ora sia il piano inclinato AC (fig. </s>

<s>6) elevato sopra <lb></lb>l&#039;orizonte, la perpendicalare CB e la orizontale AB. </s>

<s>E <lb></lb>poichè l&#039;impeto per la perpendicolare CB, all&#039;impeto per <pb xlink:href="020/01/2396.jpg" pagenum="21"></pb>l&#039;inclinata AC, sta come CB ad AC, prendasi nella AC la CD, terza propor­<lb></lb>zionale della AC, CB: l&#039;impeto dunque per CB, all&#039;impeto per AC, sta come <lb></lb>la CB alla CD. </s>

<s>Il mobile dunque, nello stesso tempo che passasse uno spazio <lb></lb>uguale alla CB nella perpendicolare CB, passerebbe uno spazio uguale alla <lb></lb>CD nell&#039;inclinata AC, ed il grado della velocità in B, al grado di velocità <lb></lb>in D, avrebbe la medesima proporzione della CB alla CD. </s>

<s>Ma il grado di ve­<lb></lb>locità in A, al grado in D, ha la medesima proporzione che la media tra AC, <lb></lb>CD, e la media tra la AC, CD è la CB; adunque i gradi in A e in B, al <lb></lb>grado in D, hanno la medesima proporzione, e però sono uguali, che è quello <lb></lb>che bisognava dimostrare. </s>

<s>” </s></p><p type="main">

<s>“ Di qui possiamo immediatamente dimostrare un&#039;altra proposizione: <lb></lb>cioè il tempo per l&#039;inclinata, al tempo per la perpendicolare, aver la mede­<lb></lb>sima proporzione di essa inclinata e perpendicolare. </s>

<s>Imperocchè diciamo che, <lb></lb>quando CA (nella solita ultima figura) sia il tempo per CA, il tempo per DC <lb></lb>sarà la media tra esse CA, DC, cioè sarà BC. </s>

<s>Ma quando il tempo per CD <lb></lb>sia CB, è anco il tempo per CB; dunque, quando AC sia il tempo per AC, <lb></lb>CB sarà il tempo per CB. Dunque, come AC a CB, così il tempo per AC al <lb></lb>tempo per CB. ” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>277-83). </s></p><p type="main">

<s>Il triumvirato della matematica Repubblica romana avrà con gran de­<lb></lb>siderio letta questa dimostrazione, la quale si faceva dipendere, com&#039;era na­<lb></lb>turale, dal Teorema meccanico, venutosi ora a restaurare dopo quella total <lb></lb>demolizione, di cui nel cap. </s>

<s>VI del Tomo precedente si narrarono le origini <lb></lb>e le vicende. </s>

<s>È a notar però che, nel suo primo libro manoscritto, Galileo <lb></lb>rimandava per quel Teorema alla <emph type="italics"></emph>Scienza meccanica,<emph.end type="italics"></emph.end> dove il processo dimo­<lb></lb>strativo è diverso, e sono altresì diversi i principii, che in questa decrepita <lb></lb>scrittura conservataci dal Nardi appariscono in abito nuovo, e con un rigo­<lb></lb>glio giovanile di vita. </s>

<s>Attendendo bene infatti è tutto il vigore impartito al <lb></lb>Teorema dal principio dei moti misti, risolvendosi la forza AF, nella quinta <lb></lb>figura qui addietro, in altre due, delle quali la sola FC rimane attiva. </s>

<s>Ora <lb></lb>essendo misurata la forza dalla quantità della materia o dal peso, moltipli­<lb></lb>cato per la velocità o per lo spazio, saran dunque nel presente caso G. FC, <lb></lb>H.FA le due forze, che si fanno insieme equilibrio, d&#039;onde G:H=FA:FC <lb></lb>che è la conclusione, da Galileo condotta e raggirata per troppo lungo di­<lb></lb>scorso. </s>

<s>D&#039;onde ancora sarebbe venuta a rendersi manifesta l&#039;intenzion prin­<lb></lb>cipale, perchè tutti gl&#039;impeti diretti per le oblique che, movendo da F, vanno <lb></lb>a raggiungere in AC l&#039;orizonte, sono uguali ciascuno all&#039;impeto per FC, e <lb></lb>perciò necessariamente uguali fra loro, che è insomma, in dimostrar la ve­<lb></lb>rità del supposto galileiano, il ragionamento che prima di tutti avea fatto <lb></lb>Luca Valerio. </s></p><p type="main">

<s>Quello però, che da noi s&#039;è chiamato vigor giovanile, mal giudicato dal <lb></lb>Nardi, non era reputato troppo sincero, come non sincero stimavalo forse il <lb></lb>Torricelli, il quale, tenendosi perciò affezionato più che mai ai modi suoi <lb></lb>proprii, nel dover mandare alla luce il libro, che tre anni prima il Castelli <lb></lb>aveva presentato a Galileo manoscritto, vi premetteva fra le altre queste pa-<pb xlink:href="020/01/2397.jpg" pagenum="22"></pb>role: “ Scio Galileum, ultimis vitae suae annis, suppositionem illam demon­<lb></lb>strare conatum, sed quia ipsius argumentatio cum libro De motu edita non <lb></lb>est, pauca haec de momentis gravium libello nostro praefigenda duximus, ut <lb></lb>appareat quod Galilei suppositio demonstrari potest ” (Opera geom., P. I, <lb></lb>Florentiae 1644, pag. </s>

<s>98). </s></p><p type="main">

<s>La torricelliana dimostrazione del supposto galileiano muove dal Teo­<lb></lb>rema meccanico, condotto però da un principio, che nella Storia della scienza <lb></lb><figure id="id.020.01.2397.1.jpg" xlink:href="020/01/2397/1.jpg"></figure></s></p><p type="caption">

<s>Figura 7.<lb></lb>apparisce del tutto nuovo. </s>

<s>È quel principio che due <lb></lb>corpi rimangono nella posizione, in cui sono equi­<lb></lb>librati, quando il loro comun centro di gravità, es­<lb></lb>sendogli impossibile scendere, si trova sempre nella <lb></lb>medesima linea orizontale. </s>

<s>Il Viviani lo illustrava mi­<lb></lb>rabilmente così, riducendolo in forma del seguente <lb></lb>teorema: </s></p><p type="main">

<s>“ Se i due pesi eguali A, B (fig. </s>

<s>7) sono legati <lb></lb>ad un filo, passato sopra una carrucola o altro soste­<lb></lb>gno, che possano scorrere; questi staranno in equili­<lb></lb>brio, dovunque si saranno situati. </s>

<s>” </s></p><p type="main">

<s>“ Perchè, se si movessero, tanto acquisterebbe <lb></lb>l&#039;uno che scendesse, quanto perderebbe l&#039;altro che <lb></lb>salisse, essendo i loro moti eguali, e per linee per­<lb></lb><figure id="id.020.01.2397.2.jpg" xlink:href="020/01/2397/2.jpg"></figure></s></p><p type="caption">

<s>Figura 8.<lb></lb>pendicolari. </s>

<s>E se è possibile si muovano dal sito A, <lb></lb>B nel sito C, D: è manifesto che, giunti li centri di <lb></lb>gravità in linea retta, il centro comune di A, B verrà <lb></lb>in mezzo, cioè in E, ed il centro comune di C, D verrà <lb></lb>in mezzo, cioè in E: perch&#039;essendo le CA, BD uguali <lb></lb>tra loro e parallele, congiunte CD, AB si segano nella <lb></lb>medesima proporzione e nel mezzo, onde il centro <lb></lb>comune non si sarà mosso, e non avrà acquistato <lb></lb>niente, sicchè i gravi A, B non si moveranno dal loro <lb></lb>sito, in che furono posti. </s>

<s>” </s></p><p type="main">

<s>“ Ma se il peso B (fig. </s>

<s>8) sarà maggiore del <lb></lb>peso A, quello scenderà, perchè il centro comune <lb></lb>loro è fuori del mezzo della BA, come in E, più vi­<lb></lb>cino al centro B, ed è in luogo che può scendere <lb></lb>sempre per la linea perpendicolare EG. ” (MSS. Gal., <lb></lb>P. V, T. VII, fol. </s>

<s>72 a tergo). </s></p><p type="main">

<s>Posto dunque questo principio, che il Viviani ci ha così ben dichiarato, <lb></lb>ecco come il Torricelli dimostra la sua prima proposizione, che cioè “ si in <lb></lb>planis inaequaliter inclinatis, eamdem tamen elevationem habentibus, duo <lb></lb>gravia constituantur, quae inter se eamdem homologe rationem habeant, <lb></lb>quam habent longitudines planorum; gravia aequale momentum habebunt ” <lb></lb>(Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>99). </s></p><p type="main">

<s>Siano AC, CD (fig. </s>

<s>9) i due piani inclinati, sopra i quali posino i due <pb xlink:href="020/01/2398.jpg" pagenum="23"></pb>gravi A, B con i loro pesi nelle dette proporzioni. </s>

<s>Avranno ugual momento <lb></lb>se, congiuntj insieme dal filo ACB, scendendo l&#039;uno in D, e risalendo l&#039;al­<lb></lb><figure id="id.020.01.2398.1.jpg" xlink:href="020/01/2398/1.jpg"></figure></s></p><p type="caption">

<s>Figura 9.<lb></lb>tro in E, il loro comun centro di gravità <lb></lb>rimanga sempre in un punto della orizon­<lb></lb>tale AB, ciò che, chiamati E, D i due <lb></lb>gravi, e da E condotta la EF parallela a <lb></lb>CD, l&#039;Autore dimostra con un discorso, <lb></lb>da noi più brevemente significato per que­<lb></lb>ste equazioni. </s>

<s>E:D=AC:CB=AE:EF <lb></lb>=BD:EF=GD:EG. </s>

<s>G dunque è il co­<lb></lb>mun centro di gravità de&#039;pesi, nè s&#039;è <lb></lb>nulla rimosso dall&#039;AB orizontale. </s></p><p type="main">

<s>Si passa di qui a proporre, in secondo luogo, che, posandosi sopra AB, <lb></lb>BC (fig. </s>

<s>10), piani diversamente lunghi ma ugualmente elevati, due pesi <lb></lb>uguali A, C, i loro momenti <emph type="italics"></emph>sunt in reciproca ratione cum longitudinibus<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2398.2.jpg" xlink:href="020/01/2398/2.jpg"></figure></s></p><p type="caption">

<s>Figura 10.<lb></lb><emph type="italics"></emph>planorum<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>100): ciò <lb></lb>che, presa D quarta proporzio­<lb></lb>nale dopo AB, BC, A, per cui i <lb></lb>momenti di A e di D sono uguali <lb></lb>per la precedente, ed osservando <lb></lb>ch&#039;essendo C, D posati sul me­<lb></lb>desimo declivio hanno i momenti <lb></lb>proporzionali alle moli, riman di­<lb></lb>mostrato dalle seguenti equazioni M.oC:M.oD=C:D=A:D=AB:BC. </s>

<s><lb></lb>Donde si conclude il Teorema meccanico nella sua propria forma: “ Mo­<lb></lb>mentum totale gravis, ad momentum quod habet in plano inclinato, est ut <lb></lb>longitudo ipsius plani inclinati ad perpendiculum ” (ibid., pag. </s>

<s>101). </s></p><p type="main">

<s>La terza proposizione che, dopo un corollario e uno scolio elegantissimi <lb></lb>relativi alla precedente, in questo libro del Torricelli, ricorre, non ha propria­<lb></lb><figure id="id.020.01.2398.3.jpg" xlink:href="020/01/2398/3.jpg"></figure></s></p><p type="caption">

<s>Figura 11.<lb></lb>mente alcuna importanza, come princi­<lb></lb>pio di mezzo a concluder la verità del <lb></lb>supposto galileiano, e solamente si scrive <lb></lb>per supplir, come l&#039;Autore credeva, al <lb></lb>difetto di Galileo. </s>

<s>Il difetto è però di <lb></lb>chi non vide la cosa nel secondo modo <lb></lb>come si dimostra la VI proposizione del <lb></lb>Dialogo terzo, benchè con processo di­<lb></lb>verso da questo qui, che è tale: s&#039;ab­<lb></lb>biano i piani AC, AB (fig. </s>

<s>11) di ugual lunghezza, ma variamente elevati in <lb></lb>C e in B: che i momenti dei gravi, posti sopra questi piani, stiano come <lb></lb>CE, BD, seni degli angoli delle elevazioni, è concluso dalle uguaglianze M.o<lb></lb>AB:M.oBF=FB:AB=FB:AC=BD:CE, osservando che M.o BF <lb></lb>=M.oAC, per essere AC, BF ugualmente inclinate. </s></p><p type="main">

<s>Il corollario, lo scolio, e il lemma, per servire a una nuova dimostra-<pb xlink:href="020/01/2399.jpg" pagenum="24"></pb>zione della Sesta galileiana, sono di una grande importanza, ma per la via <lb></lb>di concluder ciò, che ora a noi più preme, si rientra nella quarta proposizione, <lb></lb>la quale, com&#039;è presentata nel suo primo modo, non differisce per verità che <lb></lb>di pochissimo dalle dimostrazioni di Galileo, del Michelini e del Baliani. </s>

<s>Im­<lb></lb>perocchè, a provare che il tempo per BA, nella precedente figura, sta al <lb></lb>tempo per BF come BA sta a BF, presa BH terza proporzionale dopo AB, BF, <lb></lb>osserva che BF e BH sono isocrone, ond&#039;è che, dall&#039;aversi per la legge dei <lb></lb>moti accelerati T.oAB:T.oBH=√AB:√BH=AB:BF, ne concludeva an­<lb></lb>che il Torricelli, come i sopra commemorati Autori, il suo intento. </s></p><p type="main">

<s>Al Teorema meccanico, e a questa quarta bastava supplir la prima di <lb></lb>Galileo (Alb. </s>

<s>XIII, 166), per avere i mezzi necessari a dimostrar finalmente: <lb></lb>“ Gradus velocitatis ciusdem mobilis, super diversas planorum inclinationes <lb></lb>acquisiti, tunc aequales sunt, cum corumdem planorum elevationes aequales <lb></lb>sunt ” (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>108). Siano, sempre riferendosi all&#039;ultima figura, <lb></lb>AB, FB i piani aventi la medesima elevazione BD. </s>

<s>Sarà per la precedente <lb></lb>T.oAB:T.oFB=AB:FB.. Ora, qualunque ella siasi, si chiami V la velo­<lb></lb>cità, che acquista il grave giunto in A, e si chiami V′ la velocità, qualun­<lb></lb>que ella pure si sia, acquistata dal grave giunto in F. Avremo, per la ci­<lb></lb>tata prima di Galileo, T.oAB=AB/V:2, T.oBF=BF/V′:2, ossia V/2:V′/2= <lb></lb>AB/(T.oAB):BF/(T.oBF). Ma i termini di questa seconda ragione sono uguali, dunque <lb></lb>uguali sono anche i primi, e perciò V=V′ come doveva dimostrarsi. </s></p><p type="main">

<s>Ora si domanda: fu egli veramente conseguito il fine, per cui il Torri­<lb></lb>celli si dette a claborare e, intanto che si rimaneva nelle lettere private quella <lb></lb>di Galileo, divulgare in pubblico quest&#039;altra sua dimostrazione? </s>

<s>Si saranno <lb></lb>eglino, i Matematici, persuasi che il supposto principio si veniva a rendere <lb></lb>nel suo libro, per geometriche ragioni, evidente? </s>

<s>Ma se fossero bastate le <lb></lb>ragioni, il Baliani, da cinque anni, avrebbe dovuto fare l&#039;effetto, non essendo <lb></lb>la sua dimostrazione nè men bella di questa torricelliana, nè men conclu­<lb></lb>dente. </s>

<s>Nel rifiutar dunque che si faceva da tanti, prima le probabilità degli <lb></lb>sperimenti, e poi le ragioni della geometria, doveva esserci molta caparbictà, <lb></lb>della quale il Torricelli stesso ebbe a fare esperienza. </s></p><p type="main">

<s>Il Mersenno, dop&#039;aver letta la prima parte del trattato <emph type="italics"></emph>De motu gra­<lb></lb>vium naturaliter descendentium,<emph.end type="italics"></emph.end> prendeva la penna in mano per dire in <lb></lb>una sua lettera all&#039;Autore: “ Expectamus abs te postulati rationem, ab expe­<lb></lb>rientia, si fieri potest, independentem ” (MSS. Gal. </s>

<s>Disc., T. XLI, fol. </s>

<s>69). <lb></lb>— Ma non siete, padre, domandava il Torricelli maravigliato, giunto ancora <lb></lb>alla quinta proposizione del mio primo libro? </s>

<s>— E si sentiva rispondere: <lb></lb>— Io ho per nulla quella dimostrazione, condotta dal supporre i momenti <lb></lb>proporzionali alle velocità, che per me è un paralogismo vostro e di Galileo. </s>

<s>— <lb></lb>Alle quali accuse si rispondeva con l&#039;eloquenza di queste ragioni: </s></p><p type="main">

<s>“ Quod ego suppono pag. </s>

<s>104 cum Galileo adeo manifestum mihi vide­<lb></lb>tur, ut sine ulla dubitatione loco principii admitti et concedi posse videatur. <pb xlink:href="020/01/2400.jpg" pagenum="25"></pb>Ratio physica est: si fuerint a diversis planis duae sphaerae, ex. </s>

<s>gr. </s>

<s>vitreae <lb></lb>et aequales, postquam ostendero momentum unius, ad momentum alterins, <lb></lb>esse duplum, quis non concedat et velocitatem ad velocitatem esse duplam? </s>

<s><lb></lb>Dupla enim causa duplum effectum parere debet in eodem subiecto. </s>

<s>Moles <lb></lb>supponuntur aequales eiusdemque materiae, virtus vero, quae impellit alle­<lb></lb>ram molem, dupla demonstratur virtutis alterius: ergo, si dupla virtus est, <lb></lb>duplam procul dubio velocitatem efficiet ” (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>76). </s></p><p type="main">

<s>— Se così è, insisteva a questo punto del ragionamento il Mersenno, il <lb></lb>momento di C (nella figura X qui poco addietro) dovrebbe esser tanto mag­<lb></lb>giore del momento di D, quanto la mole è maggior della mole: e nonostante <lb></lb>voi, nella vostra proposizione seconda, dite che que&#039;due momenti sono uguali. <lb></lb></s>

<s>— Ma non badava, così dicendo, che i due gravi eran posati sul medesimo <lb></lb>declivio, per cui il Torricelli, a rimuovere l&#039;obiezione inconsiderata, prose­<lb></lb>guiva in tal guisa il suo discorso: </s></p><p type="main">

<s>“ Neque obstat quod obiici potest de gravibus in eodem plano consti­<lb></lb>tutis, quae, sive sint eiusdem molis, sive non, aequali tamen velocitate fe­<lb></lb>runtur. </s>

<s>Nam omnia gravia, cuiuscumque molis, ponderis et figurae sint, li­<lb></lb>bere demissa a loco absque impedimentis eadem velocitate feruntur deorsum, <lb></lb>nempe tam sphaera aurea quam lapidea, ac etiam lignea, immo et ex materia <lb></lb>laevissima eadem velocitate ex se descenderent. </s>

<s>Si vero pusillum quoddam <lb></lb>spatium graviores materiae videntur antecedere non procedit hoc ab inae­<lb></lb>qualitate virtutum moventium, quae ulla est, sed ab inaequalitate impedimen­<lb></lb>torum. </s>

<s>Tantum enim est in unoquolibet corpore virtutis moventis, quantum <lb></lb>est materiae. </s>

<s>Exempli gratia in uncia auri, atque in uncia cerae, tantumdem <lb></lb>est et materiae et virtutis moventis, licet caera appareat multum maiorem <lb></lb>locum occupare. </s>

<s>Propterea, dum quiescunt, pariter gravitant, et manifeste <lb></lb>aequalitatem virtutum indicant. </s>

<s>Quando vero moventur, aurum praecedit, sed <lb></lb>longe minus quam pro ratione specierum gravitatis, ipsam caeram, quod qui­<lb></lb>dem accidit quia, cum virtutes aequales sint in utraque materia, si altera <lb></lb>cum maiori mole ambientis medii, altera cum minori luctari debet. </s>

<s>” </s></p><p type="main">

<s>“ Quando vero consideremus duas sphaeras ciusdem materiae, sed alte­<lb></lb>ram unius unciae, alteram vero decem librarum, aequaliter hae descendunt <lb></lb>in eodem plano, quia in utraque sphaera virtutes illae arcanae, licet inac­<lb></lb>quales sint inter se, eamdem habent rationem quam resistentiae, hoc est cor­<lb></lb>pora ipsa movendo. </s>

<s>Vel si mavis, hoc modo: virtus minor, ad minus pon­<lb></lb>dus a se movendum, eamdem habet rationem quam virtus maior, ad maius <lb></lb>pondus a se movendum. </s>

<s>Exiguum illud quod videtur aliquando praecedere <lb></lb>gravius, quando maxima fuerit inter pondera proportio, oritur, non a prin­<lb></lb>cipiis intrinsecis, sed ab externis impedimentis, nempe a densitate medii, quae, <lb></lb>ut optime docet Galileus, magis impedit minores moles quam maiores, quan­<lb></lb>doquidem minores, cum maiorem superficem habeant, a maiori quantitate <lb></lb>medii retardantur. </s>

<s>” </s></p><p type="main">

<s>“ Mirum ergo non sit si metalla, lapides, ligna etc. </s>

<s>tam in descensu <lb></lb>libero, quam in eodem plano collocata, <gap></gap> eadem velocitate descendere, cum <pb xlink:href="020/01/2401.jpg" pagenum="26"></pb>omnia gravia aequalem sibi ipsis virtutem moventem habeant. </s>

<s>At in planis <lb></lb>inaequaliter inclinatis, ubi ego ostendero duas sphaeras aequales et aeque <lb></lb>graves inaequalia momenta habere, quid ni inferre possim illam, quae maius <lb></lb>habet momentum, maiori velocitate delabi pro ratione momentorum? </s>

<s>” </s></p><p type="main">

<s>“ Sed ego nimis fortasse provectus sum in hac causa, quae tanto pa­<lb></lb>trocinio mihi non videbatur indigere. </s>

<s>Satis enim erat inter pondus et mo­<lb></lb>mentum distinguere ” (ibid., fol. </s>

<s>76, 77). </s></p><p type="main">

<s>Se avesse avuto il Mersenno la mente libera da pregiudizi e l&#039;animo da <lb></lb>passioni, si sarebbe dovuto persuadere della verità delle cose, che tanto chia­<lb></lb>ramente veniva in questo discorso esponendogli il Torricelli, ma egli persi­<lb></lb>steva caparbiamente in. </s>

<s>dire che, nonostante la quinta proposizione dimostrata <lb></lb>da lui, il supposto galileiano aveva tuttavia bisogno di prove. </s>

<s>Soggiungeva <lb></lb>un&#039;altra difficoltà, ed era non si poter, dall&#039;essere i tempi proporzionali agli <lb></lb>spazi, concludere che le velocità sono uguali, altro che nei moti equabili; e <lb></lb>che avrebbero dovuto perciò Galileo e il Torricelli dimostrar che gli spazi <lb></lb>passati equabilmente dal mobile son proporzionali a quelli, che passerebbe <lb></lb>nel medesimo tempo con moto accelerato. </s>

<s>Sembrerebbe la cosa incredibile a <lb></lb>chi sa e ripensa che s&#039;incomincia a dimostrar ciò per l&#039;appunto infino dal <lb></lb>primo aprire, nel terzo dialogo delle Nuove scienze, il trattato del moto, ma <lb></lb>Michelangiolo Ricci ce ne assicura con queste parole, scritte da lui in una <lb></lb>lettera allo stesso Torricelli: </s></p><p type="main">

<s>“ Le opposizioni fatte al trattato del moto dal padre Mersenno si ridu­<lb></lb>cono a pochi capi<gap></gap> Oppone primieramente, e se ne reputa assai l&#039;Autore, a <lb></lb>quella riprova della volgare definizione data al moto accelerato, che si trova <lb></lb>a carte 164, cioè che la velocità cresce secondo lo spazio. </s>

<s>Dice esser vero <lb></lb>nel moto equabile, che, sendo le velocità in proporzione delli spazi, sono que­<lb></lb>sti passati in egual tempo, ma bisogna che il Galileo provi, il che non fa, <lb></lb>che posta la definizione volgare ne segue che la velocità, con la quale un <lb></lb>mobile passa v. </s>

<s>g. </s>

<s>BC, sia uguale ad un moto equabile, e la velocità, con <lb></lb>la quale è passato lo spazio BA dallo stesso mobile, sia uguale ad un moto <lb></lb>equabile, e poi questi due moti equabili abbiano la proporzione di BC a BA. </s>

<s><lb></lb>Oppone nel secondo luogo che l&#039;assunto primo fatto dal Galileo, ma da V. S. <lb></lb>dimostrato, sia bisognoso di prova, e perciò o probabile o improbabile, ed in <lb></lb>conseguenza le proposizioni sei seguenti asserisce esser tanto lontane dal­<lb></lb>l&#039;evidenza geometrica, quanto è impossibile aver certezza d&#039;una conclusione <lb></lb>dedotta da verosimile assunto. </s>

<s>Finalmente dice esser difficilissimo il certifi­<lb></lb>carsi dell&#039;esattezza dell&#039;esperienza fatta da Galileo, e riferita a carte 175 (mi­<lb></lb>surando gli spazi in un regolo inclinato, lungo la incavatura del quale si faceva <lb></lb>scendere una palla di bronzo, e i tempi nelle clessidre, con pesar, durante la <lb></lb>scesa, l&#039;acqua stillata) ed egli ne adduce in contrario una fallacissima, come <lb></lb>l&#039;avrà letta nella lettera del padre Mersenno. </s>

<s>Con questi fondamenti presume <lb></lb>il Gesuita d&#039;alzar rocca inespugnabile ai danni del Galileo e della sua Scuola, e <lb></lb>con mille vanti di sè medesimo e scherno del Galileo si dimostra non men leg­<lb></lb>gero ne&#039;costumi, che sia nella dottrina ” (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>116). </s></p><pb xlink:href="020/01/2402.jpg" pagenum="27"></pb><p type="main">

<s>Chiamasi qui dal Ricci il Mersenno gesuita, non perchè fosse propria­<lb></lb>mente tale nell&#039;abito esteriore, o nella profession religiosa, ma perchè con­<lb></lb>sentiva e cooperava con i gesuiti in fare ogni sforzo per non veder altri prima <lb></lb>di loro sorgere a instituire la nuova scienza del moto. </s>

<s>L&#039;ufficio però d&#039;alzar <lb></lb>rocca inespugnabile ai danni di Galileo non si stettero costoro in affidarlo <lb></lb>allo zelante Frate minimo, estraneo al loro collegio, ma se l&#039;assunsero per <lb></lb>sè medesimi, deputandone particolarmente Pietro Cazr e Niccolò Cabeo. </s>

<s>Il <lb></lb>Gesuita italiano colse l&#039;occasione d&#039;infirmare i fondamenti della Scienza ga­<lb></lb>lileiana nelle <emph type="italics"></emph>Questioni<emph.end type="italics"></emph.end> intorno ai quattro libri della meteorologia di Aristo­<lb></lb>tile, percorrendo agile e leggero, così portato com&#039;era dal vento dell&#039;ambi­<lb></lb>zione, il campo universale della Scienza. </s>

<s>Ma il Francese vi si dedicò di <lb></lb>proposito, scrivendo una dissertazione, ai paralogismi della quale non si potè <lb></lb>tener di rispondere il Gassendo, per salvar, nel difendere il vero, più l&#039;onore <lb></lb>della sua propria nazione, che quello di Galileo. </s></p><p type="main">

<s>Era un giorno il Filosofo parigino nella sua stanza di studio, col liber­<lb></lb>colo del Cazreo aperto innanzi agli occhi, alla pagina, dov&#039;ei diceva non es­<lb></lb>sere il postulato galileiano sufficientemente confermato dall&#039;esperienza, <emph type="italics"></emph>cum <lb></lb>rationes etiam non desint, quibus oppositum probabilius reddatur,<emph.end type="italics"></emph.end> e aveva <lb></lb>preso in mano la penna per seguitare a scrivere il § XIII della sua prima <lb></lb>epistola <emph type="italics"></emph>De proportione qua gravia decidentia accelerantur,<emph.end type="italics"></emph.end> affine di con­<lb></lb>futar la temeraria sentenza; quando entra a visitarlo Pietro Carcavy, nobi­<lb></lb>lissimo senatore e delle Matematiche studiosissimo, che, riconosciuta quella <lb></lb>cazreana dissertazione, e compresa l&#039;intenzion del Gassendo, gli annunziava <lb></lb>esser già comparita in Parigi una copia del trattato <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> del Torricelli, <lb></lb>dove, di quello stesso così disputato assunto galileiano, si dava la dimostra­<lb></lb>zione più vera e più concludente, che da un Geometra si potesse desiderare. <lb></lb></s>

<s>“ Praetereo autem, soggiunge esso Gassendo, ut, copia illius videndi statim <lb></lb>impetrata, deprehenderim rem confectam quinque propositionibus ” (Pari­<lb></lb>siis 1646, pag. </s>

<s>23), di ciascuna delle quali cinque torricelliane proposizioni <lb></lb>prosegue ordinatamente a trascrivere l&#039;enunciato. </s></p><p type="main">

<s>Il fatto così da esso Gassendo narrato, in tuono di solennità e d&#039;impor­<lb></lb>tanza, dice di per sè medesimo in quanta stima s&#039;avesse il Torricelli in <lb></lb>Francia, e quanto si credesse autorevole a persuadere i ritrosi con la ele­<lb></lb>gante eloquenza delle sue dimostrazioni. </s>

<s>Del Baliani non si fa motto, quasi <lb></lb>non avess&#039;egli, prima dello stesso Torricelli, dimostrato il medesimo. </s>

<s>Anzi è <lb></lb>notabile che, occorrendo al Gassendi nella citata epistola contro il Cazreo di <lb></lb>commemorare il trattato del Matematico genovese, edito in quell&#039;anno, che <lb></lb>si pubblicarono i Dialoghi di Galileo; si limiti a dir ivi che anche il Ba­<lb></lb>liani confermava essere ne&#039;declivii di uguale altezza uguali le velocità, <emph type="italics"></emph>ar­<lb></lb>gumento sumpto ab ipsis pendulorum vibrationibus.<emph.end type="italics"></emph.end> Potrebb&#039;esser che il <lb></lb>Matematico parigino avesse letto il trattatello del Nostro in una di quelle <lb></lb>prime copie, edite nel 1638, nella quale mancava la carta, fatta ristampar <lb></lb>nel Settembre dell&#039;anno dopo, aggiuntavi la dimostrazione del supposto ga­<lb></lb>lileiano, ma in ogni modo colui, che si voleva far passare per emulo invi-<pb xlink:href="020/01/2403.jpg" pagenum="28"></pb>dioso, dovè rimanersi indietro, nella fama e nella stima universale, a quel­<lb></lb>l&#039;altro, da per tutto acclamato come discepolo e promotore esimio di Galileo. </s></p><p type="main">

<s>L&#039;ingiustizia del pubblico giudizio, riconosciuta ora spassionatamente da <lb></lb>noi, doveva esser tanto più vivamente sentita da chi n&#039;era allora fatto segno, <lb></lb>onde, attribuendo forse il Baliani alla esiguità del volume, al negletto abito <lb></lb>esteriore, e alla trascuratezza della forma del libro l&#039;essere così passata inos­<lb></lb>servata ai Matematici la sua propria dimostrazione; volle tornare ancora a <lb></lb>tentare la sua fortuna, ampiando il trattato, e studiandosi di adornarlo con <lb></lb>qualche fior di eloquenza. </s>

<s>Lo distribuì in tre libri, in materia del moto dei <lb></lb>solidi, aprendosi nelle respettive prefazioni largo campo di speculare: e ve ne <lb></lb>aggiunse altri tre, in materia del moto dei liquidi, affinchè non avesse, nem­<lb></lb>meno da questa parte, a rimanersi l&#039;opera sua indietro a quella del Torri­<lb></lb>celli, che il pubblico ammirava già da due anni. </s></p><p type="main">

<s>Si sente alitar da ogni pagina, per non dire da ogni parola, quello spi­<lb></lb>rito di emulazione, che teneva agitato l&#039;animo dell&#039;Autore, ma perchè la <lb></lb>sostanza era insomma la medesima, l&#039;esser tornato a diffonderla, con tanta <lb></lb>larghezza, par che faccia l&#039;effetto de&#039;liquori a<gap></gap>acquati, i quali tanto gua­<lb></lb>dagnano nel volume, quanto scapitano nel sapore e nella fragranza. </s>

<s>Si può <lb></lb>veder l&#039;esempio di ciò, senz&#039;uscire dall&#039;argomento del nostro discorso, parago­<lb></lb>nando la dimostrazione del supposto galileiano, data nel trattatello del 1638, <lb></lb>con quella che si volle ampliare nel 1646, derivandola da più alti principii, <lb></lb>e conducendola per una serie più lunga di proposizioni. </s></p><p type="main">

<s>Pregevoli in ogni modo son nell&#039;opera del Baliani, sopra le altre, due <lb></lb>parti, che, se non si fossero trascurate dal Torricelli, gli risparmiavano le <lb></lb>opposizioni e le censure vanitosamente moleste del Merseuno. </s>

<s>Sanno i nostri <lb></lb>Lettori che la principale di quelle opposizioni nasceva dal non sapere inten­<lb></lb>dere qual relazione avessero con le velocità gl&#039;impeti o i momenti; a che il <lb></lb>Baliani fu sollecito di rispondere: “ Impetus differens est solum fortasse a <lb></lb>velocitate, quia impetus sit velocitas in actu primo, ita ut aliquo pacto im­<lb></lb>petus sit causa velocitatis ” (De motu natur., Genuae 1646, pag. </s>

<s>70). </s></p><p type="main">

<s>L&#039;altra censura del Mersenno consisteva nel dire che avrebbe dovnto il <lb></lb>Torricelli dimostrar che i moti accelerati si riducono a proporzion degli equa­<lb></lb>bili, ciò che il Baliani fa, dimostrando, in più semplice ed efficace modo di <lb></lb>Galileo, la seguente proposizione, scaturita dai più intimi seni del principio <lb></lb><figure id="id.020.01.2403.1.jpg" xlink:href="020/01/2403/1.jpg"></figure></s></p><p type="caption">

<s>Figura 12.<lb></lb>d&#039;inerzia: “ Grave in motu naturali, sive perpendiculari <lb></lb>sive inclinato, fertur sine ope gravitatis aequabili tempore <lb></lb>per duplum spatii praecedentis ” (ibid., pag. </s>

<s>58). </s></p><p type="main">

<s>Premesso ciò, e avendosi in secondo luogo per dimo­<lb></lb>strato, nell&#039;oramai noto triangolo ACB (fig. </s>

<s>12), che la nor­<lb></lb>male BD precide in D lo spazio CD isocrono con CB, si fa <lb></lb>via il Baliani a concludere la verità dell&#039;assunto galileiano, <lb></lb>con questa proposizione: “ Si linea perpendicularis et incli­<lb></lb>nata, ab codem puneto digressae, per quas idem grave naturaliter ducatur, se­<lb></lb>centur a recta normali ad inelinatam; impetus in punctis sectionis sunt ut <pb xlink:href="020/01/2404.jpg" pagenum="29"></pb>portiones linearum infra sectiones ” (ibid., pag. </s>

<s>72). Vuol dire, ritenuti i soliti <lb></lb>simboli, essere V.aB:V.aD=CB:CD, ciò che immediatamente consegue <lb></lb>dalle due premesse proposizioni, essendo per quellla V.aB=2CB/(T.oCB), V.aD= <lb></lb>2CD/(T.oCD), e per questa T.oCB=T.oCD; d&#039;onde V.aB:V.aD=CB:CD, <lb></lb>come si voleva provare, e anche V.aB:V.aD=CA:CB, per la similitu­<lb></lb>dine de&#039;triangoli ACB, DCB. </s></p><p type="main">

<s>Passa di qui il Baliani a dimostrare, in un&#039;altra proposizione, che <lb></lb>V.aA:V.aD=CA:CB, invocando per far ciò la legge dei moti accelerati, <lb></lb>che dà AC:CD=V.aA2:V.aD2; e osserva che, avendo i triangoli simili <lb></lb>ABC, CBD la medesima altezza BD, le basi AC, DC stanno come i quadrati <lb></lb>de&#039;lati omologhi AC, CB, onde V.aa2:V.aD2=AC2:CB2, ossia V.aA:V.aD= <lb></lb>CA:CB, come volevasi dimostrare. </s></p><p type="main">

<s>Per concludere poi la verità dell&#039;assunto galileiano mette il Baliani in <lb></lb>ordine un&#039;altra proposizione distinta, la quale è però superflua, avendosi <lb></lb>l&#039;intento per corollario immediato dalle due precedenti: perchè, se questa <lb></lb>dà V.aA:V.aD=CA:CB, e quella dà V.aB:V.aD=CA:CB; dunque <lb></lb>V.aA=V.aB, senza bisogno d&#039;altri discorsi. </s></p><p type="main">

<s>Dopo dieci anni, da che il Baliani veniva così più solennemente a con­<lb></lb>fermar la dimostrazione del Torricelli, usciva postuma in Bologna, inserita <lb></lb>nel terzo dialogo delle Nuove scienze, che per la prima volta si ristampava; <lb></lb>quella di Galileo, aspettata da tutti con tanto desiderio. </s>

<s>Sembrava perciò che <lb></lb>dovesse fra&#039;Matematici finalmente cessare ogni mormorio, e che dovessero <lb></lb>nella dimostrata verità quietar l&#039;intelletto, quando, in un libro venuto d&#039;Olanda, <lb></lb>e in cui l&#039;Autore, per sopredificarvi suntuosamente, veniva ricercando i fon­<lb></lb>damenti della scienza galileiana; dop&#039;esservisi dimostrato che lo spazio per­<lb></lb>corso equabilmente dal mobile, col massimo grado della velocità acquistata, <lb></lb>è doppio di quello che aveva prima passato acceleratamente, s&#039;ebbe a leg­<lb></lb>gervi con gran maraviglia soggiunte queste parole: “ Hinc vero non difficile <lb></lb>iam erit demonstrare propositionem sequentem, quam concedi sibi ut quodam­<lb></lb>modo per se manifestam Galileus postulavit. </s>

<s>Nam demonstratio illa, quam <lb></lb>postea adferre conatus est, quaeque in posteriori operum eius editione extat, <lb></lb>parum firma meo quidem iudicio videtur. </s>

<s>” </s></p><p type="main">

<s>Si leggono queste parole a pag. </s>

<s>62 del primo tomo delle Opere di Cri­<lb></lb>stiano Huyghens, stampate nel 1724 in Leida, e il nome dell&#039;Autore, e il <lb></lb>saper che dal primo libro dell&#039;<emph type="italics"></emph>Horologium oscillatorium<emph.end type="italics"></emph.end> sono state trascritte, <lb></lb>fruga vivamente la curiosità di veder com&#039;altrimenti e meglio di Galileo abbia <lb></lb>il celebre uomo, nella proposizione sua sesta, dimostrato: “ Celeritates gra­<lb></lb>vium, super diversis planorum inclinationibus descendendo acquisitae, aequa­<lb></lb>les sunt, si planorum elevationes fuerint aequales ” (ibid.). </s></p><p type="main">

<s>Siano, dice l&#039;Huyghens, AB, CB (fig. </s>

<s>13) i due piani inclinati, e AE, CD <lb></lb>le loro elevazioni uguali: se un mobile si faccia scendere ora da A, ora da C, <lb></lb>giungerà in B col medesimo grado di velocità, benchè sia l&#039;una scesa, co-<pb xlink:href="020/01/2405.jpg" pagenum="30"></pb>munque vogliasi, più precipitosa dell&#039;altra. </s>

<s>Il ragionamento che in tal forma <lb></lb>procede, secondo le parole proprie dell&#039;Autore, piglia valore dalla proposi­<lb></lb>zione IV, nella quale era già dimostrato che risalirebbe in su il mobile da B <lb></lb><figure id="id.020.01.2405.1.jpg" xlink:href="020/01/2405/1.jpg"></figure></s></p><p type="caption">

<s>Figura 13.<lb></lb>nello stesso tempo, e passando per <lb></lb>i medesimi gradi di velocità, coi <lb></lb>quali era prima sceso da C: “ Si <lb></lb>enim per CB cadens minorem ve­<lb></lb>locitatem acquirere dicitur, quam <lb></lb>cadens per AB, habeat ergo per <lb></lb>CB cadens eam dumtaxat, quam <lb></lb>per FB acquireret, posita nimirum <lb></lb>FB minore quam AB. </s>

<s>Acquiret au­<lb></lb>tem per CB cadens eam velocitatem, qua rursus por totam BC possit ascen­<lb></lb>dere. </s>

<s>Ergo, et per FB, acquiret eam velocitatem, qua possit ascendere per <lb></lb>totam BC. </s>

<s>Ideoque cadens ex F in B, si continuet motum per BC, quod re­<lb></lb>percussu ad superficiem obliquam fieri potest, ascendet usque in C, hoc est <lb></lb>altius quam unde decidit, quod est absurdum ” (ibid., pag. </s>

<s>63). </s></p><p type="main">

<s>Suppone dunque l&#039;Huyghens che, sceso il mobile da F in B, nel riflet­<lb></lb>tersi per BC o per qualunque altra inclinazione diversa, debba risalir giusto <lb></lb>a tanta altezza, quanta fu la caduta: ma questo insomma era quello che do­<lb></lb>vevasi dimostrare, e intorno a che s&#039;era sottilmente aggirato il discorso di <lb></lb>Galileo. </s>

<s>L&#039;Huyghens tiene il medesimo filo, e lo conosce e lo confessa, di­<lb></lb>cendo di voler nella sua quinta proposizione dimostrar di nuovo quel che aveva <lb></lb>già dimostrato nella seconda <emph type="italics"></emph>Galilei methodum sequendo.<emph.end type="italics"></emph.end> Quella quinta in­<lb></lb>fatti dell&#039;Orologio oscillatorio corrisponde con lo scolio alla proposizione XXIII <lb></lb>del Dialogo terzo, dove graficamente si dimostra che, se lo spazio passato <lb></lb>nello scendere acceleratamente si rappresenta dal triangolo, lo spazio passato <lb></lb>con moto equabile nel medesimo tempo, e con l&#039;ultimo grado di velocità <lb></lb>acquistato nella discesa, vien rappresentato dal rettangolo ossia dal doppio. </s></p><p type="main">

<s>Si fanno da ciò via ambedue gli Autori a considerare gli effetti del moto <lb></lb>incidente e del riflesso, così Galileo concludendo il suo sottile discorso: “ Ex <lb></lb>his igitur rationabiliter asserere possumus quod, si per aliquod planum in­<lb></lb>clinatum fiat descensus, post quem sequatur reflexio per planum elevatum, <lb></lb>mobile per impetum conceptum ascendet usque ad eandem altitudinem, seu <lb></lb>elevationem ab horizonte. </s>

<s>Ut si fiat descensus per CB (nella precedente <lb></lb>figura) feretur mobile, per planum reflexum BG, usque ad horizontalem CG ” <lb></lb>(Alb. </s>

<s>XIII, 202). Questo si fa conseguire dai principii già dimostrati, quando <lb></lb>però gli angoli dell&#039;incidenza e della riflessione siano uguali, ma Galileo sog­<lb></lb>giunge che il teorema è vero “ non tantum si inclinationes planorum sint <lb></lb>aequales, verum etiam si inaequales sint, qualis est plani AB “ (ibid.) e per <lb></lb>dimostrarlo invoca il principio, che nella prima edizione s&#039;aveva per suppo­<lb></lb>sto, ma che nella seconda postuma si concludeva con matematico ragiona­<lb></lb>mento. </s>

<s>Non dando pure a questa conclusione, come vuol l&#039;Huyghens, nessun <lb></lb>assoluto valore, è un fatto che nel <emph type="italics"></emph>Dialogo,<emph.end type="italics"></emph.end> come fu stampato nel 1638 in <pb xlink:href="020/01/2406.jpg" pagenum="31"></pb>Leyda, s&#039;ha disteso il medesimo discorso, che nell&#039;<emph type="italics"></emph>Orologio<emph.end type="italics"></emph.end> stampato nel 1673 <lb></lb>a Parigi, se non che, mentre là si supponeva un principio per la dimostra­<lb></lb>zione, qui supponesi invece quel medesimo, ch&#039;era proposto di dimostrare. </s></p><p type="main">

<s>Così essendo, sembra a noi che fosse lodevolissima l&#039;intenzione di Ales­<lb></lb>sandro Marchetti, di richiamar cioè alla memoria dei Matematici, i quali die­<lb></lb>tro la grande autorità dell&#039;Olandese avrebbero potuto deviare, le più schiette <lb></lb>e severe tradizioni della scuola italiana. </s>

<s>Dell&#039;essere esso Marchetti riuscito a <lb></lb>dare a quelle tradizioni, così variamente maneggiate, una forma nuova, con <lb></lb>troppa vanità si compiacque, e ciò dette a&#039;suoi nemici occasione di claun­<lb></lb>niarlo, e con livore impotente di strascicarlo nel fango. </s>

<s>Il Nelli, in cui aveva <lb></lb>il Grandi insufflato l&#039;odio ma non la scienza, concludeva così una sua que­<lb></lb>stione storica: “ Adunque è evidente ed innegabile che il signor Alessandro <lb></lb>Marchetti non è l&#039;autore dell&#039;opera <emph type="italics"></emph>De resistentia solidorum ”<emph.end type="italics"></emph.end> (Saggio di <lb></lb>storia letter., Lucca 1759, pag. </s>

<s>53). Il principio e i termini di mezzo per <lb></lb>questa conclusione sono assai bene strani, fondandosi sul giudizio poco favo­<lb></lb>revole fatto dai Matematici contemporanei intorno a varii opuscoli geometrici <lb></lb>dello stesso Marchetti. </s>

<s>Ma se fosse logica buona concludere da alcune pro­<lb></lb>posizioni false o men perfettamente dimostrate l&#039;inettitudine di un autore a <lb></lb>condur da sè solo un&#039;Opera, si dovrebbe dal recente esempio argomentare <lb></lb>che non è l&#039;Huyghens l&#039;autore dell&#039;Orologio oscillatorio, e a più forte ra­<lb></lb>gione dedurre, dai tanti falli notati e notabili, non esser di Galileo i libri dei <lb></lb>moti locali e dei proietti. </s></p><p type="main">

<s>Faceva dunque propriamente al Nelli più difetto il senso comune che <lb></lb>la logica, e che mancasse a lui la scienza necessaria per scriverne la storia <lb></lb>è notissimo a chi ha letto que&#039;suoi loquaci volumi; ma a cui fosse venuta <lb></lb>meno la pazienza, può servire il sapere quel ch&#039;egli dice a sfregiar le pro­<lb></lb>posizioni dal Marchetti ordinate, per concludere in ultimo la verità dell&#039;as­<lb></lb>sunto galileiano. </s>

<s>La seconda di quelle proposizioni, che dall&#039;Autore si mette <lb></lb>per <emph type="italics"></emph>Fondamento alla scienza universale del moto,<emph.end type="italics"></emph.end> è così formulata: “ Mo­<lb></lb>menta eiusdem ponderis, supra diversas planorum inclinationes, eam inter se <lb></lb>habent rationem, quam perpendiculares orizonti demissae a sublimibus eo­<lb></lb>rumdem planorum punctis, aequalesque ex ipsis longitudines abscindenti­<lb></lb>bus ” (Pisis 1674, pag. </s>

<s>9). “ Questa, dice il Nelli, la propose e dimostrò <lb></lb>prima di ogni altro a me noto il Galileo nella <emph type="italics"></emph>Scienza meccanica,<emph.end type="italics"></emph.end> dopo di <lb></lb>cui la dimostrò ancora il Torricelli nella sua III proposizione, in tempo che <lb></lb>questi, per quanto io argomento dal suo schietto parlare, non aveva ancora <lb></lb>notizia del detto trattato di Galileo ” (Saggio cit., pag. </s>

<s>24, 25). Chi scrisse <lb></lb>così non doveva aver letta mai la <emph type="italics"></emph>Scienza meccanica,<emph.end type="italics"></emph.end> perchè Galileo sup­<lb></lb>pone ivi solamente la verità del Teorema, che poi incidentalmente dimostrò <lb></lb>nella sesta proposizione del Dialogo terzo, dove non avendo il Torricelli sa­<lb></lb>puto riconoscere il già fatto, si lusingò d&#039;esser egli stato il primo. </s>

<s>Come <lb></lb>non lesse il Nelli quel trattato meccanico, così può credersi che non leggesse <lb></lb>e non intendesse gli altri di Galileo, a quel modo che non gli leggono e non <lb></lb>gl&#039;intendono tanti altri al pari di lui elogiatori del divino Uomo; ond&#039;es-<pb xlink:href="020/01/2407.jpg" pagenum="32"></pb>sendo la sentenza loro senza giudizio è meglio proceder oltre per vedere, <lb></lb>giacch&#039;è un&#039;occhiata sola, qual sia quella nuova forma, che si diceva aver <lb></lb>data il Marchetti alla sua seconda proposizione sopra annunziata, e dalla <lb></lb>quale si facevano dipendere le altre tre concludenti la verità fondamentale <lb></lb>della scienza universale del moto. </s></p><p type="main">

<s>Scendano (tale è la dimostrazione a cui l&#039;analisi ha reciso le lussuria <lb></lb><figure id="id.020.01.2407.1.jpg" xlink:href="020/01/2407/1.jpg"></figure></s></p><p type="caption">

<s>Figura 14.<lb></lb>delle parole) dallo stesso perpen­<lb></lb>dicolo BC (fig. </s>

<s>14) le vie oblique <lb></lb>AB, BD, e perchè quella è neces­<lb></lb>sariamente più lunga di questa, <lb></lb>sia dunque AF l&#039;uguale,e si con­<lb></lb>duca il perpendicolo FG: il Teo­<lb></lb>rema meccanico già nella prima <lb></lb>proposizion dimostrato, e i trian­<lb></lb>goli simili ABC, AFG danno M.oDB:M.oAB=AB:BD=AB:AF= <lb></lb>BC:FG, d&#039;onde, osservando che M.oAB=M.oAF, è conseguito il proposito. </s></p><p type="main">

<s>La terza, nella quale si dimostra che i tempi per i piani ugualmente <lb></lb>clevati son proporzionali agli spazi, e la quinta che, dall&#039;aversi i tempi pro­<lb></lb>porzionali agli spazi, conclude dover essere le velocità uguali, troppo risen­<lb></lb>tono l&#039;imitazione delle dimostrazioni date dagli Autori precedenti, perchè, <lb></lb>presa BF (nella figura 14) terza proporzionale dopo AB, BD, anche il Mar­<lb></lb>chetti dimostra che, avendo il grado della velocità in F la medesima pro­<lb></lb>porzione tanto alla velocità in A, quanto alla velocità in D, queste debbono <lb></lb>essere tra loro uguali. </s>

<s>“ Ergo gradus velocitatis in puncto F eamdem habe­<lb></lb>bit proportionem, ad gradum velocitatis in puncto A, quam ad gradum ve­<lb></lb>locitatis in puncto D: ideoque gradus velocitatis acquisiti in A et D aequales <lb></lb>sunt ” (Fundamenta cit., pag. </s>

<s>21). È vero dunque che la novità non s&#039;in­<lb></lb>trodusse dal Marchetti, altro che nella sua seconda proposizione, ma l&#039;utile <lb></lb>che conseguiva, o che poteva conseguire alla scienza da questo dispregiato <lb></lb>opuscolo del professore pisano, era quello di ridurla sui sentieri prima aperti <lb></lb>in Italia, e segnati da Galileo, dal Torricelli e dal Baliani. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Tale, quale s&#039;è da noi fin qui narrata, è la storia delle sollecite cure, <lb></lb>che si dettero i Matematici, da Galileo infino all&#039;Huyghens e al Marchetti, <lb></lb>per confermar la verità del fondamento meccanico nelle menti comhattute dal <lb></lb>dubbio. </s>

<s>L&#039;importanza dell&#039;argomento ci ha tirato fuori di quella via, alla <lb></lb>quale intendiamo ora di ritornare, per salir dietr&#039;essa nuovamente ad Ar­<lb></lb>cetri, dove lasciammo Galileo che, perduta la vista e perciò la facoltà di po­<lb></lb>tersi andare internando in più profonde speculazioni, s&#039;occupava nelle tene­<lb></lb>bre notturne intorno ai primi e principali teoremi di Meccanica, per ordinarli <pb xlink:href="020/01/2408.jpg" pagenum="33"></pb>e disporli in miglior forma ed evidenza. </s>

<s>Così dicendo egli stesso al Baliani, <lb></lb>gli soggiungeva di aver la speranza di poter migliorare e ampliare lo scritto, <lb></lb>fin allora da sè pubblicato intorno alle nuove scoperte proprietà del moto. </s></p><p type="main">

<s>Uno de&#039;primi frutti di quelle occupazioni fu il frammento dettato al Vi­<lb></lb>viani, perchè alla prima occasione di una ristampa s&#039;inserisse, dopo lo sco­<lb></lb>lio alla proposizione seconda, nel terzo dialogo delle Scienze nuove. </s>

<s>Non fu <lb></lb>quella ristampa così sollecita come si credeva, e non ebbe perciò l&#039;Autore <lb></lb>il tempo di veder l&#039;opera sua ampliata e migliorata, secondo gli studii fat­<lb></lb>tivi attorno, e secondo la conceputa speranza. </s>

<s>Anzi, quando fosse pure vis­<lb></lb>suto infino al 1656, avrebbe dovuto sentir sè, e rimandare i lettori non so­<lb></lb>disfatti, in trovar che i perfezionamenti ai Dialoghi, già tanto ammirati, si <lb></lb>riducevano alla sola dimostrazione inserita dopo il detto scolio dal nuovo edi­<lb></lb>tore di Bologna. </s>

<s>In ripensare al fatto si sentono certi dubbi nascere nella <lb></lb>mente che ci ragiona: o non son vere quelle occupazioni notturne, delle <lb></lb>quali Galileo scriveva al Baliani, o de&#039;frutti loro non si lasciò scritta o se <lb></lb>ne smarri la memoria. </s>

<s>E dall&#039;altra parte, dovendo quelle scritture esser ri­<lb></lb>maste in mano al Viviani, a cui furono dettate, com&#039;era possibile che il di­<lb></lb>scepolo zelantissimo volesse defraudare invidioso alla gloria o reluttar sacri­<lb></lb>lego alle ultime volontà del Maestro, ritenendosi que&#039;fogli, invece di mandargli <lb></lb>a Bologna al Rinaldini, che ne arricchisse la nuova edizione? </s>

<s>Nè quelle ag­<lb></lb>giunte ai Dialoghi dovevano aver minore importanza o dar minore sodisfa­<lb></lb>zione ai lettori delle lettere al Castelli e all&#039;Antonini, che dalle mani del <lb></lb>dottissimo signor Viviani, discepolo di sì gran maestro, diceva nella sua pre­<lb></lb>fazione d&#039;aver ricevute il bolognese tipografo Carlo Manolessi. </s></p><p type="main">

<s>Dietro queste considerazioni, ci si rendeva probabile che le speranze di <lb></lb>correggere e di ampliare gli scritti intorno al moto fossero, per l&#039;impotente <lb></lb>vecchiezza dell&#039;Autore, tornate vane: nonostante ci mettemmo a cercar per <lb></lb>i manoscritti galileiani con più diligenza che mai, e fu particolarmente trat­<lb></lb>tenuta la nostra attenzione sul Tomo quarto della Parte quinta. </s>

<s>Ivi ritrovansi <lb></lb>veramente di mano del Viviani scritti vari frammenti di dialogo, relativi alle <lb></lb>Nuove scienze, e la ben distinta calligrafia giovanile ci volle far credere da <lb></lb>principio che fossero in que&#039;frammenti, dettati al suo giovane ospite, rac­<lb></lb>colti da Galileo i frutti delle sue vigilie. </s>

<s>Essendo poi per la maggior parte <lb></lb>quegli argomenti riconosciuti da noi di grande importanza, e confermandoci <lb></lb>in credere impossibile che, se Galileo gli avesse dettati a quel modo coll&#039;in­<lb></lb>tenzione d&#039;inserirli nella prima nuova edizione, non avrebbe il Viviani in <lb></lb>nessun modo mancato di adempire al suo sacrosanto dovere; ci volgemmo a <lb></lb>pensare che non dettatura altrui ma esercizio proprio di chi gli scrisse fos­<lb></lb>sero quegli elaboratissimi dialogismi. </s>

<s>La probabilità poi parve ci si riducesse <lb></lb>a certezza occorrendoci a notar nelle nostre ricerche quel che ora diremo. </s></p><p type="main">

<s>Nel citato manoscritto, volume quarto, ci abbattemmo a leggere, auto­<lb></lb>grafo del Viviani, un colloquio, dove il Sagredo propone di dimostrar l&#039;equi­<lb></lb>librio nella bilancia di braccia disuguali, scansando quel comun principio dei <lb></lb>Meccanici reputato vizioso, perchè s&#039;introduceva la causa, invece dell&#039;effetto <pb xlink:href="020/01/2409.jpg" pagenum="34"></pb>presente. </s>

<s>Il Salviati approva come ragionevole il dubbio, e confessa di non <lb></lb>essere nemmen egli sodisfatto di concludere da un moto in potenza le ragioni <lb></lb>del moto attuale. </s></p><p type="main">

<s>L&#039;argomento, come ben si vede, è di grande importanza, trattandosi di <lb></lb>decidere intorno alla verità o alla falsità del famoso principio delle velocità <lb></lb>virtuali: che se il Salviati di questo frammento rappresentasse davvero il <lb></lb>Salviati del Dialogo, avremmo di qui il documento più certo che Galileo, negli <lb></lb>ultimi anni della sua vita, repudiò quel principio, di cui il Lagrange gli attri­<lb></lb>buiva la gloria dell&#039;invenzione. </s>

<s>Ma come assicurarsi dell&#039;identità della per­<lb></lb>sona, che qui e nelle Nuove scienze conversa? </s>

<s>Il leggervi scritto di mano <lb></lb>del Viviani <emph type="italics"></emph>di questo ho l&#039;originale<emph.end type="italics"></emph.end> non ci quieta, potendogli noi doman­<lb></lb>dare: a che dunque supplirvi con la copia? </s>

<s>o di quale originale si tratta, <lb></lb>essendo tolta all&#039;Autore la facoltà di scrivere da sè medesimo? </s>

<s>Ma la riso­<lb></lb>luzione di ogni dubbio ci avvenne, quando svolgendo noi, fra i manoscritti <lb></lb>dei Discepoli di Galileo, il tomo CXXXV intitolato <emph type="italics"></emph>Raccolta di esperienze <lb></lb>senz&#039;ordine e di pensieri diversi di me Vincenzio Viviani, in diversi pro­<lb></lb>positi sovvenutimi intorno a materie meccaniche, fisiche, astronomiche, filo­<lb></lb>sofiche e altro;<emph.end type="italics"></emph.end> ci abbattemmo a leggere nei fogli 8, 9 quella scrittura da <lb></lb>noi pubblicata a pag. </s>

<s>165-67 del Tomo precedente, dove la sostanza del fram­<lb></lb>mento dialogizzato s&#039;espone in discorso disteso come pensiero proprio, sov­<lb></lb>venuto allo stesso Viviani, che chiama testimone di ciò Cosimo Galilei. </s></p><p type="main">

<s>Proseguendo però nei nostri studii, che potrebbero parere di arida eru­<lb></lb>dizione, ma che servono a noi di scandaglio per misurare le profondità del <lb></lb>pensiero, e di filo per aggirarci negl&#039;intricati laberinti del cuore dell&#039;uomo, <lb></lb>ci dovremmo persuadere, contro la nostra opinione, che l&#039;aver fatti il Vi­<lb></lb>viani suoi certi pensieri non vuol dire che non fossero stati prima di Gali­<lb></lb>leo. </s>

<s>Fu deliberato atto di usurpazione o incoscienza del tempo e del modo <lb></lb>come gli erano sovvenuti i medesimi pensieri? </s>

<s>La risposta sarebbe lunga, e <lb></lb>senza alcuna probabilità di cogliere il vero, e perciò basti a noi porre i fatti, <lb></lb>senza volerne penetrar le intenzioni, che forse traspariranno da ciò, che sa­<lb></lb>remo per dire, prima che finisca il presente discorso. </s></p><p type="main">

<s>Raccolti fra&#039;<emph type="italics"></emph>Pensieri varii<emph.end type="italics"></emph.end> del Viviani si trovano, nel citato manoscritto, <lb></lb>anche alcuni in materia de&#039;proietti, ed è notabile fra questi quello, che noi <lb></lb>pubblicammo a pag. </s>

<s>569 del Tomo precedente. </s>

<s>Ora anche si osserva che alle <lb></lb>cose messe qui in discorso disteso si dà nel IV tomo della parte V forma e <lb></lb>andamento di dialogo, con manifesta intenzione d&#039;inserirlo a pag. </s>

<s>270 del­<lb></lb>l&#039;edizione di Leida, dopo la VII proposizione della quarta Giornata. </s></p><p type="main">

<s>“ SIMPLICIO. — Di grazia, prima di passar più avanti, fatemi restar ca­<lb></lb>pace in qual modo si verifichi quel concetto, che l&#039;Autore suppone come <lb></lb>chiaro ed indubitabile: dico che, venendo il proietto da alto a basso descri­<lb></lb>vendo la semiparabola, cacciato per il converso da basso ad alto si debba ri­<lb></lb>tornare per la medesima linea, ricalcando precisamente le medesime vestigia, <lb></lb>non avendo per ciò fare altro regolatore, che la direzione della semplice linea <lb></lb>retta toccante la già disegnata semiparabola: nella cui declinazione fatta dal-<pb xlink:href="020/01/2410.jpg" pagenum="35"></pb>l&#039;alto al basso l&#039;impeto trasversale orizontale mi quieta, nello ammettere la <lb></lb>molta curvazione nella sommità, ma non so intendere nè discernere come <lb></lb>l&#039;impulso fatto da basso, per una retta tangente, possa restituire un impeto <lb></lb>transversale, atto a regolare quella medesima curvità. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Voi, signor Simplicio, nel nominare la retta tangente, <lb></lb>lasciate una condizione, cioè tangente ed inclinata, la quale inclinazione è <lb></lb>bastante a fare che il proietto, in tempi eguali, si accosti orizontalmente per <lb></lb>spazi eguali all&#039;asse della parabola, come forse più a basso intenderemo. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Ma intanto, per ora, ditemi, signor Simplicio, credete voi <lb></lb>che la linea descritta da un proietto da basso ad alto, secondo qualche incli­<lb></lb>nazione, sia veramente un&#039;intera linea parabolica, e che niente importi che <lb></lb>la proiezione si faccia da levante verso ponente o per l&#039;opposito? </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Credolo, purchè la elevazione sia la medesima, e che la <lb></lb>forza del proiciente sia la stessa. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Come voi ammettete questo, fatto che si sia un tiro da <lb></lb>qualsivoglia parte, che cosa v&#039;ha mettere in dubbio che la semiparabola da <lb></lb>basso ad alto del secondo tiro, che si faccia in contrario del primo, non sia <lb></lb>la medesima, che la seconda semiparabola del primo tiro, sicchè il proietto <lb></lb>ritorni per la medesima strada? </s>

<s>Quando ciò non fosse, nè anco la parabola <lb></lb>intera del secondo tiro sarebbe simile a quella del primo. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Già intendo, e mi quieta, però seguitiamo .... ” (MSS. <lb></lb>Gal., P. V, T. IV, fol. </s>

<s>4). </s></p><p type="main">

<s>Ora è manifesto essere un tal colloquio l&#039;esplicazione di quest&#039;altro, che <lb></lb>Galileo scriveva in semplice motto, di sua propria mano, a tergo del fol. </s>

<s>106, <lb></lb>nel secondo volume della parte quinta de&#039;suoi Manoscritti. </s>

<s>Noi trascrivemmo <lb></lb>quel motto a pag. </s>

<s>568 del Tomo precedente, ma è bene ridurlo qui sotto gli <lb></lb>occhi dei nostri lettori, perchè si persuadano meglio di ciò, che ha da par­<lb></lb>tecipar valore al nostro argomento. <lb></lb><figure id="id.020.01.2410.1.jpg" xlink:href="020/01/2410/1.jpg"></figure></s></p><p type="caption">

<s>Figura 15.</s></p><p type="main">

<s>“ SIMPLICIO. — Che la palla ricacciata in su <lb></lb>descriva la medesima SX (fig. </s>

<s>15) mi par duro. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Ma se non vi par duro che, <lb></lb>descrivendo la parabola intera YXS, possa ridescri­<lb></lb>vere la SXY, non vedete che di necessità fa la SX? ” </s></p><p type="main">

<s>Dicemmo aver fatto allora di ciò Galileo questo <lb></lb>semplice motto, quasi per un memoriale, quando <lb></lb>fosse venuto a distendere il Dialogo quarto. </s>

<s>Ma, <lb></lb>comunque sia, rimastosi il pensiero indietro, se ne sentiva più che mai l&#039;im­<lb></lb>portanza, ora che andavano attorno, nella lettera al Mersennno, le invidiose <lb></lb>critiche del Cartesio. </s>

<s>Fu perciò sollecito Galileo di supplire alla sua dimen­<lb></lb>ticanza, dettando al suo giovane ospite il dialogo da noi sopra trascritto, e <lb></lb>designandone il luogo, dove ei doveva inserirlo. </s>

<s>In mezzo a quelle sollecitu­<lb></lb>dini accennava anzi all&#039;intenzione di voler fare di più, per confermar sem­<lb></lb>pre meglio le sue dottrine contro gli oppositori, dimostrando che in tempi <lb></lb>uguali il proietto s&#039;accosta orizontalmente per spazi uguali. </s>

<s>L&#039;intenzione <pb xlink:href="020/01/2411.jpg" pagenum="36"></pb>però non s&#039;è trovato che fosse mandata ad effetto, e nemmeno il Torricelli <lb></lb><figure id="id.020.01.2411.1.jpg" xlink:href="020/01/2411/1.jpg"></figure></s></p><p type="caption">

<s>Figura 16.<lb></lb>vi s&#039;applicò di proposito, benchè <lb></lb>si concluda lo stesso dalla quarta <lb></lb>proposizione del suo libro secondo; <lb></lb>imperocchè, avendosi ivi dimostrato <lb></lb>che gli spazi DE, FG, IH (fig. </s>

<s>16) <lb></lb>son passati ne&#039;medesimi tempi, dal­<lb></lb>l&#039;essere le DI, EH parallele si con­<lb></lb>clude che il proietto s&#039;accosta o si <lb></lb>discosta orizontalmente per spazi <lb></lb>uguali. </s></p><p type="main">

<s>Ma non volendoci dilungar di <lb></lb>troppo dal proposito nostro, dicia­<lb></lb>mo esser dunque un fatto certis­<lb></lb>simo che il pensiero di dimostrar <lb></lb>come sia medesima la semipara­<lb></lb>bola, o tirando di punto in bianco <lb></lb>o con direzione elevata, accolto dal Viviani fra&#039;suoi, era prima albergato nel <lb></lb>cervello di Galileo. </s>

<s>E perchè la cosa è bene assai singolare, vogliamo aggiun­<lb></lb>gere un altro esempio, pure in materia de&#039;proietti, intorno ai quali mette <lb></lb>il Viviani per sue le considerazioni, da noi pubblicate nell&#039;altro Tomo di <lb></lb>questa Storia della Meccanica. </s>

<s>Noi possiamo però assicurare i lettori che <lb></lb>quelle medesime considerazioni erano state fatte già da Galileo, dettandole <lb></lb>così come noi le trascriviamo a Marco Ambrogetti, in quel tempo che si <lb></lb>pensava a far ristampare in latino, insieme con le altre opere, anche i Dia­<lb></lb>loghi del moto. </s></p><p type="main">

<s>“ SIMPLICIO. — Summa quidem perspicuitate, atque ingenio plena sunt <lb></lb>vestra haec inventa, et si eo prorsus modo, quo mente percipiuntur, ita exe­<lb></lb>qui liceret; utilitas, et praesertim in re militari, non mediocris esset existi­<lb></lb>manda. </s>

<s>Sed ea quae extrinsecus accidentia in ipsa tractatione operis exitum <lb></lb>perturbare possunt, ita multa atque talia existunt, ut propterea fructus, qui <lb></lb>esset inde percipiendus, imminui valde videatur. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Non ideo deserendae artes vel negligendae sunt, quia <lb></lb>speratum non semper sortiantur eventum, neque enim Medicina ars ab usu <lb></lb>est abligenda, quia non omnes languores curet, vel eos ipsos quos curat non <lb></lb>tam brevi temporis spatio, et ea medicaminum quam vellemus lenitate am­<lb></lb>bigit et expellit ” (MSS. Gal., P. V, T. IV, fol. </s>

<s>13). </s></p><p type="main">

<s>Come dunque è certo che son di Galileo questi pensieri, così teniamo <lb></lb>per certo che fosse da lui stesso dettato il dialogo dell&#039;equilibrio della bilan­<lb></lb>cia di braccia disuguali, benchè anche questo discorso, insieme con gli altri <lb></lb>due relativi ai proietti si trovi, come s&#039;è detto, nella <emph type="italics"></emph>Raccolta<emph.end type="italics"></emph.end> del Viviani. </s>

<s><lb></lb>E perchè vedasi che, sebben sotto forme accidentalmente diverse, medesime <lb></lb>son qua e là le idee non solo, ma la maggior parte delle parole, e perciò uno <lb></lb>solo e medesimo l&#039;Autore: ecco il dialogo dettato da Galileo, perchè lo con-<pb xlink:href="020/01/2412.jpg" pagenum="37"></pb>fronti chi vuole col discorso, appropriatosi dall&#039;amanuense, e da noi pubbli­<lb></lb>cato a pag. </s>

<s>165 del quarto Tomo. </s></p><p type="main">

<s>“ SAGREDO. — Sia sostenuta nel punto C (fig. </s>

<s>17) la Libbra di braccia <lb></lb>disuguali, AC maggiore, CB minore. </s>

<s>Cercasi la ragione onde avvenga che, <lb></lb>posti nell&#039;estremità due pesi uguali A, B, la Libbra non resti in quiete ed <lb></lb><figure id="id.020.01.2412.1.jpg" xlink:href="020/01/2412/1.jpg"></figure></s></p><p type="caption">

<s>Figura 17.<lb></lb>equilibrio, ma inclini dalla parte del brac­<lb></lb>cio maggiore, trasferendosi come in EF. </s>

<s><lb></lb>La ragione, che comunemente se ne as­<lb></lb>segna, è perchè la velocità del peso A, <lb></lb>nello scendere, sarebbe maggiore della <lb></lb>velocità del peso B, per essere la distanza <lb></lb>CA maggiore della CB, onde il mobile A, <lb></lb>quanto al peso uguale al B, lo supera <lb></lb>quanto al momento della velocità, e però <lb></lb>gli prevale e scende sollevando l&#039;altro. </s>

<s>Dubitasi circa il valore di tal ragione, <lb></lb>la quale pare che non abbi forza di concludere, perchè è ben vero che il <lb></lb>momento di un grave si accresce congiunto con velocità sopra il momento <lb></lb>di un grave, che sia costituito in quiete, ma che, posti ambedue in quiete, <lb></lb>cioè dove non sia pur moto, non che velocità maggiore di un&#039;altra, quella <lb></lb>maggioranza, che non è ma ancora ha da essere, possa produrre un effetto <lb></lb>presente, ha qualche durezza nel potersi apprendere, ed io specialmente ci <lb></lb>sento difficoltà notabile. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — V. S. ha molto ben ragione di dubitare, ed io ancora, <lb></lb>non restando ben sodisfatto di simile discorso, trovai da quietarmi per un <lb></lb>altro verso molto semplice e speditivo, senza suppor niente, altro che la prima <lb></lb>e comunissima nozione, cioè che le cose gravi vanno all&#039;ingiù in tutte le <lb></lb>maniere che gli viene permesso. </s>

<s>Quando nella Libbra AB voi ponete due pesi <lb></lb>eguali, se voi la lascerete andare liberamente, ella se ne calerà al centro <lb></lb>delle cose gravi, mantenendo sempre il centro della sua gravità, che è il <lb></lb>punto di mezzo D, nella retta che da esso va al centro universale. </s>

<s>Ma se voi <lb></lb>a cotal moto opporrete un intoppo sotto il centro D, il moto si fermerà, re­<lb></lb>stando la Libbra con i suoi due pesi in equilibrio. </s>

<s>Ma se l&#039;intoppo si met­<lb></lb>terà fuori del centro D, come tassello in C, tale intoppo non fermerà la Bi­<lb></lb>lancia, ma devierà il centro D dalla perpendicolare, per la quale camminava, <lb></lb>e lo farà scendere per l&#039;arco DO. Insomma, la Libbra con i due pesi è un <lb></lb>corpo ed un grave solo, il cui centro della gravità è il punto D, e questo <lb></lb>solo corpo grave scenderà quanto potrà, e la sua scesa è regolata dal cen­<lb></lb>tro di gravità O: e così quel che scende è tutto il corpo o aggregato e com­<lb></lb>posto della Libbra e suoi pesi. </s>

<s>La risposta dunque propria alla interrogazione <lb></lb><emph type="italics"></emph>Perchè inclini la Libbra ecc.<emph.end type="italics"></emph.end> è perchè, come quella che è una mole sola, <lb></lb>scende e si avvicina quanto può al centro comune di tutti i gravi ” (MSS. <lb></lb>Gal., P. V, T. IV, fol. </s>

<s>41 a t.). </s></p><p type="main">

<s>Qual si fosse però il luogo, assegnato per la più opportuna inserzione <lb></lb>di questo frammento, non apparisce da nessuna parte del manoscritto, e noi <pb xlink:href="020/01/2413.jpg" pagenum="38"></pb>troviamo gran difficoltà nell&#039;indovinarlo. </s>

<s>Delle leggi delle equiponderanze, <lb></lb>nelle Libbre di braccia disuguali, si tratta a principio del secondo Dialogo, <lb></lb>dove si pongono quelle leggi per fondamento alla dottrina delle resistenze <lb></lb>dei solidi: e perchè la dimostrazione procede sull&#039;esempio di Archimede, <lb></lb>senza invocare quel principio delle velocità virtuali professato già negli avver­<lb></lb>timenti della <emph type="italics"></emph>Scienza meccanica;<emph.end type="italics"></emph.end> si direbbe che fosse il sopra scritto fram­<lb></lb>mento dettato con l&#039;intenzione d&#039;inserirlo là nel detto Dialogo, quasi per <lb></lb>render ragione dell&#039;aver tenuto altro metodo da quel primo che, concludendo <lb></lb>dalla potenza all&#039;atto, s&#039;incominciava ora da molti a tener per dubbioso. </s>

<s>Ma <lb></lb>se fossero veramente stati scelti dal Salviati i modi archimedei, per qualche <lb></lb>scrupolo natogli infin da quel tempo intorno al principio delle velocità vir­<lb></lb>tuali, perchè tornare, sul terminar della quarta Giornata, ad applicarlo alla <lb></lb>soluzion del problema dell&#039;equilibrio tra i gran pesi attaccati all&#039;estremità <lb></lb>di una corda orizontalmente distesa, e il piccolo peso che la tira nel mezzo? </s></p><p type="main">

<s>Un altro pensiero però insorge a complicare le difficoltà nella nostra <lb></lb>mente, perchè, mentre nella Scienza meccanica si dimostra il teorema delle <lb></lb>proporzioni tra il momento del grave nel perpendicolo, e il momento nel <lb></lb>piano inclinato, con aggressione diversa da Pappo, ma concludendolo dalla <lb></lb>teoria della leva angolare; ora, nel dimostrare il supposto antico e nel det­<lb></lb>tare al Viviani il discorso in proposito, torna a invocare il principio delle <lb></lb>velocità virtuali. </s>

<s>Quello è anzi il luogo, in cui si fa del detto principio la <lb></lb>professione più aperta e l&#039;applicazione più esatta, e ivi principalmente lo ri­<lb></lb>conobbe e lo additò il Lagrange, quando, a superesaltare la gloria di Gali­<lb></lb>leo, ne volle attribuire a lui l&#039;invenzione. </s></p><p type="main">

<s>Come dunque, nelle aggiunte da farsi per migliorare i Dialoghi del moto, <lb></lb>potevano stare insieme il discorso, in cui si dimostrava il Teorema meccanico <lb></lb>col principio delle velocità virtuali, e questo frammento, che dee esser pure <lb></lb>stato dettato dal medesimo Galileo, in cui al Sagredo, che trovava difficoltà ad <lb></lb>apprendere come quella causa che non è ma ha da essere possa produrre un <lb></lb>effetto presente, il Salviati risponde ch&#039;egli aveva molto ben ragione di dubitare? </s></p><p type="main">

<s>Sembra a noi non si poter risolvere la questione altrimenti che, osser­<lb></lb>vando come il mormorio contro il principio delle velocità virtuali, principio <lb></lb>antichissimo nella Scienza meccanica, incominciò in Roma fra i discepoli del <lb></lb>Castelli, e le ragioni del Nardi convinsero il Torricelli, da cui facilmente si <lb></lb>insinuarono nel Viviani, il quale ingerì lo scrupolo nello stesso Galileo, poco <lb></lb>dopo ch&#039;egli aveva dettato quel suo discorso, per dimostrar ciò che prima <lb></lb>aveva supposto. </s>

<s>Forse l&#039;intenzione di mettere il dialogo ultimamente da noi <lb></lb>trascritto non era quella di bandire addirittura dalla scienza del moto le ve­<lb></lb>locità in potenza, ma di suggerire a chi ci avesse trovato difficoltà un&#039;altra <lb></lb>maniera di dimostrar le medesime cose. </s>

<s>Si sarà questa intenzione aspettato <lb></lb>a renderla espressa, quando si fosse sul punto di pubblicar le aggiunte ai <lb></lb>colloqui, in modo da stare lì insieme senza contradirsi, ma perchè a quel <lb></lb>punto Galileo mai non giunse, rimasero que&#039;solitari pensieri, per le carte <lb></lb>disordinate, alle nostre disputazioni. </s></p><pb xlink:href="020/01/2414.jpg" pagenum="39"></pb><p type="main">

<s>Di un altro frammento, di cui il Viviani, che l&#039;aveva attinto dall&#039;oracolo <lb></lb>di Galileo, ci lasciò la copia; la destinazione, dietro le seguenti considerazioni <lb></lb>si presenta più manifesta. </s>

<s>Nel primo Dialogo, a proposito del mezzo, che im­<lb></lb>pedisce il naturale acceleramento dei gravi, era stato affermato dal Salviati <lb></lb>“ che finalmente la velocità perviene a tal segno, e la resistenza del mezzo <lb></lb>a tal grandezza che, bilanciandosi fra loro, levano il più accelerarsi e ridu­<lb></lb>cono il mobile in un moto equabile ed uniforme, nel quale egli continua poi <lb></lb>di mantenersi sempre ” (Alb. </s>

<s>XIII, 77). Ora il Cartesio, leggendo tali cose, <lb></lb>ebbe a notarle di errore, perchè con calcolo matematico dimostrava essere <lb></lb>impossibile che il cadente giunga mai mai a tal punto della sua discesa, da <lb></lb>cui, per ragguagliarsi l&#039;accelerazione della velocità con l&#039;impedimento del <lb></lb>mezzo, cominciasse il moto, d&#039;accelerato ch&#039;era prima, a diventare uniforme. </s>

<s><lb></lb>Vennero alle orecchie di Galileo queste censure, prima che si divulgassero <lb></lb>nell&#039;Epistola al Mersenno, e perchè l&#039;origine dell&#039;errore la faceva il Censore <lb></lb>principalmente dipendere dal non essersi ben definita dall&#039;Autor de&#039;dialoghi <lb></lb>nuovi la natura della forza di gravità, che è intrinseca al mobile e no stra­<lb></lb>niera, sovvenne a Galileo l&#039;arguto pensiero di confermare l&#039;asserita unifor­<lb></lb>mità del moto, concludendola da quello stesso più recondito principio, di cui <lb></lb>s&#039;era servito per investigar la causa dell&#039;accelerazion naturale. </s>

<s>Ma senten­<lb></lb>dosi contrapporre la certezza del calcolo, non poteva sperare la prevalenza <lb></lb>del suo pensiero, ch&#039;egli perciò modestamente mette in bocca a Simplicio. </s></p><p type="main">

<s>In quella prefazione dunque al trattato <emph type="italics"></emph>De motu naturaliter accelerato,<emph.end type="italics"></emph.end><lb></lb>con la quale incomincia la seconda parte del dialogo terzo, il Sagredo fa di­<lb></lb>pender l&#039;acceleramento del mobile, che cade in basso, dal prevaler che fa <lb></lb>via via sempre più la gravità al moto proiettizio in alto; a che oppone Sim­<lb></lb>plicio non potersi applicare il discorso “ se non a quei moti naturali, ai quali <lb></lb>sia preceduto un moto violento ” (ivi, pag. </s>

<s>159). Il Sagredo stesso però rispon­<lb></lb>deva all&#039;opposizione “ che il precedere alla caduta del sasso una quiete lunga <lb></lb>o breve o momentanea non fa differenza alcuna, sicchè il sasso non parta <lb></lb>sempre affetto da tanta virtù contraria alla sua gravità, quanta appunto bastava <lb></lb>a tenerlo in quiete ” (ivi, pag. </s>

<s>160). Dopo le quali parole Simplicio doveva <lb></lb>soggiunger così, secondo che Galileo stesso era venuto dettando al Viviani: </s></p><p type="main">

<s>“ Voi dite, signor Sagredo, che l&#039;accelerazione di quel sasso dipende <lb></lb>dal continuo vantaggio della sua medesima gravità sopra quella virtù con­<lb></lb>traria impressagli, che era di proibirgli lo scendere. </s>

<s>Adunque ogni volta che <lb></lb>mancasse questo vantaggio o superiorità al cadente resterebbe di più acce­<lb></lb>lerarsi: sicchè a quel grave che, partendosi dalla quiete, và con la sua gra­<lb></lb>vità superando continuamente quella virtù contraria prima datagli, e in conse­<lb></lb>guenza maggiormente prevalendosi della sua medesima gravità, e non essendo <lb></lb>quell&#039;impeto straniero infinito; dopo che si sarà consumato, non gli resterà <lb></lb>altro che la propria gravità. </s>

<s>Con l&#039;impeto dunque di quella sola seguitando <lb></lb>di moversi, non si accelererà, ma equabile si rimarrà ” (MSS. Gal., P. V, <lb></lb>T. IV, fol. </s>

<s>29). Il Salviati però, per troncare il discorso, ch&#039;ei molto ben <lb></lb>conosceva non poter competere con la matematica del Cartesio, entra di mezzo <pb xlink:href="020/01/2415.jpg" pagenum="40"></pb>a dire, come nella prima edizione di Leida e in tutte le altre, <emph type="italics"></emph>Non mi pare <lb></lb>opportuno di entrare al presente ....<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 160). </s></p><p type="main">

<s>Forse il desiderio di confermare il discorso con più esplicite ragioni ma­<lb></lb>tematiche, per dar migliore sodisfazione agli emuli Geometri valorosi di Fran­<lb></lb>cia, suggerì a Galileo un&#039;altra aggiunta, che si trova fra le copiate e distese <lb></lb>dal Viviani. </s>

<s>Nel primo Dialogo, verso la fine, vuole il Salviati persuadere a <lb></lb>Simplicio che i corpi scendono tanto più lentamente in un mezzo, quanto <lb></lb>sono più sminuzzati, perchè le superfice crescendo in maggior proporzione <lb></lb>delle moli, crescono anche secondo quella maggior proporzione, sopra la gra­<lb></lb>vità, gl&#039;impedimenti: e riducendo la cosa all&#039;esattezza geometrica afferma: <lb></lb>“ che in tutti i solidi simili le moli sono in sesquialtera proporzione delle <lb></lb>loro superfice ” (Alb. </s>

<s>XIII, 93). La proposizione s&#039;appoggia a certi calcoli <lb></lb>intorno ai cubi, ma perchè non pareva sicuro affidare una conclusion gene­<lb></lb>rale sopra due o tre esempi numerici, Galileo pensò che, dopo le parole dette <lb></lb>dal Salviati, <emph type="italics"></emph>E intanto notate, signor Simplicio, che io non equivocai, quando <lb></lb>poco fa dissi la superfice de&#039;solidi minori esser grande in comparazione <lb></lb>di quella dei maggiori<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 93), dovesse il Sagredo soggiungere così, <lb></lb>invece di quella intramessa, nella quale esso Simplicio si chiamava intera­<lb></lb>mente appagato di un teorema geometrico, confessando di non saper nulla di <lb></lb>Geometria: </s></p><p type="main">

<s>“ SAGREDO. — Notizia veramente bella, nè priva di utilità, per quanto <lb></lb>io penso, e benchè, nel caso di che si tratta, non si assesti puntualmente <lb></lb>come sarebbe in un sasso irregolare rotto in minutissime particelle irregola­<lb></lb>rissime, e perciò incognite; tuttavia l&#039;aver dimostrato il grande accrescimento, <lb></lb>che si fa di superfice, nella continuazione di spezzamento di qualsivoglia so­<lb></lb>lido, mentre si risolva in minime particelle fra di loro simili ed eguali; ci <lb></lb>assicura il somigliante dovere accadere in tutti gli altri stritolamenti. </s>

<s>Ma mi <lb></lb>par di notare un altro modo di potere, in una sola e semplice operazione, <lb></lb>ritrovare l&#039;eccesso delle superfice di molti solidi, tra di loro simili ed eguali, <lb></lb>sopra la superfice di un solo pur simile, ma uguale a tutti quelli. </s>

<s>Questo mi <lb></lb>par che ci venga dato dalla radice cuba del numero de&#039;piccoli solidi, come <lb></lb>per esempio: la superfice di mille palline quanto è maggiore della palla sola <lb></lb>uguale e simile a tutte quelle eguali e simili tra di loro? </s>

<s>Diremo esser mag­<lb></lb>giore dieci volte, per esser dieci la radice cuba di mille e dieci volte il dia­<lb></lb>metro della grande conterrà il diametro della piccola. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Questa è la vera, e vedesi finalmente che le superfice <lb></lb>sopra dette, a due lati omologhi, uno del gran solido ed uno del piccolo, si <lb></lb>rispondono contrariamente. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Ho avuto gusto grande di questo discorso .... ” (MSS. <lb></lb>Gal., P. V, T. IV, fol. </s>

<s>38). </s></p><p type="main">

<s>Sono in questi colloqui fra il Sagredo e il Salviati annunziati teoremi <lb></lb>verissimi, come si può riscontrare con facili dimostrazioni. </s>

<s>Chiamate infatti <lb></lb>M, M′ le moli di due solidi simili, S, S′ le loro superficie, e L, L′due lati <lb></lb>omologhi, abbiamo per gli elementi della Geometria M:M′=L3:L′3; S:S′= <pb xlink:href="020/01/2416.jpg" pagenum="41"></pb>L2:L′2 e perciò M2:M′2=S3:S′2 ossia M:M′=S3/2:S′3/2, che conferma <lb></lb>la verità del teorema annunziato dal Salviati <emph type="italics"></emph>esser ne&#039;solidi simili le moli <lb></lb>in sesquialtera proporzione delle loro superfice.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Chiamato inoltre A il lato di un solido, B una delle N parti, in cui è <lb></lb>stato diviso, cosicchè abbiasi A=N.B, troveremo con facile discorso inter­<lb></lb>cedere fra la superfice S del solido grande, e la somma S′ delle superfice <lb></lb>de&#039;piccoli solidi uguali e simili, in cui fu diviso, la proporzione S:S′= <lb></lb>1:N=B:A, che conferma la verità dell&#039;altro Teorema formulato dal Sal­<lb></lb>viati: <emph type="italics"></emph>le superficie, a due lati omologhi, uno del gran solido ed uno del <lb></lb>piccolo, si rispondono contrariamente.<emph.end type="italics"></emph.end> Essendo poi le moli M, M′ come i <lb></lb>cubi dei lati omologhi, ossia M′:M=B3:A3=1:N3, avremo N=3√M/M′, <lb></lb>e perciò S′=S.3√M/M′. </s>

<s>Nell&#039;esempio addotto dianzi dal Sagredo, essendosi <lb></lb>della palla grande fatto mille palline, avremo dunque M′=1, M=1000: <lb></lb>onde S′=S.3√1000=10.S, ciò che fa esatto riscontro con quel che il <lb></lb>Sagredo stesso dianzi diceva <emph type="italics"></emph>essere la superficie di mille palline dieci volte <lb></lb>maggiore di quella della palla sola, uguale e simile a tutte quelle uguali <lb></lb>e simili tra loro.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Anche questi teoremi però venivano da Galileo dimostrati per via di esempi <lb></lb>numerici, com&#039;avremo occasione di veder meglio altrove, ond&#039;è che il Viviani, <lb></lb>ripensando al Cartesio e agli altri matematici di Francia, i quali usandovi <lb></lb>l&#039;algebra gli rendevano generali, diceva a Galileo che, per dar sodisfazione <lb></lb>agli emuli, sarebbe stato bene far, di quegli annunziati teoremi intorno ai <lb></lb>solidi simili e alle loro minutissime divisioni, una dimostrazione più univer­<lb></lb>sale. </s>

<s>Approvava il buon Vecchio il pensiero, ma riconoscendosi in quelle sue <lb></lb>miserabili condizioni impotente a mandarlo ad effetto, se ne affliggeva, ciò <lb></lb>che fece risolvere il Viviani stesso d&#039;esercitarvisi attorno. </s>

<s>Una mattina entra <lb></lb>con un foglio in mano, dov&#039;era scritta la dimostrazione, nella camera di Ga­<lb></lb>lileo, il quale se ne rallegrò, compiacendosi inoltre che fosse messa in dia­<lb></lb>logo, per inserirla al suo proprio luogo, invece del frammento che avevano <lb></lb>insieme, pochi giorni fa, preparato. </s>

<s>Abbiamo il documento di ciò in una <lb></lb>carta, sopra la quale il Viviani, di sua propria mano, così scriveva: “ Fac­<lb></lb>cia 91, verso 12 (dell&#039;edizione di Leida, e faccia 93, verso 35 dell&#039;Albèri). <lb></lb>Dopo quelle parole di Simplicio, che dicono <emph type="italics"></emph>fuor che quello che concluden­<lb></lb>temente dimostrano,<emph.end type="italics"></emph.end> si potrà aggiungere quanto appresso io dimostro così, <lb></lb>contentandosene il medesimo signor Galileo: ” </s></p><p type="main">

<s>“ SAGREDO. — La verità della conclusione nei particolari si vede per <lb></lb>esperienza assai manifesta, ma io desidererei avere una dimostrazione, la <lb></lb>quale universalmente m&#039;insegnasse che, non solamente nel risolvere il solido <lb></lb>in molti simili si accresce la superficie, ma ancora secondo qual proporzione <lb></lb>ella venga moltiplicata. </s>

<s>” </s></p><pb xlink:href="020/01/2417.jpg" pagenum="42"></pb><p type="main">

<s>“ SALVIATI. — Bellissima è la proposizione, ma non men bella la dimo­<lb></lb>strazione. </s>

<s>Dico pertanto che diviso il lato di un solido in quante si vogliano <lb></lb>parti uguali, e risoluto tal solido in solidi tra di loro uguali e simili al tutto, <lb></lb>dei quali i lati omologhi siano uguali a una parte del lato omologo del tutto; <lb></lb>la superfice di tutti questi piccoli presi insieme, alla superficie del grande e <lb></lb>intero, hanno la medesima proporzione che il lato omologo del grande diviso, <lb></lb>al lato omologo di uno dei piccoli; cioè a una parte della divisione del gran <lb></lb>lato omologo: per il che dimostrare propongo questo Lemma: ” </s></p><p type="main">

<s>“ Se saranno quattro numeri continui proporzionali, il primo dei quali <lb></lb>sia l&#039;unità, il quarto di necessità sarà numero cubo, il terzo sarà quadrato, <lb></lb>il secondo sarà radice, di ambedue, il che si dimostra così: ” </s></p><p type="main">

<s>“ Essendo li tre primi proporzionali, il prodotto del primo nel terzo è <lb></lb>uguale al quadrato del secondo. </s>

<s>Ma il prodotto del primo nel terzo è l&#039;istesso <lb></lb>terzo, perchè il primo è l&#039;unità; adunque il terzo è il quadrato del secondo, <lb></lb>e questo è la sua radice. </s>

<s>E perchè il prodotto del primo nel quarto è uguale <lb></lb>al prodotto del secondo nel terzo, e il prodotto del primo nel quarto è lo <lb></lb>stesso quarto; adunque il prodotto del secondo nel terzo è uguale al quarto. </s>

<s><lb></lb>Ma il terzo è quadrato, la cui radice è il secondo, ed il prodotto del qua­<lb></lb>drato nella sua radice fa cubo; adunque il quarto è cubo, il che si doveva <lb></lb>dimostrare. </s>

<s>” (MSS. Gal., P. V., T. IX, fol. </s>

<s>92). </s></p><p type="main">

<s>Il discorso si rende per segni algebrici molto più chiaro, chiamando A, <lb></lb>B, C, D i quattro numeri continuamente proporzionali. </s>

<s>Perchè basta scrivere <lb></lb>la proporzione A:B=B:C=C:D, per vedere a colpo d&#039;occhio che, se <lb></lb>A=1, sarà B2=C, D=C.B=B3, perciò B=√C=3√D. </s>

<s>Ma ascoltiamo <lb></lb>dopo questo lemma la dimostrazione, che Galileo si contentava fosse messa <lb></lb>in bocca al suo Salviati: </s></p><p type="main">

<s>“ Dichiarato questo, verremo alla dimostrazione dell&#039;altra principal con­<lb></lb>clusione, la quale esemplificheremo per maggior chiarezza nei solidi cubi. </s>

<s><lb></lb>Intendasi la linea B esser lato di un dado, o di un cubo vogliam dir, solido, <lb></lb>diviso in quante si vogliano parti uguali, ad una delle quali sia uguale la A, <lb></lb>e di essa e del numero delle parti di B sia terzo proporzionale il numero C, <lb></lb>e quarto il D: è manifesto, per il lemma di sopra, il numero D esser cubo, <lb></lb>ed il C numero quadrato, ed il numero B lor radice. </s>

<s>E perchè li quattro <lb></lb>numeri A, B, C, D sono continui proporzionali, il numero D al numero A <lb></lb>averà tripla proporzione di quella, che gli ha il numero B. </s>

<s>Ma il solido cubo <lb></lb>del lato B, al cubo di A, ha tripla proporzione di quella del lato B ad A, <lb></lb>cioè del medesimo numero B ad A; adunque la medesima proporzione ha il <lb></lb>numero D al numero A, che il cubo solido del lato B, al cubo solido del <lb></lb>lato A. </s>

<s>Adunque tanti cubi solidi del lato A, quante sono le unità del nu­<lb></lb>mero D, saranno uguali al cubo solido del lato B. Inoltre, per essere lì tre <lb></lb>numeri A, B, C proporzionali, la proporzione del numero C all&#039;A è doppia <lb></lb>di quella del numero B all&#039;A. </s>

<s>Ma la proporzione del quadrato della linea B, <lb></lb>al quadrato della linea A, è doppia parimente della proporzione della mede-<pb xlink:href="020/01/2418.jpg" pagenum="43"></pb>sima B ad A, cioè del numero B ad A; adunque il numero C all&#039;A, unità, <lb></lb>ha l&#039;istessa proporzione del quadrato B al quadrato A. </s>

<s>Tanti quadrati dun­<lb></lb>que del lato A, quante sono le unità del numero C, sono uguali ad un solo <lb></lb>quadrato di B, ed il sescuplo al sescuplo, cioè la superfice di tanti cubi del­<lb></lb>l&#039;A, quante unità ha il numero C, sono, prese insieme, uguali alla superficie <lb></lb>del solo cubo di B. </s>

<s>Adunque le superficie di tanti cubetti di A quant&#039;è il <lb></lb>numero C.... ” (ivi). </s></p><p type="main">

<s>Il discorso rimane a questo punto interrotto, venendo meno, dopo l&#039;ul­<lb></lb>tima riga, lo spazio, e mancando nel volume la carta, nella quale dovevano <lb></lb>essere state scritte dal Viviani le poche rimanenti parole di conclusione. </s>

<s>Si <lb></lb>suppliscono queste però assai facilmente, ragionando in conseguenza de&#039;due <lb></lb>principii già dimostrati, e la verità de&#039;quali immediatamente dipende dalle <lb></lb>proporzionalità poste nel lemma. </s>

<s>Da esse infatti deriva D:A=B3:1= <lb></lb>B3:13=B3:A3, e di qui D.A3=AB3=B3; che vuol dire: <emph type="italics"></emph>tanti cubi <lb></lb>solidi del lato A, quante sono le unità del numero D, sono uguali al cubo <lb></lb>solido del lato B.<emph.end type="italics"></emph.end> Deriva pure da quelle stesse proporzionalità del Lemma <lb></lb>C:A=B2:12=B2:A2, e da ciò C.A2=B2: <emph type="italics"></emph>tanti quadrati dunque <lb></lb>del lato A, quante sono le unità del numero C, sono uguali ad un solo <lb></lb>quadrato di B.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Chi fosse nel 1639, penetrato nella villa di Arcetri, avrebbe sentito echeg­<lb></lb>giare le solitarie stanze in questi colloqui tra il Maestro e il discepolo, il <lb></lb>quale prendeva talvolta in mano, e sollevava la face a illuminar le tenebre <lb></lb>dello stesso Maestro. </s>

<s>Il fine principale di quei colloqui sapienti, quale può <lb></lb>riconoscersi ne&#039;varii esempi da noi fin qui notati, era quello che Galileo di­<lb></lb>chiarava nella sua lettera al Baliani, di ampliare cioè e di migliorare le cose <lb></lb>fin allora scritte intorno alla scienza del moto. </s>

<s>Ma presto s&#039;ebbe a fare espe­<lb></lb>rienza che non era, con quell&#039;opera sola, il fine perfettamente conseguito, <lb></lb>perchè, dopo i benevoli che, desiderosi d&#039;impossessarsi la mente di quelle <lb></lb>nuove dottrine, amavano di vederle in certe parti rese più chiare, e in certe <lb></lb>altre meglio compiute; ci erano gli emuli e gl&#039;invidiosi, dai quali null&#039;altro <lb></lb>più ardentemente si desiderava, che di cogliere que&#039;galileiani documenti in <lb></lb>difetto, e, da una piaga sola facendo tutto intero il corpo apparire morboso, <lb></lb>proclamare al mondo che tutta la Scienza nuova si fondava sul falso. </s>

<s>Era uno <lb></lb>di cotesti emuli il Cartesio, ma le censure di lui si temevano forse meno di <lb></lb>certe altre, tanto più mordaci, perchè più dissennate. </s>

<s>Il Filosofo bretone in <lb></lb>fine, se gareggiava con Galileo nel conquistare il principato della Scienza, <lb></lb>non mancava di quel valore, di che erano privi i Gesuiti, i quali con le fra­<lb></lb>gili canne peripatetiche in mano uscivano ambiziosamente in campo, a met­<lb></lb>tersi fra i nuovi conquistatori. </s></p><p type="main">

<s>Anche contro costoro bisognava difendersi, se non appuntando la spada, <lb></lb>come si farebbe con gli orsi o coi leoni, menando almeno in tresca le mani, <lb></lb>come si fa per cacciarsi le mosche, e a ciò giusto pensava Galileo nelle sue <lb></lb>tenebre, specialmente quando s&#039;incominciò a veder qualche effetto delle pre­<lb></lb>sentite molestie. </s>

<s>In un bocconcello di carta, scritta senza dubbio dal Viviani <pb xlink:href="020/01/2419.jpg" pagenum="44"></pb>sul tavolino posto a piè del letto di Galileo, o nella camera accanto dove si <lb></lb>giaceva il vecchio Maestro, sotto il titolo <emph type="italics"></emph>Domandar del Blancano<emph.end type="italics"></emph.end> si legge <lb></lb>così notato, con una certa mossa alla fiorentina: </s></p><p type="main">

<s>“ I. </s>

<s>La mi dichiari meglio, signor Galileo, come il mezzo detragga dal <lb></lb>grave; perchè la figura sferica sia contenuta sotto la minima superficie, come <lb></lb>si legge a carte 92 (della prima edizione di Leida). ” </s></p><p type="main">

<s>“ II. </s>

<s>A carte 93, l&#039;aria reprime la velocità del mobile, poichè, scari­<lb></lb>cando un archibuso da grande altezza in giù, fa minor botta, che da una <lb></lb>minore: ed in altri luoghi dice che acquista più velocità, ed in conseguenza <lb></lb>avrebbe a far maggior colpo da grande altezza, che da piccola. </s>

<s>” </s></p><p type="main">

<s>“ III. </s>

<s>Par che stia come la circonferenza alla circonferenza, così la su­<lb></lb>perficie alla superficie de&#039;cilindri ugualmente alti. </s>

<s>Carte 55: par che stia <lb></lb>come il diametro C, al diametro A, così le loro circonferenze. </s>

<s>” </s></p><p type="main">

<s>“ IV. </s>

<s>Signor Galileo, i momenti dei cilindri ugualmente grossi, ma di­<lb></lb>sugualmente lunghi, hanno eglino doppia proporzione delle loro resistenze <lb></lb>prese reciprocamente? </s>

<s>perchè pare che nella V proposizione la resistenza del <lb></lb>solido DG, a quella di DF, stia come DF a DG. ” </s></p><p type="main">

<s>“ V. </s>

<s>La settima proposizione non intendo. </s>

<s>” </s></p><p type="main">

<s>“ VI. </s>

<s>A carte 134, la considerazione di que&#039;due cilindri non la intendo. </s>

<s>” <lb></lb>(MSS. Gal., P. V, T. IV, fol. </s>

<s>14). </s></p><p type="main">

<s>Il padre Giuseppe Biancani, interpetre di Aristotile profondo, e nel va­<lb></lb>lor del quale i Gesuiti si confidavano molto, fu da loro mandato uno dei <lb></lb>primi perchè minasse l&#039;edifizio galileiano, sicuri che lo manderebbe all&#039;aria <lb></lb>con questi suoi domandari. </s>

<s>I quali che non fossero disprezzati par che sia <lb></lb>segno l&#039;averne scritto un tal memoriale, ma quel vivace ingegno giovanile <lb></lb>del Viviani volle scherzarci un poco, come se ne avvedrebbe meglio colui, a <lb></lb>chi si potesse metter sott&#039;occhio quel bocconcello di carta manoscritto, che, <lb></lb>a svolgere il volume, in luogo della <gap></gap>accia presenta il tergo. </s></p><p type="main">

<s>In ogni modo, è certo che si pensava a dar sodisfazione anche al nuovo <lb></lb>censore, ma a poco andò che il Viviani ebbe a perdere il suo tempo più in <lb></lb>consolare e in curare i languori del Vecchio infermo, che in raccoglierne i <lb></lb>parti dell&#039;ingegno. </s>

<s>Poco di poi dovè cedere il geloso ufficio al Torricelli, che <lb></lb>parve esser venuto ad Arcetri per assistere ai funerali, celebratisi infatti dopo <lb></lb>soli tre mesi. </s></p><p type="main">

<s>Anche morto però Galileo, il Viviani persistè nella generosa intenzione <lb></lb>di attendere a migliorare i dialoghi delle Nuove scienze, e se mancando l&#039;Au­<lb></lb>tore veniva a mancar chi gli darebbe legittima autorità di ampliarli, si sen­<lb></lb>tiva maggiore la libertà in emendarne, senza passione, i più notabili errori. </s>

<s><lb></lb>Procedeva dall&#039;altra parte il Viviani sicuro del fatto suo, perchè sapeva che <lb></lb>le aggiunte ei le veniva facendo secondo la mente di Galileo, e le correzioni <lb></lb>secondo le leggi del calcolo e della retta ragione. </s>

<s>Che poi fosse veramente <lb></lb>così, lo vedranno i Lettori in queste altre due parti, che rimangono al pre­<lb></lb>sente discorso. </s></p><pb xlink:href="020/01/2420.jpg" pagenum="45"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Tutto dunque in sollecitudine il Viviani di proseguir da sè solo l&#039;opera <lb></lb>incominciata insieme con Galileo, svolgeva attentamente il libro delle Nuove <lb></lb>scienze, per notarvi i punti, dove le de trine de&#039;Dialoghi qua volevano es­<lb></lb>sere dichiarate meglio, e là svolte nella bellezza e nella verità di nuove con­<lb></lb>seguenze. </s>

<s>Ei ne prendeva allora per suo uso, e ne lasciava per documento <lb></lb>alla storia il seguente memoriale: </s></p><p type="main">

<s>“ I. </s>

<s>Carte 6. SALV. — Dite pure ottuplo .... ” </s></p><p type="main">

<s>“ II. </s>

<s>Carte 11. SALV. — Ingegnosa veramente invenzione, e per intiera <lb></lb>esplicazione della sua natura mi par di scorgere, così per ombra, che qualche <lb></lb>altra speculazione si possa aggiungere .... ” </s></p><p type="main">

<s>“ III. </s>

<s>Carte 56. La dimostrazione del Torricelli dei cilindri. </s>

<s>” </s></p><p type="main">

<s>“ IV. </s>

<s>Carte 60. La dimostrazione che il poligono è medio tra due cer­<lb></lb>chi, uno inscritto e l&#039;altro isoperimetro, e la dimostrazione che qualunque <lb></lb>poligono circoscrittibile al cerchio è medio tra due qualsivogliano poligoni <lb></lb>simili, uno circoscrittibile al medesimo cerchio, e l&#039;altro isoperimetro al detto <lb></lb>poligono. </s>

<s>” </s></p><p type="main">

<s>“ V. </s>

<s>Carte 70. Nel discorso del Salviati potrebbesi aggiungere la fabbrica <lb></lb>delle due palline, e con questa occasione accennare come lo strumento per <lb></lb>conoscere le mutazioni del caldo e del freddo nell&#039;aria è invenzione del <lb></lb>Galileo. </s>

<s>” </s></p><p type="main">

<s>“ VI. </s>

<s>Carte 81. Nel secondo modo di pesar l&#039;aria si ha non solo il peso <lb></lb>di essa nel vacuo, ma dell&#039;acqua ancora nel medesimo: cosa non avvertita <lb></lb>dal Galileo, però notisi. </s>

<s>Perchè, aggiungendo al peso dell&#039;acqua il peso di <lb></lb>quell&#039;aria uscita, che è quanto l&#039;acqua, si avrà il peso dell&#039;acqua nel vacuo. </s>

<s><lb></lb>Ma perchè il lor peso nel vacuo ci vien dato da materia posta in aria, che <lb></lb>è l&#039;arena, però detto peso non sarà totalmente preciso. </s>

<s>Si averà bene da tale <lb></lb>esperienza la proporzione del peso dell&#039;acqua nel vacuo, al peso dell&#039;aria nel <lb></lb>medesimo, che sarà come il contrappeso dell&#039;acqua, con quel dell&#039;aria, a <lb></lb>quel dell&#039;aria. </s>

<s>” </s></p><p type="main">

<s>“ VII. </s>

<s>Carte 91. Dimostrazione da me trovata circa la moltiplicazione <lb></lb>delle superficie de&#039;solidi. </s>

<s>” </s></p><p type="main">

<s>“ VIII. </s>

<s>Carte 94. Dopo il discorso del Salviati circa il tiro del moschetto <lb></lb>in un corsaletto. </s>

<s>” </s></p><p type="main">

<s>“ IX. </s>

<s>Carte 254. Il pensiero di Platone, e far quel calcolo. </s>

<s>” </s></p><p type="main">

<s>“ X. </s>

<s>Carte 284. Vedi l&#039;ultimo verso che <emph type="italics"></emph>utilità<emph.end type="italics"></emph.end> volesse dire il Galileo, <lb></lb>se della misura della linea parabolica, ovvero del modo di trovare le propo­<lb></lb>sizioni dei moti de&#039;proietti. </s>

<s>” (MSS. Gal., P. V, T. IV, fol. </s>

<s>33). </s></p><p type="main">

<s>A questi dieci si riducevano i luoghi, nelle quattro giornate delle Nuove <pb xlink:href="020/01/2421.jpg" pagenum="46"></pb>scienze, presi in considerazion dal Viviani, e intorno ai quali ei si proponeva <lb></lb>di esercitare l&#039;ingegno per migliorarli, avendogli Galileo stesso detto di averci <lb></lb>riconosciuta qualche imperfezione. </s>

<s>Non sempre si è trovato però il proposito <lb></lb>messo ad effetto, o perchè così realmente avvenisse, o perchè siano andate <lb></lb>smarrite, o siano sfuggite alla nostra attenzione le schede relative. </s>

<s>Di quel <lb></lb>che abbiamo trovato renderemo ordinatamente conto qui ai nostri Lettori. </s></p><p type="main">

<s>Al proposito espresso nella nota prima sodisfaceva il Viviani, scrivendo <lb></lb>in margine alla pag. </s>

<s>6 di Leida quella postilla in lapis, che poi l&#039;Albèri in­<lb></lb>serì a pag. </s>

<s>10 nel tomo XIII della sua edizione completa. </s>

<s>Ma all&#039;ordigno <lb></lb>inventato da quel giovane parente del Sagredo, per poter con una corda ca­<lb></lb>larsi da una finestra, senza crudelmente scorticarsi le palme delle mani, non <lb></lb>par che sapesse il Viviani trovar nessuna di quelle speculazioni, che credeva <lb></lb>di poter aggiungervi così facilmente il Salviati. </s></p><p type="main">

<s>Di bene altra importanza di questo ordigno, inventato da un giovane si­<lb></lb>gnore, per rendere innocua la fuga ai giovani entrati nelle altrui case fur­<lb></lb>tivi, erano que&#039;teoremi geometrici intorno ai cilindri, a proposito de&#039;quali il <lb></lb>Viviani accennava alla dimostrazione del Torricelli. </s>

<s>Ma perchè, da quel cenno <lb></lb>così frettoloso e solitario, non è facile intendere come, trattandosi di Galileo, <lb></lb>possa entrare di mezzo il Torricelli, che par si chiami a fargli da maestro; <lb></lb>convien ravviare il discorso, perchè dietro lui si rischiarino i nostri dubbi, <lb></lb>e si manifestino meglio le altrui intenzioni. </s></p><p type="main">

<s>A proposito di dimostrar la sottigliezza estrema, a cui riducesi l&#039;oro, <lb></lb>quando si rivestano delle foglie di lui le verghe di argento, da tirarsi poi in <lb></lb>sottilissimi fili attraverso ai fori della filiera; a pag. </s>

<s>56, come nota il Viviani <lb></lb>nella edizione di Leida, si propone questo teorema: “ Le superficie dei cilin­<lb></lb>dri eguali, trattone le basi, son tra di loro in sudduplicata proporzione delle <lb></lb>loro lunghezze, ovvero in reciproca proporzione dei diametri delle basi ” <lb></lb>(Alb. </s>

<s>XIII, 56). Piacque così al Sagredo la dimostrazion del Salviati, che <lb></lb>venne a questi voglia di soggiungerne all&#039;amico un&#039;altra compagna, dimo­<lb></lb>strando quel che avvenga ai cilindri uguali di superficie, ma disuguali di al­<lb></lb>tezza, in questo così proposto secondo teorema: “ I cilindri retti, le super­<lb></lb>ficie dei quali, trattone le basi, sieno uguali, hanno fra di loro la medesima <lb></lb>proporzione, che le loro altezze contrariamente prese: ovvero in omologa pro­<lb></lb>porzione dei diametri delle basi ” (ivi, pag. </s>

<s>58). D&#039;onde si deduce per co­<lb></lb>rollario la ragione di un accidente curioso, “ ed è: come possa essere che <lb></lb>il medesimo pezzo di tela, più lungo per un verso che per l&#039;altro, se se ne fa­<lb></lb>cesse un sacco da tenervi dentro del grano, come costumano fare con un fondo <lb></lb>di tavola, terrà più, servendoci per l&#039;altezza del sacco della minor misura <lb></lb>della tela, e con l&#039;altra circondando la tavola del fondo, che facendo per l&#039;op­<lb></lb>posito ” (ivi, pag. </s>

<s>59). </s></p><p type="main">

<s>I due teoremi geometrici, oltre al parere al gusto del Sagredo belli, si <lb></lb>trovano, ciò ch&#039;è più, al giudizio dei Matematici veri; imperocchè siano <lb></lb>AC, DF (fig. </s>

<s>18) i due cilindri uguali; S, S′ le loro superficie; C, C′ le so­<lb></lb>lidità respettive: avremo S=<foreign lang="grc">π</foreign>.BC.AB, S′=<foreign lang="grc">π</foreign>.EF.DE, onde S:S′= <pb xlink:href="020/01/2422.jpg" pagenum="47"></pb>BC.AB:EF.DE(*). Sarà inoltre C=<foreign lang="grc">π</foreign>.BC2/4.AB, C′=<foreign lang="grc">π</foreign>.EF2/4.DE, le <lb></lb>quali due quantità debbon essere per supposto uguali, ossia BC2.AB= <lb></lb>EF2.DE. </s>

<s>Dunque S2:S′2=BC2.AB2:EF2.DE2=AB:DE, e perciò S:S′= <lb></lb><figure id="id.020.01.2422.1.jpg" xlink:href="020/01/2422/1.jpg"></figure></s></p><p type="caption">

<s>Figura 18.<lb></lb>√AB:√DE. </s>

<s>E anche moltiplicando la seconda <lb></lb>ragione della (*) per BC.EF, avremo S:S′= <lb></lb>BC2.AB.EF:EF2.BC.DE=EF:BC, ciò <lb></lb>che, sotto ambedue gli aspetti, verifica la pri­<lb></lb>ma proposta del Salviati. </s>

<s>Nè men vera appari­<lb></lb>sce di qui la seconda, perchè, avendosi come <lb></lb>si è ora veduto, C:C′=BC2.AB:EF2:DE, <lb></lb>per essere le superfice de&#039;cilindri uguali, ne <lb></lb>verrà BC.AB=EE.DE, e perciò C:C′= <lb></lb>BC:EF=DE:AB. </s></p><p type="main">

<s>I teoremi dunque di Galileo erano senza alcun dubbio veri, ma non pa­<lb></lb>revano al Biancani troppo chiare le dimostrazioni, e il Viviani stesso ebbe a <lb></lb>riconoscer pur troppo che si rimanevano inferiori a quella elegante facilità, <lb></lb>con la quale aveva poco fa il Torricelli condotte altre simili dimostrazioni <lb></lb>intorno alle proprietà dei cilindri, nel suo primo libro <emph type="italics"></emph>Dei solidi sferali.<emph.end type="italics"></emph.end> Nella <lb></lb>sesta proposizione si dimostra che le superficie cilindriche stanno come i ret­<lb></lb>tangoli delle sezioni, ciò che immediatamente resultaya dalla equazione da <lb></lb>noi sopra segnata con asterisco. </s>

<s>Ma il Torricelli la concludeva da altre pro­<lb></lb>posizioni, precedentemente dimostrate con quel metodo che, sebben sia ridotto <lb></lb>alla maggior facilità ed eleganza, non per questo cessa di apparir lungo a chi <lb></lb>in poche parole ora sa di riuscir a dire lo stesso. </s>

<s>La terza proposizione infatti, <lb></lb>per dimostrar la quale il Torricelli impiega una pagina e mezzo del suo <lb></lb>volume, va speditamente a concluder che, avendosi il cilindro AC, nella pre­<lb></lb>cedente figura, l&#039;altezza AB del quale sia la quarta parte del diametro della <lb></lb>sua base, la superficie cilindrica S è uguale al circolo su cui risiede; osser­<lb></lb>vando che, se AB=BC/3, la superficie S, che verrebbe espressa da <foreign lang="grc">π</foreign>.BC.AC, <lb></lb>si riduce a <foreign lang="grc">π</foreign>.BC2/4, che è l&#039;area del circolo, sopra cui posa il cilindro. </s>

<s>Qua­<lb></lb>lunque siasi poi la proporzione che passa tra la superficie S′ di questo circolo <lb></lb>base, e la superficie cilindrica S, avendosi S:S′=<foreign lang="grc">π</foreign>.BC.AB:<foreign lang="grc">π</foreign>.BC2/4= <lb></lb>AB:BC/4, resta dimostrato <emph type="italics"></emph>Cylindri recti superficies, ad circulum suae ba­<lb></lb>sis, est ut latus cylindri ad quartam partem diametri eiusdem basis,<emph.end type="italics"></emph.end> che <lb></lb>è la IV torricelliana <emph type="italics"></emph>De sphaera et solidis sphaeralibus.<emph.end type="italics"></emph.end> (Op. </s>

<s>geom., P. </s>

<s>I cit., <lb></lb>pag. </s>

<s>14). La V è di non men facile e spedita conclusione, perchè, a dimo­<lb></lb>strar che la superficie di un cilindro retto sta a un circolo qualunque come <lb></lb>il rettangolo della sezione sta al quadrato del raggio; chiamato questo rag­<lb></lb>gio R, sarà S′=<foreign lang="grc">π</foreign>R2 la superficie del cerchio, e dall&#039;equazione S:S′= <pb xlink:href="020/01/2423.jpg" pagenum="48"></pb>AB.BC:R2, che di qui e dalla espressione della superficie cilindrica S ne <lb></lb>nasce, abbiamo già conseguito l&#039;intento. </s></p><p type="main">

<s>Dovevano queste tre proposizioni servire di lemma alla VI, dimostrata <lb></lb>la quale era additato il più spedito processo di riuscire a dimostrare i teo­<lb></lb>remi di Galileo. </s>

<s>Perciò il Viviani accennava alla dimostrazione del Torricelli, <lb></lb>sull&#039;esempio della quale intendeva di ridur così, come poi fece, a più facile <lb></lb>semplicità i prolissi e involti discorsi del Salviati. </s></p><p type="main">

<s>“ Prendasi la linea G nella stessa figura 18, terza proporzionale dopo i <lb></lb>diametri BC, EF dei cerchi basi de&#039;dati cilindri. </s>

<s>E perchè questi hanno le <lb></lb>superticie curve eguali, sarà l&#039;altezza AB alla DE come il diametro EF al <lb></lb>diametro BC, o come la linea G al diametro EF. </s>

<s>Ma il cilindro AC al DF <lb></lb>ha proporzione composta del diametro BC alla terza G, e dell&#039;altezza AB <lb></lb>all&#039;altezza DE, cioè della terza G al diametro EF; adunque il cilindro AC <lb></lb>al DF sta come il diametro BC al diametro DF, omologamente presi, o come <lb></lb>le altezze DE, AB prese così reciprocamente ” (MSS. Gal., P. V, T. IX, <lb></lb>pag. </s>

<s>56). </s></p><p type="main">

<s>Questa dimostrazione, da sostituirsi col presunto permesso di Galileo a <lb></lb>quella già nel primo dialogo stampata in Leida, l&#039;aveva scritta il Viviani a <lb></lb>piè della citata pagina 56, ma in un pezzetto di carta, interfogliato tra essa <lb></lb>pagina e la seguente, ne aveva prima distesa un&#039;altra, che, poniamo fosse <lb></lb>meglio ordinata, non riusciva punto meno prolissa della stessa galileiana. </s>

<s>Per <lb></lb>dimostrar che i cilindri di superficie curve uguali son fra loro come i diame­<lb></lb>tri delle basi omologamente, o come le altezze reciprocamente prese, premet­<lb></lb>teva il Viviani un lemma, che resulta a noi dimostrato da solo moltiplicar <lb></lb>per A.B una delle ragioni dell&#039;identica A:B=A:B. </s>

<s>Quel lemma infatti <lb></lb>così proponesi, e poi si dimostra: </s></p><p type="main">

<s>“ La proporzione di due linee è composta della proporzione omologa <lb></lb>de&#039;loro quadrati, e della proporzion reciproca di loro medesime. </s>

<s>— Le date <lb></lb>linee siano A, B: dico che la ragione di A a B è composta della ragione del <lb></lb>quadrato A, al quadrato B, e della ragione della linea B alla A. </s>

<s>Prendasi C <lb></lb>terza proporzionale dopo le A, B: averà dunque A a B ragion composta della <lb></lb>ragione di A alla terza C, cioè del quadrato A at quadrato della media B, <lb></lb>e della ragione della C alla B, cioè della B alla A, il che ecc. </s>

<s>” </s></p><p type="main">

<s>Dietro ciò, propone e dimostra il Viviani il teorema: “ I cilindri retti <lb></lb>AC, CD (sempre rappresentati dalla 18a figura) de&#039;quali le superticie curve <lb></lb>sieno uguali, son fra loro in omologa proporzione de&#039;diametri BC, EF delle <lb></lb>loro basi, ed anche in proporzione reciproca delle loro altezze DE, AB. ” </s></p><p type="main">

<s>“ La curva superficie del cilindro AC è uguale al rettangolo sul lato <lb></lb>uguale alla circonferenza della base, e all&#039;altezza AB, sì come la curva del <lb></lb>DF è uguale al rettangolo sul lato uguale alla circonferenza del cerchio, che <lb></lb>ha per diametro EF, e all&#039;altezza ED. </s>

<s>Ma tali superficie curve son date uguali, <lb></lb>adunque anche questi rettangoli sono uguali, e però la circonferenza, che ha <lb></lb>per diametro BC, alla circonferenza che ha per diametro EF, cioè il diame­<lb></lb>tro BC al diametro EF sta come l&#039;altezza DE all&#039;altezza AB. </s>

<s>Ma il cilindro <pb xlink:href="020/01/2424.jpg" pagenum="49"></pb>AC al DF ha ragione composta del cerchio, che ha per diametro BC, al cer­<lb></lb>chio che ha per diametro EF, cioè del quadrato BC al quadrato EF, e del­<lb></lb>l&#039;altezza AB alla DE, cioè del diametro EF al BC: ed anche il diametro BC <lb></lb>all&#039;EF, pel passato lemma, ha ragion composta delle medesime proporzioni, <lb></lb>cioè del quadrato BC al quadrato EF, e del diametro EF al BC; adunque il <lb></lb>cilindro AC al DF sta come il diametro BC al diametro EF, ovvero come <lb></lb>l&#039;altezza DE all&#039;altezza AB, il che dovevasi dimostrare. </s>

<s>Che vuol dire che <lb></lb>i sacchi, fatti con eguali quantità di panno, quanto più son bassi, tanto più <lb></lb>tengono, e quanto sono più grossi, tanto più tengono ” (ivi). </s></p><p type="main">

<s>Gli altri teoremi, che si proponeva il Viviani di aggiungere secondo il <lb></lb>notato in quarto luogo da lui, non abbiamo trovato come fossero dimostrati, <lb></lb>ciò ch&#039;egli avrà fatto in qualche parte de&#039;suoi voluminosi manoscritti mate­<lb></lb>matici. </s>

<s>Ma dalla Geometria trapassando alla Fisica, è notabile ch&#039;egli volesse <lb></lb>dar solenne pubblicità ne&#039;Dialoghi all&#039;invenzion del Termometro, per supplire <lb></lb>a quella, ch&#039;egli credeva trascuratezza o dimenticanza di Galileo, ma che non <lb></lb>era forse altro che la coscienza di avere avuto in quella invenzione, che si <lb></lb>voleva attribuirgli, un&#039;assai piccola parte del merito. </s>

<s>Avrebbe dovuto ripen­<lb></lb>sare il Viviani che avvenne dello strumento da misurare il caldo e il freddo <lb></lb>quel che avvenne dell&#039;altro modo di trovare il peso di un corpo nel vuoto, <lb></lb>non pesandolo realmente altro che in mezzo all&#039;aria; cosa non avvertita da <lb></lb>Galileo e che perciò suggerì allo stesso Viviani quell&#039;aggiunta interfogliata <lb></lb>tra le pag. </s>

<s>82, 83 di Leida, e che poi l&#039;Albèri inserì a pag. </s>

<s>85 della sua <lb></lb>prima edizione completa. </s></p><p type="main">

<s>La settima nota del Viviani non è scritta per altro, che per assegnare <lb></lb>il proprio luogo ne&#039;Dialoghi a quella sua dimostrazione circa la moltiplica­<lb></lb>zione delle superficie de&#039;solidi, che letta a Galileo, come sopra dicemmo, era <lb></lb>stata approvata da lui: ma l&#039;ottava accenna a una questione di Meccanica <lb></lb>importantissima, e intorno alla quale vuol perciò trattenersi la nostra Storia <lb></lb>con particolar diligenza. </s></p><p type="main">

<s>Il principio fondamentale, posto alla Dinamica galileiana, è che il mo­<lb></lb>bile scendendo naturalmente passi per tutti i gradi di velocità, per cui era <lb></lb>prima passato spinto violentemente alla medesima altezza. </s>

<s>Conferito questo <lb></lb>pensiero col Sarpi, trovò subito una gran difficoltà ad essere ammesso per <lb></lb>vero, sembrando repugnante all&#039;esperienza, come il Sarpi stesso scriveva il <lb></lb>dì 9 ottobre 1604 in una sua lettera a Galileo, nella quale così cominciava: <lb></lb>“ Con occasione d&#039;inviarli l&#039;allegata, mi è venuto pensiero di proporli un <lb></lb>argomento da risolvere, e un problema che mi tiene ambiguo. </s>

<s>Già abbiamo <lb></lb>concluso che nessun grave può essere tirato all&#039;istesso termine in su, se non <lb></lb>con una forza, e per conseguente, con una velocità. </s>

<s>Siamo passati, così V. S. <lb></lb>ultimamente affermò e inventò ella, che per gli stessi termini tornerà in giù, <lb></lb>per i quali andò in su. </s>

<s>Fa non so che obiezione la palla dell&#039;archibugio: il <lb></lb>fuoco qui intorbida la forza dell&#039;istanza. </s>

<s>Ma diciamo: un buon braccio, che <lb></lb>tira una freccia con un arco turchesco, passa via totalmente una tavola, e se <lb></lb>la freccia discenderà da quella altezza, dove il braccio con l&#039;arco la può <pb xlink:href="020/01/2425.jpg" pagenum="50"></pb>trarre, farà pochisssima passata. </s>

<s>Credo che l&#039;istanza sii forse leggera, ma <lb></lb>non so che ci dire ” (Lettere raccolte da F. Polidori, Vol. </s>

<s>I, Firenze 1863, <lb></lb>pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Non sappiamo se questa istanza del Sarpi giungesse a Galileo nuova, <lb></lb>ma ei non poteva in nessun modo reputarla leggera, benchè vi rispondesse <lb></lb>poi indirettamente nel primo, e nel quarto dialogo delle Nuove scienze, attri­<lb></lb>buendo la diversità dell&#039;effetto all&#039;impedimento dell&#039;aria, risentito sì nella <lb></lb>scesa naturale, ma sopravvinto dall&#039;eccessiva furia della forza di proiezione. </s>

<s><lb></lb>Galileo anzi si serve di quella istanza del Sarpi, per confortare con qualche <lb></lb>argomento sperimentale una sua falsa opinione, che cioè l&#039;impedimento del <lb></lb>mezzo finalmente riduca il mobile all&#039;egualità, nella quale poi sempre si man­<lb></lb>tenga (Alb. </s>

<s>XIII, 96). Nel Dialogo quarto, a proposito de&#039;proietti, si ripete <lb></lb>lo stesso, e si ammette per vero il fatto affermato dal Sarpi, che cioè una <lb></lb>palla o una freccia, scendendo dall&#039;altezza, a cui fosse stata spinta dalla forza <lb></lb>del fuoco o di una molla; farebbe assai minor passata, che presso alla bocca <lb></lb>del moschetto o alla corda della balestra; benchè Galileo confessi di non aver <lb></lb>fatto una tale esperienza (ivi, pag. </s>

<s>233). </s></p><p type="main">

<s>Il Baliani, leggendo queste cose nei Dialoghi ammirati, tornava trenta­<lb></lb>cinque anni dopo a ripetere l&#039;istanza del Sarpi, aggiungendo di più che l&#039;ef­<lb></lb>fetto non credeva si potesse attribuire all&#039;impedimento del mezzo, come si <lb></lb>diceva da Galileo, a cui in una lettera da Genova del 1° Luglio 1739 scri­<lb></lb>veva, fra le altre considerazioni, anche questa: “ Da ciò che discorre, a fol. </s>

<s>94 <lb></lb>e a fol. </s>

<s>164, par che sparandosi in alto un&#039;archibugiata dovrebbe la palla <lb></lb>far l&#039;istessa passata, v. </s>

<s>g. </s>

<s>di dieci palmi, dall&#039;archibugio, tanto nello scen­<lb></lb>dere quanto nel salire, il che nè credo che riuscirebbe in fatto, nè pare che <lb></lb>si possa sciorre per la condensazione dell&#039;aria, perciocchè non è questa per <lb></lb>mio avviso tale altezza, che nello scendere il grave non osservasse la regola <lb></lb>della duplicata proporzione dei tempi uguali ” (Alb. </s>

<s>X, 334). </s></p><p type="main">

<s>Facendo riflessione sopra queste parole, ebbe a riconoscere Galileo che <lb></lb>davvero, con l&#039;introdurre l&#039;impedimento del mezzo, la difficoltà non veniva <lb></lb>sciolta: rimaneva nonostante sicuro della verità del suo principio, crollando <lb></lb>il quale, sarebbe venuto a minacciar rovina tutto intero l&#039;edifizio dei moti <lb></lb>accelerati. </s>

<s>Perciò, nella fiducia di aver pure a trovare del dubbio la risolu­<lb></lb>zion vera, e in altre più sottili osservazioni alle impugnate dottrine una con­<lb></lb>ferma, così al libero impugnatore di Genova, dopo un mese preciso, rispon­<lb></lb>deva: “ Che la palla discendente dall&#039;altezza, dove dalla forza del fuoco fu <lb></lb>cacciata, non riacquisti tornando indietro, giunta le dieci braccia vicina all&#039;ar­<lb></lb>chibugio, quell&#039;impeto, che ella ebbe quando da principio fu scaricata, da <lb></lb>me è tenuto per effetto verissimo. </s>

<s>Ma questo non altera punto la mia pro­<lb></lb>posizione, nella quale io dico che il grave discendendo da alto riacquista nei <lb></lb>medesimi luoghi della scesa quella forza, che era bastante a risospingerlo in <lb></lb>su, quando nei medesimi luoghi si ritrovò salendo, e forse, da quello che già <lb></lb>si legge nei luoghi da lei citati, raccogliere si potrebbe. </s>

<s>Ma è vero che, senza <lb></lb>aggiungere io alcune nuove osservazioni, forse non potrebbe agevolmente esser <pb xlink:href="020/01/2426.jpg" pagenum="51"></pb>compreso, ma il produrlo ricerca un poco più di ozio e di quiete di mente, <lb></lb>di quella che di presente io posseggo: lo farò altra volta, quando ella pure <lb></lb>me lo richiegga ” (Lettere per il trecentesimo natalizio, Pisa 1864, pag. </s>

<s>45). </s></p><p type="main">

<s>Il Baliani non richiese altro, dicendo di esser sodisfatto di ciò, ch&#039;era <lb></lb>detto in questa lettera e nei Dialoghi, i quali egli era perciò tornato a leg­<lb></lb>gere di nuovo: soggiungeva solamente un suo pensiero, che cioè, perdendo <lb></lb>il mobile della propria naturale velocità, per l&#039;impedimento dell&#039;aria inter­<lb></lb>posta, “ poi camminando avanti possa essere che la racquisti ” (Alb. </s>

<s>X, 361). <lb></lb>Galileo rispondeva che questo veramente sarebbe stato per lui duro a conce­<lb></lb>dere, quando non avesse esperienze e dimostrazioni in contrario (Lettere cit., <lb></lb>pag. </s>

<s>51), ma lasciando addietro questa, che era una questione incidente, ri­<lb></lb>pensava alla principale, e come ciò, che non s&#039;era curato di richiedere il <lb></lb>Baliani, poteva esser richiesto dai lettori dei Dialoghi, arretrando a que&#039;due <lb></lb>passi da noi sopra citati. </s>

<s>Conferiva queste cose col Viviani, che incorava <lb></lb>una giovanile speranza di dover finalmente sciogliere i dubbi, aiutandosi di <lb></lb>esperienze più diligenti. </s>

<s>Pareva anche a lui vero quel che vero era creduto <lb></lb>e affermato dal Sarpi, da Galileo e dallo stesso Baliani, ma non se ne poteva <lb></lb>aver certezza come di un fatto osservato. </s>

<s>Le osservazioni però voleva che si <lb></lb>facessero nelle ammaccature, non del percuziente, ma del percosso, cosicchè, <lb></lb>invece di sparar l&#039;archibugio contro una pietra, come il Salviati proponeva, <lb></lb>si sparasse contro un petto a botta, o contro un corsaletto o che altro, atto <lb></lb>a ricevere e a ritenere in sè impresse le vestigia, da congetturare del mag­<lb></lb>giore o del minor impeto della palla. </s></p><p type="main">

<s>Piacque a Galileo l&#039;esperienza, in questo nuovo modo proposta, e dietro <lb></lb>la quale si sperava di trovar la vera ragione perchè nelle cadute naturali, <lb></lb>anche da non grandi altezze, e nelle quali perciò pareva che di poco effetto <lb></lb>dovess&#039;essere l&#039;impedimento dell&#039;aria; il mobile non acquisti mai impeto <lb></lb>uguale a quello della sua proiezione. </s>

<s>Questa ragione si doveva sostituire a <lb></lb>quella messa in bocca al Salviati, ed essendo la cosa di tanta importanza, <lb></lb>perchè non dovesse rimanere indietro, in mezzo alle presenti sollecitudini di <lb></lb>migliorare e ampliare i dialoghi delle Nuove scienze, Galileo stesso ne det­<lb></lb>tava al Viviani un tal memoriale: “ Cercar di assegnar la ragione onde av­<lb></lb>venga che la palla tirata in su col moschetto, incontrando dieci o dodici brac­<lb></lb>cia lontano un pett&#039;a botta lo sfonda, sopra il quale, cadendo ella dall&#039;altezza <lb></lb>dove il moschetto la caccerebbe, percotendo nel ritorno in giù sopra il me­<lb></lb>desimo petto, assai minore effetto vi farebbe, e forse appena l&#039;ammacche­<lb></lb>rebbe un poco ” (MSS. Gal., P. V, T. IV, fol. </s>

<s>19). </s></p><p type="main">

<s>Se fosse stata veramente da Galileo e dal Viviani trovata quella ra­<lb></lb>gione, che si cercava, non potremmo noi asserire di certo, mancandoci intorno <lb></lb>a ciò il documento. </s>

<s>Anzi, come apparirà dal passo, che tra poco trascrive­<lb></lb>remo, sembra che non avessero gli Accademici fiorentini trovato da dir nulla <lb></lb>di meglio di quel che, nel primo e nel quarto dialogo delle due Scienze <lb></lb>nuove, era stato insegnato dal Salviati, nonostante l&#039;antica instanza del Ba­<lb></lb>liani, che cioè, in sì poca altezza quant&#039;è un trar d&#039;archibugio, non possa <pb xlink:href="020/01/2427.jpg" pagenum="52"></pb>l&#039;aria impedire alla palla il velocitarsi, secondo la legge degli spazi propor­<lb></lb>zionali ai quadrati dei tempi. </s></p><p type="main">

<s>Certo è però che il Viviani istitui l&#039;esperienze a quel modo che, vivente <lb></lb>Galileo, le aveva a lui stesso proposte, e come appartenenti all&#039;Accademia <lb></lb>del Cimento furon raccolte fra quelle, che si descrivono intorno ai proietti <lb></lb>nell&#039;appendice al libro dei <emph type="italics"></emph>Saggi.<emph.end type="italics"></emph.end> Ivi si ripetono dal Segretario le precise <lb></lb>parole, che si leggono nel dialogo quarto a pag. </s>

<s>164 dell&#039;edizione di Leida, <lb></lb>e a pag. </s>

<s>233 di quella dell&#039;Albèri, nelle quali parole, senz&#039;averlo ancora spe­<lb></lb>rimentato, s&#039;afferma per vero il fatto della percossa della palla dell&#039;archibu­<lb></lb>gio, presso alla bocca, maggiore di quella che la medesima palla farebbe <lb></lb>contro una pietra, tornando in giù dall&#039;altezza, a cui l&#039;archibugio stesso <lb></lb>l&#039;avrebbe verticalmente gettata, e poi nel detto libro così subito si soggiunge: </s></p><p type="main">

<s>“ Noi abbiamo fatto questa prova con un archibugio rigato, non già spa­<lb></lb>randolo contro una pietra, per osservar l&#039;ammaccatura della palla, ma bensì <lb></lb>contro un pettabbotta di ferro. </s>

<s>In esso adunque abbiamo veduto che i tiri <lb></lb>fatti da minore altezza v&#039;imprimevano forma assai più profonda di quelli, che <lb></lb>da maggiore venivano fatti: imperocchè dicevano alcuni, seguitando in ciò <lb></lb>il parere del Galileo, nel più lungo viaggio che fa la palla, fendendo l&#039;aria, <lb></lb>si va di continuo smorzando in essa quell&#039;impeto e forza soprannaturale im­<lb></lb>pressale dalla violenza del fuoco ” (Firenze 1841, pag. </s>

<s>163). </s></p><p type="main">

<s>Il parere di Galileo è notabile che fosse seguito dagli Accademici fio­<lb></lb>rentini, dopo quasi vent&#039;anni di discussione contro le istanze del Baliani o, <lb></lb>per più vero dire, contro le esperienze comuni. </s>

<s>Aveva tutta l&#039;apparenza del <lb></lb>vero che la palla del moschetto non torni in giù da tale altezza, che le debba <lb></lb>l&#039;aria togliere tanto di velocità, e nonostante non vedevano a quale altra <lb></lb>causa, fuor che all&#039;impedimento dell&#039;aria, si potesse attribuire lo stravagante <lb></lb>effetto. </s>

<s>Implicitamente dunque ammettevano costoro, insieme col Maestro, che <lb></lb>solo nel vuoto acquisterebbe il mobile, scendendo naturalmente, tutto intero <lb></lb>il primo impeto della sua proiezione, ed esplicitamente professava così il Bo­<lb></lb>relli nel suo trattato <emph type="italics"></emph>De vi percussìonis.<emph.end type="italics"></emph.end> “ Si postea removeatur omnino <lb></lb>aeris impedimentum .... spatia ascensus atque descensus, aequalibus tempo­<lb></lb>ribus, aequalia essent ” (Bononiae 1667, pag. </s>

<s>258). </s></p><p type="main">

<s>Scriveva così l&#039;Autore nella proposizione CXIV, dop&#039;aver descritta l&#039;espe­<lb></lb>rienza della palla verticalmente gettata con la saetta, l&#039;ascesa violenta della <lb></lb>qual palla dice essere stata doppia della discesa naturale nel medesimo tempo. </s>

<s><lb></lb>Ma le esperienze, che dovevano meglio persuadere, e confermare le menti <lb></lb>nella verità delle dottrine galileiane, non apparirono che sui principii del se­<lb></lb>colo XVIII, quando il Gunther faceva, innanzi all&#039;imperiale Accademia di <lb></lb>Pietroburgo, sparar con tiro verticale i cannoni, misurando il tempo e os­<lb></lb>servando l&#039;altezza, a cui faceva l&#039;impeto risalire i proietti. </s>

<s>S&#039;ebbe da una <lb></lb>di coteste esperienze l&#039;altezza di 7819 piedi inglesi, mentre, secondo i cal­<lb></lb>coli di Daniele Bernoulli, da lui stesso descritti nella dissertazione <emph type="italics"></emph>De actione <lb></lb>fluidorum in corpora solida<emph.end type="italics"></emph.end> (Comment. </s>

<s>petroburg., T. II); sarebbero nel <lb></lb>vuoto dovuti essere 58,750 piedi. </s>

<s>Aveva dunque la palla trovato tanto con-<pb xlink:href="020/01/2428.jpg" pagenum="53"></pb>trasto nell&#039;aria, da ridurre a un ottavo la sua libera salita, d&#039;onde mostrasi <lb></lb>la fallacia dell&#039;istanza del Baliani contro la dottrina di Galileo, e si risolve <lb></lb>il problema del Sarpi. </s>

<s>Perchè l&#039;impeto di proiezione non si dovrebbe com­<lb></lb>parar con l&#039;impeto della caduta naturale della palla o della freccia da quel­<lb></lb>l&#039;altezza, a cui l&#039;avevano cacciata il moschetto o la balestra, ma da un&#039;al­<lb></lb>tezza tanto maggiore, quanta si può congetturare dietro i calcoli del Bernoulli, <lb></lb>e l&#039;esperienze di Pietroburgo. </s></p><p type="main">

<s>Mancava agli Accademici fiorentini tanta perizia di calcolo, e tanta pre­<lb></lb>cisione degli strumenti, e dall&#039;altra parte l&#039;esperienze da loro istituite, die­<lb></lb>tro il suggerimento e la direzion del Viviani, e quelle stesse accennate nella <lb></lb>detta proposizione CXIV del Borelli, non avevano, per mancanza di preci­<lb></lb>sione, l&#039;efficacia che si richiedeva per rispondere alle fatte instanze, e per <lb></lb>risolvere i proposti quesiti, onde a poco si può dire che si riduca tutto quel <lb></lb>che a carte 94 si proponeva di aggiunger nel primo dialogo il Viviani, <emph type="italics"></emph>dopo <lb></lb>il discorso del Salviati circa il tiro del moschetto in un corsaletto:<emph.end type="italics"></emph.end> ma <lb></lb>l&#039;altro proposito che segue, d&#039;illustrare cioè <emph type="italics"></emph>il pensiero di Platone, e far <lb></lb>quel calcolo,<emph.end type="italics"></emph.end> ebbe a rimanersi anche in maggior difetto. </s>

<s>Nel dialogo quarto, <lb></lb>dop&#039;avere il Salviati definita la <emph type="italics"></emph>sublimità,<emph.end type="italics"></emph.end> dall&#039;impeto acquistato nella quale, <lb></lb>volto orizontalmente e cougiunto col moto naturale e accelerato della gravità, <lb></lb>il proietto descrive la semiparabola; viene in mente al Sagredo di applicar <lb></lb>quel concetto, che si confessa derivar dai placiti di Platone, alle orbite pla­<lb></lb>netarie, il moto equabile delle quali si potrebbe immaginar preceduto da un <lb></lb>moto retto accelerato, incominciatosi a far da punti più o meno sublimi, se­<lb></lb>condo la maggiore o minor velocità, che voleva il Creatore fosse impressa <lb></lb>ne&#039;pianeti. </s>

<s>Dice esso Sagredo che aveva Galileo avuto talvolta il pensiero di <lb></lb>calcolare quelle sublimità, per veder se si trovassero corrispondere alle gran­<lb></lb>dezze degli orbi e ai tempi delle rivoluzioni: a cui soggiunge il Salviati che <lb></lb>non solo aveva Galileo avuto il pensiero, ma che aveva fatto già quel com­<lb></lb>puto, “ ed anco trovatolo assai acconciamente rispondere alle osservazioni: <lb></lb>ma non averne voluto parlare, giudicando che le troppe novità da lui sco­<lb></lb>perte, che lo sdegno di molti gli hanno provocato, non accendessero nuove <lb></lb>scintille ” (Alb. </s>

<s>XIII, 238). </s></p><p type="main">

<s>Ora che era cenere, non poteva aver più nessuna paura di quell&#039;incen­<lb></lb>dio, e perciò pensava il Viviani ch&#039;era il tempo di far quel calcolo, per ador­<lb></lb>nare il concetto platonico, e anche il dialogo galileiano. </s>

<s>Non possono i Let­<lb></lb>tori astronomi non sentirsi a questo punto frugati da una grande curiosità di <lb></lb>sapere in qual modo quel calcolo fosse fatto, perchè dalla risposta scende­<lb></lb>rebbe un corollario importante alla nostra Storia dell&#039;Astronomia. </s>

<s>Quel con­<lb></lb>cetto platonico e copernicano infatti, dalla scoperta delle orbite ellittiche ve­<lb></lb>niva dimostrato falso, e poniamo che non si vedesse ancora di li conseguir <lb></lb>chiaro, come poi apparve al Newton, il sistema delle forze centrali, non si <lb></lb>poteva più pensare all&#039;equabilità del moto orbitale, succeduto al retto acce­<lb></lb>lerato, ora che si osserva di fatto andar nel perigeo il pianeta alquanto più <lb></lb>veloce che nell&#039;apogeo. </s>

<s>Galileo non volle mai credere a queste osservazioni, <pb xlink:href="020/01/2429.jpg" pagenum="54"></pb>nè il corollario storico che si diceva è questo, ma un altro anche più nota­<lb></lb>bile, perchè l&#039;essersi proposto il Viviani di far que&#039;calcoli platonici, per in­<lb></lb>serirli nel quarto dialogo delle Nuove scienze, sarebbe documento che, anche <lb></lb>dopo qualche anno la morte di Galileo, si persisteva nella scuola di lui a <lb></lb>repudiare le leggi scoperte dal Keplero. </s>

<s>Dell&#039;esser poi messo o no quel pro­<lb></lb>posito ad effetto è inutile domandare, perchè, se quei calcoli astronomici fos­<lb></lb>sero stati fatti bene secondo le dottrine platoniche e copernicane, era impos­<lb></lb>sibile che fossero <emph type="italics"></emph>trovati assai acconciamente rispondere alle osservazioni,<emph.end type="italics"></emph.end><lb></lb>per cui non par che possa andare assoluto dalla nota d&#039;inverosimile il detto <lb></lb>del Salviati. </s></p><p type="main">

<s>A terminar questo esame dei modi come il Viviani colorì que&#039;suoi pen­<lb></lb>sieri d&#039;ampliare e d&#039;illustrare le dottrine, esposte da Galileo nella prima edi­<lb></lb>zione delle Scienze nuove, in certi punti particolari; non rimane ora a dir <lb></lb>che del proposito di rispondere a una domanda, messa dallo stesso Viviani <lb></lb>in quella forma, che si lesse nella X nota del suo memoriale. </s>

<s>Accennasi quivi <lb></lb>all&#039;uso delle catenelle, di trattar delle quali si promette sulla fine del Dia­<lb></lb>logo quarto, e poi si rimanda il discorso all&#039;ultimo congresso, che sarebbe <lb></lb>in materia della forza della percossa. </s>

<s>Ma perchè dovremo di quest&#039;ultimo <lb></lb>congresso far speciale soggetto la nostra Storia, vedremo allora come rispon­<lb></lb>desse il Viviani, e com&#039;abbiamo, dietro i documenti, a rispondere noi a chi <lb></lb>fosse curioso di saper se le dette catenelle dovevano secondo Galileo sola­<lb></lb>mente servire ai Geometri, per descrivere le parabole, o anche ai militari per <lb></lb>dirigere i tiri delle artiglierie. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Due scienze, che al mondo matematico s&#039;istituivano come nuove da un <lb></lb>uomo, dotato d&#039;ingegno straordinario senza dubbio, ma non divino, come <lb></lb>tanti fanatici se lo vanno immaginando, non era possibile che, rimanendosi <lb></lb>per la naturale insufficienza da una parte in difetto, non trascorressero dal­<lb></lb>l&#039;altra in qualche errore. </s>

<s>Come fossero da Galileo stesso riconosciuti que&#039;di­<lb></lb>fetti, e come, con l&#039;aiuto del Viviani ei pensasse, in mezzo alle tenebre, di <lb></lb>supplirvi, ce l&#039;hanno fatto veder di sopra i documenti. </s>

<s>Ma quanto a cono­<lb></lb>scere e a confessare gli errori, se repugna all&#039;amor proprio di tutti gli uo­<lb></lb>mini, doveva parer cosa contro natura a colui, che sentiva quanto fosse neces­<lb></lb>sario confermare i discepoli in quella loro opinione, che avesse cioè impressa <lb></lb>quasi una certa nota d&#039;infallibilità nel suo magistero. </s></p><p type="main">

<s>Fu il giovane Viviani uno dei primi a creder con religioso ossequio a <lb></lb>una tale infallibilità del Maestro, e trasparisce viva, senza cercar altro, la sua <lb></lb>fede dal modo, com&#039;egli accolse e notò le censure del Blancano. </s>

<s>Vedemmo <lb></lb>come fossero le più pungenti di così fatte censure in materia delle resistenze <pb xlink:href="020/01/2430.jpg" pagenum="55"></pb>dei solidi, nella quinta proposizione del qual trattato si notavano dal Gesuita <lb></lb><figure id="id.020.01.2430.1.jpg" xlink:href="020/01/2430/1.jpg"></figure></s></p><p type="caption">

<s>Figura 19.<lb></lb>certe conclusioni, che parevano contradire alle <lb></lb>precedenti. </s>

<s>Si legge infatti in quella quinta di­<lb></lb>mostrazione che la resistenza R del cilindro <lb></lb>GD (fig. </s>

<s>19) sta alla resistenza R′ del cilindro <lb></lb>DF, come la lunghezza FE sta alla EG (Alb. </s>

<s>XIII, <lb></lb>123), per cui, moltiplicandosi le lunghezze per <lb></lb>le basi uguali, avremo R:R′=DF:DG, mentre la terza precedente dà la <lb></lb>proporzione omologa R:R′=EG2:FE2. </s></p><p type="main">

<s>Vivente Galileo furono anche dal Viviani queste censure, come se le <lb></lb>avesse suggerite l&#039;invidia, avute in disprezzo, ma poi, quando col progredir <lb></lb>della scienza venne a rendersi dall&#039;altrui suggezione più libero l&#039;ingegno, <lb></lb>conobbe che almeno in parte erano giuste, cosicchè, lasciando quella prima <lb></lb>cieca fede che aveva ai detti del Maestro, e richiamandoli a esame più sottile e <lb></lb>più giudizioso, ebbe a scoprir altre incredibili fallacie nell&#039;oracolo venerato. </s>

<s><lb></lb>Di qui, morto il Maestro, incomincia per il Discepolo un&#039;opera nuova, qual&#039;è <lb></lb>quella di emendare i dialoghi delle Nuove scienze dai più notabili errori. </s></p><p type="main">

<s>Ebbe quest&#039;opera principio dall&#039;esame delle proposizioni intorno alle <lb></lb>resistenze, d&#039;onde glie n&#039;era venuta l&#039;occasione, e dalla Va, censurata dal <lb></lb>Biancani, passando alla VIa, la trovò addirittura falsa, per cui, postillando <lb></lb>nella solita edizione di Leida, si proponeva di ridurla a verità più generale <lb></lb>nella seguente maniera: “ Proposizione VI del Galileo generalmente e di­<lb></lb>versamente enunciata per esser quella non vera. <emph type="italics"></emph>Dei cilindri e prismi, anzi <lb></lb>dei solidi regolari simili, il rispetto tra i momenti gravanti è sesquiterzo <lb></lb>del rispetto tra i momenti resistenti delle loro sezioni.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Siano i due solidi regolari simili AB, CD (fig. </s>

<s>20) dico ecc. </s>

<s>Prese <lb></lb><figure id="id.020.01.2430.2.jpg" xlink:href="020/01/2430/2.jpg"></figure></s></p><p type="caption">

<s>Figura 20.<lb></lb>dopo le linee A, C, uguali ai diametri <lb></lb>delle sezioni A, C, le E, F, G continue <lb></lb>proporzionali, il momento gravante del <lb></lb>solido AB, al gravante di CD, sta come <lb></lb>il quadrato della lunghezza AB, al qua­<lb></lb>drato della CD: cioè, come il quadrato <lb></lb>della linea A, al quadrato della E, per <lb></lb>esser queste proporzionali alle AB, CD, <lb></lb>stante la similitudine dei solidi, cioè <lb></lb>come la prima linea A alla quinta G. </s>

<s><lb></lb>Ed il momento resistente della sezione A, <lb></lb>al resistente della C, sta come il cubo della linea A, al cubo della C, per <lb></lb>la IVa di Galileo, cioè come la prima A alla quarta F. </s>

<s>Perchè tra A e G <lb></lb>sono quattro rispetti della prima e seconda, e tra A ed F sono tre rispetti <lb></lb>della medesima prima e seconda; adunque anco il rispetto tra il momento <lb></lb>gravante di AB, al gravante di CD, sarà sesquiterzo del rispetto tra il resi­<lb></lb>stente di A, e il resistente di C, e non è sesquialtero, come pronunziò ed <lb></lb>intese di dimostrare il Galileo ” (MSS. Gal., P. V, T. IX). </s></p><pb xlink:href="020/01/2431.jpg" pagenum="56"></pb><p type="main">

<s>Il linguaggio, più che mai insolito alle orecchie dei Matematici odierni, <lb></lb>si traduce nella seguente guisa, per confermare la verità della conclusione. </s>

<s><lb></lb>Siano date le proporzionali continue A:C=C:E=E:F=F:G, dalle <lb></lb>quali è facile ottenere A2:E2=A:G=A4:C4. </s>

<s>Chiamati dunque M, M′ i <lb></lb>momenti, avremo M:M′=A2:E2=A:G=A4:C4, e per la IVa di Ga­<lb></lb>lileo R:R′=A3:C3, rappresentando R, R′ le resistenze dei solidi contem­<lb></lb>plati. </s>

<s>Inalzata ora questa alla quarta potenza, e quella a cubo, daranno <lb></lb>R4:R′4=A12:C12, M3:M′3=A12:C12, e perciò M3:M′3=R4:R′4; ossia <lb></lb>M:M′=R4/3:R′4/3, che vuol dire i momenti delle potenze aver, secondo <lb></lb>l&#039;espression del Viviani, ragione sesquiterza delle resistenze. </s></p><p type="main">

<s>Aggiunge il Viviani stesso a questa sua proposizione un corollario, per <lb></lb>mostrar come in quella, resa così più generale, si comprenda il caso parti­<lb></lb>colare contemplato da Galileo, che pur viene a concludere una falsità, da <lb></lb>non si poter salvare, come alcuni credevano, nemmeno profferendone l&#039;enun­<lb></lb>ziazione in modo diverso. </s></p><p type="main">

<s>“ COROLLARIO. — Se dunque la linea A rappresenterà il momento gra­<lb></lb>vante del solido AB, ed anche il resistente della sua base A, che sarà quando <lb></lb>esso solido sia il minimo che rompa, la linea G rappresenterà il gravante <lb></lb>del solido CD, e la F il resistente della sua base C; sicchè il gravante CD <lb></lb>è tanto minore del suo resistente, quanto la G è minore di F, o, a propor­<lb></lb>zione, quanto è minore C di A, ovvero CD di AB. </s>

<s>Sicchè il piccolo tanto più <lb></lb>è resistente, quanto a proporzione è più corto. </s>

<s>” </s></p><p type="main">

<s>“ E per chi dubitasse che l&#039;enunziazione del Galileo si dovesse inten­<lb></lb>dere così: cioè che i momenti gravanti de&#039;cilindri simili hanno proporzione <lb></lb>sesquialtera di quella, che hanno le resistenze (assolute però e non i mo­<lb></lb>menti loro resistenti), pur si prova che, volendo paragonare il rispetto dei <lb></lb>momenti gravanti con quello delle resistenze assolute, l&#039;enunziazione sia prof­<lb></lb>ferita diversamente così, cioè: <emph type="italics"></emph>I momenti gravanti de&#039;solidi simili sono fra <lb></lb>loro in doppia proporzione delle resistenze assolute delle basi.<emph.end type="italics"></emph.end> Perchè, es­<lb></lb>sendosi provato il rispetto tra il gravante e il gravante essere come la A <lb></lb>alla G, ed essendo il rispetto tra la resistenza assoluta di A, all&#039;assoluta di <lb></lb>C, come il quadrato della linea A, al quadrato della linea C, cioè come la <lb></lb>linea A alla terza E; ed avendo A a G duplo rispetto di A ad E, che è media <lb></lb>proporzionale tra A e G, sarà manifesto quanto si propose ” (ivi). </s></p><p type="main">

<s>E anche più manifesto potrebbe rendersi, traducendo così nelle forme <lb></lb>moderne il linguaggio del Viviani: È stato già dimostrato M:M′=A2:E2; <lb></lb>R:R′=A2:C2, e dalla data serie delle continue proporzionali s&#039;ha A2:C2= <lb></lb>A:E. </s>

<s>Dunque M:M′=R2:R′2, che vuol dire: i momenti hanno doppia pro­<lb></lb>porzione delle resistenze, ossia stanno come i quadranti delle resistenze, di­<lb></lb>versamente da quello, che aveva preteso di dimostrar Galileo. </s></p><p type="main">

<s>Incominciatosi così a persuadere, con matematiche ragioni, che non era <lb></lb>da confidarsi in una verità, perchè il grande Maestro della Scienza del moto <lb></lb>l&#039;aveva messa, il Viviani passò da questa proposizione, con più libero esame, <lb></lb>a vedere anche le altre, intorno alle quali, quasi avesse creduto di offendere <pb xlink:href="020/01/2432.jpg" pagenum="57"></pb>l&#039;adorabilità di un Nume, aveva sempre cacciati i dubbi dalla sua mente. </s>

<s><lb></lb>Venne così facilmente a scoprire le tante altre fallacie, nelle quali era tra­<lb></lb>scorso Galileo, trattando delle resistenze, e aveva avvertito già lo sbaglio in <lb></lb>assegnare la figura parabolica al solido, che per tutto resiste ugualmente alla <lb></lb>pressione, qualche anno prima del Blondel e del Marchetti. </s>

<s>Tanto anzi il Vi­<lb></lb>viani stesso riconobbe il secondo dialogo delle Nuove scienze difettoso, che <lb></lb>s&#039;era proposto di riformarlo nella massima parte. </s>

<s>Di quest&#039;opera, data dallo <lb></lb>zelante discepolo, fu discorso da noi nel cap. </s>

<s>VIII dell&#039;altro tomo, per le <lb></lb>sparse pagine del quale ricorrono varie altre notizie concernenti ciò che quel <lb></lb>geloso e amorevole, ma pur libero censore, aveva scritto contro molte errate <lb></lb>dottrine de&#039;Dialoghi del moto. </s>

<s>Poco sembrerebbe perciò che rimanesse a dire <lb></lb>nel presente argomento, alla più compiuta trattazione del quale, manca nono­<lb></lb>stante un esempio, intorno a cui vogliamo trattenere i lettori, come intorno <lb></lb>a uno de&#039;più notabili fatti, da mostrar quanto fosse facile, anche ai più <lb></lb>grandi ingegni, che non presero in mano il filo di Arianna, lo smarrirsi mi­<lb></lb>seramente in questi meccanici labirinti. </s></p><p type="main">

<s>Sulla sera della quarta giornata, nella quale si trattò de&#039;proietti, e pro­<lb></lb>prio nell&#039;atto di congedarsi gl&#039;interlocutori, il Sagredo si proponeva di dimo­<lb></lb>strare un accidente simile a quel che si osserva nella palla di un cannone, <lb></lb>la quale, tirata di punto in bianco, a cagion della gravità, che mai l&#039;abban­<lb></lb><figure id="id.020.01.2432.1.jpg" xlink:href="020/01/2432/1.jpg"></figure></s></p><p type="caption">

<s>Figura 21.<lb></lb>dona, è impossibile che <lb></lb>vada per linea retta orizon­<lb></lb>tale; dicendo esser per so­<lb></lb>migliante ragione “ impos­<lb></lb>sibile distendere una corda, <lb></lb>sicchè resti tesa dirittta­<lb></lb>mente e parallela all&#039;oriz­<lb></lb>zonte, ma sempre fa sacca <lb></lb>e si piega, nè vi è forza che <lb></lb>basti a tenderla rettamen­<lb></lb>te ” (Alb. </s>

<s>XIII, 262). Con­<lb></lb>cludeva ciò come corollario <lb></lb>da un teorema di Mecca­<lb></lb>nica nuova, immaginando <lb></lb>cavalcare sopra i punti sta­<lb></lb>bili A, B (fig. </s>

<s>21) un filo <lb></lb>imponderabile, teso nella <lb></lb>dirittura orizzontale AB da due grandi pesi uguali C, C, e soggiungeva che, se <lb></lb>dal mezzo E si sospendesse qualsivoglia piccolo peso, come per esempio H, <lb></lb>la linea AB allungandosi cederebbe in qualunque modo, e costringerebbe <lb></lb>perciò i ponderosi corpi C, C a salire in alto. </s></p><p type="main">

<s>Voleva il Sagredo, per provare il suo detto, che, fattosi centro in A e <lb></lb>in B, co&#039;raggi uguali AE, BE si descrivessero due quadranti, e immaginando <lb></lb>essersi il peso H da E abbassato in F, congiunte le FA, FB, faceva osser-<pb xlink:href="020/01/2433.jpg" pagenum="58"></pb>vare che, mentre la scesa del peso piccolo veniva misurata dalla tangente EF, <lb></lb>la salita de&#039;grandi era uguale alle porzioni esterne LF delle secanti AF, FB. </s>

<s><lb></lb>Tutto si riduceva dunque a provare che il momento di H è, o può almeno <lb></lb>essere maggiore della somma de&#039;momenti C, C, richiamando perciò alla me­<lb></lb>moria di Simplicio la nota legge aristotelica delle equiponderanze, secondo <lb></lb>la quale si diceva allora avere due gravi i momenti uguali, quando sono <lb></lb>uguali i prodotti delle velocità per le moli. </s>

<s>Applicando ora il Sagredo al <lb></lb>fatto suo questa legge, voleva persuadere allo stesso Simplicio che si sarebbe <lb></lb>felicemente conseguito l&#039;intento, quando si fosse dimostrato che il prodotto <lb></lb>di H per la linea EF, dalla quale si misura la velocità della scesa, fosse o <lb></lb>potess&#039;essere maggiore del prodotto di 2 C per LF, che nello stesso tempo <lb></lb>misura la velocità della salita. </s>

<s>La dimostrazione procede in sostanza così, come <lb></lb>noi la riduciamo in più semplice forma. </s></p><p type="main">

<s>Facciasi 2 C ad H come la linea BO a un&#039;altra, che sia C, e, presa D <lb></lb>linea minore della C, dividasi in E la BO in modo, che sia OB:D=D:BE. </s>

<s><lb></lb>Menato poi il quadrante, descritto dianzi col raggio AE, per tutto il suo giro, <lb></lb>costituiscasi F a tal distanza da E che, tirata la FAG, debb&#039;aversi OE:EB= <lb></lb>GL:LF, la quale componendo darà OB:EB=GF:LF. </s>

<s>Posto poi nella <lb></lb>prima ragione di questa BE=D2/OB, e moltiplicati per LF ambedue i termini <lb></lb>della ragione seconda, verrà OB2:D2=GF.LF:LF2. </s>

<s>Ma il prodotto della <lb></lb>secante GF, per la sua porzione esterna, è uguale al quadrato della tan­<lb></lb>gente EF; dunque, sostituendo ed estraendo le radici, avremo OB:D= <lb></lb>EF:LF. </s>

<s>Ma OB:D è maggiore di OB:C, ossia di 2C:H, dunque H.EF <lb></lb>è maggiore di 2C.LF: ciò vuol dire che, prevalendo il momento del pic­<lb></lb>colo peso al momento de&#039;due grandi, questi, come dovevasi dimostrare, sa­<lb></lb>ranno in qualunque modo fatti salire da lui. </s>

<s>“ E quel che avviene alla retta <lb></lb>AB priva di gravità, conclude il Sagredo, mentre si attacchi in E qualsivo­<lb></lb>glia minimo peso H, avviene all&#039;istessa corda AB, intesa di materia pesante, <lb></lb>senza l&#039;aggiunta di alcun altro grave, poichè vi si sospende il peso stesso <lb></lb>della materia componente essa corda AB ” (ivi, pag. </s>

<s>265). </s></p><p type="main">

<s>Dicemmo esser questo un teorema di Meccanica nuova, per Galileo però, <lb></lb>perchè Leonardo da Vinci l&#039;aveva dimostrato quasi due secoli prima, come <lb></lb>si rammemoreranno coloro, che hanno letto il capitolo primo dell&#039;altra parte <lb></lb>di questa Storia. </s>

<s>L&#039;aggressione è nonostante ne&#039;due Autori molto diversa, e <lb></lb>non sarà perciò inutile il trattenersi alquanto per farne insieme il confronto. </s>

<s><lb></lb>Proponendosi a risolvere il problema del piccolissimo, che muove il grandis­<lb></lb>simo, pensava Leonardo non si potere far meglio che imitando Archimede, <lb></lb>con ricorrere alla leva, per mezzo della quale, dato il punto di appoggio, si <lb></lb>vantava che avrebbe con le sue proprie mani mosso il cielo e la terra. </s>

<s>Nè <lb></lb>a conseguir ciò, bisognava fa altro, se non dare alla leva una tale lunghezza, <lb></lb>da stare alla lunghezza della contralleva reciprocamente come il peso del­<lb></lb>l&#039;universo sta al peso di un uomo senza il cappello, perchè, a solo aggiun­<lb></lb>gervi il peso di questo, prevalendo il momento, si verrebber di fatto a com-<pb xlink:href="020/01/2434.jpg" pagenum="59"></pb>movere le fondamenta del mondo. </s>

<s>Essendo ora AE, nella precedente figura, <lb></lb>il braccio della leva, che si pone imponderabile, come ponevasi dianzi impon­<lb></lb>derabile il filo, e potendosi a qual si voglia distanza dal punto fisso A ter­<lb></lb>minare la contralleva, si comprende benissimo, diceva Leonardo, come possa <lb></lb>un capo di spillo in E sollevare in C una gran macina. </s></p><p type="main">

<s>Il discorso di Leonardo è vero, se son veri i teoremi di Archimede nel <lb></lb>libro Degli equiponderanti, ma non si può dir così di quell&#039;altro discorso, <lb></lb>che Galileo poneva in bocca al Sagredo. </s>

<s>Basta infatti questa prima conside­<lb></lb>razione, per metterci in sospetto che dee esser lì dentro una grande falla­<lb></lb>cia: La mole di H, che libera pende dal punto F, non par che possa equi­<lb></lb>ponderare alla mole di C, con la quale è congiunta per mezzo del funicolo <lb></lb>FAC, se non a patto che i due pesi, nelle dette moli, siano uguali, precisa­<lb></lb>mente com&#039;avverrebbe se fosse in F un altro punto stabile e fisso. </s>

<s>Il cal­<lb></lb>colo conferma meglio che in questa sola uguaglianza de&#039;contrappesi sussi­<lb></lb>stono le condizioni dell&#039;equilibrio, nel caso contemplato da Galileo, per cui <lb></lb>gli riusci tutt&#039;al contrario della sua intenzione, ch&#039;era quella di dimostrar <lb></lb>come mai un piccolissimo possa movere un grandissimo corpo. </s></p><p type="main">

<s>Un&#039;altra considerazione sovviene a confermare il sospetto di qualche fal­<lb></lb>lacia nel discorso di Galileo, ed è che male sembra essere applicato al caso <lb></lb>di questi pesi penduli dalle funi il principio delle velocità virtuali, come nella <lb></lb>leva, sull&#039;estremità dalla quale esercitano i pesi perpendicolarmente tutto il <lb></lb>loro momento: perchè il peso H nello schema galileiano non è libero d&#039;eser­<lb></lb>citare il momento della sua gravità per contrappesar C, C, essendo manife­<lb></lb>stamente impedito dal funicolo FB che lo frena. </s>

<s>Intanto s&#039;incomincia ora a <lb></lb>veder chiaro dove s&#039;asconde l&#039;errore di Galileo, il quale computava l&#039;effetto <lb></lb>di H come se operasse con tutta la naturale sua gravità, mentre invece la <lb></lb>gravità totale alla parziale con cui fa da contrappeso al doppio di C, sta come <lb></lb>AF ad FE. </s>

<s>Tale è appunto la ragione che passa tra il momento del grave <lb></lb>nel perpendicolo, e nel piano inclinato: che se Galileo se l&#039;avesse in tal pro­<lb></lb>posito richiamata alla memoria, si sarebbe facilmente avveduto del suo fallo, <lb></lb>e avrebbe indirizzato a miglior fine il teorema della corda tesa, specialmente <lb></lb>applicandovi ìl metodo di decomporre una forza in due, come poi fece in di­<lb></lb>mostrare uguale la velocità de&#039;cadenti per varie vie oblique, ma della me­<lb></lb>desima altezza. </s>

<s>Forse, quando scriveva e licenziava quella fine del quarto <lb></lb>Dialogo per la stampa, non aveva ancora pensato a questo nuovo modo di <lb></lb>condurre la dimostrazione del Teorema meccanico, e fa perciò più gran ma­<lb></lb>raviglia che l&#039;analogia fra questa macchina funicolare e il piano inclinato <lb></lb>non fosse avvertita poi dal Viviani, il quale, accortosi finalmente della falla­<lb></lb>cia del suo Maestro, prendendo la penna in mano per scrivergli contro, non <lb></lb>seppe nemmen egli liberarsi dal trascorrere in altra simile fallacia, ammet­<lb></lb>tendo con Galileo che per la tangente EF perpendicolare, e per la secante AF <lb></lb>obliqua eserciti il peso il suo momento totale. </s>

<s>Anzi di questo non si corresse <lb></lb>mai, nè avrebbe ai veri termini meccanici ridotte mai le altrui trasgressioni, <lb></lb>se non gli fosse provvidamente occorso a fare alcune esperienze, le quali, <pb xlink:href="020/01/2435.jpg" pagenum="60"></pb>per parer tanto aliene dalla scienza del moto, non vogliamo ancora nemmen <lb></lb>pronunziare. </s>

<s>Riconosciute dai fatti sperimentati le ragioni geometriche, e dalla <lb></lb>Fisica tornando il Viviani alla Meccanica, per sodisfare ai curiosi di sapere <lb></lb>in che modo, di promotore ch&#039;egli era della meccanica funicolare di Galileo, <lb></lb>si convertisse in contradittore; valgano le seguenti notizie, che dalle sparse <lb></lb>e informi carte manoscritte di lui passiamo a intessere nella nostra Storia. </s></p><p type="main">

<s>La prima e più ovvia promozione, che occorresse al Viviani di fare del <lb></lb>teorema di Galileo, fu quella di ridurlo a problema, perchè, data la propor­<lb></lb>zione tra il peso attaccato nel mezzo e gli altri due eguali, dai due capi della <lb></lb>fune liberamente pendenti, si determinassero le condizioni dell&#039;equilibrio. </s>

<s>Quel <lb></lb>problema veniva dal Viviani stesso così proposto: “ Sia la corda AB, nella <lb></lb>precedente figura, senza peso, orizontalmente tesa sopra le due girelle A, B <lb></lb>dal mezzo delle quali in E penda un piccol peso I, e dalla estremità di essa <lb></lb>i pesi C, C uguali tra loro, e quanto si voglia maggiori del peso I. </s>

<s>Già è ma­<lb></lb>nifesto per il Galileo che il piccolo calerà, e sarà bastante a sollevare i pesi C. </s>

<s><lb></lb>Cali per esempio in I, e sia dato un altro peso F, maggiore di I, e minore <lb></lb>di ciascuno de&#039;due pesi C, il quale si sospenda in luogo del peso I. È certo <lb></lb>che questo calerà ancora più a basso. </s>

<s>Cercasi fino a qual punto della per­<lb></lb>pendicolare EI sia per fermarsi il peso F, sollevando i pesi C ” (MSS. Gal., <lb></lb>T. CXIII, fol. </s>

<s>14). </s></p><p type="main">

<s>Il problema è risoluto così, accomodandovi opportunamente il Viviani il <lb></lb>discorso e i modi di Galileo: Facciasi F:I=C:D, rappresentando C una <lb></lb>linea; e rappresentando 2C i pesi, si faccia ancora I:2C=D:OB:avremo <lb></lb>2C:F=OB:C. </s>

<s>Prendasi OE terza proporzionale dopo OB, C, e si acco­<lb></lb>modi dentro l&#039;angolo AEF la linea AF di tal lunghezza da aversi GL:LF= <lb></lb>EB:OE. </s>

<s>Sarà F il punto cercato perchè ivi il momento F.EF del peso che <lb></lb>scende s&#039;uguaglia al momento 2C.FL dei pesi, che nello stesso tempo son <lb></lb>fatti salire. </s>

<s>Composta, l&#039;ultima scritta proporzione darà GF:LF=OB:OE, <lb></lb>e moltiplicati per LF i termini della prima ragione, e per OB i termini della <lb></lb>seconda, GF.LF:LF2=OB2:OE.OB.Ma GF.LF=FE2, OE.OB=C2, <lb></lb>dunque FE2:LF2=OB2:C2. </s>

<s>Estraendo le radici, e ponendo OB:C=2C:F, <lb></lb>avremo F.FE=2C.LF, che mostra come veramente in F, tra il peso che <lb></lb>scende e i due che salgono, s&#039;equilibrino i momenti. </s>

<s>Ma ascoltiamo il Viviani: </s></p><p type="main">

<s>“ Facciasi come il peso F all&#039;I così la linea C alla D, e come il peso I <lb></lb>ai pesi C così la linea D alla OB: sarà <emph type="italics"></emph>ex aequali<emph.end type="italics"></emph.end> il peso F ai pesi C, come <lb></lb>C ad OB, e permutando i pesi C al peso F come OB a C. </s>

<s>Inoltre delle due <lb></lb>OB, C sia terza proporzionale la OE, e si faccia come la EB ad OE, così il <lb></lb>diametro del cerchio, il cui radio AE, cioè così GL ad LF, prodotta in di­<lb></lb>ritto: che adattando la AF all&#039;angolo AEF sarà F il punto cercato. </s>

<s>Poichè, <lb></lb>essendo fatto GL ad LF come EB ad OE, sarà componendo GF ad FL, cioè <lb></lb>il quadrato di EF ad LF, come OB ad OE, cioè come il quadrato di OB a C, <lb></lb>e però la linea EF ad FL, cioè la scesa del peso F alla salita dei pesi C, <lb></lb>come la linea OB a C: cioè come i pesi C al peso F reciprocamente, e però <lb></lb>il dato peso calerà in F, e quivi si farà l&#039;equilibrio ” (ivi). </s></p><pb xlink:href="020/01/2436.jpg" pagenum="61"></pb><p type="main">

<s>Risoluto così il meccanico problema, soggiunge il Viviani un corollario, <lb></lb>per farne l&#039;applicazione a costruire quella nuova specie d&#039;Igrometri, de&#039;quali <lb></lb>parlammo a pag. </s>

<s>521 del nostro primo Tomo. </s>

<s>“ Se invece de&#039;pesi C, egli <lb></lb>dice, da sollevarsi col piccolo peso I, ci figureremo la AB essere una stri­<lb></lb>scia di carta, che priva di umido resti ben tesa e attaccata nelle estremità <lb></lb>A, B, e nel mezzo E si appenda il medesimo peso I; questo farà alquanto <lb></lb>allungare detta striscia, e cavandola dalla rettitudine, gli farà fare un tale an­<lb></lb>golo AIB, calando da E in I, e tale effetto sarà simile anzi lo stesso.... ” (ivi). </s></p><p type="main">

<s>Rimase a questo punto la scrittura interrotta, perchè, ripensando il Vi­<lb></lb>viani a un fatto poco prima osservato, incominciò ad entrargli nella mente <lb></lb>il dubbio se, nel funicolo di Galileo e nel nuovo Igrometro, l&#039;effetto fosse <lb></lb>veramente simile, anzi lo stesso. </s>

<s>Aveva fin allora con ferma fede creduto che, <lb></lb>nel detto funicolo, le scese del peso di mezzo si serbassero sempre propor­<lb></lb>zionali alle salite dei pesi dalle due parti, ciò che trovò non avverarsi nello <lb></lb>strumento, quand&#039;ebbe a compararlo con altri strumenti simili, per appli­<lb></lb>carvi la scala delle proporzioni. </s>

<s>Poniamo che sia stato segnato in I, nella <lb></lb>precedente figura, il primo grado: credeva il Viviani che, doppia umi­<lb></lb>dità facendo allungare la carta il doppio, si dovesse il secondo grado segnare <lb></lb>in F, a una distanza da E doppia del primo. </s>

<s>Gli resultava invece dalle isti­<lb></lb>tuite comparazioni che “ si ricerca più umido ad abbassare dal secondo al <lb></lb>terzo grado, che dal primo al secondo, e maggiore dal terzo al quarto, che <lb></lb>dal secondo al terzo, supposti i gradi uguali ” (MSS. Gal. </s>

<s>Disc., T. CXXXIV, <lb></lb>fol. </s>

<s>49). Cominciò allora il Viviani seco medesimo a pensare e a dire: o non <lb></lb>è vero quel che ho creduto fin qui in Fisica, che cioè la carta imbevuta di <lb></lb>doppia umidità s&#039;allunghi il doppio, o non è vero quel che m&#039;aveva Galileo <lb></lb>fatto credere in Geometria, che cioè, nella macchina funicolare descritta dal <lb></lb>Sagredo, gli allungamenti delle tangenti serbino sempre proporzione esatta <lb></lb>con gli allungamenti delle secanti. </s>

<s>E perchè questa inquisizione seconda era <lb></lb><figure id="id.020.01.2436.1.jpg" xlink:href="020/01/2436/1.jpg"></figure></s></p><p type="caption">

<s>Figura 22.<lb></lb>assai più comoda, e più concludente della <lb></lb>prima, vi s&#039;applicò con sollecita diligenza, <lb></lb>e gli riuscì facile a dimostrare che la tan­<lb></lb>gente EI, alla parte esterna IM della se­<lb></lb>cante, ha maggior proporzione della tan­<lb></lb>gente EF, alla secante FL, e così rico­<lb></lb>nobbe con sua gran compiacenza, per ra­<lb></lb>gione geometrica in perfetta conformità <lb></lb>con l&#039;esperienze, che per fare scendere <lb></lb>al peso uno spazio doppio conveniva che <lb></lb>l&#039;umidità avesse fatto allungare la carta <lb></lb>qualche cosa più del doppio, ond&#039;è che, <lb></lb>presignatasi la figura 22, la costruzione <lb></lb>della quale è facile intendere, annun­<lb></lb>ziava e dimostrava così il nuovo teorema: <lb></lb>“ Dico descensum EA ponderis H ad <pb xlink:href="020/01/2437.jpg" pagenum="62"></pb>ascensum AB ponderis L, minorem rationem habere, quam descensum FD, <lb></lb>ad ascensum DC. ” </s></p><p type="main">

<s>“ Nam, ducta AD, et producta usque ad G, et iuncta GB, et ex D ducta <lb></lb>parallela DH, erit EA ad FD ut AG ad GD, vel AB ad DH. Et, permutando, <lb></lb>EA ad AB, ut FD ad DH. </s>

<s>Sed DC, quae ad centrum M pertransit, minor <lb></lb>est DH, ut patet, ergo EA ad AB minorem habet rationem, quam FD ad DC. <lb></lb>Ergo, si pondus L ad pondus H fuerit ut EA ad AB, pondus H descendet <lb></lb>usque ad A, neque amplius descendet, cum ratio linearum FD, DC supra <lb></lb>punctum A sit semper maior, et infra A semper sit minor. </s>

<s>” (MSS. Gal. </s>

<s><lb></lb>Disc., T. CXIII, fol. </s>

<s>12). </s></p><p type="main">

<s>Poi il Viviani stesso pensò che si potevano con più facile brevità dimo­<lb></lb>strare le medesime cose in quest&#039;altra maniera: “ Se si farà come i due <lb></lb><figure id="id.020.01.2437.1.jpg" xlink:href="020/01/2437/1.jpg"></figure></s></p><p type="caption">

<s>Figura 23.<lb></lb>pesi eguali L, M (fig. </s>

<s>23), <lb></lb>al peso N, così la tan­<lb></lb>gente CF alla secante FG, <lb></lb>dico che il peso N arri­<lb></lb>verà a scendere fino in <lb></lb>F, e non passerà più ol­<lb></lb>tre a basso, perchè tutte <lb></lb>le tangenti maggiori di <lb></lb>CF, alle loro secanti, cioè <lb></lb>le scese del peso N, alle <lb></lb>salite de&#039;pesi L, M, hanno <lb></lb>minor proporzione che <lb></lb>la scesa CF alla salita <lb></lb>FC, e tutte le tangenti <lb></lb>minori di CF, a tutte le <lb></lb>loro secanti, hanno sem­<lb></lb>pre maggior proporzione <lb></lb>di detta CF alla FG. Poi­<lb></lb>chè, tirata la CG, e la DI parallela alla GF, sarà CF a FG come CC a DH. </s>

<s><lb></lb>Ma DB è minore di CH; dunque CD a BD ha maggior proporzione di CF a <lb></lb>FG. </s>

<s>Così si prova che CF a FG ha maggior proporzione di altra maggior <lb></lb>tangente CQ alla secante PQ ” (ivi). </s></p><p type="main">

<s>Lieto il Viviani di essersi incontrato in così bella, e nuova proprietà <lb></lb>geometrica, l&#039;applicava da una parte, per divisar giusti i gradi dell&#039;Igro­<lb></lb>metro, e dall&#039;altra per esplicar meglio e adornare il concetto galileiano. </s>

<s>Per <lb></lb>secondare una sua tale intenzione così scriveva in un foglio, in capo al quale <lb></lb>si legge: <emph type="italics"></emph>“ Per la proposizione del Galileo, a facce 286 nel trattato dei <lb></lb>proietti. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Se l&#039;AB, nella medesima passata figura, sarà divisa per mezzo in C, <lb></lb>e co&#039;centri A, B, ed intervalli AC, BC, siano descritti i quadranti, ai quali <lb></lb>sia tangente comune la CDF, e siano due qualsivogliano seganti AED, AGF, <lb></lb>dico che la CD alla DE ha maggior proporzione della CE alla FG. Poichè, <pb xlink:href="020/01/2438.jpg" pagenum="63"></pb>congiunta la CG, e tirata la DH parallela alla FG, che seghi la circonferenza <lb></lb>in I, sarà DE, che è la minima, minore di DI, e molto minore di DH, e <lb></lb>però CD a DE averà minor proporzione di CD a DH, cioè di CF ad FG, <lb></lb>come era da dimostrare. </s>

<s>” </s></p><p type="main">

<s>“ Che se i pesi L, M, insieme presi, al peso N averanno la medesima <lb></lb>proporzione di CF a FG, potrà il peso N calare da C sino ad F, perchè sem­<lb></lb>pre la sua scesa, avanti che ci arrivi, alla salita de&#039;pesi averà maggior pro­<lb></lb>porzione de&#039;due pesi L, M, al peso N. </s>

<s>E nota che ogni peso N, che sia <lb></lb>punto punto maggiore de&#039;due pesi L, M, averà il suo luogo nella tangente, <lb></lb>dove fermarsi ed equilibrarsi coi detti pesi, supposto però che le attaccature <lb></lb>de&#039;fili AL, BM siano tanto lunghe, che al calar del peso N possano sempre <lb></lb>salire i pesi L, M, perchè non si dà proporzione così grande tra il peso N, <lb></lb>benchè appena minor de&#039;due L, M, ed i pesi L, M, che maggiore non si <lb></lb>possa dare tra una tangente CF alla sua intercetta segante FG. </s>

<s>Ma ben è <lb></lb>vero che, subito che si dia il peso N uguale alli due insieme L, M, quello <lb></lb>non resterà di scendere per CN, finchè non averà fatto salire i pesi L, M <lb></lb>fino in A, B, e siano i fili lunghi pure quanto si voglia. </s>

<s>E questo perchè in <lb></lb>tal caso, tra la detta tangente e la porzione di segante, cioè tra la scesa del <lb></lb>peso D, e la totalità de&#039;pesi L, M, non si dà mai proporzione di egualità, <lb></lb>ma sempre di maggioranza. </s>

<s>” </s></p><p type="main">

<s>“ Che poi il peso N, equilibrando in F i due L, M, non possa scendere <lb></lb>oltre la tangente CF, così si prova nella seguente figura 24. Poichè dato per <lb></lb><figure id="id.020.01.2438.1.jpg" xlink:href="020/01/2438/1.jpg"></figure></s></p><p type="caption">

<s>Figura 24.<lb></lb>possibile che egli scenda ancora da F ad O, <lb></lb>col centro A, intervallo AF, fatto l&#039;arco FP, <lb></lb>si prova in adesso che la nuova scesa FO, <lb></lb>alla nuova salita PO ha sempre minor propor­<lb></lb>zione della tangente CF, alla porzione della <lb></lb>secante FG; cioè che i pesi L, M al peso N, <lb></lb>onde sarà sempre impossibile che il peso N <lb></lb>cali più a basso di F. Imperocchè, congiunta <lb></lb>la corda PF, e la QG prodotta sino alla se­<lb></lb>gante in R, sarà questa parallela alla PF, e <lb></lb>però il triangolo RFG sarà simile al triangolo <lb></lb>FOP, onde, come RF ad FG, così FO ad OP. </s>

<s><lb></lb>Ma RF ad FG ha minor proporzione, che CF <lb></lb>ad FG; cioè minor proporzione de&#039;pesi L, M <lb></lb>al peso N, che è quánto rimaneva a dimostrare ” (ivi, fol. </s>

<s>12, 13). </s></p><p type="main">

<s>Aveva appena cominciato il Viviani a gustare le gioie del veder con sì <lb></lb>belle geometriche invenzioni promosso il teorema di Galileo, che gli si apri­<lb></lb>rono da quelle stesse invenzioni gli occhi, per veder invece la profonda fossa <lb></lb>dell&#039;errore, in cui, come cieco ch&#039;è menato da un altro cieco, era misera­<lb></lb>mente caduto. </s>

<s>Supponiamo, diceva tenendo fisso lo sguardo sopra l&#039;ultima <lb></lb>disegnata figura, che io da C conduca equabilmente a mano il peso infino <lb></lb>a farlo scendere in O: non per questo il peso L salirà, per la ritrovata ra-<pb xlink:href="020/01/2439.jpg" pagenum="64"></pb>gione, verso A con moto equabile, ma con moto sempre più accelerato. </s>

<s>Or <lb></lb>come si può il momento di N, che si misura dal prodotto della mole per lo <lb></lb>spazio CO, comparar convenientemente col momento di L, che pur si misura <lb></lb>dal prodotto della mole per lo spazio OQ, passato nel medesimo tempo, se <lb></lb>il moto della salita dell&#039;uno è diverso dal moto della scesa dell&#039;altro? ... <gap></gap><lb></lb>quanto più ci pensava, e più si doleva che il suo Galileo l&#039;avesse così in­<lb></lb>gannato. </s>

<s>Attribuendo tutta la colpa di ciò al mal uso che delle velocità vir­<lb></lb>tuali aveva fatto il suo Maestro, volle tentare il Viviani se riusciva senza fal­<lb></lb>lacia a dimostrare le condizioni dell&#039;equilibrio nel funicolo teso, lasciando la <lb></lb>perigliosa via tenuta da Galileo, per mettersi a quell&#039;altra, che credevasi più <lb></lb>sicura, e ch&#039;era allora, allora stata aperta ai Matematici dall&#039;ingegno del Tor­<lb></lb>ricelli. </s>

<s>Sembra che, per rendersi que&#039;torricelliani principii più familiari, e <lb></lb>per volgerli a secondar meglio le sue intenzioni, s&#039;esercitasse così il Nostro <lb></lb>a confermare la verità dei due seguenti teoremi: </s></p><p type="main">

<s>“ Li pesi eguali A, B (fig. </s>

<s>25), appesi ad un filo ACDB, cavalcabile <lb></lb>sopra due girelle C, D, fermate sì, che la CD sia orizontale o inclinata, non <lb></lb><figure id="id.020.01.2439.1.jpg" xlink:href="020/01/2439/1.jpg"></figure></s></p><p type="caption">

<s>Figura 25.<lb></lb>si moveranno giammai dal sito, in che <lb></lb>vennero poste. </s>

<s>Poichè, se fosse possibile <lb></lb>che venissero nel sito EF, congiunta la <lb></lb>EF, sarebbe <emph type="italics"></emph>ob parallelas EA, BF,<emph.end type="italics"></emph.end> come <lb></lb>EA a BF, così AG a GB, e così EG a <lb></lb>GF. </s>

<s>Ma le AE, BF sono uguali, adunque <lb></lb>anco le AG, GB e le EG, GF saranno <lb></lb>uguali. </s>

<s>Ma ancora i pesi A, B sono uguali, <lb></lb>adunque il punto G è centro di gravità <lb></lb>de&#039;pesi, tanto nel sito A, B, che nel sito <lb></lb>E, F, e però tal centro comune, non acquistando niente verso il centro della <lb></lb><figure id="id.020.01.2439.2.jpg" xlink:href="020/01/2439/2.jpg"></figure></s></p><p type="caption">

<s>Figura 26.<lb></lb>Terra, anzi, non mutando luogo, i dati pesi <lb></lb>non si moveranno, ma si farà tra essi l&#039;equi­<lb></lb>librio o la quiete, in qualunque luogo verranno <lb></lb>lasciati. </s>

<s>” </s></p><p type="main">

<s>“ Ma se i pesi A, B (fig. </s>

<s>26) saranno di­<lb></lb>suguali, il peso maggiore A scenderà sempre, <lb></lb>finchè B non arriverà in D. </s>

<s>Perchè il centro <lb></lb>di gravità di essi gravi, quando venissero nel <lb></lb>sito E, F, tornerebbe in G, più vicino ad E <lb></lb>che ad F, ma più alto che H, centro de&#039;medesimi nel sito AB, il che sa­<lb></lb>rebbe un salire contro natura. </s>

<s>Ma bensì andranno verso il sito L, M, perchè <lb></lb>il centro comune I è sotto H, e sempre si troverà nella perpendicolare GHI, <lb></lb>discendendo da H verso I ” (ivi, fol. </s>

<s>21). </s></p><p type="main">

<s>Or venendo a fare il Viviani al funicolo galileiano l&#039;applicazion di que­<lb></lb>sti principii, ebbe a scoprir nel discorso del Sagredo un&#039;altra fallacia, per­<lb></lb>chè, nello scendere il peso di mezzo, e nel salire i laterali, il centro di gra­<lb></lb>vità non vien nulla acquistando verso il centro terrestre. </s>

<s>Avrebbe dovuto <pb xlink:href="020/01/2440.jpg" pagenum="65"></pb>perciò considerare che qui s&#039;opera dalla gravità, come nell&#039;esempio de&#039;pesi <lb></lb>uguali rappresentati dalla figura XXV, e gli sarebbe dovuta bastar questa <lb></lb>considerazione, per avvedersi che la radice dell&#039;errore consisteva nel suppor <lb></lb>che il peso di mezzo nel funicolo eserciti il suo momento totale per equili­<lb></lb>brar gli altri due, come s&#039;ei dipendesse da un punto stabile, e non dall&#039;an­<lb></lb>golo mobile delle due corde. </s>

<s>Persuaso in ogni modo che, per la debita appli­<lb></lb>cazion del principio torricelliano, si dovesse dar finalmente al problema la <lb></lb>desiderata risoluzione, vi s&#039;applicò con tutto il suo studio, e pentendosi di <lb></lb>aver perduto il tempo a promovere una fallacia del suo Maestro, prese la <lb></lb>penna in mano, per scrivere così <emph type="italics"></emph>Contro la dimostrazione del quarto dia­<lb></lb>logo delle due Nuove scienze:<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia il peso A (fig. </s>

<s>27) men che doppio del peso C, sicchè la metà del <lb></lb>peso A sia minore del peso C, e questo ad A abbia la proporzione della tan­<lb></lb><figure id="id.020.01.2440.1.jpg" xlink:href="020/01/2440/1.jpg"></figure></s></p><p type="caption">

<s>Figura 27.<lb></lb>gente AD alla secante DE, eccesso <lb></lb>della secante BD sopra il seno toto <lb></lb>BA, e preso CF uguale a DE si <lb></lb>giungano le AC, DF, segantisi in <lb></lb>K, e per K tirisi la ML, parallela <lb></lb>alle BC, AD, per cui dico che il <lb></lb>punto K è centro comune di gra­<lb></lb>vità, tanto della metà del peso in <lb></lb>A e del peso in C, quanto della <lb></lb>metà del medesimo A in D, e del <lb></lb>peso C in F. Perchè, come AD a <lb></lb>DE, ovvero a CF, così sta AK a <lb></lb>KC, e così DK a KF; ed AD a DE, <lb></lb>cioè a CF, sta per supposizione co­<lb></lb>me il peso C alla metà di A, e <lb></lb>come il peso F alla metà di D. Sic­<lb></lb>chè, quando i pesi erano in A, C, <lb></lb>il loro centro comune era in K, <lb></lb>dove pure egli è, quando i pesi si <lb></lb>trovano in D, F: onde, a scendere A <lb></lb>fino in D, e salir C fino in F, il centro comune loro non avrebbe acquistato <lb></lb>nulla verso il centro della terra; eppure il Galileo, per mezzo di quel suo <lb></lb>principio di considerare la scesa dell&#039;uno e la salita dell&#039;altro, conclude che <lb></lb>A scenderà in D, e C salirà in F. ” </s></p><p type="main">

<s>“ Ma qui, dico io, perchè seguir moto di questo composto di gravi, se <lb></lb>poi e&#039;si devon fermare dove il loro centro comune torna nel medesimo luogo <lb></lb>dov&#039;era prima? </s>

<s>Anzi io dimostro che prima che arrivare il peso A in D, <lb></lb>come per esempio A in G, e C in I, il centro comune, che è sempre nella <lb></lb>linea ML, si troverà sempre più basso che il punto K, com&#039;è in L; e quando <lb></lb>A è in Q, e C in P, il centro loro comune, che pure è nella ML, come in S, <lb></lb>con tutto che qui sia più alto di L, è sempre sotto K, perchè io ho provato <pb xlink:href="020/01/2441.jpg" pagenum="66"></pb>altrove che AG a GH, cioè a CI, ha maggior proporzione che AD a DE, e <lb></lb>che però, se la GI sega ML sotto K, per la medesima ragione la QP sega <lb></lb>ML sotto K. </s>

<s>Onde ne seguirebbe che se i pesi A, C potessero naturalmente <lb></lb>muoversi, e venire in D, F, come pretende il Galileo col suo principio, il lor <lb></lb>centro comune di gravità K sarebbe prima sceso per la MK, e poi tornato <lb></lb>a salire, e fermatosi nel sito più alto di quello, dove una volta ei si sia tro­<lb></lb>vato: il che par che repugni alla natura delle cose gravi. </s>

<s>” </s></p><p type="main">

<s>“ E però si esamini se si proceda con più sicurezza in questa specula­<lb></lb>zione, con quest&#039;altro principio meccanico, cioè che <emph type="italics"></emph>il composto di più gravi <lb></lb>si muoverà, sempre che il loro comune centro di gravità, nel loro moto, <lb></lb>acquisti vicinanza al centro comune delle cose gravi,<emph.end type="italics"></emph.end> perchè allora la metà <lb></lb>del peso A tirerà su, scendendo per AD, tutto il peso C, finchè amendue si <lb></lb>trovino in quel luogo, dove il centro comune loro, che sempre cammina per <lb></lb>la linea ML, si trovi nel punto più basso verso il centro della terra, e che <lb></lb>però non arriveranno mai nel sito DF, come conclude il Galileo con quel­<lb></lb>l&#039;altra maniera di considerare le scese e le salite, cioè le velocità della metà <lb></lb>del grave A e di tutto il grave C, ma bensì scenderà A e salirà C, finchè <lb></lb>il loro centro comune occupi il sito più basso sotto K, che è il centro di gra­<lb></lb>vità di quand&#039;erano in A ed in C, e di quand&#039;ei fossero in D e in F. ” </s></p><p type="main">

<s>“ Cercasi dunque qual sia il primo sito tra A e D, e quale tra C ed F, <lb></lb>come per esempio in G ed I, sicchè, giunta la diagonale GI, questa dia il <lb></lb>segamento nella MK, più infimo di K, che qualunque altra diagonale: cioè <lb></lb>trovare fin dove può scendere A e salir C, che il loro centro comune sem­<lb></lb>pre abbia sceso sotto K a segno, che se A scendesse più, e C salisse per­<lb></lb>pendicolarmente ancor più di prima, il loro centro comune cominciasse a <lb></lb>salire per LM, accostandosi al punto K. </s>

<s>Avvertasi che sempre ho inteso di <lb></lb>paragonare col peso C la metà dello A, perchè l&#039;altra metà s&#039;impiega con­<lb></lb>tro l&#039;altro peso uguale al C, pendente dall&#039;altra parte della corda, mentre <lb></lb>però A s&#039;intenda posto in mezzo della corda orizzontale...... ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. CIX, fol. </s>

<s>3). </s></p><p type="main">

<s>Non proseguì oltre il Viviani a ricercare la massima distanza da M, o <lb></lb>il minimo abbassamento sotto K del centro di gravità dei pesi, perchè inco­<lb></lb>minciò a dubitar se la nuova via presa era la diretta. </s>

<s>E benchè non fosse <lb></lb>difficile a lui, Autore del trattato <emph type="italics"></emph>De maximis et minimis,<emph.end type="italics"></emph.end> una tale ricerca, <lb></lb>non voleva nulladimeno, com&#039;aveva fatto per lo avanti in questo argomento, <lb></lb>perdere inutilmente il tempo e la fatica. </s>

<s>Scrisse perciò a Roma a Michelan­<lb></lb>giolo Ricci quella lettera del dì 21 Maggio 1675, pubblicata dal Nelli, nella <lb></lb>quale, esposte contro Galileo le difficoltà ch&#039;ei ci trovava, sì applicando alla <lb></lb>dimostrazione di lui il principio delle velocità virtuali, che quello dei centri <lb></lb>gravitativi; concludeva dicendo: “ In che consista l&#039;errore del mio discorso <lb></lb>io non penetro ancora, ma ogni poco di riflessione, che vi farà V. S. Illu­<lb></lb>strissima, sarà bastante a mostrarmelo ” (Saggio di storia letter, fiiorentina, <lb></lb>Lucca 1759, pag. </s>

<s>42). </s></p><p type="main">

<s>Il Ricci infatti rispondevagli nove giorni dopo, con sicura franchezza, <pb xlink:href="020/01/2442.jpg" pagenum="67"></pb>che l&#039;errore, riferendosi alla disegnata figura, consisteva nel considerare i <lb></lb>pesi D, F; Q, P; G, I come gravati in ambedue l&#039;estremità della bilancia <lb></lb>da forze perpendicolari, mentre in D, in Q e in G le forze del peso che di­<lb></lb>scende sono obliquamente dirette secondo le secanti BD, BQ, BG: voleva al­<lb></lb>trimenti dire che in D, in Q e in G il peso A non esercita il suo momento <lb></lb>totale, per fare equilibrio al peso C in F, in P, in I, e non correndo perciò <lb></lb>qui la regola del centro di gravità, come nella bilancia libera, è falso che <lb></lb>si trovino in R, in S e in L, lungo la medesima linea ML, quegli stessi centri <lb></lb>gravitativi: ond&#039;è che male applicato al caso torna l&#039;assunto del Torricelli. <lb></lb></s>

<s>“ Si compiaccia esaminare il mio pensiero, concludeva il Ricci, che forse lo <lb></lb>troverà sussistente e vero, e che sodisfa pienamente alle difficoltà proposte <lb></lb>da V. S. illustrissima ” (ivi, pag. </s>

<s>43). </s></p><p type="main">

<s>Quel perfetto giudizio non si era punto ingannato, e la verità rivelata <lb></lb>da lui poteva confermarsi considerando la salita del peso C, nel perpendicolo <lb></lb>BF, comparata con la scesa del peso D nel piano inclinato BD, a quel modo <lb></lb>che aveva insegnato a fare Galileo stesso nella dimostrazione, che del famoso <lb></lb>supposto dettava al Viviani. </s>

<s>Ma è da notare che presero giusto da cotesta <lb></lb>dimostrazione motivo di dubitar del principio delle velocità virtuali, il Nardi <lb></lb>e il Torricelli, ai quali s&#039;aggiunse l&#039;altra grande autorità del Cavalieri. </s>

<s>Que­<lb></lb>st&#039;ultimo, in una sua lettera, nella quale mirabilmente si compendiano le <lb></lb>controversie promosse poi dal Marchetti e dal Vanni intorno al modo di com­<lb></lb>putare i momenti di una sfera cadente lungo un piano inclinato; scriveva <lb></lb>così, dopo aver risposto alle difficoltà, che a lui faceva Gian Antonio Rocca, <lb></lb>come i due detti le facevano al Torricelli: </s></p><p type="main">

<s>“ S&#039;ella avesse comodità di fare l&#039;esperienza quanto peso ci voglia a <lb></lb>sostenere una palla in un piano inclinato 22°, 27′, che è il già considerato, <lb></lb>mi saria assai caro, per vedere pure appresso a poco quanto gravita in sul <lb></lb>piano detta palla. </s>

<s>La ragione del signor Galileo e delli altri, che trattano que­<lb></lb>sto teorema, credo sia perchè, salendo per esempio una sfera sopra un piano <lb></lb>acclive, collegata con un&#039;altra discendente perpendicolare all&#039;orizzonte, es­<lb></lb>sendo tanta la salita sopra l&#039;acclive, quanta la scesa per la detta perpendi­<lb></lb>colare, l&#039;altezza della salita, all&#039;altezza della scesa, è come la perpendicolare <lb></lb>alla inclinata. </s>

<s>Veda ora se li pare che questi alzamenti e abbassamenti per­<lb></lb>pendicolari siano sussistenti o no a determinare giustamente i loro momenti, <lb></lb>il che, come che appaia evidentissimo nella Libra, qui però non mi pare che <lb></lb>cammini con pari evidenza ” (Lettere d&#039;illustri del secolo XVII a G. A. Rocca, <lb></lb>Modena 1785, pag. </s>

<s>205, 6). </s></p><p type="main">

<s>Le medesime opinioni e i medesimi dubbi avendo intorno a ciò anche <lb></lb>il Viviani, e mancandogli in conseguenza questo efficacissimo modo di riscon­<lb></lb>trare il vero annunziatogli dal Ricci, si dette a consultar l&#039;esperienze, per <lb></lb>veder se la direzione obliqua delle forze che tirano alteri ne&#039;pesi equilibrati <lb></lb>il momento. </s>

<s>Fra certe <emph type="italics"></emph>Esperienze fatte, e riuscite,<emph.end type="italics"></emph.end> è descritta dal Viviani <lb></lb>stesso anche questa, che porta notato in fronte <emph type="italics"></emph>provata.<emph.end type="italics"></emph.end> “ Se il peso D ed E <lb></lb>(fig. </s>

<s>28) sono uguali, ed F ed E uguali, sopra le girelle A, B, C le corde CB, <pb xlink:href="020/01/2443.jpg" pagenum="68"></pb>AB saranno tirate con uguali forze, benchè CB sia più inclinata di AB, per­<lb></lb>chè... ” (MSS. Gal. </s>

<s>Disc., T. CIX, fol. </s>

<s>8). <lb></lb><figure id="id.020.01.2443.1.jpg" xlink:href="020/01/2443/1.jpg"></figure></s></p><p type="caption">

<s>Figura 28.</s></p><p type="main">

<s>Il perchè però manca: che se lo avesse <lb></lb>il Viviani trovato, non bisognava altro per <lb></lb>cavarlo di quell&#039;errore, nel quale tuttavia <lb></lb>si rimase, ingannato da varie vane appa­<lb></lb>renze. </s>

<s>Prima di tutto si osserva che para­<lb></lb>gonare l&#039;obliquità della forza CB, in questa <lb></lb>figura, con l&#039;obliquità della forza BD nella <lb></lb>figura precedente, suppone in D un punto <lb></lb>fisso, da rassomigliarsi alle pulegge C, A, <lb></lb>nel qual caso è manifesto che non potrebbe <lb></lb>sussistere l&#039;equilibrio, se non a patto che il <lb></lb>peso D sia uguale, e non minore di C, <lb></lb>come suppone il Viviani. </s></p><p type="main">

<s>Ma la fallacia nell&#039;esperienza delle funi, che cavalcando più o meno obli­<lb></lb>que sulle girelle equilibrano pesi uguali, era ben assai più sottile, perchè, a <lb></lb>veder rimanere il peso F, come il peso D, in equilibrio, si crederebbe che <lb></lb>F e D facciano sopra E la medesima forza, ma non si pensa che l&#039;equili­<lb></lb>brio può tuttavia rimanere, quando la forza che perde il peso F, nel tirare <lb></lb>il peso E in direzione obliqua, sia uguale alla diminuita resistenza, che lo <lb></lb>stesso peso E fa all&#039;esser tirato nella medesima direzione. </s>

<s>Il pensiero non <lb></lb>poteva esser suggerito da altro, che dall&#039;uso del parallelogrammo delle forze, <lb></lb>di cui mancava la Scienza meccanica di Galileo e del Viviani, per cui si ri­<lb></lb>mase così in difetto nella statica delle pulegge semplici, mentre si dia il caso <lb></lb>che la potenza non tiri in direzione parallela a quella della resistenza. </s>

<s>Fra <lb></lb>F ed E infatti permane l&#039;equilibrio, che tra D ed E era dianzi, perchè, ti­<lb></lb>rando la potenza F nella direzione obliqua BC, piuttosto che nella perpen­<lb></lb>dicolare BH, tanto perde della sua forza, quanto la linea BH perde, rispetto <lb></lb>a BC, della sua lunghezza, e il peso E dall&#039;altra parte tanto men resiste <lb></lb>all&#039;esser tirato per l&#039;obliqua BC, che per la perpendicolare BH, nella mede­<lb></lb>sima proporzione. </s></p><p type="main">

<s>Applicando queste considerazioni alla Macchina funicolare, rappresentata <lb></lb>nella figura XXVII, si vede bene che, tirando il peso D obliquamente per la <lb></lb>linea DB, piuttosto che perpendicolarmente per una linea parallela a BF, tanto <lb></lb>perde del suo momento, quanto la BF perde di lunghezza rispetto a BD: il <lb></lb>centro di gravità perciò non può essere in K, ma in un altro punto più vi­<lb></lb>cino ad F, come argutamente avvertiva il Ricci. </s>

<s>Il Viviani però non gli pre­<lb></lb>stò fede, ingannato dalle sue esperienze, non bene intese in sè, nè bene ap­<lb></lb>plicate, per cui, vinto dalle difficoltà, lasciò ai Matematici, che ne avrebbero <lb></lb>avuto notizia, l&#039;esame e il giudizio di quelle sue fallite speculazioni. </s>

<s>Vor­<lb></lb>remmo procedere addiritto a dire del resultato di quegli esami, e della forma <lb></lb>di quei giudizi, ma un incidente arresta il passo frettoloso della nostra Storia. </s></p><p type="main">

<s>Sparsasi per Firenze la voce che il Viviani aveva dimostrato aver le <pb xlink:href="020/01/2444.jpg" pagenum="69"></pb>tangenti alle secanti nel cerchio tanto maggior proporzione, quanto son di <lb></lb>lunghezza minori, al qual teorema, per le relazioni che si diceva avere con <lb></lb>le cose dimostrate da Galileo, si dava una grande importanza; Alessandro <lb></lb>Marchetti, che aveva sciolti i <emph type="italics"></emph>Problemata sex,<emph.end type="italics"></emph.end> proposti ai Matematici di Ger­<lb></lb>mania e d&#039;Italia da Cristoforo Sadlero, vi aggiunse, nel pubblicar quelle solu­<lb></lb>zioni, due teoremi geometrici, il secondo de&#039;quali era così formulato: “ Rectae <lb></lb>circulum tangentes eo maiorem rationem habent, ad rectarum secantium por­<lb></lb>tiones extra circulum, ab earumdem tangentium terminis diremptas, quo tan­<lb></lb>gentes ipsae minores sunt ” (Pisis 1675, pag. </s>

<s>45). </s></p><p type="main">

<s>Disegnata la figura, come noi la reppresentiamo nella nostra 29a, faceva <lb></lb>osservare il Marchetti ch&#039;essendo l&#039;angolo AGB, nel semicerchio, acuto, e <lb></lb><figure id="id.020.01.2444.1.jpg" xlink:href="020/01/2444/1.jpg"></figure></s></p><p type="caption">

<s>Figura 29.<lb></lb>perciò acuto essendo anche l&#039;angolo EIG, il lato EG del triangolo IEG deve <lb></lb>necessariamente esser minore del lato EI, il quale, essendo stato condotto <lb></lb>parallelo a CF, dà motivo all&#039;equazione BE/EI=BF/FH, d&#039;onde se ne conclude <lb></lb>che BE/EG deve esser maggiore di BF/FH, e con tanto più ragione maggiore di <lb></lb>BF/FC, come pure si conclude dall&#039;Autore, con più lungo però e avviluppato <lb></lb>discorso. </s></p><p type="main">

<s>Aveva inoltre sentito dire il Marchetti che il Viviani aveva mandato al <lb></lb>Ricci questo teorema, nel proporgli a risolvere una certa difficoltà natagli <lb></lb>intorno all&#039;ultima dimostrazione, posta da Galileo nel quarto dialogo delle <lb></lb>due Nuove scienze: ond&#039;è che, a prevenire anche in ciò, e a correre con <lb></lb>l&#039;emulo suo anche questo stadio della palestra, soggiungeva il Marchetti <lb></lb>stesso al dimostrato teorema delle secanti nel cerchio il seguente <emph type="italics"></emph>Monito,<emph.end type="italics"></emph.end><lb></lb>stampato in lettere che, appetto alle altre del testo, si potrebbero dir cubi­<lb></lb>tali: “ Scias velim, amicissime Lector geometra, hoc theoremate praemisso <lb></lb>tolli prorsus difficultatem, quae a rem saltem minus attente consideranti <lb></lb>apponi posset uni, ex alioquin admirandis ac propemodum divinis proposi­<lb></lb>tionibus celeberrimi ac nunquam satis laudati Galilei, ut ipsemet, si Deus <lb></lb>faxit, commodiore occasione planum faciam ” (ibid., pag. </s>

<s>48). </s></p><pb xlink:href="020/01/2445.jpg" pagenum="70"></pb><p type="main">

<s>Il Viviani che, leggendo queste parole, sentiva dare il titolo di divina a <lb></lb>una proposizione dovuta riconoscer per falsa; che sentiva dire il teorema <lb></lb>delle secanti e delle tangenti aver tolte le difficoltà, ch&#039;egli anzi avea pro­<lb></lb>vocate, non potè tenersi, scrivendo al conte Benedetto Porro, dal dirgli che <lb></lb>la dimostrazion del Marchetti procedeva con <emph type="italics"></emph>molto impaccio,<emph.end type="italics"></emph.end> e che più sem­<lb></lb>plice era la sua mandata al Ricci, e divulgatasi fra i Matematici qualche <lb></lb>mese prima della stampata nell&#039;appendice ai <emph type="italics"></emph>Sei problemi,<emph.end type="italics"></emph.end> attenente senza <lb></lb>dubbio a una proposizione di Galileo, ch&#039;era però fra tutte le altre la men <lb></lb>divina e ammiranda, e concludeva: “ io mi do a credere che il medesimo <lb></lb>signor Marchetti erri in Meccanica con troppa confidenza ” (Nelli, Saggi cit., <lb></lb>pag. </s>

<s>38). </s></p><p type="main">

<s>Che la detta proposizione proceda con molto impaccio è vero, e si po­<lb></lb>trebbe anche ammettere che l&#039;altra del Viviani abbia meno costruzione e <lb></lb>sia più breve, quando però nessuno scrupoloso chiedesse che gli fosse dimo­<lb></lb>strato quel che il Viviani stesso teneva per evidente, che cioè, di tutte le <lb></lb>linee condotte da un punto esterno alla circonferenza, la minima sia quella, <lb></lb>che prolungata passerebbe per il centro. </s>

<s>Il Marchetti però, che di tutto vo­<lb></lb>leva render ragione, ebbe a spender costruzioni e parole di più, per dimo­<lb></lb>strare che la EG nella sua figura è minore di EI, dalla minoranza degli an­<lb></lb>goli nel triangolo argomentando alla minoranza dei lati opposti. </s>

<s>Volendo esser <lb></lb>giusti insomma convien dire che, se quella dimostrazion del Marchetti cede <lb></lb>per una parte, supera dall&#039;altra la dimostrazion del Viviani, ond&#039;è che, la­<lb></lb>sciando intorno a ciò in pace i due gelosi rivali, vorremmo saper piuttosto <lb></lb>com&#039;intendesse esso Marchetti di spianar col suo teorema quelle difficoltà, <lb></lb>ch&#039;egli diceva incontrarsi da chi poco attentamente considera la divina e am­<lb></lb>miranda proposizione di Galileo. </s>

<s>E per rendere questi nostri desiderii anche <lb></lb>più modesti, vorremmo sapere in che modo s&#039;applicasse un teorema di Geo­<lb></lb>metria pura a un teorema di Meccanica nuova. </s></p><p type="main">

<s>Bisognerebbe, per rispondere prudentemente alla domanda, esser certi <lb></lb>se venne al Marchetti quella più comoda occasione, che, si <emph type="italics"></emph>Deus faxit,<emph.end type="italics"></emph.end> si <lb></lb>riprometteva: di che però confessiamo non avere altro documento da esibire <lb></lb>ai Lettori, che una nostra congettura, la notizia della quale non riuscirà in <lb></lb>ogni modo inutile in questa Storia. </s>

<s>Venne di questi ultimi giorni ad arric­<lb></lb>chire, nella R. </s>

<s>Biblioteca nazionale di Firenze, la preziosa raccolta dei Ma­<lb></lb>noscritti galileiani, un volume che, per aver ne&#039;suoi primi quaderni, trascritta <lb></lb>la lettera intorno alla <emph type="italics"></emph>Renitenza certissima dell&#039;acqua alla compressione,<emph.end type="italics"></emph.end><lb></lb>si credè che fosse del medesimo Autore, cioè di Raffaello Magiotti, anche il <lb></lb>rimanente. </s>

<s>Chi svolge però quelle pagine, con qualche attenzione, giudica <lb></lb>tutto altrimenti il libro, dentro cui si leggono di Galileo e de&#039;principali di­<lb></lb>scepoli di lui varii pensieri, non raccolti da libri stampati, ma da private <lb></lb>scritture, o dalle più approvate tradizioni orali. </s>

<s>Tale è l&#039;indole e il pregio <lb></lb>dell&#039;opera, che perciò avremo occasione di citare più volte, e non sapendo <lb></lb>per ora come designarne meglio il manoscritto, anche noi lo chiameremo il <lb></lb><emph type="italics"></emph>Magiotti.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2446.jpg" pagenum="71"></pb><p type="main">

<s>A tergo dunque del foglio 218 si vedono disegnate in margine le due <lb></lb>figure, che noi riproduciamo, lasciate alcune superfluità di linee, nella 30 e 31, <lb></lb>proposte aǵli studiosi lettori per illustrare il seguente teorema: “ Se alla <lb></lb>fune SBCR siano appli­<lb></lb><figure id="id.020.01.2446.1.jpg" xlink:href="020/01/2446/1.jpg"></figure></s></p><p type="caption">

<s>Figura 30.<lb></lb>cati i pesi S, R, e sia <lb></lb>messa la forza in D, e <lb></lb>ne&#039;luoghi B, C ruote; dico <lb></lb>che, quanto più essi pesi <lb></lb>si alzeranno, ci vorrà <lb></lb>sempre più forza ad al­<lb></lb>zargli, ed essi più facil­<lb></lb>mente si alzeranno, che <lb></lb>appesi alla fune ANR, <lb></lb>con una ruota in N, e la <lb></lb>forza in A. ” </s></p><p type="main">

<s>“ Dimostra il Galileo <lb></lb>che, se un capello, al qua­<lb></lb>le fosser sospesi ne&#039;luo­<lb></lb>ghi S. </s>

<s>R i globi lunare <lb></lb><figure id="id.020.01.2446.2.jpg" xlink:href="020/01/2446/2.jpg"></figure></s></p><p type="caption">

<s>Figura 31.<lb></lb>e terrestre, ed esso avesse resistenza per reggerli, la sua piccola <lb></lb>gravità gravitando su D, alzerebbe detti globi, ed esso capello <lb></lb>calerebbe in modo, che mai sarebbe parallelo all&#039;orizonte, sic­<lb></lb>chè ogni poco di forza nel luogo D alzerebbe qualche poco i detti <lb></lb>pesi. </s>

<s>” </s></p><p type="main">

<s>“ Se si tirerà una linea retta dal punto D al punto O, ed <lb></lb>essa prolungata segherà la linea BV di sotto al punto E (perchè, <lb></lb>se passasse per il punto L, non passerebbe per il punto O, poi­<lb></lb>chè se si pigli nella circonferenza di un cerchio due punti, la <lb></lb>linea retta che gli congiunge casca tutta dentro al cerchio) pro­<lb></lb>lunghisi e seghila in M, e da detto segamento tirisi una paral­<lb></lb>lela alla BL, quale segherà la linea VD. </s>

<s>Poichè la linea BV nel punto B <lb></lb>concorre, come sta la DL alla LO, così sta DI alla IM. F, perchè l&#039;angolo <lb></lb>esteriore BLI è maggiore che retto, ed a lui è uguale l&#039;angolo MIV, ed al <lb></lb>maggior angolo si oppone il maggior lato; sarà MV maggiore di MI. </s>

<s>E se <lb></lb>aggiungeremo ME, DL a LO avrà maggior proporzione che DV a VE, il che <lb></lb>si doveva dimostrare. </s>

<s>” </s></p><p type="main">

<s>Ora, domandiamo: raccolse il compilator del <emph type="italics"></emph>Magiotti<emph.end type="italics"></emph.end> in questa scrit­<lb></lb>tura un teorema del Marchetti? </s>

<s>La dimostrazione, come si vede, procede <lb></lb>proprio nel modo tenuto da lui, benchè con tanto minor impaccio, da emu­<lb></lb>lar non solo, ma da superare per ogni lato di pregio quell&#039;altra dimostra­<lb></lb>zione, di che tanto si pregiava il Viviani. </s>

<s>Potrebb&#039;essere il miglioramento <lb></lb>introdotto nel processo dimostrativo dallo stesso compilatore, ma chiunque <lb></lb>sia, che abbia dato opera ad applicar così le astratte linee geometriche alle <lb></lb>corde materiali tirate da pesi, convien dire che non poteva farlo con maggior <pb xlink:href="020/01/2447.jpg" pagenum="72"></pb>verità di questa, confermata da quell&#039;altra verità, certissima per le più ov­<lb></lb>vie esperienze, che cioè tanto ci vuol più di forza a tirare un carro, quanto <lb></lb>la strada è più erta, come, nell&#039;esempio del funicolo, è tirato in V il peso <lb></lb>più all&#039;erta nella direzione VB, che in L, nella direzione LB. </s>

<s>Avrebbe ciò <lb></lb>al Viviani, nel correre il periglioso mare più al largo, potuto servir di splen­<lb></lb>dido faro, senza il quale rimasto nelle tenebre ebbe a fare invece miseramente <lb></lb>naufragio. </s>

<s>Le reliquie del qual naufragio, insieme con la navicella di soccorso <lb></lb>ammannita dal Ricci, erano venute intanto alle mani di Giovan Batista Nelli, <lb></lb>il quale, apparecchiandosi nel 1759 a darne pubblica notizia, e non sapendo <lb></lb>per sè medesimo giudicare il caso da quel che si leggeva ne&#039;documenti ri­<lb></lb>masti, ne volle aver consiglio con un valoroso matematico amico suo, pro­<lb></lb>fessore nella università di Pisa. </s></p><p type="main">

<s>Tommaso Perelli, al giudizio del quale fu sottoposta la lettera del Vi­<lb></lb>viani, indirizzata il dì 21 Maggio 1675 a Michelangiolo Ricci, rispose che il <lb></lb>dubbio ivi proposto faceva molto onore all&#039;Autore, benchè si maravigliasse <lb></lb>che un Geometra così profondo non proseguisse la speculazione, ricercando <lb></lb>il massimo abbassamento del peso di mezzo nel funicolo, per costituirsi con <lb></lb>gli altri due estremi in equilibrio. </s>

<s>Questa maraviglia inopportuna incomincia <lb></lb>a ingerirci il sospetto che il professore di Pisa esaminasse la cosa con troppa <lb></lb>leggerezza, dicendo apertamente il Viviani, nell&#039;atto di congedarsi dal Ricci, <lb></lb>che <emph type="italics"></emph>non aveva già per difficile il ritrovare quel sito de&#039;gravi mossi, che dia <lb></lb>il massimo abbassamento del loro comun centro sotto il primo sito,<emph.end type="italics"></emph.end> ma <lb></lb>che non volle mettersi a cercare più oltre, <emph type="italics"></emph>perchè sarebbe stato superfluo, <lb></lb>quando fossc riconosciuto falso il suo raziocinio.<emph.end type="italics"></emph.end> (Nelli, Saggio cit., pag. </s>

<s>42). </s></p><p type="main">

<s>Ora, non doveva far altro il Perelli che esaminare se, della verità o fal­<lb></lb>sità di quel raziocinio, era giusto il giudizio del Ricci, e quand&#039;anche non <lb></lb>avesse ancora veduta la lettera di lui, far da buon matematico com&#039;aveva <lb></lb>fatto lo stesso Ricci, scoprir cioè che tutta la fallacia consisteva nello stabi­<lb></lb>lire il comun centro di gravità di uno de&#039;pesi estremi, e di quello pendente <lb></lb><figure id="id.020.01.2447.1.jpg" xlink:href="020/01/2447/1.jpg"></figure></s></p><p type="caption">

<s>Figura 32.<lb></lb>in mezzo alla fune, come se que­<lb></lb>sto gravasse con tutta la libertà <lb></lb>del suo momento. </s>

<s>Diversamente <lb></lb>però da questo, che il Perelli stesso <lb></lb>avrebbe dovuto fare, lo vediamo <lb></lb>confidente far col dubitoso Viviani <lb></lb>consorzio di errore, e, secondando <lb></lb>inconsideratamente il procedere di <lb></lb>lui, supporre <emph type="italics"></emph>due pesi qualsivo­<lb></lb>glia P, Q<emph.end type="italics"></emph.end> (fig. </s>

<s>32) <emph type="italics"></emph>legati all&#039;estre­<lb></lb>mità di una corda p A q, che passi <lb></lb>sempre per un dato punto A, i <lb></lb>quali pesi scorrano liberamente <lb></lb>per due rette date di posizione, <lb></lb>normali all&#039;orizonte ApL, CqK<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>132). </s></p><pb xlink:href="020/01/2448.jpg" pagenum="73"></pb><p type="main">

<s>Che debba il peso Q star sollevato, contro la gravità sua naturale, e <emph type="italics"></emph>libe­<lb></lb>ramente<emph.end type="italics"></emph.end> scorrere lungo la verticale CK, è supposizione che non la farebbe <lb></lb>nessun nomo da senno: eppure il Perelli ci sopredifica la sua dimostrazione, <lb></lb>dicendo che, congiunti i due pesi con la linea <emph type="italics"></emph>pq,<emph.end type="italics"></emph.end> il punto G, dov&#039;è questa <lb></lb>linea di congiunzione segata reciprocamente alle due gravità, è il loro cen­<lb></lb>tro comune. </s>

<s>Più incredibile poi è quel che soggiunge, concludendo la sna ri­<lb></lb>cerea per mezzo dell&#039;iperbola equilatera di Apollonio, che cioè il peso Q si <lb></lb>costituisce con P in equilibrio, quando il suo abbassamento è tale, da dar la <lb></lb>proporzione P:Q=A<emph type="italics"></emph>q<emph.end type="italics"></emph.end>:C<emph type="italics"></emph>q,<emph.end type="italics"></emph.end> quasi che per abbassarsi l&#039;un grave, e per <lb></lb>alzarsi l&#039;altro mutino proporzione i segmenti fatti, nella linea di congiun­<lb></lb>zione, dalla perpendicolare BG. </s>

<s>Che se sempre si serbano i detti segmenti <lb></lb>proporzionali, non si comprende come un matematico del valor del Perelli <lb></lb>potesse ammettere che due forze da equilibrarsi, le quali secondo lui riman­<lb></lb>gon le stesse, debbano una volta aver la proporzione di <emph type="italics"></emph>q<emph.end type="italics"></emph.end>G a G<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> ossia di <lb></lb><emph type="italics"></emph>q<emph.end type="italics"></emph.end>F ad AF, e un&#039;altra di A<emph type="italics"></emph>q<emph.end type="italics"></emph.end> a <emph type="italics"></emph>q<emph.end type="italics"></emph.end>C, <emph type="italics"></emph>come d&#039;altronde è noto per la dottrina <lb></lb>della composizion delle forze<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>123). </s></p><p type="main">

<s>Che se invece di accennarla così semplicemente, avesse posta quella dot­<lb></lb>trina a fondamento della sua dimostrazione, si sarebbe il Perelli incontrato <lb></lb>nel medesimo pensiero del Ricci, e la speculazion del Viviani, sgombrata cosi <lb></lb>dall&#039;errore, si sarebbe condotta a ritrovare il massimo abbassamento del peso <lb></lb>nel punto dell&#039;equilibrio, con un metodo, che avrebbe veramente fatto onore <lb></lb>ad ambedue i Matematici, perchè insomma era quello tenuto poi, nella sua <lb></lb>Meccanica analitica, dal celebre Lagrange. </s>

<s>L&#039;uso del parallelogrammo delle <lb></lb>forze infatti fu che decise appresso gli Stranieri la controversia insorta in <lb></lb>Italia, benchè sia cosa notabilissima che il Borelli, a cui parve fallace quel­<lb></lb>l&#039;uso, riuscisse, come vedremo in altro proposito, alle medesime conclu­<lb></lb>sioni. </s></p><p type="main">

<s>Possiamo di cotesti stranieri citar primo Tommaso Simpson, il quale, <lb></lb>nella sezione XVIII del suo libro, intitolata <emph type="italics"></emph>The application of Algebra to<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2448.1.jpg" xlink:href="020/01/2448/1.jpg"></figure></s></p><p type="caption">

<s>Figura 33.<lb></lb><emph type="italics"></emph>the solution of geometrical <lb></lb>problems,<emph.end type="italics"></emph.end> proponeva così il <lb></lb>XXXVIII di quegli stessi <lb></lb>problemi: “ Let A and B <lb></lb>(fig. </s>

<s>33) be two equal wei­<lb></lb>ghts, made fast to the ends <lb></lb>of a thread, or perfectly fle­<lb></lb>xible line <emph type="italics"></emph>p<emph.end type="italics"></emph.end> P <emph type="italics"></emph>n<emph.end type="italics"></emph.end> Q <emph type="italics"></emph>q,<emph.end type="italics"></emph.end> sup­<lb></lb>ported by two pins, or tacks <lb></lb>P, Q in the same horizontal <lb></lb>plane; over which pins the <lb></lb>line can freely slide either <lb></lb>way; and let C be another <lb></lb>weight, fastened to the thread, in te middle, between P and Q: now the <lb></lb>question is to find the position of the weight C, or it&#039;s distance below the <pb xlink:href="020/01/2449.jpg" pagenum="74"></pb>horizontal line PQ, to retain the other two weights A and B in equilibrio ” <lb></lb>(A treatise of algebre, London 1767, pag. </s>

<s>310). </s></p><p type="main">

<s>La soluzion del problema, che aveva dato a Galileo e al Viviani tanta <lb></lb>faccenda, da non valer nonostante a salvarli dall&#039;errore, mediante l&#039;uso del <lb></lb>parallelogrammo delle forze e l&#039;analisi algebrica occorre al Simpson spedi­<lb></lb>tamente sicura. </s>

<s>Chiamata <emph type="italics"></emph>x<emph.end type="italics"></emph.end> infatti la quantità incognita dell&#039;abbassamento <lb></lb>del peso C da R, punto di mezzo della corda PQ, in <emph type="italics"></emph>n,<emph.end type="italics"></emph.end> dove si suppone che <lb></lb>stabiliscasi in equilibrio, e fatta PR=<emph type="italics"></emph>a,<emph.end type="italics"></emph.end> l&#039;ipotenusa P<emph type="italics"></emph>n<emph.end type="italics"></emph.end> sarà uguale alla <lb></lb>√<emph type="italics"></emph>(a2+x2)<emph.end type="italics"></emph.end>. </s>

<s>Or se essa P<emph type="italics"></emph>n<emph.end type="italics"></emph.end> rappresenta la forza totale del peso A, la qual <lb></lb>forza si decomponga nelle due PR, R<emph type="italics"></emph>n,<emph.end type="italics"></emph.end> la metà del peso C non dee resistere <lb></lb>che a questa sola, essendo rintuzzata l&#039;altra dalla fermezza del punto P. </s>

<s>Sarà <lb></lb>dunque A:C/2=P<emph type="italics"></emph>n<emph.end type="italics"></emph.end>:R<emph type="italics"></emph>n<emph.end type="italics"></emph.end>=√<emph type="italics"></emph>(a2+x2)<emph.end type="italics"></emph.end>:<emph type="italics"></emph>x,<emph.end type="italics"></emph.end> ossia 2A<emph type="italics"></emph>x<emph.end type="italics"></emph.end>=C.√<emph type="italics"></emph>(a2+x2)<emph.end type="italics"></emph.end>: <lb></lb>equazione che risoluta dà <emph type="italics"></emph>x=a<emph.end type="italics"></emph.end>C/√(4A2—C2). Galileo poneva invece la rela­<lb></lb>zione A:C/2=EF:LF, nella nostra XXI figura qui poco addietro, ingan­<lb></lb>nato dal creder che i moti per la tangente e per la secante, nel medesimo <lb></lb>tempo, fossero equabili, e che il peso di mezzo equilibrasse i due estremi <lb></lb>col suo momento totale. </s>

<s>Il Viviani scoprì il primo inganno, ma, benchè ne <lb></lb>fosse avvertito dal Ricci, non riuscì a scoprire il secondo, per cui fa gran <lb></lb>maraviglia che il Frisl, accennando, in una nota all&#039;<emph type="italics"></emph>Elogio del Galileo,<emph.end type="italics"></emph.end> al <lb></lb>problema della corda tesa in fine al quarto dialogo delle due Scienze nuove, <lb></lb>scrivesse che <emph type="italics"></emph>non sussiste il dubbio cavato dall&#039;inequalità del moto de&#039;due <lb></lb>pesi<emph.end type="italics"></emph.end> (Livorno 1775, pag. </s>

<s>83), dando così intorno al fatto, che ci ha traviato <lb></lb>forse per troppo lungo cammino, giudizio non men leggero di quello dato <lb></lb>già dal Perelli. </s></p><p type="main">

<s>Ma non vogliamo, per quanto lunga, terminar la presente digressione, <lb></lb>senza osservar che Paolo Casati, informato dal suo confratello Giuseppe Fer­<lb></lb>roni dei più notabili fatti, che accadevano o erano accaduti intorno alla vita <lb></lb>scientifica del Viviani; prese parte nella questione dell&#039;equilibrio dei pesi at­<lb></lb>taccati all&#039;estremità e nel mezzo di una fune. </s>

<s>Egli che credè vera la regola <lb></lb>del parallelogrammo, e la rese contro i sofismi sicura, come si vedrà meglio <lb></lb>a suo luogo, avrebbe potuto, prima del Simpson, rettamente risolvere il pro­<lb></lb>blema, e nonostante sembra rimanesse così sedotto dagli esempi del Viviani, <lb></lb>che pensò non potersi per altra via giungere alla desiderata soluzione, che <lb></lb>comparando la tardità dei pesi estremi che salgono con la velocità del peso <lb></lb>di mezzo che scende. </s>

<s>“ Hanc vero, poi soggiunge, unius tarditatem cum al­<lb></lb>terius velocitate comparari non posse, nisi ex longitudine spatiorum, quae <lb></lb>utrumque eodem temporis intervallo percurreret. </s>

<s>Ex quo manifesta consecu­<lb></lb>tione conficitur satis esse si spatiorum inaequalitas aut aequalitas ostendatur, <lb></lb>ut praeponderatio aut aequilibritas innotescat. </s>

<s>Ac propterea satis est secan­<lb></lb>tium excessus cum tangente comparare: haec enim ponderis intermedii, illi <lb></lb>ponderum extremorum motum definiunt ” (Mechanic. </s>

<s>libri, Lugduni 1684, <pb xlink:href="020/01/2450.jpg" pagenum="75"></pb>pag. </s>

<s>349). A far la qual geometrica comparazione aveva nel cap. </s>

<s>precedente <lb></lb>ordinate X proposizioni, la IV delle quali, che è il fondamento a tutto que­<lb></lb>sto lemmatico apparecchio, si riscontra con quella, che il Marchetti ripeteva <lb></lb>pubblicamente, dop&#039;aver saputo ch&#039;era stata dimostrata in privato dal Vi­<lb></lb>viani: “ Differentia inter tangentes duorum quorumlibet angulorum maior <lb></lb>est quam differentia inter eorum secantes ” (ibid., pag. </s>

<s>340). </s></p><p type="main">

<s>Riducendoci ora dunque in via, e rammemorando ai nostri Lettori che, <lb></lb>fatto accorto dalle critiche del Biancano, ritrovò il Viviani da correggere, spe­<lb></lb>cialmente nel secondo e nel quarto dialogo di Galileo, le tante altre cose, da <lb></lb>noi notate nell&#039;ottavo e nel nono capitolo del Tomo precedente; concludiamo <lb></lb>il nostro discorso intorno all&#039;opera data dallo zelante Discepolo per restituire <lb></lb>alla sua verità la nuova Scienza del moto, e per provvedere alla gloria del <lb></lb>venerato Maestro. </s>

<s>A questa però, che fu l&#039;ultima in tal soggetto, eran pre­<lb></lb>cedute altre fatiche, intraprese con intenzione alquanto diversa, le quali giova <lb></lb>a noi riepilogar qui, per la final conclusione del nostro argomento. </s></p><p type="main">

<s>Ne&#039;suoi primi principii, lo studio di migliorare e di ampliare i dialo­<lb></lb>ghi delle due Scienze nuove non si ridusse, per parte del Viviani, che a pren­<lb></lb>der nota delle cose dettategli da Galileo, suggerendo nonostante qua e là <lb></lb>qualche pensiero di suo, che il buon Vecchio approvava, e permetteva s&#039;in­<lb></lb>serisse ne&#039;Dialoghi alla prima occasione di una ristampa. </s>

<s>Anche morto il <lb></lb>Maestro, l&#039;amorevole Discepolo, ch&#039;era penetrato oramai nelle intenzioni di <lb></lb>lui, proseguì quel primo importantissimo studio, frutto del quale si può cre­<lb></lb>dere che fossero le cinque proposizioni intorno al momento totale, decompo­<lb></lb>sto nel descensivo e nel gravitativo di una sfera cadente lungo un piano in­<lb></lb>clinato; i teoremi relativi ai pendoli di varia lunghezza, e parecchie altre cose, <lb></lb>che sono state qua e là notate da noi nella prima parte di questa Storia. </s></p><p type="main">

<s>La qualità e la natura di così fatte speculazioni, esplicitamente uscite <lb></lb>dalla bocca e approvate dallo stesso Autore dei Dialoghi nuovi, o implicita­<lb></lb>mente da lui consentite, non disdiceva che s&#039;inserissero postume nella prima <lb></lb>nuova edizione, che se ne farebbe, e lo studio del Viviani fin qui procedeva <lb></lb>giusto con questa intenzione. </s>

<s>Ma, quando si venne a notar gli errori, e le <lb></lb>correzioni si trovarono superar di mole e d&#039;importanza le aggiunte, da passar <lb></lb>per inverosimile o turpe l&#039;introdurre il medesimo personaggio in scena a dir <lb></lb>poi in diverso modo, e spesso a contradire quel che, con tanta sicurezza e <lb></lb>solennità, aveva affermato prima; allora il Viviani ebbe a mutar pensiero, e <lb></lb>lasciando star le cose, come l&#039;Elzevirio l&#039;aveva stampate, o facendo nella <lb></lb>nuova edizione sola aggiunta delle cose volute e consentite da Galileo, il ri­<lb></lb>manente, che riguardava le proposizioni non vere, e le dimostrazioni sba­<lb></lb>gliate, o che promoveva dottrine, al di là di quel che avrebbe potuto pen­<lb></lb>sar l&#039;Autore, raccogliere e stampare a nome proprio in un volume a parte. </s>

<s><lb></lb>Manifestava da sè medesimo il Viviani a un amico queste sue intenzioni, con <lb></lb>parole, da noi trascritte anche altrove (T. I, pag. </s>

<s>183) dicendo che <emph type="italics"></emph>delle sue <lb></lb>fatiche di Matematica, fatte dal 1639 al 1644, ei pensava di scegliere e <lb></lb>di pubblicar quelle, che consistevano nell&#039;illustrazione e promozione delle<emph.end type="italics"></emph.end><pb xlink:href="020/01/2451.jpg" pagenum="76"></pb><emph type="italics"></emph>opere di Galileo, suo maestro, da accoppiarsi con la descrizione della <lb></lb>sua rita.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Secondo questo proposito pochissimo cooperò il Viviani al perfeziona­<lb></lb>mento de&#039;dialoghi, quando prima occorse di ripubblicarli in Bologna, lascian­<lb></lb>done la cura a chi egli doveva sapere esser men abile di tutti gli altri, a <lb></lb>Carlo Rinaldini. </s>

<s>Nè senza dubbio s&#039;intenderebbe come le promesse giurate <lb></lb>al venerato Maestro si lasciassero sodisfare all&#039;editor bolognese in così inde­<lb></lb>bito modo, quando non avesse il Viviani avuto il pensiero d&#039;illustrarne in un <lb></lb>libro a parte o di promoverne le dottrine. </s>

<s>Com&#039;egli attendesse alacremente <lb></lb>all&#039;opera, per dedicarla a Luigi XIV, e per erigere in mezzo all&#039;aula acca­<lb></lb>demica di Parigi un monumento di gloria alla Scienza italiana, e come fosse, <lb></lb>per le rivalità del Marehetti, distolto dal mandare il generoso proposito ad <lb></lb>effetto; è stato altrove da noi stessi narrato: cosicchè, delle tante sollecitu­<lb></lb>dini, e dei tanto amorosi studii dati dall&#039;Autore e dal suo allievo, per mi­<lb></lb>gliorare i dialoghi delle due Scienze nuove (da alcune in fuori delle meno <lb></lb>importanti postille a una copia dell&#039;edizione di Leida, inserite in carattere <lb></lb>corsivo dall&#039;Albèri) ha ora il pubblico, dopo più di due secoli e mezzo, in <lb></lb>queste nostre pagine la prima notizia. </s></p><pb xlink:href="020/01/2452.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del quinto dialogo aggiunto alle due Scienze nuove <lb></lb>ossia <lb></lb>Della Scienza delle proporzioni<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Di ciò che a riformare il quinto libro di Euclide scrisse Giovan Batista Benedetti, e pensò Antonio <lb></lb>Nardi. </s>

<s>— II. </s>

<s>Come Gian Antonio Rocca porgesse occasione al Cavalieri di restaurare il princi­<lb></lb>plo alla Scienza delle proporzioni, che poi Galileo fece mettere in dialogo. </s>

<s>— III. </s>

<s>Del disteso <lb></lb>fatto dal Torricelli del quinto dialogo galileiano aggiunto alle due Scienze nuove. </s>

<s>— IV. </s>

<s>Del <lb></lb>trattato torricelliano <emph type="italics"></emph>De proportionibus,<emph.end type="italics"></emph.end> inedito, e della Scienza universale delle proporzioni <lb></lb>spiegate da V. Viviani. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La domanda, che sovverrà naturalmente a chiunque legge l&#039;intitolazione <lb></lb>del presente capitolo, com&#039;entri cioè un argomento di Geometria pura a far <lb></lb>parte della storia della Meccanica; è quella medesima, che si saranno dovuti <lb></lb>fare coloro, i quali ebbero prima a leggere nel libro del Viviani, dove si tratta <lb></lb>della <emph type="italics"></emph>Scienza universale delle proporzioni.<emph.end type="italics"></emph.end> “ Principio della quinta Giornata <lb></lb>del Galileo, da aggiungersi alle altre quattro dei Discorsi e dimostrazioni ma­<lb></lb>tematiche intorno alle due nuove Scienze, appartenenti alla Meccanica e ai <lb></lb>movimenti locali ” (Firenze 1674, pag. </s>

<s>61). Nè la risposta era difficile a darsi, <lb></lb>anche senz&#039;altre dichiarazioni, ripensando che del moto non si può avere <lb></lb>scienza assoluta per noi, che ignoriamo le cause, dalle quali è prodotto: ond&#039;è <lb></lb>che tutto quel che possiamo sapere di lui si riduce a compararne insieme gli <lb></lb>effetti. </s>

<s>E perchè tali effetti ci si rivelan principalmente dal mutar luogo, che <lb></lb>fanno i corpi, secondo certe direzioni, dalla proporzione degli spazi passati <lb></lb>nei medesimi tempi ne argomentiamo la maggiore o minore quantità degli <pb xlink:href="020/01/2453.jpg" pagenum="78"></pb>impulsi. </s>

<s>La nuova scienza perciò del Galileo non si sarebbe dovuta intitolare <lb></lb><emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> ma <emph type="italics"></emph>De proportione motus,<emph.end type="italics"></emph.end> come, con filosofica proprietà, la inti­<lb></lb>tolava Giovan Marco: tutti i loro teoremi infatti non si conducono alla con­<lb></lb>clusione per altro matematico argomento, che per quello delle linee e delle <lb></lb>quantità proporzionali. </s></p><p type="main">

<s>Riconosciutosi dunque che la verità o la falsità di quelle meccaniche con­<lb></lb>clusioni dipende in tutto dalla savia applicazione, e dal retto uso delle pro­<lb></lb>prietà geometriche, insegnate nel suo quinto libro da Euclide, era naturale <lb></lb>che, pur non dubitando della verità delle cose annunziate da lui, restasse <lb></lb>nei nuovi Matematici qualche cosa da desiderare intorno al modo di condurre <lb></lb>le dimostrazioni, e all&#039;ordine, secondo il quale si sarebbero dovute nel libro <lb></lb>altrimenti disporre le parti. </s>

<s>Dir quali si fossero cotesti desiderii, e ciò che <lb></lb>s&#039;operasse per sodisfarli, è tanta parte della storia della Meccanica, da non <lb></lb>si dover trascurare da noi. </s></p><p type="main">

<s>È oramai noto che uno dei primi e più autorevoli che, nel rinascimento <lb></lb>della Scienza, dimostrassero alcune delle principali proprietà del moto, di cui <lb></lb>Aristotile o non aveva insegnate le proporzioni, o l&#039;avea date false, fu Giovan <lb></lb>Batisia Benedetti, il quale fu perciò anche il primo che, in grazia della Mec­<lb></lb>canica, attendesse a esaminar sottilmente il quinto libro di Euclide. <emph type="italics"></emph>In quin­<lb></lb>tum Euclidis librum<emph.end type="italics"></emph.end> infatti è il titolo di una, forse delle più brevi, ma non <lb></lb>delle meno importanti scritture raccolte dal Matematico veneziano nel suo <lb></lb>libro <emph type="italics"></emph>Delle speculazioni.<emph.end type="italics"></emph.end> Premette a cotesta scrittura l&#039;Autore una prefazion­<lb></lb>cella, nella quale egli dice che, sebben verissime siano tutte le cose ivi in­<lb></lb>segnate dall&#039;antico Maestro della Geometria, non possono molti nonostante <lb></lb>non trovar difficilissime le dimostrazioni, specialmente per l&#039;astrusità della <lb></lb>quinta e della sesta definizione premesse al quinto Libro, dalle quali dipende <lb></lb>l&#039;intelligenza della massima parte dei teoremi. </s>

<s>Non fa perciò maraviglia se <lb></lb>tutti coloro, non eccettuato Galileo, i quali attesero poi alla riforma eucli­<lb></lb>diana, si trattennero principalmente intorno alle due dette definizioni, eser­<lb></lb>citandovisi però in vario modo e coll&#039;esaltarle alla dignità di teoremi, e col <lb></lb>sostituire a loro altre note meglio atte a definir la natura delle quantità pro­<lb></lb>porzionali. </s>

<s>Piacque al Benedetti di tenere altra via, non contento a riformare <lb></lb>il libro in radice, ma nelle sue varie parti, dimostrando come molte delle <lb></lb>proposizioni di Euclide si riducono all&#039;evidenza di semplici postulati. </s>

<s>“ Quan­<lb></lb>doquidem iis nostris postulatis admissis, sequentia theoremata perfacillima <lb></lb>reddentur ” (Speculat, lib., Venetiis 1599, pag. </s>

<s>198). </s></p><p type="main">

<s>Per aver tenuta questa via più larga, e assai diversa da quella de&#039;suoi <lb></lb>successori, fu il Benedetti, come vedremo, censurato da un giudice argutò: <lb></lb>nessun però ha potuto negare che i XII postulati di lui non dimostrino come <lb></lb>Euclide avesse, per più che altrettante dimostrazioni, inutilmente affaticato <lb></lb>sè, e abusato della pazienza de&#039;suoi studiosi. </s>

<s>La XXIIa, per esempio, è pro­<lb></lb>posta così, secondo la versione del Commandino: “ Se siano quante gran­<lb></lb>dezze si vogliano, e siano altre grandezze, di numero uguali a quelle, che si <lb></lb>piglino a due a due nella medesima proporzione; saranno ancora per la pro-<pb xlink:href="020/01/2454.jpg" pagenum="79"></pb>porzione uguale, nella medesima proporzione ” (Urbino 1575 a tergo del <lb></lb>fol. </s>

<s>73). E seguita dopo ciò la dimostrazione, non bastando la quale v&#039;ag­<lb></lb>giunge il traduttore anche il suo proprio commento, mentre è tutto, dice il <lb></lb>Benedetti, evidentissimo per sè nell&#039;assioma: “ Quod tota, composita ex ae­<lb></lb>quali numero partium aequalium, sunt invicem aequalia ” (Specul. </s>

<s>lib. </s>

<s>cit., <lb></lb>pag. </s>

<s>198). Or chi non riconosce, soggiunge lo stesso Benedetti, in queste pa­<lb></lb>role <emph type="italics"></emph>Le grandezze uguali alla medesima hanno la medesima proporzione, <lb></lb>e la medesima alle eguali,<emph.end type="italics"></emph.end> le note distintissime dell&#039;evidenza, senz&#039;altro bi­<lb></lb>sogno di dimostrazione, come fa Euclide nel suo VII teorema? </s></p><p type="main">

<s>L&#039;VIIIa è dal traduttore proposta in questa forma: “ Delle grandezze <lb></lb>disuguali la maggiore alla medesima ha maggior proporzione che la minore: <lb></lb>e la medesima alla minore ha maggior proporzione che alla maggiore ” (Elem. </s>

<s><lb></lb>Eucl. </s>

<s>cit., fol. </s>

<s>68). Anche questo teorema si vuol dal Benedetti ridurre al­<lb></lb>l&#039;evidenza del seguente postulato: “ Quoties plures erunt termini, quorum <lb></lb>unus fuerit maior altero, si comparentur alicui tertio eiusdem generis, pro­<lb></lb>portio maioris ad tertium illum maior erit ea, quae est minoris ad praedictum <lb></lb>tertium: et proportio illius tertii, ad maiorem, minor erit ea, quae eiusdem <lb></lb>tertii ad minorem terminum comparati ” (Specul. </s>

<s>lib. </s>

<s>cit., pag. </s>

<s>199). Potrebbe <lb></lb>però ad alcuno sembrare altrimenti, e dire che quella VIIIa euclidea è biso­<lb></lb>gnosa, o almeno suscettibile di dimostrazione. </s>

<s>Se siano infatti proposte le due <lb></lb>ragioni A/C, B/C, nelle quali A sia maggiore di B, dell&#039;esser la prima di esse <lb></lb>ragioni maggiore della seconda si può dare dimostrazione, e dire il perchè, <lb></lb>col farsi osservare che, essendo la medesima quantità divisa in egual numero <lb></lb>di parti, di queste in quella prima ragione se ne son prese di più, che nella <lb></lb>seconda. </s>

<s>Date similmente le C/A, C/B, e rimanendo il supposto di A maggiore <lb></lb>di B, si può dimostrar che la prima ragione è minore della seconda, perchè, <lb></lb>in quella, l&#039;unità è stata divisa in maggior numero di parti che in questa, <lb></lb>e di tali parti s&#039;è preso qua e là un numero uguale. </s>

<s>Risponderebbe però il <lb></lb>Benedetti all&#039;istanza che non contengono questi discorsi una vera e propria <lb></lb>dimostrazione, e non fann&#039;altro se non che dichiarare come quelle due pro­<lb></lb>poste verità si riducono a un principio noto per sè, senza altro mezzo. </s>

<s>“ Cum <lb></lb>enim hae propositiones sint ita conspicuae ipsi intellectui, ut absque dubio <lb></lb>inter obiecta ipsius intellectus connumerari possint, nullus sanae mentis eas <lb></lb>negabit ” (Specul. </s>

<s>lib. </s>

<s>cit., pag. </s>

<s>200). </s></p><p type="main">

<s>Premessi i dodici postulati, passa il riformatore di Euclide a esaminare <lb></lb>a uno a uno i teoremi del quinto libro, e una parte gli riduce ad assiomi, <lb></lb>come s&#039;è veduto di sopra in alcuni esempi, una parte gli approva come ben <lb></lb>condotti, e rimanda al testo, perchè possano da sè consultarli gli studiosi: <lb></lb>di parecchi altri poi, per restituirgli a miglior ordine logico, e a maggior <lb></lb>chiarezza, suggerisce nuove dimostrazioni. </s></p><p type="main">

<s>Chi ripensa a quei tempi, ne&#039;quali gl&#039;ingegni, viziati dagli istituti ari­<lb></lb>stotelici, di tutto volevano dare dimostrazione, perchè la scienza apparisse, <pb xlink:href="020/01/2455.jpg" pagenum="80"></pb>come il Filosofo voleva, creata dalla mente dell&#039;uomo; comprenderà l&#039;utilità <lb></lb>e l&#039;efficacia di queste speculazioni del Benedetti, agl&#039;insegnamenti del quale <lb></lb>educatosi Galileo sentenziava: “ che la più ammirabile e più da stimarsi con­<lb></lb>dizione delle scienze dimostrative è lo scaturire e pullulare da principii no­<lb></lb>tissimi ” (Alb. </s>

<s>XIII, 90). Avrebbero nonostante desiderato alcuni che, met­<lb></lb>tendosi il grande Matematico veneziano a riformare il quinto libro di Euclide, <lb></lb>avesse riconosciuto che il vizio lo tiravano la maggior parte delle proposi­<lb></lb>zioni dalla definizione quinta, come da maleficiata radice, senza risanar la <lb></lb>quale reputavano che non si potesse condur l&#039;opera alla desiderata perfezione. </s></p><p type="main">

<s>Uno di cotesti censori del Benedetti era quell&#039;Antonio Nardi, le mate­<lb></lb>matiche speculazioni del quale, tanto ammirate dal Torricelli e dal Cavalieri, <lb></lb>son rimaste per la Scienza italiana sventuratamente tesori nascosti. </s>

<s>Il Nardi <lb></lb>dunque, ingegno veramente geometrico, aveva dovuto qua e là notare alcuni <lb></lb>difetti nello studiar l&#039;unico libro, che s&#039;avesse allora da mettere innanzi a <lb></lb>chi voleva imparare i primi elementi della Geometria, e di quelle note di <lb></lb>lui s&#039;è potuto aver notizia, perchè inserite, fra le <emph type="italics"></emph>Varie osservazioni geo­<lb></lb>metriche,<emph.end type="italics"></emph.end> nella veduta ottava della sesta <emph type="italics"></emph>Scena.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nel primo degli Elementì euclidiani, ivi si legge, pongonsi imperita­<lb></lb>mente tra le domande pratiche due comuni notizie speculative, il che è er­<lb></lb>rore. </s>

<s>Anche nel VI libro trovasi, sotto il numero V, una definizione, quale è <lb></lb>dimostrabile, e devesi così apportare: <emph type="italics"></emph>La ragione di due grandezze resul­<lb></lb>tar dicesi di tante ragioni, di quante tra quelle grandezze ne stanno.<emph.end type="italics"></emph.end> Tal <lb></lb>definizione poi risponde alla decima del Vo, ove tal definizione non sta ben <lb></lb>posta, ma va nel VI<gap></gap>. </s>

<s>Servesi anche Euclide alcune volte del nome di <emph type="italics"></emph>pira­<lb></lb>mide,<emph.end type="italics"></emph.end> in cambio di quello di <emph type="italics"></emph>tetraedo,<emph.end type="italics"></emph.end> il che par cosa licenziosa in uno <emph type="italics"></emph>Ele­<lb></lb>mentario. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Se riceviamo doversi dir parte una grandezza di grandezza omogenea, <lb></lb>riceveremo anche che, se la prima della seconda, o questa di quella, sia sol <lb></lb>parte, che la terza della quarta o questa di quella; sarà la prima alla se­<lb></lb>conda, nella disegual proporzione, come la terza alla quarta; ma nella eguale <lb></lb>bisogna che la prima s&#039;agguagli alla seconda, e la terza alla quarta. </s>

<s>Incam­<lb></lb>minandoci per tale strada, potremo adoprarci in diversa maniera intorno alla <lb></lb>economia del Vo di Euclide, ma per esser ciò opera lunga, ci basti l&#039;averne <lb></lb>posti i principii. </s>

<s>” </s></p><p type="main">

<s>“ Euclide restrinse il nome di parti alla quota: noi prendiamo general­<lb></lb>mente, col nome di parte, la quota, le quote e l&#039;incommensurabile al tutto, <lb></lb>da che forse schivasi l&#039;oscurità di qualche definizione del quinto suddetto, <lb></lb>benchè altre difficoltà qui s&#039;incontrino. </s>

<s>” </s></p><p type="main">

<s>“ Non si accorse il dottissimo Commandino che una comune notizia, <lb></lb>della quale Euclide si serve nella prima del Xo, anche nella ottava del Vo aveva <lb></lb>per prima avuto luogo, e così non la notò detto Interpetre, come doveva, <lb></lb>dopo la definizione del Vo, ma dopo quella del Xo. </s>

<s>” </s></p><p type="main">

<s>“ Osservo che il dottissimo Commandino s&#039;addormentò nella decima pro­<lb></lb>posizione del IVo euclidiano, perchè, dovendo da Teone tradurre le parole <pb xlink:href="020/01/2456.jpg" pagenum="81"></pb>greche <emph type="italics"></emph>quae non est maior,<emph.end type="italics"></emph.end> traduce <emph type="italics"></emph>quae non sit maior,<emph.end type="italics"></emph.end> e così portò una <lb></lb>condizione ridicola, non che superflua alla costruzione. </s>

<s>” </s></p><p type="main">

<s>“ All&#039;ottava definizione dell&#039;XIo di Euclide suppliscasi, di mente del­<lb></lb>l&#039;Autore, <emph type="italics"></emph>prodotto per ogni banda.<emph.end type="italics"></emph.end> La IXa, la Xa e XIa dello stesso libro <lb></lb>non patiranno difficoltà, se il subietto prendasi come predicato, il che como­<lb></lb>damente far puossi, anzi devesi, per la proprietà della lingua greca, nè hanno <lb></lb>ciò avvertito gl&#039;Interpetri. </s>

<s>” </s></p><p type="main">

<s>“ Osservo che le quattro grandezze proporzionali, definite nel Vo con la <lb></lb>moltiplicazione, si possono anche, con la divisione, definire, e l&#039;un metodo, <lb></lb>nell&#039;operazione, riscontrasi con l&#039;altro ” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>844, 45). </s></p><p type="main">

<s>Questi, come si vede, eran pensieri che il Nardi frettolosamente scriveva <lb></lb>in distinte note, via via che gli sovvenivano alla mente, e che poi volle rac­<lb></lb>cogliere insieme nella citata Scena. </s>

<s>Da quei frettolosi pensieri però balena <lb></lb>chiaro il concetto della particolar riforma del quinto libro euclideo, il quale <lb></lb>si risonosce radicalmente viziato dall&#039;essere, in quinto luogo, mal definite <lb></lb>dall&#039;Autore le condizioni, che fanno consister fra loro quattro quantità omo­<lb></lb>genee proporzionali. </s>

<s>Quella quinta definizione infatti è tale, secondo le parole <lb></lb>che il traduttore premette al quinto libro: “ Le grandezze si dicono essere <lb></lb>nella medesima proporzione, la prima alla seconda e la terza alla quarta, <lb></lb>quando le ugualmente moltiplici della prima e della terza, ovvero insieme <lb></lb>avanzano le ugualmente moltiplici della seconda e della quarta, secondo qual­<lb></lb>sivoglia moltiplicazione; ovvero insieme le pareggiano; ovvero insieme sono <lb></lb>avanzate da loro ” (Elem. </s>

<s>Eucl. </s>

<s>cit., fol. </s>

<s>63). </s></p><p type="main">

<s>Esaminando bene questo discorso è facile trovare che si riduce alla forma <lb></lb>seguente: Siano date le due relazioni A/B, C/D: si vuol assegnare uno dei più <lb></lb>facili, e de&#039;più distinti caratterismi, che ce le faccia riconoscere, quando sono <lb></lb>fra loro uguali. </s>

<s>Euclide in sostanza risponde: quando, moltiplicate per la me­<lb></lb>desima quantità, la quale sia per esempio N/M; si mantengono uguali. </s>

<s>Ma per­<lb></lb>chè in dir così troppo manifesto apparirebbe il paralogismo, consistente nel <lb></lb>dare il segno da riconoscere un&#039;eguaglianza, mentre implicitamente suppo­<lb></lb>nevasi già nota; si raggirano in altre parole le medesime cose, dicendo che <lb></lb>quattro quantità sono allora proporzionali, quando i prodotti A.N, C.N, ossia <lb></lb>gli equimolteplici delle due antecedenti s&#039;accordano sempre in superare, egua­<lb></lb>gliare e mancare co&#039;prodotti B.M, D.M, ossia con gli equimolteplici delle <lb></lb>due conseguenti. </s></p><p type="main">

<s>Ora il Nardi scopriva il paralogismo anche sotto questo discorso, così <lb></lb>artificiosamente condotto, vedendo chiaro che, per moltiplicare in qualunque <lb></lb>modo, e secondo qualunque moltiplicazione, i termini, non verrebbero però <lb></lb>le due relazioni ad acquistare quella uguaglianza, che non avessero avuto <lb></lb>prima: intanto che ne concludeva non dover esser quella euclidea definizione <lb></lb>legittima, perchè applicabile indifferentemente anche alle quantità non pro­<lb></lb>porzionali. </s>

<s>Soggiungeva di più non sembrargli quella stessa definizione nem-<pb xlink:href="020/01/2457.jpg" pagenum="82"></pb>meno universale, perchè: supponiamo di avere l&#039;angolo retto, che chiame­<lb></lb>remo A, misurato dal quadrante Q del cerchio, di cui R sia il raggio: le <lb></lb>ragioni A:Q e 2:R<foreign lang="grc">π</foreign> sono senza dubbio uguali, ma benchè gli equimolte­<lb></lb>plici degli antecedenti si possano accordare facilmente insieme nel mancare <lb></lb>e nell&#039;eccedere i conseguenti, non si accorderanno in eterno nell&#039;eguagliarsi, <lb></lb>essendo la circonferenza e il raggio incommensurabili. </s>

<s>Simile dicasi del lato <lb></lb>del quadrato e della diagonale, perchè, chiamata questa D, e quello L, che <lb></lb>supponesi essere uguale a 5, D:L, e √50:√25 stanno insieme in vera e <lb></lb>propria proporzione, benchè il carattere della loro proporzionalità non si possa, <lb></lb>per la dottrina degl&#039;incommensurabili, desumer dalla regola degli equimol­<lb></lb>teplici euclidei. </s></p><p type="main">

<s>Sembravano al Nardi queste cose tanto evidenti, che si maravigliava come <lb></lb>non l&#039;avessero avvertite que&#039;così grandi Matematici dell&#039;antichità, quali erano <lb></lb>Archimede, Pappo e simili altri. </s>

<s>Ben però più si maravigliava che, nel dar <lb></lb>mano così valida a restaurare la scienza, non le avesse avvertite il Benedetti, <lb></lb>per cui soggiungeva ai sopra scritti pensieri anche il seguente, ch&#039;egli poi <lb></lb>raccoglieva fra gli altri nella medesima Scena: </s></p><p type="main">

<s>“ Il Benedetti, geometra insigne, non si accorse che, volendo riformare <lb></lb>il quinto libro di Euclide, trascurò le definizioni delle uguali e diseguali ra­<lb></lb>gioni, quale principio è il fondamento dell&#039;opera. </s>

<s>Stupiscomi certo di tanta <lb></lb>inavvertenza. </s>

<s>” </s></p><p type="main">

<s>“ Mentre io sento dirmisi che siano quattro quantità proporzionali, le <lb></lb>estreme siano maggiori delle mezzane, resto sospeso fino a che non ne fac­<lb></lb>cia il conto nei numeri noti, ed allora ragionevolmente desidero d&#039;intenderne <lb></lb>la dimostrazione, perchè l&#039;induzione, e meno l&#039;esempio, non appagano l&#039;in­<lb></lb>telletto contemplativo. </s>

<s>Che se mi si proponga due quantità uguali aver la <lb></lb>stessa proporzione ad una terza, non solo l&#039;intendo, ma vedo esser difficile <lb></lb>l&#039;insegnar, con mezzi più facili ed evidenti di quello che sia la proposta, tal <lb></lb>verità. </s>

<s>Euclide per insegnarmela assume la definizione quinta nel Vo, qual&#039;è <lb></lb>molto più difficile ad intendersi che non è la proposta: onde tal definizione <lb></lb>rende oscure tutte le prove, nelle quali direttamente s&#039;adopra. </s>

<s>” </s></p><p type="main">

<s>“ Ciò nondimeno poco m&#039;importerebbe, ma trovo qualche difficoltà per <lb></lb>mantenerla legittima. </s>

<s>Dico dunque parermi che quella definizione convenga <lb></lb>ancora alle quantità non proporzionali, il che sarebbe difetto importantissimo. </s>

<s><lb></lb>Sia qualsivoglia numero A il primo termine, e qualsivoglia numero B, mi­<lb></lb>nore, il secondo: il terzo sia l&#039;angolo retto, e il quarto l&#039;angolo nel mezzo <lb></lb>cerchio. </s>

<s>Certo che questi due angoli moltiplicati si possono superare scam­<lb></lb>bievolmente, onde hanno proporzione insieme, conforme anche ricerca Eu­<lb></lb>clide nella quarta definizione. </s>

<s>Ora dico che, presi gli equimolteplici del primo <lb></lb>e del terzo termine, in qualsivoglia modo, e così anche del secondo e del <lb></lb>quarto, avverrà che, se uno antecedente superio o manchi dal suo consegùente, <lb></lb>anche l&#039;altro supererà o mancherà dal suo, secondo qual si voglia moltipli­<lb></lb>cazione, nello stesso modo. </s>

<s>” </s></p><p type="main">

<s>“ Che se per il primo termine prendessimo Rce 50, per il secondo Rce 25, <pb xlink:href="020/01/2458.jpg" pagenum="83"></pb>per il terzo la diagonale del quadrato, per il quarto il lato dello stesso; in <lb></lb>questo caso, posti gli equimolteplici del primo e del terzo e del secondo e del <lb></lb>quarto, avverrà che se uno antecedente superi o manchi dal suo conseguente, <lb></lb>anche l&#039;altro superi o manchi dal suo. </s>

<s>È ben vero che, quantunque sian pro­<lb></lb>porzionali la diagonale e il lato, come Rce 50 e Rce 25, non però giammai av­<lb></lb>verrà che i molteplici degli antecedenti uguaglino i molteplici dei conseguenti, <lb></lb>com&#039;è noto per la dottrina degli incommensurabili: e lo stesso avviene, nel <lb></lb>caso dell&#039;angolo retto e del mezzo cerchio, e dei loro molteplici e corrispon­<lb></lb>denti. </s>

<s>Non è dunque necessario, secondo la definizione di Euclide, che le cose <lb></lb>proporzionali si possano sempre, mediante la moltiplicazione, agguagliare, al­<lb></lb>trimenti non sarebbe universale a tutte le proporzionali detta definizione. </s>

<s>” </s></p><p type="main">

<s>“ Avvezzati, o mio Lettore, a bene esaminare i detti, benchè comune­<lb></lb>mente ricevuti per veri, dei grandi uomini, e frattanto, in difesa di Euclide, <lb></lb>dico ch&#039;egli aveva bisogno di definire le quattro proporzionali con qualche <lb></lb>caratterismo, per poterle, nelle operazioni geometriche, riconoscere dalle non <lb></lb>tali: onde il definirle generalmente esser quelle, che hanno lo stesso rispetto, <lb></lb>secondo la quantità, non bastava al suo proposito. </s>

<s>Ciò supposto, piacemi che <lb></lb>alla definizione da esso data basti solo, negli scolii, aggiungere di mente sua <lb></lb>che gli eccessi o difetti della prima verso la seconda, e della terza verso la <lb></lb>quarta, sieno capaci di proporzione: cioè che moltiplicati possano superare <lb></lb>la seconda e la quarta, come vedesi volere Euclide nella ottava proposizione <lb></lb>del Vo, dove dichiara il senso di questa definizione, e così togliesi ogni dif­<lb></lb>ficoltà. </s>

<s>Vediamo ancora che Euclide propone lo scambiamento di ragione, <lb></lb>come indistintamente valido, nella X proposizione: eppure di mente sua bi­<lb></lb>sognava supplire che i termini, che si scambiano, siano di proporzione capaci, <lb></lb>altrimenti egli c&#039;insegnerebbe il falso ” (MSS. Gal., T. XX, pag. </s>

<s>846-48). </s></p><p type="main">

<s>L&#039;apparire ora queste così savie osservazioni del Nardi, dopo più che <lb></lb>due secoli e mezzo, alla luce, conferisce a farci meglio conoscere l&#039;indole di <lb></lb>quell&#039;ingegno, in mezzo ai tanti altri che, pur non essendo meno acuti di <lb></lb>lui, s&#039;eran resi però meno franchi dall&#039;altrui suggezione. </s>

<s>Il Benedetti, che <lb></lb>senti primo alitarsi in petto questo nuovo spirito di libertà, mostrò nel pre­<lb></lb>sente esempio d&#039;esser rimasto avvinto in qualche parte a quel giogo, per cui <lb></lb>non sospettò che potesse il grande Euclide essere scorso in un paralogismo, <lb></lb>di che mostrava non essersi accorto nemmeno il grandissimo Archimede. </s>

<s><lb></lb>Galileo pure passò inconsideratamente, com&#039;apparirà dal processo di questa <lb></lb>Storia, sopra quelle medesime fallacie, attraverso alle quali lo avevano con­<lb></lb>fidentemente menato i suoi antichi Maestri, ond&#039;ebbe il Nardi il merito di <lb></lb>averle egli avvertite e scansate il primo, come prezioso frutto di quel che <lb></lb>avendo già sapientemente deliberato per sè medesimo, dava poi agli altri <lb></lb>qua!&#039;utile consiglio: <emph type="italics"></emph>Avvezzati, o mio Lettore, a bene esaminare i detti, <lb></lb>benchè comunemente ricevuti per veri, dei grandi uomini.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Che veramente poi le frettolose osservazioni, raccolte dal Matematico are­<lb></lb>tino nella sua Scena, contengano, per la riforma del quinto libro di Euclide, <lb></lb>i necessari principii, che ivi dice l&#039;Autore di non si voler mettere a svol-<pb xlink:href="020/01/2459.jpg" pagenum="84"></pb>gere, <emph type="italics"></emph>per esser ciò opera lunga;<emph.end type="italics"></emph.end> apparirà manifesto da quel che saremo per <lb></lb>dire di quella medesima opera, eseguitasi nel medesimo tempo dal Cavalieri, <lb></lb>e pubblicatasi poi da Galileo, nella prima parte di quel quinto dialogo ag­<lb></lb>giunto alle due Scienze nuove, dove si pongono dal Salviati i primi fonda­<lb></lb>menti della detta riforma, null&#039;altro più facendo, nè potendosi per verità fare <lb></lb>secondo il retto giudizio, che svolgere la fondamental proposizione accennata <lb></lb>dal Nardi. </s></p><p type="main">

<s>Consisteva questa proposizione nello stabilir di fatto le condizioni di <lb></lb>quelle uguaglianze, che. </s>

<s>Euclide dava il segno di riconoscer per tali a chi <lb></lb>egli supponeva già che fossero note, dicendo, tutt&#039;altrimenti dal venerato idolo <lb></lb>antico, essere allora quattro termini proporzionali, quando il primo sia tanta <lb></lb>parte del secondo, quanta il terzo è del quarto. </s>

<s>Così venivansi ai molteplici <lb></lb>opportunamente a sostituire i divisori, e sopra così ben posto fondamento fa­<lb></lb>ceva osservare lo stesso Nardi come quel che suppone Euclide potevasi dimo­<lb></lb>strare, trasformandosi la sua quinta definizione in teorema. </s>

<s>Se A infatti sta <lb></lb>a B, come C a D, anche A.N starà a B, come C.N a D; e ancora starà <lb></lb>A.N a B.M come C.N a D.M: ciò che conclude come, essendo gli equi­<lb></lb>molteplici proporzionali, sono altresi in proporzione i semplici termini re­<lb></lb>spettivi. </s></p><p type="main">

<s>Coloro, i quali non sono avvezzi come noi, dietro i savi consigli del <lb></lb>Nardi, a bene esaminare i detti, benchè comunemente ricevuti per veri, dei <lb></lb>grandi uomini; e che anzi, fedel copia vivente dei peripatetici antichi, ten­<lb></lb>gono che una matematica proposizione sia vera, perchè è scritta nei libri di <lb></lb>Galileo, e vogliono sopra più non esserci verità, che sui principii del se­<lb></lb>colo XVII non avesse il divino uomo scoperta, e annunziata agli altri uomini, <lb></lb>giacentisi nelle tenebre universali dell&#039;ignoranza; si vedrebbero aver già le­<lb></lb>vate sospettosi le orecchie, in parer che s&#039;incammini a provare il nostro di­<lb></lb>scorso che quei, ch&#039;essi venerano qual secondo Maestro di coloro che sanno, <lb></lb>sia stato prevenuto nello stabilire la nuova Scienza delle proporzioni. </s>

<s>Noi <lb></lb>confermiamo che fu veramente così, com&#039;è intanto provato rispetto al Nardi, <lb></lb>che doveva verso il 1635 avere scritte le sue osservazioni, all&#039;esempio del <lb></lb>quale resta a soggiungere come s&#039;incontrasse in quel tempo nel medesimo <lb></lb>pensiero anche il Cavalieri, andato perciò poi soggetto a un&#039;altra usurpazione, <lb></lb>dalla quale vogliamo che vengano ora finalmente a rivendicarlo, per solo amor <lb></lb>di giustizia, il sincero giudizio, e la libera coscienza della Storia. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Noto principalmente per la solenne pubblicazione, che il Torricelli fa­<lb></lb>ceva, a pag. </s>

<s>77 della seconda parte delle Opere geometriche, di un teorema <lb></lb>di lui; Gian Antonio Rocca, gentiluomo di Reggio, fu uno dei più valorosi <lb></lb>discepoli del Cavalieri. </s>

<s>Dalla lettura dei dialoghi dei due Massimi sistemi, <pb xlink:href="020/01/2460.jpg" pagenum="85"></pb>quando non erano venuti ancora alla luce gli altri delle due Scienze nuove, <lb></lb>apprese i primi principii della Meccanica, e lo Specchio Ustorio del suo pro­<lb></lb>prio maestro gli porgeva gli esempi del modo, come si potessero, con la Geo­<lb></lb>metria nuova, illustrare e promovere quegli stessi principii galileiani. </s>

<s>Non <lb></lb>trovando, fra le altre conclusioni annunziate nel detto dialogo Del mondo, <lb></lb>nulla che si riferisse ai moti equabili, dai quali dipendono, e con i quali si <lb></lb>paragonano le altre specie di moti, volle egli medesimo applicarvisi, incerto <lb></lb>s&#039;egli fosse per supplire al difetto, o per prevenire l&#039;apparizione di ciò, che <lb></lb>nel suo nuovo trattato sarebbe per dimostrare lo stesso Galileo. </s>

<s>Comunque <lb></lb>sia, erano già da Archimede, nella prima proposizione Delle spirali, posti <lb></lb>alla nuova Scienza, che s&#039;intendeva di instaurare, i principii, e non restava <lb></lb>a far altro al Rocca, se non che a svolgerli, perchè gli venissero di lì ritro­<lb></lb>vate le conseguenti proprietà dei moti uniformi. </s></p><p type="main">

<s>In quella prima proposizione dunque Archimede vuol dimostrare il teo­<lb></lb>rema fondamentale, che cioè, essendo le velocità uguali, gli spazi stanno come <lb></lb>i tempi. </s>

<s>Per far ciò suppone che il mobile P (fig. </s>

<s>34) inceda equiveloce nella <lb></lb><figure id="id.020.01.2460.1.jpg" xlink:href="020/01/2460/1.jpg"></figure></s></p><p type="caption">

<s>Figura 34.<lb></lb>direzione AB, e dato che lo spazio CD sia passato nel tempo FG, e lo spa­<lb></lb>zio DE nel tempo GH, conclude il suo intento col provar che CD, DE e FG, <lb></lb>GH son quattro termini proporzionali. </s>

<s>Il mezzo per la dimostrazione doveva <lb></lb>esser perciò suggerito dalla Geometria pura, al maestro della quale rivolgen­<lb></lb>dosi Archimede, e trovando essere da lui insegnato che quattro termini sono <lb></lb>allora proporzionali, quando gli equimolteplici degli antecedenti s&#039;accordano <lb></lb>sempre in mancare o in uguagliare o in superare gli equimolteplici dei con­<lb></lb>seguenti, non credè il grande Siracusano che restasse a lui da far altro, se <lb></lb>non che a dimostrare come presi IC, LF equimolteplici di CD, FG, ed EK, <lb></lb>HM equimolteplici di DE e di GH, si verificassero esattamente nel suo caso <lb></lb>le condizioni, per le proporzionalità, richieste da Euclide “ Quoniam FG, così <lb></lb>David Rivault ne traduceva dal greco le parole, tempus est quo P cucurrit <lb></lb>CD, et quoties est CD in IC, toties est FG in LF, sequitur, quia motus puncti P <lb></lb>est uniformis, esse LF tempus, quo eadem celeritate punctus P decurrerit IC. </s>

<s><lb></lb>Eadem ratione est HM tempus, quo inambulaverit idem P spatium EK. <lb></lb>Proinde, si IC superaverit EK, similiter LF superabit HM. </s>

<s>Et si IC defecerit <lb></lb>ab EK, deficiet quoque LF ab HM. </s>

<s>Demum si aequalis fuerit IC alteri multi­<lb></lb>plici EK, etiam LF aequabitur tempori HM. </s>

<s>Est propterea CD ad DE ut FG ad <lb></lb>GH, ut proponebatur ” (Parisiis 1615, pag. </s>

<s>353). </s></p><p type="main">

<s>Archimede procede oltre a proporre in secondo luogo che, essendo i <pb xlink:href="020/01/2461.jpg" pagenum="86"></pb>tempi uguali, le varie velocità, con le quali incedono due mobili diversi, <lb></lb>stanno come gli spazi, e supposto che N per esempio (fig. </s>

<s>35) passi nella <lb></lb>direzione AB gli spazi AE, EG, mentre O nella direzione CD passa gli spazi <lb></lb>CF, FH; conclude il proposito col dimostrare che AE sta ad EG, come CF <lb></lb>a FH. </s>

<s>Per far ciò, essendo, egli dice, per supposizione AE, CF ed EG, FH <lb></lb>scorsi nei medesimi tempi, siano questi stessi tempi rappresentati da IK, KM: <lb></lb>avremo dunque, per la proposizion precedente, AE:BG=IK:KM. “ Atqui <lb></lb><figure id="id.020.01.2461.1.jpg" xlink:href="020/01/2461/1.jpg"></figure></s></p><p type="caption">

<s>Figura 35.<lb></lb>etiam CF est <lb></lb>ad FH, ut IK <lb></lb>ad KM; ergo <lb></lb>ut AE ad EG. <lb></lb>sic CF ad FH, <lb></lb>quod fuit <lb></lb>probandum ” <lb></lb>(ibid.). </s></p><p type="main">

<s>S&#039;arresta a questo punto il progresso archimedeo Dei moti equabili, <lb></lb>perch&#039;era sufficiente all&#039;Autore il premettere questi due soli teoremi, come <lb></lb>lemmi, per dimostrare, ciò ch&#039;era allora la sua principale intenzione, le mi­<lb></lb>rabili proprietà delle spirali. </s>

<s>Volle il Rocca proseguir l&#039;opera del Siracusano, <lb></lb>e dall&#039;aver sull&#039;esempio di lui dimostrata la prima legge fondamentale, che <lb></lb>governa i moti uniformi, ne concludeva, non solo che, essendo i tempi uguali, <lb></lb>le velocità stanno come gli spazi, ma di più che, essendo gli spazi uguali, si <lb></lb>rispondono contrariamente le velocità con i tempi; che, essendo le velocità <lb></lb>e i tempi differenti, in ragion composta di loro stanno gli spazi passati; che, <lb></lb>se sono le velocità e gli spazi disuguali, nella contraria ragion del loro com­<lb></lb>posto si rispondono i tempi: con altre simili proprietà, che l&#039;esperto Mate­<lb></lb>matico vedeva conseguire dai medesimi principii. </s></p><p type="main">

<s>Aveva il Rocca disposti in ordine di trattato questi teoremi, della legit­<lb></lb>tima dimostrazion dei quali non dubitava, quando fosse stato certo della <lb></lb>buona dimostrazione del primo, che procedeva, come s&#039;è detto, per l&#039;appli­<lb></lb>cazione degli equimolteplici a dimostrar le proporzionalità, secondo gl&#039;insegna­<lb></lb>menti di Euclide, e sopra gli esempi dello stesso Archimede. </s>

<s>Intorno a quegli <lb></lb>equimolteplici però, e non in altro, incominciarono i dubbi a tenzonar forte <lb></lb>nella solitaria mente del Rocca, perchè da una parte gli pareva chiaro, per <lb></lb>la sua propria ragione, che non fossero nè ben definite, nè ben dimostrate <lb></lb>le quantità proporzionali a quel modo; e dall&#039;altra lo atterrivano le grandi <lb></lb>autorità dei Matematici antichi, i quali concordemente lo avevano approvato. </s>

<s><lb></lb>Per quietar la sua penosa agitazione ebbe ricorso al Cavalieri, a cui, man­<lb></lb>dando il trattatello <emph type="italics"></emph>Dei moti equabili,<emph.end type="italics"></emph.end> gli esponeva anche insieme le ragioni, <lb></lb>che lo avevano fatto così dubitare e della quinta definizione euclidea premessa <lb></lb>al quinto libro degli Elementi, e dell&#039;applicazione, che ne aveva fatta Archi­<lb></lb>mede nella prima Delle spirali. </s></p><p type="main">

<s>Il Cavalieri, attentamente esaminando nei citati libri le cose, non solo <lb></lb>ebbe a convenire col Rocca, ma, persuaso di più che il trattato Dei moti <pb xlink:href="020/01/2462.jpg" pagenum="87"></pb>equabili si rimaneva a quel modo senza il suo legittimo fondamento, comin­<lb></lb>ciò a pensare, in grazia del suo discepolo e avutane occasione da lui, secondo <lb></lb>qual più vero e più noto carattere si potessero definire le ragioni proporzio­<lb></lb>nali. </s>

<s>Così di pensiero in pensiero procedendo, gli venne fatto di trovare il <lb></lb>modo, com&#039;egli avrebbe creduto si dovesse emendare il quinto libro di Eu­<lb></lb>clide, specialmente in quelle proposizioni, che rimanessero viziate dalla quinta <lb></lb>definizione. </s>

<s>Nè, essendo la verità una sola, farà punto maraviglia ch&#039;ei si <lb></lb>fosse incontrato col Nardi, così in definire l&#039;uguaglianza di due ragioni dalla <lb></lb>eguaglianza dei loro quozienti, come in ridurre la detta quinta definizione a <lb></lb>teorema da dimostrarsi. </s></p><p type="main">

<s>La novità e l&#039;importanza della pensata riforma euclidea allettavano così <lb></lb>l&#039;animo del Cavalieri, che, essendo in sul punto di terminar la stampa della <lb></lb>Geometria degl&#039;indivisibili, deliberava fra sè di coglier quell&#039;occasione, che <lb></lb>gli si porgeva così comoda e pronta di pubblicare que&#039;suoi pensieri intorno <lb></lb>alle proporzioni, come cosa anch&#039;essa geometrica, in appendice ai sette libri <lb></lb>della detta Geometria. </s>

<s>L&#039;argomento però e l&#039;indole dell&#039;aggiunta troppo es­<lb></lb>sendo diversi dal subietto, aveva pensato di dar a quella anche abito diverso, <lb></lb>mettendola in dialogo fra uno che insegna, e l&#039;altro che ascolta. </s>

<s>Il pensiero <lb></lb>d&#039;imitar Galileo, anche nell&#039;estrinseca forma del discorso, s&#039;appresentò forse <lb></lb>la prima volta alla mente del Cavalieri a quella occasione, benchè comin­<lb></lb>ciasse ad effettuarlo solo alquanti anni dopo, e in altro proposito, quando a <lb></lb>Benedetto Castelli e a Cesare Marsili, che nel dialogo della riforma di Eu­<lb></lb>clide avrebbero rappresentato il Salviati galileiano e il Sagredo, v&#039;aggiunse <lb></lb>terzo un Simplicio, applicando la goffa maschera di lui, per vendetta, sulla <lb></lb>faccia al Guldino. </s></p><p type="main">

<s>Non volle però mettersi il Cavalieri a colorir quella scena, senz&#039;averne <lb></lb>prima consulto con Galileo, da cui, prima di tutto, voleva sapere se la quinta <lb></lb>definizione di Euclide stava a rigor di logica, e se, avendo bisogno di corre­<lb></lb>zione, poteva farsi a quel modo, che si proponeva: poi voleva saper di più <lb></lb>se convenisse pubblicar la scrittura sopra tale argomento in appendice alla <lb></lb>nuova Geometria. </s>

<s>Distese perciò que&#039;suoi pensieri senz&#039;alcuno ornamento, e <lb></lb>solo, per render poi più docile la materia a improntarsi del dialogo, quando <lb></lb>fosse deciso di pubblicare il suo discorso; distinse i punti delle proposte e <lb></lb>delle obiezioni, delle domande e delle risposte. </s>

<s>Dettava poi le cose, scritte <lb></lb>così alla buona a un amanuense, il quale, trascrivendo com&#039;egli stesso e il <lb></lb>dettator pronunziavano, venne a farne una copia da spedirsi a Galileo, la <lb></lb>quale, per la sola ortografia, anche senz&#039;altri indizi, tradiva l&#039;origine propria. </s></p><p type="main">

<s>Fu fatta la spedizione <emph type="italics"></emph>da Bologna alli 19 Dicembre 1634,<emph.end type="italics"></emph.end> accompa­<lb></lb>gnando il Cavalieri il plico con una lettera, la quale così finiva: “ Di grazia <lb></lb>mi favorisca dirmi qualche cosa della mia Geometria, e se resta sodisfatto <lb></lb>o no liberamente delle mie risposte. </s>

<s>Scrivo con fretta, perciò mi scusi della <lb></lb>negligenza nello scrivere, e ciò, per avere io voluto trascrivere un pensiero <lb></lb>intorno alla definizione Va del quinto di Euclide, quale le mando per sen­<lb></lb>tirne il suo parere. </s>

<s>È cosa fatta a richiesta di un giovane studioso. </s>

<s>Se le pa-<pb xlink:href="020/01/2463.jpg" pagenum="88"></pb>resse cosa buona, avrei pensiero di metterla nel fine della mia Geometria, ma <lb></lb>desidero sentir prima il suo parere ” (Campori, Carteggio galil., Modena 1881, <lb></lb>pag. </s>

<s>423). </s></p><p type="main">

<s>La nostra curiosità fu eccitata dalla lettura di queste parole a ricercar <lb></lb>lo scritto mandato a Galileo, di cui il Cavalieri qui fa motto, e sembrandoci <lb></lb>di averlo trovato, almeno in parte, lo trascriviamo, assoggettando noi e i no­<lb></lb>stri lettori al tedio di serbare i solecismi, e la scorretta grafia dell&#039;originale: </s></p><p type="main">

<s>“ Nella dimostrazione di un certo Autore apportando nella prima pro­<lb></lb>posizione <emph type="italics"></emph>del moto equabile<emph.end type="italics"></emph.end> l&#039;operatione delli <emph type="italics"></emph>egualmente moltiplici.<emph.end type="italics"></emph.end> que­<lb></lb>sto a data occasione dessaminar la 5a e 7a definizione di Euclide. </s>

<s>” </s></p><p type="main">

<s>“ Hora per espianar la strada quanto serra possibile alla introductione <lb></lb>delle <emph type="italics"></emph>proporzionalità.<emph.end type="italics"></emph.end> suppongasi primieramente (come suppose anche Eu­<lb></lb>clide mentre le defini) che le grandezze proporzionale se trovino, cioè che <lb></lb>date in qualunque modo 3 grandezze quella proportione o quel rispetto o <lb></lb>quella relazione di quantità che ha la 1a verso la 2a l&#039;istessa possa haver <lb></lb>la 3a verso una 4a. </s>

<s>” </s></p><p type="main">

<s>“ Hora per averne una definitione vera bisogna prendere una delle lor <lb></lb>passioni, ma la più facile de tutte del quale se puol poi cavar le più recon­<lb></lb>dite. </s>

<s>Perchè la diffinitione già ditta d&#039;Euclide in questa maniera è troppo <lb></lb>imbrolliato: Allora 4 grandezze sono proporzionali quando gl&#039;egualmente <lb></lb>moltiplici della 1a e della 3a presi secondo qualunque moltiplicità si accor­<lb></lb>dano sempre nel superare mancare o paregiare gl&#039;egualmente moltiplici della <lb></lb>2a e della 4a *. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Obs.<emph.end type="italics"></emph.end> — (Chi habbia certezza che allora quando 4 grandezze sono pro­<lb></lb>porzionali gl&#039;egualmente moltiplici non si accordino sempre? </s>

<s>Overo chi me <lb></lb>assicurà che quelli egualmente moltiplici non si accordino sempre e che nul­<lb></lb>ladimeno le grandezze non siano proporzionale? </s>

<s>” </s></p><p type="main">

<s>“ Già Euclide nella precedente deffinitione haveva deliberato la propor­<lb></lb>zione tra due grandezze essere un tal rispetto o relazione tra di loro per <lb></lb>quanto appartiene alla quantità. </s>

<s>Hora avendo il lettore concepito già nel in­<lb></lb>telletto che cosa sia la proporzione fra due grandezze sarà difficile cosa che <lb></lb>egli possa intendere che quel rispetto o relatione che è fra la 1a e la 2a gran­<lb></lb>dezza allora sia simile al rispetto e relatione che si trova fra la 3a e 4a gran­<lb></lb>dezza, quando quelli egualmente moltiplici della 1a e della 3a si accordano <lb></lb>sempre nella maniera predetta con glegualmente moltiplici della 2a e della 4a. </s>

<s>” </s></p><p type="main">

<s>“ E perchè questo di Euclide è piuttosto theorema da dimostrare che una <lb></lb>definitione da premettersi. </s>

<s>” </s></p><p type="main">

<s>“ * Diremo noi allora 4 grandezze esser fra loro proporzionale, cioè haver <lb></lb>la 1a alla 2a la stessa proportione che la 3a alla 4a quando la prima sarà <lb></lb>eguale alla 2a e la 3a alla 4a. </s>

<s>Overo quando la 1a sarà tante volte moltiplice <lb></lb>della 2a quante volte precisamente la 3a è moltiplice della 4a. </s>

<s>” </s></p><p type="main">

<s>“ Similemente sono le grandezze proporzionale quando la 1a contenga <lb></lb>3 volte 1/2 per essempio la 2a et anco la 3a contenga 3 volte 1/2 la 4a, e final­<lb></lb>mente in qualsivoglia altra denominatione mentre le grandezze siano propor-<pb xlink:href="020/01/2464.jpg" pagenum="89"></pb>zionale, e perciò diremo con maggiore universalità tutto già stabilito, cioè allora <lb></lb>intendiamo 4 grandezze esser fra loro proporzionale quando l&#039;eccesso della 1a<lb></lb>sopra la 2a (qualunque egli sia) sia simile all&#039;eccesso della 3a sopra la 4a. </s>

<s>” </s></p><p type="main">

<s>“ Questo s&#039;intende quando gli antecedente sono maggiore delle lor con­<lb></lb>seguente ma in caso che la 1a sia minore della 2a e la 3a della 4a alhora <lb></lb>sarà la 2a maggiore della 1a e la 4a della 3a. </s>

<s>Però consideri con quest&#039;ordine <lb></lb>inverso e simagini che la 2a sia 1a e la 4a sia 3a. </s>

<s>Così haverà sempre le an­<lb></lb>tecedente sempre maggiore delle conseguente e laccennata diffinitione basta. </s>

<s>” </s></p><p type="main">

<s>“ Hora considerando le antecedenti maggior delle lor conseguenti di­<lb></lb>remo 1° per diffinitione in che maniera s&#039;intende le 4 grandezze esser fra <lb></lb>loro proporzionali et è questa. </s>

<s>Quando la 1a per avere alla 2a la medesima <lb></lb>proportione che la 3a alla 4a non è punto nè maggior nè minore di quello <lb></lb>che ella dovrebbe essere. </s>

<s>allora s&#039;intende aver la 1a alla seconda la mede­<lb></lb>sima proporzione che ha la 3a alla 4a. </s>

<s>” </s></p><p type="main">

<s>“ Con questa occasione definirei con modo assai simile la proportione <lb></lb>maggiore e direi così. </s>

<s>Ma quando la 1a grandezza sarà alquanto più grande <lb></lb>di quel che ella dovrebbe essere per avere alla 2a la medesima proportione <lb></lb>che ha la 3a alla 4a. </s>

<s>allora voglio che convenghiamo di dire che la 2a hab­<lb></lb>bia maggior proportione alla 2a che non ha la 3a alla 4a. </s>

<s>” </s></p><p type="main">

<s>“ Ma in caso che la 1a sia minor di quel che si ricercherebbe per avere <lb></lb>alla 2a quella medesima proportione che ha la 3a alla 4a sarà segno evi­<lb></lb>dente che la 3a è maggior del dovere per havere alla 4a quella tal propor­<lb></lb>tione che ha la 1a alla 2a. </s>

<s>Però in questo caso ancora V. S. si contenti di <lb></lb>concepir l&#039;ordine in altro modo e simmagini che quelle grandezze che erano <lb></lb>3a e 4a diventino 1a e 2a. </s>

<s>e quell&#039;altre che erano 1a e 2a V. S. le riponga <lb></lb>nei luoghi della 3a e della 4a. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Obs.<emph.end type="italics"></emph.end> — Bene adunque dimostrate con questi suoi principi tutto il 5° di <lb></lb>Euclide. </s>

<s>overo di dedurre da queste due diffinitione poste da V. S. quelle <lb></lb>altre due che Euclide mette per 5a e per 7a che sustengano il machina del <lb></lb>5° libro. </s>

<s>hora dimostrate queste come conclusioni. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Sol.<emph.end type="italics"></emph.end> — Quando le 4 grandezze sono proporzionali glegualmente molti­<lb></lb>plici della 1a e della 3a eternamente concordino etc. </s>

<s>se poterà entrar senza <lb></lb>scorta al 5° libro a intendere i theoremi delle grandezze proportionali. </s>

<s>E così <lb></lb>posta la definizione della proportione maggiore dimostrarò che in qualche <lb></lb>caso presi glegualmente moltiplici della 1a e della 3a et anco della 2a e della <lb></lb>4a quel della 1a ecceda quel della 2a ma quel della 3a non ecceda quel <lb></lb>della 4a. </s>

<s>Così questa conclusione serra la definitione della quale come prin­<lb></lb>cipio si serve Euclide. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ D.a<emph.end type="italics"></emph.end> — Quando io restassi persuaso di queste dua passioni deglegual­<lb></lb>mente moltiplici cioè che quando le 4 grandezze son proportionali quelli eter­<lb></lb>namente si accordano nel paregiare eccedere e mancare. </s>

<s>e che quando le <lb></lb>4 grandezze non son proportionali quelli in qualche caso discordano io per <lb></lb>me non ricercherei altra luce per intendere con chiarezza tutto il 5° degli <lb></lb>Elementi geometrici. </s>

<s>” </s></p><pb xlink:href="020/01/2465.jpg" pagenum="90"></pb><p type="main">

<s><emph type="italics"></emph>“ Ris.<emph.end type="italics"></emph.end> — Supponiamo che le 4 grandezze A, B, C, D siano proportio­<lb></lb>nali cioè che la 1a A alla 2a habbi l&#039;istessa proportione che la 3a C ha <lb></lb>verso la 4a D. credete che anco due della 1a verso la 2a averanno la mede­<lb></lb>sima proportione che due della 3a verso la 4a? </s>

<s>” </s></p><p type="main">

<s>“ Adunque intenderà anco con questo che 4 o 10 o 100 delle 1m<gap></gap> ad <lb></lb>una 2a averanno listessa proportione che hanno 4 o 10 o 100 della 3a ad <lb></lb>una 4a. </s>

<s>” </s></p><p type="main">

<s>“ Adunque è necessario che il moltiplice della 1a abbia listessa propor­<lb></lb>tione alla 2a che ha legualmente molteplice della 3a alla 4a cioè che la <lb></lb>1a moltiplicata quante volte si pare abbia alla 2a quella proportione istessa <lb></lb>che ha la 3a moltiplicata altrettante volte verso la 4a. </s>

<s>” </s></p><p type="main">

<s>“ Questo è per le antecedenti. </s>

<s>ma per le conseguenti credete voi che <lb></lb>date 4 grandezze proporzionali che la 1a a due della seconda abbia propor­<lb></lb>zione diversa da quella che ha la 3a a due della 1a overo a 4 o a 10? ” </s></p><p type="main">

<s>“ Ammettendo dunque voi questo confessate di restare appagato e din­<lb></lb>tendere con facilità che date 4 grandezze proporzionale A, B, C, D moltipli­<lb></lb>cate egualmente la 1a e la 3a quella proportione che ha il molteplice E della <lb></lb>1a A alla 2a B listessa ancora habbia precisamente la egualmente moltiplice <lb></lb>F della 3a C alla D. ” <lb></lb>“ E — A<emph type="sub"></emph>1<emph.end type="sub"></emph.end> B<emph type="sub"></emph>2<emph.end type="sub"></emph.end> — G <lb></lb>F — C<emph type="sub"></emph>3<emph.end type="sub"></emph.end> D<emph type="sub"></emph>4<emph.end type="sub"></emph.end> — H ”</s></p><p type="main">

<s>“ Immaginatevi dunque che queste siano le nostre 4 grandezze propor­<lb></lb>zionali E, B, F, D cioè il molteplice F della 3a sia 3a e la 4a D sia 4a V. S. <lb></lb>me ha anco detto di capire che moltiplicandosi egualmente le conseguenti <lb></lb>B, D cioè la 2a e 4a senza alterar punto le antecedenti la medesima propor­<lb></lb>tione averà la 1a al moltiplicato della 2a che ha la 3a al moltiplicato della 4a. </s>

<s><lb></lb>Ma queste 4 grandezze saranno per appunto F, F egualmente molteplice della <lb></lb>1a e della 3a e G, H egualmente molteplice della 2a e della 4a. </s>

<s>” (MSS. Gal., <lb></lb>P. V, T. V, fol. </s>

<s>81-83). </s></p><p type="main">

<s>Attentamente rimeditate queste cose, e così com&#039;erano Galileo ritrova­<lb></lb>tele vere, a predispor l&#039;animo dei nostri Lettori, curiosi già di sapere qual <lb></lb>risposta si facesse al Cavalieri, giova osservar come doveva aver l&#039;argomento <lb></lb>una particolare importanza per lui, il quale, benchè non avesse ancora pub­<lb></lb>blicato il terzo dialogo delle Scienze nuove, teneva pure fra i manoscritti di­<lb></lb>steso, parecchi anni prima del Rocca, il trattatello dei moti uniformi. </s>

<s>Il primo <lb></lb>principio della scrittura venutagli da Bologna gli aveva fatto rivolgere il pen­<lb></lb>siero a quel suo trattatello, per la buona dimostrazione, se non per la verità <lb></lb>del quale, ebbe allora a sentire una gran trepidazione, quando s&#039;abbattè ivi <lb></lb>a leggere le parole: <emph type="italics"></emph>chi mi assicura che quelli egualmente moltiplici non <lb></lb>si accordino sempre e che nulladimeno le grandezze non siano propor­<lb></lb>zionali?<emph.end type="italics"></emph.end></s></p><p type="main">

<s>A ben comprendere i sentimenti di Galileo convien osservare che i due <pb xlink:href="020/01/2466.jpg" pagenum="91"></pb>primi teoremi <emph type="italics"></emph>De motu aequabili,<emph.end type="italics"></emph.end> fedelissima imitazione delle due prime pro­<lb></lb>posizioni archimedee delle Spirali, concludono la proporzionalità fra gli spazi <lb></lb>e i tempi, essendo le velocità eguali, e la proporzionalità fra le velocità e gli <lb></lb>spazi, essendo uguali i tempi, per l&#039;applicazione degli equimolteplici. </s>

<s>“ Sunt <lb></lb>itaque quatuor magnitudines.... ac demonstratum est aeque multiplicia pri­<lb></lb>mae et tertiae vel una aequari vel una deficere, vel una excedere aeque mul­<lb></lb>tiplicia secundae et quartae. </s>

<s>Ergo prima ad secundam eamdem habet ratio­<lb></lb>nem quam tertia ad quartam ” (Alb. </s>

<s>XIII, 151). Or era venuto il Cavalieri, <lb></lb>in quelle sue carte, a far osservare che si posson bene gli equimoltiplici con­<lb></lb>tenere fra loro a quel modo, e pure non esser vero che <emph type="italics"></emph>spatium ad spatium <lb></lb>eamdem habeat rationem, quam tempus ad tempus.<emph.end type="italics"></emph.end> Non essendo vero que­<lb></lb>sto, o non ben dimostrato, non si poteva esser certi della verità del primo <lb></lb>teorema, in cui i moti accelerati si riducono agli uniformi, d&#039;onde verreb­<lb></lb>besi altresi a diffondere l&#039;incertezza sul teorema secondo, in cui, quasi per <lb></lb>un corollario del precedente, si stabilisce la legge degli spazi proporzionali <lb></lb>ai quadrati dei tempi. </s></p><p type="main">

<s>Tali sentiva Galileo dovere o poter essere le conseguenze dannose alla <lb></lb>nuova scienza del moto, com&#039;ei l&#039;aveva già nei suoi libri istituita, e che ora <lb></lb>s&#039;apparecchiava di mettere in dialogo, per palesarla finalmente al mondo: <lb></lb>ond&#039;avendo già deliberato di non lasciare in mano altrui un&#039;arme così pe­<lb></lb>ricolosa, qual vedeva spuntare dal pensiero del Cavalieri, non potendola get­<lb></lb>tare o nascondere, voleva maneggiarla egli da sè medesimo destramente a <lb></lb>suo modo. </s>

<s>Meditava fra sè in silenzio come si potesse conseguir meglio la <lb></lb>desiderata intenzione, e intanto il Rocca, il quale aveva avuto copia della <lb></lb>scrittura sulla riforma euclidea, intorno a che dicevasi di voler consultar Ga­<lb></lb>lileo, e dopo quasi più che un mese e mezzo non aveva ancora saputo altro; <lb></lb>sollecitava curioso il Cavalieri che rispondeva così da Bologna il dì 4 Gen­<lb></lb>naio: “ Scrissi già al sig. </s>

<s>Galileo e li mandai una copia della dimostrazione <lb></lb>intorno alla definizione quinta del Quinto di Euclide, da V. S. promossa, per <lb></lb>intenderne il parer suo, ed aspettone risposta: avendo cosa nuova glie ne <lb></lb>darò avviso ” (Lettere a G. A. </s>

<s>Rocca etc., Modena 1725, pag. </s>

<s>21). </s></p><p type="main">

<s>Indugiò a venire parecchi altri giorni ancora l&#039;aspettata risposta, dei <lb></lb>propri termini della quale non abbiamo precisa notizia, ma si congetturano <lb></lb>facilmente dai sentimenti, che si dovettero suscitar nell&#039;animo di Galileo, e <lb></lb>dal riscontro delle seguenti parole scrittegli dal Cavalieri in una sua lettera <lb></lb>del dì 6 Febbraio di quel medesimo anno 1635. “ Quanto all&#039;appendice in­<lb></lb>torno alla definizione V del Quinto, conforme che mi pare che inclini il suo <lb></lb>parere, la lascerò stare, non avendo veramente alcuna connessione con l&#039;opera, <lb></lb>e differirò a più opportuna occasione il pubblicarla. </s>

<s>Bene avevo gusto inse­<lb></lb>rirla nella Geometria come cosa geometrica, e maggiormente che non so se <lb></lb>più stamperò di simili materie, che da molti sono aborrite, da pochi viste, e <lb></lb>da pochissimi apprezzate ” (Campori, Carteggio gal. </s>

<s>cit., pag. </s>

<s>429). Il Cava­<lb></lb>lieri però, in quella sua ingenuità, non aveva ben comprese le segrete inten­<lb></lb>zioni nè penetrato addentro al cupo animo di Galileo, il quale poi si fece <pb xlink:href="020/01/2467.jpg" pagenum="92"></pb>intendere meglio, che di quella dimostrazione del definito da Euclide non <lb></lb>doveva far l&#039;Autore oramai più conto come di cosa sua, nè perciò pensare <lb></lb>di pubblicarla a nome suo nella Geometria nuova, nè altrove. </s>

<s>L&#039;artificio e <lb></lb>il modo cran molto diversi, ma nell&#039;effetto si rassomigliavano a quelli dei <lb></lb><emph type="italics"></emph>bravi<emph.end type="italics"></emph.end> di que&#039;tempi, i quali, dop&#039;avere usata contro un più debole qualche <lb></lb>prepotenza, lo lasciavano, sicuri d&#039;essere bene intesi, col ficcargli in viso gli <lb></lb>occhi minacciosi, e con l&#039;appuntarsi il dito su dal mento al naso. </s></p><p type="main">

<s>Divenuto Galileo con quest&#039;arti, delle quali noi ci siam fatti al mondo <lb></lb>aborriti delatori, sicuro dell&#039;usurpato possesso, resta a dire qual&#039;ei pensasse <lb></lb>llora di farne, e quale veramente ne facesse poi uso. </s>

<s>Il vederlo attendere <lb></lb>in quel tempo a trascrivere le due prime proposizioni <emph type="italics"></emph>De motu aequabili,<emph.end type="italics"></emph.end><lb></lb>così com&#039;erano state già dimostrate per l&#039;applicazione degli equimolteplici, <lb></lb>parrebbe segno ch&#039;ei non avesse riconosciuto ancora la verità dei dubbi, o <lb></lb>l&#039;importanza delle critiche del Cavalieri. </s>

<s>Ma furono certe difficoltà, le quali <lb></lb>si comprenderanno meglio fra poco, che fecero lasciare a Galileo senza ri­<lb></lb>forma i detti teoremi, di cui poteva dall&#039;altra parte riversare ogni responsa­<lb></lb>bilità sopr&#039;Archimede, loro primo e legittimo Autore. </s>

<s>Credeva allora che do­<lb></lb>vess&#039;essere sufficiente a salvarlo dalle contradizioni quella grande autorità, <lb></lb>invocata anche altrove, quando, nella dimostrazion delle traiettorie parabo­<lb></lb>liche si supponevano parallele le forze sollecitanti il proietto (Alb. </s>

<s>XIII, 228), <lb></lb>o quando si voleva da alcuni francesi mettere in dubbio se la nuova Mecca­<lb></lb>nica fosse una scienza reale o un romanzo, francamente rispondendo agli <lb></lb>oppositori, Galileo, che, pur non verificandosi le dimostrate leggi in natura, <lb></lb>non per questo perderebbero le sue dimostrazioni di forza e di concludenza, <lb></lb>“ siccome niente progiudica alle conclusioni, dimostrate da Archimede circa <lb></lb>la spirale, il non ritrovarsi in natura mobile, che in quella maniera spiral­<lb></lb>mente si muova ” (Alb. </s>

<s>VII, 157). </s></p><p type="main">

<s>Appena pubblicatisi però i Dialoghi, la critica inesorabile non volle ri­<lb></lb>conoscere autorità, e mentre da una parte s&#039;assaliva a visiera scoperta il nuovo <lb></lb>edifizio, diceudo ch&#039;era tutto fondato sopra un supposto; si sentiva dall&#039;altra <lb></lb>i minacciosi rumori di chi soggiungeva che, non solo quel meccanico fonda­<lb></lb>mento era ipotetico, ma che mancava affatto di fondamento, non essendo di­<lb></lb>mostrative delle proporzionalità fra gli spazi e i tempi le ragioni suggerite da <lb></lb>Euclide. </s>

<s>Avvenne perciò che, in mezzo all&#039;opera di perfezionare i discorsi <lb></lb>del moto stampati in Leida, una delle sollecitudini, che si dette immediata­<lb></lb>mente l&#039;Autore, dopo aver ritrovata la dimostrazione del principio supposto, <lb></lb>fu quella d&#039;assegnare altre note distintive e altre condizioni delle quantità <lb></lb>proporzionali. </s>

<s>La notizia si raccoglie certa da ciò, che soggiunge il Viviani, <lb></lb>dop aver detto come volesse Galileo che gli facesse il disteso della dimostra­<lb></lb>zion del teorema ammesso già come noto, intorno a che nel capitolo prece­<lb></lb>dente s&#039;è da noi lungamente discorso. </s></p><p type="main">

<s>“ Per una simile occasione di dubitare intorno alla quinta ed alla set­<lb></lb>tima definizione del quinto d&#039;Euclide, dice esso Viviani, mi aveva per avanti <lb></lb>conferito il Galileo la dimostrazione di quelle definizioni del quinto Libro, <pb xlink:href="020/01/2468.jpg" pagenum="93"></pb>senza però applicarla a figure, che, fermatomi poi in Arcetri, egli mi dettò <lb></lb>in dialogo, assai prima della venuta quivi del Torricelli, quando ancora il <lb></lb>Galileo non aveva risoluto di porla nella quinta Giornata, ma pensava tut­<lb></lb>tavia d&#039;aggiungerla alla quarta <emph type="italics"></emph>(così: ma voleva dire alla terza)<emph.end type="italics"></emph.end> a facce 153 <lb></lb>dell&#039;impressione di Leida, dopo la prima proposizione Dei moti equabili, nel <lb></lb>caso del ristamparsi, con le altre opere sue, quell&#039;ultima delle due nuove <lb></lb>Scienze. </s>

<s>Questa tal dettatura diede poi qualche facilità al medesimo Galileo <lb></lb>ed al Torricelli, per fare quel più ampio disteso in dialogo, che si è veduto, <lb></lb>e la medesima come inutile rimase a me, ed ancora la conservo ” (Scienza <lb></lb>univ. </s>

<s>delle proporz. </s>

<s>cit., pag. </s>

<s>100). </s></p><p type="main">

<s>Tra i frammenti di dialogo però, dettati da Galileo e notati da noi nel­<lb></lb>l&#039;altro capitolo, non s&#039;è potuto trovar questo delle proporzioni, di cui qui <lb></lb>parla il Viviani. </s>

<s>Sarà forse andato smarrito, o rimasto ai nostri occhi co­<lb></lb>perto dalla fitta selva dei fogli di que&#039;numerosi volumi, e di ciò senza dub­<lb></lb>bio ci duole, ma dalle segnate postille non è difficile ricostruire l&#039;effigie. </s>

<s>Di­<lb></lb>cendosi ivi che le cose dettate al Viviani era risoluto l&#039;Autore d&#039;inserirle dopo <lb></lb>la prima proposizione Dei moti equabili, e che dettero qualche facilità al più <lb></lb>ampio disteso in dialogo dal Torricelli, par si possa argomentare che quel <lb></lb>primo frammento si limitasse a definire le quantità proporzionali, a che si <lb></lb>riduce propriamente la prima delle tre parti, nelle quali, come si vedrà me­<lb></lb>glio, è distinto il dialogo torricelliano. </s>

<s>Che se alcuno desiderasse di sapere <lb></lb>il motivo, per cui Galileo si mutò dal primo proposito, d&#039;una semplice ag­<lb></lb>giunta ordinandone un dialogo distinto, potrebbe rimaner sodisfatto dalle se­<lb></lb>guenti considerazioni, che diffonderanno forse la loro luce anche sopr&#039;altre <lb></lb>parti di questa Storia. </s></p><p type="main">

<s>Ritessendo noi dunque con la mente le fila al discorso, che doverva es­<lb></lb>sere inserito nel terzo dialogo, dopo che il Salviati ebbe letta agli amici la <lb></lb>dimostrazione del primo teorema dei moti equabili, sappiamo che l&#039;argomento <lb></lb>si concludeva nell&#039;osservar come la regola degli equimolteplici euclidei non <lb></lb>si poteva prendere per criterio certo delle proporzionalità fra quattro termini <lb></lb>dati: ond&#039;è che si sarebbe così venuti a confessare non essere ben dimo­<lb></lb>strato quello stesso teorema dall&#039;Autore. </s>

<s>Il commento insomma che si vo­<lb></lb>leva far soggiungere agli interlocutori, non potendo non condannare o non <lb></lb>contraddire al testo, si vedeva da Galileo e dal Viviani la necessità di dimo­<lb></lb>strar che i tempi son proporzionali agli spazi, con altro mezzo e in altra <lb></lb>maniera. </s></p><p type="main">

<s>Ma qui stava la difficoltà, per ben comprender la quale giova ripensare <lb></lb>all&#039;invenzion di quel più vero principio, che i matematici posteriori a Galileo <lb></lb>sostituirono all&#039;antico paralogismo di Archimede. </s>

<s>Quel principio, che doveva <lb></lb>essere per sè noto, consisteva nel dire che due mobili sono allora ugualmente <lb></lb>veloci, quando passano spazi uguali in ugual tempo, d&#039;onde concludesi per <lb></lb>corollario immediato esser l&#039;uno più veloce dell&#039;altro, che passa in più pic­<lb></lb>col tempo il medesimo spazio. </s>

<s>La folla del popolo, spettatrice curiosa delle <lb></lb>forse dei cavalli in un prato, si serve per giudicare della vittoria di questo <pb xlink:href="020/01/2469.jpg" pagenum="94"></pb>criterio, che dunque è una verità di senso comune, espressa nella sua gene­<lb></lb>ralità dall&#039;assioma: le velocità de&#039;mobili son tanto maggiori, quant&#039;è più <lb></lb>breve il tempo e lo spazio più lungo. </s></p><p type="main">

<s>Gli elementi dunque compositori dei moti uniformi venivano così facil­<lb></lb>mente a tradursi in una formula matematica di natura frazionaria, in cui <lb></lb>sarebbero le velocità rappresentate dal quoziente, che ne resulta, dividendo <lb></lb>lo spazio per il tempo, e il simbolo algebrico della quale sarebbe V=S/T′, <lb></lb>intendendosi per V la velocità, e per S e per T gli altri due nominati ele­<lb></lb>menti. </s>

<s>Con le lettere iniziali V′, S′, T′ denominati altri elementi simili, ma <lb></lb>in quantità diversi, si compone allo stesso modo l&#039;altro simbolo V=S′/T′. </s>

<s>E <lb></lb>perchè è chiaro che tanto è più o meno grande la velocità quanto sono più <lb></lb>o meno grandi i corrispondenti spazi, relativamente ai tempi corrispondenti, <lb></lb>sarà dnnque V:V′=S/T:S′/T′, d&#039;onde si concludono, con somma facilità e <lb></lb>con retto metodo dimostrativo, i teoremi ordinati nel suo primo libro <emph type="italics"></emph>De <lb></lb>motu<emph.end type="italics"></emph.end> da Galileo. </s></p><p type="main">

<s>Questa radicale riforma, ripetiamo, non era facile introdurla allora, che <lb></lb>prevalevano i metodi antichi, proseguendo i quali, come si faceva dalla Scuola <lb></lb>galileiana, non era possibile dilungarsi un passo dagli esempi di Archimede. </s>

<s><lb></lb>Costretto Galileo stesso perciò a lasciar le due proposizioni dei moti equabili <lb></lb>così com&#039;erano state scritte nel libro, non volle mettervi a riscontro un di­<lb></lb>scorso, che tendeva a scoprirne la fallacia del metodo dimostrativo. </s>

<s>E non <lb></lb>volendo pure che si rimanesse inutile il pensiero del Cavalieri, si consigliò <lb></lb>di trattar della nuova Scienza delle proporzioni in disparte, e in modo, che <lb></lb>non apparisse l&#039;applicazione degli equimolteplici alla proporzionalità dei moti <lb></lb>equabili o falsa o inconcludente, ma oscura, intantochè colui, il quale non <lb></lb>fosse rimasto sodisfatto nel leggere que&#039;suoi primi teoremi <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> pen­<lb></lb>sasse di riformar col suo proprio ingegno, e secondo le nuove avvertenze, le <lb></lb>dimostrazioni condotte dietro l&#039;antica definizione di Euclide. </s>

<s>Che se l&#039;ar­<lb></lb>gomento delle proporzioni rimaneva scarso, per consumare il tempo di una <lb></lb>intera Giornata, in altri simili soggetti di Fisica e di Matematica troverebbe <lb></lb>il Salviati da intrattenere gli amici, perchè non oziosamente si potessero con­<lb></lb>durre a sera. </s></p><p type="main">

<s>In questo che così Galileo seco medesimo proponeva, e conferiva col gio­<lb></lb>vane Viviani, si facevano col Torricelli le trattative della sua venuta a Firenze, <lb></lb>che di fatti successe, come sappiamo, in que&#039;primi giorni di ottobre 1641. <lb></lb>Il fine, per cui fu fatto a lui mutare il soggiorno di Roma nell&#039;ospizio di <lb></lb>Arcetri, era quello di aiutare la fisica impotenza dell&#039;ospite a ripulir certe <lb></lb>sue reliquie di pensieri fisici e matematici, affinchè si potessero lasciar ve­<lb></lb>dere insieme con le altre cose meno imperfette (Alb. </s>

<s>VII, 367). Era fra quei <lb></lb>pensieri, principale senza dubbio per l&#039;argomento, e urgente per le solenni <lb></lb>promesse fatte al pubblico, quello attenente all&#039;uso delle catenelle e alla forza <pb xlink:href="020/01/2470.jpg" pagenum="95"></pb>della percossa, ond&#039;è che ognuno si sarebbe aspettato di veder in tal con­<lb></lb>giuntura ridotti alla loro tanto desiderata perfezione i dialoghi del moto. </s>

<s>Si <lb></lb>seppe invece dagli amici, e trentadue anni dopo se n&#039;ebbe pubblica testimo­<lb></lb>nianza, che il Salviati, dopo così lungo intermedio, era nuovamente tornato <lb></lb>in scena, e tutt&#039;altro che scusarsi con gli spettatori, innanzi ai quali rifinire <lb></lb>il primo interrotto discorso, divagarsi indebitamente in soggetto straniero. </s></p><p type="main">

<s>Tale è il sentimento e il giudizio degli studiosi, i quali, giunti al ter­<lb></lb>mine del dialogo quarto, sentono dire agl&#039;interlocutori che nel seguente si <lb></lb>ricercherebbero le speculazioni fatte dall&#039;Accademico intorno alla forza della <lb></lb>percossa (Alb. </s>

<s>XIII, 266), e poi svolgendo la carta trovano invece che nel <lb></lb>quinto dialogo non si tratta punto di Meccanica, ma di Geometria, e parti­<lb></lb>colarmente delle proporzioni. </s>

<s>Eppure quel titolo di <emph type="italics"></emph>Principio della quinta <lb></lb>Giornata<emph.end type="italics"></emph.end> fu stampato dal Viviani, a cui fu dato a copiare sull&#039;autografo del <lb></lb>Torricelli, il quale si dice che avesse scritto così in fronte al dialogo, per <lb></lb>espressa volontà di Galileo. </s>

<s>Che se fosse veramente stato così, bisognerebbe <lb></lb>dire che Galileo stesso, non curando gl&#039;impegni solennemente contratti col <lb></lb>pubblico avesse dismesso il pensiero di far succedere alla quarta immedia­<lb></lb>tamente un&#039;altra Giornata, dove si discorrerebbe, e si dimostrerebbero i ma­<lb></lb>ravigliosi effetti della percossa. </s>

<s>Fu anche da noi creduto un tempo così, e <lb></lb>significammo ai Lettori questa nostra opinione, ma, esaminate poi meglio le <lb></lb>cose, ci siam dovuti persuader finalmente che il titolo di <emph type="italics"></emph>Giornata quinta<emph.end type="italics"></emph.end><lb></lb>fu, non ben secondando le rimaste chiuse intenzioni di Galileo, posto dal <lb></lb>Torricelli, come apparirà dalla seguente storia del disteso fatto da lui. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Intorno a una cosa, ch&#039;è di grande importanza per l&#039;accennata storia, <lb></lb>convien prima di tutto intenderci: ed è intorno al modo, come si crede che <lb></lb>il Torricelli facesse quel suo disteso. </s>

<s>Il Viviani, che gli fu convivale in Ar­<lb></lb>cetri e collega, e perciò presente all&#039;azione e testimone del fatto, dicendo che <lb></lb>Galileo <emph type="italics"></emph>andava dettando<emph.end type="italics"></emph.end> (Scienza univ. </s>

<s>cit., pag. </s>

<s>60), non si dichiara bene <lb></lb>se la dettatura era anche della forma del discorso, o del solo semplice pen­<lb></lb>siero, come par voglia insinuarci il Serenai che, copiando, metteva questo <lb></lb>titolo: <emph type="italics"></emph>Trattato del Galileo sopra la definizione delle proporzioni di Eu­<lb></lb>clide: — Giornata quinta, da aggiungersi al,libro delle Nuove scienze, <lb></lb>distesa e spiegata dal Torricelli, vivente esso Galileo ceco, e per lui.<emph.end type="italics"></emph.end> Chi <lb></lb>però ripensa alle qualità dello scrivente, eletto fra i primi matematici del­<lb></lb>l&#039;Italia, l&#039;opera del quale non poteva perciò limitarsi a solo il meccanico <lb></lb>esercizio delle mani e degli occhi; ha già fra sè risoluta la questione. </s>

<s>e ha <lb></lb>pensato che doveva la cosa essere andata così: Galileo significava i suoi pen­<lb></lb>sieri, che poi il Torricelli distendeva a modo suo, e leggeva lo scritto da sè, <lb></lb>perchè venisse approvato. </s>

<s>Chi dall&#039;altra parte sa giudicar dello stile, sente <pb xlink:href="020/01/2471.jpg" pagenum="96"></pb>la diversità che passa tra la elegante snellezza del quinto dialogo, e la ma­<lb></lb>gnifica posa dei precedenti: ma, fuor d&#039;ogni meditata congettura e d&#039;ogni <lb></lb>sottilità di giudizio, si rende quel che si vuol conoscere per sè manifesto a <lb></lb>solo esaminar la bozza autografa, che felicemente s&#039;è conservata. </s></p><p type="main">

<s>A chi svolge il tomo quinto della quinta parte dei manoscritti di Gali­<lb></lb>leo occorre per prima cosa un quinternetto, in sesto più piccolo dei rima­<lb></lb>nenti, a cui par che manchi il principio, perchè fu per inavvertenza antepo­<lb></lb>sto all&#039;altro quinterno di maggior sesto, e della medesima calligrafia, sulla <lb></lb>prima faccia del quale comincia la scrittura del Dialogo, com&#039;usci dalla stessa <lb></lb>mano del Torricelli di primo getto. </s>

<s>Son frequentissime perciò le cassature, <lb></lb>le postille in margine e in calce, e le correzioni delle parole, consistenti bene <lb></lb>spesso nei solecismi, ne&#039;quali suol trascorrere colui, che non ha uso della <lb></lb>pronunzia e della ortografia toscana. </s>

<s>Dove, per esempio, era scritto <emph type="italics"></emph>pones­<lb></lb>simo, renovatomi, arenato,<emph.end type="italics"></emph.end> è corretto <emph type="italics"></emph>ponemmo, rinnovatomi, arrenato;<emph.end type="italics"></emph.end><lb></lb>ciò che solo basterebbe a provar, con materiale certezza, che l&#039;espressioni <lb></lb>avevano propria e particolar forma dallo scrivente, benchè altrui ne fosse il <lb></lb>concetto. </s>

<s>Intorno a ciò, com&#039;a cosa di maggiore importanza, convien tratte­<lb></lb>nere il nostro ragionamento, prima di tutto osservando che nel Dialogo tor­<lb></lb>ricelliano si distingue in tre parti quello stesso unico concetto della Scienza <lb></lb>universale delle proporzioni: nella prima si considerano le <emph type="italics"></emph>proporzioni scm­<lb></lb>plici,<emph.end type="italics"></emph.end> nella seconda le <emph type="italics"></emph>sproporzioni,<emph.end type="italics"></emph.end> e nella terza le <emph type="italics"></emph>proporzioni composte.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In che modo Galileo comunicasse al Torricelli i pensieri, per ciò che <lb></lb>s&#039;appartiene a quella prima parte del discorso, è a chiunque manifesto che, <lb></lb>anche frettolosamente, confronta il disteso di questo stesso discorso con la <lb></lb>scrittura, che da Bologua mandò il Cavalicri. </s>

<s>Il prologo infatti lo svolge il <lb></lb>Salviati da quel che s&#039;accenna in principio della detta scrittura, che l&#039;occa­<lb></lb>sione cioè di trattar delle proporzioni fu data dall&#039;esame della prima propo­<lb></lb>sizione del moto equabile, dimostrata da un certo Autore per l&#039;applicazione <lb></lb>degli ugualmente molteplici di Euclide. </s>

<s>Il Cavalieri per quell&#039;Autore inten­<lb></lb>deva il Rocca, e il protagonista del dialogo introduceva sulla scena, invece <lb></lb>di un personaggio oscuro, il famosissimo Galileo. </s></p><p type="main">

<s>Terminato il prologo, in cui anche il Salviati accenna allo studio delle <lb></lb>maravigliose spirali di Archimede, da cui ebbe lo stesso Bocca a serivere <lb></lb>quel suo trattatello il principio e l&#039;impulso; s&#039;entra nell&#039;argomento del quinto <lb></lb>libro di Euclide con queste parole, trascritte tali e quali si lessero nel foglio <lb></lb>del Cavalieri: “ Suppongasi primieramente (come le suppose anche Euclide, <lb></lb>mentre le defini) che le grandezze proporzionali si trovino... ” (Alb. </s>

<s>XIII, 290). <lb></lb>Questa medesima fedeltà di trascrizione, corretta dagli errori di ortografia e <lb></lb>dai solecismi, si riscontra anche nel progresso dell&#039;interloquio, non facendo <lb></lb>per lo più il Torricelli altro che scrivere a nome di Simplicio, del Sagredo <lb></lb>e del Salviati quelle obiezioni, quelle domande e quelle risposte, accennate <lb></lb>in margine al foglio dal bolognese amanuense. </s></p><p type="main">

<s>È dunque manifesto che il modo, come Galileo comunicò al Torricelli <lb></lb>i pensieri, espressi nella prima parte del Dialogo, fu con mettergli innanzi <pb xlink:href="020/01/2472.jpg" pagenum="97"></pb>la scrittura del Cavalieri, nella quale, come per le cose anzi dette è noto, si <lb></lb>stabilisce per caratterismo delle proporzionalità l&#039;uguaglianza del quoziente <lb></lb>nelle due ragioni: d&#039;onde poi si dimostra la definizione euclidea, che cioè, <lb></lb>essendo i quattro termini in una data proporzione, sono i loro equimolte­<lb></lb>plici altresi proporzionali. </s>

<s>Si veniva qui come là a concludere insomma che <lb></lb>la quinta delinizione di Euclide non era un principio, che si potesse ritener <lb></lb>per sè come noto, ma di un principio da preporsi come noto era piuttosto <lb></lb>la dimostrabile conseguenza. </s></p><p type="main">

<s>Per quel che poi riguarda le altre due parti del trattato delle proporzioni, <lb></lb>rimane a noi incerto il modo come Galileo comunicò al Torricelli il suo pen­<lb></lb>siero: cioè a dire se a voce o in scritto, non progredendo il discorso del Ca­<lb></lb>valieri oltre al termine, dove noi, ricopiando, l&#039;abbiamo lasciato. </s>

<s>Potrebb&#039;es­<lb></lb>ser quel termine reale, e potrebbero i fogli successivi esser venuti meno a <lb></lb>chi ebbe la cura di raccoglierli nel detto volume: cosicchè, mentre resta <lb></lb>incerto se quel che si prosegue a trattar nel dialogo delle sproporzioni e delle <lb></lb>proporzioni composte sia scritto secondo la mente del Cavalieri o di Galileo; <lb></lb>sembra sia da concluder come cosa certissima che non appartiene a Galileo, <lb></lb>nè per il concetto nè per le parole, il primo fondamento della Scienza uni­<lb></lb>versale delle proporzioni, posto nella prima parte del quinto dialogo aggiunto <lb></lb>alle due Scienze nuove. </s></p><p type="main">

<s>Comunque sia, la bozza del Torricelli termina col moffo <emph type="italics"></emph>Laus Deo,<emph.end type="italics"></emph.end> se­<lb></lb>gno che il discorso delle proporzioni, quale ivi leggesi manoscritto, era, se­<lb></lb>condo l&#039;intenzione dei due collaboratori, compiuto. </s>

<s>Essendo però appena ba­<lb></lb>stato l&#039;argomento per trattener la conversazione infin presso a mezzogiorno, <lb></lb>aveva Galileo pensato, per condurla a sera, di mettere in mano al Salviati, <lb></lb>da leggersi innanzi agli amiei, vari fogli, dove fossero dimostrati teoremi di <lb></lb>Geometria, e risoluti problemi di Fisica; ma fu impedito dalla malattia, che <lb></lb>aggravandosi sempre più, poco tempo di poi lo condusse alla morte. </s></p><p type="main">

<s>Scarsi pereiò, per la brevità del tempo che si ridusse a soli tre mesi, <lb></lb>s&#039;aspettàva che fossero i frutti raccolti ne&#039;filosofici colloqui con Galileo dal <lb></lb>Torricelli, ma, per la straordinaria eccellenza dei due uomini convenuti in­<lb></lb>sieme, tutti si ripromettevan que&#039;frutti preziosi. </s>

<s>Di qui è che, per goderne <lb></lb>o per saziarne almeno la vista, si misero attorno allo stesso Torricelli, appena <lb></lb>sceso giù dalla collina di Arcetri, gli ammiratori e gli amici, il più deside­<lb></lb>roso fra&#039;quali era il principe Leopoldo dei Medici. </s></p><p type="main">

<s>Giova in tale occasione rammemorare ch&#039;essendo esso Principe entrato <lb></lb>in gran curiosità di saper se il dialogo dell&#039;uso delle catenuzze, e della forza <lb></lb>della percossa, solennemente promesso e inutilmente atteso dall&#039;Elzevirio, si <lb></lb>preparava; ne fece, per mezzo del maestro suo don Famiano Michelini, in­<lb></lb>terrogare in proposito Galileo, il quale mandò a rispondere a Sua Altezza <lb></lb>ch&#039;egli aveva ben ritrovata la proporzione della forza della percossa, ma che, <lb></lb>per la vecchiaia e per altri accidenti, non sperava di poterla dar fuori. </s>

<s>Il <lb></lb>Principe allora, a rendere più efficaci le premure che faceva il Castelli ag­<lb></lb>giungendo il suo proprio invito, condusse il Torricelli a Firenze per questo <pb xlink:href="020/01/2473.jpg" pagenum="98"></pb>fine principalmente, perchè aiutasse Galileo a stendere il Dialogo della per­<lb></lb>cossa. </s>

<s>Desideroso ora dunque di saper qual effetto avessero avuto le sue sol­<lb></lb>lecitudini n&#039;ebbe dal Torricelli stesso per risposta che, in argomento della <lb></lb>percossa, aveva sì udito pronunziare al suo ospite alcune conclusioni impor­<lb></lb>tanti, ma di metterle in dialogo non se n&#039;era discorso, nè aveva sentito dire <lb></lb>da lui che ne avesse ridotto a perfezione il trattato. </s></p><p type="main">

<s>Abbiamo di così fatte notizie il documento in una lettera autografa del <lb></lb>principe Leopoldo, il quale rispondeva così il 9 Maggio 1665 a Michelangiolo <lb></lb>Ricci, curioso di saper se era vero che il Borelli si preparava a scrivere un <lb></lb>libro sopra la forza della percossa: “ Deve sapere che le speculazioni fatte <lb></lb>dal medesimo Borelli sopra questa esperienza della polvere credo lo abbiano <lb></lb>portato a lavorare, e speculare sopra la forza e proporzione della percossa, <lb></lb>che la buona memoria del nostro Galileo disse a me più volte aver ritro­<lb></lb>vata, ma non potè, per l&#039;età o per qualsivoglia altro accidente che ne fosse <lb></lb>cagione, darla fuori, com&#039;io le feci ben cento volte istanza, ed al qual fine <lb></lb>condussi qua il Torricelli di suo consenso, perchè potesse servire in mettere <lb></lb>in carta i suoi pensieri, ma tutto fu invano ” (MSS. Cim., T. XXIII, fol. </s>

<s>113). </s></p><p type="main">

<s>Persuaso dunque il Principe che, quanto a procurare il Dialogo della <lb></lb>percossa, le sue proprie sollecitudini fossero tornate vane, domandava curioso <lb></lb>in che altro dunque si fosse, in quella dimora d&#039;Arcetri, divagato il pensiero, <lb></lb>e il Torricelli rispondeva che in distendere in dialogo una nuova scienza <lb></lb>delle proporzioni. </s>

<s>Di veder questo Dialogo mostrò allora esso Principe vivis­<lb></lb>simo desiderio, e il Torricelli riprese in mano la bozza, con quelle corre­<lb></lb>zioni che ci aveva fatte nel leggerla, per averne l&#039;approvazione, a Galileo, <lb></lb>il quale, sperando di poter proseguir l&#039;opera, aspettava all&#039;ultimo a desi­<lb></lb>gnar del disteso il titolo e la collocazione. </s>

<s>Non si poteva però farne per il <lb></lb>Principe la copia a pulito, senza nulla scrivervi in fronte, per cui, ben sa­<lb></lb>pendo il Torricelli che il discorso intorno al quinto libro di Euclide era com­<lb></lb>piuto, e ch&#039;era fatto per aggiungersi agli altri dialoghi delle due Scienze <lb></lb>nuove, l&#039;ultimo de&#039;quali era il quarto, nè del Dialogo della percossa, che <lb></lb>sarebbe dovuto immediatamente succedere, avendo sentito mai farne motto; <lb></lb>non dubitò che, anche secondo la mente dello stesso Galileo, non fosse il <lb></lb>titolo questo: <emph type="italics"></emph>Trattato del Galileo sopra la definizione delle proporzioni di <lb></lb>Euclide — Giornata quinta da aggiungersi nel libro delle Nuove scienze.<emph.end type="italics"></emph.end><lb></lb>E così fu scritto in fronte alla copia, che di sua propria mano il Torricelli <lb></lb>condusse, per consegnarla al principe Leopoldo. </s></p><p type="main">

<s>Così essendo, non può dunque da quel titolo argomentarsi che Galileo <lb></lb>avesse dismesso il pensiero di aggiungere, dopo i primi quattro del moto, il <lb></lb>dialogo della percossa, il quale era già preparato in parte: che se avesse <lb></lb>l&#039;Autore avuto il tempo di renderlo compiuto, e il Torricelli se ne fosse tro­<lb></lb>vato in mano il disteso, non avrebbe dubitato, secondo che necessariamente <lb></lb>portava l&#039;ordine logico, d&#039;anteporlo al trattato delle proporzioni, al quale <lb></lb>avrebbe perciò scritto in fronte <emph type="italics"></emph>Giornata sesta del Galileo.<emph.end type="italics"></emph.end> Il fine e la ne­<lb></lb>cessità di queste osservazioni, che potrebbero qui ai lettori sembrar fuor di <pb xlink:href="020/01/2474.jpg" pagenum="99"></pb>proposito, si comprenderà meglio, quando in quest&#039;altro capitolo si proverà <lb></lb>di fatto che quel dialogo della percossa, di cui il Torricelli diceva di non saper <lb></lb>niente, era già cominciato, e quasi condotto a mezzo, prima ch&#039;egli venisse <lb></lb>ospite in Arcetri; e quando diremo come tra i manoscritti galileiani fosse <lb></lb>ritrovato esso Dialogo, e fosse aggiunto dagli editori delle opere agli altri <lb></lb>cinque delle due Scienze nuove. </s>

<s>Intanto riprendiamo il filo di questa storia. </s></p><p type="main">

<s>La copia, che il Torricelli consegnò al principe Leopoldo, rimase ma­<lb></lb>noscritta infino al 1674, quando il Viviani pensò di pubblicarla dopo quel <lb></lb>trattato, che ne volle scrivere per i <emph type="italics"></emph>nobili geometri principianti<emph.end type="italics"></emph.end> col titolo: <lb></lb><emph type="italics"></emph>Quinto libro degli Elementi di Euclide, ovvero Scienza universale delle <lb></lb>proporzioni.<emph.end type="italics"></emph.end> Ivi dice come venticinque anni fa, col permesso di Sua Altezza, <lb></lb>ne avesse dal detto autografo preso copia, e come nell&#039;atto del darla alle <lb></lb>stampe l&#039;avesse voluta diligentemente riscontrar sopra la bozza originale che, <lb></lb>insiem con gli altri manoscritti torricelliani, si trovava allora nelle mani di <lb></lb>Lodovico Serenai. </s>

<s>“ Ed avendola, soggiunge il Viviani stesso, ritrovata verso <lb></lb>il fine con qualche cosa di più, aggiuntavi com&#039;io credo dal Torricelli, non <lb></lb>ho voluto mancare di unirla a questa quinta Giornata, come si vedrà, in ca­<lb></lb>rattere corsivo, e quale, dopo un diligente riscontro del rimanente, mi ha <lb></lb>dettato il medesimo signor Lodovico ” (Ediz. </s>

<s>cit., pag. </s>

<s>60). Il Serenai infatti <lb></lb>che, non contento di ritrar quella prima bozza, per dir così, in <emph type="italics"></emph>fac simile,<emph.end type="italics"></emph.end><lb></lb>aveva preso altresì, col permesso del principe Leopoldo, copia del dialogo dal <lb></lb>Torricelli stesso messo a pulito; notava così sopra la prima carta, dop&#039;avervi <lb></lb>scritto il titolo: “ Ma in questa copia, oltre all&#039;esser diversa dal manoscritto <lb></lb>di esso Torricelli in molte parole di poco momento, ci mancano verso il fine, <lb></lb>a c. </s>

<s>20, circa due facce, che si leggono in detto manoscritto, e nell&#039;altra <lb></lb>copia, che ne ho fatta io ” (MSS. Gal., P. V, T. V, fol. </s>

<s>39). </s></p><p type="main">

<s>Che manchino le due facce, supplite dal Viviani e dagli altri editori in <lb></lb>carattere corsivo, è un fatto: ma non si rende chiara la ragione di tal man­<lb></lb>canza da ciò, che diceva dianzi lo stesso Viviani essere state aggiunte quelle <lb></lb>cose dal Torricelli. </s>

<s>Nella bozza originale è tutto scritto andantemente. </s>

<s>senza <lb></lb>segno alcuno di un&#039;aggiunta posteriore, e si vedono, anche per queste pagine, <lb></lb>ricorrere le solite correzioni, fatte alla presenza di Galileo, che dunque ebbe <lb></lb>approvato qui come nel resto. </s></p><p type="main">

<s>Ciò però non vorrebbe dire che non fosse propria del Torricelli l&#039;inven­<lb></lb>zione di que&#039;teoremi, con i quali concorreva a sublimare l&#039;umile scienza ga­<lb></lb>lileiana delle proporzioni. </s>

<s>I teoremi si riducono a due e noi gli vogliamo <lb></lb>ordinatamente proporre alla considerazione dei nostri Lettori, perchè, ricono­<lb></lb>scendone da loro medesimi la superiorità, confrontati con gli altri tutti ele­<lb></lb>mentarissimi nei discorsi del Sagredo e del Salviati, si venga a confermare <lb></lb>e a dichiarar meglio quel che il Viviani credeva: essere cioè quegli stessi <lb></lb>teoremi aggiunti dal Torricelli, benchè Galileo, sentendoseli leggere in mezzo <lb></lb>agli altri, si chiamasse contento e beato di lasciarli uscir fuori sotto il suo nome. </s></p><p type="main">

<s>TEOREMA I. — “ Se fra queste grandezze A e B s&#039;immaginerà che sia <lb></lb>frapposta, non una grandezza sola, ma più d&#039;una, come si vede in questi <pb xlink:href="020/01/2475.jpg" pagenum="100"></pb>segni A, C, D, B; s&#039;intenderà pure la proporzione della A alla B esser com­<lb></lb>posta di tutte le proporzioni, le quali sono intermedie fra di esse: cioè delle <lb></lb>proporzioni, che hanno la A alla C, la C alla D, e la D alla B. </s>

<s>E così, se <lb></lb>più fossero le grandezze, sempre la prima all&#039;ultima ha proporzion compo­<lb></lb>sta di tutte quelle proporzioni, le quali mediano fra di esse ” (Viviani, Scienza <lb></lb>delle prop. </s>

<s>cit., pag. </s>

<s>75). </s></p><p type="main">

<s>Il teorema è reso generale per l&#039;induzione dai casi particolari, come si <lb></lb>faceva allora in Italia, dove non s&#039;era introdotta l&#039;Aigebra cartesiana. </s>

<s>Aven­<lb></lb>dosi infatti A:C=C:B, avremo anche A:B=A.C:B.C, che resulta dal <lb></lb>moltiplicare per C la seconda ragione dell&#039;identica A:B=A:B. </s>

<s>Come pure, <lb></lb>avendosi A:C=C:D=D:B, avremo altresì A:B=A.C.D:H.C.D <lb></lb>resultante dal moltiplicar per C. </s>

<s>D la seconda ragione della detta identica <lb></lb>A:B=A:B. </s>

<s>La costanza della regola, in tutti gli altri esempi per qua­<lb></lb>lunque numero di quantità intermedie, dava logico diritto al Matematico di <lb></lb>creder la proposizione, come fa qui il Torricelli, e di pronunziarla vera in <lb></lb>universale. </s></p><p type="main">

<s>TEOREMA II. — “ Quando le proporzioni componenti sieno uguali fra di <lb></lb>loro, o per dir meglio sieno le stesse; allora la prima all&#039;ultima avrà, come <lb></lb>di sopra abbiamo detto, una tal proporzione composta di tutte le proporzioni <lb></lb>intermedie. </s>

<s>Ma perchè quelle proporzioni intermedie sono tutte uguali, po­<lb></lb>tremo esprimere il medesimo nostro senso con dire che la proporzione della <lb></lb>prima all&#039;ultima ha una proporzione tanto molteplice della proporzione, che <lb></lb>ha la prima alla seconda, quante per appunto saranno le proporzioni, che si <lb></lb>frappongono fra la prima e l&#039;ultima ” (ivi). </s></p><p type="main">

<s>Anche questo bel teorema, nuovo affatto, come l&#039;altro da cui deriva, <lb></lb>nella scienza delle proporzioni, si concludeva per induzione dai vari casi par­<lb></lb>ticolari. </s>

<s>“ Così per esempio, soggiunge, per dar ragione dimostrativa della <lb></lb>pronunziata verità, il Torricelli, se fossero tre termini, e che la medesima <lb></lb>proporzione fosse fra la prima e la seconda, che è fra la seconda e la terza; <lb></lb>allora sarebbe vero che la prima alla terza avrebbe proporzione composta <lb></lb>delle due proporzioni, le quali sono fra la prima e la seconda, e fra la se­<lb></lb>conda e la terza. </s>

<s>Ma perchè queste due proporzioni si suppongono uguali, <lb></lb>cioè le stesse, potrà dirsi che la proporzione della prima alla terza è dupli­<lb></lb>cata della proporzione, che ha la prima alla seconda ” (ivi). </s></p><p type="main">

<s>Data essendo infatti A:B=B:C, se si moltiplica per A la seconda <lb></lb>ragione dell&#039;identica A:C=A:C, avremo A:C=A2:AC. </s>

<s>Ma A. C, per <lb></lb>la data, è uguale a B2; dunque A:C=A2:B2. </s>

<s>Similmente, essendo quat­<lb></lb>tro i termini nelle proporzioni continue A:B=B:C=C:D, se per A2 si <lb></lb>moltiplicherà la seconda ragione dell&#039;identica A:D=A:D, avremo A:D= <lb></lb>A3:A2.D. </s>

<s>Ma per la data A.D=B.C, ossia A2.D=A.B.C, e per <lb></lb>essere A.C=B2 è A.C.B=B3; dunque A:D=A3:B3, per cui si po­<lb></lb>trebbe dire col Torricelli “ che la proporzione della prima alla quarta è com­<lb></lb>posta di quelle tre proporzioni intermedie, ed ancora che è triplicata della <lb></lb>proporzione della prima alla seconda ” (ivi, pag. </s>

<s>75, 76). </s></p><pb xlink:href="020/01/2476.jpg" pagenum="101"></pb><p type="main">

<s>Or essendo, dall&#039;esame di questi teoremi, confermata anche meglio l&#039;opi­<lb></lb>nion del Viviani, che cioè si fossero aggiunti, nello stender le bozze del Dia­<lb></lb>logo, dal Torricelli, per arricchirne la Scienza galileiana delle proporzioni; <lb></lb>consideriamo quel che dovette naturalmente avvenire nel ridurre, dopo la <lb></lb>morte di Galileo, quella stessa bozza a pulito, per consegnarla nelle mani del <lb></lb>principe Leopoldo. </s>

<s>Chiunque trascrive trova sempre qualche cosa da correg­<lb></lb>gere, nella scelta delle parole e nel disporle, per maggior chiarezza e armo­<lb></lb>nia, con qualche varietà negl&#039;incisi, di che il periodo s&#039;intesse. </s>

<s>Di qui nacquero <lb></lb>quelle diversità in molte parole, che diceva di aver notate il Serenai nel ri­<lb></lb>scontrar la copia con la bozza originale, soggiungendo però ch&#039;eran cose di <lb></lb>poco momento. </s>

<s>Venuto poi il Torricelli stesso al punto, dove nella terza parte <lb></lb>del Dialogo si tratta delle proporzioni composte, e dov&#039;egli aveva aggiunto <lb></lb>que&#039;suoi due teoremi, ripensando forse che Galileo era tanto ricco, da non <lb></lb>aver bisogno della roba altrni, deliberò di ritenerseli per sè, saltando nel co­<lb></lb>piare quel che prima con tanta liberalità ci aveva messo. </s>

<s>Ed ecco rivelata la <lb></lb>causa del mancar verso il fine, nella copia a pulito fatta per il principe Leo­<lb></lb>poldo, quelle due facce, che il Serenai e il Viviani avevano riscontrate nel­<lb></lb>l&#039;originale torricelliano. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La deliberazione di serbar per sè i teoremi aggiunti nel dialogo, dovette <lb></lb>esser presa dal Torricelli, quand&#039;ebbe a ripensare che Galileo, con tutto quel <lb></lb>suo discorso, non aveva fatt&#039;altro che dimostrare come il quinto libro, e <lb></lb>molte altre parti degli Elementi di Euclide, avevano bisogno di una riforma. </s>

<s><lb></lb>La riforma però non era fatta, perchè non bastava l&#039;avere osservato che la <lb></lb>regola degli egualmente moltiplici era insufficiente ad assicurarci della pro­<lb></lb>porzionalità, che passa fra quattro grandezze, ma conveniva di più insegnare <lb></lb>per quale altra via si potesse il Geometra condurre a quelle medesime con­<lb></lb>clusioni. </s>

<s>Perciocchè nessuno dubitava della verità dei Teoremi euclidei, ma <lb></lb>de&#039;termini di mezzo che s&#039;invocavano dall&#039;Autore per dimostrarli. </s></p><p type="main">

<s>Quand&#039;anche, ripensava tra sè il Torricelli, si pubblicasse questo dia­<lb></lb>logo, ch&#039;io ho qui disteso in aggiunta agli altri delle due Scienze nuove, <lb></lb>quale utilità ne potrebbero ricavare i giovani studenti della Geometria e della <lb></lb>Meccanica? </s>

<s>Null&#039;altra, dalla certezza in fuori che le prime proposizioni dei <lb></lb>moti equabili, nel terzo dialogo galileiano, e tutte le proporzionalità, che in­<lb></lb>tercedono fra linee e linee, fra superfice e linee, fra angoli e archi sottesi, <lb></lb>nei vari libri euclidei, son verità che tuttavia rimangono a dimostrarsi. </s>

<s>È <lb></lb>dunque incominciata un&#039;opera da Galileo che, per benetizio universale della <lb></lb>Scienza matematica, vuol essere compiuta: d&#039;onde, così discorrendo, venne <lb></lb>a formarsi nell&#039;animo dello stesso Torricelli il proposito di scrivere un trat­<lb></lb>tato delle proporzioni, in cui forse troverebbero luogo i due teoremi inseriti <pb xlink:href="020/01/2477.jpg" pagenum="102"></pb>nel quinto Dialogo galileiano, e in ogni modo s&#039;insegnerebbe come dimo­<lb></lb>strare altrimenti, senza gli equimolteplici, le proporzionalità geometriche, e <lb></lb>le meccaniche concernenti i moti uniformi. </s></p><p type="main">

<s>Fu il proposito mandato ad effetto in un opuscolo latino, che corse lungo <lb></lb>tempo per le mani degli amici, col titolo <emph type="italics"></emph>De proportionibus,<emph.end type="italics"></emph.end> e che servì di <lb></lb>testo nelle scuole di Geometria, per supplire al quinto, e al sesto libro degli <lb></lb>Elementi di Euclide. </s>

<s>“ L&#039;appendice al mio libretto delle proporzioni, scri­<lb></lb>veva il Torricelli il dì 24 Agosto 1647 al Ricci, è già messo al pulito. </s>

<s>Il <lb></lb>proemio mi riesce lunghissimo, particolarmente in riguardo all&#039;opera, ma è <lb></lb>pur necessario diffondersi per mostrare l&#039;insufficienza e difetto del V libro <lb></lb>di Euclide ” (MSS. Gal. </s>

<s>Disc., T. XV, fol. </s>

<s>115). Non fu mai stampato quel­<lb></lb>l&#039;opuscolo vivente l&#039;Autore, e benchè il Serenai sollecitasse tante volte e in <lb></lb>vari modi il Viviani, perchè lo pubblicasse insieme con le altre opere postume <lb></lb>del comune Amico; si rimase nella sua bozza, e nella sua copia a pulito au­<lb></lb>tografa, e si riman tuttavia nel tomo XXVI dei Discepoli di Galileo. </s>

<s>Ivi può <lb></lb>ritrovarlo intero chi vuole, o ne&#039;detti originali o nella nitid<gap></gap>sima e diligen­<lb></lb>tissima copia, che ne fece il medesimo Serenai: e perchè è documento im­<lb></lb>portantissimo, non solo della Storia della Geometria, ma e della Meccanica, <lb></lb>ritrovandovisi la prima vera logica dimostrazione della proporzionalità fra gli <lb></lb>spazi e i tempi nei moti uniformi, che in realtà manca negli antichi teoremi <lb></lb>di Archimede, e ne&#039;nuovi che Galileo ritrasse da lui; non dispiacerà ai no­<lb></lb>stri Lettori di veder qui in poche parole il riassunto della torricelliana ri­<lb></lb>forma della Scienza delle proporzioni, e delle applicazioni di lei alla Meccanica. </s></p><p type="main">

<s>Il trattato <emph type="italics"></emph>De proportionibus<emph.end type="italics"></emph.end> si divide in due parti, la prima delle quali <lb></lb>è un proemio, dove si trattien l&#039;Autore in assai lungo discorso col lettore <lb></lb>amico intorno alle geometriche definizioni. </s>

<s>Ragionando come il Nardi, e come <lb></lb>il Cavalieri, osserva la fallacia, che s&#039;asconde nel definito in quinto luogo, <lb></lb>innanzi al suo quinto libro, da Euclide, e con queste parole termina la prima <lb></lb>parte del suo discorso: “ Tandem, ut ad conclusionem accedam, pari facili­<lb></lb>tate dubitabo magnitudines non esse proportionales, licet earum aequimulti­<lb></lb>plicia imperatam concordiam constantissime servent; et esse proportionales, <lb></lb>licet ab eadem concordia aliquando recedant ” (fol. </s>

<s>56 ad t.). </s></p><p type="main">

<s>Notate le difficoltà, che s&#039;incontrano nell&#039;intendere le definizioni di Eu­<lb></lb>clide, prevede che qualche cosa di simile potrebbe alcuno ritrovar nelle sue, <lb></lb>da che s&#039;espedisce con l&#039;osservare la gran differenza che è tra l&#039;altrui me­<lb></lb>todo antico o il suo proprio nuovo. </s>

<s>“ Euclides, suppositis difficillimis prin­<lb></lb>cipiis, faciliora quaeque demonstravit: ego contra, praemissis facilioribus, no­<lb></lb>tioribusque principiis, difficillima quaeque demonstrare conatus sum ” (ibid.). </s></p><p type="main">

<s>Se l&#039;effetto l&#039;abbia poi conseguito lo lasciò il Torricelli giudicare ai <lb></lb>Lettori, passando all&#039;altra parte del trattato, o, per più propriamente dire, al <lb></lb>trattato delle proporzionali, a cui si premettono otto definizioni, e sei tra <lb></lb>supposizioni e assiomi. </s>

<s>Le prime proposizioni poi, che ricorrono a dimostrarsi, <lb></lb>son le cinque seguenti, delle quali ci contentèremo di trascrivere il semplice <lb></lb>enunciato: </s></p><pb xlink:href="020/01/2478.jpg" pagenum="103"></pb><p type="main">

<s>“ PROPOSITIO I. — Propositis duabus magnitudinibus, inaequalibus et <lb></lb>eiusdem generis, quarum una sit maior, altera vero minor; si ex maiore au­<lb></lb>feratur dimidium, et rursus ab ea quae remanet dimidium detrahatur, atque <lb></lb>iterum ex reliqua dimidium, et hoc fiat semper; relinquetur tandem quae­<lb></lb>dam magnitudo, quae minor erit proposita minori magnitudine. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO II. — Si fuerit quodcumque triangulum, cuius basis secta <lb></lb>sit in quotcumque partes inter se aequales, et ex vertice trianguli ad puncta <lb></lb>singula divisionum basis ducantur rectae lineae; erit totum triangulum di­<lb></lb>visum in triangula inter se aequalia, quod constat ex propos. </s>

<s>XXXVIII primi <lb></lb>libri: dico quamlibet summam horum triangulorum, ad reliquam, esse ut <lb></lb>basis ad basim. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO III. — Triangula eiusdem altitudinis eamdem habent ra­<lb></lb>tionem quam bases. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO IV. — Si in quocumque triangulo fuerit quaedam recta <lb></lb>parallela ad unum latus, haec parallela proportionaliter secabit ipsius trian­<lb></lb>guli latera. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO V. — Si in quocumque triangulo ABC (fig. </s>

<s>36) angulus <lb></lb>quilibet ABC bifariam secetur a recta BD, dico etiam basim AC in ratione <lb></lb><figure id="id.020.01.2478.1.jpg" xlink:href="020/01/2478/1.jpg"></figure></s></p><p type="caption">

<s>Figura 36.<lb></lb>laterum sectam esse: hoc est segmentum AD, ad <lb></lb>segmentum DC, eamdem habere rationem, quam <lb></lb>habet latus AB ad BC ” (ibid., fol. </s>

<s>61-65). </s></p><p type="main">

<s>Le altre cinque proposizioni, che si soggiungono, <lb></lb>attendono a dimostrare col medesimo metodo, indi­<lb></lb>pendentemente cioè dagli equimolteplici, che, essendo <lb></lb>date quattro linee in proporzione, convertendo, com­<lb></lb>ponendo, dividendo e permutando, rimangono pro­<lb></lb>porzionali: e finalmente che di due uguaglianze i <lb></lb>membri, comunque composti, presi nel medesimo <lb></lb>ordine, stanno fra loro in una medesima proporzione. </s></p><p type="main">

<s>“ PROPOSITIO VI. — Si quatuor magnitudines proportionales fuerint, et <lb></lb>convertendo proportionales erunt. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO VII. — Si divisae magnitudines proportionales fuerint, et <lb></lb>componendo proportionales erunt. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO VIII. — Si compositae magnitudines proportionales fuerint, <lb></lb>et dividendo proportionales erunt. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO IX. — Si quatuor magnitudines proportionales fuerint, et <lb></lb>permutando proportionales erunt. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO X. — Si fuerint quotcumque magnitudines, et aliae ipsis <lb></lb>aequales numero, quae binae in eadem ratione sumantur, et ex aequo in <lb></lb>eadem ratione erunt ” (ibid., fol. </s>

<s>61-68). </s></p><p type="main">

<s>Benchè siano le cinque precedenti proposizioni annunziate generalmente, <lb></lb>non si dimostrano dall&#039;Autore però che secondo un determinato genere di <lb></lb>quantità, fra le quali i metodi antichi portavano a sceglier le linee. </s>

<s>Così <lb></lb>però, benchè fossero esse linee assai meno determinabili dei numeri, non si <pb xlink:href="020/01/2479.jpg" pagenum="104"></pb>veniva a dare alle proposizioni quella generalità, che ricevono in sè col far <lb></lb>uso dei simboli algebrici, per cui fu costretto il Torricelli a soggiungere, alle <lb></lb>dimostrate, nuove proposizioni <emph type="italics"></emph>ut eas demonstremus universaliter veras esse, <lb></lb>etiam in omni genere quantitatis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ PROPOSITIO XI. — Si fuerint tres magnitudines, aliaeque ipsis acqua­<lb></lb>les numero, quae binae in eadem ratione sumantur, fuerit autem perturbata <lb></lb>earum proportio ex aequalitate, in eadem ratione erunt. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO XII. — Si compositae magnitudines proportionales fuerint, <lb></lb>et per conversionem rationis proportionales erunt. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO XIII. — Si fuerint ut totum ad totum, ita ablatum ad <lb></lb>ablatum, et reliqum ad reliqum erit ut erat totum ad totum. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO XIV. — Partes cum pariter multiplicibus in eadem sunt <lb></lb>ratione, si, prout sibi mutuo respondent, ita sumantur. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO XV. — Si sint magnitudines quotcumque proportionales, <lb></lb>quemadmodum se habuerit una antecedentium ad unam consequentium; ita <lb></lb>se habebunt omnes simul antecedentes ad omnes consequentes simul. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO XVI. — Eadem, ad minorem, maiorem habent rationem, <lb></lb>quam ad maiorem. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO XVII. — Si prima ad secundam eamdem habeat rationem <lb></lb>quam tertia ad quartam, habuerit autem et quinta ad secundam eamdem <lb></lb>rationem, quam sexta ad quintam; etiam composita prima cum secunda, ad <lb></lb>secundam, eamdem habebit rationem, quam tertia cum sexta ad quartam. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO XVIII. — Si quatuor magnitudines eiusdem generis pro­<lb></lb>portionales fuerint, maxima et minima reliquis duabus maiores erunt ” (ibid., <lb></lb>fol. </s>

<s>69-76). </s></p><p type="main">

<s>Qui, scrive il Torricelli dop&#039;aver dimostrata quest&#039;ultima proposizione, <lb></lb>faremo fine al trattatello delle proporzioni, in cui troveranno gli studiosi rac­<lb></lb>colto tutto quel che Euclide insegna nel suo quinto libro. </s>

<s>Benchè il numero <lb></lb>delle proposizioni euclidec ascenda a XXXIII o XXXIV, è però da osservare <lb></lb>che non son tutte quelle propriamente dell&#039;antico Autore, ma ve ne furono <lb></lb>parecchie aggiunte da chi lo commentò e lo tradusse, e perciò si possono <lb></lb>tralasciare, com&#039;abbiam fatto noi, che scriviamo per i giovani principianti. </s>

<s><lb></lb>Nonostante, prosegue a dire il Torricelli, perchè abbiamo introdotto gli stu­<lb></lb>diosi all&#039;intelligenza di alcune parti delle primc proposizioni del sesto libro, <lb></lb>vogliamo compir l&#039;opra, dimostrandole, col solito nostro metodo, intere “ ut <lb></lb>is, qui saltem libare contendit Geometriam, a sexto ipso Euclidis se citius <lb></lb>queat expediri, omissis videlicet omnino tribus primis propositionibus, iam sibi <lb></lb>notis. </s>

<s>” </s></p><p type="main">

<s>Nella prima infatti di quelle proposizioni dice Euclide che i triangoli e <lb></lb>i parallelogrammi, aventi la medesima altezza, stanno fra loro come le basi, <lb></lb>mentre nella terza torricelliana non si dimostra questa proprietà che rispetto <lb></lb>ai triangoli. </s>

<s>L&#039;Autore greco, per provare la detta proporzionalità nell&#039;une e <lb></lb>nelle altre figure, si serve degli ugualmente molteplici, e il Nostro, come <lb></lb>aveva senz&#039;essi già conclusa l&#039;annunziata proprietà nei triangoli. </s>

<s>così lo fa <pb xlink:href="020/01/2480.jpg" pagenum="105"></pb>nel seguente modo nei parrallelogrammi, applicandovi la proposizione XIV: <lb></lb>che cioè le semplici parti stanno in proporzione co&#039;multipli, i quali secondo <lb></lb>le loro mutue corrispondenze sian presi. </s></p><p type="main">

<s>Abbiansi i due parallelogrammi AC, DF (figure 37, 38) con le altezze <lb></lb>uguali: essi staranno come le basi. </s>

<s>La dimostrazione, che s&#039;avvolge in Eu­<lb></lb><figure id="id.020.01.2480.1.jpg" xlink:href="020/01/2480/1.jpg"></figure></s></p><p type="caption">

<s>Figura 37.<lb></lb><figure id="id.020.01.2480.2.jpg" xlink:href="020/01/2480/2.jpg"></figure></s></p><p type="caption">

<s>Figura 38.<lb></lb>clide per discorso lun­<lb></lb>go e inconcludente, è <lb></lb>dal Torricelli ridotta <lb></lb>alla sua massima fa­<lb></lb>cilità e speditezza. </s>

<s>Im­<lb></lb>perocchè, tirate le dia­<lb></lb>gonali GB, HE, i ret­<lb></lb>tangoli son doppi dei triangoli inscritti, e perciò, per la XIV, proporzionali. </s>

<s>Ma <lb></lb>i triangoli, per la III, stanno come le basi; dunque anche i rettangoli. </s>

<s>“ Sint <lb></lb>parallogramma AC, DF in eadem altitudine: dico esse parallelogrammum AC <lb></lb>ad DF ut basis AB, ad basim DE. </s>

<s>Ductis enim diametris BG, EH, dividen­<lb></lb>tur ab ipsis bifariam utraque parallelogramma, eruntque triangula AGB, DHE <lb></lb>pariter multiplicia, cum sint dupla. </s>

<s>Et erit, per XIV huius, parallelogrammum <lb></lb>AC ad triangulum AGB, ut parallelogrammum DF ad triangulum DHE. </s>

<s>Et <lb></lb>permutando parallelogrammum AC, ad parallelogrammum DF, ut triangu­<lb></lb>lum AGB ad triangulum DHE. </s>

<s>Sed basis AB, ad basim DE, est per IIlam<lb></lb>huius ut triangulum AGB ad triangulum DHE; ergo etc. </s>

<s>” (ibid., fol. </s>

<s>149). </s></p><p type="main">

<s>La seconda degli antichi Elementi è nella sua totalità dimostrata dalla <lb></lb>quinta del nuovo trattato, ma la terza di là non è nella quinta di qui dimo­<lb></lb>strata altro che per la sua prima parte, rimanendo tuttavia a dimostrarsi, <lb></lb>per renderla secondo Euclide compiuta, che se le parti della base abbiano la <lb></lb>medesima proporzione che gli altri lati del triangolo, la linea retta, che dalla <lb></lb>cima si tira sino al segamento della base, segherà l&#039;angolo per mezzo. </s>

<s>Ciò <lb></lb>si soggiunge appunto dal Torricelli nel suo trattato, scansando gli equimol­<lb></lb>teplici, come pure, scansando gli equimolteplici, si dimostra l&#039;ultima posta <lb></lb>da Euclide in questo sesto libro, che cioè gli angoli inscritti nel medesimo <lb></lb>cerchio son proporzionali agli archi compresi. </s></p><p type="main">

<s>Così veniva finalmente operata, negli antichi insegnamenti geometrici, <lb></lb>quella riforma, non troppo felicemente iniziata dal Benedetti, e solamente <lb></lb>proposta dal Nardi e da Galileo, o come converrebbe per giustizia dire <lb></lb>dal Cavalieri. </s>

<s>Ma l&#039;intenzione del Torricelli non era quella sola, come av­<lb></lb>vertimmo, di emendare la Geometria, ma altresì la Meccanica, i primi e <lb></lb>principali teoremi della quale, benchè verissimi, si rimanevano nel libro <lb></lb>delle Spirali e nel terzo dialogo delle Scienze nuove indimostrati. </s>

<s>La prima <lb></lb>legittima dimostrazione dunque che se ne avesse, è quale ora noi la diamo <lb></lb>alla pubbiica luce, come importantissimo documento nella storia della Scienza <lb></lb>del moto: </s></p><p type="main">

<s>“ Si punctum aliquod, aequabili semper velocitate, super aliqua recta <lb></lb>linea AB (fig. </s>

<s>39) feratur, duasque ipsius portiones AC, CB permeaverit; dico <pb xlink:href="020/01/2481.jpg" pagenum="106"></pb>portionem AC ad CB eamdem habere rationem, quam habent tempora ipsa, <lb></lb>quibus punctum portiones permeavit. </s>

<s>” </s></p><p type="main">

<s>“ Ponantur DE, EF tempora, quibus punctum permeavit rectas AC, CB: <lb></lb><figure id="id.020.01.2481.1.jpg" xlink:href="020/01/2481/1.jpg"></figure></s></p><p type="caption">

<s>Figura 39.<lb></lb>nempe DE supponatur tempus rectae <lb></lb>AC: ipsum vero EF tempus rectae <lb></lb>CB. </s>

<s>Ostendendum est rectam AC, <lb></lb>ad rectam CB, esse ut tempus DE <lb></lb>ad tempus EF. ” </s></p><p type="main">

<s>“ Nisi enim sit ita, coucipia­<lb></lb>mus, si possibile est, ut tempus DE ad EF, ita esse aliquam aliam lineam <lb></lb>IC ad eamdem CB: et erit omnino ipsa IC vel minor vel maior quam AC. ” </s></p><p type="main">

<s>“ Sit primum IC minor quam AC. </s>

<s>Secetur CB bifariam, atque iterum <lb></lb>bifariam, et hoc fiat sempen, donec remaneat quaedam CG minor quam AI: <lb></lb>dividaturque tota CB in partes aequales ipsi CG, quae quidem tota absume­<lb></lb>tur praecise. </s>

<s>Item distribuatur et ipsa CA in partes aequales eidem CG, ini­<lb></lb>tio facto ex C, et continuata divisione quousque fieri poterit. </s>

<s>Certum est ali­<lb></lb>quam divisionem casuram esse inter puncta A et I, quandoquidem recta CG <lb></lb>metiens minor facta est quam AI. </s>

<s>Cadat itaque inter A et I divisio L, et <lb></lb>quoniam rectae AC tempus est ipsum DE, erit rectae LC, quae minor est, <lb></lb>tempus minus quam DE. </s>

<s>Esto igitur rectae LC tempus OE: tunc secetur <lb></lb>tempus OE in totidem partes aequales, in quot aequales partes divisa est <lb></lb>recta CB, eruntque singulae partes temporis OE tempora singularum partium <lb></lb>aequalium rectae LC. </s>

<s>Idemque dictum sit de partibus temporis EF, et rectae <lb></lb>CB. </s>

<s>Cum autem omnes partes rectarum LC, CB omnifariam sumptae inter <lb></lb>se aequales sint, per constructionem, erunt etiam omnes partes temporum <lb></lb>OE, EF, inter se aequales, ob suppositionem, aequalis semper velocitatis, sive <lb></lb>motus aequabilis. </s>

<s>” </s></p><p type="main">

<s>“ Jam recta LC ad CB non est ut recta minor IC ad eamdem CB, sed <lb></lb>ipsa LC maior est, quam esse oporteret. </s>

<s>Ut autem recta LC ad CB, ita tem­<lb></lb>pus OE ad EF, quod infertur ex prima et sexta suppositione huius. </s>

<s>Ergo <lb></lb>etiam tempus OE maior est, quam esse oporteret. </s>

<s>Quamobrem tempus DE <lb></lb>multo maius est quam esse deberot ut ad EF eamdem habeat rationem, quam <lb></lb>habet recta IC ad CB, quod est contra suppositum ” (ibid., fol. </s>

<s>116-17). </s></p><p type="main">

<s>Che se IC si dica dover esser maggiore di AC, e allora dimostra il <lb></lb>Torricelli, con un ragionamento simile al precedente, che CB è troppo più <lb></lb>grande di quel che non dovrebb&#039;essere, perch&#039;ella possa aver con l&#039;antece­<lb></lb>dente stessa IC la ragion medesima, che ha il tempo DE al tempo EF, ciò <lb></lb>che pure è contrario alla fatta supposizione. </s>

<s>“ Patet ergo quod recta AC ad <lb></lb>CB est ut tempus DE ad EF, quandoquidem demonstravimus quam rationem <lb></lb>habet tempus DE ad EF, eamdem nullam aliam lineam, praeter AC, posse <lb></lb>habere ad CB, quod erat propositum ” (ibid.). </s></p><p type="main">

<s>La dimostrazione, lo riconosce ben da sè il Torricelli e lo confessa, non <lb></lb>è di quella facilità nè di quella eleganza, che si sarebbe desiderata, ma non <lb></lb>si poteva aspettar di meglio in chi intendeva di trattar la scienza co&#039;metodi <pb xlink:href="020/01/2482.jpg" pagenum="107"></pb>antichi, tanto alieni dalla semplicità dei principii accennati di sopra, e dai <lb></lb>quali hanno derivato i moderni le medesime conclusioni. </s>

<s>La riforma in ogni <lb></lb>modo, dal Torricelli stesso introdotta nel dimostrar le ragioni proporzionali, <lb></lb>era di tanta importanza, da desiderarsi che fosse allora maggiormente dif­<lb></lb>fusa: eppure è un fatto che la conobbero solo quei pochi, i quali erano in­<lb></lb>tervenuti alle pubbliche lezioni dell&#039;Autore, o avevano potuto prender copia <lb></lb>del manoscritto di lui. </s>

<s>Il Viviani non si risolveva di pubblicarlo, come il Se­<lb></lb>renai glie ne faceva istanza, o fosse perch&#039;egli aspettava di dare alle stampe <lb></lb>tutte insieme le opere postume dell&#039;Amico, o fosse perch&#039;egli stesso atten­<lb></lb>deva a scrivere delle proporzioni un nuovo trattato. </s>

<s>Il fine, ch&#039;ebbe di so­<lb></lb>stituire questo stesso trattato al torricelliano, non par si possa attribuire ad <lb></lb>altro, che al desiderio di esaltare il suo proprio Maestro, vedendo che il Tor­<lb></lb>ricelli non faceva li nemmeno un motto del Galileo, suo precursore, e che <lb></lb>solamente lo rammemorava, a fin di dire com&#039;avesse, per seguitar gli esempi <lb></lb>di Archimede, lasciati i primi due teoremi dei moti uniformi senza logica <lb></lb>conclusione. </s></p><p type="main">

<s>Voleva dunque il Viviani fare apparire al mondo schiettamente galileiana <lb></lb>la nuova scienza geometrica, da sostituirsi al quinto libro di Euclide, e non <lb></lb>poteva dall&#039;altra parte negare che, se l&#039;impulso era venuto da Galileo, l&#039;ese­<lb></lb>cuzion dell&#039;opera era tutto merito del Torricelli. </s>

<s>Credette perciò di potersene <lb></lb>sdebitare con l&#039;inserire nel suo trattato alcune delle proposizioni di lui, e <lb></lb>perchè il manoscritto era affidato alla custodia del Serenai, a lui ne chiese <lb></lb>prima il permesso a voce, e poi nel seguente scritto, ch&#039;egli intendeva di <lb></lb>premettere alla stampa del libro: </s></p><p type="main">

<s>“ Rappresentai ier mattina a V. S. che, nell&#039;andare disponendo con qual­<lb></lb>che nuovo ordine il trattato delle proporzioni, spiegato co&#039;principii dimo­<lb></lb>strati dal gran Galileo mio maestro, con animo di stamparlo ora prontamente, <lb></lb>sì per meglio servirne un gentilissimo cavaliere mio padrone, che mi richiese <lb></lb>copia di quello, come per renderlo comune ancora ai giovani, che in questo <lb></lb>pubblico studio si vanno introducendo nella Geometria; trovavo che mi sa­<lb></lb>rebbe tornato molto in acconcio il valermi di due di quelle dimostrazioni, <lb></lb>che il nostro caro amico signor Evangelista Torricelli, d&#039;immortal nome e me­<lb></lb>moria, soleva spiegare nel medesimo Studio, tra le altre di quel suo libretto <lb></lb>delle proporzioni, che con le altre sue cose si stamperà, le quali sono la pro­<lb></lb>posizione X e XI di quell&#039;ordine. </s>

<s>” </s></p><p type="main">

<s>“ Soggiunsile che in fine di questo trattatello averei voluto anco aggiun­<lb></lb>gere due problemi, che sono l&#039;ottavo e il nono del sesto libro di Euclide, <lb></lb>risoluti dal medesimo Torricelli con una sola costruzione e dimostrazione, <lb></lb>con brevità maestosa, e propria di quel grand&#039;Uomo. </s>

<s>E con tutto che que­<lb></lb>sta proposizione, e le altre due sopraddette, siano ormai note a molti, sì per <lb></lb>mezzo dello stesso Autore, che andò insegnandole col detto suo libro delle <lb></lb>proporzioni, del quale si valeva in luogo del quinto di Euclide, dandone e <lb></lb>lasciandone pigliar copia liberamente; come ancora per mezzo mio, che spesso <lb></lb>come cose del signor Torricelli l&#039;ho conferite a chi m&#039;è paruto opportuno; <pb xlink:href="020/01/2483.jpg" pagenum="108"></pb>lo dissi che nondimeno io mi conoscevo in obbligo di non porle alle stampe, <lb></lb>senza la precedente licenza di V. S., la quale sola tra gli altri, a titolo di <lb></lb>vero amico e di fedeltà incomparabile, nell&#039;ultima malattia del Torricelli era <lb></lb>stata scelta da esso alla custodia, non solamente di queste, che di tutte le <lb></lb>altre scritture matematiche e geometriche rimastegli da pubblicare. </s>

<s>” </s></p><p type="main">

<s>“ Quanto fino a qui le significai in voce, tanto ho pensato poi, per mi­<lb></lb>glior governo di questo fatto, di replicarle nel presente foglio, che io le invio, <lb></lb>affinchè V. S. ancora in piè di questo si contenti, come particolarmente ne la <lb></lb>prego per mia maggior quiete e sodisfazione, di confermarmi di proprio scritto <lb></lb>quella medesima cortese facoltà, che subito ella si compiacque di darmi sopra <lb></lb>di ciò, assicurandola che, oltre al far noto come devo l&#039;Autore di tali tre <lb></lb>proposizioni, insieme con questa permissione di V. S. mi s&#039;aggiungerà que­<lb></lb>sto al gran numero dei favori, de&#039;quali ormai sono trent&#039;anni che io mi <lb></lb><gap></gap>rovo in possesso, ed intanto io mi ra<gap></gap>co al solito etc. </s>

<s>” (MSS. Gal, Disc., <lb></lb>T. LXVIII, fol. </s>

<s>12). </s></p><p type="main">

<s>Nel foglio, che segue in ordine a questo nel volume ora citato, il Vi­<lb></lb>viani stesso scrisse così di sua propria mano, mettendo a suo piacere in forma <lb></lb>la risposta o l&#039;approvazione del Serenai: “ Per quelle medesime ragioni, che <lb></lb>mi mossero ier mattina a darvi subito libera facoltà in voce di poter pub­<lb></lb>blicare ogni volta queste poche cose del nostro Amico: per le medesime torno <lb></lb>volentierissimo a concedervele, ancora adesso in scritto, come desiderate, di­<lb></lb>chiarandomi con questa che, non solo mi contento che nel disporre il trat­<lb></lb>tato delle proporzioni spiegate co&#039;principii dimostrati dal Galileo, e che vo­<lb></lb>lete pubblicare prontamente, voi inseriate quelle due proposizioni X e XI del <lb></lb>signor Evangelista Torricelli, che si trovano nel suo trattato latino manoscritto <lb></lb><emph type="italics"></emph>De proportionibus,<emph.end type="italics"></emph.end> con quell&#039;altre due unite in una proposizione, che io ho <lb></lb>poi trovata nel foglio originale da me segnato di sotto col n.° 13; ma vi <lb></lb>prego inoltre con istanza particolare a non tralasciare questa opportuna oc­<lb></lb>easione, perchè, volendo voi già darle fuori per di chi elle sono, venite a <lb></lb>cooperare all&#039;onore del comune Amico, gli ponete anticipatamente in sicuro <lb></lb>quello, che per essere ormai noto a tanti potrebbe trovare chi vi s&#039;affezio­<lb></lb>nasse come a cosa propria, ed insieme beneficate il prossimo, senza scapito <lb></lb>d&#039;aleuna delle Opere postume del medesimo Autore, che a Dio piacendo si <lb></lb>sono tra poco per veder fuori, nelle quali non sarà poi errore nessuno che <lb></lb>queste tre dimostrazioni si riveggano stampate di nuovo ai luoghi loro. </s>

<s>Di <lb></lb>tanto vi prego approvando, e contentandomi, e sottoscrivendomi di propria <lb></lb>mano.... ” (ivi, fol. </s>

<s>13). </s></p><p type="main">

<s>Invece di questa risposta però, messagli in bocca dal Viviani, il Sere­<lb></lb>nai scrisse di suo proprio sentimento quell&#039;altra lettera lunga, inserita da <lb></lb>pag. </s>

<s>117-21 nella prima edizione della Scienza universale delle proporzioni; <lb></lb>pregevole lettera, per le notizie che vi si leggono relative alla storia dei ma­<lb></lb>noscritti torricelliani. </s>

<s>Questa nuova forma di concessione sostituita a quella <lb></lb>ultimamente trascritta, non si trovava oramai più in corrispondenza con la <lb></lb>formale domanda che la precedeva, per cui, come cosa fuor di luogo sop-<pb xlink:href="020/01/2484.jpg" pagenum="109"></pb>pressa, pensò il Viviani di supplirvi con quelle avvertenze, stampate in ca­<lb></lb>rattere corsivo a pag. </s>

<s>114, 116 della citata edizione. </s>

<s>Del resto, benehè due, <lb></lb>la X e l&#039;XI, fossero le proposizioni, che voleva traspor nel suo dal trattato <lb></lb>torricelliano, si contentò poi di una sola, notando in margine a pag. </s>

<s>47 che <lb></lb>quella sua XIX era senza gli equimolteplici dimostrata <emph type="italics"></emph>secondo la proposi­<lb></lb>zione XI del trattato delle proporzioni del Torricelli.<emph.end type="italics"></emph.end> Non sapremmo poi <lb></lb>dire dove, e per quale occasione fosse scritta la seguente avvertenza al Let­<lb></lb>tore, che apparisce autografa nell&#039;estremo lembo dell&#039;ultimo foglio del citato <lb></lb>volume manoscritto: </s></p><p type="main">

<s>“ Fin dall&#039;anno 1674, e di nuovo nel 1690, fu stampato in Firenze il <lb></lb>quinto libro degli Elementi di Euclide con questo titolo: <emph type="italics"></emph>Scienza uni<gap></gap>crsale <lb></lb>delle proporzioni, spiegata con la dottrina del Galilco, con nuoro ordine <lb></lb>distesa dall&#039;ultimo suo discepolo, e dedicata all&#039;A. S.ma e R.ma del principe <lb></lb>cardinale Leopoldo de&#039;Medici, beneficientissimo mecenate dci Letterati.<emph.end type="italics"></emph.end> In <lb></lb>questo libro, in cui esso Discepolo, nel dare ordine alle proposizioni procura <lb></lb>di allontanarsi men che possibile fosse da quello del proprio autore Euclide, <lb></lb>seguitato e citato come primo maestro da que&#039;Ceometri, che scrissero dopo <lb></lb>di lui; fu in più luoghi allegato in margine un trattato simile delle propor­<lb></lb>zioni, composto, pochi anni avanti la sua morte, dal celebratissimo Evange­<lb></lb>lista Torricelli, che ne aveva lasciato prender copia a molti suoi uditori. </s>

<s>” </s></p><p type="main">

<s>Così fatte notizie però riguardano più presto la storia del libro, che <lb></lb>quella della scienza, dalla quale non si veniva per verità ad accreseer di molto <lb></lb>i meriti dell&#039;Autore, confessando egli stesso di avervi atteso in un tempo, in <lb></lb>cui si ritrovava, per gravi indisposizioni di testa, inabile a più ardue con­<lb></lb>templazioni. (Scienza delle proporz. </s>

<s>cit., pag. </s>

<s>VII). L&#039;opera è assai più ri­<lb></lb>stretta e più elementare di quella del Torricelli, alla quale, come si disse, fu <lb></lb>nonostante sostituita, per avere una nuova occasione di esaltare il nome di <lb></lb>Galileo. </s>

<s>Secondo quel che infatti egli insegna nel suo quinto Dialogo, s&#039;in­<lb></lb>comincia dal Viviani a dimostrare la quinta definizione di Euclide, dalla quale <lb></lb>si svolgono poi le altre proposizioni che, ordinate in un trattato nuovo, com­<lb></lb>ponevano quella, che portava già il titolo di <emph type="italics"></emph>Scienza universale delle pro­<lb></lb>porzioni.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Che fosse l&#039;opera del Viviani più ristretta di quella del Torricelli, si <lb></lb>dimostra dall&#039;essersi la detta scienza delle proporzioni trascurato ivi di appli­<lb></lb>carla alla Meccanica, che fu la prima e principale intenzione, per cui si fece <lb></lb>la riforma cuclidea. </s>

<s>Forse esso Viviani cansò di entrare nel geloso argomento, <lb></lb>perchè la legittima dimostrazione del primo teorema galileiano dei moti uni­<lb></lb>formi, che mancava affatto ai tempi del Torricelli, era stata ora ritrovata e <lb></lb>messa in pubblico nella proposizione LXXV <emph type="italics"></emph>De vi percussionis.<emph.end type="italics"></emph.end> lvi infatti il <lb></lb>Borelli, con metodi nuovi e che nulla affatto partecipavano di quelle difficoltà, <lb></lb>per espedirsi dalle quali tanto ebbe a faticare lo stesso Autore <emph type="italics"></emph>De propor­<lb></lb>tionibus;<emph.end type="italics"></emph.end> dimostra insomma così in poche parole che due corpi uguali, mo­<lb></lb>ventisi con uguali impulsi, passano uniformemente spazi proporzionali ai tempi. </s></p><p type="main">

<s>Siano nelle figure 37 e 38, qui noco addietro disegnate, que&#039;due corni <pb xlink:href="020/01/2485.jpg" pagenum="110"></pb>uguali A, D, che, con l&#039;eguaglianza degl&#039;impulsi ricevuti, passano per tutti <lb></lb>i punti delle linee AB, DE in istanti di tempo rappresentati dalle infinite <lb></lb>linee, fra sè tutte eguali, condotte da ciascuno di que&#039;punti parallele alle <lb></lb>AG, DH. </s>

<s>Dalla somma di così fatti istanti resulta il tempo del moto, il qual <lb></lb>tempo dunque è rappresentato dalla superficie dei due rettangoli GB, HE <emph type="italics"></emph>ex <lb></lb>methodo indivisibilium Cavalerii.<emph.end type="italics"></emph.end> Ma i rettangoli, aventi per supposizione <lb></lb>altezze uguali, stanno come le basi AB, DE, che son gli spazi passati dai <lb></lb>due mobili ne&#039;due vari tempi; dunque anche essi tempi stanno come gli <lb></lb>spazi. </s>

<s>Così il Borelli, promovendo la scienza, che il Lettore desiderava nel <lb></lb>suo primo entrare al terzo dialogo delle due Scienze nuove, tacitamente ve­<lb></lb>niva a insinuare che il più risoluto metodo di trattar le più sottili questioni <lb></lb>meccaniche non era quello antico di Galileo, benchè riformato, ma l&#039;altro <lb></lb>nuovo proposto dal Cavalieri. </s></p><pb xlink:href="020/01/2486.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del sesto dialogo aggiunto alle due Scienze nuove <lb></lb>ossia <lb></lb>Della forza della percossa<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Dei principii, da cui dipende la forza della percossa, proposti da Aristotile, dal Cardano e da Ga­<lb></lb>lileo; e come fossero dimostrati falsi. </s>

<s>— II. </s>

<s>Del ritrovamento e della pubblicazione del Sesto <lb></lb>dialogo galileiano; se ne esaminano brevemente le materie, e si conclude essere snch&#039;egli in­<lb></lb>formato dai medesimi falsi principii professati in gioventù dall&#039;Autore. </s>

<s>— III. </s>

<s>Della reintegra­<lb></lb>zione del Dialogo galileiano pubblicato dal Bonaventuri. </s>

<s>— IV. </s>

<s>Degli strumenti immaginati e <lb></lb>descritti per misurare la forza della percossa. </s>

<s>— V. </s>

<s>Della nnova scienza della percossa istituita, <lb></lb>prima da Giovan Marco Marci fra gli stranieri, e poi dal Borelli nella Scuola galileiana, e di <lb></lb>ciò che conferirono a promover la detta scienza gli Accademici di Londra e di Parigi. </s>

<s>— VI. </s>

<s>Delle <lb></lb>relazioni fra gli angoli dell&#039;incidenza e della riflessione, e fra i momenti delle percosse dirette <lb></lb>e delle oblique </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il dialogo delle proporzioni andò separato dalle altre scritture sue so­<lb></lb>relle, dal 1674 al 1718, anno in cui si fece in Firenze la nuova edizione <lb></lb>delle opere di Galileo, diretta da Tommaso Bonaventuri. </s>

<s>Alle prime quattro <lb></lb>giornate delle due Scienze nuove si vide anzi allora, non solo aggiuntavi <lb></lb>questa Quinta, trasposta dal trattato del Viviani, ma una Sesta altresì, la <lb></lb>quale non poteva non metter negli animi lo stupore, che si proverebbe a ve­<lb></lb>dere improvviso comparire in piazza una persona, che da tanto tempo cre­<lb></lb>devasi morta. </s>

<s>Quella sesta Giornata infatti s&#039;intitolava <emph type="italics"></emph>Della percossa,<emph.end type="italics"></emph.end> scrit­<lb></lb>tura che tutti lamentavano, o per non avere avuto Galileo il tempo di con­<lb></lb>durla alla sua perfezione, o per essere andata smarrita fra le carte di lui: <lb></lb>lamenti universali ultimamente raccolti insieme dal Borelli come fascicolo di <pb xlink:href="020/01/2487.jpg" pagenum="112"></pb>mirra, ch&#039;egli affisse alla soglia del suo libro <emph type="italics"></emph>De vi percussionis.<emph.end type="italics"></emph.end> La curio­<lb></lb>sità perciò della strana apparizione, e l&#039;importanza dell&#039;argomento, che ci <lb></lb>promette di venire a svelarci uno dei più astrusi misteri, in che siasi tenuta <lb></lb>chiusa la scienza del moto; concorrono ad indirizzare lungo questi sentieri <lb></lb>il discorso, che, per correre al suo termine più diretto e spedito, vuol rimon­<lb></lb>tare in su dove la Storia ha il principio. </s></p><p type="main">

<s>Non riuscirà cosa nuova, nè inaspettata aì nostri Lettori, se diciamo che <lb></lb>il priucipio di questa, come dell&#039;altra scienza del moto, è nelle Questioni <lb></lb>meccaniche di Aristotile, nella XIX delle quali si domanda perchè una scure <lb></lb>gravata da un gran peso e leggermente posata su un legno, lo incide ap­<lb></lb>pena, e lo spacca così facilmente a sollevare, e a percoter con la stessa sem­<lb></lb>plice scure, benchè ora posi tanto meno di dianzi, che quel gran carico la <lb></lb>premeva? </s>

<s>“ An quia, risponde, omnia cum motu tiunt, el grave ipsum gra­<lb></lb>vitatis magis assumit, motu dum movetur, quam dum quiescit? </s>

<s>” (Operum, <lb></lb>Tomus XI, Venetiis 1560, fol. </s>

<s>34). </s></p><p type="main">

<s>S&#039;introduce dunque dal Filosofo nella Meccanica il principio, che la ve­<lb></lb>locità nel mobile aumenta il peso: principio, che alcuni poi giudicarono falso, <lb></lb>specialmente argomentando dal fatto che la percossa producesi dal martello, <lb></lb>anche menato di sotto in su contro la gravità sua naturale. </s>

<s>Ciò però non <lb></lb>sembra che possa con buone ragioni contradire a Aristotile, il quesito del <lb></lb>quale non è intorno a ogni genere di percossa, ma a quella fatta particolar­<lb></lb>mente dalla scure, menata dai boscaioli contro un legno, che le soggiaccia <lb></lb>posato sul suolo. </s>

<s>Che se per gravità si voglia intender la mole, ossia la somma <lb></lb>delle particelle materiali, da cui si misura il peso di un corpo sulle braccia <lb></lb>di una bilancia; il discorso di Aristotile si riduce all&#039;espressioue di quell&#039;al­<lb></lb><gap></gap> più vero e più generale principio, che cioè la forza della percossa è il <lb></lb>prodotto della velocità per la massa. </s>

<s>La dottrina insomma, dal Filosofo pro­<lb></lb>fessata nelle Questioni meccaniche, piuttosto che falsa, si potrebbe dire non <lb></lb>bene e non chiaramente espressa, ciò che a fare si lasciava ai futuri com­<lb></lb>mentatori del testo. </s>

<s>I commenti però si videro apparire assai tardi, e intanto <lb></lb>i Matematici, timidi di non smarrirsi, tornarono a calcar le ristrette orme <lb></lb>seguate a loro innanzi dai passi del Maestro. </s></p><p type="main">

<s>Girolamo Cardano fu il primo, che osò levarsi da una tal suggezione, <lb></lb>per secondar piuttosto i deliri della sua propria fantasia. </s>

<s>Egli ebbe, come ad <lb></lb>altre occasioni fu da noi notato, fra i fisici contemporanei e i posteriori il <lb></lb>più chiaro e più distinto concetto della compressione, e della elasticità del­<lb></lb>l&#039;aria: e avendo osservato che tra la pressione e la percossa è una tal no­<lb></lb>tabile differenza, che in quella il corpo premuto rimane in quiete, e in que­<lb></lb>sta risalta bene spesso in frautumi: pensò che non potesse quella forza di <lb></lb>risalto attribuirsi ad altro, che alla ekisticità dell&#039;aria, ond&#039;è perciò che si <lb></lb>ridusse a dire non operarsi altrimenti la percossa, che per insinuarsi a modo <lb></lb>di cuneo ne&#039;pori del percosso l&#039;aria stessa, sospintavi dal perenziente con <lb></lb>gran violenza. </s></p><p type="main">

<s>Giulio Cesare Scaligero se ne rise, nella sua CCCXXXI Esercitazione. <pb xlink:href="020/01/2488.jpg" pagenum="113"></pb>Quel Genovese dunque, diceva, che, interrogato in giudizio chi avesse am­<lb></lb>mazzato l&#039;uomo, rispondeva: le punte del forcone; avrebbe dovuto dir piut­<lb></lb>tosto, te giudice o Cardano, che invece fu l&#039;aria, e i retori dovrebbero oramai <lb></lb>lasciar di ripetere quelle loro figure, non più dicendo che fu la gioventù, la <lb></lb>notte, venere e il vino, ma l&#039;aria che commise il delitto. </s>

<s>“ Equidem didice­<lb></lb>ram, poi soggiunge, motum sicut pulsum addere ponderi. </s>

<s>Nam et absquc <lb></lb>ictu sola impressione plus affertur momenti, quam quantum eius pondus effi­<lb></lb>cere valeat. </s>

<s>Quippe rapum manus cum cultro imposita non scindet, at com­<lb></lb>pressione secabit. </s>

<s>Hoc ex nisu fit, ita etiam in ictu. </s>

<s>Aristotiles, in XIX pro­<lb></lb>positione Mechanicorum, ait: impositam securim non secare, quia pondus <lb></lb>solum habet: motum vero movere ” (Francofurti 1592, pag. </s>

<s>1060). </s></p><p type="main">

<s>Coglie di qui lo Scaligero l&#039;occasione di dire che il suo maestro Gio­<lb></lb>vanni del Giocondo, architetto nobilissimo, che solo seppe intendere ed ese­<lb></lb>guire i disegni postumi di Bramante, sciolse un giorno all&#039;imperatore Massi­<lb></lb>miliano questo problema: “ Quot pondo proportionem haberet pugnus hominis <lb></lb>ferientis, cum seipso non feriente comparatus ” (ibid., pag. </s>

<s>1061). E perchè, <lb></lb>poi soggiunge, questa, insieme con altre simili invenzioni, <emph type="italics"></emph>fortunae saevitia <lb></lb>periere,<emph.end type="italics"></emph.end> si volle studiar di recuperarle in un suo libro un Autore fran­<lb></lb>cese, le speculazioni del quale non dovevano essere tenute in poco pregio, se <lb></lb>il Viviani le tradusse di sua propria mano, e le serbò fra le sue carte come <lb></lb>memoriale di scienza. </s>

<s>Fra i Manoscritti galileiani infatti, al foglio 162 del <lb></lb>tomo 138 dei Discepoli, sotto questa avvertenza <emph type="italics"></emph>Da un libretto intitolato<emph.end type="italics"></emph.end><lb></lb>Ricreazioni scientifiche <emph type="italics"></emph>in francese,<emph.end type="italics"></emph.end> si legge: “ Problema III. </s>

<s>Dire quanto <lb></lb>pesi un colpo d&#039;un pugno, d&#039;un martello o di un&#039;ascie, in riguardo di quel <lb></lb>che peserebbe s&#039;egli stesse in riposo e senza battere. </s>

<s>” </s></p><p type="main">

<s>“ Giulio Scaligero, nella sua Esercitazione CCCXXXI contro il Cardano, <lb></lb>narra che un matematico di Massimiliano imperatore propose un giorno que­<lb></lb>sta questione, e prometteva di darne la soluzione. </s>

<s>Ma lo Scaligero non la <lb></lb>diede altrimenti, e io la risolvo in questa maniera: ” </s></p><p type="main">

<s>“ Prendete una bilancia e lasciatevi posare un pugno, un martello o <lb></lb>un&#039;asce sopra uno de&#039;gusci, o sopra un braccio della bilancia, e mettete <lb></lb>dentro l&#039;altro guscio tanto peso, quanto basta per contrappesarlo. </s>

<s>Dopo, ca­<lb></lb>ricando continuamente il guscio, e percotendo dall&#039;altra estremità col pugno, <lb></lb>martello o altro; si potrà sperimentare quanto di peso possa far sollevare <lb></lb>ciascun colpo, e conseguentemente quanto egli valga. </s>

<s>Perchè, come dice Ari­<lb></lb>stotile, il moto che si fa nel battere aggiunge gran peso, e ciò perch&#039;egli è <lb></lb>più veloce. </s>

<s>E in effetto chi mettesse mille martelli o il peso di mille libbre <lb></lb>sopra una pietra, e la stringesse con forza di vite, di leva o di altra mac­<lb></lb>china; non gli farebbe niente, in riguardo di colui che la percotesse. </s>

<s>Non <lb></lb>si ved&#039;egli che un coltello sopra il burro, o un&#039;asce posata sopra una carta, <lb></lb>senza percossa, non l&#039;intacca niente? </s>

<s>Battasi un poco sopra un legno, e si <lb></lb>vedrà che effetto ne segue. </s>

<s>” </s></p><p type="main">

<s>Il problema era dunque risoluto dall&#039;Autore francese, comparando i mo­<lb></lb>menti della gravità con quelli della percossa. </s>

<s>e riducendone le leggi delle <pb xlink:href="020/01/2489.jpg" pagenum="114"></pb>proporzioni a quelle dei pesi sulla bilancia. </s>

<s>Galileo, in quel medesimo tempo <lb></lb>o poco prima, era venuto nello stesso concetto, se non che, invece di rico­<lb></lb>noscerne l&#039;inspirazione dalle dottrine aristoteliche, come fa lo scrittore delle <lb></lb>sopra citate parole tradotte dal Viviani, incomincia, in quel suo discorso ag­<lb></lb>giunto alla <emph type="italics"></emph>Scienza meccanica,<emph.end type="italics"></emph.end> a trattare della percossa, ridendosi di Aristo­<lb></lb>tile che, alla lunghezza del manico nel martello, ne avesse attribuita l&#039;essen­<lb></lb>ziale efficacia. </s>

<s>Non cita però nelle Opere il luogo, dove dal Filosofo si dice <lb></lb>questo, che pure i Matematici, incominciando da Leonardo da Vinci, avevano <lb></lb>per verissimo, e qual legittima conseguenza del principio, che “ ab eadem <lb></lb>vi plus transfertur id extremum, quod longior a centro distat ” (ibid., fol. </s>

<s>34), <lb></lb>come giusto si verifica nel martello col manico più lungo. </s>

<s>Sembrava che <lb></lb>piuttosto avesse dovuto Galileo citar la XIX delle Questioni meccaniche, che <lb></lb>servì di documento allo Scaligero, per ridur la scienza traviata dal Cardano <lb></lb>sul suo retto sentiero, e che il Borelli stesso, benchè censore non troppo <lb></lb>indulgente, ebbe, nel proemio al suo libro Della percossa, a lodare <emph type="italics"></emph>pro sua <lb></lb>sagacitate.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Comunque sia, così Galileo avverso, come il francese Autore seguace di <lb></lb>Aristotile, riducono la forza della percossa agli effetti della stadera, e delle <lb></lb>altre macchine, nelle quali si vede “ potersi muovere qualunque gran resi­<lb></lb>stenza da ogni data piccola forza, purchè lo spazio, per lo quale si moverà <lb></lb>la resistenza, abbia quella proporzione medesima, che tra essa gran resistenza <lb></lb>e la piccola forza si trova “ (Alb. </s>

<s>XI, 124). Così, per esempio, soggiunge, <lb></lb>un martello “ il quale, avendo quattro di resistenza, vien mosso da forza <lb></lb>tale che, liberandosi da essa in quel termine dove fa la percossa, anderia <lb></lb>lontano, non trovando l&#039;intoppo, dieci passi, e viene in detto termine oppo­<lb></lb>sto un gran trave, la cui resistenza al moto è come quattromila, cioè mille <lb></lb>volte maggiore di quella del martello; fatta in esso la percossa, sarà bene <lb></lb>spinto avanti, ma per la millesima parte delli dieci passi, nei quali si sarà <lb></lb>mosso il martello ” (ivi, pag. </s>

<s>125). </s></p><p type="main">

<s>Furon queste le dottrine, che si professarono dai Matematici, fatte poche <lb></lb>eccezioni, intorno alla forza della percossa, infino a che non venne alla luce, <lb></lb>nel 1667, il trattato del Borelli. </s>

<s>Il Torricelli e il Viviani intanto esplicavano <lb></lb>quelle galileiane dottrine, illustrandole con alcuni pensieri, che dicevano di <lb></lb>avere inteso profferire dalla bocca dello stesso Galileo nei congressi di Ar­<lb></lb>cetri, e il Nardi compendiava così il Discorso aggiunto infine alla <emph type="italics"></emph>Scienza <lb></lb>meccanica,<emph.end type="italics"></emph.end> confermando la proporzione ivi assegnata tra la forza del percu­<lb></lb>ziente, e la resistenza che il percosso gli contrappone. </s></p><p type="main">

<s>“ Certo che la percossa, egli dice nella veduta XXII della Scena III, <lb></lb>tal moltiplicazione fa di forza, che quasi mirabil sembra, attesochè vediamo, <lb></lb>con un piccolo martello percotendo un chiodo, penetrarsi un legno durissimo, <lb></lb>benchè, se noi sopra il chiodo ponessimo un peso dieci e cento volte più <lb></lb>grave dello stesso martello, nulla quasi di segno c&#039;impriremmo. </s>

<s>Che diremo <lb></lb>poi se l&#039;esperienza ne dimostri che, con un piccol martello, potremo anco <lb></lb>una grandissima mole di luogo movere, se di percoterla lungo tempo du-<pb xlink:href="020/01/2490.jpg" pagenum="115"></pb>riamo? </s>

<s>Di qui veramente apparisce che gli effetti insensibili di ciascun colpo <lb></lb>moltiplicati divengono alla fine sensibili, massime nell&#039;ondeggiamento di qual­<lb></lb>che mobile, o nelle sue particelle conservato: apparisce ancora che nessuno, <lb></lb>benchè minimo atto, manca in natura di effetto. </s>

<s>” </s></p><p type="main">

<s>“ Ora, per trovare la cagione della forza, che la percossa dimostra, bi­<lb></lb>sogna considerar prima il peso del martello, e quanta in esso la resistenza <lb></lb>all&#039;esser mosso si trovi. </s>

<s>Secondo, per quanto spazio si moverebbe cacciato <lb></lb>dalla forza, se intoppo non trovasse. </s>

<s>Terzo, quanta sia la resistenza al mo­<lb></lb>vimento di quel peso, ov&#039;ei percote. </s>

<s>Quarto ed ultimo, per quanto spazio si <lb></lb>muova il corpo, che la percossa riceve. </s>

<s>Quindi tal proporzione dalla Natura <lb></lb>mantenersi il Galileo osserva che, quanto la resistenza del percosso è mag­<lb></lb>giore della resistenza del percotente, tanto minore spazio il percosso passerà <lb></lb>di quello, che trascorso il percotente si avrebbe. </s>

<s>Sia, per esempio, la resi­<lb></lb>stenza del martello 10, quella del percosso 100, e pongasi che spinto il mar­<lb></lb>tello fosse per andare innanzi 100 braccia, non trovando intoppo: avverrà <lb></lb>che, intoppando nella resistenza suddetta, la spingerà avanti un solo braccio, <lb></lb>perchè, siccome la resistenza del percotente è cento volte minore di quella <lb></lb>del percosso, così lo spazio, per il quale mosso lo stesso percotente sareb­<lb></lb>besi, è cento volte maggiore dello spazio, per cui il percosso muovesi, tal­<lb></lb>mente che, conchiudendo, diremo la forza della percossa da tal principio <lb></lb>dipendere: che quella forza, che muover può uno di resistenza per cento di <lb></lb>spazio, moverà cento di resistenza per uno di spazio ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XX, pag. </s>

<s>435, 36). </s></p><p type="main">

<s>Fra gli stranieri, a que&#039;tempi, il Mersenno, non sodisfatto di queste <lb></lb>dottrine, che si professavano nella Scuola galileiana; rinnovellò la strana <lb></lb>ipotesi del Cardano, attribuendo all&#039;aria annidata dentro i pori del corpo <lb></lb>percosso i maravigliosi effetti, che non produrrebbe il percuziente, o natu­<lb></lb>ralmente gravitando, o compresso per via di un torchio. </s>

<s>“ Quae valde con­<lb></lb>formia iis quae de cylindro ferreo deprimendo, vel depresso, in nostris <emph type="italics"></emph>Me­<lb></lb>chanicis<emph.end type="italics"></emph.end> dicta sunt: nempe motum, quo aer interiicitur, aliquid habere, quod <lb></lb>non possit a pondere, imo nec a praelis suppleri. </s>

<s>Aer siquidem interceptus <lb></lb>subiecti corporis poros ingreditur, illiusque partes ea velocitate comprimit et <lb></lb>deprimit, vel cogit, ut subsiliant, quam nullum pondus, nullave pressio sup­<lb></lb>plere potest ” (Novar. </s>

<s>Observat., T. III, Parisiis 1644, pag. </s>

<s>203). </s></p><p type="main">

<s>Ad eccezione di pochi, ai quali piaceva, come al Mersenno, di ammet­<lb></lb>tere la fantasia dove trovavan difficile il penetrare con la ragione, i più, an­<lb></lb>che fuori d&#039;Italia, professavano il principio galileiano, da cui diceva il Nardi <lb></lb>che dipende la forza della percossa. </s>

<s>Giova tra quegli stranieri annoverare <lb></lb>Isacco Vossio, il quale, scrivendo, in appendice al suo libro <emph type="italics"></emph>De Nili origine,<emph.end type="italics"></emph.end><lb></lb>una dissertazione intitolata <emph type="italics"></emph>De potentiis quibusdam mechanicis,<emph.end type="italics"></emph.end> rassegna fra <lb></lb>quelle meccaniche potenze anche la percossa, e dice esser verissimo il già <lb></lb>noto principio galileiano, ch&#039;egli anzi mette in forma di proposizione, per <lb></lb>passare con matematici argomenti a dimostrarla, ma poi soggiunge che, nè <lb></lb>da Galileo stesso, nè da nessun altro de&#039;suoi seguaci fu fatta una osserva-<pb xlink:href="020/01/2491.jpg" pagenum="116"></pb>zione importante, senza la quale non è possibile, trattandosi delle varie per­<lb></lb>cosse fatte dai corpi, ritrovar la precisa misura dei loro momenti. </s>

<s>“ De vi­<lb></lb>ribus percussionis habet nonnulla Galilaeus, vir magnae sagacitatis, qui, licet <lb></lb>propius veritatem attigerit, totam tamen difficultatem non sustulit. </s>

<s>Percus­<lb></lb>sionum efficaciam refert ille ad velocitatem et pondus corporis percutientis, <lb></lb>neglecto pondere ad ictum perpendiculari, absque quo tamen percussionum <lb></lb>momenta mensurari nequeunt ” (Hagae Comitis 1666, pag. </s>

<s>170). </s></p><p type="main">

<s>Credè insomma il Vossio di essere stato egli il primo ad osservare il <lb></lb>fatto, e a formulare la legge che <emph type="italics"></emph>omnis pressio fit a perpendiculari pon­<lb></lb>dere,<emph.end type="italics"></emph.end> benchè Leonardo da Vinci avesse descritti in una sua nota corpi di <lb></lb>vario peso che, pur essendo della stessa materia e avendo altezze perpendi­<lb></lb>colari uguali, si profondano ugualmente nel tenero fango: e il Torricelli, <lb></lb>nella quarta delle sue Lezioni accademiche, ripensando al grande effetto del­<lb></lb>l&#039;asta infilata nel ferro della picca, che pareva peso superfluo e che dovesse <lb></lb>perciò riuscire al colpo d&#039;impedimento, piuttosto che di aiuto; proponeva a <lb></lb>risolvere il problema: “ Se quel legno della picca, essendo egualmente ve­<lb></lb>locitato, facesse il medesimo effetto, mentre si adopra disteso in asta, e men­<lb></lb>tre si adoprasse raccolto in una palla. </s>

<s>Così anco se una trave egualmente <lb></lb>velocitata fosse per dare il medesimo urto, percotendo una volta per lo lungo, <lb></lb>ed un&#039;altra per traverso ” (Milano 1823, pag. </s>

<s>107). </s></p><p type="main">

<s>Ebbe il Vossio per risoluti i problemi, dicendo che la picca in asta e <lb></lb>la trave per lo lungo fanno maggior effetto, perch&#039;è dall&#039;altezza perpendi­<lb></lb>colare, che si misura la forza dell&#039;urto, ma questa era piuttosto l&#039;afferma­<lb></lb>zione di un fatto, che la conclusione di una verità dal suo proprio principio, <lb></lb>rimanendo tuttavia a sapersi il perchè e in che modo l&#039;altezza perpendico­<lb></lb>lare del percuziente conferisca a render più valido il colpo. </s>

<s>Che poi vera­<lb></lb>mente non prelucessero alle speculazioni di esso Vossio i principii necessarii <lb></lb>a promovere utilmente la scienza, apparisce dalla soluzione di quel problema, <lb></lb>agitato allora fra i curiosi dell&#039;arte cavalleresca: in qual parte cioè la spada <lb></lb>menata in giro faccia maggiore la ferita. </s>

<s>Rispondevano alcuni nella punta, <lb></lb>perchè ivi il moto è maggiormente veloce; soggiungevano altri nel centro <lb></lb>della gravità, perchè ivi raccogliesi tutta insieme la potenza della materia. <lb></lb></s>

<s>“ Sed profecto, entra a dire in mezzo ai disputanti il Vossio, omnia haec <lb></lb>sunt inania: non celeritatis tantum, sed et latitudinis et ponderis perpendi­<lb></lb>cularis singularum ensis partium habenda est ratio ” (ibid., pag. </s>

<s>166). </s></p><p type="main">

<s>Le ferite dunque, fatte nei varii punti del taglio della spada, stanno in <lb></lb>ragion composta della velocità del moto, e della larghezza della lama, cosic­<lb></lb>chè, in un bastone o in una verga in cui le sezioni fossero tutte uguali, la <lb></lb>minor percossa si farebbe presso il manico, e la maggiore verso la punta. </s>

<s><lb></lb>Così pure aveva concluso Leonardo da Vinci, e gli altri matematici, dietro <lb></lb>il principio del Filosofo che <emph type="italics"></emph>ab eadem vi plus transfertur id extremum, <lb></lb>quod longior a centro distat;<emph.end type="italics"></emph.end> ond&#039;è che il Vossio non fece di nulla essen­<lb></lb>zialmente progredire la scienza della percossa, la quale si rimase perciò tra <lb></lb>l&#039;ipotesi fisica del Cardano, e la teoria meccanica di Galileo. </s>

<s>E perciocchè <pb xlink:href="020/01/2492.jpg" pagenum="117"></pb>questa non era meno falsa di quella, non s&#039;aveva alcuna speranza di pro­<lb></lb>gresso, se non dallo sgombrarsi che farebbero le vie della verità dall&#039;uno <lb></lb>errore e dall&#039;altro. </s></p><p type="main">

<s>L&#039;ipotesi del Cardano pareva impossibile che avesse seguaci in uomini <lb></lb>di senno: eppure non mancarono alcuni, i quali si misero volentieri dietro <lb></lb>al Mersenno, principalmente sedotti dal sembrar loro che, per l&#039;intermedio <lb></lb>dell&#039;aria, si spiegassero quelle compressioni e quelle espansioni dei corpi per­<lb></lb>cossi, che non si comprendeva come potess&#039;esser l&#039;effetto della sola forza <lb></lb>immediata nei percuzienti. </s>

<s>Benemeriti perciò dell&#039;avere sgombrato dall&#039;er­<lb></lb>rore cardanico i sentieri della scienza son da dire coloro, i quali dimostra­<lb></lb>rono in che modo agisca la forza della percossa in schiacciare e allargare i <lb></lb>cedevoli corpi sotto la forza del maglio. </s>

<s>Noi non possiamo citare il nome <lb></lb>proprio dell&#039;Autore di così fatta dimostrazione, essendo di ciò solamente certi <lb></lb>che appartenne alla Scuola galileiana, trovandosi raccolte nel citato mano­<lb></lb>scritto attribuito al Magiotti, insieme con le tante altre, anche le speculazioni <lb></lb>di lui. </s>

<s>La questione è trattata nella sua generalità, sì rispetto ai vari generi <lb></lb>di corpi, sì rispetto al vario modo di agir la forza sopr&#039;essi; e solo, per <lb></lb>maggiore semplicità e per più matematica esattezza, si suppongono sferiche <lb></lb>le particelle integranti. </s></p><p type="main">

<s>“ L&#039;acqua, si legge, cadendo da alto, si slarga per tutti i versi, ed una <lb></lb>palla di terra fresca o di altra cosa tenera si schiaccia e allarga, ed ancora <lb></lb>un ferro o altro si lascia traforare ed aprire, se con qualche cosa dura sarà <lb></lb>percosso, e si distende e dilata all&#039;incudine, perchè i componenti di quella <lb></lb>tal materia (quali o siano tondi o di altra figura non importa, poichè il me­<lb></lb>desimo segue essendo dal colpo spinti) si allargano per altro verso, come <lb></lb>qui sotto si vede, e siano per adesso di figura sferica. </s>

<s>” </s></p><p type="main">

<s>“ Siano i cerchi EAG e CDB (fig. </s>

<s>40), che fra loro si tocchino, e tirisi <lb></lb><figure id="id.020.01.2492.1.jpg" xlink:href="020/01/2492/1.jpg"></figure></s></p><p type="caption">

<s>Figura 40.<lb></lb>la CG: dico che passerà ancora per <lb></lb>il toccamento. </s>

<s>Se essa non passerà per <lb></lb>il toccamento, o passerà di sopra o <lb></lb>passerà di sotto. </s>

<s>Passi prima di sotto, <lb></lb>e sia GRC. Tirisi, dal punto G al toc­<lb></lb>camento N, una linea retta, e dal me­<lb></lb>desimo toccamento al punto C un&#039;al­<lb></lb>tra linea retta. </s>

<s>Perchè la GL all&#039;LN <lb></lb>sta come la CI alla IN, e gli angoli <lb></lb>contenuti dai lati proporzionali sono <lb></lb>retti; sarà il triangolo GLN simile al triangolo GIN. </s>

<s>E perchè sopra la linea <lb></lb>retta AB vi cade una linea retta CN, farà gli angoli conseguenti uguali a due <lb></lb>retti. </s>

<s>Ma in cambio dell&#039;angolo CNI piglisi GNL, che a lui è uguale: sarà <lb></lb>la GC una linea retta, quale passerà per il toccamento. </s>

<s>Adunque due linee <lb></lb>rette, partendosi dai medesimi termini G, C, conterrebbero spazio, che è im­<lb></lb>possibile, quale si dovea dimostrare. </s>

<s>” </s></p><p type="main">

<s>“ Adunque, spingendosi per linea retta, niuno dei detti cerchi muterà <pb xlink:href="020/01/2493.jpg" pagenum="118"></pb>sito, ma è impossibile che gl&#039;infiniti componenti di un corpo tutti nel sopra <lb></lb>detto modo si urtino. </s>

<s>” </s></p><p type="main">

<s>“ Se siano aggravati due cerchi, che si tocchino per di fuori, dai punti <lb></lb>dove si aggravano e spingono tirata una linea retta, quale non passi per i <lb></lb>centri, quale ancora non passerà per il toccamento; dico che si rivolgeranno <lb></lb>l&#039;uno sopra l&#039;altro verso dove i punti presi sono fuori della linea, e più fa­<lb></lb>cilmente, quanto più ad essa linea saranno lontani. </s>

<s>” </s></p><p type="main">

<s>“ Mentre si spingano i sopraddetti cerchi per il punto M e H (nella pre­<lb></lb>cedente figura) la linea, la quale li congiunge, non passi per il toccamento: <lb></lb>mentre il cerchio MNG sia aggravato in M, girerà sopra il cerchio HND, ed <lb></lb>egli sopra MNG si rivolgerà. </s>

<s>Il medesimo faranno i componenti di qualsivo­<lb></lb>glia cosa, mentre saranno percossi: e mentre che tutti, che è impossibile, <lb></lb>non si urtino per quella linea che passa per i loro centri, si allargheranno <lb></lb>e scorreranno per diverso dove ” (fol. </s>

<s>220, 21). </s></p><p type="main">

<s>Potevano i seguaci del Cardano, per queste ragioni, persuadersi che si <lb></lb>ammaccano i corpi per effetto della forza della percossa, e non per l&#039;espan­<lb></lb>sione dell&#039;aria dentro i loro pori rinchiusa; ond&#039;è facile congetturare che <lb></lb>nessuno o pochi rimanessero, oltrepassata la metà del secolo XVII, i lusin­<lb></lb>gati dall&#039;esempio, o i soggiogati dall&#039;autorità del Mersenno. </s>

<s>Ebbe perciò ad <lb></lb>acquistare allora maggior prevalenza il principio galileiano, il quale a poco <lb></lb>andò che fu anch&#039;esso convinto di falso. </s>

<s>Ma così sottili essendo gli agguati, <lb></lb>non fu possibile eluderli, se non da poi che la Scienza si rese esperta in <lb></lb>ragionare intorno alle varie proporzioni della forza, che si comunica ai corpi <lb></lb>più o meno, secondo la quantità della loro materia. </s>

<s>Galileo, senza dubbio, <lb></lb>non avrebbe potuto contro i Peripatetici concludere l&#039;uguale velocità dei ca­<lb></lb>denti di qualunque peso, senza implicitamente ammettere che gl&#039;impulsi della <lb></lb>gravità son proporzionali alle masse, ma non seppe applicar nè estendere <lb></lb>questa legge a qualunque potenza. </s>

<s>Nel 1604 il Sarpi gli proponeva la solu­<lb></lb>zione del seguente problema: Si hanno due palle, una di oro che pesa 20 lib­<lb></lb>bre, e l&#039;altra di argento di libbre 19. Supponiamo che siano ambedue mosse <lb></lb>da forza uguale a 12: anderanno i mobili ugualmente veloci? </s>

<s>Parrebbe di <lb></lb>sì, risponde il Sarpi, applicandovi le dottrine stabilite insieme con Galileo <lb></lb>intorno al moto naturale dei gravi. </s>

<s>Ma poi conclude con approvare colui che <lb></lb>dicesse non dover essere uguali le velocità de&#039;due mobili di differente peso, <lb></lb>benchè abbia ricevuto ciascuno in sè impressione uguale di forza. </s></p><p type="main">

<s>“ Se saranno due mobili di disuguale specie, e una virtù minore di <lb></lb>quello, che sia capace ricevere qual si voglia di loro; si domanda se, comu­<lb></lb>nicandosi la virtù ad ambedue, ne riceveranno ugualmente: come se l&#039;oro <lb></lb>fosse atto di ricevere dalla somma virtù 20, e non più, e l&#039;altro 19 e non <lb></lb>più; se saranno mossi da virtù 12, se ambedue riceveranno 12. Par di sì, <lb></lb>perchè la virtù si comunica tutta; il mobile è capace: adunque l&#039;effetto è <lb></lb>lo stesso. </s>

<s>Par di no, perchè allora due mobili di specie diversa, da ugual <lb></lb>forza spinti, anderanno allo stessso termine con la stessa velocità. </s>

<s>Se uno <lb></lb>dicesse: la forza 12 moverà l&#039;argento e l&#039;oro allo stesso termine, non con <pb xlink:href="020/01/2494.jpg" pagenum="119"></pb>la stessa velocità?.... Perchè non, se ambedue sono capaci anco di mag­<lb></lb>giore, che quella qual 12 li può comunicare? </s>

<s>” (Lettere, Firenze 1863, Vol. </s>

<s>I, <lb></lb>pag. </s>

<s>14). </s></p><p type="main">

<s>Avviava così il Sarpi le questioni meccaniche in un campo nuovo e l&#039;in­<lb></lb>certezza del risolverle dipendeva come si disse dal non essersi ancora stabi­<lb></lb>lite le leggi della comunicazione dei moti, formulate già in una scienza più <lb></lb>antica. </s>

<s>Leonardo da Vinci, per esempio, dall&#039;aver posto che ogni potenza è <lb></lb>il prodotto della velocità per la quantità di materia, ne aveva concluso che, <lb></lb>essendo le potenze uguali, le velocità stanno in reciproca ragione delle masse <lb></lb>dei corpi. </s>

<s>“ Se una potenza, diceva, moverà un corpo, in alquanto tempo, <lb></lb>un alquanto spazio; la massima potenza moverà la metà di quel corpo, nel <lb></lb>medesimo tempo, due volte quello spazio: ovvero la medesima virtù moverà <lb></lb>la metà di quel corpo, per tutto quello spazio, nella metà di quel tempo ” <lb></lb>(Les Manuscrits, Man. </s>

<s>F, Paris 1389, fol. </s>

<s>26). Se fosse dunque Leonardo ri­<lb></lb>sorto, ed entrato in mezzo alle dispute insorte fra il Sarpi e Galileo, non <lb></lb>solo avrebbe confermato con certezza di scienza che due mobili l&#039;uno peso <lb></lb>come venti, e l&#039;altro come diciannove, sarebbero stati da ugual forza diver­<lb></lb>samente velocilati, ma avrebbe determinate le proporzioni di quelle diversità, <lb></lb>dicendo che la palla di argento si sarebbe mossa venti diciannovesimi più <lb></lb>veloce di quella dell&#039;oro. </s></p><p type="main">

<s>Nella risorta scienza del moto fu Niccolò Aggiunti che prese a dimo­<lb></lb>strare le prime leggi della comunicazion delle forze, per applicarla alla per­<lb></lb>cossa, <emph type="italics"></emph>la quale opera,<emph.end type="italics"></emph.end> egli dice, <emph type="italics"></emph>con la velocità e con la copia della ma­<lb></lb>teria.<emph.end type="italics"></emph.end> Non fu dunque il Borelli, se non che in pubblico, il primo a dire e <lb></lb>a dimostrare che la potenza percussiva, essendo le velocità uguali, dipende <lb></lb>dalla mole corporea, risovvenendosi i nostri Lettori di aver sentito dimostrar, <lb></lb>nel precedente Tomo di questa Storia, a pag. </s>

<s>188, 89, allo stesso Aggiunti <lb></lb>che <emph type="italics"></emph>La medesima velocità, nelle maggiori e minori quantità di materia, <lb></lb>opera più o meno potentemente, secondo la proporzione di essa materia: <lb></lb>e che, se saranno due mobili di uguale velocità, fatti della stessa mate­<lb></lb>ria, ma di quantità disuguale di essa, il momento dell&#039;uno, al momento <lb></lb>dell&#039;altro, sta come la quantità della materia dell&#039;uno alla quantità della <lb></lb>materia dell&#039;altro.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ebbe altrove il Borelli a notare che l&#039;errore di tutti i suoi antecessori <lb></lb>nella scienza della percossa dipendeva dal creder con Aristotile che gli effetti <lb></lb>del colpo fossero prodotti dal peso naturale, che nel cadere si moltiplica via via: <lb></lb>contro il quale errore poneva nel trattato <emph type="italics"></emph>De vi percussionis<emph.end type="italics"></emph.end> il cap. </s>

<s>XXXIV, <lb></lb>in cui concludeva la proposizione CXXXIV col dire essere impossibile “ ut <lb></lb>vis impetus augeat vim ponderis eiusdem corporis, et hoc profecto contingit <lb></lb>cum pila gravis sursum proiicitur perpendiculariter ad horizontem, cum e <lb></lb>contra nisus gravitatis fiat deorsum ” (Bononiae 1667, pag. </s>

<s>293). Da quegli <lb></lb>erranti antecessori però del Borelli era da escluder l&#039;Aggiunti, il quale, in <lb></lb>una Nota da noi trascritta e pubblicata nella pagina precedente alle due so­<lb></lb>pra citate, aggiungeva alla <emph type="italics"></emph>percossa naturale,<emph.end type="italics"></emph.end> di che solo s&#039;occuparono Ari-<pb xlink:href="020/01/2495.jpg" pagenum="120"></pb>stotile e Galileo, la <emph type="italics"></emph>percossa violenta,<emph.end type="italics"></emph.end> fatta dal corpo mosso di sotto in su, <lb></lb>e la <emph type="italics"></emph>media,<emph.end type="italics"></emph.end> che dice esser quella del corpo grave che, movendosi orizontal­<lb></lb>mente, percote. </s>

<s>Confermava questa sua terza definizione, proponendosi di <lb></lb>dimostrare che <emph type="italics"></emph>Anco la sola velocità, senza il peso, opera ed ha momento:<emph.end type="italics"></emph.end><lb></lb>proposizione che apparisce falsa, come noi la giudicammo, se per peso ivi <lb></lb>intendesi la materia. </s>

<s>Ma se intenderemo, secondo che deve aver inteso l&#039;Ag­<lb></lb>giunti, la materia, che non esercita il suo peso, o perchè contrariato, come <lb></lb>nel moto proiettizio all&#039;in su, o perchè equilibrato, come nel moto orizon­<lb></lb>tale; la proposizione è verissima, e le ragioni, che la dimostran tale, son più <lb></lb>semplici e più efficaci di quelle stesse addotte nel citato cap. </s>

<s>XXXIV <emph type="italics"></emph>De vi <lb></lb>percussionis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La morte arrestò nelle Note manoscritte dell&#039;Aggiunti i progressi di que­<lb></lb>ste speculazioni intorno alla nuova Scienza della percossa, a proseguir la <lb></lb>quale dette, più di trent&#039;anni dopo, opera il Borelli. </s>

<s>Egli incomincia dall&#039;os­<lb></lb>servare che la virtù partecipata al proietto dal proiciente è diffusiva di sè <lb></lb>in tutte e singole le particelle del corpo, per le quali si distribuisce ugual­<lb></lb>mente: d&#039;onde avviene che, quanto maggiore è il numero di esse particelle <lb></lb>integranti, altrettanto sia divisa la virtù motrice, e perciò minore la velocità, <lb></lb>la qual dunque sarà tale, da crescere col crescer della forza impulsiva, e col <lb></lb>diminuire della quantità di materia o della massa. </s>

<s>Le più volgari esperienze <lb></lb>confermano questa conclusione, perchè agitando in mano, per esempio, un <lb></lb>corpo diviso in frantumi di varia grandezza, e, gittandoli tutti insieme, si ve­<lb></lb>dono i più piccoli andar più lontano degli altri. </s></p><p type="main">

<s>Chiamate F, F′ le forze impresse in due vari corpi, de&#039;quali M, M′ sian <lb></lb>le respettive moli o masse, il discorso del Borelli si traduce analiticamente <lb></lb>nelle formule V=F:M, V′=F′:M′, dalle quali conseguono prima di <lb></lb>tutto le proposizioni XII e XIII, poste dall&#039;Autore per fondamento al suo <lb></lb>trattato <emph type="italics"></emph>De vi percussionis;<emph.end type="italics"></emph.end> quella che dice: “ Si duo corpora eadem velo­<lb></lb>citate moveantur, vis motiva ad vim motivam eamdem proportionem habet, <lb></lb>quam unum corpus ad aliud ” (pag. </s>

<s>36) e questa: “ Si duo corpora aequa­<lb></lb>lia inaequalibus velocitatibus moveantur, eorum virtutes motivae eamdem pro­<lb></lb>portionem habebunt, quam velocitates ” (pag. </s>

<s>38). Conseguiva altresì dal <lb></lb>sopra posto principio un&#039;altra proposizione importante, che ricorre in ordine <lb></lb>la XV, e nella quale il Borelli dimostra che, essendo le forze impulsive uguali, <lb></lb>stanno le velocità reciprocamente come le moli. </s>

<s>“ Igitur si fuerint duo cor­<lb></lb>pora inaequalia, quae impellantur ab aequalibus viribus motivis, erunt eorum <lb></lb><figure id="id.020.01.2495.1.jpg" xlink:href="020/01/2495/1.jpg"></figure></s></p><p type="caption">

<s>Figura 41.<lb></lb>velocitates reciproce proportionales magnitudinibus <lb></lb>corporum impulsorum ” (pag. </s>

<s>40). </s></p><p type="main">

<s>Questa proposizione nel manoscritto attribuito <lb></lb>al Magiotti è confermata da una bella esperienza, <lb></lb>la quale è così un poco troppo forse frettolosa­<lb></lb>mente descritta: “ Se appenderemo due palle A, <lb></lb>B (fig. </s>

<s>41) di qualsivoglia materia, una il doppio <lb></lb>più grave dell&#039;altra, e quella più leggera rimo-<pb xlink:href="020/01/2496.jpg" pagenum="121"></pb>veremo lontano dal perpendicolo il doppio della più grave, le quali lasciate <lb></lb>in libertà, acciò si urtino; una non spingerà indietro l&#039;altra, perocchè tanto <lb></lb>quanto è di lei più grave, tanto l&#039;altra è più veloce ” (fol. </s>

<s>205). </s></p><p type="main">

<s>La fretta nel descrivere, che si accennava, trasparisce dall&#039;apparente <lb></lb>improprietà dell&#039;espressione, per ridur la quale alla matematica esattezza si <lb></lb>potrà osservar che l&#039;Autore riferisce le distanze all&#039;infimo punto D del per­<lb></lb>pendicolo, a partir dal quale si deve misurar l&#039;altezza della caduta, doppia <lb></lb>in potenza, ossia il quadrato. </s>

<s>Così, se intendasi la palla A esser sollevata per <lb></lb>tutto il quadrante, e perciò scendere perpendicolamente per l&#039;altezza CD; <lb></lb>affinchè l&#039;altra palla B produca in D la metà dell&#039;urto, convien sollevarla <lb></lb>per un arco, di cui il seno verso DE sia la quarta parte di tutta DC, come <lb></lb>era per la legge galileiana notissimo all&#039;Autore, e com&#039;aveva proposto il Bo­<lb></lb>relli nel descriver una simile esperienza, la quale egli diceva esser benissimo <lb></lb>accomodata all&#039;intento, perchè i pendoli “ efficiunt transitus per arcum AC <lb></lb>(nella precedente figura) et arcum DB acquitemporaneos, et ideo, si in eo­<lb></lb>dem instanti demittantur a terminis A, B, efficientur quoque percussiones <lb></lb>in D in unico quoque instanti ” (pag. </s>

<s>202). Il Mariotte poi descrisse, dietro <lb></lb>tali esempi, in principio del suo trattato <emph type="italics"></emph>De la percussion,<emph.end type="italics"></emph.end> quella Macchina <lb></lb>di precisione, con la quale si potevano verificar questa, e altre leggi. </s></p><p type="main">

<s>Qualche cosa di simile doveva avere inventato Leonardo da Vinci, nelle <lb></lb>Note del quale vedemmo essere stata annunziata già la proposizione XV, che <lb></lb>il Borelli dava al pubblico per cosa nuova, e dall&#039;essersi ignorata la quale <lb></lb>nacquero le incertezze e i dubbi di Galileo e del Sarpi intorno alle quan­<lb></lb>tità dei moti comunicati, e nacque altresì l&#039;errore dello stesso Galileo in asse­<lb></lb>gnar le proporzioni delle velocità fra il percuziente e il percosso. </s>

<s>Diceva, <lb></lb>come già sappiamo, essere queste velocità reciproche tra la potenza del mar­<lb></lb>tello, e la resistenza del chiodo, come son reciproche ne&#039;pesi equilibrati nella <lb></lb>bilancia, o sul declivio di un piano. <emph type="italics"></emph>Sed negotium percussionis longe di­<lb></lb>versa ratione procedit,<emph.end type="italics"></emph.end> ebbe a rispondere al suo gran Maestro il Borelli, <lb></lb>giustamente osservando che, nell&#039;atto in cui si produce l&#039;effetto, il martello <lb></lb>va con velocità uguale a quella del chiodo, assai diversa dalla prima, che <lb></lb>aveva nello scender liberamente per dare il colpo. </s>

<s>E riducendo alle già di­<lb></lb>mostrate leggi nuove queste sue osservazioni, trovava che la velocità del per­<lb></lb>cuziente a quella del percosso non sta nella proporzione della semplice mole <lb></lb>di questo alla mole di quello, ma in una proporzione molto maggiore. </s>

<s>“ Si <lb></lb>igitur potentia percussiva non est facultas motus, nec vis ponderis, reliquum <lb></lb>est ut sit moles corporea, quod licet videatur incredibile, vel saltem sit igno­<lb></lb>tum, ostendetur tamen in progressu huius operis, in percussione, moles corpo­<lb></lb>reas suis velocitatibus reciproce non respondere. </s>

<s>Nam malleus, licet vehemen­<lb></lb>tissime moveatur, antequam percussionem inferat, et antequam ad contactum <lb></lb>percussi corporis perducatur, et resistentiam quiescentis corporis superet; <lb></lb>tamen, in actu percussionis, non potest malleus pristinam velocitatem reti­<lb></lb>nere. </s>

<s>Cogitur enim moveri eadem velocitate simul cum corpore percusso, <lb></lb>quandoquidem concipi nequeunt duo corpora se tangentia, et simul agitata, <pb xlink:href="020/01/2497.jpg" pagenum="122"></pb>quorum subsequens et propellens celerius moveatur, quam antecedens impul­<lb></lb>sum. </s>

<s>Itaque, si comparetur velocitas mallei, antequam percussionem inferat, <lb></lb>cum velocitate acquisita a corpore percusso, et tunc illa ad hanc velocitatem <lb></lb>maiorem proportionem habebit, quam moles percussi corporis ad molem per­<lb></lb>cutientis: habent enim eamdem proportionem quam summa corporum percussi <lb></lb>et percutientis ad corpus percutiens ” (pag. </s>

<s>IX, X). </s></p><p type="main">

<s>Dimostrava ciò il Borelli nella proposizione XIX, supponendo che un <lb></lb>corpo indifferente al moto, come sarebbe una perfetta sfera posata sopra un <lb></lb>piano perfettamente orizontale, ceda a qualunque più leggero impulso, a cui <lb></lb>nulladimeno non diminuisce la virtù motiva. </s>

<s>Sia un corpo qualunque A che, <lb></lb>movendosi con la quantità di moto A. V, ne incontri direttamente un altro B, <lb></lb>nello stato della detta indifferenza: ambedue procederanno insieme congiunti, <lb></lb>e così congiunti serberanno pure la medesima quantità di moto, la quale <lb></lb>dovrà necessariamente risultar d&#039;imminuita velocità, essendo da A in A+B <lb></lb>cresciuta la mole corporea. </s>

<s>Qualunque siasi però quella velocità, che chia­<lb></lb>meremo V′, la quantità di moto sarà espressa da (A+B)V′=A.V, e <lb></lb>perciò V/V′=(A+B)/A, che è maggior proporzione di B/A, assegnata da Ga­<lb></lb>lileo <emph type="italics"></emph>per sufficientiam iuvenilis eius ratiocinii,<emph.end type="italics"></emph.end> come disse il Borelli, il quale <lb></lb>stimò che poi vecchio si fosse ricreduto, quand&#039;ebbe a pronunziar che la <lb></lb>forza della percossa era infinita, e in un altro dialogo prometteva come tale <lb></lb>di dimostrarla. </s></p><p type="main">

<s>Quel dialogo però non ebbe la fortuna di vederlo appresso all&#039;Autore <lb></lb>vivente nessuno degli amici e dei familiari, non eccettuato lo stesso Torri­<lb></lb>celli chiamato come si sa dal principe Leopoldo, per questo effetto, nell&#039;ospi­<lb></lb>zio di Arcetri. </s>

<s>Anzi gli eredi stessi di Galileo, soggiunge il Borelli, <emph type="italics"></emph>mihi <lb></lb>retulerunt nec inter schedulas reperta est pagella, quae hoc titulo insi­<lb></lb>gniretur,<emph.end type="italics"></emph.end> cosicchè tutti coloro, i quali erano intervenuti nell&#039;Accademia della <lb></lb>Crusca ad ascoltar le torricelliane lezioni, con tanta applaudita eloquenza re­<lb></lb>citate intorno alla forza della percossa, <emph type="italics"></emph>hanc scientiam una cum Galileo <lb></lb>defunctam esse perpetuo questi sunt.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Per ristorar dunque la scienza di tanta iattura, rivolgendo spesso in <lb></lb>mente i detti di Galileo, nè potendo credere che quel grand&#039;Uomo si fosse <lb></lb>allucinato, pensò il Borelli di scrivere un libro a parte sull&#039;argomento del <lb></lb>Dialogo perduto. </s>

<s>“ At tandem, post diuturnas mentis agitationes, Dei bene­<lb></lb>ficio, hanc physicae et mathematicae partem ex integro proprio marte me <lb></lb>reperisse puto, et veram et intimam naturam energiae percussionis, eiusque <lb></lb>causas, proprietates et effectus in hoc libro luculenter demonstrasse mihi <lb></lb>videor, quae, saltem ob novitatem et materiae praestantiam, non iniucunda <lb></lb>fore censeo ” (pag. </s>

<s>XII). </s></p><p type="main">

<s>La Scienza nuova, che s&#039;istituiva nel libro <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> credeva <lb></lb>dunque l&#039;Autore fosse quella in sostanzn, che s&#039;avrebbe avuta direttamente <lb></lb>dal grande Maestro, se si fosse potuto, dopo la morte di lui, <emph type="italics"></emph>in armario <lb></lb>secretiori, inter alia scripta, hanc dissertationem, calamo exaratam, sal-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2498.jpg" pagenum="123"></pb><emph type="italics"></emph>tem non omnino completam, reperiri.<emph.end type="italics"></emph.end> E ora che la scoperta è fatta, e che <lb></lb>da quasi due secoli è stata esposta al pubblico dagli armadi segreti, possiamo <lb></lb>noi, fatti giudici con cognizione di causa, sentenziar che il Borelli s&#039;era in­<lb></lb>gannato a creder che la sua nuova Scienza della percossa fosse quella me­<lb></lb>desima di Galileo, il quale avesse nel Dialogo riparato all&#039;insufficienza del <lb></lb>suo primo giovanile giudizio. </s>

<s>Galileo invece non aveva fatto altro da vecchio <lb></lb>che confermare l&#039;errore antico, assottigliando l&#039;ingegno in speculazioni e in <lb></lb>esperienze, per dimostrar l&#039;analogia che passa fra i momenti della gravità <lb></lb>nelle macchine, e i momenti delle forze nella percossa, della quale sempre <lb></lb>ignorò le vere leggi ritrovate poi <emph type="italics"></emph>proprio marte<emph.end type="italics"></emph.end> dal Borelli: cosicchè insomma <lb></lb>il sesto dialogo aggiunto alle due Scienze nuove, che costò tante lacrime al <lb></lb>mondo, niente altro è che uno splendido tessuto di paralogismi. </s>

<s>Così resulta <lb></lb>dal libero esame, che noi sottoporremo al giudizio dei nostri liberi Lettori, <lb></lb>dop&#039;aver sodisfatta in loro la curiosità di saper come mai avvenisse la felice <lb></lb>invenzione di ciò, che quelli stessi, i quali dovevano averlo in mano, cre­<lb></lb>dettero e dissero irreparabilmente perduto: ond&#039;è che dal suo principio al <lb></lb>termine, con più spedito passo che sia possibile, ci studieremo di condurre <lb></lb>la nostra Storia. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Terminava Galileo il suo giovanile discorso <emph type="italics"></emph>Della forza della percossa<emph.end type="italics"></emph.end><lb></lb>con questa avvertenza: “ So che qui nasceranno ad alcuni delle difficoltà e <lb></lb>delle istanze, le quali però con poca fatica si torranno di mezzo, e noi le <lb></lb>rimetteremo volontariamente tra i problemi meccanici, che in fine di que­<lb></lb>sto discorso si aggiungeranno ” (Alb. </s>

<s>XI, 125). Fra i problemi meccanici <lb></lb>infatti, de&#039;quali però Galileo non lasciò che la semplice proposta, e qualche <lb></lb>frettoloso accenno alle loro soluzioni, se ne trovano alcuni relativi alla forza <lb></lb>della percossa, come i seguenti: “ Perchè le aste lunghe lanciate fanno mag­<lb></lb>gior colpo. </s>

<s>— Perchè per far diversi effetti si cerchino diverse grandezze di <lb></lb>martello e lunghezza di manichi. </s>

<s>— Quando si voglia ficcar l&#039;asta nel ma­<lb></lb>glio, meglio succederà percuotendo l&#039;asta in terra, lasciando il maglio libero, <lb></lb>che se altri brancasse il maglio con la mano e percotesse con l&#039;asta in terra ” <lb></lb>(Alb. </s>

<s>XIV, 321). </s></p><p type="main">

<s>Che siano veramente questi quei Problemi meccanici, accennati sulla fine <lb></lb>del citato <emph type="italics"></emph>Discorso,<emph.end type="italics"></emph.end> vien confermato dal veder che a risolverli s&#039;invocano dal­<lb></lb>l&#039;Autore i medesimi principii. </s>

<s>“ Se quello, scriveva, sopra il quale si vuol <lb></lb>percotere, cederà al percuziente con pari velocità della sua, la percossa sarà <lb></lb>nulla. </s>

<s>— La forza dunque della percossa vien misurata dalla velocità del per­<lb></lb>cuziente sopra la cedenza del percosso ” (ivi): nè ciò vuol dir altro, se non <lb></lb>che la potenza e la resistenza stanno reciprocamente come le loro velocità, <pb xlink:href="020/01/2499.jpg" pagenum="124"></pb>secondo che sempre accade in tutti gli altri meccanici strumenti. </s>

<s>Non si vede <lb></lb>però come qui vengano a togliersi di mezzo le difficoltà e là le istanze, che <lb></lb>potessero sovvenire alla mente di coloro, ne&#039;quali si volevano persuadere così <lb></lb>fatti principii, e ciò s&#039;intende essere avvenuto perchè rimasero que&#039;mecca­<lb></lb>nici Problemi un semplice proposito, abbandonato affatto da Galileo insieme <lb></lb>con le giovanili speculazioni della forza della percossa, le quali, quando tor­<lb></lb>narono ad agitargli la mente, pensò anche a esporre il già maturo concetto <lb></lb>sotto più nobile e splendida veste. </s></p><p type="main">

<s>L&#039;occasione, che fece Galileo già vecchio ritornar sulle abbandonate gio­<lb></lb>vanili speculazioni della percossa, apparisce manifesta da ciò, che si legge <lb></lb>nel IV dialogo, dove al Salviati, che terminava il suo lungo discorso col far <lb></lb>osservare i vari casi, e le varie condizioni di moto e di posizion del percosso, <lb></lb>che conferiscono a produrre più o men gagliardo il colpo del proietto; il <lb></lb>Sagredo soggiunge: “ Il ricordar V. S. questi colpi e queste percosse mi ha <lb></lb>risvegliato nella mente un problema, o vogliam dire questione meccanica, <lb></lb>della quale non ho trovato appresso Autore alcuno la soluzione, nè cosa che <lb></lb>mi scemi la maraviglia, o almeno in parte mi quieti l&#039;intelletto. </s>

<s>E il dub­<lb></lb>bio e lo stupor mio consiste nel non restar capace onde possa derivare, e <lb></lb>da qual principio possa dipendere l&#039;energia e la forza immensa, che si vede <lb></lb>consistere nella percossa, mentre col semplice colpo di un martello, che non <lb></lb>abbia peso maggiore di otto o dicci libbre, veggiamo superarsi resistenze tali, <lb></lb>le quali non cederanno al peso di un grave, che senza percossa vi faccia im­<lb></lb>peto solamente calcando e premendo, benchè la gravità di quello passi molte <lb></lb>centinaia di libbre ” (Alb. </s>

<s>XIII, 247). Che se fosse alcuno curioso di saper <lb></lb>con certezza il tempo, in cui le teorie dei proietti ricondussero Galileo alla <lb></lb>contemplazione degli effetti della percossa, potremmo sodisfarlo dicendo che fu <lb></lb>verso il 1634, nel Gennaio del qual anno aveva già concluso che <emph type="italics"></emph>qualun­<lb></lb>que lieve percossa aveva forza infinita:<emph.end type="italics"></emph.end> conclusione che, annunziata all&#039;Ag­<lb></lb>giunti, rispondeva essere <emph type="italics"></emph>veramente mirabilissima ”<emph.end type="italics"></emph.end> (Alb. </s>

<s>X, 13). </s></p><p type="main">

<s>L&#039;intenzione poi di proporre in dialogo, in quegli stessi discorsi intorno <lb></lb>alle due Scienze nuove, quel che aveva quarant&#039;anni prima pensato di ri­<lb></lb>durre fra i Problemi meccanici, è apertamente espressa dallo stesso Salviati, <lb></lb>il quale così rispondeva al Sagredo, mostratosi desiderosissimo di sapere quel <lb></lb>che intorno alla forza immensa della percossa avesse Galileo speculato di <lb></lb>nuovo: “ E perchè omai so che la curiosità di V. S. volentieri sentirebbe <lb></lb>quei pensieri, che si allontanano dall&#039;opinabile, non aspetterò la sua richie­<lb></lb>sta, ma le dò parola che, spedita che averemo la lettura di questo trattato <lb></lb>dei proietti, gli spiegherò tutte quelle fantasie, o vogliam dire stravaganze, che <lb></lb>dai discorsi dell&#039;Accademico mi son rimaste nella memoria ” (Alb. </s>

<s>XIII, 247). </s></p><p type="main">

<s>Sembrerebbe di qui che il primo pensiero fosse stato quello di soggiun­<lb></lb>gere il trattato della percossa in questo stesso dialogo quarto, dopo quello <lb></lb>dei proietti, al quale si voleva aggiungere, come complemento dei moti pa­<lb></lb>rabolici e dell&#039;arte di dirigere i tiri, il discorso dell&#039;uso delle catenuzze. </s>

<s>Ma <lb></lb>perchè la giornata, benchè protratta a sera, non poteva a tanto colloquio non <pb xlink:href="020/01/2500.jpg" pagenum="125"></pb>riuscire scarsa, a Simplicio, che chiedeva fosse mantenuta la data promessa <lb></lb>d&#039;esplicare qual sia l&#039;utilità, che dalle catenuzze si può ritrarre, e dopo que­<lb></lb>sto arrecare le speculazioni che si diceva essere state fatte dall&#039;Accademico <lb></lb>intorno alla forza della percossa; il Salviati così rispondeva: “ Assai per <lb></lb>questo giorno ci siamo occupati nelle contemplazioni passate: l&#039;ora, che non <lb></lb>poco è tarda, non ci basterebbe a gran segno per disbrigarci dalle nominate <lb></lb>materie: però differiremo il congresso ad altro tempo più opportuno ” (ivi, <lb></lb>pag. </s>

<s>266). </s></p><p type="main">

<s>Ciò significava che in un altro-Dialogo a parte si sarebbe trattato della <lb></lb>forza della percossa, e dell&#039;utilità delle catenuzze negli usi ballistici, di che <lb></lb>era incominciato a farsi il disteso, quando già l&#039;Elzevirio aveva finito di stam­<lb></lb>pare tutto quel che riguardava i proietti. </s>

<s>Ma perchè, alle difficoltà dell&#039;ar­<lb></lb>gomento aggiungendosi quelle della vista, che ogni giorno più si affievoliva, <lb></lb>Galileo conosceva che troppo penoso, a voler dare l&#039;opera compiuta, sarebbe <lb></lb>stato per sè e per gli editori l&#039;indugio; prese risoluzione di pubblicare in­<lb></lb>tanto i quattro dialoghi, aspettando per aggiungervi l&#039;altro l&#039;occasione, che <lb></lb>si credeva prossima, di una ristampa. </s>

<s>La difficoltà dell&#039;argomento si studiava <lb></lb>di superarla con la meditazione più intensa e, servendosi della mano di Marco <lb></lb>Ambrogetti, suppliva in parte all&#039;insufficienza della sua propria vista, Così, <lb></lb>il Dialogo, verso la fine dell&#039;Ottobre del 1638, era stato condotto infino a <lb></lb>quel punto, in cui il Salviati termina il suo discorso intorno all&#039;effetto, che <lb></lb>nasce, quando negli strettoi, allo spingere senza percossa, s&#039;aggiunge una <lb></lb>percossa, facendo un composto d&#039;ambedue (Alb. </s>

<s>XIII, 329). La proposta del <lb></lb>Viviani intorno alla dimostrazione del principio supposto divagò Galileo dal­<lb></lb>l&#039;intrapreso argomento, ma che avesse intenzione di ritornarci sopra, per ri­<lb></lb>durlo ad effetto, apparisce da ciò che scriveva il dì primo Agosto 1639 al <lb></lb>Baliani del migliorare e ampliare lo scritto e pubblicato da sè, infino a quel <lb></lb>tempo, intorno al moto “ con aggiungervi, altre speculazioncelle, ed in par­<lb></lb>ticolare quella attinente alla forza della percossa, nell&#039;investigazione della <lb></lb>quale ho consumate molte centinaia e migliaia di ore, e finalmente ridottala <lb></lb>ad assai facile esplicazione, sicchè altri, in manco di mezz&#039;ora di tempo, potrà <lb></lb>restarne capace. </s>

<s>E qui voglio tornare a dirgli che non ho memoria alcuna <lb></lb>di quelle scritture, che Ella dice essergli state mandate già come pensieri <lb></lb>del Victa, da me affermatogli essere miei: epperò desidererei di rinfrescarmi <lb></lb>col suo favore la memoria, ed in particolare dello scritto intorno alla per­<lb></lb>cossa, il quale non può essere se non imperfetto, essendochè quello, nel quale <lb></lb>io mi quieto, non è stato da me ritrovato salvo che da pochi anni in qua, <lb></lb>nè so io di averne dato fuori intera notizia ” (Lettere pel trecent. </s>

<s>natalizio <lb></lb>cit., pag. </s>

<s>46). </s></p><p type="main">

<s>Galileo dunque aveva dimenticato affatto quel suo <emph type="italics"></emph>Discorso primo ed <lb></lb>antico,<emph.end type="italics"></emph.end> ch&#039;ei volle rivendicare dal Vieta, a cui si attribuiva, benchè lo te­<lb></lb>nesse per cosa imperfetta, e da non farne perciò nessun conto. </s>

<s>Dicendo poi <lb></lb>che non s&#039;acquietava in altro, che nelle cose ritrovate da pochi anni in qua, <lb></lb>mostrava di compiacersi del nuovo dialogo, di cui diceva di non averne dato <pb xlink:href="020/01/2501.jpg" pagenum="126"></pb>fuori a nessuno notizia, e incorava una dolce speranza d&#039;aver presto a darlo <lb></lb>compiuto, premettendolo, perchè più gli premeva, e contro le prime inten­<lb></lb>zioni, al trattato delle catenuzze, benchè più immediatamente questo si rife­<lb></lb>risse ai proietti. </s>

<s>Col Viviani però, com&#039;apparisce dal primo di questi capitoli, <lb></lb>s&#039;intrattenne in migliorare e in correggere le parti già stampate, piuttostochè <lb></lb>in aggiungervene delle nuove, e, venuto il Torricelli, si sa bene che in tut­<lb></lb>t&#039;altro fu impiegato il tempo, che in speculare e scrivere sulla forza della <lb></lb>percossa. </s></p><p type="main">

<s>Certo una gran curiosità ci frugherebbe di sapere il fine, perchè Gali­<lb></lb>leo tenesse così gelosamente occulta la notizia di que&#039;fogli scritti intorno alla <lb></lb>detta forza, non a solo il Viviani, ma allo stesso Torricelli, il quale, mentre <lb></lb>da tutti si credeva esser venuto a dispensare i tesori raccolti in Arcetri, si <lb></lb>udì con grande meraviglia introdursi nell&#039;Accademia, con queste parole, a <lb></lb>leggere intorno alle proprietà e agli effetti delle percosse e degli urti: “ Se <lb></lb>la fortuna non avesse invidiata la gloria di questo scoprimento al nostro se­<lb></lb>colo, già era certo che il famosissimo Galilei lavorava questa gioia, per arric­<lb></lb>chirne il monile della toscana Filosofia. </s>

<s>Molte cose nondimeno da&#039;suoi scritti <lb></lb>e da&#039;suoi ragionamenti familiari si raccoglievano intorno alla percossa, e due <lb></lb>fra le altre: cioè una, l&#039;esperienza di certi archi, con cui s&#039;ingegnava di <lb></lb>dimostrare l&#039;immensità di detta forza: l&#039;altra erano epiteti iperbolici, coi <lb></lb>quali dava manifestamente a divedere ch&#039;egli avesse fermo concetto nell&#039;animo <lb></lb>che la forza della percossa fosse infinita ” (Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>68): e sog­<lb></lb>giungeva esser venuto per rintracciare col proprio ingegno le vestigia di quelle <lb></lb>notizie, raccolte a voce e lette in alcuni frammenti rimasti degli scritti di <lb></lb>Galileo, i quali frammenti, come si confermerà dalle cose che saremo per <lb></lb>dire, si riducevano a quelli, che si leggono dalla linea 29, a pag. </s>

<s>330, infino <lb></lb>alla fine del VI dialogo stampato nella edizione completa dell&#039;Albèri. </s></p><p type="main">

<s>Del Dialogo incominciato, disteso con l&#039;aiuto manuale dell&#039;Ambrogetti, <lb></lb>e condotto al punto che dicemmo di sopra, non ebbe dunque notizia dal suo <lb></lb>ospitatore nemmeno il Torricelli, intorno al qual fatto rimane insodisfatta la <lb></lb>nostra curiosità di sapere per qual fine, invece di proseguire addiritto, diver­<lb></lb>tisse Galileo il valido aiuto del suo ospitato intorno a un altro argomento, che, <lb></lb>se non era estraneo, non si riferiva però, se non che accidentalmente, al sog­<lb></lb>getto dei discorsi e delle dimostrazioni del moto. </s>

<s>Forse si riprometteva il <lb></lb>buon Vecchio più lunga vita, la quale venutagli inaspettatamente meno, fece <lb></lb>sì che, fra gli altri scritti postumi, rimanesse anche quello, al quale aveva <lb></lb>dato mano, inconsapevole di ciò che scriveva, l&#039;Ambrogetti. </s></p><p type="main">

<s>Colui che, avendone intelligenza, ebbe primo a veder quegli scritti, fu <lb></lb>il figliolo ed erede dell&#039;Autore Vincenzio, il quale, dettandogliene, fece pren­<lb></lb>derne copia al Viviani, ed egli sulla stessa copia scrisse poi questo titolo, e <lb></lb>questa nota: “ Ultimo congresso del signor Galileo intorno alla forza della <lb></lb>percossa, datomi a copiare dal signor Vincenzio Galilei, dopo la morte del <lb></lb>Padre. </s>

<s>Questo non è stampato, ma l&#039;originale si trova appresso gli eredi di <lb></lb>detto Vincenzio, e non mi sovviene se sia di mano del medesimo signor Ga-<pb xlink:href="020/01/2502.jpg" pagenum="127"></pb>lileo, oppure di Marco Ambrogetti, come piuttosto io mi credo, o se fosse in <lb></lb>foglio o in quarto. </s>

<s>Ne lasciai di questo pigliar copia al padre Francesco delle <lb></lb>Scuole pie, cioè a don Famiano Michelini, in tempo che egli abitava al por­<lb></lb>tone di Annalena, ed egli poi mi disse averne dato altre copie ” (Nelli, <lb></lb>Filoa IX, fol. </s>

<s>54). </s></p><p type="main">

<s>Sembra però che fossero queste copie poco diffuse, e che quelli stessi, <lb></lb>i quali le presero, le tenessero fra le loro carte dimenticate, intantochè, <lb></lb>nel 1665, nessuno in Toscana, non eccettuato lo stesso principe Leopoldo, <lb></lb>sapeva nulla di quest&#039;ultimo congresso intorno alla percossa, ritrovato fra gli <lb></lb>scritti postumi di Galileo. </s>

<s>Il Borelli perciò, per rintracciare anch&#039;egli col pro­<lb></lb>prio ingegno le vestigia di quelle cognizioni, che si lamentavano da tutti con <lb></lb>grave danno perdute, aveva seco stesso proposto di scrivere il trattato <emph type="italics"></emph>De vi per­<lb></lb>cussionis,<emph.end type="italics"></emph.end> del qual proposito dava così avviso, per lettera del dì 6 Aprile 1665 <lb></lb>da Pisa, al principe Leopoldo: “ Sono entrato a speculare la natura e la pro­<lb></lb>prietà della forza della percossa, soggetto intorno al quale il gran Galileo vi <lb></lb>speculò gran tempo, ma non ci lasciò nulla in scritto, se non che tal forza <lb></lb>fossè infinita. </s>

<s>Ora, se la passione non m&#039;inganna, mi pare d&#039;aver trovato il <lb></lb>capo di questo bandolo molto intrigato, e procurato di perfezionare e poi <lb></lb>scrivere questi concetti, se pure mi riuscirà cosa buona ” (MSS. Cim., T. XVIII, <lb></lb>fol. </s>

<s>152). </s></p><p type="main">

<s>Il Principe mandava, per lettera autografa del dì 9 Maggio appresso, la <lb></lb>bella notizia a Roma a Michelangiolo Ricci, rallegrandosi nella speranza che <lb></lb>s&#039;avesse a ristorare la toscana Filosofia della impotenza di Galileo a disten­<lb></lb>dere i suoi concetti, al qual fine soggiungeva di aver inutilmente condotto a <lb></lb>Firenze il Torricelli (ivi, T. XXIII, fol. </s>

<s>113): e il Ricci rispondeva così due <lb></lb>settimane dopo, consolandosi anch&#039;egli che al danno irreparabile s&#039;appre­<lb></lb>stasse qualche ristoro: “ Si fece gran perdita con la morte del signor Ga­<lb></lb>lileo, e specialmente della dimostrazione, tanto stimata da lui e da tutti gli <lb></lb>intendenti, della forza della percossa: materia egualmente ardua e curiosa, <lb></lb>per la quale ha ingegno molto proporzionato il signor Borelli ” (ivi, T. XVIII, <lb></lb>fol. </s>

<s>188). </s></p><p type="main">

<s>Il Viviani, che si sentiva continuo venire intorno agli orecchi il mormo­<lb></lb>rio di questi lamenti, reprimeva i desideri, e mortificava la pietà, che lo <lb></lb>avrebbe consigliato d&#039;uscire in pubblico a consolarli: e poi, dopo aver ritratto <lb></lb>lo sguardo da quella copia, che aveva presa a dettatura dal signor Vincen­<lb></lb>zio, sogghignava, leggendo così nel proemio al libro <emph type="italics"></emph>De vi percussionis:<emph.end type="italics"></emph.end><lb></lb>“ Cum autem hoc Galileus postremis suae vitae annis scripsisset, speraba­<lb></lb>tur post eius mortem in armario secretiori, inter alia scripta, hanc disserta­<lb></lb>tionem calamo exaratam, saltem non omnino completam reperiri debere: sed, <lb></lb>non sine amicorum tristitia, nec inter schedulas reperta est pagella, quae hoc <lb></lb>titulo insigneretur, ut Galilei haeredes mihi retulerunt, Idipsum testatus est <lb></lb>clarissimus Torricellius qui, ut audio, conatus est vesligia aliqua huius co­<lb></lb>gnitionis inquirere, in suis lectionibus calamo exaratis,.... et post eius mor­<lb></lb>tem stetit Florentiae de hac re altum silentium ” (pag. </s>

<s>IX, X). </s></p><pb xlink:href="020/01/2503.jpg" pagenum="128"></pb><p type="main">

<s>Le ragioni di quest&#039;alto silenzio non erano di defraudare la scienza, nè <lb></lb>d&#039;invidiare alla gloria di Galileo, cose tanto aliene dall&#039;animo del Viviani, <lb></lb>ch&#039;ebbe a farsi una gran violenza di tenere occulta la preziosa notizia, la <lb></lb>quale voleva concorresse fra le altre come pietra monumentale all&#039;edifizio, <lb></lb>che meditava di erigere al suo grande Maestro, affinchè fosse meglio cono­<lb></lb>sciuto dagli invidiosi Francesi, dedicando l&#039;opera al loro re Luigi XIV. </s>

<s>Il <lb></lb>timore di essere prevenuto, come gli avvenne di fatto riguardo al trattato <lb></lb>delle resistenze, lo consigliò a tenere quell&#039;alto silenzio anche con lo stesso <lb></lb>principe Leopoldo, e intanto, per illustrare il Dialogo che, comparendo nella <lb></lb>vita e nelle opere di Galileo inaspettato, avrebbe con sorpresa grande dì tutto <lb></lb>il mondo tolto via le lunghe e antiche querele; il Viviani pensava di dimo­<lb></lb>strare più chiaramente certe cose, e inventava e descriveva strumenti nuovi, <lb></lb>per meglio confermar quelle, che credeva ammirabili verità, insegnate intorno <lb></lb>al modo e alle ragioni della percossa in persona del Salviati. </s>

<s>E perchè insieme <lb></lb>coi laboriosi commenti avessero i Lettori sott&#039;occhio più fedele e completo il <lb></lb>testo, essendo già di Vincenzio Galilei rimasto erede il figlio Cosimo, appresso <lb></lb>al quale si ritrovavano le carte manoscritte dell&#039;avo, si rivolse a esso Cosimo <lb></lb>per collazionar la copia con l&#039;originale, e per esaminar meglio, ciò che non <lb></lb>aveva potuto fare, quando alla presenza del detto signor Vincenzio, che te­<lb></lb>neva quell&#039;originale in mano, scriveva a dettatura; se altre carte ci fossero, <lb></lb>in cui si leggessero della percossa pensieri sparsi o interlocuzioni staccate. </s></p><p type="main">

<s>Trovò, così diligentemente collazionando, essere la sua copia mancante <lb></lb>di un passo, che il dettatore dovette aver saltato per inavvertenza: e per ram­<lb></lb>memorarsi il luogo e il discorso, che voleva essere aggiunto, scriveva così in <lb></lb>una sua nota, che si legge a tergo del fol. </s>

<s>16, P. V, T. IV, de&#039;MSS di Ga­<lb></lb>lileo: “ Nel congresso ultimo mio manoscritto, a c. </s>

<s>8, dopo il nono verso, <lb></lb>deve seguitare così, secondo l&#039;originale del Galileo, alle parole che dicono: <lb></lb><emph type="italics"></emph>computandovi il primo braccio, che questo scese libero e solo<emph.end type="italics"></emph.end> — SAGR. </s>

<s>Io <lb></lb>veramente inclino a credere questo stesso, etc. </s>

<s>” (Alb. </s>

<s>XIII, dalla lin. </s>

<s>22-37 <lb></lb>della pag. </s>

<s>321). Trovò altresì, come s&#039;aspettava, alcuni pensieri sparsi, il <lb></lb>prinmo de&#039;quali trascriveva nel Tomo, e sopra la prima faccia del foglio sopra <lb></lb>citato, premettendovi questa avvertenza: <emph type="italics"></emph>“ Da un foglio originale del signor <lb></lb>Galilco, di sua mano, tra le cose della percossa.<emph.end type="italics"></emph.end> In ogni mobile, che deva <lb></lb>esser mosso violentemente, pare che siano due spezie di resistenza, etc. </s>

<s>” <lb></lb>(Alb. </s>

<s>XIII, dalla linea 33-37 della pag. </s>

<s>329, e dalla 1-23 della pag. </s>

<s>seguente). <lb></lb>Altri simili pensieri trovò pure sparsi in alcune carte slegate, ch&#039;egli dili­<lb></lb>gentemente trascrisse a c. </s>

<s>37-41 del T. III, P. VI, de&#039;citati MSS. galileiani, <lb></lb>forse con quell&#039;ordine, che aveva dato prima a loro il Torricelli, e con que­<lb></lb>sta avvertenza in principio: <emph type="italics"></emph>“ Roba copiata da un esemplare del Galileo, <lb></lb>che si trovava in mano del s̀ignor Vincenzio suo figliolo, di mano di que­<lb></lb>sto, e tutto appresso del signor Cosimo.<emph.end type="italics"></emph.end> Il momento del grave nell&#039;alto della <lb></lb>percossa, etc. </s>

<s>” (Alb. </s>

<s>XIII, dalla linea 29-37 della pag. </s>

<s>330, infino alla fine). </s></p><p type="main">

<s>Questi pensieri sparsi gli aggiunse il Viviani in fine alla copia del Dia­<lb></lb>logo, che gli aveva dettato il signor Vincenzio, e ch&#039;era quello incominciato <pb xlink:href="020/01/2504.jpg" pagenum="129"></pb>dallo stesso Galileo a distendere con l&#039;aiuto dell&#039;Ambrogetti, il termine del <lb></lb>qual Dialogo, lasciato a mezzo, è nell&#039;interlocuzion del Salviati, che termina <lb></lb>alla linea 32 della pag. </s>

<s>329 nella citata edizione completa dell&#039;Albèri. </s>

<s>Così, <lb></lb>sull&#039;originale completata la copia e corretta, la custodiva gelosamente il Vi­<lb></lb>viani per pubblicarla a suo tempo fra le opere postume di Galileo, dopo il <lb></lb>trattato delle Resistenze. </s>

<s>Andata l&#039;intenzione fallita, per le avventure da noi <lb></lb>narrate nel cap. </s>

<s>VIII del Tomo precedente, rimase, fra le altre carte scritte <lb></lb>in simile soggetto dal Viviani, abbandonato anche il Dialogo della percossa. </s>

<s><lb></lb>Avrebbe potuto cogliere nel 1674 l&#039;occasione di pubblicarlo nel dare, dopo <lb></lb>la <emph type="italics"></emph>Scienza delle proporzioni,<emph.end type="italics"></emph.end> quel suo <emph type="italics"></emph>Ragguaglio delle ultime opere del <lb></lb>Galileo,<emph.end type="italics"></emph.end> ma erano a quel tempo usciti alla luce, non il libro solo del Bo­<lb></lb>relli, ma il trattato del Wallis, dai quali manifestamente si concludeva la fal­<lb></lb>sità del concetto galileiano intorno alla natura della forza della percossa. </s>

<s>Per <lb></lb>non volgere perciò in biasimo le lodi, che dava al suo Maestro il mondo, imma­<lb></lb>ginandosi ch&#039;egli avesse speculate le verità recondite e maravigliose, ch&#039;egli <lb></lb>stesso diceva; fu contento il Viviani a fare un semplice cenno del ritrovarsi ap­<lb></lb>presso di lui quel che da tutti si rimpiangeva, con irreparabile danno, perduto. </s></p><p type="main">

<s>Narra come, rimasto erede di Galileo il figliolo di lui Vincenzio, col quale <lb></lb>seguitò a intrattenere l&#039;antica familiare amicizia; gli dettasse, perchè ne pi­<lb></lb>gliasse copia, tre diverse scritture, ritrovate inedite fra le altre carte di suo <lb></lb>padre. </s>

<s>La prima conteneva il disteso di sei Operazioni astronomiche, e la <lb></lb>seconda consisteva in dodici Problemi e Questioni spezzate. </s>

<s>“ La terza scrit­<lb></lb>tura dettatami, prosegue così a narrare lo stesso Viviani, è un altro princi­<lb></lb>pio di nuovo congresso intitolato <emph type="italics"></emph>ultimo,<emph.end type="italics"></emph.end> forse così detto dal Galileo, avanti <lb></lb>che gli venisse concetto di ridurre anche le postille a&#039;suoi oppositori in forma <lb></lb>di dialogo. </s>

<s>In questo congresso il Galileo introduce al solito per interlocutori <lb></lb>il Salviati ed il Sagredo, escludendo Simplicio, e ponendo per terzo il signor <lb></lb>Paolo Aproino, stato già suo uditore delle Matematiche in Padova. </s>

<s>Tal prin­<lb></lb>cipio è disteso in dialogo, in sei fogli in cirea, dove si spiegano alcune spe­<lb></lb>rienze fatte dal Galileo fin ne&#039;tempi ch&#039;egli era colà lettore, allora che an­<lb></lb>dava investigando la misura della forza della percossa, che in ultimo egli <lb></lb>considerò come infinita, e questa materia, dopo spiegata l&#039;esperienza, voleva <lb></lb>il Galileo trattar matematicamente in tutto il restante del Congresso, come <lb></lb>terza Scienza, dopo le due già promosse da lui medesimo, e con questa finir <lb></lb>di pubblicare il rimanente delle sue più elaborate fatiche, quale sarebbe stata <lb></lb>questa, intorno alla quale egli medesimo disse aver consumato molte migliaia <lb></lb>di ore speculando e filosofando, ed averne in fine conseguito cognizioni lon­<lb></lb>tane da&#039;nostri primi concetti, e però nuove e per la loro novità ammirande ” <lb></lb>(Scienza univ. </s>

<s>delle proporz. </s>

<s>cit., pag. </s>

<s>103). </s></p><p type="main">

<s>Divagato il Viviani di qui un poco il discorso in deplorare la perdita immensa <lb></lb>delle preziose speculazioni, rimaste entro sì ricca miniera d&#039;un tanto Filosofo <lb></lb>e Matematico, e consolatosi che fosse venuto a ristorare il danno, per ciò che <lb></lb>s&#039;appartiene alla percossa, il celebratissimo Gian Alfonso Borelli, che egre­<lb></lb>giamente trattò il subietto nella nuova opera sua; “ ma tornando, poi sog-<pb xlink:href="020/01/2505.jpg" pagenum="130"></pb>giunge, alla copia ch&#039;io mi ritrovo della scrittura intitolata <emph type="italics"></emph>Ultimo congresso,<emph.end type="italics"></emph.end><lb></lb>questa, in alcuni luoghi dov&#039;io aveva qualche difficoltà, mi fu in aiuto a ri­<lb></lb>scontrarla col proprio suo originale il molto reverendo signor Cosimo, figliolo <lb></lb>del suddetto signor Vincenzio, e degno nipote del Galileo ” (ivi, pag. </s>

<s>104). </s></p><p type="main">

<s>Coloro, ch&#039;ebbero a leggere così fatte notizie, pensarono che quest&#039;ul­<lb></lb>timo congresso, di cui qui parla il Viviani, doveva ritrovarsi postumo fra i <lb></lb>manoscritti, de&#039;quali sapevano essere stato legittimo erede il nepote di lui <lb></lb>Jacopo Panzanini. </s>

<s>Tommaso Bonaventuri perciò, che del Panzanini era amico, <lb></lb>lo richese del detto manoscritto, per aggiungerlo, insieme con quell&#039;altro <lb></lb>delle proporzioni, ai quattro dialoghi delle due Scienze nuove, nella edizione, <lb></lb>che nel 1718 stava preparando delle opere di Galileo. </s>

<s>La pubblicazione però <lb></lb>non fu fatta col criterio, che sarebbesi desiderato superiore a quello della <lb></lb>maggior parte degli editori toccati in sorte al grand&#039;Uomo. </s>

<s>Superficialmente <lb></lb>leggendo <emph type="italics"></emph>Principio della quinta Giornata,<emph.end type="italics"></emph.end> scritto in capo al dialogo delle <lb></lb>proporzioni, e <emph type="italics"></emph>Ultimo congresso<emph.end type="italics"></emph.end> intitolato quello della percossa, non dubitò <lb></lb>il Bonaventuri di posporre in ordine questo a quello, non badando all&#039;ana­<lb></lb>cronismo, in che avrebbero offeso i Lettori più attenti. </s>

<s>Bastava del resto aver <lb></lb>portata questa attenzione sopra le linee di stampa, con le quali incominciano <lb></lb>le due scritture, per avvedersi che il dialogo della percossa si rappresenta <lb></lb><emph type="italics"></emph>quindici giorni<emph.end type="italics"></emph.end> dopo il colloquio tenuto intorno ai proietti (Alb. </s>

<s>XIII, 306), <lb></lb>e quello delle proporzioni con l&#039;<emph type="italics"></emph>interposizione di qualche anno<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>288). </s></p><p type="main">

<s>La rappresentanza del dramma apparisce dunque nella prima edizione <lb></lb>fiorentina turpemente deformata, per sola colpa dell&#039;editore, il quale avrebbe <lb></lb>dovuto pensare, qualunque si fosse l&#039;autorità del titolo, che la prima auto­<lb></lb>rità era quella della ragione, la quale avrebbegli suggerito che l&#039;avvenimento <lb></lb>dopo quindici giorni precede a quello dopo qualche anno. </s>

<s>Vero è bene che <lb></lb>non era il nodo estricabile, se non a colui, che avesse avuto le necessarie <lb></lb>notizie storiche; intorno a che non sappiamo se il Bonaventuri, che poteva <lb></lb>avere a mano, come noi i documenti da rintracciarle, sia in tutto meritevole <lb></lb>di scusa: imperocchè il titolo di <emph type="italics"></emph>Giornata quinta<emph.end type="italics"></emph.end> fu posto al Dialogo delle <lb></lb>proporzioni, come si fece osservare altrove, quando ancora il Torricelli non <lb></lb>sapeva che Galileo avesse incominciato a stendere il Dialogo della percossa: <lb></lb>e il titolo di <emph type="italics"></emph>Congresso ultimo<emph.end type="italics"></emph.end> fu messo a questo stesso Dialogo della per­<lb></lb>cossa, quando Galileo non pensava ancora di lasciarlo a mezzo, per saltare <lb></lb>a scriverne, con l&#039;aiuto del Torricelli, un altro d&#039;argomento molto diverso. </s></p><p type="main">

<s>Avrebbero queste ragioni, non solo dato la licenza o il diritto, ma im­<lb></lb>posto il dovere all&#039;editore di mettere, in luogo della Giornata quinta, il trat­<lb></lb>tato della percossa, e quello delle proporzioni in ultimo luogo, non ostante <lb></lb>il titolo scritto dal Torricelli e da Galileo. </s>

<s>Ma perchè, come spesso segue, <lb></lb>l&#039;altrui autorità prevalse al proprio giudizio, s&#039;incorse in quella deformità, <lb></lb>la quale tuttavia resta, e resterà nelle opere galileiane indelebilmente impressa, <lb></lb>come le deformità del corpo, che si contraggono dalla natura. </s></p><p type="main">

<s>Tale è la storia della pubblicazione del Dialogo della percossa, che il Vi­<lb></lb>viani riguardava come una terza Scienza nuova. </s>

<s>E tale pure aspettavasi che <pb xlink:href="020/01/2506.jpg" pagenum="131"></pb>gli dovesse riuscire al giudizio anche il Borelli, il quale congetturava che, <lb></lb>non avendo trovato riscontrar le leggi della comunicazione dei moti con i <lb></lb>già ammessi giovanili principii, <emph type="italics"></emph>ab hisce difficultatibus excitatus<emph.end type="italics"></emph.end> si fosse <lb></lb>volto Galileo da vecchio a professar della natura della percossa più sane dot­<lb></lb>trine. </s>

<s>Non era questa però che una dolce lusinga, perchè della promessa <lb></lb>nuova Scienza della percossa annunziava il Sagredo così la conclusione, a <lb></lb>mezzo alla quarta Giornata: “ Io vorrei pur trovar modo di misurar la forza <lb></lb>di questa percossa, la quale non penso però che sia infinita; anzi stimo <lb></lb>ch&#039;ell&#039;abbia il suo termine, da potersi pareggiare, e finalmente regolare con <lb></lb>altre forze di gravità prementi o di leve o di viti o di altri strumenti mec­<lb></lb>canici, dei quali io a sodisfazione resto capace della moltiplicazione della forza <lb></lb>loro ” (Alb. </s>

<s>XIII, 247). </s></p><p type="main">

<s>Poteva di qui argomentare il Borelli che Galileo da vecchio non aveva <lb></lb>trovata nessuna difficoltà a professare le antiche dottrine, seguitando a com­<lb></lb>parare il moto del martello che percote coi pesi morti sostenuti sul declivio <lb></lb>dei piani, o sui bracci delle leve. </s>

<s>Vero è bene che ivi il Salviati annunzia <lb></lb>tre proposizioni, che furono poi dimostrate nel libro del Borelli, ma essendo <lb></lb>di natural senso comune, e di semplice fatto, i principii dai quali si conclu­<lb></lb>dono quelle stesse proposizioni; non si poteva congetturare di lì che Galileo <lb></lb>si fosse almeno introdotto alla scoperta delle vere leggi, dalle quali si regola <lb></lb>la forza della percossa. </s></p><p type="main">

<s>Le tre dette proposizioni corrispondono alla XXX, XXXI e XXXIV <emph type="italics"></emph>De <lb></lb>vi percussionis,<emph.end type="italics"></emph.end> ma Galileo le pronunzia com&#039;evidenti per sè medesime. </s>

<s>Chi <lb></lb>potrebbe infatti metter dubbio intorno alla prima, che dice: “ Colui che corre <lb></lb>per ferir con una lancia il suo nemico, se nel sopraggiungerlo accaderà che <lb></lb>quello si muova, fuggendo con pari velocità, non farà colpo, e l&#039;azione sarà <lb></lb>un semplice toccar senza offendere ” (Alb. </s>

<s>XIII, 245): o cercar dimostrazione <lb></lb>della seconda, che immediatamente così si soggiunge: “ Ma se la percossa <lb></lb>verrà ricevuta in un soggetto, che non in tutto ceda al percuziente, ma so­<lb></lb>lamente in parte; la percossa danneggerà, ma non con tutto l&#039;impeto, ma <lb></lb>solo con l&#039;eccesso della velocità di esso percuziente sopra la velocità della <lb></lb>ritirata e cedenza del percosso? </s>

<s>” (ivi, pag. </s>

<s>246). </s></p><p type="main">

<s>La terza proposizione che da Galileo s&#039;annunzia: “ Quando il percosso <lb></lb>si movesse con moto contrario verso il percuziente, il colpo e l&#039;incontro si <lb></lb>farebbe tanto più gagliardo, quanto le due velocità contrarie unite son mag­<lb></lb>giori, che la sola del percuziente ” (ivi); sembra che avesse bisogno d&#039;esser <lb></lb><figure id="id.020.01.2506.1.jpg" xlink:href="020/01/2506/1.jpg"></figure></s></p><p type="caption">

<s>Figura 42.<lb></lb>dichiarata con qualche discorso, come il <lb></lb>Borelli fa nella detta sua XXXIV: ma <lb></lb>basta fare una semplice riflessione per <lb></lb>riconoscerla vera. </s>

<s>Suppongansi per esem­<lb></lb>pio due corpi A e B (fig. </s>

<s>42) che, venen­<lb></lb>dosi incontro, si urtano in D con le ve­<lb></lb>locità CD, DF: è chiaro che l&#039;urto ricevuto dal corpo B in D, per essergli <lb></lb>il corpo A venuto incontro da C, è quel medesimo che riceverebbe, se fosse <pb xlink:href="020/01/2507.jpg" pagenum="132"></pb>an dato a percotere nel medesimo corpo A, rimasto immobile in C, con la <lb></lb>e locità FC. </s></p><p type="main">

<s>Da queste verità non era dunque promossa la scienza, e tanto meno era <lb></lb>promossa da ciò, che ivi appresso il Salviati soggiunge della percossa obli­<lb></lb>qua, la quale si dice dover esser più debole della diretta, <emph type="italics"></emph>e più e più se­<lb></lb>condo la maggiore obliquità<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 246), ossia secondo gli angoli del­<lb></lb>l&#039;incidenza. </s>

<s>Da nessuna parte insomma aveva intorno a ciò progredito il <lb></lb>Salviati dei Dialoghi nuovi, applicando all&#039;urto dei corpi ponderosi quel falso <lb></lb>teorema, ne&#039;primi dialoghi pronunziato intorno alla luce, dalla quale vengono <lb></lb>le superficie illuminate più o meno, <emph type="italics"></emph>secondo che i raggi illuminanti vi ca­<lb></lb>scano sopra più o meno obliquamente<emph.end type="italics"></emph.end> (Alb. </s>

<s>I, 91). Se lo sviscerato osse­<lb></lb>quio perciò, e il desiderio di magnificar tutto ciò che si riferiva al Maestro <lb></lb>non avessero fatto passare il Borelli sopra questi, che dalle cose dimostrate <lb></lb>nel suo proprio libro apparivano errori manifesti, non sarebbesi lusingato <lb></lb>d&#039;aver dovuto vedere, se la sorte non l&#039;invidiava, aggiunta alle altre due <lb></lb>nuove la terza scienza della percossa. </s>

<s>Ma le lusinghe non hanno oramai più <lb></lb>potere sopra di noi, fatti certi de&#039;pensieri di Galileo, sopra i quali vogliamo <lb></lb>dare una breve scorsa, per confermare quel che si diceva: non essere cioè <lb></lb>per altro scritto il Dialogo, che per rimovere le difficoltà e le istanze nate <lb></lb>in chi, nella <emph type="italics"></emph>Scienza meccanica,<emph.end type="italics"></emph.end> avesse letto il primo giovanile. </s>

<s>Discorso. </s></p><p type="main">

<s>Incomincia infatti l&#039;Aproino a rivelare le speculazioni dell&#039;Accademico, <lb></lb>le quali tendevano a questo principalmente: a dimostrare cioè che, come <lb></lb>nelle altre macchine, così nell&#039;operazione della percossa interviene il movi­<lb></lb>mento del percuziente congiunto con la sua velocità contro il movimento del <lb></lb>resistente, ed il suo poco o molto dovere esser mosso; ond&#039;essendo simili i <lb></lb>modi dell&#039;operare, simili anco saranno del percotere e del sollevar pesi le <lb></lb>ragioni delle misure. </s>

<s>Fu dall&#039;intenzione di dimostrar ciò che si condusse, per <lb></lb>prima cosa, a immaginar l&#039;esperienza della stadera, che da una parte risente <lb></lb>l&#039;urto fatto da un filo d&#039;acqua cadente giù da una secchia sul fondo di un&#039;al­<lb></lb>tra simile secchia a lei sottoposta, e dall&#039;altra sostiene un peso morto, per <lb></lb>misurar con esso la forza della percossa. </s>

<s>Ma perchè, ignorandosi le leggi <lb></lb>idrauliche scoperte poi dal Castelli e dal Torricelli, non si sapeva misurare <lb></lb>il peso dell&#039;acqua, rimasta in aria fra le due secchie, e non si poteva perciò <lb></lb>dedurne la quantità precisa dell&#039;urto contro il fondo della secchia inferiore, <lb></lb>dovè Galileo rivolgersi ad altre esperienze. </s></p><p type="main">

<s>Fra queste scelse quella del palo confitto dalla berta, della quale si po­<lb></lb>teva misurar la caduta, come si poteva del palo misurare a ogni colpo la <lb></lb>quantità della trafitta. </s>

<s>Supponeva che, essendo la berta cento libbre, cadendo <lb></lb>dall&#039;altezza di quattro braccia conficcasse il palo per quattro dita, la qual <lb></lb>fitta fosse parimente operata da un peso morto di mille libbre. </s>

<s>Tornando a <lb></lb>ripetere il colpo, il palo anderà ancora più giù: per minore spazio però di <lb></lb>prima, il quale supponiamo che sia ridotto a due dita. </s>

<s>Se come si è fatto, <lb></lb>serbando il medesimo peso e la medesima altezza del cadente, si tornasse a <lb></lb>soprapporre il medesimo peso morto delle mille libbre, non se ne vedrebbe <pb xlink:href="020/01/2508.jpg" pagenum="133"></pb>l&#039;effetto, se non a condizione che fosse un tal premente molto maggiore. </s>

<s>Tanto <lb></lb>poi maggiore dovrebb&#039;essere più e più, per far le fitte uguali a quelle del <lb></lb>terzo, del quarto, del quinto colpo della berta: cosicchè ritrarre si può, con­<lb></lb>clude il Salviati, <emph type="italics"></emph>la forza della percossa essere infinita, o vogliam dire inde­<lb></lb>terminata, e indeterminabile<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 314). </s></p><p type="main">

<s>Qui però, al principale intento del dimostratore, s&#039;attraversa negli ascol­<lb></lb>tanti una difficoltà, sembrando che negli ordigni meccanici non si verifichi <lb></lb>questa infinità di forza, che s&#039;attribuisce alla percossa. </s>

<s>Ma il Salviati risponde <lb></lb>ch&#039;ei perciò non credè doversi, nel percotere e nel sollevar pesi, procedere <lb></lb>dalla Natura con mezzi diversi, e conferma particolarmente il suo detto con <lb></lb>l&#039;esempio della stadera, nella quale, egli dice, “ è manifesto che un picco­<lb></lb>lissimo peso di una libbra, scendendo, alzerà un peso di cento, e di mille e <lb></lb>più quante ne piace, se noi lo costituiremo nell&#039;ago cento o mille volte e più <lb></lb>lontano dal centro, che l&#039;altro peso massimo: cioè se noi faremo che lo spa­<lb></lb>zio, per lo quale scenderà quello, sia cento e mille e più volte maggiore <lb></lb>dello spazio della salita dell&#039;altro: cioè se la velocità di quello sia cento e <lb></lb>mille volte maggiore della velocità di questo ” (ivi, 317). </s></p><p type="main">

<s>Credendo di aver così rimossa ogni difficoltà, e gl&#039;interlocutori confes­<lb></lb>sando di esserne rimasti sodisfatti, procede innanzi il Salviati col suo di­<lb></lb>scorso a considerare gli effetti della berta, che ficca il palo, i quali effetti, <lb></lb>essendo ogni volta diversi, domanda quale di questi si dovrà prendere per <lb></lb>ferma e certa misura della forza del colpo, che pure, quanto a sè, è sempre <lb></lb>il medesimo. </s>

<s>La nuova difficoltà si trova dal promotore stesso insuperabile, <lb></lb>per cui si consiglia di tentare altre esperienze e altri modi di riuscire ad <lb></lb>avere una misura costante di quegli effetti. </s>

<s>Immagina perciò di avere sopra <lb></lb>un sostegno posato un gran peso, a cui, per mezzo di una fune che passi <lb></lb>per la gola di una carrucola fissa, sia congiunto, liberamente pendulo, un <lb></lb>altro peso minore. </s>

<s>Questo è certo che stando quieto non moverà l&#039;altro, ma <lb></lb>sollevandolo, e poi lasciatolo di lì cader liberamente, darà, per l&#039;impeto con­<lb></lb>ceputo nella discesa, alla corda una tale strappata, che sarà al gran peso <lb></lb>come un colpo, che lo voglia cacciare in su. </s>

<s>Supponendo ora che la gravità <lb></lb>del gran solido posto in quiete sia per esempio cento volte maggiore della <lb></lb>gravità del piccolo peso, cadente dall&#039;altezza di un braccio, sarà, dice il Sal­<lb></lb>viati, dimostrato che si osserva nella percossa la medesima regola, che negli <lb></lb><figure id="id.020.01.2508.1.jpg" xlink:href="020/01/2508/1.jpg"></figure></s></p><p type="caption">

<s>Figura 43.<lb></lb>altri strumenti meccanici, se si troverà che il gran <lb></lb>peso sia, per la strappata del minore, sollevato per <lb></lb>un solo centesimo di braccio. </s></p><p type="main">

<s>Per giungere alla promessa conclusione, invo­<lb></lb>cando il teorema primo dimostrato nella terza gior­<lb></lb>nata, riduce il Salviati a equabili i moti accelerati <lb></lb>della caduta del piccolo peso e del balzo del grande, <lb></lb>cosicchè gli si viene lo strumento delle esperienze <lb></lb>a trasformare in un piano inclinato, sopra il quale il peso A (fig. </s>

<s>43) sia <lb></lb>sostenuto dal peso B, pendente dalla carrucola all&#039;altra estremità della corda: <pb xlink:href="020/01/2509.jpg" pagenum="134"></pb>dov&#039;è manifesto, egli dice, la resistenza del grande esser sempre ed in tutti <lb></lb>i luoghi la medesima, il che non accade nella resistenza del chiodo e del <lb></lb>palo, ne&#039;quali ella va sempre crescendo, con proporzione ignotissima, nel <lb></lb>dover penetrare il muro o il terreno. </s></p><p type="main">

<s>Suppongasi ora che CD sia cento misure o CE dieci: il piccolo grave B <lb></lb>di dieci pesi farà, secondo le note leggi meccaniche, equilibrio al grande A <lb></lb>di cento, e ogni minima aggiunta a quello basterà per muovere questo. </s>

<s>Sia <lb></lb>mosso per esempio da M in N: per altrettanto spazio sarà sceso il peso B <lb></lb>nella perpendicolare. </s>

<s>E perchè questo rappresenta il percuziente e quello il <lb></lb>peso morto, che equivale alla percossa, se ne dovranno comparare insieme le <lb></lb>velocità o gli spazi passati nelle medesime direzioni perpendicolari. </s>

<s>Condotte <lb></lb>perciò le MO, NO parallele alle DE, CE, sarà NO la misura dell&#039;ascesa perpen­<lb></lb>dicolare del corpo grave A, la quale facilmente si determina, rispetto alla ca­<lb></lb>duta perpendicolare di B, uguale a MN, dalle equazioni MN:NO=DC:CE= <lb></lb>100:10, d&#039;onde NO=MN/10. “ Adunque è manifesto, conclude il Salvlati, che <lb></lb>la caduta del peso di dieci libbre, fatta nella perpendicolare, è bastante a <lb></lb>sollevare il peso di cento libbre, pur nella perpendicolare, ma solo per lo <lb></lb>spazio della decima parte della scesa del cadente di dieci libbre. </s>

<s>Ma quella <lb></lb>forza, che può alzare un peso di cento libbre, è eguale alla forza, con la <lb></lb>quale il medesimo peso delle cento libbre calca in giù, e questa era la po­<lb></lb>tente a cacciare il palo postavi sopra e premendo; ecco dunque esplicato come <lb></lb>la caduta di dieci libbre di peso è potente a cacciare una resistenza equiva­<lb></lb>lente a quella, che ha il peso di cento libbre, per essere sollevato, ma la <lb></lb>cacciata non sarà più che per la decima parte della scesa del percuziente. </s>

<s><lb></lb>E se noi porremo la resistenza del palo essere raddoppiata e triplicata, sic­<lb></lb>chè vi bisogni per superarla la pressura di dugento o trecento libbre di peso <lb></lb>morto, replicando simil discorso, troveremo l&#039;impeto delle dieci libbre cadenti <lb></lb>a perpendicolo esser potente a cacciare, sì come la prima, la seconda e la <lb></lb>terza volta il palo: e come nella prima la decima parte della sua scesa, così <lb></lb>nella seconda volta la ventesima, e nella terza la trentesima parte della sua <lb></lb>scesa. </s>

<s>E così, moltiplicando la resistenza in infinito, sempre la medesima per­<lb></lb>cossa la potrà superare, ma col cacciare il resistente sempre per minore e <lb></lb>minore spazio, con alterna proporzione ” (ivi, pag. </s>

<s>327, 28). </s></p><p type="main">

<s>Ecco in somma qual&#039;è il processo del ragionamento, tenuto da Galileo <lb></lb>nel VI dialogo, e quale ne è la conclusione: ciò che, se avesse potuto leg­<lb></lb>gere il Borelli, avrebbe dovuto confessare di essere rimasto illuso nel suo <lb></lb>giudizio, vigendo tuttavia contro le ultime speculazioni del suo Maestro la <lb></lb>sentenza pronunziata contro le dottrine, ch&#039;egli aveva insegnate nel suo <lb></lb>primo giovanile Discorso. </s>

<s>Imperocchè la proporzione, che passa tra le ve­<lb></lb>locità e i corpi A, B, mentre l&#039;uno scende nel perpendicolo, e l&#039;altro sale <lb></lb>sul piano; è tutt&#039;affatto diversa da quella, che nel libro <emph type="italics"></emph>De vi percussio­<lb></lb>nis<emph.end type="italics"></emph.end> si dimostra dover passare fra quegli stessi termini, mentre che si con­<lb></lb>siderino i due corpi venir tra loro a conflitto. </s>

<s>Essendo dunque la conclusione <pb xlink:href="020/01/2510.jpg" pagenum="135"></pb>di Galileo manifestamente falsa non dovrebbe far maraviglia che tutto in­<lb></lb>tero il detto. </s>

<s>Dialogo niente altro sia che un bel tessuto di paralogismi, come <lb></lb>si diceva. </s></p><p type="main">

<s>Di mezzo però a quei paralogismi risalta una verità nuova, nella quale <lb></lb>consiste tutto il merito, e in cui si raccoglie il frutto unico di quelle migliaia <lb></lb>di ore, che Galileo stesso diceva di avere spese intorno al penetrare i mara­<lb></lb>vigliosi effetti della percossa. </s>

<s>Ma per prepararci a dire in che consista una <lb></lb>tal novità, ritorniamo indietro sulle ragioni, che il Salviati adduce per con­<lb></lb>cluder che la Natura, nel moltiplicare la forza sopra il piano inclinato e nella <lb></lb>percossa, procede nella medesima maniera. </s></p><p type="main">

<s>È chiaro che fra gli altri ordigni meccanici si sceglie il piano, perchè <lb></lb>meglio atto a rappresentare col peso pendulo il percuziente, e, con l&#039;altro <lb></lb>appoggiato, il peso morto che preme. </s>

<s>Avrebbe del resto il discorso condotto <lb></lb>a concludere più semplicemente il medesimo dai principii immediati della <lb></lb>leva, secondo i quali è manifesto che una piccolissima potenza vale a pa­<lb></lb>reggiare una grandissima resistenza, purchè si osservi l&#039;ordine delle di­<lb></lb>stanze, contrariamente prese dal punto di appoggio. </s>

<s>E qui torna a propo­<lb></lb>sito il famosissimo detto di Archimede: <emph type="italics"></emph>Da mihi ubi sistam, et terram <lb></lb>coelumque movebo,<emph.end type="italics"></emph.end> che Galileo applicava alla percossa, ripetendo anch&#039;egli <lb></lb>enfaticamente per somiglianza: <emph type="italics"></emph>Mettimi fuori della Terra, anzi dell&#039;uni­<lb></lb>verso riunito insieme in un globo, e lo commoverò percotendolo col mio <lb></lb>martello.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ecco la maravigliosa sentenza che l&#039;Archimede novello era venuto a pro­<lb></lb>nunziare, concludendo in forma di general proposizione, “ come qualsivoglia <lb></lb>piccolissimo peso, scendendo, faccia salire qualsivoglia immensa e gravissima <lb></lb>mole ” (ivi, pag. </s>

<s>316). La proposizione fu poi come verissima dimostrata <lb></lb>anche dall&#039;Huyghens, nella terza del suo trattato <emph type="italics"></emph>De motu corporum ex vi <lb></lb>percussionis,<emph.end type="italics"></emph.end> dove così l&#039;Autore l&#039;annunzia: “ Corpus quamlibet magnum <lb></lb>a quamlibet exiguo corpore, et qualicumque celeritate impacto, movetur ” <lb></lb>(Opuscula postuma, Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>373). Confermò pure lo stesso <lb></lb>il Mariotte nella VIII della seconda parte del suo libro <emph type="italics"></emph>De la percussion,<emph.end type="italics"></emph.end><lb></lb>esagerando anch&#039;egli come il Nostro l&#039;effetto del piccolissimo verso qualun­<lb></lb>que grandissimo col chiamarlo <emph type="italics"></emph>infinito.<emph.end type="italics"></emph.end> “ La force du choc horisontal est <lb></lb>infinie: c&#039;est-a-dire, que si un corps tres-petit en choque directement un autre <lb></lb>tres-pesant en repos par un mouvement horisontal, si lent, qu&#039;il puisse ètre; <lb></lb>il le mettra en mouvement ” (Oeuvres, T. I, A la Haye 1740, pag. </s>

<s>72). Ma <lb></lb>nè l&#039;esempio del gran naviglio, che in acqua quieta e in aria calma può <lb></lb>esser tirato a riva <emph type="italics"></emph>avec un tres-petit fil de soie, sans que le fil se rompe,<emph.end type="italics"></emph.end><lb></lb>nè l&#039;altro dell&#039;Huyghens, da somiglianti immagini desunto, hanno a che ri­<lb></lb>veder nulla con la bella dimostrazione meccanica di Galileo, ricavata dal fatto <lb></lb>della grandissima sfera pendula, il centro di gravità della quale è necessa­<lb></lb>riamente spostato dal solo toccarla, non che dal percoterla che faccia un <lb></lb>chicco di panico: dimostrazione illustrata così dal Viviani con molta sempli­<lb></lb>cità ed evidenza. </s></p><pb xlink:href="020/01/2511.jpg" pagenum="136"></pb><p type="main">

<s>“ Il grandissimo peso A (fig. </s>

<s>44), pendente dal perpendicolo RA, sarà <lb></lb>sollevato dal piccolissimo peso B, pendente dal medesimo punto R al filo RB. <lb></lb><figure id="id.020.01.2511.1.jpg" xlink:href="020/01/2511/1.jpg"></figure></s></p><p type="caption">

<s>Figura 44.<lb></lb>Perchè, congiunti i centri di gravità di <lb></lb>essi gravi, cioè quello di A, che si sup­<lb></lb>pone essere condotto nell&#039;infimo punto <lb></lb>del suo moto possibile, e quello di B colla <lb></lb>retta BA, il loro centro comune sarà in <lb></lb>essa BA, come in C, fuori del pendulo RA, <lb></lb>il qual centro C, passando per l&#039;arco del <lb></lb>suo moto fatto dal semidiametro RC, ca­<lb></lb>lerà fino che esso si ritrovi nel detto <lb></lb>piombo, e però il gran peso A verrà ne­<lb></lb>cessariamente sollevato ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXIII, fol. </s>

<s>6 a tergo). </s></p><p type="main">

<s>Nè l&#039;Huyghens nè il Mariotte pote­<lb></lb>vano aver notizia di questa proposizione, <lb></lb>che il Viviani così bene illustra sopra il <lb></lb>testo galileiano, della copia del quale egli <lb></lb>era già venuto in possesso: e pure è <lb></lb>certo che non ne aveva ancora avuto no­<lb></lb>tizia il Borelli, quando scriveva la XVI <lb></lb>e la XVII <emph type="italics"></emph>De vi percussionis.<emph.end type="italics"></emph.end> Benchè <lb></lb>dunque si trovassero, in dimostrare la medesima verità, tanti insigni ma­<lb></lb>tematici concordi, volle Onorato Fabry apporre la nota di falsità alle due <lb></lb>dette proposizioni borelliane, l&#039;Autor delle quali, per confermare l&#039;assunto <lb></lb>che, rimanendosi tuttavia inedito il Dialogo galileiano compariva nella Scienza <lb></lb>meccanica come nuovo; s&#039;incontrò in una dimostrazione, che concludeva dai <lb></lb>principii medesimi di Galileo, e si rassomigliava perciò moltissimo a quella <lb></lb>del Viviani. </s></p><p type="main">

<s>Sia GF (fig. </s>

<s>45) una libbra senza peso sostenuta nel suo mezzo A, da <lb></lb>cui penda per un filo, pur senza peso, un vastissimo globo, che movendosi <lb></lb><figure id="id.020.01.2511.2.jpg" xlink:href="020/01/2511/2.jpg"></figure></s></p><p type="caption">

<s>Figura 45.<lb></lb>qua e là descriverebbe col suo centro B il <lb></lb>semicerchio GBF. </s>

<s>Lasciato però in libera posa <lb></lb>si costituirà nel suo luogo più basso, e la lib­<lb></lb>bra FG si disporrà in perfetta linea orizon­<lb></lb>tale. </s>

<s>Aggiungasi ora in G un altro piccolo <lb></lb>corpo: il centro del sistema dovrà da B risalir <lb></lb>verso G, per la linea di congiunzione GB, infino <lb></lb>a un punto, per esempio O, che sia da G, B <lb></lb>distante per lunghezze reciproche ai pesi. </s>

<s>Ivi <lb></lb>però non potrà stabilirsi, ma scenderà, infintantochè la linea AO non si di­<lb></lb>sponga perpendicolare in AB, ciò che non può farsi, senza che il punto B <lb></lb>non risalga alquanto su per l&#039;arco BF. “ Ergo, ne conclude il Borelli, non <lb></lb>obstante illa resistentia positiva, corpus B elevabitur sursum in arcu BF. <pb xlink:href="020/01/2512.jpg" pagenum="137"></pb>Praeterea, quia perinde est si loco corpusculi G ponderosi applicetur quae­<lb></lb>libet vis motiva, sive animata, sive proiectitia, quae aequalem energiam habeat <lb></lb>quam pondus G, et illa ubicumque applicata, sive in G ant in B idem praestat <lb></lb>ac pondus G; proindeque vastum corpus pensile B a quacumque vi motiva <lb></lb>tantulum impelli sursum poterit ” (Historia incendii aetnaei, Reg. </s>

<s>Julio 1670, <lb></lb>pag. </s>

<s>149). </s></p><p type="main">

<s>Il Borelli dunque, l&#039;Huyghens e il Mariotte, a cui potremo altresì ag­<lb></lb>giungere il Wallis, non fecero altro che confermare una verità, la quale non <lb></lb>sapevano che fosse stata rivelata da Galileo, per bocca di quel suo Salviati, <lb></lb>a cui primo faceva pronunziare e dimostrare che qualunque grandissimo peso <lb></lb>può, in certe condizioni, esser mosso da qualunque minima forza. </s>

<s>Dal con­<lb></lb>siderar poi che il medesimo effetto ne segue, o tocchi il piccolo corpo il gran­<lb></lb>dissimo o lo percuota, s&#039;ingerì nello stesso Galileo il concetto che, a quel <lb></lb>modo che opera la Natura in moltiplicar la forza nelle macchine e negli urti <lb></lb>violenti, quando son le proporzioni infinite o incommensurabili; a quel me­<lb></lb>desimo modo ella operi anche nelle proporzioni definite. </s>

<s>Sarebbe come a voler <lb></lb>dire che le proprietà convenienti alla somma delle infinite linee indivisibili, <lb></lb>contessenti una superficie, convenissero a ciascuna linea particolare, commet­<lb></lb>tendo un paralogismo, che facilmente si scoprirebbe con l&#039;osservare che si <lb></lb>paragonano insieme due cose di un genere diverso. </s></p><p type="main">

<s>Dalle astratte speculazioni venivasi quel medesimo paralogismo a tradurre <lb></lb>nei fatti, quando s&#039;immaginavan da Galileo e da&#039;suoi seguaci quegli stru­<lb></lb>menti, e si eseguivano quelle esperienze ordinate a misurare la forza della <lb></lb>percossa fatta sopra uno de&#039;piatti, a proporzione del peso morto posto sul­<lb></lb>l&#039;altro piatto della bilancia. </s>

<s>È dovuto al Borelli anche il merito di aver fu­<lb></lb>gato dalla Scienza questo errore pernicioso, predominante nella Scuola alla <lb></lb>quale egli stesso apparteneva, ed è argomento degno di storia. </s>

<s>Ma prima di <lb></lb>passar oltre a trattarlo, vogliamo ripigliare il filo del nostro primo discorso <lb></lb>intorno al sesto dialogo galileiano, che vedemmo esser rimasto incompleto, <lb></lb>sì per quel che riguarda la forza della percossa, e sì per non trovarvisi fatto <lb></lb>alcun motto di quell&#039;altro promesso trattatello dell&#039;uso delle catenuzze nella <lb></lb>ballistica. </s>

<s>È come una statua di Fidia, collocata sul piedestallo in una pub­<lb></lb>blica piazza da un archeologo, a quel modo ch&#039;ei la ritrovò, sotto le mace­<lb></lb>rie, mutilata, e che noi veniamo ora a reintegrare, almeno nelle principali <lb></lb>e più distinte sue membra. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dicemmo che Galileo, distratto da altre cure suggeritegli dal Viviani e <lb></lb>dal Torricelli, lasciò il dialogo della percossa interrotto al punto, dop&#039;aver <lb></lb>dimostrato, per la somiglianza di ciò che avviene de&#039;gravi sul declivio di un <lb></lb>piano e nel perpendicolo, che i momenti del percuziente e del percosso stanno <pb xlink:href="020/01/2513.jpg" pagenum="138"></pb>reciprocamente come la velocità di questo alla velocità di quello. </s>

<s>Confermava <lb></lb>da così fatte relazioni il primario e principale suo assunto, che cioè la forza, <lb></lb>così nelle macchine che muovono, come in quelle che percotono, sia infinita. </s>

<s><lb></lb>Dicemmo altresì che, per rendere di ciò l&#039;intrapresa trattazione compiuta, <lb></lb>non aveva l&#039;Autore lasciato altro che alcune frettolose note manoscritte, ri­<lb></lb>trovate fra le carte del Viviani sotto il titolo di <emph type="italics"></emph>Roba copiata da un esem­<lb></lb>plare del Galileo.<emph.end type="italics"></emph.end> Apparisce da coteste note che voleva al Salviati far pro­<lb></lb>seguire il discorso, per confermare l&#039;infinità della potenza del colpo in ogni <lb></lb>corpo grave cadente, desumendone le ragioni dalla natura del moto accele­<lb></lb>rato. </s>

<s>E perchè si vedeva di li nascere facilmente alcune difficoltà contro l&#039;as­<lb></lb>sunto, doveva intrattenersi il Salviati stesso a rimoverle dalle dubbiose menti <lb></lb>degl&#039;interlocutori. </s></p><p type="main">

<s>I ragionamenti però, fino a questo punto tenuti fra gli amici, non ave­<lb></lb>vano avuto per subietto altro che le percosse fatte nelle cadute naturali; <lb></lb>ond&#039;è che, a voler esaurire il tema, rimaneva a dir tuttavia delle percosse <lb></lb>artificiali: di quelle cioè prodotte da qualunque forza di proiezione, o comun­<lb></lb>que sia dirette per l&#039;orizzonte o all&#039;insù, come nei martelli fabbrili, e che <lb></lb>Galileo par avesse intenzione di distinguere, comprendendone sotto il nome <lb></lb>di <emph type="italics"></emph>urti<emph.end type="italics"></emph.end> le varietà degli effetti. </s>

<s>Col dimostrar dunque che anche gli urti son <lb></lb>soggetti alle medesime leggi delle percosse naturali, e che son perciò anch&#039;essi <lb></lb>di potenza infinita, si doveva terminar l&#039;argomento, preso dai conversanti a <lb></lb>trattare in questa prima parte della giornata. </s></p><p type="main">

<s>La <emph type="italics"></emph>roba<emph.end type="italics"></emph.end> scritta, nella quale s&#039;accennava a questo proposito di proseguire <lb></lb>e di dar perfezione al trattato della percossa; prima che dal Viviani, come <lb></lb>dicemmo, era stata, vivente Galileo, copiata dal Torricelli, a cui non era, di <lb></lb>ciò che aveva speculato il suo ospite in tal soggetto, da qualche enfatica <lb></lb>espressione in fuori attinta ai familiari colloqui, pervenuta altra notizia. </s>

<s>Il <lb></lb>principe Leopoldo, che non si poteva dar pace di vedere, con sì grave danno <lb></lb>della Filosofia toscana e della Scienza universale, fallite le sue intenzioni, non <lb></lb>lasciava mai occasione d&#039;entrare intorno a ciò in discorso con lo stesso Tor­<lb></lb>ricelli, il quale ebbe finalmente un giorno a mostrare a Sua Altezza, in que&#039;fo­<lb></lb>glietti copiati, ciò che avesse Galileo lasciato scritto della percossa. </s>

<s>Gli volle <lb></lb>il Principe leggere attentamente, e trovando che contenevano pensieri, i quali <lb></lb>s&#039;accennava che sarebbero svolti, o proposizioni, che si prometteva verreb­<lb></lb>bero dimostrate, espresse il suo desiderio, per non dire il comando, che adem­<lb></lb>pisse il discepolo quel che s&#039;era proposto di fare il Maestro. </s>

<s>Si discuteva <lb></lb>intorno alla forma, e se dovessero mettersi quelle cose in dialogo: ma seni­<lb></lb>brando ciò troppo arbitrio, e vedendo tuttavia lontana l&#039;occasion di stam­<lb></lb>parlo, parve più conveniente il leggere a qualche pubblica udienza. </s>

<s>Fece perciò <lb></lb>esso Principe ammettere il Torricelli fra gli Accademici della Crusea, la quale, <lb></lb>proponendosi allora di definir le parole con la notizia delle cose, accoglieva <lb></lb>in sè quegli egregi Toscani, che sapevano scrivere elegante, perchè avevano <lb></lb>prima imparato a pensare profondo. </s>

<s>Erano quasi tutti perciò discepoli e se­<lb></lb>guaci di Galileo, per cui fu una tale adunanza creduta la più opportuna per <pb xlink:href="020/01/2514.jpg" pagenum="139"></pb>divulgarvi gli oracoli ultimamente pronunziati in Arcetri, ciò che significava <lb></lb>il banditore dicendo “ che anco l&#039;istesso Galileo s&#039;appagherebbe piuttosto di <lb></lb>questa sola udienza, che di pubblicare i frammenti de&#039;rimasti suoi scritti ” <lb></lb>(Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>69). Giova a noi credere che fossero così fatte espres­<lb></lb>sioni sincere, benchè alcuni si maravigliassero che si venisse a mescolare la <lb></lb>crusca ne&#039;sacchi del Torricelli, tutti pieni di fior di farina. </s>

<s>Il Cavalieri, ap­<lb></lb>pena avuta la notizia della nuova elezione accademica, scriveva così all&#039;eletto, <lb></lb>il di 14 Luglio 1642, in una lettera da Bologna: “ Gli Accademici della Cru­<lb></lb>sca hanno fatto un grande acquisto con l&#039;aggregazione di V. S., che gli por­<lb></lb>terà fior di roba. </s>

<s>Se non che vogliono cose piuttosto fisiche che matematiche, <lb></lb>e forse con ragione, poichè quelle assomiglierei io piuttosto alla crusca, e <lb></lb>queste al fior di farina, vero cibo e nutrimento dell&#039;intelletto. </s>

<s>Nondimeno <lb></lb>conviene accomodarsi al loro genio, anzi al genio universale ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XLI, fol. </s>

<s>126). E accomodandosi a questo genio universale anche il <lb></lb>Torricelli, incominciò a leggere dalla bugnola i suoi fisici argomenti. </s></p><p type="main">

<s>Letto appena il primo discorso, per ringraziare il Principe e gli Acca­<lb></lb>demici che lo avevano ammesso, entrò subito in argomento della percossa, <lb></lb>dimostrando ch&#039;ell&#039;è infinita, perchè infiniti son gl&#039;istanti di tempo, nei <lb></lb>quali, cadendo il corpo che ha da percotere, si moltiplica la gravità di lui, <lb></lb>che “ nei corpi naturali è come fontana, dalla quale continuamente scatu­<lb></lb>riscono momenti di peso ” (ivi, pag. </s>

<s>73): nè la dimostrazione consiste in <lb></lb>altro che nell&#039;esplicare il concetto di Galileo: “ Il momento di un grave, <lb></lb>nell&#039;atto della percossa, altro non è che un composto ed aggregato d&#039;infiniti <lb></lb>momenti, ciascuno di essi eguale al solo momento o interno e naturale di <lb></lb>sè medesimo, o estrinseco e violento, qual&#039;è quello della forza movente. </s>

<s>Tali <lb></lb>momenti, nel tempo della mossa del grave, si vanno accumulando in istante, <lb></lb>con eguale additamento, e conservando in esso, nel modo appunto che si va <lb></lb>accrescendo la velocità di un grave cadente.... ” (Alb. </s>

<s>XIII, 330, 31). </s></p><p type="main">

<s>Nasceva però contro queste dottrine un dubbio, che non si vedeva come <lb></lb>risolverlo facilmente, perchè se il momento di un grave, nell&#039;atto della per­<lb></lb>cossa, non è altro che un aggregato degl&#039;infiniti momenti acquistati negli <lb></lb>infiniti istanti del tempo della caduta, sembrava che la stessa percossa che <lb></lb>ne segue dovess&#039;essere in qualunque caso infinita: ciò che contradice all&#039;os­<lb></lb>servazione dei fatti, potendo anche un grande grave cadente produrre un pic­<lb></lb>colo colpo. </s>

<s>All&#039;istanza già preveduta accennava di voler rispondere Galileo, <lb></lb>così scrivendo fra le altre note del suo foglio: “ La forza della percossa è <lb></lb>d&#039;infinito momento, tuttavolta che ella si applichi, in un momento ed in un <lb></lb>istante, dal grave percuziente sopra materia non cedente, come si dimo­<lb></lb>strerà ” (ivi, pag. </s>

<s>331). </s></p><p type="main">

<s>La dimostrazione che manca fu supplita dal Torricelli, il quale, osser­<lb></lb>vando che l&#039;impeto conceputo da un grave nello scendere in giù è total­<lb></lb>mente estinto nel ritornare in su per altrettanto spazio, ne concluse la se­<lb></lb>guente risposta, che si conforma col pensiero di Galileo: “ Allora seguirebbe <lb></lb>l&#039;effetto infinito, ad ogni benchè piccola percossa, quando la percossa fosse <pb xlink:href="020/01/2515.jpg" pagenum="140"></pb>momentanea: cioè quando il percuziente applicasse tutto quel cumulo di mo­<lb></lb>menti, che egli ha dentro di sè aggregati insieme, che sono veramente in­<lb></lb>finiti, e gli conferisse tutti al suo resistente in un solo istante di tempo. </s>

<s>Ma <lb></lb>se nell&#039;applicargli gli applica con qualche spazio di tempo non è più neces­<lb></lb>sario che l&#039;effetto segua infinito, anzi può esser minimo, ma però nullo non <lb></lb>mai ” (Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>76). </s></p><p type="main">

<s>Che nullo veramente non sia manifesto si scorge, scriveva Galileo, <lb></lb>dall&#039;esperienza, “ poichè se con un ben piccolo martello si anderà con per­<lb></lb>cosse uniformi incontrando la testa di una grandissima trave, che sia a <lb></lb>giacere in terra, dopo molte e molte percosse si vedrà finalmente essersi <lb></lb>mossa la trave per qualche spazio percettibile: segno evidentissimo che ogni <lb></lb>percossa operò separatamente per la sua parte nello spingere la trave: poi­<lb></lb>chè, se la prima percossa non fosse a parte di tale effetto, tutte le altre sus­<lb></lb>seguenti, come in luogo di prime, niente affatto opererebbero ” (Alb. </s>

<s>XIII, <lb></lb>331, 32). Il Torricelli conferma questo stesso pensiero, asseverando niuna <lb></lb>sorta di percossa esser tanto debole, che non faccia effetto in qualunque ga­<lb></lb>gliardissima resistenza, e adduce a dimostrarlo esperienze simili, e simili ra­<lb></lb>gioni espresse talvolta con le medesime parole, che aveva lette nel manoscritto <lb></lb>galileiano. </s>

<s>“ Imperocchè se il primo colpo, egli dice, non avesse operato cosa <lb></lb>alcuna, adunque il secondo colpo si potrebbe chiamare e considerare per <lb></lb>primo. </s>

<s>Essendo poi il secondo eguale di forza al primo, e ritrovando il resi­<lb></lb>stente nella medesima disposizion per appunto, nè esso ancora opererà cosa <lb></lb>alcuna. </s>

<s>Così proveremo che nè il millesimo nè il milionesimo potrebbero <lb></lb>giammai operare, se non avesse operato anche il primo. </s>

<s>Che poi li molti <lb></lb>operino, parlino questa volta per me le porte di Agrippa e le statue del Va­<lb></lb>ti<gap></gap>ano: si vedono pure, benchè di bronzo durissimo, consumate dal solo acco­<lb></lb>stamento delle mani del popolo curioso e devoto ” (Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>94, 95). </s></p><p type="main">

<s>Altre obiezioni prevedeva il Torricelli contro la dottrina galileiana della <lb></lb>percossa infinita, e prometteva agli Accademici sarebbe venuto a ribatterle <lb></lb>in un&#039;altra tornata. </s>

<s>Consisteva la principale di quelle obiezioni nel dire che, <lb></lb>se un grave cadente avesse dentro di sè momento infinito, dovrebbe aver <lb></lb>anche velocità infinita. </s>

<s>Nè il Torricelli nega che non sia veramente così, pur­<lb></lb>chè però s&#039;intenda di una velocità assoluta, e non paragonata con altra mi­<lb></lb>nore, perchè quando il grave nella quiete avesse per esempio il momento di <lb></lb>una libbra. </s>

<s>“ allora di velocità non aveva cosa alcuna: avendo poi dopo la <lb></lb>caduta acquistato qualche velocità, questo mi pare che si possa chiamare <lb></lb>accrescimento intinito. </s>

<s>Il passaggio dall&#039;esser nulla all&#039;essere qualche cosa <lb></lb>suol giudicarsi mutazione infinita ” (ivi, pag. </s>

<s>87, 88). </s></p><p type="main">

<s>Ma per ridur l&#039;argomento contro l&#039;avversario anche più stringente, os­<lb></lb>serva il Torricelli che i momenti intrinsechi sono un che precedente, e sono <lb></lb>la vera e l&#039;unica causa della maggiore o minore velocità, per cui “ possono <lb></lb>stare e sussistere da sè stessi, senza l&#039;aiuto e la compagnia di velocità al­<lb></lb>cuna ” (ivi, pag. </s>

<s>100). Si richiama per confermar ciò ai principii meccanici, <lb></lb>da sè pubblicamente professati nel trattato <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> rispetto a ciò che av-<pb xlink:href="020/01/2516.jpg" pagenum="141"></pb>viene de&#039;gravi applicati all&#039;estremità della libbra, in distanze diverse, o po­<lb></lb>sati sopra piani con diverse inclinazioni “ dove hanno, egli dice, i diversi <lb></lb>momenti in atto, ma le diverse velocità solo in potenza. </s>

<s>Ma la velocità per <lb></lb>sè stessa non può già sussistere senza i momenti esterni ” (ivi). Qui per <lb></lb>verità non sembra che si sodisfaccia pienamente all&#039;istanza, che cioè una po­<lb></lb>tenza infinita, venendo all&#039;atto, non debba produrre effetto infinito: si toccava <lb></lb>delle velocità virtuali la gelosa questione, la quale era solamente risolubile <lb></lb>da principii tutt&#039;affatto diversi dai torricelliani, considerando la quiete non <lb></lb>come la privazione assoluta del moto, ma come il primo principio e il ter­<lb></lb>mine ultimo del moto. </s></p><p type="main">

<s>Comunque sia, aveva il Torricelli nelle due dette Lezioni esplicato il <lb></lb>pensiero galileiano per quel che riguarda la percossa naturale, ma tornò a <lb></lb>leggere agli Accademici anche la terza volta, per trattare dell&#039;urto, <emph type="italics"></emph>fratello <lb></lb>della percossa, e padre di molte speculazioni<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>106). Queste specu­<lb></lb>lazioni però, nel foglio manoscritto di Galileo, che serviva per distendere le <lb></lb>Lezioni accademiche di testo; si limitavano nell&#039;accennare ad alcune espe­<lb></lb>rienze, per le quali si mostrava “ come s&#039;imprima ne&#039;mobili, e più ne&#039;più <lb></lb>gravi, ed in essi si moltiplichi e conservi la forza, che con qualche tempo <lb></lb>gli si va comunicando ” (Alb. </s>

<s>XIII. 332). </s></p><p type="main">

<s>Da così fatte esperienze dello scaccino, che serra le porte di bronzo di <lb></lb>S. Giovanni, e del sagrestano, che, a furia di dare strappate alla fune, rie­<lb></lb>sce finalmente a far sonare una grossa campana, variate dal Torricelli negli <lb></lb>esempi del gran vascello, e della tavola di abeto che, tirati l&#039;una e l&#039;altro <lb></lb>per un cavo dalle braccia di un uomo, si fanno arrivare a percotere con va­<lb></lb>ria velocità, e con vario effetto; si deduce la teoria galileiana dell&#039;urto, che <lb></lb>dallo stesso Torricelli si riassume in queste parole: “ Abbiamo detto che la <lb></lb>forza dell&#039;urto non dipende altrimenti dalla quantità della materia, poichè se <lb></lb>ciò fosse converrebbe che la medesima palla di sessanta libbre di ferro fa­<lb></lb>cesse sempre la medesima operazione, lanciata una volta da un uomo, e una <lb></lb>volta avventata da un cannone. </s>

<s>Non dipende ne anche assolutamente dalla <lb></lb>velocità, perchè con maggior velocità urterà una tavola d&#039;abeto, tirata per <lb></lb>l&#039;acqua quiescente, che un vastissimo galeone: eppure il meno veloce farà <lb></lb>maggior violenza nell&#039;urtare ” (Lez. </s>

<s>accad. </s>

<s>cit., pag. </s>

<s>118). </s></p><p type="main">

<s>Sembra che da questi così premessi e verissimi principii ne dovesse con­<lb></lb>cludere il valent&#039;uomo che nè da sola la quantità di materia, nè da sola la <lb></lb>velocità, ma dal composto d&#039;ambedue insieme ne resulta la forza dell&#039;urto, <lb></lb>come pochi anni prima aveva concluso l&#039;Aggiunti, e scritto nei dimenticati <lb></lb>suoi fogli: eppure non sa far altro che adombrare il concetto galileiano, in­<lb></lb>vocando la renitenza della materia all&#039;esser mossa. </s>

<s>“ Ella altro non è, di­<lb></lb>ceva, che un vaso di Circe incantato, il quale serve per ricettacolo delle forze <lb></lb>e de&#039;momenti dell&#039;impeto. </s>

<s>La forza poi e gl&#039;impeti sono astratti tanto sot­<lb></lb>tili, son quintessenze tanto spiritose, che in altre ampolle non si posson rac­<lb></lb>chiudere, che nell&#039;intima corpulenza dei solidi naturali ” (ivi, pag. </s>

<s>110). E <lb></lb>come le ampolle tanto più ricevono di liquore, quanto più ne sono capaci, <pb xlink:href="020/01/2517.jpg" pagenum="142"></pb>così son atti a far maggiore conserva di forza i solidi più corpulenti; e non <lb></lb>fa perciò maraviglia che il vascello, il quale porta seco i momenti accumu­<lb></lb>lati per lo spazio di un&#039;ora dal tirar delle braccia di quell&#039;uomo, faccia mag­<lb></lb>gior effetto della tavola di abeto, la quale non portava seco altro che la forza <lb></lb>e i momenti accumulati in quaranta battute di polso. </s></p><p type="main">

<s>Soggiunge immediatamente d&#039;inclinar forse a credere “ che se fosse <lb></lb>possibile di racchiudere e restringere dentro a un vilissimo emisfero di noce, <lb></lb>ma infrangibile, tutta quella forza e fatica, che nello spazio di mezz&#039;ora è <lb></lb>stata prodotta dal traente del nostro immaginato vascello; crederei, dico, che <lb></lb>forse quel leggerisssimo guscio facesse nell&#039;atto dell&#039;urtare la medesima ope­<lb></lb>razione, che faceva l&#039;immensa mole del naviglio ” (ivi, pag. </s>

<s>111, 12). Si con­<lb></lb>ferma di qui che non era nella mente del Torricelli ben definito il concetto <lb></lb>di forza, o di quantità di moto, che sappiamo risultar dal prodotto della ve­<lb></lb>locità per la massa: che se si fossero nel discorso ora trascritto disposti gli <lb></lb>elementi secondo l&#039;ordine proprio, avrebbe dovuto dir chi lo fece che se <lb></lb>fosse impressa al guscio della noce tanta velocità, da compensare con essa <lb></lb>al difetto della mole, avrebbe, nell&#039;essere spinto a riva, prodotto la mede­<lb></lb>sima percossa del gran naviglio. </s>

<s>L&#039;incerta opinione si sarebbe trasformata <lb></lb>così in quelle leggi matematiche, della scoperta delle quali lasciarono Gali­<lb></lb>leo e il Torricelli il merito a un loro discepolo. </s></p><p type="main">

<s>Le lezioni del Torricelli fatte recitare dal principe Leopoldo, affinchè si <lb></lb>divulgassero, nel più sollecito ed efficace modo, fra i letterati e gli scienziati <lb></lb>toscani convenuti insieme ǹell&#039;Accademia della Crusca, i pensieri postumi di <lb></lb>Galileo; rimasero sconosciute al pubblico infino al 1715, quando pensò a <lb></lb>stamparle insieme in un volume in Firenze quel Tommaso Bonaventuri che, <lb></lb>raccogliendo tre anni dopo le opere galileiane, aggiunse agli altri delle due <lb></lb>Scienze nuove il dialogo sesto. </s>

<s>A lui dunque aveva dato in mano la sorte <lb></lb>quelle scritture, dalle quali riunite insieme resultavan compiute le specula­<lb></lb>zioni di Galileo intorno alla forza della percossa, non facendo altro il Torri­<lb></lb>celli che proseguire l&#039;opera del Salviati, rimasta interrotta nel manoscritto <lb></lb>copiato dal Viviani. </s>

<s>L&#039;editore fiorentino però non seppe vedere queste rela­<lb></lb>zioni, che passavano fra le Lezioni accademiche del Discepolo, e il Dialogo <lb></lb>incominciato dal Maestro, perchè altrimenti non avrebbe dubitato di unire <lb></lb>insieme le due scritture, che, sebbene apparissero sotto forme diverse, com­<lb></lb>prendevano in un solo pensiero la mente dell&#039;Autore intera e perfetta. </s>

<s>Se <lb></lb>noi dovessimo perciò, com&#039;editori che si assumono l&#039;ufficio di dar le opere <lb></lb>galileiane complete, ristampare i dialoghi delle due Scienze nuove, aggiun­<lb></lb>geremmo al sesto, dove fu lasciato interrotto dal Bonaventuri, le tre Lezioni <lb></lb>accademiche sulla forza della percossa. </s>

<s>Il disteso, è vero, è del Torricelli, ma <lb></lb>i pensieri sono di Galileo, com&#039;apparisce dalla scrittura, che servi ad esse <lb></lb>Lezioni di testo, ond&#039;è che la ragione d&#039;inserirle fra le altre opere galile­<lb></lb>iane sarebbe quella medesima, che consigliò ad inserire il quinto dialogo <lb></lb>sulla riforma di Euclide. </s>

<s>Così sarebbe riserbato a noi, condannati come rei <lb></lb>tante volte di avere infranto l&#039;idolo antico, il merito di averlo invece restau-<pb xlink:href="020/01/2518.jpg" pagenum="143"></pb>rato in uno almeno degli angoli dell&#039;altare, e di esser venuti, noi unici al <lb></lb>mondo, a tergere le lacrime al popolo devoto. </s></p><p type="main">

<s>Questo merito nonostante noi lo reputiam quasi nulla verso un altro, <lb></lb>che ci ripromettiamo di acquistare appresso agli offesi Galileiani, ai quasi si <lb></lb>annunzia che, dopo aver riconosciute e riordinate le divise scritture inte­<lb></lb>granti il VI dialogo, per quel che riguarda il trattato della percossa; abbiam <lb></lb>trovato da reintegrarlo altresì per quel che riguarda l&#039;uso delle catenelle, a <lb></lb>dar regola, senza ricorrere ai calcoli laboriosi, di dirigere i tiri delle arti­<lb></lb>glierie. </s></p><p type="main">

<s>Sulla fine della quarta Giornata il Salviati, dop&#039;aver detto che le cate­<lb></lb>nelle, lentamente sospese per le loro estremità, s&#039;incurvano in una certa sacca, <lb></lb>che moltissimo si rassomiglia alla parabola; accenna a qualche non piccola <lb></lb>utilità, alla quale potrebber così fatte catenelle servire, di che promette agli <lb></lb>interlocutori che ne avrebbe trattato appresso. </s>

<s>Speditosi poi dalla dimostra­<lb></lb>zione della corda tesa, per la quale aveva divagato il discorso, Simplicio lo <lb></lb>richiama alla fatta promessa d&#039;esplicar cioè “ qual sia l&#039;utilità, che da si­<lb></lb>mili catenelle si può ritrarre, e dopo questo arrecare quelle speculazioni, che <lb></lb>dal nostro Accademico sono state fatte intorno alla forza della percossa ” <lb></lb>(Alb. </s>

<s>XIII, 266). Ma l&#039;ora essendo così tarda, da non bastare a disbrigar le <lb></lb>nominate materie, si consiglia il Salviati <emph type="italics"></emph>di differire il congresso ad altro <lb></lb>tempo più opportuno.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Era in quel congresso dunque proposto di trattar prima delle catenelle, <lb></lb>e poi della percossa, ma fu il proposito riformato, premettendo questo a quello <lb></lb>argomento, qualunque se ne fosse la ragione, la quale non dispensava però <lb></lb>esso Salviati dal mantenere intere le sue promesse. </s>

<s>E che veramente avesse <lb></lb>intenzione di mantenerle, apparisce dall&#039;avere al colloquio così ben misurato <lb></lb>il tempo che, esaurito il primo trattato, intorno al quale anche compresa la <lb></lb>teoria degli urti si sarebbe la conversazione intrattenuta appena infino a ora <lb></lb>di nona; rimanesse tanto di sera, da passare a sodisfare i desiderosi d&#039;in­<lb></lb>tendere a quale uso mai si adoprerebbero le catenelle. </s>

<s>Ciò nonostante que&#039;de­<lb></lb>siderii, dopo più che un secolo e mezzo, si rimangono insodisfatti, nè par <lb></lb>che se ne dolesse o se ne dolga alcuno de&#039;Galileiani più infervorati. </s>

<s>Noi dun­<lb></lb>que siamo stati fra costoro i primi ed i soli, che ci siamo industriosamente <lb></lb>messi a cercare, e finalmente abbiamo trovato quella seconda parte del dia­<lb></lb>logo galileiano, la quale, soggiungendosi alla prima della percossa, dava al <lb></lb>buon Salviati materia da filosofar con gli amici infino a sera. </s>

<s>Come ci oc­<lb></lb>corresse a fare la scoperta, in mezzo a certi farraginosi manoscritti datici a <lb></lb>esaminare da un nostro amico, ci dispenseremo dal narrarlo ai nostri Let­<lb></lb>tori, i quali noi crediamo desiderosi piuttosto di veder senza indugio quel <lb></lb>che di là fu da noi ricopiato, ed è quanto appresso: </s></p><p type="main">

<s>“ SAGREDO. — I vostri ragionamenti, sig. </s>

<s>Salviati, mi hanno d&#039;ogni <lb></lb>parte così persuaso le forze delle percosse naturali e degli urti essere infi­<lb></lb>nite, che potete oramai risparmiarvi di trattenere intorno a ciò altri discorsi. </s>

<s><lb></lb>Potete dunque passar liberamente per me a mantenere l&#039;altra vostra pro-<pb xlink:href="020/01/2519.jpg" pagenum="144"></pb>messa, quale era di dirci l&#039;utilità, che sperava di ricavare il nostro Accademico <lb></lb>dalle catenuzze, applicate a punteggiare molte linee paraboliche sopra una <lb></lb>piana superficie. </s>

<s>Ma vedo qui il sig. </s>

<s>Aproino in atto di una certa maraviglia. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — Voi mi avete inteso, sig. </s>

<s>Sagredo, perchè questa vostra <lb></lb>proposta mi riesce affatto nuova. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Avete ragione: io non ho pensato che non era la S. V. <lb></lb>presente, quando, prima di congedarci la sera del passato nostro congresso, <lb></lb>il sig. </s>

<s>Salviati fece intendere a me e al sig. </s>

<s>Simplicio che appresso alla di­<lb></lb>mostrazione della forza della percossa avrebbe soggiunta la notizia delle ca­<lb></lb>tenuzze appese dalle estremità loro, le quali con la loro sacca diceva che <lb></lb>naturalmente s&#039;accomodano alla curvatura di linee paraboliche. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — A una prima maraviglia voi non fate così che aggiun­<lb></lb>germene un&#039;altra molto maggiore, per la quale sono entrato in grandissima <lb></lb>curiosità di vedere il fine di una cosa, ch&#039;era sempre rimasta senz&#039;alcuno <lb></lb>significato a&#039;miei, come a tutti gli occhi volgari. </s>

<s>Mi rivolgo perciò a fare <lb></lb>istanza insieme con voi al sig. </s>

<s>Salviati, perchè voglia senz&#039;altro indugio en­<lb></lb>trare in questo nuovo ragionamento. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Il sig. </s>

<s>Aproino, che troppo tardi è venuto a pigliar parte <lb></lb>nella nostra conversazione, non saprà forse che nell&#039;altro nostro congresso si <lb></lb>lessero le dimostrazioni dell&#039;Accademico intorno alla nuova Scienza dei pro­<lb></lb>ietti, per fondamento della quale si poneva che, fatta astrazione dagl&#039;impe­<lb></lb>dimenti dell&#039;aria, e da qualsivoglia altro estrinseco accidente, descrivono essi <lb></lb>proietti in aria una linea curva, non punto differente dalla parabola. </s>

<s>Di qui <lb></lb>venivano inaspettatamente suggerite certissime norme all&#039;arte dei bombar­<lb></lb>dieri, nel dirigere i loro tiri, cosicchè, fatto prima esperienza dell&#039;impeto, <lb></lb>ossia della forza che ha di cacciare in su nel perpendicolo, con una data mi­<lb></lb>sura di polvere, lo strumento, il sapere a qual distanza avrebbe gettata la <lb></lb><figure id="id.020.01.2519.1.jpg" xlink:href="020/01/2519/1.jpg"></figure></s></p><p type="caption">

<s>Figura 46.<lb></lb>medesima palla, nella tale o nella tal&#039;altra in­<lb></lb>clinazion della squadra, si riduceva a calcoli <lb></lb>matematici disposti dall&#039;Autore in tavole esat­<lb></lb>tissime per servigio dei militari. </s>

<s>Ma perchè l&#039;uso <lb></lb>di coteste tavole richiedeva pure qualche noti­<lb></lb>zia delle dottrine, e in ogni modo bisognava <lb></lb>ricorrere alle pagine di un libro, e a trattar <lb></lb>gli strumenti dell&#039;uomo letterato, di che non <lb></lb>può sempre aversi comodità in un accampa­<lb></lb>mento; dall&#039;avere osservato che la sacca delle <lb></lb>catenelle è una parabola, venne in mente allo <lb></lb>stesso Accademico di ridurre a un semplice <lb></lb>esercizio manuale quel che il Filosofo aveva <lb></lb>scritto ne&#039;suoi libri. </s>

<s>” </s></p><p type="main">

<s>“ Supponga, sig. </s>

<s>Aproino, di avere sopra <lb></lb>una superficie piana, come sarebbe una tavoletta di legno o un cartoncino <lb></lb>assai duro, appuntati in A e in B (fig. </s>

<s>46), all&#039;estremità di una linea ori-<pb xlink:href="020/01/2520.jpg" pagenum="145"></pb>zontale, due spilli, dai quali si faccia pendere una sottilissima calena, che <lb></lb>lenteggiando s&#039;incurverà secondo la linea ACB in figura di una parabola, <lb></lb>l&#039;altezza della quale sarà CD e AB l&#039;ampiezza. </s>

<s>S&#039;ella vorrà mantenere quella <lb></lb>medesima ampiezza, ma descrivere parabole più o meno alte, che passino <lb></lb>per un dato scopo v. </s>

<s>g. </s>

<s>per E, ella non dovrebbe far altro che ritirare la <lb></lb>catenella per uno dei suoi capi. </s>

<s>S&#039;immagini ora che coteste curve rappre­<lb></lb>sentino le vie disegnate per aria da un proietto in B: ella intenderà facil­<lb></lb>mente come si possa, conducendo le tangenti BF, BG, misurare gli angoli <lb></lb>DBF, DBG, e così sapere l&#039;elevazione del pezzo, a cui corrispondono le ri­<lb></lb>chieste ampiezze e altezze del tiro. </s>

<s>Un quadrante perciò giustamente diviso <lb></lb>e applicato alla tavoletta, col centro in B, servirebbe a risolvere così questo, <lb></lb>come altri simili problemi. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — Intendo benissimo come sarebbe un tale strumento assai <lb></lb>comodo per i militari, ai quali presterebbe non punto minor servigio del <lb></lb>Compasso di proporzione, che lo stesso Inventore descrisse e pubblicò, per <lb></lb>facilitare le operazioni geometriche e aritmetiche a quelle persone, le quali, <lb></lb>essendo in tanti altri maneggi occupate e distratte, non possono avere la pa­<lb></lb>zienza assidua, che ci vuole per seguir le regole insegnate dai libri. </s>

<s>Ma a <lb></lb>condurre le divisate operazioni ad effetto mi si presentano alcune difficoltà, <lb></lb>la prima delle quali è intorno al modo come possa la catenuzza lasciar, sulla <lb></lb>superficie da lei toccata, il vestigio. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Il modo più facile, e che pure non aberra di troppo dalla <lb></lb>richiesta precisione, è quello di punteggiare o con uno stile o con una penna; <lb></lb>ma volendo avere un disegno e serbarlo, per servirsene come di stampa, <lb></lb>usava il nostro Accademico di traforare con uno spillo il cartone lungo le <lb></lb>tracce della catena, e poi con lo spolvero ne riproduceva altrove, e quante <lb></lb>volte gli fosse piaciuto, il medesimo disegno. </s>

<s>Questo, che voi vedete così tra­<lb></lb>forato e così annerito lungo queste tre linee, sopra le quali passò il piumac­<lb></lb>cino pieno di polvere di brace; era preparato per ritrovare i gradi delle ele­<lb></lb>vazioni nelle parabole di varia altezza, e di tutte le quali fosse 465 l&#039;am­<lb></lb>piezza totale. </s>

<s>Chiesi questo cartoncino all&#039;Autore, appresso al quale era ri­<lb></lb>masto inutile, per averne fatto un altro simile e più preciso, un giorno che <lb></lb>lo trovai nel suo studio, tutto intento a questi esercizi, e, benchè vile agli <lb></lb>occhi del volgo, la Filosofia nonostante e l&#039;amicizia me lo fanno tenere in <lb></lb>grandissimo pregio. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — Io non me ne pregerei punto meno di voi, sig. </s>

<s>Salviati, <lb></lb>quanto all&#039;amicizia, ma quanto alla Filosofia io per me non troverci d&#039;acquie­<lb></lb>tarmi nell&#039;a<gap></gap>irare il pregio dell&#039;invenzione, se non allora, che mi venisse <lb></lb>dimostrato essere veramente parabolica la linea, secondo la quale s&#039;incurva <lb></lb>una catena. </s>

<s>E perchè, asseverandolo voi con tanta fiducia, non posso credere <lb></lb>che non ne abbiate qualche ragione dimostrativa, vi prego a dirmela, per­<lb></lb>chè io abbia insieme con voi a tenere da qui innanzi in quel pregio che si <lb></lb>merita, e ch&#039;io desidero, la invenzione del nostro comune amico. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — La dimostrazione, che voi richiedete, si riduce all&#039;evi-<pb xlink:href="020/01/2521.jpg" pagenum="146"></pb>denza di un fatto, perchè, se voi descriverete, con gli strumenti suggeritivi, <lb></lb>e con le regole insegnate dai Geometri, le parabole ACB, AEB, come nella <lb></lb>figura precedente, o quante altre più ve ne piacesse, e poi vi adatterete una <lb></lb>catenella; troverete che ella cammina <emph type="italics"></emph>ad unguem<emph.end type="italics"></emph.end> sopra ognuna delle para­<lb></lb>bole geometriche da voi descritte. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Io ho più volte fatta questa esperienza, ed ho trovato <lb></lb>che si verifica, specialmente nelle parabole con elevazione sotto ai 45 gradi. </s>

<s><lb></lb>Vi confesso però, sig. </s>

<s>Salviati, che questo modo di descrivere meccanicamente <lb></lb>le curve non ha ottenuto mai nella mia mente l&#039;assenso, che avrei dato a <lb></lb>una vera e propria dimostrazion matematica, e quale mi sembra si richie­<lb></lb>derebbe, per far di queste catenuzze uno strumento militare, che esattamente <lb></lb>risponda alle operazioni della Ballistica, come risponde il compasso alle ope­<lb></lb>razioni dell&#039;Aritmetica e della Geometria. </s>

<s>Sento perciò anch&#039;io di parteci­<lb></lb>pare con le difficoltà del signor Aproino. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Buon per me che io mi trovo in grado di poter dare <lb></lb>ampia sodisfazione ad ambedue, avendo io avuto dal nostro Accademico que­<lb></lb>sta matematica dimostrazione, che voi desiderate. </s>

<s>Vi dirò anzi, per vostra <lb></lb>consolazione, ch&#039;egli medesimo mi ha confessato più volte di non essersi <lb></lb>acquietato di affidare conclusione così importante alla semplice vista, nella <lb></lb>quale, e nel non risponder sempre la materia alle intenzioni dell&#039;arte, po­<lb></lb>teva sospettarsi qualche fallacia. </s>

<s>Di qui è che solo allora propose l&#039;uso del <lb></lb>suo nuovo strumento militare quando riuscì a dimostrar che la linea, nella <lb></lb>quale si dispongono gli anelli di una catena, è quella medesima, che segnano i <lb></lb>proietti per l&#039;aria: nè io v&#039;avrei promesso di darvi questo trattato, quando <lb></lb>non ne avessi avuto certezza di scienza. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — M&#039;immagino che non possa questa certezza dipendere da <lb></lb>altro, che dalle dottrine già dimostrate intorno alla nuova Scienza del moto. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Non poteva non esser così, come voi dite, e son parti­<lb></lb>colarmente così fatte dottrine derivate da una di quelle proposizioni, che voi <lb></lb>vi rammenterete di avere udita leggere da me, nel trattato delle resistenze <lb></lb>dei solidi allo spezzarsi. </s>

<s>Immaginate infatti che siano tutti gli anelli compo­<lb></lb>nenti la catena infilati in un&#039;asta orizzontale sostenuta a&#039;due estremi, la <lb></lb>quale, a un tratto, nei punti dov&#039;è gravata, si fiacchi, rimanendo esse sole <lb></lb>l&#039;estremità immobili: tutti gli altri anelli, che stavano nel mezzo, abbando­<lb></lb>nati, cadranno, e cadendo non potranno accomodarsi in quel nuovo stato di <lb></lb>equilibrio, se non a condizion che ciascuno sia sceso quanto comportava il <lb></lb>suo proprio momento. </s>

<s>E perchè l&#039;ordine di quelle scese, incominciando dal <lb></lb>secondo anello infino a quello di mezzo, è che decide della figura, secondo <lb></lb>la quale viene a incurvarsi la metà della catena, che necessariamente sarà <lb></lb>simile all&#039;altra; voi intendete che tutto si riduce a sapere con qual mo­<lb></lb>mento gravitino gli anelli, che si suppongono simili e uguali, sopra tutta <lb></lb>la lunghezza dell&#039;asta, secondo le distanze varie di qua e di là dai so­<lb></lb>stegni. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — Permettete, sig. </s>

<s>Salviati, che io aiuti la mia debole in-<pb xlink:href="020/01/2522.jpg" pagenum="147"></pb>telligenza con un poco di figura: Sia CD (fig. </s>

<s>47) l&#039;asta appoggiata nelle sue <lb></lb>estremità: supposto che i pesi di due anelli, uno in B, l&#039;altro in A, siano <lb></lb><figure id="id.020.01.2522.1.jpg" xlink:href="020/01/2522/1.jpg"></figure></s></p><p type="caption">

<s>Figura 47.<lb></lb>rappresentati dai gravi H, F, fra loro <lb></lb>uguali e pendenti nell&#039;asta da que&#039;me­<lb></lb>desimi punti B, A; voi proponete di <lb></lb>risolvere il problema qual sia il mo­<lb></lb>mento del peso H in B verso il mo­<lb></lb>mento del medesimo peso, o del suo <lb></lb>eguale F, in A. Io, nella scienza ma­<lb></lb>tematica, che ho potuto fin qui impa­<lb></lb>rare dai maestri e dai libri, non ritrovo chiari i principii per risolvere la que­<lb></lb>stione, ma in ogni modo non mi sembrano alieni dalle speculazioni meccaniche <lb></lb>intorno alla Libbra, per cui non vederei come c&#039;entrassero le proposizioni <lb></lb>delle resistenze dei solidi allo spezzarsi, anco quando avessi avuto la sorte <lb></lb>d&#039;intervenire, come il sig. </s>

<s>Sagredo, ai passati vostri congressi. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Ma la nuova Scienza delle resistenze voi dovete sapere <lb></lb>che da nessun&#039;altra dipende, che da quella antica di Archimede intorno alla <lb></lb>Libbra, purchè la linea geometrica, all&#039;estremità della quale s&#039;aggiungono i <lb></lb>pesi, si consideri come una verga solida, che debba spezzarsi. </s>

<s>Se sia la lib­<lb></lb>bra AB (fig. </s>

<s>48) col sostegno in C, voi dite, per la dottrina degli equipon­<lb></lb><figure id="id.020.01.2522.2.jpg" xlink:href="020/01/2522/2.jpg"></figure></s></p><p type="caption">

<s>Figura 48.<lb></lb>deranti, che sarà in equilibrio, <lb></lb>quando, alla potenza del peso A in <lb></lb>alzare, giustamente resista il peso <lb></lb>B all&#039;essere alzato. </s>

<s>Ma le mede­<lb></lb>sime ragioni di potenza e di resi­<lb></lb>stenza si possono applicare allo <lb></lb>strumento, considerando la linea <lb></lb>AB come una verga solida, la <lb></lb>quale consisterà in equilibrio, tutte <lb></lb>le volte che la potenza di A allo spezzare equivalga alla resistenza B all&#039;essere <lb></lb>spezzato. </s>

<s>Che se quelle due opposte virtù di operare e di resistere fossero le <lb></lb>massime in produrre il relativo effetto, qualunque minima aggiunta all&#039;una o <lb></lb>detrazione all&#039;altra basterà per turbar l&#039;equilibrio, ossia per fiaccare la verga, fa­<lb></lb>cendola abbassare e rivolgere intorno al centro C, come nella semplice Libbra. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Voi ora, sig. </s>

<s>Salviati, mi fate congetturare che la pro­<lb></lb>posizione, nel trattato delle resistenze da voi stesso poco sopra accennata, <lb></lb>possa essere la dodicesima, la quale, se ben mi ricordo, pronunziaste in que­<lb></lb>sta maniera: <emph type="italics"></emph>Se nella lunghezza di un cilindro si noteranno due luoghi, <lb></lb>sopra i quali si voglia far la frazione di esso cilindro, le resistenze di <lb></lb>detti due luoghi hanno fra di loro la medesima proporzione, che i ret­<lb></lb>tangoli fatti dalle distanze di essi luoghi contrariamente presi.<emph.end type="italics"></emph.end> Se non che <lb></lb>io vi confesso che mi trovo combattuto da due parti circa a questa propo­<lb></lb>sizione: il primo assalto mi viene dal considerarla in sè stessa, e il secondo <lb></lb>dal passare a farne l&#039;applicazione ai momenti del medesimo peso collocato <pb xlink:href="020/01/2523.jpg" pagenum="148"></pb>a varie distanze dal mezzo dell&#039;asta. </s>

<s>Io non ho infatti dubitato mai della ve­<lb></lb>rità della detta proposizione, ma del modo come da voi stesso veniva dimo­<lb></lb>strata, fondandovi sopra un supposto, secondo me dubitabile, perchè forse da <lb></lb>me non bene inteso, che cioè i momenti dei gravi appesi in una bilancia <lb></lb>hanno tra loro la proporzione composta delle distanze dal sostegno e delle <lb></lb>moli. </s>

<s>Questo quanto alla proposizione in sè stessa: quanto poi all&#039;applica­<lb></lb>zione, che si accennava di farne ai momenti dei pesi, nella Libbra appog­<lb></lb>giata alle estremità della sua lunghezza, mi teneva in dubbio il pensare che, <lb></lb>nella detta XII, il cilindro, sopra cui proponevasi di far la frazione, si con­<lb></lb>siderava invece da voi con gli appoggi nei punti di mezzo. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Non dubitate, sig. </s>

<s>Sagredo, che io troverò modo di quie­<lb></lb>tare la vostra mente intorno all&#039;uno e all&#039;altro dubbio. </s>

<s>E incominciando dal <lb></lb>primo, io non vi negherò che la proporzion dei momenti, come trasparisce <lb></lb>dalla XII proposizione del trattato delle resistenze, non lasciasse qualche cosa <lb></lb>a desiderare. </s>

<s>Si poteva però non difficilmente supplire al difetto richiaman­<lb></lb>dosi alla definizione, che dei momenti danno gli Autori della Scienza mec­<lb></lb>canica, e alle note leggi degli equiponderanti nella Libbra. </s>

<s>Resultando in­<lb></lb>fatti da quelle leggi che permane allora la macchina in equilibrio, quando, <lb></lb>come nella precedente figura, il peso A, moltiplicato per la distanza AC dal <lb></lb>sostegno, è uguale al peso B moltiplicato per la distanza BC; se voi date <lb></lb>alla propensione o all&#039;impeto di andare in basso, composto di gravità e di <lb></lb>posizione, il nome di <emph type="italics"></emph>momento,<emph.end type="italics"></emph.end> averete già concluso che i momenti nella bi­<lb></lb>lancia hanno la ragion composta delle distanze e dei pesi. </s>

<s>” </s></p><p type="main">

<s>“ Dietro queste considerazioni non stimò necessario l&#039;Autore del trat­<lb></lb>tato delle resistenze che si dimostrasse una cosa, di sì facile conclusione dagli <lb></lb>antichi teoremi di Archimede. </s>

<s>Ma nell&#039;ordinare le proposizioni ultimamente <lb></lb>da lui dimostrate, per servire di fondamento al nuovo trattatello dell&#039;uso <lb></lb>delle catenuzze, incominciandosi dall&#039;invocare i momenti, secondo la propor­<lb></lb>zion dei quali scendono più o meno gli anelli, credè bene l&#039;Accademico di <lb></lb>dover mettere espressa la proposizione, ch&#039;io vi leggerò sopra questo foglio, <lb></lb>nella forma originale, nella quale fu scritta, e che anche per noi sarà in or­<lb></lb>dine la prima di quelle, che ricorreranno via via nel nostro ragionamento. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO I. — Ponderum in Libra suspensorum momenta habent ra­<lb></lb>tionem compositam ex ratione ipsorum ponderum, et ex ratione distantiarum. </s>

<s>” </s></p><p type="main">

<s>“ Pendeant pondera DE, et F (fig. </s>

<s>49) ex distantiis AB, BC: dico mo­<lb></lb><figure id="id.020.01.2523.1.jpg" xlink:href="020/01/2523/1.jpg"></figure></s></p><p type="caption">

<s>Figura 49.<lb></lb>mentum ponderis DE, ad mo­<lb></lb>mentum ponderis F, habere <lb></lb>rationem compositam ex ra­<lb></lb>tionibus ponderis DE, ad pon­<lb></lb>dus F, et distantiae AB ad di­<lb></lb>stantiam BC. </s>

<s>Ut enim AB ad <lb></lb>BC, ita fiat pondus F ad pon­<lb></lb>dus DO: cum ergo pondera F et DO habeant rationem distantiarum AB, BC <lb></lb>permutatam, erit momentum ponderis F aequale momento ponderis DE. </s>

<s>Cum <pb xlink:href="020/01/2524.jpg" pagenum="149"></pb>igitur sint tria pondera utcumque ED, F, et DO, erit ratio ponderis ED ad <lb></lb>DO composita ex rationibus ED ad F, et F ad DO. </s>

<s>Ut autem pondus ED, ad <lb></lb>pon dus DO, ita momentum ED ad momentum DO; pendent enim ex eodem <lb></lb>puncto: igitur, cum momentum DO sit aequale momento F, ratio momenti <lb></lb>ED ad momentum F erit composita ex ratione ponderis ED ad pondus F, <lb></lb>et ponderis F ad pondus DO. </s>

<s>Factum est autem pondus F ad pondus DO ut <lb></lb>distantia AB ad distantiam BC; ergo patet momentum ponderis ED, ad mo­<lb></lb>mentum ponderis F, habere rationem compositam ex rationibus ponderum <lb></lb>ED, F, et distantiarum AB, BC. ” </s></p><p type="main">

<s>“ APROINO. — Io ringrazio voi, sig. </s>

<s>Salviati, e benedico anche insieme <lb></lb>i dubbi del sig. </s>

<s>Sagredo, che hanno dato occasione di metter fuori un teo­<lb></lb>rema, nel quale non ho memoria di essermi incontrato mai, leggendo ciò che <lb></lb>in simile materia è stato scritto dagli altri autori. </s>

<s>La conclusione io la vedo <lb></lb>poi scendere da così chiari principii, che mi fanno intravedere non poche <lb></lb>altre conseguenze utili alla dottrina dei moti. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — L&#039;utilità che voi sagacemente avete appresa, la vedrete <lb></lb>presto, sig. </s>

<s>Aproino, ricavarsi dalle applicazioni che ne faremo, ma intanto è <lb></lb>bene che passiamo a risolvere l&#039;altro dubbio del sig. </s>

<s>Sagredo, nel sereno volto <lb></lb>del quale mi par di leggere la soddisfazione, che già ha avuto del primo. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Non dite solo sodisfazione, ma compiacenza, per essere <lb></lb>anche a me, come al sig. </s>

<s>Aproino, giunta quella dimostrazione della propor­<lb></lb>zion dei momenti cosa del tutto nuova. </s>

<s>E benchè io forse potessi anche da <lb></lb>me riuscire a intendere le ragioni del trapasso, dal cilindro sostenuto nel <lb></lb>mezzo, al cilindro appoggiato negli estremi, essendo lì lì per fiaccarsi, aggra­<lb></lb>vato nell&#039;uno e nell&#039;altro modo dai medesimi pesi; aspetto che voi me ne <lb></lb>alleviate la fatica, e rendiate me, più che da me medesimo, sicuro di aver <lb></lb>veduto il vero. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Io lascerei volentieri intera a voi la compiacenza di <lb></lb>ritrovare come sia vero che s&#039;hanno le medesime condizioni d&#039;equilibrio <lb></lb>nella libbra geometrica, e nella verga rigida che vuole spezzarsi, o siano i <lb></lb>sostegni nel mezzo o negli estremi, essendo dall&#039;altra parte la cosa facilis­<lb></lb>sima a dimostrarsi. </s>

<s>Ma perchè voi volete che io sovvenga ad alleggerirvi la <lb></lb>fatica, richiamerò la vostra considerazione sopra la libbra AB, poco fa dise­<lb></lb>gnata nella figura 48, la quale voi ben sapete consistere in equilibrio intorno <lb></lb>al punto C, quando sta il peso A al peso B reciprocamente, come la distanza <lb></lb>BC alla AC. Componendo, troveremo il peso A col peso B, al semplice peso A <lb></lb>o al semplice peso B, essere come BC con AC, ossia AB, a BC o ad AC: <lb></lb>ond&#039;è manifesto che rimane la bilancia in equilibrio, tanto col sostegno in C <lb></lb>e i pesi in A, B, quanto col mettere in A e in B i sostegni, e in C la somma <lb></lb>di quegli stessi due pesi. </s>

<s>Dalla libbra geometrica facendo poi il trapasso al <lb></lb>cilindro solido, intenderete che, se A, B sono i massimi sforzi, ai quali quello <lb></lb>stesso cilindro resiste senza spezzarsi, sostenuto in C; sostenuto invece in A <lb></lb>e in B, la somma dei due pesi in C misurerà la massima forza, a cui può <lb></lb>resistere il solido all&#039;esser rotto in quel medesimo punto. </s>

<s>” </s></p><pb xlink:href="020/01/2525.jpg" pagenum="150"></pb><p type="main">

<s>“ Riduciamoci ora alla memoria la proposizione XII delle resistenze: <lb></lb>fu in quella da noi dimostrato che, se le forze A, B son minime per rom­<lb></lb>pere in C, e le E, F parimente minime per rompere in D, le forze A, B, <lb></lb>alle E, F hanno reciprocamente la medesima proporzione, che il rettangolo <lb></lb>ADB al rettangolo ACB. </s>

<s>Ma per quel che s&#039;è detto e convenuto, tant&#039;è a <lb></lb>mantenere i sostegni in D, C, e i pesi in A, B, e in E, F, quanto a traspor­<lb></lb>tare i sostegni in A, B, e i pesi A, B, riuniti insieme, in C, e gli altri E, F <lb></lb>riuniti in D; diremo dunque, e sia questa la seconda proposizione, che, aven­<lb></lb>dosi un cilindro sostenuto nelle sue estremità A, B, il peso che può rompere <lb></lb>in C, al peso che può rompere in D, ossia la resistenza in C, alla resistenza <lb></lb>in D, sta come il rettangolo ADB, al rettangolo ACB. </s>

<s>La dimostrazione perciò <lb></lb>sarebbe ora quella medesima, che fu allora, e solo si potrebbe ripetere in <lb></lb>grazia del sig. </s>

<s>Aproino, che non era presente. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — Voi mi avete così bene, sig. </s>

<s>Salviati, preparate le vie <lb></lb>co&#039;vostri dotti ragionamenti, che non diffido di riuscire da me medesimo a <lb></lb>rintracciare quella dimostrazione. </s>

<s>In ogni modo, per non indugiar di troppo <lb></lb>a venire a concludere il rimanente che è il desiderato fine del nostro collo­<lb></lb>quio, supporrò come vera la proposizione, che voi avete messa in ordine la <lb></lb>seconda. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Se così è, non rimane a fare che un passo solo, per riu­<lb></lb>scire all&#039;intento nostro principale, qual era quello di saper con quali varii <lb></lb>momenti pesino gli anelli sopra l&#039;asta, nella quale s&#039;immaginava che fossero <lb></lb>infilati, e di li dedurne le proporzioni delle scese, per concludere all&#039;ultimo <lb></lb>qual sia la linea, nella quale s&#039;incurva la catena. </s>

<s>Vi annunzio intanto, rife­<lb></lb>rendoci alla figura, per quel primo proposito disegnata, questa terza propo­<lb></lb>sizione, che dice: il momento del peso F in A, al momento del medesimo <lb></lb>peso, o di un peso uguale H in B, sta omologamente come il rettangolo CAD, <lb></lb>al rettangolo CBD. ” </s></p><p type="main">

<s>“ SAGREDO. — Cosicchè i momenti stanno contrariamente alle resistenze, <lb></lb>e l&#039;anello della catena in B averà meno impeto di scendere, che non ha <lb></lb>l&#039;anello in A, perchè quello trova, nell&#039;asta che più gli resiste, maggiore <lb></lb>l&#039;impedimento. </s>

<s>Così pure intendo perchè la catena, dal primo anello a quello <lb></lb>di mezzo, si dilunghi sempre più dalla disposizione orizontale, che aveva es­<lb></lb>sendo infilata nell&#039;asta, trovandosi poi al suo proprio peso abbandonata. </s>

<s>Mi <lb></lb>sembra anche di veder distinto l&#039;albore di quel lume di verità, che voi sa­<lb></lb>rete presto per rivelare alle nostre desiderose pupille: e perchè l&#039;indugio ne <lb></lb>riesce penoso, proseguite, sig. </s>

<s>Salviati, a dimostrare che i momenti dei pesi <lb></lb>F, H hanno tra di loro la medesima proporzione, che i rettangoli fatti dalle <lb></lb>distanze di essi luoghi omologamente presi. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — La dimostrazione, dietro quel che è stato detto fin qui, <lb></lb>e consentito da voi insieme col sig. </s>

<s>Aproino, è facile e spedita. </s>

<s>Imperocchè, <lb></lb>mantenuta sott&#039;occhio la medesima rappresentazione, supponiamo che sia il <lb></lb>peso F la misura della resistenza in A, e che la misura della resistenza in B <lb></lb>sia il peso H aggrandito in E. Sarà, per la seconda proposizione, la resistenza <pb xlink:href="020/01/2526.jpg" pagenum="151"></pb>in A, alla resistenza in B; ossia il peso F al peso E, come il rettangolo CBD <lb></lb>al rettangolo CAD. </s>

<s>Ma essendo i pesi H, E attaccati al medesimo punto della <lb></lb>Libbra, hanno la proporzion medesima dei loro momenti, cioè il momento <lb></lb>di H al momento di E (che è uguale al momento di F, per avere la mede­<lb></lb>sima virtù di rompere l&#039;asta) sta come il peso F al peso E; dunque il mo­<lb></lb>mento di H, al momento di F, sta come il rettangolo CBD al rettangolo CAD, <lb></lb>secondo quel che mi proposi di dimostrare. </s>

<s>” </s></p><p type="main">

<s>“ Ci siamo ora finalmente condotti, per questa ordinata serie di propo­<lb></lb>sizioni, a ritrovare quel che s&#039;andava cercando in fino dal principio del no­<lb></lb>stro ragionamento, e a che si diceva ridursi la somma delle cose: a sapere <lb></lb>cioè con qual momento facciano i vari anelli della catena impeto di scen­<lb></lb>dere, abbandonati dall&#039;asta che gli sosteneva. </s>

<s>Sia l&#039;asta rappresentata dalla <lb></lb>linea orizontale HD (fig. </s>

<s>50) e per l&#039;impeto o il momento, che ha l&#039;anello <lb></lb>in F, supponiamo che possa scendere in fino in E, quant&#039;è la linea perpen­<lb></lb><figure id="id.020.01.2526.1.jpg" xlink:href="020/01/2526/1.jpg"></figure></s></p><p type="caption">

<s>Figura 50.<lb></lb>dicolare FE, e parimente l&#039;anello in N possa scen­<lb></lb>dere quanto la linea MN. </s>

<s>Perchè le scese debbono <lb></lb>essere proporzionali ai loro momenti, sarà dunque, <lb></lb>per le cose già dimostrate, FE ad NM come il ret­<lb></lb>tangolo HFD al rettangolo HND. </s>

<s>Ora che altro ci ri­<lb></lb>mane per concludere che i punti E, M, e tutti gli altri <lb></lb>rispondenti agli anelli di una catena, sono veramente <lb></lb>in una parabola, se non che invocare un teorema, che <lb></lb>non troverete scritto da nessuno Autore o antico o <lb></lb>moderno, ma che il nostro Accademico dimostrò in <lb></lb>grazia del suo trattato delle resistenze? </s>

<s>Io vi voglio ora proporre quel teorema <lb></lb>che è tale: Le parallele al diametro della parabola di cui seghino perpendico­<lb></lb>larmente la base, hanno la proporzione medesima dei rettangoli fatti dai se­<lb></lb>gamenti; e così v. </s>

<s>g. </s>

<s>le NM, FE, parallele al diametro AC nella disegnata <lb></lb>figura, staranno fra loro come i rettangoli HND, HFD. ” </s></p><p type="main">

<s>“ APROINO. — Il padre Fra Bonaventura Cavalieri, quando fui poco tempo <lb></lb>fa a visitarlo a Bologna, e a proposito del mio strumento da rinforzare l&#039;udito <lb></lb>essendo entrato con lui in ragionamento dei Conici, mi disse cotesto stesso teo­<lb></lb>rema, ma non intesi bene, se come sua propria invenzione o del sig. </s>

<s>Galileo. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Potrebb&#039;esser benissimo che anche il padre Bonaventura, <lb></lb>a cui il nostro Amico è solito dare il nome di Archimede del nostro tempo, <lb></lb>si fosse incontrato in cotesta medesima passione della parabola, utilissima per <lb></lb>molte dimostrazioni di Meccanica e di Geometria: ma io posso assicurarvi <lb></lb>di avere avuto, ne&#039;colloqui coll&#039;Accademico, una tale notizia molti anni prima <lb></lb>che fosse l&#039;ingegno del Cavalieri maturo a produrre di simili frutti. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Voi mi fate ora risovvenire di avere udito questo mede­<lb></lb>simo in Padova, quando il nostro Matematico insegnava nel nostro pubblico <lb></lb>studio. </s>

<s>E perchè la verità non fa caro di sè a nessuno, che desiderosamente, <lb></lb>e per le medesime vie rette la cerca, consolateci, sig. </s>

<s>Salviati, col mostrarla <lb></lb>di nuovo ai nostri occhi svelata. </s>

<s>” </s></p><pb xlink:href="020/01/2527.jpg" pagenum="152"></pb><p type="main">

<s>“ SALVIATI. — Mi gode l&#039;animo di poter darvi piena sodisfazione, anche <lb></lb>questa volta, non ricercandosi veramente in voi altra precognizione da quella in <lb></lb>fuori, che aveste allora, quando dalla semplice generazione della parabola imme­<lb></lb>diatamente vi conclusi che le diametrali stanno come i quadrati delle applicate. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — Io ho bene a memoria la dimostrazione, che ne dà nei <lb></lb>suoi Conici Apollonio, e perciò tengo anch&#039;io come cosa già nota che la li­<lb></lb>nea AC sta alla AB, come il quadrato di CD sta al quadrato di BE. ” </s></p><p type="main">

<s>“ SALVIATI. </s>

<s>Così veramente essendo, dividiamo, e averemo AC meno AB, <lb></lb>ossia BC, ossia l&#039;uguale EF, sta ad AC, come il quadrato di CD, meno il <lb></lb>quadrato di BE, sta al quadrato di CD. </s>

<s>Ma la differenza di due quadrati es­<lb></lb>sendo uguale al rettangolo fatto dalla somma e dalla differenza delle radici, <lb></lb>secondo che facilmente si deduce dalla IVa del secondo di Euclide, sarà il <lb></lb>quadrato di CD, meno il quadrato di BE, uguale alla linea CD più BE, ossia <lb></lb>HF moltiplicata per la linea CD meno BE, ossia FD, o altrimenti la diffe­<lb></lb>renza dei due detti quadrati sarà uguale al rettangolo HFD: onde EF ad AC <lb></lb>avrà la proporzion medesima che il rettangolo HFD al quadrato di CD. </s>

<s>In <lb></lb>pari modo dimostreremo che NM ad AC ha la proporzione che il rettangolo <lb></lb>HND al quadrato di CD: onde avendo le due proporzioni i conseguenti uguali, <lb></lb>e dovendo esser perciò gli antecedenti proporzionali, si conclude che FE, MN <lb></lb>stanno insieme come i rettangoli HFD, HND, secondo ciò che io v&#039;ebbi pro­<lb></lb>messo, per satisfare al vostro desiderio. </s>

<s>” </s></p><p type="main">

<s>Il Dialogo rimane a questo punto interrotto, ma il trattato dell&#039;uso delle <lb></lb>catenuzze in ogni modo è compiuto, e ciò che si sente dovervi mancare <lb></lb>non poteva esser altro che il congedo fra gl&#039;interlocutori più o meno ceri­<lb></lb>monioso. </s>

<s>Nel consentir nonostante i nostri Lettori che si comprenda nelle <lb></lb>trascritte parole intero l&#039;argomento, potrebbero domandare a noi le ragioni, <lb></lb>che ci hanno fatto attribuire quella scrittura a Galileo. </s>

<s>Intorno a che è da <lb></lb>distinguere tra la forma e la materia, la quale che sia schiettamente gali­<lb></lb>leiana basterebbe a provarlo con certezza il fatto, che autografo dell&#039;Accade­<lb></lb>mico, nel codice e nel foglio da noi citati nel Tomo precedente all&#039;articolo IV <lb></lb>del Cap. </s>

<s>VIII, è il teorema letto dal Salviati intorno ai momenti composti <lb></lb>delle distanze e delle moli; che pure è autografa la proposizione, da noi pa­<lb></lb>rimente ivi citata, dei pesi uguali che, nell&#039;asta sostenuta all&#039;estremità, ope­<lb></lb>rano con momenti omologamente proporzionali ai rettangoli fatti sulle di­<lb></lb>stanze dai sostegni; che autografo in fine è il disegno da noi nel citato Tomo <lb></lb>e capitolo rappresentato, in cui accennava Galileo di voler applicare la pro­<lb></lb>posizione ultimamente detta agli anelli della catena, con manifesta intenzione <lb></lb>di concluderne la curvità di lei parabolica. </s></p><p type="main">

<s>Nè vogliamo proseguire oltre il nostro discorso, senza fare osservare che <lb></lb>la scoperta del Dialogo delle catenuzze, a noi felicemente in questi ultimi <lb></lb>giorni occorsa, ci ha tolti alcuni dubbi, e ka dichiarati certi fatti rimasti a <lb></lb>noi oscuri, quando nel detto Cap. </s>

<s>VIII si esponeva la nostra storia, nella quale <lb></lb>si diceva di non sapere intendere come si rimanessero fra le altre carte inu­<lb></lb>tili gli autografi dianzi commemorati; e, potendo con la materia di essi l&#039;Au-<pb xlink:href="020/01/2528.jpg" pagenum="153"></pb>tore illustrare il suo trattato delle resistenze, lo volesse nulladimeno lasciare <lb></lb>in questo difetto, perchè poi, a sovvenire ai bisogni della Scienza, vi supplis­<lb></lb>sero a gara il Cavalieri, il Torricelli e il Viviani. </s>

<s>Ora abbiamo inteso che le <lb></lb>proposizioni rimaste manoscritte erano ordinate a un trattato alquanto diverso <lb></lb>da quello proprio delle resistenze, e che, tutt&#039;altro ch&#039;esser dimostrate per <lb></lb>esser poi rifiutate, come ci parve ritrovandole così neglette, dovevano anzi ser­<lb></lb>vire di ricca trama, sopra la quale si ordirebbe il rimanente colloquio, per <lb></lb>condurre a sera con esso la giornata incominciatasi col discorso della percossa. </s></p><p type="main">

<s>Tornando ora a dire delle ragioni, per le quali si provi che l&#039;altro di­<lb></lb>scorso dell&#039;uso delle catenuzze da noi trascritto era informato ai concetti di <lb></lb>Galileo, si può aggiungere che il cartoncino traforato lungo il filo delle linee <lb></lb>paraboliche con uno spillo, per riprodurre con lo spolvero il medesimo di­<lb></lb>segno, con quelle macchie nere lasciatevi sopra dal piumaccino, e in quello <lb></lb>stato proprio che apparisce dalle parole del Salviati, si conserva tuttavia cu­<lb></lb>cito, in luogo del foglio 41, nel II Tomo della Parte V dei Manoscritti di <lb></lb>Galileo, dove ripetutamente negli angoli opposti si legge autografo <emph type="italics"></emph>amplitudo <lb></lb>tota 465.<emph.end type="italics"></emph.end> Ma la più autorevole conferma di ciò, che s&#039;intende provare, si ha <lb></lb>dalla testimonianza del Viviani, a cui crediamo di dovere attribuire il disteso <lb></lb>del dialogo, o del frammento di dialogo da noi ritrovato, in una copia, che <lb></lb>deve essere di quel tempo. </s></p><p type="main">

<s>In margine alla pag. </s>

<s>284 dell&#039;edizione di Leida, dove al Sagredo, che <lb></lb>proponeva potersi con una catenuzza punteggiare molte linee paraboliche, il <lb></lb>Salviati rispondeva <emph type="italics"></emph>potersi ct ancora con qualche utilità non piccola come <lb></lb>appresso vi dirò;<emph.end type="italics"></emph.end> il Viviani apponeva una tale postilla: “ Per mezzo di que­<lb></lb>sta catenella trovava forse il Galileo le elevazioni, per andare a ferire nello <lb></lb>scopo dato ” (MSS. Gal., P. V, T. IX). Poi, in una di quelle note, scritta <lb></lb>dal medesimo al fol. </s>

<s>23 del Tomo IV di quella stessa Parte V della colle­<lb></lb>zione, esprimeva un simile dubbio in quest&#039;altra forma: “ Vedi a carte 384 <lb></lb>l&#039;ultimo verso, che utilità volesse dire il Galileo, se della misura della linea <lb></lb>parabolica, ovvero del modo di trovare le proposizioni de&#039;moti de&#039;proietti. </s>

<s>” </s></p><p type="main">

<s>Vennero nella mente a risolversi intorno a ciò tutti i dubbi, quando i <lb></lb>foglietti autografi, ne&#039;quali erano scritte le proposizioni dei momenti fatti da <lb></lb>pesi uguali sopra la libbra sostenuta alle sue estremità, d&#039;onde si conclude­<lb></lb>vano le virtù degl&#039;impeti e le quantità della scesa in ciascuno anello della <lb></lb>catena; capitarono sotto gli occhi del Viviani. </s>

<s>Allora, ordinando coteste di­<lb></lb>sperse proposizioni, e risovvenendosi di ciò che aveva udito dire al Maestro <lb></lb>nell&#039;ospizio di Arcetri, ricompose il Viviani stesso quel trattatello dell&#039;uso <lb></lb>delle catenuzze, di cui non avevasi altra notizia, da quegli accenni in fuori <lb></lb>fatti dal Salviati in sulla sera della quarta giornata. </s>

<s>Così il congresso ultimo <lb></lb>sarebbe venuto a compiersi, secondo le date promesse, nelle sue due parti; <lb></lb>ond&#039;è perciò naturale che, ritenendo il Viviani copia della prima trattante <lb></lb>della percossa, all&#039;intenzion ch&#039;egli aveva di pubblicarla fra le opere postume, <lb></lb>dopo la vita di Galileo, da dedicarsi al re di Francia, s&#039;aggiungesse l&#039;altra <lb></lb>di ridurre il Dialogo intero, distendendo coi documenti già ritrovati quel che <pb xlink:href="020/01/2529.jpg" pagenum="154"></pb>rimaneva a dirsi dell&#039;uso delle catenuzze nell&#039;arte militare. </s>

<s>Fallite poi le spe­<lb></lb>ranze di raccogliere in un libro le opere, che per ultimo meditava di scri­<lb></lb>vere il suo Maestro, il Viviani si contentò, in quel <emph type="italics"></emph>Ragguaglio<emph.end type="italics"></emph.end> che aggiunse <lb></lb>dopo la <emph type="italics"></emph>Scienza universale delle proporzioni,<emph.end type="italics"></emph.end> di sodisfare al pubblico, anche <lb></lb>in tal proposito, con queste notizie: </s></p><p type="main">

<s>“ Restami ora a dir quant&#039;io so intorno all&#039;uso delle catenuzze, pro­<lb></lb>messo dal Galileo nel fine della quarta Giornata, riferendolo quale egli me <lb></lb>l&#039;accennò quando, presente lui, io stava studiando la sua Scienza de&#039;proietti. </s>

<s><lb></lb>Parmi dunque che egli intendesse di valersi di simili catene sottilissime pen­<lb></lb>denti dall&#039;estremità loro sopra un piano, per cavar dalle diverse tensioni di <lb></lb>esse la regola e la pratica di tirar coll&#039;artiglieria ad un dato scopo. </s>

<s>Ma di <lb></lb>questo a sufficienza e ingegnosamente scrisse il nostro Torricelli nel fine del <lb></lb>suo trattato de&#039;proietti, onde tal perdita rimane risarcita. </s>

<s>” </s></p><p type="main">

<s>“ Che poi la sacca naturale di simili catenuzze s&#039;adatti sempre alla cur­<lb></lb>vatura di linee paraboliche, lo deduceva egli, se mal non mi sovviene, da un <lb></lb>simile discorso: Dovendo i gravi scender naturalmente colla proporzione del <lb></lb>momento, che essi hanno da&#039;luoghi dove e&#039;son appesi, ed avendo i momenti <lb></lb>de&#039;gravi uguali, attaccati ai punti di una libbra sostenuta nell&#039;estremità, la <lb></lb>medesima proporzion de&#039;rettangoli delle parti di essa libbra, come il Galileo <lb></lb>stesso dimostrò nel trattato Delle resistenze, e questa proporzione essendo la <lb></lb>medesima che quella tra le linee rette, che dai punti di tal libbra, come <lb></lb>base d&#039;una parabola, si tirano parallele al diametro di tal parabola, per la <lb></lb>dottrina de&#039;Conici; tutti gli anelli della catenuzza, che son come tanti pesi <lb></lb>uguali pendenti da&#039;punti di quella linea retta, che congiugne l&#039;estremità dove <lb></lb>essa catena è attaccata, e che serve di base della parabola, dovendo in fine <lb></lb>scendere quant&#039;è loro permesso dai loro momenti e quivi fermarsi, fermar <lb></lb>si dovranno in que&#039;punti, dove le scese loro son proporzionali a&#039;propri mo­<lb></lb>menti da&#039;luoghi di dove pendono essi anelli nell&#039;ultimo stante del moto, che <lb></lb>poi son que&#039;punti, che s&#039;adattano ad una curva parabolica lunga quanto la <lb></lb>catena, ed il di cui diametro, che si parte dal mezzo di detta base, sia per­<lb></lb>pendicolare all&#039;orizonte ” (Ediz. </s>

<s>cit., pag. </s>

<s>105, 6). </s></p><p type="main">

<s>È facile vedere in queste parole compendiato il dialogo da noi trascritto, <lb></lb>la perdita del quale credeva il Viviani rimanesse risarcita dal Torricelli. </s>

<s>Ma <lb></lb>il Torricelli in verità descrive ingegnosamente, in fine al suo trattato de&#039;pro­<lb></lb>ietti, un nuovo genere di Squadra, della quale potessero praticamente valersi <lb></lb>i Bombardieri: non fa motto però dello strumento ideato da Galileo, nè del­<lb></lb>l&#039;ordine delle proposizioni, che dovevano partecipare a lui maggior certezza <lb></lb>di scienza meccanica, che non agli strumenti immaginati e descritti per mi­<lb></lb>surare la forza della percossa. </s>

<s>Il dialogo perciò, quale fu pubblicato dal Bo­<lb></lb>naventuri, si rimane in difetto della sua parte migliore, la quale non si sarebbe <lb></lb>aspettato mai il popolo devoto gli dovess&#039;essere restituita da noi, sacrileghi <lb></lb>offensori del Nume. </s>

<s>Ma così è, si vede, nella religione della scienza, come in <lb></lb>tutte le cose di questo mondo, delle quali lasciando ad altri il pensiero, noi <lb></lb>ci ridurremo sul filo del nostro primo ragionamento. </s></p><pb xlink:href="020/01/2530.jpg" pagenum="155"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Fu lasciata addietro la nostra Storia dei progressi fatti intorno alla <lb></lb>scienza della percossa nell&#039;esame del Dialogo di Galileo, il quale concludeva <lb></lb>le sue dottrine così nella seguente proposizione: “ Se l&#039;effetto che fa una <lb></lb>percossa del medesimo peso, e cadente dalla medesima altezza, caccerà un <lb></lb>resistente di resistenza sempre uguale per qualche spazio, e che per fare un <lb></lb>simile effetto ci bisogni una determinata quantità di peso morto, che senza <lb></lb>percossa prema; dico che, quando il medesimo percuziente sopra un altro <lb></lb>resistente maggiore con tal percossa lo caccerà v. </s>

<s>g. </s>

<s>per la metà dello spa­<lb></lb>zio, che fu cacciato l&#039;altro, per far questa seconda cacciata non basta la <lb></lb>pressura del detto peso morto, ma ve ne vuole altro il doppio più grave: e <lb></lb>così in tutte le altre proporzioni, quanto una cacciata fatta dal medesimo per­<lb></lb>cuziente è più breve, tanto per l&#039;opposto, con proporzione contraria, vi si ri­<lb></lb>cerca, per far l&#039;istesso, gravità maggiore di peso morto premente ” (Alb. </s>

<s>XIII, <lb></lb>326, 27). Dicemmo allora come, riscontrata questa galileiana proposizione con <lb></lb>le nuove verità dimostrate dal Borelli, si scoprisse manifestamente falsa, e <lb></lb>ora soggiungiamo che la falsità della conclusione dipendeva dalla falsità del <lb></lb>principio, consistente nel paragonare insieme due cose di genere diverso, quali <lb></lb>sono il peso morto e il grave, che cadendo percuote. </s>

<s>E perchè la più dan­<lb></lb>nosa applicazione di questo falso principio si faceva a quei vari strumenti im­<lb></lb>maginati per misurare la forza della percossa, e per concluderne di lì com&#039;ella <lb></lb>fosse infinita; giova trattenersi a descrivere i lusi dell&#039;ingegno, e a dire come <lb></lb>finalmente se ne scoprisse la fallacia. </s></p><p type="main">

<s>Quando il congresso tra il Salviati, il Sagredo e l&#039;Aproino non era a <lb></lb>nessun altro noto che al Viviani, il quale teneva di quella scrittura appresso <lb></lb>a sè copia segreta; correva largamente attorno la fama che Galileo avesse <lb></lb>inventato due insigni esperimenti, per dimostrare come la forza della per­<lb></lb>cossa si potesse veramente dire infinita. </s>

<s>Il Torricelli si fece, nella seconda <lb></lb>delle sue lezioni, organo diffusivo di quella fama, descrivendo così le inven­<lb></lb>zioni del famosissimo Vecchio ai suoi colleghi accademici della Crusca: </s></p><p type="main">

<s>“ Egli, mentre viveva, in Padova fece far di molti archi, tutti però di <lb></lb>diversa gagliardezza. </s>

<s>Prendeva poi il più debole di tutti, ed al mezzo della <lb></lb>corda di esso sospendeva una palla di piombo, di due oncie in circa, attac­<lb></lb>cata con un filo lungo per esempio un braccio: fermato l&#039;arco in una morsa, <lb></lb>alzava quella palla, e lasciandola ricadere osservava, per via d&#039;un vaso so­<lb></lb>noro sottoposto, per quanto spazio l&#039;impeto della palla incurvasse e si tirasse <lb></lb>dietro la corda dell&#039;arco: noi supporremo che fosse intorno a quattro dita. </s>

<s><lb></lb>Attaccava poi alla corda del medesimo arco un peso quiescente, tanto grande <lb></lb>che incurvasse e tirasse giù la corda dell&#039;arco per lo medesimo spazio di <lb></lb>quattro dita, e osservava che tal peso voleva essere circa dieci libbre. </s>

<s>Fatto <pb xlink:href="020/01/2531.jpg" pagenum="156"></pb>questo, prendeva un altro arco più gagliardo del primo, alla corda di esso <lb></lb>sospendeva la medesima palla di piomho col medesimo filo, e, facendola ca­<lb></lb>dere dalla medesima altezza, notava per quanto spazio ella attraesse la corda. </s>

<s><lb></lb>Attaccava poi del piombo quiescente, tanto che facesse il medesimo effetto, e <lb></lb>trovava che non bastavano più quelle dieci libbre, che bastavano prima, ma <lb></lb>volevano essere più di venti. </s>

<s>Pigliando poi di mano in mano archi sempre <lb></lb>più robusti, trovava che, per agguagliar la forza di quella medesima palla <lb></lb>di piombo e di quella medesima caduta, sempre vi voleva maggiore e mag­<lb></lb>gior peso, conforme che l&#039;esperienza si fosse fatta con archi più e più ga­<lb></lb>gliardi. </s>

<s>Adunque, diceva egli, s&#039;io piglierò un arco gagliardissimo, quella <lb></lb>palla di piombo, che non passa due once, farà effetto equivalente a mille lib­<lb></lb>bre di piombo. </s>

<s>Pigliandosi poi un arco mille volte più gagliardo di quel ga­<lb></lb>gliardissimo, quella medesima pallina farà effetto equivalente a un milione di <lb></lb>libbre di piombo: segno evidentissimo che la forza di quel poco peso, e di <lb></lb>quel braccio di caduta è infinita ” (Ediz. </s>

<s>cit., pag. </s>

<s>100-2). </s></p><p type="main">

<s>Appresso a questo soggiunge il Torricelli l&#039;altro galileiano esperimento, di <lb></lb>simile conseguenza del primo, consistente nell&#039;aver due palle uguali di piombo, <lb></lb>e messa l&#039;una sopra l&#039;incudine, per ammaccarla con la forza di un martello <lb></lb>caduto dall&#039;altezza di un braccio, far sull&#039;altra uguale ammaccatura, posan­<lb></lb>dovi sopra un peso morto, che voglia essere per esempio dieci libbre. </s>

<s>“ Ora <lb></lb>alcuno crederebbe, prosegue a leggere il nostro Accademico, che la forza di <lb></lb>quella percossa fosse equivalente al momento di quelle dieci libbre di peso <lb></lb>quiescente. </s>

<s>Ma pensutelo voi: prendasi i due medesimi pezzi di piombo egual­<lb></lb>mente ammaccati come stanno; se sopra uno di essi io poserò dieci libbre <lb></lb>di peso quiescente, certa cosa è che non si spianerà più di quello che sia, <lb></lb>avendo egli già un&#039;altra volta sostenuto il medesimo peso di dieci libbre. </s>

<s>Ma <lb></lb>se vi farò cadere il martello dalla medesima altezza come prima, farà ben <lb></lb>nuova ammaccatura, e per agguagliar questa bisognerà posare sopra l&#039;altro <lb></lb>pezzo di piombo molto maggior peso, che quel di prima, e questo succederà <lb></lb>sempre con progresso sino in infinito ” (ivi. </s>

<s>pag. </s>

<s>103). </s></p><p type="main">

<s>Venivano queste notizie oralmente divulgate in Firenze nel 1642, poco <lb></lb>dopo la morte di Galileo, e passate per le orecchie degli uditori si sarebbero <lb></lb>rimaste dimenticate ne&#039;manoscritti torricelliani, se non che le teneva fra noi <lb></lb>vive la fama, e appresso agli stranieri la commemorazione, che ne faceva <lb></lb>quattro anni dopo pubblicamente il Mersenno. </s>

<s>Egli dice, nel terzo tomo delle <lb></lb>sue <emph type="italics"></emph>Nuove osservazioni,<emph.end type="italics"></emph.end> che <emph type="italics"></emph>quae Galileus circa vim percussionis in ar­<lb></lb>cubus consideravit<emph.end type="italics"></emph.end> gliele aveva comunicate in Roma Michelangiolo Ricci. <lb></lb></s>

<s>“ Vir clariss. </s>

<s>M. A. Riccius, ad analysim natus, mecum observationem Pisis <lb></lb>a Galileo factam comunicavit, quae sic habet ” (Parisiis 1647, pag. </s>

<s>202): e <lb></lb>prosegue a descrivere l&#039;esperienza degli archi, precisamente a quel modo che <lb></lb>l&#039;aveva descritta il Torricelli, concludendo però la descrizione con queste pa­<lb></lb>role: “ Sed de illis arcus experimentis mihi dubitare liceat, donec ipse vi­<lb></lb>dero, cum aliae sint observationes, quae contrarium suadere videantur ” <lb></lb>(ibid.). Soggiunge poi l&#039;altra esperienza galileiana delle palle di piombo, am-<pb xlink:href="020/01/2532.jpg" pagenum="157"></pb>maccate ora per via della percossa, ora per via della semplice pressione, in <lb></lb>piena conformità con la notizia, che pochi anni prima ne avevano avuto gli <lb></lb>Accademici della Crusca. </s></p><p type="main">

<s>Convalidavano anche i Nostri la fama con questo pubblico documento <lb></lb>del Matematico parigino, e il Borelli, richiamando l&#039;attenzione di coloro, che <lb></lb>avrebbero letto il suo libro <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> sopra que&#039;due preclari espe­<lb></lb>rimenti di Galileo; gli descrive in quel modo, che gli trovò riferiti <emph type="italics"></emph>a Mer­<lb></lb>senno Reflexionum physico-mathematicarum cap. </s>

<s>XXIII.<emph.end type="italics"></emph.end> Tutto insomma <lb></lb>quel che s&#039;andava dicendo e scrivendo di ciò in Italia e fuori era portato <lb></lb>dalle sole ali della fama, degl&#039;incerti voli della quale, come suol sempre av­<lb></lb>venire, sarebbe segno il dirsi dal Torricelli che le magnificate esperienze fu­<lb></lb>rono fatte in Padova, mentre il Ricci al Mersenno, e il Viviani al Ferroni, <lb></lb>come tra poco vedremo, dicevano invece che erano state fatte in Pisa. </s>

<s>Nè <lb></lb>in questo caso è l&#039;incertezza del luogo di poca importanza, perchè chi chia­<lb></lb>mava il fatto pisano doveva riferirlo alle speculazioni giovanili di Galileo, <lb></lb>quando si sa che ancora non aveva concluso la forza della percossa dover <lb></lb>essere infinita. </s>

<s>E perchè è certo che non venne l&#039;Autore a una tal conclu­<lb></lb>sione, se non che verso il 1635, sembra certo altresi che nè in Pisa nè in <lb></lb>Padova fece egli fabbricare, per il nuovo uso filosofico, quegli archi più o <lb></lb>meno gagliardi, ma piuttosto in una delle suburbane ville di Firenze. </s></p><p type="main">

<s>Noi però che, invece di ascoltare la fama, abbiamo sott&#039;occhio da con­<lb></lb>sultare i fatti, possiamo esser certi che Galileo non fa, nel suo dialogo pub­<lb></lb>blicato dal Bonaventuri, nessun motto di quegli archi, dagli ammiratori <lb></lb>chiamati insigni nella scienza e preclari. </s>

<s>Anche l&#039;altra esperienza delle palle <lb></lb>di piombo ammaccate, con la sua conclusione, non si trova nel Dialogo, <lb></lb>se non che trasformata nell&#039;esempio del palo e della berta, i reiterati colpi <lb></lb>della quale si dice che non pareggiano mai il medesimo peso morto, il quale <lb></lb>anzi deve sempre esser maggiore e maggiore, <emph type="italics"></emph>d&#039;onde pare ritrar si possa <lb></lb>la forza della percossa essere infinita<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 314). </s></p><p type="main">

<s>Nè in Pisa dunque, nè in Padova, nè altrove, sembra che avesse Gali­<lb></lb>leo pensato di fare l&#039;esperienza degli archi della balestra: invece della quale <lb></lb>ne aveva immaginata e descritta un&#039;altra, da dirsi più veramente preclara, <lb></lb>benchè dal Viviani in fuori nessun altro o pochissimi, anche de&#039;più fami­<lb></lb>liari all&#039;Autore, ne avessero a que&#039;tempi notizia. </s>

<s>L&#039;esperienza alla quale ac­<lb></lb>cenniamo è quella della troscia di acqua che, dalla secchia di sopra cadendo, <lb></lb>percuote nella secchia di sotto, ambedue equilibrate da un peso morto al­<lb></lb>l&#039;estremità di una bilancia. </s>

<s>Da così fatta esperienza il Viviani stesso, non <lb></lb>curando gli archi tesi delle balestre, o le palle di piombo ammaccate, inco­<lb></lb>minciò a promovere l&#039;uso di quegli strumenti da misurare con qual mo­<lb></lb>mento, paragonato a un peso morto, naturalmente cadendo, percotano i gravi. </s>

<s><lb></lb>Ci son di queste speculazioni rimasti nei manoscritti non pochi documenti, <lb></lb>dei quali noi riferiremo intanto i più importanti, incominciando da ciò che <lb></lb>fu suggerito al Viviani stesso dalla lettura del Dialogo galileiano, dove l&#039;Aproino <lb></lb>introduce il discorso col descrivere la prima delle esperienze “ che mossero <pb xlink:href="020/01/2533.jpg" pagenum="158"></pb>l&#039;Amico ad internarsi nella contemplazione dell&#039;ammirabile problema della <lb></lb>percossa ” (Alb. </s>

<s>XIII, 308). </s></p><p type="main">

<s>“ Sia la libbra o stadera AB (fig. </s>

<s>51), sostenuta in C, e dall&#039;estremità B <lb></lb><figure id="id.020.01.2533.1.jpg" xlink:href="020/01/2533/1.jpg"></figure></s></p><p type="caption">

<s>Figura 51.<lb></lb>pendano due vasi E, F da fu­<lb></lb>nicelle, de&#039;quali quello di so­<lb></lb>pra sia pieno d&#039;acqua, ed <lb></lb>amendue si equilibrino col­<lb></lb>l&#039;altro D pendente dall&#039;altra <lb></lb>estremità A. </s>

<s>Si osservi poi <lb></lb>se, aperto il foro PQ del vaso <lb></lb>di sopra, nel tempo del ca­<lb></lb>dere dell&#039;acqua nel vaso di <lb></lb>sotto, si alteri l&#039;equilibrio: <lb></lb>perchè, se non si guasta, è <lb></lb>segno che il momento acqui­<lb></lb>stato nel moto dell&#039;acqua ca­<lb></lb>dente, e che percuote nel vaso di sotto, equivale a quella parte di acqua, che <lb></lb>è fra&#039;due vasi. </s>

<s>Ma, se la preponderazione seguisse dalle facce del vaso, sa­<lb></lb>rebbe segno che il momento acquistato per la percossa sarà maggiore del <lb></lb>momento, che si perde per il mancamento della porzione di acqua PMQN. ” <lb></lb><figure id="id.020.01.2533.2.jpg" xlink:href="020/01/2533/2.jpg"></figure></s></p><p type="caption">

<s>Figura 52.</s></p><p type="main">

<s>“ Ho fatto l&#039;esperienza, e trovato che l&#039;equilibrio <lb></lb>non si varia, ma tuttavia si mantiene in pari. </s>

<s>” </s></p><p type="main">

<s>“ E se la tavola EF (fig. </s>

<s>52), col peso B in D, <lb></lb>s&#039;equilibra col peso G in A intorno C, nel tagliare <lb></lb>il filo sostenente il peso B, mentr&#039;ei sarà per aria, <lb></lb>prepondererà il peso G, ma la percossa di B sulla <lb></lb>tavola EF restituirà l&#039;equilibrio senza passare a fare <lb></lb>inclinar più giù la stadera. </s>

<s>Ma queste esperienze <lb></lb>vanno replicate e ben considerate ” (MSS. Gal. </s>

<s>Disc., T. CXXXII, fol. </s>

<s>64). </s></p><p type="main">

<s>Replicate però e ben considerate, non sembra che il Viviani rimanesse <lb></lb><figure id="id.020.01.2533.3.jpg" xlink:href="020/01/2533/3.jpg"></figure></s></p><p type="caption">

<s>Figura 53<lb></lb>sodisfatto nè della invenzione di Galileo, nè del <lb></lb>modo assai più semplice com&#039;ei l&#039;avrebbe ri­<lb></lb>dotta, per cui si volse a immaginare un&#039;altro <lb></lb>strumento, premettendo queste parole alla nota, <lb></lb>nella quale ce lo lasciava descritto: “ Vedi se, <lb></lb>per misurare la forza della percossa possa essere <lb></lb>atto uno strumento simile a questo: ” </s></p><p type="main">

<s>“ Siano due regoli uguali AB, CD (fig. </s>

<s>53), <lb></lb>fermati saldamente s<gap></gap>tto e sopra, e tra loro pa­<lb></lb>ralleli, anzi perpendicolari all&#039;orizzonte, per i <lb></lb>quali cammini il trasversale EI, ma però dura­<lb></lb>mente, in virtù dì due molle accomodate nelle <lb></lb>incastrature E, I. </s>

<s>Al medesimo trasversale siano <lb></lb>affissi pur due regoli minori SV, TR, all&#039;estre-<pb xlink:href="020/01/2534.jpg" pagenum="159"></pb>mitâ de&#039;quali V, R sia saldamente fermata la tavoletta X, sulla quale per­<lb></lb>cuota il peso N, ovvero l&#039;O da diverse altezze: i quali percotendo in X fa­<lb></lb>ranno scorrere in giù il trasversale EI più o meno, secondo che la botta verrà <lb></lb>più o meno da alto, o secondo che il peso N sarà più o meno grave, lasciato <lb></lb>cadere dalla medesima altezza ” (ivi, fol. </s>

<s>63). </s></p><p type="main">

<s>Non apparisce da nessuna parte del manoscritto o notizia o indizio che <lb></lb>il Viviani mettesse in pratica così fatto strumento, invece del quale trovò <lb></lb>forse più comodo valersi delle spire metalliche, dalla loro maggiore o minore <lb></lb>distrazione argomentando al maggiore o minor momento di un peso, ora <lb></lb>semplicemente posato sopra la spira, ora lasciato naturalmente cadere da un <lb></lb>filo attaccato all&#039;estremo inferiore anello di essa. </s>

<s>Ne raccolse alcune conclu­<lb></lb>sioni, alle quali se non altro la novità conferisce importanza, e si riducono <lb></lb>alle seguenti: </s></p><p type="main">

<s>“ I. </s>

<s>Pesi disuguali, dalla medesima altezza, distraggono spazi nella me­<lb></lb>desima spira, che hanno la proporzione di essi pesi. </s>

<s>” </s></p><p type="main">

<s>“ II. </s>

<s>Il medesimo peso cadente da diverse altezze nella medesima spira <lb></lb>fa distrazioni disuguali, le quali hanno fra loro la medesima proporzione che <lb></lb>i momenti acquistati nelle cadute disuguali, i quali momenti sono in pro­<lb></lb>porzione sudduplicata della proporzione di dette altezze: cioè sono come le <lb></lb>radici di dette altezze. </s>

<s>” </s></p><p type="main">

<s>“ III. </s>

<s>Pesi disuguali, compensati da momento di velocità, non fanno di­<lb></lb>strazioni uguali. </s>

<s>” </s></p><p type="main">

<s>“ IV. </s>

<s>Il medesimo peso cadente dalla medesima altezza in spire di re­<lb></lb>sistenze disuguali, nella più debole fa maggior distrazione, ma non secondo <lb></lb>la proporzione delle distrazioni, che vi fa un medesimo peso morto. </s>

<s>” </s></p><p type="main">

<s>“ V. </s>

<s>Pesi morti disuguali, nella medesima spira, fanno distrazioni, che <lb></lb>hanno la proporzione di essi pesi. </s>

<s>” </s></p><p type="main">

<s>“ VI. </s>

<s>Il medesimo peso in spire disuguali fa distrazioni disuguali, e nelle <lb></lb>medesime proporzioni di esse spire: cioè, se una spira è di dodici anelli, e <lb></lb>l&#039;altra di otto, in quella distrarrà dodici punti, in questa otto ” (ivi, fol. </s>

<s>57). </s></p><p type="main">

<s>Da così fatte conclusioni sperimentali tenta il Viviani <lb></lb><figure id="id.020.01.2534.1.jpg" xlink:href="020/01/2534/1.jpg"></figure></s></p><p type="caption">

<s>Figura 54.<lb></lb>di sollevarsi all&#039;altezza, e alla dignità di qualche teorema: <lb></lb>e considerando che il momento del peso lasciato libera­<lb></lb>mente cadere dal filo, che lo teneva legato all&#039;ultimo e <lb></lb>inferiore anello della spira, cresce il suo momento se­<lb></lb>condo le ordinate nella parabola, e che la spira stessa lo <lb></lb>impedisce sempre più nello scendere, cioè proporzional­<lb></lb>mente alle ordinate nel triangolo; ne conclude che dun­<lb></lb>que la resultante dell&#039;impeto è sempre la differenza fra <lb></lb>quelle stesse ordinate. </s>

<s>“ Se il peso B (fig. </s>

<s>54) distrae con <lb></lb>la sua gravità per lo spazio AB, lasciato cadere da A, <lb></lb>distrae AC, doppia di AB. </s>

<s>Nel venire da A in B, rispetto <lb></lb>all&#039;impeto acquistato nel cadere, cresce il suo momento come le linee nella <lb></lb>parabola, ma il ritardamento della spira glielo scema secondo le linee del trian-<pb xlink:href="020/01/2535.jpg" pagenum="160"></pb>golo; onde il suo momento va secondo le linee, che sono fra la parabola e <lb></lb>il triangolo ” (ivi, fol. </s>

<s>58). </s></p><p type="main">

<s>Dagl&#039;impeti nelle cadute naturali, misuraii per via della parabola, passò <lb></lb>quella feconda e instancabile mente speculativa a proporre, per misurare essi <lb></lb>impeti ne&#039;moti proiettizi, un modo che per la sua facilità era assai lusin­<lb></lb>ghiero. </s>

<s>“ Si faccia, così lasciò scritto in un&#039;altra sua nota, la proiezione della <lb></lb>palla A (fig. </s>

<s>55) giù per il piano inclinato AB, sicchè poi si volti a far la <lb></lb>parabola BCDE, segnata in muro o sopra una tavola verticale, e si ricevano <lb></lb><figure id="id.020.01.2535.1.jpg" xlink:href="020/01/2535/1.jpg"></figure></s></p><p type="caption">

<s>Figura 55.<lb></lb>le percosse di quella ad angoli retti sopra diversi <lb></lb>pezzi piani, o lastre di sapone, C, D, E, e si osservi <lb></lb>il crescere della percossa. </s>

<s>Ma, per aggiustar me­<lb></lb>glio il tutto, si possono prima disegnare diverse <lb></lb>parabole nel muro ” (ivi, fol. </s>

<s>60). </s></p><p type="main">

<s>Tutte queste però, dal Viviani immaginate, <lb></lb>non erano altro che assai belle proposte, le quali <lb></lb>non si sapeva dall&#039;altra parte se fossero per con­<lb></lb>durre all&#039;effetto desiderato di ricavar l&#039;equivalente <lb></lb>della percossa dalla maggiore o minore penetra­<lb></lb>zione del percuziente in un corpo molle, o dalla <lb></lb>equiponderanza di esso percuziente con un peso <lb></lb>morto. </s>

<s>Mentr&#039;egli intanto pensava a qualche altro strumento, e a qualche <lb></lb>altra maniera più decisiva, si trovò prevenuto da Carlo Rinaldini, suo col­<lb></lb>lega nella prima istituzione dell&#039;Accademia del Cimento, il qual Rinaldini, <lb></lb>forse inconsapevolmente inspirato alle più antiche tradizioni della scienza, che <lb></lb>risalivano a quel Giovanni del Giocondo commemorato dallo Scaligero; pensò <lb></lb>auch&#039;egli poter essere la stadera che, ricevendo da una parte il colpo, ne mi­<lb></lb>surasse dall&#039;altra l&#039;effetto, secondo la maggiore o minor distanza del romano <lb></lb>dal centro dell&#039;equilibrio. </s></p><p type="main">

<s>Propose dunque il Rinaldini, in una sua scrittura ai Colleghi, il modo <lb></lb>di misurare la forza della percossa, valendosi della detta stadera, dal più pic­<lb></lb>colo lato della quale pendesse per un filo una palla di piombo, che nello <lb></lb>stato di quiete rimanesse in pari col romano, e poi, sollevata la palla e la­<lb></lb>sciatala liberamente cadere per tutta la lunghezza del filo, per una lunghezza <lb></lb>doppia, tripla, ecc., fare scorrere lo stesso romano, infin tanto che, come se <lb></lb>si trattasse di pesare una merce, non equiponderasse ora all&#039;una, ora all&#039;al­<lb></lb>tra maggiore strappata. </s>

<s>“ Questa esperienza, concludeva il proponente, quanto <lb></lb>sia facile e puntuale, e di quanto grande importanza, per investigare la co­<lb></lb>gnizione di quell&#039;ammirabil problema, non occorre esagerare a cotesta inge­<lb></lb>gnosissima e virtuosa Accademia: però prego a fare tale esperienza con la <lb></lb>maggiore esattezza che ricerca ” (Targioni, Notizie degli aggrandimenti ecc., <lb></lb>T. II, P. II, Firenze 1780, pag. </s>

<s>713). </s></p><p type="main">

<s>L&#039;esperienza fu fatta a&#039;di 19 Dicembre 1657, e giova credere con tutta <lb></lb>l&#039;esattezza richiesta, ma quel che se ne potè raccogliere si ridusse al sem­<lb></lb>plice fatto che qualunque strappata della corda, benchè rispondente a una <pb xlink:href="020/01/2536.jpg" pagenum="161"></pb>discesa piccolissima della palla, “ aveva facoltà di sollevare il romano, ben­<lb></lb>chè allontanato dal punto dell&#039;equilibrio, per molte libbre ” (ivi, pag. </s>

<s>668). </s></p><p type="main">

<s>Il Viviani, che dirigeva l&#039;esperienza, e che aveva forse sentito in cuore <lb></lb>il rammarico del non essergli sovvenuto un tal pensiero, di sì facile esecu­<lb></lb>zione e puntuale, come il Rinaldini diceva, e come tutti avevano creduto; <lb></lb>ebbe a restar maravigliato del vedersi innanzi fallite così belle speranze: e <lb></lb>mentre andava con gran sottigliezza, e pure inutilmente, investigando di ciò <lb></lb>la misteriosa ragione, occorsegli avventurosamente a leggere una scrittura <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>57, 58) che Lodovico Serenai aveva diligente­<lb></lb>mente copiata dall&#039;autografo del Torricelli. </s>

<s>Era una lettera indirizzata al Mer­<lb></lb>senno, nella quale si svelavano le fallacie di un&#039;esperienza fatta allora a Pa­<lb></lb>rigi, per convincere di falsità la legge galileiana dei moti accelerati. </s>

<s>E perchè <lb></lb>dagl&#039;impeti di un percuziente nella bilancia determinava quel Fisico francese <lb></lb>le relazioni fra gli spazi e i tempi, prendeva il Torricelli occasione di descri­<lb></lb>ver cose ed esporre pensieri, che corrispondevano con quelli passati allora <lb></lb>allora per la mente al Viviani, il quale fece perciò della detta lettera torri­<lb></lb>celliana, di sua propria mano, un estratto, che ci è tuttavia rimasto sotto il <lb></lb>titolo <emph type="italics"></emph>Excerptum ex quadam epistola Torricelli ad Mersennum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ ...... Certissimum est globum unius librae, si in alteram lancium <lb></lb>alicuius librae cadat a qualibet altitudine etiam minima, non solum aequalem <lb></lb>sibi globum, sed etiam centuplo maiorem ex altera bilancis parte elevaturum <lb></lb>esse. </s>

<s>Libra vero, non utcumque, sed huiusmodi esse debet, ut ipsius fila <lb></lb>nihil distrahantur, neque brachia curventur, neque materia, sive globi ca­<lb></lb>dentis sive subiectae lancis, contundantur: haec enim singula effectum impe­<lb></lb>diunt. </s>

<s>Gravitas etiam lancium et brachiorum librae experimentum minus <lb></lb>exactum reddere possunt, dum haec singula impetum seu momentum caden­<lb></lb>tis globi minuere certum est: quae omnia, si penitus vitentur, sive quoad <lb></lb>fieri poterit minuantur, procul dubio quilibet parvi globuli casus in altera <lb></lb>lancium ingens pondus ab alia parte elevabit, sed per spatium exiguum. </s>

<s>” </s></p><p type="main">

<s>“ Esto libra AB (fig. </s>

<s>56) cuius fulcrum in medio C: ex una parte pon­<lb></lb>dus centum librarum, ex alia unius tantum librae, cadatque pondus minus <lb></lb><figure id="id.020.01.2536.1.jpg" xlink:href="020/01/2536/1.jpg"></figure></s></p><p type="caption">

<s>Figura 56.<lb></lb>ex altitudine decem diametro­<lb></lb>rum suarum. </s>

<s>Quaeritur an ele­<lb></lb>vari possit pondus decem libra­<lb></lb>rum? </s>

<s>Hoc quidem nescio, sed <lb></lb>facto experimento clavum fer­<lb></lb>reum D, tenaci ligno infixum, <lb></lb>subiici lanci A, visumque est <lb></lb>pondus centum librarum non impellere ulterius clavum. </s>

<s>Globus vero ferreus <lb></lb>unius librae, cadens ab altitudine decem diametrorum, impellebat eumdem, <lb></lb>nam repetitis saepius ictibus totus clavus in ligno fixus tandem est. </s>

<s>Ergo <lb></lb>maius momentum est ictus globi minoris, quam gravitatis maioris, propterea <lb></lb>ictus minoris gravitatem maioris superare debet, quamquam, cum proportio <lb></lb>gravium maxima fuerit, spatium prae exiguitate oculis percipi nequeat, sive <pb xlink:href="020/01/2537.jpg" pagenum="162"></pb>etiam ob inflexionem librae nullum effectum facere videatur ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XXVI, fol. </s>

<s>21). </s></p><p type="main">

<s>Le osservazioni fatte dal Torricelli intorno alle qualità, che si ricercano <lb></lb>nella bilancia, perchè non debba impedire la buona riuscita dell&#039;esperimento, <lb></lb>fece mirabilmente accorto il Viviani dei difetti, che si trovavano nella sta­<lb></lb>dera proposta dal Rinaldini, al distrarsi della corda nella quale, per le strap­<lb></lb>pate della palla, attribuiva principalmente il non essersi potuta ricavare alcuna <lb></lb>notizia certa, per le più esatte misure della percossa. </s>

<s>Fatta perciò costruire <lb></lb>una libbra, come il Torricelli la prescriveva, e posata sopra la lancia A una <lb></lb>palla di cinque once, trovò che veniva sollevata per un dito, facendo dall&#039;al­<lb></lb>tezza di un braccio cadere sull&#039;altra lancia B una palla di legno del peso di <lb></lb>un&#039;oncia e mezzo. </s>

<s>Tornando poi a far cadere la medesima palla per un&#039;al­<lb></lb>tezza quadrupla, e poi nonupla, e poi sesdecupla, in modo che gl&#039;impeti delle <lb></lb>percosse crescessero via via come due, tre, e quattro, trovò che i pesi morti, <lb></lb>i quali potevano essere sollevati a quella stessa altezza di un dito, volevano <lb></lb>essere 20, 45 e 80 once, nè più nè meno, con tal legge sperimentata sem­<lb></lb>pre costante. </s>

<s>Ne esultò come di una scoperta, e n&#039;esultarono, chiamati te­<lb></lb>stimonii del fatto, i colleghi suoi accademici del Cimento, e specialmente il <lb></lb>principe Leopoldo, a cui sembrò che finalmente si fosse venuti a raccogliere <lb></lb>il frutto delle lunghe e penose speculazioni di Galileo. </s></p><p type="main">

<s>Si dimostrò l&#039;esperienza dal Viviani nell&#039;Accademia il dì 23 Dicem­<lb></lb>bre 1657; poi vennero le Feste natalizie e del capo d&#039;anno, celebratesi le <lb></lb>quali in Firenze, andò il Principe alle cacce di Pisa, dove si tratteneva pro­<lb></lb>fessore dell&#039;Università il Borelli. </s>

<s>Alla prima occasione ch&#039;ebbe esso Principe <lb></lb>di vederlo, fra i diporti e i negozi, disse per prima cosa di avere a dargli <lb></lb>una bella notizia, qual era che il Viviani, valendosi di una bilancia, secondo <lb></lb>che per quell&#039;uso era stata fatta costruire dal Torricelli, aveva trovato che <lb></lb>i momenti delle percosse, fatte sopr&#039;una delle lancie, stavano come i qua­<lb></lb>drati de&#039;pesi morti posati sull&#039;altra. </s>

<s>Anche il Borelli prese allora parte al­<lb></lb>l&#039;esultanza de&#039;suoi colleghi, dai quali era dovuto stare assente in que&#039;giorni, <lb></lb>e il di 7 Gennaio appresso scriveva così in una lettera indirizzata a Firenze <lb></lb>allo stesso Viviani: “ Al serenissimo principe Leopoldo non ho parlato fuor <lb></lb>che una volta sola, perchè le cacce e le faccende finora l&#039;han tenuto davvan­<lb></lb>taggio occupato. </s>

<s>Mi accennò in ogni modo alcune belle invenzioni di V. S., <lb></lb>e in particolare quell&#039;ammirabile effetto ed inaspettato della forza della per­<lb></lb>cossa nella stadera, ed io avrei gran curiosità di sapere se, nella lettera che <lb></lb>V. S. tiene della buona memoria del Torricelli, vi è particolarmente questa <lb></lb>osservazione, oppure è un semplice suo discorso in confermazione del con­<lb></lb>cetto del signor Galileo ” (MSS. Cim., T. XXIV, fol. </s>

<s>31). </s></p><p type="main">

<s>Il Viviani, per sodisfare alla filosofica curiosità di lui, che gli era allora <lb></lb>affezionatissimo amico, gli mandò, insieme con le relazioni delle sue espe­<lb></lb>rienze, esatta copia della lettera torricelliana, della quale il Borelli non fece <lb></lb>che una lettura superficiale. </s>

<s>Ma poi, quando si dette a specular di proposito <lb></lb>intorno all&#039;energia della percossa, per penetrarne la vera e intima natura, <pb xlink:href="020/01/2538.jpg" pagenum="163"></pb>tornò a meditar su quell&#039;estratto di lettera al Mersenno, e ci trovò dentro <lb></lb>formulata una proposizione verissima, la quale poi trasfuse in quella sua XC, <lb></lb>in cui, dietro i principii e gli sperimenti dello stesso Torricelli, intendeva di <lb></lb>dimostrare: “ Vis et energia cuiuslibet percussionis maior est quacumque <lb></lb>potentia finita, quae, absque motu locali, solummodo virtute gravitatis pre­<lb></lb>mat ” (De vi percuss. </s>

<s>cit., pag. </s>

<s>203). Quanto poi ad applicare alla misura <lb></lb>della percossa i dimostrati principii, e il descritto strumento, ebbe a notare <lb></lb>il Borelli una certa esitanza, che non poteva in tant&#039;uomo, qual era il Tor­<lb></lb>ricelli, non esser sentita senza un giusto motivo, e quel <emph type="italics"></emph>nescio<emph.end type="italics"></emph.end> che leggeva <lb></lb>seguitare alla domanda <emph type="italics"></emph>an, si cadat pondus minus ex altitudine decem <lb></lb>diametrorum suarum, elevari possit pondus decem librarum,<emph.end type="italics"></emph.end> gli parve <lb></lb>fare un singolar contrapposto con la nuova baldanza del Viviani. </s></p><p type="main">

<s>Mentre gli passavano per la mente così fatti pensieri, capitarono al Bo­<lb></lb>relli fra mano le epistole del Gassendo <emph type="italics"></emph>De proportione qua gravia deciden­<lb></lb>tia accelerantur,<emph.end type="italics"></emph.end> nella prima delle quali lesse intitolarsi un capitolo <emph type="italics"></emph>De expe­<lb></lb>rimento in Bilance facto ac aliud revera probante quam velocitates esse <lb></lb>sicut spatia.<emph.end type="italics"></emph.end> Dalla curiosità e dall&#039;importanza dell&#039;argomento invitato a pro­<lb></lb>seguir la lettura, trovò riferirsi, nelle sue testuali parole, da un discorso del <lb></lb>gesuita Pietro Cazr, la seguente conclusione sperimentale: “ Ut globus qui­<lb></lb>libet cuiuscumque materiae ex unius diametri altitudine cadens duplum sui <lb></lb>ponderis: hoc est, praeter pondus quod sine impetu in aequilibrio retineret, <lb></lb>aliud sibi aequale attollat; et ex altitudine duarum diametrorum, triplum; <lb></lb>ex tribus diametris, quadruplum, et ita deinceps ” (Parisiis 1646, pag. </s>

<s>42). <lb></lb>Soggiungeva l&#039;Autore delle dette Epistole altri passi, ne&#039;quali, dop&#039;avere il <lb></lb>Gesuita magnificata la novità della stupenda legge da sè scoperta, conclu­<lb></lb>deva dalle esperienze, contro i teoremi di Galileo, che gl&#039;incrementi delle <lb></lb>velocità hanno la proporzion medesima degli spazi passati nelle scese dei gravi. </s></p><p type="main">

<s>La curiosità di veder l&#039;esito di questo negozio frugava sempre più l&#039;animo <lb></lb>del Borelli, il quale, più avidamente applicatosi a succhiare il senso di quelle <lb></lb>pagine, leggeva ciò che, per verificare col medesimo strumento della Bilan­<lb></lb>cia, per quest&#039;uso speciale fabbricata co&#039;piatti sostenuti da robuste catene, <lb></lb>le vantate esperienze del Casreo; diceva di essere andato apparecchiando il <lb></lb>Gassendo, col far cadere i globi per altezze via via crescentì come i loro <lb></lb>quadrati, e concludendo così il ragionamento, che, tutto al contrario delle <lb></lb>opposizioni del Gesuita, confermava mirabilmente la legge di Galileo: “ Prae­<lb></lb>tereo autem quemadmodum ut globus extulit dumtaxat duplum, ex diame­<lb></lb>tris quatuor, sic etiam deinceps extulerit solummodo triplum, ex diametris <lb></lb>novem, et quadruplum ex sexdecim ” (ibid., pag. </s>

<s>48). </s></p><p type="main">

<s>A leggere questa conclusione, dalla quale appariva che gl&#039;impeti della <lb></lb>percossa stavano come i pesi morti, ebbe a maravigliarsi il Borelli come mai <lb></lb>avesse il Viviani, con somiglianti processi sperimentali trovato che stavano <lb></lb>invece come i quadrati dei pesi morti: ed essendo la verità una sola, e gli <lb></lb>sperimentatori ambedue di tal qualità, da non credere che si fossero così <lb></lb>facilmente ingannati, andava fra sè ricercando la causa delle due opposte <pb xlink:href="020/01/2539.jpg" pagenum="164"></pb>osservazioni. </s>

<s>Nè gli fu difficile ritrovarla, tornando a meditare sopra la let­<lb></lb>tera del Torricelli, dalla quale si concludeva che ogni piccolo impeto, in qua­<lb></lb>lunque più piccolo corpo, bastava per superare qualsivoglia energia di gravità <lb></lb>quiescente. </s>

<s>Vedeva inoltre essere ciò confermato dalle stesse esperienze, fatte <lb></lb>con la stadera del Rinaldini nell&#039;Accademia del Cimento, dalle quali espe­<lb></lb>rienze resultava che la palla, da qualunque minima altezza caduta, era ba­<lb></lb>stante a sollevare il romano per molte libbre di più, che non pesava in sè <lb></lb>stessa. </s>

<s>Di qui saviamente argomentava il Borelli che fra il grave in moto e <lb></lb>il grave in quiete non si poteva dar proporzione, per cui non faceva mara­<lb></lb>viglia se il Gassendo e il Viviani, partitisi ambedue da un falso principio, <lb></lb>riuscissero a conclusioni fra loro opposte. </s>

<s>“ Quoniam quilibet impetus, in <lb></lb>quolibet corpusculo inexistens, superat energiam gravitatis quiescentis, et im­<lb></lb>petu omnino privati, propterea quod ipsum impellere et elevare potest, ut <lb></lb>ostensum est; igitur, quantumvis augeatur multipliceturque simplex gravitas, <lb></lb>absque motu locali, nunquam superabit, imo nec aequabit vim impetus, et <lb></lb>ideo simplex gravitas et impetus non erunt quantitates eiusdem generis, et <lb></lb>propterea comparatio inter eas institui non potest, nec ullam proportionem <lb></lb>inter se habere possunt. </s>

<s>Sed nulla quantitas potest esse mensura quantitatis <lb></lb>alterius generis, sicut linea esse non potest mensura soni aut ponderis; igi­<lb></lb>tur pondus simplex elevatum non potest esse mensura impetus percutientis ” <lb></lb>(De vi percuss. </s>

<s>cit., pag. </s>

<s>252). </s></p><p type="main">

<s>Veniva dunque di qui data sentenza contro tutti quegli strumenti che, <lb></lb>per ridurre la forza della percossa alla misura della gravità, aveva immagi­<lb></lb>nati il Viviani, sull&#039;andare di quegli proposti da Galileo, fra quali quel degli <lb></lb>archi della balestra era famoso. </s>

<s>E anche contro questa famosa invenzione <lb></lb>s&#039;estendeva la sentenza dello stesso Borelli, il quale dunque era venuto a <lb></lb>dimostrare la falsità delle dottrine di Galileo intorno alla forza della percossa, <lb></lb>non tanto rispetto ai principii, quant&#039;altresì rispetto alle loro applicazioni spe­<lb></lb>rimentali. </s>

<s>Nè la verità di così fatta sentenza fu potuta mettere in dubbio da <lb></lb>quegli stessi, i quali avevano prima magnificate le invenzioni del famosis­<lb></lb>simo Vecchio, intorno alle quali Giuseppe Ferroni promoveva alcuni dubbi <lb></lb>in una lettera indirizzata al suo maestro Viviani, facendogli osservare che, <lb></lb>nel restituir l&#039;equilibrio tra le forze delle trazioni degli archi, e le semplici <lb></lb>gravità delle palle di piombo prementi, si venivano a paragonare due cose <lb></lb>eterogenee fra loro. </s>

<s>È notabile però che dicesse essergli entrati nella mente <lb></lb>que&#039;dubbi, per non esser rimasto sodisfatto di ciò, che aveva letto nel libro <lb></lb>del Borelli, il quale anzi, nella proposizione CXXXV aveva suggerite quelle <lb></lb>medesime osservazioni, dalle quali diceva di aver preso motivo di dubitare <lb></lb>il discepolo del Viviani. </s></p><p type="main">

<s>Nella citata proposizione infatti descrive l&#039;Autore un&#039;esperienza, ch&#039;ei <lb></lb>diceva di avere istituita, <emph type="italics"></emph>quando, communi errore detentus, impetum per­<lb></lb>cussivum ab aliquo pondere mensurari posse censebam<emph.end type="italics"></emph.end> (De vi percuss. </s>

<s>cit., <lb></lb>pag. </s>

<s>296). Consisteva nel far cadere dalla medesima altezza un&#039;accettina di <lb></lb><gap></gap>erro di tre once, ora sopra una focaccia di cera pura, ora sopra un&#039;altra <pb xlink:href="020/01/2540.jpg" pagenum="165"></pb>simile focaccia, ma più morbida, perchè composta di cera mescolata con sego. </s>

<s><lb></lb>Le ferite poi fatte sopra le due focacce, così per via della percossa, procu­<lb></lb>rava di ripeterle uguali, per via della pressione di un peso morto posato sopra <lb></lb>l&#039;accetta: e perchè trovò che undici oncie bastavano per far l&#039;incisione nella <lb></lb>focaccia più molle, e 36 nella più dura: ne concludeva, aggiungendovi il peso <lb></lb>dello strumento, che le percosse stavano come i pesi morti, ossia come 14 a 39. <lb></lb>Poi riconobbe che queste operazioni diverse dipendevano da tutt&#039;altre cause <lb></lb>che dalle pressioni, e osservava inoltre “ quod, quotiescumque applicantur cor­<lb></lb>pora ponderosa, imponunturque corporibus mollibus atque cedentibus, esse <lb></lb>omnino impossibile ut haec ab illis comprimantur absque motu locali, dum <lb></lb>corpora mollia cedunt ac stringuntur, eo tempore quo urgentur ab incum­<lb></lb>bentibus ponderibus: comprimentur ergo corpora mollia et cedentia, non a <lb></lb>ponderibus quiescentibus, sed motu locali agitatis. </s>

<s>Verum concipi non potest <lb></lb>motus localis absque velocitate, seu impetu, nec corpus grave, impetu affectum, <lb></lb>subiectum corpus comprimere potest absque percussione. </s>

<s>Igitur revera cor­<lb></lb>pora mollia quodammodo percutiuntur ab incumbentibus ponderibus, non <lb></lb>autem solummodo stringuntur, comprimunturque a vi gravitatis quiescentis ” <lb></lb>(ibid., pag. </s>

<s>297, 98). </s></p><p type="main">

<s>Nè questa osservazione giustissima del Borelli è punto diversa da quel­<lb></lb>l&#039;altra, che condusse il Ferroni a spiegare i maravigliosi effetti degli archi <lb></lb>di Galileo, <emph type="italics"></emph>senza che ne segua questo disordine, che la stessa percossa possa <lb></lb>dirsi infinita, ed equivalente a pesi sempre maggiori,<emph.end type="italics"></emph.end> che è il paralogismo, <lb></lb>in cui per tutto il dialogo s&#039;avvolgono le dimostrazioni e i discorsi del Sal­<lb></lb>viati. </s>

<s>E perchè dalla proposta del discepolo è facile argomentare alla rispo­<lb></lb>sta del Maestro, e sono ambedue documento importantissimo di questa sto­<lb></lb>ria, benchè, avendo comunicato il Ferroni i suoi pensieri al Casati, questi <lb></lb>gli pubblicasse nel cap. </s>

<s>VI del suo VII libro <emph type="italics"></emph>Mechanicorum,<emph.end type="italics"></emph.end> (Lugduni 1684, <lb></lb>pag. </s>

<s>677-81); trascriveremo qui dal suo originale la lettera scritta il dì <lb></lb>13 Aprile 1675 da Bologna, nella quale il Ferroni stesso, dopo avere annun­<lb></lb>ziata al Viviani la ricevuta del libro della Scienza universale delle propor­<lb></lb>zioni, così soggiunge e prosegue in sino alla fine: </s></p><p type="main">

<s>“ Speravo di ritrovare nel suo libro la soluzione di quella famosa espe­<lb></lb>rienza, fatta in Pisa, della palla di piombo cadente dagli archi, ne&#039;quali par <lb></lb>che si provi la forza della percossa essere infinita, mentre può equivalere a <lb></lb>pesi e pesi sempre maggiori: esperienza confermata poi dal Borelli coll&#039;ac­<lb></lb>cettina cadente sulla cera e sul sego, ove lo stesso piombo, posto in testa <lb></lb>dell&#039;accettina, non fece poi le medesime spaccature col premere, che fatte <lb></lb>furono dalla percossa cadente. </s>

<s>Or non avendo trovata la soluzione, le devo <lb></lb>dire una mia semplicità, come scolare ad un mio riverito maestro. </s>

<s>” </s></p><p type="main">

<s>“ Mi pare che, nella sperienza di Galileo fatta in Pisa, male si paragoni <lb></lb>l&#039;impeto della palla cadente dal filo attaccato alle corde degli archi, uno ri­<lb></lb>gido l&#039;altro molle, con il peso di piombo premente e sostenente le corde <lb></lb>degli archi ai segni delle discese cagionate dalla palla cadente, poichè <emph type="italics"></emph>ethe­<lb></lb>rogenea etherogeneis non comparantur, sed homogenea homogeneis.<emph.end type="italics"></emph.end> Or <pb xlink:href="020/01/2541.jpg" pagenum="166"></pb>l&#039;impeto della cadente palla, e del piombo premente col peso, sono cose ete­<lb></lb>rogenee. </s>

<s>Devesi dunque far la comparazione delle cose omogenee, come sono <lb></lb>impeto ed impeto. </s>

<s>Per tanto io paragono l&#039;impeto della palla cadente dal me­<lb></lb>desimo filo in due archi un duro l&#039;altro dolce, con l&#039;impeto, che in sè pro­<lb></lb>duce il medesimo peso di piombo attaccato alle corde dei medesimi archi, in <lb></lb>quella poca discesa, che fa con la sua pressione, per tirar gli archi ai segni <lb></lb>delle discese primarie. </s>

<s>Tra questi due impeti si trova questo divario: che la <lb></lb>palla, cadente sempre dal filo di una stessa lunghezza produce sempre in sè <lb></lb>stessa il medesimo impeto per l&#039;uguaglianza della caduta, e giunta alla re­<lb></lb>sistenza degli archi opera con tutto l&#039;impeto anticipatamente preconcetto nella <lb></lb>caduta dal filo per l&#039;aria libera, il qual impeto a poco a poco dalle resistenze <lb></lb>degli archi si va distruggendo e si annienta. </s>

<s>Ma il piombo premente attac­<lb></lb>cato agli archi opera diversamente: poichè non opera con impeto antecipa­<lb></lb>tamente preconcetto, ma incomincia nella sua piccolissima scesa a produrre <lb></lb>impeto in sè, con cui vince la forza di molla negli archi, e questo impeto <lb></lb>non si distrugge, anzi va sempre crescendo, sin che si giunge all&#039;equilibrio <lb></lb>e consistenza. </s>

<s>” </s></p><p type="main">

<s>“ Posti questi preambuli, concludo così: La palla cadente, che è la me­<lb></lb>desima e sempre cade dalla medesima altezza, opera sempre con il medesimo <lb></lb>impeto, anticipatamente preconcetto nella caduta, tanto dall&#039;arco rigido, quanto <lb></lb>dall&#039;arco pieghevole. </s>

<s>Ma le medesime, per esempio dieci once di piombo, <lb></lb>nella lor poca discesa fatta con la pressione, non operano nell&#039;uno e nell&#039;al­<lb></lb>tro caso, col medesimo impeto, ma con impeti molto diversi: poichè, attac­<lb></lb>cate le dieci once di piombo all&#039;arco duro, trovando gagliarda resistenza, co­<lb></lb>mincia ad operare con impeto debolissimo, il quale, crescendo sino all&#039;equi­<lb></lb>librio in proporzione sudduplicata del suo brevissimo spazio, poco cresce. </s>

<s>Ma <lb></lb>le medesime dieci once di piombo attaccate all&#039;arco molle, trovando resistenza <lb></lb>minore, incominciano a premere, e a scendere con grado ed impeto assai <lb></lb>maggiore di quel primo prodotto nell&#039;arco duro, e crescendo con la solita <lb></lb>proporzione, sino all&#039;equilibrio, l&#039;impeto cresce di molto. </s>

<s>Sicchè le medesime <lb></lb>dieci once di piombo premente producono più impeto nell&#039;arco dolce e soave, <lb></lb>che nell&#039;arco gagliardo, onde maraviglia non è se, per tener l&#039;arco duro a <lb></lb>quel segno ove lo trasse la percossa della palla cadente, vi vogliano forse <lb></lb>venti e più once di peso. </s>

<s>” </s></p><p type="main">

<s>“ Sicchè, paragonando impeti con impeti, mi pare di rendere la ragione <lb></lb>di questo maraviglioso fenomeno, perchè il medesimo peso con la pressione <lb></lb>non tenga le due corde degli archi a quei medesimi segni, ai quali furono <lb></lb>tratti dalla percossa della palla cadente, senza che ne segua questo disordine <lb></lb>che la stessa percossa possa dirsi infinita, ed equivalente a pesi sempre mag­<lb></lb>giori. </s>

<s>Vi vuol più peso nell&#039;arco duro, perchè il peso primiero, che produsse <lb></lb>nell&#039;arco molle impeto uguale alla percossa cadente, e perciò lo trasse e trat­<lb></lb>tenne al medesimo segno; attaccato poi all&#039;arco duro, non produce nella <lb></lb>pressione impeto uguale a quello della cadente palla, ma assai minore, e <lb></lb>questo per la maggior resistenza: e queste sono le mie semplicità. </s>

<s>” </s></p><pb xlink:href="020/01/2542.jpg" pagenum="167"></pb><p type="main">

<s>“ Io averei in pensiero di far recitare da un mio scolare un poco di pro­<lb></lb>blema sopra questa bellissima esperienza pisana del Galileo, ma, non avendo <lb></lb>trovato nel Borelli soluzione a mio gusto, e che mi oppaghi, ho speculata <lb></lb>questa bassezza, che gli ho proposto. </s>

<s>La prego a degnarsi correggermela, e <lb></lb>dirmi dintorno a detta esperienza la sua ragione, del che io la scongiuro per <lb></lb>tal uomo, che so che ella negare non mel potrà: dico per il nome glorioso <lb></lb>del nostro comune maestro, e splendore della nostra Toscana, il Galileo ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CXLVI, fol. </s>

<s>36, 37). </s></p><p type="main">

<s>Avrebbe, se così propriamente non rispose, potuto pure rispondere il <lb></lb>Viviani non averci nessun documento certo, per provar che il notato disor­<lb></lb>dine nell&#039;esperienza degli archi si dovesse attribuire al Galileo, a cui, per <lb></lb>misurare la forza della percossa, era sovvenuta una molto diversa invenzione <lb></lb>e assai più bella, dallo stesso Viviani letta in sul cominciar del Dialogo, <lb></lb>dov&#039;è messa in bocca all&#039;Aproino, il quale, dop&#039;aver descritte le due sec­<lb></lb>chie bilanciate a quel modo, che rappresentammo addietro nella figura LI, <lb></lb>così soggiunge: “ La riuscita, siccome agli altri fu inopinata, così fu mara­<lb></lb>vigliosa, imperocchè, subito aperto il foro e incominciato ad uscirne l&#039;acqua, <lb></lb>la bilancia inclinò dall&#039;altra parte del contrappeso, ma non tantosto arrivò <lb></lb>l&#039;acqua percotendo nel fondo dell&#039;inferior secchia, che, restando di più in­<lb></lb>clinarsi il contrappeso, cominciò a sollevarsi, e con un moto placidissimo, <lb></lb>mentre l&#039;acqua precipitava, si ricondusse all&#039;equilibrio, e quivi, senza pas­<lb></lb>sarlo pur di un capello, si librò e fermossi perpetuamente ” (Alb. </s>

<s>XIII, 309, 10). </s></p><p type="main">

<s>Poteva, dicevasi, rispondere il Viviani al Ferroni che la prima esperienza <lb></lb>e l&#039;unica, della quale s&#039;abbia certezza, è questa immaginata da Galileo, per <lb></lb>misurare la forza della percossa, la quale si concludeva dover essere equiva­<lb></lb>lente al momento, e al peso di quella quantità d&#039;acqua cadente, che si trova <lb></lb>in aria sospesa tra le due secchie. </s>

<s>Ma il disordine nonostante rimaneva lo <lb></lb>stesso, comparandosi <emph type="italics"></emph>etkerogenea etherogeneis,<emph.end type="italics"></emph.end> quali sono la troscia d&#039;acqua <lb></lb>in moto, da una parte della bilancia, e il contrappeso dall&#039;altra del grave <lb></lb>quiescente. </s></p><p type="main">

<s>Forse nè il Viviani stesso, nè il Ferroni, riconobbero nella esperienza <lb></lb>idraulica questo disordine, come non sembra lo riconoscesse un illustre Ma­<lb></lb>tematico recente, il quale, in alcune sue lezioni di Fisica matematica, si giovò <lb></lb>dei progressi fatti dalla scienza, per misurare la quantità dell&#039;acqua cadente, <lb></lb>e per concluderne di lì, ciò che non aveva saputo fare il Salviati, la precisa <lb></lb>misura dell&#039;urto fatto dall&#039;acqua sul fondo della secchia. </s>

<s>Fu il Newton, il <lb></lb>quale venne a togliere nello stesso Salviati quell&#039;ambiguità, per cui dovette <lb></lb>abbandonar come inutile il bello esperimento descrittogli dall&#039;Aproino: il <lb></lb>qual Newton, immaginando che la troscia sospesa in aria sia PN (fig. </s>

<s>57), e <lb></lb>la sua altezza KI, concludeva, nel secondo corollario della proposizione XXXVI <lb></lb>dimostrata nel secondo libro dei Principii di naturale Filosofia: “ Vis, qua <lb></lb>totus aquae exilientis motus generari petest, aequalis est ponderi cylindricae <lb></lb>colummae aquae, cuius basis est foramen MN, et altitudo 2 IK. </s>

<s>Nam aqua <lb></lb>exiliens, quo tempore hanc columnam aequat, pondere suo, ab altitudine <pb xlink:href="020/01/2543.jpg" pagenum="168"></pb>KI cadendo, velocitatem suam qua exilit acquirere potest ” (Genevae 1711, <lb></lb>pag. </s>

<s>291), come resulta, soggiungiamo noi per l&#039;Autore, dalla prima pro­<lb></lb><figure id="id.020.01.2543.1.jpg" xlink:href="020/01/2543/1.jpg"></figure></s></p><p type="caption">

<s>Figura 57.<lb></lb>posizione dei moti natural­<lb></lb>mente accelerati, dimostrata <lb></lb>nel terzo dialogo di Galileo. </s></p><p type="main">

<s>Ma la nuova Filosofia <lb></lb>neutoniana suggeriva un ac­<lb></lb>corgimento di più, per la più <lb></lb>esatta risoluzion del proble­<lb></lb>ma. </s>

<s>Galileo e il Viviani li­<lb></lb>mitavano alla sola scesa at­<lb></lb>tuale, nella troscia PN, la <lb></lb>quantità dell&#039;acqua, la quale <lb></lb>non gravita sulla bilancia, <lb></lb>perchè, come si mostra per <lb></lb>la bella esperienza di Leonardo da Vinci, da noi riferita a pag. </s>

<s>227 del Tomo <lb></lb>precedente, <emph type="italics"></emph>il peso grave, che libero discende, non dà di sè peso ad al­<lb></lb>cuno sostentacolo:<emph.end type="italics"></emph.end> secondo il Newton però devesi aggiungere la quantità <lb></lb>dell&#039;acqua, compresa dentro la cateratta RQ, la quale, benchè non muovasi <lb></lb>in atto, opera in potenza nello spinger l&#039;acqua dal foro MN con tal impeto, <lb></lb>come se fosse naturalmente caduta dall&#039;altezza OK, per il noto teorema del <lb></lb>Torricelli. </s></p><p type="main">

<s>L&#039;acqua dunque, che non gravita sulla bilancia, è secondo i principii <lb></lb>neutoniani uguale ad un cilindro liquido, di cui il volume è 2OI.<foreign lang="grc">π</foreign>MI2:e <lb></lb>chiamata D la densità, e <emph type="italics"></emph>g<emph.end type="italics"></emph.end> l&#039;intensione della gravità, 2OI.<foreign lang="grc">π</foreign>MI2.D<emph type="italics"></emph>g<emph.end type="italics"></emph.end> è la <lb></lb>misura del peso. </s>

<s>Che se facciasi <foreign lang="grc">π</foreign>MI2, area del foro MN, uguale ad A, e <lb></lb>invece dell&#039;altezza 2OI, chiamata <emph type="italics"></emph>v<emph.end type="italics"></emph.end> la velocità corrispondente, si sostituisca <lb></lb><emph type="italics"></emph>v2<emph.end type="italics"></emph.end>/2<emph type="italics"></emph>g,<emph.end type="italics"></emph.end> sarà il peso dell&#039;acqua, che non gravita sulla bilancia, espresso dalla <lb></lb>formula A.D. <emph type="italics"></emph>v2,<emph.end type="italics"></emph.end> “ la quale, scrisse Fabrizio Mossotti nella sua XVI lezione <lb></lb>di Fisica matematica, ci dice che l&#039;urto di una vena fluida è in generale mi­<lb></lb>surato dal prodotto della densità, dell&#039;area della sezione urtante, e del qua­<lb></lb>drato della velocità ” (Firenze 1843, T. I, pag. </s>

<s>147). Se avesse dunque, come <lb></lb>sembra, il valoroso professore di Pisa creduto potere equivalere una tale mi­<lb></lb>sura di forza viva al peso morto, che fa equilibrio alle secchie nella Bilancia <lb></lb>gelileiana, sarebbe anch&#039;egli incorso nel disordine del comparare insieme due <lb></lb>cose eterogenee, contro i precetti della logica, saviamente revocati dal Fer­<lb></lb>roni, e prima di lui dal Borelli, il quale è notabile che, prendendo a scri­<lb></lb>vere il suo libro coll&#039;intenzione di esplicare i concetti di Galileo, riuscisse <lb></lb>invece a dimostrare la falsità delle leggi, da lui assegnate alle forze della <lb></lb>percossa, e la fallacia degli strumenti da lui stesso proposti per misurarla. </s></p><pb xlink:href="020/01/2544.jpg" pagenum="169"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;esame dei fatti, indipendente e libero dalla suggezione delle prevalse <lb></lb>opinioni, può aver persuaso chiunque più ritroso che la nuova Scienza del <lb></lb>moto, per quel che riguarda l&#039;energia della percossa, è inutile andare a cer­<lb></lb>carla là, dove tutti si credevano d&#039;averla infallibilmente a ritrovare: nei di­<lb></lb>scorsi cioè e nel Dialogo postumo di Galileo. </s>

<s>Rimasta la sua prima Scuola <lb></lb>dagli errori e dalle fallacie sterilita, il Borelli poi <emph type="italics"></emph>proprio marte<emph.end type="italics"></emph.end> diceva di <lb></lb>averla recuperata, e la proponeva, nel suo trattato <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> al <lb></lb>pubblico, a cui sperava che <emph type="italics"></emph>ob novitatem et materiae praestantiam,<emph.end type="italics"></emph.end> sarebbe <lb></lb>per riuscire non ingioconda. </s>

<s>È da osservare però che, nella cultura della <lb></lb>Scienza meccanica di quei tempi, avvenne ciò che spesso avviene nella cul­<lb></lb>tura degli orti, che, vedendo uno nel suo mancare qualche albero pellegrino, <lb></lb>ve lo inserisce con la sua propria industria, mentre, per le aiuole di un altro, <lb></lb>si vedeva già da gran tempo frondeggiare, e menar fiori e frutti, propag­<lb></lb>ginatovi o scoppiato di sottoterra spontaneo dall&#039;ubertà delle preesistenti <lb></lb>radici. </s></p><p type="main">

<s>Chi crede che uno solo fosse il campo della Scienza meccanica, e quello <lb></lb>segnatamente piantato e coltivato, com&#039;oasi nel deserto, in Toscana, facil­<lb></lb>mente s&#039;inganna, avendoci oramai rivelato a tante occasioni la storia esservi <lb></lb>qua e là altre oasi sparse, alle quali erano approdati i semi e gl&#039;impostimi <lb></lb>da un primo istituito paradiso terrestre. </s>

<s>Nè a cotesto paradiso, alla custodia <lb></lb>del quale avevano i Filosofi antichi proposto Aristotile, mancarono i cultori, <lb></lb>il più benemerito fra i quali, sorto ne&#039;tempi nuovi, è Giordano Nemorario. </s>

<s><lb></lb>Si diffusero da lui quelle benefiche tradizioni, che passarono in Italia a fe­<lb></lb>condare gl&#039;ingegni nei contemporanei di Leonardo da Vinci, ma più uber­<lb></lb>tosamente rimasero ad allignare nella patria Alemagna, per mezzo alla quale, <lb></lb>essendo lungamente andate occulte e disperse, s&#039;incominciarono a raccogliere <lb></lb>e a pubblicare per gli studi solerti e la diligenza insigne di Giovan Marco <lb></lb>Marci. </s></p><p type="main">

<s>Che veramente le tradizioni, rimaste nella Scienza galileiana intercise, <lb></lb>vigessero tuttavia nel campo della scienza universale, alcuni secoli prima che <lb></lb>venisse a resuscitarle fra noi il Borelli; s&#039;argomenta dalle Note di Leonardo <lb></lb>da Vinci, in una delle quali osservammo già come si trovassero espresse le <lb></lb>quantità del moto dal prodotto della velocità per la mole, cosicchè, avendosi <lb></lb>due di quelle quantità uguali, staranno in esse le velocità in contraria ra­<lb></lb>gion delle moli. </s>

<s>Conseguiva di qui che, se le velocità sono uguali, le forze <lb></lb>delle percosse stanno direttamente come i pesi. </s>

<s>Confermava Leonardo que­<lb></lb>sta proposizione con l&#039;esperienze, per introdursi alle quali domandava “ Se <lb></lb>dieci colpi d&#039;una libbra per colpo, caduti sopra uno loco, cadendo un brac­<lb></lb>cio da alto, ficcheranno tanto uno chiodo d&#039;uno braccio, quanto farebbe un <pb xlink:href="020/01/2545.jpg" pagenum="170"></pb>peso unito di dieci libbre. </s>

<s>” Alla qual domanda faceva seguitare la facile ri­<lb></lb>sposta: “ Questo mostra di no, imperocchè, se tu volessi ficcare uno chiodo <lb></lb>col peso d&#039;un altro simile chiodo, questo sarebbe impossibile, imperocchè, se <lb></lb>tu vi battessi sopra esso diecimila simili colpi, tutti sarebbono niente. </s>

<s>E se <lb></lb>tu torrai venti tanti di peso, fia il colpo a proporzione del chiodo che voi <lb></lb>ficcare ” (Les Manuscrits etc., Manus. </s>

<s>A, Paris 1881, fol. </s>

<s>23). </s></p><p type="main">

<s>Soggiunge poi Leonardo un&#039;esperienza più diretta a confermare la ve­<lb></lb>rità dell&#039;annunziata proposizione, osservando quanto maggior trafitta si fac­<lb></lb>cia sopra una lamina di piombo da un martello di una libbra, e da un&#039;altro <lb></lb>di cento, benchè scendano ugualmente veloci, perchè lasciati ambedue an­<lb></lb>dare dalla medesima altezza. </s>

<s>“ Se tu lascerai cadere uno martello di una <lb></lb>libbra cento volte l&#039;altezza di uno braccio sopra una verga di piombo, e poi <lb></lb>tolli uno martello o altro peso, che sia della grosseza del martello, e sia tanto <lb></lb>lungo, che pesi cento libbre, e fallo medesimamente cadere l&#039;altezza di uno <lb></lb>braccio sopra una verga di piombo simile alla prima: e vederai quanto la <lb></lb>verga del colpo unito fia più trafitta che la prima ” (ivi, fol. </s>

<s>4). </s></p><p type="main">

<s>Che le altre varie proprietà della forza della percossa fossero, per legit­<lb></lb>tima conclusione immediata da queste proposizioni fondamentali, conosciute <lb></lb>da&#039;contemporanei seguaci di quella Scuola, alla quale apparteneva Leonardo; <lb></lb>non sembrerà a nessuno incredibile o maraviglioso. </s>

<s>Che se anzi si ripensa <lb></lb>come fossero quegli sconosciuti Matematici, secondo noi vissuti in un secolo <lb></lb>d&#039;ignoranza e di barbarie universale, esperti in comporre e in decomporre <lb></lb>le forze, ci potremmo aspettare di ritrovar, ne&#039;loro libri o ne&#039;loro manoscritti, <lb></lb>risoluti, anche della forza della percossa, problemi, intorno ai quali si sareb­<lb></lb>bero sgomentati di mettersi a cimento Galileo, e i discepoli di lui più valo­<lb></lb>rosi. </s>

<s>Ma che ci hann&#039;elleno luogo le espettazioni, se ne&#039;libri di Giovan Marco <lb></lb>abbiamo, di quello che si congetturava, l&#039;attestato vivo e presente? </s>

<s>Egli con­<lb></lb>fessa che, siccome di ogni altra forza, così di quella della percossa la noti­<lb></lb>zia è molto oscura, e perciò soggiunge: “ Ut in hac obscuritate aliquam lu­<lb></lb>cem consequamur, quae non nisi ex natura impulsus prius cognita clucescit, <lb></lb>de qua in libro <emph type="italics"></emph>De arcu coelesti<emph.end type="italics"></emph.end> latius disseremus, notandum hic breviter.... ” </s></p><p type="main">

<s>Così fatte parole premetteva Giovan Marco, nella proposizione XXXVII <lb></lb><emph type="italics"></emph>De proportione motus,<emph.end type="italics"></emph.end> alla recensione ordinata di quei principii fondamen­<lb></lb>tali, da&#039;quali poi, in varii corollari o porismi, si dimostrerebbero le proprietà <lb></lb>dei gravi, che percotono o si urtano insieme. </s>

<s>Gli otto <emph type="italics"></emph>Porismi<emph.end type="italics"></emph.end> però, che se­<lb></lb>guitano alla detta proposizione, ci avverte l&#039;Autore non essere altro che un <lb></lb>compendio di ciò, che più diffusamente egli stesso avrebbe trattato nel libro <lb></lb>Dell&#039;arco celeste. </s>

<s>Sembrerebbe a prima vista l&#039;argomento alieno dal presente <lb></lb>soggetto, ma ripensando poi che la luce era per gli antichi composta di tanti <lb></lb>minimi globuli, emessi dal corpo lucente, s&#039;intende come le riflessioni otti­<lb></lb>che, per esempio, si facessero cadere sotto la legge meccanica universale della <lb></lb>riflessione dei corpi duri. </s>

<s>Meccaniche infatti son parecchie proposizioni di <lb></lb>Vitellione, per condur le quali si compone e si decompone un raggio di luce, <lb></lb>come si compongono e si decompongono nel parallelogrammo le linee, prese <pb xlink:href="020/01/2546.jpg" pagenum="171"></pb>a rappresentare le forze. </s>

<s>La XL proposizione meccanica perciò, nella quale <lb></lb>Giovan Marco dimostra che l&#039;angolo dell&#039;incidenza è uguale all&#039;angolo della <lb></lb>riflessione, si comprende come non dovesse differire dalla proposizione ottica, <lb></lb>ch&#039;egli avrà in modo simile annunziata e dimostrata nel libro dell&#039;Arco ce­<lb></lb>leste, solamente intendendo applicato il moto, invece che a un globo duro <lb></lb>di ponderosa materia, a un sottile atomo di luce. </s>

<s>Parimente, in quel capi­<lb></lb>tolo, ch&#039;egli intitola <emph type="italics"></emph>De motu reflexo lapillorum ex aqua,<emph.end type="italics"></emph.end> non è difficile <lb></lb>indovinare l&#039;applicazione dei moti reflessi di una sfera, dentro le cave pareti <lb></lb>di un vaso, alle molteplici riflessioni di un raggio di luce, dentro una goc­<lb></lb>ciola rorida, per venir indi a spiegare, come talvolta si osserva, la pluralità <lb></lb>degli Archi celesti. </s></p><p type="main">

<s>Ci siamo espressi così per modo di congettura, perchè, sebbene sia un <lb></lb>fatto che Giovan Marco mantenne le sue promesse, chi ha mai veduto quel <lb></lb>suo libro <emph type="italics"></emph>De arcu coelesti?<emph.end type="italics"></emph.end> Quegli stessi pochi, che l&#039;hanno commemorato, <lb></lb>hanno dovuto confessare di non esser riusciti a consultarlo nelle sue fonti, <lb></lb>rimettendosene a quello che ne portava la pubblica fama, o se n&#039;era detto <lb></lb>dai discepoli dell&#039;Autore, o dagli ascritti al medesimo sodalizio di lui. </s>

<s>Anche <lb></lb>il libro <emph type="italics"></emph>De proportione motus<emph.end type="italics"></emph.end> è, specialmente fra noi, così raro, da doverci <lb></lb>chiamare veramente felici d&#039;averlo potuto avere ad esaminare sott&#039;occhio. </s>

<s><lb></lb>Nè qui possiamo tacere la maraviglia che proviamo, nel ripensare a quei <lb></lb>dotti Alemanni dei tempi passati e dei presenti, i quali, potendosi giusta­<lb></lb>mente gloriare di avere avuto nella loro nazione il maestro, non delle sole <lb></lb>scienze del moto e della luce insegnate nel medesimo tempo e un secolo dopo <lb></lb>da Galileo e dal Newton, ma di parecchie altre mirabili verità ignorate da <lb></lb>loro; lasciano liberamente scrivere alla Storia, benchè, riproducendo e diffon­<lb></lb>dendo le opere di Giovan Marco, la potessero convincer di menzogna, come <lb></lb>venisse d&#039;Italia e d&#039;Inghilterra la luce a illuminar le tenebre del loro set­<lb></lb>tentrione. </s></p><p type="main">

<s>Comunque sia, giacchè ci è stata favorevole la fortuna, proseguendo a <lb></lb>svolgere le preziose pagine del Matematico di Praga, per le quali trovammo <lb></lb>già dimostrate le proprietà dei moti accelerati, insieme con le leggi dei pen­<lb></lb>doli di lunghezza varia di fili, e risoluto il problema della lunghezza del pen­<lb></lb>dolo che misura i secondi; soggiungeremo quest&#039;altro insigne esempio di <lb></lb>meccaniche dottrine recateci dallo straniero, non per supplire ai difetti, ma <lb></lb>per emendare gli errori di Galileo, nell&#039;istituir che fa quegli il primo, per <lb></lb>via della detta proposizione XXXVII, la vera nuova Scienza della percossa. </s></p><p type="main">

<s>Le cose, che voleva ivi brevemente notar l&#039;Autore, perchè si potesse, in <lb></lb>tale e tanta oscurità, conseguir qualche luce, si riducono a cinque capi, l&#039;es­<lb></lb>senza dei quali si condensa in quell&#039;ultima osservazione provocata dal dub­<lb></lb>bio se una palla di legno, che lentamente si muova, possa ribattere un&#039;altra <lb></lb>palla di ferro, che a lei venga incontro con qualunque violenza. </s>

<s>“ Ad ple­<lb></lb>niorem huius atque aliarum obiectionum solutionem, risponde Giovan Marco, <lb></lb>notandum primo: Ut mobile moveatur non sufficere quamlibet impulsum, sed <lb></lb>proportionatum illi mobili. </s>

<s>Impulsus enim, quo globus ligneus ad motum con-<pb xlink:href="020/01/2547.jpg" pagenum="172"></pb>citatur, haudquaquam loco movebit pilam ferream eiusdem molis aut maio­<lb></lb>rem: at vero, si huius impulsu moveatur globus ligneus, motu agitabitur <lb></lb>multo velociore. </s>

<s>Secundo: hanc proportionem motus et impulsus non a mole <lb></lb>sed a gravitate illorum corporum determinari ” (De proport. </s>

<s>motus, Pra­<lb></lb>gae 1639, fol. </s>

<s>44, 45). </s></p><p type="main">

<s>La palla dunque di legno, mossa dalla medesima forza, va secondo i po­<lb></lb>sti principii tanto più veloce della palla di ferro, non a proporzion del volume, <lb></lb>ma della quantità di materia o della massa: cosicchè, chiamando questa M, <lb></lb>F la forza, V velocità che ne resulta, il fondamento posto da Giovan Marco alla <lb></lb>nuova Scienza della percossa, si potrebbe esprimere dalla formula V=F:M, <lb></lb>d&#039;onde ne segue che, essendo le forze e le masse uguali o fra loro propor­<lb></lb>zionali, le velocità pure dovranno resultare uguali. </s>

<s>“ Itaque globus ligneus <lb></lb>maior et glans plumbea minor, si aequiponderant, ab impulsu aequali aequali <lb></lb>velocitate moventur. </s>

<s>Simili modo, si eamdem rationem habeant impulsus quam <lb></lb>habent pondera, erit velocitas motus aequalis ” (ibid., fol. </s>

<s>45). </s></p><p type="main">

<s>Un&#039;altra osservazione, che Giovan Marco in terzo luogo soggiunge, è che <lb></lb>la percossa non si produce per il solo contatto, “ sed ex irruptione violenta, <lb></lb>qua veluti penetrat percutiens percussum ” (ibid.), cosicchè, movendosi un <lb></lb>globo contro un altro globo uguale e omogeneo, questo ch&#039;era in quiete, per <lb></lb>la nuova forza in sè trapassata, si moverà, e l&#039;altro ch&#039;era in moto diven­<lb></lb>terà quiescente. </s>

<s>L&#039;effetto, di cui chi gioca alle palle fa continua esperienza, <lb></lb>e descritto nel Porisma primo: “ Si globus alium globum percutiat qiescen­<lb></lb>tem et aequalem, illo expulso quiescit ” (ibid., fol. </s>

<s>45 ad t.) è illustrato poi <lb></lb>nel primo Problema che, proponendosi “ Globum in plano quiescentem per­<lb></lb>cutere alio globo quacumque violentia, neque tamen loco movere ” (fol. </s>

<s>47); <lb></lb>si scioglie col porre allato al globo, che ha da rimanere, un&#039;altro globo uguale <lb></lb>e omogeneo, in cui venga per così dire travasato l&#039;impulso, rimanendone <lb></lb>l&#039;altro vuoto. </s></p><p type="main">

<s>In quasi tutti i trattati di Fisica si descrive la bella esperienza dei globi <lb></lb>di avorio, tutti uguali e disposti in serie a contatto, che percosso il primo <lb></lb>l&#039;ultimo solo si risente al moto, e par che si sciolga dal rimanente monile: <lb></lb>nè ciò per altro avviene, che per secondarsi da que&#039;globi le leggi degli urti, <lb></lb>dimostrate da Giovan Marco ne&#039;suoi Porismi, dopo il quarto dei quali, ri­<lb></lb>soluto il detto problema, adducendo per ragione <emph type="italics"></emph>quia enim globus, codem<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2547.1.jpg" xlink:href="020/01/2547/1.jpg"></figure></s></p><p type="caption">

<s>Figura 58.<lb></lb><emph type="italics"></emph>momento quo percutitur, percutit globum sibi aequalem, inducet illa per­<lb></lb>cussione plagam perfectam ac proinde ex percussione quiescet<emph.end type="italics"></emph.end> (fol. </s>

<s>47 ad t.), <lb></lb>immediatamente soggiunge: “ Quod si plures globi aequales se contingant <lb></lb>in linea motus centri ut F, G, H, I (fig. </s>

<s>58), percusso F primo ab aequali E, <pb xlink:href="020/01/2548.jpg" pagenum="173"></pb>ultimus I movetur, reliquis F, G, H immotis, propterea quod, per Porisma I, <lb></lb>posterior prioris exhaurit plagam. </s>

<s>At vero si unus aequalium post se habeat <lb></lb>minores quotcumque, ut O, P, Q, percusso a K aequali L, omnes cum L <lb></lb>moto moventur ut constat per Porisma II. </s>

<s>Quod si demum percussio inci­<lb></lb>piat a minori Q v. </s>

<s>g., omnibus immotis aut reflexis, ultimus movetur per <lb></lb>Porisma III, aut, si minor est implsus gravitate, quiescit per Porisma IV ” <lb></lb>(ibid., fol. </s>

<s>48). </s></p><p type="main">

<s>Questi Porismi, e gli altri quattro che si soggiungono, non son altro <lb></lb>che conseguenze di quella prima e principal proposizione, nella quale si de­<lb></lb>finiva che le velocità son tanto più grandi, quant&#039;è maggiore l&#039;impulso dato <lb></lb>al grave e minore il suo peso. </s>

<s>La qual proposizione applica Giovan Marco a <lb></lb>ogni specie di forza, e principalmente a quella della gravità naturale, dimo­<lb></lb>strando quanto fossero in inganno Aristotile e i suoi seguaci nell&#039;affermare <lb></lb>che le velocità nei gravi cadenti son proporzionali alle quantità della mate­<lb></lb>ria. </s>

<s>“ At vero cum inferunt libras duas v. </s>

<s>g. </s>

<s>plumbi in dupla ferri celeri­<lb></lb>tate ad libram unam, falluntur, propterea quod illa gravitas in alio fit su­<lb></lb>biecto, cuius partes omnes aequali gravitate moventur. </s>

<s>Sicut enim pars extra <lb></lb>totum, v. </s>

<s>g. </s>

<s>libra una a sua gravitate movetur cum tanta velocitate; ita par­<lb></lb>tes librarum decem aut centum in toto unitae eadem velocitate moventur a <lb></lb>sua cuique propria gravitate ” (ibid., fol. </s>

<s>58 ad t.). </s></p><p type="main">

<s>Galileo per confutar ne&#039;suoi Dialoghi, e in tante altre scritture, l&#039;errore <lb></lb>dei Peripatetici, spese molte parole, che non hanno però l&#039;efficacia dello <lb></lb>stringente argomento di Giovan Marco, il quale, dal suo dimostrato principio <lb></lb>espresso dalla formula V=F:M, e dalla sua simile V′=F′:M′, se le <lb></lb>forze di gravità son proporzionali ai pesi, come le stadere lo dimostrano nelle <lb></lb>più volgari esperienze in ogni sorta di merci, ne traeva la matematica con­<lb></lb>seguenza che le velocità V, V′ di due cadenti, quanto si voglia diversi di <lb></lb>peso, si mantengono fra loro uguali. </s></p><p type="main">

<s>Passando dunque fra F ed M ed F′, M′, nelle dette formule, per le gra­<lb></lb>vità naturali, una relazione sempre costante, “ nisi gravitas, dice l&#039;Autore, <lb></lb>magis sit intensa, nihil proficiet ad velocitatem augendam illorum ” (ibid., <lb></lb>fol. </s>

<s>59). Che se si tratti d&#039;altra qualità di forze, come son quelle per esem­<lb></lb>pio che da noi s&#039;imprimono ne&#039;proietti, partecipandone una egual quantità <lb></lb>a due globi di mole diversa, nemmeno in questo caso si troverà verificato il <lb></lb>peripatetico asserto, essendo le velocità non direttamente ma reciprocamente <lb></lb>proporzionali alle grandezze. </s>

<s>“ Atque inde fit quod globus minor, accepta a <lb></lb>maiori plaga, praecurrat. </s>

<s>Quod si enim globos quotcumque ea serie dispo­<lb></lb>nas, ut continuo maiorem minor sequatur, percusso primo, videbis quasi uno <lb></lb>impetu-omnes ad motum concitari, verum celeritate, pro ratione magnitudi­<lb></lb>nis, inaequali ” (ibid.). </s></p><p type="main">

<s>S&#039;immagini che, invece di tanti globi a contatto, s&#039;abbiano tanti dischi <lb></lb>decrescenti nel medesimo ordine, e congiunti insieme per la coesion natu­<lb></lb>rale, come per esempio in un chiodo conico, che si percota nel suo cappello. </s>

<s><lb></lb>La forza, secondo Giovan Marco, va diffondendosi verso la punta come un <pb xlink:href="020/01/2549.jpg" pagenum="174"></pb>fluido, di cui giusto ella osserva le leggi, andando con velocità reciproche <lb></lb>delle sezioni. </s>

<s>Tale è la famosa legge dimostrata nell&#039;Idraulica dal Castelli, <lb></lb>e tanto prima di lui da Leonardo da Vinci, che pure, riguardando la forza <lb></lb>come un flusso che si propaga per le particelle della materia, determinava <lb></lb>secondo quella medesima legge la proporzione della velocità, con la quale va <lb></lb>ficcandosi la punta del chiodo, rispetto alla velocità, con la quale penetre­<lb></lb>rebbe la testa del martello. </s>

<s>“ Tanto quanto, egli dice, la punta del chiodo <lb></lb>entra nella testa del martello che lo batte, tanto si ficcherà più nell&#039;asse, <lb></lb>che non si ficcherebbe il martello di pari movimento e forza ” (Manus. </s>

<s>A cit., <lb></lb>fol. </s>

<s>53 a tergo). </s></p><p type="main">

<s>Lasciando d&#039;osservare, come si potrebbero queste dottrine applicare util­<lb></lb>mente alla meccanica del cuneo, appresso agli Autori così oscura, diremo, <lb></lb>per non divagar di troppo dal nostro argomento, delle loro applicazioni a un <lb></lb>problema, rimasto irresoluto anche dai più grandi maestri della scienza. </s>

<s>Ga­<lb></lb>lileo s&#039;era proposto di rendere la ragione “ Perchè le aste lunghe lanciate <lb></lb>fanno maggior colpo ” (Alb. </s>

<s>XIV, 321), ma il proposito in lui venne meno, <lb></lb>come venne meno nel Torricelli, il quale par che facesse, con gli Accade­<lb></lb>mici della Crusca, come colui che mostra un pomo al fanciullo, e poi glielo <lb></lb>nasconde. </s>

<s>“ Sarebbe forse, diceva, curioso problema l&#039;investigare se quel legno <lb></lb>della picca, essendo egualmente velocitato, facesse il medesimo effetto, men­<lb></lb>tre si adopra disteso in asta, e mentre si adoperasse raccolto in una palla: <lb></lb>così anco se una trave, egualmente velocitata, fosse per dare il medesimo <lb></lb>urto, percotendo una volta per lo lungo, ed un&#039;altra per traverso ” (Lez. </s>

<s><lb></lb>accad. </s>

<s>cit., pag. </s>

<s>107). </s></p><p type="main">

<s>Presunse il Vossio di aver fatto una grande scoperta, e di avere emen­<lb></lb>dato un grande errore di Galileo, il quale attribuiva a sola la velocità l&#039;ef­<lb></lb>ficacia della percossa, <emph type="italics"></emph>neglecto pondere ad ictum perpendiculari.<emph.end type="italics"></emph.end> Era però <lb></lb>un fatto ovvio a tutti, nelle esperienze citate dallo stesso Galileo e dal Tor­<lb></lb>ricelli, che la trave ABCD (fig. </s>

<s>59), arietando contro il muro MN, produce <lb></lb>molto maggior colpo, che se percotesselo per traverso: cosicchè il Vossio, se <lb></lb><figure id="id.020.01.2549.1.jpg" xlink:href="020/01/2549/1.jpg"></figure></s></p><p type="caption">

<s>Figura 59.<lb></lb>voleva arrogarsi il merito di aver <lb></lb>promossa la scienza, doveva ad­<lb></lb>durre non il semplice fatto già <lb></lb>benissimo noto, ma, ciò che nem­<lb></lb>men egli fa, le ragioni del fatto, <lb></lb>le quali facilmente si trovano nelle <lb></lb>dottrine professate da Leonardo, e <lb></lb>da Giovan Marco. </s>

<s>La trave AD <lb></lb>infatti, il centro di gravità della <lb></lb>quale sia O, percuote con momento uguale al suo peso, che chiameremo <lb></lb>P, moltiplicato per OE: mentre, nella posizione QN, percote con momento <lb></lb>uguale al medesimo peso P moltiplicato per ST, Le differenze dunque di <lb></lb>que&#039;momenti stanno come P.OE a P.ST, o come OE a ST, o anche come <lb></lb>AC a QP o come PN a CD, che vuol dire in ragion reciproca delle se-<pb xlink:href="020/01/2550.jpg" pagenum="175"></pb>zioni, o delle aree percosse dal medesimo percuziente nella varietà delle sue <lb></lb>giaciture. </s></p><p type="main">

<s>Altri problemi, anche più curiosi di questo, e pur rimasti difficili a molti <lb></lb>Fisici e Matematici, si risolvono con facilità professando le dottrine di Giovan <lb></lb>Marco, che cioè, propagandosi la forza come un fluido che irrompa violen­<lb></lb>temente e penetri attraverso alla materia, non opera in istante ma in tempo, <lb></lb>come si osserva nella diffusione del suono. </s>

<s>“ Notandum tertio percussionem, <lb></lb>et quae hanc sequitur plagam, non uno instanti, sed in aliquo tempore, quan­<lb></lb>tumvis imperceptibili, perfici. </s>

<s>Cum enim plaga proveniat non ex solo contactu, <lb></lb>sed ex irruptione violenta, qua veluti penetrat percutiens percussum, non esse <lb></lb>potest absque motu. </s>

<s>Cum ergo percutiens tangit, necdum est plaga sed fit, <lb></lb>cuius signum fragor a percussione non nisi in tempore proveniens ” (De <lb></lb>proport. </s>

<s>motus cit., fol. </s>

<s>45). Di qui avviene che, nel menare talvolta un mar­<lb></lb>tello, il quale lasciato andare sopra una pietra la ridurrebbe in frantumi, ri­<lb></lb>tirato subito in su, la faccia commovere appena, e co&#039;grandi magli a vapore, <lb></lb>che domano sull&#039;incudine le più dure moli del ferro, si può, non dandovi il <lb></lb>tempo, temperar l&#039;impeto in modo, che valgano appena a infrangere il gu­<lb></lb>scio di un pinocchio. </s></p><p type="main">

<s>Valorosi Matematici del secolo passato, come il Lambert, il Prony, e Gre­<lb></lb>gorio Fontana fra i nostri, vollero mettersi a supplire a un difetto, che no­<lb></lb>tarono nella Meccanica animale del Borelli, rendendo la ragione del perchè, <lb></lb>velocissimamente correndo, il corridore divenga più leggero. </s>

<s>Crederono co­<lb></lb>storo che l&#039;Autor <emph type="italics"></emph>De motu animalium<emph.end type="italics"></emph.end> avesse lasciato indietro quella cu­<lb></lb>riosa conclusione, per mancargli i principii necessari, i quali parve a loro di <lb></lb>ritrovare ne&#039;nuovi dimostrati teoremi ugeniani, per le forze centrifughe, che <lb></lb>si svolgono dalla punta de&#039;piedi verso gli archi successivamente descritti dalle <lb></lb>anche di chi muove il passo veloce. </s>

<s>Nelle dottrine di Giovan Marco però <lb></lb>avrebbero potuto ritrovar que&#039;medesimi principii assai prima, e così semplici, <lb></lb>da ricavarne una soluzione più generale al problema, essendo un fatto che <lb></lb>una tal leggerezza si osserva, non ne&#039;soli corridori, ma in qualunque corpo, <lb></lb>che orizontalmente si muova. </s></p><p type="main">

<s>Sembrerebbe si potesse dar sodisfazione col dire che la forza di gravità <lb></lb>diretta verticalmente nel mobile, componendosi con la forza orizontale del <lb></lb>corso, dà per resultante un moto, che è tanto meno obliquo, quanto la ve­<lb></lb>locità è maggiore, a che insomma si ridurrebbe la soluzione, che il Bene­<lb></lb>detti dava di questo problema, come si riferirà da noi in altro proposito, ma <lb></lb>ad alcuni Matematici del secolo XVII piacque meglio risolvere il problema, <lb></lb>invocando il principio che dice <emph type="italics"></emph>non in uno instanti, sed in aliquo tempore <lb></lb>perfici,<emph.end type="italics"></emph.end> così le percosse, come le pressioni. </s>

<s>Stefano degli Angeli, matematico <lb></lb>di Padova e discepolo del Cavalieri, distinguendo in un grave, che scenda <lb></lb>lungo un piano inclinato, il moto attuale da quello di energia, scriveva così <lb></lb>in una sua nota, che ci occorrerà di trascrivere integralmente in altra occa­<lb></lb>sione di maggiore importanza. </s>

<s>“ Può accadere che il moto attuale sia ca­<lb></lb>gione che. </s>

<s>l&#039;energia sia men sentita dal piano. </s>

<s>Poichè, essendo vero che <pb xlink:href="020/01/2551.jpg" pagenum="176"></pb><emph type="italics"></emph>omnis actio fit in tempore,<emph.end type="italics"></emph.end> il moto attuale è cagione che l&#039;energia non sia <lb></lb>esercitata sopra un luogo determinato del piano, che per un momento, ed <lb></lb>in scorrere. </s>

<s>Così è successo che, passando la ruota d&#039;una carrozza veloce­<lb></lb>mente mossa sopra un uomo, gli ha fatto poco male, ed una volta ho ve­<lb></lb>duto passar con gran prestezza una carrozza sopra un ponte debolissimo, che, <lb></lb>se questa si fosse fermata sopra l&#039;uno o sopra l&#039;altro, con la energia sua <lb></lb>avrebbe fatto gran male e fracassato ogni cosa ” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. CXIX, <lb></lb>fol. </s>

<s>17). </s></p><p type="main">

<s>Le dottrine di Giovan Marco, così riguardanti la forza della percossa e <lb></lb>i varii problemi dipendenti da lei, come le tante altre questioni di Mecca­<lb></lb>nica e di Ottica, che si trovano risolute ne&#039;suoi varii libri; rimasero sta­<lb></lb>gnanti come in ampio lago profondo, a piè di una chiusa valle, sotto un&#039;alpe <lb></lb>solitaria. </s>

<s>Il fiume della Scienza, che pure derivava da una medesima sorgente, <lb></lb>aveva preso altro corso attraverso a campi ubertosi e a popolose città, che <lb></lb>acclamavano dalle sponde e auguravano felici i progressi ai naviganti. </s>

<s>Quelle <lb></lb>acque, scese per conveniente declivio, e battute da tanti validi remi, anda­<lb></lb>vano velocemente correnti, ma in alcuni seni men late e meno profonde di <lb></lb>quell&#039;altre, rimaste morte e in disparte, così che sulla loro trauquilla super­<lb></lb>ficie, da quella del Sole in fuori, non era entrata a specchiarsi mai pu­<lb></lb>pilla viva. </s></p><p type="main">

<s>Riducendo alla realtà le immagini, la Scienza galileiana, come in altre <lb></lb>parti principalissime, così rimase in difetto, comparata con ciò che Giovan <lb></lb>Marco aveva dimestrato nella sua XXXVII proposizione <emph type="italics"></emph>De proportione mo­<lb></lb>tus:<emph.end type="italics"></emph.end> del qual difetto, se voglia eccettuarsi l&#039;Aggiunti, non par che si accor­<lb></lb>gessero i primi e più immediati discepoli dello stesso Galileo. </s>

<s>Quanto al Tor­<lb></lb>ricelli, ne fanno pubblica testimonianza le sue <emph type="italics"></emph>Lezioni,<emph.end type="italics"></emph.end> e quanto al Viviani <lb></lb>le note sparse per i suoi Manoscritti, fra le quali basti a noi citar le se­<lb></lb>guenti, a provar com&#039;anch&#039;egli secondasse l&#039;errore del Maestro in ammettere <lb></lb>che i momenti del percuziente e del percosso siano reciprocamente propor­<lb></lb>zionali alle velocità, e in commettere il disordine del chiamare la percossa <lb></lb>infinita, piuttosto che incommensurabile col peso morto, benchè avvertisse che <lb></lb>il resistente non può moversi con lui che per uguale spazio. </s>

<s>“ Il peso morto <lb></lb>non può muover la resistenza, se non per tanto spazio, quanto è il suo: ma <lb></lb>nella percossa il moto del percuziente è maggiore del moto del percosso, e <lb></lb>forse tanto, quanto il momento del percuziente è minore del momento del <lb></lb>resistente ” (MSS. Gal., T. CXXXII, fol. </s>

<s>61). — “ La campana non risuona, <lb></lb>se non quando trema: non trema, nè può tremare, senza piegarsi, e risuona <lb></lb>ad ogni minima percossa. </s>

<s>Adunque ogni minima percossa riflette il grossis­<lb></lb>simo metallo, e perciò la sua azione è come infinita ” (ivi, fol. </s>

<s>54). </s></p><p type="main">

<s>La nuova Scienza della percossa era dunque rilasciata intatta nella Scuola <lb></lb>galileiana al Borelli, il quale la ridusse alle sue ultime e più vere conclu­<lb></lb>sioni, movendo dal principio, altre volte accennato, e ritrovato già in Giovan <lb></lb>Marco espresso dalla formula, che in due corpi le velocità sono uguali alle <lb></lb>forze d&#039;impulso divise per la quantità della materia, e per la massa. </s>

<s>Dal-<pb xlink:href="020/01/2552.jpg" pagenum="177"></pb>l&#039;essere perciò V=F:M, V′=F′:M′, se ne conclude F:F′=V.M:V′.M′, <lb></lb>che corrisponde con la XXXVII proposizione <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> dal Borelli <lb></lb>così formulata: “ Si duo corpora inaequalia velocitatibus inaequalibus inci­<lb></lb>dant perpendiculariter super eiusdem corporis omnino quiescentis superficiem, <lb></lb>sintque praedicta corpora dura et inflexibilia; vires eorum percussionum pro­<lb></lb>portionem compositam habebunt ex rationibus magnitudinum et velocita­<lb></lb>tum ” (pag. </s>

<s>66). </s></p><p type="main">

<s>Si conclude altresì dalle formule stabilite, essendo le velocità uguali, <lb></lb>F:F′=M:M′, ed essendo le masse uguali, F:F′=V:V′, che riscon­<lb></lb>trano con le XXV e XXVI del citato libro, dall&#039;Autore stesso ivi proposte <lb></lb>in questa forma: “ Si duo corpora, aequali velocitate traslata, perpendicu­<lb></lb>lariter incidant in superficiem eiusdem corporis omnino immobilis, duri et <lb></lb>inflexibilis; eorum percussiones eamdem proportionem habebunt, quam moles <lb></lb>corporeae eorumdem incidentium corporum habent. </s>

<s>— Si duo corpora inter <lb></lb>se aequalia perpendiculariter incidant super alterius corporis omnino stabilis <lb></lb>superficiem, fuerintque omnia corpora dura et inflexibilia; vires percussio­<lb></lb>num proportionales erunt velocitatibus eorumdem incidentium corporum ” <lb></lb>(pag. </s>

<s>64, 65). </s></p><p type="main">

<s>Il Borelli istituisce la sua Scienza nuova sul fondamento di queste pro­<lb></lb>posizioni, nè tratta l&#039;argomento solamente in sè, ma digredisce spesso qua <lb></lb>e là, cogliendo l&#039;occasione di dimostrare le principali proprietà dei moti, che <lb></lb>in qualche modo dipendono, o che si riferiscono a quello della percossa. </s>

<s>Non <lb></lb>sempre però procedono le sue proposizioni con rigor matematico: vi s&#039;im­<lb></lb>mischia talvolta una fisica, la quale è piuttosto il parto della fantasia del­<lb></lb>l&#039;Autore, che un effetto della Natura, e fu questo forse il principale motivo, <lb></lb>per cui, non avendo avuto applauso fra gli studiosi, parve che non fossero <lb></lb>approvate le verità delle nuove dottrine. </s></p><p type="main">

<s>L&#039;Accademia di Londra propose a&#039;suoi soci di speculare intorno al me­<lb></lb>desimo soggetto, e vi concorsero il Wren e l&#039;Huyghens, che nel 1663 les­<lb></lb>sero in quelle dotte adunanze le loro dissertazioni, e vi concorse altresì il <lb></lb>Wallis che, pubblicando nel 1671 la terza parte del suo trattato <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end><lb></lb>v&#039;aggiunse il capitolo <emph type="italics"></emph>De percussione.<emph.end type="italics"></emph.end> Bene esaminando le cose però, non <lb></lb>possono i giusti estimatori non concludere il loro giudizio con dire che i tre <lb></lb>illustri Matematici stranieri non hanno fatto altro, che confermare, e in qual­<lb></lb>che parte promovere i teoremi, da tre anni conosciuti in Italia, e di lì lar­<lb></lb>gamente divulgati nel libro <emph type="italics"></emph>De vi percussionis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La dissertazione accademica dell&#039;Huyghens fu raccolta fra gli Opuscoli <lb></lb>postumi dell&#039;Autore col titolo <emph type="italics"></emph>De motu corporum ex percussione,<emph.end type="italics"></emph.end> e risulta <lb></lb>di sole XIII proposizioni, le prime delle quali non differiscono forse dalle <lb></lb>borelliane che nella forma: vi se ne aggiunge però due insigni, e perciò me­<lb></lb>ritevoli che siano notate dalla Storia. </s>

<s>La prima è la XI che dice: “ Duobus <lb></lb>corporibus, sibi mutuo occurrentibus, id quod efficitur ducendo singulorum <lb></lb>magnitudines in velocitatum suarum quadrata, simul additum, ante et post <lb></lb>occursum corporum aequale invenitur ” (Opusc. </s>

<s>posth., Lugd. </s>

<s>Batav. </s>

<s>1703, <pb xlink:href="020/01/2553.jpg" pagenum="178"></pb>pag. </s>

<s>389). Si diceva questa ugeniana proposizione insigne, non tanto per la <lb></lb>novità, quanto per aver dato occasione alle questioni famose intorno al do­<lb></lb>versi le quantità di moto misurare dal prodotto della massa per la semplice <lb></lb>velocità, o per il quadrato della velocità: queste chiamandosi forze vive e <lb></lb>quelle morte. </s></p><p type="main">

<s>L&#039;altra proposizione, alla quale la sola inaspettata novità conferisce im­<lb></lb>portanza, è la XII, dall&#039;Autore stesso così formulata: “ Si quod corpus maiori <lb></lb>vel minori quiescenti obviam pergat, maiorem ei celeritatem dabit per inter­<lb></lb>positum corpus mediae magnitudinis, itidem quiescens, quam si nullo interme­<lb></lb>dio ipsi impingatur ” (ibid., pag. </s>

<s>393). Alcuni Autori si studiarono di render <lb></lb>più facile e più breve la dimostrazione della bellissima novità così annun­<lb></lb>ziata, premettendo per lemma il teorema che <emph type="italics"></emph>percotendo un corpo un altro <lb></lb>quiescente, la velocità di quello, alla velocità impressa in questo, sta come <lb></lb>la somma d&#039;ambedue i corpi insieme a quel primo, cioè al percuziente.<emph.end type="italics"></emph.end><lb></lb>Che ciò sia il vero, non è difficile riconoscerlo, ammettendo che la forza d&#039;im­<lb></lb>pulso sia uguale a quella della resistenza, e, d&#039;ambedue insieme resultan­<lb></lb>done il colpo, concludere che questo equivale al doppio del momento del <lb></lb>percuziente, come, dietro un così semplice discorso, ebbe a concluderne il <lb></lb>Wallis nella sua VI proposizione. </s>

<s>Ora, muovasi contro B fermo il globo A, <lb></lb>con momento espresso da V.A: il colpo dato a B, chiamata V′ la velocità <lb></lb>che ne consegue, avrà per misura la quantità di moto, della quale è l&#039;ef­<lb></lb>fetto; misura espressa da V′(A+B), che è uguale a 2 V.A, per la VIa del <lb></lb>Wallis, e perciò V:V′=A+B:2A. </s></p><p type="main">

<s>Premesso il qual lemma, facciansi i globi A.B (fig. </s>

<s>60) proporzionali <lb></lb>alle linee AC, CB, e presa AD a rappresentare la velocità, con la quale A <lb></lb><figure id="id.020.01.2553.1.jpg" xlink:href="020/01/2553/1.jpg"></figure></s></p><p type="caption">

<s>Figura 60.<lb></lb>si muove contro B in quiete, si prolunghi l&#039;AC <lb></lb>in E talmente, che sia CE uguale ad AC. </s>

<s>Da <lb></lb>E poi condotta la EL parallela ad AD, si de­<lb></lb>scriva fra EA, EL, come fra asintoti, l&#039;iperbola <lb></lb>SDV: è facile dimostrare che, essendo AD la <lb></lb>velocità, come s&#039;è detto, del globo A percu­<lb></lb>ziente, sarà BS la velocità, che riceve il globo <lb></lb>B dopo la percossa. </s></p><p type="main">

<s>Abbiamo infatti, per le note proprietà della <lb></lb>curva, AD:BS=BE:AE=AC+CB:2AC, <lb></lb>sostituita invece delle linee intere BE, AE, la <lb></lb>somma delle loro parti. </s>

<s>Ma per supposizione è <lb></lb>A:B=AC:CB, ossia, componendo e dupli­<lb></lb>cando i conseguenti, A+B:2A=AC+CB: <lb></lb>2AC; dunque AD:BS=A+B:2A, ossia, per il premesso lemma, <lb></lb>AD:BS=V:V′, e ciò vuol dire appunto che, essendo dalla AD rappre­<lb></lb>sentata la velocità del percuziente, sarà dalla BS rappresentata la velocità, <lb></lb>che imprimesi nel percosso. </s></p><p type="main">

<s>Ciò premesso, la laboriosa conclusione dell&#039;Huyghens non dipende che <pb xlink:href="020/01/2554.jpg" pagenum="179"></pb>da una semplice avvertenza sopra le cose già dette. </s>

<s>Siano i tre globi A, N, B <lb></lb>(fig. </s>

<s>61) crescenti in grandezza, secondo l&#039;ordine che gli abbiamo nominati: <lb></lb>è facile vedere che il globo A, percotendo immediatamente B, gl&#039;imprime <lb></lb><figure id="id.020.01.2554.1.jpg" xlink:href="020/01/2554/1.jpg"></figure></s></p><p type="caption">

<s>Figura 61.<lb></lb>una velocità minore di quella che gl&#039;imprime­<lb></lb>rebbe percotendolo per l&#039;intermedio del globo <lb></lb>N. Imperocchè, essendo nel primo caso rappre­<lb></lb>sentata la velocità del percuziente dalla linea AD, <lb></lb>costruita l&#039;iperbola DVS fra gli asintoti EL, EN, <lb></lb>sarà da BS rappresentata la velocità del per­<lb></lb>cosso: mentre nell&#039;altro caso, che cioè il per­<lb></lb>cuziente sia il globo intermedio N, presa CH <lb></lb>uguale a CN, sarà il nuovo asintoto HG; fra il <lb></lb>quale e HN descritta l&#039;altra iperbola IVF, la ve­<lb></lb>locità impressa nel globo B verrà rappresen­<lb></lb>tata da BF, maggiore di BS, pienamente con­<lb></lb>fermando il discorso la verità della proposizione <lb></lb>ugeniana. </s></p><p type="main">

<s>Seguono da una tal proposizione due co­<lb></lb>rollarii, il primo de&#039;quali è che la massima velocità verrà allora impressa, <lb></lb>quando N globo interposto sia esattamente medio proporzionale fra i due <lb></lb>estremi A, B; e l&#039;altro, che l&#039;Huyghens stesso si proponeva in ultimo luogo <lb></lb>a dimostrar sotto questa forma: “ Quo plura corpora interponentur inter <lb></lb>duo inaequalia, quorum alterum quiescat, alterum moveatur; eo maior mo­<lb></lb>tus quiescenti conciliari poterit. </s>

<s>Maximus autem per unamquamque interpo­<lb></lb>sitorum multitudinem ita conferetur, si interposita cum extremis continuam <lb></lb>proportionalium seriem constituant ” (Opusc. </s>

<s>cit., pag. </s>

<s>397). Se per esempio <lb></lb>siano cento corpi, soggiunge l&#039;Autore, le moli de&#039;quali crescano successiva­<lb></lb>mente come i quadrati della serie dei numeri naturali, e il moto incominci <lb></lb>dal massimo, <emph type="italics"></emph>subducto calculo ad praeceptum regulae,<emph.end type="italics"></emph.end> si troverà la velo­<lb></lb>cità del minimo stare a quella del massimo prossimamente come 14,760 mi­<lb></lb>lioni ad uno. </s>

<s>Chi poi volesse applicare a qualche effetto della natura la mi­<lb></lb>rabile conclusione, ripensi che le rocce son tanto più frantumate, quanto dal <lb></lb>nucleo terrestre s&#039;ascende verso la superficie, ond&#039;è perciò dato in qualche <lb></lb>modo ad intendere com&#039;anche un leggero urto, che muova dall&#039;interno, <lb></lb>possa propagandosi all&#039;esterno del nostro globo moltiplicarsi in quelle posse <lb></lb>immense, che ci si manifestano per esempio nelle eruzioni sotterranee, e nei <lb></lb>terremoti. </s></p><p type="main">

<s>Giovanni Wallis, altro celebre accademico londinese, si tenne anche più <lb></lb>strettamente dell&#039;Huyghens a compendiar le dottrine del Borelli. </s>

<s>Le XV pro­<lb></lb>posizioni infatti, ch&#039;egli stende nel suo capitolo <emph type="italics"></emph>De percussione,<emph.end type="italics"></emph.end> si svolgono <lb></lb>essenzialmente tutte dalla seconda, che l&#039;Autore annunzia in questa maniera: <lb></lb>“ Si grave motum gravi quiescenti directe impingat, sed ita constituto, ut <lb></lb>aliunde ne moveatur non impediatur, utrumque iunctim movebitur quam cal­<lb></lb>culus, ponderum ratione et pristina celeritate rite computatis, indicabit ” (De <pb xlink:href="020/01/2555.jpg" pagenum="180"></pb>motu, cap. </s>

<s>XI, Londini 1671, pag. </s>

<s>662). L&#039;indicazione però direttamente sov­<lb></lb>viene dalla XIX borelliana, la verità della quale, chiamato A il grave in moto <lb></lb>con la velocità V, da cui s&#039;imprime la forza F nell&#039;altro grave B in quiete, <lb></lb>e vien con la velocità X trasportato nella medesima direzione; è, come al­<lb></lb>trove dicemmo, espressa dalla formula F=A.V=X(A+B) d&#039;onde <lb></lb>calcola il Wallis X=A.V/(A+B), “ nempe si momentum, ex moti gravis pon­<lb></lb>dere et celeritate compositum, per utriusque simul pondus dividatur, habe­<lb></lb>bitur futura celeritas ” (ibid.). </s></p><p type="main">

<s>Gli Accademici parigini non volendo, nel partecipare al merito di aver <lb></lb>coltivata la nuova Scienza, rimanere indietro a quelli di Londra, deputarono <lb></lb>il Mariotte, il quale scrisse il suo <emph type="italics"></emph>Traitè de la percussion, ou choc des corps,<emph.end type="italics"></emph.end><lb></lb>di cui nel 1679 era già stata fatta in Parigi la terza edizione. </s>

<s>Il nuovo Ma­<lb></lb>tematico si dilungò anche meno degli altri dai primi instituti borelliani, de­<lb></lb>rivando dalle fisiche esperienze le dimostrazioni dei principali teoremi. </s>

<s>Ma <lb></lb>imitando il nostro Italiano non sembra ne sapesse cansar que&#039;difetti, che gli <lb></lb>furono spesso ingiustamente imputati, specialmente dagli stranieri, imperoc­<lb></lb>chè, descritta esso Mariotte quella macchina di precisione, la quale era stata <lb></lb>proposta già dal Borelli nel capitolo XXIX del suo libro, come altrove osser­<lb></lb>vammo, suppone che siano esattamente isocrone le maggiori e le minori di­<lb></lb>scese dei globi penduli, nel computar ch&#039;egli fa i momenti delle loro per­<lb></lb>cosse, ora per dimostrarne direttamente, ora per verificarne le leggi. </s>

<s>“ Les <lb></lb>petits battemens d&#039;un pendule se font en des tems sensiblement égaux, quoi <lb></lb>que son plomb décrive des arcs inégaux; mais pour la facilité des demonstra­<lb></lb>tions, on suppose ici que ces tems sont precisement égaux ” (Oeuvres, T. </s>

<s>I <lb></lb>cit., pag. </s>

<s>5). </s></p><p type="main">

<s>Benchè il trattato del Mariotte, che si divide in due parti, sia molto più <lb></lb>esteso della dissertazione dell&#039;Huyghens, e del capitolo del Wallis, lascia <lb></lb>nulladimeno intatte alcune delle principali proposizioni, che strettamente si <lb></lb>riferiscono all&#039;argomento, come son quelle delle relazioni che passano fra <lb></lb>l&#039;angolo dell&#039;incidenza e l&#039;angolo della riflessione, e fra i varii momenti della <lb></lb>percossa, secondo che la direzione del moto è perpendicolare o è obliqua. </s>

<s><lb></lb>L&#039;Huyghens pure non sembra che sapesse trovar luogo a queste fra le altre <lb></lb>sue minori, benchè elaboratissime, proposizioni, e il Borelli stesso, di queste <lb></lb>verità conosciute al mondo, checchè se ne pensassero gli stranieri, primo <lb></lb>maestro; se ne passa con tal leggerezza per vero dire non conveniente alla <lb></lb>dignità e all&#039;importanza del soggetto. </s>

<s>Si direbbe che avessero dovuto tro­<lb></lb>varci qualche difficoltà quei Matematici, i quali, benchè valorosissimi, sap­<lb></lb>piamo nulladimeno che furono o ritrosi in ammettere i moti misti, o in maneg­<lb></lb>giarli inesperti; ciò che doveva render difficilissimo, per non dire impossibile, <lb></lb>il condurre a buon termine le accennate dimostrazioni. </s>

<s>Si comprende perciò <lb></lb>come alla presente intrapresa storia della percossa manchi una parte, che in <lb></lb>quest&#039;altro articolo del nostro discorso, con la maggior possibile brevità, si <lb></lb>soggiunge. </s></p><pb xlink:href="020/01/2556.jpg" pagenum="181"></pb><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Che l&#039;angolo dell&#039;incidenza sia uguale o quello della riflessione è una <lb></lb>proprietà dai più antichi Filosofi conosciuta, e sperimentata nella luce. </s>

<s>Il <lb></lb>Kepler fu il primo a darne dimostrazione, applicandovi i moti misti, e il Car­<lb></lb>tesio ne segui l&#039;esempio, appropriando agli atomi luminosi in moto i dimo­<lb></lb>strati effetti di una palla elastica, che rimbalza dalla resistenza di una dura <lb></lb>superficie. </s>

<s>Chi vuol rammemorarsi di queste cose si compiaccia di tornare indie­<lb></lb>tro a pag. </s>

<s>14, 15 del secondo Tomo della nostra Storia, rileggendo le quali <lb></lb>pagine, gli parrà di vedere in qualche modo supplito a quel difetto, che si <lb></lb>notava nella prima istituzione della scienza della percossa dei corpi ponderosi. </s></p><p type="main">

<s>Non si può senza maraviglia ripensare come rimanessero le tradizioni <lb></lb>dell&#039;Ottica inefficaci ai progressi della Meccanica, ma chi si risovviene di quel <lb></lb><emph type="italics"></emph>nescio quid subtile<emph.end type="italics"></emph.end> pronunziato dal Keplero, e di quel procedere incerto e <lb></lb>dubitoso del Cartesio, s&#039;avvedrà che tutto dipendeva dal non avere avuto fede <lb></lb>il Borelli e il Mariotte, nè dimestichezza con quelle sottigliezze dei moti mi­<lb></lb>sti. </s>

<s>Il Wallis, che fu il primo a riappiccare il filo alle prime tradizioni, ve­<lb></lb>dremo com&#039;avesse a patir contese con i matematici de&#039;suoi tempi, ignari di <lb></lb>ciò che s&#039;era luminosamente rivelato a Giovan Marco nella pace solitaria <lb></lb>de&#039;suoi pensieri. </s>

<s>Ma per apprezzar meglio le gioie passate, e sentir più vivo <lb></lb>il desiderio di un giorno sereno, descriveremo prima il nuvolo affannoso del <lb></lb>giorno dopo. </s></p><p type="main">

<s>Una via aperta, proseguendo per la quale si poteva riuscir felicemente <lb></lb>a dimostrare che, nei corpi elastici, il moto obliquo dopo la percossa si fa <lb></lb>con angolo uguale a quello prima della percossa; sembrava dovere apparire <lb></lb>innanzi al Borelli nella proposizione LXIII, nella quale egli dimostra che “ si <lb></lb>duo corpora, contrariis motibus per eamdem rectam lineam translata, reci­<lb></lb>proce proportionalia fuerint suis velocitatibus, ac se mutuo perpendiculari et <lb></lb>media incidentia percutiant, sintque ambo corpora dura et inflexibilia; re­<lb></lb>flectentur ad partes oppositas iisdem velocitatibus, quibus ante occursum fe­<lb></lb>rebantur ” (De vi percuss. </s>

<s>cit., pag. </s>

<s>120). Questa medesima proposizione fu <lb></lb>poi dimostrata dall&#039;Huyghens nella sua VIII, che dice: “ Si corpora duo sibi <lb></lb>ex adverso occurrant, quorum magnitudinibus celeritates contraria ratione <lb></lb>respondeant; utrumque eadem, qua accessit, celeritate resiliet ” (Opusc. </s>

<s>cit., <lb></lb>pag. </s>

<s>381), e fu altresi soggiunta dal Mariotte nella XV della prima parte del <lb></lb>suo Trattato, in cui, dop&#039;aver provato coi supposti principii, poi con l&#039;espe­<lb></lb>rienza conferma che “ Si deux corps à ressort se choquent directement, avec <lb></lb>des vitesses reciproques à leur poids: chacun de ces corps retournera en <lb></lb>arriere avec sa premiere vitesse ” (Oeuvres cit., pag. </s>

<s>29). </s></p><p type="main">

<s>Restava così per conseguenza dimostrato, dal consenso dei tre insigni <lb></lb>Matematici, che un corpo elastico, il quale percuota in una dura superficie, <pb xlink:href="020/01/2557.jpg" pagenum="182"></pb>ritorna indietro con la medesima velocità, con la quale era venuto, e ciò non <lb></lb>solo nella perpendicolare e media, ma in qualunque incidenza. </s>

<s>Così essendo, <lb></lb>tornava facile dimostrare che, così l&#039;incidenza, come la riflessione del moto <lb></lb>dovevano farsi con angoli uguali, ma questa facilità non fu ritrovata da nes­<lb></lb>suno, fuor che dal Wallis, applicando a condurre la sua dimostrazione, come <lb></lb>or ora vedremo, i moti misti. </s></p><p type="main">

<s>L&#039;Huyghens e il Mariotte tralasciarono l&#039;impresa, cedendo agli scrupoli, <lb></lb>ma il Borelli sembrava che si fosse, con argomento diverso dalla composi­<lb></lb>zion delle forze, aperta innanzi la porta gelosa. </s>

<s>Incomincia il cap. </s>

<s>XV del <lb></lb>suo libro con una considerazione, la quale si direbbe forse inspirata da ciò <lb></lb>che scrisse il Cartesio del non poter farsi nel punto di riflessione dal per­<lb></lb>cuziente alcuna dimora, perchè altrimenti <emph type="italics"></emph>nulla extaret causa, qua inci­<lb></lb>tante, vires resumere possent<emph.end type="italics"></emph.end> (Dioptr., Francof. </s>

<s>1692, pag. </s>

<s>47); se non si <lb></lb>sapesse esser questa l&#039;espression del principio galileiano, dimostrato contro <lb></lb>Aristotile, <emph type="italics"></emph>in puncto reflexionis non dari quietem<emph.end type="italics"></emph.end> (Op. </s>

<s>Ediz. </s>

<s>naz., Fi­<lb></lb>renze 1890, pag. </s>

<s>323). Comunque sia, l&#039;occasione immediata a quella con­<lb></lb>siderazione venne al Borelli da coloro, fra&#039;quali Giovan Marco, i quali am­<lb></lb>mettevano che il moto si estinguesse, e resuscitasse di nuovo nella resili­<lb></lb>zione. </s>

<s>“ Ut obiectioni et experientiae satisfiat, dicendum a quolibet contactu <lb></lb>impulsum deficere et expirare, novum vero a percussione determinari, qui <lb></lb>motu, eidem plagae aequali, retroagit illud mobile ” (De prop. </s>

<s>motus cit., <lb></lb>fol. </s>

<s>44 ad t.). Ma qual è la causa, domandava il Borelli, di questa estinzione <lb></lb>e di questa resurrezione? </s>

<s>E non trovandone alcuna vide la necessità di con­<lb></lb>fessare “ quod idem impetus motus incidentiae perseverat, et tantummodo, <lb></lb>impedito transitu et progressu ab obice, itineris directionem aliorsum diri­<lb></lb>git ” (De vi percuss. </s>

<s>cit., pag. </s>

<s>114). </s></p><p type="main">

<s>Ecco dunque per quali altre vie, diverse da quelle indicate nella LXIII pro­<lb></lb>posizione, riusciva il Borelli a concludere che nella riflessione persevera la <lb></lb>medesima quantità di moto che nell&#039;incidenza. </s>

<s>Si crederebbe che avesse pre­<lb></lb>parata una tal conclusione, per servirsene a dimostrare l&#039;uguaglianza degli <lb></lb>angoli ne&#039;moti che risultano uguali, tanto più che nella LIX, benchè con <lb></lb>lo scrupoloso riserbo della regola galileiana, s&#039;induce a decomporre nelle due <lb></lb><figure id="id.020.01.2557.1.jpg" xlink:href="020/01/2557/1.jpg"></figure></s></p><p type="caption">

<s>Figura 62.<lb></lb>dei cateti l&#039;unica potenza dell&#039;ipotenusa. </s>

<s><lb></lb>Con tali principii infatti, e con tali mezzi, <lb></lb>la desiderata dimostrazione sarebbe stata <lb></lb>paratissima. </s>

<s>Imperocchè, sia rappresentato <lb></lb>da AB (fig. </s>

<s>62) il moto incidente, decom­<lb></lb>posto nel perpendicolare AC, e nell&#039;ori­<lb></lb>zontale CB, e sia da BE rappresentato <lb></lb>il moto riflesso: se è vero che questo ri­<lb></lb>sulti uguale all&#039;incidente nel tutto, gli resulterà uguale altresì nelle parti <lb></lb>componenti, cosicchè, se BD è uguale a CD, anche DE dovrà essere uguale <lb></lb>ad AC, e i triangoli ACB, BDE uguali, ed uguali ABC, EBD, angoli dell&#039;in­<lb></lb>cidenza e della riflessione. </s></p><pb xlink:href="020/01/2558.jpg" pagenum="183"></pb><p type="main">

<s>È però notabile che il Borelli divaga per tutt&#039;altri sentieri, e quel che <lb></lb>diceva del perseverare il moto riflesso, con la medesima intensità dell&#039;inci­<lb></lb>dente, è termine, e non mezzo di alcuna dimostrazione. </s>

<s>Ne&#039;due capitoli ap­<lb></lb>presso insiste nel medesimo argomento, dimostrando con molte e belle ra­<lb></lb>gioni non esser possibile che il moto si distrugga in natura, e si generi di <lb></lb>nuovo, essendo la quiete stessa l&#039;effetto di due moti tuttavia vigenti e ope­<lb></lb>ranti, con direzioni però uguali e contrarie, come per esempio nel sasso, che <lb></lb>non cade, perchè l&#039;ostacolo lo trattiene. </s>

<s>“ Idemque dicendum, così termina <lb></lb>l&#039;Autore il suo ragionamento, de omnibus aliis motionibus, quae in natura <lb></lb>fiunt, ut subinde concludere liceat motum, neque gigni de novo, neque destrui <lb></lb>in natura. </s>

<s>Hoc autem nec asseveranter nec ut certe creditum me protulisse <lb></lb>quis sibi persuadeat, sed tantummodo suspicando ” (ibid., pag. </s>

<s>136). L&#039;opi­<lb></lb>nione fu anzi benissimo accolta in quello, che poi si disse <emph type="italics"></emph>principio della <lb></lb>conservazion delle forze,<emph.end type="italics"></emph.end> il qual principio era la nostra intenzione di dimo­<lb></lb>strare come fosse dal Borelli applicato ai moti riflessi. </s>

<s>Già dicemmo come <lb></lb>quello, che si credeva mezzo, era invece termine di una dimostrazione, e ora <lb></lb>è da soggiungere come si facesse in questa dimostrazione principalmente con­<lb></lb>sistere, dallo stesso Borelli, il trattato <emph type="italics"></emph>De reflessione, quae ad corporum per­<lb></lb>cussionem consequitur,<emph.end type="italics"></emph.end> lasciando indietro o dando le seconde parti a ciò, <lb></lb>che avrebbe dovuto avere le principali. </s></p><p type="main">

<s>Dop&#039;aver professato che nel moto riflesso persevera il medesimo impeto, <lb></lb>che nell&#039;incidente, soggiunge così il Nostro: “ Quod autem haec sit naturae <lb></lb>familiaris consuetudo constat ex penduli illa proprietate, quam nuper detexi ” <lb></lb>(ibid., pag. </s>

<s>114). Questa nuova proprietà del pendolo è descritta e dimostrata <lb></lb>nel cap. </s>

<s>XI del primo libro delle <emph type="italics"></emph>Theoricae Mediceorum,<emph.end type="italics"></emph.end> a proposito del ri­<lb></lb>solvere la seguente questione: Se circolando un mobile intorno a un centro <lb></lb>fisso, come i pianeti intorno al Sole o i satelliti intorno a Giove, perseve­<lb></lb>rando col medesimo vigore a rivolgersi in un cerchio più angusto faccia, come <lb></lb>dicevano alcuni, il suo moto più concitato. </s>

<s>La questione pareva per verità <lb></lb>risoluta nel quarto dialogo dei Massimi Sistemi da Galileo, dove, a proposito <lb></lb>delle ineguaglianze della Luna, dice che nella congiunzione deve passar archi <lb></lb>maggiori dell&#039;orbe magno. </s>

<s>“ Ora se è vero, dice ivi il Salviati, che la virtù, <lb></lb>che muove la Terra e la Luna intorno al Sole, si mantenga del medesimo <lb></lb>vigore, e se è vero che il medesimo mobile, mosso dalla medesima virtù, ma <lb></lb>in cerchi disuguali, in tempi più brevi passi archi simili dei cerchi minori; <lb></lb>bisogna necessariamente dire che la Luna, quando è in minor distanza dal <lb></lb>Sole, cioè nel tempo della congiunzione, archi maggiori passi dell&#039;orbe magno, <lb></lb>che quando è in maggior lontananza, cioè nell&#039;opposizione e plenilunio ” <lb></lb>(Alb. </s>

<s>I, 490). Galileo però tien per vero che la Luna, anche deviata dal suo <lb></lb>primo corso, prosegua con la medesima velocità nel giro più angusto, ma non <lb></lb>lo dimostra, ond&#039;il Borelli annunzia una tal proposizione, per supplire al di­<lb></lb>fetto: “ Aio verum non esse idem mobile, semper ab eadem virtute motiva <lb></lb>intrinseca translatum, ac modo percurrens maiorem circuli peripheriam, modo <lb></lb>vero minorem; per minorem circulum concitatiori motu cieri, quam per ma-<pb xlink:href="020/01/2559.jpg" pagenum="184"></pb>iorem: progreditur enim eadem velocitate per ambos circulos inaequales, hoc <lb></lb>est, temporibus aequalibus, aequalia spatia pertransit ” (Theoricae Medic., <lb></lb>Florentiae 1665, pag. </s>

<s>52). </s></p><p type="main">

<s>La proposizione si dimostra per mezzo di uno sperimento, <emph type="italics"></emph>aptissimum,<emph.end type="italics"></emph.end><lb></lb>dice il Borelli, <emph type="italics"></emph>ad hanc veritatem comprobandam,<emph.end type="italics"></emph.end> ed è tale: Sia AB un <lb></lb>pendolo (fig. </s>

<s>63) sospeso in A: rimosso in AC dal perpendicolo, e lasciato poi <lb></lb>andare, incontri in D un ostacolo, come per esempio un chiodo, cosicchè, con <lb></lb><figure id="id.020.01.2559.1.jpg" xlink:href="020/01/2559/1.jpg"></figure></s></p><p type="caption">

<s>Figura 63.<lb></lb>l&#039;impeto conceputo in B, prosegua il suo moto per <lb></lb>l&#039;arco GB, che verrà descritto col raggio DB raccor­<lb></lb>ciato. </s>

<s>Dice il Borelli stesso di avere in questo fatto <lb></lb>scoperto una proprietà singolare, che cioè sempre, e <lb></lb>in qualunque caso, l&#039;angolo GDB sta all&#039;angolo BAC, <lb></lb>o al suo uguale FDB, reciprocamente come la radice <lb></lb>della maggior lunghezza del pendolo sta alla radice <lb></lb>della minore: e di qui ne conclude che, per essere il <lb></lb>mobile deviato, non per questo varia la prima impres­<lb></lb>sagli velocità del suo moto. </s>

<s>La conclusione è verissima, <lb></lb>come resulta dai principii matematici del seguente di­<lb></lb>scorso. </s>

<s>Essendo gli angoli GDB, FDB proporzionali <lb></lb>agli archi intercetti, abbiamo per esperienza GB:FB=√AB:√BD, e per <lb></lb>Geometria FB:BC=DB:AB, essendo gli archi simili proporzionali alle <lb></lb>lunghezze dei raggi. </s>

<s>Moltiplicando ora insieme termine per termine queste <lb></lb>proporzioni, ne resulta GB:BC=√DB:√AB. </s>

<s>Ma per le note proprietà <lb></lb>de&#039;pendoli di varia lunghezza anche il tempo per GB sta al tempo per BC <lb></lb>come la radice di DB sta alla radice di AB; dunque i tempi son proporzio­<lb></lb>nali agli spazi. </s>

<s>“ Sed, cum tempora sunt proportionalia spatiis transactis, <lb></lb>celeritates aequales sunt inter se; ergo celeritas penduli AB aequalis est ce­<lb></lb>leritati penduli BD ” (ibid., pag. </s>

<s>54). </s></p><p type="main">

<s>Questa proprietà dei pendoli però non era ap­<lb></lb><figure id="id.020.01.2559.2.jpg" xlink:href="020/01/2559/2.jpg"></figure></s></p><p type="caption">

<s>Figura 64.<lb></lb>plicabile alla Meccanica celeste, se non che nell&#039;ipo­<lb></lb>tesi di Galileo, ma nel sistema delle forze centrali, <lb></lb>come lo professava il Borelli, era fuor di luogo, non <lb></lb>potendo il pianeta deviar dal suo corso, senza variar <lb></lb>quell&#039;impeto, che tutto dipende dalla maggior o mi­<lb></lb>nor distanza ch&#039;egli ha dal centro attrattivo; ond&#039;è <lb></lb>che, per intrinseca necessità, va nel perielio più ve­<lb></lb>loce che nell&#039;afelio. </s>

<s>Con miglior senno perciò si di­<lb></lb>rebbe applicata dall&#039;Autore la sua scoperta, nelle <lb></lb>controversie ch&#039;egli ebbe coll&#039;Angeli, rispetto al de­<lb></lb>finir la linea, che nel tendere al centro della terra <lb></lb>descrive il proietto. </s>

<s>Di lui si può dir benissimo che persevera con la sua <lb></lb>prima velocità, deviando e variamente incurvando il suo moto, come vi per­<lb></lb>severa il pendolo conico ABE (fig. </s>

<s>64), ritirando in G per esempio il filo, <lb></lb>scorrevole nella campanella B. </s>

<s>Se BG è un quarto di AB “ allora vedremo <pb xlink:href="020/01/2560.jpg" pagenum="185"></pb>dalla palla F descriversi il cerchio FG, in tempo minore, cioè la metà di <lb></lb>quello, che vi voleva a compiere il cerchio ADE; e però la velocità in FG <lb></lb>sarà la medesima, che aveva la palla A ” (Lettera a M. A. Ricci, Mes­<lb></lb>sina 1667, pag. </s>

<s>4). </s></p><p type="main">

<s>Appropriata pure è la descritta esperienza a dimostrar che, nella rifles­<lb></lb>sione, persevera la medesima quantità di moto, che nell&#039;incidenza, ond&#039;è che <lb></lb>opportunamente citavasi dallo stesso Borelli, nel cap. </s>

<s>XV <emph type="italics"></emph>De vi percussio­<lb></lb>nis,<emph.end type="italics"></emph.end> dopo di che egli ivi così soggiunge: “ Sed licet resistentia corporis duri <lb></lb>et quiescentis omnino non destruat impetum corporis in eum incidentis, ... <lb></lb>dubitari saltem potest an impetum eiusdem incidentis corporis debilitet, et <lb></lb>aliquo pacto imminuat ” (pag. </s>

<s>115), ciò che non possa essere attende a di­<lb></lb>mostrarlo nella proposizione LIX, così annunziata: “ Vis motiva incidentis <lb></lb>corporis non debilitatur, neque imminuitur a resistentia corporis firmi et <lb></lb>duri ” (ibid.). </s></p><p type="main">

<s>La proposizione però, dopo le cose dette, sembra per lo meno oziosa, <lb></lb>perchè o i corpi si suppongono perfettamente fermi e duri, e la verità del­<lb></lb>l&#039;assunto dipende dalla fatta supposizione: o i corpi si considerano secondo <lb></lb>la loro fisica realtà, e la proposizione è falsa, perchè, non essendo in nes­<lb></lb>suno di così fatti corpi la richiesta infiessibilità e durezza assoluta, è impos­<lb></lb>sibile che nel risaltare non perdano alquanto del primo impeto conceputo. </s>

<s><lb></lb>Apparirà poi la detta borelliana proposizione anche più oziosa, se si ripensa <lb></lb>che, sopra la verità di lei, era stato posto il fondamento a tutta la Meccanica <lb></lb>di Galileo, il quale, nello scolio alla proposizione XXIII del terzo dialogo delle <lb></lb>Scienze nuove, aveva dimostrato che il moto riflesso, dopo essere sceso lungo <lb></lb>un piano, non è punto diminuito dal moto incidente, avendo facoltà di ri­<lb></lb>condurre il mobile alla medesima altezza, <emph type="italics"></emph>e ciò levato ogni intoppo, che pre­<lb></lb>giudica all&#039;esperienza<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 166). </s></p><p type="main">

<s>La galileiana dimostrazione equivale alla proposizione LXIII del Borelli, <lb></lb>e alle corrispondenti dell&#039;Huyghens e del Mariotte, che pur sppongono esser <lb></lb>rimossi gli impedimenti, ammessi i quali non possono non esser false quelle <lb></lb>stesse loro proposizioni, com&#039;ebbero a riscontrare i nostri Accademici fioren­<lb></lb>tini ne&#039;rimbalzi delle palle di corno di bufalo e di avorio, che non videro <lb></lb>mai raggiungere a quella precisa altezza, da cui erano scese. </s>

<s>Del resto aveva <lb></lb>anche Galileo pensato di dimostrare che, per cangiar direzione il mobile, il <lb></lb>moto di lui non si diminuisce, osservando che una debolissima forza, impos­<lb></lb>sibile a muovere una gran mole, è pur capace, mossa che sia, di deviarla <lb></lb>dal suo sentiero. </s>

<s>“ Una palla molto grave, lasciò scritto in una nota, che fu <lb></lb>poi raccolta fra i <emph type="italics"></emph>Problemi varii;<emph.end type="italics"></emph.end> posata sopra un piano, e che percossa dal <lb></lb>vento gagliardo non gli ceda nè si muova, se la medesima sarà mossa sopra <lb></lb>quel piano, sicchè riceva il vento ad angolo retto, gli cederà deflettendo verso <lb></lb>la parte, che il vento la caccia ” (Alb. </s>

<s>XIV, 321). Ma vediamo come si di­<lb></lb>mostri dallo stesso Borelli la sopra accennata LIX proposizione. </s></p><p type="main">

<s>Tornando indietro sopra la figura 62, nella quale si rappresentava con <lb></lb>AB il moto incidente, decomposto nel perpendicolare AC e nel trasversale CB, <pb xlink:href="020/01/2561.jpg" pagenum="186"></pb><emph type="italics"></emph>quibus ille aequalis est potestate;<emph.end type="italics"></emph.end> rappresenti BE il moto riflesso, che si <lb></lb>vuol dimostrare non esser punto diminuito. </s>

<s>Perchè, se così fosse, presa del <lb></lb>trasversale una quantità BD, uguale alla CB, il perpendicolare dovrebbe re­<lb></lb>star minore di ED. </s>

<s>Sia per esempio DF: il moto riflesso diminuito sarebbe <lb></lb>dunque rappresentato da BF, per cui l&#039;angolo della riflessione FBD torne­<lb></lb>rebbe evidentemente minore dell&#039;angolo dell&#039;incidenza ABC. “ Hoc autem, dice <lb></lb>il Borelli, est falsum, et contra sensus evidentiam, quandoquidem perpetuo <lb></lb>huiusmodi anguli sunt aequales inter se ” (De vi percuss. </s>

<s>cit., pag. </s>

<s>117). </s></p><p type="main">

<s>Il teorema dunque nobilissimo, che ci si aspettava di veder dimostrato, <lb></lb>è rimesso all&#039;evidenza del fatto, e parandosi innanzi all&#039;Autore due vie, una <lb></lb>delle quali, dal suppor che il moto riflesso perseveri nel medesimo vigore <lb></lb>dell&#039;incidente, conduceva a concluder l&#039;uguaglianza degli angoli dell&#039;obliquità <lb></lb>ne&#039;due moti, e l&#039;altra che, dal supporre questa uguaglianza, menava a di­<lb></lb>mostrar come nel riflettersi quello stesso moto non diminuisce; egli prose­<lb></lb>gue a dirittura per questa, lasciando indietro quell&#039;altra. </s>

<s>In ciò consiste quel <lb></lb>che si diceva avere il Borelli posposta nell&#039;argomento la dignità e l&#039;impor­<lb></lb>tanza delle parti. </s>

<s>Che le forze, per solo cangiar direzione, non illanguidi­<lb></lb>scano il loro primo vigore, era cosa ammessa da tutti i matematici seguaci <lb></lb>delle dottrine meccaniche di Galileo, e perciò superflua si diceva tornare <lb></lb>l&#039;opera del Borelli in voler mettersi a dimostrarla, mentre poteva per quel <lb></lb>mezzo così facilmente riuscire alla tanto desiderata dimostrazione dell&#039;ugua­<lb></lb>glianza degli angoli fatti nel venir e nel tornare del percuziente dalla super­<lb></lb>ficie percossa. </s>

<s>Egli invece invoca l&#039;evidenza del senso: ma quale evidenza, <lb></lb>se il senso stesso mostra al contrario che tutti i corpi ponderosi risalgono <lb></lb>con minore obliquità di quella, con la quale erano scesi, come disse nelle <lb></lb>sue Lezioni di avere sperimentato il Torricelli, e se quella perpetuità di legge, <lb></lb>affermata dal nostro Autore, potendosi osservare in un raggio, che mettesse <lb></lb>un tempo sensibile a venire allo specchio, non si verificherebbe forse pun­<lb></lb>tualissimamente nemmen nella luce? </s></p><p type="main">

<s>Sembra nonostante che il Borelli, oltre a rimettersi al fatto, accennasse <lb></lb>a qualche dimostrazione del fatto, osservando che i corpi duri eleggono per <lb></lb><figure id="id.020.01.2561.1.jpg" xlink:href="020/01/2561/1.jpg"></figure></s></p><p type="caption">

<s>Figura 65.<lb></lb>necessità nel riflettersi la via più breve <lb></lb>di tutte. </s>

<s>“ Constat ergo ab eadem virtute <lb></lb>motiva impelli corpus incidens super ali­<lb></lb>quod corpus durum, a qua postea fertur <lb></lb>necessitate naturae <emph type="italics"></emph>brevissima via re­<lb></lb>flectendo ”<emph.end type="italics"></emph.end> (ibid. </s>

<s>pag. </s>

<s>115). Dalla qual <lb></lb>necessità naturale, supposta vera, conse­<lb></lb>gue senza dubbio che debba il mobile <lb></lb>ritornar con angolo uguale a quel che <lb></lb>venne, com&#039;è facile dimostrare. </s>

<s>Sia per <lb></lb>esempio AB (fig. </s>

<s>65) il piano, che si vuol <lb></lb>percotere, e si supponga un corpo C che, nell&#039;andare e nel tornare dalla <lb></lb>percossa, seguiti per istinto di natura la via più breve. </s>

<s>Dovendogliela noi <pb xlink:href="020/01/2562.jpg" pagenum="187"></pb>geometricamente presignare, diremo: Dal punto C si abbassino sul piano la <lb></lb>perpendicolare CA, prolungata in D per ugual tratto, e la obliqua CE: con­<lb></lb>giunta poi la DE, e prolungata in F, sarà CEF quella brevissima via, che si <lb></lb>voleva descritta. </s>

<s>Qualunque altra infatti se ne eleggesse, come per esempio <lb></lb>CGF, è facile vedere che sarebbe più lunga, perchè, congiunta la GD, DGF, <lb></lb>ossia CG+GF è evidentemente maggior linea di FD, ossia di FE+EC. </s>

<s><lb></lb>E perchè CEA, FEB sono uguali, si conclude che non può dunque il mobile <lb></lb>eleggere per necessità di natura la via brevissima, senza che sia dalla me­<lb></lb>desima necessità costretto a riflettersi con angolo uguale a quello dell&#039;in­<lb></lb>cidenza. </s></p><p type="main">

<s>Ma il Borelli, contento a porre il principio, lasciò al Leibniz il merito <lb></lb>della bellissima conclusione, intanto che, fra i primi promotori della scienza <lb></lb>della percossa, fu il Wallis il solo, che si proponesse di dimostrare: “ Si <lb></lb>grave motum in firmum obicem oblique impingat, sitque vel alterum vel <lb></lb>utrumque elasticum; resilitio eadem celeritate, et in eodem plano, ita fiet ut <lb></lb>angulus reflexionis sit angulo incidentiae aequalis ” (De motu cit., cap. </s>

<s>XIII, <lb></lb>pag. </s>

<s>692). È questa la seconda proposizione, che ricorre nel trattato <emph type="italics"></emph>De ela­<lb></lb>tere et reflexione,<emph.end type="italics"></emph.end> dop&#039;essersi dimostrato dall&#039;Autore, come aveva fatto prima <lb></lb>il Borelli nella sua LXIII, e poi l&#039;Huyghens nella VIII, e nella XV della se­<lb></lb>conde parte il Mariotte; che se un grave percote un resistente, e sia l&#039;uno <lb></lb>e l&#039;altro elastico, <emph type="italics"></emph>eadem velocitate resiliet, qua advenerat<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>687). </s></p><p type="main">

<s>Ciò premesso, ecco come succede per il Wallis la seconda detta propo­<lb></lb>sizione. </s>

<s>Sia AB (fig. </s>

<s>66) la obliquità, e la misura della forza, con la quale <lb></lb>il grave mosso percuote l&#039;obice fermo CD, e sia quella forza decomposta nella <lb></lb><figure id="id.020.01.2562.1.jpg" xlink:href="020/01/2562/1.jpg"></figure></s></p><p type="caption">

<s>Figura 66.<lb></lb>orizontale AO, e nella perpendicolare OB, <lb></lb>la quale sola offende in B, d&#039;onde ritorne­<lb></lb>rebbe, per la precedente proposizione, in <lb></lb>O, alla medesima altezza: cosicchè, men­<lb></lb>tre il mobile fosse passato orizontalmente <lb></lb>da B in D, nel medesimo tempo e per <lb></lb>spazio uguale a CB, sarebbe anche in­<lb></lb>sieme risalito verticalmente in E, ad un&#039;al­<lb></lb>tezza DE uguale ad OB, ovvero a CA, con due moti, che si ricompongono nel­<lb></lb>l&#039;unico obliquo e riflesso BE, e i triangoli rettangoli ACB, BED, coi cateti <lb></lb>uguali, daranno ABC, angolo dell&#039;incidenza uguale a DBE, angolo della ri­<lb></lb>flessione. <emph type="italics"></emph>Quae,<emph.end type="italics"></emph.end> conclude il Wallis, <emph type="italics"></emph>erant demonstranda.<emph.end type="italics"></emph.end> Ma fa subito alla <lb></lb>conclusione seguitare uno Scolio, atto benissimo a testimoniare di quelle con­<lb></lb>tradizioni, dalle quali si diceva essere stati l&#039;Huyghens e il Mariotte, fra gli <lb></lb>altri, ritenuti dal professar liberamente la dottrina dei moti composti. </s></p><p type="main">

<s>Gli studenti, così scrive l&#039;Autore nel detto Scolio, e anche alcuni, che <lb></lb>dovrebbero essere da qualche cosa più degli studenti, mi domandano con <lb></lb>qual diritto io abbia decomposto un moto retto e semplicissimo in due: o <lb></lb>pur concedendomi il licenzioso arbitrio vorrebbero sapere come mai, fra gli <lb></lb>infiniti modi di decomporre un moto, io abbia per l&#039;appunto scelto quello, <pb xlink:href="020/01/2563.jpg" pagenum="188"></pb>e non un altro. </s>

<s>“ Respondeo nullum ita simplicem esse motum posse, quin <lb></lb>in plures componentes resolvi possit. </s>

<s>Dum autem hunc prae caeteris modum <lb></lb>seligo, utor ego meo iure, qui, cum quamlibet possim, eam adhibeo compo­<lb></lb>sitionem, quae praesenti negotio sit accomoda. </s>

<s>Neque probandum erit com­<lb></lb>positionem hanc unicam esse possibilem, sed ex multis unam. </s>

<s>Liberum uti­<lb></lb>que est, pro suo cuiusque constructoris arbitrio, ex veris innumeris ea seligere, <lb></lb>quae ad rem praesentem conducant ” (ibid., pag. </s>

<s>693). E soggiunge a illu­<lb></lb>strare il fatto meccanico altri simili esempi di composizioni algebriche e geo­<lb></lb>metriche, concludendo così l&#039;apologetico suo discorso: “ Estque res haec tam <lb></lb>clara, ut nulla illustratione putaverim indiguisse, si non hoc ipsum serio <lb></lb>obiectum viderim a Viro cum tyronibus non camparando ” (ibid., pag. </s>

<s>695). </s></p><p type="main">

<s>S&#039;intendeva compresa in quell&#039;Uomo, da non mettersi coi principianti, <lb></lb>la maggior parte dei Matematici di Europa, i quali, a navigare per il peri­<lb></lb>glioso oceano della Meccanica, avevano ripudiato il più valido remo. </s>

<s>Ma con <lb></lb>questo in mano vedremo ora Giovan Marco entrare per i riposti seni, ad ap­<lb></lb>prodare ai quali peneranno ancora un secolo i novelli esploratori, conducendo <lb></lb>snellamente la sua navicella per quelle acque solitarie, non agitate dai venti, <lb></lb>sotto quella remota zona di cielo, non offuscato dalle caligini: da quelle ca­<lb></lb>ligini vogliam dire, a dissipar le quali, per tornare a vedere l&#039;alma luce del <lb></lb>sole, ebbe ad affannarsi più di una volta il Wallis. </s></p><p type="main">

<s>La proposizione XXXIX <emph type="italics"></emph>De proportione motus<emph.end type="italics"></emph.end> è dall&#039;Autore stesso così <lb></lb>pronunziata: “ Motus reflexus fit per lineam parallelam illi lineae, quae cum <lb></lb>linea perpendiculari ad contactum angulum constituit in centro, cuius sinus <lb></lb>est aequalis intervallo inter centrum gravitatis, et lineam hypomochlii ” (fol. </s>

<s>50). <lb></lb>Cada il globo CDG (fig. </s>

<s>67) sul piano obliquo ADB, e lo percota in D: dal <lb></lb>qual punto sollevata la verticale DC, che è la linea dell&#039;ipomoclio, si trovi <lb></lb><figure id="id.020.01.2563.1.jpg" xlink:href="020/01/2563/1.jpg"></figure></s></p><p type="caption">

<s>Figura 67.<lb></lb>questa lontana, per la distanza EF, dal cen­<lb></lb>tro di gravità E dello stesso globo. </s>

<s>Dentro <lb></lb>l&#039;angolo retto KEH si costruisca un angolo <lb></lb>minore HEG, di cui il seno sia HG uguale <lb></lb>ad EF. </s>

<s>Descritto il parallelogrammo HK, e <lb></lb>condotta la diagonale EG, vuol dimostrar <lb></lb>Giovan Marco che, nel riflettersi il globo <lb></lb>dopo la percossa, si move, col centro, nella <lb></lb>direzione EG, e, col punto del contatto, nella <lb></lb>direzione DI, alla stessa EG parallela. </s></p><p type="main">

<s>Rappresentato con EB il momento to­<lb></lb>tale, che vien decomposto nel DB sulla su­<lb></lb>perficie del piano, e nel DE a lei stessa per­<lb></lb>pendicolare; la dimostrazione procede così, <lb></lb>in modo che si rassomiglia nelle mosse a <lb></lb>quella del Wallis, se non che, mentre questi <lb></lb>fa precedere la proposizione che dice risalire da D in E il centro di gravità <lb></lb>del percuziente, con la medesima velocità, colla quale era da E in D dianzi <pb xlink:href="020/01/2564.jpg" pagenum="189"></pb>sceso; Giovan Marco suppone la stessa cosa come una verità conseguente <lb></lb>dall&#039;ipotesi, ch&#039;egli tiene intorno alla natura della elasticità, la quale essendo <lb></lb>perfetta restituisce al mobile tutto intero l&#039;impeto perduto nell&#039;urto. </s>

<s>Così <lb></lb>essendo, verrà dunque il centro E del globo dopo l&#039;urto sollecitato da forze <lb></lb>rappresentate per linee uguali o proporzionali alle DB, DE, ma dirette in <lb></lb>parte, che non trovino impedimento. </s>

<s>E perchè EK, EH son quelle loro pro­<lb></lb>porzionali, e hanno libero il loro esercizio, perchè son dirette alla parte av­<lb></lb>versa, e fuori dell&#039;ipomoclio del centro; trasporteranno dunque il globo, <lb></lb>com&#039;era il proposito di dimostrare, dal centro stesso nella direzione della dia­<lb></lb>gonale EG, e nella direzione DI, ad essa EG parallela, dal punto di con­<lb></lb>tatto. </s>

<s>Ma è bene, a far conoscere la precisione e la chiarezza del dimo­<lb></lb>strare, in mezzo alle verbosità di quei tempi, trascriver le parole proprie <lb></lb>dell&#039;Autore: </s></p><p type="main">

<s>“ Quia enim centrum gravitatis, dum sua mole ferit planum in puncto D, <lb></lb>per lineam ED seipsum veluti partitur: illa quidem pars quae hypomochlio <lb></lb>insistit, atque illam plagam inducit, eadem via qua impulit, et impulsu ae­<lb></lb>quali, retro agitur; reliqua vero, quae cum centro extra hypomochlium cadit, <lb></lb>per lineam fertur EK parallelam lineae DB, propterea quod haec sit proxima <lb></lb>motui gravitatis ab hypomochlio impeditae. </s>

<s>Quia ergo motus EH, EK, qui­<lb></lb>bus centrum gravitatis agitur, secundum quid sunt contrarii, propterea quod <lb></lb>angulus HEK sit minor duobus rectis; erit motus mixtus per lineam me­<lb></lb>diam inter EH, et EK, cuius intervallum determinat sinus complementi in­<lb></lb>clinationis, in ratione quam habent impulsus. </s>

<s>Est autem intervallum FE, hoc <lb></lb>est sinus DM anguli DEM, mensura gravitatis extra hypomochlio: linea vero <lb></lb>FD, sinus anguli reliqui, mensura illius, quae hypomochlio insistit, gravita­<lb></lb>tis. </s>

<s>Si fiat ut FD ad EF, ita KG, sinus complementi anguli HEG, ad HG, <lb></lb>sinum complementi anguli KEG; erit linea EG linea motus mixti ex EH, <lb></lb>et EK.... Quia ergo mobile movetur ad motum sui centri, erit motus ex D <lb></lb>reflexus per lineam parallelam illi lineae, quae cum linea perpendiculari ad <lb></lb>contactum angulum constituit in centro, cuius sinus est aequalis intervallo <lb></lb>inter centrum gravitatis, et lineam hypomochlii ” (ibid., fol. </s>

<s>50, 51). </s></p><p type="main">

<s>Si diceva che questa dimostrazione si rassomiglia nelle mosse a quella, <lb></lb>che trentadue anni dopo, fra le contradizioni dei contemporanei, conquistava <lb></lb>faticosamente alla Scienza il Wallis, ma è più generale e vien condotta da <lb></lb>Giovan Marco con tale analitico artificio, da poter da lei, come corollari, de­<lb></lb>rivar facilmente le verità più importanti, di che è a notar che il Casati in <lb></lb>Italia, dove il Matematico di Praga era affatto sconosciuto, dette i primi <lb></lb>esempi (Mechanic., libri cit., pag. </s>

<s>739-32). Essendo infatti, nella precedente <lb></lb>figura, l&#039;angolo ADC uguale all&#039;angolo FED, che pure è uguale all&#039;angolo <lb></lb>EGH, ed essendo l&#039;angolo EGH uguale all&#039;angolo IDB; apparisce manifesta <lb></lb>l&#039;uguaglianza immediata e diretta fra ADC angolo dell&#039;incidenza, e IDB an­<lb></lb>golo della riflessione: corollario, che l&#039;Autore mette in forma della propo­<lb></lb>sizione XL: <emph type="italics"></emph>Anguli incidentiae et reflexionis sunt inter se aequales<emph.end type="italics"></emph.end> (ibid., <lb></lb>fol. </s>

<s>51). </s></p><pb xlink:href="020/01/2565.jpg" pagenum="190"></pb><p type="main">

<s>Un altro corollario matematico scende dalla proposizione XXXIX di <lb></lb>Giovan Marco, ad illustrare alcuni effetti fisici, che si osservano nelle per­<lb></lb>cosse dei varii corpi: uno de&#039;quali effetti è quello, che lo stesso Giovan Marco <lb></lb>così descrive: “ Impulsus ergo pilae, cum motus centri est perpendicularis <lb></lb>ad planum ubi percussit, in hypomochlio a motu conquiescit: at vero pla­<lb></lb>num ex illa plaga in percutiente novum determinat impulsum, iuxta directio­<lb></lb>nem plagae quam infert, a quo, eadem qua venit via, retroagitur, et si qui­<lb></lb>dem duritie praestat, erit plaga, et qui hanc sequitur impulsus, in utroque <lb></lb>aequalis, ac proinde motus reflexus aequalis motui recto ” (ibid., fol. </s>

<s>44 ad t.). <lb></lb>A questa affermazione, nella quale Giovan Marco riconosceva la nota della <lb></lb>evidenza, corrispondono la proposizione prima del trattato <emph type="italics"></emph>De elatere<emph.end type="italics"></emph.end> del <lb></lb>Wallis, e la LXIII del Borelli, insieme con le altre simili dell&#039;Huyghens e <lb></lb>del Mariotte, ma dalle matematiche astrazioni trapassando alle fisiche realtà <lb></lb>lo stesso Giovan Marco, con scienza più comprensiva de&#039;suoi celeberrimi <lb></lb>successori, soggiunge: “ Deficit autem motus reflexus a motu recto, si, de­<lb></lb>fectu duritiei, minorem recipit quam dedit plagam ” (ibid.). </s></p><p type="main">

<s>Applicando l&#039;osservazione ai moti obliqui, e riferendoci sempre alla figura <lb></lb>ultimamente rappresentata, EH non avrà dunque esatta proporzione con DE, <lb></lb>se non che nel supposto della elasticità perfetta. </s>

<s>Ma se questa è in difetto, <lb></lb><emph type="italics"></emph>deficiet motus reflexus,<emph.end type="italics"></emph.end> per cui la proporzionale a DE sarà in questo caso <lb></lb>minore di EH. </s>

<s>Sia per esempio EP, rimanendo EK tuttavia del medesimo <lb></lb>vigore, perchè da nulla viene impedita: il nuovo parallelogrammo, descritto <lb></lb>sopra le due forze, sarà PK, e il moto riflesso piglierà la sua direzione se­<lb></lb>condo la diagonale ER, o secondo la sua parallela DS, intantochè l&#039;angolo <lb></lb>della riflessione BDI sarà minore dell&#039;angolo ADC dell&#039;incidenza, e tanto <lb></lb>minore, quanto sarà maggiore il difetto del percuziente dalla supposta ela­<lb></lb>sticità perfetta. </s></p><p type="main">

<s>Ecco come da questo corollario di Giovan Marco venga illustrato un fatto <lb></lb>fisico, che il Torricelli dovette contentarsi di descriver nella sua seconda Le­<lb></lb>zione della percossa, senza saper ridurlo ai principii di quella scienza, che <lb></lb>nella Scuola di Galileo tuttavia s&#039;ignorava. </s>

<s>Citeremo del passo torricelliano, <lb></lb>invece della stampa, il manoscritto, dove son rimaste le Lezioni, in quella <lb></lb>parte che richiaman qualche figura illustrativa, nella forma ch&#039;ebbero ori­<lb></lb>ginalmente, prima che l&#039;Autore stesso le correggesse, per accomodarle al­<lb></lb>l&#039;udienza, alla quale non si poteva dalla bugnola accademica comunicare le <lb></lb><figure id="id.020.01.2565.1.jpg" xlink:href="020/01/2565/1.jpg"></figure></s></p><p type="caption">

<s>Figura 68.<lb></lb>idee per via di segni visibili. </s>

<s>“ Questo sia detto, <lb></lb>leggesi dunque così nell&#039;autografo, per le proiezioni, <lb></lb>che si faranno sul piano ad angoli retti verso la <lb></lb>detta parete opposta. </s>

<s>Ma quando si scagliasse ad <lb></lb>angolo obliquo, per la linea AB (fig. </s>

<s>68), vederemmo <lb></lb>far la riflessione, non per la linea BC che fa l&#039;an­<lb></lb>golo uguale a quello dell&#039;incidenza, ma per la BED, <lb></lb>che o tocca o pochissimo va sopra il piano, come ho sperimentato con palle <lb></lb>di piombo e di creta. </s>

<s>Non è però vero che la percossa estingua quell&#039;im-<pb xlink:href="020/01/2566.jpg" pagenum="191"></pb>peto, che è nel mobile, di direzione equidistante dalla parete, ma solo smorza <lb></lb>quello, che vi è di perpendicolare alla parete, perchè questo nell&#039;urtare trova <lb></lb>la contrarietà sua, cioè che gl&#039;impedisce il suo viaggio, ma quell&#039;atro no ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XXXIX a tergo del fol. </s>

<s>16). </s></p><p type="main">

<s>Si direbbe aver questa cosa conclusa il Torricelli direttamente da una <lb></lb>proposizione simile a quella di Giovan Marco, piuttosto che dall&#039;esperienza. </s>

<s><lb></lb>Ma che, mentre il Discepolo di Galileo affermava con tanta sicurezza smor­<lb></lb>zarsi nell&#039;urto oblìquo quel tanto solo, che v&#039;è in lui di perpendicolare, non <lb></lb>s&#039;attentasse d&#039;assegnarne per scienza la proporzione; s&#039;argomenta dall&#039;incer­<lb></lb>tezza, con la quale procede in risolvere altri simili problemi. </s>

<s>In fine al suo <lb></lb>trattato <emph type="italics"></emph>De&#039;proietti<emph.end type="italics"></emph.end> proponesi di trovar la misura del colpo fatto dalla palla <lb></lb>del cannone contro il piano resistente, variato solo dalla diversità degli an­<lb></lb>goli dell&#039;incidenza, premettendo al discorso un tale avvertimento: “ Il pro­<lb></lb>blema, per quanto io sappia, è intatto; però, se si produrrà qualche cosa <lb></lb>meno sussistente, e non pura geometrica, o si compatisca, sin che altri tratti <lb></lb>meglio la dottrina, o si rifiuti affatto, che poco importa ” (Op. </s>

<s>geom., P. </s>

<s>I <lb></lb>cit., pag. </s>

<s>239). </s></p><p type="main">

<s>Ciò premesso, suppone che gli impeti nel medesimo proietto siano pro­<lb></lb>porzionali alle velocità, le quali, ne&#039;medesimi tempi, stanno come gli spazi. <lb></lb></s>

<s>“ Ciò supposto, egli dice, mentre una palla di cannone si avvicina al muro <lb></lb>opposto, la linea e dirittura del tiro o è perpendicolare al muro, o no. </s>

<s>Se è <lb></lb>perpendicolare, la percossa opera con una tal forza, che proveremo esser la <lb></lb>massima, che possa aver quel tiro: se sarà ad angoli obliqui, come la linea <lb></lb>AB (fig. </s>

<s>69) alla parete BC, io noto che, rispetto alla parete BC, sono nella <lb></lb>linea AB del proietto due moti insieme composti: uno cioè di avvicinamento <lb></lb><figure id="id.020.01.2566.1.jpg" xlink:href="020/01/2566/1.jpg"></figure></s></p><p type="caption">

<s>Figura 69.<lb></lb>perpendicolare alla parete, l&#039;altro di passaggio laterale <lb></lb>o parallelo alla stessa. </s>

<s>Il perpendicolare ci viene e mo­<lb></lb>strato e misurato dalla linea AC, il parallelo dalla linea <lb></lb>CB ” (ivi, pag. </s>

<s>240). Or perchè tanto il moto per AB, <lb></lb>quanto i moti per AC, CB son passati nel medesimo <lb></lb>tempo, staranno dunque, per le fatte supposizioni, come <lb></lb>gli spazi; ond&#039;è che, considerati gli effetti secondo le <lb></lb>direzioni perpendicolari, ed essendo l&#039;effetto di BC nullo, <lb></lb>staranno i detti moti come AB ad AC. </s>

<s>Per un&#039;altra <lb></lb>incidenza DB del medesimo tiro staranno i moti come <lb></lb>DB a DE: da che dunque inferiremo “ che le attività o <lb></lb>momenti dei tiri diversamente inclinati sono come i seni retti degli angoli <lb></lb>delle incidenze ” (ivi, pag. </s>

<s>242). Che se, diretta secondo la linea AB, “ la <lb></lb>palla s&#039;internasse tutta per l&#039;appunto nel muro, adunque, per tutte le linee <lb></lb>più elevate, non solo s&#039;immergerà tutta nella solidità, ma farà sempre mag­<lb></lb>giore passata, perchè ha maggior forza. </s>

<s>Ma delle meno elevate, perchè cia­<lb></lb>scuna averà minor forza, niuna entrerà totalmente nella parete, ma alcune <lb></lb>anco risalteranno, e sfuggiranno dall&#039;altra parte. <emph type="italics"></emph>Sia però detto tutto que­<lb></lb>sto astraendo da un certo effetto di piegamento o refrazione, che fanno i<emph.end type="italics"></emph.end><pb xlink:href="020/01/2567.jpg" pagenum="192"></pb><emph type="italics"></emph>proietti nel passar con inclinazione dal mezzo raro al mezzo più denso, <lb></lb>incurvandosi la linea al contrario della refrazione della luce e spezie vi­<lb></lb>sibili ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>243). </s></p><p type="main">

<s>Trae da quel suo teorema fondamentale il Torricelli alcuni altri corol­<lb></lb>lari, come i due seguenti, che soli basterà commemorare. </s>

<s>Il primo è che <lb></lb>“ l&#039;incidenza ad angolo di 30 gradi ha la metà della forza totale, essendo il <lb></lb>seno suo la metà del semidiametro ” (ivi, pag. </s>

<s>242): l&#039;altro, che resulta da <lb></lb>alcune considerazioni, le quali noi riferiremo, per brevità, col linguaggio e <lb></lb>co&#039;segni dei matematici odierni. </s>

<s>Siano AC, BD (fig. </s>

<s>70) le misure delle forze <lb></lb>di proiezione contro i piani resistenti BC, ED:avremo AC/AB=1/cos.BAC= <lb></lb>sec.BAC; BD/BE=1/cos.EBD=sec.EBD. Cosicchè, se sia AC:BD=sec.BAC: <lb></lb>sec.BED, dovrà essere AB=BE. </s>

<s>Ma da queste linee son misurati gl&#039;im­<lb></lb>peti fatti perpendicolarmente contro i piani resistenti nelle due proiezioni, <lb></lb><figure id="id.020.01.2567.1.jpg" xlink:href="020/01/2567/1.jpg"></figure></s></p><p type="caption">

<s>Figura 70.<lb></lb>dunque “ allora i proietti averanno la stessa forza nel per­<lb></lb>cuotere, quando gl&#039;impeti saranno come le secanti degli an­<lb></lb>goli del complemento delle incidenze ” (ivi, pag. </s>

<s>242). </s></p><p type="main">

<s>Il problema principale, da cui derivano questi e altri <lb></lb>corollari non meno importanti, aveva ragione il Torricelli <lb></lb>a dire che era intatto, non avendo Galileo, nel dialogismo <lb></lb>che succede alla quarta proposizione del quarto Dialogo delle <lb></lb>Scienze nuove, saputo far dire al suo Salviati in proposito <lb></lb>altro che questo: “ La qual positura, se sarà tale che il moto <lb></lb>del percuziente la vada a investire ad angoli retti, l&#039;impeto del colpo sarà <lb></lb>il massimo: ma se il moto verrà obliquamente, o come diciam noi a scan­<lb></lb>cio, il colpo sarà più debole, e più e più secondo la maggiore obliquità ” <lb></lb>(Alb. </s>

<s>XIII, 246). Il Maestro dunque della Scuola nuova aveva veramente la­<lb></lb>sciato irresoluto il problema, professando l&#039;errore che l&#039;impeto del colpo obli­<lb></lb>quo sia tanto più debole, quanto è minore l&#039;angolo dell&#039;obliquità, ma nella <lb></lb>Scuola antica, dal Torricelli ignorata, non era così: e noi trascrivemmo a <lb></lb>pag. </s>

<s>58 del precedente Tomo la nota, nella quale dimostrava Leonardo da <lb></lb>Vinci che i colpi stanno, non come gli angoli, ma come i seni degli angoli <lb></lb>delle inclinazioni. </s>

<s>A quella medesima scuola di Leonardo apparteneva anche <lb></lb>Giovan Marco, dalla riferita proposizione del quale, e sopra la disegnata <lb></lb>figura 67, si conclude che l&#039;impeto diretto sta all&#039;obliquo, come la linea EB <lb></lb>alla ED, ossia come il seno totale al seno dell&#039;angolo dell&#039;incidenza. </s>

<s>Ed è <lb></lb>pur notabile che, mentre i discepoli di Aristotile e del Nemorario procede­<lb></lb>vano così sicuri alla conquista del vero, il discepolo di Galileo chiedesse com­<lb></lb>patimento alle sue nuove intatte dottrine, confessando che poco gl&#039;importava <lb></lb>di vederle anche affatto rifiutare. </s></p><p type="main">

<s>Pensava in dir così il Torricelli ai suoi propri colleghi nella Scuola ga­<lb></lb>lileiana, contro i quali professava quelle dottrine, che lo condussero a riscon­<lb></lb>trarsi col Roberval nel metodo di condurre alle curve le tangenti. </s>

<s>Anzi esso <pb xlink:href="020/01/2568.jpg" pagenum="193"></pb>Roberval, benchè in pubblico conosciuto più tardi, appartiene al numero di <lb></lb>coloro, che tranquillamente facevano uso dei moti composti, non essendo in <lb></lb>Francia come in Italia sorta nessuna autorità a metter dubbio intorno alle <lb></lb>antiche tradizioni. </s>

<s>Qualche anno prima del 1640 aveva il Matematico fran­<lb></lb>cose fatto già quelle <emph type="italics"></emph>Observations sur la composition des mouvemens,<emph.end type="italics"></emph.end> che <lb></lb>il Bourdalois ridusse nel 1668 in forma di trattato, dove si legge la dimo­<lb></lb>strazione dell&#039;uguaglianza tra l&#039;angolo dell&#039;incidenza e della riflessione, decom­<lb></lb>ponendo in due il moto incidente, e ragionando in modo simile al Wallis <lb></lb>(<emph type="italics"></emph>Ouvrage de M. </s>

<s>De Roberval,<emph.end type="italics"></emph.end> a la Haye 1731, pag. </s>

<s>11, 12). È un fatto dun­<lb></lb>que che il Roberval e il Torricelli si trovarono, intorno al principio della <lb></lb>composizion delle forze, concordi: l&#039;Italiano però procedeva incerto nell&#039;appli­<lb></lb>cazione di quel principio alla misura della percossa obliqua e della diretta, <lb></lb>rassegnandosi a veder, come abbiamo ora udito, dai seguaci delle dottrine di <lb></lb>Galileo rifiutate, per esser credute false, le sue conclusioni. </s></p><p type="main">

<s>Ma vennero anzi confermate, come meritavano, e fu primo a far ciò il <lb></lb>Borelli nella XLV, e nella L <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> nella quale ultima si pro­<lb></lb>poneva l&#039;Autore di dimostrare che “ si superficies corporis ictum excipientis <lb></lb>perpendicularis fuerit ad lineam motus obliqui ipsius percutientis, erit vis <lb></lb>percussionis, ad eam quae efficitur in plano subiecto, ut sinus anguli inci­<lb></lb>dentiae ad sinum totum ” (pag. </s>

<s>97). La dimostrazione, per condur la quale <lb></lb>s&#039;invoca il principio dei moti composti, procede alquanto impacciata, nè ciò <lb></lb>fa gran maraviglia, persistendosi nella fallacia di riguardare il moto per l&#039;ipo­<lb></lb>tenusa uguale ai due per i cateti in potenza: ma fa più gran maraviglia il <lb></lb>s<gap></gap>ir dallo stesso Borelli dire, nella citata lettera a M. A. Ricci, che di <lb></lb>queste cose “ per quanto io sappia, non è stato per ancora scritto da altri ” <lb></lb>(pag. </s>

<s>11). </s></p><p type="main">

<s>Eppure era da ventitre anni stato già stampato il libro <emph type="italics"></emph>De motu proie­<lb></lb><gap></gap>orum,<emph.end type="italics"></emph.end> in fronte al quale si leggeva scritto, non il nome di un autore oscuro <lb></lb>e straniero, ma di quel celeberrimo Torricelli, in cui tutto il mondo ricono­<lb></lb>sceva specchiata la mente di Galileo, come nel suo più vivo e più prossimo <lb></lb>parelio. </s>

<s>Forse lo scansar che facevasi nel teorema torricelliano, rispetto ai <lb></lb>moti composti, i fallaci insegnamenti di Galileo, dette a intendere che non <lb></lb>fosse ben dimostrato, e lusingò chi ci aveva interesse a tener che facesse quel <lb></lb>teorema nel libro <emph type="italics"></emph>De vi percussionis<emph.end type="italics"></emph.end> la sua prima comparsa, benchè insomma <lb></lb>nessuno de&#039;due Nostri dicesse novità, la notizia della quale non s&#039;attingesse <lb></lb>da ciò, che alquanti anni prima era stato stampato in Praga. </s>

<s>Anzi la propo­<lb></lb>sizione XXXIX <emph type="italics"></emph>De proportione motus<emph.end type="italics"></emph.end> non solo era feconda dei corollari, <lb></lb>de&#039;quali si compiacevano il Torricelli e il Borelli di essere stati gli Autori, <lb></lb>ma della soluzione di alcuni problemi assai più nuovi e più curiosi, come <lb></lb>quello di determinare, in un globo pendulo, il punto della riflessione, venendo <lb></lb>da un altro simile globo pendulo percosso nel centro o fuori del centro; come <lb></lb>quell&#039;altro del determinar la resultante del moto riflesso nelle piastrelle sca­<lb></lb>gliate sulla superficie di un&#039;acqua tranquilla, in quel giochetto conosciuto fra <lb></lb>noi sotto il nome di <emph type="italics"></emph>rimbalzello;<emph.end type="italics"></emph.end> e finalmente il problema, in cui, date tre <pb xlink:href="020/01/2569.jpg" pagenum="194"></pb>palle sul piano di un biliardo, non in linea retta, si proponeva l&#039;Autore di <lb></lb>trovar nella seconda delle dette palle il punto, da cui riflessa la prima vada <lb></lb>a diritto a percotere nella terza: problemi risoluti tutti con tal sottile e destra <lb></lb>arte di decomporre e di ricomporre le forze, che, se fossero stampati in ca­<lb></lb>rattere più moderno e soppresso nel frontespizio del libro il nome dell&#039;Au­<lb></lb>tore, si direbbero opera di un Matematico, venuto a coltivar la scienza dopo <lb></lb>il Newton e l&#039;Eulero. </s></p><pb xlink:href="020/01/2570.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del settimo dialogo da aggiungersi <lb></lb>alle due Scienze nuove <lb></lb>ossia Dei problemi fisici e matematici<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del problemi, che si dovevano aggiungere dopo la <emph type="italics"></emph>Scienza meccanica,<emph.end type="italics"></emph.end> e come Galileo pensasse di <lb></lb>ridurli in Dialogo. </s>

<s>— II. </s>

<s>Di altri problemi e speculazioni intorno a varii soggetti di Fisica. </s>

<s>— <lb></lb>III. </s>

<s>Delle questioni matematiche, e dei varii teoremi e problemi di Geometria raccolti dal Vi­<lb></lb>viani. </s>

<s>— IV. </s>

<s>Del quesiti algebrici, e del misurar con la vista. </s>

<s>— V. </s>

<s>Dei teoremi di Geometria <lb></lb>avanzati alle dimostrazioni del moti locali. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Per sodisfare alla curiosità, che deve naturalmente nascere nell&#039;animo <lb></lb>di chi s&#039;abbattesse a leggere l&#039;intitolazione di questo capitolo, vogliam subito <lb></lb>rammemorare come il Viviani, raccogliendo le notizie delle opere, che per <lb></lb>ultimo meditava di scrivere Galileo, estraesse da una lettera di lui, del dì <lb></lb>7 Novembre 1637, a Pietro Carcavy di Parigi, le parole seguenti: “ Porgami <lb></lb>per sua pietà la sua mano adiutrice acciocchè, sgravato da cure che mi ten­<lb></lb>gono oppresso, io possa tornare a distendere i miei <emph type="italics"></emph>Problemi spezzati fisici <lb></lb>matematici,<emph.end type="italics"></emph.end> che sono in buon numero e tutti nuovi ” (Scienza univ. </s>

<s>delle <lb></lb>proporz., Firenze 1674, pag. </s>

<s>83). In un&#039;altra lettera poi del Gennaio appresso <lb></lb>accennava al medesimo Carcavy il suo concetto <emph type="italics"></emph>di portare quelle cose in <lb></lb>dialogo:<emph.end type="italics"></emph.end> il qual dialogo, raccogliendo le reliquie sparse degli argomenti trat­<lb></lb>tati nelle prime quattro Giornate del Mondo, e specialmente nelle altre quat­<lb></lb>tro del Moto; si sarebbe a queste aggiunto dall&#039;Autore stesso, in settimo <lb></lb>luogo, dopo i trattati della percossa e delle proporzioni. </s></p><p type="main">

<s>Avendo noi dunque detto di que&#039;trattati nei capitoli precedenti, resta, a <lb></lb>render compiuta la nostra Storia, l&#039;argomento di quel settimo dialogo, in cui <pb xlink:href="020/01/2571.jpg" pagenum="196"></pb>si porterebbero, com&#039;abbiamo inteso, i Problemi fisici e matematici. </s>

<s>Non ebbe <lb></lb>l&#039;opera meditata dal Vecchio di 74 anni, e già cieco da circa due mesi prima, <lb></lb>la sua finale intenzione quanto alla forma, ma la materia doveva esser già <lb></lb>preparata, ond&#039;è che l&#039;ufficio nostro si riduce tutto in ricercarla, e in pro­<lb></lb>porla alla notizia dei nostri lettori. </s>

<s>Non sarebbe quella ricerca per verità nè <lb></lb>difficile nè laboriosa, quando fossero complete le raccolte di quei Problemi <lb></lb>fisici e matematici procuratesi, poco dopo la morte del Maestro, dal Viviani; <lb></lb>ma in ogni modo è nelle compilate pagine manoscritte del Discepolo amoroso <lb></lb>il principal fondamento alla nostra costruzione. </s></p><p type="main">

<s>Nel tomo III della VI parte dei manoscritti di Galileo, dal folio 28 al 35, <lb></lb>son di mano dello stesso Viviani, per la maggior parte, raccolti que&#039;Problemi <lb></lb>fisici che si diceva, in fronte ai quali è dal compilatore scritta in lapis que­<lb></lb>sta Nota: “ Problemi di mano del signor Vincenzio (di Galileo) distesi da <lb></lb>lui in più fogli cuciti, in numero undici; che tre scritti, otto bianchi, e nella <lb></lb>coperta intitolati <emph type="italics"></emph>Problemi di mano del Galileo, e problemi distesi dal signor <lb></lb>Vincenzio per mano dell&#039;Ambrogetti ”,<emph.end type="italics"></emph.end> d&#039;onde viene a rendersi manifesta <lb></lb>l&#039;origine e l&#039;autenticità della detta raccolta. </s></p><p type="main">

<s>Consegnatosene il manoscritto tanti anni dopo da Jacopo Panzanini, a cui <lb></lb>era pervenuto in eredità, a Tommaso Bonaventuri, questi pubblicò nella nuova <lb></lb>edizione delle opere di Galileo alcuni di que&#039;Problemi, de&#039;quali veniva dun­<lb></lb>que allora il pubblico ad avere la prima notizia, ma in privato il Viviani <lb></lb>stesso l&#039;aveva diffusa ne&#039;suoi discepoli, fra&#039;quali Giuseppe Ferroni, che la <lb></lb>comunicò al confratello suo gesuita Paolo Casati, a cui piacque rifiorire, come <lb></lb>vedremo, di quelle galileiane curiosità sconosciute i suoi libri delle Meccani­<lb></lb>che. </s>

<s>L&#039;Albèri dopo il Bonaventuri, essendo già le carte possedute dal Pan­<lb></lb>zanini andate a riunirsi fra i codici della Biblioteca palatina di Firenze, fece <lb></lb>per la sua edizione raccolta più diligente, ch&#039;egli inserì da pag. </s>

<s>317-28 del <lb></lb>suo tomo XIV. All&#039;uno e all&#039;altro editore però mancarono i criteri neces­<lb></lb>sari, per dar ordine e conveniente scelta a quella specie di zibaldone, messo <lb></lb>insieme dal Viviani non per altro, che per servirsene come di un memo­<lb></lb>riale a&#039;suoi studi. </s>

<s>Supplendo dunque noi, come sapremo meglio, a que&#039;man­<lb></lb>cati criteri, sia, per ritrovar l&#039;ordine desiderato, il nostro primo studio rivolto <lb></lb>a investigar l&#039;occasione ch&#039;ebbe l&#039;Autore, e il tempo delle speculate ragioni <lb></lb>e de&#039;risoluti problemi. </s></p><p type="main">

<s>Si termina il trattato della <emph type="italics"></emph>Scienza meccanica<emph.end type="italics"></emph.end> con queste parole: “ So <lb></lb>che qui nasceranno ad alcuni delle difficoltà e delle istanze, le quali però con <lb></lb>poca fatica si torranno di mezzo, e noi le rimetteremo volontariamente tra <lb></lb>i <emph type="italics"></emph>Problemi meccanici,<emph.end type="italics"></emph.end> che in fine di questo discorso si aggiungeranno ” <lb></lb>(Alb. </s>

<s>XI, 125). Quel trattato si sa essere opera giovanile di Galileo, e come <lb></lb>il primo frutto raccolto dallo studio de&#039;libri del Benedetti e di Guibubaldo. </s>

<s><lb></lb>Andata la scrittura attorno originalmente infino al 1649 manoscritta, si pub­<lb></lb>blicò senza la promessa aggiunta dei Problemi meccanici, i quali dunque, se <lb></lb>vi fossero stati compresi, sarebbero de&#039;più antichi fra quelli che si raccol­<lb></lb>sero dal Viviani. </s>

<s>Il criterio poi, da riconoscerli in mezzo a quella confusione <pb xlink:href="020/01/2572.jpg" pagenum="197"></pb>è l&#039;esser di argomento meccanico, e il sentirli inspirati ai libri delle <emph type="italics"></emph>Specu­<lb></lb>lazioni<emph.end type="italics"></emph.end> del Maestro. </s></p><p type="main">

<s>Ha giusto in que&#039;libri il Benedetti una bella speculazione, per risolvere <lb></lb>il problema: onde avvenga che la trottola, girando velocissimamente, si man­<lb></lb>tenga ritta sulla sua punta, e l&#039;attribuisce alle forze centrifughe, dirette <lb></lb>orizontalmente, prevalenti così sopra la gravità naturale, che il corpo grave <lb></lb>girante ubbidisce piuttosto a quelle, che a questa. </s>

<s>“ Ab huiusmodi inclina­<lb></lb>tione rectitudinis motus partium alicuius corporis rotundi fit, ut per aliquod <lb></lb>temporis spacium trochus, cum magna celeritate seipsum circumagens, omnino <lb></lb>rectus quiescat super illam cuspidem ferri quam habet, non inclinans se ver­<lb></lb>sus mundi centrum magis ad unam partem, quam ad aliam, cum quaelibet <lb></lb>suarum partium in huiusmodi motu non inclinet omnino versus mundi cen­<lb></lb>trum, sed multo magis per transversum, ad angulos rectos cum linea directio­<lb></lb>nis, aut verticalis, aut horizontis axe, ita ut necessario huiusmodi corpus <lb></lb>rectum stare debeat ” (Speculat. </s>

<s>liber, Venetiis 1599, pag. </s>

<s>286). </s></p><p type="main">

<s>Galileo derivò manifestamente di qui le ragioni, per rispondere a quel <lb></lb>principale quesito, di cui l&#039;Albèri non stampò che la proposta: “ Qual sia <lb></lb>la ragione che le trottole o le ruzzole, girate, si mantengano ritte, e ferme <lb></lb>no, ma trabocchino ” (XIV, 321), lasciando nel manoscritto la risposta, che <lb></lb>è tale: “ Un mobile non può avere impeto verso diverse bande, e però la <lb></lb>ruzzola andando velocemente si sostien ritta, ed infine, mancando la velocità <lb></lb>per l&#039;innanzi, comincia a piegare alla banda: e però il peso nella trottola <lb></lb>lavora pochissimo, quando quella si muove velocemente, ma ben lavora assai <lb></lb>verso il fine del moto, dove egli è lento ” (MSS. Gal., P. VI, T. III, fol. </s>

<s>64). </s></p><p type="main">

<s>Da questa soluzione, che non è forse quella distesa da Galileo, ma è <lb></lb>una nota preparata per distenderla, nacque la curiosità di simili altre solu­<lb></lb>zioni di Problemi meccanici, fra&#039;quali son da notare i seguenti: </s></p><p type="main">

<s>“ Quelli che giocano alla ruzzola, mediante il filo col quale la cingono <lb></lb>tre o quattro volte, fanno tiri assai più lunghi, che non farebbero senza quel <lb></lb>filo: si domanda la causa di questo, ed appresso si cerca perchè con assai <lb></lb>minor velocità vadia la ruzzola, quando è in aria, che quando tocca terra, <lb></lb>dove velocissimamente si muove. </s>

<s>” </s></p><p type="main">

<s>“ Così risolverassi il problema: Io ho una girella forata nel centro, e <lb></lb>infilzata in un pernio: gli do su con una mano, e la fo girare su quel per­<lb></lb>nio velocissimamente. </s>

<s>Or, mentre che ella gira, la fo uscir dal pernio e ca­<lb></lb>dere in terra per taglio. </s>

<s>Che farà questa girella? </s>

<s>Certo che, in virtù del <lb></lb>moto che io gli diedi quand&#039;ella era imperniata, subito che ella arriverà in <lb></lb>terra comincerà a camminare, sicchè quel moto, che gli diedi di girare in <lb></lb>sè stessa, è cagione che in terra ella giri e cammini. </s>

<s>Ora quelli che giocano <lb></lb>alla ruzzola la circondano tre o quattro volte con un filo, e poi la tirano, e <lb></lb>in quell&#039;istante ella si svolge dal filo con somma prestezza, e per conseguenza <lb></lb>viene ad acquistare un moto velocissimo in sè stessa, onde, quand&#039;ella arriva <lb></lb>in terra, va velocissimamente, non tanto per la forza datagli dal braccio del <lb></lb>tiratore, quanto in virtù della veloce circumvoluzione, che ella ha acquistato <pb xlink:href="020/01/2573.jpg" pagenum="198"></pb>nello svilupparsi dal filo. </s>

<s>Ma quelli che tirano senza filo non danno alla ruz­<lb></lb>zola il vantaggio del girarsi in sè medesima, ma la mandano solamente con <lb></lb>la forza del loro braccio; e però tirano manco che se tirassero col filo. </s>

<s>” </s></p><p type="main">

<s>“ La causa poi perchè la ruzzola vadia con minor velocità, mentre cam­<lb></lb>mina per aria, che in terra, è perchè in aria ella va solamente con la ve­<lb></lb>locità datagli dalla forza del tiratore, e in terra cammina per la medesima <lb></lb>forza, e in virtù della vertigine veloce in sè stessa, che ella aveva innanzi <lb></lb>che arrivasse in terra, la qual vertigine in aria non opera nulla, perchè, es­<lb></lb>sendo l&#039;aria tenue e sottile, cede facilmente al girar della ruzzola, la quale, <lb></lb>non trovando alla sua revoluzione intoppo alcuno, non ha occasione di scor­<lb></lb>rere avanti con più velocità di quella, che gli dà il braccio di chi la tira. </s>

<s><lb></lb>Ma com&#039;ella arriva in terra, che è ruvida e scabrosa, trova moltissimi in­<lb></lb>toppi, ne&#039;quali, nel girare ella urta, e si risospigne addietro; onde gli è forza <lb></lb>di scorrere avanti velocemente, non solo per la forza di chi la tira, ma an­<lb></lb>cora in virtù del suo volgersi in sè medesima. </s>

<s>” </s></p><p type="main">

<s>“ Due altri Problemi hanno dependenza dal precedente, in uno de&#039;quali <lb></lb>si cerca perchè quelli che giocano alla palla tanto difficilmente rimettino le <lb></lb>palle, che gli sono mandate <emph type="italics"></emph>trinciate:<emph.end type="italics"></emph.end> e nell&#039;altro si domanda perchè, gio­<lb></lb>cando alcuni alle pallottole in una strada disuguale e sassosa, piglino la palla <lb></lb>per di sopra con la mano, dove, giocando in un pallottolaio piano e pulito, <lb></lb>la piglierebbero per di sotto. </s>

<s>” </s></p><p type="main">

<s>“ Il primo Problema si risolve così: Colui, che vuol trinciare la palla <lb></lb>al compagno che gioca seco, gli dà con la mestola o con la racchetta per di <lb></lb>sotto in tal modo che, mandandola innanzi verso il compagno, gli dà facoltà <lb></lb>di girare all&#039;indietro in sè medesima, sicchè, quand&#039;ella arriva in terra, <lb></lb>viene a fare, mercè di quel girare all&#039;indietro, il balzo verso colui che l&#039;ha <lb></lb>mandata, o almeno balza pochissimo verso quello, che aspetta di rimetterla, <lb></lb>il quale, giudicando il balzo dover esser verso di lui assai più lungo, attende <lb></lb>la palla troppo di lontano, e resta ingannato e deluso. </s>

<s>Similmente non la ri­<lb></lb>metterà di posta perchè, non essendo la palla affatto liscia e pulita, ma avendo <lb></lb>qualche risalto e scabrosità, viene, nel girare all&#039;indietro per aria, a pigliar <lb></lb>vento, onde la sua velocità alquanto si ritarda, sicchè colui che la vuol ri­<lb></lb>metter di posta l&#039;aspetta prima che ella non arriva, e pensando di coglierla <lb></lb>gli tira, e fa il colpo vano. </s>

<s>” </s></p><p type="main">

<s>“ La resoluzione del secondo problema è tale: Quelli, che giocano alle <lb></lb>pallottole per una strada sassosa, non possono, tirando la palla per terra, <lb></lb>aggiustar bene il colpo, per li molti intoppi che troverebbe la palla, ma son <lb></lb>necessitati, a guisa di quelli che fanno alle piastrelle, di procurare di avvi­<lb></lb>cinarsi al <emph type="italics"></emph>lecco,<emph.end type="italics"></emph.end> tirando di posta. </s>

<s>Ma perchè la palla non fa l&#039;effetto della <lb></lb>piastrella, che subito che ella arriva in terra si ferma, è necessario che quelli <lb></lb>che giocano trovin modo di fare che la palla si mova manco che sia possi­<lb></lb>bile dal luogo dove la tirano. </s>

<s>Ma questo gli succede col tirare, presa la palla <lb></lb>per di sopra, perchè così, mentre che è in aria, viene a girare in sè mede­<lb></lb>sima all&#039;indietro, cioè verso chi la tira: e quando ella arriva, perchè la forza <pb xlink:href="020/01/2574.jpg" pagenum="199"></pb>di chi l&#039;ha tirata la farebbe trascorrere innanzi troppo, e allontanarsi dal <lb></lb>lecco, il moto che ella aveva in sè stessa vien quasi a contrappesare la detta <lb></lb>forza, onde la palla o si ferma, o pochissimo trascorre innanzi. </s>

<s>Ma quando <lb></lb>poi si gioca ne&#039;pallottolai ben netti e puliti, si può benissimo aggiustare il <lb></lb>colpo, tirando la palla per terra, onde non è necessario il pigliarla per di <lb></lb>sopra ” (ivi, fol. </s>

<s>31, 32). </s></p><p type="main">

<s>Il problema della ruzzola tirata con lo spago ebbe solenne pubblicità dia­<lb></lb>logizzato nella seconda giornata dei Massimi Sistemi, ma gli altri due, che <lb></lb>ne dipendono, è notabile che si rimangano tuttavia nel manoscritto, nel quale <lb></lb>gli lasciarono il Bonaventuri e l&#039;Albèri. </s>

<s>Ben più notabile è però che, senza <lb></lb>saperlo, il pubblico ne avesse già da lungo tempo notizia per opera del Ca­<lb></lb>sati, a cui fu la cosa comunicata privatamente dal Viviani, come avvertimmo, <lb></lb>per mezzo del Ferroni. </s>

<s>Nel cap. </s>

<s>XI infatti del libro VII <emph type="italics"></emph>Mechanicorum,<emph.end type="italics"></emph.end> fa­<lb></lb>cendo esso Casati alcune osservazioni intorno al variarsi accidentalmente <lb></lb>gl&#039;impulsi nei moti riflessi. </s>

<s>“ Deinde, egli dice, quando reticulis luditur, non <lb></lb>raro reticulum movetur in plano aliquo horizontali, aut valde inclinato (nos <lb></lb>Itali dicimus <emph type="italics"></emph>tagliare o trinciare una palla<emph.end type="italics"></emph.end>) ita ut, dum pilam recta expel­<lb></lb>lit, illi etiam motum quemdam imprimat, quo ipsa circa suum centrum mo­<lb></lb>vetur: unde fit ut, nisi pilam excipias repellasque ante quam pavimentum <lb></lb>attingat, frustra deinde saltum illius expectes iuxta regulas reflexionis, quia <lb></lb>nimirum pila terram tangens, dum pergit moveri circa suum centrum motu <lb></lb>orbiculari, nequit a plano impediente recipere directionem illam, cuius esset <lb></lb>capax, si solum simplici motu centri mota fuisset: motus enim peripheriae <lb></lb>globi contrarius est motui centri. </s>

<s>Idem accidit, quando pila leviore astrictu <lb></lb>funem perstringit, tunc scilicet concipit motum circularem adeoque saltus <lb></lb>fallit. </s>

<s>” </s></p><p type="main">

<s>“ Quantum autem in motu valeat directiones commiscere, alteram cen­<lb></lb>tri rectam, alteram peripheriae circularem sed oppositam, satis norunt qui, <lb></lb>minoribus orbiculis ludentes, globum quasi pendentem in manu tenent, dum­<lb></lb>que illum proiiciunt manu ei motum circularem communicant, unde oritur <lb></lb>quod, ubi terram globus attigerit, vel sistit se, si directio peripheriae ad mo­<lb></lb>tum circularem est aequalis directioni centri ad motum rectum, vel tardius <lb></lb>promovetur quam si solam centri directionem haberet, prout directio centri <lb></lb>maior est directione peripheriae, quae, cum primum terram attingit, apta <lb></lb>est sua conversione retrahere centrum versus proiicientem ” (Lugduni 1684, <lb></lb>pag. </s>

<s>734, 35). </s></p><p type="main">

<s>L&#039;esempio del Casati, che così di nascosto raccoglieva le miche cadute <lb></lb>dalla lauta mensa di Galileo, ci fanno ripensare al gusto, che dovevano sen­<lb></lb>tir di così fatti Problemi que&#039;primi discepoli, per le mani dei quali correva <lb></lb>manoscritto il trattato della Scienza meccanica. </s>

<s>La forma stessa invitava i <lb></lb>curiosi a comparare le nuove scritture con le antiche Questioni aristoteliche, <lb></lb>le quali si volevano fare apparire tanto più insulse, quanto più si credeva di <lb></lb>dar quelle stesse novità risolute da&#039;più veri dimostrati principii. </s>

<s>Questa anzi, <lb></lb>di contradire alle dottrine meccaniche di Aristotile, era la principale inten-<pb xlink:href="020/01/2575.jpg" pagenum="200"></pb>zione di Galileo, a cui perciò l&#039;argomento del discorso era spesso suggerito <lb></lb>dagli argomenti medesimi del Filosofo, come quello per esempio che versa <lb></lb>intorno alle navi mosse dalle vele o dai remi. </s></p><p type="main">

<s>Se sempre i principii, dai quali si facevano dipendere le risposte a così <lb></lb>fatti quesiti, fossero, come Galileo stesso presumeva, ben dimostrati, si po­<lb></lb>trebbe per verità dubitarne, particolarmente per quel che riguarda l&#039;uso del <lb></lb>timone, e la proporzion degl&#039;impulsi, che riceve il naviglio o dalla ciurma <lb></lb>che voga, o dal vento ch&#039;enfia la vela; perchè, trattandosi di moti misti, era <lb></lb>meglio parato nelle mani del Filosofo antico che del novello il sottile argo­<lb></lb>mento, da risolvere così difficili questioni. </s>

<s>Comunque sia avrebbe dovuto Ga­<lb></lb>lileo attutire quella sua giovanile baldanza, e temperare il disprezzo con la <lb></lb>riverenza, ripensando che non avrebbe esultato dello splendor di quella nuova <lb></lb>fiamma viva, se sotto le avvilite ceneri non avesse Aristotile gelosamente cu­<lb></lb>stoditavi la scintilla. </s></p><p type="main">

<s>L&#039;esempio cade bene a proposito rispetto alle resistenze dei solidi, la <lb></lb>Scienza nuova delle quali dipendeva dall&#039;antica, che si compendiava nei mi­<lb></lb>rabili effetti della leva. </s>

<s>Così veniva ovvia a rappresentarsi alla mente di Ga­<lb></lb>lileo la distinzione fra le resistenze assolute e le respettive, della qual di­<lb></lb>stinzione furono quasi primaticci frutti due problemi, ambedue, benchè per <lb></lb>contrarie ragioni, nella storia della Scienza memorabili. </s>

<s>Una verga di me­<lb></lb>tallo, tirata fortemente per lo lungo, resiste molto più che piegata per tra­<lb></lb>verso, perchè là opera con tutta la resistenza assoluta, e qua con quella che <lb></lb>è relativa al modo di operar con la leva. </s>

<s>Eppure, anco la resistenza assoluta <lb></lb>può da proporzionato peso esser vinta: che se, invece di un peso posticcio, <lb></lb>si prolunghi essa stessa nella sua propria materia, si dovrà giungere a un <lb></lb>termine, ripensava Galileo, che quel solo aver di tanto allungata la verga <lb></lb>basti per strapparla. </s>

<s>Dunque concludeva essere alla lunghezza di qualunque <lb></lb>solido prefinito dalla Natura un limite, oltre il quale, nemmen con tutta la <lb></lb>sua forza assoluta, mai reggerebbe. </s>

<s>Dai solidi credè di poter fare libero pas­<lb></lb>saggio ai liquidi, ed ebbero da ciò occasione la proposta e la risposta al se­<lb></lb>guente Problema, leggendo il quale coloro, a cui è oramai da tanto tempo <lb></lb>nota la scoperta del Torricelli, intenderanno perchè si dicesse memorabile <lb></lb>nella Storia: </s></p><p type="main">

<s>“ Si domanda la cagione perchè le trombe, che si adoprano per cavar <lb></lb>acqua dai pozzi, non alzino l&#039;acqua, se non insino ad una certa e determi­<lb></lb>nata altezza. </s>

<s>” </s></p><p type="main">

<s>“ La cagione di tal effetto dipende da questo: Io piglio un pezzo di ca­<lb></lb>tena di ferro, un capo della quale fermo gagliardamente a una trave, ed <lb></lb>all&#039;altro incomincio ad attaccare del peso. </s>

<s>Chiara cosa è che quella catena, <lb></lb>non essendo possente di reggere un peso infinito, finalmente, se io seguiterò <lb></lb>a caricarla, si strapperà. </s>

<s>Diciamo dunque che un peso v. </s>

<s>g. </s>

<s>di mille libbre <lb></lb>appunto la facci strappare. </s>

<s>Ora, se, in cambio di attaccare alla catena un <lb></lb>peso di mille libbre, io la farò tanto più lunga, che quel pezzo che io ci ag­<lb></lb>giungo pesi le mille libbre; certo è che quella catena si strapperà, nè più <pb xlink:href="020/01/2576.jpg" pagenum="201"></pb>nè meno che si strappasse prima con le cento libbre di peso: sicchè il pro­<lb></lb>prio peso della catena è abile a farla strappare. </s>

<s>” </s></p><p type="main">

<s>“ Ora l&#039;acqua che si tira su per le trombe si regge in sè stessa sino <lb></lb>ad una tale altezza, siccome si reggerebbe la catena, alla quale io aggiun­<lb></lb>gessi un pezzo, che pesasse novecento novantanove libbre. </s>

<s>Ma se io vorrò <lb></lb>far passare all&#039;acqua quell&#039;altezza, cioè s&#039;io vorrò allungar più la sua mole, <lb></lb>a guisa della catena, alla quale io aggiugnessi un pezzo di mille libbre; si <lb></lb>strapperà per il suo proprio peso, e non potrà passare altrimenti la detta <lb></lb>altezza ” (MSS. Gal., P. VI, T. III, fol. </s>

<s>33). </s></p><p type="main">

<s>Galileo si compiacque molto di questa speculazione, occorsagli dal con­<lb></lb>siderare le resistenze assolute, e non era punto temeraria una tal compia­<lb></lb>cenza a que&#039;tempi, nei quali, non sapendosi far altro che invocare l&#039;orrore <lb></lb>al vacuo, si trovavano costretti i Filosofi a dire che non sentisse questo orror <lb></lb>la Natura, che infino a un certo punto. </s>

<s>Più ragionevolmente però poteva com­<lb></lb>piacersi di quell&#039;altro, che gli occorse al pensiero dal considerar le resistenze <lb></lb>respettive, le quali debbon esser tanto maggiori, quanto più lungo è il brac­<lb></lb>cio della contralleva. </s>

<s>Non è dunque il principale efficiente della resistenza di <lb></lb>un solido la quantità della sua propria materia, ma sì piuttosto il venir que­<lb></lb>sta in maggior ampiezza distribuita: ciò che facilmente ottenendosi col rare­<lb></lb>farla, e col lasciar qualche vacuo nel mezzo, veniva a rivelar la nuova verità <lb></lb>di un fatto, non ovvio ancora per la sola esperienza, che cioè, avendosi due <lb></lb>lance del medesimo peso, la vuota è tanto più resistente della piena, quanto <lb></lb>maggiore è il diametro di quella che di questa. </s>

<s>Fu anche il nuovo pensiero <lb></lb>disteso in forma di Problema, e possono i Lettori vederlo nel IV fra i rac­<lb></lb>colti dall&#039;Albèri (XIV, 326). </s></p><p type="main">

<s>Al medesimo ordine di quei Problemi, che dovevano aggiungersi dopo <lb></lb>il trattato della Scienza meccanica, appartengono alcuni altri, de&#039;quali trovasi <lb></lb>fatto un cenno nel citato manoscritto del Viviani in questo modo: “ Rom­<lb></lb>pesi una corda attaccata ad una gran pietra pendente da una simile corda ” <lb></lb>(MSS. cit., fol. </s>

<s>63): problema di cui il Viviani stesso dava, secondo la mente <lb></lb>di Galileo, la soluzione in quella nota, da noi trascritta a pag. </s>

<s>445 del Tomo <lb></lb>precedente. </s>

<s>Altro Problema, da mettersi in questa collezione, era quello del <lb></lb>maggior tiro, che si credeva ottenere dagli archibusi, quanto fossero più lun­<lb></lb>ghi di canna: se non che alle ragioni antiche del Cardano e del Benedetti <lb></lb>s&#039;aggiungeva da Galileo valore, introducendo il principio delle velocià pro­<lb></lb>porzionali ai tempi. </s>

<s>“ Perchè la velocità cresce secondo il tempo, gli archi <lb></lb>grandi e le cerbottane e le canne di archibuso tirano con più forza, avendo <lb></lb>tempo di accompagnare il proietto per più spazio ” (ivi, fol. </s>

<s>62). </s></p><p type="main">

<s>Di tal qualità, secondo i riferiti esempi, erano quei Problemi, i quali, <lb></lb>mostrando come si potessero applicare le leggi del moto delle macchine a <lb></lb>certi fatti naturali più ovvii e più curiosi, dovevano aggiungersi alla <emph type="italics"></emph>Scienza <lb></lb>meccanica,<emph.end type="italics"></emph.end> per dilettevole utilità dei lettori. </s>

<s>Ma Galileo accennava nel <lb></lb>passo da noi sopra trascritto particolarmente ad alcuni di quegli stessi Pro­<lb></lb>blemi, nei quali si toglierebbero di mezzo le difficoltà, e si risponderebbe <pb xlink:href="020/01/2577.jpg" pagenum="202"></pb>alle istanze, che potrebbero nascere intorno alla forza della percossa; ond&#039;è <lb></lb>che, fatti certi per questa testimonianza dell&#039;avere atteso l&#039;Autore a risolvere <lb></lb>quest&#039;altro nuovo genere di questioni, siamo stati solleciti di ricercarle nei <lb></lb>manoscritti. </s>

<s>Forse l&#039;essere stato distratto Galileo dal proseguire in quella <lb></lb>speculazione, per le ragioni accennate da noi nel capitolo precedente, fu la <lb></lb>causa per cui le cose scritte da giovane a spiegar meglio la forza della per­<lb></lb>cossa si siano in mezzo alle altre ritrovate così scarse: nonostante riferiscesi <lb></lb>all&#039;argomento la seguente nota, che è l&#039;espression di un concetto, da cui do­<lb></lb>veva svolgersi più largamente il discorso: “ Il colpo in materia cedente opera <lb></lb>meno tanto, quant&#039;è la ritirata del cedente ” (ivi, fol. </s>

<s>62). </s></p><p type="main">

<s>Quest&#039;altra nota, che ivi pure il Viviani ha raccolta, è di bene assai <lb></lb>maggiore importanza per la storia delle galileiane speculazioni intorno alla <lb></lb>forza della percossa, e intorno alle ragioni ch&#039;ebbe lo speculatore per di­<lb></lb>chiararla immensa: “ Se a un peso massimo, pendente da una corda, si ag­<lb></lb>giungerà per fianco qualsivoglia altro minimo peso, questo alzerà il massimo, <lb></lb>essendochè il piccolo scende per un arco verso il contatto, ed il massimo <lb></lb>ascende per la circonferenza: dal che ne seguirà che la sua salita sia, se­<lb></lb>condo qualsivoglia proporzione, minore della scesa del piccolo peso ” (ivi, <lb></lb>a t. </s>

<s>del fol. </s>

<s>63). </s></p><p type="main">

<s>La bellissima proposizione, quale uscì dalla mente di Galileo che fu primo <lb></lb>a pensarla, rimase ignota al pubblico infino al 1718, anno in cui il Bona­<lb></lb>venturi veniva ad aggiunger nelle Opere galileiane il sesto Dialogo agli altri <lb></lb>cinque delle Scienze nuove. </s>

<s>Come, tanto tempo prima della sua pubblica­<lb></lb>zione, potesse avere avuto il Viviani notizia di quel meccanico teorema, ch&#039;egli <lb></lb>illustrò, concorrendovi nell&#039;opera il Borelli; è facile intendere, essendo ne&#039;due <lb></lb>Discepoli quell&#039;annunzio di scienza nuova venuto per la via ordinaria delle <lb></lb>tradizioni orali e manoscritte del loro grande Maestro: ma fa maraviglia che <lb></lb>il Wallis s&#039;incontrasse in quel medesimo concetto, e, rappresentandosi nel <lb></lb>globo di Galileo pendolo da una fune il grande Globo terrestre librato in mezzo <lb></lb>allo spazio, ne concludeva, per le medesime meccaniche ragioni, che anche <lb></lb>il salto di una pulce lo avrebbe commosso. </s>

<s>“ Dato enim quod tota Telluris <lb></lb>moles, fluido aethere suspensa, cum saltu pulicis percussa sit; dicenda esset <lb></lb>loco suo tantillum dimoveri ” (De motu cit., pag. </s>

<s>663). </s></p><p type="main">

<s>Le questioni spezzate, che furono risolute da Galileo nel lungo corso <lb></lb>della sua vita scientifica, non tutte, com&#039;è da credere, erano di argomento <lb></lb>meccanico: perciò è facile intendere come rivolgendo, quasi Maestro nell&#039;offi­<lb></lb>cina, lo sguardo sui materiali rimasti indietro nella costruzione dei due grandi <lb></lb>edifizi dei Massimi Sistemi e delle Scienze nuove, ve ne dovesse rtrovar degli <lb></lb>appartenenti a ogni ordine di Scienze fisiche e matematiche. </s>

<s>E tali sono ap­<lb></lb>punto le questioni spezzate e le note sparse, che nei citati manoscritti, e in <lb></lb>altre carte galileiane, si vedono confusamente raccolte insiem con quelle, che <lb></lb>di puro argomento meccanico sono state da noi fin qui recensite. </s>

<s>Richiede­<lb></lb>rebbe forse il filo del ragionamento che si proseguisse a dar notizia ai Let­<lb></lb>tori di questa varietà di pensieri, come materiali sparsi e mezzo sepolti nel <pb xlink:href="020/01/2578.jpg" pagenum="203"></pb>terreno, che circonda i due detti grandi edifizi, ma perchè il primo e prin­<lb></lb>cipale nostro proposito fu quello di rappresentarci l&#039;Artefice, che medita di <lb></lb>dare anche a quelle sparse reliquie qualche decoro di forma; studiamoci, <lb></lb>prima di aumentar la congerie, di veder com&#039;ei lo facesse nei materiali già <lb></lb>radunati. </s></p><p type="main">

<s>Già si sa come fosse, nel citato capitolo di lettera, significata al Carcavy <lb></lb>una tale intenzione, qual&#039;era di mettere in dialogo quei pensieri, come fiori <lb></lb>in ghirlanda. </s>

<s>Ma perchè non ne seguì il meditato effetto, per gl&#039;impedi­<lb></lb>menti della cecità e della vecchiezza, se non s&#039;è avuto dunque l&#039;opera com­<lb></lb>piuta, si può domandare almeno se fu cominciata. </s>

<s>La risposta si restringe <lb></lb>intanto per noi ai Problemi meccanici, alcuni de&#039;quali avevano già trovato <lb></lb>stabile assetto nei primi e nei secondi Dialoghi già stampati. </s>

<s>Così, per esem­<lb></lb>pio il problema della ruzzola tirata col filo, e della palla tirata soprammano, <lb></lb>avevano trovato da accomodarsi nella seconda giornata dei Massimi Sistemi <lb></lb>(Alb. </s>

<s>I, 175-79) e nella prima e nella seconda delle Scienze nuove i pro­<lb></lb>blemi dell&#039;acqua nelle trombe, e nelle lance vuote più resistenti delle piene <lb></lb>(XIII, 21, 145). Tutte le altre questioni di meccanico argomento erano ri­<lb></lb>maste indietro, e s&#039;aspettava a queste di venire a intessersi ne&#039;Dialoghi no­<lb></lb>vissimi: intorno a che, stando ai soli manoscritti esistenti nella Biblioteca <lb></lb>fiorentina, non avremmo da sodisfare ai Lettori, se non col dar dell&#039;opera <lb></lb>incominciata da Galileo un segno, piuttosto che un saggio. </s></p><p type="main">

<s>S&#039;introduce nella Scienza meccanica il discorso dimostrando l&#039;utilità, <lb></lb>che si può ricavar dalle macchine: e disingannati quegli artefici, che cre­<lb></lb>devano di potere con poca forza movere e alzare pesi grandissimi, conclude <lb></lb>l&#039;Autore col dire che la principale delle dette utilità consiste nel poter solle­<lb></lb>vare tutta insieme, per via dello strumento, una gran mole, che pure si sol­<lb></lb>leverebbe, col medesimo impiego di forza, dalle semplici braccia di un uomo, <lb></lb>purchè si potesse ridurre quella tal mole trattabile col dividerla in pezzi. </s>

<s>Si <lb></lb>voleva da Galileo porgere questa stessa meccanica dottrina quasi sotto le <lb></lb>graziose forme di un apologo, nel dialogismo seguente: </s></p><p type="main">

<s>“ SALVIATI. — In proposito di quello, che è tanto semplice, che vuole <lb></lb>per via di trombe alzar tant&#039;acqua, che nel cadere poi faccia andare un mu­<lb></lb>lino, il quale non poteva andare in virtù della forza, che egli applica nel­<lb></lb>l&#039;alzare l&#039;acqua: è egli possibile che si creda di poter riavere dall&#039;acqua più <lb></lb>forza di quella, che tu gli hai prestata? </s>

<s>È possibile che tu non intenda che <lb></lb>quella forza, che bastò a alzar l&#039;acqua, basterà per mover la macina? </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Signor no: perch&#039;io ho bisogno di avere per manteni­<lb></lb>mento della mia casa uno staio di farina la settimana, ed un mio ragazzino, <lb></lb>in sei giorni, con una secchiolina mi conduce in una conserva tant&#039;acqua <lb></lb>all&#039;altezza di quattro braccia, che lasciandola poi cader sul ritrecine mi ma­<lb></lb>cina in un&#039;ora uno staio di grano ” (MSS. Gal., P. V, T. IV, fol. </s>

<s>15). </s></p><p type="main">

<s>Dicemmo ch&#039;era questo l&#039;unico esempio della forma del dialogo data da <lb></lb>Galileo alle sue Questioni meccaniche, stando ai Manoscritti palatini di Fi­<lb></lb>renze. </s>

<s>Ma noi, più attentamente rivolgendo le carte, nelle quali ritrovammo <pb xlink:href="020/01/2579.jpg" pagenum="204"></pb>il trattato dell&#039;uso delle catenuzze, ci abbattemmo a leggere un colloquio, <lb></lb>dove il Salviati e il Sagredo dimostravano a Simplicio quant&#039;avesse errato <lb></lb>il suo Aristotile, dicendo che la vela tanto più velocemente spinge la nave, <lb></lb>quanto è sollevata più in alto; e ciò per gli effetti meccanici della leva. </s>

<s>Ci <lb></lb>risovvenne allora ch&#039;era questo uno degli argomenti propostisi dallo stesso <lb></lb>Galileo a trattare nella <emph type="italics"></emph>Selva di problemi vari,<emph.end type="italics"></emph.end> dove la proposizione, rima­<lb></lb>sta come tutte le altre irresoluta, si legge così scritta: “ Se sia vero quello <lb></lb>che dice Aristotile, cioè che più gagliardamente spinga la vela, quanto è più <lb></lb>alta; e se ciò avviene per la ragione addotta da esso, presa dalla leva ” <lb></lb>(Alb. </s>

<s>XIV, 320). </s></p><p type="main">

<s>Ci sembrava venisse confermato da questo nuovo esempio che anche gli <lb></lb>altri frammenti di dialogo, ritrovati nel detto manoscritto, erano stati distesi <lb></lb>dal Viviani, a cui Galileo aveva significato i suoi propri concetti, di che ri­<lb></lb>mase la testimonianza ne&#039;libri delle Meccaniche del Casati. </s>

<s>Il confratello e <lb></lb>collega di Giuseppe Ferroni, discepolo di esso Viviani, ha, nel IV di quei <lb></lb>libri, intitolato il capitolo XVI <emph type="italics"></emph>An malus in motu navis habeat rationem <lb></lb>vectis<emph.end type="italics"></emph.end> (ediz. </s>

<s>cit., pag. </s>

<s>470), e confuta Aristotile con quelle medesime ragioni, <lb></lb>che il Salviati e il Sagredo confutano Simplicio, nel Dialogo che qui trascri­<lb></lb>viamo: </s></p><p type="main">

<s>“ SALVIATI. — È il nostro Accademico, e non il vostro Aristotile, signor <lb></lb>Simplicio, che ha istituita la nuova Scienza meccanica. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Ma pure ha anch&#039;egli imparato dal Filosofo che tutti <lb></lb>quanti gli effetti delle macchine si riducono finalmente a quello della leva, <lb></lb>e secondo ciò vedete nelle <emph type="italics"></emph>Questioni<emph.end type="italics"></emph.end> come si risolva una varietà di problemi <lb></lb>bellissimi e curiosi. </s>

<s>In quei giorni che mi trattenni ospite vostro nella vostra <lb></lb>amenissima villa delle Selve, scesi tutto solo una sera sulla riva dell&#039;Arno, <lb></lb>e mentre sedevo all&#039;ombra, guardando le acque che, per le piogge recenti, <lb></lb>scendevano giù per il fiume più del solito copiose; ecco vedo risalire i na­<lb></lb>vicelli di Signa a vele spiegate. </s>

<s>Erano così carichi, da rimanerne quasi tutti <lb></lb>inghiottiti, eppure con tanta facilità, e direi quasi snellezza, solcavano le <lb></lb>acque così fonde e con moto contrario, che io non potei non ripensare allora <lb></lb>quanto veramente mirabile dev&#039;essere la potenza della leva. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Ma, ditemi, come c&#039;entra la leva nel moto della nave <lb></lb>a vela? </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — C&#039;entra benissimo, come potete vedere in Aristotile, <lb></lb>nella sua sesta Questione, dove dice che l&#039;albero è un vette, che il luogo <lb></lb>dov&#039;egli è fisso è l&#039;ipomoclio, che il peso da movere è la stessa nave, e che <lb></lb>il vento è la forza movente. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Anch&#039;io resto maravigliato di ciò, non meno del signor <lb></lb>Salviati, e non par credibile che un tanto filosofo abbia pronunziato così fran­<lb></lb>camente sentenza, della quale nessun&#039;altra mi sembra che sia più aliena dal <lb></lb>vero. </s>

<s>Come si potrebbe infatti riconoscer l&#039;opera della leva, dove il peso e <lb></lb>l&#039;ipomoclio hanno il moto medesimo della virtù motrice? </s>

<s>Non è ella, signor <lb></lb>Simplicio, dottrina di Aristotile verissima, e confermata dall&#039;esperienza, che <pb xlink:href="020/01/2580.jpg" pagenum="205"></pb>la leva opera tanto più validamente, quanto la virtà che muove ha maggior <lb></lb>velocità, rispetto al peso che deve esser mosso? </s>

<s>Che se fossero uguali le ve­<lb></lb>locità del mosso e del movente, a nulla si ridurrebbe l&#039;efficacia dello stru­<lb></lb>mento. </s>

<s>Voi vedete dunque che, movendosi la vela e la nave con pari moto, <lb></lb>secondo le medesime dottrine del vostro Maestro, la leva, quando pure ci <lb></lb>fosse, non farebbe sulla nave nessuno effetto. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Soggiungete, signor Sagredo, che, quando ci fosse opera <lb></lb>di leva, non solo questa riuscirebbe inutile al moto della nave, ma gli sarebbe <lb></lb>anzi contraria. </s>

<s>Supponete infatti che il piè dell&#039;albero sia fermato vicino alla <lb></lb>prora: ivi sarà l&#039;ipomoclio, e intorno ad esso tenderà la vela a far girare il <lb></lb>vascello, affondando di più essa prora, che verrà perciò a ricevere maggiore <lb></lb>impedimento dall&#039;acqua, e facendo capolievare la poppa. </s>

<s>I pericoli, che cor­<lb></lb>rerebbe la navigazione per questa mobilità di equilibrio, si comprendono assai <lb></lb>facilmente, ed è perciò che i nocchieri non a caso dispongono l&#039;albero, che <lb></lb>ha da portare in alto la vela, ma sì che sempre la carena si mantenga ori­<lb></lb>zontale. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Io mi sono trattenuto più volte nei nostri porti di Ve­<lb></lb>nezia a osservare le grandi navi approdatevi d&#039;Inghilterra e d&#039;Olanda, le <lb></lb>quali hanno, specialmente il maggior albero della vela maestra, disposto in <lb></lb>modo, che riman sempre il suo piede sulla carena, fuori del comun centro <lb></lb>di gravità, e ciò col consiglio, mi credo io, che non faccia esso albero l&#039;ufficio <lb></lb>di vette, e non metta la poppa con la prora in gioco pericoloso di altalena. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Vedete dunque, signor Simplicio, come sia ben confer­<lb></lb>mato da questo esempio che, tutt&#039;altrimenti dal ricercarsi l&#039;utilità del vette <lb></lb>in sospingere più gagliardamente la nave, se n&#039;evita con ogni studio, da chi <lb></lb>sa l&#039;arte, l&#039;ingerenza nociva. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Io non so che rispondere alle vostre ragioni, ma pur <lb></lb>mi sembra che potesse rispondere per me, in favor di Aristotile, un modo, <lb></lb>che io ho veduto praticar da coloro, i quali, mancando il vento, tirano con­<lb></lb>tro il corso del fiume le navi a forza d&#039;uomini o di cavalli. </s>

<s>Ho sentito que­<lb></lb>sto chiamarsi da&#039;navicellai di Signa <emph type="italics"></emph>tirar l&#039;alzaio,<emph.end type="italics"></emph.end> il quale alzaio intesi es­<lb></lb>sere quella fune, che da un capo è legata all&#039;albero della nave, e dall&#039;altra <lb></lb>vi sono aggiunte certe brachette, che o s&#039;avvolgono intorno alle spalle degli <lb></lb>uomini, o ricingono il petto dei cavalli. </s>

<s>Ora, abbattutomi più volte a vedere <lb></lb>questa fatica, ho sempre osservato che l&#039;alzaio si lega più su che sia pos­<lb></lb>sibile all&#039;albero, di che interrogata quella buona gente, che lo tirava, mi <lb></lb>sentivo rispondere che, quanto si tien più alta la fune, tanto si muove la <lb></lb>nave con maggiore facilità, e con minore fatica. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Nè foste punto ingannato, signor Simplicio, nella rispo­<lb></lb>sta: l&#039;inganno però è tutto vostro in credere che la maggior distanza della <lb></lb>fune dal piè dell&#039;albero, come da suo ipomoclio, sia giusto procurata da <lb></lb>quella gente, per ottenere maggior favore di leva. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — O per qual altro fine dunque lo fanno, o qual ne pos­<lb></lb>sono sperare vantaggio diverso? </s>

<s>” </s></p><pb xlink:href="020/01/2581.jpg" pagenum="206"></pb><p type="main">

<s>“ SALVIATI. — Prima che io risponda a voi, rispondete voi a me, men­<lb></lb>tre vi domando se più facilmente si tira una fune libera che una impedita. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Voi volete il gioco del fatto mio. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Se dunque si tira più facilmente una fune libera, che <lb></lb>una impedita, e se tanto meglio si scansano gl&#039;impedimenti dell&#039;acqua cor­<lb></lb>rente, dei sassi, dell&#039;alveo, dei bronchi e degli sterpi delle rive, quanto la <lb></lb>fune è più in aria, intenderete che si pratica a quel modo dai tiratori d&#039;al­<lb></lb>zaio, per ragioni molto più semplici di quelle, che voi credete essere state <lb></lb>suggerite a loro dalla Filosofia. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Sia pur così, come voi volete, ma io per me non in­<lb></lb>tendo in che modo si possano coteste vostre ragioni applicare alla vela, che <lb></lb>fu il primo e principale proposito del nostro discorso: la qual vela non si <lb></lb>vede come venga a ricevere minor impedimento dallo stare spiegata sull&#039;an­<lb></lb>tenna più in alto. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — L&#039;impedimento, signor Simplicio, non è da riguardar <lb></lb>nella vela propriamente, ma nello spirito che la muove. </s>

<s>Non vedete voi che <lb></lb>il vento spira più gagliardo sulle alte torri, dove ha libero il moto, che in <lb></lb>piana terra, dove, dai tanti oggetti ch&#039;egli v&#039;incontra, ad ogni passo viene <lb></lb>impedito? </s>

<s>Non vedete voi le banderuole moversi sui campanili, anche quando <lb></lb>voi in piazza non sentite alito che vi rinfreschi? </s></p><p type="main">

<s>“ SIMPLICIO. — Volete dire insomma che la vela spinge tanto più ga­<lb></lb>gliardamente la nave, quanto è più alta, perchè in alto il vento spira sem­<lb></lb>pre più gagliardo? </s>

<s>Ma questa è ragion troppo semplice, e non meritevole <lb></lb>che v&#039;esercitasse attorno Aristotile il suo grande ingegno. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Voi credete dunque, signor Simplicio, che la Natura di­<lb></lb>sponga le sue operazioni, per dar faccenda ai Filosofi? </s>

<s>” </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Insieme coi problemi di meccanico soggetto, dei quali abbiamo discorso <lb></lb>fin qui, Galileo se n&#039;era proposti a risolvere altri di vario argomento, i quali <lb></lb>pure, facendo parte del materiale da portarsi in dialogo, vogliono esser se­<lb></lb>condo il proposito nostro raccolti, perchè possan meglio riconoscersi dai no­<lb></lb>stri Lettori. </s>

<s>Non a tutto era data la forma problematica, ma molti dei pen­<lb></lb>sieri, che si volevano dialogizzare, erano espressi in note frettolose, e in sen­<lb></lb>tenze disperse, delle quali anche daremo un saggio, come delle ultime foglie <lb></lb>e de&#039;fiori più minuti, a cui il giardiniere sa trovar qualche luogo nella già <lb></lb>imposta ghirlanda. </s></p><p type="main">

<s>Incominciando da quelle scritture di fisico argomento, le quali avevano <lb></lb>avuta già la forma determinata di problemi, per contrapporli ai <emph type="italics"></emph>Problemi<emph.end type="italics"></emph.end> di <lb></lb>Aristotile, studiati allora da tutti e da tutti creduti veri; trascriveremo i due <lb></lb>seguenti, rimasti tuttavia manoscritti, nella raccolta fattane dal Viviani. </s>

<s>Nel <pb xlink:href="020/01/2582.jpg" pagenum="207"></pb>primo “ si domanda onde avvenga che un uovo rinchiuso tra le mani per <lb></lb>punta, e stretto con grandissima forza, non si possa schiacciare ” (MSS. Gal., <lb></lb>P. VI, T. III, fol. </s>

<s>34). Alla proposta si dircbbe che anche questo problema <lb></lb>appartiene ai meccanici, ma troppo ardua cosa essendo alla scienza di allora <lb></lb>la teoria dell&#039;equilibrio delle vôlte e degli archi gravati da pesi, Galileo si <lb></lb>studiò di ridurre alla fisica la questione, si potrebbe dire ingegnosamente, <lb></lb>benchè costretto a invocar con Aristotile il falso principio che la Natura abor­<lb></lb>risce il vuoto. </s></p><p type="main">

<s>“ Il presente problema facilmente si risolverà, premettendo come prin­<lb></lb>cipii alcune vere proposizioni: La prima è che, siccome delle figure piane, <lb></lb>e che abbiano il medesimo ambito, la maggiore è il cerchio; così anco delle <lb></lb>figure solide isoperimetre la sfera è la maggiore, e la più capace delle altre. </s>

<s><lb></lb>La seconda proposizione è che la Natura grandemente aborrisce il vacuo, <lb></lb>onde in essa ei non si dà, se non con somma violenza. </s>

<s>La terza è che l&#039;aria <lb></lb>si distrae e rarefà, cosa che non può far l&#039;acqua, nè altri umori. </s>

<s>La quarta <lb></lb>è che prima s&#039;arrende un poco il guscio di un uovo, e poi si rompe. </s>

<s>” </s></p><p type="main">

<s>“ Ora da questi principii caveremo la resoluzion del problema, impe­<lb></lb>rocchè, mentre che si preme l&#039;uovo per lo lungo, e si stringono le sue punte <lb></lb>o estremità l&#039;una contro l&#039;altra, il suo guscio cede alquanto, e si arrende, <lb></lb>sicchè l&#039;uovo, che è di figura oblonga, viene ad acquistar dello sferico, e per <lb></lb>conseguenza si fa più capace, perchè, come aviamo detto delle figure solide <lb></lb>isoperimetre, la sfera è la più capace. </s>

<s>Ma perchè la roba, che è dentro del­<lb></lb>l&#039;uovo, non è cosa che si rarefaccia e distenda, per poter mantener pieno <lb></lb>l&#039;uovo, sarebbe necessario che il luogo, che acquista l&#039;uovo nel ridursi alla <lb></lb>figura sferica, rimanessi vuoto. </s>

<s>Ma la Natura, che grandemente aborrisce il <lb></lb>vacuo, repugna gagliardamente e resiste, per far che l&#039;uovo non si avvicini <lb></lb>alla figura sferica, acciò col diventar egli più capace, e per non aver dentro <lb></lb>cosa che lo possa riempiere, e per esser necessario che il suo guscio s&#039;ar­<lb></lb>renda alquanto, prima ch&#039;e&#039;si rompa; non si venga a dare il vacuo: quindi <lb></lb>è che l&#039;uovo non si può schiacciare. </s>

<s>” </s></p><p type="main">

<s>“ Per confermazione e chiarezza di questo pensiero, piglisi un uovo assai <lb></lb>scemo, sicchè dentro vi sia di molt&#039;aria, e stringasi per lo lungo: che al <lb></lb>sicuro si schiaccerà, perchè l&#039;aria che è dentro seguiterà tanto a rarefarsi, <lb></lb>e a distendersi per mantener pieno l&#039;uovo, mentre con l&#039;avvicinarsi allo sfe­<lb></lb>rico divien più capace, che il guscio, per non potere arrendersi più, si verrà <lb></lb>a rompere, ed il medesimo seguirà, se faremo nel guscio ogni piccolo foro, <lb></lb>sicchè l&#039;aria per quello possa entrare nell&#039;uovo ” (ivi, fol. </s>

<s>34 a tergo). </s></p><p type="main">

<s>All&#039;altro problema d&#039;argomento fisico, che noi qui aggiungiamo, il Vi­<lb></lb>viani apponeva la nota <emph type="italics"></emph>stampato,<emph.end type="italics"></emph.end> come quello che veramente era stato rac­<lb></lb>colto dal Rinaldini fra le Opere galileiane, nel 1655, in Bologna, col titolo <lb></lb><emph type="italics"></emph>Risposta ad un problema, proposto dall&#039;illustrissimo signor Piero Bardi <lb></lb>dei conti di Vernio, intorno all&#039;apparente diversità della temperie del­<lb></lb>l&#039;acqua.<emph.end type="italics"></emph.end> Nonostante è bene conoscerlo nella sua prima forma originale, non <lb></lb>per sola curiosità erudita, ma perchè serva di documento a dimostrar come <pb xlink:href="020/01/2583.jpg" pagenum="208"></pb>Galileo, nè prima nè poi si valse del Termometro, per risolvere una questione <lb></lb>relativa ai gradi della temperatura assoluta dell&#039;aria, e dell&#039;acqua. </s></p><p type="main">

<s>“ Uno va per bagnarsi in Arno: si spoglia, e si mette a sedere all&#039;om­<lb></lb>bra. </s>

<s>Stando così, sente un fresco comportabile e temperato. </s>

<s>Entra poi nel­<lb></lb>l&#039;acqua, e gli par di sentirla assai fredda. </s>

<s>Statovi un pezzo ne esce, torna <lb></lb>all&#039;ombra, e sente un freddo estremo. </s>

<s>Di nuovo si tuffa nell&#039;acqua e, dove <lb></lb>la prima volta gli parve molto fredda, la seconda gli apparisce piuttosto tem­<lb></lb>perata e calda. </s>

<s>Si domanda adesso la cagione di tal diversità. </s>

<s>” </s></p><p type="main">

<s>“ Il Problema si risolve così: Noi abbiamo in una stanza una tinozza <lb></lb>pi<gap></gap>a di acqua, e ci è stato v. </s>

<s>g. </s>

<s>quindici di freddura. </s>

<s>Viene uno, si spoglia <lb></lb>e entra nella tinozza. </s>

<s>Chiara cosa è ch&#039;ei sentirà assai più freddo in quel­<lb></lb>l&#039;acqua, ch&#039;ei non sentiva, innanzi ch&#039;ei v&#039;entrasse, dal che si può conclu­<lb></lb>dere che, stando l&#039;aria e l&#039;acqua in un medesimo luogo, cioè ad un istesso <lb></lb>caldo o ad un istesso freddo, sempre l&#039;acqua apparirà assai più fredda del­<lb></lb>l&#039;aria. </s>

<s>” </s></p><p type="main">

<s>“ Diciamo dunque che dei gradi di freddezza, dei quali l&#039;aria ne ha per <lb></lb>esempio due, l&#039;acqua ne abbia dieci. </s>

<s>Dunque un&#039;altr&#039;acqua, che ne abbia <lb></lb>sei, apparirà fredda, in comparazione dell&#039;aria, che ne ha due, ma ben calda <lb></lb>in relazione all&#039;acqua, che ne ha dieci. </s>

<s>” </s></p><p type="main">

<s>“ Ora, stante questo, colui che si va a bagnare in Arno, mentre sta <lb></lb>ignudo all&#039;ombra, gode il fresco temperato dell&#039;aria, che ha due soli gradi <lb></lb>di freddezza, ma, quando entra nell&#039;acqua d&#039;Arno, sente la freddezza sua, <lb></lb>che è di sei gradi (di sei dico e non di dieci, perchè il sole ardente, che <lb></lb>l&#039;ha percossa per lo spazio di molte miglia, glie ne viene ad aver levati quat­<lb></lb>tro), e però, in rispetto dell&#039;aria, che ne ha due soli, gli pare assai fredda. </s>

<s>” </s></p><p type="main">

<s>“ Esce poi costui d&#039;Arno, e torna all&#039;ombra bagnato e coperto da un <lb></lb>sottilissimo velo d&#039;acqua, la quale, per esser pochissima, non si tosto è con­<lb></lb>dotta sotto l&#039;albero all&#039;ombra, che viene ad acquistare i quattro gradi di fred­<lb></lb>dezza toltigli dal Sole, onde di sei, ch&#039;ella ne aveva innanzi, si riduce ad <lb></lb>un tratto ad averne dieci, sicchè colui che si bagua non sente più sei gradi <lb></lb>di freddezza, ma dieci. </s>

<s>E però, mentre sta sotto l&#039;albero bagnato, sente freddo <lb></lb>estremo, ma se ritorna poi a tuffarsi entro nell&#039;acqua, che ha sei gradi soli <lb></lb>di freddezza, onde, perdendo quattro gradi di freddo, gli pare di essere en­<lb></lb>trato in un bagno temperato ” (ivi, fol. </s>

<s>29). </s></p><p type="main">

<s>Anche questi due Problemi dovevano esser materia del Dialogo, e ma­<lb></lb>teria del Dialogo doveva essere altresi un argomento d&#039;assai maggiore im­<lb></lb>portanza, intorno al quale le poche risolute questioni avevano ingerito nel­<lb></lb>l&#039;animo di Galileo la speranza di averne a comporre un intero trattato. </s>

<s>Di <lb></lb>questo trattato faceva Galileo stesso menzione in una lettera a Giuliano de&#039;Me­<lb></lb>dici, a cui, dicendo di avere diversi opuscoli di soggetti naturali, ne annovera <lb></lb>in ultimo uno <emph type="italics"></emph>De animalium motu<emph.end type="italics"></emph.end> (Alb. </s>

<s>VI, 98). Sembra che allora, men­<lb></lb>tre era in Padova, emulasse l&#039;altro celebre collega suo Girolamo Fabricio <lb></lb>d&#039;Acquapendente, a cui si debbono in realtà quei trattati <emph type="italics"></emph>De sono et voce,<emph.end type="italics"></emph.end><lb></lb>e <emph type="italics"></emph>De visu et coloribus,<emph.end type="italics"></emph.end> nella sopra citata lettera a don Giuliano commemo-<pb xlink:href="020/01/2584.jpg" pagenum="209"></pb>rati. </s>

<s>Di quella emulazione si vedrà, nelle cose che saremo per dire, qualche <lb></lb>prova rispetto ai moti animali, intorno a che non rimase a Galileo, come <lb></lb>s&#039;accennava dianzi, se non che alcune questioni relative particolarmente al <lb></lb>passo dell&#039;uomo e del cavallo: questioni, il proposito di raccoglier le quali <lb></lb>e di portarle in dialogo, era stato espresso a Raffaello Magiotti, com&#039;ap­<lb></lb>parisce dalle congratulazioni di lui scritte in una lettera da Roma il di <lb></lb>21 Marzo 1637 (MSS. Gal., P. VI, T. XIII, fol. </s>

<s>14). </s></p><p type="main">

<s>Del passo del cavallo è già da qualche tempo pubblicamente nota una <lb></lb>scrittura galileiana, nella quale l&#039;Autore confuta le dottrine di Aristotile, e <lb></lb>in che modo lo faccia lo dicemmo nel cap. </s>

<s>X del terzo tomo della nostra <lb></lb>Storia, e particolarmente a pag. </s>

<s>397, 98. Son forse meno note alcune altre <lb></lb>osservazioni, che Galileo stesso faceva intorno al passo dell&#039;uomo, contro ciò <lb></lb>che Platone e Aristotile avevano insegnato nei loro libri. </s>

<s>Dicevano que&#039;due <lb></lb>grandi Filosofi che, passeggiando l&#039;uomo, la sua altezza verticale ora cresce <lb></lb>ora diminuisce, secondo che ora la persona si solleva sull&#039;un piede, per poi <lb></lb>scendere a riposarsi sull&#039;altro, sicchè la linea del moto non è retta, ma on­<lb></lb>deggiante. </s>

<s>Così fatto ondeggiamento, dicevano, si può facilmente osservare, <lb></lb>riferendo la visuale sopr&#039;una parete, parallelamente alla quale si guardi da <lb></lb>una certa distanza la testa di un che passeggia. </s></p><p type="main">

<s>La ragione, che prescriveva alla Natura questo modo indecente di ope­<lb></lb>rare, consisteva nel credere ch&#039;ella non avesse saputo, con tutto il suo sa­<lb></lb>piente magistero, far sì che le gambe si potessero allungar secondo il biso­<lb></lb><figure id="id.020.01.2584.1.jpg" xlink:href="020/01/2584/1.jpg"></figure></s></p><p type="caption">

<s>Figura 71.<lb></lb>gno, ma che sempre si dovessero mantenere <lb></lb>uguali. </s>

<s>Rappresenti AB (fig. </s>

<s>71) la colonna <lb></lb>ossea, sopra la quale si sostien l&#039;uomo, nella <lb></lb>sua stazion verticale, sul suolo CD. </s>

<s>Per mo­<lb></lb>versi innanzi fa rotare l&#039;AB intorno al cen­<lb></lb>tro A, nella posizione AB′, ond&#039;è che, per <lb></lb>andare a ritrovare e appoggiarsi sul pavi­<lb></lb>mento in G, il punto A convien che si <lb></lb>abbassi, e che poi nuovamente si rialzi, per tornar nella posizion verticale <lb></lb>parallela all&#039;AB, e così la persona non va mai di pari passo ma ondeggia. </s></p><p type="main">

<s>Galileo diceva che la Natura aveva suggerita instintivamente una bellis­<lb></lb>sima industria, sfuggita alle considerazioni di quei Filosofi, aggiungendo la <lb></lb>parte B′ G, che manca alla gamba, per andare a toccare e fermarsi nell&#039;ap­<lb></lb>poggio, col sollevare in B′ il calcagno, e col distendere e appuntare in E il <lb></lb>piede, cosicchè il punto A riman sempre alla medesima altezza, e il passo <lb></lb>dell&#039;uomo, come si conveniva alla sua dignità, si serba sempre uniforme. </s>

<s><lb></lb>Ritrovasi notato infatti fra i pensieri di Galileo “ come il camminar di noi <lb></lb>bipedi non sia a onde, ancorchè le gambe siano uguali, e che si trovino di­<lb></lb>versamente inclinate sopra l&#039;orizonte, dove par che Aristotile e Platone ab­<lb></lb>biano equivocato ” (MSS. Gal., P. VI, T. III, fol. </s>

<s>62): pensiero che vien <lb></lb>confermato dalla testimonianza, e illustrato dalle seguenti parole del Viviani: </s></p><p type="main">

<s>“ Sovviemmi aver sentito dire dal Galileo che Platone e Aristotile er-<pb xlink:href="020/01/2585.jpg" pagenum="210"></pb>rarono in dire che il moto dell&#039;uomo veniva fatto a onde, cioè che, nel mo­<lb></lb>versi e passeggiar parallelo ad una parete, osservando la testa del moventesi, <lb></lb>con riferirla con l&#039;occhio sulla muraglia, appariva che essa testa descrivesse <lb></lb>un&#039;onda ora alta ora bassa: perchè essi si credettero che le gambe fossero <lb></lb>talmente uguali, che elle non potessero mai essere disuguali. </s>

<s>Ma sono, per­<lb></lb>chè, nel posare il calcagno del piede precedente, si allunga l&#039;altra gamba, <lb></lb>alzando il suo calcagno, e levandosi in punta di piedi ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXXXV, a tergo del fol. </s>

<s>29). </s></p><p type="main">

<s>Il Borelli, esaminando, nella proposizione CLVI della prima parte <emph type="italics"></emph>De <lb></lb>motu animalium,<emph.end type="italics"></emph.end> in che modo si muova l&#039;uomo, sembra che volesse anche <lb></lb>egli indirettamente confermare le osservazioni di Galileo, contro le inconsi­<lb></lb>deratezze dei Filosofi antichi, dicendo che, sebbene possa a prima vista pa­<lb></lb>rer che le nostre gambe si rassomiglino nel moversi a quelle di un compasso, <lb></lb>è nonostante da confessar che un tale incesso ondeggiante <emph type="italics"></emph>deformis et in­<lb></lb>commodus esset<emph.end type="italics"></emph.end> (Romae 1680, pag. </s>

<s>252), ond&#039;ei ne conclude che la Natura <lb></lb><emph type="italics"></emph>faciliori et elegantiori motu machinam humani corporis promovet,<emph.end type="italics"></emph.end> e in <lb></lb>descrivere questa promozione principalmente nota, come Galileo, che ogni <lb></lb>incomodità di ondeggiamento si toglie, <emph type="italics"></emph>quia longitudo totius cruris et coxae <lb></lb>elongatur, additione longitudinis pedis<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>253). </s></p><p type="main">

<s>Nella seguente proposizione però il Borelli stesso osserva che l&#039;ondeg­<lb></lb>giamento, inevitabile al passo dell&#039;uomo, si fa propriamente a quel modo che <lb></lb>dicevano Platone e Aristotile, ma nel piano orizontale, descrittovi sopra dal <lb></lb>centro di gravità, e no nel verticale descrittovi dalla testa. </s>

<s>Che sia propria­<lb></lb>mente così, che cioè le nostre gambe non conducano l&#039;umbilico precisamente <lb></lb>nella linea retta della direzione del passo, ma che lo facciano ondeggiare ora <lb></lb>a destra ora a sinistra, il Borelli suggerisce un modo di sperimentarlo, che <lb></lb>potrebbe a chi l&#039;eseguisse riuscire, oltre che di ammaestramento di questa <lb></lb><figure id="id.020.01.2585.1.jpg" xlink:href="020/01/2585/1.jpg"></figure></s></p><p type="caption">

<s>Figura 72.<lb></lb>verità, di spettacolo curioso e giocondo. </s>

<s><lb></lb>Sia per esempio AG (fig. </s>

<s>72) la linea <lb></lb>lungo la quale, movendo da A, uno si <lb></lb>proponga di camminare, e in G sia eretta <lb></lb>la verga GH di color bianco, e in FI <lb></lb>un&#039;altra simile verga, ma di color nero, <lb></lb>cosicchè all&#039;occhio dell&#039;uomo, che sta <lb></lb>fermo in A, la bianca resti totalmente coperta dalla nera. </s>

<s>Movasi, e vedrà ad <lb></lb>ogni passo la verga bianca ora uscir fuori dalla sinistra mano ora dalla <lb></lb>destra, con continua spettacolosa vicenda, e per evidentissimo segno che, ri­<lb></lb>ferito il centro di gravità sul pavimento, vi descriverebbe la linea ondeggiante <lb></lb>ABEM, le onde o i seni della quale si vedrebbero, come BC, DE, farsi molto <lb></lb>più ampi negli uomini obesi, e nelle donne pregnanti. </s>

<s>“ Quod est argumen­<lb></lb>tum evidentissimum, così propriamente conclude il Borelli la sua proposizione, <lb></lb>dop&#039;aver descritta la curiosa esperienza; incessus hominum non fieri per <lb></lb>lineam rectam: ergo linea propensionis tortuoso et serpentino itinere tran­<lb></lb>sfertur hinc inde, ab una ad alteram parallelarum, et proinde per unicam <pb xlink:href="020/01/2586.jpg" pagenum="211"></pb>simplicem rectam lineam machina humani corporis motum progressuum in­<lb></lb>cessus efficere non potest ” (ibid., pag. </s>

<s>255). </s></p><p type="main">

<s>In proposito di così fatte questioni di Meccanica animale cade oppor­<lb></lb>tuno quel confronto, dal quale si voleva far apparire come Galileo emulasse <lb></lb>l&#039;Acquapendente. </s>

<s>Nel trattato <emph type="italics"></emph>De musculi utilitatibus<emph.end type="italics"></emph.end> è premessa dall&#039;Ana­<lb></lb>tomico nello Studio padovano la questione “ Cur musculi longiores, non so­<lb></lb>lum longiores, sed robustiores dant motus ” (Opera omnia, Lugd. </s>

<s>Batav. </s>

<s>1738, <lb></lb>pag. </s>

<s>420); e il Matematico nel medesimo Studio si proponeva pure di dimo­<lb></lb>strare “ che i tendini dei muscoli fanno maggior forza i lunghi che i brevi ” <lb></lb>(MSS. Gal., P. VI, T. III, a tergo del fol. </s>

<s>61). Ora, essendo questa propo­<lb></lb>sizione principalissima fra quelle, che dovevano comporre il trattato <emph type="italics"></emph>De ani­<lb></lb>malium motu,<emph.end type="italics"></emph.end> di cui nella storia della letteratura galileiana non è rimasto <lb></lb>che il titolo; è il tempo di dire a coloro, che ne hanno lamentata la per­<lb></lb>dita, come Galileo non progredi forse oltre in quest&#039;ordine di speculazioni, <lb></lb>perchè si trovò vinto dall&#039;emulo suo, l&#039;anatomia del quale, destramente ac­<lb></lb>coppiata con la matematica, superava i vantaggi della matematica sola, ch&#039;era <lb></lb>pur mancante dei necessari argomenti. </s></p><p type="main">

<s>Come nell&#039;Acquapendente s&#039;accoppiassero quelle due scienze, e come la <lb></lb>matematica che aveva lo fornisse dell&#039;argomento opportuno, consistente nel <lb></lb>modo di decomporre le forze, secondo gl&#039;insegnamenti di Aristotile, s&#039;accen­<lb></lb>nava in principio dell&#039;ultimo capitolo della prima parte di questa Storia della <lb></lb>Meccanica, ma vogliamo ora meglio, nella presente occasione, dichiarare le <lb></lb>cose già dette intorno al modo di risolver, nel trattato <emph type="italics"></emph>De musculi utilita­<lb></lb>tibus,<emph.end type="italics"></emph.end> la proposta questione, per concluder poi che mancavano a Galileo ve­<lb></lb>ramente, come si diceva, gli argomenti necessari, per riuscire a quella me­<lb></lb>desima soluzione. </s></p><p type="main">

<s>La soluzione dell&#039;Acquapendente si fa dipendere, come da lemma, da <lb></lb>una proposizione meccanica così formulata: “ Quo corda super vecte ela­<lb></lb>tior fuerit, idest maiorem angulum continebit, eo facilius pondus attolletur ” <lb></lb><figure id="id.020.01.2586.1.jpg" xlink:href="020/01/2586/1.jpg"></figure></s></p><p type="caption">

<s>Figura 73.<lb></lb>(Opera cit., pag. </s>

<s>420). Sia il vette AB <lb></lb>(fig. </s>

<s>73), col peso in A e col sostegno <lb></lb>in B, e per sostenerlo o sollevarlo <lb></lb>intendasi applicata in D una corda di <lb></lb>qualunque lunghezza. </s>

<s>Se inclinasi in <lb></lb>DE, in modo che l&#039;angolo EDB sia <lb></lb>minore di FDB, dice l&#039;Acquapendente <lb></lb>che anche sarà minore la forza fatta <lb></lb>dalla medesima corda, perchè allora <emph type="italics"></emph>pars virium absumitur contra fulci­<lb></lb>mentum.<emph.end type="italics"></emph.end> Costruito infatti sulla DE il rettangolo HG, la forza totale si de­<lb></lb>compone nelle due HD, DG, ed è evidente che questa <emph type="italics"></emph>absumitur contra ful­<lb></lb>cimentum,<emph.end type="italics"></emph.end> non restando attiva che l&#039;HD, minore della DF o della DE. </s>

<s>Che <lb></lb>se anche s&#039;inclini di più la corda, come in DI, è manifesto che, crescendosi <lb></lb>da una parte la forza DM, inutilmente diretta contro il fulcro, la forza utile <lb></lb>LD, che dall&#039;altra parte ne resta, è anche più che dianzi diminuita. </s>

<s>È chiaro <pb xlink:href="020/01/2587.jpg" pagenum="212"></pb>dunque che, mentre nella direzion perpendicolare non è parte alcuna della <lb></lb>forza, che non si eserciti in sollevare il peso; inclinandosi la corda sempre <lb></lb>più, anche sempre più diminuisce quella sua forza, intanto che, venendo final­<lb></lb>mente a costituirsi nella stessa linea del vette, si riduce a nulla. </s>

<s>“ Absumi­<lb></lb>tur ergo vis magna ex parte in fulcimento B expellendo: quod, si attraha­<lb></lb>tur chorda perpendicula in FD, nulla pars virium suam non exercet facultatem <lb></lb>in pondere elevando. </s>

<s>Patet etiam quod, si vectis et chorda in eadem essent <lb></lb>linea constituta, nullo pacto motus fieret ” (ibid.). </s></p><p type="main">

<s>Dimostrato ciò, per avvicinarsi più d&#039;appresso ad applicar le teorie mec­<lb></lb>caniche al caso dei muscoli che, quanto son più lunghi, tanto più facilmente <lb></lb>muovon le membra, a cui son legati; soggiunge l&#039;Acquapendente l&#039;altra pro­<lb></lb>posizione, che dice come, dovendosi un peso attaccato all&#039;estremità di un vette <lb></lb>semplicemente sostener da una corda, tanto fa l&#039;esser questa o più lunga o <lb></lb>più corta: ma se debba il peso stesso poi venir sollevato, “ dico minori vi <lb></lb>opus esse, adhibita corda longiori, quam breviori ” (ibid.). </s></p><p type="main">

<s>Per dichiarar meglio il concetto dell&#039;Autore, poniamolo sotto quest&#039;altra <lb></lb>forma: Se il peso A (fig. </s>

<s>74) debba semplicemente sostenersi, tant&#039;opera la <lb></lb><figure id="id.020.01.2587.1.jpg" xlink:href="020/01/2587/1.jpg"></figure></s></p><p type="caption">

<s>Figura 74.<lb></lb>corda AC, che la AD; ma se debba inoltre solle­<lb></lb>varsi, infino a toccar per esempio la orizontale SX, <lb></lb>più facilmente vi si porterà, e vi si manterrà dalla <lb></lb>corda più lunga, che dalla più corta. </s>

<s>La corda CA <lb></lb>infatti, girando intorno al punto C come a suo <lb></lb>centro, porterà il peso in R, e DA, girando intorno <lb></lb>a D, lo porterà in S. Ora, per concluder dietro il <lb></lb>lemma precedente che in S il peso vien sollevato più <lb></lb>facilmente che in R, basta dimostrar che l&#039;angolo <lb></lb>DSX, fatto dalla corda colla direzione del vette, è maggiore di CRX, ciò che <lb></lb>è facile a farsi conducendo le AR, AS, dai triangoli isosceli ACR, ADS de­<lb></lb>scritti dalle quali resulta essere ADS minore di ACR, d&#039;onde per necessità <lb></lb>DSX maggiore di CRX. </s>

<s>Dietro ciò, se per AC, AD intendansi due muscoli, <lb></lb>e per A il peso dell&#039;arto, a cui per moverlo son legati; il proposito è per <lb></lb>sè manifesto. </s></p><p type="main">

<s>Così risolvevasi dall&#039;Acquapendente una delle principali questioni di Mec­<lb></lb>canica animale, ritrovando nella regola di decomporre le forze, insegnatagli <lb></lb>da Aristotile, l&#039;argomento necessario per una tal soluzione. </s>

<s>Dicemmo che a <lb></lb>Galileo venne a mancare così fatto argomento, per cui dovette necessaria­<lb></lb>mente rimanere inferiore all&#039;emulo suo, ma è ora il tempo di confermare <lb></lb>quel nostro detto. </s>

<s>La somma delle cose è chiaro che si riduce alla mecca­<lb></lb>nica dei pesi sostenuti da funi, la più propizia occasione di trattar de&#039;quali <lb></lb>sarebbesi porta a Galileo, in proposito dei pendoli, ricercando in essi, quando <lb></lb>sian rimossi più o meno dal perpendicolo, la proporzion del variare i loro <lb></lb>momenti. </s></p><p type="main">

<s>Sia per esempio il pendolo BC (fig. </s>

<s>75) rimosso in BA: quanto varia <lb></lb>la forza del peso in tirare il filo nelle due posizioni? </s>

<s>Che ci dovesse essere <pb xlink:href="020/01/2588.jpg" pagenum="213"></pb>una tal varietà Galileo incominciò, come Leonardo da Vinci, ad apprenderlo <lb></lb>per esperienza, se non che, mentre all&#039;uno si rivelava il fatto dai globi ven­<lb></lb><figure id="id.020.01.2588.1.jpg" xlink:href="020/01/2588/1.jpg"></figure></s></p><p type="caption">

<s>Figura 75.<lb></lb>tilati all&#039;estremità di una bilancia, serviva <lb></lb>all&#039;altro di criterio il tatto delle proprie dita, <lb></lb>alle quali, ventilando il grave, teneva avvolto <lb></lb>o legato il filo. </s>

<s>Quel criterio poi era con <lb></lb>l&#039;esercizio divenuto sì giusto che, volendo <lb></lb>per via delle numerate vibrazioni misurare <lb></lb>il tempo, diceva di saperlo far senza errore <lb></lb>a mente, anche senza veder l&#039;andare e il <lb></lb>ritornare dello strumento. </s>

<s>“ Col misuratore <lb></lb>del tempo, troviamo scritto in una sua nota, <lb></lb>si possono numerare le vibrazioni, tenendo <lb></lb>il filo in mano, come se fosse legato a un <lb></lb>luogo stabile, e preso il tempo con la mente <lb></lb>si numereranno senza errrore, benchè non <lb></lb>si vegghino, le vibrazioni ” (MSS. Gal., P. <lb></lb>VI, T. III, fol. </s>

<s>63 a t.). </s></p><p type="main">

<s>Il fatto però era per sè solo cognizione di poco acquisto, senza che la <lb></lb>matematica venisse a definire le proporzioni, secondo le quali via via suc­<lb></lb>cede: proporzioni che noi crediamo non essere state da Galileo mai dimo­<lb></lb>strate. </s>

<s>L&#039;opinione si fonda sulla certezza che abbiamo non essere stato l&#039;ar­<lb></lb>gomento in proposito toccato, nè nei libri nè a viva voce, dal Maestro, al <lb></lb>più studioso Discepolo del quale, promotore di questa nuova scienza, doman­<lb></lb>dandosi quanta sia la violenza che patisce il filo AB, nella precedente figura, <lb></lb>rispetto a quella che patisce il filo BC, rispondeva: “ La violenza che pati­<lb></lb>sce il filo AB, essendo stirato dal grave A, credo che sia tale, quale è il <lb></lb>momento del medesimo grave, movendosi per il piano BA: cioè che la forza <lb></lb>fatta dal grave al filo, nel luogo AB, alla forza fatta al filo nel luogo BC, <lb></lb>che è la forza totale, sia come il momento del medesimo grave sopra un <lb></lb>piano inclinato quanto BA, al momento totale per la perpendicolare BC ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CXIII, fol. </s>

<s>30). </s></p><p type="main">

<s>Ma il Viviani, credendo così, credeva manifestamente il falso, com&#039;avrebbe <lb></lb>saputo dimostrare a lui e al suo proprio Maestro l&#039;Acquapendente, applican­<lb></lb>dovi, a quel modo che dianzi il rettangolo aristotelico, così in questo caso, <lb></lb>e per le medesime ragioni, il parallelogrammo. </s>

<s>Facendo infatti rappresentare <lb></lb>alla AE la forza totale, che aveva il peso in C, questa in A decomposta nelle <lb></lb>due AD, AG, non si ridurrebbe che alla sola AG, essendo che l&#039;altra AD <lb></lb><emph type="italics"></emph>absumitur contra fulcimentum.<emph.end type="italics"></emph.end> Dunque il momento totale del peso in C, <lb></lb>al parziale in A, sta come AE ad AG, o, prolungata l&#039;AG infino a incon­<lb></lb>trare in F l&#039;orizontale EF, per i triangoli simili AEG, AEF; come AF ad <lb></lb>AE, per cui la forza fatta dal peso in C, alla forza fatta in A, non sta come il <lb></lb>momento dello stesso grave nel perpendicolo, al momento lungo un piano <lb></lb>inclinato quanto AD, secondo che falsamente credeva il Viviani, ma al mo-<pb xlink:href="020/01/2589.jpg" pagenum="214"></pb>mento lungo un piano inclinato quanto AF, no nella direzione stessa del filo, <lb></lb>ma in quella a lui perpendicolare. </s></p><p type="main">

<s>L&#039;incertezza e il fallo, in cui incorse lo stesso Viviani, avevano la ra­<lb></lb>dice nella falsità del secondo teorema scritto nel IV dialogo delle Scienze <lb></lb>nuove, da cui resultava come, tutt&#039;altro che consumarsi la forza AD in ti­<lb></lb>rare inutilmente il sostegno, si faceva anzi così attiva, da rimaner per re­<lb></lb>gola della resultante del moto. </s>

<s>Ond&#039;essendo propriamente tali le fallacie del <lb></lb>Discepolo e del Maestro, abbiamo tutte le ragioni di credere che mancassero <lb></lb>all&#039;uno e all&#039;altro i principii diretti, per riuscire a dimostrar come più va­<lb></lb>lidamente operino, in movere le membra, i tendini più lunghi. </s>

<s>Dicemmo che <lb></lb>mancavano i principii diretti, perchè non è impossibile che si risolvesse la <lb></lb>questione in altri modi, secondo i quali Galileo forse intendeva di portarla <lb></lb>in dialogo, per salvar dall&#039;oblio questa reliquia delle sue speculazioni intorno <lb></lb>ai moti animali. </s></p><p type="main">

<s>Altre speculazioni intorno ai più varii soggetti della Fisica aveva da rac­<lb></lb>cogliere lo stesso Galileo, per inserirle nel suo Dialogo e salvarle anch&#039;esse <lb></lb>dall&#039;oblio, fra le quali ci sembra sia da notar fra le prime quella, che ora <lb></lb>diremo, relativa alle galleggianti. </s>

<s>Nel celebre discorso pubblicato nel 1612 in­<lb></lb>torno a questo argomento, confutava quel suo avversario Francesco Buona­<lb></lb>mico, il quale voleva confermare le sue false dottrine dal fatto, che un legno <lb></lb>inzuppato d&#039;acqua finalmente va al fondo, contrapponendo Galileo le seguenti <lb></lb>osservazioni alle fallacie del peripatetico discorso: “ Ciò accade d&#039;alcuni le­<lb></lb>gni porosi, li quali, mentre hanno le porosità ripiene di aria, o d&#039;altra ma­<lb></lb>teria men grave dell&#039;acqua, sono moli in specie manco gravi di essa acqua, <lb></lb>ma quando, partendosi tal materia leggera, succede nelle dette porosità o <lb></lb>cavernosità l&#039;acqua, può benissimo essere che allora tal composto resti più <lb></lb>grave dell&#039;acqua.... Così quel che resta del legno, partendosi l&#039;aria dalle sue <lb></lb>concavità, se sarà più grave in specie dell&#039;acqua, ripiene che saranno le sue <lb></lb>porosità d&#039;acqua, si avrà un composto d&#039;acqua e di legno, più grave del­<lb></lb>l&#039;acqua, e andrà, conforme alla dottrina d&#039;Archimede, al fondo ” (Alb. </s>

<s>XII, 32). </s></p><p type="main">

<s>In questo discorso Galileo concedeva al suo avversario la possibilità che <lb></lb>i legni inzuppati d&#039;acqua si sommergano: ciò che sarebbe senza dubbio avve­<lb></lb>nuto, quando la materia di loro che resta, partitasi l&#039;aria, fosse più grave <lb></lb>in specie dell&#039;acqua stessa. </s>

<s>Nulla però decide in proposito, non avendone <lb></lb>fatte esperienze, nè curandosi per allora di farle. </s>

<s>Ma negli ultimi anni della <lb></lb>sua vita, ritornando col pensiero sopra le cose passate, sentì nascersi una <lb></lb>viva curiosità di saper come il fatto passava, e ragionando un giorno di ciò <lb></lb>col Viviani gli soggiungeva che, se la materia legnosa fra poro e poro è spe­<lb></lb>cificamente più grave dell&#039;acqua, dell&#039;andare al fondo il legno inzuppato <lb></lb>sarebbe argomento certo il vedervene andare la segatura. </s></p><p type="main">

<s>Il desiderio di sodisfare a una tale curiosità s&#039;accendeva alla fiamma di <lb></lb>un desiderio più vivo, qual era quello di confermar che i liquidi non resi­<lb></lb>stono colla loro viscosità all&#039;esser penetrati dai corpi immersivi: perniciosa <lb></lb>dottrina, che il Salviati ripeteva nel primo Dialogo delle Scienze nuove (Alb. <pb xlink:href="020/01/2590.jpg" pagenum="215"></pb>XIII, 72), con la medesima persuasione da vecchio, che l&#039;aveva da giovane <lb></lb>professata nel sopra citato discorso idrostatico, le prolisse parole scritte nel <lb></lb>quale si possono leggere compendiate in questa nota: “ Mentre un metallo <lb></lb>è freddo, ed in conseguenza le sue parti continuate ed aderenti insieme, è <lb></lb>necessario, per dividerlo, usare strumenti gagliardi e gran forza. </s>

<s>Dopo che <lb></lb>il fuoco l&#039;ha liquefatto, restano le sue parti divise, ed un solido che si ponga <lb></lb>dentro non l&#039;ha più a dividere, ma solamente a movere. </s>

<s>Perchè irragione­<lb></lb>vol cosa sarebbe a dire che una verga di ferro o altro corpo solido dividesse <lb></lb>quello, che non ha diviso il fuoco. </s>

<s>Nel penetrar dunque i liquidi e fluidi, <lb></lb>non solamente non vi è resistenza alla divisione, ma non si ha a divider cosa <lb></lb>alcuna, ma solamente a muovere ” (MSS. Gal., P. III, T. X, fol. </s>

<s>72). </s></p><p type="main">

<s>Nel primo dialogo delle Scienze nuove, al luogo sopra citato, credeva il <lb></lb>Salviati di poter confermare queste dottrine, per via degl&#039;idrostammi, ai <lb></lb>quali è sufficiente una leggerissima variazione di temperatura nel liquido, <lb></lb>perchè vi scendano o salgano prontamente: e ora nel dialogo novissimo in­<lb></lb>tendeva di confermare quella sua antica opinione con l&#039;esempio di ciò, che <lb></lb>sarebbesi osservato nei legni massicci e nella loro limatura. </s>

<s>L&#039;esperienza non <lb></lb>sembra si facesse in tempo, e il Viviani indugiò ad eseguirla nell&#039;Accademia <lb></lb>del Cimento, contentandosi intanto di scriver per suo memoriale in questa <lb></lb>nota il pensiero comunicatogli da Galileo: “ Credo che delle cose che scen­<lb></lb>dono nell&#039;acqua, quanto più piccole sono, più stieno a scendere, ma che di <lb></lb>quelle, che mal volentieri vi scendono, siano più facili a scender le piccolis­<lb></lb>sime che le grandi, come per esempio il legno, che non vi scende, sminuz­<lb></lb>zato in sottil polvere vi scenda ” (MSS. Gal., P. V, T. IV, fol. </s>

<s>37). </s></p><p type="main">

<s>Dicemmo che questa opinion del Maestro aspettò il Viviani di verificarla <lb></lb>nell&#039;Accademia del Cimento, e ciò fu a proposito delle controversie insorte <lb></lb>fra lui e il Borelli, il quale, contro il suo collega e contro lo stesso Galileo, <lb></lb>adduceva esperienze dimostrative di un glutine, che, come quello degli altri <lb></lb>corpi, tenga insieme le particelle dell&#039;acqua. </s>

<s>Avremo intorno a questa con­<lb></lb>troversia occasion di discorso altrove: per ora qui basti dir che il Viviani, <lb></lb>propugnatore delle dottrine insegnate nel discorso delle Galleggianti, propo­<lb></lb>neva nell&#039;Accademia di “ fare una piastra tonda di cera, che salga lenta­<lb></lb>mente per taglio: posta poi per piano, si vede che la figura non è impo­<lb></lb>tente a fendere l&#039;acqua, e che in essa non ci è minima coesione e viscosità ” <lb></lb>(MSS. Cim., T. X, fol. </s>

<s>27). </s></p><p type="main">

<s>Che aggiungesse a questa il Viviani l&#039;esperienze suggeritegli da Galileo <lb></lb>resulta dal trovarsi, fra le altre rivendicazioni, scritta anche questa: <emph type="italics"></emph>Mia <lb></lb>l&#039;osservazione che tutti i legni vanno al fondo nell&#039;acqua<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>259): <lb></lb>e che non in loro stesse terminassero così fatte proposte, ma che avessero <lb></lb>il fine di dimostrare come sian continue, e non aderenti le particelle del­<lb></lb>l&#039;acqua, apparisce da un <emph type="italics"></emph>Registro di osservazioni ed esperienze varie, da <lb></lb>farsi nell&#039;Accademia in considerando l&#039;acqua come mezzo de&#039;corpi mo­<lb></lb>bili per essa<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>26). Fra quelle osservazioni è messa anche questa: <lb></lb>“ Se le materie, stimate più leggere dell&#039;acqua dal vederle galleggiare, ri-<pb xlink:href="020/01/2591.jpg" pagenum="216"></pb>dotte poi in sottilissima polvere, vi discendano: esaminar per mezzo dei corpi <lb></lb>discendenti se nel continuo dell&#039;acqua sia necessario introdurre alcun glu­<lb></lb>tine ” (ivi). Il Viviani aveva scritto a pulito questo registro da una bozza <lb></lb>pure autografa, nella quale alla medesima proposta era data quest&#039;altra forma: <lb></lb>“ Se la sottilissima limatura delle materie, stimate più leggere dell&#039;acqua <lb></lb>dal galleggiare, vi discenda, come fa il sughero e la canna, per mezzo di <lb></lb>materie discendenti: esaminare se nella continuità dell&#039;acqua sia alcun glu­<lb></lb>tine o viscosità, come alcuni hanno creduto ” (ivi, fol. </s>

<s>28). </s></p><p type="main">

<s>La materia, che avrebbero fornito al Dialogo queste esperienze, si com­<lb></lb>prende quanto fosse per riuscire importante, dall&#039;importanza stessa che poi <lb></lb>ebbe nell&#039;Accademia, la quale, sulla proposta del Viviani esaminò altresi la <lb></lb>questione dell&#039;origine delle fonti, che Galileo aveva promossa nell&#039;occasione <lb></lb>di confutar le false dottrine idrostatiche del Bonamici. </s>

<s>Diceva il Peripatetico <lb></lb>che le acque ascendono infino alle più alte cime dei monti, spintevi dalla <lb></lb>gran pressione del mare comunicante con esse per sotterranei canali. </s>

<s>Gali­<lb></lb>leo rispondeva che nei vasi comunicanti, sia l&#039;un grandissimo e l&#039;altro pic­<lb></lb>colissimo, il liquido si fa equilibrio, giunto che sia qua e là al medesimo <lb></lb>livello, e si richiamava, per confermare una tal verità, alle cose, ch&#039;egli aveva <lb></lb>già dimostrate nel suo Discorso intorno alle galleggianti. </s>

<s>Della questione, così <lb></lb>tra i Fisici controversa anche ai tempi del Guglielmini, e che doveva pure <lb></lb>porger materia al dialogo, come Galileo ne aveva data al Viviani intenzione, <lb></lb><figure id="id.020.01.2591.1.jpg" xlink:href="020/01/2591/1.jpg"></figure></s></p><p type="caption">

<s>Figura 76.<lb></lb>ci è rimasta per documento questa nota che dice: “ Aqua <lb></lb>DF (fig. </s>

<s>76) non plus premit quam BE, quod facile de­<lb></lb>monstrari potest quod consonat cum eo, quod a me scri­<lb></lb>ptum est in tractatu <emph type="italics"></emph>De insidentibus aqua,<emph.end type="italics"></emph.end> quod scilicet <lb></lb>magnum pondus ab exigua aqua sustinetur. </s>

<s>Attamen Bo­<lb></lb>namicus, pag. </s>

<s>476, contrarium opinatur: credit nam aquam <lb></lb>maris comprimendo attollere ad montium cacumina aquas, per angustas venas <lb></lb>subterraneas, ad fontes et flumina producenda ” (MSS. Gal., P. III, T. X, <lb></lb>fol. </s>

<s>71). </s></p><p type="main">

<s>Le questioni di fisica, delle quali abbiamo dato fin qui gli esempi, o <lb></lb>erano rimaste indietro, o sovvennero poi a Galileo, nel ripensare al suo di­<lb></lb>scorso <emph type="italics"></emph>Delle cose che stanno in sull&#039;acqua,<emph.end type="italics"></emph.end> ma il <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> che si può <lb></lb>riguardar come un trattato della Fisica generale di que&#039;tempi, offeriva più <lb></lb>largo campo a così fatte fisiche questioni, molte delle quali si trovano accen­<lb></lb>nate nei manoscritti, o rimaste pur esse in dietro, o sovvenute all&#039;Autore <lb></lb>dop&#039;avere scritto e pubblicato il suo libro. </s>

<s>Tale sarebbe la seguente relativa <lb></lb>all&#039;origine delle piogge e delle rugiade: </s></p><p type="main">

<s>“ Essendo che dalla terra si sollevano continuamente esalazioni sottili, <lb></lb>tenui, ascendenti, e intanto portano seco vapori più grossi ed acquei; arri­<lb></lb>vati a una certa altezza, ch&#039;è il termine dell&#039;etere nostro ambiente, e l&#039;aria <lb></lb>purissima, si dilatano e si distendono, e si trattengono o calano abbasso, <lb></lb>doppo essersi fatta una costipazione e spissitudine di questi vapori, e così si <lb></lb>fanno le piogge. </s>

<s>Ma non so in che maniera, quand&#039;è un tempo serenissimo, <pb xlink:href="020/01/2592.jpg" pagenum="217"></pb>chiaro, e&#039;si abbia subitamente a rannuvolare ogni cosa, farsi grande oscu­<lb></lb>rità, e venir milioni di botti d&#039;acqua a basso. </s>

<s>” </s></p><p type="main">

<s>“ Che continuamente si sollevino vapori si fa manifesto in più maniere <lb></lb>poichè, gettando in terra un po&#039;d&#039;acqua e guardando con l&#039;Occhiale, si ved<gap></gap><lb></lb>salir con prestezza un fumo, un vapore, e si fa manifesto nella fiamma, che <lb></lb>continuamente e con gran velocità si vede salire ad alto: e così nei carboni <lb></lb>accesi quel calore va ad alto. </s>

<s>” </s></p><p type="main">

<s>“ Le rugiade non sono altro che vapori, della medesima sorte, e cascan<gap></gap><lb></lb>la notte come abbandonati dal Sole ” (MSS. Gal., P. V, T. IV, fol. </s>

<s>28 a t.) </s></p><p type="main">

<s>Altra questione, relativa a quella trattata nel <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> è la seguente <lb></lb>intorno al rendere la ragione dell&#039;apparire gli astri di grandezza varia sul­<lb></lb>l&#039;orizonte. </s>

<s>Narrammo, nel Cap. </s>

<s>X del secondo nostro Tomo (pag. </s>

<s>397), l<gap></gap><lb></lb>controversie insorte sopra ciò tra i Filosofi, e come il Castelli si riducesse <lb></lb>ad attribuire il fenomeno alla nostra stimativa, che è varia, secondo che la <lb></lb>vista è libera, o s&#039;interpongono tra lei e l&#039;astro corpi, de&#039;quali ci sia nota <lb></lb>la grandezza e la distanza. </s>

<s>Ora è da osservar che così insomma risolvevasi <lb></lb>da Galileo la questione, come apparisce dalla nota così manoscritta: “ Non <lb></lb>si può dir che il Sole o la Luna mi appariscon grandi quanto una frittata <lb></lb>o quanto una torta, o quella cometa mi si rappresenta alla grandezza di un <lb></lb>uomo, poichè queste cose possono rappresentarsi anco alla grandezza del fond<gap></gap><lb></lb>di un tino o di un quattrino, secondo come si terranno questi lontani dal­<lb></lb>l&#039;occhio, tra esso e altri oggetti ” (ivi, fol. </s>

<s>29). </s></p><p type="main">

<s>L&#039;incontro fra il pensiero di Galileo e del Castelli gioverebbe ricerca<gap></gap><lb></lb>se fu inconsapevole e fortuito o, essendoselo insieme comunicato, a chi prim<gap></gap><lb></lb>di loro fosse sovvenuto, non sempre verificandosi il detto che il maestro sta <lb></lb>sopra al discepolo, come, per non rammemorare altri esempi, si vede essere <lb></lb>avvenuto rispetto al “ problema, perchè l&#039;acqua, nel zampillare all&#039;in su, s<gap></gap><lb></lb>separa nelle parti alte, dove il moto e<gap></gap> più lento ” (MSS. Gal., P. VI, T. II. <lb></lb>fol. </s>

<s>13). La soluzione è data nel primo libro <emph type="italics"></emph>Della misura delle acque cor­<lb></lb>renti<emph.end type="italics"></emph.end> (Bologna 1660, pag. </s>

<s>29), come corollario della proposizione ivi dimo­<lb></lb>strata, che cioè le sezioni stanno in ragion reciproca delle velocità. </s>

<s>E benchè <lb></lb>nel citato luogo autografo, Galileo non risponda a parole, sembra a noi che <lb></lb>rispondano i numeri, lungo la linea sottosignati, i quali numeri sono scritti <lb></lb>a mostrare i decrementi della velocità dello zampillo quanto giunge più alto<gap></gap><lb></lb>e il reciproco accrescimento delle sezioni, per cui si separano dalla parte di <lb></lb>sopra le particelle dell&#039;acqua, che di sotto andavano unite. </s>

<s>Sarebbe questa <lb></lb>nota, scritta così frettolosamente, documento importantissimo per coloro, i <lb></lb>quali pretendono che il principio, a cui s&#039;informa il trattato del Castelli, fosse <lb></lb>dovuto a Galileo: ma perchè di ciò avremo nella nostra Storia dell&#039;Idraulica <lb></lb>occasione a più lungo discorso, ritorniamo a quei materiali sparsi, che si ri­<lb></lb>feriscono alle cose trattate nel <emph type="italics"></emph>Saggiatore,<emph.end type="italics"></emph.end> fra le quali alcune riguardan la <lb></lb>luce in sè stessa, e ne&#039;suoi effetti. </s></p><p type="main">

<s>Meritevole di esser meditata, come quella che specchia lucidamente il <lb></lb>pensiero di Galileo intorno all&#039;essenza della luce, è la nota seguente, nella <pb xlink:href="020/01/2593.jpg" pagenum="218"></pb>quale s&#039;applicano al proposito i concetti metafisici, espressi intorno agl&#039;in­<lb></lb>divisibili infiniti nel primo dialogo delle Scienze nuove. </s>

<s>“ Che la luce sia <lb></lb>incorporea ed istantanea si potrebbe dire, poichè, avendo un pugnello di pol­<lb></lb>vere e dandogli fuoco, ella si spande in immenso, e si può vedere com&#039;è <lb></lb>ch&#039;ella sia ridotta a&#039;suoi infiniti indivisibili componenti, e fatta senza intro­<lb></lb>duzione di corpi o di posizione di vacui quanti, ma bene d&#039;infiniti indivisi­<lb></lb>bili vacui, e così non occupa luogo, e non ricerca tempo d&#039;andare da un <lb></lb>luogo a un altro ” (ivi, P. V, T. IV, fol. </s>

<s>28). </s></p><p type="main">

<s>Gli effetti della luce o son considerati nello strumento naturale che è <lb></lb>l&#039;occhio, o nell&#039;artificiale che è il Telescopio, e sovvengono opportune le note <lb></lb>sparse, relative a questo soggetto, per confermare ora gli crrori, ora il buon <lb></lb>senso, piuttosto che la scienza di Galileo. </s>

<s>Errava, quando, nelle postille alla <lb></lb><emph type="italics"></emph>Libra astronomica,<emph.end type="italics"></emph.end> si proponeva di dimostrar contro il Sarsi “ che altri­<lb></lb>menti vede l&#039;occhio di quel che i vetri portano le specie ” (MSS. Cal., P. III, <lb></lb>T. XIII, fol. </s>

<s>14). Il buon senso poi, piuttosto che la scienza delle rifrazioni, <lb></lb>gli facevan cogliere il vero, quando al Peripatetico, che diceva mostrare il <lb></lb>Canocchiale gli oggetti più grandi, col renderli più luminosi, contrapponeva <lb></lb>che “ se il medesimo oggetto ha da esser veduto sotto maggior angolo, bi­<lb></lb>sogna che il suo lume e raggi si disperghino ” (ivi). Che, se nel discorso <lb></lb>del Sarsi fosse stato verità, soggiungeva Galileo, “ gli oggetti, veduti con tra­<lb></lb>guardi di mano in mano più acuti, siccome appariscon maggiori, così dove­<lb></lb>riano apparir più lucidi, ma accade tutto l&#039;opposito ” (ivi). </s></p><p type="main">

<s>Si riferisce a questo argomento un&#039;altra nota autografa, nella quale Ga­<lb></lb>lileo proponevasi di dimostrar contro il medesimo Sarsi “ che i raggi visivi <lb></lb>camminano sempre per linee rette, e non mai per curve, dal qual principio <lb></lb>immediatamente si conclude gli oggetti visivi, in tutte le distanze quanto si <lb></lb>voglia diseguali, essere dal medesimo Telescopio sempre, secondo la mede­<lb></lb>sima proporzione, moltiplicati. </s>

<s>“ Imperocchè intendansi due raggi visivi pro­<lb></lb><figure id="id.020.01.2593.1.jpg" xlink:href="020/01/2593/1.jpg"></figure></s></p><p type="caption">

<s>Figura 77.<lb></lb>cedenti dall&#039;occhio libero, secondo le rette linee AG, <lb></lb>BH (fig. </s>

<s>77), tra le quali in diverse distanze siano <lb></lb>gli oggetti visivi AB, CD, EF, GII, li quali all&#039;occhio <lb></lb>appariranno in grandezza uguali, essendo veduti sotto <lb></lb>il medesimo angolo. </s>

<s>Intendasi poi per mezzo di un <lb></lb>Telescopio aggrandito l&#039;oggetto AB sino alla gran­<lb></lb>dezza IK, e i raggi, che vengono dal Telescopio ai <lb></lb>termini JK, s&#039;intendino prolungati secondo le linee <lb></lb>rette IP, KQ, sino alle quali si prolunghino le CD, <lb></lb>EF, GII, terminandole ne&#039;punti LM, NO, PQ, ne&#039;quali <lb></lb>punti veramente verrebbero a terminare, quando dal <lb></lb>Telescopio fossero ingrandite tutte secondo la me­<lb></lb>desima proporzione. </s>

<s>Ma, quando gli oggetti più remoti <lb></lb>fossero di mano in mano ingranditi meno, i termini delle medesime linee <lb></lb>ingranditi caderebbero dentro alle linee IP, KQ, conforme ai punti R, S; <lb></lb>T, U; X, Y ” (MSS. Gal., P. III, T. XI, fol. </s>

<s>21). </s></p><pb xlink:href="020/01/2594.jpg" pagenum="219"></pb><p type="main">

<s>Si conferma da questa proposizione, condotta sui principii della Geome­<lb></lb>tria elementare, piuttosto che su quelli propri alle rifrazioni; come Galileo, <lb></lb>nemmen negli ultimi anni della sua vita, conobbe le teorie diottriche del Ca­<lb></lb>nocchiale, cosicchè non rimane a lui altro merito, in ordine allo strumento, <lb></lb>che di averlo applicato a veder distintamente gli oggetti grandi lontani, e i <lb></lb>piccoli sotto gli occhi. </s>

<s>Quest&#039;uso fatto del Microscopio, ma più specialmente <lb></lb>del Telescopio, è tanto noto, che il volgo stesso ne sa la storia, ma non sanno <lb></lb>forse, nemmeno i più informati declamatori del grand&#039;Uomo, quel che noi <lb></lb>altrove accennammo, e che verrebbe ad accrescergli non poco questa parte <lb></lb>del merito, che cioè egli applicò il Canocchiale anche agli usi della fotome­<lb></lb>tria. </s>

<s>Nella Lettera sul candore lunare apparisce una tale applicazion manife­<lb></lb>sta, ma in quegli ultimi anni della sua vita descriveva Galileo stesso al Vi­<lb></lb>viani la composizione del Fotometro più squisito, il primo concetto del quale <lb></lb>può vedersi espresso in questa nota: “ Drizzando due cannoni, uno verso la <lb></lb>Luna quasi piena, e l&#039;altro verso l&#039;occidente, subito dopo il tramontar del <lb></lb>Sole, e ricevendo sopra due carte il lume della Luna, e quello dell&#039;aria pros­<lb></lb>sima al corpo solare, si potrà vedere quanto il lume dell&#039;aria si mostri più <lb></lb>chiaro di quel della Luna, e, secondo che il Sole si andrà abbassando, s&#039;in­<lb></lb>contreranno due lumi, della Luna e del crepuscolo, egualmente chiari ” <lb></lb>(MSS. Gal., P. III, T. X, fol. </s>

<s>75). </s></p><p type="main">

<s>Non sempre però le questioni, che si agitavano per la mente di Gali­<lb></lb>leo, erano intorno alle cose discorse ne&#039;suoi propri libri, ma talvolta entra­<lb></lb>vano nel campo altrui, come per esempio in quello del Gilberto, il pensier <lb></lb>del quale, fecondo della scienza del secolo XIX, e secondo il quale le attra­<lb></lb>zioni elettriche e le magnetiche si riducevano al medesimo principio, sem­<lb></lb>brava una stoltezza al giudizio dello stesso Galileo. </s>

<s>“ Dicere quod attractio <lb></lb>magnetis et electri sint principio simili, est idem ac dicere pinnam, dum a <lb></lb>vento agitur, ab eodem moveri principio ac avis, dum proprio nisu volat ” <lb></lb>(ivi, P. V, T. IV, fol. </s>

<s>15). </s></p><p type="main">

<s>Altre volte le proposte questioni non son risolute, cosicchè si rimangono <lb></lb>allo stato di una semplice descrizione sperimentale, e Galileo perciò si con­<lb></lb>tenta di osservare il semplice fatto, senza dirne le cause, perch&#039;egli ancora <lb></lb>non le comprende. </s>

<s>Tali sarebbero per esempio quelle relative alla pressione <lb></lb>ammosferica, e al vacuo lasciato dietro a sè nel muoversi i corpi velocissi­<lb></lb>mamente in mezzo all&#039;aria, nella notizia delle quali cause era riposta la <lb></lb><figure id="id.020.01.2594.1.jpg" xlink:href="020/01/2594/1.jpg"></figure></s></p><p type="caption">

<s>Figura 78.<lb></lb>scienza dei fatti seguenti: “ Accostando un dito o <lb></lb>mano alla fiamma o lume di candela o lucerna la­<lb></lb>teralmente, e distaccandola con velocità, la fiamma <lb></lb>ancora con gran velocità ti vien dietro lambendo <lb></lb>la mano ” (ivi, fol. </s>

<s>28). Sia AB (fig. </s>

<s>78) sifone, e <lb></lb>dalla bocca A mettasi tanta acqua, che empia la <lb></lb>parte AC: poi, turando con un dito la bocca A, l&#039;acqua AC non scorrerà <lb></lb>mai nell&#039;altra parte CB, in qualsivoglia modo io tenga il sifone, finchè io non <lb></lb>levo il dito ” (ivi, fol. </s>

<s>29). </s></p><pb xlink:href="020/01/2595.jpg" pagenum="220"></pb><p type="main">

<s>Tali essendo, nella loro più variata varietà le materie da inserirsi nei <lb></lb>Dialoghi nuovissimi, potrebbe sembrar difficile il comporle insieme in unità, <lb></lb>ma era stata giusto da Galileo scelta una tale forma di colloquio, non solo <lb></lb>per una imitazion platonica come si dice, ma principalmente perchè, come <lb></lb>egli stesso scriveva in una lettera al Carcavy (Viviani, Scienza delle propor­<lb></lb>zioni cit., pag. </s>

<s>80), quella maniera dello scrivere in dialogo gli porgeva assai <lb></lb>conveniente attacco, per inserirvi i pensieri, che via via gli cascavano in <lb></lb>mente. </s>

<s>L&#039;artificio usato in tessere quella ghirlanda così varia, che è il primo <lb></lb>dialogo delle Scienze nuove, de&#039;fiori rinascenti via via, era quello stesso che <lb></lb>doveva usarsi, in tessere questi ultimi dialoghi de&#039;fiori rimasti sparsi per <lb></lb>terra, cadutivi dal troppo colmo canestro. </s>

<s>È anzi da osservar che son nate <lb></lb>a questo modo quasi tutte le scritture di Galileo, le quali possono perciò dirsi <lb></lb>una rapsodia de&#039;pensieri, scritti sul primo foglio che capitavagli a mano, <lb></lb>prima che altro occorresse ad attutarne quel subitaneo fervore. </s>

<s>Di que&#039;fogli <lb></lb>sparsi si compongono infatti, per la massima parte, i manoscritti, che ci son <lb></lb>rimasti di lui, da&#039;quali ricopiava e puliva, e metteva in ordine i libri da <lb></lb>stamparsi. </s></p><p type="main">

<s>Che poi fosse questo modo di fare un abito contratto apparisce dal ve­<lb></lb>derlo praticato a qualunque occasione, si trattasse di scienza o di rettorica; <lb></lb>delle speculazioni della mente o delle deliberazioni dell&#039;animo; della pelle­<lb></lb>grinità del concetto o della eleganza della forma. </s>

<s>Occorrendogli, nelle con­<lb></lb>tinue controversie, di dover descrivere l&#039;indole dei Peripatetici, aveva lavo­<lb></lb>rato a parte, e teneva in serbo questa specie di apologo: “ Sembrano i <lb></lb>Peripatetici, verso Aristotile, quel vetturale, il quale, vedendo pendere la soma <lb></lb>delle mercanzie mal compartite da una banda, corre a librarla con una grave <lb></lb>pietra aggiunta dall&#039;altra, quindi di poco, cominciando a declinare dal lato <lb></lb>dove aggiunse il sasso, il qual di nuovo eccedendo in gravità, fa por nuove <lb></lb>pietre all&#039;incontro: nè trovando il poco giudizio del mulattiere il giusto equi­<lb></lb>librio, finalmente, con l&#039;aggiunger molti pesi sopra pesi, fa che il povero <lb></lb>animale si fiacca le gambe, e resta sotto l&#039;inegual soma oppresso. </s>

<s>Meglio <lb></lb>da principio cominciare a levar via della roba soverchia ” (MSS. Gal., P. III, <lb></lb>T. X, fol. </s>

<s>72). </s></p><p type="main">

<s>Que&#039;Teologi, i quali inopportunamente s&#039;ingerivano della scienza umana, <lb></lb>pensava Galileo che si potevano pungere con questo discorso: “ Ancorchè i <lb></lb>sacri Teologi siano quelli, che intendono meglio come camminano i moti del <lb></lb>Sole e delle altre stelle, che non lo sanno gli Astronomi; tuttavia, per rego­<lb></lb>lare i tempi della Pasqua e delle altre feste mobili, ricorrono, anzi si rimet­<lb></lb>tono agli Astronomi. </s>

<s>Ma perchè non regolarsi con la loro sopraeminente <lb></lb>intelligenza? </s>

<s>” (ivi, P. V, T. IV, fol. </s>

<s>15). Altri di così fatti aculei teneva <lb></lb>preparati, in ripensare alle irragionevolezze degli aristotelici, e alle loro con­<lb></lb>tradizioni. </s>

<s>“ Gli avversari tassano me, per avere scritto contro ad autore non <lb></lb>inteso da me: eppure essi medesimi cascano in questo medesimo errore, men­<lb></lb>tre contradicono a me, e tanto più gravemente, quanto è dubbio se sia vero <lb></lb>che io non abbia inteso Aristotile. </s>

<s>E non so, se lui fosse vivo, se ei mi ne-<pb xlink:href="020/01/2596.jpg" pagenum="221"></pb>gasse le mie interpetrazioni. </s>

<s>Ma io che vivo dico bene di non essere stato <lb></lb>inteso. </s>

<s>Se poi per mia colpa o di loro, questo non determinerò io. </s>

<s>Potriano <lb></lb>forse dire non mi avere inteso, perchè non metteva conto a porre studio <lb></lb>nelle cose mie, ed affaticarvisi come in quelle di Aristotile, ma io gli rispon­<lb></lb>derò che, se non metteva conto lo studiare le cose mie, meno metteva conto <lb></lb>l&#039;impugnarle ” (ivi, P. III, T. X, fol. </s>

<s>75). </s></p><p type="main">

<s>All&#039;ufficio poi di diffondere le verità della scienza, senza curarsi de&#039;suoi <lb></lb>contradittori, si sentiva Galileo generosamente eccitato da questo pensiero: <lb></lb>“ Se io doverò leggere in Studio, piccolo frutto si caverà dalle mie fatiche, <lb></lb>occupandomi con pochi in cose minime. </s>

<s>Ma se io scriverò al mondo tutto, <lb></lb>maggior gloria a me, et utilità a quello arrecherò ” (ivi, P. III, T. III, fol. </s>

<s>35). <lb></lb>E mentre il Carcavy era per metter mano alla stampa di tutte le opere sue <lb></lb>(Viviani, Scienza delle proporz. </s>

<s>cit., pag. </s>

<s>81), voleva s&#039;imprimesse sul fron­<lb></lb>tespizio queste parole, benchè nessun altro poi de&#039;successivi editori leggesse <lb></lb>o intendesse, o comunque sia mettesse in esecuzione il testamento: <emph type="italics"></emph>“ Da <lb></lb>porsi nel titolo del libro di tutte le Opere:<emph.end type="italics"></emph.end> Di qui si comprenderà in infi­<lb></lb>niti esempi qual sia l&#039;utilità delle Matematiche in concludere circa alle pro­<lb></lb>posizioni naturali, e quanto sia impossibile il poter bene filosofare, senza la <lb></lb>scorta della Geometria, conforme al vero pronunciato di Platone ” (ivi, P. III, <lb></lb>T. III, fol. </s>

<s>63 a tergo). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Oltre ai Problemi fisici, scriveva Galileo al Carcavy di averne a portare <lb></lb>in dialogo dei matematici. </s>

<s>Ora, a questo annunzio, furono le nostre diligenze <lb></lb>rivolte a cercar quali fossero, e dove potessero ritrovarsi i nuovi materiali <lb></lb>dispersi, e rimasti fuori di luogo nelle altre costruzioni. </s>

<s>In mezzo a tali sol­<lb></lb>lecitudini ci venne fatto di fermar l&#039;attenzione sul quarto tomo della parte V <lb></lb>dei manoscritti galileiani, dove ricorrono qua e là, interpolati da note di ar­<lb></lb>gomento diverso, teoremi e problemi di Geometria, i quali, benchè tutti ele­<lb></lb>mentarissimi, ci parve nulladimeno che dalla novità, e più che altro dalla <lb></lb>fama dell&#039;Autore, partecipassero qualche importanza. </s>

<s>Non son più che quin­<lb></lb>dici o sedici, ed essendo scritti dal Viviani, in quella sua ben distinta calli­<lb></lb>grafia giovanile, possiamo ragionevolmente credere che gli fossero dettati da <lb></lb>Galileo, quando cieco era costretto di rappresentarsi nella mobilità delle im­<lb></lb>magini le figure illustrative. </s>

<s>Sarebbero di ciò indizio le dimostrazioni spesso <lb></lb>spesso confuse e qualche volta sbagliate, che ci occorreranno a notare, ma in­<lb></lb>tanto si pensava fra noi che di simili teoremi ne doveva essere rimasti addie­<lb></lb>tro parecchi altri, e forse di maggiore importanza, occorsi allo stesso Galileo, <lb></lb>mentre cercava i lemmi geometrici alle sue laboriose dimostrazioni delle re­<lb></lb>ristenze dei solidi, e dei moti locali. </s>

<s>Qualche esempio, in cui ci abbattemmo <lb></lb>nell&#039;ordinare i libri dei moti accelerati, avvalorava quelle nostre congetture, <pb xlink:href="020/01/2597.jpg" pagenum="222"></pb>dalle quali poi ne conseguì la raccolta de&#039;teoremi di Algebra e di Geome­<lb></lb>tria, che daremo, come parte principalissima di quelle cose matematiche, che <lb></lb>Galileo intendeva di ridurre in dialogo, affinchè non si dovessero, con detri­<lb></lb>mento della sua gloria e della utilità degli studiosi, rimaner nell&#039;oblio. </s></p><p type="main">

<s>Essendo le nuove questioni però molto più spezzate delle fisiche e delle <lb></lb>meccaniche, pareva assai più difficile a ridurle in unità di composizione: e <lb></lb>mentre si pensava fra noi che, a superare la difficoltà avrebbe Galileo forse <lb></lb>usato il medesimo artifizio, che nella seconda, nella terza e nella quarta <lb></lb>giornata delle Scienze nuove, introducendo cioè il Salviati, che sopra alcuni <lb></lb>fogli dell&#039;Accademico legge al Sagredo e a Simplicio le varie proposizioni, <lb></lb>attenenti a que&#039;matematici soggetti; vedemmo l&#039;opinione ridursi quasi a cer­<lb></lb>tezza da un frammento di scrittura, ritrovata da noi in certe carte tanto <lb></lb>informi e disordinate, ne&#039;margini e addentro così corrose e macere dalla <lb></lb>muffa, che il Bonaventuri non seppe cavarci alcun costrutto, benchè il Pan­<lb></lb>zanini l&#039;assicurasse esser quelle tutte robe galileiane, scritte da suo zio Vin­<lb></lb>cenzio Viviani. </s>

<s>Sopr&#039;una di quelle pagine, dove si può in qualche modo in­<lb></lb>cominciare a leggerla, o diciam meglio a intenderne il significato, è scritto: </s></p><p type="main">

<s>“ SIMPLICIO. — Io non ho altra notizia di Geometria, da quella in fuori <lb></lb>che imparai essendo giovane studente sopra i libri degli Elementi di Euclide, <lb></lb>per cui temo che le cose scritte in cotesto libriccino dell&#039;Accademico, e che <lb></lb>voi, signor Salviati, volete leggerei, mi siano per riuscire di troppo difficile <lb></lb>intelligenza. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Non dubitate, signor Simplicio, di averei a trovare mag­<lb></lb>giore oscurità, che nelle dimostrazioni e discorsi intorno ai moti locali: e se <lb></lb>voi avete bene a mente Euclide vi basta, perchè possiate gustare il dolce di <lb></lb>queste vivande rimaste indietro alla mensa, come l&#039;Accademico stesso si <lb></lb>esprimeva, imbandita dai Matematici antichi nei loro trattati. </s>

<s>Se qualche cosa <lb></lb>de&#039;principii elementari vi fosse caduta col tempo dalla memoria, non man­<lb></lb>cherà di ridurvela la destrezza del signor Sagredo, che, per grande desiderio <lb></lb>di penetrare addentro ai teoremi dimostrati dal nostro Amico, s&#039;è reso fa­<lb></lb>miliari i libri, non d&#039;Euclide solo, ma di Archimede, di Apollonio e di <lb></lb>Pappo. </s>

<s>” </s></p><p type="main">

<s>La nostra Storia fa riflettere così la sua luce sopra questo frammento, <lb></lb>da non si dubitare ch&#039;egli propriamente non appartenesse a quel dialogo, in <lb></lb>cui Galileo intendeva di ridurre i Problemi matematici, e si può intendere, <lb></lb>da quel che ivi si dice, che nella raccolta matematica fatta dal Viviani a det­<lb></lb>tatura in Arcetri, ora mancano le dimostrazioni e le soluzioni, e ora vi sono <lb></lb>semplicemente accennate, perchè il Sagredo v&#039;avrebbe poi supplito, nell&#039;atto <lb></lb>di farne a Simplicio la spiegazione. </s>

<s>A noi però non riman dell&#039;opera che i <lb></lb>materiali sparsi, ma preparati dall&#039;Autore stesso per costruirla: ond&#039;è che, <lb></lb>non potendo consolar d&#039;altro i Lettori, porremo sotto ai loro occhi que&#039;ma­<lb></lb>teriali stessi, de&#039;quali faremo primi i teoremi di Geometria raccolti dal Vi­<lb></lb>viani. </s>

<s>Essendo nel manoscritto sopra indicato messi alla rinfusa, per non aver <lb></lb>gli uni dipendenza alcuna dagli altri, non si potrebbero annoverar con altr&#039;or-<pb xlink:href="020/01/2598.jpg" pagenum="223"></pb>dine, da quello assiomatico in fuori, cominciando cioè dalle linee, per pas­<lb></lb>sare alle superficie, e di lì ai solidi. </s>

<s>Così dunque faremo, non dimenticando <lb></lb>che l&#039;ufficio nostro è di storici, no di editori, e le dimostrazioni si aggiun­<lb></lb>gono, o si dichiarano in forma di note, non perchè crediamo che, in cose <lb></lb>tanto elementari, i Lettori ne abbiano bisogno, ma per dar qualche idea della <lb></lb>parte che, rappresentandosi il Dramma, Galileo avrebbe affidata al Sagredo. </s></p><p type="main">

<s>“ PROPOSITIO I, THEOREMA I. — <emph type="italics"></emph>In linea AF<emph.end type="italics"></emph.end> (fig. </s>

<s>79) <emph type="italics"></emph>moveantur duo<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2598.1.jpg" xlink:href="020/01/2598/1.jpg"></figure></s></p><p type="caption">

<s>Figura 79.<lb></lb><emph type="italics"></emph>mobilia A, B, unumquodque ubique <lb></lb>velociter: A vero moveatur velocius <lb></lb>quam B, et quam rationem habet <lb></lb>velocitas A, ad velocitatem B, hanc <lb></lb>habeat AC linea ad CB. </s>

<s>Dico codem <lb></lb>tempore puncta A, B, si moveantur versus C, punctum C conseculura <lb></lb>esse. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nisi enim A, B non convenerint in C, convenient primo, si potest fieri, <lb></lb>infra, in E. </s>

<s>Et quia velocitates sunt inter se ut spatia, per quae eodem tem­<lb></lb>poris intervallo moventur mobilia; ergo velocitas A, ad velocitatem B, erit <lb></lb>ut spatium AE ad spatium BE. </s>

<s>Erat autem et ut AC ad CB, quod est im­<lb></lb>possibile. </s>

<s>” </s></p><p type="main">

<s>“ Similiter ostendetur quod neque supra numquam convenient. </s>

<s>” </s></p><p type="main">

<s>“ Sed melius: Si quando A pervenerit in C, B non eo pervenit, aut <lb></lb>supra aut infra perveniet, ut in E, aut F. </s>

<s>Eodem ergo tempore, quo A tran­<lb></lb>sivit spatium AC, B transivit BE, aut BF: ergo velocitates.... ergo A, B <lb></lb>convenient in C ” (MSS. Gal., P. V, T. IV, fol. </s>

<s>22). </s></p><p type="main">

<s>Nel luogo, corrispondente a quello da noi punteggiato, il margine è cor­<lb></lb>roso, ma non è difficile il supplire alle parole ivi scritte, che dovevano esser <lb></lb>queste o simili: <emph type="italics"></emph>erunt ut AC ad BE, vel BF, contra propositum,<emph.end type="italics"></emph.end> cosicchè <lb></lb>nella sua integrità la conclusione sarebbe tale: “ ergo velocitates erunt ut <lb></lb>AC ad BE, vel BF, contra propositum: ergo A, B convenient in C. ” </s></p><p type="main">

<s>Il teorema si potrebbe dire un corollario, o forse meglio una trasforma­<lb></lb>zione del IIo Dei moti equabili (Alb. </s>

<s>XIII, 151), sicchè partecipa del mecca­<lb></lb>nico, come ne partecipa il seguente, a cui si riferiscono queste notizie: In <lb></lb>una lettera del dì 6 Febbraio 1635 così il Cavalieri mandava a dire a Ga­<lb></lb>lileo da Bologna: “ Io scrissi già in una mia a V. S. E. un quesito mec­<lb></lb>canico, ma perchè non me ne dice cosa alcuna, temo che la lettera non si <lb></lb>sia smarrita. </s>

<s>Il quesito era questo: Data una ruota volubile intorno al suo <lb></lb>asse, trovar modo di moverla con un&#039;altra ruota, pur volubile intorno al <lb></lb>proprio asse, in tal maniera che, perseverando la medesima velocità della <lb></lb>ruota movente, la ruota mossa vada sempre crescendo di velocità. </s>

<s>Io pensai <lb></lb>che ciò non potesse farsi con le ruote solite dentate, nè con le funi avvol­<lb></lb>tele intorno, camminando ambedue con pari velocità, ed anco con pari cir­<lb></lb>colazioni, quando sono di diametro uguale: ovvero con pari velocità e con <lb></lb>dispari circolazioni, cioè conforme alla reciproca proporzione de&#039;diametri, <lb></lb>quando questi sono diseguali. </s>

<s>E perciò venni in questo parere che bisognasse <pb xlink:href="020/01/2599.jpg" pagenum="224"></pb>fare una cosa tale, quale fanno qua a Bologna in particolare questi, che tra­<lb></lb>filano l&#039;argento falso ” (Campori, Carteggio gal., Modena 1881, pag. </s>

<s>430). </s></p><p type="main">

<s>Galileo, per rispondere al quesito, preparò una serie di proposizioni re­<lb></lb>lative al moto delle ruote, mosse da altre ruote, e delle quali non ci è ri­<lb></lb>masto memoria che della seguente, annunziata già dallo stesso Cavalieri: </s></p><p type="main">

<s>“ PROPOSITIO II, THEOREMA II. — <emph type="italics"></emph>Le circonferenze di due ruote disu­<lb></lb>guali, che girino, vanno con la medesima velocità, quando le circolazioni <lb></lb>hanno reciproca proporzione dei diametri ”<emph.end type="italics"></emph.end> (MSS. Gal., P. V, T. IV, <lb></lb>fol. </s>

<s>29. </s></p><p type="main">

<s>Il teorema, a cui manca la dimostrazione, può formularsi più chiara­<lb></lb>mente così: <emph type="italics"></emph>Due ruote di differente raggio vanno ugualmente veloci, quando <lb></lb>i numeri dei giri, fatti dall&#039;una e dall&#039;altra nel medesimo tempo, son <lb></lb>reciprocamente proporzionali alle lunghezze dei raggi.<emph.end type="italics"></emph.end> Le velocità saranno <lb></lb>uguali, quando ne&#039;medesimi tempi gli spazi sono uguali. </s>

<s>Ora, chiamati R, <emph type="italics"></emph>r<emph.end type="italics"></emph.end><lb></lb>i raggi della ruota maggiore e della minore, gli spazi percorsi nelle loro cir­<lb></lb>colazioni sono 2<foreign lang="grc">π</foreign>R, 2<foreign lang="grc">π</foreign><emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Sia N il numero, per cui, moltiplicato 2<foreign lang="grc">π</foreign><emph type="italics"></emph>r,<emph.end type="italics"></emph.end> si <lb></lb>rende uguale a 2<foreign lang="grc">π</foreign>R: avremo 1:N=<emph type="italics"></emph>r<emph.end type="italics"></emph.end>:R. </s>

<s>Ma se uno è il numero dei <lb></lb>giri della ruota maggiore, N rappresenta il numero de&#039;giri della minore, dun­<lb></lb>que è vero il teorema. </s></p><p type="main">

<s>La prima proposizione dì Geometria pura, da ordinarsi fra quelle rac­<lb></lb>colte dal Viviani, è tale: Sia il triangolo BAC (fig. </s>

<s>80), la base BC del <lb></lb><figure id="id.020.01.2599.1.jpg" xlink:href="020/01/2599/1.jpg"></figure></s></p><p type="caption">

<s>Figura 80.<lb></lb>quale intendasi prolungata indefini­<lb></lb>tivamente verso K. </s>

<s>Si tirino dal ver­<lb></lb>tice A le linee AF, AK, in modo che, <lb></lb>de&#039;triangoli, i quali vengono esse a <lb></lb>formare col lato AC, e con le inter­<lb></lb>sezioni del prolungamento della base <lb></lb>BC, il primo sia uguale, il secondo <lb></lb>doppio, il terzo triplo ecc. </s>

<s>del trian­<lb></lb>golo BAC. </s>

<s>Se dal mezzo di BC, qual <lb></lb>sia D, si conduce una parallela all&#039;AB e si prolunga, prima fino a incontrare <lb></lb>il lato AF in G, poi il lato AK in H, e via via gli altri nei punti conseguenti <lb></lb>O, P, ecc.; dimostra Galileo che DE:EG=2:1; DE:EH=3:2; DE:EO <lb></lb>=4:3; DE:EP=5:4, e così sempre: ossia, secondo il linguaggio antico, <lb></lb>che DE ad EG, ad HE, ad EO, ad EP, ecc., sta in ragion dupla, sesquialtera, <lb></lb>sesquiterza, sesquiquarta, ecc. </s></p><p type="main">

<s>“ PROPOSITIO III, THEOREMA III. — <emph type="italics"></emph>Sit triangulum ABC, cuius latus <lb></lb>BC infinite extensum ad K: sectaque BC bifariam in puncto D, ducatur <lb></lb>DH aequidistans BA, et constituatur FAC triangulum aequale CAB, cu­<lb></lb>ius latus AF secet DH in G. </s>

<s>Dico lineam DE duplam esse lineae EG. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ducatur EL aequidistans BF: et quia DE aequidistat BA, estque BD <lb></lb>aequalis DC; erit CE aequalis EA. </s>

<s>Sed aequidistat EL ipsi BF, ergo FL ae­<lb></lb>quatur LA, estque triangulum ALE simile triangulo AFC. </s>

<s>Ergo AEL est <lb></lb>quarta pars ipsius ACF et eamdem ob causam EDC erit quarta pars BAC, <pb xlink:href="020/01/2600.jpg" pagenum="225"></pb>et positum est BCA aequale ACF. </s>

<s>Ergo AEL aequatur DEC. </s>

<s>Et quia est ut <lb></lb>FB ad BD ita FA ad AG; erit AG quarta pars ipsius AF et LA dupla AG. </s>

<s><lb></lb>Quare triangulum LAE hoc est DEC, duplum trianguli AEG. </s>

<s>Et est CD linea <lb></lb>aequalis BD; ergo DE est dupla EG. ” </s></p><p type="main">

<s>“ Sed, si constituamus triangulum KAC duplum trianguli BAC, dico <lb></lb>lineam DE sesquialteram esse ipsius EH, quod simili modo ostendetur. </s>

<s>Pro­<lb></lb>ducta enim EM aequidistans BK, quia AEM est quarta pars KAC, et EDC <lb></lb>quarta pars CAB, estque ACK duplum BCA; erit MEA duplum DCE, et tri­<lb></lb>plum AEH, cum sit AH sexta pars ipsius AK, et tertia dimidiae AM. </s>

<s>Ergo <lb></lb>DCE, cum sit dimidium triplae AEH, erit ipsius AEH sesquialter: hoc est DE <lb></lb>sesquialtera EH. ” </s></p><p type="main">

<s>“ Similiter, si ponamus triangulum triplum BAC, erit DE sesquitertia <lb></lb>lineae consequentis: et, si quadruplum, sesquiquarta: et, si quintuplum, <lb></lb>sesquiquinta, et sic in infinitum. </s>

<s>” </s></p><p type="main">

<s>“ Oppositum huius theorematis facile, per reductionem ad impossibile, <lb></lb>ostendetur ” (ibid., fol. </s>

<s>21). </s></p><p type="main">

<s>“ PROPOSITIO IV, THEOREMA IV. — <emph type="italics"></emph>Dato il triangolo ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>81), <lb></lb><figure id="id.020.01.2600.1.jpg" xlink:href="020/01/2600/1.jpg"></figure></s></p><p type="caption">

<s>Figura 81.<lb></lb><emph type="italics"></emph>siano divisi i due lati AB, AC per mezzo, <lb></lb>nei punti E, D: e dagli angoli C, B tirinsi <lb></lb>le linee CE, BD, e dal punto A la linea <lb></lb>AGF. </s>

<s>Dico che la BC è dirisa per mezzo, e <lb></lb>che le parti GF, GE, GD, ciascuna di loro, <lb></lb>sono la metà dei loro rimanenti pezzi ”<emph.end type="italics"></emph.end><lb></lb>(ivi, fol. </s>

<s>28). </s></p><p type="main">

<s>Questa proposizione è lacile veder come <lb></lb>sia quella stessa, comunemente applicata dai <lb></lb>Matematici, per dimostrare dove stia il centro della gravità nel triangolo, e <lb></lb>Galileo la rende puramente geometrica, e così dimostra le relazioni, che pas­<lb></lb>sano fra le linee e fra le superficie, astraendo dal peso. </s>

<s>La dimostrazione <lb></lb>però non è bella, come quasi sempre riescon quelle condotte dagli assurdi, <lb></lb>ed è a notare, per renderla più chiara, come s&#039;usa le prime due volte la <lb></lb>parola <emph type="italics"></emph>trapezio,<emph.end type="italics"></emph.end> per indicar quello, che propriamente è un <emph type="italics"></emph>quadrilatero.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Della linea divisa in mezzo, così si dimostra: Poichè, se non è divisa <lb></lb>pel mezzo, dividasi nel punto H, e giungasi AH. </s>

<s>E perchè il triangolo BDA <lb></lb>è la metà di tutto, ed ancora il triangolo CEA è la metà di tutto; lascisi il <lb></lb>comun trapezio EGDA: rimarranno i due triangoli EGB, CDG uguali tra <lb></lb>loro, ed uguali saranno tutt&#039;a quattro i triangoli EGB, DGC, AGE, DGA, e <lb></lb>i triangoli AGC, AGB uguali. </s>

<s>Giungasi GH: il trapezio AGHC è uguale al <lb></lb>trapezio ABHG, cioè la metà di tutto il triangolo. </s>

<s>Ma ancora il triangolo AHC <lb></lb>è la metà di tutto, adunque il maggiore al minore sarà uguale. </s>

<s>È dunque <lb></lb>la BC divisa in mezzo nel punto F, e però il triangolo BGC eguale a cia­<lb></lb>scuno dei triangoli BGA. CGA, e le loro metà uguali ancora tra di loro, e <lb></lb>due di loro metà doppie di una: cioè il triangolo AGB doppio del triangolo <lb></lb>GBF: cioè la linea AG doppia della GF ” (ivi). </s></p><pb xlink:href="020/01/2601.jpg" pagenum="226"></pb><p type="main">

<s>“ PROPOSITIO V, PROBLEMA I. — <emph type="italics"></emph>Proponitur linea AB<emph.end type="italics"></emph.end> (fig. </s>

<s>82), <emph type="italics"></emph>in C <lb></lb>secta, cui perpendicularis est DB: circulum possumus describere transeun­<lb></lb>tem per signa A, C, et ipsam DB tangentem. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Dividatur AC bifariam in E, a quo erecta perpendicularis EF, media <lb></lb><figure id="id.020.01.2601.1.jpg" xlink:href="020/01/2601/1.jpg"></figure></s></p><p type="caption">

<s>Figura 82.<lb></lb>proportionalis inter AB, BC, et ab F super DB perpen­<lb></lb>dicularis FG ducatur. </s>

<s>Dico, facto centro F, intervallo FG, <lb></lb>esse petitum ” (ivi, fol. </s>

<s>25). </s></p><p type="main">

<s>La proposta soluzione sarà vera, quando prima di <lb></lb>tutto s&#039;avrà dimostrato che AF, FC, FG sono uguali, e <lb></lb>poi che alla BG competono le proprietà delle tangenti al <lb></lb>cerchio. </s>

<s>Quanto alla prima parte, la verità resulta dalla <lb></lb>seguente serie di equazioni: FC2=EF2+EC2=EF2+ <lb></lb>(EB—CB)2=EF2+EB2—2EB.CB+CB2=AB.BC+EB2— <lb></lb>2EB.CB+CB2=BC(AB+CB—2EB)+EB2. </s>

<s>Ma le quantità dentro <lb></lb>parentesi sono zero, dunque FC2=EB2, e perciò FC=EB=FG. </s>

<s>La verità <lb></lb>della seconda parte della soluzion del problema galileiano si rende manifesta <lb></lb>dall&#039;essere GB uguale alla FE, la quale per supposizione è media fra la se­<lb></lb>cante AB, e la sua parte esterna CB, e perciò, per la XXXVI del terzo di <lb></lb>Euclide, competono alla BG le proprietà delle tangenti il cerchio. <lb></lb><figure id="id.020.01.2601.2.jpg" xlink:href="020/01/2601/2.jpg"></figure></s></p><p type="caption">

<s>Figura 83.</s></p><p type="main">

<s>“ PROPOSITIO VI, THEOREMA V. — <emph type="italics"></emph>Sit sector ABDC<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>83) <emph type="italics"></emph>bifariam sectus in D: iunctis AD, BC constat <lb></lb>sectorem aequari rectangulo contento sub AD et arcu <lb></lb>BD; triangulum vero ABC aequatur rectangulo BEA. <lb></lb>Ergo, si ponatur arcus BF aequalis rectae BE, circuli <lb></lb>portio BDC aequabitur contento sub AE, DF, et con­<lb></lb>tento sub BD, ED ”<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>Abbiamo infatti BDC=AB.BD—BE.AE=(AE+ED)BD— <lb></lb>BE.AE=AE.BD+ED.BD—BE.AE=AE(BD—BE)+ED.BD. <lb></lb>Ond&#039;è che, posto BE=BF, ed essendo BD—BF=DF, si trova esser <lb></lb>vero che BDC è uguale ad AE.DF+ED.BD. </s></p><p type="main">

<s>Accennammo che queste proposizioni geometriche furono dimostrate da <lb></lb>Galileo all&#039;occasione o di studiare nei matematici antichi, o di dimostrare i <lb></lb>varii lemmi per la sua Meccanica, di che abbiamo intanto un esempio nel <lb></lb>seguente problema, nato in mezzo alle ricerche del primo lemma, preparato <lb></lb><figure id="id.020.01.2601.3.jpg" xlink:href="020/01/2601/3.jpg"></figure></s></p><p type="caption">

<s>Figura 84.<lb></lb>in servigio della XXXVI proposizione, scritta nel <lb></lb>terzo Dialogo delle Scienze Nuove. </s></p><p type="main">

<s>“ PROPOSITIO VII, PROBLEMA II. — <emph type="italics"></emph>Appli­<lb></lb>care dalla cima B<emph.end type="italics"></emph.end> (fig. </s>

<s>84) <emph type="italics"></emph>del semicircolo ABC <lb></lb>una linea, come BHG, sicchè la HG sia uguale <lb></lb>alla data LE. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Perchè, giunta KC, sarà BC lato del qua­<lb></lb>drato inscritto nel cerchio, applichisi alla linea <lb></lb>LE un rettangolo eguale al quadrato BC, che ecceda d&#039;una figura quadrata, <lb></lb>e sia questo EML. </s>

<s>E perchè il rettangolo EML è uguale al quadrato BC, <pb xlink:href="020/01/2602.jpg" pagenum="227"></pb>sarà ML minore di BC. </s>

<s>Si tiri dal punto B la BH eguale alla ML, e pro­<lb></lb>lunghisi insino in G: dico, ecc. </s>

<s>” (ivi). </s></p><p type="main">

<s>È stato fatto EM.ML=BC2, e per il detto lemma alla proposi­<lb></lb>zione XXXVI (Alb. </s>

<s>XIII, 214) anche BG.BH=BC2. </s>

<s>Dunque EM.ML= <lb></lb>BG.BH. </s>

<s>Ed essendo BH=ML per costruzione, sarà EM=BG e perciò <lb></lb>HG=LE. </s></p><p type="main">

<s>“ PROPOSITIO VIII, THEOREMA VI. — <emph type="italics"></emph>Exagonus circumscriptus exagoni <lb></lb>inscripti est sesquitertius. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Trigonus circulo circumscriptus duplus est exagoni inscripti: circum­<lb></lb>scripti vero est sesquialterus; quare exagonus circumscriptus exagoni inscripti <lb></lb>est sesquitertius ” (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>Chiamato C l&#039;esagono circoscritto, I l&#039;inscritto, e T il trigono, le due <lb></lb>equazioni T=2I, T=(1+1/2) C danno C:I=4:3. </s></p><p type="main">

<s>“ PROPOSITIO IX, THEOREMA VII. — <emph type="italics"></emph>Quodratum circulo circumscri­<lb></lb>ptum, ad circulum, minorem habet rationem quam circulus ad quadra­<lb></lb>tum inscriptum. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Patet, nam circumscriptum latus ad latus inscripti est, ut latus in­<lb></lb>scripti ad semidiametrum. </s>

<s>Sed quarta pars circumferentiae est maior latere <lb></lb>quadrati inscripti, ergo latus circumscripti, ad quartam partem peripheriae, <lb></lb>minorem habet proportionem quam quarta pars circumferentiae, ad latus <lb></lb>inscripti. </s>

<s>Est autem ut latus circumscripti, ad quartam partem peripheriae, <lb></lb>ita circumscriptum quadratum ad circulum. </s>

<s>Ut autem quarta pars periphe­<lb></lb>riae, ad latus inscripti, ita circulus ad inscriptum, ergo circumscriptum, ad <lb></lb>circulum, minorem habet rationem, quam circulus ad inscriptum ” (ibid., <lb></lb>fol. </s>

<s>28). <lb></lb><figure id="id.020.01.2602.1.jpg" xlink:href="020/01/2602/1.jpg"></figure></s></p><p type="caption">

<s>Figura 85.</s></p><p type="main">

<s>Essendo il quadrato circoscritto doppio all&#039;inscritto, <lb></lb>ossia (fig. </s>

<s>85) CD2=2AB2, avremo CD2:AB2=2:1= <lb></lb>2AO2:AO2=AB2:AO2; onde CD/AB=AB/AO. </s>

<s>Chiamata <lb></lb>Ca.AB l&#039;arco, sarà questa maggiore dell&#039;AB corda e
<lb></lb>perciò CD/(Ca.AB) &lt;AB/AO. </s>

<s>Di qui si potrebbe concluderne <lb></lb>CD/Ca.AB&lt;Ca.AB/AO, ma non si vede la ragione di quell&#039;altra disuguaglianza <lb></lb>conclusa da Galileo CD/Ca.AB&lt;Ca.AB/AB, e ch&#039;egli stesso mette sotto questa <lb></lb>forma: <emph type="italics"></emph>Ergo latus circumscripti, ad quartam partem periferiae, mi­<lb></lb>norem habet proportionem quam quarta pars circumferentiae, ad latus <lb></lb>inscripti.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Essendo inoltre CD:<foreign lang="grc">π</foreign>.AO/2=CD2:<foreign lang="grc">π</foreign>.AO.CD/2=CD2:<foreign lang="grc">π</foreign>.AO2, è <lb></lb>perciò verissimo che <emph type="italics"></emph>ut latus circumscripti ad quartam partem periferiae, <lb></lb>ita circumscriptum quadratum ad circulum,<emph.end type="italics"></emph.end> ma che poi <emph type="italics"></emph>ut quarta pars <lb></lb>periferiae, ad latus inscripti, ita circulus ad inscriptum,<emph.end type="italics"></emph.end> non ci è riu-<pb xlink:href="020/01/2603.jpg" pagenum="228"></pb>scito dimostrarlo: non ci è riuscito di dimostrare cioè come <foreign lang="grc">π</foreign>.AO/2:AB= <lb></lb><foreign lang="grc">π</foreign>.AO2:AB2, perchè essendo <foreign lang="grc">π</foreign>.AO/2:AB=<foreign lang="grc">π</foreign>.AO.AB/2:AB2 bisognerebbe <lb></lb>che fosse AB/2=AO. </s></p><p type="main">

<s>Qualcuno, accecato nella mente da quel bagliore di luce, di che la fama <lb></lb>ha circondato il nome di Galileo, o, come altrimenti si potrebbe dire, per­<lb></lb>duto il senno, non avrà forse difficoltà ad ammettere, persuaso dell&#039;infalli­<lb></lb>bile magistero dell&#039;Uomo divino, che la metà del lato del quadrato inscritto <lb></lb>nel circolo sia uguale al raggio. </s>

<s>Ma noi che siamo avvezzi oramai a farci <lb></lb>colle mani il solecchio, e che possiamo perciò vedere distintamente nella spera <lb></lb>luminosa ogni macchia, crediamo che una di queste fra le più nere consi­<lb></lb>sta nell&#039;essersi per isbaglio attribuito alle linee quel ch&#039;è proprio dei soli <lb></lb>quadrati, essendo veramente il quadrato del raggio uguale alla metà del qua­<lb></lb>drato inscritto. </s></p><p type="main">

<s>Che Galileo abbia veramente commessi sbagli, nelle più sottili questioni <lb></lb>della Meccanica, è stato, nella nuova Storia, dimostrato con tanti esempi, da <lb></lb>doverne rimanere oramai persuaso ognuno, che non abbia ereditata la ca­<lb></lb>parbietà, o, per più vero dire, la dissennatezza dei peripatetici antichi. </s>

<s>Ma <lb></lb>che il grand&#039;Uomo abbia sbagliato, anche in cose riguardanti la Geometria <lb></lb>più elementare, viene ora l&#039;occasione di mostrarlo a coloro, i quali fossero <lb></lb>rimasti o irritati o incerti intorno al giudizio, che del Nostro pronunziava il <lb></lb>Cartesio. </s>

<s>A noi non riesce d&#039;attribuir la sentenza del Filosofo francese, che <lb></lb>diceva esser Galileo poco versato nella Geometria, a rivalità o ad invidia, <lb></lb>dietro i fatti, che abbiamo a rivelare. </s></p><p type="main">

<s>Troviamo che talvolta lo sbaglio è subito riconosciuto, come per esem­<lb></lb>pio in questa proposizione, la quale, non appena Galileo ha pronunziata, che <lb></lb><figure id="id.020.01.2603.1.jpg" xlink:href="020/01/2603/1.jpg"></figure></s></p><p type="caption">

<s>Figura 86.<lb></lb>subito la condanna di falsa. </s>

<s>“ Sit <lb></lb>triangulum rectangulum ABC (figu­<lb></lb>ra 86), et AB sit aequalis BC, et se­<lb></lb>cetur bifariam AC in D, et conne­<lb></lb>ctatur BD, sitque AI ipsi CB parallela, <lb></lb>positaque AE, ipsi AB aequalis, erunt <lb></lb>CA, AE, AD continue proportionales. </s>

<s><lb></lb>Secetur CB bifariam in F, et conne­<lb></lb>ctatur EF. </s>

<s>Dico quod, si protrahatur <lb></lb>quaelibet linea, ex puncto C ad lineam AI, ut puta CGHI, esse proportionales <lb></lb>CI, IG, IH. ” Ma subito la stessa mano di Galileo, che aveva scritto, sog­<lb></lb>giunge: <emph type="italics"></emph>falsa est.<emph.end type="italics"></emph.end> (MSS. Gal., P. V, T. II, fol. </s>

<s>176). </s></p><p type="main">

<s>Talvolta però si trova che, caduto Galileo in errori ancora più pa­<lb></lb>tenti di questo, vi persiste lungamente, senza poter risorgere a proseguire <lb></lb>il cammino. </s>

<s>Riuscirebbe la cosa incredibile a noi stessi, se non ne aves­<lb></lb>simo il documento certissimo nelle carte, non dettate al Viviani, all&#039;Am-<pb xlink:href="020/01/2604.jpg" pagenum="229"></pb>brogetti o ad altri, ma scritte dalla propria mano dell&#039;Autore, con caratteri <lb></lb>così scolpiti, da non valer per scusa il non essersi potuto aiutare dei segni <lb></lb>figurativi. </s></p><p type="main">

<s>Nel quarto teorema degli Elementi Euclide si propone di dimostrare che, <lb></lb>se una linea retta sia comunque segata in due, il quadrato di tutta sarà <lb></lb>uguale ai quadrati delle parti, e al rettangolo contenuto due volte dalle dette <lb></lb>parti. </s>

<s>Galileo, volendo per suo studio confrontare questa proposizione coi nu­<lb></lb>meri, ne traeva un corollario tanto falso, che della falsità si avvedrebbe qua­<lb></lb>lunque scolaretto, a cui si dicesse che la somma de&#039;quadrati delle parti è <lb></lb>uguale al doppio del rettangolo contenuto sopra esse parti. </s>

<s>La cosa, ripetiamo, <lb></lb>ci sembrerebbe incredibile, se non avessimo sotto gli occhi il foglio, sopra <lb></lb>il quale la stessa mano propria di Galileo scrisse queste parole: </s></p><p type="main">

<s>“ Quando si domanda che proportione habbia il minor numero col mag­<lb></lb>giore, si dice un <emph type="italics"></emph>sub,<emph.end type="italics"></emph.end> come 7 a 3, <emph type="italics"></emph>dupla sesquitertia.<emph.end type="italics"></emph.end> Domandato di 3 a 7, <lb></lb>si chiamerà <emph type="italics"></emph>subdupla sesquiterlia. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Per confrontar con i numeri le proportioni del 2° Libro, come della <lb></lb>quarta, si fa a questo modo. </s>

<s>Sia una linea retta, 8 palmi per es., segata in <lb></lb>qualsivoglia modo: v. </s>

<s>g. </s>

<s>che una parte sia 5, e l&#039;altra sia 3. I quadrati della <lb></lb>linea che è 5, e di quella che è 3 sono uguali alli rettangoli contenuti due <lb></lb>volte dalle dette linee, cioè da 5 e 3, e si fa in questa maniera: si raddop­<lb></lb>piano i numeri di questi quadrati in sè stessi, come 5 via 5 fa 25, e 3 via 3 <lb></lb>nove: 25 e 9 fa 34. Così ha da tornare raddoppiandonelo ” (MSS. Gal., P. V, <lb></lb>T. IV, fol. </s>

<s>27). </s></p><p type="main">

<s>Chi crederebbe che Galileo fosse stato capace di scrivere e d&#039;insegnare <lb></lb>sul serio che, raddoppiando il cinque via tre deve tornar trentaquattro, come <lb></lb><figure id="id.020.01.2604.1.jpg" xlink:href="020/01/2604/1.jpg"></figure></s></p><p type="caption">

<s>Figura 87.<lb></lb>conferma del nuovo corollario da soggiun­<lb></lb>gersi dopo la IV del secondo di Euclide <lb></lb>in questa maniera: La somma dei quadrati <lb></lb>delle due parti, in cui sia segata una linea, <lb></lb>o diviso un numero, è uguale al doppio del <lb></lb>rettangolo contenuto, o del prodotto formato <lb></lb>dalle dette parti? </s>

<s>Che il non tornare il conto <lb></lb>del cinque via tre più cinque via tre uguale <lb></lb>a 34, non fosse bastante a persuadere quella <lb></lb>mente divina, che il corollario era falso, <lb></lb>resulta dal vederlo applicato, come una <lb></lb>verità approvatissima in Geometria, a un frammento di proposizione, scritto <lb></lb>in quel carattere così scolpito, che rivela lo stato della più valida virilità di <lb></lb>Galileo. </s></p><p type="main">

<s>Riferendosi alla nostra figura 87, quel frammento è tale: “ ▭ <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> ae­<lb></lb>quatur ▭is <emph type="italics"></emph>bf.fg<emph.end type="italics"></emph.end> et 2 ▭ <emph type="italics"></emph>bfg.<emph.end type="italics"></emph.end>pro ▭ <emph type="italics"></emph>bf<emph.end type="italics"></emph.end> sumatur ▭ <emph type="italics"></emph>hfg,<emph.end type="italics"></emph.end> erit ▭ <emph type="italics"></emph>bg<emph.end type="italics"></emph.end><lb></lb>aequale duobus ▭ <emph type="italics"></emph>bfg,<emph.end type="italics"></emph.end> ▭o <emph type="italics"></emph>bf<emph.end type="italics"></emph.end> idest ▭o <emph type="italics"></emph>hfg<emph.end type="italics"></emph.end> cum ▭ <emph type="italics"></emph>fg,<emph.end type="italics"></emph.end> id autem idem <lb></lb>est ae si dicas ▭ <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> esse aequale 2 ▭ <emph type="italics"></emph>bfg,<emph.end type="italics"></emph.end> 2 ▭ <emph type="italics"></emph>egf<emph.end type="italics"></emph.end> et 2 ▭ <emph type="italics"></emph>fg. </s>

<s>”<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2605.jpg" pagenum="230"></pb><p type="main">

<s>“ ex ▭o <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> demitur 2 ▭ <emph type="italics"></emph>bfg<emph.end type="italics"></emph.end> et 1 ▭ <emph type="italics"></emph>gf,<emph.end type="italics"></emph.end> remanet ▭ <emph type="italics"></emph>bf<emph.end type="italics"></emph.end> aequale <lb></lb>2 ▭ <emph type="italics"></emph>egf<emph.end type="italics"></emph.end> minus 1 ▭ <emph type="italics"></emph>gf,<emph.end type="italics"></emph.end> quod est ▭ <emph type="italics"></emph>hfg<emph.end type="italics"></emph.end> aequale ▭o <emph type="italics"></emph>bf .... ”<emph.end type="italics"></emph.end> (MSS. <lb></lb>Gal., P. V, T. II, a tergo del fol. </s>

<s>54). </s></p><p type="main">

<s>Essendosi dunque concluso BG2=2BFG+2EGF+2FG2, fatta la <lb></lb>indicata sottrazione, avremo BG2—2BFG—FG2=2EGF+FG2, ossia <lb></lb>BF2=2EGF+FG2. </s>

<s>Dunque “ quadratum BF aequale est duobus rectan­<lb></lb>gulis EGF <emph type="italics"></emph>plus,<emph.end type="italics"></emph.end> et non <emph type="italics"></emph>minus<emph.end type="italics"></emph.end> uno quadrato GF ” come dice rimaner dalla <lb></lb>fatta sottrazione Galileo. </s>

<s>Dall&#039;altra parte, procedendo per le vie più spedite, <lb></lb>se BF2=HFG, come si suppone, e se HF=HG+FG=2GE+FG, <lb></lb>abbiamo immediatamente BF2=(2GE+FG)FG, ossia BF2=2EGF+GF2, <lb></lb>e non 2EGF—GF2. </s>

<s>La radice del quale errore consiste nel persistere in <lb></lb>ritener per vero che il quadrato di una delle parti sia uguale al doppio del <lb></lb>rettangolo contenuto da ambedue, meno il quadrato dell&#039;altra parte. </s>

<s>Ciò poi <lb></lb>rende credibile che, nella proposizione ultimamente trascritta, avendo Gali­<lb></lb>leo sotto gli occhi un triangolo rettangolo isoscele, e preoccupato da quel <lb></lb>che solamente è vero nel Teorema pitagorico, mettesse che l&#039;ipotenusa è <lb></lb>doppia o dell&#039;uno o dell&#039;altro uguale cateto. </s>

<s>Fatta la qual digressione, per <lb></lb>secondare il genio di coloro, che amano di giudicare gli uomini, non dal­<lb></lb>l&#039;esteriore apparenza, ma dai loro più intimi affetti e pensieri; liberi di noi <lb></lb>stessi, riduciamoci in via. </s></p><p type="main">

<s>“ PROPOSITIO X, THEOREMA VIII. — <emph type="italics"></emph>Si tres lineae fuerint proportio­<lb></lb>nales, quadratum primae, ad circulum secundae, est ut periferia quadrati <lb></lb>primae, ad periferiam circuli tertiae ”<emph.end type="italics"></emph.end> (MSS., Gal., P. V, T. IV, a tergo <lb></lb>del fol. </s>

<s>23). </s></p><p type="main">

<s>Siano le tre linee A, B, C: essendo per supposizione continue propor­<lb></lb>zionali abbiamo B2=A.C, o anche AB2=A2C, d&#039;onde A2:B2=A:C, <lb></lb>ossia A2:<foreign lang="grc">π</foreign>B2/4=4A:<foreign lang="grc">π</foreign>C, Ma<foreign lang="grc">π</foreign>B2/4 esprime il circolo che ha per diame­<lb></lb><figure id="id.020.01.2605.1.jpg" xlink:href="020/01/2605/1.jpg"></figure></s></p><p type="caption">

<s>Figura 88.<lb></lb>tro B, 4A il perimetro del quadrato A, <foreign lang="grc">π</foreign>C <lb></lb>la periferia del circolo, che ha per dia­<lb></lb>metro C, <emph type="italics"></emph>unde patet propositum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In mezzo allo studio della mirabile <lb></lb>generazione delle spirali occorse a Galileo <lb></lb>un nuovo teorema di Geometria, di cui <lb></lb>ora diremo la qualità e il modo dell&#039;in­<lb></lb>venzione. </s>

<s>Sia il quadrante ABCD (fig. </s>

<s>88), <lb></lb>e tirata la CF parallela ad AD, fatto cen­<lb></lb>tro in C, e col raggio AC, descrivasi il <lb></lb>settore ACF, che è facile vedere come sia <lb></lb>uguale allo stesso quadrante, essendo questo misurato da <foreign lang="grc">π</foreign>AD2/4, e quello da <lb></lb><foreign lang="grc">π</foreign>AC2/8 e AC2=2AD2. </s>

<s>Condotta poi la secante CB, e prolungata infino a <lb></lb>incontrare in E l&#039;arco del settore AF, si serve Pappo alessandrino di questa <pb xlink:href="020/01/2606.jpg" pagenum="231"></pb>costruzione, nel problema VII del IV libro delle sue <emph type="italics"></emph>Collezioni,<emph.end type="italics"></emph.end> per dimostrare <lb></lb>la proporzionalità, che passa fra la quarta parte del circolo massimo della <lb></lb>sfera, e la porzion di spirale in essa sfera descrittta. </s>

<s>Studiando ora Galileo <lb></lb>nel libro del Matematico antico, coi commenti del Commandino, ebbe a fare <lb></lb>un&#039;osservazione, sfuggita a quello stesso eruditissimo commentatore, qual&#039;è <lb></lb>che il quadrante sta all&#039;arco del settore come la porzione BC di quello, in­<lb></lb>tersecata, sta alla porzione FE di questo, terminata dal prolungamento in E <lb></lb>della stessa linea BC intersecante. </s></p><p type="main">

<s>Abbiamo infatti, condotta la DB, e intendendo dire degli angoli, ADC= <lb></lb>ADB+BDC, FCA=ECA+ECF: e pure 2FCA=2ECA+2ECF. </s>

<s>Ma <lb></lb>ADC=2DAC=2FCA, per essere il triangolo ADC isoscele, ed FC pa­<lb></lb>rallela ad AD; dunque ADB+BDC=2ECA+2ECF. </s>

<s>Ma ADB=2ECA, <lb></lb>per la XXa del terzo di Euclide, dunque BDC=2ECF. </s>

<s>Le due equazioni perciò <lb></lb>danno ADC:BDC=FCA:ECF, e permutando ADC:FCA=BDC:ECF. </s>

<s><lb></lb>E perchè gli angoli stanno come gli archi compresi, ABC:AEF=BC:EF, <lb></lb>come conclude Galileo dal suo proprio discorso in questo modo: </s></p><p type="main">

<s>“ PROPOSITIO XI, THEOREMA IX. — <emph type="italics"></emph>Sit quadrans ACD ipsi vero DC <lb></lb>perpendicularis CF, et centro C, spatio CA, describatur circumferentia <lb></lb>AEF, et ducatur contingenter recta EC. </s>

<s>Dico quam rationem habet AF <lb></lb>ad FE, hanc habere ABC ad BC. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Jungatur BD: et quia angulus ADC duplus est anguli ACF, angulus <lb></lb>vero ADB duplus est anguli ACB; erit reliquus BDC reliquo ECF itidem <lb></lb>duplus. </s>

<s>Quare ADC angulus, ad angulum ACF, erit ut BDC angulus ad an­<lb></lb>gulum ECF. </s>

<s>Et permutando ut angulus ADC, ad angulum BDC, hoc est, ut <lb></lb>periferia ABC ad CB periferiam; ita angulus ACF ad angulum ECF: hoc <lb></lb>est periferia AEF ad periferiam EF. </s>

<s>Hanc demonstrationem non novit Coman­<lb></lb>dinus in XXXa quarti Pappi ” (MSS. Gal., P. V, T. IV, a tergo del fol. </s>

<s>25). </s></p><p type="main">

<s>“ PROPOSITIO XII, THEOREMA X. — <emph type="italics"></emph>Venduntur quaedam cartae cosmo­<lb></lb>graficae ex pluribus triangulis, quibus abscissis, possunt ipsae sphaeris <lb></lb>adaptari. </s>

<s>Trianguli vero abscissi, ad id quod reliquum est, eam habent <lb></lb>proportionem, quam habet sphaerae diameter ad excessum, quo dimidia <lb></lb>circumferentia circuli maximi excedit dictam diametrum. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nam cylindri circa sphaeram superficies, exceptis basibus, aequatur <lb></lb>superficiei sphaerae. </s>

<s>Dicta autem carta est superficies cylindri, circa sphae­<lb></lb>ram, habentis altitudinem aequalem dimidio sphaerae circumferentiae. </s>

<s>Quod, <lb></lb>si haberet altitudinem aequalem sphaerae diametro, aequaretur illius super­<lb></lb>ficiei. </s>

<s>Ex quo patet quod dicta carta excedit sphaerae superficiem secundum <lb></lb><figure id="id.020.01.2606.1.jpg" xlink:href="020/01/2606/1.jpg"></figure></s></p><p type="caption">

<s>Figura 89.<lb></lb>proportionem, quam habet dimidia circumfe­<lb></lb>rentia ad diametrum ” (ibid., fol. </s>

<s>24). </s></p><p type="main">

<s>Sia ACB (fig. </s>

<s>89) la mezza circonferenza, <lb></lb>DF uguale al diametro, e GF uguale in retti­<lb></lb>tudine alla stessa mezza circonferenza. </s>

<s>Rivol­<lb></lb>gendosi la figura tutt&#039;intorno all&#039;asse HI, il <lb></lb>mezzo cerchio descriverà una sfera, il rettangolo DB un cilindro, l&#039;esterna <pb xlink:href="020/01/2607.jpg" pagenum="232"></pb>superficie S del quale uguaglierà quella della sfera, o dei triangoli ascissi. </s>

<s>Il <lb></lb>rettangolo GI poi genererà un cilindro, la superficie esterna del quale, che <lb></lb>chiameremo S′, sarà uguale alla superficie della carta, e avremo S′= <lb></lb>2<foreign lang="grc">π</foreign>.EB.GF, S=2<foreign lang="grc">π</foreign>EB.AB, d&#039;onde S′/S=GF/AB, che vuol dire appunto <lb></lb>che la carta eccede la superficie della sfera secondo la proporzione della <lb></lb>mezza circonferenza al diametro. </s></p><p type="main">

<s>“ PROPOSITIO XIII, THEOREMA XI. — <emph type="italics"></emph>Cuiuscumque cylindri superficies, <lb></lb>exceptis basibus, sive cum basibus, minor est quam dupla superficici coni <lb></lb>in ipso descripti, excepta, sive cum basc. </s>

<s>E contra vero quorumdam co-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2607.1.jpg" xlink:href="020/01/2607/1.jpg"></figure></s></p><p type="caption">

<s>Figura 90.<lb></lb><emph type="italics"></emph>norum in cylindris inscriptorum superficies, excepta base, <lb></lb>maior est quam dupla superficiei cylindri, exceptis ba­<lb></lb>sibus ”<emph.end type="italics"></emph.end> (ibid.). </s></p><p type="main">

<s>La prima parte della proposizione si dimostra facil­<lb></lb>mente vera dal considerare il cilindro generato dal ret­<lb></lb>tangolo KI (fig. </s>

<s>90), e il cono dal triangolo BIH, mentre <lb></lb>ambedue le figure si rivolgono attorno al loro comune <lb></lb>asse HI. Imperocchè, chiamata S l&#039;esterna superficie di quel solido, S′ l&#039;esterna <lb></lb>superficie di questo, non comprese le basi, abbiamo S=2<foreign lang="grc">π</foreign>BI.KB, S′= <lb></lb><foreign lang="grc">π</foreign>BI.BH, d&#039;onde S/S′=2KB/BH, che, per essere KB/BH un rotto proprio, <lb></lb>sarà necessariamente minore di due. </s>

<s>Comprese poi le basi, sarà S= <lb></lb>2<foreign lang="grc">π</foreign>BI.KB+2<foreign lang="grc">π</foreign>BI2=2<foreign lang="grc">π</foreign>BI(KB+BI); S′=<foreign lang="grc">π</foreign>BI.BH+<foreign lang="grc">π</foreign>BI2= <lb></lb><foreign lang="grc">π</foreign>BI(HB+BI), onde S/S′,=2(KB+BI)/(HB+BI), che è pure minore di due, per la <lb></lb>medesima ragione di dianzi, per essere cioè il due moltiplicato per un rotto <lb></lb>proprio. </s></p><p type="main">

<s>Anche nell&#039;altra sua parte apparisce vero il proposto teorema, perchè <lb></lb>essendo S′/S=BH/2KB, se BH=2KB, le superficie sono uguali. </s>

<s>Se BH= <lb></lb>4KB, la superficie del cono è doppia di quella del cilindro: se poi BH è <lb></lb>maggiore di 4KB, i coni inscritti hanno tutti superficie maggior del doppio <lb></lb>di quelle dei cilindri circoscritti. </s></p><p type="main">

<s>“ PROPOSITIO XIV, THEOREMA XII. — <emph type="italics"></emph>A data sphaera, segmento plano <lb></lb>secto, ita ut segmentum ad conum basim habentem eamdem cum segmento <lb></lb>et aequalem altitudinem, datam rationem habeat; dico datam illam ra­<lb></lb>tionem debere esse necessario sesquialtera maiorem. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Così Galileo intendeva di riformare la VII archimedea, problema VI del <lb></lb>secondo libro <emph type="italics"></emph>De sphaera et cylindro,<emph.end type="italics"></emph.end> secondo ciò che leggesi nella seguente <lb></lb>nota manoscritta: “ Ex resolutione VI problematis secundi Archimedis <emph type="italics"></emph>De <lb></lb>sphaera et cylindro,<emph.end type="italics"></emph.end> patet quamlibet sphaerae portionem maiorem esse quam <lb></lb>sesquialteram coni in ipsa descripti ” (ibid., fol. </s>

<s>24). </s></p><p type="main">

<s>“ PROPOSITIO XV, PROBLEMA III. — <emph type="italics"></emph>Ex cylindro recto, ex altera parte <lb></lb>indeterminato, possumus partem sic abscindere, ut illius superficies, exceptis<emph.end type="italics"></emph.end><pb xlink:href="020/01/2608.jpg" pagenum="233"></pb><emph type="italics"></emph>basibus, ad superficiem coni in ipso descripti, excepta base, datam habeat <lb></lb>proportionem: oportet autem datam proportionem minorem esse quam <lb></lb>duplam. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sit cylindrus interminatus ABCD (fig. </s>

<s>91), axis EF; data proportio K <lb></lb>ad HG, minor quam dupla. </s>

<s>Ponatur HI aequalis HG, et ex puncto A duca­<lb></lb><figure id="id.020.01.2608.1.jpg" xlink:href="020/01/2608/1.jpg"></figure></s></p><p type="caption">

<s>Figura 91.<lb></lb>tur AF, secans axem in F, et abscindens partem FE, ad <lb></lb>quam habeat proportionem eamdem, quam GI ad K, et <lb></lb>per F aequidistans ducatur FOT. </s>

<s>Dico cylindrum AOTB <lb></lb>esse petitum. </s>

<s>” </s></p><p type="main">

<s>“ Quod enim fit ex AO in AB, et id quod fit ex <lb></lb>dimidio FA in AB, est ut OA ad dimidium FA. </s>

<s>Verum <lb></lb>quod fit ex dimidia FA in AB aequatur ei, quod fit ex <lb></lb>tota FA iu dimidia AB: hoc est in AE. </s>

<s>Contenta ergo <lb></lb>sub OA, AB, ad contentum sub FA, AE, est ut OA ad <lb></lb>dimidiam AF: hoc est ut K ad GH. Verum, ut contentum <lb></lb>sub OA, AB, ad contentum sub FA, AE, sic est superficies cylindri ad sn­<lb></lb>perficiem coni; ergo etc. </s>

<s>” (ibid., fol. </s>

<s>23). </s></p><p type="main">

<s>È dato, secondo il discorso di Galileo, AO:FA/2=K:GH, ossia AO.AB: <lb></lb>FA.AB/2=K:GH, che, moltiplicata la prima ragione per <foreign lang="grc">π</foreign> e posta AB= <lb></lb>2AE, si riduce ad AO.2<foreign lang="grc">π</foreign>AE:FA.<foreign lang="grc">π</foreign>AE=K:GH. </s>

<s>Ma nella prima ra­<lb></lb>gione il primo termine misura la superficie del cilindro, il secondo la su­<lb></lb>perficie del cono, dunque ecc. </s>

<s>Bisogna poi, com&#039;è stato avvertito nella pro­<lb></lb>posta, che sia
2AO/AF=K/GH &lt; 2, perchè, se fosse uguale, sarebbe OA=AF, <lb></lb>e gli apotemi del cilindro e del cono si confonderebbero insieme, per cui non <lb></lb>sarebbe possibile la richiesta costruzione. </s></p><p type="main">

<s>“ PROPOSITIO XVI, PROBLEMA IV. — <emph type="italics"></emph>Dato cylindro recto, in altera <lb></lb>parte indeterminato, possumus ab ipso portionem abscindere, ita ut illius <lb></lb>superficies, exceptis basibus, aequetur superficiei coni recti in ipso descripti, <lb></lb>excepta base coni. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2608.2.jpg" xlink:href="020/01/2608/2.jpg"></figure></s></p><p type="caption">

<s>Figura 92.</s></p><p type="main">

<s>“ Sit itaque cylindrus rectus indeterminatus, et <lb></lb>planum ductum per axem faciat sectionem ABCD <lb></lb>(fig. </s>

<s>92), sitque BE dupla EC, et centro C, intervallo <lb></lb>CB, describatur circuli circumferentia, quae secet CD <lb></lb>in F, et ducatur BF, quae bifariam dividatur in H, et <lb></lb>per H ducatur, BC aequidirtans, GHK. Dico, si con­<lb></lb>volvantur rectangulum KGCB, et triangulum BHC, <lb></lb>effici quod petitur. </s>

<s>” </s></p><p type="main">

<s>“ Quia enim quadratum BC triplum est quadrati <lb></lb>CF, erit BF quadratum quadruplum FC, hoc est HB <lb></lb>quadratum quadruplum quadrati BK, et linea HB dupla BK. Quare, si BC <lb></lb>bifariam dividatur in puncto I, erit ut HB ad BK, ita CB ad BI. </s>

<s>Quod ergo <pb xlink:href="020/01/2609.jpg" pagenum="234"></pb>fit ex KB in BC aequatur ei quod fit ex HB in BI. </s>

<s>Igitur mediae inter HB, <lb></lb>BI, et inter KB, BC; hoc est circuli, quorum dictae mediae sint semidiame­<lb></lb>tri, sunt aequales. </s>

<s>Ergo etc. </s>

<s>” (ibid., fol. </s>

<s>22). </s></p><p type="main">

<s>La superficie del cono, generato dalla rivoluzione del triangalo BHI in­<lb></lb>torno all&#039;asse HI, è, senza la base, <foreign lang="grc">π</foreign>BI.BH, e la superficie del cilindro, <lb></lb>generato dal rettangolo KI nel rivolgersi intorno al medesimo asse, è, senza <lb></lb>le hasi, <foreign lang="grc">π</foreign>BC.KB, per cui, se i rettangoli BI.BH, BC.KB fossero uguali, <lb></lb>sarebbe dimostrato che le due superficie sono uguali. </s>

<s>L&#039;eguaglianza poi dei <lb></lb>detti rettangoli la conclude Galileo dal supporre BC2=3CF2, dal quale sup­<lb></lb>posto ne consegue veramente BF2=3CF2+CF2=4CF2, ossia (2BH)2= <lb></lb>4(2KB)2, e in ultima riduzione BH=2BK. </s>

<s>Ma è strano il fare <emph type="italics"></emph>quadra­<lb></lb>tum BC triplum quadrati FC,<emph.end type="italics"></emph.end> perch&#039;essendo per costruzione BC, FC raggi <lb></lb>di un medesimo circolo, non possono i loro quadrati non essere uguali. </s>

<s>La <lb></lb>cosa anzi ci parve tanto strana che, dubitando di non aver bene interpetrato <lb></lb>il manoscritto, si voleva escludere questo dagli altri teoremi. </s>

<s>Essendosi però <lb></lb>ritrovato per cosa certa ch&#039;era stato propriamente messo così, come noi ri­<lb></lb>copiammo, lo adduciamo come documento storico di quei falli, nei quali ebbe <lb></lb>più volte a incorrere Galileo, principalmente per la privazion della vista, e <lb></lb>del potere adoperare la penna, “ infelicità, diceva da sè stesso, che mi accade <lb></lb>anco nel poter discorrere sopra linee, che passino oltre un triangolo, sicchè <lb></lb>nè pure posso intendere una delle mie medesime proposizioni e dimostra­<lb></lb>zioni ” (Alb. </s>

<s>VII, 236). </s></p><p type="main">

<s>Ma quest&#039;altra proposizion che scriviamo, era tanto facile, da potersi <lb></lb>contemplar con la sola mente, alla quale bastava rappresentar come il qua­<lb></lb>drato del raggio, ch&#039;entra a misurar la base di un cilindro, è uguale a esso <lb></lb>raggio moltiplicato in sè stesso. </s>

<s>Essendo infatti C, C′ due cilindri con le basi <lb></lb>di raggio R, R′, e con le altezze A, A′, avranno fra loro la proporzione <lb></lb>C:C′=A<foreign lang="grc">π</foreign>R2:A′<foreign lang="grc">π</foreign>R′2=2<foreign lang="grc">π</foreign>R..A.2R:2<foreign lang="grc">π</foreign>R′.A′.2R′, che vuol <lb></lb>dire appunto quel che Galileo proponesi di dimostrare in questo modo: </s></p><p type="main">

<s>“ PROPOSITIO XVII, THEOREMA XIII. — <emph type="italics"></emph>Cylindri proportionem habent <lb></lb>compositam ex proportione superficierum curvarum, et ex proportione <lb></lb>diametrorum basium. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nam habent proportionem compositam ex proportione altitudinum, et <lb></lb>ex proportione basium. </s>

<s>Bases autem habent proportionem compositam ex <lb></lb>circumferentiis, et ex proportione diametrorum. </s>

<s>Quare cylindrus ad cylindrum <lb></lb>habet proportionem compositam ex tribus proportionibus: nempe altitudinum. </s>

<s><lb></lb>circumferentiarum et diametrorum, quarum duae primae componunt pro­<lb></lb>portionem superficierum curvarum. </s>

<s>Quare patet propos. </s>

<s>” (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>I raccoglitori dei manoscritti attribuirono a Galileo un&#039;altra proposizione <lb></lb>geometrica, che poi il Viviani pubblicò per sua, e nel dedicarla, con la data <lb></lb>del 1668 al padre Adamo Adamando, glì diceva di averla ritrovata trent&#039;anni <lb></lb>fa, nello studiare il teorema di Pitagora, <emph type="italics"></emph>vix Geometriae liminì appulsus.<emph.end type="italics"></emph.end><lb></lb>Poi soggiungeva essere stato condotto all&#039;invenzione da così fatto pensiero: <lb></lb>“ Quum primum enim, nullo explicantis praeceptoris praesidio, ad illius <pb xlink:href="020/01/2610.jpg" pagenum="235"></pb>pithagorici inventi demonstrationent perveni, ignorans adhuc universalem <lb></lb>propositionem trigesimam primam, de similibus figuris ab Euclide in sexto <lb></lb>Elementorum allatam; excogitari coepi num, quod de figura quadrata, verum <lb></lb>quoque esset de prima ac simplicissima rectilinearum figurarum aequalium <lb></lb>pariter laterum et angulorum; nimirum de triangulo aequilatero ” (Viviani <lb></lb>Scienza delle proporz. </s>

<s>cit., pag. </s>

<s>126) </s></p><p type="main">

<s>Non si vuol da noi negar fede a queste asserzioni, perchè i frutti ren­<lb></lb>don credibile la precoce eccellenza dei fiori, sullo sbocciar dei quali avendo <lb></lb>nonostante avuto Galileo quella parte, che ha la luce e il tiepore del sole, <lb></lb>non par che aberri dal vero chi attribuisce a lui i portati primaverili della <lb></lb>giovane pianticella. </s>

<s>Se dall&#039;altra parte il modo, come fu distesa quella pro­<lb></lb>posizione nella sua prima forma originale, attesta l&#039;inesperienza del giovane <lb></lb>dimostratore, è anche indizio delle difficoltà dello stesso Galileo nel doversela <lb></lb>rappresentare in mezzo alle tenebre. </s></p><p type="main">

<s>“ PROPOSITIO XVIII, THEOREMA XIV. — <emph type="italics"></emph>Sia il triangolo rettangolo <lb></lb>ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>93), <emph type="italics"></emph>il di cui angolo retto ABC. </s>

<s>Dico il triangolo equilatero<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2610.1.jpg" xlink:href="020/01/2610/1.jpg"></figure></s></p><p type="caption">

<s>Figura 93.<lb></lb><emph type="italics"></emph>ADC, fatto sopra il lato AC opposto all&#039;an­<lb></lb>golo retto, essere uguale ai triangoli equi­<lb></lb>lateri AEB, CFB, fatti dai lati AB, BC, che <lb></lb>l&#039;angolo retto contengono. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Per provar questo, tirisi la linea retta <lb></lb>BD, e poi dal punto E tirisi la EG perpendi­<lb></lb>colare sopra la AB. </s>

<s>Tirisi inoltre la linea retta <lb></lb>GC, e finalmente tirisi un&#039;altra linea retta EC. </s>

<s><lb></lb>Considero ora i due triangoli EAC, BAD, i quali <lb></lb>hanno i lati EA, AC eguali ai due lati BA, AD, <lb></lb>l&#039;uno all&#039;altro, essendo lati di triangoli equi­<lb></lb>lateri. </s>

<s>Inoltre l&#039;angolo DAC è uguale all&#039;an­<lb></lb>golo EAB, per essere ambedue in un trian­<lb></lb>golo equilatero: aggiunto comune CAB sarà <lb></lb>tutto l&#039;angolo DAB eguale a tutto EAC, sicchè i triangoli EAC, BAD, avendo <lb></lb>due lati uguali a due lati, e l&#039;angolo compreso uguale all&#039;angolo com­<lb></lb>preso, sarà tutto il triangolo uguale a tutto il triangolo. </s>

<s>Ma il triangolo EAC <lb></lb>è composto dei tre triangoli EAG, EGC, AGC, i quali fra tutti e tre fanno <lb></lb>tutto il triangolo AEB equilatero, e mezzo il triangolo ABC rettangolo: <lb></lb>perchè, essendo la EG perpendicolare sopra la AB, sarà l&#039;angolo EGA eguale <lb></lb>all&#039;angolo EGB, essendo ambedue retti. </s>

<s>L&#039;angolo ancora EAG è uguale al­<lb></lb>l&#039;angolo EBG, per essere del triangolo equilatero. </s>

<s>Sicchè dunque i due <lb></lb>triangoli AEG, GEB saranno uguali, essendo come s&#039;è detto l&#039;angolo AGE <lb></lb>eguale all&#039;angolo EGB, e l&#039;angolo EAG eguale all&#039;angolo EBG: un lato <lb></lb>uguale a un lato del comune EG, e il lato EA uguale al lato EB, per essere <lb></lb>ambedue del triangolo equilatero. </s>

<s>Sarà dunque il triangolo EAG eguale al <lb></lb>triangolo EGB, cioè il triangolo EGB la metà di tutto l&#039;equilatero EAB. </s>

<s>Inol­<lb></lb>tre essendo ancora, per la medesima ragione, il lato AG eguale al lato GB, <pb xlink:href="020/01/2611.jpg" pagenum="236"></pb>saranno i triangoli AGC, BGC sopra basi uguali, ed hanno la medesima al­<lb></lb>tezza in C: sicchè saranno uguali fra di loro. </s>

<s>Però il triangolo AGC sarà <lb></lb>la metà di tutto il triangolo rettangolo ABC. </s>

<s>Inoltre poi, essendo l&#039;angolo <lb></lb>EGA retto, e l&#039;angolo GBC pur retto, saranno fra loro uguali. </s>

<s>Però le linee <lb></lb>EG, BC saranno parallele: però i triangoli EGC, EGB saranno fra loro uguali, <lb></lb>essendo sopra la medesima base e fra le stesse parallele. </s>

<s>Ma il triangolo EGB <lb></lb>è la metà del triangolo equilatero AEB, adunque anche il triangolo EGC sarà <lb></lb>la metà di detto triangolo equilatero. </s>

<s>Sicchè dunque i due triangoli AEG, EGC <lb></lb>sono uguali a tutto il triangolo equilatero AEB, ed il terzo triangolo AGC è <lb></lb>la metà del rettangolo ABC, e fra tutt&#039;e tre s&#039;è detto che compongono il <lb></lb>solo grande EAC. </s>

<s>Adunque il triangolo EAC è uguale al triangolo equila­<lb></lb>tero EAB, e alla metà del rettangolo ABC. </s>

<s>Ma il triangolo BAD si è provato <lb></lb>uguale al triangolo EAC, adunque anche il triangolo BAD sarà uguale al <lb></lb>triangolo equilatero EAB, e alla metà del rettangolo ABC. ” </s></p><p type="main">

<s>“ Per le medesime ragioni, e con la medesima costruzione appunto, si <lb></lb>proverà il triangolo BDC eguale all&#039;equilatero BFC, con la metà del trian­<lb></lb>golo ABC. </s>

<s>Adunque tutto il triangolo equilatero ADC, con tutto il triangolo <lb></lb>rettangolo, è uguale ai due triangoli equilateri EAB, BCF, con due metà del <lb></lb>triangolo equilatero: cioè con tutto il medesimo triangolo equilatero. </s>

<s>Ma se, <lb></lb>tanto dal solo triangolo equilatero, che dagli altri due, ne leveremo il co­<lb></lb>mune triangolo rettangolo; resterà il triangolo equilatero ADC solo eguale <lb></lb>ai due triangoli equilateri EAB, BCF. </s>

<s>Ma il triangolo ADC è il triangolo fatto <lb></lb>dalla AC, lato opposto all&#039;angolo retto del triangolo rettangolo ABC, e i trian­<lb></lb>goli EAB, BCF i triangoli fatti dai lati, che l&#039;angolo retto contengono del <lb></lb>medesimo triangolo; sicchè dunque del triangolo rettangolo il triangolo equi­<lb></lb>latero, fatto sopra il lato opposto all&#039;angolo retto, è uguale ai due triangoli <lb></lb>equilateri, fatti dai lati che l&#039;angolo retto contengono, il che si doveva pro­<lb></lb>vare ” (MSS. Gal., P. VI, T. III, fol. </s>

<s>11 a tergo e fol. </s>

<s>12). </s></p><p type="main">

<s>“ PROPOSITIO XIX, THEOREMA XV. — <emph type="italics"></emph>Ma volendosi sapere qual parte <lb></lb>del triangolo equilatero, fatta dal lato opposto all&#039;angolo retto, è uguale <lb></lb>a uno degli altri triangoli, e qual parte è uguale all&#039;altro, si opererà così: ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia il detto triangolo rettangolo ABC, come nella precedente figura, e <lb></lb>fatti i triangoli voglio provare quanto di sopra. </s>

<s>Per provar questo, tirisi dal <lb></lb>punto B la BH perpendicolare sopra la AC: congiungasi HD. </s>

<s>Dico il trian­<lb></lb>golo ADH essere eguale all&#039;equilatero AEB, l&#039;uno all&#039;altro. </s>

<s>” </s></p><p type="main">

<s>“ Tirisi la retta BD: poi tirisi la DL perpendicolare sopra AC, e con­<lb></lb>giungasi LB. </s>

<s>Tirisi inoltre la perpendicolare EG sopra la AB, e congiungasi <lb></lb>GC, e finalmente tirisi la linea retta EC. Già, per la di sopra, sappiamo il <lb></lb>triangolo AEC essere uguale al triangolo ABD, e l&#039;uno e l&#039;altro eguale al­<lb></lb>l&#039;equilatero AEB. </s>

<s>Ma essendo l&#039;angolo DEC retto uguale all&#039;altro retto AHB, <lb></lb>saranno le linee DL, BH parallele. </s>

<s>Più il triangolo DLH sarà uguale al trian­<lb></lb>golo DLB, essendo sopra la medesima base DL, e fra le stesse parallele. </s>

<s>Però, <lb></lb>pigliando in cambio di BLD il triangolo DLH, sarà tutto il triangolo DAH, <lb></lb>con ALB, eguale al triangolo AEB, con la metà del triangolo rettangolo ACB. <pb xlink:href="020/01/2612.jpg" pagenum="237"></pb>Adunque anche il triangolo ADH, con il triangolo ALB, sarà uguale al trian­<lb></lb>golo equilatero AEB, e alla metà del triangolo rettangolo ABC. </s>

<s>Ma il trian­<lb></lb>golo ALB ancora è la metà del triangolo rettangolo, per essere sopra basi <lb></lb>eguali AL, LC, avendo la medesima altezza in B. </s>

<s>Ma se tanto dal triangolo <lb></lb>equilatero AEB, che dal triangolo ADH, si tolgano le parti uguali alla metà <lb></lb>del triangolo rettangolo ABC, resterà il triangolo equilatero AEB eguale al <lb></lb>triangolo ADH, che si doveva provare. </s>

<s>” </s></p><p type="main">

<s>“ Con la medesima costruzione si proverà l&#039;altro triangolo CHD eguale <lb></lb>all&#039;altro equilatero BCF. </s>

<s>Adunque tutto ADC sarà uguale ai due ” (ivi, fol. </s>

<s>12). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Tali essendo, quali gli abbiamo ordinati ed esposti fin qui, i problemi <lb></lb>e i teoremi di Galileo raccolti dal Viviani, passiamo a ordinare quegli altri, <lb></lb>che si sono raccolti da noi, per la massima parte dagli autografi, ne&#039;quali, <lb></lb>per non aver potuto l&#039;Autore mandare ad effetto la sua intenzione, son da <lb></lb>due secoli e mezzo rimasti abbandonati. </s>

<s>Dicemmo esservene alcuni concer­<lb></lb>nenti l&#039;Algebra, per la quale intendiamo quella parte della Matematica, che <lb></lb>dimostra le relazioni esistenti fra certe date quantità, come loio proprietà <lb></lb>universali, comunque siano quelle stesse quantità definite. </s>

<s>Il modo di dimo­<lb></lb>strare così fatti teoremi consiste per lo più, appresso agli antichi, nel con­<lb></lb>cludere per induzione una regola generale da pochi fatti particolari, cosicchè <lb></lb>la fiducia, che s&#039;aveva della verità di queste soluzioni, si faceva unicamente <lb></lb>dipendere dal principio, che la Natura opera in modo sempre costante. </s>

<s>Come <lb></lb>il principio sia talvolta sicuro, e come non di rado riesca pericoloso, appa­<lb></lb>risce dagli esempi dei Matematici antichi, i quali, non sapendo dar forma <lb></lb>ai concetti universali, per poi vedervi in essi compresi i particolari, da que­<lb></lb>sti, risaliti per pochi gradi, distendono a quelli il volo ardito, soggiacendo bene <lb></lb>spesso alle sorti d&#039;Icaro, di che ebbe talvolta a fare esperienza anche Galileo. </s></p><p type="main">

<s>PROPOSITIO XX, THEOREMA XVI. — <emph type="italics"></emph>Abbiasi una progressione aritme­<lb></lb>tica che, cominciando da un numero pari, proceda costantemente per diffe­<lb></lb>renze uguali al primo termine<emph.end type="italics"></emph.end> a, <emph type="italics"></emph>alla metà del quale s&#039;agguagli il numero <lb></lb>degli stessi termini in progressione. </s>

<s>Si ponga poi una nuova progressione <lb></lb>decrescente con differenze costantemente uguali a due, e il maggior nu­<lb></lb>mero della quale sia il primo della progressione crescente, diminuito di <lb></lb>un&#039;unità, e si proceda infin tanto che, per essere quel maggior numero <lb></lb>impari, non si esaurisca nell&#039;uno. </s>

<s>Poste queste cose, si dimostra primo: <lb></lb>che il numero dei termini della progressione decrescente sarà uguale al <lb></lb>numero dei termini della crescente. </s>

<s>Secondo: che il doppio della somma <lb></lb>della stessa decrescente è uguale al primo termine della crescente, mol­<lb></lb>tiplicato per il numero dei termini in progressione.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2613.jpg" pagenum="238"></pb><p type="main">

<s>Chiamato infatti <foreign lang="grc">ω</foreign> il maggior termine della progressione decrescente, e <lb></lb><emph type="italics"></emph>d<emph.end type="italics"></emph.end> la differenza, la formula <emph type="italics"></emph>n<emph.end type="italics"></emph.end>=1+(<foreign lang="grc">ω</foreign>—<emph type="italics"></emph>a<emph.end type="italics"></emph.end>)/<emph type="italics"></emph>d<emph.end type="italics"></emph.end> dataci dai trattati di Algebra <lb></lb>si riduce ad <emph type="italics"></emph>n=a<emph.end type="italics"></emph.end>/2. Dunque il numero dei termini è veramente, come si <lb></lb>diceva, nelle due progressioni uguale. </s></p><p type="main">

<s>La formula poi <foreign lang="grc">ω</foreign>=<emph type="italics"></emph>a+d(n—1)<emph.end type="italics"></emph.end> dà per la crescente <foreign lang="grc">ω</foreign>= <lb></lb><emph type="italics"></emph>a+a(n—1)=an<emph.end type="italics"></emph.end>: mentre per la decrescente la somma <emph type="italics"></emph>s<emph.end type="italics"></emph.end> è data dalla <lb></lb>formola <emph type="italics"></emph>s=n<emph.end type="italics"></emph.end>/2(<emph type="italics"></emph>a<emph.end type="italics"></emph.end>+<foreign lang="grc">ω</foreign>) che nel presente nostro caso si riduce a 2<emph type="italics"></emph>s<emph.end type="italics"></emph.end>= <lb></lb><emph type="italics"></emph>n<emph.end type="italics"></emph.end>(1+<emph type="italics"></emph>a<emph.end type="italics"></emph.end>—1)=<emph type="italics"></emph>an.<emph.end type="italics"></emph.end> Dunque <foreign lang="grc">ω</foreign>=2<emph type="italics"></emph>s,<emph.end type="italics"></emph.end> come si doveva dimostrare. </s></p><p type="main">

<s>PROPOSITIO XXI, THEOREMA XVII. — <emph type="italics"></emph>Abbiansi le medesime cose come <lb></lb>sopra, ma il minor termine della crescente, la quale abbia tanti termini <lb></lb>in progressione, quant&#039;è la metà di a+1, sia impari, e sia perciò pari il <lb></lb>maggior della decrescente. </s>

<s>Si dimostra, così posto, che il numero dei ter­<lb></lb>mini della decrescente è sempre minore di uno del numero dei termini della <lb></lb>crescente; e che il doppio della somma di quella è uguale al numero dei <lb></lb>termini di questa moltiplicato per il suo primo termine diminuito di uno.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La formula infatti <emph type="italics"></emph>n<emph.end type="italics"></emph.end>=1+(<foreign lang="grc">ω</foreign>—<emph type="italics"></emph>a<emph.end type="italics"></emph.end>)/<emph type="italics"></emph>d,<emph.end type="italics"></emph.end> dianzi proposta, si riduce a <emph type="italics"></emph>n<emph.end type="italics"></emph.end>= <lb></lb>1+(<emph type="italics"></emph>a<emph.end type="italics"></emph.end>—1—2)/2=(<emph type="italics"></emph>a<emph.end type="italics"></emph.end>—1)/2, ciò che dimostra la verità della prima parte <lb></lb>del teorema. </s>

<s>Quanto alla seconda, l&#039;altra formula generale, che dava la <lb></lb>somma dei termini in progression decrescente, torna a 2<emph type="italics"></emph>s(n—1)(a+1)= <lb></lb>an—a+n—1=an+n—(a+1).<emph.end type="italics"></emph.end> Ma <emph type="italics"></emph>a+1=2n,<emph.end type="italics"></emph.end> dunque <lb></lb>2<emph type="italics"></emph>s=an—n=n(a—1),<emph.end type="italics"></emph.end> come dovevasi dimostrare. </s></p><p type="main">

<s>Galileo concludeva il primo dei riferiti teoremi dal veder procedere se­<lb></lb>condo la medesima regola le progressioni contrassegnate nel manoscritto con <lb></lb>le lettere D, F, E, B, A. <lb></lb>÷8:4 <lb></lb>D { <lb></lb>÷3:1 <lb></lb>÷6:12:18 <lb></lb>F { <lb></lb>÷5:3:1 <lb></lb>÷8:16:24:32 <lb></lb>E { <lb></lb>÷7:5:3:1 <lb></lb>÷10:20:30:40:50 <lb></lb>B { <lb></lb>÷9:7:5:3:1 <lb></lb>÷20:40:60:80:100:120:140:160:180:200 <lb></lb>A { <lb></lb>÷19:17:15:13:11:9:7:5:3:1 </s></p><pb xlink:href="020/01/2614.jpg" pagenum="239"></pb><p type="main">

<s>L&#039;altro teorema era pure concluso per induzione dai particolari esempi, <lb></lb>offerti e considerati nelle progressioni G, H, I, L. <lb></lb>÷5:10:15 <lb></lb>G { <lb></lb>÷4:2 <lb></lb>÷7:14:21:28 <lb></lb>H { <lb></lb>÷6:4:2 <lb></lb>÷9:18:27:36:45 <lb></lb>I { <lb></lb>÷8:6:4:2 <lb></lb>÷25:50:75:100:125:150:175:200:225:250:275:300:325 <lb></lb>L { <lb></lb>÷24:22:20:18:16:14:12:10:8:6:4:2 </s></p><p type="main">

<s>L&#039;uno e l&#039;altro poi dei detti teoremi veniva da Galileo applicato a illu­<lb></lb>strare la meccanica dei moti naturali, comparati con i violenti, com&#039;appari­<lb></lb>sce dalla seguente nota autografa, della quale è questa la fedel copia che se <lb></lb>n&#039;è presa: </s></p><p type="main">

<s><emph type="italics"></emph>“ Notabile per i proietti nel determinare quanto detragga la propen­<lb></lb>sione naturale in giù al moto preternaturale della proiezione.<emph.end type="italics"></emph.end> — Si im­<lb></lb>petus violentus disponatur secundum numeros pares, descensus naturalis demit <lb></lb>dimidium, ut constat in exemplis D, F, E, B, A. Verum, si dispositio sit se­<lb></lb>cundum numeros impares, naturalis descensus demit minus quam dimidium, <lb></lb>iuxta numerum partium dispositarum, ut patet in exemplis G, H, I, L. </s>

<s>In G <lb></lb>enim partes dispositae iuxta impetum violentum non retardatum sunt tres, <lb></lb>nempe 5, 10, 15, ex quibus in prima demitur 1, et relinquitur 4. Dempto <lb></lb>ex secunda 4, relinquitur 6. Dempto ex tertia, nempe ex 15, 9, relinquitur <lb></lb>idem numerus 6, quod deficit a dimidio 15 per 3, qui est numerus partium <lb></lb>5, 10, 15. In exemplo H numerus partium est 4: subtractiones motus na­<lb></lb>turalis sunt 6, 4, 2, quae conficiunt 12, cuius duplum deficit a 28 per 4. In <lb></lb>exemplo I subtractiones 8, 6, 4, 2 exhibent 20, cuius duplus deficit a 45 per 5, <lb></lb>quod est numerus partium. </s>

<s>In L pariter apparet subtractiones, nempe 156, <lb></lb>duplicatim deficere per 13, quod est numerus partium motus violenti, a 325 ” <lb></lb>(MSS. Gal., P. V, T. II, fol. </s>

<s>182). </s></p><p type="main">

<s>“ PROPOSITIO XXII, THEOREMA XVIII. — <emph type="italics"></emph>In numeris, ab unitate con­<lb></lb>sequentibus, summa cuiuslibet multitudinis, ad aliam summam alterius <lb></lb>multitudinis, si ab utraque dimidium maximi numeri auferatur, est ut <lb></lb>quadratum multitudinis unius, ad quadratum alterius multitudinis ”<emph.end type="italics"></emph.end> (ibid., <lb></lb>fol. </s>

<s>68). </s></p><p type="main">

<s>Anche di questo teorema, concluso da Galileo per induzione da pochi <lb></lb>esempi particolari, è manifesta la verità generale, applicandovi la formula al­<lb></lb>gebrica <emph type="italics"></emph>s=n<emph.end type="italics"></emph.end>/2(<emph type="italics"></emph>a<emph.end type="italics"></emph.end>+<foreign lang="grc">ω</foreign>), che si trasforma in <emph type="italics"></emph>s<emph.end type="italics"></emph.end>—<foreign lang="grc">ω</foreign>/2=<emph type="italics"></emph>n<emph.end type="italics"></emph.end>(<emph type="italics"></emph>a<emph.end type="italics"></emph.end>+<foreign lang="grc">ω</foreign>)/2—<foreign lang="grc">ω</foreign>/2= <pb xlink:href="020/01/2615.jpg" pagenum="240"></pb>(<emph type="italics"></emph>n<emph.end type="italics"></emph.end>(1+<foreign lang="grc">ω</foreign>)—<foreign lang="grc">ω</foreign>)/2, intendendosi per <emph type="italics"></emph>s<emph.end type="italics"></emph.end> la somma che si cerca, per <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> <foreign lang="grc">ω</foreign> il primo <lb></lb>e l&#039;ultmo termine, e per <emph type="italics"></emph>n<emph.end type="italics"></emph.end> il numero dei termini in progressione. </s>

<s>Ora es­<lb></lb>sendo <emph type="italics"></emph>a<emph.end type="italics"></emph.end>=t, e nella progressione dei numeri naturali conseguenti dall&#039;unità <lb></lb><emph type="italics"></emph>n<emph.end type="italics"></emph.end>=<foreign lang="grc">ω</foreign>, avremo <emph type="italics"></emph>s<emph.end type="italics"></emph.end>—<foreign lang="grc">ω</foreign>/2=<foreign lang="grc">ω</foreign>2/2. Per la somma <emph type="italics"></emph>s<emph.end type="italics"></emph.end>′ di un&#039;altra progressione, <lb></lb>l&#039;ultimo termine della quale sia <foreign lang="grc">ω</foreign>′, essendo <emph type="italics"></emph>s<emph.end type="italics"></emph.end>′—<foreign lang="grc">ω</foreign>′/2=<foreign lang="grc">ω</foreign>′2/2, avremo dun­<lb></lb>que <emph type="italics"></emph>s<emph.end type="italics"></emph.end>—<foreign lang="grc">ω</foreign>/2:<emph type="italics"></emph>s<emph.end type="italics"></emph.end>′—<foreign lang="grc">ω</foreign>′/2=<foreign lang="grc">ω</foreign>2:<foreign lang="grc">ω</foreign>′2, ciò ch&#039;esprime la verità che volevasi con­<lb></lb>fermare. </s></p><p type="main">

<s>“ PROPOSITIO XXIII, THEOREMA XIX. — <emph type="italics"></emph>Si fuerint quatuor lineae, <lb></lb>quarum prima et secunda simul sumptae sint aequales tertiae et quar­<lb></lb>tae simul sumptis, sint antem prima et secunda minus inter se differentes <lb></lb>quam tertia et quarta: rectangulum primae el secundae superat rectan­<lb></lb>gulum tertiae et quartae rectangulo contento ab excessu tertiae supra pri­<lb></lb>mam in excessu primae supra quartam ”<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>62 ad terg.). </s></p><p type="main">

<s>Galileo non dimostra direttamente il teorema, ma si contenta d&#039;accen­<lb></lb>nar come si veritichi nell&#039;esempio di quattro linee, la prima e la seconda <lb></lb>delle quali siano 10, 8, e la terza e la quarta 12 e 6. In questo caso è <lb></lb>veramente 10X8—12X6=2X4. È però verissima la cosa in ge­<lb></lb>nerale. </s>

<s>perchė chiamate <emph type="italics"></emph>a, b, c, d<emph.end type="italics"></emph.end> le quattro linee o i quattro numeri, se me­<lb></lb>glio piace, essendo per le poste condizioni <emph type="italics"></emph>a+b=c+d,<emph.end type="italics"></emph.end> è facile dimo­<lb></lb>strare che <emph type="italics"></emph>ab—cd=(c—a)(a—d).<emph.end type="italics"></emph.end> Sostituito infatti il valore di <lb></lb><emph type="italics"></emph>b,<emph.end type="italics"></emph.end> sarà <emph type="italics"></emph>ab—cd=a(c+d—a)—cd=ac+ad—a2—cd= <lb></lb>a(c—a)+d(a—c)=a(c—a)—d(c—a)=(c—a)(a—d),<emph.end type="italics"></emph.end><lb></lb>che conferma la verità dell&#039;annunziata proposizione. </s></p><p type="main">

<s>Seguono altri teoremi, i quali pullularono fecondi nella mente di Galileo, <lb></lb>mentre si proponeva di dimostrare con qual proporzione crescano le super­<lb></lb>ficie ne&#039;solidi sminuzzati, per concluderne poi il maggiore impedimento, che <lb></lb>ricevon questi nello scendere per varii mezzi, rispetto all&#039;impedimento, che <lb></lb>riceverebbe il solido tutto intero. </s></p><p type="main">

<s>“ PROPOSITIO XXIV, THEOREMA XX. — <emph type="italics"></emph>Dato un cubo, diviso in tre <lb></lb>parti uguali uno de&#039;suoi lati, come uno sta a tre, cosi la superficie del <lb></lb>grande alla superficie di tutti que&#039;piccoli ”<emph.end type="italics"></emph.end> (MSS. Gal., P. V, T. IV, fol. </s>

<s>37). </s></p><p type="main">

<s>Chiamato BD il lato del cubo grande, e BE il suo terzo, le superficie <lb></lb>S, <foreign lang="grc">σ</foreign> son date da S=6.BD2, <foreign lang="grc">σ</foreign>=6.BE2, onde S:<gap></gap>=BD2:BE2. </s>

<s>La <lb></lb>somma poi di tutti i cubetti, che chiameremo <foreign lang="grc">Σ</foreign>, sarà 33.6.BE2, ossia <lb></lb>27.6.BE2, e perciò <foreign lang="grc">Σ</foreign>:<foreign lang="grc">σ</foreign>=27BE2:BE2, onde S:<foreign lang="grc">Σ</foreign>=BD2:27.BE2. </s>

<s><lb></lb>E perchè BD=3BE, S:<foreign lang="grc">Σ</foreign>=9:27=1:3. La qual medesima conclu­<lb></lb>sione è dimostrata da Galileo così, con altra forma di discorso: </s></p><p type="main">

<s>“ Come la supertice del gran cubo alla superfice di un piccolo solo, cosi <lb></lb>la base del grande alla base del piccolo: e come la superfice del piccolo alla <lb></lb>sunerfice di tutti con esso, cioè a 27; cosi la sua base a 27 basi come la <pb xlink:href="020/01/2616.jpg" pagenum="241"></pb>sua. </s>

<s>Adunque <emph type="italics"></emph>ex aequali<emph.end type="italics"></emph.end> come la superfice del grande alla superfice di tutti <lb></lb>i piccoli, così la sua base grande a 27 di quelle basi piccole. </s>

<s>Ma questa ne <lb></lb>contiene nove di quelle piccole, dunque come 9 a 27, cioè come uno a tre, <lb></lb>così la superfice del grande, alla superfice di tutti que&#039;piccoli ” (ivi). </s></p><p type="main">

<s>Potevasi il teorema dimostrar facilmente nella sua generalità, chiamando <lb></lb>C il numero qualunque delle parti, nelle quali s&#039;intenda essere stato diviso <lb></lb>il lato del maggior cubo, perchè, ragionando come sopra e ritenendo le si­<lb></lb>gnificazioni di sopra, se ne concluderebbe S:<foreign lang="grc">Σ</foreign>=BD2:C3.BE2. </s>

<s>E per es­<lb></lb>sere BD=C.BE, S:<foreign lang="grc">Σ</foreign>=C2.BE2:C3.BE2=1:C=BE:BD, che <lb></lb>vuol dire: <emph type="italics"></emph>la superfice grande sta alla somma delle piccole, reciprocamente <lb></lb>come un lato di uno de&#039;piccoli cubi sta al lato del grande.<emph.end type="italics"></emph.end> La dimostra­<lb></lb>zione di questo generale teorema fu data dallo stesso Galileo, facendo uso <lb></lb>della così detta <emph type="italics"></emph>Algebra speciosa,<emph.end type="italics"></emph.end> com&#039;apparisce dal seguente frammento, in <lb></lb>cui, dietro le cose già esposte, non è difficile supplire al significato delle pa­<lb></lb>role, che mancano sul principio del manoscritto: </s></p><p type="main">

<s>“ ...... alla superfice di tanti cubetti quanto è il numero B, è la <lb></lb>medesima che quella del cubo B alla medesima dei tanti cubetti quanto è <lb></lb>il numero B. </s>

<s>Ma la superfice di tanti cubetti quanto è il numero C, a quella <lb></lb>di tanti quanto è il numero D, sta come i cubetti del numero C ai cubetti <lb></lb>del numero D, cioè come il numero C al numero D, cioè il numero A al B, <lb></lb>cioè la linea A alla linea B; adunque la superfice di tanti cubetti quanto è <lb></lb>il numero C, cioè la superfice del cubo B, alla superfice dei cubetti quanto <lb></lb>è il numero D, cioè alla superfice di tanti cubetti, che fanno il cubo mede­<lb></lb>simo B, sta come la A alla B, cioè come il lato di uno de&#039;cubetti, uguali <lb></lb>e simili al tutto, al lato del tutto, ohe è quello che si doveva dimostrare. </s>

<s>Il <lb></lb>che si deve intendere esser vero in ogni solido risoluto in solidi simili, es­<lb></lb>sendo tra di loro come i cubi de&#039;lati omologhi ” (ivi, fol. </s>

<s>38). </s></p><p type="main">

<s>Dall&#039;essere poi S:<foreign lang="grc">Σ</foreign>=1:C, secondo i simboli da noi applicati di sopra <lb></lb>a questa conclusione di Galileo, ne segue <emph type="italics"></emph>per conversionem rationis<emph.end type="italics"></emph.end> <foreign lang="grc">Σ</foreign>:S= <lb></lb>C:1, corollario del precedente, o nuovo teorema dallo stesso Galileo cosi <lb></lb>proposto e illustrato col discorso, che per noi si ricopia dal manoscritto. </s></p><p type="main">

<s>“ PROPOSITIO XXV, THEOREMA XXI. — <emph type="italics"></emph>Tutte le superfice dei piccoli <lb></lb>cubi risoluti prese insieme, alla superfice del cubo grande risoluto, hanno <lb></lb>la medesima proporzione, che il numero delle parti del lato che si sega <lb></lb>all&#039;uno. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Il numero de&#039;cubi, nei quali uno si risolve, è il numero cubo delle <lb></lb>parti, che son nel lato del cubo, che si risolve: come per esempio, diviso il <lb></lb>lato del cubo in tre o quattro parti, i cubi, che da esse parti si faranno, <lb></lb>saranno 27 o 64. Ed avendo ogni cubo sei quadrati in superfice, moltipli­<lb></lb>cando 27 per 6, e 64 pur per 6, averemo i numeri dei quadrati, che son <lb></lb>superfice dei detti cubi. </s>

<s>Di qui facilmente ne consegue quel che si diceva. </s>

<s><lb></lb>che cioè tutte le superfice dei piccoli cubi risoluti prese insieme, alla super­<lb></lb>fice del cubo grande risoluto, hanno la medesima proporzione che il numero <lb></lb>delle parti del lato che si sega all&#039;uno. </s>

<s>E così tutte le superfice dei 27 cubi, <pb xlink:href="020/01/2617.jpg" pagenum="242"></pb>alla superfice del primo massimo cubo, saranno triple, e tutte le superfice <lb></lb>delli 64 cubetti prese insieme saranno quadruple della superfice dell&#039;intero <lb></lb>gran cubo, essendo che il lato di questo fu diviso in tre parti, per cavarne <lb></lb>li 27 cubi, ed in quattro, per cavarne li cubi 64 ” (ivi, fol. </s>

<s>19). </s></p><p type="main">

<s>Osservava in simile proposito Galileo che, se il lato del quadrato è di­<lb></lb>viso in tre parti uguali, uno solo è il quadratino, che riman rinchiuso in <lb></lb>mezzo a tutti gli altri. </s>

<s>Se poi la divisione sia fatta in quattro, o in cinque <lb></lb>parti uguali, i quadratini rinchiusi saranno quattro o nove. </s>

<s>Di qui ne con­<lb></lb>cludeva per regola generale che, chiamato D il numero delle divisioni, il nu­<lb></lb>mero N de&#039;quadratini interni è (D—2)2, d&#039;onde ne conseguiva (D—2)3, <lb></lb>per il numero dei cubetti rimasti dentro al gran cubo sepolti. </s>

<s>Intorno a che <lb></lb>formulava Galileo stesso, riscontrata sopra alcuni esempi numerici, la se­<lb></lb>guente: </s></p><p type="main">

<s>“ PROPOSITIO XXVI, THEOREMA XXII. — <emph type="italics"></emph>Il numero dei cubi, che re­<lb></lb>stano sepolti nel gran cubo, si trova essere il numero cubo delle parti, <lb></lb>nelle quali si divide il lato del gran cubo, trattone due. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Onde, nascendo li 27 cubi dalla divisione in tre, tratto da questo nu­<lb></lb>mero tre, due, resta uno, ed uno solo sarà il cubo, che rimane incluso e se­<lb></lb>polto tra li 27. Otto saranno i cubi sepolti tra li 64, nascenti dalla divisione <lb></lb>del primo gran lato in quattro, imperocchè, tratto dal quattro due, resta due, <lb></lb>il cui cubo è otto. </s>

<s>E così di tutti gli altri ” (ivi). </s></p><p type="main">

<s>“ PROPOSITIO XXVII, PROBLEMA V. — <emph type="italics"></emph>Di due palle, quanto una è mag­<lb></lb>giore di un&#039;altra? </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Una palla di quattro è maggiore di una di tre, ed ha la medesima <lb></lb>proporzione che 64 a 27, facendo i cubi loro, perchè le figure simili sono <lb></lb>in tripla proporzione dei lati, cioè di 4 a 3. Di qui intenderai perchè le su­<lb></lb>perficie dei solidi simili no nell&#039;istessa proporzione, ma in minore, cioè in <lb></lb>subsesquialtera di quella di essi solidi crescono e calano ” (ivi, fol. </s>

<s>31). </s></p><p type="main">

<s>Chiamati infatti S, <emph type="italics"></emph>s<emph.end type="italics"></emph.end> i solidi, <foreign lang="grc">Σ</foreign>, <foreign lang="grc">σ</foreign> le superficie, R, <emph type="italics"></emph>r<emph.end type="italics"></emph.end> i raggi: sarà S:<emph type="italics"></emph>s<emph.end type="italics"></emph.end>= <lb></lb>R3:<emph type="italics"></emph>r3,<emph.end type="italics"></emph.end> <foreign lang="grc">Σ</foreign>:<gap></gap>=R2:<emph type="italics"></emph>r2,<emph.end type="italics"></emph.end> e perciò <foreign lang="grc">Σ</foreign>3:<foreign lang="grc">σ</foreign>3=S2:<emph type="italics"></emph>s<emph.end type="italics"></emph.end>2, ossia <foreign lang="grc">Σ</foreign>:<foreign lang="grc">σ</foreign>=S2/3:<emph type="italics"></emph>s<emph.end type="italics"></emph.end>2/3. </s></p><p type="main">

<s>Nel giugno del 1639 riceveva Galileo quel trattatello in forma di let­<lb></lb>tera, nella quale il Castelli, descrivendo il Pluviometro, diceva di essersi ser­<lb></lb>vito del nuovo inventato strumento per misurare dall&#039;altezza di lui l&#039;altezza, <lb></lb>a cui sarebbe cresciuta in tempo di pioggia la superfice del lago Trasimeno. </s>

<s><lb></lb>Era per caso allora esso Galileo tutto in pensiero de&#039;teoremi aritmetici rife­<lb></lb>riti di sopra, per ordinarli nel Dialogo, a cui parvegli si sarebbe potuta ag­<lb></lb>giungere in simile argomento un&#039;altra bellissima speculazione, qual era di <lb></lb>ritrovare il numero delle gocciole cadute sulla superfice di quello stesso lago. </s>

<s><lb></lb>E risoluto il problema, dettava intanto al Viviani così, perchè non se ne <lb></lb>avesse a perdere la memoria: </s></p><p type="main">

<s>“ In proposito del p. </s>

<s>ab. </s>

<s>don Benedetto, nel trattato del lago Trasimeno, <lb></lb>è cosa degna di esser notata quante sarebbero le gocciole dell&#039;acqua piovente <lb></lb>sopra la superfice del lago, data la distanza tra gocciola e gocciola, mante­<lb></lb>nuta sempre eguale tra ciascheduna di quelle, e dato quanto sarebbe il se-<pb xlink:href="020/01/2618.jpg" pagenum="243"></pb>midiametro uguale alla superfice del lago, cioè quante di tali distanze ne <lb></lb>conterrebbe. </s>

<s>Imperocchè, fatti due cubi, uno del numero di tutte le date di­<lb></lb>stanze con uno più, e l&#039;altro di un numero uno manco di tutto quello, e <lb></lb>sottratto questo minor numero cubo dall&#039;altro, la loro differenza è il numero <lb></lb>delle gocciole sopra il dato cerchio cadenti. </s>

<s>Per esempio la distanza tra goc­<lb></lb>ciola e gocciola sia un soldo: il semidiametro del cerchio sia soldi novan­<lb></lb>tanove. </s>

<s>Facciasi il cubo di cento, che è uno più di novantanove, che è un <lb></lb>milione, dal quale si tragga il numero cubo di novantanove, che è 970,299. <lb></lb>Tratto questo da un milione, resta 29,701 e tanto sarà il numero delle goc­<lb></lb>ciole cadenti sopra il dato cerchio ” (ivi). </s></p><p type="main">

<s>Nello stesso tempo dettava Galileo al Viviani una lettera, nella quale <lb></lb><emph type="italics"></emph>s<emph.end type="italics"></emph.end>&#039;avvisava il Castelli che il suo discorso sul lago Trasimeno aveva provocata <lb></lb>la seguente </s></p><p type="main">

<s>PROPOSITIO XXVIII, PROBLEMA VI. — <emph type="italics"></emph>Dato un cerchio, e il numero <lb></lb>delle distanze fra le gocciole nel suo raggio comprese, trovare il numero <lb></lb>di tutte le gocciole, sopra quella circolar superfice cadenti.<emph.end type="italics"></emph.end> E chiamato N <lb></lb>questo numero, e D le date distanze, diceva Galileo essere risoluto il pro­<lb></lb>hlema, in modo corrispondente alla formula N=(D+1)3—D3. </s></p><p type="main">

<s>Il Castelli fece intorno a questa soluzione qualche difficoltà, alla quale <lb></lb>Galileo così rispondeva: “ Quanto a quello, che ella tocca nella sua, in pro­<lb></lb>posito delle gocciole cadenti, che si debbano prendere non gl&#039;intervalli tra <lb></lb>gocciola e gocciola, ma i numeri di esse gocciole, è verissimo, nè io poteva <lb></lb>venire in cognizione di quanto scrissi, se non servendomi del numero delle <lb></lb>gocciole, ponendo il primo come centro, e gli altri sei come gli angoli del­<lb></lb>l&#039;esagono inscritto nel primo cerchio, e così i contenuti sono sette. </s>

<s>Presi poi <lb></lb>due punti, e fattone il cubo, che è otto, e trattone il primo cubo, che è uno, <lb></lb>restano pure sette. </s>

<s>Aggiunto il secondo cerchio, doppio in circonferenza del <lb></lb>primo e perciò contenente dodici gocciole nella circonferenza, e fatto il cubo <lb></lb>di tre punti, cioè 27, e trattone il cubo di due, che è otto, restano 19, che <lb></lb>è la somma stessa delli 12, delli sei, e dell&#039;uno del centro. </s>

<s>E seguitando con <lb></lb>quest&#039;ordine, aggiugnendo il terzo cerchio, e li 18 punti contenuti nella sua <lb></lb>circonferenza, sommandogli con gli antidetti dodici, e gli altri sei precedenti <lb></lb>a quello del centro, si fanno 37 gocciole, e tale è il numero che resta, ca­<lb></lb>vando il cubo di 3 dal cubo 4, cioè 27 da 64. E così continuando vidi la <lb></lb>continuazione della regola, ma poco potei andare innanzi, vietandomelo la <lb></lb>privazione della vista e del potere adoperar la penna: infelicità che mi accade <lb></lb>anco nel poter discorrere sopra linee, che passino oltre un triangolo, sicchè <lb></lb>neppure posso intendere una delle mie medesime proposizioni e dimostra­<lb></lb>zioni, ma tutte mi giungono come ignote e inintelligibili ” (Alb. </s>

<s>VII, 235, 36). </s></p><p type="main">

<s>I riferiti esempi, benchè pochi, possono nulladimeno bastare, per dare <lb></lb>un&#039;idea de&#039;teoremi dimostrati, e de&#039;problemi risoluti da Galileo, relativa­<lb></lb>mente a quelle proprietà, che universalmente intercedono fra certe date quan­<lb></lb>tità numeriche e lineari, e che oggidì più francamente e più generalmente <lb></lb>si dimostrerebbero per via di simboli algebrici, e con la regola nota delle <pb xlink:href="020/01/2619.jpg" pagenum="244"></pb>loro operazioni. </s>

<s>Rimarrebbe, a condurre il nostro primo proposito ad effetto, <lb></lb>di raccogliere quegli altri teoremi di Geometria, i quali occorsero alla mente <lb></lb>di Galileo, nell&#039;atto di dimostrare le proposizioni attinenti alle varie proprietà <lb></lb>dei moti: proposizioni, che, rimaste indietro nei manoscritti e fuor di luogo <lb></lb>nell&#039;opera dei dialoghi stampati, si volevano dall&#039;Autore stesso ridurre tutte <lb></lb>insieme in questo dialogo novissimo, incominciato, in mezzo alle tenebre este­<lb></lb>riori, a dettare al Viviani. </s></p><p type="main">

<s>Sembrerebbe si potesse congetturare dai fatti, in questa nostra Storia <lb></lb>più volte notati, che non fu una tal dettatura nè ordinata nè continua: ma <lb></lb>si dialogizzava uno o altro soggetto a parte, come ne veniva l&#039;occasione e il <lb></lb>tempo, con intenzione d&#039;intessere tutte insieme quelle parti nel tutto, rima­<lb></lb>nendo solo a farne le facili attaccature. </s>

<s>Per conferma di che soggiungeremo <lb></lb>qui, prima di passare a raccogliere i promessi teoremi geometrici, una delle <lb></lb>dette parti dialogizzate, nelle quali, in modo che, rispetto agl&#039;insegnamenti <lb></lb>degli altri Autori e del medesimo Galileo nelle opere stampate, si direbbe <lb></lb>nuovo; s&#039;applica la Geometria elementare ad alcune curiose insieme, e utili <lb></lb>operazioni della Geodesia: </s></p><p type="main">

<s>“ SALVIATI. — Ha il nostro Accademico in questi fogli insegnato anche <lb></lb>il modo di misurar con la vista. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Ma cotesto stesso l&#039;avevano insegnato, ne&#039;loro libri, <lb></lb>tanti altri Matematici, prima di lui. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Voi dite il vero, signor Simplicio: e bench&#039;io vi debba <lb></lb>concedere che il nostro Amico non abbia intorno a ciò insegnato nulla di <lb></lb>nuovo nella sostanza, ha nonostante il merito della novità, quanto ai modi, <lb></lb>i quali, se son più facili e più spediti degli altri, sono anche insieme di mi­<lb></lb>nore spesa, e di minore incomodo nel praticarli. </s>

<s>Ditemi: basta forse la sem­<lb></lb>plice vista, per questa maniera di operazioni? </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — No, ma vi si richiedono i necessari strumenti, come <lb></lb>sarebbero quadranti e diottre e traguardi, i quali vogliono esser fatti con <lb></lb>gran precisione dalle mani degli artefici più periti. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Ora io vi dico che il nuovo modo dispensa l&#039;operatore <lb></lb>da tutto questo: basta che egli abbia un quadrato o un rettangolo, fatto di <lb></lb>qualunque materia, con i lati ben diritti e puliti, e con gli angoli ben pie­<lb></lb>gati in perfetta squadra. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Ciò potrà forse bastare per l&#039;operazione in sè stessa, ma <lb></lb>ella richiede pure il fondamento di altre operazioni, come sarebbe quella di <lb></lb>tirare la linea del perpendicolo e l&#039;equidistante alla orizzontale, per far che <lb></lb>non vedo come possa bastare in tutto un semplice rettangolo o un quadrato, <lb></lb>e sia pure, negli angoli e ne&#039;lati, quanto vogliate, perfetto. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Voi, signor Sagredo, avete accortamente distinto il fon­<lb></lb>damento preparatorio dalla stessa propria operazione, della quale sola s&#039;in­<lb></lb>tendeva parlare: e benchè, qualunque peso pendulo da un filo sia strumento <lb></lb>paratissimo a tutti, per una delle dette operazioni; per l&#039;altra nonostante, <lb></lb>cioè per livellare, si ricerca strumento assai più artificioso. </s>

<s>Tale sarebbe un <pb xlink:href="020/01/2620.jpg" pagenum="245"></pb>sifone pieno di liquido, per la maggior precisione del quale si vorrebbe prin­<lb></lb>cipalmente che fosse assai lungo. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Io dai pratici ho sentito dire che i due rami del si­<lb></lb>fone, che si ripiegano in su, e nei quali trasparisce l&#039;acqua, debbono es­<lb></lb>sere, più che sia possibile, uguali, e che la differenza del calibro, special­<lb></lb>mente andando a restringersi i tubi, può rendere assai fallace la linea della <lb></lb>mira, ma non intendo in qual fallacia potesse indurre l&#039;esser più o meno <lb></lb>lungo il tubo disteso in piano, l&#039;acqua rinchiusa del quale non apparisce <lb></lb>al di fuori e non si guarda. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — E io, molto diversamente da quel che voi signor Sim­<lb></lb>plicio, credete, vi annunzio come cosa verissima che, quanto sarà più lungo <lb></lb>lo strumento da livellare tanto sarà minore l&#039;errore, che si potesse fare nella <lb></lb>linea di mira. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Che sia verissimo quel che il signor Salviati pronunzia <lb></lb>me lo persuade un pensiero, che m&#039;è sovvenuto pure ora alla mente, e che <lb></lb>io voglio esplicare al signor Simplicio con questo discorso: Supponete di <lb></lb>avere lo strumento prima lungo quanto AC (fig. </s>

<s>94), poi ridotto alla lun­<lb></lb>ghezza AF, e che, per essere il ramo del tubo in C più stretto del ramo <lb></lb><figure id="id.020.01.2620.1.jpg" xlink:href="020/01/2620/1.jpg"></figure></s></p><p type="caption">

<s>Figura 94.<lb></lb>in A, o per qualsivoglia altro motivo, erri la <lb></lb>linea di mira quanto DC. </s>

<s>Facendosi il me­<lb></lb>desimo errore anche in F, l&#039;effetto non è <lb></lb>però il medesimo, quanto al riferir la mira <lb></lb>per esempio sulla lunghezza della pertica BH, <lb></lb>messa innanzi per scopo. </s>

<s>È facile vedere che <lb></lb>si dilungherà dal vero punto della orizzon­<lb></lb>tale più in questo caso che in quello, ma si <lb></lb>può anche assai facilmente dimostrare se­<lb></lb>condo qual precisa proporzione si faccia l&#039;er­<lb></lb>rore, nell&#039;un caso e nell&#039;altro. </s>

<s>Perchè, presa <lb></lb>FE uguale a DC, e tirate le visuali AG, AH, le quali terminino sullo scopo <lb></lb>contrapposto in G e in H, i triangoli simili ACD, ABG danno che AB sta <lb></lb>a BG come AC a CD. Parimente, dai triangoli simili ABH, AFE, s&#039;ha che <lb></lb>AB sta a BH, come AF ad FE. </s>

<s>Se ne conclude perciò che AC verso AF ha <lb></lb>la proporzion medesima di BH verso BG, cosicchè se voi, signor Simplicio, <lb></lb>supponete che lo strumento più lungo sia per esempio sei braccia e il più <lb></lb>corto tre, quando quello facesse errore di quattro, questo invece farebbe er­<lb></lb>rore di otto. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Trattandosi di ragioni geometriche, dimostrate da Eu­<lb></lb>clide ne&#039;suoi libri degli Elementi, sarei da dire troppo stolto o troppo ca­<lb></lb>parbio, se non confessassi che il signor Sagredo mi ha persuaso col suo di­<lb></lb>scorso. </s>

<s>Passate perciò senz&#039;altro, voi signor Salviati, a levarmi la curiosità <lb></lb>di sapere come si possano misurar le distanze con la vista, non avendo altro <lb></lb>strumento a mano, che un rettangolo o un quadrato. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Vogliasi misurare un&#039;altezza, la cui radice non si ve-<pb xlink:href="020/01/2621.jpg" pagenum="246"></pb>desse, come saria l&#039;altezza del monte EF (fig. </s>

<s>95). Tirato il piano dell&#039;oriz­<lb></lb>zonte DF, pongasegli aderente per uno de&#039;suoi lati il quadrato o rettangolo <lb></lb>DC, e traguardando dall&#039;angolo D la sommità E segnisi la traccia della linea <lb></lb><figure id="id.020.01.2621.1.jpg" xlink:href="020/01/2621/1.jpg"></figure></s></p><p type="caption">

<s>Figura 95.<lb></lb>DC, ponendo in C uno scopo fisso, <lb></lb>come sarebbe per esempio uno <lb></lb>spillo. </s>

<s>Dipoi, accostiamoci verso il <lb></lb>monte, facendo strisciare il qua­<lb></lb>drato sul medesimo piano oriz­<lb></lb>zontale in modo, che l&#039;angolo, <lb></lb>che prima era in D, torni in A, e <lb></lb>si tenga conto della misura precisa <lb></lb>dell&#039;accostamento. </s>

<s>Si traguardi <lb></lb>nuovamente, e si trovi essere B <lb></lb>il punto, dove vuole esser posto <lb></lb>l&#039;occhio, perchè lo spillo e la sommità E si trovino disposti lungo la mede­<lb></lb>sima linea visuale. </s>

<s>Traccisi, allo stesso modo che dianzi, la CB sopra la su­<lb></lb>perficie del quadrato, e nessun&#039;altra operazione si richiede, fuor che misu­<lb></lb>rare le porzioni AB, CI sopra i lati dello stesso quadrato, per sapere quant&#039;è <lb></lb>l&#039;altezza FE, la quale dunque troverete con questa semplicissima regola: Par­<lb></lb>tite il fatto da CI in BD per AB, e l&#039;avvenimento sarà l&#039;altezza cercata. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Cotesta regola deve necessariamente conseguire dalla <lb></lb>proporzione AB sta a CI, come BD ad EF, ciò che poi pare a me molto fa­<lb></lb>cile a dimostrarsi, osservando che, per essere AC parallela a DE, i triangoli <lb></lb>simili ABC, DBE danno che come AB ad AC, così è BD a DE. Parimente, <lb></lb>essendo IC equidistante da FE, per li triangoli simili ACI, DEF, AC sta a <lb></lb>CI come DE ad EF, d&#039;onde viene ad aversi direttamente la proporzione, <lb></lb>sopra la quale il signor Salviati ha concluso la regola di misurare l&#039;altezza <lb></lb>del monte. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Per misurare poi una profondità, della quale non si ve­<lb></lb><figure id="id.020.01.2621.2.jpg" xlink:href="020/01/2621/2.jpg"></figure></s></p><p type="caption">

<s>Figura 96.<lb></lb>desse la radice, come se fossimo <lb></lb>sopra il monte BD (fig. </s>

<s>96), e <lb></lb>volessimo misurare la sua al­<lb></lb>tezza sopra il piano della cam­<lb></lb>pagna, non avendo noi altro stru­<lb></lb>mento che il detto quadrato, ope­<lb></lb>reremo con pari facilità in questo <lb></lb>modo: Poniamoci in C, appiè di <lb></lb>qualche casa, torre o albero, e <lb></lb>preso il quadrato in mano, dal­<lb></lb>l&#039;angolo superiore del quale sia <lb></lb>fatto pendere un filo, tirato da <lb></lb>un sassolino o da altro peso, <lb></lb>traguardiamo lungo la costola CI qualche segno, posto nel piano della cam­<lb></lb>pagna, come si vede nel punto A. </s>

<s>Segnata poi sulla superficie dello strumento <pb xlink:href="020/01/2622.jpg" pagenum="247"></pb>la traccia, lungo la direzione del filo, ascendiamo alle finestre della casa, <lb></lb>della torre, o sui rami dell&#039;albero in D, misurando la quantità dell&#039;ascesa <lb></lb>CD, e di lassù traguardando come dianzi il medesimo punto A si segni la <lb></lb>nuova direzione, che ha preso il filo, la quale sia per esempio FD. </s>

<s>Misurate <lb></lb>sopra la costola del quadrato le parti FE, EH, partite EH per AF, e l&#039;av­<lb></lb>venimento, moltiplicato per la misura dell&#039;ascesa DC, vi darà senz&#039;altro la <lb></lb>profondità del monte che si voleva. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Intendo bene che la regola è stabilita sopra la propor­<lb></lb>zione FE ad EH, come DC a CB: ma non vedo chiari questa volta i prin­<lb></lb>cipii, dai quali, voi signor Salviati, fate conseguire la verità annunziata. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Dal punto A, a cui tendono le linee delle mire CA, DA, <lb></lb>conducete la AB equidistante dalla orizontale: essendo ABC angolo retto, <lb></lb>saranno, per la XXXII del primo degli Elementi, GAB, ACB insieme uguali <lb></lb>ad un retto, e perciò CAB uguale a un retto meno ACB. </s>

<s>Ma anche ECG è <lb></lb>uguale a un retto (tale essendo l&#039;angolo del quadrato) meno ACB, dunque <lb></lb>BAG, ECG, che è il medesimo di EDH, sono uguali, e perciò i triangoli EDH, <lb></lb>BAC rettangoli saranno anche insieme equiangoli, e per la Va del VIo fra <lb></lb>loro simili. </s>

<s>” </s></p><p type="main">

<s>“ Passiamo ora a dimostrare, dietro le due citate proposizioni di Eu­<lb></lb>clide, che equiangoli pure e perciò simili sono i triangoli FED, CAD. </s>

<s>La ra­<lb></lb>gione, perchè si diceva dianzi che ECG è angolo uguale a CAB, è quella <lb></lb>medesima, per cui ora si dice che FDH è uguale a DAB, ond&#039;è che facil­<lb></lb>mente vedrete, signor Sagredo, com&#039;essendo FDE, CAD ciascuno la differenza <lb></lb>di due angoli uguali, debbon essere tra loro uguali. </s>

<s>L&#039;angolo esterno DEF <lb></lb>è uguale a un retto, con l&#039;angolo EDH, ossia CAB: ma anche l&#039;angolo <lb></lb>esterno ACD è uguale a un retto, col medesimo angolo CAB; dunque i due <lb></lb>detti esterni sono anch&#039;essi fra loro angoli uguali. </s>

<s>Il terzo angolo DFE, do­<lb></lb>vendo essere necessariamente uguale al terzo angolo ADC, non ci vuol altro <lb></lb>perchè riteniate per dimostrata l&#039;uguaglianza tra gli angoli, e la similitudine <lb></lb>tra due triangoli proposti, nei quali dunque, dovendo intercedere la pro­<lb></lb>porzionalità dei lati contrapposti agli angoli uguali, sarà EF ad EH, come DC <lb></lb>a CB, che è il fondamento della regola insegnata. </s>

<s>” </s></p><p type="main">

<s>Questa parte di Dialogo è stata da noi ritrovata fra le carte, che il Pan­<lb></lb>zanini consegnò al Bonaventuri, il quale non seppe ricavarne alcun utile per <lb></lb>la sua edizione, sgomentato dall&#039;apparirgli quelle stesse carte illeggibili, per <lb></lb>le macchie sparse e per i margini troppo addentro corrosi. </s>

<s>Fu tale anche la <lb></lb>nostra apprensione in principio, ma poi, trovando che le lacune eran tali da <lb></lb>potersi non difficilmente riempir con parole, se non identiche, equivalenti, non <lb></lb>ci siam fatti scrupolo di rassettare così l&#039;oggetto prezioso, piuttosto che get­<lb></lb>tarlo di nuovo. </s>

<s>Che sia opera di Galileo nella dettatura e nell&#039;andamento del <lb></lb>discorso ci si rende certo dalla certezza, che abbiamo essere opera del me­<lb></lb>desimo quanto alla sostanza, avendosi la proposizione degli errori negli stru­<lb></lb>menti da livellare, e le altre del misurar l&#039;altezza e la profondità colla vista, <lb></lb>autografe, in quel modo che ora trascriveremo, e ne&#039;luoghi che si citeranno, <pb xlink:href="020/01/2623.jpg" pagenum="248"></pb>quasi fretttolosi appunti e materia buona già preparata dallo stesso Galileo <lb></lb>a ricevere a suo tempo la bellezza della forma. </s></p><p type="main">

<s>“ PROPOSITIO XXIX, THEOREMA XXII. — <emph type="italics"></emph>Quanto sarà più lungo lo <lb></lb>strumento da livellare, tanto minore sarà l&#039;erŕore, che si potesse fare. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia la linea AC (nella figura 94 sopra segnata) quella del vero li­<lb></lb>vello, e dato che, con lo strumento lungo quanto AC, la linea visuale s&#039;alzi <lb></lb>sopra l&#039;estremità C quanto è la CD, con errore dal giusto livello quanto è <lb></lb>la linea BG; dico che, se si adoprerà lo strumento più corto, come AF, e <lb></lb>faccia nell&#039;estremo F l&#039;errore FE, uguale al CD, che l&#039;errore BH, fatto dalla <lb></lb>linea visuale ABH, rarà tanto maggiore del primo BG, quanto lo strumento <lb></lb>AC è più lungo dello strumento AF. Sicchè, se il primo strumento più lungo <lb></lb>sarà sei braccia, ed il primo errore sia di quattro braccia, e che il più corto <lb></lb>strumento sia tre braccia, l&#039;errore di questo sarà otto braccia. </s>

<s>Onde, tanto <lb></lb>quanto sarà più lungo lo strumento da livellare, tanto minore sarà l&#039;errore <lb></lb>che si potesse fare ” (MSS. Gal.., P. VI, T. II, fol. </s>

<s>13). </s></p><p type="main">

<s>“ PROPOSITIO XXX, PROBLEMA VII. — <emph type="italics"></emph>Per mezzo del quadrato misu­<lb></lb>rare l&#039;altezza inaccessibile FE, sopra il piano dell&#039;orizonte DE. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ut BA ad AC (riducendoci nuovamente sott&#039;occhio la figura 95, che <lb></lb>tien luogo delle molte parole non scritte da Galileo) ita BD ad DE. </s>

<s>Ut autem <lb></lb>AC ad CI, ita DE ad EF: ergo ut BA ad CI, ita BD ad EF ” (MSS. Gal., <lb></lb>P. V, T. II, fol. </s>

<s>136). </s></p><p type="main">

<s>“ PROPOSITIO XXXI, PROBLEMA VIII. — <emph type="italics"></emph>Col medesimo strumento mi­<lb></lb>surare la profondità CB, stando in C, e poi risalendo in D. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Proponendoci la figura 96, i principali tratti della soluzion del problema <lb></lb>son segnati da Galileo con queste parole: “ FE ad ED est ut DC ad CA. </s>

<s>Ut <lb></lb>autem ED ad EH, ita AC ad CB. </s>

<s>Ergo ex aequali ut FE ad EH, ita DC <lb></lb>ad CB. ” </s></p><p type="main">

<s>“ Parti EH per EF, e tante volte quant&#039;è l&#039;avvenimento entra DC <lb></lb>in CB ” (ivi, fol. </s>

<s>137). </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I teoremi geometrici, rimasti fuor di luogo, nel condurre le dimostra­<lb></lb>zioni già pubblicate nel terzo e nel quarto dialogo delle due Scienze nuove, <lb></lb>e i quali pensava Galileo negli ultimi anni della sua vita di salvar dall&#039;oblio; <lb></lb>si trovano autografi nel secondo tomo della parte quinta dei Manoscritti, dove <lb></lb>son raccolte le bozze, e d&#039;onde son ridotte a pulito per la stampa le prin­<lb></lb>cipali proposizioni dei moti accelerati e dei proietti. </s>

<s>Quanto ci abbiano gio­<lb></lb>vato coteste carte, per ritrarre in storia il concetto, gli svolgimenti graduali, <lb></lb>e le pene stesse del parto, ignorate dal pubblico, che solamente lo conobbe <lb></lb>già esposto; lo possono sapere tutti coloro, i quali hanno letto il nostro pre-<pb xlink:href="020/01/2624.jpg" pagenum="249"></pb>cedente tomo, nei capitoli VI e IX, ma è da soggiungere che il presente ar­<lb></lb>gomento porge occasione a considerar meglio, insieme col fine, l&#039;origine e <lb></lb>il tempo di certi teoremi di Meccanica notati nel detto Manoscritto, i quali, <lb></lb>accennando a un progresso del pensiero, ci mettono in gran curiosità di sa­<lb></lb>pere perchè mai Galileo non gli riducesse nei loro luoghi più convenienti, <lb></lb>per accrescer bellezza, e dar perfezione ai dialoghi da stamparsi. </s></p><p type="main">

<s>La questione, come s&#039;intende bene, è della natura di altre già da noi <lb></lb>risolute con dire che que&#039;pensieri non occorsero in tempo, per inserirsi nella <lb></lb>copia già consegnata nelle mani dell&#039;Elzevirio: e come tale fu la sorte della <lb></lb>proposizion che i momenti stanno in ragion composta delle distanze e dei <lb></lb>pesi, e che la catena si dispone in una curva, non differente dalla parabola; <lb></lb>tale è pur da dire essere stata la sorte di altre proposizioni, che ci occor­<lb></lb>rono a notare come un nuovo esempio dell&#039;aver Galileo pensato già a pro­<lb></lb>movere per sè stesso la sua propria scienza, nei medesimi modi, e anche <lb></lb>prima che vi desse opera il Torricelli. </s></p><p type="main">

<s>In un foglio del citato manoscritto, e sotto una figura, rappresentata <lb></lb>nella nostra 97, si legge scritta questa nota: “ Considera momentum in sin­<lb></lb><figure id="id.020.01.2624.1.jpg" xlink:href="020/01/2624/1.jpg"></figure></s></p><p type="caption">

<s>Figura 97.<lb></lb>gulis circumferentiae quadrantis punctis im­<lb></lb>minui, pro ratione accessus puncti perpendi­<lb></lb>cularis. </s>

<s>ut T ad centrum ” (MSS. Gal., P. V, <lb></lb>T. II, fol. </s>

<s>131) e più sotto espressa in forma <lb></lb>la proposizione seguente: </s></p><p type="main">

<s>“ PROPOSITIO XXXII, THEOREMA XXIV. — <lb></lb><emph type="italics"></emph>Momentum sub plano DC, ad totale momen­<lb></lb>tum, est ut linea TR ad RD, ducta LB ae­<lb></lb>quistante CD ”<emph.end type="italics"></emph.end> (ibid.). </s></p><p type="main">

<s>La considerazione è bene antica nella sto­<lb></lb>ria della Scienza, non essendo sfuggita alla <lb></lb>sagacia di Leonardo da Vinci, il quale, come <lb></lb>forse si ricorderanno coloro, i quali hanno letto il nostro quarto tomo, a <lb></lb>pag. </s>

<s>51, concludeva l&#039;annunziata proposizione galileiana dall&#039;osservar che la <lb></lb>sfera tanto sta in equilibrio sostenuta da un filo, quanto posata in quella di­<lb></lb>rezione sopra un piano inclinato. </s>

<s>La cosa era affatto nuova però nella scienza <lb></lb>pubblicata da Galileo, e come nuova apparve la prima volta in pubblico, nel <lb></lb>lemma dopo la seconda proposizione del primo libro del Torricelli. </s></p><p type="main">

<s>Una fra le eleganze della Meccanica torricelliana consiste nell&#039;uso del <lb></lb>semicerchio, per la invenzione delle medie proporzionali, di continuo maneg­<lb></lb>gio per risolvere i problemi dei tempi relativamente agli spazi. </s>

<s>Nè ci siamo <lb></lb>poco maravigliati che Galileo non tenesse questa via compendiosa, e di cosi <lb></lb>evidente eleganza: tanto più ripensando essere stato lui che, nella XXXIII <lb></lb>del III dialogo, e nel Lemma alla X del IV, l&#039;aveva aperta e additata allo <lb></lb>stesso Torricelli. </s>

<s>Dovremmo ora dire come si facesse quella maraviglia nel­<lb></lb>l&#039;animo nostro anche maggiore, quando prima ci abbattemmo a leggere, nel <lb></lb>suddetto codice manoscritto, il problema XV del III dialogo, per risolvere il <pb xlink:href="020/01/2625.jpg" pagenum="250"></pb>quale, invocandosi il semicerchio, a mezzo quella prolissa dimostrazione stam­<lb></lb>pata si sostituiva la snellezza del seguente processo: </s></p><p type="main">

<s>“ PROPOSITIO XXXIII, PROBLEMA IX. — <emph type="italics"></emph>Quaeritur in AC<emph.end type="italics"></emph.end> (fig. </s>

<s>98) <emph type="italics"></emph>pars <lb></lb>aequalis AB, quae conficiatur tempore aequali tempori AB. ”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2625.1.jpg" xlink:href="020/01/2625/1.jpg"></figure></s></p><p type="caption">

<s>Figura 98.</s></p><p type="main">

<s>“ Ponatur AD aequalis AB, et circa AC <lb></lb>semicirculus describatur, et ponatur AF aequa­<lb></lb>lis dimidiae DC, et ab F demittatur perpendi­<lb></lb>cularis FE, et EG ponatur aequalis AB. </s>

<s>Dico <lb></lb>EG, ex quiete in A, confici eodem tempore <lb></lb>ac AB. ” </s></p><p type="main">

<s>“ Media proportionalis inter CA, AG est <lb></lb>AI, et CI, cui aequatur EF, media inter CA, <lb></lb>AE.... ” (ibid., fol. </s>

<s>55). E a questo punto è <lb></lb>lasciata la dimostrazione interrotta, perchè do­<lb></lb>veva procedere da qui innanzi come dalla li­<lb></lb>nea 23 della stampata a pag. </s>

<s>218 del tomo XIII nella edizion dell&#039;Albèri. </s></p><p type="main">

<s>L&#039;uso del semicerchio rendeva facile e pronta a Galileo la soluzione di <lb></lb>un altro problema, simile al precedente, e di cui sarebbesi potuta arricchire <lb></lb>la raccolta delle proposizioni, lette nel terzo dialogo dal Salviati. <lb></lb><figure id="id.020.01.2625.2.jpg" xlink:href="020/01/2625/2.jpg"></figure></s></p><p type="caption">

<s>Figura 99.</s></p><p type="main">

<s>“ PROPOSITIO XXXIV, PROBLEMA X. — <emph type="italics"></emph>Quae­<lb></lb>ritur versus C<emph.end type="italics"></emph.end> (fig. </s>

<s>99) <emph type="italics"></emph>pars, quae conflciatur <lb></lb>eodem tempore ac AD. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sit tempus per AC, AC; tempus per AD <lb></lb>erit AE. </s>

<s>Ponatur GF aequalis AE, et ipsarum CA, <lb></lb>AF tertia proportionalis sit AG. </s>

<s>Dico GC esse <lb></lb>quod quaeritur. </s>

<s>” </s></p><p type="main">

<s>“ Cum enim tempus per totam AC sit AC, <lb></lb>tempus per AG erit AF, media inter CA, AG, et <lb></lb>reliqua FC erit tempus per GC. </s>

<s>Est autem FC posita aequalis AE; ergo pa­<lb></lb>tet propositum ” (ibid.). </s></p><p type="main">

<s>Un corollario però, che immediatamente si soggiunge, par che riveli la <lb></lb>fretta, dalla quale era frugato Galileo perchè non dovesse dimenticarsi la bella <lb></lb>novità trovata: ed è a questa fretta da attribuir forse l&#039;inconsideratezza delle <lb></lb>seguenti parole, alle quali si riduce il detto corollario: “ In qualibet latione <lb></lb>spacium, quod conficitur versus finem eodem tempore, ac spacium versus <lb></lb>principium, est medium proportionale inter totum lationis spatium, et ipsum <lb></lb>spatium versus principium ” (ibid). Ma la media proporzionale fra tutto lo <lb></lb>spazio, e lo spazio verso il principio, è CF, la quale non rappresenta già lo <lb></lb>spazio verso la fine, ma sì invece rappresenta il tempo, che il mobile im­<lb></lb>piega a percorrere lo spazio CG verso la fine. </s></p><p type="main">

<s>La sollecitudine in ogni modo dello scrivere così, senza tornare sopra a <lb></lb>considerare le cose scritte, è argomento che Galileo aspettava a farlo a mi­<lb></lb>glior tempo, e quando si fosse al punto d&#039;inserire i nuovi teoremi in una <lb></lb>prossima aspettata ristampa delle due Scienze nuove. </s>

<s>O forse pensava di rac-<pb xlink:href="020/01/2626.jpg" pagenum="251"></pb>coglierli nel dialogo novissimo, com&#039;è certo che pensava di raccogliervi il <lb></lb>teorema dei momenti nelle varie parti della circonferenza, intorno a che tro­<lb></lb>viamo il seguente frammento, fra le carte altre volte commemorate, e che <lb></lb>dovettero servire per l&#039;edizione del Bonaventuri: </s></p><p type="main">

<s>“ SAGREDO. — Bellissima sopra le altre mi è sembrata la considerazione <lb></lb>del nostro Accademico intorno al variar dei momenti nei singoli punti del <lb></lb>quadrante di un circolo grande, mentre la sfera tocca il piano inclinato, sopra <lb></lb>il quale sia obbligata a far la sua scesa, e perciò non vi dispiaccia, signor <lb></lb>Salviati, di dimostrare secondo qual proporzione si succedano via via, dal <lb></lb>contatto verticale all&#039;orizontale su un piano, le dette variazioni di moto. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Immaginate che sia DBC (nella precedente figura 97) il <lb></lb>quadrante, e B il punto del contatto sopra il piano LG, di cui sia GH l&#039;al­<lb></lb>tezza verticale. </s>

<s>Sapete, per la Scienza meccanica posta dal nostro Amico a <lb></lb>fondamento di queste sue nuove dottrine del moto, che l&#039;impeto dello scen­<lb></lb>dere in B sta all&#039;impeto totale, come GH sta a GL. Ora, dal punto B con­<lb></lb>ducete il raggio RB, e la BT perpendicolare all&#039;orizontale RD: vedrete fa­<lb></lb>cilmente come il triangolo rettangolo RBT sia simile al triangolo rettangolo <lb></lb>LGH, per cui l&#039;impeto, o il momento totale, che si diceva stare al parziale <lb></lb>in B come LG a GH, starà pure come RB, ossia RD, a RT sopra la mede­<lb></lb>sima lunghezza del raggio orizontale. </s>

<s>Passiamo a considerare un altro punto <lb></lb>qualunque M, a contatto col piano IE, il quale sia lungo quanto LG, e alto <lb></lb>quanto EK. </s>

<s>Fatta la medesima costruzione, e il medesimo ragionamento che <lb></lb>abbiamo fatto di sopra, troveremo essere il momento totale al parziale in M <lb></lb>come RD a RN, e di qui si conclude che i momenti, nei punti B, M del <lb></lb>quadrante, stanno come le porzioni RT, RN. Ora, perchè il discorso si ap­<lb></lb>plica a tutti e singoli i punti, compresi tra il contatto con la verticale in D, <lb></lb>e il contatto con la orizontale in C; può dunque concludersi in generale che <lb></lb>il momento nei singoli punti della circonferenza del quadrante diminuisce a <lb></lb>proporzione dell&#039;accostamento del punto perpendicolare, come T o N, al cen­<lb></lb>tro del circolo grande o della sfera. </s>

<s>” </s></p><p type="main">

<s>I riferiti esempi, che vengono ora ad aggiungersi ai parecchi altri, no­<lb></lb>tati da noi nel corso di questa storia della Meccanica, ci attestano, non solo <lb></lb>che Galileo si dava ogni sollecitudine di perfezionare i suoi trattati delle <lb></lb>Scienze nuove, ma che sarebbero que&#039;perfezionamenti in non poche parti <lb></lb>riusciti tali, da rendere inutile l&#039;opera de&#039;suoi stessi discepoli. </s>

<s>L&#039;attestazione <lb></lb>però non ci viene altro che per incidenza, in mezzo al proposito nostro pre­<lb></lb>sente, qual&#039;è di raccogliere quelle preparazioni geometriche, che servirono a <lb></lb>Galileo, per dimostrar nelle varie parti della Meccanica i più difficili teoremi. </s>

<s><lb></lb>E che propriamente non sian queste altro che preparazioni, lo dice il titolo <lb></lb>di <emph type="italics"></emph>lemma,<emph.end type="italics"></emph.end> scritto a molte in principio, come nella seguente, l&#039;enunciazion <lb></lb><figure id="id.020.01.2626.1.jpg" xlink:href="020/01/2626/1.jpg"></figure></s></p><p type="caption">

<s>Figura 100.<lb></lb>della quale è preceduta dalle parole <emph type="italics"></emph>redacta <lb></lb>est res ad hoc lemma.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ PROPOSITIO XXXV, THEOREMA XXV. — <lb></lb><emph type="italics"></emph>Sit EB<emph.end type="italics"></emph.end> (fig. </s>

<s>100) <emph type="italics"></emph>utcumque secta in A, et<emph.end type="italics"></emph.end><pb xlink:href="020/01/2627.jpg" pagenum="252"></pb><emph type="italics"></emph>inter EB, BA media sit BO, et ut EB ad BA, ita sit OB ad BN. </s>

<s>Dico <lb></lb>EB, BO, BA, BN esse continuae proportionales. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Quia enim, ut EB ad BO, ita BO ad BA, ratio EB ad BA erit dupla <lb></lb>rationis OB ad BA. </s>

<s>Et quia, ut EB ad BA, ita OB ad BN (est autem ratio <lb></lb>BE ad BA dupla rationis OB ad BA) erit quoque ratio OB ad BN dupla ra­<lb></lb>tionis BO ad BA. </s>

<s>Verum ipsa ratio OB ad BN componitur ex rationibus OB <lb></lb>ad BA, et AB ad BN; ergo ratio AB ad BN est eadem cum ratione OB ad <lb></lb>BA. </s>

<s>Ergo patet propositum ” (MSS. Gal., P. V, T. II, fol. </s>

<s>62). </s></p><p type="main">

<s>“ PROPOSITIO XXXVI, THEOREMA XXVI. — <emph type="italics"></emph>Sit linea AC<emph.end type="italics"></emph.end> (fig. </s>

<s>101) <lb></lb><figure id="id.020.01.2627.1.jpg" xlink:href="020/01/2627/1.jpg"></figure></s></p><p type="caption">

<s>Figura 101.<lb></lb><emph type="italics"></emph>maior ipsa DF, et habeat AB ad BC <lb></lb>maiorem rationem quam DE ad EF. </s>

<s><lb></lb>Dico AB ipsa DE maiorem esse. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Quia enim AB ad BC maiorem <lb></lb>rationem habet, quam DE ad EF; quam <lb></lb>rationem habet AB ad BC hane habe­<lb></lb>bit DE ad minorem quam EF. </s>

<s>Sit EG: et quia AB ad BC est ut DE ad <lb></lb>EG, erit, ut CA ad AB, ita GD ad DE. </s>

<s>Est autem CA maior DG; ergo et <lb></lb>BA ipsa DE maior erit ” (ibid., fol. </s>

<s>185). </s></p><p type="main">

<s>“ PROPOSITIO XXXVII, THEOREMA XXVII. — <emph type="italics"></emph>Secta CA<emph.end type="italics"></emph.end> (fig. </s>

<s>102) <emph type="italics"></emph>ut­<lb></lb>cumque in D, pars vero CD bifarium in I, dico quod, si fiat ut tota AC<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2627.2.jpg" xlink:href="020/01/2627/2.jpg"></figure></s></p><p type="caption">

<s>Figura 102.<lb></lb><emph type="italics"></emph>ad CI, ita ID ad DG, erit ut CA <lb></lb>ad AI, ita IA ad AG ”<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>84 <lb></lb>ad terg.). </s></p><p type="main">

<s>Galileo dimostra la proposizione <lb></lb>in due modi: il primo de&#039;quali è indiretto, e consiste nel ridurre, così, <lb></lb>l&#039;ipotesi a tesi: Sia dunque, come si vuol dimostrare, CA:AI=IA:AG: <lb></lb>dividendo, avremo CA—AI:AI=IA—AG:AG, ossia CI:AI=IG:AG, <lb></lb>e per metastasi CI:IG=AI:AG. </s>

<s>Da questa, con la prima data, si ot­<lb></lb>tiene CA:CI=AI:IG, e perchè AI=AC—IC, IG=ID—DG, <lb></lb>sarà CA:CI=AC—IC:ID—DG: ossia, moltiplicando gli estremi, ed <lb></lb>eguagliandone il prodotto al prodotto dei medii, CA.ID—CA.DG= <lb></lb>CI.AC—CI2. </s>

<s>Ora, essendo CI=ID, rimane CA.DG=CI2, ossia <lb></lb>AC:CI=CI:DG, o, sostituendo all&#039;antecedente CI della prima ragione il <lb></lb>suo uguale DI, AC:CI=DI:IG. </s>

<s>Ma cosi era fatto, dunque il fatto era vero. </s></p><p type="main">

<s>“ Si totum CA, così propriamente dice Galileo, ad totum AI est ut abla­<lb></lb>tum IA, ad ablatum AG, erit reliquum CI, ad reliquum IG, idest reliquum <lb></lb>DI, ad reliquum IG, ut totum CA ad AI, seu IA ad AG. </s>

<s>Et per conversio­<lb></lb>nem rationis ut AC ad CI. ita ID ad DG. </s>

<s>Sed ita factum est, ergo etc. </s>

<s>” <lb></lb>(ibid.). </s></p><p type="main">

<s>In altro modo diretto così Galileo dimostra la medesima proposizione: <lb></lb>Essendo dato ID:DG=AC:CI, dividendo, avremo ID—DG:ID= <lb></lb>AC—CI:AC, ossia IG:ID=AI:AC, e per essere DI=IC, e con­<lb></lb>vertendo, CA:AI=IC:IG. </s>

<s>Se poi si sostituiscono alle IC, IG le loro <lb></lb>uguali CA—AI, AI—AG, avremo CA:AI=CA—AI:AI—AG, <pb xlink:href="020/01/2628.jpg" pagenum="253"></pb>e ragguagliando il prodotto degli estremi con quello dei medii, avremo <lb></lb>AI.CA—AC.AG=AI.CA—AI2, d&#039;onde, riducendo, AC.AG= <lb></lb>AI2, ossia CA:AI=IA:AG, ch&#039;è quello appunto, che dovevasi dimo­<lb></lb>strare. </s></p><p type="main">

<s>“ Quia ID ad DG, dice Galileo, est ut AC ad CI, erit per conversionem <lb></lb>rationis ut CA ad AI, ita DI ad IG, seu IC ad IG. </s>

<s>Cum itaque sit ut totum <lb></lb>CA, ad totum AI, ita ablatum CI ad ablatum IG, erit ut reliqua IA, ad re­<lb></lb>liqua AG, ut totum CA, ad totum AI, quod erat ostendendum ” (ibid.). </s></p><p type="main">

<s>“ PROPOSITIO XXXVIII, PROBLEMA XI. — <emph type="italics"></emph>Faciendum ut AI ad IG<emph.end type="italics"></emph.end><lb></lb>(nella medesima figura 102) <emph type="italics"></emph>ita ID ad GD ”<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>84). </s></p><p type="main">

<s>È dato AC:CI=ID:DG, e dividendo AC:AC—CI=ID:ID—DG. </s>

<s><lb></lb>Fatte le sostituzioni, e ponendo IC in luogo di ID, avremo AC:AI= <lb></lb>CI:GI. Prendendo, invece di tutte le AC, AI, le loro parti, sarà AC+CI: <lb></lb>AG+IG=CI:GI, e fatto il prodotto degli estremi e de&#039;medii, e ridu­<lb></lb>cendo, AI.GI=CI.AG, d&#039;onde AI:AG=CI:GI, o, per essere CI=DI, <lb></lb>AI:AG=DI:GI. Dividendo, sarà in ultimo AI:AI—AG=DI:DI—GI, <lb></lb>e, dopo la sostituzione, AI:GI=DI:DG, come dovavasi fare. </s>

<s>Ma ascoltiamo <lb></lb>le parole proprie di Galileo. </s></p><p type="main">

<s>“ Ponatur IC aequalis ID, et fiat ut AC ad CI, ita ID ad DG. Erit, per <lb></lb>conversionem rationis, ut CA ad AI, ita DI ad IG, sen CI ad IG. </s>

<s>Et cum <lb></lb>totum CA, ad totum AI, ita ablatum CI ad ablatum IG; erit reliqua IA, ad <lb></lb>reliquum AG, ut ablatum CI, seu DI, ad IG. Et, per conversionem rationis, <lb></lb>ut AI ad IG, ita ID ad DG ” (ibid.). </s></p><p type="main">

<s>PROPOSITIO XXXIX, THEOREMA XXVIII. — <emph type="italics"></emph>Sia l&#039;angolo retto AXC<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>103), <emph type="italics"></emph>comunque diviso dalla XM, alla quale si conduca da A una per-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2628.1.jpg" xlink:href="020/01/2628/1.jpg"></figure></s></p><p type="caption">

<s>Figura 103.<lb></lb><emph type="italics"></emph>pendicolare, che la seghi in M, e si prolunghi infino all&#039;incontro della XC <lb></lb>in C. </s>

<s>Sia poi diviso l&#039;angolo CAX dalla AI in due parti uguali, e di qua<emph.end type="italics"></emph.end><pb xlink:href="020/01/2629.jpg" pagenum="254"></pb><emph type="italics"></emph>e di là da essa AI si conducano linee a piacere AL, AO, AP, ecc., le quali <lb></lb>tutte saranno intersecate dalla XM. </s>

<s>Dico che il rettangolo sotto la linea <lb></lb>AI, e sotto la sua intersezione dalla parte dell&#039;angolo A, sarà il minore <lb></lb>di tutti gli altri rettangoli sotto le altre linee, e le loro intersezioni dalla <lb></lb>medesima parte.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Rectangulum IAE esse omnium minimum LAB, OAN, PAE, etc., cum <lb></lb>angulus CAX bifariam sectus sit, pendet ex eo, quod angulus AEM trian­<lb></lb>guli AEM est aequalis angulo AIX trianguli AIX, et, quod consequens est, <lb></lb>minor omnium ALX, AOX, etc., et maior omnium API, ACI, etc. </s>

<s>” </s></p><p type="main">

<s>“ Probabitur ergo sic rectangulum IAE minus esse rectangulo LAB: <lb></lb>Cum enim angulus AME sit aequalis angulo AXI, et angulus MAE aequalis <lb></lb>angulo XAI (est enim angulus A bifariam sectus) ergo reliquus MEA reli­<lb></lb>quo XIA aequabitur. </s>

<s>Sed angulus AEM maior est angulo ABE, ergo angu­<lb></lb>lus AIL est maior angulo EBA. </s>

<s>Si igitur fiat angulus AIT angulo ABE ae­<lb></lb>qualis, erit, ob triangulortun similitudinem, ut IA ad AT, ita BA ad AE, et <lb></lb>rectangulum IAE rectangulo TAB aequale. </s>

<s>Ergo rectangulum IAE est minus <lb></lb>rectangulo LAB. ” </s></p><p type="main">

<s>“ Similiter ostendetur esse quoque minus rectangulo PAF. </s>

<s>Cum enim <lb></lb>angulus AEF, idest AIL, sit maius angulo API, erit reliquus AFE minor re­<lb></lb>liquo AIP. </s>

<s>Si igitur constituatur AIU angulo ipsi AFE aequalis, erit rectan­<lb></lb>gulum UAF rectangulo IAE aequale, ex quo patet propositum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Coroll. </s>

<s>I.<emph.end type="italics"></emph.end> — Demonstrabitur etiam quod rectangula talia, quae a li­<lb></lb>neis ex A ad lineam CX ductis, et a linea XM sectis, ea, quae fiunt a lineis <lb></lb>vicinioribus ipsi AEI, semper minora sunt illis, quae a remotioribus descri­<lb></lb>buntur lineis. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Coroll. </s>

<s>II.<emph.end type="italics"></emph.end> — Constat insuper quod media inter IAE est omnium me­<lb></lb>diarum minima, quae cadunt inter PAF, LAB, etc. </s>

<s>” (ibid., fol. </s>

<s>30 ad tergum). </s></p><p type="main">

<s>Accenna Galildo in fine al manoscritto a un&#039;altra dimostrazione dello <lb></lb>stesso teorema, che, per mezzo della descrizione di un semicerchio, e dietro <lb></lb>le note proprietà delle tangenti e delle recanti di lui, riesce assai più breve. <lb></lb><figure id="id.020.01.2629.1.jpg" xlink:href="020/01/2629/1.jpg"></figure></s></p><p type="caption">

<s>Figura 104.</s></p><p type="main">

<s>“ Aliter brevius: Posito angulo AES aequale angulo <lb></lb>EAM erit linea ES parallela AM. </s>

<s>Ergo perpendicularis ad <lb></lb>MX: eritque aequalis SA. Quare, centro S et intervallo SE, <lb></lb>circulus tanget MX in E, unde patet propositum ” (ibid., <lb></lb>fol. </s>

<s>130 ad tergum). </s></p><p type="main">

<s>PROPOSITIO XL, PROBLEMA XII. — <emph type="italics"></emph>Nel triangolo OB<gap></gap><emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>104) <emph type="italics"></emph>rettangolo in B, divisa l&#039;ipotenusa CO in parti <lb></lb>date, e data la distanza dal punto H della divisione al <lb></lb>cateto BO; trovare la lunghezza di esso cateto.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Condotta dal punto H la LH, parallela a BI, ecco come <lb></lb>Galileo risolve il facile problema: “ Detur IH, dabitur IO. <lb></lb>per ablationem quadrati IH ex quadrato HO. Deinde, ablata IH ex BC, datur <lb></lb>LC, cuius quadratum, ablatum ex quadrato CH dato, dat quadratum LH, et <lb></lb>ipsam LH, idest BI. </s>

<s>Ergo dabitur tota BO (ibid., fol. </s>

<s>132 ad t.). </s></p><pb xlink:href="020/01/2630.jpg" pagenum="255"></pb><p type="main">

<s>PROPOSITIO XLI, THEOREMA XXIX. — <emph type="italics"></emph>Alle estremità del diametro AF<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>105) <emph type="italics"></emph>condotte le tangenti AB, FE, e la secante BE, “ si ut EB ad <lb></lb>BD, ita est DB ad BC, erit ita ED ad DC: et quia EB est dupla BC, erit <lb></lb>quadratum ED duplum quadrati DC ”<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>158). <lb></lb><figure id="id.020.01.2630.1.jpg" xlink:href="020/01/2630/1.jpg"></figure></s></p><p type="caption">

<s>Figura 105.</s></p><p type="main">

<s>Se EB:BD=BD:BC, dividendo <lb></lb>avremo EB—BD:BD=BD—BC:BC, <lb></lb>ossia ED:BD=DC:BC, e per meta­<lb></lb>stasi ED:DC=BD:BC, dalla quale <lb></lb>e dalla prima s&#039;ha EB:BD=ED:DC. </s>

<s><lb></lb>Da questa, che conferma la verità della <lb></lb>prima parte del teorema, inalzata a qua­<lb></lb>drato, ed osservando che BD2=EB.BC, <lb></lb>se ne deduce EB2:EB.BC=ED2:DC2, <lb></lb>ossia EB:BC=ED2:DC2, che conferma la verità dell&#039;altra parte dello stesso <lb></lb>teorema, perch&#039;essendo EB il doppio di BC, anche ED2 sarà il doppio di DC2. <lb></lb><figure id="id.020.01.2630.2.jpg" xlink:href="020/01/2630/2.jpg"></figure></s></p><p type="caption">

<s>Figura 106.</s></p><p type="main">

<s>PROPOSITIO XLII, THEOREMA XXX. — <emph type="italics"></emph>Nel semicir­<lb></lb>colo ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>106) <emph type="italics"></emph>sia condotta la corda AB, e dalla <lb></lb>estremità di lei la BG perpendicolare al diametro: con­<lb></lb>dotta un&#039;altra corda qualunque, come AC, la quale tagli <lb></lb>in D quella stessa perpendicolare, dico che il quadrato di <lb></lb>AB è uguale al rettangolo di AC in AD.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il quadrato di AB è uguale ad AH.AG. </s>

<s>Ma condotta <lb></lb>la corda CH i triangoli simili ACH, ADG danno AH:AD= <lb></lb>AC:AG, dunque AH.AG è uguale ad AD.AC, e perciò <lb></lb>il quadrato di AB è uguale al rettangolo di AC in AD, come <lb></lb>Galileo dimostra con queste brevi parole: “ AB est media <lb></lb>inter CA, AD: nam rectangulus CAD aequatur rectangulo <lb></lb>HAG. </s>

<s>Si enim ducatur HG, erit triangulus ACH simile triangulo ADG ” <lb></lb>(ibid., fol. </s>

<s>35). </s></p><p type="main">

<s>“ PROPOSITIO, XLIII, THEOREMA XXXI. — <emph type="italics"></emph>Sit IC<emph.end type="italics"></emph.end> (fig. </s>

<s>107) <emph type="italics"></emph>perpendi­<lb></lb>cularis ad diametrum circuli AB, ductaque a puncto A quacumque linea,<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2630.3.jpg" xlink:href="020/01/2630/3.jpg"></figure></s></p><p type="caption">

<s>Figura 107<lb></lb><emph type="italics"></emph>circumferentiae et perpendiculari <lb></lb>CI occurrens, ut AID, AD, ADI, <lb></lb>dico rectangulum DAI rectangulo <lb></lb>BAC esse aequale ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Si enim iungatur recta DB, <lb></lb>erit angulus in semicirculo, ad pun­<lb></lb>ctum D, rectus, estque angulus C <lb></lb>quoque rectus, communis autem an­<lb></lb>gulus ad A. </s>

<s>Ergo triangulorum ae­<lb></lb>quiangulorum DAB, CAI latera erunt <lb></lb>proportionalia, utque BA ad AD, ita <lb></lb>IA ad AC. </s>

<s>Ergo patet propositum ” <lb></lb>(ibid.). </s></p><pb xlink:href="020/01/2631.jpg" pagenum="256"></pb><p type="main">

<s>PROPOSITIO XLIV, THEOREMA XXXII. — <emph type="italics"></emph>Sit circulus, cuius diameter AB<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>108) <emph type="italics"></emph>et ipsi parallela tangens CE, et ex termino B quaelibet linea BO<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2631.1.jpg" xlink:href="020/01/2631/1.jpg"></figure></s></p><p type="caption">

<s>Figura 108.<lb></lb><emph type="italics"></emph>in circulo applicetur. </s>

<s>Dico perpendiculares, quae <lb></lb>a termino B et O ipsi BO accommodantur, pro­<lb></lb>tractas, de linca CE partem diametro circuli ae­<lb></lb>qualem semper intercipere. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Iungantur enim A, O, et extendatur ad <lb></lb>tangentem in F, quae ad BO erit perpendicularis, <lb></lb>cui ex B parallela sit BE: demonstrandum FE <lb></lb>diametro circuli esse aequalem. </s>

<s>Id autem constat, <lb></lb>quia in parallelogrammo ABEF latera AB, FE <lb></lb>opposita aequalia sunt, ex Elementis. </s>

<s>” </s></p><p type="main">

<s>“ Vel dicas quod ducta, ex O, OG parallela <lb></lb>ipsi AB, et BG perpendiculari ad BO, abscindet <lb></lb>semper OG aequalis diametro circuli, quod patet <lb></lb>ex triangulis AOB, OBG similibus et aequalibus ” <lb></lb>(ibid., fol. </s>

<s>68). </s></p><p type="main">

<s>“ PROPOSITIO XLV, THEOREMA XXXIII. — <lb></lb><emph type="italics"></emph>Est LI ad IE<emph.end type="italics"></emph.end> (fig. </s>

<s>109) <emph type="italics"></emph>ut IA ad AE; CF autem <lb></lb>ad FE, ut FD ad DE, et sunt EF, EI aequa­<lb></lb>les: probandum est LE maiorem esse quam CE ”<emph.end type="italics"></emph.end><lb></lb>(ibid., fol. </s>

<s>61). </s></p><p type="main">

<s>Abbiamo IE/EA&gt;FE/ED perch&#039;essendo i numeratori uguali per supposizione. </s>

<s><lb></lb>EA è minore del denominatore ED. Componendo, sarà (IE+EA)/EA&gt;(FE+ED)/ED, <lb></lb>ossia AI/EA&gt;FD/ED. </s>

<s>Son dati IA/AE=LI/IE, FD/DE=CF/FE; dunque LI/IE&gt;CF/FE, e com­<lb></lb><figure id="id.020.01.2631.2.jpg" xlink:href="020/01/2631/2.jpg"></figure></s></p><p type="caption">

<s>Figura 109.<lb></lb>ponendo, LE/EI&gt;CE/EF.Ma EI=EF, dunque LE&gt;CE. <lb></lb>come dimostra Galileo con discorso simile a questo <lb></lb>nella sostanza, benchè alquanto differente nella <lb></lb>forma. </s></p><p type="main">

<s>“ Quia EA minor est ED, IE ad EA maio­<lb></lb>rem habet rationem, quam FE ad ED. Et, com­<lb></lb>ponendo, IA ad AE maiorem rationem habet quam <lb></lb>FD ad DE. Verum, ut IA ad AE, ita est LI ad IE. </s>

<s><lb></lb>Ut autem FD ad DE, ita CF ad FE. </s>

<s>Ergo LI ad IE <lb></lb>maiorem rationem habet, quam CF ad FE. Et, <lb></lb>componendo, LE ad EI maiorem habet rationem, <lb></lb>quam CE ad EF. </s>

<s>Sunt autem EF, EI aequales; <lb></lb>ergo LE maior est quam CE ” (ibid.). </s></p><p type="main">

<s>“ PROPOSITIO XLVI, THEOREMA XXXIV. — <emph type="italics"></emph>Fiat ut BA<emph.end type="italics"></emph.end> (fig. </s>

<s>110), <emph type="italics"></emph>cum <lb></lb>dupla AC, ad AC, ita CA ad AE, et ut BA ad AC, ita EA ad AR, et<emph.end type="italics"></emph.end><pb xlink:href="020/01/2632.jpg" pagenum="257"></pb><emph type="italics"></emph>ab R ducatur perpendicularis RX. </s>

<s>Dico CR, ER, RA esse proportionales <lb></lb>et amplius EA, XA aequales. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2632.1.jpg" xlink:href="020/01/2632/1.jpg"></figure></s></p><p type="caption">

<s>Figura 110.</s></p><p type="main">

<s>“ Quia enim ut BA, cum dupla AC, ad AC, ita <lb></lb>CA ad AE, dividendo erit ut BA cum AC ad AC, ita <lb></lb>CE ad EA. </s>

<s>Et quia ut BA ad AC, ita EA ad AR, erit <lb></lb>componendo ut BA, cum AC, ad AC, ita ER ad RA. </s>

<s><lb></lb>Sed ut BA, cum AC, ad AC, ita CE ad EA, ergo ut <lb></lb>CE ad EA, ita ER ad RA, et ambo antecedentia ad <lb></lb>ambo consequentia, nempe CR ad RE. </s>

<s>Sunt itaque CR, <lb></lb>ER, RA proportionales ” (ibid., fol. </s>

<s>69). </s></p><p type="main">

<s>Dalla CE:ER=EA:RA abbiamo componendo CE+ER:ER= <lb></lb>EA+RA:RA, ossia CR:ER=ER:AR. </s></p><p type="main">

<s>“ Et amplius: quia ut BA ad AC, ita positum est EA ad AR, et, propter <lb></lb>similitudinem triangulorum, ut BA ad AC, ita XA ad AR; ergo ut EA ad <lb></lb>AR, ita XA ad AR. </s>

<s>Sunt itaque EA, XA aequales ” (ibid.). </s></p><p type="main">

<s>PROPOSITIO XLVII, THEOREMA XXXV. — <emph type="italics"></emph>Nel quadrante AEB<emph.end type="italics"></emph.end> (fig. </s>

<s>111) <lb></lb><emph type="italics"></emph>tirata la corda AB, e la secante AC, sopra la quale si costituisca il punto S,<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2632.2.jpg" xlink:href="020/01/2632/2.jpg"></figure></s></p><p type="caption">

<s>Figura 111.<lb></lb><emph type="italics"></emph>in modo che AS sia terza proporzionale <lb></lb>fra AC, AE; dico che AB ad AS è come <lb></lb>il cubo di BA al cubo di AE.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Si suppone da Galileo il primo <lb></lb>Lemma alla proposizione XXXVI del <lb></lb>terzo dialogo delle due Scienze nuove, in <lb></lb>cui si dimostra che il quadrato di AB è <lb></lb>uguale al rettangolo di CA in AE, d&#039;onde <lb></lb>AB2:AE=AC:1, ossia AB2:AE2= <lb></lb>AC:AE. </s>

<s>E perchè AS è terza propor­<lb></lb>zionale dopo AC, AE avremo AB2:AE2=AC:AE=AE:AS. </s>

<s>Ma per le <lb></lb>note proprietà geometriche è, chiamato D il diametro di tutto intero il cer­<lb></lb>chio, AC2=D.AN, AE2=D.AR, dunque AB2:AE2=AE:AS= <lb></lb>AN:AR. </s>

<s>Moltiplicando la proporzione AB2:AE2=AE:AS per l&#039;identica <lb></lb>BA:AE=BA:AE, se ne conclude all&#039;ultimo AB3:AE3=BA.AE:AS.AE= <lb></lb>BA:AS, ch&#039;è la proposta di Galileo, da lui stesso dimostrata con queste pa­<lb></lb>role, che trascriviamo. </s></p><p type="main">

<s>“ Ut CA ad AB, ita AB ad AE. </s>

<s>Ergo ut quadratum CA, ad quadra­<lb></lb>tum BA, vel quadratum BA, ad quadratum AE, ita CA ad AE, vel AE ad <lb></lb>AS. </s>

<s>Fiet autem hoc, si ipsarum CA, AE accipiatur tertia proportionalis AS. </s>

<s><lb></lb>At quadratum BA, ad quadratum AE, est ut rectangulum ex diametro in AN. <lb></lb>ad rectangulum ex diametro in AR, quibus sunt aequalia; ergo ut EA ad AS, <lb></lb>ita NA ad RA, idest altitudo lineae BA, ad altitudinem lineae AE. </s>

<s>Linea <lb></lb>ergo BA ad AS est ut cubus BA ad cubum AE ” (ibid., fol. </s>

<s>188). </s></p><p type="main">

<s>“ PROPOSITIO XLVIII, THEOREMA XXXVI. — <emph type="italics"></emph>Productis lateribus AB, <lb></lb>AC<emph.end type="italics"></emph.end> (fig. </s>

<s>112) <emph type="italics"></emph>versus D, E, et erectis perpendicularibus CG, BF, ponatur <lb></lb>AN aequalis AC, et ut AB ad BN, ita fiat AL ad LC, et ipsi AL sece-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2633.jpg" pagenum="258"></pb><emph type="italics"></emph>tur aequalis AI, ipsarumque AC, IB tertia proportionalis sit CE. </s>

<s>Et dia­<lb></lb>metro AE semicirculus ducatur, secans CG in G, ductaque per E paral-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2633.1.jpg" xlink:href="020/01/2633/1.jpg"></figure></s></p><p type="caption">

<s>Figura 112.<lb></lb><emph type="italics"></emph>lela ED, occurrenti AB protractae in D, alter <lb></lb>semicirculus describatur secans perpendiculum <lb></lb>BF in F, et iungatur FA. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Primo, constat ut AB ad BD, ita esse <lb></lb>AC ad CE, et mediam BF, ad mediam CG, ut <lb></lb>AB ad AC ” (ibid., fol. </s>

<s>55). </s></p><p type="main">

<s>Consta la prima parte dall&#039;essere BC, DE <lb></lb>parallele, per cui le due linee AD, AE son ta­<lb></lb>gliate in modo, da dare la proporzione AB:BD= <lb></lb>AC:CE, d&#039;onde BD=AB.CE/AC, CE=BD.AC/AB. </s>

<s>Le due medie poi BF, CG <lb></lb>ne&#039;semicerchi danno BF:CG=√AB.BD:√AC.CE, d&#039;onde, sostituiti <lb></lb>i valori di BD, CE, consta la verità della seconda parte dell&#039;asserto, che cioè <lb></lb>BF:CG=AB:AC. </s></p><p type="main">

<s>“ Secundo, constat insuper IB esse aequale CG ” (ibid.). </s></p><p type="main">

<s>È infatti IB2=AC.CE, per costruzione, ma anche CG2=AC.CE, <lb></lb>per le note proprietà del circolo, dunque IB=CG. </s></p><p type="main">

<s>“ Tertio, cumque FB maior sit CG, ponatur BS ipsi CG aequalis. </s>

<s>Et <lb></lb>quia ut BA ad AC, seu AN, ita FB ad CG, seu BS, erit, ut AB ad BN, hoc <lb></lb>est AL, ad LC, ita BF ad FS: et rectangulum sub FB, LC erit aequale rectan­<lb></lb>gulo sub AL, FS, seu sub AI, FS ” (ibid.). </s></p><p type="main">

<s>Ci è constato in primo luogo AB:AC=FB:CG, ossia AB:AN= <lb></lb>FB:CG. </s>

<s>Dividendo e sostituendo, avremo AB:BN=FB:FS=AE:LC, <lb></lb>d&#039;onde FB.LC=AL.FS=AI.FS, in conformità con l&#039;ultima conclu­<lb></lb>sione pronunziata da Galileo. </s>

<s>Che poi fossero così fatte conclusioni geome­<lb></lb>triche preparate per dimostrare la XXXIV proposizione meccanica, scritta nel <lb></lb><figure id="id.020.01.2633.2.jpg" xlink:href="020/01/2633/2.jpg"></figure></s></p><p type="caption">

<s>Figura 113.<lb></lb>terzo dialogo delle due Scienze nuove, <lb></lb>apparisce manifesto dalla lettura dello <lb></lb>stesso Dialogo, e vien confermato dalla <lb></lb>seguente nota, scritta in margine al fo­<lb></lb>glio ultimamente citato: “ Totum opus <lb></lb>videtur esse tale: Secetur AN aequalis <lb></lb>AC, et, ut AB ad BN, ita fiat AL ad LC, <lb></lb>et ponatur AI aequalis AL, et, ut AC ad <lb></lb>IB, ita fiat IB ad CE. </s>

<s>Erit CE linea quae­<lb></lb>sita, nempe pars superior perpendiculi, ex <lb></lb>qua mobile conficiet ipsam cum AB, tem­<lb></lb>pore eodem ac solam AB. ” </s></p><p type="main">

<s>PROPOSITIO XLIX, THEOREMA XXXVII. — <emph type="italics"></emph>Sia il cerchio NDC<emph.end type="italics"></emph.end> (fig. </s>

<s>113) <lb></lb><emph type="italics"></emph>al diametro NC del quale sia condotto perpendicolare il raggio RD, che <lb></lb>prolungato venga preciso in A dalla secante CBA. </s>

<s>Dal punto D si con­<lb></lb>duca DS parallela al detto diametro, e dal punto M, metà della stessa<emph.end type="italics"></emph.end><pb xlink:href="020/01/2634.jpg" pagenum="259"></pb><emph type="italics"></emph>DS, si alzi la perpendicolare MF, che incontrerà in F la corda CD. </s>

<s>Es­<lb></lb>sendo l&#039;angolo FDM semiretto, sarà DM uguale a FM, e col centro in M, <lb></lb>intervallo DM, si descriva la circonferenza DFS. </s>

<s>Fatto ciò, Galileo nota le <lb></lb>tre seguenti proprietà geometriche, che conseguono da una tal costruzione:<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ I. — Rectangulum CDF aequatur rectangulo RC, DS; rectangulum <lb></lb>ACB aequatur rectangul<emph type="italics"></emph>o<emph.end type="italics"></emph.end> RCN; ergo rectangulum CDF, ad rectangulum ACB, <lb></lb>est ut diameter DS ad diametrum NC ” (ibid., fol. </s>

<s>149 ad terg.). </s></p><p type="main">

<s>Infatti i triangoli simili RDC, DFS danno RC:DF=CD:DS, d&#039;onde <lb></lb>DF.CD=RC.DS. </s>

<s>E condotta la NB, i triangoli simili NBC, RAC <lb></lb>danno AC:CN=RC:CB, d&#039;onde AC.CB=CN.RC. </s>

<s>E perciò avremo <lb></lb>DF.CD:AC.CB=RC.DS:RC.CN, ossia DF.CD:AC.CB= <lb></lb>DS:CN, com&#039;aveva concluso Galileo. </s></p><p type="main">

<s>“ II. — Ut autem CN ad DS ita CD ad DF, ob similitudinem portio­<lb></lb>num DBC et DF ” (ibid.). </s></p><p type="main">

<s>Dall&#039;essere infatti NC2=2DC2, DS2=2DF2, ne consegue CN:DS= <lb></lb>DC:DF. </s></p><p type="main">

<s>“ III. — Ut autem CD ad DF, ita quadratum CO ad quadratum OF ” <lb></lb>(ibid.). </s></p><p type="main">

<s>È stato fatto tacitamente CD:DO=DO;DF. Dividendo, avremo <lb></lb>CD—DO:DO=DO—DF:DF. </s>

<s>Sostituendo e trasponendo, CO:OF= <lb></lb>DO:DF, la quale equazione inalzata a quadrato dà CO2:OF2=DO2:DF2. </s>

<s><lb></lb>Ma DO2=CD.DF, per la prima, dunque CO2:OF2=CD.DF:DF2, <lb></lb>ossia CO2:OF2=CD:DF, che conferma la verità dell&#039;ultima conclusione <lb></lb>di Galileo. </s></p><p type="main">

<s>PROPOSITIO L, THEOREMA XXXVIII. — <emph type="italics"></emph>Abbiansi nel circolo EIC<emph.end type="italics"></emph.end> (fig. </s>

<s>114) <lb></lb><emph type="italics"></emph>le tangenti ED, BC parallele, e la secante DB disposta in modo che, inal-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2634.1.jpg" xlink:href="020/01/2634/1.jpg"></figure></s></p><p type="caption">

<s>Figura 114.<lb></lb><emph type="italics"></emph>zatale sopra, da A centro, una per­<lb></lb>pendicolare, questa incontri in F la <lb></lb>ED prolungata, cosicchè, descritta col <lb></lb>raggio FA la circonferenza AOP, la <lb></lb>parte esterna OD torni uguale alla <lb></lb>ID. </s>

<s>Dico che la somma delle linee <lb></lb>DF, FA, alla somma delle DA, AE <lb></lb>sta come il quadrato di AD, o di AB, <lb></lb>al quadrato di ED o di BC.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Essendo, per la XXXVI del terzo <lb></lb>di Euclide, PD.DO=AD2, ND.DI= <lb></lb>ED2, avremo dunque, rammemorandoci <lb></lb>che DO, DI sono uguali, PD:ND= <lb></lb>AD2:ED2. </s>

<s>Ma PD=DF+FA, ND= <lb></lb>EA+AD, e AD, ED sono uguali ad AB, BC: dunque DF+FA:EA+AD= <lb></lb>AD2:ED2=AB2:BC2; come in modo simile Galileo stesso dimostra col se­<lb></lb>guente discorso, che la brevità del nostro renderà forse più chiaro: </s></p><p type="main">

<s>“ Si excessus OD aequatur DI, rectangulum PDO, idest quadratum DA, <pb xlink:href="020/01/2635.jpg" pagenum="260"></pb>ad rectangulum NDI, idest ad quadratum DE, erit ut linea PD ad DN. </s>

<s>Qua­<lb></lb>dratum autem DA, ad quadratum DE, est ut quadratum AB, ad quadra­<lb></lb>tum BC; ergo faciendum est ut PD ad ND sit ut quadratum AB, ad qua­<lb></lb>dratum BC. PD autem componitur ex duobus mediis DF, FA, et ND constat <lb></lb><figure id="id.020.01.2635.1.jpg" xlink:href="020/01/2635/1.jpg"></figure></s></p><p type="caption">

<s>Figura 115.<lb></lb>ex duabus EA, AD, ita ut duae DF, FA, ad duas <lb></lb>DA, AE, sint ut quadratum AB, ad quadratum BC ” <lb></lb>(ibid., fol. </s>

<s>99). </s></p><p type="main">

<s>“ PROPOSITIO LI, PROBLEMA XIII. — <emph type="italics"></emph>Dato per­<lb></lb>pendiculo AB<emph.end type="italics"></emph.end> (fig. </s>

<s>115) <emph type="italics"></emph>et inflexa EBG, cui perpen­<lb></lb>dicularis sit BC; oportet semicirculum per E de­<lb></lb>scribere ita ut excessus mediae inter EG, GB, quae <lb></lb>est GC, seu GD, una cum perpendiculo BF, secto <lb></lb>a perpendiculari GF, sint aequales mediae inter <lb></lb>EB, BG, nempe BC. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sit factum. </s>

<s>Si CB aequatur DB, BF, posita <lb></lb>communi BG, duae CB, BG, erunt aequales duabus DG, BF; idest CG, BF ” <lb></lb>(ibid., fol. </s>

<s>97 ad tergum). </s></p><p type="main">

<s>Se CB=DB+BF, aggiunta la comune BG, sarà BG+CB= <lb></lb>DB+BF+BG=DG+BF, d&#039;onde CB=DG+BF—BG, e perciò <lb></lb>BG è l&#039;eccesso cercato. </s></p><p type="main">

<s>PROPOSITIO LII, THEOREMA XXXIX. — <emph type="italics"></emph>Nel quadrante TCN<emph.end type="italics"></emph.end> (fig. </s>

<s>116) <lb></lb><emph type="italics"></emph>prendasi una porzione TCD, dall&#039;estremità D della quale si abbassi la DX<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2635.2.jpg" xlink:href="020/01/2635/2.jpg"></figure></s></p><p type="caption">

<s>Figura 116.<lb></lb><emph type="italics"></emph>perpendicolare al diametro TM, e condotta la <lb></lb>DF, ad esso diametro parallela, se le descriva <lb></lb>sopra il mezzo cerchio DCF. </s>

<s>Condotta la corda <lb></lb>DT, e la DC prolungata in S, infino all&#039;incon­<lb></lb>tro con la tangente TS, presa poi la DE media <lb></lb>proporzionale fra DS, DC, se si congiungano <lb></lb>con E i punti S, B, C, dico che EB sarà bisset­<lb></lb>trice dell&#039;angolo SEC.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Galileo stette a principio incerto se ciò fosse <lb></lb>vero, e in capo a un primo tentativo di dimostra­<lb></lb>zione scriveva: <emph type="italics"></emph>Credo angulum SEC bifariam <lb></lb>esse sectum per EB<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>129), incominciando a ragionare, per veder <lb></lb>se la cosa riusciva, in questo modo: </s></p><p type="main">

<s>“ Angulus TDS duabus circumferentiis OC, CT insistit; ergo illae sunt <lb></lb>similes, et circumferentia DO similis est DCT. Ergo, ut linea DO ad OC, ita <lb></lb>DT ad TC. </s>

<s>Et quia rectangulum DSC aequatur quadrato ST, ergo, ut DS <lb></lb>ad ST, ita TS ad SC. </s>

<s>Ergo triangula DST, TSC similia sunt, quibus et trian­<lb></lb>gula ODC, ICB similia sunt .... ” (ibid.). </s></p><p type="main">

<s>Trovatosi da un tal discorso aggirato, Galileo lasciò la dimostrazione in­<lb></lb>terrotta, e poco di poi tornatoci sopra, ebbe dalle seguenti brevi considera­<lb></lb>zioni la desiderata conferma della propria opinione. </s>

<s>Se DS:DE=DE:DC, <lb></lb>dunque i triangoli SDE. DEC son simili. </s>

<s>Ed essendo fatta DE=DB, da <pb xlink:href="020/01/2636.jpg" pagenum="261"></pb>DS:DB=DB:DC avremo, dividendo, SD—BD:SD=DB—DC:DE, <lb></lb>d&#039;onde, per sostituzione e per trasposizione, SD:DE=SB:BC. Ma, per i <lb></lb>detti triangoli simili, SD:DE=SE:EC, dunque SE:EC=SB:BC, <lb></lb>ond&#039;è, per la terza del Sesto, EB veramente bissettrice. </s></p><p type="main">

<s>“ Quia est, scrive Galileo, ut SD ad DE, ita DE ad DC, ergo triangu­<lb></lb>lus SDE similis ert triangulo DEC, et, ut SE ad EC, ita SD ad DE, et ita <lb></lb>est SB ad BC: ergo angulus CES bifariam secatur a linea EB ” (ibid.). </s></p><p type="main">

<s>A queste proposizioni di Geometria elementare si può aggiungere la se­<lb></lb>guente, che solamente annunziamo per essere stata già trascritta dall&#039;auto­<lb></lb>grafo galileiano, a pag. </s>

<s>450 del nostro Tomo quarto: </s></p><p type="main">

<s>“ PROPOSITIO LIII, THEOREMA XL. — <emph type="italics"></emph>Sit parabola parallelogrammo <lb></lb>inscripta: dico parallelogrammum parabolae esse sesquialter; hoc est esse <lb></lb>triplum reliqui spacii extra parabolam ”<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>102 ad tergum). </s></p><p type="main">

<s>D&#039;altri teoremi di Geometria superiore non ci sono occorsi, nell&#039;esame <lb></lb>dei manoscritti, gli esempi, e dall&#039;altra parte, nella terza giornata dei Mas­<lb></lb>simi sistemi, e nella terza Lettera solare può vedersi come Galileo risolva per <lb></lb>le lunghe i triangoli, calcolandone le funzioni trigonometriche dei lati, senza <lb></lb>l&#039;uso dei logaritmi. </s>

<s>Di qui lo studio di lui di ridurre, quanto fosse possibile, <lb></lb>la Trigonometria alla Geometria semplice, come potrebbe mostrarsi dal com­<lb></lb>parare il seguente incominciato esercizio manoscritto con quel che leggesi <lb></lb>stampato nella terza Lettera al Velsero (Alb. </s>

<s>III, pag. </s>

<s>479-83), per dimo­<lb></lb>strare le incongruenze, che nascerebbero nelle proporzioni dei moti tra il Sole <lb></lb>e le sue macchie, quando queste si ponessero non aderenti alla superficie, <lb></lb>ma rivolgentisi in una sfera, concentrica col globo dello stesso Sole. </s></p><p type="main">

<s>Riferendoci alla figura, impressa in ordine la V, nella Tavola X alligata <lb></lb>infine al Tomo citato dell&#039;Albèri, son disposti in una tavoletta i seguenti va­<lb></lb>lori: IO=1000, ID=974, DO=227, DA=500, AE=2203, DL=866. <lb></lb>Di contro alla quale tavoletta sta scritto: </s></p><p type="main">

<s>“ Sian CA, AB, AD note: sarà nota anco DE e BF. </s>

<s>E perchè DH è <lb></lb>nota, sendo uguale a DE, ed essendo il triangolo HID simile al noto FBC, <lb></lb>sarà noto DI, ed è nota DL, che sono i sini degli archi HN, MN, li quali <lb></lb>però saranno noti, e le loro proporzioni. </s>

<s>” </s></p><p type="main">

<s>“ Sia il globo solare, il cui semidiametro AB, e sia l&#039;arco BL gr. </s>

<s>30: <lb></lb>sarà la linea LD 866, di quali AB è 1000. Prima è manifesto che due punti <lb></lb>B, L, posti nella superficie, passeranno i sini LD, BA nell&#039;istesso tempo. </s>

<s>È <lb></lb>inoltre chiaro che, ponendogli nelle linee DE, AC, prolungate in infinito, i <lb></lb>punti E, C traverserebbono le medesime linee BA, BD in tempi proporzio­<lb></lb>nali ad esse, sicchè, non si dando tal distanza infinita, i transiti per BA, LD <lb></lb>si faranno in tempi, che fra di loro haranno minor proporzione, che non ha <lb></lb>la linea BA alla DL. </s>

<s>E perchè, sendo DL 866, AB è 1000, et il tempo per <lb></lb>LD, al tempo per BA, deve essere come 7 a 8; facciasi come 7 a 8, così 866 <lb></lb>a un altro, che sia DI: sarà 947, e la rimanente IG sarà 53. Adattisi la IO <lb></lb>uguale a GD, e per A passi la parallela AE, che concorra con DC in E, e, <lb></lb>centro A, facciasi il cerchio CEF .... ” (ivi, fol. </s>

<s>133). </s></p><pb xlink:href="020/01/2637.jpg" pagenum="262"></pb><p type="main">

<s>Ma perchè meglio possa darsi un&#039;idea de&#039;processi trigonometrici di Ga­<lb></lb>lileo, riferiremo la formula, per così dire, che servì ai calcoli del trovar le <lb></lb>distanze assegnate, e da assegnarsi alla stella, della quale si tratta nei Mas­<lb></lb>simi sistemi, verso il mezzo della terza giornata. </s>

<s>Il problema, per risolvere <lb></lb>il quale in tutti i casi si vuol trovar la regola dell&#039;operazione, può rappre­<lb></lb>sentarsi in questa forma: </s></p><p type="main">

<s>PROPOSITIO LIV, PROBLEMA XIV. — <emph type="italics"></emph>Essendo dati gli angoli IAC, AEC<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>117) <emph type="italics"></emph>ed essendo il lato AC noto, notificare il lato EC.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>I canoni elementari della Trigonometria danno EC:AC=sen(180—IAC): <lb></lb><figure id="id.020.01.2637.1.jpg" xlink:href="020/01/2637/1.jpg"></figure></s></p><p type="caption">

<s>Figura 117.<lb></lb>sen AEC=sen IAC:sen AEC, in conformità con quel <lb></lb>che conclude Galileo nel seguente manoscritto, al quale <lb></lb>è premessa una tale osservazione: </s></p><p type="main">

<s>“ Qui sotto son notate alcune computazioni, per le <lb></lb>quali si trova la lontananza della Stella dal centro, le <lb></lb>quali computazioni son fatte sopra la parallasse delle al­<lb></lb>tezze meridiane minime, e sopra la distanza veduta della <lb></lb>Stella dal vertice. </s>

<s>Il progresso dell&#039;operazione è tale: ” </s></p><p type="main">

<s>“ La distanza dal vertice MZ mi dà l&#039;angolo IAC <lb></lb>e la parallasse data è l&#039;angolo IEC. L&#039;angolo A mi <lb></lb>dà il sino IC, nelle parti delle quali il sino tutto AC <lb></lb>è 100,000. E parimente l&#039;angolo E mi dà il sino della <lb></lb>medesima IC, nelle parti delle quali il sino tutto CE è <lb></lb>100,000. Ora, per la regola aurea, diremo: Se quando IC, come sino del­<lb></lb>l&#039;angolo E, è tanto, la CE è 100,000; quando IC, come sino dell&#039;angolo A, <lb></lb>è tanto, quanto sarà CE? </s>

<s>Moltiplica dunque il sino di A per 100,00, e parti <lb></lb>l&#039;avvenimento per il sino di E, et arai la distanza CE nelle parti, delle quali <lb></lb>il semidiametro CA è 100,000. Onde, dividendo di nuovo il quoziente tro­<lb></lb>vato per 100,000, avremo quanti semidiametri CA sono nella CE. </s>

<s>E per fare <lb></lb>l&#039;operazione brevissìma, senz&#039;altre moltiplicazioni, hasta partire il sino del­<lb></lb>l&#039;angolo A per il sino dell&#039;angolo E, ed il quoziente sarà il numero de&#039;se­<lb></lb>midiametri CA contenuti nella distanza CE. </s>

<s>Vegghiamo ora con tal regola <lb></lb>quanta venga l&#039;altezza della Stella, secondo tutte le osservazioni, comincian­<lb></lb>doci da Ticone ” (MSS. Gal., P. III, T II, fol. </s>

<s>14). </s></p><p type="main">

<s>Qui termìna dei <emph type="italics"></emph>Problemi matematici<emph.end type="italics"></emph.end> la promessa raccolta, l&#039;intenzion <lb></lb>della quale essendo, come si disse, non quella solamente di dare un&#039;idea <lb></lb>delle materie, che aveva Galileo da ridurre nel suo Dialogo novissimo, ma di <lb></lb>servire alla storia intima del pensiero di lui, e della Scienza; se ci siamo in <lb></lb>qualche parte riusciti è da attribuirlo all&#039;aver noi per i primi, e con insolita <lb></lb>diligenza, consultati i preziosi manoscritti. </s>

<s>Anzi di quell&#039;esame non abbiamo <lb></lb>dato altro che un saggio, per provocare la diligenza altrui, che dovrebbe riu­<lb></lb>scire più fruttuosa della nostra, e di quella di certi novelli editori, che, co­<lb></lb>piando materialmente senza nulla curarsi d&#039;intendere quel che leggono, ri­<lb></lb>ducono a stupidi enimmi i responsi dell&#039;Oracolo venerato. </s></p><pb xlink:href="020/01/2638.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Del trattato dei Centri di gravità <lb></lb>di Evangelista Torricelli<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Dei primi csercizi giovanili intorno ai libri baricentrici di Archimede. </s>

<s>— II. Dell&#039;invenzione de <lb></lb>centro di gravità nelle porzioni di parabola e di cerchio. </s>

<s>— III. </s>

<s>Di alcune nuove invenzioni <lb></lb>baricentricho, per via degli indivisibili. </s>

<s>— IV. </s>

<s>Del centro di gravità degli archi di cerchio. </s>

<s>e <lb></lb>delle fallacie del Guldin intorno ai centri delle callotte, delle zone e de&#039;settori sferici, notate dal <lb></lb>Cavalieri, dietro le dimostrazioni avute dal Torricelli. </s>

<s>— V. </s>

<s>Della diversità del metodo del <lb></lb>Keplero da quello del Cavalieri, e come fosse questo applicato dal Torricelli, per ritrovare in <lb></lb>vario modo il centro di gravità del cono, e di altre figure. </s>

<s>— VI. </s>

<s>Del centro di gravità dei so­<lb></lb>lidi scavati — VII. </s>

<s>Del centro di gravità dei solidi vasiformi. </s>

<s>— VIII. </s>

<s>Del centro di gravità dei <lb></lb>solidi conoidali. </s>

<s>— IX. </s>

<s>Del centro di gravità dei solidi cavalierani, e della cicloide. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>All&#039;opera di ridurre alla maggior perfezione che fosse possibile i trattati <lb></lb>delle nuove Scienze del moto, intorno a che abbiamo veduto le sollecite cure <lb></lb>datesi negli ultimi anni della sua vita da Galileo, successe quel Torricelli, <lb></lb>che abbiamo trovato in Arcetri a piè del letto, dove il vecchio maestro lan­<lb></lb>guiva, quasi rigoglioso rampollo dell&#039;albero, che è già per cadere. </s>

<s>L&#039;eccel­<lb></lb>lenza del successore si poteva fin d&#039;allora giudicar dai due libri del moto <lb></lb>dei gravi e dei proietti, i quali erano già stati scritti, e due anni dipoi, nel <lb></lb>pubblicarli, si davano come una diligente respigolatura nel campo altrui. </s>

<s>In <lb></lb>fine al volume però prometteva l&#039;Autore ai lettori, ai quali non fossero quelle <lb></lb>cose dispiaciute, che avrebbe aggiunto un trattato dei centri di gravità delle <lb></lb>superficie e dei solidi, come parti rimaste intatte nei libri del Commandino, <lb></lb>del Valerio e dello stesso Galileo. </s>

<s>Il Mersenno poi si profferse di far quel trat­<lb></lb>tato stampare a Parigi, nè il Torricelli mostrò di ricusare il favore, rispon-<pb xlink:href="020/01/2639.jpg" pagenum="264"></pb>dendo alla liberale profferta così fatte parole: “ Inventa mea geometrica <lb></lb>mechanica, hoc est nugas illas, quas inveni, sed non digessi, circa centra gra­<lb></lb>vitatis figurarum, Geometris, siquidem finita et in ordinem redacta habebo, <lb></lb>fortasse favorem et diligentiam, quam mihi tanta liberalitate offers, non re­<lb></lb>cusabo (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>76). </s></p><p type="main">

<s>Si prometteva dunque dal Torricelli una cosa, che gli avrebbe dovuto <lb></lb>accrescere di molto il merito e la gloria, perchè, dall&#039;umile condizione di <lb></lb>respigolatore nel capo altrui, veniva a sollevarsi all&#039;altezza di cultore nel <lb></lb>campo proprio. </s>

<s>Ma pur egli confessa di andar languidamente a conquistare quel <lb></lb>merito e quella gloria, distratto dagli esercizi dell&#039;arte di formare i vetri per i <lb></lb>Canocchiali, che venivano a lusingarlo con lodi molto più ambite, e a ricom­<lb></lb>pensarlo con premi assai più grandi, <emph type="italics"></emph>quandoquidem serenissimi Magni Ducis <lb></lb>effusa et vere regia liberalitas magno auri pondere donatum me non se­<lb></lb>mel voluit<emph.end type="italics"></emph.end> (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>150). Ma non è già la sete dell&#039;oro, <lb></lb>si piuttosto il gusto di avere a mano un ottimo Telescopio che, come del <lb></lb>trattato dei centri di gravità, lo fa non curante di quell&#039;altro delle propor­<lb></lb>zioni, in fine al proemio del quale così scriveva: “ Interea praestat circa vitra <lb></lb>ad usum Telescopii potius laborare, quae ab omnibus Europae partibus expe­<lb></lb>tuntur, quam circa theorematum dispositionem figurarumque accuratam de­<lb></lb>scriptionem excruciari: peracta scilicet inventione, quae sola voluptati esse <lb></lb>potest ” (MSS. Gal. </s>

<s>Disc., T. XXVI, fol. </s>

<s>59). </s></p><p type="main">

<s>L&#039;invenzione, della quale il Torricelli qui e altrove tanto si compiace, <lb></lb>consiste nell&#039;essersi, com&#039;egli dice, incontrato nella soluzione di quell&#039;ottico <lb></lb>problema <emph type="italics"></emph>tamdiu perquisiti, cuius videlicet figurae esse debeant superficies <lb></lb>vitrorum, quae ad usum Telescopii elaborantur<emph.end type="italics"></emph.end> (Op. </s>

<s>cit., pag. </s>

<s>150). Sa­<lb></lb>rebbe la compiacenza stata più giusta, se avesse scoperta e dimostrata la legge <lb></lb>delle rifrazioni, ciò ch&#039;essendo rimasto a fare allo Snellio e al Cartesio, non <lb></lb>aveva dunque il Torricelli propriamente risoluto un problema di scienza, ma <lb></lb>di semplice arte vetraria, e per emulare un occhialaio di Napoli non si curò <lb></lb>di disporre i suoi teoremi e di descrivere accuratamente le sue figure di Geo­<lb></lb>metria. </s>

<s>Giacciono infatti que&#039;teoremi confusamente scritti nelle carte disperse, <lb></lb>e abbandonati: le figure illustrative vi son neglette, e rimane appena nel­<lb></lb>l&#039;Autore una languida memoria di quelle, ch&#039;erano vere invenzioni, e che <lb></lb>gli avrebbero meritata appresso i posteri una vera gloria: cosicchè, invitato <lb></lb>un giorno a discorrerne per lettera da Michelangiolo Ricci rispondeva in fretta <lb></lb>di non saperlo fare <emph type="italics"></emph>perchè aveva la testa piena di vetri ”<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XL, fol. </s>

<s>88). </s></p><p type="main">

<s>Quelle invenzioni, nelle quali non ebbero la fortuna d&#039;incontrarsi nè <lb></lb>l&#039;antico Archimede, nè i moderni commentatori di lui, come il Commandino, <lb></lb>il Valerio, il Galileo, consistevano nei centri di gravità della callotta, del set­<lb></lb>tore e del frusto di sfera; della cicloide, e d&#039;innumerevoli altre superficie e <lb></lb>solidi, con metodi affatto nuovi: che se fosse stato tutto messo in ordine di <lb></lb>trattato alla pubblica luce, la Meccanica avrebbe avuto dal Torricelli un libro <lb></lb>non men compiuto, ma assai più bello di quel del Wallis. </s>

<s>Ebbe non poca <pb xlink:href="020/01/2640.jpg" pagenum="265"></pb>parte a quella iattura la morte, e quando furono dati al Viviani, perchè si <lb></lb>volevano in ogni modo stampare, gli scritti postumi del Torricelli, non fu­<lb></lb>rono le ultime cure rivolte ai centri di gravità, il libro de&#039;quali pensava il <lb></lb>Viviani stesso di distribuirlo nei quattro capitoli seguenti: I. De&#039;piani, cioè <lb></lb>del Settore del circolo, di alcuni piani e solidi, per gl&#039;indivisibili; del trian­<lb></lb>golo, della parabola, dei frusti e porzioni di parabola. </s>

<s>II. </s>

<s>Delle superficie <lb></lb>curve, cioè della superficie conica, della callotta e della zona sferica. </s>

<s>III. </s>

<s>Dei <lb></lb>solidi sferali, cioè dell&#039;emisferio, del settore e del frusto sferico. </s>

<s>IV. </s>

<s>Di vari <lb></lb>altri solidi, cioè del cono, del segmento conico, del frusto parabolico, del so­<lb></lb>lido cavalieriano, dei cilindri sbucati. </s></p><p type="main">

<s>Può quest&#039;ordinamento del Trattato torricelliano vedersi proposto nel <lb></lb>primo foglio del <emph type="italics"></emph>tomo XXXVI dei Discepoli,<emph.end type="italics"></emph.end> in fine al quale è fedelmente <lb></lb>eseguito in nitida copia sopr&#039;altra copia men compiuta del Serenai. </s>

<s>Si dice <lb></lb>che quella copia più moderna fosse preparata per le stampe, per le quali ne <lb></lb>fossero state già disegnate e incise le figure a parte, che perciò mancano ai <lb></lb>luoghi loro ne&#039;larghi margini bianchi del manoscritto. </s>

<s>Fu bene che non <lb></lb>avesse esecuzione il meditato disegno, perchè sarebbe stato per riuscire tale <lb></lb>sconciatura, da non si credere che vi avesse avuto parte il Viviani, alla re­<lb></lb>vision del quale non dovettero essere stati sottoposti que&#039;fogli. </s>

<s>Com&#039;è cre­<lb></lb>dibile infatti ch&#039;egli potesse dar licenza di stamparli, così com&#039;erano man­<lb></lb>canti, non solo delle aggiunte e delle illustrazioni fattevi da lui stesso con <lb></lb>tanta diligenza, ma di alcuni dei lemmi preparati già dall&#039;Autore, e senza i <lb></lb>quali non era possibile che si avessero per ben dimostrate le più importanti <lb></lb>fra quelle baricentriche proposizioni? </s></p><p type="main">

<s>I manoscritti fornirebbero il materiale necessario a chi volesse costruire <lb></lb>il trattato dei centri di gravità del Torricelli, il qual trattato altr&#039;ordine pren­<lb></lb>derebbe alle mani di un semplice compilatore, o di un che vada raccogliendo <lb></lb>quegli sparsi teoremi, per servirsene come documenti di storia. </s>

<s>Tale essendo <lb></lb>l&#039;ufficio e l&#039;intendimento nostro, non per questo saranno defraudati i Let­<lb></lb>tori di nessuna delle parti o principali o secondarie di quel trattato, in cui <lb></lb>troveranno solamente la differenza che, in vece di veder succedersi le pro­<lb></lb>posizioni via via secondo l&#039;ordine logico, le vedranno succedersi secondo l&#039;or­<lb></lb>dine cronologico: secondo il tempo cioè che le concepì la mente dell&#039;Autore, <lb></lb>sotto l&#039;influsso di queste e di quelle tradizioni, le prime e più efficaci tra le <lb></lb><figure id="id.020.01.2640.1.jpg" xlink:href="020/01/2640/1.jpg"></figure></s></p><p type="caption">

<s>Figura 118.<lb></lb>quali son quelle derivate dai libri di Archimede <emph type="italics"></emph>De <lb></lb>aequiponderantibus,<emph.end type="italics"></emph.end> e <emph type="italics"></emph>De quadratura parabolae,<emph.end type="italics"></emph.end> che <lb></lb>il Torricelli studioso commentava con questi suoi primi <lb></lb>giovanili esercizi. </s></p><p type="main">

<s>“ SUPPOSIZIONI. — Supponghiamo che le grandèzze, <lb></lb>sospese da un punto libere, cioè che possano rivoltarsi e <lb></lb>moversi, non si fermino mai, fintanto che il centro della <lb></lb>gravità di essa magnitudine non sia nell&#039;infimo punto del <lb></lb>suo cerchio. </s>

<s>Altrimenti la magnitudine si sosterrebbè da sè, potendo discen­<lb></lb>dere, il che è inverosimile. </s>

<s>Per esempio la magnitudine AB (fig. </s>

<s>118) di cui <pb xlink:href="020/01/2641.jpg" pagenum="266"></pb>centro della gravità sia C, intendasi attaccata col filo ED. È chiaro che la detta <lb></lb>grandezza non potrà mai fermarsi, fintanto che il centro C non sarà giunto <lb></lb>nel punto F, cioè nell&#039;infimo di tutti i siti, che egli possa avere, il che sarà <lb></lb>quando il punto C si sarà accomodato perpendicolarmente sotto il punto E <lb></lb>della sospensione. </s>

<s>” </s></p><p type="main">

<s>“ Supponghiamo ancora che le linee abbiano il centro della gravità, e <lb></lb>forse non sarà maggiore assurdo il considerar le linee come gravi, che il <lb></lb>considerar le superficie pesanti. </s>

<s>Già in buona Geometria non si può dire che <lb></lb>una linea sia minore di una superficie, ed io credo che tanto sia lontana <lb></lb>dall&#039;esser grave una linea, quanto una superficie. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE I. — <emph type="italics"></emph>Il centro della gravità ne&#039;triangoli sta in quella <lb></lb>linea, che dalla metà di un lato si tira all&#039;angolo opposto. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia il triangolo ABC (fig. </s>

<s>119), di cui il lato AC sia diviso per mezzo <lb></lb>in D, e tirata la BD, dico che il centro sta nella BD. </s>

<s>Se è possibile non vi <lb></lb><figure id="id.020.01.2641.1.jpg" xlink:href="020/01/2641/1.jpg"></figure></s></p><p type="caption">

<s>Figura 119.<lb></lb>stia, ma pongasi essere E. </s>

<s>Tirisi la linea IE paral­<lb></lb>lela alla BD, ed attacchisi il triangolo con la linea <lb></lb>immaginaria IE, ed accomodisi in maniera tale, che <lb></lb>la IE sia perpendicolare all&#039;orizonte. </s>

<s>Dovrà dunque <lb></lb>il triangolo star fermo, perchè il centro E sta nel <lb></lb>perpendicolo. </s>

<s>Ma producasi una linea HL parallela <lb></lb>ad AC, e divisa per mezzo in Q, e fatto centro in I, <lb></lb>ed intervallo IQ, facciasi un cerchio, del quale l&#039;in­<lb></lb>fimo punto sarà quello, che è nel perpendicolo IE, <lb></lb>e però la HL sarà in stato violento, potendo il suo <lb></lb>centro discendere ancor più. </s>

<s>È così di tutte le altre <lb></lb>linee parallele alla medesima base, le quali tutte faranno forza verso il per­<lb></lb>pendicolo, e però il triangolo non starà fermo. </s>

<s>Adunque il punto E non è <lb></lb>centro. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scolio.<emph.end type="italics"></emph.end> — Nota che questa dimostrazione, come anche quelle di Ar­<lb></lb>chimede e di altri, le quali sono indirette, non hanno forza di provare che <lb></lb>il centro della gravità sia nella linea BD, ma solo provano che non è fuori <lb></lb>di essa. </s>

<s>Che poi il centro sia nella detta linea è petizione, ed è la petizione <lb></lb>che le grandezze abbiano il centro. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE II. — <emph type="italics"></emph>Qualsivoglia figura, o sia piana o sia solida, o <lb></lb>regolare ovvero anche irregolare, purchè si possa segar con linee, ovvero<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2641.2.jpg" xlink:href="020/01/2641/2.jpg"></figure></s></p><p type="caption">

<s>Figura 120.<lb></lb><emph type="italics"></emph>piani sempre paralleli, ed i centri delle sezioni siano tutti <lb></lb>in linea retta; ha il centro della gravità nel diametro, <lb></lb>se sia piana, o nell&#039;asse, se sia solida. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia la figura ABC (120), che intendasi attaccata dal <lb></lb>punto B, ma però liberamente, sicchè si possa movere. </s>

<s>È <lb></lb>manifesto che la figura si volgerà, sino a tanto che il cen­<lb></lb>tro della gravità sia perpendicolarmente sotto al punto della <lb></lb>sospensione B. </s>

<s>Intendasi dunque la figura ridotta alla quiete, <lb></lb>ed il perpendicolo sia la linea BE, nella quale sia il centro I. </s>

<s>Dico che la linea <pb xlink:href="020/01/2642.jpg" pagenum="267"></pb>BIE è diametro della figura. </s>

<s>Poichè, se non è, sia diametro la BD, e, tirata <lb></lb>la ordinatamente applicata NO, sarà il di lei centro M, il quale, per esser <lb></lb>fuori del perpendicolo, potrà discendere e condursi all&#039;infimo punto del suo <lb></lb>giro, che è nel perpendicolo. </s>

<s>Così di tutte le ordinatamente applicate. </s>

<s>Però <lb></lb>la figura non starà ferma, ma anderà da quella parte, verso la quale spin­<lb></lb>gono tutte le applicate. </s>

<s>Perciò il punto I non sarebbe centro, che è contro <lb></lb>il supposto. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario.<emph.end type="italics"></emph.end> — Perciò è manifesto che il centro della gravità del trian­<lb></lb>golo, parallelogrammo, cerchio, ellissi, siccome della sfera, sferoide, ecc., sta <lb></lb>nel concorso dei diametri, cioè nel centro della figura. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE III. — <emph type="italics"></emph>In ogni figura solida, come prisma o paralle­<lb></lb>lepipedo, ovvero cilindro, il centro della gravità sta in quella linea, che <lb></lb>congiunge i centri delle basi opposte. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia un prisma, o parallelepipedo ovvero cilindro, ovvero altro solido <lb></lb>colonnare OI (fig. </s>

<s>121), e congiungansi i centri delle basi opposte con la retta <lb></lb>OI. </s>

<s>Se è possibile stia fuori, e facciasi la sospensione dal punto O. </s>

<s>Adunque <lb></lb><figure id="id.020.01.2642.1.jpg" xlink:href="020/01/2642/1.jpg"></figure></s></p><p type="caption">

<s>Figura 121.<lb></lb>il centro della gravità si accomoderà nel perpendicolo sotto il <lb></lb>punto O e la figura starà ferma. </s>

<s>E però segando la figura con <lb></lb>un piano AB, parallelo alle basi opposte, il centro della sezione <lb></lb>fatta sarà fuori del perpendicolo, e però non sarà nell&#039;infimo <lb></lb>punto del suo giro. </s>

<s>E così di tutte le sezioni possibili a farsi <lb></lb>parallele alle basi opposte, e perciò tutte le dette sezioni preme­<lb></lb>ranno per un verso, e la figura non starà ferma, che è contro <lb></lb>il supposto. </s>

<s>Adunque il centro non è fuori della linea OI, la <lb></lb>quale congiunge i centri delle basi opposte, e di tutte le altre <lb></lb>sezioni. </s>

<s>Che poi il centro del solido divida per mezzo la linea OI è più chiaro <lb></lb>di ogni prova, che se ne possa addurre. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE IV. — <emph type="italics"></emph>Il cono, la piramide ed ogni figura conica e <lb></lb>piramidale ha il centro della gravità in quella linea, la quale va dalla <lb></lb>cima al centro della gravità della base opposta. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia un cono, ovvero piramide, ed attacchisi dalla cima libero e s&#039;in­<lb></lb>tenda ridotto alla quiete. </s>

<s>Sarà dunque il centro nel perpendicolo sotto il <lb></lb>punto A (fig. </s>

<s>122). Dico che questo tal perpendicolo è la linea, che va dalla <lb></lb>cima al centro della base opposta. </s>

<s>Se non è, sia detta linea un&#039;altra, come <lb></lb><figure id="id.020.01.2642.2.jpg" xlink:href="020/01/2642/2.jpg"></figure></s></p><p type="caption">

<s>Figura 122.<lb></lb>la AE. </s>

<s>Adunque proverò che i centri di tutte le sezioni pos­<lb></lb>sibili parallele alla base sono nella linea AE. </s>

<s>Poichè proverò, <lb></lb>essendo cono, che il centro della sezione sta in AE, se è pi­<lb></lb>ramide proverò che nel triangolo della sezione la linea AE passa <lb></lb>per un punto, il quale sta nella retta, che vien dall&#039;angolo alla <lb></lb>metà di un lato, e la divide in proporzione dupla: e potendo <lb></lb>tutti discendere, la figura non starà ferma, che è contro il sup­<lb></lb>posto ” (MSS. Gal. </s>

<s>Disc., T. XXXVI, 5-8). </s></p><p type="main">

<s>Ai giovanili esercizi intorno ai centri di gravità appartengono quest&#039;altre <lb></lb>proposizioni, per dimostrar le quali si suppone dal Torricelli <emph type="italics"></emph>congruentium<emph.end type="italics"></emph.end><pb xlink:href="020/01/2643.jpg" pagenum="268"></pb><emph type="italics"></emph>figurarum centra gravitatis congruere: item uniuscumque figurae unicum <lb></lb>esse centrum gravitatis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ PROPOSIZIONE V. — <emph type="italics"></emph>Quodlibet parallelogrammum habet centrum gra­<lb></lb>vitatis in recta, quae bifariam secat opposita latera. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto parallelogrammum ABCD (fig. </s>

<s>123): recta bisecans opposita la­<lb></lb>tera sit EF. </s>

<s>Dico in EF esse centrum gravitatis parallelogrammi. </s>

<s>Nisi enim <lb></lb><figure id="id.020.01.2643.1.jpg" xlink:href="020/01/2643/1.jpg"></figure></s></p><p type="caption">

<s>Figura 123.<lb></lb>sit in EF, esto illud G, et producatur AB in H, DC <lb></lb>in I, FE in L. </s>

<s>Esto parallelogrammum BI aequale <lb></lb>ipsi AC. </s>

<s>Supposita ergo recta BC super AD, angu­<lb></lb>loque HBC super angulo BAD, congruet parallelo­<lb></lb>grammum BI cum parallelogrammo AC, et recta EL <lb></lb>cum FE, punctumque aliquod M in parallelogrammo <lb></lb>EI congruet cum puncto G. </s>

<s>Cumque G sit centrum <lb></lb>parallelogrammi AC, erit M centrum parallelogrammi congruentis BI. ” </s></p><p type="main">

<s>“ Invertatur iam parallelogrammum BI super eadem basi BC, ita ut <lb></lb>angulus HBC, mutato loco, sit NCB; angulus vero ICB, mutato loco, sit ipse <lb></lb>OBC, recta vero EL, mutata positione, sit eadem ac ipsa EP. </s>

<s>Punctum vero M <lb></lb>idem sit ac ipsum <expan abbr="q.">que</expan> Inclinato iam parallelogrammo BONC super paralle­<lb></lb>logrammo BADC, ita ut latus BC commune maneat, congruent, congruentque <lb></lb>parallelogrammum BP ipsi BF, et punctum Q cum aliquo puncto R in pa­<lb></lb>rallelogrammo BF. </s>

<s>Cum autem punctum Q centrum sit parallelogrammi BONC, <lb></lb>erit R centrum gravitatis parallelogrammi congruentis BADC. </s>

<s>Sed eiusdem <lb></lb>centrum gravitatis erat G, ergo etc. </s>

<s>” (idid., fol. </s>

<s>20). </s></p><p type="main">

<s>“ PROPOSIZIONE VI. — <emph type="italics"></emph>Cuiuscumque figurae, ex duobus semiparabolis <lb></lb>compositae, ita ut diametros aequales et in directum habeant, basim vero <lb></lb>communcm, centrum gravitatis est in basi. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sint duae semiparabolae ABC, CBD (fig. </s>

<s>124), quarum diametri ae­<lb></lb>quales et in directum sint AC, CD, basis vero communis CB. </s>

<s>Dico huius­<lb></lb><figure id="id.020.01.2643.2.jpg" xlink:href="020/01/2643/2.jpg"></figure></s></p><p type="caption">

<s>Figura 124.<lb></lb>modi figurae centrum gravitatis esse in basi communi <lb></lb>CB. </s>

<s>Producatur basis BC in E, ut sint aequales BC. <lb></lb>CE: tum utraque parabola perficiatur. </s>

<s>Eritque altera <lb></lb>alteri eadem parabola, et congruent n<gap></gap>tuo. </s>

<s>Secta <lb></lb>deinde BC bifariam in F, ducatur GH parallela ipsi <lb></lb>AD, iunctisque AB, BD erunt GM, NH diametri pa­<lb></lb>rabolarum AGB, BHD et erunt aequales inter se. </s>

<s><lb></lb>Sint I, L centra gravitatis parabolarum AGB, BHD, <lb></lb>eruntque acquales IM, NL. </s>

<s>Sed etiam MF, FN sunt <lb></lb>aequales, ergo totae IF, FL aequales erunt. </s>

<s>Sunt au­<lb></lb>tem aequales semiparabolae ABC, CBD cum utraque aequalis sit semipara­<lb></lb>bolae EDC, ipsa enim ABC cum EDC eadem est et congruit, ipsa vero CBD <lb></lb>cum EDC a diametro bifariam dividitur. </s>

<s>Demptis itaque aequalibus triangulis <lb></lb>erunt aequales parabolae AGB, DBH, et punctum F erit earum centrum gra­<lb></lb>vitatis. </s>

<s>Etiam trianguli ABD centrum gravitatis est in BC, ergo et totius <lb></lb>figurae, quod erat demonstrandum ” (ibid., fol. </s>

<s>26). </s></p><pb xlink:href="020/01/2644.jpg" pagenum="269"></pb><p type="main">

<s>“ PROPOSIZIONE VII. — <emph type="italics"></emph>Cuiuscumque semiparabolae centrum gravita­<lb></lb>tis est in linea basi aequidistante, et per centrum totius producta. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>A questa è premesso un lemma, che fu poi scritto in ordine l&#039;XI nel <lb></lb>libro <emph type="italics"></emph>De dimensione parabolae,<emph.end type="italics"></emph.end> dove può chi vuole leggerlo stampato sotto <lb></lb>una tal forma: “ Omnis semiparabola aequiponderat ex puncto basis, in quo <lb></lb>sic ea dividitur ut pars ad curvam terminatam sit ad reliquam ut quinque <lb></lb>ad tria ” (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>33). Dietro ciò così procede nel ma­<lb></lb>noscritto la dimostrazione della proposta: </s></p><p type="main">

<s>“ Esto parabola ABC (fig. </s>

<s>125), cuius diameter BD. </s>

<s>Centrum gravitatis <lb></lb>totius sit E, ductaque EG parallela ipsi basi DC, dico centrum gravitatis se­<lb></lb><figure id="id.020.01.2644.1.jpg" xlink:href="020/01/2644/1.jpg"></figure></s></p><p type="caption">

<s>Figura 125.<lb></lb>miparabolae DBC esse in recta EG. </s>

<s>Sit enim si possibile <lb></lb>est extra, puta I, iunctaque et producta IE, transibit ipsa <lb></lb>IE per centrum gravitatis alterius semiparabolae, per <lb></lb>lemma primum VIIIae primi Aequiponderantium. </s>

<s>Esto <lb></lb>illud F ductisque IL, FH, diametro parallelis, erunt ae­<lb></lb>quales DH, DL, sunt enim utraeque, per lemma praeced., <lb></lb>3/5 acqualium DA, DC. </s>

<s>Ideo aequales erunt etiam FE, EI, <lb></lb>et propterea semiparabolae aequales erunt. </s>

<s>Producatur <lb></lb>BD in N, ita ut sint aequales BD, DN, et per puncta <lb></lb>A, N, C transeat parabola circa diametrum ND, eritque <lb></lb>penitus eadem cum parabola ABC. </s>

<s>Nam superpositae invicem congruent. </s>

<s>Jam <lb></lb>producta IL, ut LM sit aequalis ipsi LI, erit M centrum semiparabolae CDN, <lb></lb>et ideo M congruet cum centro F, eruntque aequales FH, LM, et ideo etiam <lb></lb>FH, LI, eruntque parallelae HL, FI quod est impossibile ” (ibid., fol. </s>

<s>27). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dopo Archimede la Baricentrica era stata promossa da Federigo Com­<lb></lb>mandino e da Luca Valerio, ai trattati dei quali, se Galileo da una parte <lb></lb>faceva il commento, porgeva anche dall&#039;altra, come vedremo, gli argomenti <lb></lb>a nuove dimostrazioni. </s>

<s>In generale però sembrava che fosse ogni invenzione <lb></lb>esaurita in que&#039;libri, e Galileo stesso confessava di aver desistito dall&#039;opera, <lb></lb>perchè vedeva di non poterci far altro che ricalcar l&#039;orme segnate già dal <lb></lb>Valerio. </s></p><p type="main">

<s>Nel 1632 un gesuita spagnolo, Giovanni Della Faille, pubblicava un libro <lb></lb>di teoremi <emph type="italics"></emph>De centro gravitatis partium circuli et ellipsis,<emph.end type="italics"></emph.end> cosa affatto nuova <lb></lb>nella Scienza, avendone taciuto Archimede, e il Commandino e il Valerio <lb></lb>contentandosi di dimostrare, ciò che dall&#039;altra parte avrebbe ognuno consen­<lb></lb>tito assai facilmente, che convengono nello stesso punto i centri delle due <lb></lb>figure. </s>

<s>Narrava il Della Faille, nel proemio ai lettori, donde gli fossero de­<lb></lb>rivate le tradizioni alla sua invenzione, e diceva che, come Archimede, ritro­<lb></lb>vatone il centro di gravità, aveva facilmente conclusa la quadratura della pa-<pb xlink:href="020/01/2645.jpg" pagenum="270"></pb>rabola; così egli sperava che, ritrovato il centro di gravità di una porzione <lb></lb>di cerchio, gli verrebbe fatto di quadrare quella stessa porzione, e perciò il <lb></lb>cerchio intero. </s>

<s>La nuova quadratura meccanica riuscì, al dir di un giudice <lb></lb>competente qual era Antonio Nardi, <emph type="italics"></emph>con arte maravigliosa,<emph.end type="italics"></emph.end> ciò ch&#039;efficace­<lb></lb>mente conferì a diffondere la fama e i libri del Matematico straniero in Italia. </s>

<s><lb></lb>Il Torricelli perciò ritrovava, nel nuovo trattato dei centri di gravità delle <lb></lb>porzioni di circolo e di ellisse, un nuovo impulso, e un indirizzo nuovo ai <lb></lb>suoi studi, primo frutto de&#039;quali fu l&#039;invenzione del centro di gravità nelle <lb></lb>porzioni di parabola, invenzione forse meno strepitosa di quell&#039;altra simile <lb></lb>del padre Della Faille, ma non però meno nuova. </s></p><p type="main">

<s>“ PROPOSIZIONE VIII. — <emph type="italics"></emph>Ostendemus centrum gravitatis portionis pa­<lb></lb>rabolae qua sit in linea, et in quo ipsius puncto. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto portio parabolae ABCD (fig. </s>

<s>126), secta per lineam CD utcum­<lb></lb><figure id="id.020.01.2645.1.jpg" xlink:href="020/01/2645/1.jpg"></figure></s></p><p type="caption">

<s>Figura 126.<lb></lb>que, sive sit ad diametrum paral­<lb></lb>lela, sive non. </s>

<s>Secetur bifariam AC <lb></lb>in E, et, ducta diametro EB, sit F <lb></lb>centrum parabolae ABC, et H cen­<lb></lb>trum trianguli ACD, iunctaque F, H, <lb></lb>in FH erit centrum portionis. </s>

<s>Jun­<lb></lb>gatur BD, eritque triangulum ABC <lb></lb>ad triangulum ADC, in eadem basi, <lb></lb>ut altitudines BX, DY, sive ut BI, <lb></lb>ID per similitudinem triangulorum <lb></lb>rectangulorum BXI, IYD, et per IV <lb></lb>Sexti. </s>

<s>” </s></p><p type="main">

<s>“ Jam parabola ABC, ad triangulum ABC, est ut 4/3 rectae BI ad BI: <lb></lb>triangulum vero ABC ad ADC est ut BI ad ID, ergo ex aequo parabola ABC <lb></lb>ad triangulum ADC est ut 4/3 rectae BI ad ID, sive, sumptis subsesquiter­<lb></lb>tiis, ut recta BI ad 3/4 ID. </s>

<s>Fiat igitur ut BI ad 3/4 ID, ita reciproce HO ad <lb></lb>OF et erit O centrum gravitatis portionis ” (ibid., fol. </s>

<s>30). <lb></lb><figure id="id.020.01.2645.2.jpg" xlink:href="020/01/2645/2.jpg"></figure></s></p><p type="caption">

<s>Figura 127.</s></p><p type="main">

<s>PROPOSIZIONE IX. — <lb></lb><emph type="italics"></emph>Dato il frusto di parabola <lb></lb>ABCD<emph.end type="italics"></emph.end> (fig. </s>

<s>127), <emph type="italics"></emph>con le sue <lb></lb>basi parallele AD, BC, e <lb></lb>con la sua altezza EF cor­<lb></lb>rispondente all&#039;asse della <lb></lb>figura; trovare sopra esso <lb></lb>asse dove gravita il centro.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Questo bello e impor­<lb></lb>tante problema non è così <lb></lb>proposto, nè direttamente <lb></lb>risoluto nel manoscritto tor­<lb></lb>ricelliano fatto copiar per la stampa, dove solamente si leggono due teoremi, <lb></lb>che apparirebbero fuor di luogo e insignificanti, quando non s&#039;intendessero, <pb xlink:href="020/01/2646.jpg" pagenum="271"></pb>secondo che deve avere avuto in mente l&#039;Autore, come lemmi preparati o <lb></lb>come principii già posti per riuscire alla desiderata soluzione. </s>

<s>Ciò sempre <lb></lb>più conferma che dev&#039;essere stata preparata la detta copia per le stampe <lb></lb>senza l&#039;approvazion del Viviani, il quale non è credibile non avesse com­<lb></lb>preso che i due teoremi erano stati dimostrati per ritrovare il centro di gra­<lb></lb>vità nel frusto della parabola, tanto più che il Viviani stesso aveva già svolti <lb></lb>gli argomenti, ossia aveva fatto i calcoli per dimostrar che tornano le con­<lb></lb>clusioni pronunziate dal Torricelli. </s></p><p type="main">

<s>E perchè sui materiali, che ci son rimasti in qualche parte finiti e iǹ <lb></lb>qualche altra abbozzati, non è difficile, conforme al disegno che ne fece l&#039;ar­<lb></lb>tista, costruir l&#039;edifizio; si congiungano i punti B, C, con A, D, e tornerà <lb></lb>dalle linee AB, CD la superficie del frusto divisa in due segmenti parabolici <lb></lb>e in un trapezio. </s>

<s>Sia l&#039;asse EF segato nel mezzo in P dalla linea RS pa­<lb></lb>rallela alle basi, la quale, segando pure nel mezzo in H e in T le AB, CD, <lb></lb>saranno HL, NT, che si conducono paralleli all&#039;asse per comodità della di­<lb></lb>mostrazione, i diametri delle due parabole. </s>

<s>Se dunque si prenda HV due <lb></lb>quinti di HL, sarà per l&#039;VIII del secondo degli Equiponderanti, in V il cen­<lb></lb>tro dalla parabola ARB, come in X sarà il centro della parabola CSD, per <lb></lb>la medesima proposizion di Archimede. </s>

<s>Congiungansi V, X, e sarà in O il <lb></lb>centro delle due stesse parabole. </s>

<s>Sia poi per la XV del primo degli Equi­<lb></lb>ponderanti in K il centro di gravità del trapezio: è manifesto che s&#039;avrà <lb></lb>risoluto il problema, quando si sappia a qual punto riman dell&#039;asse il cen­<lb></lb>tro O, e qual sia la proporzione delle parabole al trapezio, perchè, chiamato T <lb></lb>questo e P quelle, se faremo come T a P così reciprocamente OZ a ZK, sarà <lb></lb>in Z il centro di gravità del frusto. </s></p><p type="main">

<s>Le due proposizioni inserite nel manoscritto torricelliano dimostrano dove <lb></lb>il punto O sia da segnarsi sull&#039;asse, e quale abbiano ragioni fra loro le dette <lb></lb>superficie. </s>

<s>Ma perchè colui che ordinò quelle proposizioni non ne intese il <lb></lb>fine, anche male le intitolò e le dispose, e, quasi fosse un tal fine principal­<lb></lb>mente quello di determinar sull&#039;asse il centro delle due parabole, volle a <lb></lb>questa dimostrazione premettere come lemma quell&#039;altra delle proporzioni <lb></lb>tra il trapezio e le due parabole adiacenti. </s>

<s>Notato ciò, non per altro che per <lb></lb>avvertire il Lettore com&#039;avendo così fallato gli altri in tanto lubriche mate­<lb></lb>rie non ci assicuriamo di aver fallato o qui o altrove anche noi; ecco in qual <lb></lb>modo compendiosamente dimostri il Torricelli dove sull&#039;asse del frusto si <lb></lb>trovi il centro delle due parabole, che ne fanno parte. </s></p><p type="main">

<s>Condotte le LI, BG, CQ parallele al detto asse, si premette dal Torri­<lb></lb>celli la seguente, per servir di lemma a ciò che vuol dimostrare: “ Osten­<lb></lb>dendum ita esse DG, ad GI ut IH ad HL. ” </s></p><p type="main">

<s>“ Recta IH ad GB èst ut IA ad AG, sive, sumpta communi altitudine, <lb></lb>ut rectangulum sub IA, GD ad rectangulum AGD. </s>

<s>Recta vero GB ad IL est <lb></lb>ut rectangulum AGD ad AID. </s>

<s>Ergo ex aequo IH ad IL erit ut rectangulum <lb></lb>sub IA, GD, ad rectangulum AID, nempe ut recta GD ad DI. Ergo, divi­<lb></lb>dendo, DG ad GI erit ut IH ad HL ” (ibid., fol. </s>

<s>28). </s></p><pb xlink:href="020/01/2647.jpg" pagenum="272"></pb><p type="main">

<s>Ciò premesso, così conclude il Torricelli essere il punto O talmente si­<lb></lb>tuato sull&#039;asse, che EO ad OF abbia quella medesima proporzione che due <lb></lb>basi maggiori del frusto con tre delle minori hanno a tre basi maggiori con <lb></lb>due delle minori. </s></p><p type="main">

<s>“ Est centrum duarum parabolarum O. </s>

<s>Ergo PO crit duae quintae ipsius <lb></lb>HL, et ideo FP ad PO, sive EP ad PO, erit ut DG ad 2/5 GI, sive ut DG <lb></lb>ad 1/5 GA. </s>

<s>Sumptisque quintuplis, erit EP ad PO ut DG quinquies ad GA <lb></lb>semel. </s>

<s>Factisque argumentis, erit EO ad OF ut DG quater, cum GQ semel, <lb></lb>ad DG quinquies, una cum GA semel. </s>

<s>Nempe ut duae bases maiores, cum <lb></lb>tribus minoribus, ad tres maiores, cum duabus minoribus ” (ibid.). </s></p><p type="main">

<s>La division dell&#039;asse nella proporzione di 4DG+GQ a 5DG+GA, <lb></lb>si dimostra così assai facilmente: In virtù del Lemma già dimostrato è <lb></lb>IH:HL=DG:GI. </s>

<s>Ma IH=PF=EP, per costruzione, e perciò, mol­<lb></lb>tiplicati i conseguenti per 2/5, e osservando che PO=HV=2/5HL; avremo <lb></lb>EP:PO=DG:2/5GI, ossia EP:PO=5DG:AG. </s>

<s>Dividendo e compo­<lb></lb>nendo, questa si riduce alle due seguenti EP—PO:PO=5DG—AG:AG; <lb></lb>EP+PO:PO=5DG+AG:AG, onde EO:FO=5DG—AG:5DG+AG. </s>

<s><lb></lb>Ma 5DG—AG=4DG+DG—AG=4DG+DG—QD=4DG+QG, <lb></lb>dunque EO:FO=4DG+QG:5DG+AG. </s></p><p type="main">

<s>Resta ora a provare come 4DG+GQ sia uguale a 2AD+3QG, e <lb></lb>come 5DG+AG sia uguale a 3AD+2QG, ciò che faremo prima di tutto <lb></lb>osservando che 4GD+GQ=4GD+GQ+2GQ—2GQ=4GD— <lb></lb><expan abbr="2GQ+3Gq.">2GQ+3Gque</expan> Ma 4GD—2GQ=4(AD—AG)—2GQ=4AD— <lb></lb>4AG—2GQ=4AD—(2AG+2QD+2QG)=4AD—2AD= <lb></lb>2AD, dunque 4GD+GQ=2AD+3QG. L&#039;altra parte poi vien pro­<lb></lb>vata con facilità dalle seguenti equazioni: 5DG+AG=3DG+2DG+ <lb></lb>GA+3GA—3GA=3(DG+AG)+2(DG—AG)=3AD+2QG. </s>

<s><lb></lb>E perciò EO:OF=2AD+3QG:3AD+2QG: “ nempe, come di­<lb></lb>ceva il Torricelli, ut duae bases maiores, cum tribus minoribus, ad tres maio­<lb></lb>res, cum duobus minoribus. </s>

<s>” </s></p><p type="main">

<s>Il Viviani illustrava la proposizione, così procedendo nel calcolo, in modo <lb></lb>poco differente dal nostro, che per l&#039;uso dell&#039;analisi ci siamo studiati di <lb></lb>render più chiaro: “ Come EP a PO, così cinque DG ad una GA, <emph type="italics"></emph>ct sumptis <lb></lb>antecedentibus duplis,<emph.end type="italics"></emph.end> come EF a PO, così dieci DG ad una GA. </s>

<s>E perchè <lb></lb>EP a PO sta come cinque DG, ad una GA; sarà, componendo, FO ad OP <lb></lb>come cinque DG, con una GA, ad una GA. <emph type="italics"></emph>Et per conversionem rationis,<emph.end type="italics"></emph.end><lb></lb>sarà PO ad OF, come una GA a cinque DG, con una GA. </s>

<s>Ma stava come <lb></lb>EF a PO, così dieci DG ad una GA, ed ora sta PO ad FO, come una GA <lb></lb>a cinque DG, con una GA: ergo <emph type="italics"></emph>ex aequo<emph.end type="italics"></emph.end> EF ad FO starà come dieci DG <lb></lb>e cinque DG, con una GH, ovvero con una <expan abbr="Dq.">Dque</expan> E, dividendo, EO ad OF <lb></lb>starà come quattro DG, con una GQ, a cinque DG, con una GA. </s>

<s>Ma in que­<lb></lb>sta DG con una GQ ci sono cinque GQ e quattro DQ, siccome in due DA, <lb></lb>con tre BC, vi sono cinque GQ, con quattro <expan abbr="Dq;">Dque</expan> adunque quattro DG, con <lb></lb>una GQ, sono uguali a due DA con tre BC. ” </s></p><pb xlink:href="020/01/2648.jpg" pagenum="273"></pb><p type="main">

<s>“ Inoltre, in cinque DG, con una GA, ci sono cinque GQ e sei GA: <lb></lb>siccome ancora, in tre DA con due BC, cioè due GQ, ci sono cinque GQ e <lb></lb>sei GA. </s>

<s>Adunque cinque DG, con una GA, sono uguali a tre DA, con due <lb></lb>BC. </s>

<s>Ma sopra abbiamo provato che EO ad OF sta come quattro DG, con <lb></lb>una GQ, a cinque DG, con una GA, ed ora si è dimostrato che quattro DG, <lb></lb>con una GQ, sono uguali a due basi maggiori DA, con tre basi minori BC, <lb></lb>e che cinque DG, con una GA, sono uguali a due basi minori BC, cou tre <lb></lb>maggiori AD; adunque BO ad OF starà come due basi maggiori, con tre <lb></lb>minori, a due minori, con tre maggiori ” (ivi, T. XXXV, fol. </s>

<s>138). </s></p><p type="main">

<s>Determinata e confermata, per i calcoli fatti, la posizione del punto O, <lb></lb>baricentro delle due parabole sopra l&#039;asse, ed essendo in K, come si disse, <lb></lb>il baricentro del trapezio; non rimane a far altro che dimostrare in qual <lb></lb>proporzione stiano quelle stesse parti fra loro, ciò che il Torricelli fa pro­<lb></lb>ponendo, e dimostrando il teorema seguente: “ Trapetium inscriptum, ad <lb></lb>reliquas parabolas frusti, ita est, ut quadratum DG, ad tertiam partem qua­<lb></lb>drati GA. ” </s></p><p type="main">

<s>“ Producatur iam diameter HL parabolae ALB usque in M, ita ut MH <lb></lb>sesquitertia sit diametro HL: erit triangulum, altitudine MH, basi vero du­<lb></lb>pla HN, aequale parabolae ALB. </s>

<s>Triangulum BAC ad parabolam ALB, sive <lb></lb>ad triangulum praedictum, rationem habebit compositam ex ratione altitudi­<lb></lb>num BG ad HM, sive IH ad duas tertias HL, sive DG ad duas tertias GI; <lb></lb>et ex ratione basium BE ad HN, sive FG ad GI. </s>

<s>Ergo triangulum BAC. ad <lb></lb>parabolam ALB, erit ut rectangulum DGF, ad rectangulum sub IG, et sub <lb></lb>duabus tertiis IG: nempe ad duas tertias quadrati GI, praedicta enim rectan­<lb></lb>gula ex iisdem rationibus componuntur. </s>

<s>Triangulum vero ACD ad BAC est <lb></lb>ut DA ad BC, vel ut DF ad FG, sive ut rectangulum FDG ad FGD. Ergo, <lb></lb>ex aequo, triangulum ACD, ad parabolam ALB, erit ut rectangulum FDG <lb></lb>ad 2/3 quadrati GI, et, per XXIV quinti, trapetium ad parabolam ut quadra­<lb></lb>tum DG ad 2/3 quadrati GI. </s>

<s>Duplicando consequentia, erit idem trapetium, ad <lb></lb>duas parabolas residuas, ut quadratum DG ad 4/3 quadrati GI, sive ad 1/3 qua­<lb></lb>drati GA, quod volebam ostendere. </s>

<s>” (ibid.). </s></p><p type="main">

<s>Se faremo dunque, in ultima conclusion del discorso, OZ:ZK=DG2: <lb></lb>4/3 GI2, sarà nel punto Z il centro di gravità del frusto parabolico, che si <lb></lb>cercava. </s></p><p type="main">

<s>Ripensando a queste nuove cose dimostrate e risolute, si compiaceva il <lb></lb>Torricelli di avere emulato il Della Faille, ma pure si trovava costretto di <lb></lb>confessare che le invenzioni di lui erano di maggior conseguenza delle sue <lb></lb>proprie. </s>

<s>Dicemmo che si riducevano quelle invenzioni al centro di gravità di <lb></lb>una porzion di cerchio e di ellisse, e ora soggiungiamo più particolarmente <lb></lb>che, dopo aver premesse XXXIII proposizioni, si veniva a concluder dall&#039;Au­<lb></lb>tore che il centro di gravità di un settore di cerchio si trova sopra il rag­<lb></lb>gio, che lo divide nel mezzo, a una distanza tale dal centro, che sia quarta <lb></lb>proporzionale dopo l&#039;arco, dopo due terzi della corda, e dopo il raggio stesso. <lb></lb></s>

<s>“ Dato quolibet sectore circuli, e centro bifariam diviso, si fiat ut sectoris <pb xlink:href="020/01/2649.jpg" pagenum="274"></pb>arcus, ad duas tertias partes rectae subtendentis arcum, ita semidiameter ad <lb></lb>quartam quamdam lineam e centro sumendam, in ea quae sectorem bifariam <lb></lb>secat; eius terminus erit centrum gravitatis sectoris propositi ” (Theoremata <lb></lb>de centro grav., Antuerpiae 1632, pag. </s>

<s>36). </s></p><p type="main">

<s>Si veniva di qui a porger facile il modo di ritrovare il centro del segmento <lb></lb>circolare, che è uguale al settore diminuito del triangolo inscritto, e nell&#039;ul­<lb></lb>time parti del libro si dimostrava come, nella medesima proporzione che nel <lb></lb>cerchio, sia segato l&#039;asse dal centro di gravità nel segmento e nel settore di <lb></lb>ellisse, intorno a che pose l&#039;Autore i due teoremi seguenti in questa forma: <lb></lb>“ Si duo segmenta data fuerint unum ellipsis, alterum circuli, et quam pre­<lb></lb>portionem habet segmentum ellipsis, ad totam ellipsim, eamdem habeat <lb></lb>segmentum circuli, ad totum circulum; centra gravitatis in eamdem propor­<lb></lb>tionem divident earum diametros. </s>

<s>— Si fuerint duo sectores unus ellipttcus, <lb></lb>alter circularis, dimidiis suis figuris minores, aequales vel maiores, et quam <lb></lb>proportionem habet unus sector ad suam figuram, eamdem habeat alter sector <lb></lb>ad suam; centrum gravitatis ipsorum in eamdem ratiònem dividet semidia­<lb></lb>metros illas, quae sectores bifariam secant ” (ibid., pag. </s>

<s>49, 51). </s></p><p type="main">

<s>Erano anche questi due teoremi una conseguenza, e posti come un&#039;ap­<lb></lb>pendice del XXIX, dove il Della Faille aveva dimostrato il modo di ritro­<lb></lb>vare il baricentro del settore di cerchio. </s>

<s>La dimostrazione procedeva secondo <lb></lb>il metodo antico degli inscritti, che menava necessariamente per le lunghe, <lb></lb>cosicchè, per preparare i principii, dai quali si potesse dedurre con rigoroso <lb></lb>discorso geometrico la conseguenza desiderata, si trovò costretto l&#039;Autore a <lb></lb>scrivere un libro intero. </s>

<s>Il Torricelli credè che ci dovesse essere una via più <lb></lb>breve, e mettendosi a cercarla la trovò, e la rifiorì delle sue proprie ele­<lb></lb>ganze, ma in sostanza rimaneva la stessa già battuta da tutti gli altri, aiu­<lb></lb>tandosi anch&#039;egli di quegli inscritti e circoscritti, ai quali erano in simili <lb></lb>bisogni ricorsi sempre i Matematici antichi. </s>

<s>Non fu perciò possibile che la <lb></lb>brevità raggiungesse quel grado, che si prometteva, e che poi si conseguì <lb></lb>con i metodi nuovi, come potranno giudicare i Lettori da ciò che ora siam <lb></lb>per trascrivere dal manoscrito torricelliano, in cui non si giunge a conclu­<lb></lb>dere il proposito, se non che per la via di dieci lemmi. <lb></lb><figure id="id.020.01.2649.1.jpg" xlink:href="020/01/2649/1.jpg"></figure></s></p><p type="caption">

<s>Figura 128.</s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma I.<emph.end type="italics"></emph.end> — Si quadrata duorum laterum <lb></lb>trianguli, simul sumpta, minora sint reliqui lateris <lb></lb>quadrato; angulus, ab illis duobus lateribus com­<lb></lb>prehensus, obtusus erit. </s>

<s>” </s></p><p type="main">

<s>“ Esto triangulum ABC (fig. </s>

<s>128), sintque qua­<lb></lb>drata AB, BC, simul sumpta, reliquo quadrato AC <lb></lb>minora: dico angulum B esse obtusum. </s>

<s>Nisi enim <lb></lb>B sit obtusus, erit certe vel rectus vel acutus. </s>

<s><lb></lb>Rectus esse non potest, nam quadrata AB, BC essent, per XLVII Primi, ae­<lb></lb>qualia quadrato AC. </s>

<s>Acutus esse non potest, quoniam quadrata AB, BC si <lb></lb>mul maiora essent quadrato AC, per XIII Secundi. </s>

<s>Superest igitur quod an­<lb></lb>gulus B sit, obtusus, quod erat propositum. </s>

<s>” </s></p><pb xlink:href="020/01/2650.jpg" pagenum="275"></pb><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Omitte, si lubet, hoc primum Lemma, tamquam satis <lb></lb>notum ex XIII Secundi Elementorum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma II.<emph.end type="italics"></emph.end> — Si fuerit circuli sector quadrante minor, perpendicu­<lb></lb>laris in triangulo, ad reliquam sagittam, magis quam dupla erit. </s>

<s>” </s></p><p type="main">

<s>“ Esto circuli sector ABCD (fig. </s>

<s>129), quadrante minor, cuius chorda <lb></lb>sit AC, et ex centro D demissa perpendicularis DE ad AC: dico DE, ad re­<lb></lb><figure id="id.020.01.2650.1.jpg" xlink:href="020/01/2650/1.jpg"></figure></s></p><p type="caption">

<s>Figura 129.<lb></lb>liquam sagittam EB, magis quam duplam esse. </s>

<s>Dupla <lb></lb>enim esse non potest, quoniam, si ponatur DE dupla <lb></lb>reliqua EB, erit BD, sive CD. ad DE, ut 3 ad 2. Ergo <lb></lb>quadratum CD ad DB erit ut 9 ad 4. Quadratum <lb></lb>vero idem DC, per conversionem rationis, ad CE erit <lb></lb>ut 9 ad 6, et duo simul quadrata CD, DA, ad qua­<lb></lb>dratum AO, erunt ut 18 ad 20. Propterea, per Lemma <lb></lb>praec., angulus ADC obtusus, quod est contra sup­<lb></lb>positum. </s>

<s>” </s></p><p type="main">

<s>“ Maius quam dupla non potest esse. </s>

<s>Quoniam, si ponatur DE minus <lb></lb>quam dupla reliquae EB, erit composita BD, sive CD, magis quam sesqui­<lb></lb>altera ipsius DE. </s>

<s>Qualium igitur partium CD est 3, ipsa DB est minus quam 2. <lb></lb>Qualium vero partium quadratum CD est 9, talium quadratum DE minus <lb></lb>erit quam 4, et talium CE quadratum erit magis quam 5. Qualium itaque <lb></lb>partium quadrata simul CD, DA sunt 18, talium quadratum AC est magis <lb></lb>quam 20. Ergo, per Lemma praec., angulus ADC est obtusus, quod est con­<lb></lb>tra suppositum. </s>

<s>Superest igitur quod recta DE, ad reliquam EB, sit magis <lb></lb>quam dupla, quod erat propositum demonstrare. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma III.<emph.end type="italics"></emph.end> — Quilibet circuli sector, sive quaelibet figura rectilinea, <lb></lb>vel intra vel circa ipsum per continuam arcus bisectionem descripta, centrum <lb></lb>gravitatis habet in axe: hoc est in recta, quae bifariam secat angulum, qui <lb></lb>ad centrum est. </s>

<s>” </s></p><p type="main">

<s>Il lemma fa riscontro esatto con la XX del Della Faille, ma vedasi <lb></lb>quanto il processo dimostrativo ne sia diverso, supposto con Archimede che <lb></lb>delle figure congruenti i centri di gravità convengano insieme. </s></p><p type="main">

<s>“ Esto circuli sector, vel figura plana qualis dicta fuit, ABCD (fig. </s>

<s>130), <lb></lb>linea vero bisecans angulum ADC sit DB: dico in recta BD esse centrum <lb></lb><figure id="id.020.01.2650.2.jpg" xlink:href="020/01/2650/2.jpg"></figure></s></p><p type="caption">

<s>Figura 130.<lb></lb>totius figurae. </s>

<s>Supponamus enim centra partium <lb></lb>esse quaelibet puncta E et F, ducaturque recta <lb></lb>EF. </s>

<s>Superpositis itaque invicem figurae partibus <lb></lb>BAD, BCD, ipsae partes congruent, ob aequali­<lb></lb>tatem omnium angulorum, omniumque laterum. </s>

<s><lb></lb>Centra igitur E et F, per suppositionem prae­<lb></lb>missam ex Archimede, congruent, quare recta <lb></lb>E, I congruet cum IF, aequalesque erunt EI, <lb></lb>IF. </s>

<s>Sunt autem et magnitudines, quarum cen­<lb></lb>tra E et F, aequales inter se. </s>

<s>Ergo magnitudinis, ex utrisque magnitudi­<lb></lb>nibus compositae, centrum gravitatis erit punctum I: punctum videlicet <pb xlink:href="020/01/2651.jpg" pagenum="276"></pb>medium librae EF. </s>

<s>Ergo centrum gravitatis est in axe BD, quod erat pro­<lb></lb>positum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma IV.<emph.end type="italics"></emph.end> — Centrum gravitatis sectoris circuli, quadrante mino­<lb></lb>ris, est inter centra triangulorum, quorum alterum inscriptum sit, alterum <lb></lb>vero ipsi sectori circumscriptum. </s>

<s>” </s></p><p type="main">

<s>“ Esto sector ABCD (fig. </s>

<s>131), quadrante minor, triangulum vero inscri­<lb></lb>ptum sit ACD, circumscriptum EFD. </s>

<s>Patet quod perpendicularis DG magis <lb></lb><figure id="id.020.01.2651.1.jpg" xlink:href="020/01/2651/1.jpg"></figure></s></p><p type="caption">

<s>Figura 131.<lb></lb>quam dupla erit ad reliquam GB. </s>

<s>Sit ergo DI <lb></lb>dupla ad IB, et DO dupla ad OG, eruntque puncta <lb></lb>I et O centra gravitatis triangulorum EFD, ACD. </s>

<s><lb></lb>Dico inter puncta O et I esse centrum gravitatis <lb></lb>sectoris ABCD. </s>

<s>Sit enim, si esse potest, centrum <lb></lb>gravitatis sectoris punctum I. </s>

<s>Cum ergo I sit cen­<lb></lb>trum totius, hoc est trianguli EFD et partis unius, <lb></lb>nempe sectoris ABCD; erit necessario centrum <lb></lb>gravitatis etiam partis alterius, nempe trilineo­<lb></lb>rum EAB, BCF, quod est absurdum. </s>

<s>Sit, si esse <lb></lb>potest, O. </s>

<s>Cum ergo O sit centrum gravitatis totius magnitudinis, nempe <lb></lb>sectoris, partisque unius, nempe trianguli ACD; erit omnino centrum etiam <lb></lb>partis alterius, nempe segmenti ABC, quod est absurdum: Sit si esse potest V. </s>

<s><lb></lb>Cum ergo I sit centrum totius magnitudinis, hoc est trianguli EFD, V vero <lb></lb>centrum partis unius, nempe sectoris; erit centrum alterius partis, nempe <lb></lb>trilineorum EAB, BCF omnino versus D, quod est impossibile. </s>

<s>Sit denique, <lb></lb>si esse potest, R. </s>

<s>Cum ergo R sit centrum totius, nempe sectoris ABCD, <lb></lb>punctum autem O partis unius, hoc est trianguli ADC; erit centrum alterius <lb></lb>partis, nempe segmenti ABC, omnino ulterius versus D, quod est absurdum. </s>

<s><lb></lb>Superest ergo quod centrum gravitatis sectoris sit inter puncta I et O, quod <lb></lb>erat propositum demonstrare. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma V.<emph.end type="italics"></emph.end> — Si figura quaelibet ABCD (fig. </s>

<s>132) in duas figuras <lb></lb>congruentes secta fuerit a linea BD, dummodo congruentium figurarum ae­<lb></lb><figure id="id.020.01.2651.2.jpg" xlink:href="020/01/2651/2.jpg"></figure></s></p><p type="caption">

<s>Figura 132.<lb></lb>quales anguli sint ad easdem partes, et supposito <lb></lb>centro gravitatis semifigurae BAD, quod sit E: si <lb></lb>ex E ducatur EI perpendicularis ad BD, dico I esse <lb></lb>centrum gravitatis totius figurae ABCD. </s>

<s>Producatur <lb></lb>enim EI, ita ut IO sit aequalis ipsi IE, eritque cen­<lb></lb>trum reliquae semifigurae punctum O. Nam, super­<lb></lb>positis figuris, puncta E et O congruent, cum rectae <lb></lb>IE, et OI perpendiculares sint ad BD, per constru­<lb></lb>ctionem, et aequales inter se. </s>

<s>Propterea centrum magnitudinis, ex utrisque ma­<lb></lb>gnitudinibus compositae, erit punctum I, quod erat propositum demonstrare. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma VI.<emph.end type="italics"></emph.end> — Si in sectore semicirculo minore figura rectilinea in­<lb></lb>scribatur, per continuam arcuum bisectionem, et circa eumdem altera similis <lb></lb>figura circumscribatur; erit centrum gravitatis sectoris inter centra prae­<lb></lb>dictarum figurarum. </s>

<s>” </s></p><pb xlink:href="020/01/2652.jpg" pagenum="277"></pb><p type="main">

<s>“ Esto sector circuli semicirculo minor ABCD (fig. </s>

<s>133), in quo, per <lb></lb>continuam arcuum bisectionem, figura rectilinea inscribatur AEBFC, et circa <lb></lb>eumdem altera similis figura circumscribatur GHILM. </s>

<s>Reperiantur centra <lb></lb><figure id="id.020.01.2652.1.jpg" xlink:href="020/01/2652/1.jpg"></figure></s></p><p type="caption">

<s>Figura 133.<lb></lb>triangulorum AED, GHD quae sint N <lb></lb>et O: inter puncta N, O erit omnino, <lb></lb>per lemma IV, centrum gravitatis secto­<lb></lb>ris AED. </s>

<s>Esto illud P. </s>

<s>Ductisque ex <lb></lb>punctis N, P, O, ad rectam DE, perpen­<lb></lb>dicularibus NQ, PS, OR, erunt puncta <lb></lb>Q, S, R, per lemma V, centra gravi­<lb></lb>tatis: nempe Q trapetii AEBD, R vero <lb></lb>trapetii GHID, et S sectoris AEDB. </s>

<s>Est <lb></lb>autem S inter Q et R, alias duae pa­<lb></lb>rallelae coinciderent, quod esse non po­<lb></lb>test. </s>

<s>Ductis iterum ex Q, S, R ad DB perpendicularibus QT, SX, RV, erunt <lb></lb>puncta T, X, V (per lemma V) centra gravitatis: nempe T figurae AEBFCD, <lb></lb>V vero figurae alterius GHILMD, X denique sectoris ABCD. </s>

<s>Estque X inter T <lb></lb>et V, alias duae parallelae convenirent, quod esse non potest, propterea cen­<lb></lb>trum gravitatis sectoris est inter centra figurarum, inscriptae scilicet et cir­<lb></lb>cumscriptae, quod erat demonstrandum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma VII.<emph.end type="italics"></emph.end> — Si fuerit sector ABCD (fig. </s>

<s>134), minor semicirculo, <lb></lb>ipsique altera figura inscribatur, et altera circumscribatur, per continuam <lb></lb><figure id="id.020.01.2652.2.jpg" xlink:href="020/01/2652/2.jpg"></figure></s></p><p type="caption">

<s>Figura 134.<lb></lb>arcus bisectionem; dico ita esse <lb></lb>perimetrum unius AEBFC, ad <lb></lb>chordam suam AC, ut est peri­<lb></lb>meter alterius GHILM, ad chor­<lb></lb>dam suam GM. ” </s></p><p type="main">

<s>“ Facto enim centro D, in­<lb></lb>tervallo DG, describi potest circu­<lb></lb>lus, qui transibit per omnia puncta <lb></lb>G, H, I, L, M. </s>

<s>Ideo anguli ACE, <lb></lb>GMH, ad peripheriam constituti, <lb></lb>aequales erunt inter se, cum sint, per XX Tertii, subdupli ciusdem anguli <lb></lb>ad centrum ADE. </s>

<s>Eadem ratione anguli EAC, HGM aequales erunt inter se, <lb></lb>et triangula EAC, HGM aequiangula. </s>

<s>” <lb></lb><figure id="id.020.01.2652.3.jpg" xlink:href="020/01/2652/3.jpg"></figure></s></p><p type="caption">

<s>Figura 135.</s></p><p type="main">

<s>“ Jam perimeter AEBFG ad AE est ut perime­<lb></lb>ter GHILM ad GH, cum sint earumdem aequimul­<lb></lb>tiplices. </s>

<s>AE vero ad AC, per IV Sexti, est ut GH <lb></lb>ad GM: ergo ex aequo perimeter AEBFC, ad chor­<lb></lb>dam suam AC, est ut perimeter GHILM, ad chordam <lb></lb>suam GM, quod erat ostendendum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma VIII.<emph.end type="italics"></emph.end> — Si fuerit trapetium ABCD <lb></lb>(fig. </s>

<s>135), constans ex duobus triangulis isoscelibus ADB, BDC, quorum et <lb></lb>latera et bases AB, BC sint aequales, ductaque AC fiat ut AB ad 2/3 ipsius <pb xlink:href="020/01/2653.jpg" pagenum="278"></pb>AE, ita perpendicularis DF ad DI; dico I esse centrum gravitatis trape­<lb></lb>tii ABCD. ” </s></p><p type="main">

<s>“ Ducatur ex I recta IO perpendicularis ad BD, eruntque duo triangula <lb></lb>orthogonia ODI, et BDF aequiangula, cum habeant communem angulum <lb></lb>BDF. </s>

<s>Sed eadem ratione triangula orthogonia ABE, BDF sunt aequiangula, <lb></lb>ergo ODI, et ABE aequiangula erunt. </s>

<s>” </s></p><p type="main">

<s>“ Jam sic: BA ad 2/3 ipsius AE, per constructionem, est ut FD ad DI. </s>

<s><lb></lb>Sed 2/3 ipsius AE, ad 2/3 ipsius AB, per IV Sexti, est ut ID ad DO; ergo <lb></lb>ex aequo AB, ad 2/3 AB, est ut FD ad DO. </s>

<s>Propterea FD sesquialtera est <lb></lb>ipsius DO. </s>

<s>Ergo O est centrum trianguli ADB. </s>

<s>Sed recta OI perpendicularis <lb></lb>est ad BD, ergo I, per lemma V, est centrum ipsius trapetii, quod erat pro­<lb></lb>positum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma IX.<emph.end type="italics"></emph.end> — Si fuerint quotcumque triangula deinceps isoscelia, <lb></lb>quorum et latera et bases aequales sint ABF, BCF, CDF (fig. </s>

<s>136), et reli­<lb></lb><figure id="id.020.01.2653.1.jpg" xlink:href="020/01/2653/1.jpg"></figure></s></p><p type="caption">

<s>Figura 136.<lb></lb>qua quae sequntur, dummodo eorum <lb></lb>numerus sit in progressione nume­<lb></lb>rorum duplorum ab unitate 1, 2, 4, <lb></lb>8, 16, etc.: fiat autem ut aggrega­<lb></lb>tum omnium basium AEG, ad 2/3 <lb></lb>chordae AG, ita FS, catetus unius <lb></lb>trianguli, ad aliam sumendam ex <lb></lb>F versus E; dico terminum huius <lb></lb>quartae proportionalis esse centrum <lb></lb>gravitatis figurae universae, ex prae­<lb></lb>dictis triangulis compositae. </s>

<s>” </s></p><p type="main">

<s>“ Esto punctum L, iuxta lemma VIII, centrum trapetii ABCF, et, ducta <lb></lb>LM perpendiculari ad CF, erit punctum M, per lemma V, centrum figurae <lb></lb>ABCDEF. </s>

<s>Ducta vero MH perpendiculari ad EF, erit H, per lemma V, cen­<lb></lb>trum totius figurae AEGF. ” </s></p><p type="main">

<s>“ In primis angulus CAO, per XX Tertii, subduplus est anguli CFE, <lb></lb>et ideo aequalis angulo EFM, et propterea triangula orthogona AOC, FML <lb></lb>sunt aequiangula. </s>

<s>Eadem ratione triangula ARE, FHM sunt aequiangula. </s>

<s>” </s></p><p type="main">

<s>“ Jam, per lemma VIII, sive per constructionem, catetus FS ad FL est <lb></lb>ut BA ad 2/3 ipsius AI, sive ut AB, BC simul ad 2/3 AC. </s>

<s>Verum LF ad FM, <lb></lb>per IV Sexti, est ut 2/3 ipsius CA, ad 2/3 AO. </s>

<s>Ergo ex aequo catetus FS, <lb></lb>ad FM, est ut AB, BC simul ad 2/3 ipsius AO, nempe ut ABCDE simul <lb></lb>ad 2/3 ipsius AE. ” </s></p><p type="main">

<s>“ Amplius FM, per IV Sexti, ad FH, est ut 2/3 AE ad 2/3 AR: ergo <lb></lb>iterum, ex aequo, catetus FS, ad FH, est ut ABCDE ad 2/3 ipsius AR, <lb></lb>sive ut omnes simul bases AEG, ad 2/3 chordae AG, quod erat proposi­<lb></lb>tum etc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma X.<emph.end type="italics"></emph.end> — Si fuerint tres magnitudines A, B, C, aliaeque ipsis <lb></lb>aequales numero D, E, F, quae binae in maiore ratione sumantur, sitque <lb></lb>perturbata earum proportio, nempe sit ratio A ad B maior ratione E ad F, <pb xlink:href="020/01/2654.jpg" pagenum="279"></pb>et B ad C maior sit ratione D ad E; dico A ad C maiorem habere ratio­<lb></lb>nem quam D ad F. ” </s></p><p type="main">

<s>“ Ponatur ut A ad B, ita E ad H, eritque, per X Quinti, magnitudo H <lb></lb>minor quam F. </s>

<s>Ponatur etiam ut B ad C, ita G ad E, oritque, per eamdem, <lb></lb>G maior quam D. ” </s></p><p type="main">

<s>“ Jam A ad C erit, per XXIII Quinti, ut G ad H. </s>

<s>Ergo necessario A <lb></lb>ad C, per VIII Quinti, maiorem rationem habebit quam D ad H: multoque <lb></lb>etiam maiorem quam D ad F, quod erat propositum. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE X. — <emph type="italics"></emph>Sifuerit circuli sector minor semicirculo, fiatque <lb></lb>ut arcus sectoris, ad 2/3 chordae eiusdem, ita semidiameter, ad aliam su­<lb></lb>mendam ex centro; terminus assumptae in axe erit centrum gravitatis <lb></lb>sectoris. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2654.1.jpg" xlink:href="020/01/2654/1.jpg"></figure></s></p><p type="caption">

<s>Figura 137.</s></p><p type="main">

<s>“ Esto circuli sector ABCD <lb></lb>(fig. </s>

<s>137), minor semicirculo, fiat­<lb></lb>que ut arcus ABC, ad 2/3 suae <lb></lb>chordae AC, ita radius BD ad DE. </s>

<s><lb></lb>Dico E punctum esse centrum <lb></lb>gravitatis sectoris. </s>

<s>Si enim pos­<lb></lb>sibile est non sit E: sit ergo cen­<lb></lb>trum gravitatis sectoris vel su­<lb></lb>pra, vel infra punctum E. </s>

<s>Esto <lb></lb>primo F, et sectori ABCD duae <lb></lb>figurae rectilineae, altera inscri­<lb></lb>batur, altera vero circumscriba­<lb></lb>tur per continuam arcus bisectionem, ita ut latus circumscriptae LM, ad <lb></lb>latus inscriptae OC, per IV <emph type="italics"></emph>De sphaera et cylindro,<emph.end type="italics"></emph.end> minorem habeat ra­<lb></lb>tionem, quam ED ad DF: fiatque ut perimeter rectilineus ANBOC, ad 2/3 <lb></lb>chordae AC, ita catetus VD, ad rectam Q: dico primum Q maiorem esse <lb></lb>quam DF. ” </s></p><p type="main">

<s>“ Nam BD ad DE est ut arcus ABC, ad 2/3 chordae AC: ergo ratio BD <lb></lb>ad BE, per XIII Quinti, maior est ratione perimetri rectilinaei ANBOC ad <lb></lb>2/3 chordae AC, sive maior est, ob constructionem, ratione VD ad <expan abbr="q.">que</expan> Am­<lb></lb>plius, ratio ED ad DF, per constructionem, maior est ratione LM ad OC, <lb></lb>sive, per IV Sexti, LD ad DO, sive ratione PD ad DV. </s>

<s>Propterea BD ad DF, <lb></lb>per lemma X, maiorem rationem habebit quam PD ad Q Maior ergo, per <lb></lb>X Quinti, est DF quam ipsa <expan abbr="q.">que</expan> ” </s></p><p type="main">

<s>“ Secetur DR aequalis ipsi Q, et erit R, per lemma IX, et ob con­<lb></lb>structionem, centrum figurae inscriptae ANBOCD. </s>

<s>Centrum vero circum­<lb></lb>scriptae adhuc ulterius erit versus B, et inter utrumque debet esse centrum <lb></lb>gravitatis sectoris. </s>

<s>Ergo centrum gravitatis sectoris non est F. ” </s></p><p type="main">

<s>“ Esto deinde centrum gravitatis sectoris, si fieri potest, infra punctum E, <lb></lb>sitque illud F (fig. </s>

<s>138). Inscribatur in sectore figura multilatera, atque al­<lb></lb>tera circumscribatur, qer continuam arcuum bisectionem, ita ut GH latus, <lb></lb>ad latus AN, per IV <emph type="italics"></emph>De Sphaera et Cylindro,<emph.end type="italics"></emph.end> minorem habeat rationem <pb xlink:href="020/01/2655.jpg" pagenum="280"></pb>quam FD ad DE. </s>

<s>Eritque ratio arcus AN ad chordam AN multo minor ra­<lb></lb>tione FD ad DE. ” </s></p><p type="main">

<s>“ Fiat, ut perimeter rectilineus GHILM ad 2/3 chordae GM, ita BD, ca­<lb></lb>tetus figurae circumscriptae, ad P. </s>

<s>Dico primum P minorem esse quam DF. <lb></lb><figure id="id.020.01.2655.1.jpg" xlink:href="020/01/2655/1.jpg"></figure></s></p><p type="caption">

<s>Figura 138.<lb></lb>Nam arcus ABC, ad 2/3 chordae <lb></lb>AC, est ut BD ad DE, per suppo­<lb></lb>sitam constructionem ab initio, <lb></lb>sed 2/3 chordae AC, ad perime­<lb></lb>trum ANBOC, per lemma VII, <lb></lb>est ut 2/3 chordae GM, ad peri­<lb></lb>metrum GHILM, sive ut P ad BD; <lb></lb>ergo, per perturbatam, erit ut ar­<lb></lb>cus ABC, ad perimetrum ANBOC, <lb></lb>ita P ad DE. </s>

<s>Sed FD ad DE, ob <lb></lb>constructionem, maiorem habet ra­<lb></lb>tionem quam arcus ABC ad peri­<lb></lb>metrum ANBOC. </s>

<s>Necesse igitur est, per X Quinti, quod P maior sit quam <lb></lb>DF. </s>

<s>Secetur ergo DT aequalis ipsi P, eritque T, per lemma IX et ob con­<lb></lb>structionem, centrum figurae circumscriptae GHILMD. </s>

<s>Centrum autem inscri­<lb></lb>ptae adhuc inferius est versus D, et inter utrumque debet esse centrum <lb></lb>gravitatis sectoris ABCD. </s>

<s>Propterea punctum F non erit centrum gravitatis <lb></lb>sectoris, sed ipsum erit E, cum demonstratum sit sectoris centrum esse non <lb></lb>posse neque supra E, neque infra. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollarium.<emph.end type="italics"></emph.end> — In quolibet circuli sectore, etiamsi semicirculo maior <lb></lb>sit, si fiat ut arcus ad 2/3 chordae, ita semidiameter ad aliam sumendam in <lb></lb>axe ex centro circuli; terminus huius assumptae erit centrum gravitatis ipsius <lb></lb>sectoris. </s>

<s>” </s></p><p type="main">

<s>“ Esto sector circuli ABCE (fig. </s>

<s>139) semicirculo maior, cuius chorda <lb></lb>AC, sectusque sit in duas partes aequales ab axe BEM. </s>

<s>Erunt ergo sectores <lb></lb><figure id="id.020.01.2655.2.jpg" xlink:href="020/01/2655/2.jpg"></figure></s></p><p type="caption">

<s>Figura 139.<lb></lb>ADBE, et BCE, uterque semicirculo minores. </s>

<s><lb></lb>Esto sectoris ADBE axis ED, fiatque ut arcus <lb></lb>ADB, ad 2/3 chordae AB, ita DE ad EI, eritque <lb></lb>I, per theorema praec., centrum gravitatis se­<lb></lb>ctoris ADBE. </s>

<s>Ductaque IO perpendiculari ad <lb></lb>BE, erit O, per lemma V, centrum totius secto­<lb></lb>ris semicirculo maioris ABCE. ” </s></p><p type="main">

<s>“ Jam triangula orthogonia IOE, ABM sunt <lb></lb>aequiangula, nam angulus IEO, ad centrum con­<lb></lb>stitutus, insistit arcui DB. </s>

<s>Angulus vero BAM <lb></lb>ad peripheriam insistit arcui duplo, nempe ipsi <lb></lb>BC. </s>

<s>Ergo anguli aequales sunt. </s>

<s>Propterea, ut <lb></lb>arcus ADB ad 2/3 chordae AB, ita BE ad EI, per constructionem. </s>

<s>Ut au­<lb></lb>tem 2/3 AB, ad 2/3 AM, ita, per IV Sexti, IE ad EO. </s>

<s>Ergo ex aequo ut <lb></lb>arcus ADB, ad 2/3 AM, sive ut arcus ABC, ad 2/3 chordae AC, ita DE, <pb xlink:href="020/01/2656.jpg" pagenum="281"></pb>sive BE, ad EO, quae quidem est inter centrum gravitatis sectoris, et cen­<lb></lb>trum circuli, quod erat demonstrandum ” (MSS. Gal. </s>

<s>Disc., T. XXXVII, <lb></lb>fol. </s>

<s>13-23). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La superiorità di questo processo dimostrativo, paragonato con quello <lb></lb>del padre Della Faille, non consiste in altro che in aver ridotti a maggiore <lb></lb>facilità i metodi antichi, e ornatigli di eleganze nuove. </s>

<s>Del resto, benchè il <lb></lb>Torricelli si compiacesse col Cavalieri di aver dimostrato in meno di un foglio <lb></lb>quel che al Matematico gesuita era, per far lo stesso, bisognato un libro; e <lb></lb>benchè tenesse i suoi lemmi e le loro applicazioni per cose tanto acute, da <lb></lb>non credere che il Guldino ci fosse potuto arrivare; nonostante troppo ben <lb></lb>comprendeva che, a correre l&#039;alto e profondo occano della Baricentrica, quelli <lb></lb>erano troppo deboli remi, e che poco era da dilungarsi dal lido, se non fosse <lb></lb>alla navicella sovvenuto altro più valido argomento. </s>

<s>Alla Geometria era già <lb></lb>felicemente incontrata questa fortuna, per la nuova invenzione del metodo <lb></lb>degl&#039;indivisibili, e alcuni tooremi, specialmente i primi fra quelli dimostrati <lb></lb>nel suo terzo libro dal Cavalieri, sembrava che si porgessero d&#039;assai facile <lb></lb>applicazione alla ricerca del centro di gravità nei cilindri scavati da una sfera <lb></lb>inscritta o da un cono. </s>

<s>Vedremo di quali conseguenze fossero nella mente <lb></lb>del Torricelli fecondi così fatti teoremi, ma intanto che il germe s&#039;incubava <lb></lb>latente ne andava discorrendo con gli amici, fra i quali Antonio Nardi, che <lb></lb>s&#039;era incontrato in que&#039;medesimi pensieri, e che, essendo per stampare un <lb></lb>libro di Geometria, aveva dato intenzione di trattarvi del modo di applicare <lb></lb>gl&#039;indivisibili ai baricentri. </s>

<s>Significava il Torricelli stesso queste intenzioni <lb></lb>dell&#039;amico e sue al Cavalieri, il quale rispondeva da Bologna, il di 30 Ot­<lb></lb>tobre 1641, così, dop&#039;aver discorso di Giovanni Beugrand venuto di Parigi a <lb></lb>ridestar nuove scintille di scienza dall&#039;ingegno dei Matematici italiani: </s></p><p type="main">

<s>“ Detto Beugrand poi, al quale molto piacque questa maniera nuova <lb></lb>degli indivisibili, aveva pensiero di praticarla in materia dei centri di gra­<lb></lb>vità, poichè mi domandava se l&#039;avevo usata io, e me ne richiedeva qualche <lb></lb>esempio. </s>

<s>Onde, se il signor Nardi vuole stampare quello che dice per gli <lb></lb>indivisibili, avrà campo ancora, se non l&#039;ha fatto, di aggiungere quello <lb></lb>dei centri di gravità, quando ci abbia gusto ” (MSS. Gal. </s>

<s>Disc., T. XLI, <lb></lb>fol. </s>

<s>114). </s></p><p type="main">

<s>Ma intanto che si facevano discorsi, volle il Torricelli venire ai fatti, il <lb></lb>primo dei quali si fu quello di applicare gl&#039;indivisibili a dimostrare il centro <lb></lb>di gravità della parabola, in quel modo che fu poi stampato nel libro della <lb></lb>sua <emph type="italics"></emph>Quadratura<emph.end type="italics"></emph.end> (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>74, 75). La nuova applicazione <lb></lb>fu come saggio sottoposta al giudizio del Cavalieri, a cui si domandava an­<lb></lb>che insieme consiglio, e nella incerta via intrapresa qualche più sicuro in-<pb xlink:href="020/01/2657.jpg" pagenum="282"></pb>dirizzo. </s>

<s>La risposta fu data in una lettera del dì 29 Ottobre 1642, in questa <lb></lb>forma: </s></p><p type="main">

<s>“ Ho vista la sua maniera di trovare il centro della parabola, la quale <lb></lb>mi è piaciuta assaissimo, e credo non si possi migliorare. </s>

<s>Gli confesso non­<lb></lb>dimeno ciò che mi è passato per la fantasia, dopo che io ebbi la lettera in <lb></lb>materia di trovare il centro di gravità di alcune figure per gl&#039;indivisibili, da <lb></lb>non compararsi però nella facilità alla sua. </s>

<s>E per dargli un poco di saggio <lb></lb>del mio pensiero apporterò per esempio il triangolo ed il conoide parabolico, <lb></lb>dai quali potrà intendere come questa maniera si possa anco applicare ad <lb></lb>altre figure. </s>

<s>” </s></p><p type="main">

<s>“ E prima non tralascerò, per il triangolo, di dire che mi pare che gl&#039;in­<lb></lb>divisibili arrechino molta facilità per ritrovare il di lui centro, poichè, essendo <lb></lb>il centro di gravità d&#039;ogni proposta linea retta, e terminata, nel mezzo di essa; <lb></lb>facilmente proveremo essere il centro del triangolo, per esempio ABD (fig. </s>

<s>140), <lb></lb><figure id="id.020.01.2657.1.jpg" xlink:href="020/01/2657/1.jpg"></figure></s></p><p type="caption">

<s>Figura 140.<lb></lb>nella AC, che divide ugualmente BD in C, poichè i centri <lb></lb>di tutte le linee parallele a BD, cioè il centro di tutto il <lb></lb>triangolo ABD, sono nella AC, il che pur anco si verificherà <lb></lb>di qual si voglia figura intorno al diametro, cioè che sarà <lb></lb>nell&#039;istesso diametro. </s>

<s>Onde, se tireremo la BE che tagli AD <lb></lb>eguàlmente in E, e la AC in O, sarà O il centro, e sarà <lb></lb>AO doppia di OC, poichè i triangoli ABE, DBE sono uguali, <lb></lb>come anco AOE, DOE, e però ABO, BOD saranno uguali, <lb></lb>cioè ABC sarà doppia di OBD, onde AO sarà doppia di OC. ” </s></p><p type="main">

<s>“ Ora vengo all&#039;altro modo, e siccome si prova facilmente che i mo­<lb></lb>menti dei gravi appesi in una bilancia hanno tra loro la proporzione com­<lb></lb>posta delle moli, supponendoli ugualmente gravi in specie, e delle distanze <lb></lb>dal sostegno; così, invece di corpi attaccandovi linee o superficie piane sup­<lb></lb>poste come gravi, riceverò per provato che pure i momenti delle prefate linee <lb></lb>avranno la detta proporzione composta. </s>

<s>” </s></p><p type="main">

<s>“ Venendo ora all&#039;applicazione, sia il medesimo triangolo che sopra ADB, <lb></lb>nel quale sia divisa BD ugualmente in C, e tirata la AC, quale sia divisa <lb></lb>in O, sicchè AO sia doppia di OC; dico il centro essere O del triangolo ABD ” <lb></lb>(ivi, fol. </s>

<s>135). E tirata la LG parallela alla BD, ciò si conclude dopo aver <lb></lb>dimostrato che il momento di tutte le linee del trapezio LD è uguale al mo­<lb></lb>mento di tutte le linee del triangolo LAG, cosìcchè conglobate queste insieme <lb></lb>in T, e quelle in P, sia il momento T.TO uguale al momento P.PO, <lb></lb>d&#039;onde T:P=PO:TO, che vuol dire essere O, nella bilancia AC, il cen­<lb></lb>tro dell&#039;equilibrio. </s></p><p type="main">

<s>“ Intenda ora DAB, nella medesima figura, prosegue a scrivere il Ca­<lb></lb>valieri, per l&#039;ambito della parabola, che passa per l&#039;asse AC del conoide <lb></lb>sopra il circolo DB, al quale ella supponga perpendicolare AC, e ciò per non <lb></lb>fare altra figura. </s>

<s>Si proverà dunque che il momento di tutti i circoli del <lb></lb>conoide ALG è uguale al momento di tutti i circoli del frusto LBDC, e per­<lb></lb>ciò sarà O centro ” (ivi, fol. </s>

<s>137). </s></p><pb xlink:href="020/01/2658.jpg" pagenum="283"></pb><p type="main">

<s>La dimostrazione però dell&#039;uguaglianza dei momenti delle linee, nel <lb></lb>triangolo, e dei momenti de&#039;cerchi nel conoide riusciva assai laboriosa e com­<lb></lb>plicata, di che troppo bene accortosi il Cavalieri così concludeva: “ La fretta <lb></lb>è cagione che io non mi possi spiegare abbastanza, ma supplirà il suo va­<lb></lb>lore al mio mancamento. </s>

<s>Mi favorisca del suo parere circa questa maniera, <lb></lb>veramente difficile, e però da non farne molto capitale. </s>

<s>Vedrà almeno come <lb></lb>riescono ancora in questa parte gl&#039;indivisibili assai fecondi, poichè, trasfor­<lb></lb>mando i momenti in rettangoli o parallelepipe di o altri solidi, possiamo rin­<lb></lb>tracciare i centri ancora, credo, d&#039;altre figure ” (ivi, fol. </s>

<s>138). </s></p><p type="main">

<s>Coloro, che hanno letto il nostro secondo capitolo scritto nel tomo IV, <lb></lb>riconoscono qui facilmente il metodo usato dal Rocca per dimostrare in qual <lb></lb>proporzione stiano fra loro il fuso parabolico e il cilindro circoscritto. </s>

<s>Ma in <lb></lb>verità il computo dei momenti rendeva difficile il processo dimostrativo, e <lb></lb>benchè non in modo da non farne capitale, come per modestia diceva il Ca­<lb></lb>valieri, certo da non si dover preferire in tutti i casi agli stessi metodi an­<lb></lb>tichi. </s>

<s>Scorto il Torricelli però da quella sua sagacia geometrica ben conobbe <lb></lb>che il metodo nuovo si poteva rendere molto più semplice e più spedito, in­<lb></lb>tendendo i pesi concentrati direttamente nel loro punto d&#039;appoggio, e non a <lb></lb>quelle distanze che si facevano dal Cavalieri e dal Rocca entrare nel com­<lb></lb>puto dei momenti. </s></p><p type="main">

<s>Nel conoide parabolico, per esempio, tutti i cerchi, come quelli di rag­<lb></lb>gio AE, BF (fig. </s>

<s>141) si possono riguardar concentrati in A, B, e ivi pon­<lb></lb>derare direttamente sull&#039;asse OG, preso per libbra. </s>

<s>E il sapere per le dimo­<lb></lb><figure id="id.020.01.2658.1.jpg" xlink:href="020/01/2658/1.jpg"></figure></s></p><p type="caption">

<s>Figura 141.<lb></lb>strazioni altrui che una tal libbra ha il suo centro di­<lb></lb>stante dal vertice O per due terzi di tutto l&#039;asse, dove <lb></lb>pur cascherebbe il centro del triangolo inscritto, fece al <lb></lb>Torricelli sovvenire un bel modo e facilissimo di di­<lb></lb>mostrare il centro dello stesso conoide, supponendolo <lb></lb>ignoto. </s>

<s>La libbra OG infatti si può per una parte con­<lb></lb>siderar gravata degl&#039;infiniti cerchi del solido parabolico, <lb></lb>e per l&#039;altra delle infinite linee della superficie trian­<lb></lb>golare, nei quali due tessuti le fila hanno uguale spessore, e sono in gravità <lb></lb>proporzionali, perchè il triangolo dà OA:OB=AC:BD, e la parabola <lb></lb>OA:OB=AE2:BF2, onde AC:BD=<foreign lang="grc">π</foreign>AE2:<foreign lang="grc">π</foreign>BF2, e così di tutte le altre <lb></lb>infinite linee del triangolo si dimostra la proporzionalità ai corrispondenti cer­<lb></lb>chi del conoideo. </s></p><p type="main">

<s>Veniva di qui facilmente suggerita una proposizione statica, la verità <lb></lb>della quale non fu difficile a dimostrarsi in quel modo, che poi si vide stam­<lb></lb>pato per servir di lemma alle quadrature della Parabola: lemma, che in or­<lb></lb>dine è il XXII del libro, messo dal Torricelli stesso in questa forma: “ Si <lb></lb>magnitudines quotcumque ad libram appensae fuerint, ex quibuscumque <lb></lb>punctis, totidemque magnitudines alterius ordinis ex iisdem punctis pendeant, <lb></lb>pariter cum praedictis magnitudinibus proportionales; erit unum idemque li­<lb></lb>brae punctum centrum aequilibrii utriusque ordinis magnitudinum ” (Op. <pb xlink:href="020/01/2659.jpg" pagenum="284"></pb>geom., P. II cit., pag. </s>

<s>61). Applicato il qual lemma, ecco in un brevissimo <lb></lb>tratto dal Torricelli condotta la dimostrazione del centro di gravità del co­<lb></lb>noide parabolico, che aveva dianzi aggirato il Cavalieri per così lungo e fa­<lb></lb>ticoso viaggio. </s></p><p type="main">

<s>“ PROPOSIZIONE XI. — <emph type="italics"></emph>Il centro del conoide parabolico sega l&#039;asse <lb></lb>nella proporzione di due a uno, provato per via del triangolo inscritto. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Poichè, sia libbra orizontale OG (nella medesima figura 141). Il cir­<lb></lb>colo di AE al circolo di BF sta come la retta AC alla BD. </s>

<s>Perciò i centri <lb></lb>divideranno la libbra nell&#039;istesso luogo ” (MSS. Gal., T. XXXVI, fol. </s>

<s>56 <lb></lb>a tergo). </s></p><p type="main">

<s>La prova, così ben riuscita nel conoide parabolico, invogliò il Torricelli <lb></lb>a tentarla anche in quell&#039;altro esempio addotto dal Cavalieri, cioè nel trian­<lb></lb>golo, dentro cui, supposto che il centro di gravità si trovi sopra qualche <lb></lb>punto della bissettrice, si potesse questa riguardar quale una bilancia, con­<lb></lb>centrativi sopra i pesi delle infinite linee, di che s&#039;intesse la detta triango­<lb></lb>lar superficie. </s>

<s>Posto ciò, nient&#039;altro rimaneva a sapere e a dimostrare, per <lb></lb>modo di lemma, se non che dove riesca il punto dell&#039;equilibrio sopra una <lb></lb>bilancia gravata per tutta la sua lunghezza da pesi, che scemino ugualmente <lb></lb>a proporzione delle distanze uguali. </s>

<s>Ma il lemma era stato dimostrato già da <lb></lb>Galileo, e posto per la prima proposizione nel suo trattato dei centri di gra­<lb></lb>vità, sotto questa forma: “ Si magnitudines quotcumque sese aequaliter exce­<lb></lb>dentes, et quarum excessus earum minimae sint aequales, ita in libra dispo­<lb></lb>nantur, ut ex distantiis aequalibus pendeant: centrum gravitatis omnium <lb></lb>libram ita demonstratur dividere, ut pars versus minores reliquae sit dupla ” <lb></lb>(Alb. </s>

<s>XIII, 267). </s></p><p type="main">

<s>E in tali condizioni si trovano per l&#039;appunto le infinite linee del trian­<lb></lb>golo ACB (fig. </s>

<s>142) parallele ad AB, e pendenti pel loro mezzo dalla libbra <lb></lb><figure id="id.020.01.2659.1.jpg" xlink:href="020/01/2659/1.jpg"></figure></s></p><p type="caption">

<s>Figura 142.<lb></lb>CE, la quale dunque sarà segata dal centro <lb></lb>di gravità D in modo, che la parte verso i <lb></lb>pesi minori, ossia CD, sia a DE doppia. </s></p><p type="main">

<s>A ridurre la conclusione assoluta rima­<lb></lb>neva dunque solamente a dimostrare il suppo­<lb></lb>sto, che cioè il centro di gravità del triangolo <lb></lb>si trova sopra un punto della linea, la quale <lb></lb>sia da un vertice fatta scendere sul mezzo del <lb></lb>lato opposto, ciò che si proponeva di fare il <lb></lb>Torricelli, dietro lo stesso principio di Galileo, <lb></lb>intitolando così la sua proposizione: <emph type="italics"></emph>Centrum gravitatis trianguli, suppo­<lb></lb>sito Galilei principio.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Nel medesimo triangolo dianzi figurato sia D il centro preso sopra la CE, <lb></lb>la quale si vuol dimostrare essere bissettrice. </s>

<s>Si consideri AB libbra, d&#039;onde <lb></lb>pendano le infinite linee ponderose parallele a CB, le quali crescendo da B <lb></lb>verso A, a proporzione delle distanze, faranno che il centro I divida essa <lb></lb>libbra in modo, che la parte AI verso i pesi minori sia doppia della IB. </s>

<s>In <pb xlink:href="020/01/2660.jpg" pagenum="285"></pb>simil guisa considerando la medesima libbra come gravata dalle infinite linee <lb></lb>parallele ad AC, queste da A scemando col detto ordine verso B concentre­<lb></lb>ranno i loro pesi in F, punto dallo stesso B distante il doppio che da A. </s>

<s>Con­<lb></lb>dotta dunque da I la IH parallela a BC e da F la FG parallela ad AC, do­<lb></lb>vendosi nella loro intersezione trovare il centro del triangolo passeranno <lb></lb>ambedue per D e la costruzione, che di qui nasce, dà facile modo a dimo­<lb></lb>strare l&#039;intento, che cioè sia in E il lato AB segato nel mezzo. </s></p><p type="main">

<s>Dall&#039;essere infatti, per le cose ora dette, BI=2AI, AF=2FB, viene <lb></lb>AI:IB=FB:FA, e, componendo, AB:IB=AB:FA, dunque IB=FA. </s>

<s><lb></lb>La similitudine dei triangoli dall&#039;altra parte dà AF:FE=CD:DE= <lb></lb>BI:IE, dunque EF=IE e perciò AE=EB, che è la conclusione desiderata, <lb></lb>in proporre e in dimostrar la quale così propriamente procede il Torricelli. </s></p><p type="main">

<s>“ PROPOSIZIONE XII. — <emph type="italics"></emph>Esto triangulum ABC, cuius gravitatis cen­<lb></lb>trum sit D, et ducta EDC, dico CE secare bifariam AB. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ducatur, per D, FDG parallela ad AC, et IDH parallela ad BC. </s>

<s>Quo­<lb></lb>niam AB est libra et ad singula ipsius puncta magnitudines pendent, nempe <lb></lb>lineae parallelae ad latus BC, habentque ipsae magnitudines inter se, ob <lb></lb>IV Sexti, eamdem rationem quam distantiae ab extremo librae puncto A, et <lb></lb>omnium centrum per suppositionem est in IH una ipsarum: item quoniam <lb></lb>AB est libra, et ex singulis ipsius punctis magnitudines pendent, nempe li­<lb></lb>neae parallelae ad latus AC, habentque magnitudines eamdem rationem quam <lb></lb>distantiae ab extremo librae puncto B, et omnium centrum est in FG per <lb></lb>suppositionem; erit libra AB secta in eadem ratione, nempe, ut AI ad IB, <lb></lb>ita BF ad FA. </s>

<s>Et componendo, AB ad BI ut BA ad AF. </s>

<s>Quare aequales <lb></lb>sunt AF, IB. </s>

<s>Quoniam vero AF ad FE est ut CD ad DE, sive ut BI ad IE, <lb></lb>erunt aequales etiam FE, EI. </s>

<s>Ergo aequales AE, EB quod erat demonstran­<lb></lb>dum ” (ibid., fol. </s>

<s>21). </s></p><p type="main">

<s>Questa maniera di applicare gl&#039;indivisibili alla ricerca del centro di gra­<lb></lb>vità, ne&#039;due esempi del conoide parabolico, e del triangolo, parve al Torri­<lb></lb>celli tanto più facile e più spedito, e da preferirsi anche in altri casi più <lb></lb>complicati a quello propostogli dal Cavalieri, che non potè tenersi dal far­<lb></lb>gliene qualche motto: a che il Cavalieri stesso rispondeva il dì 23 Dicem­<lb></lb>bre del detto anno 1642: “ La stima poi, che ella mostra di fare delle mie <lb></lb>debolezze, è da me ricevuta dall&#039;abbondanza del suo affetto, e non dal me­<lb></lb>rito di quelle, poichè sono di niuno momento, massime in comparazione di <lb></lb>qe&#039;suoi sottilissimi trovati, come stimo deva essere il modo che mi accenna <lb></lb>di ritrovare il centro di gravità per gl&#039;indivisibili, intorno al quale non man­<lb></lb>cherò di dire come il signor Giann&#039;Antonio Rocca, gentiluomo reggiano, in­<lb></lb>gegno vivacissimo e versatissimo nelle Matematiche, altre volte da me credo <lb></lb>nominato, mi mandò un altro modo assai facile di ritrovare i centri di gra­<lb></lb>vità per gl&#039;indivisibili, qùale ora non ho alle mani, ma sta rivolto fra&#039;miei <lb></lb>scartafacci, e forse potriano riscontrarsi insieme ” (ivi, T. XLI, fol. </s>

<s>140). </s></p><p type="main">

<s>Sarebbe per questa nuova storia delle Matematiche applicate alla scienza <lb></lb>del moto assai importante il sapere se il Rocca, mettendo a varie prove <pb xlink:href="020/01/2661.jpg" pagenum="286"></pb>quella sua maniera di misurare il gravitar delle linee e delle superficie dai <lb></lb>loro momenti, e trovandola complicata, s&#039;incontrasse, per renderla più sem­<lb></lb>plice, in quell&#039;altra maniera usata dal Torricelli, e l&#039;eccellenza della quale <lb></lb>principalmente consisteva nel misurare il peso degli elementi infinetisimi as­<lb></lb>solutamente in sè sulla lunghezza della libbra, e non moltiplicato per la di­<lb></lb>stanza laterale dal punto d&#039;appoggio. </s>

<s>Così si riducevano i rettangoli, presi <lb></lb>per la misura dei momenti, a semplici linee, e i parallelepipedi a quadrati, <lb></lb>il baricentro dei quali è manifestamente il medesimo che dei circoli inscritti <lb></lb>o circoscritti. </s>

<s>Sarebbe importante, ripetiamo, saper se si fosse in questo stesso <lb></lb>pensiero incontrato anche il Rocca, ma perchè a noi mancano i documenti, <lb></lb>unico o almen principale autore di questa applicazione degl&#039;indivisibili alla <lb></lb>Baricentrica non possiamo non riconoscere il Torricelli, del quale, dopo i <lb></lb>saggi fatti sul conoide e sul triangolo, è da veder quali fossero, in così fatte <lb></lb>esercitazioni, i progressi. </s>

<s>Ebbero questi non leggero impulso dal ripensare <lb></lb>alle proposizioni già dimostrate intorno al centro di gravità del settore di <lb></lb>circolo: proposizioni, le quali benchè fossero ridotte assai più semplici e a <lb></lb>minor numero di quelle che bisognarono al Della Faille per dimostrare il <lb></lb>medesimo; il metodo degli indivisibili nonostante prometteva, nell&#039;ordinarle <lb></lb>e nel condurle, d&#039;alleviare e d&#039;abbreviare anche di più la faticosa lunghezza <lb></lb>del viaggio, perchè si potrebbe, dietro gli esempi del triangolo, riguardare <lb></lb>il settore intessuto degli infiniti archi concentrici decrescenti con sempre egual <lb></lb>proporzione, via via che si dilungano dalla maggiore circonferenza, concen­<lb></lb>trando sopra il raggio, che tutti gli divide nel mezzo, come sopra una lib­<lb></lb>bra, i loro pesi. </s></p><p type="main">

<s>Gettiamo uno sguardo sul settore ABCD (fig. </s>

<s>143) segato nel mezzo dal <lb></lb>raggio DB. </s>

<s>Se si sapesse il centro di gravità degli archi che lo compongono, <lb></lb><figure id="id.020.01.2661.1.jpg" xlink:href="020/01/2661/1.jpg"></figure></s></p><p type="caption">

<s>Figura 143.<lb></lb>dal primo che sia per esempio E, infino <lb></lb>all&#039;ultimo D, è manifesto che l&#039;inven­<lb></lb>zione del centro di esso settore cade­<lb></lb>rebbe sotto quella del triangolo isoscele, <lb></lb>che avesse per sua altezza DE. </s>

<s>Tutto <lb></lb>dunque si riduce, per procedere in que­<lb></lb>sta nuova via sicuri, e con buona spe­<lb></lb>ranza di riuscita, a determinare sull&#039;asse <lb></lb>il punto estremo E della libbra, o il cen­<lb></lb>tro di gravità dell&#039;arco. </s>

<s>Il Torricelli, che <lb></lb>non aveva potuto ancora leggere la Cen­<lb></lb>trobarica del Guldino, credè che fosse <lb></lb>il problema intatto, e si dette all&#039;opera, <lb></lb>la quale felicemente riuscì, ponendo la <lb></lb>ritrovata soluzione per lemma prepara­<lb></lb>torio alla ricerca del centro di gravità del settore di circolo, per via degli <lb></lb>indivisibili, intorno a che distese quell&#039;altro trattatello, che qui appresso ri­<lb></lb>copiamo dal manoscritto. </s></p><pb xlink:href="020/01/2662.jpg" pagenum="287"></pb><p type="main">

<s><emph type="italics"></emph>“ Supponimus<emph.end type="italics"></emph.end> primo: Cuiuscumque rectae lineae terminatae gravitatis <lb></lb>centrum esse punctum, quod ipsam bifariam dividit. </s>

<s>Secundo: Congruentium <lb></lb>perimetrorum centra gravitatis congruere. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma XI.<emph.end type="italics"></emph.end> — Si aliqua figura plana ABCD (fig. </s>

<s>144) in duas con­<lb></lb>gruentes figuras BAD, BCD secta fuerit ab axe BD, dummodo aequales et <lb></lb><figure id="id.020.01.2662.1.jpg" xlink:href="020/01/2662/1.jpg"></figure></s></p><p type="caption">

<s>Figura 144.<lb></lb>sibi respondentes anguli ad easdem partes sint, suman­<lb></lb>turque BA, BC aequales utrimque perimetri partes, et <lb></lb>supposito E centro gravitatis perimetri AB; si ex E <lb></lb>ducatur EO perpendicularis ad BD, dico punctum O <lb></lb>esse centrum gravitatis perimetri ABC. ” </s></p><p type="main">

<s>“ Producatur EO in F, ita ut OF aequalis sit ipsi <lb></lb>EO. </s>

<s>Supposita deinde semifigura BAD super BCD, con­<lb></lb>gruent figurae per suppositionem, et perimeter BA con­<lb></lb>gruet cum aequali BC, punctumque E congruet cum <lb></lb>puncto F. </s>

<s>Sunt enim aequales EO, OF, et angulos <lb></lb>rectos faciunt cum BD. </s>

<s>Sed E ponitur centrum gravitatis perimetri BA, ergo <lb></lb>F centrum gravitatis erit perimetri BC. </s>

<s>Cum autem BA, BC sint aequales, <lb></lb>erit centrum gravitatis, per secundam suppositionem, commune punctum O, <lb></lb>medium scilicet punctum librae EF. </s>

<s>Patet ergo quod erat propositum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollarium.<emph.end type="italics"></emph.end> — Hinc manifestum est cuiuscumque perimetri ABC, <lb></lb>sive ex curvis, sive ex rectis lineis componatur, centrum gravitatis esse in <lb></lb>axe eius BD, nempe in recta, quae secat ipsum perimetrum in duas partes <lb></lb>congruentes ad angulos aequales. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma XII.<emph.end type="italics"></emph.end> — Cuiuscumque arcus circuli centrum gravitatis est <lb></lb>inter centra rectarum, quarum una sit ipsius chorda, altera tangens chor­<lb></lb>dae parallela. </s>

<s>” </s></p><p type="main">

<s>“ Manifestum est hoc. </s>

<s>Esto enim arcus ABC (fig. </s>

<s>145), cuius circuli <lb></lb><figure id="id.020.01.2662.2.jpg" xlink:href="020/01/2662/2.jpg"></figure></s></p><p type="caption">

<s>Figura 145.<lb></lb>centrum D, linea vero bisecans angulum arcum­<lb></lb>que sit Bd. </s>

<s>In ipsa BD erit, per corollarium lem­<lb></lb>matis praecedentis, centrum gravitatis arcus ABC. </s>

<s><lb></lb>Esto chorda AC, tangens vero EF, parallela chor­<lb></lb>dae AC: eritque G centrum gravitatis rectae AC, <lb></lb>et B erit centrum gravitatis EF. ” </s></p><p type="main">

<s>“ Jam centrum gravitatis arcus non potest <lb></lb>esse neque B, neque G: suspenso enim arcu ex <lb></lb>B, sive ex G, aequiponderaret, quod est absur­<lb></lb>dum, cum latus sit ad easdem partes. </s>

<s>Tanto mi­<lb></lb>nus potest esse extra puncta B, G, ob eamdem causam. </s>

<s>Quare patet quod <lb></lb>fuerat propositum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma XIII.<emph.end type="italics"></emph.end> — Si intra arcum circuli coaptatae fuerint quotcumque <lb></lb>rectae lineae aequales, per continuam <gap></gap>rcus bisectionem, totidemque fuerint <lb></lb>tangentes ipsis coaptatis aequidistantes; erit centrum gravitatis arcus inter <lb></lb>centra omnium coaptatarum, et omnium tangentium. </s>

<s>” </s></p><p type="main">

<s>“ Esto arcus ABC (fig. </s>

<s>146), cuius circuli centrum D. Coaptatae, per <pb xlink:href="020/01/2663.jpg" pagenum="288"></pb>continuam arcus bisectionem, sint rectae aequales AE, EB, BF, FC. </s>

<s>His vero <lb></lb>aequidistent totidem tangentes GH, HI, IL, LM, et producta DN ad con­<lb></lb><figure id="id.020.01.2663.1.jpg" xlink:href="020/01/2663/1.jpg"></figure></s></p><p type="caption">

<s>Figura 146.<lb></lb>tactum N, erunt N et P, per primam <lb></lb>suppositionem, centra gravitatis recta­<lb></lb>rum GH, AE. </s>

<s>Centrum vero arcus <lb></lb>ANE est, per lemma XII, inter pun­<lb></lb>cta N et P. </s>

<s>Ponatur illud esse O. </s>

<s><lb></lb>Ductisque PQ, OR, NS perpendicu­<lb></lb>laribus ad HD, erunt puncta Q, R, S <lb></lb>centra gravitatis: nempe Q rectarum <lb></lb>AE, EB, G tangentium GH, HI, R <lb></lb>vero arcus AEB. </s>

<s>Iterum productis QT, <lb></lb>RV, SX perpendicularibus ad ID, erit <lb></lb>V, centrum gravitatis totius arcus ABC, <lb></lb>inter puncta T et X, alias enim duae <lb></lb>parallelae convenirent: videlicet inter <lb></lb>centrum omnium coaptatarum, et omnium tangentium, quod erat propositum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma XIV.<emph.end type="italics"></emph.end> — Si arcui circuli ABC (fig. </s>

<s>147), per continuam eius­<lb></lb>dem arcus bisectionem, quotcumque rectae lineae aequales coaptatae fuerint <lb></lb>AE, EF, FG, GB, BH, HI, IL, LC, fiatque, ut omnes coaptatae lineae ad <lb></lb><figure id="id.020.01.2663.2.jpg" xlink:href="020/01/2663/2.jpg"></figure></s></p><p type="caption">

<s>Figura 147.<lb></lb>chordam AC, ita <lb></lb>D, catetus unius <lb></lb>coaptatae, ad <lb></lb>aliam sumendam <lb></lb>ex centro D, in <lb></lb>axe BD; dico ter­<lb></lb>minum huius <lb></lb>assumptae esse <lb></lb>centrum gravita­<lb></lb>tis omnium prae­<lb></lb>dictarum linea­<lb></lb>rum. </s>

<s>” </s></p><p type="main">

<s>“ Ducatur ex <lb></lb>M, puncto medio <lb></lb>rectae AE, per­<lb></lb>pendicularis MP ad ipsam ED, eritque P, per corollarium lemmatis XI, cen­<lb></lb>trum gravitatìs duarum rectarum AE, EF. </s>

<s>Ducta vero ex P recta PR per­<lb></lb>pendiculariter ad FD, erit R, per corollarium lemmatis XI, centrum gra­<lb></lb>vitatis quatuor rectarum AE, EF, FG, GB. </s>

<s>Ducta iterum ex R recta RN <lb></lb>perpendiculariter ad BD, erit N, per dictum corollarium, centrum gravitatis <lb></lb>rectarum AE, EF, FG, GB, BH, HI, IL, LC. ” </s></p><p type="main">

<s>“ Jam aequiangula triangula sunt, per VIII Sexti, EMP, PME. </s>

<s>Item ae­<lb></lb>quiangula FAT, PDR, nec non BAX, RDN, demonstraturque hoc ut in lem­<lb></lb>mate IX factum est. </s>

<s>” </s></p><pb xlink:href="020/01/2664.jpg" pagenum="289"></pb><p type="main">

<s>“ Quoniam MD ad DP est ut EM ad MP, sive ut EA ad AQ, sive ut <lb></lb>FEA ad AF, sed PD, ad DR, per IV Sexti, est ut FA ad AT; erit ex aequo <lb></lb>MD ad DR ut FEA ad AT, sive ut BGFEA ad AB: DR denique ad DN, per <lb></lb>eamdem, est ut BA ad AX. </s>

<s>Ergo ex aequo omnes rectae BG, GF, FE, EA <lb></lb>ad AX, sive omnes AE, EF, FG, GB, BH, HI, IL, LC, ad AC, sunt ut MD <lb></lb>ad DN. </s>

<s>Unde patet quod propositum fuerat. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XIII. — <emph type="italics"></emph>Centrum gravitatis cuiuscumque arcus cir­<lb></lb>culi est in axe eiusdem ita secto, ut integer axis, ad partem quae versus <lb></lb>centrum circuli est, ita sit ut arcus ad chordam. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto arcus ABC (fig. </s>

<s>148), cuius chorda AC, axis BD, fiatque, ut <lb></lb>arcus ABC ad chordam AC, ita axis BD ad DE: dico E esse centrum gra­<lb></lb><figure id="id.020.01.2664.1.jpg" xlink:href="020/01/2664/1.jpg"></figure></s></p><p type="caption">

<s>Figura 148.<lb></lb>vitatis arcus ABC. </s>

<s>Nisi enim cen­<lb></lb>trum gravitatis sit punctum E, <lb></lb>erit utique aliud punctum vel su­<lb></lb>pra, vel infra punctum. </s>

<s>” </s></p><p type="main">

<s>“ Esto primum, si possibile <lb></lb>est, F, ipsique sectori duae figu­<lb></lb>rae, per continuam arcuum bise­<lb></lb>ctionem, altera quidem circum­<lb></lb>scribatur, altera vero inseribatur <lb></lb>ea lege, per IV librì I <emph type="italics"></emph>De sphaera <lb></lb>et cylindro,<emph.end type="italics"></emph.end> ut latus OR circum­<lb></lb>scriptae, ad latus CG inscriptae, <lb></lb>minorem rationem habeat quam <lb></lb>ED ad DF. </s>

<s>Deinde fiat ut omnes <lb></lb>rectae AN, NB, BG, GC ad chordam AC, ita catetus DI ad M. </s>

<s>Ostendo pri­<lb></lb>mum M esse maiorem quam DF. ” </s></p><p type="main">

<s>“ Nam BD ad DE est ut arcus ABC ad chordam AC, ergo BD ad DE <lb></lb>maiorem habet rationem, quam perimeter ANBGC ad AC: hoc est quam DI <lb></lb><figure id="id.020.01.2664.2.jpg" xlink:href="020/01/2664/2.jpg"></figure></s></p><p type="caption">

<s>Figura 149.<lb></lb>ad M. </s>

<s>Ipsa vero DE ad DF maiorem <lb></lb>habet rationem, quam PD ad M; <lb></lb>erit itaque M maior quam DF. </s>

<s>Po­<lb></lb>natur DQ aequalis ipsi M, et erit <lb></lb>Q, per lemma XIV et per constru­<lb></lb>ctionem, centrum gravitatis perime­<lb></lb>tri ANBGD. </s>

<s>Centrum vero gravitatis <lb></lb>perimetri HKLOR adhuc ulterius est <lb></lb>versus L, et inter utrumque debet <lb></lb>esse centrum gravitatis arcus, ergo <lb></lb>centrum gravitatis arcus non est F. ” </s></p><p type="main">

<s>“ Esto deinde, si fieri potest, <lb></lb>centrum gravitatis arcus punctum S <lb></lb>(fig. </s>

<s>149), ipsique arcui duae figurae, per continuam arcus bisectionem, altera <lb></lb>quidem circumscribatur, altera vero inscribatur ea conditione, per IV libri I <pb xlink:href="020/01/2665.jpg" pagenum="290"></pb><emph type="italics"></emph>De sphaera et cylindro,<emph.end type="italics"></emph.end> ut latus circumscriptae OR, ad latus inscriptae GC, <lb></lb>minorem rationem habeat quam SD ad DE. </s>

<s>Tunc enim sine dubio ratio ar­<lb></lb>cus GPC, ad rectam GC, sive arcus ABC, ad perimetrum ANBGC, multo <lb></lb>minor erit quam sit ratio SD ad DE. ” </s></p><p type="main">

<s>“ Fiat, ut perimeter HKLOR ad HR, ita catetus PD ad M: dico pri­<lb></lb>mum M minorem esse quam DS. </s>

<s>Nam arcus ABC, ad AC, est ut BD ad <lb></lb>DE, ipsa vero AC, ad perimetrum ANBGC, per lemma VII, est ut HR ad <lb></lb>HKLOR, sive ut M ad DP. Ergo, per XXIII Quinti, arcus ABC, ad perime­<lb></lb>trum ANBGC, est ut M ad DE. </s>

<s>Sed ratio SD ad DE maior est ratione pe­<lb></lb>rimetri ANBGC ad AC; ergo ratio SD ad DE maior est ratione M ad DE. </s>

<s><lb></lb>Maior itaque est SD quam recta M. ” </s></p><p type="main">

<s>“ Ponatur DQ aequalis ipsi M, eritque Q, per lemma XIV et per con­<lb></lb>structionem, centrum gravitatis perimetri HKLOR. </s>

<s>Centrum vero perimetri <lb></lb>ANBGC adhuc inferius est versus D, et inter utrumque est omnino centrum <lb></lb>gravitatis arcus. </s>

<s>Quamobrem centrum gravitatis arcus non est S. </s>

<s>Cum ita­<lb></lb>que ostensum sit non esse neque supra neque infra E, superest quod cen­<lb></lb>trum gravitatis arcus ABC sit punctum E, quod erat propositum. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XIV. — <emph type="italics"></emph>Cenirum gravitatis sectoris circuli est in axe <lb></lb>eiusdem ita secto, ut totus axis, ad partem quae est versus circuli cen­<lb></lb>trum, sit ut arcus sectoris ad 2/3 chordae eiusdem. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto sector ABCD (fig. </s>

<s>150), cuius chorda AC, axis vero BD, fiatque, <lb></lb><figure id="id.020.01.2665.1.jpg" xlink:href="020/01/2665/1.jpg"></figure></s></p><p type="caption">

<s>Figura 150.<lb></lb>ut arcus ABC ad AC, ita BD ad DE. </s>

<s><lb></lb>Et erit E, per propositionem praece­<lb></lb>dentem, centrum gravitatis arcus ABC. </s>

<s><lb></lb>Sumpto iam in recta BD quolibet pun­<lb></lb>cto F, agatur centro D, intervallo DF, <lb></lb>arcus GFH, et fiat, ut arcus GFH ad <lb></lb>GH, ita FD ad DI, eritque punctum I, <lb></lb>per eamdem, centrum gravitatis arcus <lb></lb>GFH. ” </s></p><p type="main">

<s>“ Quoniam, ut arcus ABC ad ar­<lb></lb>cum GFH, ita semidiameter AD ad DG, <lb></lb>sive, per IV Sexti, AC ad GH; erit, <lb></lb>permutando, ut AHC ad AC, ita GFH <lb></lb>ad GH. ” </s></p><p type="main">

<s>“ Jam BD ad DE est ut ABC ad <lb></lb>AC, sive, ut GFH ad GH, vel ut FD ad DI. </s>

<s>Permutando igitur erit BD ad <lb></lb>DF ut ED ad DI, et etiam ABC ad GFH erit ut ED ad DI. ” </s></p><p type="main">

<s>“ Est itaque DE libra, ex cuius punctis singulis magnitudines quaedam <lb></lb>appensae sunt, quarum duae sunt arcus ABC, GFH, reliquae vero sunt ar­<lb></lb>cus praedictis concentrici, habentque magnitudines, ut demonstratum est, illam <lb></lb>inter se rationem, quam illarum distantiae ED, DI ab extremo puncto librae <lb></lb>D, quemadmodum etiam habent lineae alicuius trianguli. </s>

<s>Ergo libra CE, ad <lb></lb>quam applicatae sunt praedictae magnitudines, ita secabitur a centro gravi-<pb xlink:href="020/01/2666.jpg" pagenum="291"></pb>tatis omnium magnitudinum, ut secatur axis alicuius trianguli a centro gra­<lb></lb>vitatis eiusdem, nempe ea conditione, ut pars, ad extremum D terminata ver­<lb></lb>sus magnitudines decrescentes, sit, ad reliquam quae terminatur in E, centro <lb></lb>gravitatis maximae magnitudinis ABC, in proportione dupla. </s>

<s>” </s></p><p type="main">

<s>“ Secetur ergo libra DE in O, ita ut DO ad OE sit dupla, et erit O <lb></lb>centrum gravitatis omnium simul arcuum concentricorum, nempe ipsius secto­<lb></lb>ris. </s>

<s>Erit ergo arcus ABC, ad AC, ut BD ad DE. </s>

<s>Ipsa vero AC, ad 2/3 ipsius <lb></lb>AC, erit ut ED ad DO. </s>

<s>Quare ex aequo arcus ABC, ad 2/3 ipsius AC, erit <lb></lb>ut BD ad DO, nempe ut axis sectoris ad illam, quae interiicitur inter cen­<lb></lb>trum circuli, et centrum gravitatis eiusdem sectoris, quod erat propositum ” <lb></lb>(ibid., T. XXXVII, fol. </s>

<s>25-31). </s></p><p type="main">

<s>La felice riuscita di questo nuovo metodo, applicato alla ricerca del cen­<lb></lb>tro di gravità nel settore di circolo, incorò nel Torricelli una dolce speranza <lb></lb>di dovere anche più oltre promovere la Baricentrica da quel punto, a cui <lb></lb>l&#039;aveva già condotta il padre Della Faille con tanta fatica. </s>

<s>Forse, incomin­<lb></lb>ciò il Nostro a pensare, la medesima analogia, che nelle porzioni del cerchio, <lb></lb>corre nelle porzioni della sfera: e benchè sia stato dimostrato ormai il cen­<lb></lb>tro di gravità nel settore circolare e nell&#039;emiciclo, nessuno sa però ancora <lb></lb>dove stia sull&#039;asse quello del settore sferico, desunto da quello del centro <lb></lb>dell&#039;emisfero. </s>

<s>Sia questo emisfero BGC (fig. </s>

<s>151), e si riguardi, nella me­<lb></lb><figure id="id.020.01.2666.1.jpg" xlink:href="020/01/2666/1.jpg"></figure></s></p><p type="caption">

<s>Figura 151.<lb></lb>desima maniera, come composto delle in­<lb></lb>finite superficie concentriche intorno ad A: <lb></lb>si rappresentava alla mente del Torricelli <lb></lb>che, come dianzi dal centro di gravità <lb></lb>degli archi era stato facilmente condotto <lb></lb>a risolvere un problema già reso noto; <lb></lb>così ora, dal centro di gravità delle cal­<lb></lb>lotte sarebbe, per vie simili, condotto a <lb></lb>risolvere quest&#039;altro problema in una ma­<lb></lb>niera del tutto nuova. </s></p><p type="main">

<s>Sia infatti il centro di gravità della superficie emisferica BGC il punto <lb></lb>D, per il quale passi la LM perpendicolare all&#039;asse AG. </s>

<s>Descrivasi qualun­<lb></lb>que altra delle infinite superficie consentriche EPF, per il baricentro I della <lb></lb>quale si conduca la HK parallela a LM, e si compia il triangolo LMA. </s>

<s>Avremo <lb></lb>BGC:EPF=AL2:AH2=LD2:HI2=<foreign lang="grc">π</foreign>LD2:<foreign lang="grc">π</foreign>HI2, e così sempre, intan­<lb></lb>tochè sopra la libbra AD si possono intendere applicate, ne&#039;medesimi punti, <lb></lb>due vari ordini di grandezze proporzionali, e aventi ambedue perciò sopr&#039;essa <lb></lb>libbra il medesimo centro: gl&#039;infiniti circoli cioè, e le infinite callotte. </s>

<s>E per­<lb></lb>chè di queste si compone l&#039;emisfero, e di quelle il cono; dal centro di gra­<lb></lb>vità noto nell&#039;un solido, si renderà manifesto il centro di gravità nell&#039;altro. </s></p><p type="main">

<s>Tutto il forte sta dunque nel sapere dove la volta emisferica, o qualun­<lb></lb>que altra minore callotta o <emph type="italics"></emph>berrettino,<emph.end type="italics"></emph.end> come popolarmente il Torricelli la <lb></lb>chiamava, ha sull&#039;asse il suo baricentro. </s>

<s>E perchè, ricercando ne&#039;libri dei <lb></lb>Matematici antichi e dei moderni, ritrovò che nessuno ancora l&#039;aveva inse-<pb xlink:href="020/01/2667.jpg" pagenum="292"></pb>gnato, si dette il Nostro, con trepidante sollecitudine, all&#039;opera, la quale mo­<lb></lb>strava di dover rendersi assai spedita, specialmente dop&#039;essersi preparati al­<lb></lb>cuni lemmi geometrici, conclusi dal teorema noto che cioè, rivolgendosi gli <lb></lb>archi EB, AB (fig. </s>

<s>152) intorno al diametro BD descrivono due callotte pro­<lb></lb>porzionali ai quadrati delle suttese. </s>

<s>Stando infatti le dette callotte, che chia­<lb></lb><figure id="id.020.01.2667.1.jpg" xlink:href="020/01/2667/1.jpg"></figure></s></p><p type="caption">

<s>Figura 152.<lb></lb>meremo C, C′, in ragion composta delle altezze, <lb></lb>e della circonferenza di un circolo grande, o <lb></lb>del suo diametro, avremo C:C′=BF.BD: <lb></lb>BG.BD=EB2:AB2. </s>

<s>Dietro ciò dimostrava il <lb></lb>Torricelli che “ se nella sfera ABCD siano ap­<lb></lb>plicate <emph type="italics"></emph>utcumque<emph.end type="italics"></emph.end> EF, AG, sarà il berrettino <lb></lb>EBH, all&#039;ABC, come BF alla BG. ” </s></p><p type="main">

<s>“ Tirinsi ED, AD, EB, AB. </s>

<s>Il quadrato EB <lb></lb>al BD sta come la retta BF alla BD. </s>

<s>Ma il qua­<lb></lb>drato BD al BA sta come la retta DB alla BG; <lb></lb><emph type="italics"></emph>ergo ex aequo<emph.end type="italics"></emph.end> il quadrato EB al BA sta come <lb></lb>la retta BF alla BG. </s>

<s>Ma come il quadrato BE <lb></lb>al BA, così l&#039;un berrettino all&#039;altro. </s>

<s>Ergo etc. </s>

<s>” (ivi, T. XXXVI, fol. </s>

<s>32). </s></p><p type="main">

<s>Di qui, cioè da ABC:EBH=BG:BF, dividendo, abbiamo ABC—EBH: <lb></lb>EBH=BG—BF:BF, ossia che la zona AEHC sta alla EBH come l&#039;al­<lb></lb>tezza FG di quella sta all&#039;altezza FB di questa, e così per tutte le altre por­<lb></lb>zioni intercette sulla sfera fra piani paralleli, le quali dunque saranno uguali, <lb></lb>quando siano le relative altezze fra loro uguali. </s></p><p type="main">

<s>Se ora si prendano quelle altezze infinitamente piccole, ragionava il Tor­<lb></lb>ricelli, le zonule infinite intercette essendo uguali graviteranno ugualmente <lb></lb>co&#039;loro centri sopra la libbra BG, la quale per conseguenza avrà nel mezzo <lb></lb>il punto dell&#039;equilibrio, ond&#039;è che il baricentro della callotta, per esempio <lb></lb>ABC, taglierà nel mezzo la BG sua saetta. </s>

<s>Così essendo, l&#039;invenzione del <lb></lb>centro di gravità dell&#039;emisfero era ovvia, perchè, se nella figura 151 qui poco <lb></lb>addietro, D è il mezzo di AG, l&#039;altezza del cono è DA, la quale essendo di­<lb></lb>visa, a partir dal vertice, in quattro parti uguali; in P, dove si dica tornar <lb></lb>la terza divisione, sarà il centro cercato. </s>

<s>Che se anche GD similmente sia <lb></lb>quadripartito, è manifesto che GD conterrà cinque delle parti, delle quali PA <lb></lb>ne contiene tre sole. </s>

<s>Se poi BGC sia minore di una mezza circonferenza, per <lb></lb>avere il centro di gravità del settore, basta divider nel mezzo, per esempio <lb></lb>in X, la saetta, la quale prolungata infino a incontrare in A il centro della <lb></lb>sfera, da A risalendo su per la AX per tre quarti della sua intera lunghezza, <lb></lb>ivi giunti troveremo il luogo, dove il settore stesso concentra il suo peso. </s></p><p type="main">

<s>Così annunziate aveva il Torricelli distese le sue proposizioni, la verità <lb></lb>delle quali dipendendo tutta dalla verità del teorema che cioè le callotte hanno <lb></lb>il baricentro nel mezzo della saetta, ne dava, come di cosa nuova e impor­<lb></lb>tantissima avviso al Cavalieri. </s>

<s>Poi confermò questi autorevolmente nella <lb></lb>XXXIV della sua quinta Esercitazione geometrica il teorema torricelliano, ma <lb></lb>intanto rispondeva non saperne per ora altro, se non che il Guldino, nella <pb xlink:href="020/01/2668.jpg" pagenum="293"></pb>Centrobarica, era venuto a una conclusione molto diversa, dicendo che il cen­<lb></lb>tro di gravità della cupola emisferica è il medesimo che quel del circolo fatto <lb></lb>passare attraverso all&#039;asse di lei. </s></p><p type="main">

<s>Il Guldino s&#039;era senza dubbio ingannato, ma l&#039;inganno di lui, non con­<lb></lb>fermato ancora da altre simili fallacie notate nel suo libro, aveva messo il <lb></lb>Torricelli in gran sospetto che non si fosse invece ingannato egli stesso, forse, <lb></lb>per non averci bene applicati gl&#039;indivisibili, o per altre ragioni: tanto più <lb></lb>che queste gli pareva venissero avvalorate dal saper che il Nardi e il Ricci <lb></lb>avevano trovato il centro di gravità del settore sferico segar l&#039;asse in altre <lb></lb>proporzioni, da quelle ch&#039;egli aveva concluse. </s>

<s>Si volse allora a risolvere il <lb></lb>problema baricentrico delle superficie sferiche per altre vie, scansando gl&#039;in­<lb></lb>divisibili, e attenendosi ai metodi antichi, per star ne&#039;quali maggiormente <lb></lb>sicuro imitò il processo tenuto da Archimede nello Scolio alla IX proposi­<lb></lb>zione del primo degli Equiponderanti, per dimostrar che il centro di gravità <lb></lb>del parallelogrammo sta nella linea retta, dalla quale due lati opposti sian <lb></lb>segati nel mezzo (Opera cit., pag. </s>

<s>172). La dimostrazion nonostante, che qui <lb></lb>trascriviamo, confermava la verità di quel che aveva concluso per via degli <lb></lb>indivisibili, star sempre cioè il centro di gravità della callotta sferica nel <lb></lb>mezzo della saetta. </s></p><p type="main">

<s>“ Suppongo in primo luogo che, se molte grandezze averanno li centri <lb></lb>di gravità nella retta AB, tutti fra li punti A, B; che il centro comune di <lb></lb>tutte sia fra li punti A, B. </s>

<s>Suppongo in secondo luogo che, se una linea <lb></lb>retta sarà divisa in parti uguali, e di numero pari, ed in ciascuna parte di <lb></lb>essa sia il centro di gravità di altrettante grandezze uguali; che il centro di <lb></lb>tutte stia in una delle linee di mezzo. </s>

<s>Suppongo, terzo, che il berrettino e <lb></lb>le zone sferiche abbiano il centro loro di gravità nella saetta, e suppongo in <lb></lb>ultimo quel che ho già dimostrato che cioè i berrettini stanno come le saette, <lb></lb>e che perciò le zone, comprese fra piani equidistanti e paralleli, sempre sono <lb></lb>tra loro uguali. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XV. — <emph type="italics"></emph>Il centro del berrettino sferico sempre sta nel <lb></lb>mezzo della saetta. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2668.1.jpg" xlink:href="020/01/2668/1.jpg"></figure></s></p><p type="caption">

<s>Figura 153.</s></p><p type="main">

<s>“ Sia il berrettino sferico <lb></lb>ABC (fig. </s>

<s>153), e mezzo della <lb></lb>saetta D; dico ecc. </s>

<s>Se non è D <lb></lb>sia per esempio, se può, E, e di­<lb></lb>visa BD bifariam in F e poi DF <lb></lb>bifariam in G, finchè resti DG <lb></lb>minore di DE, seghisi tutta BH <lb></lb>in parti uguali alla DG, e tirinsi <lb></lb>perpendicolari alla saetta. </s>

<s>Saranno <lb></lb>dunque i berrettini come le saette, <lb></lb>cioè in proporzione aritmetica <emph type="italics"></emph>ab unitate,<emph.end type="italics"></emph.end> e però tutte le zone saranno uguali <lb></lb>al minor berrettino e fra di loro. </s>

<s>Ed avendo ciascuna il centro nel suo asse, <lb></lb>ed essendo tutte uguali, il centro di tutte dovrà essere fra il centro delle due <pb xlink:href="020/01/2669.jpg" pagenum="294"></pb>medie, cioè dovrà essere nella linea IG. </s>

<s>Ma è fuori di essa, essendo suppo­<lb></lb>sto E, ergo etc. </s>

<s>” (ivi, fol. </s>

<s>32). </s></p><p type="main">

<s>È cosa veramente singolare che nemmeno questa dimostrazione valesse <lb></lb>ad assicurare il Torricelli, il quale avrebbe potuto dall&#039;altra parte confer­<lb></lb>marsi nella verità della sua conclusione dalle proposizioni XVIII e XIX del <lb></lb>primo libro dei Solidi sferali. </s>

<s>Se è vero infatti, per la detta prima (Op. <lb></lb><figure id="id.020.01.2669.1.jpg" xlink:href="020/01/2669/1.jpg"></figure></s></p><p type="caption">

<s>Figura 154.<lb></lb>geom. </s>

<s>cit., pag. </s>

<s>28), che la superficie dell&#039;emisfero <lb></lb>descritto dal quadrante ADH (fig. </s>

<s>154) è uguale <lb></lb>alla superficie esterna del cilindro descritto dal ret­<lb></lb>tangolo FB, rivolgentesi intorno al medesimo asse <lb></lb>HB; e se è vero, per la seconda (ivi, pag. </s>

<s>30), che <lb></lb>le superficie della callotta HD e della zona DA <lb></lb>sono uguali alle curve superficie cilindriche de­<lb></lb>scritte da FC e da EB; essendo manifesto de&#039;ci­<lb></lb>lindri che il loro centro sega l&#039;asse nel mezzo, <lb></lb>sarà pur manifesto che son segate nel mezzo le <lb></lb>saette de&#039;berrettini e le altezze delle zone. </s></p><p type="main">

<s>O che non avesse il Torricelli ancora dimostrate quelle sue proposizioni <lb></lb>sferali, o che non gli sovvenisse di applicarle opportunamente alla Baricen­<lb></lb>trica, è un fatto che ne rimase il vantaggio al Wallis, il quale rendeva ge­<lb></lb>neralissimi così i teoremi torricelliani: “ Si semicircumferentiae circuli, vel <lb></lb>arcui minori, circumponatur ex continuis rectis, quae mediis suis punctis pe­<lb></lb>ripheriam contingant, conflata linea, quae ab hac linea composita circa istius <lb></lb>circuli diametrum quamvis, quae illam non secet, conversa, describitur su­<lb></lb>perficies curva; aequatur superficiei curvae cylindri recti aeque alti, basim <lb></lb>habentis exposito circulo aequalem ” (De motu, P. II, Londini 1670, pag. </s>

<s>203). <lb></lb>Di qui si deduceva, per semplice corollarìo immediato, il centro di gravità <lb></lb>delle superficie sferiche star nel mezzo dell&#039;asse, con quella sicurezza venuta <lb></lb>a mancare nel Torricelli, che pur avrebbe potuto, trent&#039;anni prima, così <lb></lb>utilmente valersi di quel medesimo argomento. </s>

<s>E che rimanesse veramente <lb></lb>esso Torricelli in timore di essersi ingannato, anche dopo aver ritrovato <lb></lb>quella così perfetta corrispondenza tra i resultati del metodo antico e degli <lb></lb>indivisibili; resulta dalla seguente lettera, scritta il dì 28 Marzo 1643 da Fi­<lb></lb>renze al Cavalieri: </s></p><p type="main">

<s>“ ...... Le scrissi che il centro delle superficie sferiche stava nel mezzo <lb></lb>dell&#039;asse corrispondente: glie ne darò un cenno, per timore di essermi ingan­<lb></lb>nato, senza indivisibili, mentre s&#039;abbia a contendere con genti, che non gli <lb></lb>accettano. </s>

<s>Le premesse, che son pedanterie meccaniche e geometriche, son <lb></lb>tali: 1.° Suppongo che i predetti centri sieno nell&#039;asse. </s>

<s>2.° Suppongo che, <lb></lb>se alquante grandezze avranno il centro di gravità nella retta AB, il centro <lb></lb>comune di tutte sia fra i punti A, B estremi. </s>

<s>3.° Suppongo che, se una sfera <lb></lb>sarà segata con piani paralleli, le superficie delle zone intercette, ed anco <lb></lb>de&#039;segamenti estremi, siano fra di loro come le porzioni degli assi corrispon­<lb></lb>denti. </s>

<s>4.° Se una linea retta AB (fig. </s>

<s>155) sarà segata in quante parti un <pb xlink:href="020/01/2670.jpg" pagenum="295"></pb>vuole, eguali e di numero pari, e che ciascuna di esse sia il centro di gra­<lb></lb>vità di altrettante grandezze uguali fra di loro; suppongo che il centro co­<lb></lb>mune di tutte sia in una delle sezioni di mezzo CE, ED, e lo provo così: <lb></lb><figure id="id.020.01.2670.1.jpg" xlink:href="020/01/2670/1.jpg"></figure></s></p><p type="caption">

<s>Figura 155.<lb></lb>Siano i centri di grandezze uguali <lb></lb>i punti F, G, H, I, N, M, L, O, <lb></lb>ciascuno dei quali sia in uno dei <lb></lb>segamenti della linea <emph type="italics"></emph>utcumque.<emph.end type="italics"></emph.end><lb></lb>Perchè dunque le grandezze, delle <lb></lb>quali esse son centri, si suppongono uguali, sarà il centro comune delle due <lb></lb>grandazze F, O il punto medio della retta FO. </s>

<s>Ma il punto medio della retta <lb></lb>FO sta nella retta CD; così anco il centro della coppia G, M sta nella retta <lb></lb>CD, ed il centro delle altre due coppie H, L ed I, N sta nella CD; adun­<lb></lb>que il centro comune di tutte sta nella CD, per la seconda supposizione. </s>

<s>” </s></p><p type="main">

<s>“ Sia la superficie di un segmento o frusto sferico, di cui sia asse BH, <lb></lb>nella medesima figura 153 qui poco addietro rappresentata, e segata per <lb></lb>mezzo BH in D, dico che D sarà centro di gravità. </s>

<s>Se non è D, sia un altro <lb></lb>per esempio E, e seghisi per mezzo BD in F, e di nuovo FD seghisi per <lb></lb>mezzo in G, e così sempre, fin che s&#039;arrivi ad una sezione DG, minore della <lb></lb>retta DE. </s>

<s>Seghisi poi tutto l&#039;asse in parti uguali alla DG, e per i punti dei <lb></lb>segamenti passino piani perpendicolari all&#039;asse. </s>

<s>Non è dubbio che tutte le <lb></lb>superficie dei frusti e del segamento ultimo saranno uguali. </s>

<s>Anzi ognuna di <lb></lb>esse averà il centro di gravità in un segamento della saetta BH, divisa in <lb></lb>parti uguali. </s>

<s>Dunque il centro comune di tutte le grandezze sarà in una <lb></lb>delle due sezioni di mezzo DG, DI. </s>

<s>Dunque il centro di tutte non è M, ma <lb></lb>necessariamente sarà D, dimostrandosi che niun altro punto della retta BH <lb></lb>può essere centro di gravità della predetta superficie sferica, di segamento o <lb></lb>di frusto che ella sia ” (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>127). </s></p><p type="main">

<s>Il Cavalieri non potè non approvare il processo dimostrativo e la verità <lb></lb>della conclusione, la quale fu, per essere ordinata con l&#039;altre nel trattato dei <lb></lb>centri di gravità, messa dallo stesso Torricelli in questa forma: </s></p><p type="main">

<s>“ PROPOSIZIONE XVI. — <emph type="italics"></emph>Centrum gravitatis zonae sphaericae, sive su­<lb></lb>perficiei curvae segmenti sphaerici, est in medio axis ipsius zonae.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La dimostrazione, che si legge manoscritta al fol. </s>

<s>33 del solito tomo XXXVI <lb></lb>crediamo di poterla tralasciare, non essendo differente da quella mandata per <lb></lb>lettera al Cavalieri, che nella forma esteriore della lingua latina. </s>

<s>E come <lb></lb>messe in ordine questa e la precedente, così messe in ordine le proposizioni, <lb></lb>che ne conseguivano, relative ai baricentri delle porzioni di sfera, tanto più <lb></lb>che in sostanza ebbe a ritrovar che anche il Nardi e il Ricci concordavano <lb></lb>seco nell&#039;ammettere la verità così pronunziata: </s></p><p type="main">

<s>“ PROPOSIZIONE XVII. — <emph type="italics"></emph>Centrum gravitatis hemisphaerii secat axem <lb></lb>ita, ut pars ad verticem sit ad reliquam sesquipartiens tertias. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma prima di trascriver la dìmostrazione vogliamo osservare che il Tor­<lb></lb>ricelli suppone il seguente lemma: Se una libbra sia per tutta la sua lun­<lb></lb>ghezza gravata da pesi, via via crescenti come i quadrati delle distanze, il <pb xlink:href="020/01/2671.jpg" pagenum="296"></pb>punto dell&#039;equilibrio la segherà in modo, che la parte verso i pesi minori <lb></lb>sia tripla della rimanente. </s>

<s>Anzi scrive in parentesi, per modo di nota: <emph type="italics"></emph>que­<lb></lb>sto bisogna premetterlo e cavarlo dal cono.<emph.end type="italics"></emph.end> In questo solido infatti gl&#039;in­<lb></lb>finiti circoli che lo compongono si possono riguardar ponderanti sopra l&#039;asse <lb></lb>come sopra una libbra, ed essi circoli stanno come i quadrati dei raggi <lb></lb>FH, DE (fig. </s>

<s>156), o delle distanze AH, AE. </s>

<s>E perchè il centro dell&#039;equili­<lb></lb>brio si sa che è sull&#039;asse a tre quarti di distanza dal vertice A; par che ne <lb></lb><figure id="id.020.01.2671.1.jpg" xlink:href="020/01/2671/1.jpg"></figure></s></p><p type="caption">

<s>Figura 156.<lb></lb>volesse di qui concludere il Torricelli che il centro di gravità <lb></lb>nella libbra è come si è detto sopra nel lemma. </s>

<s>Sarebbe stato <lb></lb>meglio però dimostrare direttamente il principio statico, e di <lb></lb>lì concluderne il centro di gravità del cono, come dianzi dal <lb></lb>principio statico di Galileo aveva concluso il centro di gravità <lb></lb>del triangolo, ma la dimostrazione dipendeva da più alti prin­<lb></lb>cipii, de&#039;quali faremo cenno in altro proposito. </s>

<s>Forse nella <lb></lb>medesima statica galileiana sarà andato il Torricelli ricercando <lb></lb>qualche cosa, che facesse al presente suo particolare bisogno, <lb></lb>con intenzion di scrivere in fronte al teorema <emph type="italics"></emph>Centrum gravitatis coni, sup­<lb></lb>posito principio Galilei,<emph.end type="italics"></emph.end> ma ebbe questo principio a trovarlo formulato molto <lb></lb>diversamente da quel che s&#039;aspettava, perchè, nella sesta proposizione, scritta <lb></lb>nell&#039;Appendice ai dialoghi delle Scienze nuove, supposta una libbra nelle <lb></lb>condizioni già dette, si dimostra che “ centrum aequilibrii libram dividit, ut <lb></lb>pars versus minores magnitudines reliquae sit maior quam tripla ” (Alb. </s>

<s><lb></lb>XIII, 280). Or qui bisognerebbe dire o che è falsa la proposizione di Gali­<lb></lb>leo, o è falso il centro di gravità del cono, come tutti l&#039;hanno insegnato, o è <lb></lb>falsa l&#039;applicazione voluta farsi degl&#039;indivisibili in questo caso. </s>

<s>E perchè il <lb></lb>Torricelli prosegue pure con gl&#039;indivisibili, e conferma il centro di gravità <lb></lb>del cono segar l&#039;asse in modo, che la parte verso il vertice sia precisamente <lb></lb>tripla, e non già più che tripla della rimanente; lasciamo ai nostri decidere <lb></lb>in giudizio, per passare a leggere nel manoscritto la dimostrazione di ciò, che <lb></lb>s&#039;è di sopra annunziato. </s></p><p type="main">

<s>“ Hemisphaerium sit ABC (fig. </s>

<s>157), cuius axis BD secetur bifariam <lb></lb>in E: eritque E centrum superficiei ABC. </s>

<s>Sumatur punctum quodvis F, et <lb></lb>dividatur bifariam FD in I, eritque I centrum superficiei GFH. ” <lb></lb><figure id="id.020.01.2671.2.jpg" xlink:href="020/01/2671/2.jpg"></figure></s></p><p type="caption">

<s>Figura 157.</s></p><p type="main">

<s>“ Superficies autem ABC, ad superficiem <lb></lb>GFH, est ut quadratum BD ad DF, sive, sumptis <lb></lb>subquadruplis, ut quadratum ED, ad DI. </s>

<s>Est ergo <lb></lb>ED libra, in qua sunt centra gravitatis infinita­<lb></lb>rum magnitudinum, quarum maxima habet cen­<lb></lb>trum in E, minima in D, suntque magnitudi­<lb></lb>nes inter se in duplicata ratione distantiarum ab <lb></lb>extremo librae D. </s>

<s>Ergo centrum omnium erit O: <lb></lb>sumpta scilicet EO 1/4 totius ED. </s>

<s>Quare BO ad OD erit ut 5 ad 3, quod <lb></lb>erat demonstrandum. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XVIII. — <emph type="italics"></emph>Esto solidus sphaerae sector ABCD<emph.end type="italics"></emph.end> (fig. </s>

<s>158), <pb xlink:href="020/01/2672.jpg" pagenum="297"></pb><emph type="italics"></emph>constans ex cono ADC, et ex segmento ABC, sectaque DF bifariam in E, <lb></lb>et ED in quatuor partes aequales, quarum una sit EO; dico centrum <lb></lb>gravitatis sectoris solidi esse O. ”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2672.1.jpg" xlink:href="020/01/2672/1.jpg"></figure></s></p><p type="caption">

<s>Figura 158.</s></p><p type="main">

<s>“ Sumatur quodvis punctum in re­<lb></lb>cta BD, puta I, et per illud agatur su­<lb></lb>perficies sphaerica HIL, bisectaque IM <lb></lb>in N, erit N centrum superficiei HIL, si­<lb></lb>cut et E est centrum superficiei ABC. ” </s></p><p type="main">

<s>“ Jam tota BD, ad totam ID, est, <lb></lb>ob aequalitatem, ut AD ad DH, sive, per <lb></lb>IV Sexti, ut FD ablata ad ablatam DM. </s>

<s><lb></lb>Quare tota BD, ad totam DI, erit ut re­<lb></lb>liqua BF ad IM, sive, sumptis subduplis, <lb></lb>ut BE ad IN. </s>

<s>Et permutando, et per con­<lb></lb>versionem rationis, crit BD ad DE ut ID <lb></lb>ad DN. </s>

<s>Et permutando BD ad DI ut ED <lb></lb>ad DN. </s>

<s>Superficies vero ABC, ad super­<lb></lb>ficiem HIL, est ut quadratum BD ad quadratum DI, sive ut quadratum ED <lb></lb>ad DN, et hoc modo semper. </s>

<s>” </s></p><p type="main">

<s>“ Pendent ergo ex libra ED magnitudines, quarum maxima centrum <lb></lb>habet E, minima vero D. </s>

<s>Suntque magnitudines inter se in duplicata ratione <lb></lb>distantiarum ab extremo librae puncto, nempe sunt inter se ut circuli ali­<lb></lb>cuius coni. </s>

<s>Propterea centrum omnium dividet libram DE in eadem ratione <lb></lb>cum centro coni, nempe ita ut pars ad D reliquae sit tripla. </s>

<s>Est itaque cen­<lb></lb>trum O, quod erat demonstrandum. </s>

<s>” <lb></lb><figure id="id.020.01.2672.2.jpg" xlink:href="020/01/2672/2.jpg"></figure></s></p><p type="caption">

<s>Figura 159.</s></p><p type="main">

<s>“ PROPOSIZIONE XIX. — <emph type="italics"></emph>Centram gravita­<lb></lb>tis solidi sectoris sphaerici est in axe, distans <lb></lb>a centro sphaerae per 3/4 axis coni, et 3/8 sa­<lb></lb>gittae segmenti. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto solidus sector sphaerae ABCF (fig. </s>

<s>159) <lb></lb>cuius axis BF, sectaque sagitta BE bifariam in D, <lb></lb>et reliqua DF quadrifariam in punctis I, H, L, <lb></lb>erit, per praecedentem, centrum sectoris I. </s>

<s>Dico <lb></lb>FI constare ex 3/4 rectae FE, et ex 3/8 rectae EB. </s>

<s><lb></lb>Quod patet: tota enim DF constat ex tota FE, et <lb></lb>ex dimidia BE, nempe constat ex 4/4 rectae FE, et ex 4/8 rectae EB. </s>

<s>Ergo sub­<lb></lb>quadrupla recta FL, constabit ex 1/4 rectae FE et 1/8 rectae EB. </s>

<s>Ipsa ergo <lb></lb>Fl, tripla FL, composita crit ex 3/4 FE, et 3/8 rectae EB, quod erat demon­<lb></lb>strandum ” (ibid., fol. </s>

<s>94, 95). </s></p><pb xlink:href="020/01/2673.jpg" pagenum="298"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Rivolgendo il Torricelli il pensiero sopra queste proposizioni, si com­<lb></lb>piaceva tutto fra sè e con gli amici di Roma, di aver fatto tant&#039;oltre pro­<lb></lb>gredire la Baricentrica, che il libro del p. </s>

<s>Della Faille, appetto a suoi pochi <lb></lb>fogli scritti, pareva ben assai misera cosa. </s>

<s>Mentre infatti gli sforzi del padre <lb></lb>non erano riusciti che a dimostrare il centro di gravità del settore di cir­<lb></lb>colo, egli aveva di più ritrovato il centro degli archi, delle callotte e delle <lb></lb>zone; de&#039;settori sferici e dello stesso emisfero. </s>

<s>Quel che il Gesuita dall&#039;altra <lb></lb>parte diceva di aver cioè determinati i centri di gravità di molte altre figure, <lb></lb>ciò che nessun altro aveva fatto prima di lui, e di aspettare a pubblicar le <lb></lb>sue invenzioni <emph type="italics"></emph>tum ut explorarem quis de his speculationibus doctorum <lb></lb>virorum futurus sit sensus, tum quod antiquorum more librum uno su­<lb></lb>biecto constare debere existimem, quale sunt circulus et ellipsisi eiusdem <lb></lb>omnino essentiae figurae;<emph.end type="italics"></emph.end> pareva al Torricelli una iattanza, la vanità della <lb></lb>quale era facilmente scoperta dallo stesso strano giudizio, che s&#039;adduceva per <lb></lb>ricoprirla. </s></p><p type="main">

<s>Dopo il gesuita accademico di Madrid, nel 1642, quando il Torricelli <lb></lb>attendeva a questi suoi studi, non si conosceva in Italia altro autore, che ne <lb></lb>avesse trattato: ciò che fa maraviglia, perchè il Guldin, in Austria, aveva <lb></lb>sette anni prima, cioè nel 1635, pubblicato il suo primo tomo della Centro­<lb></lb>barica. </s>

<s>La maraviglia cresce anzi di più, ripensando che il libro, con tanta <lb></lb>curiosità ricercato, e non potuto vedere dai Discepoli di Galileo, se non che <lb></lb>dopo tanto penare per alcuni, e per altri mai; par che fosse nelle mani <lb></lb>del loro proprio maestro. </s>

<s>Giovanni Pieroni infatti, il di primo Marzo 1636 <lb></lb>scriveva da Vienna, dove pochi mesi prima quel primo tomo era stato pub­<lb></lb>blicato, ad Arcetri, una lettera, che terminava con queste parole: “ Il padre <lb></lb>Guldini gesuita, amico di V. S., che la conobbe in Roma, e che è parziale <lb></lb>suo, ha composto un libro <emph type="italics"></emph>De centro gravitatis partium circuli,<emph.end type="italics"></emph.end> e mi ha <lb></lb>consegnato un esemplare, perchè io lo mandi a V. S., il che farò con pre­<lb></lb>sta occasione ” (Alb. </s>

<s>X, 142). </s></p><p type="main">

<s>Potrebb&#039;essere o che le promesse non fossero mantenute, o che il libro <lb></lb>si fosse smarrito per via, o che pure recapitato non se ne facesse alcun conto, <lb></lb>e si rimanesse perciò nella dimenticanza di tutti: fatto è che il Torricelli <lb></lb>riposava tranquillo nella sua gloria, senza che nessuno ancora venisse a tur­<lb></lb>bargliene i sogni. </s>

<s>Ma quando nel 1641 si pubblicò della Centrobarica il tomo <lb></lb>secondo, dove si censurava il metodo degli indivisibili, il Cavalieri divulgò <lb></lb>la notizia dell&#039;autore e dell&#039;opera fra gli amici, dandola principalmente al <lb></lb>Torricelli, le prime impressioni sull&#039;animo del quale possono giudicarsi dal <lb></lb>seguente estratto di lettera, scritta il dì 3 Febbraio 1642 al Michelini: </s></p><p type="main">

<s>“ ...... V. paternità si compiacerà di ricevere una coppia di teoremi <pb xlink:href="020/01/2674.jpg" pagenum="299"></pb>geometrici nuovi, preconizzati dal miracoloso fra Bonaventura, sebbene uno <lb></lb>di essi l&#039;ha disgustato, per essere di un suo emulo, che gli ha stampato un <lb></lb>libro contro. </s>

<s>Quel teorema dell&#039;emulo di fra Bonaventura, che è un tal <lb></lb>p. </s>

<s>Guldini gesuita, è la massima conclusione di tutte quante quelle, che io <lb></lb>abbia mai sentito fino a questo giorno, ed è tale: Se qualsivoglia figura piana <lb></lb>sia girata intorno a qualsivoglia asse, o sia l&#039;asse congiunto con la figura <lb></lb>o no, il solido rotondo descritto dalla figura sarà uguale ad un solido, la cui <lb></lb>base sia la stessa figura genitrice, ma l&#039;altezza poi sia uguale alla perife­<lb></lb>ria, che nel girare sarà stata descritta dal centro di gravità della figura ge­<lb></lb>nitrice. </s>

<s>” </s></p><p type="main">

<s>“ Di più: la superficie curva di quel solido rotondo, ancorchè irregola­<lb></lb>rissima, sarà sempre uguale ad un parallelogrammo rettangolo, un lato del <lb></lb>quale sia uguale alla linea genitrice, e l&#039;altro sia uguale alla periferia de­<lb></lb>scritta parimente dal centro di gravità di essa linea genitrice nel girare. </s>

<s>Un <lb></lb>teorema poi così grande, che è verissimo, il buon padre non lo sa dimostrare: <lb></lb>solo va provando che concorda con le dottrine di Archimede e del XII di <lb></lb>Euclide. </s>

<s>Ma fra Bonaventura ne ha la dimostrazione facilissima per via degli <lb></lb>indivisibili .... ” (MSS. Gal., T. XXVI, fol. </s>

<s>6). </s></p><p type="main">

<s>Di qui apparisce che i primi pensieri del Torricelli furono serenamente <lb></lb>rivolti a favorire l&#039;amico: ma quando quest&#039;amico, cioè il Cavalieri, gli sog­<lb></lb>giunse la notizia che, nel primo tomo dell&#039;opera del Guldin, dove non en­<lb></lb>travano per niente gl&#039;indivisibili, perchè ancora non erano conosciuti; l&#039;Au­<lb></lb>tore vi trattava profusamente dell&#039;invenzione dei centri di gravità anche delle <lb></lb>porzioni del circolo e della sfera: e allora il Torricelli rivolse il pensiero a <lb></lb>sè medesimo, e trepidante che non fosse venuto l&#039;incognito straniero a sfron­<lb></lb>dargli di sulla fronte gli allori, prese, il di 21 di Febbraio 1643, la penna, <lb></lb>per scrivere così allo stesso Cavalieri: </s></p><p type="main">

<s>“ Non ho potuto ritrovare quest&#039;ultimo libro della Centrobarica: sup­<lb></lb>plico V. P. ad avvisarmi se vi sia alcuna delle seguenti conclusioni: ” </s></p><p type="main">

<s>“ I. </s>

<s>Il solido settore della sfera, che è composto di un cono e di un <lb></lb>segmento sferico, ha il centro di gravità sull&#039;asse tanto lontano dal centro <lb></lb>della sfera, quanto sono 3/4 dell&#039;asse del cono, e 3/8 della saetta del segmento, <lb></lb>il che abbraccia l&#039;emisferio ancora. </s>

<s>” </s></p><p type="main">

<s>“ II. </s>

<s>La superficie sferica di qualunque segmento <lb></lb><figure id="id.020.01.2674.1.jpg" xlink:href="020/01/2674/1.jpg"></figure></s></p><p type="caption">

<s>Figura 160.<lb></lb>di sfera ha il centro di gravità nel mezzo della sua <lb></lb>saetta. </s>

<s>” </s></p><p type="main">

<s>“ III. </s>

<s>Ogni zona di superficie sferica, tagliata con <lb></lb>piani paralleli, ha il centro nel mezzo del segmento <lb></lb>dell&#039;asse intercetto tra i detti piani. </s>

<s>” </s></p><p type="main">

<s>“ IV. </s>

<s>Se nel settore del circolo sarà inscritta una <lb></lb>figura di molti lati uguali, mediante la continua bi­<lb></lb>sezione dell&#039;arco, se faremo come tutte le dette linee uguali ABC (fig. </s>

<s>160) <lb></lb>alla corda AC, così il cateto della figura DE alla EO; il punto O sarà cen­<lb></lb>tro di tutte le linee rette uguali ABC. ” </s></p><pb xlink:href="020/01/2675.jpg" pagenum="300"></pb><p type="main">

<s>“ V. </s>

<s>Ma se faremo come tutte le rette ABC alli 2/3 della corda AC, così <lb></lb>il cateto DE alla EI, il punto I sarà centro della figura rettilinea ABCE. ” </s></p><p type="main">

<s>“ VI. </s>

<s>Facendosi poi come l&#039;arco ABC alla corda AC, così il semidiame­<lb></lb>tro BE alla EO, il punto O sarà centro dell&#039;arco. </s>

<s>” </s></p><p type="main">

<s>“ VII. </s>

<s>E facendosi come l&#039;arco ABC, alli 2/3 della corda AC, così BE <lb></lb>alla EI: il punto l sarà centro del settore. </s>

<s>Quest&#039;ultima è del padre Della <lb></lb>Faille, dimostrata da lui con un libro di roba, ed io la dimostro con meno <lb></lb>di un foglio, in due modi diversi, per gl&#039;indivisibili e senza. </s>

<s>” </s></p><p type="main">

<s>“ Temo che quell&#039;autore della Centrobarica si sia incontrato in alcune <lb></lb>di queste verità, il che mi dispiacerebbe, non tanto perchè ne resterei privo <lb></lb>io, quauto perchè ne resterebbe padrone uno, che non è degno. </s>

<s>Così mi pare <lb></lb>di poter dire di uno, che biasima la dottrina degl&#039;indivisibili, che è la vena <lb></lb>e la miniera inesausta delle speculazioni belle, e delle dimostrazioni a priori ” <lb></lb>(ivi. </s>

<s>T. XL. fol. </s>

<s>121). </s></p><p type="main">

<s>Il Cavalieri rispose da Bologna, il dì 3 di Marzo, con una lettera, nella <lb></lb>quale, dop&#039;aver discorso d&#039;altre cose analoghe all&#039;argomento, così soggiun­<lb></lb>geva: “ Circa poi le conclusioni mandatemi devo dirle che il padre Guldini <lb></lb>le dimostra anch&#039;esso, eccettuato che non torna il centro di gravità nè del <lb></lb>solido settore della sfera, nè delle zone di essa o superficie delle porzioni. </s>

<s><lb></lb>Solo dice di stimar probabile che il centro di esse superficie sia l&#039;istesso che <lb></lb>il centro di gravità delle figure genitrici delle porzioni di sfera, o delle por­<lb></lb>zioni comprese fra piani paralleli, provandolo <emph type="italics"></emph>a simili,<emph.end type="italics"></emph.end> poichè dice: siccome <lb></lb>il centro della superficie conica, eccettuata la base, è l&#039;istesso che del trian­<lb></lb>golo per l&#039;asse; così accaderà in questi. </s>

<s>Anzi così anco dice nelle porzioni <lb></lb>di supertìcie dello sferoide, e conoide parabolico: onde credo che in questo <lb></lb>inciampi, discordando dalle sue conclusioni, che veramente mi paiono bellis­<lb></lb>sime, come anco l&#039;altro modo nuovo, con il quale pure misura le porzioni <lb></lb>di sfera, sferoidi, conoidi, etc. </s>

<s>” (ivi, T. XLI, fol. </s>

<s>157). </s></p><p type="main">

<s>Non appariva chiaro da queste prime parole se il Guldin, in dimostrare <lb></lb>il centro di gravità dell&#039;arco di cerchio, era proceduto a diritto o aveva an­<lb></lb>che in esso inciampato, ciò che principalmente premeva di sapere al Torri­<lb></lb>celli, il quale sarebbe volentieri tornato a far di ciò espressa domanda, se <lb></lb>non avesse sperato d&#039;aver presto dalla stessa lettura del libro la desiderata <lb></lb>risposta. </s>

<s>Era una tale speranza poi tanto più fondata, in quanto che fra i <lb></lb>desiderosi di aver quel libro era il giovane principe Leopoldo de&#039;Medici, che <lb></lb>studiava allora le Matematiche sotto la direzione del Michelini, a cui vedemmo <lb></lb>come fosse dianzi dato la notizia della grande Regola centrobarica: da che, <lb></lb>aggiungendosi alla propria curiosità l&#039;altrui comando, fu il Torricelli stesso <lb></lb>mosso a scrivere così al Cavalieri: “ Diedi nuova al p. </s>

<s>Francesco delle Scuole <lb></lb>pie, matematico del principe Leopoldo, del nuovo libro del Guldini, ed egli <lb></lb>mi scrive che io procuri in tutti i modi di averne uno. </s>

<s>Supplico V. P. d&#039;av­<lb></lb>visarmi se costì ve ne sarà, e almeno dov&#039;è stampato, e quando la spera <lb></lb>d&#039;aver fornita e pubblicata la <emph type="italics"></emph>Risposta ”<emph.end type="italics"></emph.end> (ivi, T. XL, fol. </s>

<s>123). </s></p><p type="main">

<s>Chi ha letto il secondo capitolo dell&#039;altro nostro tomo, già sa che l&#039;ac-<pb xlink:href="020/01/2676.jpg" pagenum="301"></pb>cennata Risposta era quella, incominciata a farsi in dialogo, alle censure dello <lb></lb>stesso Guldino, contro il quale il Torricelli sollecitava il Cavalieri a difen­<lb></lb>dersi, mentr&#039;egli intanto pensava colle offese d&#039;attutir la baldanza del ne­<lb></lb>mico. </s>

<s>Un tale animo si rivela da ciò che dice esso Torricelli in una lettera <lb></lb>scritta il di 7 Marzo 1643, cioè una settimana dopo la precedente. </s></p><p type="main">

<s>“ Dopo che io ebbi la lettera di V. P., dimostrai, anco senza indivisi­<lb></lb>bili, che il centro delle armille e zone sferiche sia nel mezzo della porzione <lb></lb>d&#039;asse, che gli corrisponde, e la dimostrazione è semplicissima, e quasi si­<lb></lb>mile alla IX del primo <emph type="italics"></emph>Degli equiponderanti.<emph.end type="italics"></emph.end> Mi darebbe poi anche il cuore <lb></lb>di dimostrare che il centro della superficie del conoide parabolico non è <lb></lb>l&#039;istesso che quello della parabola genitrice. </s>

<s>Quanto allo sferoide ed iperbo­<lb></lb>lico non ne so nulla, ma vedendo che egli si è ingannato in queste, posso <lb></lb>credere che si sia ingannato anche in quelle. </s>

<s>” </s></p><p type="main">

<s>“ Io non vorrei esser tanto prosuntuoso che ardissi di consigliarla, ma <lb></lb>almeno antepongo al suo giudizio se ella stimerà bene toccargli questo punto <lb></lb>nella <emph type="italics"></emph>Risposta,<emph.end type="italics"></emph.end> con mostrargli che egli finalmente adduce delle conclusioni <lb></lb>false. </s>

<s>Io quanto a me crederò che i metodi del Padre siano ottimi, e che <lb></lb>quello degl&#039;indivisibili di fra Bonaventura sia cattivo: so bene però per cosa <lb></lb>certa che quegli ottimi deducono delle cose false, che tali si dimostrano, e <lb></lb>che da quel cattivo non si cava se non conclusioni vere, quando si operi <lb></lb>conforme alli precetti dell&#039;arte, ed alle cose dimostrate negli Elementi. </s>

<s>” </s></p><p type="main">

<s>“ Io non posso credere che quello sia grand&#039;Uomo, mentre in cose tanto <lb></lb>gelose si lascia trasportare ad argomentare <emph type="italics"></emph>a simili.<emph.end type="italics"></emph.end> Il parallelogrammo è <lb></lb>doppio del triangolo: anco la porzione dell&#039;asse alla cima è doppia di quella <lb></lb>alla base del triangolo. </s>

<s>Il parallelogrammo è sesquialtero della parabola: anco <lb></lb>la porzion dell&#039;asse è sesquialtera. </s>

<s>Il cilindro è triplo del cono: anco la por­<lb></lb>zione dell&#039;asse alla cima è tripla della rimanente. </s>

<s>Il cilindro è doppio del <lb></lb>conoide parabolico, ed anco la porzione dell&#039;asse alla cima è dupla della <lb></lb>rimanente. </s>

<s>” </s></p><p type="main">

<s>“ Io dunque, che avrò più similitudini che non ha il Padre, seguiterò <lb></lb>ad argomentare e dirò: il cilindro è sesquialtero dell&#039;emisfero, dunque la <lb></lb>porzione dell&#039;asse dell&#039;emisfero, che è dalla cima fino al centro della gra­<lb></lb>vità, sarà sesquialtera della rimanente. </s>

<s>Ma questo è falso, stando come cin­<lb></lb>que a tre ” (ivi, fol. </s>

<s>124). </s></p><p type="main">

<s>Dismesso il primo proposito di rispondere al Guldin in dialogo, non la­<lb></lb>sciò il Cavalieri di dare effetto al consiglio dell&#039;amico nella fine del cap. </s>

<s>XIV <lb></lb>della terza Esercitazione geometrica, dove, con un esempio preso dalle inscri­<lb></lb>zioni e circoscrizioni delle superficie coniche, mostrava quant&#039;era falso l&#039;ar­<lb></lb>gomento <emph type="italics"></emph>a simili<emph.end type="italics"></emph.end> addotto nel cap. </s>

<s>X alla V proposizion centrobarica, che <lb></lb>cioè si corrispondono i centri di gravità delle dette superficie, e dei solidi <lb></lb>rotondi (Ediz. </s>

<s>cit., pag. </s>

<s>235-38). Ma la curiosità, che aveva il Torricelli di <lb></lb>riscontrar da sè queste cose nel libro, non fu in lui sodisfatta, cosicchè, di­<lb></lb>stratto dalla fabbrica dei vetri per i canocchiali, in che diceva di ritrovar <lb></lb>tutto il suo diletto, non si curò più di decidere del primato intorno all&#039;in-<pb xlink:href="020/01/2677.jpg" pagenum="302"></pb>venzione del baricentrico negli archi di cerchio. </s>

<s>Abbiam veduto quant&#039;egli <lb></lb>avesse ambito prima a una tale invenzione, la quale, non solamente comu­<lb></lb>nicò al Cavalieri, come apparisce dai documenti citati, ma a tutti i suoi amici <lb></lb>di Roma, per mezzo di Michelangiolo Ricci pregato apposta a voler dare al <lb></lb>Magiotti la nuova che “ se sarà un settore di cerchio, e facciasi, come l&#039;arco <lb></lb>a tutta la corda, così l&#039;asse a una quarta linea; nell&#039;estremità di questa sarà <lb></lb>il centro di gravità dell&#039;arco ” (ivi, fol. </s>

<s>100). </s></p><p type="main">

<s>È rimasta fra le carte del Torricelli una scrittura, che avremo occasione <lb></lb>di citar più volte, intitolata <emph type="italics"></emph>Racconto di alcune proposizioni proposte e pas­<lb></lb>sate scambievolmente tra i matematici di Francia e me, dall&#039;anno 1640 <lb></lb>in qua,<emph.end type="italics"></emph.end> nel quale anno racconta come avendo contratta col p. </s>

<s>Niceron una <lb></lb>stretta amicizia in Roma, mandasse a lui in un foglio alcune sue invenzioni <lb></lb>geometriche, accennando solo le enunciazioni, senza dimostrazione alcuna. </s>

<s>“ E <lb></lb>feci questo, soggiunge, acciò non solo il suddetto padre vedesse quel com­<lb></lb>pendio de&#039;miei studi, ma anco lo conferisse ai matematici della Francia, e <lb></lb>ne intendesse il loro giudizio ” (ivi, T. XXXII, fol. </s>

<s>21). </s></p><p type="main">

<s>Anche il baricentro dell&#039;arco fu notato tra quelle invenzioni, e, come <lb></lb>di questa, fu per i matematici francesi favorevole il giudizio delle altre pro­<lb></lb>posizioni torricelliane, infin tanto che nel 1646 non insorsero col Roberval <lb></lb>le famosè controversie intorno a chi avesse prima dimostrato il centro di <lb></lb>gravità, e definita la misura dei solidi generati dalla Cicloide. </s>

<s>In mezzo a <lb></lb>cotesta animosità, e per citar qualche altro esempio valevole a confermar <lb></lb>nell&#039;avversario l&#039;accusa di plagio, andava esso Roberval dicendo che, benchè <lb></lb>il Torricelli si fosse appropriata la&#039;dimostrazione del centro di gravità delle <lb></lb>porzioni di circonferenza, il Guldin nonostante aveva già scritto il medesimo, <lb></lb>e pubblicato nel primo libro della Centrobarica, dimostrando un&#039;altra novità <lb></lb>bellissima, che cioè la mezza circonferenza concentra il suo peso là dove la <lb></lb>Quadratrice di Nicomede ha il termine del suo moto. </s></p><p type="main">

<s>A questa prima notizia, con l&#039;animo agitato da varie passioni, forse non <lb></lb>comprese il Torricelli la relazion che passa fra il centro di gravità di un <lb></lb><figure id="id.020.01.2677.1.jpg" xlink:href="020/01/2677/1.jpg"></figure></s></p><p type="caption">

<s>Figura 161.<lb></lb>arco, e la famosa curva meccanica del Matematico antico. </s>

<s><lb></lb>Ma poi, rivolgendo le <emph type="italics"></emph>Collezioni matematiche<emph.end type="italics"></emph.end> di Pappo, <lb></lb>nel libro IV, dove si tratta della curva assunta da Dino­<lb></lb>strato e da Nicomede per la quadratura del circolo, rivolse <lb></lb>particolarmente la sua attenzione sul teorema XXIII così <lb></lb>formulato: “ Quadrato enim existente ABFC (fig. </s>

<s>161), et <lb></lb>circumferentia BC, circa centrum A, et linea quadrante BE, <lb></lb>facta sicuti dictum est; ostenditur, ut BC circumferentia, <lb></lb>ad rectam lineam AB, ita esse AB, ad ipsam AE ” (Bo­<lb></lb>noniae 1660, pag. </s>

<s>89). D&#039;ond&#039;ebbe il Torricelli a conclu­<lb></lb>dere che il punto E, dove il moto della Quadratrice ter­<lb></lb>mina sull&#039;asse, era veramente il centro di gravità della <lb></lb>semicirconferenza BCD, com&#039;egli stesso aveva concluso per vie tanto diverse. </s>

<s><lb></lb>Allora incominciò a dubitar che il Guldino avesse argomentato di qui, e che <pb xlink:href="020/01/2678.jpg" pagenum="303"></pb>fosse la sua invenzione una congettura o una supposizione, piuttosto che una <lb></lb>dimostrazione condotta dai principii della Geometria. </s>

<s>Questo gli premeva di <lb></lb>saper con certezza, per rispondere al Roberval, ond&#039;è che, dopo tre anni, <lb></lb>cioè il dì 23 Marzo 1646, tornava a farne al Cavalieri, così, ma con più tre­<lb></lb>pida sollecitudine, la domanda: </s></p><p type="main">

<s>“ Supplico V. P., se però ella se ne ricorda, a voler farmi grazia d&#039;av­<lb></lb>visarmi se quel padre gesuita della Centrobarica dimostri geometricamente <lb></lb>che, facendosi come l&#039;arco di cerchio ABC (fig. </s>

<s>162) alla sua corda AC, così <lb></lb>il semidiametro BD alla DE, il punto E sia centro dell&#039;arco ABC. </s>

<s>Mi pare <lb></lb>che V. P. mi scrivesse che egli diceva questo Teo­<lb></lb><figure id="id.020.01.2678.1.jpg" xlink:href="020/01/2678/1.jpg"></figure></s></p><p type="caption">

<s>Figura 162.<lb></lb>rema, ma non mi ricordo se ella mi dicesse se egli <lb></lb>lo dimostrava, ovvero lo supponeva ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XL, fol. </s>

<s>130). </s></p><p type="main">

<s>Rispose il Cavalieri che il Guldin dimostrava, e <lb></lb>non solamente supponeva il teorema, e nello stesso <lb></lb>tempo avvertiva l&#039;amico di ciò, che andava dicendo <lb></lb>il Roberval, per quel che aveva risaputo dal Niceron <lb></lb>di Parigi. </s>

<s>A che il Torricelli subito replicava: </s></p><p type="main">

<s>“ Apposta domandai a V. P. se il Guldini dimostrava quella proprietà <lb></lb>dell&#039;arco, per poter rispondere a monsù Roberval. </s>

<s>Mi dispiace che il Gul­<lb></lb>dini la dimostri, perchè ancor io aveva, già sono quattro anni, quella dimo­<lb></lb>strazione. </s>

<s>Io provai che, facendosi come tutti i lati uguali AE (fig. </s>

<s>163), EF, <lb></lb>FG, GB, BH, HI, IL, LC, a due terzi della corda AC, così la retta BD <emph type="italics"></emph>ad <lb></lb>aliam sumendam ex centro,<emph.end type="italics"></emph.end> il termine della presa sarebbe centro di gra­<lb></lb><figure id="id.020.01.2678.2.jpg" xlink:href="020/01/2678/2.jpg"></figure></s></p><p type="caption">

<s>Figura 163.<lb></lb>vità della figura <lb></lb>rettilinea DABC. <lb></lb>Ma, facendosi <lb></lb>come i suddetti <lb></lb>lati uguali alla <lb></lb>corda AC, così la <lb></lb>BD <emph type="italics"></emph>ad aliam su­<lb></lb>mendam ex cen­<lb></lb>tro,<emph.end type="italics"></emph.end> il termine sa­<lb></lb>rebbe stato centro <lb></lb>di tutte le rette <lb></lb>AE EF, ecc. </s>

<s>Dalla <lb></lb>prima inferivo il <lb></lb>centro del settore, <lb></lb><emph type="italics"></emph>more veterum:<emph.end type="italics"></emph.end><lb></lb>dalla seconda inferivo il centro dell&#039;arco prima, e poi il centro del settore, <lb></lb>per gl&#039;indivisibili. </s>

<s>Ma le dimostrazioni, con le quali applico il lemma, son <lb></lb>tanto acute, che non pensavo che il Guldini ci fosse potuto arrivare. </s>

<s>Giac­<lb></lb>chè V. P. ha inteso il mio mezzo termine, la supplico ad incomodarsi di <lb></lb>nuovo ad avvisarmi se va per questa strada ” (ivi, fol. </s>

<s>131). </s></p><pb xlink:href="020/01/2679.jpg" pagenum="304"></pb><p type="main">

<s>Ma il Cavalieri, quasi stanco di far risposte di questo genere, pensò di <lb></lb>mandare in prestito al requisitore, che ne aveva tanta passione, la sua pro­<lb></lb>pria copia della <emph type="italics"></emph>Centrobarica,<emph.end type="italics"></emph.end> ed ei se ne soddisfacesse a suo piacere leg­<lb></lb>gendo. </s>

<s>Di che fatto avvisato il Torricelli stesso rispondeva così, il di 28 Aprile <lb></lb>del detto anno 1646: “ Rendo infinite grazie a V. P. che, in cambio di darmi <lb></lb>solo un poco di ragguaglio intorno ai mezzi di una dimostrazione sola, si è <lb></lb>compiaciuta di mandarmi tutto il libro del Guldini, quale procurerò di re­<lb></lb>cuperar quanto prima ” (ivi, fol. </s>

<s>133). E seguitando a scrivere non aveva <lb></lb>ancora sigillata la lettera, che i volumi eran già sul suo banco di studio, dove, <lb></lb>attendendo con curiosità frettolosa a sfogliare il primo, provava nell&#039;animo <lb></lb>quella impressione, e gli passavano per la mente que&#039;pensieri, che noi vo­<lb></lb>gliamo, come parte importantissima di quest&#039;intima storia della Scienza, bre­<lb></lb>vemente descrivere ai nostri Lettori. </s></p><p type="main">

<s>Il volume è in folio, ma più della metà si spende in argomenti, che <lb></lb>poco potevano importare al Torricelli. </s>

<s>Nel cap. </s>

<s>XII si tratta dell&#039;invenzion <lb></lb>meccanica dei centri di gravità, esplicando un luogo dei commentari sulla <lb></lb>Sfera del Sacrobosco, dove il Clavio insegna a sospendere un corpo, sia pure <lb></lb>irregolare quanto si voglia, e notar la linea della direzione del filo: fatto ciò, <lb></lb>sospendeva il grave da un altro punto, e, notate le medesime cose, conclu­<lb></lb>deva che là, dove le due direzioni s&#039;incontrano, sarà il centro richiesto. </s>

<s>Poi, <lb></lb>segue, nella Centrobarica, una <emph type="italics"></emph>Dissertazione fisico-matematica<emph.end type="italics"></emph.end> superiore nel <lb></lb>concetto alla mente di un Peripatetico, dimostrandovisi che, dovendo variare <lb></lb>i corpi componenti il Globo di posizione, non può la Terra consistere nel <lb></lb>medesimo punto, perchè, mutandosi il centro di gravità, necessariamente si <lb></lb>muove. </s>

<s>S&#039;aggiungono in ultimo questioni arimmetiche, e le Tavole de&#039;qua­<lb></lb>drati dei numeri e de&#039;loro cubi dall&#039;uno al diecimila. </s></p><p type="main">

<s>Lasciate dunque indietro queste cose, e, nel trattato geometrico de&#039;centri <lb></lb>di gravità, le proposizioni, che vi si citano da altri Autori già dimostrate; <lb></lb>ebbe il Torricelli a stupire vedendo che, nelle proposizioni V e VI del cap. </s>

<s>III, <lb></lb>il Guldino preparava i lemmi a quel modo, che aveva fatto egli stesso, ri­<lb></lb>cercando il centro di gravità delle linee inscritte e circoscritte all&#039;arco di <lb></lb>cerchio, d&#039;onde poi, nella seconda proposizione del cap. </s>

<s>V, concludeva: “ Fiat <lb></lb>igitur, ut semiperipheria ad semisubtensam, ita semidiameter ad aliam quam­<lb></lb>piam, cui aequalis accipiatur AP, in semidiametro ex centro A; dico punctum P <lb></lb>centrum esse quod quaeritur ” (Centrobaricae, lib. </s>

<s>I, Viennae Austriae 1635, <lb></lb>pag. </s>

<s>59). </s></p><p type="main">

<s>Parve al Torricelli però di vedere in queste guldiniane dimostrazioni una <lb></lb>gran confusione, e un grande stento, paragonate alla elegante facilità delle <lb></lb>sue, ma più che altro vedeva prelucervi la notizia della cosa da dimostrare: <lb></lb>notizia che, seguitando a sfogliare il volume, indovinò aver avuto origine dalla <lb></lb>Quadratrice, l&#039;ultimo punto della quale, leggeva, <emph type="italics"></emph>ipsum tamen centrum esse <lb></lb>gravitatis semiperipheriae circuli nos primum mundo manifestamus<emph.end type="italics"></emph.end> (ibid., <lb></lb>pag. </s>

<s>67). Dimostra ciò, da Pappo, l&#039;Autore della Centrobarica nella propo­<lb></lb>sizione I del cap. </s>

<s>VI, ma il corollario, in cui egli fa osservare che, dato il <pb xlink:href="020/01/2680.jpg" pagenum="305"></pb>centro di gravità, s&#039;ha la quadratura, e data la quadratura s&#039;ha il centro, <lb></lb>è cosa del p. </s>

<s>Della Faille, scritta ne&#039;due primi corollari ai teoremi de&#039;cen­<lb></lb>tri di gravità del circolo e dell&#039;ellisse. </s>

<s>Dal principale teorema ivi dimostrato, <lb></lb>quale si è che l&#039;arco sta a due terzi della corda, come il raggio a una quarta <lb></lb>linea, indicatrice sull&#039;asse del baricentrico del settore; ne conclude esso Della <lb></lb>Faille che l&#039;arco, e perciò anche tutta intera la circonferenza, poteva facil­<lb></lb>mente quadrarsi, ciò che pensò il Guldin di concludere con simili ragioni <lb></lb>dal centro di gravità dell&#039;arco, come di fatti fece nel detto corollario. </s>

<s>Pro­<lb></lb>postosi dunque l&#039;altro principio che, datasi la quadratura è dato il baricen­<lb></lb>tro, pensò di ricorrere alla Quadratrice antica, argomentando che il punto <lb></lb>cercato era, di quella linea da lui chiamata <emph type="italics"></emph>mirabile,<emph.end type="italics"></emph.end> l&#039;ultimo punto. </s>

<s>L&#039;ar­<lb></lb>gomento sapeva per verità di audacia, avendo argutamente Pappo, nel citato <lb></lb>libro delle <emph type="italics"></emph>Collezioni,<emph.end type="italics"></emph.end> al problema terzo, fatto osservare che Nicomede e Di­<lb></lb>nostrato supponevan già quella proporzione tra la linea retta e la curva, che <lb></lb>si voleva cercare: e nonostante la cosa riuscì al Guldino con tanta felicità, <lb></lb>da prevenire in questo le sottili invenzioni del Torricelli, il quale in somma <lb></lb>non ebbe il torto in sospettar che il suo emulo avesse a principio supposto <lb></lb>quel che poi si studiò di dimostrare con quelle sue maniere stentate e <lb></lb>confuse. </s></p><p type="main">

<s>Costretto in ogni modo lo stesso Torricelli a dover cedere l&#039;ambita pri­<lb></lb>mizia a chi egli diceva non esserne degno, e perduto l&#039;argomento necessa­<lb></lb>rio a recidere le calunnie del Roberval dalla loro radice, non gli rimaneva <lb></lb>altra gloria che di essere rimasto il primo inventore del centro di gravità <lb></lb>delle callotte, delle zone, e de&#039;settori sferici. </s>

<s>Seguitando con questa fiducia <lb></lb>compiacente, assicuratagli dal Cavalieri, a svolgere il volume centrobarico, <lb></lb>vi leggeva, nella V proposizione del cap. </s>

<s>X, dimostrato il centro di gravità <lb></lb>delle porzioni delle superficie sferiche, sferoidee, e conoidee essere quel me­<lb></lb>desimo che delle superficie piane generatrici, per queste ragioni: “ Nam, si­<lb></lb>cuti conicae superficiei centrum gravitatis est idem, quod est trianguli, seu <lb></lb>in frusto trapezii per axem ducto; ita hic eodem modo centrum gravitatis <lb></lb>superficiei portionis sphaericae, sphaeroidicae et conoidicae, seu frusto, etiam <lb></lb>est centrum gravitatis segmenti, seu trapezii per axem ducti, basibus tamen <lb></lb>utrobique exceptis ” (ibid., pag. </s>

<s>127). </s></p><p type="main">

<s>Non rimaneva al Torricelli, per sodisfar pienamente quella sua gelosa <lb></lb>curiosità, che di vedere in qual modo indicasse il <lb></lb><figure id="id.020.01.2680.1.jpg" xlink:href="020/01/2680/1.jpg"></figure></s></p><p type="caption">

<s>Figura 164.<lb></lb>Guldin il centro di gravità del settore sferico, ciò <lb></lb>che gli occorse una sola pagina dopo quella già <lb></lb>letta, sotto il titolo della IX proposizione scritta <lb></lb>nel cap. </s>

<s>XI, dove, supposto il centro del solido <lb></lb>emisferico ABC (fig. </s>

<s>164), in I, sull&#039;asse, come <lb></lb>ve lo designa Luca Valerio, dice che, inalzata <lb></lb>da I una perpendicolare, la quale incontri in H <lb></lb>la linea EF, che bipartisce il quadrante AB in due ottanti; sarà in esso <lb></lb>H il centro di gravità del settore descritto dal rivolgersi uno dei detti ot-<pb xlink:href="020/01/2681.jpg" pagenum="306"></pb>tanti intorno alla linea FE come a suo asse. </s>

<s>Per dimostrare il quale as­<lb></lb>serto così dice: “ Res haec ut demonstretur, cum pluribus indigeat verbis <lb></lb>quam rationibus, eaeque tales sint, quae unicuique qui praecedentia intellexit <lb></lb>obviae ac manifestae sint, plura in confirmationem addere noluimus. </s>

<s>Et sic <lb></lb>satisfactum esse propositioni iudicamus ” (ibid., pag. </s>

<s>132). <emph type="italics"></emph>Bravo!<emph.end type="italics"></emph.end> fece qui <lb></lb>il Torricelli chiudendo il libro, <emph type="italics"></emph>bravo il mi&#039;bue!<emph.end type="italics"></emph.end> e ripresa in mano la let­<lb></lb>tera al Cavalieri, dianzi lasciata aperta, v&#039;aggiunse queste parole: “ Dopo <lb></lb>scritto fin qui, ho ricevuto il libro del Guldini, e scartabellato quasi tutto. </s>

<s><lb></lb>Ho veduto che adopra i medesimi mezzi, che adopro anch&#039;io, per quei cen­<lb></lb>tri, ma Dio sa con quanta confusione e stento. </s>

<s>In somma io gli pronunzio <lb></lb>che il padre Guldino, per quanto si può argomentare da questo libro, è stato <lb></lb>un bue ” (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>134). </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il secondo volume della Centrobarica, che comprendeva i libri secondo, <lb></lb>terzo e quarto, dopo i primi saggi presi poco importava di consultare al Tor­<lb></lb>ricelli, a cui il Cavalieri aveva fatta già nota la grande Regola dall&#039;Autore <lb></lb>ivi insegnata come un fatto, la verità del quale si confermava dal mostrar <lb></lb>che i resultati di lui concordavano con i teoremi della Geometria. </s>

<s>Aperto <lb></lb>nonostante il libro, sfogliando quelle undici pagine di prefazione, non potè <lb></lb>non trattenersi dalla quinta alla settima a considerar quel passo che il Gul­<lb></lb>din trascrive dal proemio del Cavalieri. </s>

<s>Vi si diceva dall&#039;Autore dei sette <lb></lb>libri della Geometria nuova come fosse rimasto preso da gran maraviglia in <lb></lb>ripensare che le ragioni stereometriche e baricentriche tra i solidi rotondi <lb></lb>non son più quelle delle superficie piane che gli hanno generati. </s>

<s>Così infatti, <lb></lb>mentre il rettangolo è doppio del triangolo, il cilindro generato è triplo del <lb></lb>cono; e mentre il centro di gravità sega l&#039;asse così che la parte verso il <lb></lb>vertice del triangolo è doppia di quella verso la base; nel cono invece si <lb></lb>trova esser tripla. </s>

<s>Di qui, prosegue lo stesso Cavalieri a dire, considerando <lb></lb>meglio le cose, conobbi che le linee, di che s&#039;intessono le superficie, e i <lb></lb>piani, di che si compaginano i solidi, non son da prender per l&#039;asse, ma pa­<lb></lb>ralleli alla base, e così si trova che gl&#039;infiniti circoli affaldati nel cilindro son <lb></lb>tripli degli infiniti circoli, che s&#039;affaldano a comporre il volume del cono. </s></p><p type="main">

<s>Ben comprese il Torricelli la ragione perchè il Guldin si studiasse di <lb></lb>cogliere questi principii di Geometria nuova in difetto: perchè per essi si <lb></lb>scoprivano le sue fallacie, le quali giusto avevano avuto origine dal cre­<lb></lb>dere che il centro di gravità delle figure condotte per l&#039;asse si mantenesse <lb></lb>il medesimo, che delle superficie dei solidi generati. </s>

<s>L&#039;esempio nonostante, <lb></lb>ch&#039;egli adduceva del triangolo e della superficie conica descritta dal rivolgi­<lb></lb>mento di lui, era vero, e il Torricelli stesso volle ciò confermare per via <lb></lb>degli indivisibili, considerando i pesi concentrati sull&#039;asse come sopra la lun-<pb xlink:href="020/01/2682.jpg" pagenum="307"></pb>ghezza di una libbra, a quel modo che aveva fatto per dimostrare il centro <lb></lb>di gravità del triangolo e del conoide parabolico. </s></p><p type="main">

<s>“ PROPOSIZIONE XX. — <emph type="italics"></emph>Centrum gravitatis superficiei<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2682.1.jpg" xlink:href="020/01/2682/1.jpg"></figure></s></p><p type="caption">

<s>Figura 165.<lb></lb><emph type="italics"></emph>conicae est in axe, ita ut pars ad verticem reliquae sit <lb></lb>dupla. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto conica superficies ABC (fig. </s>

<s>165) cuius axis BD, <lb></lb>sitque BE dupla ad ED. </s>

<s>Dico E esse centrum gravitatis. </s>

<s>Se­<lb></lb>cetur enim superficies planis FG, HI ad axem erectis ubi­<lb></lb>cumque: eritque peripheria, quae per F, ad peripheriam, <lb></lb>quae per H, ut FN ad HM, et hoc semper. </s>

<s>Ergo ad libram <lb></lb>BD pendent quaedam magnitudines, nempe peripheriae et totidem magnitu­<lb></lb>dines ipsis ex ordine proportionales, nempe lineae rectae. </s>

<s>Ergo commune <lb></lb>centrum habebunt ” (MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>31). </s></p><p type="main">

<s>Conclusa così la dimostrazione, sembrava al Torricelli di vedersi insor­<lb></lb>gere contro il Guldino o qualcun altro, come lui avverso al metodo degli <lb></lb>indivisibili, e dire: Perchè mai, avendo il triangolo e la superficie conica co­<lb></lb>mune il centro di gravità, non debbono averlo per simili ragioni la semicir­<lb></lb>conferenza e l&#039;emisfero, la parabola e il conoideo da lei descritto? </s>

<s>Suppo­<lb></lb>nete che l&#039;ambito ABC nella vostra figura sia una mezza circonferenza o una <lb></lb>parabola intorno all&#039;asse BD: condotti piani FG, HI, comunque, intercide­<lb></lb>ranno sulla superficie emisferica o conoidea circonferenze, le quali staranno <lb></lb>come i raggi HM, FN, cosicchè anche il centro di quelle superficie dovrebbe <lb></lb>segar l&#039;asse nel mezzo, ciò che, sebbene sia contro alle nostre supposizioni, <lb></lb>è altresì contrario ai vostri dimostrati teoremi. </s></p><p type="main">

<s>Rispond<gap></gap>a il Torricelli, richiamandosi alle regole insegnate dal Cavalieri, <lb></lb>una delle quali, e delle più importanti ad osservare, per non si dover tro­<lb></lb>vare ingannati, era di ricever sempre le somme di tutte le indivisibili figure <lb></lb>da paragonarsi <emph type="italics"></emph>sub quadam uniformi ratione, seu sub quodam determi­<lb></lb>nato spissitudinis aut costipationis gradu<emph.end type="italics"></emph.end> (Exercit. </s>

<s>geom., Bononiae 1647, <lb></lb>pag. </s>

<s>15). </s></p><p type="main">

<s>Gl&#039;infiniti componenti indivisibili l&#039;intelletto gli concepisce in sè stessi, <lb></lb>ma il senso gli percepisce nelle relazioni di posizione, che gli uni hanno ri­<lb></lb>spetto agli altri. </s>

<s>Così nella linea di un millimetro, come in quella di un <lb></lb>metro, per l&#039;intelletto è la medesima infinità di punti, ma per il senso è <lb></lb>questa molto più lunga di quella, perchè le distanze o i <emph type="italics"></emph>transiti<emph.end type="italics"></emph.end> son molto <lb></lb>maggiori. </s>

<s>L&#039;esempio di ciò lo abbiamo nelle proiezioni, come della linea AB <lb></lb><figure id="id.020.01.2682.2.jpg" xlink:href="020/01/2682/2.jpg"></figure></s></p><p type="caption">

<s>Figura 166.<lb></lb>(fig. </s>

<s>166) sul piano AC, in cui, dentro lo spazio AD, si <lb></lb>trovano necessariamente contratti i medesimi punti di <lb></lb>più lungo transito, compresi nello spazio AB. </s>

<s>E perchè, <lb></lb>quando la stessa linea sia risalita perpendicolarmente sul <lb></lb>piano, la proiezion di lei è un punto, è verissimo dun­<lb></lb>que sotto questo aspetto che una linea, anzi più linee <lb></lb>concorrenti possono ridursi uguali a un punto, come par si verifichi nel cono <lb></lb>luminoso, che entra o esce dal fuoco di uno specchio. </s>

<s>Ci sovviene anzi che <pb xlink:href="020/01/2683.jpg" pagenum="308"></pb>di qui Galileo inferiva dovere esser la luce incorporea e istantanea, come <lb></lb>quella che è <emph type="italics"></emph>ridotta a&#039;suoi infiniti indivisibili componenti, e fatta senza <lb></lb>introduzione di corpi o di posizione di vacui quanti, ma bene d&#039;indivisi­<lb></lb>bili vacui, e così non occupa luogo, e non ricerca tempo d&#039;andare da un <lb></lb>luogo a un altro.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Un tal concetto però della composizione dei corpi è falso, e la questione, <lb></lb>lungamente intorno a questo argomento agitata nel primo dialogo delle due <lb></lb>Scienze nuove, non si risolve nell&#039;obietto percepito, ma nel soggetto perci­<lb></lb>piente, che ora è l&#039;intelletto ora il senso. </s>

<s>Per l&#039;intelletto, che è semplice e <lb></lb>uno, l&#039;infinito si riduce a un punto, ma per il senso è diviso, e la divisione <lb></lb>è finita, o, come con Galileo si direbbe, è quanta. </s>

<s>Ecco come sia da una <lb></lb>parte l&#039;infinito innumerabile, e dall&#039;altra soggetto ai calcoli del matematico, <lb></lb>e alle circoscrizioni del Geometra: ecco come si risolvono le questioni di si­<lb></lb>mil genere, e com&#039;essendo tutte le figure geometriche sensibili sia necessa­<lb></lb>rio apprenderle nelle loro parti divise, computando la quantità della divisione <lb></lb>o le <emph type="italics"></emph>spissitudini<emph.end type="italics"></emph.end> e i <emph type="italics"></emph>transiti,<emph.end type="italics"></emph.end> come diceva il Cavalieri, e come ripeteva nello <lb></lb>Scolio alla precedente proposizione il Torricelli: </s></p><p type="main">

<s>“ Nota quod non valet argumentum, quod contra fieri posset ab his, <lb></lb>qui methodum indivisibilium non admodum intelligunt. </s>

<s>Possent enim addu­<lb></lb>cere argumentum de superficie sphaerae, aut semicirculi, quae non habent <lb></lb>commune centrum, sive de superficie conoidis parabolici et parabolae. </s>

<s>Causa <lb></lb>disparitatis est quod superficies conica eumdem transitum semper servat, sunt­<lb></lb>que omnes peripheriae, ut ita dicam, eiusdem spissitudinis, ut rectac ad BD <lb></lb>applicatae, quod non est verum in dictis superficiebus, quarum peripheriae <lb></lb>maiorem semper habent densitatem, sive spissitudinem, versus verticem, re­<lb></lb>spectu linearum applicatarum ad axem ” (ibid.). </s></p><p type="main">

<s>Il Guldin dunque e Galileo, chiamato, nella prefazione al secondo libro <lb></lb>centrobarico, per aggredire insieme il Cavalieri, in soccorso poderoso; repu­<lb></lb>tavano fallace e ripudiavano perciò il metodo degl&#039;indivisibili, perchè, secondo <lb></lb>il Torricelli, <emph type="italics"></emph>non admodum illud intelligunt.<emph.end type="italics"></emph.end> Il Torricelli stesso però stimava <lb></lb>indegni di ogni bella invenzione coloro, che un tal metodo biasimavano, essendo <lb></lb>egli, diceva, <emph type="italics"></emph>la vena e la miniera inesauribile delle speculazioni belle, e <lb></lb>delle dimostrazioni a priori.<emph.end type="italics"></emph.end> Aveva fatto di ciò particolarmente esperienza nel <lb></lb>trattare dei baricentri, non solo rispetto alla varietà dei soggetti, ma rispetto <lb></lb>altresì alla varietà dei modi di trattare il soggetto medesimo, come per esem­<lb></lb>pio il triangolo e il cono, l&#039;emisferoide e l&#039;emisfero, di che un primo saggio <lb></lb>ne porge quel capitolo intitolato nel manoscritto: <emph type="italics"></emph>Centrum gravitatis trian­<lb></lb>guli, coni et hemisphaeri, hemisphaeroidisque a priori.<emph.end type="italics"></emph.end> Ma prima di veder <lb></lb>come il metodo degl&#039;indivisibili sia applicato a dimostrar questi teoremi, con <lb></lb>elegante varietà da que&#039;medesimi già prima dimostrati; giova rimovere dalla <lb></lb>mente dei nostri lettori una fal opinione insinuata non sapremmo dire se <lb></lb>dal poco giudizio, o dal mal anìmo del Guldino. </s></p><p type="main">

<s>Nel cap. </s>

<s>IV del IV libro della Centrobarica trascrive dalla <emph type="italics"></emph>Stereometria <lb></lb>nova<emph.end type="italics"></emph.end> l&#039;interpetrazione che il Keplero dà della prima proposizione archime-<pb xlink:href="020/01/2684.jpg" pagenum="309"></pb>dea della misura del circolo. </s>

<s>Sia questo descritto col raggio AB (fig. </s>

<s>167), <lb></lb>all&#039;estremità del quale si conduca la perpendicolare BC. </s>

<s>La circonferenza, <lb></lb>dice il Kepler, ha tante parti quanti son punti, cioè infinite, su ciascuna delle <lb></lb>quali parti si considerino <lb></lb><figure id="id.020.01.2684.1.jpg" xlink:href="020/01/2684/1.jpg"></figure></s></p><p type="caption">

<s>Figura 167.<lb></lb>insistere, come sopra loro <lb></lb>base, triangoli isosceli, che <lb></lb>vadan tutti in A ad appun­<lb></lb>tarsi nel centro. </s>

<s>Estendasi <lb></lb>poi essa circonferenza in <lb></lb>dirittura, e cominciando da <lb></lb>B termini in C: se da C, da <lb></lb>E, e dagli infiniti altri ponti di divisione, si conducano ad A linee rette, è <lb></lb>manifesto che verranno a disegnarsi triangoli, pari di numero, e di superficie <lb></lb>uguali ai settori del circolo, il quale dunque sarà uguale al triangolo rettan­<lb></lb>golo ABC. <emph type="italics"></emph>Hoc vult,<emph.end type="italics"></emph.end> conclude il Keplero la sua arguta e bellissima interpe­<lb></lb>trazione, <emph type="italics"></emph>illa archimedea ad impossibile deductio: mihi sensus hic esse <lb></lb>videtur.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Parve, soggiunge qui il Guldin, ma non è: questo kepleriano è modo <lb></lb>nuovo di dimostrare, e che, sebbene non sia da disprezzarsi, non ha però <lb></lb>che a riveder nulla con quello di Archimede. </s>

<s>Poco più sotto poi, citando dalla <lb></lb>Stereometria nuova il teorema IV, dove, dall&#039;essersi dimostrato che un pri­<lb></lb>sma colonnare è triplo della piramide sollevatasi a pari altezza dalla mede­<lb></lb>sima base, ne conclude l&#039;Autore, che può il medesimo appropriarsi al cilin­<lb></lb>dro e al cono, riguardandosi quello come un prisma colonnare d&#039;infinito <lb></lb>numero di facce, e questo come una piramide; insinua il Guldino stesso che <lb></lb>a ciò insomma si riduce il metodo del Cavalieri, concludendo il suo discorso <lb></lb>in queste parole: “ Hinc enim ansam arripuit et occasionem Bonaventura <lb></lb>Cavalerius suam Methodum indivisibilium producendi ” (Centrobarycae Gul­<lb></lb>dini, Lib. </s>

<s>IV, Viennae Austriae 1641, pag. </s>

<s>325). </s></p><p type="main">

<s>Giova ora a noi esaminare così fatti giudizi, e prima di tutto, per quel <lb></lb>che spetta al Keplero, domanderemo se quel suo modo di riguardare il <lb></lb>circolo come un poligono d&#039;infinito numero di lati sia da dir propriamente <lb></lb>nuovo. </s>

<s>Il Guldin, com&#039;abbiamo inteso, lo crede, e par lo credano tutti gli <lb></lb>altri, che hanno trovato quello stesso metodo accomodatissimo ad abbreviare, <lb></lb>e a ridurre alla massima facilità i più ardui teoremi della Geometria. </s>

<s>Eppure <lb></lb>il Keplero stesso, invece di gloriarsi di questa cosa, come di sua propria in­<lb></lb>venzione, l&#039;attribuisce ad Archimede, non certamente per liberalità, ma per <lb></lb>giustizia, com&#039;onest&#039;uomo ch&#039;egli era, ed erudito della storia della Ciclome­<lb></lb>tria. </s>

<s>Da Archimede stesso direttamente anzi è notabile che apprendesse il <lb></lb>metodo Leonardo da Vinci, il quale interpetrò quella sopra citata proposi­<lb></lb>zione <emph type="italics"></emph>De circuli dimensione<emph.end type="italics"></emph.end> allo stesso modo, e tanto tempo prima del <lb></lb>Geometra alemanno. </s>

<s>“ Il cerchio, egli dice, è un parallelo rettangolo, fatto <lb></lb>del quarto del suo diametro, e di tutta la circonferenza sua: o vo&#039;dire <lb></lb>della metà del diametro, e della periferia. </s>

<s>Come se il cerchio fosse immagi-<pb xlink:href="020/01/2685.jpg" pagenum="310"></pb>nato essere resoluto in quasi infinite piramidi (triangoli isosceli), le quali poi, <lb></lb>essendo distese sopra la linea retta che tocchi la lor base, e tolto la metà <lb></lb>dell&#039;altezza e fattone un parallelo (un rettangolo); sarà con precisione uguale <lb></lb>al cerchio (MSS. K., fol. </s>

<s>80 r.). Non possiamo perciò non ci maravigliar gran­<lb></lb>demente che non avesse penetrate queste cose il Guldino, il quale compen­<lb></lb>dia nel cap. </s>

<s>I del suo secondo libro la lunga storia ciclometrica, e riferendo <lb></lb>i detti di Eutocio difende il grande Siracusano da coloro, che temerariamente <lb></lb>lo accusavano di aver data meno esatta la proporzione tra la circonferenza <lb></lb>e il diametro. </s>

<s>Dice esso Eutocio che Archimede si fermò alla iscrizione del <lb></lb>poligono di 96 lati, perchè si contentava <emph type="italics"></emph>in suo libello proposuisse id quod <lb></lb>proprinquum est invenire, propter necessarios vitae usus.<emph.end type="italics"></emph.end> Che del resto la­<lb></lb>sciava ai Matematici la fatica di spingere le divisioni infino alle parti più <lb></lb>minute, mettendoli al punto di poter concludere, come poi fecero con Tolo­<lb></lb>meo altri geometri antichi, e fra&#039;recenti il Keplero, che, riducendosi il me­<lb></lb>todo alle divisioni infinite, il circolo e il poligono inscritto si risponderebbero <lb></lb>esattamente, o per meglio dire si confonderebbero insieme. </s></p><p type="main">

<s>Comunque sia, consentendo pur col Guldin che, per essere stato un tal <lb></lb>metodo rinnovellato ed esteso dal Matematico alemanno, si possa dir <emph type="italics"></emph>keple­<lb></lb>riano;<emph.end type="italics"></emph.end> gli neghiamo però ogni somiglianza con quello elaborato dal Cava­<lb></lb>lieri, il quale citava nel proemio alla sua nuova Geometria la Stereometria <lb></lb>nuova come inspiratrice del concetto degl&#039;indivisibili, non già dalla parte <lb></lb>delle divisioni infinite, ma da quella delle sezioni parallele alla base dei so­<lb></lb>lidi rotondi, a quel modo che nell&#039;altra parte di questa Storia della Mecca­<lb></lb>nica, alla pag. </s>

<s>115, fu descritto. </s>

<s>Chi volesse poi aver della varietà de&#039;due <lb></lb>metodi un esempio efficacissimo non dovrebbe far altro che comparar l&#039;in­<lb></lb>terpetrazione della prima archimedea <emph type="italics"></emph>De circuli dimensione,<emph.end type="italics"></emph.end> data dal Keplero, <lb></lb>con quell&#039;altra che, nel proemio al trattatello <emph type="italics"></emph>De solido acuto hyperbolico,<emph.end type="italics"></emph.end><lb></lb>ne dà il Torricelli. </s>

<s>Qui non si riguarda il circolo come risoluto in infiniti <lb></lb>triangoli appuntati nel centro, ma come intessuto d&#039;infinite circonferenze con­<lb></lb>centriche, a ciascuna delle quali si dimostra essere uguali le linee, di che <lb></lb>s&#039;intesse il triangolo rettangolo avente per l&#039;un de&#039;cateti la circonferenza, e <lb></lb>per l&#039;altro il raggio. </s></p><p type="main">

<s>È anzi notabile che il Cavalieri e il Torricelli s&#039;astenessero dall&#039;usare <lb></lb>il metodo kepleriano, quasi lo reputassero abortivo da quel legittimo degli <lb></lb>indivisibili per essi professato. </s>

<s>Chi per esempio nel trattatello <emph type="italics"></emph>De centro gra­<lb></lb>vitatis sectoris circuli more veterum,<emph.end type="italics"></emph.end> da noi addietro trascritto, non avrebbe <lb></lb>consigliato il Torricelli di cansar la fatica del lungo viaggio, col fare del <lb></lb>lemma IX la proposizion principale, e di lì concluder l&#039;intento, per via di <lb></lb>corollario, senza far altro osservare, se non che l&#039;arco si può riguardar come <lb></lb>composto d&#039;infiniti latercoli rettilinei tutti uguali? </s></p><p type="main">

<s>Mirabile è la facilità, con la quale il Wallis, pur usando il metodo del <lb></lb>Keplero, dimostra il centro di gravità de&#039;settori circolari e sferici, e dello <lb></lb>stesso emisfero. </s>

<s>Nella proposizione XV del suo trattato, considerando il set­<lb></lb>tore AMBC (fig. </s>

<s>168) come composto degli infiniti triangoli isosceli appun-<pb xlink:href="020/01/2686.jpg" pagenum="311"></pb>tati in C, i centri de&#039;quali si trovan disposti nell&#039;arco DNE, presa per rag­<lb></lb>gio DC doppia di AC, dice che il punto cercato è G, centro dell&#039;arco, per <lb></lb>cui sarà DNE a DE, come CN a CG, ossia AMB ad AB come due terzi del­<lb></lb>l&#039;asse MC a CG, per giungere alla qual <lb></lb><figure id="id.020.01.2686.1.jpg" xlink:href="020/01/2686/1.jpg"></figure></s></p><p type="caption">

<s>Figura 168.<lb></lb>conclusione era bisognato al padre Della <lb></lb>Faille un libro, e al Torricelli stesso più <lb></lb>di un foglio. </s></p><p type="main">

<s>Che se AMBC rappresenta un settore <lb></lb>sferico, il servigio reso dianzi dagli infiniti <lb></lb>triangoli verrà ora supplito dalle infinite <lb></lb>piramidi esse pure appuntate in C, le quali, <lb></lb>avendo i loro centri di gravità disposti sulla <lb></lb>callotta DNE, descritta con un raggio CD, <lb></lb>che sia triplo della linea AD; faranno che <lb></lb>il punto G, mezzo della saetta della cal­<lb></lb>lotta, sia il punto cercato, il quale dimo­<lb></lb>stra il Wallis essere <emph type="italics"></emph>in axis sui illo puncto, quod a centro circuli distat <lb></lb>tribus quadrantibus radii, minus tribus octantibus altitudinis superficiei <lb></lb>cavae<emph.end type="italics"></emph.end> (De motu, P. II, Londini 1670, pag. </s>

<s>243). CG infatti è uguale a <lb></lb>CN—NG. </s>

<s>Ma CN=3/4 CM, NG=1/2 NP=3/8 <expan abbr="Mq;">Mque</expan> dunque CG= <lb></lb>3/4 CM—3/8 MQ, ciò che dall&#039;altra parte è facile vedere come concordi con <lb></lb>la invenzione del Torricelli. </s></p><p type="main">

<s>Di qui deduce lo stesso Wallis, per via di corollario, il centro di gra­<lb></lb>vità dell&#039;emisfero, il quale sarà in O, sulla metà del raggio CN, che in que­<lb></lb>sto caso è uguale alla saetta della callotta emisferica, onde, esssendo CN= <lb></lb>3/4 CM, sarà CO=3/8 CM=3/8 (CO+OM) e perciò 5 CO=3 MO, e <lb></lb>MO:CO=5:3, che vuol dire essere il centro di gravità dell&#039;emisfero in­<lb></lb>dicato da quel punto, <emph type="italics"></emph>in quo axis sic dividitur, ut pars ad verticem sit <lb></lb>ad reliquam ut quinque ad tria,<emph.end type="italics"></emph.end> secondo aveva prima di tutti dimostrato <lb></lb>Luca Valerio, nella proposizione XXXIII del secondo libro, e nella XXXV <lb></lb>del terzo, qui è là con lunga, e laboriosa preparazione di lemmi. (De centro <lb></lb>grav., Romae 1604, pag. </s>

<s>56, 61). </s></p><p type="main">

<s>Chi crederebbe che non fosse sovvenuta al Torricelli simile compendiosa <lb></lb>dimostrazione? </s>

<s>Eppure egli la rifiutò, per attenersi allo schietto metodo ca­<lb></lb><figure id="id.020.01.2686.2.jpg" xlink:href="020/01/2686/2.jpg"></figure></s></p><p type="caption">

<s>Figura 169.<lb></lb>valierano, e per dare una prova ai contradittori della <lb></lb>fecondità e della varietà di lui, applicandolo a di­<lb></lb>mostrar le medesime cose negli esempi, che ora <lb></lb>trascriveremo, incominciando dal citato capitolo, <lb></lb>dove si proponeva di dimostrare a priori il centro <lb></lb>del triangolo e del cono, dell&#039;emisferoide e del­<lb></lb>l&#039;emisfero. </s></p><p type="main">

<s>“ PROPOSIZIONE XXI. — <emph type="italics"></emph>Centrum trianguli <lb></lb>diametrum secat in ratione 2 ad 1. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sia un triangolo qualunque ABC (fig. </s>

<s>169), <pb xlink:href="020/01/2687.jpg" pagenum="312"></pb>e congiunto il vertice B con E, mezzo della base, si conducano a BE paral­<lb></lb>lele AI, CD, e si compia il parallelogrammo, sopra i due diametri del quale <lb></lb>BE, PQ graviteranno le infinite linee ponderose condotte parallele ad AC, e <lb></lb>a BE. </s>

<s>Così poi le linee AI, DC, come le LO, MP, e le infinite altre, di che <lb></lb>s&#039;intessono i triangoli esterni, le considera il Torricelli raccolte nei loro mezzi <lb></lb>gravitar, coppia per coppia, sulla bilancia BF, con quella regola, che le linee <lb></lb>del triangolo ABC pesano sopra tutta la BE, supponendo, perchè facile a di­<lb></lb>mostrarsi, il seguente lemma: <emph type="italics"></emph>Due libbre, dalle quali pendano grandezze, <lb></lb>che si eccedano a proporzione delle distanze, son tagliate dal punto del­<lb></lb>l&#039;equilibrio in parti proporzionali.<emph.end type="italics"></emph.end> Dietro ciò, così il Torricelli proponeva, <lb></lb>e dimostrava la verità sopra annunziata: </s></p><p type="main">

<s>“ Esto triangulum quodlibet ABC, sectoque bifariam AC in E, ducatur <lb></lb>BE, et compleatur figura AIDC. </s>

<s>Tum secetur bifariam BE in F, eritque F <lb></lb>centrum parallelogrammi AD. </s>

<s>Centrum vero trianguli ABC sit quodcumque H, <lb></lb>et reliquae figurae sit G. ” </s></p><p type="main">

<s>“ Jam EB est libra, ad quam pendent infinitae numero magnitudines, <lb></lb>nempe rectae ipsi AC parallelae, quarum maxima centrum habet in E, et <lb></lb>minima in B, suntque magnitudines inter se ut longitudines, ad quas pen­<lb></lb>dent, facto initio in B. Item, FB est libra, ad quam pendent magnitudines <lb></lb>numero infinitae, nempe lineae parallelae ipsi AI, in geminis triangulis AIB, <lb></lb>BDC, et maxima magnitudo centrum habet in F, minima vero in B, et sunt <lb></lb>magnitudines inter se ut iam dictae praecedentes, nam duae simul AI, CD, <lb></lb>ad duas OL, PM, sunt ut AI ad OL, sive ut AB ad BO, sive ut EB ad BN, <lb></lb>sive ut semisses earum, nempe FB ad distantiam centri duarum OL, PM a <lb></lb>puncto B. </s>

<s>Propterea centrum trianguli ABC, quod ponitur H, in eadem ra­<lb></lb>tione secabit libram BE, in qua secat libram BF centrum reliquae figurae, <lb></lb>quod est G. </s>

<s>Erit ergo ut BH ad HE, ita BG ad GF, et, componendo permu­<lb></lb>tandoque, EB ad BF ut EH ad FG, nempe EH erit dupla ad FG. </s>

<s>Sed HF, <lb></lb>FG sunt aequales, cum F sit centrum totius, et tam G quam H centra par­<lb></lb><figure id="id.020.01.2687.1.jpg" xlink:href="020/01/2687/1.jpg"></figure></s></p><p type="caption">

<s>Figura 170.<lb></lb>tium aequalium; erit EH, sive BG, dupla rectae <lb></lb>GF. </s>

<s>Ergo patet BH duplam esse ipsius HE ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>97). In modo <lb></lb>analogo a questo si dimostra l&#039;altra. </s></p><p type="main">

<s>“ PROPOSIZIONE XXII. — <emph type="italics"></emph>Centrum coni secat <lb></lb>axem in ratione 3 ad 1 ”<emph.end type="italics"></emph.end> avvertendo che, per es­<lb></lb>sere nella fig. </s>

<s>170, rappresentatrice del cono ABC, <lb></lb>a cui sia circoscritto il cilindro AE, AI:LM= <lb></lb>AB:BM, IB:LB=AB:BM, e perciò AI.IB: <lb></lb>LM.LB=AB2:BM2; le superficie cilindriche de­<lb></lb>scritte dalla conversione delle linee AI, LM intorno <lb></lb>al comune asse BD, che stanno come i rettangoli <lb></lb>delle altezze per i raggi delle basi, cioè come AI.IB <lb></lb>a LM.LB, staranno pure come AB2 a BM2. </s>

<s>Avvertasi inoltre che, supposto <lb></lb>in H il centro di gravità del cilindro scavato, e in G quello del cono, per <pb xlink:href="020/01/2688.jpg" pagenum="313"></pb>esser l&#039;uno doppio dell&#039;altro, dovrà reciprocamente la distanza FH dal cen­<lb></lb>tro F della libbra esser la metà della distanza FG. </s></p><p type="main">

<s>“ Esto conus ABC, cuius axis BD, cylindrus vero circumscriptus AE. </s>

<s><lb></lb>Centrum cylindri F, coni sit quodvis punctum G, et reliqui solidi sit H. ” </s></p><p type="main">

<s>“ Jam BD libra est, ad quam pendent infiniti numero circuli ipsi AC <lb></lb>paralleli, quoruu maximus centrum habet in D, minimus in B, suntque ma­<lb></lb>gnitudines inter se ut quadrata distantiarum, sive portionum librae initio <lb></lb>facto ex B. ” </s></p><p type="main">

<s>“ Item, FB est libra, ad quam pendent infinitae numero magnitudines, <lb></lb>hoc est superficies cylindricae circa axem BD, quarum maxima centrum <lb></lb>habet F, minima vero B, suntque magnitudines inter se ut iam dictae, nam <lb></lb>cylindrica ex AI, ad cylindricam ex ML, est ut rectangulum AIB, ad rectan­<lb></lb>gulum MLB per axem, sive ut quadratum AB ad BM, vel DB ad BO, sive <lb></lb>ut quadrata semissium ipsarum DB, BO, quae sunt distantiae centri ab <lb></lb>extremo librae B. </s>

<s>Ergo erit, ut BG ad GD, ita BH ad HF, et componendo <lb></lb>permutandoque, ut BD ad DF, ita DG ad FH. </s>

<s>Propterea DG dupla erit ipsius <lb></lb>FH. </s>

<s>Est autem GF dupla ipsius FH, nam F est centrum, ex quo aequipon­<lb></lb>derant magnitudines duplae, propterea DG, GF aequales erunt. </s>

<s>Patet totam <lb></lb>BG ad GD triplam esse ” (ibid., fog. </s>

<s>90). </s></p><p type="main">

<s>Segue alla proposizione un corollario <emph type="italics"></emph>pro centro gravitatis hemisphaeri <lb></lb>et hemisphaeroidis,<emph.end type="italics"></emph.end> il quale però suppone due cose, che vedremo in seguito <lb></lb>dimostrate. </s>

<s>Prima: che, descritta intorno all&#039;asse DB la DP quarta parte di <lb></lb>un ellisse, l&#039;ellissoide generato da lei è uguale al cilindro scavato. </s>

<s>Seconda: <lb></lb>che l&#039;emisfero e l&#039;emisferoide hanno comune il centro di gravità sull&#039;asse <lb></lb>comune. </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollarium.<emph.end type="italics"></emph.end> — Patet centrum hemisphaeri, sive hemisphaeroidis, <lb></lb>axem ita secare, ut partes sint quemadmodum 5 ad 3. Nam consideretur <lb></lb>solidum cylindricum AIEC, dempto cono ABC, non resolutum in superficies <lb></lb>cylindricas ut ante, sed in armillas circulorum parallelorum circulo IE. </s>

<s>So­<lb></lb>lidi erit idem centrum H ut ante. </s>

<s>Sed huiusmodi armillae inter se sunt ut <lb></lb>circuli sphaeroidis, cuius axis sit BD, centrum B, et apex D. </s>

<s>Ergo semisphae­<lb></lb>roidis centrum, in eadem libra BD, idem erit ac praedicti solidi, nempe erit <lb></lb>punctum H. </s>

<s>Patet iam BH ad HD esse ut 3 ad 5 ” (ibid., fol. </s>

<s>91). </s></p><p type="main">

<s>Il metodo degl&#039;indivisibili non esauriva qui la sua virtù in dimostrare <lb></lb>il centro di gravità del cono, ma al Torricelli, che così destramente sapeva <lb></lb>maneggiarlo, suggeriva intanto <lb></lb><figure id="id.020.01.2688.1.jpg" xlink:href="020/01/2688/1.jpg"></figure></s></p><p type="caption">

<s>Figura 171.<lb></lb>due altri esempi, che ora trascri­<lb></lb>veremo. </s>

<s>Per il primo si derivava <lb></lb>dalla Geometria più elementare <lb></lb>il seguente Lemma: <emph type="italics"></emph>Se AB, AC, <lb></lb>AD<emph.end type="italics"></emph.end> (fig. </s>

<s>171) <emph type="italics"></emph>son proporzionali <lb></lb>alle AE, AF, AG, e se le differenze BC, CD sono uguali, saranno pure <lb></lb>uguali le differenze EF, FG.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Abbiamo per supposizione AB:AE=AC:AF. Permutando, AB:AC= <pb xlink:href="020/01/2689.jpg" pagenum="314"></pb>AE:AF. Dividendo, AB—AC:AC=AE—AF:AF. Sostituendo, e nuo­<lb></lb>vamente permutando, BC:EF=AC:AF=AD:AG. </s>

<s>In simil guisa di­<lb></lb>mostreremo CD:FG=AD:AG, onde BC:CD=EF:FG. </s>

<s>Ma per sup­<lb></lb>posizione BC=CD, dunque EF=FG. </s>

<s>Alla qual conclusione si conduce <lb></lb>pure il Torricelli così discorrendo. </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma.<emph.end type="italics"></emph.end> — Si tres rectae lineae BA, CA, DA in aritmetica ratione <lb></lb>fuerint; et earum partes proportionales EA, FA, GA in aritmetica propor­<lb></lb>tione erunt. </s>

<s>” </s></p><p type="main">

<s>“ Esto ut ponitur, nempe BA ad AE ut CA ad AF, et ut DA ad AG. </s>

<s><lb></lb>Cum enim BA ad AE sit ut CA ad AF, erit permutando, dividendo, et rursus <lb></lb>permutando, BC ad EF ut CA ad AF, sive, ob suppositionem, ut DA ad <lb></lb>AG. </s>

<s>Sed eodemmodo ostendetur CD ad FG esse ut DA ad AG, ergo, per <lb></lb>XI Quinti, erit BC ad EF ut CD ad FG. </s>

<s>Sed antecedentia sunt aequalia, <lb></lb>ergo, etc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Aliter.<emph.end type="italics"></emph.end> — Quoniam, per suppositionem, DA ad AE est ut CA ad AF, <lb></lb>erit permutando, dividendo et convertendo, AC ad CB, sive ad aequalem CD, <lb></lb>ut AF ad FE. Amplius, quia CA ad AF est, ob suppositionem, ut DA ad <lb></lb><figure id="id.020.01.2689.1.jpg" xlink:href="020/01/2689/1.jpg"></figure></s></p><p type="caption">

<s>Figura 172.<lb></lb>AG, erit permutando, et per conversionem ratio­<lb></lb>nis, AC ad CD ut AF ad FG. Ergo, per IX Quinti, <lb></lb>aequales sunt GF, et FE, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (ibid., fol. </s>

<s>41). </s></p><p type="main">

<s>Dietro ciò, ecco qual&#039;è il concetto e il modo <lb></lb>della nuova dimostrazione. </s>

<s>Sia il cono ABC <lb></lb>(fig. </s>

<s>172), e dal mezzo E dell&#039;asse BD s&#039;intenda <lb></lb>moversi equabilmente, sempre dentro lo spazio <lb></lb>triangolare, due linee, che si mantengano nei loro <lb></lb>moti contrari equidistanti fra loro, e alla AC. </s>

<s>Se <lb></lb>sopra tutte queste linee, quante son le infinite, <lb></lb>che vanno restringendosi verso il vertice del trian­<lb></lb>golo, e allargandosi verso la base; si costruiscano <lb></lb>rettangoli per l&#039;asse, verrà dalle superficie cilin­<lb></lb>driche descritte da loro a compaginarsi il volume <lb></lb>del cono, il centro di gravità del quale sarà perciò il medesimo di quelle infi­<lb></lb>nite cilindriche superficie. </s></p><p type="main">

<s>Divisa ora ED in mezzo in O, concorreranno in quel punto i centri di <lb></lb>gravità di ciascuna coppia delle dette superficie generate in ugual fase dei <lb></lb>moti opposti. </s>

<s>Siano per esempio IG, LH due di queste fasi, in cui IG tanto <lb></lb>si sia dilungato dal centro verso il vertice, quanto se n&#039;è dilungato LH verso <lb></lb>la base. </s>

<s>Costruiti i rettangoli IP, LF, è facile veder che sono uguali, perchè <lb></lb>FD:DP=NH:MG=NB:MB=MD:ND=GP:FH, d&#039;onde FD.FH= <lb></lb>DP.GP. </s>

<s>Ed essendo i rettangoli per l&#039;asse uguali, come da questa equazion <lb></lb>duplicata si mostra, eguali pure saranno, per la VI torricelliana <emph type="italics"></emph>De solidis <lb></lb>sphacralibus,<emph.end type="italics"></emph.end> le cilindriche superficie (Op. </s>

<s>geom., P. </s>

<s>I cit., pag. </s>

<s>16). </s></p><p type="main">

<s>Se S dunque è il mezzo di ND, e V il mezzo di MD, in S e in V sa­<lb></lb>ranno i centri di gravità delle due superficie cilindriche, e sarà vero che sì <pb xlink:href="020/01/2690.jpg" pagenum="315"></pb>riduce in O il loro centro comune, quando siasi dimostrato che OV, OS <lb></lb>sono uguali. </s>

<s>Ciò che a fare è assai facile, perch&#039;essendo DE—DN=EN, <lb></lb>DM—DE=EM, ed EN, EM uguali; DN, DE, DM sono in proporzione arim­<lb></lb>metica, e in proporzione arimmetica son perciò, per il premesso lemma, an­<lb></lb>che le loro metà DS, DO, DV; onde DO—DS=DV—DO, ossia OS=OV, <lb></lb>come volevasi dimostrare. </s></p><p type="main">

<s>Ciò ch&#039;è delle linee IG, LH, verificandosi di tutte le altre infinite, prese <lb></lb>coppia per coppia nelle uguali fasi dei loro moti opposti; resta dunque così <lb></lb>dimostrato che in O, a tre quarti dell&#039;àsse a partire dal vertice, concorrono <lb></lb>i centri delle infinite superficie cilindriche componenti il cono, e però ivi con­<lb></lb>corre il centro del cono stesso, come il Torricelli annunzia e poi dimostra <lb></lb>nella seguente. </s></p><p type="main">

<s>“ PROPOSIZIONE XXIII. — <emph type="italics"></emph>Centrum gravitatis coni secat axem ut pars <lb></lb>ad verticem sit ad reliqua in ratione 3 ad 1. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Supponitur cylindricas superficies esse inter se ut earumdem rectan­<lb></lb>gula per axem, ex VI primi <emph type="italics"></emph>De solidis sphaeralibus. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto conus ABC, cuius axis BD, et ab omnibus punctis rectae DC in­<lb></lb>telligantur parallelae ad axem BD, quae quidem parallelae totidem cylindri­<lb></lb>cas superficies in revolutione describunt, quae simul omnes cylindricae su­<lb></lb>perficies idem sunt ac ipse conus. </s>

<s>Harum superficierum, si dici hoc potest, <lb></lb>extremae sunt recta DB, et peripheria, cuius diameter AC, illiusque centrum <lb></lb>est punctum E, medium axis BD, istius vero punctum D. (<emph type="italics"></emph>Quae quamvis <lb></lb>scripserim, tamen non sunt necessaria ad demonstrationem<emph.end type="italics"></emph.end>). ” </s></p><p type="main">

<s>“ Secetur libra ED bifariam in O: dico omnes praedictas cylindricas <lb></lb>superficies centrum habere gravitatis in O. </s>

<s>Sumantur IG, LH aequaliter re­<lb></lb>motae a punctis B et D, sintque ipsarum rectangula per axem PI, FL, quae <lb></lb>sunt aequalia, nam FD ad DP est ut PG ad FH. Ergo, per praemissam sup­<lb></lb>positionem, aequales erunt cylindricae superficies. </s>

<s>Sint V, S puncta media <lb></lb>rectarum MD, DN: quoniam CF aequalis est ipsi PD, sive MG, erunt, per <lb></lb>IV Sexti, aequales FH, sive DN et MB. </s>

<s>Ergo DN, DE, DM in aritmetica sunt <lb></lb>proportione, quare etiam earum semisses DS, DO, DV. </s>

<s>Si ergo sunt aequa­<lb></lb>les SO, OV, erit O centrum duarum cylindricarum superficierum FH, PG, <lb></lb>et sic semper. </s>

<s>Ergo O est centrum omnium, nempe coni, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>42). </s></p><p type="main">

<s>Per l&#039;altro modo di dimostrare, sempre con gl&#039;indivisibili, la medesima <lb></lb>proposizione, si premette dal Torricelli il seguente Lemma, per sè stesso evi­<lb></lb>dente: “ Se saranno nella libbra attaccate molte grandezze, le quali stiano <lb></lb>in equilibrio, fatta la sospensione da un punto, stanno anco in equilibrio al­<lb></lb>trettante grandezze sospese dalli medesimi punti, ciascuna delle quali sia <lb></lb>uguale a quella, che prima era nel suo luogo ” (ivi, fol. </s>

<s>10). </s></p><p type="main">

<s>Dietro ciò, l&#039;argomento, in mezzo all&#039;abbondanza nuovo, consiste in <lb></lb>inscrivere nel cono una piramide equivalente di base, e l&#039;altezza della quale <lb></lb>sia lo stesso asse del solido rotondo, il quale asse, se prendasi per libbra, da <lb></lb>cui pendano ora gl&#039;infiniti circoli del cono, ora gl&#039;infiniti triangoli della pi-<pb xlink:href="020/01/2691.jpg" pagenum="316"></pb>ramide, fra loro uguali di grandezza e di numero; è manifesto, in virtù del <lb></lb>premesso lemma, che in ambedue i casi il centro delle grandezze segherà la <lb></lb>libbra nel medesìmo punto. </s>

<s>Tutto l&#039;ingegno dunque del nuovo argomento <lb></lb><figure id="id.020.01.2691.1.jpg" xlink:href="020/01/2691/1.jpg"></figure></s></p><p type="caption">

<s>Figura 173.<lb></lb>si riduceva a risolvere il seguente problema: <lb></lb><emph type="italics"></emph>Dato un circolo, disegnarvi sopra un trani­<lb></lb>golo, che sia di superficie uguale, e in gra­<lb></lb>vità concentrico.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sia il dato circolo col centro in A <lb></lb>(fig. </s>

<s>173), per il quale facciasi passare la <lb></lb>AB di tal lunghezza, che sia un terzo della <lb></lb>periferia, e si prolunghi in C d&#039;altrettanto. </s>

<s><lb></lb>Si alzi sopra questa linea da A una per­<lb></lb>pendicolare AD, uguale a due terzi del <lb></lb>raggio, e si prolunghi al di sotto in E tal­<lb></lb>mente, che AE sia un terzo dello stesso rag­<lb></lb>gio. </s>

<s>Poi si congiungano con D i punti B, C, <lb></lb>e la linea di congiunzione, prolungata, sia in F e in G precisa dalla FG, <lb></lb>condotta alla BC equidistante. </s>

<s>La superficie del triangolo DFG, dice il Tor­<lb></lb>ricelli, è uguale alla superficie del circolo. </s>

<s>Infatti FE:AB=DE:DA=3:2. <lb></lb>Ed essendo AB uguale per costruzione a un terzo della circonferenza, sarà <lb></lb>FE uguale a un mezzo, e perciò FG uguale alla circonferenza intera. </s>

<s>La su­<lb></lb>perficie dunque del triangolo, FG.DE/2, è uguale alla circonferenza moltiplicata <lb></lb>per la metà del raggio, ossia è uguale alla superficie del circolo, ed essendo <lb></lb>AE per costruzione un terzo di AD, che sieno le due figure concentriche in <lb></lb>gravità è manifesto. </s></p><p type="main">

<s>Valgano queste osservazioni a commentare la frettolosa scrittura del Tor­<lb></lb>ricelli, che nella sua concisione potente non manca di naturale chiarezza. </s></p><p type="main">

<s>“ PROPOSIZIONE XXIV. — <emph type="italics"></emph>Il cono ha il centro nell&#039;asse e lo divide in <lb></lb>modo, che la parte ad verticem sia tripla dell&#039;altra. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia il cono, il cui centro della base in A. </s>

<s>Tirisi la BAC utcumque, e <lb></lb>sia AB uguale ad un terzo della periferia: così anco la AC, e sia la AD <lb></lb>due terzi del semidiametro, ed AE un terzo di esso, e finiscasi il triangolo, <lb></lb>il quale sarà uguale al circolo, Facciasi poi una piramide, che abbia la mede­<lb></lb>sima cima con il cono, e segandosi questa figura con piani paralleli alla base <lb></lb>sempre nascerà un circolo nel cono, ed un triangolo nella piramide uguali <lb></lb>fra di loro. </s>

<s>Però, se le grandezze triangolari equiponderano dal punto I, fatta <lb></lb>libbra la AH, anco le circolari equipondereranno dall&#039;istesso ” (ivi). </s></p><p type="main">

<s>Ora è da vedere in quale altro modo, diverso da quello già scritto nella <lb></lb>proposizione XVII qui addietro, facessero gl&#039;indivisibili trovare al Torricelli <lb></lb>il centro di gravità dell&#039;emisfero. </s>

<s>Si fa via alla nuova invenzione con due <lb></lb>proposizioni, riguardanti il centro di gravità de&#039;prismoidi o de&#039;<emph type="italics"></emph>prismali,<emph.end type="italics"></emph.end> così <lb></lb>definiti: <emph type="italics"></emph>Prismale solidum voco solidum illud, quod fit ex sectione obliqua <lb></lb>prismatis triangularis, scrvata una ex faciebus parallelogrammi<emph.end type="italics"></emph.end> (ibid., <pb xlink:href="020/01/2692.jpg" pagenum="317"></pb>fol. </s>

<s>17). Alla prima proposizione, riguardante il baricentro di così fatti pri­<lb></lb>smali, premette il Torricelli stesso il Lemma seguente: </s></p><p type="main">

<s>“ Se sarà un prisma triangolare, di cui <lb></lb><figure id="id.020.01.2692.1.jpg" xlink:href="020/01/2692/1.jpg"></figure></s></p><p type="caption">

<s>Figura 174.<lb></lb>siano le basi opposte ABC, DEF (fig. </s>

<s>174) <lb></lb>e si prolunghi un lato DB, il quale non <lb></lb>sia nelle basi opposte, e preso il punto <lb></lb>H si faccia la piramide CABH; se questa <lb></lb>figura sarà segata con un piano LM pa­<lb></lb>rallelo al parallelogrammo CE, opposto al <lb></lb>lato DB prolungato, sarà la sezione un pa­<lb></lb>rallelogrammo. </s>

<s>Poichè essendo paralleli i <lb></lb>piani LM, AF, sarà la II parallela ad AC, <lb></lb>cioè alla FE, cioè alla MN. </s>

<s>Così anco sarà <lb></lb>IM parallela a CF, cioè alla AE, cioè alla LN. </s>

<s>Quare etc. </s>

<s>” (ivi, fol. </s>

<s>13). </s></p><p type="main">

<s>“ PROPOSIZIONE XXV. — <emph type="italics"></emph>Ogni prismale ha il centro in quella linea, <lb></lb>la quale parte dal centro della base parallelogramma, e va alla metà della <lb></lb>linea opposta. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sia il prismale, la cui base AB (fig. </s>

<s>175) e centro della base C, e la <lb></lb><figure id="id.020.01.2692.2.jpg" xlink:href="020/01/2692/2.jpg"></figure></s></p><p type="caption">

<s>Figura 175.<lb></lb>DCE parallela alla FA, e si tirino dal punto <lb></lb>medio M le ME, MD. Poi, calato qualunque <lb></lb>piano GN parallelo alla base, perchè sono uguali <lb></lb>AE, EP saranno anco GH, HL: e perchè sono <lb></lb>uguali EC, CD saranno anco HI, IO. </s>

<s>Però I <lb></lb>sarà centro del parallelogrammo GN e così di <lb></lb>tutti. </s>

<s>Dunque il centro del perismale sta nella <lb></lb>retta MC, la quale parte dal centro della base <lb></lb>parallelogramma e va alla metà della linea <lb></lb>opposta. </s>

<s>La linea MC la diremo <emph type="italics"></emph>asse<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>18). </s></p><p type="main">

<s>“ PROPOSIZIONE XXVI. — <emph type="italics"></emph>Se sarà un solido, come nella passata, ma <lb></lb>che però la prolungata AB<emph.end type="italics"></emph.end> (fig. </s>

<s>176) <emph type="italics"></emph>sia uguale alla AC, il centro di <lb></lb>questo solido sarà nella linea, la quale parte da A, e va al centro della <lb></lb>figura DE, per la precedente dimostra-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2692.3.jpg" xlink:href="020/01/2692/3.jpg"></figure></s></p><p type="caption">

<s>Figura 176.<lb></lb><emph type="italics"></emph>zione, ma la divide in maniera che la <lb></lb>parte verso A, alla rimanente, sta come <lb></lb>5 a 3. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Prima di trascriver la dimostrazione <lb></lb>di questa, avvertiremo che ella conclude <lb></lb>solo in virtù del seguente teorema geo­<lb></lb>metrico, dal Torricelli supposto già di­<lb></lb>mostrato. <emph type="italics"></emph>Data la linea retta AN<emph.end type="italics"></emph.end> (quella <lb></lb>stessa che entra nella figura) <emph type="italics"></emph>e divisa nelle <lb></lb>sue parti in modo, che sia AP=PN, <lb></lb>PQ=3OQ, AO=2NO; dimostrare che AQ a QN sta come cinque <lb></lb>a tre.<emph.end type="italics"></emph.end> Infatti QN=QO+NO=QO+AO/2=QO+(PN+PQ+OQ)/2= <pb xlink:href="020/01/2693.jpg" pagenum="318"></pb>(PN+PQ+3OQ)/2=(QN+2PQ+3OQ)/2=(QN+6OQ+3OQ)/2= <lb></lb>(QN+9OQ)/2, onde avremo di qui 2QN=QN+9OQ, ossia QN=9Oq. </s>

<s><lb></lb>Rispetto a quell&#039;altra parte della linea, abbiamo AQ=AP+PQ= <lb></lb>PN+PQ=QN+PQ+PQ=QN+2PQ=QN+6Oq. </s>

<s>Sosti­<lb></lb>tuitovi il valore di QN, sarà AQ=9OQ+6OQ=15OQ, e perciò in ul­<lb></lb>timo AQ:QN=15OQ:9OQ=5:3, ciò che dimostrato, come si doveva, <lb></lb>ritorniamo a trascrivere il discorso del Torricelli. </s></p><p type="main">

<s>“ Seghisi MA, sicchè la AH sia doppia di HM, e tirato il piano GHF <lb></lb>parallelo alla faccia DG, sarà in esso il centro del prisma. </s>

<s>Segando poi MA <lb></lb><emph type="italics"></emph>bifariam<emph.end type="italics"></emph.end> in I, e tirato il piano IL parallelo al DG, saranno segate per mezzo <lb></lb>quattro linee della piramide, per la XVII dell&#039;XI, ed in esso sarà il centro <lb></lb>della piramide. </s>

<s>Ora pongasi che il centro del prisma sia R, e della piramide <lb></lb>sia S, e tirisi la RS quale segherà per forza la AN, quale va da A al cen­<lb></lb>tro della faccia DG. ” </s></p><p type="main">

<s>“ Poichè, se in NR è il centro di tutto, ed è anco in AN, però devono <lb></lb>concorrere, e sarà il concorso il centro di tutto. </s>

<s>Sia dunque Q: sarà SQ alla <lb></lb>QR come il prisma alla piramide, cioè tripla. </s>

<s>Immaginiamoci prolungato in <lb></lb>infinito il piano LI, sicchè seghi AN, v. </s>

<s>g. </s>

<s>in P. </s>

<s>Sarà dunque PQ tripla di <lb></lb><expan abbr="Oq.">Oque</expan> Ma essendo AP, PN, siccome sono AI, IM, uguali, ed essendo AO du­<lb></lb>pla di ON, siccome AH è dupla di HM; fatto il conto, sarà tutta la AQ, alla <lb></lb>QN, come 15 a 9, ovvero come 5 a 3 ” (ivi, fol. </s>

<s>186). </s></p><p type="main">

<s>“ PROPOSIZIONE XXVII. — <emph type="italics"></emph>Il centro dell&#039;emisfero è nell&#039;asse in sul <lb></lb>luogo, che sta come cinque a tre. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia il quadrante BAC (fig. </s>

<s>177), il cui asse AC. </s>

<s>Immaginisi AD uguale <lb></lb>alla semiperiferia del circolo, e sia l&#039;angolo BAD retto, e finiscasi il rettan­<lb></lb><figure id="id.020.01.2693.1.jpg" xlink:href="020/01/2693/1.jpg"></figure></s></p><p type="caption">

<s>Figura 177.<lb></lb>golo BD, che sarà uguale al suo cerchio. </s>

<s>Poi tirisi <lb></lb>la BC, e sopra il triangolo BAC facciasi il prisma <lb></lb>BGA, con l&#039;altezza AD, è prodotta AH eguale ad <lb></lb>AC tirisi la HD, sicchè seghi la CG prodotta in E, <lb></lb>e facciasi la piramide FDGE. Tirisi, tra l&#039;appli­<lb></lb>cata MN e per essa, un piano LO parallelo a <lb></lb>piano BD. ” </s></p><p type="main">

<s>“ Che il rettangolo HAC, al rettangolo HNC, <lb></lb>sia come il rettangolo BD ad LO, <emph type="italics"></emph>ratio est<emph.end type="italics"></emph.end> perchè <lb></lb>il rettangolo HAC, al rettangolo HNC, ha ragion <lb></lb>composta di AH ad HN, cioè AD ad NO, e di AC <lb></lb>a CN, ovvero AB ad NL: però sarà il rettangolo <lb></lb>LO eguale al circolo MN. ” </s></p><p type="main">

<s>“ Ora il cerchio AB, al cerchio MN, sta come <lb></lb>il quadrato AB al quadrato MN, cioè come il rettangolo HAC al rettangolo <lb></lb>HNC, ovvero come il rettangolo BD ad LO. </s>

<s>Gli antecedenti sono uguali, ergo <lb></lb>ed i consequenti. </s>

<s>” </s></p><pb xlink:href="020/01/2694.jpg" pagenum="319"></pb><p type="main">

<s>“ Fatta ora libbra AC abbiamo alla libbra attaccate grandezze rettan­<lb></lb>gole, ed altrettante circolari, ciascuna uguale a ciascuna: però li centri sa­<lb></lb>ranno nel medesimo perpendicolo, ovvero il perpendicolo, che passa per i <lb></lb>centri, dividerà la libbra nello stesso punto. </s>

<s>Ma i rettangoli equiponderano, <lb></lb>dal punto che divide la libbra, come cinque a tre; ergo anche i circoli, che <lb></lb>compongono l&#039;emisfero ” (ivi, fol. </s>

<s>15). </s></p><p type="main">

<s>Di questo modo ingegnoso, per ritrovare i baricentri delle figure note, <lb></lb>risolute in piani perpendicolari all&#039;asse, volle dare il Torricelli un altro esem­<lb></lb>pio nel conoide parabolico, adattandolo talmente al prisma triangolare, che <lb></lb>gl&#039;infiniti rettangoli di questo riuscissero proporzionali agl&#039;infiniti circoli di <lb></lb>quello, e ciò egli ottiene prendendo le facce DF, FG uguali (fig. </s>

<s>178), e l&#039;AC, <lb></lb>che sega in mezzo i lati opposti ED, FN, per asse della parabola ALB, il pa­<lb></lb>rametro della quale sia la DE stessa. </s>

<s>Prese le due ordinate BC, LM avremo, per <lb></lb>le note proprietà della curva, BC2:LM2=AC.DE:AM.DE=DF:DH= <lb></lb>FG:HI=<foreign lang="grc">π</foreign>BC2:<foreign lang="grc">π</foreign>LM2, e così essendo sempre, è <lb></lb><figure id="id.020.01.2694.1.jpg" xlink:href="020/01/2694/1.jpg"></figure></s></p><p type="caption">

<s>Figura 178.<lb></lb>dunque vero che i circoli del conoide pendenti dalla <lb></lb>libbra AC son proporzionali ai rettangoli del prisma, <lb></lb>e perciò hanno il centro dell&#039;equilibrio nel mede­<lb></lb>simo punto, per esempio in M, cosicchè AM sia a MC <lb></lb>doppia, come si propone il Torricelli stesso di dimo­<lb></lb>strare concisamente in questa maniera: </s></p><p type="main">

<s>“ PROPOSIZIONE XXVIII. — <emph type="italics"></emph>Il centro del co­<lb></lb>noide parabolico sega l&#039;asse nella proporzione di <lb></lb>due a uno. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia la parabola del conoide la AB, asse AC, <lb></lb>lato retto DE, mezzo <emph type="italics"></emph>utrimque,<emph.end type="italics"></emph.end> e, fatto il rettan­<lb></lb>golo DF, pongasi, eguale ad esso, FG, e ad angolo retto. </s>

<s>Sarà dunque il qua­<lb></lb>drato BC eguale al rettangolo DF, ovvero al rettangolo FG, ed il quadrato <lb></lb>LM sarà uguale al rettangolo DH, ovvero HI, e così di tutti. </s>

<s>Però, essendo <lb></lb>libbra AC, il centro delle une e delle altre magnitudini sarà nel medesimo <lb></lb><figure id="id.020.01.2694.2.jpg" xlink:href="020/01/2694/2.jpg"></figure></s></p><p type="caption">

<s>Figura 179.<lb></lb>perpendicolo. </s>

<s>Ma il centro del prisma sta nel <lb></lb>perpendicolo, che passa per M, quando la AM <lb></lb>è doppia di MC; adunque anche il centro del <lb></lb>conoide. </s>

<s>Ma sappiamo che anco sta nell&#039;asse, <lb></lb>ergo sarà M ” (ivi, fol. </s>

<s>56). </s></p><p type="main">

<s>A simil genere di dimostrazioni, alle quali <lb></lb>sembra che il Torricelli avesse preso gusto, <lb></lb>appartiene anche la seguente, che in questa <lb></lb>parte del trattato da noi si soggiunge come <lb></lb>ultimo esempio: </s></p><p type="main">

<s>“ PROPOSIZIONE XXIX. — <emph type="italics"></emph>Ostendemus <lb></lb>centrum gravitatis portionis parabolae qua <lb></lb>sit in linea, et in quo ipsius puncto. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto portio quaelibet ABC (fig. </s>

<s>179) parabolae, abscissa per rectam <pb xlink:href="020/01/2695.jpg" pagenum="320"></pb>BC, diametro parallelam, ductaque AB, et divisa CA bifariam in L, ductaque <lb></lb>parallela LH, fiat ut HL, ad dimldiam LI, ita CO ad OL; erit in OQ cen­<lb></lb>trum portionis ” (ibid., fol. </s>

<s>29). </s></p><p type="main">

<s>Per dimostrare che in OQ è veramente il centro della porzione ricorre <lb></lb>il Nostro a un terzo termine, che consiste nel riguardare AC come una lib­<lb></lb>bra, gravata dalle infinite linee, che contessono il segmento, a ciascuna delle <lb></lb>quali si vuol che rispondano in proporzione gl&#039;infiniti cerchi di una sfera o <lb></lb>di uno sferoide. </s>

<s>S&#039;immagini rivolgersi intorno ad AG, come ad asse, AFG, <lb></lb>semicirconferenza o semiellisse che ella sia: se dentro ad essa tirisi AF, e <lb></lb>la HL si prolunghi in M, è facile dimostrare che da una tal costruzione è <lb></lb>conseguito l&#039;intento. </s>

<s>Essendo infatti, per la parabola, HL:BC=AL.LG: <lb></lb>AC.CG, e per il circolo o la ellisse LM2:CF3=AL.LG:AC.CG; sarà <lb></lb>HL:BC=LM2:CF2. </s>

<s>Dividendo i conseguenti per 4, e osservando che <lb></lb>BC/4=LI/2, e CF2/4=LN2, sarà HL a LI/2, ossia CO ad OL, come LM2 a LN2, <lb></lb>nel qual caso, come vedremo essere dimostrato dal Torricelli in generale <lb></lb>per tutti i conoidei, O è il centro di gravità della porzione sferica descritta <lb></lb>dall&#039;arco AMF, e perciò in O batterà pure il perpendicolo calato dal centro <lb></lb>di gravità del segmento parabolico. </s></p><p type="main">

<s>“ Fiat, dice il Torricelli, circa axem sphaerois, sive sphaera AFG, et, <lb></lb>productis lineis BC, HL in F, M, ducatur AF. CO ad OL est ut HL ad se­<lb></lb>missem LI, sive HL ad 1/4 BC, sive ut quadratum ML ad 1/4 quadrati FC, <lb></lb>nempe ut ML quadratum ad quadratum LN. </s>

<s>Ergo O est centrum portionis <lb></lb>sphaeroidis, vel sphaerae FAC. ” </s></p><p type="main">

<s>“ Sed ad libram AC quaedam magnitudines pendent, quae erunt circuli <lb></lb>sphaeroidis, et aliae quaedam magnitudines, quae sunt lineae portionis pa­<lb></lb>rabolicae, praedictis circulis ex ordine proportionales. </s>

<s>Ergo centra illarum <lb></lb>similiter divident libram. </s>

<s>Propterea parabolicae portionis centrum erit in <lb></lb>recta OQ ” (ibid.). </s></p><p type="main">

<s>Resta a definire il luogo, dove precisamente il punto O si trova sul­<lb></lb>l&#039;asse, il quale dice il Torricelli essere segato in parti tali, che AO ad AC <lb></lb>“ sit ut HL cum LI ad HL. Nam, per praecedentem constructionem, cum <lb></lb>centrum sit in secta per O, erit CO ad OL, ut HL ad semissem LI. </s>

<s>Et com­<lb></lb>ponendo CL ad LO ut HL, cum semisse LI, ad semissem LI. </s>

<s>Et per con­<lb></lb>versionem rationis CL ad CO, ut HL, cum semisse LI, ad HL. </s>

<s>Et duplica­<lb></lb>tis antecedentibus AC ad CO ut bis HL, cum LI, ad HL. </s>

<s>Et dividendo AO <lb></lb>ad OC ut HL cum LI ad HL, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (ibid.). </s></p><p type="main">

<s>Così essendo, perchè il tutto si compone di due parti, l&#039;una delle quali <lb></lb>è la parabola AHB, l&#039;altra il triangolo ABC; “ iungantur, ne conclude il <lb></lb>Torricelli, centra parabolae AHB, et trianguli ABC, et ubi recta coniungens <lb></lb>concurret cum OQ, ibi erit centrum portionis ” (ibid.). </s></p><pb xlink:href="020/01/2696.jpg" pagenum="321"></pb><p type="main">

<s><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;aver dato alla Baricentrica questa varietà di metodi nuovi non quie­<lb></lb>tava l&#039;animo del Torricelli, che rivolse l&#039;operosa fecondità dell&#039;ingegno in­<lb></lb>torno a immaginar solidi nuovi, quali sarebbero gli scavati e i vasiformi. </s>

<s><lb></lb>Vedremo come di questi gli venisse l&#039;occasione da quel solido acuto iperbo­<lb></lb>lico, che non cessa, dopo due secoli e mezzo, di destar la maraviglia nei Ma­<lb></lb>tematici, ma di quelli, cioè de&#039;solidi scavati, principio alla ricerca dei centri <lb></lb>di gravità furono i centri delle porzioni di sfera, che tanto si desideravano, <lb></lb>dopo quello dei settori, a cui s&#039;erano in questo argomento arrestate le inven­<lb></lb>zioni dello stesso Torricelli. </s></p><p type="main">

<s>Luca Valerio aveva tutte esaurite le sue forze nell&#039;emisfero, ma in quel <lb></lb>secondo modo d&#039;indicarne il centro di gravità, togliendo dal cilindro circo­<lb></lb>scritto la scodella esterna, la quale si dimostrava uguale a un cono, vede­<lb></lb>vasi il Torricelli aperta innanzi la via di giungere al suo proprio intento. </s>

<s>La <lb></lb>proposizione scritta nel terzo libro <emph type="italics"></emph>De centro gravitatis solidorum,<emph.end type="italics"></emph.end> ammi­<lb></lb>rata per la sua novità, era stata resa anche più cospicua da Galileo, il quale, <lb></lb>come i nostri Lettori già sanno, la citò, nella prima giornata delle due Scienze <lb></lb>nuove, per concluder da lei che il metodo degli indivisibili era un assurdo. </s>

<s><lb></lb>Il Torricelli invece l&#039;andava predicando come la vena, e la miniera inesausta <lb></lb>delle speculazioni belle, quali giusto son queste che ora diremo, e che gli <lb></lb>occorsero alla mente dal ripensare in che modo si potessero ridurre alla fa­<lb></lb>cile brevità del metodo cavalierano i lunghi e faticosi processi del Valerio e <lb></lb>di Galileo. </s></p><p type="main">

<s>Ma il modo glielo suggeriva lo stesso Cavalieri, il quale, nel terzo libro <lb></lb>della sua Geometria nuova, dimostrava in quinto luogo questo teorema: Sia <lb></lb>BDHF (fig. </s>

<s>180) circolo o ellisse: BH, DF gli assi <lb></lb><figure id="id.020.01.2696.1.jpg" xlink:href="020/01/2696/1.jpg"></figure></s></p><p type="caption">

<s>Figura 180.<lb></lb>coniugati o i diametri, sopra l&#039;un de&#039;quali, per esem­<lb></lb>pio sopra DF, come sopra base, e circa l&#039;asse o il <lb></lb>diametro EB sian descritti il rettangolo AF e il trian­<lb></lb>golo AEC. </s>

<s>Sia dovunque, per esempio in M, perpen­<lb></lb>dicolarmente attraversato l&#039;asse dalla RV, la quale <lb></lb>seghi i lati del triangolo in N, S, e gli archi del <lb></lb>circolo o dell&#039;ellisse in I, T, e si rivolga tutta in­<lb></lb>sieme la figura intorno ad EB: “ dico ergo, scrive <lb></lb>il Cavalleri, quadratum SN aequari reliquo quadrato <lb></lb>VR, dempto quadrato TI ” (Bononiae 1635, Lib. </s>

<s>III, pag. </s>

<s>11). </s></p><p type="main">

<s>Così essendo, ragionava il Torricelli, presi i suqquadrupli, avremo SN2/4= <lb></lb>((VR+TI)/2)((VR—TI)/2), ossia SM2=VI.IR. </s>

<s>Ma il quadrato di SM stando <pb xlink:href="020/01/2697.jpg" pagenum="322"></pb>al rettangolo sotto VI, IR come il circolo descritto dal raggio SM all&#039;armilla <lb></lb>descritta da IR o da VT intorno all&#039;asse, e così essendo di tutti gl&#039;infiniti <lb></lb>circoli e delle armille infinite; sarà dunque il cono uguale alla scodella. </s></p><p type="main">

<s>Mentre che il Torricelli si compiaceva fra sè di esser giunto con tanta <lb></lb><figure id="id.020.01.2697.1.jpg" xlink:href="020/01/2697/1.jpg"></figure></s></p><p type="caption">

<s>Figura 181.<lb></lb>facilità a dimostrare ciò che al Valerio <lb></lb>e a Galileo era costato tanta fatica, <lb></lb>prendeva animo di valersi della speri­<lb></lb>mentata potenza di questo nuovo stru­<lb></lb>mento, per ritrovare il centro nelle <lb></lb>porzioni di sfera. </s>

<s>Sia dunque AGBHC <lb></lb>(fig. </s>

<s>181) la proposta porzione, la quale <lb></lb>si risolva nel cono del triangolo ABD, <lb></lb>e nel solido del bilineo AGB. </s>

<s>Sarebbe <lb></lb>il problema risoluto, quando si sapesse <lb></lb>la proporzione che hanno le armille <lb></lb>esterne, rispetto ai circoli. </s>

<s>Intorno a che <lb></lb>studiando il Torricelli riuscì a un&#039;in­<lb></lb>venzione mirabile, inaspettata, qual&#039;era <lb></lb>che il solido del bilineo si uguagliava <lb></lb>allo sferoide descritto da una semiellisse, avente per asse maggiore BD, e il <lb></lb>minore uguale alla metà di AB. </s></p><p type="main">

<s>Il mezzo poi dell&#039;invenzione è d&#039;incredibile facilità, perchè, supponen­<lb></lb>dosi essere la DFB la detta semiellisse, se il minore asse di lei FE inten­<lb></lb>dasi prolungato in G, e si conduca qualunque altra ordinata LP, s&#039;avranno, <lb></lb>per le geometriche proprietà assai ben note, le seguenti equazioni: LN.NM: <lb></lb>GI.IH=AN.NB:AI.IB=DP.PB:DE.EB=OP2:FE2. </s>

<s>Ma essendo <lb></lb>AI=IB, perchè E è il mezzo di BD, e IB=EF per costruzione, GI.IH= <lb></lb>FE2: dunque anche LN.NM=PO2. </s>

<s>Onde le armille LN, GI saranno uguali <lb></lb>ai circoli OP, FE, e, così essendo sempre, il solido del bilineo sarà uguale allo <lb></lb>sferoide, come, così avendo proposto il Torricelli, dimostrava con queste sue <lb></lb>proprie parole: </s></p><p type="main">

<s>“ Si ex segmento sphaerico ABC (nella precedente figura) dematur co­<lb></lb>nus inscriptus, erit reliquum solidum sphaericum excavatum aequale sphae­<lb></lb>roidi, cuius axis sit BD, diameter vero EF sit aequalis semissi rectae AB. ” </s></p><p type="main">

<s>“ Nam ducto plano quodlibet LM, ad axem erecto, erit rectangulum LNM, <lb></lb>ad GIH, ut ANB ad AIB, ob aequalitatem, per XXXV. Tertii, sive ut DPB <lb></lb>ad DEB, nam omnes ex iisdem rationibus componuntur, sive ut quadrata PO <lb></lb>et EF, ob ellipsim. </s>

<s>Sed conseguentia ponebantur aequalia, ob suppositionem, <lb></lb>ergo etiam antecedentia, nempe rectangulum LNM quadrato PO aequale est, <lb></lb>ideoque armilla LN circulo OP et hoc semper. </s>

<s>Ergo omnes simul armillae, <lb></lb>sive solidum sphaericum excavatum, omnibus simul circulis, nempe sphae­<lb></lb>roidi, aequales sunt ” (MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>37). </s></p><p type="main">

<s>Essendo ora in E il centro dello sferoide, e, presa BP tripla di PD, in P <lb></lb>il centro del cono; non resterebbe che a sapere la proporzione, che passa tra <pb xlink:href="020/01/2698.jpg" pagenum="323"></pb>la misura dei due solidi, per avere il centro del tutto: sembrava tendere a <lb></lb>ciò il corollario dallo stesso Torricelli ivi soggiunto: “ Solidum ergo exca­<lb></lb>vatum, ad conum ABC, erit ut sphaerois praedicta ad eumdem conum, nempe <lb></lb>ut duo quadrata FE ad quadratum AD, sive ut duo rectangula AIB ad qua­<lb></lb>dratum AD ” (ibid.). Ma volendosi riferire il ritrovato centro della porzione <lb></lb>sferica all&#039;asse, conduceva all&#039;intento direttamente quest&#039;altro teorema, di­<lb></lb>mostrato dal Cavalieri nel citato libro della Geometria nuova: “ Sit circu­<lb></lb>lus BARC cuius axis vel diameter BR, ad quem ordinatim applicetur AC, <lb></lb>abscindens utcumque portionem ABC, et centrum sit <expan abbr="q.">que</expan> Dico omnia quadrata <lb></lb>portionis ABC ad omnia quadrata trianguli ABC esse ut composita ex dimi­<lb></lb>dio totius BR, idest QR, et ipsa DR, ad eamdem DR ” (Editio cit., pag. </s>

<s>1). Di <lb></lb>qui derivava nel manoscritto torricelliano la proposizione e la pratica seguente: </s></p><p type="main">

<s>“ PROPOSIZIONE XXX. — <emph type="italics"></emph>Segmenti sphaerici ABC<emph.end type="italics"></emph.end> (sempre nella me­<lb></lb>desima figura) <emph type="italics"></emph>centrum gravitatis reperire. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Seca bifariam BD in E, et PD sit 1/3 BD, et sphaerae diameter BR <lb></lb>bifariam secetur in <expan abbr="q.">que</expan> Deinde fac ut DR ad RQ, ita ET ad TP, et erit T <lb></lb>centrum quaesitum, ” verità conseguente dai premessi principii, e confermata, <lb></lb>con questa nota illustrativa, dal Viviani: “ Nam, si intelligamus in segmento <lb></lb>conus inscriptus ABC, erit P centrum coni, et E centrum reliqui solidi, dempto <lb></lb>cono, cum alibi ostensum sit solidum genitum a bilineo AB aequari sphae­<lb></lb>roidi cuidam, cuius centrum est in E. </s>

<s>Sed totum segmentum ABC, ad co­<lb></lb>num inscriptum ABC (per Iam Tertii Geometriae Cavalerii), est ut QR cum <lb></lb>DR ad DR; ergo, dividendo, solidum bilineum AB, ad conum ABC, erit ut <lb></lb>QR ad DR. </s>

<s>Et convertendo conus ad solidum erit ut DR ad QR, vel ut ET <lb></lb>ad TP. </s>

<s>Ergo magnitudines distan­<lb></lb><figure id="id.020.01.2698.1.jpg" xlink:href="020/01/2698/1.jpg"></figure></s></p><p type="caption">

<s>Figura 182.<lb></lb>tiis e contrario respondent, idcirco <lb></lb>T erit centrum commune magni­<lb></lb>tudinum, nempe segmenti sphaerici <lb></lb>ABC, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XXXV, fol. </s>

<s>37). </s></p><p type="main">

<s>Indicato così il centro di gra­<lb></lb>vità del segmento sferico, e mo­<lb></lb>strate le ragioni perchè fosse que­<lb></lb>sta indicazione da tenersi per vera, <lb></lb>rimaneva a cercar dove si dovesse <lb></lb>collocare sull&#039;asse il centro di gra­<lb></lb>vità del frusto. </s>

<s>Rappresentandolo <lb></lb>nella figura ABCD (182) fu primo <lb></lb>pensiero del Torricelli di risolverlo <lb></lb>nel segmento EFG, la regola ba­<lb></lb>ricentrica del quale era stata dianzi indicata, e nel solido generato dal quadri­<lb></lb>lineo ABFE, che bisognava studiarsi di ridurre a qualche solido comunemente <lb></lb>noto. </s>

<s>Lo studio riuscì anche questa volta felicemente, nel modo che segue: </s></p><p type="main">

<s>“ Si ex frusto sphaerico ABCD, planis parallelis abseisso, demptum sit <pb xlink:href="020/01/2699.jpg" pagenum="324"></pb>segmentum sphaericum EFG concentricum et aequealtum, erit reliquum so­<lb></lb>lidum excavatum aequale cylindro KC, super basi BC constituto, et aequealto. </s>

<s><lb></lb>Nam, ducto ubicumque plano LM ad axem erecto, erit circulus LM, ad QV, <lb></lb>ut quadratum LN ad quadratum <expan abbr="Nq.">Nque</expan> Et, dividendo, armilla cuius latitudo <lb></lb>LQ, ad circulum QV, erit ut rectangulum LQM ad quadratum QN. </s>

<s>Sed cir­<lb></lb>culus QV, ad circulum BC, est ut quadratum QN ad BF; ergo ex aequo erit <lb></lb>armilla LQ, ad circulum BC, ut rectangulum LQM ad quadratum BF, nempe <lb></lb>aequalis est, et hoc semper. </s>

<s>Ergo omnes simul armillae, hoc est solidum <lb></lb>excavatum quale dictum est, aequales erunt omnibus simul circulis, nempe <lb></lb>cylindro KC ” (ibid., fol. </s>

<s>37). </s></p><p type="main">

<s>Dell&#039;applicazione però di questo lemma non ci è nel manoscritto torri­<lb></lb>celliano altro che il principio nell&#039;appresso </s></p><p type="main">

<s>“ PROPOSIZIONE XXXI. — <emph type="italics"></emph>Frusti sphaerici ABCD centrum reperire. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Seca FX ita ut XH sit 1/2, XI 1/3 totius FX, et centrum sphaerae sit T. </s>

<s><lb></lb>Fac ut XY ad XT, ita HO ad OI ut supra, et hoc serva.... ” (ibid., fol. </s>

<s>214). </s></p><p type="main">

<s>Il Viviani pensò di ridurre la proposizione compiuta, facendo osservare <lb></lb>che intanto era indicato in O il centro di gravità del segmento sferico, a cui <lb></lb>bisognava aggiungere il solido generato dal quadrilineo ABFE, che s&#039;è di­<lb></lb>mostrato uguale al cilindro CK. </s>

<s>Di tali due parti si compone il frusto, ma <lb></lb>si faceva dal Viviani stesso notare che il segmento e il solido descritto dal <lb></lb>trilineo ABK sono uguali, ond&#039;è che le parti componenti si riducono al detto <lb></lb>trilineo, e al cilindro inscritto. </s>

<s>Di quello il centro è O, medesimo che del <lb></lb>segmento, di questo è in H, a mezzo l&#039;asse FX. </s>

<s>Facendosi dunque come HS <lb></lb>a SO, così reciprocamente il solido del trilineo al cilindro inscritto; sarà in S <lb></lb>il centro cercato. </s></p><p type="main">

<s>“ Et erit O (soggiunge all&#039;interrotta scrittura torricelliana il Viviani) <lb></lb>centrum solidi a trilineo ABK geniti, cum sit centrum portionis sphaericae <lb></lb>EFG, quae aequatur dicto solido. </s>

<s>Sed H est centrum cylindri inscripti KC, <lb></lb>ergo centrum frusti ABCD est inter H et O. </s>

<s>Si fiat ergo ut HS ad SO, ita <lb></lb>solidum a trilineo ABK, ad cylindrum CK, erit S centrum frusti ABCD ” <lb></lb>(ibid., T. XXXV, fol. </s>

<s>138). </s></p><p type="main">

<s>Del trilineo, che è uguale al segmento, e del cilindro si possono dalla Geo­<lb></lb>metria aver le misure, alle quali son proporzionali le indicate parti dell&#039;asse, <lb></lb>e il problema sarebbe perciò risoluto. </s>

<s>Ma se il Torricelli ne lasciò la solu­<lb></lb>zione incompiuta, non dovette essere senza un motivo, che a noi giova d&#039;in­<lb></lb>vestigare. </s>

<s>Si potrebbe credere che fosse stato perchè la formula non gli riu­<lb></lb>sciva della consueta semplicità ed eleganza, e poniamo che vi concorresse <lb></lb>anche questa ragione, la principale nulladimeno fu quella di voler avere il <lb></lb>vantaggio sopra Luca Valerio. </s>

<s>Nelle due ultime proposizioni trascritte la su­<lb></lb>periorità del Torricelli consisteva solamente nel comprendersi insieme i due <lb></lb>casi, che il centro della sfera intera rimanesse così dentro, come fuori del­<lb></lb>l&#039;asse della porzione, ma si seguitava pure a distinguere il caso che la por­<lb></lb>zione contemplata avesse una sola, o due basi, porgendo della stessa sfera ora <lb></lb>un semplice segmento, ora un frusto. </s></p><pb xlink:href="020/01/2700.jpg" pagenum="325"></pb><p type="main">

<s>Si voleva dunque da esso Torricelli anche in ciò superare il Valerio, <lb></lb>che, nel suo secondo libro <emph type="italics"></emph>De centro gravitatis,<emph.end type="italics"></emph.end> aveva distinte sei proposi­<lb></lb>zioni, per dimostrare il centro di gravità delle porzioni sferiche, secondo che <lb></lb>il centro della figura intera riman dentro o fuori dell&#039;asse, e secondo che <lb></lb>esso asse tocca con ambedue le estremità i piani secanti, o ne tocca uno <lb></lb>solo, perchè l&#039;altro svanisce; comprendendo tutte queste verità in una pro­<lb></lb>posizione universalissima, a condur la quale riuscì esso Torricelli felicemente, <lb></lb>supposte le cose, per le due precedenti già dimo­<lb></lb><figure id="id.020.01.2700.1.jpg" xlink:href="020/01/2700/1.jpg"></figure></s></p><p type="caption">

<s>Figura 183.<lb></lb>strate, aggiuntovi quest&#039;altro lemma, che dice: <lb></lb>“ Se sarà un cilindro ed un cono intorno al me­<lb></lb>desimo asse, il cilindro al cono sta come tre <lb></lb>quadrati AB (fig. </s>

<s>183) al quadrato AC. </s>

<s>Poichè il <lb></lb>cilindro BE al cilindro CD sta come il quadrato <lb></lb>AB al quadrato AC, <emph type="italics"></emph>sumptisque consequentium <lb></lb>triplis,<emph.end type="italics"></emph.end> il cilindro BE al cono sta come il quadrato AB ad un terzo di AC, <lb></lb>ovvero come tre quadrati AB al quadrato AC ” (ivi, T. XXXVI, fol. </s>

<s>53). </s></p><p type="main">

<s>Ecco ora come, preparate queste cose, si dia dal Torricelli, con regola <lb></lb>universalissima, l&#039;invenzione del centro di gravità delle porzioni, comunque <lb></lb>sian segate nella sfera: </s></p><p type="main">

<s>“ PROPOSIZIONE XXXII. — <emph type="italics"></emph>Esto frustum sphaericum planis parallelis <lb></lb>AD, BC<emph.end type="italics"></emph.end> (fig. </s>

<s>184) <emph type="italics"></emph>abscissum, axis EF. </s>

<s>Dico centrum gravitatis ita secare <lb></lb>EF, ut pars ad E terminata sit ad reliquam, ut quadratum BC, cum<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2700.2.jpg" xlink:href="020/01/2700/2.jpg"></figure></s></p><p type="caption">

<s>Figura 184.<lb></lb><emph type="italics"></emph>duobus quadratis EF, duobusque AD, ad <lb></lb>quadratum AD, cum duobus FE, duobus­<lb></lb>que BC. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Fiat segmentum sphaericum GHEIL <lb></lb>concentricum et aeque altum cum frusto, in­<lb></lb>scribaturque conus GEL, et, secto axe bifa­<lb></lb>riam in M, applicetur HMI. </s>

<s>Demonstratum est <lb></lb>solidum sphaericum excavatum GHEBA ae­<lb></lb>quari cylindro, cuius basis sit circulus BC, altitudo vero EF; sive cono, cuius <lb></lb>basis sit tripla circuli BC, altitudo vero EF. </s>

<s>Ergo solidum GHEBA, ad conum <lb></lb>GEL, est ut triplum quadrati EB ad quadratum FG. </s>

<s>Solidum vero excavatum, <lb></lb>factum a bilineo GHE, ad conum eumdem GEL, demonstratum est esse ut <lb></lb>duo rectangula GNE ad quadratum FG. Ergo, per XXIV Quinti, totum simul <lb></lb>solidum ABENG, ad conum GEL, erit ut tria quadrata BE, cum duobus <lb></lb>rectangulis GNE, ad quadratum GF, sive, sumptis duplis, ut sex quadrata <lb></lb>BE, cum quadrato GE, ad duo quadrata GF. ” </s></p><p type="main">

<s>“ Secetur FM bifariam in P: eritque P centrum coni GEL, et est idem <lb></lb>centrum tam solidi GHEBA, quam etiam solidi GHE, propterea M erit cen­<lb></lb>trum totius solidi ABENG. </s>

<s>Fiat ergo ut sex quadrata BE, cum quadrato GE, <lb></lb>ad duo quadrata FG, ita reciproce recta PO ad OM, et erit O centrum gra­<lb></lb>vitatis totius frusti sphaerici. </s>

<s>” </s></p><p type="main">

<s>“ Iam argumenta sunt componendo, duplicando antecedentia, per con-<pb xlink:href="020/01/2701.jpg" pagenum="326"></pb>versionem rationis, duplicando antecedentia, dividendo, et postea facta re­<lb></lb>ductione. </s>

<s>Per constructionem est recta PO ad OM ut sex quadrata BE, cum <lb></lb>quadrato EG, ad duplum quadrati FG. Componendo, PM ad OM erit ut sex <lb></lb>quadrata BE, cum quadrato EG et duplo quadrati FG, ad duplum quadrati <lb></lb>FG. </s>

<s>Duplicando antecedentia, FM, ad MO, erit ut 12 quadrata BE, cum <lb></lb>2EG+4FG, ad 2FG. </s>

<s>Per conversionem rationis, MF ad FO ut 12BE+ <lb></lb>2EG+4FG ad 12BE+2EG+2FG. </s>

<s>Duplicando antecedentia, EF ad <lb></lb>FO ut 24BE+4EG+8FG, ad 12BE+2EG+2FG. Dividendo, EO <lb></lb>ad OF ut 12BE+2EG+6FG ad 12BE+2EG+2FG. ” </s></p><p type="main">

<s>“ Sed quoniam rectangulum AGD quadrato BE est aequale, erit diffe­<lb></lb>rentia quadratorum AF, BE. </s>

<s>Ergo potest fieri reductio talis, mutato prius <lb></lb>quadrato EG cum quadratis EF, FG. </s>

<s>Sic EO ad OF est ut 12BE+2EF+ <lb></lb>8FG, ad 12BE+2EF+4FG. Vel, facta reductione, EO ad OF est ut <lb></lb>4BE+2EF+8AF ad 8BE+2EF+4AF. Vel, facta ultima re­<lb></lb>ductione, EO ad OF est ut quadratum BC, cum duobus EF duobusque AD, <lb></lb>ad 2BC+2EF+uno AD, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (ibid., fol. </s>

<s>39). </s></p><p type="main">

<s>Notabile fra tutte le altre passate è questa proposizione, non solo riguar­<lb></lb>data in sè stessa, ma nel suo processo dimostrativo, che offre il primo esem­<lb></lb>pio, dato dal Torricelli nella Scuola galileiana, per tentar di vincere la ritrosia <lb></lb>contro i metodi analitici, ritrovati tanto utili allora dai Matematici francesi. </s>

<s><lb></lb>Se ne compiacque il Nostro non poco, e annunziando il teorema a Miche­<lb></lb>langiolo Ricci, il di 7 Marzo 1642, pochi giorni dopo averlo dimostrato, gli <lb></lb>diceva: “ Giacchè V. S. studia Luca Valerio, eccogli una proposizione, che <lb></lb>ne abbraccia molte di Luca Valerio. </s>

<s>Giudichi V. S. chi la porti meglio o egli <lb></lb>o io. </s>

<s>Se sarà un frusto di sfera ABCD (nella preced. </s>

<s>figura) tagliato co&#039;piani <lb></lb>paralleli AD, BC, o passino per il centro sì o no, o l&#039;intraprendano sì o no, <lb></lb>e sia l&#039;asse del frusto EF, e centro di gravità O; sarà la retta EO alla retta <lb></lb>OF come il quadrato AB, con due quadrati EF, e due quadrati DC, ad un <lb></lb>quadrato DC, con due quadrati EF, e due quadrati AB. </s>

<s>Se V. S. la comu­<lb></lb>nica al sig. </s>

<s>Raffaello (Magiotti) so certo che l&#039;avrà cara, perchè sui libri non <lb></lb>la troverà portata a questo modo ” (ivi, T. XL, fol. </s>

<s>100). </s></p><p type="main">

<s>Un anno dopo, dando la medesima notizia al Cavalieri si compiaceva di <lb></lb>fargli notare che il suo processo era molto più spedito che quello di Luca Va­<lb></lb>lerio, “ ed è, soggiungeva, universale, o sia intrapreso il centro o no. </s>

<s>Insomma <lb></lb>a me pare che, per via degli indivisibili, si trovino, oltre le innumerabili e <lb></lb>maravigliose di V. P., anco tuttavia delle conclusioni da non sprezzarsi, e <lb></lb>che, se io le trovassi in altri, mi parrebbero speciose. </s>

<s>Come dunque questa <lb></lb>dottrina non è da stimarsi? </s>

<s>Se costoro ammettessero le conclusioni per belle, <lb></lb>come credo che bisogni concedere, converrà pur anco approvare le dottrine: <lb></lb>ovvero, se lodano le conclusioni e non le dottrine, almeno doveranno mo­<lb></lb>strare che ve ne siano delle false, ma credo che dureranno fatica ” (ivi, <lb></lb>fol. </s>

<s>123). </s></p><p type="main">

<s>Fra i <emph type="italics"></emph>Problemi proposti ai Matematici di Francia<emph.end type="italics"></emph.end> era notato anche <lb></lb>quello del centro di gravità nel frusto sferico, e, dopo averlo enumerato, sog-<pb xlink:href="020/01/2702.jpg" pagenum="327"></pb>giungeva il Torricelli così, nel suo <emph type="italics"></emph>Racconto:<emph.end type="italics"></emph.end> “ Questa enunciazione, con po­<lb></lb>chissime mutazioni, si riduce a comprendere anco i frusti, ed i segmenti <lb></lb>della sferoide. </s>

<s>Così, in una sola e facilissima enunciazione, si vedono ristrette <lb></lb>molte e difficilissime proposizioni ignote agli antichi, ma dimostrate da L. </s>

<s>Va­<lb></lb>lerio con molte proposizioni, e con diversissime enunciazioni, non essendosi <lb></lb>accorto che, sotto una sola, semplicissima e universale, si potevano compren­<lb></lb>dere tutti i casi, sopra i quali egli forma proposizioni tanto diverse ” (ivi, <lb></lb>T. XXXII, fol. </s>

<s>23). </s></p><p type="main">

<s>Che sia veramente la proposizione torricelliana universalissima e gene­<lb></lb>rale si conferma dai seguenti corollari: Sia il frusto sferico a una sola base <lb></lb>come per esempio ABC (fig. </s>

<s>185), il quadrato dell&#039;altra <lb></lb><figure id="id.020.01.2702.1.jpg" xlink:href="020/01/2702/1.jpg"></figure></s></p><p type="caption">

<s>Figura 185.<lb></lb>base è zero, e perciò sarà in questo caso BO:OD= <lb></lb>2(BD2+AC2):AC2+2 DB2, come fa osservare lo stesso <lb></lb>Torricelli: “ In segmento sphaerico superioris figurae <lb></lb>quadratum BC (nella figura 184) penitus evanescit. </s>

<s>Ergo <lb></lb>recta BO ad OD est ut duo quadrata BD+2 AC, ad <lb></lb>quadratum AC+2 DB ” (ibid., T. XXV, fol. </s>

<s>74). </s></p><p type="main">

<s>Che se il frusto sferico ha una base sola, e questa sia uguale a un cir­<lb></lb>colo massimo, BO sta a OD come 5 a tre: ciò che conferma il già dimo­<lb></lb>strato in altri modi, essendo allora il frusto un emisfero, e si conclude dalla <lb></lb>formula della proposizion generale, illustrata dalla figura 184, e così scritta: <lb></lb>EO:OF=BC2+2(EF2+AD2):2(BC2+EF2)+AD2. </s>

<s>Essendo nell&#039;emi­<lb></lb>sfero BC2=O, AD=2EF, la detta formula si trasformerà nella seguente: <lb></lb>EO:OF=2EF2+8EF2:2EF2+4EF2=10:6=5:3. <lb></lb><figure id="id.020.01.2702.2.jpg" xlink:href="020/01/2702/2.jpg"></figure></s></p><p type="caption">

<s>Figura 186.</s></p><p type="main">

<s>Che poi in quella universalità si comprendano an­<lb></lb>che i frusti e i segmenti dello sferoide intendeva il Tor­<lb></lb>ricelli di dimostrarlo, con questa proposizione: “ In fru­<lb></lb>sto sphaeroidali ABCD (fig. </s>

<s>186) centrum gravitatis O <lb></lb>secat EF in eadem ratione, ac si esset frustum sphae­<lb></lb>ricum circa axem GH, et aeque altum ” (ibid., T. XXV, <lb></lb>fol. </s>

<s>74). Invece della dimostrazione però si trovano nel <lb></lb>manoscritto le due seguenti osservazioni: “ Ciò che si <lb></lb>dice del cerchio si può trasportare all&#039;ellisse, perchè le <lb></lb>linee tutte del cerchio hanno la medesima proporzione, <lb></lb>che quelle dell&#039;ellisse: però il punto dell&#039;equilibrio sega la libbra <emph type="italics"></emph>in eadem <lb></lb>ratione.<emph.end type="italics"></emph.end> — Quello che si dice della sfera si può trasportare alla sferoide, <lb></lb>perchè tutti i circoli della sfera sono tra di loro come tutte le ellissi della sfe­<lb></lb>roide ” (ivi, T. XXX, fol. </s>

<s>40). </s></p><p type="main">

<s>Avendosi infatti, per le note proprietà geometriche delle due figure, <lb></lb>LE2:MF2=BE2:AF2, ossia <foreign lang="grc">π</foreign>LE2:<foreign lang="grc">π</foreign> MF2=<foreign lang="grc">π</foreign> BE2:<foreign lang="grc">π</foreign>AF2, fatta EF lib­<lb></lb>bra, dovrà questa, per il lemma XXII alla XIV <emph type="italics"></emph>De dimensione parabolae<emph.end type="italics"></emph.end><lb></lb>altre volte citato, avere il medesimo punto dell&#039;equilibrio, o sia ella gravata <lb></lb>dal circolo LE, con tutti gli altri infiniti, che compongono il frusto sferico; <lb></lb>o sia gravata dal circolo BE, con tutti gli altri infiniti, che compongono il <pb xlink:href="020/01/2703.jpg" pagenum="328"></pb>frusto sferoideo, perchè ha un solido all&#039;altro la medesima proporzione. </s>

<s>“ Ergo <lb></lb>in sphaeroide (essendo BC2=4BE2=4GEH, AD2=4AF2=4HFG) <lb></lb>EO ad OF est ut duo rectangula GEH+quadrato EF+4 rectangulis <lb></lb>HEG ” (ivi, T. XXV, fol. </s>

<s>74). </s></p><p type="main">

<s>Se la base superiore svanisce, ossia se BC, e con esso GE, si riducono <lb></lb>a zero, anche il rettangolo GE.EH è zero, e la formula si trasforma nella <lb></lb>seguente EO:OF=EF2+4GFH:EF2+2GFH. </s>

<s>Che se, mentre da una <lb></lb>parte svanisce la base superiore, l&#039;inferiore diventa il circolo massimo del <lb></lb>fuso ellittico, ossia, se il frusto si riduce all&#039;emisferoide, GFH=EF2, e perciò <lb></lb>EO:OF=EF2+4EF2:EF2+2EF2=5:3, come in seguito vedremo <lb></lb>dimostrarsi dall&#039;Autore direttamente. </s></p><p type="main">

<s>Frattanto osserviamo che, mentre il Torricelli studiavasi di emulare il <lb></lb>Valerio, deduceva dalle proposizioni dell&#039;emulo, e dalle sue proprie, alcuni <lb></lb>corollari, che l&#039;avviavano a trattar l&#039;argomento indicato nel nostro somma­<lb></lb>rio. </s>

<s>Dall&#039;aver dimostrato, rivolgendo l&#039;occhio indietro sopra la figura 182, <lb></lb>che il solido descritto dal quadrilineo BE è uguale al cilindro CK di pari al­<lb></lb>tezza, risultava che il centro del solido scavato è nella metà dell&#039;asse, come <lb></lb>nello stesso cilindro. </s>

<s>“ Patet centrum gravitatis dicti solidi excavati esse idem <lb></lb>cum centro cylindri ” (ibid., T. XXXVI, fol. </s>

<s>37). E per essersi, nella figura 181, <lb></lb>dimostrato il solido generato dal bilineo AGB uguale allo sferoide, “ Patet <lb></lb>centrum etiam praedicti solidi sphaerici esse idem ac centrum sphaeroidis ” <lb></lb><figure id="id.020.01.2703.1.jpg" xlink:href="020/01/2703/1.jpg"></figure></s></p><p type="caption">

<s>Figura 187.<lb></lb>(ibid.), ossia nel mezzo dell&#039;asse, come il Torricelli stesso con­<lb></lb>fermò così, con dimostrazione diretta, e per il caso particolare <lb></lb>che il segmento contemplato fosse un emisfero. </s></p><p type="main">

<s>“ PROPOSIZIONE XXXIII. — <emph type="italics"></emph>Se dall&#039;emisfero sarà levato <lb></lb>il cono, dico che il centro del bicchiere che resta sta nel <lb></lb>mezzo dell&#039;asse AB<emph.end type="italics"></emph.end> (fig. </s>

<s>187). ” </s></p><p type="main">

<s>“ Mettasi AB per libbra, e prendansi uguali AC, DB. </s>

<s><lb></lb>Saranno anco uguali OE, IB. </s>

<s>Ma l&#039;armilla di EF, all&#039;armilla <lb></lb>di IG, le quali sono grandezze, che hanno il centro nella lib­<lb></lb>bra AB; sta come il rettango FEM, cioè OEB, <emph type="italics"></emph>ob rirculum <lb></lb>et per XXXV Tertii,<emph.end type="italics"></emph.end> cioè OIB. <emph type="italics"></emph>ob aequalitatem,<emph.end type="italics"></emph.end> cioè il rettangolo GIN, al <lb></lb>rettangolo GIN: però sono uguali <emph type="italics"></emph>et sic semper. </s>

<s>Ergo<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2703.2.jpg" xlink:href="020/01/2703/2.jpg"></figure></s></p><p type="caption">

<s>Figura 188.<lb></lb><emph type="italics"></emph>solidum vasiforme a bilineo OBG genitum, habet cen­<lb></lb>trum gravitatis in medio axis AB ”<emph.end type="italics"></emph.end> (ibid., T. XXXVI <lb></lb>fol. </s>

<s>11). </s></p><p type="main">

<s>“ PROPOSIZIONE XXXIV. — <emph type="italics"></emph>Dimostrare il mede­<lb></lb>simo anco nello sferoide. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Procederemo così: Sia la emisferoide ABC (fig. </s>

<s>188), <lb></lb>dalla quale leva il cono, e prendi uguali EM, IB, ed anco <lb></lb>EF uguale ad EM. </s>

<s>E prova genericamente, per via di <lb></lb>lemma, che il cerchio MH, alla sua armilla GH, sta come <lb></lb>il quadrato BM al rettangolo BME, preso due volte, e poi <lb></lb>seguita così.... ” (ivi, fol. </s>

<s>13). </s></p><pb xlink:href="020/01/2704.jpg" pagenum="329"></pb><p type="main">

<s>Prima però di seguitare, avvertiamo che, non essendosi il promesso <lb></lb>lemma ritrovato nel manoscritto torricelliano, il Viviani vi suppli di suo, come <lb></lb>si legge in un foglio intitolato <emph type="italics"></emph>“ Mio lemma supposto dal Torricelli.<emph.end type="italics"></emph.end> Dico <lb></lb>che il quadrato MH, alla sua armilla HG, o il cerchio MH, alla armilla HG, <lb></lb>sta sempre come il quadrato BM a due rettangoli BME. ” </s></p><p type="main">

<s>“ Prendi EF eguale ad ME: sarà il quadrato MH, al quadrato AE, come <lb></lb>il quadrato BM al quadrato BE; cioè al rettangolo BED, ed il quadrato AE, <lb></lb>al quadrato GM, <emph type="italics"></emph>ob ellipsim, vel circulum,<emph.end type="italics"></emph.end> sta come il rettangolo BED al <lb></lb>rettangolo BMD. </s>

<s>Adunque <emph type="italics"></emph>ex aequo<emph.end type="italics"></emph.end> il quadrato HM, al quadrato MG, starà <lb></lb>come il quadrato BM al rettangolo BMD; cioè, essendo BF eguale ad MD, <lb></lb>al rettangolo BMF. E, dividendo, il quadrato MH, all&#039;armilla HG, come il <lb></lb>quadrato BM al rettangolo BMF, cioè a due rettangoli BME ” (ivi, T. XXXV, <lb></lb>fol. </s>

<s>124). </s></p><p type="main">

<s>Tornando ora al Torricelli seguitiamo con lui così: “ L&#039;armilla GH, al <lb></lb>cerchio MH, sta come il rettangolo BME, preso due volte, al quadrato MB. </s>

<s><lb></lb>Il cerchio poi HM, al cerchio RI, sta come il quadrato MB, al quadrato BI, <lb></lb>ed il cerchio RI, alla sua armilla, sta come il quadrato BI al rettangolo BIE, <lb></lb>preso due volte. </s>

<s>Adunque, <emph type="italics"></emph>ex aequo et sumptis consequentium dimidiis.<emph.end type="italics"></emph.end><lb></lb>l&#039;armilla GH, alla LR, sta come il rettangolo BME al rettangolo BIE, cioè <lb></lb>uguali: e così sempre. </s>

<s>Adunque, il centro del bicchiere dell&#039;emisferoide è <lb></lb>nel mezzo dell&#039;asse EB ” (ivi, T. XXXVI, fol. </s>

<s>13). </s></p><p type="main">

<s>Di qui volle il Torricelli passare a esercitarsi intorno ai bicchieri cilin­<lb></lb>drici, considerandoli prima di tutto scavati da un cono. </s>

<s>Ne contemplò due <lb></lb>casi: il primo, in cui il cilindro avesse uguale altezza, ma base diversa dal <lb></lb>cono; il secondo, in cui l&#039;altezza e la base fossero uguali. </s>

<s>E, supposto il <lb></lb>teorema, che noi premettemmo alla XXXII qui addietro per lemma; dimo­<lb></lb>strava, e scriveva fra&#039;suoi fogli, per quel primo caso del cilindro scavato, la <lb></lb>seguente </s></p><p type="main">

<s>“ PROPOSIZIONE XXXV. — <emph type="italics"></emph>Se sarà un cilindro<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2704.1.jpg" xlink:href="020/01/2704/1.jpg"></figure></s></p><p type="caption">

<s>Figura 189.<lb></lb><emph type="italics"></emph>ed un cono intorno al medesimo asse, fa&#039;come tre <lb></lb>quadrati AC<emph.end type="italics"></emph.end> (fig. </s>

<s>189), <emph type="italics"></emph>al quadrato AB, così EI alla <lb></lb>ID<emph.end type="italics"></emph.end> (il punto 1) è mezzo di AH, ed E mezzo di AD) <lb></lb><emph type="italics"></emph>sarà il punto I centro del cilindro sbucato. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Poichè D è centro di tutto il cilindro, ma E <lb></lb>del cono. </s>

<s>Però tutto il cilindro, al cono, sta come tre <lb></lb>quadrati AC al quadrato AB, cioè, come EI ad ID. E, dividendo, il solido <lb></lb><figure id="id.020.01.2704.2.jpg" xlink:href="020/01/2704/2.jpg"></figure></s></p><p type="caption">

<s>Figura 190.<lb></lb>forato, al cono, come ED alla DI. </s>

<s>Però il punto I <lb></lb>è centro del cilindro forato ” (ivi. </s>

<s>T, XXXVI, <lb></lb>fol. </s>

<s>53). </s></p><p type="main">

<s>L&#039;altro caso del centro di gravità nel bic­<lb></lb>chiere cilindrico è d&#039;invenzione simile a quella <lb></lb>del primo. </s>

<s>Si chiami C il cilindro intero, <emph type="italics"></emph>c<emph.end type="italics"></emph.end> il <lb></lb>cono, CS il cilindro scavato. </s>

<s>Se A (fig. </s>

<s>190) è <lb></lb>il centro di gravità del cono, e B quello del cilindro, Archimede insegna <pb xlink:href="020/01/2705.jpg" pagenum="330"></pb>nella VIII degli Equiponderanti (Op. </s>

<s>cit., pag. </s>

<s>170) che, se faremo BD:AB= <lb></lb><emph type="italics"></emph>c<emph.end type="italics"></emph.end>:CS, verrà in D indicato il punto richiesto. </s>

<s>Componendo sarà AD:BD= <lb></lb>C:<emph type="italics"></emph>c<emph.end type="italics"></emph.end>=3:1. Dividendo, AB:BD=2:1. Duplicando gli antecedenti, <lb></lb>EB:BD=4:1. Componendo, ED:BD=5:1. Dividendo quella mede­<lb></lb>sima, che ora si è composta, FD:BD=3:1. D&#039;onde ED:FD=5:3. </s></p><p type="main">

<s>La medesima relazione era stata conclusa poco addietro per corollario <lb></lb>dalla XXXII, ond&#039;è che, volendo il Torricelli farne una proposizione distinta, <lb></lb>incominciò a pensare che, presa GH=FG, e sopra IG, GH disegnata una <lb></lb>semiellisse, rivolgendosi questa intorno alla IG descriverebbe un solido, il <lb></lb>centro di gravità del quale sarebbe indicato nel medesimo modo, che nel <lb></lb>bicchiere cilindrico, per cui tenne per certo che esso bicchiere e l&#039;ellissoide <lb></lb>fossero uguali. </s>

<s>Trovato che così era veramente, ne fece un lemma per questa </s></p><p type="main">

<s>“ PROPOSIZIONE XXXVI. — <emph type="italics"></emph>Centrum gravitatis hemisphaeroidis ita <lb></lb>secat axem, ut pars ad verticem sit ad reliqua ut quinque ad tria. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il detto lemma per la dimostrazione si preparava in questa maniera: <lb></lb>“ Esto cylindrus rectus ABCD (fig. </s>

<s>191) excavatus, cui nimirum demptus <lb></lb>sit conus BEC. </s>

<s>Ponatur DF aequalis ipsi DE. </s>

<s>Dico cylindrum excavatum <lb></lb><figure id="id.020.01.2705.1.jpg" xlink:href="020/01/2705/1.jpg"></figure></s></p><p type="caption">

<s>Figura 191.<lb></lb>ABECD aequalem esse hemisphaeroidi, quae fit <lb></lb>a semiellipsi DCF circa axem DC revoluta. </s>

<s>” </s></p><p type="main">

<s>“ Agatur planum GH, ad axem erectum, <lb></lb>producanturque BA, CE donec contingant in <lb></lb>N, et producatur CDO axis integer, Habebit <lb></lb>circulus AD, ad armillam LI, rationem compo­<lb></lb>sitam ex ratione rectae ED, ad LI, sive DC ad <lb></lb>CI, et ex ratione AE ad GL, sive ex ratione <lb></lb>AN ad NG, sive DO ad OI. </s>

<s>Ergo circulus AD, <lb></lb>ad armillam LI, erit ut rectangulum CDO ad <lb></lb>CIO, sive, ut quadratum DF ad IH, vel, ut <lb></lb>circulus radio DF ad circulum ex radio IH. </s>

<s><lb></lb>Sed antecedentia sunt aequalia, ergo etc. </s>

<s>Et hoc semper, ergo etc. </s>

<s>” </s></p><p type="main">

<s>“ Ho passato per noto che la retta AN sia uguale alla DO, ed è chiare, <lb></lb>perchè la DO è uguale alla DC, <emph type="italics"></emph>per constructionem,<emph.end type="italics"></emph.end> ma la AN è uguale alla <lb></lb>AB, <emph type="italics"></emph>ob parallelas,<emph.end type="italics"></emph.end> essendo BC doppia alla AE. ” </s></p><p type="main">

<s>“ Ritornando al proposito, e facendo dalla Geometria trapasso alla Mec­<lb></lb>canica, però si prova il centro della emisforoide con facilità, perchè stato <lb></lb>facile trovar quello del cilindro sbucato. </s>

<s>” </s></p><p type="main">

<s>“ Esto centrum totius cylindri B (nella figura 190 qui poco addietro) <lb></lb>coni vero ablati A. Ergo, per VIII primi Aequiponderantium, erit D centrum <lb></lb>solidi excavati, si fiat ut cylindrus ad conum, ita AD ad DB, nempe, ut tria <lb></lb>ad unum. </s>

<s>Ergo, dividendo, AB ad BD crit ut duo ad unum. </s>

<s>Et, sumptis du­<lb></lb>plis, EB ad BD ut quatuor ad unum. </s>

<s>Ergo ED ad DF erit ut quinque ad <lb></lb>tria. </s>

<s>Et in eadem ratione secat axem hemisphaeroidis centrum gravitatis ” <lb></lb>(ibid., T. XXX, fol. </s>

<s>116). </s></p><p type="main">

<s>Le medesime cose era il Torricelli riuscito a dimostrarle per altre vie, <pb xlink:href="020/01/2706.jpg" pagenum="331"></pb>non meno splendide e nuove. </s>

<s>Dalla V del III del Cavalieri si concludeva es­<lb></lb>sere la scodella esterna uguale al cono, o fosse il cilindro circoscritto alla <lb></lb>sfera, o alla sferoide, cosicchè in questo caso, togliendosi la scodella stessa, <lb></lb>rimaneva l&#039;emisferoide ignuda, della quale potevasi, con la nota regola del­<lb></lb>l&#039;VIII degli Equiponderanti, ritrovare il baricentro, conoscendosi quello del <lb></lb>tutto e di una sua parte. </s>

<s>La proporzione stereometrica poi tra l&#039;una e l&#039;al­<lb></lb>tro, cioè tra l&#039;emisferoide e il cono inscritto, era nota per la XXIX di Ar­<lb></lb>chimede nel libro <emph type="italics"></emph>De conoid. </s>

<s>et sphaer.,<emph.end type="italics"></emph.end> ma il Torricelli, per far prova della <lb></lb>superiorità del metodo degl&#039;indivisibili verso l&#039;antico, e per mostrare con <lb></lb>quanto maravigliosa facilità e speditezza si potesse giungere a quelle mede­<lb></lb>sime conclusioni, alle quali si giungeva pure dai matematici seguaci del Si­<lb></lb>racusano, ma per vie tanto aspre e affannose; si applicò a dimostrare, con <lb></lb>aggressioni nuove, che l&#039;emisfero o l&#039;emisferoide è doppia del cono inscritto, <lb></lb>premettendo tre lemmi alla proposizione. </s></p><p type="main">

<s>Il primo è compreso nella VI archimedea <emph type="italics"></emph>De conoid. </s>

<s>et sphaer.,<emph.end type="italics"></emph.end> nella <lb></lb>quale si dimostra che l&#039;ellisse sta al circolo come il rettangolo sotto gli assi <lb></lb>sta al quadrato del diametro; d&#039;onde si deriva che, se uno degli assi è uguale <lb></lb>al diametro, come suppone il Torricelli, l&#039;ellisse sta al circolo come l&#039;altro <lb></lb>asse al diametro, secondo che il Torricellì stesso proponevasi di dimostrare, <lb></lb>benchè in un modo del tutto nuovo. </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma I.<emph.end type="italics"></emph.end> — Omnis ellipsis, ad circulum qui habeat diametrum ae­<lb></lb>quale alteri axium ellipseos, eam habet proportionem, quam alter, nempe <lb></lb>inaequalis axis, ad circuli diametrum. </s>

<s>” </s></p><p type="main">

<s>“ Esto ellipsis ABC (fig. </s>

<s>192), circulus ADC, et sit axis ellipsis AC ae­<lb></lb>qualis diametro circuli AC. </s>

<s>Sitque alter axis BH: dico <lb></lb><figure id="id.020.01.2706.1.jpg" xlink:href="020/01/2706/1.jpg"></figure></s></p><p type="caption">

<s>Figura 192.<lb></lb>ellipsim ad circulum esse ut BH ad HD. </s>

<s>Ducatur enim <lb></lb>ordinatim EF, ubicumque, et erit quadratum EF, ad qua­<lb></lb>dratum BH, ut rectangulum AFC, ad rectangulum AHC. </s>

<s><lb></lb>Sed etiam quadratum IF, ad quadratum DH, est ut re­<lb></lb>ctangulum AFC ad rectangulum AHC; ergo quadratum <lb></lb>EF, ad quadratum BH, est ut quadratum IF ad quadra­<lb></lb>tum DH. </s>

<s>Ergo et lineae sunt proportionales. </s>

<s>Et, permu­<lb></lb>tando, EF ad FI est ut BH ad HD, et hoc semper. </s>

<s>Propterea erunt omnes <lb></lb>antecedentes simul, ad omnes simul consequentes, ut una antecedentium ad <lb></lb>unam consequentium, nempe ellipsis ABC, ad circulum ADC, ut BH ad HD ” <lb></lb>(idid., fol. </s>

<s>172). </s></p><p type="main">

<s>Segue l&#039;altro lemma, che, trapassando dal circolo e dall&#039;ellisse alla sfera <lb></lb>e allo sferoide, procede per gl&#039;indivisibili in modo analogo al primo. </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma II.<emph.end type="italics"></emph.end> — Omnis sphaerois, ad sphaeram, quae habeat maximum <lb></lb>circulum aequalem maximo circulo sphaeroidis, est ut axis ad axem. </s>

<s>” </s></p><p type="main">

<s>“ Esto sphaerois ABC (fig. </s>

<s>193) sphaera vero ADC quales dictae sunt: <lb></lb>maximus utriusque circulus sit AHCL. </s>

<s>Dico sphaeroidem ad sphaeram esse <lb></lb>ut axis BE ad axem ED. </s>

<s>Secetur enim utraque per centrum E, plano HBL <lb></lb>ad diametrum AC erecto, et iterum altero plano MFN, ipsi HBL parallelo <pb xlink:href="020/01/2707.jpg" pagenum="332"></pb>ubicumque. </s>

<s>Eritque, per praecedens lemma, ellipsis HBL, ad circulum HDL, <lb></lb><figure id="id.020.01.2707.1.jpg" xlink:href="020/01/2707/1.jpg"></figure></s></p><p type="caption">

<s>Figura 193.<lb></lb>ut BE ad ED. </s>

<s>Sed etiam ellipsis MFN est <lb></lb>ad circulum MIN ut FG ad GI, sive ut BE <lb></lb>ad ED, et sic semper. </s>

<s>Propterea erunt <lb></lb>omnes simul antecedentes, ad omnes con­<lb></lb>sequentes simul, ut una ad unum, nempe <lb></lb>ut ellipsis HBL ad circulum HDL, sive ut <lb></lb>axis BE ad axem ED ” (ibid., fol. </s>

<s>173). </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma III.<emph.end type="italics"></emph.end> — Sphaeroides inter <lb></lb>se sunt ut solida parallelepipeda, quorum <lb></lb>bases sunt quadrata diametrorum, altitu­<lb></lb>dines vero longitudines axium. </s>

<s>” </s></p><p type="main">

<s>“ Sint sphaeroides ABC, DEF (fig. </s>

<s>194) <lb></lb>quarum axes BG, EH, diametri vero AC, <lb></lb>DF. </s>

<s>Dico sphaeroidem ABC, ad sphaeroidem <lb></lb><figure id="id.020.01.2707.2.jpg" xlink:href="020/01/2707/2.jpg"></figure></s></p><p type="caption">

<s>Figura 194.<lb></lb>DEF, esse ut solidum parallelepipedum, basi <lb></lb>quadrato AC, altitudine vero BG, ad solidum <lb></lb>parallelepipedum, basi quadrato DF, altitudine <lb></lb>vero EH. </s>

<s>Concipiatur enim, in utraque sphae­<lb></lb>roide, sphaera aequalis diametri AIC, DOF. </s>

<s>Erit­<lb></lb>que sphaerois ABC, ad sphaeram AIC, ut recta <lb></lb>BG ad GI, per praecedens, sive, ut solidum <lb></lb>basiquadrato GI, altitudine BG, ad cubum GI. </s>

<s>Sphaera vero AIC, ad sphae­<lb></lb>ram DOF, est ut cubus GI ad cubum HO, et denique sphaera DOF, ad <lb></lb>sphaeroidem DEF, est ut cubus HO ad solidum parallelepipedum, basi qua­<lb></lb>drato HO, altitudine vero HE. </s>

<s>Ergo ex aequo patet propositum. </s>

<s>Sumptis <lb></lb>vero quadruplis, erit sphaerois ABC ad DEF ut solidum basi quadrato AC, <lb></lb>altitudine BG, ad solidnm basiquadrato DF. altitudine EH, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (ibid., <lb></lb>fol. </s>

<s>174). </s></p><p type="main">

<s>Con l&#039;aiuto de&#039;quali tre lemmi passa il Torricelli finalmente a dimo­<lb></lb><figure id="id.020.01.2707.3.jpg" xlink:href="020/01/2707/3.jpg"></figure></s></p><p type="caption">

<s>Figura 195.<lb></lb>strar la proposizione, che dice: <emph type="italics"></emph>Hemisphaerium, sive <lb></lb>hemisphaeroides dupla est coni inscripti.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto hemisphaerum sive hemisphaeroides ABC <lb></lb>(fig. </s>

<s>195), cuius axis BD, et applicata ex puncto E <lb></lb>medio axis sit FEH, conus inscriptus ABC. </s>

<s>Jam osten­<lb></lb>dimus solidum reliquum, dempto cono ABC, aequale <lb></lb>esse sphaeroidi cuidam, cuius axis sit BD, maximus <lb></lb>vero circulus sit aequalis armillae FG, nempe cuius <lb></lb>radius I medius sit inter FG, GH. ” </s></p><p type="main">

<s>“ Jam ratio sphaeroidis ABCO, ad sphaeroidem <lb></lb>cuius radius est I, axis vero BD, est, per praecedens lemma, ut solidum ba­<lb></lb>siquadrato I, altitudine BE. </s>

<s>Ergo rationem habet compositam ex ratione <lb></lb>quadrati AD, ad quadratum I, sive ad rectangulum FGH, nempe ut 4 ad 2, <lb></lb>et ex ratione altitudinis DB ad BE, nempe 2 ad 1. Ergo sphaerois ABCO, <pb xlink:href="020/01/2708.jpg" pagenum="333"></pb>ad sphaeroidem praedictam, sive ad reliquum solidum, dempto cono ABC, <lb></lb>est ut 4 ad 1. Ergo hemisphaerium, vel hemisphaeroides, ad dictum solidum, <lb></lb>est ut 2 ad 1, et, per conversionem rationis, ad conum inscriptum erit ut <lb></lb>2 ad 1, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” </s></p><p type="main">

<s>“ Che il quadrato AD sia sempre doppio del rettangolo patet, perchè il <lb></lb>quadrato FE al quadrato AD sta come il rettangolo BEO al rettangolo BDO, <lb></lb>cioè come 3 a 4, ed il quadrato AD, al quadrato GE, sta come 4 a 1. Ergo <lb></lb>ex aequo il quadrato FE, all&#039;EG, sta come 3 a 1. E, dividendo, il rettan­<lb></lb>golo FGH, al quadrato GE, sta come 2 a 1, ed al quadrato AD come 2 a 4, <lb></lb><expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (ivi, fol. </s>

<s>175). </s></p><p type="main">

<s>Sia ora CM, nella stessa figura 195, il cilindro circoscritto: se di lui si <lb></lb>tolga la scodella esterna, il rimanente è l&#039;emisferoide nuda, della quale si <lb></lb>può ritrovare il centro, perch&#039;essendo E quello del tutto, N quello della parte <lb></lb>tolta, che si sa essere uguale al cono MDP; avremo in Q il centro dell&#039;emi­<lb></lb>sferoide che si voleva, se faremo EQ a EN reciprocamente come il cono <lb></lb>inscritto alla stessa emisferoide, o, per le cose ora dimostrate, come uno a <lb></lb>due, d&#039;onde è manifesto che BQ è cinque delle parti, delle quali QD è tre <lb></lb>solamente. </s></p><p type="main">

<s>Ma, per tornare all&#039;argomento dei solidi scavati, e per mostrare la va­<lb></lb>rietà dell&#039;aspetto e delle forme, sotto le quali gli con­<lb></lb><figure id="id.020.01.2708.1.jpg" xlink:href="020/01/2708/1.jpg"></figure></s></p><p type="caption">

<s>Figura 196.<lb></lb>siderava il Torricelli, trascriveremo dal manoscritto di <lb></lb>lui quest&#039;altre proposizioni. </s></p><p type="main">

<s>“ PROPOSIZIONE XXXVII. — <emph type="italics"></emph>Esto portio circuli <lb></lb>ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>196) <emph type="italics"></emph>sive minor, sive maior semicirculi: <lb></lb>duae tangentes AD, DB, axis BM, et convertatur. </s>

<s>Dico <lb></lb>solidum vasiforme, genitum a trilineo ADB, aequale esse cono DMO. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ducta enim EI, erit rectangulum EFI, sive FEL, aequale quadrato EA, <lb></lb>per penultimam Tertii, vel quadrato GH (quadratum enim EA, ad quadra­<lb></lb>tum AD, est ut quadratum HM ad MB, sive GH ad DB, et consequentia <lb></lb>sunt aequalia). Quare armilla EF aequalis est circulo GH, propterea solidum <lb></lb>vasiforme aequalis erit cono DMO ” (ibid. </s>

<s>T. XXX, fol. </s>

<s>71). <lb></lb><figure id="id.020.01.2708.2.jpg" xlink:href="020/01/2708/2.jpg"></figure></s></p><p type="caption">

<s>Figura 197.</s></p><p type="main">

<s>“ PROPOSIZIONE XXXVIII. — <emph type="italics"></emph>Se la parabola <lb></lb>ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>197), <emph type="italics"></emph>il cui diametro BF, averà la tan­<lb></lb>gente DBE per la cima, e le tangenti AD, CE alla <lb></lb>base, e prodotta FD si giri la figura; sarà la sco­<lb></lb>della del triangolo ADF eguale al conoide, e lo <lb></lb>scodellino del trilineo DAB eguale al cono DFE, <lb></lb>e perciò medesimo sarà il centro di gravità della <lb></lb>scodella e del conoide; dello scodellino e del cono. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Tirisi l&#039;applicata GL: averà il rettangolo GIL, al quadralo AF, ra­<lb></lb>gion composta di GI ad AF, ovvero di ID a DF, ovvero di OB a BF, e di <lb></lb>IL a FC, e, perchè sono uguali, diremo di BF alla BF. </s>

<s>Sta dunque il ret­<lb></lb>tangolo GIL, al quadrato AF, come la OB alla BF, ovvero come il quadrato <lb></lb>OR al quadrato FA, e però sono uguali il rettangolo GIL e il quadrato RO, <pb xlink:href="020/01/2709.jpg" pagenum="334"></pb>ossia l&#039;armilla descritta da GI, e il circolo descritto da GO: e così essendo <lb></lb>di tutte le applicate, la scodella del triangolo ADF sarà uguale al conoide <lb></lb>parabolico, c. </s>

<s>d. </s>

<s>d. </s>

<s>” </s></p><p type="main">

<s>“ Essendosi poi provata uguale l&#039;armilla GI al quadrato RO, <emph type="italics"></emph>adde com­<lb></lb>munem<emph.end type="italics"></emph.end> l&#039;armilla IR, e sarà l&#039;armilla GR uguale al quadrato IO. </s>

<s>Essendo <lb></lb>anco provato uguale l&#039;armilla NQ al quadrato PT, <emph type="italics"></emph>deme communem<emph.end type="italics"></emph.end> l&#039;ar­<lb></lb>milla PQ, e resteranno uguali l&#039;armilla NP, e il circolo QT. </s>

<s>Dunque sarà <lb></lb>la scodellina parabolica del trilineo uguale al cono DFE ” (ivi, fol. </s>

<s>69). </s></p><p type="main">

<s>Apparterrebbero a questo medesimo argomento alcune altre proposizioni, <lb></lb>scritte per dimostrare il centro di gravità nei tronchi di cono scavati da un <lb></lb>cono solo o da più coni: ma perchè le dimostrazioni conseguono da prin­<lb></lb>cipii più alti, che si poṙranno dal Torricelli a proposito dei centri di gravità <lb></lb>dei solidi conoidali, le trascriveremo allora, per passar senza indugio alla se­<lb></lb>conda parte promessa intorno a questo argomento, che è dei centri di gra­<lb></lb>vità nei solidi vasiformi. </s></p><p type="main">

<s><emph type="center"></emph>VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dicemmo che l&#039;occasione al trattato nacque dal solido acuto iperbolico, <lb></lb>ingerendosi la fantasia a consigliar la Matematica severa di condiscendere tal­<lb></lb>volta ai lusi dell&#039;ingegno. </s>

<s>A chiunque infatti posi l&#039;occhio sulla figura geo­<lb></lb>metrica del detto solido acuto col suo asse verticale, si rappresenta, come si <lb></lb>rappresentò al Torricelli, l&#039;immagine di un piede, che quasi aspetti di so­<lb></lb>stener la coppa di un calice o di un bicchiere. </s>

<s>E perchè <emph type="italics"></emph>bicchiere<emph.end type="italics"></emph.end> era il <lb></lb>nome uscitogli più volte di bocca, per chiamare que&#039;solidi scavati, intorno <lb></lb>ai quali vedemmo come si fosse il nostro Autore esercitato, per ritrovarne <lb></lb>il centro gravitativo; sembrava dunque che la Geometria fosse, con le sue <lb></lb>proprie mani, venuta a lavorar lo strumento, per apparecchiare il convito <lb></lb>della Scienza. </s>

<s>Così, il calice, che il Torricelli pensava di porgere a Minerva <lb></lb>per celebrare i divini misteri, aveva per piede il solido acuto iperbolico, per <lb></lb>nodo una sfera, e per coppa ora una, ora un&#039;altra figura di quelle varie, che <lb></lb>possono immaginarsi descritte dal rivolgersi iperbole con gli asintoti, e pa­<lb></lb>rabole, e porzioni di ellissi e di circoli intorno ai loro proprii assi. </s>

<s>Il trat­<lb></lb>tato nuovo veniva perciò a partecipare delle festosità del ditirambo, e delle <lb></lb>grazie dell&#039;idillio, come possono sentire i lettori infin dal primo presentarlo, <lb></lb>che il Torricelli stesso faceva all&#039;amico suo Raffaello Magiotti, mentre que­<lb></lb>sti, per fuggire i calori estivi di Roma, stavasi riparato all&#039;ombra sui colli <lb></lb>tusculani. </s></p><p type="main">

<s>“ Erras, amice Magiotti, si speras in tusculanum collem seductus mea­<lb></lb>rum effugere potuisse obsidionem ineptiarum. </s>

<s>Ecce enim persequor te quo­<lb></lb>cumque fugis, solito molestiarum genere, nugis meis. </s>

<s>Libet exemplo tuo, qui <lb></lb>fusum parabolicum aliquando contemplari dignatus es, de Acu hyperbolica <pb xlink:href="020/01/2710.jpg" pagenum="335"></pb>quaedam dicere. </s>

<s>Utinam tibi libeat audire. </s>

<s>Contemplationem leges, in qua <lb></lb>fortasse acumen desiderabis, non autem in solido, cuius tanta subtilitas est <lb></lb>ut, quamvis in infinitam longitudinem producatur, exigui tamen cylindri mo­<lb></lb>lem non excedat. </s>

<s>I nunc et procul recede: aculeum habet Geometria lon­<lb></lb>giorem, quam tu ab ipso evadere possis. </s>

<s>Huius ego mucrone, non minus <lb></lb>subtili quam longo, eruditas et vere geometricas aures tuas non expungere <lb></lb>hesitabo. </s>

<s>Caeterum lege libenter hoc, quicquid est, mox enim videbis huius <lb></lb>contemplationis materiam, quae nunc cuspis est, meliore figura refusam in <lb></lb>calicem tantae capacitatis, ut sitim vel giganteam extinguere possit ” (ibid., <lb></lb>T. XXX, fol. </s>

<s>3). </s></p><p type="main">

<s>Di qui apparisce che lo scopo è principalmente quello di trovar, delle <lb></lb>varie coppe da soprapporre al piè del calice, la grandezza e no il centro, di­<lb></lb>cendo scherzevolmente al Magiotti che nel Luglio sitibondo, in cui scriveva, <lb></lb>metteva più conto di ritrovar del bicchiere da rinfrescarsi le misure della <lb></lb>capacità, che del peso. </s>

<s>Nonostante, s&#039;indica anche delle varie coppe descritte <lb></lb>il luogo del baricentro, e benchè tutte l&#039;abbiano in mezzo all&#039;asse, era pur <lb></lb>necessario dimostrarlo per vie geometriche, come il Torricelli fa in quel suo <lb></lb>modo, sempre facile ed elegante, cosicchè par che chi legge, sedotto dal de­<lb></lb>siderio di cogliere le rose, non senta più la mano pungersi dalle spine. </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma I.<emph.end type="italics"></emph.end> — Si fuerint tres lineae in continua proportione, erit ar­<lb></lb>milla, sive differentia circulorum, quorum alter fit ex semisse aggregati, alter <lb></lb>vero ex semisse differentiae extremorum; aequalis circulo, qui fit ex media <lb></lb>proportionalium linearum. </s>

<s>” <lb></lb><figure id="id.020.01.2710.1.jpg" xlink:href="020/01/2710/1.jpg"></figure></s></p><p type="caption">

<s>Figura 198.</s></p><p type="main">

<s>“ Sint tres lineae in continua ratione AB, BC, <lb></lb>BD (fig. </s>

<s>198), et ponantur extremae in directum ABD, <lb></lb>ipsa vero media BC erigatur in B ad angulos rectos. </s>

<s><lb></lb>Secta deinde AD bifariam in E, fiat ex ED, semisse <lb></lb>aggregati extremarum, circulus ACD. </s>

<s>Ex ipsa vero <lb></lb>EB, semisse differentiae extremarum, fiat circulus <lb></lb>FB. </s>

<s>Dico armillam AFCD aequale esse circulo ex BC, <lb></lb>tamquam semidiametro descripto. </s>

<s>Juncta enim EC <lb></lb>erit, ex XLVII Primi, et II Duodecimi, circulus ex EC <lb></lb>aequalis duobus simul circulis ex EB, et ex BC, ob angulum rectum EBC. </s>

<s><lb></lb>Dempto ergo communi circulo ex EB, remanebit armilla AFCD aequalis cir­<lb></lb>culo ex BC, qùod etc. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XXXIX. — <emph type="italics"></emph>Si hyperbola, una cum asymptotis, circa<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2710.2.jpg" xlink:href="020/01/2710/2.jpg"></figure></s></p><p type="caption">

<s>Figura 199.<lb></lb><emph type="italics"></emph>axem proprium convertatur, erit solidum <lb></lb>vasiforme, abscissum plano ad axem erecto, <lb></lb>aequale cylindro, qui eamdem cum solido <lb></lb>basim habeat, et eamdem altitudinem. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sit hyperbola, cuius axis AB (fig. </s>

<s>199), <lb></lb>asymptoti vero AC, AD, ipsa vero EF contin­<lb></lb>gat sectionem in E, et convertatur figura circa <lb></lb>AB. </s>

<s>Supra circulo FG intelligatur cylindrus OFGI, et secetur solidum plano <pb xlink:href="020/01/2711.jpg" pagenum="336"></pb>quodcumque CD, ad axem erecto. </s>

<s>Dico solidum, quod <emph type="italics"></emph>Vasiformem hyperbo­<lb></lb>licum<emph.end type="italics"></emph.end> appello, descriptum a revolutione quadrilinei CFEH, aequale esse cy­<lb></lb>lindro FI, super eadem basi FG, et sub eadem altitudine EB. </s>

<s>Quia nam, ex <lb></lb>X Secundi Conicorum, in continua ratione sunt CH, FE, HD, erit armilla, quae <lb></lb>fit ex revolutione lineae CH, aequalis circulo ex FE, hoc est ex OB, et hoc <lb></lb>semper. </s>

<s>Quare erunt omnes simul armillae, hoc est solidum Vasiforme hyper­<lb></lb>bolicum, aequales simul omnibus circulis, hoc est cylindro super eadem basi, <lb></lb>et sub eadem altitudine, quod etc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Ex hac propositione colligeretur mensura Conoidis hyper­<lb></lb>bolici. </s>

<s>Notus enim est conus integer circumscriptus, prout conus, et notum <lb></lb>solidum vasiforme ablatum aequale cylindro: quare reliquum etiam conoidis <lb></lb>notum esset. </s>

<s>” </s></p><p type="main">

<s>“ Item, centrum gravitatis eiusdem conoidis hyperbolici ex hac propo­<lb></lb>sitione educeretur. </s>

<s>Centrum enim coni integri circumscripti notum est; cen­<lb></lb>trum etiam solidi vasiformis in medio suo axe notum est. </s>

<s>Item, centrum parvi <lb></lb>coni FAG, quare notum esset centrum reliqui conoidis. </s>

<s>” </s></p><p type="main">

<s>“ Sed institutum nostrum est solum poculum metiri, et reliqua magnis <lb></lb>Geometris renuntiare. </s>

<s>Nihil enim nostra interest, adveniente iam canicula, <lb></lb>quantum ponderet ipsum poculum, sed quantum capiat. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE LX. — <emph type="italics"></emph>Si hyperbola cum asymptoto convertatur circa <lb></lb>axem coniugatum, erit solidum vasiforme, abscissum plano ad axem erecto, <lb></lb>aequale cylindro, qui eamdem cum solido basim habeat, eamdemque alti­<lb></lb>tudinem. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sit hyperbola AB (fig. </s>

<s>200), cuius axis coniugatus DC, asymptotus <lb></lb>vero CE, et convertatur figura circa CD. </s>

<s>Intelligatur super circulo AH cy­<lb></lb><figure id="id.020.01.2711.1.jpg" xlink:href="020/01/2711/1.jpg"></figure></s></p><p type="caption">

<s>Figura 200.<lb></lb>lindrus FAHG, et secetur solidum plano BI ad <lb></lb>axem erecto. </s>

<s>Dico solidum vasiforme, descriptum <lb></lb>a quadrilineo BACE, aequale esse cylindro AG <lb></lb>habenti basim AH, altitudinem vero CD. </s>

<s>Erunt <lb></lb>enim, per XI secundi Conicorum, in continua <lb></lb>ratione BE, CA, EI. Quare, per Lemma I, erit <lb></lb>armilla, descripta a linea BE, aequalis circulo <lb></lb>ex CA, sive ex DF, et hoc semper. </s>

<s>Quare erunt <lb></lb>omnes simul armillae, hoc est solidum vasiforme, aequales omnibus simul <lb></lb>circulis, hoc est cylindro AG, quod erat demonstrandum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Ex hac propositione totius solidi BAHI mensura, et cen­<lb></lb>trum gravitatis daretur. </s>

<s>Solidum enim vasiforme quantitate notum est: item <lb></lb>inclusus conus ECK, ergo et totum solidum. </s>

<s>” </s></p><p type="main">

<s>“ Solidi vero vasiformis centrum gravitatis est in medio suo axe: cen­<lb></lb>trum autem intercepti coni ECK notum est; quare et totius compositi solidi <lb></lb>centrum gravitatis daretur. </s>

<s>Sed nihil hoc ad nos qui, sitiente Julio, solam <lb></lb>calicis mensuram aextimamus. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma II.<emph.end type="italics"></emph.end> — Si fuerint duae parabolae aequales circa communem <lb></lb>axem AB (fig. </s>

<s>201), ducanturque ordinatim CD, EF, quarum CD sit per ver-<pb xlink:href="020/01/2712.jpg" pagenum="337"></pb>ticem inclusae parabolae, sed EF ubicumque, dummodo utranque parabolam <lb></lb>secet; dico esse ut EG ad CD, ita CD ad GF. </s>

<s>Ponatur enim AH latus rectum <lb></lb>commune, et erit, ob parabolam, rectangulum <lb></lb><figure id="id.020.01.2712.1.jpg" xlink:href="020/01/2712/1.jpg"></figure></s></p><p type="caption">

<s>Figura 201.<lb></lb>HAB aequale quadrato BE. </s>

<s>Si ergo ab aequa­<lb></lb>libus aequalia demas, nempe rectangulum sub <lb></lb>AH, CB, ex rectangulo HAB, et quadratum <lb></lb>BG ex quadrato BE, quae remanent aequalia <lb></lb>erunt, nempe rectangulum HAC, sive quadra­<lb></lb>tum CD, et rectangulum EGF. </s>

<s>Quare erit ut <lb></lb>EG ad CD, ita CD ad GF, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XLI. — <emph type="italics"></emph>Si fuerint duae <lb></lb>parabolae aequales circa communem axem, et convertatur figura, erit <lb></lb>solidum vasiforme descriptum aequale cylindro, eamdem basim cum so­<lb></lb>lido, eamdemque altitudinem habenti. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sint circa communem axem AB, uti in praeced. </s>

<s>figura, duae para­<lb></lb>bolae aequales DE, GC hoc est quarum latera recta sint aequalia, et ductis <lb></lb>ordinatim CD, BE, quarum CD tangat inclusam parabolam, BE vero secet, <lb></lb>convertatur figura circa axem AB. </s>

<s>Dico solidum vasiforme, descriptum a <lb></lb>quadrilineo EDCG, aequale esse cylindro, cuius basis sit circulus circa DO, <lb></lb>altitudo vero CB. ” </s></p><p type="main">

<s>“ Cum enim, per lemma praecedens, in continua ratione sint EG, DC, <lb></lb>GF, erit, per lemma I, armilla, ex linea EG descripta, aequalis circulo ex <lb></lb>DC, hoc est ex BH, et hoc semper. </s>

<s>Ergo omnes simul armillae, hoc est so­<lb></lb><figure id="id.020.01.2712.2.jpg" xlink:href="020/01/2712/2.jpg"></figure></s></p><p type="caption">

<s>Figura 202.<lb></lb>lidum vasiforme parabolicum, aequales <lb></lb>erunt omnibus simul circulis, hoc est cy­<lb></lb>lindro HDOL, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma III.<emph.end type="italics"></emph.end> — Si recta linea AB <lb></lb>(fig. </s>

<s>202) secetur inaequaliter bis in C <lb></lb>et D, ponaturque BE aequalis ipsi CA; erit rectangulum ADB, partium scili­<lb></lb>cet minus inaequalium, aequale duobus simul rectangulis, nempe ACB, par­<lb></lb>tium magis inaequalium, et rectangulo CDE sub intermediis sectionibus. </s>

<s>” </s></p><p type="main">

<s>“ Secetur AB bifariam in I, et erunt aequales <lb></lb><figure id="id.020.01.2712.3.jpg" xlink:href="020/01/2712/3.jpg"></figure></s></p><p type="caption">

<s>Figura 203.<lb></lb>ipsae etiam IC, IE. Sed, cum rectangulum ADB, si­<lb></lb>mul cum quadrato DI, aequale sit quadrato AI; item, <lb></lb>rectangulum ACB, cum quadrato CI, eidem quadrato <lb></lb>AI aequale sit; erunt rectangulum ADB, cum qua­<lb></lb>drato DI, aequalia rectangulo ACB cum quadrato CI. </s>

<s><lb></lb>Commune auferatur quadratum DI, erit reliquum <lb></lb>rectangulum ADB aequale reliquis duobus rectan­<lb></lb>gulis ACB, et CDE. </s>

<s>Si enim demas, ex quadralo CI, <lb></lb>quadratum DI, spatium quod relinquitur est rectan­<lb></lb>gulum CDE. </s>

<s>Ergo constat propositum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma IV.<emph.end type="italics"></emph.end> — Si fuerint circa communem <lb></lb>axem AB (fig. </s>

<s>203), et circa idem contrum C, duo <pb xlink:href="020/01/2713.jpg" pagenum="338"></pb>ellipses similes, nempe ut DC ad CE, ita BC ad CF; ordinatimque ducantur <lb></lb>FH tangens, et IL secans inclusam ellipsim; dico ita esse IM ad HF, ut HF <lb></lb>ad ML. ” </s></p><p type="main">

<s>“ Est enim quadratum IN, ad quadratum DC, ut rectangulum BNA, ad <lb></lb>rectangulum BCA: hoc est, ut quadratum BC. </s>

<s>Sed DC quadratum, ad qua­<lb></lb>dratum CE, est ut quadratum BC ad CF, et quadratum CE, ad quadratum <lb></lb>MN, est ut quadratum CF ad rectangulum ONF; quare ex aequo erit qua­<lb></lb>dratum IN, ad quadratùm MN, ut rectangulum BNA, ad rectangulum FNO. ” </s></p><p type="main">

<s>“ Iterum, quadratum idem IN, ad quadratum HF, est ut rectangulum <lb></lb>idem BNA, ad rectangulum BFA. </s>

<s>Quare erit quadratum IN, ad duo simul <lb></lb>quadrata MN, HF, ut rectangulum BNA, ad duo simul rectangula FNO, BFA. </s>

<s><lb></lb>Sed rectangulum BNA, per lemma praecedens, duobus dictis rectangulis ae­<lb></lb>quale est; ergo et quadratum IN duobus simul quadratis MN, HF aequale <lb></lb>erit. </s>

<s>Si ergo ab aequalibus commune auferas quadratum MN, reliquum re­<lb></lb>ctangulum IML aequale erit reliquo quadrato HF. </s>

<s>Propterea patet propo­<lb></lb>situm. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XLII. — <emph type="italics"></emph>Si fuerint circa communem axem CB, in <lb></lb>eadem figura, et circa idem centrum C, duo ellipses similes, et converta­<lb></lb>tur figura circa axem; erit solidum vasiforme, factum a revolutione qua­<lb></lb>drilinei DHFE, aequale cylindro eamdem ipso basi, eamdemque altitudinem <lb></lb>habenti. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Intelligatur enim super basi HP cylindrus HQ, et planum DR ad axem <lb></lb>erectum. </s>

<s>Erunt itaque, per lemma praecedens, DE, HF, ER in continua ra­<lb></lb>tione. </s>

<s>Quare, per Lemma I, erit armilla ex DE descripta aequalis circulo ex <lb></lb>HF, vel ex CS, et hoc semper. </s>

<s>Quare erunt omnes simul armillae aequa­<lb></lb>les omnibus simul circulis, nempe solidum vasiforme ellipticum aequale cy­<lb></lb>lindro. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XLIII. — <emph type="italics"></emph>Si intra parallelogrammum rectangulum <lb></lb>ABCD<emph.end type="italics"></emph.end> (fig. </s>

<s>204) <emph type="italics"></emph>sit quadrans ellipsis DB, et convertatur figura circa al­<lb></lb>terutrum vel AB vel AD; erit solidum vasiforme, factum a trilineo BDC,<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2713.1.jpg" xlink:href="020/01/2713/1.jpg"></figure></s></p><p type="caption">

<s>Figura 204.<lb></lb><emph type="italics"></emph>acquale cono CAH eamdem ipsi basim, eamdemque <lb></lb>altitudinem habenti. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Agatur enim planum EF ad axem erectum, <lb></lb>ponaturque BO axis integrae ellipsis. </s>

<s>Quadratum EI, <lb></lb>vel DA, ad quadratum LI, est ut quadratum BA, <lb></lb>ad rectangulum BIO. </s>

<s>Quadratum iterum EI, vel CB. <lb></lb>ad quadratum MI, est ut quadratum BA, ad qua­<lb></lb>dratum IA. </s>

<s>Quare erit idem quadratum EI, ad duo <lb></lb>simul quadrata LI, MI, ut quadratum BA, ad duo <lb></lb>simul spatia: rectangulum scilicet BIO et quadra­<lb></lb>tum IA. </s>

<s>Sed quadratum BA aequale est dictis duo­<lb></lb>bus spatiis, ergo et quadratum EI aequale erit duo­<lb></lb>bus quadratis LI, MI. </s>

<s>Dempto autem communi quadrato LI, erit reliquum <lb></lb>rectangulum ELF aequale quadrato MI. </s>

<s>Constat igitur, per Lemma I, armil-<pb xlink:href="020/01/2714.jpg" pagenum="339"></pb>lam, a linea EL dascriptam, aequalem esse circulo ex MI, et hoc semper. </s>

<s><lb></lb>Propterea erunt omnes simul armillae aequales omnibus simul circulis, nempe <lb></lb>solidum vasiforme aequale cono, quod etc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Hinc deduci posset sphaeroidem ut sphaeram circum­<lb></lb>scripti sibi cylindri sexquialteram esse. </s>

<s>Centrum etiam gravitatis, quod in <lb></lb>hemisphaerio et portionibus sphaerae reperit Lucas Valerius, eodem progressu <lb></lb>erueretur in hemisphaeroide, eiusque portionibus. <lb></lb><figure id="id.020.01.2714.1.jpg" xlink:href="020/01/2714/1.jpg"></figure></s></p><p type="caption">

<s>Figura 205.<lb></lb>Sed tanti non est minuta haec omnia prosequi ut <lb></lb>inceptum poculum deseramus. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XLIV. — <emph type="italics"></emph>Si fuerit in quadrato <lb></lb>ABCD<emph.end type="italics"></emph.end> (fig. </s>

<s>205) <emph type="italics"></emph>quadrans circuli DB, et conver­<lb></lb>tatur figura circa AB; erit solidum vasiforme, de­<lb></lb>scriptum a trilineo BDC, aequale cono CAE eam­<lb></lb>dem ipsi basim, eamdemque altitudinem habenti. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Agatur enim planum FH ad axem erectum, et ducatur IL parallela <lb></lb>ad AB. </s>

<s>Erit igitur rectangulum FIH, hoc est DLM, aequale quadrato LI, <lb></lb>propter circulum, sive quadrato AO, sive OP, et per Lemma I erit armilla, <lb></lb>a linea FI descripta, aequalis circulo ex OP, et hoc semper. </s>

<s>Propterea erunt <lb></lb>omnes armillae simul aequales omnibus simul circulis, nempe solidum va­<lb></lb>siforme aequale cono praedicto, quod erat etc. </s>

<s>” <lb></lb><figure id="id.020.01.2714.2.jpg" xlink:href="020/01/2714/2.jpg"></figure></s></p><p type="caption">

<s>Figura 206.</s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Lucas Valerius, Galileus et alii <lb></lb>demonstrant hanc eamdem propositionem. </s>

<s>Nos, quia <lb></lb>facit ad rem nostram, illam desumpsimus nostroque <lb></lb>modo demonstravimus. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma V.<emph.end type="italics"></emph.end> — Si fuerint circa idem centrum <lb></lb>A (fig. </s>

<s>206) duo circuli, et BC tangat inclusam pe­<lb></lb>ripheriam, DE vero secet; dico esse, ut DI ad BC, <lb></lb>ita BC ad IE. ” </s></p><p type="main">

<s>“ Ducatur enim altera tangens ML per pun­<lb></lb>ctum I: eruntque aequales inter se MI, IL, BC, cum <lb></lb>circuli sint concentrici. </s>

<s>Erit igitur rectangulum DIE aequale rectangulo MIL, <lb></lb>secant enim se intra circulum, hoc est quadrato MI, sive BC. </s>

<s>Quare constat <lb></lb>propositum. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XLV. — <emph type="italics"></emph>Si fuerint circa idem centrum A<emph.end type="italics"></emph.end> (fig. </s>

<s>207) <lb></lb><emph type="italics"></emph>duo circuli, et ductis BC, DE parallelis, ipsa BC tangat interiorem peri­<lb></lb>pheriam, ipsa vero DE secet, et circa CE axem<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2714.3.jpg" xlink:href="020/01/2714/3.jpg"></figure></s></p><p type="caption">

<s>Figura 207.<lb></lb><emph type="italics"></emph>convertatur figura; dico salidum vasiforme, quod <lb></lb>a quadrilineo DBCF describitur, aequale esse <lb></lb>cylindro eamdem ipsi basim, eamdemque alti­<lb></lb>tudinem habenti. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Concipiatur enim cylindrus, uti dictum est, <lb></lb>IBHL: et quia, per Lemma praecedens, sunt in <lb></lb>continua ratione DF, BC, FM, erit, per Lemma I, armilla, descripta a linea <lb></lb>DF, aequalis circulo ex BC, sive ex EI, et hoc semper. </s>

<s>Propterea erunt <pb xlink:href="020/01/2715.jpg" pagenum="340"></pb>omnes simul armillae aequales omnibus simul circulis, hoc est solidum va­<lb></lb>siforme sphaericum aequale cylindro praedicto, quod etc. </s>

<s>” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XXX, fol. </s>

<s>18-25). </s></p><p type="main">

<s><emph type="center"></emph>VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il trattatello elegante della stereometria e della baricentrica dei solidi <lb></lb>vasiformi, di cui abbiamo dal manoscritto torricelliano scelto i teoremi prin­<lb></lb>cipali, s&#039;incontrava in qualche parte nelle medesime cose dimostrate da al­<lb></lb>tri, come dal Commandino, dal Valerio e dal Galileo; ma il Torricelli faceva <lb></lb>notare che le sue dimostrazioni procedevano in modo nuovo, e che si face­<lb></lb>vano derivare da principii più generali, comprendenti in una somma unità <lb></lb>i vari casi particolari. </s>

<s>Si compiaceva di ciò molto a ragione il Nostro, perchè <lb></lb>il merito della novità non consisteva semplicemente nel compendiare, o nel <lb></lb>ridurre a maggior facilità le cose da trattarsi, ma nel premostrare ai Mate­<lb></lb>matici quel vigore potente, che si verrebbe a infondere nella Scienza dal li­<lb></lb>bero uso dell&#039;analisi, applicata al Metodo degli indivisibili in quel che si <lb></lb>chiamerebbe poi Calcolo differenziale. </s>

<s>Un esempio di ciò l&#039;aveva lo stesso <lb></lb>Torricelli dato a proposito del centro di gravità nella sfera, comunque ella <lb></lb>venisse ridotta o in segmenti o in frusti, e lo udimmo poco fa quasi com­<lb></lb>passionare il Valerio, per non essersi accorto che la fatica del ritessere tante <lb></lb>volte il viaggio potevasi risparmiare movendo a dirittura dal suo primo prin­<lb></lb>cipio. </s>

<s>Un altro simile incomodo, di divagar nei particolari senz&#039;aver ricono­<lb></lb>sciuta la generalità, nella quale potevano tutti esser compresi, ebbe a notarla <lb></lb>nell&#039;argomento del centro di gravità dei solidi conoidali, intorno a che il <lb></lb>Valerio e Galileo avevano sudato tanto, per dimostrare alcune proposizioni, ri­<lb></lb>maste ne&#039;loro libri come membra sparse e inerti, perchè non ricongiunte a <lb></lb>quel principio, che avrebbe dovuto in esse far refluire la vita. </s></p><p type="main">

<s>Nel numero dei Problemi, proposti e passati scambievolmente tra i ma­<lb></lb>tematici di Francia, il Torricelli racconta di aver messo anche questo: “ Se <lb></lb>sarà il solido CFAHD (fig. </s>

<s>208), nato dalla rivoluzione di una sezione conica, <lb></lb>o sia perabola o iperbola o porzione di circolo, ovvero di ellisse, e sia tirato il <lb></lb><figure id="id.020.01.2715.1.jpg" xlink:href="020/01/2715/1.jpg"></figure></s></p><p type="caption">

<s>Figura 208.<lb></lb>piano FH parallelo alla base CD, e che seghi per <lb></lb>mezzo l&#039;asse nel punto E; chiameremo il cerchio <lb></lb>FH media sezione, e intorno a ciò si dimostrarono <lb></lb>e si proposero i due teoremi seguenti: I. </s>

<s>Il solido <lb></lb>predetto, al suo cono inscritto, sarà come una sua <lb></lb>base, con quattro medie sezioni, e due sue basi. </s>

<s><lb></lb>II. </s>

<s>Ma facendosi come una base, con due medie <lb></lb>sezioni, a due medie sezioni, così la retta AO alla <lb></lb>OB; sarà il punto O centro di gravità di quel tale solido. </s>

<s>” </s></p><p type="main">

<s>“ Nella prima di queste due enunciazioni sta compendiata ùna gran <pb xlink:href="020/01/2716.jpg" pagenum="341"></pb>parte delle dottrine di Archimede, cioè la sostanza principale delli libri <emph type="italics"></emph>De <lb></lb>sphaera et cylindro,<emph.end type="italics"></emph.end> et <emph type="italics"></emph>De sphaer. </s>

<s>et conoidibus:<emph.end type="italics"></emph.end> nella seconda poi sta gran­<lb></lb>dissima parte della dottrina di Luca Valerio, del Commandino e del Galileo, <lb></lb>i quali, con numero grandissimo di proposizioni, hanno cercato i centri di <lb></lb>gravità nei solidi delle sezioni coniche, i quali da noi in una sola proposi­<lb></lb>zione sono stati ristretti. </s>

<s>L&#039;uno e l&#039;altro dei predetti teoremi si dimostra <lb></lb>con una sola dimostrazione. </s>

<s>La proposta fu lodata in Francia, ma non già <lb></lb>sciolta, ed io qualche anno dopo conferii la dimostrazione con gli amici d&#039;Ita­<lb></lb>lia ” (MSS. Gal. </s>

<s>Disc., T. XXXII, fol. </s>

<s>25). Uno de&#039;qùali amici, e de&#039;primi, <lb></lb>dee essere stato il Michelini, a cui, il di 3 Febbraio 1642, annunziava, in­<lb></lb>sieme col teorema centrobarico generale del Guldin, anche i due sopra nar­<lb></lb>rati, chiamandoli <emph type="italics"></emph>nuovi preconizzati dal miracoloso fra Bonaventura:<emph.end type="italics"></emph.end> e <lb></lb>in che modo s&#039;avverasse il preconio lo diranno i seguenti tratti di storia. </s></p><p type="main">

<s>Riuscito a quella inaspettata trasformazione del solido descritto dal bi­<lb></lb>lineo (nato in un segmento di circolo, a cui sia <lb></lb><figure id="id.020.01.2716.1.jpg" xlink:href="020/01/2716/1.jpg"></figure></s></p><p type="caption">

<s>Figura 209.<lb></lb>stato inscritto un triangolo), in una certa sfe­<lb></lb>roide, come si vide in principio del paragrafo VI <lb></lb>del presente capitolo; il Torricelli presenti che <lb></lb>forse le medesime cose s&#039;avveravano qualunque <lb></lb>fosse la sezione conica generatrice del solido <lb></lb>rotondo, come infatti poi dimostrò aiutandosi <lb></lb>di questo lemma: “ Se in una sezione conica <lb></lb>qualunque linea AB (fig. </s>

<s>209), terminata da <lb></lb>ambe le parti nella sezione, segherà due linee <lb></lb>rette parallele CD, EF, terminanti parimente nella sezione; il rettangolo CGD, <lb></lb>al rettangolo EHF, sarà come il rettangolo AGB al rettangolo AHB ” (ivi, <lb></lb>T. XL, fol. </s>

<s>26). </s></p><p type="main">

<s>Per la dimostrazione si cita il libro archimedeo <emph type="italics"></emph>De conoid. </s>

<s>et sphaer.,<emph.end type="italics"></emph.end><lb></lb>dalle proposizioni XIII, XIV e XV del quale resulta che, condotta la tan­<lb></lb>gente IL, parallela ad AB, e la ML parallela ad EF, i rettangoli CGD, EHF, <lb></lb><figure id="id.020.01.2716.2.jpg" xlink:href="020/01/2716/2.jpg"></figure></s></p><p type="caption">

<s>Figura 210.<lb></lb>e parimente i rettangoli AGB, AHB stanno <lb></lb>come i quadrati ML, LI: d&#039;onde immedia­<lb></lb>tamente si conclude il proposito, che cioè <lb></lb>quegli stessi quattro rettangoli sono in pro­<lb></lb>porzione fra loro. </s>

<s>Dietro ciò passava così il <lb></lb>Torricelli a proporre, e a dimostrare il di­<lb></lb>vinato teorema: </s></p><p type="main">

<s>“ Sia una sezione di cono, il cui asse <lb></lb>AB (fig. </s>

<s>210), triangolo inscritto CAD, e gi­<lb></lb>risi la figura: dico che il residuo del solido, levatone il cono inscritto, sarà <lb></lb>uguale ad una tale sferoide, il cui asse sia AB. ” </s></p><p type="main">

<s>“ Sia il quadrato FB doppio al quadrato BC, e congiunta AF seghi la <lb></lb>sezione in E, ed applicata EG facciasi, per li punti A, I, B, una ellisse in­<lb></lb>torno all&#039;asse AB, e girisi, Intendasi poi la figura segata con un piano LP <pb xlink:href="020/01/2717.jpg" pagenum="342"></pb>parallelo alla base. </s>

<s>Essendo ora il quadrato FB doppio del BC, sarà EG dop­<lb></lb>pio del GI, e però il rettangolo EIH eguale al quadrato IG, e però l&#039;armilla <lb></lb>EI eguale al cerchio IG. </s>

<s>Ma l&#039;armilla LM, all&#039;armilla EI, sta come il ret­<lb></lb>tangolo LMP al rettangolo EIH, ovvero, per il lemma precedente, come il <lb></lb>rettangolo CMA al rettangolo CIA, cioè, come il rettangolo BOA al rettan­<lb></lb>golo BGA, cioè come il quadrato ON al quadrato GI. </s>

<s>Ma i conseguenti sono <lb></lb>uguali, però anche gli antecedenti, cioè l&#039;armilla LM sarà uguale al cerchio <lb></lb>ON, et sic semper, ergo patet propositum ” (ivi). </s></p><p type="main">

<s>Così, il conoide si veniva a risolvere in due figure, delle quali era nota <lb></lb>la stereometria, e si poteva con gran facilità, componendo, ricavarne la pro­<lb></lb>porzione di tutto il solido a una delle sue parti componenti, come per esem­<lb></lb>pio al cono inscritto, intorno a che il Torricelli si proponeva di dimostrare: <lb></lb>“ Se sarà una porzione di sfera o sferoide, ovvero conoide parabolico, op­<lb></lb>pure iperbolico, di cui asse sia AB (nella figura 208 qui poco addietro) e <lb></lb>cono inscritto CAD, e dal mezzo dell&#039;asse sia applicata la EF; dico che tutto <lb></lb>il solido al cono sta come il quadrato FE, col quadrato EG, al doppio del <lb></lb>quadrato EG ” (ivi). </s></p><p type="main">

<s>Per la dimostrazione supponesi un lemma, taciuto dall&#039;Autore per al­<lb></lb>cune ragioni, che appariranno in seguito da questa intima storia svelate, ma <lb></lb>intanto quel lemma è tale: <emph type="italics"></emph>La sferoide è doppia del rombo solido inscritto,<emph.end type="italics"></emph.end><lb></lb>verità, che si conclude per corollario immediato dalla XXIX archimedea <emph type="italics"></emph>De <lb></lb>conoid. </s>

<s>et sphaer.,<emph.end type="italics"></emph.end> semplicemente osservando che, se le due emisferoidi sono <lb></lb>uguali ciascuna al doppio del cono inscritto, sarà la sferoide intera uguale <lb></lb>al doppio del rombo solido, composto di quegli stessi due coni, la misura dei <lb></lb>quali essendo AB.<foreign lang="grc">π</foreign>GE2/3=AB.<foreign lang="grc">π</foreign>FG.GH/3, sarà perciò AB.2<foreign lang="grc">π</foreign>.FG.GH/3 <lb></lb>la misura della sferoide o del bilineo, che chiameremo Bo, tra il quale e <lb></lb>Co, che vuol dire il cono CAD inscritto e misurato da AB.<foreign lang="grc">π</foreign>CB2/3; interce­<lb></lb>derà la proporzione Bo:Co=2FG.GH:CB2, la quale, per essere CB= <lb></lb>2EG, e perciò CB2=4EG, sostituendo, <emph type="italics"></emph>et sumptis dimidiis,<emph.end type="italics"></emph.end> si trasformerà <lb></lb>in quest&#039;altra Bo:Co=FG.GH:2EG2. </s>

<s>Poi, componendo, e osservando che <lb></lb>il bilineo insieme col cono compongono tutto il solido So, avremo So:Co= <lb></lb>FG.GH+2EG2:2EG2. </s>

<s>Sostituendo in fine, in luogo del rettangolo, la diffe­<lb></lb>renza de&#039;quadrati espressa da FE2—EG2, avremo So:Co=FE2+EG2:2 ES2, <lb></lb>come concisamente viene il Torricelli a dimostrare così, col suo proprio di­<lb></lb>scorso: </s></p><p type="main">

<s>“ Il solido descritto dal bilineo CFA già è uguale ad una sferoide, il <lb></lb>cui asse sia BA, ed il cui massimo cerchio sia uguale all&#039;armilla FG, ovvero, <lb></lb>risolvendo la sferoide in cono, è uguale ad un cono, la cui altezza sia BA, <lb></lb>ed il quadrato del semidiametro della base fosse due rettangoli FG.GH, <lb></lb>perchè allora la base del cono sarà doppia dell&#039;armilla FG, e però doppia <lb></lb>del massimo cerchio della sferoide. </s>

<s>Dunque il solido del detto bilineo CFA, <lb></lb>al cono inscritto, sta come due rettangoli FG.GH al quadrato CB, cioè a <pb xlink:href="020/01/2718.jpg" pagenum="343"></pb>quattro quadrati EG: ovvero <emph type="italics"></emph>sumptis dimidiis,<emph.end type="italics"></emph.end> come il rettangolo FGH a <lb></lb>due quadrati GE. <emph type="italics"></emph>Et componendo patet propositum ”<emph.end type="italics"></emph.end> (ivi). </s></p><p type="main">

<s>Nel <emph type="italics"></emph>Raćconto<emph.end type="italics"></emph.end> dei problemi proposti ai Matematici francesi udimmo dianzi <lb></lb>il teorema formulato dal Torricelli in altra maniera, alla quale è facile ri­<lb></lb>durre questa, ora espressa dalla relazione So:Co=FE2+EG2:2EG2, <lb></lb>perch&#039;essendo EG=CB/2, sostituendo, e moltiplicando per <foreign lang="grc">π</foreign>, avremo So:Co= <lb></lb><foreign lang="grc">π</foreign>FE2+<foreign lang="grc">π</foreign>CB2/4:CB2/2=<foreign lang="grc">π</foreign>CB2+4<foreign lang="grc">π</foreign>FE2:2<foreign lang="grc">π</foreign>CB2, che vuol dire appunto, <lb></lb>rammemorandoci che la FE sega l&#039;asse nel mezzo, stare il solido al cono <lb></lb>inscritto come una sua base, con quattro medie sezioni, a due basi. </s></p><p type="main">

<s>Udimmo pure, in quel Racconto, il Torricelli compiacersi di avere in <lb></lb>questo suo teorema compendiata una gran parte delle dottrine di Archimede, <lb></lb>per conferma di che, specialmente contro i dubitanti della verità delle con­<lb></lb>clusioni, alle quali conduceva il metodo del Cavalieri; faceva notare come il <lb></lb>detto teorema universalissimo, applicato ai vari casi particolari, concordava <lb></lb>con le proposizioni dimostrate ne&#039;libri <emph type="italics"></emph>De sphaera et cylindro,<emph.end type="italics"></emph.end> e <emph type="italics"></emph>De conoid. </s>

<s><lb></lb>et sphaeralibus.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto conoides parabolicum CFAHD (nella medesima figura 298), conus <lb></lb>inscriptus CAD, axis AB sectus bifariam in E, et applicata EF. </s>

<s>Dixi conoi­<lb></lb>des ad conum esse ut duo quadrata ex EF, EG, ad duplum quadrati EG, ut <lb></lb>ostensum est. </s>

<s>Dico convenire cum Archimedis XXIII <emph type="italics"></emph>De con. </s>

<s>et spaer.<emph.end type="italics"></emph.end> Pona­<lb></lb>tur enim quadratum EF esse ut duo: erit AD ut quatuor, et ideo EG ut <lb></lb>unum. </s>

<s>Quare, componendo sumptisque consequentium duplis, erit quadratum <lb></lb>FE, cum quadrato EG, ad duo quadrata ex EG, ut 3 ad duo. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Che la proposizione universalissima concordi con quella della Sfera, <lb></lb>et con la XXIX De con. </s>

<s>et spaer.:<emph.end type="italics"></emph.end> Sit hemisphaerium, vel hemisphaeroides <lb></lb>ABC (fig. </s>

<s>211), conus inscriptus ABC, axis BD sectus <lb></lb><figure id="id.020.01.2718.1.jpg" xlink:href="020/01/2718/1.jpg"></figure></s></p><p type="caption">

<s>Figura 211.<lb></lb>sit bifariam in E, et applicata EF. </s>

<s>Dixi hemisphaerium <lb></lb>ad conum inscriptum esse ut duo quadrata ex FE et ex <lb></lb>EG, ad duplum quadrati EG. </s>

<s>Probo convenire cum Ar­<lb></lb>chimede. </s>

<s>Esto axis integer BH, ponaturque quadratum <lb></lb>FE esse 3. Quadratum FE, ad quadratum AD, est ut <lb></lb>rectangulum BFH, ad rectangulum BDH, nempe ut <lb></lb>3 ad 4. Quadratum vero AD ad EG est ut 4 ad 1. Ergo <lb></lb>ex aequo quadratum FE, ad EG, est ut 3 ad 1. Ergo, <lb></lb>componendo, sumptisque consequentium duplis, patet duo quadrata FE, EG, <lb></lb>ad duo quadrata EG, esse ut 4 ad 2 ” (MSS. Gal. </s>

<s>Disc., T. XXX, fol. </s>

<s>184). </s></p><p type="main">

<s>Soggiunse il Torricelli a queste due un&#039;altra Nota, per provar <emph type="italics"></emph>che la <lb></lb>dimostrazione universalissima, nel conoide iperbolico e nella porzion di <lb></lb>sferoide, concordi con la volgata di Archimede XXVII e XXXI De conoid. </s>

<s><lb></lb>et sphaer.<emph.end type="italics"></emph.end> (ivi). Rappresenti AIBC (fig. </s>

<s>212) una delle iperbole, l&#039;asse DB <lb></lb>della quale sia prolungato infino a incontrare in E il vertice dell&#039;altra iper­<lb></lb>bola. </s>

<s>Sia L il centro, ed EO uguale ad EL, cosicchè insomma sia BO ses-<pb xlink:href="020/01/2719.jpg" pagenum="344"></pb>quialtera della BE, ossia quella stia a questa come tre a due. </s>

<s>Chiamato S <lb></lb><figure id="id.020.01.2719.1.jpg" xlink:href="020/01/2719/1.jpg"></figure></s></p><p type="caption">

<s>Figura 212.<lb></lb>il solido, C il cono inscritto, dimostra nella <lb></lb><figure id="id.020.01.2719.2.jpg" xlink:href="020/01/2719/2.jpg"></figure></s></p><p type="caption">

<s>Figura 213.<lb></lb>detta XXVII Archimede che So:Co= <lb></lb>OD:DE. </s></p><p type="main">

<s>Rappresenti in simil guisa AIBC (fi­<lb></lb>gura 213) una porzion di sferoide, l&#039;asse BE <lb></lb>della quale sia prolungato in fin tanto che, <lb></lb>giunto in O, la BO non sia, come dianzi, <lb></lb>sesquialtera della BE. </s>

<s>Dimostra Archimede, <lb></lb>nella XXXI del libro citato, che il solido <lb></lb>al cono “ hanc habet rationem, quam li­<lb></lb>nea composita ex dimidio axe sphaeroidis, <lb></lb>et ex axe maioris portionis, habet ad axem <lb></lb>maioris portionis ” (Opera cit., pag. </s>

<s>322), ossia si dimostra So:Co= <lb></lb>BE/2+ED:ED. </s>

<s>Ma è facile vedere ch&#039;essendo per supposizione OB= <lb></lb>3/2 BE, OD=OB—BD=OB—BE+ED=3/2 BE—BE+ED= <lb></lb>BE/2+ED: onde in ambedue i casi bastò al Torricelli di dimostrar che la <lb></lb>proporzione So:Co=OD:DE di Archimede concordava con la sua, come <lb></lb>egli fece così scrivendo: </s></p><p type="main">

<s>“ Abbiamo provato che il solido tutto, al cono inscritto, sta come i due <lb></lb>quadrati insieme IG, GH al doppio del quadrato GH. </s>

<s>Mostrerò ora che li due <lb></lb>quadrati IG, GH, al doppio del quadrato GH, sono come la OD alla DE, <lb></lb>presa OB sesquialtera di BE. ” </s></p><p type="main">

<s>“ Il quadrato IG, al quadrato AD, sta come il rettangolo EGB al ret­<lb></lb>tangolo EDB, <emph type="italics"></emph>et sumptis consequentium subquadruplis,<emph.end type="italics"></emph.end> il quadrato IG, al <lb></lb>quadrato GH, sta come il rettangolo EGB al rettangolo LGB, ovvero come <lb></lb>la retta EG alla GL. E, componendo, il quadrato IG, con il quadrato GH, al <lb></lb>quadrato GH, sta come EG con GL alla GL, cioè come OD alla GL. <emph type="italics"></emph>Et <lb></lb>sumptis consequentium duplis,<emph.end type="italics"></emph.end> il quadrato IG, col quadrato GH, al doppio <lb></lb>del quadrato GH, sta come la retta OD alla DE, <expan abbr="q.">que</expan> e. </s>

<s>d. (ivi, fol. </s>

<s>186). </s></p><p type="main">

<s>La principale intenzione del Torricelli però era quella di applicare così <lb></lb>fatte questioni stereometriche alla Baricentrica, ciò che, ritornando al primo <lb></lb>proposito e alla rappresentazione di lui nella figura 208, si conseguirà col <lb></lb>dire che, costituitosi sopra l&#039;asse un punto O, in modo che sia BO:OE= <lb></lb>FE2:GE2, sarebbe in quello stesso punto O il centro di gravità del tutto. <lb></lb>“ Iisdem positis dico, si fiat ut quadratum FE, ad quadratum EG, ita BO <lb></lb>ad OE; dico, inquam, O esse centrum gravitatis totius solidi. </s>

<s>” </s></p><p type="main">

<s>“ Secetur BE bifariam in I: eritque I centrum gravitatis coni inscri­<lb></lb>pti. </s>

<s>Centrum autem reliqui solidi, dempto cono, est in medio axe, quando­<lb></lb>quidem demonstratum est singulas eiusdem solidi armillas aequales esse sin­<lb></lb>gulis circulis unius sphaeroidis, circa axem AB constitutae. </s>

<s>” </s></p><p type="main">

<s>“ Jam BO ad OE est ut quadratum FE ad quadratum EG. Et, com-<pb xlink:href="020/01/2720.jpg" pagenum="345"></pb>ponendo, erit BE ad EO ut quadrata FE, EG, ad quadratum EG, vel ut duo <lb></lb>quadrata FE, cum duobus EG, ad duo quadrata EG. </s>

<s>Sumptisque anteceden­<lb></lb>tium dimidiis, erit IE ad EO ut quadratum FE, cum quadrato EG, ad duo <lb></lb>quadrata EG: nempe ut totum solidum ad conum inscriptum. </s>

<s>Puncta vero <lb></lb>I, E sunt centra partium, ergo O erit centrum totius ” (ivi, T. XL, fol. </s>

<s>27). </s></p><p type="main">

<s>Nel Racconto de&#039;problemi ai Francesi era questo teorema, come si ram­<lb></lb>menteranno i Lettori, formulato altrimenti, ond&#039;è che, a mostrarne la con­<lb></lb>cordanza, il Torricelli stesso così ragionava: “ Esto BE ad OE ut quadra­<lb></lb>tum FE ad EG. Ergo, componendo, BE ad EO erit ut quadrata FE, EG ad <lb></lb>quadratum EG. Convertendo, OE ad EA ut quadratum EG ad duo quadrata <lb></lb>FE, EG. Et, componendo, AO ad AE ut quadrata EG, FE, EG ad duo qua­<lb></lb>drata FE, EG. </s>

<s>Sumptis vero consequentium duplis, erit OA ad AB ut qua­<lb></lb>drata EG, EG, FE ad quadrata EG, EG; FE, FE. </s>

<s>Et convertendo erit BA <lb></lb>ad AO ut quadrata EG, EG; FE, FE, ad quadrata EG, EG; FE ” (ivi, <lb></lb>T. XXXVI, fol. </s>

<s>219), ossia, facendo uso dei segni analitici, BA:AO= <lb></lb>2GE2+2FE2:2EG2+FE2. </s>

<s>Dividendo, riducendo e trasponendo, AO:BO= <lb></lb>2EG2+FE2:FE2=4<foreign lang="grc">π</foreign>EG2+.2<foreign lang="grc">π</foreign>FE2:2<foreign lang="grc">π</foreign>FE2=<foreign lang="grc">π</foreign>CB2+2<foreign lang="grc">π</foreign>FE2:2<foreign lang="grc">π</foreign>FE. </s>

<s><lb></lb>Alla qual riduzione accennava così lo stesso Torricelli: “ Nota che AO ad OB <lb></lb>sta come quattro quadrati EG, con due quadrati FE, a due quadrati FE: <lb></lb>ovvero, come il quadrato CB, con due quadrati FE, a due quadrati FE: cioè, <lb></lb>ed è il mio intento, come un cerchio CD, con due FH, a due FH ” (ivi): <lb></lb>a seconda del quale intento aveva stabilito di formulare così quella che, dopo <lb></lb>le altre da noi scritte, era in ordine la </s></p><p type="main">

<s>“ PROPOSIZIONE XLVI. — <emph type="italics"></emph>Centrum gravitatis cuiuscumque conoidalis, <lb></lb>verticem habentis, dividit axem solidi, ita ut pars ad verticem terminata, <lb></lb>ad reliquam, sit ut basis solidi, cum duobus circulis qui axem bifariam <lb></lb>secant, ad duos circulos, qui axem bifariam secant ”<emph.end type="italics"></emph.end> (ivi, T. XXV, fol. </s>

<s>58). </s></p><p type="main">

<s>Essendo dunque AB l&#039;asse del conoide, con l&#039;una estremità A al ver­<lb></lb>tice, e con l&#039;altra B alla base, e chiamato B il circolo di essa base, S quello <lb></lb>della media sezione, il punto O, dove riesce il centro di gravità del solido, <lb></lb>sarà indicato dalla relazione AO/BO=(B+2S)/2S. </s>

<s>Con ciò poneva il Torricelli <lb></lb>il fondamento alla nuova baricentrica dei conoidei, ai progressi della quale <lb></lb>gli soccorreva opportuna un&#039;altra proposizione stereometrica, suggeritagli da <lb></lb>Michelangiolo Ricci. </s>

<s>Gli scriveva questi da Roma una lettera, nel di 16 Gen­<lb></lb>naio 1644, per descrivergli il modo com&#039;aveva dimostrato che un frusto co­<lb></lb>nico, toltine due coni appuntati insieme sull&#039;asse, fosse uguale a un terzo <lb></lb>cono, che avesse per base la superficie laterale involgente il solido intero, e <lb></lb>per altezza la perpendicolare, condotta dal vertice comune ai due detti coni <lb></lb>sopra uno degli apotemi del frusto. </s>

<s>Nel processo della dimostrazione s&#039;in­<lb></lb>voca più volte un teorema, non con altro segno indicato che di un asteri­<lb></lb>sco, intorno al quale teorema il Ricci stesso così si dichiarava: “ Devo solo <lb></lb>avvertire V. S. che, dove vedrà questo asterisco, denota il bisogno di una <lb></lb>proposizione, che mi trovo aver dimostrata in tre maniere, della quale feci <pb xlink:href="020/01/2721.jpg" pagenum="346"></pb>a V. S. un cenno questa Pasqua passata: cioè che il frusto conico è uguale <lb></lb>a tre coni, che abbiano la medesima altezza del frusto, ma che due basi siano <lb></lb>le medesime che del frusto, e l&#039;altra del terzo cono sia media proporzionale <lb></lb>tra quelle ” (ivi, T. XLII, fol. </s>

<s>3). </s></p><p type="main">

<s>In un&#039;altra lettera, scritta pur da Roma il di 18 Giugno di quel me­<lb></lb>desimo anno, nella quale il Ricci stesso trascriveva una sua proposizione in­<lb></lb>torno ai frusti parabolici, iperbolici, etc., come si vedrà meglio altrove; diceva <lb></lb>al Torricelli di essersi valuto di quel medesimo teorema, in cui risolveva lo <lb></lb>stesso frusto in tre coni, ma non resulta, nè di qui, nè da altre carte ca­<lb></lb>duteci sott&#039;occhio, che ne comunicasse la dimostrazione all&#039;amico, il quale <lb></lb>ebbe a ritrovarla da sè, senz&#039;alcuna difficoltà, aiutandosi dei due lemmi se­<lb></lb>guenti: </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma I.<emph.end type="italics"></emph.end> — Si a circulo duo circuli demantur, ita ut duo diametri <lb></lb>simul demptorum circulorum totam alterius circuli diametrum exaequent; <lb></lb>erit reliqua perforata lunula, ad assumptum circulum quemlibet, ut semissis <lb></lb><figure id="id.020.01.2721.1.jpg" xlink:href="020/01/2721/1.jpg"></figure></s></p><p type="caption">

<s>Figura 214.<lb></lb>rectanguli, sub diametris dempto­<lb></lb>rum circulorum contenti, ad qua­<lb></lb>dratum radii assumpti circuli. </s>

<s>” </s></p><p type="main">

<s>“ Esto etc. </s>

<s>et sint centra to­<lb></lb>tius circuli C, demptorum B et E <lb></lb>(fig. </s>

<s>214), et intelligatur primo <lb></lb>demptus solum circulus AD: erit­<lb></lb>que reliqua integra lunula aequa­<lb></lb>lis armillae unius rectanguli FEA. </s>

<s><lb></lb>Erit ergo integra lunula, ad cir­<lb></lb>culum FD, ut rectangulum FEA, <lb></lb>sive DEA, ad quadratum DE. Et, <lb></lb>dividendo, lunula perforata, ad <lb></lb>eumdem circulum DF, erit ut re­<lb></lb>ctangulum EDA ad quadratum <lb></lb>DE. </s>

<s>Circulus vero DF, ad circu­<lb></lb>lum OS, est ut quadratum DE ad quadratum OS: ergo ex aequo patet pro­<lb></lb>positum. </s>

<s>Nam lunula perforata erit ad circulum OS ut rectangulum EDA, <lb></lb>nempe, ut semissis rectanguli FDA, sub diametris demptorum circulorum <lb></lb>contenti, ad quadratum OS ” (ivi, T. XXXVI, fol. </s>

<s>47). </s></p><p type="main">

<s>Per intelligenza della qual dimostrazione, al solito tirata giù dal Torri­<lb></lb>celli più per suo memoriale, che per esser veduta da altri in quell&#039;abito <lb></lb>trasparentissimo, ma negletto, discorreremo così, facendo uso del linguaggio, <lb></lb>e dei segni dei Matematici odierni: Abbiamo per costruzione AB+DE= <lb></lb>AC, onde DE=AC—AB=BC. </s>

<s>Chiamata <emph type="italics"></emph>L<emph.end type="italics"></emph.end> la lunula, sarà <emph type="italics"></emph>L<emph.end type="italics"></emph.end>= <lb></lb><foreign lang="grc">π</foreign>AC2—<foreign lang="grc">π</foreign>AB2=<foreign lang="grc">π</foreign>(AC+AB)(AC—AB). Ma AC+AB=AB+ <lb></lb>BC+AB=AB+BC+BD=AB+BD+DE=AE. </s>

<s>Quanto al­<lb></lb>l&#039;altro coefficiente, AC—AB=DE=EF, dunque <emph type="italics"></emph>L<emph.end type="italics"></emph.end>=<foreign lang="grc">π</foreign>AE.EF. </s>

<s>Ma <lb></lb>anche l&#039;armilla EF=<foreign lang="grc">π</foreign>CF2—<foreign lang="grc">π</foreign>CE2=<foreign lang="grc">π</foreign>(CF+CE)(CF—CE)= <pb xlink:href="020/01/2722.jpg" pagenum="347"></pb><foreign lang="grc">π</foreign>AE.EF; dunque <emph type="italics"></emph>lunula integra est aequalis armillae unius rectanguli <lb></lb>AEF,<emph.end type="italics"></emph.end> come l&#039;Autore dianzi diceva. </s></p><p type="main">

<s>Chiamato C il circolo dal diametro FD, ed L al solito la lunula, <lb></lb>avremo dunque L:C=AE.EF:DE2. </s>

<s>Dividendo, sarà L—C:C= <lb></lb>AE.EF—DE2:DE2=AE.ED—DE2:DE2=ED(AE—DE):DE2= <lb></lb>ED.DA:DE2. </s>

<s>Chiamisi ora C′ un altro circulo qualunque, di raggio OS: <lb></lb>avremo C′:C=OS2:DE2, e di qui L—C:C′=ED.DA:CB2, e sostituito <lb></lb>DE=DF/2, L—C:C′=FD.DA/2:OS2. </s>

<s>Ma L—C rappresenta la lunula <lb></lb>perforata dal circolo DF, e C′ il circolo assunto, dunque si conferma di qui <lb></lb>la verità del lemma torricelliano. </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma II.<emph.end type="italics"></emph.end> — Perforatae lunulae, quales ante dicebamus, sunt inter <lb></lb>se ut rectangula sub diametris demptorum circulorum contenta. </s>

<s>” </s></p><p type="main">

<s>“ Esto etc.: erit <lb></lb><figure id="id.020.01.2722.1.jpg" xlink:href="020/01/2722/1.jpg"></figure></s></p><p type="caption">

<s>Figura 215.<lb></lb>ergo lunula perforata <lb></lb>AMP (fig. </s>

<s>215), ad cir­<lb></lb>culum FH, ut rectan­<lb></lb>gulum ABC ad qua­<lb></lb>dratum FI. </s>

<s>Sed circu­<lb></lb>lus FH, ad lunulam <lb></lb>perforatam EOR, est ut <lb></lb>quadratum FI ad re­<lb></lb>ctangulum EFI; ergo <lb></lb>ex aequo lunula perfo­<lb></lb>rata AMP, ad lunulam perforatam EOR, est ut rectangulum ABC ad rectan­<lb></lb>gulum EFI, sive, sumptis duplis, ut rectangulum ABD ad rectangulum EFH ” <lb></lb>(ibid.). </s></p><p type="main">

<s>Premessi i quali due lemmi, passa il Torricelli a dimostrare, in una sua <lb></lb>prima proposizione, che, tolti dal frusto conico i due coni designati dal Ricci, <lb></lb>quel che riman del solido uguaglia una sferoide, la quale dimostra, in un&#039;al­<lb></lb><figure id="id.020.01.2722.2.jpg" xlink:href="020/01/2722/2.jpg"></figure></s></p><p type="caption">

<s>Figura 216.<lb></lb>tra proposizione, risolversi in quel terzo <lb></lb>cono, dallo stesso Ricci designato per me­<lb></lb>dio proporzionale tra gli altri due. </s></p><p type="main">

<s><emph type="italics"></emph>Proposizione prima.<emph.end type="italics"></emph.end> — “ Si a seg­<lb></lb>mento conico demantur duo coni, aeque <lb></lb>alti cum segmento, et super utraque ipsius <lb></lb>basi constituti, reliquum solidum erit ae­<lb></lb>quale sphaeroidi cuidam, eamdem cum <lb></lb>segmento conico altitudinem habenti. </s>

<s>” </s></p><p type="main">

<s>“ Esto segmentum coni ABCD (fig. </s>

<s>216), cuius axis EF, et ab ipso de­<lb></lb>mantur duo coni ABD, BDC, etc. </s>

<s>Ponatur quadratum PH duplum quadrati <lb></lb>GH, et per PO intelligatur planum oppositis basibus parallelum: eritque lu­<lb></lb>nula perforata PO, demptis circulis PH, HO, aequalis circulo, cuius radius <lb></lb>GH, ob constructionem, et ex demonstratis ” (ibid., fol. </s>

<s>48). </s></p><pb xlink:href="020/01/2723.jpg" pagenum="348"></pb><p type="main">

<s>La lunula PO infatti, perforata da circoli uguali, che hanno per diametro <lb></lb>ciascuno la metà di PO, ossia PH, ovvero OH, chiamata al solito L, sarà uguale <lb></lb>a <foreign lang="grc">π</foreign>PH2—<foreign lang="grc">π</foreign>PH2/4—<foreign lang="grc">π</foreign>OH2/4=<foreign lang="grc">π</foreign>PH2/2. Ma perchè si è fatto PH2=2GH2, <lb></lb>sarà dunque L=<foreign lang="grc">π</foreign>PH2/2=<foreign lang="grc">π</foreign>GH2, e perciò sarà la lunula uguale a un cir­<lb></lb>colo, che abbia per raggio GH, come dice l&#039;Autore. </s></p><p type="main">

<s>Ora è chiaro che, riguardando il proposto frusto conico come compagi­<lb></lb>nato d&#039;infiniti circoli eretti all&#039;asse, verrà il solido dai due coni ABD, BDC <lb></lb>terebrato in modo, che di ciascun di que&#039;circoli riman solo una lunula per­<lb></lb>forata, ciascuna delle quali dimostra il Torricelli equivalere al circolo della <lb></lb>sferoide, descritta da una semiellisse, che passi per i punti E, G, F, e che <lb></lb>si rivolga intorno alla EF, come a suo proprio asse. </s></p><p type="main">

<s>Sia, fra quegli infiniti circoli, in che si assomma il frusto, considerata <lb></lb>la sezione LN. È facile dimostrare che la lunula perforata è uguale al circolo <lb></lb>dell&#039;ellissoide, descritto dal raggio IQ intorno all&#039;asse. </s>

<s>Sarà infatti, per il <lb></lb>secondo lemma, significando la lunula col solito simbolo <emph type="italics"></emph>L, L<emph.end type="italics"></emph.end>.PN:<emph type="italics"></emph>L<emph.end type="italics"></emph.end>.PO= <lb></lb>LM.MN:PH.HO. Ma, per ragion delle parallele LN.PO, abbiamo le due <lb></lb>proporzioni LM:PH=EI:EH; MN:HO=IF:FH, le quali, moltiplicate <lb></lb>termine per termine, danno LM.MN:PH.HO=EI.IF:EH.HF; ond&#039;è <lb></lb>che <emph type="italics"></emph>L<emph.end type="italics"></emph.end>.LN:<emph type="italics"></emph>L<emph.end type="italics"></emph.end>.PO=EI.IF:EH.HF. Ma, per la natura dell&#039;ellisse, <lb></lb>EI.IF=IQ2, EH.HF=GH2; dunque <emph type="italics"></emph>L<emph.end type="italics"></emph.end>.LN:<emph type="italics"></emph>L<emph.end type="italics"></emph.end>.PO=<foreign lang="grc">π</foreign>IQ2:<foreign lang="grc">π</foreign>GH2. </s>

<s><lb></lb>Ora è per supposizione <emph type="italics"></emph>L<emph.end type="italics"></emph.end>.PO=<foreign lang="grc">π</foreign>GH2, dunque anche <emph type="italics"></emph>L<emph.end type="italics"></emph.end>.LN=<foreign lang="grc">π</foreign>IQ2, e <lb></lb>ciò a qualunque punto sia fatta la sezione LN, cosicchè sempre la lunula <lb></lb>perforata sarà uguale al circolo, e perciò tutte le lunule perforate compor­<lb></lb>ranno un solido uguale all&#039;ellissoide intera, come nel suo manoscritto il Tor­<lb></lb>ricelli stesso dimostra con queste parole: </s></p><p type="main">

<s>“ Fiat per puncta EGF ellipsis circa axem EF, et convertatur, sectoque <lb></lb>segmento per planum LN, basibus parallelum, erit lunula perforata LN, ad <lb></lb>lunulam perforatam PO, ut rectangulum LMN ad rectangulum PHO, nempe <lb></lb>rationem compositam habebit ex rationibus LM ad PH, et MN ad HO, sive <lb></lb>ex rationibus IE ad EH, et IF ad FH, quae sunt aeedem cum praedictis. </s>

<s><lb></lb>Ergo perforata lunula LN, ad perforatam lunulam PO, erit ut rectangulum <lb></lb>FIE ad rectangulum FHE, sive, ut circulus ex IQ, ad circulum ex HG. Con­<lb></lb><figure id="id.020.01.2723.1.jpg" xlink:href="020/01/2723/1.jpg"></figure></s></p><p type="caption">

<s>Figura 217.<lb></lb>sequentia vero ex constructione sunt aequalia, quare <lb></lb>et lunula perforata LN aequalis erit circulo ex IQ, <lb></lb>et hoc semper. </s>

<s>Quare patet propositum ” (ibid.). </s></p><p type="main">

<s><emph type="italics"></emph>Proposizione seconda.<emph.end type="italics"></emph.end> — “ Dico huiusmodi <lb></lb>sphaerois medio loco proportionalis esse inter abla­<lb></lb>tos conos. </s>

<s>” </s></p><p type="main">

<s>“ Secetur axis MN (fig. </s>

<s>217) bifariam in F, <lb></lb>ab applicata EH: eritque perforata lunula EH ae­<lb></lb>qualis maximo circulo praedictae sphaeroidis. </s>

<s>Sit quadratum I aequale re­<lb></lb>ctangulo EGH, eritque circulus, cuius radius I, ad lunulam perforatam HE, <pb xlink:href="020/01/2724.jpg" pagenum="349"></pb>ut quadratum I ad semissem rectanguli EGH, nempe duplus. </s>

<s>Propterea co­<lb></lb>nus, cuius radius basis sit I, altitudo vero MN, aequalis erit sphaeroidi, sive <lb></lb>reliquo segmenti conici, demptis duobus conis ” (ibid.). </s></p><p type="main">

<s>Sia dunque, come vuole il Torricelli, I2=EG.GH. </s>

<s>Avremo per il <lb></lb>lemma primo, significati con <emph type="italics"></emph>C<emph.end type="italics"></emph.end> il circolo, e con <emph type="italics"></emph>L<emph.end type="italics"></emph.end> la lunula, <emph type="italics"></emph>C<emph.end type="italics"></emph.end>.I:<emph type="italics"></emph>L<emph.end type="italics"></emph.end>.EH= <lb></lb>I2:EG.GH/2, che vuol dire il circolo esser doppio della lunula, e perciò il <lb></lb>cono, la base del quale abbia per raggio I, con l&#039;altezza MN, sarà, per fa­<lb></lb>cile corollario dalla XXIX archimedea <emph type="italics"></emph>De conoid. </s>

<s>et sphaer.,<emph.end type="italics"></emph.end> uguale alla <lb></lb>sferoide. </s></p><p type="main">

<s>È il presente proposito quello di dimostrare che una tale sferoide, o il <lb></lb>cono a lei equivalente, è medio proporzionale fra i due coni ABD, BDC, le­<lb></lb>vati dal frusto, i quali coni, per avere altezza uguale, stanno come i qua­<lb></lb>drati de&#039;raggi delle basi, ossia come AN2 a BM2. </s>

<s>Ma anche il terzo cono, a <lb></lb>cui s&#039;è detto uguagliarsi la sferoide, ha la medesima altezza degli altri due; <lb></lb>dunque tutto si riduce a dimostrare che il quadrato del raggio I, ossia il <lb></lb>rettangolo EG.GH è medio proporzionale tra AN2 e BM2, ciò che si può <lb></lb>fare in questa maniera: Abbiamo, per ragion delle parallele, NF:FM= <lb></lb>AE:EB. Componendo, NF+FM:FM=AE+EB:EB, ossia NM:FM= <lb></lb>AB:EB. </s>

<s>Ma NM=2FM, dunque AB=2EB, e perciò AD=2EG, ossia <lb></lb>AN=EG, come, per le medesime ragioni, GH=BM. </s>

<s>Ora EG:GH= <lb></lb>EG2:EG.GH=EG.GH:GH2, per cui, sostituendo AN2 ad EG2, se ne <lb></lb>concluderà il proposito, come il Torricelli stesso lo conclude con questo di­<lb></lb>scorso: </s></p><p type="main">

<s>“ Conum autem praedictum I medium proportionalem esse inter ABD, <lb></lb>BDC, patet. </s>

<s>Nam, cum rectangulum EGH medium sit inter quadratum AN, <lb></lb>BM, etiam quadratum I medium erit inter eadem. </s>

<s>Et propterea conus I, sive <lb></lb>sphaerois illa media proportionalis erit inter demptos conos. </s>

<s>Erit enim, ob <lb></lb>parallelas, ut NF ad FM, ita AE ad EB. </s>

<s>Et componendo etc. </s>

<s>Sed NM dupla <lb></lb>est MF; ergo AB dupla est BE, et propterea AD dupla EG. </s>

<s>Quare AN et <lb></lb>EG sunt aequales, et GH, BM sunt aequales. </s>

<s>Quadratum vero EG, ad rectan­<lb></lb>gulum EGG, est ut EG ad GH, et rectangulum EGH, ad quadratum GH, <lb></lb>est ut EG ad GH. </s>

<s>Quare patet propositum ” (ibid.). </s></p><p type="main">

<s>Così dimostrava il Torricelli, con la fecondità del suo proprio ingegno, <lb></lb>in una maniera forse diversa da quelle tre usate dal Ricci, la risoluzione del <lb></lb>frusto conico in tre coni di altezze uguali. </s>

<s>Se non che al terzo cono di mezzo <lb></lb>sostituiva una sferoide, perchè l&#039;intento suo principale era quello di trasporre <lb></lb>la bella proposizione, dal campo della Stereometria pura, dove lo stesso Ricci <lb></lb>l&#039;aveva lasciata, in quello della Baricentrica. </s>

<s>Riducendosi infatti il centro di <lb></lb>gravità di essa sferoide nel mezzo dell&#039;asse, si venivano a render più sem­<lb></lb>plici, nella libbra gravata delle parti, nelle quali era il solido risoluto, le ra­<lb></lb>gioni delle equiponderanze. </s></p><p type="main">

<s>Venne al nostro Autore l&#039;occasione di far ciò, essendo intorno a esami­<lb></lb>nare le proposizioni galileiane <emph type="italics"></emph>De centro gravitatis,<emph.end type="italics"></emph.end> alcuna delle quali essen-<pb xlink:href="020/01/2725.jpg" pagenum="350"></pb>dosi da lui sospettata per falsa, volle d&#039;altre confermare la verità, in chi ne <lb></lb>avesse dubitato, per averle forse trovate di non facile intelligenza. </s>

<s>Tale parve <lb></lb>la X, nella quale, premesso un lemma geometrico, Galileo dimostrava che, <lb></lb>nel frusto di un cono o di una piramide, il centro di gravità sega talmente <lb></lb><figure id="id.020.01.2725.1.jpg" xlink:href="020/01/2725/1.jpg"></figure></s></p><p type="caption">

<s>Figura 218.<lb></lb>l&#039;asse, che la parte verso la base minore <lb></lb>stia all&#039;altra, “ ut tripla minoris basis, <lb></lb>cum spatio duplo medii geometrici inter <lb></lb>basin maiorem et minorem, una cum basi <lb></lb>minori; ad triplam minoris basis eum eo­<lb></lb>dem duplo spatii medii, ac una cum basi <lb></lb>maiori ” (Alb. </s>

<s>XIII, 286). O altrimenti, <lb></lb>rappresentandosi dalla figura 218 il frusto <lb></lb>proposto, con l&#039;asse EF parallelo alla lib­<lb></lb>bra AL, e significandosi con B la maggior basè AD, con B′ la minore BC, e <lb></lb>con B″ una media proporzionale fra ambedue; vuol Galileo dimostrare che <lb></lb>il centro Q dell&#039;equilibrio è indicato dalla relazione QL/AQ=(3B+B′+2B″)/(B+3B′+2B″). <lb></lb>Ora il Torricelli applicava al caso le dimostrate risoluzioni del frusto conico, <lb></lb>e confermava esser veramente tale nel solido la ragion dell&#039;equiponderanza, <lb></lb>con la seguente illustrazione stupenda delle dottrine di Galileo: </s></p><p type="main">

<s>“ PROPOSIZIONE XLVII. — <emph type="italics"></emph>Segmentum coni habet centrum gravitatis, <lb></lb>ut ait Galileus propos. </s>

<s>ultima appendicis<emph.end type="italics"></emph.end> De centro gravitatis solidorum. </s>

<s>” </s></p><p type="main">

<s>“ Esto frustum coni ABCD (nella precedente figura) cuius axis FE, <lb></lb>appensumque sit ad libram AL, ita ut circuli, qui per AD, BC ducuntur, <lb></lb>perpendiculares sint ad horizontem. </s>

<s>Tum, secta FE in quatuor partes aequa­<lb></lb>les per puncta H, G, I, ducantur perpendicula OH, MG, NI, LE. </s>

<s>Trium ergo <lb></lb>magnitudinum ad libram appensarum centra gravitatis erunt in rectis OH, <lb></lb>MG, NI: nempe, coni ACD, in OH; coni BAC in NI, reliqui vero solidi in <lb></lb>GM, quandoquidem ostensum est singulas ipsius perforatas lunulas aequales <lb></lb>esse singulis circulis alicuius sphaeroidis, cuius axis erat FE. ” </s></p><p type="main">

<s>“ Centrum vero praedictarum trium magnitudinum sic habebitur: In­<lb></lb>telligatur unaquaeque dictarum magnitudinum divisa in quatuor partes ae­<lb></lb>quales, et concipiantur appendi ad libram, ita ut coni ACD 3/4 pendeant ex <lb></lb>A, reliqua vero 1/4 ex L. </s>

<s>Coni vero BAC 3/4 pendeant ex L, reliqua vero <lb></lb>1/4 ex A. </s>

<s>Reliqui tandem solidi 2/4 pendeant ex A. et 2/4 ex L. </s>

<s>Manifestum <lb></lb>est punctum aequilibrii harum trium magnitudinum sectarum idem prorsus <lb></lb>futurum esse, quod erat ante illarum sectionem, quandoquidem ipsarum cen­<lb></lb>tra gravitatis, propter sectionem a nobis factam, non mutaverunt dispositionem <lb></lb>neque inter se, neque ad libram comparata. </s>

<s>” </s></p><p type="main">

<s>“ Esto illud Q, ergo, centrum gravitatis. </s>

<s>Q secabit libram AL, ita ut sit <lb></lb>AQ ad QL, quemadmodum est magnitudo, appensa ex L, ad magnitudinem <lb></lb>appensam ex A: nempe ut 3/4 coni BAC, 2/4 reliqui solidi, et 1/4 coni ACD, <lb></lb>ad 3/4 coni ACD, cum 2/4 reliqui solidi, et 1/4 coni BAC, sive, sumptis qua­<lb></lb>druplis, ut tres coni BAC, cum duobus ex reliquis solidis, et uno cono ACD, <pb xlink:href="020/01/2726.jpg" pagenum="351"></pb>ad tres conos ACD, duos ex reliquis solidis, et unum conum BAC: sive, ut <lb></lb>eorum bases, quae sunt in continua proportione, quod proposuerat Galileus. </s>

<s><lb></lb>Ostendimus enim dictum reliquum solidum cuidam sphaeroidi aequale esse, <lb></lb>quae quidem sphaerois medio loco proportionalis est inter illos duos conos. </s>

<s><lb></lb>Ergo, si ipsa reducatur ad conum aeque altum, erit ipsius basis medio loco <lb></lb>proportionalis inter bases conorum, sive inter bases segmenti nostri coni ” <lb></lb>(ibid., T. XXXVI, fol. </s>

<s>49). </s></p><p type="main">

<s>La conclusione dunque del Torricelli è analiticamente espressa da que­<lb></lb>sti segni, chiamando R quel che riman del frusto, toltine i coni sulle sue due <lb></lb>basi, QL:AQ=3/4ACD+1/4ACB+2/4R:1/4ACD+3/4ACB+2/4R. </s>

<s><lb></lb>Sostituiti gli elementi geometrici, considerando che le altezze de&#039;coni ACD, <lb></lb>ACB sono uguali, e che perciò stanno essi coni come le basi B, B′: osser­<lb></lb>vando di più che R equivale a una sferoide, o a un cono, la base del quale <lb></lb>B″ sia media fra le altre due B, B′, e l&#039;altezza sia la medesima; sarebbe un <lb></lb>perdere il tempo e le parole a dire che la formula del Torricelli si riduce <lb></lb>a quella medesima di Galileo. </s></p><p type="main">

<s>Sul finir della giornata quarta delle due Scienze nuove diceva il Sal­<lb></lb>viati, quasi proemiando a quell&#039;<emph type="italics"></emph>Appendice,<emph.end type="italics"></emph.end> che sarebbe per leggere intorno <lb></lb>ai centri di gravità, com&#039;avesse l&#039;Accademico intrapreso da giovane un tale <lb></lb>studio, per supplire a quello che si desiderava nel libro del Commandino, col <lb></lb>pensiero di andar seguitando la materia, anco negli altri solidi non tocchi da <lb></lb>lui: ma che poi, incontratosi nel trattato di Luca Valerio, non seguitò più <lb></lb>avanti, benchè fossero le sue aggressioni per istrade molto diverse (Alb. </s>

<s><lb></lb>XIII, 266). Apparisce di questa diversità, nella proposizione fin qui discorsa, <lb></lb>il più chiaro esempio, avendo esso Valerio nella XXV del suo terzo libro già <lb></lb>dimostrato il centro di gravità del frusto conico. </s>

<s>Sembra anzi che sia que­<lb></lb>sta tanto più facile e breve, che si direbbe superflua l&#039;opera aggiuntavi da <lb></lb>Galileo, se non si ripensasse che la diversità fra l&#039;una e l&#039;altra aggressione <lb></lb>non è puramente accidentale, o di semplice forma. </s>

<s>Mentre infatti il Valerio <lb></lb>chiedeva si perfezionasse il cono, per riferire a un punto preso sull&#039;asse in­<lb></lb>tero di lui il centro di gravità della porzione, Galileo invece lo riferiva alle <lb></lb>estremità dell&#039;asse proprio del frusto terminato in sè stesso. </s></p><p type="main">

<s>Ora, non contento il Torricelli di avere in sì bel modo illustrato il suo <lb></lb>Maestro, volle di più emularlo, proseguendo per quell&#039;altre strade tanto più <lb></lb>agevoli e spedite, ch&#039;egli già per sè erasi aperte. </s>

<s>Veniva di qui condotto a <lb></lb>riguardare il frusto come un bicchiere scavato da un cono. </s>

<s>La speculazione <lb></lb>era già balenata anche alla mente del Valerio, nella proposizione X del ci­<lb></lb>tato suo libro terzo, ma perchè gli mancavano gli argomenti necessari a di­<lb></lb>mostrare il centro di gravità nel detto solido scavato, dovettero quelle sue <lb></lb>speculazioni rimanersi nel campo della Geometria, limitandosi ad assegnare <lb></lb>la proporzione tra il frusto e il cono inscritto sulla base maggiore. </s></p><p type="main">

<s>I processi torricelliani si vedono in fin da questo punto già disegnati: <lb></lb>il bicchiere e il cono pendono come da libbra dall&#039;asse, e non occorre far <lb></lb>altro che ritrovare il centro di gravità delle parti, e le ragioni stereometri-<pb xlink:href="020/01/2727.jpg" pagenum="352"></pb>che intercedenti, per aver fra l&#039;estremità della detta libbra indicato il punto, <lb></lb>dove il solido tutto intero concentra il suo peso. </s>

<s>Il primo passo perciò si fa <lb></lb>dimostrando la seguente <lb></lb><figure id="id.020.01.2727.1.jpg" xlink:href="020/01/2727/1.jpg"></figure></s></p><p type="caption">

<s>Figura 219.</s></p><p type="main">

<s>“ PROPOSIZIONE XLVIII. — <emph type="italics"></emph>Reliquum <lb></lb>segmenti conici, dempto cono maioris basis, <lb></lb>centrum habet in axe, si fiat, ut quatuor <lb></lb>diametri maiores cum quatuor minoribus, <lb></lb>ad duos maiores cum uno minori, ita axis <lb></lb>AB ad BC ”<emph.end type="italics"></emph.end> (fig. </s>

<s>219). </s></p><p type="main">

<s>In aiuto alla dimostrazione soccorre un <lb></lb>lemma, in cui si dimostra che, dato il segmento conico ABCD (fig. </s>

<s>220), <lb></lb>scavato dal cono AED, prolungate le AE, DC infino all&#039;incontro in H, e da <lb></lb>questo punto condotta una linea parallela ad EC, che incontri il prolunga­<lb></lb>mento dell&#039;asse EF in G; se per G, C, F si farà passare una semiellisse, <lb></lb>dalla rivoluzion della quale intorno a EF si descriva una sferoide; il rima­<lb></lb>nente del segmento conico, toltone il cono della maggior base, sarà equiva­<lb></lb>lente a CFB, porzione della detta sferoide. </s></p><p type="main">

<s>Si dimostra ciò dal Torricelli co&#039;soliti modi suoi proprii, che si com­<lb></lb>pendiano ne&#039;seguenti. </s>

<s>È per ragion delle parallele BE:IM=AE:AM= <lb></lb><figure id="id.020.01.2727.2.jpg" xlink:href="020/01/2727/2.jpg"></figure></s></p><p type="caption">

<s>Figura 220.<lb></lb>EF:FL, e anche insieme BE:MO=EC:MO= <lb></lb>CH:HO=EG:GI. Dunque, moltiplicando termine a <lb></lb>termine, e per le proprietà dell&#039;ellisse, BE3:IM.MO= <lb></lb>FE.EG:FL.LG=BE2:NL2, e perciò <foreign lang="grc">π</foreign>IM.MO= <lb></lb><foreign lang="grc">π</foreign>NL2, ossia l&#039;armilla IM è uguale al circolo LN. </s>

<s><lb></lb>Così essendo di tutte le altre sezioni resta dimo­<lb></lb>strata vera l&#039;eguaglianza tra la sferoide e il bic­<lb></lb>chiere. </s></p><p type="main">

<s>“ Reliquum segmenti conici (frettolosamente il <lb></lb>Torricelli scriveva) dempto cono maioris basis, est sphaerois, cuius axis in­<lb></lb>teger habebitur si fiat, ut FD ad EC, ita FG ad GE. ” </s></p><p type="main">

<s>“ Fiat, et per CBF transeat ellipsis, ex qua fiat sphaerois. </s>

<s>Ductaque IO, <lb></lb>parallela ad AD, habebit quadratum BE, ad rectangulum IMO, compositam <lb></lb>rationem ex rationibus BE ad IM, sive EA ad AM, sive EF ad FL, et ex <lb></lb>ratione BE ad MO, vel EC ad MO, vel CH ad HO, vel EG ad GL. </s>

<s>Quare <lb></lb>quadratum BE, ad rectangulum IMO, est ut rectangulum FEG ad rectangu­<lb></lb>lum FLG, sive ut quadratum idem BE ad quadratum NL. </s>

<s>Sunt ergo aequa­<lb></lb>lia rectangulum IMO, et quadratum NL; quare armilla IM aequatur cir­<lb></lb>culo NL ” (MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>43). </s></p><p type="main">

<s>Riducendoci ora nuovamente sott&#039;occhio la figura 219, si costruisca, <lb></lb>secondo la regola ora insegnata, la sferoide, alla porzione EIAF della quale <lb></lb>sappiamo equivalere quel che riman del tronco, tolto il cono inscritto DBG. </s>

<s><lb></lb>Sia C il centro della descritta porzione sferoidea, che sarà anche insieme il <lb></lb>centro del solido scavato: rimane a dimostrare che C sta veramente sull&#039;asse <lb></lb>AB in quel punto, che il Torricelli annunziava. </s></p><pb xlink:href="020/01/2728.jpg" pagenum="353"></pb><p type="main">

<s>Per la proposizione XLV, qui addietro scritta, essendo BC:AC= <lb></lb>2IM2:2IM2+EB2, è facile dedurne BC:CM=IM2:ML2. </s>

<s>Ma, per il <lb></lb>precedente lemma, <foreign lang="grc">π</foreign>IM2=<foreign lang="grc">π</foreign>HI.IN; dunque IM2=HI.IN; e dall&#039;altra <lb></lb>parte ML2=HI2, per essere HN parallela alla base e bissettrice dell&#039;asse: <lb></lb>onde BC:CM=HI.IN:HI2=IN:HI=4IN:4IH. </s>

<s>Ma IH=EB/2= <lb></lb>EF/4, e perciò 4IH=EF. </s>

<s>Di più essendo IN=HN—IH=(EF+DG)/2—EF/4, <lb></lb>sarà 4IN=2EF+2DG—EF=2DG+EF. </s>

<s>Dunque BC:CM= <lb></lb>2DG+EF:EF. Componendo, BC+CM:BC=2DG+2EF:2DG+EF. </s>

<s><lb></lb>Sostituendo a BC+CM, BM, e duplicando gli antecedenti, 2BM:BC= <lb></lb>4DG+4EF:2DG+EF, ossia AB:BC=4DG+4EF:2DG+EF, <lb></lb>come da principii frettolosamente posti conclude, nelle seguenti parole, il Tor­<lb></lb>ricelli, ripigliando il costrutto da noi di sopra nell&#039;annunziata proposizione <lb></lb>lasciato interrotto. </s></p><p type="main">

<s>“ Nam sit centrum praedictum C: erit ergo BC ad CM ut quadratum <lb></lb>IM ad ML, sive, ob aequalitatem, ut rectangulum HIN ad quadratum HI, <lb></lb>nempe ut recta NI ad IH. </s>

<s>Sumptisque quadruplis, ut duo diametri maiores <lb></lb>DG, cum uno minori EF, ad EF. </s>

<s>Et convertendo, componendoque, sumptisque <lb></lb>antecedentibus duplis, erit AB ad BC ut quatuor EF, cum quatuor DG, ad <lb></lb>DG bis, cum EF semel, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (ibid., fol. </s>

<s>45). </s></p><p type="main">

<s>Il secondo passo, che bisognava fare, perchè, procedendo per questa via, <lb></lb>potesse il Torricelli conseguire il suo intento, era quello di dimostrare qual <lb></lb><figure id="id.020.01.2728.1.jpg" xlink:href="020/01/2728/1.jpg"></figure></s></p><p type="caption">

<s>Figura 221.<lb></lb>ragione avesse il solido generato dal trian­<lb></lb>golo ABE (fig. </s>

<s>221) al solido del triangolo <lb></lb>AEF, rivolgendosi ambedue le figure intorno <lb></lb>all&#039;asse EF: ragione, ch&#039;esso Torricelli an­<lb></lb>nunzia essere di BC(BC+AD) a 2AD2. </s>

<s><lb></lb>Qui però è uno sbaglio manifesto, occasionato <lb></lb>senza dubbio dalla fretta nello scrivere, per­<lb></lb>chè il quarto termine della relazione, secondo il calcolo rettamente condotto, <lb></lb>è AD2 semplicemente, e non 2AD2. </s></p><p type="main">

<s>Seguitiamo infatti l&#039;Autore, da cui si suppone per già dimostrato avere <lb></lb>il segmento della sferoide, che significheremo con <emph type="italics"></emph>S<emph.end type="italics"></emph.end>.BFC, al cono BFC, la <lb></lb>proporzione di MG2+GN2 a GN2. </s>

<s>Duplicando i termini della seconda ra­<lb></lb>gione, sarà <emph type="italics"></emph>S<emph.end type="italics"></emph.end>.BFC:BFC=2MG2+2GN2:4GN2=2MG2+2GN2:BE2. </s>

<s><lb></lb>Ma AED:BFC=AF2:BE2, dunque <emph type="italics"></emph>S<emph.end type="italics"></emph.end>.BFC:AED=2MG2+2GN2:AF2. </s>

<s><lb></lb>Ora MG2=HI.IL, come fu dimostrato nel lemma alla precedente, e NG2= <lb></lb>HI2, per essere HL bissettrice dell&#039;asse, e perciò 2MG2+2GN2= <lb></lb>2HI(IL+IH)=2HI.HL. </s>

<s>Sarà dunque, sostituendo, <emph type="italics"></emph>S<emph.end type="italics"></emph.end>.BFC:AED= <lb></lb>2HI.HL:AF2. </s>

<s>Ma HI=BC/4, HL=(BC+AD)/2, per cui 2MG2+2GN2= <lb></lb>2.BC/4((BC+AD)/2)=BC/4(BC+AD), e in conclusione <emph type="italics"></emph>S<emph.end type="italics"></emph.end>.BFC:AED= <pb xlink:href="020/01/2729.jpg" pagenum="354"></pb>BC(BC+AD):4AF2=BC(BC+AD):AD2. </s>

<s>E perchè <emph type="italics"></emph>S<emph.end type="italics"></emph.end>.BFC, per il <lb></lb>lemma alla precedente, è uguale al solido generato dalla conversione del trian­<lb></lb>golo ABE intorno all&#039;asse EF; dunque questo solido, o tronco di cono sca­<lb></lb>vato, al cono descritto dal triangolo AEF, ha la proporzione di BC(BC+AD) <lb></lb>a AD2, e non a 2AD2, come, per uno sbaglio di calcolo, fu condotto a con­<lb></lb>cludere il Torricelli dalla dimostrazione, che qui trascriviamo. </s></p><p type="main">

<s>“ Secetur axis EF bifariam in G, appliceturque GH. </s>

<s>Erit segmentum <lb></lb>sphaeroidis BFC, ad conum BFC, ut quadrata MG, GN simul, ad duo qua­<lb></lb>drata GN. </s>

<s>Sumptisque duplis, ut duo quadrata MG, cum duobus NG, ad <lb></lb>quatuor NG, sive ad quadratum BE. </s>

<s>Conus vero BFC, ad conum AED, est <lb></lb>ut quadratum BE ad quadratum AF. </s>

<s>Ergo ex aequo segmentum sphaeroi­<lb></lb>dis, ad conum AED, erit ut duo quadrata MG, cum duobus quadratis NG, <lb></lb>sive, ut duo rectangula HIL, quae aequantur duobus quadratis MG, sive col­<lb></lb>lectim, ut duo tantum rectangula IHL ad quadratum AF. </s>

<s>Sumptisque octu­<lb></lb>plis, erit ut rectangulum, ex minori basi in minorem maioremque simul, ad <lb></lb>duplum quadrati maioris basis ” (ibid., fol. </s>

<s>44). </s></p><p type="main">

<s>Se avesse avuto l&#039;occasione e il tempo di tornare sopra questo disteso, <lb></lb>si sarebbe senza dubbio dal Torricelli ritrovato e corretto lo sbaglio, tanto <lb></lb>più che ne lo avrebbe potuto fare accorto lo stesso Luca Valerio, il quale <lb></lb>aveva, nella X proposizione del suo terzo libro, dimostrato che “ omne fru­<lb></lb>stum coni, ad conum cuius basis est eadem, quae maior basis frusti et eadem <lb></lb>altitudo, est ut rectangulum contentum basium diametris, una cum tertia parte <lb></lb>quadrati differentiae eorumdem diametrorum, ad tertiam partem quadrati, ex <lb></lb>diametro maioris basis ” (De centro grav., Lib. </s>

<s>III, Romae 1604, pag. </s>

<s>14). </s></p><p type="main">

<s>Chiamato dunque F il frusto, C il cono, e segnato sopra AD, nella pro­<lb></lb>posta figura, il punto O, in tal parte che AO sia uguale a BC, e perciò OD <lb></lb>la differenza de&#039;diametri delle basi; sarebbe la relazione espressa da F:C= <lb></lb>AD.AO+DO2/3:AD2/3, ciò che, triplicati i termini della seconda ragione, <lb></lb>dividendo, e sostituendo BC ad AO, si riduce a F—C:C=3AD.BC+ <lb></lb>DO2—AD2:AD2. </s>

<s>Ma, essendo per costruzione DO=AD—BC, avremo <lb></lb>DO—AD=—BC, DO+AD=2AD—BC, e perciò la differenza dei <lb></lb>quadrati, ch&#039;è uguale a (DO+AD)(DO—AD), sarà BC(BC—2AD). <lb></lb>Sostituendo, se ne concluderà dunque, per Luca Valerio, F—C:C= <lb></lb>3AD.BC—2AD.BC+BC2:AD2=BC2+AD.BC:AD2, che vuol <lb></lb>dire “ segmentum coni ABCD dempto cono maioris basis AD, ad conum AED <lb></lb>maioris basis, est ut quadratum diametri minoris basis, cum rectangulo sub <lb></lb>utraque, ad quadratum maioris ” e non <emph type="italics"></emph>ad duplum quadrati maioris,<emph.end type="italics"></emph.end> come <lb></lb>annunziava, e si credeva di aver dimostrato il Torricelli, per cui va corretta <lb></lb>la proposizione, che ora trascriveremo di lui, e a dimostrar la quale erano <lb></lb>ordinate le precedenti. </s></p><p type="main">

<s>“ PROPOSIZIONE XLIX. — <emph type="italics"></emph>Centrum gravitatis segmenti coni BC<emph.end type="italics"></emph.end> (fig. </s>

<s>222) <lb></lb><emph type="italics"></emph>habetur in axe EF, si fiat primo, ut CD quater, cum AB quater, ad CD bis <lb></lb>et AB semel sumptis; ita FE ad EG; iterumque, sumpta FH 1/4 axis,<emph.end type="italics"></emph.end><pb xlink:href="020/01/2730.jpg" pagenum="355"></pb><emph type="italics"></emph>fiat, ut quadratum AB cum rectangulo AB in CD, ad duo quadrata CD, <lb></lb>ita HI ad IG, eritque centrum I. ”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2730.1.jpg" xlink:href="020/01/2730/1.jpg"></figure></s></p><p type="caption">

<s>Figura 222.</s></p><p type="main">

<s>“ Nam, ex demonstratis, erit G centrum reliqui, <lb></lb>dempto cono maioris basis, H vero centrum est prae­<lb></lb>dicti coni, demonstratumque est reliquum illud, ad di­<lb></lb>ctum conum, esse ut quadratum AB, cum rectangulo <lb></lb>AB in CD, ad duo quadrata CD: nempe, ex suppo­<lb></lb>sitione, ut HI ad IG. </s>

<s>Quare centrum erit I ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>46). </s></p><p type="main">

<s>Dal frusto del cono volle il Torricelli passare al frusto del conoide para­<lb></lb>bolico, e benchè il Valerio, nella XLII del secondo libro, ne avesse, con una <lb></lb>dimostrazione assai semplice, indicato il centro; non patì il Nostro di rima­<lb></lb>nergli indietro, formulando la proposizion nel medesimo modo, ma dimostran­<lb></lb>dola diversamente da&#039;suoi proprii principii, e secondo il metodo usato. </s></p><p type="main">

<s>“ PROPOSIZIONE L. — <emph type="italics"></emph>Esto frustum conoidis parabolici ABCD<emph.end type="italics"></emph.end> (fig. </s>

<s>223), <lb></lb><emph type="italics"></emph>cuius axis EF, centrum O: dico EO ad OF esse ut quadratum BC, cum <lb></lb>duobus quadratis AD, ad quadratum AD, cum duobus BC. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Compleatur parabola AID, et fiat parabola GEH idem habens latus <lb></lb>rectum cum AID. </s>

<s>Concipiatur ex frusto ABCD demptum conoides paraboli­<lb></lb>cum GEH, in quo inscriptus sit conus GEH, et, secta EF bifariam in L, appli­<lb></lb>cetur <expan abbr="NLq.">NLque</expan> ” </s></p><p type="main">

<s>“ Jam solidum factum a quadrilineo GNEBA, per lemma II ad prop. </s>

<s>XLI, <lb></lb>aequalis est cylindro, cuius basis circulus BC, altitudo vero EF: sive cono, <lb></lb><figure id="id.020.01.2730.2.jpg" xlink:href="020/01/2730/2.jpg"></figure></s></p><p type="caption">

<s>Figura 223.<lb></lb>cuius basis sit tripla circuli BC, altitudo vero <lb></lb>sit ipsa FE. </s>

<s>Solidum vero factum a bilineo GNE, <lb></lb>ad conum GEH, est, per lemma ad propos. </s>

<s>XLV, <lb></lb>ut duo rectangula NPQ, ad quadratum GF. </s>

<s><lb></lb>Ergo simul, per XXIV Quinti, totum solidum <lb></lb>ABEG, ad conum GEH, est ut 3 quadrata BE, <lb></lb>cum duobus rectangulis NPQ, ad quadratum <lb></lb>GF. </s>

<s>Sed in parabola rectangulum NPQ aequale <lb></lb>est quadrato PL (perchè PL è il raggio del cir­<lb></lb>colo massimo della sferoide) ergo solidum ABEG, ad conum GEH, est ut tria <lb></lb>quadrata BE, cum duobus quadratis PL, ad quadratum FG, sive, ut sex qua­<lb></lb>drata BE, cum quadrato FG, ad duo quadrata FG. ” </s></p><p type="main">

<s>“ Centrum gravitatis solidi GNEBA est L, nam ostensae sunt singulae <lb></lb>ipsius armillae aequales singulis unius cylindri circulis: solidi vero GNE cen­<lb></lb>trum est L, nam singulae ipsius armillae ostensae sunt aequales singulis <lb></lb>unius sphaeroidis circuli; ergo totius solidi GEBA centrum est L. </s>

<s>Sed coni <lb></lb>GEH est M, sempta FM dimidia ipsius FL; ergo, si fiat ut sex quadrata BE, <lb></lb>cum quadrato FG, ad duo quadrata FG, ita reciproce MO ad OL; erit O <lb></lb>centrum totius. </s>

<s>” </s></p><p type="main">

<s>“ Jam quinque erunt argumenta, praeter reductionem: Per constructio­<lb></lb>nem, MO ad OL est ut sex quadrata BE, cum quadrato FG, ad duo qua-<pb xlink:href="020/01/2731.jpg" pagenum="356"></pb>drata FG. Componendo, ML ad LO est ut sex quadrata BE, cum tribus qua­<lb></lb>dratis FG, ad duo quadrata FG. </s>

<s>Duplicando antecedentia, FL ad LO ut <lb></lb>12 quadrata BE+6 quadratis FG, ad 2FG. </s>

<s>Per conversionem rationis, LF <lb></lb>ad FO ut 12 quadrata BE+6 quadratis FG, ed 12BE+4FG. </s>

<s>Dupli­<lb></lb>cando antecedentia, EF ad FO ut 24 quadrata BE+12FG, ad 12BE+4FG. <lb></lb>Dividendo, EO ad OF ut 12BE+8FG ad 12BE+4FG. ” </s></p><p type="main">

<s>“ Sed quia rectangulum AGD, per lemma II ad propos. </s>

<s>XL, aequale <lb></lb>est quadrato BE, erit quadratum FG differentia inter quadratum AF, BE. </s>

<s><lb></lb>Ergo fieri poterit talis reductio: EO ad OF est ut 4BE, cum 8FA, ad 8BE <lb></lb><figure id="id.020.01.2731.1.jpg" xlink:href="020/01/2731/1.jpg"></figure></s></p><p type="caption">

<s>Figura 224.<lb></lb>cum 4FA: vel, ut quadratum BC, cum 2AD, ad <lb></lb>quadratum AD, cum 2BC, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (ibid., fol. </s>

<s>50). </s></p><p type="main">

<s>Ma, per comprendere tutte le conoidali in una <lb></lb>proposizione universalissima, premetteva il seguente <lb></lb><emph type="italics"></emph>Lemma:<emph.end type="italics"></emph.end> “ Se sarà un solido o conoidale o porzione <lb></lb>di sfera o sferoide ABC (fig. </s>

<s>224), cni asse sia BD, <lb></lb>cono inscritto ABC, tangenti AE, ed EB, segmento <lb></lb>conico AEFC; dico che il cono inscritto, il solido <lb></lb>intermedio e la scodella esterna sono in continua proporzione. </s>

<s>” </s></p><p type="main">

<s>“ Concepiscasi il cono EDF il quale, nella XXXVII, è stato provato <lb></lb>eguale alla scodella esterna, fatta dalla tangente. </s>

<s>Si è anco dimostrato, nella <lb></lb>proposizione seconda premessa alla XLVI come lemma, che, se dal segmento <lb></lb>conico leveremo li due coni ABC, EDF, il rimanente è medio proporzionale <lb></lb>fra essi coni. </s>

<s>Dunque, levando il cono ABC o scodella esterna, il rimanente <lb></lb>sarà medio proporzionale fra esso cono e la scodella ” (ivi, fol. </s>

<s>112). Ciò, <lb></lb>chiamato I il detto solido medio proporzionale, potrà scriversi sotto la forma <lb></lb>ABC:I=I:EDF. </s>

<s>Ma ABC:EDF=AD2:EB2, dunque EDF=EB2.ABC/AD2, <lb></lb>e perciò I2=ABC.EDF=ABC2.EB2/AD2, ossia I2:ABC2=EB2:AD2, ed <lb></lb>estratta la radice e trasponendo, ABC:I=AD:EB. </s></p><p type="main">

<s>Il centro di gravità del cono ABC è in N, punto noto; del solido inter­<lb></lb>medio I, ossia del bilineo AGB equivalente a una sferoide, è in M nel mezzo <lb></lb>dell&#039;asse. </s>

<s>Se dunque si supponga in O il centro del tutto, sarà questo indi­<lb></lb>cato dalla relazione ABC:I, ossia (<emph type="italics"></emph>a<emph.end type="italics"></emph.end>) AD:EB=MO:ON. </s>

<s>Moltiplicando <lb></lb>l&#039;una e l&#039;altra ragione di questa per 3/2, e componendo, avremo (<emph type="italics"></emph>b<emph.end type="italics"></emph.end>) 3AD+ <lb></lb>2EB:2EB=3MO+2NO:2NO. </s>

<s>Moltiplicando per 2 i conseguenti di (<emph type="italics"></emph>a<emph.end type="italics"></emph.end>), <lb></lb>AD:2B=MO:2NO, la quale, per composizione, darà AD+2EB:2EB= <lb></lb>MO+2NO:2NO; ond&#039;è che si trasformerà la (<emph type="italics"></emph>b<emph.end type="italics"></emph.end>) in 3AD+2EB:AD+ <lb></lb>2EB=3MO+2NO:MO+2NO. </s>

<s>Ma 3MO+2NO=3(BO—BM)+ <lb></lb>2(BN—BO)=3BO—3BM+2BN—2BO=BO—3BM+2BN= <lb></lb>BO, e dall&#039;altra parte MO+2NO=MD—OD+2(OD—ND)=OD+ <lb></lb>MD—2ND=OD; dunque 3AD+2EB:2EB+AD=BO:DO, ed è <lb></lb>ciò che appunto intende di dimostrare il Torricelli in questa sua </s></p><p type="main">

<s>“ PROPOSIZIONE LI. — <emph type="italics"></emph>Poste le medesime cose che nella precedente<emph.end type="italics"></emph.end><pb xlink:href="020/01/2732.jpg" pagenum="357"></pb><emph type="italics"></emph>figura, dico che, se si farà come tre delle AD, con due delle EB, a due <lb></lb>delle EB çon una delle AD, così BO ad OD; che il punto O è il centro <lb></lb>del solido conoidale, o della porzione di sfera o di sferoide.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Perchè il cono ABC, al cono EDF, sta come il quadrato AD al qua­<lb></lb>drato EB: però il cono inscritto ABC, al solido intermedio, sarà come la retta <lb></lb>AD alla retta EB. </s>

<s>Se dunque segheremo BD in quattro parti uguali BI, IM, <lb></lb>MN, ND, sarà M centro del solido AGB, ed N centro del cono. </s>

<s>E se faremo, <lb></lb>come AD alla BE, così MO ad ON <emph type="italics"></emph>reciproce,<emph.end type="italics"></emph.end> sarà O centro di tutto. </s>

<s>Però <lb></lb>sarà come tre delle AD, con due delle EB, a due delle EB, con una delle <lb></lb>AD; così BO ad OD, c. </s>

<s>d. </s>

<s>d. </s>

<s>” (ivi, fol. </s>

<s>237). </s></p><p type="main">

<s>Soggiunge il Torricelli, dopo questa, un corollario <emph type="italics"></emph>pro centro gravitatis<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2732.1.jpg" xlink:href="020/01/2732/1.jpg"></figure></s></p><p type="caption">

<s>Figura 225.<lb></lb><emph type="italics"></emph>hyperbolici, et segmenti sphaerae, aut sphaeroidis tantum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto conois hyperbolicum, sive sphaerae aut sphae­<lb></lb>roidis portio ABC (fig. </s>

<s>225), cuius diameter BG, axis BD, <lb></lb>centrum H, tangentes AF, BF. </s>

<s>Suppono quod, si fiat ut tri­<lb></lb>pla AD, cum dupla BF, ad duplam BF, cum AD, ita BO <lb></lb>ad OD; O esse centrum gravitatis, ut ostendimus in praece­<lb></lb>denti. </s>

<s>His positis, fiat ut tripla axis BD, cum quadrupla diame­<lb></lb>tri BG, ad duplam diametri BG cum BD, ita BO ad OE: dico <lb></lb>iterum O esse centrum gravitatis conoidis, sive portionis. </s>

<s>” </s></p><p type="main">

<s>“ Ducatur enim FI parallela ad BD. </s>

<s>Erit ergo AI ad ID <lb></lb>ut DB ad BE: nempe, ob tangentem sectionis coni AE, ut <lb></lb>DH ad HB. Et, componendo, erit AD ad FB ut DG ad GH: <lb></lb>quare, ut tripla AD, cum dupla FB, ad duplam FB, cum AD; ita tripla DG, <lb></lb>cum dupla GH, ad duplam GH cum GD: nempe ita tripla BD, cum quadru­<lb></lb>pla BG, ad duplam BG, cum BD, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (ibid., fol. </s>

<s>214). </s></p><p type="main">

<s>Istituiscasi il calcolo, tenendo dietro al processo dell&#039;Autore. </s>

<s>Abbiamo, <lb></lb>per la natura della tangente alla sezione conica, essendone in H segnato il <lb></lb>centro, DB:BE=DH:HB. </s>

<s>E condotta la FI parallela all&#039;asse, AI:DI= <lb></lb>DB:BE; dunque AI:DI=DH:HB, relazione che, componendo e sosti­<lb></lb><figure id="id.020.01.2732.2.jpg" xlink:href="020/01/2732/2.jpg"></figure></s></p><p type="caption">

<s>Figura 226.<lb></lb>tuendo gli equivalenti, si trasforma nell&#039;altra (<emph type="italics"></emph>a<emph.end type="italics"></emph.end>) AD:FB= <lb></lb>DG:GH. </s>

<s>Triplicando in questa gli antecedenti, e duplicando <lb></lb>i conseguenti, avremo 3AD:3FB=3DG:2GH, dalla <lb></lb>quale deriverà per composizione la (<emph type="italics"></emph>b<emph.end type="italics"></emph.end>) 3AD+2FB:2FB= <lb></lb>3DG+2GH:2GH. </s>

<s>Duplicando i conseguenti della (<emph type="italics"></emph>a<emph.end type="italics"></emph.end>) e <lb></lb>componendo, avremo anche insieme AD+2FB:2FB= <lb></lb>DG+2GH:2GH, e da questa e dalla (<emph type="italics"></emph>b<emph.end type="italics"></emph.end>) ne conseguirà <lb></lb>3AD+2FB:AD+2FB=3DG+2GH:DG+2GH. </s>

<s><lb></lb>Ma 3DG+2GH=3(GB—BD)+BG=4BG—3BD, e <lb></lb>2GH+DG=GB+GB—BD=2GB—BD; dunque <lb></lb>3AD+2FB:AD+2FB=4BG—3BD:2BG—BD. </s></p><p type="main">

<s>Questa conclusione è manifestamente diversa da quella, <lb></lb>che abbiamo letta di sopra nel Torricelli, la quale non s&#039;appro­<lb></lb>pria ad altra sezione che all&#039;iperbola. </s>

<s>In tal caso, com&#039;apparisce dalla fig. </s>

<s>226, <pb xlink:href="020/01/2733.jpg" pagenum="358"></pb>in cui le indicazioni del centro, dell&#039;asse, del diametro e di tutto il resto cor­<lb></lb>rispondono con quelle della figura 225; DG=BG+GD. Ma, nel caso della <lb></lb>sferoide o della sfera, DG non è uguale alla somma delle due dette por­<lb></lb>zioni del diametro, ma com&#039;è evidente, alla loro differenza; e perciò la for­<lb></lb>mula, applicabile ai tre casi contemplati dal Torricelli, si dovrebbe scrivere <lb></lb>BO:OE=4BG±3BD:2BG±BD, nella quale il segno di sopra vale <lb></lb>per l&#039;iperbola, o per il conoidale iperbolico, e quel di sotto per la sferoide e <lb></lb>per la sfera. </s></p><p type="main">

<s><emph type="center"></emph>IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I solidi conoidei, intorno ai quali aveva il Valerio fatte prove ammi­<lb></lb>rande ai matematici de&#039;suoi tempi, venivano, per lo studio del Torricelli, <lb></lb>compresi così in una formula universale, che se ne poteva calcolare il centro <lb></lb>di gravità, fossero que&#039;corpi descritti da qualunque sezione conica, o si ri­<lb></lb>manessero interi o ridotti nei loro frusti. </s>

<s>La Baricentrica perciò era, per via <lb></lb>di queste torricelliane proposizioni, fatta notabilmente progredire sopra quella <lb></lb>degli antichi, e s&#039;avviava a vestir lo splendore e l&#039;agilità di quell&#039;abito nuovo, <lb></lb>che le avrebbero presto assettato in dosso l&#039;analisi cartesiana e il calcolo <lb></lb>differenziale. </s>

<s>Nè per solo il metodo è il Nostro benemerito della scienza, ma <lb></lb>per la varietà de&#039;soggetti discorsi, e delle fogge dei solidi immaginati, fra&#039;quali <lb></lb>si sono in questo trattato veduti apparire i bicchieri e i calici, dentro i quali <lb></lb>viene a infondere Minerva agl&#039;ingegni sitibondi, con larga mano, l&#039;ambrosia. </s></p><p type="main">

<s>Rimangon però ancora, a condurre il presente trattato alla sua perfe­<lb></lb>zione, altre fogge di solidi, e altre figure di superficie, non più immaginate <lb></lb>o conosciute agli antichi, intorno ai centri di gravità delle quati s&#039;esercitò <lb></lb>con gloriosa riuscita il Torricelli. </s>

<s>Son tra que&#039;solidi principalmente da anno­<lb></lb>verare i così detti <emph type="italics"></emph>cavalieriani,<emph.end type="italics"></emph.end> e fra quelle superficiali figure le cicloidali, <lb></lb>che ci vogliono brevemente trattenere in discorso, in quest&#039;ultima parte del <lb></lb>presente capitolo. </s></p><p type="main">

<s>In una lettera a Michelangiolo Ricci, della quale è rimasto solo l&#039;estratto, <lb></lb><figure id="id.020.01.2733.1.jpg" xlink:href="020/01/2733/1.jpg"></figure></s></p><p type="caption">

<s>Figura 227.<lb></lb>senza alcuna data precisa, scriveva così il Torricelli circa <lb></lb>l&#039;anno 1644: “ Il padre fra Bonaventura mi scrisse la set­<lb></lb>timana passata, e aggiungerò qui un capitolo della sua let­<lb></lb>tera: <emph type="italics"></emph>Con tale occasione dissi al p. </s>

<s>Mersenno che io ero in­<lb></lb>torno a speculare sopra un quesito, non ancora digerito, <lb></lb>quale bisognò dirgli, facendomene instanza, per conferirlo <lb></lb>al signor Robervallio. </s>

<s>Io dissi che non era quesito da un <lb></lb>par suo: tuttavia volle che io glielo dicessi, ed è tale: Sia <lb></lb>sopra la parabola ACB<emph.end type="italics"></emph.end> (fig. </s>

<s>227), <emph type="italics"></emph>come base, il corpo co­<lb></lb>lonnare o cilindrico, come lo chiamo nella mia Geometria, <lb></lb>ADEBCF, sicchè DFE sia l&#039;opposta base, ed anche essa parabola simile,<emph.end type="italics"></emph.end><pb xlink:href="020/01/2734.jpg" pagenum="359"></pb><emph type="italics"></emph>uguale e similmente posta come ACB. </s>

<s>Stendasi poi un piano per la retta <lb></lb>AB, e per la cima F della parabola DFE: ora io dissi che cereaco la <lb></lb>proporzione delli due frusti di detto corpo, fatti dal piano AFB. </s>

<s>Io poi non <lb></lb>l&#039;ho più pensato, ma per una certa analogia stimai che fussero fra di loro <lb></lb>come cinque a due.<emph.end type="italics"></emph.end> Queste sono le precise parole di fra Bonaventura. </s>

<s>Io vi <lb></lb>pensai subito, e trovai subito la dimostrazione, ed il medesimo giorno, che <lb></lb>ebbi la lettera, gli mandai la risposta. </s>

<s>Parteciperò anche a V. S. il mio pen­<lb></lb>siero, rimettendomi a lei il parteciparlo a cotesti signori, se lo stimerà degno. <lb></lb><emph type="italics"></emph>Esto figura quaelibet ABC.... ”<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>107). </s></p><p type="main">

<s>Nel <emph type="italics"></emph>Racconto<emph.end type="italics"></emph.end> poi dei problemi mandati ai Matematici francesi, più volte <lb></lb>da noi citato, dop&#039;avere scritto il quesito, lo stesso Torricelli soggiunge: <lb></lb>“ Questo fu da me sciolto universalmente, e non solo risposi che il solido <lb></lb>a me proposto era segato in proporzion sesquialtera, e non in ragione di <lb></lb>5 a 3, come il Cavalieri credette per isbaglio stare il frusto maggiore al mi­<lb></lb>nore; ma in una annunciazione, facile e universalissima, dissi a esso Cava­<lb></lb>lieri qual proporzione abbiano le parti di tale solido, anco quando le basi <lb></lb>opposte siano qualunque altra sorta di figura, purchè abbiano diametro. </s>

<s>Gli <lb></lb>mandai la brevissima dimostrazione, come anco la mandai agli altri amici <lb></lb>d&#039;Italia ” (ivi, T. XXXII, fol. </s>

<s>41). </s></p><p type="main">

<s>Sarebbe nonostante rimasta nel pubblico ignorata di ciò la notizia, se <lb></lb>il Cavalieri stesso, nella sua Quinta esercitazione geometrica, dop&#039;aver dimo­<lb></lb>strata la proposizione XVII, non avesse in uno scolio accennato al quesito, <lb></lb><figure id="id.020.01.2734.1.jpg" xlink:href="020/01/2734/1.jpg"></figure></s></p><p type="caption">

<s>Figura 228.<lb></lb>ch&#039;egli aveva proposto già di risolvere al Tor­<lb></lb>ricelli, e non avesse soggiunta la dimostra­<lb></lb>zione, ehe n&#039;ebbe da lui per risposta. </s>

<s>“ Et <lb></lb>quia demonstratio elegantissima est, et ad­<lb></lb>ducta brevior, ideo hic eam subnectere libuit, <lb></lb>quae talis est ” (Bononiae 1647, pag. </s>

<s>365). <lb></lb>Tale però crediamo che fosse la dimostrazione <lb></lb><emph type="italics"></emph>ex Torricellio<emph.end type="italics"></emph.end> quivi addotta, quanto alla so­<lb></lb>stanza, non però quanto alla forma, che il <lb></lb>Cavalieri ridusse più geometricamente ordi­<lb></lb>nata. </s>

<s>Ma perchè la dimostrazione, rimasta nel <lb></lb>manoscritto, è anche più breve, e non meno <lb></lb>chiara, e dalla universalità della figura, sopra <lb></lb>la quale s&#039;erige il solido colonnare, passa in <lb></lb>uno scolio l&#039;Autore a contemplare il caso par­<lb></lb>ticolare, che la base del detto solido sia para­<lb></lb>bolica come s&#039;era contentato di proporgli il <lb></lb>Cavalieri; pensiamo di pubblicar, nella sua <lb></lb>propria original forma, quella medesima tor­<lb></lb>ricelliana proposizione, che è tale: </s></p><p type="main">

<s>“ PROPOSIZIONE LII. — <emph type="italics"></emph>Esto figurae ABC<emph.end type="italics"></emph.end> (228) <emph type="italics"></emph>diameter BE, centrum <lb></lb>vero gravitatis sit F. </s>

<s>Dico frustum, quod sub tribus planis curvague su-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2735.jpg" pagenum="360"></pb><emph type="italics"></emph>perficie continebitur, ad reliquum sub duobus planis et curva quadam <lb></lb>superficie contentum; esse ut recta BF ad FE. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nam producatur FH, axis totius solidi, ductaque IOL, quae bifariam <lb></lb>secet latera EG, BD, connectantur EL, DI. </s>

<s>Patet primo: quod centrum to­<lb></lb>tius solidi erit punctum O, medium scilicet totius axis FH. </s>

<s>Centrum vero <lb></lb>frusti superioris ACBD erit in recta EL, et reliqui frusti in recta DI. </s>

<s>Facile <lb></lb>probatur hoc, nam, si totum solidum secetur plano, ad planum CP parallelo, <lb></lb>quodlibet parallelogrammum, quod nascetur in superiori frusto, centrum habe­<lb></lb>bit in recta EL, et reliquum parallelogrammum, quod fiet in frusto inferiori, <lb></lb>centrum habebit in recta DI. </s>

<s>Propterea omnia simul parallelogramma supe­<lb></lb>rioris frusti, sive ipsum superius frustum, centrum habebunt in recta EL, et <lb></lb>sic de reliquo inferiori. </s>

<s>” </s></p><p type="main">

<s>“ Esto iam centrum gravitatis frusti ACBD punctum quodlibet M, in <lb></lb>recta EL, productaque MON, erit omnino N centrum reliqui frusti, eritque <lb></lb>frustum inferius, ad frustum superius, reciproce, ut MO ad ON, sive ut LO <lb></lb>ad OI: hoc est ut BF ad FE, quod erat propositum ” (ibid., T. XXXVI, <lb></lb>fol. </s>

<s>239). </s></p><p type="main">

<s>Suppongasi ora che ACB, come proponeva il Cavalieri, sia una parabola: <lb></lb>se con F s&#039;indica tuttavia il centro, sarà per le notissime cose BF:FE= <lb></lb>3:2. Condotta poi FD, il centro di gravità del frusto superiore si dovrà tro­<lb></lb>vare sopra un punto di lei, e per le cose giè dette anche insieme sopra un <lb></lb>punto della EL: dunque in R, dove ambedue quelle linee concorrono: cosic­<lb></lb>chè la parte intersecata ER stia all&#039;altra RL, come quattro sta a tre. </s>

<s>Con­<lb></lb>ducansi infatti le ED, BR: i triangoli EDF, FDB, appnntati in D, e pari­<lb></lb>mente i triangoli ERF, FRB, appuntati in R, stanno come le respettive basi: <lb></lb>cioè, come due a tre, e stanno nella medesima proporzione i rimanenti, tolti <lb></lb>i triangoli col vertice in R da quegli altri col vertice in D: cioè ERD:BRD= <lb></lb>2:3. Dividendo per due i conseguenti, e osservando che la metà del trian­<lb></lb>golo BRD è LRD, avremo ERD:LRD=4:3. E i triangoli con uguale al­<lb></lb>tezza stando come le loro basi, sarà dunque, come si diceva, ER:RL= <lb></lb>4:3. Se infine conducasi ancora da R, attraverso a O, la linea RS, sarà in S <lb></lb>il centro di gravità del frusto inferiore, il quale starà al superiore reciproca­<lb></lb>mente come RO ad OS, o come LO ad OI, cioè come FB ad EF, in sesquial­<lb></lb>tera proporzione, secondo che il Torricelli annunziava, correggendo lo sba­<lb></lb>glio del Cavalieri, e secondo si conclude da questo scolio, che alla proposizion <lb></lb>precedente si soggiunge nel manoscritto: </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Quando vero huiusmodi solidum ab aliqua parabola ortum <lb></lb>ducat, et oporteat centrum partium reperire; centrum gravitatis frusti ACBD <lb></lb>habebitur producta recta DF in communi concursu cum recta EL. Nam, si <lb></lb>secetur planis ad oppositas bases parallelis, sectiones omnes parabolae erunt, <lb></lb>omniumque et singularum centra gravitatis erunt in recta DF. </s>

<s>Ergo frusti <lb></lb>centrum erit in DF. </s>

<s>Sed erat etiam in EL, ergo in communi concursu R. ” </s></p><p type="main">

<s>“ Amplius dico ER ad RL esse ut 4 ad 3. Nam triangulum BDF, ad <lb></lb>triangulum EDF, est ut 3 ad 2. Item, ablatum BRF ad ablatum ERF: ergo <pb xlink:href="020/01/2736.jpg" pagenum="361"></pb>reliquum BRD, ad reliquum ERD, est ut 3 ad 2 etc. </s>

<s>Si denique ab hoc <lb></lb>communi concursu R producatur recta quaedam linea per O usque ad rectam <lb></lb>DI; habebitur centrum reliqui frusti ” (ibid., fol. </s>

<s>240). </s></p><p type="main">

<s>Dop&#039;aver raccontatò in che modo, e a quale occasione gli proponesse il <lb></lb>Cavalieri il problema, risoluto così nella sua generalità e ne&#039;suoi particolari, <lb></lb>soggiungeva il Torricelli in tal guisa nella scrittura sopra citata: “ Il me­<lb></lb>desimo padre fra Bonaventura mi ha fatto istanza più di una volta, in diversi <lb></lb>tempi, acciò che io volessi trovare la dimostrazione di un altro quesito, che <lb></lb>neanco egli sapeva, ed è così definito: ” </s></p><p type="main">

<s>“ Se sarà un solido, nato e segato come il precedente, ma che le basi <lb></lb>opposte siano figure composte di due mezze parabole ABC, ABF (fig. </s>

<s>229), <lb></lb>congiunte con la base comune AB, e che le cime siano C ed F; si cerca il <lb></lb>centro di gravità delle due parti del solido. </s>

<s>” </s></p><p type="main">

<s>“ Io dimostrai che, facendosi DA alla DB come 8 a 7, nel caso propo­<lb></lb>stomi, e tirando la DE parallela alla BI, e di nuovo facendo OD alla OE <lb></lb><figure id="id.020.01.2736.1.jpg" xlink:href="020/01/2736/1.jpg"></figure></s></p><p type="caption">

<s>Figura 229.<lb></lb>come 8 a 7; il punto Q, cioè il mezzo della retta <lb></lb>OD, era centro della parte di sopra del solido se­<lb></lb>gato. </s>

<s>Ma la mia dimostrazione essendo univer­<lb></lb>sale, provavo che, se il solido nasceva dalla prima <lb></lb>parabola, che è il triangolo, la retta BD alla DA <lb></lb>era come 6 a 6. Se della seconda parabola, era <lb></lb>come 8 a 7; se della terza, come 9 a 8; se della <lb></lb>quarta, come 10 a 9, et sic semper. </s>

<s>La retta poi <lb></lb>ED va segata nella medesima proporzione che <lb></lb>la BA, e si troverà il punto O. </s>

<s>E segando per <lb></lb>mezzo la OD in Q, sarà Q centro della parte su­<lb></lb>periore del solido segato. </s>

<s>” </s></p><p type="main">

<s>“ Quanto al centro della parte inferiore non <lb></lb>soggiungerò altro, poichè, essendo dato il centro <lb></lb>di tutto, e di una parte, con la proporzione delle <lb></lb>parti, è dato ancora il centro della parte rima­<lb></lb>nente, per la VIII del primo degli Equiponde­<lb></lb>ranti. </s>

<s>La dimostrazione di questo è stata da me <lb></lb>conferita solo al medesimo fra Bonaventura, il <lb></lb>quale me l&#039;ha chiesta ” (ivi, T. XXXII, fol. </s>

<s>42). <lb></lb>E allo stesso fra Bonaventura fu da questa sug­<lb></lb>gerita la dimostrazione della XXI della sua quinta Esercitazione geometrica, <lb></lb>ma la originale proposizione torricelliana è, per quel che da noi si sappia, al <lb></lb>pubblico ignota, per cui ci sentiamo tanto più fortemente invogliati di pub­<lb></lb>blicarla, come corona e fastigio delle precedenti. </s>

<s>Ciò facciamo altresì perchè <lb></lb>quella si tira dietro queste altre due proposizioni, che le servon per lemmi, <lb></lb>il secondo dei quali specialmente è, per la sua universalità, nella Baricentrica <lb></lb>di non lieve importanza. </s></p><p type="main">

<s>PROPOSIZIONE LIII. — <emph type="italics"></emph>Di due mezze parabole simili e uguali, con-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2737.jpg" pagenum="362"></pb><emph type="italics"></emph>giunte con la base comune, il centro di gravitù sega essa base con tal <lb></lb>proporzione, che la parte verso il vertice stia alla rimanente come cinque <lb></lb>sta a tre.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Deriva per corollario dal lemma XI, e dalla proposizione XXI <emph type="italics"></emph>De di­<lb></lb>mensione parabolae<emph.end type="italics"></emph.end> (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>33, 84), imperocchè, se siano <lb></lb><figure id="id.020.01.2737.1.jpg" xlink:href="020/01/2737/1.jpg"></figure></s></p><p type="caption">

<s>Figura 230.<lb></lb>le due mezze parabole AHB, AMN (fig. </s>

<s>230) con­<lb></lb>giunte con la base comune AC, la quale sia anche <lb></lb>insieme asse dell&#039;emisfero descritto dal quadrante <lb></lb>ARC, compiuto il semicircolo sul diametro AF, e <lb></lb>descritte intere le ABF, ANF, abbiamo per la para­<lb></lb>bola IIL:BC=AL.LF:AC.CF=HM:BN, <lb></lb>e per il circolo LP2:CR2=AL.LF:AC.CF. </s>

<s><lb></lb>Dunque HM:BN=<foreign lang="grc">π</foreign>LP2:<foreign lang="grc">π</foreign>CR2, che vuol dire <lb></lb>essere le infinite linee, delle quali s&#039;intessono le <lb></lb>due mezze parabole, proporzionali ai cerchi, di che <lb></lb>si compagina l&#039;emisfero: e perciò il centro del­<lb></lb>l&#039;equilibrio nella superficie e nel solido segherà la <lb></lb>libbra AC nella medesima proporzione. </s>

<s>Ond&#039;essendo <lb></lb>nell&#039;emisfero, per le cose già dimostrate, nella proporzione di cinque a tre: <lb></lb>dunque anche nelle due mezze parabole sarà tale. </s></p><p type="main">

<s>Ma l&#039;annunziata proposizione deriva più prossimamente dalla XXIX di <lb></lb>questo trattato, nella quale si comprende come nella sua formula generale, <lb></lb>espressa da AO:OC=HL+LI:HL, sostituitivi i valori particolari, che <lb></lb>sono LI=BC/2, HL=3/4BC, come, osservando che BC sega nel mezzo la <lb></lb>AF, e HL la AC, resulta dalla proporzione CB:HL=AC.CF:AL.LF= <lb></lb>4:3. Fatte le sostituzioni s&#039;ha veramente AO:OC=3/4CB+1/2CB: <lb></lb>3/4CB=5:3, in conferma di quel che sentiremo tra poco asserirsi dal <lb></lb>Torricelli, come legittima conseguenza di principii già dimostrati. </s></p><p type="main">

<s>PROPOSIZIONE LIV. — <emph type="italics"></emph>De&#039;trilinei, formati da qualunque parabola, il <lb></lb>centro di gravità sega l&#039;asse con tal proporzione, che la parte verso il ver­<lb></lb>tice, alla rimanente, stia come il grado della parabola, eresciuto di un&#039;unità, <lb></lb>all&#039;unità stessa.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Che ciò sia il vero, <emph type="italics"></emph>ostenditur,<emph.end type="italics"></emph.end> dice il Torricelli, <emph type="italics"></emph>in doctrina parabo­<lb></lb>larum.<emph.end type="italics"></emph.end> Ma perchè a voler tener dietro all&#039;Autore in quelle dottrine saremm<gap></gap><lb></lb>tirati troppo in lungo, e fuori del campo nostro, ci contenteremo di far osser­<lb></lb>vare come l&#039;annunziata verità si confermi per induzione da alcuni esempi. </s></p><p type="main">

<s>Nel triangolo, ch&#039;è il trilineo formato dalla parabola di primo grado, è <lb></lb>stato già da tanti e in tanti modi dimostrato che il centro di gravità sega <lb></lb>l&#039;asse così, che la parte verso il vertice stia a quella verso la base come uno <lb></lb>più uno, ossia due, sta a uno. </s>

<s>Verificarsi poi nel trilineo della seconda pa­<lb></lb>rabola l&#039;annunziata regola generale fu primo a dimostrarlo Luca Valerio, <lb></lb>nella XXII del suo terzo libro, che dice esser segato dal centro dell&#039;equili­<lb></lb>brio il diametro della figura <emph type="italics"></emph>ita, ut pars quae est ad verticem sit tripla<emph.end type="italics"></emph.end><pb xlink:href="020/01/2738.jpg" pagenum="363"></pb><emph type="italics"></emph>reliquae<emph.end type="italics"></emph.end> (pag. </s>

<s>43), ossia come due, grado della parabola, più uno, è ad uno. </s>

<s><lb></lb>Il Torricelli poi v&#039;applicò il metodo degl&#039;indivisibili, e riuscì alla medesima <lb></lb>conclusione, supponendo noto il centro di gravità del cono. </s></p><p type="main">

<s>Sia infatti CAG (fig. </s>

<s>231) il trilineo proposto: condotta la AC, e pro­<lb></lb>lungata in E l&#039;ascissa NB, avremo, per la parabola da una parte, e per la <lb></lb>similitudine dei triangoli dall&#039;altra, CI:BN=AI2:AN2=IC2:NE2, d&#039;onde, <lb></lb>moltiplicando per 2 la prima ragione, e per <foreign lang="grc">π</foreign> la seconda, CG:BM=<foreign lang="grc">π</foreign>IC2: <lb></lb><figure id="id.020.01.2738.1.jpg" xlink:href="020/01/2738/1.jpg"></figure></s></p><p type="caption">

<s>Figura 231.<lb></lb><foreign lang="grc">π</foreign>NE2, che vuol dire essere le infinite li­<lb></lb>nee del trilineo proporzionali agl&#039;infiniti <lb></lb>circoli di un cono, avente sopra quello <lb></lb>descritto col raggio IC la base, e in A il <lb></lb>vertice: per cui avrà la libbra AI, nel me­<lb></lb>desimo punto, per ambedue le figure, il <lb></lb>centro dell&#039;equilibrio. </s>

<s>E perchè nel cono <lb></lb>quel centro sega l&#039;asse così, che la parte verso il vertice è tripla della <lb></lb>rimanente, dunque anche nell&#039;asse del trilineo tale è la sezione. </s></p><p type="main">

<s>Il Cavalieri divulgò questo modo, avuto privatamente dal Torricelli, nella <lb></lb>propos. </s>

<s>XXIX della sua quinta Esercitazione, benchè con ordine inverso, ser­<lb></lb>vendosi del centro del trilineo per indicare quello del cono: e fu lo stesso <lb></lb>Cavalieri che, nella XXX appresso, rese al pubblico nota l&#039;altra bella ma­<lb></lb>niera di ritrovare il centro del conoide parabolico, da quello del triangolo, <lb></lb>come si vide fare al nostro Autore nella XI di questo trattato. </s></p><p type="main">

<s>Ma tornando al proposito, se CI:BN=AI3:AN3, e la parabola è perciò <lb></lb>del terzo grado, o è cubica, come si dice; il Torricelli dimostrò che la parte <lb></lb>dell&#039;asse verso il vertice sta alla rimanente come 3+1, ossia 4, sta ad uno. </s>

<s><lb></lb>Se CI:BN=AI4:AN4, e perciò la parabola è biquadratica, le due dette <lb></lb>porzioni dell&#039;asse stanno come 4+1 a uno, ossia l&#039;una è quintupla del­<lb></lb>l&#039;altra, e così sempre con regola universale, <emph type="italics"></emph>ut ostenditur in doctrina pa­<lb></lb>rabolarum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Si consideri dunque AI come una libbra gravata da grandezze, che si <lb></lb>eccedono via via a proporzione delle distanze uguali, come nel triangolo, o a <lb></lb>proporzion de&#039;quadrati, de&#039;cubi, de&#039;quadrato-quadrati, o di qualsivoglia altra <lb></lb>potenza, come ne&#039;trilinei formati da parabole ordinarie, cubiche, biquadra­<lb></lb>tiche ecc.; resterà dimostrato da queste dottrine torricelliane il medesimo <lb></lb>teorema generalissimo proposto di sopra, messo però sotto quest&#039;altra forma: <lb></lb><emph type="italics"></emph>Se si disporranno in una libbra grandezze eccedentisi l&#039;una sopra l&#039;altra, <lb></lb>a proporzione delle semplici distanze uguali, de&#039;quadrati, de&#039;cubi, de&#039;bi­<lb></lb>quadrati o di qualsivoglia altra potenza di esse distanze; sarà la detta <lb></lb>libbra segata dal centro dell&#039;equilibrio con tal ragione, che la parte verso <lb></lb>le grandezze minori stia alla rimanente, come il grado della potenza, cre­<lb></lb>sciuto di un&#039;unità, sta all&#039;unità stessa.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Galileo non riuscì, nella sua prima proposizione <emph type="italics"></emph>De centro gravitatis,<emph.end type="italics"></emph.end><lb></lb>a dimostrare il teorema, se non che nel caso che la potenza sia uno. </s>

<s>Per le <lb></lb>seconde potenze cadde in una fallacia, come apparisce in quel suo medesimo <pb xlink:href="020/01/2739.jpg" pagenum="364"></pb>trattato dalla proposizlone VI, ma dimostrar la regola universalissima, da va­<lb></lb>lere per qualunque potenza, non era riserbato che alla potenza matematica <lb></lb>del Torricelli. </s></p><p type="main">

<s>Così dunque preparatesi le vie, potè esso Torricelli riuscire a risolvere <lb></lb>anche il secondo problema, propostogli dal Cavalieri con questa, che nel ma­<lb></lb>noscritto è così intitolata: <emph type="italics"></emph>Demonstratio centri gravitatis cuiusdam solidi, <lb></lb>a parabola geniti, cuius dimidium tantum depinximus.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ PROPOSIZIONE LV. — <emph type="italics"></emph>Esto parabola quaelibet ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>232), <emph type="italics"></emph>cuius <lb></lb>vertex A, diameter AD, basis vero DC (nos hic, facilitatis gratia et bre­<lb></lb>vitatis causa, parabolam ipsam quadraticam supponemus) et super hac <lb></lb>concipiatur cylindricum parabolicum, cuius oppositae bases sint ABCD,<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2739.1.jpg" xlink:href="020/01/2739/1.jpg"></figure></s></p><p type="caption">

<s>Figura 232.<lb></lb><emph type="italics"></emph>EFG: intelligaturque <lb></lb>sectum huiusmodi soli­<lb></lb>dum plano ADFH, per <lb></lb>diametrum AD, et <lb></lb>extremam ipsius pa­<lb></lb>rallelam EH, in oppo­<lb></lb>sita base ducto. </s>

<s>Quae­<lb></lb>ritur centrum gravita­<lb></lb>tis alterius partis, puta <lb></lb>superioris ABCDF. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Circumscribatur <lb></lb>ipsi cylindrico parabo­<lb></lb>lico solidum parallele­<lb></lb>pipedum AICDGEHF. </s>

<s><lb></lb>Secetur solidum alio <lb></lb>plano HO, ubicumque <lb></lb>sit, dummodo plano DE <lb></lb>aequidistet, nasceturque <lb></lb>parallelogrammum BHLM in frusto solidi parabolici, et parallelogrammum <lb></lb>BMON in quodam solido, cuius basis est CIHF, apex vero A. </s>

<s>Huiusmodi so­<lb></lb>lidum vocabimus <emph type="italics"></emph>Pyramidale,<emph.end type="italics"></emph.end> licet quatuor tantum ipsius superficies planae <lb></lb>sint, reliqua vero curva ” (MSS. Gal. </s>

<s>Disc., T. XXXI, fol. </s>

<s>293). </s></p><p type="main">

<s><emph type="italics"></emph>His suppositis,<emph.end type="italics"></emph.end> soggiunge il Torricelli, procederemo alla nostra dimo­<lb></lb>strazione: della quale però chi ha letto il principio non intende quanto po­<lb></lb>tesse riuscire utile complicarla anche di più con quella circoscrizione. </s>

<s>Eppure <lb></lb>sta tutta qui la macchina, disposta co&#039;suoi organi in modo, che può, dalla <lb></lb>VIII del primo degli Equiponderanti, ricevere l&#039;impulso e la regola del moto. </s>

<s><lb></lb>In quella archimedea proposizione infatti, dato il contro di gravità di qua­<lb></lb>lunque grandezza, e di una parte, in cui sia stata divisa; s&#039;insegna a ritro­<lb></lb>vare il centro dell&#039;altra. </s></p><p type="main">

<s>Anche nel presente caso, per via della circoscrizione, il prisma triango­<lb></lb>lare, che nasce dalla bisezione fatta dal piano DH nel parallelepipedo, si <lb></lb>compone di due solidi: del frusto parabolico e del piramidale, i quali chia-<pb xlink:href="020/01/2740.jpg" pagenum="365"></pb>meremo F e P, e immagineremo pendere insieme con le altre loro metà <lb></lb>dalla libbra DC, sopra la quale, essendo Q il centro dell&#039;equilibrio del prisma, <lb></lb>in R quello della parte tolta, ossia del piramidale; il centro del rimanente, <lb></lb>cioè di quel che si cerca, supposto essere in S, verrà indicato dalla rela­<lb></lb>zione (*) QS:QR=P:F. </s>

<s>Di qui si vede che sarà allora risoluto il pro­<lb></lb>blema, quando siano i punti Q, R determinati sopra la libbra, e sia tra P, F <lb></lb>ritrovata la proporzione della grandezza. </s></p><p type="main">

<s>Il punto Q, da cui pendendo s&#039;equilibra il prisma triangolare, sega la <lb></lb>libbra in modo, che la parte DQ sia alla QC doppia, com&#039;è noto per le cose <lb></lb>già dimostrate, e si potrebbe concludere dalla universalità del principio for­<lb></lb>mulato nella precedente proposizione, dalla quale è dato pure con facilità <lb></lb>ritrovare il centro, intorno a cui s&#039;equilibra il piramidale. </s>

<s>S&#039;osservi infatti <lb></lb>che CH:BO=CI.IH:BN.NO. </s>

<s>Ma CI:BN=AI2:AN2, per la parabola, <lb></lb>e IH:NO=AI:AN, per la similitudine dei triangoli; dunque CH:BO= <lb></lb>AI3:AN3, e ciò significa che i parallelogrammi del piramidale son propor­<lb></lb>zionali alle linee di un trilineo cubico, ond&#039;è che quelli segheranno l&#039;asse <lb></lb>nella medesima proporzione di questi, in modo cioè che la parte verso il ver­<lb></lb>tice sia quadrupla della rimanente. </s>

<s>Se perciò intendasi lo spigolo AI traspor­<lb></lb>tato in DC, e ivi lo stesso piramidale raddoppiato; sarà il punto R così di­<lb></lb>sposto sopra la libbra DC, che la parte di lei DR stia all&#039;altra RC come <lb></lb>quattro sta a uno. </s></p><p type="main">

<s>S&#039;ha dunque di qui notificato, colla formula segnata con asterisco, il <lb></lb>valore di QR. </s>

<s>Resta a notificarsi la proporzione tra P e F, per che fare <lb></lb>applicheremo le proposizioni già poco fa scritte: che se dalla LIII veniva <lb></lb>dimostrato che il centro di gravità delle semiparabole, congiunte per la base, <lb></lb>è a tal distanza da C, che stia a quella da D come cinque a tre; dalla LII <lb></lb>si conclude che anche il frusto inferiore, o nel suo tutto o nella sua metà, <lb></lb>quale ora solamente viene in considerazione, sta al frusto superiore F, come <lb></lb>cinque sta a tre: cosicchè chiamato <emph type="italics"></emph>CP<emph.end type="italics"></emph.end> tutto intero il solido colonnare parabo­<lb></lb>lico, sarà F=3/8<emph type="italics"></emph>CP.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Dai medesimi principii si concluderà pure che, avendo il trilineo AIC <lb></lb>il suo centro di gravità a tre quarti dal vertice, il frusto superiore di lui, <lb></lb>chiamandosi <emph type="italics"></emph>CT<emph.end type="italics"></emph.end> il colonnare intero, sarà P=3/4<emph type="italics"></emph>CT.<emph.end type="italics"></emph.end> Consideriamo ora che <lb></lb>il colonnare <emph type="italics"></emph>CP<emph.end type="italics"></emph.end> è doppio di <emph type="italics"></emph>CT,<emph.end type="italics"></emph.end> perchè, avendo ambedue i solidi la mede­<lb></lb>sima altezza, la base parabolica DAC è doppia della trilinea AIC, e perciò <lb></lb>F=3/8.2<emph type="italics"></emph>CT<emph.end type="italics"></emph.end>=3/4<emph type="italics"></emph>CT<emph.end type="italics"></emph.end>=P. </s>

<s>Se dunque P=F, per la sopra contrasse­<lb></lb>gnata con asterisco, sarà anche QS=QR, e son con ciò fatte note tutte <lb></lb>quelle porzioni, che bisognano per riferire il punto S alle due estremità della <lb></lb>libbra. </s>

<s>Abbiamo infatti DS=DQ—QR=DQ—(DR—DQ)=2DQ—DR; <lb></lb>SC=QC+QR=QC+QC—RC=2QC—RC. </s>

<s>Ma 2DQ—DR= <lb></lb>2.2/3DC—4/5DC=8/15DC; 2QC—RC=2/3DC—1/5DC=7/15DC; <lb></lb>dunque DS:SC=8:7. </s></p><p type="main">

<s>Così viene ad essere dimostrata la verità, che il nostro Autore solamente <lb></lb>annunziava in quelle parole poco addietro da noi trascritte, e illustrate dalla <pb xlink:href="020/01/2741.jpg" pagenum="366"></pb>figura 229, nella quale sappiamo ora per certa scienza che la distanza AD <lb></lb>è 8/15 di tutta intera la libbra. </s>

<s>Se perciò s&#039;immagina sospeso il frusto dal <lb></lb>punto D, il centro di gravità dovrà trovarsi lungo il perpendicolo DE, e, per <lb></lb>le cose dette nella proposizione LII, anche lungo la linea AH, che attraversa <lb></lb>il centro di tutte le figure parallelogramme componenti lo stesso frusto, di <lb></lb>cui dunque il centro gravitativo tornerà in Q, dove le due dette linee hanno <lb></lb>il loro concorso. </s>

<s>Di un tal concorso è poi facile indicar la posizione nel per­<lb></lb>pendicolo DE, attraversato in O dalla AI diagonale, perchè i triangoli simili <lb></lb>già disegnati danno AD:DB=AO:OI=OD:OE=8:7, per cui è OD <lb></lb>8/15 di DE, e DQ, che è metà di DO, com&#039;è BH, metà di BI, 4/15. Riferito <lb></lb>insomma il centro di gravità del frusto agli assi ortogonali AD, DE, che siano <lb></lb>ciascuno divisi in quindici parti uguali, s&#039;avrà l&#039;ascissa a otto, e l&#039;ordinata <lb></lb>a quattro di quelle parti. </s></p><p type="main">

<s>La medesima proposizione VIII del primo libro degli Equiponderanti, <lb></lb>che ne ha guidato in questa ricerca, vale per buona regola anche nell&#039;altra: <lb></lb>nella ricerca cioè del centro di gravità del solido inferiore. </s>

<s>Presa infatti BK <lb></lb>5/8 di AB, e condotto il perpendicolo KN, che sia attraversato dalla HP in L, <lb></lb>sarà L il centro di gravità del solido colonnare. </s>

<s>Ma essendo Q quello della <lb></lb>parte tolta, prolungato QL così in fino in M, che stia LM a LQ reciproca­<lb></lb>mente come il frusto superiore sta all&#039;inferiore, ossia come tre sta a cinque; <lb></lb>sarà in M il centro di gravità del rimanente, ossia del frusto inferiore che <lb></lb>si voleva. </s></p><p type="main">

<s>Le coordinate ortogonali, che indicano la situazione del punto M, sono <lb></lb>IT=IN+TN e TM=SE—LR. </s>

<s>Ora IN è porzione nota dell&#039;asse IV, <lb></lb>ed SE è la metà del perpendicolo ED. </s>

<s>La TN poi, ossia la MR, e la LR sono <lb></lb>notificate dai triangoli simili LMR, QLS, i quali danno RM=ML/Lq.LS= <lb></lb>3/5LS; LR=ML/Lq.OQ=3/5OQ, ed LS è uguale a LH—SH; OQ= <lb></lb>OD—DQ tutte quantità note. </s>

<s>Per quantità tutte note verrà dunque a in­<lb></lb>dicarsi dalle dette coordinate ortogonali il centro di gravità del frusto infe­<lb></lb>riore. </s>

<s>Valga questo nostro discorso, qualunque egli sia, a illustrare per qualche <lb></lb>parte, e a rendere per qualche altra compiuta la dimostrazione scritta dal <lb></lb>Torricelli per suo memoriale, e per parteciparla al Cavalieri, che curioso <lb></lb>gliela aveva chiesta, intanto che l&#039;Autore di lei aspettava a ripulirla, e a met­<lb></lb>terla in ordine per la stampa quell&#039;occasione, che invidiosamente gli tolse la <lb></lb>morte. </s>

<s>La detta dimostrazione poi, supposte le cose già annunziate di sopra, <lb></lb>è tale: </s></p><p type="main">

<s>“ His suppositis, esto parallelepipedum 12: eritque cylindricum parabo­<lb></lb>licum integrum, ad reliquam partem, ut basis ad basim, ob eamdem altitu­<lb></lb>dinem: nempe ut parabola ABCD ad trilineum externum ABCI; hoc est, in <lb></lb>nostro casu, ut 8 ad 4. Pars inferior cylindri parabolici, ad superiorem ABCDF, <lb></lb>est ut 5 ad 3, ut ostendimus iam pridem. </s>

<s>Si enim intelligantur duae semipa­<lb></lb>rabolae ad eamdem basim CD coniunctae cum suo solido atque sectione, uti <pb xlink:href="020/01/2742.jpg" pagenum="367"></pb>supra dictum est, erit centrum basis, hoc est duarum semiparabolarum in <lb></lb>recta CD, ita secta, ut pars ad C terminata sit ad reliquam ut 5 ad 3. Ergo <lb></lb>etiam solidum inferius ad superius erit, in eo casu, ut 5 ad 3. Quare etiam, <lb></lb>sumptis tantum dimidiis, erit in nostro casu pars inferior, ad superiorem <lb></lb>ABCDF, ut 5 ad 3. ” </s></p><p type="main">

<s>“ Remanet cylindricum trilineare, cuius oppositae bases sunt ABCI, <lb></lb>EPFH. </s>

<s>Pars eius inferior, ad superiorem quam Pyramidale vocamus, est ut <lb></lb>unum ad 3. Si enim intelligantur duo trilinea ad eamdem rectam AI com­<lb></lb>posita, cum suo solido atque sectione, uti supra explicatum est, erit centrum <lb></lb>basis, hoc est duorum trilineorum, in recta AI ita secta, ut pars ad I sit ad <lb></lb>reliquam ut unum ad tria. </s>

<s>Ratio est quia omnes lineae in trilineo, quales <lb></lb>sunt IC, NB, etc., inter se erunt ut circuli alicuius coni, qui axem habeat <lb></lb>AI, et verticem A. </s>

<s>Quare etiam pars inferior, ad superiorem, erit in eo casu <lb></lb>ut unum ad tria. </s>

<s>Ergo, sumptis etiam tantum dimidiis, erit in nostro casu <lb></lb>pars inferior ad superiorem, sive ad nostrum pyramidale CIHFA, ut unum <lb></lb>ad tria. </s>

<s>” </s></p><p type="main">

<s>“ Ostensum itaque est quod, si ponatur parallelepipedum 12, pars su­<lb></lb>perior solidi cylindrici parabolici erit 3. Itemque ipsum sibi adiacens pyrami­<lb></lb>dale erit 3. Propterea huiusmadi solida, quando parabola quadratica fuerit, <lb></lb>sunt aequalia. </s>

<s>” </s></p><p type="main">

<s>“ Pyramidale CIHFA centrum gravitatis habet in plano basi parallelo, <lb></lb>quod quidem planum secat AI rectam in ratione quadrupla: nempe ita ut <lb></lb>pars ad A sit ad reliquam ut 4 ad 1. Ratio est quia parallelogrammum CH, <lb></lb>ad BO, rationem habet compositam ex ratione rectae CI ad rectam BN, sive <lb></lb>ex ratione quadrati IA ad AN, ob parabolam quadraticam, et ex ratione rectae <lb></lb>IH ad NO, sive ex ratione rectae IA ad AN. </s>

<s>Quare parallelogrammum BO <lb></lb>erit ut cubus IA ad cubum AN, et hoc semper. </s>

<s>Propterea omnia simul pa­<lb></lb>rallelogramma, sive ipsum pyramidale, centrum gravitatis habebit in eodem <lb></lb>plano, in quo est centrum gravitatis trilinei externae parabolae cubicae, cum <lb></lb>plana pyramidalis inter se sint ut lineae trilinei cubici. </s>

<s>Trilineum autem cu­<lb></lb>bicum centrum gravitatis habet in quadam aequidistante ipsi IC, quae qui­<lb></lb>dem secat rectam AI in ratione quadrupla, ut ostenditur in <emph type="italics"></emph>doctrina para­<lb></lb>bolarum.<emph.end type="italics"></emph.end> Quare centrum gravitatis pyramidalis erit in plano, quod secat <lb></lb>tangentem AI in ratione ut 4 ad 1. ” </s></p><p type="main">

<s>“ Ponamus iam omnia corpora a nobis delineata duplicari etiam ex al­<lb></lb>tera parte ad rectam DC. </s>

<s>Ponaturque rectam DC esse libram quamdam, <lb></lb>divisam in quindecim partes aequales. </s>

<s>Centrum aequilibrii prismatis, cuius <lb></lb>dimidium est AHFDIC, erit punctum Q, in quo libra dividitur in ratione <lb></lb>dupla. </s>

<s>Magnitudines enim appensae sunt infinita parallelogramma, quorum <lb></lb>unum est HO, inter se eamdem rationem servantia, quam servant lineae <lb></lb>trianguli DCF, quarum una est HL. </s>

<s>At centrum aequilibrii duorum pyrami­<lb></lb>dalium, quorum unum est CIHFA, erit punctum R, in quo libra dividitur <lb></lb>in ratione quadrupla, uti ante explicatum est, ergo centrum aequilibrii re­<lb></lb>liqui solidi, cuius dimidium est ABCDF, erit S, nempe, sumpta QS, quae sit <pb xlink:href="020/01/2743.jpg" pagenum="368"></pb>aequalis ipsi QR, cum demonstraverimus ipsum pyramidale aequale esse so­<lb></lb>lido ABCDF in parabola quadratica. </s>

<s>Propterea centrum gravitatis solidi pro­<lb></lb>positi erit in recta, quae ex puncto S demittitur aequidistanter ipsi CF. </s>

<s>Est <lb></lb>autem etiam in recta, quae ex D producitur ad punctum medium ipsius CF, <lb></lb>ergo in communi concursu. </s>

<s>In nostro casu punctum S secat rectam DC in <lb></lb>ratione 8 ad 7. ” </s></p><p type="main">

<s>“ Si quis vero desideret centrum gravitatis etiam partis inferioris, ipsam <lb></lb>habebit per VIII libri primi Aequiponderantium, cum datum sit centrum <lb></lb>totius in medio axis integri solidi, centrumque unius partis, una cum ratione <lb></lb>partium ” (ibid., fol. </s>

<s>294, 95). </s></p><p type="main">

<s>Rimane a dire dell&#039;invenzione del centro di gravità dentro lo spazio ci­<lb></lb>cloidale, intorno a che avrà la nostra Storia, in altro proposito, occasione a <lb></lb>lungo e importante discorso, l&#039;argomento del quale si vedrà intanto accen­<lb></lb>nato dalle seguenti parole, che il Torricelli stesso scriveva nel raccontar le <lb></lb>vicende subite da&#039;suoi varii problemi, proposti ai matematici di Francia: </s></p><p type="main">

<s><emph type="italics"></emph>“ Il centro di gravità della cicloide sta nell&#039;asse e lo sega in pro­<lb></lb>porzione di sette a cinque.<emph.end type="italics"></emph.end> Avendo io avvisato la sola annunciazione di <lb></lb>quest&#039;ultimo teorema in Francia, mi fu risposto dal p. </s>

<s>Mersenno, che allora <lb></lb>era l&#039;interpetre tra monsù Roberval e me, che io in questo avevo prevenuto <lb></lb>il loro geometra Roberval, il quale circa alla cicloide aveva dimostrata ogni <lb></lb>altra cosa, fuor che il centro di gravità, e il solido intorno all&#039;asse: e che <lb></lb>riconoscevano da me, come da primo inventore, questa invenzione del centro <lb></lb>di gravità della cicloide, e che non credevano che geometricamente potesse <lb></lb>esser vera la mia proposta. <emph type="italics"></emph>Dubitat Robervallius noster an mechanice tan­<lb></lb>tum centrum gravitatis inveneris, quod tamen geometrice falsum suspi­<lb></lb>catur. </s>

<s>Docebis num demonstrationem habeas<emph.end type="italics"></emph.end> con altre confessioni simili, <lb></lb>come appare in lettere di propria mano del p. </s>

<s>Mersenno, le quali sono ap­<lb></lb>presso di me. </s>

<s>In queste confessa apertamente che monsu Roberval non aveva <lb></lb>quel teorema, se ne chiamano debitori a me, e parlando di Roberval dice <lb></lb>queste parole: <emph type="italics"></emph>Qui cum tuas postremas literas legisset praedictum centrum <lb></lb>gravitatis tibi debere fatetur qui primus invenisti,<emph.end type="italics"></emph.end> e mi prega più di una <lb></lb>volta, acciò che io voglia mandargli la dimostrazione, con promettermi che <lb></lb>si sarebbe messa fra quelle di monsù Roberval, e così per l&#039;appunto seguì. </s>

<s>” </s></p><p type="main">

<s>“ Io subito gli mandai, e questo fu la state del 1644, in una lunga <lb></lb>scrittura, non solo la dimostrazione del centro di gravità, ma anco la dimo­<lb></lb>strazione del teorema seguente, poichè serviva per lemma alla dimostrazione <lb></lb>mia: <emph type="italics"></emph>Se due figure piane saranno girate intorno a due lince come assi, <lb></lb>gli solidi fatti dalla revoluzione averanno fra di loro la proporzione com­<lb></lb>posta della proporzione, che hanno le figure piane genitrici, e della pro­<lb></lb>porzione, che hanno le distanze del centro di gravità delle medesime dal­<lb></lb>l&#039;asse della revoluzione.<emph.end type="italics"></emph.end> Essi hanno tardato due anni a rispondere, ed ora, <lb></lb>dimenticati delle lettere passate, e confidando che io, avendole sprezzate, non <lb></lb>le abbia più, scrivono che le predette dimostrazioni, mandategli da me a loro <lb></lb>istanza, le avevano un pezzo fa. </s>

<s>Ora si sta controvertendo questo punto, e <pb xlink:href="020/01/2744.jpg" pagenum="369"></pb>se essi persisteranno in dire che, avanti a me avevano le predette due dimo­<lb></lb>strazioni, io sono risoluto di far riconoscere le lettere, le quali sono notis­<lb></lb>sime a molti in Italia, e stamparle, insieme con le ragioni mie, acciò il mondo <lb></lb>veda che furto vergognoso hanno tentato di farmi ” (MSS. Gal. </s>

<s>Disc., T. XXXII, <lb></lb>fol. </s>

<s>39). </s></p><p type="main">

<s>Troppo semplici bisognerebbe dire i nostri Lettori, se credessero, come <lb></lb>alcuni hanno fatto, che sia decisa la sentenza così dietro le ragioni dette a <lb></lb>favor suo da uno solo dei litiganti. </s>

<s>Ascolteremo altrove anche l&#039;altra parte, <lb></lb>e, se non c&#039;inganniamo, sarà allora che la Storia ci avrà dato della causa <lb></lb>cognizione perfetta, pronunziato finalmente il giudizio secondo giustizia. </s>

<s>In­<lb></lb>tanto, messa la proposizione del centro di gravità della cicloide in forma, per <lb></lb>aggiungersi a questo trattato, vediamo come l&#039;Autore l&#039;avesse dimostrata. </s></p><p type="main">

<s>“ PROPOSIZIONE LVI. — <emph type="italics"></emph>Centrum gravitatis cycloidis dividit axem ita, <lb></lb>ut pars ad verticem terminata sit ad reliqua ut 7 ad 5. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Vi è premesso un lemma simile, e di non men facile dimostrazion di <lb></lb>quell&#039;altro, che in primo luogo precede al secondo teorema <emph type="italics"></emph>De dimensione <lb></lb>Cycloidis<emph.end type="italics"></emph.end> (Op. </s>

<s>geom., P. II cit., pag. </s>

<s>87): il detto lemma è tale: </s></p><p type="main">

<s>“ Si super lateribus oppositis alicuius parallelogrammi rectanguli ABCD <lb></lb>(fig. </s>

<s>233), duo semicirculi descripti sint, figuram mixtam AEBCFD <emph type="italics"></emph>arcuatum<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2744.1.jpg" xlink:href="020/01/2744/1.jpg"></figure></s></p><p type="caption">

<s>Figura 233.<lb></lb>appello, lineasque rectas AD, BC ipsius bases. </s>

<s>Quando <lb></lb>vero arcuatum iam dictum sectum fuerit ab aliqua <lb></lb>recta EF, basibus parallela, utramque figuram a se­<lb></lb>ctione factam <emph type="italics"></emph>arcuatum<emph.end type="italics"></emph.end> item appello. </s>

<s>” </s></p><p type="main">

<s>“ Unnmquodque arcuatum aequale est rectangulo <lb></lb>super eadem basi, et sub eadem altitudine constituto: <lb></lb>facile probatur hoc per subtractionem, additionemque. </s>

<s><lb></lb>Ergo patet quod arcuata, super aequalibus basibus <lb></lb>constituta, erunt inter se ut altitudines. </s>

<s>” </s></p><p type="main">

<s>“ Denique si alicuius arcuati AEFD altitudo HD <lb></lb>bifariam secetur in I, suppono centrum gravitatis arcuati esse in ea linea, <lb></lb>quae per I ducitur aequidistanter basibus arcuati. </s>

<s>Quod quidem utraque ra­<lb></lb>tione, nova veterique, facile probari potest: facilius tamen concedi et omitti ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XXXIV, fol. </s>

<s>275). </s></p><p type="main">

<s>Che per semplice addizione e sottrazione sia veramente la cosa dimo­<lb></lb>strabile, resulta, chiamando A l&#039;arcuato, dall&#039;equazione A=<foreign lang="grc">π</foreign>BA2/2+ <lb></lb>BI.IH—<foreign lang="grc">π</foreign>CD2/2=BI.IH. </s>

<s>E ciò che del tutto essendo vero altresì delle <lb></lb>parti corrispondenti, sarà l&#039;arcuato CBEF uguale al rettangolo BH, e l&#039;ar­<lb></lb>cuato ADFE uguale al rettangolo AH: ond&#039;è che sulla linea, condotta dal <lb></lb>mezzo di HD parallela alla base comune, si troverà il centro di gravità del­<lb></lb>l&#039;una e dell&#039;altra figura. </s></p><p type="main">

<s>Se ora dell&#039;emicicloide ABCD (fig. </s>

<s>234) si divida in F, nel mezzo, la <lb></lb>semibase AD, e sopra il diametro FG si disegni una metà del circolo geni-<pb xlink:href="020/01/2745.jpg" pagenum="370"></pb>tore, e poi dal punto B, dove la circonferenza di lui sega la cicloide, si con­<lb></lb>duca la BE parallela alla base; è manifesto che questa passerà per i centri <lb></lb><figure id="id.020.01.2745.1.jpg" xlink:href="020/01/2745/1.jpg"></figure></s></p><p type="caption">

<s>Figura 234.<lb></lb>L, E, e che con una tal costruzione <lb></lb>si verrà lo spazio cicloidale a dividere <lb></lb>in quattro parti, che sono: il semi­<lb></lb>circolo CHD, l&#039;arcuato BHDF e i due <lb></lb>trilinei CBH, ABF. L&#039;arcuato, che è <lb></lb>per il precedente lemma uguale al ret­<lb></lb>tangolo FE, ossia a FD quarta parte <lb></lb>della circonferenza moltiplicata per il <lb></lb>raggio ED, sarà dunque uguale a mezzo il circolo CHD: e perchè tutto lo spa­<lb></lb>zio si compone di tre tali mezzi circoli, dunque i due trilinei insieme equi­<lb></lb>varranno al terzo. </s></p><p type="main">

<s>Oltre alle proporzioni delle aree di due delle parti componenti, sappiamo <lb></lb>anche il centro di gravità in quale ordinata egli sia, e il centro di CHD <lb></lb>semicircolo essere in EB, e dell&#039;arcuato in IM. </s>

<s>E ciò tanto basta, senza che <lb></lb>sia determinato in quelle linee il punto preciso, perch&#039;essendo la presente <lb></lb>invenzione rivolta, non alla mezza cicloide particolarmente, ma alla cicloide <lb></lb>intera; basta a noi sapere dove la linea, che ricongiunge i centri di gravità <lb></lb>delle due parti in distanze uguali dall&#039;asse, sega l&#039;asse stesso: nel qual punto <lb></lb>della sezione ha in ogni modo a ritrovarsi il centro di gravità del tutto. </s>

<s>Si <lb></lb>riduce dunque il negozio a dimostrare in quale ordinata si trovi il centro di <lb></lb>gravità dei due trilinei, intorno a che tutto si affaticò il Torricelli a quel <lb></lb>modo, e con quella riuscita, che i Lettori qui appresso intenderanno. <lb></lb><figure id="id.020.01.2745.2.jpg" xlink:href="020/01/2745/2.jpg"></figure></s></p><p type="caption">

<s>Figura 235.</s></p><p type="main">

<s>“ Esto dimidium lineae cycloidis ABC (fig. </s>

<s>235), cuius axis CD, basis <lb></lb>vero sit AD, et ordinata, per punctum axis medium, sit EB. </s>

<s>Transeat autem <lb></lb>per B circulus genitor FBG, contingens basim in F lineamque CG in G. </s>

<s><lb></lb>Patet quod aequales erunt AF, FD, nam, cum arcus FB, BG quadrantis sint, <pb xlink:href="020/01/2746.jpg" pagenum="371"></pb>recta AF aequalis est arcui BF: recta vero GC aequalis est arcui GB, utra­<lb></lb>que ob naturam cycloidis primariae. </s>

<s>Cum vero latera opposita arcuati FBHD <lb></lb>aequalia sint, nempe BH, FD erunt aequales, et rectae AF, BH. </s>

<s>Secetur ita­<lb></lb>que utraque illarum in partes quotcumque aequales, et erunt in recta BH <lb></lb>partes totidem quot sunt in AF. </s>

<s>Transeat iam per unumquodque sectionum <lb></lb>punctum peripheria circuli genitoris, et super singulis basibus HI, IL, etc., <lb></lb>item super singulis basibus FM, MN, etc., concipiantur constituta arcuata <lb></lb>usque ad cycloidem lineam, ita ut arcuata tangant, sed non excedant lineam <lb></lb>cycloidalem. </s>

<s>Manifestum est quod numerus arcuatorum, quot sunt in trili­<lb></lb>neo ABF, aequalis erit numero arcuatorum, quot sunt in trilineo BCH, nam <lb></lb>super singulis partibus rectae AF, excepta extrema quae terminatur ad A, <lb></lb>item, super singulis partibus rectae BH, excepta extrema quae terminatur <lb></lb>ad B, singula arcuata erecta sunt. </s>

<s>Dico universa huiusmodi arcuata centrum <lb></lb>commune gravitatis habere in recta BE, quae per medium axis punctum in <lb></lb>cycloide applicatur. </s>

<s>” </s></p><p type="main">

<s>“ Sumantur enim duo quaelibet ex praedictis arcuatis MP, IO, quorum <lb></lb>bases NM, LI aequaliter remotae sunt a punctis A et B: tum producantur <lb></lb>ordinatim PQ, OR, ducaturque ST parallela ad axem, et secentur bifariam <lb></lb>QD in V, RE in X, ST in Y, et HT in Z. Jam, ob naturam cycloidis, arcus <lb></lb>OK aequalis est rectae KC, sed quadrans LK rectae GC: ergo reliquus ar­<lb></lb>cus LO rectae GK aequalis erit, sive rectae BL, sive rectae AN, ob suppo­<lb></lb>sitionem, bases enim sumptorum arcuatorum aequaliter distant ab A et B <lb></lb>punctis; sive arcui PN, ob cycloidem. </s>

<s>Ergo, cum aequales sint arcus OL, PN, <lb></lb>aequales erunt eorum sagittae, sive sinus versi HT, QD, quod memento. </s>

<s>” </s></p><p type="main">

<s>“ Quoniam tota HW, et tota HE est ut ablata HT ad TZ, nempe dupla, <lb></lb>erit reliqua TW dupla reliquae ZE. </s>

<s>Arcuatum vero MP, ad arcuatum IO, <lb></lb>est ut altitudo QD ad ST, sive ut HT ad TS, sive, ob circulum, ut TS ad <lb></lb>TW, sive, sumptis subduplis, ut TY ad ZE, sive, sumptis aequalibus, ut XE <lb></lb>ad EV. </s>

<s>Est autem centrum gravitatis arcuati MP in linea applicata ex V, et <lb></lb>centrum arcuati OI est in linea applicata ex puncto X, ostendimusque arcua­<lb></lb>tum MP, ad IO, esse ut recta XE ad EV, reciproce. </s>

<s>Propterea commune illo­<lb></lb>rum centrum erit in recta BE, ubicumque tamdem sit. </s>

<s>Sic ostendetur cen­<lb></lb>trum omnium reliquorum, si bina sumantur, ea lege ut sumptorum bases <lb></lb>aequaliter distent a punctis A et B; ostendetur, inquam, centrum gravitatis <lb></lb>omnium esse in eadem recta BE. </s>

<s>Propterea et commune centrum gravitatis <lb></lb>universorum, simul sumptorum, erit in BE. ” </s></p><p type="main">

<s>“ Amplius, dico commune centrum gravitatis duorum trilineorum ABF, <lb></lb>BCH esse in eadem recta BE. </s>

<s>Si enim possibile est, ponatur extra rectam <lb></lb>BE, ubicumque, puta <foreign lang="grc">β. </foreign></s>

<s>Ducatur ordinatim recta <foreign lang="grc">αβ. </foreign></s>

<s>Tum inscribantur intra <lb></lb>ipsa trilinea duae figurae, constantes ex arcuatis aeque altis, et numero ae­<lb></lb>qualibus, utrimque, ita tamen ut trilinea ipsa, ad differentiam, quae inter <lb></lb>ipsa et inscriptas figuras est, maiorem habeant rationem, quam CE ad E<foreign lang="grc">α. </foreign></s>

<s><lb></lb>Quod autem hoc fieri possit, constat: nam, supponamus ita esse duo trilinea, <lb></lb>ad aliquod spatium <foreign lang="grc">Σ</foreign>, uti est CE ad E<foreign lang="grc">α</foreign>: tum inscribantur intra ipsa trili-<pb xlink:href="020/01/2747.jpg" pagenum="372"></pb>nea duae figurae, constantes ex arcuatis aeqealtis, ita ut defectus figurarum <lb></lb>inscriptarum a trilineis minor sit spatio <foreign lang="grc">Σ. </foreign></s>

<s>Tunc enim erit ratio trilineorum, <lb></lb>ad differentiam, maior ratione CE ad E<foreign lang="grc">α. </foreign></s>

<s>” </s></p><p type="main">

<s>“ Factum ergo sit, supponamusque inscriptas in trilineis esse duas figu­<lb></lb>ras, ex arcuatis compositas, uti iussum est. </s>

<s>Ex demonstratis, erit centrum <lb></lb>gravitatis incriptarum figurarum in recta BE. </s>

<s>Esto illud punctum quodcum­<lb></lb>que <foreign lang="grc">γ</foreign>, ducaturque recta <foreign lang="grc">γβ</foreign>, et extendatur. </s>

<s>Fiat deinde ut ipsa duo trilinea <lb></lb>ABF, BCH, ad praedictam differentiam, ita recta quaedam <foreign lang="grc">εγ</foreign> ad <foreign lang="grc">γβ</foreign>: patet <lb></lb>quod recta <foreign lang="grc">εγ</foreign> maior erit quam <foreign lang="grc">δγ</foreign>, nam ratio <foreign lang="grc">εγ</foreign>, ad <foreign lang="grc">γβ</foreign>, eadem est ac ratio <lb></lb>trilineorum ad differentiam, quae quidem ratio, per constructionem, maior <lb></lb>est ratione CE ad E<foreign lang="grc">α</foreign>: hoc est ratione <foreign lang="grc">δγ</foreign> ad <foreign lang="grc">γβ. </foreign></s>

<s>Ergo recta <foreign lang="grc">εγ</foreign> maior est <lb></lb>quam recta <foreign lang="grc">δγ. </foreign></s>

<s>Dividendo itaque, erunt figurae inscriptae in arcuatis constan­<lb></lb>tes, ad illam differentiam, ut recta <foreign lang="grc">εβ</foreign> ad <foreign lang="grc">βγ. </foreign></s>

<s>Sed <foreign lang="grc">β</foreign> centrum gravitatis est <lb></lb>totius, et <foreign lang="grc">γ</foreign> figurarum inscriptarum; ergo <foreign lang="grc">ε</foreign> erit centrum gravitatis differen­<lb></lb>tiae, absurdum. </s>

<s>Non est ergo centrum gravitatis trilineorum extra rectam BE, <lb></lb>sed in ipsa, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” (ibid., fol. </s>

<s>275, 76). </s></p><p type="main">

<s>Essendosi così dunque dimostrato che il centro di gravità d&#039;ambedue i <lb></lb>trilinei è sopra l&#039;ordinata BE (rivolgendo l&#039;occhio indietro sulla figura 234) <lb></lb>in E dunque, sull&#039;asse, saranno i centri di gravità di questi, come degli altri <lb></lb>due trilinei a questi uguali, che son dentro l&#039;altro spazio cicloidale: e in E, <lb></lb>centro della figura, sarà pure il centro di gravità del circolo intero, a cui <lb></lb>i detti quattro trilinei, e i due arcuati col centro comune in I, sono uguali. </s>

<s><lb></lb>Delle tre pari grandezze dunque, delle quali si compone lo spazio cicloidale, <lb></lb>due pendono in E, e una in I, ond&#039;è che, se la libbra EI si divide ugual­<lb></lb>mente in tre parti, due delle quali ne abbia IO, e la terza EO; in O sarà <lb></lb>il centro di gravità del tutto, ossia della Cicloide. </s>

<s>Se poi anche ID nello stesso <lb></lb>modo si tripartisca, e in sei, come riman divisa questa metà, si divida pa­<lb></lb>rimente anche l&#039;altra metà dell&#039;asse; è manifesto che, delle dodici parti, CO <lb></lb>ne contien 7, e OD 5, come già il Torricelli annunziava in principio, e in <lb></lb>fine alla sua dimostrazione ora conclude con queste parole: </s></p><p type="main">

<s>“ Praeterea, cum arcuatum FBHD aequale sit rectangulo FLED, et se­<lb></lb>micirculus CHD eidem rectangulo aequalis sit; aequales erunt inter se tres <lb></lb>figurae, nempe semicirculus CHD, arcuatum FBHD, et reliqua duo trilinea <lb></lb>ABF, BCH simul sumpta. </s>

<s>Secetur ED bifariam in I, et EI in tres partes <lb></lb>aequales EO, OP, PI: manifestum est quod centrum gravitatis arcuati FBHD <lb></lb>est in applicata ex puncto I, et reliquarum duarum magnitudinum, nempe <lb></lb>semicirculi trilineorumque, centrum gravitatis est in applicata BE, estque ar­<lb></lb>cuatum FBHD, ad reliquas figuras, subduplum, hoc est ut EO ad OI reci­<lb></lb>proce. </s>

<s>Ergo centrum gravitatis compositae emicicloidis erit in applicata, quae <lb></lb>per O ducitur. </s>

<s>Propterea centrum gravitatis integrae cicloidis erit ipsummet <lb></lb>punctum O. </s>

<s>Quod autem CO ad OD sit ut numerus 7 ad 5, manifestum est <lb></lb>ex imperata divisione ” (ibid., fol. </s>

<s>276). </s></p><pb xlink:href="020/01/2748.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Di varie altre cose di Meccanica <lb></lb>lasciate dal Torricelli<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Di alcune proposizioni relative al trattato <emph type="italics"></emph>De motu.<emph.end type="italics"></emph.end> — II. </s>

<s>Di alcune altre proposizioni relative al <lb></lb>trattato <emph type="italics"></emph>De momentis.<emph.end type="italics"></emph.end> — III. </s>

<s>Del modo meccanico di condur le tangenti, e di varii altri teo­<lb></lb>remi di Meccanica nuova. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Se non avesse il Torricelli lasciato altro di manoscritto che le proposi­<lb></lb>zioni dei centri di gravità, delle quali nel precedente capitolo ci siamo stu­<lb></lb>diati di ordinare e di esporre la storia, basterebbe questo solo per giustificare <lb></lb>le sollecitudini del principe Leopoldo de&#039;Medici, il quale, persuasosi che fos­<lb></lb>sero quelle carte non intelligibili che al loro proprio autore, e rappresenta­<lb></lb>tive così informi di un disegno, che nessun altro saprebbe mettere in ese­<lb></lb>cuzione; avrebbe voluto che nella Biblioteca laurenziana fossero custodite, <lb></lb>dentro un&#039;arca fatta fabbricare con regia munificenza, le preziose reliquie. </s>

<s><lb></lb>Lodovico Serenai però, benchè fossero morti il Cavalieri e il Ricci, che il <lb></lb>Torricelli stesso aveva designati della sua scientifica eredità esecutori testa­<lb></lb>mentari, non aveva perduta affatto la speranza di veder que&#039;teoremi, in <lb></lb>qualche parte compiuti e in qualche altra illustrati, messi in ordine di trat­<lb></lb>tato così, da supplire nel miglior modo possibile a quella perdita, che da tutti <lb></lb>si deplorava. </s>

<s>Aveva il verde di una tale speranza fondate le sue radici nella <lb></lb>perizia delle cose, e nella affezione che, come discepolo verso l&#039;autore di loro, <lb></lb>tutti riconoscevano nel Viviani. </s>

<s>Da lui perciò i Matematici di Europa, i quali <lb></lb>avevano con tanto applauso e con tanta ammirazione accolte le Opere geo­<lb></lb>metriche stampate nel 1644, aspettavano di veder sodisfatti i loro desiderii. <pb xlink:href="020/01/2749.jpg" pagenum="374"></pb>E quasi fosse divenuto intollerabile ogni più lungo indugio, Erasmo Bartho­<lb></lb>lin, che trattenendosi in Italia aveva con lo stesso Viviani contratta partico­<lb></lb>lare amicizia, veniva da Padova con sue lettere sollecitando il fiorentino amico, <lb></lb>perchè gli volesse intanto trascrivere la nota degli argomenti, intorno a che <lb></lb>verserebbero le opere postume del Torricelli. </s>

<s>Il qual desiderio era sodisfatto <lb></lb>così, con lettera del dì 4 Settembre 1655 da Firenze: </s></p><p type="main">

<s>“ Invio a V. S. la qui inclusa nota delle opere postume originali del <lb></lb>signor Torricelli, che, dalla morte di esso in qua, si trovano appresso il signor <lb></lb>Lodovico Serenai, il quale, per ratificare in parte al desiderio e alla curio­<lb></lb>sità di V. S., ha trascritto dal proemio del libro <emph type="italics"></emph>Delle proporzioni<emph.end type="italics"></emph.end> quant&#039;ella <lb></lb>vede in proposito del trattato <emph type="italics"></emph>De lineis novis,<emph.end type="italics"></emph.end> che il medesimo signor Tor­<lb></lb>ricelli prometteva di dar fuori. </s>

<s>Non so già se l&#039;improvvisa morte di lui gli <lb></lb>abbia tolto il poter colorire e perfezionare così peregrini e maravigliosi di­<lb></lb>segni, quali egli va leggermente toccando in detto suo proemio, non avendo <lb></lb>io avuto per ancora appresso di me copia di alcun foglio di detta materia. </s>

<s><lb></lb>Dubito però che, per essere i primi abbozzi ed i primi delineamenti di così <lb></lb>alte meditazioni, ci sia, oltre al disordine, ed errori e imperfezioni dell&#039;opera <lb></lb>stessa, la quale forse non ha finita e dimostrata in ogni sua parte, ma solo <lb></lb>in molti luoghi accennata. </s>

<s>” </s></p><p type="main">

<s>“ Alle due prime necessità procurerò di ovviare, nella maniera che ho <lb></lb>fatto intorno alla copia di altre cose geometriche del medesimo Autore, che <lb></lb>ultimamente ho avuto alle mani, avendogli dato il miglior ordine a me pos­<lb></lb>sibile, per essersi trovate confusissime, correttele ne&#039;luoghi difettosi, e nei <lb></lb>trascorsi di penna, soliti farsi per lo più nelle prime bozze, tolte via quelle <lb></lb>che sono già stampate da lui medesimo o da altri, e che <emph type="italics"></emph>ad institutum non <lb></lb>faciunt,<emph.end type="italics"></emph.end> e ridotte finalmente a vero senso quelle, che per avventura propon­<lb></lb>gono o concludono il falso. </s>

<s>” </s></p><p type="main">

<s>“ Quanto alla terza, lascerò che venga supplito da altri, assai più di me <lb></lb>esercitato in queste nuove speculazioni, con dimostrare e aggiungere ciò che <lb></lb>potesse mancarci, trovandomi da dieci anni, o piuttosto dalla morte del signor <lb></lb>Galileo mio maestro in qua, per varie disavventure e pessime contingenze, <lb></lb>nemici, domestici affari, etc., quasi affatto alienato da simili studi, che per <lb></lb>altro sariano proporzionatissimi al genio mio, se non alla mia inclinazione. </s>

<s><lb></lb>Intanto V. S., insieme con gli altri acutissimi geometri d&#039;Europa, aspetti in <lb></lb>breve la pubblicazione di tali opere, e compatisca a qualche poca di dila­<lb></lb>zione, non essendo in potestà mia il disporre delle altrui cose ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. CXLII, fol. </s>

<s>4). </s></p><p type="main">

<s>Quella dilazione però, che si prometteva si poca, era giunta a ben ven­<lb></lb>titre anni, dopo il qual tempo così scriveva il Viviani stesso in una sua let­<lb></lb>tera del dì 7 Giugno 1678 al p. </s>

<s>Antonio Baldigiani gesuita, che attendeva <lb></lb>allora a scrivere gli elogi di Galileo, e de&#039;più illustri discepoli di lui: “ Ve­<lb></lb>nendo ora all&#039;acutissimo geometra Torricelli, il quale, benchè di nazione non <lb></lb>toscano, illustrò mirabilmente il posto del suo predecessore Galileo, ed in <lb></lb>conseguenza la nostra Toscana con le sue speculazioni; io son pur certo che <pb xlink:href="020/01/2750.jpg" pagenum="375"></pb>di questo ancora, essendovi assaissimo da commendare, assai ella e felicis­<lb></lb>simamente avrà detto. </s>

<s>Di questo le Opere pubblicate sin ora son comprese <lb></lb>in un tomo in quarto, stampato in Firenze nel 1644, ecc. </s>

<s>” (ivi, fol. </s>

<s>272), e <lb></lb>seguitando a enarrare i titoli delle Opere varie, poi così soggiunge: </s></p><p type="main">

<s>“ Le opere rimanenti da stamparsi ora saranno sotto questo titolo: <lb></lb>EVANGELISTAE TORRICELLI FAVENTINI — MATHEMATICI OLIM SERENISS. — FER­<lb></lb>DINANDI-II. M. E. D. — OPERA POSTHUMA MATHEMATICA — QUAE EXTANT OMNIA <lb></lb>— IN TRES PARTES DIVISAS — QUARUM PRIMA, STYLO VETERUM CONTINET — <lb></lb><emph type="italics"></emph>Miscellanea circa magnitudines planas, curvas, ac solidas — Mechanica <lb></lb>quaedam — De tactionibus et de proportionibus libros cum enarratione <lb></lb>quorundam problematum geometricorum.<emph.end type="italics"></emph.end> — SECUNDA CONTINET, INDIVISI­<lb></lb>BILIUM METHODO, <emph type="italics"></emph>Stereometria et eentrobaryca.<emph.end type="italics"></emph.end> — TERTIA, <emph type="italics"></emph>Tractatus de li­<lb></lb>neis novis. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ In quarto luogo saranno alcune <emph type="italics"></emph>Lezioni Accademiche<emph.end type="italics"></emph.end> italiane e Let­<lb></lb>tere familiari. </s>

<s>Ciò che io abbia faticato e contribuito a quest&#039;Opere si cono­<lb></lb>scerà apertamente, ma non mai tanto, quanto da chi le vedde disordinate e <lb></lb>imperfette ” (ivi). </s></p><p type="main">

<s>Sono ormai passati, dalla data di questa lettera al Baldigiani, dugento <lb></lb>e vent&#039;anni, e delle opere postume del Torricelli, quivi annunziate e solen­<lb></lb>nemente promesse come di prossima pubblicazione, non si son vedute che <lb></lb>le Lezioni accademiche, per cura di tutt&#039;altri che del Viviani. </s>

<s>Erano forse <lb></lb>una menzogna le sue promesse, o era vero quel che dissero alcuni, che cioè <lb></lb>vi si trovasse contro sua voglia impegnato, e che per invidia e per rivalità <lb></lb>col Torricelli menasse così la cosa in lungo, da riuscire a eludere i deside­<lb></lb>rii del Serenai, e i comandi del principe Leopoldo? </s></p><p type="main">

<s>La calunnia si dissipa senz&#039;altro, osservando che non fa maraviglia se <lb></lb>mancò al Viviani, per curare le opere altrui, quel tempo o quella comodità, <lb></lb>che non seppe trovar per le proprie: benchè non si venga a togliere con ciò <lb></lb>qualche dubbio, che rimarrebbe intorno alla sincerità del titolo, che tenevasi <lb></lb>preparato per mettersi innanzi alla stampa del libro. </s>

<s>S&#039;avevano veramente <lb></lb>in ordine tutti i trattati matematici secondo le tre parti, nelle quali il dili­<lb></lb>gente compilatore pensava di distribuire le opere postume del Torricelli? </s>

<s>Si <lb></lb>risponderebbe di no, se la maggior parte de&#039;fascicoli non manca ne&#039;raccolti <lb></lb>volumi manoscritti. </s>

<s>E fra quei che ci sono abbiamo avuto occasione nel pre­<lb></lb>cedente capitolo di parlare dei centrobarici, confessando di averli trovati così <lb></lb>negligentemente condotti nelle parti loro più sostanziali, da non sembrar cre­<lb></lb>dibile che avesse permesso di stamparli a quel modo il Viviani. </s>

<s>Il medesimo <lb></lb>giudizio è, secondo noi, da fare di quegli altri trattatelli, per i quali si ri­<lb></lb>chiedeva l&#039;opera del compilatore in compiere, in ordinare e in illustrare i <lb></lb>varii teoremi. </s>

<s>E perchè fra questi i più importanti per noi son quelli di argo­<lb></lb>mento meccanico, intorno ad essi soli restringeremo le nostre osservazioni. </s></p><p type="main">

<s>All&#039;argomento ora detto appartiene principalmente quel trattatello inti­<lb></lb>tolatosi dal Viviani <emph type="italics"></emph>De motu ac momentis,<emph.end type="italics"></emph.end> di cui ci è rimasto un abbozzo <lb></lb>informe, e che, sebbene abbia ripescato per tutto il campo della scienza del <pb xlink:href="020/01/2751.jpg" pagenum="376"></pb>moto, de&#039;solidi non solo, ma e de&#039;liquidi; non giunge più che a diciassette <lb></lb>o a diciotto proposizioni. </s>

<s>Ci sarebbe ne&#039;manoscritti torricelliani materia da <lb></lb>raddoppiarne senza dubbio, e da triplicarne, non forse il numero solo ma <lb></lb>l&#039;importanza, e noi avremmo anche volentieri presa a fare questa fatica, se <lb></lb>l&#039;ufficio nostro di storici, e non di editori, non ci consigliasse di tener, nella <lb></lb>scelta e nell&#039;ordine dei teoremi, quelle ragioni, dalle quali appariscano i pro­<lb></lb>gressi fatti fare o preparati alla scienza meccanica dal Torricelli. </s>

<s>Quelle cose <lb></lb>perciò, che si riferiscono alle leggi e alle proprietà del moto in generale, <lb></lb>abbiamo voluto presentar separate da quell&#039;altre, che si riferiscono partico­<lb></lb>larmente ai momenti, e sacrificando all&#039;ubertà della messe, che volentieri <lb></lb>lasciamo a chi vorrà dietro a noi tornare a respigolare nei manoscritti; ci <lb></lb>siamo solamente curati di fare apparir come il pensiero dell&#039;Autore s&#039;in­<lb></lb>grada via via, e si estende nella varietà degli esempi. </s>

<s>Tende efficacemente <lb></lb>a conseguire il fine, che ci siamo proposti, la terza parte aggiunta alle due <lb></lb>dette dei moti e dei momenti, nella qual terza parte si metteranno i teoremi <lb></lb>relativi a quella, che dai Francesi, quasi un secolo dopo, si appellò col nome <lb></lb>di Meccanica nuova. </s></p><p type="main">

<s>I primi esempi, che da noi qui si scelgono per il trattatello <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end><lb></lb>si tenevano dall&#039;Autore preparati per inserirsi, e per aggiungersi come co­<lb></lb>rollari alle proposizioni del primo libro <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> quand&#039;occorresse <lb></lb>di far dell&#039;opera una ristampa, e perciò il risaperli non par che serva se <lb></lb>non a sodisfare alla curiosità degli eruditi. </s>

<s>Nè, trattandosi di un Torricelli, <lb></lb>si può così fatta erudizione reputare aliena dagli uffici della Storia, i quali <lb></lb>sarebbero in ogni modo scusati, in grazia di quegli altri uffici, ch&#039;ella passa <lb></lb>a fare di maggiore importanza, mostrandoci quel che avesse speculato il Tor­<lb></lb>ricelli stesso intorno all&#039;impeto dei punti geometrici in descrivere il circolo <lb></lb>e l&#039;iperbola, e sull&#039;esempio loro altre curve; intorno al dimostrar che la <lb></lb>catena, insenandosi, s&#039;adatta alla figura di una parabola, e intorno al crear <lb></lb>nuove leggi nel moto accelerato, per cui le parabole descritte dai proietti na­<lb></lb>turali si variano in parabole di qualunque potenza, descritte da corpi appar­<lb></lb>tenenti a mondi immaginari, ma ai quali pure la Geometria prescrive, non <lb></lb>men che per il presente nostro mondo reale, certezza impreteribile di leggi. </s></p><p type="main">

<s>Cominciando dunque dai primi promessi esempi ci occorre a notare nel <lb></lb>nostro Autore un concetto nuovo, per concluder che la forza in sè stessa è <lb></lb>infinita: imperocchè, diviso il subietto materiale in ch&#039;ella si propaga, in <lb></lb>parti minutissime infinite, non perciò rimette nulla del suo primo vigore, ma <lb></lb>si mantiene in ciascuna divisione intera, e sempre uguale a sè stessa. </s>

<s>Ciò si <lb></lb>dimostra particolarmente avvenire nel tirare una corda, fatta però un&#039;ipo­<lb></lb>tesi, la quale non si vede come possa facilmente verificarsi nella materia. </s></p><p type="main">

<s>“ PROPOSIZIONE I. — <emph type="italics"></emph>Che la forza sia infinita. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia il gran sasso A (fig. </s>

<s>236) e sia attaccata ad esso una lunga corda <lb></lb>BG. </s>

<s>Io suppongo che un uomo abbia forza di tirare la corda BG, cioè di <lb></lb>conferire a tutta essa corda una tal tensione, qualunque ella si sia: e questo <lb></lb>si vede per esperienza. </s>

<s>” </s></p><pb xlink:href="020/01/2752.jpg" pagenum="377"></pb><p type="main">

<s>“ Io considero qui primieramente che tutta la corda BG averà la me­<lb></lb>desima tensione in ogni sua parte, cioè tanto sarà tirata nel principio B, <lb></lb><figure id="id.020.01.2752.1.jpg" xlink:href="020/01/2752/1.jpg"></figure></s></p><p type="caption">

<s>Figura 236.<lb></lb>quanto nel mezzo D, e quanto verso <lb></lb>il fine C. </s>

<s>Questo è assai chiaro, <lb></lb>astraendo però da qualche varietà, <lb></lb>che potesse fare il proprio peso <lb></lb>della corda, ed anco astraendo dalla <lb></lb>differenza, che potesse nascere dal <lb></lb>toccamento della corda sopra il piano a lei sottoposto, che però la consi­<lb></lb>dereremo in aria, e senza la gravità propria. </s>

<s>Non di meno si può con questo <lb></lb>discorso dimostrar così: ” </s></p><p type="main">

<s>“ L&#039;uomo traente conferisce al punto B tanta forza, quanta ne ha esso <lb></lb>uomo: il punto B tira poi con tanta forza il punto E suo congiunto, quanta <lb></lb>ne ha esso B, cioè quanta è la forza dell&#039;uomo, e il punto E tira il punto <lb></lb>F suo congiunto con quanta ne ha esso E, cioè quanta è la forza del­<lb></lb>l&#039;uomo, e così si può andar discorrendo di tutti i punti, cioè di tutta <lb></lb>la corda BG, e concluderemo che l&#039;ultimo punto G, e perciò il gran sasso <lb></lb>A, vien tirato con altrettanta forza per appunto con quanta vien tirato il <lb></lb>punto B, cioè con la forza dell&#039;uomo traente, non accresciuta nè diminuita. </s>

<s>” </s></p><p type="main">

<s>“ Stabiliremo dunque questo principio: che qualunque volta avremo una <lb></lb>lunghezza, cioè una estensione di punti continuati, e che il primo di essi <lb></lb>punti venga tirato e spinto con una tal forza, anco tutti gli altri successi­<lb></lb>vanıente saranno tirati e spinti con la medesima forza, senz&#039;accrescerla o <lb></lb>diminuirla, ma trasmettendola sino al fine. </s>

<s>” </s></p><p type="main">

<s>“ Consideriamo poi che, se fosse possibile tagliar la corda BG in due <lb></lb>parti, senza guastargli quella tensione, che ella aveva avanti fosse tagliata, <lb></lb>e se si potesse attaccare la parte tagliata BE in F, e fosse vero che l&#039;una <lb></lb>e l&#039;altra corda, tanto BE, quanto EF, ritenesse la medesima tensione di prima; <lb></lb>sarebbe vero che il punto F verrebbe tirato, non più da una, ma da due <lb></lb>forze uguali a quella dell&#039;uomo traente. </s>

<s>Nello stesso modo, chi facesse, non <lb></lb>due parti della corda, ma dieci o cento, e le attaccasse tutte nel punto F, e <lb></lb>ciascuna parte ritenesse la medesima tensione, che aveva la corda avanti <lb></lb>fosse divisa in parti; certo è che il punto F sarebbe tirato con forza dieci, <lb></lb>e cento volte maggiore di quella, dalla quale era tirato in principio. </s>

<s>Gli altri <lb></lb>punti poi susseguenti tutti sarebbero tirati dalle medesime forze, che vien <lb></lb>tirato il punto F, e così per conseguenza il sasso ancora ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XXXVII, fol. </s>

<s>123). </s></p><p type="main">

<s>A questa, che intende ad esplicare la recondita natura della forza, fa­<lb></lb>remo succedere un&#039;altra proposizion generale, da premettersi alle dimostra­<lb></lb>zioni dei moti accelerati, conducendola dal principio degl&#039;indivisibili. </s>

<s>La detta <lb></lb>proposizione è scritta <emph type="italics"></emph>pro confirmanda prima Galilei,<emph.end type="italics"></emph.end> e per mostrare a co­<lb></lb>loro, i quali non si fidavano del metodo del Cavalieri, come anche i punti, <lb></lb>benchè indivisibili, hanno ragioni fra loro infinite, come tutte le altre ter­<lb></lb>minate grandezze. </s>

<s>“ Quod puncta, et reliqua indivisibilia, così preavverte <pb xlink:href="020/01/2753.jpg" pagenum="378"></pb>l&#039;Autore, habeant rationes inter se infinitas, sicuti habent magnitudines ter­<lb></lb>minatae, atque divisibiles, mihi iam satis superque patet, quamquam semper <lb></lb>sint indivisibilia ” (ivi, T. XXXI, fol. </s>

<s>61). </s></p><p type="main">

<s>“ PROPOSIZIONE II. — <emph type="italics"></emph>Esto tempus AB<emph.end type="italics"></emph.end> (fig. </s>

<s>237), <emph type="italics"></emph>moveaturque mobile, <lb></lb>et tempore AB percurrat rectas GF, OH, ted rectam GF currat motu <lb></lb>aequabili, cum gradu velocitatis semper eodem AV, rectam vero OH cur-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2753.1.jpg" xlink:href="020/01/2753/1.jpg"></figure></s></p><p type="caption">

<s>Figura 237.<lb></lb><emph type="italics"></emph>rat motu non aequabili, cum gradibus velocitatis homo­<lb></lb>logis ad lineas AC, sive ME; dico spatium OH, ad <lb></lb>GF, esse ut figura ACDB, ad figuram AVDB. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nam totidem sunt puncta in spatio GF, quot <lb></lb>sunt in spatio OH: nempe totidem, quot fuerunt in­<lb></lb>stantes eiusdem temporis, sed illa puncta sunt inae­<lb></lb>qualia. </s>

<s>Jam, sumpto quolibet instanti temporis, puta M, <lb></lb>sint puncta peracta hoc instanti ipsa L et N, eritque ut <lb></lb>recta MI ad ME, hoc est, ut impetus, ita spatium L ad <lb></lb>spatium N, et hoc semper. </s>

<s>Suntque antecedentes aequales, ergo, ut AVDB ad <lb></lb>ACDB, ita quantitas omnium punctorum GF, ad quantitatem omnium, nempe <lb></lb>totidem punctorum OH, sive ita GF ad OH ” (ibid.). </s></p><p type="main">

<s>Che questa propriamente, nella sua universalità, confermi il vero della <lb></lb>prima proposizione galileiana <emph type="italics"></emph>De motu naturaliter accelerato,<emph.end type="italics"></emph.end> è manifesto, <lb></lb>perchè, se il moto comincia in D dalla quiete, e vanno le velocità crescendo <lb></lb>a proporzione dei tempi, la DEC è una linea retta, e la figura DVC un trian­<lb></lb>golo. </s>

<s>Se suppongasi inoltre che la linea EG, nel medesimo tempo AB, sia <lb></lb>corsa con moto equabile, così cioè che i gradi delle velocità sian sempre <lb></lb>i medesimi, e tutti uguali a VC, ultimo grado della velocità accelerata­<lb></lb>mente acquistata; sarà la figura AD doppia della DVC, e tale anco sarà <lb></lb>l&#039;uno spazio all&#039;altro, come nella detta proposizione prima si dimostra da <lb></lb>Galileo. </s></p><p type="main">

<s>In tal proposizione, che si legge scritta nel terzo diologo delle due <lb></lb>Scienze nuove, è noto come sia costituito uno de&#039;fondamenti alle dottrine <lb></lb>galileiane dei moti accelerati, ma il principale di quei fondamenti è nel Teo­<lb></lb><figure id="id.020.01.2753.2.jpg" xlink:href="020/01/2753/2.jpg"></figure></s></p><p type="caption">

<s>Figura 238.<lb></lb>rema così detto <emph type="italics"></emph>meccanico,<emph.end type="italics"></emph.end> il quale si vo­<lb></lb>leva dal Torricelli illustrare nel modo che <lb></lb>segue: </s></p><p type="main">

<s>“ PROPOSIZIONE III. — <emph type="italics"></emph>Qual si coglia <lb></lb>gran peso da qualunque piccola forza può <lb></lb>essere tirato su, per un piano clevato <lb></lb>utcumque. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia nel piano dato l&#039;orizontale AB <lb></lb>(fig. </s>

<s>238), e ad essa la perpendicolare CE, e sia in E il peso dato, quale pon­<lb></lb>gasi essere come EC, e la data forza sia come FH, minore di CD, perchè, se <lb></lb>fosse come CD, moverebbe il peso per tutta la linea del piano dato. </s>

<s>Fac­<lb></lb>ciasi dal centro E, con l&#039;intervallo EC, il semicircolo ACB nel piano, e si <lb></lb>tiri l&#039;orizontale FI, e per la linea EI si potrà tirare il peso dalla forza FH, <pb xlink:href="020/01/2754.jpg" pagenum="379"></pb>ovvero IL, poichè, se il peso è come EC, ovvero EI, sarà in EI come IL, <lb></lb>e però la forza IL lo agguaglierà. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario I.<emph.end type="italics"></emph.end> — Di qui si ricava che le strade più oblique dei monti <lb></lb>sono tanto più agevoli, quanto la IL è minore della CD, ovvero la IM della <lb></lb>CE, essendo simili CED, IML. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario II.<emph.end type="italics"></emph.end> — Però, quando l&#039;angolo IEB sarà gradi 30, allora la <lb></lb>salita per EI sarà la metà più agevole, che per EC, essendo il sino IM di <lb></lb>gradi 30 la metà del sino toto EC: ovvero inferisci che la fatica della salita <lb></lb>sarà come i sini degli angoli, che farà la strada con la orizontale. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario III.<emph.end type="italics"></emph.end> — I pesi dei corpi nostri, e delle cose che porteremo, <lb></lb>saranno per le strade EC, EI come CD, IL, ovvero, come CE, IM, che sono <lb></lb>i sini suddetti ” (ivi, T. XXXIII, fol. </s>

<s>87). </s></p><p type="main">

<s>Questa proposizione la dicemmo semplicemente illustrativa del Teorema <lb></lb>meccanico, la dimostrativa del quale è la prima del trattato stampato, la <lb></lb>quale si conduce dal celebre principio che due pesi stanno allora fra loro in <lb></lb>equilibrio, quando congiunti insieme, a rimoverli dalla loro prima stazione, <lb></lb>il centro di gravità rimane sulla medesima linea orizontale. </s>

<s>Condizioni di un <lb></lb>tale equilibrio si dimostra esser che i pesi abbiano omologa proporzione con <lb></lb>le lunghezze dei piani inclinati: che, se varia l&#039;inclinazione, i pesi stessi ne­<lb></lb>cessariamente si muovono, e il Torricelli investiga così qual via si farebbe <lb></lb>dal comun centro di gravità nel moto. </s></p><p type="main">

<s>“ PROPOSIZIONE IV. — <emph type="italics"></emph>Si plana AB, BC<emph.end type="italics"></emph.end> (fig. </s>

<s>239) <emph type="italics"></emph>fuerint utcumque <lb></lb>inclinata, et gravia A, C aequalia, aequaliterque a puncto B remota; erit <lb></lb>AC via centri gravitatis. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Venerint enim in D et E, et erunt aequales AD, CE: dico centrum <lb></lb>esse F. </s>

<s>Agatur EH parallela ipsi BD: erit, ut CB ad BA, ita CE ad EH, <lb></lb><figure id="id.020.01.2754.1.jpg" xlink:href="020/01/2754/1.jpg"></figure></s></p><p type="caption">

<s>Figura 239.<lb></lb>vel DA ad EH. Sed, cum CB, BA sint aequales, erunt <lb></lb>DA, EH aequales, et erunt parallelae. </s>

<s>Quare EF, FD <lb></lb>aequales erunt. </s>

<s>Ergo etc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Quando vero gravia non sint ae­<lb></lb>qualia, aptentur gravia ita, ut sit ut grave A ad grave <lb></lb>C, ita AB ad BC, et erit iterum AC via centri. </s>

<s>Mo­<lb></lb>veantur usque in D et E: eruntque DA, CE aequales. </s>

<s><lb></lb>At grave A, ad grave C, est ut AB ad BC, vel HE <lb></lb>ad EC, vel HE ad AD, vel FE ad FD reciproce; est <lb></lb>ergo F centrum ” (ivi, T, XXXVII, fol. </s>

<s>72). </s></p><p type="main">

<s>Vedremo, nel seguente trattato <emph type="italics"></emph>De momentis,<emph.end type="italics"></emph.end> an­<lb></lb>che più spiegatamente condotta questa proposizione, che <lb></lb>sarà premessa per lemma ad altre proposizioni, ma per ora, proseguendo il <lb></lb>divisato ordine nostro, raccoglieremo le poche cose seguenti, relative alle pro­<lb></lb>porzioni che passano tra le velocità e i tempi de&#039;mobili nei piani inclinati, <lb></lb>quasi fragrante mazzolino di fiori, di che la Meccanica severa non sdegnerà <lb></lb>ornarsene il seno. </s></p><p type="main">

<s>“ PROPOSIZIONE V. — <emph type="italics"></emph>Si duo circuli se se in infimo puncto tangant,<emph.end type="italics"></emph.end><pb xlink:href="020/01/2755.jpg" pagenum="380"></pb><emph type="italics"></emph>erunt tempora per AB, DC<emph.end type="italics"></emph.end> (fig. </s>

<s>240), <emph type="italics"></emph>aequalia. </s>

<s>Item, cum tota tempora <lb></lb>aequalia sint, et ablata ablatis, erunt reliqua BE, CE, etiam si non sint <lb></lb>ex quiete, aequalia ”<emph.end type="italics"></emph.end> (ivi, T. XXXIII, fol. </s>

<s>82). <lb></lb><figure id="id.020.01.2755.1.jpg" xlink:href="020/01/2755/1.jpg"></figure></s></p><p type="caption">

<s>Figura 240.</s></p><p type="main">

<s>Di ciò che è scritto, insieme con tant&#039;altre cose messe <lb></lb>alla rinfusa in quel volume, intitolato dal Torricelli <emph type="italics"></emph>Campo <lb></lb>di tartufi:<emph.end type="italics"></emph.end> manca la dimostrazione, perchè forse troppo <lb></lb>facile a ritrovarsi dietro i teoremi meccanici di Galileo, e <lb></lb>la CVI del VII libro delle Matematiche collezioni, nella <lb></lb>quale Pappo dimostra (ediz. </s>

<s>cit., pag. </s>

<s>334) che le corde <lb></lb>AB, ED son parallele, e perciò AC:BC=AD:BE. Ma, <lb></lb>per le note leggi, stando i tempi come le radici degli spazi, <lb></lb>cioè To.AC:To.AD=√AC:√AD, To.BC:To.BE= <lb></lb>√BC:√BE, abbiamo To.AC:To.BC=To.AD:To.EB. </s>

<s>Dunque essendo <lb></lb>i tempi per AC, BC uguali, anco uguali saranno i tempi per AD, BE, come <lb></lb>voleva dimostrarsi. </s></p><p type="main">

<s>Che se le AC, BC intere sono isocrone, e isocrone le loro parti AD, BE; <lb></lb>isocrone dovranno essere per conseguenza anche le DC, EC rimanenti: non <lb></lb>inutile corollario, in cui la verità dimostrata da Galileo nel caso, che il mo­<lb></lb>bile si parta in D e in E dalla quiete, si conferma, anche quando esso mobile <lb></lb>abbia un moto antecedente, e quello per l&#039;appunto, che ha il principio in <lb></lb>A, B, sull&#039;altra circonfcrenza di contatto. </s></p><p type="main">

<s>“ PROPOSIZIONE VI. — <emph type="italics"></emph>Si duo circuli se exterius tangant, in puncto <lb></lb>sublimiori et infimo, erunt tempora AB, MD<emph.end type="italics"></emph.end> (fig. </s>

<s>241) <emph type="italics"></emph>aequalia. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La proposizione si dimostrerebbe speditamente dalla CII del citato lib. </s>

<s>VII <lb></lb>di Pappo (pag. </s>

<s>334), secondo la quale, essendo la AD parallela alla MB, se <lb></lb><figure id="id.020.01.2755.2.jpg" xlink:href="020/01/2755/2.jpg"></figure></s></p><p type="caption">

<s>Figura 241.<lb></lb>questa si prolunghi infino a incontrare <lb></lb>in H la AH condotta parallela a MD; la <lb></lb>figura HD sarà un rettangolo, e perciò <lb></lb>AH=MD, e il tempo per l&#039;una uguale <lb></lb>al tempo per l&#039;altra, ond&#039;ei non restava <lb></lb>al Torricelli che a invocare il lemma alla <lb></lb>sua XIII stampata, per concluder senz&#039;al­<lb></lb>tro l&#039;intento. </s>

<s>E nonostante seguì una via <lb></lb>più lunga e indiretta, dimostrando prima, <lb></lb>per modo di lemma, che, tirata la BE pa­<lb></lb>rallela alla MD, le FE, ID erano uguali <lb></lb>“ nam, iunctis AD, DE, una eademque <lb></lb>recta erunt, alias, continuata AD, faceret <lb></lb>angulum rectum extra E, quod est absur­<lb></lb>dum ” (MSS. Gal., T. XXXIII, fol. </s>

<s>82). </s></p><p type="main">

<s>Dalla dimostrata uguaglianza delle FE, ID, conclude il Torricelli il suo <lb></lb>proposito, lasciati sottintesi i principii di mezzo, i quali si riducono a que­<lb></lb>sti: ch&#039;essendo i tempi per le FE, ID, e per le FB, IM uguali, saranno pure <lb></lb>uguali i tempi per le intere MD, EB. </s>

<s>Ma EB nel cerchio è isocrona al diame-<pb xlink:href="020/01/2756.jpg" pagenum="381"></pb>tro AB, dunque isocrona allo stesso diametro sarà la MD, ciò che doveva <lb></lb>provarsi. </s></p><p type="main">

<s>“ PROPOSIZIONE VII. — <emph type="italics"></emph>Si latus exagoni sit AC<emph.end type="italics"></emph.end> (fig. </s>

<s>242), <emph type="italics"></emph>erit velo-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2756.1.jpg" xlink:href="020/01/2756/1.jpg"></figure></s></p><p type="caption">

<s>Figura 242.<lb></lb><emph type="italics"></emph>citas, sive maximum momentum in AB, duplum momenti <lb></lb>in AC, qui eodem tempore duplum spatium peragit ”<emph.end type="italics"></emph.end><lb></lb>(ivi, T. XXXVII, fol. </s>

<s>94). </s></p><p type="main">

<s>Infatti, per essere i tempi uguali, le velocità stanno <lb></lb>come gli spazi. </s>

<s>Ma lo spazio AB, diametro, è doppio dello <lb></lb>spazio AC, lato dell&#039;esagono; dunque anche la velocità per <lb></lb>quella via sarà doppia alla velocità per questa. </s></p><p type="main">

<s>“ PROPOSIZIONE VIII. — <emph type="italics"></emph>Si angulus A<emph.end type="italics"></emph.end> (fig. </s>

<s>243) <emph type="italics"></emph>fuerit angulus trian­<lb></lb>guli aequilateri, erit momentum in AC duplum momenti per AB ”<emph.end type="italics"></emph.end> (ibid.). </s></p><p type="main">

<s>Esser A angolo del triangolo equilatero non vuol dir altro che esser di <lb></lb>60 gradi. </s>

<s>Dunque, supponendosi AC verticale, e BC orizontale, e perciò ACB <lb></lb><figure id="id.020.01.2756.2.jpg" xlink:href="020/01/2756/2.jpg"></figure></s></p><p type="caption">

<s>Figura 243.<lb></lb>angolo retto; sarà ABC 30 gradi. </s>

<s>Si prolunghi AC di altret­<lb></lb>tanto in D, e si congiunga la DB: è manifesto che ABD è il <lb></lb>triangolo equilatero. </s>

<s>“ Si fuerit AB dupla ipsius AC, erit an­<lb></lb>gulus A angulus trianguli aequilateri. </s>

<s>Producatur CD aequalis <lb></lb>ipsi CA, et erunt aequalia latera BA, AD. Sed, per IV Primi, <lb></lb>etiam BD aequatur ipsi BA; ergo etc. </s>

<s>” (ibid.). E qui s&#039;ar­<lb></lb>resta il discorso del Torricelli, che facilmente si compie col <lb></lb>seguente costrutto: Il momento o la velocità per AC, al momento o alla ve­<lb></lb>locità per AB, sta come la AC alla AB. </s>

<s>Ma AB è doppia di AC, dunque <lb></lb>anche quella velocità nel perpendicolo sarà doppia a questa nell&#039;inclinata, <lb></lb>com&#039;era il proposito di dimostrare. </s></p><p type="main">

<s>Queste ultime quattro proposizioni non sono altro per verità che ele­<lb></lb>ganze, preparate dal Torricelli per ornare il suo proprio, e il trattato di Ga­<lb></lb>lileo, e l&#039;Autore stesso, in certe sue note interpolate nel manoscritto, le qua­<lb></lb>lificava per bagattelle. </s>

<s>Comunque sia, hanno ben altra importanza le proposi­<lb></lb>zioni, che si soggiungeranno, incominciando da quelle intitolate <emph type="italics"></emph>Dell&#039;impeto <lb></lb>de&#039;punti.<emph.end type="italics"></emph.end> L&#039;origine, che queste speculazioni ebbero nel nostro Torricelli e <lb></lb>nel Roberval comune, è manifestamente dallo studio della spirale di Archi­<lb></lb>mede, intorno alla quale tratterremo il discorso più a lungo nella terza parte <lb></lb>di questo capitolo, contentandoci di notar per ora che, così il Nostro come <lb></lb><figure id="id.020.01.2756.3.jpg" xlink:href="020/01/2756/3.jpg"></figure></s></p><p type="caption">

<s>Figura 244.<lb></lb>il Matematico di Francia, ammettevano, con il grande <lb></lb>Maestro siracusano, che la resultante de&#039;due moti, dai <lb></lb>quali insieme composti viene a descriversi la curva, sia <lb></lb>diretta secondo la tangente al punto della curva stessa, <lb></lb>la quale proseguirebbe perciò indi il suo moto in li­<lb></lb>nea retta. </s></p><p type="main">

<s>“ PROPOSIZIONE IX. — <emph type="italics"></emph>Si recta AB<emph.end type="italics"></emph.end> (fig. </s>

<s>244) <lb></lb><emph type="italics"></emph>super DC perpendicularis semper existat, in eodem­<lb></lb>que plano, et moveatur motu progressivo aequabili, simulque aliquod <lb></lb>ipsius punctum A moveatur in recta AB, ita ut velocitas puncti A, ad<emph.end type="italics"></emph.end><pb xlink:href="020/01/2757.jpg" pagenum="382"></pb><emph type="italics"></emph>velocitatem lineac AB sit semper ut recta DB ad BA; punctum A cir­<lb></lb>culum describet. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto enim tangens lineae curvae in A ipsa AC: et quia impetus puncti A <lb></lb>versus B, ad impetum lineae AB versus C, est ut DB ad BA; erit etiam, ob <lb></lb>leges motuum, AB ad BC ut BD ad BA: ergo angulus DAC rectus est, sed <lb></lb>AD tangens; ergo figura circulus est ” (ivi, T. XXXI, fol. </s>

<s>86). </s></p><p type="main">

<s>È scritto in principio di questa, dalla mano dello stesso Torricelli: <emph type="italics"></emph>Porta <lb></lb>la conversa, perchè così non prova,<emph.end type="italics"></emph.end> e la conversa si potrebbe formulare, e <lb></lb>facilmente provare in questa maniera: <emph type="italics"></emph>Nel punto mobile, che descrive il <lb></lb>circolo, l&#039;impeto discensivo al progressivo sta come il coseno, al seno del­<lb></lb>l&#039;angolo dell&#039;inclinazione.<emph.end type="italics"></emph.end> Si consideri il punto A, nella medesima figura 244, <lb></lb>con l&#039;inclinazione ADB. </s>

<s>Condotta la tangente AC, resultante del moto, le <lb></lb>componenti di lei saranno AB misura dell&#039;impeto D discensivo e DB misura <lb></lb>dell&#039;impeto P progressivo, onde avremo D:P=AB:BC. </s>

<s>Ma i triangoli si­<lb></lb>mili ABC, ADB danno AB:BC=DB:AB, dunque D:P=DB:AB: e <lb></lb>di qui è che, sempre che si verifichi questa proporzione fra i moti descri­<lb></lb>venti una curva, la curva stessa sarà un circolo, come il Torricelli si pro­<lb></lb>poneva di dimostrare nella sua diretta. </s></p><p type="main">

<s>Intendono bene i Lettori come si sarebbe facilmente potuta applicare <lb></lb>questa proposizione ai pendoli, per risolvere il problema, in cui si domanda <lb></lb>secondo qual proporzione diminuisca la forza in tirare il filo, via via che il <lb></lb>pendolo si rimove dal suo perpendicolo. </s>

<s>Eppure non si vede balenar di ciò <lb></lb>nessuna idea nella mente del Torricelli, per cui si rimase il Viviani in quelle <lb></lb>incertezze, e poi si volse a seguitar quell&#039;errore, da noi notato qui addietro, <lb></lb>nella seconda parte del capitolo quarto. </s></p><p type="main">

<s>Passa nella seguente il nostro Autore a dimostrar che gl&#039;impeti puri, <lb></lb>misurati in due vari punti del medesimo circolo, stanno reciprocamente come <lb></lb>le loro tangenti. </s>

<s>La dimostrazione, chiamati I.oA, I.oC (fig. </s>

<s>245) gl&#039;impeti <lb></lb><figure id="id.020.01.2757.1.jpg" xlink:href="020/01/2757/1.jpg"></figure></s></p><p type="caption">

<s>Figura 245.<lb></lb>puri in A e in C, e chiamato I.o AD l&#039;impeto pro­<lb></lb>gressivo equabile della linea AD; procede in questa <lb></lb>guisa: Abbiamo per la precedente I.oA:I.oAD= <lb></lb>BD:DA; I.oAD:I.oC=CE:EB, le quali due <lb></lb>proporzioni moltiplicate termine per termine, danno <lb></lb>I.oA:I.oC=BD.CE:DA.EB. </s>

<s>Per la similitu­<lb></lb>dine dei triangoli BAD, BAG e BCE, ECF è altresi <lb></lb>BD:DA=BA:AG; CE:EB=FC:CB, dalla quale per moltiplicazione resulta <lb></lb>BD.CE:DA.EB=BA.FC:AG.CB=FC:AG, d&#039;onde I.oA:I.oC= <lb></lb>FC:AG, come propone e dimostra il Torricelli nella seguente </s></p><p type="main">

<s>“ PROPOSIZIONE X. — <emph type="italics"></emph>Impetus descendens purus in A<emph.end type="italics"></emph.end> (nella medesima <lb></lb>figura passata), <emph type="italics"></emph>ad impetum descendentem purum in C, est ut tangens <lb></lb>CF ad AG. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nam impetus in A ad impetum lineae AD, est ut BD ad DA: impe­<lb></lb>tus autem lineae, qui semper idem est, ad impetum puncti C est ut CE ad <lb></lb>EB. </s>

<s>Ergo impetus descendens puncti A, ad impetum in C, rationem habet <pb xlink:href="020/01/2758.jpg" pagenum="383"></pb>compositam ex ratione BD ad DA, et ex ratione CE ad EB, sive, ex ratione <lb></lb>FC ad CB, et ex ratione BA ad AG. </s>

<s>Sed medii termini CB, BA sunt aequa­<lb></lb>les, ergo patet propositum ” (ibid.). </s></p><p type="main">

<s>“ PROPOSIZIONE XI. — <emph type="italics"></emph>Si recta AB<emph.end type="italics"></emph.end> (fig. </s>

<s>246), <emph type="italics"></emph>cum eadem semper in­<lb></lb>clinatione insistat super CD, inoveaturque motu aequabili in eodem plano,<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2758.1.jpg" xlink:href="020/01/2758/1.jpg"></figure></s></p><p type="caption">

<s>Figura 246.<lb></lb><emph type="italics"></emph>et punctum aliquod ipsius moveatur sur­<lb></lb>sum vel deorsum, ita ut velocitates sint in­<lb></lb>ter se, ut quadrata distantiarum ipsius a <lb></lb>recta CD; hyperbola erit ”<emph.end type="italics"></emph.end> (ibid.). </s></p><p type="main">

<s><emph type="italics"></emph>Porta la conversa,<emph.end type="italics"></emph.end> si legge notato in <lb></lb>margine nel manoscritto. </s>

<s>E infatti si dimo­<lb></lb>stra che, supposto essere la curva un&#039;iper­<lb></lb>bola, i punti nel descriverla si muovono con <lb></lb>la legge assegnata. </s>

<s>Di qui è che ogni volta <lb></lb>si verifichi nei punti mobili una tal regola di <lb></lb>andamento, si conclude dover essere un&#039;iperbola la linea descritta dal loro moto. </s></p><p type="main">

<s>“ Esto hyperbola AE, cuius axis CA, asymptoti CF, CH, et sit punctum <lb></lb>A, quod supponimus pervenisse ad E. </s>

<s>Ducantur tangentes FG, IH. </s>

<s>Erit im­<lb></lb>petus compositus puncti E secundum lineam EH. </s>

<s>Ergo impetus progressivus <lb></lb>lineae, ad impetum descendentem puncti, erit ut DH ad DE (applicandovi la <lb></lb>regola del parallelogrammo delle forze come si vedrà meglio appresso) sive <lb></lb>ut CD ad DE, sunt enim aequales, ob hyperbolam, IE, EH, et CD, DH. </s>

<s>Jam <lb></lb>impetus descendens in A, ad progressivum in A, aequalis est, nempe ut AB <lb></lb>ad BC: progressivus vero, ad descendentem in E, est ut CD ad DE. </s>

<s>Ergo <lb></lb>ex aequo impetus descendens in A, ad descendentem in E, rationem habet <lb></lb>compositam ex ratione AB ad BC, et CD ad DE. </s>

<s>Ergo est ut CD ad DE, <lb></lb>nam termini AB, BC sunt aequales, sive ut rectangulum CDE ad quadra­<lb></lb>tum DE, sive ut rectangulum CBA, vel quadratum BA, ad quadratum DE, <lb></lb>quod volebam. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Quando est hyperbola, cum praedictis iis velocitatum <lb></lb>legibus punctum movetur: propterea, etiam quando movetur ex se, hyper­<lb></lb>bolam describet: alias idem punctum motum iisdem semper velocitatibus per <lb></lb>diversas inter se lineas curreret, quod probatur esse absurdum ” (ibid., ad. </s>

<s>t.). </s></p><p type="main">

<s>Quel detto che la Natura è geometrica non par s&#039;illustri con altro più <lb></lb>efficace esempio, che col descriver ch&#039;ella fa al proietto, il quale può riguar­<lb></lb>darsi come condensato in un punto, linee curve, con regole simili a quelle, <lb></lb>che nelle due precedenti proposizioni il Geometra ha speculato. </s>

<s>E perchè la <lb></lb>Natura sempre all&#039;Arte è di nuove invenzioni maestra, immaginiamo, pen­<lb></lb>sava il Torricelli, che le velocità non crescano secondo la semplice propor­<lb></lb>zione de&#039;tempi, come Galileo dimostrò nei gravi sulla superficie di questo <lb></lb>nostro Globo cadenti, ma secondo la proporzion de&#039;quadrati, dei cubi, dei <lb></lb>quadrato quadrati, o di qualsivoglia altra potenza: è certo che dal moto, com­<lb></lb>posto del descensivo con tali leggi e del progressivo equabilmente per l&#039;oriz­<lb></lb>zonte, resulteranno descritte curve appartenenti senza dubbio alla medesima <pb xlink:href="020/01/2759.jpg" pagenum="384"></pb>famiglia delle parabole quadratiche o naturali. </s>

<s>Intorno a che il Torricelli <lb></lb>dimostrò che, se la velocità è quadratica, la parabola che descriverebbe il <lb></lb>proietto è cubica: se la velocità è cubica, la parabola è biquadratica, e in <lb></lb>generale, se la velocità è di grado <emph type="italics"></emph>n,<emph.end type="italics"></emph.end> sarà di grado <emph type="italics"></emph>n+1<emph.end type="italics"></emph.end> la potenza della <lb></lb>parabola relativa. </s>

<s>Sebbene sia il concetto assai pellegrino, è nonostante di <lb></lb>molto facile dimostrazione, come apparisce dal seguente esempio, applicato al <lb></lb>caso della parabola cubica, premessovi questo problema per lemma: <lb></lb><figure id="id.020.01.2759.1.jpg" xlink:href="020/01/2759/1.jpg"></figure></s></p><p type="caption">

<s>Figura 247.</s></p><p type="main">

<s>“ Si mobile moveatur deorsum tempore AC <lb></lb>(fig. </s>

<s>247), et tempore AB, et augeatur velocitas qua­<lb></lb>dratice, quaeritur ratio spatiorum. </s>

<s>” </s></p><p type="main">

<s>“ Dico sic: Spatia peracta habent rationem <lb></lb>compositam ex ratione velocitatum, et ex ratione <lb></lb>temporum. </s>

<s>Sint spatia peracta AB, AC, tempora <lb></lb>vero DE, DF. </s>

<s>Supponamus mobile in B et in C <lb></lb>converti horizontaliter. </s>

<s>Jam impetus in B, ad im­<lb></lb>petum in C, erit ut quadratum temporis DE, ad <lb></lb>quadratum DF. </s>

<s>Ergo spatium BH, factum tempore casus AB, ad spatium CI, <lb></lb>factum tempore casus AC, rationem habebit compositam rectae DE ad DF, <lb></lb>et quadrati DE ad quadratum DF. </s>

<s>Ergo spatium BH ad CI erit ut cubus DE <lb></lb>ad DF. </s>

<s>Sed ut spatia BH, CI, ita sunt spatia AB, AC, ipsorum submultiplicia <lb></lb>aequaliter, ergo patet etc. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE XII. — <emph type="italics"></emph>Cadat mobile aliquod horizontaliter concitatum <lb></lb>ex plano DA<emph.end type="italics"></emph.end> (fig. </s>

<s>248), <emph type="italics"></emph>ita ut duos impetus habeat, alterum aequabilem<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2759.2.jpg" xlink:href="020/01/2759/2.jpg"></figure></s></p><p type="caption">

<s>Figura 248.<lb></lb><emph type="italics"></emph>horizontalem versus partes EC. alterum de­<lb></lb>scendentem acceleratum quadratice. </s>

<s>Dico pa­<lb></lb>rabolam cubicam fieri. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Hoc ex dictis patet. </s>

<s>Nam consideretur <lb></lb>mobile in quibuslibet punctis B, C. </s>

<s>Cum im­<lb></lb>petus horizontalis externus sit et aequabilis, <lb></lb>erunt CI, BH ut tempora casuum. </s>

<s>Sed spatia <lb></lb>peracta EC, FB sunt ut cubi temporum; ergo <lb></lb>cubi rectarum CI, BH erunt ut EC, FB, sive <lb></lb>ut IA ad AH ” (ibid., T. XXXI, fol. </s>

<s>341). </s></p><p type="main">

<s>Perchè dunque la proposta verità, dato il lemma, è patente, si può quello <lb></lb>stesso lemma dimostrare nella sua universalità, d&#039;onde ne derivi la univer­<lb></lb>salità sua anche la proposizione ora scritta. </s>

<s>Chiamati S, S′, V, V′, T, T′ due <lb></lb>spazi, due varie velocità, due vari tempi, abbiamo, per le note leggi del moto, <lb></lb>S:S′=V.T:V′.T′. </s>

<s>Che se l&#039;accelerazione è lineare, ossia se V:V′= <lb></lb>T:T′, sarà S:S′=T2:T′2; se l&#039;accelerazione è quadratica, e perciò V:V= <lb></lb>T2:T′2, sarà S:S′=T3:T′3: se poi l&#039;accelerazione è cubica, e V:V′= <lb></lb>T3:T′3, sarà S:S′=T1:T′1, e in generale, se l&#039;accelerazione è di grado <emph type="italics"></emph>n,<emph.end type="italics"></emph.end><lb></lb>sarà S:S′=T<emph type="italics"></emph>n+1<emph.end type="italics"></emph.end>:T′

<emph type="italics"></emph>n+1<emph.end type="italics"></emph.end>.</s> 

<s>Cosicchè, facendone l&#039;applicazione alla para­<lb></lb>bola, rappresentata dalla stessa ultima figura, sarà l&#039;equazione di lei espressa <lb></lb>da AH:AI=HB</s>

<s><emph type="italics"></emph>n+1<emph.end type="italics"></emph.end>:IC<emph type="italics"></emph>n+1<emph.end type="italics"></emph.end>.</s></p><pb xlink:href="020/01/2760.jpg" pagenum="385"></pb><p type="main">

<s>Il concetto, che rifulge assai chiaro per la Geometria di Euclide, e se­<lb></lb>condo il quale sarebbero le varie figure descritte da un punto, che con certe <lb></lb>determinate leggi si muove; ha nella precedente del Torricelli l&#039;applicazione <lb></lb>più bella, che si potesse fare alla genesi meccanica delle infinite parabole, <lb></lb>comprese fra il triangolo e il parallelogrammo. </s>

<s>Di qui si vede che la Geo­<lb></lb>metria è meccanica, come la Meccanica è geometrica: anzi può dirsi che la <lb></lb>Scienza, della quale scriviamo la Storia, è una Geometria particolare, di cui <lb></lb>i punti mobili, che descrivono le figure, son gravi, soggetti cioè per naturale <lb></lb>necessità a ubbidire a certe leggi proprie del moto, dipendenti dall&#039;attra­<lb></lb>zione centrale della Terra, cosicchè i proietti sulla superficie di lei, tra le <lb></lb>infinite parabole possibili, descrivono le quadratiche. </s></p><p type="main">

<s>Si può dunque riguardar la proposizione poco fa dimostrata come il prin­<lb></lb>cipio generalissimo, a cui s&#039;informa il quarto dialogo delle due Scienze nuove, <lb></lb>che, non potutosi maturare da Galileo, in quegli ultimi anni della sua vec­<lb></lb>chiezza, fu mirabilmente illustrato e compiuto dal Torricelli. </s>

<s>Egli fu il primo <lb></lb>ad applicar la parabola ai moti naturali, come Galileo stesso l&#039;aveva appli­<lb></lb>cata ai moti violenti, e son di questi nuovi teoremi così pieni i due libri <emph type="italics"></emph>De <lb></lb>motu gravium<emph.end type="italics"></emph.end> fra le altre Opere geometriche di lui già stampati, da non <lb></lb>avere speranza di trovarne dei rimasti indietro nei manoscritti. </s>

<s>Non ci sem­<lb></lb>bra nonostante che siano di leggera importanza quest&#039;altre poche cose che <lb></lb>soggiungiamo, la prima delle quali appartiene a quel libretto indirizzato in <lb></lb>forma di lettera a Raffaello Magiotti, il qual libretto, che insieme col trat­<lb></lb>tato <emph type="italics"></emph>De motu proiectorum<emph.end type="italics"></emph.end> passerebbe per proemio e per introduzione; così <lb></lb>disgiunto da lui, diceva il Torricelli stesso per modestia, non contenere che <lb></lb>baie. </s>

<s>Una di queste, che i Lettori ritroveranno tutt&#039;altro che una baia, man­<lb></lb>data a esso Magiotti nel libretto a lui dedicato, sarebbe la seguente, con le <lb></lb>parole, che trascriviamo premesse alla proposizione: </s></p><p type="main">

<s>“ Perchè il foco delle parabole ha che fare in alcuni teoremi dei pro­<lb></lb>ietti più che qualcuno non pensa, l&#039;inserisco nel mio libretto, e mi pare di <lb></lb><figure id="id.020.01.2760.1.jpg" xlink:href="020/01/2760/1.jpg"></figure></s></p><p type="caption">

<s>Figura 249.<lb></lb>dimostrarlo assai più facilmente che Vitellione, <lb></lb>Marin Ghetaldo e fra Bonaventura, i quali appor­<lb></lb>tano tutti la medesima dimostrazione: però non <lb></lb>vorrei arrogarmi una dimostrazione non mia. </s>

<s><lb></lb>Mando questa copia a V. S. acciò mi faccia gra­<lb></lb>zia di vedere se confronta con quella di Oronzio <lb></lb>Fineo, se ben credo che lui ancora porterà la <lb></lb>comune di Vitellione, che va per via di quei quat­<lb></lb>tro rettangoli del Secondo di Euclide. </s>

<s>Oltre a <lb></lb>questi quattro autori non so che altri tratti del <lb></lb>foco delle parabole. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Proprietà della Parabola, Lemma.<emph.end type="italics"></emph.end> — Se <lb></lb>sarà la parabola, il cui asse AB (fig. </s>

<s>249), e la quarta parte del lato retto <lb></lb>sia AC, e preso qualunque punto E si tirino due tangenti AD, ED; dico che <lb></lb>l&#039;angolo HDC è retto. </s>

<s>” </s></p><pb xlink:href="020/01/2761.jpg" pagenum="386"></pb><p type="main">

<s>“ Tirisi l&#039;ordinatamente applicata EB: e perchè le AB, AH sono uguali, <lb></lb>ed EB, AD parallele, sarà il quadrato EB quadruplo del quadrato AD. </s>

<s>Lo <lb></lb>stesso quadrato EB è quadruplo del rettangolo BAC, cioè HAC; adunque il <lb></lb>quadrato AD è uguale al rettangolo HAC: però l&#039;angolo HDC è retto. </s>

<s>” </s></p><p type="main">

<s>Mostrato questo, cioè che la linea, che dal punto C va al concorso delle <lb></lb>due tangenti, sempre fa angoli retti con la tangente, la quale <emph type="italics"></emph>non est per <lb></lb>verticem parabolae;<emph.end type="italics"></emph.end> si mostra la proprietà del foco, per la quarta proposi­<lb></lb>zione del primo libro di Euclide. </s></p><p type="main">

<s><emph type="italics"></emph>“ Proposizione.<emph.end type="italics"></emph.end> — Sia la parabola, il cui asse AB (nella medesima <lb></lb>figura) ed AC sia la quarta parte del lato retto. </s>

<s>Prendasi qualunque punto <lb></lb>E, e sia EG parallela all&#039;asse, e tirinsi le tangenti ED, AD, e si congiun­<lb></lb>gano CE, CD: dico che gli angoli GEF, CED sono uguali. </s>

<s>” </s></p><p type="main">

<s>“ Poichè, tirata la ordinatamente applicata BE, perchè le BE, AD sono <lb></lb>parallele, e BA, AH uguali, saranno ancora ED, DH uguali fra loro, e la DC <lb></lb>è comune, e gli angoli in D sono retti. </s>

<s>Adunque, per la quarta del primo <lb></lb>di Euclide, l&#039;angolo CED è uguale all&#039;angolo DHC, cioè al GEF. ” </s></p><p type="main">

<s>“ In questa dimostrazione il caso è unico, ma nella comune sono tre <lb></lb>casi, e sempre bisogna variar la dimostrazione, poichè o la BE casca tra il <lb></lb>foco e la cima, ovvero alla parte opposta, ovvero sul foco stesso ” (MSS. <lb></lb>Gal., T. XL, fol. </s>

<s>20). </s></p><p type="main">

<s>Avuto forse in risposta dal Magiotti che il modo di dimostrare era nuovo, <lb></lb>e da non reputarsi perciò una baia, pensò il Torricelli di metter così la pro­<lb></lb>posizione in miglior forma, per inserirla nel primo libro <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end><lb></lb>innanzi alla XIX, nella quale l&#039;invenzion del foco si suppone per ritrovar <lb></lb>dalla distanza di lui sull&#039;asse della parabola le ordinatamente applicate, che <lb></lb>s&#039;han da prendere per la misura degl&#039;impeti, in ciascun punto della curva. </s></p><p type="main">

<s>“ PROPOSIZIONE XIII. — <emph type="italics"></emph>Sit parabola AE<emph.end type="italics"></emph.end> (sempre nell&#039;ultima figura) <lb></lb><emph type="italics"></emph>axis AB, ipsique parallela EG. </s>

<s>Ponatur AC quarta pars lateris recti, <lb></lb>ductisque tangentibus EH, AD, iungantur CD, EC. </s>

<s>Dico angulos GEF, <lb></lb>CED aequales esse. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ducatur ordinatim BE: cum enim aequales sint BA, AH, erit qua­<lb></lb>dratum AD quarta pars quadrati BE. </s>

<s>Rectangulum etiam CAB est quarta <lb></lb>pars eiusdem quadrati BE. </s>

<s>Quare quadratum AD aequatur rectangulo CAB, <lb></lb>hoc est CAH. </s>

<s>Erit igitur angulus HDC in semicirculo, et ideo rectus. </s>

<s>Sed <lb></lb>cum latera DH, DC aequalia sint lateribus ED, DC, utrumque, et anguli in <lb></lb>D recti; erunt reliqua aequalia, per quartam Primi, nempe angulus CHD, <lb></lb>sive GEF, aequalis angulo DEC, quod erat demonstrandum ” (ibid. </s>

<s>ad t.). </s></p><p type="main">

<s>Dimostrato così che il foco è veramente sull&#039;asse della parabola, a una <lb></lb>distanza dal vertice uguale alla quarta parte del parametro, si confermavano <lb></lb>dal Torricelli tutte quelle sue proposizioni, scritte a illustrare i teoremi letti <lb></lb>nel quarto Dialogo dal Salviati. </s>

<s>Ma un altro ufficio, ben assai più impor­<lb></lb>tante, erasi assunto il Discepolo valoroso, ed era quello di perfezionare l&#039;opera <lb></lb>del suo proprio Maestro, lasciata di parecchie altre parti, ma principalmente <lb></lb>del trattato delle catenuzze ballistiche in difetto. </s>

<s>Non deve nemmen egli il <pb xlink:href="020/01/2762.jpg" pagenum="387"></pb>Torricelli aver saputa da quali principii meccanici, e per quali vie riuscisse <lb></lb>Galileo a dimostrare che quelle stesse catenuzze si dispongono in figura di <lb></lb>parabola: o forse volle alla non facile dimostrazione trovare da sè stesso altri <lb></lb>modi, se veramente concludenti, e da doversi preferire ai galileiani, lo giu­<lb></lb>dicheranno i Lettori. </s>

<s>Si pone per fondamento al discorso un teorema statico, <lb></lb>a cui preluce il seguente <lb></lb><figure id="id.020.01.2762.1.jpg" xlink:href="020/01/2762/1.jpg"></figure></s></p><p type="caption">

<s>Figura 250.</s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma.<emph.end type="italics"></emph.end> — Si angulus ABC (fig. </s>

<s>250) <lb></lb>sectus bifariam sit a linea BD, ductaque sit quae­<lb></lb>libet AC, et sumatur AE aequalis ipsi BC, inde <lb></lb>EH parallela sit ipsi BD; dico AH, DC aequa­<lb></lb>les esse. </s>

<s>” </s></p><p type="main">

<s>“ Est enim, per tertiam Sexti, ut AD ad DC, <lb></lb>ita AB ad BC, vel AB ad AE, vel AD ad AH. </s>

<s>Quare aequales sunt AH, DC. ” </s></p><p type="main">

<s>“ PROPOSIZIONE XIV. — <emph type="italics"></emph>Sit angulus quilibet GBF<emph.end type="italics"></emph.end> (nella medesima <lb></lb>figura) <emph type="italics"></emph>et loca centrorum extrema G, F, linea bisecans angulum sit BD. <lb></lb>Deinde, moto loco, sit linea centrorum AC, sumaturque AH aequalis ipsi <lb></lb>DC: dico H esse centrum loci. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nam ut totum locum ad totum, ita dimidium AB ad dimidium BC, <lb></lb>vel, per tertiam Sexti, AD ad DC, vel, per praec. </s>

<s>lemma, HC ad AH reci­<lb></lb>proce. </s>

<s>Quare H centrum est gravitatis loci sic positum ” (ibid., T. XXXVII, <lb></lb>fol. </s>

<s>115). </s></p><p type="main">

<s>La difficoltà, che debbono tutti i lettori trovare in intendere queste ra­<lb></lb>gioni, dipende dal non essersi ben definito dal Torricelli il significato della <lb></lb>parola <emph type="italics"></emph>loco,<emph.end type="italics"></emph.end> nè del suo centro gravitativo, ond&#039;è che opportunamente soc­<lb></lb>corre in aiuto nostro il Viviani con questa nota, intitolata <emph type="italics"></emph>Mia raba, per <lb></lb>chiarezza della precedente.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia l&#039;angolo MBN (fig. </s>

<s>251) fatto da due piani MB, NB, e sia la fune <lb></lb>o catena MB, ora distesa da B sino ad M, ora da B sino ad N: è chiaro che <lb></lb><figure id="id.020.01.2762.2.jpg" xlink:href="020/01/2762/2.jpg"></figure></s></p><p type="caption">

<s>Figura 251.<lb></lb>il più lontano luogo de&#039;centri di gravità <lb></lb>della catena, posta in MB, sarà il punto <lb></lb>di mezzo A, ed il più lontano luogo del <lb></lb>centro, quando la catena sia in BN, sarà <lb></lb>il punto di mezzo C; sicchè questi A, C <lb></lb>si diranno <emph type="italics"></emph>loca centrorum extrema.<emph.end type="italics"></emph.end> Ma, <lb></lb>movendo la catena in modo che pigli del­<lb></lb>l&#039;uno e dell&#039;altro piano, nel sito per esem­<lb></lb>pio OBP, il centro della parte OB sarà <lb></lb>nel mezzo E, e della parte BP nel mezzo <lb></lb>H, sicchè, giunta la EH, questa si può dire <lb></lb><emph type="italics"></emph>linea centrorum moti loci,<emph.end type="italics"></emph.end> perchè con­<lb></lb>giunge i centri di gravità delle parti della catena mossa di luogo. </s>

<s>E perchè <lb></lb>la EH congiunge i centri delle parti della catena, in essa EH sarà il centro <lb></lb>di tutto, ed in luogo, che la parte verso H, alla parte verso E, sia come la <lb></lb>parte OB della catena, alla parte BP, cioè come la metà EB, alla metà BH. <pb xlink:href="020/01/2763.jpg" pagenum="388"></pb><emph type="italics"></emph>Ergo,<emph.end type="italics"></emph.end> dice il Torricelli, <emph type="italics"></emph>ut totum locum ad totum,<emph.end type="italics"></emph.end> cioè <emph type="italics"></emph>ut totum OB ad <lb></lb>totum BP, ita dimidium EB ad dimidium BH, vel EI ad IH, vel HL <lb></lb>ad LE reciproce. </s>

<s>Ergo L centrum gravitatis est loci ”<emph.end type="italics"></emph.end> (ibid., fol 115). </s></p><p type="main">

<s>Queste cose premesse e dimostrate, vuole il Torricelli che le condizioni <lb></lb>dell&#039;equilibrio della catena, parte disposta sul piano comunqu e inclinato MB, <lb></lb>e parte sul piano BN, siano quelle medesime, che se si tenesse sospesa per <lb></lb>i punti estremi A, e C liberamente pendula. </s>

<s>La supposizione fatta dal Disce­<lb></lb>polo è senza dubbio non meno arbitraria di quell&#039;altra fatta dal Maestro, ma <lb></lb>è certo che, come dal concedersi a Galileo che gli anelli sian discesi nella <lb></lb>catena insaccata, secondo la ragion de&#039;momenti, che avrebbe ciascuno di essi <lb></lb>in romper l&#039;asta, nella quale si supponessero orizontalmente infilati, resta <lb></lb>legittimamente dimostrato che quella tal saccaia è in figura di parabola; così, <lb></lb>dal concedere al Torricelli quella sua ipotesi già detta, si vien pur legittima­<lb></lb><figure id="id.020.01.2763.1.jpg" xlink:href="020/01/2763/1.jpg"></figure></s></p><p type="caption">

<s>Figura 252.<lb></lb>mente alla medesima conclusione, premesso il <lb></lb>seguente <emph type="italics"></emph>Lemma,<emph.end type="italics"></emph.end> relativo alle proprietà di <lb></lb>certe linee, con premeditata intenzione tirate <lb></lb>intorno, e dentro alla Parabola. </s></p><p type="main">

<s>“ Sia la parabola ABC (fig. </s>

<s>252), il cui <lb></lb>asse BH, ed ordinatamente applicata AC, e, <lb></lb>presa BD uguale a BH, tirinsi AD, CD, che <lb></lb>saranno tangenti. </s>

<s>Preso poi qualunque punto <lb></lb>E, tirisi l&#039;altra tangente FEG; dimostreremo <lb></lb>più cose: ” </s></p><p type="main">

<s>“ Per i punti F, E, G tirinsi parallele <lb></lb>all&#039;asse FM, NP, IL, e si prolunghi AD, che <lb></lb>concorra con LG in I, e si tiri AP parallela <lb></lb>a FE. </s>

<s>Perchè si è preso nella parabola un punto E, e la EP parallela al­<lb></lb>l&#039;asse, e la AP parallela alla tangente FE, e la AF tangente in A; saranno <lb></lb>uguali PE, EN, e però saranno uguali AF, FN fra le stesse parallele. </s>

<s>” </s></p><p type="main">

<s>“ Perchè poi l&#039;angolo ADC è diviso bifariam dalla HD, e la GI paral­<lb></lb>lela alla HD, saranno uguali GD, DI. ” </s></p><p type="main">

<s>“ Perchè CG ad AF ha proporzione subdupla di GL a FM, sarà, come <lb></lb>CG ad AF, così GE ad EF, ovvero IN ad NF. </s>

<s>Ma perchè i conseguenti AF, <lb></lb>NF sono uguali, saranno uguali gli antecedenti CG, NI. </s>

<s>Ed aggiunta la co­<lb></lb>mune DG sarà CD, ovvero AD, uguale alle NI, DG. </s>

<s>E levata la comune ND, <lb></lb>sarà AN uguale alle ID, DG, e però la metà AF uguale alla metà DG. ” <lb></lb><figure id="id.020.01.2763.2.jpg" xlink:href="020/01/2763/2.jpg"></figure></s></p><p type="caption">

<s>Figura 253.</s></p><p type="main">

<s>“ Stante questo, dico che anco FE sarà uguale <lb></lb>ad OG. S&#039;è mostrato che GE a EF sta come CG <lb></lb>ad AF, ovvero come FD a DG, ovvero FO ad OG, <lb></lb><emph type="italics"></emph>ob angulum D bifariam sectum.<emph.end type="italics"></emph.end> Come dunque GE <lb></lb>ad EF, così FO ad OG. </s>

<s>E componendo, GF ad FE, <lb></lb>come FG a GO, e così sono uguali FE, GO. ” </s></p><p type="main">

<s>“ PROPOSIZIONE XV. — <emph type="italics"></emph>Siano i due centri <lb></lb>primarii A, B<emph.end type="italics"></emph.end> (fig. </s>

<s>253) <emph type="italics"></emph>e sia mossa la catena,<emph.end type="italics"></emph.end><pb xlink:href="020/01/2764.jpg" pagenum="389"></pb><emph type="italics"></emph>sicchè i centri siano C, D, e sia la EF che seghi l&#039;angolo bifariam, e <lb></lb>prendasi DI uguale a CF: è chiaro che I sarà il centro comune. </s>

<s>Dico <lb></lb>ora che I sta nella parabola. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Se non ci sta, passi la parabola sulla MIN, parallela all&#039;asse EF in <lb></lb>L, e si prenda LN uguale ad LM, e si tiri la retta DLO. È certo che, es­<lb></lb>sendo uguali MD, DA, come ora proverò, ed uguali NL, LM, saranno paral­<lb></lb>lele AN, DL. </s>

<s>Dunque DLO sarà la seconda tangente della parabola, e per la <lb></lb>proposizion precedente saranno uguali AD, EO, <emph type="italics"></emph>quod est absurdum<emph.end type="italics"></emph.end> perchè <lb></lb>AD, EC sono uguali. </s>

<s>” </s></p><p type="main">

<s>“ Provo ora che MD, DA sono uguali fra loro. </s>

<s>Sono uguali AD ed EC <lb></lb><emph type="italics"></emph>per hypothesim,<emph.end type="italics"></emph.end> e CF, DI <emph type="italics"></emph>per constructionem.<emph.end type="italics"></emph.end> Ora ED a DA sta come ED <lb></lb>a EC, vel DF ad FC, vel FD ad DI, vel ED ad DM. </s>

<s>Però sono uguali AD, <lb></lb>DM, come avevo promesso di dimostrare ” (ivi, T. XXXVII, fol. </s>

<s>122). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Abbiamo riserbato a parte il trattar de&#039;momenti sì per essere argomento <lb></lb>nella nostra Storia della principale importanza, e sì per avere intorno a tali <lb></lb>dottrine patito il Torricelli le maggiori contradizioni. </s>

<s>Incominciarono queste, <lb></lb>lui vivente, in Francia, per opera del Roberval, con l&#039;intermedio del padre <lb></lb>Mersenno, e le resuscitò, contro lui già morto, in Italia, Alessandro Mar­<lb></lb>chetti. </s>

<s>Il Borelli ammoniva il discepolo suo prediletto che, almeno per l&#039;av­<lb></lb>venire, imparasse a procedere <emph type="italics"></emph>con più cautela e modestia<emph.end type="italics"></emph.end> (Tondini, Let­<lb></lb>tere, T. I, Macerata 1782, pag. </s>

<s>90), e Sfefano Angeli, tirato dagli stessi amici <lb></lb>suoi e del Marchetti a prender parte al pericoloso giudizio, inclinava a di­<lb></lb>fendere il Torricelli (ivi, pag. </s>

<s>131). </s></p><p type="main">

<s>Ma il Torricelli stesso, che conosceva non dipendere da altro le censure, <lb></lb>che dall&#039;aver lasciate in qualche parte mancanti, e in qualche altra non bene <lb></lb>spiegate le sue proposizioni; col ritornar sopra l&#039;opera già stampata, per <lb></lb>perfezionarla, intendeva di difendersi, nel migliore e più virtuoso modo, con­<lb></lb>tro i Francesi. </s>

<s>Col fatto poi veniva dal silenzioso sepolcro a sbugiardare i <lb></lb>vanti del Marchetti, il quale erasi compiaciuto a principio di aver egli dimo­<lb></lb>strato il primo che i momenti hanno la ragion composta delle distanze e dei <lb></lb>pesi: poi, fatto avvertito che la dimostrazione l&#039;aveva data parecchi anni <lb></lb>prima, e in una solenne opera sua stampata il Cavalieri, si consolava che <lb></lb>non gli avrebbe nessuno contesa la gloria dell&#039;avere egli veramente il primo <lb></lb>applicato alle dottrine del moto il teorema. </s>

<s>Ma il Serenai e il Viviani ma­<lb></lb>neggiavano intanto quelle carte torricelliane, nelle quali leggevano fatta già <lb></lb>dall&#039;Autore la stessa applicazione ad alcune nuove proposizioni baricentriche, <lb></lb>e per dimostrar dai principii geometrici la regola centrobarica del Guldino. </s>

<s><lb></lb>Di qui nasce la triplice partizion delle cose, che s&#039;ordineranno in questa se-<pb xlink:href="020/01/2765.jpg" pagenum="390"></pb>conda parte del presente capitolo, per servire alla storia de&#039;concetti postumi <lb></lb>del Torricelli, e dei loro svolgimenti fecondi. </s></p><p type="main">

<s>Incominciamo dalla prima parte, in cui ci si rappresenta il Nostro tutto <lb></lb>in sollecitudine di aggiungere la desiderata perfezione a quelle proposizioni <lb></lb><emph type="italics"></emph>De motu gravium naturaliter descendentium,<emph.end type="italics"></emph.end> nelle quali si dimostrano le <lb></lb>proprietà e le leggi de&#039;momenti dei gravi, mentre scendono lungo i piani <lb></lb>inclinati. </s>

<s>Dipendono queste leggi, come da loro universale principio, dal <emph type="italics"></emph>Teo­<lb></lb>rema meccanico,<emph.end type="italics"></emph.end> che dice stare allora due gravi in equilibrio, sopra due piani <lb></lb>ugualmente alti, quando le loro lunghezze siano alle gravità omologamente <lb></lb>proporzionali. </s>

<s>Alla dimostrazione di ciò, che in primo luogo ricorre nel libro <lb></lb>stampato, voleva il Torricelli aggiungere un tal corollario: “ Ergo gravia <lb></lb>tunc habebunt aequalia momenta, quando ipsa fuerint ut secantes comple­<lb></lb>mentorum anguli elevationis. </s>

<s>Posito enim sinu toto AB (fig. </s>

<s>254) erunt AC, <lb></lb>AD dictae secantes ” (MSS. Gal. </s>

<s>Disc., T. XXXIII, fol. </s>

<s>83). È infatti AC:AB= <lb></lb>1:cos.CAB=sec.CAB:1; AD:AB=1:cos.BAD=sec.BAD:1. <lb></lb>D&#039;onde AC:AD=sec.CAB:sec.BAD. <lb></lb><figure id="id.020.01.2765.1.jpg" xlink:href="020/01/2765/1.jpg"></figure></s></p><p type="caption">

<s>Figura 254.</s></p><p type="main">

<s>Nella seconda <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> avendo già di <lb></lb>mostrato l&#039;Autore che i momenti di due gravi uguali, <lb></lb>sopra due piani di uguale altezza, stanno come le <lb></lb>loro lunghezze reciproche; poi pensò di mettere la <lb></lb>medesima conclusione sotto altra forma, dicendo <lb></lb>che que&#039;momenti hanno la proporzione omologa <lb></lb>dei seni degli angoli delle elevazioni. </s>

<s>Si trova il pensiero sotto il n.o XXX <lb></lb>del citato <emph type="italics"></emph>Campo di tartufi,<emph.end type="italics"></emph.end> notato in questa forma: “ Quando vero gravia <lb></lb>aequalia fuerint, erunt momenta ut sinus angulorum elevationis. <emph type="italics"></emph>Nota che <lb></lb>vi è (nel libro stampato), ma la prova è più bella così:<emph.end type="italics"></emph.end> nam, cum sint <lb></lb>momenta ut ED, FD (fig. </s>

<s>255), hae sunt sinus angulorum DAC, DBC ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. XXXIII, fol. </s>

<s>82). </s></p><p type="main">

<s>Come però AD, BD, a cui contrariamente rispondono i momenti, abbian <lb></lb>la proporzion medesima delle loro porzioni DF, DE, segate dal mezzo cerchio, <lb></lb><figure id="id.020.01.2765.2.jpg" xlink:href="020/01/2765/2.jpg"></figure></s></p><p type="caption">

<s>Figura 255.<lb></lb>che sia descritto intorno a DC; non si <lb></lb>trova dimostrato, e non si trova pur di­<lb></lb>mostrato come le due corde intercette <lb></lb>siano uguali ai seni dell&#039;angolo dell&#039;incli­<lb></lb>nazione de&#039;piani. </s>

<s>Nè si può la prima di <lb></lb>queste due verità supporre nota dall&#039;iso­<lb></lb>cronismo delle sottese al circolo, non di­<lb></lb>mostrato ancora, per cui s&#039;argomenta che <lb></lb>dalle proprietà geometriche, e non dalle <lb></lb>meccaniche, intendesse il Torricelli che fosse da concludere la proporzionalità <lb></lb>reciproca tra le lunghezze de&#039;piani AD, BD, e le loro porzioni intersecate. </s>

<s><lb></lb>Essendo infatti la BC tangente, la DB secante, e il triangolo BDC rettangolo <lb></lb>in C, abbiamo, per le notissime proprietà geometriche, BC2=BD.BF= <lb></lb>DB2—DC2, e perciò DC2=DB (DB—BF)=DB.FD. </s>

<s>Nel medesimo <pb xlink:href="020/01/2766.jpg" pagenum="391"></pb>modo si troverebbe DC2=AD.ED. Che, se dunque AD.ED=DB.FD, <lb></lb>AD:DB=FD:ED. </s></p><p type="main">

<s>La seconda torricelliana si sarebbe potuta perciò mettere anche sotto <lb></lb>quest&#039;altra forma, dicendo che i momenti del medesimo grave, sopra i piani <lb></lb>AD, BD, stanno omologamente come le loro parti intersecate dal semicerchio, <lb></lb>d&#039;onde il corollario bellissimo che, essendo per DF, DE gl&#039;impeti o le velo­<lb></lb>cità proporzionali agli spazi, i tempi sono uguali, per venire alla qual con­<lb></lb>clusione ebbe Galileo a prepararsi la macchina di parecchie laboriose pro­<lb></lb>posizioni. </s></p><p type="main">

<s>Ma la presente intenzione del Nostro era, come si diceva, quella di <lb></lb>dimostrar che i momenti son proporzionali ai seni degli angoli delle eleva­<lb></lb>zioni. </s>

<s>Forse la dimostrazione era la medesima o simile, che nel lemma pre­<lb></lb>messo alla proposizione IV (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>106), ma più facile e più <lb></lb>diretta sovviene dal considerar l&#039;uguaglianza del triangolo HID (nella fatta <lb></lb>costruzione) col CED, e del GMD col DFC, d&#039;onde il lato ED viene a dimo­<lb></lb>strarsi uguale a LH, seno dell&#039;angolo LDH, o del suo uguale DAC, secondo <lb></lb>cui s&#039;inclina il piano AD sopra l&#039;orizontale AC; e il lato FD uguale al lato <lb></lb>GM, seno di MDG, o del suo uguale DBC, angolo dell&#039;inclinazione dell&#039;al­<lb></lb>tro piano. </s></p><p type="main">

<s>A così fatte dimostrazioni, mancanti nel manoscritto, pensò di supplir <lb></lb>di buon&#039;ora il Viviani, il quale ordinò così quella, che, fra le occorseci in <lb></lb>questo proposito, si contrassegna da noi per la proposizione prima. </s></p><p type="main">

<s>“ PROPOSIZIONE I. — <emph type="italics"></emph>Momenta gravium aequalium super plana DA, <lb></lb>DB<emph.end type="italics"></emph.end> (nella medesima figura), <emph type="italics"></emph>sunt ut sinus angulorum elevationis. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Quod, per primum, momenta gravium aequalium super plana DA, DB, <lb></lb>de quibus Auctor loquitur, sint inter se ut ipsorum segmenta ED, FD, in <lb></lb>semicirculo DEC inscripta, dum sit DC ad horizontalem AC perpendicula­<lb></lb>ris; patet sic: Nam iunctis CE, CF, rectangula ADE, BDF inter se sunt ae­<lb></lb>qualia, utrumque enim aequatur quadrato diametri DC. </s>

<s>Quare ut BD ad DA, <lb></lb>ita est ED ad DF. </s>

<s>Sed ut BD ad DA, ita est reciproce momentum gravis <lb></lb>super DA, ad momentum aequalis gravis super DB, per secundam proposi­<lb></lb>tionem eiusdem libri primi <emph type="italics"></emph>De motu;<emph.end type="italics"></emph.end> ergo ut ED ad DF, ita est momen­<lb></lb>tum super DA, ad momentum super DB. ” </s></p><p type="main">

<s>“ Insuper, quod ipsae DE, DF sint sinus angulorum elevationis DAC, <lb></lb>DBC, ita ostenditur: Descripto enim, ex centro D, ac intervallo DC, qua­<lb></lb>drante circuli DCI, secante plana in G, H, atque ex GH ductis GM, HL, si­<lb></lb>nubus angulorum GDI, HDI, vel sibi aequalium DBC, DAC; hi aequantur <lb></lb>ipsis inscriptis DF, DE, singuli singulis, quoniam, in triangulis DLH, CED, <lb></lb>angulus LDH, a tangente et secante constitutus, aequatur angulo in alterna <lb></lb>portione ECD: anguli ad M, E sunt recti, latus vero DH aequatur lateri DC, <lb></lb>cum utrumque sit radius quadrantis; ideoque et latus HL aequatur lateri DE. </s>

<s><lb></lb>Eademque ratione GM aequale ipsi DF, quod supererat, demonstratur ” (ibid., <lb></lb>T. XXXVII, fol. </s>

<s>93). </s></p><p type="main">

<s>Di qui si conclude, intendendo significato con Mo il momento, e riferen-<pb xlink:href="020/01/2767.jpg" pagenum="392"></pb>doci alla medesima figura, Mo.DB:Mo.DC=sen.DBC:sen.DCB= <lb></lb>DC:DB, che vuol dire il momento parziale sopra il piano inclinato stare al <lb></lb>totale, nel perpendicolo, contrariamente come la lunghezza di esso perpen­<lb></lb>dicolo sta alla lunghezza del piano. </s>

<s>Che se il grave s&#039;immagini essere una <lb></lb>sfera, posata sul declivio BG (fig. </s>

<s>256), e si faccia dal diametro di lei rap­<lb></lb><figure id="id.020.01.2767.1.jpg" xlink:href="020/01/2767/1.jpg"></figure></s></p><p type="caption">

<s>Figura 256.<lb></lb>presentare il momento totale, sarà il parziale, dice il <lb></lb>Torricelli nel corollario alla citata proposizione (Op. </s>

<s><lb></lb>geom. </s>

<s>cit., pag. </s>

<s>102), rappresentato dalla corda AB, co­<lb></lb>sicchè, intendendosi significati con Mo.T, Mo.P i due <lb></lb>detti momenti, avremo Mo.T:Mo.P=HB:AB. </s>

<s><lb></lb>Moltiplicando ora la seconda ragione per la circonfe­<lb></lb>renza di un cerchio massimo, e osservando che essa cir­<lb></lb>conferenza moltiplicatà per il diametro è uguale a tutta <lb></lb>intera la superficie sferica, e moltiplicata per la corda AB è uguale all&#039;ar­<lb></lb>milla descritta dall&#039;arco AB, supposto che la rivoluzione si faccia intorno al <lb></lb>diametro EF; avremo dimostrata la proposizione che segue: </s></p><p type="main">

<s>“ PROPOSIZIONE II. — <emph type="italics"></emph>Momentum totale ad momentum in hoc situ<emph.end type="italics"></emph.end><lb></lb>(quale cioè vien rappresentato dalla figura) <emph type="italics"></emph>est ut tota sphaerae superficies <lb></lb>ad armillarem sphaerae superficiem, quam subtendit AB,<emph.end type="italics"></emph.end> si <emph type="italics"></emph>sphaera vol­<lb></lb>vatur circa EF ”<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. XXX, fol. </s>

<s>79). </s></p><p type="main">

<s>Questa e la precedente, incluse come in loro principio nelle proposizioni <lb></lb>già divulgate, aggiungevano al trattato eleganza, ma quella, che ora in terzo <lb></lb>luogo porremo, suppliva una notizia importante, della quale anche Galileo <lb></lb>aveva lasciato il suo dialogo in difetto, ed è: secondo qual proporzione stiano <lb></lb>i momenti, quando, essendo i piani quali si sono descritti, i mobili però sono <lb></lb>in mole e in gravità differenti: per rispondere al quale quesito aveva il Tor­<lb></lb>ricelli distesa la seguente </s></p><p type="main">

<s>“ PROPOSIZIONE III. — <emph type="italics"></emph>Si AB, BC<emph.end type="italics"></emph.end> (fig. </s>

<s>257) <emph type="italics"></emph>duo plana fuerint inae­<lb></lb>qualiter inclinata, et AC horizontalis, sintque in planis duo gravia quae-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2767.2.jpg" xlink:href="020/01/2767/2.jpg"></figure></s></p><p type="caption">

<s>Figura 257.<lb></lb><emph type="italics"></emph>cumque D, et E; dico momentum D, ad mo­<lb></lb>mentum E, compositam habere rationem ex <lb></lb>ratione molis D, ad molem E homologe, et <lb></lb>ex ratione longitudinis CB ad BA, reci­<lb></lb>proce. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ponatur enim grave F aequale ipsi D, in <lb></lb>altero plano BC, et erit, per propositionem secundam libelli nostri <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end><lb></lb>momentum D, ad momentum F, ut est CB ad BA. </s>

<s>At momentum F, ad <lb></lb>momentum E, est ut molis F ad molem E; ergo momentum D, ad momen­<lb></lb>tum E, compositam rationem habet ex ratione CB ad BA, et ex ratione mo­<lb></lb>lis D ad E, <expan abbr="q.">que</expan> e. </s>

<s>d. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Sed quia CB ad BA est ut sinus anguli A, ad sinum <lb></lb>anguli C, dicemus etiam rationem momenti D, ad momentum E, componi <lb></lb>ex ratione molis D, ad molem E, et ex ratione sinus elevationis plani AB, <lb></lb>ad sinum elevationis plani CB ” (ibid., T. XXXVII, fol. </s>

<s>72). </s></p><pb xlink:href="020/01/2768.jpg" pagenum="393"></pb><p type="main">

<s>Aveva il Mersenno rimproverato, in una sua lettera, il Torricelli perchè <lb></lb>egli suppone nel corollario, dopo la propozione terza, una cosa, senz&#039;altri­<lb></lb>menti dimostrarla. </s>

<s>Di che avendo esso Torricelli giustamente riconosciuto <lb></lb>essere il suo trattato in difetto, pensò di supplirvi in questa maniera: </s></p><p type="main">

<s>“ PROPOSIZIONE IV. — <emph type="italics"></emph>Posita cadem figura, quae in libello<emph.end type="italics"></emph.end> (per noi <lb></lb>la 258), <emph type="italics"></emph>dico momentum A, ad momentum B, ita esse ut CD ad DE. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sumantur enim ID, DH aequales ipsis CD, DE, et in punctis I, H <lb></lb><figure id="id.020.01.2768.1.jpg" xlink:href="020/01/2768/1.jpg"></figure></s></p><p type="caption">

<s>Figura 258.<lb></lb>duae sphaerae constituantur aequales, tum inter <lb></lb>se, tum ipsis B, A, et connectatur recta BH, <lb></lb>quae tamquam libra concipiatur. </s>

<s>Patet quod <lb></lb>recta BH bifariam secabitur in L, per secun­<lb></lb>dam Sexti, ergo punctum L erit centrum gra­<lb></lb>vitatis gravium B, H, et est L in perpendiculo <lb></lb>per punctum suspensionis ducto: ergo gravia <lb></lb>sic connexa, sive colligentur recta BH, sive linea <lb></lb>inflexa BDH, non movebuntur, nulla enim maior <lb></lb>ratio est cur ad dextram descendant, potius quam ad sinistram. </s>

<s>Si manent, <lb></lb>ergo momentum in B aequale est momento in H. ” </s></p><p type="main">

<s>“ Idem dicendum de gravibus A, I. </s>

<s>Propterea momenta in A, B erunt <lb></lb>ut momenta in I, H, nempe ut distantiae ID, DH, sive ut CD, DE ” (ibid., <lb></lb>T. XL, fol. </s>

<s>77). </s></p><p type="main">

<s>Il Torricelli per far prova della sua fecondità in quello stesso, che da&#039;suoi <lb></lb>proprii censori si giudicava difetto, volle dimostrare così la medesima cosa. <lb></lb><figure id="id.020.01.2768.2.jpg" xlink:href="020/01/2768/2.jpg"></figure></s></p><p type="caption">

<s>Figura 259.<lb></lb>anche in un altro modo assai più bello, per <lb></lb>via della costruzione, ch&#039;è data assai facil­<lb></lb>mente ad intendere dalla nostra figura 259, <lb></lb>senza che ci sia bisogno di altre parole: <lb></lb>“ Momentum partiale descensivum per DF, <lb></lb>ad totale per DK, est ut DK ad DF, vel ut <lb></lb>AK ad AD, vel AC: et totale per DK, vel EI, <lb></lb>ad partiale descensivum per EG, est ut EG <lb></lb>ad EI, vel ut AE ad AI, vel ut AC ad AI. </s>

<s>Ergo ex aequali partiale descen­<lb></lb>sivum per DF, ad partiale descensivum per EG, est ut AK ad AI, vel ut <lb></lb>totale appensum in K, ad totale idem appensum in I ” (ibid., T. XXXIV, <lb></lb>fol. </s>

<s>134). </s></p><p type="main">

<s>Così gl&#039;importanti corollari della proposizione terza venivano ad essere <lb></lb>anche meglio nella loro verità confermati. </s>

<s>Ma il Torricelli pensava di ar­<lb></lb>ricchire anche più questa parte del suo trattato, aggiungendovi le seguenti, <lb></lb>che noi raccoglieremo qui fra le nostre proposizioni meccaniche dei mo­<lb></lb>menti. </s></p><p type="main">

<s>“ PROPOSIZIONE V. — <emph type="italics"></emph>Sint duo plana utcumque AB, AC<emph.end type="italics"></emph.end> (fig. </s>

<s>260) <emph type="italics"></emph>et <lb></lb>duo gravia utcumque B, C. </s>

<s>Iungatur BC, et fiat ut grave B ad C, ita CD <lb></lb>ad DB. </s>

<s>Tum per D ducatur EF, ita ut secet ipsas EA, AF in ratione gra­<lb></lb>vis B ad grave C: dico EF esse viam centri aravitatis. </s>

<s>”<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2769.jpg" pagenum="394"></pb><p type="main">

<s>“ Primo ostendemus BE, FC aequales esse. </s>

<s>Ducatur BI parallela ad AC: <lb></lb><figure id="id.020.01.2769.1.jpg" xlink:href="020/01/2769/1.jpg"></figure></s></p><p type="caption">

<s>Figura 260.<lb></lb>erit EB ad BI ut EA ad EF, hoc est <lb></lb>CD ad DB, hoc est FC ad BI eam­<lb></lb>dem. </s>

<s>Quare aequales erunt EB, FC. ” </s></p><p type="main">

<s>“ Moveantur iam gravia, et sint <lb></lb>B in L, C in M: erunt aequales totae <lb></lb>EL, FM. </s>

<s>Ducatur LO parallela ad <lb></lb>AM, et iungatur LM. </s>

<s>Erit grave L, ad <lb></lb>grave M, ut EA ad AF, vel EL ad LO, <lb></lb>vel MF ad LO, vel MP ad PL. </s>

<s>Ergo <lb></lb>centrum est P ” (ibid., T. XXXVII, <lb></lb>fol. </s>

<s>69). </s></p><p type="main">

<s>“ PROPOSIZIONE VI. — <emph type="italics"></emph>Datis ut supra, fiat ut grave A<emph.end type="italics"></emph.end> (fig. </s>

<s>261), <emph type="italics"></emph>ad <lb></lb>grave B, ita quaelibet CD ad DE: et erit planum CE tale planum, quod <lb></lb>si in ipso grave A sit, erit momentum gravis A in plano CE idem ac <lb></lb>momentum gravis A in plano CD ”<emph.end type="italics"></emph.end> (ibid.). </s></p><p type="main">

<s>La dimostrazione è taciuta, perchè forse la credeva il Torricelli ovvia <lb></lb>alla mente di ognuno, che vada ripensando come, per la prima <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> i <lb></lb><figure id="id.020.01.2769.2.jpg" xlink:href="020/01/2769/2.jpg"></figure></s></p><p type="caption">

<s>Figura 261.<lb></lb>due gravi rimarrebbero allora fra loro sopra i due piani <lb></lb>in equilibrio, ossi asenza momento, quando la linea di <lb></lb>congiunzione CE tornasse in posizione orizontale. </s>

<s>E se <lb></lb>sopra essa orizontale s&#039;intendesse posato il grave A o E <lb></lb>rimarrebbe ivi egli pure senza momento. </s>

<s>Inclinando poi <lb></lb>la figura, in quel modo che si è rappresentata, è ma­<lb></lb>nifesto che l&#039;impeto di discendere lungo il piauo DC è, per il grave A con­<lb></lb>giunto col grave B, quel medesimo che sarebbe di scendere lungo il piano <lb></lb>CE, essendo A libero. </s>

<s>Che se fosse la figura piegata e volta alla parte con­<lb></lb>traria, in modo cioè che il punto E si abbassasse, anche il grave E sarebbe <lb></lb>quello disposto a scendere col già detto momento. </s></p><p type="main">

<s>Questa, con la precedente, della quale non è che un corollario, servi­<lb></lb>vano a preparare la proposizione che segue, la quale doveva inserirsi nel li­<lb></lb><figure id="id.020.01.2769.3.jpg" xlink:href="020/01/2769/3.jpg"></figure></s></p><p type="caption">

<s>Figura 262.<lb></lb>bretto stampato, dopo la dimostrazione <lb></lb>che, passandosi le corde, nel circolo col <lb></lb>diametro verticalmente eretto, nel mede­<lb></lb>simo tempo; le velocità o i momenti son <lb></lb>per esse corde proporzionali agli spazi <lb></lb>passati. </s></p><p type="main">

<s>“ PROPOSIZIONE VII. — <emph type="italics"></emph>Sit planum <lb></lb>AB<emph.end type="italics"></emph.end> (fig. </s>

<s>262) <emph type="italics"></emph>utcumque inclinatum, et <lb></lb>grave D sit in ipso, sitque aliud plannm <lb></lb>BC utlibet inclinatum. </s>

<s>Fiat circulus qui­<lb></lb>libet, cuius tamen infimum punctum sit in AB, et concipiatur momentum <lb></lb>gravis D esse ut AB: si ponatur grave aliud E connexum cum D, et fiat, ut <lb></lb>grave D ad E, ita AB ad BC, erit AH momentum gravis D connexi ”<emph.end type="italics"></emph.end> (ibid.). </s></p><pb xlink:href="020/01/2770.jpg" pagenum="395"></pb><p type="main">

<s>La dimostrazione, che manca nel manoscritto, si supplisce assai facil­<lb></lb>mente dopo le cose già dette, imperocchè il momento di D in AB, al mo­<lb></lb>mento di D in AH, sta come AB ad AH. </s>

<s>Ma il momento di D sopra il piano <lb></lb>AH è, per la V di questo, uguale al momento di D congiunto con E sopra <lb></lb>il piano AB; dunque il momento di D libero, al momento di D congiunto, <lb></lb>sta come AB ad AH, ciò che dimostra la verità di quel che il Torricelli <lb></lb>dianzi annunziava. </s></p><p type="main">

<s>Le sette proposizioni intorno ai momenti, fin qui da noi raccolte dai <lb></lb>manoscritti del Torricelli, sono ordinate alla storia del trattato <emph type="italics"></emph>De motu gra­<lb></lb>vium,<emph.end type="italics"></emph.end> secondo la prima nostra data intenzione. </s>

<s>La seconda era quella di <lb></lb>mostrar come avesse lo stesso Torricelli, tanto prima del Marchetti, non so­<lb></lb>lamente saputo dedurre dai principii statici che i momenti hanno la ragion <lb></lb>composta delle distanze e dei pesi, ma come egli ne avesse, nel medesimo <lb></lb>tempo, fatta l&#039;applicazione ad alcuni teoremi concernenti la Baricentrica e <lb></lb>la Centrobarica guldiniana. </s>

<s>Di che il primo documento, per quel che riguarda <lb></lb>i centri di gravità, ci è offerto dalla seguente lettera, scritta da Firenze il <lb></lb>di 7 Aprile 1646 al Cavalieri:. </s></p><p type="main">

<s>“ Quando, nella lettera di V. P., veddi che ella trattava di quei centri <lb></lb>di gravità intorno a quel suo solido, ebbi paura che ella mi avesse scoperta <lb></lb>una passione, che io trovai. </s>

<s>Ora perchè ella non abbia a trovarla, io la dirò: <lb></lb>Il centro della gravità, in tutte le figure piane e solide, purchè abbiano l&#039;asse <lb></lb>o il diametro, sega sempre l&#039;asse, o il diametro che sia, con la medesima <lb></lb>regola. </s>

<s>La Natura non è così ricca d&#039;invenzioni, come a noi sembra per la <lb></lb>nostra propria debolezza. </s>

<s>Ella non bada che la proporzione delle parti del <lb></lb>diametro in alcune figure sia dupla, in altre tripla, in altre sesquialtera, come <lb></lb>cinque a tre, come sette a cinque, e tante altre sorti di proporzioni, anco <lb></lb>incommensurabili. </s>

<s>” </s></p><p type="main">

<s>“ Questi sono corollari, ma il Teorema universale non so se sia sovve­<lb></lb>nuto ancora a nessuno: anzi credo che nessuno abbia mai pensato che ci <lb></lb>possa essere, eppure vi è, ed è tale: </s></p><p type="main">

<s>“ PROPOSIZIONE VIII. — <emph type="italics"></emph>Centrum gravitatis in qualibet figura, sive <lb></lb>plana sive solida, dummodo axem habeat vel diametrum, secat axem vel <lb></lb>diametrum semper hac lege, ut pars versus verticem sit ad reliquam que­<lb></lb>madmodum sunt omnes ductus applicatorum, in omnes axis vel diametri <lb></lb>portiones versus verticem abscissas, ad omnes ductus eorumdem applica­<lb></lb>torum in reliquas axis vel diametri portiones. </s>

<s>Intelligimus autem, nomine <lb></lb>applicatorum, in figuris planis, lineas applicatas, in solidis, plana. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ella vede che quelli <emph type="italics"></emph>ductus<emph.end type="italics"></emph.end> in figure piane saranno rettangoli, in so­<lb></lb>lidi poi saranno solidi. </s>

<s>Ella conoscerà subito che questo è un corollario della <lb></lb>dimostrazione, ch&#039;io gli mandai intorno al solido segato per traverso in un <lb></lb>piano, che passi <emph type="italics"></emph>per extremas applicatas.<emph.end type="italics"></emph.end> Infatti, esto semifigura qualis de­<lb></lb>finita est ABC (fig. </s>

<s>263), cuius diameter AB, vertex B, fiatque suum solidum <lb></lb>cylindricum cavalerianum BD, ita ut altitudo AE sit aequalis diametro AB, <lb></lb>seceturque plano ACG. </s>

<s>Ostensum est a nobis quod, si F sit centrum gravi-<pb xlink:href="020/01/2771.jpg" pagenum="396"></pb>tatis totius figurae, ita esse solidum ADEG, ad reliquum, ut BF ad FA. </s>

<s>His <lb></lb><figure id="id.020.01.2771.1.jpg" xlink:href="020/01/2771/1.jpg"></figure></s></p><p type="caption">

<s>Figura 263.<lb></lb>positis, omnia rectangula, quorum unum HL <lb></lb>(nempe sub applicata HI et sub IL, sive sub por­<lb></lb>tione IG diametri abcissae versus verticem), ad <lb></lb>omnia rectangula, quorum unum LP (nempe sub <lb></lb>applicata OP, et OL, sive reliqua portione dia­<lb></lb>metri OA) sunt ut solidum ADEG, ad solidum <lb></lb>ABCG: ergo patet ita esse BF ad FA ut omnia <lb></lb>praedicta rectangula. </s>

<s>Benchè dunque si potesse <lb></lb>dal solido cavaleriano dimostrare in questo modo <lb></lb>il Teorema, nulladimeno io ne ho trovata un&#039;al­<lb></lb>tra dimostrazione apposta, ed è tale: ” </s></p><p type="main">

<s>“ Esto figura quaelibet ABCD (fig. </s>

<s>264), sive plana sive solida, dum­<lb></lb>modo axem vel diametrum habeat AC, sitque centrum gravitatis E: dico CE <lb></lb>ad EA esse ut dictum est supra. </s>

<s>” </s></p><p type="main">

<s>“ Nam ponatur ei in directum alia similis et aequalis figura CFGH, <lb></lb>cuius centrum sit I, sumaturque homologa applicatae LB, MF, et intelliga­<lb></lb><figure id="id.020.01.2771.2.jpg" xlink:href="020/01/2771/2.jpg"></figure></s></p><p type="caption">

<s>Figura 264.<lb></lb>tur suspensa libra ex C, sive aequipon­<lb></lb>deret, sive non. </s>

<s>” </s></p><p type="main">

<s>“ Jam, ex principiis mechanicis, <lb></lb>erit momentum applicati LB, ad mo­<lb></lb>mentum applicati MF, ut ductus appli­<lb></lb>cati LB in distantiam LC, ad ductum <lb></lb>applicati MF, in distantiam MC, et hoc <lb></lb>semper verum est, ubicumque sumpta fuerint homologa applicata. </s>

<s>Ergo mo­<lb></lb>mentum omnium applicatorum, seu figurarum ABCD, ad momentum figurae <lb></lb>CFGH, erit ut omnes ductus applicatorum, quorum unum est LB, in omnes <lb></lb>diametri vel axis portiones versus verticem abscissas, quarum una est LC; <lb></lb>ad omnes ductus eorumdem applicatorum, quorum unum est MF, in reli­<lb></lb>quas diametri portiones, quorum una est MC. </s>

<s>Sed momentum figurae ABCD, <lb></lb>ad momentum figurae CFGH, est ut distantia EC ad distantiam CI; ergo <lb></lb>EC ad CI, hoc est EC ad EA, erit ut omnes praedicti illi ductus, quorum <lb></lb>unum est BL in LC, ad omnes praedictos ductus, quorum unum est MF in <lb></lb>MC, quod erat domonstrandum. </s>

<s>” </s></p><p type="main">

<s>“ Nelle figure solide basta mutar nome all&#039;applicato, che non è linea <lb></lb>ma piano, e però anco il rettangolo si muterà in solido. </s>

<s>La stessa proposi­<lb></lb>zione abbraccia il centro anche delle linee e delle superficie, ma, in cambio <lb></lb>delle porzioni del diametro, si adoprano le tangenti. </s>

<s>Supplico V. P. a non <lb></lb>conferire la cosa con alcuno, perchè proposi il teorema agli amici di Roma, <lb></lb>e forse lo proporrò in Francia, e non l&#039;ho conferita se non a V. P. ” (ivi, <lb></lb>T. XL, fol. </s>

<s>132). </s></p><p type="main">

<s>Si sente da queste espressioni che il Torricelli faceva gran conto della <lb></lb>sua invenzione, la quale nonostante il Cavalieri diceva che sarebbe da pre­<lb></lb>giare anche di più, quando vi s&#039;insegnasse il modo di trovare le proporzioni <pb xlink:href="020/01/2772.jpg" pagenum="397"></pb>fra gli uni e gli altri di que&#039;prodotti. </s>

<s>Ma il Torricelli ingenuamente rispon­<lb></lb>deva: “ quanto al trovar la proporzione di quelli <emph type="italics"></emph>omnes ductus, ad omnes <lb></lb>ductus,<emph.end type="italics"></emph.end> io non ci ho nulla, e non ho cercato altro, stimandola assai intri­<lb></lb>cata materia ” (ivi, fol. </s>

<s>133). Nonostante, dando poco tempo dopo notizia al <lb></lb>Carcavy di questo teorema, dop&#039;averglielo formulato così, soggiungeva: “ Haec <lb></lb>est regula, ex qua centra gravitatis exprimo, cum habeam methodum, non <lb></lb>adeo difficilem, pro invenienda ratione, quam habent praedicti omnes ductus, <lb></lb>ad omnes ductus ” (ibid., fol. </s>

<s>39). Potrebb&#039;essere che si fosse messo a ricer­<lb></lb>care il metodo, e che fosse riuscito a trovarlo, dop&#039;aver tutt&#039;altrimenti con­<lb></lb>fessato al Cavalieri, ma non se ne conosce da noi il documento, che giustifi­<lb></lb>chi la vantazione datasi innanzi all&#039;illustre Senator parigino, in una sua <lb></lb>lettera, dove sono altre vantazioni, che appariranno dalla Storia non giuste. </s></p><p type="main">

<s>Ma, per non interrompere ora il filo del nostro discorso, diremo come <lb></lb>applicasse il Torricelli il teorema dei momenti a dimostrare la Regola cen­<lb></lb>trobarica. </s>

<s>Non aveva intorno a ciò insegnato altro il Guldino, se non che ogni <lb></lb>solido rotondo è uguale alla figura genitrice, moltiplicata per il viaggio fatto <lb></lb>dal centro di gravità di lei nella sua conversione. </s>

<s>Il Cavalieri fu il primo <lb></lb>a dimostrare la verità di quella Regola universalissima, per via degl&#039;indivi­<lb></lb>sibili, e il Torricelli, come già faceva allora anche il Nardi, pensò che si po­<lb></lb>teva concludere il medesimo dai più elementari principii della Geometria e <lb></lb>della Meccanica, proponendosi intanto questo semplice esempio: </s></p><p type="main">

<s>Si rivolgano co&#039;loro centri di gravità, posti nelle distanze FE, DE (fig. </s>

<s>265) <lb></lb><figure id="id.020.01.2772.1.jpg" xlink:href="020/01/2772/1.jpg"></figure></s></p><p type="caption">

<s>Figura 265.<lb></lb>dall&#039;asse comune AE, i due rettangoli AB, BC: <lb></lb>è manifesto che si descriverà da quello un cilin­<lb></lb>dro solido, e da questo un anello circolare o ci­<lb></lb>lindro forato, la misura del quale sarà, secondo <lb></lb>la Regola guldiniana, BC.2<foreign lang="grc">π</foreign>DE, come sarà <lb></lb>AB.2<foreign lang="grc">π</foreign>FE la misura delll&#039;altro: ond&#039;è che colui, <lb></lb>il quale si proponesse di voler avere i due solidi <lb></lb>uguali, dovrebbe fare AB a BC reciprocamente <lb></lb>come DE a FE. </s>

<s>Ora è appunto ciò che intende <lb></lb>di dimostrare il Torricelli nella seguente, per <lb></lb>accordare la centrobarica alla geometria. </s></p><p type="main">

<s>“ PROPOSITIONE IX. — <emph type="italics"></emph>Si fuerit ut rectan­<lb></lb>gulum AB ad BC, ita reviproce recta DE ad <lb></lb>EF, nempe distantia centri gravitatis rectan­<lb></lb>guli BC, ad distantiam centri gravitatis re­<lb></lb>ctanguli AB ab axe AE, convertaturque utra­<lb></lb>que figura circa axem AE; dico solida aequalia <lb></lb>circumscribi: nempe cylindrum, ex AB factum, aequalem esse solido annu­<lb></lb>lari, sive cylindrico excavato, ex BC facto. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ponatur HL aequalis ipsi CE, et fiat ut LB ad BH, ita BH ad BI, et <lb></lb>compleantur figurae ut in schemate. </s>

<s>Jam spatium AB ad BC est ut recta <lb></lb>DE ad EF, per suppositionem, sive, in duplis, ut CE, EG, simul, ad EG: <pb xlink:href="020/01/2773.jpg" pagenum="398"></pb>nempe ut LB ad BH, sive ut HB ad BI, per constructionem; hoc est ut spa­<lb></lb>tium idem AB ad NI. </s>

<s>Propterea aequalia sunt NI, BC, et eorum latera re­<lb></lb>ciproce, nempe NB ad BG erit ut recta OB ad BI, sive, sumpta BL communi <lb></lb>altitudine, ut rectangulum OBL ad rectangulum IBL, hoc est, ut rectangu­<lb></lb>lum OBL ad quadratum BH. </s>

<s>Et componendo erit NG ad GB ut quadratum <lb></lb>OH ad BH, sive ut circulus ex OH ad circulum ex BH. </s>

<s>Cylindrorum itaque, <lb></lb>factorum ex AG et HC circa axem AE, reciprocantur bases et altitudines; <lb></lb>quare aequales sunt. </s>

<s>Et, dempto communi cylindro facto ex HG, reliqua so­<lb></lb>lida aequalia erunt ” (ibid., T. XXXI, fol. </s>

<s>38). </s></p><p type="main">

<s>Il discorso è chiarissimo, se non che, giunto a concludere la propor­<lb></lb>zione NB:EG=OB.BL:BH2, dalla quale s&#039;ha, componendo, NG:BG= <lb></lb>OB.BL+BH2:BH2, suppone il Torricelli che il terzo termine proporzio­<lb></lb>nale di questa sia uguale al quadrato di OH, come cosa che dall&#039;altra parte <lb></lb>così assai facilmente si dimostra: Abbiamo OB.BL=OB(BH+HL)= <lb></lb>OB.BH+OB.HL. </s>

<s>Dunque OB.BL+BH2=OB.BH+OB.HL+BH2= <lb></lb>BH (OB+BH)+OB.HL=BH.OH+OB.HL. </s>

<s>Ma HL=OH, dunque <lb></lb>OB.BL+BH2=OH (BH+OB)=OH.OH=OH2. </s></p><p type="main">

<s>In questo esempio però le superficie genitrici son regolari, e regolari <lb></lb>son per conseguenza i solidi generati. </s>

<s>Ma la Regola guldiniana si diceva va­<lb></lb>lere per qualunque figura, ciò che rimaneva al Torricelli da dimostrare, spe­<lb></lb>cialmente allora, che si disponeva a ritrovar la misura dei solidi rotondi <lb></lb>descritti dagli spazi cicloidali. </s>

<s>Si conseguiva poi il laborioso intento per via <lb></lb><figure id="id.020.01.2773.1.jpg" xlink:href="020/01/2773/1.jpg"></figure></s></p><p type="caption">

<s>Figura 266.<lb></lb>delle tre proposizioni, che si mettono da noi l&#039;ultime fra <lb></lb>le raccolte qui, per servire alla Storia, e per compilarne <lb></lb>insieme il promesso trattato postumo <emph type="italics"></emph>De momentis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ PROPOSIZIONE X. — <emph type="italics"></emph>Si rectangulum aliquod AB<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>266) <emph type="italics"></emph>libratum, sive suspensum sit super aliqua <lb></lb>recta ED, lateribus parallela, erunt momenta partium <lb></lb>rectanguli ut quadrata laterum homologe: hoc est mo­<lb></lb>mentum figurae AD, ad momentum figurae EB, erit <lb></lb>ut quadratum CD, ad quadratum DB. ”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2773.2.jpg" xlink:href="020/01/2773/2.jpg"></figure></s></p><p type="caption">

<s>Figura 267.</s></p><p type="main">

<s>“ Ponantur enim centra gravitatis par­<lb></lb>tium esse I et O, habebiturque momentum <lb></lb>AD, ad momentum EB, rationem composi­<lb></lb>tam ex ratione magnitudinum, et ex ratione <lb></lb>distantiarum: nempe ex ratione figurae AD <lb></lb>ad EB, sive rectae CD ad DB, et ex ratione <lb></lb>rectae IH, ad HO, vel CD ad DB. </s>

<s>Ergo mo­<lb></lb>mentum AD, ad momentum EB, erit ut qua­<lb></lb>dratum CD, ad quadratum DB ” (ibid., <lb></lb>T. XXXIV, fol. </s>

<s>277). </s></p><p type="main">

<s>“ PROPOSIZIONE XI. — <emph type="italics"></emph>Si quaelibet <lb></lb>figura ABCD<emph.end type="italics"></emph.end> (fig. </s>

<s>267), <emph type="italics"></emph>habens perimetrum <lb></lb>in easdem partes cavum, super aliqua re-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2774.jpg" pagenum="399"></pb><emph type="italics"></emph>cta AD aequilibretur cum rectangulo AE, hoc est aequale momentum ha­<lb></lb>beat tam figura ACD, quam rectangulum AE; dico solida rotunda, quae <lb></lb>circa axem AD fiunt, tam a figura ABCD, quam a rectangulo AE, aequa­<lb></lb>lia esse inter se. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Supponendo che siano GO, NP le distanze dei centri di gravità delle due <lb></lb>figure dall&#039;asse, avere esse figure il momento uguale non vuol dir altro che <lb></lb>essere ABCD.NP=AE.GO, ossia ABCD.2<foreign lang="grc">π</foreign>NP=AE.2<foreign lang="grc">π</foreign>GO, Ora, per <lb></lb>chi ammette la Regola centrobarica, l&#039;uguaglianza fra&#039;due solidi rotondi è <lb></lb>di qui manifesta. </s>

<s>Ma il Torricelli vuole, indipendentemente da ogni altro <lb></lb>principio che non sia geometrico, dimostrare l&#039;uguaglianza dei due solidi ro­<lb></lb>tondi, per confermare la verità della stessa Regola centrobarica. </s></p><p type="main">

<s>“ Nisi enim (cosi egli infatti per la via obliqua procede, perchè la di­<lb></lb>retta era evidente) aequalia sint, erit solidum figurae ABCD vel maius vel <lb></lb>minus cylindri rectanguli AE. Esto, si potest, primum maius, et intra ipsum <lb></lb>describatur figura solida constans ex cylindris aeque altis, ita ut inscripta <lb></lb>etiam figura solida maior sit cylindro facto ex rectangulo AE: quod hoc pos­<lb></lb>sit fieri, et quomodo, notissimum iam est apud Geometras. </s>

<s>Tunc enim erit <lb></lb>cylindrus ex DL, ad cylindrum ex DI, ut quadratum LF ad FI, sive ut mo­<lb></lb>mentum rectanguli DL, ad momentum DI, et hoc verum erit de reliquis <lb></lb>omnibus cylindrulis et rectangulorum momentis, excepto ultimo AM. </s>

<s>Suntque <lb></lb>omnes primi ordinis magnitudines, omnesque tertii aequales, propterea erunt, <lb></lb>per lemma XVIII libelli nostri <emph type="italics"></emph>De dimensione parabolac,<emph.end type="italics"></emph.end> omnes primae, hoc <lb></lb>est omnes cylindri ex MD simul sumpti, ad figuram solidam inscriptam ex <lb></lb>cylindris constantem, ut omnes simul tertiae: hoc est ut momentum collectum <lb></lb>omnium rectangulorum MD ad momentum figurae planae inscriptae. </s>

<s>Sed <lb></lb>omnes cylindri ex AE, ad omnes ex MD, sunt ut momentum omnium rectan­<lb></lb>gulorum AE, ad momentum omnium MD; ergo ex aequo omnes cylindri ex <lb></lb>AE, ad figuram solidam inscriptam, sunt ut momenta figurae planae AE, ad <lb></lb><figure id="id.020.01.2774.1.jpg" xlink:href="020/01/2774/1.jpg"></figure></s></p><p type="caption">

<s>Figura 268.<lb></lb>momentum figurae planae intra ABCD descriptae, hoc <lb></lb>est maiores, quod est contra suppositum. </s>

<s>” </s></p><p type="main">

<s>“ Quando vero solidum rotundum ex ABCD pona­<lb></lb>tur minus cylindro ex AE facto, tunc circumscribenda <lb></lb>erit ipsi solido figura quaedam, ex cylindris aeque altis <lb></lb>constans, ita ut circumscripta figura minor sit eodem <lb></lb>cylindro ex AE facto, quod fieri potest more solito, <lb></lb>eademque demonstratio praecedens adhiberi poterit, <lb></lb>brevior tamen et facilior, siquidem numerus cylindro­<lb></lb>rum et rectangulorum utrimque idem erit, et argu­<lb></lb>mentum illud ex aequo evanescit. </s>

<s>Cum ergo solidum <lb></lb>figurae ABCD non possit esse neque maius neque <lb></lb>minus cylindri rectanguli AE, erit aequale, quod erat <lb></lb>ostendendum ” (ibid., T. XXVI, fol. </s>

<s>41, 42). </s></p><p type="main">

<s>“ PROPOSIZIONE XII. — <emph type="italics"></emph>Solidum rotundum ex qualibet figura plana <lb></lb>ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>268), <emph type="italics"></emph>cuius tamen perimeter sit ad easdem partes cavus, circa<emph.end type="italics"></emph.end><pb xlink:href="020/01/2775.jpg" pagenum="400"></pb><emph type="italics"></emph>axem AC factum, ad cylindrum ex rectangulo quolibet DC circa eumdem <lb></lb>axem factum, rationem habet compositam ex ratione figurae planae ABC, <lb></lb>ad rectangulum DC, et ex ratione distantiae GE ad distantiam GF: nempe <lb></lb>centri gravitatis E et F ab axe communi AC. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ponatur rectangulum AH, cuius centrum I, quod aequale momentum <lb></lb>habeat cum figura plana ABC, eritque figura ABC ad AH reciproce ut IG <lb></lb>ad GE, cum aequiponderent. </s>

<s>Fiat etiam ut IG ad GF, ita EG ad GO. </s>

<s>Jam <lb></lb>ex praeced. </s>

<s>patet quod cylindrus factus ex AH aequalis erit solido rotundo <lb></lb>ex figura ABC. </s>

<s>Propterea solidum ex ABC, ad cylindrum ex DC, erit ut <lb></lb>cylindrus ex AH, ad cylindrum ex DC: nempe ut quadratum IG, ad qua­<lb></lb>dratum GF. </s>

<s>Ratio itaque solidi rotundi ex ABC, ad cylindrum ex DC, com­<lb></lb>ponitur ex ratione rectae IG ad GF, bis sumpta, sive ex ratione rectae IG <lb></lb>ad GF semel, et ex ratione restae EG ad GO, per constructionem. </s>

<s>Ergo so­<lb></lb>lidum ex ABC, ad cylindrum ex DC, erit ut rectangulum IGE ad rectangu­<lb></lb>lum FGO, nempe rationem habebit compositam ex ratione laterum IG ad GO, <lb></lb>vel, ut infra ostendam, figurae planae ABC ad DC, et ex ratione distantiae <lb></lb>EG ad GF, quod erat ostendendum. </s>

<s>” </s></p><p type="main">

<s>“ Quod promisimus ostendemus sic: figura plana ABC ad AH est ut <lb></lb>IG ad GE: sed figura AH ad DC est ut IG ad GF, vel ut EG ad GO; ergo <lb></lb>ex aequo erit figura plana ABC, ad DC, ut recta IG ad GO ” (ibid., fol. </s>

<s>43). </s></p><p type="main">

<s>Queste proposizioni erano, come dicemmo, state preparate dal Torricelli <lb></lb>per applicarle a ritrovare la proporzione che passa tra il solido rotondo, ge­<lb></lb><figure id="id.020.01.2775.1.jpg" xlink:href="020/01/2775/1.jpg"></figure></s></p><p type="caption">

<s>Figura 269.<lb></lb>nerato dallo spazio cicloidale, <lb></lb>e il cilindro del rettangolo <lb></lb>circoscritto, rivolgendosi am­<lb></lb>bedue le figure insieme in­<lb></lb>torno al medesimo asse. </s>

<s>Es­<lb></lb>sendo infatti FE (fig. </s>

<s>269) la <lb></lb>distanza del centro di gra­<lb></lb>vità del rettangolo, e GE quella del centro della Cicloide, come il Torricelli <lb></lb>stesso ha insegnato a ritrovarlo nella proposizione LVI da noi scritta nel ca­<lb></lb>pitolo precedente; dalla passata resulta che il solido rotondo ha verso il cilin­<lb></lb>dro circoscritto la ragion composta delle figure AD, ABC, e delle distanze <lb></lb>EF, EG de&#039;respettivi centri dall&#039;asse della rivoluzione. </s>

<s>Ma perchè di ciò avrà <lb></lb>da intrattenersi altrove la nostra Storia in discorso importante, passeremo <lb></lb>senz&#039;altro a raccogliere dai Manoscritti torricelliani i promessi teoremi di <lb></lb>Meccanica nuova. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quel maraviglioso argomento meccanico di comporre e decomporre le <lb></lb>forze fu dai Matematici francesi, sul finir del secolo XVII, creduto cosa nuova, <lb></lb>perchè il lungo decorrer dei secoli, e la giovanile baldanza dei progressi, <pb xlink:href="020/01/2776.jpg" pagenum="401"></pb>avevano fatto dimenticare e disprezzare le antiche tradizioni della Scienza. </s>

<s><lb></lb>Scaturivano quelle tradizioni dalle fonti aristoteliche, le quali poi vennero a <lb></lb>formare due rivi, sullo scoperto margine dell&#039;un de&#039;quali scendevano ad abbe­<lb></lb>verarsi i Matematici, più seguaci del vero che di questo o di quel Maestro. </s>

<s><lb></lb>L&#039;altro rivo parve disperdersi sotto terra, e ivi dentro, quasi a mantenervi <lb></lb>perpetua la verdura, ricircolare invisibile nel Libro archimedeo delle Spirali. </s>

<s><lb></lb>La XVIII proposizione di questo, e la prima Della dimensione del circolo, <lb></lb>per volerne penetrare il segreto, posero, da che riapparirono al mondo, a <lb></lb>tortura gl&#039;ingegni dei primi interpetri, i quali vi s&#039;affaticarono inutilmente, <lb></lb>perchè, non curando i libri aristotelici, non era a loro venuta a mano la <lb></lb>chiave per aprir quei misteri. </s>

<s>Ond&#039;a ripensar che fra cotesti non curanti era <lb></lb>anche il Torricelli, sarebbe da dir miracoloso il suo ingegno, perch&#039;egli fu, <lb></lb>almeno tra noi, il primo a scoprir che il segreto della XVIII delle Spirali <lb></lb>dipendeva tutto dal principio dei moti composti. </s>

<s>Il miracolo però svanisce <lb></lb>osservando che al difetto delle tradizioni aristoteliche supplirono le galileiane, <lb></lb>benchè non legittime, come più qua vedremo. </s>

<s>Ma per dichiarar meglio i fatti <lb></lb>recenti giova risalir col discorso a quell&#039;alta sfera, dove il contemplativo Si­<lb></lb>racusano ha il suo cielo, se i troppo acuti raggi non c&#039;impediranno la de­<lb></lb>bole vista. </s></p><p type="main">

<s>Da che nacque la Geometria sino al tempo nostro (scriveva Antonio <lb></lb>Nardi in un suo libro rimasto manoscritto, e di cui daremo qualche notizia <lb></lb>in quest&#039;altro capitolo) s&#039;è senza successo cercata la misura precisa del cer­<lb></lb>chio, e del suo perimetro. </s>

<s>È fra cotesti cercatori il più celebre Archimede, <lb></lb>gli sforzi del quale, benchè fossero senza successo in ordine al fine che di­<lb></lb>rettamente s&#039;era prefisso, pur lo condussero per via indiretta a quella geo­<lb></lb>metrica invenzione stupenda, nei più riposti segreti della quale osa ora di <lb></lb>penetrare la nostra Storia. </s></p><p type="main">

<s>Ritornando indietro per XXII secoli, troveremo il nostro Matematico <lb></lb>lungo il solitario lido siracusano sedersi contemplativo innanzi alla figura di <lb></lb>un circolo, ch&#039;egli ha descritto sopra l&#039;arena. </s>

<s>La cura, che al presente lo <lb></lb>preme, è di misurare la precisa lunghezza delle linee rette, dall&#039;ambito delle <lb></lb>quali si racchiuda uno spazio uguale a quello, che dentro sè racchiude l&#039;am­<lb></lb>bito della curva. </s>

<s>Il primo pensiero che lo lusinga è quello d&#039;inscrivere un <lb></lb>poligono regolare, a cui solo mancano, per uguagliarsi al circolo, gli spazi <lb></lb>rimasti presi tra i lati inscritti e gli esterni archi sottesi: spazi, che vanno <lb></lb>sempre più ad assottigliarsi, quanto i lati del poligono son più suddivisi. </s>

<s>Così <lb></lb>la circolar superficie differirebbe di poco da quella di altrettanti triangoli, <lb></lb>appuntati tutti nel centro, e perciò tutti aventi la medesima altezza poco dif­<lb></lb>ferente dal raggio, quanti sono i lati del poligono, che a ciascun triangolo <lb></lb>servon di base. </s>

<s>E qui gli balenò alla mente che si potevano que&#039;tanti trian­<lb></lb>goli ridurre a uno solo, stirando in dirittura il perimetro dello stesso poli­<lb></lb>gono inscritto. </s>

<s>Anzi, perchè non si potrebbe far ciò della medesima circon­<lb></lb>ferenza? </s>

<s>la quale immagina Archimede essere diventata un filo flessibile, con <lb></lb>le due estremità toccantisi in B (fig. </s>

<s>270), l&#039;una delle quali tenuta in B <pb xlink:href="020/01/2777.jpg" pagenum="402"></pb>ferma, prende l&#039;altra, e la svolge, e la stira nella dirittura BC in modo, che <lb></lb>faccia con AB un angolo retto. </s>

<s>Or che rimane altro a fare, se non che ricon­<lb></lb><figure id="id.020.01.2777.1.jpg" xlink:href="020/01/2777/1.jpg"></figure></s></p><p type="caption">

<s>Figura 270.<lb></lb>giungere i punti A, C, per <lb></lb>annunziare questa verità <lb></lb>al mondo maravigliato? <lb></lb><emph type="italics"></emph>Omnis circulus aequalis <lb></lb>est triangulo rectangulo, <lb></lb>cuius radius est par uni <lb></lb>eorum, quae sunt circa <lb></lb>rectum angulum; circumferentia vero basi.<emph.end type="italics"></emph.end> (Opera cit., pag. </s>

<s>128). </s></p><p type="main">

<s>Conseguiva di qui una verità, la quale, benchè non riuscisse ai Geome­<lb></lb>tri nuova, aveva nonostante abito nuovo, e maniera più familiare, perchè, <lb></lb>come sapevasi che il triangolo ha per misura la base moltiplicata per la metà <lb></lb>dell&#039;altezza, così rendevasi ora manifesto che lo spazio circolare è misurato <lb></lb>dal prodotto della circonferenza per la metà del raggio. </s>

<s>Il principale intento <lb></lb>però, con quella meccanica stiratura violenta, non era conseguito, dovendosi, <lb></lb>tra la curvità e la rettitudine, trovar piuttosto la proporzion naturale nei le­<lb></lb>gittimi termini della Geometria. </s>

<s>Parve allora ad Archimede che l&#039;astrusa <lb></lb>questione si risolverebbe, quando, invece di dare il punto C alla AC deter­<lb></lb>minato, fosse ella stessa che lo determinasse sopra la BC, condottavi per una <lb></lb>certa necessità di legge: a ricercar la qual legge, essendo ora rivolti gli studi <lb></lb>del Matematico, dobbiam dire come e quale ei la trovasse. </s></p><p type="main">

<s>L&#039;avevano nell&#039;ardua via preceduto Dinostrato e Nicomede, la quadra­<lb></lb>trice famosa proposta dai quali porse al Nostro occasione di formulare, e di <lb></lb>dimostrare matematicamente le leggi dei moti uniformi. </s>

<s>Essendo una di co­<lb></lb>teste leggi che, dove i tempi sono uguali, le velocità stanno come gli spazi, <lb></lb><figure id="id.020.01.2777.2.jpg" xlink:href="020/01/2777/2.jpg"></figure></s></p><p type="caption">

<s>Figura 271.<lb></lb>ebbe, assai prima di Pappo, ad accorgersi che <lb></lb>nel meccanismo della Quadratrice, inventato ap­<lb></lb>posta per uso della Ciclometria, quel che s&#039;an­<lb></lb>dava cercando già supponevasi noto. </s>

<s>Giovò nono­<lb></lb>stante ad Archimede l&#039;invenzione de&#039;due Geome­<lb></lb>tri, che gli fece rivolgere la mente sopra le curve <lb></lb>descritte dalla mistion di due moti. </s>

<s>Parve a tutti <lb></lb>fra coteste curve sopra ogni altra bellissima quella, <lb></lb>che a testimonianza di Pappo (Collect. </s>

<s>mathem. </s>

<s><lb></lb>cit., pag. </s>

<s>82) aveva già Conone Hamio immagi­<lb></lb>nato descriversi da un punto, il quale, mentre, a <lb></lb>mover dal centro, passa equabilmente tutto intero <lb></lb>il raggio, nel medesimo tempo compia intorno a <lb></lb>esso centro il suo giro. </s></p><p type="main">

<s>Suppongasi, diceva Archimede, che sia in B <lb></lb>(fig. </s>

<s>271) il termine del moto composto, e che <lb></lb>di lì in poi sia il punto mobile lasciato in libertà: avverrà di lui quel che <lb></lb>avviene del sasso, nell&#039;atto di sciogliersi dai legami della fionda, o del fango <pb xlink:href="020/01/2778.jpg" pagenum="403"></pb>schizzato dal carro, nel veloce rivolgersi della ruota: avverrà cioè che i detti <lb></lb>mobili proseguiranno col preconcetto impeto il loro viaggio in linea retta tan­<lb></lb>gente il punto, dove si separarono dalla curva. </s>

<s>Era appunto questa tangente <lb></lb>la linea, che Archimede cercava, perchè, resultando per essa il moto unico <lb></lb>composto dei due, uno proporzionale alla lunghezza del raggio, e l&#039;altro pro­<lb></lb>porzionale alla circonferenza; tirata al raggio AB, o al suo uguale BC, perpen­<lb></lb>dicolare una linea indefinita, basta condur da B una tangente al circolo, o <lb></lb>all&#039;elice, perchè ella intersechi sopra quella linea lasciata indefinita una lun­<lb></lb>ghezza precisamente uguale alla stessa circonferenza. </s>

<s>Erano dall&#039;altra parte <lb></lb>ad Archimede noti i principii, per giunger direttamente a una tal conclusione, <lb></lb>avendo Aristotile insegnato, anzi riconosciuto come cosa per sè manìfesta, <lb></lb><emph type="italics"></emph>quod id, quod secundum diametrum duobus fertur lationibus, necessario <lb></lb>secundum laterum proportionem fertur:<emph.end type="italics"></emph.end> onde il punto, mosso dianzi con <lb></lb>impeto proporzionale al raggio BC, e alla circonferenza rettificata CD, che sono <lb></lb>i lati del triangolo o del mezzo rettangolo; ora ch&#039;egli è libero sarà neces­<lb></lb>sariamente trasportato secondo il diametro BD. </s></p><p type="main">

<s>La nuova bellissima proprietà così scoperta s&#039;annunziava nella XVIII pro­<lb></lb>posizione del libro delle Spirali, ma chi legge ivi il modo com&#039;è dimostrata <lb></lb>direbbe che qualche malevolo abbia sostituita alla vera quest&#039;altra dimostra­<lb></lb>zione, andante per vie oblique e intralciate, quasi per trarre studiosamente <lb></lb>in agguato l&#039;ingenuo lettore. </s>

<s>E avvenne infatti così, perchè i commentatori <lb></lb>e gl&#039;interpetri non riuscirono a indovinare qual si potess&#039;essere la mente <lb></lb>dell&#039;Autore. </s>

<s>Alcuni fra costoro, come il Rivault in Francia, e il nostro <lb></lb>Nardi, crederono che la detta proposizione XVIII fosse ordinata alla quadra­<lb></lb>tura del circolo, non per concluderla direttamente, ma per mostrare che <lb></lb>ell&#039;era possibile. </s>

<s>L&#039;inganno sarebbesi potuto fin d&#039;allora sospettar facilmente, <lb></lb>perchè da nessuna parte del libro delle Spirali trasparisce che tal si fosse <lb></lb>l&#039;intenzion dell&#039;Autore: ma si rende ora manifesto dall&#039;investigata storia <lb></lb>dell&#039;invenzione, la quale, benchè avvenisse propriamente in grazia del cir­<lb></lb>colo, riconosciuta per lui inutile ancella, fu costituita in dignità propria, indi­<lb></lb>pendente e signora. </s>

<s>Rimase in ogni modo, per tanti secoli infino al Torri­<lb></lb>celli, una tale notizia occulta, come occulta rimane tuttavia la ragione, perchè <lb></lb>Archimede, alle facili vie dirette, preferisse le oblique. </s></p><p type="main">

<s>Il Nardi fa in proposito un&#039;osservazione importante, dicendo, in una <lb></lb>delle sue <emph type="italics"></emph>Ricercate geometriche,<emph.end type="italics"></emph.end> che, se le dimostrazioni indirette o all&#039;as­<lb></lb>surdo possono nelle menti generare certezza, non valgono nulladimeno a dare <lb></lb>alle verità dimostrate evidenza. </s>

<s>“ E però, soggiunge, io me ne asterrei sem­<lb></lb>pre, quando potessi per altra via arrivare al proprio fine. </s>

<s>Imperocchè, pochi <lb></lb>penetrando la forza di tali dimostrazioni, dubitasi talvolta del loro fondamento. </s>

<s><lb></lb>Archimede con tutto ciò non solo non s&#039;astenne, ma incredibilmente amò tal <lb></lb>maniera di dimostrare. </s>

<s>Non fu già il primo a servirsene, poichè dal XII degli <lb></lb>Elementi l&#039;apprese, dove materie simili a quelle ch&#039;egli tratta si trattano <lb></lb>nella stessa guisa, sicchè il contrario di quello che scrisse scriver doveva Luca <lb></lb>Valerio, mentre diverso dallo stile di Euclide giudicò quello di Archimede. <pb xlink:href="020/01/2779.jpg" pagenum="404"></pb>Piacque ad Archimede tal metodo, non tanto perchè in pronto non avesse <lb></lb>forse sempre il diretto, e pur volesse far uniforme delle sue dimostrazioni il <lb></lb>metodo; quanto per più mirabili far le sue proposte apparire, il che non così <lb></lb>conseguito avrebbe con l&#039;altro. </s>

<s>” </s></p><p type="main">

<s>Non tutti forse di questo discorso resteranno sodisfatti, ma comunque <lb></lb>sia è tempo di venire al proposito nostro, ch&#039;era quello di narrar come fosse <lb></lb>il Torricelli il primo a scoprire che, procedendo per la via de&#039;moti compo­<lb></lb>sti, s&#039;incontrò Archimede in quell&#039;ammirabile proprietà delle Spirali. </s>

<s>Qual <lb></lb>si fosse l&#039;occasione della scoperta è dal Torricelli stesso detto in una lettera <lb></lb>a Galileo, scritta da Roma il dì 29 Giugno 1641. “ Questi giorni passati, <lb></lb>leggendo un manoscritto d&#039;un amico virtuoso, notai uno sforzo ch&#039;egli fa, <lb></lb>per trovar l&#039;origine della proposizione XVIII della Spirale di Archimede. </s>

<s>Mi <lb></lb>parve che io ne cavassi poco frutto, onde ripensandovi dopo mi venne so­<lb></lb>spetto che quella dottrina pendesse dalla Scienza del moto, e in particolare <lb></lb>da una proposizione di V. S. E., posta nel principio <emph type="italics"></emph>Dei proietti,<emph.end type="italics"></emph.end> la quale <lb></lb>facilmente le sovverrà nelle sue tenebre luminose, per essere un semplicis­<lb></lb>simo triangolo rettangolo, e tratta di questo: che se un mobile camminerà <lb></lb>di due moti ecc. </s>

<s>il momento della velocità sarà in potenza uguale a quelli <lb></lb>due ” (Alb. </s>

<s>X, 423, 24). E con queste parole accompagna al Maestro il Tor­<lb></lb>riselli <emph type="italics"></emph>un suo discorsetto,<emph.end type="italics"></emph.end> in cui veniva applicando il detto teorema dei Pro­<lb></lb>ietti a dimostrar la proposizione, ch&#039;è in ordine la XVIII dell&#039;antico libro <lb></lb>delle Spirali, e la prima di questo nuovo, formulata così nello stesso modo <lb></lb>archimedeo: </s></p><p type="main">

<s>“ PROPOSITIO I. — <emph type="italics"></emph>Si spiralem, ex prima circumvolutione ortam, recta <lb></lb>linea tetigerit in termino Spirae, a puncto vero, quod est in principio <lb></lb>spirae, quaedam ducatur ad angulos rectos ei, quae est principium revo­<lb></lb>lutionis; ducta incidet in tangentem et ipsius, quae pars media erit inter <lb></lb>tangentem et principium spirae, aequalis erit periferiae primi circuli ”<emph.end type="italics"></emph.end><lb></lb>(Opera cit., pag. </s>

<s>377). </s></p><p type="main">

<s>“ Domandiamo che se un mobile sarà trasportato con impeto per alcuna <lb></lb>linea curva, liberato ch&#039;egli sia dal legame, che lo necessitava a camminar <lb></lb>per la curva, seguiti il suo moto per linea retta, non avendo egli nuova oc­<lb></lb>casione di piegare il suo viaggio da alcuna parte. </s>

<s>” </s></p><p type="main">

<s>“ Domandiamo ancora che tal retta sia tangente della linea curva, in <lb></lb>quel punto d&#039;essa, nel quale sarà stato liberato il mobile dalla precedente <lb></lb>curvità. </s>

<s>” </s></p><p type="main">

<s>“ Fu la verità di questa domanda provata già con acuti discorsi dal <lb></lb>signor Galileo, in altre sue opere. </s>

<s>Noi solamente l&#039;esemplificheremo così: <lb></lb>Intendasi in un piano orizontale incavato un canalino, e sia di pianta cir­<lb></lb>colare, o parabolica o spirale. </s>

<s>Se una palla di metallo perfettamente liscia <lb></lb>sarà da qualche impulso spinta nel canaletto, ella trascorrerà in esso, ed obbe­<lb></lb>dirà necessariamente alla piegatura degli argini suoi, sin tanto che durerà <lb></lb>l&#039;incassamento di essi. </s>

<s>Ma subito finito il canale, mentre la palla resti li­<lb></lb>bera sopra il piano orizontale, dimenticata della strada precedente, seguiterà <pb xlink:href="020/01/2780.jpg" pagenum="405"></pb>con il suo impeto a correre, non più per circolo o per elice, ma sì bene per <lb></lb>linea retta. </s>

<s>Sarà poi per appunto tal linea retta tangente alla curva del ca­<lb></lb>naletto in quel punto, dove il mobile si sarà liberato dalla sua piegatura. </s>

<s>” </s></p><p type="main">

<s>“ Definizione: <emph type="italics"></emph>Si recta linea in plano sit ducta, et, quiescente altero <lb></lb>eius termino, aequali velocitate circumferatur, donec restituatur in eum <lb></lb>locum, unde moveri coeperat, et simul cum linea circumlata punctum fe­<lb></lb>ratur aequali velocitate ipsum sibi ipsi, et per se secundum dictam lineam <lb></lb>latum, incipiens a termino quiescente; punctum hoc describit in plano <lb></lb>lineam, quam Spiralem, sive Helicem vocamus ”<emph.end type="italics"></emph.end> (Archim. </s>

<s>ad propos. </s>

<s>XII <lb></lb>De lineis spiralibus). </s></p><p type="main">

<s>“ Stante questo, io dico che quel punto mobile, il quale descrive l&#039;Elice, <lb></lb>averà nel fine della prima revoluzione un momento tale d&#039;impeto, che, se <lb></lb>seguitasse a camminare di moto equabile con quello, trascorrerebbe, in al­<lb></lb>trettanto tempo quanto ne ha speso nella prima conversione, due spazi, uno <lb></lb>però progressivo e l&#039;altro laterale, ed il progressivo sarebbe uguale al semi­<lb></lb>diametro del circolo della prima revoluzione, l&#039;altro, cioè il laterale, sarebbe <lb></lb>uguale alla periferia dello stesso circolo. </s>

<s>” </s></p><p type="main">

<s>“ La prova di questo sarà facile, se noi separeremo con l&#039;astrazione i <lb></lb>due momenti d&#039;impeto l&#039;uno dall&#039;altro. </s>

<s>Immaginiamoci dunque che nel­<lb></lb>l&#039;estremo della prima circolazione il punto mobile seguiti a camminare pro­<lb></lb>gressivamente per il semidiametro, slongato fuori del circolo, ma che intanto <lb></lb>il semidiametro medesimo stia fermo. </s>

<s>Non è dubbio che, in altrettanto tempo <lb></lb>quanto il punto mobile averà speso nella prima conversione, camminerà fuori <lb></lb>del circolo altrettanto spazio progressivo quanto ne averà camminato nella <lb></lb>prima conversione, cioè precisamente un semidiametro del primo circolo. </s>

<s>” </s></p><p type="main">

<s>“ Astragghiamo ora al contrario, ed immaginiamoci che, nella medesima <lb></lb>estremità della prima conversione, il punto mobile si fermi nel semidiame­<lb></lb>tro, e resti senza alcun moto progressivo, ma però che il semidiametro se­<lb></lb>guiti il suo moto conversivo. </s>

<s>È chiaro che il punto mobile camminerà ora <lb></lb>per la periferia del primo circolo, e la scorrerà tutta precisamente in altret­<lb></lb>tanto tempo, quanto egli ne aveva speso nella prima conversione. </s>

<s>” </s></p><p type="main">

<s>“ Parmi abbastanza provato che il punto mobile di Archimede, nella <lb></lb>estremità della prima revoluzione, abbia un tale momento composto di due <lb></lb>momenti, ovvero impeti, cioè uno progressivo e dilungativo dal centro, e <lb></lb>l&#039;altro laterale, sicchè questi due impeti abbiano una particolar proporzione <lb></lb>fra di loro, come quella del semidiametro alla periferia: cioè tale, che nello <lb></lb>stesso tempo, nel quale il punto mobile si avanzerà di moto progressivo, <lb></lb>quanto è lungo un semidiametro; in quello stesso tempo per l&#039;appunto si <lb></lb>spingerà lateralmente per tanto spazio, quanto è lunga la periferia dello stesso <lb></lb>circolo. </s>

<s>” </s></p><p type="main">

<s>“ Si proponga ora la XVIII delle Spirali. </s>

<s>Immaginiamoci che il semi­<lb></lb>diametro AB (nella precedente figura 271), nel quale è il principio e fine <lb></lb>dell&#039;Elice, sia prodotto e prolungato fuori del circolo altrettanto, quanto è <lb></lb>esso semidiametro, sicchè la BC sia uguale alla AB, e per l&#039;estremo punto <pb xlink:href="020/01/2781.jpg" pagenum="406"></pb>della prolungata tirisi una linea CD ad angolo retto con essa, da quella <lb></lb>parte, verso dove camminano l&#039;ultime parti della Spirale. </s>

<s>Supponiamo ora <lb></lb>che il punto mobile di Archimede, subito giunto all&#039;estremità della prima <lb></lb>rivoluzione in B, resti libero dal semidiametro suo deferente, e dalla Spirale <lb></lb>fin là descritta, e seguiti a camminare con tutto l&#039;acquistato momento delli <lb></lb>suoi impeti: conforme alle petizioni premesse, questo punto continuerà la <lb></lb>sua lazione per una linea retta, e questa linea retta sarà tangente alla Spi­<lb></lb>rale. </s>

<s>Dico che questa tangente concorrerà con la perpendicolare da noi ti­<lb></lb>rata CD, e che la porzione CD di detta perpendicolare, intercetta tra il con­<lb></lb>corso della tangente e il semidiametro prolungato, sarà uguale alla periferia. </s>

<s>” </s></p><p type="main">

<s>“ Quanto al primo, che la retta tangente prolungata concorre con CD, <lb></lb>è manifesto: poichè se non concorresse, essendo retta, averebbe dunque il <lb></lb>punto mobile perso l&#039;impeto progressivo, ch&#039;egli in B aveva verso la linea <lb></lb>CD, contro supposizione. </s>

<s>” </s></p><p type="main">

<s>“ Concorra dunque per esempio in D: proverò che la porzione tagliata <lb></lb>CD sia uguale alla periferia del primo circolo. </s>

<s>Poichè, se fosse disuguale, <lb></lb>averebbe il punto mobile compito <emph type="italics"></emph>eodem tempore<emph.end type="italics"></emph.end> per la diagonale BD tanto <lb></lb>di spazio progressivo, quanto è il semidiametro BC, ma non già tanto di la­<lb></lb>terale, quanto la periferia. </s>

<s>E però conseguentemente, quando il punto mo­<lb></lb>bile restò libero in B, non averebbe avuto in sè quel momento, che da noi <lb></lb>si dimostrò avere, cioè di correre <emph type="italics"></emph>eodem tempore<emph.end type="italics"></emph.end> due spazi, uno progres­<lb></lb>sivo quanto il semidiametro, e l&#039;altro laterale quanto la periferia. </s>

<s>” </s></p><p type="main">

<s>“ Che poi il triangolo BCD sia lo stesso che quello di Archimede, seb­<lb></lb>bene contrariamente posto, non ci è difficoltà. </s>

<s>Nello stesso modo si dimostra <lb></lb>la verità delle due seguenti proposizioni, nel maraviglioso libro delle Spirali. </s>

<s><lb></lb>A noi basterà di avere accennato per qual via Archimede possa essere ve­<lb></lb>nuto in cognizione d&#039;una verità tanto astrusa, e per così dire inopinabile, <lb></lb>come la suddetta. </s>

<s>Credo certo che l&#039;Autore a bello studio volesse occultare <lb></lb>ed inviluppare la dimostrazione del teorema a segno tale, che non si potesse <lb></lb>conoscere da che origine glie n&#039;era derivata la cognizione. </s>

<s>Però nel corso <lb></lb>di tanti secoli non fu mai capita evidentemente questa passione della Spi­<lb></lb>rale, non per altro, che per la mancanza della dottrina <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> nota be­<lb></lb>nissimo fino ne&#039;suoi tempi all&#039;Archimede antico, ma pubblicata solamente <lb></lb>ne&#039;nostri dal Moderno. </s>

<s>” </s></p><p type="main">

<s>“ Che i mezzi, dei quali l&#039;Autore si serve nella dimostrazione, siano <lb></lb>per così dire improprii, e che altrettanto appropriati siano quelli, che pro­<lb></lb>cederanno con la dottrina del moto, si può argomentare dalla definizione <lb></lb>stessa, la quale altro non contiene che l&#039;immaginazione di due movimenti, <lb></lb>dalla mistione dei quali resulta poi quel viaggio spirale. </s>

<s>Perciò chi con le <lb></lb>cose poste nella definizione, cioè con la scienza del moto, cercasse di pro­<lb></lb>vare anco i teoremi dipendenti da quella, mi pare ch&#039;egli si servirebbe dei <lb></lb>mezzi propri per arrivare alle conclusioni, e che però produrrebbe scienza <lb></lb>evidente, o come dicono, <emph type="italics"></emph>a priori.<emph.end type="italics"></emph.end> Al contrario, dimostrandosi indirettamente <lb></lb>tali proprietà, con mezzi alieni dalla definizione, oltre l&#039;oscurità e la lun-<pb xlink:href="020/01/2782.jpg" pagenum="407"></pb>ghezza, nella quale s&#039;incorrerà, si produrrà al lettore una scienza in certo <lb></lb>modo accidentale, di tal sorta che egli conoscerà bene di non poter contra­<lb></lb>dire a quella proposta, ma non intenderà già come, e per qual causa, quella <lb></lb>conclusione sia necessariamente vera ” (MSS. Gal. </s>

<s>Disc., T. XXXIV, fol. </s>

<s>201-5). </s></p><p type="main">

<s>Stato con grande attenzione ad ascoltare questo discorso, dettò Galileo <lb></lb>per risposta essergli sembrato maraviglioso il concetto, sovvenuto al Torri­<lb></lb>celli per dimostrare, con tanta facilità e leggiadria, quello, che Archimede, <lb></lb>con strada tanto inospite e travagliosa, investigò nelle sue Spirali: “ strada, <lb></lb>soggiungeva, la quale a me parve sempre tanto astrusa e recondita, che, dove <lb></lb>con lo studio per avventura di cento anni non mi sarei disperato del tutto <lb></lb>di trovare l&#039;altre conclusioni del medesimo Autore, di questa sola non mi <lb></lb>sarei promessa l&#039;invenzione in molti anni, nè in perpetuo. </s>

<s>Ora giudichi V. S. <lb></lb>quale mi sia riuscito il suo gentilissimo trovato ” (Alb. </s>

<s>VII, 366). Delle quali <lb></lb>parole di lode, e della lettera in cui furono scritte, tanto si compiacque il <lb></lb>Torricelli, che, nello scolio alla sua XVIII del primo libro <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> ne volle <lb></lb>fare solenne commemorazione. (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>121). </s></p><p type="main">

<s>Notabilissima cosa è che in quello stesso Scolio, sottilmente esaminando, <lb></lb>si trova una confutazione di quelle dottrine galileiane <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> dimostrate <lb></lb>nel Dialogo dei proietti, che il Torricelli diceva essergli servite di chiave per <lb></lb>aprire il segreto archimedeo delle Spirali. </s>

<s>Il teorema infatti del Maestro inse­<lb></lb>gnava che il moto per l&#039;ipotenusa era uguale in potenza alla somma dei <lb></lb>moti per i cateti, e il Discepolo, nello Scolio citato, par che voglia correg­<lb></lb><figure id="id.020.01.2782.1.jpg" xlink:href="020/01/2782/1.jpg"></figure></s></p><p type="caption">

<s>Figura 272.<lb></lb>gere l&#039;errore, dicendo che, non uguali in potenza, ma <lb></lb>proporzionali ai due lati BD, DC (fig. </s>

<s>272) di un paral­<lb></lb>lelogrammo son le due forze resultanti nell&#039;unica dire­<lb></lb>zione della diagonale. </s>

<s>Ma intorno a ciò, dovendoci tratte­<lb></lb>nere altrove, trapasseremo per ora a dire come, applicando <lb></lb>esso Torricelli i principii dimostrati in quel medesimo Sco­<lb></lb>lio, risolvesse varii problemi di Meccanica nuova, incominciando da quello <lb></lb>delle tangenti. </s></p><p type="main">

<s>L&#039;invenzione di condurre per via meccanica le tangenti alle curve occorse <lb></lb><figure id="id.020.01.2782.2.jpg" xlink:href="020/01/2782/2.jpg"></figure></s></p><p type="caption">

<s>Figura 273.<lb></lb>al Nostro, come anche al Roberval in Francia, a pro­<lb></lb>posito della Spirale, d&#039;onde venne facilmente il pensiero <lb></lb>di farne alla Parabola de&#039;proietti l&#039;applicazione imme­<lb></lb>diata. </s>

<s>Sia AB (fig. </s>

<s>273) la curva descritta, al punto B <lb></lb>della quale si vuol condurre la tangente. </s>

<s>Sarà tale, per <lb></lb>le supposizioni premesse alla precedente proposizione, la <lb></lb>resultante unica de&#039;due impeti, dai quali è sollecitato <lb></lb>il mobile in B, uno progressivo secondo BC, e l&#039;altro <lb></lb>discensivo secondo AC, ond&#039;è che tornerà allora sciolto <lb></lb>il problema, quando sian ritrovate fra quegli stessi due <lb></lb>impeti le proporzioni. </s>

<s>Dovendo in ogni modo essere <lb></lb>ambedue proporzionali agli spazi passati, se il progressivo è rappresentato <lb></lb>da BC, il discensivo sarà, per il primo teorema dimostrato nel terzo dia-<pb xlink:href="020/01/2783.jpg" pagenum="408"></pb>logo di Galileo, rappresentato dal doppio di AC. </s>

<s>Si prolunghi perciò la CB <lb></lb>per altrettanto spazio in D, e si conduca BE, che sia alla AC doppia e pa­<lb></lb>rallela: compiuto il parallelogrammo DE, e tirata la diagonale BF, se si im­<lb></lb>magini essere il mobile in B abbandonato a un tratto dall&#039;impeto violento, <lb></lb>proseguirà naturalmente nella direzione BF il suo viaggio, tangente in B la <lb></lb>curva, da cui s&#039;è sciolto. </s>

<s>È dunque la BF o la sua uguale BG la linea cer­<lb></lb>cata, la quale poteva descriversi con più facile costruzione, duplicando in G <lb></lb>la lunghezza AC dell&#039;asse della parabola, e congiungendo i punti G, B, come <lb></lb>avrebbe insegnato di fare la Geometria. </s></p><p type="main">

<s>Così è sciolto dal Torricelli il problema, quando l&#039;incremento della ve­<lb></lb>locità nel moto discensivo è lineare, e la parabola descritta è perciò la na­<lb></lb>turale, ossia la quadratica. </s>

<s>Che se il detto incremento invece è quadratico, <lb></lb>cubico, biquadratico, ecc., e le parabole, per quel che fu dimostrato nella <lb></lb>XII proposizione della prima parte di questo capitolo, son cubiche, biquadra­<lb></lb>tiche, cuboquadratiche, ecc., immaginando che sia il proietto attratto al cen­<lb></lb>tro con qualunque fra gli assegnati gradi di accelerazione, prosegue il Tor­<lb></lb>ricelli ad applicare il medesimo metodo per condur le tangenti anco a queste <lb></lb>curve paraboliche, che s&#039;ingradano via via. </s>

<s>Qualunque poi sia questo grado, <lb></lb>l&#039;impeto progressivo è sempre rappresentato da un&#039;ordinata simile alla BC, <lb></lb>nella precedente figura, ond&#039;è che tutto si riduce a sapere ne&#039;vari casi qual <lb></lb>sia la proporzione, che ha la BE verso l&#039;AC, perchè così anche sapremo <lb></lb>quali sono i lati del parallelogrammo, dal diametro del quale è designata la <lb></lb>tangente richiesta. </s>

<s>Per dimostrar dunque con qual varia proporzione crescon <lb></lb>gli spazi, passati equabilmente nel medesimo tempo che si passa lo spazio <lb></lb>AC, co&#039;vari gradi di accelerazion discensiva; si premette dal Torricelli per <lb></lb>lemma un teorema, che, fra quelli mandati in Francia, è sotto il numero LI <lb></lb>formulato in questa maniera: </s></p><p type="main">

<s>“ Se sarà il parallelogrammo ABCD (fig. </s>

<s>274), col suo triangolo ACD, <lb></lb>tutte le infinite linee del parallelogrammo, a tutte le infinite linee del trian­<lb></lb><figure id="id.020.01.2783.1.jpg" xlink:href="020/01/2783/1.jpg"></figure></s></p><p type="caption">

<s>Figura 274.<lb></lb>golo, sono duple: ma tutti i quadranti sono tripli di <lb></lb>tutti i quadrati; tutti i cubi sono quadrupli di tutti i <lb></lb>cubi, tutti i quadratoquadrati sono quintupli di tutti <lb></lb>i quadratoquadrati, ecc., in infinitum in tutte le infinite <lb></lb>dignità dell&#039;algebra ” (MSS. Gal. </s>

<s>Disc., T. XXXIII, <lb></lb>fol. </s>

<s>39). I matematici moderni formulerebbero così, <lb></lb>nel loro proprio linguaggio, il medesimo teorema: <emph type="italics"></emph>La <lb></lb>somma di tutte le potenze dell&#039;ordine<emph.end type="italics"></emph.end> n <emph type="italics"></emph>di una quan­<lb></lb>tità, continuamente crescente, è alla somma di altrettante potenze simili <lb></lb>della quantità massima nella proporzione medesima di<emph.end type="italics"></emph.end> 1 <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> n+1. </s></p><p type="main">

<s>Il Frisi, nelle Operette scelte dal Silvestri di Milano (1825, pag. </s>

<s>239), <lb></lb>attribuisce questo teorema al Cavalieri, di cui fa l&#039;elogio: ed è un fatto che <lb></lb>nella quarta Esercitazione geometrica le proposizioni XIX, XX e XXI dimo­<lb></lb>strano verificarsi la cosa annunziata, particolarmente per le potenze lineari, <lb></lb>quadratiche e cubiche. </s>

<s>Nella XXII poi si propone similmente il Cavalieri di <pb xlink:href="020/01/2784.jpg" pagenum="409"></pb>dimostrare che “ Omnia quadratoquadrata parallelogrammi quintupla sunt <lb></lb>omnium quadratoquadratorum trianguli, per diametrum constituti ” (Bono­<lb></lb>niae 1647, pag. </s>

<s>274), ma la via da lui presa non lo porta più oltre, ond&#039;è <lb></lb>vera l&#039;osservazione storica dopo le parole da noi sopra trascritte, così dallo <lb></lb>stesso Torricelli soggiunta: </s></p><p type="main">

<s>“ Questo teorema fu primieramente inventato e proposto da fra Bona­<lb></lb>ventura Cavalieri, ma però da esso non fu ritrovata la dimostrazione uni­<lb></lb>versale, avendo egli presa una strada che, per quanto intendo, cammina solo <lb></lb>infino alli cubi, ovvero alli quadratoquadrati. </s>

<s>Il primo, che abbia dimostrato <lb></lb>il teorema universalmente in tutte le infinite dignità dell&#039;algebra, è stato <lb></lb>monsù Beugrand francese, che ora è morto. </s>

<s>La sua dimostrazione però cam­<lb></lb>mina per via di algebra. </s>

<s>Dopo questo, per quel ch&#039;io sappia, nessuno ha <lb></lb>dimostrato il teorema, fuor che me, e la mia dimostrazione procede senz&#039;al­<lb></lb>gebra, per sola Geometria, e non solo è universalissima, come quella di monsù <lb></lb>Beugrand, ma è infinite volte più universale ” (MSS. Gal. </s>

<s>Disc., T. XXXII, <lb></lb>fol. </s>

<s>40). </s></p><p type="main">

<s>Essendo alieno dal presente nostro proposito, non ci tratterremo qui a <lb></lb>dire in qual modo si dimostrasse dal Torricelli, per sola Geometria, il Teo­<lb></lb>rema, contentandoci più quà di riferire, per i quadrati particolarmente, un <lb></lb>esempio. </s>

<s>Tenendo perciò il detto Teorema, quale fu proposto ai Francesi, per <lb></lb>dimostrato, è da vedere come servisse di lemma a ritrovare quanto della AC, <lb></lb>rappresentata nella figura 273 qui poco addictro, debba essere in qualunque <lb></lb>parabola molteplice la CG, che s&#039;ha da prendere per la misura dell&#039;impeto <lb></lb>verticale, costruendosi sopr&#039;essa, e sopra un&#039;ordinata simile alla BC, il pa­<lb></lb>rallelogrammo delle forze. </s>

<s>Il Torricelli conclude essere la richiesta moltipli­<lb></lb>plicità uguale al grado della parabola, con un discorso che brevemente ri­<lb></lb>ducesi a questo: </s></p><p type="main">

<s>Se le velocità crescono come i semplici tempi, lo spazio, che equabil­<lb></lb>mente è passato dal mobile con l&#039;ultimo grado dell&#039;accelerazione, è doppio, <lb></lb>per il teorema primo di Galileo, di quello stesso passato acceleratamente nel <lb></lb>medesimo tempo, ossia sta come le infinite linee del parallelogrammo ulti­<lb></lb>mamente disegnato, alle infinite linee del triangolo inscritto. </s>

<s>Ma se le velo­<lb></lb>cità crescono come i quadrati dei tempi, lo spazio allo spazio sta come i <lb></lb>quadrati ai quadrati, ossia, per il passato lemma, come tre a uno: se le ve­<lb></lb>locità crescono come i cubi, lo spazio sta allo spazio, come i cubi ai cubi, <lb></lb>ossia come quattro a uno: e in generale, se le velocità crescono come la po­<lb></lb>tenza <emph type="italics"></emph>n<emph.end type="italics"></emph.end> dei tempi, lo spazio allo spazio starà come <emph type="italics"></emph>n+1,<emph.end type="italics"></emph.end> ossia, per le <lb></lb>cose dimostrate, come l&#039;esponente della parabola ad uno. </s>

<s>Di qui la regola <lb></lb>torricelliana <emph type="italics"></emph>Pro tangentibus infinitarum parabolarum,<emph.end type="italics"></emph.end> formulata nell&#039;ap­<lb></lb>presso </s></p><p type="main">

<s>“ PROPOSITIO II. — <emph type="italics"></emph>Esto in parabola quaelibet AB<emph.end type="italics"></emph.end> (nella passata <lb></lb>figura 273), <emph type="italics"></emph>cuius diameter AC, applicata CB: fiat ut esponens ad uni­<lb></lb>tatem, ita CG ad AC. </s>

<s>Dico ductam BG esse tangentem. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nam, quaecumque sit parabola, velocitas puncti mobilis crescit secun-<pb xlink:href="020/01/2785.jpg" pagenum="410"></pb>dum rationem dignitatis parabolae: hoc est, in quadratica, velocitas crescit <lb></lb>in ratione duplicata temporum; in cubica vero crescit in triplicata etc. </s>

<s>Ergo, <lb></lb>per iam dicta, si mobile B, dum est in B, per tangentem procedat, et re­<lb></lb>currat motu aequabili, debet, quo tempore recurrit BC, hoc est tempore ca­<lb></lb>sus, duplam, triplam, quadruplam, ipsius AC recurrere, secundum rationem <lb></lb>dignitatis parabolae. </s>

<s>Ergo tangens pertinet ad G ” (MSS. </s>

<s>Gal Disc., T. XXXI, <lb></lb>fol. </s>

<s>342). </s></p><p type="main">

<s>Il processo di questa dimostrazione si trova ordinatamente disposto nel <lb></lb>manoscritto esemplificato nelle tangenti la parabola cubica, per dimostrar la <lb></lb>via da seguirsi in qualunque altro caso proposto. </s>

<s>Mostreremo ora qual sia <lb></lb>quel processo nelle sue varie parti, cominciando dal seguente lemma, pre­<lb></lb>parato apposta dal Torricelli per dimostrar che gl&#039;infiniti quadrati delle linee, <lb></lb>che compongono il parallelogrammo, son tripli degli infiniti quadrati, fatti <lb></lb>sulle linee del triangolo inscritto. </s></p><p type="main">

<s>Abbiasi un parallelepipedo, quale si rappresenta nella figura 275, e sopra <lb></lb>la medesima base DL si inscriva una piramide appuntata in B, il lato AB <lb></lb>della quale farà nel parallelogrammo CD da diametro. </s>

<s>Siano ambedue i so­<lb></lb><figure id="id.020.01.2785.1.jpg" xlink:href="020/01/2785/1.jpg"></figure></s></p><p type="caption">

<s>Figura 275.<lb></lb>lidi, a qualsivoglia punto della loro altezza, <lb></lb>attraversati da un medesimo piano, che faccia <lb></lb>nel parallelepipedo la sezione FH, e la FI <lb></lb>nella piramide. </s>

<s>È facile dimostrare che il <lb></lb>quadrato della linea EF, la quale è una delle <lb></lb>infinite del parallelogrammo CD, sta al qua­<lb></lb>drato della GF, una delle infinite linee com­<lb></lb>ponenti il triangolo ADB, come la sezione FH <lb></lb>sta alla sezione FI. </s>

<s>Chiamate infatti S, S′ le due <lb></lb>dette sezioni, sarà S:S′=EF.EH:GF.GI. <lb></lb>Ma, per la similitudine de&#039;triangoli, abbiamo <lb></lb>AL:GI=AB:BG=AD:GF, e AL= <lb></lb>EH, AD=EF; dunque EH:GI=EF:GF, e perciò S:S′=EF2:GF2, <lb></lb>come si doveva dimostrare. </s>

<s>Così poi sempre essendo, per qualunque sezione, <lb></lb>si potrà concluderne che gl&#039;infiniti quadrati del parallelogrammo stanno agli <lb></lb>infiniti quadrati del triangolo, come gl&#039;infiniti piani tutti uguali a FH, com­<lb></lb>ponenti il parallelepipedo, stanno agl&#039;infiniti piani simili ad FI, componenti <lb></lb>la Piramide, ossia come tre sta a uno. </s></p><p type="main">

<s>“ Posta la figura come qui (così, attraverso alle parole che trascriviamo, <lb></lb>come attraverso a interrotti globi metallici fa il Torricelli passar la folgore <lb></lb>del suo pensiero) dico che tutti i quadrati del parallelogrammo AB son tri­<lb></lb>pli di tutti quelli del triangolo ADB. Perchè, tirata la EF a caso, dirai: Il <lb></lb>quadrato EF all&#039;FG sta come il piano FH ad FI, et hoc semper, e gli an­<lb></lb>tecedenti sono uguali sempre, dunque etc. </s>

<s>Come il parallelepipedo alla pi­<lb></lb>ramide, così tutti i quadrati del parallelogrammo a tutti i quadrati del trian­<lb></lb>golo, quod etc. </s>

<s>” (ivi, T. XXXV, fol. </s>

<s>13). </s></p><p type="main">

<s>“ PROPOSITIO III. — <emph type="italics"></emph>Gravia descendunt ita ut temporibus aequalibus<emph.end type="italics"></emph.end><pb xlink:href="020/01/2786.jpg" pagenum="411"></pb><emph type="italics"></emph>aequaliter crescant velocitates, ut optime docet Galileus. </s>

<s>Supponamus iam <lb></lb>mobile aliquod descendere ita ut velocitates crescant ut quadrata tempo­<lb></lb>rum. </s>

<s>Ex. </s>

<s>gr. </s>

<s>esto CD<emph.end type="italics"></emph.end> (nella passata figura 274), <emph type="italics"></emph>tempus descensionis, et sit <lb></lb>quadratum AD velocitas, quam habet mobile in fine descensionis. </s>

<s>Peracto <lb></lb>tempore CE, debebit eius velocitas esse ut quadratum EF, nam quadratum <lb></lb>AD et EF sunt ut quadrata temporum CD, CE. </s>

<s>Esto GH spatium peracto <lb></lb>tempore CD, quaeritur: si grave in fine descensionis convertatur horizon­<lb></lb>taliter, cum impetu AD, quodnam spatium conficiet tempore aequali tem­<lb></lb>pori descensus? </s>

<s>Dico triplum. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nam, quando mobile, tempore CD, adhibet tot tantasque velocitates, <lb></lb>quot quantaque sunt omnia quadrata trianguli ACD, peragit spatium GH. </s>

<s><lb></lb>Sed quando eodem tempore adhibet tot tantasque velocitates, quot quantasque <lb></lb>sunt omnia quadrata parallelogrammi BD, triplum spatium conficere debe­<lb></lb>bit, nam, per praecedentem demonstrationem, quadrata quadratorum sunt tri­<lb></lb>pla. </s>

<s>Idem dicas de reliquis algebrae dignitatibus ” (ibid., T. XXXI, fol. </s>

<s>341). </s></p><p type="main">

<s>“ PROPOSITIO IV. — <emph type="italics"></emph>Esto parabola quaelibet ex. </s>

<s>gr. </s>

<s>cubica AB<emph.end type="italics"></emph.end> (nella <lb></lb>figura 273), <emph type="italics"></emph>cuius ad punctum B quaero tangentem. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sumatur CG multiplex ipsius AC iuxta dignitatem parabolae; hoc est <lb></lb>in casu nostro tripla, et, iuncta GB, tangens erit. </s>

<s>Nam punctum mobile B, <lb></lb>quod parabolam describit, in loco B duos impetus habet, alterum horizonta­<lb></lb>lem secundum AH, tangentem, alterum perpendicularem secundum diame­<lb></lb>trum AC, quorum rationem inquiro hoc modo: Impetus horizontalis, tempore <lb></lb>casus, peragit spatium CB: impetus vero perpendicularis, per iam dicta, si <lb></lb>aequabilis conservetur, tempore casus, curreret triplum ipsius casus AC spa­<lb></lb>tium. </s>

<s>Ergo motus, sive directio puncti B, quae componitur ex duobus velo­<lb></lb>citatibus, quae sunt ut BC ad CG, erit iuxta lineam BG. </s>

<s>Propterea BG non <lb></lb>secat curvam, sed tangit. </s>

<s>Quae vero, brevitatis causa, exemplivificavimus in <lb></lb>cubica, dici posset de quacumque parabola ” (ibid., fol. </s>

<s>341). </s></p><p type="main">

<s><emph type="italics"></emph>Haec demonstratio peculiaris est pro parabola<emph.end type="italics"></emph.end> poteva qui ripetere il <lb></lb>Torricelli, com&#039;aveva scritto nello Scolio alla XVIII proposizione del primo <lb></lb>libro <emph type="italics"></emph>De motu gravium<emph.end type="italics"></emph.end> (Op. </s>

<s>geom., P. I, pag. </s>

<s>121), dove, dopo la detta <lb></lb>osservazione, soggiunge ch&#039;egli aveva altresì un metodo di condur le tan­<lb></lb>genti universale per tutte le sezioni coniche, per la Spirale archimedea, e <lb></lb>per simili altre curve; fra le quali anche la Cicloide. </s>

<s>Riguardo alla Spirale <lb></lb>il metodo è stato esposto nella prima proposizione di questa terza parte: ri­<lb></lb>guardo al circolo e all&#039;iperbola, fra le sezioni coniche, nella IX, X e XI della <lb></lb>prima parte del presente capitolo, e tra poco ne vedremo fatta l&#039;applicazione <lb></lb>alla Cicloide. </s>

<s>Ma perchè così fatte invenzioni matematiche del Torricelli com­<lb></lb>pariscono ora, dopo due secoli e mezzo, nella nostra Storia, alla luce; e il <lb></lb>metodo del Roberval, infino dal 1668, era stato in Francia dal Bourdelois <lb></lb>fatto noto; invece di disputare a quale de&#039;due Matematici si convenga il pri­<lb></lb>mato, giova per ora osservare com&#039;ambedue, partiti dai medesimi principii, <lb></lb>procedessero indipendenti per vie diverse, ma che pure s&#039;incontrano spesso <lb></lb>spesso, come quelle che tendevano al medesimo fine. </s></p><pb xlink:href="020/01/2787.jpg" pagenum="412"></pb><p type="main">

<s>Il principio comune al Roberval e al Torricelli è il parallelogrammo <lb></lb>delle forze, proposto e dimostrato così nel sopra citato scolio <emph type="italics"></emph>De motu gra­<lb></lb>vium,<emph.end type="italics"></emph.end> che il latino di lui sembra essere una traduzione del teorema primo <lb></lb><emph type="italics"></emph>Des mouvemens composez:<emph.end type="italics"></emph.end> “ Si un mobile est porté par deux divers mou­<lb></lb>vemens, chacun droit et uniforme, le mouvement composé de ces deux sera <lb></lb>un mouvement droit et uniforme diffèrent de chacun d&#039;eux, mais toutefois <lb></lb>en mesme plan, en sorte que la ligne droite que décrira le mobile sera le <lb></lb>diamètre d&#039;un parallelogramme, les costez duquel seront entre eux comme <lb></lb>les vitesses de ces deux mouvemens, et la vitesse du composé sera à cha­<lb></lb>cun des composans comme le diamètre a chacun des costez ” (Roberval, <lb></lb>Ouvrages a la Haye, 1731). </s></p><p type="main">

<s>Così l&#039;Accademico di Parigi, come quel di Firenze, considerando che le <lb></lb>curvità delle linee geometriche risultano di due moti misti, si proposero di <lb></lb>sceverarli ne&#039;due lati opposti di un parallelogrammo, per aver dalla diago­<lb></lb>nale di lui la direzione delle tangenti. </s>

<s>Sono i detti moti per le curve in ge­<lb></lb>nerale ambedue uniformi, cosicchè i punti mobili, che le descrivono nel me­<lb></lb>desimo tempo, vanno con velocità proporzionali agli spazi. </s>

<s>Ma nella parabola <lb></lb>in particolare, riguardando il punto mobile come un proietto, uno di que&#039;moti <lb></lb>è accelerato, cosicchè, partecipando la linea alle proprietà della Meccanica <lb></lb>naturale, sembrava che ad esser trattata col metodo nuovo, dovesse esser la <lb></lb>prima. </s>

<s>Così fu veramente per il Torricelli, il quale anzi ne derivò un metodo <lb></lb>generalissimo per le infinite parabole, da vincere di gran lunga il Roberval, <lb></lb>che, facendone anch&#039;egli la prima applicazione alla parabola ordinaria, non <lb></lb>la considerò come descritta dalla Natura, ma dall&#039;arte, a quel modo che nella <lb></lb>proposizione XXV del suo secondo libro insegnava il Mydorgio. </s></p><p type="main">

<s>Per le altre curve la differenza fra&#039;due Autori consiste nella varietà degli <lb></lb>esempi, in cui il Francese ha il vantaggio, avendogli estesi a tutte le sezioni <lb></lb>coniche, alla coclea, alla spirale, alla cissoide, alla concoide, alla quadratrice, <lb></lb>alla parabola cartesiana: e consiste nella facilità, nella quale insuperabile è <lb></lb>il Nostro, benchè sia in ambedue simile il processo dimostrativo, specialmente <lb></lb>trattandosi di curve della più facile composizione, qual sarebbe la Cicloide, per <lb></lb>condurre le tangenti alla quale la regola del Torricelli, come ora vedremo, è <lb></lb>conclusa dal Roberval in queste parole: “ Pour trouver la tangente de la Rou­<lb></lb>lette en un point donné, je tire du dit point une touchante au cercle, qui pas­<lb></lb><figure id="id.020.01.2787.1.jpg" xlink:href="020/01/2787/1.jpg"></figure></s></p><p type="caption">

<s>Figura 276.<lb></lb>seroit par le dit point, car chaque point <lb></lb>de cercle se meut selon la touchante de <lb></lb>ce cercle. </s>

<s>Je considere ensuite le mouve­<lb></lb>ment, que nous avons donné a nostre <lb></lb>point, emporté par le diamétre marchant <lb></lb>parallelement a soy mesme. </s>

<s>Tirant du <lb></lb>mesme point la ligne de ce mouvement, si <lb></lb>je paracheve le parallelogramme, qui doit <lb></lb>toujours avoir les quatre costez égaux, <lb></lb>lors que le chemin du point F (fig. </s>

<s>276) <pb xlink:href="020/01/2788.jpg" pagenum="413"></pb>par la circonférence est égal au chemin du diamétre FB par la ligne AF, et <lb></lb>si du mesme point je tire la diagonale, j&#039;ay la touchante de la figure, qui a <lb></lb>eù ces deux mouvemens pour sa composition, scavoir le circolaire et le di­<lb></lb>rect ” (Ouvrages cit., pag. </s>

<s>211). </s></p><p type="main">

<s>La regola è nel <emph type="italics"></emph>Traité des indivisibles<emph.end type="italics"></emph.end> così semplicemente descritta, per­<lb></lb>chè dipende dai principii già dimostrati nelle <emph type="italics"></emph>Observations sur la composi­<lb></lb>tion des mouvemens:<emph.end type="italics"></emph.end> principii per applicare i quali al caso presente si <lb></lb>suppone questo facilissimo lemma: <emph type="italics"></emph>Se abbiasi un cerchio col diametro per­<lb></lb>pendicalarmente eretto all&#039;orizonte, tutte le corde, condotte dalla sommità <lb></lb>di esso diametro a un punto della circonferenza, dividono nel mezzo l&#039;an­<lb></lb>golo fatto dalla tangente e dalla orizontale in quel punto.<emph.end type="italics"></emph.end> Sia IEL, nella <lb></lb>medesima figura, il cerchio come s&#039;è detto, E il punto, da cui vengon ti­<lb></lb>rate la orizontale EM, la tangente EN, e la corda EI: è manifesto che gli <lb></lb>angoli NEI, IEM hanno per misura ciascuno la metà dell&#039;arco IE, o del suo <lb></lb>uguale, e che perciò l&#039;angolo NEM è dalla IE diviso nel mezzo. </s></p><p type="main">

<s>Considerando ora il punto E moventesi nella Cicloide, le EN, EM se­<lb></lb>gnano la direzione dei moti componenti, i quali sono fra loro uguali, avendo <lb></lb>il circolo nel progredire per la FA quel medesimo impeto, che nel rivolgersi <lb></lb>intorno al suo centro. </s>

<s>E di qui è che, presa EM uguale ad EN, e costruito <lb></lb>il parallelogrammo, la diagonale ED, diretta secondo EI, sarà la resultante <lb></lb>del moto, e la tangente richiesta nel dato punto. </s></p><p type="main">

<s>Il metodo meccanico fa esatto riscontro col geometrico, il quale dimo­<lb></lb>stra che la tangente alla Cicloide nel punto E è parallela alla corda GH del <lb></lb>circolo genitore descritto intorno all&#039;asse. <emph type="italics"></emph>Quae Cycloidem contingit recta <lb></lb>est correspondenti circuli genitoris circa Cycloidis axem positi chordae ad <lb></lb>verticem terminatae, parallela.<emph.end type="italics"></emph.end> Il teorema così proposto fu dimostrato, dopo <lb></lb>il Cartesio e il Fermat, dal Wallis, nella prima parte della XXII <emph type="italics"></emph>De centro <lb></lb>gravitatis<emph.end type="italics"></emph.end> (Mechanica, P. II, Londini 1670, pag. </s>

<s>424 e 23), ma il Viviani, <lb></lb>tuttavia giovanetto, aveva in Italia preceduto tutti costoro. </s>

<s>Fece di ciò so­<lb></lb>lenne testimonianza il Torricelli, il quale, in una lettera scritta sul finir del­<lb></lb>l&#039;Ottobre 1643 al Roberval, gli diceva: “ Tangentem Cycloidi iam ostende­<lb></lb>rat mihi Vincentius Vivianus Vivianus florentinus, clarissimi Galilaei alumnus, etiam <lb></lb>nunc adolescens ” (Roberval, ouvrages cit., pag. </s>

<s>360). Alla dimostrazione geo­<lb></lb>metrica del Viviani aggiunse poi il Torricelli la sua meccanica, della quale <lb></lb>non pubblicò che l&#039;enunciato in questa forma: </s></p><p type="main">

<s>“ PROPOSITIO V. — <emph type="italics"></emph>Tangens ad datum quodlibet punctum primariae <lb></lb>Cycloidis ducitur ex puncto sublimiori genitoris circuli, per ipsum datum <lb></lb>punctum transeuntis ”<emph.end type="italics"></emph.end> (Op. </s>

<s>geom. </s>

<s>cit., P. II, pag. </s>

<s>92). </s></p><p type="main">

<s>La dimostrazione però è rimasta fin qui sconosciuta in una lettera, scritta <lb></lb>da Firenze il di 27 Febbraio 1643 a Michelangiolo Ricci. </s>

<s>Ivi anzi è annun­<lb></lb>ziato un altro teorema, del quale non fece il Torricelli allora nessun conto, <lb></lb>benchè ne avrebbe indi potuto dedur per corollario immediato il tautocro­<lb></lb>nismo della Cicloide. </s>

<s>Così, prevenendo l&#039;Huyghens in una scoperta di tanta <lb></lb>importanza, si sarebbe meritata molto maggiore, e più sincera gloria, di <pb xlink:href="020/01/2789.jpg" pagenum="414"></pb>quella che s&#039;aspettava dall&#039;invenzion del modo di ripulire per i Telescopi le <lb></lb>superficie de&#039;vetri, de&#039;quali diceva al Ricci di aver piena la testa. </s>

<s>Quella <lb></lb>torricelliana proposizione poi è tale: </s></p><p type="main">

<s>“ PROPOSITIO VI. — <emph type="italics"></emph>Se una ruota si rivolgerà sopra un piano, le ve­<lb></lb>locità degl&#039;infiniti punti di lei sono come le corde, che da quei punti vanno <lb></lb>al contatto. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sia della ruota DBC (fig. </s>

<s>277) il contatto col piano il punto C, da cui, <lb></lb>come da centro, e con gl&#039;intervalli DC, AC, BC, si descrivano archi infini­<lb></lb>tesimi sulla periferia della ruota: la proposizione è manifesta, considerando <lb></lb><figure id="id.020.01.2789.1.jpg" xlink:href="020/01/2789/1.jpg"></figure></s></p><p type="caption">

<s>Figura 277.<lb></lb>che i punti D, A, B si movono nel medesimo istante come <lb></lb>sopra le circonferenze di tre ruote concentriche, le velocità <lb></lb>delle quali, essendo il moto comune, hanno la medesima pro­<lb></lb>porzione dei raggi. </s></p><p type="main">

<s>Passando ora ad applicare la proposizione alla ruota, che <lb></lb>descrive la Cicloide nella figura 276, qui poco addietro già <lb></lb>disegnata; la velocità dunque del punto G sta alla velocità del <lb></lb>punto E, come GA ad EL, o come GHA ad EKL, ossia come AF a FL: <lb></lb>ond&#039;essendo le velocità come gli spazi, debbono i tempi necessariamente <lb></lb>essere uguali, e perciò la curva cicloidale FEG è <emph type="italics"></emph>tautocrona.<emph.end type="italics"></emph.end> Il documento <lb></lb>di questa, e della precedente proposizione torricelliana, è nella detta lettera <lb></lb>al Ricci, che ora diamo alla luce, lasciate indietro le cose, che non appar­<lb></lb>tengono al soggetto presente: </s></p><p type="main">

<s>“ Dirò a V. S. due bagattelle: Se una ruota si volgerà sopra un piano, <lb></lb>come quella delle carrozze, ovvero la ruzzola, le velocità degl&#039;infiniti punti <lb></lb>della ruota sono come le corde, che da quei punti vanno al contatto: cioè <lb></lb>la velocità di A (nella figura 277) a quella di B, sta come AC alla CB. </s>

<s>Ma <lb></lb>la dirittura dell&#039;impeto è comune a tutti gl&#039;infiniti punti della ruota, poichè <lb></lb>tutti sono diretti verso il punto D. </s>

<s>La ruota però va considerata come una <lb></lb>semplice periferia. </s>

<s>” </s></p><p type="main">

<s>“ Di qui nasce che la tangente EI della Cicloide, nella figura 276, passa <lb></lb>sempre per il punto sublime I del cerchio, che passa per il contatto E. </s>

<s>Di­<lb></lb>scorro così: il punto E <emph type="italics"></emph>duplici latione fertur, nempe directa aequidistan­<lb></lb>ter rectae FL, per rectam EM, et circulariter per periferiam, hoc est per <lb></lb>tangentem EN, suntque impetus huiusmodi lationum, sive ipsae lationes, <lb></lb>aequales. </s>

<s>Ergo neutri illarum obediet, sed aequaliter feretur inter utram-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2789.2.jpg" xlink:href="020/01/2789/2.jpg"></figure></s></p><p type="caption">

<s>Figura 278.<lb></lb><emph type="italics"></emph>que directionem, nempe per lineam EI, quae bifa­<lb></lb>riam secat angulum NEM.<emph.end type="italics"></emph.end> Mi scusi per grazia, perchè <lb></lb>ho la testa piena di vetri ” (MSS. Gal. </s>

<s>Disc., T. XL, <lb></lb>fol. </s>

<s>88). </s></p><p type="main">

<s>“ PROPOSITIO VII. — <emph type="italics"></emph>Sia AB<emph.end type="italics"></emph.end> (fig. </s>

<s>278) <emph type="italics"></emph>un muro <lb></lb>eretto al piano dell&#039;orizonte BC, e sia AC una trave <lb></lb>appoggiata al muro: cercasi la proporzione del mo­<lb></lb>mento, che averanno queste due forze, e dico che la forza A, alla C, sarà <lb></lb>come la linea CB alla BA, permutatamente prese.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2790.jpg" pagenum="415"></pb><p type="main">

<s>Questa medesima proposizione fu da noi trascritta nel Tomo quarto a <lb></lb>pag. </s>

<s>64, dove la dimostrazione, rimasta nel manoscritto torricelliano inter­<lb></lb>rotta, si vede supplita dal Viviani, dietro que&#039;cenni, che il Torricelli stesso, <lb></lb>in una lettera del dì 20 Gennaio 1643, soggiungeva così a M. A. Ricci, dopo <lb></lb>avergli annunziata la scoperta: “ La dimostrazione non l&#039;ho scritta, ma pende <lb></lb>dalla velocità, poichè movendosi la stanga AC radente le due linee dell&#039;an­<lb></lb>golo retto ABC, la velocità, nella quale sta costituito il punto A, alla velo­<lb></lb>cità, nella quale sta costituito il punto C, sta come BC alla BA ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>82). </s></p><p type="main">

<s>Benchè dunque sia certo che il Torricelli intendeva di dimostrare dai <lb></lb>principii statici la verità sopra annunziata, abbiamo voluto nonostante racco­<lb></lb>gliere la proposizione fra le altre di Meccanica nuova, perchè dette ai Mate­<lb></lb>matici, sul cominciare di questo secolo, occasione d&#039;applicarvi il principio <lb></lb>delle forze composte. </s>

<s>L&#039;applicazione però, secondo i varii Autori, fu varia, e <lb></lb>il problema, proposto già da Leonardo da Vinci, e rinnovellato dal discepolo <lb></lb>di Galileo, ebbe, per le complicanze del nodo, maggiori di quel che non par­<lb></lb>rebbe, soluzioni diverse. </s>

<s>Sembra nonostante a noi la più razionale quella, <lb></lb>che ne dette Giuseppe Venturoli, desumendola dalle leggi di un sistema ri­<lb></lb>gido in equilibrio, sollecitato da forze parallele. (Elementi di Meccanica, Na­<lb></lb>poli 1852, pag. </s>

<s>40). </s></p><p type="main">

<s>Rappresentino la verticale AC (fig. </s>

<s>279) e la orizzontale CB il profilo <lb></lb>del muro, e del pavimento, a cui s&#039;appoggia una trave con le sue testate <lb></lb><figure id="id.020.01.2790.1.jpg" xlink:href="020/01/2790/1.jpg"></figure></s></p><p type="caption">

<s>Figura 279.<lb></lb>A, B. </s>

<s>Sia in G raccolto il peso P di <lb></lb>essa trave e, fatta per G passare la ver­<lb></lb>ticale TP, limitata in P dalla orizontale <lb></lb>MP, intendasi in P trasportato il peso, di <lb></lb>cui la forza PQ sia decomposta nelle due <lb></lb>EP, PD, applicate in AM, BN ai due <lb></lb>punti d&#039;appoggio. </s>

<s>Si vuol sapere in qual <lb></lb>proporzione debbano stare queste forze <lb></lb>tra loro, e rispetto al peso, perchè la <lb></lb>trave rimanga in equilibrio. </s></p><p type="main">

<s>Si decomponga nuovamente la BN <lb></lb>nelle due BX, BZ, e rimossi gli ap­<lb></lb>poggi sieno le forze applicate in direzioni contrarie, così cioè che AM tiri <lb></lb>da sinistra a destra, BX da destra a sinistra, e BZ di sotto in su. </s>

<s>Le solle­<lb></lb>citanti al moto orizontalmente il sistema sono le AM, BX, mentre le P, BZ <lb></lb>lo spingono verticalmente. </s>

<s>A farlo poi rotare intorno al centro C, prese le <lb></lb>AC, CB per gli assi, tendono da sinistra a destra le forze AM, P, con mo­<lb></lb>menti uguali a AM.CA, P.CT: e a farla rotare da destra a sinistra tende <lb></lb>la forza BZ con momento uguale a BZ.BC. </s></p><p type="main">

<s>Perchè dunque tutto rimanga in equilibrio, dovranno aversi le tre se­<lb></lb>guenti equazioni: 1.a AM—BX=O; 2.a P—BZ=O; 3.a P.CT+ <lb></lb>AM.CA—BZ.BC=O. </s>

<s>Dalla prima delle quali si apprende che s&#039;ugua-<pb xlink:href="020/01/2791.jpg" pagenum="416"></pb>gliano le due contrarie spinte fatte orizontalmente: e dalla seconda, che il <lb></lb>peso della trave preme con tutto sè il pavimento. </s>

<s>Dalla terza poi, sostitui­<lb></lb>tovi P in luogo di BZ, e risoluta rispetto ad AM, avremo AM=BX= <lb></lb>P.BT/CA.E perchè, chiamato <foreign lang="grc">φ</foreign> l&#039;angolo BAC, BT=BG sen <foreign lang="grc">φ</foreign>, AC=AB cos <foreign lang="grc">φ</foreign>; <lb></lb>sarà AM=BX=P.BG/AB tang <foreign lang="grc">φ</foreign>, e ciò vuol dire che la spinta orizontale <lb></lb>sta al peso della trave, come la distanza del centro di gravità di lei dal pa­<lb></lb>vimento, moltiplicata per la tangente dell&#039;angolo dell&#039;inclinazione sul muro, <lb></lb>sta alla total lunghezza della stessa trave. </s></p><p type="main">

<s>Il Torricelli nonostante, avendo a modo suo risoluto il problema, inten­<lb></lb>deva d&#039;applicarlo a simili altri problemi di Meccanica nuova, e principal­<lb></lb>mente a quella, che qui segue in ordine: </s></p><p type="main">

<s>“ PROPOSITIO VIII. — <emph type="italics"></emph>Si cerca per che causa un piccol cerchio di ferro, <lb></lb>che fascia una colonna fessa, come nel cortile del palazzo de&#039;Medici, e<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2791.1.jpg" xlink:href="020/01/2791/1.jpg"></figure></s></p><p type="caption">

<s>Figura 280.<lb></lb><emph type="italics"></emph>sotto le logge degli Ufizi, sia bastante a tenere quella co­<lb></lb>lonna che non s&#039;apra, e per conseguenza a reggere quella <lb></lb>macchina, acciò non rovini. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia la colonna fessa AB (fig. </s>

<s>280) quale si consideri in <lb></lb>quattro parti divisa. </s>

<s>Certo è che, premendo il peso della fab­<lb></lb>brica soprapposta in AC, la colonna procurerà di slargarsi in <lb></lb>EF, non potendo AC discendere, se nelle parti di mezzo la <lb></lb>fessura della colonna non si slarga. </s>

<s>Ora io dico che, ovviandosi <lb></lb>presto al disordine, ogni minima forza basterà per fermarla, <lb></lb>e che, lasciando fare l&#039;apertura grande, ci vorrà una volta forza eguale al <lb></lb>peso, e può anche essere che una volta vi si ricerchi forza mille volte mag­<lb></lb>giore del peso. </s>

<s>” </s></p><p type="main">

<s>“ Sia la fessura ABCD (fig. </s>

<s>281), l&#039;apertura o larghezza della quale sia <lb></lb>BD, e linea perpendicolare sia AC. </s>

<s>Per le cose dimostrate nella precedente <lb></lb><figure id="id.020.01.2791.2.jpg" xlink:href="020/01/2791/2.jpg"></figure></s></p><p type="caption">

<s>Figura 281.<lb></lb>ponendo un peso in A, ed una potenza uguale in D, il <lb></lb>momento della potenza, a quello del peso, sta come la <lb></lb>AO alla OD. </s>

<s>Per far dunque che i momenti siano uguali, <lb></lb>pongasi una potenza, che al peso sia come DO ad AO. </s>

<s><lb></lb>Così poi diremo in questo modo: la potenza piccola alla <lb></lb>grande sta come DO ad AO, ma la grande al peso stava <lb></lb>come AO a DO; ergo ex aequo la potenza piccola è uguale <lb></lb>al peso. </s>

<s>” </s></p><p type="main">

<s>“ Si cava dunque che, per tenere unite le colonne, <lb></lb>che non s&#039;aprano maggiormente, ci vuole una forza, la quale al peso abbia <lb></lb>la proporzione, che ha il diametro della figura BD, alla perpendicolare AC ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XXXVII, fol. </s>

<s>78). </s></p><p type="main">

<s>Sembra che la proposizione sia confermata, anche applicandovi diretta­<lb></lb>mente la regola del parallelogrammo, dalla diagonale AC del quale sia rappre­<lb></lb>sentato il peso. </s>

<s>Nella figura ABCD, per far l&#039;equilibrio, ci vogliono due forze <pb xlink:href="020/01/2792.jpg" pagenum="417"></pb>uguali a DA, AB, o ad AB, BC; ma, se la fessura s&#039;allarga in AECF, le <lb></lb>forze necessarie a resistere son cresciute come AE, AF, o come AE, EC, e <lb></lb>quelle prime stanno a queste, come la diagonale ED sta ad EF. </s>

<s>Tali insomma, <lb></lb>quali noi gli abbiamo nel fertile campo dissepolti, sono i germi di Mecca­<lb></lb>nica nuova che, spuntati appena nella mente del Torricelli, risecchirono mi­<lb></lb>seramente sotto il gelo della morte. </s></p><pb xlink:href="020/01/2793.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Di altri Discepoli di Galileo <lb></lb>promotori della Scienza del moto<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. — Di Antonio Nardi, e particolarmente delle sue <emph type="italics"></emph>Ricercate geometriche:<emph.end type="italics"></emph.end> di Michelangiolo Ricci. </s>

<s><lb></lb>II. </s>

<s>Digressione intorno alla Cicloide: delle proprietà di leì scoperte dal Roberval, e da altri <lb></lb>Matematici francesi. </s>

<s>— III. </s>

<s>Di ciò che dimostrarono intorno alla Cicloide il Nardi, il Torricelli <lb></lb>e il Ricci. </s>

<s>— IV. </s>

<s>Delle controversie insorte fra il Robervai e il Torricelli, prima intorno alla <lb></lb>quadratura, poi intorno al baricentro della Cicloide. </s>

<s>— V. </s>

<s>Di ciò che a illustrare, a compiere <lb></lb>e a divulgare le dottrine galileiane del moto operarono il Cavalieri, il Borelli e il Viviani. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>A solo sentirsi annunziare il soggetto del presente discorso non può, <lb></lb>chiunque legge, non precorrere con la mente a pensare ai nomi del Cava­<lb></lb>lieri, del Viviani e del Borelli, che son, per le opere e per la fama, i più <lb></lb>conosciuti dopo il Torricelli fra i discepoli di Galileo. </s>

<s>La cosa è per sè tanto <lb></lb>naturale, che null&#039;altro s&#039;indovinerebbe con maggiore certezza, ma benchè <lb></lb>sia un fatto che debbono i tre ora commemorati entrare nell&#039;argomento, non <lb></lb>si faranno però i primi, essendo la notizia di essi men desiderata di quella <lb></lb>di altri loro colleghi, non punto men valorosi, e rimasti al pubblico scono­<lb></lb>sciuti. </s></p><p type="main">

<s>Di Antonio Nardi aretino non è stato fin qui oscuro fra i Matematici il <lb></lb>nome, per essersi scolpito in fronte ai libri torricelliani Dei solidi sferali, ma <lb></lb>chi ivi legge, con riconoscenza di discepolo, commemorato l&#039;acutissimo scru­<lb></lb>tatore dei libri di Archimede non può non sentirsi nascere il desiderio di <lb></lb>conoscere, o di avere almeno un saggio delle opere matematiche di colui, <lb></lb>che ispirò e dette impulso alla maggiore opera matematica del Torricelli. </s>

<s>A <pb xlink:href="020/01/2794.jpg" pagenum="419"></pb>sodisfare al qual desiderio ha conferito in parte la nostra Storia a varie occa­<lb></lb>sioni, e particolarmente discorrendo dei Baricentri, dove si ordinarono dai <lb></lb>manoscritti le proposizioni dimostrate dal Nardi, per confermare geometrica­<lb></lb>mente la verità della regola meccanica del Guldino. </s>

<s>Altra occasione, per so­<lb></lb>disfare ai desiderosi di conoscere un tale uomo, ci si porgeva ora, che tro­<lb></lb>vavasi esso Nardi aver precorso, e in ogni modo concorso col Torricelli nel­<lb></lb>l&#039;invenzione dei centri di gravità di alcune figure, o rimasti ai Matematici <lb></lb>fin allora ignoti, o dimostrati con troppo lunghi e faticosi processi. </s>

<s>Vorremmo <lb></lb>senza indugio dar opera a raccogliere e ordinare così fatti teoremi baricen­<lb></lb>trici, se non si credesse opportuno il premettere alcune notizie intorno ai <lb></lb>manoscritti, da cui sono stati raccolti. </s></p><p type="main">

<s>Questi manoscritti son le <emph type="italics"></emph>Scene accademiche,<emph.end type="italics"></emph.end> penseranno i Lettori, se <lb></lb>pur ce ne sono, che dal nostro Discorso preliminare fin qui ci hanno tenuto <lb></lb>dietro, e ai quali è noto essere quelle Scene, negli argomenti i più varii, <lb></lb>così disordinate, da parere un caos filosofico, piuttosto che un libro. </s>

<s>Per tale <lb></lb>anzi si riconobbe, e con tal nome si chiamò l&#039;opera dal suo proprio Autore, <lb></lb>il quale così ripensava fra sè, e notava in una pagina, giunto a scrivere <lb></lb>mezzo il grosso volume: </s></p><p type="main">

<s>“ Oh quanto confuse sono queste accademiche Scene! Parrebbero l&#039;idea <lb></lb>della confusione, se idea la confusione avesse. </s>

<s>Ma se ordinate fossino non <lb></lb>sarebbero formate da un confuso. </s>

<s>Io per me stimo che siano un caos filo­<lb></lb>sofico, il quale facilmente ordinar si possa, purchè la mente gli soprarrivi. </s>

<s><lb></lb>Certo che mi sono abbattuto in un luogo loro, d&#039;onde non affatto senz&#039;or­<lb></lb>dine sembravano. </s>

<s>Sovviemmi che, quand&#039;era giovanetto, soleva per ischerzo <lb></lb>fingere alcuni disegni che a caso delineati, fuorchè da un sol punto, sem­<lb></lb>bravano. </s>

<s>Lo stesso quasi parmi che in questi componimenti accada, di cui <lb></lb>la forma un filosofico quasi e tetracordo sistema mi rappresenta. </s>

<s>La prima <lb></lb>corda è matematica, sopra la quale ricercansi teorie spettanti al numero, mi­<lb></lb>sura, momento, movimento ed apparenza delle cose: qual punto della Filosofia <lb></lb>con nome di Arismetrica, Geometria, Meccanica, Astronomia e con altri an­<lb></lb>cora si addita. </s>

<s>Quindi la seconda corda segue, che più al concreto ed all&#039;in­<lb></lb>timo delle cose corporee pertiene, nella quale ricercasi la natura dei veraci <lb></lb>corpi, e i loro principii e passioni. </s>

<s>Nella stessa maniera si arriva alle parti­<lb></lb>colari nature, incominciando dalle più comuni e men degne, insino all&#039;anima <lb></lb>ragionevole si giunge. </s>

<s>Qui s&#039;attacca la corda metafisica, ove dell&#039;ente gene­<lb></lb>ralmente e de&#039;suoi principii, e del supremo di ogni Ente, con gli aiuti della <lb></lb>Natura e della Grazia, discorresi. </s>

<s>L&#039;ultima corda aggiunta è varia di criti­<lb></lb>che, per lo più, e morali materie ” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>745). </s></p><p type="main">

<s>Di qui si comprende come non fossero le Scene scritte per stamparsi a <lb></lb>quel modo, ma per raccogliervi i materiali, da ordinarsi in un libro, dove <lb></lb>si ricercherebbero cose di matematica, di fisica, di metafisica e di morale, <lb></lb>quasi riducendo la verità nèll&#039;armonia di un tetracordo. </s>

<s>A raccogliere e a <lb></lb>far copiare, tra così fatte <emph type="italics"></emph>Ricercate,<emph.end type="italics"></emph.end> le matematiche, per darsi alle stampe, <lb></lb>attendeva il Nardi nel 1641, come si rileva dalle seguenti parole scritte dal <pb xlink:href="020/01/2795.jpg" pagenum="420"></pb>Cavalieri in una lettera del dì primo Novembre di quell&#039;anno a Giann&#039;An­<lb></lb>tonio Rocca: “ Gli dò poi nuova che mi scrive il Torricelli trovarsi di stanza <lb></lb>dal sig. </s>

<s>Galileo, ed aspettare in Firenze il sig. </s>

<s>Antonio Nardi, credo genti­<lb></lb>luomo aretino, che ha da stampare un libro di Geometria, nel quale pre­<lb></lb>tende con modi nuovi di mostrare tutte le cose di Archimede, per via degli <lb></lb>indivisibili, quale dice avere fatto una grandissima pratica sopra la mia Geo­<lb></lb>metria ” (Lettere a G. A. Rocca, Modena 1785, pag. </s>

<s>268). </s></p><p type="main">

<s>Il proposito di venire a Firenze, per aver consiglio col Torricelli, e di­<lb></lb>videre con lui le cure della stampa, non sembra fosse dal Nardi mandato ad <lb></lb>effetto. </s>

<s>Un anno e mezzo dopo era tuttavia in Arezzo, dove, scriveva il Tor­<lb></lb>ricelli stesso al Cavalieri, attendeva “ a far copiare il suo libro geometrico per <lb></lb>mandarlo qua a me, acciò io lo faccia pervenire anco in mano di V. P. per <lb></lb>sentire una parola del suo purgatissimo giudizio ” (MSS. Gal. </s>

<s>Disc., T. XL, <lb></lb>fol. </s>

<s>127). A mezzo l&#039;anno 1645, avendo già il Nardi messo in ordine la parte <lb></lb>metafisica del suo libro, attendeva alla fisica, ma gli rimaneva tuttavia da tor­<lb></lb>nare sopra alla matematica, come si raccoglie da queste parole, che M. A. </s>

<s>Ricci <lb></lb>scriveva al Torricelli: “ Il sig. </s>

<s>Antonio Nardi fatica intorno l&#039;opera sua. </s>

<s>Ha <lb></lb>dato perfezione alla parte metafisica, ora è d&#039;intorno alla fisica, e poi rive­<lb></lb>drà la matematica, il che non potrà seguir prima di dieci mesi, ovvero un <lb></lb>anno. </s>

<s>E mi duole che tardi tanto ad uscire in luce Opera, che si spera debba <lb></lb>essere doviziosa di tutte le speculazioni, cioè pasto per ogni sorta di profes­<lb></lb>sori di Scienza ” (ivi, T. XLII, fol. </s>

<s>121). </s></p><p type="main">

<s>Benchè fossero le Ricercate matematiche state a copiarsi le prime, dice <lb></lb>nonostante il Ricci che volle tornar l&#039;Autore in dietro a rivederle, perchè ci <lb></lb>aveva certe cose da aggiungere, alcune delle quali, come vedremo, importan­<lb></lb>tissime. </s>

<s>Passarono del resto i dieci mesi e l&#039;anno, e le durate fatiche, qua­<lb></lb>lunque se ne fosse la ragione, riuscirono infruttuose. </s>

<s>La copia delle Ricer­<lb></lb>cate geometriche, con correzioni e postille autografe, rimase per due secoli <lb></lb>e mezzo dimenticata in Arezzo, dove si ritrovarono in questi ultimi giorni <lb></lb>alcuni pochi fascicoli mutilati e dispersi, de&#039;quali (non sapremmo con qual <lb></lb>consiglio, se non fu quello di mantenere fra le sventurate carte la dispersione) <lb></lb>parte fu donato da un Aretino alla Biblioteca nazionale di Firenze, e parte a <lb></lb>quella di Roma. </s>

<s>Nè ha perciò l&#039;una città nulla da invidiare o da reclamare <lb></lb>all&#039;altra, la quale possiede, nella raccolta de&#039;manoscritti galileiani, le Scene <lb></lb>intere, inclusevi le Ricercate, no nei loro materiali solamente, ma nell&#039;or­<lb></lb>dine, secondo il quale volevano essere disposti dallo stesso Autore. </s>

<s>È dunque <lb></lb>poco da lamentar la perdita, e meno da esultar per l&#039;acquisto, benchè l&#039;aver <lb></lb>noi potuto consultare e collazionar con le Scene i manoscritti, donati alle due <lb></lb>dette Biblioteche, abbia conferito a darci alcuni utilissimi documenti di sto­<lb></lb>ria, come sarebbe per esempio quel che riguarda gli studi fatti dal Nardi <lb></lb>intorno alla Cicloide. </s>

<s>Così, dall&#039;aver letto nella prima copia delle Ricercate <lb></lb>geometriche essersi ritrovata la misura dello spazio cicloidale, per sola mec­<lb></lb>canica esperienza; abbiamo potuto ragionevolmente argomentare che, dopo <lb></lb>il 1641, attese il Nardi a dimostrare geometricamente le proprietà della curva. </s></p><pb xlink:href="020/01/2796.jpg" pagenum="421"></pb><p type="main">

<s>Vedremo più qua l&#039;importanza di una tale notizia: ora è da tornar sopra <lb></lb>quello, che si diceva, dell&#039;ordine delle materie da trattarsi nelle Ricercate, il <lb></lb>quale ordine resulta dagl&#039;indici particolari, scritti dal Nardi stesso per cia­<lb></lb>scun sistema del suo Tetracordo. </s>

<s>Quel che a noi nel presente proposito più <lb></lb>importa è l&#039;indice delle Ricercate matematiche, le quali sono otto: le prime <lb></lb>tre ordinate a riformare le dimostrazioni di Euclide, le quattro seguenti a <lb></lb>dimostrar le ragioni del curvo e del retto, con altro metodo da quello ar­<lb></lb>chimedeo, e l&#039;ultima intorno alla dottrina meccanica dei momenti e dei mo­<lb></lb>vimenti, alla quale propriamente si riferisce il soggetto del nostro discorso. </s></p><p type="main">

<s>Di questa ottava Ricercata matematica l&#039;indice delle materie è così scritto: <lb></lb><emph type="italics"></emph>I. </s>

<s>Divisione delle Meccaniche. </s>

<s>— II. </s>

<s>Se Archimede supponga un falso mec­<lb></lb>canico nella quadratura parabolica. </s>

<s>— III. </s>

<s>Centro di gravità di alcuni <lb></lb>rettilinei, mostrati diversamente dal metodo di Archimede. </s>

<s>— IV. </s>

<s>Centro <lb></lb>di gravità dei triangoli e dei coni. </s>

<s>— V. </s>

<s>Centro di gravità d&#039;un frusto <lb></lb>parabolico. </s>

<s>— VI. </s>

<s>Centro di gravità del settore di cerchio. </s>

<s>— VII. </s>

<s>Cen­<lb></lb>tro di gravità d&#039;un settore di sfera. </s>

<s>— VIII. </s>

<s>Centro della potenza, o di <lb></lb>gravità, della Cicloide nostra. </s>

<s>— IX. </s>

<s>Teorema generale meccanico. </s>

<s>— <lb></lb>X. </s>

<s>Forza della percossa. </s>

<s>— XI. </s>

<s>Di un principio meccanico di Galileo. </s>

<s>— <lb></lb>XII. </s>

<s>Varie osservazioni meccaniche. </s>

<s>— XIII. </s>

<s>Della scienza esatta del moto. <lb></lb></s>

<s>— XIV. </s>

<s>Parere del Galilei intorno al moto dei grari cadenti.<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s><lb></lb>Disc., T. XX, pag. </s>

<s>745). </s></p><p type="main">

<s>Intorno a varie, fra queste così indicate proposizioni, abbiamo avuto più <lb></lb>qua e più là occasione di riferire i pensieri del Nardi, cosicchè non ci ri­<lb></lb>mane altro a dire, che del metodo come furono mostrati dal Nostro i cen­<lb></lb>tri di gravità delle varie figure, diversamente da Archimede fra gli antichi, <lb></lb>e dal Torricelli fra i matematici moderni. </s>

<s>Sarà il trattatello da noi distinto <lb></lb>in due parti, secondo che l&#039;invenzione del baricentrico ha per soggetto le <lb></lb>figure ordinarie, o quella particolarmente inventata dal Nardi, e che perciò <lb></lb>designeremo col nome di <emph type="italics"></emph>Cicloide nardiana.<emph.end type="italics"></emph.end> La prima di queste parti si <lb></lb><figure id="id.020.01.2796.1.jpg" xlink:href="020/01/2796/1.jpg"></figure></s></p><p type="caption">

<s>Figura 282.<lb></lb>compone dei seguenti XII teoremi, da noi rac­<lb></lb>colti, e qui appresso ordinati: </s></p><p type="main">

<s>“ TEOREMA I. — <emph type="italics"></emph>Nel triangolo VCQ<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>282) <emph type="italics"></emph>dalla cima C cada CO nella base <lb></lb>VQ, dividendola ugualmente: dico che il <lb></lb>centro dì gravità di esso triangolo è nel <lb></lb>punto X, il quale divide CO in modo, che CX <lb></lb>è doppio di XO. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Dividansi ugualmente CV, CQ nei punti <lb></lb>F, G, e tirate OFI, OGR, s&#039;eguaglino all&#039;al­<lb></lb>tezza C, sicchè la retta IR passi per C, e sia <lb></lb>parallela alla base <expan abbr="Vq.">Vque</expan> Tirisi anche FG, che <lb></lb>in H divida CO. </s>

<s>I triangoli dunque IFC, CGR <lb></lb>sono simili, uguali e similmente posti in riguardo di CH; onde egualmente <lb></lb>gravano in CH. </s>

<s>Nello stesso modo avviene degli altri VFO, OGQ, che egual-<pb xlink:href="020/01/2797.jpg" pagenum="422"></pb>mente gravano in HO, e ancora il trapezio FVGQ eguale, simile e contrap­<lb></lb>posto all&#039;altro FIRG, e così graveranno ugualmente in FG, come parimente <lb></lb>i triangoli FCG, FOG, o veramente OFC, OGC. </s>

<s>Il punto H dunque è centro <lb></lb>della figura, e perchè X è centro del triangolo VCQ, il quale è simile a CGR, <lb></lb>ed agli altri collaterali e opposti, sarà in essi il centro similmente posto. </s>

<s>” </s></p><p type="main">

<s>“ Sia D il eentro di CGR, e intendasi tirata da D una retta al centro <lb></lb>del triangolo IFC, la quale seghi HC in T, e sarà HT uguale a GD. </s>

<s>E per­<lb></lb>chè la retta CX è doppia di XO, anche GD o HT sarà doppia di DS o TC: <lb></lb>T poi è il centro della gravità composta dei due triangoli IFC, CGR. </s>

<s>Dun­<lb></lb>que tolti questi, scorrerà il centro H in X, sicchè HX ad HT sarà come i <lb></lb>due triangoli al triangolo <expan abbr="VCq.">VCque</expan> Ma HT è dupla di HX, adunque il triangolo <lb></lb>VCQ sarà duplo degli altri due, il che è vero, perchè è vero che il trian­<lb></lb>golo VCQ è doppio degli altri due ” (ivi, pag. </s>

<s>49). </s></p><p type="main">

<s>La conclusione, forse dal Nardi non troppo chiaramente scritta, dipende <lb></lb>da un principio assai per sè noto, qual&#039;è che due grandezze uguali e simil­<lb></lb>mente poste gravano ugualmente sopra la libbra, e si può ridurre al seguente <lb></lb>discorso: Dalla libbra XT col centro in H pendono, dalla parte di T, due <lb></lb>sole grandezze uguali, che sono i triangoli IFC, CGR, e dalla parte di X ne <lb></lb>pendono quattro di così fatte grandezze, tutte eguali fra loro e alle altre due, <lb></lb>che sono i triangoli VFO, FOC, e OGQ, COG. </s>

<s>Dunque TH=2XH, e perciò <lb></lb>XH=TC, CX=CT+TH+XH=4XH, XO=CT+TH—HX= <lb></lb>2XH, d&#039;onde CX:XO=4:2=2:1, come dal Nardi intendevasi di dimo­<lb></lb>strare. </s></p><p type="main">

<s>Dipendono da questo primo altri due teoremi, i quali, benchè risalgano <lb></lb>a un tratto a figure assai più composte, pur crediamo di doverli ordinar qui, <lb></lb>perchè strettamente si ritengono con quello, per modo o di corollari o di <lb></lb>scolii. </s></p><p type="main">

<s>TEOREMA II. — <emph type="italics"></emph>Del trapezio, segato da un triangolo per una linea <lb></lb>che ne divide nel mezzo i lati, il centro di gravità così sega l&#039;asse, che la <lb></lb>parte verso la maggior base stia a quella verso la minore come quattro <lb></lb>sta a cinque.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Nella precedente figura è GV il trapezio, quale viene proposto, di cui si <lb></lb>supponga essere in Z il centro. </s>

<s>La libbra ZT, sospesa in X, è dalla parte <lb></lb>T gravata del solo triangolo FCG, e dalla parte Z dei tre triangoli VFO, <lb></lb>FOG, OGQ, tutti uguali insieme, e con quel primo. </s>

<s>Avremo perciò ZX:XT= <lb></lb>1:3, ossia ZX=XT/3=2/3 XH. Ora, essendo ZH=ZX+HX= <lb></lb>2/3 HX+3/3 HX=5/3 XH; ZO=HO—ZH=3XH—5/3 XH=4/3 XH; <lb></lb>se ne concluderà l&#039;intento cioè OZ:HZ=4:5. </s></p><p type="main">

<s>La medesima conclusione si sarebbe, osserva il Nardi, ottenuta dalla <lb></lb>XV archimedea del primo libro degli Equiponderanti, applicandovi la for­<lb></lb>mula generale quivi proposta ZO:HZ=2FG+VQ:2VQ+FG, impe­<lb></lb>rocchè, fatto VQ=4, e perciò FG=2, sarà ZO:HZ=4+4:8+2= <lb></lb>8:10=4:5. </s></p><pb xlink:href="020/01/2798.jpg" pagenum="423"></pb><p type="main">

<s>TEOREMA III. — <emph type="italics"></emph>Del frusto che riman del cono, segato per un piano <lb></lb>erettamente condotto sulla metà dell&#039;asse, il centro di gravità divide la <lb></lb>porzion di esso asse in modo, che la parte verso la base minore sia a quella <lb></lb>verso la base maggiore, come 17 a 11.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Rappresentando, sempre nella medesima figura, VCQ il cono, di cui il <lb></lb>centro di gravità X sia, per le note regole, già determinato; apparirà in FQ <lb></lb>il tronco proposto, sull&#039;asse HO del quale vuole ora indicarsi il luogo Z del <lb></lb>centro. </s>

<s>Essendo CVQ=<foreign lang="grc">π</foreign>VQ2.OC/3=4<foreign lang="grc">π</foreign>FH2.2CH/3; CFG=<foreign lang="grc">π</foreign>FH2.CH/3, <lb></lb>avremo CVQ:CFG=8:1. E, dividendo, CVQ—CFG:CFG=7:1, co­<lb></lb>sicchè il frusto applicato in Z essendo settuplo del cono applicato in T, verrà <lb></lb>la libbra TZ, col sostegno in Z, a esser divisa talmente, da aversi ZX:XT= <lb></lb>1:7; ossia ZX=XT/7. Suppongasi ora diviso tutto l&#039;asse CO in 56 parti <lb></lb>uguali: sarà HO=CH=28; XH=14; HT=7; XT=21; XZ=3. <lb></lb>Dunque HZ=HX+ZX=14+3=17; ZO=HO—HZ=28—17= <lb></lb>11, e perciò HZ:OZ=17:11, com&#039;era proposto. </s></p><p type="main">

<s>Vuole omologamente il Nardi far osservare che ě incluso anche questo <lb></lb>caso nella generalità, proposta in ultimo luogo da Galileo nell&#039;Appendice dei <lb></lb>centri di gravità (Alb. </s>

<s>XIII, 286), sotto la forma <lb></lb>HZ:ZO=2<foreign lang="grc">π</foreign>VO2+<foreign lang="grc">π</foreign>FH2+2<foreign lang="grc">π</foreign>VO.FH:3<foreign lang="grc">π</foreign>FH2+<foreign lang="grc">π</foreign>VO2+<foreign lang="grc">π</foreign>VO.FH. </s>

<s><lb></lb>Dividendo infatti la seconda ragione per <foreign lang="grc">π</foreign>, fatto VO=2, e sostituiti i valori, <lb></lb>avremo HZ:ZO=12+1+4:3+4+4=17:11. Ma è bene prose­<lb></lb>guire di là, dove fu da noi lasciato interrotto, a trascrivere il manoscritto, <lb></lb>per vedervi i due teoremi dimostrati nelle loro forme originali. </s></p><p type="main">

<s>“ Per trovare il centro del cono, soggiunge il Nardi, altri si potrà incam­<lb></lb>minare con proporzional metodo: e qui solo noterò che, nel trapezio FGQV, <lb></lb>il centro di gravità, posto per ora Z, divide HO con tal ragione, che ZH ad <lb></lb>OZ sia come il doppio di VQ con FG al doppio di EG con <expan abbr="Vq.">Vque</expan> Imperocchè, <lb></lb>tolto dal triangolo CVQ l&#039;altro FCG, sarà XZ all&#039;aggregato di XH, HT, posto <lb></lb>T centro del triangolo FCG, come il triangolo FCG al trapezio <expan abbr="VFGq;">VFGque</expan> cioè <lb></lb>come uno a tre. </s>

<s>E così OZ ad HZ sarà come quattro a cinque, cosicchè, <lb></lb>posto HT tre, XH tre, sarà l&#039;aggregato sei, e ZX due. </s>

<s>Ma posto VQ quat­<lb></lb>tro, sarà il suo doppio otto. </s>

<s>Ed aggiuntoli FG due, sarà dieci. </s>

<s>Qual somma, <lb></lb>al doppio di FG, cioè a quattro e a VQ quattro ha la ragione di cinque a <lb></lb>quattro. </s>

<s>” </s></p><p type="main">

<s>“ Anche raccorrassi che del frusto solido VFGQ il centro Z divide HO <lb></lb>in modo, che ZH a ZO sia come il triplo del cerchio, di cui diametro VQ, <lb></lb>col cerchio, di cui diametro FG, e con due proporzionali di mezzo, al triplo <lb></lb>del cerchio di FG, col cerchio di VQ, e con due di mezzo, qual proporzione <lb></lb>è di 17 a 11, come qui si vede: ” </s></p><p type="main">

<s>“ Posto VQ quattro, sarà FG due, e i loro quadrati saranno come otto <lb></lb>a due. </s>

<s>Dunque il triplo di otto, con due e con otto, cioè 34, al triplo di due <pb xlink:href="020/01/2799.jpg" pagenum="424"></pb>con otto due volte, cioè 22, sono come 51 a 33, o come 17 a 11. Ma tal <lb></lb>corollario suppone essere il cono VCQ ottuplo dell&#039;altro FCG, e che, essendo X <lb></lb>il centro del cono VCQ, sia CX triplo di XO, di che altrove. </s>

<s>E frattanto <lb></lb>avvertiremo come dalle più semplici e regolari figure l&#039;intelletto nostro saglia <lb></lb>alle più irregolari e composte, per poi generalmente le stesse proprietà nelle <lb></lb>une e nelle altre dimostrare ” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>50). </s></p><p type="main">

<s>TEOREMA IV. — <emph type="italics"></emph>Cuiuscumque parallelogrammi centrum gravitatis est <lb></lb>in recta linca coniungente opposita parallelogrammi latera, bifariam secta.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Abbiamo annunziato il teorema nelle forme proprie, e con le medesime <lb></lb>parole di Archimede, perch&#039;era l&#039;intenzione del Nardi di rendere assai più <lb></lb>semplice la proposizione IX del primo libro <emph type="italics"></emph>De aequiponderantibus,<emph.end type="italics"></emph.end> conclu­<lb></lb>dendola da un principio evidente, a cui poi riducesi la petizione X dal Si­<lb></lb>racusano premessa al detto libro primo, che cioè due grandezze eguali s&#039;equi­<lb></lb>librano sull&#039;asse, intorno a cui siano similmente disposte, e sopra esso asse, <lb></lb>come sopra loro libra, hanno il centro comune. </s></p><p type="main">

<s>Sia il parallelogrammo AD (fig. </s>

<s>283) segato nelle due uguali grandezze <lb></lb>AB, CD dall&#039;asse CB, che prolungato seghi allo stesso modo il parallelo­<lb></lb><figure id="id.020.01.2799.1.jpg" xlink:href="020/01/2799/1.jpg"></figure></s></p><p type="caption">

<s>Figura 283.<lb></lb>grammo EH, uguale in tutto e <lb></lb>per tutto all&#039;AD. </s>

<s>Preso nel mezzo <lb></lb>di CF il punto O, sarà ivi il cen­<lb></lb>tro comune, che si rimarrà tale <lb></lb>avvicinandosi con egual moto i <lb></lb>due parallelogrammi, infintanto­<lb></lb>chè i loro lati non giungano a toccarsi e a confondersi nell&#039;unico ED della <lb></lb>figura AH, della quale rimane pur in O il centro, ond&#039;è manifesto che que­<lb></lb>sto segherà, come dovevasi dimostrare, la linea ED nel mezzo. </s></p><p type="main">

<s>“ Siano, così dice propriamente il Nardi, due simili ed uguali paralle­<lb></lb>logrammi AD, EH, i quali abbiano paralleli i lati omologhi. </s>

<s>Dunque, sospesi <lb></lb>dai centri della loro gravità in una retta, di cui il mezzo sia O, peseranno <lb></lb>ugualmente da O. </s>

<s>Intendasi ora avvicinarsi egualmente l&#039;uno all&#039;altro, senza <lb></lb>mutare inclinazione: adunque avverrà che resti sempre l&#039;equilibrio, sino a <lb></lb>che il lato D si faccia uno con l&#039;omologo E, e così di due si formerà un <lb></lb>solo lato ED, e un parallelogrammo solo AH ” (ivi, pag. </s>

<s>1282). </s></p><p type="main">

<s>TEOREMA V. — <emph type="italics"></emph>Il centro di gravità di una superficie emisferica è nel <lb></lb>mezzo dell&#039;asse.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Essere il centro di gravità di una superficie emisferica nel mezzo del­<lb></lb>l&#039;asse, in che sbagliossi il Guldino, provasi da me facilmente con dividere <lb></lb>detto asse in particelle eguali, e ciascuna minore della distanza, che l&#039;avver­<lb></lb>sario vuole dal mezzo. </s>

<s>Quindi, tirati piani paralleli alla base, per dette divi­<lb></lb>sioni si tagliano parti uguali di superficie, quali, per essere uniformemente <lb></lb>gravi, peseranno ugualmente, ed averà ciascuna il centro dentro i termini <lb></lb>della sua particella di asse, e quindi dedurrassi brevemente l&#039;assurdo ” (ivi, <lb></lb>pag. </s>

<s>1360). </s></p><p type="main">

<s>Era dunque la dimostrazione del Nardi quella medesima, che il Torri-<pb xlink:href="020/01/2800.jpg" pagenum="425"></pb>celli diceva di avere imitata da Archimede, ma nell&#039;osservazione aggiunta <lb></lb>e che dice <emph type="italics"></emph>trovarsi anche facilmente il centro delle superficie coniche e <lb></lb>cilindriche,<emph.end type="italics"></emph.end> è intesa la dimostrazione a priori, ossia per via degli indivisi­<lb></lb>bili, secondo la quale, considerandosi le due dette superficie rotonde come <lb></lb>composte delle infinite circonferenze proporzionali ai raggi, il centro della <lb></lb>superficie conica si riduce a quello di un triangolo, e della superficie cilin­<lb></lb>drica a quello di un parallelogrammo. </s></p><p type="main">

<s>Un&#039;altra osservazione anche vi si soggiunge di maggiore importanza, ed <lb></lb>è che col <emph type="italics"></emph>Teorema generale meccanico,<emph.end type="italics"></emph.end> ossia con la regola centrobarica del <lb></lb>Guldino si poteva con facilità inaspettata, dimostrare il seguente </s></p><p type="main">

<s>TEOREMA VI. — <emph type="italics"></emph>Il centro di gravità della mezza circonferenza DAF<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2800.1.jpg" xlink:href="020/01/2800/1.jpg"></figure></s></p><p type="caption">

<s>Figura 284.<lb></lb>(fig. </s>

<s>284), <emph type="italics"></emph>divisa nel mezzo in A, è in X, punto così <lb></lb>collocato, che sia CX quarta proporzionale, dopo essa <lb></lb>mezza circonferenza, il diametro e il raggio.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Valgano per una dimostrazione di ciò le parole: <lb></lb><emph type="italics"></emph>ed in questa ossservasi la medesima analogia, chi ben <lb></lb>l&#039;intende, che nella superficie emisferica<emph.end type="italics"></emph.end> (ivi). Chia­<lb></lb>mata infatti S questa superficie, la Geometria dà S= <lb></lb>DF.<foreign lang="grc">π</foreign>AC, e la Centrobarica S=DAF.<foreign lang="grc">π</foreign>CX, d&#039;onde DAF:DF=AC:CX. </s></p><p type="main">

<s>Si diceva essere questa invenzione di maggiore importanza delle altre, <lb></lb>non solamente perchè nuova, ma perchè vi si faceva uso di un argomento <lb></lb>nuovo, non avvertito nè dallo stesso Guldino, nè ancora dal Torricelli, nè da <lb></lb>nessun altro prima del Wallis, preceduto di tanto tempo dal Nardi, il quale <lb></lb>avvertiva, nel citato luogo, altresì che, <emph type="italics"></emph>con l&#039;aiuto di questa centrobarica, <lb></lb>si discende alle più particolari proposte intorno alla stessa materia.<emph.end type="italics"></emph.end> Ve­<lb></lb>dremo di così fatte proposte un esempio insigne applicato alla misura dei <lb></lb>solidi rotondi generati dalla Cicloide, ma intanto è da proseguire nel nostro <lb></lb>proposito, qual&#039;era di mostrare come il Nardi concorresse col Torricelli in <lb></lb>facilitare e in promovere la Scienza dei precursori. </s>

<s>E quanto alla facilità, <lb></lb>abbiamo ora da proporre l&#039;esempio del baricentrico nel frusto di parabola, <lb></lb><figure id="id.020.01.2800.2.jpg" xlink:href="020/01/2800/2.jpg"></figure></s></p><p type="caption">

<s>Figura 285.<lb></lb>e nel settore di circolo, <lb></lb>da preferirsi alle lunghe <lb></lb>e stentate dimostrazioni di <lb></lb>Archimede, e del Della <lb></lb>Faille. </s></p><p type="main">

<s>TEOREMA VII. — <emph type="italics"></emph>Nel <lb></lb>frusto parabolico ARBCD<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>285) <emph type="italics"></emph>siano inscritte <lb></lb>le parabole ARB, CSD <lb></lb>col centro comune in O, <lb></lb>e il trapezio ABCD col <lb></lb>centro in K: se, come il <lb></lb>trapezio alle parabole, così faremo reciprocamente OZ a ZK, dico che in Z <lb></lb>sarà il centro di gravità del frusto.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2801.jpg" pagenum="426"></pb><p type="main">

<s>Il teorema s&#039;è veduto già dimostrato dal Torricelli nella IX proposizione <lb></lb>da noi raccolta nel capitolo V, e il Nardi accennava con queste parole al <lb></lb>medesimo processo dimostrativo: “ Difficilissime di gran lunga, fra tutte le <lb></lb>altre di Archimede, sono le due ultime del secondo libro dei superficiali equi­<lb></lb>libri (così traduce l&#039;Autore il titolo, a cui comunemente corrisponde quello <lb></lb><emph type="italics"></emph>De aequiponderantibus<emph.end type="italics"></emph.end>) delle quali la prima serve per lemma della seguente, <lb></lb>ove s&#039;investiga il centro d&#039;un frusto parabolico, potendosi in altro modo pro­<lb></lb>porre, e facilissimamente trovare lo stesso quesito, con dire per esempio <lb></lb>così: D&#039;ogni frusto parabolico il centro di gravità sta nell&#039;asse suo collocato <lb></lb>tra il centro del trapezio in esso descritto, e tra quello delle due parabole <lb></lb>collaterali in modo, che la distanza del centro del frusto a quella delle pa­<lb></lb>rabole, alla distanza del centro del frusto a quella del trapezio, sia come il <lb></lb>trapezio alle parabole. </s>

<s>Il tutto s&#039;intende e si dimostra con ridursi un tratto <lb></lb><figure id="id.020.01.2801.1.jpg" xlink:href="020/01/2801/1.jpg"></figure></s></p><p type="caption">

<s>Figura 286.<lb></lb>alla VIa del primo <emph type="italics"></emph>Dei superficiali equili­<lb></lb>brii,<emph.end type="italics"></emph.end> come alla fine fa Archimede, e così <lb></lb>risparmiamo cento sillogismi ” (ivi, p. </s>

<s>935). </s></p><p type="main">

<s>Passeremo ora al <emph type="italics"></emph>Centro di gravità <lb></lb>del settore di cerchio,<emph.end type="italics"></emph.end> dopo il qual titolo il <lb></lb>Nardi così soggiunge: <emph type="italics"></emph>Dell&#039;invenzione mia <lb></lb>del mezzo per provare tal teorema nel modo <lb></lb>che segue; Il lettore conoscerà quanto ab­<lb></lb>breviato siasi il progresso del p. </s>

<s>Faille.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ TEOREMA VIII. — <emph type="italics"></emph>Nel settore AECD<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>286), <emph type="italics"></emph>o maggiore o minore di un <lb></lb>niezzo cerchio, sia inscritto il quadrila <lb></lb>tero ABCD, ed essendo AB, BC lati uguali, <lb></lb>intendansi dal centro D tirate a que&#039;lati le perpendicolari DF, DG, e si <lb></lb>congiunga DB. </s>

<s>I centri di gravità dei triangoli ABD, BDC siano K, P, i <lb></lb>quali si connettano con la KP segante BD in L, che sarà centro del­<lb></lb><figure id="id.020.01.2801.2.jpg" xlink:href="020/01/2801/2.jpg"></figure></s></p><p type="caption">

<s>Figura 287.<lb></lb>l&#039;inscritto quadrilatero. </s>

<s>Dico che <lb></lb>FD a DL sarà come AB+BC a <lb></lb>2/3 AC, sottesa dell&#039;arco ABC. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Perchè ne&#039;triangoli rettan­<lb></lb>goli ABE, KDL l&#039;angolo al centro <lb></lb>KDL è uguale all&#039;angolo CAB, <lb></lb>alla periferia insistente sopra dop­<lb></lb>pio arco. </s>

<s>Dunque KD a DL, come <lb></lb>AB ad AE; FD a KD, come AE a <lb></lb>2/3 AE; dunque, per l&#039;ugualità per­<lb></lb>turbata, FD a DL, come AB a 2/3 <lb></lb>AE, ovvero AB+BC a 2/3 AC. ” </s></p><p type="main">

<s>“ TEOREMA IX — <emph type="italics"></emph>Stando la <lb></lb>medesima costruzione, immagi­<lb></lb>niamoci ne&#039;settori AGBD, BHCD<emph.end type="italics"></emph.end> (fig. </s>

<s>287) <emph type="italics"></emph>i quadrilateri segnati con le<emph.end type="italics"></emph.end><pb xlink:href="020/01/2802.jpg" pagenum="427"></pb><emph type="italics"></emph>medesime lettere, de&#039;quali siano i centri di gravità L, R e si connetta <lb></lb>LSR, che seghi BD in S, il quale S sarà centro di gravità di tutto il po­<lb></lb>ligono equilatero inscritto nell&#039;ABCD. </s>

<s>Ad un lato AG sia tirata dal cen­<lb></lb>tro perpendicolarmente DI. </s>

<s>Dico che DI a DS, è come l&#039;aggregato de&#039;lati <lb></lb>del poligono a 2/3 AC. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Imperocchè AG+GB a 2/3 AB è come ID a DL, per l&#039;antecedente. </s>

<s><lb></lb>LD a DS come 2/3 AB a 2/3 AE, per la similitudine dei triangoli ABE, SLD, <lb></lb>essendo LDS al centro insistente alla metà dell&#039;arco AB, ovvero BC; e gli <lb></lb>angoli ad E, S retti. </s>

<s>Adunque, per l&#039;ugualità di ragione, ID a DS, come <lb></lb>AG+GB a 2/3 AE, ovvero AG+GB+BH+HC a 2/3 AC, che sono i <lb></lb>doppi, ond&#039;è chiaro etc. </s>

<s>” </s></p><p type="main">

<s>“ Volendo continuare la inscrizione faremo un quadrilatero nel settore <lb></lb>AMGD, un altro nel GNBD, ove ne resulterà un poligono di doppi lati, uno <lb></lb>de&#039;quali pongasi AM. </s>

<s>Per le cose ora dimostrate sarà la perpendicolare dal <lb></lb>centro D nel lato AM, alla DLT, supposto che T sia centro del poligono <lb></lb>inscritto ultimamente in AGBD, come tutti i lati di esso poligono a 2/3 AB. </s>

<s><lb></lb>Tirando poi da T la TV perpendicolare alla BD, si costituiranno, come sopra, <lb></lb>i triangoli rettangoli simili ABE, TDV, dal che segue di nuovo TD a DV <lb></lb>come 2/3 AB a 2/3 AE, o per l&#039;ugualità la perpendicolare nel lato AM, alla <lb></lb>DV, come tutti i lati del detto poligono a 2/3 di AE. E, presi i doppi, come <lb></lb>tutti i lati del poligono inscritto in ABCD, uno de&#039;quali AM, a 2/3 AC. </s>

<s>E così <lb></lb>continueremo l&#039;inscrizione in infinito, essendo sempre vero che il perimetro <lb></lb>del poligono, inscritto nel settore nel modo suddetto, a due terzi della sut­<lb></lb>tesa AC, sia come la perpendicolare del centro di un lato alla distanza dal <lb></lb>centro di gravità del poligono dal centro del cerchio. </s>

<s>Il che etc. </s>

<s>Ma ad ogni <lb></lb>poligono regolare simile ai suddetti si puote circoscrivere un settore di cer­<lb></lb>chio; adunque sarà generalmente conchiuso in ogni poligono, e quindi si passa <lb></lb>al settore. </s>

<s>Avvertisco poi come la mia invenzione di tal mezzo si faciliti nelle <lb></lb>prove dal p. </s>

<s>Ricci ” (ivi, pag. </s>

<s>1003-5). </s></p><p type="main">

<s>A dimostrare il centro di gravità del settore, ch&#039;era l&#039;intento princi­<lb></lb>pale, si passa dunque secondo il Nardi per corollario dai teoremi precedenti, <lb></lb>e specialmente dall&#039;ultimo, perchè, continuata l&#039;inscrizione all&#039;infinito, i lati <lb></lb>del poligono si confondono con l&#039;arco, e il cateto uguaglia il raggio, con cui <lb></lb>l&#039;arco stesso è stato descritto. </s>

<s>Di qui è che il centro di gravità viene in que­<lb></lb>sto caso indicato dall&#039;estremo punto di una linea, che muova dal centro del <lb></lb>circolo, e che sia quarta proporzionale dopo l&#039;arco, i due terzi della corda <lb></lb>che lo sottende, e il&#039;raggio. </s></p><p type="main">

<s>Se il Ricci facilitò anche di più la prova del mezzo usato dal Nardi, <lb></lb>s&#039;intende quanto si rimanessero i due amici superiori al Torricelli, il quale <lb></lb>non riuscì ad abbreviare il Della Faille, se non che anch&#039;egli scrivendo, per <lb></lb>il baricentrico del settor circolare, quasi un libro. </s>

<s>Nè punto inferiori si ri­<lb></lb>masero i due detti al valoroso emulo loro, quando vennero insieme con lui <lb></lb>al cimento di ritrovare il centro di gravità del settore sferico. </s></p><p type="main">

<s>“ Nell&#039;aver fatto trascrivere le opere mie (tale avvertenza premette il <pb xlink:href="020/01/2803.jpg" pagenum="428"></pb>Nardi alla sua dimostrazione) occorse che ultimamente si perdesse un qua­<lb></lb>derno di molta importanza, in riguardo di esse, imperocchè contenevasi in <lb></lb>quello il meglio delle mie geometriche contemplazioni, delle quali nemmeno, <lb></lb>il che importa, copia ritenuto m&#039;avea. </s>

<s>La memoria per alquanto m&#039;è ser­<lb></lb>vita, ma non il tempo, sicchè, per ristorarne i danni, mi è stato di sommo <lb></lb>aiuto il signor M. A. Bicci, gentiluomo mio amicissimo, e col quale comu­<lb></lb>nico da alquanto tempo in qua, cioè da che conosco un giovane di così alto <lb></lb>intelletto, le debolezze de&#039;miei discorsi. </s>

<s>Egli non solo ha supplito al bisogno <lb></lb>mio, ma anche, più sottilmente e copiosamente di quel che fatto avevomi, <lb></lb>ha ristorato ogni perdita, e da vantaggio altre sue nobilissime contemplazioni <lb></lb>ha aggiunto alla mia selva, di che a luogo per luogo faccio menzione. </s>

<s>Fuor <lb></lb>di modo poi me li conosco obbligato, per la dimostrazione rinvenuta di que­<lb></lb>sto mio, forse non volgare, teorema. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Definizioni.<emph.end type="italics"></emph.end> — I. </s>

<s>Sotto il nome di <emph type="italics"></emph>cilindrico<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>conico<emph.end type="italics"></emph.end> intendo di <lb></lb>comprendervi il cilindro e la porzione cilindrica, il cono e la porzione conica. </s>

<s>” </s></p><p type="main">

<s>“ II. </s>

<s>Segandosi una sfera o sferoide con piano eretto all&#039;asse, l&#039;una e <lb></lb>l&#039;altra delle due parti fatte io chiamo assolutamente <emph type="italics"></emph>segamento,<emph.end type="italics"></emph.end> di cui sarà <lb></lb>base un cerchio o un ellisse. </s>

<s>” </s></p><p type="main">

<s>“ III. </s>

<s>Per <emph type="italics"></emph>solido settore<emph.end type="italics"></emph.end> intendo un segamento maggiore o minore del­<lb></lb>l&#039;emisfero o emisferoide, insieme con un conico, ovvero toltone un conico, <lb></lb>quando il segamento è maggiore, la cui cima sia nel centro di essa sfera o <lb></lb>sferoide, e la base sia quella stessa del segamento, e questo segamento si <lb></lb>dirà segamento del settore. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma geometrico.<emph.end type="italics"></emph.end> — Espongasi un solido settore HABCKD (fig. </s>

<s>288), <lb></lb>ossia il suo segamento minore o maggiore di una mezza sfera, intorno l&#039;asse <lb></lb><figure id="id.020.01.2803.1.jpg" xlink:href="020/01/2803/1.jpg"></figure></s></p><p type="caption">

<s>Figura 288.<lb></lb>BF, ovvero BDF, il quale asse, prodotto <lb></lb>nel primo caso fino al centro della sfera <lb></lb>o sferoide in D, sia segato in F dalla base <lb></lb>del detto segamento: Dico che il settor so­<lb></lb>lido, al residuo AHDKC, sarà in ragione <lb></lb>di BF ad FD. ” </s></p><p type="main">

<s>“ Intendasi descritto il cilindro AE <lb></lb>intorno il segamento ABC, ed intorno il <lb></lb>segamento del settore il cilindrico GE, con <lb></lb>simile ed egual base, ed intorno il mede­<lb></lb>simo asse con l&#039;AE. </s>

<s>Immaginiamoci in­<lb></lb>torno DF come asse tre conici, col vertice <lb></lb>D e la base nel piano GFI. </s>

<s>Il cerchio o <lb></lb>ellisse base del primo abbia per diametro GI, il secondo HK, il terzo una <lb></lb>retta che pareggi di quadrato l&#039;eccesso del quadrato GI sopra il quadrato <lb></lb>HK. </s>

<s>In riguardo però dell&#039;ellisse bisognerà che i diametri siano omologhi. </s>

<s>” </s></p><p type="main">

<s>“ Ora, dei tre conici suddetti, il secondo e il terzo insieme presi s&#039;ag­<lb></lb>guagliano al primo, per l&#039;egualità delle basi e delle altezze; ma il terzo <lb></lb>conico è uguale al cilindrico AI, senza la porzione AHFKC, per la XIVa del <pb xlink:href="020/01/2804.jpg" pagenum="429"></pb>terzo di Luca Valerio. </s>

<s>Adunque il cilindrico AI, senza la detta porzione, preso <lb></lb>insieme col secondo conico HDK, è uguale al primo conico, e conseguente­<lb></lb>mente un terzo del cilindrico AI intero, del quale sarà due terzi la residua <lb></lb>porzione AHDKC e questa residua porzione sarà doppia del primo conico. </s>

<s><lb></lb>Adunque, essendo il cilindrico AE, al segamento ABC, come il cilindrico AI, <lb></lb>alla residua porzione AHDKC, cioè in ragion sesquialtera; segue, per la XIX <lb></lb>del Quinto, nel primo caso, e per la XII nel secondo caso, che nella mede­<lb></lb>sima ragione sia il cilindrico GE al solido settore, cioè in ragion sesquial­<lb></lb>tera. </s>

<s>E finalmente, permutando e convertendo, il cilindrico GE, al cilindrico <lb></lb>AI, cioè l&#039;asse BF all&#039;asse FD, come il solido settore alla residua porzione <lb></lb>AHDKC. </s>

<s>Il che etc. </s>

<s>” </s></p><p type="main">

<s>“ TEOREMA X. — Nella medesima figura dividasi DF nel mezzo in L, <lb></lb>ed LF nel mezzo in O, che DO sia tripla di OF. </s>

<s>Sarà L centro di gravità <lb></lb>del cilindrico AI, ed O del secondo conico HDK, ed anco del cilindrico AI, <lb></lb>senza la porzione AHKC, secondo che dimostra Luca Valerio nel libro citato, <lb></lb>alla proposizion XXVII. </s>

<s>Facciasi LN, che sia metà di LO. </s>

<s>Siccome il secondo <lb></lb>conico, insieme col cilindrico AI senza la porzione AHKC, è metà della re­<lb></lb>sidua porzione AHDKC, per le cose dimostrate nell&#039;antecedente lemma; sarà, <lb></lb>per la ragion reciproca dei pesi con le distanze LN, LO, N centro di gra­<lb></lb>vità della suddetta porzion residua AHDKC. </s>

<s>E supponendo DF esser otto, <lb></lb>sarà LO due, LN uno, FN cinque, ed ND tre. </s>

<s>Per la qual cosa N divide <lb></lb>l&#039;asse DF in ragione di cinque a tre. </s>

<s>” </s></p><p type="main">

<s>“ TEOREMA XI. — Espongasi il sopra detto settore HBKD, e tutto il <lb></lb>resto della figura, lasciando però i cilindrici e le divisioni fatte in L ed O. </s>

<s><lb></lb>Prendasi PD tre ottavi della BD, e saranno P ed N i centri di gravità del <lb></lb>segamento ABC, e della residua porzione AHDKC. </s>

<s>Nel primo caso facciasi <lb></lb>NP a PQ come BF a FD, cioè come il solido settore alla detta residua por­<lb></lb>zione, reciprocamente, e sarà Q centro di gravità del settore. </s>

<s>Nel secondo <lb></lb>caso, dividasi PN in Q, che NQ a PQ sia come BD a FB, ovvero, come il <lb></lb>segamento ABC alla residua porzione AHDKC, e similmente Q sarà centro <lb></lb>di gravità del settore, com&#039;è manifesto. </s>

<s>Dico che, prendendosi tre ottavi del <lb></lb>semidiametro BD, e tre ottavi della parte FD, l&#039;aggregato loro nel primo <lb></lb>caso, o la differenza nel secondo caso, sarà uguale alla distanza DQ, cioè del <lb></lb>centro di gravità del settore dal centro della sfera o sferoide. </s>

<s>” </s></p><p type="main">

<s>“ Imperocchè, essendo PB le medesime parti di BD, che DN di DF, <lb></lb>sarà permutando BD a DF, come PB a DN. </s>

<s>E dividendo nel primo caso, <lb></lb>componendo nel secondo, BF a FD, ovvero NP a PQ, come la medesima NP <lb></lb>a ND. </s>

<s>Adunque PQ è uguale a ND, e però DQ sarà uguale nel primo caso <lb></lb>a DP+DN, cioè a 3/8 di BD+3/8 di FD, e nel secondo caso a DP—DN, <lb></lb>cioè a 3/8 di BD—3/8 di FD, il che etc. </s>

<s>Quindi verremo alla dimostrazione <lb></lb>del proposto ” </s></p><p type="main">

<s>“ TEOREMA XII. — Sia nella medesima figura il settor di sfera HBKD, <lb></lb>il cui centro di gravità il punto Q, il centro della sfera D, l&#039;asse BE, la su­<lb></lb>perficie sferica del settore HBK. </s>

<s>Tirisi la retta HB, e sarà il quadrato di HB, <pb xlink:href="020/01/2805.jpg" pagenum="430"></pb>al quadrato di HF, o il rettangolo EBF al rettangolo EFB, o la base EB alla <lb></lb>base EF, per esser comune BF, come la superficie sferica HBK, al cerchio <lb></lb>del semidiametro HF. </s>

<s>Ma questo cerchio, a tre suoi quarti, è come EF a tre <lb></lb>quarti dello stesso EF; adunque, per la eguale, la superficie sferica ABK, a <lb></lb>tre quarti del cerchio descritto con la distanza HF, è come la retta EB a tre <lb></lb>quarti di essa EF. E, presa la metà, come BD a tre ottavi della stessa FE, <lb></lb>poichè un ottavo è la metà di un quarto, e tre ottavi la metà di tre quarti, <lb></lb>ovvero, nel primo caso, 3/8 di ED+DF, cioè 3/8 di ED+3/8 di EF; e nel <lb></lb>secondo caso, 3/8 di ED—DF, ovvero 3/8 di ED—3/8 di DF. </s>

<s>Ma tale an­<lb></lb>cora è BQ, per le cose dette, adunque la superficie sferica HBK, a tre quarti <lb></lb>del cerchio descritto dal semidiametro HF, sarà come BD a DQ, il che etc. </s>

<s>” <lb></lb>(ivi, pag. </s>

<s>372-76). </s></p><p type="main">

<s>Della conclusione, appena ritrovatasi, dette il Nardi notizia al Torricelli, <lb></lb>il quale così scriveva in un poscritto di lettera indirizzata il dì 7 Marzo 1640 <lb></lb>al Cavalieri: “ Il signor Antonio Nardi mi avvisa di aver dimostrato il cen­<lb></lb>tro di gravità del settore solido di sfera, con conclusione più bella della mia, <lb></lb>ed è questa: <emph type="italics"></emph>Facciasi come la superficie sferica del settore alli tre quarti <lb></lb>del cerchio sua base, così il semidiametro ad un&#039;altra da prendersi dal <lb></lb>centro della sfera, che quel punto sarà centro,<emph.end type="italics"></emph.end> ed è verissima e concorda <lb></lb>con la mia ” (MSS. Gal. </s>

<s>Dis., T. XL, fol. </s>

<s>125). </s></p><p type="main">

<s>Smarritesi poi le carte, dove il Nardi aveva disteso quel suo teorema, e <lb></lb>volendo anche questo, come uno de&#039;più importanti, inserire nelle <emph type="italics"></emph>Ricercate <lb></lb>geometriche,<emph.end type="italics"></emph.end> vi suppli il Ricci, che, mettendosi a ricercare i centri di gra­<lb></lb>vità nel settor circolare e nello sferico, era con grandissima facilità riuscito <lb></lb>alle medesime conclusioni. </s>

<s>Sulla fine del 1645, nel mandare esso Ricci, per­<lb></lb>chè fossero stampati nelle dette Ricercate, i suoi teoremi baricentrici; ne <lb></lb>dava compiacentesi avviso al Torricelli, che rispondeva così da Firenze, il dì <lb></lb>due di dicembre: </s></p><p type="main">

<s>“ Mi rallegro che con tanta facilità abbia trovato i centri di gravità delle <lb></lb>parti del cerchio e della sfera: taccio l&#039;ellissi e la sferoide, perchè vanno <lb></lb>sotto la medesima invenzione. </s>

<s>Non so se ella vedesse certi fogliacci, che io, <lb></lb>già sono due anni, mandai al signor Raffaello (Magiotti). Dimostravo il cen­<lb></lb>tro di gravità nel settore del cerchio in due modi, e brevemente, cioè <emph type="italics"></emph>more <lb></lb>veterum,<emph.end type="italics"></emph.end> e per gl&#039;indivisibili. </s>

<s>Quanto al centro di gravità del settore di sfera, <lb></lb>mi scrisse il signor Antonio Nardi di Arezzo di averlo mostrato, e annun­<lb></lb>ziato come fa V. S. </s>

<s>Io gli risposi di averlo mostrato e annunziato in un altro <lb></lb>modo, cioè che sia nell&#039;asse del settore lontano dal centro della sfera per tre <lb></lb>quarti dell&#039;asse del cono, e tre ottavi della saetta del segmento. </s>

<s>V. S. intende <lb></lb>già che il settore è composto di un cono, e di un segmento. </s>

<s>La medesima <lb></lb>enunciazione credo che mi paresse adattarla anco alla sferoide, ma ora ho <lb></lb>la testa lontanissima da simili cose. </s>

<s>Dimostrai la concordanza tra la propo­<lb></lb>sizione del signor Nardi e la mia, e devo averla in scritto ” (ivi, fol. </s>

<s>101). </s></p><p type="main">

<s>Noi infatti abbiamo ritrovato cotesto scritto, in cui le due apparentemente <lb></lb>diverse indicazioni del centro di gravità del settore sferico si conciliano fa-<pb xlink:href="020/01/2806.jpg" pagenum="431"></pb>cilmente insieme, con questo discorso, riducendoci la figura 289 sott&#039;occhio. </s>

<s><lb></lb>Posto che sia il centro di gravità del settore ABCD collocato in F, mezzo <lb></lb>della saetta BE, a una distanza X dal centro della figura, il Torricelli dà <lb></lb>X=3/4 DF, e il Nardi X=3<foreign lang="grc">π</foreign>AE2.BD/4.ABC, ond&#039;è che la ragion della con­<lb></lb>cordanza si riduce a dimostrare che <foreign lang="grc">π</foreign>AE2.BD/ABC è uguale a DF. </s>

<s>La dimo­<lb></lb>strazione poi è assai facile, perchè BD:DF=2BD:2DF=BG:GE= <lb></lb><figure id="id.020.01.2806.1.jpg" xlink:href="020/01/2806/1.jpg"></figure></s></p><p type="caption">

<s>Figura 289.<lb></lb><foreign lang="grc">π</foreign>BG.BE:<foreign lang="grc">π</foreign>GE.BE. </s>

<s>Ma il primo termine di <lb></lb>quest&#039;ultima ragione è uguale alla callotta ABC, e il <lb></lb>secondo al circolo di raggio AE; dunque BD:DF= <lb></lb>ABC:<foreign lang="grc">π</foreign>AE2, d&#039;onde DF=<foreign lang="grc">π</foreign>AE2.BD/ABC, come in <lb></lb>sostanza scrisse così di aver ritrovato il Torricelli <lb></lb>stesso, benchè con altre parole: </s></p><p type="main">

<s>“ Sia il settore ABCD, e divisa BE bifariam <lb></lb>in F, sarà il centro di gravità nelli tre quarti di <lb></lb>DF (ait Torricellius). ” </s></p><p type="main">

<s>“ Facciasi come la superficie ABC, alli tre <lb></lb>quarti del cerchio AC, così BD ad un&#039;altra, da <lb></lb>pigliarsi dal centro: il termine di questa sarà centro (ait Nardius). ” </s></p><p type="main">

<s>“ Congiungansi AB, AG. </s>

<s>E perchè tutta GB, a tutta BD, sta come la <lb></lb>levata EB, alla levata BF; sarà la rimanente GE, alla rimanente DF, come <lb></lb>tutta a tutta, cioè doppia. </s>

<s>” </s></p><p type="main">

<s>“ Jam BD ad DF est ut, sumptis duplis, BG ad GE, sive, ut quadra­<lb></lb>tum BG ad GA, sive ut quadratum BA ad AE, sive, ut superficies ABC ad <lb></lb>circulum AC. </s>

<s>Sumptis vero consequentium subsesquitertiis, erit ut BD ad <lb></lb>rectam Torricellii, ita superficies ABC ad 3/4 circuli AC. </s>

<s>Eadem ergo est recta <lb></lb>Torricellii cum recta Nardii ” (MSS. Gal. </s>

<s>Disc., T. XXXVI, fol. </s>

<s>96). </s></p><p type="main">

<s>Apparisce dalle cose fin qui esposte che, mentre si credeva di dare i <lb></lb>teoremi baricentrici del Nardi, abbiamo dati anche insieme quelli del Ricci, <lb></lb>quasi in una mente sola, come in un sol cuore, si fossero trasfusi i due <lb></lb>amici. </s>

<s>Essi perciò fra i promotori della Scienza meccanica non vogliono es­<lb></lb>sere separati fra loro, come non vogliono essere separati dal Torricelli, in­<lb></lb>sieme col quale compongono quel triumvirato glorioso, che la nostra Storia <lb></lb>ha collocato nel suo proprio seggio. </s>

<s>Intorno al Ricci sono state le notizie più <lb></lb>scarse che intorno agli altri due, perchè, non essendo suo fine di stampare, <lb></lb>protestava <emph type="italics"></emph>di disprezzare le sue speculazioni come in sè stesse di nulla <lb></lb>estimazione, e di non scriverne se non che qualcuna, per mantenere il. </s>

<s><lb></lb>commercio col Torricelli.<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>60). </s></p><p type="main">

<s>Son fra queste speculazioni notabili, per il presente nostro argomento, <lb></lb>le considerazioni intorno i frusti conoidali segati con due piani paralleli, com­<lb></lb>prendendosi dal Ricci, sotto una sola universalissima, varie proposizioni dello <lb></lb>stesso Torricelli. </s>

<s>Sia richiesto il centro di gravità del frusto AKBCD (fig. </s>

<s>290) <pb xlink:href="020/01/2807.jpg" pagenum="432"></pb>intero, o scavato dal cono AHD. </s>

<s>Per risolvere il problema, il metodo era <lb></lb>quello di dimostrare qual proporzione abbia il tutto verso la parte, ossia il <lb></lb><figure id="id.020.01.2807.1.jpg" xlink:href="020/01/2807/1.jpg"></figure></s></p><p type="caption">

<s>Figura 290.<lb></lb>frusto verso il cono inscritto: proporzione, <lb></lb>che il Ricci annunziava in questa forma: <lb></lb>“ In detto frusto intendasi il frusto conico, <lb></lb>ovvero di porzione conica ABCD, il cui asse <lb></lb>HE sia diviso nel mezzo dall&#039;applicata KL, <lb></lb>e la MI sia differenza delle rette AE, GI. </s>

<s><lb></lb>Dico il frusto AKBCD, al suo cono inscritto <lb></lb>AHD, essere in proporzione di due quadrati KI ed un quadrato GI col qua­<lb></lb>drato MI, al quadrato AE ” (ivi, T. XLII, fol. </s>

<s>29). </s></p><p type="main">

<s>Suppone il Ricci, per dimostrare che il suo teorema è veramente con­<lb></lb>cluso nella formula esposta, due proposizioni, la prima delle quali è che il <lb></lb>residuo del frusto AKBCD, toltone il frusto conico, sia verso il cono AHD <lb></lb>come due rettangoli KGL al quadrato di AE: e la seconda, che il frusto <lb></lb>ABCD, al cono AHD, stia come i quadrati di AE, BH con un medio tra loro, <lb></lb>al quadrato di AE. </s>

<s>Riconosce della prima proposizione autore il Torricelli, <lb></lb>se non che, invece di ridurre il solido annulare, descritto dal bilineo AKB <lb></lb>intorno all&#039;asse, a uno sferoide, ciò che suppone la notizia de&#039;solidi sferali, <lb></lb>per non uscir dalle dottrine dei Conici, pensò il Ricci di ridurre il detto so­<lb></lb>lido annulare a un cilindro come RQ (fig. </s>

<s>291), il quale, avendo pari altezza <lb></lb><figure id="id.020.01.2807.2.jpg" xlink:href="020/01/2807/2.jpg"></figure></s></p><p type="caption">

<s>Figura 291.<lb></lb>a quella del frusto, e per base un circolo di raggio RE, o TI <lb></lb>a mezzo l&#039;asse, il quadrato del quale uguagli il rettangolo <lb></lb>KGL; fosse scavato dai due coni PIQ, RIS. </s>

<s>La proporzione <lb></lb>del resto fra il solido annulare e il cono AHD riman tut­<lb></lb>tavia quella del doppio rettangolo KGL, al quadrato di AE, <lb></lb>data dal Torricelli, perchè, chiamato S quel solido, e C il <lb></lb>cono, essendo S=<foreign lang="grc">π</foreign>TI2.EH—<foreign lang="grc">π</foreign>TI2.EH/3=2/3<foreign lang="grc">π</foreign>XGL.EH, <lb></lb>e C=<foreign lang="grc">π</foreign>AE2.EH/3, abbiamo S:C=2KGL:AE2. </s></p><p type="main">

<s>L&#039;altra proposizione poi, che risolve il frusto conico in tre coni, rite­<lb></lb>neva, com&#039;era giusto, il Ricci per sua, sapendo di averla egli il primo co­<lb></lb>municata al Torricelli, benchè questi poi la dimostrasse di sua propria indu­<lb></lb>stria, riducendo ad uno sferoide il terzo cono proporzionale, come si vide <lb></lb>nell&#039;ordinare la proposizione XLVI, qui addietro, nel capitolo quinto. </s>

<s>Così <lb></lb>essendo, premettiamo per maggiore intelligenza gli argomenti analitici alla <lb></lb>fedel trascrizione del proposto teorema universale dei conoidali. </s></p><p type="main">

<s>Son date le due equazioni AKBCD—ABCD:AHD=2KGL:AE2; <lb></lb>ABCD:AHD=AE2+F2+BH2:AE2, intendendosi per F2 il medio <lb></lb>proporzionale fra AE2, BH2. </s>

<s>Conseguono da queste due le tre seguenti: </s></p><p type="main">

<s><emph type="center"></emph>AKBCD—ABCD:ABCD=2KGL:AE2+F2+BH2; <lb></lb>AKBCD:ABCD=2KGL+AE2+F2+BH2:AE2+F2+BH2; <lb></lb>AKBCD:AHD=2KGL+AE2+F2+BH2:AE2.<emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/2808.jpg" pagenum="433"></pb><p type="main">

<s>Facciansi NE, OE uguali alle rette GI, BH. </s>

<s>Avremo AE+BH=2GI= <lb></lb>2NE, d&#039;onde AE=2NE—BH=2NE—OE, ossia AE—NE=NE—OE, <lb></lb>e in conclusione AN=NO. </s></p><p type="main">

<s>AE2=(AN+NE)2=AN2+2ANE+NE2; OE2=(NE—NO)2= <lb></lb>NE2—2ENO+NO2. </s>

<s>Sommando queste due equazioni, e sostituendo AN <lb></lb>a NO, avremo AE2+OE2=2NE2+2AN2=AE2+BH2. </s></p><p type="main">

<s>F2=AE.BH=AEO, e perciò F2+AN2=AEO+AN2=NE2. </s>

<s><lb></lb>Dunque AE2+BH2+F2=3NE2+AN2+AN2+F2=3NE2+AN2= <lb></lb>3NE+MI2. </s></p><p type="main">

<s>E in ultimo, 2KGL+AE2+BH2+F2=2KGL+3NE2+MI2= <lb></lb>2(KI2—IG2)+3IG2+MI2=2KI2+IG2+MI2. </s></p><p type="main">

<s>“ Sia il quadrato di F (per dar la dimostrazione con le parole proprie <lb></lb>del Ricci) medio proporzionale tra li quadrati AE, BH. </s>

<s>E perchè il frusto <lb></lb>AKBCD, toltone il frusto ABCD, al cono AHD sta come due rettangoli KGL, <lb></lb>al quadrato AE, e il frusto ABCD, al cono medesimo, come li tre quadrati <lb></lb>AE, F, BH al medesimo quadrato AE; dunque tutto il frusto AKBCD, al <lb></lb>cono AHD, è come due rettangoli KGL, con li quadrati AE, F, BH, al qua­<lb></lb>drato AE. ” </s></p><p type="main">

<s>“ Ora, per ridurli alli termini detti nella proposizione, facciansi NE, OE <lb></lb>uguali alle rette GI, BH. </s>

<s>Saranno gli eccessi AN, NO uguali, e perciò li qua­<lb></lb>drati AE, OE, insieme, uguali a due quadrati NE e due quadrati NA, per <lb></lb>la X del Secondo. </s>

<s>Inoltre, essendo li quadrati AE, F, RH proporzionali, sa­<lb></lb>ranno anche i lati, e il quadrato della media F, uguale al rettangolo AEO, <lb></lb>giuntovi uno de&#039;quadrati NA, ovvero NO, doventerà uguale al quadrato NE. </s>

<s><lb></lb>Sicchè ridotti sono li tre quadrati AE, F, BH a tre quadrati NE ed uno AN, <lb></lb>ovvero MI. </s>

<s>E congiunti con li due rettangoli KGL, averemo due quadrati KI, <lb></lb>un quadrato GI, ed uno MI (in luogo di due rettangoli KGL, e dei tre qua­<lb></lb>drati AB, F, BH) al quadrato AE, in proporzione medesima che il frusto <lb></lb>AKBCD al cono AHD, <emph type="italics"></emph>quod proponebatur. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Che il residuo del frusto AKBCD, toltone il frusto conico, sia verso <lb></lb>il cono AHD come due rettangoli KGL al quadrato AE, suppongo dimostrato <lb></lb>da V. S. (cioè dal Torricelli a cui si rivolge il discorso) molto egregiamente, <lb></lb>e la maniera mia poco varia, avendolo io dimostrato uguale al qui descritto <lb></lb>cilindro intorno l&#039;asse stesso del frusto, e che il suo quadrato TI sia uguale <lb></lb>al rettangolo KGL; al cilindro dico, toltine li coni PIQ, RIS, e mi vaglio <lb></lb>della medesima proposizione presa dai Conici. </s>

<s>Che poi il frusto ABCD, al <lb></lb>cono AHD, stia come que&#039;tre quadrati al quadrato AE, il raccolgo da una <lb></lb>proposizione mia altre volte accennata a V. S., che un tal frusto sia uguale <lb></lb>a tre coni, con l&#039;altezza HE, e sopra i cerchi descritti dagl&#039;intervalli AE, <lb></lb>F, BH ” (ivi, fol. </s>

<s>30, 31). </s></p><p type="main">

<s>Queste ultime parole destarono nell&#039;animo del Torricelli un sentimento, <lb></lb>che si direbbe di gelosia, non quale però è generata dall&#039;impotenza, ma dalla <lb></lb>prepotenza. </s>

<s>Contenne per allora in silenzio i primi moti della sua passione, <lb></lb>ma quando il Ricci impaziente tornò una settimana dopo a scrivere in una <pb xlink:href="020/01/2809.jpg" pagenum="434"></pb>lettera queste parole: <emph type="italics"></emph>un&#039;altra volta la pregherò a voler vedere una mia <lb></lb>proposizione intorno li frusti parabolici, iperbolici, sferici, compresi sotto <lb></lb>una sola proposizione<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>27); il Torricelli risoluto rispose che anzi <lb></lb>quella universale proposizione era sua, e non poteva patire che nessun altro <lb></lb>se la fosse appropriata. </s>

<s>S&#039;è veduto quanto equamente avesse nella prima let­<lb></lb>tera il Ricci distribuite le parti del merito, e perchè di esse non ne toccava al­<lb></lb>trui che le secondarie, rimanendo le principali per sè; con buon diritto po­<lb></lb>teva chiamar sua la proposizione delle conoidali. </s>

<s>Facile nonostante a cedere, <lb></lb>e disposto a riversare nel pingue erario del Torricelli anche questa moneta <lb></lb>ingiusta, presa occasione da altre cose, che aveva a dire, così soggiungeva: </s></p><p type="main">

<s>“ Passo all&#039;altra lettera, per la quale pare che V. S. mi accenni di so­<lb></lb>spettare un poco che io voglia attribuirmi l&#039;invenzione di cotesta sua pro­<lb></lb>posizione dei solidi conoidali. </s>

<s>Non piaccia a Dio che io faccia mai simile <lb></lb>azione. </s>

<s>Si ricordi pure V. S. di una lettera, che io le scrissi molte setti­<lb></lb>mane sono, dove le dicevo di aver considerato che il modo usato da V. S. <lb></lb>per li frusti sferici poteva portarsi in modo più generale: intendo quanto alla <lb></lb>sfera scavata dal cono e dal cilindro. </s>

<s>Secondariamente dissi a V. S. che, <lb></lb>dovendo un tal solido escavato essere uguale ad una tale sferoide, non po­<lb></lb>teva servire alla proposizion generale, nella quale si cercasse la proporzione <lb></lb>di sfera, sferoide, conoide etc. </s>

<s>al cono inscritto, poichè bisognava supporre <lb></lb>come noto la sferoide essere doppia del rombo inscrittole. </s>

<s>Ed a questo pre­<lb></lb>tesi poi di ovviare io con dimostrare que&#039;solidi uguali ad un cilindro, con <lb></lb>le determinazioni già avvisatele nell&#039;ultima mia. </s>

<s>Si tolga dunque dall&#039;animo <lb></lb>tali pensieri. </s>

<s>Che se mai avessi neppur ombra che V. S. mi tenesse in con­<lb></lb>cetto di arrogarmi nemmeno un ette d&#039;altrui, vorrei imporre alli miei stu­<lb></lb>dii perpetuo silenzio, poichè con essi è solo il mio fine di spassarmi, e di <lb></lb>continuare il commercio con V. S., a me senza modo dilettevole..... Roma, <lb></lb>16 Luglio 1644 ” (ivi, fol. </s>

<s>36). </s></p><p type="main">

<s>Non abbiamo voluto lasciar l&#039;occasione di rivelar verso i più cari amici <lb></lb>quell&#039;animo, il mal abito del quale vedremo esser portato dal Torricelli an­<lb></lb>che in pubblico, nelle contese ch&#039;egli ebbe con gli stranieri. </s>

<s>Dopo ciò, ritor­<lb></lb>nando sopra il nostro sentiero, si dovrebbe per le fatte promesse aggiungere <lb></lb>la seconda parte di quel trattato dei centri di gravità, a cui dette opera il <lb></lb>Nardi, dicendo com&#039;egli investigasse il centro delle potenze nella sua propria <lb></lb>Cicloide. </s>

<s>L&#039;ordine cronologico però, secondo il quale ha da svolgersi questa <lb></lb>nobilissima parte della Storia, ci consiglia a non introdurci ancora dietro il <lb></lb>Nostro nel campo, senza prima riconoscere la cultura, e saggiare i frutti rac­<lb></lb>coltivi da uno straniero, facendo invece una breve sosta fuor della chiusa <lb></lb>siepe, in faccia al callare, per osservar gli strumenti che lo dettero aperto. </s></p><p type="main">

<s>Principalissimi fra questi sono il Teorema meccanico universale, ossia la <lb></lb>Regola centrobarica, e il metodo degl&#039;indivisibili. </s>

<s>Nell&#039;altro Tomo e nel pre­<lb></lb>sente abbiam veduto come prendesse il Nardi quel primo strumento dalla <lb></lb>officina guldiniana, e com&#039;ei lo temprasse e affinasse alla fucina della Geo­<lb></lb>metria, facendo le prime prove delle virtù di lui nel baricentro della mezza <pb xlink:href="020/01/2810.jpg" pagenum="435"></pb>circonferenza. </s>

<s>Quanto al metodo degli indivisibili si lusingava il buon Cava­<lb></lb>lieri di essere egli stato il primo a insegnarlo, ma il Nardi riconosce di così <lb></lb>fatte dottrine, che apparvero nuove, più antichi e autorevoli maestri. </s>

<s>La cosa, <lb></lb>come s&#039;intende, è di tale e tanta importanza, da non doversene passare con <lb></lb>sentenza sì asciutta. </s></p><p type="main">

<s>La seconda Ricercata geometrica, qual si legge nel manoscritto donato <lb></lb>alla Biblioteca di Roma, conclude le risposte alle obiezioni contro Archimede <lb></lb>col pronunziare che queste son nulle, o per lo più leggere. </s>

<s>Si direbbe no­<lb></lb>nostante, soggiunge l&#039;Autore, essersi il Siracusano messo a inchieste ardue <lb></lb>e lubriche, se non si pensasse agl&#039;impulsi ch&#039;egli ebbe, nello speculare e <lb></lb>nell&#039;inventare, dalle precedenti tradizioni, e al molto aiuto che gli venne <lb></lb>dall&#039;usare il metodo degli indivisibili, e dal praticar l&#039;esperienze. </s>

<s>A queste, <lb></lb>risolvendo le questioni accennate da noi nel secondo capitolo della prima <lb></lb>parte di questa Storia, attribuisce l&#039;invenzione del centro di gravità nella <lb></lb>rettangola conoidale, supposto noto nella IIa del secondo libro <emph type="italics"></emph>De insiden­<lb></lb>tibus humido:<emph.end type="italics"></emph.end> e a quello, cioè al metodo degl&#039;indivisibili, il segreto di tante <lb></lb>geometriche verità, da parer quasi rivelazioni di un Nume. </s></p><p type="main">

<s>Da Archimede confessa dunque il Nardi di avere appresa la dottrina del­<lb></lb>l&#039;infinito, riducendo per essa le quantità lineari a tal piccolezza da trasfor­<lb></lb>mare il curvo nel retto. </s>

<s>Ma delle particolari applicazioni del metodo gli sparse <lb></lb>nella mente i primi semi una pellegrina dimostrazione di Pappo, chi ripensi <lb></lb>alla quale sentesi compreso da uno stupore, com&#039;a vedere sotto il sol me­<lb></lb>ridiano scintillare una stella in mezzo al cielo profondo. </s>

<s>È data quella dimo­<lb></lb>strazione dal Matematico alessandrino nel teorema XXI del quarto libro delle <lb></lb><emph type="italics"></emph>Collezioni,<emph.end type="italics"></emph.end> per concluderne che lo spazio, compreso tra la spirale e la linea <lb></lb><figure id="id.020.01.2810.1.jpg" xlink:href="020/01/2810/1.jpg"></figure></s></p><p type="caption">

<s>Figura 292.<lb></lb>condotta al centro dal princi­<lb></lb>pio della circolazione, è la ter­<lb></lb>za parte della superficie del <lb></lb>cerchio. </s></p><p type="main">

<s>Sia lo spazio da misurare <lb></lb>BEFAB, nella figura 292. Di­<lb></lb>visa tutta la circonferenza in <lb></lb>parti uguali, sian due di que­<lb></lb>ste AC, CD, dalle quali e dalle <lb></lb>loro concentriche FG, EH sian <lb></lb>chiusi quattro settori. </s>

<s>Espon­<lb></lb>gasi anche insieme un rettangolo KL, di cui i lati KP, KN sian divisi in tante <lb></lb>parti uguali, in quante fu divisa la stessa circonferenza, ed essendo due di <lb></lb>queste parti KR, RQ sopra l&#039;un lato, KM, MS sopra l&#039;altro; si conducano <lb></lb>RT, QV parallele a KN, e MZ, SO parallele a KP. </s></p><p type="main">

<s>Per la genesi della spirale archimedea, per supposizione e per costru­<lb></lb>zione, sarà, chiamata C la circonferenza, BC:CF=C:CA=KP:KR= <lb></lb>KL:KZ=RT:RZ. </s>

<s>Dividendo la prima e l&#039;ultima ragione e de&#039;loro ter­<lb></lb>mini facendo il quadrato, BC2:BF2=RT2:TZ2. </s>

<s>Con simile ragione dimo-<pb xlink:href="020/01/2811.jpg" pagenum="436"></pb>streremo DB2:BE2=QV2:VO2, e così sarà vero passando a ricercare le <lb></lb>altre parti. </s>

<s>Ora essendo ai quadrati de&#039;raggi de&#039;circoli proporzionali i set­<lb></lb>tori, e ai quadrati de&#039;raggi delle basi proporzionali i cilindri ugualmente alti, <lb></lb>si potrà concluderne che ciascun settore circoscritto sta al corrispondente, <lb></lb>inscritto nella spirale, come ciascun cilindro circoscritto sta all&#039;inscritto nel <lb></lb>triangolo KNL, rivolgendosi i rettangoli genitori intorno all&#039;asse NL. </s>

<s>E perchè <lb></lb>in tutte le proporzionali così dimostrate i primi e i terzi termini sono uguali, <lb></lb>staranno dunque le somme dei settori ai settori come le somme dei cilindri <lb></lb>ai cilindri, ossia la superficie del circolo, alla somma dei settori inscritti nella <lb></lb>spirale, come il cilindro del rettangolo NP, alla somma de&#039;cilindri, de&#039;quali <lb></lb>si costruisce il conoide gradinato. </s>

<s>Supponendo poi Pappo che sian prese così <lb></lb>minime le divisioni, da sparire i trilinei FGA, EHF .... e le addentellature <lb></lb>KMZ, ZXO .... riduce in ultimo la proporzione a dire: <emph type="italics"></emph>circulum, ad eam <lb></lb>figuram, quae inter lineam spiralem et rectam AB intercipitur, ita esse <lb></lb>ut cylindrus ad conum<emph.end type="italics"></emph.end> (editio cit., pag. </s>

<s>84) cioè come tre a uno. </s>

<s>Nella qual <lb></lb>supposizione vide il Nardi il metodo degl&#039;indivisibili nascosto come in un nido, <lb></lb>da cui, incubato sotto le ali del suo proprio ingegno, vide con lieta maravi­<lb></lb>glia uscirne un modo nuovo di quadrar la parabola. </s></p><p type="main">

<s>Sia la mezza figura 293 intorno al diametro AO, e sopra la base OX, <lb></lb>con la quale e col centro in O sia descritto il quadrante OCX, a cui e alla <lb></lb>semiparabola circoscrivansi i rettangoli OL, OM. </s>

<s>Presa una minima parte <lb></lb>AD, si conduca da D una parallela ad AO, e si prolunghi in I. </s>

<s>Dai punti <lb></lb>poi E, H, ne&#039;quali la detta linea incontra le due curve, si conducano ordinata­<lb></lb>mente FE, GH. </s>

<s>Avremo OD:OE=DR:RE=AO:RE=OX2:OX.RX= <lb></lb>OC2:RH2=<foreign lang="grc">π</foreign>OC2:<foreign lang="grc">π</foreign>RH2. </s>

<s>E perciò OD:OE=<foreign lang="grc">π</foreign>OC2.OR:<foreign lang="grc">π</foreign>RH2.OR. <lb></lb><figure id="id.020.01.2811.1.jpg" xlink:href="020/01/2811/1.jpg"></figure></s></p><p type="caption">

<s>Figura 293.<lb></lb>E così per tutte le altre infinite divisioni saranno simili <lb></lb>proporzionalità fra i rettangoli della figura superiore e i <lb></lb>cilindri della inferiore, supponendo questa rivolgersi intorno <lb></lb>alla linea OX come a suo proprio asse. </s>

<s>Ora, osservando <lb></lb>che in ognuna delle dette proporzionalità i primi e i terzi <lb></lb>termini sono uguali, avremo la somma di tutti i rettangoli, <lb></lb>ai rettangoli, come la somma di tutti i cilindri ai cilindri; <lb></lb>ossia il rèttangolo OM, alla semiparabola, come il cilindro <lb></lb>all&#039;emisfero, che vuol dire, come tre a due. </s>

<s>Ma ascoltiamo <lb></lb>il Nardi, che non solamente discorre così, ma aggiunge altre <lb></lb>importanti notizie al suo discorso. </s></p><p type="main">

<s>“ Una pellegrina dimostrazione di Pappo, ove egli, con <lb></lb>l&#039;aiuto dei solidi e col ridurli occultamente agl&#039;indivisibili, <lb></lb>prova la ragione del cerchio allo spazio elico, mi diede oc­<lb></lb>casione, per la conformità dei soggetti, di pensar con lo <lb></lb>stesso metodo alla ragione di un rettilineo alla parabola, il che felicemente <lb></lb>successemi. </s>

<s>” </s></p><p type="main">

<s>“ Sia una mezza parabola AXO, di cui il diametro AO, e la mezza base <lb></lb>OX sia semidiametro d&#039;un cerchio, di cui un quadrante OCB, centro O, e <pb xlink:href="020/01/2812.jpg" pagenum="437"></pb>il rettangolo OL sia circoscritto ad esso quadrante. </s>

<s>Dividasi ora tanto la retta <lb></lb>AM, quanto la uguale CL, in parti minime, sicchè, essendo una di loro AD, <lb></lb>manchi DM da AM meno di ogni proponibile distanza, e lo stesso avvenga <lb></lb>di LI rispetto ad LC. ” </s></p><p type="main">

<s>“ Ciò supposto, tirisi DR parallela ad AO, e seghi la curva parabolica <lb></lb>in E, e sia FE applicata alla mezza parabola. </s>

<s>Lo stesso accada nel rettan­<lb></lb>golo OL, dove, tirata IR parallela al semidiametro, seghi la periferia nel <lb></lb>punto H, e quindi nel semidiametro cada la perpendicolare HG. È poi vero <lb></lb>che il parallelogrammo OD, all&#039;altro OE, è come DR ad RE, o come il qua­<lb></lb>drato OC al quadrato HR, o come il cilindro CR all&#039;altro HO. Adunque, <lb></lb>come tutti i minimi rettangoli circoscritti o inscritti nella mezza parabola, ad <lb></lb>essa mezza parabola; così tutti i minimi cilindri circoscritti o inscritti nel <lb></lb>quadrante di sfera, ad esso quadrante. </s>

<s>Onde di nuovo sarà il parallelogrammo <lb></lb>OM, alla mezza parabola, come il cilindro OL al quadrante di sfera. </s>

<s>È poi il <lb></lb>cilindro sesquialtero del quadrante di sfera; adunque il parallelogrammo sarà <lb></lb>sesquialtero della mezza parabola. </s>

<s>E però, essendo il triangolo inscritto nella <lb></lb>mezza parabola tre di quelle parti, delle quali il parallelogrammo OM è sei, <lb></lb>e la mezza parabola quattro; sarà questa sesquiterza del triangolo inscritto. </s>

<s>” </s></p><p type="main">

<s>“ E qui ultimamente ho osservato aver avuto l&#039;occhio il dottissimo Tor­<lb></lb>ricelli, nel X e XIII modo di quadrar la parabola. </s>

<s>Ma, tornando alla dimo­<lb></lb>strazione di Pappo, confesso che quella fra le antiche fu la prima, che spar­<lb></lb>semi nella mente i semi della retta maniera di dimostrare le ragioni del <lb></lb>curvo e del retto, e della dottrina degl&#039;indivisibili, quale poi da&#039;moderni, e <lb></lb>in particolare dall&#039;ingegnosissimo p. </s>

<s>Cavalieri, ho veduta coltivata lauta­<lb></lb>mente ” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>141). </s></p><p type="main">

<s>Avremmo voluto rendere questo documento sopra gli altri anche più <lb></lb>cospicuo, a ritirare il dubbio da noi altrove, per insufficiente esame, emesso, <lb></lb>che cioè fosse il Nardi non troppo favorevole al metodo cavalierano, mentre <lb></lb>è un fatto ch&#039;egli ne aveva prevenuta già l&#039;invenzione. </s>

<s>Non fa perciò ma­<lb></lb>raviglia se con tale argomento in mano, aggiuntavi la Regola centrobarica, <lb></lb>fosse il Nostro in Italia de&#039;primi a penetrare i segreti della Cicloide, aperti <lb></lb>con argomenti uguali o simili qualche anno prima in Francia. </s>

<s>Ma la sen­<lb></lb>tenza, che da noi s&#039;anticipa, intorno a una questione delle più vivamente <lb></lb>agitate fra i Matematici, dopo la prima metà del secolo XVII, e che non ha <lb></lb>avuto fin qui altra regola delle preconcette opinioni in fuori, e dell&#039;amor <lb></lb>nazionale; vuol essere confermata dai fatti, che sinceramente passeremo a <lb></lb>narrare dai loro principii. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le prime dispute insorsero intorno all&#039;inventore della Cicloide, dicen­<lb></lb>dosi comunemente in Italia essere stato costui Galileo. </s>

<s>E veramente sembre­<lb></lb>rebbe favorire una tale opinione un documento prezioso, ritrovato da noi in <pb xlink:href="020/01/2813.jpg" pagenum="438"></pb>alcuni manoscritti, derivati senza dubbio dalla libreria del p. </s>

<s>ab. </s>

<s>Guido Grandi, <lb></lb>col titolo: <emph type="italics"></emph>Roba del gran Galileo, in parte copiata dagli originali, e in <lb></lb>parte dettata da lui cieco a me Vincenzio Viviani, mentre dimoravo nella <lb></lb>sua casa di Arcetri.<emph.end type="italics"></emph.end> Quel documento, che si diceva, è dettato e scritto in <lb></lb>dialogo, per inserirsi nella prima giornata delle due Scienze nuove “ a facce 25 <lb></lb>(dell&#039;edizione di Leida) dopo le parole che dice il Sagredo <emph type="italics"></emph>Il negozio è vera­<lb></lb>mente molto intrigato .... però diteci quel che ne conviene. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ SALVIATI. — Prima però di dirvi una mia opinione, non voglio la­<lb></lb>sciare indietro di proporvi un fatto, che mi occorse a notare, speculando io <lb></lb>intorno al modo di risolvere, forse più ragionevolmente di quel che non avesse <lb></lb>fatto Aristotile, questo problema della ruota veramente ammirando. </s>

<s>Per ri­<lb></lb>durmi la cosa più sotto i sensi, e per aiutare la mia immaginazione, feci <lb></lb>quell&#039;esagono, che vi ho detto, di cartone ben sodo, mettendomi a ruzzolarlo <lb></lb>lungo una riga, tenuta ferma applicata contro un foglio, sopra il quale due <lb></lb>punte di spillo, una infissa nel centro del poligono esterno, l&#039;altra nel sog­<lb></lb>giacente angolo del poligono interno e concentrico, mi avrebbero lasciate <lb></lb>impresse le vestigie degli archi continui e de&#039;saltuari, dei quali ho discorso. </s>

<s><lb></lb>Trasformando poi i due esagoni in due cerchi, pur col medesimo centro, per <lb></lb>ridurmi più d&#039;appresso alla contemplazione della ruota di Aristotile, mi ven­<lb></lb>nero messi i due spilli in C e in B (fig. </s>

<s>294), e facendo rivolgere la ruota <lb></lb><figure id="id.020.01.2813.1.jpg" xlink:href="020/01/2813/1.jpg"></figure></s></p><p type="caption">

<s>Figura 294.<lb></lb>sopra la riga BF per una intera circolazione, trovai con una certa maravi­<lb></lb>glia tracciate sopra il foglio le due curve linee BIF, CHE, quali vedete rap­<lb></lb>presentate in questa figura. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Elegantissime curve in vero, le quali, insistendo sopra <lb></lb>due corde di uguale lunghezza, e soprastando ad esse con differente altezza; <lb></lb>sembra che possano adattarsi alla costruzione dei ponti, ai quali, mantenendo <lb></lb>la medesima luce, si volesse dare o maggiore o minore il rigoglio. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Così parve anche a me, e a proposito del disegno del <lb></lb>nuovo ponte di Pisa, che si voleva fare di un arco solo, avrei volentieri sug­<lb></lb>gerito all&#039;architetto una centina di quella figura, che mi aveva tanto bel <lb></lb>garbo. </s>

<s>Ma le mie speranze erano principalmente rivolte a promovere la scienza, <lb></lb>ch&#039;era mia professione, perchè forse, dallo spazio compreso fra l&#039;arco della <pb xlink:href="020/01/2814.jpg" pagenum="439"></pb>curva e la base, ne sarebbe potuta derivare qualche utile notizia per la tanto <lb></lb>desiderata misura dello spazio circolare. </s>

<s>Vero è bene che, partecipando na­<lb></lb>turalmente ciascun generato delle qualità dei generanti, dubitai non fossero <lb></lb>tra loro le due quantità incommensurabili, e fu per questa ragione che, prima <lb></lb>di applicarmi agl&#039;incerti e faticosi argomenti della Geometria, volli averne <lb></lb>qualche consiglio con l&#039;esperienza. </s>

<s>Scelsi dunque un cartone, della più uni­<lb></lb>forme solidità e superficie che mi fosse possibile ritrovare, e di una parte <lb></lb>di esso incisi, come seppi far meglio, una perfettissima ruota. </s>

<s>Sopra il ri­<lb></lb>manente poi con esquisito macchinamento, disegnai la curva, a fil della quale <lb></lb>e della linea, ch&#039;era lungo la sottoposta riga servita di base, diligentemente <lb></lb>tagliai il cartone. </s>

<s>Avuta in fine una bilancetta da orafi, delle più esatte e <lb></lb>gelose, pesai, più accuratamente che se fossero stati oro o margarite preziose, <lb></lb>i due incisi cartoni, e poco mancò che l&#039;uno non fosse il triplo dell&#039;altro. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Se fossi stato chiamato io a consulto, quando si posero <lb></lb>l&#039;origini delle cose, vi confesso, signor Salviati, la mia temerità, che avrei <lb></lb>consigliato la Geometria a fare una tal proporzione esattamente tripla, attem­<lb></lb>perando all&#039;armonia universale anco questa corda, fin qui rimasta non tocca. </s>

<s><lb></lb>Ma ditemi, non si potrebbe attribuire la differenza a qualche inesattezza nello <lb></lb>sperimentare, o non potrebbe dipendere dal non avere scelta conveniente <lb></lb>materia? </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Io usai d&#039;incidere le figure anche sopra lamine di me­<lb></lb>tallo, ma sempre l&#039;un peso mi riuscì qualche poco men che triplo dell&#039;altro. </s>

<s><lb></lb>Se la differenza avesse avuto origine dall&#039;imperfezione della materia, o dal <lb></lb>poco esatto strumento, o dalla mia propria imperizia nel maneggiarlo, non <lb></lb>sembra anche a voi che, conseguendo da così fatti inevitabili difetti il dar <lb></lb>talvolta di meno, non si fosse tal altra dovuto aver qualche cosa più del <lb></lb>giusto? </s>

<s>Or perchè accordarsi perpetuamente in andar nel medesimo eccesso, <lb></lb>se non per intrinseca natura della cosa, e perchè insomma le due proposte <lb></lb>grandezze non hanno fra loro nessuna misura comune? </s>

<s>E così, parendomi <lb></lb>esser certo, abbandonai l&#039;impresa, che mi s&#039;era prima presentata con spe­<lb></lb>ranza così lusinghiera. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Se da questa speculazione non può ricavarsi alcun utile <lb></lb>per la Geometria, come voi dite, la lascieremo anche noi volentieri, per tor­<lb></lb>nare a pregarvi, signor Salviati, ci diciate quel che convenga a noi di pen­<lb></lb>sare intorno alla ragione dello scorrere il cerchio minore una linea tanto <lb></lb>maggiore della sua circonferenza. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Io ricorrerei alla considerazione dei poligoni sopra con­<lb></lb>siderati etc. </s>

<s>” </s></p><p type="main">

<s>Quanto è certo che fu dettato e disteso questo frammento di dialogo sui <lb></lb>principii dell&#039;anno 1639, altrettanto è dubbio quando occorresse a osservare <lb></lb>la Cicloide primaria e la secondaria, tracciate sul foglio dal moto dello stru­<lb></lb>mento descritto dal Salviati. </s>

<s>Quel che fu detto, essere cioè stata fatta l&#039;os­<lb></lb>servazione infino dal 1600, è una congettura, una reminiscenza, una giacu­<lb></lb>latoria de più devoti discepoli di Galileo. </s>

<s>È certo altresì che, sotto il nome <pb xlink:href="020/01/2815.jpg" pagenum="440"></pb>volgare di <emph type="italics"></emph>Roulette,<emph.end type="italics"></emph.end> si trattava della nuova curva in Parigi, infino dal 1628, <lb></lb>e il Roberval attesta averne udito ivi parlare al Mersenno come di cosa in­<lb></lb>torno alla quale, benchè inutilmente, s&#039;erano da molti anni travagliati gl&#039;in­<lb></lb>gegni. </s>

<s>Hanno alcuni voluto confermare, dietro questa notizia, l&#039;antichità e <lb></lb>il primato dell&#039;invenzione galileiana, ma come, essendo fra noi rimasta di­<lb></lb>menticata, pellegrinasse a que&#039;tempi in Francia, e ritrovasse fra gli stranieri <lb></lb>quell&#039;accoglienza, che non ebbe fra&#039;suoi; secondo l&#039;ordine naturale delle <lb></lb>cose, non si comprende. </s></p><p type="main">

<s>Ben assai più conforme a quest&#039;ordine è il pensare che il caso occorso <lb></lb>al Salviati fosse occorso tante volte prima a quei Matematici, i quali, non <lb></lb>avendo altro maestro che Aristotile, e da&#039;libri di lui attingendo i principii <lb></lb>da risolvere le più ardue questioni, pensavano di risolvere anche quella della <lb></lb>quadratura del circolo dallo speculare intorno alla Ruota famosa, e alla linea <lb></lb>descritta, nel rivolgersi, da un punto fisso della sua circonferenza. </s>

<s>Inutili co­<lb></lb>nati è vero, ma da&#039;quali si può argomentare come dovesse ai contemporanei <lb></lb>di Leonardo da Vinci, del Cardano e del Vieta appresentarsi spontanea, nel <lb></lb>meditare sopra la XXIV questione meccanica del Filosofo, la curva gentile. <lb></lb></s>

<s>È da ripensare anzi alle occasioni forse più efficaci e immediate d&#039;incontrarsi <lb></lb>nella Cicloide, studiando quella meccanica quadratura del circolo, che i Ma­<lb></lb>tematici infin dal secolo XIV leggevano con tanto gusto in Archimede, quando <lb></lb>s&#039;incominciò a divulgare la prima collezione delle opere di lui. </s>

<s>“ Dal moto <lb></lb>del carro, scriveva in una sua Nota Leonardo, ci è sempre stato dimostro <lb></lb>dirizzare la circonferenza de&#039;cerchi. </s>

<s>La mezza circonferenza della rota, della <lb></lb>quale la grossezza sia uguale al suo semidiametro, lascia di sè vestigio eguale <lb></lb>alla quadratura del suo cerchio ” (MSS. E, fol. </s>

<s>25 v.). </s></p><p type="main">

<s>Comunque sia, da Galileo in Firenze, e dal Mersenno in Parigi ha i suoi <lb></lb>principii storici la Cicloide, che però non va, nè all&#039;un celebre uomo nè <lb></lb>all&#039;altro, debitrice de&#039;suoi progressi. </s>

<s>Il Francese nonostante, a cui non ne <lb></lb>venne mai meno la speranza, fu di così fatti progressi assai più benemerito <lb></lb>dell&#039;Italiano, che distolse dall&#039;applicarvisi gl&#039;ingegni, reputando la quadra­<lb></lb>tura della Cicloide problema non men disperato di quell&#039;altro della quadra­<lb></lb>tura del circolo genitore. </s>

<s>Di qui è che fu causa l&#039;inganno di Galileo del­<lb></lb>l&#039;essersi indugiato fra noi a riconoscere il vero una diecina di anni dopo i <lb></lb>Francesi, come si vedrà resultare dai fatti, che passiamo a narrare imparziali. </s></p><p type="main">

<s>Egidio Roberval era assai giovane, quando il Mersenno gli propose di <lb></lb>studiare intorno alle proprietà della curva, descritta dal rivolgersi della Ruota <lb></lb>aristotelica, e perciò difficilissima apparvegli allora la proposta. </s>

<s>Seguitando <lb></lb>intanto gli amati esercizi, apprese dal divino Archimede quella dottrina del­<lb></lb>l&#039;infinito, che poi il Cavalieri chiamò degl&#039;indivisibili, col retto metodo dei <lb></lb>quali sciolse alcuni de&#039;più ardui problemi geometrici, qual&#039;era quello di mi­<lb></lb>surare la superficie conica di uno scaleno. </s>

<s>Erano in questo passati sei anni, <lb></lb>e il Mersenno tornò a battere sulla Trochoide, rimproverando il giovane amico <lb></lb>ch&#039;egli avesse lasciato indietro un così nobile studio, quasi si confessasse <lb></lb>dalle difficoltà esser vilmente rimasto atterrito. </s>

<s>“ Ego sic castigatus, coepi <pb xlink:href="020/01/2816.jpg" pagenum="441"></pb>sedulo ipsam (trochoidem) inspicere, ac tunc quidem, quae absque indivisi­<lb></lb>bilibus difficillima visa erat, ipsis opitulantibus nullo negotio patuit ” (<emph type="italics"></emph>Ro­<lb></lb>bervallii epist. </s>

<s>ad Torricellium,<emph.end type="italics"></emph.end> Oouvrages cit., pag. </s>

<s>369). </s></p><p type="main">

<s>Le proposizioni, che con l&#039;aiuto degli indivisibili il Roberval dimostrò <lb></lb>intorno alla Trocoide, furono lette privatamente in scuola, e comunicate agli <lb></lb>amici, nè si resero di pubblica ragione, se non che molto tardi, qua e là <lb></lb>disperse per le Opere, raccolte poi fra le memorie dell&#039;Accademia di Parigi. </s>

<s><lb></lb>Noi ordineremo quelle proposizioni, con i lemmi, da cui alcune son prece­<lb></lb>dute, e di molto abbrevieremo il discorso, usando il metodo analitico, e in­<lb></lb>troducendo il segno Ŗ nel calcolo delle quantità indivisibili, perchè, non es­<lb></lb><figure id="id.020.01.2816.1.jpg" xlink:href="020/01/2816/1.jpg"></figure></s></p><p type="caption">

<s>Figura 295.<lb></lb>sendo altro esse quantità che i <lb></lb>differenziali dei Matematici mo­<lb></lb>derni, la loro somma dunque <lb></lb>corrisponde a una vera e pro­<lb></lb>pria integrazione. </s></p><p type="main">

<s>“ PROPOSITIO I. — <emph type="italics"></emph>Semi­<lb></lb>trochoides AFD<emph.end type="italics"></emph.end> (fig. </s>

<s>295) <emph type="italics"></emph>sinus <lb></lb>versi IL est quadrupla, seu <lb></lb>diametri IH dupla ”<emph.end type="italics"></emph.end> (De tro­<lb></lb>choide, Ouvrages cit., pag. </s>

<s>342). </s></p><p type="main">

<s>Conclude il Roberval il suo <lb></lb>assunto col dimostrar che, presa <lb></lb>qualsivoglia porzione AF della <lb></lb>curva, alla quale corrisponda l&#039;arco circolare IMF, essa porzione è uguale al <lb></lb>quadruplo del seno verso IQ della metà IM dell&#039;arco. </s>

<s>Son mezzi della di­<lb></lb>mostrazione tre principii, il primo geometrico, il secondo meccanico, e il terzo, <lb></lb>che partecipa dell&#039;uno e dell&#039;altro modo. </s></p><p type="main">

<s>Il primo principio, di cui fa l&#039;Autore frequenti applicazioni, si trova fa­<lb></lb>cilmente dimostrato nel <emph type="italics"></emph>Traité des indivisibles,<emph.end type="italics"></emph.end> ed è tale: Sia del semicer­<lb></lb>chio ADB (fig. </s>

<s>296) presa qualunque parte, come per es. </s>

<s>CD o AC: diviso <lb></lb>l&#039;arco AC ugualmente in E, F, G .... e da ciascun punto della divisione <lb></lb>abbassati i seni EL, FM, GN .... “ je dis que la ligne AH est à la circon­<lb></lb>ference AC comme tous les sinus ensemble sont à autant des sinus totaux, <lb></lb>ou demidiamètres ” (pag. </s>

<s>212). </s></p><p type="main">

<s>Il secondo principio dipende dal metodo di condur le tangenti, applican­<lb></lb>dovi la regola del parallelogrammo delle forze, a quel modo che vedemmo <lb></lb><figure id="id.020.01.2816.2.jpg" xlink:href="020/01/2816/2.jpg"></figure></s></p><p type="caption">

<s>Figura 296.<lb></lb>nella proposizione V della Meccanica nuova <lb></lb>del Torricelli. </s>

<s>Secondo questa dottrina si <lb></lb>trovano in F, nella figura 295, raccolte le <lb></lb>velocità degl&#039;infiniti punti dell&#039;arco IF, e <lb></lb>della porzion di cicloide AF: velocità, che <lb></lb>resultano delle infinite respettive tangenti. </s>

<s><lb></lb>E perchè nei moti equabili le velocità son <lb></lb>proporzionali agli spazi AF, FMI, passati nel <pb xlink:href="020/01/2817.jpg" pagenum="442"></pb>medesimo tempo “ ut ergo omnes tangentes curvae AF ad omnes tangentes <lb></lb>arcus IMF, sic ipsa curva AF ad ipsum arcum IMF (pag. </s>

<s>341). </s></p><p type="main">

<s>A instituire i terzo principio, essendo FG tangente al circolo nel punto <lb></lb>F, FH tangente alla curva, e perciò resultante del moto, si conducano il rag­<lb></lb>gio FL, e la corda FI. </s>

<s>I triangoli simili FGH, FLI danno FH ad FG, come <lb></lb>IF ad FL. </s>

<s>Se ora intendansi fatte nell&#039;arco IMF, e nella porzione di curva <lb></lb>AF, le medesime infinite divisioni, e, condotte le medesime infinite tangenti, <lb></lb>se ne prenda le somme; ne concluderemo, con l&#039;Autore, per terzo principio, <lb></lb>“ chordas illas omnes simul sumptas, ad radium FL toties sumptum, sic se <lb></lb>habere, ut omnes tangentes curvae AF simul, ad omnes tangentes arcus IMF <lb></lb>simul, hoc est, per secundum notatum, ut curva ipsa AF, ad arcum ipsum <lb></lb>IMF ” (pag. </s>

<s>341). </s></p><p type="main">

<s>Premonstrati i quali principii, così facilmente si conduce il Roberval alla <lb></lb>desiderata conclusione. </s>

<s>Dagli infiniti punti di divisione dell&#039;arco IM, metà di <lb></lb>IMF, si conducano sul raggio LI gl&#039;infiniti seni retti corrispondenti, ciascun <lb></lb>de&#039;quali essendo la metà della corda, la metà pure sarà quella di questa loro <lb></lb>somma. </s>

<s>Se perciò si chiamino <emph type="italics"></emph>s.r<emph.end type="italics"></emph.end> i seni retti, <emph type="italics"></emph>e<emph.end type="italics"></emph.end> le corde, e con Ŗ si signi­<lb></lb>fichi la loro somma, avremo 2Ŗ<emph type="italics"></emph>s.r<emph.end type="italics"></emph.end>=Ŗc. </s>

<s>E se con Ŗ<emph type="italics"></emph>r<emph.end type="italics"></emph.end> si rappresenti la <lb></lb>somma dei raggi, sarà, per il terzo premesso principio, Ŗ<emph type="italics"></emph>c<emph.end type="italics"></emph.end>:Ŗ<emph type="italics"></emph>r<emph.end type="italics"></emph.end>=AF:IMF= <lb></lb>2Ŗ<emph type="italics"></emph>s.r<emph.end type="italics"></emph.end>:Ŗ<emph type="italics"></emph>r.<emph.end type="italics"></emph.end> E perchè, per il primo degli stessi premessi principii, Ŗ<emph type="italics"></emph>s.r<emph.end type="italics"></emph.end>:Ŗ<emph type="italics"></emph>r<emph.end type="italics"></emph.end>= <lb></lb>IQ:IM, ossia 2Ŗ<emph type="italics"></emph>s.r<emph.end type="italics"></emph.end>:Ŗ<emph type="italics"></emph>r<emph.end type="italics"></emph.end>=2IQ:IM; dunque AF:IMF=2IQ:IM= <lb></lb>4IQ:2IM=4IQ:IMF, ond&#039;è veramente AF=4Iq. </s></p><p type="main">

<s>Potendosi ora una tale dimostrazione applicare a qualunque punto della <lb></lb>mezza Cicloide, comunque sia dall&#039;origine A distante, supponiamo che il dato <lb></lb>punto sia D. </s>

<s>Troveremo ancora, col medesimo processo, AFD=4IL=2IH, <lb></lb>ciò che vuol dire essere, così com&#039;era il proposito di dimostrare, la mezza <lb></lb>Cicloide doppia al diametro del circolo genitore. </s></p><p type="main">

<s><emph type="italics"></emph>Corollario.<emph.end type="italics"></emph.end> — Diviso l&#039;arco IR nel mezzo in P, come nel mezzo M è <lb></lb>stato diviso l&#039;arco IF, e condotte le due corde FP, RM, è facile vedere che <lb></lb>queste s&#039;intersecheranno fra loro e col diametro HI nel punto T, in modo <lb></lb>che sia HF=HT=HI—IT=HI—2IQ, d&#039;onde 2HF+4IQ=2HI= <lb></lb>AFD, essendo la semicicloide, per le cose già dimostrate, uguale al doppio del <lb></lb>diametro. </s>

<s>E perch&#039;è stato altresì dimostrato che la porzione AF è uguale al <lb></lb>quadruplo del seno verso IQ, dunque 2HF=AFD—AF=DF, ciò che <lb></lb>vuol dire essere ogni porzione, presa dal vertice, uguale al doppio della tan­<lb></lb>gente. </s>

<s>Così il Wallis, quell&#039;<emph type="italics"></emph>Anglus vir doctissimus, qui et praelo per se, <lb></lb>vel per amicos suo nomine vulgavit<emph.end type="italics"></emph.end> (pag. </s>

<s>344), formulò la seconda parte <lb></lb>della proposiz. </s>

<s>XXII, nel cap. </s>

<s>V della sua <emph type="italics"></emph>Mechanica:<emph.end type="italics"></emph.end> “ Curvae semicycloi­<lb></lb>dis portio quaevis, ad verticem terminata, est dupla subtensae corresponden­<lb></lb>tis arcus circuli genitoris ” (Londini 1741, pag. </s>

<s>424). </s></p><p type="main">

<s>“ PROPOSITIO II. — <emph type="italics"></emph>In rota simplici spatium trochoidis triplum est <lb></lb>eiusdem rotae ”<emph.end type="italics"></emph.end> (Ouvr. </s>

<s>cit., pag. </s>

<s>310). </s></p><p type="main">

<s>La facilità della dimostrazione dipende dall&#039;invenzion di quella curva, <lb></lb>che il Roberval chiamava la <emph type="italics"></emph>Compagne de la roulette,<emph.end type="italics"></emph.end> e noi la <emph type="italics"></emph>Comite<emph.end type="italics"></emph.end> della <pb xlink:href="020/01/2818.jpg" pagenum="443"></pb>Cicloide. </s>

<s>“ Pour décrire cette ligne, dice l&#039;Autore, ayant tiré des point de la <lb></lb>Roulette des lignes paralleles à AC (fig. </s>

<s>297), si dans chacune de ces lignes, <lb></lb>a commencer aux points de la Roulette, l&#039;on prend une ligne égale à la por­<lb></lb>tion de la mesme ligne comprise entre la demi-circonference du cercle et <lb></lb>son axe, l&#039;on avra les points par lesquels cette ligne est décrite. </s>

<s>Ainsi tirant <lb></lb>comme nous avons dit la ligne GHI, si dans la mesme ligne vous prenez GN <lb></lb><figure id="id.020.01.2818.1.jpg" xlink:href="020/01/2818/1.jpg"></figure></s></p><p type="caption">

<s>Figura 297.<lb></lb>égale a HI, vous avrez le point N, par lequel passe la compagne de la Tro­<lb></lb>choide. </s>

<s>De mesme prenant dans KLM la ligne KO égale à LM, vous avrez <lb></lb>un autre point O de la mesme ligne. </s>

<s>Et si par le centre E vous tirez EF <lb></lb>perpendiculaire a BD, et si vous la prolongez en P, jusqu&#039;à la Roulette, <lb></lb>ayant pris de P vers F la ligne PQ égale à EF, dans la mesme ligne PF <lb></lb>vous avrez le point Q, qui est le milieu de cette ligne-cy, et auquel elle <lb></lb>change de courbure ” (pag. </s>

<s>64). </s></p><p type="main">

<s>Apparisce in primo luogo da una tal descrizione che lo spazio rinchiuso <lb></lb>fra la cicloide e la comite è diviso dalla linea PQ in due parti uguali, come <lb></lb>quelle che sono intessute de&#039;seni retti di due quadranti del medesimo cir­<lb></lb>colo, con transiti, non equabili, ma simili qua e là nelle due figure, ond&#039;è <lb></lb>che tutto il detto spazio è uguale a quello dello stesso mezzo cerchio. </s>

<s>2.o Dai <lb></lb>punti N, O, Q abbassando perpendicolari sulla base AD, saranno queste linee <lb></lb>i seni versi corrispondenti ai seni retti già presi. </s>

<s>3.o La parte superiore QB <lb></lb>della comite sarà uguale all&#039;inferiore ANQ, perchè tutte le linee condotte <lb></lb>parallelamente alla base son tagliate in parti contrariamente uguali, e di qui <lb></lb>è ch&#039;essa comite divide il rettangolo nel mezzo, come l&#039;AB diagonale. </s>

<s>Con­<lb></lb>segue in ultimo dalla fatta costruzione che i due bilinei ANQA, QBQ sono <lb></lb>uguali, e che perciò uguale spazio rinchiudono dentro l&#039;angolo retto ADB la <lb></lb>comite e la diagonale. </s></p><p type="main">

<s>La superficie dunque, che si propone a quadrare, è composta di quella <lb></lb>compresa tra la cicloide e la comite, e dell&#039;altra occupata dal triangolo mi­<lb></lb>stilineo AQBD, uguale al rettilineo ABD, che ha per misura AD.BD/2= <lb></lb><foreign lang="grc">π</foreign>DB/2.DB/2=<foreign lang="grc">π</foreign>DB2/4, ossia uguale al circolo di diametro BD. </s>

<s>Aggiunta a <lb></lb>questa l&#039;altra superficie, compresa tra la linea cicloidale e la comite, e che <pb xlink:href="020/01/2819.jpg" pagenum="444"></pb>vedemmo essere uguale al mezzo cerchio, “ toute la figure de la Cycloide <lb></lb>vaudra trois fois le cercle ” (ivi, pag. </s>

<s>211). </s></p><p type="main">

<s><emph type="italics"></emph>Corollario.<emph.end type="italics"></emph.end> — Di qui è patente che i quattro spazi compresi tra l&#039;asse e il <lb></lb>semicircolo, tra il semicircolo e la comite, tra la comite e la cicloide, tra la ci­<lb></lb>cloide e il rettangolo circoscritto; sono uguali, e che perciò il detto rettangolo <lb></lb>contiene quattro di quelle parti, delle quali la cicloide ne contiene tre sole. </s></p><p type="main">

<s>Ecco come veramente il Roberval avesse <emph type="italics"></emph>nullo negotio<emph.end type="italics"></emph.end> risoluto il pro­<lb></lb>blema della quadratura della Cicloide, che Galileo aveva abbandonato come <lb></lb>impresa, non solo difficilissima, ma disperata. </s>

<s>La stereometria però de&#039;solidi, <lb></lb>generati dal rivolgersi la figura col suo rettangolo circoscritto intorno alla <lb></lb>base, intorno a una tangente al vertice, intorno all&#039;asse; era altro negozio, <lb></lb>a trattare il quale, non bastando le forze naturali, bisognava, come a rimo­<lb></lb>vere un corpo troppo ponderoso, ricorrere all&#039;aiuto dei macchinamenti. </s>

<s>Il <lb></lb>Torricelli, come vedremo, ritrovò questi validissimi aiuti nella Regola cen­<lb></lb>trobarica, ma il Roberval, o che non avesse ancora veduti i libri del Gul­<lb></lb>dino, o che sdegnasse di ricorrere agli stranieri soccorsi della Meccanica, <lb></lb>volle tutto ricavare dagl&#039;intimi seni della Geometria pura, dimostrando la <lb></lb>seguente proposizione, da servire, alla stereometria de&#039;cicloidali, di primo e <lb></lb>principalissimo lemma: </s></p><p type="main">

<s>“ Si on decrit alentour d&#039;une figure un parallelogramme (nous avons <lb></lb>pris un cercle en cet exemple) et qu&#039;on fasse tourner le tout sur un des <lb></lb>costez du parallelogramme; le solide fait par ce parallelogramme est au so­<lb></lb>lide fait par la figure, comme le plan du parallelogramme est au plan de la <lb></lb>figure ” (pag. </s>

<s>222). </s></p><p type="main">

<s>Essendo un circolo, col quadrato a lui circoscritto, come nella fig. </s>

<s>298, <lb></lb>e HF l&#039;asse della rivoluzione, è manifesto che saranno i solidi generati un <lb></lb><figure id="id.020.01.2819.1.jpg" xlink:href="020/01/2819/1.jpg"></figure></s></p><p type="caption">

<s>Figura 298.<lb></lb>anello stretto e un cilindro, la pro­<lb></lb>porzion tra i quali e le figure ge­<lb></lb>nitrici si dimostra in questo caso <lb></lb>assai facilmente. </s>

<s>L&#039;anello infatti si <lb></lb>compone delle infinite armille QM, <lb></lb>VN .... come il cilindro dei corri­<lb></lb>spondenti circoli SO, TP .... Inten­<lb></lb>dendosi ora con <emph type="italics"></emph>a<emph.end type="italics"></emph.end> significata l&#039;armilla <lb></lb>abbiamo <emph type="italics"></emph>a<emph.end type="italics"></emph.end> QM=<foreign lang="grc">π</foreign>SQ2—<foreign lang="grc">π</foreign>MS2= <lb></lb><foreign lang="grc">π</foreign>(SQ+MS)(SQ—MS)= <lb></lb><foreign lang="grc">π</foreign>SO.QM. </s>

<s>Troveremo allo stesso <lb></lb>modo <emph type="italics"></emph>a<emph.end type="italics"></emph.end> VN=<foreign lang="grc">π</foreign>TP.VN, e così di <lb></lb>tutte le altre. </s>

<s>La somma dunque di <lb></lb>tutte queste infinite armille, delle <lb></lb>quali si compone l&#039;anello A, sarà, osservando che TP=SO, A= <lb></lb>SO(QM+VN...). </s></p><p type="main">

<s>Il circolo poi descritto da SO è uguale a <foreign lang="grc">π</foreign>SO2 come il circolo di TP <lb></lb>a <foreign lang="grc">π</foreign>TP2. </s>

<s>Della somma di tutti questi circoli componendosi il cilindro C, sarà <pb xlink:href="020/01/2820.jpg" pagenum="445"></pb>dunque C=<foreign lang="grc">π</foreign>SO(SO+TP...) e perciò A:C=QM+VN...:SO+TP... <lb></lb>Ma di questa seconda ragione il primo termine è la somma di tutte le linee, <lb></lb>che intessono il circolo, e il secondo è la somma di tutte le linee, che intes­<lb></lb>sono il quadrato; dunque i solidi rotondi stanno come le figure. </s></p><p type="main">

<s>Tale dimostrazione però non s&#039;adatta che al circolo, o a figure segate <lb></lb>dall&#039;AB in due parti, non solamente uguali, ma simmetriche intorno all&#039;asse. </s>

<s><lb></lb>Però volendo il Roberval dare dimostrazione più generale, applicabile a qua­<lb></lb>lunque figura divisa in due parti uguali, o simmetriche o no intorno all&#039;asse, <lb></lb>procede in quest&#039;altra maniera, considerando l&#039;armilla QM composta delle due <lb></lb>parti IM, IQ, quella uguale a <foreign lang="grc">π</foreign>IS2—<foreign lang="grc">π</foreign>SM2, questa uguale a <foreign lang="grc">π</foreign>SQ2—<foreign lang="grc">π</foreign>SI2. </s>

<s><lb></lb>Si tratta ora di riunire insieme queste due armille, al quale intento si giunge <lb></lb>così, abbreviando la via tenuta dall&#039;Autore: </s></p><p type="main">

<s>IS2—SM2=MI2+2IM.MS=MI(MI+MS)+IM.MS= <lb></lb>MI.IS+IM.MS, onde (*) IS2—SM2+IQ2=MI.IS+IM.MS+IQ2= <lb></lb>MI.IS+MI.MS+MI2=MI.IS+MI(MS+MI)=MI.IS+MI.IS= <lb></lb>2MI.IS. </s>

<s>Abbiamo inoltre SQ2—SI2—IQ2=2SI.IQ=2SI.IM, la quale, <lb></lb>sommata con quella notata sopra con asterisco, darà IS2—SM2+SQ2—SI2= <lb></lb>4SI.IM. </s>

<s>Troveremo nello stesso modo TK2—TN2+TV2—TK2=4TK.NK <lb></lb>e così di tutte le altre infinite armille, che sommate insieme comporranno l&#039;anello <lb></lb>A=<foreign lang="grc">π</foreign>SI(IM+KN...)=2<foreign lang="grc">π</foreign>SI2(IM+KN...)=<foreign lang="grc">π</foreign>SO(MQ+NV...). </s></p><p type="main">

<s>Venendo ai circoli, quello descritto da SO sarà <foreign lang="grc">π</foreign>SO2; quello descritto <lb></lb>da TP=<foreign lang="grc">π</foreign>TP2, e così di tutti gli altri infiniti, i quali sommati insieme <lb></lb>comporranno il cilindro C=<foreign lang="grc">π</foreign>SO(SO+TP...), onde </s></p><p type="main">

<s><emph type="center"></emph>A:C=MQ+NV...:SO+TP...<emph.end type="center"></emph.end><lb></lb>Ma nel secondo membro di questa equazione il primo termine è la somma <lb></lb>di tutte le infinite linee tessenti il circolo, il secondo la somma di tutte le <lb></lb>infinite linee tessenti il rettangolo; dunque l&#039;anello sta al cilindro, come il <lb></lb>circolo al rettangolo circoscritto. </s></p><p type="main">

<s><emph type="italics"></emph>Corollario I.<emph.end type="italics"></emph.end> — Qualunque sia la figura inscritta nel rettangolo, purchè <lb></lb>venga dalla linea AB, parallela all&#039;asse di rotazione, segata in due parti <lb></lb>uguali, com&#039;esso rettangolo; i solidi rotondi saranno sempre proporzionali <lb></lb>ai piani da cui son generati. </s></p><p type="main">

<s><emph type="italics"></emph>Scolio.<emph.end type="italics"></emph.end> — “ Nous trouverons la mesme chose en faisant tourner toute <lb></lb>la figure sur la ligne YZ ” (pag. </s>

<s>224) e tirate le sezioni come dianzi, per <lb></lb>esempio la UO, si dimostra dall&#039;Autore in simile modo che “ le quadruple <lb></lb>du rectangle UIO sera au quarré de EY comme le cylindre, ou plutost le <lb></lb>rouleau GEFH, est au cylindre total EGZY ” (ivi, pag. </s>

<s>225). </s></p><p type="main">

<s>Se dunque son vere le cose dimostrate, anche quando l&#039;asse della rivo­<lb></lb>luzione sia una parallela a HF, come per esempio ZY, chiamato Ro il rotondo, <lb></lb>che descrive il parallelogrammo Po, e Ao l&#039;anello descritto dal circolo Co; <lb></lb>avremo Ro:Ao=Po:Co. </s>

<s>Moltiplicando la seconda ragione per 2<foreign lang="grc">π</foreign>LP, <lb></lb>ossia per la circonferenza descritta dal raggio LR, sarà </s></p><p type="main">

<s><emph type="center"></emph>Ro:Ao=Po.2<foreign lang="grc">π</foreign>LR:Co.2<foreign lang="grc">π</foreign>LR.<emph.end type="center"></emph.end><pb xlink:href="020/01/2821.jpg" pagenum="446"></pb>Ora il Roberval dimosta che, essendo Ro=Po.2<foreign lang="grc">π</foreign>LR, è anche in conse­<lb></lb>guenza Ao=Co.2<foreign lang="grc">π</foreign>LR, ciò che dà luogo a formulare la proposizione: <lb></lb>“ Je dis que la roule GF est egal au solide qui a pour base le parallelo­<lb></lb>gramme GF, et pour hauteur la circonference d&#039;un cercle, qui a pour demi­<lb></lb>diametre la ligne LR ” (pag. </s>

<s>228). </s></p><p type="main">

<s>Concludesi dall&#039;Autore l&#039;uguaglianza tra EFGH.2<foreign lang="grc">π</foreign>LR e Ro.EFGH <lb></lb>(ossia il rotondo descritto dal rettangolo EH) dimostrando che ambedue si <lb></lb>uguagliano a un terzo solido Co.GY, che vuol dire al cilindro descritto dal <lb></lb>rettangolo GY. </s>

<s>La dimostrazione procede facilmente per questa via: </s></p><p type="main">

<s><emph type="center"></emph>Co.GY=<foreign lang="grc">π</foreign>GZ.GZ.HF; EFGH.2<foreign lang="grc">π</foreign>LR=HF.GH.2<foreign lang="grc">π</foreign>LR,<emph.end type="center"></emph.end><lb></lb>onde EFGH.2<foreign lang="grc">π</foreign>LR:Co.GY=GH.2LR:GZ2=4GB.BZ:GZ2. </s>

<s><lb></lb>Ma per lo Scolio precedente 4GB.BZ sta a GZ2 come il rotondo di EGFH <lb></lb>sta a Co.GY; dunque questo rotondo è uguale al solido, che ha per base <lb></lb>EFGH, e per altezza 2<foreign lang="grc">π</foreign>LR. </s>

<s>E perciò dall&#039;essersi così dimostrato Ro= <lb></lb>Po.2<foreign lang="grc">π</foreign>LR, ne consegue Ao=Co.2<foreign lang="grc">π</foreign>LR, che vuol dire insomma equiva­<lb></lb>lere i due solidi a due prismi di pari altezza, uguale alla circonferenza de­<lb></lb>scritta dal raggio LR distesa in dirittura, ma l&#039;un dei quali avesse per base <lb></lb>il rettangolo, e l&#039;altro il circolo, dal rivolgimento de&#039;quali furono quelli stessi <lb></lb>solidi generati. </s></p><p type="main">

<s>Questo teorema, che il Roberval intitola <emph type="italics"></emph>Des anneaux,<emph.end type="italics"></emph.end> apparirà a chiun­<lb></lb>que vi ripensi notabilissimo, avuto riguardo alla Regola centrobarica, o non <lb></lb>conosciuta allora in Francia, o trasposta così di proposito, dal campo della <lb></lb>Meccanica, in quello della Geometria, qualche tempo prima che, a confortar <lb></lb><figure id="id.020.01.2821.1.jpg" xlink:href="020/01/2821/1.jpg"></figure></s></p><p type="caption">

<s>Figura 299.<lb></lb>di matematiche ragioni le proposte del Gul­<lb></lb>dino, si pensasse in Italia. </s>

<s>Ma lasciando stare <lb></lb>le applicazioni feconde, che di questo teorema <lb></lb>robervalliano della trasformazion de&#039;solidi annu­<lb></lb>lari in prismi si poteva fare alla Stereometria; <lb></lb>il principale intento, per cui lo troviamo rac­<lb></lb>colto fra queste proposizioni, è quello di ser­<lb></lb>vire di lemma principale alla misura dei solidi <lb></lb>cicloidali. </s>

<s>Altri due lemmi però, per agevolar <lb></lb>l&#039;ardua via, e da nessune altre orme segnata, <lb></lb>erano necessari, e il Roberval così se gli pro­<lb></lb>poneva a dimostrar facilmente, aiutandosi degli <lb></lb>indivisibili. </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma II.<emph.end type="italics"></emph.end> — Les quarrez des sinus sont <lb></lb>au quarre du diametre pris autant de fois comme <lb></lb>1 à 8 ” (pag. </s>

<s>251). </s></p><p type="main">

<s>Sia il quadrante FLN (fig. </s>

<s>299) diviso in un numero infinito di parti <lb></lb>uguali. </s>

<s>Noi considereremo le tre divisioni fatte in M, L, K, dalle quali si <pb xlink:href="020/01/2822.jpg" pagenum="447"></pb>conducano i seni retti GM, HL, IK, e i seni retti KQ, LP, MO dei loro com­<lb></lb>plementi. </s>

<s>Avremo </s></p><p type="main">

<s><emph type="center"></emph>DM2=GM2+GD2<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DL2=HL2+HD2<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DK2=KI2+ID2<emph.end type="center"></emph.end><lb></lb>… <lb></lb>Sommando queste equazioni, e osservando che tutti i loro primi membri sono <lb></lb>uguali al raggio R, avremo ŖR2=GM2+HL2+KI2...+GD2+HD2+ID2... <lb></lb>Ma nel secondo rispetto la prima somma è quella de&#039;quadrati de&#039;seni retti, <lb></lb>che potrà significarsi con Ŗ<emph type="italics"></emph>s.r2,<emph.end type="italics"></emph.end> la seconda è quella dei complementi de&#039;seni <lb></lb>retti, ed è manifestamente in numero e in quantità uguale all&#039;altra; e perciò <lb></lb>ŖR2=2Ŗ<emph type="italics"></emph>sr2.<emph.end type="italics"></emph.end> Ora, intendendosi per D il diametro, R2 è uguale a D2/4: <lb></lb>dunque ŖD2/4=2Ŗ<emph type="italics"></emph>sr2,<emph.end type="italics"></emph.end> ossia Ŗ<emph type="italics"></emph>sr2:<emph.end type="italics"></emph.end>ŖD2=1:8. </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma III.<emph.end type="italics"></emph.end> — Le quarré du diametre pris autant de fois est aux <lb></lb>quarrez des sinus verses commè 8 à 3 ” (pag. </s>

<s>252). </s></p><p type="main">

<s>Osservando che FE2=(FI+IE)2=FI2+IE2+2FI.IE, e che <lb></lb>FI.IE=IK2, e così di tutte le altre infinite sezioni del diametro EF; <lb></lb>avremo </s></p><p type="main">

<s><emph type="center"></emph>EF2=FI2+IE2+2IK2<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>EF1=FH2+HE2+2HL2<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>EF2=FG2+GE2+2GM2<emph.end type="center"></emph.end><lb></lb>… <lb></lb>Sommando e osservando che FI2+FH2+FG2.... è la somma di tutti i <lb></lb>quadrati dei seni versi, che significheremo con Ŗ<emph type="italics"></emph>s.v2;<emph.end type="italics"></emph.end> e IE2+HE2+GE2.... <lb></lb>la somma de&#039;loro complementi, e che perciò tutti questi sono uguali a tutti <lb></lb>quelli; avremo ŖEF2=2Ŗ<emph type="italics"></emph>s.v2<emph.end type="italics"></emph.end>+2(IK2+KL2+GM2....). Ma la <lb></lb>somma dentro parentesi è, per il lemma precedente, uguale 1/8 ŖEF2, dun­<lb></lb>que ŖEF2—1/4 ŖEF2=2Ŗ<emph type="italics"></emph>s.v2,<emph.end type="italics"></emph.end> d&#039;onde 3ŖEG2=8Ŗ<emph type="italics"></emph>s.v2,<emph.end type="italics"></emph.end> ossia <lb></lb>ŖEF2:Ŗ<emph type="italics"></emph>s.v2<emph.end type="italics"></emph.end>=8:3. </s></p><p type="main">

<s>Premessi i quali tre lemmi, le proporzioni, che passano tra i solidi e i <lb></lb>cilindri circoscritti, rivolgendosi le figure intorno alla base, e intorno alle <lb></lb>tangenti o al vertice o all&#039;origine della Cicloide; tornarono al Roberval così, <lb></lb>come noi le compendieremo con discorso analitico, d&#039;assai facile invenzione. <lb></lb><figure id="id.020.01.2822.1.jpg" xlink:href="020/01/2822/1.jpg"></figure></s></p><p type="caption">

<s>Figura 300.</s></p><p type="main">

<s>“ PROPOSITIO III. — <emph type="italics"></emph>La <lb></lb>raison de 5 à 8 est celle du <lb></lb>solide, que fait la roulette <lb></lb>AIB<emph.end type="italics"></emph.end> (fig. </s>

<s>300) <emph type="italics"></emph>au cylindre <lb></lb>AM, le tout tournant sur <lb></lb>ACB ”<emph.end type="italics"></emph.end> (pag. </s>

<s>267). </s></p><p type="main">

<s>Considera l&#039;Autore il so­<lb></lb>lido proposto resultar di due parti: di quella descritta dallo spazio AFIRA, <pb xlink:href="020/01/2823.jpg" pagenum="448"></pb>compreso tra la cicloide e la comite, e dell&#039;altra, che vien descritta dal tri­<lb></lb>lineo AFIC. </s>

<s>Ora la prima detta figura è, per il corollario della seconda pro­<lb></lb>posizione, un quarto del rettangolo AI, ed ha, come il detto rettangolo, il <lb></lb>centro sopra la GD, che sega in due parti uguali ambedue le figure, ed è <lb></lb>parallela all&#039;asse AB della revoluzione. </s>

<s>Dunque i solidi rotondi, per il co­<lb></lb>rollario primo del primo lemma, stanno come le figure piane, e perciò il solido, <lb></lb>che chiameremo S, al cilindro C, come uno a quattro, o come due a otto. </s></p><p type="main">

<s>La figura poi AFIC è per costruzione intessuta delle infinite linee pa­<lb></lb>rallele a IC, ossia degli infiniti seni versi del mezzo circolo IEC, ed è nel <lb></lb>terzo lemma stato dimostrato che la somma de&#039;quadrati di tutti questi seni <lb></lb>versi, o de&#039;circoli da essi descritti, sta alla somma de&#039;quadrati del diame­<lb></lb>tro IC, o de&#039;circoli da lui descritti e presi altrettante volte, come 3 a 8. Ora, <lb></lb>essendo manifesto che la somma de&#039;primi circoli costituisce il solido T del <lb></lb>trilineo, e la somma dei secondi il solido C del cilindro; avremo T:C=3:8. <lb></lb>Ma è altresì S:C=2:8, dunque S:T=2:3. Componendo S+T:T= <lb></lb>5:3, d&#039;onde S+T:C<gap></gap>5:8. </s></p><p type="main">

<s>Di qui manifestamente resultando </s></p><p type="main">

<s><emph type="center"></emph><foreign lang="grc">π</foreign>KV2+<foreign lang="grc">π</foreign>ON2+<foreign lang="grc">π</foreign>RQ2...:<foreign lang="grc">π</foreign>ZV2+<foreign lang="grc">π</foreign>PN2+<foreign lang="grc">π</foreign>SQ2=5:8,<emph.end type="center"></emph.end><lb></lb>avremo, dividendo per <foreign lang="grc">π</foreign>, KV2+ON2...:ZV2+PN2...=5:8. </s></p><p type="main">

<s>“ PROPOSITIO IV. — <emph type="italics"></emph>Maintenant il faut voir quelle raison il y avra <lb></lb>entre le solide de la mesme roulette a son cylindre, lors qu&#039;elle tourne <lb></lb>sur LM<emph.end type="italics"></emph.end> (uella medesima figura) <emph type="italics"></emph>parallele à AB, qui est celle de 7 à 8 ”<emph.end type="italics"></emph.end><lb></lb>(pag. </s>

<s>268). </s></p><p type="main">

<s>Considera l&#039;Autore che il solido descritto dallo spazio cicloidale, in que­<lb></lb>sto caso, uguaglia il cilindro, toltone il solido generato dai trilinci ALI, IMB, <lb></lb>a trovar la misura del quale si riduce il presente negozio. </s>

<s>E perchè resulta <lb></lb>la detta misura dalla somma degl&#039;infiniti circoli, come sarebbro quelli de­<lb></lb>scritti da ZK, PO, SR, ecc., convien prima dunque con le seguenti equa­<lb></lb>zioni predisporre per ciascuno i valori </s></p><p type="main">

<s><emph type="center"></emph>ZK2=ZV2+KV2—2VZ.VK<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>PO2=PN2+ON2—2PN.ON<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SR2=SQ2+RQ2—2Sq.RQ<emph.end type="center"></emph.end><lb></lb>… <lb></lb>Sommando tutte queste equazioni, e osservando che <expan abbr="ZV+PN+Sq.">ZV+PN+Sque</expan>..= <lb></lb>ŖIC, avremo </s></p><p type="main">

<s><emph type="center"></emph>ZK2+PO2+SR2=ŖIC2+KV2+ON2...—2ŖIC(VK+ON...).<emph.end type="center"></emph.end><lb></lb>Ma, per il corollario della precedente, KV2+ON2...=5/8 ŖIC2, e, per il <lb></lb>corollario della seconda, VK+ON...=3/4 ŖIC; dunque </s></p><p type="main">

<s><emph type="center"></emph>ZK2+PO2...=8/8 ŖIC2+5/8 ŖIC2—12/8 ŖIC2=1/8 ŖIC2.<emph.end type="center"></emph.end><lb></lb>Moltiplicando per <foreign lang="grc">π</foreign>, <foreign lang="grc">π</foreign>KZ2+<foreign lang="grc">π</foreign>PO2...=1/8<foreign lang="grc">π</foreign>ŖIC2. </s>

<s>Ond&#039;è che, compo-<pb xlink:href="020/01/2824.jpg" pagenum="449"></pb>nendosi degl&#039;infiniti circoli di raggio KZ, PO, ecc., come si disse, il solido T <lb></lb>descritto dal trilineo ALI, e degl&#039;infiniti circoli, tutti di raggio uguale a IC, <lb></lb>il cilindro C; avremo C:T=8:1. Dividendo, C—T:T=7:1, d&#039;onde <lb></lb>C—T:C=7:8. </s></p><p type="main">

<s>“ PROPOSITIO V. — <emph type="italics"></emph>Il faut maintenant considerer les solides, qui se <lb></lb>font quand la figure tourne sur LA. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Où on remarquera que la ligne IC, parallele à la dite LA, coupe le <lb></lb>parallelogramme AM et la figure AIB en deux egalement, et partant les so­<lb></lb>lides sont entr&#039;eux comme les plans, et ainsi le solide fait par AIB sera au <lb></lb>cylindre, formé par le parallelogramme AM, comme le plan de l&#039;un est au <lb></lb>plan de l&#039;autre. </s>

<s>Mais les plans sont entr&#039;eux comme 4 à 3, partant le cylin­<lb></lb>dre sera au solide de la roulette comme 4 à 3 ” (pag. </s>

<s>269). </s></p><p type="main">

<s>“ Haec et multa alia, conclude il Roberval, circa annos 1635 et 1640, <lb></lb>vigente animi vigore, detexi ” (pag. </s>

<s>342). Tentò altresì la misura del solido <lb></lb>generato dalla mezza cicloide e dal cilindro circoscritto, facendosi la rivolu­<lb></lb>zione intorno all&#039;asse, ma lasciò allora l&#039;impresa per disperata, sembrandogli <lb></lb>essere i due solidi fra loro incommensurabili. </s>

<s>Vi tornò poi sopra, quando il <lb></lb>Torricelli annunziò di aver avuta in proporzioni definite quella misura, di <lb></lb>che diremo altrove, prima di por termine a questa digressione. </s></p><p type="main">

<s>Intanto lo stesso Roberval e il Mersenno andavano tutti compiacenti <lb></lb>diffondendo fra i Matematici la notizia di queste scoperte, e principalmente <lb></lb>della quadratura della Cicloide, facendosi intendere com&#039;ella fosse stata di­<lb></lb>mostrata precisamente tripla del circolo genitore. </s>

<s>Ne sentirono allegrezza gli <lb></lb>amici, e livore gli emuli e gl&#039;invidiosi, sfogandosi col dire che la cosa era <lb></lb>poi tanto facile, da non meritar che se ne facesse tutto quel gran rumore, <lb></lb>non ripensando costoro che una tale facilità dipendeva dall&#039;essersi per il Ro­<lb></lb>berval l&#039;ipotesi ridotta a tesi, che ciascuno era certo di poter dimostrare. <lb></lb><figure id="id.020.01.2824.1.jpg" xlink:href="020/01/2824/1.jpg"></figure></s></p><p type="caption">

<s>Figura 301.</s></p><p type="main">

<s>Essendo infatti due le vie, che na­<lb></lb>turalmente si paravano innanzi, l&#039;una <lb></lb>delle quali consisteva nel decomporre <lb></lb>lo spazio cicloidale DGABD (fig. </s>

<s>301), <lb></lb>nel triangolo rettilineo DAB; e nel bi­<lb></lb>lineo DGAD; e l&#039;altra nel decomporre <lb></lb>quel medesimo spazio nel mezzo cerchio <lb></lb>DHA, e nel trilineo DGAHB; è ma­<lb></lb>nifesto che, dovendo essere il tùtto uguale a tre mezzi cerchi, de&#039;quali il <lb></lb>triangolo, che ha per base la mezza circonferenza e per altezza il diametro, <lb></lb>è due; tutto si riduceva a trovar modo di dimostrare come li bilineo fosse <lb></lb>uguale a uno, e il trilineo a due di quei mezzi cerchi. </s>

<s>Tenne questa via il <lb></lb>Fermat, e quella il Cartesio, il quale, in comunicarne la dimostrazione al <lb></lb>Mersenno, così gli scriveva: “ Inchoasti per inventionem d. </s>

<s>De Roberval de <lb></lb>spatio comprehenso in linea curva, quam describit punctum aliquod circum­<lb></lb>ferentiae circuli, qui concipitur rotari aut currere super plano quodam, quam <lb></lb>mihi fateor nunquam in mentem venisse, et eius annotationem perelegantem <pb xlink:href="020/01/2825.jpg" pagenum="450"></pb>esse. </s>

<s>Caeterum non video rem tanti esse, quae buccina vulgetur, cum sit in­<lb></lb>ventu facilis, quamque vel mediocriter in Geometria versatus certo invenire <lb></lb>potest, si eam quaerit ” (<emph type="italics"></emph>Epistolae,<emph.end type="italics"></emph.end> P. III, Amstelod. </s>

<s>1683, pag. </s>

<s>240). </s></p><p type="main">

<s>Chiunque infatti può facilmente dimostrare che tutte le infinite linee <lb></lb>come GH, EI (nella medesima figura) equidistanti alla FC, che parallela­<lb></lb>mente alla base attraversa il centro; son coppia a coppia uguali alla corda, <lb></lb>come KL, condotta parallelamente al diametro, a una distanza MC, che si <lb></lb>uguagli alla NC. </s>

<s>Or perchè di quelle infinite linee accoppiate si compone il <lb></lb>bilineo, e delle infinite corde, corrispondenti a ciascuna di quelle coppie, il <lb></lb>semicerchio; dunque le due superficie sono uguali. </s></p><p type="main">

<s>Riduce ingegnosamente il Cartesio a maggior facilità la cosa, disponendo <lb></lb>le coppie GH, EI, e tutte le altre infinite in continuità lungo una medesima <lb></lb>direzione, col trasportar lo spazio DFO, che nella figura 301 riman di sotto, <lb></lb>invece allato, come ACD nella figura 302. Resulta da una tale disposizione <lb></lb><figure id="id.020.01.2825.1.jpg" xlink:href="020/01/2825/1.jpg"></figure></s></p><p type="caption">

<s>Figura 302.<lb></lb>che la linea FD, divisa nel mezzo in B, uguaglia EH diametro del semicir­<lb></lb>colo EIH, da cui è generata la cicloide, e che tutte le corde, come KL, sono <lb></lb>uguali alle infinite linee, una delle quali è GC essendo queste tanto distanti <lb></lb>da FD, quanto dal centro O sono distanti quelle. </s>

<s>Ciò che evidentemente prova, <lb></lb>dice il Cartesio, essere le due superficie uguali a chi non ignora che due <lb></lb>figure, aventi la medesima base e la medesima altezza, e tutte le linee rette <lb></lb>parallele, inscritte nell&#039;una, uguali alle infinite inscritte nell&#039;altra; si disten­<lb></lb>dono nello spazio ugualmente. </s>

<s>“ Verum, poi soggiunge, cum fortasse sint qui <lb></lb>theoremati isti non applaudant, pergendum duxi hoc modo (ibid., pag. </s>

<s>228). <lb></lb>Il modo consiste nel comune e antico degl&#039;inscritti, facendo osservare che <lb></lb>sono uguali qua e là i triangoli EIH, FAD, insistenti con pari altezza sopra <lb></lb>basi uguali: e uguali i triangoli SAP, QAC insieme, ai triangoli KIM, INL <lb></lb>insieme, e anche il triangolo FGP+QCD uguale al triangolo EKM+NLH, <lb></lb>per le medesime assai patenti ragioni. </s>

<s>Così essendo vero di tutti i triangoli, <lb></lb>che resultano dal moltiplicare all&#039;infinito le iscrizioni, resta provato che lo <lb></lb>spazio FGAD, da cui si rappresenta il bilineo della Cicloide, è uguale a mezzo <lb></lb>il circolo genitore. </s></p><p type="main">

<s>Non vogliamo proseguire il discorso, senza arrestarci un poco a ripen­<lb></lb>sare come il Cartesio è il terzo, dopo il Roberval e il Nardi, a far uso degli <lb></lb>indivisibili, prima che se ne istituisse il metodo nella <emph type="italics"></emph>Geometria nuova.<emph.end type="italics"></emph.end> I <lb></lb>primi due commemorati, benchè confessassero di aver non da altri che <pb xlink:href="020/01/2826.jpg" pagenum="451"></pb>da Archimede e da Pappo derivata la dottrina dell&#039;infinito, pur non de­<lb></lb>trassero poi nulla alla gloria del Cavalieri, la Geometria del quale parve <lb></lb>al Nardi <emph type="italics"></emph>oṕera gigantea, così oscure verità discopre e in sì nobile maniera<emph.end type="italics"></emph.end><lb></lb>(MSS. Gal., T. XX, pag. </s>

<s>1895), e il Roberval, che pure avrebbe potuto chia­<lb></lb>marsi a parte col Cavalieri nel merito dell&#039;invenzione, così generosamente <lb></lb>si protestava in pubblico con queste parole: “ Ego tanto viro, tantae ac tam <lb></lb>sublimis doctrinae inventionem non eripiam, nec possum, nec si possim fa­<lb></lb>ciam. </s>

<s>Ille prius vulgavit, ille hoc iure suam fecit: ille hoc iure habeat, atque <lb></lb>possideat, ille tandem hoc iure inventoris nomine gaudeat ” (Ouvrages cit., <lb></lb>pag. </s>

<s>367). </s></p><p type="main">

<s>Il Cartesio però, nè fra gli antichi nè fra i moderni, non conosce mae­<lb></lb>stro: il metodo degli indivisibili è parto del suo proprio cervello, per cui si <lb></lb>ride e sente compassione di questo povero Cavalieri. </s>

<s>Nell&#039;Aprile del 1646, <lb></lb>essendo in Leida, gli si fa incontro il professore Schoten, il giuniore, per <lb></lb>dirgli ch&#039;era recapitata quivi d&#039;Italia la <emph type="italics"></emph>Geometria nuova.<emph.end type="italics"></emph.end> Prende il Car­<lb></lb>tesio fra le mani il libro, e lo svolge non più che per un quarto d&#039;ora, <emph type="italics"></emph>qua­<lb></lb>drantis horae spatio,<emph.end type="italics"></emph.end> eppure ciò gli basta per formarsi il giudizio che non <lb></lb>si faceva lì dall&#039;Autore altro che ripetere cose viete, dimostrandole in quel <lb></lb>modo, con cui aveva egli stesso dimostrata la quadratura della Cicloide. </s>

<s>Poi <lb></lb>si mette a dire che alla chiave di questo Cavalieri mancavano per aprire gli <lb></lb><figure id="id.020.01.2826.1.jpg" xlink:href="020/01/2826/1.jpg"></figure></s></p><p type="caption">

<s>Figura 303.<lb></lb>ingegni. </s>

<s>“ Ego enim multa plura novi maio­<lb></lb>ris ponderis, quorum vim magnam in meam <lb></lb>Geometriam contuli: ille autem ea non facile <lb></lb>inveniet, neque intelliget unum ex illis, nisi <lb></lb>prolixo volumine explicatum ” (Epistol., P. III <lb></lb>cit., pag. </s>

<s>343). Ma vediamo come il Fermat <lb></lb>dimostrasse, non men facilmente del Cartesio, <lb></lb>che il trilineo ABFD (fig. </s>

<s>303) nella mezza ci­<lb></lb>cloide è in superficie uguale al circolo genitore. </s></p><p type="main">

<s>Essenziale proprietà della curva è che, a partire dal vertice B, dove in­<lb></lb>tendasi fermato il diametro BD del circolo genitore con la sua semicircon­<lb></lb>ferenza DLFD; tutte le ordinate, come IL, EF, sono uguali agli archi inter­<lb></lb>cetti LB, BLF: ond&#039;è che se le due dette ordinate sono ugualmente distanti <lb></lb>dal centro C, sommate insieme, saranno uguali alla stessa semicirconferenza, <lb></lb>e così sarà vero delle infinite simili coppie. </s>

<s>Qui il metodo degl&#039;indivisibili <lb></lb>avrebbe somministrato al Fermat una dimostrazione, da non si paragonare, <lb></lb>nella brevità e nella eleganza, nè a quella del Cartesio, nè del Torricelli <lb></lb>stesso o di qualunque altro avesse voluto concorrere nell&#039;argomento. </s>

<s>Impe­<lb></lb>rocchè, soprammesse tutte quelle mezze circonferenze, comporrebbero la mezza <lb></lb>superficie convessa di un cilindro, descritto da un quadrato, di cui fosse il <lb></lb>lato uguale al raggio CD del circolo genitore, la qual superficie convessa es­<lb></lb>sendo uguale a uno de&#039;circoli, che fanno da base al medesimo cilindro, an­<lb></lb>che il trilineo AIBFD sarà dunque uguale a quel circolo. </s></p><p type="main">

<s>Ma, o che il Fermat non conoscesse questo metodo, o che non l&#039;appro-<pb xlink:href="020/01/2827.jpg" pagenum="452"></pb>vasse, ricorse a un altro espediente, molto allora in voga per gli esempi <lb></lb>datine dal Keplero, qual era quello di pigliar delle curve così minime parti, <lb></lb>da poterle riguardar come rette. </s>

<s>Così dunque divisi i raggi CD, CB nel me­<lb></lb>desimo numero di particelle, tutte fra loro uguali, e da ciascun punto di divi­<lb></lb>sione, sotto e sopra, a ugual distanza dal centro C, condotti seni come FG, LH, <lb></lb>prodotti nelle ordinate FE, LI; la figura ED si potrà riguardar come un tra­<lb></lb>pezio, e tale pure, cioè come un trapezio, la minor base del quale sia ridotta <lb></lb>a zero, si potrà riguardare il triangolo ILB, e così dicasi delle altre infinite <lb></lb>simili figure intercette. </s>

<s>Chiamati ora T, <emph type="italics"></emph>t,<emph.end type="italics"></emph.end> que&#039;trapezi ED, ILB, con le al­<lb></lb>tezze GD, BH uguali, e ugualmente distanti dal mezzo C; sommati insieme <lb></lb>daranno T+<emph type="italics"></emph>t<emph.end type="italics"></emph.end>=GD/2(AD+EF+IL)=GD.<foreign lang="grc">π</foreign>CD. </s>

<s>Suppongasi ora <lb></lb>essere <emph type="italics"></emph>n<emph.end type="italics"></emph.end> il numero delle divisioni, corrispondente al numero delle coppie dei <lb></lb>trapezi descritti nel trilineo AIBFD, e per questo numero <emph type="italics"></emph>n<emph.end type="italics"></emph.end> si moltiplichi la <lb></lb>trovata equazione. </s>

<s>Verrà <emph type="italics"></emph>n<emph.end type="italics"></emph.end>(T+<emph type="italics"></emph>t<emph.end type="italics"></emph.end>)=<emph type="italics"></emph>n<emph.end type="italics"></emph.end>GD<foreign lang="grc">π</foreign>CD. </s>

<s>Ma <emph type="italics"></emph>n<emph.end type="italics"></emph.end>(T+<emph type="italics"></emph>t<emph.end type="italics"></emph.end>) è mani­<lb></lb>festamente uguale alla superficie S del detto trilineo, e <emph type="italics"></emph>n<emph.end type="italics"></emph.end> GD=CD; dun­<lb></lb>que S=<foreign lang="grc">π</foreign>CD2. </s></p><p type="main">

<s>Tale facilità di via aprì il Roberval ai matematici di Francia, i quali <lb></lb>avevano già nel 1641, infino al punto che abbiam veduto, promossa la scienza <lb></lb>della Cicloide. </s>

<s>Ma fra noi si rimaneva in quel tempo tuttavia stagnante, im­<lb></lb>peditone il libero corso da quell&#039;argine contrappostole da Galileo, e descritto <lb></lb>dal Salviati nel frammento di dialogo sopra trascritto, il quale argine ora è <lb></lb>a narrare quando, da chi e con quali conati fosse superato, d&#039;onde scesero <lb></lb>le acque di sopra a irrigar largamente anche i nostri campi. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il dì 14 Febbraio 1640 scriveva il Cavalieri in una lettera, indirizzata a <lb></lb>Galileo da Bologna, queste parole rimasteci come certissimo documento della <lb></lb>prima occasione, che il Roberval, aiutato dalle ingerenze del Mersenno, dette <lb></lb>ai nostri Matematici di risolvere i problemi intorno alla linea, allo spazio e <lb></lb>ai solidi generati dalla Cicloide: “ Mi sono stati mandati da Parigi due que­<lb></lb>siti da quei Matematici, circa de&#039;quali temo di farmi poco onore, perchè mi <lb></lb>paiono cure disperate. </s>

<s>L&#039;uno è la misura della superficie del cono scaleno, <lb></lb>l&#039;altro la misura di quella linea curva, simile alla curvatura di un ponte, <lb></lb>descritta dalla rivoluzione di un cerchio, sino che scorra con tutta la sua cir­<lb></lb>conferenza una linea retta, e dello spazio piano compreso da quella, e del <lb></lb>corpo generato per la rivoluzione intorno all&#039;asse e alla base: il che mi ri­<lb></lb>cordo che una volta mi domandò lei, ma che infruttuosamente mi vi affati­<lb></lb>cai. </s>

<s>Di grazia mi dica se sa che queste due cose sieno state dimostrate da <lb></lb>nessuno, perchè, per quello che io vedo, mi paiono difficilissime. </s>

<s>” </s></p><pb xlink:href="020/01/2828.jpg" pagenum="453"></pb><p type="main">

<s>“ L&#039;occasione è stata che, passando un padre di S. </s>

<s>Francesco di Paola <lb></lb>(<emph type="italics"></emph>il padre Niceron<emph.end type="italics"></emph.end>) qua da Bologna, che è di Parigi, e molto intendente delle <lb></lb>matematiche, nel discorrere seco di diverse cose gli venni a dire che avevo <lb></lb>trovata la misura del corpo parabolico nato dalla rivoluzione della parabola <lb></lb>intorno alla base, e che avevo trovato che il cilindro, generato dal paralle­<lb></lb>logrammo circoscritto alla parabola, era al detto corpo come 15 a 8, sebbene <lb></lb>uno dei principali gesuiti matematici mi aveva già un pezzo fa scritto che <lb></lb>era doppio. </s>

<s>Ora il detto Padre disse: Lasci di grazia che io lo scriva a quei <lb></lb>matematici di Parigi, per vedere se rincontrano questa verità, e così l&#039;hanno, <lb></lb>dice, trovata come 15 a 8. E questa è stata l&#039;occasione di propormi questi <lb></lb>altri problemi, da me reputati di difficilissima risoluzione, per quel poco che <lb></lb>io vedo ” (Alb. </s>

<s>X, 379, 80). </s></p><p type="main">

<s>Galileo rispose, dopo dieci giorni, parere anche a lui i problemi man­<lb></lb>dati di Francia difficilissimi, nè sapere che ancora fossero sciolti, e soggiun­<lb></lb>geva: “ Quella linea arcuata sono più di cinquant&#039;anni che mi venne in <lb></lb>mente il descriverla, e l&#039;ammirai per una curvità graziosissima, per adat­<lb></lb>tarla agli archi d&#039;un ponte. </s>

<s>Feci sopra di essa, e sopra lo spazio da lei e <lb></lb>dalla sua corda compreso, diversi tentativi per dimostrarne qualche passione, <lb></lb>e parvemi da principio che tale spazio potesse esser triplo del cerchio che <lb></lb>lo descrive, ma non fu così, benchè la differenza non sia molta. </s>

<s>Tocca all&#039;in­<lb></lb>gegno del p. </s>

<s>Cavalieri e non d&#039;altro il ritrovarne il tutto, e mettere tutti li <lb></lb>speculativi in disperazione di poter venire a capo di questa contemplazione ” <lb></lb>(Dati, <emph type="italics"></emph>Lettera ai Filaleti,<emph.end type="italics"></emph.end> Firenze 1663, pag. </s>

<s>4, 5). </s></p><p type="main">

<s>Invece il Cavalieri aveva, dietro queste parole, messo sè medesimo in più <lb></lb>disperazione che mai. </s>

<s>Chi avrebbe creduto ciò dell&#039;Autore degli indivisibili? </s>

<s><lb></lb>Fosse allora venuto uno a mostrargli con quanta facilità conduceva il me­<lb></lb>todo da lui stesso iusegnato a riconoscere, com&#039;aveva fatto il Cartesio, che <lb></lb>il bilineo compreso fra la diagonale del rettangolo circoscritto e la mezza ci­<lb></lb>cloide uguaglia il semicircolo che la descrive; o che il trilineo compreso fra <lb></lb>le due mezze curve è uguale alla metà della superficie convessa di un cilin­<lb></lb>dro, descritto dal rivolgersi di un quadrato costruitosi sul raggio del circolo <lb></lb>genitore! Ma il saper che in tale esercizio s&#039;era per cinquant&#039;anni inutil­<lb></lb>mente straccato Galileo, e il credere con lui che le proposizioni venute di <lb></lb>Parigi fossero problemi da risolversi, e non teoremi già dimostrati, fu causa <lb></lb>che il Cavalieri adombrasse puerilmente così, da ritrarsi dalla nobile impresa. </s></p><p type="main">

<s>La viltà del capitano impaurì anche gli altri militi, fra quali il Nardi, <lb></lb>ch&#039;era pure uno dei più coraggiosi, nè mancò di giovare quel poco di co­<lb></lb>raggio, di che egli dava gli esempi. </s>

<s>Discepolo fedelissimo di Archimede, che <lb></lb>aveva secondo lui ritrovato il centro di gravità nel conoide, e in altre strane <lb></lb>figure per via di meccaniche esperienze, tornò il Nardi a tentare le prove, <lb></lb>che a Galileo non erano mai riuscite. </s>

<s>Se non che pensò di paragonare il <lb></lb>peso della cicloide con quello del rettangolo circoscritto, piuttosto che del cir­<lb></lb>colo genitore. </s>

<s>Così le rasure, dalle quali si temeva che principalmente dipen­<lb></lb>dessero le fallacie, riuscivano molto minori di quelle fatte da Galileo, e d&#039;av-<pb xlink:href="020/01/2829.jpg" pagenum="454"></pb>vantaggio s&#039;avevano due riscontri: prima col rettangolo intero, e poi co&#039;due <lb></lb>triangoli aventi un lato curvilineo opposto all&#039;angolo retto, e rimasti dal re­<lb></lb>cider la cicloide dal rettangolo stesso. </s>

<s>Fatta dunque l&#039;operazione, trovò il <lb></lb>Nardi che il peso del rettangolo era a quello della cicloide come quattro a <lb></lb>tre, d&#039;onde credeva se ne potesse concludere esser essa cicloide esattamente <lb></lb>tripla del circolo, che movendosi la descrive. </s>

<s>Ma rimanendo tuttavia incerto <lb></lb>se dicesse il vero la sua o la bilancetta di Galileo, lasciò anch&#039;egli ai geo­<lb></lb>metri il dar sentenza finale. </s></p><p type="main">

<s>L&#039;invenzione meccanica della quadratura della Cicloide occorse al Nardi <lb></lb>nel 1641, quando faceva copiare la seconda Ricercata geometrica, nella quale <lb></lb>era scritto: “ Osservo, per le meccaniche esperienze, che un rettangolo di <lb></lb>ugual base e altezza con la cicloide sia sesquiterzo di essa, da che, quando <lb></lb>vero sia, vero anche sarà che la cicloide sia tripla di quel cerchio da cui <lb></lb>descrivesi. </s>

<s>” E si termina dall&#039;Autore questo discorso della Cicloide con le <lb></lb>seguenti parole: “ Finalmente non stimo gettarsi il tempo che s&#039;impieghi <lb></lb>nel coltivare tal campo della Geometria, in grazia d&#039;agguagliare il cerchio <lb></lb>ad un rettilineo. </s>

<s>Ma chiunque per questa strada arriverà a tal segno saprà <lb></lb>forse anche trovare la proporzione della linea cicloide verso la base sua, come <lb></lb>anche quella del solido e superficie prodotti mentre intorno alla base o al­<lb></lb>l&#039;asse si rivolga lo spazio clcloidale. </s>

<s>Lasciamo dunque tali contemplazioni agli <lb></lb>altri, e ripigliamo il nostro discorso. </s>

<s>” </s></p><p type="main">

<s>L&#039;esperienza meccanica, dalla quale resultava essere la cicloide esatta­<lb></lb>mente tripla del circolo che l&#039;ha descritta, fu dal Nardi annunziata al Tor­<lb></lb>ricelli, il quale incominciò allora a dubitare che Galileo si fosse ingannato. </s>

<s><lb></lb>Da ciò prese animo di posporre l&#039;autorità di lui alla legittima della Geome­<lb></lb>tria, dalla quale, interrogata, ebbe il responso di quel teorema, che, in più <lb></lb>maniere, e tutte concludentissime, confermava la verità dell&#039;esperienza. </s>

<s>Ben­<lb></lb>chè la dimostrazione riuscisse, per via degli indivisibili, assai facile, com&#039;ap­<lb></lb>parisce dall&#039;appendice <emph type="italics"></emph>De dimensione Cycloidis,<emph.end type="italics"></emph.end> nella seconda parte delle <lb></lb>Opere geometriche, pur il Torricelli, ch&#039;era così felicemente riuscito in un&#039;im­<lb></lb>presa da&#039;suoi grandi maestri creduta disperata, esultò della scoperta, annun­<lb></lb>ziandola senza indugio, sulla fine del Marzo 1643, agli amici e agli stranieri. </s>

<s><lb></lb>Ciò che rispondessero questi, ossia i Francesi, ai quali non riusciva la cosa <lb></lb>punto nuova, si dirà altrove, per trattenerci ora a narrare qual effetto pro­<lb></lb>ducesse nell&#039;animo, e nella mente dei nostri Italiani. </s></p><p type="main">

<s>Il Cavalieri si rimase passivo da uno stupore molto simile a quello di <lb></lb>colui, che, avendo intorno a un segreto ritrovato scarso ogni sforzo delle mani <lb></lb>e delle braccia, veda entrare un altro ad aprirlo col dito, a un legger tocco <lb></lb>di molla. </s>

<s>Trasparisce un tal sentimento da ciò, che il dì 23 Aprile 1643 così <lb></lb>rispondeva all&#039;annunzio: “ Finalmente ho sentito nell&#039;ultima sua la misura <lb></lb>dello spazio cicloidale, con molta mia maraviglia, essendo stato sempre sti­<lb></lb>mato problema di molta difficoltà, che straccò già il Galileo: siccome io pure, <lb></lb>parendomi assai difficile, lo lasciai andare, ond&#039;ella ne averà non poca lode <lb></lb>di questo, oltre le tante sue maravigliose invenzioni, che gli daranno eterna <pb xlink:href="020/01/2830.jpg" pagenum="455"></pb>fama. </s>

<s>Non resterò poi di dirle intorno a questo che il signor Galileo mi <lb></lb>scrisse una volta di avervi applicato quarant&#039;anni fa, e che non aveva po­<lb></lb>tuto trovar niente, e che s&#039;era persuaso che il detto spazio fosse triplo del <lb></lb>circolo suo genitore, ma che poi gli pareva che non fosse precisamente, se <lb></lb>mal non mi ricordo, poichè, per quanto abbi cercato nelle mie scritture, non <lb></lb>ho mai potuto tal lettera ritrovare. </s>

<s>Sicchè, se sta, come mi pare di ricor­<lb></lb>darmi, bisogna che esso molto s&#039;ingannasse a credere che fosse altrimenti <lb></lb>che triplo ” (MSS. Gal. </s>

<s>Disc., XLI, fol. </s>

<s>171). </s></p><p type="main">

<s>Ma il Nardi si pentì di avere a così bella e facile contemplazione la­<lb></lb>sciato altrui correre il campo, in cui, trovandosi ora a dover fare da respi­<lb></lb>golatore, si studiò di portarvisi da par suo. </s>

<s>E come il Roberval alla deside­<lb></lb>rata quadratura s&#039;agevolò la via con la invenzion della comite, così il Nostro <lb></lb>inventò al medesimo effetto una cicloide nuova, in tale artificioso modo de­<lb></lb><figure id="id.020.01.2830.1.jpg" xlink:href="020/01/2830/1.jpg"></figure></s></p><p type="caption">

<s>Figura 304.<lb></lb>scritta, che l&#039;eccesso CFHAGC di <lb></lb>lei (fig. </s>

<s>304), sopra il triangolo CAD, <lb></lb>fosse uguale al semicircolo genitore. </s>

<s><lb></lb>Di qui essendo manifesto che tanto <lb></lb>questa curva, quanto la volgare <lb></lb>CFEA, circoscrivono uguale spazio, <lb></lb>benchè con andamento diverso, e <lb></lb>dall&#039;altra parte sapendosi con cer­<lb></lb>tezza che il triangolo al semicircolo <lb></lb>è doppio; immediatamente si con­<lb></lb>clude il tutto dover esserne triplo. </s>

<s><lb></lb>Nè qui, per confermare altri esempi, è da passare inosservato l&#039;incontro, <lb></lb>senza dubbio fortuito, del Matematico francese col Nostro, il quale notava <lb></lb>come i seni del semicircolo applicati sopra la diagonale AC terminano di <lb></lb>fuori nella cicloide nuova, ma, applicati sulla cicloide volgare, terminano di <lb></lb>dentro in una curva, simile a un Ŗ inclinata, che evidentemente è la comite <lb></lb>robervalliana. </s></p><p type="main">

<s>Furono le inclinazioni del Nardi, come negli altri studi geometrici così <lb></lb>in questo, secondate dal Ricci, il quale dette anzi alla linea, vagheggiata fin <lb></lb>qui solitaria, una nobile famiglia di curve, che gli piacque chiamar <emph type="italics"></emph>cicloi­<lb></lb>dali.<emph.end type="italics"></emph.end> Nel Settembre del 1645 conferiva col Torricelli queste sue nuove spe­<lb></lb>culazioni, dicendogli che rimaneva in dubbio da qual principio far ad esse <lb></lb>curve dipendere la <emph type="italics"></emph>limitazion<emph.end type="italics"></emph.end> necessaria. </s>

<s>Che del resto, “ quanto a quel che <lb></lb>ella dice, scriveva all&#039;amico e al maestro, che la lor quadratura è troppo re­<lb></lb>condita, pare a me che sia teorema non dispregevole il dire che in tutte le <lb></lb>suddette figure l&#039;eccesso della cicloidale, sopra il triangolo, sia uguale alla <lb></lb>figura genitrice. </s>

<s>E V. S. non si maravigli se queste figure non osservano le <lb></lb>leggi delle cicloidali considerate da lei, perchè a quelle son come genere alla <lb></lb>sua specie, e sarebbe strano allora che le osservassero, ovvero che le cicloi­<lb></lb>dali di V. S. non avessero le condizioni generali delle figure da me consi­<lb></lb>derate. </s>

<s>La facilità, o diciamo la sincerità della mia <emph type="italics"></emph>definizione,<emph.end type="italics"></emph.end> che scopre a <pb xlink:href="020/01/2831.jpg" pagenum="456"></pb>prima vista tutto il segreto, sappia V. S. che è stata procurata da me, pia­<lb></lb>cendomi assai più di rendere facilissime le cose, dove gli altri hanno affet­<lb></lb>tato l&#039;oscurità, o che non hanno saputo ritrovare il suo natural principio; <lb></lb>che di renderle oscure, perchè altri ammiri in questa oscurità quel che non <lb></lb>ci si trova ” (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>138). </s></p><p type="main">

<s>Quel principio generale poi, o quella limitazion necessaria, che il Ricci <lb></lb>fra il dubbio ricercava, pensò di stabilirla, definendo le relazioni fra la figura <lb></lb><figure id="id.020.01.2831.1.jpg" xlink:href="020/01/2831/1.jpg"></figure></s></p><p type="caption">

<s>Figura 305.<lb></lb>genitrice ECDB <lb></lb>(fig. </s>

<s>305) e la <lb></lb>generata AXC <lb></lb>in modo, che <lb></lb>tutto il perime­<lb></lb>tro CDB, alla <lb></lb>sua parte EC o <lb></lb>CD, avesse la <lb></lb>proporzion me­<lb></lb>desima che la <lb></lb>AB, alla EG o alla DF, questa e quella supposte parallele alla base. </s>

<s>Se dunque si <lb></lb>costruisce sopra i lati AB, BC il rettangolo MB, e sopra la AM la figura MHIA, <lb></lb>uguale e simile alla CEDB, e le due ordinate GE, FD sian condotte equidi­<lb></lb>stanti dal centro O; avremo, per la fatta supposizione, AB:EG=BEC:EC= <lb></lb>HE:EG. Dividendo, HE:HG=BEC:EDB=BEC:CED=AB:FD. </s>

<s>Ma <lb></lb>HE=AB, dunque HG=FD, d&#039;onde GE=IF. </s></p><p type="main">

<s>Con queste medesime ragioni dimostrandosi che tutte le altre infinite <lb></lb>ordinate, prese a coppia a coppia a ugual distanza dal centro O, son tagliate <lb></lb>dalla cicloidale in parti contrariamente uguali; se ne concluderà l&#039;uguaglianza <lb></lb>de&#039;trilinei CMIAC, CFABEC, ciascun de&#039;quali sarà perciò la metà del qua­<lb></lb>drilineo CMIABEC. </s>

<s>Ma questo quadrilineo è manifestamente uguale al ret­<lb></lb>tangolo MB, di cui è metà il triangolo ABC; dunque un tal triangolo e il <lb></lb>trilineo corrispondente sono uguali, e perciò l&#039;eccesso dello spazio cicloidale, <lb></lb>sopra il detto triangolo rettilineo, uguaglierà lo spazio della figura genitrice. </s></p><p type="main">

<s>Suppongasi ora che questa figura sia un mezzo cerchio, la semicircon­<lb></lb>ferenza del quale sia stesa nella dirittura AB. </s>

<s>La curva AXC sarà allora una <lb></lb>cicloide primaria, essenzial proprietà della quale è, non solamente l&#039;ugua­<lb></lb>glianza tra AB e BEC, ma tra GE ed EC, da cui vien ordinata la propor­<lb></lb>zione AB:GE=BEC:EC. </s>

<s>Dunque anche la cicloide primaria è generata <lb></lb>al modo delle altre curve, secondo la data definizione, e dovendo necessaria­<lb></lb>mente esser proprio di lei quel che delle altre sue congeneri s&#039;è dimostrato; <lb></lb>l&#039;eccesso. </s>

<s>dunque dello spazio cicloidale, sopra il triangolo ACB uguaglierà il <lb></lb>semicircolo, e tutto intero esso spazio cicloidale a quel medesimo semicir­<lb></lb>colo sarà triplo. </s></p><p type="main">

<s>Una tale uguaglianza tra la base e il perimetro del circolo genitore, e <lb></lb>tra qualunque ordinata e l&#039;arco intercetto, a partire dal vertice, passa anche <lb></lb>in tutte le cicloidi secondarie, allungate che siano o contratte, e perciò di esse <pb xlink:href="020/01/2832.jpg" pagenum="457"></pb>pure, come appartenenti alla famiglia delle curve descritte, sarà vero che <lb></lb>l&#039;eccesso dello spazio sopra il triangolo uguaglia la superficie del semi­<lb></lb>cerchio. </s></p><p type="main">

<s>È da notare però che il Ricci non segue queste vie dirette, ma le obli­<lb></lb>que, riducendo le sue dimostrazioni agli assurdi, e ciò forse con l&#039;intenzione <lb></lb>di supplire al difetto, in cui aveva il Torricelli lasciata la scienza delle ci­<lb></lb>cloidi secondarie, confermandone la verità dei principii e delle conseguenze <lb></lb>anche nella mente di coloro, che non avessero accettata la dottrina degl&#039;in­<lb></lb>divisibili. </s>

<s>Nello scolio infatti all&#039;appendice <emph type="italics"></emph>De dimensione cycloidis<emph.end type="italics"></emph.end> s&#039;annun­<lb></lb>ziano tre teoremi, ne&#039;quali si suppone che lo spazio di qualunque cicloide <lb></lb>si componga d&#039;un triangolo e d&#039;un bilineo, ambedue i quali presi insieme <lb></lb>pareggino il triplo del semicerchio. </s>

<s>Chiamati T il triangolo, B la sua base, <lb></lb>R il raggio del circolo genitore, S lo spazio cicloidale, resulta dalle proposizioni <lb></lb>del Ricci T=B.R, S=B.R+<foreign lang="grc">π</foreign>R2, onde S:T=B.R+<foreign lang="grc">π</foreign>R2:B.R= <lb></lb>B+<foreign lang="grc">π</foreign>R:B=2B+2<foreign lang="grc">π</foreign>R:2B, che conferma la verità del primo teorema <lb></lb>torricelliano, annunziato a pag. </s>

<s>92 della seconda parte delle Opere geome­<lb></lb>triche. </s>

<s>Il secondo, chiamato C il circolo, trova espressa la sua verità dalla <lb></lb>seguente equazione: S:C=B.R+<foreign lang="grc">π</foreign>R2:<foreign lang="grc">π</foreign>R2=2B+2<foreign lang="grc">π</foreign>R:2<foreign lang="grc">π</foreign>R. </s>

<s><lb></lb>Il terzo finalmente, ritenute le denominazioni di sopra, e per S′, B′, R′ in­<lb></lb>tendendosi il secondo spazio cicloidale, la sua base e il raggio del circolo <lb></lb>genitore; si conclude facilmente così, dai principii dimostrati dal Ricci, S= <lb></lb>B.R+<foreign lang="grc">π</foreign>R2, S′=B′.R′+<foreign lang="grc">π</foreign>R′2, onde </s></p><p type="main">

<s><emph type="center"></emph>S:S′=R(B+<foreign lang="grc">π</foreign>R):R′(B′+<foreign lang="grc">π</foreign>R′)= <lb></lb>2R(2B+2<foreign lang="grc">π</foreign>R):2R′(2B′+2<foreign lang="grc">π</foreign>R′).<emph.end type="center"></emph.end><lb></lb>È perchè 2R, 2R′ son de&#039;due spazi le respettive altezze, è patente che <lb></lb><emph type="italics"></emph>cuiuscumque cycloidalis spatii, ad quodlibet spatium cycloidale, ratio com­<lb></lb>ponitur ex ratione altitudinis ad altitudinem, et ex ratione dupli basis <lb></lb>cum periphaeria genitrice, ad duplum basis cum periphaeria genitrice,<emph.end type="italics"></emph.end><lb></lb>come annunziava il Torricelli, tacendone la dimostrazione, perchè, essendosi <lb></lb>messo per vie tanto più lunghe di quelle del Ricci, diceva che l&#039;appendice <lb></lb>gli si sarebbe trasformata in un libro. </s></p><p type="main">

<s>Comuni essendo del Matematico di Arezzo e di quel di Roma gli studi, <lb></lb>nemmeno in pubblico volevano andar separati, e perciò il Nardi, riformando <lb></lb>nella seconda Ricercata geometrica il discorso intorno alla Cicloide, e facen­<lb></lb>dolo copiare per darlo alle stampe; soggiungeva dopo le sue le speculazioni <lb></lb>del Ricci, che trascriviamo qui con fedeltà e con amore, riducendole nella <lb></lb>nostra Storia come gemme preziose, che la Scienza italiana viene ora per noi <lb></lb>ad aggiungere al suo ricco monile. </s></p><p type="main">

<s>“ Del rettangolo BD (nella figura 304 qui poco addietro) sia un lato <lb></lb>CD uguale alla circonferenza del mezzo cerchio AID, di cui il diametro sia <lb></lb>l&#039;altro lato AD del rettangolo. </s>

<s>In questo intendasi la mezza cicloide COEA, <lb></lb>qual viene disegnata dal punto A, mentre il mezzo cerchio si ruzzola una <lb></lb>volta sopra il piano CD. </s>

<s>Quando dunque il mezzo cerchio abbia trascorso la <pb xlink:href="020/01/2833.jpg" pagenum="458"></pb>metà di DC, si troverà il punto A in F, il qual punto F tanto più oltre <lb></lb>della metà trovasi di DC, ovvero della uguale KL, quanto è il semidiametro <lb></lb>IK: da che raccogliesi essere KF uguale alla retta IK, ed alla quarta parte <lb></lb>di periferia cioè a ID. </s>

<s>Con lo stesso metodo bisogna investigare gli altri siti <lb></lb>in altre date distanze. </s>

<s>” </s></p><p type="main">

<s>“ È poi stato da altri insegnato che lo spazio della cicloide CEAD è tri­<lb></lb>plo del mezzo cerchio AID, da cui descrivesi, e per dimostrar tal conclu­<lb></lb>sione serve ancora una nuova, e forse piu naturale cicloide da noi inventata, <lb></lb>la cui origine è questa: Del mezzo cerchio AID sia diametro AD, e dagli <lb></lb>estremi di esso diametro si partano le tangenti AB, DC, delle quali ciascuna <lb></lb>si agguagli alla periferia AID. </s>

<s>Intendasi poi la retta AD moversi, senza mu­<lb></lb>tare inclinazione, sino a che arrivi in BC, onde descrivasi il rettangolo BD, <lb></lb>e nello stesso tempo A trascorra con moto eguale la retta AD, dall&#039;accop­<lb></lb>piamento de&#039;quali due moti si descriva la retta AC, e finalmente da ogni <lb></lb>punto di AC si continui verso BC una retta posta in dirittura con la sua <lb></lb>corrispondente ed eguale nel mezzo cerchio. </s>

<s>E così per esempio la retta FG <lb></lb>sia a dirittura con la sua corrispondente ed eguale IK. </s>

<s>Dunque tutte le or­<lb></lb>dinate nel mezzo cerchio s&#039;agguagheranno a tutte le ordinate nella figura <lb></lb>CFHAG, e l&#039;altezza è uguale; adunque il mezzo cerchio s&#039;agguaglierà alla <lb></lb>figura suddetta, ed in quella trasformerassi. </s>

<s>Il triangolo poi ADC è duplo <lb></lb>dello stesso mezzo cerchio, come nella misura del cerchio insegnammo, e ora <lb></lb>piacemi anche in quest&#039;altro modo provare, acciò si osservi la varietà delle <lb></lb>invenzioni. </s>

<s>Intendasi ad un cerchio circoscritto qualsivoglia regolar poligono, <lb></lb>e siano il cerchio e il poligono basi co&#039;loro perimetri di una superficie di <lb></lb>cilindro e di prisma retti, quali abbiano per altezza il semidiametro del cer­<lb></lb>chio. </s>

<s>Adunque sarà la superficie del prisma il doppio del poligono, e ciò è <lb></lb>vero in infinito, sino al trasformarsi il poligono in cerchio, e la superficie <lb></lb>del prisma in cilindrica. </s>

<s>Adunque di nuovo, per le cose mostrate la super­<lb></lb>ficie cilindrica sarà anch&#039;essa doppia del cerchio. </s>

<s>Questa superficie poi s&#039;ag­<lb></lb>guaglia, come altrove provammo, ad un rettangolo, di cui un lato sia il se­<lb></lb>midiametro, l&#039;altro lato il perimetro del suddetto cerchio, e del medesimo <lb></lb>rettangolo è metà un triangolo rettangolo, che abbia seco comuni i lati com­<lb></lb>prendenti l&#039;angolo retto. </s>

<s>Adunque tal triangolo o il suo uguale ACD s&#039;ag­<lb></lb>guaglierà al cerchio predetto, ossia a due mezzi cerchi AID. </s>

<s>Adunque tutta <lb></lb>la mezza cicloide sarà tripla dello stesso mezzo cerchio. </s>

<s>” </s></p><p type="main">

<s>“ Qui considerisi come, dal rivolgersi una volta il perimetro del qua­<lb></lb>drato sopra di una linea retta, descriverassi una figura composta di due trian­<lb></lb>goli, e di tre quarte di cerchio. </s>

<s>Di queste le due estreme hanno per semidia­<lb></lb>metro il lato del quadrato, e la di mezzo ha il diametro dello stesso. </s>

<s>Appellisi <lb></lb>tal figura <emph type="italics"></emph>Cicloide falsa.<emph.end type="italics"></emph.end> Negli altri regolari poligoni il simile proporzional­<lb></lb>mente avviene, ed osservisi che dagli isoperimetri al cerchio descrivesi mag­<lb></lb>giormente la linea curva, e tanto più quanto meno numero di lati ottengono. </s>

<s><lb></lb>Ma quanto più s&#039;avvicinano alla condizione del circolo i poligoni, col numero <lb></lb>e con la parità de&#039;lati, più regolare la formano. </s>

<s>Ma i contrari a questi la <pb xlink:href="020/01/2834.jpg" pagenum="459"></pb>formano più sregolata, sebbene tutti la formano di porzioni circolari, una <lb></lb>meno di numero dei lati del descrivente poligono. </s>

<s>” </s></p><p type="main">

<s>“ Or non è cosa mirabile che gli estremi dei cateti o semidiametri dei <lb></lb>poligoni descrivano porzioni di cerchi e di periferia, e che gli estremi pro­<lb></lb>porzionali del cerchio descrivano altre linee e figure! Notisi di più che nelle <lb></lb>cicloidi, descritte da poligoni di numero pari di lati, le porzioni di cerchio <lb></lb>sono impari, e la maggiore altezza è nel mezzo delle basi, e s&#039;agguaglia al <lb></lb>diametro del poligono. </s>

<s>Ma negli impari poligoni le porzioni sono pari di nu­<lb></lb>mero, e l&#039;altezza maggiore non è nel mezzo. </s>

<s>” </s></p><p type="main">

<s>“ Di nuovo, nella figura 304, la curva AHFC rappresenti la linea della <lb></lb>cicloide regolare e la curva AEFOC rappresenti la linea della volgare. </s>

<s>La <lb></lb>differenza consiste perchè, tirata FG parallela a BA, lato del rettangolo com­<lb></lb>prendente la mezza cicloide, sicchè seghi, prodotta, il diametro AC ugual­<lb></lb>mente; la volgare racchiude tra BAFG la regolare, e tra FGCD è racchiusa <lb></lb>dalla stessa. </s>

<s>Parimente la linea simile ad uno Ŗ inclinato significa co&#039;suoi <lb></lb>punti i termini delle applicate nella volgare, ma i termini delle applicate nella <lb></lb>regolare sono nella AC. </s>

<s>La cagione poi di tal differenza scorgesi, per tro­<lb></lb>varsi nella volgare il diametro del cerchio descrivente essa cicloide (qual <lb></lb>diametro si supponga parallelo ad AD) avanti CA, verso DC, mentre egli <lb></lb>trascorra tra il punto G e il lato AD, ma tra il punto G e il lato BC è posto <lb></lb>dopo, e solo nel punto G conviene l&#039;uno e l&#039;altro diametro. </s>

<s>Quindi le appli­<lb></lb>cate s&#039;avanzano in una parte e si ritirano nell&#039;altra, con la stessa propor­<lb></lb>zione, e dando in un luogo quanto tolgono nell&#039;altro, mediante la condizione <lb></lb>del cerchio, s&#039;agguagliano tutte le applicate nella suddetta parte della vol­<lb></lb>gare a tutte le applicate nella parte della nostra cicloide. </s>

<s>E si osservi come <lb></lb>anche sopra basi circolari si possono formare altre cicloidi, di che esempi <lb></lb>non mancano nei moti annui e diurni dei mondani corpi. </s>

<s>A queste conside­<lb></lb>razioni, per ultimo, aggiungeremo quest&#039;altra del signor M. A. Ricci. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma I.<emph.end type="italics"></emph.end> — Sia CPB (nella passata 305) una figura intorno all&#039;asse <lb></lb>PO, la quale manchi verso la parte P, e l&#039;ordinatamente applicata COB le <lb></lb>serva di base, in cui sian prese due porzioni uguali CK, LB, dagli estremi <lb></lb>di essa C, B. S&#039;alzino dai punti K, L le perpendicolari KE, LD, che seghino <lb></lb>del perimetro EC, DB. </s>

<s>Dico che EC, DB sono uguali, come si prova facil­<lb></lb>mente con la sopraposizione. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Definizione.<emph.end type="italics"></emph.end> — Sia BDC una figura intorno l&#039;asse, che manchi verso <lb></lb>la parte P, col cavo indentro, il convesso di fuori, e BC sia una delle ordi­<lb></lb>natamente applicate. </s>

<s>Pongasi BA perpendicolare alla BC, e di che lunghezza <lb></lb>si vuole, e nel perimetro della figura sia preso qualsivoglia altro punto E, <lb></lb>e supponendo che tutto il perimetro BDC, alla parte CE ovvero CD, stia <lb></lb>come AB all&#039;EG, e siano GE, DF equidistanti alla BA; si formerà in tal ma­<lb></lb>niera una figura AFGCEDB, la quale chiamo triangolo curvilineo; AB sua <lb></lb>base, e la figura BPC figura genitrice. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma II.<emph.end type="italics"></emph.end> — Sia dunque il suddetto triangolo curvilineo, con la sua <lb></lb>genitrice BDC, ed al punto A della base AB sia eretta la AM, base della <pb xlink:href="020/01/2835.jpg" pagenum="460"></pb>figura MHA, simile ed uguale alla medesima genitrice. </s>

<s>Si prendano nella BC <lb></lb>le parti KC, BL, e si passino le HK, LI parallele alla BA, le quali seghino <lb></lb>il triangolo in E, G; D, F, e la MHA ne&#039;punti H ed I. </s>

<s>Dico che FD sarà <lb></lb>uguale a GH, e GE ad FI. </s>

<s>Imperocchè DL, KE segano, per il primo Lemma, <lb></lb>le parti BD, EC uguali: dunque BEC ad EC come AB ad EG, cioè HE ad EG. </s>

<s><lb></lb>E per conversion di ragione, HE ad HG come BEC a BE, ovvero il suo <lb></lb>uguale DC: e così AB a DF. </s>

<s>Dunque HE ad HG come AB a DF. </s>

<s>Ma BA, <lb></lb>HE sono uguali, dunque ancora HG, DF, e conseguentemente i loro residui <lb></lb>GE, FI, il che etc. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE. — <emph type="italics"></emph>Supposte le medesime cose, dico che il triangolo <lb></lb>curvilineo ACB sarà uguale all&#039;altro ACM. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Perchè altrimenti sarà maggiore o minore. </s>

<s>Pongasi prima eccedente <lb></lb>della quantità Y, e si divida con rette parallele alla BA il curvilineo parallelo­<lb></lb>grammo AHMCEB, finchè troviamo il parallelogrammo IADB minore della Y. </s>

<s><lb></lb>Poi s&#039;inscriva nei triangoli una figura composta di parallelogrammi curvili­<lb></lb>nei, egualmente con l&#039;IADB altì, intendendo che per F passi la figura ge­<lb></lb>nitrice con la applicata perpendicolare alla BA, della qual figura, per il primo <lb></lb>lemma, LDF ne segherà le parti uguali e congruenti FN, DB, che forme­<lb></lb>ranno un parallelogrammo curvilineo inscritto: e similmente formeranno gli <lb></lb>altri inscritti, come MHGS, facendo passar la genitrice figura per il puuto G. </s>

<s><lb></lb>Ma questi curvilinei hanno le altezze uguali BL, KC, e le basi FD, GH pur <lb></lb>uguali; dunque saranno uguali. </s>

<s>Il simile proveremo delli altri parallelogrammi <lb></lb>inscritti, egualmente lontani dalle basi AB ed MC. </s>

<s>Dunque le inscritte figure <lb></lb>ne&#039;triangoli sono uguali e minori de&#039;triangoli, ne&#039;quali s&#039;inscrivono. </s>

<s>” </s></p><p type="main">

<s>“ Inoltre, il parallelogrammo curvilineo FX è uguale all&#039;FR, per l&#039;ugua­<lb></lb>lità delle basì e delle altezze: XG al ZR, CG al ZB. </s>

<s>Dunque l&#039;eccesso della <lb></lb>figura circoscritta al trilineo ACB, sopra l&#039;inscritto nel medesimo, è uguale <lb></lb>ad IADB, e minore di Y. </s>

<s>Sarà dunque molto minore di Y l&#039;eccesso del­<lb></lb>l&#039;ACB sopra la sua inscritta, e però detta inscritta ancora eccedente l&#039;altro <lb></lb>triangolo, il che è impossibile, poichè si è provata minore del triangolo. </s>

<s>Dun­<lb></lb>que ACB triangolo non è maggiore dell&#039;altro ACM. L&#039;istesso progresso ci <lb></lb>varrà per dimostrare che ACM non sia maggiore di ACB, dunque sono uguali, <lb></lb>il che etc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario I.<emph.end type="italics"></emph.end> — Essendo che facilmente si dimostra il curvilineo AMCB <lb></lb>essere uguale al rettilineo parallelogrammo MB, segue che MB sia doppio <lb></lb>del triangolo ACB curvilineo, e però uguale al rettilineo triangolo ABC, <lb></lb>quando si giunga la retta AC. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario II.<emph.end type="italics"></emph.end> — Perchè la figura AGCKB è uguale al triangolo cur­<lb></lb>vilineo ACB, insieme con la figura genitrice, e il triangolo detto è uguale al <lb></lb>triangolo rettilineo ABC; dunque l&#039;eccesso della figura AGCKB, sopra il trian­<lb></lb>golo rettilineo ABC, sarà uguale alla figura genitrice. </s>

<s>” </s></p><p type="main">

<s>“ Or noto che, ponendosi BDC essere un semicerchio, e la base AB <lb></lb>uguale alla sua periferia; la AGCKB sarà una primaria semicicloide. </s>

<s>Perchè <lb></lb>allora sarà AB, a tutta la periferia BEC, come FD alla DEC, e però la parte <pb xlink:href="020/01/2836.jpg" pagenum="461"></pb>residua FI, ovvero AN, sarà uguale alla parte residua BD, ovvero FN, se­<lb></lb>condo la passione della Cicloide primaria. </s>

<s>” </s></p><p type="main">

<s>“ Immaginiamoci poi sopra l&#039;AB rivolgersi il semicerchio OHN (fig. </s>

<s>306), <lb></lb>per descrivere col punto H una semicicloide primaria AHCB, ed il mezzo <lb></lb><figure id="id.020.01.2836.1.jpg" xlink:href="020/01/2836/1.jpg"></figure></s></p><p type="caption">

<s>Figura 306.<lb></lb>cerchio concentrico KGL, in <lb></lb>quel moto, descriva, con uno <lb></lb>de&#039;suoi punti G, la semicicloide <lb></lb>secondaria, di cui sia base DE, <lb></lb>uguale all&#039;AB. </s>

<s>Mentre OH avrà <lb></lb>calcata la parte AO, il punto <lb></lb>concentrico avrà calcata la parte <lb></lb>DL, con la sua parte GL, la quale <lb></lb>è simile alla OH, per l&#039;angolo <lb></lb>GIL al centro comune. </s>

<s>Dunque <lb></lb>LGK a GK, ovvero OHN all&#039;arco <lb></lb>HN è come AB, ovvero DE, <lb></lb>all&#039;HR o al suo uguale OB, ovvero GF. </s>

<s>Dunque EFS ad FS come DE a GF, <lb></lb>ed è il punto S vertice della secondaria cicloide, DE sua base. </s>

<s>Adunque tanto <lb></lb>la cicloide primaria quanto la secondaria sono specie della figura da noi pro­<lb></lb>posta nel principio, e per conseguenza l&#039;eccesso della semicicloide, o prima­<lb></lb>ria o secondaria, sopra il triangolo rettilineo, i lati del quale sono la base e <lb></lb>l&#039;altezza di detta semicicloide; è uguale al semicircolo genitore, il che etc. </s>

<s>” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>951-59). </s></p><p type="main">

<s>In queste geometriche speculazioni del Ricci, il merito e l&#039;importanza <lb></lb>delle quali si conosceranno facilmente dai nostri Lettori, termina la storia <lb></lb>de&#039;progressi fatti in Italia intorno alla quadratura della Cicloide. </s>

<s>Non si te­<lb></lb>neva però ancora per assoluta la scienza di lei, tuttavia rimanendo a defi­<lb></lb>nire le proporzioni, che passano tra i solidi rotondi generati dallo spazio ci­<lb></lb>cloidale, e i cilindri a lui circoscritti. </s>

<s>Ora è notabile questo passaggio dalla <lb></lb>Geometria pura alla Stereometria, a che non pensarono punto da principio <lb></lb>nè Galileo nè il Mersenno; ond&#039;è a ricercar l&#039;occasione, per cui dalle sem­<lb></lb>plici superficie si venne, col proporre i solidi, a complicare il problema. </s></p><p type="main">

<s>Quell&#039;occasione dai recati documenti è manifesta: ella risale al teo­<lb></lb>rema dal Niceron proposto a dimostrarsi ai Matematici suoi francesi, avutene <lb></lb>in Bologna le conclusioni dal Cavalieri. </s>

<s>Al Roberval dunque, tutto allora in­<lb></lb>torno alla Cicloide, cadde facilmente in pensiero che si potesse circoscrivere <lb></lb>a lei un rettangolo, come intorno alla parabola, e il bel teorema nuovo ve­<lb></lb>nuto d&#039;Italia, delle proporzioni che passano tra il fuso parabolico e il cilin­<lb></lb>dro circoscritto, dette all&#039;ingegnoso Parigino motivo di dimostrare intorno al <lb></lb>solido cicloidale un altro simile, e non men bello e nuovo teorema. </s>

<s>Anzi il <lb></lb>giovanile ardor della mente lo portò a considerare che poteva farsi il rivol­<lb></lb>gimento non solo intorno alla base, ma intorno agli altri lati del rettangolo <lb></lb>circoscritto, d&#039;onde venissero a nascer solidi di varia forma e misura, tra&#039;quali <lb></lb>egli ebbe pure a trovare le proporzioni. </s></p><pb xlink:href="020/01/2837.jpg" pagenum="462"></pb><p type="main">

<s>Di qui avvenne che, scambiatesi tra il Cavalieri e il Roberval le pro­<lb></lb>poste, quegli le partecipasse non a Galileo solo, ma ai discepoli e agli amici <lb></lb>compiute nel numero e nell&#039;ordine dei quesiti, sempre confermando gli altri <lb></lb>nella propria opinione, che cioè fossero così fatte proposte francesi problemi <lb></lb>da risolversi in Italia, e non teoremi già dimostrati. </s>

<s>Con questo falso con­<lb></lb>cetto nella mente, da cui ebbero poi precipua causa i litigi che diremo, s&#039;era <lb></lb>il Torricelli messo all&#039;impresa, nella quale aveva appena fatto il primo passo, <lb></lb>che ne volle dare al Roberval l&#039;annunzio, dicendogli com&#039;avesse in cinque <lb></lb>varie maniere dimostrata la misura dello spazio cicloidale. </s>

<s>Ma del resto, sog­<lb></lb>giungeva il di primo ottobre 1643, <emph type="italics"></emph>quoad solida nihil habeo,<emph.end type="italics"></emph.end> ond&#039;è a nar­<lb></lb>rare come e quando gli occorresse l&#039;ambita invenzione, con la quale in mano <lb></lb>lo vedremo tornare innanzi allo stesso Roberval, compiacendosi d&#039;aver della <lb></lb>Cicloide ritrovata tutta intera la scienza da lui proposta. </s></p><p type="main">

<s>Venne anche questa volta la prima occasione dal Nardi, il quale, come <lb></lb>si rammemoreranno coloro, che nel Cap. </s>

<s>II del precedente nostro Tomo hanno <lb></lb>letto il paragrafo IV; aveva dimostrato in che facile modo si potesse, con la <lb></lb>regola centrobarica, ritrovar la misura del fuso parabolico rispetto al cilin­<lb></lb>dro circoscritto. </s>

<s>I problemi perciò dei solidi cicloidali, quali venivano propo­<lb></lb>sti dai Francesi, vide bene esso Nardi che sì sarebbero potuti risolvere con <lb></lb>la medesima facilità, quando però si sapesse, come della parabola, il centro <lb></lb>di gravità della Cicloide. </s>

<s>Si poteva dentro lo spazio inscrivere un triangolo <lb></lb>di pari base e altezza della curva, ma rimaneva tuttavia incerto il centro <lb></lb>de&#039;bilinei laterali, essendo la Cicloide volgare. </s>

<s>Nella regolare però, novamente <lb></lb>inventata, era quel centro manifestamente il medesimo che del circolo geni­<lb></lb>tore descritto intorno all&#039;asse, sopra il quale asse il centro di gravità del <lb></lb>tutto, per i noti teoremi archimedei, necessariamente consegue da quello delle <lb></lb>parti, Propostasi dunque questa sua Cicloide non ebbe il Nardi alcuna diffi­<lb></lb>coltà in ritrovar la stereometria dei solidi rotondi, con quel metodo centro­<lb></lb><figure id="id.020.01.2837.1.jpg" xlink:href="020/01/2837/1.jpg"></figure></s></p><p type="caption">

<s>Figura 307.<lb></lb>barico, di cui fu egli il primo <lb></lb>a farne, in così fatti quesiti, <lb></lb>l&#039;applicazione, sia diretta­<lb></lb>mente dal centro di gravità <lb></lb>desumendo i solidi e le su­<lb></lb>perficie dei rivolgimenti, sia <lb></lb>conversamente da&#039;solidi e <lb></lb>dalle superficie revolute de­<lb></lb>sumendone i centri. </s></p><p type="main">

<s>Abbiasi la Cicloide nardiana DHEF, (fig. </s>

<s>307) col vertice in E, e con la <lb></lb>base DF, dal mezzo L della quale s&#039;alzi perpendicolarmente LE, asse della <lb></lb>figura e diametro del circolo genitore, di cui il centro A sarà, per la natural <lb></lb>costruzione della curva, centro di gravità de&#039;bilinei laterali, i quali ugua­<lb></lb>gliano, per le cose già dimostrate, la superficie dello stesso circolo genitore. </s>

<s><lb></lb>Se CE è doppia di CL, avverrà in C il centro di gravità del triangolo DEF, <lb></lb>onde il centro di tutto lo spazio cicloidale sarà in B, talmente situato, che <pb xlink:href="020/01/2838.jpg" pagenum="463"></pb>AB abbia a BC la proporzione di due a uno, come reciprocamente ha tal <lb></lb>proporzione il triangolo ai due bilinei insieme, o al circolo solo. </s>

<s>Che se di­<lb></lb>vidasi LE in 36 parti uguali, AL sarà di queste parti 18, LB 14, e BE 22. </s></p><p type="main">

<s>Sia circoscritto ora alla cicloide il rettangolo GF, e si rivolgano ambedue <lb></lb>le figure intorno alla DF loro base comune. </s>

<s>Verrà da così fatto rivolgimento <lb></lb>generato un solido rotondo, che chiameremo S, e che, secondo la regola <lb></lb>guldiniana dallo stesso Nardi confermata con le ragioni della Geometria, è <lb></lb>uguale a un prisma avente per base il piano cicloidale, e per altezza la cir­<lb></lb>conferenza ridotta in dirittura, e quale si descriverebbe dal raggio LB, di­<lb></lb>stanza del centro di gravità di esso piano dall&#039;asse della revoluzione. </s>

<s>Sarà <lb></lb>nello stesso tempo generato un cilindro C, uguale per le medesime ragioni a <lb></lb>un parallelepipedo avente per base il rettangolo GF, e per altezza la circonfe­<lb></lb>renza descritta dal raggio AL, cosicchè, dietro le equazioni S=DHEIF.2<foreign lang="grc">π</foreign>BI., <lb></lb>e C=GF.2<foreign lang="grc">π</foreign>AL, potrà scriversi la proporzione S:C=DHEIF.BL:GF.AL, <lb></lb>la quale, essendo lo spazio cicloidale al rettangolo circoscritto come 3 a 4, e <lb></lb>BL=14, AL=18; si riduce alla proporzione definita in numeri S:C= <lb></lb>3.14:4.18=7:12. </s></p><p type="main">

<s>Se il rivolgimento si facesse intorno alla GK, tangente il vertice, è ma­<lb></lb>nifesto che rimarrebbero le cose come di sopra, eccettuato che il prisma, a <lb></lb>cui s&#039;uguaglia il solido cicloidale, invece di aver per altezza la circonferenza <lb></lb>di LB, avrà quella descritta da EB, e la proporzione si trasformerà nella se­<lb></lb>guente S:C=DHEIF.EB:GF.AE=3.22:4.18=11:12. Che se in­<lb></lb>vece si supponga rivolgersi le figure intorno alla GD, parallela all&#039;asse, i <lb></lb>solidi rotondi che indi nascono uguaglieranno due prismi aventi la medesima <lb></lb>altezza, perchè le distanze de&#039;centri di gravità dall&#039;asse tornano uguali: ond&#039;è <lb></lb>ch&#039;essi rotondi staranno come le rispettive basi prismali, cioè come 3 a 4. </s></p><p type="main">

<s>Di conseguire con un tal metodo la proporzione de&#039;solidi intorno l&#039;asse <lb></lb>non era speranza, bisognandovi il centro di gravità della mezza cicloide, <lb></lb>ignoto al Nardi, così nella sua, come nella volgare. </s>

<s>Ond&#039;è che soli questi <lb></lb>tre problemi fece, così come noi gli trascriviamo, mettere nelle <emph type="italics"></emph>Scene,<emph.end type="italics"></emph.end> per <lb></lb>poi ridurli ai loro luoghi insieme, con le altre matematiche invenzioni, e <lb></lb>pubblicarli nelle sue Ricercate: </s></p><p type="main">

<s>“ Sia la Cicloide nostra, che <emph type="italics"></emph>regolare<emph.end type="italics"></emph.end> nominiamo, DHEIF, nella mede­<lb></lb>sima figura, di cui la base DF, la sommità E, l&#039;asse EL, ed in essa descri­<lb></lb>vasi il triangolo DEF, e intorno alla stessa il rettangolo GF. Ora, posto es­<lb></lb>sere EL 18, sarà la metà sua AE 9, ed il punto A sarà centro delle due <lb></lb>porzioni DHE, FIE, come per le cose altrove dimostrate, si può intendere. </s>

<s><lb></lb>Ma posta EC 12, sarà il punto C centro del triangolo DEF. </s>

<s>E perchè questo, <lb></lb>alle due porzioni, ha la ragione di due a uno; sarà EB, posta 11, centro <lb></lb>della Cicloide. </s>

<s>” </s></p><p type="main">

<s>“ Dunque il cilindro, nato dalla revoluzione del rettangolo intorno a DF, <lb></lb>al solido, nato dalla revoluzione della Cicloide intorno alla stessa DF, sarà <lb></lb>come 12 a 7. Ma intorno a GE sarà come 12 a 11, e intorno a GD come <lb></lb>4 a 3. “ (Mss. </s>

<s>Gal. </s>

<s>Disc. </s>

<s>T. XX, pag. </s>

<s>149). </s></p><pb xlink:href="020/01/2839.jpg" pagenum="464"></pb><p type="main">

<s>Fu la nuova invenzione del Nardi prima, che a ogni altro, comunicata al <lb></lb>suo carissimo Ricci, il quale facevagli osservare che l&#039;ultimo dei tre teoremi <lb></lb>si verifica anche nella Cicloide volgare, essendo il solido, nato di lei mentre <lb></lb>ch&#039;ella si rivolge intorno al lato del rettangolo parallelo all&#039;asse, al cilindro <lb></lb>circoscritto, come l&#039;una all&#039;altra figura genitrice, cioè come tre a quattro, <lb></lb>ossia, secondo che egli diceva, in ragione subsesquiterza. </s>

<s>Di qui avvenne che <lb></lb>il Nardi, ai tre teoremi relativi alla sua cicloide nuova, v&#039;aggiungesse il <lb></lb>quarto relativo alla cicloide antica, nell&#039;annunziargli che fece al Torricelli, <lb></lb>il quale, credendo che fosse quell&#039;osservazione sovvenuta allo stesso Nardi, <lb></lb>gliene volle rendere pubblica testimonianza, quasi in segno di gratitudine <lb></lb>verso colui, che avevagli aperta e dimostrata la via, da giungere al termine <lb></lb>desiderato. </s>

<s>Che altro infatti gli rimaneva, per risolvere i problemi venuti di <lb></lb>Francia, se non che a ritrovare il centro di gravità della cicloide, coraggio­<lb></lb>samente affrontando quelle difficoltà, innanzi alle quali s&#039;erano arretrati, o <lb></lb>l&#039;avevano tentate solamente di traverso, gli amici suoi pur così valorosi? </s>

<s><lb></lb>Come riportasse il Torricelli di ciò lieta vittoria fu veduto nella proposi­<lb></lb>zione LVI, scritta da noi nel capitolo V qui addietro, nella qual proposizione <lb></lb>l&#039;Autor dimostrava che il centro di gravità della Cicloide così divide l&#039;asse, <lb></lb>che la parte al vertice stia a quella verso la base, come sette sta a cinque. </s></p><p type="main">

<s>Or s&#039;intenda nella solita figura 307, disegnata in DHEIF la cicloide <lb></lb>volgare, col suo baricentro in B. </s>

<s>Essendo EB=7, BL=5, e AL=6, non <lb></lb>rimane a far altro che a sostituire questi numeri nelle formule già poste dal <lb></lb>Nardi, le quali, per i solidi intorno alla base si riducono a S:C=3.5:4.6= <lb></lb>5:8, e per i solidi intorno al lato opposto alla base a S:C=3.7:4.6= <lb></lb>7:8. Il primo de&#039;quali teoremi, tralasciando l&#039;altro perchè facilissimo con <lb></lb>somiglianti metodi a dimostrarsi, si legge manoscritto così, in fine al trat­<lb></lb>tatello torricelliano della Cicloide: </s></p><p type="main">

<s>“ Solidum cycloidale circa basim revolutum ad cylindrum circumscriptum <lb></lb>est ut 5 ad 8. “ </s></p><p type="main">

<s>“ Esto cycloidale spatium DHEIF, cuius axis EL, centrum gravitatis B, <lb></lb>rectangulum vero circumscriptum sit GF, ipsiusque centrum gravitatis sit A. </s>

<s><lb></lb>Demonstratum iam est NL ad BL esse ut 6 ad 5, et spatium GF, ad spa­<lb></lb>tium DHEIF, esse ut 4 ad 3. (Hoc in appendice ad libellum <emph type="italics"></emph>De dimensione <lb></lb>parabolae.<emph.end type="italics"></emph.end>) ” </s></p><p type="main">

<s>“ Convertatur iam utraque figura circa basim DF, habebitque solidum <lb></lb>ex DHEIF, ad cylindrum ex GF, rationem compositam ex ratione figurae <lb></lb>planae DHEIF ad rectangulum GF, nempe ex ratione numeri 15 ad 20, et <lb></lb>ex ratione distantiarum BL ad AL, nempe ex ratione 20 ad 24. Ergo soli­<lb></lb>dum cycloidale circa basim, ad cylindrum sibi circumscriptum, erit ut 15 <lb></lb>ad 24, sive in minimis ut 5 ad 8, quod ostendere volebam. </s>

<s>” (ibid., T. XXXIV, <lb></lb>fol. </s>

<s>278). </s></p><p type="main">

<s>De&#039;solidi intorno alla GK parallela alla base dicemmo come il Torri­<lb></lb>celli ne lasciasse a concludere facilmente la proporzione di 7 a 8, richiaman­<lb></lb>dosi al teorema del Nardi, per i solidi nati dal rivolgersi le due figure in-<pb xlink:href="020/01/2840.jpg" pagenum="465"></pb>torno al lato GD del rettangolo circoscritto. </s>

<s>Rimaneva, per aver questo <lb></lb>trattatello cicloidale compiuto, a ritrovar la proporzione che passa tra il so­<lb></lb>lido e il cilindro generati ambedue dalla rivoluzione intorno all&#039;asse, ciò che <lb></lb>non potevasi con l&#039;intrapreso metodo conseguire, senz&#039;aver prima determinato <lb></lb>il punto, in cui la mezza cicloide concentra il suo peso. </s>

<s>Da B condotta una <lb></lb>parallela alla base, era certissimo che doveva sopra questa linea cadere quel <lb></lb>punto, ma a qual distanza precisamente dall&#039;asse pareva difficilissimo, per non <lb></lb>dire impossibile, a dimostrare. </s>

<s>E nonostante volle il Torricelli far credere <lb></lb>di avere anche di ciò certissima matematica dimostrazione, dalla quale, per <lb></lb>l&#039;applicazione della Regola guldiniana, conseguiva essere il solido della mezza <lb></lb>cicloide, al cilindro circoscritto, nella proporzion medesima di 11 a 18. Tro­<lb></lb>viamo una tal presunzione espressa in pubblico nel documento che citeremo <lb></lb>e in un estratto di lettera privata a Raffaello Magiotti, a cui il Torricelli <lb></lb>stesso così diceva: </s></p><p type="main">

<s>“ Il solido della Cicloide rivolta intorno all&#039;asse, al cilindro circoscritto, <lb></lb>è come 11 a 18, dimostrazione difficilissima. </s>

<s>Il solido <emph type="italics"></emph>circa basim,<emph.end type="italics"></emph.end> al suo <lb></lb>cilindro è come 5 a 8 è più facile. </s>

<s>Pur l&#039;una e l&#039;altra si trova per via di <lb></lb>meccanica, trovato prima il centro di gravità della figura genitrice, in che <lb></lb>linea stia, or parallela alla base, che è difficilissimo, ed or parallela all&#039;asse, <lb></lb>che è peggiore. </s>

<s>” </s></p><p type="main">

<s>“ Trovato questo centro, ho poi la dimostrazione dei solidi. </s>

<s>La proposi­<lb></lb>zione è questa: <emph type="italics"></emph>Date due figure piane<emph.end type="italics"></emph.end> DK, (nella ultima figura 307) <emph type="italics"></emph>di cui <lb></lb>sia centro A, e DETF, di cui sia centro M, e si rivolgano intorno al­<lb></lb>l&#039;asse DF; il solido di DK, al solido di DEIF, avrà proporzione composta <lb></lb>della figura DK alla DEIF, e della distanza AL alla distanza MN.<emph.end type="italics"></emph.end> Però, <lb></lb>supposta questa proposizione che da me si dimostra, (come si vede nella pro­<lb></lb>posizione XII <emph type="italics"></emph>De momentis,<emph.end type="italics"></emph.end> da noi ordinata nel capitolo precedente) o per <lb></lb>dirla è piuttosto invenzione d&#039;altri che mia, e trovato i centri della cicloide <lb></lb>e semicicloide, sapendosi già la proporzione delle figure piane e la propor­<lb></lb>zione delle distanze dall&#039;asse; si trova la proporzione composta, che è quella <lb></lb>dei solidi. </s>

<s>La dimostrazione del solido <emph type="italics"></emph>circa basim<emph.end type="italics"></emph.end> l&#039;ebbe il signor Nardi e <lb></lb>il signor Ricci dal 1644. ” (ivi T. XL, fol. </s>

<s>23). </s></p><p type="main">

<s>Erano di una tal dimostrazione in gran desiderio i due amici, special­<lb></lb>mente dietro quel che avevano letto fra le varie Opere geometriche, nello <lb></lb>Scolio alla proposizione XVIII del primo libro <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> in fine al <lb></lb>quale Scolio, dop&#039;aver detto il Torricelli che ometteva la dimostrazione delle <lb></lb>tangenti, de&#039;solidi e de&#039;centri di gravità degli spazi cicloidali, <emph type="italics"></emph>ad evitandam <lb></lb>molem,<emph.end type="italics"></emph.end> soggiungeva in tal guisa: “ Satis sit interea lectorem hic admo­<lb></lb>nuisse quod, si Cycloidis spatium circa basim convertatur, erit solidum ad <lb></lb>cylindrum circumscriptum ut 5 ad 8: si vero circa tangentem basi paralle­<lb></lb>lam ut 7 ad 8. Centrum Cycloidis axem secat, ita ut partes sint ut 7 ad 5. <lb></lb>Demonstratur etiam ratio solidi circa axem, ad cylindrum circumscriptum: <lb></lb>item in qua linea axi parallela sit centrum semicycloidis. </s>

<s>Clar. </s>

<s>vir Antonius <lb></lb>Nardi ostendit quod, si cyclois circa tangentem axi parallelam convertatur, <pb xlink:href="020/01/2841.jpg" pagenum="466"></pb>solidum ad suum cylindrum erit subsesquitertium. </s>

<s>” (pag. </s>

<s>121, 22). Le quali <lb></lb>parole leggendo il Ricci nel settembre del 1644 ringraziava l&#039;Autore dell&#039;aver­<lb></lb>gli donato il libro, in cui trovava tutte quelle proposizioni ammirabili, fa­<lb></lb>cendogli questa osservazione. </s>

<s>“ Ho poi veduto citare una proposizione tale: <lb></lb><emph type="italics"></emph>Il solido nato dalla Cicloide, girata intorno una tangente all&#039;asse paral­<lb></lb>lela, del suo cilindro è subsesquiterza:<emph.end type="italics"></emph.end> cosa dimostrata da me fin da prin­<lb></lb>cipio che sentii nominar la Cicloide, e, per la facilità con che si dimostra, <lb></lb>non ne ho mai fatta stima veruna. </s>

<s>” (MSS. Gal. </s>

<s>Tom. </s>

<s>XLII, fol. </s>

<s>50). </s></p><p type="main">

<s>Non deve averne fatta grande stima nemmeno il Nardi, per cui non <lb></lb>pensò di avvertire il Torricelli che il teorema del solido intorno alla tangente <lb></lb>parallela all&#039;asse era del Ricci. </s>

<s>Il sentirsi ora attribuire cosa di sì poco mo­<lb></lb>mento, senza far motto del metodo ch&#039;era proprio suo, avuto il quale, il <lb></lb>merito del Torricelli non riusciva che secondario; deve essere dispiaciuto al <lb></lb>Nardi, il quale però non fece, che da noi si sappia, di ciò lagnanza con nes­<lb></lb>suno. </s>

<s>Rimase perciò nell&#039;animo dello stesso Torricelli dell&#039;ambita invenzione <lb></lb>la compiacenza intera, la quale venne nonostante a diminuirsegli da un&#039;altra <lb></lb>parte, quando il Mersenno, a proposito della quadratura, gli soggiungeva in <lb></lb>una lettera del dì 13 giugno 1644, aver il Roberval da qualche anno dimo­<lb></lb>strato che il solido cicloidale intorno alla base sta al cilindro circoscritto <lb></lb>come 5 a 8. </s></p><p type="main">

<s>Se fosse stata dal Matematico parigino ritrovata la proporzione anche <lb></lb>fra gli altri solidi il Torricelli era incerto, ma pure si lusingava che no, <lb></lb>fermamente credendo che il centro di gravità della Cicloide, e l&#039;applicazione <lb></lb>della regola centrobarica, non fosser cose note che a lui. </s>

<s>Di qui è che al­<lb></lb>l&#039;unico teorema annunziatogli dal Mersenno aggiungeva la nota dei parecchi <lb></lb>altri da sè dimostrati intorno alle proprietà della cicloide, nella qual nota <lb></lb>mandata in Francia parve al Roberval di sentire alitarvi uno spirito di ar­<lb></lb>roganza. </s>

<s>Altre occasìoni s&#039;aggiunser poi ad irritare sempre più gli animi <lb></lb>de&#039;due matematici, che finirono per accusarsi obbrobriosamente a vicenda <lb></lb>d&#039;usurpazione e di plagio. </s>

<s>— Ora imparo a credere, scriveva il Torricelli del <lb></lb>Roberval, ch&#039;ei non avesse la quadratura della Cicloide, <emph type="italics"></emph>ma la prendesse <lb></lb>dalla mia.<emph.end type="italics"></emph.end> — E dop&#039;aver minutamente raccontato come passassero le cose <lb></lb>fra lui, e quei signori francesi, concludeva, invocando a suo giudice il mondo <lb></lb>scientifico: <emph type="italics"></emph>vedete che furto vergognoso hanno tentato di farmi!<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il Roherval di rincontro, descritte l&#039;arti degli invidiosi e degli emuli, da <lb></lb>lui rassomigliati ai fuchi, che non sapendo elaborare il dolce miele, inva­<lb></lb>dono i favi delle api: “ his artibus, soggiungeva, ipsa trochoides, eiusque <lb></lb>tangentes, et plana, sed et solida ferme omnia mihi erepta sunt. </s>

<s>” (<emph type="italics"></emph>DeTro­<lb></lb>choide.<emph.end type="italics"></emph.end> Ouvr. </s>

<s>cit. </s>

<s>p. </s>

<s>343). E perchè non apparisse dubbio essere contro il <lb></lb>Torricelli propriamente diretta l&#039;accusa di furto diceva di serbare ancora le <lb></lb>lettere di lui: di lui, <emph type="italics"></emph>qui prae caeteris sapere videri volebat,<emph.end type="italics"></emph.end> ed ebbesi al <lb></lb>contrario, rispetto al solido intorno l&#039;asse, scoperta la propria ignoranza, d&#039;onde <lb></lb>gli nacque nell&#039;animo quella indignazione e quella rabbia! (ivi.) </s></p><p type="main">

<s>S&#039;ingerirono nella lite avvocati, difensori naturalmente delle ragioni dei <pb xlink:href="020/01/2842.jpg" pagenum="467"></pb>loro clienti, e prima uscì in francese un libretto intitolato <emph type="italics"></emph>Histoire de la <lb></lb>Roulette,<emph.end type="italics"></emph.end> che per dargli anche maggior diffusione, fu tradotto in latino. </s>

<s>Si <lb></lb>voleva dimostrare in esso che aveva la Cicloide avuto in Parigi la nascita e <lb></lb>l&#039;educazione, e che perciò il Torricelli bugiardamente diceva esser sua figlia <lb></lb>naturale quella, che in verità non era che adottiva. </s>

<s>Carlo Dati, nella sua <lb></lb><emph type="italics"></emph>Lettera a&#039;Filaleti,<emph.end type="italics"></emph.end> stampata in Firenze nel 1663 sotto il nome di <emph type="italics"></emph>Timauro <lb></lb>Antiate,<emph.end type="italics"></emph.end> rispose alle accuse dello storico francese, che sentenziava senza re­<lb></lb>car documenti, con i quali in mano concludeva esso Dati col dire che, non <lb></lb>dubitando punto della verità delle invenzioni robervelliane e del loro pri­<lb></lb>mato, si negava però che il Torricelli fosse giunto a ritrovar le medesime <lb></lb>cose, dietro la notizia di quel che era stato fatto dagli altri. </s></p><p type="main">

<s>L&#039;apologia del Dati è pienamente confermata dalla nostra Storia, la quale <lb></lb>ha già contato passo per passo i progressi fatti dalla scienza della Cicloide, <lb></lb>prima in Parigi e poi in Firenze, dove le prime mosse furon date da Ga­<lb></lb>lileo. </s>

<s>L&#039;incertezze e le fallacie dell&#039;esperienza meccanica essendo state tolte <lb></lb>dal Nardi, venne da ciò a incorarsi la speranza della quadratura nel Torri­<lb></lb>celli, che riuscì a dimostrarla con feconda facilità, e con geometrica accura­<lb></lb>tezza. </s>

<s>Persuasi da questo fatto i dubitosi Galileiani che il problema era so­<lb></lb>lubile per ragioni di Geometria, il Nardi stesso vi s&#039;applicò, immaginando <lb></lb>la Cicloide regolare, la quale, per la facile invenzione del suo centro di gravità, <lb></lb>dette modo al suo Autore di ritrovar con la regola centrobarica le propor­<lb></lb>zioni tra i solidi, e i cilindri circoscritti, rivolgendosi le figure ora intorno <lb></lb>alla base, e ora intorno alla tangente all&#039;origine e alla cima. </s>

<s>Da ciò prese <lb></lb>l&#039;esempio il Torricelli di trattar col medesimo metodo la Cicloide volgare, e <lb></lb>datosi a ricercare il centro di gravità di lei, e ritrovatolo esattamente, gli <lb></lb>vennero con facilità conclusi per questa figura i tre teoremi de&#039;solidi, che <lb></lb>analogamente il Nardi aveva conclusi per la sua. </s></p><p type="main">

<s>In Parigi l&#039;ufficio di ostetricante fu fatto dal Mersenno, ma il parto lo <lb></lb>dette alla luce il Roberval da sè solo, avuta da Archimede la dottrina degli <lb></lb>indivisibili, e col teorema geometrico <emph type="italics"></emph>Degli anelli<emph.end type="italics"></emph.end> supplendo al servigio reso <lb></lb>in Italia dal teorema del Guldino. </s>

<s>Benchè dunque vari fossero gl&#039;inlzi, e vari <lb></lb>gli istrumenti, è un fatto ormai dimostrato dalla Storia che si condussero <lb></lb>i due Matematici a scoprire le medesime verità, senza che l&#039;uno sapesse <lb></lb>nulla dell&#039;altro. </s>

<s>E perciò si diceva che l&#039;apologia del Dati era giusta, in quanto <lb></lb>l&#039;Autore difendeva il suo proprio amico e maestro dall&#039;accusa d&#039;aver rubato <lb></lb>nulla allo straniero. </s>

<s>Ma i Lettori imparziali sentono già nella loro propria <lb></lb>coscienza che la giustizia non può dirsi intera, infintantoche non sia anche <lb></lb>lo Straniero purgato dall&#039;accusa di furto mossagli dal Nostro. </s></p><p type="main">

<s>Il Dati manca di far ciò, e anzi conferma le ragioni, con le quali pre­<lb></lb>tendeva il Torricelli che il Roberval si fosse appropriato il centro di gravità <lb></lb>della Cicloide, e l&#039;applicazione di lui al metodo di ritrovare i solidi rotondi. </s>

<s><lb></lb>L&#039;affezione doveva senza dubbio aver fatto velo al giudizio, ma è da aggiun­<lb></lb>gere di più che il Dati non potè ascoltare, o non avrebbe forse avuta tanta <lb></lb>sincerità di mente, da apprezzar le ragioni, che l&#039;irritato Francese adduceva <pb xlink:href="020/01/2843.jpg" pagenum="468"></pb>per dimostrar ch&#039;era suo il metodo inverso di concluder dai dati solidi il <lb></lb>baricentro, e altre cose che si possono ora legger da noi fra le Opere rober­<lb></lb>valliane; nell&#039;ultima epistola stampata <emph type="italics"></emph>ad Torricellium.<emph.end type="italics"></emph.end> Di questa epistola <lb></lb>sappiamo aver esso Dati fatto ricerca appresso il Ricci, a cui scriveva: “ Mi <lb></lb>par di sentire che m. </s>

<s>Roberval già minacciasse di rispondere con una pie­<lb></lb>nissima lettera a quella che scrisse il Torricelli sotto il dì 7 Luglio 1646, <lb></lb>risentendosi dell&#039;usurpato centro di gravità della Cicloide, la quale però non <lb></lb>so se mai comparisse, nulla trovando fra le scritture di esso Torricelli, nè <lb></lb>incontrando chi l&#039;abbia veduta o sentita nominare. </s>

<s>Onde supplico V.S.I. a <lb></lb>compiacersi, per l&#039;amore della reputazione dell&#039;amico e della verità, a darmi <lb></lb>non solamente notizia di questa lettera di m. </s>

<s>Roberval, se però è nel mondo, <lb></lb>ma avendola a farmene fare una copia. </s>

<s>” (MSS. Palatini, Raccolta Baldovi­<lb></lb>netti n.° 258, fasc. </s>

<s>2°.) Ma nè il Ricci sapendone nulla, non potè il Dati <lb></lb>esaminar le ragioni dell&#039;imputato, le quali imparzialmente s&#039;esamineranno <lb></lb>ora da noi, facendo da&#039;suoi principii derivare il processo di questa lite famosa. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Racconta il Torricelli come, ritrovandosi in Roma nel 1640, avesse occa­<lb></lb>sione di conoscere il padre Giovan Francesco Niceron, de&#039;frati Minimi, va­<lb></lb>lentissimo matematico francese e pittore, con cui, anche trasferito che si fu <lb></lb>a Parigi, mantenendo esso Torricelli qualche commercio di virtuosa amicizia, <lb></lb>ciò dette opportunità di mandare al detto padre la nota di alcune sue inven­<lb></lb>zioni geometriche, proponendole semplicemente senz&#039;alcuna dimostrazione. </s>

<s><lb></lb>Erano fra quelle proposizioni, ridotte al numero di venti, incluse anche quelle <lb></lb>del Solido acuto iperbolico, e della quadratura della Cicloide, che richiama­<lb></lb>rono particolarmente l&#039;attenzione del Roberval, all&#039;esame del quale le aveva <lb></lb>il Niceron sottoposte, per mezzo del coufrate suo Marino Mersenno. </s></p><p type="main">

<s>Nella ferma persuasione che non fosse la Cicloide nota altro che in Fran­<lb></lb>cia, ebbe il Roberval a maravigliarsi, ripensando in che modo fosse potuta <lb></lb>pellegrinare in Italia, e, non trovando in che altro sodisfare la sua curiosità, <lb></lb>sospettò che il Beaugrand, ne&#039;suoi viaggi, ne avesse comunicata la notizia <lb></lb>o a Galileo o al Castelli o al Cavalieri. </s>

<s>In ogni modo la XIV delle dette <lb></lb>proposizioni, cioè quella del solido iperbolico, gli parve tanto elegante, che <lb></lb>volle applicarvisi a dimostrarla, in che felicemente essendo riuscito, si volse <lb></lb>con lieto animo a ringraziare il Mersenno, che gli avesse fatto conoscere un <lb></lb>tant&#039;Uomo, da non posporsi, diceva, allo stesso Archimede, e degno di esser <lb></lb>fatto conoscere al Fermat, e al Cartesio. </s>

<s>Con queste enfatiche espressioni <lb></lb>terminava una lettera latina indirizzata allo stesso Mersenno, il quale non <lb></lb>indugiò a mandarne fedel copia a Firenze, rallegrandosi col Torricelli che <lb></lb>fosse da que&#039;dottissimi Matematici tanto applaudito. </s>

<s>Il Torricelli corrispose <lb></lb>con non minore ardore dell&#039;animo, andando direttamente a ritrovare il Ro-<pb xlink:href="020/01/2844.jpg" pagenum="469"></pb>berval, e contraccambiandogli il titolo di Apollo dei Geometri. </s>

<s>Con tali sen­<lb></lb>timenti scriveva a Parigi in una lettera latina, sottoscritta da Firenze il di <lb></lb>primo Ottobre 1643, ma fra gli amici si lagnava che si fosse il Roberval <lb></lb>arrogato il primato della quadratura della Cicloide, e dicesse che il Beaugrand <lb></lb>ne aveva recata la notizia in Italia: lagnanze, che il Cavalieri veniva a con­<lb></lb>solare nell&#039;animo dell&#039;amico con queste parole: </s></p><p type="main">

<s>“ Mi è giunto nuovo il nome del Robervallio, tuttavia non lo stimo io <lb></lb>manco, mentre ella lo giudica soggetto eminente, il che non può essere di <lb></lb>meno, avendogli dimostrate le cose che dice, e massime le sue maravigliose <lb></lb>proposizioni.... Mi rallegro poi-seco che la fama delle sue ammirabili pro­<lb></lb>posizioni sia arrivata in Francia, sebbene mi dispiace che il detto Roberval­<lb></lb>lio si arroghi il primato circa la Cicloide, o almeno che da esso sia venuta <lb></lb>a notizia di V. S., e immeritatamente incolpa in questo il Beaugrand, quale <lb></lb>non parlò di tal cosa nè a me, nè credo neanco al Galileo o al padre don <lb></lb>Benedetto, quando venne in Italia, o scrisse mai, che io sappia, di tal cosa, <lb></lb>poichè ne averei pure avuto qualche sentore. </s>

<s>Fu bene il Nicerone, che pro­<lb></lb>pose a me tal quesito, al quale però non applicai, spaventato dalla lettera <lb></lb>del Galileo, quale mi avvisava d&#039;avervi pensato indarno molto e molto tempo, <lb></lb>come credo che altra volta gli scrivessi. </s>

<s>Se poi fosse il primo il Galileo a <lb></lb>pensare a un tal quesito, o gli fosse proposto da altri, veramente non lo so.... <lb></lb>È ben vero che, scrivendo ultimamente al p. </s>

<s>Nicerone, gli dissi come V. S. <lb></lb>aveva dimostrato la misura dello spazio cicloidale in tre modi, ma non ac­<lb></lb>cennai già qual fosse la proporzion ritrovata, nè altro mi ricordo di avere <lb></lb>scritto colà, parendomi che da questo solo, come <emph type="italics"></emph>ex ungue leonem,<emph.end type="italics"></emph.end> potes­<lb></lb>sero essere ragguagliati di qual sorta d&#039;ingegni produca l&#039;Italia, e che pro­<lb></lb>gressi farebbono, se qua vi fosse il fervore in questa scienza, che tra quei <lb></lb>virtuosi e studiosi di Parigi ” (MSS. Gal. </s>

<s>Disc., T. XLI, fol. </s>

<s>177-81). </s></p><p type="main">

<s>La causa tra&#039;due competitori, nella quale, a favore del Torricelli, en­<lb></lb>trava, così, testimone di mezzo il Cavalieri; s&#039;agitò da principio sommessa­<lb></lb>mente, o come si direbbe dietro le spalle: in faccia il Roberval non si fece <lb></lb>altro uscire dalla bocca, che queste parole: “ In cycloide Torricellii agnosco <lb></lb>nostram trochoidem, nec recte percipio quomodo ipsa ad Italos pervenerit, <lb></lb>nobis nescientibus ” (Epist. </s>

<s>Rob. </s>

<s>ad Mersennum. </s>

<s>Ouvrages cit., pag. </s>

<s>350): <lb></lb>a che il Torricelli stesso rispondeva che una tal linea così <emph type="italics"></emph>natura familia­<lb></lb>ris erat<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>360), da non far maraviglia ch&#039;ella fosse pubblicamente <lb></lb>nota, senza che nessuno l&#039;avesse mostrata, e voleva con ciò insinuare che <lb></lb>le tradizioni erano ben più antiche e più universali di quelle, che correvano <lb></lb>allora tra i Francesi. </s></p><p type="main">

<s>Dicemmo che così passarono tra il Roberval e il Torricelli le cose sul <lb></lb>principio, ma poi tornarono a rinfacciarsi acerbamente le accuse di plagio, <lb></lb>quando ne&#039;solidi e nel centro di gravità della Cicloide venne ad aggropparsi <lb></lb>la lite, che ora a noi resta a enodare. </s></p><p type="main">

<s>Ricevuta il Roberval la lettera da Firenze del dì primo Ottobre 1643, <lb></lb>da noi sopra commemorata, ne sentì gran piacere, esprimendo questi suoi <pb xlink:href="020/01/2845.jpg" pagenum="470"></pb>sensi al Mersenno, il quale, dop&#039;avergli significati al Torricelli in una let­<lb></lb>tera da Parigi del dì 13 Gennaio 1644, così soggiungeva: “ Trochoidis vero <lb></lb>naturam, vel ut vis Cycloidis, ita penetravit Robervallius noster nihil ut ele­<lb></lb>gantius, vel profundius videris: eiusque solidum cum super base convertitur, <lb></lb>ad cylindrum eiusdem altitudinis, demonstravit esse ut 5 ad 8 ” (Lett. </s>

<s>a&#039;Fi­<lb></lb>laleti, pag. </s>

<s>11). </s></p><p type="main">

<s>Il Torricelli che pochi mesi fa, ritrovato il baricentro della Cicloide, aveva <lb></lb>col metodo del Nardi dimostrato non solamente la proporzione tra il solido <lb></lb>e il cilindro circa la base, ma circa le tangenti all&#039;origine e alla cima, e <lb></lb>anche, come si lusingava di far credere, intorno all&#039;asse; per contrapporre <lb></lb>a quella, che appariva aridità nel Francese, la sua vena feconda, prese, il dì <lb></lb>primo del Maggio 1644, in mano la penna. </s>

<s>per annunziare al Mersenno, e <lb></lb>mediante lui al Roberval la serie di questi teoremi, dal primo in fuori com­<lb></lb>piacendosi che tutti gli altri fossero sue proprie invenzioni. </s></p><p type="main">

<s>“ Solidum, quod fit a spatio cycloidali circa tangentem axi aequidistan­<lb></lb>tem revoluto, ad cylindrum eiusdem altitudinis eiusdemque diametri, est sub­<lb></lb>sesquitertium. </s>

<s>Demonstratio non est mea, sed inventum demonstratumque <lb></lb>fuit hoc ab Antonio Nardio, patritio aretino, olim Galilei amicissimo. </s>

<s>Reli­<lb></lb>qua mea sunt. </s>

<s>” </s></p><p type="main">

<s>“ Solidum, quod fit a spatio cycloidali circa tangentem basi parallelam re­<lb></lb>voluto, est ad cylindrum eiusdem altitudinis et diametri, subsesquiseptimum. </s>

<s>” </s></p><p type="main">

<s>“ Solidum, quod fit a spatio cycloidali circa axem revoluto, ad cylindrum <lb></lb>eiusdem axis et diametri, est ut 11 ad 18. Solidum idem circa axem, ad so­<lb></lb>lidum circa basim, est ut circulus aliquis ad quadratum sibi circumscriptum. </s>

<s>” </s></p><p type="main">

<s>“ Hinc est solidum etiam circa basim, ad cylindrum eiusdem axis et <lb></lb>diametri, ut 5 ad 8. ” </s></p><p type="main">

<s>“ Centrum gravitatis spatii cycloidalis axem ita dividit, ut pars, quae <lb></lb>ad verticem, sit ad reliquam ut 7 ad 5 ” (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>42 <lb></lb>ad tergum). </s></p><p type="main">

<s>Presentata questa nota di teoremi al Roberval, i nostri Lettori, che hanno <lb></lb>già vedute le cinque proposizioni, dimostrate da lui infino dal 1640 in que­<lb></lb>sto medesimo soggetto, indipendentemente dalla Regola centrobarica, allora <lb></lb>a lui forse ignota; possono indovinar facilmente che nulla gli dovesse appa­<lb></lb>rire, fra quelle cose, nuovo, fuor che il centro di gravità della Cicloide, e il <lb></lb>solido circa l&#039;asse. </s>

<s>Il teorema degli anelli dispensandolo dal pensiero di quello, <lb></lb>e intorno a questo abbandonato ogni studio, per parergli la proporzione <lb></lb>incommensurabile, confessò ingenuamente, e secondo il giudizio che poteva <lb></lb>farne allora dietro quelle semplici enunciazioni, che il Torricelli l&#039;aveva pre­<lb></lb>venuto nelle due dette cose, nel dimostrar cioè il centro cicloidale, e il so­<lb></lb>lido circa l&#039;asse, delle quali due dimostrazioni perciò ei generosamente lo <lb></lb>riconosceva primo e prestantissimo autore. </s>

<s>E così, come disse al Mersenno, <lb></lb>così il Mersenno scrisse al Torricelli con queste parole: “ qui, cum tuas <lb></lb>postremas legisset, praedictum solidum, et centrum gravitatis tibi debere fa­<lb></lb>tetur, qui primus invenisti ” (Lett. </s>

<s>a&#039;Filaleti, pag. </s>

<s>12). </s></p><pb xlink:href="020/01/2846.jpg" pagenum="471"></pb><p type="main">

<s>Ma si sentì il Roberval, ripensando a que&#039;teoremi torricelliani, frugato <lb></lb>da una gran curiosità di sapere com&#039;entrasse il centro di gravità della Ci­<lb></lb>cloide nelle proposizioni de&#039;solidi generati da lei, per cui, non sapendo se <lb></lb>l&#039;invenzione apparteneva come l&#039;altre alla Geometria, o resultava da qualche <lb></lb>meccanica esperienza, il Mersenno, che anch&#039;egli era incerto della risposta, <lb></lb>interrogò in proposito il Torricelli, così soggiungendo dopo le riferite parole: <lb></lb>“ Dubitat noster Robervallius an mechanice tantum centra gravitatis Cycloi­<lb></lb>dis inveneris, quae geometrice falsa suspicantur: docebis num ipsius rei de­<lb></lb>monstrationem habeas? </s>

<s>” (ibid.). Che si debbano intendere queste dure frasi <lb></lb>mersenniane come noi abbiam detto, non è dubbio, così avendole intese da <lb></lb>principio anche lo stesso Torricelli, ma poi, perchè faceva gioco alla sua <lb></lb>causa, le interpetrò troppo materialmente, facendo dire a&#039;due francesi la stra­<lb></lb>nezza che possa essere una cosa meccanicamente vera, e geometricamente <lb></lb>falsa, quasichè la quadratura della cicloide, ritrovata meccanicamente dal <lb></lb>Nardi, non fosse anche vera in Geometria, e quella di Galileo, errata nel­<lb></lb>l&#039;esperienza, anche alla Geometria non riuscisse ugualmente falsa. </s></p><p type="main">

<s>Ma non interrompendo il filo della storia, vediamo come rispondesse il <lb></lb>Torricelli interrogato se aveva esatta dimostrazione geometrica de&#039;baricentri <lb></lb>cicloidali, e del solido circa l&#039;asse. </s>

<s>Quanto ai primi fu largo, ordinando le <lb></lb>proposizioni, insieme con la dimostrazione dei solidi rotondi, i quali stanno <lb></lb>in ragion composta delle figure genitrici e delle distanze de&#039;loro centri di <lb></lb>gravità dall&#039;asse della rotazione, tutto premettendo per lemmi al teorema del <lb></lb>solido circa la base: e così disposto il trattatelo, quale si legge fra i mano­<lb></lb>scritti appartenenti ai discepoli di Galileo, nell&#039;autografo e nelle copie del <lb></lb>Viviani e del Serenai; lo mandò a Parigi al Mersenno, accompagnando la <lb></lb>scrittura con una lettera, nella quale diceva: “ Heri (24 Luglio 1644) ad me <lb></lb>delatae fuerunt literae tuae, Vir clarissime, ideoque inter paucas horas pro­<lb></lb>positiunculas, quas nunc mitto, composui conscripsique. </s>

<s>Constitueram propo­<lb></lb>sitiones de centro grav. </s>

<s>cycloidis, semicicloidisque, quas in mente tantum <lb></lb>tenebam, nulli per aliquot menses communes facere. </s>

<s>Attamen victus alteram <lb></lb>earum mitto, nempe Cycloidis. </s>

<s>Sileo alteram, cum ex ea pendeat demonstra­<lb></lb>tionem solidi circa axem, victus autem fui, quando in illa verba incidi: Du­<lb></lb>bitat Robervallius noster geometrica ne, an aliqua mechanica ratione, de­<lb></lb>monstrationem habeas de centro gravitatis ” (Lett. </s>

<s>a&#039;Fil., pag. </s>

<s>12). </s></p><p type="main">

<s>Soprabbondando dunque nel rispondere alla prima parte della domanda, <lb></lb>tacque il Torricelli affatto rispetto alla seconda, nè s&#039;intenderebbe il perchè, <lb></lb>se non si cominciasse fin d&#039;ora a sospettare che il centro di gravità della <lb></lb>semicicloide lo doveva aver davvero, non in altro che nella mente, non po­<lb></lb>tend&#039;essere nella realtà delle cose. </s>

<s>Bastò nulladimeno al Roberval l&#039;accenno, <lb></lb>che dal detto centro della semicicloide dipendeva la dimostrazione del solido <lb></lb>circa l&#039;asse, come gli bastò la lettura delle rimanenti proposizioni, per inten­<lb></lb>dere quale ingerenza avesse negli altri solidi il centro di gravità della Ci­<lb></lb>cloide intera, d&#039;onde vennegli giusto motivo di riformare, intorno all&#039;Autore <lb></lb>dei due detti teoremi, quel primo fatto giudizio: cosa che poi tanto dispiacque <pb xlink:href="020/01/2847.jpg" pagenum="472"></pb>a chi ci aveva interesse, qualificandola per una contradizione indegna, e per <lb></lb>una meditata rapina. </s></p><p type="main">

<s>Il Torricelli, come in questa apparisce e in molte altre parti della Sto­<lb></lb>ria, era troppo geloso, sospettoso e prepotente in rivendicare a sè quel che <lb></lb>non aveva sempre ragione di chiamar suo, e nonostante avrebbe forse rico­<lb></lb>nosciuto giusto o scusato almeno quel rivoltar giubba, siaci permesso il detto, <lb></lb>se il Roberval gli avesse mandate a esaminare le sue cinque proposizioni, <lb></lb>come l&#039;altro aveva a Parigi mandato le sue. </s>

<s>Tardi riconobbe da sè stesso il <lb></lb>Roberval che sarebbe stato bene di far così, per evitare i litigi, e per assi­<lb></lb>curarsi la proprietà delle invenzioni, e pubblicamente ne disse sua colpa. <lb></lb></s>

<s>“ Negligentia mea, quod nihil praelo committerem, factum est ut quidam <lb></lb>extranei nationis nostrae aemuli, vel potius eidem invidi,... multa mea mibi <lb></lb>eripere conarentur, eaque sibi tribuere ” (<emph type="italics"></emph>De Trochoide,<emph.end type="italics"></emph.end> Ouvrages cit., p. </s>

<s>343). <lb></lb>E non solamente si sarebbe assicurato dai furti, ma avrebbe meglio provve­<lb></lb>duto ai progressi e agl&#039;incrementi della Scienza, la quale perciò professa <lb></lb>maggior gratitudine al Geometra nostro, che a lui. </s>

<s>Eppure anche il Torri­<lb></lb>celli, temendo di andar troppo per le lunghe, non fece della maggior parte <lb></lb>delle cose da sè dimostrate intorno alla Cicloide altro che un motto, il quale <lb></lb>nulladimeno bastò a produrre il suo effetto, largamente diffondendosi da due <lb></lb>centri impulsivi: in Italia dall&#039;appendice <emph type="italics"></emph>De cycloide,<emph.end type="italics"></emph.end> in fine alla seconda <lb></lb>parte delle Opere geometriche torricelliane; e in Francia dai <emph type="italics"></emph>Cogitata phi­<lb></lb>sico mathematica,<emph.end type="italics"></emph.end> dov&#039;è notabile che il Mersenno, a proposito dei solidi ci­<lb></lb>cloidali, citi non il suo Matematico ma il nostro, forse perchè questi aveva <lb></lb>aggiunto agli altri teoremi e dimostrato “ solidum factum a spatio cycloidali <lb></lb>circa axem revoluto esse ad cylindrum ut 11 ad 18, atque ideo rationem <lb></lb>ineffabilem habere ad solidum circa basim, quippe quae componatur ex ra­<lb></lb>tione 44 ad 45, et rationem circuli alicuius ad quadratum circumscriptum ” <lb></lb>(Mechan., Parisiis 1644, pag. </s>

<s>24). </s></p><p type="main">

<s>Due anni dopo, nel 1646, era in tutto da que&#039;Francesi mutata sentenza. </s>

<s><lb></lb>Il Mersenno, scrivendo le <emph type="italics"></emph>Riflessioni fisico-matematiche,<emph.end type="italics"></emph.end> che l&#039;anno appresso <lb></lb>comparirebbero in Parigi alla luce, cantava la palinodia, sostituendo al sot­<lb></lb>tilissimo Torricelli il chiarissimo Roberval, che si proclamava primo e solo <lb></lb>autore della Trocoide, della quadratura, e de&#039;solidi di lei, particolarmente di <lb></lb>quello circa l&#039;asse, che non sta altrimenti al cilindro circoscritto come 11 <lb></lb>a 18, ma come tre quarti del quadrato della mezza base “ si dematur ter­<lb></lb>tia pars quadrati altitudinis, ad ipsum dimidiae basis quadratum ” (Pari­<lb></lb>siis 1647, pag. </s>

<s>71). Il Roberval scriveva dall&#039;altra parte, privatamente allo <lb></lb>stesso Torricelli, essere dal Beaugrand pervenuta la notizia della quadratura <lb></lb>della Cicloide in Italia; aver da gran tempo, per la ricerca de&#039;centri di gra­<lb></lb>vità, dati i solidi o le figure piane, il metodo universalissimo, e finalmente <lb></lb>essersi scoperto che la proporzione di 11 a 18 era minor della vera, che si <lb></lb>dava formulata dal Roberval in questa lettera nei medesimi termini, pub­<lb></lb>blicati poco di poi dal Mersenno nel detto libro delle Riflessioni. </s></p><p type="main">

<s>Il sospetto, nato nel 1643, che si fosse dal Beaugrand recata la notizia <pb xlink:href="020/01/2848.jpg" pagenum="473"></pb>della Cicloide in Italia, torna ora pel Roberval, sotto l&#039;aspetto di una cer­<lb></lb>tezza, aggiuntevi le particolari circostanze del fatto. </s>

<s>Il Du-Verdus di Roma <lb></lb>aveva ad esso Beaugrand mandati i tre modi di quadrar la Cicloide, quali si <lb></lb>leggono stampati nell&#039;appendice alla seconda parte delle Opere geometriche <lb></lb>del Torricelli: e perchè il primo di que&#039;modi aveva una certa somiglianza <lb></lb>con quello seguito dal Cartesio, e che a&#039;nostri Lettori è ben noto, ciò bastò <lb></lb>al Roberval per dire che il Beaugrand aveva consegnato in mano di Gali­<lb></lb>leo, e da questi era venuta nel Torricelli, quella dimostrazion cartesiana. </s>

<s>Ma <lb></lb>rispondeva a ciò il Torricelli con tali ragioni, che il Roberval stesso s&#039;ebbe <lb></lb>facilmente a persuadere non avere il suo sospetto e i suoi commenti nessuna <lb></lb>corrispondenza col vero. </s>

<s>Rispondeva: se la quadratura della Cicloide Galileo <lb></lb>l&#039;ebbe in mano dimostrata, come mai persistè in fino alla morte in dire che <lb></lb>non la sapeva? </s>

<s>Maggiore insistenza faceva il Nostro contro quel che il Fran­<lb></lb>cese diceva ora del baricentro cicloidale, contrapponendogli quel che aveva <lb></lb>detto prima al Mersenno, e confessando di non sapere intendere come po­<lb></lb>tesse il Roberval sospettar falsa geometricamente l&#039;indicazione del detto ba­<lb></lb>ricentro, se era vero ch&#039;ei ne avesse avuto certezza. </s></p><p type="main">

<s>Notabile in questa lettera, pubblicata da Timauro Antiate a pag. </s>

<s>15, che <lb></lb>il Torricelli non fa cenno di risposta a ciò che gli si rinfacciava aver egli <lb></lb>data la proporzione tra il solido circa l&#039;asse, e il cilindro circoscritto, non <lb></lb>esatta. </s>

<s>Sembra anzi gli si rintuzzasse da ciò così l&#039;animo, da diffondere anche <lb></lb>sopra gli altri punti della difesa un avvilimento, e una fiacchezza, simile a <lb></lb>quella di un che sia rimasto stordito da un gran colpo, benchè minore ne <lb></lb>dovesse sentir la ferita, per averlo previsto. </s>

<s>Il Ricci, sotto il dì 23 Giu­<lb></lb>gno 1645, fra le altre cose, gli scriveva: “ Ho poi lettere del p. </s>

<s>Mersenno, <lb></lb>che saluta caramente V. S., e l&#039;avvertisce come monsù de Roberval ha dimo­<lb></lb>strato che il solido, fatto dalla rivoluzione di una Cicloide intorno l&#039;asse, non <lb></lb>osservi la ragione di 11 a 18 verso il cilindro circoscrittogli, ma, posto che <lb></lb>sia questo 11, il cilindro sarà più che 18 ” (MSS. Gal. </s>

<s>Disc., T. XLII, <lb></lb>fol. </s>

<s>155). La robervalliana dimostrazione di ciò è tanta parte di questa Sto­<lb></lb>ria, che dobbiam trattenerci ad avvolgere intorno a lei il filo del nostro <lb></lb>discorso. </s></p><p type="main">

<s>Entriamo nella segreta stanza, dove il Matematico parigino è con grande <lb></lb>attenzione a leggere il manoscritto <emph type="italics"></emph>Della cicloide,<emph.end type="italics"></emph.end> venuto da Firenze, e in­<lb></lb>doviniamo i pensieri, che gli passano per la mente. </s>

<s>La curiosità vuol prima <lb></lb>di tutto sodisfarla rispetto al centro di gravità dello spazio cicloidale, e ora <lb></lb>finalmente intende il perchè di un tal centro, e quale principale importanza <lb></lb>egli abbia nella dimostrazione dei solidi rotondi. </s>

<s>Ora è che si leva da quella <lb></lb>lettura, per ricercar notizie, e per erudirsi intorno alla Regola centrobarica, <lb></lb>con lieta maraviglia ripensando ai riscontri, ch&#039;ella ha col suo proprio teo­<lb></lb>rema degli Anelli. </s>

<s>Al diritto, che da ciò glie ne consegue, non ha il tempo <lb></lb>di pensar ora, che si vede messo sulla via d&#039;intender quello che più gli pre­<lb></lb>meva, come procedesse cioè il Torricelli a dimostrare il solido circa l&#039;asse. </s></p><p type="main">

<s>Ritorniamo anche noi indietro con l&#039;occhio sopra la figura 307, dise-<pb xlink:href="020/01/2849.jpg" pagenum="474"></pb>gnata nel manoscritto torricelliano, e nella quale il punto B sull&#039;asse indica <lb></lb>il centro di gravità della Cicloide. </s>

<s>Ha inteso il Roberval, e per la sua faci­<lb></lb>lità anche ammirato il metodo ivi tenuto, per giunger dalla proporzione com­<lb></lb>posta delle distanze BL, AL, e delle figure piane, a quella dei solidi, facen­<lb></lb>dosi il rivolgimento intorno alla base. </s>

<s>Volendosi per la medesima via riuscire <lb></lb>a dimostrare i solidi circa l&#039;asse, ben comprese come doveva il Torricelli <lb></lb>attendere a ritrovare il centro di gravità della semicicloide, in che linea stia, <lb></lb>ora parallela alla base, e ora parallela all&#039;asse. </s>

<s>Quanto alla prima, resultava <lb></lb>dalle cose, già dimostrate per la Cicloide intera, dover essere la BP, ma la <lb></lb>difficoltà stava nella seconda linea, da tirarsi parallela all&#039;asse, la quale no­<lb></lb>nostante voleva far credere il Torricelli di averla trovata, benchè a tutti e <lb></lb>sempre ne tacesse il modo e la ragione. </s>

<s>Ma sia pure qual si voglia OQ Ia <lb></lb>detta linea, ella dee necessariamente, per sodisfare alle posizioni, esser tale, <lb></lb>da incontrare la BP in R, a una distanza RB dall&#039;asse, che stia alla SA, <lb></lb>come 22 a 27. Chiamati infatti S, C il solido e il cilindro circoscritto, gene­<lb></lb>rati dal rivolgersi la semicicloide DHEL e il rettangolo GL intorno ad EL, <lb></lb>e stando i detti solidi in ragion composta delle figure piane, ossia di 3 a 4, <lb></lb>e delle distanze BR, AS; è manifesto che, per aver la proporzione S:C= <lb></lb>11:18, dev&#039;essere RB=22, e AS=27. Se ora la proporzione RB:AS= <lb></lb>22:27 dal Torricelli si dà per esatta, e tale ei la pretende, essendo AS la <lb></lb>quarta parte della circonferenza, anche la circonferenza intera tornerà dun­<lb></lb>que esattamente per lui rettificata. </s>

<s>Laonde ebbe qui il Roberval a dire: o <lb></lb>questo Torricelli ha trovato l&#039;impossibile, o vuol dare a credere ai Matema­<lb></lb>tici cose non vere. </s>

<s>Il dilemma era solubile assai facilmente, ma colui, che <lb></lb>se l&#039;era proposto, volle con ragioni geometriche assicurarsi della fallacia, di­<lb></lb>mostrando come la proporzione di 11 a 18 non si concilia con quest&#039;altro <lb></lb>teorema, annunziato così dallo stesso Torricelli, nella nota scritta al Mer­<lb></lb>senno: <emph type="italics"></emph>“ Solidum, quod fit a spatio cycloidali circa axem revoluto, ad <lb></lb>solidum circa basim, est ut circulus aliquis ad quadratum sibi circum­<lb></lb>scriptum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma una tal proporzione l&#039;hanno anche i respettivi cilindri circoscritti. </s>

<s><lb></lb>Chiamato infatti C quello generato dal rivolgersi il rettangolo GL intorno <lb></lb>ad EL, abbiamo C=<foreign lang="grc">π</foreign>DL2.EL, e chiamato C′ l&#039;altro cilindro, fatto dal <lb></lb>rettangolo GF intorno a DF, avremo C′=<foreign lang="grc">π</foreign>EL2.2DL, donde C:C′= <lb></lb>DL2.EL:EL2.2DL=DL:2EL=DL.EL/2:EL2=2DL.EL/4:EL2, ossia <lb></lb>come il circolo che ha generata la Cicloide, al quadrato del diametro. </s>

<s>Se <lb></lb>dunque intendansi con S.A, S.B significati i solidi circa l&#039;asse, e circa la <lb></lb>base avremo S.A:S.B=C:C′. </s></p><p type="main">

<s>Ritengansi ora per vere le date posizioni torricelliane S.A=11/18.C, <lb></lb>S.B=5/8.C′:verrà da ciò ordinata la proporzione </s></p><p type="main">

<s><emph type="center"></emph>S.A:S.B=11/18C;5/8C′=44/72C=45/72C′,<emph.end type="center"></emph.end><lb></lb>giunto alla quale, il Roberval così ragionava: o non son veri i teoremi, che <pb xlink:href="020/01/2850.jpg" pagenum="475"></pb>il solido circa l&#039;asse al solido circa la base sta come un circolo al quadrato <lb></lb>del suo diametro, e che il solido circa la base è 45/72 del cilindro circoscritto; <lb></lb>o è falso che il solido circa l&#039;asse sia 44/72 del respettivo cilindro. </s>

<s>Ma perchè <lb></lb>i due primi teoremi son verissimi, dunque è falso il terzo, dando egli minor <lb></lb>proporzione della vera, la quale dovrebbe essere non 44, ma 45/72, com&#039;è <lb></lb>manifesto. </s></p><p type="main">

<s>Cosi essendo, proseguiva addirittura il Roberval nel suo ragionamento, <lb></lb>non è possibile che il Torricelli abbia avuto, come per la cicloide intera, <lb></lb>l&#039;indicazione esatta del centro di gravità della semicicloide dal legittimo ma­<lb></lb>gistero della Geometria, ma egli deve averla ricavata per approssimazione <lb></lb>dall&#039;esperienza; e credendo non si poter da nessuno dimostrare la ragione <lb></lb>esatta, si confidò che nessuno avrebbe saputo scoprire che la sua era falsa. </s>

<s><lb></lb>Così, come seco medesimo pensava, disse al Mersenno, e riferì al Torricelli, <lb></lb>con queste precise parole, quello che aveva detto: “ Quid ergo, iniquit Mer­<lb></lb>sennus, dices de clarissimo Torricellio? </s>

<s>nonne insignium adeo theorematum <lb></lb>cognitionem ipsi te debere fateberis? </s>

<s>— Faterer, respondi, si vera essent, at <lb></lb>talia non esse certus sum. </s>

<s>Miror sane quod vir talis falsum pro vero nobis <lb></lb>velit obtrudere, nec aliud suspicari possum nisi quod ille mechanica quadam <lb></lb>ratione, per approximationem, huiusmodi rationem, a vero non admodum <lb></lb>longe aberrantem, invenerit, existimaveritque veram rationem non posse de­<lb></lb>tegi, ac proinde suam haud veram esse a nemine posse demonstrari. </s>

<s>” (Ou­<lb></lb>vrages cit. </s>

<s>pag. </s>

<s>377-78). </s></p><p type="main">

<s>Il sospetto era fondato sopra buone ragioni, nè qualunque sia tra i più <lb></lb>gelosi della fama del Torricelli saprebbe secondo noi rispondere all&#039;accusa: <lb></lb>chi avrebbe creduto mai un così nobile geometra, <emph type="italics"></emph>aliquid pure geometricum <lb></lb>sine demonstatione affirmare voluisse?<emph.end type="italics"></emph.end> (ibid. </s>

<s>p. </s>

<s>394). </s></p><p type="main">

<s>La dimostrazione del centro di gravità della semicicloide non l&#039;abbiamo <lb></lb>potuta trovare, per quanto abbiamo frugato, in nessuna parte dei manoscritti <lb></lb>da noi consultati, eppure il Torricelli faceva conto di averla fra le sue carte, <lb></lb>benchè a nessuno, o familiare o estraneo, riuscisse mai di vederla, e richie­<lb></lb>stone l&#039;Autore ne sapeva uscir sempre con qualche scusa. </s>

<s>Ma più che una <lb></lb>scusa (ce lo perdoni il grand&#039;Uomo) trasparisce l&#039;arte di un furbo, per non <lb></lb>dire la stizza di un imputato dal seguente poscritto, taciuto, per non esser <lb></lb>forse conveniente a un apologista, da <emph type="italics"></emph>Timauro Antiate,<emph.end type="italics"></emph.end> nel trascrivere dalla <lb></lb>bozza originale, e nel pubblicar la lettera intera: “ Lecta iterum epistola <lb></lb>cl. </s>

<s>Robervallii et obsignata iam mea ad ipsum data, animadverto me nihil <lb></lb>respondisse de solido cycloidis circa axem, sed neque responsum quodpiam <lb></lb>dari necesse existimo. </s>

<s>Tunc enim quisquam iure arguere poterit me, quando <lb></lb>in paralogismos meos incidet. </s>

<s>Habemus apud Archimedem, propos. </s>

<s>II, <emph type="italics"></emph>De <lb></lb>circuli dimensione,<emph.end type="italics"></emph.end> circulum ad quadratum diametri esse ut 11 ad 14: quaero <lb></lb>ab ipso unde nam putet me habuisse rationem, quam ad numeros 11 et 18 <lb></lb>reducebam? </s>

<s>Si vero eo dicit, ut ego demonstrationes iterum ultro mittam, <lb></lb>fallitur. </s>

<s>” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XL, fol. </s>

<s>44). </s></p><p type="main">

<s>E noi credemmo che si fosse rimasto il Torricelli di rispondere all&#039;ac-<pb xlink:href="020/01/2851.jpg" pagenum="476"></pb><gap></gap>usa dell&#039;errore intorno al solido circa l&#039;asse, perchè lo avesse riconosciuto, <lb></lb>ora che da altri si vedeva scoperto. </s>

<s>Abbiamo invece da lui stesso ora inteso <lb></lb>che tuttavia persiste in far credere di aver la dimostrazione del centro di <lb></lb>gravità della semicicloide, e del teorema stereometrico che ne consegue; che <lb></lb>se non lo manda al Roberval, ne abbiamo udìta la ragione, la quale, diceva <lb></lb>il sagace Francese sentir <emph type="italics"></emph>redolere totius epistolae acerbitatem.<emph.end type="italics"></emph.end> Ma perchè in <lb></lb>ogni modo non era possibile levar le accuse, senza mandar quella dimostra­<lb></lb>zione, e il Torricelli non la mandò mai, perchè non l&#039;aveva, pensò che i suoi <lb></lb>diritti si potrebbero ridurre almeno al centro di gravità della Cicloide, di <lb></lb>che, lasciato il resto, si contentò di rivendicarsi il primato dell&#039;invenzione. </s>

<s><lb></lb>In tal proposito così scriveva il dì 14 luglio 1646 da Firenze, in una lettera <lb></lb>al Cavalieri: </s></p><p type="main">

<s>“ Faccio sapere a V.P. come in questi giorni mi trovo due liti, una col <lb></lb>Robervallio di Francia, il quale sfacciatissimamente e vergognosissimamente <lb></lb>scrive aver avuto il centro di gravità della Cicloide, avanti che io gli man­<lb></lb>dassi la dimostrazione, e non solo il centro predetto della gravità della Ci­<lb></lb>cloide, ma dice che anco aveva quel metodo, da me dimostrato e mandato <lb></lb>da me in mano sua, dove io mostravo che, dato il centro di gravità e qua­<lb></lb>dratura di un piano, si dà il solido. </s>

<s>Esso l&#039;ha rivoltata, e dice che aveva il <lb></lb>metodo di trovare il centro di gravità, data la quadratura e il solido. </s>

<s>” </s></p><p type="main">

<s>“ Quando avvisai in Francia la sola enunciazione di quel centro, dicendo <lb></lb>che sta nell&#039;asse segato come 7 a 5, il p. </s>

<s>Mersenno mi scrisse una lettera <lb></lb>piena d&#039;iperbole di lodi, confessando che io ho prevenuto in questo il loro <lb></lb>geometra Robervallio: mi prega a mandar la dimostrazione: mi dice che <lb></lb>Robervallio ha dimostrato ogni cosa fuor che questa, mi dice che i suoi Geo­<lb></lb>metri non credono queste cose si siano trovate, e parlando di Robervallio <lb></lb>dice: <emph type="italics"></emph>qui cum tuas postremas legisset, praedictum solidum et centrum gra­<lb></lb>vitatis tibi fatetur debere, qui primus invenisti. </s>

<s>Rogamus tamen an cen­<lb></lb>trum gravitatis etc.<emph.end type="italics"></emph.end> Ed in ultimo della lettera lunghissima scrive: <emph type="italics"></emph>Dubitat <lb></lb>noster Robervallius an mechanice tantum centra gravitatis Cycloidis, et <lb></lb>semicicloidis inveneris, quae geometrice falsa suspicantur. </s>

<s>Docebis num <lb></lb>istius rei demonstrationem habeas.<emph.end type="italics"></emph.end> E molte altre simili confessioni, le quali <lb></lb>sono in una lunghissima lettera, che io ho stimato da quaresima in qua per <lb></lb>persa. </s>

<s>Finalmente, dopo moltissime diligenze l&#039;ho trovata, ed ho scritto le <lb></lb>mie ragioni in Francia, con copia delle lettere loro, e la testimonianza delle <lb></lb>recognizioni, e quando occorrerà le farò riconoscere da otto o dieci letterati, <lb></lb>e le stamperò con le ragioni mie. </s>

<s>” </s></p><p type="main">

<s>“ L&#039;altra lite l&#039;ho col signor M. A. </s>

<s>Ricci di Roma. </s>

<s>Al suddetto signore <lb></lb>mandai la dimostrazione da me adattata alle figure infinitamente lunghe di <lb></lb>Robervallio, fin di marzo passato. </s>

<s>Alla settimana passata io mandai al me­<lb></lb>desimo la stessa dimostrazione, applicata alla quadratura delle infinite para­<lb></lb>bole, in due modi. </s>

<s>Quando aspetto che mi ringrazi, trovo che egli dice avere <lb></lb>adattata ancor lui quella mia dimostrazione alla quadratura delle parabole, ed <lb></lb>ora vi pretende il medesimo gius che ci ho io. </s>

<s>Primieramente, la dimostra-<pb xlink:href="020/01/2852.jpg" pagenum="477"></pb>zione fondamentale è mia, senza controversia, ed egli lo confessa. </s>

<s>Avanti <lb></lb>ch&#039;egli me ne dia motivi gli mando l&#039;applicazione alle parabole, ed ora nella <lb></lb>risposta mi dice che quella applicazione l&#039;aveva e quel che più mi duole mi <lb></lb>dice che già era accordato di stampar questa sua cosa nel libro, che uscirà <lb></lb>presto del sig. </s>

<s>Antonio Nardi. </s>

<s>Dico il fatto mio all&#039;uno e all&#039;altro, cioè al <lb></lb>Roberval e al Ricci. </s>

<s>” (MSS. Gal. </s>

<s>Disc. </s>

<s>T. XL, fol. </s>

<s>138, 39). </s></p><p type="main">

<s>L&#039;essersela il Torricelli presa col Ricci, di cui si conoscono i generosi <lb></lb>atti, e i nobili portamenti, quando prima cadde in sospetto di volersi appro­<lb></lb>priare i teoremi de&#039;solidi conoidali, predispone i nostri lettori a credere che, <lb></lb>come esso Torricelli ebbe il torto a risentirsi contro l&#039;amico, così lo dovesse <lb></lb>avere anche risentendosi contro lo straniero. </s>

<s>Si faceva in questa seconda lite <lb></lb>forte di due ragioni: prima, perchè il Roberval aveva indugiato due anni a <lb></lb>rispondere; poi perchè avuto il metodo di dimostrare i solidi, dati i centri <lb></lb>di gravità e le quadrature; pretendeva d&#039;appropriarsi il metodo inverso di <lb></lb>dimostrare il centro di gravità, dati i solidi e le figure piane, da cui sono <lb></lb>essi solidi generati. </s></p><p type="main">

<s>Ma il Roberval credeva di aver data sufficiente ragione di quell&#039;indugio, <lb></lb>attribuendolo alle difficoltà incontrate nel ritrovar la vera proporzione geo­<lb></lb>metrica tra il solido circa l&#039;asse, e il cilindro circoscritto. </s>

<s>“ Ne vero mireris <lb></lb>quod tantum temporis in unico problemate solvendo consumpserimus, illud <lb></lb>enim ex iis est, quae et longa inquisitione indigent, et acrem pertinacis geo­<lb></lb>metrae requirunt operam, nec memini me aliuid unquam demonstrasse, quod <lb></lb>cum eo conferri posset. </s>

<s>” (Lettera a&#039;Filaleti, p. </s>

<s>13). Il Torricelli invece at­<lb></lb>tribuiva quell&#039;indugio a ciò, che il Roberval si confidava dover essere andata <lb></lb>in tanto tempo smarrita la lettera, mandata a Firenze dal Mersenno, per cui <lb></lb>non si potessero contestare le contradizioni. </s>

<s>Giustizia ora vuole che si tolga <lb></lb>dal Francese una tale ingiuria, dimostrando ch&#039;ebbe di fatto a penar così <lb></lb>lungamente, com&#039;egli dice, prima d&#039;assicurarsi di aver propriamente ridotta <lb></lb>all&#039;esattezza geometrica la poco accurata proporzione torricelliana. </s></p><p type="main">

<s>Alla dimostrazione, che si promette, porgono i documenti necessari le <lb></lb>Opere robervelliane, per le quali troviamo in tre modi, e in termini sempre <lb></lb>diversi assegnate le proporzioni tra il solido cicloidale e il cilindro circoscrit­<lb></lb>togli intorno all&#039;asse. </s>

<s>La cosa pare strana in sè, e tanto più rispetto alla ve­<lb></lb>rità geometrica, la quale non può essere che una sola, ma si comprende come <lb></lb>ciò accadesse, ripensando che furono raccolti insieme dagli Editori parigini i <lb></lb>trattati, rimasti inediti, e scritti dal loro Accademico in vari tempi, nella suc­<lb></lb>cessione de&#039;quali, esaminate meglio le cose, giunse finalmente a conquistare <lb></lb>la verità, ravvedendosi dei primi errori. </s>

<s>Di qui è che abbiamo, nei vari trat­<lb></lb>tati robervalliani della Cicloide, segnate così l&#039;orme dei passi, da creder fa­<lb></lb>cilmente lungo dover essere stato il tempo, che, per giungere al termine <lb></lb>faticoso, venne a spender l&#039;Autore. </s></p><p type="main">

<s>Nel trattato <emph type="italics"></emph>De trochoide<emph.end type="italics"></emph.end> aveva detto il solido stare al cilindro <emph type="italics"></emph>ut differentia <lb></lb>inter quadratum quadrantis et<emph.end type="italics"></emph.end> 4/3 <emph type="italics"></emph>quadrati radii, ad quadratum ipsius se­<lb></lb>micircumferentiae<emph.end type="italics"></emph.end> (Ouvrages cit. </s>

<s>pag. </s>

<s>319): cosicchè, chiamati S il detto solido, <pb xlink:href="020/01/2853.jpg" pagenum="478"></pb>C il cilindro, e riferendoci alla figura 308, nella quale AC s&#039;uguaglia alla mezza <lb></lb>circonferenza, e CI è il raggio della ruota; sarebbe quella ragione espressa da <lb></lb>S:C=AC2/4—4/3CI2:AC2. </s>

<s>Questì termini però non riscontrano con quegli <lb></lb>altri, che si deducono col calcolo, componendo insieme le proporzioni, che hanno <lb></lb>i solidi generati dagli spazi compresi tra la cicloide e la comite, e tra la co­<lb></lb>mite e l&#039;asse, verso il cilindro circoscritto, che per ambedue manifestamente <lb></lb>è lo stesso. </s>

<s>Quanto a quel primo solido, che chiameremo S′ “ patet itaque <lb></lb>(così conclude il Roberval la sua dimostrazione) continere portionem, quae <lb></lb>ad ipsum totum cylindrum eam habet rationem, quam 2/3 quadrati semidia­<lb></lb>metri, ad quadratum semicircumferentiae ” (ibid. </s>

<s>pag. </s>

<s>322): conclusione, che <lb></lb>scritta per simboli è tale S′:C=2/3CI2:AC2. </s>

<s>Dell&#039;altro solido S″ descritto <lb></lb>dalla comite nel rivolgersi intorno all&#039;asse, dallo stesso Roberval si dimostra <lb></lb>“ ad cylindrum cui inscribitur eamdem rationem habere, quam dimidium <lb></lb>quadrati semicircumferentiae rotae, dempto dimidio quadrati diametri, ad <lb></lb>integrum quadratum semircumferentiae ” (ibid. </s>

<s>p. </s>

<s>332) ossia S″:C= <lb></lb>AC2/2—CF2/2:AC2. </s>

<s>Or da questa e dalla precedente omologa proporzione, in <lb></lb>cui i secondi e quarti termini sono uguali, s&#039;ha S′:S″=2/3CI2:AC2/2—CF2/2, <lb></lb>e componendo, S′+S″:S′=2/3CI2—CF2/2+AC2/2:2/3CI2. </s>

<s>E però <lb></lb>S′+S″:C=2/3CI2—CF2/2+AC2/2:AC2=AC2/2+2/3CI2—2CI2:AC2= <lb></lb>AC2/2—4/3CI2:AC2. </s></p><p type="main">

<s>Essendo S=S′+S″, si vede bene che la discordanza, tra questa e la <lb></lb>proporzion precedente, non cade in altro, che nel terzo termine, il quale, se <lb></lb>non è vero in quella, non si può credere però che sia venuto a correggersi <lb></lb>in questa, conclusa dal Roberval dietro un principio, ch&#039;esaminato bene si <lb></lb>scopre falso. </s>

<s>Dice l&#039;Autore che la somma degli infiniti quadrati KM, BH, <lb></lb><expan abbr="Tq.">Tque</expan>... al quadrato di CA preso altrettante volte, ossia a ŖAC2, <emph type="italics"></emph>rationem <lb></lb>habet, quam sphaera rotae ad totum cylindrum<emph.end type="italics"></emph.end> (ibid. </s>

<s>pag. </s>

<s>321). Ora, es­<lb></lb>sendo la sfera uguale alla terza parte del raggio moltiplicata per la super­<lb></lb>ficie, che è quadrupla di un circolo grande, sarà la solidità di essa sfera <lb></lb>espressa da 4/3<foreign lang="grc">π</foreign>CI2, e quella del cilindro da 2<foreign lang="grc">π</foreign>AC2. </s>

<s>CI per cui i due so­<lb></lb>lidi staranno fra loro come 2/3 CI2 ad AC2. </s>

<s>E perchè, dice esso Roberval, tale <lb></lb>esser pure la ragione del solido S′ al medesimo cilindro C, avremo dunque <lb></lb>KM2+BH2....:ŖAC2=2/3CI:AC2=S′:C=S′:<foreign lang="grc">π</foreign>ŖAC2.D&#039;onde S′= <lb></lb><foreign lang="grc">π</foreign>(KM2+BH2....) ciò che non sembra esser vero, dimostrandosi il solido S′ <lb></lb>uguale alla somma degli infiniti circoli descritti dai raggi KM, BM .... in­<lb></lb>torno alla comite, aggiuntavi la quarta parte del cilindro totale, anche se­<lb></lb>condo lo stesso calcolo robervalliano. </s></p><p type="main">

<s>Il solido infatti, che si descrive dallo spazio, compreso tra la cicloide e <pb xlink:href="020/01/2854.jpg" pagenum="479"></pb>la comite nel rivolgersi intorno all&#039;asse, è composto delle infinite armille KM, <lb></lb>BH, TQ .... il valor delle quali, chiamate A, A′, A″, si troverà così assai <lb></lb>facilmente: A=<foreign lang="grc">π</foreign>EK2—<foreign lang="grc">π</foreign>EM2=<foreign lang="grc">π</foreign>(KM2+ME2+2KME—ME2)= <lb></lb><foreign lang="grc">π</foreign>KM2+2<foreign lang="grc">π</foreign>KME. </s>

<s>Troveremo con simile discorso A′=<foreign lang="grc">π</foreign>BH2+2<foreign lang="grc">π</foreign>BHI, <lb></lb>A″=<foreign lang="grc">π</foreign>TQ2+2<foreign lang="grc">π</foreign>TQS .... Sommate ora insieme tutte queste armille, il <lb></lb>solido delle quali si compone sarà </s></p><p type="main">

<s><emph type="center"></emph>S′=<foreign lang="grc">π</foreign>(KM2+BH2+QT2....)+2<foreign lang="grc">π</foreign>(KME+BHI+TQS....)<emph.end type="center"></emph.end></s></p><p type="main">

<s>Giunti a questo punto, rispetto alla somma degl&#039;infiniti rettangoli, com­<lb></lb>presi fra parentesi, ascoltiamo come il Roberval ne ragioni: “ At dupla illa <lb></lb>rectangula aequivalent semel omnibus rectangulis sub EL, sive CA et KM; <lb></lb>sub IG, sive CA et HB; sub SN, sive CA et QT .... propterea quod omnes <lb></lb>rectae EM, IH, SQ .... bis sumptae aequivalent omnibus rectis EL, IG, <lb></lb>SN .... semel sumptis; hoc est rectae BA toties sumptae: et haec rectan­<lb></lb>gula constituunt quartam partem quadrati CA toties sumpti. </s>

<s>” (ibid. </s>

<s>pag. </s>

<s>321). <lb></lb>Stabilisce dunque il Roberval questa equazione: 2(KME+BHI+TQS....)= <lb></lb>2(ME+HI+QS....) (<expan abbr="KM+BH+Tq.">KM+BH+Tque</expan>...) dietro la quale, supponen­<lb></lb>dola vera, in tal guisa prosegue il suo discorso: Della somma delle infinite <lb></lb>linee ME, HI, QS .... s&#039;intesse la superficie del trilineo AFC, che sappiamo <lb></lb>essere uguale all&#039;altro trilineo AFD, e perciò quella somma, presa due volte, <lb></lb>equivarrà allo spazio circoscritto dal rettangolo DC, ossia a ŖAC. </s>

<s>Della <lb></lb>somma poi delle linee infinite KM, BH, TQ s&#039;intesse la figura disegnata <lb></lb>dalla cicloide e dalla sua comite, la qual figura, essendo, come si sa, la quarta <lb></lb>parte del rettangolo intero, equivarrà dunque a ŖAC/4, d&#039;onde verrà ad essere <lb></lb>trasformata così l&#039;equazione lasciata di sopra: </s></p><p type="main">

<s><emph type="center"></emph>S′=<foreign lang="grc">π</foreign>(KM2+BH2+QT2....)+<foreign lang="grc">π</foreign>ŖAC2/4.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Se il calcolo robervalliano sia condotto secondo le buone regole alge­<lb></lb>briche sel vedono i Matematici lettori, ma in ogni modo si deve l&#039;Autore <lb></lb>stesso essere accorto, dalla fallacia dei mezzi, dell&#039;inesattezza dei resultati, <lb></lb>ridotti finalmente alla ragione S:C=3/4AC2—CF2/3:AC2, che è quella <lb></lb>creduta, sopra le altre due precedenti, per vera, e che sotto questa formula <lb></lb>fu definitivamente annunziata nella lettera al Torricelli. </s>

<s>Non fu dunque per <lb></lb>quel malizioso fine, che ingiuriosamente al Roberval s&#039;imputava, l&#039;indugio di <lb></lb>quasi due anni a far la risposta, ma per la difficoltà della ricerca, che ri­<lb></lb>chiese veramente dal pertinace Geometra, com&#039;ei diceva, opera cosi lunga e <lb></lb>faticosa. </s></p><p type="main">

<s>La causa però s&#039;agitava principalmente, e con grande ardore degli animi, <lb></lb>circa al centro di gravità della Cicloide, che il Torricelli difendeva come sua <lb></lb>propria invenzione, contro le usurpazioni del Roberval, a cui, diceva quegli, <lb></lb>non passò tal cosa mai per la mente. </s>

<s>A questo capo di accusa così giungeva <lb></lb>solenne da Parigi a Firenze la risposta. </s></p><pb xlink:href="020/01/2855.jpg" pagenum="480"></pb><p type="main">

<s>“ Dum ais me nunquam ne verbum quidem fecisse de centro gravitatis <lb></lb>Trochoidis, cum interea tantopere, et quidem merito, gloriarer de omnibus <lb></lb>aliis, quadratura, tangentibus, solidis etc., nec verisimile esse, cum reliqua <lb></lb>omnia proponerem, de unico centro gravitatis siluisse, si illud tantum spe­<lb></lb>ravissem, quod quidem problema, tuo iudicio nulli reliquorum posthabendum <lb></lb>videtur; dum haec ais, inquam, Vir clarissime, ex tuo genio loqueris: nos, <lb></lb>dum scripsimus, ex nostro etiam genio scripsimus. </s>

<s>Tu, cum magnifaceres <lb></lb>centra, quia ex iis solida deducere posse confidebas, solida autem praecipue <lb></lb>intendebas, ideo centrorum inventionem magnifice extulisti, nec caeteris post­<lb></lb>habendam, immo praehabendam iudicasti. </s>

<s>Ego contra, quia sine centris solida <lb></lb>et quaesivi et via geometrica inveni, datis autem solidis, statim et absque la­<lb></lb>bore centra sequebantur. </s>

<s>Ideo centra ne respexi quidem, neque ad ea un­<lb></lb>quam animum applicui, certus omnino, ex praemissa nostra methodo, dato <lb></lb>plano quod dudum habebam, sola solida mihi quaerenda superesse, centra <lb></lb>autem simul cum plano et solidis haberi. </s>

<s>” (ibid. </s>

<s>pag. </s>

<s>376). </s></p><p type="main">

<s>Ora, che cosa potrebbesi trovare in questa risposta, che non riscontri <lb></lb>con la verità dei fatti? </s>

<s>Era ad ambedue i Matematici data la Regola cen­<lb></lb>trobarica, dalla quale si deduceva per corollario immediato che i solidi ro­<lb></lb>tondi stanno in ragion composta delle figure piane, e delle distanze dei loro <lb></lb>centri di gravità dall&#039;asse della rivoluzione. </s>

<s>Se sia data dunque la quadratura, <lb></lb>o se in altre parole sia detto secondo qual proporzione stanno fra loro le <lb></lb>superficie genitrici, il teorema universalissimo del Guldino non solo porgeva <lb></lb>facile il modo di risolvere direttamente il problema: dati i centri di gravità <lb></lb>trovare i solidi; ma conversamente di risolver l&#039;altro: dati i solidi trovare i <lb></lb>centri. </s>

<s>E come il Torricelli pretendeva essere sua propria quella soluzione <lb></lb>diretta, così sua propria diceva il Roberval essere questa conversa, la quale, <lb></lb>se ci avesse pensato, o sentitone il bisogno, lo conduceva, assai prima del suo <lb></lb>rivale, a dimostrare il centro di gravità della Cicloide <emph type="italics"></emph>statim et absque la­<lb></lb>bore.<emph.end type="italics"></emph.end> Riducendoci infatti sott&#039;occhio la figura 307, se con S, C si rappresen­<lb></lb>tano il solido e il cilindro circa la base, che nella terza proposizione rober­<lb></lb>valliana erano stati già ritrovati stare come 5 a 8, e se con T, R si significhino <lb></lb>la trochoide e il rettangolo, che, nel corollario della proposizione precedente <lb></lb>alla citata, si trovarono aver tra loro la proporzione di 3 a 4; subito vera­<lb></lb>mente e senza alcuna fatica s&#039;ha indicato il punto B sull&#039;asse dalla propor­<lb></lb>zione BL.T:AL.R=3BL:4AL=S:C=5:8, la quale si riduce a <lb></lb>BL:AL=5:6, secondo che, per altra via laboriosissima, era giunto pure <lb></lb>a concludere il Torricelli. </s>

<s>Con quanta coscienza poi potesse questi affermare <lb></lb>nella citata lettera al Mersenno: <emph type="italics"></emph>Misi etiam demonstrationem meam et vere <lb></lb>meam, pro methodo, quae inservit ad inveniendum centrum gravitatis ex <lb></lb>dato solido, sive solidum ex dato centro;<emph.end type="italics"></emph.end> lo lasciamo giudicare ai nostri <lb></lb>Lettori, i quali sanno oramai troppo bene che quel medodo era invece del <lb></lb>Nardi. </s></p><p type="main">

<s>Nè il Roberval, dall&#039;altra parte, era meno illuso, quando dal suo teo­<lb></lb>rema <emph type="italics"></emph>Des anneaux<emph.end type="italics"></emph.end> credeva potersi, per la ricerca de&#039;centri di gravità, dati <pb xlink:href="020/01/2856.jpg" pagenum="481"></pb>i solidi, derivare il metodo universalissimo. </s>

<s>Quel teorema invece, supponendo <lb></lb>le superficie piane concentriche, non suppliva se non che parzialmente alla <lb></lb>Regola centrobarica, nel solo caso cioè che i centri di gravità delle figure <lb></lb>fossero ugualmente distanti dall&#039;asse della rivoluzione. </s>

<s>Di qui nacquero senza <lb></lb>dubbio alcuni errori di lui, come sarebbe quello, che è a notar nel calcolo del <lb></lb>solido generato dallo spazio intercetto tra la Cicloide e la comite, nel rivol­<lb></lb>gersi intorno all&#039;asse, del qual solido dice; <emph type="italics"></emph>patet continere quartam partem <lb></lb>totius cylindri<emph.end type="italics"></emph.end> (Ouvrag. </s>

<s>cit. </s>

<s>pag. </s>

<s>322). </s></p><p type="main">

<s>Sarebbe la cosa patente, quando le due superficie piane, rappresentateci <lb></lb>dal rettangolo DC e dal bilineo AMFT, nella figura 308, avessero ì loro centri <lb></lb><figure id="id.020.01.2856.1.jpg" xlink:href="020/01/2856/1.jpg"></figure></s></p><p type="caption">

<s>Figura 308.<lb></lb>di gravità a ugual distanza dalla FC, <lb></lb>perchè allora, stando i solidi com&#039;esse <lb></lb>superficie semplicemente, starebbero <lb></lb>anche insieme come uno a quattro. </s>

<s><lb></lb>Ma chi sa in qual punto della BH cade <lb></lb>il centro del detto bilineo, o qual <lb></lb>fiducia può aversi che coincida col <lb></lb>punto di mezzo della GI, dove il ret­<lb></lb>tangolo DC concentra il suo peso? </s>

<s><lb></lb>Non avvertì il Roberval essere la cosa <lb></lb>molto diversa, quando il rivolgimento si fa intorno alla base, perchè allora <lb></lb>il bilineo e il rettangolo, raddoppiati dall&#039;altra parte dell&#039;asse, riescono con­<lb></lb>centrici in I, e il metodo, solamente applicabile in questo caso, lo credè <lb></lb>universale. </s></p><p type="main">

<s>Così sembra a noi venga dato imparziale giudizio intorno al torto e al <lb></lb>diritto di questa lite, la quale non si sarebbe forse agitata così diuturna e <lb></lb>fervente, se ambedue i grandi Uomini non avessero falsamente creduto al­<lb></lb>l&#039;impossibilità del riscontrarsi, per vie diverse, nella medesima invenzione <lb></lb>due ingegni, senza che all&#039;uno fossero in qualunque modo noti i progressi <lb></lb>dell&#039;altro. </s>

<s>Fu da un tal dannoso pregiudizio mosso principalmente il Torri­<lb></lb>celli, quando, posate appena le armi contro il Roberval, le riprese subito in <lb></lb>mano, per usarle contro il Ricci, da cui intendeva di rivendicarsi il primato <lb></lb>e la proprietà del metodo per la quadratura delle infinite parabole. </s>

<s>Ma il <lb></lb>Ricci, con coscienza non men sincera e dignitosa del Roberval, rispondeva <lb></lb>così francamente alle pretensioni: </s></p><p type="main">

<s>“ Passo dunque al punto principale, cioè che la quadratura delle infi­<lb></lb>nite parabole io deva totalmente riconoscerla come sua, benchè io scriva di <lb></lb>averla molto prima, che ella mi scrivesse la sua, che quasi è la medesima, <lb></lb>e benchè io l&#039;abbia ritrovata prima di lei, per quel che posso congetturare <lb></lb>da una sua lettera, che mi scrisse il marzo passato, dove disprezzava l&#039;in­<lb></lb>venzione del Robervallio. </s>

<s>E fu allora che io le risposi che io non potevo non <lb></lb>estimarla assai come fecondo principio di bellissime conseguenze, alludendo <lb></lb>alla quadratura suddetta, di che avevo preso motivo da quella invenzione, e <lb></lb>alla invenzione de&#039;centri di gravità della stessa parabola, con altri misteri, <pb xlink:href="020/01/2857.jpg" pagenum="482"></pb>ai quali scorgevo aperta la strada. </s>

<s>Questa ultima però dei centri di gravità <lb></lb>non la perfezionai, stante l&#039;indisposizione, che allora mi travagliava. </s>

<s>” </s></p><p type="main">

<s>“ Le ragioni di V. S. son due: la prima, che sarà giudicato impossi­<lb></lb>bile che ci siamo incontrati ambedue nel medesimo metodo così precisamente, <lb></lb>senza che uno di noi abbia veduto il progresso dell&#039;altro, e di poco l&#039;abbia <lb></lb>alterato, essendo troppo fuori dell&#039;usato quel modo di provare. </s>

<s>La seconda <lb></lb>vuole che io non possa avere quella quadratura generalmente, perchè vi si <lb></lb>richiederebbe il teorema delle tangenti, a questo il teorema de&#039;massimi, il <lb></lb>quale io confesso di non aver generalmente trovato per ancora. </s>

<s>” </s></p><p type="main">

<s>“ Io dico a V. S. che la proposta di Robervallio mi fu comunicata dal <lb></lb>sig. </s>

<s>Raffaello Magiotti, per ordine di lei, e ne ammirai la dimostrazione, che <lb></lb>ella subitamente vi fece, come a V. S. ne scrissi in quel tempo. </s>

<s>Da questo <lb></lb>io presi occasione di mostrare la quadratura delle infinite parabole, non lo <lb></lb>metto in dubbio. </s>

<s>Se poi si giustificherà impossibile (cosa che V. S. non disse <lb></lb>mai) il dedurre questa quadratura, io avrò fatto l&#039;impossibile, e il sig. </s>

<s>An­<lb></lb>tonio Nardi me ne farà fede. </s>

<s>Ma perchè V. S. non dirà che sia difficile, ma <lb></lb>facilissimo il dedurla dalla proposizione di Robervallio, anzi una cosa mede­<lb></lb>sima, io replico che ciò non sarà agevolmente ammesso da chi saprà che <lb></lb>Robervallio, avendo dimostrata la proposizione, stimò ardua impresa il ca­<lb></lb>varne la quadratura della sola parabola vulgata, come V. S. mi significò nella <lb></lb>sua de&#039;28 di Maggio prossimo. </s>

<s>Ed aggiungo quel che di sopra dicevo, che <lb></lb>ella avrebbe fatto stima grandissima di quella proposta, quando ne avesse <lb></lb>dedotta la detta quadratura, che, sebbene ora mostra di prezzar poco, allora <lb></lb>era uno dei massimi teoremi, che fossero in volta. </s>

<s>” </s></p><p type="main">

<s>“ Circa poi all&#039;essere una cosa medesima la proposta di Robervallio e <lb></lb>la quadratura, onde seguirebbe che la dimostrazione di questa io non potessi <lb></lb>appropriarmi, quando avessi con poca alterazione da quella proposta preso <lb></lb>fondamento alla mia dimostrazione; le ridurrò solamente a memoria il suo <lb></lb>senso, avvisatomi nella lettera poco dianzi mentovata. </s>

<s>Ella mi comunica due <lb></lb>maniere per dimostrare le infinite quadrature, l&#039;una delle quali ha il me­<lb></lb>desimo progresso con la mia maniera, e piglia per fondamento una dimo­<lb></lb>strazione, da quella della proposta di Robervallio poco differente, come V. S. <lb></lb>asserisce. </s>

<s>L&#039;altra si serve espressamente della proposta di Robervallio, con <lb></lb>la dimostrazione fattale da V. S., e conclude la lettera: <emph type="italics"></emph>Noi da quelle sue <lb></lb>figure,<emph.end type="italics"></emph.end> cioè di Robervallio, <emph type="italics"></emph>caviamo la quadratura di tutte le parabole, <lb></lb>come apparve in quest&#039;ultima: ed in modo poco differente con invenzione <lb></lb>propria affatto, senza nulla d&#039;altri come la precedente, dimostriamo un&#039;al­<lb></lb>tra volta il medesimo.<emph.end type="italics"></emph.end> Ecco dunque che, variandosi un poco la dimostra­<lb></lb>zione adattata alla proposta di Robervallio, e da questa derivandosi la qua­<lb></lb>dratura delle infinite parabole (ed io poi non solo vario il poco di V. S. ma <lb></lb>forse assai più) si può, per detto di lei, chiamare invenzione senza nulla <lb></lb>d&#039;altri. </s>

<s>” </s></p><p type="main">

<s>“ Ma non è da tacere che nella dimostrazione di V. S. fanno gioco prin­<lb></lb>cipale le tangenti, delle quali, non solamente io posso dirmi il primo, per la <pb xlink:href="020/01/2858.jpg" pagenum="483"></pb>verità che generalmente le partecipai; ma per il metodo generale ancora, <lb></lb>dal quale confessa ella d&#039;aver avuto motivo per la dimostrazione fattane dopo <lb></lb>per via del moto. </s>

<s>Ella scrive, sotto li 26 di Febbraio dell&#039;anno passato, in <lb></lb>questo tenore, rispondendo alla lettera, con la quale avvisavo l&#039;invenzione <lb></lb>delle suddette tangenti: <emph type="italics"></emph>Ho bene io imparato dalle sue lettere cose, che <lb></lb>forse non avrei avvertite mai, perchè, tornando iersera con le lettere di <lb></lb>V. S. in mano, mi entrò in testa che quelle tangenti non potesssero essere. </s>

<s><lb></lb>Ciò fu causa che feci non so che figure, e trovai poi ch&#039;era verissimo, e <lb></lb>ne scrissi la dimostrazione universale, per via del moto.<emph.end type="italics"></emph.end> Se dunque io non <lb></lb>posso per l&#039;un rispetto attribuirmi questa quadratura, ella pare a me che <lb></lb>non vorrà attribuirsela, avendo riguardo a quest&#039;altro rispetto. </s>

<s>Sicchè re­<lb></lb>sterà come effetto di mutua causalità, per favellar con le scuole, e non si <lb></lb>dirà nè suo nè mio parto proprio e totale, essendo ella primo in un genere <lb></lb>ed io primo in un altro. </s>

<s>” </s></p><p type="main">

<s>“ Alla seconda ragione rispondo che io facevo due conti, in caso che <lb></lb>mi fosse succeduto di provare quel lemma generalmente: cioè di supplicar <lb></lb>V. S. che me ne favorisse, conforme all&#039;intenzione che me ne diede l&#039;anno <lb></lb>passato, quando mi mandò il medesimo lemma dimostrato, ma in casi par­<lb></lb>ticolari; ovvero di proporre il metodo e darne come un esempio in que&#039;casi <lb></lb>che posso, avvertendo che, riducendo qual si voglia caso all&#039;invenzione dei <lb></lb>massimi, si trova generalmente la ragione di tutto. </s>

<s>” </s></p><p type="main">

<s>“ Mando a V. S. parte della mia dimostrazione nel proposito nostro, <lb></lb>stimandola sufficiente per questo che si pretende, cioè di scoprire la conve­<lb></lb>nienza de&#039;metodi, e giuro a V. S. che questa è la medesima dimostrazione, <lb></lb>che io scrissi nel marzo passato: solo qualche paroluccia ho mutato nel tra­<lb></lb>scrivere.... Ella si ricorderà, due mesi sono, che mi avvisò una sua pro­<lb></lb>posizione dimostrata da lei in modo recondito, eppure io l&#039;indovinai..... <lb></lb>Roma, 7 Luglio 1646. ” (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>162-66). </s></p><p type="main">

<s>Da queste ragioni giova a noi credere che rimanesse persuaso il Tor­<lb></lb>ricelli, nel quale è certo che tornò presto la consueta serenità verso il Ricci, <lb></lb>come pure giova similmente credere che facesse col Roberval accettando <lb></lb>l&#039;amicizia da lui generosamente proffertagli, <emph type="italics"></emph>litibus valere iussis<emph.end type="italics"></emph.end> (Ouvrages, <lb></lb>pag. </s>

<s>398) dalla naturale bontà dell&#039;animo, e dal presentimento della morte <lb></lb>vicina. </s></p><p type="main">

<s>Chi potrebbe in ogni modo negare ai due grandi Matematici l&#039;aver <lb></lb>concorso con pari merito, l&#039;uno a istituire, l&#039;altro a diffondere quella scienza <lb></lb>della Cicloide, che avrebbe poco di poi, per il Pascal, pel Wallis e per l&#039;Huy­<lb></lb>ghens progredito tant&#039;oltre? </s>

<s>Che se l&#039;ultimo commemorato, nello scolio al­<lb></lb>l&#039;ottava proposizione della terza parte dell&#039;<emph type="italics"></emph>Orologio oscillatorio,<emph.end type="italics"></emph.end> compen­<lb></lb>diando questa Storia non ricorda del Torricelli nemmeno il nome, l&#039;altro, <lb></lb>il Wallis, nella prefazione al suo <emph type="italics"></emph>Trattato della Cicloide<emph.end type="italics"></emph.end> confessa di averne <lb></lb>da solo il Torricelli imparata la quadratura, non pensando nemmen per sogno <lb></lb>che il Roberval, nulla avendo dato ancora alla luce, si fosse esercitato nel <lb></lb>medesimo soggetto. </s></p><pb xlink:href="020/01/2859.jpg" pagenum="484"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La storia della Cicloide, perchè troppo importante in sè stessa, e per­<lb></lb>chè troppo bisognosa di essere illustrata nelle sue origini, rimaste fin qui <lb></lb>occulte nei manoscritti; è stata in questo capitolo una assai lunga digressione <lb></lb>da quella via, sopra la quale siam solleciti ora di ritornare, per accennar <lb></lb>frettolosamente all&#039;opera, data dai colleghi e dai discepoli del Torricelli in <lb></lb>promovere la Meccanica galileiana. </s>

<s>Si disse già, infin dal principio del pre­<lb></lb>sente discorso, ch&#039;erano principalmente da annoverare fra cotesti promotori <lb></lb>il Cavalieri, il Borelli e il Viviani, i quali tre insigni personaggi sono oramai <lb></lb>tante volte compariti sopra la scena, come principali attori del dramma, e i <lb></lb>nostri Lettori perciò gli debbono conoscere così bene, che alla tela, sopra la <lb></lb>quale è disegnata la loro effige, manca solamente l&#039;essere circoscritta, e ter­<lb></lb>minata dalla sua propria cornice. </s></p><p type="main">

<s>Il Cavalieri, avutone l&#039;impulso dalla lettura dei dialoghi dei Due mas­<lb></lb>simi sistemi, esordì i suoi studi con lo <emph type="italics"></emph>Specchio ustorio,<emph.end type="italics"></emph.end> dimostando che, <lb></lb>nelle naturali scese dei gravi, gli spazi crescono come i quadrati dei tempi, <lb></lb>in un modo nuovo e affatto geometrico, come pure ei fu il primo a dimo­<lb></lb>strar, nella parabola de&#039;proietti, i ludi geometrici della Natura. </s>

<s>Galileo, o <lb></lb>fossero le sue espressioni sincere, o tinte della gelosa paura di un potente <lb></lb>rivale; designava per suo successore nella Scienza del moto lo stesso Cava­<lb></lb>lieri, che rispondeva nel Giugno del 1635 in questi termini, interpetrando <lb></lb>meglio il suo proprio genio, che le intenzioni degli altrui onorevoli inviti: <lb></lb><emph type="italics"></emph>Quanto alla qualità degli studi, ai quali sia ora per applicarmi, se io <lb></lb>riguardo al mio gusto, mi saria piaciuto applicarmi io ancora alla dot­<lb></lb>trina del moto, parendomi cosa di gran momento, ed il compendio della <lb></lb>vera Filosofia:<emph.end type="italics"></emph.end> ma soggiunge che, per badare alla sodisfazione del luogo, <lb></lb>ossia della cattedra bolognese, nella quale era stato il Magini suo anteces­<lb></lb>sore tanto onorato, gli sarebbe convenuto piuttosto attendere a calcolare le <lb></lb>Effemeridi per gli anni prossimi futuri (Campori, Carteggio gal., Modena 1881). <lb></lb>Da un&#039;altra lettera, scritta allo stesso Galileo pochi giorni appresso, traspa­<lb></lb>risce più chiaramente essere una delle principali ragioni, che lo ritengono <lb></lb>dal coltivare gli studi della Meccanica, quella di non far nascere nuove om­<lb></lb>bre di gelosia nel mal disposto animo del suo Maestro, scusandosi con lui, <lb></lb>un&#039;altra volta fra le tante, del disgusto, che gli potesse ignorantemente aver <lb></lb>dato con l&#039;occasione dello <emph type="italics"></emph>Specchio ustorio<emph.end type="italics"></emph.end> “ nel quale, prosegue a dire, ve­<lb></lb>nendomi così bene a taglio la linea descritta dal proietto per le sezioni co­<lb></lb>niche, pensando che ella non ne facesse conto più che tanto, mi presi licenza <lb></lb>d&#039;inserirla in quel libro, credendo che le proposte mie, fatte in quello, che <lb></lb>era cosa imparata da lei, dovessero piuttosto cagionarle piacere che dispia­<lb></lb>cere ” (ivi, pag. </s>

<s>442). </s></p><pb xlink:href="020/01/2860.jpg" pagenum="485"></pb><p type="main">

<s>Non è il tempo nè il bisogno di tornare indietro sopra la storia odiosa <lb></lb>di quella incredibile usurpazione, dalla quale si derivò grave danno ai pro­<lb></lb>gressi della Scienza del moto, abbandonata dal Cavalieri afflitto e sbigottito. </s>

<s><lb></lb>Non abbiamo infatti su quel soggetto, dopo quel che ne toccò l&#039;Autore nello <lb></lb>Specchio ustorio, altro che la Quinta esercitazione geometrica, nella quale <lb></lb>pure s&#039;intravede una trepida sollecitudine di non mettere il pie&#039;nel campo <lb></lb>galileiano, limitandosi a percorrerne, nella statica dei momenti e dei centri <lb></lb>di gravità, le estreme prode. </s>

<s>Notabile, a proposito dell&#039;invenzione di questi <lb></lb>centri, che fosse il Cavalieri il primo e l&#039;unico a riguardare i corpi in gra­<lb></lb>vità come <emph type="italics"></emph>uniformemente disformi,<emph.end type="italics"></emph.end> ciò che si meriterebbe il nome, scritto <lb></lb>nel titolo, di una pura esercitazione geometrica, se in qualche caso, da con­<lb></lb>siderarsi forse meglio dai Fisici, non se ne vedesse possibile l&#039;applicazione, <lb></lb>come per esempio nella ricerca de&#039;centri di gravità delle grandi moli solle­<lb></lb>vate dalle forze endogene della Terra, supponendo che la densità degli strati <lb></lb>sia proporzionale alle pressioni o alle attrazioni, le quali crescano reciproca­<lb></lb>mente alle distanze dal centro. </s></p><p type="main">

<s>Altra cosa notabile è che, delle tante invenzioni comunicategli dal Tor­<lb></lb>ricelli intorno ai centri di gravità delle varie figure, non faccia il Cavalieri <lb></lb>motto che del solido colonnare insignito del suo proprio nome; e, nella pro­<lb></lb>posizione XVII, del centro di gravità della callotta sferica, <emph type="italics"></emph>quod novissime <lb></lb>probavit Torricellius,<emph.end type="italics"></emph.end> e, nella XXXIV, del centro di gravità dell&#039;emisfero, <lb></lb>dimostrato per via degl&#039;indivisibili con eleganze, che poco paion diverse dalle <lb></lb>torricelliane. </s>

<s>La ragione scusabilissima di questo silenzio sarà stata, perchè <lb></lb>sperava che avrebbe il Torricelli stesso presto dato ordine e pubblicità al <lb></lb>suo libro <emph type="italics"></emph>De centro gravitatis,<emph.end type="italics"></emph.end> il quale, rimastosi invece per due secoli e <lb></lb>mezzo ne&#039;suoi materiali disordinato e disperso, oggi finalmente ha preso qui <lb></lb>addietro nella nostra Storia, men per noi che per i pregi suoi propri, bel­<lb></lb>lezza nuova di forma. </s></p><p type="main">

<s>Il Borelli, fra i discepoli di Galileo, attese allo studio della Meccanica <lb></lb>sopra tutti gli altri, dando in quell&#039;argomento alla luce quattro opere insi­<lb></lb>gni, quali sono <emph type="italics"></emph>De vi percussionis, De motionibus naturalibus a gravitate <lb></lb>pendentibus, Theoricae Mediceorum<emph.end type="italics"></emph.end> e <emph type="italics"></emph>De motu animalium.<emph.end type="italics"></emph.end> Nelle prime <lb></lb>due l&#039;intento dell&#039;Autore non è che di promovere le dottrine del suo Mae­<lb></lb>stro, ma nelle altre due rimanenti apre campi nuovi alla Scienza, e dai pic­<lb></lb>coli gravi terrestri risale arditamente alle grandi moli de&#039;pianeti, e da&#039;moti <lb></lb>apperenti nella materia bruta deriva leggi, che rivelano gli occulti misteri <lb></lb>della vita. </s></p><p type="main">

<s>Del trattato della percossa e degli urti, e come il Borelli, prima del Wal­<lb></lb>lis, del Mariotte e dell&#039;Huyghens ne dimostrasse le leggi, fu detto qui addie­<lb></lb>tro nel capitolo III quanto ne pare a sufficienza per la storia dell&#039;invenzione, <lb></lb>se non del libro, che, sospingendone la via, lasciamo alle cure degli eruditi. </s></p><p type="main">

<s>Nè solamente rispetto alla forza della percossa lasciava da desiderare la <lb></lb>Scienza galileiana, ma rispetto ancora ad altre dottrine più fondamentali, che <lb></lb>il Borelli si studiò di confermare, e di esplicare nel libro <emph type="italics"></emph>De motionibus na-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2861.jpg" pagenum="486"></pb><emph type="italics"></emph>turalibus.<emph.end type="italics"></emph.end> Gli errori di Aristotile intorno alle cadute naturali dei gravi erano <lb></lb>stati scoperti liberamente da Galileo, il quale fu il primo ad annunziare <lb></lb>quella proposizione, apparita a tutti ammirabile, che cioè nel vuoto i corpi, <lb></lb>di qualunque mole e di qualunque figura, scenderebbero nel medesimo tempo <lb></lb>spazi uguali. </s>

<s>“ Eam tamen propositionem, soggiunge il Borelli, Galileus non <lb></lb>demonstravit, sed coniecturis et probabilibus tantummodo rationibus confir­<lb></lb>mare conatus est. </s>

<s>Quia vero huiusmodi propositio usum habet in hac phy­<lb></lb>sicee parte, quam praemanibus habemus, propterea operae pretium duxi fir­<lb></lb>mis demonstrationibus eam confirmare ” (Regio Julio 1670, pag. </s>

<s>439, 40). </s></p><p type="main">

<s>Le dimostrazioni però dell&#039;Autore, come si può facilmente indovinare, <lb></lb>erano di ragion pura e non sperimentali, mancando anche a lui, come a <lb></lb>Galileo, della Macchina pneumatica l&#039;invenzione e l&#039;uso. </s>

<s>Nulladimeno saga­<lb></lb>cemente avvertiva che del fatto, solamente operantesi nel vuoto, si poteva <lb></lb>aver qualche indizio certo o almeno probabile anche nel pieno, quando le <lb></lb>cadute si osservino in distanze talmente piccole, che poco sia l&#039;impedimento <lb></lb>opposto dalla consistenza o viscosità del mezzo. </s>

<s>Di qui apparisce, soggiunge <lb></lb>il Borelli, l&#039;imperizia di coloro, da&#039;quali non è escluso lo stesso Galileo, che, <lb></lb>volendo investigare se i corpi inegualmente gravi discendono inegualmente, <lb></lb>pensanò doversi sperimentare facendo cadere i gravi dalle altissime torri <lb></lb>“ ubi velocitates plumbi et argillae valde differunt inter se, cum tamen in <lb></lb>brevioribus altitudinibus nullo sensu distingui possint eorum inaequalitates, <lb></lb>cum ambo eodem tempore ferri videantur ” (ibid., pag. </s>

<s>500). </s></p><p type="main">

<s>Non sempre però il Borelli si contenta di confermare, come fa qui, le <lb></lb>dottrine del suo Maestro, ma altrove anche le compie, annunziando e dimo­<lb></lb>strando proposizioni nuove, qual sarebbe per esempio la seguente: “ Si fue­<lb></lb>rint duo cylindri homogenei aqua demersi, aequalium basium et inaequalium <lb></lb>altitudinum, semperque eorum latera perpendicularia sint ad horizontem; <lb></lb>tempora, quibus aequalia spatia ascendendo vel descendendo percurrunt, eam­<lb></lb>dem proportionem reciprocam habebunt, quam subduplicata ratio altitudinum <lb></lb>fuerit ” (ibid., pag. </s>

<s>470). La proposizione è contro Antonio Oliva, il quale <lb></lb>aveva proposto nell&#039;Accademia del Cimento alcune esperienze, per confer­<lb></lb>mare una sua opinione, che cioè le velocità de&#039;corpi, o discendenti o ascen­<lb></lb>denti nell&#039;acqua, osservino la proporzion diretta delle loro altezze. </s></p><p type="main">

<s>Erano altri, nè sappiamo se fosse tra costoro lo stesso Oliva, che nega­<lb></lb>vano l&#039;accelerarsi i corpi nell&#039;andare al fondo, o nel risalir pur per l&#039;acqua. </s>

<s><lb></lb>L&#039;errore aveva avuto occasione e veniva confermato da quell&#039;altro errore di <lb></lb>Galileo, che insegnava giungere nelle prolisse cadute il grave a ricevere dal <lb></lb>mezzo tale impedimento, da vietargli di più accelerarsi, cosicchè il moto pro­<lb></lb>cede di lì in poi sempre uniforme. </s>

<s>Credettero que&#039;Fisici che impedimento di <lb></lb>tal qualità e potenza fosse al mobile l&#039;acqua, e il Borelli non volle lasciar <lb></lb>l&#039;occasione di scoprire con due belle esperienze quella loro fallacia, dimo­<lb></lb>strata già dai calcoli del Cartesio. </s>

<s>A un vaso aveva spalmato il fondo di cera, <lb></lb>e riempiutolo del liquido, vi faceva da varie altezze cadere una palla di <lb></lb>piombo, infissovi sotto un ago. </s>

<s>Osservò che la punta era entrata nella cera <pb xlink:href="020/01/2862.jpg" pagenum="487"></pb>tanto più addentro, quanto la palla era venuta più d&#039;alto. </s>

<s>A far poi espe­<lb></lb>rienza del medesimo, nel risalire, affondava, per via di un bastoncello, un <lb></lb>cannellino, a cui era zavorra un globetto di piombo, che lasciato libero si <lb></lb>vedeva risaltar più o meno sull&#039;acqua, secondo ch&#039;era stato più o meno som­<lb></lb>merso. </s>

<s>“ Unde patet, ne conclude il Borelli, quod saltus altior produci de­<lb></lb>buit a vehementiori velocitate eiusdem calami, acquisita in eius ascensu pro­<lb></lb>lixiori ” (ibid., pag. </s>

<s>501). </s></p><p type="main">

<s>Le due opere di Meccanica pura, esaminate o per più vero dire ridotte <lb></lb>alla memoria dei nostri Lettori, erano nell&#039;intendimento dell&#039;Autore una <lb></lb>preparazione, e dovevano quasi servir di proemio alla grande opera dei moti <lb></lb>animali. </s>

<s>La celebrità di lei dispensa la nostra Storia dall&#039;entrare ne&#039;più mi­<lb></lb>nuti particolari, e da un altro lato, nel Tomo III, sono inseriti in gran nu­<lb></lb>mero documenti, che mostrano quali progressi venisse a fare la Fisiologia, <lb></lb>per le speculazioni e per l&#039;esperienze del Borelli. </s>

<s>De&#039;tanti lemmi premess <lb></lb>alle varie proposizioni, per preparar dalle forze che tendon le funi il pas­<lb></lb>saggio alle forze che contraggono i tendini e i muscoli, abbiamo avuto oc­<lb></lb>casione di toccare in vario proposito, e cose anche di maggiore importanza <lb></lb>ci occorreranno a dire più qua nel capitolo IX: ond&#039;è che sole le <emph type="italics"></emph>Theori­<lb></lb>cae Mediceorum<emph.end type="italics"></emph.end> ci rimangono a ridurre dentro la cornice del quadro. </s></p><p type="main">

<s>Non si possono l&#039;importanza e il fine di quest&#039;Opera nuova di Mecca­<lb></lb>nica celeste pienamente comprendere, senza risalire, e intrattener la mente <lb></lb>nella grande riforma astronomica del Keplero. </s>

<s>L&#039;orbita ellittica, dimostrata <lb></lb>da lui nella stella di Marte come cosa di fatto, aprì gli occhi via via agli <lb></lb>osservatori del Cielo, i quali presto ebbero a persuadersi che in simil modo <lb></lb>ricircolano intorno al Sole tutti gli altri pianeti, e i satelliti stessi intorno a <lb></lb>Giove. </s>

<s>Venivano così a dissiparsi de&#039;costruttori dei mondani sistemi le mac­<lb></lb>chine incantate, ma restava a spiegarsi come mai le circolanti moli s&#039;appres­<lb></lb>sassero e si dilungassero, con vicenda incessante, dai loro centri. </s>

<s>Il Keplero <lb></lb>s&#039;era immaginato che una faccia del Pianeta fosse amica al Sole, e l&#039;altra <lb></lb>nemica, d&#039;onde ora avvenisse un&#039;attrazione, ora una repulsione, a somi­<lb></lb>glianza di quel che il magnete, dagli opposti poli, fa verso il ferro: e com&#039;era <lb></lb>una strana immaginazione, così a buon diritto si repudiò dagli Astronomi. </s></p><p type="main">

<s>Con nessun diritto però s&#039;ostinarono altri a negare l&#039;esistenza del fatto, <lb></lb>perchè non ne intendevano le ragioni, di che Galileo dette al mondo, ne&#039;dia­<lb></lb>loghi dei Due massimi sistemi, esempio così famoso. </s>

<s>Si condannarono cote­<lb></lb>sti Dialoghi dalla Curia, instigata dai professori del Collegio romano, ma gli <lb></lb>aveva prima con più legittima autorità condannati la Scienza, la quale, per <lb></lb>le prove del moto della Terra, prolissamente ridotte all&#039;intelligenza dei Sim­<lb></lb>plicii, non seppe perdonare le inverosimiglianze e le irragionevolezze del si­<lb></lb>stema copernicano, per vedersi liberata dalle quali aveva fatto dianzi così <lb></lb>gran plauso al Keplero. </s>

<s>Di qui è che gli Astronomi, i quali, benchè per ra­<lb></lb>gioni diverse, si trovarono esser concorsi nella medesima sentenza col Santo <lb></lb>Uffizio, non fecero que&#039;reclami, di che poi assordarono il mondo tanti scrit­<lb></lb>tori, quando nell&#039;argomento veniva a porgersi alla loro rettorica un sì favo-<pb xlink:href="020/01/2863.jpg" pagenum="488"></pb>rito esercizio. </s>

<s>Nè furono quegli astronomi solamente i Roberval e i Cartesii, o <lb></lb>altri stranieri indifferenti o plaudenti agl&#039;immolatori della vittima del loro ri­<lb></lb>vale, ma gli stessi discepoli di Galileo più assennati e più liberi, fra&#039;quali, <lb></lb>da che s&#039;è imparato a conoscerlo in questa Storia, è de&#039;primi Antonio Nardi. </s></p><p type="main">

<s>Più forse del libro <emph type="italics"></emph>De revolutionibus<emph.end type="italics"></emph.end> del Copernico conferì a persuadere <lb></lb>che, non la Terra ma il Sole, sia centro de&#039;moti planetari l&#039;Arenario di Ar­<lb></lb>chimede, intorno al quale il Nardi, nella sua <emph type="italics"></emph>Ricercata seconda,<emph.end type="italics"></emph.end> sotto il ti­<lb></lb>tolo: “ Del sistema del mondo sopra quelle parole di Archimede nell&#039;Are­<lb></lb>nario <emph type="italics"></emph>Supponit Aristarchus inerrantia sidera et Solem non moveri, Terram <lb></lb>vero ferri in gyrum circa Solem, qui in medio stadio iaceat;<emph.end type="italics"></emph.end> scriveva la <lb></lb>seguente osservazione, compendiando una delle pagine più importanti della <lb></lb>Storia filosofica dell&#039;Astronomia: </s></p><p type="main">

<s>“ Molto rozzo, e molto nell&#039;apparenza dalla verisimilitudine repugnante, <lb></lb>parmi il sistema del Mondo, che per vero al tempo di Archimede da molti <lb></lb>si riceveva, poichè credevasi con Anassimandro il mondo essere una sfera, <lb></lb>di cui il centro fosse quello della Terra, e il semidiametro quella linea, che <lb></lb>dalla Terra andasse al Sole. </s>

<s>Platone con tutto ciò ed altri avevano creduto <lb></lb>diversamente, a&#039;quali, dopo Archimede, accostossi Ipparco Rodio, a cui To­<lb></lb>lomeo, e a Tolomeo gli altri tutti, sino all&#039;età de&#039;nostri avi, si sottoscris­<lb></lb>sero. </s>

<s>Ma Filolao da Crotone e Iceta Siracusano erano stati avanti Platone <lb></lb>inventori in parte di un paradosso sistema, il quale da Aristarco Samio fu <lb></lb>molto coltivato e perfezionato, di tal maniera che Archimede ad Aristarco il <lb></lb>parto di tal sistema attribuisce. </s>

<s>Ma tal parto morì quasi in fasce, se non che <lb></lb>Niccolò Copernico, dopo il giro dintorno a diciotto secoli, lo cavò dal sepol­<lb></lb>cro, e all&#039;età nostra, per le osservazioni del Telescopio, si è grandemente <lb></lb>avanzato nella credenza di molti. </s>

<s>” </s></p><p type="main">

<s>“ È ben vero che alla Santa Romana Chiesa tal sistema è per gravis­<lb></lb>sime cagioni sospetto, di che per ora ragionare non è mio proposito, e solo <lb></lb>avvertirò come, anche col semplice lume naturale discorrendo, parmi che il <lb></lb>sistema del Copernico in molte cose sia difettoso. </s>

<s>Egli in prima asserisce il <lb></lb>Sole e le fisse Stelle essere in tutto immobili, e per il contrario diè tante e <lb></lb>così strane maniere di movimenti alla Terra, senz&#039;addurne almeno qualche <lb></lb>ingegnosa, se non vera cagione, che sembra l&#039;opinion sua una fantasia troppo <lb></lb>fantastica, e pareva molto meglio il dare a ciascun corpo il suo moto, poichè <lb></lb>de&#039;corpi è comune accidente il moversi, che ad alcuni in tutto levandolo, e <lb></lb>troppi ad altri assegnandone, disturbare il mondano concerto. </s>

<s>” </s></p><p type="main">

<s>“ Impossibili dunque paiono quelle copernicane posizioni intorno a tanti <lb></lb>e sì diversi commovimenti, che come propri attribuisce alla Terra. </s>

<s>Quindi <lb></lb>ancora non lè librazioni sole e l&#039;inclinazioni, quali esso le finge, stimeran­<lb></lb>nosi da molti cose adulterine, ma ancora molto più quel forzato discorri­<lb></lb>mento, che per diritta linea in giù e in sù fa Mercurio. </s>

<s>S&#039;aggiunga ancora <lb></lb>che, essendo cose immaginarie, i centri degli Orbi descrivono con tutto ciò <lb></lb>appo il Copernico altri cerchi, e seco ne rapiscono gli orbi loro, il che è <lb></lb>inverosimile grande. </s>

<s>Lascio che in tal caso, mentre saglie e discende l&#039;Orbe, <pb xlink:href="020/01/2864.jpg" pagenum="489"></pb>che egli dice inconsideratamente Magno; offenderà il maggiore di Marte, e <lb></lb>quello di Venere, se però non voglia che fra l&#039;uno orbe e l&#039;altro ci sia molto <lb></lb>spazio vano, il che lo sproposito accresce: come anco a volere che insieme <lb></lb>si confondessero o si condensassero o rarefacessero. </s>

<s>Il vedersi ancora alcuni <lb></lb>mondani movimenti avere i loro periodi ubbidienti ai movimenti di altri corpi, <lb></lb>come per esempio il trovarsi Venere e Mercurio prossimi o lontani da un <lb></lb>certo punto, mentre la Terra in una tal linea si trovi; dà di chimerica po­<lb></lb>sizione indizio, sicchè almeno bisogna scansare, se non torre in tutto questo <lb></lb>inverosimile. </s>

<s>Ma supera tutti gl&#039;inverosimili l&#039;immensa distanza eterea fra <lb></lb>le fisse e i pianeti, poichè la sola ragione delle rifrazioni orizontali poteva <lb></lb>rimediare a molte apparenze, senza per così dire disgiungere il mondo da <lb></lb>sè medesimo, acciò di notte non si veda meno che mezzo. </s>

<s>” </s></p><p type="main">

<s>“ Tolomeo, dall&#039;altra banda, molto seccamente s&#039;inventò e abbracciò <lb></lb>quei cerchi, che irregolarmente sopra il suo, e regolarmente sopra gli altri <lb></lb>centri si muovono. </s>

<s>Pare ancora che nulla di naturale artifizio abbiano gli <lb></lb>orbi vuoti e di grossezza disuguale, per dove gli eccentri scorrano: oltrechè <lb></lb>troppo il rendere ragione è difficile come, gli uni combaciandosi con gli altri, <lb></lb>possano o congiunti o separati movimenti ottenere. </s>

<s>È anche strano a inten­<lb></lb>dersi come l&#039;ottavo cielo, contiguo a Saturno, comunichi a Saturno il suo <lb></lb>moto, ma Saturno non comunichi il suo a Giove, massime che la Luna co­<lb></lb>munica il suo al fuoco, se ci sia, e all&#039;aria, nature dalla quinta essenza to­<lb></lb>lemaica dissimili e fra sè ancora, e che, di più, propria origine di movi­<lb></lb>mento, e diverso dal circolare, ottengono in tale ipotesi. </s>

<s>Moversi ancora <lb></lb>l&#039;ottavo Orbe di movimento si tardò, e il settimo contiguo sì veloce, e di <lb></lb>velocissimo il nono; moversi ancora il secondo, il terzo e il quarto di eguale, <lb></lb>non ha del probabile in modo alcuno, come nemmeno che la Luna sia, nella <lb></lb>quarta, nell&#039;imo apside dell&#039;eccentro, e non riluca quattro volte più di quello <lb></lb>che fa, e ancora che si muova nell&#039;epiciclo, e che mostri l&#039;istessa faccia a <lb></lb>noi. </s>

<s>Certo che Tolomeo, purchè in qualche maniera alle apparenze dei moti <lb></lb>(questo è suo fine) sodisfaccia, poco della mondana armonia e convenienza <lb></lb>gli cale. </s>

<s>Quindi anco vediamo che poco la mal proporzionata proporzione <lb></lb>degli epicicli di Marte e di Venere gli prema, e così anche, ora gli eccentri <lb></lb>e gli epicicli, ora l&#039;epiciclo dell&#039;epiciclo e l&#039;eccentro epiciclo ei prenda nella <lb></lb>gran composizione, senza di tal differenza briga prendersi, in che, come in <lb></lb>altri inconvenienti, ha Tolomeo compagno il Copernico, e massime nel far <lb></lb>movere i pianeti intorno a centri immaginari. </s>

<s>” </s></p><p type="main">

<s>“ Meglio fece Aristotile a voler che i pianeti si movessero intorno alla <lb></lb>Terra come intorno a proprio centro, ma in tal caso bisogna render qualche <lb></lb>ragione dell&#039;avvicinarsi e discostarsi i Pianeti da esso centro, il che ha ten­<lb></lb>tato di fare in altra ipotesi il Keplero. </s>

<s>Delle cagioni poi di cotesti moti non <lb></lb>si trova parola appo Tolomeo e il Copernico, ma lasciano di ciò la briga ai <lb></lb>Fisici, i quali per lo più ricorrono alle macchine. </s>

<s>” </s></p><p type="main">

<s>“ In ultimo, mercè di tante apparenze nuovamente manifestateci, e per <lb></lb>essersi nuovi corpi mondani, e nuovi movimenti scoperti, o meglio i vecchi <pb xlink:href="020/01/2865.jpg" pagenum="490"></pb>osservati; bisogna non solo poco probabili stimare molte supposizioni degli <lb></lb>antichi, ma ancora in molte parti false. </s>

<s>Ticone di due sistemi ha fatto una <lb></lb>mal digerita confusione. </s>

<s>Non voglio esaminare tal suo parto, perchè, dal solo <lb></lb>aspetto, mostruoso apparisce. </s>

<s>Marte solo, rompendo col suo un altro giro, <lb></lb>impaurisce chiunque abbracciar dette posizioni volesse. </s>

<s>Ma di queste materie <lb></lb>nel mio sistema più accuratamente trattasi. </s>

<s>” </s></p><p type="main">

<s>Il sistema planetario, immaginato dal Nardi, metteva, come quel di Ari­<lb></lb>starco, nel Sole il centro dei moti, ma scansava gl&#039;inconvenienti del Coper­<lb></lb>nico, non considerati da Galileo, più filosoficamente del quale sentiva il Di­<lb></lb>scepolo come giovasse al progredir dell&#039;Astronomia investigar le ragioni <lb></lb>del discendere e del risalire i pianeti dal Sole, senza introdurre gli epicicli <lb></lb>e gli equanti. </s>

<s>Vero è bene che parve anche a lui cosa dura ammettere le <lb></lb>orbite kepleriane schiettamente ellittiche, ma per non mostrarsi, in rifiutar <lb></lb>ciò che si proponeva come cosa di fatto, o dissennato o caparbio, pensò che <lb></lb>di ellittico non avessero esse orbite che l&#039;apparenza o la similitudine, essendo <lb></lb>in realtà una trasformazione da certe figure elicali, che sarebbero secondo <lb></lb>lui le vere orbite descritte dai pianeti. </s>

<s>Troviamo questa opinione accennata <lb></lb>così per incidenza, trattandosi dall&#039;Autore <emph type="italics"></emph>Delle spirali o elici di Archimede:<emph.end type="italics"></emph.end><lb></lb>“ E chi sa che ancora i Pianeti non descrivano, intorno al Sole loro centro, <lb></lb>porzioni di elice, mentre ora da quello meno tirati discendono, ora, in virtù <lb></lb>dell&#039;attrazione e del consenso con gli altri membri del mondo, risagliono con <lb></lb>reciproche vibrazioni? </s>

<s>Certo che tal mio parere è forse non meno verosi­<lb></lb>mile che l&#039;introdurre gli epicicli e gli equanti, o il dare il moto ai punti <lb></lb>immaginari del centro, o finalmente inventare i moti ellittici. </s>

<s>” </s></p><p type="main">

<s>Ma perchè, in dimostrare la verosomiglianza di questo parere, si ridu­<lb></lb>ceva, del Sistema astronomico del Nardi, la maggiore importanza e il me­<lb></lb>rito principale; attese a farlo di proposito in una veduta delle sue <emph type="italics"></emph>Scene,<emph.end type="italics"></emph.end><lb></lb>introducendovi il principio delle forze centrali, immaginate spirar dal Sole a <lb></lb>guisa di un vento perpetuo, che meni in giro una nave. <lb></lb><figure id="id.020.01.2865.1.jpg" xlink:href="020/01/2865/1.jpg"></figure></s></p><p type="caption">

<s>Figura 309.</s></p><p type="main">

<s>“ Sia, egli dice, il cerchio ABC (fig. </s>

<s>309) di cui <lb></lb>centro F, diametro AB. </s>

<s>Intendasi il centro esser occu­<lb></lb>pato dal Sole ed un pianeta A, per esempio Giove, <lb></lb>il suo centro abbia nella periferia. </s>

<s>Giove, per la pro­<lb></lb>pria forma, moversi in sè stesso circolarmente pon­<lb></lb>gasi, ed anco intorno al Sole. </s>

<s>D&#039;avvantaggio pongasi <lb></lb>che il Sole e la sua forma, essendo quasi cuore ed <lb></lb>anima del mondo planetario, muovano in qualche <lb></lb>modo e formino i moti degli altri membri, e in con­<lb></lb>seguenza più veloci moveranno i più vicini. </s>

<s>Il loro muovere non sarà im­<lb></lb>pulso esterno, ma una informazione interna o vitale, mediante la virtù pro­<lb></lb>pria e solare, che muove equabilmente, ed in conseguenza perpetuamente. </s>

<s><lb></lb>Vento, che stabile. </s>

<s>gonfi ed animi una vela per un tranquillo orizonte, <lb></lb>cagionerà, nel movere egualmente in giro una nave, certa somiglianza dello <lb></lb>effetto solare nei circostanti corpi. </s>

<s>” </s></p><pb xlink:href="020/01/2866.jpg" pagenum="491"></pb><p type="main">

<s>“ Ma perchè Giove aspira, nel suo condursi in giro per la periferia ABC, <lb></lb>all&#039;accostamento verso il suo centro, quindi è che nel circolare sopraggiunge <lb></lb>il retto moto, il quale è congiunto dello accoppiarsi delle virtù gioviale e <lb></lb>solare, e così ancora avviene nel grave cadente, il quale, dalla propria forma <lb></lb>e dal consenso delle sottoposte cose, è rapito al centro, e sempre con impeto <lb></lb>più accelerato s&#039;avanza. </s>

<s>Lo stesso forse fa Giove, se non che l&#039;impeto suo <lb></lb>non si accelera evidentemente nell&#039;accostarsi al Sole, perchè la lontananza <lb></lb>e grandezza sua fanno diversa ragione di accelerarsi, che non fa la piccolezza di <lb></lb>un sasso cadente, e la vicinanza alle altre parti congeneri che l&#039;attraggono. </s>

<s>” </s></p><p type="main">

<s>“ Il moto dunque composto di circolare e diretto non par altro che una <lb></lb>spira, e questa tanto s&#039;avvicina al centro, quanto mirando la causa finale <lb></lb>comporta la convenienza e il bisogno di Giove in riguardo del Sole, onde, <lb></lb>arrivato al termine, ritorna alla medesima altezza. </s>

<s>Ma perchè verso la stessa <lb></lb>parte concorrono i moti del Sole e di Giove in sè stessi, e di più quello di <lb></lb>Giove è messo in giro diverso; avvien forse che la spira del punto A non <lb></lb>termini in un punto del diametro AB, ma trascorra alquanto più in là, come <lb></lb>in E, onde, restituendosi il periodo della risalita, anch&#039;egli alquanto mag­<lb></lb>giore di quello della scesa, trascorrerà anche A, punto dell&#039;auge, secondo <lb></lb>l&#039;ordine de&#039;segni in D, e segherassi ne&#039;punti A, D la prima spira dalla se­<lb></lb>conda. </s>

<s>Vento che, uniforme spirando, spieghi la chioma di qualche albero <lb></lb>sino a certo segno, onde quella per sè stessa ritorni in altrettanta inclina­<lb></lb>zione verso della contraria parte, e che di nuovo alternando si lasci dal vento <lb></lb>spiegare; somiglia al meglio che può tra le cose nostre l&#039;ordine e la ragione <lb></lb>delle celesti spire. </s>

<s>Tal maniera poi di spira, poichè le spire sono d&#039;infinite <lb></lb>sorti, riscontrasi, almeno prossimamente, con una ellisse, in uno dei cui fochi <lb></lb>sia il Sole. </s>

<s>E tanto secondo questi principi apportato sia, poichè anche in <lb></lb>questa via si trovano intoppi ” (MSS. Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>291-94). </s></p><p type="main">

<s>Gl&#039;intoppi erano per questa via inevitabili, come a colui che si trovava <lb></lb>costretto ad ammettere una conseguenza di fatto, senza conoscerne i prin­<lb></lb>cipii. </s>

<s>Di qui è che lo studio del Nardi si ridusse a dimostrare in qualche <lb></lb>modo come le orbite ellittiche fossero una trasformazione dalle circolari. </s>

<s>Il <lb></lb>Boulliaud non seppe tenere altra via diversa da questa, immaginando quel <lb></lb>suo aereo cono scaleno, per dare ad intendere come dai circoli, descritti in­<lb></lb>torno all&#039;asse di lui dal pianeta, che dal vertice equabilmente discende verso <lb></lb>la base; venga a disegnarsi sulla superficie di esso cono un&#039;ellisse, che in <lb></lb>uno de&#039;suoi fochi abbia il Sole. </s></p><p type="main">

<s>Di non lieve importanza apparirà perciò il passo, che fece fare il Bo­<lb></lb>relli alla Scienza, ammettendo che l&#039;eccentricità sia all&#039;orbite congenita, e <lb></lb>non avventizia. </s>

<s>Di qui è che il problema si poteva proporre ne&#039;suoi veri ter­<lb></lb>mini, avviandolo a ricercare d&#039;onde resultin le forze che, sollecitando i sa­<lb></lb>telliti e i pianeti, gli fanno rivolgere non più in circoli ma in ellissi. </s>

<s>Alla <lb></lb>ricerca però non conseguì per il Nostro la desiderata invenzione, perchè, seb­<lb></lb>bene egli avesse felicemente sottoposti i moti celesti all&#039;azione delle forze <lb></lb>centrifughe e delle centripete, ignorò le loro vere leggi, credendo che queste <pb xlink:href="020/01/2867.jpg" pagenum="492"></pb>attraessero secondo la ragion semplice reciproca delle distanze, e quelle non <lb></lb>sapendo risolvere nelle loro direzioni tangenziali, d&#039;onde il moto iniziale si <lb></lb>veniva a ridurre a una certa proiezione. </s>

<s>Cosi ebbe anch&#039;egli a giocare di <lb></lb>fantasia come il Nardi, ripetendo con lui che il Sole volge in giro intorno a <lb></lb>sè il pianeta, spirandogli la forza, <emph type="italics"></emph>ad instar venti alicuius perpetui.<emph.end type="italics"></emph.end> (Flo­<lb></lb>rentiae 1665, pag. </s>

<s>61). </s></p><p type="main">

<s>Ignorata la ragione del moto proiettizio ne&#039;suoi principii, da&#039;quali re­<lb></lb>sultava che un mobile attratto a un centro, con forze reciprocamente pro­<lb></lb>porzionali ai quadrati delle distanze, descrive intorno a esso centro una curva, <lb></lb>che dal circolo via via si trasformerebbe in ellisse, in parabola, in iperbola, <lb></lb>secondo che sempre maggiore si facesse la proiezione iniziale; il Borelli si <lb></lb>trovò anche un&#039;altra volta a dover imitare le immaginazioni del Nardi. </s>

<s>E <lb></lb>come questi avea fatto ricorso all&#039;azion del Sole, che interrottamente spi­<lb></lb>rando i suoi effluvi fa ondeggiare il pianeta, come il vento la chioma di un <lb></lb>albero; così il Borelli rassomigliò esso pianeta galleggiante nell&#039;etere a un <lb></lb>cilindro galleggiante nell&#039;acqua, che, sommerso una volta più giù di quel che <lb></lb>non importi alla sua gravità in specie, ritorna in su reciprocando le sue vi­<lb></lb>brazioni di andare e di venire con vicenda, che sarebbe perpetua, se non tro­<lb></lb>vasse impedimento nel peso e nella viscosità del liquido, come, secondo che <lb></lb>credevasi allora, non ne trovano nel sottilissimo etere i vaganti corpi celesti. </s>

<s><lb></lb>Di qui è a concludere che le <emph type="italics"></emph>Theoricae Mediceorum<emph.end type="italics"></emph.end> preparano quelle vie al <lb></lb>Newton, che esse stesse trovarono dal Nardi già preparate, e così la luce <lb></lb>venuta a illuminare le tenebre del mondo, apparita in Germania, non si di­<lb></lb>resse verso l&#039;Inghilterra fortunata, se non che dopo essersi, come da spec­<lb></lb>chio, riflessa dall&#039;Italia. </s></p><p type="main">

<s>Del Viviani sembrerebbe che poco rimanesse a dire, non essendosi in <lb></lb>questa lunga Storia della Meccanica toccato quasi argomento, in cui egli non <lb></lb>sia entrato, e non v&#039;abbia preso gran parte. </s>

<s>Un intento unico però, quasi <lb></lb>meta de&#039;suoi desideri, abbiamo fin qui scorto nell&#039;opera di lui, qual è di <lb></lb>esplicare, di correggere e di promovere i teoremi (non sempre dimostrati, <lb></lb>ma talvolta solamente proposti da Galileo) in commentari, da sottoscriversi <lb></lb>in note, e in appendici ai dialoghi delle Due Scienze nuove. </s>

<s>Prelude­<lb></lb>vano a questi, chi ben considera, gli altri dialoghi del Mondo, in cui le <lb></lb>leggi più generali del moto, richiamate destramente dai conversanti a pro­<lb></lb>posito del moto della Terra, si dimostravano con discorsi accomodati all&#039;in­<lb></lb>telligenza delle menti volgari. </s>

<s>Ma se queste ne ritraevano utilità con diletto, <lb></lb>ai Filosofi frettolosi di passar dai principii alla conclusione riuscivano quelle <lb></lb>lunghe digressioni di tedio, e divagatrici del pensiero: incomode poi torna­<lb></lb>vano agli studiosi, i quali avrebbero voluto meglio apprendere così fatte dot­<lb></lb>trine da un libro, scritto con la brevità e con l&#039;ordine di un trattato. </s></p><p type="main">

<s>A tale ufficio desideratissimo attese dunque il Viviani, e con tale inten­<lb></lb>zione fu incominciata da lui quella scrittura, che nel Tomo VII, Parte V <lb></lb>de&#039;Manoscritti di Galileo, si legge dal foglio 89 al 95, sotto il titolo <emph type="italics"></emph>Varie <lb></lb>proprietà del moto dei gravi naturale e violento.<emph.end type="italics"></emph.end> Raccoglie quivi e dà or-<pb xlink:href="020/01/2868.jpg" pagenum="493"></pb>dine l&#039;Autore alle principali proposte, che ricorrono nella terza giornata delle <lb></lb>Due nuove Scienze, e riducendo il trattatello a un semplice memoriale, con <lb></lb>mettere solamente e dichiararne le tesi, apre ai lettori la via di ritrovarne <lb></lb>per sè medesimi le dimostrazioni. </s>

<s>Nel Tomo XXXIV de&#039;Manoscritti del Ci­<lb></lb>mento, dal foglio 54 al 113, si trovan raccolti i materiali, per trattare <emph type="italics"></emph>Delle <lb></lb>gravità specifiche e assolute,<emph.end type="italics"></emph.end> e ivi pure, dal foglio 114 al 145, e dal foglio <lb></lb>204 al 208, si trova il principio posto a due altri libri, il primo de&#039;quali <lb></lb>s&#039;intitolava <emph type="italics"></emph>Del moto dei gravi,<emph.end type="italics"></emph.end> e il secondo <emph type="italics"></emph>De momentis gravium in ge­<lb></lb>nere.<emph.end type="italics"></emph.end> Per chi poi volesse avere un saggio della lucida brevità, con la quale <lb></lb>il Viviani esponeva le dottrine meccaniche del suo Maestro, sceglieremo da <lb></lb>varie Note le due seguenti, perchè si possano confrontare con que&#039;lunghi <lb></lb>discorsi tenuti da Galileo ne&#039;Dialoghi, e in varie altre scritture minori, per <lb></lb>confutar gli errori, che intorno alle cadute naturali dei gravi erano stati detti <lb></lb>già da Aristotile, e che tuttavia si ripetevano dai seguaci di lui: </s></p><p type="main">

<s>“ I. </s>

<s>Si domanda ai signori Peripatetici se, lasciando cadere a basso mille <lb></lb>particole di legno, come per esempio una giumella di segatura, ei credano <lb></lb>che tutte scendessero con pari velocità. </s>

<s>Credo sian per rispondere di si. </s>

<s>Se <lb></lb>dunque queste particole si accosteranno insieme, e si attaccassero in modo, <lb></lb>che tra loro non restasse aria (che è il mezzo nel quale si pone che si muo­<lb></lb>vano) domandisegli se credono che queste continuassero il moto con la me­<lb></lb>desima velocità di prima, poichè non potendo altri, anche per detto loro, <lb></lb>conferir più di quello che esso ha, non mi pare che assegnar si possa quali <lb></lb>fossero quelle particole, che augumentassero la velocità alle altre loro simi­<lb></lb>lissime e ugualissime. </s>

<s>” </s></p><p type="main">

<s>“ Diranno forse che, quando altro acquisto non ci fosse, vi sarebbe la <lb></lb>diminuzione della superficie, la maggior parte della quale si occulta nelle <lb></lb>attaccature. </s>

<s>E concedendo che la confricazione del mezzo con la superficie <lb></lb>del mobile ritarda la di lui velocità, soggiungeranno che perciò quelle molte <lb></lb>particole, ridotte in un sol corpo di superficie grandemente minore, acqui­<lb></lb>steranno velocità nel moto. </s>

<s>” </s></p><p type="main">

<s>“ Se tale sarà la risposta loro, diranno benissimo, perchè basta che <lb></lb>eglino concedano e sian capaci che, non per accrescimento di velocità, ma <lb></lb>per diminuzione di superficie, cioè, per diminuzione dell&#039;impedimento del <lb></lb>mezzo, si cresce la velocità. </s>

<s>E se di ciò volessero anche più chiara esperienza <lb></lb>considerino come una foglia d&#039;oro battuto, che sotto così gran superficie <lb></lb>discende per aria lentissimamente, ridotta poi in un piccolo globetto scende <lb></lb>cento volte più veloce, benchè il peso sia lo stesso. </s>

<s>Ma quanto importi l&#039;im­<lb></lb>pedimento del mezzo si ha manifesto da una palla, che venga cacciata dalla <lb></lb>artiglieria, alla quale l&#039;impedimento di non molte braccia di acqua, che ella <lb></lb>incontri dopo il moto per l&#039;aria, talmente ritarda la sua velocità, che la sua <lb></lb>percossa ne resta fiacchissima. </s>

<s>Eppure l&#039;acqua, come priva in tutto di tena­<lb></lb>cità, non resiste con altro che col doversi movere lateralmente, come a lungo <lb></lb>dimostrò il Galileo nel suo trattato delle Galleggianti ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXXXV, fol. </s>

<s>15). </s></p><pb xlink:href="020/01/2869.jpg" pagenum="494"></pb><p type="main">

<s>“ II. </s>

<s>Dicunt aliqui gravia, quae deorsum feruntur, magis semper intendi <lb></lb>in motu, quia pauciores partes aeris sibi scindendae restant, quod quidem <lb></lb>falsu m videtur. </s>

<s>Nam, si tunc grave velocius fertur, quando pauciores partes <lb></lb>aeris sunt scindendae; ergo, si aliquod grave ab altissimo loco demittatur, <lb></lb>ut ab aliqua turri, cuius altitudo sit 100, idem autem demittatur ab alio <lb></lb>loco, cuius altitudo sit 10; celerius movebitur in fine huius altitudinis, quae <lb></lb>est 10, quam in medio altioris altitudinis, puta ut 50, quod absurdum vi­<lb></lb>detur ” (ibid., fol. </s>

<s>25). </s></p><p type="main">

<s>Da queste e da simili altre Note, dai titoli de&#039;trattati dianzi trascritti, <lb></lb>dai teoremi dimostrati intorno ai pendoli, ai momenti de&#039;gravi lungo i piani <lb></lb>inclinati, alle resistenze de&#039;solidi, per tacere di tante altre cose; si conferma <lb></lb>esser quale si disse la principale intenzione di questi studi intorno alla <lb></lb>Scienza meccanica fatti dal Viviani. </s>

<s>Ma venivano spesso spesso a stimolarlo <lb></lb>gli esempi degli altri Colleghi suoi, ritrovatori di verità nuove, in campi non <lb></lb>punto meno fertili di quegli stessi coltivati da Galileo, com&#039;era per esempio <lb></lb>la Centrobarica, che apparita maravigliosa in sè stessa prometteva di aprir <lb></lb>la via a cento altre non meno mirabili invenzioni. </s>

<s>Ciò fu che mosse il Vi­<lb></lb>viani a comporre quel trattatello <emph type="italics"></emph>Dei centri di gravità,<emph.end type="italics"></emph.end> e a distendere quelle <lb></lb>proposizioni spicciolate, che s&#039;hanno raccolte ne&#039;tomi LXXI, XCII della ci­<lb></lb>tata collezion manoscritta dei Discepoli di Galileo. </s>

<s>E per chi credesse non <lb></lb>esser nulla rimasto a chi, dopo il Torricelli e il Nardi, il Cavalieri e il Ricci, <lb></lb>s&#039;assideva al medesimo convivio; sceglieremo dal detto manoscritto le sei pro­<lb></lb><figure id="id.020.01.2869.1.jpg" xlink:href="020/01/2869/1.jpg"></figure></s></p><p type="caption">

<s>Figura 310.<lb></lb>posizioni seguenti, dalle quali apparirà <lb></lb>come ben sapesse l&#039;Autore una eser­<lb></lb>citazione già fatta trattare con metodi <lb></lb>nuovi, o promoverla oltre a quel che <lb></lb>non aveva ancora pensato nessuno dei <lb></lb>predecessori: e le relazioni date da <lb></lb>loro in funzioni algebriche, per alcune <lb></lb>figure circoscritte da qualche arco di <lb></lb>cerchio, riducesse a numeri, quanto <lb></lb>più prossimamente era possibile, de­<lb></lb>terminati. </s></p><p type="main">

<s>“ PROPOSITIO I. — <emph type="italics"></emph>Centrum gra­<lb></lb>vitatis curvae superficiei coni recti <lb></lb>ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>310), <emph type="italics"></emph>cuius axis BD, hanc <lb></lb>dividit in E, ita ut BE sit dupla ED, adeo ut idem sit centrum gravitatis <lb></lb>curvae, et centrum gravitatis trianguli per axem coni. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Producta axe BD, sumatur ipsi aequalis DG, ac DF aequalis DE, et <lb></lb>quaevis DM aequalis DI: sumptaque DH aequali circumferentiae circuli AC, <lb></lb>basis coni, iungatur GH, et in triangulis ABC, GDH sint per I, E, et per <lb></lb>F, M ductae OP, QR, FL, MN parallelae ipsi AC:BG vero concipiatur tam­<lb></lb>quam libra horizontalis appensa ex D. ” </s></p><p type="main">

<s>“ Jam, cum sit DE tertia pars DB, et DF erit pars tertia DG, ac ideo <pb xlink:href="020/01/2870.jpg" pagenum="495"></pb>centrum gravitatis trianguli rectanguli GDH sui momentum exercet per li­<lb></lb>neam FL. </s>

<s>Et cum sit DH ad FL ut DG ad GF, vel, ob aequalitatem, ut DB <lb></lb>ad BE; vel, ob homologorum laterum in similibus triangulis ADB, QEB pro­<lb></lb>portione laterum, ut DA, radius basis coni, ad EQ, radium circuli in cono <lb></lb>per E ducti, vel ut periferia AC in conica superficie ad superficiem QR in <lb></lb>cadem conica utcumque sit secta, DH aequalis periferiae ADC, ex constru­<lb></lb>ctione; erit quoque recta FL aequalis periferiae QR. </s>

<s>Sed illa gravitat in F, <lb></lb>haec vero in E, suntque distantiae DF, DE inter se aequales, prout sunt ma­<lb></lb>gnitudines; ergo in D inter se aequiponderant. </s>

<s>” </s></p><p type="main">

<s>“ Eadem penitus ratione ostendetur recta MN aequalis esse, et aequi­<lb></lb>ponderare in D cum periferia OP, ex aequalibus distantiis DI, DM, et hoc <lb></lb>semper. </s>

<s>Ergo omnes simul rectae in triangulo GDH, sive ipsum triangulum, <lb></lb>aequale est ac aequale momentum habet circa D cum omnibus simul peri­<lb></lb>feriis, hoc est cum conica superficie curva ABC. </s>

<s>Quare ipsarum superficie­<lb></lb>rum centra gravitatis aeque distant a D. </s>

<s>Sed centrum trianguli gravitat in F, <lb></lb>ergo centrum curvae conicae est in E, prout ostendere propositum fuit. </s>

<s>” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. LXVI, fol. </s>

<s>99). </s></p><p type="main">

<s>Il Torricelli in tre modi dimostrò questa medesima proposizione, e il Viviani <lb></lb>volle far vedere che non perciò la fecondità era esaurita. </s>

<s>Ma così esso Torricelli, <lb></lb>come tutti gli altri, si limitarono alla ricerca del centro di gravità della sola <lb></lb>superficie conica convessa, e il Nostro pensò che si poteva anche oltre pro­<lb></lb>moverla, comprendendovi il circolo base. </s>

<s>Così, del centro della universale su­<lb></lb>perficie del solido, riuscì a dare elegantemente questa nuova indicazione. </s></p><p type="main">

<s>“ PROPOSITIO II. — <emph type="italics"></emph>Centrum gravitatis universae superficiei coni recti <lb></lb>sic dividit axem, ut pars ad verticem coni sit ad reliquam ad basim ut <lb></lb>tres radii basis, cum duplo lateris coni, ad latus idem coni. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto ABC (fig. </s>

<s>311) triangulum per axem BD, quo secto in E, ut DE <lb></lb>sit pars tertia totius BD, constat in E esse centrum gravitatis curvae coni­<lb></lb><figure id="id.020.01.2870.1.jpg" xlink:href="020/01/2870/1.jpg"></figure></s></p><p type="caption">

<s>Figura 311.<lb></lb>cae ABC, et in D centrum gravitatis circuli suae basis. </s>

<s><lb></lb>Sed curva conica ad basim est ut latus BA ad AD, ergo, <lb></lb>si DE secetur in F, ita ut DF ad FE sit ut BA ad AD, <lb></lb>erit F centrum gravitatis utriusque superficiei. </s>

<s>Sed BF <lb></lb>constat ex duabus DF, et ex tribus FE; FD vero ex <lb></lb>unica FD: duo autem DF exhibent duo latera AB, et <lb></lb>tres FE exhibent tres AD, ac unica DF unicam AB, <lb></lb>quod sit DF ad FE ut BA ad AD. </s>

<s>Quare BF ad FD <lb></lb>est ut duo DF, cum tribus FE, ad ipsum FD, vel ut duo <lb></lb>latera AB, cum tribus radiis AD, ad idem latus AB, quod etc. </s>

<s>” (ibid., fol. </s>

<s>102). </s></p><p type="main">

<s>Abbiamo infatti BF=BE+EF=2DE+EF=2(DF+EF)+EF= <lb></lb>2DF+3EF, e di qui la proporzione BF:DF=2DF+3EF:DF. </s>

<s>Ma <lb></lb>essendo per la legge delle equiponderanze DF:EE=AB:AD, sarà anche <lb></lb>insieme 2DF:3FE=2AB:3AD. Componendo, 2DF+3FE:2DF= <lb></lb>2AB+3AD:2AB. </s>

<s>Dividendo i conseguenti per due, se ne conclude imme­<lb></lb>diatamente la relazione BF:DF=2AB+2AD:AB. </s></p><pb xlink:href="020/01/2871.jpg" pagenum="496"></pb><p type="main">

<s>Anche il centro di gravità della callotta sferica era stato ritrovato dal <lb></lb>Torricelli per la sola parte curva della figura, escluso il circolo base, ma il <lb></lb>Viviani passò oltre a indicarne così il punto sull&#039;asse, dove gravita la su­<lb></lb>perficie universale. </s></p><p type="main">

<s>“ PROPOSITIO III. — <emph type="italics"></emph>Centrum gravitatis universae superficiei portionis <lb></lb>sphaericae sic dividit axem, ut pars ad polum terminata sit ad reliquam, <lb></lb>ut axis portionis reliquae, cum semiaxe sphaerae, ad ipsum semiaxem:<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2871.1.jpg" xlink:href="020/01/2871/1.jpg"></figure></s></p><p type="caption">

<s>Figura 312.<lb></lb><emph type="italics"></emph>vel, ut duplum basis portionis sphaericae, una cum <lb></lb>eius curva superficie, ad ipsam curvam. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Esto ABC (fig. </s>

<s>312) sphaerae portio, cuius <lb></lb>axis BD, diameter basis AC, et axis totius sphaerae <lb></lb>BE. </s>

<s>Jam constat quod, secto BD bifariam in F, id <lb></lb>est centrum gravitatis curvae superficiei ABC. </s>

<s>Sed D <lb></lb>est centrum circuli AC, ergo utriusque simul super­<lb></lb>ficiei centrum gravitatis est inter F et D, ut in G. </s>

<s><lb></lb>Dico BG ad GD esse ut axis DE, cum dimidio axis <lb></lb>EB, ad ipsum dimidium. </s>

<s>” </s></p><p type="main">

<s>“ Jungantur AB, AE. </s>

<s>Erit ergo, ob aequilibrium in G curvae ABC cum <lb></lb>circulo AC, FG ad GD ut circulus AC ad curvam ABC, vel ut quadratum <lb></lb>radii DA ad quadratum radii BA, cuius circulus aequatur ipsi curvae super­<lb></lb>ficiei ABC, vel, ob triangulorum DAB, DEA similitudinem, ut quadratum DE <lb></lb>ad quadratum EA, vel ut linea DE ad tertiam proportionalem EB in semi­<lb></lb>circulo BAE. </s>

<s>Et componendo, FD ad DG ut DE cum EB ad EB. </s>

<s>Et divi­<lb></lb>dendo, BG ad GD ut duplum DE cum EB ad EB, vel, sumptis horum di­<lb></lb>midiis, ut una DE cum dimidio EB, seu cum semiaxe sphaerae, ad dimidium <lb></lb>EB, vel ad ipsum semiaxem, quod erat primo etc. </s>

<s>” (ibid., fol. </s>

<s>108). </s></p><p type="main">

<s>Per passare al secondo modo, o alla seconda forma, sotto la quale la <lb></lb>medesima verità propone l&#039;Autore a dimostrarsi, si osservi che fu già con­<lb></lb>cluso FG:GD=DE:EB. </s>

<s>Ma AE2=EB.ED, EB2=EB2 d&#039;onde ED:EB= <lb></lb>AE2:EB2=DA2:AB2=<foreign lang="grc">π</foreign>DA2:<foreign lang="grc">π</foreign>AB2, e perciò FG:GD=<foreign lang="grc">π</foreign>DA2:<foreign lang="grc">π</foreign>AB2. </s>

<s><lb></lb>Componendo, FD:DG=<foreign lang="grc">π</foreign>DA2+<foreign lang="grc">π</foreign>AB2:<foreign lang="grc">π</foreign>AB2. </s>

<s>Duplicando gli antecedenti, <lb></lb>BD:DG=2<foreign lang="grc">π</foreign>DA2+2<foreign lang="grc">π</foreign>AB2:<foreign lang="grc">π</foreign>AB2. </s>

<s>E in ultimo dividendo, BG:GD= <lb></lb>2<foreign lang="grc">π</foreign>DA2+<foreign lang="grc">π</foreign>AB2:<foreign lang="grc">π</foreign>AB2. </s>

<s>Ora essendo la superficie di una callotta sferica <lb></lb>uguale al prodotto della sua altezza per la circonferenza di un circolo grande, <lb></lb>ossia essendo uguale a <foreign lang="grc">π</foreign>BD.BE=<foreign lang="grc">π</foreign>AB2, e dall&#039;altra parte rappresentan­<lb></lb>dosi da <foreign lang="grc">π</foreign> DA2 il circolo descritto col raggio AD, sopra il quale la cupola <lb></lb>risiede; è manifesto che il punto G sega così l&#039;asse, che la parte verso il polo <lb></lb>abbia alla rimanente la proporzion medesima, che la doppia base con la callotta <lb></lb>ha alla callotta sola, secondo che così il Viviani soggiunge nel suo foglio: </s></p><p type="main">

<s>“ Sed DE ad EB est ut quadratum AE ad quadratum EB, vel ut qua­<lb></lb>dratum DA ad quadratum AB, vel ut circulus ex radio DA seu basis por­<lb></lb>tionis ABC, ad circulum ex radio AB, vel ad curvam superficiem portionis; <lb></lb>ergo BG ad GD est quoque ut duae bases portionis sphaericae ABC, cum <lb></lb>curva eius superficie, ad ipsam curvam ” (ibid.). </s></p><pb xlink:href="020/01/2872.jpg" pagenum="497"></pb><p type="main">

<s>Che se BE=2BD, ossia se la callotta sia emisferica, tornerà la su­<lb></lb>perficie di lei, ch&#039;era 2<foreign lang="grc">π</foreign>BD2, ossia <foreign lang="grc">π</foreign>AB2, espressa da 2<foreign lang="grc">π</foreign>DA2, e perciò <lb></lb>BG:GD=2<foreign lang="grc">π</foreign>DA2+2<foreign lang="grc">π</foreign>DA2:2<foreign lang="grc">π</foreign>DA2=2:1, come il Viviani stesso <lb></lb>soggiunge in questo suo <emph type="italics"></emph>Corollario:<emph.end type="italics"></emph.end> “ Hinc centrum gravitatis universae <lb></lb>superficiei haemisphaericae sic axem dividit, ut pars ad polum terminata sit <lb></lb>ad reliquam, ut duo ad unum: tunc enim duae bases aequantur uni curvae, <lb></lb>et duae bases cum curva duplae sunt unica curva, adeoque et pars ad polum <lb></lb>terminata reliquae ad centrum basis dupla erit ” (ibid.). </s></p><p type="main">

<s>“ PROPOSITIO IV. — <emph type="italics"></emph>Centrum gravitatis E<emph.end type="italics"></emph.end> (fig. </s>

<s>313), <emph type="italics"></emph>quadrantis cir­<lb></lb>culi ABCD, cuius centrum D, axis DB, ita hunc secat, ut totus BA, ad<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2872.1.jpg" xlink:href="020/01/2872/1.jpg"></figure></s></p><p type="caption">

<s>Figura 313.<lb></lb><emph type="italics"></emph>partem DE attingentem centrum D arcus ABC, sit <lb></lb>quam proxime ut 5 ad 3. Circumscripto vero qua­<lb></lb>dranti huic quadrato ADCF, centrum gravitatis G <lb></lb>trilinei ABCF sic dividit axem DF, ut radius DB <lb></lb>ad DG sit quam proxime ut 10 ad 11. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Quoad primum, diameter FD secetur bifariam <lb></lb>in I, atque ex G, I, E super DA ducantur perpen­<lb></lb>diculares GL, IK, EH, et concipiatur figura converti <lb></lb>circa AD. ” </s></p><p type="main">

<s>“ Jam constat cylindrum a quadrato AC, ad hemisphaerium a quadrante <lb></lb>ABCD, esse ut 3 ad 2, sive ut 42 ad 28. Sed ipse cylindrus ad ipsum hemi­<lb></lb>sphaerium, ex Centrobaryca, rationem habet compositam ex ratione quadrati <lb></lb>ad quadrantem, sive ex ratione proxime 14 ad 11, sive ex ratione 42 ad 33, <lb></lb>et ex ratione distantiae IK ad distantiam EH centrorum gravitatis quadrati <lb></lb>et quadrantis ab axe revolutionis AD, atque etiam 42 ad 28 rationem habet <lb></lb>compositam ex 42 ad 33, et ex ratione 33 ad 28, et ratio quadrati ad qua­<lb></lb>drantem est ut 42 ad 33; ergo ratio distantiae IK, ad rationem EH, est ut <lb></lb>33 ad 28, velut ut 9 ad 7+7/11. Qualium ergo partium IK est 9, talium <lb></lb>EH est 7+7/11, et talium DC, quae dupla est ipsius IK, quae est 9, erit 18. ” </s></p><p type="main">

<s>“ Sed DB vel DC latus quadrati AC, ad diametrum DF, vel ad AC <lb></lb>chordam arcus ABC, est ut 5 ad 7+1/14, vel ut 18 ad 25+16/35; ergo tam <lb></lb>DF quam AC, cum sit DB partium 18, erit earumdem 25+16/35, et DI, <lb></lb>dimidium ipsius DF, erit 12+51/70. Sed IK 9, ad EH 7+7/11, est ut DI <lb></lb>12+51/70 ad DE, quae invenitur partium earumdem 10+4/5, et DB in­<lb></lb>venta est earumdem partium 18; ergo radius BD, ad distantiam DE a cen­<lb></lb>tro quadrantis ad eius centrum gravitatis, est ut 18 ad 10+4/5, vel at 90 <lb></lb>ad 54, vel ut 10 ad 6, vel ut 5 ad 3, quod erat primo demonstrandum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Cum sit arcus ABC quadrantis, ad 2/3 chordae AC, ut <lb></lb>BD ad DE, quod E sit centrum gravitatis quadrantis, vel ut 5 ad 3, ex modo <lb></lb>assertis, vel ut 10 ad 6; erit idem arcus ad totam chordam ut 10 ad 9. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollarium.<emph.end type="italics"></emph.end> — Hinc, sumptis quadruplis, perimeter circuli, ad pe­<lb></lb>rimetrum quadrati inscripti, est proxime ut 90 ad 36, vel ut 10 ad 9 ” (ibid., <lb></lb>T. XCII, fol. </s>

<s>21). </s></p><p type="main">

<s>“ Quod vero ad secundum, hoc in theoremate propositum, cylindrus a <pb xlink:href="020/01/2873.jpg" pagenum="498"></pb>quadrato AC revoluto circa AD, ad rotundum a trilineo ABCF circa AD, est, <lb></lb>ex eadem Centrobaryca, in ratione composita quadrati AC ad trilineum ABCF, <lb></lb>hoc est in ratione 14 ad 3 proxime, vel 42 ad 9, et ex ratione distantiae IK <lb></lb>ad distantiam GL eorum centrorum gravitatis I, G ab axe AD. </s>

<s>Sed cylin­<lb></lb>drus ad rotundum est ut 3 ad 1, vel ut 42 ad 14; ergo 42 ad 14 rationem <lb></lb>habet compositam ex ratione 42 ad 9, et ex ratione earumdem distantiarum <lb></lb>IK, GL. </s>

<s>Sed 42 ad 14 habet queque rationem compositam ex 42 ad 9, et <lb></lb>ex 9 ad 14, et ex his prima ratio est ea, quae inter quadratum et trilineum; <lb></lb>ergo secunda ratio inter 9 et 14 erit ratio distantiarum IK, GL. </s>

<s>Sed IK in­<lb></lb>venta est partium 9, qualium DB erit 18; ergo GL est earumdem 14. Sed <lb></lb>IK ad GL est ut DI ad DG, ergo etiam DI ad DG est ut 9 ad 14. Sed DI <lb></lb>inventa est earumdem partium 12+51/70, si fiat ergo ut 9 ad 14, ita 12+51/70 <lb></lb>ad aliam, quae est 19+4/5 totidem partium, erit ipsa DG, ad quam radius <lb></lb>DB erit ut 18 ad 19+4/5, vel ut 90 ad 99, vel ut 10 ad 11, quod erat se­<lb></lb>cundo ostendendum ” (ibid., fol. </s>

<s>18). </s></p><p type="main">

<s>“ PROPOSITIO V. — <emph type="italics"></emph>Centrum gravitatis G, in eadem figura, trilinei <lb></lb>ABCF sic dividit rectam FD iungentem eius verticem F, et centrum D <lb></lb>sui arcus ABC, ut tota FD ad DG sit quam proxime ut 9 ad 7. — In­<lb></lb>super ipsum centrum gravitatis G trilinei AGCF sic dividit eius axem <lb></lb>FD, ut pars FG ad F, ad partem GB ad B, sit quam proxime ut 22 <lb></lb>ad 7, vel ut circuli periferia ad diametrum. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Et primo, cum sit IK 9 et GL 14, sitque DI 12+51/70, cumque ut <lb></lb>IK ad GL ita sit DI ad DG; erit DG 19+28/35. Sed tota DF est 25+16/35, <lb></lb>ergo DF ad DG erit ut 25+16/35 ad 19+28/35, vel ut 891 ad 693, vel ut <lb></lb>99 ad 77, vel ut 9 ad 7. Et convertendo, DG, ad DF ut 7 ad 9, quocirca <lb></lb>centrum gravitatis trilinei ABCF distat a centro D sui ipsius per distantiam <lb></lb>DG, ad quam tota diameter FD quadrati circumscripti proprio quadranti sit <lb></lb>quam proxime ut 9 ad 7. ” </s></p><p type="main">

<s>“ Secundo, cumque DB ad DG sit quam proxime ut 10 ad 11, et DG <lb></lb>ad DF, ex nuper ostensis, quam proxime ut 7 ad 9, vel ut 11 ad 14+1/7; <lb></lb>tres DB, DG, DF erunt ut 10, 11, 14+1/7, vel ut 70, 77, 99. Quare ipsa­<lb></lb>rum differentiae BG, GF erunt ut hi numeri 7, 22, adeoque centrum gra­<lb></lb>vitatis G trilinei ABCF secat sic eius axem FB, ut pars ad F, ad partem <lb></lb>ad B, sit quam proxime ut 22 ad 7, vel ut circuli periferia ad suam dia­<lb></lb>metrum. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Propterea cum qualium partium DB ponitur 10, ta­<lb></lb>lium DE sit quam proxime 6, et DI 7+1/14, et DB 10, et DG 11, et DF <lb></lb>14+2/14; ipsae DE, DI, DB, DG, DF erunt ut hi numeri 84, 99, 140, <lb></lb>154, 198. Et, cum DE, DB, DG sint ut 84, 140, 154, in minimis terminis <lb></lb>essent ut 6, 10, 11 ” (ibid., fol. </s>

<s>19). </s></p><p type="main">

<s>Termineremo questo breve ordine di proposizioni baricentriche con una <lb></lb>relativa alla Cicloide, e che senza dubbio è posteriore al trattato wallisiano <lb></lb><emph type="italics"></emph>De centro gravitatis,<emph.end type="italics"></emph.end> supponendovisi la rettificazion della curva, pubblicata <lb></lb>quivi dal Matematico inglese nella seconda parte della proposizione XXII, <pb xlink:href="020/01/2874.jpg" pagenum="499"></pb>benchè il Roberval, come si vide, l&#039;avesse dimostrata assai prima. </s>

<s>Vi si sup­<lb></lb>pone altresì noto il centro di gravità della linea semicicloidale: ma nè lo <lb></lb>stesso Pascal sdegnerebbe di vedere aggiunto alla sua ricca e pellegrina co­<lb></lb>rona di teoremi questo fiore elegante, colto nella medesima aiola dal nostro <lb></lb>Viviani. </s></p><p type="main">

<s>“ PROPOSITIO VI. — <emph type="italics"></emph>Esto ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>314) <emph type="italics"></emph>Cyclois primaria, cuius dia­<lb></lb>meter BD, sitque rectangulum BDAE, et curvae AIB sit centrum G, a <lb></lb>quo demittatur GF perpendicularis super BD, sumaturque HF aequalis<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2874.1.jpg" xlink:href="020/01/2874/1.jpg"></figure></s></p><p type="caption">

<s>Figura 314.<lb></lb><emph type="italics"></emph>dimidio AD, et fiat revo­<lb></lb>lutio circa BD: cylindrica <lb></lb>superficies ab AE, ad ro­<lb></lb>tundam semicycloidis AIB, <lb></lb>est ut FH ad FG distan­<lb></lb>tia centri gravitatis arcus <lb></lb>AIB ab axe BD. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Nam, sumpta rotunda <lb></lb>a recta AE, ad rotundam AIB, esse in ratione composita rectae AE ad cur­<lb></lb>vam AIB, sive 1 ad 2, sive FH ad AD, et ex distantia AD centri gravitatis <lb></lb>AE a BD, ad FG distantiam centri gravitatis curvae AIB: hae rationes con­<lb></lb>ficiunt rationem rectae FH ad FG, quod erat demonstrandum ” (ibid., fol. </s>

<s>32). </s></p><p type="main">

<s>Nè a queste sole eleganze s&#039;arrestano le ricerche intorno ai centri di <lb></lb>gravità, fatte dal Viviani, le quali si estesero all&#039;emiperboloide, alla lunula, <lb></lb>e ad altre figure, rimaste inscritte ne&#039;cerchi; come furono altresì frutto degli <lb></lb>infaticabili studii di lui que&#039;teoremi, che si dimostrano intorno a questo <lb></lb>stesso argomento in varii fogli, rilegati insieme nel volume manoscritto, che <lb></lb>è il CIX dei Discepoli di Galileo. </s>

<s>Anzi in tutti gli altri nove, che vanno sotto <lb></lb>il titolo di <emph type="italics"></emph>Meccanica dei solidi,<emph.end type="italics"></emph.end> sarebbero da raccogliere documenti di non <lb></lb>poca importanza. </s>

<s>Nel CVI, per esempio, varii assiomi, con proposizioni e co­<lb></lb>rollari, intorno alle forze de&#039;pesi sostenuti da corde; nel CVIII, un tratta­<lb></lb>tello intorno all&#039;arte dei pesi nella stadera; e per tutti i volumi sparsi teo­<lb></lb>remi, dimostrativi delle proporzioni, secondo le quali si velocitano i gravi <lb></lb>discendenti per i piani inclinati, ordinati per verità a illustrare, piuttosto che <lb></lb>a promovere la scienza di Galileo o del Torricelli. </s>

<s>E tra per questa ragione, <lb></lb>e per essere condotte le dimostrazioni per le solite vie oblique, senza far uso <lb></lb>cioè del principio della composizion delle forze, abbiamo creduto dover ba­<lb></lb>stare questo cenno, affinchè possano dalla Storia i nostri Lettori far più giu­<lb></lb>sto giudizio dell&#039;opera, data, in coltivar la Meccanica, dal Viviani. </s></p><pb xlink:href="020/01/2875.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dei Matematici stranieri <lb></lb>principali promotori della Scienza del moto<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Degli otto libri della Statica del Roberval, e come il Wallis e il Mariotte confermarono la Dina­<lb></lb>mica galileiana, che l&#039;Huyghens coronò di nuovi teoremi. </s>

<s>— IL Delle proprietà meccaniche della <lb></lb>Cicloide. </s>

<s>— III. </s>

<s>De centri delle percosse e delle oscillazioni. </s>

<s>— IV. </s>

<s>Delle forze centrifughe. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>S&#039;è narrato fin qui quale e quanta si fosse la cultura della Scienza del <lb></lb>moto in Italia, dove Galileo, con l&#039;insegnamento orale e co&#039;libri, s&#039;era fatto <lb></lb>maestro. </s>

<s>Ne giunse la fama anche appresso gli stranieri, ne&#039;quali parve na­<lb></lb>scere allora un gran fervore di applicarsi a quei medesimi studii, particolar­<lb></lb>mente in Francia, dove fiorivano più che altrove gl&#039;ingegni. </s>

<s>Le dottrine ga­<lb></lb>lileiane, raccomandate là dal Peiresc, dal Carcavy, e dal Beaugrand, in tutti e <lb></lb>tre i quali, dalla probità della vita, e dalla dignità del grado si rendeva più <lb></lb>autorevole la Scienza; furono accolte in modi e con effetti sì varii, che vo­<lb></lb>gliono essere principalmente notati. </s></p><p type="main">

<s>Per alcuni, e furono de&#039;primi, rassomigliasi l&#039;accoglienza a quella di un <lb></lb>ospite illustre, a cui non s&#039;attende che a fare onore, e si vuol che tutti gli <lb></lb>altri di casa facciano il somigliante, aspramente garrendo coloro, che osas­<lb></lb>sero di contradire. </s>

<s>Tale immagine sembra a noi rendersi dal Gassendo, la <lb></lb>Meccanica del quale è unicamente istituita a confermare le dottrine galile­<lb></lb>iane, sia co&#039;ragionamenti, sia con l&#039;esperienze. </s>

<s>Abbiamo avuto più volte oc­<lb></lb>casione di citar di lui l&#039;epistole contro Pietro Cazr <emph type="italics"></emph>De proportione, qua<emph.end type="italics"></emph.end><pb xlink:href="020/01/2876.jpg" pagenum="501"></pb><emph type="italics"></emph>gravia decidentia accelerantur,<emph.end type="italics"></emph.end> scritte per confermar che quella proporzione, <lb></lb>con cui crescono gli spazi, è veramente secondo i quadrati, come Galileo di­<lb></lb>ceva, e non secondo i semplici tempi, come presumevasi dal Gesuita. </s></p><p type="main">

<s>Il contradittore, che voleva il Gassendo così confutare, insorse da poi <lb></lb>che la legge, annunziata ne&#039;primi dialoghi del Mondo, venne a esplicarsi e <lb></lb>a dimostrarsi matematicamente ne&#039;secondi dialoghi del Moto, ma intanto che <lb></lb>aspettavasi la pubblicazione di questo libro s&#039;apprendevano dall&#039;altro, che <lb></lb>l&#039;aveva preceduto, le principali nozioni di Dinamica nuova. </s>

<s>Le verità però <lb></lb>si proponevan quivi semplicemente senza dimostrazione: erano conclusioni <lb></lb>delle quali i principii, per lo più, rimanevano occulti, e invogliavano gli stu­<lb></lb>diosi a mettersi per sè stessi a ritrovarli. </s>

<s>Quanto giovasse una tale palestra, <lb></lb>in esercitare gl&#039;ingegni, si può facilmente immaginare, anche senza i fatti <lb></lb>narrati: poi, venendosi a leggere in pubblico le Due Scienze nuove, parve <lb></lb>facesse Galileo quel che fa il Maestro, quando mette a cimento col proporre <lb></lb>una tesi agli scolari, i quali, riscontrando le proprie con le dimostrazioni di <lb></lb>lui, son lieti o d&#039;aver colto nel vero, o di vedersi aperti gli occhi a ricono­<lb></lb>scere il falso. </s></p><p type="main">

<s>Una particolar dottrina però avvertì il Gassendo che rimaneva nei nuovi <lb></lb>Dialoghi dimenticata così, da desiderarsi di udire ancora il Salviati dispu­<lb></lb>tare intorno al farsi tutti i nostri moti, sul veicolo in cui sediamo, sempre <lb></lb>allo stesso modo, o egli corra velocissimamente, o stia fermo. </s>

<s>Così fatta di­<lb></lb>menticanza, comunque sia, non fu volontaria, ma suggerita dal giudizio, non <lb></lb>potendosi quel che si dice nella seconda Giornata dei Due massimi sistemi <lb></lb>intorno ai proietti conferire con i teoremi, nel quarto dialogo delle nuove <lb></lb>Scienze poi dimostrati. </s>

<s>Nella detta Giornata infatti si discorre a lungo del <lb></lb>moto impresso dal motore, concludendovisi che la palla, tirata con direzione <lb></lb>perpendicolare, torna in giù alla bocca del cannone, o stia egli fermo o sia <lb></lb>con qualunque velocità tirato sopra una carretta. </s>

<s>Il fatto era in sè notissimo <lb></lb>anche ai fanciulli, i quali, correndo per via, si gettan sulla testa un pomo, <lb></lb>che ritorna a loro in giù nella mano: ma la scienza del fatto dipendeva dalla <lb></lb>composizion di due moti, dai quali non seppe Galileo altro dedurre se non <lb></lb>che il pomo non rimane indietro, correndo il fanciullo, perchè, sebbene sem­<lb></lb>bri che esso pomo vada e venga nel perpendicolo, ei propriamente descrive <lb></lb>in aria una linea <emph type="italics"></emph>trasversale.<emph.end type="italics"></emph.end> Forse il Gassendo non penetrò più addentro, <lb></lb>e quella linea trasversale benignamente interpetrò per una parabola. </s>

<s>Ma che <lb></lb>parabola fosse restava a dimostrarsi, ed è ciò ch&#039;egli intese di fare in quelle <lb></lb>sue epistole <emph type="italics"></emph>De motu impresso a motore translato.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ipse recensui obiter (scriveva l&#039;Autore nell&#039;Epistola prima, dopo po­<lb></lb>che parole d&#039;introduzione) tum observata propria, tum quae Galileus con­<lb></lb>gessit adstruendo illi theoremati: <emph type="italics"></emph>Si id corpus, cui insistimus, transferatur; <lb></lb>omnes nostros motus, rerumque a nobis mobilium, perinde fieri appare­<lb></lb>reque, ac si illud quiesceret.....<emph.end type="italics"></emph.end> Experimentum vero facillimum est ut dum <lb></lb>deambulabis pilam lusoriam, aliumve globum manu tenens, remque explo­<lb></lb>res ” (Opusc. </s>

<s>philos., Florentiae 1727, pag. </s>

<s>436). Più mirabile e più diffi-<pb xlink:href="020/01/2877.jpg" pagenum="502"></pb>cile a intendere ti sembrerà, soggiunge a Pietro Puteano, ciò che avviene, <lb></lb>quando tu, correndo velocemente sopra un cavallo, apri la mano, in cui te­<lb></lb>nevi una palla, la quale tu vedi cadere a perpendicolo sotto la sella, benchè <lb></lb>avesse cominciato a moversi in giù tanto di più lontano. </s>

<s>Ella dunque t&#039;ha <lb></lb>seguito in tutto il cammino, inflettendosi per una linea che, se avesse la­<lb></lb>sciata di sè visibile traccia per l&#039;aria, troveresti essere la trasversale non <lb></lb>retta ma curva. </s>

<s>“ Causa vero cur motus pilae a rectitudine deflectatur, et <lb></lb>curvam sequatur describatque lineam, illius compositio est, quatenus ex du­<lb></lb>plici vi motrice originem habet ” (ibid., pag. </s>

<s>438), e da questa duplice virtù <lb></lb>motrice dimostra resultarne una semiparabola. </s></p><p type="main">

<s>Per l&#039;amore, con cui il Gassendo accolse, commentò e diffuse le dot­<lb></lb>trine di Galileo, si meritò la riconoscenza dei Discepoli, i quali più volte <lb></lb>commemorarono solennemente il Filosofo francese nella loro Accademia fio­<lb></lb>rentina. </s>

<s>E quasi, per far eco alle applaudite epistole <emph type="italics"></emph>De motu impresso,<emph.end type="italics"></emph.end><lb></lb>instituirono e descrissero nel loro libro dei <emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> quelle esperienze, in con­<lb></lb>fermazione di quel che asserisce in più luoghi il medesimo Galileo “ che la <lb></lb>virtù impressa ne&#039;proietti, per novella direzione di moto, non si distrugge ” <lb></lb>(Firenze 1841, pag. </s>

<s>163). </s></p><p type="main">

<s>Ci furono però in Francia, insieme col Gassendo, altri, che delle dot­<lb></lb>trine, insegnate ne&#039;dialoghi dei due Massimi sistemi intorno alle proprietà <lb></lb>del moto, si fecero acuti e liberi censori. </s>

<s>A un geometra così profondo, come <lb></lb>era il Fermat, non sfuggì quello, in cui era trascorso Galileo, quando asse­<lb></lb>gnò l&#039;orbita circolare al sasso cadente dall&#039;alto di una torre, movendosi in <lb></lb>giro la Terra, e dette al Carcavy, perchè la mandasse a leggere allo stesso <lb></lb>Galileo, la dimostrazione che la detta orbita, nel medesimo supposto, doveva <lb></lb>rassomigliarsi invece a una spirale. </s>

<s>Consapevole di tutto ciò era il Mersenno, <lb></lb>quel buon padre, disse il Dati, atto meglio a raccogliere e a promovere le <lb></lb>altrui invenzioni, che a mettere in luce le proprie “ facendo come quei mer­<lb></lb>catanti che, per iscarsezza di loro avere, malamente potendo far negozi, sfo­<lb></lb>gano il genio loro guadagnando pure assai nel contrattare, e mettere in ven­<lb></lb>dita le merci altrui ” (Lettera a&#039;Filaleti cit., pag. </s>

<s>6). Si potrebbe anche bene <lb></lb>rassomigliare a quell&#039;aure instabili, o a quegl&#039;insetti faccendieri, che traspor­<lb></lb>tano il polline per fecondarne qua e là gli aperti fiori; il qual ufficio e il <lb></lb>qual genio mostrò il Padre di averlo veramente esercitato e portato in tutti <lb></lb>i libri che scrisse, incominciando dai primi, ch&#039;egli fuse poi in quel volu­<lb></lb>mone in foglio, intitolato <emph type="italics"></emph>De la nature des sons, des mouvemens, et de <lb></lb>leurs proprietez,<emph.end type="italics"></emph.end> stampato a Parigi nel 1635. Fu qui che, negoziando la <lb></lb>scrittura fatta dal Fermat sopra la linea, che descrive il cadente, cavando la <lb></lb>dimostrazione dallo scrigno privato, per metterla in pubblico corso; esaminò <lb></lb>prima il Mersenno, nella III proposizione del secondo suo libro, quel che <lb></lb>Galileo dice del peso, che scendendo dall&#039;alto di una torre giungerebbe a <lb></lb>toccare il centro terrestre, passando per una mezza circonferenza, e poi sog­<lb></lb>giunse immediatamente una proposizione così formulata: “ Monstrer qu&#039;il <lb></lb>est impossible que les corps pesans, descendans iusques au centre de la <pb xlink:href="020/01/2878.jpg" pagenum="503"></pb>Terre, descrivent le demicercle precedant, et donner la ligne, par la quelle <lb></lb>ils descendroient si la Terre tournoit en 24 heures auteur de son assieu ” <lb></lb>(pag. </s>

<s>96). </s></p><p type="main">

<s>Ma la linea descritta dai cadenti si riduceva a una speculazione geome­<lb></lb>trica, che aveva il suo fondamento nella composizione dei moti, per cui non <lb></lb>fa maraviglia che avesse intorno ad essa fallato quel Galileo, dal quale erasi <lb></lb>data la sentenza non si poter comporre di due moti retti un moto circolare <lb></lb>(Alb. </s>

<s>I, 446). Le nuove cose di Meccanica però, che si proponevano ne&#039;dia­<lb></lb>loghi dei Due massimi sistemi, non tutte erano di questa natura: vi si de­<lb></lb>finiva per esempio il tempo, che impiega un grave a passare lo spazio di <lb></lb>cento braccia; la proporzion dei momenti de&#039;mobili lungo i piani più o meno <lb></lb>inclinati; l&#039;equidiuturnità de&#039;pendoli di varia mole, per qualunque ampiezza <lb></lb>d&#039;arco oscillanti, e simili altre cose, la verità delle quali si pretendeva, non <lb></lb>senza ragione, che dovess&#039;essere confermata dall&#039;esperienza. </s>

<s>Ora parve a quei <lb></lb>censori Parigini che troppo confidentemente avesse Galileo asserite le sue <lb></lb>proposizioni, le quali perciò messero in dubbio, avendole trovate, non sola­<lb></lb>mente non riscontrare, ma spesso contradire ai fatti osservati. </s>

<s>Il Mersenno, <lb></lb>alla proposizione VII del secondo libro citato, scritta per dimostrare il mo­<lb></lb>mento dei pesi lungo i piani inclinati, e per determinare se il cadente passa, <lb></lb>come diceva Galileo, per tutti gl&#039;infiniti gradi di tardità; aggiunse un tal <lb></lb>corollario: </s></p><p type="main">

<s>“ Je doute que le sieur Galilee ayt fait les experiences des cheutes sur <lb></lb>le plan, puis qu&#039;il n&#039;en parle nullement, et que la proportion qui donne con­<lb></lb>tradit souvent l&#039;experience: et desire que plusieurs esprouvent la mesme <lb></lb>chose sur des plans differens avec toutes les precautions, dont ils pourront <lb></lb>s&#039;aviser, afin qu&#039;ils voyent si leurs experiences respondront aux nostres, et <lb></lb>si l&#039;on en pourra tirer assez de lumiere pour faire un theorema en faveur <lb></lb>de la vitesse de ces cheutes obliques, dont les vitesses pourroient estre me­<lb></lb>surees par les differens effets du poids, qui frappera dautant plus fort que <lb></lb>le plan sera moins incliné sur l&#039;horizon, et qu&#039;il approchera davantage de la <lb></lb>ligne perpendiculaire ” (ivi, pag. </s>

<s>112). </s></p><p type="main">

<s>Le censure del Mersenno potevano approvarsi per quel che riguarda il <lb></lb>tempo speso dal cadente a passare le cento braccia, o l&#039;isocronismo dei pen­<lb></lb>doli, qualunque fosse l&#039;ampiezza dell&#039;arco descritto dalle loro vibrazioni. </s>

<s>Ma <lb></lb>rispetto alla proporzion dei momenti, con cui scendono i gravi lungo i piani <lb></lb>inclinati, non potevano l&#039;esperienze infirmare la verità dei teoremi galileiani, <lb></lb>avendo supposto l&#039;Autore che venisse dal mobile rimosso tutto ciò che, per <lb></lb>via dell&#039;attrito dell&#039;aria, o di qualsivoglia altro accidente ne impedisce la li­<lb></lb>bera caduta. </s>

<s>Di qui è che, sembrando impossibile sperimentare nel vuoto, e <lb></lb>senza che dal grave si tocchi, almeno in alcuni punti, il piano soggetto, si <lb></lb>vede la necessità del non corrispondere esattamente alle leggi inatematiche <lb></lb>i fatti osservati. </s>

<s>Presto per tal rispetto cessarono i dubbi, ma intanto le li­<lb></lb>bere censure del Mersenno, dop&#039;aver tolta agl&#039;insegnamenti di Galileo quella <lb></lb>fedeltà di ossequio, con cui gli aveva accolti il Gassendo, suscitarono nel-<pb xlink:href="020/01/2879.jpg" pagenum="504"></pb>l&#039;animo dei Matematici parigini un baldanzoso spirito di emulazione. </s>

<s>Non <lb></lb>sappiamo per verità con qual coscienza il Cartesio potesse dir sua la sco­<lb></lb>perta delle leggi, con cui si accelerano i gravi, e suoi, nella Dinamica nuo­<lb></lb>vamente instituita in Italia, tanti altri teoremi: ma, mentre tutto il mondo <lb></lb>applaudiva all&#039;opera del nostro Italiano, consentendogli volentieri che le due <lb></lb>Scienze ivi istituite fossero propriamente nuove; non si può non ascoltare <lb></lb>con maraviglia il Roberval vantarsi di queste cose col Torricelli: “ At Me­<lb></lb>chanicam a fundamentis ad fastigium novam extruximus, reiectis omnibus, <lb></lb>praeter paucos admodum, antiquis lapidibus, quibus illa constahat ” (Ouvr. </s>

<s>cit., <lb></lb>pag. </s>

<s>396). E soggiunge di non ammettere nessun nuovo postulato, come fa <lb></lb>Galileo, e come fai tu. </s>

<s>“ Vir clarissime, qui propositione prima libri primi <lb></lb><emph type="italics"></emph>De motu gravium descendentium<emph.end type="italics"></emph.end> ad id demonstrandum novo postulato usus <lb></lb>es, quod quivis non facile concesserit, quia pondera, quae proponis, non libra <lb></lb>rigida et recta, ut fieri solet, sed fune molli ac perfecte plicabili invicem alli­<lb></lb>gantur. </s>

<s>Nos autem ad hoc libra utimur modo usitato disposita, cuius bene­<lb></lb>ficio propositionem illam non aliter demonstramus, quam aut vectem aut <lb></lb>axem in peritrochio. </s>

<s>Eam autem iam ante quindecim annos invenimus, atque <lb></lb>anno 1636, tamquam Mechanicae nostrae prodromum, praelo commisimus <lb></lb>atque vulgavimus, sed gallico idiomate ” (ibid., pag. </s>

<s>397). La notizia è tale, <lb></lb>da non si passar per noi senza un breve esame questa nuova Meccanica ro­<lb></lb>bervalliana condotta come si dice dai fondamenti al suo più alto fastigio, <lb></lb>senza che da Galileo o da nessun altro degli antichi sia stato preso per l&#039;edi­<lb></lb>fizio altro che qualche pietra. </s></p><p type="main">

<s>È divisa l&#039;opera in otto libri, in ciascuno de&#039;quali dice il Roberval esser <lb></lb>questi i soggetti via via trattati: I. </s>

<s>Se si dia un centro delle virtù potenziali <lb></lb>in universale. </s>

<s>II. </s>

<s>Della Libbra, e degli Equiponderanti. </s>

<s>III. </s>

<s>Dei centri di gra­<lb></lb>vità dellè varie figure. </s>

<s>IV. </s>

<s>Di alcune mirabili proprietà delle forze applicate <lb></lb>alle funi. </s>

<s>V. </s>

<s>Delle macchine, e degli strumenti. </s>

<s>VI. </s>

<s>Delle potenze, che agi­<lb></lb>scono in vari mezzi. </s>

<s>VII. </s>

<s>Dei moti composti. </s>

<s>VIII. </s>

<s>Dei centri delle percosse. </s></p><p type="main">

<s>Per dar di queste cose al Torricelli qualche saggio, sceglieva il Rober­<lb></lb>val dal quarto libro alcuni teoremi, fra&#039;quali quello della fune tesa, che gra­<lb></lb>vata nel mezzo da un peso anche piccolissimo o s&#039;inflette o si rompe, senza <lb></lb>che sia possibile a qualunque gran forza ridurla mai in dirittura. </s>

<s>Nè temeva <lb></lb>gli rinfacciasse il Torricelli che la questione era già trattata da Galileo, <lb></lb>avendo pronta la risposta col dire ch&#039;essendo il problema, infine al quarto <lb></lb>dialogo delle nuove Scienze, mal risoluto, egli era propriamente il primo, che <lb></lb>ne avesse data la risoluzion vera, applicandovi il principio dei moti compo­<lb></lb>sti. </s>

<s>Ma due altri teoremi soggiungeva lo stesso Roberval, per confermare che <lb></lb>veramente maravigliosa era questa nuova meccanica delle funi. </s>

<s>Il primo si <lb></lb>annunziava in questa maniera: “ Si tres potentiae, totidem funibus, ad com­<lb></lb>munem nodum religatis, agentes (nodus est quodvis punctum in fune) aequi­<lb></lb>librium constituant; tunc describi poterit triangulum, cuius centrum gravitatis <lb></lb>sit nodus ipse, tres autem anguli ad tria funium puncta alicubi terminentur <lb></lb>(infinita quidem describerentur triangula sed omnia similia): erunt autem <pb xlink:href="020/01/2880.jpg" pagenum="505"></pb>tunc tres potentiae in eadem ratione cum tribus rectis a centro trianguli ad <lb></lb>tres angulos terminatis, ita ut quaelibet potentia homologa sit ei rectae, quae <lb></lb>in fune ipsius existit ” (ibid). </s></p><p type="main">

<s>L&#039;elegantissimo teorema si può, più semplicemente, proporre sotto quest&#039;al­<lb></lb>tra forma: Sia nel triangolo ABC (fig. </s>

<s>315) il centro di gravità F, da cui si <lb></lb><figure id="id.020.01.2880.1.jpg" xlink:href="020/01/2880/1.jpg"></figure></s></p><p type="caption">

<s>Figura 315.<lb></lb>conducano le AF, FC, FB ai tre vertici. </s>

<s>Se queste tre <lb></lb>linee rappresentano tre funi annodate in F, e si supponga <lb></lb>che vengano ciascuna tirate da forze proporzionali alle <lb></lb>lunghezze, il nodo rimarrà in equilibrio. </s>

<s>Costruito infatti <lb></lb>il parallelogrammo BFCD, la diagonale di lui FD è la <lb></lb>resultante delle forze BF, FC, che tirano in giù, ed è <lb></lb>manifestamente essa diagonale in dirittura, contrapposta, <lb></lb>e uguale alla AF, essendo ambedue doppie della EF. </s>

<s>Se <lb></lb>ai lati AB, AC, CB si conducano esternamente o inter­<lb></lb>namente, a qual si voglia distanza, e quanti più piaccia <lb></lb>lati paralleli; gl&#039;infiniti triangoli, che ne nascono, son tutti simili, e perciò le <lb></lb>distanze dal comun centro di gravità ai respettivi vertici tutte proporzionali. </s></p><p type="main">

<s>L&#039;altro teorema analogo così dal Roberval si proponeva: “ Si quatuor <lb></lb>potentiae, non existentes in eodem plano, totidem funibus ad communem <lb></lb><figure id="id.020.01.2880.2.jpg" xlink:href="020/01/2880/2.jpg"></figure></s></p><p type="caption">

<s>Figura 316.<lb></lb>nodum religatis agentes, aequilibrium consti­<lb></lb>tuant; tunc quod supra de triangulo dictum est de <lb></lb>quadam pyramide tetragona verum erit ” (ibid.). </s></p><p type="main">

<s>Sia ABCD (fig. </s>

<s>316) la piramide tetragona, <lb></lb>col vertice in A, e avente per base il triangolo <lb></lb>BDC, col centro di gravità in E. </s>

<s>Congiunta la <lb></lb>AE, la quale sia segata in F talmente, che AF <lb></lb>riesca tripla di FE, sarà in F il centro di gra­<lb></lb>vità della piramide. </s>

<s>Se ora, come ad A la AF, <lb></lb>si conducano dal medesimo punto F agli altri <lb></lb>tre vertici in basso le FD, FB, FC, e s&#039;intenda <lb></lb>esser queste altrettante funi applicate a tirare <lb></lb>il nodo F, con forze proporzionali alle rispettive <lb></lb>lunghezze; dice il Roberval che le forze traenti <lb></lb>in basso equivalgono a quell&#039;unica AF, che tira <lb></lb>in alto, per cui il nodo F starà fermo. </s></p><p type="main">

<s>Che sia vera l&#039;asserita uguaglianza tra le <lb></lb>forze opposte, si dimostra assai facilmente, com­<lb></lb>ponendo le BF, FC nella FG, e questa con la <lb></lb>DF nella FH, costruendo il parallelogrammo DG, <lb></lb>di cui essa FH sarà diagonale, che procederà <lb></lb>nella medesima dirittura con la AF, e sarà la resultante unica delle tre <lb></lb>forze inferiori. </s>

<s>Che poi questa resultante sia uguale ad AF, per cui le due <lb></lb>forze, tirando contrariamente, deve il nodo F permanere nell&#039;equilibrio, <lb></lb>consegue dalla similitudine dei triangoli DEH, FEI i quali danno la pro-<pb xlink:href="020/01/2881.jpg" pagenum="506"></pb>porzione DE:EI=EH:EF. </s>

<s>Ma DE è doppia di EI, dunque anche EH è <lb></lb>doppia di EF, della quale essendo FH e AF ambedue triple, saranno dunque <lb></lb>queste due linee, o le due forze che rappresentano, fra loro uguali. </s></p><p type="main">

<s>Tali erano le eleganze, che il Roberval dava al Torricelli, per saggio del <lb></lb>IV libro della sua Meccanica. </s>

<s>Dal V poi sceglieva la dimostrazione di un tal <lb></lb>paradosso: se un corpo A (fig. </s>

<s>317) sia dal piano BC premuto con quanta <lb></lb><figure id="id.020.01.2881.1.jpg" xlink:href="020/01/2881/1.jpg"></figure></s></p><p type="caption">

<s>Figura 317.<lb></lb>forza si voglia sul piano inclinato DE, e i due piani si <lb></lb>suppongano perfettamente rigidi e fra sè paralleli, il <lb></lb>detto corpo interposto scenderà in ogni modo lungo il <lb></lb>declivio DE, se da qualche forza straniera non vi sia <lb></lb>ritenuto. </s>

<s>Altra cosa di minor curiosità, ma di maggiore <lb></lb>importanza, faceva il Roberval notare in questo suo <lb></lb>libro, ed era che, nel trattar de&#039;gravi scendenti lungo <lb></lb>i piani inclinati, “ non tantum casum consideravimus, <lb></lb>qui solus ab omnibus attenditur, cum scilicet potentia pondus in plano in­<lb></lb>clinato positum retinens, agit per lineam directionis ipsi plano parallelam, <lb></lb>sed et dum eadem linea directionis aliam quamcumque positionem obtinue­<lb></lb>rit, quo pacto ratio ponderis ad potentiam infinite mutatur ” (Ouvrag. </s>

<s>cit., <lb></lb>pag. </s>

<s>397). </s></p><p type="main">

<s>Sia sul piano inclinato AC (fig. </s>

<s>318) posto il peso D; tutti i Matema­<lb></lb>tici, dice il Roberval, dimostrano che questo sta al suo contrappeso come <lb></lb><figure id="id.020.01.2881.2.jpg" xlink:href="020/01/2881/2.jpg"></figure></s></p><p type="caption">

<s>Figura 318.<lb></lb>AC, lunghezza dello stesso piano, <lb></lb>sta all&#039;AB sua elevazione, tacita­<lb></lb>mente supponendo che le forze <lb></lb>agiscano in direzioni parallele alle <lb></lb>due dette linee. </s>

<s>Supponiamo invece <lb></lb>che il peso venga sostenuto, con <lb></lb>direzione diversa, dalla fune DE, la <lb></lb>quale sia presa lunga quanto AC: <lb></lb>non sarà mica vero che si possa <lb></lb>come dianzi con questa lunghezza <lb></lb>misurare la forza, ma sarà tanto <lb></lb>diversa, soggiungeva lo stesso Ro­<lb></lb>berval, quanto ED diagonale del <lb></lb>parallelogrammo è diversa da DG <lb></lb>lato di lui, condotto parallelamente <lb></lb>all&#039;inclinazione del piano. </s></p><p type="main">

<s>Con simil ragione, proseguiva a dire l&#039;Autore di questa meccanica nuova, <lb></lb>diversifica la cosa se il contrappeso F, invece di tirare verticalmente in di­<lb></lb>rezione parallela ad AB, come tutti suppongono, tiri obliquamente secondo <lb></lb>IH, perch&#039;essendo in quel primo caso rappresentata la forza da IK uguale <lb></lb>ad AB, dovrà èsser nell&#039;altro rappresentata da una linea tanto maggiore, <lb></lb>quanto la diagonale IH è maggiore del lato IK del parallelogrammo, con le <lb></lb>solite regole costruito. </s></p><pb xlink:href="020/01/2882.jpg" pagenum="507"></pb><p type="main">

<s>Se avesse il Roberval ragione di credersi primo autore di questa novità <lb></lb>introdotta nella Statica del piano inclinato, lo vedremo nel capitolo appresso. </s>

<s><lb></lb>Ma di fatto egli riaccendeva la face di quella tradizione, che parve essersi <lb></lb><figure id="id.020.01.2882.1.jpg" xlink:href="020/01/2882/1.jpg"></figure></s></p><p type="caption">

<s>Figura 319.<lb></lb>spenta nella memoria de&#039;suoi contemporanei, e de&#039;loro <lb></lb>discepoli più immediati. </s>

<s>Nel qual proposito ci oc­<lb></lb>corre a notare la proposizione LXIII della prima <lb></lb>parte <emph type="italics"></emph>De motu animalium,<emph.end type="italics"></emph.end> dove, considerandosi dal <lb></lb>Borelli le condizioni dell&#039;equilibrio tra le potenze <lb></lb>T ed R (fig. </s>

<s>319), tendenti obliquamente la fune <lb></lb>DE, ne conclude dover essere le due dette potenze <lb></lb>uguali. </s>

<s>Ma non aveva pronunziata la conclusione, <lb></lb>che soggiunge un lungo scolio, per avvertire i lettori <lb></lb>che il suo teorema non contradice all&#039;altro <emph type="italics"></emph>ab <lb></lb>omnibus receptum<emph.end type="italics"></emph.end> (Romae 1880, pag. </s>

<s>120), e se­<lb></lb>condo il quale si dice che il peso R sta al contrappeso T come la lun­<lb></lb>ghezza AC del piano sta all&#039;altezza BC, essendo questo da quell&#039;altro con­<lb></lb>templato caso molto diverso. </s></p><p type="main">

<s>Poteva, con efficace brevità, far osservare l&#039;Autore che il peso R opera <lb></lb>nel medesimo modo che se pendesse in E da una puleggia sola con direzion <lb></lb>verticale, parallela alla CB, il qual caso è assai diverso dall&#039;altro, quando la <lb></lb>direzione fosse obliqua come ED, perchè allora, costruito il parallelogrammo <lb></lb>FH, il contrappeso R dovrebbe esser tanto maggiore del peso T, quanto la <lb></lb>ED diagonale è maggiore del lato EF del descritto parallelogrammo, ciò che <lb></lb>torna come se il detto peso esercitasse no il suo momento totale, ma quale <lb></lb>gli converrebbe posato che fosse sul declivio AC del piano. </s>

<s>Così, ripetiamo, <lb></lb>poteva il Borelli, come avrebbe fatto il Roberval in simile occorrenza, discor­<lb></lb>rere nel suo scolio, e invece si conduce per vie lunghe e oblique a dimo­<lb></lb>strare il suo intento, riducendo i due casi alle varie condizioni dell&#039;equili­<lb></lb>brio, che si osservano nella leva diritta e nella angolare. </s></p><p type="main">

<s>Nel suo ottavo libro diceva il Roberval trattarsi dei centri delle percosse, <lb></lb>e come saggio annunziava intanto al Torricelli un teorema dimostrativo del <lb></lb>punto, da cui, percotendo, si fa il massimo colpo in un settore di cerchio <lb></lb>ondeggiante intorno al centro della figura intera alla quale egli appartiene, <lb></lb>dicendo che si troverebbe quel punto col fare “ ut chorda arcus sectoris, ad <lb></lb>ipsum arcum, ita tres quadrantes semidiametri circuli ad rectam inter ipsius <lb></lb>circuli centrum et centrum percussionis sectoris interceptam ” (ibid., pag. </s>

<s>398). <lb></lb>Di ciò avremo occasione di dir altrove più di proposito, ma per ora è da <lb></lb>ripensare a questa Meccanica robervalliana, che non a torto il suo autore <lb></lb>chiamava nuova, ritrovandosi veramente tale per la massima parte, se si pa­<lb></lb>ragona con ciò che delle macchine e delle altre statiche questioni scrissero <lb></lb>Galileo, e i Matematici contemporanei nei loro libri. </s>

<s>Vero è che la Sparto­<lb></lb>statica era stata precedentemente istituita dallo Stevino, ma il Roberval di­<lb></lb>mostrò la regola del parallelogrammo delle forze da&#039;suoi veri principii, e <lb></lb>l&#039;applicò a risolvere nuovi mirabili problemi intorno all&#039;equilibrio de&#039;pesi o <pb xlink:href="020/01/2883.jpg" pagenum="508"></pb>tirati o sostenuti da funi. </s>

<s>Come fosse poi rispetto a ciò difettosa la Scienza <lb></lb>galileiana, lo sanno oramai troppo bene coloro, che hanno letto addietro la <lb></lb>nostra Storia. </s>

<s>La teoria del piano inclinato, da cui le altre macchine dove­<lb></lb>vano prender la legge, vedemmo come fosse stata dimostrata già dal Tarta­<lb></lb>glia, a cui Galileo stesso e il Cartesio e il Torricelli non aggiunsero in so­<lb></lb>stanza nulla di nuovo, prima che il Roberval venisse a considerare il caso, <lb></lb>in cui le potenze sostenenti il peso hanno qualunque direzione diversa da <lb></lb>quella del perpendicolo, e del piano o del suo declivio. </s>

<s>Ma de&#039;centri delle <lb></lb>percosse le questioni erano affatto intatte, specialmente appresso i seguaci <lb></lb>della Scuola galileiana, per non avere intorno a ciò il loro Maestro proposto <lb></lb>se non che principii falsi, e alla nuova inquisizione in qualunque modo insuf­<lb></lb>ficienti. </s></p><p type="main">

<s>Molto più dunque sarebbe da confessare aver progredito la Meccanica <lb></lb>in Francia che in Italia, ma que&#039;progressi riguardavano solamente la Sta­<lb></lb>tica, mentre la Dinamica si rimaneva tutta intera nelle mani di Galileo, come <lb></lb>conseguenza feconda del principio da lui professato che cioè, nelle libere ca­<lb></lb>dute, le velocità de&#039;gravi crescono come i tempi. </s>

<s>Il Cartesio fece a quel prin­<lb></lb>cipio, verissimo in sè e nella sua forma, alcune cavillose osservazioni, ma il <lb></lb>Roberval sembra che lo negasse affatto, come trasparisce da queste parole <lb></lb>scritte dal Ricci, nel chiudere una sua lettera indirizzata da Roma al Tor­<lb></lb>ricelli: “ In ultimo prego V. S. che voglia rispondere alle lettere di quel <lb></lb>gesuita (cioè del Mersenno, così spesso chiamato dal Ricci, poi cardinale, non <lb></lb>perchè il Padre professasse de&#039;gesuiti la religione, ma perchè, secondo lui, <lb></lb>ne imitava l&#039;ipocrisia) che impugna le dottrine del moto, conforme già ne <lb></lb>ragguagliai V. S., e soggiunge alcuni pensieri di Robervallio in questa parte, <lb></lb>con caratteri poi così sconci, che finora non ho potuto trovare persona, che <lb></lb>ne possa dar chiara interpetrazione. </s>

<s>E per me vado considerando che Ro­<lb></lb>bervallio sia contrario alle posizioni del Galileo in materia dell&#039;augumento <lb></lb>di velocità nei gravi cadenti, e contrario in modo, che neghi ogni posizione <lb></lb>del Galileo. </s>

<s>Ma di questo ha promesso di scriverne il suo parere, ed allora, <lb></lb>per mezzo del Mersenno, intenderemo il tutto ” (MSS. Gal. </s>

<s>Disc., T. XLII, <lb></lb>fol. </s>

<s>156). </s></p><p type="main">

<s>Rimase per queste ragioni nel Roberval la Dinamica così sterilita, che <lb></lb>non fa maraviglia se non sì vide menare i frutti aspettati, per raccogliere i <lb></lb>quali, essendo stato necessario tornare a Galileo, da ciò si segna il terzo passo, <lb></lb>che, poco dopo la metà del secolo XVII, fecero gl&#039;insegnamenti di lui appresso <lb></lb>gli stranieri. </s>

<s>Si videro allora sorgere principali il Wallis in Inghitterra, il <lb></lb>Mariotte in Francia e l&#039;Huyghens nell&#039;Olanda, al quale ultimo va massima­<lb></lb>mente debitrice la Scienza del moto dell&#039;avere in provincie nuove esteso il <lb></lb>suo antico dominio. </s>

<s>Ma a preparare l&#039;opera di lui giovarono grandemente <lb></lb>quelle degli altri due commemorati, e in special modo del Wallis, che, trat­<lb></lb>tandone con regole di calcolo più precise i teoremi, confermò, contro gli oppo­<lb></lb>sitori e i dubitanti, la Scienza galileiana nella geometrica verità de&#039;suoi <lb></lb>principii. </s></p><pb xlink:href="020/01/2884.jpg" pagenum="509"></pb><p type="main">

<s>I capitoli perciò, dove il celebre Professor saviliano tratta del moto in <lb></lb>generale, della discesa dei gravi, e della libbra, se son per matematica po­<lb></lb>tenza notabili, non hanno però altra ragione che di commenti a verità pre­<lb></lb>cedentemente già dimostrate; come pure colà, dove tratta delle percosse e <lb></lb>degli urti, non sembra facesse altro il Wallis che dar miglior ordine e chia­<lb></lb>rezza, e forma più rigorosamente matematica alle proposizioni del nostro <lb></lb>Borelli. </s>

<s>Ma il trattato <emph type="italics"></emph>De centro gravitatis,<emph.end type="italics"></emph.end> che comprende esso solo due <lb></lb>terzi della intera Meccanica wallisiana, dovette apparire al mondo opera nuova, <lb></lb>rimanendosi allora, e per più di due secoli appresso, sconosciuto e seppel­<lb></lb>lito ne&#039;manoscritti ciò che dai nostri Matematici erasi scritto in quel mede­<lb></lb>simo soggetto. </s>

<s>Che se le invenzioni del Torricelli, del Nardi e del Ricci fos­<lb></lb>sero state raccolte e pubblicate in un libro dai loro propri autori, s&#039;intende <lb></lb>come l&#039;Italia avrebbe avuto della Baricentrica un trattato compiuto, venti <lb></lb>anni prima dell&#039;Inghilterra. </s>

<s>Anche al Wallis, come agli Italiani che l&#039;ave­<lb></lb>vano preceduto, serve di strumento, per domar la durezza del campo da <lb></lb>dissodarsi, la dottrina degli indivisibili, ch&#039;egli, con i più celebri matematici <lb></lb>stranieri, approva, e l&#039;ha dal suo proprio inventore per ben dimostrata. <lb></lb></s>

<s>“ Atque hanc <emph type="italics"></emph>De indivisibilibus<emph.end type="italics"></emph.end> doctrinam, nunc passim receptam atque <lb></lb>post Cavallerium a celeberrimis Mathematicis approbatam, pro veterum con­<lb></lb>tinua figurarum adscriptione substituire visum est ” (Mechan., P. II, Lon­<lb></lb>dini 1670, pag. </s>

<s>112). </s></p><p type="main">

<s>Il Mariotte men predilesse i calcoli sottili, che le fisiche esperienze, ma <lb></lb>l&#039;Huyghens parve comprendere in sè le virtù de&#039;suoi predecessori, non ri­<lb></lb>manendosi inferiore al Wallis nella Matematica, e dall&#039;altra parte applicando <lb></lb>i teoremi di lei a dar fermezza di leggi ai fuggevoli fatti osservati. </s>

<s>Nel terzo <lb></lb>dialogo delle due Nuove Scienze, come altrove osservammo, si proponeva una <lb></lb>lunga serie di principii, da&#039;quali poi non si vedeva conseguir la finale inten­<lb></lb>zione dell&#039;Autore, ch&#039;era quella di dimostrare l&#039;isocronismo dei pendoli per <lb></lb>qualunque ampiezza delle loro vibrazioni. </s>

<s>Tutta quella gran mole di teoremi, <lb></lb>congesta nel detto dialogo, non era per altro servita, che per dimostrare <lb></lb>quello stesso isocronismo nelle corde, d&#039;onde Galileo lasciava a concluderne <lb></lb>l&#039;isocronismo per gli archi circolari sottesi. </s>

<s>Ma la conclusione, non essendo <lb></lb>logica, riusciva perciò tutt&#039;insieme anche falsa, e fu l&#039;Huyghens che ridusse <lb></lb>nella via retta, e dette perfezione alla Scienza galileiana, dimostrando che <lb></lb>dall&#039;esser le suttese tautocrone conseguiva, secondo le buone regole ragionando, <lb></lb>il tautocronismo, non per gli archi dei circoli, ma per quelli della cicloide. </s></p><p type="main">

<s>Si riformò per la nuova scoperta la costruzione degli Orologi, che dal­<lb></lb>l&#039;umile arte fabbrile si sollevarono alle più alte dignità della Geometria. </s>

<s>Se­<lb></lb>condo qual più giusta regola si dovesse prefinire la lunghezza del pendolo, <lb></lb>sanno bene i nostri Lettori come fosse questione antica, avendola allo stesso <lb></lb>Galileo proposta il Pieroni, quando prima pensò di valersi di quel semplice <lb></lb>strumento, per le osservazioni celesti: e gli stessi Accademici fiorentini, qua­<lb></lb>rant&#039;anni dipoi, essendo tuttavia nella incertezza, si studiavano d&#039;assicurarsi <lb></lb>prudentemente dalle fallacie, col far sottilissimo il filo, e col ridurre sotto <pb xlink:href="020/01/2885.jpg" pagenum="510"></pb>la minor mole possibile la gravità del peso ondeggiante. </s>

<s>Benchè alcuni Ma­<lb></lb>tematici stranieri facessero derivar quella regola dai centri delle percosse, fu <lb></lb>nonostante l&#039;Huyghens il primo che, all&#039;occasion di descrivere il suo nuovo <lb></lb>Orologio oscillatorio, ne dette dimostrazione propria e diretta. </s>

<s>“ Occasio vero <lb></lb>ad haec denuo tentanda ex pendulorum automati nostri temperandorum ra­<lb></lb>tione oblata est, dum pondus mobile, praeter id quod in imo est, illis ap­<lb></lb>plico ” (Opera varia, T. I, Lugd. </s>

<s>Batav. </s>

<s>1724, pag. </s>

<s>118). </s></p><p type="main">

<s>Altra occasione, da questo stesso Orologio, venne all&#039;Huyghens di spe­<lb></lb>cular cose di Meccanica nuova, dall&#039;osservar che il pendolo, menando qua e <lb></lb>là per l&#039;ambito di un circolo il peso, gl&#039;imprime una forza, <emph type="italics"></emph>quam centri­<lb></lb>fugam vocare libet,<emph.end type="italics"></emph.end> e che sopravvien nel mobile ad alterargli in qualche <lb></lb>modo la gravità naturale. </s>

<s>“ Unde aliud quoque Horologii commentum de­<lb></lb>duximus ” (ibid., pag. </s>

<s>185), formulando intanto <emph type="italics"></emph>De vi centrifuga ex motu <lb></lb>circulari<emph.end type="italics"></emph.end> tredici teoremi, ai quali poi negli Opuscoli postumi ebbe la Geo­<lb></lb>metria meccanica a rallegrarsi di veder fatte le dimostrazioni. </s>

<s>Con questi <lb></lb>teoremi e con quegli altri relativi ai centri delle oscillazioni, e alle proprietà <lb></lb>meccaniche della Cicloide, aggiungeva il Matematico olandese, a quelle isti­<lb></lb>tuite già da Galileo, tre nuove Scienze, intorno alle quali ha da trattenersi <lb></lb>ora particolarmente la nostra Storia con breve discorso. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il tautocronismo della Cicloide vedemmo come derivasse per corollario <lb></lb>dalla proposizione XI torricelliana di <emph type="italics"></emph>Meccanìca nuova,<emph.end type="italics"></emph.end> scritta qui addietro <lb></lb><figure id="id.020.01.2885.1.jpg" xlink:href="020/01/2885/1.jpg"></figure></s></p><p type="caption">

<s>Figura 320.<lb></lb>nel § 3° del <lb></lb>capitolo se­<lb></lb>sto. </s>

<s>Ma con­<lb></lb>segue anche <lb></lb>immediatamente <lb></lb>dai teoremi gali­<lb></lb>leiani dei moti ac­<lb></lb>celerati, dietro le <lb></lb>proprietà geome­<lb></lb>triche della curva dimo­<lb></lb>strate dal Roberval, una <lb></lb>delle quali proprietà è <lb></lb>che qualunque porzione <lb></lb>di essa curva, presa dal ver­<lb></lb>tice, è uguale al doppio della <lb></lb>tangente. </s>

<s>Gl&#039;impeti infatti <lb></lb>acquistati dal medesimo mobile, nello scendere da B (fig. </s>

<s>320) in I e in <lb></lb>A sul piano orizontale AI, sono uguali, o sia fatta la scesa per l&#039;arco <pb xlink:href="020/01/2886.jpg" pagenum="511"></pb>cicloidale AB, o per la tangente BI: e proseguirebbe esso mobile equabil­<lb></lb>mente passando, nel medesimo tempo impiegato a venire da B in I, uno <lb></lb>spazio doppio di BI, ossia uguale all&#039;arco AB. </s>

<s>Lo stesso dicasi di qualunque <lb></lb>altro punto, da cui partendosi il grave acquisterebbe, giunto in A per la <lb></lb>concavità cicloidale, tal impeto, da passare equabilmente uno spazio uguale <lb></lb>a quello del cammin curvo, acceleratamente descritto in quel medesimo tempo, <lb></lb>che sarebbe venuto giù per la tangente: onde essendo gl&#039;impeti o le velo­<lb></lb>cità, in qualunque caso, proporzionali agli spazi, i tempi necessariamente sono <lb></lb>uguali. </s></p><p type="main">

<s>E per dire come dal tautocronismo delle scese per le corde dei cerchi <lb></lb>si potesse concludere a quello per gli archi della cicloide, e non degli stessi <lb></lb>cerchi, come fece Galileo; si osservi essere le cadute dai vari punti della <lb></lb>curva CA quelle medesime, che per le loro tangenti o per le corde, nel cir­<lb></lb>colo DVA condotte a loro uguali e parallele, come la AV per esempio alla <lb></lb>BI: ond&#039;essendo, per i teoremi galileiani, esse corde tautocrone, tautocrona <lb></lb>sarà dunque anche la Cicloide. </s></p><p type="main">

<s>Si può veder di qui quale stretta dipendenza avesse con la precedente <lb></lb>la Meccanica ugeniana, ma l&#039;Autore aveva dimostrato della curva altre pro­<lb></lb>prietà meccaniche più generali, dalle quali faceva come per corollario deri­<lb></lb>vare non solamente il tautocronismo, ma anche insieme altre verità non men <lb></lb>nuove e maravigliose. </s>

<s>Quella generale proposizione è la XXV della seconda <lb></lb>parte dell&#039;<emph type="italics"></emph>Orologio oscillatorio,<emph.end type="italics"></emph.end> in cui dimostrasi dall&#039;Autore che, disposta <lb></lb>la Cicloide con la base orizontale, come la rappresenta la passata figura, il <lb></lb>tempo della scesa di un grave, da qualunque punto della concavità all&#039;imo <lb></lb>vertice, sta al tempo della scesa per l&#039;asse come la semicirconferenza sta al <lb></lb>suo diametro. </s>

<s>Servono per lemma a questa le due proposizioni precedenti, <lb></lb>la prima delle quali è così annunziata: </s></p><p type="main">

<s>“ Sit cyclois ABC (nella medesima figura) cuius vertex A deorsum con­<lb></lb>versus sit, axe AD ad perpendiculum erecto: sumptoque in ea quolibet puncto <lb></lb>B, ducatur inde deorsum recta BI, quae cycloidem tangat, termineturque <lb></lb>recta horizontali AI, recta vero BF ad axem perpendicularis agatur, et, di­<lb></lb>visa bifariam FA in X, super ea describatur semicirculus FHA. </s>

<s>Ducta deinde <lb></lb>per punctum quodlibet G, in curva BA sumptum, recta <foreign lang="grc">Σ</foreign>G, parallela BF, <lb></lb>quae circumferentiae FHA occurrat in H, axi AD in <foreign lang="grc">Σ</foreign>; intelligantur per pun­<lb></lb>cta G et H rectae tangentes utriusque curvae, earumque tangentium partes, <lb></lb>iisdem duabus horizontalibus MS, NT interceptae, sint MN, ST. </s>

<s>Iisdemque <lb></lb>rectis MS, NT includantur tangentis BI pars OP, et axis DA pars QR. </s>

<s>Qui­<lb></lb>bus ita se habentibus, dico tempus quo grave percurret rectam MN, celeri­<lb></lb>tate aequabili quanta acquiritur descendendo per arcum cycloidis BG, fore <lb></lb>ad tempus quo percurretur recta OP, celeritate aequabili dimidia eius, quae <lb></lb>acquiritur descendendo per totam tangentem BI; sicut est tangens ST ad <lb></lb>partem axis QR ” (ibid., pag. </s>

<s>79, 80). </s></p><p type="main">

<s>Si compia la costruzione descrivendo intorno al diametro AD il semicir­<lb></lb>colo AVD, che incontrerà le parallele <foreign lang="grc">Σ</foreign>G, BF ne&#039;punti <emph type="italics"></emph>f,<emph.end type="italics"></emph.end> V, e si congiunga <pb xlink:href="020/01/2887.jpg" pagenum="512"></pb>A con V per una linea, la quale intersecherà nel suo passaggio le PR, G<foreign lang="grc">Σ</foreign>, <lb></lb>OQ in K, L, E. </s>

<s>Si congiungano poi con H i punti F, A, X, e il punto A <lb></lb>con <emph type="italics"></emph>f<emph.end type="italics"></emph.end> per una linea, che attraverserà la PR in <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> e prolungata raggiungerà <lb></lb>la OQ in <emph type="italics"></emph>d.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ciò fatto, sappiamo per i teoremi galileiani che il tempo equabilmente <lb></lb>passato per la MN, al tempo per la OP, passato con la mezza celerità detta, <lb></lb>ha la ragion composta diretta degli spazi, e reciproca delle velocità: cosicchè, <lb></lb>chiamati To.MN, To.OP quegli stessi tempi e, Va.MN, Va.OP/2 le velocità <lb></lb>corrispondenti; avremo To.MN:To.OP=MN.Va.OP/2:OP.Va.MN. </s>

<s>Ma <lb></lb>perchè tutta intera la velocità equabile per OP è quella conveniente alla ca­<lb></lb>duta da B in I, e la velocità per MN è quella dovuta al cadente, con moto <lb></lb>accelerato da B in G, o da F in <foreign lang="grc">Σ</foreign>; dunque, essendo per le note leggi della <lb></lb>Dinamica le velocità proporzionali alle radici degli spazi, avremo </s></p><p type="main">

<s><emph type="center"></emph>Va.OP:Va.MN=√AF:√F<foreign lang="grc">Σ</foreign>=AF:√AF.F<foreign lang="grc">Σ</foreign>=AF:FH.<emph.end type="center"></emph.end><lb></lb>Dividendo gli antecedenti per due, e facendo le sostituzioni, la ritrovata re­<lb></lb>lazion de&#039;tempi si trasformerà nell&#039;altra </s></p><p type="main">

<s><emph type="center"></emph>To.MN:To.OP=MN.FX:OP.FH.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Ora essendo, per le parallele e i parallelogrammi da esse circoscritti, <lb></lb>MN=<emph type="italics"></emph>dp,<emph.end type="italics"></emph.end> OP=EK, abbiamo MN:OP=<emph type="italics"></emph>dp<emph.end type="italics"></emph.end>:EK=<emph type="italics"></emph>d<emph.end type="italics"></emph.end>A:EA=<emph type="italics"></emph>f<emph.end type="italics"></emph.end>A:LA. </s>

<s><lb></lb>E perchè congiunti V, <emph type="italics"></emph>f,<emph.end type="italics"></emph.end> il triangolo AV<emph type="italics"></emph>f<emph.end type="italics"></emph.end> che ne nasce essendo simile al <lb></lb>triangolo AL<emph type="italics"></emph>f,<emph.end type="italics"></emph.end> dà la proporzione AV:A<emph type="italics"></emph>f<emph.end type="italics"></emph.end>=A<emph type="italics"></emph>f<emph.end type="italics"></emph.end>:AL; sarà dunque MN:OP= <lb></lb>AV:A<emph type="italics"></emph>f,<emph.end type="italics"></emph.end> la qual seconda ragione facilmente si dimostra esser quella mede­<lb></lb>sima di FA ad AH. </s>

<s>Imperocchè AV2=DA.AF e A<emph type="italics"></emph>f<emph.end type="italics"></emph.end>2=DA.A<foreign lang="grc">Σ</foreign>, d&#039;onde <lb></lb>AV2:A<emph type="italics"></emph>f<emph.end type="italics"></emph.end>2=AF:A<foreign lang="grc">Σ</foreign>=AF2:AF.A<foreign lang="grc">Σ</foreign>=AF2:AH2, e perciò AV:A<emph type="italics"></emph>f<emph.end type="italics"></emph.end>= <lb></lb>AF:AH. </s>

<s>Essendo poi, per la similitudine dei triangoli FAH, FH<foreign lang="grc">Σ</foreign>, la ragione <lb></lb>di AF ad AH uguale a quella di FH a H<foreign lang="grc">Σ</foreign>; questa sarà dunque anche la <lb></lb>ragione di MN a OP, che, sostituita nella relazione de&#039;tempi ultimamente <lb></lb>scritta, la trasformerà nell&#039;altra To.MN:To.OP=FX.FH:H<foreign lang="grc">Σ</foreign>.FH= <lb></lb>FX:H<foreign lang="grc">Σ</foreign>=HX:H<foreign lang="grc">Σ</foreign>, la quale, osservando che, condotta la T<emph type="italics"></emph>b<emph.end type="italics"></emph.end> perpendico­<lb></lb>lare sopra SQ, i triangoli simili ST<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> TH<foreign lang="grc">Σ</foreign> danno HX:H<foreign lang="grc">Σ</foreign>=ST:T<emph type="italics"></emph>b<emph.end type="italics"></emph.end>= <lb></lb>ST:QR; si riduce finalmente a To.MN:T.OP=ST:QR, d&#039;onde appa­<lb></lb>risce vera la conclusione dall&#039;Huyghens stesso espressa in questa forma: <lb></lb>“ Igitur tempus motus qualem diximus per MN, ad tempus per OP, constat <lb></lb>esse sicut ST ad QR, quod erat demonstrandum ” (ibid., pag. </s>

<s>81). </s></p><p type="main">

<s>Se la porzione QR fosse stata presa infinitesima, gli archi del semicir­<lb></lb>colo e della semicicloide, intercetti fra le parallele OQ, PR, si sarebbero <lb></lb>confusi con le tangenti ST, MN, ond&#039;è che la medesima conclusione uge­<lb></lb>niana poteva mettersi in altra forma, dicendo che il tempo della scesa per <lb></lb>l&#039;arco cicloidale MN sta al tempo della scesa per la porzione di tangente OP, <lb></lb>come l&#039;arco ST del circolo sta alla porzione QR dell&#039;asse. </s>

<s>E perchè, divi-<pb xlink:href="020/01/2888.jpg" pagenum="513"></pb>dendo tutto intero il diametro AF in parti infinitamente piccole, e tutte uguali <lb></lb>a QR, la dimostrazione fatta per questa particolar divisione è applicabile a <lb></lb>ciascuna delle altre infinite, è manifesto che verrebbero da ciò ordinate al­<lb></lb>trettante proporzioni, in cui i secondi termini, che sono i tempi impiegati a <lb></lb>passare equabilmente spazi tutti uguali ad OP, ed i quarti termini, ossia le <lb></lb>porzioni dell&#039;asse AF, sono tutti fra loro uguali. </s>

<s>Ora, non sarebbe bisognato <lb></lb>all&#039;Huyghens che d&#039;invocare il <emph type="italics"></emph>Teorema integrale,<emph.end type="italics"></emph.end> per conseguir dalle cose <lb></lb>già dimostrate la sua principale intenzione. </s></p><p type="main">

<s>Che se giungesse a qualcuno oscura la nuova denominazione, sappia che <lb></lb>da noi si chiama Teorema integrale quello, che fu già proposto in questa <lb></lb>forma: “ Si fuerit ut prima magnitudo ad secundam, ita tertia ad quartam, <lb></lb>et hoc quotiescumque libuerit, fuerintque omnes primae inter se, item omnes <lb></lb>tertiae magnitudines inter se aequales; erunt omnes primae simul, ad omnes <lb></lb>secundas, ut sunt omnes tertiae simul, ad omnes quartas magnitudines ” <lb></lb>(Torricelli, Op. </s>

<s>geom. </s>

<s>cit., P. II, pag. </s>

<s>50). Il Roberval suppose ciò come <lb></lb>dimostrato, per facile corollario, da due proposizioni del quinto libro Degli <lb></lb>elementi, e il Torricelli ne fece una dimostrazione particolare, da lui stesso <lb></lb>inserita nel luogo sopra citato, come XVIII lemma <emph type="italics"></emph>De dimensione parabolae.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Che poi convenga al detto teorema il titolo d&#039;integrale, adempiendo agli <lb></lb>uffici del calcolo, che per le posteriori istituzioni prese quel nome, è mani­<lb></lb>festo dall&#039;uso, che ne fecero i due stessi promotori insigni del metodo degli <lb></lb>indivisibili ora commemorati, e segnatamente il Torricelli, nelle varie occor­<lb></lb>renze di ricercare i centri di gravità delle varie figure, e le dimensioni delle <lb></lb>parabole. </s>

<s>Prendasi per esempio, da questo Libro torricelliano, quella propo­<lb></lb>sizione XIII, il modo di dimostrar la quale disse il Nardi di averlo qualche <lb></lb>tempo prima imparato da Pappo. </s>

<s>Essendo ABC <lb></lb><figure id="id.020.01.2888.1.jpg" xlink:href="020/01/2888/1.jpg"></figure></s></p><p type="caption">

<s>Figura 321.<lb></lb>(fig. </s>

<s>321) una parabola, intorno alla base AC della <lb></lb>quale sia descritto il semicircolo ANC, e AD, AE <lb></lb>rettangoli circoscritti alle due figure, si dimostra <lb></lb>dall&#039;Autore che FG:GI=<foreign lang="grc">π</foreign>GL2:<foreign lang="grc">π</foreign>GM2, e così <lb></lb>sempre, qualunque siano, fra le infinite linee <lb></lb>uguali equidistanti dal diametro BN, quelle che <lb></lb>incontrano la parabola, la base di lei, e il circolo <lb></lb>ne&#039;punti dei loro passaggi. </s>

<s>Ora essendo, secondo <lb></lb>il metodo cavalierano, risolute nelle infinite linee costanti come FG, e nelle <lb></lb>infinite variabili come GI le superficie del rettangolo e della parabola, e si­<lb></lb>milmente negli infiniti circoli di costante raggio GL, e di variabile GM, essendo <lb></lb>risoluti i solidi rotondi generati dal rivolgersi intorno ad AC il semicircolo e il <lb></lb>rettangolo a lui circoscritto; è manifesto che i termini FG, GI; <foreign lang="grc">π</foreign>GL2, <foreign lang="grc">π</foreign>GM2<lb></lb>sono altrettante quantità differenziali, che si scriverebbero, seeondo i sim­<lb></lb>boli usati dai matematici moderni, <emph type="italics"></emph>da:dx=db:dy,<emph.end type="italics"></emph.end> rappresentando <emph type="italics"></emph>a<emph.end type="italics"></emph.end> e <emph type="italics"></emph>x<emph.end type="italics"></emph.end><lb></lb>il rettangolo e la parabola, <emph type="italics"></emph>b<emph.end type="italics"></emph.end> e <emph type="italics"></emph>y<emph.end type="italics"></emph.end> il cilindro e la sfera. </s>

<s>Dall&#039;analisi differen­<lb></lb>ziale della funzione si risale alla sintesi integrale, per via della somma, in <lb></lb>virtù del Teorema sopra accennato, da cui resulta che la somma delle infi-<pb xlink:href="020/01/2889.jpg" pagenum="514"></pb>nite quantità, tutte uguali a <emph type="italics"></emph>da, db,<emph.end type="italics"></emph.end> uguaglia <emph type="italics"></emph>a, b:<emph.end type="italics"></emph.end> e la somma delle infinite <lb></lb>flussioni di <emph type="italics"></emph>x<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>y<emph.end type="italics"></emph.end> uguaglia agli stessi <emph type="italics"></emph>x, y,<emph.end type="italics"></emph.end> precisamente come nel cal­<lb></lb>colo recente Ŗ <emph type="italics"></emph>da,<emph.end type="italics"></emph.end> Ŗ <emph type="italics"></emph>dx,<emph.end type="italics"></emph.end> Ŗ <emph type="italics"></emph>db,<emph.end type="italics"></emph.end> Ŗ <emph type="italics"></emph>dy<emph.end type="italics"></emph.end> sono uguali ad <emph type="italics"></emph>a, x, b, y,<emph.end type="italics"></emph.end> non te­<lb></lb>nuto conto delle costanti. </s></p><p type="main">

<s>Ritornando ora indietro sopra l&#039;ultima conclusione dell&#039;Huyghens, nel <lb></lb>supposto che fossero le due parallele OQ, PR condotte infinitamente poco <lb></lb>distanti fra loro, e quantità infinitamente piccole perciò riuscissero così gli <lb></lb>archi ST, MN del semicircolo e della semicicloide, come le porzioni QR, OP <lb></lb>dell&#039;asse e della tangente; si sarebbero potute istituire infinite equazioni diffe­<lb></lb>renziali, che s&#039;integrerebbero assai facilmente applicandovi il Teorema del <lb></lb>Torricelli, da cui per via diretta resulterebbe che il tempo speso a passare <lb></lb>per gl&#039;infiniti tratti della curva AB, ossia per tutto l&#039;arco cicloidale AB, sta <lb></lb>al tempo per le infinite parti della tangente IB, ossia per tutta intera la tan­<lb></lb>gente IB, come la somma di tutte le infinite porzioni degli archi circolari, <lb></lb>ossia tutto il semicerchio AHF, sta alla somma di tutte le porzioni, ossia <lb></lb>a tutto il diametro AF. </s></p><p type="main">

<s>Essendo poi il tempo speso a passare equabilmente la BI, con la mezza <lb></lb>velocità che si sarebbe acquistata dal mobile dopo la caduta naturale per la <lb></lb>stessa BI, uguale al tempo speso a passare equabilmente uno spazio doppio, <lb></lb>con la velocità intera; è chiaro esser medesimo il tempo di passare equabil­<lb></lb>mente la BI con velocità dimidiata, e il tempo di passarla con moto acce­<lb></lb>lerato, partendosi il mobile dalla quiete. </s>

<s>Ma il tempo della caduta accelerata <lb></lb>per BI, ossia per AV, è, per i noti teoremi galileiani, uguale al tempo per <lb></lb>l&#039;asse AD; dunque rimarrebbe, senz&#039;altro discorso, dimostrata la verità, così <lb></lb>dall&#039;Huyghens stesso in XXV luogo, nel citato libro, proposta: “ In cycloide, <lb></lb>cuius axis ad perpendiculum erectus est, vertice deorsum spectante, tempora <lb></lb>descensus, quibus mobile a quocumque in ea puncto dimissum ad punctum <lb></lb>imum verticis pervenit, sunt inter se aequalia, habentque ad tempus casus <lb></lb>perpendicularis per totum axem cycloidis eam rationem, quam semicircum­<lb></lb>ferentia circuli ad diametrum ” (Op. </s>

<s>et Tom. </s>

<s>cit., pag. </s>

<s>87). </s></p><p type="main">

<s>Ma l&#039;Huyghens non procede per le vie da noi disegnate, e che a quei <lb></lb>tempi apparivano nuove: calcando invece le orme dei Matematici antichi, <lb></lb>egli si attiene piuttosto alle circoscrizioni, affaticandosi di giungere al suo <lb></lb>intento, col far uso di quel metodo obliquo, e perciò lungo, con cui si vede <lb></lb>esser penosamente condotta da lui la XXIV proposizione. </s>

<s>La cosa è veramente <lb></lb>notabile, dopo gli esempi pubblicamente dati dal Roberval, dal Torricelli, dal <lb></lb>Wallis e da altri insigni promotori degl&#039;indivisibili, ma è dall&#039;altra parte un <lb></lb>segno manifesto della poca fede, che s&#039;aveva nella sincerità di quel metodo, <lb></lb>pochi anni prima del Leibniz e del Newton: e anche l&#039;Huyghens se ne <lb></lb>astenne, si perchè voleva non cadesse ombra di dubbio sopra la verità dei <lb></lb>suoi teoremi, e si per dar prova del suo proprio valore, nel riuscire a dimo­<lb></lb>strar cose tanto nuove e tanto difficili, non valendosi d&#039;altro, che de&#039;vecchi <lb></lb>rugginosi strumenti. </s></p><p type="main">

<s>La novità però delle invenzioni ugeniane non apparisce, da quel che se <pb xlink:href="020/01/2890.jpg" pagenum="515"></pb>n&#039;è detto fin qui, che per una parte sola, in quanto cioè, dall&#039;avere il tempo <lb></lb>della scesa da qualunque punto della Cicloide al tempo della caduta per <lb></lb>l&#039;asse, una proporzione sempre costante, qual&#039;è quella della circonferenza al <lb></lb>diametro; se ne concludeva per corollario il tautocronismo della stessa Ci­<lb></lb>cloide: ma ben altre verità più importanti faceva l&#039;Autor conseguire dalle <lb></lb>verità dimostrate, in ordine al cadere i gravi ora liberamente, ora vibrando <lb></lb>sospesì dai fili dei pendoli. </s></p><p type="main">

<s>S&#039;accennò di sopra che, dall&#039;essere isocrone le cadute per le corde dei <lb></lb>circoli, male a ragione inferiva Galileo l&#039;isocronismo per gli archi sottesi, <lb></lb>non essendo l&#039;illazione logicamente valida, se non che rispetto agli archi ci­<lb></lb>cloidali: ciò che, rimastosi nella stessa Meccanica galileiana latente, fu primo <lb></lb>l&#039;Huyghens a produrre alla luce. </s>

<s>Sarebbe però da stimarsi la scoperta non <lb></lb>più che per una bella speculazione, quando non si fosse potuta applicare alla <lb></lb>misura dei minimi tempi, nè si vedeva possibile dall&#039;altra parte la deside­<lb></lb>rata applicazione, se non col trovare il modo di far descrivere ai pendoli <lb></lb>archi, non più di cerchio, ma di cicloide. </s>

<s>L&#039;invenzione, che avrebbe tratte­<lb></lb>tenuto intorno a un semplice fatto fisico un ingegno volgare, aprì all&#039;Huy­<lb></lb>ghens quel campo nuovo nella Geometria, ch&#039;egli chiamò <emph type="italics"></emph>Delle evolute,<emph.end type="italics"></emph.end> per­<lb></lb>chè, data una curva, sulla convessità della quale s&#039;intendesse applicato un <lb></lb>filo di ugual lunghezza, si proponeva l&#039;Autore di mostrar la linea, che de­<lb></lb>scriverebbe il capo di esso filo, svolgendosi in modo, che sempre la lunghezza <lb></lb>svolta si serbasse tangente. </s>

<s>Il particolar teorema poi di questo trattato, dal­<lb></lb>l&#039;applicazione del quale dipendeva la trasformazione degli archi circolari dei <lb></lb>pendoli in archi cicloidali, si trova così proposto nella citata terza parte del­<lb></lb><figure id="id.020.01.2890.1.jpg" xlink:href="020/01/2890/1.jpg"></figure></s></p><p type="caption">

<s>Figura 322.<lb></lb>l&#039;Orologio oscil­<lb></lb>latorio: “ Semi­<lb></lb>cycloidis evolu­<lb></lb>tione, a vertice <lb></lb>coepta, alia se­<lb></lb>micyclois de­<lb></lb>scribitur, evolu­<lb></lb>tae aequalis et <lb></lb>similis, cuius <lb></lb>basis est in ea <lb></lb>recta, quae cy­<lb></lb>cloidem evolu­<lb></lb>tam in vertice <lb></lb>contingit ” (pa­<lb></lb>gina 96). </s></p><p type="main">

<s>Sia ABC <lb></lb>(fig. </s>

<s>322) semi­<lb></lb>cicloide, asse <lb></lb>AD, base DC, AHD semicircolo genitore, a cui in A giunga la GA tangente. </s>

<s><lb></lb>Sia sulla convessità della curva applicato il filo ABC, di cui il capo A, svolto <pb xlink:href="020/01/2891.jpg" pagenum="516"></pb>intorno a C, si vuol dimostrare che descrive, nella sua evoluzion progressiva, <lb></lb>una linea AEF eguale e simile all&#039;evolvente, cioè un&#039;altra semicicloide. </s></p><p type="main">

<s>Si consideri giunta l&#039;evoluzione a un punto qualunque, per esempio E, <lb></lb>cosicchè la lunghezza del filo svolto sia BE, intersecante in K l&#039;AG. </s>

<s>Dai <lb></lb>punti K, E s&#039;alzino alle AG, EK le perpendicolari KM, EM, le quali s&#039;in­<lb></lb>contrino in M, disegnando il triangolo EMK. </s>

<s>Da B poi si conduca una pa­<lb></lb>rallela alla base, e raggiunga il semicircolo in H, d&#039;onde si tiri la corda HD. </s>

<s><lb></lb>Il triangolo rettangolo AHD, che ne nasce, e il triangolo EMK sono uguali, <lb></lb>essendo in primo luogo equiangoli perchè per le note proprietà della Cicloide, <lb></lb>la tangente EB è parallela alla corda AH, e perciò EM, DH lati paralleli, e <lb></lb>paralleli KM, AD: in secondo luogo poi EK è uguale ad AH, perchè EB <lb></lb>uguaglia per supposizione la porzion di curva AB, la quale, per il corollario <lb></lb>alla Prima robervalliana, nel capitolo precedente ordinata, è doppia di KB, e <lb></lb>perciò EK è uguale a BK, ossia ad AH. </s>

<s>Se son dunque veramente, come si <lb></lb>diceva, i due triangoli rettangoli MEK, AHD uguali, uguali pure saranno i <lb></lb>semicircoli ad essi circoscritti, onde, a concluder l&#039;intento, riman solo a dimo­<lb></lb>strare come E sia un punto nella semicicloide generata dallo stesso MEK, ciò <lb></lb>che poi è in conseguenza dell&#039;essere l&#039;arco EK uguale alla porzion di base <lb></lb>AK, com&#039;è di fatto, essendo esso arco uguale all&#039;arco AH, a cui, per quel <lb></lb>che hanno inteso i Lettori dalle dimostrazioni del Ricci e del Nardi, s&#039;ugua­<lb></lb>glia l&#039;ordinata HB, ossia la AK. Così, comprendendo le proposizioni uge­<lb></lb>niane IV, V e VI, nella terza parte dell&#039;Opera citata, si dimostrerebbe che <lb></lb>qualunque altro punto della evoluta AEF è in una semicicloide generata dal <lb></lb>ruzzolarsi la ruota HEM su per la via AG, e perciò è una curva uguale e <lb></lb>simile alla ABC semicicloide evolvente. </s></p><p type="main">

<s>Dicemmo che da questa dimostrata proprietà dipendeva la trasformazione <lb></lb>degli archi circolari nei cicloidali, descritti dai pendoli oscillatorii. </s>

<s>Immagi­<lb></lb>nando infatti di aver la disegnata figura capovolta, e intorno a C, punto di <lb></lb>sospensione del pendolo CF, applicate le due lamine cicloidali CB, CO, conse­<lb></lb>gue dalle cose fin qui discorse e dimostrate che, svolgendosi e avvolgendosi <lb></lb>il filo nel vibrare, descrive archi di cicloide uguali e simili a BC, OC, e sem­<lb></lb>pre fra loro isocroni, qualunque sia l&#039;ampiezza della vibrazione. </s>

<s>Così, com&#039;è <lb></lb>noto, prescriveva di fare l&#039;Huyghens stesso ai costruttori degli Orologi della <lb></lb>nuova invenzione, e così i teoremi astratti della Meccanica venivano applicati <lb></lb>agli strumenti, da misurare con la massima esattezza i più piccoli tempi. </s></p><p type="main">

<s>Un&#039;altra importantissima applicazione si soggiungeva avere avuto i me­<lb></lb>desimi teoremi ugeniani, a determinare cioè, si direbbe quasi, l&#039;istante, in <lb></lb>cui cade un grave da un&#039;altezza osservabile. </s>

<s>I predecessori dell&#039;Huyghens <lb></lb>furono tutti costretti a ricorrere alle esperienze, le quali quanto fossero pe­<lb></lb>nose e fallaci s&#039;è veduto nell&#039;altro Tomo di questa Storia della Meccanica, <lb></lb>per gli esempi di Galileo e del Riccioli. </s>

<s>Ma ora, che è stato dimostrato avere <lb></lb>il tempo di qualunque vibrazione intera del pendolo cicloidale, al tempo della <lb></lb>scesa naturale per l&#039;asse della curva, la proporzione medesima che ha la <lb></lb>circonferenza al diametro; non occorre di saper altro, per risolvere esatta-<pb xlink:href="020/01/2892.jpg" pagenum="517"></pb>mente il geloso problema, se non che quanto vada lungo il pendolo dei se­<lb></lb>condi. </s>

<s>Sia questa lunghezza, nella medesima figura, la CF, la metà GC della <lb></lb>quale uguaglierà l&#039;asse, che secondo l&#039;Huyghens torna precisamente 18 once <lb></lb>del piede orario. </s>

<s>Si potrà senz&#039;altro avere il tempo X, impiegato da un grave <lb></lb>a scendere dall&#039;altezza perpendicolare di quelle 18 once, dalla formula T:X= <lb></lb>C:D, intendendosi per T il tempo di un secondo, ossia di 60tʹ, e per C, D <lb></lb>la circonferenza e il suo diametro, la ragion tra&#039;quali è presa di 355 a 113. <lb></lb>Dunque X=T.D/C=19tʹ+1/10=19tʹ, 1, molto prossimamente. </s>

<s>Di qui, <lb></lb>essendo per i noti Teoremi galileiani, gli spazi proporzionali ai quadrati dei <lb></lb>tempi, si può facilmente rispondere a chi volesse sapere da quanta altezza <lb></lb>sia sceso nel perpendicolo un grave, in un minuto secondo. </s>

<s>Perchè, come il <lb></lb>quadrato di 19, 1, a quello di 60, ossia di 191 a 600, che sono i quadrati <lb></lb>dei tempi; così lo spazio delle 18 once, a quello che si cerca, e che dovendo <lb></lb>essere quarto proporzionale dopo 36481, 360000 e 18, si troverebbe di 14 piedi, <lb></lb>9 once e 6 linee del piede orario, ossia di 15 piedi e un oncia prossimamente, <lb></lb>fatta la riduzione al piede parigino. </s></p><p type="main">

<s>“ Quia igitur (per riferir con le parole proprie dell&#039;Autore la nuova mi­<lb></lb>rabile invenzione) penduli ad secunda scrupula longitudinem diximus esse <lb></lb>pedum horariorum 3, tempus autem unius oscillationis minimae est ad tem­<lb></lb>pus descensus perpendicularis ex dimidia penduli altitudine ut circumferentia <lb></lb>circuli ad diametrum, hoc est ut 355 ad 113; si fiat ut numerus horum prior <lb></lb>ad alterum, ita tempus unius secundi scrupuli, sive sexaginta tertiorum, ad <lb></lb>aliud, fiet 19tʹ+1/10 tempus descensus per dimidiam penduli altitudinem, <lb></lb>quae nempe est pedis unciarum 18. Sicut autem quadrata temporum ita sunt <lb></lb>spatia illis temporibus peracta, ergo, si fiat ut quadratum ex 19+1/10, ad <lb></lb>quadratum ex 60, hoc est ut 36481 ad 360000, ita 18 unciae ad aliud; fient <lb></lb>ped. </s>

<s>14, unc. </s>

<s>9, lin. </s>

<s>6 altitudo descensus perpendicularis tempore unius se­<lb></lb>cundi. </s>

<s>Cum autem pes horarius sit ad parisiensem ut 881 ad 864, erit eadem <lb></lb>altitudo, ad hanc mensuram reducta, proxime pedum 15, et unciae unius ” <lb></lb>(ibid., pag. </s>

<s>282, 83). </s></p><p type="main">

<s>In un tempo, in cui si seguitava tuttavia da alcuni Matematici a dubitar <lb></lb>se le leggi dimostrate da Galileo fossero ipotetiche o realmente corrispon­<lb></lb>denti con i fatti osservati, si comprende quale efficace modo porgesse l&#039;in­<lb></lb>venzione ugeniana di verificare le dette leggi. </s>

<s>Ma non si sarebbe potuto recare <lb></lb>alla Scienza questo benefizio, se prima non si rimovevano dagli sperimenti <lb></lb>le occasioni delle fallacie, le quali principalmente consistevano nell&#039;incertezza <lb></lb>di definire, a giudizio dell&#039;occhio, il preciso punto del tempo, in cui il grave <lb></lb>termina la sua caduta. </s>

<s>Si volse perciò l&#039;Huyghens a disporre le cose con <lb></lb>tale ingegno, che il pendolo stesso, nell&#039;atto del suo moto, fosse tutto insieme <lb></lb>misuratore del tempo, e dello spazio. </s></p><p type="main">

<s>Sia AB (fig. </s>

<s>323) il profilo di una parete o di un&#039;asse di legno, per­<lb></lb>pendicolarmente eretta, a cui in A sia raccomandato il capo del pendolo ci­<lb></lb>cloidale AC che, con la sua mezza oscillazione CD, ha da misurare il tempo <pb xlink:href="020/01/2893.jpg" pagenum="518"></pb>della caduta del grave, tenuto fermo in D, come il pendolo in C, da un te­<lb></lb>nuissimo filo, che gli congiunge ambedue. </s>

<s>Al cadente poi nel perpendicolo <lb></lb>è legato un secondo filo, l&#039;altro capo del quale è raccomandato a una stri­<lb></lb><figure id="id.020.01.2893.1.jpg" xlink:href="020/01/2893/1.jpg"></figure></s></p><p type="caption">

<s>Figura 323.<lb></lb>sciola di carta, col suo lembo inferiore toccante il punto D, <lb></lb>e applicata alla parete in modo, da cedere facilmente al ti­<lb></lb>rare del filo stesso, non preso così lungo, che nel secondar <lb></lb>la caduta sia tutto scorso, quando da C il pendolo è ve­<lb></lb>nuto in D, compiuta la sua mezza vibrazione. </s>

<s>Dunque esso <lb></lb>pendolo batte sulla striscia di carta, e vi lascia impresso <lb></lb>il vestigio, perchè la palla C era stata poco prima tinta di <lb></lb>filiggine o d&#039;atramento. </s>

<s>Di qui è manifesto potersi, anche <lb></lb>finito il caso, osservare lo spazio passato nel tempo della <lb></lb>mezza scorsa del pendolo, il quale spazio sarà giusto quant&#039;è <lb></lb>la lunghezza del filo tirato, aggiuntavi la lunghezza della <lb></lb>striscia di carta sotto il segno. </s>

<s>E perchè importa massi­<lb></lb>mamente alla precisione dell&#039;esperienza che la scesa del <lb></lb>pendolo e la caduta naturale del grave incomincino nel <lb></lb>medesimo istante, ciò otteneva l&#039;Huyghens abbruciando, <lb></lb>con accostarvi la fiamma di un cerino, il sopra detto te­<lb></lb>nuissimo filo di congiunzione. </s>

<s>Così potè l&#039;Huyghens stesso <lb></lb>riscontrar le cose, e dire che le teorie <emph type="italics"></emph>cum accuratissimis <lb></lb>experimentis nostris prorsus conveniunt ”<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>183). </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Dei centri delle oscillazioni, che subito si dissero essere una medesima <lb></lb>cosa con i centri delle percosse, la Meccanica anch&#039;ebbe dall&#039;Huyghens la <lb></lb>teoria generale. </s>

<s>Vi s&#039;erano nulladimeno esercitati i Matematici molto prima, <lb></lb>per rispondere alle domande importune de&#039;gladiatori e dei duellanti, curiosi <lb></lb>di sapere a qual punto dovessero appioppare il bastone sulle spalle dell&#039;av­<lb></lb>versario, perchè ne dovesse maggiore sentir la percossa. </s>

<s>Quei che nelle Mec­<lb></lb>caniche di Aristotile cercavano i principii, per risolvere il problema, dice­<lb></lb>vano, come Leonardo da Vinci, che quel punto era verso la cima, perchè <lb></lb>ivi il moto è più veloce. </s>

<s>Poi più tardi lo ritirarono verso il centro di gravità, <lb></lb>sapendo che quivi concorre d&#039;ogni parte all&#039;effetto la materia del legno. </s>

<s>Ve­<lb></lb>nivano però l&#039;esperienze a mettere in dubbio ambedue le soluzioni, e spe­<lb></lb>cialmente la seconda, essendo facile accorgersi dall&#039;altra parte che vi si con­<lb></lb>siderava, piuttosto la semplice gravità del bastone, che la gravità di lui, <lb></lb>congiunta con l&#039;impeto del braccio che lo mena. </s></p><p type="main">

<s>Il principio professato dal Filosofo, che cioè il moto accresce peso al <lb></lb>grave mosso, rettamente interpetrato, fu primo ad aprire le vie all&#039;ingegno <lb></lb>speculativo, il quale ebbe a ripensare che, movendosi nella lunghezza del <pb xlink:href="020/01/2894.jpg" pagenum="519"></pb>bastone le sezioni materiali via via dalla mano alla cima sempre più veloci, <lb></lb>era come se diventassero via via sempre più gravi. </s>

<s>Conseguiva di qui dover <lb></lb>essere il centro delle forze che si cercava, nel legno mosso, diverso dal cen­<lb></lb>tro di gravità del legno fermo, e s&#039;intese come non si potrebbe avere altri­<lb></lb>menti la ragione di questa diversità, che ritrovando le proporzioni, secondo <lb></lb>le quali, nell&#039;agitarsi la verga, crescono i pesi o i momenti alle particelle <lb></lb>distribuite in tutta la sua lunghezza. </s></p><p type="main">

<s>Si prevede bene, dietro queste considerazioni, come la soluzion del pro­<lb></lb>blema del centro della percossa nella clava dovesse occorrere a quei soli Ma­<lb></lb>tematici, che avessero chiara notizia della statica dei momenti, misurati dal <lb></lb>prodotto dei pesi nelle respettive distanze dai loro punti d&#039;appoggio, d&#039;onde <lb></lb>ne conseguiva la misura delle forze, o degli impeti, da quegli stessi pesi, <lb></lb>moltiplicatisi per le velocità o per gli spazi passati. </s>

<s>Ma si doveva, anche dopo <lb></lb>una tale notizia, trovar non poca difficoltà nell&#039;applicarla, essendo la clava <lb></lb>tutto un corpo solo: nè giovava riguardare la sua gravità dispersa adunata <lb></lb>in un centro, richiedendovisi, per riuscir nell&#039;intenzione, la più giusta mi­<lb></lb>sura degl&#039;incrementi proporzionali di moto nelle singole particelle, le quali <lb></lb>essendo infinite non promettevano di darsi resolute, se non a colui, che avesse <lb></lb>avuta la dottrina matematica degl&#039;infiniti. </s>

<s>La scienza necessaria perciò, a <lb></lb>dimostrare il centro della percossa, non sarebbe mancata nè al Cavalieri, nè <lb></lb>al Nardi, nè al Torricelli: eppure è notabile, nella storia della Meccanica, <lb></lb>che lasciassero que&#039;tre grandi nostri Matematici, per sè e per i loro succes­<lb></lb>sori, la questione intatta, della quale perciò rimase tutto il merito agli stra­<lb></lb>nieri. </s>

<s>Sappiamo che il Roberval diceva di aver trattato, nell&#039;ottavo libro della <lb></lb>sua Meccanica riformata, <emph type="italics"></emph>De centro percussionis potentiarum mobilium,<emph.end type="italics"></emph.end> e <lb></lb>ora è il tempo per noi di narrare i principii e i progressi fatti dal Mate­<lb></lb>matico francese nell&#039;istituire, e nell&#039;aggiungere alla Scienza della percossa <lb></lb>questa nuova e nobilissima parte, di che il Borelli stesso trentatre anni di <lb></lb>poi la lascerebbe in difetto. </s></p><p type="main">

<s>Per risponder dunque con geometrici argomenti alla proposta, che aveva <lb></lb>dato occasione a queste speculazioni, riguardava il Roberval il bastone cilin­<lb></lb><figure id="id.020.01.2894.1.jpg" xlink:href="020/01/2894/1.jpg"></figure></s></p><p type="caption">

<s>Figura 324.<lb></lb>drico ridotto a una linea materiale, <lb></lb>che, affissa in una delle sue estremità, <lb></lb>ondeggi liberamente dall&#039;altra. </s>

<s>Sia <lb></lb>AC (fig. </s>

<s>324) la detta linea, che ri­<lb></lb>mossa dal suo perpendicolo in AB <lb></lb>incontri, nello scendere e nel ridursi <lb></lb>alla sua prima stazione, un ostacolo, <lb></lb>contro cui si vuol sapere in qual punto <lb></lb>concentra le forze della percossa. </s>

<s>Qui <lb></lb>il metodo degl&#039;indivisibili suggeriva <lb></lb>di riguardare la linea oscillante riso­<lb></lb>luta in infiniti uguali punti ponderosi, come G, E, B, i momenti dei quali <lb></lb>vanno via via crescendo a proporzion degli spazi passati nel medesimo tempo, <pb xlink:href="020/01/2895.jpg" pagenum="520"></pb>ossia degli archi GNK, ELH, BCD, cosicchè, riducendo a pesi questi stessi <lb></lb>momenti, mentre nella quiete erano tutti uguali, ora nell&#039;agitazione son cre­<lb></lb>sciuti nelle dette proporzioni, e perciò il centro dell&#039;equilibrio, che dianzi <lb></lb>era nel mezzo, si deve ora esser mutato, e rimane a sapere dove sia sceso. </s></p><p type="main">

<s>A ciò invocava il Roberval questo teorema, d&#039;assai facile conclusione dai <lb></lb>principii archimedei: <emph type="italics"></emph>Due libbre caricate d&#039;ugual numero di pesi, di gran­<lb></lb>dezze proporzionali, e disposti in distanze proporzionali, son segate dal <lb></lb>centro dell&#039;equilibrio in parti proporzionali.<emph.end type="italics"></emph.end> Ora essendo gli archi GNK, <lb></lb>ELH, BCD proporzionali alle loro corde GK, EH, BD, e queste e quelli di­<lb></lb>sposti dal centro A in distanze proporzionali; è manifesto che la libbra AB <lb></lb>gravata di tutti i suoi infiniti momenti oscillatorii e la libbra AP gravata <lb></lb>delle linee BD, EH, GK, e di tutte le altre infinite, che contessono il trian­<lb></lb>golo ABD, son segate dai loro centri dell&#039;equilibrio o delle gravità in parti <lb></lb>proporzionali. </s>

<s>“ Centrum autem gravitatis trianguli ABD (conclude il Ro­<lb></lb>berval il suo ragionamento) dividit AP in Q, adeo ut AQ duplum sit <expan abbr="Pq.">Pque</expan> <lb></lb>uti demonstravit Lucas Valerius in tractatu suo <emph type="italics"></emph>De centro gravitatis,<emph.end type="italics"></emph.end> itaque <lb></lb>et O centrum agitationis rectae AB dividit AB in O, adeo ut AO duplum <lb></lb>sit BO, atque ita inventum est centrum percussionis rectae AB, quod erat <lb></lb>demonstrandum ” (Epist. </s>

<s>cartes., P. III, Amstelodami 1683, pag. </s>

<s>330). </s></p><p type="main">

<s>La bella dimostrazione fu inserita nel luogo citato col titolo soprascrit­<lb></lb>tovi: <emph type="italics"></emph>Centrum percussionis lineae rectae AB, circulariter rotatum circa <lb></lb>punctum fixum A, per D. </s>

<s>Roberval anno 1646,<emph.end type="italics"></emph.end> nel qual tempo l&#039;ebbe il <lb></lb>Cartesio, ma ell&#039;era stata ritrovata già da qualche anno, e certamente prima <lb></lb>del 1644, perchè, mostrata al Mersenno, questi se ne rallegrò, e prese ne&#039;suoi <lb></lb><emph type="italics"></emph>Cogitata physico-mathem.,<emph.end type="italics"></emph.end> a proposito della Meccanica, occasione d&#039;inserir <lb></lb>la notizia per decidere la questione, che vivamente s&#039;agitava intorno al cen­<lb></lb>tro della percossa nel bastone o nella spada, pronunziando risolutamente <lb></lb>questa sentenza: “ Ensis, cuius percussio maxima est, neque est in illius <lb></lb>centro gravitatis, neque in mucrone, sed versus ensis dodrantem, a cuspide <lb></lb>incipiente ” (Parisiis 1644, pag. </s>

<s>84). </s></p><p type="main">

<s>Ma il Roberval, ritornando sopra a considerare le oscillazioni di quella <lb></lb>sua linea, vedeva aprirsi la via a speculazioni di ben altra importanza, e <lb></lb>d&#039;altra nobiltà, rappresentandoglisi nel moto di lei l&#039;oscillare di un pendolo. </s>

<s><lb></lb>Riconobbe allora che il centro della percossa di quella era una medesima <lb></lb>cosa col centro di agitazione di questo, riguardate le forze sotto vario aspetto: <lb></lb>o in quanto cioè si concentrano nella linea o nella verga cilindrica, per perco­<lb></lb>tere con la massima energia in un ostacolo, che le sia contrapposto; o in <lb></lb>quanto si concentrano nel pendolo, a dare e a mantenere l&#039;impulso di reci­<lb></lb>procare le sue vibrazioni. </s>

<s>Resultava intanto alla mente del Roberval che le <lb></lb>vibrazioni del cilindro AB sono isocrone a quelle di un pendolo semplice, <lb></lb>lungo quanto AO, avendo ambedue in A il centro della sospensione. </s></p><p type="main">

<s>Era, in questa nuova e inaspettata notizia, come la prima e più lusin­<lb></lb>ghiera promessa di aver finalmente a risolvere un problema desideratissimo <lb></lb>dalla Cronometria, e il Roberval, <emph type="italics"></emph>vigente animi ardore,<emph.end type="italics"></emph.end> proseguì con l&#039;in-<pb xlink:href="020/01/2896.jpg" pagenum="521"></pb>trapreso metodo a ricercare i centri dell&#039;agitazione nelle superficie e ne&#039;so­<lb></lb>lidi, scegliendo, per non trovarsi impedito o arretrato ne&#039;primi passi, le <lb></lb>figure più semplici e più regolari, come i triangoli isosceli, le piramidi o <lb></lb>i coni. </s></p><p type="main">

<s>Sia il triangolo ABD, nella medesima figura, che oscilli avanti e indie­<lb></lb>tro intorno al vertice A: risoluto nelle sue linee infinite, tre delle quali siano <lb></lb>GK, FH, BD, i momenti ridotti a pesi, e de&#039;quali intendasi esser gravata la <lb></lb>libbra AP, stanno come le porzioni di superficie cilindriche descritte nel­<lb></lb>l&#039;oscillazione dalle dette linee, ossia come i rettangoli GK.AR, FH.AQ, <lb></lb>BD.AP, o come i quadrati di AR, AQ, AP, o finalmente come le ordinate <lb></lb>ER, IN, LM nel trilineo parabolico acuto AML, il centro di gravità del quale <lb></lb>essendo in una ordinata, che sega in Q l&#039;asse, talmente che sia AQ tre quarti <lb></lb>della AP, come Luca Valerio dimostra nella XXII proposizione del III libro <lb></lb><emph type="italics"></emph>De centro gravitatis;<emph.end type="italics"></emph.end> dunque in Q sarà pure il centro della percossa, nel <lb></lb>triangolo agitato. </s></p><p type="main">

<s>Se BAD rappresenta una piramide o un cono, le sezioni de&#039;piani o dei <lb></lb>circoli aventi per diametri GK,.FH, BD stanno come i quadrati delle distanze <lb></lb>AR, AQ, AP dal vertice, e perciò i loro momenti avranno la ragion com­<lb></lb>posta di essi quadrati e delle loro radici, ossia staranno come i cubi delle <lb></lb>distanze AR, AQ, AP, ossia come le ordinate ER, IN, ML nel trilineo AML, <lb></lb>supposto che la semiparabola AIM sia cubicale. </s>

<s>Di qui è che il centro della <lb></lb>percossa del solido sarà in Q, dove cade sulla libbra AP quell&#039;ordinata, che <lb></lb>passa per il centro di gravità del trilineo acuto. </s></p><p type="main">

<s>A indicar la posizione di questo centro sull&#039;asse occorreva opportuna la <lb></lb>proposizione LIV del trattato <emph type="italics"></emph>Dei centri di gravità<emph.end type="italics"></emph.end> del Torricelli, pubblicato <lb></lb>da noi qui addietro nel capitolo V: proposizione che l&#039;Autore diceva di aver <lb></lb>a quel modo generalmente conclusa <emph type="italics"></emph>ex doctrina parabolarum.<emph.end type="italics"></emph.end> Fosse nota <lb></lb>o no al Roberval questa generalissima dottrina, è un fatto che, nel caso par­<lb></lb>ticolare della parabola cubica, sapeva benissimo il Matematico parigino che <lb></lb>il centro di gravità del trilineo circoscritto da tale curva sega l&#039;asse così, <lb></lb>che la parte al vertice stia alla rimanente come quattro sta a uno: e tale <lb></lb>concludeva essere l&#039;indicazione del centro della percossa nella piramide o nel <lb></lb>cono. </s>

<s>Per la teoria de&#039;pendoli poi derivava il Roberval stesso dalle sue pro­<lb></lb>posizioni il seguente corollario: <emph type="italics"></emph>I pendoli semplici, isocroni ai composti della <lb></lb>figura ABD, che ora sia triangolo, ora piramide o cono, vanno lunghi nel <lb></lb>primo caso per tre quarti dell&#039;altezza del triangolo, e nel secondo per quat­<lb></lb>tro quinti dell&#039;altezza del cono.<emph.end type="italics"></emph.end> Nel caso però che la sospensione fosse fatta <lb></lb>dal mezzo P della base, il Roberval forse non ritrovò il centro della percossa <lb></lb>altro che per il triangolo, dicendo che divide l&#039;asse in due parti uguali, a <lb></lb>una delle quali perciò corrisponderebbe la lunghezza del pendolo, che fa nel <lb></lb>medesimo tempo il medesimo numero di vibrazioni. </s></p><p type="main">

<s>Dicemmo che forse fu così, perchè la regola fin qui seguita veniva, nelle <lb></lb>dette figure sospese per la base, a complicarsi di troppo: ond&#039;ebbe il Ro­<lb></lb>berval a cercare altre vie, quando volle proporsi figure di diversa indole dalle <pb xlink:href="020/01/2897.jpg" pagenum="522"></pb>precedenti, come per esempio il settor di cilindro, che, essendo un solido co­<lb></lb>lonnare ogni sezion del quale è un settore di circolo va sotto la medesima <lb></lb>invenzione di esso settor circolare. </s></p><p type="main">

<s>Se sia, nella medesima figura, AFLH il detto settore, col raggio per­<lb></lb>pendicolare AL sospeso dal punto A, intorno al quale si supponga oscillare <lb></lb>avanti e indietro dal piano, sopra cui s&#039;è disegnato; ritrovò il Roberval che <lb></lb>il centro della percossa nella figura cade in P, a una distanza da A, che sia <lb></lb>quarta proporzionale dopo la corda, l&#039;arco sotteso, e tre quarti del raggio; <lb></lb>cosicchè, fatto AQ=3/4 AL, sarebbe quel centro indicato dalla relazione <lb></lb>FH:FLH=AQ:AP. </s>

<s>Di qui resulta: I.o Che, essendo l&#039;arco di grandezza <lb></lb>finita, e perciò sempre maggiore della sua corda, il punto P riman sempre <lb></lb>al di sotto di <expan abbr="q.">que</expan> II.o Che, quando fosse FLH=4/3 FH, tornerebbe AP=AL, <lb></lb>ossia il centro della percossa sarebbe sceso nell&#039;infimo punto del settore. </s>

<s><lb></lb>III.o Finalmente che, quando la proporzione dell&#039;arco alla sua corda fosse <lb></lb>maggiore di quattro a tre, AP allora sarebbe maggiore di AL, e ciò vorrebbe <lb></lb>dire che il centro della percossa è passato fuori del settore, con esempio non <lb></lb>raro, ma pur notabile nella risoluzione di così fatti problemi, che, applicati <lb></lb>ai pendoli propri, dicono che il pendolo semplice isocrono può talvolta andar <lb></lb>più lungo di quello composto. </s></p><p type="main">

<s>Se avesse il Roberval, in questo soggetto, dimostrato altri teoremi non <lb></lb>è ora a investigarsi da noi, lasciandone la cura ai dotti Francesi, che, am­<lb></lb>biziosi di primeggiare sopra le altre nazioni, reintegrando, così per ciò che <lb></lb>riguarda i centri delle percosse, come per le altre sue sette parti, la Mecca­<lb></lb>nica robervalliana, darebbero un esempio ammirabile al mondo di quell&#039;alto <lb></lb>fastigio, a cui diceva il loro connazionale, contemporaneo a Galileo, di avere <lb></lb>eretta dai fondamenti la Scienza nuova del moto. </s>

<s>A noi basti di aver rac­<lb></lb>colti questi pochi materiali, preparati per soprapporsi come pietre angolari <lb></lb>nel superbo edifizio, ma rimasti, a quel che sembra, senza forma e dispersi <lb></lb>nella gelosa officina, alla quale non fu lasciato entrare che al solo Marino <lb></lb>Mersenno. </s>

<s>Egli, secondando quel suo genio, che per altre parti di questa <lb></lb>Storia è oramai ben conosciuto, proponeva a risolvere i problemi de&#039;centri <lb></lb>delle oscillazioni o delle percosse a quanti matematici incontrava, non per­<lb></lb>donando, per esempio, a Onorato Fabry, benchè sapesse il capo strambo <lb></lb>ch&#039;egli era, nè a Cristiano Huyghens, benchè lo vedesse ancora così giova­<lb></lb>netto. </s>

<s>Ma il Roberval, che sotto sotto stimolava il Frate, ardeva di un gran­<lb></lb>dissimo desiderio ch&#039;entrasse nell&#039;agone, per cimentarne le forze, il Carte­<lb></lb>sio, allora e sempre odiosissimo suo rivale, e il Cartesio rispondeva all&#039;invito <lb></lb>in una lettera sottoscritta il di 2 Marzo 1646, stabilendo al Mersenno, che <lb></lb>glie ne aveva fatto richiesta pochi giorni prima, per l&#039;invenzion de&#039;centri <lb></lb>delle percosse, le tre regole seguenti: </s></p><p type="main">

<s>I. </s>

<s>Se il corpo ha una sola dimensione sensibile, quale si può supporre <lb></lb>avere un cilindro, che sia pochissimo gresso, “ centrum eius agitationis est <lb></lb>in illo loco huius corporis, quod transit per centrum gravitatis trianguli ABCD <lb></lb>(nella medesima figura) cum describit triangulum illum per motum suum, <pb xlink:href="020/01/2898.jpg" pagenum="523"></pb>nimirum in puncto P, quod relinquit trientem longitudinis AC versus basin ” <lb></lb>(Epist., P. III cit., pag. </s>

<s>317). — II. </s>

<s>Se il corpo ha due dimensioni sensibili, <lb></lb>come la superficie del triangolo isoscele ABD, “ tum centrum agitationis illius <lb></lb>est in puncto lineae AP perpendicularis basi BD, quod transit per centrum <lb></lb>gravitatis pyramidis, quam describit triangulum, tum cum se movet circa <lb></lb>punctum A, nimirum in puncto Q, adeo ut QP sit quadrans lineae AP ” (ibid.). </s></p><p type="main">

<s>Passa il Cartesio a dare la terza regola, quando cioè il corpo abbia tre <lb></lb>dimensioni sensibili: regola, che poi spiegò meglio, quando il Mersenno, met­<lb></lb>tendosi a riscontrare le cose lette, le trovò discordare dalla esperienza. </s>

<s>Di ciò <lb></lb>sparse voce fra gli amici, nel numero de&#039;quali era il signore di Cavendisck, <lb></lb>gentiluomo inglese, che si trovava allora a Parigi, e il Cavendisck si rivolse <lb></lb>direttamente allo stesso Cartesio, che il di 30 Marzo di quello stesso anno 1646 <lb></lb>gli rispondeva in questa sentenza: Non deve far maraviglia se le mie regole <lb></lb>non rispondono ai fatti, concorrendo ad alterarle gl&#039;impedimenti, che il corpo <lb></lb>oscillante ha dal sostegno, e principalmente dal mezzo dell&#039;aria. </s>

<s>Del resto <lb></lb>il mio modo di ragionare è geometrico, e non può indurre in fallacie. </s>

<s>Se sia <lb></lb>un corpo solido, comunque irregolare, ABCD (fig. </s>

<s>325) sospeso in A, e avente <lb></lb><figure id="id.020.01.2898.1.jpg" xlink:href="020/01/2898/1.jpg"></figure></s></p><p type="caption">

<s>Figura 325.<lb></lb>nel perpendicolo AO il centro della sua gravità <lb></lb>naturale, io lo considero diviso in infinite sezioni <lb></lb>parallele all&#039;orizonte, le quali nell&#039;agitarsi descri­<lb></lb>vono porzioni di superficie cilindriche, ch&#039;io riduco <lb></lb>a piramidi tutte appuntate in A, e che, stando in <lb></lb>ragion composta delle basi e delle altezze, mi danno <lb></lb>la proporzione dei loro momenti. </s>

<s>“ Vis enim agita­<lb></lb>tionis earum, non saltem ex modo celeritatis earum <lb></lb>aextimatur, cuius differentia repraesentatur per di­<lb></lb>versas altitudines horum solidorum; verum etiam per diversam quantitatem <lb></lb>materiae ipsarum, quae per diversas magnitudines basium repraesentatur ” <lb></lb>(ibid., pag. </s>

<s>322). Poi da ciascuno degli infiniti punti dell&#039;asse AO immaginò che <lb></lb>sian segate nel mezzo, condotte perpendicolarmente a lui, altrettante linee <lb></lb>tutte proporzionali alle piramidi che iusiston sopr&#039;esse, come per esempio <lb></lb>sarebbero le linee FG, HI, e dice che nel centro di gravità della figura <lb></lb>piana AFHOIG, tessuta delle dette linee infinite, sta il centro dell&#039;agitazione <lb></lb>che si cercava. </s></p><p type="main">

<s>Questa, e l&#039;altra epistola cartesiana, che 28 giorni prima aveva diretta­<lb></lb>mente ricevuta, il Mersenno mostrò al Roberval, il quale notò che le prime <lb></lb>due regole in conseguenza riscontravano con le sue: Voleva però esaminarne <lb></lb>più sottilmente le ragioni, e intanto, non sazio ancora di tentare intorno a <lb></lb>ciò le forze dell&#039;ingegno matematico del Cartesio, — domandategli, padre, <lb></lb>diceva a esso Mersenno, se sa dirvi dove stia il centro della percossa nel <lb></lb>triangolo isoscele, quando sia sospeso dal mezzo della base, o quanta sia la <lb></lb>lunghezza del pendolo, che va sotto il medesimo tempo di un cono sospeso <lb></lb>per la cima. </s>

<s>— </s></p><p type="main">

<s>Il Mersenno, qualunque poi ne fosse la ragione, fece a nome suo far la <pb xlink:href="020/01/2899.jpg" pagenum="524"></pb>richiesta a una terza persona, alla quale il Cartesio francamente rispondeva <lb></lb>che, quanto al triangolo, il centro della percossa divide l&#039;asse in due parti <lb></lb>uguali. </s>

<s>“ Nam sumptis ad libitum in perpendiculari CD (fig. </s>

<s>326) punctis <lb></lb>E, H a medio E aequaliter distantibus, tum, ductis lineis FG, HI parallelis <lb></lb>basi, rectangulum CFG, semper aequale est rectangulo CHI, et consequenter <lb></lb><figure id="id.020.01.2899.1.jpg" xlink:href="020/01/2899/1.jpg"></figure></s></p><p type="caption">

<s>Figura 326.<lb></lb>figura, cuius centra gravitatis quaerenda essent, ex prae­<lb></lb>scripto regulae meae ad habendum centrum agitationis <lb></lb>huius trianguli, foret quadrangularis, et haberet centrum <lb></lb>suum gravitatis in puncto E ” (ibid., pag. </s>

<s>336). Quanto al <lb></lb>pendolo isocrono al cono, soggiungeva il Cartesio, a che <lb></lb>me ne richiede il Mersenno? </s>

<s>Non aveva egli quella lun­<lb></lb>ghezza dalla mia terza regola, con faeile calcolo, di che <lb></lb>perciò a lui, e al signore di Roberval ne lasciavo la cura? </s>

<s><lb></lb>Ma se vogliono risparmiarsi questa fatica, dirò a loro <lb></lb>la cosa, ch&#039;è tale: “ nimirum, tum cum pyramis aut conus per apicem su­<lb></lb>spensus est, altitudo eius debet esse, secundum longitudinem funependuli, <lb></lb>veluti quinque ad quatuor ” (ibid.). </s></p><p type="main">

<s>Esaminatesi dal Roberval le tre regole cartesiane, con quell&#039;animosità <lb></lb>che gl&#039;intorbidava il giudizio, sentenziò che i principii, dietro i quali erano <lb></lb>state condotte, non potevano approvarsi, perchè, venendo a farne l&#039;applica­<lb></lb>zione ai centri della percossa ne&#039;settori di cilindro o di cerchio, conducevano <lb></lb>a conseguenze false. </s>

<s>Ritornando infatti alla figura 324, che ha in AFLH di­<lb></lb>segnato un settor circolare, la superficie, dal centro di gravità della quale <lb></lb>sarebbe, secondo la regola cartesiana, indicato nel detto settore il centro della <lb></lb>percossa, è il trilineo parabolico AML, per cui tornerebbe esso centro in Q, <lb></lb>distante da A per tre quarti di AL. </s>

<s>Ma io ho dimostrato, diceva il Rober­<lb></lb>val, che il punto richiesto deve essere di Q sempre più basso, qual sarebbe <lb></lb>per esempio P, nè può questo concorrere mai con quello, se non a patto <lb></lb>che l&#039;arco del settore sia uguale alla corda, ossia quando l&#039;angolo FAH fosse <lb></lb>minimo così, da poter aversi la figura per un triangolo isoscele, in cui vera­<lb></lb>mente il centro della percossa cade sull&#039;asse a tre quarti di distanza dal <lb></lb>punto di sospensione. </s>

<s>Ma per il settore di grandezza finita, che naturalmente <lb></lb>è quello sopra cui può cader l&#039;invenzione, il metodo cartesiano, sentenzio­<lb></lb>samente concludeva il Roberval, è manifestamente falso. </s></p><p type="main">

<s>Pervenute a notizia del Cartesio queste censure, diceva per risposta che <lb></lb>sarebbero allora convinte di falsità le sue conclusioni, quando quelle dell&#039;av­<lb></lb>versario si dovessero aver per indubitate. </s>

<s>Ma perchè ciò non apparisce dal <lb></lb>suo discorso, “ nihil me iudice aliud probat quam quod praetendat ut plus <lb></lb>authoritati eius, quam meis rationibus tribuam ” (ibid., pag. </s>

<s>331). Nella epi­<lb></lb>stola infatti, nella quale si facevano al Cavendisck notare gli errori del Car­<lb></lb>tesio, lasciò il Roberval di dimostrare la proposizione del centro della per­<lb></lb>cossa nei settori, <emph type="italics"></emph>quia aequo longior esset<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>326), ma egli era <lb></lb>sicuro della verità di lei, confermata poi da tutti i Matematici, e principal­<lb></lb>mente dall&#039;Huyghens, nella propos. </s>

<s>XXI della quarta parte dell&#039;Orologio oscil-<pb xlink:href="020/01/2900.jpg" pagenum="525"></pb>latorio, dove dice che il pendolo isocrono al settore di circolo ha lunghezza <lb></lb><emph type="italics"></emph>trium quartarum rectae, quae sit ad radium ut arcus ad subtensam<emph.end type="italics"></emph.end><lb></lb>(pag. </s>

<s>159). Nè l&#039;Huyghens però nè nessun altro di que&#039;matematici avrebbero <lb></lb>così assolutamente sentenziato contro il Cartesio, come fece il Roberval, esa­<lb></lb>minando la questione con più sincero giudizio di lui. </s></p><p type="main">

<s>La prima regola per verità, scritta nella Lettera al Mersenno, appresso <lb></lb>un rigido Geometra non troverebbe scusa, perchè quel che si chiama trian­<lb></lb>golo è un settore di cerchio, e si sa bene quanto sia diverso il centro di <lb></lb>gravità nelle due figure, quando siano, come sempre si suppone in questi <lb></lb>esempi, di grandezze finite. </s>

<s>Anche la seconda non si può dlre esattamente <lb></lb>descritta, ma la colpa maggiore è della terza, lusingatrice come chi prometta <lb></lb>di torre uno di difficoltà, mettendolo in un&#039;altra maggiore; quasi che il tro­<lb></lb>var il centro di gravità nelle superfice piane fosse più facile, che trovar nel <lb></lb>solido direttamente il centro della percossa. </s></p><p type="main">

<s>Nel caso però che il solido fosse di figura regolare, e fosse di più de­<lb></lb>terminato il modo della sua sospensione, come nel cono pendulo dalla cima, <lb></lb>il metodo era per sè sufficiente, e aveva infatti condotto il Cartesio a una <lb></lb>conclusione, confermata da tutti per vera. </s>

<s>Nè differiva questo metodo carte­<lb></lb>siano in sostanza da quello del Roberval, come non ne differiva l&#039;altro, con <lb></lb>cui si ricercava il centro della percossa nel triangolo isoscele pendulo dalla <lb></lb>base, applicandosi qui alla libbra i pesi proporzionali alle piramidi, o alle <lb></lb>linee rette nella figura piana, mentre là le si applicavano que&#039;medesimi pesi <lb></lb>ridotti all&#039;egualità dinamica dei momenti. </s>

<s>Ma la virtù di concludere derivava <lb></lb>in ambedue gli autori dall&#039;essere i rettangoli, fatti delle equidistanti dal mezzo <lb></lb>dell&#039;asse e dalle rispettive distanze dai punti di sospensione, uguali, come, <lb></lb>prese per esempio nella medesima figura 326 le due FG, HI, o le loro duple <lb></lb>GM, IN, si vede conseguire dall&#039;equazione GM:IN=DF:DH=CH:CF. </s>

<s><lb></lb>Il Roberval considerava la libbra CD gravata de&#039;momenti <foreign lang="grc">π</foreign>GM.CF, <foreign lang="grc">π</foreign>IN.CH, <lb></lb>i quali eguagliandosi insieme essi stessi, come pure s&#039;uguagliano gli altri loro <lb></lb>simili infiniti, debbono avere nel mezzo di essa CD il centro del loro equi­<lb></lb>librio. </s>

<s>Il Cartesio trasformava i momenti in piramidi, le basi delle quali rap­<lb></lb>presentassero la quantità di materia, e le altezze la velocità: e trovate que­<lb></lb>ste piramidi uguali, le linee, secondo la regola prese ad esse proporzionali, <lb></lb>intessono il rettangolo PQ, e gravitando tutte ugualmente sopra la libbra CD, <lb></lb>s&#039;equilibrano perciò intorno al centro della figura. </s></p><p type="main">

<s>Dunque il Roberval, condannando senza discrezione il Cartesio, condan­<lb></lb>nava insieme anche sè stesso: che se voleva esser più giusto doveva dire <lb></lb>piuttosto che la terza regola cartesiana non era così generale come l&#039;Autore <lb></lb>la spacciava, ma solamente applicabile in alcuni esempi più semplici di figure <lb></lb>regolari, e così confessare che nè egli nè il suo emulo, guali che si fossero <lb></lb>i progressi fatti, non avevano però ancora trovato il metodo universale di ri­<lb></lb>solvere questo nuovo genere di problemi. </s></p><p type="main">

<s>Que&#039;progressi nonostante non giovarono alla Scienza, perchè ne rimase <lb></lb>per qualche tempo ne&#039;soli privati commerci epistolari la notizia: e avendo <pb xlink:href="020/01/2901.jpg" pagenum="526"></pb>il Mersenno nel 1644 annunziato, senza dir le ragioni, che il centro della <lb></lb>percossa nella spada o nella verga cade in parte, distante dalla punta il dop­<lb></lb>pio che dalla impugnatura; Isacco Vossio nel 1666, come aveva condannate <lb></lb>tutte le altre opinioni, così non risparmiava quella di coloro “ qui maximam <lb></lb>statuunt percussionem provenientem ab ea parte ensis, quae dodrante abest <lb></lb>a mucrone ” (<emph type="italics"></emph>De Nili orig.,<emph.end type="italics"></emph.end> Hagae Com. </s>

<s>1666, pag. </s>

<s>165-66). </s></p><p type="main">

<s>Poco prima che si pubblicasse l&#039;Orologio oscillatorio, e in quel tempo <lb></lb>che il Wallis attendeva a dar perfezione alla terza parte della sua Mecca­<lb></lb>nica, si divulgarono le epistole al Mersenno e al Cavendisck, dove il Car­<lb></lb>tesio e il Roberval stabilivano le regole, e annunziavano le conclusioni dei <lb></lb>loro teoremi. </s>

<s>O si fosse inspirato a coteste letture, o fosse il frutto di spe­<lb></lb>culazioni sue proprie, è un fatto ch&#039;esso Wallis, aggiungendo in fine al suo <lb></lb>trattato <emph type="italics"></emph>De percussione<emph.end type="italics"></emph.end> la proposizione XV, nella quale si sottoponevano al <lb></lb>calcolo le forze, che si concentrano in un punto a dare la massima percossa; <lb></lb>non fa altro se non che ordinare i teoremi cartesiani o robervalliani, dimo­<lb></lb>strandoli col medesimo metodo e ripetendone talvolta gli errori, come per <lb></lb>esempio intorno al centro dell&#039;oscillazione della piramide o del cono, indi­<lb></lb>cato al medesimo modo che dal Cartesio e dal Roberval, ma tanto diversa­<lb></lb>mente da quel che poi trovò l&#039;Huyghens, nella XXII proposizione della P.IV <lb></lb>dell&#039;<emph type="italics"></emph>Orologio oscillatorio<emph.end type="italics"></emph.end> (ediz. </s>

<s>cit., pag. </s>

<s>166, 67), che Giacomo Bernoulli <lb></lb>ebbe ad accusar pubblicamente il Wallis di avere sbagliato: “ Wallisius in <lb></lb>cono ex. </s>

<s>gr. </s>

<s>aliud percussionis, Hugenius aliud oscillationis centrum assignat. </s>

<s><lb></lb>Fallitur enim Wallisius in eo quod integrae basi coni, circulisque basi pa­<lb></lb>rallelis, non maiorem distantiam ab axe rotationis, celeritatemque tribuit, ea <lb></lb>quam ipsa horum circulorum centra obtinent ” (<emph type="italics"></emph>Opera,<emph.end type="italics"></emph.end> T. I, Genevae 1744, <lb></lb>pag. </s>

<s>464). Il Wallis infatti (chiamato <emph type="italics"></emph>a<emph.end type="italics"></emph.end> l&#039;asse, <emph type="italics"></emph>b<emph.end type="italics"></emph.end> il raggio della base del <lb></lb>cono) aveva indicata la distanza D del centro dell&#039;oscillazione dal vertice con <lb></lb>l&#039;equazione D=4/5<emph type="italics"></emph>a,<emph.end type="italics"></emph.end> mentre è veramente D=4/5<emph type="italics"></emph>a<emph.end type="italics"></emph.end>+<emph type="italics"></emph>b2<emph.end type="italics"></emph.end>/5<emph type="italics"></emph>a,<emph.end type="italics"></emph.end> per cui l&#039;in­<lb></lb>dicazion wallisiana è in difetto dalla vera dimostrata dall&#039;Huyghens del quinto <lb></lb>della terza proporzionale, dopo l&#039;altezza del cono, e il raggio della base. <lb></lb><figure id="id.020.01.2901.1.jpg" xlink:href="020/01/2901/1.jpg"></figure></s></p><p type="caption">

<s>Figura 327.</s></p><p type="main">

<s>Si propone anche il Wallis in primo luogo <lb></lb>il centro della percossa nella linea materiale o <lb></lb>nella sottilissima verga cilindrica AB (fig. </s>

<s>327), <lb></lb>la quale egli immagina rotarsi intorno al <lb></lb>punto A, per cadere liberamente sul piano AC. </s>

<s><lb></lb>Divide essa verga in infinite sezioni uguali, <lb></lb>che crescono via via i loro momenti a propor­<lb></lb>zione delle distanze, come le linee del trian­<lb></lb>golo ACD: e ne conclude che, essendo AC <lb></lb>libbra sopra la quale s&#039;intendano gravare, a <lb></lb>proporzione di esse linee, i momenti; il ri­<lb></lb>chiesto centro della percossa, nella detta verga, risponde in E, dove cade <lb></lb>la linea, che passa per il centro di gravità del piano triangolare. </s></p><pb xlink:href="020/01/2902.jpg" pagenum="527"></pb><p type="main">

<s>Se il percuziente è un triangolo isoscele, appuntato in A con l&#039;apice, le <lb></lb>sezioni e le velocità crescono come le distanze, e perciò i momenti come i <lb></lb>quadrati di esse distanze, o come le ordinate del trilineo parabolico ACD <lb></lb>(fig. </s>

<s>328), ond&#039;è che se FE è tra queste ordinate quella, che passa per il <lb></lb>baricentro di esso trilineo, in E caderà il centro della percossa. </s>

<s>Se poi <lb></lb>suppongasi il triangolo AB trasformato in un cono, <lb></lb><figure id="id.020.01.2902.1.jpg" xlink:href="020/01/2902/1.jpg"></figure></s></p><p type="caption">

<s>Figura 328.<lb></lb>crescendo le sezioni di lui come i quadrati delle di­<lb></lb>stanze, e le velocità come le semplici distanze dal <lb></lb>centro della rotazione, i momenti progrediranno <lb></lb>come i cubi delle distanze medesime, e dal punto <lb></lb>E pure, da cui s&#039;intenda pendere nella libbra l&#039;or­<lb></lb>dinata, che passa per il centro di gravità del trilineo <lb></lb>parabolico cubico ACD; verrà indicato il luogo, dove <lb></lb>il cono percote con la massima energia. </s></p><p type="main">

<s>Mirabile è in verità la legge dinamica di questi <lb></lb>progressi: un punto, come sarebbe F nella fig. </s>

<s>327, <lb></lb>acquista movendosi per percotere la potenza della <lb></lb>linea GH, ossia della parabola di grado zero; la linea <lb></lb>acquista la potenza di un triangolo, ossia della pa­<lb></lb>rabola di grado uno; il triangolo quella di una parabola di grado due, e <lb></lb>il cono o la piramide di una parabola di grado tre. </s>

<s>Il centro poi della per­<lb></lb>cossa, nell&#039;ingradarsi così il percuziente dal punto alla linea, dalla linea <lb></lb>alla superficie, dalla superficie al solido; sega così la libbra, che la parte al <lb></lb>vertice stia alla rimanente come uno a due, come due a tre, come tre a <lb></lb>quattro, come quattro a cinque: intanto che, lusingato il Wallis dal mirabile <lb></lb>ordinamento di questa serie, credè che seguitasse anche al di là de&#039;pochi, <lb></lb>e così semplici esempi considerati. </s>

<s>“ Atque ad eamdem formam, mutatis <lb></lb>mutandis, procedendum erit, quaecumque fuerit figura corporis moti, sive <lb></lb>ordinata sive utcumque inordinata, et ubicumque ponatur centrum rotationis <lb></lb>“ (Londini 1871, pag. </s>

<s>679). Ma avrebbe il Roberval anche a lui ripetute le <lb></lb>obiezioni fatte al Cartesio, e noi concluderemo che nessuno dei tre grandi <lb></lb>Matematici s&#039;era ancora incontrato in quella regola universale, che si desi­<lb></lb>derava, e dalla quale solamente si deciderebbe con autorità di scienza se <lb></lb>sian sempre e in tutti i casi una medesima cosa i centri dell&#039;oscillazione, <lb></lb>e della percossa. </s></p><p type="main">

<s>Intanto quel giovanetto, a cui aveva il Mersenno proposto a risolvere i <lb></lb>problemi robervalliani, era divenuto l&#039;autore dell&#039;<emph type="italics"></emph>Orologio oscillatorio,<emph.end type="italics"></emph.end> nella <lb></lb>introduzione alla quarta parte della quale opera narrava come, arretratosi da <lb></lb>principio alle difficoltà nel primo aggresso incontrate, poi le superasse feli­<lb></lb>cemente, all&#039;occasione di cercare una regola matematica, per temperare i pesi <lb></lb>al pendolo del suo nuovo automato, deducendo quella stessa regola da prin­<lb></lb>cipii più certi, e più generali di quel che non avessero fatto i suoi prede­<lb></lb>cessori. </s>

<s>Erano cotali principii illustrati dall&#039;Huyghens per definizioni, e sta­<lb></lb>biliti sopra ipotesi nuove, d&#039;onde venivasi a concluder l&#039;intento nella quinta <pb xlink:href="020/01/2903.jpg" pagenum="528"></pb>proposizione dell&#039;opera e della parte citata, apparecchiatesi già le quattro <lb></lb>precedenti per lemmi. </s></p><p type="main">

<s>Siano i due pesi A, B (fig. </s>

<s>329) sulla leva AC: tenderanno a scendere <lb></lb>intorno al centro C, con momenti misurati da A.AC+B.BC. </s>

<s>Ma se nei <lb></lb>punti A′, B′ si sospenderanno due <lb></lb><figure id="id.020.01.2903.1.jpg" xlink:href="020/01/2903/1.jpg"></figure></s></p><p type="caption">

<s>Figura 329.<lb></lb>altri pesi A′, B′, uguali ai primi <lb></lb>e a distanze uguali dal centro, si <lb></lb>farà l&#039;equilibrio. </s>

<s>Ora, essendo in D <lb></lb>il centro di gravità dei detti pesi <lb></lb>A, B, è manifesto che rimarrà pure <lb></lb>fra questi l&#039;equilibrio, ridotti che <lb></lb>siano in esso centro, e perciò i <lb></lb>momenti di A′ e di B′, ossia di A <lb></lb>e di B, equivarranno al momento <lb></lb>unico di A e di B concentrati in <lb></lb>D insieme, e sarà insomma A.AC+B.BC=(A+B)DC, come per <lb></lb>altre vie più oblique dimostra l&#039;Huyghens, nella sua prima proposta, in que­<lb></lb>sta forma: <emph type="italics"></emph>Ponderibus quotlibet, ad eamdem partem plani existentibus, si <lb></lb>a singulorum centris gravitatis agantur in planum illud perpendiculares; <lb></lb>hae singulae in sua pondera ductae tantundem simul efficient, ac perpen­<lb></lb>dicularis, a centro gravitatis ponderum omnium in planum idem cadens, <lb></lb>ducta in pondera omnia<emph.end type="italics"></emph.end> (pag. </s>

<s>123). </s></p><p type="main">

<s>Che se A, B sono uguali, dalle cose dimostrate tornerà AC+BC= <lb></lb>2 DC, per facile corollario, di cui nonostante fece l&#039;Huyghens soggetto alla <lb></lb>sua proposizione seconda: <emph type="italics"></emph>Positis quae prius, si pondera omnia sint aequa­<lb></lb>lia, dico summam omnium perpendicularium aequari perpendiculari a cen­<lb></lb>tro gravitatis ductae, secundum ponderum numerum<emph.end type="italics"></emph.end> (pag. </s>

<s>125). </s></p><p type="main">

<s>Rimossi A′, B′ contrappesi della leva, i pesi A, B insieme col punto D <lb></lb>scenderanno per gli archi AF, BE, DH dalle altezze perpendicolari CF, CE, CH, <lb></lb>uguali alle distanze AC, BC, DC: e perciò, sostituite queste distanze nell&#039;equa­<lb></lb>zione data dalla prima, riman senz&#039;altro dimostrata la terza proposizione <lb></lb>ugeniana: <emph type="italics"></emph>Si magnitudines quaedam descendant omnes vel ascendant, licet <lb></lb>inaequalibus intervallis; altitudines descensus vel ascensus cuiusque, in <lb></lb>ipsam magnitudinem ductae, efficient summam productorum aequalem ei, <lb></lb>quae fit ex altitudine descensus vel ascensus centri gravitatis omnium ma­<lb></lb>gnitudinum, ducta in omnes magnitudines<emph.end type="italics"></emph.end> (ibid.). </s></p><p type="main">

<s>Di qui, e dal principio fondamentale dinamico, che cioè un grave, scen­<lb></lb>dendo e riflettendo in alto il suo moto, giunge alla precisa altezza perpen­<lb></lb>dicolare da cui fu sceso, e non più in alto, perchè la forza non può dar più <lb></lb>di quel ch&#039;ella ha, e non più in basso dando essa forza di meno, perchè si <lb></lb>suppone che di lei nulla si perda, e che produca tutto il suo effetto; l&#039;Huy­<lb></lb>ghens conclude la sua quarta proposizione, che è tale: Siano i tre corpi <lb></lb>A, B, C (fig. </s>

<s>330) connessi colla verga senza peso DC, nell&#039;atto di girare <lb></lb>intorno al centro D, per sceudere a quietarsi nel perpendicolo DF: e giunti <pb xlink:href="020/01/2904.jpg" pagenum="529"></pb>i detti corpi in G, H, K, supponiamo che incontrino un ostacolo, in cui ur­<lb></lb>tando si sciolgano dai loro legami, e risaltino A in L, B in M, C in N, dove <lb></lb>essendo, risponda in P il loro comun centro di gravità, mentre trovavasi <lb></lb><figure id="id.020.01.2904.1.jpg" xlink:href="020/01/2904/1.jpg"></figure></s></p><p type="caption">

<s>Figura 330.<lb></lb>dianzi in E, quand&#039;erano connessi con la verga: è <lb></lb>manifesto, dalle cose dimostrate e supposte, che non <lb></lb>può il punto P essere risalito nè a maggiore, nè a <lb></lb>minore altezza perpendicolare del punto E. </s></p><p type="main">

<s>Premesse le quali cose, abbiasi il pendolo com­<lb></lb>posto dei tre pesi A, B, C (fig. </s>

<s>331): il pendolo <lb></lb>semplice corrispondente, dice l&#039;Huyghens, avrà tale <lb></lb>precisa lunghezza quale resulta dal dividere la somma <lb></lb>de&#039;prodotti de&#039;pesi ne&#039;quadrati delle distanze dal­<lb></lb>l&#039;asse dell&#039;oscillazione, per il prodotto della somma <lb></lb>dei detti pesi nella distanza del loro centro di gra­<lb></lb>vità dal medesimo asse, cosicchè, posta essere DL la <lb></lb>richiesta lunghezza, sia <lb></lb>DL=(A.AD2+B.BD2+C.CD2)/DE(A+B+C). </s></p><p type="main">

<s>Dimostrar ciò, dice l&#039;Autore, vale quanto dimostrare che, presa FG <lb></lb>nella figura 332 uguale a DL, e fatto l&#039;angolo GFH uguale ad LDK, in tutti <lb></lb><figure id="id.020.01.2904.2.jpg" xlink:href="020/01/2904/2.jpg"></figure></s></p><p type="caption">

<s>Figura 331.<lb></lb>i punti, come P, O, similmente situati negli <lb></lb>archi LN, GM, le velocità sono uguali: cosic­<lb></lb>chè, giunto G in O, abbia concepito tale im­<lb></lb>peto, da sollevarsi all&#039;altezza perpendicolare <lb></lb>OY, uguale alla PS. </s></p><p type="main">

<s>Se ciò che si asserisce non è vero, pro­<lb></lb>segue così l&#039;Huyghens a ragionare, ammettasi <lb></lb>dunque che la velocità in P sia diversa da <lb></lb>quella in O, e in primo luogo si supponga <lb></lb>maggiore, cosicchè l&#039;altezza, a cui può solle­<lb></lb>varsi il mobile, scioltosi dal suo vincolo, sia <lb></lb>maggiore della PS. </s>

<s>Presi AT, EQ, BV, CX <lb></lb>archi tutti simili a LP, chiamate Va.P, <lb></lb>Va.T le velocità in P e in T, e invocata <lb></lb>la nota legge de&#039;quadrati delle velocità proporzionali agli spazi, avremo <lb></lb>Va.P:Va.T=DL:AD, e insieme Va.P2:Va.T2=DL2:AD2= <lb></lb>SP:TZ. </s>

<s>Ma perchè si vuole che il mobile nello scendere abbia, giunto <lb></lb>ch&#039;egli sia in P, acquistato tal impeto, da sollevarsi ad altezza maggiore di PS; <lb></lb>sarà dunque TZ&gt;SP.AD2/DL2, e anche, per simili ragioni, VZ′&gt;SP.BD2/DL2, <lb></lb>e XZ″&gt;SP.CD2/DL2, d&#039;onde </s></p><p type="main">

<s><emph type="center"></emph>A.TZ+B.VZ′+CXZ″&gt;SP(A.AD2+B.BD2+C.CD2)/DL2.<emph.end type="center"></emph.end><pb xlink:href="020/01/2905.jpg" pagenum="530"></pb>Or, essendosi posto DL=(A.AD2+B.BD2+C.CD2)/DE(A+B+C), dal moltiplicarsi <lb></lb>questa stessa equazione per SP s&#039;ottiene </s></p><p type="main">

<s><emph type="center"></emph>SP(A.AD2+B.BD2+C.CD2)/DL2=SP.DE(A+B+C)/DL,<emph.end type="center"></emph.end><lb></lb>e in conseguenza A.TZ+B.VZ′+CXZ″&gt;SP.DE(A+B+C)/DL. </s>

<s><lb></lb>Posto poi in R′ il centro di gravità de&#039;pesi risaliti in Z, Z′, Z″, sarà <lb></lb>A.TZ+B.VZ′+CXZ″=QR′(A+B+C) e dall&#039;essere LD:ED= <lb></lb>SP:QR s&#039;ha QR=SP.ED/LD, e perciò QR′(A+B+C)&gt;QR(A+B+C). <lb></lb>E perchè il primo termine della disuguaglianza esprime la quantità di moto <lb></lb>nell&#039;ascesa del sistema, e il secondo la quantità di moto nella discesa; ne <lb></lb>verrebbe per conseguenza l&#039;assurdo che questo sia maggiore di quello. </s>

<s>A un <lb></lb>simile assurdo condurrebbe il supposto che la velocità in P, nel percorrere <lb></lb>l&#039;arco LN, sia minore della velocità in O, nel percorrere l&#039;arco GM; dun­<lb></lb>que riman da ciò dimostrata la celebre proposizione quinta ugeniana: <emph type="italics"></emph>Dato <lb></lb>pendulo ex ponderibus quotlibet composito, si singula ducantur in qua­<lb></lb>drata distantiarum suarum ab axe oscillationis, et summa productorum <lb></lb>dividatur per id quod fit, ducendo ponderum summam in distantiam cen­<lb></lb>tri gravitatis communis omnium ab eodem axe oscillationis; orietur lon­<lb></lb>gitudo penduli simplicis composito isochroni, sive distantia inter axem et <lb></lb>centrum oscillationis ipsius penduli compositi<emph.end type="italics"></emph.end> (pag. </s>

<s>127, 28). </s></p><p type="main">

<s>Di qui è che se i pesi, qualunque sia il loro numero N, son tutti uguali, <lb></lb>rappresentati da P; se le distanze di ciascuno dal punto di sospensione del <lb></lb>sistema si chiamino A, B, C...., e sia D la distanza del comun centro di <lb></lb>gravità di essi pesi dal detto punto di sospensione; la lunghezza X del <lb></lb>pendolo semplice, isocrono al composto, sarà data dalla formula X= <lb></lb>P(A2+B2+C2....)/N.P.D=(A2+B2+C2....)/N.D, secondo quel che s&#039;annun­<lb></lb>ziava dall&#039;Huyghens stesso nella sua VI proposizione: <emph type="italics"></emph>Dato pendulo, ex <lb></lb>quotcumque ponderibus aequalibus composito, si summa quadratorum facto­<lb></lb>rum a distantiis, quibus unumquodque pondus abest ab axe oscillationis, <lb></lb>applicetur ad distantiam centri gravitatis communis ab eodem oscillatio­<lb></lb>nis axe, multiplicem secundum ipsorum ponderum numerum; orietur lon­<lb></lb>gitudo penduli simplicis composito isochroni<emph.end type="italics"></emph.end> (pag. </s>

<s>131). </s></p><p type="main">

<s>Si disse la quinta di queste recondite proposizioni ugeniane celebre, non <lb></lb>tanto per l&#039;importanza ch&#039;ell&#039;ebbe ne&#039;progressi della Scienza del moto, <lb></lb>quanto per le contradizioni da varie parti subite, e dalle quali finalmente <lb></lb>riuscì vittoriosa. </s>

<s>Il padre Deschales, dop&#039;aver nel trattato VIII del suo <emph type="italics"></emph>Mun­<lb></lb>dus mathematicus<emph.end type="italics"></emph.end> proposti vari teoremi, attinenti al centro delle percosse, <lb></lb>ne&#039;quali per verità non s&#039;aggiungeva nulla di nuovo a ciò, che avevano dimo­<lb></lb>strato il Roberval e il Cartesio, e che oramai per l&#039;opera del Wallis era <lb></lb>stato fatto pubblicamente noto; soggiungeva, nel seguente trattato IX, al-<pb xlink:href="020/01/2906.jpg" pagenum="531"></pb>cune cose concernenti i centri delle oscillazioni, proponendosene principal­<lb></lb>mente l&#039;invenzione in un pendolo composto di due globi uguali. </s></p><p type="main">

<s>Se questi globi, quali s&#039;intendono rappresentati per B, C (fig. </s>

<s>332), fos­<lb></lb>sero in quiete, il centro del moto sarebbe nel mezzo di BC. </s>

<s>Ma perchè C è <lb></lb>più lontano dal punto A di sospen­<lb></lb><figure id="id.020.01.2906.1.jpg" xlink:href="020/01/2906/1.jpg"></figure></s></p><p type="caption">

<s>Figura 332.<lb></lb>sione, intorno a cui si move più <lb></lb>veloce, è come se fosse più peso di <lb></lb>B, secondo la ragion dei momenti, <lb></lb>i quali sono C.AC, B.AB, e per­<lb></lb>ciò il centro del moto dividerà la <lb></lb>linea BC in D talmente, che deb­<lb></lb>ba aversi la proporzion reciproca <lb></lb>B.AB:C.AC=CD:DB, ossia, <lb></lb>nel presente supposto, AB:AC= <lb></lb>CD:DB, dalla quale s&#039;avrà indi­<lb></lb>cato il punto D, in cui termina la <lb></lb>lunghezza del pendolo semplice iso­<lb></lb>crono al composto. </s></p><p type="main">

<s>Maggior difficoltà, prosegue il <lb></lb>Deschales a dire, s&#039;incontra, met­<lb></lb>tendosi a ricercare il centro dell&#039;o­<lb></lb>scillazione in un triangolo isoscele <lb></lb>o in un cono, sospesi ora per l&#039;apice, <lb></lb>ora per la base: ma difficilissima è <lb></lb>questa medesima invenzione, quan­<lb></lb>do tutto intero il triangolo o il cono <lb></lb>si facciano oscillare pendenti da un <lb></lb>filo, “ quae tantum innuere volui ut is cui licebit per otium examinet, haec <lb></lb>autem non sunt ita constituta, ut iis acquiescam. </s>

<s>Profert regulam aliquam <lb></lb>D. Eughens, nempe ut multiplicetur pondus quodlibet per quadratum suae <lb></lb>distantiae, fiatque summa productorum: haec summa dividatur per sum­<lb></lb><gap></gap>am momentorum ” (Lugduni, editio alt. </s>

<s>1690, T. II, pag. </s>

<s>322): regola <lb></lb>che il Deschales confessa aver esatto riscontro con la sua data di sopra, <lb></lb>a proposito del pendolo composto di due pesi uguali. </s>

<s>Se sia infatti AB= <lb></lb>2, AC=8, B=C=4, e per conseguenza BC=6, sostituiti que­<lb></lb>sti valori numerici nell&#039;equazione AB:AC=CD:DB, o nella compo­<lb></lb>sta da lei AB+AC:AB=CD+DB:CD, avremo CD=2.6/10=1+1/5, <lb></lb>e perciò AD=AC—CD=8—1—1/5=6+4/5, precisamente come <lb></lb>s&#039;ha dalla regola ugeniana, secondo la quale condotto il calcolo s&#039;ha pure <lb></lb>AD=(4+64)/10=6+4/5. </s></p><p type="main">

<s>Ma potevasi il riscontro fra le due regole dimostrare più generalmente, <lb></lb>concludendo il valore di AD dall&#039;equazione AB:AC=CD:DB, la quale <pb xlink:href="020/01/2907.jpg" pagenum="532"></pb>dà per composizione AB+AC:AB=CD+DB:CD=BC:CD= <lb></lb>AC—AB:CD, d&#039;onde CD=AB(AC—AB)/(AC+AB), e perciò AC—CD=AD= <lb></lb>AC—AB(AC—AB)/(AC+AB)=(AC2+AB2)/(AC+AB), che è la formula stessa stabilita dal­<lb></lb>l&#039;Huyghens nella sua VI proposizione. </s></p><p type="main">

<s>Non per questo credè il Deschales di dover revocare contro lo stesso <lb></lb>Huyghens la sua sentenza, ma anzi, considerando il pendolo composto, nel <lb></lb>caso che i due globi uguali comprendessero nel mezzo il centro dell&#039;oscilla­<lb></lb>zione, concluse da parecchie esperienze, istituite col variare ai pesi grandezze <lb></lb>e distanze, <emph type="italics"></emph>in omnibus regulam D. </s>

<s>Eughens non ad amussim experien­<lb></lb>tiis respondere<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>323) a cui il signor Huyghens contrapponeva che <lb></lb>la non rispondenza fra la teoria e la pratica, notata dal Padre, dipendeva da <lb></lb>ciò che, ne&#039;suoi computi, <emph type="italics"></emph>rationem non habuit, ut debebat, ponderis ba­<lb></lb>culi cui pondera erant appensa<emph.end type="italics"></emph.end> (Op. </s>

<s>et T. cit., pag. </s>

<s>225). Nè l&#039;inconsi­<lb></lb>deratezza del. </s>

<s>Deschales fu sola, ma ebbe anche altri matematici seguaci, <lb></lb>da&#039;quali non si può escludere il Mariotte, che, nella seconda parte del suo <lb></lb>trattato <emph type="italics"></emph>De la percussion,<emph.end type="italics"></emph.end> proponendosi di trovare <emph type="italics"></emph>le centre d&#039;agitation d&#039;une <lb></lb>partie d&#039;une ligne, qui se meut a l&#039;entour d&#039;un de ses points extremes, et <lb></lb>le centre de percussion d&#039;un pendule compost<emph.end type="italics"></emph.end> (Oeuvres, T. I, a l&#039;Haye, <lb></lb>pag. </s>

<s>89, 91); si limitava ai pochi e più facili esempi toccati dallo stesso <lb></lb>Deschales, e fedelmente ne imitava i processi dimostrativi. </s></p><p type="main">

<s>Ma sorsero altri in mezzo alla controversia, per dire che la teorica uge­<lb></lb>niana non corrisponde con l&#039;esperienza, perch&#039;è falsa, essendo il modo del­<lb></lb>l&#039;agire la gravità nei pesi congiunti diverso dal modo dell&#039;agire nei sepa­<lb></lb>rati. </s>

<s>Primo a movere questa difficoltà fu l&#039;abate Catelani, d&#039;onde nacque tra <lb></lb>lui e l&#039;Huyghens un&#039;altra controversia, agitata più assai della prima, e nella <lb></lb>quale prese gran parte Giacomo Bernoulli. </s>

<s>Esaminando egli bene la propo­<lb></lb>sta questione, dimostrò che veramente due corpi, ponderando a varie distanze <lb></lb>dal centro sul braccio di una libbra, percorrono, abbandonati a sè stessi, nel <lb></lb>medesimo tempo, uguali spazi, o cadendo liberamente o rimanendo con essa <lb></lb>libbra congiunti. (<emph type="italics"></emph>Controversia de hugen. </s>

<s>centri oscill. </s>

<s>determinatione,<emph.end type="italics"></emph.end><lb></lb>Op. </s>

<s>et T. cit., pag. </s>

<s>240). E come da questa parte favoriva l&#039;Huyghens, così <lb></lb>dall&#039;altra confermava le opposizioni del Catelani, concludendo dalla detta di­<lb></lb>mostrazione che la somma delle altezze, alle quali risalgono i gravi separa­<lb></lb>tamente componenti il pendolo, è minore della somma delle altezze, dalle <lb></lb>quali erano quegli stessi gravi congiuntamente discesi (ivi, pag. </s>

<s>241). Il mar­<lb></lb>chese De l&#039;Hòpital ebbe a maravigliarsi, vedendo che dai medesimi princi­<lb></lb>pii ugeniani si traevano inaspettatamente conclusioni, che contradicevano alle <lb></lb>verità de&#039;teoremi dimostrati da lui; ond&#039;è che, esaminate meglio le cose, <lb></lb>ritrovò nascondersi nel discorso del Bernoulli una fallacia, consistente nel <lb></lb>considerare le velocità acquistate, piuttosto che le virtuali, come si fa in di­<lb></lb>mostrare le ragioni dell&#039;equilibrio nel vette, quando i pesi non sono uguali <lb></lb>(ivi, pag. </s>

<s>245). Usciva l&#039;Huyghens da questa controversia dicendo che solo <pb xlink:href="020/01/2908.jpg" pagenum="533"></pb>il De l&#039;Hòpital s&#039;era più di tutti avvicinato alla vera soluzion del problema: <lb></lb>reputar del resto difficilissimo il risolverlo con altro metodo diverso dal suo, <lb></lb>com&#039;avevano tentato di fare il Wallis, il Deschales e il Mariotte, i quali <lb></lb>“ quaesiverunt tantum centrum percussionis, nec potuerunt demonstrare idem <lb></lb>esse cum centro oscillationis, licet id revera se habeat ” (ibid., pag. </s>

<s>246). </s></p><p type="main">

<s>La sentenza però dell&#039;Huyghens è pronunziata in forma troppo assoluta: <lb></lb>essere il centro della percossa una medesima cosa col centro dell&#039;oscillazione <lb></lb>resultava dalla definizione del Roberval e del Cartesio assai manifesto, senz&#039;aver <lb></lb>bisogno di essere dimostrato, benchè non valessero così fatte definizioni, se <lb></lb>non che in certi esempi particolari. </s>

<s>Così, anche il Wallis scriveva nello Scolio <lb></lb>alla proposizione citata: “ Atque hinc ad funependula aextimanda via patet: <lb></lb>nempe cuiuscumque figurae sit suspensum solidum, vibrationem quod spectat, <lb></lb>tantae longitudinis reputandum esse, quanta est distantia a suspensionis puncto <lb></lb>ad centrum ” (pag. </s>

<s>681) e il Mariotte s&#039;era limitato a dimostrare, nel luogo <lb></lb>sopra citato, che “ Les centres de vibration, agitation et percussion sont un <lb></lb>mème point dans un triangle, qui se meut sur sa base ” (pag. </s>

<s>93). </s></p><p type="main">

<s>Restava a confermare la verità, non per il triangolo solo o per le altre <lb></lb>figure contemplate già dal Roberval, dal Cartesio, dal Deschales e dal Wal­<lb></lb>lis, ma per ogni sistema di pesi in generale, ciò che pretendeva di aver fatto <lb></lb>l&#039;Huyghens, benchè le ragioni di lui si riconoscessero più tardi, quando sul <lb></lb>principio del secolo XVIII si resero i Matematici nel calcolare più esperti. </s>

<s><lb></lb>Allora fu che, ricercandosi in un sistema di corpi, solidamente attaccati a <lb></lb>distanze invariabili sopra un piano materiale, supposto senza peso e senza <lb></lb>inerzia, il punto dove tutte si concentrano le forze per operare contro un re­<lb></lb>sistente con la massima energia; si riuscì a dimostrare che quel punto è a <lb></lb>una distanza dall&#039;asse, precisamente uguale a quella data dalla formula uge­<lb></lb>niana per il centro dell&#039;oscillazione. </s></p><p type="main">

<s>Col calcolo infinitesimale poi riuscì facile a dimostrare che la regola, <lb></lb><figure id="id.020.01.2908.1.jpg" xlink:href="020/01/2908/1.jpg"></figure></s></p><p type="caption">

<s>Figura 333.<lb></lb>insegnata nella V proposizione della parte quarta dell&#039;Oro­<lb></lb>logio oscillatorio, riscontra esattamente con la verità dei <lb></lb>teoremi robervalliani. </s>

<s>Era il primo di questi teoremi in­<lb></lb>torno al centro di una linea come AB (fig. </s>

<s>333), che si <lb></lb>farà per comodo uguale ad <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> agitata mentr&#039;è sospesa dalla <lb></lb>sua estremità superiore. </s>

<s>Preso di AP, uguale ad <emph type="italics"></emph>x,<emph.end type="italics"></emph.end> un <lb></lb>elemento infinitesimale <emph type="italics"></emph>dx,<emph.end type="italics"></emph.end> moltiplicato questo per il qua­<lb></lb>drato della distanza dal punto A, sarà il prodotto <emph type="italics"></emph>x2 dx,<emph.end type="italics"></emph.end><lb></lb>e sarà la somma di tutti gli altri infiniti prodotti simili Ŗ <emph type="italics"></emph>x2 dx,<emph.end type="italics"></emph.end> che, in­<lb></lb>tegrato ed esteso l&#039;integrale a tutta la linea, ossia fatto <emph type="italics"></emph>x=a;<emph.end type="italics"></emph.end> dà <lb></lb><emph type="italics"></emph>a2<emph.end type="italics"></emph.end>/3, e così abbiamo il dividendo della formula ugeniana. </s>

<s>Il divisore poi sarà <lb></lb>dato dalla somma degl&#039;infiniti punti ponderosi componenti la linea, molti­<lb></lb>plicati per la distanza del loro centro comune di gravità, ossia sarà dato dal <lb></lb>prodotto <emph type="italics"></emph>a.a<emph.end type="italics"></emph.end>/2=<emph type="italics"></emph>a2<emph.end type="italics"></emph.end>/2, ond&#039;è che per il quoziente, da cui viene indicato il <pb xlink:href="020/01/2909.jpg" pagenum="534"></pb>centro richiesto, troveremo <emph type="italics"></emph>a3<emph.end type="italics"></emph.end>/3:<emph type="italics"></emph>a2<emph.end type="italics"></emph.end>/2=2/3.a, com&#039;aveva ritrovato per altra <lb></lb>via il Roberval, e dopo lui tutti gli Autori. </s></p><p type="main">

<s>Rispetto al secondo teorema robervalliano, che considera il triangolo ABC, <lb></lb>nella medesima figura, agitato intorno al vertice A, fatta AH=<emph type="italics"></emph>a,<emph.end type="italics"></emph.end> BC=<emph type="italics"></emph>b,<emph.end type="italics"></emph.end><lb></lb>AP=<emph type="italics"></emph>x,<emph.end type="italics"></emph.end> e condotte le due DE, GF parallele alla base, e distanti fra loro <lb></lb>della quantità infinitesimale PQ=<emph type="italics"></emph>dx;<emph.end type="italics"></emph.end> essendo DE=<emph type="italics"></emph>bx/a,<emph.end type="italics"></emph.end> sarà l&#039;elemento <lb></lb>superficiale DG del triangolo uguale a <emph type="italics"></emph>bx dx/a,<emph.end type="italics"></emph.end> e il prodotto di lui nel qua­<lb></lb>drato della sua distanza dal punto A, <emph type="italics"></emph>bx3 dx/a:<emph.end type="italics"></emph.end> cosicchè Ŗ <emph type="italics"></emph>bx3 dx/a<emph.end type="italics"></emph.end> sarà la somma <lb></lb>di tutti gl&#039;infiniti prodotti simili, che integrata, ed esteso l&#039;integrale a tutto <lb></lb>il triangolo, ossia fatto <emph type="italics"></emph>x=a,<emph.end type="italics"></emph.end> sarà <emph type="italics"></emph>ba3/4.<emph.end type="italics"></emph.end> Dovendosi ora questa quantità, se­<lb></lb>condo la regola ugeniana, dividere per <emph type="italics"></emph>ab<emph.end type="italics"></emph.end>/2.<emph type="italics"></emph>2a<emph.end type="italics"></emph.end>/3, che è la somma degli infi­<lb></lb>niti elementi ponderosi del triangolo, moltiplicati per la distanza del loro centro <lb></lb>di gravità dal punto di sospensione; avremo per quoziente <emph type="italics"></emph>ba3<emph.end type="italics"></emph.end>/4:<emph type="italics"></emph>ba2<emph.end type="italics"></emph.end>/3=3/4<emph type="italics"></emph>a,<emph.end type="italics"></emph.end><lb></lb>non altrimenti da quel che tanti anni prima aveva lo stesso Roberval dimo­<lb></lb>strato al Mersenno. </s></p><p type="main">

<s>Non potevano questi, e altri simili riscontri, che, secondo il medesimo <lb></lb>ordine erano facili a farsi, non avere una grande efficacia in persuadere i <lb></lb>dissidenti, ma s&#039;agitava allora vivamente la questione delle forze vive, dal <lb></lb>principio della conservazion delle quali era condotta la dimostrazione del Teo­<lb></lb>rema ugeniano. </s>

<s>Pensarono perciò i Matematici di valersi d&#039;altri principii, che <lb></lb>non fossero controversi, e Giov. </s>

<s>Bernoulli, applicando le leggi che muovono <lb></lb>il vette a quello stesso Teorema, giungeva a una formula, dopo scritta la <lb></lb>quale così notava: “ Id quod omnino conforme est Regulae hugenianae, quam­<lb></lb>vis elicitae ex principio indirecto, fundato in aequalitate descensus et ascen­<lb></lb>sus communis centri gravitatis, quod redit ad suppositionem <emph type="italics"></emph>Conservationis <lb></lb>virum vivarum ”<emph.end type="italics"></emph.end> (Opera omnia, Lausannae 1742, pag. </s>

<s>261). Il D&#039;Alembert <lb></lb>poi rese la dimostrazion del Bernoulli anche più semplice, facendola deri­<lb></lb>vare dalla soluzion del seguente problema: “ Trouver la vitesse d&#039;une verge <lb></lb>fixe, et chargée de tant de corps, qu&#039;on voudra, en supposant que ces corps, <lb></lb>si la verge ne les en empechoit, decrivissent dans des tems egaux les lignes <lb></lb>infiniment petites perpendiculaires a la verge ” (<emph type="italics"></emph>Traitè de Dinamique,<emph.end type="italics"></emph.end> a <lb></lb>Paris 1758, pag. 96). </s></p><p type="main">

<s>In cotesto tempo, da certe iattanze degl&#039;Inglesi, presero i Matematici oc­<lb></lb>casione di definir nei loro precisi termini le relazioni, che passano tra il cen­<lb></lb>tro dell&#039;oscillazione e quello della percossa. </s>

<s>L&#039;Huyghens, come udimmo, aveva <lb></lb>detto che nè il Wallis, nè nessun altro de&#039;suoi predecessori, era riuscito a <lb></lb>dimostrar l&#039;identità, benchè fosse verissima, dei due detti centri, ma lo Stone, <pb xlink:href="020/01/2910.jpg" pagenum="535"></pb>accademico reale di Londra, citando quel documento, che noi pure trascri­<lb></lb>vemmo dallo Scolio alla XV proposizion wallisiana <emph type="italics"></emph>De percussione,<emph.end type="italics"></emph.end> preten­<lb></lb>deva che, per avere esso Wallis riconosciuta quella identità, avesse ragione <lb></lb>di precedenza sull&#039;Huyghens intorno alla teoria de&#039;centri oscillatorii. </s>

<s>Soste­<lb></lb>neva queste sue pretensioni in un libro, stampato nel 1735 in Parigi, col <lb></lb>titolo di <emph type="italics"></emph>Analyse des infinimens petits,<emph.end type="italics"></emph.end> e scritto con la principale intenzione <lb></lb>di rivendicare al Newton il primato dell&#039;invenzione del Calcolo infinitesimale. </s>

<s><lb></lb>A quel libro facendo Giov. </s>

<s>Bernoulli alcune argute postille, mentre mostrava <lb></lb>da una parte l&#039;opera, che avevano dato seco il Leibniz, l&#039;Hòpital e altri non <lb></lb>Inglesi a istituir l&#039;analisi degl&#039;infinitamente piccoli, toglieva dall&#039;altra al Wal­<lb></lb>lis, quanto all&#039;invenzion dei centri d&#039;oscillazione, ogni diritto di precedenza, <lb></lb>col negar che sia, come leggermente si credeva da tutti, tra esso centro e <lb></lb>quello della percossa alcuna connession necessaria: a persuadersi di che egli <lb></lb>dice “ il n&#039;y a qu&#039;a considérer ces deux choses: 1.° La nature du centre <lb></lb>d&#039;oscillation dépend entiérement de la nature et de l&#039;action de la pesanteur, <lb></lb>au lieu que, dans la theorie du centre de percussion, la pesanteur n&#039;entre <lb></lb>aucunement en consideration, mais seulement la matiere et la vitesse, quoi­<lb></lb>que uniforme, de ses parties. </s>

<s>De-là il arrive qu&#039;un pendule compose de plu­<lb></lb>sieurs corps de differentes densités, agité dans l&#039;air, a son centre d&#039;oscillation <lb></lb>different de celui qu&#039;il avroit, s&#039;il etoit agité dans une liqueur, par éxemple <lb></lb>dans l&#039;eau. </s>

<s>Mais le centre de pércussion sera le même dans l&#039;air et dans <lb></lb>l&#039;eau. </s>

<s>2.° Au contraire, si les corps se meuvent dans un même milieu, le <lb></lb>centre d&#039;oscillation est quelque chose d&#039;absolu et independant de toute rela­<lb></lb>tion, au lieu que le centre de percussion varie selon la diversité de situa­<lb></lb>tion du corps choqué, ensorte qu&#039;il y a une mutuelle dépendance entre les <lb></lb>corps choquans et choqués ” (Opera cit., pag. 180). </s></p><p type="main">

<s>A ridur ne&#039;precisi termini la questione accennava anche il D&#039;Alembert, <lb></lb>dop&#039;aver risoluto il problema, da cui si disse ch&#039;egli faceva dipendere l&#039;in­<lb></lb>venzione dei centri oscillatorii. </s>

<s>“ Il est a remarquer qu&#039;on ne s&#039;exprimeroit <lb></lb>pas exactement en disant, avec quelques auteurs, que la distance du centre <lb></lb>d&#039;oscillation est toujours la même, soit que le milieu resiste, soit qu&#039;il ne <lb></lb>resiste pas. </s>

<s>” E ciò perchè nella formula ritrovata entrano quantità “ qui, <lb></lb>dependent de la pesanteur, ne sont pas les mêmes que dans le vuide, par­<lb></lb>ceque la pesanteur de chaque corps est diminuée par celle du fluide, et <lb></lb>qu&#039;elle l&#039;est differentment a raison de la densité, du volume et de la figure <lb></lb>de chaque corps ” (<emph type="italics"></emph>Traité de Dinamique<emph.end type="italics"></emph.end> cit., pag. </s>

<s>100). </s></p><p type="main">

<s>Ma a far queste considerazioni erano predisposte le menti dalle dottrine <lb></lb>dell&#039;Herman, il quale, dopo aver notato che, se il pendolo è composto di <lb></lb>corpi di differente gravità specifica, il centro dell&#039;oscillazione varia nella varia <lb></lb>densità dei mezzi, per cui rimprovera coloro, che inconsideratamente con­<lb></lb>fondono questo col centro della percossa; passa a dimostrare nel 1.° libro <lb></lb>della <emph type="italics"></emph>Foronomia<emph.end type="italics"></emph.end> la proposizione XXXVI, che dice: non verificarsi l&#039;identità <lb></lb>del centro dell&#039;oscillazione col centro della percossa, se non nel caso partico­<lb></lb>lare, che i pesi componenti il pendolo siano proporzionali alle masse. </s>

<s>“ Iden-<pb xlink:href="020/01/2911.jpg" pagenum="536"></pb>titas centri oscillationis et percussionis eo casu, quo singularum penduli com­<lb></lb>positi partium pondera massis eorumdem proportionalia sunt ” (Amstelo­<lb></lb>dami 1716, pag. </s>

<s>108). E cosi può dirsi che, per opera e studio de&#039;Matematici <lb></lb>stranieri, giungesse al suo ultimo perfezionamento l&#039;invenzione ugeniana. </s></p><p type="main">

<s>In Italia, dove Galileo aveva insegnate intorno alla forza della percossa <lb></lb>dottrine false, e insufficienti, ad emendare e a restaurar le quali aveva tutte <lb></lb>esaurite le sue forze il Borelli; rimasero intatte queste importantissime que­<lb></lb>stioni, cosicchè il Torricelli ebbe e restarsi muto a certe domande, che in <lb></lb>una lettera del dì 6 Novembre 1646 gli faceva da Parigi il Mersenno: “ Ab <lb></lb>hinc anno plurimum laboravimus in regulis inveniendis, quibus agnoscitur <lb></lb>et determinatur centrum percussionis cuiuslibet corporis alicui clavo ita ap­<lb></lb>pensi, ut libere hinc inde instar funependuli moveri possit... punctum seu <lb></lb>centrum percussionis seu virtutis, hoc est in quo vehementissime percutiat <lb></lb>vel, quod eodem recidit, putamus quantae longitudinis debet esse funependu­<lb></lb>lum ut moveatur seu vibretur aequali tempore ac praedictum triangulum. </s>

<s><lb></lb>Vide ut mihi significes an Galileus ea de re cogitavit et si regulam invene­<lb></lb>rit ” (MSS. Gal. </s>

<s>Disc., T. XLI, f. </s>

<s>28). </s></p><p type="main">

<s>Nè solamente non aveva trovata la regola Galileo, ma non l&#039;avevano <lb></lb>trovata nemmeno gli Accademici del Cimento, quando già potevano aver no­<lb></lb>tizia delle invenzioni del Roberval e del Cartesio, le quali è certo che fu­<lb></lb>rono comunicate, nell&#039;Agosto del 1646, al Torricelli per lettera scrittagli di <lb></lb>Parigi dal Mersenno: “ Sit baculus sive quadratus, sive rotundus: dico fu­<lb></lb>nependulum longitudine subsesquialtera longitudini baculi suas habere vibra­<lb></lb>tiones aequales tempore. </s>

<s>Itaque dividatur cylindrus sive baculus in tres par­<lb></lb>tes: funependulum duorum erit partium. </s>

<s>Regula generalis, quam nobis <lb></lb>D. </s>

<s>Cartesius a nobis rogatus misit, haec est: omnia corpora, praeter cen­<lb></lb>trum gravitatis, aliud centrum percussionis, sive agitationis habere ” (ibid., <lb></lb>fol. </s>

<s>59). Nonostante i nostri Accademici fiorentini non sapevano ancora dire <lb></lb>con certezza di scienza quanta parte dell&#039;asse della pallina d&#039;oro dovesse <lb></lb>aggiungersi al filo di seta, per aver la lunghezza esatta del loro pendolo pre­<lb></lb>diletto. </s>

<s>Abbiamo di ciò il documento in una nota autografa del Viviani, scritta <lb></lb>per insegnare il modo di <emph type="italics"></emph>trovare qual punto del pendolo sia quello, dal <lb></lb>quale si regola il moto.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Prendi egli dice, una palla di piombo come A (fig. </s>

<s>334) e sospendila <lb></lb>ad un filo di qualunque lunghezza come BC. </s>

<s>Con questa fa vibrare il pen­<lb></lb>dolo, e numera le vibrazioni, che esso fa in un tal tempo, v. </s>

<s>g. </s>

<s>in cento vi­<lb></lb>brazioni di un altro qualsiasi pendolo esploratore, che siano v. </s>

<s>g. </s>

<s>60, con il <lb></lb>filo AH e palla A. </s>

<s>Prova poi ad accorciare il filo quanto DC, in modo che <lb></lb>le vibrazioni del medesimo peso A col filo DC siano la metà meno, cioè 30, <lb></lb>nel tempo che l&#039;esploratore ne faceva pur cento. </s>

<s>Dividi poi il residuo del <lb></lb>filo BD in tre parti uguali, ed una divisione dal punto D gettala verso A: <lb></lb>chè, dove il punto A termina, questo sarà il regolatore del moto del detto <lb></lb>pendolo, e si troverà che detta misura della terza parte di BD arriva ad A, <lb></lb>centro di gravità della palla, quando essa sarà omogenea, e il filo sia sotti-<pb xlink:href="020/01/2912.jpg" pagenum="537"></pb>lissimo. </s>

<s>Ma quando anche non arrivi al centro, ma termini sopra A, ovvero <lb></lb>sotto A, tal punto sarà nondimeno quello, che dà regola alle vibrazioni del <lb></lb>detto pendolo ” (MSS. Cim., T. X, fol. </s>

<s>48). <lb></lb><figure id="id.020.01.2912.1.jpg" xlink:href="020/01/2912/1.jpg"></figure></s></p><p type="caption">

<s>Figura 334.</s></p><p type="main">

<s>Da quali principii concludesse il Viviani questa sua regola <lb></lb>non ci è noto, ma è certissimo in ogni modo che il punto <lb></lb>regolatore delle vibrazioni del pendolo deve necessariamente <lb></lb>esser più basso di A. Perchè, intendendosi divisa la palla in <lb></lb>due emisferi soprapposti, quel di sotto, nell&#039;agitazione, acqui­<lb></lb>sta maggiore momento. </s>

<s>Che se siano dei due detti emisferi i <lb></lb>centri di gravità in E, F, la regola semplicissima di ritrovare <lb></lb>in G il punto, da cui si regola il moto, è data, com&#039;insegnava <lb></lb>il Deschales, dalla proporzione GE:GF=BF:BE. </s></p><p type="main">

<s>Dopo gli Accademici del Cimento, fu forse, nel 1684, il <lb></lb>primo in Italia a trattare de&#039;centri delle oscillazioni e delle <lb></lb>percosse Paolo Casati. </s>

<s>In qual modo però ciò facesse può giu­<lb></lb>dicarlo chi legge il capitolo IX del VII libro della sua Mec­<lb></lb>canica. </s>

<s>Proponendosi egli l&#039;invenzione del centro della percossa <lb></lb>in un cilindro sottilissimo, o in una verga girevole intorno ad <lb></lb>una sua estremità, considerava che i momenti andavano cre­<lb></lb>scendo a proporzion de&#039;seni degli archi concentrici, ma non <lb></lb>sapendo applicarvi, come il Roberval, il Cartesio e il Wallis il <lb></lb>metodo degli indivisibili, non riuscì a determinare il punto della <lb></lb>maggiore energia delle forze, che dentro certi limiti, usandovi <lb></lb>un metodo di falsa posizione. </s>

<s>E più da fisico che da matematico raccoglie il fiore <lb></lb>delle sue dottrine nell&#039;insegnar che il centro della percossa di un sistema, <lb></lb>per esempio di una clava, è a tanta distanza dall&#039;asse della sospensione, quant&#039;è <lb></lb>la lunghezza di un pendolo isocrono, composto di un sottilissimo filo di rame, <lb></lb>e di un piccolo globo, avvertendo che “ si una perpendiculi vibratio diutur­<lb></lb>nior sit quam una clavae vibratio, decurtandum est filum, si brevior, produ­<lb></lb>cendum usque eo, dum perpendiculi vibrationes singulae singulis clavae vi­<lb></lb>brationibus isochronae fuerint ” (Mechanic. </s>

<s>libri, Lugduni 1684, pag. </s>

<s>716). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Rimane a dire, secondo l&#039;ordine propostoci, delle Forze centrifughe, a <lb></lb>dimostrar la natura e le proprietà delle quali anche venne all&#039;Huyghens <lb></lb>l&#039;occasione dall&#039;Orologio oscillatorio. </s>

<s>I teoremi nuovi relativi a questo argo­<lb></lb>mento, e solamente pubblicati dall&#039;Autore per dar perfezione di scienza al <lb></lb>nuovo automato, sparsero nelle menti dell&#039;Hook, del Newton, c di altri Ma­<lb></lb>tematici inglesi i germi fecondi della Meccanica celeste, d&#039;onde è facile ar­<lb></lb>gomentare all&#039;importanza della presente parte della nostra Storia, la quale, <lb></lb>aprendosi a un tratto, poco dopo la metà del secolo XVII, com&#039;alveo a rice­<lb></lb>vere un gran fiume, ebbe pure da lontani e sottilissimi rivoli la sua sorgente. </s></p><pb xlink:href="020/01/2913.jpg" pagenum="538"></pb><p type="main">

<s>Quella forza, a cui piacque all&#039;Huyghens di dare il nome di <emph type="italics"></emph>centrifuga,<emph.end type="italics"></emph.end><lb></lb>si rimase per lunghissimo tempo implicata così ne&#039;moti di rotazione, che <lb></lb>l&#039;ufficio nostro si riduce ora a narrar come e quando riuscissero finalmente <lb></lb>i Matematici a distinguerla, e a misurare la proporzione ch&#039;ell&#039;ha all&#039;altra <lb></lb>sua componente. </s>

<s>Le prime speculazioni perciò versarono intorno a que&#039;moti <lb></lb>violenti, de&#039;quali Aristotile, nella sua XII questione meccanica, era venuto a <lb></lb>porgere i primi esempi. </s>

<s>Si propone quivi il Filosofo di rendere la ragione <lb></lb>perchè un proietto vada con tanto maggior impeto, girato nella fionda, che se <lb></lb>fosse gettato dalla semplice mano: e dice che ciò forse avviene, perchè quel <lb></lb>che si getta, nella mano, si parte dalla quiete, e nella fionda con velocità <lb></lb>precedente: <emph type="italics"></emph>omnia autem, cum in motu sunt, quam cum quiescunt, faci­<lb></lb>lius moventur<emph.end type="italics"></emph.end> (Operum, T. XI, Venetiis 1560, fol. </s>

<s>32 ad t.). Ma un&#039;altra <lb></lb>ragione soggiunge a questa il Filosofo, ed è che la mano fa da centro del <lb></lb>moto, e la fionda si dilunga dal centro: <emph type="italics"></emph>quanto autem productius fuerit id <lb></lb>quod a centro est, tanto citius movetur<emph.end type="italics"></emph.end> (ibid.). </s></p><p type="main">

<s>Il principio aristotelico era l&#039;unico, che senz&#039;altra dichiarazione s&#039;appli­<lb></lb>casse, in simili questioni meccaniche, dai Matematici, fra quali basti citare <lb></lb>il Cardano, che, nel capitolo LVI dell&#039;XI libro <emph type="italics"></emph>De rerum varietate,<emph.end type="italics"></emph.end> lo for­<lb></lb>mulava con queste parole: “ Omne quod movetur violenter eo velocius mo­<lb></lb>vetur, quo celerius et per longius spatium ab eo a quo movetur ” (Op. </s>

<s>omnia, <lb></lb>T. III, Lugduni 1663, pag. </s>

<s>214). </s></p><p type="main">

<s>Anche Giovan Batista Benedetti ripetè poi che <emph type="italics"></emph>quanto maior est ali­<lb></lb>qua rota tanto maiorem quoque impetum, et impressionem motus eius cir­<lb></lb>cumferentiae partes recipiunt<emph.end type="italics"></emph.end> (Speculationum liber, Venetiis 1599, pag. </s>

<s>159), <lb></lb>ma egli ha il merito di avere speculato un principio più prossimo e più im­<lb></lb>mediato, da concluder la proposta verità del teorema. </s>

<s>Credè di aver egli ri­<lb></lb>trovato quel principio in un fatto, <emph type="italics"></emph>quod a nemine adhuc, quod sciam, in <lb></lb>trocho est observatum,<emph.end type="italics"></emph.end> ed è che, immaginando essa trottola, mentre gira <lb></lb>velocissimamente sul suo punzone, esser ridotta in minute schegge, queste <lb></lb>non cadono a perpendicolo, ma vanno per linea retta orizontale, e tangente <lb></lb>a quel punto del giro, da cui furono scisse: ciò che dall&#039;altra parte si vede <lb></lb>avvenire ordinariamente nelle ruote de&#039;carri, e in qualunque altro corpo, <lb></lb>che sia da estrinseco moto violentemente circondotto. </s>

<s>Intorno ai quali moti <lb></lb>rotatorii il Matematico veneziano stabilisce le dottrine seguenti: “ Quaelibet <lb></lb>pars corporea, quae a se movetur, impetu eidem a qualibet extrinseca vir­<lb></lb>tute movente impresso, habet naturalem inclinationem ad rectum iter, non <lb></lb>autem curvum. </s>

<s>Unde, si a dicta rota particula aliqua suae circumferentiae <lb></lb>disiungeretur, absque dubio per aliquod temporis spatio pars separata recto <lb></lb>itinere ferretur per aerem, ut exemplo a fundis, quibus iaciuntur lapides, <lb></lb>sumpto, cognoscere possumus. </s>

<s>In quibus impetus motus impressus naturali <lb></lb>quadam propensione rectum iter peragit, cum evibratus lapis per lineam re­<lb></lb>ctam contiguam giro, quem primo faciebat, in puncto in quo dimissus fuit, <lb></lb>rectum iter instituit ” (ibid.). </s></p><p type="main">

<s>Posto così il principio che il mobile, per inclinazion sua naturale, è di-<pb xlink:href="020/01/2914.jpg" pagenum="539"></pb>sposto d&#039;andare in linea retta, tangente al punto del giro, da cui si scioglie, <lb></lb>ed essendo facil cosa a concedere che tanto sia maggiore il moto, quanto è <lb></lb>più secondato dalla sua propria natura; conclude il Benedetti dovere essere <lb></lb>nella ruota maggiore, maggiore altresì l&#039;impeto della proiezione, perchè la <lb></lb>sua curvatura, più che nella ruota minore, s&#039;accosta alla linea retta. </s>

<s>“ Quia, <lb></lb>quanto maior est diameter unius circuli, tanto minus curva est eiusdem cir­<lb></lb>cumferentia, et tanto propius accedit ad rectitudinem linearem. </s>

<s>Unde earum­<lb></lb>dem partium dictae circumferentiae motus ad inclinationem sibi a natura <lb></lb>tribulam, quae est incedendi per lineam rectam, magis accedit ” (ibid.). </s></p><p type="main">

<s>In questi moti giratorii però, come per esempio in quello volgare della <lb></lb>fionda, s&#039;osserva, dice il Benedetti, un certo effetto <emph type="italics"></emph>notatu dignus,<emph.end type="italics"></emph.end> ed è che, <lb></lb>quanto più cresce l&#039;impeto del corpo girato, tanto più è necessario che, me­<lb></lb>diante la fune, si senta a lui tirare la mano. </s>

<s>Ecco dunque proporsi alla <lb></lb>mente dello speculatore la question della forza centrifuga propriamente detta, <lb></lb>che par nascere dall&#039;impeto di proiezione, ma egli non sa far altro intorno <lb></lb>a ciò che applicare il professato principio, dicendo essere di quel notabile <lb></lb>effetto la ragione “ quia, quanto maior impetus impressus, tanto magis cor­<lb></lb>pus ad rectum iter peragendum inclinatur: unde, ut recta incedat, tanto <lb></lb>maiore vi trahit ” (ibid., pag. </s>

<s>161). </s></p><p type="main">

<s>Di qui si vede che il Benedetti aveva fatto un notabilissimo progresso, <lb></lb>riducendo l&#039;impeto del mobile alla forza della sua proiezione per la tan­<lb></lb>gente, ma non perciò era entrato addentro al mistero di queste forze, non <lb></lb>penetrabile se non a colui, che avesse saputo decomporre quell&#039;unico moto <lb></lb>proiettizio in due: uno che mena il mobile in giro, e l&#039;altro che nello stesso <lb></lb>tempo lo farebbe rifuggire dal centro, se un&#039;arcana forza di attrazione non <lb></lb>lo tenesse a sè immobile e fisso. </s>

<s>Questa forza, che poi si disse <emph type="italics"></emph>centripeta,<emph.end type="italics"></emph.end><lb></lb>e che è una delle componenti il moto tangenziale, fu primo a riconoscerla <lb></lb>Galileo, che ne&#039;dialoghi dei due Massimi Sistemi, fra i promotori di questa <lb></lb>scienza, immediatamente succede all&#039;Autor del libro delle Speculazioni. </s>

<s>Nella <lb></lb>seconda Giornata, in proposito di rispondere all&#039;obiezione, che, quando la <lb></lb>Terra girasse in sè stessa, il moto della superficie, verso il circolo massimo, <lb></lb>come incomparabilmente più veloce dei paralleli, dovrebbe estrudere ogni <lb></lb>cosa verso il cielo; proponeva e dimostrava poi agl&#039;interlocutori il seguente </s></p><p type="main">

<s>TEOREMA. — <emph type="italics"></emph>“ Quanto più si cresce la ruota, tanto si scema la causa <lb></lb>della proiezione. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Siano due ruote diseguali intorno al centro A (fig. </s>

<s>335), e della mi­<lb></lb>nore sia la circonferenza BG, e della maggiore CE, e il semidiametro ABC <lb></lb>sia eretto all&#039;orizonte, e per i punti B, C segniamo le rette linee tangenti <lb></lb>BF, CD, e negli archi BG, CE sieno prese due parti eguali BG, CE, e in­<lb></lb>tendasi le due ruote esser girate sopra i loro centri con eguali velocità, sic­<lb></lb>chè i due mobili, quali sariano v. </s>

<s>g. </s>

<s>due pietre poste ne&#039;punti B e C, ven­<lb></lb>gano portate per le circonferenze BG, CE con eguali velocità, talchè, nel­<lb></lb>l&#039;istesso tempo che la pietra B scorrerebbe per l&#039;arco BG, la pietra C <lb></lb>passerebbe l&#039;arco CE: dico adesso che la vertigine della minor ruota è molto <pb xlink:href="020/01/2915.jpg" pagenum="540"></pb>più potente a far la proiezione della pietra B, che non è la vertigine della <lb></lb>maggior ruota della pietra C. ” </s></p><p type="main">

<s>“ Imperocchè dovendosi, come già si è dichiarato, far la proiezione per <lb></lb><figure id="id.020.01.2915.1.jpg" xlink:href="020/01/2915/1.jpg"></figure></s></p><p type="caption">

<s>Figura 335.<lb></lb>la tangente, quando le pietre B, C dovessero sepa­<lb></lb>rarsi dalle lor ruote, e cominciare il moto della proie­<lb></lb>zione dai punti B, C, verrebbero dall&#039;impeto conce­<lb></lb>pito dalla vertigine scagliate per le tangenti BF, CD. </s>

<s><lb></lb>Per le tangenti dunque BF, CD hanno le due pietre <lb></lb>eguali impeti di scorrere, e vi scorrerebbero, se da <lb></lb>qualche altra forza non ne fossero deviate, la qual <lb></lb>forza non può essere che la propria gravità. </s>

<s>” </s></p><p type="main">

<s>“ Ora considerate che, per deviar la pietra della <lb></lb>minor ruota dal moto della proiezione, che ella fa­<lb></lb>rebbe per la tangente BF, e ritenerla attaccata alla <lb></lb>ruota; bisogna che la propria gravità la ritiri per quanto è lunga la se­<lb></lb>gante FG, ovvero la perpendicolare tirata dal punto G sopra la linea BF, <lb></lb>dovecchè, nella ruota maggiore, il ritiramento non ha da essere più che si <lb></lb>sia la segante DE, ovvero la perpendicolare tirata dal punto E sopra la tan­<lb></lb>gente DC, minor assai della FG, e sempre minore e minore, secondo che la <lb></lb>ruota si facesse maggiore. </s>

<s>E perchè questi ritiramenti si hanno a fare in <lb></lb>tempi eguali, cioè mentre che si passano li due archi uguali BG, CE, quello <lb></lb>della pietra B, cioè il ritiramento FG, dovrà esser più veloce dell&#039;altro DE, <lb></lb>e però molto maggior forza si ricercherà, per tener la pietra B congiunta <lb></lb>alla sua piccola ruota, che la pietra C alla sua grande: che è il medesimo <lb></lb>che dire che tal poca cosa impedirà lo scagliamento nella ruota grande, che <lb></lb>non lo proibirà nella piccola. </s>

<s>È manifesto dunque ecc. </s>

<s>” (Alb. </s>

<s>I, 238, 39). </s></p><p type="main">

<s>Trattandosi di ruote artificiali, non si potrebbe dire esser la gravità la <lb></lb>forza, che tira la ruota al centro, nemmen quando, come qui si vuole, i se­<lb></lb>midiametri AB, AC fossero eretti all&#039;orizonte. </s>

<s>Ma, essendo la principale inten­<lb></lb>zione di questo teorema quella di applicarlo al moto rotatorio intorno all&#039;asse <lb></lb>della Terra, della quale A fosse il centro, e intorno a lui i due archi dise­<lb></lb>gnati; il concetto di Galileo riscontra mirabilmente con le dottrine neuto­<lb></lb>niane, secondo le quali propriamente la forza centripeta della pietra, in un <lb></lb>circolo concentrico con la Terra, non è che la gravità sua naturale. </s>

<s>Torna <lb></lb>in ogni modo benissimo, a conferire il discorso di Galileo co&#039;teoremi del <lb></lb>Newton, che i ritiramenti al centro, o le forze centripete, sòn proporzionali <lb></lb>alle parti esterne FG, DE delle secanti, o alle perpendicolari GH, EL, o ai <lb></lb>seni versi BN, MC: cosicchè non rimaneva a far altro ne&#039;dialoghi del Mondo, <lb></lb>per prevenire la conclusione annunziata nel V corollario della IV proposi­<lb></lb>zione, scritta nel Tomo primo dei Principii di Filosofia naturale, che dimo­<lb></lb>strar la ragione delle linee GH, EL, o delle loro uguali. </s></p><p type="main">

<s>Nemmeno il Mersenno, inserendo nella XVIII proposizione del suo libro <lb></lb><emph type="italics"></emph>Du mouvement des corps,<emph.end type="italics"></emph.end> pubblicato in Parigi nel 1635, questa medesima <lb></lb>argomentazione contro chi, per gli effetti della proiezion superficiale, negava <pb xlink:href="020/01/2916.jpg" pagenum="541"></pb>la diurna vergine terrestre; promoveva di un passo le dottrine galileiane <lb></lb>verso la teoria delle forze centrali, limitandosi a tradurre fedelmente in fran­<lb></lb>cese l&#039;interlocuzion del Salviati. </s></p><p type="main">

<s>Forse opponeva qualche difficoltà a questa promozione la Geometria ele­<lb></lb>mentare, mentre quella degli indivisibili, se avesse incontrato il favore di <lb></lb>Galileo, gli avrebbe di un intuito rivelato che la proporzione tra BN e CM <lb></lb>è quella reciproca dei raggi. </s>

<s>Se BG, CE infatti son archi così minimi, da <lb></lb>confondersi con le loro sottese, BG2 è uguale a 2AB.BN, e CE2=2AC.CM; <lb></lb>ond&#039;essendo per supposizione BG=CE, ne consegue senz&#039;altro BN:CM= <lb></lb>AC:AB. </s></p><p type="main">

<s>A chi poi fosse curioso di sapere se fu veramente qualche difficoltà, <lb></lb>incontrata nella dimostrazione, o il pensiero di non divagar dal soggetto del <lb></lb>discorso, che fece a Galileo lasciar l&#039;occasione di concluder nel luogo citato <lb></lb>la verità del nuovo e bellissimo teorema; inclineremmo a dire essere stato <lb></lb>piuttosto quel motivo che questo. </s>

<s>Perchè vinte, nel caso de&#039;ritiramenti al <lb></lb>centro sulle ruote di varia grandezza, ma ugualmente veloci, le difficoltà geo­<lb></lb>metriche, che si paravano nel dimostrar l&#039;altro caso; troviamo, tra i copiati <lb></lb>dal Viviani, il teorema di Galileo, che i ritiramenti o le forze centripete, o <lb></lb>le centrifughe a loro uguali e contrarie, stanno direttamente come i semi­<lb></lb>diametri delle ruote. </s></p><p type="main">

<s>“ Siano le due circonferenze AB, DE (fig. </s>

<s>336), sopra le quali s&#039;inten­<lb></lb>dano in B e in E posati due gravi, quali sariano due pietre, e rivolgendosi <lb></lb>intorno al centro O le due ruote, vengano le dette pietre per la vertigine <lb></lb><figure id="id.020.01.2916.1.jpg" xlink:href="020/01/2916/1.jpg"></figure></s></p><p type="caption">

<s>Figura 336.<lb></lb>estruse secondo le direzioni delle tangenti BH, <lb></lb>EL. </s>

<s>Dico che il ritiramento AH, al ritiramento <lb></lb>LD, o la perpendicolare AM, uguale alla BC, alla <lb></lb>perpendicolare DN, uguale alla EF, ha la propor­<lb></lb>zion medesima che il semidiametro OB, al semi­<lb></lb>diametro OE. ” </s></p><p type="main">

<s>“ Imperocchè, tirate le suttese AB, ED, i <lb></lb>triangoli simili danno che AB a DE è come OB <lb></lb>ad OE, ed anche, che il quadrato di AB, al qua­<lb></lb>drato di DE, è come il quadrato di OB al qua­<lb></lb>drato di OE. Dall&#039;altra parte il quadrato di AB <lb></lb>è uguale al doppio di BO moltiplicato per BC, e <lb></lb>il quadrato di ED è uguale al doppio di EO mol­<lb></lb>tiplicato per EF. </s>

<s>Dunque diremo che il quadrato di AB sta al quadrato di <lb></lb>ED, come il rettangolo di BO e di BC sta al rettangolo di EC e di EF, ossia <lb></lb>come il-quadrato di BO sta al quadrato di EO. </s>

<s>E di qui è manifesto che BC <lb></lb>ad EF ha egual proporzione che BO ad EO, com&#039;era il proposito di dimo­<lb></lb>strare. </s>

<s>” <emph type="italics"></emph>(Roba del gran Galileo, in parte copiata dagli originali, e in <lb></lb>parte dettata da lui cieco a me Vincenzio Viviani, mentre dimoravo nella <lb></lb>sua casa d&#039;Arcetri).<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Rimasto questo teorema dimenticato ne&#039;manoscritti, e l&#039;altro della se-<pb xlink:href="020/01/2917.jpg" pagenum="542"></pb>conda giornata dei Massimi Sistemi chiuso nel suo germe, e perciò non appa­<lb></lb>rente, si può dir che non dette Galileo nessuno impulso a far progredire la <lb></lb>Scienza delle forze centrali, che intanto dalle umili fionde, e dalle ruote dei <lb></lb>carri, il Borelli sublimava alle ruote celesti. </s>

<s>A coloro che opponevano non <lb></lb>poter la Terra moversi dal suo proprio luogo, perchè, non avendo chi la <lb></lb>sostenti, cadrebbe; si rispondeva, come da Galileo stesso a quel peripatetico <lb></lb>cappuccino veronese, essere una tale opposizione ridicola, “ quasi che il moto <lb></lb>velocissimo per l&#039;opposto non sia quello, che vieta il cadere agli uccelli vo­<lb></lb>lanti, a&#039;sassi scagliati, alle trottole dei fanclulli. </s>

<s>Ma non dicono i Filosofi <lb></lb>che la Luna e le altre stelle non cadono, perchè la velocità del loro moto <lb></lb>le trattiene? </s>

<s>” (Alb. </s>

<s>VII, 61). </s></p><p type="main">

<s>Questa vera Filosofia però non fu prima insegnata che dal libro <emph type="italics"></emph>Theo­<lb></lb>ricae Mediceorum,<emph.end type="italics"></emph.end> dicendovisi che la Luna non cade sulla Terra, nè i sa­<lb></lb>telliti su Giove, nè i pianeti sul Sole, perchè la forza magnetica dell&#039;attra­<lb></lb>zione, sola causa efficiente di quelle cadute, viene equilibrata dalla contra­<lb></lb>ria forza centrifuga, che svolgesi nel girare. </s>

<s>Ma il Borelli pretendeva di più <lb></lb>che, dalla composizione di queste forze contrarie, dipendesse la maggiore <lb></lb>o minore velocità del pianeta nel perielio e nell&#039;afelio: “ Ex compositione <lb></lb>dictorum motuum efficitur vis quaedam et impetus compositus, ex quo pen­<lb></lb>det periodus celeritatis acquisitae a planeta, quae a remotissimo termino, <lb></lb>usque ad proprinquissimum, augetur ca proportione, quo distantiae decre­<lb></lb>scunt ” (Florentiae 1665, pag. </s>

<s>77). E in ciò il valent&#039;uomo aberrava, per­<lb></lb>chè dalla composizione di quelle due forze opposte, quando l&#039;una fosse stata <lb></lb>maggiore dell&#039;altra, non poteva nascere un moto progressivo nell&#039;orbita, ma <lb></lb>solo un avvicinarsi o un dilungarsi del pianeta dal centro. </s>

<s>Da che è mani­<lb></lb>festo che l&#039;Autore, nonostante che la lettura del secondo dialogo dei Mas­<lb></lb>simi Sistemi l&#039;avesse potuto avviare alla scoperta del vero, confondeva la <lb></lb>forza centrifuga con quella di proiezione. </s></p><p type="main">

<s>Duravano dunque ancora nel 1665 le tenebre, che involgevano il cielo <lb></lb>aristotelico, non rischiarato che da&#039;lampi del Benedetti e di Galileo, quando <lb></lb>apparve alla luce l&#039;Orologio oscillatorio, nelle ultime pagine del quale l&#039;Huy­<lb></lb>ghens, dopo avere accennato a un&#039;altra costruzione dell&#039;automato con pen­<lb></lb>dolo circolare, così soggiungeva: “ Et constitueram quidem descriptionem <lb></lb>horum cum iis demum edere, quae ad motum circularem et <emph type="italics"></emph>Vim centrifu­<lb></lb>gam,<emph.end type="italics"></emph.end> ita enim eam vocare libet, attinent, de quo argumento plura dicenda <lb></lb>habeo, quam quae hoc tempore exequi vacet. </s>

<s>Sed ut nova nec inutili spe­<lb></lb>culatione maturius fruantur harum rerum studiosi, Theoremata traduntur ad <lb></lb>vim centrifugam pertinentia, demonstratione ipsorum in aliud tempus di­<lb></lb>lata ” (Op., T. cit., pag. </s>

<s>185, 86): i quali teoremi, così solamente annun­<lb></lb>ziati, son di numero tredici, i primi cinque relativi alle forze centrifughe, <lb></lb>quando i raggi vettori son sul piano di rotazione, come nei cerchi, e gli altri <lb></lb>otto, quasi tutti, quando essi raggi son fuori del piano della rotazione, come <lb></lb>nei pendoli conici. </s></p><p type="main">

<s>Era per l&#039;Huyghens quasi un tentar le forze dei Matematici in ritro-<pb xlink:href="020/01/2918.jpg" pagenum="543"></pb>vare la dimostrazione di quei teoremi, i quali parvero anche di maggiore <lb></lb>importanza, dappoichè aveva il Borelli additato che dipendevano da essi prin­<lb></lb>cipalmente le leggi dei moti celesti. </s>

<s>A scoprir così fatte leggi attendevano <lb></lb>allora intensamente i matematici inglesi Wren, Hook, Halley, i quali perciò, <lb></lb>rimeditando le conclusioni dei teoremi ugeniani, ne raccolsero per primo <lb></lb>frutto la notizia distinta delle forze centrifughe, per cui si avvidero facil­<lb></lb>mente della fallacia, in ch&#039;era incorso lo stesso Borelli. </s>

<s>Dall&#039;uso della fionda, <lb></lb>pensavano, s&#039;impara due essere le forze: una che mena in giro la pietra, <lb></lb><figure id="id.020.01.2918.1.jpg" xlink:href="020/01/2918/1.jpg"></figure></s></p><p type="caption">

<s>Figura 337.<lb></lb>e l&#039;altra che tira la mano, le quali due forze, percioc­<lb></lb>chè si riducono in una, quando il mobìle esce fuori del­<lb></lb>l&#039;orbita, in direzion tangenziale; non può dunque esser <lb></lb>altra quest&#039;unica forza così diretta, che la resultante <lb></lb>dalla composizione di quelle stesse due. </s>

<s>E applicandovi <lb></lb>la regola dei moti composti, era tale il discorso: Sia <lb></lb>AB (fig. </s>

<s>337) la forza tangenziale, e l&#039;arco AE si prenda <lb></lb>così piccolo, da riguardarsi come una linea retta: co­<lb></lb>struito il parallelogrammo DE, vien da AE rappresen­<lb></lb>tata la forza di circolazione, e da AD la centrifuga, co­<lb></lb>sicchè, soiogliendosi il grave da&#039;suoi legami, la stessa <lb></lb>forza tangenziale AB è quella che resulta dal comporsi <lb></lb>insieme le due AE, AD. </s>

<s>Il Borelli dunque, e tutti i se­<lb></lb>guaci di Aristotile, s&#039;ingannavano in questo: che cre­<lb></lb>devan esser le forze centrifughe una delle cause del <lb></lb>moto nell&#039;orbita, mentre in verità non ne son che l&#039;effetto. </s></p><p type="main">

<s>Conseguiva per facile calcolo, dall&#039;altra parte, dai teoremi annunziati <lb></lb>dall&#039;Huyghens, della verità de&#039;quali si poteva aver fede, anche senza le di­<lb></lb>mostrazioni; che le forze centrifughe di due pianeti stanno direttamente <lb></lb>come i prodotti delle masse e de&#039;raggi delle orbite, e reciprocamente come <lb></lb>i quadrati dei tempi periodici, cosicchè, chiamate F, <emph type="italics"></emph>f;<emph.end type="italics"></emph.end> M, <emph type="italics"></emph>m;<emph.end type="italics"></emph.end> R, <emph type="italics"></emph>r;<emph.end type="italics"></emph.end> T, <emph type="italics"></emph>t<emph.end type="italics"></emph.end><lb></lb>le dette forze, le masse, i raggi e i tempi; la legge di queste stesse forze è <lb></lb>scritta da F:<emph type="italics"></emph>f<emph.end type="italics"></emph.end>=M.R/T2:<emph type="italics"></emph>m.r/t2.<emph.end type="italics"></emph.end> Se dunque i quadrati dei tempi, seguitava <lb></lb>l&#039;Hook a ragionare, stanno, secondo la terza legge kepleriana, come i cubi <lb></lb>dei raggi, sarà F:<emph type="italics"></emph>f<emph.end type="italics"></emph.end>=M<emph type="italics"></emph>r2<emph.end type="italics"></emph.end>:MR2, ond&#039;è che, per un medesimo pianeta, le <lb></lb>forze centripete o di attrazione stanno in reciproca ragione de&#039;quadrati delle <lb></lb>distanze. </s></p><p type="main">

<s>Se ora si risovvengano i Lettori delle cose da noi narrate, nel cap. </s>

<s>XIV <lb></lb>del secondo tomo, intorno alle proporzioni del diffondersi la luce, la virtù <lb></lb>magnetica e le forze cosmiche, allo stesso modo irradianti, e che, nonostante <lb></lb>la certezza geometrica del crescer le superficie sferiche come i quadrati dei <lb></lb>raggi, si credeva che le forze radianti da un centro diminuissero d&#039;intensità <lb></lb>col semplice crescer dei raggi, per cui, non tornando il calcolo del cader della <lb></lb>Luna, aveva abbandonato il Newton le sue sublimi speculazioni; si possono <lb></lb>immaginare quale efficace impulso a ritornar sulla sua via ricevesse lo stesso <pb xlink:href="020/01/2919.jpg" pagenum="544"></pb>Newton per la notizia partecipatagli dall&#039;Hook, che cioè, ammesse le sco­<lb></lb>perte del Kepler, conseguiva da&#039;nuovi canoni ugeniani crescer le forze, che <lb></lb>farebbero cader la Luna, non secondo i semplici avvicinamenti, ma secondo <lb></lb>i quadrati degli avvicinamenti di lei alla Terra. </s></p><p type="main">

<s>Germogliarono di qui i Principii matematici di Filosofia naturale, per <lb></lb>fondamento de&#039;quali si prevede, dal filo delle idee, come dovesse l&#039;Autore <lb></lb>porre la dimostrazione dei teoremi dell&#039;Huyghens, e delle leggi dei moti, da <lb></lb>cui, come da principii generali, scendessero i fatti dal Keplero osservati, e <lb></lb>come tali da lui stesso descritti. </s>

<s>Il Newton non solamente s&#039;accorse, come <lb></lb>l&#039;Hook e i suoi connazionali, che le forze centrifughe conseguono com&#039;effetto <lb></lb>necessario dal moto circolatorio, ma che di più quell&#039;effetto nasce sempre e <lb></lb>per la medesima necessità, quando il moto, dalla retta direzione passa alla <lb></lb>curva, qualunque poi siasi una tale curvità o di circolo o di ellisse o d&#039;altra <lb></lb>linea anche più irregolare. </s>

<s>Nè il caratterismo di un tale effetto gli parve si <lb></lb>trovasse espresso meglio, che dalla seconda legge kepleriana delle aree pro­<lb></lb>porzionali ai tempi impiegati a descriverle dai raggi vettori. </s>

<s>Il primo teorema <lb></lb>infatti dimostrato dal Newton è tale: “ Areas, quas corpora, in gyros acta radiis <lb></lb>ad immobile centrum virium, describunt, et in planis immobilibus consistere, <lb></lb>et esse temporibus proportionales ” (Genevae 1739, pag. </s>

<s>89). Conversamente <lb></lb>poi dimostrò nel secondo: “ Corpus omne, quod movetur in linea aliqua curva, <lb></lb>in plano descripta, et radio ducto ad punctum vel immobile vel motu rectilineo <lb></lb>uniformiter progrediens, describit areas circa punctum illud temporibus propor­<lb></lb>tionales; urgetur a vi centripeta tendente ad idem punctum ” (ibid., pag. </s>

<s>92). </s></p><p type="main">

<s>Sia ora il circolo intorno a cui si fa il moto: è dunque già dimostrato <lb></lb>che il grave corpo circolante è ritirato al centro, con una certa forza, della <lb></lb>quale il Newton, che sempre vuol risalire alla universalità dei principii, at­<lb></lb>tende a ritrovar la misura. </s>

<s>Sarebbe stata l&#039;impresa di difficile, anzi d&#039;im­<lb></lb>possibile esecuzione, mentre che si durava a confondere le forze centrifughe <lb></lb>con le tangenziali. </s>

<s>Ma pure era a Galileo riuscita bene la misura delle forze <lb></lb>dei ritiramenti dagli spazi passati ne&#039;medesimi tempi. </s>

<s>Il prodotto della massa <lb></lb>per la velocità, che vale per la misura dei moti equabili e retti, non basta <lb></lb>trattandosi dei curvi, i quali variano per altre ragioni, non difficili a sco­<lb></lb>prirsi nelle rappresentazioni, esibiteci dalle figure 337 e 335. Se la velocità <lb></lb>è come AE, la forza centrifuga è come AD. </s>

<s>Ma se la velocità diminuisce, <lb></lb>riducendosi per esempio ad AL, anche la forza centrifuga diminuisce, ridu­<lb></lb>cendosi ad AF, ond&#039;è che esse forze, nel medesimo circolo, dipendono dalle <lb></lb>varie velocità, a cui sono direttamente proporzionali. </s>

<s>Se poi s&#039;eguagliano le <lb></lb>velocità, e differiscono i circoli, come nella figura 335, le forze centrifughe <lb></lb>variano anche per un&#039;altra ragione, che è quella reciproca dei raggi. </s>

<s>Ond&#039;è <lb></lb>a concludere che, per aver la misura dell&#039;intensità delle dette forze, non <lb></lb>basta il prodotto della massa e della velocità, ma bisogna aggiungervi per <lb></lb>fattore il quoziente della velocità divisa per il raggio, cosicchè resulti tutto <lb></lb>insieme quel che si cerca espresso dalla massa moltiplicata per il quadrato <lb></lb>della velocità, e divisa per lo stesso raggio. </s></p><pb xlink:href="020/01/2920.jpg" pagenum="545"></pb><p type="main">

<s>Il Newton però sostituiva a questo un ragionamento non men semplice, <lb></lb>e non men concludente. </s>

<s>Diceva che ne&#039;moti diretti le forze son proporzio­<lb></lb>nali ai prodotti delle masse e delle velocità, ma ne&#039;curvi la proporzione deve <lb></lb>essere anche più composta, riguardando la curvità come linee poligonari in­<lb></lb>finilatere, per gli angoli delle quali, dovendo entrare e uscire continuamente <lb></lb>nel suo viaggio, il mobile ha bisogno di esser sospinto al moto da un im­<lb></lb>pulso maggiore. </s>

<s>Or perchè cotesti angoli son tanti più di numero, quanto <lb></lb>l&#039;arco è più grande, e son tanto meno incavati quant&#039;è maggiore la curva­<lb></lb>tura, o il raggio che la descrive; la maggioranza dunque dell&#039;impulso richie­<lb></lb>sto dovrà essere proporzionale direttamente alle velocità, e reciprocamente ai <lb></lb>raggi, per cui le forze, che osservavano nel moto retto la semplice ragion <lb></lb>composta delle masse e delle velocità, sopravvenendo il curvo, si compon­<lb></lb>gono anche di più della ragione delle velocità divise per i raggi: ossia sarà <lb></lb>la loro proporzion definita quella delle masse e de&#039;quadrati delle velocità, <lb></lb>divisi per essi raggi. </s>

<s>“ Haec est vis centrifuga, qua corpus urget circulum, <lb></lb>et huic aequalis est vis contraria, qua circulus continuo repellit corpus cen­<lb></lb>trum versus ” (Principia mathem. </s>

<s>cit., pag. </s>

<s>104). </s></p><p type="main">

<s>Ma volendosi aver di ciò una dimostrazion matematica, il Newton sodi­<lb></lb>sfa i Lettori nel suo IV teorema, con facile ragionamento, che si può ridurre <lb></lb>alla seguente forma, ritornando indietro sopra la figura 336. Essendo le forze <lb></lb>centrifughe, ne&#039;gravi uguali, misurate da&#039;seni versi EF, BC, non rimane <lb></lb>altro a fare, che a determinare i loro valori in funzione degli elementi dei <lb></lb>circoli, e ciò si consegue immediatamente dai canoni della Geometria più <lb></lb>elementare, riducendo gli archi ED, AB a una piccolezza infinitesima, o come <lb></lb>diceva il Newton alla <emph type="italics"></emph>evanescenza,<emph.end type="italics"></emph.end> cosicchè, confondendosi essi archi con le <lb></lb>loro suttese, avremo EF=DE2/2EO, BC=AB2/2BO. </s>

<s>E perchè, essendo uguali i <lb></lb>tempi, come qui suppone, le velocità V, <emph type="italics"></emph>v<emph.end type="italics"></emph.end> son proporzionali agli spazi, e son <lb></lb>proporzionali agli spazi, ossia alle circonferenze o ai loro raggi divisi per i <lb></lb>tempi T, <emph type="italics"></emph>t,<emph.end type="italics"></emph.end> essendo essi tempi diversi; ritenute del resto le solite denomi­<lb></lb>nazioni, sarà la legge delle forze centrifughe espressa dalla formula generale <lb></lb>F:<emph type="italics"></emph>f<emph.end type="italics"></emph.end>=V2/R:<emph type="italics"></emph>v2/r<emph.end type="italics"></emph.end>=R/T2:<emph type="italics"></emph>r/t2.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Di qui deduce il Newton in forma di corollarii, e conferma la verità dei <lb></lb>primi cinque teoremi, annunziati in fine all&#039;Orologio oscillatorio. </s>

<s>Se i tempi <lb></lb>sono uguali, F:<emph type="italics"></emph>f<emph.end type="italics"></emph.end>=R:<emph type="italics"></emph>r,<emph.end type="italics"></emph.end> cioè: <emph type="italics"></emph>Si mobilie duo aequalia, aequaiibus tem­<lb></lb>poribus circumferentias inaequales percurrant, erit vis centrifuga in ma­<lb></lb>iori circumferentia, ad eam quae in minori, sicut ipsae inter se circum­<lb></lb>ferentiae vel eorum diametri.<emph.end type="italics"></emph.end> Se le velocità sono uguali, F:<emph type="italics"></emph>f<emph.end type="italics"></emph.end>=<emph type="italics"></emph>r:<emph.end type="italics"></emph.end>R, <lb></lb>secondo che l&#039;Huyghens aveva pronunziato così ìn secondo luogo: <emph type="italics"></emph>Si duo <lb></lb>mobilia aequalia, aequali celeritate ferantur in circumferentiis inaequali­<lb></lb>bus; erunt eorum vires centrifugae in ratione contraria diametrorum.<emph.end type="italics"></emph.end> Se <lb></lb>i raggi sono uguali, F:<emph type="italics"></emph>f<emph.end type="italics"></emph.end>=V2:<emph type="italics"></emph>v2,<emph.end type="italics"></emph.end> e se le forze centrifughe sono uguali, <lb></lb>T2:<emph type="italics"></emph>t2<emph.end type="italics"></emph.end>=R:<emph type="italics"></emph>r,<emph.end type="italics"></emph.end> ossia T:<emph type="italics"></emph>t<emph.end type="italics"></emph.end>=√R:√<emph type="italics"></emph>r,<emph.end type="italics"></emph.end> ciò che perfettamente corrisponde <pb xlink:href="020/01/2921.jpg" pagenum="546"></pb>col III e col IV ugeniano: <emph type="italics"></emph>Si duo mobilia aequalia in circumferentiis ae­<lb></lb>qualibus ferantur, celeritate inaequali, sed utraque motu aequabili, qua­<lb></lb>lem in his omnibus intelligi volumus; erit vis centrifuga velocioris, ad <lb></lb>vim tardioris, in ratione duplicata celeritatum. </s>

<s>— Si mobilia duo aequa­<lb></lb>lia, in circumferentiis inaequalibus circumlata, vim centrifugam aequalem <lb></lb>habuerint; erit tempus circuitus in maiori circumferentia, ad tempus <lb></lb>circuitus in minori, in subdupla ratione diametrorum.<emph.end type="italics"></emph.end> (Opera, T. cit., <lb></lb>pag. </s>

<s>188, 89). </s></p><p type="main">

<s>Il teorema V aveva pel Newton una singolare importanza, direttamente <lb></lb>entrando nell&#039;ordine delle sue speculazioni, per cui ne volle, nello scolio alla <lb></lb>citata proposizione IV de&#039;suoi <emph type="italics"></emph>Principii,<emph.end type="italics"></emph.end> far solenne commemorazione con <lb></lb>queste parole: “ Datur autem ex descensu gravium et tempus revolutionis <lb></lb>unius, et arcus, dato quovis tempore descriptus, per huius corollarium IX. </s>

<s><lb></lb>Ex huiusmodi propositionibus Hugenius, in eximio suo tractatu <emph type="italics"></emph>De horolo­<lb></lb>gio oscillatorio,<emph.end type="italics"></emph.end> vim gravitatis cum revolventium viribus centrifugis contu­<lb></lb>lit ” (pag. </s>

<s>103). </s></p><p type="main">

<s>Il corollario IX, che qui si cita, e per mezzo del quale si poteva, come <lb></lb>aveva fatto l&#039;Huyghens, conferire la gravità con la forza centrifuga, è scritto <lb></lb>dall&#039;Autore in questa forma: <emph type="italics"></emph>Ex eadem demonstratione consequitur etiam <lb></lb>quod arcus, quem corpus in circulo, data vi centripeta, uniformiter re­<lb></lb>volvendo tempore quovis describit; medius est proportionalis inter diame­<lb></lb>trum circuli, et descensum corporis, eadem data vi, eodemque tempore <lb></lb>cadendo confectum ”<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>101, 2). </s></p><p type="main">

<s>Sia ABG (fig. </s>

<s>338) il circolo, e la forza centripeta, che urge il mobile <lb></lb><figure id="id.020.01.2921.1.jpg" xlink:href="020/01/2921/1.jpg"></figure></s></p><p type="caption">

<s>Figura 338.<lb></lb>in esso, sia pari a quella che ne sollecita la discesa <lb></lb>lungo il diametro AG, come lo solleciterebbe la gravità <lb></lb>naturale, della quale dunque subirà il detto mobile le <lb></lb>medesime leggi, rispetto ai tempi e agli spazi passati. </s>

<s><lb></lb>Sia descritto l&#039;arco AF, nel tempo della discesa AL: <lb></lb>consegue, dice il Newton, dalla mia dimostrazione che <lb></lb>AF2 è uguale ad AL.AG. </s>

<s>Preso infatti un arco mini­<lb></lb>mo AB, in cui la forza centrifuga sappiamo essere mi­<lb></lb>surata dal seno verso AC, per le note leggi dinamiche <lb></lb>gli spazi AC, AL stanno come i quadrati dei tempi, o <lb></lb>delle velocità, o degli spazi percorsi nel circolo, essendo <lb></lb>per supposizione in esso i moti uniformi. </s>

<s>Cosicchè, divisi ambedue i termini della <lb></lb>seconda ragione per AG, avremo AC:AL=AB2/AG:AF2/AG. </s>

<s>E perchè, essendo <lb></lb>l&#039;arco AB evanescente, uguaglia la sua sottesa, d&#039;onde AB2=AC.AG, ossia <lb></lb>AC=AB2/AG; dunque anche AL=AF2/AG, e AL:AF=AF:AG, secondo quel <lb></lb>che veramente il Newton diceva conseguire dalla sua dimostrazione. </s></p><p type="main">

<s>Se la forza, che urge il mobile per farlo scendere lungo il diametro del <lb></lb>circolo, è quella della sua gravità naturale, si giunge per facile via, dalla <pb xlink:href="020/01/2922.jpg" pagenum="547"></pb>stessa dimostrazion newtoniana, a concludere che la forza centripeta del mo­<lb></lb>bile, a quella del suo peso, sta come la metà del raggio del circolo, allo spa­<lb></lb>zio percorse nel tempo, che esso mobile, sollecitato dalla forza centripeta, <lb></lb>passerebbe quel medesimo mezzo raggio. </s>

<s>Cosicchè, chiamato S questo stesso <lb></lb>spazio, F la forza centripeta, G la gravità del mobile o il peso, e finalmente <lb></lb>R il raggio, avremo F:G=R/2:S. </s>

<s>Che se S=R/2, F e G pure sono <lb></lb>uguali, secondo il detto quinto teorema, che l&#039;Autore dell&#039;Orologio oscillato­<lb></lb>rio aveva proposto a dimostrare ai Matematici in questa forma: <emph type="italics"></emph>Si mobile <lb></lb>in circumferentia circuli feratur, ea celeritate, quam acquirit cadendo ex <lb></lb>altitudine, quae sit quartae parti diametri aequalis; habebit vim centrifu­<lb></lb>gam suae gravitati aequalem: hoc est eadem vi funem, quo in centro de­<lb></lb>tinetur, intendit, atque cum ex co suspensum est<emph.end type="italics"></emph.end> (pag. </s>

<s>189). </s></p><p type="main">

<s>Nel 1701 il marchese De l&#039;Hòpital aveva dimostrati questi medesimi <lb></lb>teoremi innanzi all&#039;Accademia di Parigi, quando già l&#039;Huyghens era morto <lb></lb>da sei anni. </s>

<s>Ma bene era vivo nel 1687, quando il Newton pubblicò per la <lb></lb>prima volta la sua sublime Filosofia naturale, cosicchè vedendovi esso Huy­<lb></lb>ghens la sua scienza delle forze centrifughe, non solamente conclusa da prin­<lb></lb>cipii più generali, ma così altamente promossa alla Meccanica celeste, stimò <lb></lb>inutile oramai il suo trattatello, che perciò Burchero De Volder e Bernardo <lb></lb>Fullen, a&#039;quali fu commessa la cura di pubblicarlo, insieme con gli altri <lb></lb>opuscoli postumi dell&#039;Autore, dissero di aver trovato <emph type="italics"></emph>nequaquam convenienti <lb></lb>ordine dispositum.<emph.end type="italics"></emph.end> Nonostante hanno un carattere loro proprio, che li rende <lb></lb>degni di storia, i teoremi delle forze centrifughe ne&#039;pendoli conici, che l&#039;Huy­<lb></lb>ghens fa dipendere principalmente da alcuni teoremi, la verità de&#039;quali, egli <lb></lb>dice, <emph type="italics"></emph>constat ex Mechanicis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sia il corpo C (fig. </s>

<s>339) posato sul declivio AB, e la forza che ve lo <lb></lb>trattiene tiri secondo la direzione orizontale CE: la proporzione di questa <lb></lb>forza, a quella della gravità assoluta del detto corpo, s&#039;avrà decomponendo <lb></lb>la CD, condotta perpendicolare al piano AB, nella CF, diretta secondo l&#039;azione <lb></lb>della gravità, e nella CG, diretta secondo l&#039;azione della potenza. </s>

<s>Dalla qual <lb></lb><figure id="id.020.01.2922.1.jpg" xlink:href="020/01/2922/1.jpg"></figure></s></p><p type="caption">

<s>Figura 339.<lb></lb>decomposizione resulta, osservando che CG=FD, e <lb></lb>chiamando <emph type="italics"></emph>a<emph.end type="italics"></emph.end> l&#039;angolo CDF, G la gravità, e P la po­<lb></lb>tenza; G:P=FC:FD=sen <emph type="italics"></emph>a<emph.end type="italics"></emph.end>:cos <emph type="italics"></emph>a<emph.end type="italics"></emph.end>=tang <emph type="italics"></emph>a<emph.end type="italics"></emph.end>:1, <lb></lb>d&#039;onde è manifesto che, se l&#039;inclinazione del piano <lb></lb>AB sull&#039;orizonte è ad angolo semiretto, ossia se <emph type="italics"></emph>a<emph.end type="italics"></emph.end>= <lb></lb>45°, G=P, e ciò vuol dire che sono uguali in quel <lb></lb>caso la gravità del corpo, e la forza necessaria a te­<lb></lb>nerlo sul declivio. </s>

<s>Per un&#039;altra inclinazione qualun­<lb></lb>que <emph type="italics"></emph>a′<emph.end type="italics"></emph.end> si troverebbe, fra la gravità e la nuova po­<lb></lb>tenza, la proporzione G:P′=tang <emph type="italics"></emph>a′<emph.end type="italics"></emph.end>:1, d&#039;onde si <lb></lb>conclude che le potenze debbono essere proporzio­<lb></lb>nali alle tangenti degli angoli delle inclinazioni. </s>

<s>Se invece che dal piano in­<lb></lb>clinato s&#039;immagini poi il grave sorretto dal filo HC, come nel pendolo, fatta <pb xlink:href="020/01/2923.jpg" pagenum="548"></pb>rappresentare da HC la forza della trazione, questa si risolverebbe nella ver­<lb></lb>ticale KC, e nella orizontale HK, in proporzion delle quali starebbe la gravità <lb></lb>del pendolo stesso rispetto alla forza che lo sostiene in C, rimosso dalla sta­<lb></lb>zion sua naturale. </s></p><p type="main">

<s>Premessi i quali principii meccanici, passa l&#039;Huyghens a dimostrare: <lb></lb><emph type="italics"></emph>In curva superficie Conoidis parabolici, quod axem ad perpendiculum <lb></lb>erectum habeat, circuitus omnes mobilis circumferentias horizonti paral­<lb></lb>lelas percurrentis, sive parvae, sive magnae fuerint, aequalibus temporibus <lb></lb>peraguntur, quae tempora singula aequantur binis oscillationibus penduli, <lb></lb>cuius longitudo sit dimidium lateris recti parabolae genitricis<emph.end type="italics"></emph.end> (Opuscula <lb></lb>posthuma, Lugd. </s>

<s>Batav. </s>

<s>1703, pag. </s>

<s>416). Questa è la VII proposizione <emph type="italics"></emph>De <lb></lb>vi centrifuga,<emph.end type="italics"></emph.end> rispondente alla VI dell&#039;Orologio oscillatorio, la dimostrazion <lb></lb>della quale leggendo innanzi all&#039;Accademia parigina, il marchese De l&#039;Hô­<lb></lb>pital, osservava che mancavano nella proposta dell&#039;Autore due condizioni, <lb></lb>senza le quali si rimaneva indeterminata: <emph type="italics"></emph>prima, ut filum semper sit <lb></lb>superficiei Conoidis perpendiculare, altera, ut semper fiat gyratio ad per­<lb></lb>pendicularem altitudinem dimidii lateris recti.<emph.end type="italics"></emph.end> Il De Volder rispondeva <lb></lb>che, se mai, la condizione mancante è una sola, riducendosi manifestamente <lb></lb>la seconda alla prima; ma che in effetto la proposizione ugeniana non è li­<lb></lb>mitata da condizioni, essendo ella universalissima, come <emph type="italics"></emph>patet ex demonstra­<lb></lb>tione, quam hic libellus exhibet.<emph.end type="italics"></emph.end> In sostanza il De Volder aveva ragione, <lb></lb>ma riuscirebbe ai Lettori del libretto la cosa anche più patente, quando alla <lb></lb>dimostrazione, per non aver tenuto l&#039;Autore le vie più semplici, non fosse <lb></lb>venuta a mancare quella chiarezza, che sarebbesi potuta secondo noi conse­<lb></lb>guire, dimostrando indipendentemente l&#039;una dall&#039;altra le due parti, nelle <lb></lb>quali è distinto il teorema. </s></p><p type="main">

<s>Quanto alla prima, essendo nella semiparabola HDB (fig. </s>

<s>340) rappre­<lb></lb>sentata la sezion del Conoide, sul quale s&#039;appoggi in H il corpo, condotta <lb></lb><figure id="id.020.01.2923.1.jpg" xlink:href="020/01/2923/1.jpg"></figure></s></p><p type="caption">

<s>Figura 340.<lb></lb>la tangente HF, e la perpendicolare HG, consegue dai <lb></lb>principii meccanici già dimostrati che la potenza, o la <lb></lb>forza centrifuga F che l&#039;eguaglia, e che è necessaria a <lb></lb>sostenere il detto corpo in H, sta alla gravità naturale <lb></lb>di lui come HG a GF: o, riguardato pendulo dal filo <lb></lb>HL, come l&#039;ordinata HK alla sunnormale LK. </s>

<s>In un&#039;al­<lb></lb>tra posizione, per esempio M, la proporzione tra la forza <lb></lb>centrifuga F′, e la gravità, sarebbe quella dell&#039;ordinata <lb></lb>MN, alla sunnormale NO: e perchè, per la proprietà <lb></lb>della curva, le sunnormali s&#039;eguaglian tutte fra loro, <lb></lb>sarà dunque F:F′=HK:MN. Ond&#039;essendo le forze <lb></lb>centrifughe, in queste e in tutte le altre posizioni sulla <lb></lb>concavità del Conoide, proporzionali ai raggi delle ro­<lb></lb>tazioni, saranno, per la conversa della prima <emph type="italics"></emph>De vi cen­<lb></lb>trifuga,<emph.end type="italics"></emph.end> i tempi periodici uguali. </s></p><p type="main">

<s>Di qui, osservando che i pendoli H, M, e tutti gli altri, descrivono coni <pb xlink:href="020/01/2924.jpg" pagenum="549"></pb>tutti aventi la medesima altezza uguale alla sunnormale, o alla metà del pa­<lb></lb>rametro della parabola; veniva per corollario, senza trattenervi come fa l&#039;Huy­<lb></lb>ghens altro discorso, dimostrata la seguente proposizione VIII: <emph type="italics"></emph>Si mobilia <lb></lb>duo ex filis inaequalibus suspensa gyrentur, ita ut circumferentias hori­<lb></lb>zonti parallelas percurrant, capite altero fili manente immoto, fuerint au­<lb></lb>tem conorum, quorum superficiem fila hoc motu describunt, axes sive al­<lb></lb>titudines aequales; tempora quoque, quibus utrumque mobile circulum <lb></lb>suum percurrit, aequalia erunt ”<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>418). Conversamente poi, dimo­<lb></lb>strata questa, si sarebbe potuta per corollario dimostrar la VII, quanto alla <lb></lb>sua prima parte, osservando che i pendoli H, M descrivono, rotando intorno <lb></lb>all&#039;asse del Conoide parabolico, coni tutti di pari altezza. </s></p><p type="main">

<s>Venendo alla seconda parte della proposizione VII, supposto essere in A <lb></lb>il foco della parabola, per le proprietà di lei, particolarmente dimostrate dal <lb></lb>Torricelli, nella VII e VIII del primo libro <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> sappiamo che <lb></lb>l&#039;ascissa AB è uguale a un quarto, e l&#039;ordinata AD alla metà del lato retto, <lb></lb>ossia del parametro, e, prolungato l&#039;asse in E, cosicchè AB e HE siano <lb></lb>uguali, sappiamo pure che la linea condotta fra D ed E è tangente alla curva, <lb></lb>e che, il triangolo BAE essendo isoscele, l&#039;angolo ADE è semiretto, per cui <lb></lb>la forza centrifuga in D, e la gravità naturale del corpo che ivi riposa, per <lb></lb>i lemmi meccanici poco fa commemorati, sono uguali. </s>

<s>Di qui è che, per la <lb></lb>conversa della quinta di questo libretto, e dell&#039;Orologio oscillatorio, il tempo, <lb></lb>in cui il corpo D compie il suo giro, sta al tempo della discesa naturale di <lb></lb>lui da pari altezza alla metà del raggio DA, come la circonferenza sta a quel <lb></lb>suo medesimo raggio: cosicchè, chiamati To.P, To.AD/2 i detti tempi, avremo <lb></lb>To.P:To.AD/2=2<foreign lang="grc">π</foreign>AD:AD. </s>

<s>Riguardato poi D come un pendolo, che <lb></lb>faccia le sue minime oscillazioni in archi di circoli osculatori alla Cicloide, <lb></lb>dalla XXV della seconda parte dell&#039;Orologio oscillatorio sappiamo che il tempo <lb></lb>di una di queste minime oscillazioni, al tempo della scesa perpendicolare per <lb></lb>la metà della lunghezza del pendolo, ha la proporzione della circonferenza <lb></lb>al diametro: cosicchè chiamato To.O il tempo della detta minima oscilla­<lb></lb>zione, avremo To.O:To.AD/2=2<foreign lang="grc">π</foreign>AD:2AD, ossia To.2O:To.AD/2= <lb></lb>2<foreign lang="grc">π</foreign>AD:AD, dalla quale, paragonata con la precedente, resulta To.P= <lb></lb>To.2O.E perchè il tempo periodico del corpo in D è uguale al tempo del <lb></lb>medesimo corpo in M, in H, o in qual si voglia altro punto della concavità <lb></lb>del Conoide; si conclude generalmente così la proposizione, con le parole <lb></lb>stesse dell&#039;Huyghens: “ Tempus ergo gyrationis in Conoide parabolico ae­<lb></lb>quatur tempori, quo binae peraguntur oscillationes penduli, cuius longitudo <lb></lb>sit DA, dimidium lateris recti parabolae genitricis ” (ibid., pag. </s>

<s>417). </s></p><p type="main">

<s>Le osservazioni dunque del De l&#039;Hòpital non hanno più luogo, data così <lb></lb>altra forma più semplice e più chiara alla VII proposizione <emph type="italics"></emph>De vi centrifuga.<emph.end type="italics"></emph.end><lb></lb>Ma fa gran maraviglia che a quegli acuti censori parigini passasse inosser-<pb xlink:href="020/01/2925.jpg" pagenum="550"></pb>vata la proposizione XVI di questo stesso libretto, corrispondente con la XIII <lb></lb>e ultima dell&#039;Orologio oscillatorio, che un nostro Matematico, trent&#039;anni e <lb></lb>più dopo, sentì subodorare di falsa, così come l&#039;Autore la pronunziava: <emph type="italics"></emph>Si <lb></lb>pendulum simplex oscillatione laterali maxima agitetur, hoc est, si per to­<lb></lb>tum circuli quadrantem descendat, ubi ad punctum imum circumferen­<lb></lb>tiae pervenerit, triplo maiori vi filum suum trahet, quam si ex illo sim­<lb></lb>pliciter suspensum foret<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>425). </s></p><p type="main">

<s>L&#039;occasione di sospettare che in questo teorema ugeniano s&#039;ascondesse <lb></lb>una fallacia venne al Grandi, quando il Bonaventuri, esaminando varie pic­<lb></lb>cole carte, nelle quali aveva il Viviani scritte certe cose di Meccanica, che <lb></lb>dovevano aggiungersi per illustrare le materie in simile argomento trattate <lb></lb>dal suo Maestro; ebbe a notarvi, a proposito del pendolo, quel che ivi dice <lb></lb>l&#039;Autore del manoscritto, che cioè la forza, che fa esso pendolo tirando il <lb></lb>filo, quando sta perpendicolare all&#039;orizonte, “ alla forza ch&#039;egli fa tirandolo, <lb></lb>se si pone il filo obliquo, rimovendolo dal perpendicolo, sta come il momento <lb></lb>totale al momento discensivo, che avrebbe nel piano inclinato secondo l&#039;obli­<lb></lb>quità del medesimo filo. </s>

<s>Il che però non si trova esser vero, se non quando <lb></lb>il filo obliquamente posto si tien fermo, ma non già quando vibrando si <lb></lb>muove, perchè allora la forza centrifuga fa stirare viepiù il filo, benchè sia <lb></lb>obliquo, di quando è semplicemente nella sua quiete nel perpendicolo ” <lb></lb>(Alb. </s>

<s>XI, 132, 33). </s></p><p type="main">

<s>Noi trattammo già, nella prima parte del cap. </s>

<s>IV di questo Tomo, la <lb></lb>presente questione, alla quale non rimane ora da aggiungere se non che, <lb></lb>conferite il Bonaventuri le sue osservazioni col Grandi, questi prese motivo <lb></lb>di correggere, e di perfezionare il teorema propostosi dal Viviani, dimostrando <lb></lb>che le forze centrifughe, ne&#039;pendoli variamente inclinati all&#039;orizonte, stanno <lb></lb>come i seni degli angoli delle inclinazioni. </s>

<s>Poco esperto esso Grandi nel ma­<lb></lb>neggio dei moti misti, di che in altre parti di questa Storia vedremo gli <lb></lb>esempi, si condusse a ritrovare il vero per certe vie oblique, le quali nondi­<lb></lb>meno tornano alle dirette, perchè, rimosso il pendolo AB (fig. </s>

<s>341), dalla <lb></lb>sua stazione perpendicolare, in C, col filo AC inclinato all&#039;orizzonte per l&#039;an­<lb></lb><figure id="id.020.01.2925.1.jpg" xlink:href="020/01/2925/1.jpg"></figure></s></p><p type="caption">

<s>Figura 341.<lb></lb>golo CAD, che chiameremo <emph type="italics"></emph>a<emph.end type="italics"></emph.end>; decomposta <lb></lb>la gravità CE, espressa con G, nella CF, <lb></lb>secondo la direzione del filo, e perciò mi­<lb></lb>suratrice della forza centrifuga F, e nell&#039;al­<lb></lb>tra CG, ad esso filo perpendicolare; avremo <lb></lb>F:G=CF:CE=CH:AC=sen <emph type="italics"></emph>a<emph.end type="italics"></emph.end>:1. <lb></lb>Per un altro angolo d&#039;inclinazione <emph type="italics"></emph>a′<emph.end type="italics"></emph.end> si <lb></lb>trova allo stesso modo, tra la nuova forza <lb></lb>centrifuga F e la gravità naturale, la pro­<lb></lb>porzione F′:G=sen <emph type="italics"></emph>a′<emph.end type="italics"></emph.end>:1, e perciò F:F=sen <emph type="italics"></emph>a<emph.end type="italics"></emph.end>:sen <emph type="italics"></emph>a′<emph.end type="italics"></emph.end>. </s></p><p type="main">

<s>Con questo teorema il Grandi, così studioso dell&#039;Huyghens, ebbe a con­<lb></lb>ferire la detta proposizione XVI <emph type="italics"></emph>De vi centrifuga,<emph.end type="italics"></emph.end> e avendo trovato che il <lb></lb>pendolo in B, dop&#039;essere sceso da D, ha una forza centrifuga proporzionale <pb xlink:href="020/01/2926.jpg" pagenum="551"></pb>ad AB, alla quale è pure proporzionale la gravità del peso fermo; <emph type="italics"></emph>parmi,<emph.end type="italics"></emph.end><lb></lb>ne concluse, <emph type="italics"></emph>che caduto il globo per tutto il quadrante DCB, dovrà tirare <lb></lb>il centro A doppiamente di quando gli era attaccato fermo.<emph.end type="italics"></emph.end> (Instituz. </s>

<s>mec­<lb></lb>caniche, Firenze 1739, pag. </s>

<s>128). E così, per verità, pare anche a noi, ra­<lb></lb>gionando pure al modo dell&#039;Huyghens, bench&#039;egli dica che tripla, piuttosto <lb></lb>che doppia essere la ritirata del centro <emph type="italics"></emph>ad amussim experientiae consentit,<emph.end type="italics"></emph.end><lb></lb>perchè, immaginando esser la forza del peso fermo in B quella, che lo fa­<lb></lb>rebbe passare equabilmente lo spazio BK, uguale ad AB, nel tempo della <lb></lb>discesa naturale per la stessa AB; venendo il medesimo peso da D per l&#039;arco, <lb></lb>o da A per il perpendicolo, passerebbe equabilmente con l&#039;impeto concepito, <lb></lb>secondo le note leggi dinamiche, spazio doppio di BK, e non triplo. </s></p><p type="main">

<s>Gli altri teoremi de&#039;pendoli conici, che si dimostrano nel trattatello uge­<lb></lb>niano, dipendono più o meno da questi, e avendo le loro particolari appli­<lb></lb>cazioni alla fabbrica degli Orologi, cedono d&#039;importanza a que&#039;primi, sopra <lb></lb>il metro de&#039;quali, trasferitosi in cielo, temperava il Newton le danze degli Dei. </s></p><pb xlink:href="020/01/2927.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della proposta di una Meccanica nuova <lb></lb>e della composizione dei moti<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della <emph type="italics"></emph>Nouvelle Macanique<emph.end type="italics"></emph.end> di Pietro Varignon: degli errori del Cartesio e di Galileo intorno alle <lb></lb>proprietà dei moti composti, dimostrate da Giovan Marco Marci. </s>

<s>— II.<gap></gap>i ciò che operarono <lb></lb>i Matematici stranieri, per confutare il Cartesio, e per dimostrar come debba usarsi, e come <lb></lb>sia vera la regola del parallelogrammo. </s>

<s>— III. </s>

<s>Come le fallacie di Galileo seducessero il Tor­<lb></lb>ricelli e il Viviani, e come fossero solennemente dal Borelli confermate co&#039;suoi paralogismi. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le promozioni date alla Scienza meccanica dagli Stranieri, nella seconda <lb></lb>metà del secolo XVII, parvero esser giunte al loro più alto fastigio, quando <lb></lb>Pietro Varignon, avendo prima inserita nella sua <emph type="italics"></emph>Histoire de la Repubbli­<lb></lb>que des Lettres<emph.end type="italics"></emph.end> una dissertazione, dove le condizioni dell&#039;equilibrio nelle pu­<lb></lb>legge si dimostravano col principio dei moti composti; leggeva poco dipoi, <lb></lb>innanzi all&#039;Accademia parigina, la proposta di trattar tutte le macchine col <lb></lb>medesimo principio: proposta, che venne postuma alla luce nel 1725, col <lb></lb>titolo di <emph type="italics"></emph>Nouvelle Mechanique.<emph.end type="italics"></emph.end> Gli editori fecero preceder l&#039;Opera, che si <lb></lb>raccolse in due grossi volumi, da un discorso, in cui diceva l&#039;Autore come, <lb></lb>ripensando al metodo tenuto da Archimede, dal Cartesio e dal Wallis, nello <lb></lb>stabilire le leggi dell&#039;equilibrio nelle macchine semplici, gli parve che quegli <lb></lb>insigni Matematici s&#039;arrestassero piuttosto a provar la necessità di esso equi­<lb></lb>librio, che il modo com&#039;egli avviene: d&#039;onde si sentì nascere il desiderio <lb></lb>d&#039;investigar le cose più addentro, mettendosi dietro a nuove speculazioni, <lb></lb>delle quali passa a narrare il progresso. </s></p><p type="main">

<s>Dice che <emph type="italics"></emph>le premier obiet qui me vint à l&#039;esprit ce fut un poids qu&#039;une <lb></lb>puissance soûtient sur un plan incliné,<emph.end type="italics"></emph.end> intorno a che vennegli considerato <pb xlink:href="020/01/2928.jpg" pagenum="553"></pb>che l&#039;impressione, fatta dal grave sul piano, è misurata dalla diagonale del <lb></lb>parallelogrammo, di cui siano i lati presi proporzionali al peso, e alla forza <lb></lb>che lo sostiene, d&#039;onde vide aprirsi la mente a <emph type="italics"></emph>choses toutes nouvelles.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Apres avoir ainsi trouvé, prosegue a dire, la maniere dont l&#039;equilibre <lb></lb>se fait sur des plans inclinez, je cherche, par le même chemin, comment des <lb></lb>poids soù tenus avec des cordes soulement, ou appliquez à des poulies, ou <lb></lb>bien à des leviers, font équilibre entr&#039;eux, au avec les puissances qui les <lb></lb>soûtiennent, et j&#039;apperçûs de même que tout cela se faisent encore par la <lb></lb>voye des mouvemens composez, et avec tant d&#039;uniformitè, que je ne pus <lb></lb>m&#039;empêcher de croire que cette voye ne fùt veritablement celle, que fait la <lb></lb>nature dans le concours d&#039;action de deux poids, ou de deux puissances, en <lb></lb>faisent que leurs impressions particulieres, quelque proportions qu&#039;elles ayent, <lb></lb>se confondent en une soule, qui se décharge toute entiere sur se point, ou <lb></lb>se fait cet equilibre: de sorte que la raison physique des effets, qu&#039;on admire <lb></lb>le plus dans les machines, me paruit être justement celle des mouvemens <lb></lb>composez. </s>

<s>” </s></p><p type="main">

<s>Chi legge però queste cose dubita se siano veramente, come vuole il <lb></lb>Varignon, le sue speculazioni <emph type="italics"></emph>toutes nouvelles,<emph.end type="italics"></emph.end> e ripensa al Roberval, che <lb></lb>aveva anch&#039;egli, un mezzo secolo prima, dimostrate le proporzioni dei gravi <lb></lb>sopra i piani inclinati, con questi stessi principii di Meccanica nuova: e ri­<lb></lb>pensa all&#039;Huyghens che, ne&#039;lemmi alla VII, e nella XV proposizione <emph type="italics"></emph>De vi <lb></lb>centrifuga,<emph.end type="italics"></emph.end> dava, come cosa nota appresso i Meccanici, la regola di misurare <lb></lb>l&#039;impressione di un corpo sopra un piano inclinato dalla diagonale del pa­<lb></lb>rallelogrammo, descritto sopra due linee, l&#039;una delle quali fosse proporzio­<lb></lb>nale al peso, e l&#039;altra alla forza necessaria a tenerlo sul declivio. </s>

<s>Che se si <lb></lb>volesse dire non essere ancora, nel 1685, quando fece il Varignon la sua <lb></lb>prima proposta, queste cose del Roberval e dell&#039;Huyghens pubblicamente <lb></lb>note, si potrebbe rispondere che nota era senza dubbio la <emph type="italics"></emph>Spartostatica<emph.end type="italics"></emph.end> dello <lb></lb>Stevino, e notissimo il Corso matematico dell&#039;Herigonio. </s>

<s>Ma nè perciò, fa­<lb></lb>rebbero tuttavia istanza alcuni, sarebbe a diminuire il pregio della novità <lb></lb>nella proposta dell&#039;Accademico di Parigi, non avendo lo Stevino applicato il <lb></lb>principio della composizione delle forze a tutte le macchine, nè essendosi di­<lb></lb>mostrati dall&#039;Herigonio i principii, da&#039;quali consegue la verità del suo teorema. </s></p><p type="main">

<s>Comunque sia, la disputa, che troppo andrebbe in lungo, vien final­<lb></lb>mente decisa dalla Storia, la quale si propone in questo capitolo a narrare <lb></lb>come la regola del parallelogrammo delle forze fosse antichissima, e come, <lb></lb>avendo pacificamente per tanti secoli regnato nel campo della Meccanica, <lb></lb>giunto a un terzo del suo corso il secolo XVII, due potentissimi nemici le <lb></lb>movessero guerra. </s>

<s>Contro la quale essendo andate per alcun tempo deboli <lb></lb>le difese, perchè soggiogate dalla prepotenza e disperse dal timore, insorsero <lb></lb>poi più animose e tutte insieme raccolte nel Varignon, il quale, benchè non <lb></lb>fosse propriamente altro che il restauratore, pure ebbe il nome, e s&#039;acqui­<lb></lb>stò appresso i più il merito di novello instauratore dei moti composti, e delle <lb></lb>loro più ammirabili applicazioni. </s></p><pb xlink:href="020/01/2929.jpg" pagenum="554"></pb><p type="main">

<s>Che fosse veramente antichissima la regola del parallelogrammo si ram­<lb></lb>memorò da noi stessi ai Lettori, infin dai principii di questa Storia della <lb></lb>Meccanica, dove, nella prima parte del capitolo primo dell&#039;altro tomo, si ci­<lb></lb>tava dalle Meccaniche di Aristotile la questione, risolutasi dal Filosofo con <lb></lb>dire che, se un corpo è spinto nel medesimo tempo da due forze proporzio­<lb></lb>nali ai lati di un parallelogrammo, il moto unico che ne resulta è diretto <lb></lb>secondo la diagonale. </s>

<s>Che veramente poi si tenessero dai Matematici queste <lb></lb>dottrine per certe, e che s&#039;applicassero a risolvere i più difficili problemi <lb></lb>della Scienza, si mostrò per gli esempi di Leonardo da Vinci e di Vitellione, <lb></lb>i quali, come cosa notissima ai Meccanici; e perciò da loro universalmente <lb></lb>accettata, senza prendersi altra cura di dimostrarla; decomponevano le forze <lb></lb>dei pesi, e le velocità dei raggi di luce, fatte rappresentare alla diagonale di <lb></lb>un parallelogrammo, in due altre forze o velocità o moti, che avessero ad <lb></lb>essa diagonale la proporzione dei lati. </s></p><p type="main">

<s>Così operando, non credevano nè Leonardo nè Vitellione d&#039;ingannarsi, <lb></lb>sembrando a loro le ragioni del Filosofo dimostrative, come per dimostrative <lb></lb>l&#039;ebbe pure, un secolo e più dopo lo Stevino, ìl quale instituiva la sua nuova <lb></lb>Spartostatica confermando la verità dell&#039;aristotelico teorema. </s>

<s>Ma i dubbi erano <lb></lb>incominciati qualche tempo prima, quando si vollero sottilizzar col discorso <lb></lb>quelle prime apprensioni di verità, così ben rispondenti al senso comune, e <lb></lb>confermate dalle esperienze. </s>

<s>Girolamo Cardano, nel libro IX dei <emph type="italics"></emph>Paralipo­<lb></lb>meni,<emph.end type="italics"></emph.end> ha il capitolo X intitolato <emph type="italics"></emph>De motibus mirabilibus,<emph.end type="italics"></emph.end> fra le quali ma­<lb></lb>raviglie scriveva anche questa: </s></p><p type="main">

<s><emph type="italics"></emph>“ Si duobus motibus rectis idem feratur eodem modo altero ad alte­<lb></lb>rum, ad rectum stante, movebitur secundum reclam per rectangulum, iuxta <lb></lb>proportionem dimetientis. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sit A (fig. </s>

<s>342) motum ad B, et eodemmodo, idest aequaliter, in <lb></lb>aequalibus temporibus, et regula, in qua est A, quae est AB, moveatur ver­<lb></lb>sus CD ita, quod sit aliqua proportio inter AB et AC et ducatur AD dime­<lb></lb>tiens: dico quod A feretur perpetuo his duobus motibus per AGD. </s>

<s>Feratur <lb></lb><figure id="id.020.01.2929.1.jpg" xlink:href="020/01/2929/1.jpg"></figure></s></p><p type="caption">

<s>Figura 342.<lb></lb>enim in E: igitur si regula feratur in F erit ex sup­<lb></lb>posito AC ad AF ut AB ad AE. </s>

<s>Cumque commu­<lb></lb>nicent rectangula in A recto, erunt similia, igitur <lb></lb>circa eamdem dimetientem. </s>

<s>Igitur punctum G cadet <lb></lb>in recta AD. </s>

<s>Quod si A moveretur aequaliter in AB, <lb></lb>ut AB regula versus CD, manifestum esset quod A <lb></lb>ferretur per dimetientem quadrati, et superficies <lb></lb>ABCD esset quadrata ” (<emph type="italics"></emph>Opera omnia,<emph.end type="italics"></emph.end> T. X, Lugduni 1663, pag. </s>

<s>516). </s></p><p type="main">

<s>La dimostrazion del Cardano, come di tutti gli Autori infino al Newton, <lb></lb>e lo vedremo, somiglia quella di Aristotile. </s>

<s>Ma mentre il Filosofo insegnava <lb></lb>andar sotto la medesima regola la composizione dei moti, qualunque si fosse <lb></lb>l&#039;angolo del loro concorso, il Cardano soggiungeva quest&#039;altro teorema: “ Si <lb></lb>vero eodemmodo idem punctum moveatur, sed motibus non ad rectum an­<lb></lb>gulum constitutis, efficiet punctum istud lineam obliquam ” (ibid., pag. </s>

<s>517). <pb xlink:href="020/01/2930.jpg" pagenum="555"></pb>E dai paralogismi di questa cardanica dimostrazione ebbero origine que&#039;dubbi, <lb></lb>i quali parve non lasciassero la mente quieta nemmeno al Keplero, quando, <lb></lb>introducendo nell&#039;Ottica il metodo usato da Vitellione, di decomporre il rag­<lb></lb>gio incidente in due, l&#039;uno perpendicolare e l&#039;altro parallelo alla superficie <lb></lb>dello specchio; chiamava con una certa espressione, che non sfugge all&#039;at­<lb></lb>tenzion dei Lettori, quello stesso metodo una finzione, <emph type="italics"></emph>commentum.<emph.end type="italics"></emph.end> Ma nei <lb></lb>primi quarant&#039;anni del secolo XVII i dubbi, avutane già la spinta dal Car­<lb></lb>dano, rovinarono in tali errori, che, insiem con gli sforzi per ritirarli in sul <lb></lb>retto sentiero, formano in questa Storia un quadro notabile, di cui con brevi <lb></lb>tocchi daremo il disegno. </s></p><p type="main">

<s>Quando il Cartesio volle, nel suo celebre discorso <emph type="italics"></emph>Del metodo,<emph.end type="italics"></emph.end> restaurar <lb></lb>l&#039;Ottica, pensò di applicare alle sue dimostrazioni, sull&#039;esempio di Vitellione, <lb></lb>rinnovellato poco fa dal Keplero, il principio dei moti composti. </s>

<s>Ma per poca <lb></lb>considerazione intorno ai teoremi già dimostrati dai suoi predecessori, ch&#039;egli <lb></lb>al solito disprezzava, credè che il moto resultante per esempio secondo la <lb></lb>diagonale del quadrato AB (fig. </s>

<s>343) dovesse equivalere alla somma dei moti <lb></lb>componenti fatti per AH, AC, cosicchè, supposto avere questi due moti cia­<lb></lb>scuno un grado di velocità, il mobile ne avesse in B acquistati due. </s>

<s>Simil­<lb></lb>mente, facendosi il moto per AH con un grado di velocità, e per l&#039;AD con <lb></lb>due, credeva che per la diagonale AG andasse il mobile con velocità di <lb></lb>tre gradi. </s></p><p type="main">

<s>Secondo questa opinione le due diagonali dunque starebbero fra loro <lb></lb>come due a tre, ciò che contradice apertamente ai canoni della Geometria, <lb></lb>perchè AB2=2AH2, e AG2=5AH2, d&#039;onde AB:AG=√4:√10= <lb></lb>2:√10. Avrebbe dovuto di qui avvedersi il Filosofo che, non potendo non <lb></lb>dire il vero la Geometria, quella sua opinione doveva esser falsa, ma, non <lb></lb>permettendogli ciò il filosofico orgoglio, ricorse allo strattagemma di riguar­<lb></lb><figure id="id.020.01.2930.1.jpg" xlink:href="020/01/2930/1.jpg"></figure></s></p><p type="caption">

<s>Figura 343.<lb></lb>dar le linee come quelle che determinano la via, e no che <lb></lb>misurano la quantità del moto. </s>

<s>Ma perchè il metodo ch&#039;egli <lb></lb>seguiva supponeva le dette linee proporzionali alle quantità, <lb></lb>non bastò al Cartesio l&#039;aver sostituito i nomi alle cose, per <lb></lb>ricoprire il paralogismo del suo discorso, nel quale, ammet­<lb></lb>tendosi la coesistenza delle due equazioni AB:AG=2:3, <lb></lb>e AB:AG=2:√10, veniva a dirsi che tre è uguale alla <lb></lb>radice di dieci. </s>

<s>Che poi di fatto ammettesse paralogizzando il <lb></lb>Cartesio una tale coesistenza, si ricava dalle sue proprie pa­<lb></lb>role, scritte in una epistola al Mersenno, per rispondere a <lb></lb>un suo censore, che lo aveva accusato di poca chiarezza nel chiamar <emph type="italics"></emph>de­<lb></lb>terminazione al moto<emph.end type="italics"></emph.end> quel che si sarebbe dovuto piuttosto dire <emph type="italics"></emph>moto deter­<lb></lb>minato.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ In primis ait me clarius locuturum fuisse, si pro determinatione mo­<lb></lb>tum determinatum dixissem, qua in re ipsi non assentior. </s>

<s>Etsi enim dici <lb></lb>possit velocitatem pilae ab A ad B componi ex duabus aliis, scilicet ab A <lb></lb>ad H, et ab A ad C; abstinendum tamen esse putavi ab isto modo loquendi, <pb xlink:href="020/01/2931.jpg" pagenum="556"></pb>ne forte ita intelligeretur, ut istarum velocitatum, in motu sic composito, <lb></lb>quantitas et unius ad alteram proportio remaneret, quod nullo modo est ve­<lb></lb>rum. </s>

<s>Nam si, exempli causa, ponamns pilam ab A ferri dextrorsum uno <lb></lb>gradu celeritatis, et deorsum uno etiam gradu, perveniet ad B cum duobus <lb></lb>gradibus celeritatis, eodem tempore quo alia, quae ferretur etiam ab A <lb></lb>dextrorsum uno gradu celeritatis, et deorsum duobus, perveniet ad G cum <lb></lb>tribus gradibus celeritatis: unde sequeretur lineam AB esse ad AG ut 2 <lb></lb>ad 3, quae tamen est ut 2 ad √10 ” (<emph type="italics"></emph>Epist. </s>

<s>cartes.,<emph.end type="italics"></emph.end> P. III, Amstelodami 1683, <lb></lb>pag. </s>

<s>69). </s></p><p type="main">

<s>L&#039;error del Cartesio in credere che, facendosi separatamente il moto per <lb></lb>la AH con un grado, e per l&#039;AD con due, fosse nel composto per l&#039;AG con <lb></lb>tre gradi di velocità, esattamente serbando la somma dei due componenti; <lb></lb>fu comune, affinchè imparino i Lettori a credere alla divinità dell&#039;ingegno <lb></lb>degli uomini, anche a Galileo, a cui il Lagrange attribuiva l&#039;invenzione dei <lb></lb>moti composti, e poi soggiungeva: <emph type="italics"></emph>mais il paroît en même tems que Ga­<lb></lb>lilee n&#039;a pas connu toute l&#039;importance de ce theorême dans la theorie de <lb></lb>l&#039;equilibre,<emph.end type="italics"></emph.end> e ciò dice perchè, dimostrando esso Galileo le proporzioni dei pesi <lb></lb>nel perpendicolo e sopra il piano inclinato, lo vede ricorrere ai principii sta­<lb></lb>tici della leva, piuttosto che alla regola del parallelogrammo (<emph type="italics"></emph>Mechanique <lb></lb>anal.,<emph.end type="italics"></emph.end> Paris 1788, pag. </s>

<s>8). Ma non deve il celebre Matematico torinese aver <lb></lb>bene considerato quel teorema II, ch&#039;egli cita dal IV dialogo delle Scienze <lb></lb>nuove, perchè altrimenti l&#039;ammirazion dell&#039;invenzione si sarebbe convertita <lb></lb>nella compassione del paralogismo che l&#039;informa: paralogismo tanto men per­<lb></lb>donabile che al Cartesio, ripensando alle tradizioni più prossime, che Gali­<lb></lb>leo ebbe di quelle dottrine. </s></p><p type="main">

<s>Accenna a così fatte tradizioni l&#039;interloquio, che succede al detto teo­<lb></lb>rema, e in cui fa a Simplicio difficoltà l&#039;ammetter che l&#039;impeto composto <lb></lb>in B (nell&#039;ultima figura) sia maggiore del semplice in C, mentre altrove era <lb></lb>stato detto, e poi dimostrato, che dovevano essere que&#039;due impeti uguali. </s>

<s><lb></lb>Alla quale difficoltà risponde il Salviati essersi dimostrata una tale ugua­<lb></lb>glianza, no nel caso che il grave si muova equabilmente di moto composto, <lb></lb>ma quando, partendosi in A dalla quiete, scende acceleratamente lungo l&#039;AB <lb></lb>inclinata sull&#039;orizonte: intorno a che si sovverranno i Lettori come Galileo <lb></lb>interpellasse Luca Valerio, il quale, in una lettera scritta da Roma il di 18 Lu­<lb></lb>glio 1609, confermava, dimostrandola così col principio dei moti composti, <lb></lb>la verità dell&#039;assunto: </s></p><p type="main">

<s>“ Essendo il moto del corpo grave D (fig. </s>

<s>344), mosso per l&#039;AC al­<lb></lb>l&#039;orizonte BC, mobile verso la BC, e l&#039;altro per una perpendicolare all&#039;ori­<lb></lb>zonte, essa ancor mobile; cosa chiara è che, quando D sarà in C, avrà acqui­<lb></lb>stato tanto impeto, o inclinazione a velocemente moversi, che è la quantità <lb></lb>dell&#039;effetto (in quanto effetto, dico, di quella parte del moto composto, che si <lb></lb>fa per la perpendicolare mobile eguale alla stabile AB) quanto avrebbe acqui­<lb></lb>stato, se D si fosse mosso per la sola perpendicolare AB ” (Alb. </s>

<s>VIII, 47, 48). </s></p><p type="main">

<s>Da questo discorso dunque, i principii che informano il quale dovevano <pb xlink:href="020/01/2932.jpg" pagenum="557"></pb>esser veri, perchè si vedevano condurre a conseguenze, che Galileo stimava <lb></lb>verissime; resultava che il moto composto non era uguale alla somma, ma <lb></lb>a uno solo dei componenti, rimanendosi l&#039;altro senza effetto. </s>

<s>E perchè, non <lb></lb><figure id="id.020.01.2932.1.jpg" xlink:href="020/01/2932/1.jpg"></figure></s></p><p type="caption">

<s>Figura 344.<lb></lb>in questo caso solo, ma in tutti gli altri, dove le forze <lb></lb>sono angolari, qualche parte di esse necessariamente si <lb></lb>elide, avrebbe dovuto persuadersi Galileo che il moto mi­<lb></lb>sto non può essere uguale, ma sempre minor della somma <lb></lb>dei moti semplici separati. </s>

<s>Tutt&#039;altrimenti da ciò, che <lb></lb>avrebbe suggerito il retto discorso, leggiamo annunziato <lb></lb>così dall&#039;Autore il teorema: <emph type="italics"></emph>Si aliquod mobile duplici <lb></lb>motu aequabili moveatur, nempe orizontali et perpen­<lb></lb>diculari, impetus seu momentum lationis, ex utroque motu compositae, erit <lb></lb>potentia aequalis ambobus momentis priorum motuum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Moveatur enim aliquod mobile aequabiliter duplici latione, et motioni <lb></lb>perpendiculari respondeat spatium AB (nella medesima ultima figura) lationi <lb></lb>vero horizontali, eodem tempore confectae, respondeat BC. </s>

<s>Cum igitur, per <lb></lb>motus aequabiles, conficiantur eodem tempore spatia AB, BC, erunt harum <lb></lb>lationum momenta inter se ut ipsae AB, BC. </s>

<s>Mobile vero, quod secundum <lb></lb>hasce duas motiónes movetur, describit diagonalem AC: erit momentum suae <lb></lb>velocitatis ut AC ” (Alb. </s>

<s>XIII, 234). Chiamate dunque F, F′, F″ quelle forze, <lb></lb>o quei momenti di velocità, sarebbe secondo questo discorso F:F′=AB:BC, <lb></lb>e anche F:F″=AB:AC, d&#039;onde F+F′:F″=AB+BC:AC. </s>

<s>Così <lb></lb>(anche Galileo ripetendo i medesimi paralogismi del Cartesio) si può dire <lb></lb>che è, ma non lo permette la Geometria, perchè, dovendo le due parti F, F′ <lb></lb>tornare uguali al tutto F″, parrebbe che i cateti all&#039;ipotenusa, o la linea <lb></lb>spezzata ABC dovesse tornare uguale alla AC linea retta. </s>

<s>Onde, a salvar da <lb></lb>una parte il suo proprio errore, e dall&#039;altra la verità geometrica, Galileo <lb></lb>ricorse a uno strattagemma, ch&#039;è poi un equivoco non men meschino di <lb></lb>quello del Cartesio, dicendo che AB, BC, AC non son linee, ma potenze, e <lb></lb>sta bene che le potenze, o i quadrati di AB e di BC, uguaglino insieme la <lb></lb>potenza o il quadrato di AC diagonale. </s>

<s>“ Verum AC potentia aequatur ipsis <lb></lb>AB, BC: ergo momentum, compositum ex utrisque momentis AB, BC, est <lb></lb>potentia tantum illis simul sumptis aequale, quod erat ostendendum ” (ibid.). </s></p><p type="main">

<s>Quando Galileo accomodava così questa sua dimostrazione aveva sot­<lb></lb>t&#039;occhio il terzo tomo del <emph type="italics"></emph>Cursus Mathematicus<emph.end type="italics"></emph.end> di Pietro Herigon, stam­<lb></lb>pato per la prima volta in Parigi nel 1634, e dove è inserito un trattatello <lb></lb>di Meccanica, la XII proposizione del quale è così espressa: <emph type="italics"></emph>Dato pondere, <lb></lb>duobus funibus suspenso, invenire quantum ponderis singuli funes ferant.<emph.end type="italics"></emph.end><lb></lb>La soluzion del problema è data, per dir così, alla mutola, per via di segni, <lb></lb>che sono una figura simile alla nostra (fig. </s>

<s>345) allato alla quale e sotto sono <lb></lb>scritte le equazioni: A=1000, C=800, D=600, EB:BF=A:C, <lb></lb>EB:BG=A:D. </s>

<s>Un corollario vi s&#039;aggiunge, che dice: Se C=D= <lb></lb>A=100, il quadrilatero FG è una losanga, e perciò FBG=120°. </s></p><p type="main">

<s>Galileo e qualunque altro lettore deduceva da quelle equazioni BF:BG= <pb xlink:href="020/01/2933.jpg" pagenum="558"></pb>C:D: e componendo, BF+BC:BF=C+D:A, d&#039;onde, se veramente <lb></lb>le parti rimanendo intere dovessero tornare uguali al tutto, se cioè C+D=A, <lb></lb>come lo stesso Galileo credeva, ne sarebbe dal Teorema herigoniano venuto <lb></lb>per conseguenza BF+BC=BF+FE=EB, ciò che, conferito con l&#039;al­<lb></lb><figure id="id.020.01.2933.1.jpg" xlink:href="020/01/2933/1.jpg"></figure></s></p><p type="caption">

<s>Figura 345.<lb></lb>tro teorema recitato nel Dialogo dal Salviati, conduceva <lb></lb>necessariamente a dire o che non è incluso in questo <lb></lb>esso teorema herigoniano, o ch&#039;egli è un&#039;aperta fallacia, <lb></lb>perchè, non essendo l&#039;angolo in F retto, le potenze di <lb></lb>BF e di EF insieme non sono uguali alla potenza di <lb></lb>BE sola. </s>

<s>Non si sa come la pensasse intorno a ciò Ga­<lb></lb>lileo, ma nei discepoli di lui prevalse, come vedremo, <lb></lb>l&#039;opinione che la regola seguita dall&#039;Herigonio si do­<lb></lb>vesse sospettare di falsa, e che perciò non fosse lecito <lb></lb>comporre i moti dei lati nella diagonale del parallelogrammo, altro che nel <lb></lb>caso delle forze ortogonali. </s></p><p type="main">

<s>Si potrebbe qui opportunamente ripetere da noi ai Lettori quel che <lb></lb>disse l&#039;Hobbes al Mersenno, a proposito del Cartesio: vedete quanto sia fa­<lb></lb>cile anche ai dottissimi uomini, per troppo confidar di sè, il cadere in pa­<lb></lb>ralogismi. </s>

<s>Ma giova, per amor della dignità dell&#039;ingegno umano e della <lb></lb>Scienza, rammemorare un altro dottissimo uomo, che sanamente ragionava <lb></lb>in mezzo ai delirii incredibili del Cartesio e di Galileo. </s>

<s>A Giovan Marco <lb></lb>Marci, matematico di Praga, si deve il merito di aver dimostrate le leggi <lb></lb>della composizione dei moti con tal perfezione, da rimaner tuttavia superiore, <lb></lb>a nostro giudizio, agli stessi autori più moderni. </s></p><p type="main">

<s>Due moti si possono, dice Giovan Marco, mescere in uno solo, e questo <lb></lb>novamente sceverarsi ne&#039;due, non così però che la miscela torni esattamente <lb></lb>alla somma delle parti, come a pesare con la stadera due corpi, ma facendo <lb></lb>de&#039;componenti una terza cosa, che non è nè l&#039;uno nè l&#039;altro di quelli, ben­<lb></lb>chè ne partecipi delle qualità, come a mescere insieme due colori. </s>

<s>E perchè <lb></lb>del moto quel che può sapersi è la direzione e l&#039;intensità, il proposito del­<lb></lb>l&#039;Autore è quello di dimostrare come sia diretta, e quanta sia la grandezza <lb></lb>della linea, che rappresenta il moto misto, rispetto alla direzione e alla gran­<lb></lb>dezza delle linee, che rappresentano i moti semplici componenti. </s>

<s>I principii <lb></lb>della dimostrazione si desumono dai teoremi premessi intorno ai moti o alle <lb></lb>forze, che produce ne&#039;corpi la gravità naturale, con la continua e regolare <lb></lb>successione de&#039;suoi impulsi. </s>

<s>Ora, supposto che un&#039;altra forza qualunque operi <lb></lb>in modi simili a quello della gravità, saranno simili anche le proporzioni dei <lb></lb>moti, qualunque sia la loro direzione assoluta, diversa da quella, che è al <lb></lb>centro della Terra. </s>

<s>Le forze poi, che hanno generalmente, nel rettangolo <lb></lb>della massa e della velocità del corpo mosso, la loro misura, fa più sempli­<lb></lb>cemente Giovan Marco rappresentar dai quadrati, ossia dalle potenze delle <lb></lb>linee geometriche, sapientemente però riducendo alla verità logica i paralo­<lb></lb>gismi di Galileo. </s></p><p type="main">

<s>Benchè sia cosa da tutti gli autori chiesta, e da tutti i lettori facilmente <pb xlink:href="020/01/2934.jpg" pagenum="559"></pb>concessa come assioma, pure il Matematico di Praga si propone per prima <lb></lb>cosa di dimostrare che <emph type="italics"></emph>Ab impulsu contrario et aequali nullus est motus; <lb></lb>ab impulsu vero contrario et inaequali motus est aequalis excessus maio­<lb></lb>ris (De proportione motus,<emph.end type="italics"></emph.end> Pragae 1639, fol. </s>

<s>36 ad t.). Dopo la qual pro­<lb></lb>posizione passa l&#039;Autore, nella XXXI appresso, a stabilire per fondamento <lb></lb>alle sue dottrine: <emph type="italics"></emph>Motus secundum quid contrarii per lineam fiunt me­<lb></lb>diam, cuius intervallum determinat sinus complementi inclinationis, in <lb></lb>ratione quam habent impulsus<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>37). </s></p><p type="main">

<s>Se il mobile dal medesimo punto A (fig. </s>

<s>346) si muova per le linee <lb></lb>AB, AF, inclinate fra loro ad angolo maggiore o minore di un retto, “ erunt <lb></lb>hi motus secundum quid contrarii, ac proinde, in eo quo sunt contrarii, tol­<lb></lb>lunt aut impediunt suum contrarium. </s>

<s>Impulsus ergo in AF, ab impulsu in <lb></lb>AB, et hic ab impulsu in AF retractus, quia idem mobile esse non potest <lb></lb>in pluribus locis, ac proinde neque pluribus motibus agitari; movebitur motu <lb></lb>inter utrumque medio, cuiusmodi linea motus AD. </s>

<s>Dico huius lineae inter­<lb></lb>vallum lineis extremis AB, AF esse sinum complementi angulorum FAD, <lb></lb><figure id="id.020.01.2934.1.jpg" xlink:href="020/01/2934/1.jpg"></figure></s></p><p type="caption">

<s>Figura 346.<lb></lb>BAD, in ratione quam habet impulsus AB ad impul<gap></gap>um <lb></lb>AF ” (ibid.). Condotte infatti dai punti F, B sopra la <lb></lb>AD le perpendicolari FC, BE, e chiamate AF, AB due <lb></lb>forze qualunque, proporzionali ai momenti della gravità <lb></lb>naturale del medesimo corpo, o di due corpi uguali, <lb></lb>scendenti lungo i piani inclinati AF, AB; aveva Gio­<lb></lb>van Marco dimostrato nella sua XIV, corrispondente con <lb></lb>la III del primo libro <emph type="italics"></emph>De motu gravium<emph.end type="italics"></emph.end> del Torricelli, <lb></lb>essere AF:AB=AC:AE=sen AFC:sen ABE=cos FAD:cos BAD. </s></p><p type="main">

<s>Siano ora i due moti fatti per AB, AE (fig. </s>

<s>347) lati del parallelo­<lb></lb>grammo BE: ossendo AD il seno del complemento, ossia il coseno dell&#039;an­<lb></lb>golo dell&#039;inclinazione DAE, e AC il coseno dell&#039;angolo dell&#039;inclinazione BA, <lb></lb>la direzion della resultante sarà dunque per l&#039;ACD secondo la diagonale. </s>

<s>E <lb></lb>perchè, condotte dai punti E, B le perpendicolari ED, BC sopra la linea della <lb></lb>notata direzione, il moto per l&#039;AE e per l&#039;AD, come anche per l&#039;AB e per <lb></lb>l&#039;AC, o per la sua uguale DF, secondo la XIII di Giovan Marco, e più di­<lb></lb>rettamente secondo il lemma dopo la XII del sopra citato libro primo del <lb></lb><figure id="id.020.01.2934.2.jpg" xlink:href="020/01/2934/2.jpg"></figure></s></p><p type="caption">

<s>Figura 347.<lb></lb>Torricelli, si fanno in tempi eguali; è manifesto che nel tempo <lb></lb>che il mobile sarebbe, co&#039;moti semplici separati, portato da <lb></lb>A in E, e da A in B, mescendosi insieme quegli stessi due <lb></lb>moti, sarà portato per AD+DF=AF, ossia per la diago­<lb></lb>nale del parallelogrammo. </s>

<s>E perchè, essendo i tempi eguali, <lb></lb>gl&#039;impeti per AB, AE, AF, che si chiameranno B, E, F, stanno <lb></lb>come gli spazi; sarà dunque B:F=AB:AF, E:F=AE:AF, <lb></lb>d&#039;onde B:E=AB:AE. Componendo, B+E:E= <lb></lb>AB+AE:AE, e perciò B+E:F=AB+AE:AF. </s>

<s>Così dava G. </s>

<s>Marco ma­<lb></lb>tematica dimostrazione di quel che aveva semplicemente asserito nella pro­<lb></lb>posizione III, che cioè, uscita fuor dell&#039;arco la saetta, “ quia a nullo deti-<pb xlink:href="020/01/2935.jpg" pagenum="560"></pb>netur, per lineam fit mediam inter tangentem et lineam rectam, sive per <lb></lb>diametrum parallelogrammi, cuius latera sunt in proportione illorum mo­<lb></lb>tuum ” (ibid., fol. </s>

<s>12). </s></p><p type="main">

<s>Rimaneva ancora all&#039;Autoro, nella presente dottrina dei moti misti, a <lb></lb>risolvere una questione importante: qual proporzione cioè abbia il moto per <lb></lb>i lati a quello per la diagonale. </s>

<s>Il Cartesio e Galileo avevano creduto essere <lb></lb>una tal proporzione di perfetta uguaglianza, ma in mezzo a loro così ingan­<lb></lb>nati sorgeva G. </s>

<s>Marco ad annunziare in nome della verità: <emph type="italics"></emph>Motus perfecte <lb></lb>mixtus fit per diametrum parallelogrammi, cuius latera constituit motus <lb></lb>simplex, et, ex impulsu quidem aequali, est aequalis semissi, ex inaequali <lb></lb>vero, maior semisse eiusdem motus<emph.end type="italics"></emph.end> (ibid., fol. </s>

<s>37 ad t.). </s></p><p type="main">

<s>Chiama moto perfettamente misto quello, che resulta di due moti sem­<lb></lb>plici uguali e similmento contrari, come sarebbe in un mobile sollecitato da <lb></lb>forze proporzionali, e dirette secondo i lati di una figura quadrata. </s>

<s>Sia AD <lb></lb>questa figura (348) nella quale AD, BC diametri, intersecantisi in E. </s>

<s>Es­<lb></lb>sendo AE2=AC2—CE2, dunque, benchè sia vero che per AE, AC i moti <lb></lb>sono eguali nel tempo, differiscono nulladimeno in grandezza, e CE2, ossia <lb></lb>AE2 è questa differenza. </s>

<s>Similmente, AB2 differisce da AE2 di BE2, ossia di <lb></lb>ED2, onde il moto per la diagonale AD è AE2+ED2=AD2/2. E perchè <lb></lb>AD2=AC2+CD2=AC2+AB2, dunque il moto misto nella diagonale <lb></lb><figure id="id.020.01.2935.1.jpg" xlink:href="020/01/2935/1.jpg"></figure></s></p><p type="caption">

<s>Figura 348.<lb></lb>è la metà de&#039;moti semplici componenti. </s>

<s>“ Est autem (per <lb></lb>citar le parole proprie dell&#039;Autore da noi commentate) mo­<lb></lb>tus in AB et AC, duratione quidem, aequalis motui in AE, <lb></lb>per proposit. </s>

<s>XIII, magnitudine vero minor, cuius excessus <lb></lb>quadratum EB et EC, seu AE et ED. </s>

<s>At vero duo quadrata <lb></lb>AE, ED sunt semisses quadrati AD: hoc est motus in AB, <lb></lb>AC, cui aequale est quadratum AD, propterea quod AD sit <lb></lb>dupla AE aut ED; igitur motus aequaliter mixtus fit per diametrum paral­<lb></lb>lelogrammi, et, ab aequali impulsu, est aequalis semissi utriusque motus <lb></lb>simul sumpti ” (ibid., fol. </s>

<s>38). </s></p><p type="main">

<s>Suppongasi in secondo luogo, presegue G. </s>

<s>Marco a dire, che i due moti <lb></lb>siano differenti, e precisamente FE (fig. </s>

<s>349) doppio di EG. </s>

<s>Condotte dai <lb></lb>vertici G, F le perpendicolari GO, FL alla diagonale EH, sarà, per i teo­<lb></lb>remi della Geometria elementare, EF:FH=EL:LF=LF:LH, e anche <lb></lb>insieme EF2:FH2=EL2:LF2=LF2:LH2. </s>

<s>Avendosi poi, per le cose sup­<lb></lb>poste, EF2=2EG2=2FH2, avremo anche LF2=2LH, ossia LF2+LH2= <lb></lb>FH2=3LH2: e, duplicando, 2FH2=6LH2. </s>

<s>Ora, perchè EH2=EF2+FH2, <lb></lb>ed EF2=2FH2, si trasformerà la trovata uguaglianza del quadrato di EH, <lb></lb>fatte le sostituzioni, in EH2=3FH2=9LH2, e perciò EH2/2=(4+1/2)LH2. </s>

<s><lb></lb>Dalla prima quadratica poi dianzi istituita resulta EL2=LF2.EF2/FH2: e perchè, <lb></lb>come si disse, EF2=2FH2, e si trovò LF2=2LH2, si trasformerà quella <pb xlink:href="020/01/2936.jpg" pagenum="561"></pb>eguaglianza del quadrato di EL, aggiuntovi il quadrato di LH, in EL2+LH2= <lb></lb>5LH2. </s>

<s>Dunque EL2+LH2&gt;EH2/2. Ed essendo EL2+LH2 il moto nella dia­<lb></lb>gonale, ed EH2=EG2+GH2=EG2+EF2 la somma dei moti semplici <lb></lb>componenti, quello sarà maggiore della metà di questi, come G. </s>

<s>Marco erasi <lb></lb>proposto di dimostrare. </s></p><p type="main">

<s>Concludesi questa teoria col rendere la ragione del perchè il moto re­<lb></lb>sultante non sia nè possa essere uguale, come il Cartesio e Galileo crede­<lb></lb>vano, ma si trovi sempre in difetto verso la somma dei componenti. </s>

<s>“ Causa <lb></lb>vero huius defectus, dice l&#039;Autore, est contrarietas illorum motuum, ex an­<lb></lb>gulis proveniens, cum quibus augetur et minuitur quousque angulus latescens <lb></lb>aequalis sit duobus rectis, in quo summa est contrarietas, ac proinde nullus <lb></lb>esse potest motus. </s>

<s>Angulo vero decrescente augetur similitudo motus, quou­<lb></lb>sque, angulo deficiente, fiat una linea motus, in qua perfecta similitudo, <lb></lb>nulla autem contrarietas. </s>

<s>Itaque motus aequalis motum auget in cadem ra­<lb></lb>tione: totus quidem totum, pars vero partem sibi aequalem ” (ibid., fol. </s>

<s>39). <lb></lb>Ciò che poi si rende evidente per la stessa figura, nella quale, diminuendo <lb></lb>l&#039;angolo GEF, diminuiscono anche le perpendicolari GO, LF, e al contrario <lb></lb>crescono col crescer dell&#039;angolo stesso. </s>

<s>Di quelle perpendicolari poi si dice <lb></lb>che misurano il difetto del moto: <emph type="italics"></emph>ductae lineae perpendiculares FL, GO <lb></lb><figure id="id.020.01.2936.1.jpg" xlink:href="020/01/2936/1.jpg"></figure></s></p><p type="caption">

<s>Figura 349.<lb></lb>metientur defectum motus in EII<emph.end type="italics"></emph.end> (fol. </s>

<s>38). <lb></lb>E infatti, osservando bene, rappresentano due <lb></lb>forze che si fanno insieme equilibrio, essendo <lb></lb>uguali e contrarie, per cui, son veramente la <lb></lb>misura dell&#039;elisione, quando le forze stesse, di <lb></lb>concorrenti o di contrarie che erano, diventano <lb></lb>angolari. </s>

<s>Si rende la cosa anche più manifesta, <lb></lb>costruendo i rettangoli LM, ON, in cui le forze <lb></lb>opposte EM, EN, che uguagliano le dette per­<lb></lb>pendicolari, sono contrariamente applicate al <lb></lb>medesimo punto E. </s>

<s>Dalla qual costruzione si confermano altresì le cose <lb></lb>da G. </s>

<s>Marco già dimostrate, perchè EF2=EM2+MF2=EM2+EL2, <lb></lb>ed EG2=EN2+NG2=EN2+EO2, d&#039;onde, sommando e osservando che <lb></lb>EM2+EN2 è uguale a zero, EF2+EG2=EH2=EL2+EO2=EL2+LH2. </s></p><p type="main">

<s>Tali cose insegnava il Matematico tedesco, e sarebbero le dottrine di lui <lb></lb>potute esser segno di stella ai naviganti nel periglioso oceano della Mecca­<lb></lb>nica. </s>

<s>Ma, rimastosi quel solitario splendore velato dalle nebbie settentrionali, <lb></lb>predominarono nelle scuole gli errori del Cartesio e di Galileo, che, com­<lb></lb>battuti dai matematici delle straniere nazioni, e dannosamente secondati in <lb></lb>Italia, porgono soggetto importante al seguito, e al termine del presente ca­<lb></lb>pitolo di storia. </s></p><pb xlink:href="020/01/2937.jpg" pagenum="562"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quel valoroso emulo del Cartesio, che fu il Roberval, l&#039;abbiamo dovuto <lb></lb>più volte ammirare per le sue invenzioni, non con altro argomento felice­<lb></lb>mente da lui conseguite, che con quello dei moti composti, come nel metodo <lb></lb>di condur le tangenti alle curve, nella teoria del piano inclinato, quando la <lb></lb>potenza non è diretta secondo il declivio, e negli elegantissimi teoremi del <lb></lb>nodo delle funi, che tirato sta fermo, quando le forze son proporzionali alle <lb></lb>linee condotte dal centro di gravità ai vertici del triangolo e della piramide. </s>

<s><lb></lb>Or, quello stesso Roberval aveva dimostrati i principii, de&#039;quali faceva così <lb></lb>le applicazioni, in un libro <emph type="italics"></emph>Sur la composition des mouvemens,<emph.end type="italics"></emph.end> in cui parve <lb></lb>che le antiche tradizioni della scienza riprendessero, dopo il Cardano, il loro <lb></lb>naturale e libero corso. </s>

<s>S&#039;aggiungeva al detto libro il <emph type="italics"></emph>Projet d&#039;un livre de <lb></lb>Mechanique traitant des mouvemens composez,<emph.end type="italics"></emph.end> fecondo seme di specula­<lb></lb>zioni larghe e profonde, gettato dalla frettolosa mano dell&#039;Autore nel campo <lb></lb>della scienza, e destinato a crescere e a fruttificare nei secoli futuri, come <lb></lb>per esempio il seguente: <emph type="italics"></emph>La nature en général possede les principes des <lb></lb>mouvemens simples, dont il s&#039;en compose una infinité d&#039;autres dans les <lb></lb>animaux, vegetaux, mineraux etc.<emph.end type="italics"></emph.end> (Ouvrages de Mathem. </s>

<s>a la Haye 1731, <lb></lb>pag. </s>

<s>68). Ma lo splendore di tutti questi pensieri sparsi accendesi, come a <lb></lb>scintilla viva, a un tale teorema, posto per fondamento al trattato rober­<lb></lb>valliano: </s></p><p type="main">

<s>“ Soit le mobile A (nella figura 347 qui poco addietro) porté par deux <lb></lb>divers mouvemens, desquels les lignes de direction soient AB, AE faisant <lb></lb>l&#039;angle BAE, et que les mouvemens droits et uniformes soient tels, qu&#039;en <lb></lb>mesme temps, que l&#039;impression AB auroit porté le mobile en B, en mesme <lb></lb>temps l&#039;impression AE l&#039;eust portée en E. </s>

<s>Je dis que le mobile, porté par <lb></lb>le mouvement compose de ces deux, sera porté le long du diametre AF du <lb></lb>parallelogramme AF, duquel les deux lignes AB, AE son les deux costez, <lb></lb>et que le mouvement, qu&#039;il aura sur le diametre AF, sera uniforme. </s>

<s>” </s></p><p type="main">

<s>“ Ce que nous comprendrons, si nous imaginons que la ligne AB de­<lb></lb>scendant toûjours uniformement et parallelament a la ligne EF, jusqu&#039;a ce <lb></lb>qu&#039;elle ne soit qu&#039;une mesme ligne avec la ligne EF, e la ligne AE se mou­<lb></lb>vent vers la ligne BF en la mesme facon; nostre mobile A ne fait autre <lb></lb>chose que se rencontrer à tout moment en la commune section de ces deux <lb></lb>lignes. </s>

<s>Or il est assez clair que les points de cette commune section sont <lb></lb>tous dans le diamétre AF, ce que nous démonstrerons encore mieux par cette <lb></lb>consideration ” (ivi, pag. </s>

<s>6, 7): considerazione, che è poi quella stessa fattta <lb></lb>dal Cardano, e prima di lui da Aristotile, per condurre le loro dimostrazioni. </s></p><p type="main">

<s>Di qui si vede aprirsi, soggiungeva il Roberval, <emph type="italics"></emph>un champs d&#039;une in­<lb></lb>finité de belles speculations,<emph.end type="italics"></emph.end> come sarebbero quelle, che riguardano le ri-<pb xlink:href="020/01/2938.jpg" pagenum="563"></pb>flessioni e le rifrazioni dei corpi obliquamente incidenti in una superficie, <lb></lb>che ne impedisca o ne debiliti il moto. </s>

<s>Sia AB (fig. </s>

<s>350) la direzione di <lb></lb>questo moto decomposto ne&#039;due AH, AC: la riflessione dal punto B del <lb></lb>piano BCE, dice il Roberval, si farà con angolo uguale, o minore o mag­<lb></lb>giore dell&#039;angolo dell&#039;incidenza ABC, secondo che il mobile in B acquista <lb></lb>impeto di risalire precisamente ad H, o sotto o sopra a questo punto, come <lb></lb>per esempio in G o in I, perchè nel primo caso la resultante del moto com­<lb></lb>posto dell&#039;orizontale BE e del verticale BH, è BF; nel secondo è BL, e nel <lb></lb>terzo BM. </s>

<s>Rispetto poi alle rifrazioni, soggiunge lo stesso Roberval, si può <lb></lb>supporre che nel punto dell&#039;incidenza B il moto o aumenti o scemi la sua <lb></lb>prima energia, cosicchè, rimanendosi invariato il moto orizontale, il verticale <lb></lb>si riduca a BO maggiore di AC, o a BQ minore, nel qual primo caso la re­<lb></lb>sultante del moto, o la rifrazione, sarebbe diretta secondo la linea BS, e nel­<lb></lb>l&#039;altro secondo la linea BR. </s></p><p type="main">

<s>Si presente con facilità che in queste osservazioni aveva il Roberval di <lb></lb>mira l&#039;Ottica del Cartesio, contro la quale infatti si sentono apertamente <lb></lb>pronunziare poco più sotto le seguenti parole: “ Or il faut remarquer avec <lb></lb>soin cette facon de composer, et mesler les mouvemens, puis que nous vo­<lb></lb><figure id="id.020.01.2938.1.jpg" xlink:href="020/01/2938/1.jpg"></figure></s></p><p type="caption">

<s>Figura 350.<lb></lb>yons que des personnes, les plus exercées dans la ré­<lb></lb>cherche des veritez mathematiques, se sont trompées <lb></lb>en cet endroit. </s>

<s>Ainsi M. Des-Cartes, pour expliquer la <lb></lb>reflexion, décrit un cercle du centre B, qui passe par <lb></lb>A, et trouve que le point de la circonférence, auquel le <lb></lb>mobile retournera en autant de temps, qu&#039;il a mis à <lb></lb>aller de A vers B; doit estre F, au lieu que, d&#039;un rai­<lb></lb>sonnemeut semblable au nostre, il devoit en tirer comme <lb></lb>une conséquence que le point F dans cette hypothese <lb></lb>se rencontrera dans la circonference du cercle décrit du <lb></lb>centre B par A. </s>

<s>Secondement expliquant la réfraction <lb></lb>de la bale dans l&#039;eau, il a confondu les termes d&#039;im­<lb></lb>pression ou vistesse, et de determination, lesquels pourtant il avoit distinguez <lb></lb>peu auparavant, car en la pag. </s>

<s>17, ligne derniere, il dit <emph type="italics"></emph>et puis qu&#039;elle ne <lb></lb>perd rien du tout de la determination.... ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>13, 14). </s></p><p type="main">

<s>Scriveva il Roberval queste censure in tale forma, da proporsi al giu­<lb></lb>dizio del pubblico nel suo libro, ma privatamente si dirigevano epistole al <lb></lb>Mersenno, dove gli si facevano notare i.medesimi falli, perchè gli riferisse <lb></lb>al Cartesio. </s>

<s>L&#039;Hobbes erasi fra tutti gli altri maravigliato del discorso poco <lb></lb>logico fatto dall&#039;Autore della logica del <emph type="italics"></emph>Metodo,<emph.end type="italics"></emph.end> che cioè una cosa manife­<lb></lb>stamente falsa si potesse dir vera, e dimostrava come invece la falsità con­<lb></lb>sistesse nel credere che la quantità del moto composto fosse uguale alla <lb></lb>somma dei componenti, dovendo essere in realtà quella sempre minore di <lb></lb>questa, perchè nelle direzioni angolari tanto più delle forze si elide, quanto <lb></lb>maggiore è l&#039;angolo del concorso. </s>

<s>E per dimostrare anche meglio questa eli­<lb></lb>sione, supposto essere le due forze proporzionali ad AB, AC (fig. </s>

<s>351), con-<pb xlink:href="020/01/2939.jpg" pagenum="564"></pb>correnti in A ad angolo retto, le decomponeva ciascuna in altre due AF, FB; <lb></lb>AE, EC, e osservava che si perdono nella resultante del moto per la BC le <lb></lb>due forze FB, EC, operanti in diversa, anzi opposta direzione. </s>

<s>Di qui con­<lb></lb>cludeva che i moti composti nella figura 343 stanno come le diagonali AB, <lb></lb>AG, ossia, nell&#039;esempio del Cartesio, come due alla radice di dieci, e non <lb></lb>come due a tre, secondo che il Cartesio stesso credeva si potesse dire, stra­<lb></lb>namente paralogizzando. </s></p><p type="main">

<s>“ Nam et si pilam (per riferir le parole scritte dall&#039;Hobbes di Parigi, <lb></lb>il di 7 Febbraio 1641 al Mersenno) ponamus ferri ab A (nella figura 343) <lb></lb>dextrorsum uno gradu celeritatis, et deorsum uno etiam gradu, non tamen <lb></lb><figure id="id.020.01.2939.1.jpg" xlink:href="020/01/2939/1.jpg"></figure></s></p><p type="caption">

<s>Figura 351.<lb></lb>perveniet ad B duobus gradibus celeritatis: similiter, si <lb></lb>A feratur dextrorsum uno gradu, deorsum duobus, non <lb></lb>tamen perveniet ad G tribus gradibus, ut D. </s>

<s>Descartes <lb></lb>supponit. </s>

<s>Supponamus enim duas rectas constitutas ad <lb></lb>angulum rectum BAC (come nella figura 351) sitque <lb></lb>velocitas ab A versus B in ratione, ad velocitatem ab <lb></lb>A versus C, quam habet ipsa AB ad ipsam AC: hae <lb></lb>duae velocitates componunt velocitatem, quae est a B versus C. </s>

<s>Dico veloci­<lb></lb>tatem a B versus C esse ad velocitatem ab A versus C, vel ab A versus B, <lb></lb>ut recta BC ad rectam AC, vel AB. ” </s></p><p type="main">

<s>“ Ducatur ab A recta AD perpendicularis ad BC, et per A recta FAE <lb></lb>eidem BC parallela: item BF, CE perpendiculares ad FE. </s>

<s>Quoniam igitur <lb></lb>motus ab A ad B componitur ex motibus ab F ad A, et ab F ad B, non <lb></lb>contribuet motus compositus AB plus celeritatis ad motum a B versus C, <lb></lb>quam possunt contribuere componentes FA, FB. </s>

<s>Sed motus FB nihil con­<lb></lb>tribuit motui a B versus C, motus enim ille determinatur deorsum, nec <lb></lb>omnino tendit a B versus C; solus igitur motus FA dat motum a B ver­<lb></lb>sus C. ” </s></p><p type="main">

<s>“ Similiter probatur AC dare motum a D versus C, in virtute solius <lb></lb>AE. </s>

<s>Sed celeritas, quam participat AB ab AF, et qua operatur a B versus C, <lb></lb>est ad celeritatem totam AB in proportione FA, vel BD, ad AB: item cele­<lb></lb>ritas, quam habet AC virtute AE est, ad celeritatem totam AC, ut AE vel <lb></lb>DC ad AC; sunt ergo ambae celeritates iunctae, quibus fit motus a B ver­<lb></lb>sus C, ad celeritatem simpliciter sumptam in AC vel AB, ut tota BC ad AC, <lb></lb>vel AB. </s>

<s>Quare sumpta figura 343, erunt celeritates per AB, AG ut ipsae AB, <lb></lb>AG, hoc est ut √2 ad √5, hoc est ut √4 ad √10, hoc est ut 2 ad √10, <lb></lb>et non ut 2 ad 3. Non igitur sequitur absurdum illud ab isto modo loquendi, <lb></lb>quod probat D. Descartes. </s>

<s>Vide, Pater, quam pronum sit, etiam doctissimis <lb></lb>viris, per nimiam securitatem, quandoque in paralogysmos incidere. </s>

<s>” (<emph type="italics"></emph>Epist. </s>

<s><lb></lb>cart.,<emph.end type="italics"></emph.end> P. III cit., pag. </s>

<s>73, 74). </s></p><p type="main">

<s>La dimostrazione che, per essere così chiara, e perciò così efficace ad <lb></lb>aprire le menti a conoscere il vero dei moti misti, abbiamo voluto riferire <lb></lb>nella sua integrità; l&#039;applicava l&#039;Hobbes al teorema cartesiano della rifles­<lb></lb>sion della luce, per scoprir la fallacia del ragionamento. </s>

<s>In quel medesimo <pb xlink:href="020/01/2940.jpg" pagenum="565"></pb>tempo il Fermat notava simili fallacie, nelle quali il Cartesio stesso era in­<lb></lb>corso a proposito delle rifrazioni, il teorema relativo alle quali si fondava <lb></lb>principalménte sul supposto che rimanesse la medesima velocità nel raggio <lb></lb>rifratto, benchè l&#039;angolo di lui colla perpendicolare variasse da quel primo <lb></lb>fatto nell&#039;incidenza. </s>

<s>Era come a dire che le diagonali BR, BS, nella fig. </s>

<s>350, <lb></lb>sono uguali alla AB. </s>

<s>E perchè ben conosceva il Fermat nascere un tale er­<lb></lb>rore, nell&#039;Autor del discorso intorno al Metodo, per non aver compresa la <lb></lb>natura dei moti semplici, relativamente al loro composto; si mette a spie­<lb></lb>garla in una epistola diretta al Mersenno, incominciando dal rammemorargli <lb></lb>come di una tal qualità di moti avessero fatto uso Archimede, e altri ma­<lb></lb>tematici antichi nel comporre le loro Elici, e poi soggiunge: “ verum quia <lb></lb>motus ille compositus non ita frequenter in usum cadit, oportet ut alio modo <lb></lb>consideretur, et ut specialis de eo meditatio fiat ” (ibid., pag. </s>

<s>97). </s></p><p type="main">

<s>La prima parte di questa meditazione è tale: Supposto che il mobile A <lb></lb><figure id="id.020.01.2940.1.jpg" xlink:href="020/01/2940/1.jpg"></figure></s></p><p type="caption">

<s>Figura 352.<lb></lb>(fig. </s>

<s>352) passi lo spazio AN in un minuto d&#039;ora e <lb></lb>lo spazio AC nel medesimo tempo; con ragioni molto <lb></lb>simili a quelle del Roberval si conclude: “ Fiet ergo <lb></lb>motus compositus super linea AB, et possumus as­<lb></lb>serere grave illud percursurum lineam AR in mi­<lb></lb>nuto horae ” (ibid., pag. </s>

<s>98). Cosicchè, essendo i <lb></lb>moti equabili, e perciò le velocità, supposta l&#039;egua­<lb></lb>glianza dei tempi, proporzionali agli spazi, il moto <lb></lb>per AB starà al moto per AN, o per AC, come la <lb></lb>stessa AB alle stesse AN, AC. </s></p><p type="main">

<s>Nella seconda parte del ragionamento considera il Fermat l&#039;angolo CAN <lb></lb>variare, e diventar per esempio maggiore qual&#039;è C′ AN′, e da ragioni simili <lb></lb>a quelle dette di sopra è portato a concludere: “ quod eadem erit propor­<lb></lb>tio velocitatis motus compositi in prima figura, ad velocitatem motus com­<lb></lb>positi in secunda, quae est longitudinis lineae AB in prima ad longitudinem <lb></lb>lineae AB′ in secunda ” (ibid.). E perchè AB′ è manifestamente, e con fa­<lb></lb>citità potrebbe provarsi dover esser necessariamente minore di AB, riman <lb></lb>dunque così dimostrata la verità del parallelogrammo delle forze, e scoperto <lb></lb>l&#039;errore del Cartesio. </s></p><p type="main">

<s>Queste censure dell&#039;Hobbes e del Fermat erano scritte, come si disse, <lb></lb>privatamente al Mersenno, al quale pure erano dirette le difese che, per la <lb></lb>propria causa, faceva lo stesso Cartesio, aggiuntevi quelle degli amici e dei <lb></lb>seguaci delle dottrine di lui, col non far altro insomma che avvolgersi dispe­<lb></lb>ratamente in nuovi paralogismi. </s>

<s>Ma il Mersenno ebbe tanto giudizio e tanta <lb></lb>coscienza, da non avere nessun riguardo all&#039;amico, per difendere contro lui <lb></lb>la verità, pubblicamente annunziata agli erranti nella XXXII proposizione <lb></lb>della sua <emph type="italics"></emph>Ballistica.<emph.end type="italics"></emph.end> Ivi, a proposito dei moti composti, considerati nella <lb></lb>figura 343 qui poco addietro, com&#039;era stata disegnata dall&#039;Hobbes, veniva <lb></lb>così saviamente ripetendo le osservazioni lette e meditate nell&#039;epistola di lui. <lb></lb></s>

<s>“ Ubi notandum est grave A latum vel impulsum uno gradu velocitatis <pb xlink:href="020/01/2941.jpg" pagenum="566"></pb>dextrorsum ad H, et uno gradu velocitatis deorsum in C, quibus pervenit <lb></lb>ad B, non acquisivisse duos gradus velocitatis, aut tres gradus in puncto G, <lb></lb>cum duobus gradibus celeritatis motum est ab A ad D, et uno ab A ad H <lb></lb>per rectam AG pervenit ad G, alioqui recta AB esset ad rectam AG ut 2 <lb></lb>ad 3, cum linea sit ad lineam ut celeritas ad celeritatem, quod verum non <lb></lb>est, quandoquidem est AB ad AG ut 2 ad radicem 10, vel ut radix 2 ad <lb></lb>radicem 5, hoc est: celeritas ab A ad B, ad celeritatem ab A ad G, non est <lb></lb>ut composita ex AH et HB, ad compositam ex AH et HG: sunt enim velo­<lb></lb>citates ut subtensae AB, AG ” (Parisiis 1644, pag. </s>

<s>110). </s></p><p type="main">

<s>Utilissimi sarebbero tornati agli studiosi questi mersenniani avvertimenti, <lb></lb>se la prepotente autorità del Cartesio e l&#039;aforismo, male applicato al caso, <lb></lb>che cioè le parti debbono uguagliare il tutto, non avessero congiurato così <lb></lb>ai danni della Scienza, da consigliarla a provocare poco di poi per ristorar­<lb></lb>sene l&#039;opera poderosa di Giovanni Wallis. </s>

<s>Egli infatti intitolava <emph type="italics"></emph>De motibus <lb></lb>compositis, acceleratis, retardatis et proiectorum<emph.end type="italics"></emph.end> il capitolo X della terza <lb></lb>parte del suo trattato <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> nel qual capitolo formulava così la VI pro­<lb></lb>posizione: “ Si mobile, ob duas causas motrices, duos concipiat directos im­<lb></lb>petus, puta secundum duas rectas positione datas angulum facientes, celeri­<lb></lb>tatibus in se aequalibus, ad invicem vero eisdem ut parallelogrammi lateribus <lb></lb>longitudine datis proportionalibus; feretur mobile per parallelogrammi dia­<lb></lb>gonium ea celeritate, quae sit ad datas ut diagonium illud ad respectiva <lb></lb>latera. </s>

<s>” </s></p><p type="main">

<s>“ Adeoque tantumdem est, lationem quod spectat, sive feratur mobile <lb></lb>motu ex duobus composito, qui directiones habeant secundum parallelogrammi <lb></lb>latera, et celeritatibus ipsis proportionales, sive motu simplici secundum eius­<lb></lb>dem diagonium et celeritate proportionali: quippe utrovis modo, eodem tem­<lb></lb>pore, per eumdem tramitem eadem celeritate feretur. </s>

<s>” </s></p><p type="main">

<s>“ Ideoque motui ex pluribus composito similiter accommodabitur, sive <lb></lb>directiones habeant in eodem plano omnes, sive secus, potestque idem pro­<lb></lb>pterea motus infinitis modis componi. </s>

<s>” (Londini 1671, pag. </s>

<s>654). </s></p><p type="main">

<s>E passa il Wallis a dimostrare la proposizione nelle sue tre distinte <lb></lb>parti, benchè le ultime due dipendano dalla prima condotta anch&#039;essa, ad <lb></lb>imitazione de&#039;precedenti Autori, dal considerar che a qualunque punto preso <lb></lb>in distanze proporzionali nelle linee de&#039;moti semplici, diretti secondo i lati <lb></lb>del parallelogrammo, corrisponde il moto composto in un punto della dia­<lb></lb>gonale. </s>

<s>Ma rende l&#039;Autore in così fare l&#039;immagine di colui, che perorando <lb></lb>si guarda sospettoso all&#039;intorno, perchè sa di trovarsi in mezzo a contradit­<lb></lb>tori ostinati, ai quali direttamente rivolge la parola nello Scolio dopo la pro­<lb></lb>posizione seconda <emph type="italics"></emph>De elatere.<emph.end type="italics"></emph.end> Domandavano codesti contradittori al Wallis <lb></lb>chi gli avesse dato autorità di decomporre un moto unico in due, presi a <lb></lb>capriccio e secondo gli tornava meglio, per accomodare il negozio: a&#039;quali <lb></lb>il Matematico rispondeva avere avuto una tale autorità da chi l&#039;aveva data <lb></lb>a loro di decomporre per esempio il numero 8 nelle parti 2X4, o nelle <lb></lb>2X2X2, o nelle altre infinite, quali resulterebbero da fattori frazionari, <pb xlink:href="020/01/2942.jpg" pagenum="567"></pb>scegliendo fra queste infinite scomposizioni quella, che più accomoda al cal­<lb></lb>colo, certi che in ogni modo la libertà della scelta non offende le leggi o le <lb></lb>ragioni del vero. </s></p><p type="main">

<s>S&#039;argomenta di qui che nel 1670 duravano quelle contradizioni dei Car­<lb></lb>tesiani, delle quali ebbero a fare esperienza l&#039;Hobbes e il Fermat trent&#039;anni <lb></lb>prima, ed è anche resa di qui la ragione di un certo riserbo, notabile ne&#039;Ma­<lb></lb>tematici di que&#039;tempi, di non professare apertamente la regola del paralle­<lb></lb>logrammo, benchè intendessero e volessero essere intesi che quel loro me­<lb></lb>todo, riconosciuto da tutti per vero, conduceva ai medesimi resultati di <lb></lb>quell&#039;altro, che si diceva sbagliato. </s>

<s>Citeremo per primo esempio, tra quei <lb></lb>Matematici, Niccolò Witsen, il quale, nel suo libro <emph type="italics"></emph>Del modo di costruire <lb></lb>e di dirigere i bastimenti,<emph.end type="italics"></emph.end> pubblicato nel 1671, risolveva il problema <emph type="italics"></emph>In <lb></lb>qual modo più profittevole si voltino le vele ai venti.<emph.end type="italics"></emph.end> Ma il Witsen era <lb></lb>discepolo dello Stevin, che egli cita, e dalla XIX proposizione statica del quale <lb></lb>aveva appreso il modo e la ragione di risolvere i moti nei due lati di un <lb></lb>triangolo, di cui l&#039;altro lato fosse la diagonale del parallelogrammo doppio. </s>

<s><lb></lb>La detta proposizione steviniana è celebre nella storia del piano inclinato, <lb></lb>per esservi dimostrata la proporzion dei momenti dall&#039;equilibrio della catena <lb></lb>posata su due pendenze di uguale altezza, ma ben si meriterebbero maggior <lb></lb>celebrità di lei i corollari, de&#039;quali se si fosse rammemorato il Roberval non <lb></lb>lo avremmo udito vantarsi di essere egli stato il primo a dimostrare qual <lb></lb>proporzione abbia alla resistenza la potenza, che tira in direzione non pa­<lb></lb>rallela al declivio. </s></p><p type="main">

<s>Dop&#039;aver concluso generalmente lo Stevino, nel terzo dei corollari ci­<lb></lb>tati, che la resistenza assoluta del grave sta alla potenza che l&#039;equilibra, come <lb></lb>la lunghezza del piano sta alla sua altezza; passa nel quarto a considerare <lb></lb>quello stesso grave configurato in un rettangolo, che, per dargli qualche <lb></lb>aspetto di materialità, vuol s&#039;intenda come la sezione di un cilindro o di <lb></lb>una colonna. </s>

<s>Sia dunque HG (fig. </s>

<s>353) l&#039;asse di questa colonna, al centro <lb></lb>di gravità della quale D venga applicata la fune DF, che impedisce al peso <lb></lb><figure id="id.020.01.2942.1.jpg" xlink:href="020/01/2942/1.jpg"></figure></s></p><p type="caption">

<s>Figura 353.<lb></lb>di scendere col contrappeso E: “ il appert que comme <lb></lb>AB à BC ainsi la colonne D au poids E ” (Oeuvres <lb></lb>mathem., Leyde 1634, pag. </s>

<s>449). E ciò detto, così <lb></lb>l&#039;Autore soggiunge nel corollario V: “ Soit icy menée <lb></lb>une perpendiculaire par le centre de la colonne D <lb></lb>comme DK, coupant le costé d&#039;icelle en L: alors le <lb></lb>triangle LDI sera semblable au triangle ABC, car les <lb></lb>angles ACB et LID sont droits, et LD est parallele à <lb></lb>BC, et DI à AB, par quoy comme AB à BC ainsi LD <lb></lb>à DI ” (ivi). E perchè, condotta la LQ parallela ed <lb></lb>uguale à DI, il parallelogrammo è compiuto; è mani­<lb></lb>festo dunque che lo Stevin fu il primo a riconoscere quell&#039;importanza del <lb></lb>teorema della composizione dei moti <emph type="italics"></emph>dans la theorie de l&#039;equilibre,<emph.end type="italics"></emph.end> che il <lb></lb>Lagrange lamentava essere sfuggita alla considerazione di Galileo, “ qui au <pb xlink:href="020/01/2943.jpg" pagenum="568"></pb>lieu d&#039;employer le principe de la composition du mouvement pour deter­<lb></lb>miner directement la gravité relative d&#039;un corps sur un plan inclinée, il <lb></lb>rappelle le plan incliné au levier ” (<emph type="italics"></emph>Mechanique anal.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>8). </s></p><p type="main">

<s>Ma lo Stevino rimaneva allo stesso Galileo superiore per un&#039;altra ra­<lb></lb>gione, per aver cioè dimostrate le condizioni dell&#039;equilibrio, non solamente <lb></lb>quando la potenza agisce in direzion parallela, ma altresì quand&#039;ella con­<lb></lb>corre secondo qualunque obliquità col declivio. </s>

<s>Sia DO (nella medesima <lb></lb>figura) questa direzione, e il peso M della colonna sia equilibrato dal con­<lb></lb>trappeso P: condotto il piano BN, con l&#039;inclinazione CBN uguale a IDO, <lb></lb>sarà per le cose dimostrate AB:BN=M:P. “ Aussi, dice lo Stevin, LD <lb></lb>à DO seront comme les pesanteurs y appartenans, c&#039;est à dire comme M <lb></lb>à P ” (Oeuvr. </s>

<s>cit., pag. </s>

<s>449), a quel modo che se fosse compiuto, secondo <lb></lb>le regole note, il parallelogrammo OR. </s>

<s>A che, in guisa di Scolio soggiungesi <lb></lb>dall&#039;Autore: “ Ce que dessus peut aussi estre entendu d&#039;un globe sur la <lb></lb>ligne AB (fig. </s>

<s>354) comme icy joignant, là où nous dirons comme devant: <lb></lb>que comme LD à DO, ainsi M à P (pourveu que CL soit en angles droits <lb></lb>sur AB, c&#039;est à dire parallele à l&#039;axe HG du globe D) et partant comme LD <lb></lb>à DO, ainsi la pesanteur du globe à P ” (ivi). </s></p><p type="main">

<s>Insegnavasi dunque dallo Stevino, come poi dal Roberval e dai Mate­<lb></lb><figure id="id.020.01.2943.1.jpg" xlink:href="020/01/2943/1.jpg"></figure></s></p><p type="caption">

<s>Figura 354.<lb></lb>matici moderni, a usar la regola in questo modo: Inal­<lb></lb>zate dal centro di gravità la verticale DL, che rap­<lb></lb>presenti il peso assoluto del globo, o la forza che lo <lb></lb>tien sollevato nel perpendicolo (<emph type="italics"></emph>elevant direct<emph.end type="italics"></emph.end>) e so­<lb></lb>pr&#039;essa DI come diagonale costruite un triangolo o <lb></lb>un parallelogrammo intero, con un de&#039;lati perpendi­<lb></lb>colare al piano inclinato, come HD, e con l&#039;altro se­<lb></lb>condo la direzione della potenza o della forza, che tira <lb></lb>obliquamente a sollevare lo stesso globo (<emph type="italics"></emph>elevation <lb></lb>oblique<emph.end type="italics"></emph.end>), come DO: e qual proporzione è tra la linea <lb></lb>DL e la DO, tale sarà tra il peso assoluto, e la potenza che lo tiene equi­<lb></lb>librato sul declivio. </s></p><p type="main">

<s>A così fatta scuola ammaestrato il Witsen, francamente risolveva il suo <lb></lb>problema navale, rassomigliando la vela, e il vascello spinto da lei lungo il <lb></lb>solco apertogli dal timone, a un piano o a una riga come CD (fig. </s>

<s>355), <lb></lb>spingente il globo A contro l&#039;ostacolo CB, che rende immagine dell&#039;ostacolo <lb></lb><figure id="id.020.01.2943.2.jpg" xlink:href="020/01/2943/2.jpg"></figure></s></p><p type="caption">

<s>Figura 355.<lb></lb>opposto dall&#039;acqua al moto laterale dello stesso va­<lb></lb>scello. </s>

<s>Rappresentata con FE la forza, che spinge <lb></lb>la riga, o lo strale del vento, che dà nella vela, <lb></lb>decompone esso Witsen, secondo la regola steviniana, <lb></lb>la detta forza unica nelle due FD, ED: e perchè <lb></lb>quella non fa nessuno effetto nello spingere, riman <lb></lb>questa sola, che opera sopra la CD con tutta l&#039;ener­<lb></lb>gia, essendole condotta perpendicolare. </s>

<s>Una tale ener­<lb></lb>gia poi si comunicherebbe tutta intera al globo A, se <pb xlink:href="020/01/2944.jpg" pagenum="569"></pb>l&#039;ostacolo non ne rintuzzasse una parte, che il Witsen ha dal suo Maestro <lb></lb>imparato a misurare dalla FG, lato del triangolo FGB o del parallelogrammo <lb></lb>a lui doppio, fatta dalla diagonale FB rappresentare quella stessa energia <lb></lb>intera, cosicchè non rimane che la GB, altro lato di quel medesimo paralle­<lb></lb>logrammo, a rappresentar l&#039;attività e la direzion della forza, con cui la riga <lb></lb>sospinge innanzi il globo, o la vela il vascello. </s></p><p type="main">

<s>Premessi così fatti principii statici in generale, passa il Witsen ad ap­<lb></lb>plicargli alla particolar soluzione del suo problema, considerando che la più <lb></lb>favorevole disposizion della riga è quando della forza, che immediatamente <lb></lb>riceve, se ne perde meno, e perciò se ne partecipa più che sia possibile: <lb></lb>ciò che comprendesi facilmente dovere avvenire quando sia EF/DE=FB/GB=CB/BF <lb></lb>Ma FE/DE=1/sen EFD, CB/BF=1/sen BCF; dunque EFD, ossia CFG, e BCF, ossia <lb></lb>GCE, debbono essere uguali, ed uguali anche perciò CG e GF, affinchè il <lb></lb>vento sopra la vela, e la vela sopra il vascello possano produrre il loro mag­<lb></lb>gior possibile effetto, come con particolari esempi numerici si dimostra dal­<lb></lb>l&#039;Autore nella sua V proposizione. </s>

<s>Il modo, con cui questa è distesa, insieme <lb></lb>con le altre che la precedono, lo vedrenio apparirci tra poco domestico in <lb></lb>lingua italiana, nelle carte private del Viviani, e intanto possiam renderci di <lb></lb>qui la ragione del perchè l&#039;Huyghens, olandese anch&#039;egli come lo Stevino <lb></lb>e il Witsen, trattasse qual cosa nota e consentita dai Matematici della sua <lb></lb>nazione quel modo di comporre e decomporre nel parallelogrammo le forze, <lb></lb>che appresso altri Matematici era penosamente dubbioso, e fieramente con­<lb></lb>troverso. </s></p><p type="main">

<s>Queste patrie tradizioni della Scienza le vedemmo invocate dallo stesso <lb></lb><figure id="id.020.01.2944.1.jpg" xlink:href="020/01/2944/1.jpg"></figure></s></p><p type="caption">

<s>Figura 356.<lb></lb>Huyghens, nel suo trattato <emph type="italics"></emph>De vi centrifuga,<emph.end type="italics"></emph.end> e nell&#039;O­<lb></lb>rologio oscillatorio, ma non possiam tacere un altro no­<lb></lb>tabile esempio di ciò, offertoci dalla prima proposizione <lb></lb><emph type="italics"></emph>De potentiis fila funesve trahentibus,<emph.end type="italics"></emph.end> che s&#039;informa al <lb></lb>teorema seguente di Geometria: Siano le due linee AB, <lb></lb>AC (fig. </s>

<s>356), concorrenti nell&#039;angolo A, prese secondo <lb></lb>qualunque moltiplicità, per esempio AF=N.AB, AG= <lb></lb>O.AC, e si costruisca sui lati AF, AG il parallelo­<lb></lb>grammo, di cui AP sia la diagonale intersecata in E <lb></lb>dalla linea BC: dico che AP=AE(N+O). Condotte infatti le FQ, GR <lb></lb>parallele a BC, avremo AE:AR=1:O, AE:AQ=1:N, d&#039;onde <lb></lb>AR:AQ=O:N, e componendo </s></p><p type="main">

<s><emph type="center"></emph>AR+AQ:AQ=O+N:N.<emph.end type="center"></emph.end><lb></lb>Osservando poi che, per essere i triangoli PFQ, ARG simili, PQ=AR, e <lb></lb>perciò AR+AQ=AP, tornerà la scritta proporzione composta ad AP:AQ= <lb></lb>O+N:N, e da questa, AP:AE=O+N:1, d&#039;onde AP=AE(O+N) <lb></lb>com&#039;erasi detto. </s></p><pb xlink:href="020/01/2945.jpg" pagenum="570"></pb><p type="main">

<s>Ora l&#039;Huyghens vuol dimostrare che, se le fila AB, AC son tirate da <lb></lb>forze proporzionali ad AB.N, AC.O, ossia ad AF, AG, la resultante o l&#039;equi­<lb></lb>valente di queste due forze insieme è quell&#039;unica proporzionale ad AE(N+O), <lb></lb>ed è il mezzo della dimostrazione il citato teorema geometrico, che cioè l&#039;AE, <lb></lb>presa molteplice secondo la somma di N con O, uguaglia la diagonale di quel <lb></lb>parallelogrammo, che, per le regole assai note, è atto, dice l&#039;Autore, a rap­<lb></lb>presentare le forze, ond&#039;egli così ne conclude la propostasi verità con que­<lb></lb>ste parole: “ Cum ergo potentiae fila AB, AC trahentes sint ut AF, AG, <lb></lb>quibus acquipollet attractio per filum AE, a potentia quae sit ut AP, <emph type="italics"></emph>ex <lb></lb>theoremate mechanico satis noto;<emph.end type="italics"></emph.end> manifesta est proposita veritas ” (<emph type="italics"></emph>Opera <lb></lb>varia<emph.end type="italics"></emph.end> et T. </s>

<s>I cit., pag, 287). </s></p><p type="main">

<s>Non poteva nonostante l&#039;Huyghens ignorare le contradizioni, alle quali <lb></lb>andava soggetto quel meccanico teorema appresso i Matematici, che igno­<lb></lb>ravano o negavan fede agli insegnamenti dello Stevino, per cui parve inten­<lb></lb>desse di confermare nella verità i diffidenti, dimostrando come per altre vie <lb></lb>si giungesse a quella medesima conclusione, alla quale era giunto il Rober­<lb></lb>val con applicarvi direttamente la regola del parallelogrammo. </s>

<s>“ Et hine pa­<lb></lb>tet (conclude la sua proposizione seconda <emph type="italics"></emph>De potentiis fila funesve trahen­<lb></lb>tibus<emph.end type="italics"></emph.end>) veritas theorematis robervalliani. <emph type="italics"></emph>Si a centro gravitatis pyramidis <lb></lb>fila tendantur ad quatuor angulos, quae trahantur a potentiis, quae sint <lb></lb>inter se ut filorum ipsorum longitudines; fieri acquilibrium, manente nodo <lb></lb>in dicto gravitatis centro ”<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>290). </s></p><p type="main">

<s>La medesima intenzione dell&#039;Huyghens ebbe anche il De-la-Hire, quando, <lb></lb>nella proposizione XXI del suo <emph type="italics"></emph>Traité de Mecanique,<emph.end type="italics"></emph.end> risolveva, dietro i prin­<lb></lb>cipii statici precedentemente dimostrati, il problema robervalliano: “ Il faut <lb></lb>trouver trois puissances, qui tirant un point par trois directions données, <lb></lb>soient en equilibre entr&#039;elles ” (A Paris 1695, pag. </s>

<s>70). Che se siano que­<lb></lb>ste tre potenze nel vigore proporzionali e dirette secondo le linee KC, KD, <lb></lb>KE (fig. </s>

<s>357), “ je dis que les trois puissances cherchees seron entr&#039;elles <lb></lb><figure id="id.020.01.2945.1.jpg" xlink:href="020/01/2945/1.jpg"></figure></s></p><p type="caption">

<s>Figura 357.<lb></lb>comme les trois lignes EF ou GK son egale, EG ou KF, et EK, <lb></lb>qui son prises dans le meme ordre, et qui sont paralleles, ou <lb></lb>qui son partie des directions des puissances ausquelles elles re­<lb></lb>spondent ” (ivi, pag. </s>

<s>70, 71): secondo dunque la medesima <lb></lb>regola prescritta da coloro, che applicano direttamente alla so­<lb></lb>luzion del problema, imitando il Roberval, la costruzione del <lb></lb>parallelogrammo, ai due lati del quale prese proporzionali due <lb></lb>qualunque delle date potenze, facesse a queste insieme equilibrio la terza, <lb></lb>presa a proporzion della diagonale. </s></p><p type="main">

<s>Ma nella patria dell&#039;Herigon e del Roberval altri matematici avevano <lb></lb>preceduto il De-la-Hire, dimostrando che dai principii statici del vette e del <lb></lb>piano inclinato si giungeva alle medesime conclusioni, che col far uso del <lb></lb>parallelogrammo. </s>

<s>Fra cotesti matematici è da annoverare principalmente Ga­<lb></lb>stone Pardies, a cui par che accenni il Borelli là, dove esamina il modo come <lb></lb>s&#039;intendeva da&#039;vari autori di confermare la verità dei teoremi dello stesso <pb xlink:href="020/01/2946.jpg" pagenum="571"></pb>Herigonio, e dello Stevino. </s>

<s>Ciò vedremo particolarmente fra poco, osservando <lb></lb>intanto che il Pardies, il De-la-Hire, l&#039;Huyghens, il Wallis, e gli altri com­<lb></lb>memorati nel nostro discorso, preparavano e concorrevano all&#039;opera del Va­<lb></lb>rignon, i benefizi arrecati dalla quale alla Scienza si comprenderanno anche <lb></lb>meglio, quando gli vedremo diffondersi nella nostra Italia, dove, per i falsi <lb></lb>insegnamenti di Galileo, viziate le menti, erano più che altrove ritrose a <lb></lb>riconoscere quella verità, della quale l&#039;Accademico di Parigi proclamava al <lb></lb>mondo la finale vittoria. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Viziata nelle sue più profonde radici si può dire una cosa, quando nè <lb></lb>la pronta, nè la facile correzione le giova, come si vede essere avvenuto alle <lb></lb>menti dei discepoli di Galileo, in proposito delle dottrine intorno ai moti <lb></lb>composti. </s>

<s>Che pronte poi e facili fossero quelle correzioni agli errori, inse­<lb></lb>gnati dal loro Maestro, si vede per l&#039;esempio del Mersenno, il quale fu dei <lb></lb>primi a praticarle in sè stesso, a quel tempo e con quella occasione, che gli <lb></lb>aveva fatto riconoscere il medesimo error nel Cartesio. </s></p><p type="main">

<s>Nella proposizione XXII della sua Meccanica dimostrava così il Mersenno <lb></lb>che un moto semplice si può dir generato da due moti diversi: “ Sit enim <lb></lb>motus AB (fig. </s>

<s>358) simplex, quo globus vel aliud quodvis mobile feratur <lb></lb>aequabili motu ab A ad B: certum est motum illum posse componi sive ge­<lb></lb>nerari ex motu A in D, et ex motu A in C. </s>

<s>Enim vero sint duo venti ae­<lb></lb>quales, quorum unus ab A in C, alius ab A in D sufflet in mobile A, cuius <lb></lb>partes omnes sunt aequaliter mobiles. </s>

<s>Mobile non perveniet in C vel in D, <lb></lb>sed in B: cumque pervenerit ad I, erit in medio sui motns.... Quamquam <lb></lb>AB motus dici potest aequalis potentia duobus motibus AD, AC, ut est dia­<lb></lb>meter duobus suis costis potentia aequalis ” (Parisiis 1644, pag. </s>

<s>79-81). </s></p><p type="main">

<s>Erano già stampati e approvati i fogli del volume, sopra i quali aveva <lb></lb><figure id="id.020.01.2946.1.jpg" xlink:href="020/01/2946/1.jpg"></figure></s></p><p type="caption">

<s>Figura 358.<lb></lb>inconsideratamente il Mersenno lasciate cader dalla penna <lb></lb>queste parole, quando le censure dell&#039;Hobbes al Cartesio <lb></lb>lo fecero tutto insieme accorto della fallacia di Galileo, in <lb></lb>scoprire anche meglio la quale si aiutava così col suo proprio <lb></lb>discorso: Sottoponiamo in C un corpo alla percussion di un <lb></lb>martello, che ora venga equabilmente mosso per la diago­<lb></lb>nale DC, ora per la GC uguale alla somma de&#039;due lati AD, <lb></lb>AC: com&#039;è possibile che faccia nel percotere il medesimo <lb></lb>effetto, con impeti tanto diversi, quanto la DC è diversa <lb></lb>dalla GC? </s>

<s>Non è egli manifesto che, concorrendo i due moti <lb></lb>in A ad angolo retto, si elidono insieme, e che l&#039;elisione è <lb></lb>tanta, quant&#039;è la differenza tra le due dette lunghezze lineari? </s></p><p type="main">

<s>Persuaso dunque il Mersenno, per queste evidentissime ragioni, della fal-<pb xlink:href="020/01/2947.jpg" pagenum="572"></pb>sità di ciò, che era trascorso a scrivere nel testo della sua Meccanica, che <lb></lb>cioè i due moti per l&#039;AD e per l&#039;AC insieme equivalgono in potenza al moto <lb></lb>unico per l&#039;AB; pensò di premettere alquante pagine innumerate, e stam­<lb></lb>pate dopo il volume, nelle quali, fra le altre correzioni e ritrattazioni, a chi <lb></lb>fosse per leggere, scriveva anche questa: “ Rursus quod pagina 81, linea 28, <lb></lb>dicitur AB motum dici posse aequalem potentia duobus motibus AD et AC, <lb></lb>est ex mente Galilaei, pag. </s>

<s>250 Dialogorum, quod tamen minime verum esse <lb></lb>videtur. </s>

<s>Sit enim aliquid in puncto C percutiendum, malleusque percussu­<lb></lb>rus a puncto D ad C, per DC diametrum, ita moveatur, ut motus per DC <lb></lb>componatur ex motu D in A, et D in B, seu A in C. </s>

<s>Si duo illi motus DA, <lb></lb>AC simul ita iungantur, ut malleus per lineam AC motus eodem tempore <lb></lb>percurreret lineam AC duplam, hoc est lineam GC, quo prius percurrebat <lb></lb>diametrum DC, certum est eo fortius a malleo per GC, quam a malleo per <lb></lb>DC, motum percussum iri, tantoque fortius, quanto recta GC longior est <lb></lb>recta DC, cum eo maior censeatur percussio, quo fit maiore velocitate, sit­<lb></lb>que eo maior velocitas quo malleus percussurus, et uniformiter motus, spa­<lb></lb>tium maius, eodem vel aequali tempore, percurrerit. </s>

<s>Hine fit ut ex motibus <lb></lb>per AD, AC, ex quibus AB motus componi supponitur, tantumdem perire <lb></lb>videatur quanto AB brevius est AD bis sumpta, et omnes motus, qui a suis <lb></lb>lineis rectis recedunt, semper aliquid amittent ” (<emph type="italics"></emph>Praefatio ad Mechan.<emph.end type="italics"></emph.end> cit.). </s></p><p type="main">

<s>Il fatto di queste perdite di forza, avvertito dal Mersenno, è tanto ma­<lb></lb>nifesto, da persuadersene facilmente qualunque ingegno volgare, e non privo <lb></lb>effatto di senso comune. </s>

<s>Imperocchè, supponiamo che A sia un sasso, e AD <lb></lb>una fune soprammessa a un&#039;altra fune, tirate ambedue da uomini ugual­<lb></lb>mente validi, o nella medesima direzione. </s>

<s>Chi direbbe che seguitano con pari <lb></lb>forza a tirare quel peso le due funi, anche quando, invece di star come <lb></lb>dianzi soprammesse, si sian dilungate per un quadrante di cerchio, cosicchè <lb></lb>uno degli uomini sia in D, e l&#039;altro in C? </s>

<s>Secondo il calcolo di Giovan <lb></lb>Marco questo secondo sforzo è ridotto alla metà del primo, ma anche senza <lb></lb>troppi calcoli insegna l&#039;esperienza ai manuali di tirare, stando più uniti che <lb></lb>sia possibile, perchè sanno che tanto è minore l&#039;effetto delle funi, quanto <lb></lb>maggiore è l&#039;angolo del loro concorso. </s>

<s>E il grande Galileo invece insegnava <lb></lb>che due uomini, posti in B all&#039;estremità della fune AB, hanno ugual po­<lb></lb>tenza di tirare il masso A, che posti in D e in C all&#039;estremità delle funi <lb></lb>AD, AC. </s>

<s>Questo pare incredibile in tant&#039;uomo, ma è più incredibile che si <lb></lb>lasciassero cader cecamente nel medesimo errore di lui altri uomini come il <lb></lb>Torricelli, il Viviani e il Borelli, intorno a&#039;quali ci duole di dover tratte­<lb></lb>nerci a misurar quelle loro cadute, piuttosto che a contarne, come altre volte, <lb></lb>i progressi. </s></p><p type="main">

<s>Nello scolio alla proposizione XVIII del primo libro <emph type="italics"></emph>De motu gravium<emph.end type="italics"></emph.end><lb></lb>il Torricelli, quasi per digressione dal suo principale soggetto, metteva que­<lb></lb>sto teorema: <emph type="italics"></emph>“ Si mobile aliquod A<emph.end type="italics"></emph.end> (fig. </s>

<s>359) <emph type="italics"></emph>ex angulo parallelogrammi <lb></lb>alicuius, vel ex quolibet puncto diametri, feratur aequabiliter duplici si­<lb></lb>mul latione, nempe progressiva secundum lineam AC, et laterali secun-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2948.jpg" pagenum="573"></pb><emph type="italics"></emph>dum AB, utcumque inclinatam, sitque proportio duarum vclocitatum ca­<lb></lb>dem ac proportio laterum AC ad AB homologe; dico mobile iturum esse <lb></lb>secundum diametrum AD, hoc est per ipsam diametrum. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Si enim possibile est, feratur mobile extra diametrum per aliquod <lb></lb><figure id="id.020.01.2948.1.jpg" xlink:href="020/01/2948/1.jpg"></figure></s></p><p type="caption">

<s>Figura 359.<lb></lb>punctum E, ducaturque EG parallela ad AB. </s>

<s>Ergo quam pro­<lb></lb>portionem habent spatia peracta a mobili, eam habebunt et <lb></lb>impetus: nempe, ut spatium progressivum peractum AG, ad <lb></lb>laterale peractum GE, ita impetus progressivus ad impetum <lb></lb>lateralem, ideoque, ut AG ad GE, ita AC ad AB, ob suppo­<lb></lb>sitionem, sive AC ad CD, sive AG ad GI. </s>

<s>Essent ergo aequa­<lb></lb>les GE et EI, totum et pars. </s>

<s>” (Op. </s>

<s>geom., P. </s>

<s>I cit., pag. </s>

<s>120). </s></p><p type="main">

<s>Riconoscono bene i nostri Lettori esser questo del Torricelli quel me­<lb></lb>desimo teorema, posto dal Roberval per fondamento alle sue osservazioni <lb></lb><emph type="italics"></emph>Sur la composition des mouvemens,<emph.end type="italics"></emph.end> con la differenza che il Nostro tiene <lb></lb>in dimostrar le vie oblique, piuttosto che le dirette, e sono altresì in am­<lb></lb>bedue gli Autori medesime l&#039;intenzioni d&#039;applicar cioè la detta proposizione <lb></lb>meccanica al metodo di condur le tangenti alle curve. </s></p><p type="main">

<s>Da un tale Scolio. </s>

<s>col solo intermedio di un brevissimo lemma, si passa <lb></lb>alla XIX proposizione torricelliana, nella quale si dimostra dall&#039;Autore che <lb></lb>gl&#039;impeti, ne&#039;varii punti della parabola, non son precisamente proporzionali <lb></lb>alle loro proprie ordinate, ma si ad altre ordinate più distanti dal vertice, <lb></lb>quant&#039;è la quarta parte del parametro della curva, e adduce per ragione di <lb></lb>ciò che queste seconde ordinate son sempre l&#039;ipotenuse di triangoli, che hanno <lb></lb>per cateti le ordinate stesse de&#039;punti respettivi, e l&#039;ordinata del foco: d&#039;onde, <lb></lb>invocando il teorema galileiano, che cioè la somma de&#039;momenti per i cateti <lb></lb>equivale in potenza al momento per l&#039;ipotenusa, ne conclude il suo intento. <lb></lb><figure id="id.020.01.2948.2.jpg" xlink:href="020/01/2948/2.jpg"></figure></s></p><p type="caption">

<s>Figura 360.<lb></lb>L&#039;impeto insomma nel punto C (fig. </s>

<s>360), della parabola ACD, <lb></lb>della quale F sia il foco, e FH la sua ordinata; dice il Torri­<lb></lb>celli esser proporzionale all&#039;ordinata DE, presa BE uguale ad <lb></lb>AF. “ Impetus enim, qui simul sunt in C, sunt CB, HF. </s>

<s>Ergo <lb></lb>momentum impetus, ex ipsis compositum, debet esse potentia <lb></lb>ipsis aequale, per 2am Galilaei <emph type="italics"></emph>De motu accelerato.<emph.end type="italics"></emph.end> Sed et recta <lb></lb>DE aequatur potentia ipsis CB, HF, per lemma praecedens, ergo <lb></lb>momentum DE est momentum, sive impetus compositus ex duo­<lb></lb>bus illis, qui sunt in puncto C ” (ibid.). </s></p><p type="main">

<s>Seguitando a svolgere il volume di queste Opere geometriche del Tor­<lb></lb>ricelli, ci abbattiamo a leggere, in sul terminar della scrittura distesa in ita­<lb></lb>liano, e aggiunta al trattato <emph type="italics"></emph>De motu proiectorum;<emph.end type="italics"></emph.end> quelle belle considera­<lb></lb>razioni intorno al misurar quanto varino gl&#039;impeti, fatti da una palla di <lb></lb>cannone contro un piano resistente, secondo il variar degli angoli dell&#039;inci­<lb></lb>denza: e supposto, per esempio, che sia AC, nella passata figura 358, una <lb></lb>muraglia, e AB la direzione del tiro, “ io noto, dice il Torricelli, che, ri­<lb></lb>spetto alla parete AC, sono nella linea AB del proietto due moti insieme <lb></lb>composti: uno cioè di avvicinamento perpendicolare alla parete, l&#039;altro di <pb xlink:href="020/01/2949.jpg" pagenum="574"></pb>passaggio laterale, o parallelo alla stessa. </s>

<s>Il perpendicolare ci viene e mo­<lb></lb>strato e misurato dalla linea BC, il parallelo dalla linea AC, poichè nel me­<lb></lb>desimo tempo vengono passati dalla palla ambedue gli spazi BC, AC ” (ivi, <lb></lb>pag. </s>

<s>240). </s></p><p type="main">

<s>E perchè, soggiungiamo noi a questo discorso, essendo anche la BA pas­<lb></lb>sata nel medesimo tempo, l&#039;impeto per essa è proporzionale allo spazio, ne <lb></lb>consegue che questo stesso impeto sta alla somma degl&#039;impeti per BC, AC <lb></lb>come la linea AB sta alle due linee BC e AC, prese insieme. </s>

<s>Ma i detti im­<lb></lb>peti sono in potenza uguali, secondo la dottrina di Galileo, fedelmente se­<lb></lb>guita dal Torricelli, dunque AB è uguale a BC con AC: l&#039;ipotenusa cioè alla <lb></lb>somma dei cateti, una linea retta alla spezzata. </s></p><p type="main">

<s>Come un sì grande Matematico non si avvedesse di un tale assurdo, a <lb></lb>cui precipitosamente menava il suo ragionamento, è cosa tanto da stupire, <lb></lb>che ne invoglia di ricercar la causa di sì incredibile paralogismo: ricerca <lb></lb>che si riduce a intendere come mai potesse il Torricelli conciliare insicme <lb></lb>il teorema del Roberval, dimostrato nello Scolio alla proposizione XVIII, con <lb></lb>quell&#039;altro di Galileo citato nella proposizione seguente, senza considerar che, <lb></lb>se l&#039;uno era vero, l&#039;altro necessariamente doveva esser falso. </s>

<s>Nè, avendo <lb></lb>esso Torricelli, nel discorso intorno alla Spirale archimedea, riconosciuto Ga­<lb></lb>lileo qual restauratore dei moti composti, e imitatine gli esempi; si potrebbe <lb></lb>intendere quel che sì diceva senza ammetter che la notizia del teorema ro­<lb></lb>verballiano fosse pervenuta al Nostro di Francia, d&#039;onde si verrebbe a de­<lb></lb>cidero <emph type="italics"></emph>a priori<emph.end type="italics"></emph.end> a favore del Roberval la lite famosa intorno a chi di loro <lb></lb>due fosse stato primo inventore del metodo delle tangenti. </s>

<s>Imperocchè è ma­<lb></lb>nifesto che non poteva quel metodo essere spontaneamente sovvenuto nella <lb></lb>mente di uno, che professava dottrine fatte apposta per contradirlo. </s>

<s>Che se <lb></lb>il Torricelli, senza pur contradirlo, lo accolse, e lo applicò a risolvere que&#039;suoi <lb></lb>vari problemi di <emph type="italics"></emph>Meccanica nuova,<emph.end type="italics"></emph.end> fu, con buona pace dì sì grand&#039;uomo, <lb></lb>inconsideratezza, la quale si direbbe consigliata, per una parte, da quella <lb></lb>cieca fede che aveva alle dottrine di Galileo, e per l&#039;altra da uno sfrenato <lb></lb>ardor di contendere e di non rimanere, o almeno di non apparire in nulla <lb></lb>inferiore al suo rivale. </s></p><p type="main">

<s>E così, come volle apparire, fu creduto il Torricelli dai discepoli e dagli <lb></lb>amici, fra&#039;quali perciò s&#039;ingerì l&#039;opinione ch&#039;egli avesse introdotto nella <lb></lb>Meccanica, e applicato alla Geometria il parallelogrammo per la composizione <lb></lb>dei moti; e ch&#039;egli avesse nel medesimo tempo, con la sua nuova autorità, <lb></lb>confermate le dottrine insegnate da Galileo nel secondo teorema dei proietti. </s>

<s><lb></lb>Nè dubitavano punto che l&#039;una opinione repugnasse con l&#039;altra, perchè, trat­<lb></lb>tenendo la mente sulla proposizione XIX <emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> non pensavano <lb></lb>a quel che aveva dimostrato l&#039;Autore poco prima, o a quel ch&#039;egli aveva <lb></lb>soggiunto di poi, tanto è vero che al Borelli, come i nostri Lettori già sanno, <lb></lb>passò così inosservato quel che era stato scritto nell&#039;appendice al libro tor­<lb></lb>ricelliano <emph type="italics"></emph>De motu proiectorum,<emph.end type="italics"></emph.end> ch&#039;egli si compiaceva di essere stato il primo <lb></lb>a dimostrar che, nelle direzioni oblique, gl&#039;impeti delle percosse son pro-<pb xlink:href="020/01/2950.jpg" pagenum="575"></pb>porziali ai seni degli angoli delle incidenze. </s>

<s>Il Ricci, a cui furono dall&#039;amico <lb></lb>e dal Maestro comunicati, insiem col metodo di condur le tangenti alla Ci­<lb></lb>cloide, altri problemi di Meccanica nuova; fu della prima opinione, ma la <lb></lb>seconda s&#039;apprese così tenacemente nel Viviani e nel Borelli, che serbarono <lb></lb>intorno a ciò pari fede agli oracoli dei loro due grandi maestri, benchè fos­<lb></lb>sero in altre cose fieramente discordi. </s></p><p type="main">

<s>Era da queste discordie sollecitato nel Viviani il proposito di servirsi <lb></lb>della scienza anatomica del suo amico Stenone, per prevenir l&#039;opera <emph type="italics"></emph>De motu <lb></lb>animalium,<emph.end type="italics"></emph.end> che il Borelli allora faticosamente ammanniva. </s>

<s>Ma lo Stenone, <lb></lb>educato alla scuola dello Stevino, trovava comodo e ragionevole, in calcolar <lb></lb>la potenza de&#039;muscoli, rassomigliati a corde, che sostengono o che tirano <lb></lb>pesi; far uso del triangolo o del parallelogrammo intero, costruito sulle di­<lb></lb>rezioni delle leve, con tal regola, che, sospettata dal Viviani fallace, fu pre­<lb></lb>cipua causa del rimanersi que&#039;suoi così ardenti propositi senza effetto. </s>

<s>Una <lb></lb>mattina, andato a far visita allo Stenone, lo trovò seduto nella sua solita <lb></lb>stanza innanzi a un banco, sopra il quale era posato un volumone in foglio, <lb></lb>legato in cartapecora, che tiratoselo con familiare libertà innanzi il soprav­<lb></lb>venuto aprì, e nel frontespizio leggeva, o quasi si direbbe compitava, con­<lb></lb>tornate da figure simboliche e da fregi, così fatte parole: <emph type="italics"></emph>Scheepsbouw en <lb></lb>Bestier, door Nicolaes Witsen, t&#039;Amsterdam 1671.<emph.end type="italics"></emph.end> — Oh questo, disse il <lb></lb>Viviani, è per me un linguaggio molto simile a quello usato in Dante dalla <lb></lb>voce chioccia di Pluto. </s>

<s>— A cui sorridendo lo Stenone rispondeva: — Si <lb></lb>potrebbe tradurre <emph type="italics"></emph>De re navali veterum et hodierna commentarium Ni­<lb></lb>colai Witsen:<emph.end type="italics"></emph.end> me l&#039;hanno mandato, pochi giorni sono, i miei amici d&#039;Olanda, <lb></lb>ed è libro di una varietà di cose dilettevolissime, ora di pellegrina erudi­<lb></lb>zione, ora di sottilissima scienza. </s>

<s>Qui a facce 141 ho trovato sciolto un pro­<lb></lb>blema utilissimo ai naviganti, e ne fa il Witsen dipendere la soluzione da <lb></lb>certi teoremi, ai quali so che voi non fareste buon viso, ma che io non posso <lb></lb>non approvare e, almeno matematicamente, tenerli per veri. </s>

<s>— E proseguiva <lb></lb>così a esporli sommariamente, ma con tanto calore, che il Viviani disse gli <lb></lb>avrebbe voluti volentieri esaminare con pace, se avesse avuto intelligenza <lb></lb>della lingua, nella quale erano scritti. </s>

<s>Allora lo Stonone si esibì di tradur­<lb></lb>glieli in lingua italiana, giacchè non eran più che cinque proposizioni, le <lb></lb>prime delle quali assai brevi, e il Viviani, presa la penna in mano, scriveva <lb></lb>a dettatura sopra certi fogli, che ci sono rimasti, e in fronte ai quali, tor­<lb></lb>nato a casa, aggiungeva la nota, che ricopieremo qui fedelmente col resto, <lb></lb>quasi esotica pianticella trasposta ora in mezzo alle nostre aiole: </s></p><p type="main">

<s>“ Da Niccolò Witsen, a faccie 141, stampato in.... traduzionè detta­<lb></lb>tami dal signor Niccolò Stenonè: <emph type="italics"></emph>In qual modo più profittevole si voltino <lb></lb>le vele ai venti. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Per far questo facciasi che una linea retta, tirata dal di dietro della <lb></lb>vela parallela allo strale del vento, sino all&#039;opposta banda del vascello; sia <lb></lb>lunga quanto una linea intercetta tra la vela e la prima linea: per esempio, <lb></lb>nella figura 361, la linea CD sia lo strale del vento, BA la vela. </s>

<s>Per fare <pb xlink:href="020/01/2951.jpg" pagenum="576"></pb>quel che si cerca, di presentare cioè nel miglior modo la vela al vento, dico <lb></lb>che DL deve essere uguale alla HL, il che si dimostra per mezzo delle se­<lb></lb>guenti proposizioni, come si vedrà alla fine di esse. </s>

<s>Come parimente con <lb></lb>quello si dimostra in che modo si possa sapere, essendo cognita la forza del <lb></lb>vento, lo strale e il corso del vascello, quanto meno tutti i venti laterali, <lb></lb>secondo la loro natura, spingano meno il vascello, che se venissero a dar per­<lb></lb>pendicolarmente sopra la vela, supposto che il vento perpendicolare dia la <lb></lb>massima velocità al vascello. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE I. — <emph type="italics"></emph>Se un corpo sopra un piano orizontale viene <lb></lb>spinto da un altro piano perpendicolare ad esso orizonte, detto corpo dal <lb></lb>piano impellente si allontanerà secondo la linea perpendicolare. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia, nella medesima figura 361, il piano perpendicolare AB spinto se­<lb></lb><figure id="id.020.01.2951.1.jpg" xlink:href="020/01/2951/1.jpg"></figure></s></p><p type="caption">

<s>Figura 361.<lb></lb>condo la linea CD, ed incontri in D il corpo E, e sia DF <lb></lb>perpendicolare ad AB; dico che il corpo E scorrerà secondo <lb></lb>la linea DF. </s>

<s>Imperocchè la spinta del piano AB non può far <lb></lb>forza sopra il corpo E per moverlo verso A o verso B, per­<lb></lb>chè, essendo egli egualmente piano per tutto, non vi è mag­<lb></lb>gior ragione che deva il corpo moversi per altra via, che per <lb></lb>quella che perpendicolarmente l&#039;allontana dal corpo, che im­<lb></lb>mediatamente lo tocca, benchè obliquamente venga mosso. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE II. — <emph type="italics"></emph>Se un piano sarà spinto da una linea obliqua, <lb></lb>la forza spingente, alla resistenza del piano spinto, sta come la detta linea <lb></lb>obliqua ad un&#039;altra, tirata perpendicolarmente dall&#039;estremità di detta <lb></lb>obliqua. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia il detto piano AB (fig. </s>

<s>362), la linea obliqua CD, secondo la quale <lb></lb>venga spinta la AB. </s>

<s>Sia DE perpendicolare ad AB: dico che la forza, con <lb></lb>la quale il piano AB viene spinto per la linea DC, alla resistenza di detto <lb></lb>piano, sta come CD a DE. ” </s></p><p type="main">

<s>“ Per dimostrar questo, sia ABD una colonna; DB una leva obliqua, <lb></lb><figure id="id.020.01.2951.2.jpg" xlink:href="020/01/2951/2.jpg"></figure></s></p><p type="caption">

<s>Figura 362.<lb></lb>DC una leva diritta, e sia la forza traente per CF uguale <lb></lb>alla forza spingente per CD: il piano BA averà la mede­<lb></lb>sima resistenza alla forza traente, che alla spingente. </s>

<s>Ora <lb></lb>se il piano si tirerà per la linea EG talmente, che il piano <lb></lb>AB da questa forza traente patisca lo stesso che dalla <lb></lb>traente per CF, o dalla spingente per CD, cioè se la forza <lb></lb>traente per EG fosse dell&#039;istesso vigore con quella di CF; <lb></lb>per la XIX proposizione della Statica di Stevino, la forza <lb></lb>traente per CF, o spingente per CD, alla forza traente per EG, o alla resi­<lb></lb>stenza del piano, starà come CD a DE. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario.<emph.end type="italics"></emph.end> — Di qui è che in un corpo, spinto come nella I proposi­<lb></lb>zione, la linea CD alla CG starà come la forza, che si applica per la linea <lb></lb>CD sopra il corpo E, al moto che riceve il medesimo corpo E. ” </s></p><p type="main">

<s>“ PROPOSIZIONE III. — <emph type="italics"></emph>Se un corpo E<emph.end type="italics"></emph.end> (fig. </s>

<s>363) <emph type="italics"></emph>sopra un piano ori­<lb></lb>zontale si moverà verso un muro o qualche impedimento AB da un piano<emph.end type="italics"></emph.end><pb xlink:href="020/01/2952.jpg" pagenum="577"></pb><emph type="italics"></emph>ad esso corpo perpendicolare, e secondo la linea DF perpendicolare al <lb></lb>piano CD; la forza per DF, alla forza o resistenza del corpo E, starà <lb></lb>come AB ad AD, quando ADF è perpendicolare a DB. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Imperocchè sia BD come un piano obliquo, secondo la passata pro­<lb></lb><figure id="id.020.01.2952.1.jpg" xlink:href="020/01/2952/1.jpg"></figure></s></p><p type="caption">

<s>Figura 363.<lb></lb>posizione, e sia EG parallela alla linea DF, ed <lb></lb>EH parallela ad AB, ed LK perpendicolare ad <lb></lb>AB. </s>

<s>Sia EL una leva d&#039;una forza traente in <lb></lb>G, che tanto ritenga il corpo, quanto esso viene <lb></lb>spintogli contro dal piano CDB, il che si può <lb></lb>supporre, ed EM sia una leva d&#039;una forza <lb></lb>traente in H, che parimente ritenga il corpo <lb></lb>E in equilibrio, con la forza spingente il me­<lb></lb>desimo corpo. </s>

<s>” </s></p><p type="main">

<s>“ Questo così supposto, di nuovo, secondo la proposizione XIX della <lb></lb>Statica di Stevino, sarà EL ad EM come la forza in G o la spinta in FD <lb></lb>alla forza in H, o alla spinta del corpo E secondo la linea HME. </s>

<s>Ma per <lb></lb>essere EM ed EL parallele alle AB ed AD, gli angoli I ed A sono uguali, <lb></lb>siccome sono uguali EML, ADB per essere retti; e perciò li due triangoli <lb></lb>EML, ADB sono simili. </s>

<s>Onde ne segue che AB ad AD, come EL ad EM, <lb></lb>cioè come la forza traente in G, o la spinta in FD, alla forza traente in H, <lb></lb>ovvero alla forza, che spinge il corpo E. ” </s></p><p type="main">

<s>“ PROPOSIZIONE IV. — <emph type="italics"></emph>Trovar la forza, con la quale un corpo cam­<lb></lb>mina sopra un piano orizontale lungo un impedimento, quando sia mosso <lb></lb>da un piano, che sia spinto obliquamente. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia, come di sopra, il corpo E (fig. </s>

<s>364), l&#039;impedimento AB, il piano <lb></lb>spingente AC secondo la linea GH: si cerca la forza, con la quale il corpo <lb></lb><figure id="id.020.01.2952.2.jpg" xlink:href="020/01/2952/2.jpg"></figure></s></p><p type="caption">

<s>Figura 364.<lb></lb>E viene spinto lungo l&#039;impedimento AB. </s>

<s><lb></lb>Per esempio, se in GH fosse un peso di <lb></lb>10 libbre, essendo GC perpendicolare ad <lb></lb>AC, e BDF perpendicolare alla medesima <lb></lb>AC, e sia trovato che HG a GC stia come <lb></lb>5 a 4: sarà come 5 a 4 così 19 libbre <lb></lb>ad 8, le quali in FD bisogneranno per <lb></lb>spingere il corpo E con una forza uguale <lb></lb>a 10 libbre per la linea GH, per la se­<lb></lb>conda dimostrata proposizione. </s>

<s>Ora sia <lb></lb>trovato AB a BD stare come 4 a 3: starà <lb></lb>come 4 a 3, così 8 libbre in FD, a libbre 6, che è la forza cercata, cioè quella, <lb></lb>con la quale il corpo E viene ad essere spinto da una spinta obliqua se­<lb></lb>condo GH di 10 libbre lungo l&#039;impedimento AB, per la terza proposizione. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE V. — <emph type="italics"></emph>Data una linea, per la quale un piano debba <lb></lb>essere spinto per far camminare un corpo lungo un dato impedimento, <lb></lb>trovare lo stato, il sito o inclinazione del piano spingente, per far cam­<lb></lb>minare il detto corpo con la massima forza possibile. </s>

<s>”<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/2953.jpg" pagenum="578"></pb><p type="main">

<s><emph type="italics"></emph>“ Primo caso.<emph.end type="italics"></emph.end> — Sia il corpo A (nella figura 355 poco addietro rap­<lb></lb>presentata) l&#039;impedimento BC, la linea, per la quale si fa la forza, EFG, po­<lb></lb>sta perpendicolare all&#039;impedimento CB. </s>

<s>Volendo dare una tal situazione a <lb></lb>CD, che faccia la maggior possibile forza contro il corpo A, si tiri la linea <lb></lb>CFD in modo, che CG sia uguale a GF, e quella sarà la linea desiderata, <lb></lb>secondo la quale si deve situare il piano, per spingere il corpo A con la <lb></lb>maggiore forza possibile. </s>

<s>” </s></p><p type="main">

<s>“ Imperocchè, essendo i due lati GC, GF uguali del triangolo CGF, e <lb></lb>ciascuno mezzo retto, e similmente gli angoli DFE, DEF uguali fra loro nel <lb></lb>triangolo EDF, siccome gli angoli FCB, FBC nel triangolo FBC, per essere <lb></lb>questi tre triangoli simili fra loro; dico dunque che posta EF libbre 2, a <lb></lb>ED 1, così libbre 10, che è la forza per EF, alle 5 libbre; questa sarà la <lb></lb>forza spingente il piano. </s>

<s>Inoltre, come BC 2 a BF 1, così libbre 10 spingenti <lb></lb>il piano, a libbre 5, e questa sarà la forza, con la quale viene spinto il <lb></lb>corpo A. ” </s></p><p type="main">

<s>“ Ponghiamo adesso CG maggiore di GF nella proporzione, per esem­<lb></lb>pio, di 4 a 3, ossia ponghiamo che il quadrato di CG stia al quadrato di GF <lb></lb>come 16 a 9: essendo il triangolo CGF rettangolo in G, il quadrato di CF <lb></lb>sarà 25, e CF 5, onde EF ad ED sarà come 5 a 4, per essere gli angoli <lb></lb>GFC, DFE uguali, e gli angoli FGC, FDE retti, e però i triangoli simili. </s>

<s><lb></lb>Parimente, avendo i triangoli FGC, BCF un angolo comune C, e ciascuno <lb></lb>un retto FGC e BFC, saranno essi triangoli simili tra loro, onde BC a BF <lb></lb>sta come 5 a 3. ” </s></p><p type="main">

<s>“ Facciasi dunque come EF 5 a DE 4, così 10 libbre di forza ad 8 di <lb></lb>resistenza del piano: inoltre si faccia come BC 5 a BF 3, così 8 libbre di <lb></lb>resistenza a 4+4/5 di forza, con la quale il corpo A viene spinto, la quale <lb></lb>è minore delle cinque libbre trovate nel primo supposto. </s>

<s>Nel medesimo modo, <lb></lb>se ponghiamo GC minore di GF, troveremo 4+4/5 per la forza premente <lb></lb>il corpo A, posto cioè che GC a GF stia come 3 a 4, sicchè, quando GC <lb></lb>e GF sono uguali, la spinta per EF sarà la più vantaggiosa. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Secondo caso.<emph.end type="italics"></emph.end> — Sia dato il corpo A, (fig. </s>

<s>365) la linea, per la quale si <lb></lb>fa la forza, FDG, l&#039;impedimento BC non perpendicolare ad FG: per trovare <lb></lb><figure id="id.020.01.2953.1.jpg" xlink:href="020/01/2953/1.jpg"></figure></s></p><p type="caption">

<s>Figura 365.<lb></lb>quel che si domanda facciasi GC uguale a GD, e <lb></lb>giunta la linea CDE, questa sarà la desiderata <lb></lb>situazione del piano. </s>

<s>Imperocchè DF ad EF stia <lb></lb>come 5 a 3, come è lecito di supporre secondo <lb></lb>il caso di Stevino. </s>

<s>Facciasi dunque come 5 a 3, <lb></lb>così 10 libbre di forza in FD, a 6 libbre di re­<lb></lb>sistenza del piano, e per essere GC, GD uguali <lb></lb>saranno anco uguali gli angoli GDC, GCD. </s>

<s>Ma <lb></lb>GDC è anco uguale all&#039;EDF, dunque EDF è <lb></lb>uguale a GCD, ovvero BBD, e gli angoli BDG, <lb></lb>DEF son retti, onde i triangoli BDC, FED sono simili: sicchè, come CB a <lb></lb>BD, così DF ad FE, cioè come 5 a 3. Si faccia dunque come BC 5 a BD 3, <pb xlink:href="020/01/2954.jpg" pagenum="579"></pb>così libbre sei di resistenza del piano, a libbre 3 3/5, che sarà la forza, con <lb></lb>cui il corpo A viene spinto. </s>

<s>Ma posto GC maggiore, ovvero minore di GD, <lb></lb>il corpo A non verrà spinto con tanta forza, come si prova per il calcolo, <lb></lb>e perciò questa è la situazione più vantaggiosa del piano DC. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario I.<emph.end type="italics"></emph.end> — Per la quarta proposizione si è dimostrato il modo <lb></lb>di trovare per mezzo del calcolo la forza, con la quale un vascello viene <lb></lb>spinto, quando sia data la forza del vento contro la vela, e lo strale del vento, <lb></lb>e la situazione della vela. </s>

<s>Imperocchè sia AB (fig. </s>

<s>366) un vascello, che per <lb></lb><figure id="id.020.01.2954.1.jpg" xlink:href="020/01/2954/1.jpg"></figure></s></p><p type="caption">

<s>Figura 366.<lb></lb>mezzo del timone viene forzato a cammi­<lb></lb>nare lungo la linea AB, ovvero FG, lo <lb></lb>strale del vento sia CD, la vela EF, e sia <lb></lb>il vento di mille libbre di peso, ovvero sia <lb></lb>la sua forza bastante a operare come se <lb></lb>fosse di tanto peso, il qual vento per la <lb></lb>linea CD, o altra parallela ad essa, urti <lb></lb>nella vela, e sia dato che DC ad EC stia <lb></lb>come 5 a 3. Facciasi come DC 5 ad EC 3, così libbre mille a seicento, che <lb></lb>questa sarà la resistenza della vela. </s>

<s>” </s></p><p type="main">

<s>“ Di nuovo, sia per esempio che GF a GD stia come 5 a 4. Si faccia <lb></lb>come 5 a 4, così seicento libbre a quattrocento ottanta, che questa sarà la <lb></lb>forza spingente il vascello, il che chiaramente apparisce per la quarta pro­<lb></lb>posizione. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario II.<emph.end type="italics"></emph.end> — Dalla quinta proposizione si cava come la vela deve <lb></lb>esser situata col maggiore avvantaggio, quando sia data la linea del vento. </s>

<s>” </s></p><p type="main">

<s>“ Sia di nuovo, nella medesima figura, il vascello AB andante da B <lb></lb>in A, sia FG l&#039;impedimento, HG la linea del vento, FE la vela, la quale si <lb></lb>deve situare in tal maniera, che FG sia uguale a GD, tirando la vela da F <lb></lb>per D ad E, il qual tiramento, per la quinta proposizione, darà la maggior <lb></lb>forza per far camminare il vascello, il che è quello, che io mi sono propo­<lb></lb>sto di dimostrare. </s>

<s>” </s></p><p type="main">

<s>“ E questo da tutti i marinari può essere praticato, misurando la lun­<lb></lb>ghezza della banda dal luogo, dove vien segata dalla vela, sino al luogo, dove <lb></lb>la linea del vento taglia l&#039;istessa banda, facendo quella uguale con la linea <lb></lb>tirata dal luogo della banda, che vien tagliata dalla linea del vento, sino al <lb></lb>corpo della vela. </s></p><p type="main">

<s>“ Qui non paia strano che si misuri il vento a libbre, giacchè si può <lb></lb>pesarlo, o almeno la di lui forza. </s>

<s>Ma caso che la parola di peso vi dispiac­<lb></lb>cia, valetevi di quella de&#039;gradi in suo luogo, e dite un vento di tanti gradi <lb></lb>di forza o potenza. </s>

<s>” </s></p><p type="main">

<s>“ Vero è bene che, a voler praticar ciò, non si troverebbe sempre che <lb></lb>tutto a capello riuscisse con quella esattezza, che qui si è scritto, il che ac­<lb></lb>caderebbe, perchè di rado la forza del vento è uniforme per lungo tempo, e <lb></lb>i vascelli per alcune ragioni talvolta deviano dalla linea del loro cammino, <lb></lb>e per l&#039;incostanza degli impedimenti, e per non essere la situazione della <pb xlink:href="020/01/2955.jpg" pagenum="580"></pb>vela simile a quella delle tavole, fermandosi queste nella situazione che si <lb></lb>dà loro, laddove le vele vengono stravolte da ogni minimo moto. </s>

<s>” (MSS. <lb></lb>Gal., T. CLXI, fol. </s>

<s>1-6). </s></p><p type="main">

<s>Qual si fosse il giudizio riportato dal Viviani dopo la diligente lettura <lb></lb>di questi teoremi del Witsen, e dopo le istanze fattegliene dallo Stenone, <lb></lb>non si potrebbe dir con esattezza, ma noi crediamo che si rimanesse tuttavia <lb></lb>fedele agl&#039;insegnamenti di Galileo, sedotto, e confermatovi forse da quelle <lb></lb>esperienze, che gli fecero eludere gli avvedimenti saggiamente suggeritigli <lb></lb>da Michelangiolo Ricci, quando si trattava di risolvere, con miglior ragione <lb></lb>di quella addotta nell&#039;ultimo Dialogo dal Salviati, il problema della corda <lb></lb>tesa. </s>

<s>Da un tal fatto, che si narrò da noi nel capitolo I di questo Tomo, da <lb></lb>pag. </s>

<s>60-67, apparisce che fu esso Ricci l&#039;unico a que&#039;tempi, nella scuola <lb></lb>galilciana, che con libertà di giudizio intendesse la natura dei moti compo­<lb></lb>sti, e che ne sentisse la grandissima utilità delle applicazioni. </s>

<s>Ricevuta, per <lb></lb>mezzo del principe Leopoldo dei Medici, una di quelle scritture, nelle quali <lb></lb>il Borelli dava saggio de&#039;progressi che sarebbe presto per fare nella Scienza <lb></lb>del moto, ringraziato esso Principe, che gli avesse fatte gustare così profonde <lb></lb>e belle speculazioni, gli soggiungeva: “ E saria forse bene che s&#039;applicasse <lb></lb>il signor Borelli a dare in luce un trattato della composizione dei moti, e <lb></lb>dell&#039;aumento e diminuzione loro, giacchè tant&#039;oltre si è internato nella ma­<lb></lb>teria, perchè quivi pescano molti che oggidì vanno speculando per le cose <lb></lb>geometriche, astronomiche e fisiche. </s>

<s>Vostra Altezza si ricorderà quanto ca­<lb></lb>pitale ne faceva il Torricelli, e quanto se ne sia valso il Robervallio, ed altri <lb></lb>matematici famosi, e Des-Cartes in filosofia, e Keplero nell&#039;astronomia. </s>

<s>Così <lb></lb>verrebbe egli a farsi autore di tante verità, che s&#039;inventeranno con l&#039;aiuto <lb></lb>di quelle dottrine dei moti, che sono innumerabili ” (Fabbroni, <emph type="italics"></emph>Lettere di <lb></lb>uomini illustri,<emph.end type="italics"></emph.end> T. II, Firenze 1765, pag. </s>

<s>127). </s></p><p type="main">

<s>Le invenzioni con questi aiuti si fecero veramente e innumerevoli, come <lb></lb>il Ricci divinava, ma da tutti altri autori da quello, in cui egli aveva ripo­<lb></lb>ste le sue speranze, il quale, riducendo con logica inesorabile, e più incon­<lb></lb>siderata di quella de&#039;suoi colleghi, il teorema galileiano alle sue ultime con­<lb></lb>seguenze, disse che i moti per i lati si possono ben comporre nel moto per <lb></lb>la diagonale, quando si fanno i loro concorsi ad angolo retto, come nel qua­<lb></lb>drato o nel rettangolo, ma non già, quando concorrono secondo qualunque <lb></lb>angolo, come nella losanga o nel parallelogrammo, non verificandosi in que­<lb></lb>ste figure, come in quelle, la ragione addotta da Galileo dell&#039;equivalere cioè <lb></lb>la potenza della resultante alla somma delle due componenti. </s>

<s>Nè lo disse il <lb></lb>Borelli in privato discorso con gli amici, ma al pubblico in quel solenne an­<lb></lb>fiteatro della sua Scienza, che è l&#039;Opera dei Moti animali. </s></p><p type="main">

<s>Nella proposizione LXIX della Prima Parte, si voleva dimostrar dall&#039;Au­<lb></lb>tore: “ Duae potentiae sustinentes, ad resistentiam, erunt ut longitudines <lb></lb>funium obliquae, quae proportionales sint conterminalibus potentiis, ad ea­<lb></lb>rum sublimitates ” (Romae 1680, pag. </s>

<s>131). Cioè: essendo le due potenze <lb></lb>R, S (fig. </s>

<s>367), che per mezzo delle funi AC, BC sostengono il peso T, con <pb xlink:href="020/01/2956.jpg" pagenum="581"></pb>forze proporzionali ad AC, CM, se dai punti A, M si conducono sulla ver­<lb></lb>ticale FC, sicchè la raggiungano in D e in O le due perpendicolari AD, MO, <lb></lb>chiama il Borelli le sezioni CD, CO le <emph type="italics"></emph>sublimità,<emph.end type="italics"></emph.end> alle quali dice essere le <lb></lb>contermine potenze proporzionali, d&#039;onde in ultimo conclude così il ragiona­<lb></lb>mento: “ Ergo duae potentiae R, S simul sumptae, ad resistentiam T, eam­<lb></lb>dem rationem habebunt quam duae AC, CM simul, ad duas DC, OC simul ” <lb></lb>(ibid., pag. </s>

<s>132). </s></p><p type="main">

<s>A questo punto il Lettore, che non sa nulla ancora, crederebbe avesse <lb></lb>voluto il Borelli trasformare così la sua proposizione per mostrar che la nuova <lb></lb>regola da lui insegnata è quella medesima, a cui avrebbe direttamente con­<lb></lb><figure id="id.020.01.2956.1.jpg" xlink:href="020/01/2956/1.jpg"></figure></s></p><p type="caption">

<s>Figura 367.<lb></lb>dotto il parallelogrammo, costruito sui lati AC, CM. </s>

<s>Ti­<lb></lb>rata infatti dal punto A una parallela a CM, che incontri <lb></lb>la verticale, e il punto F di tale incontro congiunto <lb></lb>con M, è facile riconoscere, nella figura AM che ne <lb></lb>resulta, la proprietà del parallelogrammo, essendo per <lb></lb>le parallele AF, MC; AD, MO gli angoli opposti uguali. </s>

<s><lb></lb>Uguali anche essendo DA a MO, e OC a FD, d&#039;onde <lb></lb>viene DC+OC=FC, che è la diagonale del detto <lb></lb>parallelogrammo; la proporzionalità dunque ultimamen­<lb></lb>te conclusa dal Borelli si riduce a R+S:T= <lb></lb>AC+CM:FC, conforme a quel che avevano insegnato lo Stevino e l&#039;He­<lb></lb>rigonio. </s></p><p type="main">

<s>Ma mentre aveva creduto il Lettore essere l&#039;intenzion del Borelli quella <lb></lb>di dimostrare una tale conformità, con sua gran maraviglia proseguendo s&#039;in­<lb></lb>contra in una digressione così intitolata: “ Quia Stevinus et Herigonius et <lb></lb>alii viri doctissimi alia longe diversa via hanc eamdem propositionem se de­<lb></lb>monstrasse putant, cogor paucis innuere rationes, quibus methodum a Viris <lb></lb>praeclaris servatam, non omnino tutam et legitimam censuerim ” (ibid., <lb></lb>pag. </s>

<s>133). </s></p><p type="main">

<s>La maraviglia cresce tanto più, in quanto che il Borelli, per dimostrare <lb></lb>che non era legittimo il metodo dello Stevino e dell&#039;Herigonio, incomincia <lb></lb>dal riferire i discorsi di quei Matematici, che ne avevano dovuta confermare <lb></lb>la verità, riducendolo ai principii statici del piano inclinato e del vette. </s>

<s>Il <lb></lb>secondo di que&#039;discorsi il Borelli l&#039;attribuisce a un <emph type="italics"></emph>insigne Geometra neo­<lb></lb>terico,<emph.end type="italics"></emph.end> per il quale par che debba intendersi il Pardies, nella sua <emph type="italics"></emph>Statique, <lb></lb>ou Scienc des forces mouvantes,<emph.end type="italics"></emph.end> libro stampato in Parigi nel 1673: ma il <lb></lb>primo l&#039;attribuisce espressamente all&#039;Herigonio, e si può facilmente conce­<lb></lb>dere al Borelli che sia in questa sua digressione il discorso <emph type="italics"></emph>aliler et clarius <lb></lb>ostensus,<emph.end type="italics"></emph.end> perchè in esso Herigonio non apparisce di ciò nessuna esplicita <lb></lb>dimostrazione. </s>

<s>Si dubiterebbe anzi se l&#039;Autor della detta digressione avesse <lb></lb>veduto mai il libro oggetto alle sue contradizioni, il quale forse conosceva <lb></lb>solamente per fama, e per le raccomandazioni, che ne faceva il Cavalieri <lb></lb>a&#039;suoi discepoli, come particolarmente al Rocca, con queste parole: “ Di li­<lb></lb>bri nuovi non ho nuova alcuna, ma non so se ella abbi visto il <emph type="italics"></emph>Cursus ma-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2957.jpg" pagenum="582"></pb><emph type="italics"></emph>thematicus<emph.end type="italics"></emph.end> di Pietro Herigoni, matematico di Parigi, diviso in cinque tomi, <lb></lb>stampato a Parigi, nel quale, con maniera molto breve, professa insegnare <lb></lb>tutte le Matematiche, ed è degno di esser visto, ed opera nuova ” (<emph type="italics"></emph>Lettere <lb></lb>d&#039;uomini illustri a G. A. Rocca,<emph.end type="italics"></emph.end> Modena 1785, pag. </s>

<s>153). </s></p><p type="main">

<s>In qualunque modo, ecco quali erano, secondo il Borelli, i ragionamenti, <lb></lb>che si facevano dai Matematici de&#039;suoi tempi, per confermare, dai principii <lb></lb>statici universalmente consentiti, la verità dell&#039;uso di ricomporre nella diagonale <lb></lb>del parallelogrammo i moti, che s&#039;intendessero fatti per i due lati. </s>

<s>Il globo T <lb></lb>(fig. </s>

<s>368), sorretto per il centro C dalle potenze R, S, applicate alle funi AC, <lb></lb>BC, starebbe egualmente in equilibrio sopra i due piani IH, IG, inclinati <lb></lb>nelle direzioni delle tangenti VH, OG: e le relazioni tra il peso assoluto T, <lb></lb>e il suo momento MoT sul piano OG, son date, secondo le note leggi, da <lb></lb>T:MoT=IG:IP. </s>

<s>Si disegni il parallelogrammo MN, e sul prolungamento <lb></lb>di DM si abbassi dal centro C la perpendicolare CL:il triangolo DLC, che <lb></lb>indi nasce, è simile al triangolo IPG, e perciò T:MoT=DC:CL. </s>

<s>Se ora <lb></lb>si conduca da O perpendicolarmente la OQ sopra VC, i triangoli MLC, COQ <lb></lb>danno, per la loro similitudine, LC:CM=QO:OC. </s>

<s>E considerando essere <lb></lb><figure id="id.020.01.2957.1.jpg" xlink:href="020/01/2957/1.jpg"></figure></s></p><p type="caption">

<s>Figura 368.<lb></lb>OC la lunghezza del vette, che appoggiandosi col so­<lb></lb>stegno in O fa ruzzolare il globo sul piano; consi­<lb></lb>derato inoltre che OQ è la distanza della direzione <lb></lb>obliqua della potenza R da esso sostegno, per cui <lb></lb>OC è la misura assoluta di R, e OQ è la misura <lb></lb>di lei, che equilibra il momento di T sul declivio, <lb></lb>tirando in direzione non parallela, ma convergente <lb></lb>con esso declivio; avremo LC:CM=QO:OC= <lb></lb>Mo.T:R. Ora, moltiplicata questa Mo.T:R= <lb></lb>LC:CM per l&#039;altra già trovata T:Mo.T=DC:CL, <lb></lb>ne conseguirà T:R=DC:CM. </s>

<s>Con simile ragio­<lb></lb>namento, soggiunge il Borelli, trovano pure questi <lb></lb>Matematici T:S=DC:CN, e perciò R:S= <lb></lb>CM:CN:e ancora, R+S:T=CM+CN:DC, d&#039;onde intendono costoro <lb></lb>di confermare la regola insegnata dallo Stevino e dall&#039;Herigonio, per com­<lb></lb>porre in uno solo due moti, con qualunque angolo concorrenti. </s></p><p type="main">

<s>L&#039;altra dimostrazione, attribuita a quell&#039;insigne Geometra neoterico, è <lb></lb><figure id="id.020.01.2957.2.jpg" xlink:href="020/01/2957/2.jpg"></figure></s></p><p type="caption">

<s>Figura 369.<lb></lb>riferita dal Borelli stesso con tal discorso, che si può <lb></lb>compendiare in questo modo: Le funi AC, BC (fig. </s>

<s>369) <lb></lb>si riguardino come due vetti appuntati in C, e co&#039;so­<lb></lb>stegni in A, B, cosicchè il peso T tiri in giù il vette <lb></lb>AC, con momento, che starà al peso assoluto come <lb></lb>la lunghezza AC dello strumento sta alla distanza AD <lb></lb>della direzione obliqua dall&#039;ipomoclio, mentre dall&#039;al­<lb></lb>tra parte è sostenuto esso vette, uguale in potenza ad <lb></lb>S, con momento, che sta alla forza assoluta, la quale tenderebbe a far girare il <lb></lb>peso T intorno al centro A; come la distanza AE sta al raggio AC, per cui si <pb xlink:href="020/01/2958.jpg" pagenum="583"></pb>avranno le equazioni T:Mo.S=CA:DA, Mo.S:S=EA:CA:e, co­<lb></lb>struito il parallelogrammo MN, T:S=EA:DA=<emph type="italics"></emph>sen<emph.end type="italics"></emph.end> ACE:<emph type="italics"></emph>sen<emph.end type="italics"></emph.end> ACD= <lb></lb><emph type="italics"></emph>sen<emph.end type="italics"></emph.end> DNC:<emph type="italics"></emph>sen<emph.end type="italics"></emph.end> CDN=DC:CN. </s>

<s>Il ragionamento, per dimostrare che T sta ad <lb></lb>R, come DC a MC, è simile a questo, e perciò si giunge anche di qui a quel <lb></lb>medesimo, che i Matematici detti di sopra avevano già concluso per altre vie. </s></p><p type="main">

<s>Ora ognuno si aspetterebbe, dopo aver riferite così queste dimostrazioni, <lb></lb>che il Borelli avesse da scoprirci dentro qualche fallacia. </s>

<s>Ma, tutt&#039;altrimenti <lb></lb><figure id="id.020.01.2958.1.jpg" xlink:href="020/01/2958/1.jpg"></figure></s></p><p type="caption">

<s>Figura 370.<lb></lb>da ciò, confessa che non è in esse nessuna fal­<lb></lb>lace argomentazione, <emph type="italics"></emph>nec quicquam assumptum <lb></lb>est praeceptis mechanicis repugnans.<emph.end type="italics"></emph.end> — Oh <lb></lb>dunque, perchè non debbono valere que&#039;discorsi <lb></lb>a confermar la verità della regola herigoniana? <lb></lb></s>

<s>— E risponde il Borelli che così è per due ra­<lb></lb>gioni: la prima delle quali è l&#039;esperienza, invo­<lb></lb>cata da me, egli dice, a confermare quel che al­<lb></lb>trove ho dimostrato, “ quod duae potentiae R <lb></lb>et S (fig. </s>

<s>370), oblique sustinendo pondus T, <lb></lb>cum eodem aequilibrari possunt, licet R ad S habeat quamcumque pro­<lb></lb>portionem, ac proinde maiorem aut minorem ea, quam CM habet ad CN, <lb></lb>et licet duae potentiae R et S simul sumptae, ad pondus T, habeant quam­<lb></lb>cumque diversam proportionem ab ea, quam CM et CN simul sumptae ha­<lb></lb>bent ad DC ” (Loco cit., pag. </s>

<s>138). </s></p><p type="main">

<s>Aggiungasi, prosegue a dire lo stesso Borelli, che, fatte le medesime <lb></lb>ipotesi di quei Matematici, si giunge, ragionando dai loro medesimi princi­<lb></lb>pii, a concludere che il peso assoluto T sta alle due potenze R, S insieme, <lb></lb>come CO ad OP, ossia come CD a DX. “ Hoc autem nedum est evidenter <lb></lb>falsum, sed etiam contra eosdem praeclaros auctores, qui censent pondus T, <lb></lb>ad duas potentias R et S, esse ut DC ad MC, et CN simul sumptas, quae <lb></lb>multo maiores sunt, quam DX, ut facile ostendi potest ” (ibid., pag. </s>

<s>141). <lb></lb>Di qui si passa immediatamente a concludere che, se fossero legittimi i pro­<lb></lb>gressi di quegli stessi preclarissimi Autori, si dovrebbe, fra le due potenze <lb></lb>e il peso che sostengono, sempre avere la medesima proporzione, e non dif­<lb></lb>ferente. </s>

<s>Che se ciò non avviene, non può, dice, attribuirsi ad altro, che al­<lb></lb>l&#039;essere quelle fatte supposizioni nè possibili nè vere, “ quod nimirum duo <lb></lb>termini funium A et B, sigillatim vel coniunctim, ut centra fixa vectium <lb></lb>usurpari possint, et quod sola potentia R, vel sola potentia S, aequari possit <lb></lb>momento totius resistentiae T ” (ibid., pag. </s>

<s>142). </s></p><p type="main">

<s>Verrebbe di qui facile sulla bocca di ognuno la risposta che quei Ma­<lb></lb>tematici non trattavano di una uguaglianza, ma di una certa proporzionalità, <lb></lb>che passa tra ciascuna parzial potenza, e la resistenza totale. </s>

<s>In qualunque <lb></lb>modo però s&#039;avvedono i Lettori che debbono essere le esperienze del Bo­<lb></lb>relli fallacie, e paralogismi i suoi ragionamenti. </s>

<s>Non mancarono Matematici, <lb></lb>anche tra noi, i quali ebbero questi avvedimenti, ma il più libero, e il più <lb></lb>eloquente in denunziarli, fu il Varignon, il quale scrisse, e aggiunse in fine <pb xlink:href="020/01/2959.jpg" pagenum="584"></pb>alla sua <emph type="italics"></emph>Nouvelle mecanique,<emph.end type="italics"></emph.end> un opuscolo critico, diviso in due capitoli, e <lb></lb>intitolato: <emph type="italics"></emph>Examen de l&#039;opinion de M. </s>

<s>Borelli sur les proprietez des poids <lb></lb>suspendus par des cordez.<emph.end type="italics"></emph.end> Quanto all&#039;esperienza, osserva saviamente il Va­<lb></lb>rignon, che, in fatto d&#039;esattezza e di precisione, “ ne prouve rien, sur tout <lb></lb>ici, ou la resistance, qui vient du frottement des poulies avec leurs pivons etc., <lb></lb>rend ces sortes d&#039;experiences possibles en tant de manieres differentes, qu&#039;il <lb></lb>n&#039;y a presque point de sentiment, pour ou contre le quel on n&#039;en puisse <lb></lb>faire à son gré ” (A Paris, T. II, 1725, pag. </s>

<s>454). </s></p><p type="main">

<s>Quanto poi al ragionamento, in cui pretende il Borelli di dimostrare <lb></lb>che il peso assoluto sta alle due potenze che lo sostengono, come CO ad OP, <lb></lb>nella medesima figura 370, soggiunge lo stesso Varignon ch&#039;egli è condotto <lb></lb>da varie supposizioni o principii, tutti manifestamente falsi. </s>

<s>Il Critico fran­<lb></lb>cese però non entrò addentro a ricercar la radice di queste fallacie, che perciò <lb></lb>non si crederebbero in un ingegno, come è quello dell&#039;Autore dei Moti ani­<lb></lb>mali, ma che, piuttosto ch&#039;esser proprie di lui solo, appartennero a tutta in­<lb></lb>tera quella Scuola dominatrice, nella quale si teneva con fermissima fede non <lb></lb>aver Galileo insegnato mai nulla, che non fosse vero e perfetto. </s>

<s>Di qui è che <lb></lb>o non si curavano, o si disprezzavano gl&#039;insegnamenti di quell&#039;altra Scuola, <lb></lb>più umile e più dispersa, istituita dallo Stevino, negli insegnamenti del quale <lb></lb>si sarebbe dovuto piuttosto, principalmente per ciò che concerne i moti com­<lb></lb>posti, cercar quella verità e quella perfezione, che non si trovava affatto nella <lb></lb>Scienza meccanica di Galileo. </s></p><p type="main">

<s>L&#039;applicazione del parallelogrammo delle forze alla teoria del piano in­<lb></lb>clinato non era da lamentar negletta, come sembra facesse il Lagrange, per­<lb></lb>chè avrebbe dato a Galileo maggior facilità di dimostrare, ma perchè glie ne <lb></lb>sarebbe derivata perfezione di scienza, in distinguere le varietà, e in misu­<lb></lb>rar le grandezze dei momenti, con cui il grave preme il piano, e lunghesso <lb></lb>discende: e ciò non solamente nel caso, che sia sostenuto da potenza con <lb></lb>direzion parallela, ma comunque convergente con la linea del declivio. </s>

<s>Nello <lb></lb>Stevino basta tornare in dietro sulla figura 353, per vedervi distinti que&#039;due <lb></lb>momenti e le loro proporzioni, rispetto al peso assoluto della colonna, il qual <lb></lb>peso essendo rappresentato dalla diagonale DL, vengono dai lati QD, DI a <lb></lb>rappresentarsi i respettivi momenti, con cui la colonna stessa preme, o stri­<lb></lb>scerebbe giù lungo il piano. </s>

<s>Che se la direzione della potenza non è, come <lb></lb>DF, parallela, ma, come DB, convergente con la linea AB del declivio, la <lb></lb>diagonale DL e il lato DO, nel parallelogrammo RO nuovamente costruito, <lb></lb>daranno la proporzione tra il peso assoluto del grave, e la forza bastante a <lb></lb>trattenerlo in quel sito: proporzione che, ridotta in forma trigonometrica, è <lb></lb>tale:LD:DO=<emph type="italics"></emph>sen<emph.end type="italics"></emph.end> LOD:<emph type="italics"></emph>sen<emph.end type="italics"></emph.end> DLO. </s>

<s>E perchè LOD, ossia IQD, è uguale <lb></lb>a 90°—IDO, e DLO=BAC; dunque LD:DO=<emph type="italics"></emph>cos<emph.end type="italics"></emph.end> IDO:<emph type="italics"></emph>sen<emph.end type="italics"></emph.end> BAC, se­<lb></lb>condo che il Dechales, infino dal 1673, annunziava nella prima edizione del <lb></lb>suo <emph type="italics"></emph>Mundus mathematicus<emph.end type="italics"></emph.end> agli studiosi della Statica steviniana: <emph type="italics"></emph>“ Pondus, <lb></lb>in plano inclinato consistens, se habet ad pondus aequalis momenti, tra­<lb></lb>hens linea plano non parallela, ut sinus complementi anguli tractionis,<emph.end type="italics"></emph.end><pb xlink:href="020/01/2960.jpg" pagenum="585"></pb><emph type="italics"></emph>ad sinum anguli inclinationis plani ”<emph.end type="italics"></emph.end> (T. II, editio altera, Lugduni 1690, <lb></lb>pag. </s>

<s>204). </s></p><p type="main">

<s>“ Et de mesme seroit, per citar le parole proprie dello Stevino, si BN <lb></lb>estoit de l&#039;altre coste de la perpendicolaire BC, assavoir entre AB, BC, et <lb></lb>sembleblament DO entre DL et DI ” (Ouvr. </s>

<s>cit., pag. </s>

<s>449), ossia, se la fune <lb></lb>DB, invece di convergere con B, converge con A dalla parte opposta, come <lb></lb>nell&#039;esempio esibitoci dalla 354a figura, dove, essendo LOD=180°—DOF= <lb></lb>180°—(90°—ODF)=90°—ODF, s&#039;ha DL:LO=<emph type="italics"></emph>sen<emph.end type="italics"></emph.end> LOD:<emph type="italics"></emph>sen<emph.end type="italics"></emph.end> DLO= <lb></lb><emph type="italics"></emph>cos<emph.end type="italics"></emph.end> ODF:<emph type="italics"></emph>sen<emph.end type="italics"></emph.end> BAC, ossia, come dianzi, il peso sta alla potenza che lo sostiene <lb></lb>come il coseno dell&#039;angolo della trazione sta al seno dell&#039;angolo dell&#039;incli­<lb></lb>nazion del piano sull&#039;orizonte. </s></p><p type="main">

<s>Galileo invece insegnava che il peso sta alla potenza come il seno to­<lb></lb>tale, ossia il raggio, sta al seno dell&#039;angolo dell&#039;inclinazione, con teorema, <lb></lb>che rimanendosi nello stato, in cui la Scienza lo aveva avuto già dal Tar­<lb></lb>taglia, così assolutamente pronunziato è, a confronto di quello dello Stevino, <lb></lb>da dire addirittura falso, non verificandosi che nel caso dell&#039;angolo della tra­<lb></lb>zione uguale a zero, perchè allora il coseno di zero torna veramente alla <lb></lb>lunghezza del raggio. </s></p><p type="main">

<s>Dall&#039;avere il Maestro, dietro un esempio particolare, formulato un teo­<lb></lb>rema generalissimo, s&#039;ingerì ne&#039;Discepoli l&#039;opinione che si mantenesse sem­<lb></lb>pre uguale la forza applicata a una fune secondo qualunque direzione, e il <lb></lb>Viviani, come vedemmo (pag. </s>

<s>67, 68 di questo Tomo) istituiva per confer­<lb></lb>marla esperienze, e il Borelli se ne serviva come principio, da concluderne tra <lb></lb>la potenza e il peso una proporzione, diversa da quella che passa tra i lati <lb></lb>e la diagonale del parallelogrammo. </s>

<s>E dal non aver saputo Galileo decom­<lb></lb>porre il peso assoluto del grave sopra il piano ne&#039;suoi momenti parziali, de­<lb></lb>rivò nel Borelli, benchè fosse per le medesime vie oblique giunto a dimo­<lb></lb>strare i teoremi del Viviani (vedi il nostro Tomo IV, pag. </s>

<s>244, 45), quella <lb></lb>confusione d&#039;idee, che trasparisce dal suo ragionamento. </s>

<s>Fra gli altri prin­<lb></lb>cipii quivi assunti è notabile quello, che suppone la resultante divider nel <lb></lb>mezzo l&#039;angolo del concorso, anco quando i moti componenti non sono uguali: <lb></lb>supposizione affatto gratuita, ma che è in conseguenza delle dottrine profes­<lb></lb>sate dall&#039;Autore, nello scolio alla proposizione LXIX di questa prima parte <lb></lb><emph type="italics"></emph>De motu animalium:<emph.end type="italics"></emph.end> “ Manifeste colligitur, ex dictis propositionibus, quod <lb></lb>duae quaelibet potentiae, sive aequales sive inaequales inter se fuerint, pos­<lb></lb>sunt aequilibrari alicui resistentiae, trahendo funes obliquos, efficientes cum <lb></lb>directione resistentiae angulos acutos, sive aequales, sive inaequales inter se ” <lb></lb>(pag. </s>

<s>132). Ma tutte queste fallacie dipendevano dalla massima e principale, <lb></lb>introdotta da Galileo in questa Scienza dei moti composti, che cioè, dovendo <lb></lb>le parti essere in ogni modo uguali al tutto, le potenze sostenitrici debbono, <lb></lb>senz&#039;alcuna diminuzione, equivalere al tutto. </s></p><p type="main">

<s>Il Varignon dunque, senza curarsi, come si diceva, di cercar d&#039;onde <lb></lb>avessero avuto origine, notava nel <emph type="italics"></emph>Remarque,<emph.end type="italics"></emph.end> in fine al capitolo I del citato <lb></lb><emph type="italics"></emph>Examen<emph.end type="italics"></emph.end> queste fallacie, incominciando da ciò che il Borelli soggiunge, dopo <pb xlink:href="020/01/2961.jpg" pagenum="586"></pb>aver detto che, riguardandosi la corda AC (fig. </s>

<s>371) come una verga rigida, <lb></lb>girevole intorno al punto fisso A, e all&#039;estremitè C della quale sia attaccato <lb></lb>il peso T; questo peso è da essa verga sostenuto come se riposasse sul piano <lb></lb><figure id="id.020.01.2961.1.jpg" xlink:href="020/01/2961/1.jpg"></figure></s></p><p type="caption">

<s>Figura 371.<lb></lb>CI perpendicolare ad AC, e con l&#039;elevazione <lb></lb>IL: <emph type="italics"></emph>patet quod pondus T, ad vim qua idem <lb></lb>T innitur, et comprimit planum IC, est <lb></lb>ut IC ad CL<emph.end type="italics"></emph.end> (pag. </s>

<s>139). “ Cela seroit vrai, <lb></lb>osserva qui il Varignon, si BC etoit paral­<lb></lb>lele a CI perpendiculaire à AC, mais non <lb></lb>pas, lorsqu&#039;elle lui est oblique, comme ici, <lb></lb>ou le poids S aide au poids T a charger <lb></lb>le plan CI, qui ne le seroit qui par ce poids <lb></lb>T, si BC lui étoit parallele ” (<emph type="italics"></emph>Nouvelle mechan.,<emph.end type="italics"></emph.end> T. </s>

<s>I cit., pag. </s>

<s>461). </s></p><p type="main">

<s>È chiaro infatti che la corda AC equilibra il momento gravitativo sul <lb></lb>piano, ma il discensivo viene equilibrato dall&#039;altra corda BC: e se quello è <lb></lb>secondo il Borelli proporzionale a LC, questo deve necessariamente esser pro­<lb></lb>porzionale a LI. </s>

<s>Cosicchè egli viene a dire che T sta ad S come il raggio <lb></lb>CI sta al seno LI dell&#039;inclinazione, ciò che non è assolutamente vero, come <lb></lb>si credeva dai discepoli di Galileo s<gap></gap>ll&#039;autorità del Maestro, ma nel solo caso <lb></lb>particolare che CB sia parallela a CI: cosa che non si verifica in questo <lb></lb>esempio, in cui la proporzione tra T ed S è quella del coseno dell&#039;angolo <lb></lb>della trazione ICB, e non del raggio, al seno dell&#039;angolo dell&#039;inclinazione <lb></lb>del piano, secondo il teorema generalissimo e verissimo dimostrato dallo <lb></lb>Stevino. </s></p><p type="main">

<s>In un&#039;altra fallacia, simile a questa, notava il Varignon essere incorso <lb></lb>il Borelli, quando, dop&#039;avere abbassata nella figura. </s>

<s>370 la CP perpendico­<lb></lb>lare sopra la KG, soggiungeva: <emph type="italics"></emph>Idem pondus absolutum T, ad vim qua com­<lb></lb>primit planum CO, eamdem rationem habebit quam CO ad OP<emph.end type="italics"></emph.end> (pag. </s>

<s>141). <lb></lb>“ Cela seroit vrai, si ce poids T étoit retenu sur CO par une puissance d&#039;une <lb></lb>direction parallele à CO ” (ivi, pag. </s>

<s>462). Ritornando infatti sopra la fig. </s>

<s>353, <lb></lb>ritratta dalla Statica dello Stevino, si vede che il momento gravitativo della <lb></lb>colonna sul piano è proporzionale a LI, coseno dell&#039;angolo dell&#039;inclinazione, <lb></lb>nel solo caso contemplato da Galileo e dal Borelli, e da loro supposto gene­<lb></lb>ralissimo, che la fune DF tiri con direzione parallela al declivio. </s>

<s>Ma se tira <lb></lb>con altra direzione, o sotto o sopra a quella, come DB, DV, il detto mo­<lb></lb>mento gravitativo o cresce come LO, o scema come LS, seni dell&#039;angolo fatto <lb></lb>dalla trazione con la linea verticale. </s></p><p type="main">

<s>“ Dans la critique, prosegue il Varignon, qu&#039;il (M. Borelli) fait ensuite <lb></lb>du raisonnement d&#039;Hérigone, de Stevin, etc., après avoir regardé le poids T <lb></lb>(nella figura 370) soûtenu par les cordes AC et BC, comme s&#039;il l&#039;étoit sur <lb></lb>les plans CK perpendiculaire à AC, et CG perpendiculaire à CB, inegale­<lb></lb>ment inclinez, il dit, pag. </s>

<s>141. <emph type="italics"></emph>Tunc pondus T, dum moveri niteretur per <lb></lb>duas rectas inclinatas CK et CG, cogeretur moveri, aut nisum exercere <lb></lb>per diagonalem CO, secantem angulum GCK bifariam.<emph.end type="italics"></emph.end> Pour cela il fau-<pb xlink:href="020/01/2962.jpg" pagenum="587"></pb>droit que ces deux plans CK, CG fussent également inclinez, et conseguen­<lb></lb>tement aussi les directions AC, BC, qu&#039;on leur suppose perpendiculaires ” <lb></lb>(ivi, pag. </s>

<s>461, 62). </s></p><p type="main">

<s>L&#039;ultima osservazione si fa dal Critico francese alle parole del Nostro: <lb></lb><emph type="italics"></emph>Vis, quam patitur planum CO<emph.end type="italics"></emph.end> (nella medesima figura 370) <emph type="italics"></emph>a compressione <lb></lb>ponderis T, aequalis est viribus ambarum potentiarum R et S, quae su­<lb></lb>stinendo idem pondus in tali situ plani CO inclinati vicem supplent.<emph.end type="italics"></emph.end><lb></lb>“ Cela est faux. </s>

<s>La force resultante du concours des deux autres (ripete il <lb></lb>Varignon al Borelli quel che tanto tempo prima avevano detto l&#039;Hobbes al <lb></lb>Cartesio, e il Mersenno a Galileo) est toujours moindre que leur somme, <lb></lb>tant que leurs directions font quelque angle entr&#039;elles. </s>

<s>Outre que cette force <lb></lb>resultante le long du plan CO, étant ainsi parallele a ce plan, ne seroit pas <lb></lb>celle de sa compression, qui résulteroit du concours de cette force parallele, <lb></lb>et de la pesanteur du poids soûttenu par elle sur ce plan ” (ivi, pag. </s>

<s>462). </s></p><p type="main">

<s>Supponiamo ora che il Borelli fosse sopravvissuto a questo esame, che <lb></lb>del suo ragionamento faceva così l&#039;Accademico parigino. </s>

<s>Si crederebb&#039;egli <lb></lb>forse che avesse riconosciuto e confessato il suo errore? </s>

<s>Noi per verità met­<lb></lb>tiamo la cosa in dubbio, ripensando a quei così tenaci pregiudizi della sua <lb></lb>Scuola, che tuttavia durano dopo due secoli e mezzo. </s>

<s>Dall&#039;altra parte l&#039;os­<lb></lb>servazione da noi fatta di sopra, che cioè il metodo, con cui egli si studiò <lb></lb>di dimostrar le potenze proporzionali alle sublimità, conduceva alla medesima <lb></lb>regola del parallelogrammo, non sarebbe dovuta bastar per sè sola a per­<lb></lb>suaderlo? </s>

<s>E quell&#039;altra sua opinione del non si poter comporre i moti per i <lb></lb>lati in quello per la diagonale, altro che nel caso dei concorsi ortogonali, non <lb></lb>gli si sarebbe potuta dissipar dalla mente come nebbia al chiaro sole di un così <lb></lb>fatto ragionamento? </s>

<s>Concorrano secondo qualunque angolo GCH (fig. </s>

<s>372) le <lb></lb>due potenze R, S a sostenere il peso T. Costruito, secondo qualunque pro­<lb></lb>porzione, un parallelogrammo, come per esempio GH, lo Stevino e l&#039;Heri­<lb></lb>gonio dicevano che le due potenze rappresentate da GC, CH equivalgono in­<lb></lb>sieme alla potenza unica rappresentata dalla diagonale CD, e il Borelli osti­<lb></lb>natamente ciò negava, perchè GCH non è, come prescrivevasi da Galileo, un <lb></lb><figure id="id.020.01.2962.1.jpg" xlink:href="020/01/2962/1.jpg"></figure></s></p><p type="caption">

<s>Figura 372.<lb></lb>angolo retto. </s>

<s>Or bene: si abbassino dai punti G, H, perpen­<lb></lb>dicolari sull&#039;orizontale MN, le GM, HN, e le due forze GC, <lb></lb>CH equivarranno, secondo il precetto galileiano, alle quattro <lb></lb>GM, HN; MC, CN. </s>

<s>E perchè queste è facile veder che sono <lb></lb>uguali e contrarie, rimangono attive quelle sole, ossia le loro <lb></lb>uguali QC, PC, ossia l&#039;intera DC, diagonale del parallelo­<lb></lb>grammo, che dunque equivale in potenza alle potenze dei lati. </s>

<s><lb></lb>Notabile è poi che il Borelli non s&#039;avvede come nel metodo, <lb></lb>ch&#039;egli dice suo proprio, e che consiste nel pigliar le linee <lb></lb>delle potenze proporzionali alle sublimità, si fa sempre la ri­<lb></lb>duzione, dalle forze concorrenti con qualunque angolo, alle forze ortogonali, <lb></lb>e che da questa riduzione, la quale senza volerlo, anzi reluttante lo conduce <lb></lb>alla regola del parallelogrammo, dipende la verità di quasi tutte le sue pro-<pb xlink:href="020/01/2963.jpg" pagenum="588"></pb>posizioni, e l&#039;aver principalmente risoluto, al modo del Simpson, il problema <lb></lb>della corda tesa, che dette al Viviani, come si narrò, tanto travaglio. </s></p><p type="main">

<s>E qui cade opportuno riferire le belle osservazioni, fatte dal Varignon <lb></lb>in questo proposito, del decomporre ciascuna delle forze concorrenti in altre <lb></lb>due ortogonali, come nell&#039;esempio illustrato dall&#039;ultima figura: “ Si M. Bo­<lb></lb>relli, egli dice, eùt fait reflexion que les puissances R et S n&#039;agissent pas <lb></lb>seulement contre le poids T, mais aussi l&#039;une contre l&#039;autre, et que de même <lb></lb>qu&#039;elles concourent ensemble pour empêcher que ce poids n&#039;attire a lui le <lb></lb>noeud C, de mème aussi chacune d&#039;elles concourt avec lui pour empècher <lb></lb>que l&#039;autre ne l&#039;emporte; si dis-je il avoit fait cette reflexion, il avroit vù <lb></lb>sans doute que chacune de ces puissances fait impression sur ce noeud, non <lb></lb>seulement suivant la direction du poids qu&#039;elles soutiennent pour le tenir <lb></lb>toùjours a mème hauteur, mais aussi suivant l&#039;horisontale MCN, pour em­<lb></lb>pècher qu&#039;aucune d&#039;elles ne l&#039;attire ni à droit ni à gauche. </s>

<s>D&#039;ou il avroit <lb></lb>infailliblement conclu que ces impressions horisontales étant diametralement <lb></lb>opposées doivent toùjours etre egales. </s>

<s>De-là voyant qu&#039;elles augmentent on <lb></lb>diminuent necessairement à mesure que les angles, que font les cordes de <lb></lb>ces puissances avec la ligne de direction du poids qu&#039;elles soutiennent, s&#039;ap­<lb></lb>prochent ou s&#039;eloignent de l&#039;angle droit; il avroit enfin apper<gap></gap>ù l&#039;impossibi­<lb></lb>lité de faire, si non aucun, du moins un tel changement a leurs directions, <lb></lb>sans en rompre l&#039;equilibre ” (ivi, pag. </s>

<s>477). </s></p><p type="main">

<s>Avrebbe anche di più conosciuto il Borelli, soggiungiamo noi, che mal<gap></gap><lb></lb>s&#039;applicava da Galileo l&#039;aforismo che dice dover le parti essere uguali al <lb></lb>tutto, e ch&#039;è un tale aforismo solamente vero, quando le parti stesse si pren­<lb></lb>dono tutte, e non diminuite come qui, con diminuzione misurata dalla linea <lb></lb>MC, o dalla CN sua eguale e contraria, la quale evidentemente riesce mag­<lb></lb>giore o minore, secondo che maggiore o minore è l&#039;angolo del concorso. </s>

<s><lb></lb>Questa osservazione, che sarebbe stata della maggiore importanza, perchè in­<lb></lb>somma tutte le fallacie in questo argomento derivavano dalla massima delle <lb></lb>fallacie, contenutasi nel secondo Teorema galileiano, e intorno a che si passò <lb></lb>il Varignon assai leggermente; questa osservazione, voleva dirsi, era stata <lb></lb>fatta assai tempo prima, che il Critico francese pubblicasse il suo opuscolo <lb></lb>sul Borelli, dal nostro piacentino Paolo Casati, il quale, a proposito del peso <lb></lb>sostenuto da due funi, pronunziava, in mezzo ai comuni errori, la salutare <lb></lb>sentenza, <emph type="italics"></emph>re autem ipsa quod ex iis componitur momentum, non ex ipso­<lb></lb>rum momentorum additione conflatur, sed ex ipsis temperatur.<emph.end type="italics"></emph.end> (<emph type="italics"></emph>Mechanic. </s>

<s><lb></lb>libri,<emph.end type="italics"></emph.end> Lugduni 1684, pag. </s>

<s>103). Sia A (fig. </s>

<s>373) il detto peso, e AB, AC le <lb></lb>due funi, che lo sostengono, e che supporremo essere di lunghezze uguali. </s>

<s><lb></lb>Abbassate da B, C, sulla orizontale DE le BD, CE perpendicolari, osserva il <lb></lb>Casati che, recisa la fune AC, il pendolo AB scenderebbe con momento pro­<lb></lb>porzionale ad AD, e similmente, con momento proporzionale ad AE scende­<lb></lb>rebbe il pendolo AC, venendogli a mancare la fune AB, che lo tien solle­<lb></lb>vato. </s>

<s>Si conducano le tangenti AR, AG, uguali alle DA, AE, immaginando <lb></lb>quelle sottoposte dall&#039;una e dall&#039;altra parte al globo, quasi piani inclinati <pb xlink:href="020/01/2964.jpg" pagenum="589"></pb>alle sue libere scese: “ ex quo fit corpus A, suspensum hac ratione, mo­<lb></lb>menta descendendi habere in diversas partes abeuntia AR, AG. </s>

<s>Perfecto igi­<lb></lb>tur parallelogrammo ARNG, ex duobus illis momentis temperatur momen­<lb></lb>tum AN ” (ibid., pag. </s>

<s>104). </s></p><p type="main">

<s>Ora essendo DA, AE i seni degli angoli delle inclinazioni DBA, ACE <lb></lb>delle funi, i quali si suppongono noti, s&#039;ha dalle Tavole trigonometriche AE, <lb></lb><figure id="id.020.01.2964.1.jpg" xlink:href="020/01/2964/1.jpg"></figure></s></p><p type="caption">

<s>Figura 373.<lb></lb>ossia AG, 81496, e DA, ossia AR, 37784; dai quali <lb></lb>numeri essendo rappresentati i momenti parziali, <lb></lb>verrà perciò la loro somma rappresentata da 119280. <lb></lb>Ma il triangolo ANG, in cui son noti i lati AG, <lb></lb>GN, e noto è altresì l&#039;angolo G da essi compreso, <lb></lb>perchè conoscesi l&#039;angolo RAG, e il suo opposto N, <lb></lb>che resultano ambedue dalla somma de&#039;comple­<lb></lb>menti degli angoli delle inclinazioni delle funi; può <lb></lb>risolversi rispetto al lato AN, diagonale del paralle­<lb></lb>logrammo, la quale trovasi 81613. “ Ex quibus <lb></lb>apparet (ne conclude il Casati da questo suo cal­<lb></lb>colo, che pare istituito apposta per dimostrar quanto fosse falso il teorema <lb></lb>di Galileo, e falsi i corollari che ne traeva il Borelli) descendendi momen­<lb></lb>tum, quod componitur ex momentis in planis inctinatis, non esse 119280 ex <lb></lb>corum summa, sed ita temperari, ut longe minus sit, videlicet solum 81613 ” <lb></lb>(ibid., pag. </s>

<s>105). </s></p><p type="main">

<s>Ma il Casati che, come gesuita, non apparteneva a nessuna nazione, e <lb></lb>che, come peripatetico, era inviso alla nuova Scuola, non ebbe co&#039;suoi in­<lb></lb>segnamenti nessuna efficacia in ridurre gli erranti sulla retta via; tanto è <lb></lb>vero che, quando il Vanni avventò contro Galileo quel suo <emph type="italics"></emph>Specimen<emph.end type="italics"></emph.end> famoso, <lb></lb>i Galieiani si trovarono impacciati nelle difese, le quali avrebbero potuto tro­<lb></lb>var paratissime nel primo degli otto libri Meccanici dell&#039;Autor piacentino. </s>

<s><lb></lb>Anzi noi preghiamo i nostri Lettori a voler tornare indietro sul capitolo IV <lb></lb>del nostro Tomo di storia, che precede a questo, dove là troveranno, in pro­<lb></lb>posito del rispondere al Vanni, descritto lo stato, in cui si trovava la Scienza <lb></lb>dei moti composti appresso i principali Matematici dell&#039;Europa, sul finir del <lb></lb>secolo XVII. </s>

<s>E ripensando alle cose lette, e a quelle che poi leggeranno nella <lb></lb>Storia dell&#039;Idraulica intorno ai trascorsi del Michelini, del Guglielmini e del <lb></lb>Grandi, in materie gravissime; comprenderanno quanto benefica riuscisse <lb></lb>l&#039;opera del Varignon, a cui veramente vi deve l&#039;aver, per la sua più man­<lb></lb>chevole parte, rinnovellata la Meccanica di Galileo. </s></p><p type="main">

<s>La Scienza, nella quale era stato per due secoli assoluto principe quel­<lb></lb>l&#039;Uomo, rimaneva per lui in difetto anche da due altre parti, quali erano <lb></lb>l&#039;analisi algebrica, e la dottrina dell&#039;infinito, da quella aborrendo, perchè <lb></lb>recideva i nervi dell&#039;eloquenza, e da questa, a quel che ci ha rivelato la sto­<lb></lb>ria, per non aver l&#039;animo e la mente disposti a penetrare addentro alle pro­<lb></lb>fonde speculazioni del Cavalieri. </s>

<s>N&#039;ebbero di que&#039;difetti a risentirsi natu­<lb></lb>ralmente i Discepoli, e specialmente del primo, che si trovaron costretti a <pb xlink:href="020/01/2965.jpg" pagenum="590"></pb>dover confessare, e a riconoscere che di gran lunga rimanevan per quel mo­<lb></lb>tivo superati dai loro emuli d&#039;oltremonte. </s>

<s>Il Cavalieri, avuta dal Rocca la so­<lb></lb>luzione algebrica di un problema, gli rispondeva: “ Mi sentii un prurito di <lb></lb>applicarmi per vedere se geometricamente si poteva sciogliere tal problema, <lb></lb>e mi ci applicai tanto più, che io le confesso ingenuamente che le opera­<lb></lb>zioni algebraiche non le ho troppo alle mani, non vi avendo fatto molto stu­<lb></lb>dio ” (<emph type="italics"></emph>Lettere a C. A. Rocca<emph.end type="italics"></emph.end> cit., pag. </s>

<s>188). E Michelangiolo Ricci si rac­<lb></lb>comandava al Marchetti, per l&#039;onore della Scienza italiana, che sopprimess<gap></gap><lb></lb>o ritirasse la stampa di que&#039;suoi sciagurati <emph type="italics"></emph>Problemata Sex,<emph.end type="italics"></emph.end> “ perchè vi è <lb></lb>molto che dire, e non vorrei che i Virtuosi oltramontani, dei quali assais­<lb></lb>simi hanno emulazione grande con gl&#039;Italiani, com&#039;ella sa, pigliassero mo­<lb></lb>tivo di biasimare, sì perchè nelle cose di V. S. ritroveranno che riprendere, <lb></lb>sì ancora in vedere che ella ne faccia tanto conto, con aver messo alle stampe <lb></lb>quelle soluzioni di problemi, i quali sono veramente difficili, ma essi, che <lb></lb>possiedono l&#039;Algebra, in un giorno e francamente gli risolverebbero, e però <lb></lb>meno gli stimano..... Frascati, 4 giugno 1675. ” (Nelli <emph type="italics"></emph>Saggio di storia <lb></lb>letter.,<emph.end type="italics"></emph.end> Lucca 1749, pag. </s>

<s>32). </s></p><p type="main">

<s>La mirabile facilità del metodo degli indivisibili, applicato a risolvere <lb></lb>problemi nuovi di Geometria, da tutti reputati difficilissimi, aveva nel Tor­<lb></lb>ricelli e nel Nardi fatte chiudere le orecchie a quelle arguzie eloquenti, con <lb></lb>le quali pretendeva Galileo di dimostrare che il metodo cavalierano condu­<lb></lb>ceva all&#039;assurdo di ragguagliare una circonferenza, grande quanto l&#039;orbe <lb></lb>magno, a un semplice punto. </s>

<s>Ma si trovarono que&#039;due Autori, e tutti gli <lb></lb>altri che ne avevano seguiti gli esempi, chiusa la via di progredire piu oltre, <lb></lb>non avendo saputo nemmen essi trattare le questioni geometriche con quel­<lb></lb>l&#039;analisi algebrica, senza la quale il metodo stesso non pigliava l&#039;agilità ne­<lb></lb>cessaria a sublimarsi, e a spaziare per le regioni dell&#039;infinito. </s></p><p type="main">

<s>È un fatto che Galileo, a cui pur tanto deve la Scienza del moto, le <lb></lb>aveva anche insieme recisi così i germi, da non poter aprirsi in rami no­<lb></lb>velli, costringendola a rimanersi perpetuamente nella statura di quell&#039;arbo­<lb></lb>scello, ch&#039;egli aveva educato ne&#039;Dialoghi delle due nuove Scienze. </s>

<s>O fosse <lb></lb>presunzione di voler col suo prescrivere i limiti all&#039;ingegno umano, o per­<lb></lb>suasione del non v&#039;essere altri mezzi, da quelli in fuori da sè usati in far <lb></lb>progredire la Meccanica; questa ebbe a rinnovellarsi, oltre a ciò che con­<lb></lb>cerne i moti composti, per altre due parti, per l&#039;uso cioè dell&#039;analisi alge­<lb></lb>brica e della infinitesimale. </s>

<s>E come fu quel primo rinnovellamento fatto dal <lb></lb>Varignon, questi altri due pure furono opera di Matematici stranieri, i quali <lb></lb>perciò tolsero, sul finir del secolo XVII, il principato di questa Scienza al­<lb></lb>l&#039;Italia. </s>

<s>Così vien tolto anche insieme di mano a noi l&#039;argomento di questa <lb></lb>Storia, alla quale non rimane oramai che di gettare uno sguardo sopra quella <lb></lb>superba mole, a cui i Nostri abbiam veduto come ponessero i fondamenti, e <lb></lb>per cui raccolsero la maggiore, e più eletta parte dei materiali. </s></p><pb xlink:href="020/01/2966.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO X.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dei progressi fatti dalla Meccanica nuova<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Dei <emph type="italics"></emph>Principii matematici di Filosofia naturale<emph.end type="italics"></emph.end> del Newton. </s>

<s>— II. </s>

<s>Della <emph type="italics"></emph>Foronomia<emph.end type="italics"></emph.end> dell&#039;Her­<lb></lb>mann. </s>

<s>— III. </s>

<s>Del parallelogrammo delle forze, e del Calcolo infinitesimale nella Meccanica <lb></lb>nuova. </s>

<s>— IV. </s>

<s>Della Meccanica analitica dell&#039;Euler, del D&#039;Alembert e del Lagrange. </s>

<s>— V. </s>

<s>Brevi <lb></lb>parole di conclusione. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Come, quando è nato un animale o una pianta, non si pensa più al­<lb></lb>l&#039;uovo o al seme, ma tutta la nostra ammirazione è rivolta all&#039;apparizione <lb></lb>di quella nuova gioventù di vita, che si manifesta nella varietà dei moti, e <lb></lb>nella sagacia degl&#039;istinti, o nella lussuria dei rami e nella ubertà dei fiori <lb></lb>e de&#039;frutti; così, tra lo scader del secolo XVII e il cominciar del seguente, <lb></lb>l&#039;ammirazione dei Matematici si rivolse tutta alla Meccanica nuova, non sem­<lb></lb>plicemente rinnovellata per quella agilità, che le aveva il Varignon infuso <lb></lb>nelle vecchie membra, ma per nuovi organi aggiunti, quasi ali sul dorso a <lb></lb>chi fin allora era andato col solo passo dei piedi. </s>

<s>La palingenesi maravigliosa <lb></lb>apparve nei <emph type="italics"></emph>Principii matematici di Filosofia naturale<emph.end type="italics"></emph.end> del Newton, intorno <lb></lb>ai quali però il tempo e l&#039;intento nostro non ci permetton di fare che una <lb></lb>brevissima storia. </s></p><p type="main">

<s>È noto che se ne fecero in Londra, vivente l&#039;Autore, tre edizioni: nel 1686, <lb></lb>nel 1713 e nel 1725 sempre con nuove aggiunte e con nuove correzioni, infin <lb></lb>tanto che l&#039;Opera non si rimase distinta in quei tre Tomi, i quali sono og­<lb></lb>gidì per le mani degli studiosi. </s>

<s>E perchè nel secondo Tomo si tratta delle <lb></lb>resistenze opposte al moto dai mezzi fluidi, e delle proprietà statiche e di­<lb></lb>namiche di essi fluidi, e nel terzo si mostra come si applichino particolar­<lb></lb>mente al circolar dei corpi celesti i teoremi di Meccanica astratta esposti nel <pb xlink:href="020/01/2967.jpg" pagenum="592"></pb>Tomo primo; al solo esame di questo dunque si limita il soggetto del no­<lb></lb>stro discorso. </s></p><p type="main">

<s>Il trattato è diviso in XIV sezioni, nelle quali tutto è nuovo. </s>

<s>La Mec­<lb></lb>canica antica sta compendiata in poche pagine a parte: e perchè non con­<lb></lb>tien per l&#039;Autore se non che principii comunemente ricevuti dai Matematici, <lb></lb>e confermati dalle esperienze; ei la raccoglie sotto il titolo di <emph type="italics"></emph>Assiomi,<emph.end type="italics"></emph.end> ossia <lb></lb><emph type="italics"></emph>Leggi del moto.<emph.end type="italics"></emph.end> La prima legge è quella che, dopo il Keplero, si chiamò <lb></lb><emph type="italics"></emph>d&#039;inerzia,<emph.end type="italics"></emph.end> e dalla quale dipende la seconda, che dice come le mutazioni son <lb></lb>proporzionali alle forze motrici impresse, e dirette per la linea, lungo la quale <lb></lb>fu fatta l&#039;impressione. </s>

<s>Ma la terza legge, che cioè, all&#039;azione, sempre uguale <lb></lb>e contraria è la reazione, è avuta dal Newton per cosa di maggiore impor­<lb></lb>tanza, e nello Scolio scritto dopo i corollari si trattiene a far vedere come <lb></lb>abbia quella terza legge, non solamente l&#039;applicazione alla teoria degli urti <lb></lb>e delle riflessioni, ma come altresì si riducano a lei le condizioni generali <lb></lb>dell&#039;equilibro tra la potenza e la resistenza in tutte le Macchine, l&#039;efficacia <lb></lb>delle quali, egli dice, non consiste in altro, che in aumentar la forza col <lb></lb>diminuire la velocità. </s>

<s>“ Unde solvitur, in omni aptorum instrumentorum <lb></lb>genere, problema: <emph type="italics"></emph>Datum pondus data vi movendi, aliamve datam resisten­<lb></lb>tiam vi data superandi.<emph.end type="italics"></emph.end> Nam si Machinae ita formentur, ut velocitates agen­<lb></lb>tis et resistentis sint reciproce ut vires, agens resistentiam sustinebit, et ma­<lb></lb>iori cum velocitatum disparitate eamdem vincit ” (Genevae 1739, pag. </s>

<s>59). </s></p><p type="main">

<s>Questo non era altro però che il principio antico professato da Galileo, <lb></lb>e che il Newton faceva derivar da un assioma troppo volgare, e non bene <lb></lb>confacentesi con la Scienza nuova, all&#039;altezza e alla dignità della quale fu <lb></lb>il primo che pensasse di ridurvelo Giovanni Bernoulli. </s>

<s>Questi inviava, sot­<lb></lb>toscritta nel dì 26 Gennaio 1717, una lettera al Varignon, nella quale inco­<lb></lb>mincia dal proporgli un nuovo modo per misurar l&#039;energia, valendosi di <lb></lb>quelle, ch&#039;egli incominciò allora a chiamare <emph type="italics"></emph>velocità virtuali.<emph.end type="italics"></emph.end> Sia P (fig. </s>

<s>374) <lb></lb>un punto qualunque, in un sistema di forze in equilibrio, ed F una di queste <lb></lb>forze, che spinga innanzi o ritiri in dietro, nella direzione FP, il detto punto. </s>

<s><lb></lb>Sopravvenendo un piccolissimo moto, la FP sarà trasportata in <emph type="italics"></emph>fp,<emph.end type="italics"></emph.end> mante­<lb></lb>nendosi questa sempre parallela a quella, se il sistema tutto insieme si muove <lb></lb>parallelamente a una linea data: o, prolungate le due direzioni, concorre­<lb></lb>ranno con un angolo infinitamente piccolo, se il moto del detto sistema si <lb></lb>facesse intorno ad un centro fisso. </s>

<s>“ Tirez donc (così propriamente scriveva <lb></lb>il Bernoulli al Varignon) PC perpendiculaire sur <emph type="italics"></emph>fp,<emph.end type="italics"></emph.end> et vous avrez C<emph type="italics"></emph>p<emph.end type="italics"></emph.end> pour <lb></lb>la <emph type="italics"></emph>vitesse virtuelle<emph.end type="italics"></emph.end> de la force F, en sorte que F. C<emph type="italics"></emph>p<emph.end type="italics"></emph.end> fait ce quoi j&#039;appelle <lb></lb><emph type="italics"></emph>energie. </s>

<s>”<emph.end type="italics"></emph.end> Osservate, soggiunge qui lo stesso Bernoulli, che la C<emph type="italics"></emph>p<emph.end type="italics"></emph.end> può es­<lb></lb>sere o <emph type="italics"></emph>positiva<emph.end type="italics"></emph.end> o <emph type="italics"></emph>negativa<emph.end type="italics"></emph.end> rispetto alle altre forze: Venendo il punto P <lb></lb>spinto innanzi è positiva, se l&#039;angolo FP<emph type="italics"></emph>p<emph.end type="italics"></emph.end> è ottuso, ed è negativa, se acuto. </s>

<s><lb></lb>Ma quando il punto fosse invece tirato indietro, C<emph type="italics"></emph>p<emph.end type="italics"></emph.end> è negativa, se l&#039;angolo è <lb></lb>ottuso, ed è positiva se acuto: ciò che facilmente si comprende dal pensar <lb></lb>che, con quelle contrarietà di segni, si vogliono dal Bernoulli distinguere i <lb></lb>moti, che al punto C tendono, da quelli che ne rifuggono. </s></p><pb xlink:href="020/01/2968.jpg" pagenum="593"></pb><p type="main">

<s>“ Tout cela etant bien entendu, je forme, dit M. Bernoulli, cette pro­<lb></lb>position generale: <emph type="italics"></emph>En tout equilibre de forces quelconque, en quelque ma­<lb></lb>niere qu&#039;elles soient appliquées, et suivant quelques directions qu&#039;elles agis-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.2968.1.jpg" xlink:href="020/01/2968/1.jpg"></figure></s></p><p type="caption">

<s>Figura 374.<lb></lb><emph type="italics"></emph>sent les unes sur les autres, ou mediatement, ou immediate­<lb></lb>ment; la somme des energies affirmatives sera egale à la <lb></lb>somme des energies negatives prises affirmativement ”<emph.end type="italics"></emph.end> (<emph type="italics"></emph>Nou­<lb></lb>velle Mecan.,<emph.end type="italics"></emph.end> T. cit., pag. </s>

<s>176). Questa proposizione mi parve, <lb></lb>dice il Varignon, così semplice e così bella, che, vedendo com&#039;ella <lb></lb>si poteva benissimo derivare dalla teoria dei moti composti, pen­<lb></lb>sai d&#039;introdurla nella mia Meccanica nuova, dimostrandola co&#039;miei <lb></lb>proprii principii applicati a ritrovar le condizioni dell&#039;equilibrio <lb></lb>nelle varie Macchine. </s>

<s>E così veramente egli fece nella Sezione IX, <lb></lb>soggiunta all&#039;opera, come generale corollario delle teorie prece­<lb></lb>denti, ed ebbe così la notizia del Teorema bernulliano la diffusion più de­<lb></lb>siderata, e la verità di lui la più solenne conferma. </s></p><p type="main">

<s>Ma di quella terza Legge del moto, per tornare al Newton, si fa dal­<lb></lb>l&#039;Autore apparir l&#039;importanza, che si diceva, in que&#039;sei corollari compren­<lb></lb>denti in sè tutte le leggi scoperte dalla Meccanica antica, inclusavi la stessa <lb></lb>riforma varignoniana. </s>

<s>Nel primo corollario infatti si propone la Regola del <lb></lb>parallelogrammo delle forze, e nel secondo, dop&#039;aver applicata quella regola <lb></lb>a dimostrar le condizioni dell&#039;equilibrio nella Libbra, nel Vette, nell&#039;Asse, e <lb></lb>nel Cuneo e nella Vite; ne conclude così, in poche parole, il fatto di quella <lb></lb><emph type="italics"></emph>Nouvelle mecanique,<emph.end type="italics"></emph.end> allora solamente proposta dall&#039;Accademico di Parigi: <lb></lb>“ Usus igitur Corollarii huius latissime patet, et late patendo veritatem eius <lb></lb>evincit, cum pendeat ex iam dictis Mechanica tota ab Auctoribus diversi­<lb></lb>mode domonstrata. </s>

<s>Ex hisce enim facile derivantur vires Machinarum quae, <lb></lb>ex rotis, tympanis, trochleis, vectibus, nervis tensis et ponderibus, directe vel <lb></lb>oblique ascendentibus, caeterisque potentiis mechanicis componi solent, ut et <lb></lb>vires tendinum ad animalium ossa movenda ” (pag. </s>

<s>30). </s></p><p type="main">

<s>Il terzo corollario, applicabile agli urti e alle riflessioni de&#039;corpi duri, <lb></lb>col ridurre in una le leggi dimostrate dal Borelli; poteva anche tacersi, senza <lb></lb>grave scapito della Scienza, dopo i teoremi del Wallis. </s>

<s>Ma il corollario IV <lb></lb>che segue apparve a tutti i Matematici nuovo, e anche i censori stessi lo <lb></lb>trovarono elegantissimo. </s>

<s>È dall&#039;Autore così proposto: “ Commune gravitatis <lb></lb>centrum corporum duorum vel plurium, ab actionibus corporum inter se, <lb></lb><figure id="id.020.01.2968.2.jpg" xlink:href="020/01/2968/2.jpg"></figure></s></p><p type="caption">

<s>Figura 375.<lb></lb>non mutat statum suum vel motus vel <lb></lb>quietis, et propterea corporum omnium <lb></lb>in se mutuo agentium, exclusis actioni­<lb></lb>bus et impedimentis externis, commune <lb></lb>centrum gravitatis vel quiescit, vel mo­<lb></lb>vetur uniformiter in directum ” (p. </s>

<s>36). <lb></lb>Ciò che si può spiegare così in poche parole: Sia C (fig. </s>

<s>375) il centro di <lb></lb>gravità dei corpi A, B: sostenuto il sistema in C, starà in quiete: abban­<lb></lb>donato a sè stesso, cadrà lungo la linea CD verticale. </s>

<s>E ciò sarà vero, an-<pb xlink:href="020/01/2969.jpg" pagenum="594"></pb>che quando i detti corpi si attraggano o si respingano a vicenda con eguale <lb></lb>quantità di moto, ossia in modo che i prodotti delle velocità per le masse, <lb></lb>di qua e di là, tornino uguali. </s>

<s>Se infatti AA′XA=BB′XB, è facile ve­<lb></lb>dere che il centro C della gravità non si muta. </s>

<s>Lo stesso dicasi, nel caso <lb></lb>che i corpi sian tre o più, componendo i loro centri di gravità nei so­<lb></lb>liti modi. </s></p><p type="main">

<s>Abbiamo accennato che questo Corollario del Newton ebbe censori, <lb></lb>fra quali s&#039;indovina facilmente dover essere Giovanni Bernoulli, che, pur non <lb></lb>mancando di riverenza verso il grande Matematico inglese, non poteva patire <lb></lb>che egli, e forse peggio i suoi, volessero tirare a sè tutto il merito de&#039;pro­<lb></lb>gressi, che veniva facendo la nuova Filosofia matematica. </s>

<s>Il Bernoulli dun­<lb></lb>que sentì che il Corollario neutoniano non si dimostrava dal suo Autore se­<lb></lb>condo quella generalità, con la quale era stato proposto. </s>

<s>E infatti non sembra <lb></lb>avesse il Newton in mente, quando lo formulò, che di farne l&#039;applicazione <lb></lb>alla proposizione LXV, e alle altre simili, delle quali intendeva poi valersi <lb></lb>nel Tomo terzo, per illustrare la teoria delle perturbazioni dei corpi celesti. </s>

<s><lb></lb>I Matematici invece si credettero a prima vista di avere avuto un Teorema <lb></lb>dinamico generale, e il Bernoulli ne scoprì sagacemente l&#039;inganno, facendo <lb></lb>osservare che <emph type="italics"></emph>etsi hoc Theorema, elegantissimum quidem, in generali sensu <lb></lb>sit propositum, demonstratio tamen Newtoni minime est generalis.<emph.end type="italics"></emph.end> E ciò <lb></lb>perchè, prosegue a dire, in quel suo lungo discorso non si contempla altro <lb></lb>caso che quello, in cui i corpi concorrano a due a due, o due o più insieme <lb></lb>combinati con un terzo, ma non si mette mai in considerazione il caso, che <lb></lb>tre o più corpi si sospingano a vicenda in varie direzioni, tutti a una volta, <lb></lb>e nel medesimo istante, <emph type="italics"></emph>cuius casus neglectio, relinquit sane demonstra­<lb></lb>tionem Newtoni longe imperfectissimam, quae vix periculum praestat eius <lb></lb>quod promittitur in propositione generali.<emph.end type="italics"></emph.end> Per supplire al qual difetto, sog­<lb></lb>giunge, è da tenere altra via, la quale è quella che mi ha menato a formu­<lb></lb>lare e a dimostrar questo, che è veramente generale Teorema, da sostituirsi <lb></lb><figure id="id.020.01.2969.1.jpg" xlink:href="020/01/2969/1.jpg"></figure></s></p><p type="caption">

<s>Figura 376.<lb></lb>all&#039;altro annunziato dal Newton in quel suo Corol­<lb></lb>lario quarto: <emph type="italics"></emph>Si dati corporis ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>376) <emph type="italics"></emph>cen­<lb></lb>trum gravitatis Q sollicitatur a pluribus potentiis, <lb></lb>seu viribus motricibus, quarum directiones et quan­<lb></lb>titates designentur per rectas datas OD, OE, OF, <lb></lb>OG etc, sitque punctum P centrum commune gra­<lb></lb>vitatis punctorum D, E, F, G, instar ponderum <lb></lb>aequalium consideratorum; dico rectam OP fore <lb></lb>directionem, secundum quam movebitur centrum gravitatis O corporis <lb></lb>ABC, et quidem motu sibi semper parallelo, sive accedendo versus P, <lb></lb>sive ab eodem recedendo, prout vires motrices sunt vel trahentes vel pel­<lb></lb>lentes<emph.end type="italics"></emph.end> (Op. </s>

<s>omnia, T. cit., pag. </s>

<s>341). </s></p><p type="main">

<s>Il Leibniz poi aveva reso anche più perfetto il bellissimo Teorema, sog­<lb></lb>giungendo che la resultante del moto, non solamente è diretta lungo la OP, <lb></lb>ma è altresì misurata dalla OP stessa, presa molteplice secondo il numero <pb xlink:href="020/01/2970.jpg" pagenum="595"></pb>de&#039;punti gravi, de&#039;quali P sia, com&#039;è detto, nel centro. </s>

<s>Dette esso Leibniz, <lb></lb>in una epistola al Wallis, l&#039;annunzio della invenzione, senza però dimostrarla, <lb></lb>ma non indugiarono molto gli studiosi ad aver la desiderata dimostrazione <lb></lb>dall&#039;Hermann, il quale anzi promosse la cosa tant&#039;oltre, da riuscire a tro­<lb></lb>var la ragione ultima dell&#039;uguagliarsi insieme i momenti nella Libbra ar­<lb></lb>chimedea: nè vogliam qui tacerne ai nostri Lettori il modo, riferendosi stret­<lb></lb>tamente alla storia del Corollario neutoniano, da cui insomma ebbero que­<lb></lb>ste alte speculazioni il principio. </s></p><p type="main">

<s>Esposto in brevi, ma chiarissime parole, e in pochi segni il Teorema <lb></lb>del Leibniz, si propone l&#039;Hermann a risolvere un tal problema: <emph type="italics"></emph>Invenire <lb></lb>mediam directionem solicitationum quarumvis AG, BG, CG, DG<emph.end type="italics"></emph.end> (fig. </s>

<s>377) <lb></lb><emph type="italics"></emph>quibus puncta A, B, C, D lineae rectae inflexilis AD urgentur<emph.end type="italics"></emph.end> (Forono­<lb></lb><figure id="id.020.01.2970.1.jpg" xlink:href="020/01/2970/1.jpg"></figure></s></p><p type="caption">

<s>Figura 377.<lb></lb>mia cit,, pag. </s>

<s>18), e la pratica, della <lb></lb>quale passa poi a dimostrar la ra­<lb></lb>gione e la verità, è così comandata. </s>

<s><lb></lb>Prendete fuori della verga rigida un <lb></lb>centro qualunque O, da cui irrag­<lb></lb>gino, passando per A, B, C, D ... <lb></lb>altrettante linee prefinite, ne&#039;punti <lb></lb>omonomi F, dalle respettive linee <lb></lb>GF, condotte, dalle estremità G delle <lb></lb>potenze, parallele alla direzione AD <lb></lb>della verga. </s>

<s>Fate gl&#039;intervali OA′, <lb></lb>OB′, OC′, OD′ ... uguali ad AF, <lb></lb>BF, CF, DF, e, de&#039;punti A′, B′, C′, <lb></lb>D′ ... essendo baricentro E′, per <lb></lb>questo punto e per O fate passare <lb></lb>una linea, che prolungata attraversi <lb></lb>in E la verga stessa, d&#039;onde la pro­<lb></lb>lungherete ancora, in fin tanto che <lb></lb>non vada EM lunga quanto OE′, <lb></lb>presa molteplice secondo il numero <lb></lb>de&#039;punti A′, B′, C′, D′ ... All&#039;ul­<lb></lb>timo, condotta la ML parallela ad <lb></lb>AD, e presa di tal lunghezza tanto <lb></lb>che valga quanto tutte insieme le FG, congiungete i punti L, E, e avrete <lb></lb>nella LE, non solamente la direzione, ma anche la misura della resultante <lb></lb>unica delle varie potenze applicate a sollecitare il sistema, di cui dunque E <lb></lb>sarà il centro, intorno al quale o si moverà o permarrà in equilibrio. </s></p><p type="main">

<s>Rispetto a questo centro dell&#039;equilibrio avverte l&#039;Herman una certa pro­<lb></lb>prietà, per farne nel corollario secondo un&#039;applicazione importante, ed è che, <lb></lb>abbassate dai punti A, B, C, D ... le AH, BH, CH. DH ... perpendicolari <lb></lb>sui prolungamenti delle FG, i rettangoli fatti da queste perpendicolari, e dalle <lb></lb>respettive distanze dal centro E da una parte, sommati insieme, sono uguali <pb xlink:href="020/01/2971.jpg" pagenum="596"></pb>alla somma dei rettangoli, che in modo simile si facesser dall&#039;altra: cioè <lb></lb>AH.AE+BH.BE=DH.DE+CH.CE. </s></p><p type="main">

<s>L&#039;applicazione importante che si diceva è al vette sollecitato dalle po­<lb></lb>tenze oblique AG, BG; DG, CG (fig. </s>

<s>378), intorno al centro E dell&#039;equili­<lb></lb>brio, da cui conducendosi sui prolungamenti delle linee rappresentanti esse <lb></lb>potenze le perpendicolari EP, <expan abbr="Eq;">Eque</expan> ES, ER, i triangoli simili, che per que­<lb></lb>sta costruzione vengono a disegnarsi, danno i rettangoli AH.AE, BH.BE, <lb></lb>DH.DE, CH.CE rispettivamente uguali ai rettangoli AG.EP, BG.EQ, <lb></lb>DG.ES, CG.ER. </s>

<s>Ma AG.EP+BG.EQ è, per le cose dimostrate, uguale <lb></lb>a DG.ES+CG.ER; dunque AH.AE+BH.BE=DH.DE+CH.CE, <lb></lb>ossia, per le condizioni dell&#039;equilibrio, la somma dei momenti, che solleci­<lb></lb>tano il vette da una parte, deve essere uguale alla somma dei momenti, che <lb></lb>lo sollecitano dall&#039;altra. </s>

<s>E ciò concluso, soggiunge l&#039;Herman questo che, per <lb></lb>la storia del quarto Corollario del Newton, è notabilissimo Scolio: “ Casus <lb></lb>Corollarii huius secundi obtinet non solum tunc cum linea AD est recta, cui <lb></lb><figure id="id.020.01.2971.1.jpg" xlink:href="020/01/2971/1.jpg"></figure></s></p><p type="caption">

<s>Figura 378.<lb></lb>potentiae obliquae AG, BG ... <lb></lb>applicantur, sed etiam in casu, <lb></lb>quo ipsa linea applicatas poten­<lb></lb>tias habens est curva, immo e­<lb></lb>tiam in rotis aliisque eiusmodi <lb></lb>organis. </s>

<s>Uno verbo <emph type="italics"></emph>si circa ali­<lb></lb>quod punctum potentiae aut <lb></lb>solicitationes quaecumque in ae­<lb></lb>guilibrio sunt; momenta potentiarum, quae agunt in unam partem, aequa­<lb></lb>lia sunt momentis potentiarum, quae agunt in partem oppositam,<emph.end type="italics"></emph.end> atque <lb></lb>sic inopinato incidimus in demonstrationem directam et immediatam prin­<lb></lb>cipii Archimedei de aequalitate momentorum, in casu aequilibrii potentia­<lb></lb>rum inter se commissarum, quod varii varie demonstrare conati sunt ” (Fo­<lb></lb>ron. </s>

<s>cit., pag. </s>

<s>21). </s></p><p type="main">

<s>Al quarto Corollario che l&#039;Herman, il Leibniz e il Bernoulli promossero <lb></lb>così com&#039;abbiamo veduto, ne fa seguitare il Newton altri due d&#039;assai minore <lb></lb>importanza, dopo i quali riassume il suo discorso in uno Scolio, e che co­<lb></lb>mincia: “ Hactenus principia tradidi a Mathematicis recepta et experientia <lb></lb>multiplici confirmata. </s>

<s>Per leges duas primas et corollaria duo prima Gali­<lb></lb>leus invenit descensum gravium esse in duplicata ratione temporis, et mo­<lb></lb>tum proiectorum fieri in parabola ” (pag. </s>

<s>45, 46), che sono gli argomenti <lb></lb>trattati nel terzo e nel quarto Dialogo delle due nuove Scienze, ritirati qui <lb></lb>a piè della nuova Filosofia matematica, quasi soggetta valle disegnata nel <lb></lb>quadro, perchè possa l&#039;occhio misurare la superba altura del monte. </s>

<s>E per­<lb></lb>chè non si può aver la misura giusta del fastigio, senza ricercarne il prin­<lb></lb>cipio e la radice, premettiamo queste considerazioni. </s></p><p type="main">

<s>Due massimi problemi, su quella via per la quale s&#039;erano messi i suoi <lb></lb>nuovi studi, ebbe a trovare il Newton irresoluti: il primo de&#039;quali era per­<lb></lb>chè i pianeti circondassero il Sole, e i satelliti Giove, in orbite ellittiche, e <pb xlink:href="020/01/2972.jpg" pagenum="597"></pb>il secondo, in cui si domandava quale curvità di linea descriverebbe un pro­<lb></lb>ietto, che a movere dalla superficie andasse finalmente a quetar nel centro <lb></lb>della Terra. </s></p><p type="main">

<s>Benchè commenti indegni della Scienza gli dovessero sembrar le ragioni <lb></lb>del Keplero, e le opinioni del Boulliaud e del Borelli cose molto somiglianti <lb></lb>ai romanzi, nonostante il Newton non aveva ancora trovato nulla di meglio, <lb></lb>per risolvere il primo dei detti problemi, quando gli si rivelò, dalle specu­<lb></lb>lazioni del Wren, dell&#039;Hook e dell&#039;Halley intorno alle forze centrali, che il <lb></lb>Sole attrae i pianeti e Giove i satelliti con forze, che diminuiscono, non col <lb></lb>crescere delle semplici distanze, ma de&#039;quadrati delle distanze dal centro <lb></lb>dell&#039;attrazione. </s>

<s>Allora, come emendò, e trovò che tornava bene il calcolo <lb></lb>della velocità, con cui sarebbe caduta sulla Terra la Luna; così pensò che, <lb></lb>del non aver saputo gli Astronomi suoi precursori render la ragione geome­<lb></lb>trica dell&#039;eccentricità delle orbite, fosse stata potissima causa l&#039;ignorar la <lb></lb>vera legge del variar le forze centripete, rispetto al variare delle distanze. </s>

<s><lb></lb>Ond&#039;è che, mettendosi a cercare in qual curva si volgerebbe un proietto, il <lb></lb>quale fosse continuamente ritirato verso un punto, con forze reciprocamente <lb></lb>proporzionali ai quadrati delle distanze; trovò con ineffabile compiacenza che <lb></lb>quella curva era un&#039;ellisse, in un foco della quale risedesse il centro del­<lb></lb>l&#039;attrazione. </s>

<s>Contrariamente, dato che un corpo vada in giro per un&#039;ellisse, <lb></lb>attratto continuamente a uno de&#039;fochi; trovò che le forze centripete erano <lb></lb>reciprocamente proporzionali ai quadrati delle distanze. </s></p><p type="main">

<s>Intorno al secondo problema sopra notato i Matematici, a&#039;tempi del <lb></lb>Newton, erano molto discordi. </s>

<s>Galileo, prima di aver veduto lo <emph type="italics"></emph>Specchio <lb></lb>ustorio<emph.end type="italics"></emph.end> del Cavalieri, credè verosimile che un grave cadente dall&#039;alto di una <lb></lb>torre, menata in giro dalla vertigine della Terra, giungerebbe al centro di <lb></lb>lei per una mezza circonferenza. </s>

<s>Poi non dubitò di asserire che, almeno per <lb></lb>qualche tratto, quel moto composto del retto accelerato e del circolare equa­<lb></lb>bile si farebbe per una parabola, ma il Fermat pretese di dimostrare che, <lb></lb>non potendo esser parabolica una linea, la quale ritorna all&#039;asse, da cui si <lb></lb>era partita; era invece una spirale, non difforme da quella di Archimede. </s>

<s><lb></lb>Il Borelli, nella proposizione LVII <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> sentenziò che tutte e <lb></lb>tre queste opinioni erano false. </s>

<s>Falsa quella prima di Galileo, perchè le scese <lb></lb>starebbero come i seni versi delle metà degli archi passati, e perciò in pro­<lb></lb>porzione assai minore di quella dei quadrati dei tempi: falsa anche la se­<lb></lb>conda dello stesso Galileo, e incompetente nella questione, non potendo evi­<lb></lb>dentemente esser parabolica una curva, che ritorna in sè stessa. </s>

<s>Ma falsa <lb></lb>concludeva all&#039;ultimo essere anche l&#039;opinione del Fermat, il quale, egli dice, <lb></lb>s&#039;ingannò a credere che, col medesimo impeto trasversale, il mobile in tempi <lb></lb>uguali percorra spazi sottendenti al centro angoli uguali. </s>

<s>Or perchè è un <lb></lb>fatto che quegli crescono successivamente, secondo che diminuiscono via via <lb></lb>le distanze da esso centro, <emph type="italics"></emph>constat curvam lineam non esse regularem.<emph.end type="italics"></emph.end> (Bo­<lb></lb>noniae 1667, pag. </s>

<s>109). </s></p><p type="main">

<s>Il Newton senti che il Borelli da una parte aveva ragione, stando egli <pb xlink:href="020/01/2973.jpg" pagenum="598"></pb>nell&#039;ipotesi comune della gravità, che sollecita il mobile con impulso uni­<lb></lb>forme, ma sentì dall&#039;altra che non si decideva nulla in proposito, non es­<lb></lb>sendo verosimile che il cadente venga attratto, come supponevasi da Galileo, <lb></lb>dal Fermat e dallo stesso Borelli, sempre con la medesima forza, a qualun­<lb></lb>que distanza dal centro. </s>

<s>E perchè non aveva forse pensato ancora ad asse­<lb></lb>gnar la legge naturale di quelle forze, per sciogliere direttamente il problema; <lb></lb>si limitò a darne una soluzione indiretta: <emph type="italics"></emph>Gyretur corpus in spirali secante <lb></lb>radios omnes in angulo dato: requiritur lex vis centripetae tendentis ad <lb></lb>centrum spiralis<emph.end type="italics"></emph.end> (pag. </s>

<s>136), e il frutto della ricerca fu che le forze centri­<lb></lb>pete debbono esser reciprocamente proporzionali ai cubi delle distanze. </s></p><p type="main">

<s>Poi la detta legge naturale la desunse immaginando un grave, che giri <lb></lb>in orbite circolari o ellittiche, ora più lontane, ora più vicine al centro, da <lb></lb>cui venga attratto, e trovò che la legge dell&#039;attrazione in questo caso era <lb></lb>quella diretta delle distanze. </s>

<s>Conseguiva di qui che, trasformandosi l&#039;ellisse <lb></lb>in parabola, coll&#039;andare il centro infinitamente distante dal vertice della nuova <lb></lb>sezione; le forze centripete, che tutte hanno verso l&#039;infinito la medesima <lb></lb>proporzione, divengono uniformi, e così la presente questione ricade in quella <lb></lb>particolare di Galileo intorno ai proietti. </s>

<s>“ Si ellipsis, centro in infinitum <lb></lb>abeunte, vertatur in parabolam, corpus movebitur in hac parabola, et vis, ad <lb></lb>centrum infinite distans iam tendens, evadet aequabilis. </s>

<s>Hoc est theorema <lb></lb>Galilei ” (pag. </s>

<s>149). Dunque, nell&#039;ipotesi della gravità uniforme, la pietra <lb></lb>che cade dall&#039;alta torre viene attratta a un punto, che è a una distanza infi­<lb></lb>nita, e che perciò non può essere il centro della Terra: ond&#039;è chiaro che <lb></lb>la detta pietra descriverà una parabola, non per un tratto solo, come pensò <lb></lb>Galileo, ma per tutto il suo viaggio, che dovrebbe proseguire in infinito. </s></p><p type="main">

<s>Traspariva da queste speculazioni che, nella Dinamica galileiana, si <lb></lb>contemplava il solo caso particolare, in cui i corpi son continuamente sol­<lb></lb>lecitati da impulsi di gravità sempre uguali, e sentì perciò il Newton che <lb></lb>la Scienza, com&#039;ei l&#039;aveva trovata, era tuttavia ne&#039;suoi principii, e che ri­<lb></lb>maneva a promoverla in assai più vasto e più nobile campo, dimostrando le <lb></lb>leggi universalissime de&#039;moti, nel caso che gl&#039;impulsi gravitativi, ossia le <lb></lb>forze centripete, variassero ora secondo le semplici distanze, ora secondo i <lb></lb>quadrati delle distanze, ora secondo qualsiasi proporzione. </s>

<s>Ecco l&#039;indole della <lb></lb>nuova Dinamica neutoniana, della quale tutte le cose scoperte, e tutti i teo­<lb></lb>remi dimostrati dai Matematici, che avevano preceduto l&#039;Autore infino a Ga­<lb></lb>lileo e all&#039;Huyghens; non sarebbero stati più che semplici corollari: ecco il <lb></lb>compasso da misurar giusta l&#039;estensione e la sublimità, a cui giunse la <lb></lb>Scienza del moto nei <emph type="italics"></emph>Principii matematici di Filosofia naturale.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Se l&#039;uno di que&#039;due massimi problemi, da&#039;quali si diceva aver avuto <lb></lb>questa nuova Filosofia gli inizii, dette occasione al Newton di ritrovar le <lb></lb>leggi delle forze centripete, nel corpo che gira in una spirale, in un&#039;ellisse, <lb></lb>in una parabola, d&#039;onde si veniva a definir la linea descritta dal cadente, <lb></lb>che non arrestasse il moto sulla superficie terrestre; l&#039;altro dei detti pro­<lb></lb>blemi porgeva allo stesso Autore un argomento d&#039;assai maggiore importanza, <pb xlink:href="020/01/2974.jpg" pagenum="599"></pb>qual&#039;è il trattato del moto dei corpi nelle sezioni coniche eccentriche. </s>

<s>E fu <lb></lb>appunto per questa importanza che v&#039;intrattenne intorno il Newton più dif­<lb></lb>fusamente il discorso, com&#039;egli stesso dice, ripensando a quel sesto corolla­<lb></lb>rio della proposizione IV, in cui era stato concluso che, essendo i tempi pe­<lb></lb>riodici nelle ellissi proporzionali ai cubi dei grandi assi, le forze centripete <lb></lb>son reciprocamente proporzionali ai quadrati dei raggi vettori: “ Casus co­<lb></lb>rollarii sexti obtinet in corporibus coelestibus, ut seorsum collegerunt etiam <lb></lb>nostrates Wrennus, Hockius et Hallaeus, et propterea quae spectant ad vim <lb></lb>centripetam decrescentem in duplicata ratione distantiarum a centris, decrevi <lb></lb>fusius in sequentibus exponere ” (pag. </s>

<s>103): che è l&#039;argomento sopra accen­<lb></lb>nato, e che sì svolge ne&#039;teoremi della terza sezione. </s></p><p type="main">

<s>Piglia dunque motivo questo argomento dalle tre celebri leggi del Ke­<lb></lb>plero, astraendo dalle particolari osservazioni dei corpi celesti, e considerando <lb></lb>il moto di un semplice punto fisico o materiale, continuamente sollecitato da <lb></lb>forze centripete, che diminuiscono d&#039;intensità col crescere dei quadrati delle <lb></lb>distanze. </s>

<s>Alla nuova Dinamica razionale preluceva nei fatti naturali osser­<lb></lb>vati la notizia certa delle conclusioni, ma rimaneva al Newton a ritrovarne <lb></lb>i principii. </s>

<s>E perchè in que&#039;fatti era una intima dipendenza di ragioni fra <lb></lb>i tempi periodici, e le linee delle orbite, e le forze attrattive, cosicchè l&#039;una <lb></lb>poteva indifferentemente prendersi per principio, da cui conseguissero le <lb></lb>altre; pose esso Newton per fondamento al suo trattato l&#039;osservazione fatta <lb></lb>dal Keplero intorno ai pianeti, che cioè le aree son proporzionali ai tempi, <lb></lb>riducendola a dimostrarsi matematicamente in quel teorema, che è il primo <lb></lb>e principale della Sezione seconda, e da cui si svolgono tutte le altre pro­<lb></lb>posizioni relative alle forze centripete, che sollecitano i corpi, mentre girano <lb></lb>intorno ai centri di una spirale, e delle varie sezioni di un cono. </s></p><p type="main">

<s>La Sezione terza, come si disse, è propriamente quella, in cui si tratta <lb></lb>astrattamente del moto di qualunque corpo, supposto ch&#039;egli pesi verso un <lb></lb>dato punto, come i pianeti verso il Sole, e i satelliti verso Giove: e dop&#039;aver <lb></lb>dimostrate le proporzioni di quel peso, nel moversi ora in una, ora in un&#039;altra <lb></lb>delle sezioni coniche eccentriche, passa a propor la soluzione di questo mas­<lb></lb>simo problema: “ Posito quod vis centripeta sit reciproce proportionalis qua­<lb></lb>drato distantiae locorum a centro, et quod vis illius quantitas absoluta sit <lb></lb>cognita; requiritur linea, quam corpus describit de loco dato, cum data ve­<lb></lb>locitate, secundum datam rectam egrediens ” (pag. </s>

<s>170). </s></p><p type="main">

<s>Esca il corpo P (fig. </s>

<s>379) con la velocità data, secondo la tangente PR, <lb></lb>e subito sia costretto dalla forza centripeta, diretta verso il punto S, a de­<lb></lb>scrivere la curva PQ, che per le cose dimostrate appartien senza dubbio a <lb></lb>una sezione conica, avente in S uno de&#039;fochi, e della quale si vuol determi­<lb></lb>nare la specie. </s>

<s>Facciasi RPH complementare dell&#039;angolo RPS a due angoli <lb></lb>retti: sopra un punto della PH si dovrà trovare l&#039;altro foco della sezione, <lb></lb>che supponesi essere H. </s>

<s>Congiunti S e H, e dal vertice S del triangolo che <lb></lb>indi nasce condotta la SK, perpendicolare sul lato opposto PH, e chiamato L <lb></lb>il lato retto, ossia il parametro della curva, a qualunque sezion del cono ella <pb xlink:href="020/01/2975.jpg" pagenum="600"></pb>appartenga; riesce il Newton, calcolando, all&#039;equazione L (SP+PH)= <lb></lb>PH (2SP+2KP), d&#039;onde L:2SP+2KP=PH:SP+PH. </s>

<s>Ora può <lb></lb>darsi il caso che il corpo esca con tal impeto tangenziale da far sì che L, <lb></lb>ossia il parametro, manchi, uguagli o superi il doppio della somma SP+KP, <lb></lb>nel qual caso anche PH mancherà, uguaglierà o supererà SP+PH: cioè <lb></lb>la linea SP sarà o positiva o nulla o negativa, e secondo che questo o quello <lb></lb>o quell&#039;altro caso avviene, la sezione conica dell&#039;orbita sarà o un&#039;ellisse o <lb></lb>una parabola o una iperbola. </s>

<s>“ Si ea sit corporis in P velocitas, ut latus <lb></lb>rectum L minus fuerit quam 2SP+2KP, iacebit PH ad eamdem partem <lb></lb><figure id="id.020.01.2975.1.jpg" xlink:href="020/01/2975/1.jpg"></figure></s></p><p type="caption">

<s>Figura 379.<lb></lb>tangentis PR cum linea PS, ideoque <lb></lb>figura erit ellipsis, et, ex datis umbilicis <lb></lb>S, H et axe principali SP+PH, da­<lb></lb>bitur. </s>

<s>Sin tanta sit corporis velocitas, ut <lb></lb>latus rectum L aequale fuerit 2SP+ <lb></lb>2KP, longitudo PH infinita erit, et prop­<lb></lb>terea figura erit parabola, axem habens <lb></lb>GH parallelum lineae PK, et inde dabi­<lb></lb>tur. </s>

<s>Quod si corpus maiori adhuc cum <lb></lb>velocitate de loco suo P exeat, capienda erit longitudo PH ad alteram par­<lb></lb>tem tangentis, ideoque, tangente inter umbilicos pergente, figura erit hyper­<lb></lb>bola, axem habens principalem aequalem differentiae linearum SP et PH, et <lb></lb>inde dabitur ” (pag. </s>

<s>172, 73). </s></p><p type="main">

<s>Applicato questo Teorema alla Meccanica celeste, non solamente confer­<lb></lb>mava la ragion geometrica della orbite ellittiche, in cui si rivolgono i satelliti <lb></lb>e i pianeti, ma rivelava inoltre il mistero di altri corpi celesti, come delle <lb></lb>Comete, le quali, avendo ricevuto il primo impulso tangenziale più forte dei <lb></lb>satelliti detti e de&#039;pianeti, descriverebbero parabole: ed, essendo quell&#039;im­<lb></lb>pulso anche più forte, iperbole; cosicchè vedute una volta in cielo non appa­<lb></lb>rirebbero mai più ad occhio mortale. </s></p><p type="main">

<s>La sublimità del pensiero destò in tutti la maraviglia, ed in alcuni po­<lb></lb>chi uno spirito d&#039;emulazione, da cui furono stimolati a dire che non aveva <lb></lb>il Newton dimostrato bene come il corpo, uscito con quell&#039;impeto tangen­<lb></lb>ziale, e con quella legge d&#039;attrazione al centro, non potesse moversi in altra <lb></lb>curva diversa da una sezione del cono. </s>

<s>Fu perciò che Giov. </s>

<s>Bernoulli e il <lb></lb>Leibniz e il Varignon vollero tentare il problema inverso, ricercando cioè in <lb></lb>qual curva s&#039;avvierebbe un proietto, con un dato impulso tangenziale, e at­<lb></lb>tratto a un centro fisso in reciproca ragione dei quadrati delle distanze. </s>

<s><lb></lb>L&#039;Euler si maravigliò di queste censure, quasi non resultasse ad evidenza, <lb></lb>da quella XVII proposizion neutoniana, nessun altra curva, da una sezione <lb></lb>conica in fuori, poter sodisfare al quesito, e si compiaceva di aver nel primo <lb></lb>tomo della sua <emph type="italics"></emph>Mechanica analitice exposita<emph.end type="italics"></emph.end> data della cosa tal risoluzione, <lb></lb>“ qua Newtoni assertio extra dubium ponitur ” (Petropoli 1746, pag. </s>

<s>271). <lb></lb>Ma era quella risoluzione stata data alquanto prima dall&#039;Herman, il quale, <lb></lb>proponendosi <emph type="italics"></emph>invenire canonem generalem determinandae gravitatis va-<emph.end type="italics"></emph.end><pb xlink:href="020/01/2976.jpg" pagenum="601"></pb><emph type="italics"></emph>riabilis seu leges solicitationum centralium pro omnibus curvis algebraicis <lb></lb>in infinitum, quantitatibus finitis expressum<emph.end type="italics"></emph.end> (Foron. </s>

<s>cit., pag. </s>

<s>74); osserva <lb></lb>poi in uno Scolio che, se la legge delle dette sollecitazioni è la reciproca dei <lb></lb>quadrati delle distanze, l&#039;equazion generale della curva algebrica è propria­<lb></lb>mente quella, che si riferisce alle Sezioni del cono, concludendo così il suo <lb></lb>discorso “ Ergo in hac hypothesi centrum virium, seu solicitationum gravi­<lb></lb>tatis, sunt umbilici Sectionum conicarum, quod iam omnibus constat egre­<lb></lb>gie conspirare cum iis, quae demonstrata sunt ab illustr. </s>

<s>Newtono, Leibni­<lb></lb>tio, Varignonio ed aliis, circa vires, quas vocant centripetas, in Sectionibus <lb></lb>conicis methodis directis ” (ibid., pag. </s>

<s>79). </s></p><p type="main">

<s>Tre sono le ipotesi in tal proposito, alle quali rispondono i fatti che si <lb></lb>osservano, o che si sperimentano nella Natura: quella delle sollecitazioni <lb></lb>della gravità sempre uguali ne&#039;cadenti sulla superficie terrestre, e quella <lb></lb>delle sollecitazioni della gravità, che variano in ragion diretta delle semplici <lb></lb>distanze, e in reciproca de&#039;quadrati delle distanze, come s&#039;argomenta de&#039;corpi <lb></lb>tendenti al centro della Terra, sotto la sua superficie, e si osserva de&#039;Pia­<lb></lb>neti attratti al centro del Sole. </s>

<s>S&#039;arresta forse qui ne&#039;primi termini la pro­<lb></lb>gressione, e ne&#039;primi gradi è rotta la foga dell&#039;ascesa: o ripensando alla <lb></lb>instancabile operosità, e alla onnipotenza della somma Virtù creativa, si cre­<lb></lb>derebbe piuttosto che fosse il Sole anch&#039;egli un pianeta, attratto a un centro <lb></lb>da forze decrescenti via via coll&#039;aumentar de&#039;cubi delle distanze, e che que­<lb></lb>sto centro, a cui move il Sole, tenda a moversi anch&#039;egli alla sua volta a <lb></lb>un altro centro più lontano, che con tanto più debole forza l&#039;attragga, quanto <lb></lb>secondo i quadrato quadrati n&#039;è cresciuta la lontananza? </s>

<s>Chi potrebbe im­<lb></lb>por limite a questo ingradarsi sempre più in alto gli ordinamenti del Cosmo, <lb></lb>innanzi alla pensata immensità del quale sentendosi rintuzzare il filosofico <lb></lb>orgoglio dell&#039;uomo, par che volesse prepotentemente reagire nel Newton, <lb></lb>quando si propose l&#039;invenzion dell&#039;orbite, nelle quali si rivolgerebbero i corpi <lb></lb>sollecitati da forze centripete, secondo qualunque ragione operanti. </s>

<s>“ Posita <lb></lb>cuiuscumque generis vi centripeta, et concessis figurarum curvilinearum qua­<lb></lb>draturis, requiruntur tum traiectoriae, in quibus corpora movebuntur, tum <lb></lb>tempora motuum in traiectoriis inventis ” (pag. </s>

<s>318). Così era risalito il <lb></lb>Newton, con l&#039;ala del suo proprio ingegno, a descriver le vie, che percor­<lb></lb>rerebbero nello spazio immenso gl&#039;incogniti mondi, usciti dalla mano del <lb></lb>Creatore con qualunque forza gli fosse piaciuto di sollevare, nel gettarli, il <lb></lb>suo braccio; mentre Galileo erasi rimasto nel suo quarto Dialogo a inse­<lb></lb>gnare ai militari il modo di dirigere i tiri delle bombarde, per distrugger <lb></lb>queste povere nostre figuline! </s></p><p type="main">

<s>A pari sublime altezza promoveva il Newton la scienza del terzo dia­<lb></lb>logo galileiano, dalle pallottole di argilla cadenti dalla cima del campanile di <lb></lb>Pisa sollevando il pensiero al cader della Luna sopra la Terra, della Terra <lb></lb>sopra il Sole, del Sole sopra il suo centro: e finalmente, lasciate libere le <lb></lb>ali all&#039;ardito volo, misurare i gradi della velocità, con cui, da qualunque <lb></lb>legge di gravità sollecitati cadrebbero i rilucenti globi dal firmamento. </s>

<s>“ Po-<pb xlink:href="020/01/2977.jpg" pagenum="602"></pb>sita cuiuscumque generis vi centripeta, et concessis figurarum curvilinearum <lb></lb>quadraturis, requiritur corporis recta ascendentis vel discendentis tum velo­<lb></lb>citas in locis singulis, tum tempus quo corpus ad locum quemvis perveniet, <lb></lb>et e contra ” (pag. </s>

<s>305). </s></p><p type="main">

<s>Dai due Dialoghi di Galileo sopra commemorati la Dinamica, poco dopo <lb></lb>la metà del secolo XVII, non avrebbe forse sperato di avanzarsi tant&#039;oltre, <lb></lb>quanto fece per opera dell&#039;Huyghens nell&#039;<emph type="italics"></emph>Orologio oscillatorio.<emph.end type="italics"></emph.end> Si rimaneva <lb></lb>però quivi l&#039;Autore tuttavia a considerare i gravi sulla superficie terrestre, <lb></lb>come sollecitati continuamente dagl&#039;impulsi della gravità naturale, che si sup­<lb></lb>ponevano, ma che di fatto non potevano essere uniformi. </s>

<s>La Cicloide poi, <lb></lb>ch&#039;era la curva, sopra le proprietà meccaniche della quale, nuovamente sco­<lb></lb>perte e dimostrate, si volevano costruire i nuovi Orologi; appariva, a consi­<lb></lb>derarla bene, come un&#039;opera dell&#039;arte piuttosto che della Natura, la quale <lb></lb>non porge mai alla ruota genitrice una via piana, ma incurvata nell&#039;arco di <lb></lb>qualche circolo massimo della Terra. </s>

<s>I teoremi ugeniani non uscivan dunque <lb></lb>fuori di que&#039;limiti, dentro i quali Archimede aveva circoscritta la Scienza, <lb></lb>e il Newton, per volerla promovere alle sue generalità anche da questa parte, <lb></lb>ricercò la Cicloide naturale, e in lei quelle leggi de&#039;pendoli, delle qnali le <lb></lb>scoperte dall&#039;Huyghens non potevano essere che un caso particolare. </s></p><p type="main">

<s>Sia C (fig. </s>

<s>380) il centro, e CB l&#039;intervallo, con cui è descritto l&#039;areo <lb></lb>ABL del cerchio massimo di un globo, sulla convessità, e sulla concavità del <lb></lb>quale arco passeggiando una ruota, descriverà due distinte curve cicloidee, <lb></lb>e il nome di <emph type="italics"></emph>epicicloide<emph.end type="italics"></emph.end> dato dall&#039;inventore a quella, suggerisce a noi di <lb></lb>chiamare <emph type="italics"></emph>ipocicloide<emph.end type="italics"></emph.end> quest&#039;altra. </s>

<s>Essendosi da A partita la detta ruota, giunta <lb></lb>in B, abbia descritto l&#039;arco d&#039;epicicloide AP. </s>

<s>Prolungato il raggio CB di una <lb></lb>lunghezza uguale al diametro BV, e congiunti V e P, il Newton trovò essere <lb></lb>essenziale proprietà della nuova linea che AP a BV—VP, e 2CE a CB <lb></lb>hanno insieme la medesima proporzione. </s></p><p type="main">

<s>Dal centro E si abbassi sul mezzo dell&#039;arco BGP la EG, che segherà <lb></lb>perpendicolarmente la corda in F, e al segamento EF tornerà la VP paral­<lb></lb>lela e doppia, essendo anche BV diametro doppio del raggio EB. Ora, perchè <lb></lb>FG=EG—EF=(2EB—VP)/2=(BV—VP)/2, sarà 2FG=BV—VP, <lb></lb>ond&#039;è che la proporzione sopra annunziata dal Newton si potrà scrivere nella <lb></lb>forma AP:2FG=2CE:CB. </s>

<s>Ma 2EG è il duplo seno verso della metà <lb></lb>dell&#039;arco BGP, 2CE è la somma de&#039;diametri del globo e della ruota, e CB <lb></lb>è il raggio della stessa ruota; dunque è vero quel che aveva l&#039;Autore, nella <lb></lb>proposizione XLVIII, annunziato, che cioè “ longitudo itineris curvilinei, quod <lb></lb>punctum quodvis in rotae perimetro datum, ex quo globum tetigit, confecit, <lb></lb>quodque <emph type="italics"></emph>cycloidem vel epycicloidem<emph.end type="italics"></emph.end> nominare licet; erit ad duplicatum si­<lb></lb>num versum arcus dimidii, qui globum ex eo tempore inter eumdem teti­<lb></lb>git, ut summa diametrorum globi et rotae, ad semidiametrum globi ” (p. </s>

<s>364). <lb></lb>Per l&#039;ipocicloide ricorre una simile proporzione, se non che il terzo termine, <lb></lb>invece d&#039;essere come dianzi la somma dei diametri, è la differenza. </s></p><pb xlink:href="020/01/2978.jpg" pagenum="603"></pb><p type="main">

<s>Il pensiero della nuova curva così generata era balenato in mente anche <lb></lb>al Nardi, quando, dop&#039;avere accennato alle infinite cicloidi secondarie, descritte <lb></lb>dagli infiniti circoli concentrici alla ruota, soggiungeva: <emph type="italics"></emph>Osservo anche po­<lb></lb>tersi la stessa linea cicloidale fra due periferie, ad imitazione dell&#039;elice, <lb></lb>disegnare.<emph.end type="italics"></emph.end> Ma il Newton aveva ben altre intenzioni che alla Geometria pura, <lb></lb>benchè nella sua Cicloide nuova si comprendessero anche le proprietà geo­<lb></lb>metriche della volgare, la quale s&#039;intende bene come non sia altro che la <lb></lb>stessa Cicloide neutoniana, nel caso che il raggio BC sia infinito, e che perciò <lb></lb>l&#039;arco ABL si riduca a una linea retta. </s>

<s>Se CB infatti è infinita, si rimarrà <lb></lb>tale anche aggiungendovi il piccolo raggio BE della ruota, e perciò, essendo <lb></lb>CR, CE uguali, la sopra trovata proporzione si trasforma in quest&#039;altra: <lb></lb>AP:BV—VP=2:1, d&#039;onde AP=2 (BV—VP), in cui si sa che <lb></lb>BV—VP è il doppio seno verso della metà dell&#039;arco BGP. </s>

<s>Quando il punto <lb></lb>P, giunto in S, abbia descritta la mezza cicloide AS, allora la metà dell&#039;arco <lb></lb>BGP è divenuta un quadrante, il seno verso del quale uguagliando il raggio, <lb></lb>farà AS=2BS, e 2AS=4BS, ossia tutta intera la curva uguale al <lb></lb>diametro quadruplicato della ruota; notissima proprietà della Cicloide or­<lb></lb>dinaria. </s></p><p type="main">

<s>Le intenzioni però del Newton, come si diceva, non erano rivolte alla <lb></lb><figure id="id.020.01.2978.1.jpg" xlink:href="020/01/2978/1.jpg"></figure></s></p><p type="caption">

<s>Figura 380.<lb></lb>Geometria, ma sì alla Mec­<lb></lb>canica, per promoverla al di <lb></lb>là di quel termine, dove l&#039;a­<lb></lb>veva lasciata l&#039;Huyghens. </s>

<s>Si <lb></lb>supponeva da lui nell&#039;<emph type="italics"></emph>Oro­<lb></lb>logio oscillatorio<emph.end type="italics"></emph.end> che fosse <lb></lb>il pendolo sollecitato dagli <lb></lb>impulsi della gravità sempre <lb></lb>uniformi, ciò che dunque <lb></lb>prescriveva allo strumento <lb></lb>una sola particolare e im­<lb></lb>mutabile stazione, la quale <lb></lb>dall&#039;altra parte non era pos­<lb></lb>sibile ritrovar qui sulla su­<lb></lb>perficie della Terra, che in <lb></lb>effetto non è piana, ma curva. </s>

<s><lb></lb>Oscilli dunque il pendolo, disse il Newton, no nella volgare cicloide ugeniana, <lb></lb>ma nella nostra, e le forze di gravità che lo sollecitano siano proporzionali alle <lb></lb>distanze dal centro attrattivo: allora solamente io dimostrerò che quel pendolo <lb></lb>è isocrono. </s>

<s>“ Si vis centripeta, tendens undique ad globi centrum, sit in locis <lb></lb>singulis ut distantia loci cuiusque a centro, et hac sola vi agente corpus oscil­<lb></lb>letur in perimetro Cycloidis; dico quod oscillationum utcumque inaequalium <lb></lb>aequalia erunt tempora ” (pag. </s>

<s>374). </s></p><p type="main">

<s>Di qui scendevano corollarii mirabili inaspettati: Decrescendo la gravità, <lb></lb>dalla superficie della Terra in giù, in ragion semplice, e dalla superficie della <pb xlink:href="020/01/2979.jpg" pagenum="604"></pb>Terra in su in ragion de&#039;quadrati delle distanze, non son dunque propria­<lb></lb>mente isocroni altro che i pendoli ipocicloidali, oscillanti ne&#039;fondi delle mi­<lb></lb>niere e delle caverne: non però gli epicicloidali sulla superficie terrestre, e <lb></lb>gl&#039;ipercicloidali sulle alture de&#039;monti, e oscillino pure nella Cicloide neuto­<lb></lb>niana o nella volgare. </s>

<s>“ Aptantur autem propositiones a nohis demontratae <lb></lb>ad veram constitutionem Terrae, quatenus rotae, eundo in eius circulis maxi­<lb></lb>mis, descrihunt motu clavorum, perimetris suis infixorum, Cycloides extra <lb></lb>globum, et pendula, inferius in fodinis et cavernis Terrae suspensa, in Cy­<lb></lb>cloidibus intra globos oscillari debent ut oscillationes omnes evadant isochro­<lb></lb>nae. </s>

<s>Nam gravitas, ut in Libro tertio docebitur, decrescit in progressu a su­<lb></lb>perficie Terrae, sursum quidem in duplicata distantiarum a centro eius, <lb></lb>deorsum vero in ratione simplici ” (pag. </s>

<s>383). </s></p><p type="main">

<s>Non vogliamo, per la sua importanza, lasciar questo argomento, senza <lb></lb>osservare che il Newton soggiunse nel suo Libro secondo le leggi del moto <lb></lb>oscillatorio, anche avuto riguardo all&#039;impedimento del mezzo, dimostrando <lb></lb>che il pendolo cicloidale è solamente isocrono allora, ch&#039;esso mezzo gli re­<lb></lb>siste in ragion semplice della velocità. </s>

<s>Ma se le resistenze si fanno propor­<lb></lb>zionali ai quadrati delle velocità, e allora, “ oscillationes breviores sunt ma­<lb></lb>gis isochronae. </s>

<s>et brevissimae iisdem temporibus peraguntur, ac in medio <lb></lb>non resistente, quam proxime: earum vero, quae in maioribus arcubus fiunt, <lb></lb>tempora sunt paulo maiora ” (pag. </s>

<s>201). Conseguiva di qui che, resistendo <lb></lb>l&#039;aria, come resulta dalle esperienze, in duplicata ragione delle celerità, nem­<lb></lb>meno i pendoli ugeniani, secondo l&#039;uso che se ne può fare da noi, sono iso­<lb></lb>croni. </s>

<s>“ Cyclois igitur, scriveva in tal proposito l&#039;Eulero, quae ab Hugenio <lb></lb>apta est demonstrata ad isochronismum pendulorum producendum, hanc pro­<lb></lb>prietatem in medio resistente in duplicata celeritatum ratione amittit, et hanc <lb></lb>ob rem in aere non inservit, nisi vel oscillationes sint valde parvae, vel inter <lb></lb>se proxime aequales ” (Mechan., T. II, Petropoli 1736, pag. </s>

<s>291): ciò che <lb></lb>verificandosi pure ne&#039;semplici pendoli circolari, ci fa intender come e perchè <lb></lb>andassero così presto in disuso i magnificati Orologi nuovi olandesi. </s></p><p type="main">

<s>L&#039;opera dunque dell&#039;Huyghens aveva più conferito ai progressi della <lb></lb>Geometria e della Meccanica, che non a quelli della Fisica, alla quale eran <lb></lb>principalmente rivolte le intenzioni dell&#039;Autore. </s>

<s>Ma la Meccanica stessa del­<lb></lb>l&#039;Huyghens, come abbiamo veduto, aveva bisogno di essere ritirata verso la <lb></lb>generalità de&#039;principii, da&#039;quali dipendeva essa, e la Meccanica galileiana in­<lb></lb>sieme con lei, ciò che fece il Newton in quel modo, che da noi sommaria­<lb></lb>mente s&#039;è esposto. </s>

<s>Non ci siamo però curati nel nostro discorso che di dare <lb></lb>un saggio della materia, cosicchè la forma è rimasta solamente <gap></gap>isibile a co­<lb></lb>loro, che hanno avuto per le mani e studiato il primo libro dei Principii di <lb></lb>Filosofia naturale. </s></p><p type="main">

<s>Quanti possano essere oggidi così fatti studiosi non è difficile indovinare, <lb></lb>benchè la scarsità presente non sia forse punto minore di quella, che si notò <lb></lb>nel suo primo venire il libro alla luce: messe ne&#039;più lo stupore, e per qual­<lb></lb>che tempo si rimase incompreso. </s>

<s>Lo stupore nasceva dalla novità inaspettata <pb xlink:href="020/01/2980.jpg" pagenum="605"></pb>delle conclusioni, e il parere impossibile che potessero queste capire nella <lb></lb>mente di un uomo le fece giudicare incomprensibili a chi, con quelle del­<lb></lb>l&#039;Autore, misurava le forze del proprio ingegno. </s>

<s>Ma consistevano altre e più <lb></lb>forti ragioni di queste difficoltà dell&#039;intenderle, nel modo com&#039;erano esposte <lb></lb>e dimostrate le nuove dottrine. </s>

<s>In Galileo rimaneva riparato l&#039;apparente di­<lb></lb>sordine dalla forma del dialogo, unificatrice presso a poco, come l&#039;impasto <lb></lb>nel mosaico a scaglie, ma l&#039;Huyghens, che usciva fuori nel semplice e suc­<lb></lb>cinto abito del Matematico, distribuiva il suo <emph type="italics"></emph>Orologio<emph.end type="italics"></emph.end> in cinque parti di­<lb></lb>stinte, descrivendo nella prima lo strumento, e nella seconda dimostrando <lb></lb>que&#039;teoremi <emph type="italics"></emph>De descensu gravium,<emph.end type="italics"></emph.end> che giovarono, col loro ordine e con la <lb></lb>loro brevità, a diffondere la notizia della nuova Scienza galileiana, meglio <lb></lb>de&#039;prolissi ragionamenti del Salviati. </s>

<s>Dalle leggi delle scese de&#039;gravi nelle <lb></lb>linee rette e nelle oblique si passa poi a dimostrare le nuove leggi della <lb></lb>scesa de&#039;gravi nella Cicloide. </s>

<s>Qui dunque è tutto bene ordinato quanto al <lb></lb>principio, al mezzo e al fine: è una figura tutta intera dalla pianta de&#039;piedi <lb></lb>ai capelli, mentre nel Newton non vedi del gran gigante altro che il torso, <lb></lb>e qualcuna delle membra principali contratte, per una sublime sdegnosità <lb></lb>michelangiolesca, e perchè mancava il marmo a rappresentar nella sua inte­<lb></lb>grità la sconfinata ampiezza del concetto. </s>

<s>Il metodo poi non è nè quello <lb></lb>schiettamente sintetico di Galileo, nè quell&#039;altro dell&#039;Huyghens, qualche cosa <lb></lb>partecipante dell&#039;analisi cartesiana; ma, fra questa e la nuova analisi infini­<lb></lb>tesimale, fa sui più l&#039;effetto di una nuvola molesta innanzi agli occhi, e in <lb></lb>altri pochi provoca un disgusto espresso, somigliante a quello che si prove­<lb></lb>rebbe nel mangiare una frutta di squisitissima qualità, ma tuttavia legnosa <lb></lb>e acerbetta. </s></p><p type="main">

<s>Questi secondi si riducevano a que&#039;tre o quattro Tedeschi, che vole­<lb></lb>vano sopra gl&#039;Inglesi rivendicare alla loro nazione l&#039;invenzion del calcolo <lb></lb>infinitesimale: e di quel disgusto che si diceva abbiamo più volte veduto <lb></lb>l&#039;esempio in Giovanni Bernoulli, il quale, non solamente perfezionò alcuni <lb></lb>teoremi neutoniani, ma in qualche parte trovatili sbagliati gli emendò, come <lb></lb>quando, nel secondo libro <emph type="italics"></emph>De principii,<emph.end type="italics"></emph.end> proponendosi l&#039;Autore di trovare la <lb></lb>resistenza, che farebbe liberamente movere un corpo nella periferia di un <lb></lb>circolo, chiamata G la forza assolutamente uniforme, R la resistenza incon­<lb></lb>t<emph type="italics"></emph>v<emph.end type="italics"></emph.end>ata dal punto M mobile in un quadrante, l&#039;ordinata ortogogona del quale <lb></lb>fosse QM, preso il raggio AC per asse delle ascisse, con l&#039;origine al con­<lb></lb>tatto della curva; assegnò tra G ed R la proporzion medesima, che è tra <lb></lb>AC e QM, mentre il Bernoulli dimostrò che doveva esser invece l&#039;altra, che <lb></lb>è tra 2AC e 3QM, e il Newton docilmente corresse, nelle successive edi­<lb></lb>zioni, il suo errore. </s>

<s>La moltitudine degli studiosi però si rimaneva tuttavia <lb></lb>atterrita dalle difficoltà, e perchè queste dipendevano come si disse dalla <lb></lb>mancanza dell&#039;ordine, e dalla qualità del metodo, con cui il libro era scritto; <lb></lb>que&#039;che avevano amore ai progressi della Scienza pensarono di ordinare in <lb></lb>compendio, e di trattare con più facili aggressioni i teoremi del Newton, ri­<lb></lb>ducendoli all&#039;intelligenza della stessa gioventù, che frequentava le scuole. </s></p><pb xlink:href="020/01/2981.jpg" pagenum="606"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il merito di aver fatto così riprendere il corso al cavallo, che aveva <lb></lb>adombrato, è principalmente dovuto a Giacomo Herman. </s>

<s>Chiamato da Ba­<lb></lb>silea sua patria a leggere le Matematiche nel nostro studio di Padova, elesse <lb></lb>per soggetto delle sue lezioni l&#039;Idrostatica. </s>

<s>Trovò che aveva questa scienza <lb></lb>da Archimede in poi progredito molto per opera e studio di Galileo, del Tor­<lb></lb>ricelli, del Pascal, del Boyle, e molto più ancora per quel che avevano il <lb></lb>Castelli e il Guglielmini insegnato intorno alle acque correnti. </s>

<s>“ Sed quia, <lb></lb>egli dice, eximia haec inventa in variis diariis aliisque libris dispersa et ex <lb></lb>diversis, saepe principiis elicila sunt, gratum me iis facturum, qui hisce rebus <lb></lb>delectantur, existimavi, si omnia iuxta genuinum ordinem in unum collecta, <lb></lb>ex paucis iisque simplicibus principiis deducta et aucta publicae luci siste­<lb></lb>rem ” (<emph type="italics"></emph>Phoron. </s>

<s>cit. </s>

<s>praefatio<emph.end type="italics"></emph.end>). </s></p><p type="main">

<s>Da queste parole si rivela espressamente l&#039;indole del magistero dell&#039;Her­<lb></lb>man, il quale prosegue a dire che dovendo, per risalire alla desiderata gene­<lb></lb>ralità, richiamar molte dottrine appartenenti alla Meccanica pura, e non <lb></lb>volendo rimandare i giovani suoi lettori a ricercarle altrove, pensò di premet­<lb></lb>tere quello de&#039;solidi al trattato del moto e dell&#039;equilibrio de&#039;fluidi, e così <lb></lb>gli venne ripartita in due libri l&#039;opera, alla quale impose il titolo di Legge <lb></lb>delle forze o di <emph type="italics"></emph>Phoronomia, sive de viribus et motibus corporum solidorum <lb></lb>et fluidorum.<emph.end type="italics"></emph.end> Essendo sua principale intenzione l&#039;ordine, ei fu il primo a <lb></lb>trattar separatamente, prima dell&#039;equilibrio e poi del moto dei corpi, dalla <lb></lb>qual proprietà delle cose si venne poi a introdurre nell&#039;uso la proprietà delle <lb></lb>parole. </s>

<s>Ai tempi di Galileo per Meccanica s&#039;intendeva il trattato delle mac­<lb></lb>chine: poi si messe fuori il nome di Statica, così mal definito però, come <lb></lb>si vede nel Deschales, e in altri scrittori. </s>

<s>Ma dopo l&#039;Herman la parola <emph type="italics"></emph>Mec­<lb></lb>canica<emph.end type="italics"></emph.end> si usò a significare in generale la Scienza del moto, la quale si di­<lb></lb>vise nella <emph type="italics"></emph>Statica<emph.end type="italics"></emph.end> e nella <emph type="italics"></emph>Dinamica,<emph.end type="italics"></emph.end> secondo che si trattava del moto in po­<lb></lb>tenza e impedito, o nel suo attuale e libero esercizio. </s></p><p type="main">

<s>La prima sezione dunque del primo libro della Foronomia è un trat­<lb></lb>tato di Statica, che in sole XIV brevissime proposizioni comprende tutti i <lb></lb>progressi fatti dalla Scienza, da Archimede in fino a que&#039;tempi. </s>

<s>E perchè <lb></lb>uno di questi più notabili progressi consisteva nell&#039;applicar i moti composti, <lb></lb>incominciò l&#039;Herman dal dimostrare che la resultante di due forze angolari <lb></lb>è diretta e misurata dalla diagonale del parallelogrammo. </s>

<s>L&#039;ammirata bre­<lb></lb>vità poi e la lucidezza nascono dalle generalità de&#039;principii, da cui i parti­<lb></lb>colari teoremi scendono dimostrati con facilità, in semplici corollari: si può <lb></lb>dir anzi che la Statica venisse per l&#039;Herman ridotta a un unico principio <lb></lb>supremo, qual&#039;è quello dell&#039;eguaglianza de&#039;momenti delle potenze, applicate <lb></lb>di qua e di là dal centro della Libbra. </s></p><pb xlink:href="020/01/2982.jpg" pagenum="607"></pb><p type="main">

<s>Di ben altra comprensione e importanza è la Dinamica, trattata dal­<lb></lb>l&#039;Herman nella Sezione seconda. </s>

<s>I teoremi sparsi nel terzo e quarto dialogo <lb></lb>delle due nuove Scienze; nella seconda, terza e quarta parte dell&#039;Orologio <lb></lb>oscillatorio, e nel primo libro de&#039;Principii di Filosofia naturale; si trovan <lb></lb>tutti ordinati qui in queste XLIII proposizioni, che son quasi altrettante fonti <lb></lb>scaturite dalle alture del monte a irrigar largamento i campi della Scienza <lb></lb>del moto. </s>

<s>E come chi ha raggiunta la fonte riceve comodamente nella ca­<lb></lb>vità della mano tutta l&#039;acqna, che anderà poi a diffrangersi fra&#039;sassi del ru­<lb></lb>scello; così avviene a chi legge il libro dell&#039;Herman. </s></p><p type="main">

<s>Mosse la restaurata Scienza dal fondamento di due supposizioni, l&#039;una <lb></lb>delle quali diceva che si raggiunge sempre uguale velocità ne&#039;cadenti dalla <lb></lb>medesima altezza, e l&#039;altra che le velocità son proporzionali ai tempi. </s>

<s>Come <lb></lb>Galileo, il Torricelli e l&#039;Huyghens fossero stati solleciti di confermare quel <lb></lb>primo fondamento della Scienza con qualche ragione dimostrativa, ben se lo <lb></lb>sanno i nostri Lettori, ma chi pensò mai o sperò di riuscire a dimostrare <lb></lb>quell&#039;altro principio fondamentale della Dinamica galileiana<emph type="italics"></emph>?<emph.end type="italics"></emph.end> Che sapeva o <lb></lb>poteva egli rispondere Galileo stesso al Baliani, quando opponeva parergli <lb></lb>più ragionevole l&#039;ammetter che le velocità crescessero come gli spazi? </s>

<s>niente <lb></lb>altro se non che l&#039;esperienze confermavano le sue supposizioni. </s>

<s>E così come <lb></lb>sentì l&#039;Herman che la Scienza pativa difetto ne&#039;suoi più vitali principii; così <lb></lb>pensò d&#039;infonderveli derivandoli dalle altissime fonti. </s></p><p type="main">

<s>Sia la linea retta AD (fig. </s>

<s>381) con qualunque curva MON, e fatto cen­<lb></lb><figure id="id.020.01.2982.1.jpg" xlink:href="020/01/2982/1.jpg"></figure></s></p><p type="caption">

<s>Figura 381.<lb></lb>tro in D, si descrivano <lb></lb>gli archi di cerchio NE, <lb></lb>OP, MA. S&#039;immagini <lb></lb>che il medesimo mobile <lb></lb>o due mobili uguali, <lb></lb>partendosi dalla quiete <lb></lb>in A e in M, discendano <lb></lb>per le due dette linee <lb></lb>attratti al centro D con <lb></lb>forze, che saranno u­<lb></lb>guali in N, E; O, P; <lb></lb>M, A, per esser punti <lb></lb>situati respettivamente <lb></lb>a distanze uguali dal <lb></lb>centro dell&#039;attrazione. </s>

<s><lb></lb>Sia la forza centripeta, <lb></lb>che sollecita il punto N, <lb></lb>rappresentata da NB, la quale si decomponga nella tangenziale NC, e nel­<lb></lb>l&#039;altra BC, perpendicolare a lei, e perciò non considerata in questo calcolo <lb></lb>come inulile a produrre il moto discensivo. </s>

<s>Da E alzata sopra la AD una <lb></lb>linea ad angolo retto, si prenda in essa ES=NB, e in simile modo, cer­<lb></lb>cate le forze tangenziali in O, e in tutte le altre parti della curva, le linee <pb xlink:href="020/01/2983.jpg" pagenum="608"></pb>che le rappresentano si applichino in P, e negli altri punti corrispondenti: <lb></lb>è manifesto che la curva AS sarà la scala delle velocità tangenziali. </s></p><p type="main">

<s>Così definite le cose, l&#039;Herman si propone di dimostrare questo teorema: <lb></lb>“ Si mobilia M, et A ex punctis M, et A in curva MON et recta AD a quiete <lb></lb>cadere incipiant, celeritates ipsorum in punctis N, E; O, P etc. </s>

<s>acquisitae <lb></lb>erunt aequales ” (pag. </s>

<s>58). La proposizione essendo universalissima, deve <lb></lb>esser vera a qualunque distanza trovisi il punto D. </s>

<s>Che se questa distanza <lb></lb>è infinita, gli archi AM, PO, EN torneranno nelle rettitudini AM′, PO′ EN′, <lb></lb>e perciò le velocità tangenziali in M′, O′, N′ saranno quelle medesime delle <lb></lb>discensive in A, P, E. “ Adeoque celeritates in diversis planorum et curva­<lb></lb>rum continuam curvaturam habentium inclinationibus descensu acquisitae, <lb></lb>aequales sunt in omni gravitatis variabilis et uniformis hypothesi, si plano­<lb></lb>rum vel curvarum elevationes aequales fuerint ” (ibid., pag. </s>

<s>62). </s></p><p type="main">

<s>Ecco in qual modo il famoso supposto galileiano è dimostrato vero, e <lb></lb>no solamente nel caso della gravità uniforme, ma in qualunque ipotesi della <lb></lb>gravità variabile; cosicchè i corpi raggiungono velocità uguali, dopo cadute <lb></lb>uguali, così sulla superficie e nell&#039;interno della nostra Terra, come è nei <lb></lb>mondi, che si governassero con altre leggi. </s>

<s>E qui vien voglia di domandare <lb></lb>se qualunque legge di gravità sia possibile. </s>

<s>Chi non lo crederebbe, pensando <lb></lb>alla Onnipotenza del Creatore? </s>

<s>Eppure la Matematica risponde di no, per la <lb></lb>contrarietà che talvolta non lo consente, come non consentirebbe a nessuna <lb></lb>potenza di far che un circolo sia quadrato, e di qui è che essa Matematica <lb></lb>decise esser solamente possibile la proposta in que&#039;casi, ne&#039;quali il calcolo <lb></lb>dà un resultato reale; impossibile poi in tutti gli altri, per i quali s&#039;hanno <lb></lb>resultati assurdi e immaginari. </s>

<s>Per questa via sottilmente apertasi và l&#039;Her­<lb></lb>man a decidere tra la ipotesi di Galileo e quella del Baliani, e così nello <lb></lb>stesso tempo gli vien conclusa la dimostrazione, che le velocità son propor­<lb></lb>zionali ai tempi e non agli spazi. </s></p><p type="main">

<s>Stando infatti la velocità <emph type="italics"></emph>u<emph.end type="italics"></emph.end> in ragion diretta dello spazio <emph type="italics"></emph>s,<emph.end type="italics"></emph.end> e reciproca <lb></lb>del tempo <emph type="italics"></emph>t,<emph.end type="italics"></emph.end> e la forza sollecitante <emph type="italics"></emph>g<emph.end type="italics"></emph.end> della gravità in ragion diretta della <lb></lb>velocità, e pur essa reciproca del tempo; dalle equazioni <emph type="italics"></emph>u=ds:dt, g= <lb></lb>du:dt<emph.end type="italics"></emph.end> abbiamo <emph type="italics"></emph>u:g=ds:du,<emph.end type="italics"></emph.end> ossia <emph type="italics"></emph>gds=udu.<emph.end type="italics"></emph.end> Poniamo, come vuole <lb></lb>il Baliani, <emph type="italics"></emph>u=s<emph.end type="italics"></emph.end> o <emph type="italics"></emph>u2=s2,<emph.end type="italics"></emph.end> d&#039;onde viene, differenziando, <emph type="italics"></emph>udu=sds= <lb></lb>gds,<emph.end type="italics"></emph.end> e perciò <emph type="italics"></emph>g=s.<emph.end type="italics"></emph.end> Dunque, essendo <emph type="italics"></emph>s=o,<emph.end type="italics"></emph.end> sarà anche <emph type="italics"></emph>g=o,<emph.end type="italics"></emph.end> e ciò vuol <lb></lb>dire che, venendo meno nell&#039;atto della discesa l&#039;impulso della gravità, il <lb></lb>corpo, come non potrebbe cominciare, così sarebbe impossibile che prose­<lb></lb>guisse nel moto. </s>

<s>Di più, nella formula <emph type="italics"></emph>dt=du:g<emph.end type="italics"></emph.end> posto <emph type="italics"></emph>g=s,<emph.end type="italics"></emph.end> avremmo <lb></lb>secondo l&#039;ipotesi del Baliani <emph type="italics"></emph>dt=ds:s,<emph.end type="italics"></emph.end> la quale equazione integrata dà <lb></lb><emph type="italics"></emph>t=log.s,<emph.end type="italics"></emph.end> cosicchè, essendo <emph type="italics"></emph>s=o,<emph.end type="italics"></emph.end> e il logaritmo di zero infinito; ne con­<lb></lb>seguirebbe che il mobile impiegasse un tempo infinito nella quiete, ossia che <lb></lb>assolutamente non si movesse, <emph type="italics"></emph>adeoque Baliani hypothesis impossibilis et <lb></lb>imaginaria est.<emph.end type="italics"></emph.end> (Phoron., pag. </s>

<s>65). </s></p><p type="main">

<s>Questa ipotesi fu poi sostenuta da altri, fra i quali il Cazr, il Descha­<lb></lb>les, il Lana, tutti gesuiti: e perchè dalle cose narrate nel capitolo terzo di <pb xlink:href="020/01/2984.jpg" pagenum="609"></pb>questo Tomo apparisce quanto fossero insufficienti l&#039;esperienze a decidere la <lb></lb>questione; si comprende come giungesse opportuno, a confermare i fonda­<lb></lb>menti della Scienza galileiana, il calcolo dell&#039;Herman, ripetuto poi dall&#039;Eulero <lb></lb>nel primo tomo della sua Meccanica analitica, al secondo Scolio dopo la pro­<lb></lb>posizione XV, concludendovi col dire che la legge supposta da Galileo era <lb></lb>necessaria, e che perciò ne escludeva ogni altra diversa. </s>

<s>“ Ex data vero pro­<lb></lb>blematis solutione unde consequitur celeritatis incrementa fore temporibus <lb></lb>quibus producuntur proportionalia, intelligitur legem inventam necessariam <lb></lb>esse, neque ullam aliam vi principii contradictionis existere posse ” (pag. </s>

<s>54). </s></p><p type="main">

<s>L&#039;Herman aveva particolarmente notate alcune altre di queste ipotesi, <lb></lb>dimostrandole in contradizion con la vera, perchè, ridotte nella formula, da­<lb></lb>vano resultati anch&#039;esse impossibili e immaginari, e dopo ciò così dice: <lb></lb>“ Hactenus generalia motuum acceleratorum habuimus: dispiciendum restat <lb></lb>quid ex una alteraque gravitatis hypotesi sequi debeat ” (pag. </s>

<s>65). Le ipo­<lb></lb>tesi della gravità allora ammesse si riducevano a quella del Newton per l&#039;in­<lb></lb>terno della Terra, dove le forze sollecitanti son proporzionali alle distanze, <lb></lb>e a quella di Galileo comunemente professata ne&#039;cadenti sulla superficie della <lb></lb>Terra, sollecitati da impulsi di gravità sempre uniformi. </s>

<s>Essendo manifesta­<lb></lb>mente in quella prima ipotesi la scala delle forze in un triangolo, si propose <lb></lb>l&#039;Herman di trovar la scala delle relative velocità, ciò che gli riuscì di fa­<lb></lb>cile invenzione, dietro il teorema XIX illustrato dalla figura 381, e in cui <lb></lb>si dimostrava che, essendo IHG la scala delle gravità, i quadrati delle linee <lb></lb>PO′, EN′, e delle altre simili, che espongono le velocità, equivalgono al dop­<lb></lb>pio delle aree IAPH, IAEG. </s></p><p type="main">

<s>Ciò posto, e dato che sia AD (fig. </s>

<s>382) la linea della scesa d&#039;un corpo <lb></lb>attratto al punto D, con forze proporzionali alle distanze, e perciò anche alle <lb></lb>ordinate del triangolo ADQ, dalla DQ con qualunque angolo al centro de­<lb></lb>scritto; per concluder che la scala delle velocità è il quadrante ASR di una <lb></lb>ellisse, il semiasse maggior della quale sia AD, e DR=√AD.AQ semiasse <lb></lb>minore; non occorr<gap></gap> dimostrar altro se non che, segnata ordinatamente qua­<lb></lb>lunque linea ES, il quadrato di questa uguaglia il doppio dell&#039;area del trape­<lb></lb>zio AC, a che facilmente conduce la costruzione del quadrante circolare AFL, <lb></lb>e del triangolo isoscele AGD, dal qual triangolo e dall&#039;altro inscrittogli AQD, <lb></lb>prolungata la ES, in F da una parte, e in B dall&#039;altra; avremo per le pa­<lb></lb>rallele AG, BE, AG:BE=AQ:CE. </s>

<s>Componendo e trasponendo, sarà <lb></lb>AG+BE:AQ+CE=AG:AQ=2T:2<emph type="italics"></emph>t,<emph.end type="italics"></emph.end> intendendosi per T, <emph type="italics"></emph>t<emph.end type="italics"></emph.end> i <lb></lb>trapezii, de&#039;quali AG+BE, AQ+CE son la somma delle basi parallele. </s>

<s>Ora <lb></lb>essendo, per le proprietà del circolo e dell&#039;ellisse, EF2:ES2=DL2:DR2= <lb></lb>AG2:AG.AQ=AG:AQ=2T:2<emph type="italics"></emph>t,<emph.end type="italics"></emph.end> ed EF2=DF2—DE2=DA2—DE2= <lb></lb>AH—EI=AGHIBE=2T; dunque ES2=2<emph type="italics"></emph>t,<emph.end type="italics"></emph.end> com&#039;era l&#039;intenzione di di­<lb></lb>mostrare. </s>

<s>In qual modo poi si derivi di qui, quasi per corollario, la XLVII pro­<lb></lb>posizione del Newton (T. I, pag. </s>

<s>362) è cosa per sè tanto manifesta, che <lb></lb>hasti averla avvertita. </s></p><p type="main">

<s>Nella comune ipotesi della gravità uniforme, D andando infinitamente <pb xlink:href="020/01/2985.jpg" pagenum="610"></pb>distante da A, le due linee AD, QD diventano parallele, e l&#039;area AC trasfor­<lb></lb>mandosi in un rettangolo riduce l&#039;equazione alla forma 2Aq.AE=ES2, <lb></lb>che è l&#039;equazione di una parabola, col parametro <expan abbr="2Aq.">2Aque</expan> Donde è manifesto <lb></lb>che la scala delle velocità, in questa ipotesi, è nella parabola; e perchè le <lb></lb>ascisse rappresentan gli spazii, e le ordinate le velocità o i tempi; questi <lb></lb>stanno dunque come le radici di essi spazi. </s>

<s>Così l&#039;Herman, derivandola da <lb></lb>principii universali, confermava la verità della X proposizione del primo libro <lb></lb><emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> del Torricelli, il quale fu il primo a designar la parabola per la <lb></lb>scala delle velocità de&#039;corpi, secondo la legge di Galileo naturalmente cadenti. </s></p><p type="main">

<s>Ipotesi si possono, e anzi, a rigore di Matematica, si debbono dire le <lb></lb>leggi della gravità sulla superficie e nell&#039;interno della Terra, ma per gli <lb></lb>spazi planetarii il Keplero e il Newton avevano ridotte le leggi, secondo le <lb></lb>quali gravitano i pianeti nel Sole, a certissima tesi: di certezza fisica per le <lb></lb>osservazioni dèl primo de&#039;commemorati astronomi, e di certezza matematica <lb></lb><figure id="id.020.01.2985.1.jpg" xlink:href="020/01/2985/1.jpg"></figure></s></p><p type="caption">

<s>Figura 382.<lb></lb>per i teoremi del se­<lb></lb>condo, che applica al <lb></lb>moto iniziale dei Pia­<lb></lb>neti le proprietà dina­<lb></lb>miche de&#039;proietti. </s>

<s>La <lb></lb>dinamica nuova neu­<lb></lb>toniana era senza dub­<lb></lb>bio più generale di <lb></lb>quella insegnata da <lb></lb>Galileo nel suo Dialo­<lb></lb>go quarto, dove si <lb></lb>suppone che il cen­<lb></lb>tro attrattivo sia a <lb></lb>una distanza infinita <lb></lb>dal mobile, ma pure si limitava a rendere la ragione di un fatto particolare, <lb></lb>quale si osserva nella Natura. </s>

<s>L&#039;Herman volle dare a questo problema della <lb></lb>Scienza la sua massima generalità, proponendosi di trovare in qual curva si <lb></lb>volgerebbe un proietto, attratto al centro con qualunque legge di gravità va­<lb></lb>riabile, senza richiedere altra condizione, se non che la detta curva sia alge­<lb></lb>brica e non trascendente. </s>

<s>Così i teoremi scritti nella terza sezione de&#039;Principii <lb></lb>di Filosofia naturale si derivano come semplici corollarii da questa univer­<lb></lb>salissima proposizione dell&#039;Herman, e accennammo di sopra come in uno di <lb></lb>questi stessi corollarii, in cui si concludeva che, variando la gravità recipro­<lb></lb>camente ai quadrati delle distanze, il proietto si volgerebbe in una sezione <lb></lb>conica; le censurate dottrine del Newton trovarono la loro più autorevole <lb></lb>conferma. </s></p><p type="main">

<s>Non sempre si porge all&#039;Herman l&#039;occasione di sublimare di più queste <lb></lb>assai per sè stesse sublimi speculazioni neutoniane, ma sempre però si stu­<lb></lb>dia e giunge a renderle di più facile trattato, e più chiare. </s>

<s>Potremo, fra&#039;tanti <lb></lb>esempi di ciò, citar le leggi delle sollecitazioni centrali nelle orbite mobili, <pb xlink:href="020/01/2986.jpg" pagenum="611"></pb>e del <emph type="italics"></emph>Moto degli apsidi.<emph.end type="italics"></emph.end> Sia ABE (fig. </s>

<s>383) qualunque orbita immobile, uguale <lb></lb>e simile all&#039;orbita A′B′E′, descritta da un proietto, che si volga in essa e <lb></lb>con essa, la quale si suppone che giri intorno al centro C dell&#039;attrazione con <lb></lb><figure id="id.020.01.2986.1.jpg" xlink:href="020/01/2986/1.jpg"></figure></s></p><p type="caption">

<s>Figura 383.<lb></lb>tal legge, che l&#039;angolo ACA′, rotatorio dell&#039;asse, all&#039;an­<lb></lb>golo A′CB′ sotteso dall&#039;arco A′B′ passato dal proietto <lb></lb>nel medesimo tempo, che fu descritto l&#039;angolo della <lb></lb>rotazione ACA′; stia in qualunque ragion data, per <lb></lb>esempio ACA′:A′CB′=H:F, o componendo B′CA: <lb></lb>A′CB′=H+F:F=G:F, facendo per semplicità <lb></lb>H+F=G. </s>

<s>Il moto dell&#039;asse A′E′ è un esempio di <lb></lb>quello che si chiama <emph type="italics"></emph>Moto degli apsidi,<emph.end type="italics"></emph.end> e che vien <lb></lb>determinato dalla ragione di F a G, per trovar la quale <lb></lb>il Newton ricorre al suo teorema delle serie conver­<lb></lb>genti infinite: “ Sed quid, entra qui a dire l&#039;Herman, <lb></lb>si modum facillimum aperuero, quo idem, absque ulla <lb></lb>serierum infinitarum auxilio, obtineri queat, imo longe <lb></lb>plura, quandoquidem praebet canonem generalem, quaecumque solicitationis <lb></lb>centripetae sit lex, rationem F ad G manifestantem? </s>

<s>” (pag. </s>

<s>99). </s></p><p type="main">

<s>Bastano questi, senz&#039;aver bisogno di aggiungere altri esempi, a persua­<lb></lb>derci che la facilità, con cui l&#039;Herman dimostrava i teoremi di Galileo e del <lb></lb>Newton, oltre tanti altri, che non si trovano compresi nelle loro proposizioni, <lb></lb>dipendeva dall&#039;essere risalito agli altissimi principii. </s>

<s>Dicemmo che di mezzo <lb></lb>a que&#039;due grandi promotori della Scienza stava l&#039;Huyghens, l&#039;opera del <lb></lb>quale, benchè forse ristretta, parve nulladimeno insigne, per aver quietate le <lb></lb>affannose ambagi dei Matematici, col definir la vera natura della curva tau­<lb></lb>tocrona. </s>

<s>Ripensando l&#039;Herman anche sopra questa nuova ammirata inven­<lb></lb>zione, si domandava se il tautocronismo fosse proprietà di sola la cicloide, e <lb></lb>a chi gli avesse risposto di sì, almeno nell&#039;ipotesi della gravità uniforme, <lb></lb>sentiva di poter citare i progressi fatti dal Newton in questa stessa specu­<lb></lb>lazione, supposto che la gravità sia variabile ora come le distanze, ora come <lb></lb>i quadrati delle distanze dal centro dell&#039;attrazione. </s>

<s>Ma dato che si facessero <lb></lb>queste variabilità in qualunque modo, qual sarebbe la curva, nella quale scen­<lb></lb>dendo un grave per archi o maggiori o minori gli passerebbe nonostante <lb></lb>tutti nel medesimo tempo? </s>

<s>Ecco ciò che cercava di far l&#039;Herman, con sol­<lb></lb>lecitudine che si sarebbe detta un&#039;incredibile audacia, se il fine così felice­<lb></lb>mente conseguito non avesse con lo stupore soppresso ogni alito della voce. </s></p><p type="main">

<s>Circa l&#039;asse CA (fig. </s>

<s>384) descrivasi la IKLN, che sia la scala della <lb></lb>gravità variabile sollecitatrice al centro O. </s>

<s>Da A, dove si pone il loro prin­<lb></lb>cipio, vadano le ordinate XZ, HR, GQ e le altre simili via via crescendo con <lb></lb>tal legge, che i loro quadrati uguaglino il doppio delle aree XN, HN, GN...: <lb></lb>gli estremi punti Z, R, <expan abbr="q.">que</expan>.. delle dette ordinate si troveranno in una curva <lb></lb>continua AZRQD, che per le cose dette è la scala delle velocità. </s>

<s>Ora, a par­<lb></lb>tire dal punto A, pure intorno all&#039;asse AC, descrivasi una terza curva BEA, <lb></lb>di tal figura che, menati col centro in O e con gl&#039;intervalli CO, GO, HO... <pb xlink:href="020/01/2987.jpg" pagenum="612"></pb>gli archi di cerchio BC, FG, EH..., i curvilinei BFEA, FEA, EYA ... alle <lb></lb>ordinate CD, GQ, HR stiano come un numero qualunque N all&#039;unità: la­<lb></lb>sciato un grave cadere, nella concavità disegnata, da R, da F, da Y o da <lb></lb>qualsivoglia altro punto, giungerà in A sempre nel medesimo tempo, e perciò <lb></lb>la BEA sarà la curva tautocrona, con qualunque legge la gravità del corpo <lb></lb>ne vada sollecitando la discesa. </s></p><p type="main">

<s>La dimostrazione non costa all&#039;Herman che una pagina di scritto, la <lb></lb>quale anche si potrebbe ridurre alla metà, introducendovi i simboli algebrici, <lb></lb>e gli usati segni convenzionali: eppure è in quelle pagine condensata tutta <lb></lb>la scienza dell&#039;Huyghens, con le sue più notabili conseguenze. </s>

<s>Infatti se la <lb></lb>gravità è uniforme la linea curva ILN torna a una linea retta parallela al­<lb></lb>l&#039;asse, e la scala ARD delle velocità si riduce a una parabola conica: gli <lb></lb>archi BC, FG, YX..., essendo O a una distanza infinita, si rettificano nelle <lb></lb>corde, le quali ordinatamente riferiscono all&#039;asse AC la curva tautocrona AEB, <lb></lb>che dunque è una Cicloide ordinaria. </s>

<s>Di qui anche consegue che il tempo <lb></lb>impiegato dal mobile a passare la metà della curva, è al tempo della scesa <lb></lb>perpendicolare per l&#039;asse, come la semicirconferenza al diametro. </s></p><p type="main">

<s>L&#039;Huyhens non ebbe altra intenzione, in cercare nel tautocronismo della <lb></lb><figure id="id.020.01.2987.1.jpg" xlink:href="020/01/2987/1.jpg"></figure></s></p><p type="caption">

<s>Figura 384.<lb></lb>Cicloide il pendolo isocrono, che di ap­<lb></lb>plicarlo alla misura del tempo, prin­<lb></lb>cipale e unico ufficio commessogli da <lb></lb>Galileo. </s>

<s>Poi il Newton dette ingerenza <lb></lb>allo strumento di misurare le varia­<lb></lb>bili distanze della superficie dal centro <lb></lb>della Terra, e di scandagliare, per le <lb></lb>segrete viscere di lei, la quantità e qua­<lb></lb>lità della materia: nè ciò bastando, il <lb></lb>Bernoulli additò in lui le virtù stesse <lb></lb>dell&#039;areometro, dalla gravità assoluta <lb></lb>passando a rivelar la specifica dei corpi. </s>

<s><lb></lb>Tutte queste proprietà, sparsamente di­<lb></lb>mostrate dai vari autori, son comprese <lb></lb>nel teorema generale dell&#039;Herman, il <lb></lb>quale, ripensando da una parte alla <lb></lb>dignità dell&#039;argomento, e dall&#039;altra <lb></lb>all&#039;insufficienza de&#039;principii, con cui <lb></lb>si era trattato; ebbe ragione di scrive­<lb></lb>re, compiacentesi, queste parole: “ Ex <lb></lb>corollariis proxime antecedentibus satis elucere existimo quantae utilitatis sit <lb></lb>Theorema nostrum generale isochronismi corporum in curvis, assignata lege <lb></lb>descriptis, descendentium, cum ex ea omnia, quae ad pendulorum motus <lb></lb>spectant, tanta facilitate deducantur ” (<emph type="italics"></emph>Phoron.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Sia infatti, nella medesima figura 384 illustrativa di quel teorema ge­<lb></lb>nerale, T il centro del circolo osculatore alla curva nel tratto AY: se dal <pb xlink:href="020/01/2988.jpg" pagenum="613"></pb>raggio TA, come da filo attaccato in T o da verga, vada pendulo il globo A, <lb></lb>farà questo le sue vibrazioni isocrone, ond&#039;è che tutte le minime vibrazioni <lb></lb>circolari si fanno nel medesimo tempo, non solamente sulla superficie terre­<lb></lb>stre, ma dovunque le sollecitazioni della gravità sian variabili secondo qua­<lb></lb>lunque ragione. </s>

<s>Chiamato T il tempo di due delle dette minime vibrazioni, <lb></lb>M la massa del corpo A, P il suo peso, l&#039;Herman ha per facile corollario <lb></lb>dal suo teorema: T=2<emph type="italics"></emph>r<emph.end type="italics"></emph.end><foreign lang="grc">π</foreign>√M.TA.AO/P.TO, equazione, che vale per tutti <lb></lb>i pendoli, da qualunque variabile forza acceleratrice siano sollecitati, e dalla <lb></lb>quale resulta che i tempi delle oscillazioni di due pendoli varii stanno in <lb></lb>ragion diretta delle radici delle masse, delle lunghezze e delle minori distanze <lb></lb>dal centro dell&#039;attrazione; e in ragion contraria delle radici dei pesi e delle <lb></lb>distanze de&#039;punti di sospensione dal detto centro. </s>

<s>“ Haec determinatio, dice <lb></lb>l&#039;Herman, probe consentit cum assertionibus paulo specialioribus Neutoni, <lb></lb>propos. </s>

<s>LH libri primi Phil. </s>

<s>Natur. </s>

<s>” (ibid., pag. </s>

<s>85). Il Newton infatti non <lb></lb>giunge quivi a questa determinazione dalla curva isocrona universale, ma <lb></lb>dalle particolari proprietà dimostrate nel suo pendolo ipocicloidale, in quello <lb></lb>cioè che oscilla in un arco della cicloide, generata dal ruzzolarsi la ruota <lb></lb>nella concavità del cerchio massimo di un globo. </s>

<s>Ed essendo V di esso globo <lb></lb>la forza assoluta, trova che i tempi delle oscillazioni <emph type="italics"></emph>“ sunt in ratione, quae <lb></lb>componitur ex subduplicata ratione longitudinis fili directe, et subdupli­<lb></lb>cata ratione distantiae inter punctum suspensionis, et centrum globi in­<lb></lb>verse, et subduplicata ratione vis absolutae globi etiam inversae ”<emph.end type="italics"></emph.end> (pag. </s>

<s>381): <lb></lb>ossia, come √AT/OT.V Ora, avendosi <emph type="italics"></emph>g<emph.end type="italics"></emph.end>=AO.V, perchè la forza accelera­<lb></lb>trice <emph type="italics"></emph>g<emph.end type="italics"></emph.end> cresce col crescere della distanza dal centro attrattivo, e della forza <lb></lb>assoluta, ed essendo <emph type="italics"></emph>g<emph.end type="italics"></emph.end>=P/M, verrà 1/V=AO.M/P, che sostituito riduce l&#039;asser­<lb></lb>zione del Newton manifestamente alla determinazione dell&#039;Herman. </s></p><p type="main">

<s>Bellissime cose fin qui, senza dubbio, ma inutili a noi, che non abitiamo <lb></lb>nè sotto terra, nè nel mondo delle astrazioni. </s>

<s>Pensiamo perciò ai pendoli, <lb></lb>disse l&#039;Herman, che si possono trattar con le nostre proprie mani, e per i <lb></lb>quali (le forze acceleratrici supposte uniformi, e AO infinita rendendosi uguale <lb></lb>a TO) la formula del tempo, chiamata L la lunghezza del filo, si riduce a <lb></lb>T=2<emph type="italics"></emph>r<emph.end type="italics"></emph.end><foreign lang="grc">π</foreign>√M.L/P, d&#039;onde T:T′=√M.L/P:√M′.L′/P′. </s>

<s>Che se le lun­<lb></lb>ghezze dei fili sono uguali, T:T′=√M/P:√M′/P′; se i pesi a quelle stesse <lb></lb>lunghezze son proporzionali, T:T′=√M:√M′; e se di più anche le masse <lb></lb>ad essi pesi sono proporzionali, se cioè √M.L/P=√M′.L′/P′; e i tempi <lb></lb>pure anderanno uguali. </s>

<s>Avremo all&#039;ultimo, in pendoli ugualmente lunghi, <lb></lb>M:M′=PT2:P′T′2. </s>

<s>“ Atque hoc ipsum est, dice l&#039;Herman, propos. </s>

<s>XXVII <pb xlink:href="020/01/2989.jpg" pagenum="614"></pb>libri II Princ. </s>

<s>Phil. </s>

<s>Natur. </s>

<s>qua usus est cl. </s>

<s>Vir ad explorandum utrum pon­<lb></lb>dera corporum ipsorum massis proportionalia sint nec ne ” (<emph type="italics"></emph>Phoron.,<emph.end type="italics"></emph.end> pag. </s>

<s>85): <lb></lb>la qual proposizione corrisponde, nelle posteriori edizioni, alla XXIV così for­<lb></lb>mulata: <emph type="italics"></emph>“ Quantitates materiae in corporibus funependulis, quorum cen­<lb></lb>tra oscillationum a centro suspensionis aequaliter distant, sunt in ratione <lb></lb>composita ex ratione ponderum, et ex ratione duplicata temporum oscil­<lb></lb>lationum in vacuo ”<emph.end type="italics"></emph.end> (pag. </s>

<s>189). E perchè, essendo i pesi uguali, le masse <lb></lb>stanno direttamente come i quadrati dei tempi, ed essendo le masse uguali <lb></lb>i pesi stanno reciprocamente come i detti quadrati; “ hinc liquet, conclude <lb></lb>il Newton, ratio tum comparandi corpora inter se, quoad quantitatem mate­<lb></lb>riae in singulis, tum comparandi pondera eiusdem corporis in diversis locis, <lb></lb>ad cognoscendam variationem gravitatis. </s>

<s>Factis autem experimentis quam <lb></lb>accuratissimis, inveni semper quantitatem materiae in corporibus singulis <lb></lb>eorum ponderi proportionalem esse ” (pag. </s>

<s>194). </s></p><p type="main">

<s>Perchè poi è un fatto che due diversi pendoli, quanto son più lesti, <lb></lb>tanto fanno, nel medesimo tempo, un più gran numero N, N′ di vibrazioni, <lb></lb>ossia, avendosi per esperienza N:N′=T′:T; sostituiti i valori di T′, T, <lb></lb>verrà N:N′=√M′.T′/P′:√M.L/P, e anche, perchè M/P=1/<emph type="italics"></emph>g,<emph.end type="italics"></emph.end> N:N′= <lb></lb>√L′/<emph type="italics"></emph>g′<emph.end type="italics"></emph.end>:√L/<emph type="italics"></emph>g,<emph.end type="italics"></emph.end> d&#039;onde, in pendoli da gravità uguali sollecitati; N:N′= <lb></lb>√L′:√L, e in pendoli ugualmente lunghi, N:N′=√<emph type="italics"></emph>g<emph.end type="italics"></emph.end>:√<emph type="italics"></emph>g′.<emph.end type="italics"></emph.end> “ Atque <lb></lb>hoc posterius (che cioè i numeri delle vibrazioni di due pendoli, con lun­<lb></lb>ghezze uguali, stanno come le radici delle gravità sollecitanti) ad amussim <lb></lb>convenit cum regula, quam Bernoullius in elegantissimo suo schediasmate, <lb></lb>Act. </s>

<s>Lips. </s>

<s>1713 m. </s>

<s>februario inserto, tradit paragrapho 16, ex qua deinceps <lb></lb>gravitates specificas eruere docet ex pendulorum experimentis, modo plane <lb></lb>novo nec antea cognito ” (<emph type="italics"></emph>Phoron.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>86). </s></p><p type="main">

<s>Il capitolo ultimo della Meccanica dell&#039;Herman s&#039;intitola <emph type="italics"></emph>De regulis <lb></lb>motus in collisione corporum,<emph.end type="italics"></emph.end> dove per verità, piuttosto che promovere la <lb></lb>scienza de&#039;suoi precursori, ne rende la trattazione più facilè e più ordinata. </s>

<s><lb></lb>Notabile è nonostante q&#039;ipotesi della conservazione delle forze assolute, che <lb></lb>egli crede liberamente di poter professare, in mezzo alla controversie, e cita <lb></lb>il Leibniz e l&#039;Huyghens, per dare autorità alla sua opinione, benchè sarebbe <lb></lb>stato forse più giusto citar prima di loro il Borelli, il quale aveva concluso <lb></lb>il cap. </s>

<s>XVII del suo libro <emph type="italics"></emph>De vi percussionis<emph.end type="italics"></emph.end> col dire: <emph type="italics"></emph>motum neque gigni <lb></lb>de novo, neque destrui in natura<emph.end type="italics"></emph.end> (pag. </s>

<s>136). </s></p><p type="main">

<s>Non ritorneremo sopra la formula generale data dall&#039;Herman, per cal­<lb></lb>colare i centri delle oscillazioni, nè sopra quel ch&#039;egli aggiunse, per appli­<lb></lb>carla direttamente ai pendoli, e alla teoria delle forze centrifughe, già sufficien­<lb></lb>temente illustrata dall&#039;Hopital e dal Newton, essendo oramai tempo di con­<lb></lb>cludere il nostro discorso, col rassomigliare la Foronomia, nella vita della <lb></lb>Scienza, al ventricolo del cuore, in cui, scesovi dalle vene, s&#039;è raccolto nella <lb></lb>diastole il sangue. </s>

<s>Nel successivo moto di sistole quel sangue già vivificato <pb xlink:href="020/01/2990.jpg" pagenum="615"></pb>si diffonderà a irrigare le membra rigogliose per la grande arteria della Mec­<lb></lb>canica analitica, alla quale ci rimarrebbe a rivolgere uno sguardo. </s>

<s>Ma per­<lb></lb>chè si vuole che questi spiriti vitali vi siano suscitati, quasi come da fer­<lb></lb>mento, dalle Regole dei moti composti e del calcolo infinitesimale; diremo <lb></lb>prima qualche cosa di loro, nell&#039;ammetterle che fecero i Matematici ai ser­<lb></lb>vigi della Meccanica nuova. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>O consapevoli o no i novelli Matematici, nel dimostrare le leggi dei moti <lb></lb>composti, non si dilungarono dalla semplicità dei metodi antichi. </s>

<s>Supposto che <lb></lb>un corpo venga sollecitato insieme da due forze angolari, proporzionate ai <lb></lb>lati di un parallelogrammo, il Varignon, il Newton e l&#039;Herman procedevano, <lb></lb>in concluder che la resultante è rappresentata in direzione e in grandezza <lb></lb>dalla diagonale, in quel modo ch&#039;erano già proceduti Aristotile, il Cardano, <lb></lb>il Roberval, il Torricelli e il Wallis. </s>

<s>Ma il Newton sopra gli altri riduceva <lb></lb>la dimostrazion del teorema da lui formulato: <emph type="italics"></emph>Corpus viribus coniunctis <lb></lb>diagonalem parallelogrammi eodem tempore describere quo latera sepa­<lb></lb>ratis<emph.end type="italics"></emph.end> (<emph type="italics"></emph>Principia<emph.end type="italics"></emph.end> cit., T. I, pag. </s>

<s>24) a quella così efficace semplicità, che de­<lb></lb>rivava nel suo discorso dalla precisione, e dall&#039;evidenza de&#039;premessi assiomi, <lb></lb>o com&#039;egli stesso gli chiamava <emph type="italics"></emph>Leggi dei moti.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La prima legge è quella così detta dell&#039;inerzia, in virtù della quale un <lb></lb>corpo già mosso persevera uniformemente a moversi in diretto: cosicchè se <lb></lb>prima era per esempio in A (fig. </s>

<s>385), e poi in D, possiamo esser certi che <lb></lb>non è mai uscito dalla rettitudine DA del precedente viaggio. </s>

<s>La seconda <lb></lb>legge, dipendente dalla prima, è che la velocità di un corpo non muta nè <lb></lb>grado nè direzione, per sopravvenirgli un altro impulso in direzione diversa: <lb></lb>cosicchè, se il punto A per esempio si move nell&#039;AC uniformemente, con <lb></lb>una data velocità; con questa seguiterà a moversi parallelamente a se stesso, <lb></lb>anche trasportato che sia nella direzione AB: assioma, che giovò ridurre alla <lb></lb>mente di coloro, i quali, tuttavia sofisticando intorno all&#039;impedirsi che fanno <lb></lb>in concorrere insieme due forze, si mettevano al pericolo di errare, quando <lb></lb>si trattava di definir l&#039;essere, e la ragion della resultante. </s></p><p type="main">

<s>Ciò premesso, sia, dice il Newton, in un dato tempo, per la sola forza <lb></lb>M, il corpo A uniformemente portato da A in B, e, per la sola forza N, da <lb></lb>A in C. </s>

<s>Compiuto il parallelogrammo, perciocchè, per la seconda legge, la <lb></lb>forza che agisce nella direzione AC non muta la velocità di avvicinarsi alla <lb></lb>linea BD, dovrà in qualche punto di questa, alla fine del dato tempo, ritro­<lb></lb>varsi il mobile A, e dovrà per le medesime ragioni trovarsi anche insieme <lb></lb>in qualche punto della CD; dunque nel loro concorso D: e il mobile stesso, <lb></lb>che a principio era in A, non può, in virtù della prima legge, non esser pas­<lb></lb>sato per la rettitudine AD, diagonale del parallelogrammo. </s></p><pb xlink:href="020/01/2991.jpg" pagenum="616"></pb><p type="main">

<s>Il Varignon, nei principii che premette alla <emph type="italics"></emph>Nouvelle mecanique,<emph.end type="italics"></emph.end> invoca, <lb></lb>più espressamente del Newton, l&#039;assioma che <emph type="italics"></emph>les espaces parcourus de vi­<lb></lb>tesses uniformes en tems egaux par des corps quelconques sont entr&#039;eux <lb></lb>comme ces memes vitesses<emph.end type="italics"></emph.end> (T. </s>

<s>I cit., pag. </s>

<s>5), e simile fa l&#039;Herman nel teo­<lb></lb>rema III del primo libro della Foronomia, cosicchè le loro dimostrazioni pro­<lb></lb>cedon nel modo medesimo di quella del Newton, ma con diverso andamento, <lb></lb>il quale consiste nel considerare che, mentre il mobile ha passato, nella di­<lb></lb>rezione AC, lo spazio AK, deve nella direzione AB aver passato tale altro <lb></lb>spazio KG, che sia AC:CD=AK:KG, cosicchè G è il punto, dove si trova <lb></lb>il mobile alla fine di quei due moti. </s>

<s>S&#039;avranno allo stesso modo indicati i <lb></lb>punti G′, G″ .... dove esso mobile è giunto alla fine dei moti AK′, K′G′; <lb></lb>AK″, K″G″ .... ed è facile vedere come tutti questi punti sian disposti lungo <lb></lb>la diagonale AD del parallelogrammo, la quale dunque indica la direzione, e <lb></lb>misura la quantità del moto unico, che resulta dai due componenti. </s></p><p type="main">

<s>Era il bel teorema, per tanti secoli quanti se ne contano da Aristotile <lb></lb>all&#039;Herman, andato attorno in quest&#039;abito semplice e schietto, bene accolto <lb></lb>da tutti e onorato, quando Giovanni Bernoulli uscì fuori con giovanile bal­<lb></lb>danza a dire che quell&#039;abito non era il suo, e che bisognava tagliargliene <lb></lb><figure id="id.020.01.2991.1.jpg" xlink:href="020/01/2991/1.jpg"></figure></s></p><p type="caption">

<s>Figura 385.<lb></lb>un&#039;altro, che s&#039;adattasse me­<lb></lb>glio al suo dosso. </s>

<s>“ Peccant <lb></lb>qui confundunt compositio­<lb></lb>nem virium cum compositione <lb></lb>motuum. </s>

<s>Vis enim vel poten­<lb></lb>tia, utpote consistens in solo <lb></lb>nisu vel conatu, ad motum <lb></lb>generandum, nullam sane ve­<lb></lb>locitatem actualem, ne mini­<lb></lb>mam quidem, producit, si cor­<lb></lb>pus in quod agit est immobile. </s>

<s>Ubi perfectum est aequilibrium, ibi nullus <lb></lb>adest motus. </s>

<s>Qui ergo considerari possit motus, in aequilibrii natura expli­<lb></lb>canda, non video ” (<emph type="italics"></emph>De composit. </s>

<s>et resolut. </s>

<s>virium,<emph.end type="italics"></emph.end> Op. </s>

<s>omnia, T. IV cit., <lb></lb>pag. </s>

<s>256). </s></p><p type="main">

<s>Non vedeva ciò il Bernoulli, perchè non aveva letto, o aveva dimenti­<lb></lb>cato quel ch&#039;era stato scritto da alcuni Matematici insigni, essere cioè nel­<lb></lb>l&#039;equilibrio due moti uguali e contrari, e perciò la quiete non altro che ap­<lb></lb>parente. </s>

<s>Il Borelli, nel cap. </s>

<s>XVII del suo libro <emph type="italics"></emph>De vi percussionis,<emph.end type="italics"></emph.end> pronunziava <lb></lb>questa, non sentenza assoluta, ma probabile opinione: “ Si vero conside­<lb></lb>retur actio illa, quae vera destructio motus appellatur, profecto in ea nil <lb></lb>omnino destruitur, sed tantummodo imprimitur motus contrarius, ita ut post­<lb></lb>modum in eodem subiecto duo impetus et motus contrarii vigentes et perse­<lb></lb>verantes apparentiam quietis pariant, et sic videantur ambo destructi, cum <lb></lb>tamen utrumque vivere ac existere in natura non videatur improbabile: et <lb></lb>universe, quotiescumque corpus aliquod post eius motum quiescere conspi­<lb></lb>citur, tunc dicendum est ab obstaculo vel impedimento eidem impressum <pb xlink:href="020/01/2992.jpg" pagenum="617"></pb>fuisse gradum impetus contrarium omnino aequalem ei quo prius fereba­<lb></lb>tur ” (Editio cit., pag. </s>

<s>135). </s></p><p type="main">

<s>Del resto non si vede che gran peccato facessero coloro, i quali ave­<lb></lb>vano confusa la composizione dei moti con quella delle forze. </s>

<s>Confondere le <lb></lb>azioni si sarebbe stato gran vizio logico, perchè le forze son le cause e i <lb></lb>moti l&#039;effetto: ma qui si tratta di una passione, che sopravviene ai loro <lb></lb>composti, nè si vede per qual ragione s&#039;avesse a condannar chi dicesse che <lb></lb>la causa e l&#039;effetto possono, in certe loro passioni, rassomigliarsi. </s>

<s>“ Quaeri­<lb></lb>tur enim, soggiunge ivi il Bernoulli, cur tres potentiae C, B, F (nella fig. </s>

<s>385) <lb></lb>commune punctum A sollicitantes, ea qua dictum est conditione (cioè che la <lb></lb>diagonale del parallelogrammo, descritto sopra due qualunque delle date forze, <lb></lb>sia uguale e direttamente contraria alla terza) perfectum inter se servent <lb></lb>aequilibrium? </s>

<s>Quomodo igitur introduci possit ulla velocitas, ubi perfecta <lb></lb>adest quies, non video. </s>

<s>” </s></p><p type="main">

<s>Ma suppongasi che le AB, AC, AF (nella medesima figura) siano tre <lb></lb>funi, che mantengono il nodo A in equilibrio: recisa l&#039;AF, l&#039;equilibrio è <lb></lb>rotto, e succede il moto nella direzione AD resultante dalla composizione dei <lb></lb>moti per AB, AC. </s>

<s>Ecco per qual ragione i Matematici anteriori al Bernoulli <lb></lb>erano trapassati a introdurre le velocità, dov&#039;era quiete perfetta. </s>

<s>Anzi tanto <lb></lb>facile e naturale si presentava questo passaggio, che il Bernoulli stesso, nella <lb></lb>sua dimostrazione, come vedremo, non potè astenersi dal farlo. </s>

<s>Il teorema <lb></lb>insomma si può proporre in due vari modi: nel primo, che dice restare in <lb></lb>quiete il punto A sollecitato dalle tre forze AB, AC, AF, se la diagonale AD <lb></lb>è uguale e direttamente contraria alla terza forza AF; e nel secondo modo <lb></lb>così: il punto A, che, divisamente, si moverebbe con le velocità AB, AC, <lb></lb>compostamente, è diretto e va con velocità rappresentata dalla diagonale AD <lb></lb>del parallelogrammo. </s>

<s>In quel primo modo proposto il teorema apparterrebbe <lb></lb>alla Statica, ma alla Dinamica nel secondo. </s></p><p type="main">

<s>Ora, sarebbe stato il Bernoulli assai più giusto censore, se avesse detto <lb></lb>che il Varignon, il Newton e l&#039;Herman confondevano la Statica con la Di­<lb></lb>namica: o meglio, se avesse rimproverato a quegli Autori, per aver trattato <lb></lb>dell&#039;equilibrio, con l&#039;invocare le leggi del moto. </s>

<s>Il Varignon per esempio pre­<lb></lb>mette come principio assiomatico della sua dimostrazione che, nei moti uni­<lb></lb>formi, essendo i tempi uguali, le velocità son proporzionali agli spazi. </s>

<s>Ma <lb></lb>questo non è, nè può citarsi come assioma, essendo un teorema da dimo­<lb></lb>strarsi in una Scienza superiore. </s>

<s>Parimente l&#039;Herman dimostra la regola di <lb></lb>comporre in uno due moti, nella prima sezione del primo libro della Foro­<lb></lb>mia, ossia nella Statica, dove anch&#039;egli cità quella proprietà dei moti uni­<lb></lb>formi, dicendola manifesta: <emph type="italics"></emph>manifestum est.<emph.end type="italics"></emph.end> E poniamo che tale ei la dica <lb></lb>per le cose già dimostrate infin da Archimede nel libro delle Spirali, non <lb></lb>potrebbe però apparir tale alla mente de&#039;suoi lettori, i quali si suppone che <lb></lb>non sappiano ancora nulla della Dinamica, di che si tratterà nella Sezione <lb></lb>seconda. </s>

<s>Quivi era logico ammettere per cosa nota, perchè recentemente di­<lb></lb>mostrata da Galileo e dall&#039;Huyghens, che <emph type="italics"></emph>spatiola, aequabili motu percursa,<emph.end type="italics"></emph.end><pb xlink:href="020/01/2993.jpg" pagenum="618"></pb><emph type="italics"></emph>sunt in composita ratione temporum et velocitatum<emph.end type="italics"></emph.end> (Phoron., pag. </s>

<s>55): non <lb></lb>logico però sembra a noi che sia suppor la notizia di quelle leggi de&#039;moti <lb></lb>equabili, nel teorema terzo degli equilibri. </s></p><p type="main">

<s>Ma come da un&#039;altra parte trattar dei moti, senza presupporne le leggi? <lb></lb></s>

<s>— A che bene a proposito ci vien la risposta dal Bernoulli: — Scansate di <lb></lb>trattar dei moti, e attenetevi alle semplici forze. </s>

<s>— E così, come egli disse, <lb></lb>anche insegnò di fare con assai bella dimostrazione, non da altri principii <lb></lb>condotta che dalla statica del vette. </s>

<s>“ Archimedes, aliique ex veteribus, ad <lb></lb>vectis indolem recurrcrunt ut phaenomena gravitationum, se mutuo in aequi­<lb></lb>librio vel quiete retinentium, demonstrarent. </s>

<s>Nos eorum exemplum secuti <lb></lb>idem fecimus, dum potentiarum compositionem ad vectis leges, utpote a longo <lb></lb>adeo tempore dmonstratas atque receptas, reduximus, reiecto nempe expli­<lb></lb>candi modo recentiorum Geometrarum, ut Cartesii, Stevini, Newtoni, Vari­<lb></lb>gnonii, Hermanni aliorumque, qui velocitatem saltem initialem in auxilium <lb></lb>vocarunt, ad principii elegantissimi veritatem stabiliendam; ubi tamen nulla <lb></lb>prorsus adest velocitas ” (Op. </s>

<s>cit., pag. </s>

<s>256). </s></p><p type="main">

<s>La dimostrazion del Bernoulli, che nella scrittura di lui forse appari­<lb></lb>sce prolissa, si può rendere così in poche parole. </s>

<s>Siano le tre potenze A, B, D <lb></lb><figure id="id.020.01.2993.1.jpg" xlink:href="020/01/2993/1.jpg"></figure></s></p><p type="caption">

<s>Figura 386.<lb></lb>(fig. </s>

<s>386) rappresentate dalle linee AP, BP, DP, con­<lb></lb>correnti a mantenere il punto P in equilibrio. </s>

<s>È ma­<lb></lb>nifesto che, rimossa una qualunque delle dette po­<lb></lb>tenze, per esempio D, il punto P si moverà con <lb></lb>direzione, dice il Bornoulli, e con forza rappresen­<lb></lb>tata dalla diagonale del parallelogrammo AB, co­<lb></lb>struito sulle direzioni delle due forze rimaste. </s></p><p type="main">

<s>Esser questa veramente e non altra la direzione <lb></lb>resulta dall&#039;aversi AP a BP contrariamente, come <lb></lb>il seno dell&#039;angolo BPC al seno dell&#039;angolo APC: <lb></lb>ciò che dall&#039;Autore si dimostra prolungando le AP, <lb></lb>PB, e sopra i loro prolungamenti abbassando dal <lb></lb>punto C le perpendicolari CE, CF. Allora, trasferite <lb></lb>le potenze A, B, D in E, F, C, la ECF si può ri­<lb></lb>guardar come una leva angolare coll&#039;ipomoclio in <lb></lb>C, e in cui, per le note leggi, è A:B=CF:EC=BC:AC=AP:BP= <lb></lb>sen BPC:sen APC. </s></p><p type="main">

<s>Supponendo ora invece rimossa l&#039;AP, il moto resultante dalle D, R sarà <lb></lb>dunque, per le cose già dimostrate, diretto secondo PG, in modo che sia <lb></lb>B:D=senDPG:senGPB=senAPC:senPAC=AC:PC=PB:PC. </s>

<s><lb></lb>E perchè PB rappresenta la potenza B, dunque PC rappresenterà la po­<lb></lb>tenza D, e perciò veramente si farà il moto nella direzione e nella misura <lb></lb>che s&#039;era detto, cioè lungo, e per tutta intera la diagonale del parallelo­<lb></lb>grammo. </s></p><p type="main">

<s>Chi potrebbe negare che questa dimostrazione non si addica meglio alla <lb></lb>Statica di quell&#039;altre del Varignon e dell&#039;Herman? </s>

<s>Anzi, perchè così que-<pb xlink:href="020/01/2994.jpg" pagenum="619"></pb>ste, come quelle de&#039;precedenti autori, eccettuatone Giov. </s>

<s>Marco, son tutte <lb></lb>uscite dal medesimo antico stampo aristotelico, è da dire che incontrò prima <lb></lb>al Bernoulli, non contento degli altrui processi, di dare alla dimostrazione del <lb></lb>bello e importantissimo teorema un processo del tutto nuovo. </s></p><p type="main">

<s>Un secondo e simile incontro ebbe poco di poi in Italia Vincenzo Ric­<lb></lb>cati, benchè per vario, ma forse più giusto e più generoso motivo, quale si <lb></lb>fu di persuadere la verità a quelle poche e sparse reliquie de&#039;Galileiani, i <lb></lb>quali duravano ostinati a dire che nella regola del parallelogrammo non si <lb></lb>osserva la necessaria equivalenza tra le potenze componenti e la resultante. </s>

<s><lb></lb>Per dare alla sua dimostrazione la maggiore evidenza, pensò il Riccati d&#039;in­<lb></lb>trodurre le potenze direttamente, invece delle velocità o delle forze, come <lb></lb>avevano fatto gli altri. </s>

<s>E per rendere meno astratte queste matematiche spe­<lb></lb>culazioni, finse cotali potenze in corde elastiche, come quelle delle cetre, le <lb></lb>quali corde, essendo state prima stirate, poi nel contrarsi rapiscono violen­<lb></lb>temente a sè un corpo, a cui si fossero applicate. </s>

<s>Se sia dunque A (fig. </s>

<s>387) <lb></lb>un punto mobile, e AS una corda, che con potenza rappresentata da AB lo <lb></lb>tira un istante per lo spazio infinitamente piccolo A <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> verrà l&#039;azione di essa <lb></lb>potenza rappresentata dal rettangolo AB. </s>

<s>A <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> essendo AB, come s&#039;è detto, <lb></lb>la forza, e A <emph type="italics"></emph>p<emph.end type="italics"></emph.end> la velocità virtuale. </s></p><p type="main">

<s>Ciò premesso, il Riccati raggiunge il suo intento, qual&#039;era di dimostrare <lb></lb><figure id="id.020.01.2994.1.jpg" xlink:href="020/01/2994/1.jpg"></figure></s></p><p type="caption">

<s>Figura 387.<lb></lb>che, qualunque sia l&#039;angolo del concorso, il <lb></lb>moto per la diagonale uguaglia in potenza <lb></lb>il moto per i due lati del parallelogrammo, <lb></lb>in virtù di due lemmatiche proposizioni, la <lb></lb>prima delle quali è questa: Insieme con AS <lb></lb>(nella medesima figura) potente come AB, <lb></lb>sia un&#039;altra corda AT, potente come AC, ap­<lb></lb>plicate ambedue al punto A, il quale sia co­<lb></lb>stretto a moversi nella direzione AD, quasi <lb></lb>ritenutovi dalle sponde di un canaletto o <lb></lb>solco inciso sul piano BC: “ Se da&#039;punti B, <lb></lb>C, nella direzione AD si menino le normali <lb></lb>BH, CK, e si tagli HD uguale ad AK, dico che la retta AD rappresenterà <lb></lb>la potenza equipollente alle due potenze AB, AC ” (<emph type="italics"></emph>Dialogo delle forze vive,<emph.end type="italics"></emph.end><lb></lb>Bologna 1749, pag. </s>

<s>221, 22). </s></p><p type="main">

<s>S&#039;immagini che, rapito dal concorso delle due corde il punto A, in un <lb></lb>primo istante abbia passato lo spazio infinitamente piccolo A <emph type="italics"></emph>a:<emph.end type="italics"></emph.end> col centro S, <lb></lb>intervallo S<emph type="italics"></emph>a,<emph.end type="italics"></emph.end> e col centro T, intervallo T<emph type="italics"></emph>a,<emph.end type="italics"></emph.end> descritti gli archetti <emph type="italics"></emph>ap, aq,<emph.end type="italics"></emph.end> è <lb></lb>manifesto che gli spazioli A<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> A<emph type="italics"></emph>q<emph.end type="italics"></emph.end> misurano i ritiramenti delle corde o le <lb></lb>loro velocità virtuali: ond&#039;essendo AB.A<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> AC.A<emph type="italics"></emph>q<emph.end type="italics"></emph.end> le azioni delle potenze <lb></lb>AB, AC, e AD.A<emph type="italics"></emph>a<emph.end type="italics"></emph.end> l&#039;azione della potenza AD; s&#039;avrà conclusa la proposi­<lb></lb>zione quando sia dimostrato AB.A<emph type="italics"></emph>p<emph.end type="italics"></emph.end>+AC.A<emph type="italics"></emph>q<emph.end type="italics"></emph.end>=AD.A<emph type="italics"></emph>a,<emph.end type="italics"></emph.end> ciò che poi <lb></lb>è d&#039;assai facile conseguenza, imperocchè i triangoli simili ABH, A <emph type="italics"></emph>ap<emph.end type="italics"></emph.end> da una <lb></lb>parte, e AKD, A<emph type="italics"></emph>aq<emph.end type="italics"></emph.end> dall&#039;altra, danno l&#039;equazioni AB:AH=A<emph type="italics"></emph>a<emph.end type="italics"></emph.end>:A<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> ossia <pb xlink:href="020/01/2995.jpg" pagenum="620"></pb>AH.A<emph type="italics"></emph>a<emph.end type="italics"></emph.end>=AB.A<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> e AC:AK=A<emph type="italics"></emph>a<emph.end type="italics"></emph.end>:A<emph type="italics"></emph>q,<emph.end type="italics"></emph.end> ossia AK.A<emph type="italics"></emph>a<emph.end type="italics"></emph.end>=AC.A<emph type="italics"></emph>q,<emph.end type="italics"></emph.end><lb></lb>d&#039;onde AB.A<emph type="italics"></emph>p<emph.end type="italics"></emph.end>+AC.A<emph type="italics"></emph>q<emph.end type="italics"></emph.end>=A<emph type="italics"></emph>a<emph.end type="italics"></emph.end>(AH+AK)=A<emph type="italics"></emph>a<emph.end type="italics"></emph.end>.AD, la quale ugua­<lb></lb>glianza, venendo così a dimostrarsi vera, non significa altro, se non che <lb></lb>l&#039;azione della potenza AD uguaglia le azioni delle due potenze AB, AC, e <lb></lb>però quella potenza a questa verrà ad essere equipollente, come il Riccati <lb></lb>s&#039;era proposto di dimostrare. </s></p><p type="main">

<s>Nell&#039;altra proposizione, che si diceva essere stata insieme con questa da <lb></lb>esso Riccati preparata, per riuscire con facilità all&#039;intenzion principale; si <lb></lb>considerano gl&#039;incitamenti, che ha il punto mobile di delirare dal solco, e <lb></lb>si conclude che, essendo così fatti incitamenti uguali e contrari, il punto pro­<lb></lb>cederebbe liberamente nel suo viaggio. </s>

<s>La conclusione ovvia a chi riguardi <lb></lb>la contrarietà nelle forze poste in dirittura fra loro, e perpendicolarmente alla <lb></lb>linea AD, la trae il Riccati dal suo solito principio che cioè l&#039;azione equivale <lb></lb>alla potenza di una corda elastica, d&#039;ond&#039;egli viene a sapere che il punto A <lb></lb>allora sarà libero di ubbidire alla sollecitazione delle potenze AB, AC, e di <lb></lb>dirigere e contemperare ai loro impulsi il suo moto, quando le BH, CK, prese <lb></lb>a rappresentare due forze contrarie perpendicolarmente dirette sulla linea AD, <lb></lb>sono uguali. </s>

<s>Dopo ciò un solo e breve passo rimane a farsi, per giungere <lb></lb>al termine desiderato. </s>

<s>Congiungansi con D i punti B, C: i triangoli BHD, <lb></lb>AKC rettangoli, e con i cateti uguali, sono uguali, e perciò il quadrilatero BC <lb></lb>è un perfetto parallelogrammo. </s>

<s>“ Questa per l&#039;appunto, dice il Riccati, è la <lb></lb>legge ordinaria della composizione e risoluzion delle forze, ed essa è dedotta <lb></lb>dal principio dell&#039;egualità tra le azioni delle potenze laterali, e l&#039;azione del­<lb></lb>l&#039;equipollente: cioè dal principio dell&#039;egualità tra la cagione e l&#039;effetto, tanto <lb></lb>è falso che, nella legge della composizione e risoluzion delle forze, cotal prin­<lb></lb>cipio non si mantenga ” (ivi, pag. </s>

<s>225). </s></p><p type="main">

<s>Qual efficacia avessero queste nuove dimostrazioni del Riccati e del Ber­<lb></lb>noulli, in por suggello di verità, e nel dare ordine dimostrativo al Teorema <lb></lb>del parallelogrammo, non si saprebbe dir da noi con certezza. </s>

<s>Ma è un fatto <lb></lb>che il D&#039;Alembert, pochi anni appresso, notava queste cose che trascriviamo, <lb></lb>dop&#039;avere distesa di quello stesso Teorema una dimostrazione sua nuova: <lb></lb>“ La dimonstration qu&#039;on apporte d&#039;ordinaire du Th<gap></gap>orème précédent, con­<lb></lb>siste à imaginer que le point A (nella figura 385 qui poco addietro) se meuve <lb></lb>uniformément sur une regle AB avec la vitesse qu&#039;il a recùe suivant AB, et <lb></lb>qu&#039;en mème tems la ligne ou regle AB se meuve suivant AC, avec la vi­<lb></lb>tesse que le corps A a recùe suivant AC. </s>

<s>On prouve très-bien dans cette <lb></lb>supposition, que le point mobile A décrit la diagonale AD ” (<emph type="italics"></emph>Traitè de Dy­<lb></lb>namiqae,<emph.end type="italics"></emph.end> a Paris 1758, pag. </s>

<s>37). </s></p><p type="main">

<s>Si direbbe che il D&#039;Alembert non fece conto delle censure del Bernoulli, <lb></lb>se non si ripensasse che, trattando esso D&#039;Alembèrt della Dinamica sola, <lb></lb>trovò le supposizioni fatte dal Varignon, dal Newton e dall&#039;Herman non punto <lb></lb>fuori del suo proposito, ond&#039;ei potè senz&#039;altro riguardo aver ragione di dire <lb></lb>che da quegli Autori si provavano a quel modo le cose <emph type="italics"></emph>très-bien.<emph.end type="italics"></emph.end> Ma ascol­<lb></lb>tiamo quel che ivi soggiunge: “ En général la plùpart des démonstrations <pb xlink:href="020/01/2996.jpg" pagenum="621"></pb>communes de cette proposition sont fondées sur ce qu&#039;on regarde les deux <lb></lb>puissances suivant AB et AC (nella detta figura) comme agissant sur le <lb></lb>corps A, pendant tout le tems de son mouvement, ce qui n&#039;est pas précisé­<lb></lb>ment l&#039;etat de la question. </s>

<s>Car l&#039;hypothese est que le corps A tend à se <lb></lb>mouvoir au premier instant suivant AB et AC à la fois, et l&#039;on demande la <lb></lb>direction et la vitesse, qu&#039;il doit avoir en vertu du concours d&#039;action des <lb></lb>deux puissances. </s>

<s>Dès qu&#039;il a pris une direction moyenne AD, les deux ten­<lb></lb>dances suivant AB et AC n&#039;existent plus: il n&#039;y a plus de réel que sa ten­<lb></lb>dance suivant AD ” (pag. </s>

<s>37, 38). </s></p><p type="main">

<s>Per prevenir dunque anche questa difficoltà, ne&#039;malcontenti e ne&#039;ritrosi <lb></lb>di professare la Meccanica nuova, pensò il D&#039;Alembert di dimostrare che il <lb></lb>corpo A prende, in virtù dei moti componenti, sempre la medesima direzione, <lb></lb>sia che le due potenze agiscano un istante sopra lui, e poi lo abbandonino, <lb></lb>sia che l&#039;accompagnino in tutto il suo viaggio. </s>

<s>Ammesse per buone le ra­<lb></lb>gioni di coloro, che dimostravano essere nel secondo caso quella direzione <lb></lb>lungo la diagonale del parallelogrammo; per concluder che tale dovesse esser <lb></lb>pure anche nel primo, parve a principio al D&#039;Alembert bastasse considerare <lb></lb>che, ricevuto il primo impulso, il mobile, anche abbandonato a sè stesso, <lb></lb>prosegue nella medesima dirittura, la quale, se era dunque secondo la dia­<lb></lb>gonale nel principio, non devierà da essa nel mezzo e nella fine, o sia breve <lb></lb>il tempo o sia lungo. </s></p><p type="main">

<s>Poi, essendo questo un teorema così fondamentale della Dinamica, de­<lb></lb>liberò il d&#039;Alembert di darne una prova diretta, e ricercandola nel subietto, <lb></lb>arido per sè stesso e da altri autori sfruttato, gli venne fatto di rinvenirla <lb></lb>a giudizio nostro ingegnosa. </s>

<s>Era senza dubbio difficile paragonare insieme la <lb></lb>resultante con le componenti, se, quando quella incomincia a nascere, que­<lb></lb>ste già non son più, ma fu la difficoltà superata col fare in modo, che il <lb></lb>mobile fosse in continuo conato di moversi, eppure si rimanesse in quiete <lb></lb>nello spazio assoluto. </s>

<s>Nè le condizioni di ciò potevano esser altre, se non che <lb></lb>a ogni conato se ne opponesse un altro uguale in grado e in direzione con­<lb></lb>traria, come se per esempio il punto A (sempre nella medesima figura 385) <lb></lb>posato sopra un piano fosse sollecitato a moversi con la direzione, e con la <lb></lb>velocità AD, e il piano stesso, con quella medesima velocità, si movesse e <lb></lb>con la direzion resultante DA in contrario. </s></p><p type="main">

<s>S&#039;immagini dunque il detto punto A sollecitato dai conati instantanei <lb></lb>AB, AC, e il piano ABDC, su cui s&#039;immagina posato, moversi con l&#039;assi­<lb></lb>stenza continua delle forze DB, DC, uguali e parallele alle AC, AB, sicchè <lb></lb>il detto piano è un parallelogrammo. </s>

<s>Si rimarrà dunque A in quiete nello <lb></lb>spazio assoluto, ma ciò non potrebb&#039;essere, se al suo conato al moto non si <lb></lb>contrapponesse, con uguale velocità e direzione, il moto attuale del piano. </s>

<s>Ora <lb></lb>questa velocità e questa direzione si tengon dal D&#039;Alembert per benissimo <lb></lb>dimostrate dai Matematici, nell&#039;ipotesi fatta da loro che sian misurate e in­<lb></lb>dicate dalla diagonale DA; dunque tanto negli impulsi istantanei, quanto <lb></lb>nella continua assistenza delle forze. </s>

<s>il viaggio del punto A è il medesimo, <pb xlink:href="020/01/2997.jpg" pagenum="622"></pb>secondo che l&#039;Autore, per prevenire ogni difficoltà, aveva creduto bene di <lb></lb>dover dimostrare. </s>

<s>“ J&#039;ai donc crù devoir prevenir cette difficulté, et faire <lb></lb>voir que le chemin du corps A est le mème, soit que les deux puissances <lb></lb>n&#039;agissent sur lni que dans le premier instant, soit qu&#039;elles agissent conti­<lb></lb>nuellement toutes deux à la fois sur le corps. </s>

<s>C&#039;est à quoi je crois ètre par­<lb></lb>venu dans la demonstration que j&#039;ai donnée ci-dessus ” (pag. </s>

<s>38). </s></p><p type="main">

<s>Più tardi, quando la sperimentata efficacia del Teorema in risolvere le <lb></lb>più intricate questioni della Meccanica glie ne crebbe la dignità e l&#039;im­<lb></lb>portanza, si credè di doverlo nobilitare, assumendolo alla gloria del nuovo <lb></lb>calcolo infinitesimale. </s>

<s>Dopo Daniele Bernoulli, che ne dette il primo esempio, <lb></lb>il Teorema del parallelogrammo uscì tante volte fuori in quest&#039;abito sun­<lb></lb>tuoso, ch&#039;essendo superfluo, per giudicarne la convenienza, il mostrarlo in <lb></lb>tutte le sue comparse, basterà vederlo in quella sola, che è la più magnifica <lb></lb>di tutte, nella <emph type="italics"></emph>Mecanique celeste.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Siano, dice il Laplace, <emph type="italics"></emph>x<emph.end type="italics"></emph.end> e <emph type="italics"></emph>y<emph.end type="italics"></emph.end> (fig. </s>

<s>388) due forze ortogonali sollecitanti <lb></lb><figure id="id.020.01.2997.1.jpg" xlink:href="020/01/2997/1.jpg"></figure></s></p><p type="caption">

<s>Figura 388.<lb></lb>il punto M, e <emph type="italics"></emph>z<emph.end type="italics"></emph.end> la loro resul­<lb></lb>tante, che faccia con <emph type="italics"></emph>x<emph.end type="italics"></emph.end> un an­<lb></lb>golo <foreign lang="grc">θ. </foreign></s>

<s>Dalle date <emph type="italics"></emph>x, y<emph.end type="italics"></emph.end> si tratta <lb></lb>di determinar <foreign lang="grc">θ</foreign>, e con esso <emph type="italics"></emph>z<emph.end type="italics"></emph.end><lb></lb>che ne dipende. </s>

<s>Divise le due <lb></lb>componenti in quantità infini­<lb></lb>tamente piccole, cosicchè vada­<lb></lb>no successivamente crescendo <lb></lb>secondo i termini delle serie <lb></lb><emph type="italics"></emph>dx,<emph.end type="italics"></emph.end> 2<emph type="italics"></emph>dx,<emph.end type="italics"></emph.end> 3<emph type="italics"></emph>dx..., dy,<emph.end type="italics"></emph.end> 2<emph type="italics"></emph>dy,<emph.end type="italics"></emph.end><lb></lb>3<emph type="italics"></emph>dy...,<emph.end type="italics"></emph.end> è manifesto che l&#039;an­<lb></lb>golo <foreign lang="grc">θ</foreign> riman sempre il medè­<lb></lb>simo, e che la resultante cre­<lb></lb>sce nella medèsima proporzione, cioè secondo i termini della serie <emph type="italics"></emph>dz,<emph.end type="italics"></emph.end><lb></lb>2 <emph type="italics"></emph>dz,<emph.end type="italics"></emph.end> 3 <emph type="italics"></emph>dz....<emph.end type="italics"></emph.end> ed è manifesto altresi che, ne&#039;successivi incrementi delle tre <lb></lb>forze, le relazioni di <emph type="italics"></emph>x<emph.end type="italics"></emph.end> e <emph type="italics"></emph>y<emph.end type="italics"></emph.end> a <emph type="italics"></emph>z<emph.end type="italics"></emph.end> saranno costantemente date in funzione di <foreign lang="grc">θ</foreign>, <lb></lb>e che perciò si avranno le due equazioni <emph type="italics"></emph>x=z<foreign lang="grc">φ</foreign>(<foreign lang="grc">θ</foreign>), y=z<foreign lang="grc">φ</foreign>(90°—<foreign lang="grc">θ</foreign>).<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Riguardando poi la <emph type="italics"></emph>x<emph.end type="italics"></emph.end> come la resultante delle due forze ortogonali <lb></lb><emph type="italics"></emph>x′, x″,<emph.end type="italics"></emph.end> perciocchè quella è sopr&#039;essa resultante inclinata con l&#039;angolo <foreign lang="grc">θ</foreign>, e <lb></lb>questa con l&#039;angolo 90°—<foreign lang="grc">θ</foreign>; avremo dunque di <emph type="italics"></emph>x′,<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>x″<emph.end type="italics"></emph.end> due altre equa­<lb></lb>zioni simili a quelle scritte di sopra, cioè <emph type="italics"></emph>x′=x<foreign lang="grc">φ</foreign>(<foreign lang="grc">θ</foreign>)=x2/z, x″= <lb></lb>x<foreign lang="grc">φ</foreign>(90°—<foreign lang="grc">θ</foreign>)=xy/z.<emph.end type="italics"></emph.end> Parimente, decomposta la <emph type="italics"></emph>y<emph.end type="italics"></emph.end> nelle due ortogonali <emph type="italics"></emph>y, y″,<emph.end type="italics"></emph.end><lb></lb>inclinate con gli angoli 90°—<foreign lang="grc">θ</foreign>, e <foreign lang="grc">θ</foreign>, sarà <emph type="italics"></emph>y′=y<foreign lang="grc">φ</foreign>(90°—<foreign lang="grc">θ</foreign>)=y2/z, y″= <lb></lb>y<foreign lang="grc">φ</foreign>(<foreign lang="grc">θ</foreign>)=xy/z.<emph.end type="italics"></emph.end> Alle due <emph type="italics"></emph>x, y<emph.end type="italics"></emph.end> si potranno dunque sostituire le quattro forze <lb></lb><emph type="italics"></emph>x′, y′; x″, y″.<emph.end type="italics"></emph.end> E perchè le due ultime, oltre a essere uguali, son diretta-<pb xlink:href="020/01/2998.jpg" pagenum="623"></pb>mente contrarie, e l&#039;uguaglianza tra <emph type="italics"></emph>x′z<emph.end type="italics"></emph.end> e <emph type="italics"></emph>y′<emph.end type="italics"></emph.end> produce tra <emph type="italics"></emph>x′+y′,<emph.end type="italics"></emph.end> ossia tra <lb></lb><emph type="italics"></emph>(x2+y2)/z<emph.end type="italics"></emph.end>e <emph type="italics"></emph>z,<emph.end type="italics"></emph.end> un&#039;altra uguaglianza; dunque <emph type="italics"></emph>x2+y2=z2.<emph.end type="italics"></emph.end> “ D&#039;ou il suit, dice <lb></lb>il Laplace, que la resultante des deux forces <emph type="italics"></emph>x<emph.end type="italics"></emph.end> et <emph type="italics"></emph>y<emph.end type="italics"></emph.end> est representée pour la <lb></lb>quantité par la diagonale du rectangle, dont les cotes representent ces for­<lb></lb>ces ” (<emph type="italics"></emph>Traité de Mecanique celeste,<emph.end type="italics"></emph.end> a Paris, T. I, an. </s>

<s>VII, pag. </s>

<s>5). </s></p><p type="main">

<s>Rimane a determinare l&#039;angolo <foreign lang="grc">θ</foreign>, e per far ciò immagina il Laplace <lb></lb>che la <emph type="italics"></emph>x<emph.end type="italics"></emph.end> cresca della quantità infinitesima <emph type="italics"></emph>dx,<emph.end type="italics"></emph.end> rimanendosi l&#039;altra <emph type="italics"></emph>y<emph.end type="italics"></emph.end> inva­<lb></lb>riabile. </s>

<s>Per maggiore chiarezza di ciò che dice l&#039;Autore, appongasi l&#039;incre­<lb></lb>mento <emph type="italics"></emph>dx<emph.end type="italics"></emph.end> non a <emph type="italics"></emph>x<emph.end type="italics"></emph.end> direttamente, ma alla sua uguale e parallela <emph type="italics"></emph>yz,<emph.end type="italics"></emph.end> e questo <lb></lb>incremento infinitesimale di forza così apposto decompongasi ne&#039;due ortogo­<lb></lb>nali <emph type="italics"></emph>dx′, dx″.<emph.end type="italics"></emph.end> Poi <emph type="italics"></emph>dx′<emph.end type="italics"></emph.end> si prolunghi di una quantità uguale a <emph type="italics"></emph>z:<emph.end type="italics"></emph.end>è manife­<lb></lb>sto che le forze sollecitanti il punto M sono le due <emph type="italics"></emph>z+dx′, dx″,<emph.end type="italics"></emph.end> sopra le <lb></lb>quali costruito un rettangolo, la diagonale di lui <emph type="italics"></emph>z′<emph.end type="italics"></emph.end> sarà la resultante, che <lb></lb>farà l&#039;angolo <emph type="italics"></emph>dx″z′z=d<foreign lang="grc">θ</foreign>,<emph.end type="italics"></emph.end> e l&#039;angolo <emph type="italics"></emph>dx″zz′=90°—d<foreign lang="grc">θ</foreign>.<emph.end type="italics"></emph.end> Dunque per­<lb></lb>chè, omologamente a quel che s&#039;è fatto di sopra, <emph type="italics"></emph>dx″=z′<foreign lang="grc">φ</foreign>(90°—d<foreign lang="grc">θ</foreign>= <lb></lb>—z′kd<foreign lang="grc">θ</foreign><emph.end type="italics"></emph.end> (essendo <emph type="italics"></emph>k<emph.end type="italics"></emph.end> una costante arbitraria, e indipendente dall&#039;angolo <foreign lang="grc">θ</foreign>) <lb></lb>e anche <emph type="italics"></emph>dx″=dx<foreign lang="grc">φ</foreign>(90°—<foreign lang="grc">θ</foreign>)=ydx/z;<emph.end type="italics"></emph.end> avremo <emph type="italics"></emph>ydx/z=—z′kd<foreign lang="grc">θ</foreign>,<emph.end type="italics"></emph.end> d&#039;onde, <lb></lb>considerando che <emph type="italics"></emph>z′<emph.end type="italics"></emph.end> e <emph type="italics"></emph>z,<emph.end type="italics"></emph.end> per differire di una quantità infinitesima sono uguali, <lb></lb><emph type="italics"></emph>d<foreign lang="grc">θ</foreign>=(—ydy)/kz2.<emph.end type="italics"></emph.end> Se poi in questa si cambi <emph type="italics"></emph>x<emph.end type="italics"></emph.end> in <emph type="italics"></emph>y, y<emph.end type="italics"></emph.end> in <emph type="italics"></emph>x,<emph.end type="italics"></emph.end> e <foreign lang="grc">θ</foreign> in 90°—<foreign lang="grc">θ</foreign>, <lb></lb>avremo per la variazione di <emph type="italics"></emph>y,<emph.end type="italics"></emph.end> rimanendosi <emph type="italics"></emph>x<emph.end type="italics"></emph.end> costante, <emph type="italics"></emph>d<foreign lang="grc">θ</foreign>=xdy/kz2,<emph.end type="italics"></emph.end> cosicchè, <lb></lb>per il simultaneo variar di <emph type="italics"></emph>x<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>y,<emph.end type="italics"></emph.end> la variazione totale dell&#039;angolo <foreign lang="grc">θ</foreign> sarà <lb></lb><emph type="italics"></emph>d<foreign lang="grc">θ</foreign>=(xdy—ydx)/kz2.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Questa ultima integrata rende <emph type="italics"></emph>y/x<emph.end type="italics"></emph.end>=tang.(<emph type="italics"></emph>k<emph.end type="italics"></emph.end><foreign lang="grc">θ</foreign>+C), ossia <emph type="italics"></emph>y2= <lb></lb>x2<emph.end type="italics"></emph.end>tang2(<emph type="italics"></emph>k<emph.end type="italics"></emph.end><foreign lang="grc">θ</foreign>+C)=<emph type="italics"></emph>z2—x2,<emph.end type="italics"></emph.end> d&#039;onde <emph type="italics"></emph>x=z<emph.end type="italics"></emph.end>√1/tang2(<emph type="italics"></emph>k<foreign lang="grc">θ</foreign><emph.end type="italics"></emph.end>+C)= <lb></lb><emph type="italics"></emph>z<emph.end type="italics"></emph.end>cos(<emph type="italics"></emph>k<emph.end type="italics"></emph.end><foreign lang="grc">θ</foreign>+C), nè rimane a far altro che a determinare le due costanti. </s>

<s>Se <lb></lb><emph type="italics"></emph>y<emph.end type="italics"></emph.end> è zero, evidentemente <emph type="italics"></emph>z=x,<emph.end type="italics"></emph.end> e <foreign lang="grc">θ</foreign>=0, nel qual caso l&#039;equazione si ri­<lb></lb>duce a cos C=<emph type="italics"></emph>x/z<emph.end type="italics"></emph.end>=1, d&#039;onde C=360°, che sostituito dà </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>x=z<emph.end type="italics"></emph.end>cos(360+<emph type="italics"></emph>k<foreign lang="grc">θ</foreign>)=z<emph.end type="italics"></emph.end>cos<emph type="italics"></emph>k<emph.end type="italics"></emph.end><foreign lang="grc">θ</foreign>.<emph.end type="center"></emph.end><lb></lb>Se invece è zero <emph type="italics"></emph>x,<emph.end type="italics"></emph.end> l&#039;uguaglianza tra <emph type="italics"></emph>z<emph.end type="italics"></emph.end> e <emph type="italics"></emph>y,<emph.end type="italics"></emph.end> e tra <foreign lang="grc">θ</foreign> e 90° che ne resulta, <lb></lb>riduce cos <emph type="italics"></emph>k<emph.end type="italics"></emph.end><foreign lang="grc">θ</foreign>=0, equazione non esistente se no nel caso che <emph type="italics"></emph>k<emph.end type="italics"></emph.end> sia un <lb></lb>numero impari (quale si suol esprimere con 2<emph type="italics"></emph>n<emph.end type="italics"></emph.end>+1) e <foreign lang="grc">θ</foreign> sia uguale <foreign lang="grc">θ</foreign><lb></lb>90°:2<emph type="italics"></emph>n<emph.end type="italics"></emph.end>+1. Ma nella fatta supposizione che <emph type="italics"></emph>x<emph.end type="italics"></emph.end> sia nullo evidentemente a <lb></lb>deve essere uguale a 90°; dunque, affinchè sia 90°=90°:2<emph type="italics"></emph>n<emph.end type="italics"></emph.end>+1, biso­<lb></lb>gna che <emph type="italics"></emph>n<emph.end type="italics"></emph.end> sia zero, e perciò <emph type="italics"></emph>k<emph.end type="italics"></emph.end>=1, il quale valore sostituito riduce final­<lb></lb>mente l&#039;integrata equazione alla forma <emph type="italics"></emph>y=zcos<foreign lang="grc">θ</foreign>.<emph.end type="italics"></emph.end> “ De là il suit, ne con-<pb xlink:href="020/01/2999.jpg" pagenum="624"></pb>clude il Laplace, que la diagonale du rectangle construit sur les droites qui <lb></lb>representent les deux forces <emph type="italics"></emph>x<emph.end type="italics"></emph.end> et <emph type="italics"></emph>y,<emph.end type="italics"></emph.end> represente non seulement la quantité, <lb></lb>mais encore la direction de leur resultante ” (ivi, pag. </s>

<s>6). </s></p><p type="main">

<s>Abbiamo esposta la dimostrazione non solo agli occhi, ma al giudizio <lb></lb>dei nostri Lettori, ai quali sembrerà forse come a noi di trovarci quel difetto <lb></lb>capitalissimo, rimproverato da altri al Duchayle, di supporre cioè come noto <lb></lb>quel che si proponeva di dimostrare. </s>

<s>L&#039;ipotesi non è altro che la conversa <lb></lb>della tesi: si vuol concludere che la risultante di due forze ortogonali è la <lb></lb>diagonale del rettangolo, e per far ciò si suppone che le componenti siano <lb></lb>i lati del rettangolo stesso. </s>

<s>È poi vero che dal caso delle forze concorrenti <lb></lb>insieme ad angolo retto si può facilmente passare agli altri casi che sia qua­<lb></lb>lunque l&#039;angolo del detto concorso, ma la proposizione del Laplace in ogni <lb></lb>modo è particolare, e volendola ridurre alla sua generalità, il calcolo istituito <lb></lb>da lui riuscirebbe assai più complicato. </s>

<s>Ma rimanendosi pure in quella mas­<lb></lb>sima semplicità di differenziali e d&#039;integrazioni, si domanda qual maggiore <lb></lb>evidenza e fermezza viene a darsi al Teorema trattato a quel modo, verso <lb></lb>l&#039;altra trattazione del Newton, che si spedisce in così poche parole, e per <lb></lb>intender le quali basta la notizia della Geometria più elementare? </s></p><p type="main">

<s>Si direbbe che è cominciato il tempo, in cui si crederà colla potenza <lb></lb>del calcolo di soggiogar l&#039;esperienza e la ragione, ma alcuni Matematici fe­<lb></lb>cero senno, e pensarono che al Teorema del parallelogrammo era avvenuto <lb></lb>come agli animali domestici e alle piante, che bene spesso si ammalano per <lb></lb>volerle troppo curare. </s>

<s>Il Varignon, il Newton e l&#039;Herman, che furono i primi <lb></lb>a riconoscere dì quel gran Teorema l&#039;importanza, avrebbero senza dubbio <lb></lb>saputo darne dimostrazione più elaborata, e al D&#039;Alembert per esempio non <lb></lb>mancava del calcolo più sublime nè l&#039;uso nè il senso della potenza: eppure, <lb></lb>avvisando nella prefazione alla sua Dinamica i Lettori di aver trattato del <lb></lb>principio della composizion delle forze in una maniera nuova, soggiungeva <lb></lb>di essersi guardato in essa “ de ne pas deduire d&#039;un grand nombre de pro­<lb></lb>positions compliquées un principe qui, etant l&#039;un des premiers de la Mecha­<lb></lb>nique, doit nécessairement ètre appuyé sur des preuves simples et faciles ” <lb></lb>(pag. </s>

<s>XIII). Di questo medesimo parere fu il Lagrange, ond&#039;è che si ridus­<lb></lb>sero alla primiera semplicità molti autori, fra&#039;quali è particolarmente da com­<lb></lb>memorare quel Marie, tanto benemerito in Francia e fuori dell&#039;ordinamento <lb></lb>delle Matematiche nelle Scuole di que&#039;tempi. </s></p><p type="main">

<s>I savi metodi proposti alla gioventù pigliavano autorità dal vederli se­<lb></lb>guiti anche dai provetti, come dal Prony, il quale, ponendo per fondamento <lb></lb>alla sua <emph type="italics"></emph>Nouvelle architecture hydrauliche<emph.end type="italics"></emph.end> la regola del parallelogrammo, <lb></lb>suppone di avere un corpo in quiete posato sopra un piano, che equabil­<lb></lb>mente si muove. </s>

<s>“ Cela posé, poi soggiunge, si on concoit qu&#039;une force quel­<lb></lb>conque agisse sur lui (cioè sul detto corpo mobile rappresentato da A nella <lb></lb>figura 385 qui poco addietro) selon la direction AC, et lui imprime una vi­<lb></lb>tesse telle que dans une unité de temps il puisse parcourir l&#039;espace AC uni­<lb></lb>formement, on ne peut douter qu&#039;en vertu de cette premiere impression, qui <pb xlink:href="020/01/3000.jpg" pagenum="625"></pb>lui est proprie, il ne doive se trouver au point C, lorsque cette unité de <lb></lb>temps finira. </s>

<s>Mais comme en vertu du mouvement du plan la ligne AC <lb></lb>s&#039;avance d&#039;un mouvement parallele et uniforme vers BD, et qu&#039;elle doit reel­<lb></lb>lement se confondre avec BD au bout d&#039;une unité de temps; il est clair que <lb></lb>le point C se confondra avec le point D ” (A Paris 1790, pag. </s>

<s>25). Così da <lb></lb>questi medesimi principii, concludendo al medesimo modo che nell&#039;introdu­<lb></lb>zione al primo libro della matematica Filosofia naturale, restituiva il Prony, <lb></lb>dopo un secolo ai meritati onori la repudiata semplicità della dimostrazion <lb></lb>neutoniana. </s></p><p type="main">

<s>Nonostante pensarono alcuni che tanta faccenda dei Matematici intorno <lb></lb>al nobile e insigne Teorema non doveva esser riuscita senza frutto, il quale <lb></lb>era ben raccogliere sceverato da&#039;bozzacchioni e dalle fronde. </s>

<s>Attendendo <lb></lb>da una parte a rendere il metodo semplice e facile, e dall&#039;altra a partir da <lb></lb>principii evidenti, e non complicati con le idee di moto e di tempo, si chie­<lb></lb>deva principalmente e unicamente si concedesse per vero che la resultante <lb></lb>divide nel preciso mezzo l&#039;angolo fatto da due componenti uguali. </s>

<s>Chi vuol <lb></lb>che tutto sia dimostrato pretenderà forse di aver dimostrazione anche di que­<lb></lb>sto, ma chi più saviamente ripensa che un punto di partenza è necessario <lb></lb>alla possibilità logica di ogni discorso, non dubiterà di concedere il postu­<lb></lb>lato, dipendente da quell&#039;altro non saputosi ancora negar da nessuno, che <lb></lb>cioè la direzion della resultante è media fra la direzion delle due compo­<lb></lb>nenti, le quali, se si uguagliano, par dunque evidente che la medietà debba <lb></lb>esser perfetta. </s></p><p type="main">

<s>Dietro ciò è manifesto che la resultante delle due forze uguali AB, AC <lb></lb>(fig. </s>

<s>389) è diretta secondo la AD, diagonale del rombo CB, e nel modo che <lb></lb>si dirà ragionando, facilmente si dimostra che alla stessa AD deve essere <lb></lb><figure id="id.020.01.3000.1.jpg" xlink:href="020/01/3000/1.jpg"></figure></s></p><p type="caption">

<s>Figura 389.<lb></lb>inoltre la detta resultante uguale: Sia, se è possibile, <lb></lb>minore. </s>

<s>Divisa tutta la AD in parti uguali, grandi o <lb></lb>piccole a piacere, come le D<emph type="italics"></emph>a, ab, bc ....<emph.end type="italics"></emph.end> dicasi per <lb></lb>esempio che la resultante è A<emph type="italics"></emph>a.<emph.end type="italics"></emph.end> Si inscrivano nel mag­<lb></lb>gior rombo i rombi EK, FI .... GH: come della A<emph type="italics"></emph>a<emph.end type="italics"></emph.end><lb></lb>son le componenti AB, AC, così della A<emph type="italics"></emph>b<emph.end type="italics"></emph.end> saranno AE, <lb></lb>AK, e su su procedendo della resultante, che s&#039;è già <lb></lb>in A esaurita, rimarranno le componenti AG, AH, ciò <lb></lb>che è assurdo. </s>

<s>Se poi si dice che la resultante è mag­<lb></lb>giore di AD, ragionando in simile modo, e sopr&#039;ana­<lb></lb>loga costruzione, giungeremo a un&#039;ultima resultante <lb></lb>senza più le componenti, altro assurdo manifesto. </s>

<s>Non <lb></lb>potendo esser dunque la resultante delle forze uguali AB, AC nè minore nè <lb></lb>maggiore di AD, sarà l&#039;AD stessa, e avremo perciò, non solamente la dire­<lb></lb>zione, ma la grandezza altresì di lei rappresentata dalla diagonale del rombo. </s></p><p type="main">

<s>Di qui concluderemo per la conversa che all&#039;unica AD equivalgono le <lb></lb>due forze AB, AC, e si potranno all&#039;occorrenza sostituir le une alle altre. </s></p><p type="main">

<s>Da questo corollario, e da quel lemma, vien aperta la via alla dimostra-<pb xlink:href="020/01/3001.jpg" pagenum="626"></pb>zione, quando le forze son di differente grandezza, e retto o acuto ne sia <lb></lb>l&#039;angolo del concorso. </s>

<s>Nel primo caso infatti (fig. </s>

<s>390) che rappresenta il <lb></lb>rettangolo AD, in cui son tirate le diagonali AD, BC, e intorno a cui son <lb></lb><figure id="id.020.01.3001.1.jpg" xlink:href="020/01/3001/1.jpg"></figure></s></p><p type="caption">

<s>Figura 390.<lb></lb>disegnati i rombi EG, FG; chi cercasse la <lb></lb>resultante X delle due componenti date, la <lb></lb>troverebbe facilmente osservando che all&#039;una <lb></lb>AC equivalgono le due forze AE, AG, e al­<lb></lb>l&#039;altra AB le due AF, AG, onde X= <lb></lb>AC+AB=AE+AG+AF+AG. </s>

<s><lb></lb>E perchè AE, AP sono uguali e contrarie, e <lb></lb>2AG=AD, dunque X=AD. </s></p><p type="main">

<s>Se poi l&#039;angolo del concorso è acuto, (fig. </s>

<s>391) e allora, costruiti i ret­<lb></lb>tangoli EF, HG, sarà, per l&#039;applicazione del caso precedente, X=AC+AB= <lb></lb>AF+AE+AG+AH. </s>

<s>E perchè AE, AH sono uguali e contrarie, e AF= <lb></lb>GD, sarà ancora X=AD. </s></p><p type="main">

<s>Diventando l&#039;angolo BAC ottuso si giunge anche in questo caso a con­<lb></lb>cludere similmente, dietro una omologa costruzione, e perciò sempre, siano <lb></lb>le forze uguali o diverse, e con qualunque angolo concorrenti, la resultante <lb></lb>avrà direzione e grandezza proporzionali alla diagonale del parallelogrammo <lb></lb>fatto sulle due componenti. </s></p><p type="main">

<s>Così conducendo la dimostrazione sì soddisfaceva a coloro, che la vo­<lb></lb><figure id="id.020.01.3001.2.jpg" xlink:href="020/01/3001/2.jpg"></figure></s></p><p type="caption">

<s>Figura 391.<lb></lb>levano indipendente da qualunque idea di <lb></lb>moto, e dall&#039;altra parte era così semplice e <lb></lb>facile, da bastare per la piena intelligenza <lb></lb>di lei le prime nozioni della Geometria. </s>

<s>Tali <lb></lb>essendo le avventure del Teorema, quando, <lb></lb>tra il finir del secolo XVII e il cominciar <lb></lb>del seguente, s&#039;ingerì nella Meccanica nuo­<lb></lb>va; non ci rimane a dir, secondo il propo­<lb></lb>sito fatto, che del Calcolo infinitesimale, altro massimo efficiente di quel rin­<lb></lb>novamento della Scienza. </s></p><p type="main">

<s>Come dalle tradizioni antiche di Pappo e di Archimede derivasse, nel <lb></lb>nostro Nardi e nel francese Roberval, la dottrina dell&#039;infinito, non è neces­<lb></lb>sario ripeterlo a chi ha letto i fatti da noi narrati in questo stesso Tomo. </s>

<s><lb></lb>Sull&#039;esempio offertogli dalla XXI proposizione del IV libro delle Matemati­<lb></lb>che collezioni anche il Nardi riguardava le superficie come composte d&#039;in­<lb></lb>finiti rettangoli, e i solidi rotondi d&#039;infiniti cilindri: di rettangoli cioè e di <lb></lb>cilindri, le altezze de&#039;quali fossero minime, o indivisibili come dicevasi al­<lb></lb>lora. </s>

<s>È notabile la definizione data da esso Nardi di questi indivisibili, di­<lb></lb>cendo tali precise parole, nella sua Quadratura nuova della parabola, da noi <lb></lb>altrove integralmente trascritte dall&#039;originale: <emph type="italics"></emph>Dividasi la retta AM in parti <lb></lb>minime, sicchè, essendo una di loro AD, manchi DM da AM meno di ogni <lb></lb>proposta distanza:<emph.end type="italics"></emph.end> notabile si diceva, perchè fa esatto riscontro con i <emph type="italics"></emph>dif­<lb></lb>ferenziali<emph.end type="italics"></emph.end> leibniziani. </s></p><pb xlink:href="020/01/3002.jpg" pagenum="627"></pb><p type="main">

<s>L&#039;essere delle parti indivisibili componenti le linee, le superficie e i so­<lb></lb>lidi, era definito, a quel modo che Pappo suggeriva al Nardi, anche dal Ro­<lb></lb>berval, il quale così conclude nell&#039;introduzione al suo <emph type="italics"></emph>Traité des indivisibles:<emph.end type="italics"></emph.end><lb></lb>“ Par tout ce discours on peut comprendre que la multitude infinie de points <lb></lb>se prend pour une infinité de petites lignes, et compose la ligne intiere. </s>

<s>L&#039;in­<lb></lb>finité des lignes represente l&#039;infinité des petites superficies qui composent la <lb></lb>superficie totale. </s>

<s>L&#039;infinité des superficies represente l&#039;infinité de petites so­<lb></lb>lides, qui composent ensemble le solide total ” (<emph type="italics"></emph>Ouvrages de Matem.<emph.end type="italics"></emph.end> cit., <lb></lb>pag. </s>

<s>209), </s></p><p type="main">

<s>Benchè il Nardi e il Roberval, non riconoscendo altri Maestri che gli <lb></lb>antichi, si potessero compiacere di essere stati i primi a istituire il nuovo <lb></lb>metodo degli indivisibili, concessero nonostante generosamente ambedue le <lb></lb>prime parti del merito al Cavalieri, il quale si lasciò incautamente uscir di <lb></lb>bocca che di punti si compongon le linee, di linee le superficie, e di super­<lb></lb>ficie i solidi. </s>

<s>Farebbe maraviglia il trovare, dopo le opposizioni di Galileo, <lb></lb>rimasta questa improprietà di linguaggio nel libro della Geometria nuova, se <lb></lb>non si ripensasse che non avrebbe creduto mai l&#039;Autore d&#039;incontrarsi in let­<lb></lb>tori tanto indiscreti, e se forse non avesse temuto, col rifare il libro, di per­<lb></lb>dere l&#039;opportunità di dedicarlo a que&#039;signori, padroni suoi di Bologna. </s>

<s>L&#039;in­<lb></lb>discretezza, a cui si accennava, consisteva nell&#039;interpetrare rigidamente che <lb></lb>i punti, non aventi nessuna dimensione, potessero generar la linea, e la li­<lb></lb>nea, con una dimensione sola, la superficie che ne ha due, e la superficie il <lb></lb>solido, che ne ha tre: del qual rigore indiscreto dava il primo esempio Ga­<lb></lb>lileo nell&#039;obiezione famosa, tolta dal considerar l&#039;esaustione della scodella in <lb></lb>un circolo, e del cono inscritto in un punto. </s></p><p type="main">

<s>Dalle risposte fatte, come si narrò a pag. </s>

<s>123 del Tomo precedente, appa­<lb></lb>risce chiaro che il Cavalieri negava terminarsi la scodella in un circolo, e il <lb></lb>cono in un punto, perchè il punto che genera la linea, e la linea che ge­<lb></lb>nera la superficie debbono, secondo le sue definizioni, aver ciascuno una di­<lb></lb>mensione minima, quella di lunghezza e questa di altezza, cosicchè, venendo <lb></lb>a mancare un tal minimo elemento da una parte e dall&#039;altra, l&#039;orlo della <lb></lb>scodella non si riduce a un circolo, nè l&#039;apice del cono a un punto, ma am­<lb></lb>bedue svaniscono, e anche nell&#039;evanescenza perciò sono uguali. </s></p><p type="main">

<s>Che tale fosse veramente il concetto del Cavalieri si dichiara da quelle <lb></lb>parole scritte in risposta a Galileo, e sopra le quali giova ritornar col pen­<lb></lb>siero per meditarle: “ Al suo dubbio della scodella pareami ancora si po­<lb></lb>tesse risponder così: che nel concetto di tutte le linee d&#039;una figura piana, <lb></lb>o di tutti i piani di un corpo, non si debbono, secondo le mie definizioni, <lb></lb>intendere le estreme, benchè paiano del medesimo genere, poichè chiamo <lb></lb>tutte le linee d&#039;una figura piana le comuni sezioni del piano segante la figura <lb></lb>nel moto fatto da esso da un estremo all&#039;altro, o da una tangente infino al­<lb></lb>l&#039;opposta tangente. </s>

<s>Ora poi che il principio e termine del moto non è moto, <lb></lb>perciò non si debbono computare le estreme tangenti fra tutte le linee, e <lb></lb>così non è maraviglia, intendendo lo stesso per i piani ne&#039;solidi, che questi <pb xlink:href="020/01/3003.jpg" pagenum="628"></pb>estremi restino diseguali, come nel suo esempio della scodella ” (Campori, <lb></lb><emph type="italics"></emph>Carteggio gal.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>422, 423). </s></p><p type="main">

<s>Ecco in queste parole il metodo degli indivisibili, presentato sotto il me­<lb></lb>desimo aspetto di quello delle <emph type="italics"></emph>flussioni,<emph.end type="italics"></emph.end> che il Newton giusto immaginò per <lb></lb>evitar le censure fatte al Cavalieri. </s>

<s>E perchè l&#039;ultimo termine della flussione <lb></lb>è nella evanescenza, come il Newton è sollecito d&#039;avvertire che la infinita <lb></lb>piccolezza della quantità non si considera, quando è svanita, perchè allora è <lb></lb>nulla, ma nell&#039;atto della evanescenza; così similmente avverte il Cavalieri <lb></lb>che il termine del moto non è moto. </s></p><p type="main">

<s>Se il Newton, togliendosi dal numero degli indiscreti, indovinava questo <lb></lb>consenso, non avrebbe, per parergli troppo dura, rifiutata l&#039;ipotesi degl&#039;in­<lb></lb>divisibili, come non la rifiutarono il Torricelli e il Cartesio co&#039;loro nume­<lb></lb>rosi e valenti seguaci, i quali non si può credere che fossero di così debole <lb></lb>ingegno, da non conoscere che un punto senza alcuna dimensione, non può, <lb></lb>nemmeno moltiplicandosi all&#039;infinito, prodursi nella lunghezza di una linea. </s>

<s><lb></lb>Del proprio senno supponevano que&#039;valentuomini ne partecipassero anche i <lb></lb>loro lettori, nella mente de&#039;quali perciò non sospettarono il dubbio che linee <lb></lb>disegnate a intessere una superficie avessero la sola dimensione della lun­<lb></lb>ghezza: benchè quella della larghezza la mettessero così piccola, da non sem­<lb></lb>brar conveniente il farla apparire, e quasi che col tacerla credessero di si­<lb></lb>gnificar meglio, e di farne meglio intendere l&#039;incomprensibile piccolezza. </s></p><p type="main">

<s>Al Torricelli e al Cartesio si può aggiungere il Roberval, il quale, benchè <lb></lb>avesse dal canto suo scansato ogni occasione alle censure, dichiarava quelle <lb></lb>fatte al Cavalieri per ingiuste, e le diceva mosse dall&#039;invidia di certi scioli, <lb></lb>che si metton fra&#039;piedi a&#039;valentuomini per indugiarne i progressi. </s>

<s>La difesa <lb></lb>è tanto più eloquente, in quanto che esso Roberval la faceva, dop&#039;aver detto <lb></lb>d&#039;essersi già servito degli indivisibili, per risolver non pochi difficilissimi <lb></lb>problemi, cinque anni prima che il Cavalieri pubblicasse la sua nuova Geo­<lb></lb>metria. </s>

<s>“ Illa ergo indivisibilia an ante nos clarissimus Cavalerius invenerit <lb></lb>nescio: certe illud scio me integro quinquennio, antequam in lucem emise­<lb></lb>rit, ea doctrina usum fuisse in solvendis multis iisque plane arduis proposi­<lb></lb>tionibus. </s>

<s>Attamen ergo tanto viro non eripiam, nec possum, nec si possem <lb></lb>faciam.... Est autem inter clarissimi Cavalerii methodum et nostra exigua <lb></lb>quaedam differentia. </s>

<s>Ille enim cuiusvis superficiei indivisibilia secundum in­<lb></lb>finitas lineas, solidi autem indivisibia secundum infinitas superficies conside­<lb></lb>rat. </s>

<s>Unde ex vulgaribus Geometris plerique, sed et quidam ex superbis illis <lb></lb>sciolis, qui soli docti haberi volunt, quique si nihil aliud certe hoc unum sa­<lb></lb>tis habent ut in magnorum Virorum opera insurgant, quod a se minime <lb></lb>profecta esse invideant; occasionem carpendi Cavalerii arripuerunt, tamquam <lb></lb>si ille aut superficies ex lineis, aut solida ex superficiebus reyera constare <lb></lb>vellet ” (<emph type="italics"></emph>Epist. </s>

<s>ad Torricellium,<emph.end type="italics"></emph.end> Ouvrages cit., pag. </s>

<s>367, 68). </s></p><p type="main">

<s>Che tra que&#039;geometri volgari e fra quegli scioli superbi intendesse il <lb></lb>Roberval di comprendere Galileo, noi non lo crediamo, ma è un fatto che <lb></lb>Galileo fu il primo a cogliere in fallacia il Cavalieri, quasi egli avesse vo-<pb xlink:href="020/01/3004.jpg" pagenum="629"></pb>luto dire di fatto che le linee constan di punti, come di linee le superficie, <lb></lb>e di superficie i solidi. </s>

<s>La zizania, sparsa ne&#039;dialoghi delle due nuove Scienze <lb></lb>da quel nimico uomo del Salviati, crebbe in mezzo alla buona sementa del <lb></lb>Cavalieri, specialmente per opera del celebre Maclaurin, il quale scrisse con­<lb></lb>tro la Matematica degli infiniti un libro, che il D&#039;Alembert condannò col ti­<lb></lb>tolo di malvagio: <emph type="italics"></emph>mauvais livre contré la certitude de la Geométrie.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Insorsero contro queste insane calunnie i Matematici, e mentre da una <lb></lb>parte ne rimproveravano agramente i colpevoli, si consigliarono dall&#039;altra di <lb></lb>levarne ogni ooccasione, con usare una maggiore proprietà di linguaggio, e <lb></lb>con definire più precisamente le matematiche ragioni dell&#039;infinito. </s>

<s>Un certo <lb></lb>Autore, per citar qualche esempio, volle mettersi a commentare l&#039;<emph type="italics"></emph>Analyse <lb></lb>des infiniment petits<emph.end type="italics"></emph.end> del marchese De l&#039;Hopital, e mandò a Giovanni Ber­<lb></lb>noulli, per averne da lui il giudizio, il suo commentario. </s>

<s>Era quell&#039;Autore <lb></lb>fra il numero de&#039;congiurati ai danni dell&#039;Analisi infinitesimale, non per de­<lb></lb>liberato animo, ma per ignoranza, e il Bernoulli, fattegli prima notare certe <lb></lb>espressioni, che suonano troppo dure a un orecchio geometrico, seguitava <lb></lb>così a dirgli liberamente: “ Elles jettent plûtot dans l&#039;erreur, et dans le <lb></lb>prejugé, ou on est avant que d&#039;etre Geometre, comme si le corps étoit com­<lb></lb>posé de surfaces, la surface composée de lignes, et la lìgne composée de <lb></lb>points: prejuge fort difficile à détruire dans les jeunes gens, et qui les em­<lb></lb>péche de comprendre les démonstrations sur les figures geometriques. </s>

<s>Car <lb></lb>qu&#039;est-ce qui les trouble d&#039;avantage, que quand ils ne savent pas distinguer, <lb></lb>par exemplé, la surface d&#039;avec les lignes qui la terminent? </s>

<s>Il ne faudroit <lb></lb>donc pas se servir de ces facons de parler, qui noutrissent les prejugés au <lb></lb>lieu de les détruire ” (<emph type="italics"></emph>Opera omnia,<emph.end type="italics"></emph.end> T. IV cit., pag. </s>

<s>162). </s></p><p type="main">

<s>Il D&#039;Alembert credeva che anche da un&#039;altra parte derivassero i pre­<lb></lb>giudizi, dal non essersi cioè ben definito il concetto delle quantità infinita­<lb></lb>mente piccole, le quali, egli diceva, non sono qualche cosa di reale, come <lb></lb>dai più si crede, ma una semplice idea di relazione. </s>

<s>“ Le methode des infi­<lb></lb>niment petits n&#039;est autre chose que la méthode des raisons premieres et <lb></lb>dernieres, c&#039;est-a-dire des rapports des limites des quantités finies. </s>

<s>Quan­<lb></lb>d&#039;on a bien concù l&#039;esprit et les principes de cette Methode, alors il est <lb></lb>utile de la mettre en usage pour parvenir à des solutions élégantes ” (<emph type="italics"></emph>Traité <lb></lb>de Dynam.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>50). </s></p><p type="main">

<s>In questo stato d&#039;incertezze, di ostacoli e di battaglie, quale da questi <lb></lb>esempi ci si rappresenta, nel primo quarto e nella prima metà del secolo; <lb></lb>era il Calcolo infinitesimale anche nel principio, quando la Meccanica nuova <lb></lb>cominciò a chiamarlo in suo aiuto. </s>

<s>Il Newton, trovatoselo innanzi con l&#039;abito <lb></lb>messogli addosso dal Cavalieri, giudicandolo poco decente, volle da sè rive­<lb></lb>stirlo di un abito nuovo. </s>

<s>“ Contractiores enim redduntur demonstrationes per <lb></lb>methodum indivisibilium. </s>

<s>Sed quoniam durior est indivisibilium hypothesis, <lb></lb>et propterea methodus illa minus geometrica censetur; malui demonstratio­<lb></lb>nes rerum sequentium ad ultimas quantitatum evanescentium summas et <lb></lb>rationes, primasque nascentium, idest ad limites summarum et rationum de-<pb xlink:href="020/01/3005.jpg" pagenum="630"></pb>ducere, et propterea limitum illorum demonstrationes, qua potui brevitate, <lb></lb>praemittere ” (<emph type="italics"></emph>Principia Philos.<emph.end type="italics"></emph.end> cit., L. I, pag. </s>

<s>80, 81). </s></p><p type="main">

<s>Il Newton dunque credè di aver migliorato e corretto il metodo degli <lb></lb>indivisibili, non riguardando le quantità crescenti per apposizione di parti, <lb></lb>ma per un moto continuo, o per un continuo flusso del punto nel generar <lb></lb>la linea, della linea nel generare la superficie, della superficie nel generare <lb></lb>il solido, e dell&#039;angolo per la rotazione di un lato, dalla qual genesi mec­<lb></lb>canica è manifesto perchè venisse al metodo il nome delle <emph type="italics"></emph>flussioni.<emph.end type="italics"></emph.end> Un tal <lb></lb>metodo però non è in sostanza diverso da quello del Cavalieri, il quale, come <lb></lb>abbiamo veduto e come si potrebbe notar nel suo libro, ripete spesso i nomi <lb></lb>di esaustione, di esinanizione e di moto, equivalenti a quelli delle evane­<lb></lb>scenze, de&#039;limiti, e delle flussioni neutoniane. </s>

<s>Forse nel metodo dell&#039;Inglese <lb></lb>è più unità di concetto, e più matematica precisione, ma l&#039;avere introdotto <lb></lb>l&#039;elemento straniero del moto, che si fa col tempo, il quale ha la sua mi­<lb></lb>sura dalla velocità e dallo spazio, fece sì che i processi non si rendessero <lb></lb>direttamente applicabili altro che alla Geometria, a cui si limitava la istitu­<lb></lb>zione del Cavalieri. </s>

<s>Dentro questi limiti poi veniva a trattenere e a risospin­<lb></lb>gere il metodo riformato il principio dominatore di lui, ch&#039;escludeva le quan­<lb></lb>tità assolute, per considerarne solamente la relazione, tanto è vero che il <lb></lb>Newton non insegnò a differenziare altro che equazioni. </s></p><p type="main">

<s>In considerar queste cose si troverebbe forse la norma ai giudizi da <lb></lb>farsi intorno alle pretese degli Inglesi, per l&#039;invenzione del Calcolo infinite­<lb></lb>simale. </s>

<s>Ma lasciando le dispute altrui, per passare ai fatti nostri, esaminiamo <lb></lb>qual uso facesse di quel Calcolo il Newton, e quali vantaggi ne ritraesse per <lb></lb>dimostrare que&#039;suoi sublimi teoremi di Meccanica nuova: e dall&#039;esame re­<lb></lb>sulterà confermato che i vantaggi venuti dallo strumento rifatto erano quelli <lb></lb>stessi che i precedenti Matematici avevano avuto dall&#039;originale. </s>

<s>Anzi, chi <lb></lb>paragoni co&#039;trattati robervalliani della Cicloide, e con quegli altri torricel­<lb></lb>liani delle seconde quadrature delle parabole e dei baricentri, le proposizioni <lb></lb>scritte nel primo libro dei Principii di Filosofia naturale, non esita a decider <lb></lb>che la Matematica piglia più agile, più largo e più robusto il volo là per <lb></lb>gl&#039;indivisibili, che qua per le flussioni. </s></p><p type="main">

<s>I Tedeschi hanno senza dubbio maggior merito nell&#039;invenzione, ma <lb></lb>anch&#039;essi nel pretenderlo sembran troppo dimentichi de&#039;benefizi ricevuti dalle <lb></lb>prime tradizioni. </s>

<s>Ascoltiamo il Leibniz: “ L&#039;analyse des infinis est intiere­<lb></lb>ment differente de la Geometrie des indivisibles de Cavalieri, et de l&#039;Arithme­<lb></lb>tique des infinis de M. Wallis. </s>

<s>Car cette Geometrie de Cavalieri, qui est <lb></lb>tres-bornie d&#039;ailleurs, est attachée aux figures, ou elle cherché les sommes <lb></lb>des ordonnées; et M. </s>

<s>Wallis pour faciliter cette recherche nous donné par <lb></lb>induction les sommes de certains rangs de nombres; au lieu que l&#039;analyse <lb></lb>nouvelle des infinis ne regarde ni les figures, ni les nombres, mais les gran­<lb></lb>deurs en general, comme fait la spacieuse ordinaire ” (<emph type="italics"></emph>Opera omnia,<emph.end type="italics"></emph.end> T. III, <lb></lb>Genevae 1768, pag. </s>

<s>260, 61). </s></p><p type="main">

<s>Più proprio è far tra la Geometria del Cavalieri e l&#039;Analisi infinitesi-<pb xlink:href="020/01/3006.jpg" pagenum="631"></pb>male la differenza, che è tra la fanciullezza e la virilità, rimanendo sempre <lb></lb>medesima la persona. </s>

<s>E come di questa medesimezza potrebb&#039;essere una <lb></lb>prova l&#039;abito che sta bene addosso nelle due varie età, solamente a ridurne <lb></lb>le proporzioni del taglio; così sarebbe prova dell&#039;identità de&#039;due metodi <lb></lb>l&#039;adattarsi proporzionatamente agl&#039;indivisibili le fogge stesse dei differenziali. </s>

<s><lb></lb>La prova fu fatta dall&#039;Herman sul teorema centrobarico del Guldino, pre­<lb></lb>messovi per lemma il teorema ugeniano che cioè la somma de&#039;momenti di <lb></lb>più corpi divisi equivale al momento unico di essi corpi insieme, dal loro <lb></lb>comun centro di gravità ponderanti. </s></p><p type="main">

<s>Quanto da quel lemma derivasse facilità nelle dimostrazioni che il Nardi, <lb></lb>il Cavalieri e il Torricelli dettero della Regola guldiniana, si può compren­<lb></lb>dere dal confrontare que&#039;loro lunghi e laboriosi discorsi con questo, che si <lb></lb>spedisce così in due parole: Sia AB (fig. </s>

<s>392) l&#039;asse, intorno a cui si ri­<lb></lb>volge la figura ACFB, per generare il solido rotondo, che s&#039;affalda de&#039;cir­<lb></lb>coli descritti dai raggi DC, EF, o di tutti gli altri infiniti: cosicchè, chiamato <lb></lb>quel solido S; sarà S=<foreign lang="grc">π</foreign>(DC2+EF2....)=2<foreign lang="grc">π</foreign>(DC.DC/2+EF.EF/2...). <lb></lb>Ma le quantità dentro parentesi son la somma de&#039;momenti delle infinite linee <lb></lb>ponderose, che s&#039;immaginano concentrate nel loro mezzo, i quali momenti <lb></lb>sono uguali, pel Teorema ugeniano, al momento che resulta dal moltiplicar <lb></lb>le dette infinite linee ponderose, ossia la figura F, per la distanza D del <lb></lb>suo centro di gravità dall&#039;asse; dunque S=2<foreign lang="grc">π</foreign>D.F, come per la regola <lb></lb>del Guldino. <lb></lb><figure id="id.020.01.3006.1.jpg" xlink:href="020/01/3006/1.jpg"></figure></s></p><p type="caption">

<s>Figura 392.</s></p><p type="main">

<s>Al corollario, che immediatamente deriva da questa pro­<lb></lb>posizione, e che dice stare i solidi rotondi in ragion composta <lb></lb>delle figure genitrici, e delle distanze de&#039;loro centri di gra­<lb></lb>vità, o delle circonferenze da esse distanze, come raggi, descritte <lb></lb>intorno all&#039;asse della rotazione; si giungerebbe, per la me­<lb></lb>desima via brevissima, dal teorema del Rocca, secondo il quale <lb></lb>i solidi S, S′ stanno come i momenti dellè figure F, F′ (Tor­<lb></lb>ricelli, <emph type="italics"></emph>Op. </s>

<s>Geom.<emph.end type="italics"></emph.end> cit., P. II, pag. </s>

<s>76). Ma questi momenti <lb></lb>sono, secondo il detto Teorema ugeniano, uguali al prodotto <lb></lb>di quelle stesse figure, e delle distanze D, D′ de&#039;loro centri <lb></lb>di gravità dall&#039;asse; dunque S:S′=D.F:D′.F′=2<foreign lang="grc">π</foreign>D.F:2<foreign lang="grc">π</foreign>D′.F′. </s></p><p type="main">

<s>L&#039;Herman sostituì, come il Nardi e il Roberval, alle linee genitrici dei <lb></lb>circoli i rettangoli generatori dei cilindri, le lunghezze de&#039;quali rettangoli <lb></lb>chiama <emph type="italics"></emph>y,<emph.end type="italics"></emph.end> e le altezze <emph type="italics"></emph>dx,<emph.end type="italics"></emph.end> essendo <emph type="italics"></emph>x<emph.end type="italics"></emph.end> l&#039;asse, cosicchè la figura F, che re­<lb></lb>sulta dalla somma di cotesti infiniti rettangoli, verrà data da <emph type="italics"></emph>Ŗydx.<emph.end type="italics"></emph.end> Essendo <lb></lb>poi la somma degli infiniti momenti de&#039;rettangoli ponderosi <emph type="italics"></emph>Ŗ1/2y2 dy,<emph.end type="italics"></emph.end> dun­<lb></lb>que, chiamata D la distanza del centro di gravità della figura dall&#039;asse, sarà <lb></lb>D.Ŗ<emph type="italics"></emph>ydx<emph.end type="italics"></emph.end>=D.F=Ŗ1/2<emph type="italics"></emph>y2dx,<emph.end type="italics"></emph.end> ossia 2<foreign lang="grc">π</foreign>D.F=Ŗ<foreign lang="grc">π</foreign><emph type="italics"></emph>y2dx.<emph.end type="italics"></emph.end> Ma questa <lb></lb>significa la somma degl&#039;infiniti cilindri, che compongono il solido rotondo, <lb></lb>ossia lo stesso solido rotondo S; dunque S=2<foreign lang="grc">π</foreign>D.P. “ Figura genitrix <lb></lb>dicatur F, distantia centri eius gravitatis ab axe rotationis D, ordinata figu-<pb xlink:href="020/01/3007.jpg" pagenum="632"></pb>rae <emph type="italics"></emph>y<emph.end type="italics"></emph.end> ad axem rotationis, <emph type="italics"></emph>dx<emph.end type="italics"></emph.end> elementum axis, solidum, ex conversione figu­<lb></lb>rae F circa axem <emph type="italics"></emph>x,<emph.end type="italics"></emph.end> dicatur S, eius elementum <emph type="italics"></emph>d<emph.end type="italics"></emph.end> S. </s>

<s>Quibus positis, per prae­<lb></lb>sentem propositionem, erit D.F aequale summae momentorum elementorum <lb></lb>magnitudinis F=Ŗ1/2<emph type="italics"></emph>yydx,<emph.end type="italics"></emph.end> nam elementum ipsius F est <emph type="italics"></emph>ydx,<emph.end type="italics"></emph.end> et huius <lb></lb>momentum 1/2<emph type="italics"></emph>yydx.<emph.end type="italics"></emph.end> Sit <emph type="italics"></emph>p<emph.end type="italics"></emph.end> circumferentia circuli, cuius radius est I, et du­<lb></lb>catur antecedens aequatio in <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> ut fiat <emph type="italics"></emph>p<emph.end type="italics"></emph.end>D.F=Ŗ1/2<emph type="italics"></emph>pyydx.<emph.end type="italics"></emph.end> Iam <emph type="italics"></emph>p<emph.end type="italics"></emph.end> D est <lb></lb>circumferentia radii D, et <emph type="italics"></emph>py<emph.end type="italics"></emph.end> circumferentia radii <emph type="italics"></emph>y,<emph.end type="italics"></emph.end> atque adeo. </s>

<s>1/2<emph type="italics"></emph>pyy<emph.end type="italics"></emph.end><lb></lb>area circuli eiusdem radii <emph type="italics"></emph>y,<emph.end type="italics"></emph.end> et per cousequens 1/2<emph type="italics"></emph>pyydx<emph.end type="italics"></emph.end> cylindrulus so­<lb></lb>lido S inscriptus, seu eius elementum <emph type="italics"></emph>d<emph.end type="italics"></emph.end> S. </s>

<s>Ergo <emph type="italics"></emph>p<emph.end type="italics"></emph.end>D.F=Ŗ<emph type="italics"></emph>d<emph.end type="italics"></emph.end>S=S, quod <lb></lb>erat ostendendum (<emph type="italics"></emph>Phoron.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>15). </s></p><p type="main">

<s>Il libro, in cui si dava questa dimostrazione, era dedicato al Leibniz, in <lb></lb>quel tempo che più calorosamente i connazionali di lui agitavano la questione <lb></lb>con i connazionali del Newton, intorno a chi si dovesse de&#039;due grandi uo­<lb></lb>mini dir primo inventore del Calcolo infinitesimale. </s>

<s>L&#039;Herman volle forse <lb></lb>insinuare che l&#039;invenzione era più antica, e che, essendo stata già fatta, non <lb></lb>era maraviglia che per opera del Newton e del Leibniz, l&#039;uno inconsapevole <lb></lb>dell&#039;altro, avesse nel medesimo tempo presa un&#039;educazione diversa. </s>

<s>Se non <lb></lb>fu questa l&#039;intenzione dell&#039;Herman difficilmente si spiegherebbe com&#039;egli in­<lb></lb>tegrasse gli elementi delle figure genitrici de&#039;solidi rotondi, riguardando le <lb></lb>ordinate <emph type="italics"></emph>y<emph.end type="italics"></emph.end> come tutte invariabili, ciò che renderebbe dimostrativa la propo­<lb></lb>sizione solamente nel caso che il solido generato dalla figura fosse un cilin­<lb></lb>dro: e dall&#039;altra parte si vedeva impossibile l&#039;integrare le dette ordinate, <lb></lb>variabili senz&#039;alcuna legge, come nelle figure irregolari. </s>

<s>Il solo pensiero di <lb></lb>queste variabili, che in un medesimo termine possono esser più d&#039;una, e le <lb></lb>regole ritrovate per differenziarle e integrarle nelle serie ordinate, bastava per <lb></lb>far comprendere quanto avesse progredito l&#039;Analisi nuova sopra il Metodo <lb></lb>degl&#039;indivisibili, e perciò l&#039;Herman, nello Scolio all&#039;XI proposizione, si con­<lb></lb>tenta di dare un&#039;idea della istituzion leibniziana con qualche esempio, accen­<lb></lb>nando come quella stessa ardua istituzione dipendeva dal seguente principio <lb></lb>semplicissimo, e che parrebbe a primo aspetto di nessun uso: “ Si fuerint <lb></lb>quotcumque decrescentes magnitudines A, B, C, D, F, erunt omnium differen­<lb></lb>tiae simul sumptae aequales excessui maximae supra minimam ” (<emph type="italics"></emph>Phoron.<emph.end type="italics"></emph.end> cit., <lb></lb>pag. </s>

<s>37). </s></p><p type="main">

<s>L&#039;intenzione di scrivere, non per i Geometri provetti ma per i giovani <lb></lb>principianti, al genio de&#039;quali più che le algebriche par che s&#039;addicano le <lb></lb>dimostrazioni lineari, fu cagione che l&#039;Herman così sobriamente usasse il <lb></lb>Calcolo infinitesimale, e questo con metodi, che s&#039;avvicinavano in qualche <lb></lb>modo ai geometrici del Cavalieri. </s>

<s>L&#039;uso esteso, continuo e sicuro di quello <lb></lb>stesso Calcolo, che parve essere divenuto la ruota maestra del carro, inco­<lb></lb>minciò a farsi da&#039;successori, i progressi de&#039;quali, che ora ci rimangono a <lb></lb>esaminare, si rassomigliavano al moto del sangue nelle arterie, che succede <lb></lb>a quel delle vene, raccolto e vivificato, come nel ventricolo del cuore, nella <lb></lb>Foronomia del Matematico di Basilea. </s></p><pb xlink:href="020/01/3008.jpg" pagenum="633"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nel 1736 usciva in Pietroburgo alla luce, dalla tipografia dell&#039;Accade­<lb></lb>mia delle Scienze, un&#039;Opera in due tomi, nel titolo de&#039;quali prometteva l&#039;Au­<lb></lb>tore che s&#039;esporrebbe la Meccanica in una maniera affatto nuova. <emph type="italics"></emph>Mechanica, <lb></lb>sive motus scientia, analytice exposita, auctore Leonhardo Eulero.<emph.end type="italics"></emph.end> In che <lb></lb>consista la novità promessa lo scopre facilmente il Lettore, il quale non aveva <lb></lb>avuto fin allora tra mano che il Newton e l&#039;Herman, a solamente svolgere <lb></lb>le nuove pagine, così magre di parole e tutte infarcite de&#039;segni proprii al­<lb></lb>l&#039;analisi algebrica, ma principalmente alla infinitesimale. </s>

<s>In vent&#039;anni s&#039;è <lb></lb>fatto un gran cambiamento d&#039;idee intorno al modo più conveniente di trat­<lb></lb>tare la Scienza. </s>

<s>L&#039;Herman avvertiva, nella prefazione alla Foronomia, di aver <lb></lb>seguìto il metodo geometrico, perchè col benefizio di lui <emph type="italics"></emph>multa elegantius <lb></lb>obtinentur, quam calculis analyticis,<emph.end type="italics"></emph.end> mentre l&#039;Eulero professava che senza <lb></lb>i calcoli analitici è impossibile affatto aver delle proprietà del moto chiara <lb></lb>cognizione e distinta. </s>

<s>Ascoltiamo le sue proprie parole, scritte nella prefa­<lb></lb>zione, subito dop&#039;aver commemorati l&#039;Herman e il Newton, ne&#039;libri de&#039;quali <lb></lb>diceva non si trovar la Meccanica se non che sinteticamente trattata col me­<lb></lb>todo degli antichi. </s>

<s>“ Sed quod omnibus scriptis, quae sine analysi sunt com­<lb></lb>posita, id potissimum Mechanicis obtingit ut lector, etiamsi de veritate eo­<lb></lb>rum quae proferuntur convincatur, tamen non satis claram et distinctam <lb></lb>eorum coguitionem assequatur, ita ut easdem quaestiones, si tantillum immu­<lb></lb>tentur, proprio marte vix resolvere valeat, nisi ipse in analysim inquirat, <lb></lb>easdemque propositiones analytica methodo evolvat. </s>

<s>” </s></p><p type="main">

<s>Per verità l&#039;esperienza fatta sopra noi stessi sembrerebbe che provasse <lb></lb>tutto il contrario. </s>

<s>Abbiamo anche noi da giovani imparato la Meccanica <emph type="italics"></emph>ana­<lb></lb>lytice exposita:<emph.end type="italics"></emph.end> eppure dobbiamo ingenuamente confessare di non esserci <lb></lb>fatta un&#039;idea chiara delle particolari proprietà dei moti, se non da poi che <lb></lb>le vedemmo dimostrate ne&#039;libri del Torricelli, dell&#039;Huyghens, del Newton, <lb></lb>dell&#039;Herman, con i sintetici metodi antichi. </s>

<s>I moderni pedagogisti poi con­<lb></lb>fermano che questo s&#039;è confessato da noi avviene in tutti gli altri per legge <lb></lb>di natura, dietro l&#039;osservazione, dalla quale stabiliscono per regola doversi la <lb></lb>mente dell&#039;alunno dai particolari far risalire alla notizia degli universali. </s>

<s>Tale <lb></lb>anzi è il processo della mente umana nell&#039;acquisto di qualunque genere di <lb></lb>cognizioni, come questa nostra, e ogni altra storia delle Scienze chiaramente <lb></lb>ci dimostra. </s></p><p type="main">

<s>Dalle sensate osservazioni, e non già da&#039;sistemi de&#039;Filosofi, si scopre <lb></lb>questo esser vero: che cioè nell&#039;universale, incompreso ancora e incosciente, <lb></lb>vediamo i particolari, i quali poi ci fanno per riflessione risalire a compren­<lb></lb>dere, e ad aver chiara e distinta scienza dell&#039;universale. </s>

<s>Nello spazio etereo, <lb></lb>fuor d&#039;ogni vista degli oggetti terreni, l&#039;occhio è in mezzo ai raggi del sole, <pb xlink:href="020/01/3009.jpg" pagenum="634"></pb>eppure ei non se ne avvede, e non s&#039;avvede della presenza del solo stesso, <lb></lb>se non che quando riflette que&#039;suoi raggi da qualche parte, tanto più facen­<lb></lb>done la rivelazion luminosa, quanto è più largo e costipato il campo delle <lb></lb>riflessioni. </s>

<s>I particolari perciò non formano la vera scienza, la quale consi­<lb></lb>ste nel veder com&#039;essi dipendano da quell&#039;universale, che per mezzo loro <lb></lb>s&#039;è saputo riconoscere, e s&#039;è potuto contemplare. </s></p><p type="main">

<s>Par che volesse intendere ciò l&#039;Euler, quando diceva che non si possono <lb></lb>risolvere le questioni meccaniche, se co&#039;metodi analitici la mente non le <lb></lb>svolge. </s>

<s>La notizia de&#039;vari teoremi spicciolati non fa il Matematico, come la <lb></lb>notizia de&#039;vari individui, o animali o piante o minerali, non fa il Naturali­<lb></lb>sta. </s>

<s>Osservano diligentemente gli studiosi della Natura in quali caratteri con­<lb></lb>vengano più individui, e ne forman le specie, i generi e le classi, in che ri­<lb></lb>conoscono poi le particolari proprietà degl&#039;individui stessi. </s>

<s>E come, senza <lb></lb>aver fatto prima questo ordinamento, al veder qualche nuovo organo acci­<lb></lb>dentalmente sopravvenuto in una pianta, non saprebbe il Botanico più qua­<lb></lb>lificarla; così, dice l&#039;Eulero, se un tantin si rimovano le condizioni a un pro­<lb></lb>blema, la mente nel risolverlo si trova impacciata. </s></p><p type="main">

<s>Questo discorso però non sembra che si possa giustamente applicare al <lb></lb>Newton e all&#039;Herman, i quali sempre ebbero per principale intento di risa­<lb></lb>lire alle generalità, dalle quali le particolari questioni, trattate da Galileo e <lb></lb>dall&#039;Huyghens, si facevano scendere, come semplici corollari. </s>

<s>Si direbbe che <lb></lb>l&#039;Eulero facesse essenzialmente consistere il metodo analitico nel calcolo, con­<lb></lb>fondendo l&#039;opera con lo strumento. </s>

<s>Se sia giusta l&#039;accusa contro un tant&#039;uomo, <lb></lb>forse molti ne dubiteranno, ma è un fatto che, dopo lui, tanto s&#039;incominciò <lb></lb>ad esagerare la potenza del calcolo, da farlo prevalere al raziocinio e all&#039;espe­<lb></lb>rienza. </s>

<s>Gli esageratori però sempre hanno male interpetrate le parole, che <lb></lb>citano con grand&#039;enfasi dallo stesso Eulero: <emph type="italics"></emph>quidquid autem sit, hic calculo <lb></lb>potius quam nostro iudicio est fidendum,<emph.end type="italics"></emph.end> e la mala interpetrazione consi­<lb></lb>ste nel farle così sonare fuori del loro contesto, e contro l&#039;intenzion dell&#039;Au­<lb></lb>tore. </s>

<s>Chi legge il passo intero, com&#039;è scritto nel primo tomo della Mecca­<lb></lb>nica analitica, al secondo Scolio dopo la XXXV proposizione, trova esser <lb></lb>diversa, e più con la verità conforme, la sentenza. </s>

<s>Si propone ivi l&#039;Autore <lb></lb>di trovare la velocità in ogni punto del viaggio di un corpo, attratto con <lb></lb>qualunque ragion di forze al suo centro, e il calcolo porta che, giunto il <lb></lb>mobile in esso centro con velocità infinita, non può proseguire oltre nella <lb></lb>medesima direzione. </s>

<s>La conseguenza sembra senza dubbio, dice l&#039;Eulero, assai <lb></lb>strana, ma comunque sia, poi soggiunge, <emph type="italics"></emph>“ hic calculo potius quam nostro <lb></lb>iudicio est fidendum, atque statuendum nos saltum, si sit ex infinito in <lb></lb>finitum, penitus non comprehendere ”<emph.end type="italics"></emph.end> (pag. </s>

<s>108). </s></p><p type="main">

<s>La sentenza dunque euleriana non è assoluta, ma da pronunziarsi so­<lb></lb>lamente colà, dove si tratti di un trapasso dal finito all&#039;infinito, che per noi <lb></lb>è incomprensibile. </s>

<s>Ma come, si dirà, è incomprensibile l&#039;infinito matematico <lb></lb>all&#039;ingegno dell&#039;uomo, se egli è che lo crea? </s>

<s>Si risponde che non si tratta <lb></lb>dell&#039;infinito in sè stesso, ma del giudizio che si fa di lui, trapassando alle <pb xlink:href="020/01/3010.jpg" pagenum="635"></pb>cose finite. </s>

<s>Noi non siamo avvezzi a vedere i corpi cadere, che per uno spa­<lb></lb>zio determinato, e giunto a un termine, con una certa velocità, non si du­<lb></lb>bita se, non essendo impedito, proseguirebbe oltre nella medesima direzione <lb></lb>il suo viaggio. </s>

<s>Ciò che avverrebbe però, quando quella velocità fosse infinita, <lb></lb>non si può, dice l&#039;Eulero, giudicare da noi, che non abbiamo veduto mai <lb></lb>andare un corpo con velocità infinita. </s>

<s>Il mondo creato dal calcolo è molto <lb></lb>diverso da questo mondo reale, e si governa con altre leggi, che il calcolo <lb></lb>solo, avendole create, ha il diritto d&#039;interpetrare. </s>

<s>Ecco in quali casi esso cal­<lb></lb>colo prevale all&#039;esperienza nostra e al nostro giudizio! onde il fallo di molti <lb></lb>consiste nell&#039;aver dato all&#039;Analisi la medesima potenza sopra le quantità al­<lb></lb>gebriche, e sopra le infinitesimali; e nell&#039;aver creduto che risegga in essa <lb></lb>la virtù di partecipare la verità a tutti i nostri discorsi. </s>

<s>Se fu l&#039;Euler che <lb></lb>pose il lubrico di cadere in queste fallacie, si deve dir però che cautamente <lb></lb>trattenne sull&#039;orlo il piede, benchè anch&#039;egli s&#039;illuse, credendo che le solu­<lb></lb>zioni generali de&#039;vari problemi di Meccanica, ottenute per via dell&#039;analisi, <lb></lb>equivalessero alla generalità di quei principii, che, premostrati da lui, si vol­<lb></lb>sero a ricercare i suoi successori. </s></p><p type="main">

<s>Stava infatti da alquanti anni sollevato innanzi all&#039;ammirazione de&#039;Matema­<lb></lb>tici questo grande edifizio della Meccanica euleriana, e nonostante il D&#039;Alem­<lb></lb>bert lamentava che si fosse pensato piuttosto a sollevare il fastigio della gran <lb></lb>mole, che a dare al fondamento di lei la stabilità conveniente. </s>

<s>I principii, <lb></lb>ne&#039;quali consiste un tal fondamento, sono, diceva <emph type="italics"></emph>“ ou obseurs par eux­<lb></lb>memes, ou énoncés et démonstrés d&#039;une maniere obscure ”<emph.end type="italics"></emph.end> (<emph type="italics"></emph>Traité de <lb></lb>Dinam. </s>

<s>cit., Discours prelim.,<emph.end type="italics"></emph.end> pag. </s>

<s>IV). È necessario perciò, soggiungeva, <lb></lb>stabilire la scienza sopra principii semplici e chiari. </s>

<s>Ma se ciò solo baste­<lb></lb>rebbe a chi volesse confermare i teoremi della Meccanica, fin qui dimostrati, <lb></lb>non basta però a chi attenda insieme a provvedere ai progressi di lei, e perciò <lb></lb>vogliono que&#039;principii inoltre essere scelti tali, da accomodarsi ai nuovi usi, <lb></lb>e rifiutar quelli, che inutilmente vi si fossero introdotti. </s></p><p type="main">

<s>Ai tempi del D&#039;Alembert, cioè verso la metà del secolo XVIII, non s&#039;era <lb></lb>ancora ricomposta con pace una gran questione, incominciata fra i Matema­<lb></lb>tici a&#039;principii del secolo, intorno alle ragioni del misurare le forze, che di­<lb></lb>stinguevano in <emph type="italics"></emph>morte<emph.end type="italics"></emph.end> e <emph type="italics"></emph>vive:<emph.end type="italics"></emph.end> questione, alla quale si dava grande impor­<lb></lb>tanza, ma che lo stesso D&#039;Alembert riponeva nel numero delle altre cose inu­<lb></lb>tili alla Meccanica. <emph type="italics"></emph>“ La question de la mesure des forces est intierement <lb></lb>inutile à la Méchanique, et meme sans aucun obiet réel ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>XXIV). <lb></lb>La sentenza in conclusione è giusta, ma perchè tale non potrebbe apparire <lb></lb>a chi così asciuttamente se l&#039;udisse pronunziare, giova ridursi alla memoria <lb></lb>il commento storico, relativo alle forze vive, e alla più giusta ragione del <lb></lb>misurarle. </s></p><p type="main">

<s>Ripensando il Leibniz alle contrarietà, alle quali era andata soggetta la <lb></lb>verissima teoria ugeniana del centro delle oscillazioni, scopri che dipende­<lb></lb>vano da una fallacia de&#039;contradittori, la quale consisteva nel misurare per <lb></lb>la quantità di moto il grado e l&#039;intensità di qualunque forza. </s>

<s>Ma altro è, <pb xlink:href="020/01/3011.jpg" pagenum="636"></pb>diceva, la forza, che opera con semplice conato, come nella libbra, altro è <lb></lb>la forza, che produce un moto attuale, come nella percossa di un cadente da <lb></lb>maggiore o minore altezza. </s>

<s>Concedasi, soggiungeva il Leibniz, che in ambedue <lb></lb>i casi la quantità di moto, ossia la forza, sia misurata dal prodotto della <lb></lb>massa per lo spazio passato, ma perchè nella libbra, dove la forza è morta, <lb></lb>esso spazio sta come la velocità, e nel cadente, dove la forza è viva, sta <lb></lb>come il quadrato della velocità; dunque è falso che dal prodotto della massa <lb></lb>per la velocità si possa, come alcuni fanno, misurare allo stesso modo la <lb></lb>forza morta e la viva. </s>

<s>Il principio cartesiano perciò, che tanta forza ci vuole <lb></lb>a sollevare un peso di una libbra a due gradi di altezza, quanto a sollevare <lb></lb>a un grado solo il peso di due libbre, non vale che per le macchine in equi­<lb></lb>librio. </s>

<s>Ma negli altri casi, diceva il Leibniz, essendo una verità già dimo­<lb></lb>strata da Galileo, e confermata dall&#039;Huyghens, <emph type="italics"></emph>Corpus cadens ex certa al­<lb></lb>titudine acquirere vim eousque rursus assurgendi, uti in pendulorum motu <lb></lb>evidens est;<emph.end type="italics"></emph.end> la vera regola, da sostituirsi alla cartesiana, è questa: <emph type="italics"></emph>Tanta <lb></lb>vi aptus est ad elevandum corpus A unius librae ad altitudinem quatuor <lb></lb>ulnarum, quanta opus est ad elevandum corpus B quatuor librarum <lb></lb>usque ad altitudinem unius ulnae.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Annunziava serenamente il Leibniz agli amatori della verità queste cose, <lb></lb>negli atti degli Eruditi di Lipsia del mese di Marzo 1686. Ma quel Catelan, <lb></lb>oppositore dell&#039;Huyghens, che vedeva così essere sottilmente scoperta l&#039;ori­<lb></lb>gine delle sue fallacie, fieramente se ne risentì, e si risentì insieme con lui <lb></lb>Dionigi Papin, appartenente alla setta dei Cartesiani. </s>

<s>Si conosceva bene che <lb></lb>in ambedue i fumi dell&#039;orgoglio eran saliti a far velo al giudizio, e perchè <lb></lb>il Leibniz, vedendo scendere così chiara la conclusione dai premessi princi­<lb></lb>pii. </s>

<s>non s&#039;era dato troppa cura di confermarla con altri argomenti, vi s&#039;ap­<lb></lb>plicò sollecitamente Giov. </s>

<s>Bernoulli, dimostrando che se un corpo, con un <lb></lb>grado di velocità, tende un elastro, con due gradi ne tende quattro, con tre <lb></lb>nove, e così di seguito, d&#039;onde ne concludeva <emph type="italics"></emph>vires corporum aequalium <lb></lb>csse in duplicata ratione celeritatum,<emph.end type="italics"></emph.end> come comunicò per lettera al Wolf, <lb></lb>il quale, nel secondo tomo degli Elementi di Matematica universale, pubblico <lb></lb>la nuova bernulliana dimostrazione. (Genevae 1746, pag. </s>

<s>62). </s></p><p type="main">

<s>Il Leibniz intanto era entrato nell&#039;agone a difendersi contro i suoi ne­<lb></lb>mici, e specialmente contro il Papin, a cui raccomandava di meditar meglio <lb></lb>come stavan le cose. </s>

<s>Prese di questo modo di procedere tanta maraviglia il <lb></lb>nostro Poleni, che volle consigliare lo stesso Leibniz d&#039;usar co&#039;caparbi non <lb></lb>parole ma fatti. </s>

<s>Se i quadrati delle velocità son la vera misura delle forze vive <lb></lb>debbono, diceva, mostrarcelo le esperienze, e ripensando al miglior modo di <lb></lb>farle, trovò questo, che poi descrisse nel suo libro <emph type="italics"></emph>De Castellis,<emph.end type="italics"></emph.end> pubblicato <lb></lb>in Padova nel 1718. Prese un vaso pieno di sego rappreso, sulla piana su­<lb></lb>perficie del quale fece, da due fili, pender due globi di ugual volume, ma <lb></lb>l&#039;uno peso il doppio dell&#039;altro, e così disposti, che il più leggiero rimanesse <lb></lb>dal sego stesso distante il doppio. </s>

<s>Tagliate le sospensure, i globi caddero, e <lb></lb>scavarono nella cedente materia sottoposta due callotte, che si trovarono <pb xlink:href="020/01/3012.jpg" pagenum="637"></pb>uguali. </s>

<s>Ripetuta l&#039;esperienza più volte, col variare i pesi e le altezze delle <lb></lb>cadute, dietro la costanza de&#039;resultati ottenuti credè il Poleni doversi con­<lb></lb>cludere in generale: “ Tunc aequales vires corporum cadentium esse, cum <lb></lb>ipsorum propria pondera rationem habent reciprocam eius, quam habent <lb></lb>spatia ab iisdem corporibus cadendo emensa ” (pag. </s>

<s>57). Cosicchè, chiamate <lb></lb>F, <emph type="italics"></emph>f<emph.end type="italics"></emph.end> le forze, P, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> i pesi, e A, <emph type="italics"></emph>a<emph.end type="italics"></emph.end> le altezze, le quali stanno come i quadrati <lb></lb>delle velocità V, <emph type="italics"></emph>v;<emph.end type="italics"></emph.end> l&#039;equazione F:<emph type="italics"></emph>f<emph.end type="italics"></emph.end>=PV2:<emph type="italics"></emph>pv2,<emph.end type="italics"></emph.end> che resulta dalla espe­<lb></lb>rienza, conferma pienamente la teoria leibniziana. </s></p><p type="main">

<s>Piacque allo &#039;s Gravesande così la bella e nuova esperienza del Poleni, <lb></lb>che costruì per ripeterla quello strumento di precisione, ch&#039;ei descrisse nel <lb></lb>capitolo terzo del secondo libro de&#039;suoi Elementi di fisica matematica, sotto <lb></lb>il titolo di “ Machina, qua corporum directe cadentium vires conferuntur ” <lb></lb>(<emph type="italics"></emph>Physices elem. </s>

<s>mathem.,<emph.end type="italics"></emph.end> T. I, Leidae 1748, pag. </s>

<s>235). Consisteva in una <lb></lb>cassetta parallelepipeda di legno, piena rasa fino all&#039;orlo di molle argilla, <lb></lb>sugli angoli della quale cassetta quattro ritti formavano come due spalliere <lb></lb>di seggiola, sulle traverse delle quali, poste a uguali distanze, s&#039;appoggia­<lb></lb>vano regoli per sostenere i pesi, d&#039;onde poi si lasciavan cadere, penetrando <lb></lb>nella sottoposta mollizie più o meno, secondo il maggiore o minor impeto <lb></lb>delle cadute. </s>

<s>Que&#039;pesi constavano di tre globi di rame d&#039;un pollice e mezzo <lb></lb>di diametro ciascuno, composti di emisferi, che si ricongiungano a vite, ma <lb></lb>le loro diverse gravità stanno come uno, due, e tre. </s>

<s>Eseguitasi più volte <lb></lb>l&#039;esperienza, da altezze diverse, resultò in generale, come al Poleni, che le <lb></lb>cavità non differivano, “ quando altitudines sunt inverse ut massae, in quo <lb></lb>casu vires sunt aequales ” (ibid., pag. </s>

<s>237). </s></p><p type="main">

<s>Vincenzo Riccati ridusse all&#039;analisi matematica queste esperienze dello <lb></lb>&#039;s Gravesande e del Poleni. </s>

<s>Si chiamino <emph type="italics"></emph>m,<emph.end type="italics"></emph.end> M le masse, <emph type="italics"></emph>c,<emph.end type="italics"></emph.end> C le celerità ini­<lb></lb>ziali degli scavamenti: <emph type="italics"></emph>r,<emph.end type="italics"></emph.end> R le resistenze della materia molle, o argila, o sego, <lb></lb><emph type="italics"></emph>n,<emph.end type="italics"></emph.end> N le profondità delle fosse scavate. </s>

<s>Dalle note formole <emph type="italics"></emph>m<foreign lang="grc">φ</foreign>ds=mudu,<emph.end type="italics"></emph.end><lb></lb>M<foreign lang="grc">φ</foreign><emph type="italics"></emph>d<emph.end type="italics"></emph.end>S=MV<emph type="italics"></emph>d<emph.end type="italics"></emph.end>V, osservando che <emph type="italics"></emph>m<foreign lang="grc">φ</foreign>=—rn,<emph.end type="italics"></emph.end> M<foreign lang="grc">φ</foreign>=—R.N, per es­<lb></lb>sere le forze delle resistenze ritardatrici, avremo <emph type="italics"></emph>rnds=—mudu,<emph.end type="italics"></emph.end> RN<emph type="italics"></emph>d<emph.end type="italics"></emph.end>S= <lb></lb>—MV<emph type="italics"></emph>d<emph.end type="italics"></emph.end>V, le quali integrate danno </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>rns<emph.end type="italics"></emph.end>=—<emph type="italics"></emph>m(u2<emph.end type="italics"></emph.end>/2+P), RNS=—M(V2/2+Q).<emph.end type="center"></emph.end><lb></lb>Per determinare le costanti P, Q osserviamo che, quando <emph type="italics"></emph>u,<emph.end type="italics"></emph.end> V sono uguali <lb></lb>a <emph type="italics"></emph>c,<emph.end type="italics"></emph.end> C, le quantità <emph type="italics"></emph>s,<emph.end type="italics"></emph.end> S divengono zero, e perciò <emph type="italics"></emph>rns=(mc2—mu2<emph.end type="italics"></emph.end>)/2, RNS= <lb></lb>(MC2—MV2)/2. Ma quando <emph type="italics"></emph>u,<emph.end type="italics"></emph.end> V sono zero, <emph type="italics"></emph>s,<emph.end type="italics"></emph.end> S tornano uguali a uno; dunque <lb></lb><emph type="italics"></emph>rn<emph.end type="italics"></emph.end>:RN=<emph type="italics"></emph>mc2<emph.end type="italics"></emph.end>:MC2. </s>

<s>“ Ecco pertanto, ne conclude il Riccati, che la pro­<lb></lb>fondità delle fosse per la costante resistenza moltiplicata, che altro non è se <lb></lb>non l&#039;effetto che si vede e che si tocca con mano, riesce proporzionale alla <lb></lb>massa, e al quadrato della velocità ” (<emph type="italics"></emph>Dialogo delle forze vive<emph.end type="italics"></emph.end> cit., pag. </s>

<s>49). </s></p><p type="main">

<s>Tutto questo faticar dunque di speculazioni, d&#039;esperienze e di calcoli, di <pb xlink:href="020/01/3013.jpg" pagenum="638"></pb>cui i citati da noi non son che pochissimi esempi, diceva il D&#039;Alembert non <lb></lb>ebbe altro scopo che di risolvere una question di parole, e perciò affatto inu­<lb></lb>tile alla Meccanica, per le seguenti ragioni: Chi misura l&#039;intensità di una <lb></lb>forza dalla velocità, che imprime in un corpo, mette in considerazione piut­<lb></lb>tosto l&#039;effetto che l&#039;intrinseca causa, essendo chiaro che quel corpo va più <lb></lb>o meno veloce, secondo il maggiore o minor numero degli ostacoli, che in­<lb></lb>contra nel suo viaggio. </s>

<s>Ora questi ostacoli possono essere o insuperabili <lb></lb>affatto, o tali che facciano la resistenza precisamente necessaria ad arrestare <lb></lb>per un momento il moto, come nel caso dell&#039;equilibrio, o tali finalmente, da <lb></lb>impedire al mobile il corso a poco a poco, come ne&#039;moti ritardati. </s>

<s>I primi <lb></lb>dei detti ostacoli è chiaro che non possono servire a misurare la forza, che <lb></lb>da essi stessi è distrutta, ma quanto agli altri, “ tout le monde, dice il <lb></lb>D&#039;Alembert, convient qu&#039;il y a équilibre entre doux corps, quand les pro­<lb></lb>duits de leurs masses par leurs vitesses virtuelles, c&#039;est-à-dire par les vi­<lb></lb>tesses avec lesquelles ils tendent à se mouvoir, sont égaux de part et d&#039;au­<lb></lb>tre. </s>

<s>Donc dans l&#039;équilibre le produit de la masse par la vitesse, ou, ce qui <lb></lb>est la même chose, la quantité de mouvement, peut représenter la force. </s>

<s><lb></lb>Tout le mond convient aussi que dans le mouvement retardé le nombre des <lb></lb>obstacles vaincus est comme le quarré de la vitesse.... d&#039;ou les partisans <lb></lb>des forces vives concluent que la force des corps, qui se meuvent actuelle­<lb></lb>ment, est en général comme le produit de la masse par le quarré de la vi­<lb></lb>tesse ” (pag. </s>

<s>XX). A che disputar dunque di cose, dice il D&#039;Alembert, di <lb></lb>cui tutto il mondo-conviene? </s></p><p type="main">

<s>La conclusione in sostanza è giusta, e tutti que&#039;valentuomini, che in­<lb></lb>torno al misurar le forze esercitarono l&#039;ingegno e la mano, avrebbero fatto <lb></lb>cosa inutile davvero, quando, essendo tutti i Matematici concordi nell&#039;ammet­<lb></lb>tere i principii, avessero anche ugualmente concordato nella logica delle con­<lb></lb>seguenze. </s>

<s>Ma perchè non avvenne così, ecco qual si fu la ragione, il merito <lb></lb>e l&#039;utilità del disputare. </s>

<s>Che del resto, ne&#039;precisi termini del D&#039;Alembert, <lb></lb>aveva alquanti anni prima ridotta la questione il Wolf, il quale, in due di­<lb></lb>stinti teoremi, che sono il XXXVI e il XLIX degli elementi di Meccanica, <lb></lb>nel citato secondo tomo della Matematica universale, aveva dimostrato che <lb></lb>le forze morte e le vive stanno in ragion composta delle masse, e delle sem­<lb></lb>plici velocità quelle, ma de&#039;quadrati delle velocità queste, concludendo che <lb></lb>facevano le dimostrate verità contro coloro “ qui promiscue vires omnes in <lb></lb>ratione composita massarum et velocitatum esse statuunt ” (pag. </s>

<s>61): errore, <lb></lb>soggiungeva, che fu primo il Leibniz a scoprire e ad emendare. </s></p><p type="main">

<s>Se poi sia vero quel che dice il D&#039;Alembert, che cioè per questo fatto <lb></lb>esso Leibniz “ a cru pouvoir se faire honneur comme d&#039;une découverte ” <lb></lb>(pag. </s>

<s>XVII) non possiamo dir niente, ma sappiamo di certissimo che la sco­<lb></lb>perta era stata fatta da più di un mezzo secolo in Italia. </s>

<s>Il primo infatti a <lb></lb>commettere l&#039;errore di misurar promiscuamente, con una medesima regola, <lb></lb>le forze morte e le vive, fu Galileo, seguito poi dal Viviani, quando intesero <lb></lb>ambedue concordi d&#039;assegnar la proporzione tra gli effetti de&#039;pesi morti e <pb xlink:href="020/01/3014.jpg" pagenum="639"></pb>delle percosse: errore, che non fu scoperto nè emendato dal Leibniz, ma dal <lb></lb>Borelli, il quale osservò che le semplici gravità e gl&#039;impeti son due cose di <lb></lb>genere diverso, come di genere diverso, e perciò non comparabili insieme, <lb></lb>sono i moti uniformi e gli accelerati (<emph type="italics"></emph>De vi percuss.,<emph.end type="italics"></emph.end> Cap. </s>

<s>XXXIII). Più de­<lb></lb>cisiva era stata la questione rispetto ai liquidi, le velocità de&#039;quali nel fluire <lb></lb>da&#039;vasi erano da Galileo e dal Castelli misurate proporzionalmente alle al­<lb></lb>tezze morte, ma il Torricelli dimostrò che dovevano essere invece propor­<lb></lb>zionali alle radici delle altezze vive. </s>

<s>È notabile a questo proposito un teo­<lb></lb>rema dell&#039;Herman, in cui stare gl&#039;impeti de&#039;liquidi erompenti dai fori in <lb></lb>ragion composta delle moli e de&#039;quadrati delle velocità si conclude dalla nota <lb></lb>proposizion del Castelli, che le quantità son proporzionali alle velocità mol­<lb></lb>tiplicate per le sezioni. </s>

<s>Or perchè gl&#039;impeti son misurati dal prodotto delle <lb></lb>quantità per le velocità respettive, è manifesto che stanno in ragion compo­<lb></lb>sta delle sezioni, ossia delle moli liquide in esse comprese, e de&#039;quadrati delle <lb></lb>velocità. </s>

<s>Più notabile poi è che di questo si serva l&#039;Herman, per dimostrare <lb></lb>il principio idrodinamico del Torricelli, che cioè gl&#039;impeti degli zampilli <lb></lb>stanno come le radici delle altezze vive. </s></p><p type="main">

<s>Così fatte questioni, che ritorneranno nella Storia dell&#039;Idrodinamica, non <lb></lb>furono certamente di semplici parole, e intesero i savi che non si sarebbero <lb></lb>potute altrimenti risolvere, che per via delle esperienze, come intese il Po­<lb></lb>leni di risolvere, a quello stesso modo, la question delle forze vive. </s>

<s>Ma forse <lb></lb>il D&#039;Alembert prese di qui occasione a riputare inutile le dispute tra il <lb></lb>Leibniz e il Papin, perchè la contingenza de&#039;principii, d&#039;onde movevasi da <lb></lb>una parte e dall&#039;altra, “ ruineroit la certitude de la Méchanique, et la re­<lb></lb>duiroit à n&#039;etre plus qu&#039;une science experimentale ” (pag. </s>

<s>XII). E perchè il <lb></lb>principale intento dell&#039;Autore era quello di ridur la Meccanica stessa a una <lb></lb>scienza puramente razionale, e perciò volle che i principii, posti a lei per <lb></lb>fondamento, fossero tutti di verità necessarie, e non contingenti. </s></p><p type="main">

<s>L&#039;Eulero aveva creduto di sollevare la Scienza a quella dignità, fra gli <lb></lb>altri argomenti estrinseci, col riguardare i corpi come ridotti a punti mate­<lb></lb>riali, e in fatti chi bene osserva le astratte proprietà meccaniche degli urti <lb></lb>e delle riflessioni non si verificano esattamente che ne&#039;globuli della luce, e <lb></lb>gli stessi teoremi più fondamentali, come quello del piano inclinato, non sono <lb></lb>in ogni loro parte applicabili, che ai semplici punti ponderosi. </s>

<s>Le censure e <lb></lb>i vaniloquì del Marchetti, e di altri, non si sarebbero potuti evitare altri­<lb></lb>menti, perchè il corpo che ha sensibili dimensioni o rotola o scivola, secondo <lb></lb>che la perpendicolare, abbassata dal suo centro di gravità, cade dentro la <lb></lb>base o fuori; e ruzzolando e scivolando non serba secondo la teoria la co­<lb></lb>stante ragione esatta del suo proprio momento. </s>

<s>Il D&#039;Alembert dunque, che <lb></lb>non parve contentarsi del fatto dall&#039;Eulero, volle rendere la Meccanica una <lb></lb>scienza puramente razionale, costituendola sul fondamento di tre principii, <lb></lb>reputati da lui semplici e di verità necessaria, quali sarebbero la forza d&#039;iner­<lb></lb>zia, la composizione dei moti, e l&#039;equilibrio che si fanno insieme due corpi, <lb></lb>di masse uguali, e d&#039;uguali velocità virtuali e contrarie. </s>

<s>“ Le principe de <pb xlink:href="020/01/3015.jpg" pagenum="640"></pb>l&#039;equilibre, joint à ceux de la force d&#039;inertie, et du mouvement composé, <lb></lb>nous conduit à la solution de tous les problemes, ou l&#039;on considere le mou­<lb></lb>vement d&#039;un corps ” (pag. </s>

<s>XV). </s></p><p type="main">

<s>Che, ne&#039;principii dell&#039;inerzia e della composizion delle forze, possa avere <lb></lb>i suoi fondamenti la Dinamica, si comprende con facilità, ripensando che per <lb></lb>via di quello ritrovò Galileo le leggi della caduta de&#039;gravi, e per via di que­<lb></lb>sto ebbero i Matematici in mano il filo di Arianna, per non smarrirsi ne&#039;mec­<lb></lb>canici laberinti. </s>

<s>Più difficile, anzi quasi impossibile sembrava l&#039;altro assunto <lb></lb>del D&#039;Alembert, di derivar cioè dalla quiete le leggi universali del moto. </s>

<s>La <lb></lb>difficoltà nondimeno può solo sulla mente di coloro, i quali riguardano nella <lb></lb>quiete il moto come estinto, mentre in verità non è che contrariato. </s>

<s>Il pen­<lb></lb>siero profondo del Borelli trovò la sua più splendida applicazione nel metodo <lb></lb>di ritrovare il centro oscillatorio secondo Giacomo Bernoulli, il quale, consi­<lb></lb>derando essere le parti componenti il pendolo alcune più ritardate e altre <lb></lb>più velocitate, che se oscillassero con libertà dal medesimo punto, le une in­<lb></lb>dipendenti dalle altre; vide che il problema si riduceva alle condizioni del­<lb></lb>l&#039;equilibrio nella leva. </s>

<s>Il D&#039;Alembert poi rese generale il metodo bernoul­<lb></lb>liano, applicandolo a ritrovare la resultante del moto in più corpi, che agiscono <lb></lb>comunque gli uni sopra gli altri, e concludendolo in una regola così espressa: <lb></lb>“ Décomposes les mouvemens A, B, C..., imprimés a chaque corps, cha­<lb></lb>cun en deux autres <emph type="italics"></emph>a, a′, b, b′, c, c′...;<emph.end type="italics"></emph.end> qui soient tels que, si l&#039;on n&#039;eùt <lb></lb>imprimé aux corps que les mouvemens <emph type="italics"></emph>a, b, c...,<emph.end type="italics"></emph.end> ils eussent pù conser­<lb></lb>ver ces mouvemens sans se nuire reciproquement, et que, si on ne leur eùt <lb></lb>imprimè que les mouvèmens <emph type="italics"></emph>a′, b′, c′...,<emph.end type="italics"></emph.end> le systeme fùt demeure en repos. </s>

<s><lb></lb>Il est clair que <emph type="italics"></emph>a, b, c...<emph.end type="italics"></emph.end> seront les mouvemens, que ces corps prendront <lb></lb>en vertu de leur action ” (pag. </s>

<s>74, 75). </s></p><p type="main">

<s>Così tutte le leggi del moto venivano a ridursi a quelle dell&#039;equilibrio <lb></lb>de&#039;corpi. </s>

<s>La Statica e la Dinamica, che parevano contenere in sè una con­<lb></lb>tradizion naturale, si unirono per opera del D&#039;Alembert a comporre insieme <lb></lb>una scienza sola, cosicchè le distinzioni, così utilmente introdotte dall&#039;Her­<lb></lb>man, non rimasero che di nome. </s></p><p type="main">

<s>Ripensando alle cose fin qui discorse concluderemo che all&#039;analisi aveva <lb></lb>l&#039;Eulero educato la Meccanica, più co&#039;calcoli che coi principii; il D&#039;Alembert <lb></lb>più coi principii che con i calcoli; ma il Lagrange congiunse insieme e con­<lb></lb>temperò così bene le due virtù, che la Meccanica analitica si può dire giun­<lb></lb>gesse finalmente per lui alla sua perfezione. </s>

<s>Ei lo sente e se ne compiace, <lb></lb>infin dalle prime parole premesse all&#039;opera, facendovi notar come cosa nuova <lb></lb>che il metodo proseguito da lui l&#039;ha dispensato dall&#039;usar le figure illustra­<lb></lb>tive, cosicchè il trattato procede ne&#039;ragionamenti geometrici o meccanici, so­<lb></lb>lamente con operazioni algebriche, regolare e uniforme. </s>

<s>“ Ceux qui aiment <lb></lb>l&#039;analyse, soggiunge e termina così quelle brevi parole, verront avec plaisir <lb></lb>la Mechanique en devenir une nouvelle branche, et me sauront gré d&#039;en avoir <lb></lb>étendu ainsi le domaine ” (<emph type="italics"></emph>Mechan. </s>

<s>anal.,<emph.end type="italics"></emph.end> a Paris 1788, pag. </s>

<s>VI). </s></p><p type="main">

<s>Ma il metodo, più che dalla forma esteriore del calcolo, prende effica-<pb xlink:href="020/01/3016.jpg" pagenum="641"></pb>cia dalla generalità dei principii, che anche il Lagrange riduce sommaria­<lb></lb>mente a tre: a quello dell&#039;equilibrio nella leva, a quello della composizion <lb></lb>delle forze, e all&#039;altro infine delle velocità virtuali. </s>

<s>Il D&#039;Alembert, come ve­<lb></lb>demmo, dietro l&#039;esempio dei predecessori, aveva ridotto questi due ultimi a <lb></lb>uno solo, ma il Nostro vide tanta essere l&#039;importanza del principio delle <lb></lb>velocità virtuali, che da lui, reso universale, fece principalmente dipendere <lb></lb>tutta la Scienza del moto. </s>

<s>Il primo uso, che se ne fece nelle questioni mec­<lb></lb>caniche, lo ravvisa nel trattato delle macchine di Galileo, con quanta ragione <lb></lb>poi se lo sanno oramai bene i nostri Lettori, a&#039;quali giova rammemórare in <lb></lb>proposito i dubbi de&#039;Discepoli, che si volsero, per dar più fermo fondamento <lb></lb>alla Statica, a cercare e a sostituire altri principii diversi da quello delle <lb></lb>velocità virtuali, creduto da loro contenere in sè una fallacia. </s>

<s>Nè que&#039;dubbi <lb></lb>erano irragionevoli, allora che Galileo stesso proponeva intorno alle quantità <lb></lb>infinitamente piccole dottrine così imperfette, anzi false, e insegnava a diffi­<lb></lb>dare della bontà de&#039;nuovi metodi del Cavalieri. </s>

<s>Di qui è che il principio <lb></lb>delle velocità virtuali, benchè verissimo in sè stesso, era ai discepoli di Ga­<lb></lb>lileo indimostrabile, e perciò non si potè farne sicuro uso nella Meccanica, <lb></lb>se non da poi che s&#039;istitui, e si diffuse il calcolo infinitesimale. </s>

<s>Primo infatti <lb></lb>a proporlo in forma ben definita fu Giovanni Bernoulli, come dice il La­<lb></lb>grange, e come si riferì da noi in altra occasione, citando la lettera, in cui <lb></lb>esso Bernoulli comunicava al Varignon il suo proprio Teorema. </s>

<s>Da questa <lb></lb>scrittura del Matematico di Basilea s&#039;aprì la mente al Nostro, il quale rico­<lb></lb>nobbe che le velocità virtuali porgevano al Matematico un principio sem­<lb></lb>plice, e nello stesso tempo così preciso, da esser l&#039;unico possibile a tradursi <lb></lb>in una equazion generale, in cui si comprenderebbe tutta la varietà de&#039;teo­<lb></lb>remi, che si potrebbero proporre intorno all&#039;equilibrio dei gravi. </s>

<s>“ Nous al­<lb></lb>lons exposer cette formule dans toute son étendue; nous tàcherons mème <lb></lb>de la présentér d&#039;une maniere èncore plus générale qu&#039;on ne l&#039;a fait jusqu&#039;à <lb></lb>present, et d&#039;en donner des applications nouvelles ” (pag. </s>

<s>12). Fra queste <lb></lb>nuove applicazioni forse è la più notabile quella fatta all&#039;equilibrio di più <lb></lb>forze, in un sistema di punti connessi con un filo flessibile o con una verga <lb></lb>rigida, ma dal proposto disegno, che poi nella prima parte dell&#039;Opera si vede <lb></lb>dall&#039;Autore maestrevolmente eseguito, si possono giudicare le promozioni ve­<lb></lb>nute alla Statica per opera del Lagrange. </s></p><p type="main">

<s>Rispetto alla Dinamica il teorema generalissimo proposto dal D&#039;Alem­<lb></lb>bert, e che consisteva, come si disse, nel dedurre dalle precedenti condizioni <lb></lb>dell&#039;equilibrio, per via indiretta, le equazioni necessarie a risolvere qual si <lb></lb>voglia problema concernente il moto; era senza dubbio assai seducente, ma, <lb></lb>in venire a farne l&#039;applicazione, s&#039;ebbe più volte a incontrarvi non poche <lb></lb>difficoltà, per determinar le forze che debbono esser distrutte, e a fare espe­<lb></lb>rienza che la legge dell&#039;equilibrio fra esse forze menava troppo spesso alla <lb></lb>conclusione per vie intralciate e penose. </s>

<s>A ridurle perciò più agevoli, e più <lb></lb>spedite, il Lagrange sperò che gioverebbero le velocità virtuali, le quali, come <lb></lb>lo avevano così facilmente condotto a risolvere tutte le questioni della Sta-<pb xlink:href="020/01/3017.jpg" pagenum="642"></pb>tica; così lo condurrebbero similmente a risolvere le questioni della Dina­<lb></lb>mica. </s>

<s>Se non che, mentre là bastava quel principio solo, qui voleva esser <lb></lb>congiunto con un altro, dalla qual congiunzione glie ne venne a resultare <lb></lb>un metodo nuovo, molto simile al primo, cosicchè le due Scienze dell&#039;equi­<lb></lb>librio e del moto de&#039;gravi, se naturalmente avevano abito vario, non si po­<lb></lb>teva però dire che l&#039;avessero diverso. </s></p><p type="main">

<s>Volendo il Lagrange stesso, nella prima sezione della seconda parte del­<lb></lb>l&#039;Opera, dare una certa idea di quel metodo a&#039;suoi Lettori, riduce alla loro <lb></lb>memoria che il principio delle velocità virtuali consiste in ciò che, essendo <lb></lb>un sistema di punti fisici, e sollecitato da qualunque forza, in equilibrio, se <lb></lb>diasi al detto sistema un piccolissimo impulso, e tale da promovere ciascun <lb></lb>punto per uno spazio infinitesimo; la somma delle forze, moltiplicate a una <lb></lb>a una per il respettivo spazio percorso, deve sempre essere uguale a zero. </s>

<s><lb></lb>Se inoltre si suppone il sistema esser mosso, e il moto particolare, che cia­<lb></lb>scuno dei punti componenti ha in un dato istante, si decomponga in due, <lb></lb>l&#039;un de&#039;quali sia quello che prenderà il punto stesso nell&#039;istante successivo; <lb></lb>si vedrà facilmente che l&#039;altro deve esser distrutto, per l&#039;azion reciproca dei <lb></lb>punti materiali, e per quella delle forze motrici, dalle quali sono attualmente <lb></lb>sollecitati. </s>

<s>Dovendo poi queste forze equilibrarsi con le resistenze opposte, <lb></lb>ne consegue che, per applicare a un sistema in moto la formula del suo pro­<lb></lb>prio equilibrio, basta aggiungervi i termini rappresentativi di quelle stesse <lb></lb>forze motrici. </s></p><p type="main">

<s>“ Or si on considere, prosegue a dire il Lagrange, ainsi que nous l&#039;avons <lb></lb>déja fait plus haut, les vitesses, que chaque corps a suivant trois directions <lb></lb>fixes et perpendiculaires entr&#039;elles, les décroissemens de ces vitesses repré­<lb></lb>senteront les mouvemens perdue suivant les mèmès directions, et leurs <lb></lb>accroissemens seront par consequent les mouvemens perdus dans des di­<lb></lb>rections opposées. </s>

<s>Donc les pressions resultantes de ces mouvemens perdus <lb></lb>seront exprimées en général par la masse multipliée par l&#039;élément de la vi­<lb></lb>tesse, et divisée par l&#039;élément de tems, et auront des directions directement <lb></lb>contraires à celles des vitesses. </s>

<s>De cette maniere on pourra exprimer anali­<lb></lb>tiquement les termes dont il s&#039;agit, et l&#039;on aura une formule generale pour <lb></lb>le mouvement des corps, la quelle renformera la solution de tous les pro­<lb></lb>blemes de Dynamique, comme on le verra dans la suite de cet traité ” <lb></lb>(<emph type="italics"></emph>Mechan. </s>

<s>anal.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>181, 82). </s></p><p type="main">

<s>E quei che seguitano a leggere e a meditare il trattato non posson non <lb></lb>ammirar la profondità, a cui si ridusse la Meccanica per opera dell&#039;Autore. <lb></lb></s>

<s>È una profondità quasi direbbesi paurosa, simile a quella di una immensa <lb></lb>cisterna, attraverso alle limpide acque della quale scorge l&#039;occhio ogni og­<lb></lb>getto giacente sul fondo: sono i brividi, che mette addosso il pensiero del­<lb></lb>l&#039;infinito, e che fanno quasi rifuggire dal contemplarlo. </s>

<s>E come all&#039;infinito <lb></lb>non si può aggiungere nulla di più, così nulla di più sembrava si potesse <lb></lb>oramai aggiungere alla Meccanica analitica del Lagrange. </s>

<s>Che se anche que­<lb></lb>sto, come tutti gli altri discorsi, che prescrivono un limite al progredir del-<pb xlink:href="020/01/3018.jpg" pagenum="643"></pb>l&#039;ingegno, sembrasse una esagerazione, si ripensi che i progressi fatti di poi <lb></lb>dall&#039;analisi applicata alla Scienza del moto riguardano piuttosto la facilità <lb></lb>de&#039;calcoli, e la semplicità de&#039;metodi, che la universalità de&#039;principii in­<lb></lb>formativi. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;indole della Meccanica analitica è, per le cose fin qui discorse, defi­<lb></lb>nita in sè stessa, e si vede consistere nel ridur la Scienza del moto alla cer­<lb></lb>tezza della verità matematica. </s>

<s>La parte fisica o sperimentale è sparita affatto, <lb></lb>e si direbbe piuttosto ch&#039;è dissipata, come a un calore intenso si dissipa un <lb></lb>corpo, di cui non riman che l&#039;ultima e sottilissima essenza. </s>

<s>Ciò che ne av­<lb></lb>verte dover essersi già posto il termine alla nostra Storia, la quale nulladi­<lb></lb>meno, non contenta di esser risalita sul monte, ha voluto anche mostrar come <lb></lb>su quella cima fermato il piede spiccassero i Matematici il volo sublime. </s>

<s>E <lb></lb>ora che quel termine è giunto realmente, vogliam dare uno sguardo fuggi­<lb></lb>tivo indietro alla via lunga e faticosa, che vi ci ha condotti. </s></p><p type="main">

<s>Della lunghezza non diciamo, ma della fatica può farsi un&#039;idea chiun­<lb></lb>que ripensi che della Meccanica mancava fin qui una Storia ordinata, e che <lb></lb>avesse particolar riguardo alla cultura datasi a questa Scienza in Italia. </s>

<s>Ma <lb></lb>mentre si meditava da noi l&#039;ardua impresa, e si significava per le pagine <lb></lb>dei due Tomi, che son sotto gli occhi del pubblico, i nostri pensieri; nella <lb></lb>dotta Germania si leggevano dalle cattedre scritti, e si stampavano libri sullo <lb></lb>stesso argomento. </s>

<s>I nostri, che non si risolvono a far nulla se non venga a <lb></lb>loro l&#039;esempio dagli stranieri, hanno incominciato a delibare il soggetto, non <lb></lb>curato fin qui, benchè le istituzioni meccaniche formino una delle glorie più <lb></lb>insigni della Scienza italiana. </s>

<s>Come poi que&#039;tali prendono dagli altri gli im­<lb></lb>pulsi a fare, così del fare ne imitano fedelmente i modi. </s>

<s>Ora, hanno trovato <lb></lb>i sapienti d&#039;oltremonti un modo di risolvere facilmente qualunque più arduo <lb></lb>problema della Scienza, in quella, ch&#039;essi chiamano legge dell&#039;evoluzione, e <lb></lb>per la quale si dà ad intendere come una semplice cellula siasi andata in­<lb></lb>gradando via via, da venire all&#039;essere di una pianta e di un animale. </s>

<s>Il prin­<lb></lb>cipio informativo e regolatore di così fatti progressi consiste in ciò che, degli <lb></lb>organi accidentalmente sopravvenuti, non rimangono se non che quelli, che <lb></lb>favoriscono il ben essere dell&#039;individuo, e stringono meglio insieme le rela­<lb></lb>zioni ch&#039;egli ha co&#039;suoi simili, per cui prosperano quegli organi, e prospe­<lb></lb>rando si perfezionano; a differenza degli altri, che vanno a perdersi a poco <lb></lb>a poco o a ridursi nello stato di rudimenti. </s>

<s>Così, per questo provvido istinto <lb></lb>di sceglier sempre il migliore, e di repudiare il peggiore, tutti gli esseri na­<lb></lb>turali son giunti via via dall&#039;infimo al più alto grado e perfetto. </s></p><p type="main">

<s>Chi veramente abbia infuso quell&#039;istinto nella Natura, e da chi sia re­<lb></lb>golato, la maggior parte de&#039;settatori di queste nuove dottrine non lo sa e <pb xlink:href="020/01/3019.jpg" pagenum="644"></pb>non lo dice, per cui lasciano mancare alla loro scienza il primo fondamento. </s>

<s><lb></lb>Ma i più savi la riconoscono da un Dio creatore, e nelle loro mani quella <lb></lb>stessa Scienza, per tanti altri così desolata, come viene ad aver fermezza di <lb></lb>principii, così ha o potrebbe avere speranza di più lieti progressi. </s>

<s>A torto <lb></lb>perciò alcuni, per il solito vezzo di recalcitrare a ogni novità, condannano <lb></lb>il sistema dell&#039;evoluzione, per il quale è venuta a&#039;nostri giorni a ricevere <lb></lb>tanto incremento la Storia naturale, e anche maggiore ne potrebbe ricevere, <lb></lb>se con più senno si procedesse dagli uomini in questo mondo. </s>

<s>Fin qui sven­<lb></lb>turatamente ci troviamo stare tra i due eccessi con coloro, che da una parte <lb></lb>rifuggono dal così detto darvinismo come da una empietà, e con quegli altri <lb></lb>che lo vogliono con incredibile imprudenza costituire a principio supremo di <lb></lb>ogni ordine di cose, o sieno percettibili per gli occhi o per la mente, o si <lb></lb>tratti insomma di Fisica o di Psicologia. </s>

<s>Allo svolgersi del pensiero nel cer­<lb></lb>vello di un uomo s&#039;intende applicar le medesime leggi, che allo svolgimento <lb></lb>dell&#039;ovulo in un nido, o del seme in un orto. </s></p><p type="main">

<s>Dal pensiero dell&#039;individuo era naturale il trapasso a farne l&#039;applica­<lb></lb>zione al pensiero di tutto il genere nella Storia delle scienze, fra le quali è <lb></lb>toccato finalmente la sorte anche alla Meccanica. </s>

<s>Le minute notizie partico­<lb></lb>lari si stimano oramai cose indegne de&#039;novelli scrittori, l&#039;alto ufficio de&#039;quali <lb></lb>si è quello di descrivere le lotte, in cui son dovuti entrare l&#039;un contro l&#039;al­<lb></lb>tro i vari principii assunti via via da&#039;vari autori, per farne conseguire le <lb></lb>verità dei loro teoremi: lotte, nelle quali, rimasero sopra gli altri vittoriosi, <lb></lb>fra i predetti principii, quelli, che più facilmente si porgevano a risolvere le <lb></lb>proposte questioni. </s>

<s>Così spiegasi come ai tempi per esempio del Lagrange <lb></lb>toccasse la fortunata vittoria al principio delle velocità virtuali. </s></p><p type="main">

<s>Noi, dietro i canoni di una Filosofia più antica, e confermata anch&#039;essa <lb></lb>dalle osservazioni dei fatti, abbiamo riconosciute le ragioni di quel progre­<lb></lb>dire che ha fatto la Meccanica dall&#039;invenzion de&#039;principii, scelti dagli Au­<lb></lb>tori fra i più semplici e universali, ma quella scelta l&#039;abbiamo veduta di­<lb></lb>pendere e regolarsi con una legge tutta propria dell&#039;intelletto, e che non ha <lb></lb>con la selezion darviniana altra analogia, da quella in fuori che passa tra il <lb></lb>mondo fisico e il mondo morale. </s>

<s>I novelli Filosofi gli confondono in un mondo <lb></lb>solo, e in ciò consiste quella imprudenza che si diceva. </s>

<s>Si persuadono co­<lb></lb>storo che medesimi siano gli organi inservienti alla vita intellettiva e all&#039;a­<lb></lb>nimale, perchè credono che cotesti organi si riducano solamente a quelli, <lb></lb>che si possono dissecare col coltello anatomico, o vedere col microscopio, e <lb></lb>che perciò son composti di solidi e di liquidi, in mezzo a&#039;quali se ne sco­<lb></lb>prono altri aerei e vaporosi. </s>

<s>Ma in queste esalazioni, non difficili a racco­<lb></lb>gliersi e a esaminarsi, termina la serie de&#039;corpi conoscibili da noi con l&#039;uso <lb></lb>dei nostri sensi, benchè si comprenda dover essere in natura altre sostanze, <lb></lb>più sottili per dir così e più raffinate, e delle quali, come dell&#039;elettricità, non <lb></lb>abbiamo altra notizia che dagli effetti osservabili da noi nelle materie crasse. </s>

<s><lb></lb>Or chi sa di quante altre varie essenze e proprietà son fluidi eterei in na­<lb></lb>tura? </s>

<s>Eppure, dovendo essere essi gli organi immediati della vita, bisogne-<pb xlink:href="020/01/3020.jpg" pagenum="645"></pb>rebbe conoscerli nella loro più intima essenza, per decider prudentemente, <lb></lb>se medesimi essendo della vita fisiologica e della psicologica gli organi e le <lb></lb>funzioni, si possano i loro svolgimenti assoggettare alle medesime leggi. </s>

<s>In <lb></lb>tanta incertezza la filosofica prudenza ci consiglia di starcene all&#039;osservazione <lb></lb>de&#039;fatti, da&#039;quali apparisce che son diverse qua e là le funzioni, e che per­<lb></lb>ciò diverse, nell&#039;uno ordine di cose e nell&#039;altro, debbon essere le leggi degli <lb></lb>svolgimenti. </s></p><p type="main">

<s>Ma o si seguano intorno a ciò le più sane antiche dottrine, o si corra <lb></lb>inconsideratamente dietro alle nuove, sembra la questione in ogni modo o <lb></lb>affatto estranea, o non toccar che indirettamente la Storia, ufficio della quale <lb></lb>è di narrare i principii, da cui mosse la Scienza, e i termini a cui giunse <lb></lb>finalmente vittoriosa, dopo il travaglio dei dubbi combattuti, e l&#039;esperienza <lb></lb>dei patiti errori. </s>

<s>Lo storico insomma non può dispensarsi dal dar notizie, <lb></lb>rese dalle testimonianze certe, e dalla critica sincere. </s>

<s>La maggior parte degli <lb></lb>scrittori è vero ha male adempiuto fin qui a un tale ufficio, facendo per lo <lb></lb>più consistere la storia nel descriver la vita civile e letteraria de&#039;varii au­<lb></lb>tori, senza curarsi di penetrare addentro alla vita del pensiero, o leggendola, <lb></lb>no negli originali, ma nelle relazioni di questo o di quello, desunte senza <lb></lb>giudizio da altre precedenti relazioni. </s></p><p type="main">

<s>Riconosciuta l&#039;imperfezione del metodo, tutto rivolto a rappresentar le <lb></lb>cose nel solo abito esterno, o nelle loro più insignificanti minuzie; s&#039;è cre­<lb></lb>duto di emendarlo, con risalir d&#039;un tratto a ritrovar le supreme leggi in­<lb></lb>formative di que&#039;fatti particolari: e invece della Storia son venuti que&#039;dotti <lb></lb>stranieri a darci una Filosofia della Storia. </s>

<s>Ma se questa Filosofia, a qua­<lb></lb>lunque soggetto storico si riferisca, suppone com&#039;è ragionevole la notizia dei <lb></lb>fatti particolari, da&#039;quali si vuol risalire al principio universale che gl&#039;in­<lb></lb>forma, per dedurne la legge degli svolgimenti; è manifesto che si crede da <lb></lb>costoro essere cotali fatti bene accertati, perchè altrimenti sarebbero senza <lb></lb>fondamento le loro speculazioni. </s>

<s>Ora a noi sembra questa opinione inconsi­<lb></lb>derata, e ci fa maraviglia che non se ne siano accorti que&#039;valentuomini, se <lb></lb>fu la detta imperfezione de&#039;metodi storici precedenti, che gli consigliò così <lb></lb>risolutamente a repudiarli. </s>

<s>E se gli avessero per ciò solo repudiati, perchè <lb></lb>si trattenevano in minuzie, si potrebbe dire che una certa boria filosofica fu <lb></lb>che ve gl&#039;indusse, perchè avrebbero dovuto invece prima esaminare se quelle <lb></lb>sparse e minuziose notizie almeno erano vere, e sopra quelle riconosciute ve­<lb></lb>rità, come sopra stabile fondamento, edificare la nuova Storia filosofica. </s></p><p type="main">

<s>Quell&#039;esame, dannosamente trascurato dai nostri predecessori, l&#039;abbiamo <lb></lb>voluto istituir noi, non facendo alcun conto delle relazioni altrui, ma ricer­<lb></lb>cando i pensieri e le scoperte de&#039;varii autori nelle loro opere originali. </s>

<s>E <lb></lb>perchè di que&#039;pensieri e di quelle scoperte, per ciò che particolarmente con­<lb></lb>cerne la Scuola italiana, rimaneva tuttavia la miglior parte nei manoscritti, <lb></lb>abbiamo usato una special diligenza nel produrli alla luce con i loro com­<lb></lb>menti storici, superate le difficoltà, che avevano fatto fin qui arretrar dal­<lb></lb>l&#039;impresa tanti altri, senza dubbio più valorosi di noi, ma forse meno pazienti. </s></p><pb xlink:href="020/01/3021.jpg" pagenum="646"></pb><p type="main">

<s>Nè del trascrivere da quelli, che volgarmente si chiamerebbero scara­<lb></lb>bocchi, tante proposizioni, e anzi trattati interi, fu solo il nostro pensiero <lb></lb>quello di far note al mondo le importanti verità dimostrate, ma di aggiun­<lb></lb>gere esempi nuovi di ciò, che valesse alle mani di quegli antichi il calcolo <lb></lb>infinitesimale, sotto l&#039;abito geometrico degl&#039;indivisibili cavalierani. </s>

<s>I canoni <lb></lb>di questo metodo si desumono con facilità da pochi teoremi degli Elementi <lb></lb>di Euclide, cosicchè possono speditamente maneggiarlo anehe i giovani prin­<lb></lb>cipianti, e con esso risolvere in Geometria e in Meccanica grandissima parte <lb></lb>de&#039;più ardui problemi. </s>

<s>Ora, cotesti problemi non si propongono alla gio­<lb></lb>ventù studiosa, se non che dopo quel lungo e periglioso tirocinio, che è ne­<lb></lb>cessario per giungere a trattar le regole de&#039;calcoli differenziale e integrale. </s>

<s><lb></lb>Si sperava perciò da noi che non inutili riuscirebbero gli esempi del Rober­<lb></lb>val, del Torricelli, del Nardi e degli altri, che ricorrono in questa Storia, se <lb></lb>consigliassero qualche maestro a imitarli, e a suoi giovani discepoli, che hanno <lb></lb>appena varcate le soglie della Geometria, facesse pregustare molte di quelle <lb></lb>verità, il penetrar le quali non si crede possibile a nessuno, che non abbia <lb></lb>in mano le chiavi della Matematica più sublime. </s>

<s>La fallacia di una tale <lb></lb>opinione fu primo a riconoscerla, e a mostrarla l&#039;Herman, il quale, come si <lb></lb>legge nella sua prefazione alla <emph type="italics"></emph>Foronomia,<emph.end type="italics"></emph.end> per molteplici esperienze ammae­<lb></lb>strato fornirsi dalla meditazione delle figure soluzioni più semplici ed ele­<lb></lb>ganti che dall&#039;analisi speciosa; applicò gli stessi segni e simboli leibniziani <lb></lb>allo schietto metodo geometrico del Cavalieri. </s></p><p type="main">

<s>Per quel che riguarda poi i documenti ricavati da&#039;libri, che sono alla <lb></lb>pubblica luce, non ci siam contentati d&#039;indicar semplicemente le pagine del­<lb></lb>l&#039;Opere via via citate, ma ne abbiamo trascritte le parole proprie, perchè <lb></lb>rimeditandole possano per sè medesimi giudicare i Lettori se le abbiamo sem­<lb></lb>pre interpetrate a dovere, o se ci fossimo anche più spesso ingannati. </s>

<s>In tali <lb></lb>inganni, quando qualcuno ve gli scoprisse, confessiamo che consisterebbe il <lb></lb>maggior difetto della nostra Storia, la quale, qualunque ella si sia, presen­<lb></lb>tiamo al pubblico perchè, o approvandola o correggendola, possa stare in <lb></lb>quel giusto mezzo in cui ci siamo studiati di metterla, cosicchè da una parte <lb></lb>supplisca alle notizie o false o insufficienti, date da chi ci ha preceduto, e <lb></lb>dall&#039;altra possa fornire a chi ci succede materia di più sublimi storiche spe­<lb></lb>culazioni. </s></p><pb xlink:href="020/01/3022.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICI<emph.end type="center"></emph.end><pb xlink:href="020/01/3023.jpg"></pb></s></p><pb xlink:href="020/01/3024.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE DEI CAPITOLI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Delle correzioni e delle riforme ne&#039;Dialoghi delle due Scienze nuove.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Del supposto principio delle velocità uguali dopo cadute uguali, e come sortisse a Ga­<lb></lb>lileo, al Michelini, al Baliani finalmente di dimostrarlo <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 7 </s></p><p type="main">

<s>II Del supposto galieiano confermato per le dimostrazioni del Torricelli, del Baliani, del­<lb></lb>l&#039;Huyghens e del Marchetti ” 18 </s></p><p type="main">

<s>III Di alcune aggiunte, da farsi ai Dialoghi, dettate da Galileo al Viviani suo ospite in Ar­<lb></lb>cetri ” 32 </s></p><p type="main">

<s>IV Dell&#039;opera di ampliare le dottrine esposte ne&#039;Dialoghi del moto, proseguita dal Viviani, <lb></lb>dopo la morte di Galileo ” 45 </s></p><p type="main">

<s>V Delle correzioni di alcuni falsi teoremi di Galileo, che fecero finalmente risolvere il Vi­<lb></lb>viani d&#039;illustrare e di promovere, in un&#039;Opera a parte, le dottrine del suo Maestro ” 54 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del quinto Dialogo aggiunto alle due Scienze nuove, <lb></lb>ossia della Scienza delle proporzioni.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Di ciò che, a riformare il quinto libro di Euclide, scrisse Giovan Batista Benedetti, e <lb></lb>pensò Antonio Nardi <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end> 77 </s></p><p type="main">

<s>II Come Giovan Antonio Rocca porgesse occasione al Cavalieri di restaurare il principio alla <lb></lb>Scienza delle proporzioni, che poi Galileo fece mettere in dialogo ” 84 </s></p><p type="main">

<s>I Del disteso fatto dal Torricelli del quinto dialogo galileiano, aggiunto alle due Scienze <lb></lb>nuove ” 95 </s></p><p type="main">

<s>IV Del trattato torricelliano <emph type="italics"></emph>De proportionibus,<emph.end type="italics"></emph.end> inedito, e della Scienza universale delle <lb></lb>proporzioni spiegata da V. </s>

<s>Viviani ” 101 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del sesto Dialogo aggiunto alle due Scienze nuove, <lb></lb>ossia della forza della percossa.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Dei principii, da cui dipende la forza della percossa, proposti da Aristotile, dal Cardano <lb></lb>e da Galileo, e come fossero dimostrati falsi <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>111 </s></p><p type="main">

<s>II Del ritrovamento e della pubblicazione del sesto dialogo galileiano: se ne esaminano <lb></lb>brevemente le materie, e si conclude essere anch&#039;egli informato dai medesimi falsi <lb></lb>principii professati in gioventù dall&#039;Autore ” 123 </s></p><p type="main">

<s>III Della reintegrazione del Dialogo galileiano, pubblicato dal Bonaventuri ” 137 </s></p><p type="main">

<s>IV Degli strumenti immaginati e descritti per misurare la forza della percossa ” 155 </s></p><pb xlink:href="020/01/3025.jpg" pagenum="650"></pb><p type="main">

<s>V Della nuova Scienza della percossa, istituita prima da Giovan Marco Marci tra gli stra­<lb></lb>nieri, e poi dal Borelli nella Scuola galileiana, e di ciò che conferirono a promover <lb></lb>la detta Scienza gli Accademici di Londra e di Parigi <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>169 </s></p><p type="main">

<s>VI Delle relazioni fra gli angoli dell&#039;incidenza e della riflessione, e fra i momenti delle per­<lb></lb>cosse dirette e delle oblique ” 181 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del settimo Dialogo da aggiungersi alle due Scienze nuove, <lb></lb>ossia dei Problemi fisici e matematici.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Dei problemi, che si dovevano aggiungere dopo la <emph type="italics"></emph>Scienza meccanica,<emph.end type="italics"></emph.end> e come Galileo <lb></lb>pensasse di ridurli in Dialogo <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>195 </s></p><p type="main">

<s>II Di altri problemi e speculazioni intorno a varii soggetti di Fisica ” 206 </s></p><p type="main">

<s>III Delle questioni matematiche, e dei varii teoremi e problemi di Geometria raccolti dal <lb></lb>Viviani ” 221 </s></p><p type="main">

<s>IV Dei quesiti algebrici, e del misurar con la vista ” 237 </s></p><p type="main">

<s>V Dei Teoremi di Geometria avanzati alle dimostrazioni dei moti locali ” 248 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Del trattato dei centri di gravità di Evangelista Torricelli.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Dei primi esercizi giovanili intorno ai libri baricentrici di Archimede <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>263 </s></p><p type="main">

<s>II Dell&#039;invenzione dei centri di gravità, nelle porzioni di parabola e di cerchio ” 269 </s></p><p type="main">

<s>III Di alcnne nuove invenzioni haricentriche, per via degli indivisibili ” 281 </s></p><p type="main">

<s>IV Dei centro di gravità degli archi di cerchio, e delle fallacie del Guldin intorno ai centri <lb></lb>delle callotte, delle zone e de&#039;settori sferici, notate dal Cavalieri, dopo le dimostra­<lb></lb>zioni avute dal Torricelli ” 298 </s></p><p type="main">

<s>V Della diversità del metodo del Keplero da quello del Cavalieri, e come fosse questo ap­<lb></lb>plicato dal Torricelli per ritrovare in vario modo il centro di gravità del cono, e di <lb></lb>altre figure ” 306 </s></p><p type="main">

<s>VI Del centro di gravità dei solidi scavati ” 321 </s></p><p type="main">

<s>VII Del centro di gravità dei solidi vasiformi ” 334 </s></p><p type="main">

<s>VIII Del centro di gravità dei solidi conoidali ” 340 </s></p><p type="main">

<s>IX Del centro di gravità dei solidi cavalierani e della Cicloide ” 358 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Di varie altre cose di Meccanica lasciate dal Torricelli.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Di alcune proposizioni relative al trattato <emph type="italics"></emph>De motu Pag.<emph.end type="italics"></emph.end>373 </s></p><p type="main">

<s>II Di alcune altre proposizioni relative al trattato <emph type="italics"></emph>De momentis ”<emph.end type="italics"></emph.end> 389 </s></p><p type="main">

<s>III Del modo meccanico di condur le tangenti, e di vari altri teoremi di Meccanica nuova ” 400 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Di altri Discepoli di Galileo, promotori della Scienza del moto.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Di Antonio Nardi, e particolarmente delle sue <emph type="italics"></emph>Ricercate geometriche:<emph.end type="italics"></emph.end> di Michelangiolo <lb></lb>Ricci <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>418 </s></p><p type="main">

<s>II Digressione intorno alla Cicloide: delle proprietà di lei scoperte dal Roberval, e da altri <lb></lb>Matematici francesi ” 437 </s></p><pb xlink:href="020/01/3026.jpg" pagenum="651"></pb><p type="main">

<s>III Di ciò che dimostrarono, intorno alla Cicloide, il Nardi, il Torricelli e il Ricci <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>452 </s></p><p type="main">

<s>IV Delle controversie insorte fra il Roberval e il Torricelli, prima intorno alla quadratura, <lb></lb>poi intorno al baricentro della Cicloide ” 468 </s></p><p type="main">

<s>V Di ciò che, a illustrare, a compiere e a divulgare le dottrine galileiane del moto, opera­<lb></lb>reno il Cavalieri, il Borelli e il Viviani ” 484 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO VIII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dei matematici stranieri principali promotori della Scienza del moto.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Degli otto libri della Statica del Roberval, e come il Wallis e il Mariotte confermarono <lb></lb>la Dinamica galileiana, che l&#039;Huyghens coronò di nuovi teoremi <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>500 </s></p><p type="main">

<s>II Delle proprietà meccaniche della Cicloide ” 510 </s></p><p type="main">

<s>III De&#039;centri delle percosse e delle oscillazioni ” 518 </s></p><p type="main">

<s>IV Delle forze centrifughe ” 537 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO IX.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Della proposta di una Meccanica nuova, e della composizione dei moti.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Della <emph type="italics"></emph>Nouvelle mecanique<emph.end type="italics"></emph.end> di Pietro Varignon: degli errori del Cartesio e di Galileo <lb></lb>intorno alle proprietà dei moti composti, dimostrate da Giovan Marco Marci <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>552 </s></p><p type="main">

<s>II Di ciò che operarono i Matematici stranieri per confutare il Cartesio, e per dimostrar <lb></lb>come debba usarsi, e come sia vera la regola del parallelogrammo ” 562 </s></p><p type="main">

<s>III Come le fallacie di Galileo seducessero il Torricelli e il Viviani, e come fossero solen­<lb></lb>nemente dal Borelli confermate co&#039;suoi paralogismi ” 571 </s></p><p type="main">

<s><emph type="center"></emph>CAPITOLO X.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Dei progressi fatti dalla Meccanica nuova.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>I Dei <emph type="italics"></emph>Principii matematici di Filosofla naturale<emph.end type="italics"></emph.end> del Newton <emph type="italics"></emph>Pag.<emph.end type="italics"></emph.end>591 </s></p><p type="main">

<s>II Della <emph type="italics"></emph>Foronomia<emph.end type="italics"></emph.end> dell&#039;Herman ” 606 </s></p><p type="main">

<s>III Del parallelogrammo delle forze e del Calcolo infinitesimale nella Meccanica nuova ” 615 </s></p><p type="main">

<s>IV Della Meccanica analitica dell&#039;Euler, del D&#039;Alembert, e del Lagrange ” 633 </s></p><p type="main">

<s>V Brevi parole di conclusione ” 643 </s></p><pb xlink:href="020/01/3027.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEI DOCUMENTI ESTRATTI DAI MANOSCRITTI GALILEIANI <lb></lb>E NOTATI SECONDO L&#039;ORDINE DEI CAPITOLI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Da una lettera di Famiano Michelini, che chiedeva a Galileo la dimostrazione di un suo supposto <lb></lb>principio meccanico, pag. </s>

<s>13. </s></p><p type="main">

<s>Cenno, estratto da una lettera del Viviani al Rinaldini, relativo alla pubblicazione delle opere di Ga­<lb></lb>lileo 17. </s></p><p type="main">

<s>Motto, dal Ricci fatto al Torricelli, intorno a una dimostrazione del supposto galileiano 18. </s></p><p type="main">

<s>Scrittura mandata da Galileo ad Antonio Nardi, e nella quale si dimostrava il principio mec­<lb></lb>canico 19-21. </s></p><p type="main">

<s>Due teoremi del Viviani, in cui si dichiara la verità di un nuovo principio meccanico professato dal <lb></lb>Torricelli 22. </s></p><p type="main">

<s>Ii Mersenno chiede al Torricelli una dimostrazione del supposto galileiano, indipendente dall&#039;espe­<lb></lb>rienza 24, come rispondesse il Torricelli alla richiesta 24-26. </s></p><p type="main">

<s>Da una lettera al Torricelli, dove il Ricci nota alcune censure temerariamente fatte dal Mersenno al <lb></lb>trattato del moto di Galileo 26. </s></p><p type="main">

<s>Frammento di dialogo, di mano del Viviani 34, 35, il quale è un&#039;esplicazione di quell&#039;altro autografo <lb></lb>accennato da Galileo 35. </s></p><p type="main">

<s>Frammento di Dialogo in latino, dettato da Galileo a Marco Ambrogetti 36. </s></p><p type="main">

<s>Dialogo galileiano, in cui, messo in dubbio il principio delle velocità virtuali, se ne propone un&#039;altro <lb></lb>diverso, per dimostrare le condizioni dell&#039;equilibrio nelle bilance 37, 38. </s></p><p type="main">

<s>Passo da inserirsi nel primo dialogo delle Scienze nuove, e in cui Galileo intendeva di rispondere <lb></lb>al Cartesio 39, 40. </s></p><p type="main">

<s>Frammento da inserirsi nei detto dialogo primo, perchè Galileo voleva rendere più generale un esem­<lb></lb>pio numerico 40. </s></p><p type="main">

<s>Aggiunta di ciò che aveva dimostrato il Viviani, per inserirsi verso la fine del medesimo dialogo <lb></lb>primo, contentandosene il signor Galileo 42, 43. </s></p><p type="main">

<s><emph type="italics"></emph>Domandari del Blaneano,<emph.end type="italics"></emph.end> notati dal Viviani, in dichiarazione di alcuni dubbi contro le dottrine ga­<lb></lb>lileiane del moto 44. </s></p><p type="main">

<s>Luoghi nelle Scienze nuove, notati dal Viviani, con l&#039;intenzione di correggerli e di esplicarli 45. </s></p><p type="main">

<s>Dimostrazione della capacità dei sacchi cilindrici, che il Viviani voleva sostituire a quella di Ga­<lb></lb>lileo 48, 49. </s></p><p type="main">

<s>Memoriale di un argomento da trattarsi, scritto dal Viviani ad istanza di Galileo 51. </s></p><p type="main">

<s>Proposizione VI delle resistenze del Galileo, generalmeate e diversamente enunciata dal Viviani, per <lb></lb>esser quella non vera 55, e corollario di questa proposizione 56. </s></p><p type="main">

<s>Prima promozione, occorsa a far dal Viviani, del teorema galileiano della corda tesa 60. </s></p><p type="main">

<s>Note del Viviani, relative a un nuovo Igrometro 61. </s></p><pb xlink:href="020/01/3028.jpg" pagenum="653"></pb><p type="main">

<s>Teoremi del Viviani, relativi allo scendere di un peso attaccato in mezzo a una fune, e al salire dei <lb></lb>pesi pendenti dagli estremi 62, 63. </s></p><p type="main">

<s>Teoremi dimostrati dal Viviani, per confermare la verità del principio torricelliane, da sostituirsi a <lb></lb>quello delle velocità virtuali 64. </s></p><p type="main">

<s>Scrittura cominciata dal Viviani, contro la dimostrazione uitima del quarto dialogo galileiano delle due <lb></lb>Nuove Scienze 65, 66. </s></p><p type="main">

<s>Esperienza del Viviani, per dimostrar che due funi tirano con egual forza, nella direzione obliqua e <lb></lb>nella perpendicolare 67. </s></p><p type="main">

<s>Applicazione dell&#039;ultimo tcorema dimostrato da Galileo nel quarto dialogo delle due Nuove Scienze 71. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo II.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Varie osservazioni di Antonio Nardi intorno alla Scienza delle proporzioni, pag. </s>

<s>80, 82. </s></p><p type="main">

<s>Scrittura intorno alla riforma del quinto libro di Euclide, che il Cavalieri mandò a Galileo 88-90. </s></p><p type="main">

<s>Estranto di lettera del principe Leopoldo dei Medici, dove dice di aver chiamato a Firenze il Torri­<lb></lb>celli, perchè aiutasse Galileo, già vecchio e cieco, a distendere il dialogo <emph type="italics"></emph>Della percossa<emph.end type="italics"></emph.end> 98. </s></p><p type="main">

<s>Motto fatto dal Torricelli, in proposito del suo trattato <emph type="italics"></emph>De proportionibus<emph.end type="italics"></emph.end> 102. </s></p><p type="main">

<s>Compendio del trattato torricelliano <emph type="italics"></emph>De proportionibus<emph.end type="italics"></emph.end> 102-6. </s></p><p type="main">

<s>Licenza, richiesta al Serenai dal Viviani, d&#039;inserire nella sua Scienza delle proporzioni alcune pro­<lb></lb>posizioni del Torricelli 107-8, e permesso ricevutone 108. </s></p><p type="main">

<s>Accenno fatto dal Viviani al trattato torricelliano <emph type="italics"></emph>De propoctionibus<emph.end type="italics"></emph.end> 109. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo III.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Passo, intorno al misurar la forza della percossa, estratto da un libretto intitolato <emph type="italics"></emph>Ricreazioni scien­<lb></lb>tifu he,<emph.end type="italics"></emph.end> in francese, e tradotto dal Viviani, pag. </s>

<s>113. </s></p><p type="main">

<s>Pensieri del Nardi intorno al confermare le proporzioni, assegnate da Galileo tra la forza del percu­<lb></lb>ziente e la resistenza del percosso, 114. </s></p><p type="main">

<s>Dimostrazione dello schiaccialsi i corpi sotto i colpi delle percosse 117, 18, e ove descrivesi nel me­<lb></lb>desimo manescritto un&#039;esperienza, per confermare la legge dell&#039;urto dei corpi 120. </s></p><p type="main">

<s>Titolo e osservazioni del Viviani, intorno all&#039;ultimo congresso di Galileo 126, 27. </s></p><p type="main">

<s>Il Borelli dá notizia al principe Leopoldo dei Medici di essere entrato a speculare intorno alla na­<lb></lb>tura, e alla proprietà della forza della percossa: notizia che, passata nel Ricci, questi se ne <lb></lb>rallegra 127. </s></p><p type="main">

<s>Appunti manoscritti del Viviani, relativi alla collazione fatta della copia del Dialogo della percossa, <lb></lb>con l&#039;originale di Galileo 128. </s></p><p type="main">

<s>Dimostrazione data dal Viviani, che qualunque piecolissimo può movere qualunque altro grandissimo <lb></lb>corpo 136. </s></p><p type="main">

<s>Estratto di lettera del Cavalieri, il quale si congratula col Torricelli che sia stato eletto Accademico <lb></lb>della Crusca 139. </s></p><p type="main">

<s>Trattato delle proprietà delle catenelle, da applicarsi agli usi ballistici, disteso in dialogo, per aggiun­<lb></lb>gersi al trattoto della percossa, finalmente ritrovato fra i manoscritti galileiani, e qui pubblicato <lb></lb>da pag. </s>

<s>143-52. </s></p><p type="main">

<s>Postille del Viviani, relative all&#039;uso che Galileo intendeva fare delle catenuzze 153. </s></p><p type="main">

<s>Strumnti inventati, e sperienze fatte e descritte dal Viviani, per misurare la forza della percossa 158-60. </s></p><p type="main">

<s><emph type="italics"></emph>Exscerptum ex quadam epistola Torricelli ad Mersennum<emph.end type="italics"></emph.end> fatto e di sua propria mano trascritto <lb></lb>dal Viviani 161. </s></p><p type="main">

<s>Da una lettera, nella quale il Borelli domanda al Viviani schiarimenti intorno alla stadera del Tor­<lb></lb>ricelli, per misurar la forza della percossa 162. </s></p><p type="main">

<s>Lettera al Viviani, dove Giuseppe Farroni espone alcuni suoi dubbi intorno all&#039;esperienza, che si di­<lb></lb>ceva esser fatta da Galileo, per misurare la forza della percossa 165-67. </s></p><p type="main">

<s>Passo, in cui Stefano Angeli spiega la leggerezza del correre 176. </s></p><p type="main">

<s>Due note sentenziose del Viviani intorno alla forza della percossa 176. </s></p><p type="main">

<s>Passo autografo, trascritto dalle Lezioni accademiche del Torricelli, concernente la ragion degli angoli <lb></lb>dell&#039;incidenza e della riflessione 190, 91. </s></p><pb xlink:href="020/01/3029.jpg" pagenum="654"></pb><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo IV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Problemi di mano del signor Vincenzo di Galileo, pag. </s>

<s>196: della trottola, perchè girando stia ritta 197, <lb></lb>delle ruzzole girate col filo, delle palle gettate in aria con la racchetta, e per i pallottolai in piana <lb></lb>terra 197-99: delle trombe, che sollevano l&#039;acqua solamente infino a una certa altezza 200, 1: del <lb></lb>rompersi delle corde tirate da pesi, e della maggior portata degli <gap></gap> baano le canno <lb></lb>più lunghe, 201: della percossa e di qualunque grandissimo peso moss<gap></gap> da lei 202. </s></p><p type="main">

<s><gap></gap> apologo meccanico dialogizzato da Galileo, 203. </s></p><p type="main">

<s>Dialogo di Galileo, dove si discute se l&#039;albero delle navi, trasportato dalla vela, fa l&#039;ufficio di <lb></lb>vette 201-6. </s></p><p type="main">

<s>Problemi di vario argomento risoluti da Galileo: dell&#039;uovo, che premutone il guscio non si schiac­<lb></lb>cia 207: della varia temperatura, che pare aver l&#039;acqua d&#039;estate nell&#039;entrare e nell&#039;uscire dal <lb></lb>bag<gap></gap> 208. </s></p><p type="main">

<s>Intorno al passo dell&#039;uomo: pensioro di Galileo illustrato dal Viviani 209, 10. Proposizione intorno al <lb></lb>tirar dei tendini, solamente annunziate da Galileo 211. Moti del pendolo da Galileo misura<gap></gap> col <lb></lb>semplice tatto 213. </s></p><p type="main">

<s>Proposizione falsa del Viviani intorno alle forze centrifughe dei pendoli 213. </s></p><p type="main">

<s>Pensieri di Galileo, illustrati dal Viviani, intorno alla viscosità dell&#039;acqua, argomentata dalle scendervi <lb></lb>la limatura dei corpi galleggianti 215, 16. </s></p><p type="main">

<s>Nota, nella quale Galileo confuta l&#039;opinione del Bonamici intorno all&#039;origine delle fonti 216. </s></p><p type="main">

<s>Ragioni delle piogge e delle rugiade, notate da Galileo 216, 17, e del parer più grande la luna vicino <lb></lb>all&#039;orizzonte 217, e dell&#039;ingrossare in alto i fili degli zampili <emph type="italics"></emph>ivi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Note sparse di Galileo intorno all&#039;essenza della luce, e a corte proprietà di lei, nell&#039;occhio naturale <lb></lb>e nel Telescopio 218. </s></p><p type="main">

<s>Compendiosa descrizione fatta da Galileo di un Fotometro perfetto: un pensiero di lui intorno all&#039;al­<lb></lb>trazion del magnete, e alcune osservazioni di fatti dipendenti dalla pressione dell&#039;aria 210. </s></p><p type="main">

<s>Detti satiri<gap></gap>i di Galileo contro i Peripatetici, i Teologi, i suoi oppositori: proposito di scrivere in pub­<lb></lb>bli<gap></gap>, e senzenza che voleva si scrivesse nel titolo delle sue Opere, pubblicandosi tutte in­<lb></lb>sieme 220, 21. </s></p><p type="main">

<s>Frammento appartenente al Dialogo, in cui voleva Galileo portare i Problemi matematiri 222. </s></p><p type="main">

<s>Proposizioni XIX di Geometria, che dalla bocca e dagli scritti di Galileo raccolse il Viviani 223-37. </s></p><p type="main">

<s>Una proposizione riconosciuta falsa da Galileo, e due altre falsissime da lui stesso credute per <lb></lb>vere 228, 29. </s></p><p type="main">

<s>Proposizioni IX di algebra, quasi tutto autograle di Galileo, con un frammento di Dialogo intorno al <lb></lb>misurar con la vista 237-48. </s></p><p type="main">

<s>Teoremi XXIII di Geometria, occorsi alla mente di Galileo, nell&#039;atto di dimostrare le proposizioni <lb></lb>attinenti alle varie propriotà dei moti 249-62. </s></p><p type="main">

<s>Frammento di Dialogo, in cui il Salviati dimostra la varictà de&#039;momenti di un circolo o di una sfera, <lb></lb>nelle scendere lungo piani variamente inclinati 251. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo V.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Passo di lettera, in cui il Torricelli ringrazia il Mersenno dolla pro<gap></gap>erta di fare stampare a Parigi il <lb></lb>trattato dei centri di gravità, pag. </s>

<s>264. </s></p><p type="main">

<s>Eatratto dal pro<gap></gap>io al trattato Delle proporzioni, dove il Torricelli esprime la fatta deliberazione di <lb></lb>lasciare i teoremi della geometria, per attendere ai vetri del Canocchiali <emph type="italics"></emph>ivi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Proposizioni VII, che si riferiscono ai primi giovanili esercizi del Torricelli intorno ai centri di gra­<lb></lb>vità 265-69. </s></p><p type="main">

<s>Proposizioni due del Torricelli, dimostrative del centro di gravità nelle porzioni, e ne&#039;frusti di pa­<lb></lb>rabola 270-73. </s></p><p type="main">

<s>Lemmi X, con i quali si prepara il Torricelli le vie a dimostrere il centro di gravità del settore di <lb></lb>circolo, proseguendo il metodo degl&#039;inscritti e dei circoscritti: e dimostrazione di esso centro con <lb></lb>un unico teorema 274-81. </s></p><pb xlink:href="020/01/3030.jpg" pagenum="655"></pb><p type="main">

<s>Estratto di lettera al Torricelli, in cui il Cavalieri propone l&#039;applicazione degli indivisibili alla ricerca <lb></lb>dei centri di gravità 281. </s></p><p type="main">

<s>Altro estratto di lettera al medesimo, dove il Cavalieri propone il modo, come si potrebbero appl­<lb></lb>care gl&#039;indivisibili alla ricerca del centro di gravità del triangolo, e del conoide parabolico 282, 83. </s></p><p type="main">

<s>Proposizione, nella quale speditamente il Torricelli dimostra il centro di gravità del conoide parala­<lb></lb>lico, da quello del triangolo inscritto 284. </s></p><p type="main">

<s>Altra proposizione, in cui dal medesimo si dimostra il centro di gravità del triangolo da un teorema <lb></lb>s<gap></gap>atico di Galileo 283. </s></p><p type="main">

<s>Da una lettera dove, a proposito di Baricentrica, il Cavalieri accenna alla possibilità del riscontrarsi <lb></lb>il metodo del Torricelli con quello del Rocca, 285. </s></p><p type="main">

<s>Proposizizne del Torricelli, preceduta da quattro lemmi, per dimostrare il centro di gravità di qua­<lb></lb>lunque arco di cerchio 287-90: dietro la qual proposizione, in altro medo dal precedente, cioè, per <lb></lb>via degli indivisibili, si dimostra il centro di gravità del settore di circolo 290, 91. </s></p><p type="main">

<s>Studi del Torricelli per l&#039;invenzione del centro di gravità delle callotte, che poi dimostrò star nel <lb></lb>mezzo della sactta 291-94. </s></p><p type="main">

<s>Da una lettera del Torricelli, nella quale espone al Cavalieri le ragioni del centro di gravità nelle <lb></lb>callotte, dubitando di essersi ingannato 391, 95; delle quali ragioni poi esso Torricelli si servi, per <lb></lb>dimostrare il centro di gravità dell&#039;emisfero e del settore sferico 295-97. </s></p><p type="main">

<s>Estratto di lettera, in cui il Torricelli dà al Michelini notizia del Teorema centrobarico del Gul­<lb></lb>dino 298, 99. </s></p><p type="main">

<s>Domande del Torricelli se VII sue proposizioni baricentriche erano state dimostrate dal Guldino, e <lb></lb>risposte del Cavalieri 299-300, che attizzarono le rivalità di esso Torricelli contro alcuni errori <lb></lb>dell&#039;Autore della Centrobarica 301. </s></p><p type="main">

<s>Nuove istanze fatte appresso il Cavalieri dal Torricelli, per assicurarsi in che modo avesse il Guldino <lb></lb>desunto il centro di gravità della semicirconferenza dalla Quadratrice di Dinostrato, e per poter <lb></lb>indi rispondere alle accuse del Roberval 303. </s></p><p type="main">

<s>Giudizio poco favorevole del Torricelli, dop&#039;avere sfogliata la Centrobarica del Guldino 306. </s></p><p type="main">

<s>Centro di gravità della superficie conica: nuova dimostrazione del Torricelli 307. </s></p><p type="main">

<s>Nuovo modo di dimostrare, per via degli indivisibili, il centro di gravità del triangolo e del cono 311-16: <lb></lb>similmene, dell&#039;emisfero e dell&#039;emisferoide 313: e, premesso a ciascuno un lemma, due altri modi, <lb></lb>suggeriti dagli indivisibili al Torricelli, di dimostrare il centro di gravità del cono 314-16. Con <lb></lb>simil metodo, premessa l&#039;invenzione del centro di gravità dei prismali, si trovano dal medesimo <lb></lb>Autore i centri nell&#039;emisfero, nel conoide parabolico, e nelle porzioni di parabola 317-20. </s></p><p type="main">

<s>Torricelliane dimostrazioni del centro di gravità de&#039;segmenti e de&#039;frusti sferici, con alcuni supple­<lb></lb>menti del Viviani 322-26: della brevità e universalità delle quali dimostrazioni sopra quelle di <lb></lb>L. </s>

<s>Valerio si compiace l&#039;Autore col Ricci, col Cavalieri e con altri 326-28, e da ciò piglia occa­<lb></lb>sione di ritrovare il centro di gravità ne&#039;solidi scavati, premessovi un lemma, la dimostrazione <lb></lb>del quale in supplita dal Viviani 328-30. </s></p><p type="main">

<s>Dimostrazione del Torricelli, col metodo degli indivisibili, e premessivi tre lemmi geometrici, che <lb></lb>l&#039;emistero e l&#039;emisferoide son doppi del cono inscritto 331-33, dopo la qual dimostrazione si torna <lb></lb>dal medesimo Autore a ricercare, per via del solito metodo degl&#039;indivisibili, il centro di gravità <lb></lb>ne&#039;solidi scavati 333, 34. </s></p><p type="main">

<s>Varie proposizioni, raccolte dal Trattato del Torricelli, <emph type="italics"></emph>Della misura e del centro di gravità dei so­<lb></lb>lidi vasiformi<emph.end type="italics"></emph.end> 335-40. </s></p><p type="main">

<s>Teorema universalissimo del Torricelli, comprendente le dottrine degli Sferici e de&#039;Conoidali di Ar­<lb></lb>chimede: dal qual Teorema stereometrico se ne deriva un altro, pure universalissimo, per l&#039;in­<lb></lb>venzione del centro di gravità di qualunque solido conoideo 340-45: per giungere alla quale inven­<lb></lb>zione, esso Torricelli dimostra che un frusto conico si compone di tre coni, come gli aveva <lb></lb>annunziato il Ricci, e applica questa dimostrazione a confermar la formulà, con la quale da Ga­<lb></lb>lileo s&#039;indicava il centro di gravità di esso frusto 345-51. </s></p><p type="main">

<s>Proposizioni IV, nelle quali il medesimo Torricelli dimostra dove stia il centro di gravità nei segmenti <lb></lb>conici scavati e interi, nel frusto di conoide parabolico, sferico, e iperbolideo 352-57. </s></p><p type="main">

<s>Estratto di una lettera del Torricelli a M. A. Ricci, relativa alle sezioni del solido cavalierano 358, 59. </s></p><p type="main">

<s>Teorema, in cui il Torricelli, correggendo uno sbaglio del suo inventore, dimostra in qual propor­<lb></lb>zione sia, secondo la proposta, segato il solido cavalierano 359-61. </s></p><p type="main">

<s>Ricerca del centro di gravità nel solido colonnare, che ha per base due mezze parabole, premessavi <lb></lb>l&#039;invenzione del centro di gravità di esse mezze parabole congiunte per la base, e del trilineo <lb></lb>parabolico, in tre proposizioni dimostrate dal Torricelli 361-68. </s></p><p type="main">

<s>Centro di gravità della Cicloide, indicato per una proposizione del Torricelli 369-72. </s></p><pb xlink:href="020/01/3031.jpg" pagenum="656"></pb><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo VI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Lettera di V. </s>

<s>Viviani a Erasmo Bartholin, relativa alle opere inedite del Torricelli, pag. </s>

<s>374. </s></p><p type="main">

<s>Da una lettera del medesimo al p. </s>

<s>Baldigiani, sopra lo stesso argomento 374, 75. </s></p><p type="main">

<s>Proposizione, in cui si dimostra dal Torricelli che la forza è infinita 376, 77. </s></p><p type="main">

<s>Proposizioni due dimostrate dal Torricelli, per render più generale, e per confermare il fondamento <lb></lb>della Dinamica galileiana 378, 79, con un teorema, soggiunto dal medesimo, per designar la via, <lb></lb>che fa il centro di gravità di due corpi congiunti per un filo, e moventisi lungo piani comunque <lb></lb>inclinati 379. </s></p><p type="main">

<s>Proposizioni IV, relative alle proporzioni, che passano tra le velocità e i tempi dei mobili ne&#039;piani <lb></lb>inclinati, dimostrate dal Torricelli, per aggiungerle al suo trattato <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> 379-31. </s></p><p type="main">

<s>Dell&#039;impeto dei punti, nel descrivere il circolo e l&#039;iperbola: tooremi dimostrati dal Torricelli 381-33. </s></p><p type="main">

<s>Delle infinite parabole: teoremi dimostrati dal Torricelli, per estendere a qualunque legge di accele­<lb></lb>razione la teoria de&#039;proietti 384, 85. </s></p><p type="main">

<s>Del feco, e di altre proprietà della parabola, nell&#039;use de&#039;proietti, e per applicarle alla catenaria: <lb></lb>lemmi e proposizioni dimostrate dal Torricelli 385-89. </s></p><p type="main">

<s>Illustrazione del Viviani al teorema torricelliano della catenaria 387, 88. </s></p><p type="main">

<s>Note intorno ai momenti de&#039;gravi, scritte dal Torricelli, per aggiungerle e dar perfezione al suo trat­<lb></lb>tato <emph type="italics"></emph>De motu gravium<emph.end type="italics"></emph.end> 389-91. </s></p><p type="main">

<s>Proposizioni VII, dimostrate dal Torricelli intorno ai momenti dei gravi sopra i piani inclinati 391-94. </s></p><p type="main">

<s>Proposizioni IV, nelle quali applica il Torricelli alla Baricentrica i teoremi de&#039;momenti dei gravi 395-400. </s></p><p type="main">

<s>Giudizio del Nardi intorno a preferirsi da Archimede i metodi obliqui ai diretti 403, 4. </s></p><p type="main">

<s>Discorso del Torricelli, in cui, a dimostrare le proprietà della Spirale archimedea, s&#039;applica il prin­<lb></lb>cipio della composizione dei moti 404-7. </s></p><p type="main">

<s>Regola del Torricelli <emph type="italics"></emph>pro tangentibus infinitarum parabolarum<emph.end type="italics"></emph.end> 409, 10. </s></p><p type="main">

<s>Lemma premesso dal Torricelli, per poi dimostrare un teorema, riguardante lo spazio passato ori­<lb></lb>zontalmente da un mobile, supposto che l&#039;antecedento velocità fosse cresciuta come i quadrati <lb></lb>dei tempi 410, 11. </s></p><p type="main">

<s>Modo insegnato dal Torricelli, per condurre una tangente alla parabola cubica 411. </s></p><p type="main">

<s>Proposizioni due, nelle quali il Torricelli insegna il modo di condur meccanicamente le tangenti alla <lb></lb>Cicloide, e pone i principii, da concluderne il tautocronismo di lei 413, 14. </s></p><p type="main">

<s>Problemi risoluti dal Torricelli: trovar lo sforzo fatto da una trave, appoggiata al muro, e la causa <lb></lb>perchè a una colonna fessa s&#039;impedisca l&#039;aprirsi di più e il rovinare, con una semplice fascia­<lb></lb>tura 414-17. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo VII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Giudizio, che da sè dà il Nardi delle sue Scene, pag 419. </s></p><p type="main">

<s>Cenni, dal Torricelli fatti al Cavalieri, e dal Ricci al Torricelli, relativi a un libro, che voleva stam­<lb></lb>pare il Nardi 420. </s></p><p type="main">

<s>Indice della VIII Ricercata matematica del Nardi 421. </s></p><p type="main">

<s>Tooremi XII, de&#039;quali si compila il trattato <emph type="italics"></emph>Dei centri di gravità<emph.end type="italics"></emph.end> di Antonio Nardi, con le cose <lb></lb>supplitevi da M. A. </s>

<s>Ricci 421-30. </s></p><p type="main">

<s>Centro di gravità del settore di sfera, commemorato in alcune sue lettere dal Torricelli, e concor­<lb></lb>danza della indicazione data da lui con quella del Nardi 430, 31. </s></p><p type="main">

<s>Del centro di gravità nei frusti conoidali universalmente: teorematiche indicazioni del Ricci, che su­<lb></lb>scitarono la gelosia nell&#039;animo del Torricelli 431-34. </s></p><p type="main">

<s>Quadratura della parabola, col metodo degli indivisibili, che dice il Nardi di avere imparato da Pappo <lb></lb>Alessandrino 436, 37. </s></p><p type="main">

<s>Dialogo, intorno all&#039;invenzione della Cicloide, dettato da Galileo al Viviani, per inserirlo nella prima <lb></lb>Giornata delle que nuove Scienze, nell&#039;occasione di una ristampa 438, 39. </s></p><p type="main">

<s>Passi estratti dalle <emph type="italics"></emph>Ricercate,<emph.end type="italics"></emph.end> dove il Nardi accenna alla quadratura meccanica della Cicloide, da sè <lb></lb>ritrovata, e ai problemi intorno ai solidi cicloidali 454. </s></p><pb xlink:href="020/01/3032.jpg" pagenum="657"></pb><p type="main">

<s>Estratto di lettera, nella quale il Cavalieri si rallegra col Torricelli delle ritrovate misure dello spazio <lb></lb>cicloidale, e narra come Galileo intorno a ciò si fosse ingannato 454, 55. </s></p><p type="main">

<s>Passo di una lettera del Ricci al Torricelli, concernente le curve cicloidali 455, 56. </s></p><p type="main">

<s>Discorso del Nardi intorno alla Cicloide, e in cui si comprendono le proposizioni dimostrate dal <lb></lb>Ricci 457-61. </s></p><p type="main">

<s>Luogo estratto dalle <emph type="italics"></emph>Scene,<emph.end type="italics"></emph.end> in cui il Nardi dimostra le proporzioni, che hanno i solidi ai cilindri cir­<lb></lb>coscritti nella sua propria cicloide 463. </s></p><p type="main">

<s>Conclusione scritta dal Torricelli, relativa alla misura, che ha il solido cicloidale circa la base, verso <lb></lb>il cilindro a lui circoscritto 464. </s></p><p type="main">

<s>Conclusioni, relative ai solidi cicloidali, scritte dal Torricelli al Magiotti 465. </s></p><p type="main">

<s>Osservazione del Ricci, relativa alla facilità, con cui dice al Torricelli di aver dimostrato il solido ci­<lb></lb>cloidale circa la tangente parallela all&#039;asse 466. </s></p><p type="main">

<s>Da una lettera, nella quale il Dati fa premure al Ricci, per aver notizia dell&#039;Epistola robervalliana <lb></lb><emph type="italics"></emph>ad Torricellium<emph.end type="italics"></emph.end> 468. </s></p><p type="main">

<s>Da una lettera del Cavalieri al Torricelli: notizie relative alla cicloide 469. </s></p><p type="main">

<s>Teoremi cicloidali annunziatì dal Torricelli al Mersenno 470. </s></p><p type="main">

<s>Poscritto importante, in una lettera del Torricelli, tralasciato, nel pubblicarla, dal Dati 475. </s></p><p type="main">

<s>Il Torricelli scrive com&#039;avesse insieme due fiere liti, l&#039;una col Roberval, l&#039;altra col Ricci 476, 77. </s></p><p type="main">

<s>Lettera, nella quale il Ricci si difende dall&#039;accusa datagli dal Torricelli di avergli usurpato il metodo <lb></lb>di quadrare le infinite parabole 481-83. </s></p><p type="main">

<s>Discorso, in cui Antonio Nardi compendia una parte importantissima della storia filosofica dell&#039;Astro­<lb></lb>nomia 488-90. </s></p><p type="main">

<s>Due passi estratti dalle <emph type="italics"></emph>Scene accademiche,<emph.end type="italics"></emph.end> rlative ai pianeti, nel primo de&#039;quali il Nardi professa <lb></lb>il principio delle forze centrali, e nel secondo dimostra che le orbite sono spirali molto simili <lb></lb>alle ellissi 490, 91. </s></p><p type="main">

<s>Note due, nelle quali il Viviani esplica alcune proposizioni meccaniche fondamentali di Galileo 493, 94. </s></p><p type="main">

<s>Proposizioni sei, intorno ai centri di gravità, dimostrate dal Viviani 494-99. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo VIII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Da una lettera del Ricci, dove accenna al Torricelli che il Mersenno e il Roberval contradicevano ai <lb></lb>principii fondamentali della Dinamica di Galileo, pag. </s>

<s>508. </s></p><p type="main">

<s>Da una lettera, nella quale il Mersenno domanda al Torricelli se Galileo aveva trovata la regola di <lb></lb>ridurre al pendolo semplice un pendolo composto 536. </s></p><p type="main">

<s>Regola data dal Viviani, per trovare qual punto del pendolo sia quello, dal quale si regola il <lb></lb>moto 536, 37. </s></p><p type="main">

<s>Teorema, in cui Galileo aveva dimostrato che le forze centripete stanno direttamente come i raggi <lb></lb>delle ruote 541. </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Nel Capitolo IX.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Da Niccolò Witsen: traduzione dettata da Niccolò Stenone a Vincenzo Viviani: <emph type="italics"></emph>In qual modo più <lb></lb>profittevole si voltino le vele ai venti,<emph.end type="italics"></emph.end> pag. </s>

<s>375-80. </s></p><pb xlink:href="020/01/3033.jpg"></pb><p type="main">

<s><emph type="center"></emph>INDICE ALFABETICO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DEGLI AUTORI E DELLE COSE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Co&#039;numeri s&#039;accenna alle pagine<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Accademici di Londra<emph.end type="bold"></emph.end> ripetono, intorno alla forza della percossa, in sostanza, le dottrine del Bo­<lb></lb>relli 77. </s></p><p type="main">

<s><emph type="bold"></emph>Acquapendente (d&#039;) Girolamo Fabricio,<emph.end type="bold"></emph.end> teoremi di Meccanica animale da lui dimostrati 211. </s></p><p type="main">

<s><emph type="bold"></emph>Aggiunti Niccolò<emph.end type="bold"></emph.end> previene il Borelli nel determinar la misura dei momenti, e delle quantità di <lb></lb>moto 119. </s></p><p type="main">

<s><emph type="bold"></emph>Alemanni<emph.end type="bold"></emph.end> non curanti del loro connazionale Giovan Marco Marci 171. </s></p><p type="main">

<s><emph type="bold"></emph>Alembert (d&#039;),<emph.end type="bold"></emph.end> sua nuova dimostrazione del parallelogrammo delle forze 621. </s></p><p type="main">

<s><emph type="bold"></emph>Analisi algebrica,<emph.end type="bold"></emph.end> come ne difettassero i Discepoli di Galileo 590. </s></p><p type="main">

<s><emph type="bold"></emph>Archimede,<emph.end type="bold"></emph.end> si scopre il segreto della XVIII proposizione dimostrata da lui intoruo alle proprietà delle <lb></lb>Spirali 401, e qual relazione ell&#039;abbia con la quadratura del circolo 402, perchè, in dimostrare le <lb></lb>proprietà delle Spirali, seguisse il metodo obliquo invece del diretto 403. </s></p><p type="main">

<s><emph type="bold"></emph>Aria,<emph.end type="bold"></emph.end> quanto impedisca il risalir de&#039;proietti nei tiri verticali 53. </s></p><p type="main">

<s><emph type="bold"></emph>Ariete,<emph.end type="bold"></emph.end> ragione della forza della sua percossa 174. </s></p><p type="main">

<s><emph type="bold"></emph>Aristotile,<emph.end type="bold"></emph.end> primo a propor la questione della forza della percossa 112. </s></p><p type="main">

<s><emph type="bold"></emph>Atomi della luce,<emph.end type="bold"></emph.end> si applicano ad essi le leggi del moto dei corpi ponderosi 471. </s></p><p type="main">

<s><emph type="bold"></emph>Baliani Giovan Batista,<emph.end type="bold"></emph.end> ingiusto giudizio dei meriti di lui rivendicato 28, trova difficoltà d&#039;attribuire <lb></lb>all&#039;aria la varia passata di una palla esplosa da un moschetto, presso alla bocca di lui, e in di­<lb></lb>stanza 50. </s></p><p type="main">

<s><emph type="bold"></emph>Benedetti Giovan Batista,<emph.end type="bold"></emph.end> riforma del V libro di Euclide proposta da lui 78, sue speculazioni impor­<lb></lb>tanti intorno alle forze centrifughe 539. </s></p><p type="main">

<s><emph type="bold"></emph>Beriguardi Claudio<emph.end type="bold"></emph.end> come dimostrasse un teorema fondamentale della Meccanica, indipendentemente, <lb></lb>e prima di Galileo 14. </s></p><p type="main">

<s><emph type="bold"></emph>Bernoulli Giovanni<emph.end type="bold"></emph.end> censura un corollario del Newton 594, sua nuova dimostrazione del parallelo­<lb></lb>grammo delle forze 616. </s></p><p type="main">

<s><emph type="bold"></emph>Bilancia<emph.end type="bold"></emph.end> delle due secchie, immaginata da Galileo per misurar la forza della percossa, ridotta alle <lb></lb>sue ragioni idrostatiche 168. </s></p><p type="main">

<s><emph type="bold"></emph>Bonaventuri Tommaso,<emph.end type="bold"></emph.end> doveva, nella pubblicazione delle opere di Galileo, premettere al Dialogo detla <lb></lb>percossa quello della riforma di Euclide, e perchè 130. </s></p><p type="main">

<s><emph type="bold"></emph>Borelli Giovann&#039;Alfonso,<emph.end type="bold"></emph.end> come applicasse il metodo degl&#039;indivisibili, per superare le difficoltà, in­<lb></lb>contrate da Galileo e dal Torricelli, nel dimostrare il teorema fondamentale dei moti uniformi 110, <lb></lb>sue proposizioni intorno alla forza della percossa 120, 122, 163, qual fosse l&#039;intenzione che lo <lb></lb>mosse a scrivere il trattato <emph type="italics"></emph>De vi percussionis<emph.end type="italics"></emph.end> 122, come dimostri che qualunque piccolissimo <lb></lb>corpo può movere un grandissimo 136, scopre l&#039;origine della fallacia in alcune esperienza del <lb></lb>Gassendo e del Viviani 164, sue esperienze della percossa sopra focacce più o meno molli 165, <lb></lb>esperienza proposta da lui per dimostrar l&#039;ondeggiamento de&#039;passi dell&#039;uomo 210, sue due opere <lb></lb>di Meccanica pura, brevemente esaminate 485-87, suo libro <emph type="italics"></emph>Theoricae Mediceorum<emph.end type="italics"></emph.end> 487-92, come <pb xlink:href="020/01/3034.jpg" pagenum="659"></pb>confondesso la forza centrifuga con quella di proiezione 542, sue fallacie relative al modo di com­<lb></lb>porre le forze, ripudiando la regola del parallelogrammo 580-88, primo a dimostrar la misura vera <lb></lb>delle forze vivo 639. </s></p><p type="main">

<s><emph type="bold"></emph>Cabeo Niccolò,<emph.end type="bold"></emph.end> sua opposizione a un principio meccanico fondamentale supposto da Galileo 9. </s></p><p type="main">

<s><emph type="bold"></emph>Calcolo astronomico,<emph.end type="bold"></emph.end> propostosi da Galileo e dal Viviani, per adornare un concetto platonico 54. </s></p><p type="main">

<s><emph type="bold"></emph>Cardano Girolamo,<emph.end type="bold"></emph.end> suoi teoremi intorno ai moti composti 554. </s></p><p type="main">

<s><emph type="bold"></emph>Cartesio Renato,<emph.end type="bold"></emph.end> suoi paralogismi in soggetto de&#039;moti composti 555. </s></p><p type="main">

<s><emph type="bold"></emph>Casati Paolo,<emph.end type="bold"></emph.end> come risolva il problema del funicolo gravato nel mezzo 74, scioglie uno dei problemi <lb></lb>naturali di Galileo 199, primo a dimostrar la verità del parallelogrammo delle forze, contro le <lb></lb>fallacie de&#039;seguaci di Galileo 588. </s></p><p type="main">

<s><emph type="bold"></emph>Catenelle,<emph.end type="bold"></emph.end> loro usa nella Ballistica, trattato in dialogo di Galileo, ora da noi ritrovato 143. </s></p><p type="main">

<s><emph type="bold"></emph>Cavalieri Bonaventura<emph.end type="bold"></emph.end> intraprende, a istanza di G. A. Rocca, la riforma di Euclide 87, proposizioni <lb></lb>geomotriche di lui, che aprirono la via alle invenzioni baricentriche del Torricelli 321-23, pro­<lb></lb>pone un teorema intorno alle potenze algebriche, dal Torricelli poi dimostrato universalmente 408, <lb></lb>riassunto di eiò ch&#039;egli operasse intorno alla Meccanica 484, raccomanda ai suoi scolari il Corso <lb></lb>matematico dell&#039;Herigonio 581, sua geometria paragonata con l&#039;Analisi infinitesimale 631. </s></p><p type="main">

<s><emph type="bold"></emph>Cazr Pletro,<emph.end type="bold"></emph.end> esperienza, da cui vuol concludere esser faisa la legge galileiana dei gravi naturalmente <lb></lb>cadenti 163. </s></p><p type="main">

<s><emph type="bold"></emph>Centri<emph.end type="bold"></emph.end> dell&#039;oscillazione e della percossa, come si dimostrasse che non sono identici 535. </s></p><p type="main">

<s><emph type="bold"></emph>Centrigfuhe (forze),<emph.end type="bold"></emph.end> prime osservazioni fatte intorno ad esse 538, da quali considerazioni il Newton <lb></lb>ne rieavasse l&#039;equazione, e ne concludesse i principali teoremi ugeniani 545-47, loro proprietà di­<lb></lb>mostrate dall&#039;Huyghens ne&#039;pendoli conici 547-49. </s></p><p type="main">

<s><emph type="bold"></emph>Centro della<emph.end type="bold"></emph.end> percossa nelle varie figure, primi teoremi dimostrati dal Roberval 520, regole stabilite <lb></lb>dal Cartesio, e loro applicazione 522, esame di queste regole 525. </s></p><p type="main">

<s><emph type="bold"></emph>Centrebarico (teorema)<emph.end type="bold"></emph.end> come speditamente dimostrato dall&#039;Herman 631. </s></p><p type="main">

<s><emph type="bold"></emph>Cicloide,<emph.end type="bold"></emph.end> origine della sua invenzione 440, liti, accuse e difese fra il Torricelli e il Roberval intorno <lb></lb>al primato delle scoperte proprietà di lei 466, e particolarmente intorno al centro di gravità della <lb></lb>figura, e del solido circa l&#039;asse 469-73, come il Roberval, esaminando la proporzione del solido <lb></lb>circa l&#039;asse al cilindro circoscritto, data dal Torricelli, la trovasse falsa 473-75, come il Roberval, <lb></lb>dopo penosi indugi, trovasse la proporzione vera 478, tautocronismo di lei dimostrato dall&#039;Huy­<lb></lb>ghens 510-14. </s></p><p type="main">

<s><emph type="bold"></emph>Cimento (Accademia del),<emph.end type="bold"></emph.end> esperienza fatta in essa con un archibugio rigato, per confermare che alla <lb></lb>palla, nel tornare in giù naturalmente, è impedito il coipo dall&#039;aria 52. </s></p><p type="main">

<s><emph type="bold"></emph>Colpi<emph.end type="bold"></emph.end> obliqui e diretti, leggi delle loro forze dimostrate dal Torricelli 191. </s></p><p type="main">

<s><emph type="bold"></emph>Comite<emph.end type="bold"></emph.end> della Cicloide 442, a quale occasione se ne intraprendesse lo studio in Italia, 542. </s></p><p type="main">

<s><emph type="bold"></emph>Conservazione<emph.end type="bold"></emph.end> della forza creduta razionale dal Borelli 183. </s></p><p type="main">

<s><emph type="bold"></emph>Corda<emph.end type="bold"></emph.end> tesa orizontalmente, qualunque minimo peso posto nel mezzo di lei vale a sollevarne due <lb></lb>grandissimi pendenti dagli estremi 58. </s></p><p type="main">

<s><emph type="bold"></emph>Cuneo,<emph.end type="bold"></emph.end> sua ragion meccanica derivata dalle dottrine di Giovan Marco Marci, e di Leonardo da <lb></lb>Vinci 174. </s></p><p type="main">

<s><emph type="bold"></emph>Dialeghi<emph.end type="bold"></emph.end> galileiani Del moto, come nella stampa degli Elzeviri rimanessero incompiuti 8. </s></p><p type="main">

<s><emph type="bold"></emph>Dialege V,<emph.end type="bold"></emph.end> delle due nuove Scienze, suo titolo proprio scritto dal Torricelli in fronte a una copia, da <lb></lb>presentarsi al principe Leopoldo de&#039;Medici 98. </s></p><p type="main">

<s><emph type="bold"></emph>Differenziali<emph.end type="bold"></emph.end> leibniziani definiti dal Nardi 626. </s></p><p type="main">

<s><emph type="bold"></emph>Elasticità<emph.end type="bold"></emph.end> imperfetta, perchè renda l&#039;angolo della riflessione minore di quello dell&#039;incidenza 190. </s></p><p type="main">

<s><emph type="bold"></emph>Esperimenti<emph.end type="bold"></emph.end> insigni, per misurare la forza della percossa, inventati da Galileo e descritti dal Torri­<lb></lb>celli 155, pubblicati dal Mersenno 156, delle due secchie, dove l&#039;acqua cadente da quella di sopra <lb></lb>percote il fondo dell&#039;altra di sotto 167. </s></p><p type="main">

<s><emph type="bold"></emph>Euler Leonardo,<emph.end type="bold"></emph.end> interpetrazione di un passo della Meccanica analitica di lui 634. </s></p><p type="main">

<s><emph type="bold"></emph>Evolute<emph.end type="bold"></emph.end> delle curve, e specialmente della Cicloide 315. </s></p><p type="main">

<s><emph type="bold"></emph>Faille (della) Giovannl,<emph.end type="bold"></emph.end> suo trattato de&#039;centri di gravità delle porzioni di circolo e di ellisse 269, primo <lb></lb>a indicare il centro di gravità nei semmenti, e nei settori di circolo e di ellisse 274. </s></p><p type="main">

<s><emph type="bold"></emph>Flussioni,<emph.end type="bold"></emph.end> metodo del Newton, non diverso da quello del Cavalieri 631. </s></p><p type="main">

<s><emph type="bold"></emph>Forze<emph.end type="bold"></emph.end> centrali, come si riconoscesse che variano d&#039;intensità in ragion reciproca de quadrati delle <lb></lb>distanze, 543, Composte, applicate alla teoria del piano inclinato 584, Vive, questione intorno al <lb></lb>più giusto modo di misurarle 635-39. </s></p><pb xlink:href="020/01/3035.jpg" pagenum="660"></pb><p type="main">

<s><emph type="bold"></emph>Frammento,<emph.end type="bold"></emph.end> da inserirsi nel III dialogo delle due nuove Scienze, dopo la prima proposizione dei <lb></lb>moti equabili 93. </s></p><p type="main">

<s><emph type="bold"></emph>Galilei Galileo,<emph.end type="bold"></emph.end> come scoprisse una fallacia dell&#039;ingegner Bartolotti 10, come iu un caso simile per­<lb></lb>suadesse Guidubaldo del Monte 11, con quali arti usurpasse la riforma del V libro d&#039;Euclide al <lb></lb>Cavalieri 91, per qual ragione pensasse di fare un dialogo a parte intorno alla Scienza delle pro­<lb></lb>porzioni 93, non appartiene a lui il fondamento della Scienza delle proporzioni, nè quanto al con­<lb></lb>cetto. </s>

<s>nè quanto alla forma 97, suo errore nell&#039;assegnare le proporzioni delle velocità fra i corpi, <lb></lb>prima e dopo l&#039;urto 122, per quale occasione, e quando riprendesse le speculazioni intorno alla <lb></lb>forza della percossa 124, a che punto, nell&#039;ottobre del 1638, avesse condotto il dialogo della per­<lb></lb>cossa 125, suo tre proposizioni intorno all&#039;urto dei corpi 131, processo del ragionamento di lui, nel <lb></lb>Dialogo della percossa 132-34, suo mirabile detto, confermato dall&#039;Huyghens e dal Mariotte 135, <lb></lb>suoi sbagli in cose di Matematica più elementare 228, sua proposizione lemmatica dei centri di <lb></lb>gravità, subodorata falsa dal Torricelli 296, relazioni di lui col Guldino 298, suo teorema relativo <lb></lb>alle forze centripete 539, suo teorema de&#039;moti composti, che si riconosce falso, paragonato con <lb></lb>quello dell&#039;Herigonio 557. </s></p><p type="main">

<s><emph type="bold"></emph>Gassendo Pietro<emph.end type="bold"></emph.end> accolse, commentò e diffuse le dottrine dinamiche di Galileo 501. </s></p><p type="main">

<s><emph type="bold"></emph>Guldin Paolo,<emph.end type="bold"></emph.end> sue false proposizioni baricentriche, esaminate dal Torricelli 305, quale origine avesse, <lb></lb>secondo lui, il metodo del Cavalieri 309. </s></p><p type="main">

<s><emph type="bold"></emph>Herman Giacomo<emph.end type="bold"></emph.end> dimostra generalmento un corollario neutoniano 595, esame della <emph type="italics"></emph>Foronomia<emph.end type="italics"></emph.end> di <lb></lb>lui 606-15, con gl&#039;indivisibili del Cavalieri, e co&#039;segni del Leibniz, usa il calcolo infinitesi­<lb></lb>male 632. </s></p><p type="main">

<s><emph type="bold"></emph>Hire (de la)<emph.end type="bold"></emph.end> come risolvesse il problema robervalliano del nodo della fune, che rimane in equilibrio, <lb></lb>tirato da tre potenze 570. </s></p><p type="main">

<s><emph type="bold"></emph>Hopital (de l&#039;),<emph.end type="bold"></emph.end> sue censure al VII teorema ugeniano <emph type="italics"></emph>De vi centrifuga,<emph.end type="italics"></emph.end> e loro difesa 548, suo teo­<lb></lb>rema <emph type="italics"></emph>De potentiis fila funesve trahentibus<emph.end type="italics"></emph.end> dimostrato col principio della composizione delle <lb></lb>forze 569. </s></p><p type="main">

<s><emph type="bold"></emph>Huyghens Cristiano,<emph.end type="bold"></emph.end> suo trattato <emph type="italics"></emph>De motu corporum ex percussione<emph.end type="italics"></emph.end> 177-79, primo a risolvere, con <lb></lb>metodo generale, i problemi del centro delle oscillazioni e delle percosse 528, sua XVI proposf­<lb></lb>zione <emph type="italics"></emph>De vi centrifuga,<emph.end type="italics"></emph.end> riconosciata falsa 450. </s></p><p type="main">

<s><emph type="bold"></emph>Indivisibili,<emph.end type="bold"></emph.end> metodo, secondo il Nardi, usato da Archimede e da Pappo 435, il Roberval ne riconosce <lb></lb>autore il Cavalieri, ma il Cartesio ne attribuisce il merito dell&#039;invenzione a sè stesso 451, usato <lb></lb>dal Wallis, e dai principali Matematici d&#039;Europa 509, definito dallo stesso Cavalieri, per rispon­<lb></lb>dere alle critiche di Galileo 627, corrisponde alle flussioni del Newton 628, pregiudizi di alcuni <lb></lb>intorno ad esso 629. </s></p><p type="main">

<s><emph type="bold"></emph>Integrale<emph.end type="bold"></emph.end> (teorema) di cui fecero uso principalmente il Torricelli e il Roberval, per sommare le quan­<lb></lb>tità indivisibili 513. </s></p><p type="main">

<s><emph type="bold"></emph>Kepler Giovanni,<emph.end type="bold"></emph.end> come interpetri la I2 archimedea <emph type="italics"></emph>De dimensione circuli<emph.end type="italics"></emph.end> 309. </s></p><p type="main">

<s><emph type="bold"></emph>Lagrange Luigi,<emph.end type="bold"></emph.end> sua Meccanica analitica 640-42. </s></p><p type="main">

<s><emph type="bold"></emph>Laplace,<emph.end type="bold"></emph.end> sua nuova dimostrazione del parallelogrammo delle forze, condotta per via del calcolo infi­<lb></lb>nitesimale 622. </s></p><p type="main">

<s><emph type="bold"></emph>Leggerezza<emph.end type="bold"></emph.end> del correre, dimostrata da vari principii meccanici 175. </s></p><p type="main">

<s><emph type="bold"></emph>Lexioni accademiche<emph.end type="bold"></emph.end> del Torricelli intorno alla forza della percossa: loro occasione e intendimento <lb></lb>dell&#039;Autore 138, loro sommario 139-42, completano il dialogo della percossa, lasciato interrotto da <lb></lb>Galileo 142. </s></p><p type="main">

<s><emph type="bold"></emph>Lemiti,<emph.end type="bold"></emph.end> loro metodo applicato dal Nawton agli indivisibili 629. </s></p><p type="main">

<s><emph type="bold"></emph>Magiotti Eaffaelle,<emph.end type="bold"></emph.end> notizie di un manoscritto di lui aggiunto alla raccolta de&#039;galileiani 70. </s></p><p type="main">

<s><emph type="bold"></emph>Magli<emph.end type="bold"></emph.end> a vapore, come si spieghino i varii effetti curiosi delle loro percosse 175. </s></p><p type="main">

<s><emph type="bold"></emph>Marchetti Alessandro,<emph.end type="bold"></emph.end> suo teorema delle tangeati e delle secanti nel circolo, dimostrato in concor­<lb></lb>renza col Viviani 69. </s></p><p type="main">

<s><emph type="bold"></emph>Marci Giovan Marce,<emph.end type="bold"></emph.end> opere di lui poco conosciute 171, instituisce la nuova Scienza della percossa, e <lb></lb>della comunicazione dei moti 172, sue leggi degli urti dei corpi <emph type="italics"></emph>ivi,<emph.end type="italics"></emph.end> come, dalle sue formule, l&#039;er­<lb></lb>rore peripatetico delle velocità proporzionali alle masse sia meglio confutato, che dai lunghi ra­<lb></lb>gionamenti di Galileo 173, confronto di alcuni suoi teoremi con quelli del Borelli 177, come dimo­<lb></lb>stri le ragioni dell&#039;uguaglianza dell&#039;angolo dell&#039;incidenza con quello della riflessione, per via dei <lb></lb>moti composti 189, primo a dar la dimostrazion razionale dei moti composti 558-61. </s></p><pb xlink:href="020/01/3036.jpg" pagenum="661"></pb><p type="main">

<s><emph type="bold"></emph>Mariotte Edmondo,<emph.end type="bold"></emph.end> suo trattato della percossa 180. </s></p><p type="main">

<s><emph type="bold"></emph>Martello,<emph.end type="bold"></emph.end> modo e forza della percossa fatta da lui 114. </s></p><p type="main">

<s><emph type="bold"></emph>Mersenno Marino<emph.end type="bold"></emph.end> censura alcune proposizioni dinamiche di Galileo 502, professa con Galileo che la <lb></lb>resultante debba uguagliar la somma delle componenti, e poi riconosce il suo errore 571. </s></p><p type="main">

<s><emph type="bold"></emph>Moto<emph.end type="bold"></emph.end> non muore, nè rinvivisce, ma si conserva latente 182. </s></p><p type="main">

<s><emph type="bold"></emph>Nardi Antonio,<emph.end type="bold"></emph.end> suo savio avvertimento intorno al giudicare i grandi uomini 83, notizie de&#039;mano­<lb></lb>scritti di lui 419-21, trova per via meccanica la quadratura della Cicloide esatta 453, immagina <lb></lb>una Cicloide nuova, per la quadratura della volgare 455, 58. </s></p><p type="main">

<s><emph type="bold"></emph>Newton Isacco,<emph.end type="bold"></emph.end> storia del primo tomo de&#039;suoi Principii matematici di Filosofia naturale 591-605. </s></p><p type="main">

<s><emph type="bold"></emph>Ottica<emph.end type="bold"></emph.end> cartesiana, censure relative ai moti composti, fatte dal Roberval, dall&#039;Hobbes e dal Fer­<lb></lb>mat 563-65. </s></p><p type="main">

<s><emph type="bold"></emph>Pappo Alessandrino,<emph.end type="bold"></emph.end> dimostrazione di lui condotta col metodo degli indivisibili 435. </s></p><p type="main">

<s><emph type="bold"></emph>Parallelogrammo<emph.end type="bold"></emph.end> delle forze, come dimostrato dal Newton 615, come dal Varignen e dall&#039;Herman 616, <lb></lb>come dal Prony 624, come da altri, comprendendo le virtù delle dimostrazioni precedenti 625. </s></p><p type="main">

<s><emph type="bold"></emph>Pendolo<emph.end type="bold"></emph.end> semplice, una proprietà di lui scoperta dal Borelli 183, come l&#039;Huyghens riuscisse a fargli <lb></lb>descrivere arehi cicloidali 516, composto, come si riduce al semplice 528-30, regola di questa <lb></lb>riduzione data dall&#039;Huyghens, che il Deschales non riconosce vera, se non in alcuni casi parti­<lb></lb>colari 531, obiexioni fatte all&#039;Huyghens in questo proposito da altri Matematici 532, finalmente la <lb></lb>verità della Regola ugeniana vien confermata, per via del calcolo infinitesimale 533, e derivan­<lb></lb>dola da principii diversi da quello della conservazione delle forze vive 534. </s></p><p type="main">

<s><emph type="bold"></emph>Percossa,<emph.end type="bold"></emph.end> forza di lei paragonata da Galileo con quella delle Macchine 114, quali false idee ne avesse <lb></lb>il Mersenno 115, distinta dall&#039;Aggiunti in naturale, violenta e media 119, leggi di lei, che si lu­<lb></lb>singò di avere scoperte il Viviani, usando una stadera costruita sopra un disegno del Torri­<lb></lb>celli 162. </s></p><p type="main">

<s><emph type="bold"></emph>Perelli Tommaso<emph.end type="bold"></emph.end> erra insieme col Viviani nel risolvere il problema della corda tesa, gravata nel <lb></lb>mezzo da un piccolissimo peso 72. </s></p><p type="main">

<s><emph type="bold"></emph>Pietroburge,<emph.end type="bold"></emph.end> esperienze ivi fatte per dimostrare il grande impedimento, che ricevon dall&#039;aria i pro­<lb></lb>ietti nei tiri verticali 53. </s></p><p type="main">

<s><emph type="bold"></emph>Platone,<emph.end type="bold"></emph.end> suo concetto voluto ridurro a calcolo da Galileo e dal Viviani 53. </s></p><p type="main">

<s><emph type="bold"></emph>Poleni Giovanni,<emph.end type="bold"></emph.end> sue esperienze per la misura delle forze vive 636. </s></p><p type="main">

<s><emph type="bold"></emph>Postulate,<emph.end type="bold"></emph.end> principio meccanico di Galileo 11, come da Galileo stesso dimostrato 12, come dal Miche­<lb></lb>lini 14, come dal Baliani 15, come dal Torricelli, invocando un principio nuovo 23, come, in di­<lb></lb>verso modo da quel che che aveva fatto nella prima edizione, il Baliani lo dimostrasse nella <lb></lb>seconda 29, come lo dimostrasse l&#039;Huyghens che, malcontento di Galileo, cade in un paralogi­<lb></lb>smo 29, come finalmente lo dimostrasse A. </s>

<s>Marchetti 32. </s></p><p type="main">

<s><emph type="bold"></emph>Problemi naturali,<emph.end type="bold"></emph.end> occasione che Galileo ebbe di scriverli 196. </s></p><p type="main">

<s><emph type="bold"></emph>Quadratura<emph.end type="bold"></emph.end> della Cicloide, come fosse dimostrata dal Cartesio e dal Fermat 449-52. </s></p><p type="main">

<s><emph type="bold"></emph>Riccati Vincenzo,<emph.end type="bold"></emph.end> come dimostrl il parallelogrammo delle forze 619, sottopone al calcolo l&#039;esperienza <lb></lb>dimostrativa della vera misura delle forze vive 637. </s></p><p type="main">

<s><emph type="bold"></emph>Ricci Michelangiolo<emph.end type="bold"></emph.end> risolve al Viviani un dubbio meccanico, per il principio dei moti composti 67, <lb></lb>esorta il Borelli a trattare della composizione dei moti 580. </s></p><p type="main">

<s><emph type="bold"></emph>Riflessione<emph.end type="bold"></emph.end> conserva, secondo il Borelli, la stessa quantità di moto dell&#039;incidenza 186, segue nel suo <lb></lb>viaggio la via più breve <emph type="italics"></emph>ivi.<emph.end type="italics"></emph.end></s></p><p type="main">

<s><emph type="bold"></emph>Rimbalzello,<emph.end type="bold"></emph.end> sua ragione data da G. M. </s>

<s>Marci 193. </s></p><p type="main">

<s><emph type="bold"></emph>Rimbalzi<emph.end type="bold"></emph.end> non giungono mai alla precisa altezza, da cui scesero i corpi 185. </s></p><p type="main">

<s><emph type="bold"></emph>Roberval Egidio,<emph.end type="bold"></emph.end> sue proposizioni dimostrative delle proprietà della Cicloide, raccolte e ordinata­<lb></lb>mente narrate 441, suo notabile teorema <emph type="italics"></emph>Des anneaux<emph.end type="italics"></emph.end> 446, lemmi premessi, per dimostrare in <lb></lb>tre distinte proposizioni la proporzion che passa tra i solidi cicloidali e i cilindri circoscritti 446-49, <lb></lb>come si difendesse dall&#039;accuse mossegli dal Torricelli di avergli usurpata l&#039;invenxione del cen­<lb></lb>tro di gravità della Cicloide 480, degli otto libri di Meccanica nuova, pubblicati da lui 504-8, suo <lb></lb>trattato Dei moti composti 562, riconosce il Cavalieri autore degli indivisibili 628. </s></p><p type="main">

<s><emph type="bold"></emph>Rocca Giovann&#039;Antonio,<emph.end type="bold"></emph.end> suo trattato dei moti equabili 86. </s></p><p type="main">

<s><emph type="bold"></emph>Sarpi Paolo,<emph.end type="bold"></emph.end> sue istanze contro un principio fondamentale della Meccanica di Galileo 50, propone <lb></lb>a Galileo un problema relativo alle quantità di moto 118, il qual problema era stato risoluto già <lb></lb>da Leonardo da Vinci 119. </s></p><pb xlink:href="020/01/3037.jpg" pagenum="662"></pb><p type="main">

<s><emph type="bold"></emph>Scaligero G. Cesare,<emph.end type="bold"></emph.end> qual opposizione facesse alle opinioni del Cardano intorno alla forza della per­<lb></lb>cossa 113. </s></p><p type="main">

<s><emph type="bold"></emph>Secchie,<emph.end type="bold"></emph.end> per la misura della forza della percossa, esperienza di Galileo illustrata 168. </s></p><p type="main">

<s><emph type="bold"></emph>Simpson Tommaso<emph.end type="bold"></emph.end> applica il principio della composizion delle forze a dimostrare il teorema gali­<lb></lb>leiano della corda tesa 73. </s></p><p type="main">

<s><emph type="bold"></emph>Spada,<emph.end type="bold"></emph.end> in qual parte della sua lunghezza faccia, secondo Isacco Vossio, maggiore la ferita 116. </s></p><p type="main">

<s><emph type="bold"></emph>Stadera<emph.end type="bold"></emph.end> per la misura della forza della percossa, proposta dal Rinaldini nell&#039;Accademia del Ci­<lb></lb>mento 160. </s></p><p type="main">

<s><emph type="bold"></emph>Stenone Niccolò,<emph.end type="bold"></emph.end> colloquio di lui col Viviani, relativo ai moti composti 575. </s></p><p type="main">

<s><emph type="bold"></emph>Stevino Simeone,<emph.end type="bold"></emph.end> primo a dimostrar geometricamente il teorema della scesa di un grave per un <lb></lb>piano inclinato, qualunque sia la direzione, che la potenza fa col declivio 567. </s></p><p type="main">

<s><emph type="bold"></emph>Tangenti,<emph.end type="bold"></emph.end> loro descrizione meccanica 407. </s></p><p type="main">

<s><emph type="bold"></emph>Teoremi<emph.end type="bold"></emph.end> due, inseriti dal Torricelli, annuente e compiacentesi Galileo, nel Dialogo delle propor­<lb></lb>zioni 99, perchè manchino nella copia originate di detto Dialogo fatta dal Torricelli per il prin­<lb></lb>cipe Leopoldo de&#039;Medici 101. </s></p><p type="main">

<s><emph type="bold"></emph>Tempo<emph.end type="bold"></emph.end> impiegato dal grave a passare naturalmente uno spazio determinato, come misurato dall&#039;Huy­<lb></lb>ghens 517. </s></p><p type="main">

<s><emph type="bold"></emph>Termometro,<emph.end type="bold"></emph.end> come l&#039;invenzione di lui, attribuita a Galileo, pensasse il Viviani di commemorar nei <lb></lb>dialoghi delle due nuove Scienze 49. </s></p><p type="main">

<s><emph type="bold"></emph>Torricelli Evangellsta,<emph.end type="bold"></emph.end> il libro di lui <emph type="italics"></emph>De motu<emph.end type="italics"></emph.end> presentato a Galileo 19, quanto fosse stimato in Fran­<lb></lb>cia si dà a giudicar da ciò, che si narra esser passato fra il Carcary e il Gassendo 27, in che <lb></lb>modo distese a dettatura il dialogo delle proporzioni 95, descrizione de&#039;pensieri, che gli passa­<lb></lb>rono per la mente, nel leggero i libri della Centrobarica guldiniana, mandatigli dal Cavalieri, e <lb></lb>in cui notò vari falsi teoremi 304, suoi teoremi de&#039;moti composti esaminati 573. </s></p><p type="main">

<s><emph type="bold"></emph>Trottole,<emph.end type="bold"></emph.end> perchè girando stien ritte 197. </s></p><p type="main">

<s><emph type="bold"></emph>Ultimo<emph.end type="bold"></emph.end> congresso di Galileo, storia relativa a lui narrata dal Viviani 129. </s></p><p type="main">

<s><emph type="bold"></emph>Uniforme,<emph.end type="bold"></emph.end> moto, sue principali proprietà dimostrate da Archimede 85. </s></p><p type="main">

<s><emph type="bold"></emph>Valerio Luca<emph.end type="bold"></emph.end> applica il principio della composizion delle forze a dimostrare il supposto meccanico <lb></lb>di Galileo 21, 556. </s></p><p type="main">

<s><emph type="bold"></emph>Varignon Pietro,<emph.end type="bold"></emph.end> sua <emph type="italics"></emph>Nouvelle mecanique<emph.end type="italics"></emph.end> 552, suo esame critico dell&#039;opinion del Borelli intorno <lb></lb>alle proporzioni de&#039;pesi pendenti le corde 584-87. </s></p><p type="main">

<s><emph type="bold"></emph>Velocità virtuoli,<emph.end type="bold"></emph.end> dubbi intorno ad esse mossi da Galileo e dalla sua Scuola 38, e segnatamente dal <lb></lb>Cavalieri 67, come le definisse Giovanni Bernoulli, che così fu il primo a chiamarle 682. </s></p><p type="main">

<s><emph type="bold"></emph>Vinci (da) Leonardo,<emph.end type="bold"></emph.end> suoi teoremi relativi alle quantità di moto e ai loro effetti 119, 170, relativi alla <lb></lb>forza della percossa 270, 74, aveva interpetrato allo stesso modo del Kepler la Ia archimedea <emph type="italics"></emph>De <lb></lb>circuli dimensione<emph.end type="italics"></emph.end> 309. </s></p><p type="main">

<s><emph type="bold"></emph>Viviani Viucenzo,<emph.end type="bold"></emph.end> come facesse ia prima conoscenza di Galileo in Arcetri, e gli proponesse alcuni <lb></lb>suoi dubbi 9, come s&#039;avvedesse che i dialoghi delle due nuovo Scienze avevano bisogno d&#039;esser <lb></lb>corretti 55, si rivolge a M. A. Ricci, per aver da lui la soluzione meccanica di un suo dubbio 66, <lb></lb>intento principale degli studii, dati da lui alla meccanica 492. </s></p><p type="main">

<s><emph type="bold"></emph>Vessio Isacco,<emph.end type="bold"></emph.end> come si lusingasse di aver suggerito certe considerazioni intorno al modo più van­<lb></lb>vantaggioso di disporre le parti de&#039;corpi, che han da operar la percossa 116. </s></p><p type="main">

<s><emph type="bold"></emph>Wallis Giovanni,<emph.end type="bold"></emph.end> suo trattato <emph type="italics"></emph>De percussione<emph.end type="italics"></emph.end> 179, come dimostrasse l&#039;uguaglianza fra l&#039;angolo del­<lb></lb>l&#039;incidenza e della riflessione, e rispondesse a coloro, che chiamavano una temerità la composi­<lb></lb>zione e scomposizione delle forze 187, conclude come Galileo che anche il salto di una pulce <lb></lb>commoverebbe la Terra 202, generalizza alcuni teoremi del Torricelli, per applicarli all&#039;inven­<lb></lb>zione del centro di gravità delle superficie curve 294, applica il metodo kepleriano all&#039;invenzione <lb></lb>de&#039;centri di gravità dei settori circolari e sferici 210, rispetto al centro della percossa usa il me­<lb></lb>todo, e conferma le conclusioni del Roberval e del Cartesio 526, suo teorema, e difesa de&#039;moti <lb></lb>composti 568. </s></p><p type="main">

<s><emph type="bold"></emph>Witsen Niccolò,<emph.end type="bold"></emph.end> come, applicandovi i teoremi steviniani della composizion dei moti, sciogliesse il <lb></lb>problema del voltar, nel modo più profittevole, le vele ai venti 568. <pb xlink:href="020/01/3038.jpg"></pb><pb xlink:href="020/01/3039.jpg"></pb></s></p><pb xlink:href="020/01/3040.jpg"></pb><p type="main">

<s>Finito di stampare in Bologna presso la <lb></lb>Libreria Editrice Forni nel Giugno 1970 </s></p><pb xlink:href="020/01/3041.jpg"></pb></chap><chap><p type="main">

<s>350478 Storia Del Metodo Sperimentale Italia </s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Editor-in-Chief: Harry Woolf<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Willis K. </s>

<s>Shepard Professor of the History of <lb></lb>Science, The Johns Hopkins University<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/3042.jpg"></pb><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph><emph type="italics"></emph>Storia del Metodo <lb></lb>Sperimentale in Italia<emph.end type="italics"></emph.end><emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>by RAFFAELLO CAVERNI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>in Six Volumes<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Volume VI<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>THE SOURCES OF SCIENCE, NO. 134<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>NEW YORK LONDON 1972<emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/3043.jpg"></pb><p type="main">

<s>Reproduced here is the Florence edition of 1891-1900. </s></p><p type="main">

<s>This sixth volume of the <emph type="italics"></emph>Storia del Metodo Sperimentale <lb></lb>in Italia<emph.end type="italics"></emph.end> was published posthumously and is incomplete. </s>

<s><lb></lb>It breaks off suddenly on page 464. </s></p><figure id="id.020.01.3043.1.jpg" xlink:href="020/01/3043/1.jpg"></figure><p type="main">

<s><emph type="center"></emph>Copyright © 1972 by Johnson Reprint Corporation All rights reserved <lb></lb>Library of Congress Catalog Card Number: 70-178235<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT CORPORATION<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>111 Fifth Avenue, New York, N.Y. 10003, U.S.A.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>JOHNSON REPRINT COMPANY LTD.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>Shipton Group House, 24/28 Oval Road, London, NW17DD, England<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>Printed in Italy<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><pb xlink:href="020/01/3044.jpg"></pb><p type="main">

<s><emph type="center"></emph>DEL METODO SPERIMENTALE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>APPLICATO<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>ALLA SCIENZA DEL MOTO DELLE ACQUE<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>PARTE PRIMA<emph.end type="center"></emph.end><pb xlink:href="020/01/3045.jpg"></pb></s></p><pb xlink:href="020/01/3046.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO I.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della Scienza dell&#039;equilibrio e del moto delle acque <lb></lb>da&#039;suoi principii infino a tutto il secolo XVI<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Della partizione di questa Storia: di Archimede, e del suo primo libro delle Galleggianti. </s>

<s>— II. </s>

<s>Del <lb></lb>secondo libro archimedeo delle Galleggianti. </s>

<s>— III. </s>

<s>Della Scienza del moto delle acque da Sesto <lb></lb>Giulio Frontino a Leonardo da Vinci. </s>

<s>— IV. </s>

<s>Delle dottrine idrauliche di L. da Vinci, parago­<lb></lb>nate con quello di Girolamo Cardano. </s>

<s>— V. De&#039;progressi fatti dall&#039;Idrostatica nella seconda <lb></lb>metà del secolo XVI. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Chiamare <emph type="italics"></emph>acque<emph.end type="italics"></emph.end> i liquidi, come arie i corpi gazosi, potrebbe sembrare <lb></lb>improprio, o almen basso, nell&#039;artificioso linguaggio, di che fanno uso gli <lb></lb>scienziati moderni. </s>

<s>Ma pure, amando noi di essere anche nelle parole sem­<lb></lb>plici e chiari, abbiam creduto di non doverci dilungare in ciò dall&#039;esempio <lb></lb>di quei buoni antichi, i quali, per non coniar vocaboli strani e non intesi, <lb></lb>davano a tutta una specie il nome stesso di uno degli oggetti, che, fra&#039;com­<lb></lb>presi in essa, fosse de&#039;più comuni. </s>

<s>E qual cosa infatti è più comune e più <lb></lb>nota dell&#039;acqua, alla quale tutti sappiamo doversi attribuire, nelle piante e <lb></lb>negli animali, quella che propriamente si dice freschezza di vita? </s>

<s>Aggiun­<lb></lb>gasi che parte principalissima della Scienza, di cui siamo per narrare la Sto­<lb></lb>ria, consiste nell&#039;investigare le ragioni e i modi del correre le acque sull&#039;al­<lb></lb>veo, e dentro gli argini dei fiumi. </s></p><p type="main">

<s>Ma o siano acque o di qualunque altra natura i liquidi, per questo si <lb></lb>distinguono, e formano una specie a parte dagli altri trattabili corpi, perchè, <lb></lb>sebben rimangano quanto al volume costanti, son, quanto alla forma, conti­<lb></lb>nuamente variabili, accomodandosi, quando sono in quiete, a prendere quella, <pb xlink:href="020/01/3047.jpg" pagenum="8"></pb>qualunque ella si sia, dei recipienti. </s>

<s>È di qui manifesto che se il recipiente <lb></lb>ha figura regolare, come di cono o di sfera, il liquido infusovi, in quanto è <lb></lb>grave, tende al centro terrestre secondo la direzione, e con la intensità di un <lb></lb>solido, che fosse denso ugualmente, e il centro di gravità si troverebbe perciò <lb></lb>nello stesso punto, che nel cono solido o nella sfera. </s>

<s>Ma se le pareti si rom­<lb></lb>pono, e il contenuto si versa, è impossibile a sapere oramai più dove sia an­<lb></lb>dato il centro di gravità, sì perchè la mole liquida ha preso una figura irre­<lb></lb>golare, e sì perchè questa stessa figura ad ogni istante si varia. </s></p><p type="main">

<s>Può intravedersi di qui una di quelle difficoltà, che la Scienza trova <lb></lb>assai maggiore in investigar le leggi del moto ne&#039;liquidi, che ne&#039;solidi. </s>

<s>Ma <lb></lb>non è la sola, imperocchè ogni particella liquida com&#039;è premuta per la pro­<lb></lb>pria gravità, e per il peso delle soprastanti, così ripreme col medesimo im­<lb></lb>pulso tutte le altre, che le stanno all&#039;intorno, ond&#039;è in tutta la mole un&#039;in­<lb></lb>finità d&#039;infinite forze intestine, fra le quali può turbar l&#039;equilibrio ogni più <lb></lb>lieve accidente. </s>

<s>Si presentano perciò allo scienziato a risolvere problemi di <lb></lb>un&#039;infinita infinità d&#039;incognite, fortunato se può riuscire a determinarne qual­<lb></lb>cuna, e più fortunato che mai se la travagliata determinazion particolare è <lb></lb>la vera. </s></p><p type="main">

<s>Tante altre considerazioni, che si potrebbero fare in simile proposito, <lb></lb>predispongono i nostri Lettori ad ascoltare una storia, in cui il Metodo spe­<lb></lb>rimentale, quando non si confesserà insufficiente a scoprire la verità deside­<lb></lb>rata, darà le prove estreme della sua propria bontà e del suo valore. </s>

<s>Di qui <lb></lb>è che, mentre la Meccanica de&#039;solidi era giunta alla perfezione, che si vide <lb></lb>ne&#039;Dialoghi delle due nuove Scienze; quella de&#039;liquidi si può dire che ri­<lb></lb>maneva tuttavia nell&#039;infanzia. </s>

<s>Nè de&#039;progressi fatti poco di poi si deve tutto <lb></lb>il merito attribuire agli sperimenti, ma pure si furon questi, che addirizza­<lb></lb>rono il filo alle speculazioni, e che ne assicurarono della rettitudine in tanti <lb></lb>casi, come per esempio quando s&#039;applicò agli efflussi dai vasi le scoperte <lb></lb>leggi delle cadute naturali dei gravi, e dei getti parabolici. </s>

<s>Si prese da ciò <lb></lb>fiducia di ridur la Scienza del moto de&#039;liquidi a partecipar de&#039;progressi così <lb></lb>felicemente fatti dalla Scienza del moto dei corpi duri, ma tanti dubbi assa­<lb></lb>lirono le menti, e tante cause concorsero a rompere i ritrosi vincoli di quei <lb></lb>connubii, che le stesse esperienze più diligenti ebbero a travagliarsi lunga­<lb></lb>mente in stabilirgli, e no assolutamente, ma in certe date condizioni. </s></p><p type="main">

<s>In ogni modo partecipano i liquidi co&#039;solidi una proprietà essenziale, che <lb></lb>consiste nell&#039;essere ambedue le specie de&#039;corpi similmente gravi; ond&#039;è che, <lb></lb>se questa forza di gravità è ritenuta da qualche ostacolo, come dalle pareti <lb></lb>di un recipiente, il liquido rimane in quiete, ma lasciato in libertà si muove, <lb></lb>scendendo, per la più breve e diretta via, al comun centro terrestre. </s>

<s>Anche <lb></lb>questa Scienza perciò andò soggetta a quelle due massime distinzioni, che si <lb></lb>fecero della Meccanica, chiamandosi <emph type="italics"></emph>Idrostatica<emph.end type="italics"></emph.end> l&#039;una parte, che tratta del­<lb></lb>l&#039;equilibrio, e <emph type="italics"></emph>Idrodinamica<emph.end type="italics"></emph.end> quell&#039;altra, che tratta del moto. </s>

<s>Le leggi idro­<lb></lb>statiche e idrodinamiche, dai Matematici dimostrate co&#039;calcoli, e da&#039;Fisici <lb></lb>verificate con l&#039;esperienze, s&#039;appropriano a ogni specie di liquidi, che si con-<pb xlink:href="020/01/3048.jpg" pagenum="9"></pb>tengano in piccoli vasi, da&#039;fori aperti ne&#039;quali fluiscano liberamente o dentro <lb></lb>tubi aggiunti, o in artificiosi canali. </s>

<s>Ma ci è un liquido, fra i mondani elementi <lb></lb>diffusissimo, e uno de&#039;maggiori ministri deputato dalla Natura a dispensare <lb></lb>sul nostro globo la vita; liquido, che ha per suoi propri vasi i laghi e i <lb></lb>mari, sull&#039;ampia superficie de&#039;quali corre e ricorre senza mai posa tra invi­<lb></lb>sibili sponde, che gli si vedono poi distinte negli argini de&#039;fiumi e negli <lb></lb>alvei, da sè stesso scavatisi con provvido istinto a&#039;suoi liberi flussi perenni. </s></p><p type="main">

<s>Sembrerebbe a prima vista che, essendo le velocità indipendenti dalla <lb></lb>maggiore o minor mole della materia, e dal più lungo o breve spazio per­<lb></lb>corso, fossero con pari legge velocitate le acque, sia ch&#039;ell&#039;escano da piccol <lb></lb>vaso o da larga fonte, e s&#039;avviino a scendere giù pel declivio di un tavolato <lb></lb>manufatto o di un alveo naturale, senz&#039;altra differenza che degli impedi­<lb></lb>menti nel più lungo corso, e nel declivio più scabroso, maggiormente ritar­<lb></lb>datori del moto. </s>

<s>Ma ripensando poi che ne&#039;fiumi le sezioni premono tanto <lb></lb>più fortemente sopra sè medesime, e incalzano le sezioni seguenti, quanto <lb></lb>più crescono le loro altezze, come si vede avvenir nelle piene, cosicchè non <lb></lb>si verifica la legge delle velocità indipendenti dalle moli; si potrà da ciò solo <lb></lb>argomentare che tante altre cause concorrono a far differire il flusso del­<lb></lb>l&#039;acqua dai vasi, e il loro correr per gli alvei dei fiumi, da render neces­<lb></lb>sario d&#039;aggiungere alla Scienza una terza parte distinta, che è quella pro­<lb></lb>priamente chiamata col nome di <emph type="italics"></emph>Idraulica.<emph.end type="italics"></emph.end> Così dunque, come tripartita è <lb></lb>la Scienza stessa, tripartiremo noi la sua propria Storia, dell&#039;Idrostatica e <lb></lb>dell&#039;Idrodinamica trattando in questo tomo, e dell&#039;Idraulica nel seguente. </s></p><p type="main">

<s>Secondo i limiti, che ci siamo prefissi, dovrebbe la nostra narrazione <lb></lb>incominciare da quel risorgimento intellettuale, che sul finir del secolo XVI <lb></lb>si rese più cospicuo e ammirato. </s>

<s>Ma come, a conoscer bene un albero, e a <lb></lb>giudicar del portato de&#039;suoi frutti, è necessario andare a ricercarne le intime <lb></lb>radici; così, per conoscer meglio i portati della mente speculativa, e dell&#039;arte <lb></lb>sperimentale in quel tempo, è ben risalire alle prime tradizioni. </s>

<s>Si trova, <lb></lb>così facendo, quel ch&#039;è consueto osservarsi in tutti gli svolgimenti naturali <lb></lb>dal loro proprio principio, che cioè, prima d&#039;apparire distintamente le varie <lb></lb>membra organiche, sono insieme confuse. </s>

<s>Ne&#039;tempi infatti, che precederono <lb></lb>al risorgere della Scienza, le speculazioni intorno all&#039;equilibrio e al moto <lb></lb>de&#039;liquidi, intorno alle loro leggi del fluire dentro i tubi o dentro gli alvei <lb></lb>de&#039;fiumi, benchè si distinguano ora da noi per la varietà dell&#039;obbietto, si <lb></lb>comprendevano nonostante dai loro Autori in un solo esercizio, ond&#039;è che <lb></lb>in questo rapido sguardo, che siam per dare indietro alla lunga via, ci verrà <lb></lb>tutt&#039;insieme in considerazione quel che intorno all&#039;Idrostatica, all&#039;Idrodina­<lb></lb>mica e all&#039;Idraulica fu speculato, e sperimentato dai precursori dello Stevino <lb></lb>e del Castelli. </s></p><p type="main">

<s>Il più antico documento che abbiamo, e che, nel decorrere di tanti secoli, <lb></lb>e in mezzo a tanti progressi, riman colle sue proprie note distinto, quasi ra­<lb></lb>dice maestra, che tuttavia duri a infondere i vitali umori nell&#039;albero della <lb></lb>Scienza; è fra le opere di Archimede quella, che tratta del galleggiare dei <pb xlink:href="020/01/3049.jpg" pagenum="10"></pb>corpi. </s>

<s>Di sottile e difficile materia dissero di averla trovata sempre tutti gli <lb></lb>studiosi, e coloro, che non lo confessarono con le parole, lo mostraron co&#039;fatti <lb></lb>ne&#039;loro infelici commentarii. </s>

<s>Si direbbe che tali difficoltà sono inevitabili in <lb></lb>uno scrittore antico, le opere del quale non ci son pervenute, che nelle copie <lb></lb>di amanuensi inesperti, e si soggiungerebbe che sono ai più dotti critici insu­<lb></lb>perabili, per la impossibilità delle collazioni, se non si ripensasse che assai <lb></lb>leggeri sono i difficili incontri, per ragion del testo o guasto o corrotto, e <lb></lb>del processo delle dimostrazioni disordinato, rispetto a quelli, che si parano <lb></lb>innanzi alla mente dell&#039;interpetre, per la sottigliezza dell&#039;argomento. </s>

<s>A dif­<lb></lb>fondere perciò su tante tenebre qualche raggio di luce poco possono giovare <lb></lb>le più diligenti cure di rendere quant&#039;è possibile genuina la lezione, in­<lb></lb>torno a che par che consùmino tutta l&#039;opera loro i critici e i commentatori, <lb></lb>ma bisogna penetrare addentro al segreto e profondo pensiero dell&#039;Autore, <lb></lb>per poi ritrarne l&#039;indole propria dell&#039;esposizione. </s></p><p type="main">

<s>L&#039;intenzion nostra presente non è alle cose geometriche, ma alle fisiche <lb></lb>e meccaniche, e più particolarmente a quelle, che riguardano il galleggiare <lb></lb>dei corpi. </s>

<s>L&#039;indole della trattazione archimedea intorno a un tale soggetto <lb></lb>si può conoscere in precedenza, ripensando esser egli stato fedel seguace di <lb></lb>quel Platone, che reputava indegno del Filosofo il trattenersi a contemplare <lb></lb>le vili e variabili passioni della materia. </s>

<s>Passando poi a leggere si trova con­<lb></lb>fermata la verità del preconcetto, imperocchè quell&#039;ingegno ogni volta che <lb></lb>ripiega le ali, per scendere a posarsi sulla materia, è studioso di sceglierne <lb></lb>il fiore, quasi ape, che ne trasforma la nativa insipidezza in ambrosia celeste. </s>

<s><lb></lb>La sua trutina, per esempio, è quasi un invisibile genio, che distende per <lb></lb>sostenere i pesi le impalpabili braccia. </s>

<s>Le piu disperse virtù di que&#039;pesi si <lb></lb>riducono per Archimede in un punto, a cui vanno, e da cui vengono i moti <lb></lb>dispensati con ordine e con misura, come cuore o punto saliente, da cui <lb></lb>escono, e in cui rientrano gli spiriti della vita. </s>

<s>Il liquido, in che egli imma­<lb></lb>gina galleggiare i corpi, non è acqua propriamente, nè altro di simile e par­<lb></lb>ticolare natura, ma quasi una stillata essenza di tutte le loro proprietà, a <lb></lb>cui non si saprebbe, e non s&#039;è saputo dare altro nome che di <emph type="italics"></emph>umido.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma pure una fama antica, e di riflesso in riflesso fattasi infino a noi <lb></lb>sempre più diffusa, ci rappresenta Archimede quale uno de&#039;più affaccendati <lb></lb>in voler ridurre alla sua suggezione le forze più ritrose della materia. </s>

<s>Egli <lb></lb>inventore di macchine prodigiose, da offendere i nemici, e da difendere la <lb></lb>sua patria dai loro assalti: egli costruttore sul mobile mare di un edifizio, <lb></lb>da render più comodo e delizioso il soggiorno del Re, che in mezzo ai giar­<lb></lb>dini di Siracusa. </s>

<s>Non le sentine sole de&#039;vascelli, ma i laghi stessi si asciu­<lb></lb>gano con la sua Coclea: le più gravi moli si trasportano con facilità, per il <lb></lb>felice accoppiamento ch&#039;egli ha pensato di fare dell&#039;elice con la ruota: e ri­<lb></lb>salendo ardito infino a invadere i dominii del Sole, lo costringe a conden­<lb></lb>sare il potente calore de&#039;suoi raggi, per abbruciare in mezzo alle acque i <lb></lb>navigli nemici dei Romani. </s>

<s>E che più? </s>

<s>ci vien dipinto ebro della sua scienza <lb></lb>correre per le vie ad annunziare la scoperta inaspettatamente sovvenutagli <pb xlink:href="020/01/3050.jpg" pagenum="11"></pb>della quantità dell&#039;argento, furtivamente sostituito dall&#039;orefice all&#039;oro, che <lb></lb>egli aveva avuto dal suo Re, per costruirne una corona yotiva. </s></p><p type="main">

<s>Si dirà forse che Archimede sapeva, per colmo delle sue virtù, congiun­<lb></lb>gere insieme la contemplazione e l&#039;azione? </s>

<s>Ma perchè in tutti i suoi libri <lb></lb>serba sempre il carattere di filosofo platonico, e in mezzo a tante astratte <lb></lb>verità specu̇late non si legge fatto mai nemmeno un cenno a qualcuna di <lb></lb>quelle pratiche applicazioni, che la fama gli ha attribuito? </s>

<s>Com&#039;è possibile <lb></lb>non riconoscere una diversità fra le opere endoteriche e le esoteriche, ben­<lb></lb>chè vadano sotto il medesimo nome di Archimede Siracusano? </s>

<s>E da un&#039;altra <lb></lb>parte, perchè le notizie sparse da così nobili scrittori, quali sono Diodoro, <lb></lb>Polibio, Ateneo non possono non essere sostentate da qualche aura di vero;, <lb></lb>giova ricercar da qual parte sia quella sottile aura spirata. </s>

<s>Nè difficile ci si <lb></lb>presenta la ricerca, ripensando a quelle leggi d&#039;induzione e di deduzione, <lb></lb>secondando le quali il pensiero, con moto simile all&#039;andare e al ritornar di <lb></lb>una spola, va intessendo la sua sottilissima tela. </s>

<s>Archimede induce per astra­<lb></lb>zione dalle cose fisiche una proprietà geometrica, da cui potrà chi vuole de­<lb></lb>durne la notizia dei vari fatti particolari. </s>

<s>Tra le prime sensibili apprensioni, <lb></lb>e questa notizia acquistata così per riflessione, ci è la differenza che passa <lb></lb>tra uno, che lavora un oggetto a mano, e un altro, che si trova già prepa­<lb></lb>rata la forma. </s>

<s>E come chi ha preparato la forma si può giustamente dire <lb></lb>autore della statua, che dentro vi s&#039;è gettata; così può dirsi Archimede au­<lb></lb>tore di tutte le invenzioni, che gli studiosi stessi contemporanei attinsero <lb></lb>da&#039;suoi libri. </s>

<s>Chi trova ragionevoli queste considerazioni si vedrà facilmente <lb></lb>risoluti molti problemi, e fra gli altri quello del non parer credibile che, <lb></lb>all&#039;invenzione e all&#039;esecuzione di tante maraviglie, potesse bastar la vita di <lb></lb>un Filosofo. </s>

<s>Quel Filosofo dunque inventò, e altri eseguirono: gli autori delle <lb></lb>opere endoteriche e delle esoteriche son diversi, e nonostante sta bene che <lb></lb>s&#039;attribuiscano a uno solo. </s></p><p type="main">

<s>Passiamo ora a considerare particolarmente, fra quelle opere, il trattato <lb></lb>delle Galleggianti. </s>

<s>Che questo insigne monumento della Scienza avesse occa­<lb></lb>sione dal sentirsi l&#039;autore alleggerire il corpo nel bagno, e dal pensiero che <lb></lb>si sarebbe quella leggerezza potuta misurare per la quantità dell&#039;acqua river­<lb></lb>satasi dalla tinozza; saranno anche i nostri Lettori disposti a non reputarlo <lb></lb>oramai più che quale un apologo nella Storia. </s>

<s>Ben più alti furono que&#039;prin­<lb></lb>cipii, e più degni della Filosofia. </s>

<s>Avvezzo Archimede, infin da fanciullo, a <lb></lb>vedere i porti della sua Siracusa tutto intorno assiepati di navi, non era pos­<lb></lb>sibile che non rivolgesse poi le sue speculazioni a macchine così suntuose, <lb></lb>e dalle quali principalmente dipendevano le sorti della sua terra, per l&#039;uti­<lb></lb>lità de&#039;commerci, e per la sicurezza dagli assalti nemici. </s>

<s>E quanto, e da <lb></lb>quante parti porgevan materia da specular quelle moli, così intorno alle ra­<lb></lb>gioni del loro galleggiare sull&#039;acque, come del mantenere sulle mobili onde <lb></lb>fermezza di equilibrio fra la prora e la poppa? </s></p><p type="main">

<s>Il soggetto attraeva tanto più fortemente Archimede a contemplarlo, in <lb></lb>quanto che l&#039;ebbe a trovare intatto, e anzi da gravissimi errori deturpato <pb xlink:href="020/01/3051.jpg" pagenum="12"></pb>nella scuola del Filosofo, il quale, domandandosi, nel problema secondo della <lb></lb>XXIII sezione, <emph type="italics"></emph>Cur navigia onustioria in portu, quam in altu esse viden­<lb></lb>tur;<emph.end type="italics"></emph.end> rispondeva: “ An quia plus aquae quam minus reniti validius potest, <lb></lb>pauca nam oppressa onere cedit, ut demergi necesse sit: multa e contrario <lb></lb>repellit ac sustinet ” (<emph type="italics"></emph>Aristot. </s>

<s>Opera,<emph.end type="italics"></emph.end> T. IX, Venetiis 1550, fol. </s>

<s>316). Archi­<lb></lb>mede invece veniva, co&#039;suoi nuovi teoremi, a insegnare che del galleggiar <lb></lb>più o meno, e dell&#039;affondare un solido dentro un liquido non è altra ragione <lb></lb>dalla proporzionalità in fuori, che passa tra la gravezza di esso solido im­<lb></lb>merso e la gravezza del liquido, in cui quello per l&#039;immersione occupa il <lb></lb>luogo, intantochè o egli giungerà al livello del vaso o soprastarà o precipi­<lb></lb>terà sott&#039;esso, secondo che sarà la detta proporzione o d&#039;eguaglianza o di <lb></lb>eccesso. </s>

<s>Non dalla quantità dunque dell&#039;acqua, come insegnava Aristotile, ma <lb></lb>dalla sua sola gravità in specie dipende il fatto, ond&#039;è che, riducendo ne&#039;ter­<lb></lb>mini della verità il problema, deve il mare, di un medesimo vascello e ugual­<lb></lb>mente carico, inghiottir meno che un lago o un fiume, avendo maggiore gra­<lb></lb>vità specifica l&#039;acqua salsa che la dolce. </s>

<s>Ma non condiscendeva a così fatte <lb></lb>minuzie il genio di Archimede, le proposizioni del quale comprendono nella <lb></lb>loro universalità ogni sorta di acqua, anzi ogni liquefatta sostanza, purchè <lb></lb>ell&#039;abbia le proprietà generali dell&#039;umido, di giacersi cioè in superficie ori­<lb></lb>zontale e di ceder le parti men premute alle più compresse. </s>

<s>Del problema <lb></lb>proposto da Aristotile, e di altri simìli, lasciava l&#039;Autore ricavarne per co­<lb></lb>rollario la soluzione agli studiosi, i quali impararono, fra le altre cose, a ri­<lb></lb>trovare il peso specifico de&#039;vari corpi, e la proporzione de&#039;loro misti, d&#039;onde <lb></lb>ebbe l&#039;origine, come si spiegherà meglio altrove, il famoso apologo dell&#039;in­<lb></lb>venzione della quantità dell&#039;argento sostituito dall&#039;oretice del re Gerone all&#039;oro <lb></lb>della corona. </s></p><p type="main">

<s>È tale, cioè del semplice galleggiamento, la prima parte del trattato ar­<lb></lb>chimedeo. </s>

<s>Ma la seconda è d&#039;assai più sottile speculazione e di maggiore <lb></lb>importanza nella pratica, proponendovisi l&#039;Autore di dimostrare le ragioni <lb></lb>dello stabile equilibrio dei galleggianti. </s>

<s>Ch&#039;egli avesse anche qui di mira la <lb></lb>Nautica si può ragionevolmente argomentare dall&#039;avere scelto, fra&#039;solidi ro­<lb></lb>tondi, il settore di sfera principalmente e il conoide parabolico, che son le <lb></lb>forme geometriche astratte, alle quali più prossimamente ci può rassomi­<lb></lb>gliare e ridurre la mole di una nave. </s>

<s>D&#039;applicarne poi la teoria alle costru­<lb></lb>zioni negli arsenali lasciava Archimede l&#039;ufficio agl&#039;ingegneri, i quali non <lb></lb>mancarono di adempirlo, come discepoli diligenti, e fu la loro ammirabile <lb></lb>solerzia simboleggiata in quel palazzo incantato, che essere stato costruito <lb></lb>dallo stesso Archimede sulle onde marine, per variar le delizie alla dimora <lb></lb>del re Gerone, scrive, ne&#039;suoi <emph type="italics"></emph>Dinnosofisti,<emph.end type="italics"></emph.end> Diogene Laerzio. </s></p><p type="main">

<s>Ma dai simboli passando alla realtà, è un fatto che i Siracusani avevano, <lb></lb>sotto le discipline di Archimede, molto progredito e nella costruzione e nel <lb></lb>governo delle belliche navi, di che ebbe a fare esperienza più volte, venendo <lb></lb>a cimento con loro, l&#039;armata dei Romani. </s>

<s>Rimasti questi vittoriosi, ed eser­<lb></lb>citando la loro prepotenza in ridurre in schiavitù non le membra ma l&#039;in-<pb xlink:href="020/01/3052.jpg" pagenum="13"></pb>gegno dei vinti, tradussero nella loro propria lingua, col titolo <emph type="italics"></emph>De insidenti­<lb></lb>bus aquae,<emph.end type="italics"></emph.end> il libro, da cui tant&#039;arte pericolosa era derivata ne&#039;loro nemici, <lb></lb>non riserbandosi dell&#039;originale, che perciò andò miseramente smarrito; altro <lb></lb>che le figure illustrative. </s></p><p type="main">

<s>La storia dell&#039;Architettura navale di que&#039;tempi ci potrà narrare qual <lb></lb>pro sapesse ritrarre dalle male conquistate teorie l&#039;arte dei Romani, ma nel <lb></lb>campo della Filosofia naturale è più facile ritrovare intorno a ciò i docu­<lb></lb>menti, de&#039;quali ci contenteremo citar da Seneca uno, in cui si può dir che <lb></lb>s&#039;interpetrano, e si compendiano le proposizioni, dall&#039;appresso Siracusano <lb></lb>dimostrate nella prima parte delle sue Galleggianti. </s>

<s>Voleva Seneca confer­<lb></lb>mare quella verissima sentenza della Filosofia platonica non essere cioè una <lb></lb>cosa leggera o grave, secondo la nostra stima, ma in comparazione col mezzo, <lb></lb>e di ciò fare prende occasione nel terzo libro delle <emph type="italics"></emph>Questioni naturali,<emph.end type="italics"></emph.end> dove, <lb></lb>nel cap. </s>

<s>XXV, spiegò così il perchè in alcuni laghi il corpo di un uomo, <lb></lb>anche senza notare, e in qualche stagno i mattoni stessi rimangano a galla: <lb></lb>“ Huius rei palam causa est. </s>

<s>Quamcumque vis rem expende, et contra aquam <lb></lb>statue, dummodo utriusque par sit modus. </s>

<s>Si aqua gravior est, leviorem rem <lb></lb>quam ipsa est fert, et tanto supra se extollit, quanto erit levior. </s>

<s>Graviora de­<lb></lb>scendunt. </s>

<s>At si aquae et eius rei quam contra pensabis par pondus erit, nec <lb></lb>pessum ibit nec extabit, sed aequabitur aquae et natabit quidem, sed pene <lb></lb>mersa ac nulla eminens parte. </s>

<s>Hoc est cur quaedam tigna supra aquam pene <lb></lb>tota efferantur, quaedam ad medium submissa sint, quaedam ad aequilibrium <lb></lb>aquae descendant. </s>

<s>Nam, cum utriusque pondus par est, neutra res alteri ce­<lb></lb>dit. </s>

<s>Graviora descendunt, leviora gestantur. </s>

<s>Grave autem et leve est, non <lb></lb>aestimatione nostra, sed comparatione eius, quo vehi debet. </s>

<s>Itaque, ubi aqua <lb></lb>gravior est, hominis corpore aut saxi, non sinit id quo non vincitur mergi ” <lb></lb>(Venetiis 1522, fol. </s>

<s>30). </s></p><p type="main">

<s>Da Vitruvio poi, e da qualche altro autore di que&#039;tempi, si raccoglie che <lb></lb>i principii archimedei, dimostrati nel primo libro <emph type="italics"></emph>De insidentibus aquae,<emph.end type="italics"></emph.end> si <lb></lb>applicavano alla invenzione delle gravità specifiche dei varii corpi, ma il se­<lb></lb>condo libro parve si rimanesse oscuro a quegli stessi, che s&#039;erano confidati <lb></lb>di far romana la scienza di dare stabilità d&#039;equilibrio sul mare agli agitati <lb></lb>vascelli. </s>

<s>Diciamo così perchè si vedono qualche tempo dopo que&#039;baldanzosi <lb></lb>tornare a ricercar fra le spoglie dei vinti altri trattati dello stesso Archimede, <lb></lb>scegliendo principalmente quelli, ne&#039;quali si dimostrano le leggi dell&#039;equili­<lb></lb>brio de&#039;gravi nell&#039;aria, mossi dalla speranza che verrebbe luce di lì a intender <lb></lb>meglio le leggi dell&#039;equilibrio ne&#039;galleggianti sull&#039;acqua. </s>

<s>Di qui ebbe ori­<lb></lb>gine quella prima collezione delle Opere archimedee, che si componeva del­<lb></lb>l&#039;<foreign lang="grc">Ε<gap></gap>ΕΔΩΝ ΙΣΟΠΠΟ<gap></gap>ΩΝ</foreign> tradotto, o per dir meglio interpetrato <emph type="italics"></emph>Liber de cen­<lb></lb>tro gravium,<emph.end type="italics"></emph.end> del <foreign lang="grc">ΤΕΤΠΑΓΩΝΙΣΜΟΣ ΡΛΠΑΒΟΛΕΣ</foreign>, a cui rimase il titolo asso­<lb></lb>luto di <emph type="italics"></emph>Tetragonismus, e De insidentibus aquae.<emph.end type="italics"></emph.end> Chiameremo questa raccolta <lb></lb><emph type="italics"></emph>Romana,<emph.end type="italics"></emph.end> per distinguerla da quell&#039;altra, che si fece molto più tardi, e alla <lb></lb>quale, per la legittimità dell&#039;origine, ci sia lecito dare il nome di <emph type="italics"></emph>Siracu­<lb></lb>sana.<emph.end type="italics"></emph.end> Si comprendono in questa tutte le opere, che per la diligenza degli <pb xlink:href="020/01/3053.jpg" pagenum="14"></pb>eruditi, nell&#039;epoca del Rinascimento, si poterono ritrovare, ma in quella si <lb></lb>scelsero, come s&#039;è inteso, i soli trattati in materia di Meccanica, dal <foreign lang="grc">ΚΥΚΛΟΥ <lb></lb>ΜΕΤΠΗΣΙΣ</foreign> in fuori, che, per esser breve e di facile e maravigliosa inven­<lb></lb>zione, s&#039;inserì quasi parte dell&#039;altro Tetragonismo. </s></p><p type="main">

<s>Nel tempo del decadimento, come andarono dimenticati e dispersi gli <lb></lb>altri documenti della Scienza antica, e della letteratura; così incontrò alle <lb></lb>Opere di Archimede, che si ricercarono poi con desiderio, nel secolo XV, <lb></lb>quando da Cicerone e da Plutarco, da Vitruvio e da Polibio, insieme coi <lb></lb>tanti altri autori latini e greci resuscitati, se ne udì magnificare così l&#039;eccel­<lb></lb>lenza. </s>

<s>È facile indovinare, dietro ciò che s&#039;è detto, e secondo i naturali avve­<lb></lb>nimenti delle cose, come dovesse esser prima a trovarsi, e a richiamare a sè <lb></lb>l&#039;attenzione degli studiosi, la collezione Romana, della quale una copia si fece, <lb></lb>con la maggior diligenza possibile, a richiesta e a spese del vescovo di Pa­<lb></lb>dova, quando s&#039;incominciò a istituire qu̇ella Biblioteca, assegnata poi al Se­<lb></lb>minario, e che fu una delle prime e delle più benemerite degli studii in Italia. </s>

<s><lb></lb>Si diffusero di li come da centro le altre copie, che se ne fecero via via, fra <lb></lb>le quali son memorabili quelle, sopra cui studiarono Leonardo da Vinci, e <lb></lb>Niccolò Tartaglia. </s>

<s>Superate con l&#039;esercizio le prime difficoltà, che ebbe a in­<lb></lb>contrare l&#039;arte della stampa, pensò esso Tartaglia, nella povertà munifico, di <lb></lb>pubblicare a sue spese, per comun benefizio, come poi fece in Venezia nel 1543, <lb></lb>il manoscritto, intitolandolo <emph type="italics"></emph>Opera Archimedis Siracusani per Nicolaum <lb></lb>Tartaleam multis erroribus emendata.<emph.end type="italics"></emph.end> Questa non è, come si disse, altro <lb></lb>che la parzial Collezione romana, comprendente le sole Opere in materia di <lb></lb>Meccanica: anzi, perchè l&#039;intenzion principale de&#039;collettori fu rivolta al <emph type="italics"></emph>De <lb></lb>insidentibus aquae,<emph.end type="italics"></emph.end> a cui il libro de&#039;Centri di gravità e il Tetragonismo non <lb></lb>servivano che di preparazione; intorno al <emph type="italics"></emph>De insidentibus aquae<emph.end type="italics"></emph.end> versò prin­<lb></lb>cipalmente lo studio anche del Tartaglia, il quale vi si mostrò meno editor <lb></lb>diligente, che sottile e acuto commentatore. </s>

<s>Di ciò diremo più qua, ma in­<lb></lb>tanto non è da passare sotto silenzio un errore, che un nostro eloquente sto­<lb></lb>rico delle Matematiche può facilmente avere insinuato ne&#039;suoi Lettori. </s></p><p type="main">

<s>Guglielmo Libri, discorrendo nel suo secondo libro del Tartaglia, dice <lb></lb>che “ on lui doit le traité <emph type="italics"></emph>De insidentibus<emph.end type="italics"></emph.end> d&#039;Archimede, dont il connaissait <lb></lb>l&#039;original grec, qui a été perdu depuis ” (<emph type="italics"></emph>Histoire des Sciences mathem.,<emph.end type="italics"></emph.end><lb></lb>T. III, a Paris, pag. </s>

<s>165). Come fosse quell&#039;originale greco perduto assai <lb></lb>tempo prima fu detto da noi di sopra, e cì fa gran maraviglia non avesse <lb></lb>quel valent&#039;uomo fatto attenzione che il Tartaglia stesso conferma di non <lb></lb>avere avuto, del testo archimedeo, notizia, in quella lettera al conte Antonio <lb></lb>Landriani, dedicatoria del suo primo <emph type="italics"></emph>Ragionamento.<emph.end type="italics"></emph.end> Dichiarasi in questo il <lb></lb>libro di Archimede Siracusano <emph type="italics"></emph>De insidentibus aquae,<emph.end type="italics"></emph.end> e perchè, essendo così <lb></lb>fatta traduzione dal greco in molte parti oscura, esso conte, per collazionarla <lb></lb>coll&#039;originale, voleva mettersi a ogni costo a ricercarlo; il Tartaglia, che re­<lb></lb>putava questa di lui fatica inutile, e opera perduta, così, nella detta lettera <lb></lb>dedicatoria, gli soggiungeva: “ Onde, per levar questa fatica a V. S. di stare <lb></lb>a ricercare tale original greco, qual forse più oscuro ed incorretto ritroverà <pb xlink:href="020/01/3054.jpg" pagenum="15"></pb>della detta traduzione latina, ho dichiarata e minutamente dilucidata tal parte <lb></lb>in questo mio primo Ragionamento ” (Venetia 1551). </s></p><p type="main">

<s>Il Libri deve senza dubbio esser rimasto ingannato da quel che dice il <lb></lb>compar Riccardo, sulla fine di quel primo ragionamento in dialogo, rispetto <lb></lb>alla figura illustrativa della VIII proposizion di Archimede, la qual figura, <lb></lb>essendo mal disegnata, voleva esso Riccardo che fosse nel ricopiarla corretta, <lb></lb>ma a lui Niccolò rispondeva: “ Voi dite la verità, ma perchè così era quella <lb></lb>figura nell&#039;esempio greco, non m&#039;è parso di contraffarla, ancorchè fosse stato <lb></lb>meglio ” (ivı, pag. </s>

<s>21). L&#039;inganno dello Storico dunque stette nel credere <lb></lb>che con quell&#039;<emph type="italics"></emph>esempio greco<emph.end type="italics"></emph.end> s&#039;appellasse al testo, e non alle tavole unica­<lb></lb>mente rimaste, come si disse, e com&#039;è confermato dal Commandino, il quale, <lb></lb>supplendo di suo alla detta VIII del primo libro archimedeo, e alla seconda <lb></lb>del secondo, che per l&#039;ingiuria de&#039;tempi si desideravano; dice di averle re­<lb></lb>stituite <emph type="italics"></emph>ad mentem Archimedis ex figuris, quae remanserunt<emph.end type="italics"></emph.end> (Archimedis, <lb></lb><emph type="italics"></emph>De his quae vehuntur in aqua,<emph.end type="italics"></emph.end> Rononiae 1565, fol. </s>

<s>7 et 11). Non vediamo <lb></lb>poi come possa eludere la forza di questi argomenti Carlo Thurot, il quale <lb></lb>supponeva che si fosse il Tartaglia fatto tradurre per suo servigio i libri <lb></lb>idrostatici di Archimede da qualcuno, quanto dotto della lingua greca, altret­<lb></lb>tanto ignaro della Matematica (<emph type="italics"></emph>Revue archeol.,<emph.end type="italics"></emph.end> 1868, 69). </s></p><p type="main">

<s>Nelle collezioni archimedee, che via via si completarono, con l&#039;aggiunta <lb></lb>delle Opere geometriche in greco, o in latino col testo a fronte, i soli due <lb></lb>libri <emph type="italics"></emph>De insidentibus aquae<emph.end type="italics"></emph.end> si rimanevano scritti in una lingua, che si può <lb></lb>dire straniera all&#039;Autore, e fu primo tra gli editori David Rivault, che osasse <lb></lb>di restituirla alle imitate forme del dialetto dorico. </s>

<s>Fu lo stesso Rivault anche <lb></lb>il primo a movere questioni intorno al titolo, che, per relazion di Strabone, <lb></lb>era <foreign lang="grc">ΡΕΠΙ ΤΩΝ ΟΧΟΥΜΕΝΩΝ</foreign>, ma Pappo, soggiunge l&#039;editor francese sulla fine <lb></lb>del suo proemio, per togliere ogni ambiguità, e per dichiarar sopra che cosa <lb></lb>particolarmente farebbesi l&#039;insidenza, v&#039;aggiunse <foreign lang="grc">υφ&#039;υδατος. </foreign></s>

<s>Io poi, conclude <lb></lb>il proemiatore, volentieri starei con Pappo, se non temessi di far contro allo <lb></lb>stesso Archimede, che non fece motto mai particolarmente dell&#039;acqua, ma <lb></lb>sempre usò la parola <emph type="italics"></emph>umido:<emph.end type="italics"></emph.end> onde, a rendere il titolo più universale, e più <lb></lb>conforme con l&#039;intenzion dell&#039;Autore, direi che si dovesse piuttosto aggiun­<lb></lb>gere <foreign lang="grc">εφ&#039;υγρων. </foreign></s></p><p type="main">

<s>La questione, che par di semplici parole, è, come vedremo, di gran <lb></lb>conseguenza, per le strette relazioni, che le parole stesse hanno con le cose. </s>

<s><lb></lb>L&#039;aggiunta della parola <emph type="italics"></emph>acqua,<emph.end type="italics"></emph.end> per denotare il subietto del galleggiante o <lb></lb>l&#039;insidenza, fu fatta dal traduttore latino, forse prima che da Pappo, il quale <lb></lb>non sembra a noi che avesse l&#039;intenzione, attribuitagli dal Rivault, di defi­<lb></lb>nir cioè il titolo dell&#039;Archimede, essendo manifesto ch&#039;egli intende piuttosto <lb></lb>di dichiarare ai lettori il suo proprio discorso. </s>

<s>Nel proemio infatti all&#039;ottavo <lb></lb>libro delle <emph type="italics"></emph>Matematiche collezioni<emph.end type="italics"></emph.end> annovera l&#039;Autore i vari inventori delle <lb></lb>macchine, e il vario modo d&#039;esercitarle: “ alii quidem per spiritus, ut Hero <lb></lb><foreign lang="grc">πνευματιχοις</foreign>, alii per nervos et funes, ut Hero ad <foreign lang="grc"><gap></gap>ομα οις χαι ξ γιοις</foreign>, alii vero <lb></lb>per ea quae in aqua vehuntur, ut Archimedes <foreign lang="grc">οχονμενοις. </foreign></s>

<s>” (Bononiae 1660, <pb xlink:href="020/01/3055.jpg" pagenum="16"></pb>pag. </s>

<s>448): onde s&#039;intende come al Commandino stesso, che così traduceva, <lb></lb>sovvenisse di dare il titolo, ai due libri del Siracusano, <emph type="italics"></emph>De his quae vehun­<lb></lb>tur in aqua.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>È notabile a questo proposito che il Nardi riprendesse esso Comman­<lb></lb>dino, per aver seguitato così autorevoli esempi, invece di correggere il titolo, <lb></lb>posto in fronte alla stessa antichissima versione latina. </s>

<s>“ La traduzione di <lb></lb>Archimede <emph type="italics"></emph>Delle cose che stanno nell&#039;umido<emph.end type="italics"></emph.end> mentisce il titolo, perchè dice <lb></lb><emph type="italics"></emph>nell&#039;acqua,<emph.end type="italics"></emph.end> e non so perchè il Commandino non correggessela. </s>

<s>Non si parla <lb></lb>dell&#039;acqua in detto libro, ne è vero che l&#039;acqua sia sinceramente umida, <lb></lb>onde molti, non attendendo lo scopo di Archimede, hanno preteso che egli <lb></lb>abbia dimostrato, o voluto dimostrare, che la superficie dell&#039;acqua sia per­<lb></lb>fettamente sferica, il che non è vero. </s>

<s>L&#039;Autore semplicemente suppone tro­<lb></lb>varsi l&#039;umido in natura, cioè una sostanza grave e scontinuata, o senza vi­<lb></lb>scosità di parti. </s>

<s>Nè sapere gl&#039;importa se tale squisitamente sia l&#039;acqua, o <lb></lb>altro liquore, od anche il vapore o l&#039;etere: nemmeno saper gl&#039;importa se <lb></lb>tal qualità di umido si trovi sincera o rimescolata, onde per le mescolate <lb></lb>ragioni della viscosità si alterino gli effetti, bastandogli che sia in atto natu­<lb></lb>ralmente, e che con l&#039;intelletto si separi dalla mistione ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. XX, pag. </s>

<s>846). </s></p><p type="main">

<s>Avrebbe potuto il Commandino rispondere che non corresse il titolo, per <lb></lb>la ragione che non l&#039;aveva prima di lui corretto il Tartaglia, il quale osser­<lb></lb>vava che, verificandosi le proposizioni archimedee per ogni qualità di umido, <lb></lb>si poteva questo universalmente significare col nome di acqua, <emph type="italics"></emph>essendo l&#039;acqua <lb></lb>la principale di tutte le cose umide<emph.end type="italics"></emph.end> (Ragionam. </s>

<s>I cit., pag. </s>

<s>6). Ma il Nardi, <lb></lb>nell&#039;accennare a que&#039;molti, che non avevano inteso Archimede, aveva piu <lb></lb>ragione che di riprendere il Commandino, benchė il titolo non corretto da <lb></lb>lui avesse dato motivo di riguardar l&#039;acqua come un umido astratto, e di <lb></lb>negarle perciò una delle più importanti sue proprietà naturali, qual&#039;è d&#039;es­<lb></lb>sere tegnente nelle particelle componenti, o viscosa. </s>

<s>Vedremo di ciò notabili <lb></lb>fatti nel corso della nostra Storia, ma per ora è da ritornare al titolo im­<lb></lb>presso, o da imprimersi a&#039;due libri idrostatici del Siracusano, concludendo <lb></lb>che il riferitoci da Strabone dev&#039;esser propriamente quello scritto in fronte <lb></lb>al codice originale. </s>

<s>Supponiamo che qualche nostro scrittore intitolasse un <lb></lb>suo trattato <emph type="italics"></emph>Delle galleggianti.<emph.end type="italics"></emph.end> Gli si potrebbe domandare: galleggianti in <lb></lb>che? </s>

<s>nell&#039;acqua, nel mercurio, o piuttosto nella cera, o nella pece liquefatta? </s>

<s><lb></lb>Ma ei risponderebbe: sopra nessuna di queste cose in particolare; io intendo <lb></lb>di trattar del galleggiamento dei corpi in generale. </s>

<s>Ora, essendo precisa­<lb></lb>mente questa l&#039;intenzione di Archimede, è manifesto quanto fosse bene ap­<lb></lb>propriato a significarla il titolo assoluto di <foreign lang="grc">ΗΕΠΙ ΟΧΟΥΜΕΝΩΝ</foreign>, purchè questa <lb></lb>voce avesse nel comune uso, oltre al general significato d&#039;<emph type="italics"></emph>insidente,<emph.end type="italics"></emph.end> anche <lb></lb>quello, che particolarmento si dà da noi al nome di <emph type="italics"></emph>galleggiante.<emph.end type="italics"></emph.end> I latini <lb></lb>non avevano forse una parola, che rispondesse a quella di Archimede come <lb></lb>la nostra, e traducendola nel general significato che ha la frase <emph type="italics"></emph>De insiden­<lb></lb>tibus,<emph.end type="italics"></emph.end> o <emph type="italics"></emph>De his quae vehuntur,<emph.end type="italics"></emph.end> furono costretti a dichiarare che l&#039;insidenza <pb xlink:href="020/01/3056.jpg" pagenum="17"></pb>o il sostentamento doveva intendersi particolarmente su un liquido, a rappre­<lb></lb>sentare il quale scelsero l&#039;acqua, a quel modo che i nostri Autori intitolano <lb></lb>i loro libri <emph type="italics"></emph>Del moto delle acque,<emph.end type="italics"></emph.end> benchè di qualunque altro liquido si ve­<lb></lb>rifichi quel che attendono a dimostrare. </s>

<s>Dunque è <foreign lang="grc">ΗΕΠΙ ΟΧΟΥΜΕΝΩΝ</foreign> il vero <lb></lb>titolo dell&#039;Opera di Archimede, che per noi si traduce, con mirabile fedeltà, <lb></lb>in quello <emph type="italics"></emph>Delle galleggianti:<emph.end type="italics"></emph.end> e tanto bastando, per quel che riguarda la que­<lb></lb>stione delle parole, è tempo oramai di passare a dir delle cose. </s></p><p type="main">

<s>È diviso il trattato, come s&#039;è accennato più volte, e come tutti sanno, <lb></lb>in due libri, de&#039;quali intanto esamineremo il primo, che procede con una <lb></lb>semplicità e facilità, veramente maravigliose in così sottile e delicato argo­<lb></lb>mento. </s>

<s>Una tale semplicità poi del processo, e una tale facilità della dimo­<lb></lb>strazione, non da altro dipendono che dall&#039;aver saputo Archimede ridurre il <lb></lb>modo di pesare i corpi nell&#039;acqua a quello ordinario di pesare i solidi nel­<lb></lb>l&#039;aria, per mezzo della Bilancia. </s>

<s>E come avviene in questo strumento che il <lb></lb>peso, posto in un de&#039;bacini, si dice uguale, o più leggero, o più grave del <lb></lb>contrappeso nell&#039;altro, secondo che fa rimanere uguale o sollevare o abbas­<lb></lb>sare il giogo; così un corpo immerso si dice, ed è ugualmente grave, o più <lb></lb>lieve o più ponderoso del liquido stesso, secondo che ne pareggia il livello, <lb></lb>o lo sovrasta, o gli sottostà, seguitando a precipitare infino al fondo del vaso. </s>

<s><lb></lb>La somiglianza però tra i due modi è solamente evidente rispetto a ciò, che <lb></lb>anche i liquidi son come i solidi gravi, e tendono perciò tutti ugualmente <lb></lb>al comun centro terrestre. </s>

<s>Ma non è chiaro in che si corrispondano i due <lb></lb>strumenti, dove cioè sia nell&#039;umido l&#039;ipomoclio, e cos&#039;è che rappresenta in <lb></lb>esso, e fa l&#039;ufficio del giogo, e de&#039;bacini della Bilancia, come quando si pe­<lb></lb>sano i corpi nell&#039;aria. </s>

<s>In dichiarar dunque tuttociò consiste la dottrina di <lb></lb>questo libro, che si compendia nella prima supposizione. </s>

<s>In essa infatti si <lb></lb>dice che le parti componenti ogni liquido son per loro natura continue, ed <lb></lb>equigiacenti, ossia si dispongono in superficie orizzontali concentriche, in cia­<lb></lb>scuna delle quali si può mettere il giogo della Bilancia. </s>

<s>Il qual giogo liquido, <lb></lb>se sia o più o meno premuto da una parte che dall&#039;altra, necessariamente <lb></lb>s&#039;abbassa o si alza. </s>

<s>E perchè anche il liquido è grave, o egli naturalmente <lb></lb>discenda o sia premuto da qualche forza straniera, le discese e le pressioni <lb></lb>non hanno in ogai modo altra direzione diversa dalla linea perpendicolare. <lb></lb></s>

<s>“ Ponatur humidi cam esse naturam ut, partibus ipsius aequaliter iacenti­<lb></lb>bus et continuatis, inter sese minus pressa a magis pressa expellatur. </s>

<s>Una­<lb></lb>quaeque auteni pars eius premitur humido supra ipsam existente ad per­<lb></lb>pendiculum, si humidum sit descendens in aliquo, aut ab alio aliquo pres­<lb></lb>sum ” (Archimedis, Opera, Parisiis 1615, pag. </s>

<s>491). </s></p><p type="main">

<s>Sembrerebbe che la desiderata Bilancia liquida si dovesse spontanea­<lb></lb>mente offerire alle speculazioni di Archimede nel sifone di braccia uguali. </s>

<s><lb></lb>In esso infatti il liquido omogeneo si livella, o sottostà o sovrastà, se ciò che <lb></lb>vi s&#039;è infuso è più grave, o più leggero da una parte che dall&#039;altra, come <lb></lb>se per esempio si fosse riversato mereurio o olio sull&#039;acqua. </s>

<s>Nonostante Ar­<lb></lb>chimede scelse una via più semplice, che consiste nel ridurre all&#039;equilibrio <pb xlink:href="020/01/3057.jpg" pagenum="18"></pb>le braccia uguali della Bilancia, supponendo il vaso di figura regolare, e <lb></lb>l&#039;umor contenutovi diviso in due parti uguali da un piano, che l&#039;attraversi <lb></lb>nel mezzo. </s>

<s>La detta regolarità si sarebbe potuta ottenere formando un vaso <lb></lb><figure id="id.020.01.3057.1.jpg" xlink:href="020/01/3057/1.jpg"></figure></s></p><p type="caption">

<s>Figura 1.<lb></lb>parallelepipedo, orizzontalmente posato con la sua base, <lb></lb>come si rappresenta nella figura 1, nella quale, essendo <lb></lb>CD il piano, che divide nel mezzo il liquido contenuto <lb></lb>nel vaso AB, con le pareti AE, FB verticali; in qua­<lb></lb>lunque sezione liquida orizzontale, come in GH, può <lb></lb>stabilirsi il giogo immaginario della Bilancia, col soste­<lb></lb>gno in I, intorno al quale sta in equilibrio, perchè si <lb></lb>suppone che il peso AI da una parte sia uguale al peso CH dall&#039;altra. </s></p><p type="main">

<s>Ma è notabile che quell&#039;Archimede, il quale non badò tanto in suppor <lb></lb>parallele le direzioni dei pesi attaccati alle braccia della Bilancia solida, si <lb></lb>mostri ora nella Bilancia liquida così scrupoloso, in descriver sempre quelle <lb></lb>medesime direzioni come convergenti, cosicchè il vaso, in ch&#039;egli intende <lb></lb>contenersi l&#039;umido, non è composto sulla regola di un parallelepipedo, ma <lb></lb>di un cono o di una piramide, che, avendo la base sulla superficie della <lb></lb><figure id="id.020.01.3057.2.jpg" xlink:href="020/01/3057/2.jpg"></figure></s></p><p type="caption">

<s>Figura 2.<lb></lb>Terra, scenda precisamente infino ad appuntarsi nel cen­<lb></lb>tro B della sfera, qui disegnata nella figura 2. In questa <lb></lb>la superficie AOC non è piana, ma convessa, e le braccia <lb></lb>DF, FE, benchè uguali, perchè la OB divide nel mezzo <lb></lb>la sezione ABC del vaso; non son però in linea retta, <lb></lb>ma curvate in archi di cerchio. </s></p><p type="main">

<s>Qualunque si fosse l&#039;intenzion di Archimede, che in dimostrare i suoi <lb></lb>teoremi volle sempre eleggere questa teorica posizione, è un fatto che in <lb></lb>realtà non è possibile il considerare, del gran vaso piramidale ABC, altro <lb></lb>che una minima parte, cosicchè la superficie dell&#039;umido, ristretta nella por­<lb></lb>zion tangenziale alla grande sfera terrestre, sia piana; le pareti AB, BC, in <lb></lb>così breve tratto, convergano tanto poco, da potersi avere per parallele; e <lb></lb>l&#039;arco DFE, ridotto a essere quasi infinitesimo, si confonda con la rettitu­<lb></lb>dine della sua propria tangente. </s>

<s>Ond&#039;è che, per maggiore semplicità ed evi­<lb></lb>denza, riferiremo i Teoremi archimedei con le loro proprie ragioni, suppo­<lb></lb>nendo parallelepipedo, come nella prima figura, il vaso; piana la superficie <lb></lb>dell&#039;umido, e rettilineo perciò il giogo della Bilancia. </s>

<s>Le quali cose tutte <lb></lb>presupposte, sarà facile intendere per prima cosa come sia vero che un corpo, <lb></lb><figure id="id.020.01.3057.3.jpg" xlink:href="020/01/3057/3.jpg"></figure></s></p><p type="caption">

<s>Figura 3.<lb></lb>d&#039;eguale peso specifico a quello di un liquido, si <lb></lb>sommerga in esso così, che nulla ne resti sopra, <lb></lb>ma senza andare più al fondo. </s></p><p type="main">

<s>Sia un quadrato solido S (fig. </s>

<s>3) lasciato sulla <lb></lb>superficie del detto liquido, di cui si suppone essere <lb></lb>esso solido ugualmente grave in specie: è certo che <lb></lb>vi si sommergerà tutto, come si rappresenta nella <lb></lb>indicata figura, e quivi permarrà in equilibrio, perchè, preso un quadrato <lb></lb>liquido L, uguale e a ugual distanza dal punto I della bilancia CD, pesano <pb xlink:href="020/01/3058.jpg" pagenum="19"></pb>ugualmente le due grandezze sulle braccia di lei. </s>

<s>A ciò si riduce insomma <lb></lb>la ragion del Teorema, che vien terzo nell&#039;ordinamento del libro, perchè suc­<lb></lb>cede a due lemmi di Geometria, ma che veramente è il primo fra gl&#039;idrosta­<lb></lb>tici, da Archimede stesso così proposto: “ Solidarum magnitudinum, quae, <lb></lb>aequalem molem habentes, aeque graves sunt atque humidum; in humidum <lb></lb>demissae mergentur, ita ut ex humidi superficie nihil extet, non tamen <lb></lb>adhuc deorsum ferentur ” (Archim., Opera, Parisiis 1615, pag. </s>

<s>493). </s></p><p type="main">

<s>Che se S, stante la medesima figura, è più leggero di L, è patente che <lb></lb>questo preponderando s&#039;abbasserà, e farà sollevar quello in modo, che ne <lb></lb>rimanga qualche parte fuori dell&#039;umido, secondo che, fra&#039;teoremi idrostatici <lb></lb>di Archimede, si legge scritto così in secondo luogo: “ Solidarum magnitu­<lb></lb>dinum quaecumque levior humido fuerit, demissa in humidum, non demer­<lb></lb>getur tota, sed aliqua pars ipsius ex humidi superficie extabit ” (ibid., <lb></lb>pag. </s>

<s>496). </s></p><p type="main">

<s>Suppongasi il proposto solido esser sollevato sulla superficie dell&#039;umido <lb></lb>infino in EF (fig. </s>

<s>4), e che lì giunto rimangasi in equilibrio. </s>

<s>Essendo che <lb></lb><figure id="id.020.01.3058.1.jpg" xlink:href="020/01/3058/1.jpg"></figure></s></p><p type="caption">

<s>Figura 4.<lb></lb>pur in equilibrio si rimarrebbe la bilancia, <lb></lb>quando, estrattone il solido, si riempisse del­<lb></lb>l&#039;umido circostante la pozzetta lasciata da lui; <lb></lb>è dunque vero quel che nel suo terzo teorema <lb></lb>idrostatico propone lo stesso Archimede: “ So­<lb></lb>lidarum magnitudinum quaecumque levior hu­<lb></lb>mido fuerit, demissa in humidum, usque eo demergetur, ut tanta moles <lb></lb>humidi, quanta est partis demersae, eamdem quam tota magnitudo gravita­<lb></lb>tem habeat ” (ibid.). </s></p><p type="main">

<s>La forza poi dell&#039;impeto di L, nella terza figura, per far sollevare S, è <lb></lb>manifesto esser tanta, quant&#039;è l&#039;eccesso della gravità, che ha quella gran­<lb></lb>dezza sopra questa, secondo che Archimede stesso pronunziò in questa forma: <lb></lb>“ Solidae magnitudines humido leviores, in humidum impulsae, sursum fe­<lb></lb>runtur tanta vi, quanto humidum, molem hadens magnitudini aequalem, gra­<lb></lb>vius est ipsa magnitudine ” (ibid., pag. </s>

<s>497). </s></p><p type="main">

<s>Sia all&#039;ultimo S più grave di L, nella figura 3a. </s>

<s>Si immagini essere S <lb></lb>trasformato in umido così, che si debba aggiungere a lui il peso P, per egua­<lb></lb>gliare il peso suo primo. </s>

<s>È facile vedere come S e L equilibrandosi, la bi­<lb></lb>lancia prepondererà in forza del solo peso P, che è la differenza tra il peso <lb></lb>del solido e quello di un ugual mole dell&#039;umido, in cui egli è sommerso: <lb></lb>d&#039;onde riman provata la verità dell&#039;ultima proposizione idrostatica di Ar­<lb></lb>chimede, che dice: “ Solidae magnitudines humido graviores, demissae in <lb></lb>humidum, ferentur deorsum donec descendant, et erunt in humido tanto le­<lb></lb>viores, quanta est gravitas humidi, molem habens solidae magnitudini aequa­<lb></lb>lem ” (ibid., pag. </s>

<s>498). </s></p><p type="main">

<s>S&#039;è detto che questa è l&#039;ultima proposizione idrostatica, dimostrata da <lb></lb>Archimede nel suo libro primo, benchè, nella Collezione romana e in tutte <lb></lb>le altre edizioni, che si fecero poi su quell&#039;esempio, se ne aggiunga un&#039;al-<pb xlink:href="020/01/3059.jpg" pagenum="20"></pb>tra, che è l&#039;ottava segnata nell&#039;ordinamento primo di quello stesso libro. </s>

<s>Ma <lb></lb>chi ben attende si persuade con facilità che la detta proposizione appartiene <lb></lb>all&#039;argomento, dall&#039;Autore stesso trattato nel libro secondo, e che ella anzi <lb></lb>contiene in sè il principio, da cui si svolgono, e a cui s&#039;informa il processo <lb></lb>dimostrativo di tutte le altre. </s>

<s>La supposizione, premessa qui sul fine, piut­<lb></lb>tostochè in principio del libro, insieme e subito dopo la prima; avrebbe do­<lb></lb>vuto far accorti gli editori e i commentatori che si preparava già fin di li <lb></lb>la trattazione di un argomento diverso, ma nessuno ebbe questa felice rive­<lb></lb>lazione all&#039;intelletto, per cui le dottrine archimedee nel secolo XVIII si ri­<lb></lb>manevano tuttavia non comprese. </s>

<s>A chi poi sembrasse questa asserzion teme­<lb></lb>raria sodisfaranno forse le considerazioni qui appresso. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>All&#039;uno e all&#039;altro libro dunque del trattato delle Galleggianti è premesso <lb></lb>un principio proprio e distinto, e a riconoscer l&#039;importanza di ciascuno par <lb></lb>che nocesse non poco il titolo di <emph type="italics"></emph>supposizione.<emph.end type="italics"></emph.end> Tale è veramente quella <lb></lb>prima, nella quale si suppone un fatto, e si ricercano tali proprictà fisiche <lb></lb>dell&#039;umido, concesse le quali ne conseguono necessariamente i teoremi idro­<lb></lb>statici, di cui s&#039;è discorso. </s></p><p type="main">

<s>Il principio però premesso al secondo libro ha indole e significazione <lb></lb>molto diversa da quella, che gli si suol dare comunemente, e che, primo <lb></lb>fra&#039;commentatori di Archimede, gli fu data dal Tartaglia: di principio cioè <lb></lb>per sè noto e indimostrabile, come son quelli “ che alcuni gli dicono pe­<lb></lb>titioni, e gli altri chiamano dignità, ovver supposizioni ” (Ragionamento <lb></lb>primo cit., pag. </s>

<s>4). Chi si persuaderebbe infatti di ricever tra i principii di <lb></lb>senso comune, o fra gli assiomi, questo così formulato, secondo la trascri­<lb></lb>zione dello stesso Tartaglia? </s>

<s>“ Supponatur corum, quae in humido sursum <lb></lb>feruntur, unumquodque sursum ferri secundum perpendicularem, quae per <lb></lb>centrum gravitatis ipsorum producitur ” (ivi, pag. </s>

<s>18). </s></p><p type="main">

<s>Vero è bene che nemmen l&#039;Autore di questo primo Ragionamento idro­<lb></lb>statico sembra che se ne persuadesse, giacchè egli accenna al suo interlocu­<lb></lb>tore, compar Riccardo, quel che Archimede stesso aveva dimostrato nell&#039;altro <lb></lb>suo libro <emph type="italics"></emph>De centro gravitatis.<emph.end type="italics"></emph.end> Trasparisce di qui intanto che il Tartaglia <lb></lb>non dà al premesso principio valor proprio di assioma, ma di verità, che, <lb></lb>sebbene non sia per sè nota, pur supponesi tale, perchè fu altrove già dimo­<lb></lb>strata. </s>

<s>Nell&#039;indicato libro però non avrebbe trovato messer Riccardo da sodi­<lb></lb>sfare la sua curiosità, se non che circa al modo di determinare il centro gra­<lb></lb>vitativo ne&#039;piani, o circoscritti da linee rette, o da curve paraboliche, men­<lb></lb>tre nella pronunziata supposizione apparisce definito esso centro come il punto <lb></lb>dell&#039;applicazion di una forza unica, resultante da tutte insieme quelle che <lb></lb>risospingono in su un solido, tutto sommerso in un umido specificamente più <pb xlink:href="020/01/3060.jpg" pagenum="21"></pb>grave. </s>

<s>È certo insomma che Archimede suppone avere i suoi Lettori la no­<lb></lb>tizia di quel che i moderni chiamano <emph type="italics"></emph>Centro delle pressioni,<emph.end type="italics"></emph.end> che è giusto <lb></lb>il punto, a cui s&#039;applica la resultante di tutte le forze parallele, che nascono <lb></lb>dal riflettersi in su le pressioni idrostatiche. </s>

<s>Or trattandosi di una scienza, <lb></lb>la quale non refulse chiara agli intelletti, se non che a mezzo il secolo XVIII, <lb></lb>come apparirà dalla Storia, s&#039;intende di quanta curiosità, e di quanta im­<lb></lb>portanza sia il saper come Archimede a&#039;suoi tempi la supponesse già nota. </s></p><p type="main">

<s>Egli deve senza dubbio averla già dimostrata, e perchè ne tace qui nel <lb></lb><emph type="italics"></emph>De insidentibus aquae,<emph.end type="italics"></emph.end> e negli stessi libri <emph type="italics"></emph>De aequiponderantibus<emph.end type="italics"></emph.end> si sup­<lb></lb>pongono le verità de&#039;medesimi o di simili altri pronunziati; si può doman­<lb></lb>dare se la dimostrazione fu fatta in un libro, che sia andato smarrito, o che <lb></lb>Archimede avesse intenzione di scrivere, ma che poi la morte o altro caso <lb></lb>glielo impedisse. </s>

<s>Di questo vezzo, del supporre vera cioè una proposizione <lb></lb>da dimostrarsi, ne abbiamo nel nostro Autore, in altro proposito, notabili <lb></lb>esempi. </s>

<s>Nessuno, che da noi si sappia, potrebbe decidere con certezza quale <lb></lb>delle due opere, intorno agli Equiponderanti e alla Quadratura della para­<lb></lb>bola, fosse scritta o messa in ordine per la prima. </s>

<s>Se fu tale quella degli <lb></lb>Equiponderanti, nel Problema premesso al secondo libro si suppone essere <lb></lb>il piano parabolico sesquiterzo al triangolo inscritto, che è l&#039;ultima conclu­<lb></lb>sione, a cui si giunge dopo quella lunga serie di proposizioni, dimostrate nel <lb></lb>libro della Quadratura della parabola. </s>

<s>Che se altri volesse dire invece aver <lb></lb>la scrittura di questo preceduto a quella del libro degli Equiponderanti, si <lb></lb>trova supposto là come noto il centro di gravità del triangolo e del trape­<lb></lb>zio, che qua sarebbesi dimostrato. </s></p><p type="main">

<s>Ma lasciando per ora addietro la questione se Archimede pronunziasse <lb></lb>la verità fondamentale, premessa al suo secondo libro delle Galleggianti, come <lb></lb>cosa dimostrata o da dimostrarsi; l&#039;importante sta nell&#039;investigare da quali <lb></lb>principii movesse, e per quali mezzi fosse condotta la desiderata dimostra­<lb></lb>zione. </s>

<s>Rispetto a che giova principalmente osservare che la detta premessa <lb></lb>è quasi il corollario di un&#039;altra più generale, concernente le cadute naturali <lb></lb>dirette secondo la perpendicolare, che passa per il centro di gravità del ca­<lb></lb>dente. </s>

<s>Una tal direzione unica delle varie parti, che compongono il grave, si <lb></lb>può ammettere come cosa di fatto, da cui argomentar che gl&#039;impulsi gravi­<lb></lb>tativi distribuiti per le sparse particelle della materia si raccolgano in qualche <lb></lb>punto di quella stessa retta perpendicolare. </s>

<s>E perchè in un&#039;altra simile per­<lb></lb>pendicolare si raccoglierebbe quella medesima somma d&#039;impulsi, variando al <lb></lb>corpo la posizione; sarebbe lecito concludere che dalla intersecazion delle due <lb></lb>linee viene indicato il punto, intorno a cui gravita tutta intera la mole. </s>

<s>L&#039;in­<lb></lb>venzione però del centro di gravità fatta in questo modo non era punto conforme <lb></lb>col genio di Archimede, che dalle nuvolose questioni della Fisica risale sempre <lb></lb>alle serene alture della Geometria. </s>

<s>E della Geometria pur valendosi nella <lb></lb>proposta inquisizione, non sembra aver potuto tenere altra via, da quella dei <lb></lb>Matematici moderni, con la differenza forse di qualche più comodo veicolo, e, <lb></lb>per essere stati battuti per tanti secoli, con la facilità de&#039;più appianati sentieri. </s></p><pb xlink:href="020/01/3061.jpg" pagenum="22"></pb><p type="main">

<s>I moderni dunque si sa che riducono la questione a trovare la resul­<lb></lb>tante, e il centro di più forze parallele, in un modo che può ridirsi così in <lb></lb>poche parole: Siano alla verga inflessibile AB (fig. </s>

<s>5) applicate le due forze <lb></lb><figure id="id.020.01.3061.1.jpg" xlink:href="020/01/3061/1.jpg"></figure></s></p><p type="caption">

<s>Figura 5.<lb></lb>parallele AP, <expan abbr="Bq.">Bque</expan> Aggiuntene due altre AM, <lb></lb>BN, nella stessa direzion della verga uguali ed <lb></lb>opposte, si possono, invece delle quattro forze, <lb></lb>considerare le lore resultanti AC, BD, o, pro­<lb></lb>lungatene le direzioni concorrenti in S, le loro <lb></lb>uguali SE, SF, che si possono decomporre <lb></lb>nelle SI, SK, e nelle SG, SH, queste alla linea <lb></lb>AB perpendicolari, e quelle parallele. </s>

<s>Protratta <lb></lb>poi la SG, e dal punto O, in cui ella incontra <lb></lb>la verga, presa la OL=SG+SH, è manifesto <lb></lb>che, intesa questa applicata in O, è la resul­<lb></lb>tante cercata delle due forze parallele, verso <lb></lb>esse stesse parallelamente diretta, e uguale alla <lb></lb>loro somma. </s>

<s>E perchè EG:AO=SG:SO, e HF:OB=SH:SO, d&#039;onde, <lb></lb>essendo EG, HF uguali, consegue AO:OB=SH:SG=BQ:AP; è ma­<lb></lb>nifesto che il punto O, a cui viene applicata la resultante, divide la verga in <lb></lb>due parti, che sono alle due forze componenti reciprocamente proporzionali. </s>

<s><lb></lb>Anche più manifestamente poi ne consegue che, se le due forze componenti <lb></lb>sono uguali, il punto dell&#039;applicazione della loro resultante divide la verga <lb></lb>AB nel mezzo. </s></p><p type="main">

<s>S&#039;immagini ora che A, B (fig. </s>

<s>6) sian due corpi congiunti insieme, o <lb></lb>due distinte porzioni di un medesimo corpo, e con esse altre due porzioni <lb></lb><figure id="id.020.01.3061.2.jpg" xlink:href="020/01/3061/2.jpg"></figure></s></p><p type="caption">

<s>Figura 6.<lb></lb>C, D, o quante più se ne voglia, sol­<lb></lb>lecitate ciascuna dai propri impulsi <lb></lb>gravitativi, rappresentati dalle verti­<lb></lb>cali AP, BQ, CR, DS. </s>

<s>Congiunto A <lb></lb>con B, e divisa la linea di congiun­<lb></lb>zione in O, cosicchè OB ad AO stia <lb></lb>reciprocamente come AP a <expan abbr="Bq;">Bque</expan> nel­<lb></lb>l&#039;unica V s&#039;assommano le potenze di <lb></lb>P e di Q, come nell&#039;unica X s&#039;as­<lb></lb>sommano le due R, V, fatta in M, <lb></lb>della linea CO, secondo le medesime contrarietà, la divi­<lb></lb>sione: e s&#039;assommano all&#039;ultimo nell&#039;unica Z le quattro <lb></lb>forze componenti, divisa la MD in N come dianzi. </s></p><p type="main">

<s>Simile essendo il processo del ragionamento, quando <lb></lb>le porzioni, in cui s&#039;intenda esser diviso il corpo, fossero <lb></lb>ridotte all&#039;infinito numero delle minime particelle di lui <lb></lb>componenti; è manifesto, trattenendosi nella semplicità <lb></lb>del proposto esempio, che N è il punto, intorno a cui si raccolgono i pesi, <lb></lb>ossia è il centro di gravità, e che il tutto prende una direzione unica se-<pb xlink:href="020/01/3062.jpg" pagenum="23"></pb>condo NZ. </s>

<s>Di qui perciò torna geometricamente dimostrato perchè i moti in <lb></lb>giù son diretti lungo la linea perpendicolare, che passa per il centro di gra­<lb></lb>vità del cadente, E perchè, ne&#039;moti in su, non è da fare altra variazione al <lb></lb>discorso, che di considerare le forze P, Q, R e tutte le altre, quante ce ne <lb></lb>fossero, in verso opposto; ecco da quali principii deriva la scienza, che si <lb></lb>presuppone da Archimede nel suo secondo libro delle Galleggianti: scienza, <lb></lb>che si riduce dunque a saper comporre in una qualunque numero, o finito <lb></lb>o infinito di forze parallele, e che, sebbene sia resa così nelle sue conclu­<lb></lb>sioni evidente, potrebbe fare alcun dubitare se vi giunse propriamente il suo <lb></lb>Autore per le vie da noi disegnate: per l&#039;una cioè del parallelogrammo delle <lb></lb>forze, e per l&#039;altra della risoluzion del continuo nelle minime parti indivi­<lb></lb>sibili. </s>

<s>Abbiamo giusta ragione di temer di que&#039;dubbi, ripensando come pre­<lb></lb>valga anche oggidì in molti l&#039;idea, che il parallelogrammo sia d&#039;invenzione <lb></lb>recente, e leggendo in alcuni commentatori moderni che Archimede costan­<lb></lb>temente rifuggì da ogni speculazione, che sapesse d&#039;infinitesimale. </s>

<s>Quanto <lb></lb>al primo, il libro delle Spirali, e le precedenti invenzioni di simili altre curve <lb></lb>meccaniche, persuadono essere antichissima la notizia de&#039;moti composti, di <lb></lb>che s&#039;addussero, nella passata Storia della Meccanica, tali documenti, da es­<lb></lb>sere oramai soverchio spendervi attorno altri discorsi. </s>

<s>Di maggiore curiosità <lb></lb>e importanza è il saper se sia vero, come si dice, che Archimede aborrisse <lb></lb>dall&#039;ammettere nelle quantità continue la possibile divisione all&#039;infinito. </s>

<s>Per <lb></lb>verità sembrerebbe invece che dovess&#039;essere un tal genere di speculazioni <lb></lb>propriamente conforme col suo genio, e non mancano fatti, che da più parti <lb></lb>sovvengono a confermarne il giudizio. </s></p><p type="main">

<s>Le tradizioni del nuovo metodo più immediate vennero al Cavalieri dal <lb></lb>Kepler, e il Guldin argutamente notava che la quadratura Kepleriana del <lb></lb>circolo si concludeva per via degli indivisibili. </s>

<s>Ma perchè esso Kepler pro­<lb></lb>testava di non aver fatto altro che commentare una proposizion di Archimede, <lb></lb>rimasta alquanto oscura, e variamente interpetrata; egli insomma veniva ad <lb></lb>attribuire allo stesso Archimede l&#039;invenzione e l&#039;uso del metodo cavalierano. </s></p><p type="main">

<s>Il Matematico di Praga ne deve essere stato inconsapevole, ma è un fatto <lb></lb>che l&#039;avevano prevenuto i Matematici del secolo precedente nell&#039;interpetrare, <lb></lb>con la dottrina degli infinitamente piccoli, la recondita ciclometria del Sira­<lb></lb>cusano. </s>

<s>“ Il cerchio, scriveva Leonardo da Vinci, è una figura parallela, per­<lb></lb>chè tutte le linee rette prodotte dal centro alla circonferenza sono eguali, e <lb></lb>caggiono in nella lor linea circonferenziale infra angoli eguali eretti sferici. </s>

<s><lb></lb>Il cerchio è simile a un parallelo rettangolo, fatto del quarto del suo diame­<lb></lb><figure id="id.020.01.3062.1.jpg" xlink:href="020/01/3062/1.jpg"></figure></s></p><p type="caption">

<s>Figura 7.<lb></lb>tro, e di tutta la circum­<lb></lb>ferentia sua, o vo&#039;dir e <lb></lb>della metà del diametro, e <lb></lb>della periferia. </s>

<s>Come se il <lb></lb>cerchio EF (fig. </s>

<s>7) fusse <lb></lb>immaginato essere reso­<lb></lb>luto in quasi infinite pi-<pb xlink:href="020/01/3063.jpg" pagenum="24"></pb>ramidi, le quali poi essendo distese sopra la linea retta, che tocchi la loro <lb></lb>base BD, e tolto la metà dell&#039;altezza, e fatto il parallelo ABCD; sarà con <lb></lb>precisione eguale al circolo EF ” (MSS. K, fol. </s>

<s>80 r.). </s></p><p type="main">

<s>In simile modo quadrava Leonardo il settor circolare ABC (fig. </s>

<s>8) divi­<lb></lb>dendolo in altri settori infinitesimi. </s>

<s>Poi dirizzava l&#039;arco, col farlo movere <lb></lb><figure id="id.020.01.3063.1.jpg" xlink:href="020/01/3063/1.jpg"></figure></s></p><p type="caption">

<s>Figura 8.<lb></lb>sopra la linea retta DE, per <lb></lb>cui veniva esso settore ad <lb></lb>aprirsi, e allargarsi nel ret­<lb></lb>tangolo DF duplicando il suo <lb></lb>proprio spazio, così meccani­<lb></lb>camente riquadrato. </s>

<s>“ E que­<lb></lb>sta, ne concludeva, è la sola <lb></lb>e vera regola da dare la quadratura d&#039;ogni porzion di cerchio, minore del <lb></lb>semicircolo, della quale nulla scientia vale, se non col moto predetto ” (MSS. <lb></lb>E, fol. </s>

<s>25 r.). </s></p><p type="main">

<s>Con la medesima regola, applicandovi cioè il metodo degl&#039;indivisibili, <lb></lb>tacitamente supposto da Archimede, insegnava Leonardo a quadrare la su­<lb></lb>perficie della sfera, come si vede in varie sue Note, e specialmente in quella, <lb></lb>che si legge nel MSS. E, a tergo del foglio 24. Nè di altre simili applica­<lb></lb>zioni manca, in questi preziosi documenti Vinciani della Scienza, l&#039;esempio. </s>

<s><lb></lb>Nella prima faccia del foglio 73 del medesimo manoscritto è formulata que­<lb></lb>sta proposizione: <emph type="italics"></emph>“ Il descenso del grave situato per qualunque obliquità <lb></lb>sempre fia per diritta linea. </s>

<s>”<emph.end type="italics"></emph.end> S&#039;immagina l&#039;Autore di avere la trave AB <lb></lb><figure id="id.020.01.3063.2.jpg" xlink:href="020/01/3063/2.jpg"></figure></s></p><p type="caption">

<s>Figura 9.<lb></lb>(fig. </s>

<s>9) di uniforme figura e peso, e perciò <lb></lb>col centro di gravità nel suo mezzo. </s>

<s>Ora, a pro­<lb></lb>vare che, sebbene si giaccia obliqua, essa trave <lb></lb>caderà nonostante per la rettitudine CD della <lb></lb>sua perpendicolare; divide il cadente in minime <lb></lb>particelle, di uniforme figura e peso, nella <lb></lb>piccolezza delle quali perciò l&#039;obliquità del tutto <lb></lb>sparisce. </s>

<s>E perchè ciascuna delle dette parti­<lb></lb>celle è sollecitata dal proprio impulso gravita­<lb></lb>tivo, rappresentato da altrettante linee perpen­<lb></lb>dicolari uguali, come si vede nella figura dise­<lb></lb>gnata nel citato foglio in margine; ne conclude <lb></lb>Leonardo che la resultante delle parti è la mede­<lb></lb>sima linea perpendicolare CD, applicata al centro di gravità della trave. </s>

<s>“ Pro­<lb></lb>vasi per la settima di questo che dice: Li gravi d&#039;uniforme figura e peso, che <lb></lb>descenderanno per mezzo eguale, saranno d&#039;egual velocità. </s>

<s>Adunque, se il <lb></lb>trave d&#039;uniforme figura e peso sarà diviso in parti eguali, e simili per di­<lb></lb>rezione, sarà di velocità uguale e simile, E quel che fa la parte farà il tutto. </s>

<s>” <lb></lb>Chi, penetrando addentro al significato di queste parole, non vi riconosce <lb></lb>schietto il principio della composizion delle forze parallele, rappresentanti la <lb></lb>velocità della caduta, o il peso delle particelle, in cui è lecito immaginar di-<pb xlink:href="020/01/3064.jpg" pagenum="25"></pb>viso qualunque corpo? </s>

<s>E da che può avere appreso Leonardo una tale scienza, <lb></lb>se non dalla V proposizione archimedea <emph type="italics"></emph>De aequiponderantibus,<emph.end type="italics"></emph.end> la quale, <lb></lb>lasciando immaginar qualunque numero di grandezze, pendenti intorno al <lb></lb>centro di gravità, nella verga che le sostiene; confermava in quella medesima <lb></lb>verità gli studiosi, anche quando fosse a loro piaciuto di ridurre quelle stesse <lb></lb>grandezze a un numero infinito? </s></p><p type="main">

<s>A questo punto i Lettori, a cui non sia passato dalla memoria quel che <lb></lb>da noi stessi fu scritto a pag. </s>

<s>104, 105 del Tomo IV, troveranno da notare <lb></lb>una contradizione, la quale però non è temeraria, avendoci le nuove cose <lb></lb>meglio considerate fatto ritrattare le prime opinioni. </s>

<s>Anche la sentenza ivi <lb></lb>citata dal Torricelli ci parve poi verissima, messa specialmente a riscontro <lb></lb>di altri documenti, che s&#039;addurranno fra poco. </s>

<s>Ma la questione concernente <lb></lb>Leonardo è di tale importanza, da non lasciar l&#039;occasione di ritornarvici <lb></lb>sopra. </s></p><p type="main">

<s>Il Libri notò che <emph type="italics"></emph>le Peintre toscan<emph.end type="italics"></emph.end> era stato il primo a indicare il cen­<lb></lb>tro di gravità della piramide, decomponendola in piani paralleli alla base, <lb></lb>come si rileva dalle figure dimostrative. </s>

<s>Ripetiamo che di qui non si rileva <lb></lb>propriamente altro, se non che la proposizione si voleva concludere dall&#039;in­<lb></lb>tersecarsi gli assi, condotti dagli opposti vertici sopra le respettive basi, a <lb></lb>quel modo che, nella sua XXII <emph type="italics"></emph>De centro gravitatis,<emph.end type="italics"></emph.end> fa il Commandino, la <lb></lb>figura del quale è similissima a quella dello stesso Leonardo. </s>

<s>Questa XXII <lb></lb>però si faceva, come da principal lemma, dipendere dalla XIV fra le prece­<lb></lb>denti, nella quale si dimostrava che il centro di gravità di qualunque solido <lb></lb>piramidale si ritrova necessariamente in qualche punto sull&#039;asse. </s>

<s>La dimo­<lb></lb>strazione, che ne dà di ciò esso Commandino, procede all&#039;assurdo, per le so­<lb></lb>lite vie lunghe e faticose degl&#039;inscritti e dei circoscritti, mentre Leonardo è <lb></lb>da credere se ne spedisse, decomponendo la piramide o il cono in infiniti <lb></lb>piani triangolari o circoli, i centri di ciascun de&#039;quali essendo disposti lungo <lb></lb>l&#039;asse, sull&#039;asse stesso era necessario che cadesse pure il centro di gravità <lb></lb>del tutto. </s>

<s>E perchè le medesime ragioni manifestamente valevano, da qua­<lb></lb>lunque vertice si conducessero i detti assi sopra l&#039;opposta base triangolare; <lb></lb>legittimo era concluderne che dovesse essere il richiesto punto quello della <lb></lb>loro comune intersezione. </s></p><p type="main">

<s>Ecco in qual modo si può dir che il Pittore toscano applicasse alla Ba­<lb></lb>ricentrica stereometrica il metodo degl&#039;indivisibili, ciò che non s&#039;argomenta <lb></lb>mica dalle figure, ma dal ripensare che dovette esser venuta a Leonardo, <lb></lb>come poi venne al Roberval, l&#039;inspirazione da quel loro profondo meditare <lb></lb>sui libri di Archimede, da cui intesero esser proposti i piani ponderosi, non <lb></lb>come superficie astratte, ma come solidi veri, con le loro altezze infinitesi­<lb></lb>mali. </s>

<s>E giacchè il Libri, anzi tutti gl&#039;interpetri dei Manoscritti vinciani, trat­<lb></lb>tandosi di Matematiche, non possono trascurar le figure, bene spesso signifi­<lb></lb>cative ora del concetto, ora del processo dimostrativo di qualche teorema; a <lb></lb>noi pare di vedere in que&#039;segni, dalla scienza insieme e dall&#039;arte resi cosi <lb></lb>eloquenti, un proposito anche più ardito di quel che si sia annunziato fin qui, <pb xlink:href="020/01/3065.jpg" pagenum="26"></pb>ed è che il Nostro, oltre alla piramide intera, o al cono, instituiva un me­<lb></lb>todo, da ritrovare il centro di gravità ne&#039;loro frusti: metodo, che non è so­<lb></lb>lamente più facile e più elegante, ma anche più diretto e più universale di <lb></lb>quelli stessi usati di poi dal Commandino, dal Valerio e da Galileo. </s>

<s>Dell&#039;esser <lb></lb>diretto n&#039;è prova la derivazione immediata dalla VIII archimedea del primo <lb></lb>libro <emph type="italics"></emph>Degli Equiponderanti,<emph.end type="italics"></emph.end> e dell&#039;essere universale l&#039;estendersi per analo­<lb></lb>gia dal triangolo genitore, che Leonardo chiamò <emph type="italics"></emph>piramide di due lati equi­<lb></lb>distanti,<emph.end type="italics"></emph.end> al cono, da lui stesso detto <emph type="italics"></emph>piramide di lati piramidali.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Nel manoscritto E, a tergo del fol. </s>

<s>X, è una nota che dice: “ Sia con <lb></lb>un taglio diviso il triangolo equidistante alla base in due parti uguali. </s>

<s>Que­<lb></lb>sto è provato nella sesta del 3° <emph type="italics"></emph>De ponderibus. </s>

<s>”<emph.end type="italics"></emph.end> Tale era il titolo che, ad <lb></lb>imitazione del loro più prossimo maestro Giordano Nemorario, si dava ai trat­<lb></lb>tati di Meccanica dagli Autori di que&#039;tempi, e così anche Leonardo, richia­<lb></lb>mandosi a quel suo libro, che sarebbesi potuto compilar delle sue note sparse, <lb></lb>mentalmente se lo rappresentava come già scritto, e lo intitolava <emph type="italics"></emph>De pon­<lb></lb>deribus.<emph.end type="italics"></emph.end> La prova poi, o la soluzion del problema dipendeva dalla proposta <lb></lb><figure id="id.020.01.3065.1.jpg" xlink:href="020/01/3065/1.jpg"></figure></s></p><p type="caption">

<s>Figura 10.<lb></lb>di un problema più generale, che si trova altrove <lb></lb>scritto così in una nota: <emph type="italics"></emph>“ Io voglio saper quante <lb></lb>piramide CED<emph.end type="italics"></emph.end> (fig. </s>

<s>10) <emph type="italics"></emph>entra nella piramide <lb></lb><expan abbr="CVq.">CVque</expan><emph.end type="italics"></emph.end> — Io multiplicherò la linea CV in sè, la <lb></lb>quale avendo la parte EV per sua parte aliquota, <lb></lb>troverai tal piramide grande contenere in sè <lb></lb>tante delle piramidi piccole, quant&#039;è la somma, <lb></lb>che resulta dalle parti, in che è partita la linea <lb></lb>CV, che son simili alla linea CE, come dire la <lb></lb>linea DE eqidistante alla linea <expan abbr="Vq.">Vque</expan> E il lato CE <lb></lb>entra 8 volte nel lato CV. </s>

<s>Dirai dunque: 8 via <lb></lb>8 fa 64, e tanto fia il numero delle piramide <lb></lb>CED, che entrano nella piramide maggiore ” (K, fol. </s>

<s>6 r.). </s></p><p type="main">

<s><emph type="italics"></emph>E questo modo,<emph.end type="italics"></emph.end> soggiunge Leonardo, <emph type="italics"></emph>è regola generale.<emph.end type="italics"></emph.end> Condotto in­<lb></lb>fatti l&#039;asse CO, abbiamo CED:CVQ=CI.EI:CO.VO.E perchè tanto <lb></lb>CI a CO, quanto EI a VO stanno come EC a CV; dunque ECD:CVQ= <lb></lb>EC2:CV2.E prendendo CE per unità di misura, CVQ=FCD.CV2, onde <lb></lb>essendo CV=8, come suppone Leonardo, è manifesto che, de&#039;piccoli trian­<lb></lb>goli isosceli CED, se ne contengono nel maggiore CVQ, 64. Se poi la figura <lb></lb>è un cono, si ha, per l&#039;omologa regola generale ECD:CVQ=EC3:CV3. </s>

<s><lb></lb>Trasponendo e dividendo, EQ:ECD=CV3—EC3:EC3, e per il triangolo <lb></lb>EQ:ECD=CV2—EC2:EC2. </s>

<s>Che se EQ=ECD, sarà per l&#039;una figura <lb></lb>CV=EC.3√2, e per l&#039;altra CV=EC.√2, d&#039;onde vien la regola per <lb></lb>sapere dove debba farsi il taglio, che divida il triangolo, equidistante alla <lb></lb>base, in due parti uguali, secondo il proposto problema, per la prova del <lb></lb>quale rimandava Leonardo al suo libro <emph type="italics"></emph>De ponderibus.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma trattandosi di un teorema puramente geometrico, qual relazione, vien <pb xlink:href="020/01/3066.jpg" pagenum="27"></pb>fatto di domandare, può aver egli con un libro di Meccanica? </s>

<s>La risposta <lb></lb>al quesito incomincia ad apparire da quest&#039;altra nota: “ La piramide ha tre <lb></lb>centri, de&#039;quali uno è centro della magnitudine, l&#039;altro è centro della gra­<lb></lb>vità accidentale, e il terzo è centro della gravità naturale. </s>

<s>Centro della ma­<lb></lb>gnitudine è quello, che divide la lunghezza della piramide in due uguali <lb></lb>parti. </s>

<s>E centro della gravità naturale è quello, nel quale sospendendo la pi­<lb></lb>ramide fa che essa piramide sta nel sito dell&#039;egualità colli stremi della sua <lb></lb>linea centrale. </s>

<s>Centro della gravità naturale è detto quello, sopra del quale, <lb></lb>dividendo la piramide per linea retta per qualunque verso, sempre resta di­<lb></lb>visa in due parti d&#039;egual peso. </s>

<s>Ma lo centro della gravità naturale, per qua­<lb></lb>lunque verso sarà tocco dalla linea retta, che divide la piramide; sempre <lb></lb>sarà di 5/9 di tutta la piramide, di verso la base, ed è posto il centro d&#039;essa <lb></lb>gravità accidentale nel terzo della lunghezza di verso la base, essendo pira­<lb></lb>mide di due lati equidistanti, e, se ella piramide fusse di lati piramidali, il <lb></lb>centro della sua gravità accidentale sarà nel quarto della sua lunghezza di <lb></lb>verso la base ” (K, fol. </s>

<s>89). </s></p><p type="main">

<s>La dicitura impropria e confusa non toglie nulla alla verità del concetto, <lb></lb>che si conferma per corollario dal Teorema geometrico, preparato dianzi dallo <lb></lb>stesso Leonardo, per fondamento di questa conclusione. </s>

<s>Se nella formula in­<lb></lb>fatti CED:CVQ=CE2:CV2, si fa CE=2/3CV (nel qual caso, essendo <lb></lb>CE a CV, come CI a CO, il punto I sarebbe sceso nel centro di gravità del <lb></lb>triangolo) avremo CED:CVQ=4/9:1, ossia CED=4/9CVQ, e perciò <lb></lb>sarà la parte EQ di verso la base 5/9 di tutta la piramide, onde il trapezio <lb></lb>al triangolo viene a essere come 5 a 4. Che se la formula è CED:CVQ= <lb></lb>CE3:CV3, fatto CE=3/4CV (nel qual caso il punto I sarebbe sceso nel <lb></lb>centro di gravità del cono) sarà CED:CVQ=27/64:1. E come la parte <lb></lb>CED è 27/64, così la rimanente EQ deve essere 37/64 del tutto, e perciò il fru­<lb></lb>sto al minor cono otterrebbe la proporzione di 37 a 27. </s></p><p type="main">

<s>Ora, come avrebbe Leonardo, in proposito <emph type="italics"></emph>De ponderibus,<emph.end type="italics"></emph.end> cercato le <lb></lb>geometriche proporzioni delle parti, in cui la linea e il piano, che passano <lb></lb>per i centri di gravità, segano il triangolo e il cono; se non perchè, appli­<lb></lb>candovi la proposizione VIII del primo libro <emph type="italics"></emph>Degli equiponderanti,<emph.end type="italics"></emph.end> voleva <lb></lb>istituire una reogla generale, da ritrovare il punto, intorno a cui gravitano <lb></lb>il trapezio, e il frusto rimasti dal segamento delle due dette figure, che pur <lb></lb>s&#039;osservano nel Manoscritto, benchè senz&#039;altra dichiarazione? </s>

<s>La regola dal­<lb></lb>l&#039;altra parte riusciva di tal bellezza d&#039;ordine e di semplicità, da far mara­<lb></lb>viglia che sfuggisse all&#039;industria di que&#039;tre valorosi, poco fa commemorati, <lb></lb>i quali, tra la seconda metà e il finir del secolo XVI, ripresero a trattare <lb></lb>l&#039;arduo soggetto. </s></p><p type="main">

<s>Sia il triangolo isoscele VOQ (nella precedente figura) il cui centro di <lb></lb>gravità X, e sia segato esso triangolo, secondo qualunque proporzione, dalla <lb></lb>linea FG in due parti: cioè nel triangolo CFG, col centro in T, e nel tra­<lb></lb>pezio FQ, di cui si cerca sull&#039;asse HO il centro Z. </s>

<s>Fatta CO=<emph type="italics"></emph>m,<emph.end type="italics"></emph.end> HC=<emph type="italics"></emph>n,<emph.end type="italics"></emph.end><lb></lb>abbiamo, per il Teorema geometrico di Leonardo, FCG:FQ=<emph type="italics"></emph>n2:m2—n2,<emph.end type="italics"></emph.end><pb xlink:href="020/01/3067.jpg" pagenum="28"></pb>e, per la VIII proposizione meccanica di Archimede, ZX:XT=<emph type="italics"></emph>n2:m2—n2,<emph.end type="italics"></emph.end><lb></lb>onde ZX=(<emph type="italics"></emph>n2<emph.end type="italics"></emph.end>XT)/(<emph type="italics"></emph>m2—n2<emph.end type="italics"></emph.end>). Ma perchè XH=XC—CH=<emph type="italics"></emph>2/3m—n,<emph.end type="italics"></emph.end> e HT= <lb></lb><emph type="italics"></emph>1/3n;<emph.end type="italics"></emph.end> dunque XT=XH+HT=<emph type="italics"></emph>2/3m—n+n/3=2/3(m—n),<emph.end type="italics"></emph.end> il qual <lb></lb>valore sostituito, dà ZX=<emph type="italics"></emph>2n2/(3(m+n)),<emph.end type="italics"></emph.end> onde </s></p><p type="main">

<s><emph type="center"></emph>ZH=ZX+HX=<emph type="italics"></emph>2n2/(3(m+n))+2/3m—n.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Per l&#039;altra porzione dell&#039;asse abbiamo </s></p><p type="main">

<s><emph type="center"></emph>ZO=HO—HZ=<emph type="italics"></emph>m—n—2n2/(3(m+n))—2/3m+n=1/3(m—2n2/(m+n))<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><lb></lb>e di qui viene a istituirsi la proporzione </s></p><p type="main">

<s><emph type="center"></emph>OZ:HZ=<emph type="italics"></emph>1/3(m—2n2/(m+n)):2n2/(3(m+n))+2/3m—n= <lb></lb>(m2—2n2+mn):(2m—n2—mn).<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>Volendosi avere la relazione in funzion della base maggiore, che chia­<lb></lb>meremo <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> e della minore, che chiameremo <emph type="italics"></emph>b;<emph.end type="italics"></emph.end> perchè <emph type="italics"></emph>a:b=m:n,<emph.end type="italics"></emph.end> avremo </s></p><p type="main">

<s><emph type="center"></emph>OZ:HZ=<emph type="italics"></emph>(a2—2b2+ab):(2a2—b2—ab)= <lb></lb>[(a—b)(a+b)+b(a—b)]:[(a+b)(a—b)+a(a—b)]= <lb></lb>(a—b)(a+2b):(a—b)(2a+b)=(a+2b):(2a+b)<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><lb></lb>che è la formula, con la quale Archimede, e dietro lui i Meccanici sogliono <lb></lb>indicare il centro di gravità del trapezio. </s></p><p type="main">

<s>Se <emph type="italics"></emph>m<emph.end type="italics"></emph.end>=2, e <emph type="italics"></emph>n<emph.end type="italics"></emph.end>=1, tanto da questa, quanto dalla formula di Leo­<lb></lb>nardo, s&#039;ha OZ:HZ=4:5, com&#039;aveva trovato il Nardi. </s>

<s>Se <emph type="italics"></emph>m<emph.end type="italics"></emph.end>=3, e <lb></lb><emph type="italics"></emph>n<emph.end type="italics"></emph.end>=2, nel qual caso la sezione FG passa per il centro di gravità del trian­<lb></lb>golo grande, OZ:HZ=7:8. Se poi VQ2:FG2=OC2:HC2=2:1, ossia <lb></lb>OC:HC=√2:1=<emph type="italics"></emph>m:n,<emph.end type="italics"></emph.end> per cui <emph type="italics"></emph>m=n√2;<emph.end type="italics"></emph.end> sostituito questo valore <lb></lb>di <emph type="italics"></emph>m<emph.end type="italics"></emph.end> nella formula di Leonardo, viene OZ:HZ=√2:3—√2. </s></p><p type="main">

<s>Queste cose però, che non promovevano, ma illustravano la Scienza, <lb></lb>erano da Leonardo preparate in grazia del centro di gravità del frusto co­<lb></lb>nico, l&#039;invenzion del quale il Commandino si credè che fosse nuova, e Ga­<lb></lb>lileo si compiacque di averla perfezionata. </s>

<s>Per il teorema stereometrico in­<lb></lb>fatti, che dice avere il cono maggiore, e il minore segato da lui con un piano <lb></lb>parallelo alla base, la proporzion de&#039;cubi dei loro assi, il valore di ZX si <lb></lb>trasforma in quello di (<emph type="italics"></emph>n3<emph.end type="italics"></emph.end>XT)/(<emph type="italics"></emph>m3—n3<emph.end type="italics"></emph.end>). E perchè XT=<emph type="italics"></emph>3/4(m—n),<emph.end type="italics"></emph.end> e XH= <lb></lb><emph type="italics"></emph>3/4(m—n);<emph.end type="italics"></emph.end> dunque ZX=<emph type="italics"></emph>n3/(m3—n3).3/4(m—n)<emph.end type="italics"></emph.end> e perciò ZH=ZX+XH= <lb></lb><emph type="italics"></emph>n3/(m3—n3).3/4(m—n)+3/4m—n=(n

<gap></gap>+3m

<gap></gap>—4nm
<gap></gap>)/(4(m3—n3)).<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/3068.jpg" pagenum="29"></pb><p type="main">

<s>Si trova poi, per l&#039;altra porzione dell&#039;asse, ZO—HO—ZH— <lb></lb><emph type="italics"></emph>m—n=n3/(m3—n3).3/4(m—n)—3/4m+n=(m

<gap></gap>+3n

<gap></gap>—4mn3)/(4(m3—n3)),<emph.end type="italics"></emph.end><lb></lb>d&#039;ondè HZ:ZO=<emph type="italics"></emph>(n

<gap></gap>+3m

<gap></gap>—4nm3):(m<gap></gap><gap></gap>3n

<gap></gap>—4mn3).<emph.end type="italics"></emph.end> E po­<lb></lb>tendosi agli assi <emph type="italics"></emph>m, n,<emph.end type="italics"></emph.end> sostituire le basi <emph type="italics"></emph>a, b<emph.end type="italics"></emph.end> loro proporzionali, avremo <lb></lb>un&#039;analoga relazione espressa dalla formula </s></p><p type="main">

<s><emph type="center"></emph>HZ:ZO=<emph type="italics"></emph>(b<gap></gap>+3a<gap></gap>—4a3b):(a<gap></gap>+3b<gap></gap>—4ab3)<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><lb></lb>la quale è facile vedere come si riduca a quella che Galileo dà nel suo tral­<lb></lb>tatello (Alb. </s>

<s>XIII, 286): </s></p><p type="main">

<s><emph type="center"></emph>HZ:ZO=<emph type="italics"></emph>(3a2+b2+2ab):(3b2+a2+ab).<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><lb></lb>Che se <emph type="italics"></emph>a<emph.end type="italics"></emph.end>=2, e <emph type="italics"></emph>b<emph.end type="italics"></emph.end>=1, tanto dalla formula di Galileo, quanto da quella <lb></lb>di Leonardo, s&#039;ha il centro di gravità del frusto conico indicato dalla rela­<lb></lb>zione HZ:ZO=17:11. </s></p><p type="main">

<s>Chi non ha dimenticato il precedente nostro Tomo, nella prima parte <lb></lb>del capitolo VII, sa che questa medesima indicazione era stata data da An­<lb></lb>tonio Nardi, e il comparare il metodo di lui con quello di Leonardo, che ha <lb></lb>dato luogo a questa forse lunga, ma non inutile digressione, giova a confer­<lb></lb>mare come derivasse in ambedue una tale elegante facilità, anche ne&#039;me­<lb></lb>todi ordinarii, da quello principalissimo degli indivisibili, di cui dunque esso <lb></lb>Leonardo conterma l&#039;antichità dell&#039;origine. </s></p><p type="main">

<s>Benchè irragionevole sarebbe il pensare altrimenti, nondimeno abbiamo <lb></lb>la più efficace, e più espressa testimonianza di ciò, che intendiamo provare, <lb></lb>da que&#039;due stessi, i quali nella nostra Storia appariscono del Cavalieri pre­<lb></lb>cursori immediati, anzi nella istituzione del metodo degl&#039;indivisibili compe­<lb></lb>titori con lui. </s>

<s>Il Nardi, ora commemorato, in quella sua <emph type="italics"></emph>Ricercata seconda<emph.end type="italics"></emph.end><lb></lb>sopra Archimede, nella quale risponde alle obiezioni, che si fanno all&#039;opere <lb></lb>di lui, dop&#039;aver concluso che nulle per lo più, o leggere almeno sono tali <lb></lb>obiezioni, così soggiunge: “ Eppure ad inchieste così ardue egli si pone, che <lb></lb>molto difficile il non mai sdrucciolare apparisce. </s>

<s>È vero che molto dal me­<lb></lb>todo degli indivisibili, se però io posso ben giudicare, o veracemente mo­<lb></lb>strare in quest&#039;opera cosa alcuna, ed anche dagli sperimenti meccanici Ar­<lb></lb>chimede fu in parte aiutato per l&#039;investigazione di tante astruse verità, il <lb></lb>che da più capi argomento, e in particolare dai proemii delle Conoidali e <lb></lb>delle Spirali, ed anco dal supporre noto il centro della gravità nella rettan­<lb></lb>gola conoidale. </s>

<s>” </s></p><p type="main">

<s>La testimonianza dell&#039;altro, dopo il Nardi, a cui s&#039;accennava di sopra, <lb></lb>è quella del Roberval, che, ne&#039;documenti riferiti da noi a varie occasioni, <lb></lb>fu udito confessare apertamente aver dal divino Archimede appresa quella <lb></lb>Scienza matematica dell&#039;infinito, la quale egli poi applicò alla soluzione dei <lb></lb>più ardui problemi, <emph type="italics"></emph>integro quinquennio<emph.end type="italics"></emph.end> prima, che si pubblicasse il me­<lb></lb>todo del Cavalieri. </s>

<s>Non cita però il Roberval nessun libro particolare, e nes­<lb></lb>suna proposizione, d&#039;onde almen trasparisca aver Archimede riguardate le <lb></lb>superficie come composte della somma d&#039;infinite linee, o il solido della somma <pb xlink:href="020/01/3069.jpg" pagenum="30"></pb>d&#039;infinite superficie indivisibili, per cui si crederebbe un&#039;invenzione l&#039;asserto <lb></lb>del Matematico francese, che, per non parere secondo al Nostro, pensò astu­<lb></lb>tamente di sottöporre sè e lui a un&#039;autorità tanto maggiore. </s>

<s>La sincerità <lb></lb>nonostante e la generosità dell&#039;animo, che si dimostra nell&#039;epistola al Tor­<lb></lb>ricelli, non facendo lecito un tal giudizio, s&#039;andava ripensando fra noi da <lb></lb>qual parte delle opere del Siracusano potess&#039;esser derivata la Scienza degli <lb></lb>indivisibili robervalliani, e finalmente parve avere il nostro proposito risolu­<lb></lb>zione dalla risoluzione stessa di quel famoso problema, in cui domandavasi <lb></lb>com&#039;è possibile che le superficie sian gravi, secondo che sempre supponesi <lb></lb>da Archimede, nell&#039;uno e nell&#039;altro libro de&#039;Piani equiponderanti. </s></p><p type="main">

<s>Il Nardi nella Ricercata seconda sopra citata, tocca così frettolosamente <lb></lb>la sottile questione: “ Suppone parimente egli (Archimede) nella stessa opera <lb></lb>della Quadratura della parabola, e nei Superficiali equilibri, che le superfice <lb></lb>gravi siano, il che ad alcuno parve sproposito sì grave, che per fuggirlo ne <lb></lb>commesse un gravissimo, col sostituire i corpi in luogo delle superficie. </s>

<s>Ma <lb></lb>se a chi separa le considerazioni sue dal materiale non si permette tal li­<lb></lb>bertà, nemmeno si permetterà il far muovere una linea o una superficie.... <lb></lb>Ma alcuni, superficiali nella dottrina peripatetica, intendono sinistramente il <lb></lb>detto del loro Maestro, mentr&#039;egli serive che il Matematico astrae dal moto, <lb></lb>cioè dal naturale e concreto, e non dall&#039;astratto e immaginario, altrimenti <lb></lb>avverria che Euclide non saria geometra, quando l&#039;origine di tante figure <lb></lb>riconosce dal moto. </s>

<s>” </s></p><p type="main">

<s>Colui che volle correggere lo sproposito di Archimede, e a cui il Nardi <lb></lb>accennava, è senza dubbio David Rivault, il quale avvertiva nella sua ver­<lb></lb>sione, e nel suo commento all&#039;opera <emph type="italics"></emph>De aequiponderantibus,<emph.end type="italics"></emph.end> dopo il primo <lb></lb>lemma del libro primo: “ Caeterum, licet in sequentibus agatur de planis, <lb></lb>tamen ne planae superficies intelligerentur, quae pondus habere non cer­<lb></lb>nuntur, figuras ut corpora adsignavimus ” (Archim., Opera illustrata, Pari­<lb></lb>siis 1615, pag. </s>

<s>169). Sempre infatti egli embreggia le figure in modo, che <lb></lb>rappresentano non piani, ma prismi o prismoidi o solidi colonnari, non av­<lb></lb>vedendosi dell&#039;errore veramente gravissimo, in cui veniva a compromettere <lb></lb>il suo Archimede, perchè in queste rappresentazioni di corpi solidi, doven­<lb></lb>dosi il centro di gravità ridurre nel preciso mezzo dell&#039;asse, tutte le propo­<lb></lb>sizioni archimedee, manifestamente riuscirebbero false. </s></p><p type="main">

<s>Che se errata è la soluzion del problema, data dal Rivault, non è per <lb></lb>questo punto più accettevole l&#039;altra, suggerita dallo stesso Nardi, il quale <lb></lb>diceva esser lecito per astrazione attribuire alle superficie il peso, com&#039;Eu­<lb></lb>clide, e tutti i geometri, per astrazione attribuiscono a loro stesse il moto. </s>

<s><lb></lb>Rispetto a che giova invocare l&#039;antica distinzion metafisica tra forma e ma­<lb></lb>teria, e rammemorar che la forma, a cui si riferiscono le superficie, non <lb></lb>pesa, come, valendosi degli stessi principii idrostatici di Archimede, Galileo <lb></lb>dimostrò contro i Peripatetici, e come ce he persuadono l&#039;esperienze, pesando <lb></lb>nel vuoto qualche plasmabile corpo, trasfigurato in qualunque maniera. </s>

<s>Se <lb></lb>il peso dunque è inerente e proprio alla sola materia, è irragionevole attri-<pb xlink:href="020/01/3070.jpg" pagenum="31"></pb>buirlo alle superficie, rese per astrazione immateriali. </s>

<s>Si può inoltre osser­<lb></lb>vare che, se il peso è causa produttrice del moto, non ogni moto però, com&#039;è <lb></lb>quello della linea che genera la superficie, è l&#039;effetto del peso. </s>

<s>Una tale ge­<lb></lb>nerazione meccanica infatti, suggerita ai Geometri dall&#039;esempio di un punto <lb></lb>discreto e luminoso, che movendosi velocissimo apparisce una continuata stri­<lb></lb>scia di luce; ha relazione piuttosto con la forma imponderabile, che con la <lb></lb>gravità essenzialmente propria della materia. </s></p><p type="main">

<s>Antonio Rocca avrebbe, secondo il Rivault, introdotto nella Baricentrica <lb></lb>un altro sproposito più grosso di quello di Archimede, facendo, non solo le <lb></lb>superficie, ma le linee stesse pesanti. </s>

<s>Eppure il Torricelli non dubitò d&#039;imi­<lb></lb>tarne gli esempi, e chi ha letto, nel Tomo precedente, il trattato dei Centri <lb></lb>di gravità di lui, si rammenterà di aver trovata anche questa, fra le altre <lb></lb>supposizioni: “ Supponghiamo ancora che le linee abbiano il centro di gra­<lb></lb>vità, e forse non sarà maggiore assurdo il considerare le linee come gravi, <lb></lb>che il considerar le superficie pesanti. </s>

<s>Già in buona Geometria non si può <lb></lb>dire che una linea sia minore di una superficie, ed io credo che tanto sia <lb></lb>lontano dall&#039;esser grave una linea, quanto una superficie. </s>

<s>” </s></p><p type="main">

<s>Il discorso dunque del Torricelli riesce a questo: non esser ragionevole <lb></lb>negare il peso alle linee, se si concede alle superficie. </s>

<s>E perciò sembra che, <lb></lb>senza troppo travagliarsene, volesse risolvere il problema col dire: Archi­<lb></lb>mede l&#039;ha supposto, i Matematici in generale hanno menata buona quella <lb></lb>sua supposizione; sia dunque anche a noi lecito ammettere che le superfi­<lb></lb>cie, e perciò anche le linee, gravitano intorno al sostegno delle loro bilance. </s>

<s><lb></lb>Il ragionamento del Torricelli è quello insomma, che s&#039;è fatto sempre, e si <lb></lb>fa tuttavia dagli Scrittori, i quali si propongono nei loro trattati di trovare <lb></lb>il centro di gravità del triangolo, per esempio, e della parabola, come un <lb></lb>esercizio usato infin dagli antichissimi tempi, senza ripensare alla vanità del­<lb></lb>l&#039;opera loro, quando si terminasse l&#039;inquisizione in quelle figure, e senza <lb></lb>pur sospettare che le cose dimostrate da Archimede non son veramente pro­<lb></lb>posizioni, ma lemmi. </s></p><p type="main">

<s>I reconditi sensi del Siracusano sembra a noi che fossero penetrati dal­<lb></lb>l&#039;acutissimo Roberval, il quale, unico forse, comprese che i piani, di cui si <lb></lb>tratta ne&#039;libri degli Equiponderanti, son solidi: il triangolo, sì, un prisma, <lb></lb>la parabola un cilindroide, non però con altezze definite, come le metteva il <lb></lb>Rivault, ma infinitamente piccole, indivisibili. </s>

<s>Par che si voglia il centro di <lb></lb>gravità di piani, e l&#039;invenzione è invece ai solidi colonnari, che si possono <lb></lb>costruire con soprapporre essi piani infiniti, il centro di gravità de&#039;quali so­<lb></lb>lidi essere in mezzo all&#039;asse, alla linea cioè che congiunge i centri di gra­<lb></lb>vità delle basì, è più chiaro, diceva il Torricelli, di ogni prova, che se ne <lb></lb>potesse addurre. </s>

<s>Ecco perchè, convien che il Roberval dicesse, volendo Ar­<lb></lb>chimede indicare il centro di gravità del prisma triangolare, o del paralle­<lb></lb>lepipedo, o del cilindroide parabolico, si limita a trovar que&#039;medesimi centri <lb></lb>nel triangolo, nel parallelogrammo, e nella parabola: perchè di li, come da <lb></lb>lemmi, chiunque avrebbe potuto con facilità concluderne il fine delle pro-<pb xlink:href="020/01/3071.jpg" pagenum="32"></pb>posizioni. </s>

<s>Fattosi così pervente a esso Roberval lo spirito di Archimede, <lb></lb>s&#039;intende come ammirato lo salutasse col titolo di divino. </s>

<s>A lui era debi­<lb></lb>tore, non solamente d&#039;aver appresa la scienza dell&#039;infinito, e di averla insti­<lb></lb>tuita in un metodo nuovo, ma di esser felicemente riuscito a scansar le cri­<lb></lb>tiche, che incontrò il Cavalieri, malignamente inconsiderate, non intendendo <lb></lb>come lui il solido compaginato d&#039;infinite superficie, ma d&#039;infiniti piani con <lb></lb>altezze indivisibili, e quali volevano esser quelli del suo divino premonstra­<lb></lb>tore, affinchè si potessero dire, e trattar come gravi. </s></p><p type="main">

<s>Benchè queste cose sian forse trapassate fin qui dai critici inosservate, <lb></lb>non sembrano a noi però meno evidenti, e mentre la scoperta del Rober­<lb></lb>val da una parte conferma l&#039;origine antica del metodo degl&#039;indivisibili, de­<lb></lb>rivata direttamente da Archimede ne&#039;contemporanci di Leonardo, e nel Ro­<lb></lb>berval, e per riflesso dalle Collezioni di Pappo nel Nardi, e dalla Stereometria <lb></lb>o dalla Ciclometria del Kepler nel Cavalieri; dall&#039;altra riduce a ragionevoli <lb></lb>termini una nuova questione, come Archimede cioè ritrovasse il centro di <lb></lb>gravità nel solido parabolico. </s>

<s>Il Commandino fu primo ad avvertire la mi­<lb></lb>rabile invenzione. </s>

<s>Pervenutogli alle mani il trattato delle Galleggianti, “ ani­<lb></lb>madverti, egli dice nel dedicare il suo libro del centro di gravità de&#039;solidi <lb></lb>al cardinale Farnese, dubitari non posse quin Archimedes, vel de hac ma­<lb></lb>teria scripsisset, vel aliorum mathematicorum scripta perlegisset; nam in iis <lb></lb>tum alia nonnulla, tum maxime illam propositionem ut evidentem, et alias <lb></lb>probatam assumit: centrum gravitatis in portionibus conoidis rectanguli axem <lb></lb>ita dividere, ut pars, quae ad verticem terminatur, alterius partis, quae ad <lb></lb>basim, dupla sit ”: proposizione che, sebbene non sia dall&#039;Autore espressa­<lb></lb>mente formulata, pur s&#039;argomenta dall&#039;enunziato della seconda, e dalle altre <lb></lb>proposizioni, che seguono nel secondo libro. </s>

<s>Il Nardi insinuava, come udimmo <lb></lb>poco fa, che l&#039;invenzion del punto gravitativo nel Conoide occorresse ad Ar­<lb></lb>chimede, per via dell&#039;esperienza, ciò che sembra alieno dall&#039;istituto schiet­<lb></lb>tamente geometrico di lui, sempre avverso alla scienza somministrata dai <lb></lb>sensi, i quali ei reputava fallaci, e non senza ragione, per le prove che se ne <lb></lb>ebbe a far poi, come da Galileo, quando volle colla bilancia tentare il centro <lb></lb>di gravità della cicloide. </s>

<s>Or si comprende come l&#039;incertezza del fatto venisse <lb></lb>a togliersi con facilità, per via della speculazione, ammettendo che proce­<lb></lb>desse anche Archimede, nell&#039;invenzion del centro di gravità del Conoide, a <lb></lb>quel modo, che vedemmo già fare al Torricelli. </s>

<s>Il metodo degl&#039;indivisibili <lb></lb>rivelava così patente l&#039;analogia fra il triangolo ed essa Conoidale, da dover <lb></lb>concluderne con tutta la certezza geometrica essere gli assi del piano e del <lb></lb>solido segati dal centro di gravità, secondo la medesima proporzione. </s></p><p type="main">

<s>Deve il Commandino, dietro quella prima avvertenza, averne fatta anche <lb></lb>un&#039;altra, ed è che Archimede, nella figura illustrativa l&#039;ottava proposizione <lb></lb>del primo libro, indicava il centro di gravità del settore sferico con quella <lb></lb>precisione, che poi sarebbe per indicare il centre della Conoidate. </s>

<s>Al Mate­<lb></lb>matico urbinate però questa volta non servì, per la difticile inquisizione, la <lb></lb>Geometria ordinaria, ond&#039;ei non seppe dir altro, se non che il richiesto cen-<pb xlink:href="020/01/3072.jpg" pagenum="33"></pb>tro di gravità del settore trovavasi su qualche punto dell&#039;asse. </s>

<s>A questa vaga <lb></lb>indicazione si sarebbe dovuto star senza dubbio contento anche Archimede, <lb></lb>quando non avesse invocati i soccorsi della Geometria infinitesimale, in modo <lb></lb>simile a quel che fecero il Nardi, il Cavalieri, il Torricelli e il Wallis, i <lb></lb>quali, immaginando essere il solido composto d&#039;infinite callotte concentriche, <lb></lb>vinsero del problema quella gran ritrosia, di che il Tartaglia e il Comman­<lb></lb>dino ebbero a fare non vincibile prova. </s></p><p type="main">

<s>Che Archimede avesse penetrato, con l&#039;acume degl&#039;indivisibili, il centro <lb></lb>di gravità del conoide parabolico e del settore di sfera, sembra che lo cre­<lb></lb>desse anche lo stesso Torricelli, il quale anzi si persuase che gli antichi aves­<lb></lb>sero in quel metodo, e nel principio della composizione de&#039;moti, un segreto <lb></lb>efficacissimo, per aprire in Geometria i più reconditi misteri. </s>

<s>Di questo me­<lb></lb>desimo parere fu anche il Wallis, come apparisce dal commentario di lui <lb></lb>sopra il libro archimedeo <emph type="italics"></emph>De circuli dimensione,<emph.end type="italics"></emph.end> e prima dell&#039;Inglese e del <lb></lb>Nostro aveva il Nunnez, nel suo trattato di algebra in lingua spagnola, sen­<lb></lb>tenziato non doversi reputar da nessuno che le proposizioni di Euclide e di <lb></lb>Archimede fossero trovate per quelle medesime vie che appariscono ne&#039;loro <lb></lb>libri (Antuerpiae 1567, pag. </s>

<s>114). Occultassero quest&#039;arcano dell&#039;arte, per <lb></lb>non soggiacere all&#039;invidia, e alle contradizioni, come disse il Torricelli (Opera <lb></lb>geom., P. II, pag. </s>

<s>56), o per far più mirabili apparire i loro trovati, come <lb></lb>pensò il Nardi, o per qualsivoglia altra ragione molto difficile a indovinarsi <lb></lb>da noi, gente tanto diversa da quella di que&#039;tempi; sarebbe vano, secondo <lb></lb>le riferite opinioni, aspettare l&#039;apparizion di que&#039;libri, dove Archimede dimo­<lb></lb>strerebbe la natura e le proprietà de&#039;centri gravitativi, che si presuppongono <lb></lb>ai teoremi <emph type="italics"></emph>De aequiponderantibus,<emph.end type="italics"></emph.end> e il principio della composizion delle <lb></lb>forze parallele, da cui resulta che il moto in su si fa nella direzion della <lb></lb>perpendicolare, che passa per il centro di gravità del galleggiante. </s>

<s>Anche in <lb></lb>quel trattato <foreign lang="grc">Ρερι ξυγω̄ν</foreign>, che tanto si desidera dai cultori di Archimede, si <lb></lb>troverebbe forse, quando finalmente apparisse alla luce, essersi dall&#039;Autore <lb></lb>mantenuto quel segreto geloso, che ora gli studii ci hanno scoperto, e per <lb></lb>cui può svelarsi la scienza, rimasta fin qui coperta dal pellucido tessuto delle <lb></lb>supposizioni. </s></p><p type="main">

<s>Ammessa infatti la dottrina degli infinitesimi, e l&#039;uso del parallelogrammo <lb></lb>delle forze, abbiamo potuto rintracciare le sottilissime vie, per le quali si <lb></lb>condusse Archimede (riguardando le infinite particelle materiali come solle­<lb></lb>citate da forze parallele) a ritrovare il punto, dov&#039;è applicata l&#039;unica forza <lb></lb>resultante dalla somma delle componenti infinite: punto, che riferito ai pesi, <lb></lb>è quel centro di gravità, che dal chiuso pensiero dell&#039;Autore sale a un tratto, <lb></lb>com&#039;acqua da nascosta vena, a irrigar largamente i campi della Statica ar­<lb></lb>chimedea. </s>

<s>La famosa dimostrazione del vette e quella, che più al vivo ri­<lb></lb>tragga in sè l&#039;immagine della teoria, da cui con occulto parto fu esposta, <lb></lb>sostituendo i pesi, moltiplicabili all&#039;infinito, alle forze parallele, il centro delle <lb></lb>quali vedemmo segar la linea di congiunzione (che per la Va del primo libro <lb></lb><emph type="italics"></emph>De aequiponderantibus<emph.end type="italics"></emph.end> si trasforma nel vette) in parti reciprocamente pro-<pb xlink:href="020/01/3073.jpg" pagenum="34"></pb>porzionali alle stesse forze sollecitanti, sì considerate in astratto, e sì come <lb></lb>applicate a rappresentare le gravità delle appese grandezze. </s></p><p type="main">

<s>Abbiasi ora, per ridursi più da vicino al nostro proposito, in AB (fig. </s>

<s>11) <lb></lb>un corpo, che supporremo in forma di quadrato, e di tale gravità in specie <lb></lb>da cader liberamente nell&#039;aria, e siaci proposto a ritrovare la direzione e <lb></lb><figure id="id.020.01.3073.1.jpg" xlink:href="020/01/3073/1.jpg"></figure></s></p><p type="caption">

<s>Figura 11.<lb></lb>l&#039;intensità di una tale caduta. </s>

<s>Risoluto il <lb></lb>detto quadrato in infiniti rettangoli, nel <lb></lb>mezzo C della linea ED, che ricongiunge <lb></lb>i centri di gravità di ciascuna grandezza, <lb></lb>deve, per la citata quinta proposizion di <lb></lb>Archimede, ritrovarsi il centro di gravità <lb></lb>del tutto, e sostituite altrettante forze pa­<lb></lb>rallele a rappresentare le sollecitazioni in <lb></lb>tutti gl&#039;infiniti elementi, la resultante CM, <lb></lb>uguale a tutte insieme le forze parziali, e <lb></lb>a esse stesse parallela, misura la intensità <lb></lb>e la direzione della caduta. </s></p><p type="main">

<s>S&#039;immagini poi esser messo il corpo AB in fondo a un liquido, di cui <lb></lb>sia specificatamente men grave: è un fatto che il moto, dianzi discensivo, <lb></lb>ora si converte in ascensivo, ciò che non può avvenire altrimenti, se non per <lb></lb>essere le forze sollecitanti ciascuna particella rivolte in direzione opposta, e <lb></lb>per aver raggiunta proporzion maggiore verso le prime. </s>

<s>Dovendo poi l&#039;in­<lb></lb>cremento in ciascuna essere uguale, il centro delle nuove forze parallele potrà <lb></lb>essere il medesimo, e la medesima direzione, benchè con più gagliardo moto, <lb></lb>avrà la resultante CN, la quale è alla CM direttamente opposta. </s>

<s>D&#039;onde è <lb></lb>manifesto i corpi più leggeri del liquido, in cui sono immersi, <emph type="italics"></emph>sursum ferri <lb></lb>secundum perpendicularem, quae per centrum gravitatis eorum ducitur,<emph.end type="italics"></emph.end><lb></lb>come dice Archimede, supponendo i principii, dall&#039;investigazione de&#039;quali <lb></lb>s&#039;è veduta scaturire questa stessa conclusione. </s></p><p type="main">

<s>Giunto il corpo immerso alla sommità del liquido, e sopra il livello di <lb></lb>lui sollevatosi tanto, quanto dalla Va del primo libro archimedeo delle Gal­<lb></lb>leggianti è prescritto; ivi si rimane, ciò che non può essere, se non perchè <lb></lb>la forza, che violentemente lo sospingeva in alto, s&#039;è fatta uguale a quella <lb></lb>che lo portava in basso, e qui giova trattenersi alquanto in considerare le <lb></lb>condizioni di un tale equilibrio. </s></p><p type="main">

<s>Sia il solido, quietandosi nel termine della sua ascesa, rimasto nella po­<lb></lb>sizione rappresentata per la medesima figura, nella quale FO segna la linea <lb></lb>del livello. </s>

<s>Si potrebbe ritrovare la causa della sua stazione, immaginando <lb></lb>che il peso de&#039;prismetti infinitesimi, componenti esso solido, uno de&#039;quali <lb></lb>AH, sia uguale al peso degl&#039;infiniti filetti liquidi, simili a LH, in modo però <lb></lb>che questi tendano non verso M, ma verso N, centro contrapposto a quello <lb></lb>della Terra. </s>

<s>La speculazione sarebbe senza dubbio conforme a quel che è <lb></lb>stato dimostrato nella proposizione V del primo libro <emph type="italics"></emph>De insidentibus aquae,<emph.end type="italics"></emph.end><lb></lb>essendo manifesto che di quegli infiniti filetti liquidi componesi una mole di <pb xlink:href="020/01/3074.jpg" pagenum="35"></pb>umido uguale alla parte del solido sommersa, e che pesa quanto esso solido <lb></lb>intero. </s>

<s>Tale fu appunto la speculazion di Archimede, ma rimase per molti <lb></lb>secoli incompresa, d&#039;onde ebbero origine le vicende, che ci porgeranno argo­<lb></lb>mento, anzi saranno come il polo, intorno a cui s&#039;aggira la storia dell&#039;Idro­<lb></lb>statica: per ora non è da interrompere il filo del discorso. </s></p><p type="main">

<s>Il quadrato o altro solido qualunque ABCD (fig. </s>

<s>12) galleggiante sul <lb></lb>liquido, sia tenuto per forza con l&#039;asse BD inclinato alla superficie FO del <lb></lb><figure id="id.020.01.3074.1.jpg" xlink:href="020/01/3074/1.jpg"></figure></s></p><p type="caption">

<s>Figura 12.<lb></lb>livello: consegue da&#039;premessi principii <lb></lb>la ragion meccanica perchè, abbando­<lb></lb>nato a sè stesso, si dirizza naturalmente <lb></lb>coll&#039;asse perpendicolare. </s>

<s>Essendo infatti <lb></lb>in X il centro di gravità del tutto, e <lb></lb>in Z quello della parte sommersa, il <lb></lb>galleggiante è spinto in basso dalla <lb></lb>forza ZY, e in alto dalla forza a lei <lb></lb>uguale TU, trasportata da Z in T sopra <lb></lb>l&#039;asse, e basta osservare al loro modo di agire, per concluder che non ces­<lb></lb>seranno di far rotare il solido, da destra a sinistra, infintanto che non giun­<lb></lb>gano a contrapporsi lungo la medesima linea, diretta al centro della Terra. </s></p><p type="main">

<s>Proprietà simili a queste si proponeva Archimede a dimostrare nel suo <lb></lb>secondo libro, in galleggianti scelti di tal figura, che potessero accomodarsi <lb></lb>all&#039;intenzione dell&#039;Opera. </s>

<s>Posto dunque, come principio, fondamentale, esser <lb></lb>portati in su i corpi nell&#039;umido, secondo la perpendicolare, che dal loro cen­<lb></lb>tro di gravità si produce, è secondo la traduzion latina, edita dal Tartaglia, <lb></lb>formulata così la proposizione, che, secondo l&#039;ordine logico, si disse dover <lb></lb>esser la prima: “ Si aliqua solida magnitudo habens figuram portionis sphae­<lb></lb>rae in humidum demittatur, ita ut basis portionis non tangat humidum, figura <lb></lb>insidebit recta, ita ut axis portionis secundum perpendicularem sit: et si ab <lb></lb>aliquo trahitur figura, ita ut basis portionis tangat humidum, non manet de­<lb></lb>clinata, secundum dimittatur, sed recta restituatur. </s>

<s>” </s></p><p type="main">

<s>Doveva il testo ragionevolmente avere: <emph type="italics"></emph>sed, cum dimittitur, recta resti­<lb></lb>tuctur,<emph.end type="italics"></emph.end> e ciò osservatosi per fare accorto chi legge de&#039;tanti errori scorsi nella <lb></lb>trascrizione, da qualunque mano abbiano avuto origine, seguitiamo a leggere <lb></lb>nella stessa copia del Tartaglia scritto così, che pare incominci la dimostra­<lb></lb>zione del proposto teorema: “ Et igitur, si figura levior existens humido de­<lb></lb>mittatur in humidum, ita ut basis ipsius tota sit in humido; figura inside­<lb></lb>bit recta ita, ut axis ipsius sit secundum perpendicularem. </s>

<s>Intelligatur enim <lb></lb>aliqua magnitudo in humidum demissa: intelligatur etiam etc. </s>

<s>” proseguen­<lb></lb>dovisi a dimostrare in che modo il segmento sferico, che sia messo con tutta <lb></lb>la base nell&#039;umido, rimosso dal perpendicolo, vi ritorna. </s>

<s>La dimostrazion di­<lb></lb>retta perciò della proposta è taciuta, e forse Archimede, dall&#039;esposte ragioni <lb></lb>dell&#039;equilibrio nel segmento con la base nell&#039;umido, lasciava a&#039;suoi studiosi <lb></lb>la facile applicazione al primo proposito, ch&#039;era del segmento stesso, con la <lb></lb>base fuori dell&#039;umido. </s>

<s>E perchè, primo fra quegli studiosi, fu lo stesso Tar-<pb xlink:href="020/01/3075.jpg" pagenum="36"></pb>taglia, non mancò di mettersi, nel Ragionamento primo sopra la sua <emph type="italics"></emph>Tra­<lb></lb>vagliata invenzione,<emph.end type="italics"></emph.end> a un tale esercizio. </s>

<s>Quivi, esposto il teorema tutto in­<lb></lb>sieme nelle due parti, incomincia dal dimostrar la seconda, proponendosi il <lb></lb>caso di un segmento maggiore dell&#039;emisfero, come si rappresenta dalla no­<lb></lb><figure id="id.020.01.3075.1.jpg" xlink:href="020/01/3075/1.jpg"></figure></s></p><p type="caption">

<s>Figura 13.<lb></lb>stra figura 13, nella quale ACD è la super­<lb></lb>ficie sferica dell&#039;umido, col centro in L, e <lb></lb>HNE il galleggiante, ora con l&#039;asse eretto <lb></lb>secondo NL, ora, secondo ZT, inclinato, la <lb></lb>porzione emersa del qual gaìleggiante abbia <lb></lb>raccolto in R il suo peso, che per la RL è <lb></lb>diretto in L suo stesso centro. </s>

<s>“ Il restante <lb></lb>dunque di tal figura, dice il Tartaglia, cioè <lb></lb>quella parte, che è nell&#039;umido sommersa, <lb></lb>averà il centro della sua gravità, per la sesta <lb></lb>proposizione del libro <emph type="italics"></emph>De centro gravium,<emph.end type="italics"></emph.end> nella linea CR, prodotta in diretto <lb></lb>dalla banda del C, tolta talmente, che la parte allungata, alla CR, abbia la me­<lb></lb>desima proporzione, che ha la gravità di quella parte di figura, che è di fuori <lb></lb>dell&#039;umido, alla gravità di quella parte, che è nell&#039;umido sommersa. </s>

<s>Or po­<lb></lb>niamo che tal centro di detta figura sia il punto O, e per il detto centro O <lb></lb>sia protratta la perpendicolare LO. </s>

<s>Adunque la gravità della parte che è fuora <lb></lb>dell&#039;umido premerà di suso in giuso, secondo la perpendicolare RL, e la <lb></lb>parte della figura, che è sommersa nell&#039;umido, premerà di sotto in suso, <lb></lb>per la seconda supposizione, secondo la perpendicolare LO. </s>

<s>Adunque tal figura <lb></lb>non rimarrà, ma le parti della figura, che sonò verso H, saranno portate in <lb></lb>giuso, e quelle che sono verso E saranno portate in suso, e questo sarà, per <lb></lb>fino a tanto che l&#039;assis ZT sia fatto secondo la perpendicolare. </s>

<s>E questa tal <lb></lb>dimostrazione si verifica ancora nella mezza sfera, che stia nell&#039;umido con <lb></lb>tutta la base.... e si verifica ancora nella porzion minore della mezza sfera. </s>

<s>” </s></p><p type="main">

<s>“ Con questi medesimi argomenti si <lb></lb><figure id="id.020.01.3075.2.jpg" xlink:href="020/01/3075/2.jpg"></figure></s></p><p type="caption">

<s>Figura 14.<lb></lb>dimostra il medesimo, quando che queste <lb></lb>sopraddette figure siano lasciate nell&#039;umido <lb></lb>talmente, che le base di quelle stiano in suso, <lb></lb>cioè che niuna di quelle tocchi l&#039;umido, con­<lb></lb>chiudendo quasi con parole contrarie a quelle <lb></lb>di sopra narrate, cioè che la parte della figu­<lb></lb>ra, che è fuora dell&#039;umido, premerà di suso <lb></lb>in giuso, secondo la perpendicolare LS (figu­<lb></lb>ra 14) per la prima supposizione. </s>

<s>E la parte <lb></lb>della figura summersa premerà di sotto in <lb></lb>suso, secondo la perpendicolare LR, per la <lb></lb>seconda supposizione. </s>

<s>Adunque tal figura, secondo quest&#039;altra posizione, non <lb></lb>starà: anzi le parti di tutta la figura, che sono verso E, saranno premute <lb></lb>di suso in giuso, e quelle che sono verso H saranno urtate e spinte di sotto <lb></lb>in suso, e questo persevererà per fino a tanto che l&#039;assis ZT sia fatta se-<pb xlink:href="020/01/3076.jpg" pagenum="37"></pb>condo la perpendicolare più volte detta, che è il proposito vero ” (Vene­<lb></lb>tia 1551, pag. </s>

<s>20, 21): ossia è la parte principale della proposizione. </s>

<s>Che se <lb></lb>il Tartaglia ne pospose l&#039;ordine, fu per mantenersi fedele al testo, e per <lb></lb>tener dietro alla scorta delle figure, le quali si succedevano nella tavola, ri­<lb></lb>masta dell&#039;originale greco, in due gruppi, il primo de&#039;quali rappresentava <lb></lb>il galleggiante ora uguale all&#039;emisfero, poi maggiore, e all&#039;ultimo minore, <lb></lb>con la base immersa nell&#039;umido, mentre le tre analoghe figure dell&#039;altro <lb></lb>gruppo rappresentavano que&#039;medesimi segmenti sferici con la base emersa. </s>

<s><lb></lb>Per questo stesso amore di fedeltà s&#039;indusse a porre l&#039;asse ZT, non secondo <lb></lb>il suo debito stare, cioè nella metà dell&#039;arco della figura, ma alquanto obli­<lb></lb>quo, e benchè conoscesse che a quel modo <emph type="italics"></emph>saria più naturale e più chiaro,<emph.end type="italics"></emph.end><lb></lb>nonostante <emph type="italics"></emph>perchè,<emph.end type="italics"></emph.end> dice, <emph type="italics"></emph>così erano tali figure nell&#039;esempio greco, non me <lb></lb>parso di contrafar quelle, anchor che fusse stato meglio<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>Il Commandino non ebbe tanti scrupoli. </s>

<s>Ridusse le figure al loro de­<lb></lb>bito stare, come s&#039;è fatto da noi con le linee punteggiate: ritoccò qua e là <lb></lb>la forma dell&#039;enunciato, e corresse gli sbagli della trascrizione dal codice la­<lb></lb>tino. </s>

<s>Poi, benchè la licenza paresse oltrepassare il necessario, di una propo­<lb></lb>sizione unica divisa in due parti, ne volle fare due distinte proposizioni, la <lb></lb>prima delle quali così diceva: “ Si aliqua magnitudo solida, levior humido, <lb></lb>quae figuram portionis sphaerae habeat, in humidum demittatur, ita ut ba­<lb></lb>sis portionis non tangat humidum: figura insidebit recta, ita ut axis portio­<lb></lb>nis sit secundum perpendicularem. </s>

<s>Et si ab aliquo inclinetur figura, ut basis <lb></lb>portionis humidum contingat, non manebit inclinata, si demittatur, sed recta <lb></lb>restituetur. </s>

<s>” L&#039;altra proposizione viene appresso così formulata: “ Quod si <lb></lb>figura humido levior in humidum demittatur, ut basis tota sit in humido; <lb></lb>insidebit recta, ita ut axis ipsius secundum perpendicularem constituatur. </s>

<s>” <lb></lb>La qual verità così proposta si passa a dimostrare in quel modo, che aveva <lb></lb>fatto Archimede: modo con tanta facilità applicabile a dimostrar la prece­<lb></lb>dente, che, anche quando non si fosse l&#039;Autore curato di vedere il Ragiona­<lb></lb>mento del Tartaglia, parrebbe una vanagloria lo scrivere in margine <emph type="italics"></emph>Sup­<lb></lb>pleta a Federico Commandino,<emph.end type="italics"></emph.end> e si direbbe adulazione quella di un valoroso <lb></lb>Critico tedesco, il quale annotava: <emph type="italics"></emph>Demonstrationem de suo adiecit Com­<lb></lb>mandinus<emph.end type="italics"></emph.end> (Heiberg. </s>

<s>Archim. </s>

<s>Op., Vol. </s>

<s>II, Lipsiae 1881, pag. </s>

<s>371). </s></p><p type="main">

<s>Nè maggior ragione di compiacersi sembra avesse lo stesso Comman­<lb></lb>dino, nell&#039;annunziar che di suo proprio s&#039;era pure supplito alla parte, man­<lb></lb>cante nel primo di quei teoremi, in cui proponevasi il galleggiante in figura <lb></lb>di un solido conoidale. </s>

<s>Intorno a ciò è da osservare che, nel segmento sfe­<lb></lb>rico, non s&#039;attendeva ad altro, che a dimostrare il gioco delle forze, e come <lb></lb>per-il modo dell&#039;agir di loro fosse costretto a rotare in sè stesso il galleg­<lb></lb>giante, non quietandosi infin tanto che le dette forze non venissero a con­<lb></lb>trapporsi lungo la medesima verticale. </s>

<s>Anche in questo caso però potrebbe <lb></lb>darsi che l&#039;equilibrio si facesse, ma che non fosse stabile, ond&#039;è che le con­<lb></lb>dizioni di una tale stabilità, trascurate dianzi nel segmento sferico, si ven­<lb></lb>gono ora a considerar particolarmente da Archimede nel solido parabolico. </s></p><pb xlink:href="020/01/3077.jpg" pagenum="38"></pb><p type="main">

<s>Sia il detto solido, quale, nella sua sezione AOL, ce lo rappresenta la <lb></lb>figura 15. Immerso nel liquido col suo vertice, vi si manterrà stabilmente <lb></lb>eretto, ogni volta che il suo centro di gravità rimanga alquanto di sotto al <lb></lb><emph type="italics"></emph>centro della pressione.<emph.end type="italics"></emph.end> E perchè una condizion tale dipende, non solamente <lb></lb><figure id="id.020.01.3077.1.jpg" xlink:href="020/01/3077/1.jpg"></figure></s></p><p type="caption">

<s>Figura 15.<lb></lb>dalla proporzione, che ha la gravità spe­<lb></lb>cifica del solido al liquido, ma e dal pa­<lb></lb>rametro della parabola genitrice, o dalla <lb></lb>distanza fra l&#039;apice del cono, e il punto, <lb></lb>in cui cade sull&#039;apotema il vertice della <lb></lb>sezione, distanza che Archimede chiama <lb></lb><emph type="italics"></emph>linea all&#039;asse;<emph.end type="italics"></emph.end> e perchè il centro di gra­<lb></lb>vità del conoideo sega così l&#039;asse di lui, <lb></lb>che il tutto sia sesquialtero della parte, <lb></lb>che è verso il vertice, ossia che stia a que­<lb></lb>sta come tre sta a due; è perciò che si <lb></lb>dice l&#039;annunziato fatto verificarsi, quando la porzione del conoideo rettangolo <lb></lb>abbia l&#039;asse minore che <emph type="italics"></emph>sesquialtero<emph.end type="italics"></emph.end> (dal greco latinamente trasvestito in <emph type="italics"></emph>emio­<lb></lb>lium<emph.end type="italics"></emph.end>) della linea stessa che è all&#039;asse. <emph type="italics"></emph>“ Recta portio rectanguli conoida­<lb></lb>lis,<emph.end type="italics"></emph.end> così è nella edizione del Tartaglia, <emph type="italics"></emph>quando axem habuerit non mino­<lb></lb>rem, quam emiolium eius, quae usque ad axem, omnem proportionem <lb></lb>habens ad humidum in gravitate, dimissa in humido ita, ut basis ipsius <lb></lb>non tangat humidum, posita inclinata, non manet inclinata, sed restitue­<lb></lb>tur recta: rectam dico consistere talem portionem, quando, quod secuit <lb></lb>ipsam, fuerit aequidistanter superficiei humidi. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Le parole che seguitano si crederebbe che fossero il principio della di­<lb></lb>mostrazione, ma di questa propriamente non sono che l&#039;<emph type="italics"></emph>ipotesi:<emph.end type="italics"></emph.end> non si fa <lb></lb>cioè altro con esse che dichiarare esser l&#039;asse del solido veramente inclinato, <lb></lb>come si vuole, alla superficie del liquido, perchè non fa con essa da una <lb></lb>parte e dall&#039;altra angoli uguali. </s>

<s>La dimostrazione però manca affatto, e il <lb></lb>Commandino al solito nota in margine di averla supplita di suo, concludendo <lb></lb>che se R, nella proposta figura, è il centro di gravità del tutto, H della parte <lb></lb>immersa, e G della emersa; la forza applicata in H, e che spinge in alto, <lb></lb>insieme con quella applicata in G, e che spinga in basso, faranno rotare il <lb></lb>solido, infin tanto che il suo asse ON non torni nella dirittura RT della per­<lb></lb>pendicolare. </s></p><p type="main">

<s>A questa conclusione però sarebbero bastati i principii, premessi per il <lb></lb>segmento sferico, cosicchè inutile, e tutto affatto fuor del proposito, appari­<lb></lb>sce quel che il Commandino, dall&#039;essere la linea RO minore di quella che <lb></lb>è all&#039;asse, argomenta: che cioè l&#039;angolo RT<foreign lang="grc">Ω</foreign> è acuto, e che perciò il punto T <lb></lb>della perpendicolare alla superficie del livello cade tra P e <foreign lang="grc">Ω. </foreign></s>

<s>Di qui è ma­<lb></lb>nifesto che il benemerito commentatore di Urbino non comprese come quei <lb></lb>principii erano da Archimede premessi, e presupposte quelle condizioni, non <lb></lb>a dimostrar che l&#039;effetto resultante dalle due forze contrariamente applicate <lb></lb>in H o in G, è quello di dirizzare il conoideo, ma che esso conoideo, venuto <pb xlink:href="020/01/3078.jpg" pagenum="39"></pb>a mettersi in dirittura, anche vi permarrebbe, perchè il centro H della pres­<lb></lb>sione riman di sopra al centro R, intorno a cui s&#039;intende gravitar tutta <lb></lb>la mole. </s></p><p type="main">

<s>Si può dietro questo giudicare qual fiducia debba aversi ai commenti, <lb></lb>fatti dal Commandino intorno alle seguenti parti del Trattato archimedeo, <lb></lb>le proposizioni del quale si vanno via via sempre più complicando, da smar­<lb></lb>rirsi ne&#039;sottilissimi laberinti anche i matematici, a cui benevola Arianna, non <lb></lb>avesse dato in mano il suo filo. </s>

<s>Non poche difficoltà dipendono senza dubbio <lb></lb>da quella sciagurata traduzione latina, ma son queste un nulla, appetto a <lb></lb>quell&#039;altre, che si sono incontrate dai commentatori, per avere smarrito il <lb></lb>filo, veramente arianneo, delle archimedee tradizioni: smarrimento che, av­<lb></lb>venuto poco dopo i tempi dell&#039;Autore, riapparve nel risorgere della Scienza <lb></lb>manifesto, lasciamo stare per ora Leonardo da Vinci, nei commentarii stessi <lb></lb>del Commandino. </s>

<s>La conclusione della proposizione ottava del primo libro, <lb></lb>nella quale si dice che la porzion del segmento sferico, rappresentato nella <lb></lb>figura 14a qui poco addietro, fuori dell&#039;umido, sarà per la retta SL spinta <lb></lb><emph type="italics"></emph>deorsum,<emph.end type="italics"></emph.end> e l&#039;altra porzion che è nell&#039;umido, per la retta RL, <emph type="italics"></emph>sursum;<emph.end type="italics"></emph.end> è <lb></lb>da esso Commandino dichiarata con queste parole: “ Magnitudo enim, quae <lb></lb>in humido demersa est, tanta vi per lineam RL sursum fertur, quanta quae <lb></lb>extra humidum per lineam SL deorsum: id quod ex propositione sexta huius <lb></lb>libri constare potest. </s>

<s>Et quoniam feruntur per alias, atque alias lineas, neutra <lb></lb>alteri obsistit quominus moveatur, idque continenter fiet dum portio in rectum <lb></lb>fuerit constituta. </s>

<s>Tunc enim utrorumque magnitudinum gravitatis centra in <lb></lb>unam eamdemque perpendicularem conveniunt, videlicet in axem portionis. </s>

<s><lb></lb>Et quanto conatu impetuve ea quae in humido est sursum, tanto quae extra <lb></lb>humidum deorsum, per eamdem lineam, contendit. </s>

<s>Quare, cum altera alte­<lb></lb>ram non superet, non amplius movebitur portio, sed consistet manebitque <lb></lb>in eodem semper situ, nisi forte aliqua causa extrinsecus accesserit ” (<emph type="italics"></emph>De <lb></lb>iis quae veh. </s>

<s>in aqua<emph.end type="italics"></emph.end> cit., fol. </s>

<s>7, 8). </s></p><p type="main">

<s>Ora, è notabile l&#039;errore del Commandino, il quale fa le due forze RL, <lb></lb>SL eguali, e da esse sole perciò dipendere l&#039;equilibrio. </s>

<s>Ma ben assai più <lb></lb>notabile è quel richiamarsi alla proposizione VI, senz&#039;avvedersi il valent&#039;uomo <lb></lb>che questa, e più manifestamente la quinta che la precede, scoprono anzi la <lb></lb>fallacia di quella sua posizione. </s>

<s>Imperocchè, se son le spinte uguali e con­<lb></lb>trarie della porzione immersa e della emersa del galleggiante, che lo fanno <lb></lb>rimanere in quiete, e allora non sarebbe vera quella stessa quinta proposi­<lb></lb>zione citata, la quale ammette l&#039;uguaglianza in gravità, o rispetto alle forze <lb></lb>de&#039;pesi, non tra la mole dell&#039;umido uguale alla porzione immersa, e la sola <lb></lb>porzione emersa, ma tra quella e la gravità di tutta intera la mole. </s>

<s>Cosic­<lb></lb>chè, secondo il vero senso delle tradizioni archimedee, le due forze che si <lb></lb>equilibrano sono quella diretta in giù, secondo XL, e l&#039;altra diretta in su, <lb></lb>secondo RL. </s></p><p type="main">

<s>L&#039;origine dell&#039;inganno consiste nel non avere il Commandino avvertito <lb></lb>che, essendo la XL decomposta nelle SL, RL, ambedue dirette al centro della <pb xlink:href="020/01/3079.jpg" pagenum="40"></pb>Terra, vengono a trovarsi lungo la medesima direzione RL, e applicate al <lb></lb>medesimo punto R due forze differenti e contrapposte: l&#039;una dovuta alla <lb></lb>gravità naturale della porzione BRG immersa, e l&#039;altra dovuta alla spinta <lb></lb>che si farebbe dal peso riflesso in su di un egual mole di liquido, la quale <lb></lb>spinta il Commandino ammetteva che fosse una forza semplice, e non resul­<lb></lb>tante dalla differenza di lei con un&#039;altra forza opposta. </s></p><p type="main">

<s>I commentatori che successero, non solo non emendarono l&#039;errore, ma <lb></lb>volsero le cose in peggio, non facendo nessun conto della pressione idrosta­<lb></lb>tica <emph type="italics"></emph>sursum,<emph.end type="italics"></emph.end> da Archimede stesso richiesta come principio necessario nella <lb></lb>sua seconda supposizione. </s>

<s>Cosicchè le forze sollecitanti il galleggiante incli­<lb></lb>nato si riducevano per costoro alle sole SL, RL, ambedue dirette al cen­<lb></lb>tro L con impeti uguali. </s>

<s>La restituzione perciò del segmento sferico alla prima <lb></lb>sua rettitudine la facevano dipendere dalla medesima causa, che fa restituire <lb></lb>orizzontale una bilancia di braccia, e di momenti uguali, quando il centro <lb></lb>di gravità, torna in qualche punto della linea verticale e inferiore alla so­<lb></lb>spensura. </s>

<s>Così, mentre il Commandino, intendendo a mezzo Archimede, non <lb></lb>riconosceva lungo la direzione RL che una forza <emph type="italics"></emph>sursum,<emph.end type="italics"></emph.end> questi altri non <lb></lb>riconobbero che una sola forza <emph type="italics"></emph>deorsum,<emph.end type="italics"></emph.end> contro la manifesta intenzion dello <lb></lb>stesso Archimede, il quale, per aprirsi la via alle future e più complicate <lb></lb>proposizioni de&#039;galleggianti conoidei, incominciava fin d&#039;ora a considerare, <lb></lb>invece della forza unica XL, applicata al centro di gravità del tutto, le SL, <lb></lb>RL applicate al centro di gravità delle parti. </s>

<s>Quando dunque l&#039;asse TZ, <lb></lb>scendendo si sia abbattuto sulla NL, le forze che ve lo fanno rimanere, e <lb></lb>che si possono intendere applicate tutte nel punto X′, son tre: due diretta­<lb></lb>mente concorrenti e, sommate insieme, proporzionali alla gravità di tutta la <lb></lb>grandezza, e una ad esse contraria, e proporzionale alla reazione del peso <lb></lb>di una mole di umido uguale a quella della parte sommersa. </s>

<s>E ciò fa esatto <lb></lb>riscontro con quel che, per altre vie molto diverse, era stato dallo stesso <lb></lb>Archimede dimostrato nella sua proposizione quinta, la quale si può, secondo <lb></lb>questo nuovo ordine di speculazioni, rendere più evidente, immaginando che <lb></lb>le due dette forze concorrenti vengano assommate nella X′R, e che la terza <lb></lb>sia rappresentata dalla X′K, le quali due forze così ridotte, essendo uguali <lb></lb>e contrarie, manterranno il punto X′, intorno a cui s&#039;aduna il peso di tutta <lb></lb>la magnitudine, in stabilità di equilibrio. </s>

<s>La cosa insomma, sotto questo <lb></lb>aspetto, torna a quel più semplice caso, illustrato addietro dalla figura 12.a</s></p><p type="main">

<s>Intendasi perciò il galleggiante ABCD restituito, per l&#039;azion delle forze <lb></lb>Y, U componenti una di quelle che il Poinsot chiamava <emph type="italics"></emph>coppie,<emph.end type="italics"></emph.end> nella retti­<lb></lb>tudine del suo asse, e così stando s&#039;immagini essere violentemente profondato <lb></lb>esso galleggiante sotto il livello FO del liquido più grave in specie. </s>

<s>È ma­<lb></lb>nifesto che, rimanendo la Y sempre la medesima, la contraria forza U cre­<lb></lb>sce via via, secondo che il corpo via via più s&#039;immerge, ond&#039;è che lasciato <lb></lb>in libertà torna in su con tant&#039;impeto, quant&#039;è dovuto alla differenza che <lb></lb>passa fra&#039;due impulsi contrarii, in piena conformità con quel ch&#039;era stato <lb></lb>detto nella proposizione sesta: <emph type="italics"></emph>“ Solidae magnitudines humido leviores, in<emph.end type="italics"></emph.end><pb xlink:href="020/01/3080.jpg" pagenum="41"></pb><emph type="italics"></emph>humidum impulsae, sursum feruntur tanta vi, quanto humidum, molem <lb></lb>habens magnitudini aequalem, gravius est ipsa magnitudine. </s>

<s>”<emph.end type="italics"></emph.end> Come poi <lb></lb>si possano da questi medesimi principii concludere con facilità tutti gli altri <lb></lb>teoremi, proposti nel primo libro <emph type="italics"></emph>De insidentibus,<emph.end type="italics"></emph.end> è così agevole a com­<lb></lb>prendere, che ce ne passiamo senz&#039;altri discorsi. </s></p><p type="main">

<s>Nè son questi principii dell&#039;antichissimo Maestro dell&#039;Idrostatica punto <lb></lb>differenti da quelli professati sui principii del secolo XVIII, nel capitolo III <lb></lb>del secondo libro della <emph type="italics"></emph>Foronomia,<emph.end type="italics"></emph.end> dove l&#039;Herman, dop&#039;aver concluso in un <lb></lb>corollario della sua proposizione XIII universalissima che, per non essere le <lb></lb>due forze Y, U congruenti, il galleggiante è costretto a convertirsi in sè me­<lb></lb>desimo, infin tanto che l&#039;asse di lui non sia tornato perpendicolare alla su­<lb></lb>perficie del liquido; soggiunge: “ Atque in hoc corollariolo fundantur ferme <lb></lb>omnes regulae, quas Autores circa aequilibria solidorum cum fluidis homo­<lb></lb>geneis subinde tradunt ” (Amstelodami 1716, pag. </s>

<s>155), </s></p><p type="main">

<s>La conclusione dunque è quella medesima, a cui giungemmo dianzi dal­<lb></lb>l&#039;aver bene addentro esaminata la dottrina ascosta ne&#039;teoremi archimedei: <lb></lb>eppure l&#039;Herman crede esservi giunto per vie affatto nuove, e incognite ai <lb></lb>suoi predecessori, fra&#039;quali nomina espressamente il Pascal, che dimostrò <lb></lb>le ragioni degli idrostatici equilibri col principio delle velocità virtuali: prin­<lb></lb>cipio, dice l&#039;Herman, indiretto, e difficilmente applicabile ai fluidi eterogenei <lb></lb>(ivi, Schol. </s>

<s>II, pag. </s>

<s>157). </s></p><p type="main">

<s>La Storia conferma esser verissimo pur troppo quel che da una parte <lb></lb>asserisce il Matematico di Basilea, ma dall&#039;altra gli contende la compiacenza <lb></lb>del credersi autore di que&#039;principii diretti, de&#039;quali, benchè non sapessero <lb></lb>far uso nè il Pascal, nè altri, si trova pure il documento nell&#039;antichissimo <lb></lb>Siracusano. </s>

<s>I due libri di lui hanno indole alquanto diversa, riconoscibile, <lb></lb>chi sottilmente penetra il mistero, nelle due distinte supposizioni, separata­<lb></lb>mente premesse innanzi all&#039;un libro e all&#039;altro. </s>

<s>Nel primo libro i galleggia­<lb></lb>menti e le sommersioni de&#039;corpi si riducono alle ragioni de&#039;loro pesi, mi­<lb></lb>surabili con la bilancia, ma nel secondo, invece de&#039;pesi, si considerano le <lb></lb>forze, che le ponderose moli traggono al centro, per cui può dirsi che quella <lb></lb>prima parte dottrinale sta a questa seconda, come la Fisica sta alla Geome­<lb></lb>tria. </s>

<s>Le geometriche sottigliezze però si stavano così sotto la crassizie fisica <lb></lb>velate, che sino all&#039;Herman, in tanti secoli, nessun Matematico valse a rico­<lb></lb>noscerle. </s>

<s>Se tutti i corpi son ponderosi, e perciò tendono in basso, e se anche <lb></lb>ogni umido è un corpo, com&#039;è possibile, dicevano, che contro alla comun <lb></lb>legge naturale debba spingere in alto? </s>

<s>La riflessione delle pressioni idro­<lb></lb>statiche verticali rimase, anche dopo il Torricelli, per qualche tempo, dalla <lb></lb>maggior parte de&#039;Fisici, incompresa, come incomprese rimasero pure per <lb></lb>molti le pressioni laterali: ond&#039;è che, lusingati da quel che pareva porgere <lb></lb>la prima supposizion di Archimede, si credè che il liquido non premesse altro <lb></lb>che il fondo del vaso. </s></p><p type="main">

<s>A questa estrema conseguenza, preparata già dal prevaler delle prece­<lb></lb>denti opinioni, giunse Famiano Michelini, secondato e difeso da quel Viviani <pb xlink:href="020/01/3081.jpg" pagenum="42"></pb>che, nell&#039;atto di correggersene, faceva complice dell&#039;errore Archimede, accu­<lb></lb>sandolo di aver trattato l&#039;Idrostatica con principii poco universali, perchè il <lb></lb>progresso delle sue dimostrazioni, diceva, non vale, se non in caso che le <lb></lb>parti infime del fluido si trovino ugualmente poste in continuazione fra loro, <lb></lb>e premute dalla mole che le sovrasta perpendicolarmente. </s>

<s>Il quale esempio <lb></lb>ci basti per ora a provar che in sul declinare del secolo XVII, si teneva dai <lb></lb>più insigni cultori della Scienza che unico modo di dimostrar le leggi idro­<lb></lb>statiche fosse quello tenuto dall&#039;antico Maestro, nel suo primo fisico libro. </s>

<s><lb></lb>E come il Viviani stesso, dando mano a scrivere il suo trattatello <emph type="italics"></emph>Degli ab­<lb></lb>bassamenti e de&#039;sollevamenti dei corpi ne&#039;fluidi,<emph.end type="italics"></emph.end> non sospettò che l&#039;opera <lb></lb>sua era simile a quella di chi fa riapparire una scrittura su un palinsesto; <lb></lb>così parve non ne sospettare nemmeno l&#039;Herman. </s>

<s>Ond&#039;è alla nostra Storia <lb></lb>affidato tale ufficio che, sebbene non sia affatto nuovo, ha qualche cosa di <lb></lb>straordinario: a noi incombe narrare i delirii lunghi e affannosi di venti <lb></lb>secoli, prima che l&#039;Idrostatica si riduca nella rettitudine de&#039;sentieri ar­<lb></lb>chimedei. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Si direbbe che Archimede, da quella parte, nella quale insegnava essere <lb></lb>il galleggiante sostenuto da forze, suscitatesi nell&#039;umido contrariamente a <lb></lb>quelle della gravità naturale; fosse rimasto incompreso da quegli stessi, che <lb></lb>convissero con lui, o che gli successero poco di poi. </s>

<s>Scarsi e languidi, per <lb></lb>la lunga oblivione, ci sono i documenti, ma qualcuno che n&#039;è rimasto, e che <lb></lb>non è sfuggito alla nostra scarsa erudizione, par che dia ragionevole fonda­<lb></lb>mento al nostro giudizio. </s></p><p type="main">

<s>Herone Alessandrino, nel proemio al suo libro <emph type="italics"></emph>Degli spiritali,<emph.end type="italics"></emph.end> propone <lb></lb>un problema, che fra gl&#039;idrostatici è uno de&#039;più famosi, e che serve quasi <lb></lb>di metro a misurare i progressi di questa scienza: onde avvenga che coloro, <lb></lb>i quali notano nel profondo del mare, avendo un peso d&#039;acqua inestimabile <lb></lb>sopra le spalle, non ne vengano oppressi. </s>

<s>E l&#039;Autore, per la soluzione della <lb></lb>proposta, invoca Archimede, non già là, dove dimostra che le pressioni deor­<lb></lb>sum sono equilibrate da quelle sursum, perchè eguali e contrarie, ma là <lb></lb>dove, dai teoremi del primo libro, si raccoglie che l&#039;acqua non pesa in sè <lb></lb>stessa, e nè perciò sopra il corpo del marangone, secondo qualunque pro­<lb></lb>fondità a lei soggetto. </s>

<s>Nè a principii punto diversi da questi è informata, nel <lb></lb>capitolo I dei detti <emph type="italics"></emph>Spiritali,<emph.end type="italics"></emph.end> la teoria del sifone ritorto, la quale, invece che <lb></lb>sopra le pressioni idrostatiche, e sopra le ragioni del loro equilibrio, si fonda <lb></lb>inopportunamente sul principio che deve l&#039;acqua disporsi necessariamente in <lb></lb>una superficie sferica, “ il centro della quale sia l&#039;istesso con il centro della <lb></lb>Terra, perciocchè, se la superficie di qualche acqua è sferica, ed ha l&#039;istesso <lb></lb>centro della Terra, essa si posa, ma se è possibile non posi .... ” (<emph type="italics"></emph>Tradu-<emph.end type="italics"></emph.end><pb xlink:href="020/01/3082.jpg" pagenum="43"></pb><emph type="italics"></emph>zione di A. Giorgi,<emph.end type="italics"></emph.end> Urbino 1592, fol. </s>

<s>14), e seguita ripetendo il senso di <lb></lb>Archimede, nella proposizione seconda del primo libro. </s></p><p type="main">

<s>Trapassando ad altra nazione, ad altre discipline, e ad altri tempi, da&#039;li­<lb></lb>bri di Seneca s&#039;attinge un&#039;altra prova del ridursi tutta la scienza degli idro­<lb></lb>statici equilibrii a un fatto, non dissimile da quello, che si osserva, pesando <lb></lb>i corpi solidi sulla bilancia. <emph type="italics"></emph>Quamcumque vis rem expende, et contra aquam <lb></lb>statute, dummodo utriusque par sit modus.<emph.end type="italics"></emph.end> Or che altro significano così <lb></lb>fatte parole, se non quella parità di modi, che s&#039;otteneva da Archimede nelle <lb></lb>proposizioni del suo primo libro, col divider l&#039;umido in due settori uguali, <lb></lb>quasi bilancia, che nel punto di mezzo sostiene il giogo, sopra cui s&#039;intenda <lb></lb>da una parte posato il galleggiante, e dall&#039;altra un&#039;egual mole di liquido, <lb></lb>che lo contrappesa? </s></p><p type="main">

<s>Seneca invocava, come avvertimmo, queste dottrine, per confermare i <lb></lb>placiti della Filosofia platonica, nella quale s&#039;insegnava non essere i corpi o <lb></lb>gravi o leggeri, secondo la nostra stima, ma per comparazione del mezzo, <lb></lb>da cui son portati. </s>

<s>La Filosofia però non era la Scienza più gradita a quei <lb></lb>tempi, ne&#039;quali, piuttosto che alla speculazione s&#039;andava dietro a ciò, che <lb></lb>potesse in qualche modo servire alle utilità, e ai comodi della vita. </s>

<s>E spen­<lb></lb>tasi quella face, che precorreva nelle mani di Archimede, a dimostrare i <lb></lb>sottili e ascosti sentieri, per i quali si sarebbe dovuta metter l&#039;arte dell&#039;ar­<lb></lb>chitettura navale; non si vedeva quale altro vantaggio riceverebbero le co­<lb></lb>munanze civili dalla Scienza delle acque, se non imparando a regolarne <lb></lb>equamente la dispensa, ne&#039;domestici usi, e per la irrigazione delle campa­<lb></lb>gne. </s>

<s>Ma nè Archimede stesso, nè nessun altro avevano ancora insegnato nulla <lb></lb>intorno a ciò, per cui unica regola, intorno a un fatto di così grande impor­<lb></lb>tanza alla vita sociale, si rimaneva la volgare esperienza. </s></p><p type="main">

<s>I primi suggerimenti, che di qui vennero all&#039;arte, furono quelli di re­<lb></lb>golar le dispense secondo la maggiore o minore ampiezza delle bocche, ma <lb></lb>non potè nello stesso tempo sfuggire alla considerazione de&#039;legislatori quel <lb></lb>che dall&#039;altra parte era notissimo ai villici, e a&#039;canovai, che cioè da una me­<lb></lb>desima cannella s&#039;attinge in ugual tempo maggior misura di vino dalla botte <lb></lb>piena, che dalla scema, passando con maggior impeto il liquido in quella, che <lb></lb>in questa. </s>

<s>Si trova perciò che furono, infin dagli antichissimi moderatori, <lb></lb>avvertite alcune fra le cause principali del crescere e del diminuire la rapi­<lb></lb>dità del corso dell&#039;acque, d&#039;onde, venendosi a dare ai privati meno o più del <lb></lb>convenuto, o farebbe ingiustizia il Principe, o ne riceverebbe danno lo Stato. </s></p><p type="main">

<s>I Romani, fra le antiche nazioni, furono, in costruire acquedotti, spe­<lb></lb>cialmente per la loro città, i più suntuosi, e ne eleggevano a prefetto uno <lb></lb>de&#039;cittadini più principali. </s>

<s>Sotto gl&#039;imperi di Nerva e di Traiano cotesta <lb></lb>prefettura delle acque venne in Sesto Giulio Frontino che, zelantissimo del <lb></lb>commessogli ufficio, e letterato, scrisse quel Commentario <emph type="italics"></emph>De aquaeducti­<lb></lb>ctibus Urbis Romae,<emph.end type="italics"></emph.end> da cui ci viene il primo documento di ciò, che sapesse <lb></lb>la Scienza, e praticasse l&#039;arte, intorno al regolar le misure delle acque <lb></lb>correnti. </s></p><pb xlink:href="020/01/3083.jpg" pagenum="44"></pb><p type="main">

<s>Incomincia Frontino dal descrivere gli Acquidotti, col nome proprio a <lb></lb>ciascuno, e poi dice d&#039;onde movessero, quanto corressero per giungere alla <lb></lb>Città, quanto rimanessero incavati entrando sottoterra, e quanti archi gli so­<lb></lb>stenessero, uscendo fuori all&#039;aperto. </s>

<s>Seguita poi a narrare quant&#039;acqua porti <lb></lb>ciascun condotto, o dentro o fuori della Città, quante siano le piscine o i <lb></lb>conservatoi, quanto se ne dispensasse di lì ai laghi, quanto a nome di Ce­<lb></lb>sare, quanto ad uso de&#039;privati, per benefizio del Principe. </s>

<s>Venivano le di­<lb></lb>stribuzioni regolate col crescere o col diminuire le bocche delle fistole, la più <lb></lb>comune tra le quali era detta <emph type="italics"></emph>quinaria,<emph.end type="italics"></emph.end> per essere un circolo inciso in una <lb></lb>lamina di piombo, e d&#039;un diametro di cinque quarte di digito del piede <lb></lb>romano. </s></p><p type="main">

<s>È un fatto dunque che la regola si riduceva principalmente a moderare <lb></lb>le luci, ma che inoltre la maggiore o minore velocità del corso conferisse ad <lb></lb>alterare le misure dell&#039;acqua era cosa che Frontino, come insisteva, perchè <lb></lb>non la dimenticassero i suoi ufficiali; così voleva rammemorarla ai suoi let­<lb></lb>tori: “ Meminerimus omnem aquam, quotiens ex altiore loco venit, et intra <lb></lb>breve spatium in castellum cadit, non tantum respondere modulo suo, sed <lb></lb>etiam ex superare: quotiens vero ex humiliore, idest minore pressura, lon­<lb></lb>gius ducatur, segnitia ductus modum quoque deperdere: ideo, secundum hanc <lb></lb>rationem, aut onerandam esse erogationem, aut relevandam ” (<emph type="italics"></emph>S. I. </s>

<s>Fron­<lb></lb>tini Comment. </s>

<s>restitutus atque explicatus op. </s>

<s>ct studio I.<emph.end type="italics"></emph.end> Poleni, Pata­<lb></lb>vii 1722, pag. </s>

<s>100-2). </s></p><p type="main">

<s>Il Poleni, in questa riconosciuta necessità di onerare o di relevare l&#039;ero­<lb></lb>gazione, ossia, com&#039;egli interpetra, di ampliare o di restringere il modulo o <lb></lb>la sezion della bocca, secondo che maggiore o minore è la natural velocità <lb></lb>dell&#039;acqua che passa; argomenta non essere ignoto a Frontino il principio <lb></lb>delle velocità medie, benchè non sapesse farne l&#039;applicazione. </s>

<s>Ma comunque <lb></lb>sia per ora di ciò, le parole, che immediatamente seguono alle citate, con­<lb></lb>tengono un altro avvedimento che, sebbene ora sembri a noi ovvio, doveva <lb></lb>nonostante allora valere per una sottigliezza, ed è che i <emph type="italics"></emph>calici,<emph.end type="italics"></emph.end> ossia quei <lb></lb>tubi, che si mettevano nel grosso della muratura de&#039;conservatoi, e che si <lb></lb>facevano di bronzo, perchè gli attriti e le fraudi non ne dovessero alterar la <lb></lb>misura; facevano differenza nella portata, secondo la loro collocazione ri­<lb></lb>spetto alla linea orizontale, o alla direzione dell&#039;acqua. </s>

<s>“ Sed et calicis po­<lb></lb>sitio habet momentum: in rectum, et ad libram collocatus, modum servat: <lb></lb>ad cursum aquae oppositus et devexus amplius rapit: ad latus praetereuntis <lb></lb>aquae conversus et supinus, nec ad haustum pronus, segniter exiguum su­<lb></lb>mit ” (ibid., pag. </s>

<s>102, 3). </s></p><p type="main">

<s>Per un&#039;altra varietà di collocamento, soggiunge altrove Frontino, fanno <lb></lb>i calici differenza nella portata, cioè, per non essere tutti disposti nella me­<lb></lb>desima linea orizontale, ma alcuni più bassi, altri più alti; intorno a che <lb></lb>mette questa avvertenza: “ Circa collocandos quoque calices observari opor­<lb></lb>tet, ut ad lineam ordinentur; nec alterius inferior calix, alterius superior po­<lb></lb>natur. </s>

<s>Inferior plus trahit; superior, quia cursus aquae ab inferiore rapitur, <pb xlink:href="020/01/3084.jpg" pagenum="45"></pb>minus ducit ” (ibid., pag. </s>

<s>197-99). La ragione del trar più l&#039;inferiore che <lb></lb>il superiore, perchè in quello vien l&#039;acqua più rapidamente che in questo; <lb></lb>è la stessa, che dicemmo esser nota anche alla gente volgare, la quale sa <lb></lb>altresì molto bene, come Frontino, che del gettar più lo zipolo di sotto, che <lb></lb>quello di sopra, è immediata causa la maggiore o minore altezza del vino, <lb></lb>che fa, in dargli esito, maggiore o minore la pressura. </s>

<s>Dalla collazione del <lb></lb>qual passo, con quello primo citato, par se ne ricavi un&#039;interpetrazione di­<lb></lb>versa, da quella datagli dal Poleni, cosicchè <emph type="italics"></emph>onerare<emph.end type="italics"></emph.end> o <emph type="italics"></emph>relevare<emph.end type="italics"></emph.end> l&#039;erogazione <lb></lb>non significhi direttamente allargare o restringere il modane, ma aumentare <lb></lb>o diminuire l&#039;altezza, e con essa la pressione e l&#039;impulso velocitativo, infino <lb></lb>a ridur la cosa al suo temperamento. </s></p><p type="main">

<s>Benchè così chiari, e derivati dalle loro legittime fonti, ne siano i do­<lb></lb>cumenti, s&#039;accusava nulladimeno, da un autorevolissimo giudice, Frontino di <lb></lb>non aver bene considerato quanto conferiscano le velocità in mutar le mi­<lb></lb>sure della medesima acqua corrente. </s>

<s>Fondamento all&#039;accusa era quel che <lb></lb>si legge all&#039;articolo LXIV del citato Commentario degli acquedotti di Roma, <lb></lb>che qui trascriviamo: “ Persecutus ea quae de modulis dici fuit necessarium, <lb></lb>nunc ponam quem modum quaeque Aqua, ut Principum commentariis com­<lb></lb>prehensum est, usque ad nostram curam habere visa sit, quantumque ero­<lb></lb>gaverit; deinde quem ipsi scrupulosa inquisitione, praeeunte providentia optimi <lb></lb>diligentissimique principis Nervae, invenerimus. </s>

<s>Fuere ergo in commenta­<lb></lb>riis in universo quinariarum XII millia DCCLVI: in erogatione XIV millia <lb></lb>XVIII; plus in distributione, quam in accepto, computabantur quinariae <lb></lb>MCCLXIII. </s>

<s>Huius rei admiratio, cum praecipuum officii opus in exploranda <lb></lb>fide Aquarum atque copia crederem, non mediocriter me convertit ad scru­<lb></lb>tandum, quemadmodum amplius erogaretur, quam in patrimoni, ut ita di­<lb></lb>cam, esset. </s>

<s>Ante omnia itaque capita ductuum metiri aggressus sum, sed <lb></lb>longe, idest circiter quinariis X millibus, ampliorem, quam in commentariis <lb></lb>modum inveni: ut per singulas demonstrabo ” (ibid., pag. </s>

<s>112-15). </s></p><p type="main">

<s>Il conto si riduce a questo, come, per ciascun acqua, si raccoglie dai <lb></lb>successivi articoli del Commentario: Dall&#039;Appia, quinarie 1825; dal Teve­<lb></lb>rone, 4398; dalla Marcia, 4690; dalla Tepula, 445: dalla Giulia, 1206; dalla <lb></lb>Vergine, 2504; dalla Claudia, 4607; dal Tevere, 4738: in tutto quinarie 24413. <lb></lb>Onde essendo nell&#039;erogazione quinarie 14018, la trovata differenza era di <lb></lb>10395 quinarie, <emph type="italics"></emph>idest,<emph.end type="italics"></emph.end> preso il numero tondo, <emph type="italics"></emph>circiter quinariis X millibus,<emph.end type="italics"></emph.end><lb></lb>come dice Frontino, a cui venne perciò il sospetto che quel di più se l&#039;aves­<lb></lb>sero usurpato <expan abbr="ĩ">im</expan> ministri o i partecipanti. </s></p><p type="main">

<s>“ La qual cosa, soggiunge in tal proposito il Castelli, poteva essere in <lb></lb>parte, perchè pur troppo è vero che il pubblico quasi sempre è ingannato. </s>

<s><lb></lb>Con tutto ciò io penso ancora assolutamente che, oltre le fraudi di quelli <lb></lb>officiali, le velocità dell&#039;acqua nei luoghi, ne&#039;quali Frontino le misurò, po­<lb></lb>tessero essere diverse da quelle velocità, che si ritrovavano nelli altri luoghi <lb></lb>misurati da altri per avanti, e perciò le misure dell&#039;acque potevano, anzi do­<lb></lb>vevano necessariamente essere diverse, essendosi da noi stato dimostrato che <pb xlink:href="020/01/3085.jpg" pagenum="46"></pb>le misure della medesima acqua fluente hanno reciproca proporzione delle <lb></lb>loro velocità. </s>

<s>Il che non considerando bene Frontino, e ritrovando l&#039;acqua <lb></lb><emph type="italics"></emph>in commentariis<emph.end type="italics"></emph.end> 12755 quinarie, <emph type="italics"></emph>in erogatione<emph.end type="italics"></emph.end> 14018, e nella propria mi­<lb></lb>sura, fatta da sè medesimo <emph type="italics"></emph>ad capita ductuum,<emph.end type="italics"></emph.end> 22755 (<emph type="italics"></emph>così è scritto, ma <lb></lb>veramente è 24413, come torna alla somma de&#039;numeri dati dallo stesso <lb></lb>Frontino<emph.end type="italics"></emph.end>) quinarie in circa; pensò che in tutti questi luoghi passasse diversa <lb></lb>quantità d&#039;acqua, cioè maggiore <emph type="italics"></emph>ad capita ductuum<emph.end type="italics"></emph.end> di quella, che era <emph type="italics"></emph>in <lb></lb>erogatione,<emph.end type="italics"></emph.end> e questa giudicò maggiore di quella, che era <emph type="italics"></emph>in commentariis ”<emph.end type="italics"></emph.end><lb></lb>(<emph type="italics"></emph>Della Misura delle acque correnti,<emph.end type="italics"></emph.end> Bologna 1660, pag. </s>

<s>29, 30). </s></p><p type="main">

<s>Ora, alcuni zelantissimi partigiani dell&#039;antico Scrittore si risentirono <lb></lb>acerbamente contro il Castelli, e allegando i passi da noi sopra alligati ne <lb></lb>concludevano che l&#039;accusa era ingiusta, e che il Console romano aveva dato <lb></lb>la vera regola di misurare le acque, tanti secoli prima, e più esattamente <lb></lb>del Discepolo di Galileo. </s>

<s>A suo tempo la Storia darà intorno alla passionata <lb></lb>questione definitiva sentenza, e per ora si conceda liberamente agli amici, e <lb></lb>agli ammiratori di Frontino, come cosa di fatto, aver egli avuto qualche no­<lb></lb>tizia del Teorema, che dice stare le quantità dell&#039;acque erogate in ragion <lb></lb>composta delle velocità e delle sezioni. </s>

<s>Anzi soggiungeremo per conferma di <lb></lb>ciò che, sebbene Frontino stesso ne faccia qualche cenno, si trova nelle leggi <lb></lb>degli antichi pretori di Roma espresso di quel generale teorema idrodina­<lb></lb>mico sopra formulato una importantissima conseguenza, qual&#039;è che, avendosi <lb></lb>quantità d&#039;acque uguali, stanno le loro velocità reciprocamente come le se­<lb></lb>zioni. </s>

<s>La notizia era stata data in una scrittura idraulica dal padre Guido <lb></lb>Grandi, le parole del quale trascriviamo qui tanto più volentieri, in quanto <lb></lb>che sono tutt&#039;insieme illustrative della Scienza, e interpetrative dell&#039;antica <lb></lb>legge pretoria. </s></p><p type="main">

<s>“ L&#039;acqua corrente, egli scrive, con somma facilità si adatta a più e <lb></lb>diverse aperture, compensando colla velocità ciò che manca alla grandezza <lb></lb>della sezione, per cui è obbligata a passare. </s>

<s>Così il medesimo fiume passa da <lb></lb>un luogo più largo ad uno più stretto, e viceversa dal più angusto al più am­<lb></lb>pio, e passa sotto gli archi de&#039;ponti tutta quella piena, che pare non possa <lb></lb>capire nell&#039;alveo inferiore più dilatato, e che talvolta lo trabocca. </s>

<s>E però <lb></lb>una minor sezione, o per larghezza o per altezza, o per entrambe, non è sem­<lb></lb>pre segno di minor quantità d&#039;acqua, che passi per essa, ma per lo più, <lb></lb>secondo le circostanze del caso, di cui si parla, indica solamente maggiore <lb></lb>velocità della medesima quantità di acqua. </s>

<s>E così, nella Legge: <emph type="italics"></emph>Ait prae­<lb></lb>tor ff. </s>

<s>ne quid in flum. </s>

<s>publ.,<emph.end type="italics"></emph.end> dicesi che, senza mutare la quantità dell&#039;acqua <lb></lb>corrente, si fa innovazione nel fiume, con farla correre per sezione o più <lb></lb>bassa o più stretta, rendendola con questo più rapida e più veloce. <emph type="italics"></emph>Si mu­<lb></lb>tetur aquae cursus, dum vel depressior vel arctior fiat aqua, ac per hoc <lb></lb>rapidior sit ...:<emph.end type="italics"></emph.end> non dovendosi attendere chi legge in questo luogo <emph type="italics"></emph>altior<emph.end type="italics"></emph.end><lb></lb>ovvero <emph type="italics"></emph>auctior,<emph.end type="italics"></emph.end> ma bensì <emph type="italics"></emph>arctior,<emph.end type="italics"></emph.end> come sta nelle Pandette fiorentine, il che <lb></lb>meglio corrisponde al sentimento di quella legge ” (<emph type="italics"></emph>Raccolta di Autori che <lb></lb>trattano del moto delle acque,<emph.end type="italics"></emph.end> ediz. 2a, Firenze 1774, T. IX, pag. 274). </s></p><pb xlink:href="020/01/3086.jpg" pagenum="47"></pb><p type="main">

<s>I regolamenti, che poteva suggerire la Scienza nella pubblica dispensa <lb></lb>dell&#039;acque, si mantennero quali ce li porgono Frontino ne&#039;suoi commenta­<lb></lb>rii, e nelle loro leggi i Pretori romani, senza nessun progresso, in tutto il <lb></lb>tempo della decadenza. </s>

<s>E anche, ne&#039;primi albori del Rinascimento, non si <lb></lb>sapeva aggiungere nulla di più alle avvertenze date in proposito dagli anti­<lb></lb>chi. </s>

<s>“ La cannella, dice Leon Batista Alberti nel X libro della sua <emph type="italics"></emph>Architet­<lb></lb>tura,<emph.end type="italics"></emph.end> che sarà messa a piano e diritta, manterrà il modine, ed hanno tro­<lb></lb>vato che detta cannella, per lo attingere, dirò così, si consuma ” (<emph type="italics"></emph>Tradu­<lb></lb>zione di C. Bartoli,<emph.end type="italics"></emph.end> Milano 1833, pag. </s>

<s>364). E aveva poco prima lo stesso <lb></lb>Autore notato che “ i buchi delli sboccatoi si variano per versare le acque, <lb></lb>secondo il concorso deli&#039;acqua che viene, e secondo i doccioni. </s>

<s>Perciocchè <lb></lb>quanto più l&#039;acqua sarà presa da un largo e veloce fiume, e quanto ella <lb></lb>sarà condotta per canali e vie più spedite, e quanto ella sarà per esse stretta <lb></lb>insieme, tanto più bisognerà allargare il modine da versare ” (ivi). In que­<lb></lb>ste parole si comprendono dall&#039;Alberti le due massime leggi, da sì lungo <lb></lb>tempo già note, che cioè le quantità dell&#039;acqua stanno in ragion composta <lb></lb>delle velocità e delle sezioni, ond&#039;è perciò che, avendosi quantità uguali, esse <lb></lb>stesse velocità e sezioni si corrispondono in ragion contraria. </s>

<s>Ma non era <lb></lb>però questa altro che una semplice notizia sperimentale, e come non si sa­<lb></lb>peva da quegli Autori mettere nella sua precisa forma il Teorema, così man­<lb></lb>cava a loro il modo di dimostrarlo scientificamente dai suoi principii. </s></p><p type="main">

<s>Il primo tentativo di una dimostrazione geometrica sembra a noi che, <lb></lb>fra gli Autori più noti, s&#039;incontri ne&#039;libri di Girolamo Cardano. </s>

<s>Mentre la <lb></lb>Idrostatica si teneva nel trattato di Archimede come perfetta, per cui non si <lb></lb>ridussero in tanti secoli le promozioni di lei, che a mettere le verità pro­<lb></lb>poste dal Siracusano sotto altra forma; l&#039;Idrodinamica, verso la metà del <lb></lb>secolo XVI, fa la sua prima pubblica comparsa. </s>

<s>Diciamo così, perchè il Car­<lb></lb>dano stesso mostra di non esser venuto a dire cose del tutto nuove; anzi <lb></lb>alcune delle sue proposizioni non hanno altro scopo, che di contradire a ciò, <lb></lb>che intorno al moto delle acque avevano insegnato i suoi predecessori. </s></p><p type="main">

<s>Or chi erano costoro, che avevano preceduto l&#039;Autore <emph type="italics"></emph>De rerum varie­<lb></lb>tate?<emph.end type="italics"></emph.end> E, nella mancanza di pubblici documenti, chi altri si penserebbe che <lb></lb>potessero essere, se non i discepoli di Giordano Nemorario, i quali, appli­<lb></lb>cando ai liquidi la promossa scienza del moto, istituirono l&#039;Idrodinamica? </s>

<s><lb></lb>Così fatte promozioni ebbero efficacissimo impulso dalla benefica resurrezione <lb></lb>dei libri meccanici di Archimede, ciò che, mentre vale a determinar l&#039;epoca <lb></lb>in cui esso Giordano scrisse, e incominciò a fiorir la sua scuola; mostra <lb></lb>quanto poco probabile sia l&#039;opinione di chi fa un tale autore molto più an­<lb></lb>tico, e dice essere il trattato di lui <emph type="italics"></emph>De ponderibus<emph.end type="italics"></emph.end> tradotto dal greco. </s>

<s>La sto­<lb></lb>ria della Meccanica ci ha narrato che in cotesto libro s&#039;insegnava a misu­<lb></lb>rare le forze e i loro momenti dal prodotto della massa e della rettitudine <lb></lb>del discenso, ossia dalla massa e dalla velocità, la quale per un medesimo <lb></lb>tempo è proporzionale allo spazio: nè con diversa formola, secondo quegli <lb></lb>insegnamenti, si misurava ciò che i Matematici odierni chiamano <emph type="italics"></emph>quantità<emph.end type="italics"></emph.end><pb xlink:href="020/01/3087.jpg" pagenum="48"></pb><emph type="italics"></emph>di moto.<emph.end type="italics"></emph.end> Ora, essendo anche i liquidi corpi, soggetti come gli altri agli im­<lb></lb>pulsi della gravità naturale, s&#039;intende facilmente che le loro quantità nel­<lb></lb>l&#039;uscire dai vasi, o nel passar per i fiumi, corrispondevano ad altrettante <lb></lb>quantità di moto, le quali perciò volevano essere misurate dalla massa (pro­<lb></lb>porzionale alla grandezza del foro o della sezione dell&#039;alveo) e dalla velocità, <lb></lb>con cui il liquido stesso era mosso. </s>

<s>Che se il corso, invece di essere libero, <lb></lb>si facesse dentro il chiuso di tubi inclinati, la nuova Scienza meccanica <lb></lb>aveva insegnato a desumerne il grado della velocità, non secondo la mag­<lb></lb>giore o minor lunghezza di essi tubi, ma secondo la quantità della discesa <lb></lb>verticale, cosicchè con pari impeto esca l&#039;acqua da bocche disposte lungo <lb></lb>una medesima linea orizontale, qualunque sia l&#039;obliquità del loro scen­<lb></lb>dere dal medesimo punto della conserva. </s>

<s>Quanto fosse questo principio fe­<lb></lb>condo d&#039;importantissime conseguenze, trattandosi di fiumi, che andando o <lb></lb>diretti o tortuosi allo sbocco, è come se corressero in un alveo più o meno <lb></lb>obliquo; si può preveder facilmente anche prima, che venga la storia a dimo­<lb></lb>strarcelo col fatto. </s></p><p type="main">

<s>Così ebbe le sue prime istituzioni, e fece i suoi progressi quella Scienza <lb></lb>idrodinamica, che il Cardano in parte volle confutare, e in parte promovere <lb></lb>nei suoi libri, benchè non apparisca il filo, a cui si riappiccano le sue tra­<lb></lb>dizioni. </s>

<s>Confutando infatti, o accettando le dottrine correnti, non nomina mai, <lb></lb>da Frontino in fuori, nessun Autore particolare. </s>

<s>Nè poteva nominarli, perchè <lb></lb>i Maestri si confondevano nella Scuola, gl&#039;insegnamenti della quale erano <lb></lb>orali e non scritti, o, se scritti, in carte senza l&#039;impronta pubblica della <lb></lb>stampa, benchè non fossero perciò tra gli studiosi di allora meno diffusi. </s>

<s>Di <lb></lb>qui s&#039;intende quanto benefica, a rischiarare il buio di que&#039;secoli, tornasse <lb></lb>l&#039;apparizione dei manoscritti di Leonardo da Vinci, in cui si specchia, non <lb></lb>la particolare sapienza dell&#039;uomo, ma e del tempo in cui visse, e di quello <lb></lb>che più prossimamente l&#039;aveva preceduto. </s></p><p type="main">

<s>Quell&#039;apparizione, dopo tre secoli, parve che suscitasse nell&#039;animo degli <lb></lb>studiosi un senso molto simile a quello che, a incontrarsi nel cappello d&#039;oro <lb></lb>di un fungo, in mezzo alla borraccina e alle foglie secche del bosco, prova <lb></lb>la villanella, la quale stupisce lieta dell&#039;improvvisa apparizion solitaria, per­<lb></lb>chè nulla aveva mai visto, e nulla saputo della sottilissima rete del micelio. </s>

<s>Gli <lb></lb>stupefatti lettori proclamarono allora Leonardo creatore dal nulla della Scienza <lb></lb>enciclopedica, e lo adorarono come un Dio più vero e onnipotente di quello <lb></lb>descrittoci da Mosè, che dianzi avevano deriso. </s>

<s>I più temperati si contenta­<lb></lb>rono di dire che non prima d&#039;oggidi s&#039;è rivolto lo studio ai manoscritti di­<lb></lb>vini, perchè a tanta altezza non era possibile risalisse l&#039;ingegno degli stu­<lb></lb>diosi, se non da poi che gli avessero impennate le ali Galileo e il Newton, <lb></lb>non inventori in realtà, ma banditori o espositori di una sapienza più antica. </s>

<s><lb></lb>Strane opinioni, che non s&#039;intenderebbe come potessero essere invalse in <lb></lb>tempi, in cui la teoria delle evoluzioni lente e progressive, dalla storia na­<lb></lb>turale, s&#039;è tanto audacemente estesa alla psicologia; se non si ripensasse che <lb></lb>i sistemi filosofici più declamati sempre anche sono i meno compresi. </s></p><pb xlink:href="020/01/3088.jpg" pagenum="49"></pb><p type="main">

<s>Sembrerebbe dunque che fosse ora il tempo di dimostrare, come nem­<lb></lb>meno l&#039;ingegno di Leonardo da Vinci si sottrasse all&#039;impero di una legge, <lb></lb>che è generalissima, e naturale a tutte le cose. </s>

<s>E perchè, concedendo che <lb></lb>sia così, è necessario ammettere un subietto, che venendo a perfezionarsi, in <lb></lb>virtù dell&#039;evoluzione, doveva essere prima difettivo in sè stesso; a ogni passo, <lb></lb>fra le ammirate scritture di Leonardo, ne ricorrono alcune, che accennano <lb></lb>all&#039;imperfezione, e ai difetti proprii alle scienze, specialmente fisiche, le quali <lb></lb>abbiano incominciato pur ora a movere dai loro principii. </s></p><p type="main">

<s>In questi giorni Teodoro Sabachnikoff ha pubblicato, dai manoscritti <lb></lb>della R. biblioteca di Windsor, i primi fogli <emph type="italics"></emph>Dell&#039;anatomia,<emph.end type="italics"></emph.end> e Mathias Duval <lb></lb>vi premette un discorso, in cui magnifica le scoperte fatte da Leonardo in­<lb></lb>torno alla descrizione delle membra umane, e alla fisiologia delle loro fun­<lb></lb>zioni, senz&#039;avvedersi ch&#039;eran piuttosto le scoperte degli anatomici e de&#039;fisio­<lb></lb>logi di quel tempo, de&#039;quali, insieme con alcune verità, Leonardo stesso <lb></lb>ripete i moltissimi errori. </s></p><p type="main">

<s>Tutte quelle note, che ricorrono ne&#039;primi fogli del MSS. H, del Ra­<lb></lb>vaisson, in soggetto di storia naturale, non sono altro che apologhi, o fatti <lb></lb>ingegnosamente trasportati al morale: e se possono essere un esempio, imi­<lb></lb>tabile anche dagli scrittori d&#039;oggidi, di stile descrittivo, non oltrepassano la <lb></lb>credula semplicità delle narrazioni di Plinio. </s>

<s>In fatto di biologia, la genera­<lb></lb>zione spontanea, e la trasformazione immediata di un essere insensitivo in <lb></lb>un animale, era una di quelle semplicità, che Leonardo aveva comuni col <lb></lb>volgo. </s>

<s>“ La setola del bue, egli scrive, messa in acqua morta di state, pi­<lb></lb>glia sensitività e moto per sè medesima, e paura e fuga, e sente dolore. </s>

<s>E <lb></lb>prova sia che stringendola, e si storce, e si divincola. </s>

<s>Ma riaila nell&#039;acqua: <lb></lb>essa, come di sopra, ripiglia fuga, e levasi dal pericolo ” (MSS. K, fol. </s>

<s>81). </s></p><p type="main">

<s>Senza dubbio i Naturalisti moderni commettono peccato più grave, e <lb></lb>meno scusabile di quello di Leonardo, quando, ingannati dalle medesime <lb></lb>apparenze, concedono l&#039;animalità a certi infusorii. </s>

<s>Ma lasciando star ciò, se <lb></lb>esso Leonardo credeva così facilmente alla trasformazione degli esseri vege­<lb></lb>tanti ne&#039;sensitivi, non fa maraviglia che secondasse la comune opinione, in­<lb></lb>torno alla trasformazione degli elementi. </s>

<s>“ Quando l&#039;aria, si legge altrove, <lb></lb>si converte in pioggia, essa farebbe vacuo, se l&#039;altr&#039;aria non lo proibisse col <lb></lb>suo soccorso, lo quale fa con impetuoso moto, e questo è quel vento, che <lb></lb>nasce di state insieme colle furiose piogge ” (MSS. E, in fine). </s></p><p type="main">

<s>Non è tutta di questa qualità è vero, nè tutta consiste qui la scienza <lb></lb>di Leonardo, ma anche là dove annunzia una proposizione vera, e descrive <lb></lb>qualche fatto osservato, non è poi cosa di tanta maraviglia, che trascenda la <lb></lb>virtù naturale, e la possibile cultura dell&#039;ingegno. </s>

<s>In materia di ottica, per <lb></lb>esempio, è notabile la riduzione di certi fenomeni al principio della persi­<lb></lb>stenza delle immagini sopra la retina. </s>

<s>“ Se l&#039;occhio, che risguarda la stella, <lb></lb>si volta con prestezza in contraria parte, li parrà che quella stella si com­<lb></lb>ponga in una linea curva infocata, e questo accade perchè l&#039;occhio riserva <lb></lb>per alquanto spazio la similitudine della cosa che splende. </s>

<s>E perchè tale im-<pb xlink:href="020/01/3089.jpg" pagenum="50"></pb>pressione dello splendore della stella è più permanente nella pupilla, che non <lb></lb>fu il tempo del suo moto; è che tale impressione dura insieme col moto <lb></lb>in tutti i siti, che passano a riscontro della stella ” (MSS. K, fol. </s>

<s>120). L&#039;in­<lb></lb>crociamento de&#039;raggi, che passano per un piccolo foro, e gli effetti, che ne <lb></lb>conseguono rispetto al modo di vedere l&#039;oggetto, come si descrivono, fra&#039;tanti <lb></lb>luoghi, nel foglio 127 del MSS. K, son delicatissime osservazioni; e i Teo­<lb></lb>remi di prospettiva, sparsi per queste pagine, son tanto numerosi, da avan­<lb></lb>zarne largamente alla compilazione di un libro, ma non sono altro in sostanza <lb></lb>che illustrazioni, o promozioni de&#039;teoremi di Euclide, concernenti le proprietà <lb></lb>della sola luce riflessa. </s>

<s>Della luce rifratta però, e delle applicazioni di lei <lb></lb>agli strumenti ottici, e alla visione, non se ne legge fatto negli ammirati vo­<lb></lb>lumi il minimo cenno, ond&#039;è a concludere che l&#039;Autore sapesse di ottica <lb></lb>quanto ne potessero sapere gli altri più dotti uomini di que&#039;tempi, ignari <lb></lb>tuttavia come lui de&#039;teoremi diottrici dello Snellio, e del Cartesio. </s></p><p type="main">

<s>Fra le note di Leonardo, che possono richiamar l&#039;attenzione de&#039;lettori <lb></lb>e la maraviglia, una delle principali sembra a noi che sia questa: “ La figura <lb></lb>del corpo luminoso, ancora che partecipassi del lungo, in lunga distantia pa­<lb></lb>rerà di rotondo corpo. </s>

<s>Questo si prova nel lume della candela che, benchè <lb></lb>sia lungo pure in lunga distantia pare rotondo. </s>

<s>E questo medesimo può acca­<lb></lb>dere alle stelle, che ancora che fussino come la luna cornute, la lunga di­<lb></lb>stantia le farebbe parere rotonde ” (MSS. C, fol. </s>

<s>8). Chi tali parole rileg­<lb></lb>gendo avrebbe il coraggio di negare a Leonardo il merito di aver prevenuto <lb></lb>Galileo, la principale opera di cui, in confermare la verità della Sintassi co­<lb></lb>pernicana, si riduce in aver dimostrato di fatto che Venere è corniculata, <lb></lb>benchè sempre all&#039;occhio nudo apparisca rotonda? </s>

<s>La difficoltà, allo stesso <lb></lb>Copernico irresolubile, prima della invenzione del Canocchiale, dovette pa­<lb></lb>rarsi alla mente degli Astronomi, infin da quando s&#039;ebbe a tener per certo <lb></lb>che Venere e Mercurio son collocati fra la Terra e il Sole: certezza che, <lb></lb>insieme con Dante e con la massima parte degli uomini dotti, ebbe anche <lb></lb>Leonardo, nonostante che i due detti pianeti apparissero sempre rotondi, ciò <lb></lb>che egli attribuiva come Galileo alla irradiazione ascitizia. </s>

<s>“ Se l&#039;occhio ri­<lb></lb>guarda il lume di una candela lontana 400 braccia, esso lume apparirà a <lb></lb>esso occhio suo riguardatore cresciuto 100 volte la sua vera quantità. </s>

<s>Ma se <lb></lb>li poni dinanzi un bastone (<emph type="italics"></emph>Galileo invece usava una cordicella<emph.end type="italics"></emph.end>) alquanto <lb></lb>più di esso lume grosso, esso bastone occuperà quel lume, che pareva largo <lb></lb>due braccia. </s>

<s>Adunque questo errore viene dall&#039;occhio, che piglia le spetie <lb></lb>luminose, non solamente per lo punto della luce, ma etiam con tutta essa <lb></lb>luce ” (MSS. C, fol. </s>

<s>60). Che se il Nostro avesse anche fatto professione di <lb></lb>copernicanismo perfetto, non sarebbe cosa da stupire, avendo il sistema del <lb></lb>Sole, posto nel centro e immoto, attirato a sè l&#039;attenzione de&#039;più eletti in­<lb></lb>gegni, infin da quando, fra le resuscitate opere di Archimede, s&#039;incominciò <lb></lb>a leggere, e a meditar l&#039;Arenario. </s></p><p type="main">

<s>Chi si crede d&#039;aver ritrovato in Leonardo tutta la scienza del Coper­<lb></lb>nico, di Galileo, e del Newton, o non ha pensato che doveva averla deri-<pb xlink:href="020/01/3090.jpg" pagenum="51"></pb>vata dalle precedenti tradizioni immediate, o ha fatto dire all&#039;Autore altri­<lb></lb>menti, da quel che egli intendeva, specialmente trattenendosi in una sen­<lb></lb>tenza staccata dal contesto. </s>

<s>In un familiare colloquio udimmo una volta un <lb></lb>uomo assai dotto magnificare con grand&#039;enfasi Leonardo da Vinci, per aver <lb></lb>notato ne&#039;suoi volumi che la Terra è di figura sferoidea, più sollevata sotto <lb></lb>il circolo equinoziale, che intorno ai poli. </s>

<s>E perchè possano i nostri Lettori <lb></lb>avvedersi da sè medesimi come si fosse quel buon uomo illuso, trascriveremo <lb></lb>dal foglio 12 del MSS. </s>

<s>E il passo, ch&#039;egli citava, e dove, fra i sommari dei <lb></lb>capitoli trattanti del moto dell&#039;acqua, mette Leonardo stesso anche quello, <lb></lb>in cui si direbbe “ come l&#039;acqua delli mari equinoziali è più alta che le <lb></lb>acque settentrionali, ed è più alta sotto il corpo del Sole, che in nessuna <lb></lb>parte del circolo equinoziale, come si sperimenta sotto il calore dello Stizzo <lb></lb>infocato l&#039;acqua, che mediante tale stizzo bolle, e l&#039;acqua circostante al cen­<lb></lb>tro di tal bollore sempre discende con onda circolare: e come l&#039;acque set­<lb></lb>tentrionale son più basse, che li altri mari, e tanto più, quanto esse son più <lb></lb>fredde, in sin che si convertano in ghiaccio. </s>

<s>” </s></p><p type="main">

<s>Ma cotesto citato libro <emph type="italics"></emph>Delle acque<emph.end type="italics"></emph.end> è quello, che più strettamente si <lb></lb>riferisce al presente nostro discorso, ond&#039;è che dovendosi da noi, come prin­<lb></lb>cipal documento di storia, sottoporre ad esame, dobbiamo prima di tutto <lb></lb>osservar che l&#039;Autore non dette esecuzione al proposito più volte espresso <lb></lb>di metterlo in ordine, ma ne lasciò i materiali, che si trovano per le nu­<lb></lb>merose sue carte informi e dispersi. </s></p><p type="main">

<s>Come rimanessero queste carte, dopo la morte di Leonardo, nella villa <lb></lb>Melzi di Vaprio dimenticate, e come poi la miglior parte di loro venisse alle <lb></lb>mani di Galeazzo Arconati; son cose oramati tanto note, ch&#039;è superfluo il <lb></lb>ripeterle. </s>

<s>Alla famiglia degli Arconati apparteneva il padre Luigi Maria, frate <lb></lb>domenicano, il quale, mettendosi a esaminare e a studiare i curiosi volumi, <lb></lb>ebbe a restar maravigliato di trovar, fra gli scritti di un pittore, tanta copia <lb></lb>di quella Scienza idraulica, dell&#039;istituzion della quale tutta la lode e il me­<lb></lb>rito si dava allora al Castelli. </s>

<s>Con l&#039;intenzione di mostrare a chi fossero tali <lb></lb>lodi e tali meriti per giustizia dovuti, il p. </s>

<s>Arconati, raccogliendo le sparse <lb></lb>note le ordinò in un libro, ch&#039;egli intitolava <emph type="italics"></emph>Del moto e della misura delle <lb></lb>acque.<emph.end type="italics"></emph.end> Il manoscritto pervenne alla Biblioteca barberiniana di Roma, dove, <lb></lb>contro l&#039;intenzione del laborioso compilatore, si rimase dimenticato, infin <lb></lb>tanto che il Venturi, andato a Parigi a ritrovare gl&#039;involati volumi, e mosso <lb></lb>da&#039;medesimi sentimenti, ebbe a ripetere, non meno maravigliato, che da Leo­<lb></lb>nardo era stata l&#039;Idraulica più copiosamente, e più perfettamente trattata che <lb></lb>dal Castelli. </s>

<s>Mossi da queste voci i Raccoglitori d&#039;Autori italiani, che trattano <lb></lb>del moto dell&#039;acque, pubblicarono in Bologna, nel 1828, il manoscritto, che l&#039;Ar­<lb></lb>conati aveva preparato 185 anni prima. </s>

<s>L&#039;edizione, fattasi in tempi, in cui era <lb></lb>difficile il collazionare in Italia le trascrizioni con le note originali; è scorret­<lb></lb>tissima, e nonostante ha giovato agli studiosi, e può giovare tuttavia, non <lb></lb>foss&#039;altro per aver tutto insieme raccolto quel che si squaderna ne&#039;sei volumi <lb></lb>in foglio del Ravaisson-Mollien, e negli altri pubblicati dopo e da pubblicarsi. </s></p><pb xlink:href="020/01/3091.jpg" pagenum="52"></pb><p type="main">

<s>Riducendosi ora sul filo del nostro ragionamento, così l&#039;Arconati come <lb></lb>il Venturi, dal confronto che facevano del Castelli con Leonardo, intendevano <lb></lb>concluderne che questi avesse precorsi i fioritissimi tempi della scuola di Ga­<lb></lb>lileo, e, incominciatosi così a dar fiato alla tuba, se ne diffuse largamente il <lb></lb>suono in quelle esagerazioni, che poco fa si diceva. </s>

<s>Il proposto confronto tra <lb></lb>i due Autori non è cosa da spedirsi in brevi parole, e noi lo rimetteremo <lb></lb>al giudizio, che ne proverrà dalla Storia: basti per ora confermare quel che <lb></lb>altra volta abbiamo accennato, che cioè Leonardo non è creatore, e nem­<lb></lb>meno istitutore della Scienza idraulica, ma cultore e promotore di lei, quanto <lb></lb>ne potess&#039;essere uno studioso di Archimede, qual maestro dell&#039;Idrostatica, e <lb></lb>del Nemorario, qual premostratore della Idrodinamica. </s>

<s>Onde, essendo le scuole <lb></lb>pubbliche, si comprende come Leonardo dovesse avere condiscepoli, sopra i <lb></lb>quali non si vede che s&#039;avvantaggiasse per tanto spazio smisurato. </s>

<s>Se nel <lb></lb>trattare dell&#039;equilibrio de&#039;liquidi ne avesse considerate le pressioni, e la loro <lb></lb>uguaglianza per tutti i versi; se nel trattar del moto avesse scoperta la legge <lb></lb>delle velocità, e ne avesse fatta l&#039;applicazione ai getti parabolici; avrebbe <lb></lb>dato qualche ragionevole motivo di ammirazione, e ne sarebbe in qualche <lb></lb>modo giustificato, o scusato il titolo d&#039;ingegno creatore. </s>

<s>Ma se i Teoremi <lb></lb>archimedei non sa interpetrarli con altro, che con ammettere la leggerezza <lb></lb>positiva, e se ne fa da essa conseguire a dirittura le più false dottrine pe­<lb></lb>ripatetiche; se dagli insegnamenti del Nemorario non sa ricavarne altro, se <lb></lb>non che l&#039;acqua è velocitata a proporzione del numero degli strati soprop­<lb></lb>posti, o delle altezze; e se delle elevazioni e delle ampiezze de&#039;getti liquidi, <lb></lb>fatti con varia inclinazione de&#039;tubi, non sa dar che una regola a caso, o <lb></lb>come egli stesso confessa in di grosso; come dubitar se sia vero ch&#039;egli non <lb></lb>oltrepassò i limiti della Scuola, alla quale s&#039;era educato l&#039;ingegno? </s>

<s>Ma per­<lb></lb>chè si potrebbe dubitare dell&#039;esistenza di questa Scuola, noi ne osserveremo <lb></lb>le tradizioni riversarsi, come sotteraneo fiume che scaturisce, ne&#039;libri del <lb></lb>Cardano, di cui nessuno sospetterà che avesse veduti i Manoscritti di Leo­<lb></lb>nardo da Vinci, per attingerne le dottrine idrauliche, o per confutarle: d&#039;onde <lb></lb>verrà altresì efficacemente provato che del patrimonio della Scienza, benchè <lb></lb>in moneta senza pubblica impronta, si faceva in fin d&#039;allora comune e libe­<lb></lb>rale commercio fra&#039;dotti, e non ingiusto e sterile monopolio. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il libro <emph type="italics"></emph>Del moto delle acque<emph.end type="italics"></emph.end> di Leonardo da Vinci, comunque siasi <lb></lb>dall&#039;Arconati ordinato, contiene l&#039;Idrostatica, l&#039;Idrodinamica, e le applica­<lb></lb>zioni di lei alla così detta <emph type="italics"></emph>misura dell&#039;oncia,<emph.end type="italics"></emph.end> e al regolamento dei fiumi. </s>

<s><lb></lb>La prima parte resulta dai primi teoremi di Archimede, i quali hanno il loro <lb></lb>principal fondamento nella proposizione che la superficie dell&#039;acqua è sfe­<lb></lb>rica, e concentrica con la Terra: proposizione, che Leonardo commentava <pb xlink:href="020/01/3092.jpg" pagenum="53"></pb>con questo discorso: “ Dico che nessuna parte della superficie dell&#039;acqua <lb></lb>per sè non si muove, se ella non discende. </s>

<s>Adunque la spera dell&#039;acqua, non <lb></lb>avendo superficie in nessuna parte da potere scendere, gli è necessario che <lb></lb>per sè essa non si muova. </s>

<s>E se tu ben consideri ogni minima particula di <lb></lb>tal superficie, tu la troverai circondata da altre simili particule, le quali sono <lb></lb>di egual distantia in fra loro dal centro del mondo, e della medesima distan­<lb></lb>tia da esso centro è quella particula, che da queste è circondata. </s>

<s>Adunque <lb></lb>tal particula dell&#039;acqua da sè non si moverà, per essere circondata da sponde <lb></lb>d&#039;uguale altezza. </s>

<s>E così ogni circulo di tali particule si fa vaso alla parti­<lb></lb>cola, che dentro a tal circolo si racchiude, il qual vaso ha circuizione de&#039;sua <lb></lb>labbri d&#039;uguali altezze, e per questo tal particula, insieme con tutte le altre <lb></lb>simili, di che è composta la superficie della spera dell&#039;acqua, per necessità <lb></lb>sarà per sè senza moto, e per conseguenza, essendo ciascuna d&#039;uguale al­<lb></lb>tezza dal centro del mondo, necessità fa essa superficie essere sferica ” <lb></lb>(MSS. F, fol. </s>

<s>26). </s></p><p type="main">

<s>La dimostrazione è, come s&#039;è inteso, condotta dal principio che <emph type="italics"></emph>la su­<lb></lb>perficie dell&#039;acqua per sè non si muove, se ella non discende,<emph.end type="italics"></emph.end> e non di­<lb></lb>scende, se non per la linea del suo moto, ossia per la perpendicolare, se­<lb></lb>condo la prima supposizion di Archimede. </s>

<s>La cosa male interpetrata fu <lb></lb>occasione di gravissimi errori, qual&#039;è quello che s&#039;accennava del Michelini, <lb></lb>e da cui non in tutto andò esente Leonardo. </s>

<s>“ Il centro del fondo del vaso, <lb></lb>egli dice, riceve più peso dell&#039;acqua, che altro loco ” (MSS. H, fol. </s>

<s>68). No­<lb></lb>nostante ciò, la quotidiana volgare esperienza del versare i liquidi anche dalle <lb></lb>pareti de&#039;recipienti, era argomento certo del loro premere, non sul fondo <lb></lb>solo, ma anche lateralmente: e intorno a due figure di vasi, il primo dei <lb></lb>quali s&#039;intendesse pieno d&#039;acqua o d&#039;altra cosa liquida, e il secondo di mi­<lb></lb>glio, di rena o di altra cosa discontinua, nel fol. </s>

<s>62 del MSS. I, si legge: <lb></lb>“ Io voglio sapere quanta forza e peso faran le cose contenute dai due vasi <lb></lb>in tutti i lati de&#039;vasi, cioè che differenza è del peso, che riceve il fondo, e <lb></lb>quanto le pareti, benchè tutto il peso si carica sul fondo. </s>

<s>” </s></p><p type="main">

<s>Non era nemmeno sfuggito alla considerazione di Leonardo che le pres­<lb></lb>sioni laterali crescono via via, secondo la profondità del liquido, intorno a <lb></lb>che, oltre all&#039;averne esperienza nel maggior impeto, con cui si vede uscire <lb></lb>il vino delle botti dal foro più basso, era confermato da ciò, che veniva os­<lb></lb>servando e speculando sui vortici o sui ritrosi. </s>

<s>Domandavasi: “ qual causa <lb></lb>fa l&#039;acqua de&#039;ritrosi stare più alta, che il fondo d&#039;esso ritroso, che in sin <lb></lb>li è pien d&#039;aria? </s>

<s>” (MSS. F, fol. </s>

<s>14). E rispondeva Leonardo esser questa <lb></lb>la causa medesima, per cui sta ritta la trottola, “ che, per la velocità del <lb></lb>suo circonvolubile, perde la potenza, che ha l&#039;inegualità della sua gravezza <lb></lb>intorno al centro del suo circonvolubile, per causa dello impeto, che signo­<lb></lb>reggia esso corpo ” (MSS. E, fol. </s>

<s>5). Ma nell&#039;acqua è col moto centrifugo <lb></lb>congiunto un moto centripeto, dovuto alle spinte laterali. </s>

<s>E perchè l&#039;acqua <lb></lb>spinge più in basso che di sopra, essa restringe più la vacuita al ritroso ” <lb></lb>(<emph type="italics"></emph>Compilazione dell&#039;Arconati,<emph.end type="italics"></emph.end> Bologna 1828, pag. </s>

<s>356). </s></p><pb xlink:href="020/01/3093.jpg" pagenum="54"></pb><p type="main">

<s>Di qui può concludersi che Leonardo non negava farsi le pressioni an­<lb></lb>che lateralmente sui vasi, ma le reputava minime, rispetto a quelle, che si <lb></lb>ricevon dal fondo. </s>

<s>Ond&#039;è che la sentenza <emph type="italics"></emph>L&#039;acqua non pesa manco per <lb></lb>traverso, che per la sua perpendicolare<emph.end type="italics"></emph.end> (MSS. H, fol. </s>

<s>68) non deve già in­<lb></lb>tendersi che le due pressioni siano uguali, ma che per l&#039;una non è da esclu­<lb></lb>dersi l&#039;altra, quasi la giusta interpetrazione del detto si fosse questa: L&#039;acqua <lb></lb>non solamente pesa per la perpendicolare, ma anche per traverso. </s>

<s>O meglio, <lb></lb>si dovrebbe intendere: l&#039;acqua pesa perpendicolarmente, con forza propor­<lb></lb>zionale a quella, che si fa per traverso, secondo il principio idrodinamico, <lb></lb>professato da Leonardo stesso, come vedremo. </s></p><p type="main">

<s>Proseguendo per ora il cominciato argomento, si trovano dal nostro Au­<lb></lb>tore formulate le seguenti proposizioni: “ Tanto peso d&#039;acqua si fuggirà dal <lb></lb>suo sito, quanto è la somma del peso, che essa acqua caccia. </s>

<s>— Tanto fia <lb></lb>il peso, che si sostien sopra l&#039;acqua, quanta è la somma del peso dell&#039;acqua, <lb></lb>che dà luogo a esso peso ” (MSS. H, fol. </s>

<s>92). — L&#039;acqua, che manca nel <lb></lb>loco che occupa la nave, pesa quanto tutto il resto del navilio che la cac­<lb></lb>cia (ivi, fol. </s>

<s>69). Sono in queste sentenze compendiati senza dubbio i teoremi <lb></lb>idrostatici di Archimede, e in sè stesse considerate son vere. </s>

<s>Ma i pesi del­<lb></lb>l&#039;acqua nell&#039;acqua, troppo strettamente rassomigliati ai pesi de&#039;corpi solidi <lb></lb>nell&#039;aria, fanno molto lungi dal vero aberrare Leonardo, il quale misura le <lb></lb>quantità delle pressioni idrostatiche dalla quantità del liquido circonfuso, come <lb></lb>dal resistere al contrappeso suol misurarsi il peso di un corpo posto sopra <lb></lb>l&#039;altro bacino della bilancia. </s>

<s>Di qui è che, nel libro Del moto delle acque, <lb></lb>si trovano proposti e dimostrati i due seguenti falsissimi teoremi: “ I. Del­<lb></lb>l&#039;acque di pari profondità quella, che sarà più stretta, sosterrà meno peso <lb></lb>sopra di sè. </s>

<s>— II. Dell&#039;acque di pari larghezza, quella sosterrà men peso, <lb></lb>che fia più bassa. </s>

<s>” (<emph type="italics"></emph>Compilazione<emph.end type="italics"></emph.end> cit., pag. </s>

<s>412). </s></p><p type="main">

<s>Si venivano a rinnovellare così le peripatetiche fallacie antiche, lusin­<lb></lb>gando la ragione con questo discorso: “ Provasi la prima, perchè, ficcan­<lb></lb>dosi la barca nell&#039;acqua, per il peso da lei contenuto, s&#039;alza l&#039;acqua. </s>

<s>Ma <lb></lb>con questa differenza che, quando è l&#039;acqua larga che s&#039;alza v. </s>

<s>g. </s>

<s>un palmo, <lb></lb><figure id="id.020.01.3093.1.jpg" xlink:href="020/01/3093/1.jpg"></figure></s></p><p type="caption">

<s>Figura 16.<lb></lb>per la barca, che col suo peso si ficca <lb></lb>verso il fondo, anche, per tale profon­<lb></lb>darsi della barca l&#039;altezza di un palmo, <lb></lb>un palmo l&#039;acqua si viene ad alzare, e <lb></lb>gran peso acquista. </s>

<s>E quanto maggior <lb></lb>peso acquista, tanto maggior peso sostiene. </s>

<s><lb></lb>Ma quando è stretta, per essere poca <lb></lb>somma di acqua, che nel profondarsi della <lb></lb>barca s&#039;alza; ancora poco peso acquista, <lb></lb>e poco peso può sostenere. </s>

<s>E per questo <lb></lb>l&#039;acqua qui da basso (fig. </s>

<s>16) del vaso <lb></lb>minore DH, quale con la sua acqua circonda il peso posto sopra l&#039;aria, non pesa <lb></lb>sopra essa aria, quanto fa il peso, che le è posto di sopra, sopra essa acqua, <pb xlink:href="020/01/3094.jpg" pagenum="55"></pb>come fa l&#039;acqua del vaso maggiore, la quale è fatta tanto alta sopra a tal aria, <lb></lb>che sostiene il peso, ed ha acquistato per tale altezza tanto peso, che ella <lb></lb>è potente a spingere l&#039;aria in su, con il peso che le è posto di sopra, quanto <lb></lb>sia potente tal peso a premerla in giù ” (ivi). Da questi medesimi principii <lb></lb>si concludono le ragioni dell&#039;altro annunziato teorema, per intender bene <lb></lb>le quali è da sapere che Leonardo professava, insieme con altri falsi prin­<lb></lb>cipii peripatetici, anche questo: “ Tutti gli elementi, fuori del loro sito, de­<lb></lb>siderano a esso sito ritornare, e massime aria e fuoco, acqua e terra ” <lb></lb>(MSS. C, fol. </s>

<s>26): e come in questi riconosceva una gravità naturale; così <lb></lb>a quelli attribuiva una leggerezza positiva. </s>

<s>Di qui è che, trattandosi de&#039;so­<lb></lb>lidi immersi ne&#039;liquidi, sempre attribuisce l&#039;Autore le spinte sursum all&#039;aria, <lb></lb>la quale tanto più efficacemente è costretta a operare, quanto alla tendenza <lb></lb>sua naturale s&#039;aggiunge l&#039;estrusione, provocata dal peso dell&#039;acqua che la <lb></lb>circonda. </s>

<s>Ed essendo il peso proporzionale alla massa, è facile intendere come <lb></lb>da così falsi principii conseguissero le falsità de&#039;sopraddetti due teoremi. </s></p><p type="main">

<s>Da questi medesimi principii, sostituiti a quello delle pressioni idrosta­<lb></lb>tiche riflesse, ragionando Leonardo, spiegava come mai un corpo specifica­<lb></lb>mente più grave dell&#039;acqua, qual&#039;è la materia, di che si compongono le navi, <lb></lb>così facilmente galleggi, in virtù cioè, egli diceva, della leggerezza dell&#039;aria, <lb></lb>che si contrappone, e fa equilibrio alla gravità del composto del legno duro <lb></lb>e del ferro, che per sè andrebbe necessariamente al fondo. </s>

<s>“ Tutto il peso <lb></lb>della barca, posto al livello dell&#039;acqua, è fatto uguale ad altrettant&#039;acqua, <lb></lb>computato la levità dell&#039;aria, che li sta di sotto, la quale la tiene in tale al­<lb></lb>tezza. </s>

<s>Questa proposizione resta provata così: Imperocchè, a fare che l&#039;aria <lb></lb>della barca resti a livello con l&#039;acqua che la circonda, necessità vuole che, <lb></lb>quanto l&#039;aria della barca supera in levità la detta acqua, che la circonda, <lb></lb>tanto il peso della barca venga proporzionatamente a superare il peso del­<lb></lb>l&#039;acqua, sicchè, tra la levità dell&#039;aria, e gravità del peso nella barca, si faccia <lb></lb>un misto di tanta gravità, quanto è quella dell&#039;acqua ” (<emph type="italics"></emph>Compilaz.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>410). </s></p><p type="main">

<s>Le obiezioni, che poi fecero gli Accademici del Cimento, per confutare <lb></lb>con le loro esperienze l&#039;errore della leggerezza positiva, anche si pararono <lb></lb>innanzi alla mente di Leonardo. </s>

<s>Ma egli vi si trovò impacciato, e per dar­<lb></lb>sele in qualche modo risolute, s&#039;acquietò finalmente in un paralogismo: <lb></lb>“ Egli è un pozzo, così scrive, il quale ha nel suo fondo un otro di tal <lb></lb>grandezza, e in tal modo situato, che di sotto e da lato non si trova più di <lb></lb>un dito di grossezza d&#039;acqua, in modo che l&#039;acqua, che riposa sul fondo, <lb></lb>pesa libbre 100, e quella, che si posa sopra della baga, pesa libbre 10,000. <lb></lb>Se così è, la baga scoppierà, avendo sopra sè tanto peso. </s>

<s>E se quel peso non <lb></lb>la preme, che lo sostiene? </s>

<s>E se pure esso fussi sostenuto, perchè avrebbe <lb></lb>a passare l&#039;otre sopra l&#039;acqua? </s>

<s>E se pure l&#039;acqua carica sopra il suo fondo, <lb></lb>perchè non patisce passione un uomo, passione di peso, stando sopra il suo <lb></lb>fondo? </s>

<s>Adunque, se la baga sostiene l&#039;acqua, la baga toglie il peso di essa <lb></lb>acqua al fondo del pozzo ” (MSS. A, fol. </s>

<s>25). </s></p><p type="main">

<s>L&#039;ipotesi, in un&#039;altra nota, si riduce, e si presenta così sotto forma di <pb xlink:href="020/01/3095.jpg" pagenum="56"></pb>tesi: “ Io ti voglio mostrare in che modo l&#039;acqua può essere sostenuta dal­<lb></lb>l&#039;aria, essendo da quella divisa e separata. </s>

<s>Certo se tu hai in te ragione, io <lb></lb>credo che tu non mi negherai che, essendo una baga nel fondo dell&#039;acqua <lb></lb>di un pozzo, la qual baga tocchi tutti i lati del fondo d&#039;esso pozzo, in modo <lb></lb>che acqua non possi passare sotto lei; questa baga, essendo piena di aria, <lb></lb>non farà minor forza d&#039;andare alla superficie dell&#039;acqua a ritrovare l&#039;altra <lb></lb>aria, che si facci l&#039;acqua a volere toccare il fondo del pozzo. </s>

<s>E se questa <lb></lb>baga vuole andare in alto, ella spingerà in alto l&#039;acqua a lei soprapposta, e <lb></lb>levando l&#039;acqua in alto ella scarica il fondo del pozzo, onde quasi esso pozzo, <lb></lb>a questa ragione, potrebbe stare senza fondo ” (MSS. C, fol. </s>

<s>26); </s></p><p type="main">

<s>La verità si è che il fondo è gravato invece da tutt&#039;insieme il peso della <lb></lb>baga, e dell&#039;acqua che le sovrasta, ed è notabile che Leonardo non faccia <lb></lb>differenza dal primo esempio, in cui si supponeva che l&#039;otre avesse l&#039;acqua <lb></lb>da&#039;lati e di sotto, a questo, in cui la baga l&#039;ha solamente di sopra: e non <lb></lb>attendesse il fatto che là si vede l&#039;aria essere spinta alla superficie, e qua <lb></lb>rimanersi immobile nel fondo, sopra cui scoppierebbe necessariamente, quando, <lb></lb>per la grande altezza del liquido superiore, non potesse resisterne la pressione. </s></p><p type="main">

<s>Si vede che il divino uomo, l&#039;ammirabile ingegno non sempre seppe <lb></lb>sollevarsi sulla volgare turba peripatetica, vizio della quale era di accomo­<lb></lb>dar l&#039;esperienze alle preconcette opinioni: e se si debba giudicare da&#039;ma­<lb></lb>noscritti di lui si direbbe che l&#039;Idrostatica, tutt&#039;altro ch&#039;esservi creata o <lb></lb>promossa, è anzi ritirata indietro da quella dirittura, a che l&#039;avevano avviata <lb></lb>i Platonici, i quali, come s&#039;ha per l&#039;esempio di Seneca, applicarono i teo­<lb></lb>remi archimedei a dimostrare sperimentalmente che non si dà leggerezza <lb></lb>positiva, e che gravi e lievi non son le cose per sè stesse, ma che, per com­<lb></lb>parazione col mezzo, si dicono tali. </s></p><p type="main">

<s>L&#039;Idrodinamica dicemmo esser nata nel secolo XV, per l&#039;applicazione <lb></lb>che si fece a&#039;liquidi delle nuove dimostrate proprietà del moto dei gravi. </s>

<s><lb></lb>Leonardo stesso cita il libro <emph type="italics"></emph>De proportionibus<emph.end type="italics"></emph.end> di Alberto di Sassonia, in <lb></lb>cui si formulava la legge delle potenze, le quali stanno in ragion composta <lb></lb>delle velocità e delle masse. </s>

<s>“ Dice Alberto di Sassonia, nel suo <emph type="italics"></emph>Di propor­<lb></lb>tione,<emph.end type="italics"></emph.end> che, se una potentia move un mobile con certa velocità, che moverà <lb></lb>la metà di esso mobile in duplo veloce. </s>

<s>La qual cosa a me non pare, im­<lb></lb>perocchè lui non mette che questa tale potentia adoperi l&#039;ultima sua vale­<lb></lb>tudine ” (MSS. I, fol. </s>

<s>120). </s></p><p type="main">

<s>Si censura dunque dal Nostro la proposizione del Sassone, discepolo del <lb></lb>Nemorario, come poco precisa, e no come falsa. </s>

<s>Anzi, pur che s&#039;intenda che <lb></lb>la potenza venga nel mobile tutta esaurita, riconosceva la proposizione stessa <lb></lb>per così vera, che dava per altrettante verità i corollari immediati di lei. </s>

<s><lb></lb>Chiamata P la potenza, M il mobile e V la velocità, se sostituiscasi alla ve­<lb></lb>locità stessa la relazione tra lo spazio S, e il tempo T, avremo quella me­<lb></lb>desima equazione espressa sotto l&#039;altra forma P=(M.S)/T, e perchè (M.S)/T= <lb></lb>M/2.2S/T=M/2.S:T/2, di qui si vede la ragione de&#039;corollari, che da Leonardo <pb xlink:href="020/01/3096.jpg" pagenum="57"></pb>stesso si trovano così scritti: I. </s>

<s>Se una potentia move un corpo, nun quanto <lb></lb>tempo, la medesima potentia moverà la metà di quel corpo, nel medesimo <lb></lb>tempo, due volte quello spatio. </s>

<s>II. </s>

<s>Se alcuna virtù moverà alcun mobile, per <lb></lb>alcuno spatio, ine qual tempo, (<emph type="italics"></emph>in qualche tempo<emph.end type="italics"></emph.end>) la medesima virtù mo­<lb></lb>verà la metà di quel mobile, in tutto quello spatio, la metà di quel tempo ” <lb></lb>(MSS. F, fol. </s>

<s>51). </s></p><p type="main">

<s>Come poi l&#039;equazione della potenza, data dal Nemorario, e applicata da <lb></lb>Alberto, si teneva che fosse vera per sè anche dal Nostro; così secondo la <lb></lb>verità s&#039;applicava da lui stesso al moto delle acque. </s>

<s>In due fiumi dunque, <lb></lb>o in due distinte sezioni di un medesimo fiume, le potenze motrici son mi­<lb></lb>surate dal prodotto delle moli dell&#039;acqua, contenuta in esse sezioni, e delle <lb></lb>velocità respettive, di modo che, essendo simboleggiate da P, P′ le dette po­<lb></lb>tenze, e da V, V′ le velocità, secondo le quali son sollecitate le corrispon­<lb></lb>denti sezioni S, S′, abbiamo le due equazioni P=S.V, P′=S′.V′. </s></p><p type="main">

<s>Ora, nel libro dell&#039;Arconati che teniamo sott&#039;occhio, si trova compilata <lb></lb>anche questa proposizione: “ Il moto d&#039;ogni fiume, con egual tempo, dà in <lb></lb>ogni parte della sua lunghezza egual peso d&#039;acqua. </s>

<s>E questo accade perchè, <lb></lb>se il fiume nello sboccamento che fa scarica un tanto peso d&#039;acqua, in tanto <lb></lb>tempo, necessità vuole che, in luogo dell&#039;argine scaricata, succeda un altret­<lb></lb>tanto peso di acqua, in altrettanto tempo, quale si muova dalla parte imme­<lb></lb>diatamente antecedente, e così successivamente, in luogo di quest&#039;altra acqua, <lb></lb>succeda un altrettanto peso, insintanto che s&#039;arrivi alla prima parte della <lb></lb>lunghezza del fiume. </s>

<s>Altrimenti, se nello sboccamento si scaricasse maggior <lb></lb>somma di acqua, di quella che si trova al principio del fiume; seguirebbe <lb></lb>che nel mezzo del canale l&#039;acqua di continuo s&#039;andasse sminuendo. </s>

<s>E per <lb></lb>il contrario, se nel medesimo sboccamento passasse minor somma di acqua, <lb></lb>di quella che entra al suo nascimento; l&#039;acqua di mezzo crescerebbe conti­<lb></lb>nuamente. </s>

<s>Ma l&#039;uno e l&#039;altro è manifestamente falso, dunque il moto di ogni <lb></lb>fiume, con ugual tempo, dà in ogni parte della sua larghezza uguale peso <lb></lb>di acqua ” (pag. </s>

<s>427): ossia, riducendosi alla formula sopra scritta, P è <lb></lb>uguale a P′, e perciò S:S′=V′:V, conseguenza che Leonardo, nel suo <lb></lb>proprio linguaggio, significava: “ Tanto quanto crescerai il fiume di lar­<lb></lb>ghezza, tanto diminuirai la qualità del suo movimento: Tanto quanto di­<lb></lb>minuirai la larghezza del fiume, tanto crescerai la qualità del suo movi­<lb></lb>mento ” (ivi). </s></p><p type="main">

<s>Così, il teorema principalissimo, che le velocità e le sezioni si rispon­<lb></lb>dono contrariamente, veniva provato per ragion matematica, ma Leonardo <lb></lb>soggiungeva che poteva confermarsi altresì per le esperienze, o per gli esempi, <lb></lb>fra&#039;quali ne sceglie uno assai efficace, tolto da un esercito costretto a pas­<lb></lb>sare per varie ampiezze di luogo, che, a voler mantenersi unito, debbono i <lb></lb>soldati tanto affrettare il passo di più, quanto il luogo stesso è più stretto. <lb></lb></s>

<s>“ Se fia uno loco, che abbi tre varie larghezze, le quali si contengano in­<lb></lb>sieme, e la prima minore di larghezza entri nella seconda quattro volte, e <lb></lb>la seconda entri due volte nella terza; dico che li uomini, che compieranno <pb xlink:href="020/01/3097.jpg" pagenum="58"></pb>colle loro persone i detti lochi, che avranno a essere in continuo cammino; <lb></lb>che, quando li uomini del maggiore loco faranno uno passo, che quelli della <lb></lb>seconda minore stantia ne faran due; e quelli del terzo loco, che è minore <lb></lb>il quarto che il secondo loco, in quel medesimo tempo, faranno otto passì, <lb></lb>e che questa medesima proportione troverai in tutti i movimenti, che pas­<lb></lb>sano per varie larghezze di lochi ” (MSS. A, fol, 37). Fra&#039;quali movimenti <lb></lb>Leonardo non annovera solamente quelli fatti dai liquidi, <emph type="italics"></emph>non condensabili <lb></lb>nè rarefattibili<emph.end type="italics"></emph.end> (MSS. E, fol. </s>

<s>71), ma quelli stessi fatti dai fluidi elastici, <lb></lb>come dall&#039;aria. </s>

<s>“ Il vento, nel passare gli stremi dei monti, si fa veloce e <lb></lb>denso, e quando discorre di là dalli monti si fa raro e tardo, a similitudine <lb></lb>dell&#039;acqua, che sbocca di stretto canale in largo pelago ” (ivi, fol. </s>

<s>54). </s></p><p type="main">

<s>La legge universalissima, applicata a ogni sorta di fluidi, che abbiamo <lb></lb>trovata scritta da Leonardo da Vinci, era comunemente nota nella Scuola, <lb></lb>alla quale egli apparteneva, e da essa la ricevè il Cardano, e la divulgò nel <lb></lb>cap. </s>

<s>VI del primo libro <emph type="italics"></emph>De rerum varietate<emph.end type="italics"></emph.end> dove, trattando delle acque, dice <lb></lb>che le ragioni de&#039;loro moti, così utili a sapersi, dipendono essenzialmente da <lb></lb>questi due principii: “ alterum quod iuxta foraminis amplitudinem aqua de­<lb></lb>fertur; alterum quod iuxta impetum. </s>

<s>Nam si reliqua paria sint, quae per <lb></lb>angustum foramen et lente exit paucior est: contra, quae per ampliora et <lb></lb>patentiora loca maioreque impetu. </s>

<s>Porro ratio foraminis, si ad basim refe­<lb></lb>ratur, eamdem retinebit proportionem, atque ideo simplicissima est. </s>

<s>Ponatur <lb></lb><figure id="id.020.01.3097.1.jpg" xlink:href="020/01/3097/1.jpg"></figure></s></p><p type="caption">

<s>Figura 17.<lb></lb>enim quod AB (fig. </s>

<s>17), inxta altitudinem AC, qua­<lb></lb>dratam, ita ut AB sit unum, et locus super quem <lb></lb>aqua transit, emittat unciam aquae: dico quod non <lb></lb>mutato situ si BD, DE, EF aequales sint AB, <lb></lb>quod iuxta eamdem altitudinem profluunt unciae <lb></lb>singulae. </s>

<s>Ita, quod per AD unciae duae, per AE <lb></lb>tria, per AF quatuor, et ita de aliis quotquot fuerint. </s>

<s>Nam seorsum per BD, <lb></lb>ex supposito, flueret uncia et per DF, et per EF, ubi adessent latera et al­<lb></lb>titudo quanta est AC. </s>

<s>Sed aqua, quae fluit per AB, nec impedit nec iuvat <lb></lb>eam quae fluit per BD, nec, quae per BD, eam quae per DE, atque ita de <lb></lb>aliis. </s>

<s>Constat igitur quod ut multiplex, aut quam proportionem habebit AF <lb></lb>ad AB, seu AD, aut alia quaepiam; eamdem proportionem habebit aqua <lb></lb>fluens secundum latitudinem AF, vel AD, altitudinem autem AC ad unciam ” <lb></lb>(Basilaee 1581, pag. </s>

<s>61, 62). </s></p><p type="main">

<s>Questo dice il Cardano, per quel che riguarda l&#039;ampiezza delle sezioni. </s>

<s><lb></lb>Per quel che poi riguarda le proporzioni degl&#039;impeti, soggiunge che questi <lb></lb>sono secondo l&#039;altezze delle discese, come si vede ne&#039;vasi vinarii: “ Impe­<lb></lb>tus vero aquae fit, vel ob descensus magnitudinem, vel quia protruditur. </s>

<s><lb></lb>Unde videmus in vinariis vasis, per siphunculos in medio et imo aequales, <lb></lb>celerius impleri cirneas, quam per eos, qui in suprema parte positi sunt ” <lb></lb>(ibid., pag. </s>

<s>62). E perchè “ quae velocius labitur maiore etiam copia exit ” <lb></lb>(ibid., pag. </s>

<s>63), e son le velocità proporzionali alle altezze; saranno ad esse <lb></lb>altezze pure proporzionali le quantità d&#039;acqua uscita in pari tempo dalla me-<pb xlink:href="020/01/3098.jpg" pagenum="59"></pb>desima, o da uguale sezione: ciò che esattamente riscontra con la proposi­<lb></lb>zione scritta da Leonardo: “ Dell&#039;acqua, che non manca di una ordinata <lb></lb>altezza nella sua superficie, tale sarà la quantità dell&#039;acqua, che versa per <lb></lb>un dato spiracolo in un dato tempo, quale quella della data altezza di esso <lb></lb>spiracolo. </s>

<s>Dico che se B (fig. </s>

<s>18) versa in un tempo una quantità d&#039;acqua, <lb></lb><figure id="id.020.01.3098.1.jpg" xlink:href="020/01/3098/1.jpg"></figure></s></p><p type="caption">

<s>Figura 18.<lb></lb>che C verserà due tanti acqua, nel medesimo tempo, perchè ha <lb></lb>due tanti più peso d&#039;acqua sopra di sè ” (MSS. F, fol. </s>

<s>53). </s></p><p type="main">

<s>La legge delle velocità proporzionali alle pressioni derivava <lb></lb>immediatamente dalla prima supposizion di Archimede. </s>

<s>E per­<lb></lb>chè sembrava che non si dovessero ammettere, secondo queste <lb></lb>dottrine, altre pressioni, che le perpendicolari sul fondo dei vasi, <lb></lb>e l&#039;esperienze dimostravano manifestamente che si fanno anche <lb></lb>sui lati; di qui nascevano difficoltà, da mettere a dura prova <lb></lb>gl&#039;ingegni speculativi. </s>

<s>Il Cardano si propone, fra gli altri, a risolvere <lb></lb>anche il problema: “ Cur aquae a lateribus etiam stantium paludum effu­<lb></lb>sae, per rimas tabularum impetum secum afferant ” (<emph type="italics"></emph>De rerum var.<emph.end type="italics"></emph.end> cit., <lb></lb>pag. </s>

<s>69). E risponde che sarebbe cosa di facile spiegazione, contentandoci di <lb></lb>dire, come avevano detto i suoi predecessori, fra&#039;quali abbiamo ritrovato an­<lb></lb>che Leonardo da Vinci; che l&#039;acqua superiore preme anche dai lati. </s>

<s>“ Ve­<lb></lb>rum ex nodo, immediatamente soggiunge, nodus oritur, nam verisimile non <lb></lb>est premi a tota aqua, neque enim proportio motus servari videtur, cum <lb></lb>ex vase vinario tam parvo nec pleno adeo celeriter vinum effundatur, ut, si <lb></lb>iuxta proportionem multitudinis totius aquae id fieret, necesse esset impetum <lb></lb>illum esse multo maiorem, ac pene insuperabilem. </s>

<s>Si vero non a tota aqua <lb></lb>compressio fiet, questio manet. </s>

<s>Dicimus itaque aquam totam premi, et ut <lb></lb>premitur premere, sed non adeo vehementer, quia, dum premuntur partes, <lb></lb>et ipsae premunt, quamobrem pars illa quae exit a tota premitur, sed a re­<lb></lb>motiore multo minus: vehementer vero a proxima, nec etiam aequaliter ab <lb></lb>aequaliter distantibus, sed vehementer ab ea, quae in directo est effluentis, <lb></lb>usque ad adversam ripam: parum vero ab ea, quae est a laterihus, et iuxta <lb></lb>fluminis aut rivi longitudinem posita, nec ab hac etiam aequaliter, sed ab ea <lb></lb>quae antecedit nullo modo. </s>

<s>Ab ea autem, quae in superiore loco, adhuc di­<lb></lb>versa ratione, siquidem a proximiore plus, a remotiore autem minus ” (ibid.). </s></p><p type="main">

<s>Benchè il problema non sia a questo modo risoluto, pure è molto lo­<lb></lb>devole il Cardano, per aver fatto sforzi così generosi, i quali avrebbero po­<lb></lb>tuto rendergli buon frutto, se avesse saputo fermarsi in quella verità, bale­<lb></lb>natagli alla mente, <emph type="italics"></emph>aquam totam premi et ut premitur premere.<emph.end type="italics"></emph.end> Leonardo, <lb></lb>dall&#039;altra parte, come fu più leggero in questa contemplazione, così, nell&#039;ap­<lb></lb>plicarla alle curve descritte dai getti liquidi, parve più audace. </s>

<s>Egli si fa <lb></lb>questa domanda: “ Se una botte ha in sè il vino alto quattro braccia, e <lb></lb>getta il vino lontano da sè quattro braccia; se quando il vino sarà nel ca­<lb></lb>lare disceso all&#039;altezza di due braccia della botte, getterà ella il vino per la <lb></lb>medesima cannella ancora due braccia: cioè, se il calo e l&#039;empito del get­<lb></lb>tare della cannella diminuisce con uguale proporzione o no; e se, essendo la <pb xlink:href="020/01/3099.jpg" pagenum="60"></pb>botte piena, e s&#039;empierà per la sua cannella due boccali per ora, se doverà <lb></lb>a questa ragione empiere un sol boccale per ora, colla medesima cannella <lb></lb>che versava ” (MSS. I, fol. </s>

<s>73). </s></p><p type="main">

<s>Il problema fu risoluto affermativamente in questa nota, scritta di rin­<lb></lb>contro a una figura simile alla nostra 19. “ È in natura che una medesima <lb></lb><figure id="id.020.01.3099.1.jpg" xlink:href="020/01/3099/1.jpg"></figure></s></p><p type="caption">

<s>Figura 19.<lb></lb>canna può gettare lontan da sè infinita distantia, perchè infi­<lb></lb>nita può essere l&#039;altezza ingorgata dell&#039;acqua, che carica sopra <lb></lb>tale uscita di acqua, come fa la canna BAC, che può essere <lb></lb>d&#039;infinita altezza coll&#039;immaginazione, e in ogni grado d&#039;altezza <lb></lb>la canna AC acquista gradi di distantia nel gettare da lon­<lb></lb>tano ” (ivi, fol. </s>

<s>14). </s></p><p type="main">

<s>Il teorema consegue immediatamente dal principio, che <lb></lb>ammette le velocità proporzionali alle altezze, ma l&#039;applica­<lb></lb>zione, che se ne fa agli efflussi laterali, è arbitraria, come <lb></lb>arbitraria è la seguente proposizione, insieme col problema che ne dipende: <lb></lb><figure id="id.020.01.3099.2.jpg" xlink:href="020/01/3099/2.jpg"></figure></s></p><p type="caption">

<s>Figura 20.<lb></lb>“ Quella proporzione, che averà BC (fig. </s>

<s>20) con AC, tale <lb></lb>proporzione troverai nelle due quantità del vino, che si <lb></lb>trova in nel vasello, che cagione desse di versar più presso <lb></lb>o lontano: cioè se il vino del vasello prima versava in C, <lb></lb>essendo pieno, e quando era quasi vuoto versava in A; sappi <lb></lb>che, quando e&#039;verserà in mezzo fra A e C, nel punto B, <lb></lb>il vasello sarà appunto mezzo ” (MSS. C, fol. </s>

<s>5). “ Di qui <lb></lb>puossi conoscere quando sia tratto il vino d&#039;un vasello più <lb></lb>alto o più basso e quanto, sapendo solamente il diametro <lb></lb>di esso. </s>

<s>Fa&#039;così: ricevi il vino, quando è caduto fuori del vasello, e dopo che <lb></lb><figure id="id.020.01.3099.3.jpg" xlink:href="020/01/3099/3.jpg"></figure></s></p><p type="caption">

<s>Figura 21.<lb></lb>la sua curvazione s&#039;è ridotta alquanto perpendicolare <lb></lb>linea, e ricevi in prima AN (fig. </s>

<s>21) nel luogo N, e <lb></lb>nota il punto N. </s>

<s>Dipoi ricevi B nel punto M, e poni <lb></lb>col filo piombato F a punto, dove il vino di dentro <lb></lb>confina dinanzi col suo vasello. </s>

<s>E tanto quanto AO <lb></lb>entra in OP, tanto FN entrerà a proporzione in FM <lb></lb><figure id="id.020.01.3099.4.jpg" xlink:href="020/01/3099/4.jpg"></figure></s></p><p type="caption">

<s>Figura 22.<lb></lb>appunto, essendo i buchi <lb></lb>del vasello di egual gran­<lb></lb>dezza, e così il legno di <lb></lb>grossezza ” (ivi, fol. </s>

<s>6). </s></p><p type="main">

<s>Che poi queste propo­<lb></lb>sizioni non avessero in sè certezza alcuna di scienza <lb></lb>lo riconosce pur troppo bene, e lo confessa Leo­<lb></lb>nardo, nel provarsi a dar regola delle ampiezze, <lb></lb>che secondo le varie inclinazioni delle fistole descri­<lb></lb>vono per aria gli zampilli. </s>

<s>Sotto una figura, imi­<lb></lb>tata qui da noi nella 22, è scritto: “ Prova per fare regola di questi moti. </s>

<s><lb></lb>Faraila con una baga piena di acqua, con molte cannelle di pari busi, posti <lb></lb>per una linea. </s>

<s>Io giudico, così in di grosso, che quanto C si leva più alto <pb xlink:href="020/01/3100.jpg" pagenum="61"></pb>che D, tanto il mezzo dell&#039;arco D si ritroverà più lontano sotto il suo per­<lb></lb>pendicolare in H. Cioè: tanto, quanto D fia più basso di C, tanto H fia più <lb></lb>lontano da O che G. </s>

<s>Vero è che le cannelle, che gettano l&#039;acqua, vogliono <lb></lb>tutte nascere su un piano a livello, e di medesima lunghezza, e poi piegate <lb></lb>a diversi siti ” (ivi, fol. </s>

<s>7). </s></p><p type="main">

<s>Il Cardano non ebbe il coraggio di entrare in così fatte questioni, per­<lb></lb>chè si sentiva mancare la scienza necessaria a risolverle, e dall&#039;altra parte <lb></lb>troppo ben comprendeva che quelle ordinate non si sarebbero potute riferire <lb></lb>a una linea curva, e tanto meno a un arco di cerchio, secondo la curvità <lb></lb>del quale si credeva inflettersi lo zampillo, come in un arco di cerchio si cre­<lb></lb>deva insenarsi le corde lentamente sospese dai due loro estremi. </s>

<s>“ L&#039;arco, <lb></lb>scrive Leonardo, che si genera dalla corda, che s&#039;estende infra le due car­<lb></lb>rucole, poste nel sito della egualità; è una parte della circonferentia di un <lb></lb>cerchio ” (MSS. E, fol. </s>

<s>62). Il Cardano vedeva invece in quella incurvatura <lb></lb>l&#039;apparenza di una parabola e atterrito dalla difficoltà di dimostrarla geome­<lb></lb>tricamente tale, si contentò di osservare che, uscendo l&#039;acqua libera dalla <lb></lb>bocca di un sifone, non prosegue nella sua prima dirittura, nè cade perpen­<lb></lb>dicolare, ma tiene una via di mezzo, descrivendo nelle prime parti del suo <lb></lb><figure id="id.020.01.3100.1.jpg" xlink:href="020/01/3100/1.jpg"></figure></s></p><p type="caption">

<s>Figura 23.<lb></lb>moto una linea, che si rassomiglia molto <lb></lb>a un arco di parabola. </s>

<s>“ Aquae, quae <lb></lb>per canales efferuntur, media linea effluunt <lb></lb>inter lineam descensus et rectam. </s>

<s>Velut <lb></lb>aqua per canalem delata AB (fig. </s>

<s>23) <lb></lb>deberet, toto impetu servato, effundi per <lb></lb>BC. </s>

<s>Et si nullum haberet impetum, per <lb></lb>BD, quod videmus in aquis, quae a late­<lb></lb>ribus canalium, non ab ore effunduntur. </s>

<s>Igitur, iuxta rationem mediam, <lb></lb>feretur primum per partem BE. </s>

<s>Inde eo magis removebitur a C, quo etiam <lb></lb>a B, et ita ad F: infra vero F, recta, per aequidistantem BD ” (<emph type="italics"></emph>De rerum <lb></lb>var.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>65). </s></p><p type="main">

<s>Se però era tuttavia lontano colui, che avrebbe dimostrata la teoria pa­<lb></lb>rabolica de&#039;proietti, il&#039;Nemorario aveva dato già fondamento alla futura Di­<lb></lb>namica galileiana, ponendo il principio che i cadenti lungo piani, comunque <lb></lb>siansi inclinati, raggiungono in fine la medesima velocità, come se fossero <lb></lb>venuti per linea perpendicolare. </s>

<s>Non bisognava per ciò far altro che ridurre <lb></lb>i piani inclinati a canali o a sifoni, perchè, essendo anche l&#039;acqua un corpo <lb></lb>grave, fiorisse nella scuola dello stesso Nemorario questo capitalissimo teo­<lb></lb><figure id="id.020.01.3100.2.jpg" xlink:href="020/01/3100/2.jpg"></figure></s></p><p type="caption">

<s>Figura 24.<lb></lb>rema d&#039;Idrodinamica, da Leonardo così annun­<lb></lb>ziato: “ La obliquità del corso dell&#039;acqua adopera <lb></lb>come se fussi perpendicolare: tanto fa l&#039;obliquità <lb></lb>AM (fig. </s>

<s>24), quanto il perpendicolare AN ” <lb></lb>(MSS. H, fol. </s>

<s>73). Il Cardano poi esplicava il con­<lb></lb>cetto, frettolosamente qui espresso, e da&#039;sifoni <lb></lb>chiusi passando ai canali aperti, mostrava che <pb xlink:href="020/01/3101.jpg" pagenum="62"></pb>ne&#039;vari punti B, C, D.... (fig. </s>

<s>25) le velocità dell&#039;acqua son quelle con­<lb></lb>venienti alle loro cadute, cosicchè giungono allo sbocco E con impeto, come <lb></lb><figure id="id.020.01.3101.1.jpg" xlink:href="020/01/3101/1.jpg"></figure></s></p><p type="caption">

<s>Figura 25.<lb></lb>se fossero da A scese in F, per altezza per­<lb></lb>pendicolare. </s>

<s>“ Cum igitur fluxerit per lon­<lb></lb>gius iter, lineam que eamdem rectam, quanto <lb></lb>magis a principio ortus distiterit, eo velo­<lb></lb>cius movebitur. </s>

<s>Sit enim aqua, quae fluat <lb></lb>per ABCDE. </s>

<s>Sit FE libella, seu AG, ferme <lb></lb>aequidistans: dico ergo quod, cum CL sit dupla BH, et DL eidem tripla, <lb></lb>et GE quadrupla; quod motus etiam erit velocior, quo remotior aqua a <lb></lb>fonte ” (<emph type="italics"></emph>De rerum var.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>72). </s></p><p type="main">

<s>Si sa oramai dalla storia della Meccanica che ambedue i commemorati <lb></lb>Autori professavano il principio, altro fondamento alla dinamica galileiana, <lb></lb>che un corpo sferico, posato sopra un piano perfettamente orizontale, astra­<lb></lb>zion fatta da ogni altro impedimento, può esser mosso da qualunque minima <lb></lb>forza; e che, così essendo mosso, proseguirebbe sempre colla medesima ve­<lb></lb>locità il suo viaggio. </s>

<s>Fatta l&#039;applicazione di questo stesso principio al corso <lb></lb><figure id="id.020.01.3101.2.jpg" xlink:href="020/01/3101/2.jpg"></figure></s></p><p type="caption">

<s>Figura 26.<lb></lb>dell&#039;acqua dentro il tubo AM, perfettamente <lb></lb>livellato (fig. </s>

<s>26), ne&#039;punti A, M, e in tutti <lb></lb>gli altri, variamente distanti dal principio del <lb></lb>moto R; passerà dunque l&#039;acqua ugualmente <lb></lb>veloce; ond&#039;essendo per supposizione i sifoni <lb></lb>AN, MO egualmente inclinati, e di uguale lunghezza, tanto sarà veloce, e <lb></lb>perciò in tanta copia uscirà l&#039;acqua dalla bocca N, quanta ne esce dalla <lb></lb>bocca O, come in una sua nota scrive Leonardo: “ Se tu torrai l&#039;acqua da <lb></lb>una altra acqua, che sia di pari livello, con uguale obliquità, sappi che tanto <lb></lb>fia a torla vicino al loco R, con la caduta AN, quanto lontano in MO ” <lb></lb>(MSS. N, fol. </s>

<s>87). </s></p><p type="main">

<s>Altro corollario del medesimo Teorema è il seguente: Se saranno due <lb></lb>sifoni ugualmente inclinati, ma di varia lunghezza come, AM, AP (nella <lb></lb>passata figura 24) dalla bocca P del più lungo uscirà l&#039;acqua maggiormente <lb></lb>veloce, che dalla bocca M del più corto, perchè l&#039;altezza AQ, alla AN, ha <lb></lb>maggior proporzione. </s>

<s>“ L&#039;acqua cadente da un mdesimo livello, per canali <lb></lb>di eguali obliquità, quella sarà di più veloce corso, che fia di maggiore lun­<lb></lb>ghezza ” (MSS. H, fol. </s>

<s>39). </s></p><p type="main">

<s>Dietro i quali principii è facile intendere come risolvesse Leonardo al­<lb></lb>cuni problemi, che si trovano ne&#039;manoscritti di lui semplicemente proposti, <lb></lb><figure id="id.020.01.3101.3.jpg" xlink:href="020/01/3101/3.jpg"></figure></s></p><p type="caption">

<s>Figura 27.<lb></lb>quali sarebbero per esempio i due seguenti: <lb></lb>I. “ L&#039;acqua AB (fig. </s>

<s>27), che discende, quanto <lb></lb>monterà in BC? ” (MSS. K, fol. </s>

<s>99). La ri­<lb></lb>sposta a ciò, dietro i professati principii, è <lb></lb>manifestamente tale: essendo la discesa retta <lb></lb>AD, l&#039;acqua salirà fino a tal punto O, che le <lb></lb>perpendicolari OE, AD tornino uguali. </s>

<s>— <pb xlink:href="020/01/3102.jpg" pagenum="63"></pb>II. “ L&#039;acqua CN (fig. </s>

<s>28) è piana: domando quanto verserà più presto essa <lb></lb>aqua il canale AC, che il canale BC ” (MSS. H, fol. </s>

<s>89). Un discepolo, così <lb></lb><figure id="id.020.01.3102.1.jpg" xlink:href="020/01/3102/1.jpg"></figure></s></p><p type="caption">

<s>Figura 28.<lb></lb>interrogato, darebbe questa risposta, con piena <lb></lb>sodisfazion del Maestro: Essendo gli spazi AC, <lb></lb>BC, per supposizione uguali, e perciò avendo i <lb></lb>tempi reciproca ragione delle velocità, le quali <lb></lb>stanno come le altezze; l&#039;acqua dunque tanto si <lb></lb>verserà più presto dalla bocca B, che dalla bocca <lb></lb>A, quanto l&#039;altezza CE è maggiore della CD. </s></p><p type="main">

<s>Ritornando sul problema primo, l&#039;acqua giunta in O rimarrà nelle due <lb></lb>canne AB, BO, con congiunzione angolare, senza movimento, e ciò “ perchè, <lb></lb>dice Leonardo, tanto pesa l&#039;acqua AB, quanto l&#039;acqua BO ” (<emph type="italics"></emph>Arconati,<emph.end type="italics"></emph.end><lb></lb>pag. </s>

<s>436). E poi soggiunge nel capitoletto appresso: “ Tal movimento farà <lb></lb>l&#039;acqua per la cicognola qua di sopra ABO qual&#039;essa farebbe se corresse <lb></lb>per la linea AB ” (ivi). Dunque l&#039;elemento liquido A giunto in B ha con­<lb></lb>cepito per la discesa tant&#039;impeto, da risalire in O alla medesima altezza, se­<lb></lb>condo i principii, che poi si professerebbero da Galileo. </s>

<s>Dipende senza dub­<lb></lb><figure id="id.020.01.3102.2.jpg" xlink:href="020/01/3102/2.jpg"></figure></s></p><p type="caption">

<s>Figura 29.<lb></lb>bio da tali principii il teorema noto del Torricelli, <lb></lb>intorno a cui anche Leonardo pensava che, ne&#039;vasi <lb></lb>comunicanti rappresentati per noi dalla fig. </s>

<s>29, il <lb></lb>libero zampillo A, e l&#039;acqua dentro la canna B do­<lb></lb>vevano giungere al livello C del liquido, da cui sono <lb></lb>spinti. </s>

<s>Poi gli venne dubbio se la forza del getto fosse <lb></lb>alquanto maggiore, per non essere impedita dalle <lb></lb>confregazioni con le pareti del tubo, come apparisce da questa nota: “ Se <lb></lb>l&#039;acqua, schizzata in A dalla canna, è mossa da maggior potentia, che da <lb></lb>quella della canna B ” (MSS. K, fol. </s>

<s>98): dubbio risoluto poi dalle espe­<lb></lb>rienze del Mariotte, che confermarono essere veramente così, come Leonardo <lb></lb>stesso aveva sospettato. </s></p><p type="main">

<s>Tanto basti per avere un&#039;idea dello stato, in cui, tra il secolo XV e <lb></lb>il XVI, si trovava l&#039;Idrodinamica. </s>

<s>Ora è da dire delle applicazioni di lei, e <lb></lb>prima di tutto al modo di misurare le acque nel dispensarle a once, per gli <lb></lb>usi del pubblico e dei privati. </s></p><p type="main">

<s>Essendo stato dimostrato che le quantità hanno la ragion composta delle <lb></lb>velocità e delle sezioni, veniva per conseguenza che fossero esse quantità alle <lb></lb>semplici velocità proporzionali, passando l&#039;acqua per la medesima bocca. </s>

<s>“ La <lb></lb>misura dell&#039;once, dice Leonardo, che si danno nelle bocche dell&#039;acqua, son <lb></lb>maggiori o minori, secondo le maggiori o minori velocità dell&#039;acqua, che per <lb></lb>essa bocca passa. </s>

<s>Doppia velocità dà doppia acqua, in un medesimo tempo, <lb></lb>e così tripla velocità, in un medesimo tempo, darà tripla quantità d&#039;acqua ” <lb></lb>(MSS. F, fol. </s>

<s>16). </s></p><p type="main">

<s>Questa legge sarebbe assoluta, se non fossero le velocità soggette ad al­<lb></lb>terazioni, delle quali alcune cause furono avvertite già da Frontino, e dai <lb></lb>Pretori romani, ma assai più ne pensarono i Fisici del secolo XV, alle quali <pb xlink:href="020/01/3103.jpg" pagenum="64"></pb>il nostro Leonardo ne aggiunse altre di suo, riducendole a uu buon numero, <lb></lb>che nonostante sperava di accrescere anche di più, com&#039;apparisce dalla cifra <lb></lb>lasciata in bianco nell&#039;elenco, che di queste XVII intanto lasciava, così, in <lb></lb>una sua nota ordinatamente descritto: “ L&#039;acqua, che versa per una mede­<lb></lb>sima quantità di bocca, si può variare di quantità maggiore o minore per .... <lb></lb>modi, de&#039;quali il I è da essere più alta o più bassa la superficie dell&#039;acqua <lb></lb>sopra la bocca d&#039;onde versa. </s>

<s>— II. </s>

<s>Da passare l&#039;acqua con maggiore o mi­<lb></lb>nore velocità da quell&#039;argine, dov&#039;è fatta essa bocca. </s>

<s>— III. </s>

<s>Da essere più <lb></lb>o meno obliquo il lato di sotto della grossezza della bocca, dove l&#039;acqua <lb></lb>passa. </s>

<s>— IV. </s>

<s>Dalla varietà dell&#039;obliquità de&#039;lati di tal bocca. </s>

<s>— V. </s>

<s>Dalla <lb></lb>grossezza del labbro di essa bocca. </s>

<s>— VI. </s>

<s>Per la figura della bocca: cioè <lb></lb>da essere tonda o quadra o rettangolare o lunga. </s>

<s>— VII. </s>

<s>Da essere posta <lb></lb>essa bocca in maggiore o minore obliquità d&#039;argine, per la sua lunghezza. <lb></lb></s>

<s>— VIII. </s>

<s>Per essere posta tal bocca in maggiore o minore obliquità d&#039;argine, <lb></lb>per la sua altezza. </s>

<s>— IX. </s>

<s>Da essere posta nella concavità o convessità del­<lb></lb>l&#039;argine. </s>

<s>— X. </s>

<s>Da essere posta ovvero in maggiore, o minore larghezza del <lb></lb>canale. </s>

<s>— XI. </s>

<s>Se l&#039;altezza del canale ha più velocità nell&#039;altezza della bocca, <lb></lb>o più tardità che altrove. </s>

<s>— XII. </s>

<s>Se il fondo ha globosità o convessità, a <lb></lb>riscontro di essa bocca o più alte o più basse. </s>

<s>— XIII. </s>

<s>Se l&#039;acqua, che <lb></lb>passa per tal bocca, piglia vento o no. </s>

<s>— XIV. </s>

<s>Se l&#039;acqua, che cade fuor <lb></lb>dalla bocca, cade in fra l&#039;aria, ovvero rinchiusa da un lato, o da tutti, salvo <lb></lb>la fronte. </s>

<s>— XV. </s>

<s>Se l&#039;acqua, che cade rinchiusa, sarà grossa nel suo peso <lb></lb>o sottile. </s>

<s>— XVI. </s>

<s>Se l&#039;acqua che cade, essendo rinchiusa, sarà lunga di ca­<lb></lb>duta o breve. </s>

<s>— XVII. </s>

<s>Se i lati del canale, d&#039;onde discende tale acqua, <lb></lb>saran solli o globulosi ” (ivi, fol. </s>

<s>9). </s></p><p type="main">

<s>Il Cardano, delle cause, che fanno variar le velocità, e perciò le misure <lb></lb>delle acque correnti; non ne annovera molte di più di quelle, venute in <lb></lb>mente a Frontino, a cui volentieri concede che, tanto più se ne attinga da <lb></lb>un fiume, quanto egli è più alto e veloce. </s>

<s>Ma son notabili, fra così fatte cause <lb></lb>modificatrici delle velocità, quelle, che egli attribuisce allo spirare de&#039;venti, <lb></lb>e alla disposizione e figura dei tubi addizionali, benchè sembrino strani gli <lb></lb>effetti, da lui stesso attribuiti alla qualità della materia, di che si compon­<lb></lb>gono essi tubi. </s>

<s>“ Venti enim, si quandoque possint obesse, solent et pro­<lb></lb>desse. </s>

<s>Constat ergo, ubi venti certi regnant, aliquos plus accipere, aliquos <lb></lb>minus longe quam debeant. </s>

<s>Plurimum quoque referre an aqua a latere rivi, <lb></lb>an ab ore sumatur. </s>

<s>Sed haee minora videntur, quandoquidem referat Fron­<lb></lb>tinus, Nervae aetate, Romanos adeo oscitanter aquarum rationem tractasse, <lb></lb>ut dimidio aberrarent. </s>

<s>Plurimum quoque refert si per fistulam, quae plerum­<lb></lb>que metallo constat, aut tubis fietilibus, aut canali ligneo, nam, non ob ma­<lb></lb>teriam differunt, sed quia canalis haud clausus est, verum respirat. </s>

<s>Educuntur <lb></lb>tamen aquae plerumque tubis aut fistulis, quoniam canalis aquam effluen­<lb></lb>tem spargit, ob id igitur privat<gap></gap>rum usus a fistulis et tubis, non autem ea­<lb></lb>ualibus, sumuntur. </s>

<s>Multum quoque refert quomodo calix collo<gap></gap>tur, ut inquit <lb></lb>Frontinus. </s>

<s>Circa collocandos quoque calices observari oportet ut ad lineam <pb xlink:href="020/01/3104.jpg" pagenum="65"></pb>ordinentur, nec alterius inferior calix, alterum superior ponatur: inferior plus <lb></lb>trahit, superior minus ducit, quia cursus aquae ab inferiore rapitur. </s>

<s>Haec <lb></lb>ille ” (<emph type="italics"></emph>De rérum var.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>66). </s></p><p type="main">

<s>Altre cause ritardatrici delle velocità riconosce il Cardano, alcune delle <lb></lb>quali son fra quelle annoverate da Leonardo, ma di cui quegli spesso rende <lb></lb>la&#039;ragione, dedotta da principii fisici più sani, e che risentono talora il leg­<lb></lb>gero alitare di una scienza lontana. </s>

<s>C&#039;incontreremo e c&#039;intratterremo sopra <lb></lb>qualche più notabile esempio di ciò nel ritornare all&#039;elenco di esso Leonardo, <lb></lb>per ritrovarvi i vestigi lasciativi dalla Scienza, talvolta nelle sue cadute, ma <lb></lb>più spesso ne&#039;suoi progressi, primo a notar fra&#039;quali è l&#039;osservazione intorno <lb></lb>al variarsi le velocità, per la varietà del perimetro di una sezione, pur ser­<lb></lb>bandosi dall&#039;area di lei la medesima ampiezza. </s>

<s>La cosa, accennata dianzi <lb></lb>nel sesto numero del detto elenco, è spiegata altrove così, nella sua ragione <lb></lb>geometrica: “ Fra le bocche dell&#039;acqua, poste in altezze uguali sotto la su­<lb></lb><figure id="id.020.01.3104.1.jpg" xlink:href="020/01/3104/1.jpg"></figure></s></p><p type="caption">

<s>Figura 30.<lb></lb>perficie dell&#039;acqua del suo bottino, quella che ha men con­<lb></lb>tatto con l&#039;acqua, che per li passa, meno impedirà il tran­<lb></lb>sito a essa acqua. </s>

<s>A e B (fig. </s>

<s>30) siano le bocche uguali, <lb></lb>A quadrato, e B circolo. </s>

<s>Dico che l&#039;acqua, che passa per <lb></lb>la bocca circolare, arà men contatto che l&#039;acqua, che <lb></lb>passa per il quadrato, uguale a esso circolo, perchè più <lb></lb>lunga è la linea, che circuisce il quadrato, che quella, <lb></lb>che circuisce il tondo ” (MSS. F, fol. </s>

<s>55). </s></p><p type="main">

<s>Da questa proposizione vedeva opportunamente Leonardo scendere un <lb></lb>corollario, che gli dava modo a risolvere il seguente problema: “ Che figura <lb></lb>arà una medesima quantità d&#039;acqua, movendosi per una medesima obliquità <lb></lb>di fondo, a farsi più veloce che sia possibile? </s>

<s>— Fia quella che arà minore <lb></lb>contatto col suo fondo, cioè mezzo cerchio ” (MSS. E, fol. </s>

<s>105). </s></p><p type="main">

<s>In questo argomento osservava il Nostro un&#039;altra cosa importante, messa <lb></lb>così in forma di proposizione: “ Delle bocche uguali, e di uguale altezza, <lb></lb>quella verserà più acqua, in pari tempo, che arà maggiore somma di sè, <lb></lb>nella sua parte inferiore, che nella parte di sopra ” (MSS. F, fol. </s>

<s>54). La <lb></lb>dimostrazione di ciò è affidata tutta all&#039;eloquenza de&#039;segni, rappresentativi <lb></lb>il medesimo triangolo isoscele, ora colla base in alto, ora col vertice, come <lb></lb><figure id="id.020.01.3104.2.jpg" xlink:href="020/01/3104/2.jpg"></figure></s></p><p type="caption">

<s>Figura 31.<lb></lb>si vede in A, B <lb></lb>(fig. </s>

<s>31). Siano le <lb></lb>loro altezze per­<lb></lb>pendicolaritaglia­<lb></lb>te nel mezzo dal­<lb></lb>la orizontale CD. </s>

<s><lb></lb>La EP è maggior <lb></lb>somma della par­<lb></lb>te GHI, e perchè <emph type="italics"></emph>inferior plus rapitur,<emph.end type="italics"></emph.end> secondo lo stesso Frontino, è dun­<lb></lb>que maggiore la quantità dell&#039;acqua velocitata in B, che in A, e perciò <lb></lb>quella, in pari tempo, verserà più di questa. </s></p><pb xlink:href="020/01/3105.jpg" pagenum="66"></pb><p type="main">

<s>Si dispongano similmente il circolo L, e il quadrato M, in modo cioè <lb></lb>che le loro estremità inferiori insistano sulla medesima linea orizontale NO. <lb></lb>È manifesto che la parallela a questa, fatta passare per il centro Q del qua­<lb></lb>drato, prolungata riman sotto al centro P del circolo, per cui, essendo la <lb></lb>quantità dell&#039;acqua RST tutta insieme men premuta della sua uguale quan­<lb></lb>tità UVX, quella passerà men veloce di questa, e perciò in tal caso il cir­<lb></lb>colo, dal mezzo in giù, verserà, in pari tempo, alquanto men del quadrato. </s>

<s><lb></lb>Di qui, comparando le portate di queste due bocche con quell&#039;altre due trian­<lb></lb>golari già dette, si comprende secondo qual ragione sentenziasse Leonardo: <lb></lb>“ Queste quattro bocche sono in fra loro uguali, e co&#039;loro estremi posti in <lb></lb>altezze uguali. </s>

<s>L versa meno, dal mezzo in giù, di M, e men A che B ” <lb></lb>(MSS. F, fol. </s>

<s>54). A che, per rendere queste sperimentali verità più com­<lb></lb>piute, può aggiungersi l&#039;altra conclusione: “ Delle bocche di ugual lar­<lb></lb>ghezza, figura e altezza, quella verserà più acqua in pari tempo, che sarà <lb></lb>in più sottile pariete, ovvero che averà più breve contatto co&#039;lati della sua <lb></lb>bocca ” (ivi, fol. </s>

<s>55). </s></p><p type="main">

<s>In simile proposito, e dietro simili considerazioni, concludeva anche il <lb></lb>Cardano: “ Constat igitur aquarum ductus, non ex fistularum magnitudine <lb></lb>consistere, sed si proportio latitudinis servetur ” <emph type="italics"></emph>(De rer. </s>

<s>var.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>73). <lb></lb>Sia, ritornando indietro sulla XVII figura, CB la bocca dell&#039;oncia, e si vo­<lb></lb>glia quadruplicarla. </s>

<s>Geometricamente si conseguirebbe ciò tanto col quadru­<lb></lb>plicare la semplice larghezza AB, quanto col duplicar questa, e insieme l&#039;al­<lb></lb>tezza AC. </s>

<s>Or benchè, per le cose dimostrate da Euclide, le due aree siano <lb></lb>perfettamente uguali, non si creda però, dice il Cardano, che quattr&#039;oncie <lb></lb>sian versate dall&#039;una, ugualmente che dall&#039;altra, ma faranno differenza no­<lb></lb>tabile, dipendente dalla varia distanza, in cui rimangono i centri delle due <lb></lb>figure sotto il livello del recipiente. </s>

<s>“ Quare solum quadratas superficies <lb></lb>iuxta latitudinem basis commensurare licebit aquam, non secundum lineas <lb></lb>proportionales medias ” (ihid.). </s></p><p type="main">

<s>Ma ritornando sopra l&#039;elenco ordinato da Leonardo, ci occorre a consi­<lb></lb>derare quel che dice sotto il numero VIII, spiegato meglio così, nella com­<lb></lb>pilazione dell&#039;Arconati: “ Quanto l&#039;argine, dove è posta la bocca dell&#039;oncia <lb></lb>dell&#039;acqua, fia più obliqua nella sua altezza inverso la caduta della bocca <lb></lb>dell&#039;acqua, tanto maggior quantità d&#039;acqua verserà la sua bocca. </s>

<s>Provasi, <lb></lb>perchè l&#039;acqua nella bocca in tal caso caderebbe per linea più obliqua, e <lb></lb>per la XXI del V quell&#039;acqua è più veloce, che discende per linea più obli­<lb></lb>qua, e per la XXVIII del medesimo l&#039;acqua, che cade per linea più vicina <lb></lb>alla perpendicolare, più presto discende ” (pag. </s>

<s>426, 27). </s></p><p type="main">

<s>Le due proposizioni qui citate, e che non è possibile riscontrare, perchè <lb></lb>la stesura di que&#039;due libri rimase nel pensiero; son quelle medesime, che il <lb></lb>Cardano riduceva così a postulati: “ Constat etiam quod velocissimus mo­<lb></lb>tus est, qui fit ex maiore altitudine, in aequali spacio, aut aequali altitudine, <lb></lb>in minore spacio ” <emph type="italics"></emph>(De rer. </s>

<s>var.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>63). Ma come, si domanderà, sono <lb></lb>applicabili all&#039;obliquità degli argini così fatti principii? </s>

<s>Nè si può dare al <pb xlink:href="020/01/3106.jpg" pagenum="67"></pb>quesito la sua debita risposta, senza esplicare il concetto di Leonardo, che <lb></lb>è tale: S&#039;immagini l&#039;argine con la sponda esterna AE (fig. </s>

<s>32) perpendi­<lb></lb>colare, ma con l&#039;interna ora più obliqua, come AB, ora meno, come AC, e <lb></lb><figure id="id.020.01.3106.1.jpg" xlink:href="020/01/3106/1.jpg"></figure></s></p><p type="caption">

<s>Figura 32.<lb></lb>una fistola DC penetri attraverso esso argine, da cui at­<lb></lb>tinga ora dalla bocca, B, ora dalla C l&#039;acqua del fiume. </s>

<s><lb></lb>Dice il Nostro che, scendendo per la linea AB, più vicina <lb></lb>alla perpendicolare, il liquido più veloce, che per la linea <lb></lb>AC; anche più veloce imboccherà per B, che per C. </s>

<s>La <lb></lb>conclusione è falsa in se, e in contradizione con le cose <lb></lb>precedentemente dimostrate dal medesimo Autore, secondo <lb></lb>le quali, essendo in B e in C l&#039;acqua scesa dalla me­<lb></lb>desima altezza, dovrebbe avervi anche acquistati impeti <lb></lb>uguali. </s>

<s>Ma non faccia maraviglia che rimanesse un Fisico <lb></lb>del secolo XV irretito in una fallacia, alla quale furon presi, come vedremo, <lb></lb>alcuni fra i più eletti discepoli di Galileo. </s></p><p type="main">

<s>Fra le cause, che fanno variare le velocità dell&#039;acqua, annovera Leo­<lb></lb>nardo, in IX luogo, l&#039;esser poste le fistole in argine concavo. </s>

<s>E quivi in <lb></lb>verità, come specialmente s&#039;osserva nelle piene, la superficie dell&#039;acqua è <lb></lb>più alta che altrove, ma è un inganno il credere che da tale altezza si pro­<lb></lb>duca maggior pressione, e perciò maggiore velocità nella fistola sottoposta. </s>

<s><lb></lb>La velocità straordinaria, con cui per la forza centrifuga, son dentro alla detta <lb></lb>concavità spinti gli strati liquidi, gli fa essere specificamente più leggeri, e <lb></lb>perciò debbono sollevarsi, come l&#039;olio nel sifone, per mettersi in equilibrio <lb></lb>con gli strati acquei comunicanti, e più gravi. </s></p><p type="main">

<s>Da questa medesima fallacia è informata l&#039;osservazione XI, ma la XIII <lb></lb>è giusta, specialmente ridotta alle ragioni, che si spiegano altrove: “ L&#039;acqua, <lb></lb>che cade per linea perpendicolare si fa acuta in una parte del suo descenso, <lb></lb>e il condotto d&#039;onde cadea resta vacuo. </s>

<s>E qui combatte l&#039;aria con l&#039;acqua, <lb></lb>come si dirà a suo loco, ma non dimenticherò però di dire che tal descenso <lb></lb>d&#039;acqua è impedito dalla condensazione dell&#039;aria nel condotto di essa acqua ” <lb></lb>(MSS. E, fol. </s>

<s>103). </s></p><p type="main">

<s>Ciò che si dice sotto i numeri XIV, XV e XVI ha maggiore importanza <lb></lb>storica, toccandovisi questioni, che si crede essere state solamente risolute <lb></lb>dagli Idraulici moderni, come quella, per esempio, che, dentro i tubi, scende <lb></lb>l&#039;acqua da pari altezza più veloce che fra l&#039;aria. </s>

<s>Anche le cause modifica­<lb></lb>trici delle velocità, secondo la ragion della lunghezza o della grossezza delle <lb></lb>canne, e le varietà fatte dall&#039;andar l&#039;acqua per canale tutt&#039;intorno chiuso, <lb></lb>o di sopra aperto; riconosciute così bene infin da que&#039;tempi, son degne di <lb></lb>nota. </s>

<s>“ L&#039;acqua, che per diretto discense si move, per canna di uniforme <lb></lb>larghezza, sarà tanto più veloce, quanto tal canna fia più lunga. </s>

<s>— L&#039;acqua, <lb></lb>che per diretto descenso si move per canne di uguali lunghezze, fia di tanto <lb></lb>più veloce moto, quanto tali canne fiano di maggiori larghezze. </s>

<s>E questo si <lb></lb>prova, perchè la linea centrale di tale acqua è più remota dalla confreca­<lb></lb>tione della canna larga, che della stretta, e per questo il suo moto è meno <pb xlink:href="020/01/3107.jpg" pagenum="68"></pb>impedito, e per questo si fa più veloce. </s>

<s>— L&#039;acqua, che si move per canna <lb></lb>equigiacente, è più grossa che quella, che corre per canale scoperto, e mas­<lb></lb>sime, quando tal canna riceve l&#039;acqua perpendicolare, e la lascia perpendi­<lb></lb>colare ” (ivi, fol. </s>

<s>12). </s></p><p type="main">

<s>Nella compilazione dell&#039;Arconati s&#039;aggiunge, per provare la verità qui <lb></lb>in terzo luogo proposta: “ Questo accade per quello, che è detto nella XX <lb></lb>del V, perchè quella parte dell&#039;acqua cadente, che è contigua all&#039;aria, si <lb></lb>mischia con l&#039;aria, e si fa più lieve. </s>

<s>E quanto è più lieve, più si tarda ” <lb></lb>(pag. </s>

<s>431). Ma il Cardano aveva intorno a ciò idee molto più sane. </s>

<s>” Itaque, <lb></lb>egli dice, haud dubium est aquas, quae per fistulas et siphones deducuntur, <lb></lb>et impetu et continuitate agi. </s>

<s>Quae vero per canales, rivos et locos paten­<lb></lb>tes, solo impetu. </s>

<s>Quamobrem velocius semper fertur aqua per siphones, quam <lb></lb>per rivos, pari ratione, paribusque auxiliis ac impedimentis constitutis ” <emph type="italics"></emph>(De <lb></lb>rer. </s>

<s>var.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>63). La ragione del doversi l&#039;acqua mantenere ne&#039;tubi <lb></lb>continua, e andarvi perciò più veloce che nel canale scoperto, il Cardano la <lb></lb>riconosce nell&#039;aria, alla quale egli attribuisce il peso, come a tutti gli altri <lb></lb>corpi, mentre Leonardo la faceva positiva causa della leggerezza. </s>

<s>Nella teoria <lb></lb>del sifone ritorto spiega meglio esso Cardano l&#039;azione del peso dell&#039;aria, che <lb></lb>efficacemente concorre a mantenervi il flusso continuo, così dicendo: “ Deni­<lb></lb>que tota haec contemplatio absolvitur hoc argumento: quod aqua, quae debet <lb></lb>trahere aliam aquam secum, oportet ut vase contineatur, quoniam sine illo <lb></lb>convelli nequit, sed ab aere iuvatur adveniente, et ut corpus continuum ad <lb></lb>aequilibrium perveniat ” <emph type="italics"></emph>(De subtilitate,<emph.end type="italics"></emph.end> Lugduni 1580, pag. </s>

<s>25). Le quali <lb></lb>dottrine, inspirate forse da Herone Alessandrino, aspettavano di ricevere dalla <lb></lb>scoperta del Torricelli la loro ultima perfezione. </s></p><p type="main">

<s>Finalmente, per esaurir questo esame intorno all&#039;elenco di Leonardo, <lb></lb>osserveremo che l&#039;ultima assegnata causa, per cui una medesima bocca di <lb></lb>erogazione può variare di quantità, l&#039;abbiamo trascritta: <emph type="italics"></emph>Se i lati del ca­<lb></lb>nale, d&#039;onde discende tale acqua, saran solli o globulosi.<emph.end type="italics"></emph.end> L&#039;Arconati in­<lb></lb>terpetrò <emph type="italics"></emph>sodi o globulosi<emph.end type="italics"></emph.end> (pag. </s>

<s>420), nè punto meglio sembra a noi tradu­<lb></lb>cesse il Ravaisson-Mollien <emph type="italics"></emph>mous ou bossues,<emph.end type="italics"></emph.end> ma è un fatto che deve inten­<lb></lb>dersi solli o globulosi, cioè levigati o aspri. </s></p><p type="main">

<s>Le XVII recensite cause, che fanno variare le portate, erano altrettanti <lb></lb>avvedimenti suggeriti ai dispensatori delle acque, e qui si arrestavano i be­<lb></lb>nefizi della Scienza, la quale s&#039;apparecchiava di farne altri migliori, intorno <lb></lb>al modo di regolare il corso dei fiumi. </s>

<s>I moderni Idraulici fecero il gran <lb></lb>passo, applicando a questì le scoperte leggi degli efflussi da&#039;vasi; e come il <lb></lb>Wolf, per esempio, nel corollario V dopo il XXVIII teorema della sua Idrau­<lb></lb>lica (Elem. </s>

<s>Matheseos univ., T. II, Genevae 1746, pag. </s>

<s>374), intendeva che <lb></lb>la velocità nel punto E dell&#039;alveo (fig. </s>

<s>25 qui addietro) fosse quella mede­<lb></lb>sima, con cui uscirebbe ivi da un foro aperto nel vaso ACE l&#039;acqua sta­<lb></lb>gnante; così la intendeva il Cardano, di cui vedemmo essere dalla medesima <lb></lb>figura XXV illustrato il concetto, e la intendeva pure Leonardo da Vinci, il <lb></lb>quale, applicando il teorema <emph type="italics"></emph>che in ogni grado di altezza la canna acqui-<emph.end type="italics"></emph.end><pb xlink:href="020/01/3108.jpg" pagenum="69"></pb><emph type="italics"></emph>sta gradi di distantia, nel gettar da lontano,<emph.end type="italics"></emph.end> alle acque correnti ne&#039;fiumi; <lb></lb>concludeva questa sua proposizione: “ Se un sostegno dà sopra di sè il tran­<lb></lb>sito a una data quantità d&#039;acqua di due once di grossezza, e vi s&#039;aggiunge <lb></lb>una terza oncia, allora l&#039;oncia di sotto raddoppia la potenza, la velocità e la <lb></lb>quantità della prima acqua. </s>

<s>Provasi per la seguente, che mostra, delle acque <lb></lb>correnti sopra li fondi de&#039;fiumi d&#039;uniforme obliquità, tali essere le propor­<lb></lb>zioni della velocità del moto, quale è quella delle loro altezze. </s>

<s>Adunque, se <lb></lb>la prima oncia detta di sopra fia premuta da un&#039;altra oncia, e poi da due <lb></lb>once, senza dubbio la potenza che preme è duplicata, e per conseguenza, come <lb></lb>è detto, la velocità e la quantità è raddoppiata ” <emph type="italics"></emph>(Arconati,<emph.end type="italics"></emph.end> pag. </s>

<s>422). Que­<lb></lb>sta proposizione, come fu bene da altri osservato, fa esatto riscontro con la <lb></lb>II del II libro del Castelli: “ Se un fiume, movendosi con una velocità per <lb></lb>un suo regolatore, averà una data altezza viva, e poi, per nuova acqua cre­<lb></lb>scerà il doppio; crescerà ancora il doppio la velocità ” <emph type="italics"></emph>(Della misura delle <lb></lb>acque corr.,<emph.end type="italics"></emph.end> Bologna 1660, pag. </s>

<s>82). </s></p><p type="main">

<s>Simili applicazioni, che mettevano sulla via d&#039;intendere la natura dei <lb></lb>fiumi, si fecero da&#039;tubi agli alvei, negli uni de&#039;quali e negli altri si ritenne <lb></lb>che la velocità allo sbocco fosse quella conveniente alla discesa perpendico­<lb></lb>lare. </s>

<s>Ma così questa, come l&#039;altra proposizione rinnovellata dal Castelli, non <lb></lb>son vere, se non che nella loro assoluta ragione, ossia, astraendo da ogni <lb></lb>sorta d&#039;impedimenti, inevitabili in ogni caso, o si confreghi la corrente con <lb></lb>le pareti de&#039;tubi, o col ghiareto, e con le ripe degli alvei. </s>

<s>“ Quanto l&#039;acqua, <lb></lb>dice Leonardo, sarà più distante dal fondo, tanto più libera sarà nel suo na­<lb></lb>tural moto (MSS. H, fol. </s>

<s>72). L&#039;acqua, che corre presso al fondo, tra le rive, <lb></lb>sarà più tarda che l&#039;altra (ivi, fol. </s>

<s>77). L&#039;acqua di sotto obbedisce manco <lb></lb>al suo naturale corso, che quella di sopra, e questo accade perchè l&#039;acqua, <lb></lb>che confina con l&#039;aria, non è aggravata da alcun peso, onde semplicemente, <lb></lb>senz&#039;alcuno impedimento, ubbidisce al suo natural corso: quella di sotto è <lb></lb>aggravata e premuta ” (ivi, fol. </s>

<s>85). E tante altre cause incomputabili rico­<lb></lb>nosceva Leonardo stesso concorrere ad alterare le velocità naturali, che ebbe <lb></lb>a uscire in questa sentenza: “ Pochissime son le parti delle acque correnti, <lb></lb>che si trovano in fra la superficie e il fondo suo, che corrano a un mede­<lb></lb>simo aspetto ” (MSS. F, fol., 47). </s></p><p type="main">

<s>Tutto questo, che si diceva dal Nostro, e in che consentivano gli altri, <lb></lb>non era però che il frutto della speculazione, la quale sembrava ai più che <lb></lb>contendesse co&#039;fatti osservati. </s>

<s>Se non corrono le parti dell&#039;acqua tutte a un <lb></lb>medesimo aspetto, com&#039;è, dicevano costoro, che si mantengono unite, e con­<lb></lb>tinuo si vede andare al suo termine il fiume? </s>

<s>La difficoltà era tale che, per <lb></lb>assicurarsi della verità di quelle speculate conclusioni, fu necessario ricor­<lb></lb>rere alle esperienze. </s>

<s>Una delle prime, occorse fra le pensate, dee essere stata <lb></lb>quella descritta così nella compilazione dell&#039;Arconati: “ Se vuoi vedere dove, <lb></lb>in alcun luogo sopra la superficie, ed in alcuno sotto la superficie sia più <lb></lb>veloce, getta acqua tinta, insieme con olio, sopra l&#039;acqua corrente, ed avverti <lb></lb>al fine del corso chi prima giunge: cioè, se giunge prima l&#039;olio, l&#039;acqua <pb xlink:href="020/01/3109.jpg" pagenum="70"></pb>corre più di sopra che di sotto; se giunge prima l&#039;acqua tinta, il fiume corre <lb></lb>più di sotto, che di sopra ” (pag. </s>

<s>307). </s></p><p type="main">

<s>L&#039;esperienza però non era praticabile, che ne&#039;piccoli canali, e quand&#039;an­<lb></lb>che si fosse riusciti in questi a riconoscere il vero, poteva rimaner dubbio <lb></lb>nel passare ad applicarlo ai grandi corsi de&#039;fiumi, intorno ai quali s&#039;aggi­<lb></lb><figure id="id.020.01.3109.1.jpg" xlink:href="020/01/3109/1.jpg"></figure></s></p><p type="caption">

<s>Figura 33.<lb></lb>rava tutta l&#039;importanza della questione. </s>

<s>Di qui ebbe origine <lb></lb>quel primo Idrometro, l&#039;invenzion del quale s&#039;attribuisce al <lb></lb>Cabeo, ma che, a tergo del fol. </s>

<s>42 del MSS. A, Leonardo <lb></lb>rappresentava con questo disegno (fig. </s>

<s>33) dichiarandone così <lb></lb>le parti “ N sughero — AQ canna: falla avanzare in AN uno <lb></lb>braccio, acciò che per la piega del quadrello si veda quella <lb></lb>di AN. ” Quanto poi all&#039;uso di un tale strumento si trova <lb></lb>nell&#039;<emph type="italics"></emph>Arconati<emph.end type="italics"></emph.end> così descritto: “ Di una bacchetta, che sia di <lb></lb>sopra infilata in baga, e di sotto in sasso, quella parte, che <lb></lb>avanza di sopra alla baga, se penderà in verso all&#039;avvenimento <lb></lb>dell&#039;acqua, correrà l&#039;acqua più in fondo che di sopra: e, se detta bacchetta <lb></lb>penderà inverso il fuggimento dell&#039;acqua, correrà il fiume più di sopra che <lb></lb>di sotto: e, se resta diritta la bacchetta, il corso sarà di pari velocità di <lb></lb>sotto e di sopra ” (pag. </s>

<s>306). </s></p><p type="main">

<s>Fu in questo modo esplorato che, quando la corrente è bassa, la super­<lb></lb>ficie e il fondo restano uguali in velocità, ma che, vicino alle cascate, è più <lb></lb>veloce la superficie che il fondo: fatto verissimo, a cui poi gli Idraulici det­<lb></lb>tero il nome di <emph type="italics"></emph>chiamata allo sbocco,<emph.end type="italics"></emph.end> e che anco Leonardo sembra attri­<lb></lb>buisse alla viscosità dell&#039;acqua. </s>

<s>“ Coll&#039;antidetta ragione, scriveva, si dimo­<lb></lb>stra come i fiumi d&#039;ugual fondo e larghezza, i quali ruinano il lor fine, che <lb></lb>corrono più di sopra che di sotto, perchè nel fine l&#039;acqua di sopra è più ve­<lb></lb>loce nel cadere, che quella di sotto: onde l&#039;acqua superiore, che successiva­<lb></lb>mente s&#039;appoggia a quella è necessario che sia di tal moto, quanto fu quello <lb></lb>che è detto ” (MSS, I, fol. </s>

<s>89). </s></p><p type="main">

<s>Non tutti però erano, di queste speculazioni, e di queste conclusioni spe­<lb></lb>rimentali sodisfatti, e, durando tuttavia le controversie, ci entrò di mezzo il <lb></lb>Cardano. </s>

<s>Le prime difficoltà, che avevano fatto dubitare altrui se gli strati <lb></lb>acquei corressero tutti, come si diceva, a vario aspetto; ei l&#039;ebbe in ogni <lb></lb>modo per decisive, “ quia necesse esset ut altior et humilior appareret, quod <lb></lb>tamen non contingit, nisi vel, dum alveus inaequalis est, vel flante vento ” <lb></lb><emph type="italics"></emph>(De rer. </s>

<s>var.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>66). E aggiuntavi l&#039;osservazione che nelle cascate <lb></lb>l&#039;acqua non prosegue per la sua prima dirittura BC (fig. </s>

<s>23 qui addietro), <lb></lb>nè cade perpendicolare lungo BD, ma tiene la via di mezzo BE; si confer­<lb></lb>mava nell&#039;opinione che tutti gli strati, dall&#039;imo al sommo, corressero in­<lb></lb>sieme a un medesimo aspetto, ossia con tale uniforme velocità, che, tra la <lb></lb>massima e la minima delle parti, resultasse al tutto la media. </s>

<s>“ Quamobrem <lb></lb>dicendum est aequaliter moveri imum aquae et supremum, in alveis aequa­<lb></lb>libus, quoniam, dum effunditur a canali, etiam videntur partes aequaliter <lb></lb>ferri ” (ibid.). </s></p><pb xlink:href="020/01/3110.jpg" pagenum="71"></pb><p type="main">

<s>Ma si citavano in contrario le esperienze idrometriche, sull&#039;andare di <lb></lb>quelle, che registrava ne&#039;suoi quaderni Leonardo, a che rispondeva il Car­<lb></lb>dano che lo strumento non diceva il vero, e che l&#039;esser egli più violente­<lb></lb>mente spinto in basso, che in alto, o al contrario, non era segno certo che <lb></lb>la corrente fosse, su e giù, o più o meno veloce, dovendosi attribuir ciò piut­<lb></lb>tosto a un effetto necessario, dipendente dalla natura del vette. </s>

<s>“ Moveri au­<lb></lb>tem velocius aquam in imo quam in summo, argumentum non est quod ba­<lb></lb><figure id="id.020.01.3110.1.jpg" xlink:href="020/01/3110/1.jpg"></figure></s></p><p type="caption">

<s>Figura 34.<lb></lb>culus in imo sentiatur vehementer agi, atque abduci, ut <lb></lb>in C (fig. </s>

<s>34) quam in B; nam C longius ab hypomoclio <lb></lb>distat, ideo aequaliter fluere videtur ” (ibid., pag. </s>

<s>67). </s></p><p type="main">

<s>Queste opposizioni del Cardano, contro le esperienze <lb></lb>dell&#039;Idrometro, forse erano state fatte da altri, ma rico­<lb></lb>nosciutesi insussistenti, si confermarono gl&#039;Idraulici nella <lb></lb>verità, che gli strati, dalla superficie al fondo, nelle varie <lb></lb>condizioni del fiume, corressero a vario aspetto. </s>

<s>Così poi <lb></lb>questo principio, come gli altri concernenti la teoria delle <lb></lb>velocità, si applicarono a regolare il corso naturale dell&#039;acqua. </s></p><p type="main">

<s>È davvero notabile come potesse il Castelli lusingar sè, e tutto il mondo <lb></lb>scientifico, che questa a&#039;suoi tempi fosse una scienza nuova. </s>

<s>Si poneva dal­<lb></lb>l&#039;Autore, per uno de&#039;principali corollarii di lei, la considerazione dei venti, <lb></lb>i quali, imboccando un fiume, e spirando contro la corrente, <emph type="italics"></emph>ritardano il <lb></lb>suo corso e la sua velocità ordinaria, per cui vengono necessariamente ad <lb></lb>ampliar la misura del medesimo fiume (Misura delle acque corr.,<emph.end type="italics"></emph.end> Lib. </s>

<s>I <lb></lb>cit., pag. </s>

<s>13): parole, nelle quali non si fa poi che rendere dilavato il con­<lb></lb>cetto stesso di Seneca: “ Si crebrioribus ventis ostium caeditur, et rever­<lb></lb>beratur fluctis, amnis resistit, qui crescere videtur, quia non effunditur ” <lb></lb><emph type="italics"></emph>(Quaest. </s>

<s>natur.<emph.end type="italics"></emph.end> cit. </s>

<s>fol. </s>

<s>30). </s></p><p type="main">

<s>Ma molto più di vicino al Castelli il Cardano, come udimmo, aveva detto <lb></lb>essere una delle principali cause, che modificano le velocità, e perciò le mi­<lb></lb>sure dell&#039;acqua, i venti, sia che soffino avversi, o a seconda della sua libera <lb></lb>corrente. </s>

<s>Che se, contro al corollario di esso Castelli, si moveranno difficoltà, <lb></lb>sembrando che le correnti dell&#039;aria non possano far altro, che increspar leg­<lb></lb>germente la superficie dell&#039;acqua; aveva ad esse Leonardo preparata la ri­<lb></lb>sposta due secoli prima: “ I fiumi, egli dice, che si moveranno contro ai <lb></lb>corsi dei venti, fieno di tanto maggiore corso di sotto, che di sopra, quanto <lb></lb>la sua superfitie si fa più tarda, essendo sospinta da&#039;venti, che prima. </s>

<s>La <lb></lb>ragione di questo si è che, essendo i fiumi d&#039;eguale profondità e latitudine, <lb></lb>di pari corso in sul fondo che in superficie, necessaria cosa è che la recal­<lb></lb>citazione, che fa il vento contro alla corrente superficie, faccia quella tor­<lb></lb>nare indietro, e non bastando a esse onde alquanto elevarsi in alto, che al <lb></lb>fine cadendo entran sotto le altre, e vanno al fondo, dove, trovando l&#039;altra cor­<lb></lb>rente del fondo, s&#039;accompagna con essa. </s>

<s>E perchè l&#039;argine non è capace di questa <lb></lb>multiplicazione, è necessario che esso fondale corso si raddoppi, se no l&#039;acqua <lb></lb>verrebbe a elevarsi molto fuori delle argini di essi fiumi ” (MSS. C, fol. </s>

<s>25). </s></p><pb xlink:href="020/01/3111.jpg" pagenum="72"></pb><p type="main">

<s>In un altro corollario della nuova Scienza delle acque correnti faceva il <lb></lb>Castelli notare un puerile errore dell&#039;architetto Giovanni Fontana, il quale, <lb></lb>a spiegar come fosse una gran piena del Tevere passata sotto il ponte di <lb></lb>Quattrocapi, diceva che tra quelle angustie v&#039;era l&#039;acqua premuta, quasi <lb></lb>fosse bombice o lana. </s>

<s>Ma, mentre Galileo si studiava di difendere l&#039;Archi­<lb></lb>tetto romano, rassomigliando lo scorso di essa acqua <emph type="italics"></emph>al nocciolo di ciliega, <lb></lb>che premuto dalle dita scappa<emph.end type="italics"></emph.end> (Alb. </s>

<s>VI, 324), e il Castelli seguitava ad <lb></lb>accampare quel suo principio, nella generalità indeterminato; Leonardo asse­<lb></lb>gnava, di quella sopravvenuta velocità nello stretto della sezione, la causa <lb></lb>vera e immediata, dicendo che la piena passa liberamente per gli archi dei <lb></lb>ponti “ perchè l&#039;acqua, che passa per tali archi, cresce l&#039;impeto, per avere <lb></lb>gran peso di sopra ” (MSS. I, fol. </s>

<s>87). La ragion poi di un tale accresci­<lb></lb>mento d&#039;impeto, per il peso che sovrasta, è meglio spiegata altrove, e con­<lb></lb>fermata dal fatto delle corrosioni degli argini e del fondo, nella proposizione, <lb></lb>che Leonardo stesso così scriveva; “ Ogni canale d&#039;acqua, d&#039;uguale obli­<lb></lb>quità e profondità e larghezza, che sarà in alcun luogo restretto, roderà il <lb></lb>fondo dell&#039;argine, dopo il transito di essa strettezza. </s>

<s>Questo accade perchè, <lb></lb>dove l&#039;acqua è ristretta, ella s&#039;alza di rietro a essa strettura, e, passando per <lb></lb>esso loco stretto, vi passa con furore, perchè dichina: trova l&#039;acqua di sotto, <lb></lb>che non corre, e riceve impedimento, onde, seguitando la linea del suo de­<lb></lb>scenso, vassene al fondo, e li cava, e con ritrose circulazioni si volta all&#039;ar­<lb></lb>gine, e quello sotto cavando lo fa ruinare ” (MSS. H, fol. </s>

<s>85). </s></p><p type="main">

<s>Quando le nuove istituzioni idrauliche del Castelli mossero Galileo a <lb></lb>scrivere la celebre lettera sul fiume Bisenzio, i discepoli di lui immediati e <lb></lb>i successori salutarono in quella scrittura le prime applicazioni, fatte all&#039;acque, <lb></lb>della teoria de&#039;gravi scendenti lungo i piani inclinati. </s>

<s>Ma questa teoria, e <lb></lb>quella applicazione, si sa bene oramai essere cosa molto più antica, avendo <lb></lb>noi letto, ne&#039;fogli manoscritti di Leonardo, e nelle pagine stampate del Car­<lb></lb>dano, che in ugual caduta perpendicolare sbocca l&#039;acqua dai tubi ugualmente <lb></lb>veloce. </s>

<s>Ciò che però volevano quegli Autori s&#039;intendesse delle velocità asso­<lb></lb>lute, e no delle relative alle resistenze, cosicchè, sebbene in teoria sia vero <lb></lb>che in B e in C (fig. </s>

<s>35) i due tubi AB, AC gettano con pari impeto; no­<lb></lb><figure id="id.020.01.3111.1.jpg" xlink:href="020/01/3111/1.jpg"></figure></s></p><p type="caption">

<s>Figura 35.<lb></lb>nostante si vede in pratica uscire da C il liquido con <lb></lb>minor foga, rallentatagli dalla più lunga confregazione <lb></lb>contro le pareti del tubo. </s>

<s>E perchè un medesimo fiume, <lb></lb>che corresse al medesimo sbocco ora diritto ora torto, <lb></lb>sarebbe come se ci venisse per un canale ora corto <lb></lb>ora lungo; di qui presero quegli Idraulici la regola di <lb></lb>torcere o di raddirizzare un alveo, secondo il riconosciuto bisogno di velo­<lb></lb>citar o di raffrenare l&#039;impeto della corrente, come si legge in un capitolo <lb></lb>di Leonardo, così intitolato: <emph type="italics"></emph>“ Del modo di dirizzare i fiumi, essendo con <lb></lb>tardi corsi.<emph.end type="italics"></emph.end> Perchè, quanto il fiume è più diritto, esso si fa più veloce e rode <lb></lb>più forte e consuma l&#039;argine e il fondo, onde a questi tali fiumi è necessario <lb></lb>allargarli forte, o veramente mandarli per molte torture, o dividerli in molti <pb xlink:href="020/01/3112.jpg" pagenum="73"></pb>rami. </s>

<s>E se il fiume, per molte torture si facesse pigro e paludoso, allora tu <lb></lb>lo debbi in modo dirizzare, che l&#039;acque piglino sufficiente moto, e non che <lb></lb>abbia a dare ruina di ripe o di argini. </s>

<s>E quando sarà profondità vicino ad <lb></lb>alcuna argine, allora si debbe tale loco riempire di gabbioni con fascine, e <lb></lb>giova, acciò non cavi in modo sotto l&#039;argine, che rovinandola abbia poi il <lb></lb>fiume a fare un gomito nella tua possessione o villa, e raddirizzarvi suo corso ” <lb></lb>(MSS. I, fol. </s>

<s>82). </s></p><p type="main">

<s>Dire che, in queste brevi parole, si conclude la scienza della Lettera sul <lb></lb>fiume Bisenzio non è tutta, nè la miglior parte del vero: bisogna soggiun­<lb></lb>gere che quella stessa scienza vi è corretta da&#039;suoi errori più radicali, e per­<lb></lb>fezionata a quel modo, che poi fece il Viviani, costretto a ripudiare gl&#039;inse­<lb></lb>gnamenti del suo Maestro, troppo astratti dalla presente realtà delle cose. </s>

<s>E <lb></lb>la famosa questione della Laguna veneta, e de&#039;benefizi o de&#039;danni, che ri­<lb></lb>ceverebbe dalla diversione dei fiumi, non si trova ella, più magistralmente, <lb></lb>che da&#039;lunghi e battaglieri discorsi del Castelli, risoluta dalla brevità senten­<lb></lb>ziosa di questi motti?: “ Se la superchia grandezza de&#039;fiumi guasta e rompe <lb></lb>i liti marittimi, devesi tali fiumi, poichè non si possono voltare in altri lochi, <lb></lb>disfarli in minuti rivicelli ” (MSS. I, fol. </s>

<s>111). E altrove, anche più a pro­<lb></lb>posito, scriveva lo stesso Leonardo: “ Lo atterramento de&#039;paduli sarà fatto, <lb></lb>quando in essi paduli fien condotti li fiumi torbidi. </s>

<s>Questo si prova perchè, <lb></lb>dove il fiume corre, di lì lieva il terreno, e dove si ritarda qui lascia la sua <lb></lb>turbolentia. </s>

<s>E per questo, e perchè nei fiumi mai l&#039;acqua si ritarda, come <lb></lb>nei paduli, nei quali le acque son di moto insensibile; mai in essi paduli il <lb></lb>fiume debbe entrare per loco basso e stretto, e uscirne per ispazio largo e <lb></lb>di poca profondità. </s>

<s>E questo è necessario; perchè l&#039;acqua corrente del fiume <lb></lb>è più grossa e terrestre di sotto che di sopra, e l&#039;acqua tarda de&#039;paduli an­<lb></lb>cora è il simile, ma molto è differente la levità superiore delli paduli, alla <lb></lb>gravità sua inferiore, che non è nella corrente de&#039;fiumi, nelli quali la levità <lb></lb>superiore poco si varia dalla gravità inferiore ” (MSS. E, fol. </s>

<s>5). </s></p><p type="main">

<s>Dietro queste cose, messe insieme con tutte le altre, che si son da noi <lb></lb>particolarmente discorse, intorno alla scienza idraulica di Leonardo da Vinci; <lb></lb>s&#039;intende come, paragonandolo col Castelli, giustamente il Venturi, nel suo <lb></lb>ben noto <emph type="italics"></emph>Essai,<emph.end type="italics"></emph.end> concludesse: <emph type="italics"></emph>Le primier me paróit dans cette partie su­<lb></lb>perieur de beaucoup à l&#039;autre, que l&#039;Italie cependant a regardé comme <lb></lb>le fondateur de l&#039;Hydraulique.<emph.end type="italics"></emph.end> Dopo, fu un continuo ripeter l&#039;acclamazione, <lb></lb>ma si esagerò, non solamente in credere che fosse Leonardo inventore della <lb></lb>scienza, ma in attribuirgli certi meriti, che son dovuti propriamente al Ca­<lb></lb>stelli, e i quali non consistono nell&#039;aver egli avvertite le velocità, ma nel­<lb></lb>l&#039;avere insegnato il modo pratico di misurarle. </s></p><p type="main">

<s>Quegli avvertimenti vedemmo che furono dati dagli stessi antichi Ro­<lb></lb>mani, e s&#039;aveva dopo tanti secoli un bel predicare: “ Tu, che compri l&#039;acqua <lb></lb>a once, sappi che tu ti puoi forte ingannare. </s>

<s>Imperocchè, se tu tolli un&#039;on­<lb></lb>cia in acqua morta, e un&#039;oncia in acqua corrente contro al buso della tua <lb></lb>oncia; un&#039;oncia averai vicino alla superficie, un&#039;oncia vicino al fondo, una <pb xlink:href="020/01/3113.jpg" pagenum="74"></pb>in traverso alla corsia ” (MSS. H, fol. </s>

<s>78). Tali erano de&#039;patiti inganni le <lb></lb>remote cause generali, senza le parecchie altre, dallo zelante nostro Filosofo <lb></lb>riconosciute. </s>

<s>Ma quali rimedi si suggerivano da lui ai poveri ingannati? </s>

<s>Il <lb></lb>Castelli penetrò la causa prossima e particolare del malefizio, riducendola al <lb></lb>trascurar che si faceva, nel misurare un solido, la sua lunghezza: ciò che <lb></lb>egli dava ad intendere con l&#039;esempio dell&#039;oro o di altro metallo, tirato alla <lb></lb>trafila. </s>

<s>Ci sovviene che anche Leonardo si volse a un simile esempio, non <lb></lb>meno argutamente, ma in proposito molto diverso, qual&#039;è di dimostrare, in <lb></lb>una maniera meccanica, che in solidi uguali stanno le altezze reciprocamente <lb></lb>alle basi. </s>

<s>Abbiasi, diceva, una quantità di materia dilatabile, come cera, e <lb></lb>se ne formi un parallelepipedo con base quadrata. </s>

<s>Trafilando la cera per un <lb></lb>foro quadrato, che sia la quarta parte della detta base, ne uscirà un altro <lb></lb>parallelepipedo, che alla misura si troverà quattro volte più lungo. </s>

<s>E rispon­<lb></lb>dendo sempre i particolari esempi con simile ragione, concludeva da ciò in <lb></lb>generale: “ Il corpo uniforme, che uniformemente si restringe, tanto acqui­<lb></lb>sta di lunghezza, quanto e&#039;perde della sua larghezza ” (MSS. E, fol. </s>

<s>8). </s></p><p type="main">

<s>Il Castelli, in quell&#039;allungamento del corpo duttile, quale pure è l&#039;acqua <lb></lb>che si restringe, riconobbe l&#039;espressione della velocità, o dello spazio che lo <lb></lb>misura, in relazione col tempo; cosicchè la questione della più giusta di­<lb></lb>spensa dell&#039;acqua si veniva a risolvere per lui con l&#039;orologio alla mano. </s>

<s>Ma <lb></lb>Leonardo non seppe sollevarsi punto sopra alla turba volgare, la quale non <lb></lb>capiva come si potesse definir la lunghezza a un corpo, che mai non cessa <lb></lb>di scorrere. </s>

<s>E adducendo l&#039;esempio dello schizzatoio, <emph type="italics"></emph>che, quando il ma­<lb></lb>schio si move un dito, l&#039;acqua di fuori si è allontanata due braccia;<emph.end type="italics"></emph.end> ne parla <lb></lb>come di cosa ipotetica, e d&#039;impossibile esperienza <emph type="italics"></emph>(Arconati,<emph.end type="italics"></emph.end> pag. </s>

<s>428, 29). </s></p><p type="main">

<s>Il gelo della critica è finalmente venuto a bruciare le fronde tenerelle <lb></lb>della Rettorica, ma se Leonardo, da inventore della Scienza, n&#039;è rimasto un <lb></lb>semplice cultore, coltivandola, la promosse forse più al di là di ogni altro <lb></lb>discepolo di Giordano, perchè possedeva le virtù necessarie in grado più <lb></lb>eccellente. </s>

<s>La prima e principale di queste virtù noi la riconosciamo nella <lb></lb>grande perizia, ch&#039;ebbe delle Matematiche. </s>

<s>È cosa veramente notabile che, <lb></lb>mentre tutti si affaccendano a indicare ne&#039;Manoscritti del Nostro specula­<lb></lb>zioni, scoperte e invenzioni di ogni genere, e tutte ammirande; nessuno abbia <lb></lb>ancora avvertito la grande arte di lui, in maneggiar l&#039;algebra e la geome­<lb></lb>tria, da emulare, e da superare talvolta gli stessi metodi odierni, per la fa­<lb></lb>cilità delle dimostrazioni, e per l&#039;eleganza. </s></p><p type="main">

<s>Un&#039;altra virtù consisteva in quella diligente pazienza d&#039;osservare i vari <lb></lb>fatti naturali, che non gli lasciava fuggire all&#039;occhio la minima cosa. </s>

<s>Una <lb></lb>buona parte del libro, compilato dall&#039;Arconati, s&#039;impiega a descrivere le <lb></lb>figure bizzarre e capricciose, alla superficie e nell&#039;interno dell&#039;acqua, che <lb></lb>movendosi incontra ostacoli al suo libero corso, e secondo il modo di questi <lb></lb>incontri ora si riflette, ora si rifrange, ora s&#039;affila e intesse panneggiamenti, <lb></lb>ora s&#039;avvolge e fa vortici, girandole e cirri, da importar forse meno alla <lb></lb>scienza, che all&#039;arte della pittura. </s>

<s>A questa artistica curiosità nondimeno de-<pb xlink:href="020/01/3114.jpg" pagenum="75"></pb>vesi l&#039;osservazione della vena contratta, del meccanismo, che produce i ven­<lb></lb>tri e i nodi in un fil d&#039;acqua che cada, e di tanti altri fenomeni, osservati <lb></lb>da Leonardo in recipienti con pareti diafane, immersevi polveri o altri mi­<lb></lb>nuti galleggianti colorati, per rendersi meglio visibili i complicati moti inte­<lb></lb>stini. </s>

<s>Ond&#039;è facile intendere come giungesse così a fare scoperte, l&#039;onor delle <lb></lb>quali poi si distribul fra il Mariotte, il Newton e il Poleni. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Le tradizioni di quella Scienza, la quale ora desta in noi la maraviglia, <lb></lb>non sapremmo dire se più per i grandi progressi fatti da lei, o per essere <lb></lb>stata dimenticata; derivarono, come da triplice fonte, da Archimede, da Fron­<lb></lb>tino e dal Nemorario. </s>

<s>Ma la vena intima alimentatrice si può dire che fosse <lb></lb>una sola: quella cioè, che si sentiva scorrere in mezzo a&#039;due libri <emph type="italics"></emph>De insi­<lb></lb>dentibus aquae.<emph.end type="italics"></emph.end> E perchè la loro pubblicazione era naturale che venisse a <lb></lb>dare nuovo e validissimo impulso a questi studii, l&#039;importanza dell&#039;argo­<lb></lb>mento c&#039;invita a trattenerci attorno più particolarmente il discorso. </s></p><p type="main">

<s>Si disse già come fosse condotta la versione latina del trattato <foreign lang="grc">περι <lb></lb>ὸχουμένων</foreign>, e come questa pervenisse nella penisola insieme con le altre Opere <lb></lb>meccaniche di Archimede. </s>

<s>Rimasto il codice lungamente negletto, nel se­<lb></lb>colo XIV si dette opera a copiarlo, e il copiatore premetteva, ripetendola in­<lb></lb>nanzi a ogni libro distinto, un&#039;avvertenza, nella quale scusavasi delle lacune, <lb></lb>e de&#039;frantesi, per essere, com&#039;egli diceva, il codice, in certi punti, così la­<lb></lb>cero, da non si poter leggere in nessun modo. </s>

<s>Altre copie se ne presero, <lb></lb>conformi in tutto e per tutto con questa, e n&#039;ebbe una il Vescovo di Pa­<lb></lb>dova, d&#039;onde si diffusero le altre, venute a mano di Leonardo da Vinc, e <lb></lb>un poco più tardi del Tartaglia, e del cardinale Cervini, poi papa Marcello II, <lb></lb>che ne fece dono al Commandino. </s></p><p type="main">

<s>Sentì il Tartaglia tanto gusto della bellezza matematica di quelle dot­<lb></lb>trine, che per comun benefizio pensò di pubblicarle. </s>

<s>Ma se la Scienza da <lb></lb>una parte lo confortava, veniva dall&#039;altra a disanimarlo la Filologia, a che, <lb></lb>non potendo reprimere l&#039;incredibile ardore, trovò rimedio, pubblicando le <lb></lb>sole cose in latino, come l&#039;aveva trovate, e scusandosene a quel modo, che <lb></lb>aveva fatto il primo copiatore, l&#039;avvertenza del quale trasfuse nella sua pre­<lb></lb>fazione. </s>

<s>Anzi, perchè il libro secondo <emph type="italics"></emph>De insidentibus aquae<emph.end type="italics"></emph.end> era di così sot­<lb></lb>tile e oscura materia, da non giovare a bene interpetrarlo nemmeno la <lb></lb>scienza; trovatosi il poco esperto editore da ambedue le parti sopraffatto e <lb></lb>vinto, pensò di lasciarlo indietro, non riducendo nella sua compilazione che <lb></lb>il primo. </s></p><p type="main">

<s>Morto nel 1557 il Tartaglia, furono i manoscritti di lui venduti a Cur­<lb></lb>zio Troiano, tipografo-editore in Venezia, il quale, avendo tra quelle com­<lb></lb>prate carte ritrovata la trascrizione del secondo libro <emph type="italics"></emph>De insidentibus hu-<emph.end type="italics"></emph.end><pb xlink:href="020/01/3115.jpg" pagenum="76"></pb><emph type="italics"></emph>mido,<emph.end type="italics"></emph.end> non esitò di darlo, nella sua propria officina, alla pubblica luce. </s>

<s>Nel <lb></lb>dedicare l&#039;opuscolo a Fabrizio de Nores, dop&#039;aver detto che si crederebbe <lb></lb>meritevole di riprensione, se egli, che aveva in mano le rimaste scritture del <lb></lb>grandissimo Tartaglia, ne avesse dinegato lo studio agli uomini letterati; così <lb></lb>soggiungeva: “ Quare, cum habeam adhuc apud me Archimedem <emph type="italics"></emph>De insi­<lb></lb>dentibus aquae,<emph.end type="italics"></emph.end> ab ipso Nicolao in lucem revocatum, et quantum ab ipso <lb></lb>fieri potuit ab erroribus librarii emendatum, et suis lucubrationibus illustra­<lb></lb>tum; videor fraudare omnes literatos sua possessione, ni omnia, quae huius <lb></lb>ingeniosissimi viri apud me restant, in lucem emisero, et omnibus ea com­<lb></lb>municavero. </s>

<s>” </s></p><p type="main">

<s>J. L. Heiberg, dando alla Biblioteca teubneriana di Lipsia le opere di <lb></lb>Archimede, da sè recensite, tradotte in latino e illustrate; al titolo <emph type="italics"></emph>De iis <lb></lb>quae in humido vchuntur<emph.end type="italics"></emph.end> sottoponeva questa nota: “ Librum I primus <lb></lb>edidit N. Tartalea, Venetiis 1543. Deinde ex schedis eius et primum et se­<lb></lb>cundum librum edidit Troianus Curtius, Venetiis 1565. Hanc interpetratio­<lb></lb>nem emendavit F. Commandinus, Bononiae 1565 ” (Vol. </s>

<s>II, 1881, pag. </s>

<s>359). </s></p><p type="main">

<s>Ma com&#039;è possibile che il Commandino conducesse in pochi mesi quella <lb></lb>sua, che da ogni parte apparisce penosissima emendazione, e anzi dì più ri­<lb></lb>trovasse, in tal brevissimo tempo, quelle sue laboriosissime proposizioni dei <lb></lb>centri di gravità de&#039;solidi, l&#039;argomento delle quali confessa essergli stato <lb></lb>suggerito dalla meditazione del secondo libro idrostatico di Archimede? </s>

<s>Il <lb></lb>Torelli, nella prefazione a tutte le Opere del Siracusano, suppose che il <lb></lb>Tartaglia e il Commandino s&#039;abbattessero ne&#039;libri <foreign lang="grc">περι οχομένων</foreign> quasi nel me­<lb></lb>desimo tempo, benchè l&#039;uno indipendentemente dall&#039;altro. </s>

<s>“ Caeterum, egli <lb></lb>dice, cum Commandinus in libros, quos memoravimus, eodem fere tempore <lb></lb>incidisset, quo illos Tartalea invenit; egregiam in iis operam insumpsit ” <lb></lb>(Oxonii 1792, pag. </s>

<s>XVIII). Cosicchè, verso l&#039;anno 1543, suppone il To­<lb></lb>relli che i libri idrostatici di Archimede capitassero alle mani del Matema­<lb></lb>tico di Urbino. </s>

<s>Ma in questo caso non si comprenderebbe perchè non gli <lb></lb>raccogliesse fra le altre opere del medesimo Autore, le quali egli stesso pub­<lb></lb>blicava nel 1558, con tant&#039;amorosa diligenza, in Venezia. </s>

<s>Fu da questo no­<lb></lb>tato difetto anzi indotto ìl cardinale Cervini a fare il dono al diligentissimo <lb></lb>editore, il quale, dicendo di averlo ricevuto non molti anni prima del 1565 <lb></lb>(Lettera dedic. </s>

<s>del libro <emph type="italics"></emph>De centro gravitatis),<emph.end type="italics"></emph.end> ne fa con certezza argomen­<lb></lb>tare che ciò accadesse circa l&#039;anno 1560, diciassette o diciotto anni dopo il <lb></lb>Tartaglia. </s></p><p type="main">

<s>Così, anche quei cinque anni, che precedettero la pubblicazione, essendo <lb></lb>tempo sufficiente a commentare i libri <emph type="italics"></emph>De iis quae vehuntur in aqua,<emph.end type="italics"></emph.end> e a <lb></lb>preparare il trattato <emph type="italics"></emph>De centro gravitatis solidorum,<emph.end type="italics"></emph.end> si vengono a togliere <lb></lb>l&#039;inconvenienze, che nascono dalle posizioni del valoroso, e benemerito pro­<lb></lb><gap></gap>essore di Copenaghen, il quale, se avesse ripensato a queste cose, si sarebbe <lb></lb>anche insieme deliberata la mente da que&#039;suoi dubbi, espressi ne&#039;Prolego­<lb></lb>meni al Commentario di Eutocio, dove si fa maraviglia che il Commandino, <lb></lb>successore immediato nell&#039;ufficio di editore al Tartaglia, non ne profferisca <pb xlink:href="020/01/3116.jpg" pagenum="77"></pb>mai il nome. </s>

<s>“ Is (Commandinus) in praefatione editionis librorum <foreign lang="grc">περι <lb></lb>οχουμένων,</foreign> fol. </s>

<s>2, hacc habet: <emph type="italics"></emph>Cum enim graecus Archimedis codex nondum <lb></lb>in lucem venerit, non solum is qui eum latinitate donavit multis in locis <lb></lb>foede lapsus est, verum etiam codex ipse, ut etiam interpres fatetur, ve­<lb></lb>tustate corruptus et mancus est.<emph.end type="italics"></emph.end> His verbis Tartaleam et descriptionem co­<lb></lb>dicis eius, quam ex praefatione eius supra attuli, significari adparet, et mi­<lb></lb>ramur cur nomen eius non nominaverit ” (Archim., <emph type="italics"></emph>Op. </s>

<s>omnia,<emph.end type="italics"></emph.end> Vol. </s>

<s>III, <lb></lb>pag. </s>

<s>XXXII). Alla pagina XXIX infatti aveva l&#039;Heiberg trascritte queste <lb></lb>parole, con le quali il Tartaglia cominciava la sua prefazione all&#039;edizione <lb></lb>delle Opere meccaniche d&#039;Archimede: “ Cum sorte quadam ad manus meas <lb></lb>pervenissent fracti, et qui vix legi poterant, quidam libri manu graeca scripti <lb></lb>illius celeberrimi philosophi Archimedis..... ” Ma queste medesime espres­<lb></lb>sioni vedemmo essere nell&#039;avvertenza del copiatore antico, la quale av­<lb></lb>vertenza leggendo il Commandino riportata nel suo manoscritto credè che <lb></lb>fosse di colui, che aveva fatta la traduzione latina, direttamente dal testo <lb></lb>greco. </s></p><p type="main">

<s>La maraviglia dunque dell&#039;illustre editore tedesco dipende tutta dal­<lb></lb>l&#039;avere ingerita l&#039;opinione che il Commandino avesse condotte le sue recen­<lb></lb>sioni sopra la pubblicazion del Tartaglia, nella quale consistesse il libro do­<lb></lb>natogli dal cardinale Cervini: opinione comunemente invalsa, e che fu tenuta <lb></lb>anche da noi, prima di considerare che il detto libro era il manoscritto, di <lb></lb>cui s&#039;è discorso di sopra, e che il Cardinale consegnava al Matematico di <lb></lb>Urbino, raccomandandogliene la pubblicazione, quando quella del Tartaglia <lb></lb>giudicavasi troppo informe, e ritrovavasi mancante della sua seconda parte. </s>

<s><lb></lb>Se, nella dedica infatti del libro <emph type="italics"></emph>De centro grav.,<emph.end type="italics"></emph.end> quelle parole <emph type="italics"></emph>non multos <lb></lb>abhinc annos Mareellus Il Pont. </s>

<s>Max., cum abhuc cardinalis esset, mihi, <lb></lb>quae sua erat humanitas, libros Archimedis de iis quae vehuntur in aqua <lb></lb>latine redditos dono dedit,<emph.end type="italics"></emph.end> lasciano ambiguo il lettore intorno all&#039;essere il <lb></lb>libro, di cui si parla, o manoscritto o stampato; dalla dedica del <emph type="italics"></emph>De iis quae <lb></lb>vehuntur in aqua<emph.end type="italics"></emph.end> chiaramente apparisce che si trattava della pubblicazione <lb></lb>di un codice, simile a quella, che l&#039;Autore stesso ivi dice avere già fatta <lb></lb>degli analemmi di Tolomeo. </s>

<s>“ Quod tibi (al card. </s>

<s>Ranuccio Farnese, a cui <lb></lb>l&#039;edizione si dedicava) superioribus diebus pollicitus sum, cum libellum Pto­<lb></lb>lomaei De analemmate in lucem proferrem, brevi fore ut Archimedis etiam <lb></lb>libri De iis quae in aqua vehuntur et emendatiores, et fortasse opera mea <lb></lb>illustriores ederentur..... ” </s></p><p type="main">

<s>Essendo così dichiarata l&#039;indipendenza della pubblicazione del Comman­<lb></lb>dino, da quella del Tartaglia, si può giudicare quanto fuori del segno co­<lb></lb>gliessero le congetture dell&#039;Heiberg, per risolvere gli esposti dubbi, e altri <lb></lb>nuovi, che nascevano intorno alla questione, la quale quanto più maneggia­<lb></lb>vasi, per trovare il bandolo della matassa, e più si arruffava. </s>

<s>“ His omnibus <lb></lb>rebus adductus, nunc in eam potius partem inclinaverim, ut putem Tarta­<lb></lb>leam, ex Codice illo graeco antiquo et dilacerato, ceteros libros ipsum latine <lb></lb>interpetratum esse. </s>

<s>Sed librum I <emph type="italics"></emph>De insidentibus aquae,<emph.end type="italics"></emph.end> sicut etiam li-<pb xlink:href="020/01/3117.jpg" pagenum="78"></pb>brum II ei e graeco latine conversum, nescio quo modo oblatum esse ” <lb></lb><emph type="italics"></emph>(Op. </s>

<s>Archim.,<emph.end type="italics"></emph.end> Vol. </s>

<s>III cit., pag. </s>

<s>XXXII). </s></p><p type="main">

<s>La nuova risoluta questione, intorno ai due primi editori de&#039;libri idro­<lb></lb>statici di Archimede, giova a risolvere definitivamente anche quell&#039;altra, che <lb></lb>riguarda il codice greco. </s>

<s>Quando il Tartaglia diceva, in quella sua prefa­<lb></lb>zione, essergli per sorte pervenuti alcuni libri di Archimede, <emph type="italics"></emph>manu graeca <lb></lb>scripti,<emph.end type="italics"></emph.end> era da eccettuare il trattato <emph type="italics"></emph>De insidentibns aquae,<emph.end type="italics"></emph.end> di cui trovò la <lb></lb>sola traduzione latina, senza il testo greco a fronte, come avevano gli altri. </s>

<s><lb></lb>Nè ciò è un induzione, ma un fatto attestato dallo stesso Tartaglia, chi ben <lb></lb>l&#039;intende, nella lettera dedicatoria al conte Landriani. </s>

<s>Il medesimo fatto poi <lb></lb>è confermato dal Commandino, il quale, benchè credesse, come avvertimmo, <lb></lb>essere il codice che aveva fra mano quello, in cui si dava la version di Ar­<lb></lb>chimede, fatta direttamente dal testo greco; il vero testo greco nonostante <lb></lb>dice che <emph type="italics"></emph>nondum in lucem venit.<emph.end type="italics"></emph.end> E come s&#039;ha, dalle stesse parole del Tar­<lb></lb>taglia, espressa la notizia che di quel codice nient&#039;altro era rimasto, che le <lb></lb>figure illustrative; così è ripetuto dal Commandino, nel luogo da noi citato <lb></lb>dal suo Commentario. </s></p><p type="main">

<s>Ciò basti a noi aver detto, per quel che s&#039;appartiene alla storia di una <lb></lb>pubblicazione, la quale tanto efficacemente sarebbe concorsa a promovere la <lb></lb>scienza idrostatica. </s>

<s>Son fra que&#039;primi promotori senza dubbio da annove­<lb></lb>rare ambedue coloro, che tanto cooperarono a diffondere la notizia, e lo stu­<lb></lb>dio dei libri archimedei, benchè ne siano i meriti, nell&#039;estimazione e nel <lb></lb>grado, molto diversi. </s>

<s>Il Commandino supera di gran lunga, nella diligenza <lb></lb>e nella critica necessaria a un editore, il Tartaglia, così rude in ogni genere <lb></lb>di letteratura, da far veramente maraviglia che l&#039;Heiberg se lo immagini <lb></lb>tutto intento a compulsare codici greci e latini, con gli avvedimenti dell&#039;arte, <lb></lb>e con la minuziosa pazienza di un moderno critico tedesco. </s>

<s>Esso Heiberg non <lb></lb>potè passar senza nota l&#039;errore lasciato trascorrere in fronte, nella prima <lb></lb>aperta del libro: <emph type="italics"></emph>Incipit liber Archimenidis de centris gravium valde pla­<lb></lb>nis aequerepentibus,<emph.end type="italics"></emph.end> e l&#039;attribuisce alla negligenza del tipografo. </s>

<s>Ma ripen­<lb></lb>sando come costui era quel veneziano Venturino Ruffinelli, che tanto cor­<lb></lb>rettamente poi stampò i nove libri intitolati <emph type="italics"></emph>Quesiti et inventioni diverse,<emph.end type="italics"></emph.end><lb></lb>si direbbe piuttosto che la differenza nasceva dallo stampare nel materno <lb></lb>vernacolo lombardo, o nella lingua latina, rispetto alla quale essendo, edi­<lb></lb>tore e tipografo, simili a un cieco, che si facesse guida a un altro cieco, non <lb></lb>fa maraviglia che ambedue cadessero nella medesima fossa. </s>

<s>Un tal giudizio <lb></lb>vien confermato da altri esempi, come da questo: <emph type="italics"></emph>Explicet liber Archime­<lb></lb>dis de centrum gravitatis vel duplationis aequerepentibus (Opera Archim. </s>

<s><lb></lb>per N. Tartaleam,<emph.end type="italics"></emph.end> Venetiis 1543, fol. </s>

<s>19). E perchè tali erano per così dire <lb></lb>le rubriche, dall&#039;editore aggiunte al manoscritto, si può di qui giudicare <lb></lb>quanto valesse il Tartaglia nella lingua latina, persuaso talmente essere il <lb></lb>vero titolo de&#039;libri di Archimede, intorno agli Equiponderanti, qual&#039;egli lo <lb></lb>faceva stampare al Ruffinelli, senz&#039;avvedersi del bisogno che v&#039;era di cor­<lb></lb>reggervi <emph type="italics"></emph>vel de planis<emph.end type="italics"></emph.end> sulle bozze di stampa; che torna, nel Ragionamento <pb xlink:href="020/01/3118.jpg" pagenum="79"></pb>primo sopra la sua <emph type="italics"></emph>Travagliata inventione,<emph.end type="italics"></emph.end> a citare i detti libri, con la stessa <lb></lb>sicurtà e franchezza, <emph type="italics"></emph>De centro gravium valde planis aequerepentibus<emph.end type="italics"></emph.end><lb></lb>(pag. </s>

<s>18). E un tal uomo si vuol far credere il traduttore dal latino di un <lb></lb>codice greco?! Ma se il Tartaglia è inferiore al Commandino, in letteratura, <lb></lb>ei lo supera lungamente nella scienza, perchè mentre l&#039;uno non è che un <lb></lb>semplice commentator di Archimede, e non sempre felice come vedemmo, <lb></lb>l&#039;altro lo promove a tal punto, che è bene segnar con lapide, perchè sem­<lb></lb>bra essere stato sepolto dalle sabbie portatevi sepra dai venti del deserto. </s>

<s><lb></lb>Intendiamo dire della tooria e della pratica di ritrovare i pesi specifici dei <lb></lb>varii corpi, che rimaste, per pregiudizi e per ambizione, dimenticate, riap­<lb></lb>parvero un mezzo secolo dopo, nel Ghetaldo e nel Galileo, come nuove. </s></p><p type="main">

<s>Dalle varie scritture dello stesso Tartaglia si ricava qual si fosse l&#039;ori­<lb></lb>gine, e l&#039;occasione di dimostrare la scienza, e d&#039;insegnar l&#039;arte da misurare <lb></lb>quanto un solido o un liquido fossero, rispetto all&#039;acqua, più o meno gravi. </s>

<s><lb></lb>Egli era a Brescia sua patria, quando giunse la notizia che una nave carica <lb></lb>erasi affondata presso a Malamocco, nè, per qualunque arte vi si fosse usata <lb></lb>attorno, era stato possibile recuperarla. </s>

<s>Un&#039;altra nave, che similmente affondò <lb></lb>poco dopo, e, per l&#039;esperienze fattesi nella prima, perduta ogni speranza di <lb></lb>riaverla, benchè ne rimanessero a fior d&#039;acqua la poppa e la prora; si de­<lb></lb>cretò di ridurla in pezzi, e sgombrarne poi il porto da&#039;rottami. </s>

<s>“ Ond&#039;io, <lb></lb>dice il Tartaglia al doge Francesco Donato, considerando di quanto danno <lb></lb>era il rompere un simil vaso, oltre la perdita del cargo, deliberai da inve­<lb></lb>stigare qualche modo, over regola da sovenire a tai dannose occorrentie. </s>

<s><lb></lb>Onde, havendone ritrovata una generale et indubitata, me apparso per co­<lb></lb>mun benefitio di questa magnifica Città da dichiarare, et figuralmente delu­<lb></lb>cidare tal regola, nella presente operina ” che nel 1551 si dava, nella stessa <lb></lb>Venezia, alla luce, col titolo di <emph type="italics"></emph>Travagliata inventione.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>È divisa la detta operina in tre brevissimi libri, benchè l&#039;argomento sia <lb></lb>quanto alla sostanza esaurito nel primo, ìn cui, supponendo la media gravità <lb></lb>specifica del carico della nave ridotta a quella di un solido omogeneo, come <lb></lb>terra cotta, marmo, ferro, piombo, rame, oro, ecc., si assegnano le minime <lb></lb>dimensioni al vacuo di un vaso di legno, perchè, caricatosi di un determi­<lb></lb>nato volume del tale o del tale altro solido, potesse ivi dentro sostenersi a <lb></lb>galla. </s>

<s>Ma sembrando difficile l&#039;imbragare, per via di strumenti, il solido <lb></lb>sommerso per sollevarlo, senza l&#039;assistente mano dell&#039;uomo; immaginò l&#039;Au­<lb></lb>tore, e poi descrisse nel secondo libro una macchina, nella quale a tutto si <lb></lb>provvedeva, per calarsi a lavorare giù sul fondo marino, fuor che alla cosa <lb></lb>principale, qual&#039;era il modo di respirare in un piccolo vaso chiuso: modo, <lb></lb>che, conseguitosi pol senza molta difficoltà, dette l&#039;invenzione del Tartaglia <lb></lb>perfezionata in quell&#039;utilissimo strumento peschereccio, da gran tempo co­<lb></lb>nosciuto sotto il nome di <emph type="italics"></emph>Campana del palombaro.<emph.end type="italics"></emph.end> Nel terzo libro final­<lb></lb>mente si raccolgono, da varii autori e dalle tradizioni popolari, i segni delle <lb></lb>mutazioni dell&#039;aria o dei tempi. </s></p><p type="main">

<s>Ma ritornando alla parte sostanziale dell&#039;invenzione, “ acciocchè, dice il <pb xlink:href="020/01/3119.jpg" pagenum="80"></pb>Tartaglia, se ne habbia generale dottrina, per recuperare ogni specie di co­<lb></lb>losso affondato, cioè de ogni specie di corpo solido, o sia di pietra, over di <lb></lb>ferro, over di stagno, over di rame, over di piombo, over di argento, over <lb></lb>di oro (come che facilmente occorrer potria di affondarlo volontariamente, <lb></lb>in tempo di guerra, per salvarlo, e da poi saperlo anchora con ragion recu­<lb></lb>perare) bisogna tener questa regola: Sel solido per longo tempo affondato <lb></lb>fosse de pietra cotta (detta matone, over quadrello) da poi che afferrato fusse, <lb></lb>saria necessario a tuor tanti para di navi over navigli, barche over burchii, <lb></lb>che tutti li vacui de quelli in summa non fussen men che quadruppli al­<lb></lb>l&#039;area corporale di quel tal solido affondato. </s>

<s>E se per sorte il solido, già <lb></lb>longo tempo affondato, fusse di pietra marmorina, bisogneria che l&#039;area cor­<lb></lb>porale de tutti li vacui di detti legni over vasi in summa non fusseno men <lb></lb>che settupli all&#039;area corporale de l&#039;affondato solido, cioè sette volte tanto ” <lb></lb>(pag. </s>

<s>67). E seguita a dar similmente la regola, nel caso che il solido affon­<lb></lb>dato fosse ferro, piombo, rame, argento, oro. </s>

<s>Una tal regola poi facilmente <lb></lb>si comprende come fosse fondata nell&#039;invenzione dei pesi specifici delle dette <lb></lb>terre e metalli, ma, non essendo quivi il luogo di renderne le ragioni, il Tar­<lb></lb>taglia vi supplì con alcuni Ragionamenti, ne&#039;quali si dava scienza di ciò, che <lb></lb>solo praticamente aveva prima insegnato ai marangoni. </s>

<s>E perchè tale scienza <lb></lb>derivava necessariamente dai principii idrostatici, per l&#039;antico Maestro già <lb></lb>dimostrati, nel Ragionamento primo sopra le cose dette nel principio della <lb></lb><emph type="italics"></emph>Travagliata inventione<emph.end type="italics"></emph.end> “ sè dichiara volgarmente quel libro di Archimede <lb></lb>siracusano, detto <emph type="italics"></emph>De insidentibus aquae,<emph.end type="italics"></emph.end> materia di non poca speculatione <lb></lb>et intellettual dilettatione ” ciò che l&#039;Autore fa risaltar dalle parafrasi e dai <lb></lb>commenti, a cui gli porge occasione quel suo compare Riccardo Ventvorth, <lb></lb>insiem col quale dialogizzando si studia di abbellire in qualche modo il di­<lb></lb>scorso. </s></p><p type="main">

<s>Questo primo ragionamento serviva di preparazion fondamentale alle <lb></lb>dottrine, che si dimostrerebbero nel secondo, intorno al determinar la forza <lb></lb>necessaria per sollevar la nave sommersa, e distingue il caso importante che <lb></lb>il fondo di lei sia circondato dall&#039;acqua, come avviene quando fosse caduto <lb></lb>sui sassi, o sia da essa acqua escluso, come quando riman confitto nell&#039;arena. </s>

<s><lb></lb>Dicevasi questa distinzione importante, perchè si riduceva alla question della <lb></lb>baga di Leonardo da Vinci messa in fondo all&#039;acqua del pozzo, dal modo di <lb></lb>risolver la quale si deciderebbe de&#039;progressi che, nel riconoscere l&#039;azione <lb></lb>delle pressioni <emph type="italics"></emph>sursum,<emph.end type="italics"></emph.end> per riflessione delle pressioni <emph type="italics"></emph>deorsum,<emph.end type="italics"></emph.end> avrebbe fatto <lb></lb>in quel tempo la Scienza, la quale si può dunque concludere che si rima­<lb></lb>nesse stazionaria, perchè il Tartaglia attribuisce la maggiore o minore diffi­<lb></lb>coltà di riaver la nave, nei due detti casi, a ragioni immaginarie, sostituite <lb></lb>in luogo delle vere non conosciute. </s></p><p type="main">

<s>“ Hor perchè, egli dice, sia mo tanto e tanto difficile separare il corpo <lb></lb>da un fondo pantanoso, over arenoso, da quello che sia da un sassoso; la <lb></lb>causa è questa: Che in un fondo sassoso tutto il detto affondato corpo è <lb></lb>abbrazato et circondato dal&#039;acqua, accettuando quella poca parte, che tocca <pb xlink:href="020/01/3120.jpg" pagenum="81"></pb>il detto fondo sassoso, la qual parte ancora, quanto che è più accuta, cioè <lb></lb>che tocca manco del detto fondo, tanto è più facile a separarlo da quello, <lb></lb>perchè l&#039;acqua, che ha da empire quel luoco, che lassarà il detto corpo nella <lb></lb>sua assensione; è ivi presente, cioè che non ha da venire da loco molto lon­<lb></lb>tano, e però il detto corpo, non ha tanta difficoltà a tirare da longinque <lb></lb>parti, come che gli occorreria, quando che fusse in gran parte sepulto nel <lb></lb>pantano, over sabbia, nella qual positione gli bisogneria tirare la detta acqua <lb></lb>dalla suprema parte di quella sua cassa pantanosa, over arenosa, per fin nella <lb></lb>infima parte di quella. </s>

<s>E perchè tal acqua non puol così immediate, over <lb></lb>in un istante, discorrere in tal parte infima, ma solamente in tempo, e la <lb></lb>Natura non permette che un loco possi restar vacuo per alcuno minimo spa­<lb></lb>cio di tempo; e perciò è cosa molto e molto più difficultosa a separare un <lb></lb>corpo grave da un fondo pantanoso, di quello sarà in un fondo sassoso ” <lb></lb>(pag. </s>

<s>27). </s></p><p type="main">

<s>Smossa che sia l&#039;arrenata mole dal fondo, la maggiore o minor forza, <lb></lb>che tuttavia ve la trattiene, dipende solamente dal maggiore o minore peso <lb></lb>specifico, cosicchè, conosciutosi questo, s&#039;avrà anche insieme la misura di <lb></lb>quella, e della contraria potenza sollevatrice. </s>

<s>Or il Tartaglia annunzia di <lb></lb>aver trovati i pesi specifici di varie sorta di corpi, quale annunzio destò in <lb></lb>Riccardo la curiosità di sapere com&#039;avesse fatto a misurarli con tanta pre­<lb></lb>cisione, che pareva sì difficile ad ottenersi co&#039;metodi antichi. </s>

<s>Qe&#039;metodi in­<lb></lb>fatti, derivando dalle tradizioni archimedee, consistevano nel pesare il corpo <lb></lb>in aria, e poi, sommersolo in un vaso pieno, pesar l&#039;acqua versata, non poca <lb></lb>parte della quale, come quella rimasta a bagnar le pareti, andando dispersa, <lb></lb>era potissima causa del non si corrispondere esattamente insieme i due com­<lb></lb>parati volumi. </s>

<s>Il Tartaglia rimediò a questo, e ad altri inconvenienti, pe­<lb></lb>sando il medesimo corpo prima in aria, poi in acqua, e desumendone la <lb></lb>gravità specifica dalla differenza de&#039;due pesi, in virtù della VII proposizione <lb></lb>archimedea. </s>

<s>Così egli fu il primo a inventare, e a far uso della <emph type="italics"></emph>Bilancetta <lb></lb>idrostatica,<emph.end type="italics"></emph.end> ch&#039;egli stesso così deserive, per sodisfare alla sopra accennata <lb></lb>curiosità del suo Riccardo: </s></p><p type="main">

<s>“ Ve dirò, compare, volendomi certificare che proportion havesse la pie­<lb></lb>tra cotta (detta matone over quadrello) in gravità con l&#039;acqua. </s>

<s>Io pesai due <lb></lb>pietre cotte, over quadrelli, sottili, li quali trovai essere libbre 7, once 2 alla <lb></lb>grossa, et da poi li legai con uno spagheto longheto attacato a li ancini della <lb></lb>stadera, over piombino, et questo feci, acciò che li detti ancini non intras­<lb></lb>seno nell&#039;acqua, dove faceva conto di pesarli, et così con tal cautella li ri­<lb></lb>pesai in un vaso di acqua dolce, ed in quella li trovai esser solamente lib­<lb></lb>bre 3, once 5, onde, per la VII di Archimede, tanta acqua, quanto saria li <lb></lb>detti due quarelli, veneria a pesare libbre 3, once 9, cioè la differentia, che <lb></lb>è fra le libbre 7, once 2, che, pesò in aere, e le libbre 3, once 9, che pesò <lb></lb>in acqua. </s>

<s>Per la qual cosa io conclusi che la proportione della pietra cotta <lb></lb>all&#039;acqua, in gravità, fusse come da once 86 a 41, che saria più che dop­<lb></lb>pia in gravità. </s>

<s>Ma, per certificarmi meglio, il giorno seguente ripesai li dui <pb xlink:href="020/01/3121.jpg" pagenum="82"></pb>medesimi quarelli, li quali trovai in aere essere libbre 7, once 9, cioè cre­<lb></lb>scerno once 7, per essere imbeverati di acqua, et da poi li ripesai in acqua, <lb></lb>e li retrovai libbre 3, once 9. La differentia di questi due pesi saria libbre 4, <lb></lb>onde, secondo questa seconda sperientia, la proportione di tal pietra cotta <lb></lb>all&#039;acqua in gravità saria come once 93 a 48, cioè men che doppia. </s>

<s>Onde, <lb></lb>per esser molto il variare di tal sorta di quadrelli, e tal hor uno è più grave <lb></lb>de l&#039;altro per la humidità e siccità, pigliai il mezzo di queste due sperien­<lb></lb>tie, cioè conclusi che la proportione della detta pietra cotta in gravità con <lb></lb>l&#039;acqua essere circa doppia ” (pag. </s>

<s>30). </s></p><p type="main">

<s>Di poi, seguita a dire il Tartaglia, pesai una palla di marmo, e la tro­<lb></lb>vai in aria once 7, e in acqua once 5, di modo che ne conclusi stare il peso <lb></lb>del marmo, a quello di un ugual volume di acqua, come 7 a 2. E come 19 <lb></lb>a 3 trovò per il ferro, come 65 a 10 per il rame, come 30 a 3 per il piombo, <lb></lb>come 313 a 32 per l&#039;argento, e finalmente come 17 a 1, per l&#039;oro. </s>

<s>“ Ces <lb></lb>pesanteurs, osserva il Libri, semblent en general un peu trop flaibles, mais <lb></lb>il faut remarquer que non seulement Tartaglia, qui les determinait en obser­<lb></lb>vant combien un corps perduit de son poids lorsqu&#039;on le plongeait dans l&#039;eau, <lb></lb>ne se servait pas d&#039;eau distillée, mais que de plus, faisant ses experiences a <lb></lb>Venise, dans le dessein surtout de les appliquer au sauvetage des vaisseaux <lb></lb>submergés, il employait peut-<gap></gap>tre l&#039;eau de la mer pour unité ” <emph type="italics"></emph>(Histoire des <lb></lb>sciences mathem.,<emph.end type="italics"></emph.end> T. III, a Paris 1840, pag. </s>

<s>166). </s></p><p type="main">

<s>Se l&#039;acqua in cui immergeva i corpi il Tartaglia, non era distillata, sap­<lb></lb>piamo però da lui stesso che era pura; “ Sel fusse possibile a formare un <lb></lb>cubo di <emph type="italics"></emph>acqua pura,<emph.end type="italics"></emph.end> che fusse poniamo un piede per fazza, formandone poi <lb></lb>un altro simile, et uguale in quantità di detta pietra cotta, dico che il detto <lb></lb>cubo di pietra cotta pesaria circa il doppio di quello, che pesaria quel cubo <lb></lb>di acqua ” (pag. </s>

<s>28). Che se lo Storico dalle Matematiche in Italia potè so­<lb></lb>spettar che il Tartaglia riferisse le proporzioni de&#039;pesi all&#039;acqua marina, <lb></lb>convien dire ch&#039;ei non leggesse questa avvertenza, premessa dall&#039;Autore alla <lb></lb>descrizione della Bilancietta idrostatica, e alla tavola de&#039;pesi specifici ritro­<lb></lb>vati con essa: “ Tutte queste proportioni delli detti corpi materiali con l&#039;acqua <lb></lb>sono state da me ritrovate con l&#039;acqua comune di pozzo, cioè dolce e non <lb></lb>salsa, e però, essendo la salsa alquanto più grave della dolce, varierà al­<lb></lb>quanto, ma poco ” (pag. </s>

<s>30). Per cui, se i pesi, nella detta Tavola descritti, <lb></lb>non solo sembrano, ma son veramente <emph type="italics"></emph>un peu trop faibles;<emph.end type="italics"></emph.end> non è da at­<lb></lb>tribuir ciò ad altro che all&#039;impurità de&#039;metalli sottoposti alle esperienze: <lb></lb>considerazione che non poteva essere sfuggita al Tartaglia, il quale perciò <lb></lb>non intese dare i pesi specifici del rame, dell&#039;argento e dell&#039;oro puri, ma <lb></lb>quali ei gli trovò alligati nelle monete, che erano allora in corso nel Regno <lb></lb>veneto, come bagatini, mocenighi, ducati: così, nella proposta Tavola, qua­<lb></lb>lificatisi, per prevenire i dubbi di chi fosse per ritrovare altre proporzioni, <lb></lb>in oggetti formati di metalli, che vanno sotto que&#039;medesimi nomi. </s></p><p type="main">

<s>Fin qui non esce fuori il Tartaglia del campo della Fisica, ma egli vuol <lb></lb>coronare la sua invenzione di quattro Teoremi, che egli giudica degni di <pb xlink:href="020/01/3122.jpg" pagenum="83"></pb>essere aggiunti a quelli dello stesso Archimede. </s>

<s>“ Quattro altre ingegnose <lb></lb>proposizioni, compare honorando, oltre quelle dette da Archimede, vi voglio <lb></lb>in questo loco narrare dimostrativamente, delle quale la prima è questa: <lb></lb><emph type="italics"></emph>La proportione de ogni dui corpi gravi in grandezza, o sia de un mede­<lb></lb>simo, overo de diversi generi, è si come la differentia del peso de luno de <lb></lb>quelli in aere al peso de quel medesimo in acqua, alla differentia del peso <lb></lb>del altro in aere al peso di quello medesimo in acqua. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia uno de dui corpi A, et sia C tanta acqua a quel eguale in gran­<lb></lb>dezza, et il peso di tal acqua sia E. </s>

<s>Et sia simelmente B l&#039;altro corpo, et D <lb></lb>sia l&#039;acqua a quello uguale in grandezza, et F sia il peso di quella acqua. </s>

<s><lb></lb>Perchè adunque, compare carissimo, l&#039;acqua C è uguale al corpo A in gran­<lb></lb>dezza, e similmente l&#039;acqua D è uguale al corpo B; permutatamente la pro­<lb></lb>portione del A al B sarà siccome del C al D, e la proportione, che è dalla <lb></lb>acqua C alla acqua D, quella medesima sarà del suo peso E al peso F. Adun­<lb></lb>que, per la XI del V di Euclide, la proportione del peso E al peso F sarà <lb></lb>si come del corpo A al corpo B in grandezza. </s>

<s>E perchè il peso E, per la VII <lb></lb>del nostro Archimede, viene a esser la differentia del peso del corpo A in <lb></lb>aere, al peso di quel medesimo in acqua, e così il peso F vien a esser la <lb></lb>differentia del peso del corpo B in aere, al peso di quel medesimo in acqua; <lb></lb>per il che seguita il proposito ” (pag. </s>

<s>31, 32). </s></p><p type="main">

<s>Si possono dunque scrivere, secondo questo discorso del Tartaglia, le <lb></lb>proporzioni A:B=C:D=E:F, nelle quali A, B sono i volumi di due <lb></lb>corpi, a cui corrispondono due uguali volumi di acqua C, D: ed E, F sono <lb></lb>le differenze de&#039;pesi di quegli stessi corpi in aria e in acqua. </s>

<s>Chiamate <lb></lb>P—<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> P′—<emph type="italics"></emph>p′<emph.end type="italics"></emph.end> queste differenze, V, <emph type="italics"></emph>v<emph.end type="italics"></emph.end> i volumi, avremo perciò V:<emph type="italics"></emph>v<emph.end type="italics"></emph.end>= <lb></lb>P—<emph type="italics"></emph>p<emph.end type="italics"></emph.end>:P′—<emph type="italics"></emph>p′.<emph.end type="italics"></emph.end> Ora, perchè, secondo la loro naturale definizione, le gra­<lb></lb>vità specifiche stanno come i pesi assoluti, divisi per i volumi; dunque sta­<lb></lb>ranno anche com&#039;essi pesi assoluti, divisi per le differenze de&#039;pesi in aria e <lb></lb>in acqua, d&#039;onde una nuova espressione della gravità specifica. </s></p><p type="main">

<s>Da questa proposizione trae il Tartaglia un nuovo e importantissimo co­<lb></lb>rollario: Se <emph type="italics"></emph>v<emph.end type="italics"></emph.end> è il volume noto di un cubo, rispetto al quale siasi, per mezzo <lb></lb>della Bilancetta, trovato il valore di P′—<emph type="italics"></emph>p′,<emph.end type="italics"></emph.end> e se V è il volume incognito <lb></lb>di qualunque forma irregolare di corpo, per cui siasi col medesimo stru­<lb></lb>mento determinato il valore di P—<emph type="italics"></emph>p;<emph.end type="italics"></emph.end> è manifesto che, per la superiore <lb></lb>equazione, sarà noto il valore di V. </s>

<s>Per cui, specialmente ripensando che il <lb></lb>Mantovani e il Viviani darebbero questa come una loro novità, s&#039;intende <lb></lb>quant&#039;avesse giusta ragione il Tartaglia di far dire all&#039;interlocutore suo Ric­<lb></lb>cardo: “ Compare, questa è stata certamente una bellissima e utile propo­<lb></lb>sitione et demostratione, perchè con grandissima facilità se può cognoscere <lb></lb>l&#039;area corporale de ogni strania forma di corpo, il che importa assai, perchè <lb></lb>saria impossibile a poterla investigare, nè sapere, per i semplici termini di <lb></lb>Geometria ” (ivi, pag. </s>

<s>32). </s></p><p type="main">

<s>Nella sua seconda proposizione il Tartaglia insegna a trovare il peso <lb></lb>specifico di due liquidi, per esempio acqua e olio. </s>

<s>Presi de&#039;due detti liquidi <pb xlink:href="020/01/3123.jpg" pagenum="84"></pb>volumi uguali, non è dubbio che, dalle due equazioni G=P:V, <emph type="italics"></emph>g=p:v,<emph.end type="italics"></emph.end><lb></lb>si ha le gravità specifiche proporzionali ai pesi assoluti. </s>

<s>Ond&#039;è che s&#039;otter­<lb></lb>rebbe con facilità la desiderata invenzione, per via della Stadera ordinaria, <lb></lb>pesando il medesimo vaso, per esempio un fiasco, prima pieno d&#039;acqua, e <lb></lb>poi di olio. </s>

<s>Ma vuole il Nostro, anche in questo caso, applicar la Bilancetta, <lb></lb>osservando che, per la VII del primo di Archimede, i valori, rappresentati <lb></lb>con P, <emph type="italics"></emph>p<emph.end type="italics"></emph.end> si possono avere dalle differenze che ne resultano, pesando il me­<lb></lb>desimo oggetto, di qualunque materia egli sia, prima nell&#039;aria, e poi nell&#039;un <lb></lb>liquido e nell&#039;altro, per cui quella sua detta proposizione seconda fu dal­<lb></lb>l&#039;Autore stesso così formulata: <emph type="italics"></emph>“ Se la proportione del peso de alcun corpo <lb></lb>in duoi diversi liquori et in aere sarà nota; la proportione della gravità <lb></lb>de l&#039;uno de quei liquori, alla gravità de laltro secondo la specie, sarà <lb></lb>manifesta ”<emph.end type="italics"></emph.end> (pag. </s>

<s>32). </s></p><p type="main">

<s>Dalla stabilita proporzione poi V:<emph type="italics"></emph>v<emph.end type="italics"></emph.end>=P—<emph type="italics"></emph>p<emph.end type="italics"></emph.end>:P′—<emph type="italics"></emph>p′,<emph.end type="italics"></emph.end> e da quell&#039;al­<lb></lb>tra G:<emph type="italics"></emph>g<emph.end type="italics"></emph.end>=P/P—<emph type="italics"></emph>p<emph.end type="italics"></emph.end>:P′/P′—<emph type="italics"></emph>p′.<emph.end type="italics"></emph.end> conclusa già nella prima di queste proposi­<lb></lb>zioni, scende senz&#039;altro dimostrata la III dello stesso Tartaglia: <emph type="italics"></emph>“ Se li pesi <lb></lb>in aere et in acqua de dui qual si voglia corpi, poniamo di oro e di ar­<lb></lb>gento, saranno noti; le proportioni de quelli medesimi corpi, in grandezza <lb></lb>et secondo la specie, saranno note ”<emph.end type="italics"></emph.end> (ivi). </s></p><p type="main">

<s>Nella quarta proposizione, pur procedendo analiticamente, come nella <lb></lb>passata, si cerca una formula generale, che renda possibile la risoluzione di <lb></lb>questo problema: <emph type="italics"></emph>“ Ritrovare la proportione della grandezza, et la pro­<lb></lb>portione della gravità, secondo la specie, de dui corpi, di quali l&#039;uno sia <lb></lb>di natura più grave di lacqua, come è il ferro, et l&#039;altro di natura più <lb></lb>leggier di lacqua, come è la cera. </s>

<s>”<emph.end type="italics"></emph.end> Risoluto il problema, così l&#039;Autore <lb></lb>immediatamente soggiunge: “ Con la evidentia di questa propositione egli <lb></lb>è possibile, de un corpo misto di dui corpi differenti in gravità, poniamo di <lb></lb>oro e di argento; a dichiarare quanto vi sia dentro dell&#039;uno, e quanto del­<lb></lb>l&#039;altro ” (ivi, pag. </s>

<s>33, 34). </s></p><p type="main">

<s>La formula infatti, alla quale conduce il ragionamento del Tartaglia, si <lb></lb>traduce facilmente in quest&#039;altra, chiamata G la gravità specifica del misto, <lb></lb><emph type="italics"></emph>p, p′<emph.end type="italics"></emph.end> i pesi assoluti dell&#039;oro e dell&#039;argento, <emph type="italics"></emph>v, v′<emph.end type="italics"></emph.end> i volumi: G=<emph type="italics"></emph>(p+p′)/(v+v′).<emph.end type="italics"></emph.end><lb></lb>E perchè, supponendo esser P il peso assoluto del detto misto, è manifesta­<lb></lb>mente <emph type="italics"></emph>p′<emph.end type="italics"></emph.end>=P—<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> e <emph type="italics"></emph>v=p/g, v′=p′/g′,<emph.end type="italics"></emph.end> intendendosi per <emph type="italics"></emph>g, g′<emph.end type="italics"></emph.end> le respettive <lb></lb>gravità specifiche dell&#039;oro e dell&#039;argento; avremo dunque G=P:<emph type="italics"></emph>(p/g<emph.end type="italics"></emph.end>+(P—<emph type="italics"></emph>p)/g′)<emph.end type="italics"></emph.end>, <lb></lb>d&#039;onde <emph type="italics"></emph>p<emph.end type="italics"></emph.end>=P<emph type="italics"></emph>g (g′<emph.end type="italics"></emph.end>—G)/G <emph type="italics"></emph>(g′—g)<emph.end type="italics"></emph.end>. </s>

<s>Ora, avendosi il valore di P dalla Stadera, e dalla <lb></lb>Bilancetta idrostatica i valori di G, <emph type="italics"></emph>g, g′<emph.end type="italics"></emph.end>; sarà dunque noto <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> ossia il peso <lb></lb>dell&#039;oro, e verrà per esso notificato altresì il peso dell&#039;argento, perchè <emph type="italics"></emph>p′<emph.end type="italics"></emph.end>= <lb></lb>P—<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> “ la qual regola, giustamente ne conclude il Tartaglia, sarà molto e <pb xlink:href="020/01/3124.jpg" pagenum="85"></pb>molto piu certa et men fallace di quella, che nara Vitruvio et altri autori <lb></lb>haver trovata Archimede, per cognoscer la fraude del artefice nell&#039;aurea co­<lb></lb>rona di Hierone. </s>

<s>Perchè tal sua via non servirà, salvo che in una gran massa <lb></lb>di oro. </s>

<s>Ma con questa se potrà conoscere tal fraude pontualmente, in un du­<lb></lb>cato, et men de un ducato doro, domente che (purchè) si sia diligenti nel <lb></lb>operare ” (pag. </s>

<s>34). </s></p><p type="main">

<s>La critica, fatta così dal Tartaglia al metodo attribuito ad Archimede, <lb></lb>è giusta, per le ragioni accennate di sopra, e perchè, se l&#039;oggetto è piccolo, <lb></lb>può essere che, nell&#039;infonderlo, o non si versi nulla dell&#039;acqua del vaso colmo, <lb></lb>o che non si versi tutta, perchè la pellicola superficiale, prima di squarciarsi, <lb></lb>rigonfia, e non versa che dalla parte, dov&#039;è avvenuto lo squarcio. </s>

<s>Così fatti <lb></lb>inconvenienti si evitano manifestamente con l&#039;uso della Bilancetta, la quale, <lb></lb>dando in ogni modo la differenza del peso, per qualunque minimo corpo, <lb></lb>fa che senza difficoltà, e con tutta la precisione, se ne possa conseguire <lb></lb>l&#039;intento. </s></p><p type="main">

<s>Tali erano le utilissime promozioni che dopo la prima metà del se­<lb></lb>colo XVI, ebbe l&#039;idrostatica di Archimede. </s>

<s>Ma perchè s&#039;aggiungevano a que­<lb></lb>ste tradizioni antiche quelle altre, derivate da Frontino, anche da tal parte <lb></lb>fu, in quel medesimo tempo, la scienza utilmente promossa. </s>

<s>Nel 1554, in­<lb></lb>sieme con altri opuscoli geometrici di Giovanni Buteone, ne uscì in Lione <lb></lb>alla luce uno, che s&#039;intitolava <emph type="italics"></emph>De fluentis aquae mensura.<emph.end type="italics"></emph.end> L&#039;Autore, dopo <lb></lb>avervi diligentemente esaminati i Commentarii sopra gli Acquedutti romani, <lb></lb>conclude che così Frontino come tutti gli altri Scrittori, prima e dopo lui, <lb></lb>quant&#039;erano stati solleciti, in avvertire alcune cause alteratrici della velocità <lb></lb>delle acque correnti, e perciò della loro misura; altrettanto s&#039;erano dimo­<lb></lb>strati incerti, in suggerirne i rimedii. </s>

<s>“ Multa igitur, poi soggiunge, scru­<lb></lb>pulose mihi denique cogitanti, illa tandem subiit animum cogitatio ut que­<lb></lb>madmodum tempus ipsum aqua stillante metitur, sic et fluentis aquae <lb></lb>modum mensura temporis veluti mutua posse constitui ” <emph type="italics"></emph>(J. </s>

<s>Buteonis Qp. </s>

<s>geo­<lb></lb>metrica, nunc primum impressa,<emph.end type="italics"></emph.end> Lugduni 1554, pag. </s>

<s>71). E il modo, che <lb></lb>suggerisce, consiste nel dar, nel medesimo istante, esito all&#039;acqua della con­<lb></lb>serva e della clessidra, cosicchè il riempimento di un vaso di nota capacità, <lb></lb>per esempio di un piede cubico, corrisponda a un determinato tempo, come <lb></lb>sarebbe un minuto. </s>

<s>Chiamandosi la detta capacità, per conformarsi con Fron­<lb></lb>tino, quinaria, è certo, dice il Buteone, che, volendosi dare due, o tre o <lb></lb>quattro quinarie, si farà passar l&#039;acqua dalla medesima cannella per due, o <lb></lb>tre o quattro minuti, e così verranno misurate giustamente le dispense dalla <lb></lb>preparata conserva, che sempre si mantenesse alla medesima altezza, misu­<lb></lb>rando le parti proporzionali del tempo. </s>

<s>“ His itaque rationibus et exemplis, <lb></lb>ni fallor, et antiquorum error manifestus, et emendatio probabilis erit. </s>

<s>Et ita <lb></lb>ad fluentis aquae mensuram se nostrum habet inventum ” (ibid., pag. </s>

<s>72). </s></p><p type="main">

<s>Oltre a quelle, raccolte dai libri di Archimede e di Frontino, proveni­<lb></lb>vano altre nuove tradizioni alla Scienza dagli insegnamenti del Nemorario, <lb></lb>la fecondità de&#039;quali vedemmo rigogliosamente apparire ne&#039;Manoscritti di Leo-<pb xlink:href="020/01/3125.jpg" pagenum="86"></pb>nardo da Vinci, e nelle pubbliche opere del Cardano. </s>

<s>Ma, dopo la prima <lb></lb>metà del secolo XVI, parve che di queste ultime tradizioni, per cui si vi­<lb></lb>dero applicate ai liquidi le velocità, che sollecitano tutti i gravi cadenti; ne <lb></lb>rimanesse spenta ogni notizia. </s>

<s>Basti a provar ciò l&#039;esempio del Benedetti, <lb></lb>in quella, che egli intitolava: <emph type="italics"></emph>Nova solutio problematis de vase pleno li­<lb></lb>quoris. (Speculat. </s>

<s>liber. </s>

<s>Epistolae,<emph.end type="italics"></emph.end> Venetiis 1599, pag. </s>

<s>289). </s></p><p type="main">

<s>Proponevasi il caso di un tino pieno, con tre cannelle al fondo di varia <lb></lb>grandezza, la prima delle quali valesse a evacuarlo in un&#039;ora, la seconda in <lb></lb>due, e la terza in tre: domandavasi in quanto tempo, lasciando dette can­<lb></lb>nelle aperte tutt&#039;e tre insieme, voterebbero quel medesimo vaso. </s>

<s>“ Ad hoc <lb></lb>volo, risponde il Benedetti, ut quaèratur primo quanta pars aquae unaquae­<lb></lb>que fistula evacuabit in aliquo dato tempore, quod facile est, ut puta prima <lb></lb>fistula spatio dimidiae horae evacuabit dimidium vas, eo quod spatio inte­<lb></lb>grae horae potest totum evacuare: secunda fistula, eodem temporis spatio, <lb></lb>evacuabit quartam partem ipsius vasis; tertia vero fistula, eodemmet spatio <lb></lb>temporis dimidiae horae, evacuabit sextam partem ipsius vasis ” (ibid.). </s></p><p type="main">

<s>Pare impossibile che un tale uomo profferisse cose tanto contrarie alla <lb></lb>ragione e all&#039;esperienza, e, se non avessimo questa certezza di documenti, <lb></lb>non si crederebbe che le proposizioni, dimostrate dal Cardano intorno al­<lb></lb>l&#039;acque fluenti da&#039;vasi, o correnti lungo i canali, si rimanessero così total­<lb></lb>mente sepolte nell&#039;oblio, che le potessero il Castelli e Galileo dare per nuove <lb></lb>apparizioni. </s>

<s>Ma capitali, in questa nobilissima parte dello scientifico istituto, <lb></lb>rimanevano, prima e dopo il Cardano, i teoremi di Archimede, i quali, se <lb></lb>porgevano facilissimo il modo a spiegar come l&#039;acqua s&#039;equilibrasse in un <lb></lb>sifone, co&#039;due rami di ugual calibro, lasciavano tuttavia inesplicato e ine­<lb></lb>splicabile il fatto del serbarsi parimente l&#039;equilibrio, anche quando l&#039;uno dei <lb></lb>detti rami fosse straordinariamente più capace dell&#039;altro. </s>

<s>Questo, che ha <lb></lb>l&#039;aria di un paradosso, e che giusto è andato, e va nella Scienza idrosta­<lb></lb>tica, sotto un tal nome, famoso, richiamò a sè, tra il finir del secolo XVI e <lb></lb>il cominciar del seguente, l&#039;ingegno e lo studio dei Matematici, e parve esau­<lb></lb>rirli tutti così, da non lasciarli in libertà di attendere ad altre simili spe­<lb></lb>culazioni. </s>

<s>Vedremo infatti come fosse questo l&#039;oggetto, a cui si rivolsero, e <lb></lb>da cui si svolsero le nuove istituzioni idrostatiche dello Stevino e di Galileo, <lb></lb><figure id="id.020.01.3125.1.jpg" xlink:href="020/01/3125/1.jpg"></figure></s></p><p type="caption">

<s>Figura 36.<lb></lb>ma prima è da mostrare come fossero, all&#039;uno e all&#039;al­<lb></lb>tro autore, aperte prima le vie dallo stesso Benedetti. </s></p><p type="main">

<s>In una delle sue epistole a Giovan Paolo Capra si <lb></lb>propone di dimostrare perchè, avendosi un largo vaso o <lb></lb>mortaio come AB (fig. </s>

<s>36), a cui sia annessa una gracile <lb></lb>fistola C, la piccola acqua contenuta in questa possa far <lb></lb>resistenza alla gran mole dell&#039;altra. </s>

<s>“ Hoc autem evenit, <lb></lb>egli dice, ex eo quod aqua AB non impellit aquam C toto <lb></lb>suo pondere, propterea quod pondus dividitur proportionaliter supra basim <lb></lb>vasis ” <emph type="italics"></emph>(Specul. </s>

<s>lib.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>187, 88). Come poi sia vero che il peso vien <lb></lb>distribuito proporzionalmente sopra il fondo del vaso si studia di provarlo <pb xlink:href="020/01/3126.jpg" pagenum="87"></pb>con questo discorso: Sia un tal vaso in figura di tronco di cono, come DBNM <lb></lb>(fig. </s>

<s>37), e il diametro BD della base maggiore sia multiplo del diametro <lb></lb>della base minore, poniamo triplo, cosicchè BF. FG, GD siano uguali insieme <lb></lb><figure id="id.020.01.3126.1.jpg" xlink:href="020/01/3126/1.jpg"></figure></s></p><p type="caption">

<s>Figura 37.<lb></lb>e con NM. </s>

<s>Dipoi si abbassino dai punti S, G, F, O <lb></lb>perpendicolari in R, M, N, T, per le quali s&#039;imma­<lb></lb>gini passare le superficie coniche, che circumcingono <lb></lb>il cilindro FM. </s>

<s>Ciò fatto, si consideri l&#039;acqua com­<lb></lb>presa tra GM, SR, il peso della quale si dispensa <lb></lb>sopra MR, latitudine maggiore della GS. “ Cogi­<lb></lb>temus igitur MC, così soggiunge con le sue proprie parole il Benedetti, ae­<lb></lb>qualem esse GS: manifestum erit quod MC non sustinebit totum pondus <lb></lb>aquae, quae inter GM et SR reperitur, eo quod omnis pars aquae ad per­<lb></lb>pendiculum inclinat versus mundi centrum, quapropter fundus, seu basis <lb></lb>MN, non sustinet aliud pondus, quam aquae FM ” (ibid., pag. </s>

<s>188). </s></p><p type="main">

<s>Così concludesi la dimostrazione, per confermar la quale si soggiunge <lb></lb>la risoluzion di un dubbio, che potrebbe nascere dal supporre il fondo alleg­<lb></lb>gerito dalle pressioni, che l&#039;acqua laterale fa sull&#039;interna FM. “ Sed si quis <lb></lb>hoc in dubium revocaret dicens quod aqua, circumscribens situm corporis <lb></lb>aquei FM, impellit lateraliter dictum corpus aqueum, respondendum est quod <lb></lb>ex aequo huius corporis FM aqua impellit etiam aquam circumstantem, eo <lb></lb>quod sunt corpora homogenea, cum in corporibus homogeneis aequales par­<lb></lb>tes habeant aequales vires ” (ibid.). </s></p><p type="main">

<s>Dunque il Benedetti suppone che l&#039;acqua laterale sia di parti uguali, e <lb></lb>perciò di pari forza all&#039;interna: o se fosse maggiore o minore? </s>

<s>E anche ri­<lb></lb>tenendo per dimostrati questi principii, e per evidente che la porzion di pa­<lb></lb>rete MC non sostien tutta l&#039;acqua compresa fra GM, SR, chi da ciò vede <lb></lb>conseguir le ragioni del paradosso idrostatico, secondo che l&#039;Autore s&#039;era <lb></lb>proposto? </s>

<s>Nasce l&#039;oscurità da quel combattersi, che facevano, dentro la mente <lb></lb>del Benedetti, le idee vecchie, così tenacemente radicate nella prima suppo­<lb></lb>sizion di Archimede, con le nuove: combattimento che più affannoso appa­<lb></lb>risce ne&#039;lettori studiosi, che nell&#039;Autore stesso del libro delle Speculazioni. </s>

<s><lb></lb>Basti, tra il numero di così fatti studiosi, additare il Porta, il quale così scri­<lb></lb>veva, nel primo libro de&#039;suoi <emph type="italics"></emph>Spiritali,<emph.end type="italics"></emph.end> al cap. </s>

<s>X, per dimostrare che ogni <lb></lb>parte dell&#039;umido preme sè stessa a perpendicolo: </s></p><p type="main">

<s>“ Bisogna ancora un&#039;altro assioma, per la ragion de&#039;principii. </s>

<s>Ogni <lb></lb>parte dell&#039;umido, che sta in alcun vaso, non ognuna preme ognuna, ma cia­<lb></lb>scuna preme quella sola parte, la quale le sta sotto a perpendicolo. </s>

<s>Noi ne <lb></lb>porremo un esempio assai bastevole. </s>

<s>Sia alcun vaso piramidale, di cui il cono <lb></lb>sia sotto, e la base di sopra, e sia la cima rotta NM (nella precedente figura) <lb></lb>e si tirino le linee GM, FN. </s>

<s>Dico che l&#039;acqua, che starà in GD, in quella <lb></lb>parte della piramide DGM; che solo preme col suo peso l&#039;acqua DM, perchè <lb></lb>le sta sotto a perpendicolo, e non preme la GF ovvero MN, nè s&#039;intromette <lb></lb>ne&#039;luoghi GF, MN, se non che, cacciata l&#039;acqua dal suo luogo, da GD sia <lb></lb>forzata passare in FG, o MN. </s>

<s>Ma ne seguirebbe da questo che la parte <pb xlink:href="020/01/3127.jpg" pagenum="88"></pb>FGMN sarebbe premuta dall&#039;acqua GDM di fuori del suo luogo, il che è <lb></lb>impossibile, per esser l&#039;acqua corpo di una medesima specie, e le sue parti <lb></lb>uguali hanno forze uguali ” (Napoli 1606, pag. </s>

<s>25). Il simile, soggiunge, è <lb></lb>da dire di un esperimento, che egli passa a descrivere, ed è quello del mor­<lb></lb>taio, proposto dal Benedetti, ch&#039;esso Porta conferma e illustra in altri due <lb></lb>modi: col far cioè osservare che rimosso il tubo C (nella figura XXXVI) lo <lb></lb>zampillo risale sempre alla medesima altezza, per allargare o restringere il <lb></lb>vaso AB quanto si vuole; poi riducendo alla mente le frodi di taluni, i quali, <lb></lb>cavato vin dalla botte, la riempiono, per un sottilissimo cannello, con altret­<lb></lb>tanta acqua, la quale ha nonostante virtù di movere e di sostituirsi alla gran <lb></lb>mole, purchè sia fatta scendere da tale altezza, che superi il livello del li­<lb></lb>quido nella stessa botte. </s></p><p type="main">

<s>Lo scioglimento e il progresso di queste dottrine non si poteva sperare, <lb></lb>nè aversi, che dal ridurre alla sua massima generalità la particolare ipotesi <lb></lb>di Archimede, riconoscendo cioè che l&#039;umido non preme solo a perpendi­<lb></lb>colo, ma per tutti i versi. </s>

<s>Che se il Benedetti poneva tra i principii dimo­<lb></lb>strativi del paradosso idrostatico le pressioni, che soffrono le pareti, erette <lb></lb>sopra il fondo del vaso; non faceva che mostrar la chiave da aprire il mi­<lb></lb>stero. </s>

<s>Rimaneva però a lavorarne l&#039;ingegno, e ciò fece Simeone Stevino, <lb></lb>venuto dalla lontana Bruges a inserire mirabilmente, nel tronco della scienza, <lb></lb>un surculo nuovo. </s></p><pb xlink:href="020/01/3128.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO II.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dell&#039;Idrostatica nei principii del secolo XVII<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. Dell&#039;Idrostatica negli <emph type="italics"></emph>Elementi<emph.end type="italics"></emph.end> di Simeone Stevino. </s>

<s>— II. Dell&#039;Idrostalica nei varii seritti di Ga­<lb></lb>lileo, e particolarmente nel Discorso intorno alle galleggianti. </s>

<s>— III. Dell&#039;Idrostatica nei com­<lb></lb>menti di Marino Ghetaldo, di David Rivault, e di altri, sopra i libri di Arehimede. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Mentre il Benedetti, e gli studiosi delle Speculazioni di lui, ripetevano <lb></lb>quel che sempre s&#039;era detto da tutti, giurandolo sull&#039;autorità di Archimede, <lb></lb>che <emph type="italics"></emph>omnis pars aquae ad perpendiculum inclinat:<emph.end type="italics"></emph.end> lo Stevino, migliore in­<lb></lb>terpetre degli antichi insegnamenti, e non da altra autorità soggiogato, che <lb></lb>da quella della ragione; usciva il primo a pronunziare con libera sicurtà la <lb></lb>sentenza nuova: “ que l&#039;eau proposée soit de tout costé de pesanteur uni­<lb></lb>forme ” <emph type="italics"></emph>(Oeuvres mathem.<emph.end type="italics"></emph.end> a Leyde 1634, pag, 485), e perciò che essa acqua <lb></lb>inclina, ed è premuta, non solo <emph type="italics"></emph>ad perpendiculum,<emph.end type="italics"></emph.end> ma di sotto e di sopra <lb></lb>ugualmente, e da&#039;lati, e insomma per tutti i versi. </s>

<s>Da che faceva l&#039;Autore <lb></lb>conseguire la proposizione, posta da lui per fondamento al trattato suo nuovo <lb></lb><emph type="italics"></emph>Des elemens hydrostatiques,<emph.end type="italics"></emph.end> sotto la forma: “ L&#039;eau proposée tient telle po­<lb></lb>sition, qu&#039;on voudra dans l&#039;eau ” (ivi). </s></p><p type="main">

<s>Se l&#039;acqua dunque, contenuta in un vaso, pesa per tutti i versi, pre­<lb></lb>merà non solamente il fondo, ma le pareti di lui laterali, ciò che, sebbene <lb></lb>molti riconoscessero esser vero, persuasi dalla esperienza, non ne avevano <lb></lb>però certezza alcuna di scienza, la quale si riduceva a dire con qual legge <lb></lb>e misura si facessero quelle pressioni. </s>

<s>Lo Stevino perciò attese principal­<lb></lb>mente a ritrovare una tale scienza, proponendosi di dimostrarla tanto rispetto, <pb xlink:href="020/01/3129.jpg" pagenum="90"></pb>al premere, che fa il liquido contro una parete, da lui detta <emph type="italics"></emph>convenant,<emph.end type="italics"></emph.end><lb></lb>quanto contro pareti di qualunque figura: “ Fond convenant, poi, come dal­<lb></lb>l&#039;Autore stesso si definisce, est celuy duquel chaque deux mottiez conve­<lb></lb>nient: ou pourroit dire que c&#039;est celuy, dont tous les diametres sont coupez <lb></lb>en deux egalement par le centre ” (ivi): e tali sarebbero i circoli, le ellissi, <lb></lb>i parallelogrammi, i poligoni regolari di pari numero di lati, anche mi­<lb></lb>stilinei. </s></p><p type="main">

<s>Incominciando dal dimostrar le leggi, e le misure delle pressioni, fatte <lb></lb>dall&#039;acqua sopra i detti fondi <emph type="italics"></emph>convenant,<emph.end type="italics"></emph.end> o simmetrici, distingue lo Stevino <lb></lb>due casi: il primo de&#039;quali è che il piano del fondo laterale sia a perpen­<lb></lb>dicolo sotto il livello del liquido sostenuto, e il secondo, che lo stesso piano <lb></lb>fondale sia obliquo. </s>

<s>In ogni caso però dimostra esser vero ciò che si pro­<lb></lb>pone, così dicendo: “ Sur un fond convenant, duquel le plus haut poinct <lb></lb>est a fleur d&#039;eau, repose un poids egal à la demi-colomne d&#039;eau, de la quelle <lb></lb>la base est pareille au dit fond, et sa hauteur egale a la perpendicle com­<lb></lb>prise entre les niveaux, qui passent par le plus haut, et plus bas poinct du <lb></lb>dit fond ” (ivi, pag. </s>

<s>488). </s></p><p type="main">

<s>Sia AB (fig. </s>

<s>38) un vaso pieno, e la parete laterale AD un rettangolo, <lb></lb>perpendicolarmente eretto alla orizzontale, col supremo lato AC a fior d&#039;acqua: <lb></lb>presa DH uguale a DC, e condotta la CH, si vuol dallo Stevino dimostrare <lb></lb>che la pressione contro la parete AD è quella medesima, che si farebbe dal <lb></lb><figure id="id.020.01.3129.1.jpg" xlink:href="020/01/3129/1.jpg"></figure></s></p><p type="caption">

<s>Figura 38.<lb></lb>prisma triangolare EACDH, se fosse <lb></lb>un solido di pari gravità all&#039;acqua, po­<lb></lb>sato sopra lo stesso fondo AD, suppo­<lb></lb>sto mobile, e ridotto a giacitura oriz­<lb></lb>zontale. </s>

<s>La dimostrazione è condotta <lb></lb>per via degli inscritti e dei circoscritti, <lb></lb>secondo il metodo antico, il quale, o <lb></lb>si chiami de&#039;lìmiti, come oggidì si fa, <lb></lb>o delle esaustioni, ridotto ai suoi più <lb></lb>semplici termini, si riscontra con quel­<lb></lb>lo degl&#039;indivisibili. </s>

<s>Invece infatti di di­<lb></lb>vider la base AD prima in quattro, poi <lb></lb>in otto, poi in sedici parti uguali, e così procedere, infin tanto che i paral­<lb></lb>lelepipedi inscritti e circoscritti, riposanti sopra quelle così moltiplicate sud­<lb></lb>divisioni di basi, <emph type="italics"></emph>differeroyent moins qu&#039;aucun corps donné;<emph.end type="italics"></emph.end> si può diret­<lb></lb>tamente considerare la colonna acquea, o il prisma triangolare EACDH, come <lb></lb>diviso in infiniti piani rettangolari, via via decrescenti, e tutti paralleli al <lb></lb>massimo AD: o anche, come diviso in triangoli infiniti, tutti uguali al DCH, <lb></lb>e a lui stesso paralleli. </s>

<s>Così, la proposizione viene a dimostrarsi per via assai <lb></lb>facile e breve, perchè, dovendo le pressioni crescere come le profondità, la <lb></lb>loro scala è data dalle infinite ordinate nel triangolo CDH, parallele a DH. <lb></lb>Or, intessendosi esso triangolo di queste stesse ordinate infinite, è manife­<lb></lb>sto che la pressione, fatta sul latercolo CD, è uguale al peso della colonna <pb xlink:href="020/01/3130.jpg" pagenum="91"></pb>acquea triangolare CDH. </s>

<s>E intessendosi dall&#039;altra parte degli infiniti piani <lb></lb>triangolari, tutti uguali a CDH, la colonna acquea o il prisma EACDH, mi­<lb></lb>surato dal prodotto della base AD, e della metà dell&#039;altezza DH, o DC; ri­<lb></lb>mane dimostrato senz&#039;altro il proposito dello Stevino. </s></p><p type="main">

<s>Si può con pari facilità dimostrare quanta sia la pressione, fatta su <lb></lb>qualche parte della parete AD, verso il fondo, pur rimanendosi come dianzi <lb></lb>il vaso, infino al supremo orlo AC, pieno. </s>

<s>Vogliasi per esempio sapere qual <lb></lb>peso d&#039;acqua preme la porzion di parete GD. </s>

<s>Condotta la IK parallela a DH, <lb></lb>e la KL parallela a DC, è manifesto che il latercolo ID è premuto dal peso <lb></lb>del rettangolo acqueo IL, e del triangolo KLH, e però tutta la parete GD, <lb></lb>che s&#039;intesse degl&#039;infiniti latercoli tutti uguali ad ID, verrà premuta da un <lb></lb>parallelepipedo acqueo, e da un prisma triangolare, ambedue risiedenti sopra <lb></lb>base uguale, ma quello alto quanto DL, ossia IC, e questo alto quanto LH, <lb></lb>ossia ID, la qual linea si supponga esser tagliata nel mezzo in M. </s>

<s>Sarà dun­<lb></lb>que la somma dei due solidi GD.IC+GD.ID/2=GD(IC+CM), se­<lb></lb>condo che proponevasi lo Stevino di dimostrare in questa forma: “ Estant <lb></lb>un fond convenant dans l&#039;eau, ayant son extremité superieure sous fleur <lb></lb>d&#039;eau, le poids qui repose a l&#039;encontre est egal a la pesanteur de la colomne <lb></lb>d&#039;eau, ayant le dit fond pour base et pour hauteur la perpendiculaire entre <lb></lb>la fleur d&#039;eau, et le plus haut poinct du fond: et d&#039;avantage la moitié de la <lb></lb><figure id="id.020.01.3130.1.jpg" xlink:href="020/01/3130/1.jpg"></figure></s></p><p type="caption">

<s>Figura 39.<lb></lb>perpendule depuis le pius haut poinct <lb></lb>du fond, jusques au niveau passant <lb></lb>par le plus bas ” (pag. </s>

<s>491). </s></p><p type="main">

<s>Come poi si verifichino le due di­<lb></lb>mostrate proposizioni altresì nel caso, <lb></lb>che la parete, invece di essere perpen­<lb></lb>dicolare al livello del liquido, gli sia <lb></lb>obliqua; è facile certificarsene, per­<lb></lb>chè, trasformata nella 39 la prece­<lb></lb>dente figura, il triangolo DCH ha <lb></lb>sempre la medesima base DH, uguale <lb></lb>a DC, e per altezza la perpendicolare <lb></lb>CO, abbassata fra il livello del liquido, <lb></lb>e il più basso fondo orizontale del vaso. </s>

<s>Come pure al rettangolo IL, e al <lb></lb>triangolo KLH, riman la medesima base ID, ma l&#039;altezza, nel primo di <lb></lb>que&#039;due solidi, è ridotta a PQ, e a QH nel secondo, le quali due altezze, <lb></lb>come resultino uguali alle CN, NO, è manifesto dalla punteggiata costru­<lb></lb>zione della figura. </s></p><p type="main">

<s>Sia nel rettangolo AD (fig. </s>

<s>39) inscritta un&#039;ellisse, in cui suppongasi <lb></lb>trasformata la parete, sopra la quale si vuol misurar la pressione. </s>

<s>È mani­<lb></lb>festo che questa, per un discorso simile a quello fatto dallo Stevino, è quella <lb></lb>che vi si produrrebbe dal peso di un cilindroide, avente per base l&#039;ellisse <lb></lb>stessa, e per altezza la perpendicolare CD: cilindroide che, essendo di pari <pb xlink:href="020/01/3131.jpg" pagenum="92"></pb>gravità all&#039;acqua, fosse segato dal piano diametrale, che passa per CH. </s>

<s>Quel <lb></lb>che dicesi dell&#039;ellisse è facile vedere come sia applicabile a tutte le altre <lb></lb>figure qualunque, purchè simmetriche intorno a un asse. </s>

<s>Ma anche per le <lb></lb>figure asimmetriche o <emph type="italics"></emph>inconvenants<emph.end type="italics"></emph.end> lo Stevino stesso insegna a misurar le <lb></lb>pressioni idrostatiche fatte sopr&#039;esse, mediante la soluzione del seguente pro­<lb></lb>blema: “ Estant dans l&#039;eau un fond plat, de figure quelconque, trouver un <lb></lb>corps d&#039;eau equiponderant au poids reposant contre le dit fond ” (ivi, <lb></lb>pag. </s>

<s>494). </s></p><p type="main">

<s>Premessi i quali principii, si può facilmente intendere perchè si faccia <lb></lb>l&#039;equilibrio tra l&#039;acqua del mortaio, e quella della fistola annessa, secondo <lb></lb>la proposizione del Benedetti: “ parquoy la petite eau CDE (nella figura 36) <lb></lb>pousse autant contre le fond HB, que la grande eau AB ” (ivi, pag. </s>

<s>499). <lb></lb>Abbassate infatti sulla orizontale FD, che passa per il centro E della parete <lb></lb>acquea HB, le perpendicolari GF, CD; la pressione fatta dalla piccola acqua <lb></lb>CDE, sulla detta parete, è, per le cose già dimostrate, HB.CD, e la pres­<lb></lb>sione, fatta sulla medesima dalla grande acqua AB, è per le stesse ragioni <lb></lb>HB.GF. </s>

<s>Ma CD, GF sono uguali, dunque il velo acqueo HB, essendo pre­<lb></lb>muto da due forze uguali e contrarie, s&#039;intende perchè non può muoversi, <lb></lb>nè passare egli e i successivi a ingrosssre l&#039;acqua del più piccolo recipiente. </s></p><p type="main">

<s>Così riduceva lo Stevino a ragioni matematiche quel che il Benedetti <lb></lb>diceva distribuirsi il peso proporzionalmente sopra il fondo del vaso, e solo <lb></lb>parzialmente sopra le pareti laterali di lui. </s>

<s>Ma perchè la nuova Scienza idro­<lb></lb>statica era universale, si poteva per essa ugualmente bene rivelare il mistero <lb></lb><figure id="id.020.01.3131.1.jpg" xlink:href="020/01/3131/1.jpg"></figure></s></p><p type="caption">

<s>Figura 40.<lb></lb>della Natura, anche presentandosi sotto altri varii <lb></lb>aspetti, come quando per esempio il vaso conico <lb></lb>avesse la sua maggior base in basso. </s>

<s>Suppongasi <lb></lb>essere un tal vaso ABCD (fig. </s>

<s>40): lo Stevino <lb></lb>aveva ne&#039;suoi principii ritrovate le ragioni, per <lb></lb>cui il fondo CD riceve ugual pressione dalla pic­<lb></lb>cola acqua ABCD, e dalla grande EFCD. </s></p><p type="main">

<s>Non difficilmente poteva occorrere al pensiero anche degli studiosi del <lb></lb>Benedetti, che come, stando la minor base del vaso in basso, il fondo era <lb></lb>dalle pareti alleggerito, così in questa nuova posizione fosse invece aggra­<lb></lb>vato: per cui la pressione contro esso fondo là fosse meno, è qua più di <lb></lb>quella fatta da tutta l&#039;acqua del recipiente. </s>

<s>Il concetto, vero in sè stesso, <lb></lb>voleva come tale essere dimostrato, ciò che poteva facilmente farsi così, ap­<lb></lb>plicandovi le proposizioni dello stesso Stevino: Consideriamo sopra il fondo <lb></lb>CD un punto qualunque M, il quale sarebbe premuto da solo il peso del <lb></lb>filetto liquido GM, se questo fosse in stato naturale. </s>

<s>Ma egli è invece in <lb></lb>stato violento, tendendo a risalire in su, come si vedrebbe avvenire di fatto, <lb></lb>se nel punto G la parete avesse un foro. </s>

<s>Dunque essa parete ripreme il <lb></lb>filetto in giù, ed è causa, cosi facendo, d&#039;accrescergli nuovo peso sopra il <lb></lb>suo proprio e naturale. </s>

<s>Or perchè la repressione è tanta, quanta è la pres­<lb></lb>sione, la quale, essendosi l&#039;area parietale ridotta a un punto, è per la pro-<pb xlink:href="020/01/3132.jpg" pagenum="93"></pb>posizione dello stesso Stevino uguale al gravitar del filetto liquido GL; tanto <lb></lb>sarà il peso, che aggiungesi al peso naturale del filetto GM: cosicchè il punto <lb></lb>M sarà premuto da tutto intero il filetto ML. </s>

<s>Col medesimo ragionamento <lb></lb>si dimostrerebbe che, non solo il punto N, ma tutti gli altri infiniti, com­<lb></lb>ponenti la sezione CD del fondo, son premuti ciascuno dal peso de&#039;respet­<lb></lb>tivi filetti liquidi, che risalgono in fin su all&#039;altezza del livello. </s>

<s>Ma dalla <lb></lb>somma di cotali filetti infiniti resulta la mole acquea EFDC; dunque è da <lb></lb>questa premuto il detto fondo, come da quella, benchè tanto minore, che <lb></lb>realmente ritiene in sè il vaso fra le sue sponde. </s></p><p type="main">

<s>Che se fosse esso vaso configurato come nella 41, è facile vedere che <lb></lb>al peso naturale dei filetti AB, CD, e degli altri simili infiniti, aggiungen­<lb></lb><figure id="id.020.01.3132.1.jpg" xlink:href="020/01/3132/1.jpg"></figure></s></p><p type="caption">

<s>Figura 41.<lb></lb>dosi le repressioni fatte da&#039;punti A, C del coperchio, le <lb></lb>quali equivalgono alle pressioni dei filetti AE, CF; il <lb></lb>fondo GH è premuto così dalla piccola acqua MHGNO, <lb></lb>come dalla grande EGHM. Cosicchè, qualunque forma <lb></lb>abbiasi il recipiente, e o poco o molto, mantenendo il <lb></lb>medesimo fondo e la medesima altezza, sia il liquido con­<lb></lb>tenuto, si può con lo Stevino concludere in generale: “ Sur <lb></lb>le fond de l&#039;eau, parallele a l&#039;horizon, repose un poids <lb></lb>egal a la pesanteur de l&#039;eau, qui est egal à la colomne, dont la base est le <lb></lb>fond susdit, et la hauteur la perpendicle sur l&#039;horizon, entre le fond et la <lb></lb>fleur de l&#039;eau ” (ivi, pag. </s>

<s>487). </s></p><p type="main">

<s>La dimostrazione dell&#039;Autore però procede in altra maniera, da quella <lb></lb>che s&#039;è detta, e più accomodata alla qualità de&#039;Filosofi di que&#039;tempi, tut­<lb></lb>tavia alieni dal professare il metodo degli indivisibili, e meglio che dalla ra­<lb></lb>gion matematica disposti a persuadersi dalla naturale semplicità di queste <lb></lb><figure id="id.020.01.3132.2.jpg" xlink:href="020/01/3132/2.jpg"></figure></s></p><p type="caption">

<s>Figura 42.<lb></lb>osservazioni: Sia il vaso ADCE (fig. </s>

<s>42): che il suo fondo <lb></lb>DC sia premuto dal peso di una colonna d&#039;acqua, la <lb></lb>quale abbia per base DC, e per altezza la perpendicolare <lb></lb>AD; è cosa tanto per sè manifesta, da rendere superfluo <lb></lb>ogni discorso, intorno al quale perciò non trova lo <lb></lb>Stevino altro modo di procedere, che dall&#039;assurdo. </s></p><p type="main">

<s>Così essendo, come da ogni parte apparisce il vero, <lb></lb>si separi nella massa del liquido la porzione GHIE, e non per questo ver­<lb></lb>ranno alterate le prime condizioni dell&#039;equilibrio, le quali anzi seguiteranno <lb></lb>a rimaner tali, anche quando, alla mole acquea GI, si sostituisca un solido <lb></lb>di pari gravità, e talmente aderente e fisso alle contigue pareti, che la capa­<lb></lb>cità del vaso si riduca all&#039;acqua ADCIHG. </s>

<s>Dunque sarà così premuto il <lb></lb>fondo DC da questa sola, come da tutta l&#039;AC. </s></p><p type="main">

<s>Da una tal proposizione fa lo Stevino scendere un corollario importante, <lb></lb>ed è che, trovandosi il velo acqueo HI premuto dal peso della colonna GI, <lb></lb>e pur non movendosi in basso; è necessario che sia risospinto in alto con <lb></lb>forza uguale, di che si vedrebbe l&#039;effetto manifesto, quando lo spazio GI <lb></lb>restasse vuoto, e il coperchio HI del vaso fosse in qualche punto forato. </s></p><pb xlink:href="020/01/3133.jpg" pagenum="94"></pb><p type="main">

<s>Come queste fisiche conclusioni si riscontrino con le dimostrazioni ma­<lb></lb>tematiche dette di sopra, si comprende assai facilmente. </s>

<s>Ma la ragione s&#039;ar­<lb></lb>rendeva così malvolentieri a consentire ugual peso a un&#039;oncia d&#039;acqua, e a <lb></lb>mille libbre, e così pareva ritrosa ad ammetter nel liquido la spinta in su, <lb></lb>contro la gravità sua naturale; che lo Stevino pensò di dover l&#039;uno e l&#039;al­<lb></lb><figure id="id.020.01.3133.1.jpg" xlink:href="020/01/3133/1.jpg"></figure></s></p><p type="caption">

<s>Figura 43.<lb></lb>tro paradosso confermare con l&#039;esperienza. </s>

<s>Che la <lb></lb>poca acqua della fistola contrappesi alla molta del <lb></lb>mortaio appariva, nello strumento del Benedetti, come <lb></lb>cosa di fatto. </s>

<s>Ma esso Stevino soggiunge, a questi, due <lb></lb>altri esempi, in cui si parrebbe operar piuttosto&#039;dal­<lb></lb>l&#039;arte magica, che dalla Natura. </s></p><p type="main">

<s>Un cilindro DE (fig. </s>

<s>43), cavo e pien d&#039;acqua, <lb></lb>sia contrappesato dal grave P sul braccio di una bi­<lb></lb>lancia, sostenuta in C. </s>

<s>Si cali, per via del filo FG, <lb></lb>un cilindro solido, che non riempia tutta la cavità <lb></lb>del vaso sottoposto, facendone versare tutta l&#039;acqua, ma lasciandovene in­<lb></lb><figure id="id.020.01.3133.2.jpg" xlink:href="020/01/3133/2.jpg"></figure></s></p><p type="caption">

<s>Figura 44.<lb></lb>torno alle pareti e sul fondo un velo, il quale, benchè ri­<lb></lb>dotto a un&#039;estrema sottigliezza, pur mostra di pesar quanto <lb></lb>tutta l&#039;acqua che v&#039;era prima, giacchè si vede che la bi­<lb></lb>lancia non s&#039;è mossa. </s>

<s>Siano inoltre due vasi con fondi <lb></lb>circolari uguali, e traforati ugualmente nel centro, ma <lb></lb>l&#039;uno sia cilindrico, come AB (fig. </s>

<s>44), l&#039;altro tubulare, <lb></lb>come DEF (fig. </s>

<s>45). Si coprano i fori de&#039;<gap></gap>ondi con ro­<lb></lb><figure id="id.020.01.3133.3.jpg" xlink:href="020/01/3133/3.jpg"></figure></s></p><p type="caption">

<s>Figura 45.<lb></lb>telle GH, fatte del medesimo legno, e di uguale diametro, <lb></lb>e s&#039;infonda l&#039;acqua infin che non giunga a pari altezza, <lb></lb>nell&#039;un recipiente e nell&#039;altro. </s>

<s>Dovrebbero le dette rotelle, <lb></lb>secondo le cose dimostrate, esser premute ugualmente, ben­<lb></lb>chè l&#039;una abbia sopra sè la poca acqua del tubo, e l&#039;altra <lb></lb>quella del gran cilindro: “ ce qu&#039;on peut recognoistre par <lb></lb>experience, dice lo Stevino, en attachant des poids elevans <lb></lb>egaux T, S, equiponderans a l&#039;eau que l&#039;assiette GH supporte ” (ivi, pag. </s>

<s>499). </s></p><p type="main">

<s>L&#039;altro paradosso del sospingere in su l&#039;acqua, che pure, come tutti i <lb></lb>gravi tende naturalmente in basso, benchè reso dagli zampilli evidente, si <lb></lb>studiava lo Stevino di confermare con una esperienza così semplice e dimo­<lb></lb>strativa, che dopo tre secoli si dura tuttavia a ripetere nelle Scuole. </s>

<s>Consi­<lb></lb>steva nell&#039;apporre a un tubo di vetro per fondo posticcio una rotella di mate­<lb></lb>ria grave, come sarebbe di piombo, la quale rotella, mentre che il tubo sta <lb></lb>in aria, non gli si può tenere applicata, se non tirandovela per un filo, ma, <lb></lb>immersa con tutto il tubo nell&#039;acqua, vi si vede esser sostenuta dalla pres­<lb></lb>sione in su, senza altro aiuto. </s></p><p type="main">

<s>Questa pressione, che evidentemente appariva operare dal basso in alto, <lb></lb>notava lo Stevino non dipender punto dalla quantità dell&#039;acqua circumfusa, <lb></lb>ma dalla sola sua altezza, cosicchè un sottil filo di acqua perpendicolare <lb></lb>avrebbe potuto vincere quella di tutto l&#039;oceano, com&#039;egli stesso particolar-<pb xlink:href="020/01/3134.jpg" pagenum="95"></pb>mente descriveva con questo esempio: “ Soit ABCD (fig. </s>

<s>46) un vaisseau <lb></lb>plein d&#039;eau, avec un pertuis EF au fond DC, sur le quel repose une assiette <lb></lb><figure id="id.020.01.3134.1.jpg" xlink:href="020/01/3134/1.jpg"></figure></s></p><p type="caption">

<s>Figura 46.<lb></lb>minugrave a l&#039;eau: la mesme pressera le <lb></lb>fond comme il a esté dit cy dessus. </s>

<s>Soit <lb></lb>puis apres IKL un petit canal, dont le trou <lb></lb>superieur I soit de mesme hauteur que AB, <lb></lb>et son trou inferieur soit EF. </s>

<s>Et remplis­<lb></lb>sant ce canal plein d&#039;eau, ce peu d&#039;eau <lb></lb>poussera autant contre l&#039;assiette par des­<lb></lb>sous, que la grande eau par dessus, car <lb></lb>alors l&#039;assiette GH s&#039;elevera en haut. </s>

<s>Tel­<lb></lb>lement que 1 lb. </s>

<s>d&#039;eau (je pose qu&#039;autant <lb></lb>contienne le canal IKL) fera plus d&#039;effort <lb></lb>contre l&#039;assiette GH, que non pas 100,000 lb.: ce qu&#039;on pourroit estimer <lb></lb>un mystere en la Nature, si la cause estoit incognue ” (ivi, pag. </s>

<s>500). </s></p><p type="main">

<s>Ed ecco venir di qui la soluzion vera al problema, che tanto dette tra­<lb></lb>vaglio a Leonardo da Vinci e al Tartaglia. </s>

<s>Se DC, nella medesima figura 46, <lb></lb>rappresenta il fondo del pozzo, e GH la baga, è manifesto, per queste dot­<lb></lb>trine dello Stevino, che, non comunicando con l&#039;acqua la parte inferiore EF <lb></lb>di essa baga, sarà premuta sul fondo con tutto il suo proprio peso, e con <lb></lb>quello del liquido soprapposto. </s>

<s>Mentre invece, se vi è qualche comunicazion <lb></lb>da&#039;lati e di sotto, questa fa l&#039;effetto del tubo IKL, e la baga stessa risale <lb></lb>a galla per la sua propria leggerezza. </s>

<s>Può similmente DC rappresentare il <lb></lb>fondo marino, e GH la nave sommersa, secondo il problema propostosi dal <lb></lb>Tartaglia, e la maggiore difficoltà del riavere essa nave, quando è arrenata, <lb></lb>che quando semplicemente riposa sui sassi, corrisponde alle difficoltà, che si <lb></lb>provano nel voler ritirare in su l&#039;assicella, tanto maggiori, quando la sua <lb></lb>inferiore superficie ne è esclusa, che quando comunica con l&#039;acqua supe­<lb></lb>riore, per via del sottilissimo tubo. </s></p><p type="main">

<s>Nel ricercare la ragione delle pressioni, che soffre l&#039;otre pien d&#039;aria <lb></lb>posto in fondo al pozzo, occorreva a Leonardo a risolvere un altro simile <lb></lb>problema: perchè, cioè, l&#039;uomo, stando in luogo dell&#039;otre, non sente pas­<lb></lb>sione dal gran peso dell&#039;acqua, che gli sovrasta. </s>

<s>La speculazione è di an­<lb></lb>tica data, e si trova, come accennammo altrove, proposta da Herone Ates­<lb></lb>sandrino, nel proemio al suo libro <emph type="italics"></emph>Degli spiritali,<emph.end type="italics"></emph.end> dove si legge: “ Dicono <lb></lb>dunque certi, a proposito del non essere oppressi i notanti nel fondo del <lb></lb>mare, che ciò avviene, perchè l&#039;acqua in sè stessa è ugualmente grave. </s>

<s>Ma <lb></lb>questi non vengono punto ad assegnare altra ragione del fatto, la quale fa <lb></lb>di mestieri dimostrarla in questa guisa. </s>

<s>Immaginiamoci la parte superiore <lb></lb>dell&#039;acqua dalla superficie, che tocca il corpo in essa immerso, e sopra la <lb></lb>quale seguita l&#039;acqua; essere una mole o corpo egualmente grave come <lb></lb>l&#039;acqua, e che abbi conforme figura al resto dell&#039;acqua che è di sopra, ed <lb></lb>immaginiamoci che questa mole sia mossa nel resto dell&#039;acqua, di modo che <lb></lb>la superficie sua inferiore si accosti al corpo immerso, e sia quasi come una <pb xlink:href="020/01/3135.jpg" pagenum="96"></pb>cosa stessa con quello, e che successivamente vi sia sopra la parte superiore <lb></lb>dell&#039;acqua: è chiara cosa che questa mole immersa non sovrasta tanto o <lb></lb>quanto al resto dell&#039;acqua, e meno è sommersa sotto la superficie superiore <lb></lb>di essa. </s>

<s>È poi per certo stato da Archimede dimostrato, nel Libro che fa <lb></lb><emph type="italics"></emph>Delle cose che vanno per acqua,<emph.end type="italics"></emph.end> che li corpi ugualmente gravi, e l&#039;acqua <lb></lb>immersa nell&#039;altr&#039;acqua non seprastà punto all&#039;acqua, nè meno viene da <lb></lb>questa depressa. </s>

<s>Adunque non calcherà le a lei sottoposte cose, e, levatone <lb></lb>di sopra tutto quello che premere averia potuto, nondimeno quel corpo se <lb></lb>ne starà nell&#039;istesso loco. </s>

<s>Per qual conto dunque premerà quel corpo, che <lb></lb>non appetisce di calare in altro più basso loco? (Traduz. </s>

<s>cit., fol. </s>

<s>10, 11). </s></p><p type="main">

<s>Il ragionamento di Herone sembra a prima vista ridursi a quello dello <lb></lb>Stevino, messo così da lui in forma di sillogismo: “ Tout pressement qui <lb></lb>blesse le corps pousse quelque partie du corps hors de son lieu naturel. </s>

<s>Ce <lb></lb>pressement causè par l&#039;eau ne pousse aucune partie du corps hors de son <lb></lb>lieu naturel; Ce pressement donc causé par l&#039;eau ne blesse nullement le <lb></lb>corps. </s>

<s>La mineure est manifeste par l&#039;experience, don la raison est que s&#039;il <lb></lb>y avoit quelque chose qui soit poussée hors de son lieu, il faudroit que cela <lb></lb>rentrast en un autre lieu, mais ce lieu n&#039;est pas dehors, a cause que l&#039;eau <lb></lb>presse de tout costé egalement (quant à la partie de dessous elle est un <lb></lb>peu plus pressée que celle de dessus par la XI proposition des Elemens hy­<lb></lb>drostatiques, ce qui n&#039;est d&#039;aucune estime, d&#039;autant que telle difference ne <lb></lb>peut pousser aucune partie hors de son lieu naturel) ce lieu n&#039;est pas aussi <lb></lb>dedans le corps, car il n&#039;y a rien de vuide non plus que dehors; d&#039;ou il <lb></lb>s&#039;ensuit que les parties s&#039;entre poussent egalement, pource que l&#039;eau a une <lb></lb>mesme raison a l&#039;entour du corps. </s>

<s>Ce lieu-la done n&#039;est dehors ny dedans <lb></lb>le corps et par consequent en nulle part, ce qui fait que nulle partie n&#039;est <lb></lb>poussée hors de son lieu, et partant ne blesse nullement le corps ” (ivi, <lb></lb>pag. </s>

<s>500). </s></p><p type="main">

<s>Dicemmo che la soluzione dell&#039;antico Autore e del moderno sembran <lb></lb>ridursi ai medesimi principii, ma ripensandoci bene vi si trova una sostan­<lb></lb>ziale differenza, perchè, sebbene Herone par che voglia confutare coloro, i <lb></lb>quali dicevano esser l&#039;acqua ugualmente grave in sè stessa, pur egli riesce <lb></lb>a dire il medesimo, dai Teoremi archimedei concludendo che l&#039;acqua nel­<lb></lb>l&#039;acqua non pesa. </s>

<s>Questo principio, così assolutamente pronunziato, è falso, <lb></lb>e perciò vi si sostituisce dallo Stevino quell&#039;altro verissimo dell&#039;uguaglianza <lb></lb>delle pressioni per ogni verso. </s>

<s>Esser poi falso che l&#039;acqua nell&#039;acqua non <lb></lb>pesa, per cui non si può con tale supposto spiegare perchè non sia oppresso <lb></lb><figure id="id.020.01.3135.1.jpg" xlink:href="020/01/3135/1.jpg"></figure></s></p><p type="caption">

<s>Figura 47.<lb></lb>chi nota per un pelago profondo; si dimostrava dallo <lb></lb>stesso Stevino immaginando di avere un gran vaso ABCD <lb></lb>(fig. </s>

<s>47) campato in aria, con un foro E aperto nel fondo. </s>

<s><lb></lb>Turato il foro, sopra il quale si supponga giacere un <lb></lb>uomo, rappresentato nell&#039;assicella F; riempiasi per tutta <lb></lb>la sua altezza il detto vaso. </s>

<s>Si vuole che quell&#039;uomo non <lb></lb>patisca, perchè l&#039;acqua nell&#039;acqua non pesa. </s>

<s>Ma levisì il <pb xlink:href="020/01/3136.jpg" pagenum="97"></pb>turo E: riman sempre l&#039;acqua nell&#039;acqua, eppure ella si sentirebbe ora pesar <lb></lb>tanto, che il misero marangone a questo patto ne sarebbe schiacciato. </s>

<s>“ Soit <lb></lb>ABCD (così scrive propriamente lo Stevino, riferendo alla medesima figura, <lb></lb>per noi 47a, il discorso) une eau, ayant au fond DC un trou formé d&#039;une <lb></lb>broche E, sur le quel fond gist un homme F, ayant son dos sur E. </s>

<s>Ce <lb></lb>qu&#039;estant ainsi, l&#039;eau le pressant de tout costé, celle qui est dessus luy ne <lb></lb>pousse aucune partie hors de son lieu. </s>

<s>Mais si on veut voir par effect que <lb></lb>cecy est la cause veritable, il ne faut qu&#039;oster la broche E. </s>

<s>Alors il n&#039;y aura <lb></lb>aucun poussement contre son dos en E, comme aux autres lieux de son <lb></lb>corps, pourtant aussi son corps patira là une compression voire aussi forte, <lb></lb>comme il a esté demonstré au troisiesme exemple de la II proposition du <lb></lb>present livre: assavoir autant que pese la colomne d&#039;eau, ayant le trou E <lb></lb>pour base et AD hauteur et ainsi le dessein est demonstré apertement ” (ivi). </s></p><p type="main">

<s>Potrebbe questo solo esempio esser sufficiente a dimostrare quanto si <lb></lb>fosse la scienza dello Stevino avvantaggiata sopra quella di Leonardo da Vinci, <lb></lb>e del Tartaglia. </s>

<s>Eppure furono dalle medesime ombre oscurati così gli Ele­<lb></lb>menti idrostatici dell&#039;olandese, come i Manoscritti del Pittore toscano, e i <lb></lb>discorsi intorno alla Tavagliata invenzione del Matematico di Brescia. </s>

<s>Men­<lb></lb>tre, sorti i novelli promotori di Archimede, sedevano di queste cose maestri, <lb></lb>e da un&#039;elettissima scuola e numerosa s&#039;ascoltavano come oracoli i loro in­<lb></lb>segnamenti; il solitario di Bruges s&#039;additava dalla lontana col suo turbante <lb></lb>di mago in capo, e ravvolto nella sua toga nera, men pauroso che sospetto, <lb></lb>per avere insegnato a far sì che un&#039;oncia di liquido pesasse quanto cento­<lb></lb>mila libbre sul piatto della stadera. </s>

<s>Apparve nondimeno una volta con tutto <lb></lb>il suo abito filosofale in Toscana. </s>

<s>E perchè vi furono approvati i suoi detti, <lb></lb>e vi fecero ravvedere uno de&#039;nostri più gran Savii, giova accennare all&#039;oc­<lb></lb>casione, e al modo di quella visita clandestina. </s></p><p type="main">

<s>Chi ha letto la terza parte del capitolo IX, scritto da noi nel Tomo che <lb></lb>precede a questo, sa come il Viviani venisse, per mezzo dello Stenone, ad <lb></lb>aver notizia e intelligenza nella sua propria lingua di alcuni teoremi di Mec­<lb></lb>canica, da Niccolò Witsen dimostrati nel suo libro, scritto in lingua olan­<lb></lb>dese, intorno al modo di costruire e di governare le navi. </s>

<s>Ricorrevano in <lb></lb>quel medesimo volume del connazionale e discepolo dello Stevino altri teo­<lb></lb>remi d&#039;Idrostatica, dimostrati sull&#039;andare di quelli del suo Maestro, e anche <lb></lb>sopra questi volle lo Stenone richiamar l&#039;attenzione del Viviani, il quale, <lb></lb>gustandovi dentro tale Scienza, che gli sembrava non solo promovere, ma <lb></lb>correggere in parte quella stessa, che aveva imparata da Archimede e da <lb></lb>Galileo; chiese all&#039;amico gli dettasse anche di questa la traduzione italiana. </s>

<s><lb></lb>Di che gentilmente compiaciuto, scrisse di sua propria mano, sopra certi fogli <lb></lb>che ci son rimasti, ordinatamente, queste otto proposizioni: </s></p><p type="main">

<s>PROPOSIZIONE I. — <emph type="italics"></emph>“ Sopra un fondo parallelo alla superficie del­<lb></lb>l&#039;acqua riposa un peso uguale al peso di una colonna o cilindrico, la di <lb></lb>cui base è uguale al fondo dato, e l&#039;altezza uguale alla perpendicolare <lb></lb>della superficie dell&#039;acqu<gap></gap> sopra il fondo dato. </s>

<s>”<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/3137.jpg" pagenum="98"></pb><p type="main">

<s>“ Sia, nelle figure 48 e 49, ABCD l&#039;acqua, AB la superficie, GH il <lb></lb>fondo parallelo ad AB: dico che sopra GH riposa una colonna d&#039;acqua EFGH. <lb></lb><figure id="id.020.01.3137.1.jpg" xlink:href="020/01/3137/1.jpg"></figure></s></p><p type="caption">

<s>Figura 48.<lb></lb>Nella figura 48 la proposizione per sè è manifesta; nella 49 così <lb></lb><figure id="id.020.01.3137.2.jpg" xlink:href="020/01/3137/2.jpg"></figure></s></p><p type="caption">

<s>Figura 49.<lb></lb>si dimostra: Sia in essa un corpo solido EFGH, <lb></lb>della medesima gravità in specie dell&#039;acqua. </s>

<s>Egli <lb></lb>è evidente che il corpo galleggiante nell&#039;acqua <lb></lb>preme l&#039;acqua, che è sotto GH, col peso del corpo <lb></lb>EFGH. </s>

<s>Bisogna dunque che l&#039;acqua ancora prema <lb></lb>verso GH coll&#039;istesso peso, altrimenti il corpo non <lb></lb>si quieterebbe in quel luogo. </s>

<s>Ora, se il corpo <lb></lb>EFGH fosse attaccato al lato AD, questo non farebbe alterazione alcuna. </s>

<s><lb></lb>Sicchè un peso uguale al peso d&#039;un prisma d&#039;acqua, grande quanto EFGH, <lb></lb>riposa sopra il fondo GH. </s>

<s>Il che ecc. </s>

<s>” </s></p><p type="main">

<s>PROPOSIZIONE II. — <emph type="italics"></emph>“ Sopra un fondo quadrato, non parallelo alla <lb></lb>superficie dell&#039;acqua, il di cui lato più alto è sotto la superficie dell&#039;acqua, <lb></lb>riposa un peso più leggiero d&#039;una colonna d&#039;acqua, la di cui base è uguale <lb></lb>al fondo prescritto, e l&#039;altezza alla linea perpendicolare tra la superficie <lb></lb>dell&#039;acqua, e del più basso lato del dato fondo, e più grave di una co­<lb></lb>lonna d&#039;acqua della stessa base, ma di altezza uguale alla perpendicolare <lb></lb>tra la superficie dell&#039;acqua, e del più alto lato del dato fondo. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia, nella figura 50, dato il fondo EF, e siano EG, FH uguali ad EF, <lb></lb>e parallele alla superficie dell&#039;acqua AB: dico che sopra EF riposa un peso <lb></lb>minore che FHIA, e maggiore che EGIA ” (MSS. Gal., T. CXLI, fol. </s>

<s>7). <lb></lb><figure id="id.020.01.3137.3.jpg" xlink:href="020/01/3137/3.jpg"></figure></s></p><p type="caption">

<s>Figura 50.</s></p><p type="main">

<s>Prima di trascrivere la dimostrazione, giova osser­<lb></lb>vare che, in questa e nelle seguenti, si procede dal­<lb></lb>l&#039;Autore per via degl&#039;indivisibili, considerando della <lb></lb>parete uno degl&#039;infiniti latercoli, di cui essa s&#039;intesse, <lb></lb>rappresentato nel profilo EF. </s>

<s>Come pure egli intende <lb></lb>esser esso profilo gravato da infiniti filetti liquidi, fra <lb></lb>sè paralleli, e a&#039;due estremi GE, HF. </s>

<s>Giova osservare <lb></lb>inoltre che la stessa dimostrazione, specialmente nella <lb></lb>sua seconda maniera, si conduce da un principio assai <lb></lb>evidente, ed è che dal mezzo di EF in su i filetti liquidi, che premono la <lb></lb>parete, son di numero maggiori di quelli compresi nel rettangolo EI, e dal <lb></lb>mezzo in giù minori di quelli compresi in IF. </s>

<s>Le medesime ragioni poi sono <lb></lb>tanto evidentemente applicabili anche al caso che il fondo laterale, invece <lb></lb>di essere perpendicolare alla superficie del liquido, come qui si rappresenta, <lb></lb>sia obliqua; che s&#039;è creduto inutile farne avvertiti i Lettori a parole, o di­<lb></lb>segnandone, come l&#039;Autore fa, una figura apposta. </s></p><p type="main">

<s>“ Pongasi, così seguita nel Manoscritto la traduzione del Witsen, che <lb></lb>l&#039;acqua EFGH non abbia peso. </s>

<s>Il che essendo, l&#039;acqua è premuta verso EG <lb></lb>col peso della colonna d&#039;acqua AIGE, e per ragioni conosciute l&#039;acqua EFGH <lb></lb>preme verso EG col peso eguale, essendo che l&#039;acqua di sotto coll&#039;istessa <lb></lb>forza resiste a quella di sopra, con la quale l&#039;acqua di sopra preme contro <pb xlink:href="020/01/3138.jpg" pagenum="99"></pb>di essa, mentre restano in tale stato di quiete (Veggasi la X proposizione di <lb></lb>Stevino nella Statica). Nondimeno, per la fluidità dell&#039;acqua, verrà l&#039;istessa <lb></lb>pressione sopra EF ed FH, e l&#039;acqua in EG, GH, essendo premuta, pre­<lb></lb>merà coll&#039;istessa forza tuttociò che la sostiene, considerato che l&#039;acqua (ol­<lb></lb>tre al suo peso, che solamente preme in giù, del che qui non si parla, e <lb></lb>che senza impedimento considerabile può trascurarsi nella pratica) è anco <lb></lb>fluida, la qual fluidità dell&#039;acqua, per esser premuta verso tutte le bande <lb></lb>con egual forza, cerca di ripremere, e per conseguenza preme con egual <lb></lb>forza verso i quattro lati. </s>

<s>Ma per esser l&#039;acqua in EFGH anco grave è che <lb></lb>questa gravità verso EF più preme che nulla, e meno che verso FH. </s>

<s>Per <lb></lb>questo anco riposerà più peso, verso EF, che la colonna d&#039;acqua EGAI, e <lb></lb>meno che la colonna d&#039;acqua FHIA, il che si doveva dimostrare. </s>

<s>” </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>“ Altrimenti. </s>

<s>”<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>“ Verso l&#039;angolo E riposa tanto, quanto verso qualsivoglia altro luogo <lb></lb>uguale ad esso nella linea EG, imperocchè ogni punto nell&#039;acqua, in quanto <lb></lb>alla sua fluidità, viene ad essere premuto ugualmente verso tutte le bande <lb></lb>(Vedi Stevino sopra ciò). E verso l&#039;angolo di qualsivoglia altra linea, tirata <lb></lb>parallela con la linea EG, tanto riposa, quanto verso altro luogo nell&#039;istessa <lb></lb>linea. </s>

<s>E perchè riposa più verso qualunque linea che verso EG, e meno che <lb></lb>verso FH; seguita che verso gli angoli inferiori riposa più che verso l&#039;an­<lb></lb>golo E, e meno che verso l&#039;angolo F, e per conseguenza verso tutti gli an­<lb></lb>goli, cioè verso la linea EF (imperocchè tutti gli angoli o punti solidi com­<lb></lb>pongono la linea EF) più che verso EG, e meno che verso FH. ” </s></p><p type="main">

<s>PROPOSIZIONE III. — <emph type="italics"></emph>“ Verso un fondo quadrato, il di cui lato supe­<lb></lb>riore è nella superficie dell&#039;acqua, riposa un peso eguale alla metà d&#039;una <lb></lb>colonna d&#039;acqua, la cui base è uguale al fondo dato, e l&#039;altezza uguale <lb></lb>alla perpendicolare tra la superficie dell&#039;acqua, ed il lato inferiore del <lb></lb>fondo dato. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia nella figura 51 l&#039;acqua ABCD, la superficie AB, il fondo AD: <lb></lb>dico che verso AD riposa la metà di una colonna d&#039;acqua, il cui fondo o <lb></lb>base fosse AD, o DE, posta uguale ad AD; ovvero, che è l&#039;istesso, una co­<lb></lb>lonna trilatera d&#039;acqua ADE. ” </s></p><p type="main">

<s>“ Per dimostrar ciò, si divida AD e DE <lb></lb><figure id="id.020.01.3138.1.jpg" xlink:href="020/01/3138/1.jpg"></figure></s></p><p type="caption">

<s>Figura 51.<lb></lb>in parti uguali, e da&#039;punti delle divisioni si <lb></lb>tirino linee parallele ad AB, e ad AD. </s>

<s>Dalla <lb></lb>passata proposizione è evidente che sopra AF <lb></lb>riposa più che niente, e meno che la co­<lb></lb>lonna d&#039;acqua FL. Parimente, sopra FG ri­<lb></lb>posa più che FL o GR, e meno che GL o <lb></lb>MN. </s>

<s>Come anche sopra GH più che GL o <lb></lb>HS, e meno che HL o HN, e così sopra HI <lb></lb>più che IT, e meno che IO. </s>

<s>Sopra IK più <lb></lb>che KV, e meno che KP, e finalmente sopra <pb xlink:href="020/01/3139.jpg" pagenum="100"></pb>KD più che DZ, e meno che <expan abbr="Dq.">Dque</expan> Adunque il peso, che riposa sopra AD, è <lb></lb>sempre più che tutte queste inscritte colonne d&#039;acqua, che toccano la linea <lb></lb>AE, e meno che tutte le circoscritte colonne. </s>

<s>Ma quanto sono più piccole le <lb></lb>parti, nelle quali si divide le AD, DE, tanto sarà minore la differenza, e tanto <lb></lb>più si accosteranno al triangolo ADE. </s>

<s>Ora si può dividere AD e DE in tante <lb></lb>parti, che all&#039;ultimo la loro differenza sarà minore di qualunque quantità <lb></lb>data, il che si riduce nella pratica quasi al niente. </s>

<s>Nondimeno, resta la co­<lb></lb>lonna trilatera d&#039;acqua sempre dimostrata tra il meno e il più, cioè tra le <lb></lb>inscritte e le circoscritte, e perciò riposa verso AD un peso grave quanto la <lb></lb>detta colonna d&#039;acqua ADE, o la metà di una colonna d&#039;acqua, il di cui <lb></lb>fendo sia AD, e l&#039;altezza la perpendicolare tra la superficie dell&#039;acqua, e il <lb></lb>suo più basso fondo, il che ecc. </s>

<s>” </s></p><p type="main">

<s>PROPOSIZIONE IV. — <emph type="italics"></emph>“ Verso un fondo quadrato, il di cui lato supe­<lb></lb>riore è sotto la superficie dell&#039;acqua, riposa il peso di una colonna di <lb></lb>acqua, la di cui base è uguale al fondo dato, e l&#039;altezza alla perpendi­<lb></lb>colare tra la superficie dell&#039;acqua, e il mezzo del fondo dato. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia, nella figura 52, l&#039;acqua ABCD, la sua superficie AB, il fondo <lb></lb>dato DE, il di cui mezzo I: dico che sopra DE riposa un peso eguale al peso <lb></lb><figure id="id.020.01.3139.1.jpg" xlink:href="020/01/3139/1.jpg"></figure></s></p><p type="caption">

<s>Figura 52.<lb></lb>di una colonna d&#039;acqua, la di cui base è ED, <lb></lb>e l&#039;altezza è la IK. Imperocchè, per la prece­<lb></lb>dente, la colonna trilatera d&#039;acqua ADH riposa <lb></lb>sopra AD, ed AEF riposa sopra AE. </s>

<s>Adunque <lb></lb>il triangolo ADH, diminuito del triangolo AEF, <lb></lb>riposa sopra ED, cioè la colonna d&#039;aqua EFHD. </s>

<s><lb></lb>Ma questa è uguale alla colonna, la di cui base <lb></lb>è ED, e altezza IK. Imperocchè, tirata LN nel <lb></lb>mezzo di GH, parallela ad AD, e prolungata <lb></lb>EF in N; EDLN sarà uguale ad EFHD. </s>

<s>Tirata <lb></lb>poi LM perpendicolare sopra AD, o alla sua prolungata; EDLN è una co­<lb></lb>lonna, la di cui base ED e altezza LM. </s>

<s>Se dunque IK è uguale ad LM, sarà <lb></lb>provata la proposizione. </s>

<s>Ciò si dimostra così: AE è uguale ad EF o DG, <lb></lb>ed AD a DH, onde ED è uguale a GH, e le loro metà anco uguali, cioè EI <lb></lb>a GL, ed AI a DL, e gli angoli LDM, KAI sono uguali, per essere AK e DL <lb></lb>parallele, e l&#039;angolo DML all&#039;AKI, per essere retti, ed i triangoli, e le LM, <lb></lb>IK uguali. </s>

<s>” </s></p><p type="main">

<s>PROPOSIZIONE V. — <emph type="italics"></emph>“ Di due fondi quadrati di acqua, d&#039;ugual lar­<lb></lb>ghezza, ma di lunghezza ineguale, i lati de&#039;quali più alti e più bassi <lb></lb>stiano ugualmente sotto la superficie dell&#039;acqua; i <lb></lb>pesi, che riposano verso essi, hanno fra loro la pro­<lb></lb>porzione, che tra la loro lunghezza. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Siano, nella figura 53, i dati fondi CE, DF, <lb></lb>la superficie dell&#039;acqua AB: dico che CE sta a DF, <lb></lb>come il peso, posante sopra CE, al peso sopra DF. </s>

<s>Im­<lb></lb>perocchè siano G, H il mezzo de&#039;fondi dati CF, DF, <lb></lb><figure id="id.020.01.3139.2.jpg" xlink:href="020/01/3139/2.jpg"></figure></s></p><p type="caption">

<s>Figura 53.<pb xlink:href="020/01/3140.jpg" pagenum="101"></pb>e si tirino GI, HK perpendicolari ad AB. </s>

<s>Sarà il peso sopra CE la colonna <lb></lb>d&#039;acqua, la di cui base sarà CE, e l&#039;altezza GI: e sopra DF la colonna, la <lb></lb>di cui base DF, ed altezza HK, o GI, per le due passate proposizioni. </s>

<s>Ma que­<lb></lb>ste colonne sono fra loro come CE, DF; e per conseguenza anco i pesi, che <lb></lb>posano sopra essi fondi, il che ecc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scolio I.<emph.end type="italics"></emph.end> — Nota che nella III proposizione, alla quale si applica que­<lb></lb>sta stessa figura, si è parlato di una mezza colonna d&#039;acqua, la di cui base <lb></lb>sia CE, ovvero DF, e l&#039;altezza la perpendicolare tra la superficie dell&#039;acqua <lb></lb>AB, e il punto E, ovvero F. </s>

<s>Ed è chiaro che queste mezze colonne sono <lb></lb>uguali alle colonne intere, le di cui basi sono le stesse CE e DF, e l&#039;altezza <lb></lb>la metà delle dette perpendicolari, cioè le linee intere GI, e HK, e perciò <lb></lb>resta la dimostrazione la stessa. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scolio II.<emph.end type="italics"></emph.end> — Nota inoltre che ho indicato i fondi per mezzo di linee, <lb></lb>per le quali bisogna intendere quadrati, di quella lunghezza, che uno gli vuol <lb></lb>dare. </s>

<s>E che questo non apporti alcuna variazione, si vede per sè medesimo, <lb></lb>ond&#039;è superfluo farne altra menzione ” (ivi, fol. </s>

<s>8, 9). </s></p><p type="main">

<s>Le proposizioni, dimostrate fin qui dal Witsen, corrispondono a quelle <lb></lb>dello Stevino, il quale però sempre suppone che i fondi e le pareti dei re­<lb></lb>cipienti siano superficie piane, come si conveniva alla natura del suo trat­<lb></lb>tato, in cui s&#039;astraeva dai casi particolari, che quegli stessi fondi ora spor­<lb></lb>gessero, ora rientrassero con andamenti sinuosi, de&#039;quali offrono giusto l&#039;esem­<lb></lb>pio i fianchi nell&#039;interno delle navi. </s>

<s>E potendo quegli andamenti essere in <lb></lb>varii piani, il Witsen ne considera i principali distintamente in due propo­<lb></lb>sizioni. </s></p><p type="main">

<s>PROPOSIZIONE VI. — <emph type="italics"></emph>“ Contro un fondo, il di cui lato superiore e l&#039;in­<lb></lb>feriore ciascuno è in un piano parallelo alla superficie dell&#039;acqua, ma <lb></lb>l&#039;uno e l&#039;altro piegato egualmente, però in tal modo, che tutte le linee, <lb></lb>da certi punti del lato superiore tirate verso altrettanti punti del lato in­<lb></lb>feriore, siano tutte linee parallele fra loro; vi riposa tanto peso, quanto <lb></lb>riposerebbe contro un fondo quadrato piano d&#039;egual lunghezza, e larghezza <lb></lb>e profondità sotto l&#039;acqua. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia, nella figura 54, l&#039;acqua ABCD, la superficie AB, i due piani EF, <lb></lb>CD paralleli alla superficie AB. </s>

<s>Nel piano EF sia il lato superiore del fondo <lb></lb>AEGILC, e su CD il lato inferiore BFHKMD, i due estremi AB, CD. </s>

<s>Dico <lb></lb>che, verso questo fondo serpeggiante, riposa un peso, che riposerebbe verso <lb></lb><figure id="id.020.01.3140.1.jpg" xlink:href="020/01/3140/1.jpg"></figure></s></p><p type="caption">

<s>Figura 54.<lb></lb>un fondo piano, largo quanto AB o CD, e <lb></lb>lungo quanto AEGILC, ovvero BFHKMD. <lb></lb>ed ugualmente profondo nell&#039;acqua. </s>

<s>Im­<lb></lb>perocchè siano AC, BD divise in tante <lb></lb>parti uguali, che le parti tra le divisioni <lb></lb>diventino linee rette, come in EG, IL ecc. </s>

<s><lb></lb>ed FH, KM ecc., e sian tirate le EF, GH, <lb></lb>IK, LM ecc., di maniera che il fondo ser­<lb></lb>peggiante sia diviso in fondi quadrati. <pb xlink:href="020/01/3141.jpg" pagenum="102"></pb>come sarebbe ABFE. </s>

<s>Nello stesso modo si potrebbe anco dividere i fondi <lb></lb>piani in altrettanti ed uguali fondi quadrati, i quali ugualmente sono pre­<lb></lb>muti, per la IV proposizione, e conseguentemente tutti i quadrati del fondo <lb></lb>serpeggiante saranno premuti altrettanto, quanto tutti i quadrati del fondo <lb></lb>piano. </s>

<s>Il che ecc. </s>

<s>” </s></p><p type="main">

<s>PROPOSIZIONE VII. — <emph type="italics"></emph>“ Contro un fondo piegato, i di cui lati supe­<lb></lb>riori ed inferiori sono paralleli alla superficie dell&#039;acqua, e i due altri <lb></lb>lati paralleli fra loro, e similmente piegati; riposa un peso eguale a quello, <lb></lb>che riposerebbe contro un fondo piano, dell&#039;istessa lunghezza, larghezza, <lb></lb>e profondità sotto l&#039;acqua ”<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>10, 11). </s></p><p type="main">

<s>La diversità di questa proposizione dalla precedente consiste nel consi­<lb></lb>derare le pieghe, con la loro longitudine orizzontale, ciò che meglio si potrà <lb></lb><figure id="id.020.01.3141.1.jpg" xlink:href="020/01/3141/1.jpg"></figure></s></p><p type="caption">

<s>Figura 55.<lb></lb>intendere, immaginando il fondo ondulato, che <lb></lb>si rappresentava in ABCD, nella passata figura, <lb></lb>essere eretto in modo, che i due lati estremi AB, <lb></lb>CD riescano paralleli al livello dell&#039;acqua LO, <lb></lb>come nella figura 55. Supponiano che le linee <lb></lb>BD, AC spiegate, s&#039;allunghino quanto le FH, <lb></lb>EG, e che le due superficie tra esse comprese, <lb></lb>la piana cioè e la piegata, rimangano profon­<lb></lb>date ugualmente sotto l&#039;acqua, come la figura 56, ne&#039;loro profili OA, OB, <lb></lb>le rappresenta. </s>

<s>Rimanendo alle due prementi colonne liquide ampiezza pari <lb></lb>di base e pari altezza, è manifesto che saranno <lb></lb><figure id="id.020.01.3141.2.jpg" xlink:href="020/01/3141/2.jpg"></figure></s></p><p type="caption">

<s>Figura 56.<lb></lb>uguali, come il Witsen ha già proposto, e poi <lb></lb>così dimostra: </s></p><p type="main">

<s>“ Sia, nella figura 55, la superficie del­<lb></lb>l&#039;acqua LO, i fondi dati ABDC, ed EFHG, dei <lb></lb>quali AB, DC; EF, HG sono uguali fra loro, e <lb></lb>tutti paralleli alla superficie dell&#039;acqua OL. </s>

<s>I <lb></lb>lati AB ed EF siano ugualmente profondi sotto <lb></lb>l&#039;acqua, come anco i lati CD, GH. </s>

<s>Dico che contro ABDC, ed EFHG, ri­<lb></lb>posa l&#039;istesso peso di acqua. </s>

<s>Imperocchè, dividansi AC, BD in parti uguali, <lb></lb>e tirinsi le linee, e così sarà diviso il fondo in diversì fondi quadrilateri. </s>

<s><lb></lb>Dividansi parimente le EG, FH: ne segue, per le proposizioni III e IV, che, <lb></lb>verso i quadrati superiori di ABDC, riposa lo stesso peso, che sopra i qua­<lb></lb>drati superiori di EFHG, e verso i susseguenti dell&#039;uno, che verso i susse­<lb></lb>guenti dell&#039;altro; e per conseguenza verso tutti dell&#039;uno, che verso tutti <lb></lb>dell&#039;altro. </s>

<s>” </s></p><p type="main">

<s>PROPOSIZIONE VIII. — <emph type="italics"></emph>“ In due fondi, ugualmente profondi sotto la <lb></lb>superficie dell&#039;acqua, e di ugual larghezza, e de&#039;quali uno sia piegato e <lb></lb>l&#039;altro no; la lunghezza alla lunghezza così sta, come la pressione alla <lb></lb>pressione. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sian, nella figura 57, i fondi dati AB, CD, sia A a C egualmente pro­<lb></lb>fondo sotto la superficie dell&#039;acqua LO, come anco B a D. Dico: come la <pb xlink:href="020/01/3142.jpg" pagenum="103"></pb>lunghezza del fondo piegato AB, alla lunghezza del diritto CD; così il peso, <lb></lb>che riposa verso AB, al peso che riposa verso CD. Imperocchè, siano AB, <lb></lb>CD divisi in più fondi quadrati, come nella passata, e sarà, per i fondi qua­<lb></lb>drati superiori, AE a CF, come il peso contro AE, al <lb></lb><figure id="id.020.01.3142.1.jpg" xlink:href="020/01/3142/1.jpg"></figure></s></p><p type="caption">

<s>Figura 57.<lb></lb>peso contro CF, per la V proposizione. </s>

<s>E similmente <lb></lb>EG ad FH come il peso contro EG, al peso contro FH. </s>

<s><lb></lb>Onde tutti i piccoli quadrati del fondo piegato, e tutti <lb></lb>i quadrilateri del fondo diritto, saranno premuti con <lb></lb>la proporzione, che è tra la lunghezza della linea in­<lb></lb>tera dell&#039;uno, alla lunghezza della linea intera del­<lb></lb>l&#039;altro fondo. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scolio.<emph.end type="italics"></emph.end> — Di qui è che, se il fondo AB fosse piegato nel modo che <lb></lb>nella VI e VII proposizione, sempre si conserverà le medesime proporzioni ” <lb></lb>(ivi, fol. </s>

<s>12). </s></p><p type="main">

<s>Rimeditando il Viviani su questi fogli, che tornandosene dalla casa dello <lb></lb>Stenone recava seco manoscritti, si persuase sempre più della verità di que­<lb></lb>ste nuove dottrine, e se prima aveva distese proposizioni, per dimostrare che <lb></lb>il liquido non preme niente contro le pareti laterali dei vasi, in difesa del <lb></lb>Michelini; ora dava mano a scrivere un trattato, in cui, per supplire ai di­<lb></lb>fetti di Archimede, si concluderebbe, da principii meccanici più certi, e con <lb></lb>tutto il rigore geometrico, che la mole di esso liquido preme non solo in giù, <lb></lb>ma ugualmente per ogni verso. </s>

<s>Racconteremo in seguito i fatti relativi alla <lb></lb>scrittura di questo trattato, per ora semplicemente osservando che il Viviani, <lb></lb>per non parere di detrar nulla al suo Maestro, non osservò la debita giu­<lb></lb>stizia verso i meriti, che si&#039;dovevano allo Stevino. </s>

<s>Nè più giusti verso lui si <lb></lb>mostrarono i contemporanei e i successori, i quali, sotto il sol meridiano <lb></lb>dello stesso Galileo e del Torricelli, del Boyle e del Pascal, avevano perduto <lb></lb>affatto di vista quella solitaria stella lontana, de&#039;raggi della quale s&#039;erano <lb></lb>rischiarate le tenebre del mattino. </s></p><p type="main">

<s>Nonostante, pochi anni prima che terminasse il secolo XVIII, sorgeva <lb></lb>il Lagrange a commemorare solennemente gli <emph type="italics"></emph>Hypomnemata mathematica,<emph.end type="italics"></emph.end><lb></lb>e sarebbe potuto bastare esso solo a far perdonare all&#039;Autore, e a rivendi­<lb></lb>carlo della lunga ingiustizia patita. </s>

<s>Ma il Lagrange stesso ebbe a risentirsi <lb></lb>del malefico influsso, e, o riferisse sopra le relazioni altrui, o ricorrendo al­<lb></lb>l&#039;originale lo consultasse con troppa fretta; i teoremi idrostatici dello Stevino <lb></lb>sono esposti da lui in maniera impropria, e sotto mendaci forme si porgono <lb></lb>le più importanti verità dimostrate. </s>

<s>Non si crederebbe ciò, ma è un fatto, e <lb></lb>noi non vogliamo passarci d&#039;esaminarlo, fra gli altri motivi, affinchè si per­<lb></lb>suadano alcuni che, senza sufficiente criterio, s&#039;è trattata fin qui la Storia <lb></lb>della Scienza, anche dagli scrittori piu celebri, e da&#039;giudici più competenti <lb></lb>di questa materia. </s></p><p type="main">

<s>Là dove dunque il Lagrange descrive il quadro storico, per rappresen­<lb></lb>tare ai Lettori quel che s&#039;era fatto nell&#039;Idrostatica da tutti coloro, che l&#039;ave­<lb></lb>vano preceduto, incominciando da Archimede, e affinchè si potessero giusta-<pb xlink:href="020/01/3143.jpg" pagenum="104"></pb>mente apprezzare gl&#039;impulsi, ch&#039;egli stesso, con la sua <emph type="italics"></emph>Meccanica analitica<emph.end type="italics"></emph.end><lb></lb>nuova, avrebbe dato alla Scienza; si legge: — Dai principii di Archimede <lb></lb>si desumono facilmente le pressioni sui fondi, e sopra le pareti dei vasi: lo <lb></lb>Stevino nonostante è il primo che l&#039;abbia fatto, e che abbia scoperto il <emph type="italics"></emph>Pa­<lb></lb>radosso idrostatico.<emph.end type="italics"></emph.end> È nel terzo tomo degli <emph type="italics"></emph>Hypomnemata mathematica,<emph.end type="italics"></emph.end><lb></lb>tradotto dall&#039;olandese per lo Snellio, e pubblicato a Leyda nel 1608, che si <lb></lb>trova l&#039;Idrostatica dello Stevino. </s>

<s>Egli immagina un vaso rettangolare pieno <lb></lb>d&#039;acqua, in cui sia immerso un solido del medesimo peso, sotto un egual <lb></lb>volume, il quale corpo, occupando il posto dell&#039;acqua, lascia che si faccia la <lb></lb>medesima pressione sul fondo, anco quando non vi resti del fluido che un <lb></lb>sottilissimo filo. </s>

<s>Ora esso Stevino osserva che, supponendo questo solido fer­<lb></lb>mato al suo posto, non può resultarne alcuna varietà nell&#039;azion dell&#039;acqua <lb></lb>contro il fondo del vaso. </s>

<s>Dunque, ei ne conclude, la pressione sopra questo <lb></lb>fondo sarà sempre uguale al peso della medesima colonna d&#039;acqua, e sia <lb></lb>qualunque la figura del recipiente. </s>

<s>Passa di qui l&#039;Autore a determinare la <lb></lb>pressione del liquido sopra pareti verticali o inclinate, e, applicandovi il me­<lb></lb>todo dei limiti, dimostra che la detta pressione è uguale al peso di una co­<lb></lb>lonna d&#039;acqua, di cui la base fosse la stessa parete, e l&#039;altezza la metà del­<lb></lb>l&#039;altezza del vaso. </s></p><p type="main">

<s>Dette le quali cose il Lagrange, nel suo proprio linguaggio, così, dello <lb></lb>Stevino, soggiunge: “ Il determine ensuite la pression sur une partie quel­<lb></lb>conque d&#039;une paroi plane inclinée, et il la trouve égale au poids d&#039;une co­<lb></lb>lonne d&#039;eau, qui saroit formèe en appliquant perpendiculairement a chaque <lb></lb>point de cette partie des droites egales a la profondeur de ce point sous <lb></lb>l&#039;eau ” (<emph type="italics"></emph>Mechan, analit.,<emph.end type="italics"></emph.end> a Paris 1788, pag. </s>

<s>126). Lo Stevino, è vero, de­<lb></lb>termina nel suo X teorema le pressioni, fatte sopra qualunque porzion di <lb></lb>parete inclinata, ma la sua dimostrazione vale altresi, quando la detta pa­<lb></lb>rete sia perpendicolare, nel qual caso la colonna che preme è propriamente <lb></lb>formata degl&#039;infiniti filetti liquidi orizzontali, aventi ciascuno lunghezza uguale <lb></lb>alla sua respettiva profondità sotto la linea del livello. </s>

<s>Così, ritornando in­<lb></lb>dietro sopra la figura 38, è manifesto che la colonna IDHK si compone degli <lb></lb>infiniti filetti liquidi, compresi fra IK, e DH, i quali due estremi, come gli <lb></lb>altri infiniti di mezzo, son perpendicolari al profilo parietale CD, e sono uguali <lb></lb>ciascuno alle respettive profondità CI, CD. </s>

<s>Ma quando la parete è inclinata, <lb></lb>che è il caso particolarmente riferito dal Lagrange, gli omonimi filetti IK, <lb></lb>DH nella figura 39 non sono altrimenti perpendicolari, nè la loro lunghezza <lb></lb>uguaglia la profondità sotto l&#039;acqua, ma la lunghezza della parete sopra­<lb></lb>stante, dal punto del loro contatto con essa, infin su a fior d&#039;acqua. </s>

<s>Così, <lb></lb>IK, DH non sono uguali ai perpendicoli delle profondità CN, CO, ma alle <lb></lb>oblique CI, CD, ossia ai profili delle pareti. </s></p><p type="main">

<s>“ Ce theoreme, prosegue a dire il Lagrange, étant ainsi demontré pour <lb></lb>des surfaces planes quelconques, situées comme l&#039;on voudra, il est facile de <lb></lb>l&#039;etendre à des surfaces courbes quelconques, et d&#039;en conclure que la pres­<lb></lb>sion exercée par un fluide pesant contre une surface quelconque, a pour me-<pb xlink:href="020/01/3144.jpg" pagenum="105"></pb>sure le poids d&#039;une colonne de ce mème fluide, la quelle auroit pour base <lb></lb>cette mème surface convertie en une surface plane, s&#039;il est necessaire, et <lb></lb>dont les hauteurs, répondantes aux différens points de la base, seroient les <lb></lb>mèmes que les distances des points correspondens de la surface a la ligne <lb></lb>de niveau du fluide; ou, ce qui revient au mème, cette pression sera mesu­<lb></lb>rée par le poids d&#039;une colonne, qui auroit pour base la surface pressée, et <lb></lb>pour hauteur la distance verticale du centre de gravité de cette meme sur­<lb></lb>face, a la surface superieure de fluide ” (ivi). </s></p><p type="main">

<s>Ma il teorema dello Stevino è formulato bene altrimenti, e chi vuol per­<lb></lb>suadersene legga quel ch&#039;egli così propriamente dice, nel secondo esempio, <lb></lb>dopo la XII proposizione: “ Soit AB (fig. </s>

<s>58) un fond <lb></lb><figure id="id.020.01.3144.1.jpg" xlink:href="020/01/3144/1.jpg"></figure></s></p><p type="caption">

<s>Figura 58.<lb></lb>convenant, ayant son plus haut poinct A sous fleur d&#039;eau C, <lb></lb>et AD perpendicle de A sur le niveau passant par le plus <lb></lb>bas poinct B, et prolongée jusques à fleur d&#039;eau C. </s>

<s>Soit E <lb></lb>au milieu de AD: Ie dis que le poids, qui repose con­<lb></lb>tre AB, est egal a la pesanteur de la colonne, ayant le dit <lb></lb>fond AB pour base, et CE pòur bauteur ” (Elemens hydr, <lb></lb>cit., pag. </s>

<s>494). Ora è chiaro che il punto E non è centro <lb></lb>di gravità del fondo <emph type="italics"></emph>convenant<emph.end type="italics"></emph.end> AB, altro che per acci­<lb></lb>dente, e non s&#039;intende come questo stesso centro possa <lb></lb>entrare in questione, se la parete del vaso, sopra cui riposa l&#039;acqua, non fa <lb></lb>altro ufficio che della libbra, alla quale sono attaccati i pesi o applicate le <lb></lb>forze. </s>

<s>Nè lo Stevino dall&#039;altra parte invoca la Baricentrica, se non colà, dove <lb></lb>si mette a ricercare il centro della pressione, in due proposizioni, che il La­<lb></lb>grange, a voler dare perfezione al suo quadro storico, rappresentandovi le <lb></lb>cose nella loro integrità sostanziale; non avrebbe dovuto lasciar di comme­<lb></lb>morare. </s></p><p type="main">

<s>Volgiamo ancora indietro lo sguardo sopra la figura 38. Si può la CD <lb></lb>riguardare come una libbra, gravata di pesi via via crescenti da C verso D, <lb></lb>a proporzione delle distanze, perchè tali in verità sono, e talmente operano <lb></lb>i filetti liquidi orizzontali, prementi contro la detta porzione indivisibile della <lb></lb>parete. </s>

<s>Ma si sa dalla Meccanica che il centro dell&#039;equilibrio sega così la <lb></lb>libbra, in questo caso, che la parte verso i pesi minori sia doppia di quella <lb></lb>verso i pesi maggiori; dunque il centro della pressione, fatta contro CD, è <lb></lb>in M, se DM è la metà di CM. </s>

<s>Lo Stevino però giunge a questa medesima <lb></lb>conclusione, immaginando che il triangolo CDH, trasformato in un solido di <lb></lb>pari gravità all&#039;acqua sia fatto rivolgere così in sè stesso, che CD base rie­<lb></lb>sca orizzontale. </s>

<s>In questo caso è manifesto che il centro di gravità di detto <lb></lb>solido batte pure in M. </s>

<s>E perchè sopra la linea MN, parallela ad AC, bat­<lb></lb>tono per le medesime ragioni i centri di gravità di tutti gl&#039;infiniti piani <lb></lb>triangolari, componenti il prisma EACDH; nel mezzo dunque di MN batterà <lb></lb>il centro di esso prisma, e ivi perciò caderà il centro della pressione, che la <lb></lb>prismatica colonna d&#039;acqua fa contro la parete parallelogramma, secondo che <lb></lb>si propone lo Stevino di dimostrare in questa forma: “ Si le fond d&#039;une eau <pb xlink:href="020/01/3145.jpg" pagenum="106"></pb>n&#039;est a niveau, estant parallelogramme, du quel le plus haut costé soit à <lb></lb>fleur d&#039;eau, et de son milieu au milieu de son costé opposite est menée une <lb></lb>ligne; le centre de gravité (du pressement de l&#039;eau congregé contre le fond) <lb></lb>divise ceste ligne de telle sorte, que la partie haute à la basse est en rai­<lb></lb>son double ” (ivi, pag. </s>

<s>495). </s></p><p type="main">

<s>Passa di qui lo Stevino a dimostrare in qual punto risponda il centro <lb></lb>della pressione, dentro la porzione ID della parete, come nella 39, qui addie­<lb></lb>tro, è prefigurata. </s>

<s>E osservando che una tale pressione si deve al peso del <lb></lb>piano acqueo, composto del parallelogrammo IL, e del triangolo KLH, aventi <lb></lb>quello e questo i centri di gravità, che riposano ne&#039;punti P ed R, sul mezzo, <lb></lb>e ai due terzi della base ID; ne conclude che il centro della gravità del <lb></lb>piano, o della pression del liquido, risponde al punto Q, fermato sulla PR <lb></lb>con tal ragione, che la parte QR stia alla QP, reciprocamente, come il pa­<lb></lb>rallelogrammo sta al triangolo; ossia, per le cose già dimostrate, come CI <lb></lb>sta ad IP, o come CN a NS. </s>

<s>E perchè di tutti gl&#039;infiniti piani, uguali e pa­<lb></lb>ralleli a IDHK, s&#039;affalda la colonna liquida, premente la parete parallelo­<lb></lb>gramma, il superior lato e l&#039;inferior della quale, suppongasi essere dalla ID <lb></lb>divisi nel mezzo; nello stesso punto Q, com&#039;è stato geometricamente indi­<lb></lb>cato, risponde il punto che si cercava, quello cioè, in cui si concentra tutto <lb></lb>insieme il peso della detta colonna, secondo che così propriamente lo Ste­<lb></lb>vino stesso annunziava: “ Estant un fond dans l&#039;eau, parallelogramme, non <lb></lb>a niveau, et son plus haut costé sous fleur d&#039;eau, et a niveau, du milieu du <lb></lb>quel costé au milieu de son opposite on mene une ligne; en icelle ligne est <lb></lb>le centre de gravité de compression congregée contre le fond la divisant en­<lb></lb>tre deux certains poincts, dont celuy d&#039;en-haut est centre du fond, l&#039;autre <lb></lb>divise la ligne totale en raison double. </s>

<s>Or entre ces deux poincts le dit cen­<lb></lb>tre se trouve diviser l&#039;intervalle ainsi que la partie inferieure à la superieure <lb></lb>est comme la ligne a plomb, entre fleur d&#039;eau et le plus haut costé du fond, <lb></lb>a la moitie de la ligne a plomb (<emph type="italics"></emph>così propriamente si deve leggere e non <lb></lb>semplicemente<emph.end type="italics"></emph.end> à la ligne a plomb, <emph type="italics"></emph>com&#039;è trascorso in questa edizione<emph.end type="italics"></emph.end>) en­<lb></lb>tre le dit plus haut costé, et le niveau qui passe sous son costé opposite ” <lb></lb>(ivi, pag. </s>

<s>496). </s></p><p type="main">

<s>Tali erano le importanti novità, che si venivano per lo Stevino a intro­<lb></lb>durre nell&#039;Idrostatica, la precipua fra le quali consisteva in aver messe nella <lb></lb>loro più piena evidenza le pressioni in su e per ogni verso, rimaste a tutti <lb></lb>un&#039;enimma dentro la seconda supposizion di Archimede. </s>

<s>D&#039;onde è facile <lb></lb>persuadersi che sarebbe giunta questa Scienza, già fino dal cominciar del <lb></lb>secolo XVII, a quella perfezione, a cui la ridusse l&#039;Hermann, se l&#039;autorità <lb></lb>del magistero non fosse tutta passata nelle mani di Galileo, l&#039;opera posta <lb></lb>dal quale intorno all&#039;Idrostatica, fin qui forse mal giudicata, apparirà quale <lb></lb>si fosse in effetto nella seguente Storia. </s></p><pb xlink:href="020/01/3146.jpg" pagenum="107"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quale occasione avesse Galileo di applicarsi, ne&#039;suoi anni giovanili, allo <lb></lb>studio dei teoremi idrostatici di Archimede, lo racconta da sè stesso in quel <lb></lb>dialogo latino, che fu per la prima volta pubblicato dall&#039;Albèri, in cui si <lb></lb>gettavano dall&#039;Autore i semi della nuova Scienza del moto. </s>

<s>Quivi dice, per <lb></lb>mezzo del suo interlocutore sotto il nome di Alessandro, che la ragion vera, <lb></lb>secondo la quale un corpo ci apparisce grave o leggero, dipende dalla pro­<lb></lb>porzione ch&#039;egli ha col mezzo, a quel modo che s&#039;era studiato di dimostrare <lb></lb>“ cum veram rationem invenire tentassem, qua possimus, in mixto ex duo­<lb></lb>bus metallis, singuli metalli exactissimam proportionem assignare: quorum <lb></lb>theorematum licet non dissimilia ab Archimede demonstrata sint, demon­<lb></lb>strationes minus mathematicas, et magis physicas in medium afferam ” <lb></lb>(Alb. </s>

<s>XI, 21). L&#039;occasione dunque di ritrovare queste prime fisiche dimo­<lb></lb>strazioni de&#039;medesimi teoremi archimedei venne a Galileo, mentre, circa al­<lb></lb>l&#039;anno 1587, attendeva all&#039;invenzione di quella Bilancetta idrostatica, per <lb></lb>l&#039;applicazion della quale si sarebbe potuto praticamente risolvere uno de&#039;più <lb></lb>mirabili e più curiosi problemi, fra quanti se ne raccontino dallle più anti­<lb></lb>che Storie della Scienza. </s></p><p type="main">

<s>La narrazione di ciò, più autorevole e più diffusa, è quella fattaci da <lb></lb>Vitruvio, il quale, dopo aver detto come Gerone re dei Siracusani, avendo <lb></lb>dato una massa di oro a un orefice perchè glie ne formasse una corona vo­<lb></lb>tiva, ed entrato poi in sospetto che fosse impiegata nell&#039;opera una parte di <lb></lb>argento, ricorresse ad Archimede, affinchè gli scoprisse per via di scienza la <lb></lb>ragione del furto; “ tunc is, Vitruvio stesso soggiunge, cum haberet eius rei <lb></lb>curam, casu venit in balneum, ibique, cum in solium descenderet, animad­<lb></lb>vertit quantum corporis sui in eo insideret tantum aquae extra solium ef­<lb></lb>fluere. </s>

<s>Itaque, cum eius rei rationem explicationis offendisset, non est mora­<lb></lb>tus, sed exilivit gaudio motus de solio, et nudus vadens domum versus, <lb></lb>significabat clara voce invenisse quod quaereret. </s>

<s>Nam currens identidem <lb></lb>graece clamabat <foreign lang="grc">ἐυρπχα, ἐυρπχα. </foreign></s>

<s>Tum vero ex eo inventionis ingressu duas <lb></lb>dicitur fecisse massas aequo pondere, quo etiam fuerat corona, unam ex auro, <lb></lb>alteram ex argento. </s>

<s>Cum ita fecisset, vas amplum ad summa labra imple­<lb></lb>vit aqua, in quo demisit argenteam massam. </s>

<s>Cuius quanta magnitudo in vase <lb></lb>depressa est, tantum aquae effluxit. </s>

<s>Ita exempta massa quanto minus factum <lb></lb>fuerat refudit, sextario mensus, ut eodem modo quo prius fuerat ad labra <lb></lb>aequaretur. </s>

<s>Ita ex eo invenit quantum, ad certum pondus argenti, certa aquae <lb></lb>mensura responderet. </s>

<s>Cum id expertus esset, tum auream massam similiter <lb></lb>pleno vase dimisit, et ea exempta, eadem ratione mensura addita, invenit ex <lb></lb>aqua non tantum defluxisse, sed tantum minus quantum minus magno cor­<lb></lb>pore eodem pondere auri massa esset quam argenti. </s>

<s>Postea vero repleto vase, <lb></lb>in eadem aqua ipsa corona demissa, invenit plus aquae defluxisse in coro-<pb xlink:href="020/01/3147.jpg" pagenum="108"></pb>nam, quam in auream eodem pondere massam, et ita, ex eo quod plus de­<lb></lb>fluxerat aquae in corona quam in massa, ratiocinatus deprehendit argenti in <lb></lb>auro mixtionem, et manifestum furtum redemptoris ” (<emph type="italics"></emph>Architecturae,<emph.end type="italics"></emph.end> Lib. </s>

<s>IX, <lb></lb>Cap. </s>

<s>III). </s></p><p type="main">

<s>Il Fazello, in un passo dell&#039;<emph type="italics"></emph>Istoria Siciliana,<emph.end type="italics"></emph.end> riferitoci dall&#039;Hodierna, <lb></lb>aggiunge così al racconto alcune particolarità degne di nota: “ Lucio Pol­<lb></lb>lione scrive che Archimede fu inventore di questa cosa, che si dirà adesso. </s>

<s><lb></lb>Jerone minore, re di Siracusa, avendo fatto voto di mettere una corona d&#039;oro <lb></lb>in un certo tempio, diede l&#039;oro ad un orefice perchè la facesse. </s>

<s>Ma egli con <lb></lb>tanta gran maestria mise l&#039;argento sotto l&#039;oro, che ella pareva veramente <lb></lb>tutta d&#039;oro. </s>

<s>Ma avendo il Re qualche sospetto di questo, per averlo udito <lb></lb>dir dalle spie, e non potendo per sè stesso <gap></gap> il furto, pregò Archi­<lb></lb>mede che volesse scoprire la malignità dell&#039;orefice, e convincerlo. </s>

<s>Onde egli, <lb></lb>pigliando tal carico sopra di sè, venne a caso nel bagno .... ” (<emph type="italics"></emph>Archimede <lb></lb>redivivo,<emph.end type="italics"></emph.end> Palermo 1644, pag. </s>

<s>9) e prosegue a narrare come da ciò gli ve­<lb></lb>nisse suggerita l&#039;invenzione, aiutandosi delle esperienze, a quel medesimo <lb></lb>modo, che Vitruvio le descrive. </s></p><p type="main">

<s>Si disse esser questo nella Storia un apologo, il significato proprio del <lb></lb>quale si raccoglierà facilmente, ripensando a que&#039;primi studiosi delle dottrine <lb></lb>idrostatiche di Archimede, le quali, nelle loro astratte generalità, pur sì mo­<lb></lb>stravano così feconde delle più nuove e più utili applicazioni. </s>

<s>Una di coteste <lb></lb>utilità nella Fisica si riconosceva principalmente dal saper secondo qual più <lb></lb>esatta proporzione si corrispondano le gravità di due o più corpi, sotto uguali <lb></lb>ampiezze di moli: ciò che vedevasi direttamente conseguire dalla Scienza ar­<lb></lb>chimedea, nella quale dimostravasi che i solidi immersi tanto perdono della <lb></lb>loro propria gravità, quant&#039;è quella dell&#039;umido, di cui occupano il luogo. </s>

<s>Che <lb></lb>se quest&#039;umido è l&#039;acqua, dalla sola perdita, che subisce un corpo nell&#039;im­<lb></lb>mersione, s&#039;avrebbe verso un egual mole di lei, e secondo la più precisa <lb></lb>verità, la proporzione desiderata. </s>

<s>Non occorreva altro a farsi poi che un com­<lb></lb>puto numerico, perchè, dato il peso di una massa, per esempio composta di <lb></lb>oro e di argento, si potesse da que&#039;medesimi principii archimedei certamente <lb></lb>concludere quanto fosse nel misto, distintamente, il peso dell&#039;un metallo e <lb></lb>dell&#039;altro. </s>

<s>E il computo que&#039;primi discepoli e promotori di Archimede non <lb></lb>penarono a farlo, di che lasciarono, com&#039;era giusto, tutta attribuire al Mae­<lb></lb>stro la gloria, cantatagli innanzi, sopra la lira di Bione e di Mosco, con quel­<lb></lb>l&#039;idillio, che in più rozze note ci ha trasmesso Vitruvio. </s></p><p type="main">

<s>Dietro l&#039;esperienza delle gravità specifiche de&#039;due metalli, e del loro <lb></lb>composto, il calcolo della quantità dell&#039;argento, sostituito all&#039;oro nella corona <lb></lb>del re Gerone, certissimamente fu fatto, e si può, dietro questa certezza, ar­<lb></lb>gomentare quanto amorosi e intensi fossero gli studii dati all&#039;Idrostatica dai <lb></lb>contemporanei di Archimede, o da&#039;successori immediati di lui, benchè quel <lb></lb>calcolo non dovesse poi parer tanto difficile a chi meditava e aveva intelligenza <lb></lb>dei libri <emph type="italics"></emph>Della sfera e cilindro, Dei conoidi e sferoidei.<emph.end type="italics"></emph.end> Nonostante non sap­<lb></lb>piamo altro da Vitruvio, se non che la proporzione de&#039;due metalli nel misto <pb xlink:href="020/01/3148.jpg" pagenum="109"></pb>fu ritrovata <emph type="italics"></emph>ratiocinando,<emph.end type="italics"></emph.end> ma nessuno aveva ancora detto in qual modo fosse <lb></lb>fatta, o si potesse fare questa raziocinazione o questo calcolo, prima del Tar­<lb></lb>taglia, a cui pure venne primo in pensiero d&#039;istituirlo sopra più precisi dati <lb></lb>sperimentali, inventando l&#039;uso della Bilancetta. </s></p><p type="main">

<s>Che in mezzo a tanto squisita cultura di lettere umane le rozze pagine <lb></lb>del Matematico di Brescia andassero dimenticate, non fa maraviglia, ma ben <lb></lb>fa maraviglia che le potessero così disprezzare coloro, i quali incominciarono <lb></lb>nel secolo appresso a infondere nelle parole un succo di verità nuove, come <lb></lb>ristorativo sapore di frutto in mezzo al vano susurrar delle fronde. </s>

<s>Comun­<lb></lb>que sia, benchè Galileo ostentasse il suo disprezzo, come sopra tutti gli altri <lb></lb>che lo avevano preceduto, così e sopra il Tartaglia; è un fatto che s&#039;intro­<lb></lb>dusse in questi studii delle gravità specifiche con l&#039;aggiungere qualche per­<lb></lb>fezione a quello stesso strumento, che da quasi cinquant&#039;anni tutti legge­<lb></lb>vano, o potevano leggere in quel secondo ragionamento, fatto dall&#039;Autore <lb></lb>intorno alla sua propria <emph type="italics"></emph>Travagliata invenzione.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Già ben sanno i nostri Lettori, a cui poco addietro si commemorava, <lb></lb>come fosse quello strumento idrostatico inventato dal Tartaglia, a evitar le <lb></lb>fallacie, inevitabili nel metodo, che, per trovare i pesi specifici de&#039;vari corpi, <lb></lb>si diceva avere usato Archimede: e che tale pure si fosse il primo passo <lb></lb>fatto da Galileo intorno alla Bilancetta, apparisce da una sua nota, la quale, <lb></lb>essendo scritta in mezzo a quella salva di <emph type="italics"></emph>Problemi varii,<emph.end type="italics"></emph.end> che poi risoluti <lb></lb>si sarebbero voluti inserire nel <emph type="italics"></emph>Dialogo novissimo:<emph.end type="italics"></emph.end> ne fa presentir l&#039;origine <lb></lb>e la ragione di quel frammento, che più qua pubblicheremo. </s>

<s>In quella nota <lb></lb>dunque si legge: “ Esperienza di Archimede falsa intorno alla Corona di <lb></lb>Jerone, con l&#039;esplicazione della Bilancia, per trovare i pesi delle diverse ma­<lb></lb>terie ” (MSS. Gal., P. III, T. III, fol. </s>

<s>62). E appunto è questa quella Bilan­<lb></lb>cia, che si diceva non essere di originale invenzione, ma un perfezionamento <lb></lb>di quell&#039;altra del Tartaglia. </s>

<s>Un documento, ritrovato da noi nelle <emph type="italics"></emph>Aggiunte <lb></lb>ai Manoscritti galileiani, esistenti nella R. </s>

<s>Biblioteca nazionale di Firenze,<emph.end type="italics"></emph.end><lb></lb>e che ora siam per trascrivere, conferma il nostro asserto. </s>

<s>Prima che l&#039;Ho­<lb></lb>dierna pubblicasse la scrittura autografa di Galileo, non si sapeva della Bi­<lb></lb>lancetta di lui se non ciò che, per tradizione orale, ne venivano dicendo i <lb></lb>Discepoli, le particolarità de&#039;quali detti in proposito possono raccogliersi dal <lb></lb>documento, inserito nelle <emph type="italics"></emph>Aggiunte<emph.end type="italics"></emph.end> sopra annunziate, prezioso organo di tante <lb></lb>altre tradizioni scientifiche, ignote, della Scuola galileiana. </s>

<s>In quel documento <lb></lb>manoscritto dunque si dice: </s></p><p type="main">

<s>“ Il signor Galileo trovò una invenzione per pesare le materie più gravi <lb></lb>dell&#039;acqua, abbiano che figura si vuole, ed è facendo una Bilancia, anzi Sta­<lb></lb>dera, con ispazi giustissimi e minuti, <lb></lb><figure id="id.020.01.3148.1.jpg" xlink:href="020/01/3148/1.jpg"></figure></s></p><p type="caption">

<s>Figura 59.<lb></lb>ed i metalli o altro si pongono sopra <lb></lb>la Bilancia immersi dentro all&#039;acqua, <lb></lb>appesi per un filo di seta cruda, ov­<lb></lb>vero capello, e si legano alla stadera <lb></lb>mel punto B (fig. </s>

<s>59). E per fare li <pb xlink:href="020/01/3149.jpg" pagenum="110"></pb>scompartimenti giustissimi fanno l&#039;ago BD tondo, e sopra ci avvolgono a <lb></lb>spira un filo di metallo, tirato alla filiera, che benissimo si accosti, quale, <lb></lb>per essere grosso tutto ugualmente, e tra loro toccarsi le spire, viene a fare <lb></lb>li scompartimenti uguali fra loro. </s>

<s>” </s></p><p type="main">

<s>“ Per fare il computo della gravità dell&#039;argento si sospenderà un pezzo <lb></lb>di argento C ad un capello, alla testa della stadera B, ed immerso nell&#039;acqua <lb></lb>chiara, ed ivi si tiri il guscio F, che serve invece di romano, in luogo che <lb></lb>stia in equilibrio, e sia per esempio al decimo scompartimento (quali si con­<lb></lb>tano toccandoli con la punta di un ago, ovvero con il taglio di un coltello) <lb></lb>e se non starà perfettamente in equilibrio, cavisi ovvero aggiungasi della pol­<lb></lb>vere di piombo o altro grave, che in detto guscio si deve ponere, fino a che <lb></lb>ugualmente bilanci. </s>

<s>Cavisi poi detto argento fuori dell&#039;acqua, e si lasci asciu­<lb></lb>gare al sole o altrimenti, e si tiri tanto avanti il guscio, che serve per ro­<lb></lb>mano, in fino a che stia in equilibrio, e sia v. </s>

<s>g. </s>

<s>a venti gradi o scompar­<lb></lb>timenti. </s>

<s>Io dico che la gravità dell&#039;argento a quella dell&#039;acqua starà come <lb></lb>venti a dieci, perchè infondendolo nell&#039;acqua noi abbiamo detratto dal suo <lb></lb>peso totale dieci gradi di gravità. </s>

<s>Ma l&#039;acqua non detrae dalle materie gravi <lb></lb>altro che quanto peserebbe una mole di acqua per l&#039;appunto, uguale a quella <lb></lb>che s&#039;immerge, abbia che figura si vuole, perchè l&#039;acqua nell&#039;acqua non <lb></lb>pesa; adunque l&#039;argento sarà il doppio più grave dell&#039;acqua. </s>

<s>E permutan­<lb></lb>dosi, a volere che l&#039;argento fosse uguale di peso all&#039;acqua, sarebbe neces­<lb></lb>sario che quel medesimo pezzo fussi di superficie due volte maggiore. </s>

<s>” </s></p><p type="main">

<s>“ Dicono che la stadera, per esser comoda, vorrebbe esser lunga un <lb></lb>gran palmo, e di robustezza basta che possa sostenere un&#039;oncia di peso: il <lb></lb>filo di ottone o di acciaio vuol essere sottilissimo, e la bilancia gelosa, che <lb></lb>ogni poco di grave la muova. </s>

<s>” </s></p><p type="main">

<s>“ Per fare la bilancia assai gelosa, si faccia che il fulcimento sia fuora <lb></lb>della traversa, e tanto quanto sarà alle braccia della bilancia o traversa lon­<lb></lb>tano, tanto sarà piu gelosa. </s>

<s>Come per esempio nella bilancia ABC (fig. </s>

<s>60), <lb></lb><figure id="id.020.01.3149.1.jpg" xlink:href="020/01/3149/1.jpg"></figure></s></p><p type="caption">

<s>Figura 60.<lb></lb>se in cambio di porre il pernio del fulcimento nel <lb></lb>luogo B, come si usa, lo porremo lontano alle brac­<lb></lb>cia AB, BC, e lo porremo nel luogo D, ella sarà più <lb></lb>gelosa e mobile: tanto più, quanto dal luogo B sta <lb></lb>lontano l&#039;ago. </s>

<s>Allora, ogni tantino che esca la Bi­<lb></lb>lancia dall&#039;equilibrio, farà molto maggior mutazione, <lb></lb>ed è meglio, invece di fare il buco nel luogo D, ed il fulcimento o pernio <lb></lb>farlo nel sostegno, che detta Bilancia sostiene; farlo nel sostegno: e nelì&#039;ago <lb></lb>della Bilancia in D farvi un coltello tagliente. </s>

<s>” </s></p><p type="main">

<s>Queste ultime osservazioni sono di non lieve importanza, per la storia <lb></lb>della costruzione, e delle leggi statiche applicate alla Bilancia, benchè al­<lb></lb>quanto fuori del presente proposito, qual&#039;era di confermare che la princi­<lb></lb>pale intenzione, per cui Galileo costruì la sua Bilancetta idrostatica, fu <emph type="italics"></emph>per <lb></lb>trovare i pesi in specie delle varie materie,<emph.end type="italics"></emph.end> non altrimenti da quel che un <lb></lb>mezzo secolo prima aveva pure inteso di fare il Tartaglia. </s>

<s>Quali modifica-<pb xlink:href="020/01/3150.jpg" pagenum="111"></pb>zioni poi all&#039;invenzione di questo facesse l&#039;altro, dalla precedente descrizione <lb></lb>è manifesto: allo <emph type="italics"></emph>spaghetto lunghetto<emph.end type="italics"></emph.end> si sostituì uu filo di seta cruda, o un <lb></lb>capello, e alla inesattezza delle divisioni, segnate con le tacche ordinarie sul­<lb></lb>l&#039;ago della Stadera <emph type="italics"></emph>ovver piombino,<emph.end type="italics"></emph.end> si provvide ingegnosamente, riducendo <lb></lb>l&#039;ago stesso quasi a vite micrometrica, co&#039;sottili e stretti avvolgimenti di un <lb></lb>filo di metallo. </s></p><p type="main">

<s>Con un tale strumento, ridotto così, per via dei detti artificii, squísito, <lb></lb>Galileo sperimentò le gravità specifiche dei varii corpi, e, in ordine al pro­<lb></lb>blema della corona, dava per risolverlo fondamenti assai più sicuri di quelli, <lb></lb>che si proponevano dagli Antichi. </s>

<s>Quella completa soluzion nonostante ri­<lb></lb>maneva tuttavia affidata a un calcolo, come nella prima istituzion di Archi­<lb></lb>mede, e fu propriamente Galileo, che dispensò da ogni esercizio matematico, <lb></lb>insegnando a chi ne fosse stato curioso di ritrovare le proporzioni de&#039;due <lb></lb>metalli nel misto, col semplice uso manuale del suo strumento. </s>

<s>Tutto ciò, <lb></lb>insieme con altri particolari, da cui si viene a illustrare la storia della Bilan­<lb></lb>cetta galileiana, s&#039;intenderà meglio da un frammento di Dialogo, che si rende <lb></lb>ora per noi alla pubblica notizia dal manoscritto altre volte citato: <emph type="italics"></emph>Roba del <lb></lb>gran Galileo, in parte copiata dagli originali, e in parte dettata da lui <lb></lb>cieco a me Vincenzo Viviani, mentre dimoravo nella sua casa di Arcetri.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ SALVIATI. — Ammiranda, sopra tutte le altre che si leggono nelle an­<lb></lb>tiche scritture, mi è sembrata sempre l&#039;invenzion di Archimede, per la quale <lb></lb>scopri il furto della corona di Jerone, e tanto più mi s&#039;accresce di ciò la <lb></lb>maraviglia, quanto più vo fra me ripensando come il nostro Accademico ri­<lb></lb>dusse l&#039;operazione assai più facile e più precisa. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Io n&#039;ho sentito anch&#039;io tante volte parlare, e a chi non <lb></lb>è noto oramai quel famoso <emph type="italics"></emph>eurika, eurika?<emph.end type="italics"></emph.end> Non intendo però come a sco­<lb></lb>prir se un oggetto è di oro puro, o mescolato con altro, ci sia bisogno di <lb></lb>una scienza così pellegrina. </s>

<s>Non era ella forse nota a que&#039;tempi la pietra <lb></lb>del paragone? </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Era anzi notissima sotto il nome di pietra eraclèa o lidia, <lb></lb>e se ne trovano descritte le maravigliose virtù da Teofrasto, antichissimo <lb></lb>scrittore greco. </s>

<s>Poco o nulla però poteva giovare il ricorrere a un tale espe­<lb></lb>diente, trattandosi, non di scoprir la natura de&#039;metalli, ma di sapere secondo <lb></lb>qual proporzione si trovassero nel composto, ciò che si desiderava principal­<lb></lb>mente, per far la giusta ragione del furto. </s>

<s>Del qual furto gl&#039;indizi non ve­<lb></lb>nivano dall&#039;aspetto esteriore, o da qualche esame che si fosse fatto intorno <lb></lb>alla parte sostanziale della corona, la quale, come mostrava, così era al di <lb></lb>fuori tutta aurea, e rispondeva esattamente al peso del metallo puro conse­<lb></lb>gnato all&#039;orefice, perchè ne conducesse il lavoro. </s>

<s>Sembra piuttosto, a quel <lb></lb>che si può, con la ragione e con la prudenza, congetturare di un fatto da <lb></lb>noi tanto remoto, che i cortigiani sapessero qualche cosa di certo, e che, <lb></lb>susurrandone in palazzo, facessero entrare nel Re il sospetto che a una buona <lb></lb>parte dell&#039;oro fosse furtivamente sostituito altrettanto peso di argento, cosic­<lb></lb>chè la materia della corona resultasse del loro misto. </s>

<s>” </s></p><pb xlink:href="020/01/3151.jpg" pagenum="112"></pb><p type="main">

<s>“ SAGREDO. — Mi sembrerebbe, essendo così, che dal solo colore si sa­<lb></lb>rebbe potuto sospettar dell&#039;inganno, perchè, mescolandosi insieme due pol­<lb></lb>veri, l&#039;una delle quali tirasse al giallo rossigno dell&#039;oro, e l&#039;altra al bianco <lb></lb>cenerino dell&#039;argento; se ne vedrebbe nascere un terzo colore, che non è <lb></lb>bene nè questo schietto, nè quello. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Voi, signor Sagredo, mostrate di participar con l&#039;opi­<lb></lb>nione di molti, che la mescolanza dei due metalli nella corona fosse fatta <lb></lb>per fusione, e per effetto del fuoco. </s>

<s>Ma non fu propriamente così: anzi vi <lb></lb>dico che così non può essere stato, perchè altrimenti sarebbono riuscite fal­<lb></lb>laci le liberali applicazioni della scienza, nel far le quali necessariamente si <lb></lb>presuppone che le densità, da cui dipendono le moli de&#039;due metalli, separa­<lb></lb>tamente e nel misto, si mantengano inalterate. </s>

<s>Voi dovete sapere che sono <lb></lb>in tutti i corpi sparsi vacuetti, dal maggiore o minor numero de&#039;quali, e <lb></lb>dalla loro maggiore o minore grandezza, dipende l&#039;essere alcuni solidi, sotto <lb></lb>parità di superficie, più o meno gravi di altri. </s>

<s>È perchè togliendo due palle <lb></lb>di diametro uguale, ma la prima d&#039;oro e la seconda d&#039;argento, si trova es­<lb></lb>ser quella notabilmente più grave di questa; convien dire che nell&#039;argento <lb></lb>siano que&#039;vacuetti in più larga copia disseminati, che in mezzo all&#039;oro. </s>

<s>Ora <lb></lb>accade che, fondendosi insieme i due metalli, nelle maggiori vacuità dell&#039;uno <lb></lb>penetra, assottigliata dal fuoco, la sostanza dell&#039;altro, intanto che il misto <lb></lb>viene a ridursi sotto mole assai minore di quella, che avevano prima i due <lb></lb>metalli separati. </s>

<s>Così essendo, il ragionamento di Archimede, che partivasi <lb></lb>da falsi principii, sarebbe giunto a conseguenze false. </s>

<s>Nè potendosi ciò pre­<lb></lb>supporre in un ingegno tanto eccellente, mi fa con certezza asseverare che <lb></lb>fossero i due metalli insieme nella corona per semplice apponimento di parti, <lb></lb>e non per fusione: come a dire che l&#039;armilla e i raggi, consolidati dentro <lb></lb>nella materia dell&#039;argento, fossero tutti ricoperti di fuori, e fasciati, da una <lb></lb>foglia di purissimo oro. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Se così stanno, signor Salviati, le cose, come voi dite, <lb></lb>non aveva bisogno Jerone di ricorrere alla sapienza del grande Archimede: <lb></lb>qualunque artefice, co&#039;suoi strumenti acuti e taglienti, rimovendo la foglia <lb></lb>dell&#039;oro, gli avrebbe reso visibile l&#039;argento che v&#039;era sotto, e senza indugio <lb></lb>scoperta la ragione del furto. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Pensate però, signor Simplicio, che si sarebbe così gua­<lb></lb>stato il lavoro, con finissima arte e diligenza condotto, e da questa parte <lb></lb>giusto ne pare maravigliosa la scienza di Archimede, perchè, mentre non <lb></lb>rendeva men certo e men patente il fatto, che a metterlo sotto gli occhi; <lb></lb>lasciava, secondo il desiderio del Re, l&#039;opera dell&#039;artefice intatta. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Il signor Simplicio, col suo stesso silenzio, mostra di es­<lb></lb><gap></gap> sodisfatto. </s>

<s>Vi resta ora, signor Salviati, a dare sodisfazione anche a me <lb></lb>intorno a due dubbii, che mi son nati, ascoltando il vostro discorso. </s>

<s>Il primo <lb></lb>si è che io non posso persuadermi avere metalli così compatti, come sono <lb></lb>l&#039;oro e l&#039;argento, vacuetti o pori aperti in mezzo alla loro sostanza, come <lb></lb>si vede ne&#039;legni o in altri corpi, che galleggiano sopra l&#039;acqua. </s>

<s>Il secondo <pb xlink:href="020/01/3152.jpg" pagenum="113"></pb>è che io non intendo come, non serbando i due metalli nel misto la mede­<lb></lb>sima proporzion di mole, che separati, fallaci, come voi dite, ne dovessero <lb></lb>riuscire i giudizi di Archimede, o di chiunque altro si volesse mettere a imi­<lb></lb>tarne gli esempi. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — L&#039;esperienze del nostro Accademico vi risolveranno il <lb></lb>primo dubbio. </s>

<s>Il secondo ve lo troverete per voi medesimo risoluto, da poi <lb></lb>che io vi avrò descritto il processo della maravigliosa invenzione, che, se­<lb></lb>condo ne riferiscono gli Scrittori, sarebbe questo: Avendo Archimede, men­<lb></lb>tre era tutto in pensiero della proposta fattagli da Jerone, scoperto che il suo <lb></lb>proprio corpo, immerso nell&#039;acqua della tinozza piena, tanto perdeva della <lb></lb>sua gravità naturale, quant&#039;era il peso dell&#039;acqua versata; prese una massa <lb></lb>di oro schietto, e separatamente una massa di argento, ambedue di pari peso <lb></lb>a quello, che dava la corona, posta sopra una squisitissima Bilancia. </s>

<s>Poi <lb></lb>riempì un vaso di acqua, e vi tuffò la massa dell&#039;oro, la quale ne fece tra­<lb></lb>boccar tanta, quant&#039;era precisamente la propria mole, tenendo esattissimo <lb></lb>conto del peso dell&#039;acqua versata. </s>

<s>Similmente operò con l&#039;argento, e con la <lb></lb>corona, la quale fu trovata versar meno acqua dell&#039;argento stesso, e più di <lb></lb>quello, che non avesse fatto l&#039;oro solo, e da questo più o meno dell&#039;acqua, <lb></lb>ne&#039;detti versamenti con diligenza raccolta, riuscì poi, per via di calcolo, Ar­<lb></lb>chimede a saper quanto più o meno dell&#039;un metallo o dell&#039;altro avesse im­<lb></lb>piegato l&#039;orefice nel suo lavoro. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Or ben comprendo, signor Salviati, che, non potendosi <lb></lb>paragonare insieme due cose di natura diversa, male avrebbe Archimede ri­<lb></lb>soluto il problema, se le moli ai pesi, de&#039;due metalli separati e nel misto, <lb></lb>non avessero osservata la medesima proporzione. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Quanto a me confesso che, dal discorso del signor Sal­<lb></lb>viati, mi si rappresenta il furto della corona di così facile ritrovato, che io <lb></lb>non intendo com&#039;egli abbia potuto destar nel mondo tanta ammirazione. </s>

<s><lb></lb>Trattandosi di versar acqua in un vaso, e di farvela traboccare col tuffarvi <lb></lb>dentro un oggetto, mi pare che tutto si riduca a un gioco da fanciulli, nè <lb></lb>so quale gloria potesse guadagnarne il nostro Accademico, a ingerirsi di que­<lb></lb>ste bagattelle, per renderle, come voi dite, più facili e più precise. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Bagattelle si potrebbero forse dire in sè stesse, non con­<lb></lb>siderata la loro intenzione finale, che se voi poteste, signor Simplicio, pene­<lb></lb>trar col vostro cervello, vi farebbe dare di queste cose ben altro giudizio. </s>

<s>Vi <lb></lb>concedero; in ogni modo che sia ovvio infondere l&#039;acqua in un vaso, e per <lb></lb>l&#039;immersione di una mole straniera farla riversar fuori dal suo labbro. </s>

<s>Ma, <lb></lb>per la bontà dell&#039;operazione, è necessario saper la misura esatta di quel ver­<lb></lb>samento. </s>

<s>Ripensate ora a quel che in tale atto rimane attaccato agli orli, e <lb></lb>alle pareti esterne, e vi persuaderete che il liquido così raccolto non è pre­<lb></lb>cisamente tutto quello, di cui la mole straniera è sottentrata a prendere il <lb></lb>luogo. </s>

<s>Nè a punto minor pericolo di fallacie menava il metodo, che si dice <lb></lb>aver tenuto Archimede. </s>

<s>Egli lasciava liberamente versar l&#039;acqua, infin tanto <lb></lb>che non fosse la mole tutta immersa. </s>

<s>Poi estraeva questa dal vaso, che ne-<pb xlink:href="020/01/3153.jpg" pagenum="114"></pb>cessariamente si rimaneva scemo, e l&#039;acqua, che poi ci bisognava a colmarlo, <lb></lb>era la misura di quella dianzi versata. </s>

<s>” </s></p><p type="main">

<s>“ Questa operazione dispensava è vero da ogni cura lo sperimentatore, <lb></lb>per quella parte dell&#039;acqua che si perdeva, rimanendo nel versare attaccata <lb></lb>agli orli, e alle pareti del vaso: ma se ne perdeva pure in altra maniera, <lb></lb>in quel velo cioè, di che tornavano rivestite le moli, nel tirarle fuori dal ba­<lb></lb>gno, e specialmente la corona, con tutti que&#039;suoi incavi e risalti, sfuggimenti <lb></lb>e trafori. </s>

<s>E nell&#039;atto stesso di colmare il vaso, dopo l&#039;estrazione, a quanti <lb></lb>scorsi non andava ella soggetta la mano incerta? </s>

<s>Bisognava badar bene che <lb></lb>l&#039;acqua non traboccasse: eppure, se non traboccava, non si poteva esser certi <lb></lb>che il vaso era colmo. </s>

<s>Giunto il liquido all&#039;orlo supremo, si poteva, colla <lb></lb>sestaria o con altra ampolla di misura nota, seguitare a infondere a gocciola <lb></lb>a gocciola, e una e due e quattro non bastano, in fin tanto che, squarcian­<lb></lb>dosi a un tratto quella specie di pellicola, che involge, e che, quasi vi fosse <lb></lb>cucita in giro, trattiene il colmo; tutto va giù a precipizio. </s>

<s>Ond&#039;ei non è <lb></lb>possibile sapere, con quella precisione che pur si richiede, quant&#039;è l&#039;acqua <lb></lb>versata dall&#039;ampolla, a riempire lo scemo, rimasto dentro il vaso, dall&#039;estrarne <lb></lb>fuori i metalli. </s>

<s>E anche, nel misurar l&#039;acqua dell&#039;ampolla dopo il riempi­<lb></lb>mento, altra nuova occasione a fallacie. </s>

<s>Perchè, non valendoci le misure di <lb></lb>capacità, e dovendosi ricorrere alla Stadera, ci bisognavano due pesate: una <lb></lb>prima, e un&#039;altra dopo l&#039;infusione, a fin di argomentare, dalla trovata dif­<lb></lb>ferenza, quanto sia il peso dell&#039;acqua, di mole uguale a quella dell&#039;oro, del­<lb></lb>l&#039;argento, e della corona. </s>

<s>” </s></p><p type="main">

<s>“ Ora il nostro Accademico, ripensando a ciò, e specialmente che per <lb></lb>l&#039;operazione era la Stadera strumento indispensabile, si maravigliò che Ar­<lb></lb>chimede eleggesse modi così complicati e fallaci, invece di quegli altri tanto <lb></lb>più semplici, e più sicuri, che pareva dover essergli suggeriti da&#039;suoi stessi <lb></lb>teoremi. </s>

<s>In uno di questi infatti dimostra che un solido immerso nell&#039;umido <lb></lb>perde tanto di gravità, quant&#039;è la gravità dell&#039;umido, di cui dentro il vaso <lb></lb>egli occupa il luogo. </s>

<s>Immaginate dunque essere BD (nella figura 59) la sta­<lb></lb>dera, con la quale si è pesato il solido C, o oro o argento che egli sia, o un <lb></lb>composto di tutt&#039;e due, e che siasi quel peso v. </s>

<s>g. </s>

<s>trovato venti libbre. </s>

<s>Non <lb></lb>rimovete nulla dal suo posto: se mai, allungate il filo BC, che ha da essere <lb></lb>sottilissimo e resistente come d&#039;acciaio, infin tanto che il solido C, da cui <lb></lb>pende, non vada a tuffarsi tutto nell&#039;acqua di un vaso, sottopostogli a que­<lb></lb>sto effetto. </s>

<s>Perderà, così stante, del suo proprio peso, e quanto ne perderà <lb></lb>per l&#039;appunto si potrà saperlo dal ritirare indietro il romano, il quale sup­<lb></lb>poniamo che faccia l&#039;equilibrio, giunto sul segno delle dieci libbre. </s>

<s>La diffe­<lb></lb>renza è dunque dieci, e tanto è il giusto peso di una mole di acqua, uguale <lb></lb>alla mole C, che, per ritrovarlo, si facevano quelle penose e incerte opera­<lb></lb>zioni da me narrate. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Io rimango veramente stupito, nel ripensare al modo delle <lb></lb>antiche e delle nuove esperienze. </s>

<s>In queste il solido imprime nell&#039;umido la <lb></lb>sua propria stampa, intanto che la mole di questo, corrispondente alla mole <pb xlink:href="020/01/3154.jpg" pagenum="115"></pb>di quello, si può dire che sia esattamente ritrovata dalla stessa Natura, non <lb></lb>rimanendo all&#039;arte altra faccenda, che di ritirare innanzi e indietro il con­<lb></lb>trappeso della stadera. </s>

<s>Mirabilmente si viene per questa via a scansare ogni <lb></lb>fallacia, da quella in fuori che può nascer dal filo. </s>

<s>Ma pur, lasciandone tuffare <lb></lb>assai poco, ed essendo sottilissimo, come avete prescritto, non può produrre <lb></lb>che qualche minimo effetto. </s>

<s>Io non avrei avuto il coraggio di dire, come il <lb></lb>signor Simplicio, che queste erano bagattelle, ma non avrei nemmeno creduto <lb></lb>che fossero invenzioni così pellegrine e ammirande, come ora intendo. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — E anch&#039;io pronunziai quel giudizio, perchè da tanti avevo <lb></lb>sentito parlare di questo furto, fatto nella corona del re Jerone, ma nes­<lb></lb>suno me ne aveva ancora spiegato così bene il modo, com&#039;avete fatto voi, <lb></lb>signor Salviati, a cui raccomando di congratularvi di ciò con l&#039;Accademico, <lb></lb>a nome mio. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Aspettate a far questo di avere inteso il tutto, non essen­<lb></lb>dosi detto fin qui da me che il principio, a movere dal quale sia fatto il <lb></lb>primo passo, considerando che col metodo nuovo è possibile ritrovare la pro­<lb></lb>porzione, che, al peso di un&#039;egual mole di acqua, ha il peso di qualunque <lb></lb>più piccolo oggetto, come sarebbe per esempio di una margarita. </s>

<s>Se non <lb></lb>che si richiede al proposito una stadera assai delicata, e con la lunghezza <lb></lb>divisa in minime parti, le quali vogliono essere tutte puntualissimamente <lb></lb>uguali. </s>

<s>Una tal precisione, difficile ad aversi dall&#039;arte fabbrile, si conseguiva <lb></lb>dal nostro Accademico, avvolgendo intorno al ferro tondo dell&#039;ago un filo <lb></lb>sottilissimo di acciaio, passato alla filiera, e stringendone le spire l&#039;una con­<lb></lb>tro l&#039;altra a esquisitissimo contatto. </s>

<s>Così, alle tacche ordinarie si sostituivano <lb></lb>i passi di una vite, i quali, per essere così brevi, e perciò non bene discer­<lb></lb>nibili alla vista, abbarbagliata di più dai riflessi; si contano dagli scatti della <lb></lb>punta di un ago o del taglio di un coltello strisciativi sopra. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Strumento gentilissimo in vero, e a quel che intendo di <lb></lb>uso assai più universale di quello, che a prima vista non sembrerebbe. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Serve infatti a ritrovare le gravità in specie di qualun­<lb></lb>que corpo con tal precisione, che il nostro Accademico ebbe a notare essere <lb></lb>gli sperimentatori, avanti a lui, proceduti, intorno a ciò troppo in di grosso, <lb></lb>benchè possa anch&#039;egli aver talvolta fallato, specialmente rispetto a certi me­<lb></lb>talli, per non esserglisi sempre offerti purissimi, com&#039;avrebbe voluto. </s>

<s>La pron­<lb></lb>tezza poi e la facilità dell&#039;operazione è manifesta, dietro ciò che io vi ho <lb></lb>detto, e ritornando con l&#039;occhio sopra questo foglio, disegnatovi dianzi, per <lb></lb>darvi a intendere la costruzione e il modo della Bilancia. </s>

<s>Imperocchè, se la <lb></lb>mole C è oro, che in aria stia col contrappeso in H, distante dal perpendi­<lb></lb>colo E, quant&#039;è la linea EH, e poi in acqua voglia essere ritirato in G; <lb></lb>dalla proporzione delle due linee EH, GH, che è quella de&#039;numeri degli scatti <lb></lb>ascoltati, nel fare strisciare, ora sopra l&#039;una lunghezza ora sopra l&#039;altra, <lb></lb>l&#039;aguto; s&#039;averà la proporzione della gravità in specie dell&#039;oro, alla gra­<lb></lb>vità di una egual mole di acqua, o di altro liquore. </s>

<s>E con questo è venuto <lb></lb>il proposito di dirvi in che modo si certificasse il nostro Accademico che, <pb xlink:href="020/01/3155.jpg" pagenum="116"></pb>in mezzo alla sostanza dell&#039;oro e dell&#039;argento, per non dire di altri metalli <lb></lb>meno densi, siano disseminati pori, benchè tanto piccoli, da sfuggire alla <lb></lb>vista più acuta. </s>

<s>” </s></p><p type="main">

<s>“ Sia novamente C o palla o cubo di oro, che pesato, come si è detto, <lb></lb>prima in aria e poi in acqua, abbia data la differenza GH. </s>

<s>Prendeva poi <lb></lb>l&#039;Amico nostro quel medesimo cubo, e, posatolo sopra un&#039;incudine, gli fa­<lb></lb>ceva dare gagliardissimi colpi con un martello di acciaio. </s>

<s>Tornando poi a <lb></lb>sospendere alla bilancia l&#039;oro così ammaccato, e tuffandolo in acqua, trovava <lb></lb>che il contrappeso voleva essere ritirato alquanto più distante dal perpendi­<lb></lb>colo, che non era il punto G; segno evidentissimo che nell&#039;ammaccatura la <lb></lb>mole era diminuita, e ciò non per altro, che per essere entrata la materia <lb></lb>a occupare gli spazi prima rimasti vacui. </s>

<s>Il rientramento poi e il ritiramento <lb></lb>della mole in sè stessa fu a proporzione anche maggiore nell&#039;argento, in si­<lb></lb>mile modo ammaccato. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Bellissima e delicata esperienza, da cui si conferma che <lb></lb>non dovevano essere i due metalli confusi nella corona di Jerone, ma sem­<lb></lb>plicemente congiunti. </s>

<s>Da tutto quel che avete detto però, signor Salviati, <lb></lb>non vedo come ne resultino le proporzioni dell&#039;oro all&#039;argento, di rassegnar <lb></lb>le quali era il fine principalissimo di questa invenzione. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Archimede ci andò per via di calcolo, tutta la precision <lb></lb>del quale dipendendo dalle sperimentate gravità in specie, ci aveva il Nostro <lb></lb>opportunamente provveduto, valendosi di quel suo perfettissimo strumento. </s>

<s><lb></lb>Da principio si contentò di questa semplice promozione, lasciando anch&#039;egli <lb></lb>alle ragioni numeriche concludere il rimanente. </s>

<s>E perchè queste ragioni non <lb></lb>si sa come propriamente Archimede le istituisse, e i commentatori di lui si <lb></lb>erano messi per vie tanto intralciate, da non si parer confacevoli col genio <lb></lb>nobilissimo del Matematico antico; il comune Amico nostro ridusse tutto alla <lb></lb>semplicità di quella regola, per la quale, dati essendo tre termini in pro­<lb></lb>porzione, è possibile a ritrovar sempre il quarto termine ignoto. </s>

<s>Il primo <lb></lb>dunque di quei termini è l&#039;eccesso della gravità in specie dell&#039;oro, sopra la <lb></lb>gravità in specie, dell&#039;argento, diviso per la gravità in specie dell&#039;argento: <lb></lb>il secondo è l&#039;eccesso della gravità in specie dell&#039;oro, sopra la gravità in <lb></lb>specie del composto, diviso per la gravità in specie del composto: il terzo è <lb></lb>la gravità in aria di esso composto, che per supposizione è la medesima che <lb></lb>la gravità delle parti separate, e che può aversi dalla Bilancia ordinaria, <lb></lb>come pure dalla Bilancia, per trovare i pesi nell&#039;acqua, s&#039;avranno gli altri <lb></lb>due detti termini. </s>

<s>Ond&#039;ei potranno tutti e tre sapersi, e sapersi con essi in­<lb></lb>sieme anche il quarto, che è il peso dell&#039;argento. </s>

<s>Il peso dell&#039;oro ne verrà <lb></lb>in conseguenza, perchè, se il composto è v. </s>

<s>g. </s>

<s>sessanta libbre, e che l&#039;ar­<lb></lb>gento si sia trovato venti; è manifesto che l&#039;oro sarà quaranta. </s>

<s>Ma poi pensò <lb></lb>che queste stesse proporzioni si potevano direttamente conoscere, mediante <lb></lb>lo strumento, senza far altro che contarne i segni, sopra la lunghezza del­<lb></lb>l&#039;ago compresi fra le varie distanze dai punti, dove, per ottener l&#039;equilibrio, <lb></lb>s&#039;erano fatti rimanere i contrappesi. </s>

<s>” </s></p><pb xlink:href="020/01/3156.jpg" pagenum="117"></pb><p type="main">

<s>“ SIMPLICIO. — Questo mi piace, ed essendo così, l&#039;invenzione mi rie­<lb></lb>sce bellissima, e praticabile a tutti, che come me non sanno, o non vogliono <lb></lb>tornare a stillarsi il cervello sopra il quinto libro di Euclide. </s>

<s>Ditemi dun­<lb></lb>que, signor Salviati, in che modo io potessi ritrovare, in un oggetto compo­<lb></lb>sto di oro e di argento, la proporzione dei due metalli, senz&#039;avere a far al­<lb></lb>tro, che pesare alla stadera, con l&#039;arte semplicissima di chi vende sopra le <lb></lb>piazze o nelle botteghe. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Nella figura (61) che io, per vostra maggiore intelligenza, <lb></lb>vo&#039;disegnarvi su questo foglio, immaginate che in E stia il perpendicolo della <lb></lb><figure id="id.020.01.3156.1.jpg" xlink:href="020/01/3156/1.jpg"></figure></s></p><p type="caption">

<s>Figura 61.<lb></lb>stadera, e che il vostro og­<lb></lb>getto, rappresentato con A, <lb></lb>e pendente in F da uno <lb></lb>estremo, sia dall&#039;altro C <lb></lb>esattamente contrappesato <lb></lb>in aria dal grave B, il quale <lb></lb>suppongo che faccia da con­<lb></lb>trappeso a due separate <lb></lb>quantità di oro e di argento, che, remosso A, si facessero una per volta pen­<lb></lb>dere dal punto F. </s>

<s>Sia dunque, prima, A oro puro, che tuffato in acqua faccia <lb></lb>ritirare il grave B da C in D, e si noti diligentemente questo punto. </s>

<s>Si levi <lb></lb>poi l&#039;oro, e si metta in suo logo l&#039;argento, che, dall&#039;aria passando in acqua, <lb></lb>voglia il ritiramento nel punto G, il quale similmente si noti con diligenza. </s>

<s><lb></lb>Tornando all&#039;ultimo a sospendere l&#039;oggetto A, che si faccia anch&#039;egli scen­<lb></lb>dere sotto l&#039;acqua, si può con assai facilità prevedere come, essendo più lieve <lb></lb>che se fosse oro pretto, e più grave, che se fosse pretto argento; farà tal­<lb></lb>mente ritirare il contrappeso, che tra D e G consista in qualche punto di <lb></lb>mezzo, quale, venendo al fatto, si trovi essere H. </s>

<s>Contate ora i passi, che fa <lb></lb>il filo di acciaio tra G e H, e poi tra H e D; e quant&#039;è il numero di quelli, <lb></lb>rispetto al numero di questi, altrettante direte, signor Simplicio, essere le parti <lb></lb>dell&#039;oro, rispetto a quelle dell&#039;argento. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — La conclusione è semplicissima in vero, e deve il nostro <lb></lb>Accademico esservi giunto per via di qualche ragionamento geometrico, che, <lb></lb>se non supera la mia capacità, vi prego a riferirmelo secondo il suo proprio <lb></lb>processo. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Il ragionamento anzi è facilissimo, nè richiede altra pre­<lb></lb>cognizione, che de&#039;primi principii della Scienza meccanica, da cui si con­<lb></lb>duce in poche parole. </s>

<s>Rimangano infatti le medesime supposizioni, ma in A <lb></lb>siano distintamente contrassegnate due parti: una I dell&#039;oro, contrappesata <lb></lb>in aria dalla porzione M, e l&#039;altra L dell&#039;argento, contrappesata dalla por­<lb></lb>zione N. </s>

<s>Fatto dal filo attaccato in F calare l&#039;oggetto A nell&#039;acqua, il riti­<lb></lb>ramento si trovò essere in H, da cui pendono dunque congiunti insieme M <lb></lb>ed N. </s>

<s>Stante ciò, immaginate che venga remossa da A la parte L: l&#039;altra <lb></lb>che rimane sarà contrappesata da M in D. </s>

<s>Rimovete invece la parte I, e ciò <lb></lb>che di A rimane sarà contrappesato da N in G. </s>

<s>Dunque il medesimo og-<pb xlink:href="020/01/3157.jpg" pagenum="118"></pb>getto A si trova sopra la libbra ugualmente bene in equilibrio, tanto a far <lb></lb>pendere collettivamente i due pesi M ed N da H, quanto a far distributiva­<lb></lb>mente pendere M da D, ed N da G. </s>

<s>Dunque è, per la Scienza meccanica, <lb></lb>H il centro dell&#039;equilibrio, dal qual punto debbono le distanze HG e DH <lb></lb>stare reciprocamente come il peso M, al peso N, ossia, come il peso dell&#039;oro <lb></lb>al peso dell&#039;argento, secondo che da me poco fa si diceva al signor Simpli­<lb></lb>cio, nel descrivergli la sola arte pratica dell&#039;operazione. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Quest&#039;arte ora, in grazia del vostro discorso dimostra­<lb></lb>tivo, mi è tornata chiarissima, e se io fossi quell&#039;Archimede, a cui fu pro­<lb></lb>posto di scoprire la ragione del furto famoso, sospenderei dalla bilancia in F, <lb></lb>prima la corona del re Jerone, poi un pezzo di oro, poi un pezzo di argento, <lb></lb>che tutti e tre in aria valessero il medesimo peso B. Poi, tuffando le tre moli <lb></lb>una per volta nell&#039;acqua, farei i ritiramenti in H, in D, e in G: e se, a <lb></lb>strisciare la punta dello stiletto da G fino in H, ne contassi 21 scatto, e da <lb></lb>H in D ne contassi 40; direi che la parte dell&#039;oro puro sta alla parte del­<lb></lb>l&#039;argento, furtivamente sostituito dall&#039;orafo, come 40 sta a 21. Che se, po­<lb></lb>niamo, tutto il peso della corona fosse stato 61 libbra, direi che certissima­<lb></lb>mente 40 libbre erano oro, e 21 argento. </s>

<s>Ma in qualunque numero fosse <lb></lb>dato quel peso, lo partirei per 61, e l&#039;avvenimento in once, e in divisioni <lb></lb>di oncia, moltiplicato per 40, e poi per 21, mi scoprirebbe il peso dell&#039;oro <lb></lb>e dell&#039;argento in once, o in altre più minute divisioni di oncia, e mi ren­<lb></lb>derebbe la ragione esattamente matematica del furto. </s>

<s>” </s></p><p type="main">

<s>“ SIMPLICIO. — Dunque non si può, nemmeno operando con lo stru­<lb></lb>mento, evitare il calcolo, come il signor Salviati ci aveva promesso. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Ma è un calcolo, da non superare l&#039;abilità di un fan­<lb></lb>ciullo, che abbia rivedute appena le prime pagine dell&#039;abbaco: nè molto più <lb></lb>difficile, a dire il vero, mi parve quell&#039;altro, che voi diceste, signor Salviati, <lb></lb>essere stato ridotto dal nostro Accademico alla semplicità della regola aurea. </s>

<s><lb></lb>Vorrei però sapere da voi se si può essere certi, che la regola dell&#039;arimme­<lb></lb>tica, e la pratica operazione con lo strumento, conducono infallibilmente a <lb></lb>concludere il medesimo. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Il riscontro che voi, signor Sagredo, desiderate, si riduce <lb></lb>insomma a dimostrare che la proporzione tra i pesi e le distanze, segnate <lb></lb>sopra la lunghezza della libbra, è la stessa che tra i pesi, e quegli eccessi <lb></lb>di gravità in specie, e loro quoti, a quel modo che vi pronunziai. </s>

<s>Fu con­<lb></lb>cluso per la Scienza meccanica che GH sta a DH, come il peso dell&#039;oro al <lb></lb>peso dell&#039;argento. </s>

<s>Componendo, averemo GH con DH, ossia DG, a DH, come <lb></lb>il peso dell&#039;oro, insieme col peso dell&#039;argento, ossia, come tutto il peso della <lb></lb>corona, al peso dell&#039;argento solo. </s>

<s>Per la concordanza dunque delle due re­<lb></lb>gole si deve dimostrare che GD, verso DH, ha la medesima proporzione, che <lb></lb>l&#039;eccesso della gravità in specie dell&#039;oro, sopra la gravità in specie dell&#039;ar­<lb></lb>gento, diviso per la gravità in specie dell&#039;argento; ha verso l&#039;eccesso della <lb></lb>gravità in specie dell&#039;oro, sopra la gravità in specie della corona, diviso per <lb></lb>la gravità in specie della corona. </s>

<s>Alla dimostrazione di che ci condurrà fa-<pb xlink:href="020/01/3158.jpg" pagenum="119"></pb>cilmente un principio, quale io vi propongo così in forma di lemma: Se la <lb></lb>mole A, sospesa in F dalla bilancia, ora sia oro, ora sia argento del mede­<lb></lb>simo peso B in aria, e che, successivamente tuffate le due moli in acqua, <lb></lb>quella faccia ritirare da C in D, e questa da C in G; dico che la gravità in <lb></lb>specie dell&#039;oro, alla gravità in specie dell&#039;argento, averà tal proporzione, <lb></lb>quale ha GC alla CD. </s>

<s>La proposta verità si conclude immediata da ciò, che <lb></lb>su tal proposito in precedenza fu detto, che cioè la gravità in specie dell&#039;oro, <lb></lb>alla gravità in specie dell&#039;acqua, è come la EC alla CD. </s>

<s>E similmente, la <lb></lb>gravità in specie dell&#039;acqua, alla gravità in spece dell&#039;argento, come la CG <lb></lb>alla EC: onde ex aequali, per la perturbata, la gravità in specie dell&#039;oro averà, <lb></lb>alla gravità in specie dell&#039;argento, la medesima proporzione, che la CG <lb></lb>alla CD. E, supponendo che le moli considerate siano ugualmente gravi alla <lb></lb>corona di Jerone, il ritiramento della quale in acqua sia da C in D; si pro­<lb></lb>durrà similmente che la gravità in specie dell&#039;oro, alla gravità in specie della <lb></lb>corona, sta come la CH alla CD. Ora, dividendo queste due proporzioni, tro­<lb></lb>verete che, come l&#039;eccesso della gravità in specie dell&#039;oro, sopra la gravità <lb></lb>in specie dell&#039;argento, alla gravità in specie dell&#039;argento; così è l&#039;eccesso <lb></lb>della GC sopra la CD, ossia la DG alla CD. </s>

<s>In pari modo l&#039;eccesso della <lb></lb>gravità in specie dell&#039;oro, sopra la gravità in specie della corona, è, alla gra­<lb></lb>vità in specie della corona, come l&#039;eccesso della CH sopra la CD, ossia la <lb></lb>DH, sopra la DC. </s>

<s>Dunque ex aequali, per la perturbata, l&#039;eccesso della gra­<lb></lb>vità in specie dell&#039;oro, sopra la gravità in specie dell&#039;argento, diviso per la <lb></lb>gravità in specie dell&#039;argento, sta all&#039;eccesso della gravità in specie dell&#039;oro, <lb></lb>sopra la gravità in specie della corona, diviso per la gravità in specie della <lb></lb>corona, come la GD, divisa per la CD, sta alla DH, divisa per la medesima <lb></lb>CD: ossia, come la GD sola sta alla DH sola, secondo che, per sodisfare <lb></lb>alla curiosità filosofica del nostro signor Sagredo, si voleva che io dimo­<lb></lb>strassi. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Son gratissimo alla vostra cortesia. </s>

<s>Io ho tenuto così <lb></lb>dietro a tutto il vostro discorso, da cui siamo stati condotti a conclusioni tanto <lb></lb>belle nella Scienza, e ad applicazioni così curiose nella pratica; che, per non <lb></lb>interromperlo, mi sono tante volte astenuto di manifestarvi un mio pensiero, <lb></lb>sovvenutomi improvvisamente, in mezzo a quel descriver che ci faceste le <lb></lb>esperienze di Archimede, per ritrovar le moli dell&#039;acqua, esattamente uguali <lb></lb>a quelle dei due metalli e della corona. </s>

<s>Ora quel pensiero, quell&#039;idea lusin­<lb></lb>gatrice, era questa: che, se il vaso fosse stato perfettamente prismatico, un <lb></lb>corpo, per quanto si voglia irregolare, o formato con tutt&#039;altra regola, da <lb></lb>quella così semplice, che prescrive ne&#039;suoi solidi la Geometria, quale sarebbe <lb></lb>stata giusto quella corona; averebbe trovato nello scemo dell&#039;acqua dentro <lb></lb>il vaso la sua quadratura prontissima e perfetta. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Il medesimo sovvenne a me, nè saprei ben definire se, <lb></lb>dell&#039;esserci così incontrati insieme in questa speculazione, io senta maggiore <lb></lb>in me o la compiacenza o la maraviglia. </s>

<s>Procurai di avere un vaso, tirato <lb></lb>più esattamente che fosse possibile in forma di cubo, e, in mezzo al vano di <pb xlink:href="020/01/3159.jpg" pagenum="120"></pb>lui fatto sospendere un esattissimo cilindro, colmai il detto vaso di acqua, e <lb></lb>poi ne estrassi il solido, che, per essere stato scelto da me di materia più <lb></lb>grave in specie, era tutto rimasto sommerso. </s>

<s>Il vuoto, da lui lasciato in figura <lb></lb>di un prisma, corrispondeva dunque esattamente alla mole cilindrica, la cir­<lb></lb>colar base della quale mi si veniva perciò a trasformare in base quadrata. </s>

<s><lb></lb>Entrato in questa curiosità, passai anche più oltre. </s>

<s>Feci il vaso, da ricevere <lb></lb>l&#039;acqua, cilindrico, è con esso un cono e una sfera, di tali diametri il cir­<lb></lb>colo grande di questa, e la base di quello, che entrassero esattamente a riem­<lb></lb>pire la cavità del cilindro, sol lasciandovi intorno quant&#039;è grosso un capello, <lb></lb>per la penetrazione del sottilissimo liquido, e per la libertà del suo passarvi <lb></lb>attraverso. </s>

<s>Estratte le due moli, mi si venivano a trasformare in due cilin­<lb></lb>dri vacui, i quali, potendosi comodamente da me misurare, mi fecero cu­<lb></lb>rioso di veder come si corrispondessero questi modi meccanici con i teoremi <lb></lb>dimostrati dalla Geometria. </s>

<s>Sapete bene da Euclide che il cono uguaglia un <lb></lb>cilindro di pari base, ma con la sola terza parte dell&#039;altezza. </s>

<s>Quanto alla <lb></lb>sfera poi, si ricava per corollario dalla XXXI proposizione del libro, in cui <lb></lb>Archimede trattò di queste cose, essere ella uguale a un cilindro, che avesse <lb></lb>per base un circolo grande, e per altezza quattro terzi del semidiametro di <lb></lb>esso circolo grande, ossia due terzi del diametro intero. </s>

<s>Ora, venuto al mi­<lb></lb>surare, con quella maggiore diligenza che mi fu possibile, i vacui cilindrici <lb></lb>lasciati, per avere estratte dall&#039;acqua le due dette moli; trovai tale corrispon­<lb></lb>denza con le conclusioni dei Matematici, da superare ogni mia aspettazione, <lb></lb>ripensando a quante fallacie potevano essere andate soggette le mie proprie <lb></lb>esperienze. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Son senza dubbio così fatti esercizi manuali soggetti a <lb></lb>fallacie, ma chi sa che non potessero tornare di qualche utilità ai Geome­<lb></lb>tri, benchè pur troppo sia vero che le imperfezioni della materia son po­<lb></lb>tenti a contaminare le purissime dimostrazioni della Matematica? </s>

<s>Ripensando <lb></lb>come tante invenzioni di Archimede son così pellegrine da ciò, che l&#039;inge­<lb></lb>gno di un uomo avrebbe senza altri indizi potuto per sè solo prevedere, du­<lb></lb>bitai che, siccome giova allo statuario, per rifinire l&#039;opera nel marmo, l&#039;es­<lb></lb>sersene messo innanzi nella rozza creta l&#039;esempio:.... ” </s></p><p type="main">

<s>Qui termina lo scritto a tergo nel foglio, a cui manca il seguente, e <lb></lb>perciò rimane interrotto il costrutto, non però così, che non si possa facil­<lb></lb>mente supplire, intendendo che Archimede, per l&#039;investigazione di così astruse <lb></lb>verità geometriche, si potesse essere in parte aiutato con l&#039;esperienze. </s>

<s>Tale si <lb></lb>fu pure l&#039;opinione del Nardi, nè è necessario ripetere le ragioni, per cui si <lb></lb>giudicò da noi poco probabile: ma l&#039;invenzione di trasformare i solidi, e di <lb></lb>quadrarne i volumi e le superficie per via dell&#039;acqua, è notabile, e vedremo <lb></lb>qual partito per sè ne sapesse trarre il Viviani. </s></p><p type="main">

<s>Altre cose, di non minore curiosità e importanza, ricorrono in questo <lb></lb>Dialogo, che non si vuol lasciare senza pure notarle, e sia prima fra tutte <lb></lb>la negazione espressa di un supposto, che alcuni dissero implicito ne&#039;discorsi <lb></lb>di Archimede e di Galileo. </s>

<s>Il Nardi, troppo inconsideratamente fuor del suo <pb xlink:href="020/01/3160.jpg" pagenum="121"></pb>solito, scriveva anche questa fra le altre libere censure al grande Siracu­<lb></lb>sano: “ Anco Archimede, nell&#039;investigare il furto della corona, non consi­<lb></lb>derò, per quanto sappiamo, che due insieme fusi metalli occupino minor mole <lb></lb>che separati, poichè dal più rado di essi imbevesi il più denso, come l&#039;espe­<lb></lb>rienza insegna. </s>

<s>E veramente non devesi dal natural Filosofo trascurare tal <lb></lb>punto, e non dovevasi da Archimede ” (MSS. Gal., T. XX, pag. </s>

<s>879, 80). <lb></lb>Ma ben assai più inconsiderato ne par quel Domenico Mantovani, il quale, <lb></lb>in alcune sue annotazioni sopra la scrittura autografa di Galileo, descrittiva <lb></lb>della Bilancetta, diceva supporsi ivi dall&#039;Autore, nel risolvere il problema, <lb></lb>“ che il composto di due metalli conservi l&#039;istessa proporzione in grandezza <lb></lb>nel composto, che prima avevano li due metalli semplici che lo compon­<lb></lb>gono ” (Alb. </s>

<s>XIV, 206). </s></p><p type="main">

<s>La storia, che da Lucio Pollione raccolse il Fazello, basta a confermare <lb></lb>l&#039;inconsideratezza del Nardi. </s>

<s>Quanto poi al Mantovani si può dire essere stato <lb></lb>egli il primo, e non Galileo, a supporre che i due metalli nella loro fusione <lb></lb>mantengono la medesima mole che separati; giacchè esso Galileo chiama <lb></lb><emph type="italics"></emph>misto<emph.end type="italics"></emph.end> la composizione dell&#039;oro e dell&#039;argento nella corona del re Gerone, e <lb></lb>come si debba per questo misto intendere la semplice soprapposizion delle <lb></lb>parti dal trascritto Dialogo è manifesto. </s>

<s>Giova anzi avvertire in tal proposito <lb></lb>che il Viviani, a quelle parole inserite nelle sue <emph type="italics"></emph>Osservazioni<emph.end type="italics"></emph.end> dall&#039;editore <lb></lb>Albèri, e che dicono: “ tanto si è che il peso sia composto dell&#039;oro e del­<lb></lb>l&#039;argento separatamente, quanto che sia l&#039;oro mescolato per infusione, poichè <lb></lb>non si altera nè il peso assoluto nè la mole, e per conseguenza nemmen <lb></lb>la gravità in specie ” (ivi, pag. </s>

<s>214), scrisse in margine <emph type="italics"></emph>fanne esperienza<emph.end type="italics"></emph.end><lb></lb>(MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>65). Era poi in grado di apprezzar l&#039;impor­<lb></lb>tanza di questa postilla quel Viviani, che aveva trascritto il Dialogo di Ga­<lb></lb>lileo, e che, pur essendo persuaso non andar nemmeno i metalli esenti dai <lb></lb>pori, poteva dubitare se questi si riempissero sempre nella fusione, cosicchè <lb></lb>talvolta la lega serbasse inalterato il volume dei metalli componenti. </s></p><p type="main">

<s>In ogni modo, fra le cose notabili in questo Dialogo, sembra a noi prin­<lb></lb>cipalissima la dimostrazione sperimentale dei così detti <emph type="italics"></emph>pori fisici<emph.end type="italics"></emph.end> dei corpi, <lb></lb>alla quale dette forse occasione una lettera, che il 14 Maggio 1611 scriveva <lb></lb>in questa sentenza allo stesso Galileo, da Bruxelles, Daniele Antonini: “ Sono <lb></lb>stato questi giorni in Anversa, dove ho veduto una cosa degna di scrivere <lb></lb>a V. S. </s>

<s>Un certo, il quale è sopra la zecca di questo serenissimo Signore, <lb></lb>fa a chi vuol vederla questa prova. </s>

<s>Lui piglia una pallina di oro, e la fa <lb></lb>pesare a chi vuole sopra una bilancia giustissima ed esatta. </s>

<s>Poi batte detta <lb></lb>pallina, e ne fa una focaccetta. </s>

<s>Si ritorna a pesare, e pesa sempre tre, e <lb></lb>anche quattro grani più che prima. </s>

<s>La comune opinione di costoro è che la <lb></lb>forma pesi. </s>

<s>Non mancano di quelli, che dicono che vi resta del ferro del <lb></lb>martello nell&#039;oro, ma sono opinioni ridicolose, pare a me. </s>

<s>Questa cosa mi <lb></lb>conferma l&#039;opinione di V. S. che ci siano de&#039;vacuetti ne&#039;corpi, li quali, per <lb></lb>il battere del martello, si riempino, onde il corpo non occupi poi tanto loco <lb></lb>nell&#039;aria, e per conseguenza non sia tanto sostenuto dal medio e pesi più. <pb xlink:href="020/01/3161.jpg" pagenum="122"></pb>Non so quello che circa questo giudicaria V. S., nè ho altro di nuovo ” <lb></lb>(MSS. Gal., P. VI, T. VIII, fol. </s>

<s>14). </s></p><p type="main">

<s>Alcuni, tra le prime prove sperimentali dell&#039;esistenza de&#039;pori fisici nei <lb></lb>corpi, citano il terzo degli sperimenti descritti nel libro de&#039;<emph type="italics"></emph>Saggi di natu­<lb></lb>rali esperienze<emph.end type="italics"></emph.end> intorno alla compressione dell&#039;acqua. </s>

<s>E veramente non è que­<lb></lb>sto altro che un saggio, sopra il solo argento, di parecchie esperienze fatte <lb></lb>sopra varie specie di metalli, le quali, essendo attribuite al granduca Ferdi­<lb></lb>nando, si può credere che appartenessero a quel primo periodo dell&#039;Acca­<lb></lb>demia medicea, che pigliava essere e forma dal Torricelli. </s>

<s>“ Che l&#039;acqua, <lb></lb>come acqua, scriveva il Viviani, non si possa, nemmeno con qualsivoglia <lb></lb>violenza, condensare per minima parte; l&#039;ha sperimentato il Serenissimo <lb></lb>Granduca. </s>

<s>Ha fatto gettare d&#039;ogni metallo, come argento, rame, ottone ecc. </s>

<s><lb></lb>più palle vote per di dentro, e di grossezza di orbe intorno a quella di una <lb></lb>piastra d&#039;argento, quali poi, per un foro fattovi a vite, ha fatte empir d&#039;acqua, <lb></lb>e, serrato con vite di simili metalli strettissimamente il foro di dette palle, <lb></lb>le ha poi fatte posare sopra un&#039;incudine, e fattogli dare colpi gagliardi con <lb></lb>un martello di acciaio, e ha osservato S. A. che l&#039;acqua inclusa, per non <lb></lb>poter patire condensazione alla violenza de&#039;colpi, trasudava fuori delle palle <lb></lb>per i pori del metallo ” (MSS. Gal. </s>

<s>Disc., T. 134, fol. </s>

<s>5 a t.). Il Borelli, par­<lb></lb>lando con più proprietà, non disse che il Granduca fece l&#039;esperienza, ma <lb></lb><emph type="italics"></emph>iussit<emph.end type="italics"></emph.end> che fosse fatta (<emph type="italics"></emph>De motion, natur.,<emph.end type="italics"></emph.end> Regio Julio 1670, pag. </s>

<s>333) e il <lb></lb>comandamento non poteva averlo ricevuto che il Torricelli. </s></p><p type="main">

<s>In ogni modo però, non essendo queste che dimostrazioni indirette, la <lb></lb>esperienza direttamente dimostrativa dell&#039;esistenza dei pori fisici si può dire <lb></lb>che fosse primo a farla Galileo, come s&#039;argomenta dalla lettera a lui dell&#039;An­<lb></lb>tonini, e con certezza si conferma dal Dialogo trascritto, sopra cui riman­<lb></lb>gono solamente a fare alcune osservazioni circa alla disposizione microme­<lb></lb>trica dei fili spirali. </s>

<s>Il Mantovani, dietro alcuni trascorsi, ch&#039;egli attribuisce <lb></lb>ai copiatori dell&#039;originale galileiano; immaginò un sistema di comporre, e <lb></lb>di numerare essi fili arbitrario, e tutt&#039;affatto fuor del proposito. </s>

<s>Ma nemmeno <lb></lb>dalla lezione emendata, come ce la dette l&#039;Albèri, si vengono a togliere i <lb></lb>dubbi, perch&#039;essendo parata la Bilancia per determinati pesi di oro e di ar­<lb></lb>gento, i punti D e G, nella figura 61, sono prestabiliti, e non occorrendo, <lb></lb>per aver la proporzione del misto, che di misurare il loro intervallo, basta <lb></lb>che questo solo sia ricoperto dal filo, e perciò tanto fa ch&#039;egli sia o di ot­<lb></lb>tone o di acciaio. </s>

<s>Che se si volesse parar la Bilancia, per pesi differenti da <lb></lb>A, i punti D e G torneranno sull&#039;ago di lei o più innanzi o più indietro, <lb></lb>cosicchè si dovrebbe riempir del filo uno spazio diverso da DG. Onde, a evi­<lb></lb>tar l&#039;incomodo, tornava meglio avvolgere un filo solo andante sopra tutta la <lb></lb>lunghezza della libbra, ciò che si suppone esser fatto nello strumento pro­<lb></lb>posto dal Salviati, il dialogo del quale soccorre dunque opportuno a illustrare <lb></lb>e a correggere la stessa frettolosa scrittura autografa di Galileo, tutto allora <lb></lb>in distenderla studioso, come udimmo, di produrre dimostrazioni de&#039;teoremi <lb></lb>idrostatici, più fisiche e meno matematiche di quelle di Archimede. </s></p><pb xlink:href="020/01/3162.jpg" pagenum="123"></pb><p type="main">

<s>“ Dico primum solidas magnitudines, aeque graves ac aqua, in aquam <lb></lb>demissas, totas demergi, non autem adhuc deorsum ferri magis quam sur­<lb></lb>sum ” (Alb. </s>

<s>XI, 22). Il ragionamento di Galileo per la dimostrazione si ri­<lb></lb>duce al seguente: Sia il primo stato dell&#039;acqua CD (figura 62), e infusa nel <lb></lb>vaso la mole B non si sommerga, se è possibile, tutta, <lb></lb><figure id="id.020.01.3162.1.jpg" xlink:href="020/01/3162/1.jpg"></figure></s></p><p type="caption">

<s>Figura 62.<lb></lb>ma ne resti la parte A sollevata, ascendendo per l&#039;im­<lb></lb>mersione la superficie del liquido da CD in FG. </s>

<s>Allora <lb></lb>avremo che il peso di FD fa nella bilancia equilibrio al <lb></lb>peso AB, ma quello è minore di questo, perchè ugua­<lb></lb>glia una sola parte di lui qual&#039;è B; dunque ecc. </s></p><p type="main">

<s>“ Hoc itaque demonstrato, sequitur ut ostendamus <lb></lb>solidas magnitudines aqua leviores, in aquam demissas, <lb></lb>non demergi totas, sed earum aliquam partem extare ex aqua ” (ibid., pag. </s>

<s>23). <lb></lb>Perchè, se si demergesse tutta, avremmo, dice Galileo, nella bilancia, equili­<lb></lb>brio fra un peso più grave, qual&#039;è l&#039;acqua, e un più leggero, qual&#039;è la gran­<lb></lb>dezza demersa. </s></p><p type="main">

<s>“ Demonstrato igitur solidas magnitudines aqua leviores non demergi <lb></lb>totas, expedit nunc ostendere quaenam illarum partes demergantur. </s>

<s>Dico igi­<lb></lb>tur quod solidae magnitudines, aqua leviores, in aquam demissae, usque eo <lb></lb>demerguntur, ut tanta moles aquae, quanta est moles partis demersae ma­<lb></lb>gnitudinis, eamdem quam tota magnitudo habeat gravitatem ” (ibid., pag. </s>

<s>24). <lb></lb>Sia il primo stato della superficie CD, come nella passata figura, e della <lb></lb>grandeza s&#039;immerga la sola parte B, restandone l&#039;altra A fuori, cosicchè il <lb></lb>livello salga da CD in FG, e ivi giunto si faccia l&#039;equilibrio. </s>

<s>Dunque i pesi <lb></lb>di FD e di AB sono uguali, ma anche i volumi FD e di B sono uguali, <lb></lb>dunque ecc. </s></p><p type="main">

<s>“ Nunc autem, prosegue Galileo, antequam ad demonstrationem solido­<lb></lb>rum aqua graviorum accedamus, demonstrandum est quanta vi solida ma­<lb></lb>gnitudo aqua levior sursum feratur, si tota vi sub aquam demergatur. </s>

<s>Dico <lb></lb>igitur solidas magnitudines aqua leviores, in aquam impulsas, ferri sursum <lb></lb>tanta vi, quanto aqua, cuius moles aequetur moli demersae magnitudinis, <lb></lb>ipsa magnitudine gravior erit ” (ibid., pag. </s>

<s>25). Se il solido, nella medesima <lb></lb>figura 62, faccia la prima superficie del liquido risalire per l&#039;immersione da <lb></lb>CD in FG, il qual livello egli affiori con la parte sua superiore GA, abbiamo <lb></lb>da una parte, nella bilancia, FD uguale in mole a B, ma, essendo maggiore <lb></lb>di peso per supposizione, farà perciò traboccare dalla sua parte essa bilan­<lb></lb>cia, con la forza della sua propria prevalenza, <emph type="italics"></emph>quod,<emph.end type="italics"></emph.end> dice Galileo, <emph type="italics"></emph>fuit de­<lb></lb>monstrandum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Ex his autem quae demonstrata sunt, poi soggiunge, satis perspicuum <lb></lb>est solidas magnitudines aqua graviores deorsum ferri, si in aqua demittan­<lb></lb>tur. </s>

<s>Nisi enim ferantur deorsum, aut earum aliqua pars extabit, aut sub <lb></lb>aqua manebunt, nec sursum aut deorsum ferentur. </s>

<s>At earum nulla pars <lb></lb>extabit, essent enim, ut demonstratum est, aqua leviores, nec in aqua ma­<lb></lb>nebunt, quia essent aeque graves ac aqua. </s>

<s>Restat ergo quod deorsum feran-<pb xlink:href="020/01/3163.jpg" pagenum="124"></pb>tur. </s>

<s>Nunc autem quanta vi deorsum ferantur ostendamus: dico igitur soli­<lb></lb>das magnitudines aqua graviores, in aquam demissas, ferri deorsum tanta <lb></lb>vi, quanto aqua, molem habens moli ipsius magnitudinis aequalem, levior <lb></lb>est ipsa magnitudine ” (ibid., pag. </s>

<s>26). Sia AE (fig. </s>

<s>63) uguale in mole alla <lb></lb>grendezza solida BL: e perchè il peso di quella si è supposto minore del <lb></lb><figure id="id.020.01.3163.1.jpg" xlink:href="020/01/3163/1.jpg"></figure></s></p><p type="caption">

<s>Figura 63.<lb></lb>peso di questa, sia AO la quantità del liquido, che ci bi­<lb></lb>sogna per l&#039;equilibrio. </s>

<s>Alla BL poi s&#039;immagini essere con­<lb></lb>giunta una grandezza LM, più leggera dell&#039;acqua, e la mole <lb></lb>della quale, uguagliandosi alla mole AO, pesi quanto la <lb></lb>parte AE. </s>

<s>Dunque AE con AO, e BL con LM, si faranno <lb></lb>sulla bilancia equilibrio, ciò che non potrebbe essere, se la <lb></lb>forza, con cui BL tende a scendere, non fosse pari a quella, <lb></lb>con cui LM tende a salire. </s>

<s>Ma, per la precedente, questa <lb></lb>forza è uguale all&#039;eccesso del peso dell&#039;acqua AO sopra il peso dell&#039;acqua DO, <lb></lb>ossia al peso dell&#039;acqua AE; dunque ecc. </s></p><p type="main">

<s>Tali sono quelle dimostrazioni fisiche, che Galileo si studiava di sosti­<lb></lb>tuire alle altre di Archimede, stimate da lui più matematiche, benchè pro­<lb></lb>priamente non sian tali che in apparenza, o nella forma, facilmeute riducibile <lb></lb>a quella data a loro dallo stesso Galileo, come si riferi da noi sui principii <lb></lb>del precedente capitolo. </s>

<s>Così fatte dimostrazioni nuove furon poi il frutto <lb></lb>degli studii giovanili, quando il novello professore di Pisa attendeva al a fab­<lb></lb>brica e all&#039;uso della sua Bilancetta. </s></p><p type="main">

<s>Ma in ogni modo l&#039;Idrostatica, con queste invenzioni, non veniva so­<lb></lb>stanzialmente promossa. </s>

<s>Dai teoremi idrostatici, benchè riformati, non si ve­<lb></lb>deva direttamente conseguir la ragione di quel paradosso, che il Benedetti, <lb></lb>piuttosto che spiegare, pareva voler proporre alla spiegazione de&#039;suoi succes­<lb></lb>sori. </s>

<s>Questa riforma infatti si riduceva a considerare il peso delle grandezze <lb></lb>da una parte, e il peso dell&#039;acqua da un&#039;altra, come posati sui bacini di <lb></lb>una bilancia di braccia uguali, ciò che, se poteva bastare a spiegar l&#039;equili­<lb></lb>brio ne&#039;due rami del sifone d&#039;ugual calibrio, faceva arretrar la ragione in­<lb></lb>nanzi al fatto della poca acqua nella gracile <expan abbr="cãnna">cannna</expan>, che pur vale a sostener <lb></lb>la grandissima nel mortaio. </s>

<s>Allora Galileo pensò a quel che similmente ac­<lb></lb>cade nella bilancia di braccia disuguali, ossia nel vette, in virtù di cui qua­<lb></lb>lunque piccolissimo peso può fare equilibrio a un grandissimo, purchè i loro <lb></lb>momenti siano uguali: ond&#039;ei non è maraviglia, disse fra sè, che la velo­<lb></lb>cissima salita della poca acqua resista alla tardissima scesa della molta. </s>

<s>“ Ac­<lb></lb>cade dunque in questa operazione, poi soggiungeva esplicandosi nella mente <lb></lb>quel primo concetto, lo stesso a capello che nella stadera, nella quale un peso <lb></lb>di due libbre ne contrappeserà un altro di 200, tuttavolta che, nel tempo <lb></lb>medesimo, quello si dovesse movere per ispazio cento volte maggiore che <lb></lb>questo, il che accade, quando l&#039;un braccio della libbra sia cento volte più <lb></lb>lungo dell&#039;altro ” (Alb. </s>

<s>XII, 26). </s></p><p type="main">

<s>Esultando Galileo d&#039;aver conclusa così la ragione del paradosso famoso, <lb></lb>dalla generalità dei principii meccanici da sè professati, pensò che, potendosi <pb xlink:href="020/01/3164.jpg" pagenum="125"></pb>questi anche applicare alla bilancia di braccia uguali; de&#039;comuni teoremi ar­<lb></lb>chimedei si potevano dare altresi nuove dimostrazioni. </s>

<s>Perchè infatti, immer­<lb></lb>gendosi più e più il solido, via via gli si solleva maggiore quantità d&#039;acqua <lb></lb>all&#039;intorno, basta conferire i momenti della resistenza del liquido all&#039;essere <lb></lb>alzato, co&#039;momenti della grandezza che lo preme, “ e se i momenti della <lb></lb>resistenza dell&#039;acqua, soggiunge Galileo stesso, pareggiano i momenti del <lb></lb>solido, avanti la sua totale immersione; allora senza dubbio si farà l&#039;equi­<lb></lb>librio, nè più oltre si tufferà il solido. </s>

<s>Ma se il momento del solido supe­<lb></lb>rerà sempre i momenti, co&#039;quali l&#039;acqua scacciata va successivamente fa­<lb></lb>cendo resistenza; quello, non solamente si sommergerà tutto sott&#039;acqua, ma <lb></lb>discenderà sino al fondo. </s>

<s>Ma se finalmente, nel punto della total sommer­<lb></lb>sione, si farà l&#039;aggiustamento tra i momenti del solido premente e dell&#039;acqua <lb></lb>resistente, allora si farà la quiete, e esso solido, in qualunque luogo del­<lb></lb>l&#039;acqua, potrà indifferentemente fermarsi ” (ivi, pag. </s>

<s>17). </s></p><p type="main">

<s>Per conferire i detti momenti invoca Galileo dalla Statica due principii, <lb></lb>i quali però dipendono da uno solo più universale, conosciuto e praticato <lb></lb>dai precedenti Autori, ma che esso Galileo non seppe ridurre alla sua pro­<lb></lb>pria forma, nè perciò valersi di lui a dare quella efficace brevità, che manca <lb></lb>a tante sue conclusioni. </s>

<s>Agli esempi, che ricorrono di ciò nelle Storie pas­<lb></lb>sate, s&#039;aggiunge ora questo de&#039;principii fondamentali, posti dall&#039;Autore al <lb></lb>suo trattato Delle galleggianti, i quali principii, benchè si distinguano in due, <lb></lb>sono inclusi nulladimeno, come si diceva, in un altro più generale, e secondo <lb></lb>cui i momenti, o quelle che poi si chiameranno forze morte, si misurano dal <lb></lb>prodotto delle velocità e de&#039;pesi assoluti. </s>

<s>È facile infatti veder che di qui si <lb></lb>ha, per conclusione immediata, come, essendo i pesi e le velocità uguali, <lb></lb>anche i momenti sono uguali; e dall&#039;altra parte, essendo i momenti uguali, <lb></lb>le velocità rispondono contrariamente ai pesi, che sono i due principii, di­<lb></lb>stintamente assunti da Galileo per fondamento alle sue idrostatiche dimo­<lb></lb>strazioni, in servigio delle quali si premette pure il seguente lemma: “ I pesi <lb></lb>assoluti de&#039;solidi hanno la proporzione composta delle proporzioni delle lor <lb></lb>gravità in specie, e delle lor moli ” (ivi, pag. </s>

<s>21). </s></p><p type="main">

<s>La verità della proposta, più brevemente che nel discorso di Galileo, si <lb></lb>conclude dalla definizione stessa delle gravità specifiche, le quali si dicono <lb></lb>tanto essere maggiori le une delle altre, quanto più gran peso è raccolto <lb></lb>sotto minor volume, cosicchè, intendendosi per G, P, M, e per G′, P′, M′, le <lb></lb>dette gravità, i pesi e le moli, o i volumi di due corpi diversi; dalle equa­<lb></lb>zioni G=P:M, G′=P′:M′, ossia, dalle altre P=M.G, P′=M′.G′, <lb></lb>se ne conclude il proposito immediatamente. </s>

<s>Che se G&gt;G′, e allora sarà <lb></lb>P:M&gt;P′:M′, ossia P:P′&gt;M:M′, ciò che vuol dire aver maggiore pro­<lb></lb>porzione il peso assoluto al peso assoluto, che no il volume al volume: co­<lb></lb>rollario pure invocato a varie occasioni da Galileo, come vedremo. </s></p><p type="main">

<s>Ciò premesso, s&#039;immagini di avere un vaso prismatico, dentro l&#039;acqua <lb></lb>del quale sia immerso un solido, pure prismatico: nella disposizione, che ha <lb></lb>quello di scendere, e questo di salire, riconosce Galileo una specie di libra-<pb xlink:href="020/01/3165.jpg" pagenum="126"></pb>mento, soggetto alle medesime leggi statiche de&#039;libramenti ordinari, e come <lb></lb>questi perciò dimostrabile col principio delle velocità virtuali. </s>

<s>Da un tal princi­<lb></lb>pio infatti è informato il <emph type="italics"></emph>Discorso intorno alle cose che stanno in sull&#039;acqua, <lb></lb>o che in quella si muovono,<emph.end type="italics"></emph.end> di cui tale è l&#039;ordine delle proposizioni: </s></p><p type="main">

<s>PROPOSIZIONE I. — <emph type="italics"></emph>“ La mole dell&#039;acqua, che si alza nell&#039;immergere <lb></lb>un prisma o cilindro solido, o che s&#039;abbassa nell&#039;estrarlo; è minore della <lb></lb>mole di esso solido demersa o estratta, e ad essa ha la medesima pro­<lb></lb>porzione, che la superficie dell&#039;acqua circonfusa al solido, alla medesima <lb></lb>superficie circonfusa, insieme con la base del solido ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>18). </s></p><p type="main">

<s>Sia EH (fig. </s>

<s>64) il primitivo naturale livello dell&#039;acqua, la quale siasi <lb></lb>sollevata in NM, mentre che il solido si è abbassato in IK. </s>

<s>Essendo LG, NG <lb></lb><figure id="id.020.01.3165.1.jpg" xlink:href="020/01/3165/1.jpg"></figure></s></p><p type="caption">

<s>Figura 64.<lb></lb>due parallelepipedi, con altezze uguali, sta­<lb></lb>ranno dunque come LM, NM, loro respettive <lb></lb>basi. </s>

<s>Considerando poi che NG, mole del­<lb></lb>l&#039;acqua sollevata, è uguale ad EK, parte del <lb></lb>solido sotto il primo livello sommersa, per <lb></lb>cui LG, LK tornano uguali; s&#039;avrà senz&#039;altro <lb></lb>concluso essere la mole LK del solido som­<lb></lb>mersa, alla mole NG dell&#039;acqua, come la su­<lb></lb>perficie LM, alla superficie NM. </s></p><p type="main">

<s>Si dimostrerebbe, con simile compendioso <lb></lb>discorso, esser medesima la proporzione tra le <lb></lb>moli e le superficie, quando il solido, diversamente da quel che si è fin qui <lb></lb>supposto, sale, e il liquido scende: ciò che dall&#039;altra parte si sarebbe potuto <lb></lb>facilmente prevedere da solo ripensar che il solido riman sommerso, per ca­<lb></lb>lare egli stesso, e tutt&#039;insieme per sollevarglisi l&#039;acqua all&#039;intorno, d&#039;onde <lb></lb>viene a rendersi altresì la ragione della prima parte della proposta. </s></p><p type="main">

<s>PROPOSIZIONE II. — <emph type="italics"></emph>“ Quando in uno dei vasi sopraddetti, di qua­<lb></lb>lunque larghezza, benchè immensa o angusta, sia collocato un tal prisma <lb></lb>o cilindro circondato da acqua, se alzeremo tal solido a perpendicolo, <lb></lb>l&#039;acqua circumfusa s&#039;abbasserà, e l&#039;abbassamento dell&#039;acqua, all&#039;alza­<lb></lb>mento del prisma, avrà la medesima proporzione, che l&#039;una delle basi <lb></lb>del prisma, alla superficie dell&#039;acqua circumfusa ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>19). </s></p><p type="main">

<s>Sia la base superiore del prisma, prima a <lb></lb>un medesimo livello AE (fig. </s>

<s>65) con l&#039;acqua <lb></lb><figure id="id.020.01.3165.2.jpg" xlink:href="020/01/3165/2.jpg"></figure></s></p><p type="caption">

<s>Figura 65.<lb></lb>infusa nel vaso, e poi il detto prisma si sollevi <lb></lb>per l&#039;altezza GA, abbassandosegli l&#039;acqua infino <lb></lb>ad AO. </s>

<s>Essendo le moli HA, AN uguali, ossia <lb></lb>HG.AG=AE.AO, è manifesto che HG:AE= <lb></lb>AO:AG, com&#039;era proposto di dimostrare. </s>

<s>E per­<lb></lb>chè gli AO, AG, passati nel medesimo tempo, <lb></lb>son la misura delle velocità, scende altresì dalle <lb></lb>cose dimostrate per corollario che le velocità <lb></lb>hanno reciproca ragion delle moli. </s></p><pb xlink:href="020/01/3166.jpg" pagenum="127"></pb><p type="main">

<s>PROPOSIZIONE III. — <emph type="italics"></emph>“ Un prisma o cilindro retto, di materia in spe­<lb></lb>cie men grave dell&#039;acqua, se sarà circondato dall&#039;acqua secondo tutta la <lb></lb>sua altezza, non resterà sotto, ma si solleverà, benchè l&#039;acqua circonfusa <lb></lb>fosse pochissima, e di gravità assoluta quanto si voglia inferiore alla gra­<lb></lb>vità di esso prisma ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>20). </s></p><p type="main">

<s>Sia il prisma AF (fig. </s>

<s>66) tutto immerso nell&#039;acqua CE del vaso prisma­<lb></lb>tico BD. </s>

<s>Chiamate G, G′ le gravità in specie di esso <lb></lb><figure id="id.020.01.3166.1.jpg" xlink:href="020/01/3166/1.jpg"></figure></s></p><p type="caption">

<s>Figura 66.<lb></lb>prisma e dell&#039;acqua, e ritenute le medesime deno­<lb></lb>minazioni, usate in precedenza, abbiamo per sup­<lb></lb>posizione G′&gt;G, e però, per il corollario del pre­<lb></lb>messo lemma, P′:P&gt;M′:M. Ma, per il corol­<lb></lb>lario della precedente, chiamate V′, V le volocità; <lb></lb>è M′:M=V:V′, dunque P′:P&gt;V:V′, ossia <lb></lb>P′.V′&gt;P.V, che significa prevalere il momento <lb></lb>dell&#039;acqua a quello del prisma, il quale perciò non <lb></lb>starà sotto, ma si solleverà. </s>

<s>Ond&#039;essendo mede­<lb></lb>sime le conclusioni, qnalunque siasi la maggioranza della gravità specifica <lb></lb>sopra la gravità specifica, e qualunque sia pure la grandezza della mole del­<lb></lb>l&#039;acqua; riman così la proposizione dimostrata per ogni sua parte. </s></p><p type="main">

<s>PROPOSIZIONE IV. — <emph type="italics"></emph>“ Se un cilindro o prisma solido sarà men grave <lb></lb>in specie dell&#039;acqua, posto in un vaso come di sopra, di qualsivoglia gran­<lb></lb>dezza, e infusa poi l&#039;acqua, resterà il solido senz&#039;esser sollevato, sin che <lb></lb>l&#039;acqua arrivi a tal parte dell&#039;altezza di quella, alla quale tutta l&#039;al­<lb></lb>tezza del prisma abbia la medesima proporzione, che la gravità in specie <lb></lb>dell&#039;acqua, alla gravità in specie di esso solido. </s>

<s>Ma infondendo più acqua, <lb></lb>il solido si solleverà ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>22). </s></p><p type="main">

<s>Sia il vaso NL (fig. </s>

<s>67), e in esso sia collocato il prisma MD, e qual <lb></lb>proporzione ha la gravità in specie dell&#039;acqua, a quella del prisma, tale <lb></lb><figure id="id.020.01.3166.2.jpg" xlink:href="020/01/3166/2.jpg"></figure></s></p><p type="caption">

<s>Figura 67.<lb></lb>abbia l&#039;altezza DF all&#039;altezza FB: dice Galileo <lb></lb>che, infondendosi liquido sino all&#039;altezza FB, <lb></lb>il solido non si solleverà, ma ben sarà ridotto <lb></lb>all&#039;equilibrio, cosicchè ogni poco più d&#039;acqua <lb></lb>che gli si aggiunga farà sollevarlo. </s>

<s>Abbiamo <lb></lb>infatti, per supposizione e per ragioni ste­<lb></lb>reometriche, ritenute le solite denominazioni, <lb></lb>G:G′=BF:FD=BG:DG. </s>

<s>Moltiplicate la <lb></lb>prima e l&#039;ultima ragione di questa per l&#039;identica <lb></lb>GD:AF=GD:AF, e fatte le riduzioni, avre­<lb></lb>mo G.GD:G′.AF=BG:AF. </s>

<s>Ma G.GD= <lb></lb>P, G′.AF=P′, per il premesso Lemma in <lb></lb>principio, e BG ad AF sta come la superficie EM alla superficie BA, le quali <lb></lb>stanno, per la seconda, come la scesa dell&#039;acqua o la sua velocità V′, alla <lb></lb>salita del solido o alla sua velocità V; dunque P:P′=V′:V. Ond&#039;è, che <lb></lb>stando i pesi contrariamente alle velocità, i momenti si fanno uguali, e perciò <pb xlink:href="020/01/3167.jpg" pagenum="128"></pb>il solido, com&#039;era proposto, rimane in quiete, e solo allora si solleva, accre­<lb></lb>sciuto che gli sia, con qualunque piccola mole di acqua, un tantino del suo <lb></lb>momento. </s></p><p type="main">

<s>Chiamato P′ il peso assoluto di una mole di acqua, uguale a BG, e P <lb></lb>il peso assoluto del prisma DG, abbiamo, per il premesso lemma, P′:P= <lb></lb>BG.G′:DG.G. Ma, per le cose ora dimostrate, G′:G=DG:BG; dun­<lb></lb>que P′:P=BG.DG:DG.BG, e perciò P′=P: vale a dire tant&#039;acqua <lb></lb>in mole, quant&#039;è il solido BG, pesa assolutamente quanto tutto il solido DG, <lb></lb>d&#039;onde si fa manifesto “ come i solidi men gravi in specie dell&#039;acqua si <lb></lb>sommergono solamente, sin tanto che tanta acqua in mole, quanta e la <lb></lb>parte del solido sommersa, pesi assolutamente quanto tutto il solido ” (ivi, <lb></lb>pag. </s>

<s>23). </s></p><p type="main">

<s>PROPOSIZIONE V. — <emph type="italics"></emph>“ Riguardando il solido M<emph.end type="italics"></emph.end> (fig. </s>

<s>68) <emph type="italics"></emph>ora immerso <lb></lb>nel piccolissimo vaso ES, ora nel grandissimo AC, dico che, nell&#039;alzarsi <lb></lb><figure id="id.020.01.3167.1.jpg" xlink:href="020/01/3167/1.jpg"></figure></s></p><p type="caption">

<s>Figura 67.<lb></lb>esso solido, l&#039;abbassamento della pochissima <lb></lb>acqua ES si muove tanto più velocemente della <lb></lb>grandissima mole dell&#039;acqua AC, quanto ap­<lb></lb>punto questa è più di quella ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Si ehiami <emph type="italics"></emph>u<emph.end type="italics"></emph.end> la velocità dell&#039;abbassamento <lb></lb>della pochissima mole <emph type="italics"></emph>m<emph.end type="italics"></emph.end> dell&#039;acqua, V′ la velo­<lb></lb>cità dell&#039;abbassamento della grandissima mole d&#039;acqua M′, e V la velocità <lb></lb>del sollevamento della mole M: abbiamo, per la seconda di questo, <emph type="italics"></emph>u<emph.end type="italics"></emph.end>:V= <lb></lb>M:<emph type="italics"></emph>m,<emph.end type="italics"></emph.end> V′:V=M:M′, d&#039;onde <emph type="italics"></emph>mu<emph.end type="italics"></emph.end>=V′.M′, ossia <emph type="italics"></emph>u<emph.end type="italics"></emph.end>:V′=M′:<emph type="italics"></emph>m,<emph.end type="italics"></emph.end> come <lb></lb>voleva Galileo dimostrare, e come di fatti dimostrò col suo lungo discorso, <lb></lb>proponendo così di questa, come delle altre proprietà de&#039;corpi galleggianti, <lb></lb>nuove ragioni. </s>

<s>Che se nella prima maniera non faceva altro che renderle, <lb></lb>come udimmo più fisiche, in questa seconda diceva di <emph type="italics"></emph>averle ridotte a prin­<lb></lb>cipii più intrinseci e immediati<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>14), quali son quelli della Statica, <lb></lb>ch&#039;egli si lusingava di veder corrispondere <emph type="italics"></emph>a capello<emph.end type="italics"></emph.end> con le leggi dell&#039;Idro­<lb></lb>statica. </s>

<s>Se avesse ripensato però che i solidi e i liquidi, benchè convengano <lb></lb>nell&#039;esser gravi, diversificano sostanzialmente nelle loro proprietà naturali; <lb></lb>avrebbe con facilità riconosciuto che que&#039;suoi professati principii, tutt&#039;altro <lb></lb>che essere intrinseci e immediati, venivano, in certi casi specialmente, a in­<lb></lb>vocarsi così fuor di proposito, da condurre a manifesti e dannosissimi errori, <lb></lb>di che basti a noi citare i due esempi seguenti. </s></p><p type="main">

<s>Se un solido più grave dell&#039;acqua dimori in quiete sopra il fondo di <lb></lb>un vaso, “ benchè, dice Galileo, si aggiungesse poi grandissima quantità <lb></lb>d&#039;acqua sopra il livello di quella, che pareggia l&#039;altezza del solido, non però <lb></lb>si accresce la pressione o aggravamento delle parti circonfuse al detto solido, <lb></lb>per la quale maggior pressione egli avesse ad esser cacciato ” (ivi, pag. </s>

<s>27). <lb></lb>E nel seguito del medesimo Discorso anche si legge quest&#039;altra espression <lb></lb>sentenziosa: “ Il dir poi che l&#039;acqua possa accrescer peso alle cose che in <lb></lb>essa sieno collocate è falsissimo, perchè l&#039;acqua nell&#039;acqua non ha gravità <lb></lb>veruna, poichè ella non vi discende ” (ivi, pag. </s>

<s>50). </s></p><pb xlink:href="020/01/3168.jpg" pagenum="129"></pb><p type="main">

<s>A chiunque verrebbe voglia qui di rispondere che, se tutti i corpi, i <lb></lb>quali non scendono, non son gravi; dunque gli oggetti posati sopra una ta­<lb></lb>vola non son gravi? </s>

<s>Dal veder che l&#039;acqua nell&#039;acqua non scende non può <lb></lb>perciò inferirsi che ella non è grave, ma si dirà piuttosto aver sotto chi la <lb></lb>sostiene, come dal veder che un corpo non scende, posato sul bacino di una <lb></lb>bilancia, nessuno crederebbe ch&#039;egli non pesi, ma direbbe che del peso non <lb></lb>apparisce l&#039;effetto, per essere dall&#039;altra parte esattamente contrappesato. </s>

<s>Ciò <lb></lb>che vale altresì a scoprire la fallacia di Galileo nell&#039;altro esempio: fallacia <lb></lb>simile a quella di colui, il quale, a una bilancia equilibrata con un&#039;oncia di <lb></lb>qua e di là, sopraggiungendo altr&#039;once via via sempre uguali di numero da <lb></lb>una parte e dall&#039;altra, e non vedendo allo strumento perciò fare alcun moto; <lb></lb>dicesse che da quell&#039;aggiunta di peso non si cresce la pressione e l&#039;aggra­<lb></lb>vamento del giogo. </s>

<s>Ritorniamo indietro sopra la figura 42, ch&#039;essendo ser­<lb></lb>vita per lo Stevino citiamo apposta, perchè si faccia il confronto delle verità <lb></lb>di lui con le fallacie nel Nostro, e supponendo che GI sia il solido, posato <lb></lb>in fondo al vaso, non però così che alquanto di acqua non gli penetri sotto, <lb></lb>s&#039;aggiunga sopra il livello EG, che pareggia l&#039;altezza del detto solido, nuova <lb></lb>acqua via via, nè importa pure che sia grandissima, per veder se è vero <lb></lb><emph type="italics"></emph>che non si accresce la pressione o l&#039;aggravamento delle parti circonfuse <lb></lb>al solido,<emph.end type="italics"></emph.end> come diceva Galileo. </s></p><p type="main">

<s>Delle dannose conseguenze, che venivano dal professar principii estrin­<lb></lb>seci e insufficienti, ebbe Galileo stesso a fare esperienza nel risolvere un pro­<lb></lb>blema, che insomma è l&#039;argomento principale del suo Discorso. </s>

<s>Perchè una <lb></lb>pentola di rame o di terra, ma vuota, galleggia, ne concludevano alcuni Pe­<lb></lb>ripatetici contro Archimede non esser vero che galleggino i soli corpi più <lb></lb>gravi in specie dell&#039;acqua: e dal veder che una palla d&#039;ebano s&#039;affonda, ma <lb></lb>ridotta in una larga e sottil tavoletta galleggia, vollero dire esser causa del <lb></lb>galleggiamento di alcuni corpi la loro stessa figura. </s>

<s>A costoro Galileo con­<lb></lb>trapponeva che l&#039;aria contenuta nel vaso è quella, che lo sostiene a galla <lb></lb>“ avvegnachè di lei e del rame si faccia un composto men grave di altret­<lb></lb>tanta acqua, e il luogo che occupa il vaso sott&#039;acqua, mentre galleggia, non <lb></lb>è uguale al rame solo, ma al rame e all&#039;aria insieme, che riempie quella <lb></lb>parte del vaso, che sta sotto il livello dell&#039;acqua ” (ivi, pag. </s>

<s>51). Quanto <lb></lb>poi alle tavolette di ebano, che messe sotto l&#039;acqua seguitano a scendere fino <lb></lb>in fondo, e posatevi su leggermente rimangono a galla; soggiungeva non <lb></lb>avvenir ciò, per ragione della loro figura, ma “ perchè quello che si mette <lb></lb>nell&#039;acqua è la pura falda d&#039;ebano, che, per esser più grave dell&#039;acqua va <lb></lb>al fondo, e quello, che si posa sull&#039;acqua, è un composto d&#039;ebano e di tanta <lb></lb>aria, che fra ambedue sono in specie men gravi dell&#039;acqua, e però non di­<lb></lb>scendono ” (ivi, pag. </s>

<s>60). </s></p><p type="main">

<s>Chi, leggendo tali passi nel Discorso intorno alle galleggianti, non si <lb></lb>persuaderebbe essere per questi espressa la verità, secondo la quale il peso <lb></lb>dell&#039;aria, aggiungendosi al peso della materia del vaso o dell&#039;assicella, sono <lb></lb>ambedue insieme equilibrati dal contra stante peso dell&#039;acqua? </s>

<s>Eppure, se-<pb xlink:href="020/01/3169.jpg" pagenum="130"></pb>guitando una sola pagina dopo, sorprende il lettore a trovarci scritto che <lb></lb>l&#039;aria, nella cavità del vaso, o nella fossetta scavatasi dentro l&#039;acqua dal­<lb></lb>l&#039;assicella, nè alleggerisce il solido nè l&#039;aggrava, cosicchè par che per <emph type="italics"></emph>aria<emph.end type="italics"></emph.end><lb></lb>non si debba intendere il noto elemento, ma riceversi la parola nel signi­<lb></lb>ficato di <emph type="italics"></emph>area<emph.end type="italics"></emph.end> o di spazio non occupato da nessun corpo. </s>

<s>Che anzi l&#039;Autore <lb></lb>la intenda propriamente così ne possiamo esser certi dal proporsi ch&#039;egli fa <lb></lb>l&#039;assicella IS (fig. </s>

<s>69), la quale, se sia il doppio più <lb></lb>grave dell&#039;acqua, e di tal grossezza IO, da uguagliarsi <lb></lb>alla massima altezza degli arginetti, che le fanno <lb></lb>sponda all&#039;intorno; dimostra come, posta che sia nel­<lb></lb>l&#039;acqua, non si sommergerà per queste ragioni: “ Im­<lb></lb>perocchè, essendo l&#039;altezza AI eguale all&#039;altezza IO, <lb></lb>sarà la mole dell&#039;aria ABCI eguale alla mole del so­<lb></lb>lido CIOS, e tutta la mole AOSB doppia della mole IS. <lb></lb><figure id="id.020.01.3169.1.jpg" xlink:href="020/01/3169/1.jpg"></figure></s></p><p type="caption">

<s>Figura 69.<lb></lb>E avvegnachè la mole dell&#039;aria AC <emph type="italics"></emph>non cresca o diminuisca la gravità <lb></lb>della mote IS,<emph.end type="italics"></emph.end> e il solido IS si pone doppio in gravità all&#039;acqua: adunque <lb></lb>tant&#039;acqua, quanta è la mole sommersa AOSB, composta dell&#039;aria AICB e <lb></lb>del solido IOSC, pesa appunto quanto essa mole sommersa AOSB ” (ivi, <lb></lb>pag. </s>

<s>61, 62). E nella seguente proposizione, affermandosi che la gravità del <lb></lb>solido IS è la medesima che la gravità del solido AS, ne fa manifestamente <lb></lb>intendere Galileo che la gravità dell&#039;aria, compresa dentro lo spazio AC, si <lb></lb>debba ritenere, non già come insensibile, ma come nulla affatto. </s></p><p type="main">

<s>La maraviglia cresce poi anche di più, leggendosi in questo stesso Di­<lb></lb>scorso che, non solamente l&#039;aria non aggrava col suo proprio peso l&#039;assi­<lb></lb>cella sottoposta, ma che anzi, aderendo al solido, ella è che lo tiene a galla. </s>

<s><lb></lb>Cosicchè quest&#039;aderenza dell&#039;aria farebbe l&#039;ufficio della leggerezza positiva <lb></lb>attribuitale da Leonardo da Vinci, e sostituita alle pressioni idrostatiche, non <lb></lb>avvertite nè dall&#039;uno nè dall&#039;altro Autore. </s>

<s>A chi avesse domandato perchè, <lb></lb>penetrata l&#039;acqua, l&#039;assicella non seguita a profondarsi, Galileo rispondeva: <lb></lb>“ Perchè nel sommergersi, finchè la sua superficie arriva al livello di quella <lb></lb>dell&#039;acqua, ella perde una parte della sua gravità, e il resto poi lo va per­<lb></lb>dendo nel profondarsi e abbassarsi oltre alla superficie dell&#039;acqua, la quale <lb></lb>intorno intorno li fa argine e sponda, e tale perdita fa ella mediante il ti­<lb></lb>rarsi dietro, e far seco discendere l&#039;aria superiore, e a sè stessa per lo con­<lb></lb>tatto aderente ” (ivi, pag. </s>

<s>49). </s></p><p type="main">

<s>La nuova causa assegnata al galleggiamento de&#039;corpi è tanto strana, <lb></lb>che potrebbero i gelosi della fama dell&#039;Autore ricorrere a qualche più be­<lb></lb>nigna interpetrazione. </s>

<s>Ma, per togliere ad essi ogni refugio, Galileo stesso <lb></lb>esplica il suo proprio senso e lo conferma col suggello di tali parole, che <lb></lb>giova a noi trascrivere nella loro integrità, benchè non brevi: “ Forse, egli <lb></lb>dice, alcuno di quei signori, che dissentono da me, si maraviglierà che io <lb></lb>affermi che l&#039;aria contigua superiore sia potente a sostener quella laminetta <lb></lb>di rame o d&#039;argento, che su l&#039;acqua si trattiene, come che io voglia in un <lb></lb>certo modo dare una quasi virtù di calamita all&#039;aria di sostenere i corpi <pb xlink:href="020/01/3170.jpg" pagenum="131"></pb>gravi, co&#039;quali ella è contigua. </s>

<s>Io per sodisfare, per quanto m&#039;è permesso, <lb></lb>a tutte le difficoltà, sono andato pensando di dimostrare, con qualche altra <lb></lb>sensata esperienza, come veramente quella poca d&#039;aria contigua e superiore <lb></lb>sostien que&#039;solidi, che, essendo per natura atti a discendere al fondo, posti <lb></lb>leggermente su l&#039;acqua non si sommergono, se prima non si bagnano in­<lb></lb>teramente, e ho trovato che, sceso che sia uno di tali corpi al fondo, col <lb></lb>mandargli senza altrimenti toccarlo un poco d&#039;aria, la quale colla sommità <lb></lb>di quello si congiunga, ella è bastante non solo, come prima si faceva, a <lb></lb>sostenerlo, ma a sollevarlo e ricondurlo ad alto, dove nella stessa maniera <lb></lb>si ferma e resta, sin che l&#039;aiuto dell&#039;aria congiuntagli non gli vien manco. </s>

<s><lb></lb>E a questo effetto ho fatta una palla di cera, e fattala con un poco di piombo <lb></lb>tanto grave, che lentamente discende al fondo, facendo di più la sua super­<lb></lb>ficie ben tersa e pulita, e questa posata pian piano sull&#039;acqua si sommerge <lb></lb>quasi tutta, restando solamente un poco di sommità scoperta, la quale, sin <lb></lb>che starà congiunta con l&#039;aria, tratterrà la palla in alto, ma tolta la con­<lb></lb>tiguità dell&#039;aria col bagnarla discenderà al fondo, e quivi resterà. </s>

<s>Ora, per <lb></lb>farla, in virtù dell&#039;aria medesima, che dianzi la sosteneva, ritornare ad alto, <lb></lb>e fermarvisi appresso; spingasi nell&#039;acqua un bicchiere rivolto, cioè colla <lb></lb>bocca in giù, il quale porterà seco l&#039;aria da lui contenuta, e questo si muova <lb></lb>verso la palla, abbassandolo tanto che si vegga, per la trasparenza del vetro, <lb></lb>che l&#039;aria contenuta dentro arrivi alla sommità della palla. </s>

<s>Dipoi ritirisi in <lb></lb>su lentamente il bicchiere, e vedrassi la palla risorgere e restare anche di <lb></lb>poi ad alto, se con diligenza si separerà il bicchiere dall&#039;acqua, sicchè ella <lb></lb>non si commova e agiti di soverchio. </s>

<s>” </s></p><p type="main">

<s>“ È dunque tra l&#039;aria e gli altri corpi una certa affinità, la quale gli <lb></lb>tiene uniti, sicchè, non senza qualche poco di violenza, si separano. </s>

<s>Lo stesso <lb></lb>parimente si vede nell&#039;acqua, perchè, se tufferemo in essa qualche corpo, sì <lb></lb>che si bagni interamente; nel tirarlo poi fuor piano piano vedremo l&#039;acqua <lb></lb>seguitarlo, e sollevarsi notabilmente sopra la sua superficie, avanti che da <lb></lb>quello si separi. </s>

<s>I corpi solidi ancora, se saranno di superficie in tutto si­<lb></lb>mili, sicchè esquisitamente si combagino insieme, nè tra di loro resti aria, <lb></lb>che si distragga nella separazione, e ceda sin che l&#039;ambiente succeda a riem­<lb></lb>pier lo spazio; saldissimamente stanno congiunti, nè senza gran forza si se­<lb></lb>parano. </s>

<s>Ma perchè l&#039;aria, l&#039;acqua e gli altri liquidi molto speditamente si <lb></lb>figurano al contatto de&#039;corpi solidi, si che la superficie loro esquisitamente <lb></lb>s&#039;adatta a quella de&#039;solidi, senza che altro resti tra loro; però più manife­<lb></lb>stamente e frequentemente si riconosce in loro l&#039;effetto di questa copula e ade­<lb></lb>renza, che ne&#039;corpi duri, le cui superficie di rado congruentemente si con­<lb></lb>giungono. </s>

<s>Questa è dunque quella virtù calamitica, la quale con salda copula <lb></lb>congiunge tutti i corpi, che senza interposizione di fluidi cedenti si toccano. </s>

<s>E <lb></lb>chi sa che un tal contatto, quando sia esquisitissimo, non sia bastante cagione <lb></lb>dell&#039;unione e continuità delle parti del corpo naturale? </s>

<s>” (ivi, pag. </s>

<s>42-54). </s></p><p type="main">

<s>Qualche anno dopo, l&#039;assegnare, per causa del galleggiare le tavolette <lb></lb>di ebano o di metallo sull&#039;acqua, le virtù calamitiche dell&#039;aria, parve anche <pb xlink:href="020/01/3171.jpg" pagenum="132"></pb>a Galileo ipotesi tanto strana, che avrebbe voluto ritirarla. </s>

<s>Ma perchè era <lb></lb>messa oramai fuori, e non volendo dall&#039;altra parte, non solamente confes­<lb></lb>sare, ma nemmeno parere di avere sbagliato; bisognava ricorrere a qual­<lb></lb>cuna di quelle arti, che da&#039;più destri si sogliono usare in simili casi. </s>

<s>Non <lb></lb>dirà come poi, per salvarsi dall&#039;accusa di avere errato intorno alla linea dei <lb></lb>proietti, che ne&#039;dialoghi dei due Massimi Sistemi se n&#039;era scritto per celia, <lb></lb>ma, riducendo le cose alle parole, afferma che il termine di <emph type="italics"></emph>virtù calamitica<emph.end type="italics"></emph.end><lb></lb>attribuita all&#039;aria in sostener le assicelle galleggianti, non era suo, ma di un <lb></lb>cavalier principale discorde dalla sua opinione (Alb. </s>

<s>XII, 104). E nell&#039;armeg­<lb></lb>gìo di questa ritirata si perdè il bel pensiero dell&#039;attrazione molecolare, da <lb></lb>cui dipende la coesione dei corpi, e che sarebbe nel primo dialogo delle due <lb></lb>Nuove scienze per cedere il luogo alle chimere della repugnanza del vacuo. </s></p><p type="main">

<s>La ritirata, che si diceva, fu fatta qualche anno dopo nella lettera a <lb></lb>Tolomeo Nozzolini, dove s&#039;incomincia da Galileo a riconoscere il peso del­<lb></lb>l&#039;aria, e gli effetti di lei nel galleggiamanto delle assicelle e de&#039;vasi vuoti <lb></lb>specificamente più gravi dell&#039;acqua. </s>

<s>È dunque in sostanza la detta Lettera <lb></lb>una corrèzione fatta al Discorso intorno alle galleggianti, benchè si voglia <lb></lb>studiosamente non farla apparir tale nella forma. </s>

<s>Ma perchè così fatte cor­<lb></lb>rezioni non riguardano altro che dottrine secondarie, e la scrittura dove si <lb></lb>fecero non venne alla luce che in sui primi anni del secolo XVIII; i nuovi <lb></lb>insegnamenti idrostatici di Galileo si tramandarono ai discepoli tali, quali si <lb></lb>hanno ancora nel citato Discorso al granduca Cosimo secondo, e furono le <lb></lb>seconde instituzioni, che si videro a que&#039;tempi, dopo quelle dello Stevino. </s>

<s><lb></lb>Galileo dunque e lo Stevino sono i principali promotori di Archimede, ben­<lb></lb>chè altri precedessero, altri succedessero a loro nell&#039;ufficio, i quali tutti, <lb></lb>avendo pure e non lievemente concorso a far progredire la Scienza, non vo­<lb></lb>gliono essere perciò dimenticati in questa Storia. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nel 1603 vedeva in Roma la luce un libretto, col titolo di <emph type="italics"></emph>Promotus <lb></lb>Archimedes.<emph.end type="italics"></emph.end> Marino Ghetaldo, che n&#039;era l&#039;Autore, diceva, in una delle prime <lb></lb>pagine, a&#039;suoi lettori che il comparare il peso assoluto de&#039;corpi co&#039;loro vo­<lb></lb>lumi gli era sembrato argomento così giocondo, e così utile notizia, da in­<lb></lb>vogliarlo a scriverne un trattato, tanto più che da nessun, diceva, prima di <lb></lb>lui, almeno diffusamente, ancora non s&#039;era fatto. </s>

<s>Quel dir però la proposta <lb></lb>scienza <emph type="italics"></emph>nec fuse a quopiam explicata,<emph.end type="italics"></emph.end> forse era vero, perchè il Tartaglia <lb></lb>s&#039;intrattiene piuttosto in dar fondamento alle dottrine, che in applicarle ai <lb></lb>fatti particolari, intorno a che si diffonde il Ghetaldo. </s>

<s>Ma perchè la Scienza <lb></lb>non consiste propriamente nel descrivere cotali particolari esperienze, o in <lb></lb>ordinar le numerose Tavole delle varie gravità specifiche; non doveva il <lb></lb>novello Promotor di Archimede dimenticare chi l&#039;aveva preceduto di ben <pb xlink:href="020/01/3172.jpg" pagenum="133"></pb>52 anni, nè tacere che la <emph type="italics"></emph>Bilancetta idrostatica,<emph.end type="italics"></emph.end> ch&#039;ei diceva essere <emph type="italics"></emph>operae <lb></lb>praetium,<emph.end type="italics"></emph.end> e quale si descrive da lui nell&#039;esempio dopo l&#039;ottava proposizione; <lb></lb>non era cosa punto nuova, se forse la novità non si fosse fatta consistere <lb></lb>nell&#039;aver sostituito allo <emph type="italics"></emph>spaghetto lunghetto<emph.end type="italics"></emph.end> del primo inventore un crino di <lb></lb>cavallo, per essere in specie quasi ugualmente grave all&#039;acqua. </s>

<s>“ Corpus, <lb></lb>quod ponderandum proponitur, seta equina ex altera librae lance appenda­<lb></lb>tur. </s>

<s>In altera lance ponantur pondera, et corpus appensum demittatur in <lb></lb>aqua, et ita ponderetur, ac si in aere penderet ” (<emph type="italics"></emph>Promotus Archim.,<emph.end type="italics"></emph.end> pag. </s>

<s>10). </s></p><p type="main">

<s>A imitazion del Tartaglia anche il Ghetaldo si serve dello strumento, <lb></lb>per risolvere il problema della corona di Gerone, dop&#039;avere anch&#039;egli notato <lb></lb>le inesattezze, a cui inevitabilmente conducevano i modi, che Vitruvio rife­<lb></lb>risce aver tenuti Archimede. </s>

<s>Quanto al calcolo poi, da instituirsi sopra le <lb></lb>fatte operazioni, molti, dice il Ghetaldo, ne hanno scritto, “ longa tamen <lb></lb>methodo atque difficili usi sunt, et quod maximam confusionem et obscuri­<lb></lb>tatem parit, nullum operationis tradunt praeceptum firmum ac stabile ” (ivi, <lb></lb>pag. </s>

<s>54). Ciò che forse non avrebbe potuto dire in coscienza, se si fosse ri­<lb></lb>cordato della quarta proposizione dimostrata dal Tartaglia nel suo secondo <lb></lb>Ragionamento, benchè forse con la regola del tre, che il Ghetaldo stesso <lb></lb>passa a proporre, si vada per via più semplice e piana. </s>

<s>“ Ego autem unica <lb></lb>tantum proportionis ratiocinatione, seu regula trium, ut vulgo dicitur, bre­<lb></lb>viter et expedite idem consequor, eamque geometrica ratione demonstro ” <lb></lb>(ibid.). La qual geometrica dimostrazione si dà infatti nel X teorema così <lb></lb>proposto: </s></p><p type="main">

<s>“ Si trium corporum, aeque gravium, primum et tertium fuerint gene­<lb></lb>ris diversi, secundi autem portio fuerit eiusdem generis cum corpore primo, <lb></lb>reliqua vero eiusdem generis cum corpore tertio: fuerint etiam tres quan­<lb></lb>titates aquae praedictis corporibus aequales, prima videlicet corpori primo, <lb></lb>secunda secundo, et tertia tertio; erit ut differentia gravitatum primae et <lb></lb>tertiae quantitatis aquae, ad gravitatem corporis secundi, ita differentia gra­<lb></lb>vitatum primae et secundae quantitatis aquae, ad gravitatem portionis cor­<lb></lb>poris secundi, quae est eiusdem generis cum corpore tertio. </s>

<s>Et ita differen­<lb></lb>tia gravitatum secundae et tertiae quantitatis aquae, ad gravitatem portionis <lb></lb>eiusdem generis cum corpore primo ” (ibid., pag. </s>

<s>56). </s></p><p type="main">

<s>Abbiansi tre corpi A, B+C, D, di peso assoluto tutti uguali a P, e <lb></lb>il primo e il terzo di questi corpi siano di natura diversa, ma le parte B <lb></lb>(la gravità assoluta della quale chiameremo <emph type="italics"></emph>p<emph.end type="italics"></emph.end>) sia del genere di A, e l&#039;altra <lb></lb>parte C, la gravità della quale chiameremo <emph type="italics"></emph>p′,<emph.end type="italics"></emph.end> sia del genere di D. </s>

<s>Si pren­<lb></lb>dano, uguali alle tre dette moli, altre tre moli di acqua, la prima delle quali <lb></lb>R pesi come G, la terza Q pesi come H, e le parti Q+L corrispondenti <lb></lb>alle parti B+C abbiano un peso respettivamente rappresentato da F, V. </s>

<s>Si <lb></lb>propone il Ghetaldo di dimostrare che si verificano le due seguenti equa­<lb></lb>zioni: H—G:P=(V+F)—G:<emph type="italics"></emph>p′,<emph.end type="italics"></emph.end> e H—G:P=H—(V+F):<emph type="italics"></emph>p.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>La seconda dimostrazion dell&#039;Autore, assai più breve e più matematica <lb></lb>della prima, procede in questa maniera: Osservando che due equazioni danno <pb xlink:href="020/01/3173.jpg" pagenum="134"></pb>sempre una proporzione, e che, trattandosi di corpi omogenei, i volumi ri­<lb></lb>spondono proporzionalmente ai pesi assoluti; sarà D:C=Q:L, e P:<emph type="italics"></emph>p′<emph.end type="italics"></emph.end>= <lb></lb>H:V. </s>

<s>Similmente A:B=R:O, e P:<emph type="italics"></emph>p<emph.end type="italics"></emph.end>=G:F. </s>

<s>Dividendo quest&#039;ultima, <lb></lb>e osservando che P—<emph type="italics"></emph>p<emph.end type="italics"></emph.end>=<emph type="italics"></emph>p′,<emph.end type="italics"></emph.end> verrà P:<emph type="italics"></emph>p′<emph.end type="italics"></emph.end>=G:C—F, e perciò H:V= <lb></lb>G:G—F, ossia H:G=V:G—F, la quale per divisione darà la (*) <lb></lb>H—G:G=V+F—G:G—F, d&#039;onde si riesce, per composizione <lb></lb>e per riduzione, alla H:G=V:G—F. </s>

<s>Questa pure, divisa e permutata, <lb></lb>si riduce alla H—G:V+F—G=G:G—F, e, per la segnata con <lb></lb>asterisco, all&#039;altra H—G:V+F—G=P:P—<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> che, per nuova per­<lb></lb>mutazione e sostituzione di <emph type="italics"></emph>p′<emph.end type="italics"></emph.end> a P—<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> rende finalmente H—G:P= <lb></lb>(V+F)—G:<emph type="italics"></emph>p′,<emph.end type="italics"></emph.end> che è la prima equazione promessa. </s></p><p type="main">

<s>Quanto alla seconda, essendo P:<emph type="italics"></emph>p′<emph.end type="italics"></emph.end>=H:V, s&#039;ha da questa per divi­<lb></lb>sione P:P—<emph type="italics"></emph>p′<emph.end type="italics"></emph.end>=H:H—V, ossia P:<emph type="italics"></emph>p<emph.end type="italics"></emph.end>=H:H—V=G:F (per una <lb></lb>delle prime equazioni prestabilite al calcolo precedente) e anche insieme <lb></lb>H:G=H—V:F, la quale vien, dividendo, H—G:G=H—V—F:F, <lb></lb>e permutando, H—G:H—V—F=G:F. </s>

<s>In ultimo, perciocchè G:F= <lb></lb>P:<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> ancora permutando, ne resulterà H—G:P=H—(V+F):<emph type="italics"></emph>p,<emph.end type="italics"></emph.end> con­<lb></lb>forme a ciò che il Ghetaldo erasi proposto di dimostrare in secondo luogo, <lb></lb>benchè la prima equazione, anche sola, bastasse a sciogliere il problema. </s>

<s><lb></lb>Essendo infatti noti, con l&#039;uso della Stadera e della Bilancetta idrostatica, i <lb></lb>valori di H, di G, di P, e di V+F; s&#039;ha, per essa equazione, il valore di <lb></lb><emph type="italics"></emph>p′,<emph.end type="italics"></emph.end> ossia del peso dell&#039;argento, e il valore di <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> peso dell&#039;oro, si deduce im­<lb></lb>mediatamente dall&#039;equazione <emph type="italics"></emph>p<emph.end type="italics"></emph.end>=P—<emph type="italics"></emph>p′.<emph.end type="italics"></emph.end> Supposto essere P=95, e la <lb></lb>Bilancetta dare G=5, V+F=6, H=9+6/31, come, nel primo esem­<lb></lb>pio dopo la proposizione XVIII, ponesi dal Ghetaldo (ivi, pag. </s>

<s>56), si tro­<lb></lb>verà <emph type="italics"></emph>p′<emph.end type="italics"></emph.end>=22+17/26, ond&#039;è che, per sola differenza e senz&#039;altro computo, <lb></lb>si conclude <emph type="italics"></emph>p<emph.end type="italics"></emph.end>=72+9/26. </s></p><p type="main">

<s>Nonostante, dalle due equazioni insieme, scende per corollario </s></p><p type="main">

<s><emph type="center"></emph>H—(V+F):(V+F)—G=<emph type="italics"></emph>p:p′,<emph.end type="italics"></emph.end><emph.end type="center"></emph.end><lb></lb>nuova formula, che tirò a sè l&#039;attenzione di Galileo, e che gli suggeri il modo <lb></lb>di risolvere meccanicamente il problema della corona. </s>

<s>Ritornando sopra la <lb></lb>figura 61, qui addietro, è facile vedere che il valore di H, nella formula del <lb></lb>Ghetaldo, è rappresentato dalla lunghezza della linea CG, sull&#039;ago della Bi­<lb></lb>lancetta di Galileo; il valore di V+F, dalla lunghezza di CH, e quello di <lb></lb>GD, dalla linea CD. </s>

<s>Sarà dunque, scambiando i simboli di <emph type="italics"></emph>p, p′,<emph.end type="italics"></emph.end> in quelli <lb></lb>di M, N; CG—CH:CH—CD=M:N, ossia HG:DH=M:N, che è <lb></lb>la regola di ritrovare le proporzioni del peso de&#039;metalli nel misto, secondo <lb></lb>l&#039;invenzione dello stesso Galileo. </s></p><p type="main">

<s>Vien di qui dunque un nuovo documento a illustrare la storia di que­<lb></lb>sta invenzione. </s>

<s>Il Viviani poneva di sua propria mano, in fronte alla nota <lb></lb>scrittura galileiana, il titolo seguente: <emph type="italics"></emph>Fabbrica ed uso di una esatta Bi­<lb></lb>lancia da saggiatore, per ritrovare la proporzione di due metalli, con altre <lb></lb>curiosità, inventata nel 1586 dal signor Galileo Galilei, ne&#039;suoi primi<emph.end type="italics"></emph.end><pb xlink:href="020/01/3174.jpg" pagenum="135"></pb><emph type="italics"></emph>studi intorno alle opere di Archimede<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>60), <lb></lb>e tutti sono andati e vanno tuttavia, senza discrizione, ripetendo in tal modo. </s>

<s><lb></lb>Ma le cose fin qui narrate ne fanno accorti essere da distinguer nell&#039;inven­<lb></lb>zione due progressi: uno, che riguarda lo Strumento come semplicemente <lb></lb>parato alla ricerca delle gravità specifiche de&#039;vari corpi, ciò che potè esser be­<lb></lb>nissimo occorso a Galileo nel 1586, in assai facile modo, non trattandosi d&#039;al­<lb></lb>tro, che di perfezionare, con l&#039;aggiunta di organi noti, quali eran le spire dei <lb></lb>sottilissimi fili micrometrici, la Bilancetta descritta e usata già dal Tartaglia. </s></p><p type="main">

<s>Il secondo progresso riguarda lo Strumento come parato a ritrovare le <lb></lb>proporzioni di due metalli nel misto, al quale effetto si presupponeva di ne­<lb></lb>cessità il fondamento di quella scienza, che si veniva a rendere per dir così <lb></lb>manuale, come il Compasso di proporzione presupponeva la Geometria di <lb></lb>Euclide, e la Catenella per i bombardieri il quarto dialogo delle due nuove <lb></lb>Scienze. </s>

<s>Or perchè il fondamento all&#039;arte di ritrovare i pesi nel misto si ve­<lb></lb>niva a porre nel problema IX, e nella proposizione XIX del Ghetaldo, com­<lb></lb>parse in pubblico nel 1603; sembra ragionevole concluder che, dopo quel­<lb></lb>l&#039;anno, venisse in pensiero a Galileo di applicare la Bilancetta stessa, ser­<lb></lb>vita già per le semplici gravità in specie, a risolvere anche il problema, più <lb></lb>complicato, della Corona. </s></p><p type="main">

<s>Vorranno dire alcuni che Galileo sciolse geometricamente quello stesso <lb></lb>problema, o primo, o facendosi a sè stesso maestro, senza il Ghetaldo, alla <lb></lb>quale opinione consentiremmo anche noi volentieri, quando se ne producesse <lb></lb>qualche prova di fatto. </s>

<s>Dall&#039;altra parte non s&#039;ha questo esempio solo degli <lb></lb>studiosi commenti, che il giovane professore di Pisa e di Padova faceva sopra <lb></lb>le proposizioni del provetto Matematico di Ragusa: lo stesso Discorso intorno <lb></lb>alle galleggianti si può dire non essere altro che un commentario prolisso <lb></lb>di ciò, che si legge nell&#039;<emph type="italics"></emph>Archimede promosso.<emph.end type="italics"></emph.end> Mentre questo opuscolo era <lb></lb>sotto i torchi (avverte quivi l&#039;Autore, dopo l&#039;esempio soggiunto alla propo­<lb></lb>sizione XV) venne un dottissimo uomo a dirmi che, dall&#039;immergere i corpi <lb></lb>nell&#039;acqua, non si può desumere la ragion vera dei loro pesi, se non forse, <lb></lb>quando avessero i detti corpi uguale o simile figura, perchè, se uno sia per <lb></lb>esempio disteso in forma di tavoletta, e l&#039;altro appuntato a guisa di cono, <lb></lb>benchè nell&#039;aria pesassero il medesimo, posti nonostante in acqua si trove­<lb></lb>rebbe questo, per la più facile penetrazione, essere più leggero di quella. <lb></lb></s>

<s>“ Hoc argumentum, licet primo aspectu probabile videatur, tamen falso con­<lb></lb>cludit. </s>

<s>Verum est quod aqua sustentat magis corpns planum quam conum; <lb></lb>ipsum tamen sustentat ne tanta velocitate feratur deorsum, non ideo ipsius <lb></lb>gravitati aliquid detrahit. </s>

<s>Neque enim ex velociori motu simpliciter inferri <lb></lb>potest maior gravitas, illud enim valeret etiam in aere, quod est falsum. </s>

<s>Sed <lb></lb>ne huiusmodi dubitatio veritatis specie aliquem decipiat, sequenti theoremate <lb></lb>eam destruere aggrediar: <emph type="italics"></emph>Corpora eiusdem generis et gravitatis graviora <lb></lb>quam aqua, etsi dissimilia, uequalem in aqua gravitatem habent ”<emph.end type="italics"></emph.end> (ibid., <lb></lb>pag. </s>

<s>28). Ed è questo il teorema che in vario modo dimostra, e, secondo <lb></lb>altri più minuti particolari, esplica Galileo nel suo celebre Discorso. </s></p><pb xlink:href="020/01/3175.jpg" pagenum="136"></pb><p type="main">

<s>Quarant&#039;anni dopo, quasi fossero in questo tempo rimaste morte le pa­<lb></lb>role di Marino Ghetaldo, e l&#039;ufficio di mantenere in vita la Scienza fosse <lb></lb>passato nel solo Galileo, avvenne che Giovan Batista Hodierna, a cui, per <lb></lb>mezzo di Benedetto Castelli suo maestro, era pervenuta la scrittura, dove <lb></lb>suscitavasi <emph type="italics"></emph>l&#039;inventione di quel famoso Siragosano in trovare il furto del­<lb></lb>l&#039;oro nella corona di Hierone;<emph.end type="italics"></emph.end> pensasse di pubblicarla co&#039;commenti da sè <lb></lb>aggiuntivi, e così far rivivere l&#039;Archimede antico, in quello, che s&#039;andava <lb></lb>predicando da tutti <emph type="italics"></emph>Archimede nuovo di Fiorenza.<emph.end type="italics"></emph.end> Nel 1644 infatti si vide <lb></lb>uscire in Palermo alla luce un opuscolo, col titolo in fronte di <emph type="italics"></emph>Archimede <lb></lb>redivivo.<emph.end type="italics"></emph.end> Premesso per testo il discorso galileiano, soprascrittovi: <emph type="italics"></emph>Fabbrica <lb></lb>di un nuovo strumento detto dall&#039;Autore Bilancetta;<emph.end type="italics"></emph.end> segue un <emph type="italics"></emph>Annota­<lb></lb>mento di varie considerazioni intorno alla proposta dottrina del signor <lb></lb>Galileo:<emph.end type="italics"></emph.end> considerazioni per verità di assai lieve momento, quali possono essere <lb></lb>quelle intorno al modo di contare il numero delle spire, nel sottilissimo filo <lb></lb>avvolto intorno all&#039;ago della Stadera, preferendo all&#039;uso dell&#039;orecchio, in <lb></lb>ascoltare gli scatti strisciandovi sopra l&#039;aguto, quello direttamente dell&#039;occhio, <lb></lb>aiutato da uno squisitissimo microscopio. </s></p><p type="main">

<s>In altre considerazioni, piuttosto che rimettersene a quel che aveva detto <lb></lb>il Ghetaldo, per voler troppo sminuzzare le cose, e darle a intendere al volgo; <lb></lb>trascorre incredibilmente l&#039;Hodierna in errori, da non si perdonare a uno <lb></lb>scolaretto, che avesse veduti appena gli Elementi di Euclide. </s>

<s>Vuol far notare <lb></lb>la fallacia dell&#039;esperienze, attribuite ad Archimede, per via di quel colmo, <lb></lb>in che risorge l&#039;acqua intorno intorno agli orli del vaso, prima di strapparsi <lb></lb>e di traboccare. </s></p><p type="main">

<s>“ Ma vedasi, egli dice, con un esempio quanto importi questa fallacia, <lb></lb>per non potersi mai determinare, per questa via incerta, quel che si va cer­<lb></lb>cando. </s>

<s>Avendo io preso un vaso d&#039;argento, il cui orificio circonferenziale si <lb></lb>stendeva per diametro precisamente un palmo, e accomodandolo al livello <lb></lb>dell&#039;orizonte, dop&#039;averlo già pieno d&#039;acqua con esattezza fino all&#039;orlo, se­<lb></lb>guendo poi con una ampolla di vetro d&#039;aggiungervi acqua, prima che l&#039;ec­<lb></lb>cesso aggiuntovi cominciasse a traboccare dall&#039;orlo; si ritrovò quattr&#039;once <lb></lb>d&#039;acqua, che altrettanto di oro in mole peserebbe libbre sei e due terzi, che <lb></lb>sono once otto, come appresso anderemo dimostrando. </s>

<s>Ora, secondo questa <lb></lb>esperienza, quando si desse un vaso con l&#039;orificio assai più largo, come do­<lb></lb>veva esser quello, nel quale Archimede doveva immergere la corona di Je­<lb></lb>rone, che si crede essere stata assai grande; quant&#039;acqua credete voi se le <lb></lb>possa aggiungere? </s>

<s>Suppongasi però che l&#039;orificio del vaso sia stato in diame­<lb></lb>tro non più largo di due palmi: allora, perchè l&#039;area di quella ampiezza sa­<lb></lb>rebbe stata quasi quadrupla a quella d&#039;un palmo, conseguentemente avrebbe <lb></lb>potuto sostentare l&#039;eccesso di <emph type="italics"></emph>sedici<emph.end type="italics"></emph.end> once d&#039;acqua, montata sopra il livello <lb></lb>dell&#039;orlo. </s>

<s>Ma altrettanta massa di oro importerebbe di peso libbre 26, e once <lb></lb>otto, avendo il peso dell&#039;oro al peso dell&#039;acqua la stessa proporzione di 20 a <lb></lb>uno, come appresso si farà manifesto ” (pag. </s>

<s>12, 13). </s></p><p type="main">

<s>La copia del libro, da cui s&#039;è così trascritto, ha un pregio singolare, <pb xlink:href="020/01/3176.jpg" pagenum="137"></pb>per aver fatto parte della biblioteca di Vincenzio Viviani, il quale, avendo <lb></lb>contrassegnata la parola <emph type="italics"></emph>sedici,<emph.end type="italics"></emph.end> messa nel testo, per dire quanto sia in once <lb></lb>l&#039;eccesso d&#039;acqua sostentata; vi sottoscriveva di sua propria mano questa <lb></lb>nota: “ Anzi di 32 once, perchè, se tutti i massimi colmi dell&#039;acqua sopra <lb></lb>vasi circolari di bocca, oppur di altre figure simili, pigliano figura di lenti, <lb></lb>o di altro corpo, simili fra di loro; essendo i solidi simili in tripla propor­<lb></lb>zion de&#039;lati omologhi, ed essendo posto il diametro del primo vaso un palmo, <lb></lb>e il diametro del secondo due palmi, la base dell&#039;uno alla base dell&#039;altro <lb></lb>sarà come il cubo di uno, al cubo di due: cioè come uno a otto. </s>

<s>Ma quello <lb></lb>di un palmo pesava 4 once, adunque quello di due palmi peserà once 32. ” </s></p><p type="main">

<s>Il malcontento del Viviani, per gli annotamenti che l&#039;Hodierna s&#039;era <lb></lb>messo a fare intorno alle dottrine del suo Maestro, si rivela da un&#039;altra po­<lb></lb>stilla, scritta in margine della pagina appresso. </s>

<s>Ivi dice così l&#039;Autore del­<lb></lb>l&#039;Archimede redivivo: “ Chi volesse intendere qual sia veramente l&#039;intrin­<lb></lb>seca passione, che induce le materie più gravi dell&#039;acqua all&#039;andare al fondo, <lb></lb>e le men gravi al galleggiar sopra l&#039;acqua, siccome anco, d&#039;onde sia che <lb></lb>l&#039;acqua nell&#039;acqua non è grave nè lieve; io li direi ciò avvenire dalla mag­<lb></lb>giore o minore, ovvero eguale inclinazione ed appetito delle materie gravi <lb></lb>tra di loro al discendere ” (pag. </s>

<s>15). E il Viviani: “ Per me tanto me ne <lb></lb>intendo a chiamarla intrinseca passione, che appetito o inclinazione o appe­<lb></lb>tenza: e credete pure, signor Hodierna, che così saremo sempre da capo. </s>

<s>” </s></p><p type="main">

<s>Segue in questo opuscolo, ai detti annotamenti, con assai lungo ordine <lb></lb>di definizioni, di petizioni e di supposizioni, premesse per dimostrare sei pro­<lb></lb>posizioncelle; un discorso intitolato: <emph type="italics"></emph>Archimede siracusano; delle cose che <lb></lb>pesano nell&#039;acqua, interpetrato nella lingua italiana da Giovan Batista <lb></lb>Hodierna<emph.end type="italics"></emph.end> (pag. </s>

<s>32). È una composizione indigesta, una confusion discordante <lb></lb>de&#039;teoremi del Ghetaldo, e delle proposizioni del Tartaglia, alcune delle quali <lb></lb>son fedelmente ricopiate, riducendovisi qualche parola dal dialetto bresciano <lb></lb>al palermitano, senza farne un motto, quasi credesse che, de&#039;Ragionamenti <lb></lb>intorno alla Travagliata invenzione, fosse spenta in ogni altro la memoria, <lb></lb>e non ne rimanesse al mondo altra copia da leggervi su, che la sua: tanto <lb></lb>l&#039;aver Galileo reciso il filo delle tradizioni, con taglio così prepotente, aveva <lb></lb>infuso baldanza ne&#039;suoi seguaci! </s></p><p type="main">

<s>La proposizione IV è annunziata come il problema IX del Ghetaldo, <lb></lb>tradotto dal latino, e si conclude così nella forma stessa del corollario, che <lb></lb>ne deriva, dal paragonare le due equazioni dimostrate nel X teorema da esso <lb></lb>Ghetaldo: “ Dico che la parte del misto, che in esso sarà del genere più <lb></lb>grave, la proporzione all&#039;altra sua parte, la quale è del genere più lieve, <lb></lb>sarà come la proporzione della differenza del misto al peso del più lieve, alla <lb></lb>differenza del peso dello stesso misto al peso del più grave ” (ivi, pag. </s>

<s>41). <lb></lb>Notabile che, per dimostrar ciò, non segue i modi del Ghetaldo, ma del Tar­<lb></lb>taglia, senz&#039;avvedersi che la conclusione dell&#039;uno era in forma diversa da <lb></lb>quella dell&#039;altro, o curarsi di dimostrare che, essendo pure nella forma di­<lb></lb>verse, concordavano le soluzioni de&#039;due Autori nella sostanza. </s>

<s>Chi vuole, per <pb xlink:href="020/01/3177.jpg" pagenum="138"></pb>curiosità, vedere il gioco, che del povero Tartaglia fece l&#039;Hodierna, legga di <lb></lb>questo le proposizioni V e VI, dove è ricopiato non l&#039;ordine solo, non le <lb></lb>sole parole, nè i corpi da pesarsi scelti ad esempio: ma perfino le stesse <lb></lb>lettere dell&#039;alfabeto, da significarne i nomi e le proprietà. </s>

<s>Vorremmo anche <lb></lb>nello stesso tempo pregar que&#039;curiosi di attendere a queste parole, che si <lb></lb>leggono nell&#039;appendice alla proposizione IV: “ Da questa par che il signor <lb></lb>Galilei abbia cavato il modo, e trovato l&#039;artificio, che tenne Archimede nello <lb></lb>scoprire il furto dell&#039;orefice dell&#039;oro della corona di Hierone, con avervi ag­<lb></lb>giunto l&#039;artificioso strumento, come insegna nel suo Discorso ” (pag. </s>

<s>41, 42): <lb></lb>vorremmo, dicevasi, pregare di ciò i curiosi, perchè quindi si conferma essere <lb></lb>l&#039;uso della Bilancetta, per la ricerca delle porzioni di due metalli nel misto, <lb></lb>suggerita da&#039;teoremi del Ghetaldo: documento di non poca importanza, per <lb></lb>chi specialmente ripensa che l&#039;Hodierna eruttava, intorno a Galileo, le no­<lb></lb>tizie imbevute da Benedetto Castelli. </s></p><p type="main">

<s>D&#039;altri promotori di Archimede, fioriti prima che il secolo XVII giun­<lb></lb>gesse al suo mezzo, non tratterremo più in lungo il discorso, perchè le loro <lb></lb>promozioni non sono altro che intorno al primo libro <emph type="italics"></emph>De insidentibus in <lb></lb>aqua,<emph.end type="italics"></emph.end> e alle applicazioni de&#039;teoremi di lui all&#039;invenzione delle gravità in <lb></lb>specie. </s>

<s>Il Ghetaldo e l&#039;Hodierna, il Villanpando e il Ventimiglia s&#039;affaccen­<lb></lb>darono in costruirne Tavole, che ai metalli, ai liquidi, alle pietre preziose e <lb></lb>alle materie terree estendevano i pochi saggi datine dal Tartaglia, ma è inu­<lb></lb>tile sperare di ritrovarvi quell&#039;esattezza, che s&#039;attendeva pure a conseguire <lb></lb>con tanto ostinata fatica, non sperimentandosi nel vuoto, nè con l&#039;acqua <lb></lb>distillata. </s>

<s>Il Barometro, il Termometro e l&#039;Areometro parlavano un linguag­<lb></lb>gio allora non compreso, ma che in ogni modo annunziava l&#039;impossibilità del <lb></lb>concordare due esperienze, fatte in varie costituzioni di aria, di acqua e di <lb></lb>temperatura, indipendentemente dalla perizia o dalla diligenza degli speri­<lb></lb>mentatori, e dalla perfezione dei loro strumenti. </s></p><p type="main">

<s>Nelle inchieste, delle quali è il presente discorso, gli strumenti, oltre alla <lb></lb>Bilancetta, sono quegli Idrostammi, de&#039;quali, sulla fine del primo tomo, si <lb></lb>fece la descrizione storica. </s>

<s>Per quel che poi riguarda la loro teoria, ella fu <lb></lb>da&#039;Matematici conclusa tutta nella proposizione così formulata dall&#039;Herman: <lb></lb>“ Diversae partes unius eiusdemque corporis, diversis liquoribus homogeneis <lb></lb>immersae, in casu aequilibrii, sunt in reciproca ratione densitatum, seu gra­<lb></lb>vitatum specificarum liquorum, quibus idem corpus successive immersum <lb></lb>esse ponitur ” (<emph type="italics"></emph>Foron. </s>

<s>Amstelod.,<emph.end type="italics"></emph.end> 1716, pag. </s>

<s>155). Chiamandosi infatti P il <lb></lb>peso assoluto del solido, e G, G′ le gravità specifiche, ch&#039;egli ha rispetto a <lb></lb>due liquidi, nell&#039;un de&#039;quali s&#039;immerga per la parte V, e nell&#039;altro per la <lb></lb>parte V′ del suo proprio volume; avremo G=P:V, G′=P′:V′, d&#039;onde <lb></lb>G.V=G′.V′, ossia V′:V=G:G′, secondo il proposito. </s></p><p type="main">

<s>I cenni storici, dati sin qui, possono bastare a farsi un&#039;idea di cio, che <lb></lb>fu operato nei primi decenni del secolo XVII per promovere l&#039;Idrostatica di <lb></lb>Archimede. </s>

<s>Quelle promozioni però non riguardavano che la parte, per dir <lb></lb>così, fisica della scienza, trattata nel primo libro <emph type="italics"></emph>De insidentibus humido,<emph.end type="italics"></emph.end><pb xlink:href="020/01/3178.jpg" pagenum="139"></pb>come preparazione all&#039;altra parte matematica, trattata nel secondo, e in cui <lb></lb>coronavasi l&#039;opera dell&#039;Autore. </s>

<s>Le applicazioni perciò de&#039;teoremi, a trovar <lb></lb>le proporzioni fra i pesi e i volumi dei corpi, e a scoprire l&#039;impurità di al­<lb></lb>cuni metalli, benchè gioconde, come parvero al Ghetaldo, e utili alla vita <lb></lb>cìvile, come le disse l&#039;Hodierna; sembrano nulladimeno non avere che la <lb></lb>ragione di semplici corollarii, verso la proposizion principale, che attendeva <lb></lb>a dimostrare secondo qual legge galleggerebbero, o si salverebbero dal pe­<lb></lb>ricolo di sommergersi le navi sugl&#039;instabili flutti ondeggianti. </s></p><p type="main">

<s>Unico, fra i promotori, che avesse qualche sentore essere principalissima <lb></lb>intenzion di Archimede quella di volere applicati alla Nautica i suoi astratti <lb></lb>teoremi, fu lo Stevino, il quale perciò coronò i suoi Elementi idrostatici con <lb></lb>quella parte, ch&#039;egli intitolava <emph type="italics"></emph>Des acrobatiques ou des pesanteurs au som­<lb></lb>met du flottant,<emph.end type="italics"></emph.end> e che si conclude tutta in questo unico teorema: “ Un corps <lb></lb>flottant sur l&#039;eau prend telle position, que son centre de gravitè est en la <lb></lb>perpendicle de gravité du creux d&#039;eau qu&#039;il occupa ” (Oeuvres cit., pag. </s>

<s>512). </s></p><p type="main">

<s>Immagina che il corpo galleggiante sia una nave, rappresentata da BCD <lb></lb>(fig. </s>

<s>70) e il centro di gravità della quale sia O, per il qual pnnto, fatta pas­<lb></lb><figure id="id.020.01.3178.1.jpg" xlink:href="020/01/3178/1.jpg"></figure></s></p><p type="caption">

<s>Figura 70.<lb></lb>sare la perpendicolare MN, dice <lb></lb>che dentro questa linea si deve <lb></lb>trovare il punto L, centro di gra­<lb></lb>vità della fossa, che il solido na­<lb></lb>viculare si scava nell&#039;acqua: per­<lb></lb>chè, se si trovasse fuori, come <lb></lb>per esempio in P, non potrebbe <lb></lb>ciò avvenire, se non che trasfor­<lb></lb>mandosi la detta fossa, e perciò <lb></lb>abbassandosi la sponda, e alzan­<lb></lb>dosi l&#039;opposta, contro la supposizione. </s></p><p type="main">

<s>Di qui fa derivar lo Stevino alcuni corollarii importanti: “ I. </s>

<s>Il appert <lb></lb>que; quand le centre de gravité du corps est dessus celuy du creux de l&#039;eau, <lb></lb>que le sommet flottant est chargé, et que tout renverse (c&#039;est assavoir s&#039;il <lb></lb>n&#039;est soustenu) jusqu&#039;à ce que son centre soit dans la perpendicle de gravité <lb></lb>du creux de l&#039;eau. </s>

<s>II. </s>

<s>Il est evident que, mettant quelque poids dans un bat­<lb></lb>teau, ou quelque vaisseau, ayant changé de place dans iceluy, que le creux <lb></lb>change aussi de figure, et le centre de gravité d&#039;iceluy creux change de lieu. </s>

<s><lb></lb>III. </s>

<s>Il est aussi manifeste que, mettant une pesanteur sous le plan de gra­<lb></lb>vité (parallele a l&#039;horizon) du creux de l&#039;eau, qu&#039;icelle pesanteur cause plus <lb></lb>de fermeté au cours du navire, et au sommet d&#039;iceluy; et au contraire, le <lb></lb>pesanteur estant mise au dessus du dit plan de gravité (a niveau), telle pe­<lb></lb>santeur surcharge le sommet du navire tellement, qu&#039;il en est moins ferme ” <lb></lb>(ivi, pag. </s>

<s>513). </s></p><p type="main">

<s>Termina poi l&#039;Autore il suo trattatello con questa osservazione: Se i <lb></lb>due centri di gravità, egli dice, della nave e della fossa scavata nell&#039;acqua, <lb></lb>fossero di facile invenzione, egli è certo che si potrebbe per teoria, prima <pb xlink:href="020/01/3179.jpg" pagenum="140"></pb>della pratica, sapere <emph type="italics"></emph>quelle disposition un batteau, navire, ou autre vais­<lb></lb>seau, tiendroit sur l&#039;eau, et s&#039;il se tiendroit droit ou oblique, et si l&#039;eau, <lb></lb>entreroit par les bords ou non<emph.end type="italics"></emph.end> (ivi). E perciò Archimede scelse i segmenti <lb></lb>sferici, e i conoidei parabolici, de&#039;quali sapeva geometricamente indicare il <lb></lb>centro di gravità. </s>

<s>Questa osservazione però la lascia lo Stevino a&#039;suoi let­<lb></lb>tori, l&#039;ingegno de&#039;quali par che volesse mettere ad esercizio, col tenere, di­<lb></lb>mostrando il suo teorema, le vie oblique all&#039;assurdo, invece delle dirette, che <lb></lb>tutti avrebbero potuto ritrovar da lui stesso disegnate nel libro degli <emph type="italics"></emph>Ele­<lb></lb>menti.<emph.end type="italics"></emph.end> Dal terzo corollario infatti della IX proposizione di questi resultava <lb></lb>“ que centre C (fondo della nave nell&#039;ultima figura) y a un effort, qui le <lb></lb>pousse enhaut, de mesme que la colonne d&#039;eau (o il solido BCD a lei equi­<lb></lb>valente) pousse le mesme fonde C embas ” (ivi, pag. </s>

<s>488). E perchè que­<lb></lb>sto secondo sforzo è concentrato in O, e l&#039;altro in L, che è quel centro della <lb></lb>pressione, le ragioni di ritrovar geometricamente il quale son simili alle di­<lb></lb>mostrate quivi nelle proposizioni XVIII e XIX; dunque, se ai punti O, L <lb></lb>s&#039;immagini essere attaccati due pesi, o applicate due forze uguali e contra­<lb></lb>rie, si ridurranno agli effetti di queste le ragioni dell&#039;equilibrio della mole gal­<lb></lb>leggiante. </s>

<s>Così ragionando, come tacitamente lo Stevino insinuava, venivasi <lb></lb>ad avere la dimostrazione diretta del teorema acrobatico, e de&#039;suoi corollarii, <lb></lb>a solo considerare il gioco delle forze, le quali non si possono equilibrare, <lb></lb>se non che nella direzion connaturata a loro, ossia nella medesima verticale. </s>

<s><lb></lb>Cosicchè, inclinando violentemente la nave, secondo che si rappresenta a de­<lb></lb>stra della figura; è manifesto come, lasciata in libertà, si debba necessaria­<lb></lb>mente dirizzare, e restituirsi nella prima posizione, rappresentata nella figura <lb></lb>a sinistra, per effetto degli sforzi, che la sollecitano ugualmente nella natu­<lb></lb>rale direzione a opposte parti. </s></p><p type="main">

<s>Che se, invece di considerar tutto il peso della nave concentrato in O, <lb></lb>si assegnassero, in P e in Q, i centri delle parti in acqua e in aria; o al­<lb></lb>trimenti, se l&#039;unica forza OT si decomponesse nelle due parallele PS, QU; <lb></lb>verrebbe il teorema dello Stevino ridotto alla precisa forma di quello di Ar­<lb></lb>chimede, e tal sarebbe per l&#039;uno, quale è indicata per l&#039;altro, la vera e di­<lb></lb>retta via della dimostrazione. </s>

<s>Or essendo così, chi non direbbe che i cul­<lb></lb>tori della Idrostatica, ne&#039;primi anni del secolo XVII, dovevano avere negli <lb></lb>Elementi steviniani ritrovata la chiave, da aprir finalmente il mistero del <lb></lb>secondo libro <emph type="italics"></emph>De insidentibus humido,<emph.end type="italics"></emph.end> e avvedersi insieme quanto male il <lb></lb>Tartaglia e il Commandino, ne&#039;loro commenti, l&#039;avessero interpetrato? </s>

<s>Ma <lb></lb>vediamo qual corrispondenza le congetture abbian coi fatti. </s></p><p type="main">

<s>Il primo, fra i commentatori di Archimede, che nel secolo XVII ci si <lb></lb>presenti, è quel David Rivault, il quale, raccogliendo e ordinando le opere <lb></lb>del Siracusano, prometteva di darle <emph type="italics"></emph>novis demonstrationibus, commenta­<lb></lb>riisque illustrata.<emph.end type="italics"></emph.end> Avrebbe forse fatto meglio a tenersi fedelmente alle di­<lb></lb>mostrazioni antiche, e salvare così la sua propria reputazione dalle censure <lb></lb>di molti, i quali avrebbero amato meglio di veder procedere la venerata <lb></lb>figura dell&#039;Autore, colla spedita franchezza del suo passo, che vederglielo <pb xlink:href="020/01/3180.jpg" pagenum="141"></pb>misurato nella dialettica pedanteria delle <emph type="italics"></emph>ipotesi<emph.end type="italics"></emph.end> e degli <emph type="italics"></emph>emporasmi,<emph.end type="italics"></emph.end> delle <lb></lb><emph type="italics"></emph>catatasi<emph.end type="italics"></emph.end> e delle <emph type="italics"></emph>apodisi.<emph.end type="italics"></emph.end> Ma, lasciando stare la forma, il peggio sta nella <lb></lb>sostanza, che ha spesso spesso all&#039;oro antico sostituito l&#039;orpello, per cui non <lb></lb>a torto dissero alcuni il Rivault commentatore infelicissimo. </s>

<s>La quale infe­<lb></lb>licità, più che in altra parte, apparisce intorno alla VIII proposizione del <lb></lb>primo libro <emph type="italics"></emph>De insidentibus humido,<emph.end type="italics"></emph.end> dopo l&#039;enunciazion della quale il Com­<lb></lb>mentatore scrive questo scolio: “ Quoniam huius propositionis antiqua de­<lb></lb>monstratio, quae fuerat Archimedis, ne quidem veteribus translationibus ad <lb></lb>nos pervenit, et quoniam a Federico Commandino suppleta fuerit, ut aliae <lb></lb>quae similiter perierant; visum est eius vestigiis inhaerere primum, deinde <lb></lb>aliam subiungere, erutam ex antea demonstratis ab Archimede, ut magis ac <lb></lb>magis a seipso lumen accipiat ” (Parisiis 1615, pag. </s>

<s>500). </s></p><p type="main">

<s>Le vestigia però del Commandino, che i nostri Lettori hanno oramai <lb></lb>vedute impresse in questa Storia, non è vero sian calcate dal Rivault; che <lb></lb>anzi par che le sciupi, sbadatamente passandovi sopra col suo piede. </s>

<s>Sola­<lb></lb>mente l&#039;ipotesi e il simporasma concordano con la dimostrazione del Mate­<lb></lb>matico di Urbino, il quale del resto si sdegnerebbe che gli fossero fatte dir <lb></lb>cose, tanto più aliene dal vero delle sue, e contro la propria intenzione. </s></p><p type="main">

<s>Sia la sfera dell&#039;umido ABC (fig. </s>

<s>71), e la porzione sferica galleggiante <lb></lb>e inclinata EFH, con la sua inferior parte BZCF immersa, la quale sia dalla <lb></lb><figure id="id.020.01.3180.1.jpg" xlink:href="020/01/3180/1.jpg"></figure></s></p><p type="caption">

<s>Figura 71.<lb></lb>corda BC divisa così in due parti, che l&#039;una <lb></lb>abbia il centro di gravità in Y, e l&#039;altra in Z, <lb></lb>mentre tutto il peso di detta parte immersa <lb></lb>suppongasi concentrato in R, e concentrato <lb></lb>in X il peso di tutto il solido galleggiante. <lb></lb></s>

<s>“ Educta linea a centro Y, dice il Rivault, <lb></lb>ad centrum reliquae partis portionis, quae <lb></lb>manet in aere, quod sit S; transibit neces­<lb></lb>sario per centrum X totius portionis ” (ibid). <lb></lb>La conseguenza è manifestamente falsa, non <lb></lb>essendo possibile che passi per X la linea <lb></lb>congiungente S con Y, ma con R, secondo <lb></lb>la catasasi vera del Commandino, il quale si sarebbe maravigliato che il Ri­<lb></lb>vault gli attribuisse un discorso simile a questo: “ Cum ergo ponderet pars <lb></lb>in humido secundum linam YL, pars vero quae in aerem secundum lineam <lb></lb>SL, et demum tota portio secundum perpendicularem, quae ab X ad L edu­<lb></lb>ceretur; non manebit portio quousque haec tria centra et punctum L, quod <lb></lb>est ceutrum Terrae, recta linea iungantur, quod non fiet quin ambae lineae <lb></lb>LK et FK in unam incidant: scilicet, deorsum ruentibus partibus quae sunt <lb></lb>ad E, et ascendentibus sursum iis quae sunt ad H, secundum diversas li­<lb></lb>neas, quarum situs paulatim movetur quousque radii XS, XY fiant aequales <lb></lb>et aequilibrium accidat. </s>

<s>Vis autem movens in hac titubatione est tam gra­<lb></lb>vitas ponderis, quae aequamentum quaerit, cum premat in diversis centris, <lb></lb>quam humidi ponderositas maior quam sit portionis ” (ibid.). </s></p><pb xlink:href="020/01/3181.jpg" pagenum="142"></pb><p type="main">

<s>Ma, se la ponderosità dell&#039;umido fosse maggiore di quella della por­<lb></lb>zione, dovrebbe questa nell&#039;inclinarsi sollevarsi anche di più, ciò che non è <lb></lb>consentito nè dalla ragione e nè dalla esperienza, per cui falsamente si sup­<lb></lb>pone, che le lunghezze de&#039;raggi XS, XY vadano ad uguagliarsi, perchè av­<lb></lb>venga l&#039;equilibrio. </s>

<s>Questo equilibrio poi si studia il Rivault di ridurlo al­<lb></lb>l&#039;esperienza della Bilancia, rimandando i Lettori a quel che aveva scritto <lb></lb>addietro, in un lungo Scolio, dopo la proposizione VI <emph type="italics"></emph>De quadratura pa­<lb></lb>raboles,<emph.end type="italics"></emph.end> per dimostrare come ragionevolmente supponesse Archimede tirare <lb></lb>i pesi, per così brevi distanze, in direzioni parallele, benche in effetto con­<lb></lb>vergano al centro terrestre. </s>

<s>In quello Scolio dunque così dicevasi dell&#039;equi­<lb></lb>librio della Bilancia, per applicarlo all&#039;equilibrio della porzion galleggiante <lb></lb>di sfera: “ Caeterum duobus modis centra gravitatum et suspensionum, in <lb></lb>eadem perpendiculari constituta, pariunt et aequipondium et ponderum sta­<lb></lb>tum ac quietem: primo, nempe cum in statera radii sunt ponderum reci­<lb></lb>proce proportionales; secundo, cum pondera, sive aequalia sive inaequalia, <lb></lb>et sive in reciprocis radiis, sive in non reciprocis, ita sursum deorsumque <lb></lb>feruntur, ut earum perpendiculares suspensionum, vel quibus gravitant, in <lb></lb>unam conveniant ” (ibid.). </s></p><p type="main">

<s>Come però si possano questi principii statici applicare al teorema idro­<lb></lb>statico di Archimede è dubbio, ripensando che, per avere i pesi in S e in Y <lb></lb>momenti uguali, la bilancia è in condizione di equilibrio indifferente, e perciò <lb></lb>la porzione dovrebbe galleggiando stare così bene o diritta o inclinata, ciò <lb></lb>che pure consegue dalla dimostrazione del Commandino. </s>

<s>Un&#039;aperta discor­<lb></lb>danza poi fra i due commentatori, e più notabile delle altre, apparisce dal <lb></lb>fatto che il Rivault mette i pesi ambedue tendere in giù, mentre il Com­<lb></lb>mandino, stando ad Archimede, faceva solo tendere in giù la parte del gal­<lb></lb>leggiante in aria, e in su l&#039;altra parte sommersa. </s>

<s>Ma, per vedere come il <lb></lb>Francese, dilungandosi dal Nostro, si dilunghi anche di più dalla verità delle <lb></lb>cose; seguitiamolo nel secondo modo di dimostrare, ch&#039;egli crede più con­<lb></lb>facevole colla mente di Archimede. </s></p><p type="main">

<s>La dimostrazione è ridotta a una tale semplicità, che conferisce a ren­<lb></lb>dere l&#039;errore più manifesto. </s>

<s>Siano, come dianzi, la sfera dell&#039;umido e l&#039;emi­<lb></lb>sfero galleggiante HFJ, il cui centro di gravità R, e della parte sommersa <lb></lb>sia centro gravitativo L, della emersa sia M, cosicchè la linea, che congiunge <lb></lb>questi due stessi centri, sia divisa nel punto K (per cui necessariamente <lb></lb>passa) con tal ragione, che il raggio LK, al raggio KM, reciprocamente stia <lb></lb>come la porzione dell&#039;emisferio in aria, alla porzione di lui in acqua: “ quo­<lb></lb>niam L (così, fatta l&#039;ipotesi, passa il Rivault all&#039;apodisi della sua dimostra­<lb></lb>zione) est centrum partis demersae, ponderat secundum perpendicularem EL, <lb></lb>uti non demersa secundum perpendicularem EM; totum vero haemisphae­<lb></lb>rium secundum lineam EK, et puncto K videtur fieri suspensio, et esse li­<lb></lb>bride ML: punctum vero suspensionis G, centrum nempe magnitudinis. </s>

<s><lb></lb>Ergo M, quae sursum est in suspendio, mittetur deorsum, punctum vero <lb></lb>L ascendet sursum, ita ut tandem tria puncta E, K, G abeant in rectam <pb xlink:href="020/01/3182.jpg" pagenum="143"></pb>lineam, et sit axis FG in perpendiculari EK, ut vult propositio ” (ibid., <lb></lb>pag. </s>

<s>501). </s></p><p type="main">

<s>La necessità del costituirsi i punti L, M nella medesima verticale col <lb></lb>punto K di sospensione, la fa conseguire il Rivault dal secondo principio <lb></lb>statico, formulato nello Scolio dopo la VI proposizione del Tetragonismo della <lb></lb>parabola: principio, che non è però applicabile, se non al caso che i mo­<lb></lb>menti intorno al punto di sospensione siano diversi, perchè allora prevalendo <lb></lb>il maggiore, e facendo abbassare la bilancia dalla sua parte, la fa necessa­<lb></lb>riamente sollevare dall&#039;altra. </s>

<s>Ma come può esser questo il motivo della re­<lb></lb>stituzione nell&#039;emisfero inclinato, se i momenti, stando le gravità per ipo­<lb></lb>tesi reciprocamente come le distanze, sono uguali, in piena conformità col <lb></lb>primo principio statico, formulato nel detto scolio? </s>

<s>In questo caso, comun­<lb></lb>que l&#039;emisfero s&#039;inclini, ivi si rimarrebbe allo stesso modo che dianzi eretto, <lb></lb>come la bilancia di momenti uguali, e col centro di gravità nel punto della <lb></lb>sospensione, si rimane indifferentemente, comunque sia volta. </s></p><p type="main">

<s>Anche apparisce di qui più espressamente tendere in basso ambedue le <lb></lb>forze applicate in M e in L, secondo il Rivault, il quale non sa compren­<lb></lb>dere come Archimede, e il Commandino che lo segue, possano aver detto <lb></lb>che il punto L è spinto in su. </s>

<s>“ Possemus, sicut Archimedes, dicere M ferri <lb></lb>deorsum, et L ferri sursum, et tandem axem GF uniri perpendiculari EK, <lb></lb>verum unde fiat elatio puncti L sursum non videtur constare ” (ibid., pag. </s>

<s>501). <lb></lb>Sarebbe potuto ciò constare dalla seconda supposizione, se avesse inteso il Ri­<lb></lb>vault a qual fine Archimede, invece di aggiungerla alla prima in principio <lb></lb>del primo libro, la mettesse a mezzo, innanzi alla proposizione VIII. </s>

<s>Il no­<lb></lb>vello sapiente volle insegnare all&#039;antico Maestro com&#039;avrebbe dovuto ordinar <lb></lb>meglio il suo libro: “ Hanc positionem, egli dice, Archimedes subiungit post <lb></lb>VIII propositionem huius. </s>

<s>Ego vero malui hic adponere, tum quod positio­<lb></lb>num ut datarum hic locus sit, tum quia etiam primis propositionibus deser­<lb></lb>vit. </s>

<s>Caeterum Archimedes posuerat tantum de iis quae sursum feruntur; <lb></lb>ego vero addidi, et de iis quae deorsum tendunt ” (ibid., pag. </s>

<s>492). E in­<lb></lb>fatti così, con incredibile temerità, sciaguattava in queste parole la limpi­<lb></lb>dezza del pensiero archimedeo: “ Ponatur eorum, quae in humido sursum <lb></lb>vel deorsum feruntur, unumquodque sursum vel deorsum ferri, secundum <lb></lb>perpendicularem, quae per centrum gravitatis ipsorum ducitur ” (ibid.). </s></p><p type="main">

<s>Questo era, per servirsi di un&#039;altra immagine, un ridurre l&#039;ingegno ela­<lb></lb>boratissimo della chiave alla uniforme crassizie del martello, ond&#039;ei non è <lb></lb>maraviglia se il Rivault, invece di aprir la porta, l&#039;andò tormentando con <lb></lb>inutili colpi, e, come altre volte si disse, volse in peggio le illustrazioni o le <lb></lb>divinazioni del Commandino. </s>

<s>Da questa parte perciò ne, sembra assai com­<lb></lb>mendevole Isacco Barrow che, nel suo libro <emph type="italics"></emph>Archimedis opera methodo nova <lb></lb>illustrata, et succincte demonstrata,<emph.end type="italics"></emph.end> venendo al <emph type="italics"></emph>De insidentibus humido,<emph.end type="italics"></emph.end><lb></lb>restituì la supposizione seconda al suo luogo, come in questo, così nel rima­<lb></lb>nente protestandosi di seguir l&#039;orme di quel Federigo Commandino, <emph type="italics"></emph>de li­<lb></lb>teris hisce optime meritum<emph.end type="italics"></emph.end> (Londini 1675, pag. </s>

<s>245), da cui compendiò il <pb xlink:href="020/01/3183.jpg" pagenum="144"></pb>modo di dimostrare l&#039;VIII proposizione, e così dietro lui la concluse: “ Cum <lb></lb>igitur pars immersa sursum feratur secundum rectam EL (nella medesima <lb></lb>figura 72) pars vero extans deorsum, secundum ME, neque hae lationes sibi <lb></lb>invicem ullatenus obsistant, utpote per alias, aliasque lineas peractae; non <lb></lb><figure id="id.020.01.3183.1.jpg" xlink:href="020/01/3183/1.jpg"></figure></s></p><p type="caption">

<s>Figura 72.<lb></lb>quiescet portio donec haec centra, cum cen­<lb></lb>tro terrae, in unam rectam incidant: hoc <lb></lb>est, donec axis GF sit secundum perpendi­<lb></lb>cularem. </s>

<s>Tum vero quiescent, quia quanto <lb></lb>impetu quae in humido est pars sursum, <lb></lb>tanto quae extra deorsum per eamdem li­<lb></lb>neam contendit ” (ibid., pag. </s>

<s>249). </s></p><p type="main">

<s>Pare impossibile che un sì gran ma­<lb></lb>tematico, qual&#039;era il maestro del Newton, <lb></lb>si fosse così lasciato irretire ne&#039;paralogismi <lb></lb>del Commandino, a sciogliersi da&#039;quali sa­<lb></lb>rebbegli bastato osservare che l&#039;impeto, fatto <lb></lb>in su dall&#039;umido, non eguaglia quello fatto <lb></lb>in giù dalla sola parte emersa, ma da tutta intera la porzione sferica, se­<lb></lb>condo che Archimede stesso aveva poco innanzi insegnato, nella sesta pro­<lb></lb>posizione. </s>

<s>Ma pure è un fatto che, sebbene il Barrow ammetta col Comman­<lb></lb>dino essere il punto L respinto in su, nonostante anch&#039;egli fra sè diceva: <lb></lb><emph type="italics"></emph>Verum unde fiat elatio ista sursum non videtur constare,<emph.end type="italics"></emph.end> ciò che si con­<lb></lb>ferma dalla seguente nota, nella quale, come dimostra di partecipare ai dubbi <lb></lb>del Rivault, così si studia di acquetarsi la mente nelle medesime o in simili <lb></lb>soluzioni. </s>

<s>“ Recta LM lìbram repraesentat, in qua duo gravia BFC, HBCI <lb></lb>diversimode ponderant (levior est enim pars immersa illa quae extat). Su­<lb></lb>spensio fit ex puncto K, radii sunt KL, KM. </s>

<s>Descendit M, attolletur L, donec, <lb></lb>puncto K in EG constituto, contingat aequilibrium ” (ibid.). </s></p><p type="main">

<s>L&#039;espressione <emph type="italics"></emph>diversimode ponderant,<emph.end type="italics"></emph.end> e il far consistere la diversità del <lb></lb>modo nella maggior leggerezza, ne fa ragionevolmente argomentare che il <lb></lb>Barrow in questo tenesse più col Rivault, che col Commandino, per cui non <lb></lb>fa maraviglia se in seguito, abbandonato affatto il commentatore di Urbino, <lb></lb>si tenesse dietro dai più a quell&#039;altro di Fluranzia. </s>

<s>Anche in Italia se n eb­<lb></lb>bero vari esempi, fra&#039;quali basti a noi citare il seguente. </s>

<s>Quando si fece la <lb></lb>Raccolta fiorentina degli <emph type="italics"></emph>Autori, che trattano del moto delle acque,<emph.end type="italics"></emph.end> il primo <lb></lb>posto naturalmente fu riserbato a Archimede. </s>

<s>E perchè tutti i trattati, in <lb></lb>qualunque lingua fossero originalmente scritti, dovevan esser tradotti nella <lb></lb>italiana, fu la traduzione del <emph type="italics"></emph>De insidentibus humido<emph.end type="italics"></emph.end> affidata all&#039;elegante <lb></lb>penna di Giovanni Bottari, il quale, non sentendosi così forte in matematica, <lb></lb>come in letteratura, condusse l&#039;opera con l&#039;assistenza di Guido Grandi. </s>

<s>Il <lb></lb>qual Grandi poi non si fece nessuno scrupolo di seguire il Rivault nella te­<lb></lb>merità e ne&#039;falli. </s>

<s>Tolse perciò anch&#039;egli la seconda petizione dal suo proprio <lb></lb>luogo, e la fece succedere alla prima, in principio del libro, rimpastandovi <lb></lb>i moti <emph type="italics"></emph>sursum<emph.end type="italics"></emph.end> coi <emph type="italics"></emph>deorsum,<emph.end type="italics"></emph.end> come aveva fatto colui, che aveva preso ad esem-<pb xlink:href="020/01/3184.jpg" pagenum="145"></pb>pio, e da cui lasciò che il Bottari traducesse così fedelmente la restaurata <lb></lb>VIII proposizione: </s></p><p type="main">

<s>“ Sia la parte BFC (nella medesima figura 72) della porzione sferica <lb></lb>HFI, immersa nel liquido ABC. </s>

<s>E perchè il centro di gravità della detta por­<lb></lb>zione è nell&#039;asse FG, sia il punto K, e si congiunga L, centro della parte <lb></lb>immersa, con M, centro della parte che resta fuori, con una retta linea, che <lb></lb>passi pel centro K di tutta la porzione sferica, e sarà obliqua alla linea FG, <lb></lb>supponendosi la figura inclinata. </s>

<s>E perchè L è centro della parte sommersa, <lb></lb>questa farà forza in giù per la EL, perpendicolare al liquido, e la parte emer­<lb></lb>gente per la perpendicolare ME, posto E centro della terra, e tutta la por­<lb></lb>zione sferica graviterà per la linea EK. </s>

<s>Adunque nel punto K si fa la so­<lb></lb>spensione della libbra ML, ed M, che nella libbra è in su, scenderà, e per <lb></lb>conseguenza salirà L, sicchè i tre punti E, K, G rimangano in una linea <lb></lb>retta, e venga l&#039;asse FG soprapposta alla perpendicolare EK. </s>

<s>Adunque ecc. </s>

<s>” <lb></lb>(<emph type="italics"></emph>Raccolta cit.,<emph.end type="italics"></emph.end> Ediz. 2a, T. I, Firenze 1755, pag. 5). </s></p><p type="main">

<s>Ecco come, in un secolo e mezzo, vennero a imbozzacchire i dolci pomi <lb></lb>dello Stevino. </s>

<s>Se ne attribuirà forse la causa all&#039;essersi condotta per vie <lb></lb>oblique, come si disse, l&#039;Acrobatica di lui: e senza dubbio, se avesse a di­<lb></lb>rittura chiamato centro della pressione quello, ch&#039;egli volle chiamar piutto­<lb></lb>sto <emph type="italics"></emph>centro di gravità della fossa,<emph.end type="italics"></emph.end> sarebbesi fatto intendere assai meglio, e <lb></lb>avrebbe ovviato all&#039;errore del credersi che ambedue le forze tendessero in <lb></lb>giù al centro della Terra, come vi tendono tutte le gravità naturali. </s>

<s>Ma, a <lb></lb>rendere il magistero dello Stevino inefficace, conferì un altro magistero, che <lb></lb>gli successe, e che rimase trionfatore per un complesso di cause, che lungo <lb></lb>sarebbe e difficile a dire, ma principalmente per la seduzion dell&#039;eloquio, e per <lb></lb>essersi l&#039;Autore, con l&#039;uso del canocchiale, e presa occasione dal discorrer <lb></lb>delle galleggianti, fatto messaggero alla terra di nuovi mondi celesti. </s>

<s>Del resto <lb></lb>Galileo aveva alla scienza spennate le ali, che lo Stevino avevale felicemente <lb></lb>restituite, per farla risalire alle alture archimedee. </s>

<s>Questi argomenti per l&#039;ar­<lb></lb>duo volo consistevano nel principio della composizione delle forze parallele, <lb></lb>nel metodo degl&#039;indivisibili, e principalmente nel fatto dell&#039;uguaglianza delle <lb></lb>pressioni: argomenti, de&#039;quali, come Archimede aveva fatto uso, così furono <lb></lb>restaurati tutti dallo Stevino. </s></p><p type="main">

<s>Non giova qui ripetere quali, e quanto gravi danni ricevessero le dot­<lb></lb>trine dei moti composti e degli indivisibili negli insegnamenti di Galileo, per <lb></lb>trattenerci intorno a ciò, che più nocque ai progressi dell&#039;Idrostatica, volu­<lb></lb>tasi incautamente ridurre tutta alle leggi della Statica pura. </s>

<s>Così avvenne che <lb></lb>de&#039;liquidi, come de&#039;solidi, non si considerò altro che il peso, e trascuratasi <lb></lb>la mobilità delle particelle, di che sono essi liquidi composti, e in cui con­<lb></lb>siste il dirsi e l&#039;essere propriamente tali; si confusero con i centri di gra­<lb></lb>vità i centri delle pressioni. </s>

<s>Esaminando infatti a qual principio s&#039;informano <lb></lb>le dimostrazioni di Galileo si troverà che il liquido, secondo lui, non reagi­<lb></lb>sce attivamente, ma solo resiste al solido immerso, e non gli resiste per al­<lb></lb>tro, che per contrapporgli il suo proprio peso. </s>

<s>Fu tale poi il principio stesso, <pb xlink:href="020/01/3185.jpg" pagenum="146"></pb>che prevalse nelle scuole, e che fece sventuratamente smarrir la via, per la <lb></lb>quale l&#039;Idrostatica era stata rimessa dallo Stevino. </s>

<s>L&#039;esempio di ciò più no­<lb></lb>tabile lo abbiamo nel Rivault, il quale essere imbevuto degli insegnamenti <lb></lb>galileiani si mostra nello scolio, ch&#039;egli scrisse dopo la proposizione I del <lb></lb>secondo libro <emph type="italics"></emph>De insidentibus humido.<emph.end type="italics"></emph.end> Conforme a questi insegnamenti è la <lb></lb>ragione, ch&#039;egli ivi adduce del non saper comprendere come Archimede dica <lb></lb>che il centro della parte sommersa della porzione sferica è spinto in alto. <lb></lb></s>

<s>“ Nam, licet magnitudo humido levior assurgat tanta vi, quanto humidum, <lb></lb>molem habens magnitudini aequalem, gravius est ipsa magnitudine; tamen <lb></lb>elatio fit potius ex gravitate magnitudinis immersae, quae centrum quaerit, <lb></lb>quam ex impulsione humidi ” (Archim., Op. </s>

<s>cit., pag. </s>

<s>501). </s></p><p type="main">

<s>La negazione dell&#039;impulsione dell&#039;umido, e la sua resistenza passiva, <lb></lb>erano conseguenze necessarie della statica del vette, invocata da Galileo, e <lb></lb>alla resistenza della quale da una parte si contrappone la potenza dall&#039;altra. </s>

<s><lb></lb>Consiste in ciò principalmente, come s&#039;è detto più volte, il vizio radicale <lb></lb>delle istituzioni idrostatiche di lui, ma è quasi per una infezione di questo <lb></lb>stesso vizio, che si dice l&#039;umido non premere che in giù, e non gravitare <lb></lb>in sè stesso, come nè l&#039;aria o altro fluido si insegnava non esser gravi nel <lb></lb>loro proprio elemento. </s>

<s>Ripensando ai quali dannosissimi errori, s&#039;intenderà <lb></lb>qual grave e geloso ufficio lasciasse Galileo a&#039;suoi discepoli, i quali l&#039;adem­<lb></lb>pirono con filosofica libertà, per amor del vero, rinunziando a ogni ossequio, <lb></lb>come passeremo a narrare nel seguente capitolo di storia, in cui sembrerà <lb></lb>di veder descritta l&#039;opera lunga e affannosa di quei, che si affaccendassero <lb></lb>intorno a una nave, per riaverla dal fondo e rimetterla in corso, squarciate <lb></lb>le vele, scavigliati i remi, e rotto o irrigidito sui cardini il timone. </s></p><pb xlink:href="020/01/3186.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO III.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Dei ravviamenti e dei progressi fatti dall&#039;Idrostatica <lb></lb>dopo le istituzioni di Galileo<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>De&#039;teoremi di Archimede, non assolutamente veri, se non quando, sopra l&#039;umida superficie, sia <lb></lb>il vuoto. </s>

<s>— II. </s>

<s>Di ciò che specularono i Matematici, e sperimentarono i Fisici, per dimostrare, <lb></lb>contro i Peripatetici e contro Galileo, che l&#039;acqua, l&#039;aria e ogni altro fluido pesa anche nel suo <lb></lb>proprio elemento. </s>

<s>— III. Dell&#039;equilibrio de&#039;liquidi fra loro: de&#039;promotori. </s>

<s>e degli oppositori al <lb></lb>metodo usato da Galileo per dimostrarlo. </s>

<s>— IV. Dell&#039;equilibrio de&#039;liquidi co&#039;solidi immersi, e <lb></lb>come, riconosciuto fallace il nuovo metodo usato da Galileo per dimostrarlo, si tornasse all&#039;an­<lb></lb>tico di Archimede. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quel che rimaneva a fare ai discepoli di Galileo, per ravviare la scienza <lb></lb>sulla rettitudine dei sentieri, da cui l&#039;aveva fatta traviare il Maestro, ridu­<lb></lb>cevasi dunque a riconoscere principalmente l&#039;insufficienza della statica della <lb></lb>leva, applicata a dimostrare le leggi dell&#039;equilibrio de&#039;liquidi, con sè stessi <lb></lb>comunicanti e co&#039;solidi immersi. </s>

<s>S&#039;incominciò dal dubitare se fosse vero il <lb></lb>principio delle velocità virtuali, introdotto da Galileo nella scienza degli equi­<lb></lb>librii, e alcuni lo ripudiarono come non a proposito delle dimostrazioni, per <lb></lb>le quali, o tornarono agli antichi modi di Archimede, o gli promossero col <lb></lb>principio della composizion delle forze, o paragonando i liquidi ai solidi, ri­<lb></lb>dotti in una polvere di minutissime ed esattissime sfere. </s>

<s>Altri però accetta­<lb></lb>rono quel principio, purchè però si trattassero le velocità virtuali, non co&#039;me­<lb></lb>todi antichi, ma con quello degl&#039;indivisibili, da cui mostrarono di ricavarne <lb></lb>ottimi servigi, fra&#039;quali anche quello di riuscire a dar matematica dimostra­<lb></lb>zione del principio dell&#039;uguaglianza delle pressioni. </s>

<s>Concorsero a esercitarsi <lb></lb>intorno a una tale varietà di argomenti i cultori dell&#039;Idrostatica, dopo le isti­<lb></lb>tuzioni di Galileo, per tutto il rimanente secolo XVII: e avendo avuto quei <pb xlink:href="020/01/3187.jpg" pagenum="148"></pb>loro esercizi la prima occasione e l&#039;impulso dalla proposta di un quesito, la <lb></lb>soluzion del quale fu di grande importanza; vuol di qui perciò cominciare <lb></lb>il presente capitolo di storia. </s></p><p type="main">

<s>Nel più volgar modo di dimostrare i teoremi di Archimede, e special­<lb></lb>mente il VII, s&#039;immagina che lo spazio occupato dal solido rimanga vuoto, <lb></lb>e che poi sia riempito di altrettanto liquido. </s>

<s>Similmente nell&#039;esperienza, per <lb></lb>trovare le gravità specifiche, o secondo il modo narrato da Vitruvio, per ri­<lb></lb>solvere il problema della corona, o con l&#039;uso della Bilancetta, si suppone che <lb></lb>il peso dell&#039;acqua versata, e di cui s&#039;alleggerisce il contrappeso dello stru­<lb></lb>mento, corrisponda esattamente al peso della mole liquida, in luogo della <lb></lb>quale è sottentrato il solido immerso. </s>

<s>Ma è da fare intorno a ciò un&#039;osser­<lb></lb>vazione importante, ed è che lo spazio scavato in seno al liquido, nel primo <lb></lb>caso, è rimasto assolutamente vuoto, come, nel secondo, il solido sottentra <lb></lb>in uno spazio, che deve esser pure, in forza della supposizione, assoluta­<lb></lb>mente vuoto. </s>

<s>Ond&#039;ei non par vero che la mole d&#039;acqua, la quale stava den­<lb></lb>tro al vaso in perfetto vuoto, pesi precisamente tanto, quanto versata fuori, <lb></lb>e gravitante nel mezzo dell&#039;aria. </s></p><p type="main">

<s>Si può il presente discorso dichiarar meglio con l&#039;esempio della Bilan­<lb></lb>cia idrostatica, parata a quel modo che tutti sanno, per dimostrar la seconda <lb></lb>parte della VII proposizione archimedea. </s>

<s>Si chiami P il contrappeso del ci­<lb></lb><figure id="id.020.01.3187.1.jpg" xlink:href="020/01/3187/1.jpg"></figure></s></p><p type="caption">

<s>Figura 73.<lb></lb>lindro A (fig. </s>

<s>73) e del secchio B in aria. </s>

<s><lb></lb>Immerso il detto cilindro, che si suppone <lb></lb>essere in tale stato ridotto al peso <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> e re­<lb></lb>stituito l&#039;equilibrio, col riempire il secchio <lb></lb>del medesimo liquido di quello, in cui si fa <lb></lb>l&#039;immersione, e che sia di peso <emph type="italics"></emph>p′<emph.end type="italics"></emph.end>; si os­<lb></lb>servi che, nell&#039;infondere in esso secchio il <lb></lb>liquido, è stata scacciata l&#039;aria, che dentro <lb></lb>ci gravava, con un tal peso, quale poniamo <lb></lb>sia <emph type="italics"></emph>p″,<emph.end type="italics"></emph.end> ond&#039;è che avremo <emph type="italics"></emph>p+p′—p″<emph.end type="italics"></emph.end>=P, <lb></lb>ossia <emph type="italics"></emph>p<emph.end type="italics"></emph.end>=P—(<emph type="italics"></emph>p′—p″<emph.end type="italics"></emph.end>). Dunque il so­<lb></lb>lido cilindro non è alleggerito solamente del <lb></lb>peso <emph type="italics"></emph>p<emph.end type="italics"></emph.end> di una mole liquida, uguale a quella <lb></lb>che ha egli stesso, ma di <emph type="italics"></emph>p′—p″,<emph.end type="italics"></emph.end> ossia della differenza tra la detta mole <lb></lb>liquida, e una corrispondente mole di aria. </s>

<s>La qual mole di aria si può forse <lb></lb>da&#039;Fisici reputare di peso insensibile, ma è l&#039;esperienza stessa trasformabile <lb></lb>in modo, da provar anche fisicamente che la perdita del peso, subita dal corpo <lb></lb>immerso, non è quale propriamente dice Archimede, ma quale nella sopra <lb></lb>scritta formula fu conclusa. </s>

<s>S&#039;immagini infatti d&#039;operare con la Bilancia in <lb></lb>un&#039;ammosfera di olio, galleggiante sopra l&#039;acqua del vaso C o in un&#039;am­<lb></lb>mosfera di acqua, galleggiante sopra il mercurio, di cui si fosse ripieno il <lb></lb>medesimo vaso. </s>

<s>Allora il secchio, votandosi d&#039;olio e riempiendosi d&#039;acqua <lb></lb>nel primo caso, o votandosi d&#039;acqua e riempiendosi di mercurio nel secondo, <lb></lb>è manifesto che il valore di <emph type="italics"></emph>p″,<emph.end type="italics"></emph.end> ossia di tant&#039;olio o di tant&#039;acqua, quanta ne <pb xlink:href="020/01/3188.jpg" pagenum="149"></pb>può capire nel secchio, non dovrebb&#039;essere insensibile a nessuna Bilancia, e <lb></lb>riuscirebbe perciò necessariamente fallace l&#039;esperienza di chiunque lo tra­<lb></lb>scurasse. </s>

<s>Or, dovendo essere i teoremi idrostatici universalmente veri, vien <lb></lb>di qui a proporsi il quesito che si diceva: Son da accusar forse di false le <lb></lb>cose dimostrate nel primo libro <emph type="italics"></emph>De insidentibus humido,<emph.end type="italics"></emph.end> o si verificano so­<lb></lb>lamente negli umidi non costituiti in aria, ma nel vuoto assoluto? </s></p><p type="main">

<s>La risposta era stata data da quel sottilissimo ingegno dello Stevino. </s>

<s><lb></lb>Chi, al primo aprire il libro degli <emph type="italics"></emph>Elementi<emph.end type="italics"></emph.end> di lui, legge, fra le numerose <lb></lb>definizioni scritte, le ultime due, cioè la XI e la XII: <emph type="italics"></emph>Vuide est un lieu <lb></lb>ou il n&#039;y a nul corps — Vuide est un vase ou il n&#039;y a que de l&#039;air de­<lb></lb>dans;<emph.end type="italics"></emph.end> e dopo queste passa alla petizione prima che dice: <emph type="italics"></emph>La pesanteur pro­<lb></lb>pre d&#039;un corps soit celle, de la quelle il est trouvé estre pesant en l&#039;air, <lb></lb>mais dans l&#039;eau qu&#039;elle soit dite sa constitution en icelle;<emph.end type="italics"></emph.end> chi legge que­<lb></lb>ste cose, voleva dirsi, può crederle prenozioni superflue, o avvertenze scru­<lb></lb>polose, e perciò disprezzate dagli autori moderni. </s>

<s>Ma poi quando uno giunge <lb></lb>a intendere il fine, per cui tali definizioni e petizioni s&#039;eran premesse, è co­<lb></lb>stretto a confessare che gli stessi moderni autori son trascurati, e che la loro <lb></lb>scienza non giunge a quella precisione mirabile, e a quella finezza, con cui, <lb></lb>tre secoli prima, l&#039;aveva trattata il Matematico di Bruges. </s>

<s>Egli propone così, <lb></lb>nel suo libro <emph type="italics"></emph>Des elemens hydrostatiques,<emph.end type="italics"></emph.end> il VII teorema: “ Tout corps so­<lb></lb>lide est plus leger dans l&#039;eau, qu&#039;en l&#039;air, de la pesanteur de l&#039;eau egale en <lb></lb>grandeur a iceluy ” (pag. </s>

<s>487), e lo dimostra supponendo che sia dentro <lb></lb>l&#039;acqua scavata una fossa, esattamente capace del solido, il quale deve dun­<lb></lb>que trovarvisi in mezzo tanto men grave, quanto era il peso dell&#039;acqua vo­<lb></lb>tata. </s>

<s>Intorno al qual vuoto rimasto occorrono a fare le osservazioni accen­<lb></lb>nate di sopra, e che lo Stevino stesso fa nel capitolo V dell&#039;<emph type="italics"></emph>Appendice de <lb></lb>la Statique.<emph.end type="italics"></emph.end> A vederlo procedere snello e sicuro per il lubrico, sopra cui Ga­<lb></lb>lileo tante volte scivolò e cadde, ne vien voglia di far risonare alle orecchie <lb></lb>dei nostri lettori, nella loro integrità, le parole di lui, benchè non brevi, ac­<lb></lb>ciocchè riconoscano quanto immeritamente fossero dimenticate. </s></p><p type="main">

<s>“ Il a esté dit, en la susdite VIII proposition, <emph type="italics"></emph>que tout corps solide est <lb></lb>d&#039;autant plus leger dans l&#039;eau qu&#039;en l&#039;air qu&#039;emporte la pesanteur de l&#039;eau <lb></lb>égale a iceluy.<emph.end type="italics"></emph.end> D&#039;ou quelqu&#039;un voudroit tirer en consequence que <emph type="italics"></emph>tout corps <lb></lb>solide est d&#039;autant plus leger dans l&#039;argent-vif qu&#039;en l&#039;eau qu&#039;emporte la <lb></lb>pesanteur de l&#039;argent-vif egal a iceluy.<emph.end type="italics"></emph.end> Ou bien ainsi: <emph type="italics"></emph>que tout corps so­<lb></lb>lide est d&#039;autant plus leger dans l&#039;eau qu&#039;en l&#039;huile qu&#039;emporte la pesan­<lb></lb>teur de l&#039;eau egale a iceluy.<emph.end type="italics"></emph.end> Et ainsi des autres, les quelles consequences <lb></lb>necessaires sembleroyent du commencement estre contre l&#039;experience. </s>

<s>Car <lb></lb>une livre de plomb ne sera (selon la maniere ordinaire) pas plus legere dans <lb></lb>l&#039;eau qu&#039;en l&#039;huile qu&#039;emporte le pesanteur de l&#039;eau egale a iceluy, mais seu­<lb></lb>lement plus legere que la difference des deux corps d&#039;eau et d&#039;huyle egaux <lb></lb>à iceluy. </s>

<s>Toutefois regardant de plus près, et posant les choses, comme on <lb></lb>dit <emph type="italics"></emph>ceteris paribus,<emph.end type="italics"></emph.end> le tout se trouvera estre en son extreme perfection. </s>

<s>Car <lb></lb>il faut remarquer qu&#039;en la premiere petition des <emph type="italics"></emph>Elemens hydrostatique<emph.end type="italics"></emph.end> on <pb xlink:href="020/01/3189.jpg" pagenum="150"></pb>requiert que <emph type="italics"></emph>la pesanteur des corps en l&#039;air soit dite estre leur propre.<emph.end type="italics"></emph.end> Et <lb></lb>en la cinquiesme <emph type="italics"></emph>que le vasiforme plein d&#039;eau estant icelle ostée demeure <lb></lb>vuide,<emph.end type="italics"></emph.end> c&#039;est a dire plein d&#039;air selon la XI definition. </s>

<s>Partant prenant que les <lb></lb>deux moyens, argent-vif et eau, soyent en la place des autres, qui sont l&#039;eau <lb></lb>et l&#039;air, assavoir l&#039;argent-vif au lleu de l&#039;eau, et l&#039;eau au lieu de l&#039;air; on <lb></lb>poutra faire de telles petitions: <emph type="italics"></emph>Que la propre pesanteur des corps soit celle <lb></lb>qu&#039;ils ont en l&#039;eau. </s>

<s>Aussi le vasiforme plein d&#039;argent-vif estant vuide de­<lb></lb>meure plein d&#039;eau.<emph.end type="italics"></emph.end> Alors les propositions susdites au commencement seront <lb></lb>veritables. </s>

<s>Et prenant le cas qu&#039;un homme soit bien profondement sous l&#039;eau <lb></lb>ayant une Balance, de l&#039;or aussi et de l&#039;argent-vif, que l&#039;eau luy soit comme <lb></lb>a nous l&#039;air, alors il est certain que l&#039;or sera d&#039;autant plus leger dans l&#039;ar­<lb></lb>gent-vif qu&#039;en l&#039;eau, qu&#039;emporte la pesanteur de l&#039;argent-vif egal a iceluy. </s>

<s>Il <lb></lb>est bien vray que si l&#039;on prenoit que <emph type="italics"></emph>la vraye pesanteur des corps dans le <lb></lb>vuide soit leur propre,<emph.end type="italics"></emph.end> comme il est en simple apparence, on pourroit dite <lb></lb>que <emph type="italics"></emph>tout corps est d&#039;autant plus leger en l&#039;eau, qu&#039;au vuide, qu&#039;emporte <lb></lb>la pesanteur d&#039;eau egale a iceluy.<emph.end type="italics"></emph.end> Mais remarquant les circostances de no­<lb></lb>stre maniere vulgaire à peser (a la quelle la theorie doit tousiours aspirer) <lb></lb>ne se fait pas au vuide, mais en l&#039;air; il sera donc plus a propos de dire, <lb></lb>selon la premiere maniere, que la propre pesanteur des corps est faite en <lb></lb>l&#039;air. </s>

<s>Et au regard d&#039;icelle la VIII proposition susdite, et celles qui s&#039;en en­<lb></lb>suivent, sont en leur extreme perfection, comme nous avions entrepis de <lb></lb>declairer ” (Ouvrages cit., pag. </s>

<s>503). </s></p><p type="main">

<s>Dalla qual dichiarazione si rileva la risposta al proposto quesito: rispo­<lb></lb>sta che, per detto dello Stevino, è tale: I teoremi dimostrati da Archimede <lb></lb>son veri fisicamente, ossia secondo il comun modo di pesare, che da noi si <lb></lb>fa sempre nell&#039;aria. </s>

<s>Matematicamente però non si verificano, se non che <lb></lb>quando l&#039;umido, o le solide grandezze che vi galleggiano, o che vi s&#039;immer­<lb></lb>gono, siano costituite nel vuoto. </s></p><p type="main">

<s>La medesima questione, risoluta così dal Fisico olandese, tornò, sessanta <lb></lb>anni dopo, ad agitarsi in Italia, a proposito di un dubbio nato parecchio tempo <lb></lb>prima (ne&#039;primi cinque mesi dell&#039;anno 1627) in alcuni studiosi di Archi­<lb></lb>mede, nuovamente illustrato da Galileo: se cioè l&#039;acqua, aggiunta all&#039;ar­<lb></lb>gento vivo, faccia che il ferro o si rimanga o s&#039;attuffi o galleggi maggior­<lb></lb>mente. </s>

<s>Alcuni, ripensando che i Teoremi archimedei erano assoluti, ne con­<lb></lb>cludevano che il ferro si rimarrebbe: altri dicevano che, gravato dal peso <lb></lb>dell&#039;acqua, s&#039;affonderebbe di più: altri poi invece che, per la circumpulsione <lb></lb>dell&#039;acqua stessa sopra infusavi, si solleverebbe di alquanto. </s>

<s>Fu proposta dai <lb></lb>disputanti a dimostrare la verità al venerato comun loro maestro Benedetto <lb></lb>Castelli, il quale decise che il ferro si solleverebbe, e anche determinò se­<lb></lb>condo qual proporzione. </s></p><p type="main">

<s>Del sollevamento era facile ritrovar la ragione, a quel modo che poi fece <lb></lb>il Viviani, in una bozza di teorema, dove dice “ che, se sia il ferro infuso <lb></lb>nell&#039;argento vivo sino a un certo livello, sopranfusagli acqua, sicchè lo rico­<lb></lb>pra abbondantemente, tal solido di ferro si solleverà ancora più di prima ” <pb xlink:href="020/01/3190.jpg" pagenum="151"></pb>(MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>44) e la ragione di ciò la ritrovò semplicis­<lb></lb>sima, osservando che la parte del ferro emersa, per trovarsi più leggera nel­<lb></lb>l&#039;acqua che nell&#039;aria, come più leggera dunque sarebbesi sollevata alquanto <lb></lb>più nell&#039;argento vivo, e perciò insieme con lei si solleverebbe anche tutto <lb></lb>il ferro. </s>

<s>Ma secondo qual proporzione farebbesi un tale sollevamento era più <lb></lb>difficile inchiesta. </s>

<s>Il Baliani la discorreva così col Castelli, ringraziandolo del­<lb></lb>l&#039;offerta fattagli della risoluzion del quesito: “ Se il ferro non fosse più grave <lb></lb>dell&#039;acqua non è dubbio che in tal caso sarebbe tutto fuori dell&#039;argento vivo. </s>

<s><lb></lb>Ma perchè è più grave uscirà fuori dell&#039;argento vivo alla rata, cioè per l&#039;ot­<lb></lb>tava parte della sua propria quantità, attesochè il ferro pesa più dell&#039;acqua <lb></lb>otto volte tanto, come sa meglio di me ” (Alb. </s>

<s>IX, 144). </s></p><p type="main">

<s>Questa soluzion del Baliani però si prevede facilmente che doveva essere <lb></lb>sbagliata, perch&#039;egli non attese se non a ciò che il ferro, circumpulso più <lb></lb>in su dall&#039;acqua che non dall&#039;aria, anche di più s&#039;alleggerisce, senza punto <lb></lb>pensare che l&#039;alleggerimento si fa sentire in una bilancia, sopra cui gravano <lb></lb>insieme il mercurio e l&#039;acqua. </s>

<s>Di qui è che esso ferro non uscirà fuori alla <lb></lb>rata della sola gravità specifica dell&#039;acqua, ma di quella di lei e del mer­<lb></lb>curio: o, per usare il linguaggio de&#039;moderni, la proporzione del solleva­<lb></lb>mento non sarà data in funzione della gravità specifica del solo liquido <lb></lb>sopra infuso, ma e del liquido soggiacente altresì, fra&#039;quali due il solido gal­<lb></lb>leggia. </s></p><p type="main">

<s>Il fallo del Baliani, e in cui tanti altri erano caduti insieme con lui, <lb></lb>fece, ne&#039;discepoli e negli amici del Castelli, nascere il desiderio <emph type="italics"></emph>di veder la <lb></lb>dimostrazione più distinta<emph.end type="italics"></emph.end> (ivi) datane da lui, il quale perciò la distese or­<lb></lb>dinatamente, aggiuntovi un corollario importante, in una scrittura, dedicata <lb></lb>a Giovanni Ciampoli, e che noi vogliamo produrre qui alla notizia dei nostri <lb></lb>Lettori. </s></p><p type="main">

<s>“ Il quesito, che mi fu fatto intorno alla materia delle cose, che stanno <lb></lb>nell&#039;umido, trattata da Archimede, e dal signor Galileo, nel suo particolare <lb></lb>Discorso; fu di questo tenore: Il ferro, per essere meno grave in spezie del­<lb></lb>l&#039;argento vivo, non si sommerge tutto, ma parte di esso resta fuori dell&#039;ar­<lb></lb>gento vivo, e parte ne resta tuffato. </s>

<s>Ora si ricerca se, infondendosi acqua nel <lb></lb>vaso, dove stiano come si è detto i medesimi corpi, sicchè l&#039;acqua li copra <lb></lb>del tutto; si ricerca dico se il ferro resterà nell&#039;istessa positura di prima, <lb></lb>cioè colla medesima porzione nell&#039;argento vivo, oppure se in parte si solle­<lb></lb>verà fuori di detto argento vivo, o finalmente se si sommergerà nell&#039;argento <lb></lb>vivo con maggior porzione di quella, che era avanti all&#039;infusione dell&#039;acqua, <lb></lb>stante che l&#039;acqua sopra infusa col suo peso lo veniva a comprimere, per <lb></lb>così dire, più a basso. </s>

<s>Al qual quesito io rispondo così: Se un solido più <lb></lb>grave in spezie dell&#039;acqua, e men grave dell&#039;argento vivo, sarà posto nell&#039;ar­<lb></lb>gento vivo, e dopo, sopra infusa l&#039;acqua, sicchè sopravanzi la parte superiore <lb></lb>di tal solido; tal solido non istarà, come nella prima positura, collocato nel­<lb></lb>l&#039;argento vivo, ma si solleverà per qualche spazio. </s>

<s>La qual proposizione fu <lb></lb>da me dimostrata con aver prima notati i tre seguenti lemmi. </s>

<s>” </s></p><pb xlink:href="020/01/3191.jpg" pagenum="152"></pb><p type="main">

<s><emph type="italics"></emph>“ Lemma I.<emph.end type="italics"></emph.end> — Se saranno quattro grandezze proporzionali, gli antece­<lb></lb>denti delle quali siano maggiori de&#039;conseguenti, e dalle prime due ne siano <lb></lb>levate parti uguali; il rimanente della prima, al rimanente della seconda, <lb></lb>averà maggior proporzione, che la terza alla quarta. </s>

<s>” </s></p><p type="main">

<s>“ Sia l&#039;AB (fig. </s>

<s>74) alla CD come EF a GH, e AB maggiore di CD, e <lb></lb>perciò ancora la EF maggiore di GH, e siano dall&#039;AB e dalla CD levate <lb></lb><figure id="id.020.01.3191.1.jpg" xlink:href="020/01/3191/1.jpg"></figure></s></p><p type="caption">

<s>Figura 74.<lb></lb>parti uguali BI, DK. </s>

<s>Dico che la rimanente AI, alla <lb></lb>rimanente CK, averà maggior proporzione che EF <lb></lb>a GH. </s>

<s>Facciasi come AB a CD così IB a LD: adun­<lb></lb>que, per essere AB maggiore di CD, sarà ancora IB <lb></lb>maggiore della LD. </s>

<s>F perchè, come tutta AB a tutta <lb></lb>la CD, così la levata via IB alla levata via ID; adun­<lb></lb>que la rimanente AI, alla rimanente CL, sarà come <lb></lb>tutta AB a tutta la CD, cioè come EF alla GH. </s>

<s>Ma perchè IB è maggiore <lb></lb>di LD, come si è dimostrato, ed uguale alla KD; perciò sarà CL maggiore <lb></lb>di CK. </s>

<s>Adunque la AI a CK averà maggior proporzione che la stessa AI <lb></lb>alla CL, cioe che la EF alla GH, che si dovea dimostrare. </s>

<s>” (MSS. Gal. </s>

<s><lb></lb>Disc., T. I, fol. </s>

<s>144, 45). </s></p><p type="main">

<s>Questo lemma è un caso particolare del seguente più generale, ma ele­<lb></lb>mentarissimo teorema: <emph type="italics"></emph>Ai due termini di una frazione aggiungendo quan­<lb></lb>tità uguali, il quoziente cresce o scema, secondo che la frazione è appa­<lb></lb>rente o propria: e avviene tutto il contrario, se la medesima quantità dai <lb></lb>due detti termini invece si tolga.<emph.end type="italics"></emph.end> Abbiasi, per esempio, A/B=Q, e (A±<emph type="italics"></emph>a<emph.end type="italics"></emph.end>)/(B±<emph type="italics"></emph>a<emph.end type="italics"></emph.end>)= <lb></lb>Q′. </s>

<s>Per vedere in quali casi Q sia maggiore o minore di Q′, si riducano le <lb></lb>frazioni al medesimo denominatore, per cui si trasformeranno in </s></p><p type="main">

<s><emph type="center"></emph>(A.B±A.<emph type="italics"></emph>a<emph.end type="italics"></emph.end>)/(B(B±<emph type="italics"></emph>a<emph.end type="italics"></emph.end>))=Q, (A.B±B.<emph type="italics"></emph>a<emph.end type="italics"></emph.end>)/(B(B±<emph type="italics"></emph>a<emph.end type="italics"></emph.end>))=Q′.<emph.end type="center"></emph.end><lb></lb>È di qui manifesto che, valendo il segno di sopra, se A&gt;B, ossia se la <lb></lb>frazione è apparente, Q&gt;Q′. </s>

<s>E se A&lt;B, anche Q&lt;Q′. </s>

<s>Valendo poi il <lb></lb>segno di sotto ed essendo la frazione propria, manifestamente è Q&gt;Q′. </s>

<s>Al <lb></lb>contrario poi Q&lt;Q′, se la frazione è apparente, che è il caso particolar­<lb></lb>mente contemplato dal Castelli in questo suo lemma, la dimostrazion del <lb></lb>quale, supponendosi A/B=C/D, vien dalla disuguaglianza (A—<emph type="italics"></emph>a<emph.end type="italics"></emph.end>)/(B—<emph type="italics"></emph>a<emph.end type="italics"></emph.end>)&lt;C/D. </s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma II.<emph.end type="italics"></emph.end> — Quando nell&#039;umido sono sommersi due corpi, più gravi <lb></lb>in specie dell&#039;umido, nel quale sono immersi, perdono ugual momento di <lb></lb>gravità in specie. </s>

<s>Il che è manifesto, perchè quel che si perde dall&#039;uno e <lb></lb>dall&#039;altro ciascheduno è uguale alla gravità in specie dell&#039;acqua, come si <lb></lb>deduce dalle cose dimostrate da Archimede, nel primo libro <emph type="italics"></emph>De insidentibus <lb></lb>humido. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s><emph type="italics"></emph>“ Lemma III.<emph.end type="italics"></emph.end> — Se saranno due prismi o cilindri, simili ed uguali in <lb></lb>mole, e dell&#039;istessa gravità in specie, immersi similmente nello stesso umido <pb xlink:href="020/01/3192.jpg" pagenum="153"></pb>più grave in specie di essi prismi e cilindri; l&#039;altezza della parte sommersa <lb></lb>dell&#039;uno sarà uguale all&#039;altezza della parte sommersa dell&#039;altro. </s>

<s>Il che, seb­<lb></lb>bene pare in certo modo noto per sè stesso, tuttavia si può dimostrare in <lb></lb>questa maniera: Siano due prismi o cilindri AB, CD (fig. </s>

<s>75) simili, eguali <lb></lb>di mole, e della stessa gravità in specie, e siano posti similmente nello stesso <lb></lb><figure id="id.020.01.3192.1.jpg" xlink:href="020/01/3192/1.jpg"></figure></s></p><p type="caption">

<s>Figura 75.<lb></lb>umido, più grave in specie di essi solidi, e siano <lb></lb>sommersi fino alle altezze BE, DF. </s>

<s>Dico che BE <lb></lb>è uguale alla DF. </s>

<s>Imperocchè la GB alla BE ha <lb></lb>la medesima proporzione, che la gravità in specie <lb></lb>del solido AB (come dimostra il signor Galileo nel <lb></lb>Discorso delle cose che galleggiano nell&#039;umido) <lb></lb>cioè, come la stessa gravità in specie dell&#039;umido, <lb></lb>alla gravità in specie del solido CD, giacchè i solidi sono di gravità in specie <lb></lb>uguali. </s>

<s>Ma come la gravità in specie dell&#039;umido, alla gravità in specie del <lb></lb>solido CD, così l&#039;altezza HD all&#039;altezza DF; e però, come GB alla BE, così <lb></lb>è HD alla DF. E, per essere la prima GB uguale alla terza HD sarà ancora <lb></lb>EB uguale alla FD, che era il proposito. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE. — <emph type="italics"></emph>Stanti le suddette cose, dico che, se un solido più <lb></lb>grave in specie dell&#039;acqua, e men grave dell&#039;argento vivo, sarà posto nel­<lb></lb>l&#039;argento vivo, e dopo sopra infusa l&#039;acqua, sicchè sopravanzi la parte <lb></lb>superiore del solido; tal solido non starà, come nella prima posizione, <lb></lb>posto nell&#039;argento vivo, ma si solleverà per qualche spazio. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia il cilindro ovvero prisma ABCD (fig. </s>

<s>76) di ferro, ovvero di al­<lb></lb>cuna materia più grave in specie dell&#039;acqua, e meno dell&#039;argento vivo, im­<lb></lb><figure id="id.020.01.3192.2.jpg" xlink:href="020/01/3192/2.jpg"></figure></s></p><p type="caption">

<s>Figura 76.<lb></lb>merso nell&#039;argento vivo sino al livello HG, nel vaso EF, <lb></lb>e il rimanente AGHD resti nell&#039;aria. </s>

<s>Intendasi di più, <lb></lb>per maggior chiarezza, un altro prisma, ovvero cilin­<lb></lb>dro della medesima gravità in specie, e uguale e si­<lb></lb>mile al solido AC, e sia IKLM (fig. </s>

<s>77) immerso si­<lb></lb>milmente (cioè col lato LK omologo al lato CB posto <lb></lb>nella parte inferiore) nell&#039;argento vivo, sino al livello <lb></lb>NO, nel vaso PR, ed il rimanente IONM intendasi come prima in aria. </s>

<s>Chiara <lb></lb>cosa è che l&#039;altezza GB è uguale all&#039;altezza OK, per il terzo lemma. </s>

<s>Ora <lb></lb><figure id="id.020.01.3192.3.jpg" xlink:href="020/01/3192/3.jpg"></figure></s></p><p type="caption">

<s>Figura 77.<lb></lb>dico che, infondendosi acqua nel vaso PR fino al li­<lb></lb>vello PQ, sicchè sopravanzi la parte superiore del so­<lb></lb>lido MK, il solido MK si solleverà per qualche spazio. </s>

<s><lb></lb>Imperocchè l&#039;altezza IK, all&#039;altezza KO, è come la <lb></lb>gravità in specie dell&#039;argento vivo alla gravità in <lb></lb>specie del cilindro, posti l&#039;uno e l&#039;altro sotto l&#039;acqua <lb></lb>del vaso PR, come dimostra il signor Galileo. </s>

<s>E per­<lb></lb>chè, avanti all&#039;infusione dell&#039;acqua, la gravità in spe­<lb></lb>cie dell&#039;argento vivo nel vaso PR, alla gravità in specie della MK, era come <lb></lb>la gravità in specie dell&#039;argento vivo nel vaso EF, alla gravità in specie del <lb></lb>solido DB, a tal che erano quattro grandezze proporzionali, e gli antecedenti <pb xlink:href="020/01/3193.jpg" pagenum="154"></pb>erano maggiori dei conseguenti, e di poi, per l&#039;infusione dell&#039;acqua nel vaso <lb></lb>PR, si sono levate parti uguali di gravità in specie, pel secondo lemma; <lb></lb>adunque, per il primo lemma, il residuo dell&#039;antecedente, cioè la gravità in <lb></lb>specie dell&#039;argento vivo nel vaso PR, alla gravità in specie del solido MK, <lb></lb>averà maggior proporzione che la gravità in specie dell&#039;argento vivo nel <lb></lb>vaso EF, alla gravità in specie del solido DB. </s>

<s>Adunque ancora la linea IK, <lb></lb>cioè AB, alla KO, ha maggior proporzione che la gravità in specie dell&#039;ar­<lb></lb>gento vivo, nel vaso EF, alla gravità in specie del solido DB, cioè che AB <lb></lb>alla BG, e però KO è minore della GB. </s>

<s>Adunque il solido MK è stato solle­<lb></lb>vato per l&#039;infusione dell&#039;acqua, come si doveva provare ” (ivi, fol. </s>

<s>145, 46). </s></p><p type="main">

<s>Questo apparato geometrico fu prescelto forse dal Castelli, per dare quasi <lb></lb>autentico suggello di verità alla conclusione, alla quale vedeva nonostante con­<lb></lb>dursi assai facilmente, non dilungandosi dalla fisica semplicità dei metodi ar­<lb></lb>chimedei, come fa, soggiungendo immediatamente così al suo primo discorso: </s></p><p type="main">

<s>“ Sia un vaso con argento vivo fino al segno AB (fig. </s>

<s>78) e sia un ferro <lb></lb>galleggiante in esso CD, la cui parte C sia immersa, e la D scoperta. </s>

<s>Si cerca <lb></lb><figure id="id.020.01.3193.1.jpg" xlink:href="020/01/3193/1.jpg"></figure></s></p><p type="caption">

<s>Figura 78.<lb></lb>che cosa farà questo ferro, dop&#039;esser ricoperto <lb></lb>d&#039;acqua. </s>

<s>Sia infusa l&#039;acqua sino al segno EF, <lb></lb>ed il ferro CD, se è possibile, resti fermo nel <lb></lb>sito, nel quale stava prima, avanti l&#039;infusione <lb></lb>dell&#039;acqua. </s>

<s>Immaginiamoci la mole acquea G <lb></lb>simile ed uguale alla mole D, e la mole d&#039;ar­<lb></lb>gento vivo H simile ed uguale alla C. È chiaro <lb></lb>per Archimede che il solo argento vivo H pesa <lb></lb>tanto, quanto pesa tutto il ferro CD. </s>

<s>Adunque <lb></lb>tutta la figura HG, essendovi aggiunta l&#039;acqua <lb></lb>G, peserà più che il ferro CD. </s>

<s>Seghiamo ora <lb></lb>il vaso col piano IL: e perchè l&#039;umido LBO <emph type="italics"></emph>magis pressum est quam humi­<lb></lb>dum LAO, non quiescet sed impelletur sursum tanta vi, quanta est gra­<lb></lb>vitas aquae molem habentis figurae G aequalem;<emph.end type="italics"></emph.end> non resterà dunque fermo <lb></lb>il ferro, dopo l&#039;infusione dell&#039;acqua, ma spingerà all&#039;in su, con tanta forza o <lb></lb>momento, quant&#039;è il peso d&#039;una mole d&#039;acqua eguale alla G, ovvero alla D. ” </s></p><p type="main">

<s>“ Ma più brevemente: sia il ferro AB (fig. </s>

<s>79), ed il livello dell&#039;ar­<lb></lb>gento vivo CD, ed avanti l&#039;infusione dell&#039;acqua stia il ferro colla parte B <lb></lb><figure id="id.020.01.3193.2.jpg" xlink:href="020/01/3193/2.jpg"></figure></s></p><p type="caption">

<s>Figura 79.<lb></lb>tuffata, e la A scoperta. </s>

<s>Infondasi poi l&#039;acqua, e resti il <lb></lb>ferro come prima senza moversi. </s>

<s>È chiaro che se la figura A <lb></lb>acquea, e la figura B fosse argento vivo, tutta la composta <lb></lb>figura AB starebbe senza moversi. </s>

<s>Ma essendo la detta fi­<lb></lb>gura AB, non d&#039;acqua o d&#039;argento vivo, ma di ferro, sarà <lb></lb>meno grave che non è quella composta d&#039;acqua e d&#039;ar­<lb></lb>gento vivo, perchè tutta la figura di ferro pesa solamente <lb></lb>quanto la figura B d&#039;argento vivo. </s>

<s>Adunque al ferro AB manca, per potere <lb></lb>star fermo, il peso dell&#039;acqua A, onde <emph type="italics"></emph>feretur sursum tanto impetu, quanto <lb></lb>est gravitas aquae molem habentem aequalem figurae<emph.end type="italics"></emph.end> A ” (ivi, fol. </s>

<s>146). </s></p><pb xlink:href="020/01/3194.jpg" pagenum="155"></pb><p type="main">

<s>Era, con tali ragioni fisiche e matematiche, risposto a quella prima <lb></lb>parte del quesito, intorno alla quale nè il Baliani nè altri, avveduti come <lb></lb>lui, non ammettevano dubbi. </s>

<s>Rimaneva come più difficile di rispondere al­<lb></lb>l&#039;altra, quanta sia, cioè, la parte del ferro che, per l&#039;infusione dell&#039;acqua, <lb></lb>s&#039;inalza sopra il livello dell&#039;argento vivo, e il Castelli ci si metteva così ra­<lb></lb>gionando: </s></p><p type="main">

<s>“ Sia il ferro AB (fig. </s>

<s>80), di figura prismatica o cilindrica, <lb></lb><figure id="id.020.01.3194.1.jpg" xlink:href="020/01/3194/1.jpg"></figure></s></p><p type="caption">

<s>Figura 80.<lb></lb>immerso nell&#039;argento vivo sino al segno CD, e dopo l&#039;infusione <lb></lb>dell&#039;acqua s&#039;alzi sino a qualche segno EF: si cerca la quantità <lb></lb>dell&#039;alzamento DF. ” </s></p><p type="main">

<s>“ Perchè il ferro AB, sommerso nell&#039;argento vivo sino al <lb></lb>segno CD, galleggiava, sarà il peso dell&#039;argento vivo AD eguale <lb></lb>al peso di tutto il ferro, per Archimede. </s>

<s>Perchè poi, dopo l&#039;in­<lb></lb>fusione dell&#039;acqua, il ferro sollevato sta fermo colla parte AF nell&#039;argento <lb></lb>vivo, e colla rimanente FH in acqua, peseranno le due figure, AF d&#039;argento <lb></lb>vivo ed FH d&#039;acqua insieme, quanto tutto il ferro. </s>

<s>Adunque egualmente pe­<lb></lb>sano la mole d&#039;argento vivo AD, e le due moli AF d&#039;argento vivo, ed FH <lb></lb>d&#039;acqua insieme. </s>

<s>Levata poi la comune AF, peserà tanto l&#039;argento vivo ED, <lb></lb>quanto l&#039;acqua EB. </s>

<s>Ma quando i pesi assoluti sono uguali, le gravità in spe­<lb></lb>cie sono come le moli contrariamente prese, secondo il Galileo; adunque la <lb></lb>mole EB, alla ED, cioè la linea BF, alla FD, sarà come la gravità in specie <lb></lb>dell&#039;argento vivo, alla gravità in specie dell&#039;acqua. </s>

<s>Ma perchè la BD è nota, <lb></lb><figure id="id.020.01.3194.2.jpg" xlink:href="020/01/3194/2.jpg"></figure></s></p><p type="caption">

<s>Figura 81.<lb></lb>cioè la parte scoperta del ferro, avanti si coprisse di acqua; <lb></lb>saranno note ancora le BF, DF, poichè, <emph type="italics"></emph>data proportione et <lb></lb>differentia duorum magnitudinum, ipsae etiam magnitu­<lb></lb>dines dantur. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Quando il ferro non fosse prisma o cilindro ma solido <lb></lb>irregolare, come ADBC (fig. </s>

<s>81), tuffato nell&#039;argento vivo colla <lb></lb>parte ACB, facciasi come la gravità in specie dell&#039;argento <lb></lb>vivo, alla gravità in specie dell&#039;acqua, così la mole DEF alla <lb></lb>mole EABF, e la porzione EABF sarà quella che, dopo l&#039;infusione dell&#039;acqua, <lb></lb>si solleverà sopra il livello dell&#039;argento vivo ” (ivi, fol. </s>

<s>146, 47). </s></p><p type="main">

<s>Che così veramente, come diceva il Castelli, sia risoluto il problema, <lb></lb>può dichiararsi meglio col seguente discorso, dop&#039;aver concluso che l&#039;argento <lb></lb>vivo, di pari mole alla porzione ED della mole del cilindro di ferro, ugua­<lb></lb>glia al peso della mole EB d&#039;acqua, il luogo della quale è occupato dalla <lb></lb>porzione EB dello stesso cilindro. </s>

<s>Imperocchè, dove i pesi sono uguali, le <lb></lb>gravità specifiche stanno contrariamente ai volumi, o alle loro altezze, es­<lb></lb>sendo prismi o cilindri di basi uguali. </s>

<s>Chiamate dunque G, G′ le gravità <lb></lb>specifiche del mercurio e dell&#039;acqua, sarà BF:DE=G:G′. </s>

<s>Dividendo, <lb></lb>BF—DF:DF=G—G′:G′, d&#039;onde, sostituito BD a BF—DF, viene <lb></lb>(G′.BD)/(G—G′). Ma G e G′ son note, per mezzo della Bilancetta idrostatica, e BD, <lb></lb>che è uguale a CH, può aversi dalla proporzione C:G″=AH:CH, intesa <pb xlink:href="020/01/3195.jpg" pagenum="156"></pb>per G″ la gravità specifica del ferro, o per misura diretta; dunque DF, quan­<lb></lb>tità dell&#039;alzamento, prodotto nel cilindro di ferro, per l&#039;infusione dell&#039;acqua <lb></lb>sul mercurio, è nota, ed è perciò, come si diceva, risoluto il problema. </s></p><p type="main">

<s>“ Per corollario (soggiunge il Castelli in fine del suo Discorso) si scio­<lb></lb>glie un problema, in cui alcuno proponesse di trovare due moli, una d&#039;acqua <lb></lb>e l&#039;altra d&#039;argento vivo, le quali insieme prese fossero uguali e di mole e <lb></lb>di peso ad un dato ferro: ovvero si proponesse il vaso AB, nella figura 80, <lb></lb>da empirsi d&#039;acqua e d&#039;argento vivo in tal modo, che il vaso pieno pesi <lb></lb>tanto, quanto peserebbe se fosse tutto ferro. </s>

<s>” </s></p><p type="main">

<s>“ Facciasi come la gravità in specie dell&#039;argento vivo, alla gravità in <lb></lb>specie del ferro, così HA ad AC. </s>

<s>Di più, come la medesima gravità in spe­<lb></lb>cie dell&#039;argento vivo, alla gravità in specie dell&#039;acqua, così la EH alla EC, <lb></lb>ed il vaso AB, pieno fino al segno HB d&#039;acqua, peserà quanto se fosse tutto <lb></lb>ferro. </s>

<s>Nè vi è altro segno che il trovato EF, il quale seghi il vaso in modo <lb></lb>che, riempiutane una parte d&#039;argento vivo, e l&#039;altra d&#039;acqua; faccia che <lb></lb>tutto il composto pesi tanto, quanto peserebbe, se fosse ferro assoluto ” (ivi, <lb></lb>fol. </s>

<s>147). </s></p><p type="main">

<s>Se il cilindro di ferro AB, immerso nel vaso, in cui il livello del mer­<lb></lb>curio lo sega nel determinato segno EF, e l&#039;acqua ne pareggia la sommità <lb></lb>BH, sta in equilibrio; è manifesto che, se la parte EB si trasformasse in <lb></lb>acqua, e la AF in mercurio, l&#039;equilibrio stesso perciò non sarebbe turbato. </s>

<s><lb></lb>Ond&#039;essendo il peso del ferro uguale al peso di quest&#039;acqua e di questo <lb></lb>mercurio, il problema proposto dal Castelli è risoluto, quando sia nota l&#039;al­<lb></lb>tezza AE. Ora, supponendo che l&#039;altezza del livello del mercurio senz&#039;acqua <lb></lb>fosse AC, abbiamo AE=AC—CE. Cosicchè, chiamandosi G, G′ le gra­<lb></lb>vità in specie del mercurio e dell&#039;acqua, AC è nota, perchè G:G′=HA:AC. <lb></lb>È anche poi EC nota, per la formula ritrovata di sopra, dunque è risoluto il <lb></lb>problema. </s></p><p type="main">

<s>Del teorema, dimostrato dal Castelli in questo Discorso, fu diffusa la no­<lb></lb>tizia per le varie copie, che del manoscritto lasciò il Ciampoli prendere agli <lb></lb>amici, ma principalmente per gl&#039;insegnamenti del Borelli, il quale, leggendo <lb></lb>in pubblica scuola gli elementi dell&#039;Idrostatica, faceva notare che le propo­<lb></lb>sizioni di Archimede, e specialmente la V, son vere solamente, quando la so­<lb></lb>lida grandezza, come suppone l&#039;Autore, galleggi sopra un fluido solo più <lb></lb>denso, senza che la parte emersa si trovi in mezzo a un più raro. </s>

<s>E così, <lb></lb>come oralmente il Borelli insegnava, diffuse poi per le stampe i medesimi <lb></lb>insegnamenti nel libro <emph type="italics"></emph>De motionibus naturalibus,<emph.end type="italics"></emph.end> dove, avendo fatto osser­<lb></lb>vare come, per la forza che respinge in su il solido piu leggero dell&#039;umido, <lb></lb>e di cui si tratta nella VI del primo libro <emph type="italics"></emph>De insidentibus,<emph.end type="italics"></emph.end> non si deve in­<lb></lb>tendere il moto attuale, ma l&#039;energia o il conato al moto; soggiunge: “ Prae­<lb></lb>terea altera Archimedis propositio, quod nimirum moles fluidi, aequalis so­<lb></lb>lidi natantis parti demersae, aeque ponderet ac solidum ipsum; vera est, <lb></lb>nisi hypothesis varietur. </s>

<s>Oportet enìm, ex vi hypothesis, ut solidum innatet <lb></lb>supra unum fluidum, nam, si omnino sit demersum intra rarius, et innatet <pb xlink:href="020/01/3196.jpg" pagenum="157"></pb>supra aliud densius fluidum, propositio alteratur, ut docuit praeceptor meus <lb></lb>Benedictus Castellus, qui demonstravit quod ferrum supra mercurium natans, <lb></lb>si aqua quoque cooperiatur, tunc quidem altius elevabitur quam prius, pro­<lb></lb>pterea quod pondus aquae collateralis auget magis hydrargyri compressionem, <lb></lb>quam ferri pondus augeat, proindeque ferrum aliquantisper altius elevat ” <lb></lb>(<emph type="italics"></emph>Regio Julio<emph.end type="italics"></emph.end> 1670, pag. </s>

<s>477, 78). </s></p><p type="main">

<s>Fra gli uditori della Lezione, in cui il Borelli così diceva, era quel vi­<lb></lb>vacissimo ingegno di Donato Rossetti, il quale condusse alle ultime sue con­<lb></lb>seguenze il discorso udito fare al Maestro. </s>

<s>E l&#039;aria stessa, pensava fra sè, <lb></lb>non è ella un fluido più raro dell&#039;acqua, o di altr&#039;umido, in cui il solido <lb></lb>s&#039;immerga? </s>

<s>Dunque le proposizioni <emph type="italics"></emph>De insidentibus<emph.end type="italics"></emph.end> son false nelle espe­<lb></lb>rienze di tutti coloro, che fisicamente se ne servono per loro assiomi, e si <lb></lb>verificano, come par che supponga Archimede stesso, solamente nel vuoto, <lb></lb>perchè ivi solamente le solide grandezze soprannotano a un unico fluido. </s>

<s>Così <lb></lb>appunto, come il Rossetti pensò, disse in questa forma pubblicamente: <emph type="italics"></emph>Il <lb></lb>concetto di Archimede che il galleggiante si sommerga sotto il livello del­<lb></lb>l&#039;acqua, fin tanto che una mole d&#039;acqua, uguale alla parte sommersa, <lb></lb>pesi assolutamente quanto tutto il galleggiante; è falsissimo.<emph.end type="italics"></emph.end> (<emph type="italics"></emph>Dimostra­<lb></lb>zione fisica-matem.,<emph.end type="italics"></emph.end> Firenze 1668, pag. </s>

<s>3). Pronunziata la qual sentenza, <lb></lb>passa l&#039;Autore a dimostrare che il galleggiante non uguaglia in peso asso­<lb></lb>luto il peso della detta mole dell&#039;acqua, ma di questa, insieme con una mole <lb></lb>d&#039;aria, pari a quella della parte, che in esso galleggiante soprannota. </s>

<s>La di­<lb></lb>mostrazione è simile, anzi è sostanzialmente la medesima di quella fatta dal <lb></lb>Castelli, nella seconda sua fisica maniera, sostituito un umido qualunque al <lb></lb>mercurio, e all&#039;acqua sopra infusagli l&#039;aria. </s></p><p type="main">

<s>Si fecondò nel Rossetti questo primo concetto, estendendolo, dall&#039;equi­<lb></lb>librio de&#039;liquidi, a tutti gli altri equilibrii in generale, di che pure, ne&#039;suoi <lb></lb>libri <emph type="italics"></emph>De aequiponderantibus,<emph.end type="italics"></emph.end> aveva trattato Archimede. </s>

<s>E perchè il fonda­<lb></lb>mento a questa causa degli equilibri si poneva da lui nel centro di gravità <lb></lb>de&#039;corpi, osservò il nuovo arguto commentatore che, nell&#039;invenzione di que­<lb></lb>sto centro, si supponeva essere il grave costituito no in aria, ma nel vuoto <lb></lb>assoluto. </s>

<s>Ne toglieva l&#039;esempio dal triangolo, dalla piramide, dal cono, e da <lb></lb>somiglianti figure <emph type="italics"></emph>in alteram partem deficientes,<emph.end type="italics"></emph.end> nelle quali il centro di <lb></lb>gravità, variando col variare la densità del mezzo, l&#039;indicazione, datane da <lb></lb><figure id="id.020.01.3196.1.jpg" xlink:href="020/01/3196/1.jpg"></figure></s></p><p type="caption">

<s>Figura 82.<lb></lb>Archimede e da&#039;promotori di lui, non potrebb&#039;essere <lb></lb>così, come si ritiene, di assoluta verità matematica. </s>

<s>Nel <lb></lb>triangolo ABC, per esempio (fig. </s>

<s>82), si determina geo­<lb></lb>metricamente il centro di gravità in tal punto della bis­<lb></lb>settrice AF, che la parte AO sia due terzi della rima­<lb></lb>nente. </s>

<s>Cosicchè, sospesa la figura dal punto O, e fatta <lb></lb>per lui passare una linea parallela alla base, si dice che il tutto sta in equi­<lb></lb>librio, perchè tanto pesa il triangolo ADE da una parte, quanto il trapezio EB <lb></lb>dall&#039;altra. </s>

<s>Ma che ciò si verifichi solamente nel vuoto, e no nell&#039;aria o in <lb></lb>altro mezzo più denso, come sarebbe l&#039;acqua, è manifesto dall&#039;esperienza <pb xlink:href="020/01/3197.jpg" pagenum="158"></pb>Perchè, lasciando liberamente cadere in alcuno dei detti mezzi, ma special­<lb></lb>mente nel secondo, il detto triangolo solido, ossia il prisma triangolare so­<lb></lb>pr&#039;esso costruito; si osserva che l&#039;equilibrio non si mantiene, ma che co­<lb></lb>stantemente il vertice volge in basso, e si dirizza in alto la base, evidente <lb></lb>segno che il triangolo non è ugualmente peso, ma più grave del trapezio <lb></lb>a lui contrapposto. </s>

<s>Che poi causa di ciò sia il mezzo si comprenderà facil­<lb></lb>mente, osservando che per essere il triangolo in superficie un quinto men del <lb></lb>trapezio (giacchè si sa che l&#039;uno sta all&#039;altro come 4 sta a 5) riceve anche <lb></lb>un quinto meno d&#039;impedimento, e perciò prepondera sopra l&#039;altro per un <lb></lb>quinto, rimasto libero della sua gravità naturale. </s></p><p type="main">

<s>Dietro le quali osservazioni è necessario concludere col Rossetti <emph type="italics"></emph>che <lb></lb>Archimede non concepì le sue proposizioni per la Fisica, ma per la Mate­<lb></lb>matica.<emph.end type="italics"></emph.end> “ Dal che è più che necessario il dedurne, soggiunge lo stesso Ros­<lb></lb>setti, che in errore siano vissuti sinora tutti quelli, che fisicamente se ne <lb></lb>servirono per loro assiomi. </s>

<s>Dal che si deduce anche la cagione perchè molte <lb></lb>cose non abbiano in fatti corrisposto a quanto da questa proposizione si aspet­<lb></lb>tava, non solo intorno alle materie che dovevano galleggiare, ma ancora in <lb></lb>quelle che, in aria sospese, dovevano bilanciarsi intorno al loro centro di <lb></lb>gravità ” (ivi). </s></p><p type="main">

<s>Benche fossero tutte queste conclusioni verissime, è un fatto però che <lb></lb>i più non le ascoltarono, e alcuni le contraddissero. </s>

<s>I Fisici, che sperava di <lb></lb>far ravvedere il Rossetti, si rimasero nell&#039;antico errore intorno alle galleg­<lb></lb>gianti, come si par dall&#039;uso, che tuttavia seguitano a fare della Bilancia idro­<lb></lb>statica, la quale non è esattamente dimostrativa della settima proposizione <lb></lb>archimedea (in cui supponesi che sopra l&#039;umido non sia fluido alcuno e nem­<lb></lb>men l&#039;aria) se non che quando il secchio B, della figura 73, sia esso pure <lb></lb>affatto senz&#039;aria. </s>

<s>Può concedersi che il peso di questa sia insensibile nella <lb></lb>bilancia ordinaria, ma sperimentando con quella mobilissima e squisitissima, <lb></lb>descritta dallo&#039;s Gravesande nel primo Tomo de&#039;suoi Elementi matematici <lb></lb>di Fisica (Leida 1748, pag. </s>

<s>423, 24), non sarebbe male tener qualche conto <lb></lb>di questi avvertimenti del Rossetti, che son poi quelli stessi dati tanti anni <lb></lb>prima dallo Stevino. </s></p><p type="main">

<s>Fra i contradittori, a cui s&#039;accennava di sopra, abbiamo a notar Gemi­<lb></lb>niano Montanari, che educatosi in altra scuola, pare ignorasse, o non fosse <lb></lb>persuaso della soluzion del problema, data dal Castelli nel discorso al Ciam­<lb></lb>poli. </s>

<s>Cosicchè, proposto il caso della cera galleggiante nell&#039;acqua, sopra in­<lb></lb>fusovi olio, non sapeva comprendere il Montanari come questo non oppri­<lb></lb>messe col suo proprio peso il galleggiante soggetto, il quale vedevasi anzi <lb></lb>sollevarsi alquanto sopra il primo livello: nè poteva comprendere la verità <lb></lb>della tesi sostenuta dal Rossetti, il quale andava ripetendo così al suo con­<lb></lb>tradittore la dimostrazion del Castelli. </s>

<s>Inteso che i settori ELI, ILF, della <lb></lb>figura 78, siano pieni d&#039;acqua infino al livello AOB, e il resto, infino al li­<lb></lb>vello EIF, dove prima era aria, in mezzo alla quale emergeva la parte G del <lb></lb>galleggiante di cera, sia messo olio; nell&#039;infondere questo, dice il Rosseti <pb xlink:href="020/01/3198.jpg" pagenum="159"></pb>“ più peso si pone sopra la superficie AO, che sopra la OB, perchè l&#039;olio <lb></lb>EO eccede l&#039;olio OF dell&#039;olio G, che è in mole uguale alla parte sopranna­<lb></lb>tante della cera GH. </s>

<s>E per questo, essendo più premuta la superficie AO <lb></lb>che la OB, quella discenderà, col far salir questa, in quel modo appunto che <lb></lb>nella bilancia sale quel braccio, ove è meno di peso, quando l&#039;altro braccio <lb></lb>più aggravato scende ” (<emph type="italics"></emph>Insegnamenti fisico-matem.,<emph.end type="italics"></emph.end> Livorno 1669, pag. </s>

<s>135). </s></p><p type="main">

<s>Il Montanari dunque non poteva esser disposto a penetrare le argute <lb></lb>osservazioni del Rossetti, per mancargli i principii necessari. </s>

<s>Ma principal­<lb></lb>mente giocava nella fantasia di lui quel pregiudizio comune a tanti, che cioè <lb></lb>sia infallibile criterio della verità di una cosa l&#039;essere approvata da tutti, e <lb></lb>specialmente dai grandi uomini, fra&#039;quali bastava citare il solo Galileo. </s>

<s>E da <lb></lb>un&#039;altra parte si faceva Galileo entrare bene a proposito nella questione, per <lb></lb>quel ch&#039;egli aveva insegnato rispetto all&#039;efficacia dell&#039;aria, in concorrere a <lb></lb>sostener le assicelle d&#039;ebano galleggianti. </s>

<s>Si notò più addietro la stravaganza <lb></lb>di queste dottrine, perchè, essendo un fatto che anche l&#039;aria pesa, non vi <lb></lb>si teneva poi nessun conto del peso di lei: stranezza che il Rossetti si stu­<lb></lb>diava di togliere col dire che, non essendo l&#039;aria nell&#039;altr&#039;aria nè grave nè <lb></lb>leggera, Galileo dunque intendeva di pesarla nel vuoto. </s>

<s>“ Vi ricorderete, <lb></lb>scriveva, che Galileo non fece altre esperienze, in quel suo Trattato delle <lb></lb>galleggianti, se non di cose, che di sua natura scendono nell&#039;acqua come <lb></lb>d&#039;ebano e di metalli: e vi ricorderete che queste materie, ridotte in lar­<lb></lb>ghissime falde, venivano posate leggermente e con gran diligenza sopra <lb></lb>l&#039;acqua in modo, che si mantenevano a galla, del quale effetto gli avversari <lb></lb>del Galileo avevano preteso che ne fosse la causa quella figura così ampia, <lb></lb>ed il Galileo, fondato sopra la dottrina de&#039;galleggianti, provava e dimostrava <lb></lb>ciò avvenire, perchè tanto pesava quella falda di ebano o di metallo, atten­<lb></lb>dete bene, <emph type="italics"></emph>con quell&#039;aria, che veniva rinchiusa tra quegli argini, che fa <lb></lb>l&#039;acqua intorno alla detta falda sino al superior livello dell&#039;acqua; quanto <lb></lb>pesava una mole di acqua uguale alla detta falda ed aria.<emph.end type="italics"></emph.end> Sicchè se il <lb></lb>Galileo, in queste sue esperienze, pesò o intese di pesare, lo fece col met­<lb></lb>tere da una parte della Bilancia una mole d&#039;acqua, e nell&#039;altra una falda <lb></lb>di qualche materia più grave dell&#039;acqua, con qualche massa di aria. </s>

<s>Ma <lb></lb>l&#039;aria nell&#039;aria non si può pesare; adunque dovè pesarla ove si potesse pe­<lb></lb>sare, sicchè bisogna concludere che la pesasse o intendesse pesarla nel <lb></lb>vuoto ” (ivi, pag. </s>

<s>112, 13). </s></p><p type="main">

<s>Il Montanari negava esser questa la vera intenzione di Galileo, e te­<lb></lb>stualmente citando, dal Discorso intorno alle galleggianti, i passi illustrati <lb></lb>dalla figura 69, qui addietro: <emph type="italics"></emph>Et avvegnachè la mole dell&#039;aria AC non <lb></lb>cresca, nè diminuisca la gravità della mole IS,<emph.end type="italics"></emph.end> e poco più basso, <emph type="italics"></emph>E per­<lb></lb>chè l&#039;aria AC non cresce o scema il peso del solido IS;<emph.end type="italics"></emph.end> ne concludeva, <lb></lb>contro il Rossetti, apparire di qui ben chiaro che Gahleo “ non pone in conto <lb></lb>il peso dell&#039;aria, se dice che ella non opera cosa alcuna, perchè infatti l&#039;aria <lb></lb>nell&#039;aria non ha momento veruno, il che non potrebbe egli dire, se inten­<lb></lb>desse quell&#039;acqua pesata nel vuoto, perchè quivi sarebbe necessario mettere <pb xlink:href="020/01/3199.jpg" pagenum="160"></pb>in conto il peso d&#039;altrettant&#039;aria. </s>

<s>Altrimenti la proposizione non si verifi­<lb></lb>cherebbe, e sarebbe un paralogismo: laddove dimostrata e vera rimane, se <lb></lb>si considera il peso assoluto nell&#039;aria. </s>

<s>Resta dunque provato che il Galileo <lb></lb>intese per peso assoluto il peso de&#039;corpi in aria, e no nel vuoto “ (<emph type="italics"></emph>Lezione <lb></lb>accademica,<emph.end type="italics"></emph.end> Torino 1678, pag. </s>

<s>8). </s></p><p type="main">

<s>Se queste dispute non hanno grande importanza per sè stesse, l&#039;hanno <lb></lb>però, e non piccola, per noi, i quali siamo intanto fatti certi di due cose: <lb></lb>la prima è che i paralogismi di Galileo, intorno al galleggiare i corpi più <lb></lb>gravi in specie dell&#039;acqua, dipendevano dall&#039;aver egli incautamente profes­<lb></lb>sato il principio peripatetico che ogni elemento, nel suo proprio elemento, <lb></lb>non è nè grave nè leggero: la seconda, che oltrepassata di non pochi anni <lb></lb>la prima metà del secolo XVII, de&#039;paralogismi del novello Archimede non <lb></lb>s&#039;erano ancora accorti due non ignobili seguaci di lui. </s>

<s>Che se ritornisi col <lb></lb>pensiero al Borelli e al Viviani, difensori ingenui delle fallacie del Michelini, <lb></lb>se ne dovrà concludere che Galileo aveva, co&#039;suoi nuovi insegnamenti idro­<lb></lb>statici, tenute lungamente soggiogate alla tirannia peripatetica le più nobili <lb></lb>intelligenze della sua scuola. </s>

<s>Il fatto apparisce tanto più deplorabile, in <lb></lb>quanto che una mano di valorosi stranieri era venuta a infrangere coteste <lb></lb>catene. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il Pascal v&#039;aveva menato sopra tanti colpi potenti, quante sono le varie <lb></lb>esperienze, immaginate e descritte da lui, per dimostrare che l&#039;acqua nel­<lb></lb>l&#039;acqua preme per tutti i versi i solidi immersi, e tanto più gagliardamente <lb></lb>gli preme, quanto vi scendono più profondi. </s>

<s>Se il tubo AB (fig. </s>

<s>83), tenu­<lb></lb>tagli chiusa la bocca B con un dito, s&#039;immerga in un vivaio fino al livello <lb></lb>CD, e così stando s&#039;empia di mercurio, e poi tolgasi il dito; il mercurio <lb></lb><figure id="id.020.01.3199.1.jpg" xlink:href="020/01/3199/1.jpg"></figure></s></p><p type="caption">

<s>Figura 83.<lb></lb>verserà dalla bocca B, scendendo sotto l&#039;altra A, fino a un <lb></lb>certo punto. </s>

<s>“ Si on enforce le tuyau plus avant, le vif ar­<lb></lb>gent remonte, car le poids de l&#039;eau est plus grand, et si on <lb></lb>le hausse au contraire le vif argent baisse, car son poids <lb></lb>surpasse l&#039;autre ” (<emph type="italics"></emph>De l&#039;equilibre des liqueurs,<emph.end type="italics"></emph.end> a Paris, 1663, <lb></lb>pag. </s>

<s>19). Un manticino da focolare, sommerso tutto così, che <lb></lb>la bocca del cannello assai lungo sopravanzi il livello del­<lb></lb>l&#039;acqua, s&#039;apre più difficilmente, essendogli stata chiusa l&#039;ani­<lb></lb>mella, che in mezzo all&#039;aria “ a cause du poids de la masse <lb></lb>de l&#039;eau, qui le presse. </s>

<s>Aussi plus il est avant dans l&#039;eau, plus <lb></lb>il est difficile à ouvrir, parce qu&#039;il y a une plus grande hauteur d&#039;eau a sup­<lb></lb>porter ” (ivi, pag. </s>

<s>31). Similmente, strinta la bocca di una borsa di pelle <lb></lb>intorno a un cannello di vetro, aperto da ambedue le parti, poi tutto ripieno <lb></lb>di mercurio, e tuffato nell&#039;acqua; si vede il mercurio stesso risalir su per il <pb xlink:href="020/01/3200.jpg" pagenum="161"></pb>detto cannello, e tanto più altamente, quanto si fa calare più al fondo, “ a <lb></lb>cause que le poids de l&#039;eau, pressant le balon de tous costez le vif argent <lb></lb>qu&#039;il contient, est presse egalement en tous ses points ” come a strizzarlo <lb></lb>con una mano più o meno forte (ivi, pag. </s>

<s>31, 32). </s></p><p type="main">

<s>Il Boyle nel suo VII Paradosso proponevasi di dimostrare “ Corpus <lb></lb>fluido immersum sustinere pressionem lateralem a fluido, eamque auctam <lb></lb>prout corporis immersi infra superficiem fluidi profunditas augetur ” (<emph type="italics"></emph>Pa­<lb></lb>radoxa hydrost. </s>

<s>Roterodami,<emph.end type="italics"></emph.end> 1670, pag. </s>

<s>197). La dimostrazione è simile alla <lb></lb>prima, fra quelle dianzi descritte dal Pascal, sostituito l&#039;olio al mercurio, e <lb></lb>la bocca B, invece di rivoltarsi in su, aperta da lato. </s>

<s>Ma la cosa essendo di <lb></lb>tanta importanza pose ai Paradossi una prima appendice, per rispondere a <lb></lb>sette obiezioni, sovvenute a un recente scrittore, onde confermar la dottrina <lb></lb>del Cartesio, che cioè le parti superiori dell&#039;acqua non premono le inferiori. </s>

<s><lb></lb>Data la risposta alle quali obiezioni, soggiunge il Boyle un&#039;esperienza nuova, <lb></lb>per dimostrare che non solo l&#039;acqua pesa nell&#039;acqua, ma che ella vi pesa, <lb></lb>quasi con la medesima forza come se fosse in aria. </s>

<s>Si soffi, egli dice, una <lb></lb>bolla di vetro alla fiamma, lasciandole fuori un picciolo, mentre dentro ri­<lb></lb>mane vuota di aria, e, aggiungendole un piombino, si tuffi nell&#039;acqua, te­<lb></lb>nendola sospesa per un filo a un braccio di una esattissima bilancia equili­<lb></lb>brata. </s>

<s>Poi si rompa colla tanaglia il picciolo alla detta bolla, che s&#039;empirà <lb></lb>d&#039;acqua, attratta di mezzo all&#039;altr&#039;acqua, la quale che veramente pesi, e <lb></lb>quanto, si parrà dalla bilancia stessa, e da ciò che le si deve aggiungere per <lb></lb>restituirìa al primo equilibrio. </s>

<s>Alla quale aggiunta poi si troverebbe, con po­<lb></lb>chissima differenza, corrispondere il peso dell&#039;acqua contenuta nella bolla <lb></lb>stessa, quando questa, detratto il vetro, si pesasse nell&#039;aria. </s>

<s>“ Unde liquet <lb></lb>(così il Boyle stesso ne conclude) non modo aquam gravitare sub aqua, sed <lb></lb>eam vel fere, vel plane tantum inibi ponderare, ac ipsa illa portio liquoris <lb></lb>ponderaret in aere ” (ibid., pag. </s>

<s>213). </s></p><p type="main">

<s>Pochi anni dopo la pubblicazione originale, fatta in Oxford, di questi <lb></lb>Paradossi boileiani, correva per le mani de&#039;curiosi un libro, col titolo <emph type="italics"></emph>Ars <lb></lb>nova et magna gravitatis et levitatis,<emph.end type="italics"></emph.end> scritto in dialoghi, nel quinto de&#039;quali <lb></lb>l&#039;Autore, ch&#039;era Giorgio Sinclaro, si proponeva di trattare un tale argomento: <lb></lb>“ Ex novo illo Urinatorum machinamento, recens excogitato, cui nomen <emph type="italics"></emph>Cam­<lb></lb>panae,<emph.end type="italics"></emph.end> eiusque usu, invictissimae eruuntur rationes, quibus elementum aquae <lb></lb>in suo loco gravitare ostenditur ” (<emph type="italics"></emph>Roterodami,<emph.end type="italics"></emph.end> 1669, pag. </s>

<s>230). Vi si in­<lb></lb>comincia a narrare com&#039;essendo nel 1558 affondata, presso una delle isole <lb></lb>boreali della Scozia, una gran nave, spedita dal re di Spagna in Inghilterra, <lb></lb>ivi si rimanesse per 77 anni arrenata, infin tanto che un ardito palombaro <lb></lb>non venne a profferirsi di saperne recuperare dal fondo marino il ricchis­<lb></lb>simo carico, per via di un macchinamento da sè allora inventato: macchi­<lb></lb>namento, che consisteva in quella Campana, più di un secolo prima propo­<lb></lb>sta già al medesimo uso dal Tartaglia, ma che si rendeva praticabile, per <lb></lb>essere costruita di tale capacità, da bastar l&#039;aria dentro rinchiusa a respi­<lb></lb>rarvi in mezzo un uomo, almen per un&#039;ora. </s>

<s>Non era, come quella del No-<pb xlink:href="020/01/3201.jpg" pagenum="162"></pb>stro, chiusa tutta all&#039;intorno, ma aperta in fondo, e potrebbe aver l&#039;esempio <lb></lb>nel bicchiere, dentro cui, rovesciato e spinto con la mano in fondo a una <lb></lb>vasca, si vede tanto solo entrar d&#039;acqua, quanto glie lo permetta la conden­<lb></lb>sazione dell&#039;aria. </s>

<s>“ Ope, et auxilio huiuscemodi machinamentorum, sed in <lb></lb>primis Campanae (prosegue a dire il Sinclaro) multa experiri possumus, quae <lb></lb>adeo extra omnem controversiae aleam aquae marinae pondus et gravitatem, <lb></lb>quam in suo exercet loco, demonstrant, ut postea vix supersit alicui dubi­<lb></lb>tandi locus ” (ibid., pag. </s>

<s>230). </s></p><p type="main">

<s>I descritti esperimenti, per il Sinclaro, si riducono a cinque. </s>

<s>Vuole in <lb></lb>primo luogo che il marangone porti seco un Barometro, o Baroscopio come <lb></lb>ei lo chiama, e gli promette che vedrà, via via discendendo con la Cam­<lb></lb>pana, sollevarsi invece dentro il tubo il mercurio. </s>

<s>Poi, gonfiata prima di scen­<lb></lb>dere una vescica, e fortemente turata una bottiglia vuota, gli giura non dover <lb></lb>giungere a posarsi sul fondo del mare, senza che quella non sia ridotta flac­<lb></lb>cida, e questa in frantumi. </s>

<s>Quivi stando, suggerisce al Palombaro, in quarto <lb></lb>luogo, che prenda un&#039;altra simile bottiglia, ben bene anch&#039;essa turata, e gli <lb></lb><figure id="id.020.01.3201.1.jpg" xlink:href="020/01/3201/1.jpg"></figure></s></p><p type="caption">

<s>Figura 84.<lb></lb>predice che se la vedrà scoppiare sotto gli occhi, prima <lb></lb>che sia tornato su a galla. </s>

<s>Dice in ultimo a quel suo <lb></lb>uomo sottomarino che si prepari uno strumento, simile a <lb></lb>quello che si rappresenta qui da noi nella 84 figura, e, <lb></lb>rinchiudendolo nella sua stanza, indovina che, appena <lb></lb>incominciato a scendere nel mare, vedrà l&#039;acqua della <lb></lb>tinozza A risalire su per il sifone BC, infin tanto che <lb></lb>tutta venga a travasarsi in E. </s>

<s>Dai quali esperimenti, dice <lb></lb>il Sinclaro, si raccoglie per certo “ quod Campanae aeris <lb></lb>elaterium descendendo multum intendatur, multumque ascendendo remitta­<lb></lb>tur, quod in omne aevum inexplicabile manebit, nisi id ex aquae pressura <lb></lb>oriri dicas ” (ibid., pag. </s>

<s>239). </s></p><p type="main">

<s>Cotali esperienze non son facili è vero a farsi da un Filosofo, non av­<lb></lb>vezzo ai disagi, e non esperto dell&#039;arte dei marangoni. </s>

<s>Suggerisce perciò il <lb></lb>Sinclaro che si costruisca una Campana in piccolo, tanto ch&#039;ella possa ca­<lb></lb>pire in se un Barometro, e, senza dover profondarsi insieme con lo stru­<lb></lb>mento nè sotto l&#039;acqua de&#039;laghi, nè sotto quella de&#039;mari; seduti comoda­<lb></lb>mente sulla sponda di un vivaio, osservarne gli effetti. </s>

<s>In ogni modo qua­<lb></lb>lunque Filosofo più delicato potrebbe rendere visibile a sè, e a&#039;suoi scolari, <lb></lb>l&#039;inflaccidirsi della vescica, fatta entrare, mentre era gonfia, in un bicchiere, <lb></lb>il quale arrovesciato si spinga colla mano, più profondamente che sia pos­<lb></lb>sibile, sotto l&#039;acqua ricevuta in un vaso di vetro. </s></p><p type="main">

<s>Il Pascal, il Boyle e il Sinclaro, con gli sperimenti fin qui descritti, ba­<lb></lb>stano a persuaderci che i Fisici di Europa avevano cacciati già dalla scienza <lb></lb>i pregiudizi peripatetici, quando ancora i nostri, imbevuti degl&#039;insegnamenti <lb></lb>di Galileo, ripetevano con sicurtà che nessun fluido pesa nel suo proprio ele­<lb></lb>mento. </s>

<s>È da notare però che i tre Autori commemorati non pretendevano <lb></lb>di esser venuti a insegnare nulla di nuovo, contenti a confermare una ve-<pb xlink:href="020/01/3202.jpg" pagenum="163"></pb>rità combattuta, con la più evidente prova dei fatti. </s>

<s>Così, il Boile non fa altro <lb></lb>che moltiplicare le sperienze dello Stevino, e renderle più concludenti, ma <lb></lb>il Pascal e il Sinclaro, oltre a quelle dello Stevino, seguono altre più pros­<lb></lb>sime tradizioni, ravvivate da quel concorrere che facevasi d&#039;ogni parte a il­<lb></lb>lustrare l&#039;esperienza famosa del Torricelli. </s>

<s>La cosa insomma si riduce a que­<lb></lb>sto: che fu propriamente in Italia fabbricata l&#039;arme, per abbattere l&#039;orgo­<lb></lb>glio peripatetico di un colpo, e furono d&#039;Italiani le braccia, che lo menarono, <lb></lb>non lasciando ai successori altro che il merito di finir di uccidere il nemico <lb></lb>caduto, o la baldanza di fare intorno al suo cadavere festa e tripudio. </s>

<s>Che <lb></lb>se la vittoria s&#039;attribuisce agli stranieri è perchè il Torricelli non appari­<lb></lb>sce che quale inventore dell&#039;esperienza, lo splendor della quale invenzione <lb></lb>ecclissò in lui un merito molto maggiore, di aver cioè speculate altresì le <lb></lb>ragioni dell&#039;esperienza: ragioni che, riferendosi alle proprietà de&#039;fluidi, seco <lb></lb>stesso comunicanti o con altri, illustravano mirabilmente, quasi sopraesal­<lb></lb>tandole, le comuni leggi dell&#039;Idrostatica. </s></p><p type="main">

<s>Un tale tesoro di speculazioni fu riversato nel privato erario di Miche­<lb></lb>langiolo Ricci, amico e maestro a quel Tommaso Cornelio, che, ancora gio­<lb></lb>vane e sconosciuto, pubblicava nel 1648, col titolo <emph type="italics"></emph>De platonica circumpul­<lb></lb>sione,<emph.end type="italics"></emph.end> una sua epistola pregevolissima, perche vi si raccoglieva, ordinava e <lb></lb>illustrava tutto ciò che, intorno all&#039;Idrodinamica, e, a proposito della teoria <lb></lb>del Barometro, intorno all&#039;Idrostatica, aveva il Torricelli insegnato a voce e <lb></lb>per lettere al Ricci. </s>

<s>I quali insegnamenti rimeditando io, dice il Cornelio, <lb></lb>“ sequens experimentum tentavi: Vitreum orbem, exiguo pertusum foramine, <lb></lb>in profundiorem aquam mergebam, ostiolumque deorsum vergens digito obtu­<lb></lb>rabam, ut mox orbis in auras evectus indicaret semper maiorem atque ma­<lb></lb>iorem aquae copiam in eumdem ingestam, qno profundius ille penetrasset. </s>

<s><lb></lb>Et res quidem ex sententia successit. </s>

<s>Nam aqua eo maiori nisu, per orbis <lb></lb>foramen, intruditur, quo illa fuerit altior, atque interea aer in orbe conten­<lb></lb>tus in minus atque minus spatium cogitur, donec impulsus, a superstantis <lb></lb>aquae pondere proveniens, sit aequalis conatui, quo aer resistit ne violenter <lb></lb>comprimatur, unde, aperto deinde foramine, ac deorsum spectante, aqua fo­<lb></lb>ras extruditur a vi aeris, iuxta debitam mensuram, se se iterum expanden­<lb></lb>tis ” (<emph type="italics"></emph>Appendix ad Progymn.,<emph.end type="italics"></emph.end> Neapoli 1688, pag. </s>

<s>343). </s></p><p type="main">

<s>Dice il Cornelio tanto esser piaciute le speculazioni, e l&#039;esperienze messe <lb></lb>nel suo libretto, che alcuni se le appropriarono. </s>

<s>Non potremmo asserir con <lb></lb>certezza se, fra&#039;complici di queste usurpazioni, fosse anche il Borelli, il quale, <lb></lb>a dimostrar che l&#039;acqua gravita in sè stessa, e con tanto maggior forza, <lb></lb>quanto è più profonda; adduceva, fra le altre, come di sua propria inven­<lb></lb>zione, l&#039;esperienza descritta trent&#039;anni prima dal suo concittadino. </s>

<s>Comun­<lb></lb>que sia, a ravvedersi di ciò, che credeva esser vero sull&#039;autorità di Galileo, <lb></lb>concorsero nel Borelli altre cause, fra le quali, come nel Pascal e nel Sin­<lb></lb>claro, lo studio de&#039;fenomeni barometrici. </s>

<s>Nel fare il vuoto, specialmente con <lb></lb>l&#039;acqua, s&#039;ebbe a osservare un brulichio nel tubo, simile a quel che fa l&#039;acqua <lb></lb>stessa bollendo al fuoco: brulichio che, quanto più saliva, tanto più mostra-<pb xlink:href="020/01/3203.jpg" pagenum="164"></pb>vasi fervoroso. </s>

<s>Il Borelli spiegava il fatto col dire che l&#039;aria, chiusa dentro <lb></lb>alle bollicelle, essendo, via via che si sale, meno compressa dal peso del­<lb></lb>l&#039;acqua ambiente, si dilata, e perciò si rendono esse bollicelle più cospicue, <lb></lb>e appariscono più frequenti. </s>

<s>“ In pulcherrimo instrumento torricelliano, in <lb></lb>quo vacuum mediante aqua efficitur, videmus ab aqua tantam copiam am­<lb></lb>pullarum aerearum egredi, ut repraesentet ebullitionem, quam efficere solet <lb></lb>fervor ignis in eadem aqua. </s>

<s>Et hoc pendet ex eo quod particulae minimae <lb></lb>aeris, ibidem, non ut prius comprimuntur ab ingenti pondere aereae regio­<lb></lb>nis, sed solummodo ab exigua gravitate aquae incumbentis, quod persuade­<lb></lb>tur ex eo, quod profundiora granula aeris, quae ob parvitatem fere incon­<lb></lb>spicua erant, quo magis ad summitatem aquae accedunt, eo magis amplian­<lb></lb>tur, inflantur, grandioresque ampullas constituunt, prout magis vis elastica <lb></lb>aeris, libertatem nacta, ampliare dilatareque easdem ampullas potest ” (<emph type="italics"></emph>De <lb></lb>motion natur.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>552). </s></p><p type="main">

<s>Ai Peripatetici, fra&#039;quali possiam citare il gesuita Daniello Bartoli, osti­<lb></lb>nati in professare il principio che l&#039;acqua in mezzo all&#039;acqua non pesa, non <lb></lb>piacque punto la ragion del Borelli, e confessando pure essere stato ciò detto <lb></lb>da lui ingegnosamente, non però toglie, soggiungevano, il potersi recare il <lb></lb>fatto ad un&#039;altra ragione, “ cioè al venirsi scontrando, in quei diciassette <lb></lb>cubiti di salita, in altre bolle d&#039;aria, e con esse unendosi formarne di mol­<lb></lb>tissime piccole una grande ” (<emph type="italics"></emph>Del ghiaccio,<emph.end type="italics"></emph.end> Roma 1681, pag. </s>

<s>147). </s></p><p type="main">

<s>Ma la principale occasione di riconoscere, e detestare la falsità dell&#039;as­<lb></lb>sunto peripatetico, venne al Borelli ne&#039;frequentati congressi dell&#039;Accademia <lb></lb>del Cimento, quando si volle discutere la questione della leggerezza positiva. </s>

<s><lb></lb>Potrebb&#039;essere che il Cornelio, toltasi dal volto la maschera di Timeo Lo­<lb></lb>crese, e fattosi riconoscere per colui, che tanti meriti s&#039;era venuto acqui­<lb></lb>stando in tutti gli ordini della Fisica sperimentale; avesse, con l&#039;epistola <emph type="italics"></emph>De <lb></lb>circumpulsione<emph.end type="italics"></emph.end> raccolta in un volume co&#039;Proginnasmi, eccitato l&#039;ingegno dei <lb></lb>suoi connazionali. </s>

<s>In ogni modo le parole, dal segretario dell&#039;Accademia pre­<lb></lb>messe all&#039;argomento, commemorano Platone, autor del Dialogo del Timeo, <lb></lb>come precursore antico della verità, che si voleva confermare con le nuove <lb></lb>esperienze. </s>

<s>Ma di queste, come di tutte le altre naturali esperienze, si dà <lb></lb>dagli Accademici solamente un <emph type="italics"></emph>saggio<emph.end type="italics"></emph.end> di quel tanto più, e forse meglio, che <lb></lb>da loro s&#039;era operato. </s>

<s>Gli operatori poi più efficaci, a cotesto tempo, si sa <lb></lb>che erano il Borelli e il Viviani, i quali tanto ebbero a persuadersi del bi­<lb></lb>sogno di assicurare la scienza del moto dalle pericolose incursioni peripate­<lb></lb>tiche, che s&#039;affaccendarono a speculare ragioni, e ad ammannire esperienze, <lb></lb>per provare che non vi è leggerezza positiva, e che l&#039;acqua, l&#039;aria e ogni <lb></lb>altro fluido insomma fa dentro il proprio fluido la medesima forza all&#039;in giù, <lb></lb>che fuori di esso. </s>

<s>E perchè tali argomenti, nel libro scritto a nome di tutta <lb></lb>l&#039;Accademia, non potevano aver luogo, gli fece il Borelli, per suo proprio <lb></lb>conto, pubblicamente noti nell&#039;opera <emph type="italics"></emph>De motionibus naturalibus a gravitate <lb></lb>pendentibus,<emph.end type="italics"></emph.end> benchè gli altri del Viviani si rimangano tuttavia sconosciuti. </s>

<s><lb></lb>E perciò noi gli daremo ora alla luce, nella loro propria scrittura, essendoci <pb xlink:href="020/01/3204.jpg" pagenum="165"></pb>bastata la pazienza di ricavarla dal manoscritto più informe, e più penosa­<lb></lb>mente leggibile, di quanti altri mai ci siano fin qui capitati. </s></p><p type="main">

<s>“ PROPOSIZIONE I. — <emph type="italics"></emph>Il peso di qualsisia porzione di fluido grave sta­<lb></lb>gnante fa attualmente, dentro il proprio fluido, la medesima forza allo <lb></lb>in giù, che fuori di esso.<emph.end type="italics"></emph.end> Imperocchè il peso non è proprio, libero e indi­<lb></lb>pendente, ma necessario. </s>

<s>Onde non per elezione o per accidente fa forza <lb></lb>allo in giù, ma per necessità. </s>

<s>Per lo che, dovunque egli si sia o dentro <lb></lb>o fuori del proprio fluido, è necessario che faccia la medesima forza allo <lb></lb>in giù. </s>

<s>” </s></p><p type="main">

<s>“ Il medesimo si dimostra con l&#039;esperienza. </s>

<s>Imperocchè se, dentro qual­<lb></lb>sisia fluido stagnante sul fondo di uua bilancia, s&#039;infonderà una mole del <lb></lb>medesimo fluido, che sia di doppio peso; è manifesto che sforzerà attual­<lb></lb>mente la bilancia detta con doppia forza allo in giù. </s>

<s>Dunque è manifesto che <lb></lb>il peso della mole aggiunta fa attualmente nel proprio fluido la medesima <lb></lb>forza allo in giù, che fuori di esso. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE II. — <emph type="italics"></emph>Tutto il peso di un fluido grave stagnante ag­<lb></lb>grava perpendicolarmente il fondo, perpendicolarmente sottoposto.<emph.end type="italics"></emph.end> È evi­<lb></lb>dente per l&#039;esperienza. </s>

<s>Imperocchè se, alla forza del di lui peso non averà <lb></lb>il fondo dato momento di resistenza bastante, verrà da questo sforzato ma­<lb></lb>nifestamente a cedere. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE III. — <emph type="italics"></emph>Il peso di qualunque porzione superiore di un <lb></lb>fluido grave stagnante aggrava perpendicolarmente la porzione inferiore, <lb></lb>perpendicolarmente sottopostale. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sul fondo AB (fig. </s>

<s>85) intendasi stagnante qualsiasi <lb></lb><figure id="id.020.01.3204.1.jpg" xlink:href="020/01/3204/1.jpg"></figure></s></p><p type="caption">

<s>Figura 85.<lb></lb>porzione di fluido EB e sopra EB qualsiasi altra porzione <lb></lb>perpendicolarmente sovrappostale. </s>

<s>Dico che il peso di CD ag­<lb></lb>grava perpendicolarmente la porzione EB, perpendicolarmente <lb></lb>sottopostale. </s>

<s>Imperocchè, se è possibile, non sia dal peso della <lb></lb>porzione CD aggravata perpendicolarmente la porzione EB. </s>

<s><lb></lb>Dunque non potrà EB che col proprio peso aggravare perpen­<lb></lb>dicolamente il fondo. </s>

<s>Dunque non sarà il fondo detto, dal peso di tutto il <lb></lb>fluido CB, perpendicolarmente aggravato. </s>

<s>Il che è impossibile per quel che <lb></lb>si è dimostrato. </s>

<s>” </s></p><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>“ Il medesimo direttamente. </s>

<s>”<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>“ Tutto il peso del fluido BC aggrava perpendicolarmente il fondo AB, <lb></lb>perpendicolarmente sottopostoli. </s>

<s>Dunque tutto il peso di CB fa forza perpen­<lb></lb>dicolarmente verso AB. </s>

<s>Dunque per necessità il peso ancora della porzione <lb></lb>CD fa perpendicolarmente forza verso AB. </s>

<s>Ma è impossibile far forza per­<lb></lb>pendicolarmente verso AB, perpendicolarmente sottoposto, senza far forza <lb></lb>perpendicolarmente verso la porzione EB, posta perpendicolarmente fra essa <lb></lb>ed AB; dunque è necessario che il peso della porzione CD, facendo forza <lb></lb>perpendicolarmente verso AB, la faccia ancora verso ED, e perciò perpendi­<lb></lb>colarmente l&#039;aggravi. </s>

<s>” </s></p><pb xlink:href="020/01/3205.jpg" pagenum="166"></pb><p type="main">

<s><emph type="center"></emph><emph type="italics"></emph>“ Il medesimo altrimenti. </s>

<s>”<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s>“ Imperocchè, per qualunque cagione altri dica la superficie ED, dal <lb></lb>peso della mole sovrastante CD, non essere attualmente aggravata; cagione <lb></lb>certo non dirà esserne la di lui fluidezza. </s>

<s>Ma, presupposta la superficie ED <lb></lb>consistente, è manifesto, per le cose dette, che, di qualunque natura o gra­<lb></lb>vezza in specie si dia la mole ED, sarà dal peso di CD attualmente aggra­<lb></lb>vata; dunque, data ancora invece della consistenza la fluidezza, di qualun­<lb></lb>que natura o gravità in specie la ED si supponga; non meno del peso della <lb></lb>mole sovrastante attualmente è aggravata. </s>

<s>” </s></p><p type="main">

<s>“ Le quali cose sì per minuto ci siamo sforzati di mostrare, perchè si <lb></lb>possa vedere se contro la ragione sia o no l&#039;affermare il contrario, cioè che <lb></lb>il fluido nel fluido proprio attualmente non gravi, nè perciò le parti inferiori <lb></lb>di esso siano, dal peso delle superiori, attualmente aggravate. </s>

<s>” </s></p><p type="main">

<s>“ Il principal motivo di dubitare della verità sopraddetta furono alcune <lb></lb>esperienze, sì manifestamente a prima vista contrarie, che non è maraviglia <lb></lb>se, contro la ragione assai per altro evidente, avesse luogo nell&#039;animo di <lb></lb>molti la contraria opinione. </s>

<s>” </s></p><p type="main">

<s>“ Perchè dunque, se possibile fia, ogni scrupolo tor si possa intorno alla <lb></lb>verità di punto così importante, dal quale, come vedremo appresso, gran parte <lb></lb>della naturale Filosofia dipende, egli è sopratutto necessario che, deposta ogni <lb></lb>propria passione, sopra di essa diligente riflessione facciamo. </s>

<s>Imperocchè mi <lb></lb>do a credere che se a sufficienza mostreremo gli effetti, in esse esperienze <lb></lb>contenuti, non essere alla detta verità, se non in apparenza, contrari, e tanto <lb></lb>esser lontano che all&#039;attuale aggravamento delle parti fluide nel proprio fluido <lb></lb>repugni che, da esso presupposto, questo e altri fatti necessariamente pro­<lb></lb>vengano; mi do a credere, dico, che basterà, per fare, in chi altrimenti fin <lb></lb>ora ha creduto, cessare ogni dubbio. </s>

<s>L&#039;esperienze dunque son queste: ” </s></p><p type="main">

<s>“ I.a I marangoni, stando sott&#039;acqua, non sentono peso dall&#039;acqua, che <lb></lb>all&#039;altezza talvolta di venti o di più braccia gli sovrasta. </s>

<s>Dal che pare a ta­<lb></lb>luno evidente che il peso dell&#039;acqua non aggravi i corpi, che in essa sono <lb></lb>e per conseguenza che ella nel proprio luogo attualmente non pesi. </s>

<s>Ma, per <lb></lb>la Ia, la conseguenza è falsa. </s>

<s>Che il peso dell&#039;acqua aggravi e prema attual­<lb></lb>mente i corpi, che in essa sono, è per altro dalla esperienza manifesto. </s>

<s>Im­<lb></lb>perocchè pongasi sotto l&#039;acqua un mantice dilatato, e per tutto ben chiuso, <lb></lb>e si vedrà chiaramente che, quanto maggior copia di acqua vi s&#039;andrà di <lb></lb>sopra aggiungendo, tanto maggiormente verrà dal di lei peso abbassato e <lb></lb>ristretto. </s>

<s>Inoltre pongasi ferma sott&#039;acqua una palla di sottilissimo vetro ben <lb></lb>chiusa, e si vedrà che, aggiungendo nova acqua, verrà finalmente, per il di <lb></lb>lei peso, a schiacciarsi e a rompersi. </s>

<s>” </s></p><p type="main">

<s>“ II.a Una secchia piena d&#039;acqua, essendo nell&#039;acqua, si tira su con la <lb></lb>medesima, anzi minor forza, che fuori vuota: eppure, oltre il proprio peso, <lb></lb>vi è ancora quello di tutta la mole che le sovrasta. </s>

<s>Ciò stante, come dun­<lb></lb>que dicono eglino che l&#039;acqua nell&#039;acqua attualmente pesa? </s>

<s>” </s></p><pb xlink:href="020/01/3206.jpg" pagenum="167"></pb><p type="main">

<s>“ Ma perchè con un simile effetto resti chiara la verità rispondano ora <lb></lb>a me. </s>

<s>Una secchia piena d&#039;acqua, essendo nella bilancia, se dalla banda op­<lb></lb>posta ve ne sarà similmente un&#039;altra, si tira su colla medesima forza, anzi <lb></lb>minore, che fuori vuota. </s>

<s>Come dunque ciò stante l&#039;acqua nella bilancia at­<lb></lb>tualmente pesa? </s>

<s>E che attualmente dentro di essa pesi lo dichiarano il fondo e <lb></lb><figure id="id.020.01.3206.1.jpg" xlink:href="020/01/3206/1.jpg"></figure></s></p><p type="caption">

<s>Figura 86.<lb></lb>i fili che la sostengono, quando, non facendo al <lb></lb>di lei peso resistenza bastante, sforzati finalmente <lb></lb>si strappano. </s>

<s>Che diremo di ciò? </s>

<s>Non altro certo, <lb></lb>se non che la secchia piena d&#039;acqua pesi attual­<lb></lb>mente nella bilancia. </s>

<s>Ma perchè l&#039;altra opposta <lb></lb>pesa attualmente ancor ella, e con quella contrap­<lb></lb>pesando la sostenta, fa conseguentemente che, a <lb></lb>tirarla su, alcuna resistenza non si senta. </s>

<s>Ora, <lb></lb>il medesimo a capello nel caso nostro succede. </s>

<s><lb></lb>Imperocchè, posta la secchia piena dentro l&#039;acqua, viene il di lei peso, insieme <lb></lb>col peso della mole che le sovrasta, a contrappesarsi col peso di una mole <lb></lb>opposta, che per di sotto la sostenta. </s>

<s>Il che per chiarezza accenneremo con <lb></lb>la seguente figura (86). ” </s></p><p type="main">

<s>“ Sia AB superficie dell&#039;acqua stagnante AC, dentro la quale intendasi <lb></lb>il vaso S, la cui superficie inferiore DGE, con l&#039;acqua sovrastante, costitui­<lb></lb>sca la mole FGL. </s>

<s>Pesando dunque FGL, e facendo forza allo in giù, sfor­<lb></lb>zerà la mole perpendicolarmente sottoposta HGN, e questa non può cedere <lb></lb>se non si riflette e spigne allo in su una mole, quale sia per es. </s>

<s>NB. </s>

<s>Ma il <lb></lb>peso di questa fa resistenza ad esser mosso allo in su, alla forza dunque allo <lb></lb>in giù del peso FGL s&#039;oppone di sotto la forza del peso GHN, e perciò la <lb></lb>mole HB, con la mole FN contrappesandosi, come appresso dimostreremo, <lb></lb>la viene di sotto a sostentare. </s>

<s>Onde non si può, a tirare su il vaso S, alcuna <lb></lb>resistenza sentire, non altrimenti che nella bilancia succede. </s>

<s>” </s></p><p type="main">

<s>“ E perchè chiaramente si vegga come, dal sostentamento dell&#039;acqua <lb></lb>contrappesantesi per di sotto, tal mancamento di resistenza provenga, pon­<lb></lb>gasi di maniera il vaso S nell&#039;acqua, che l&#039;acqua GHN o altra non lo possa <lb></lb><figure id="id.020.01.3206.2.jpg" xlink:href="020/01/3206/2.jpg"></figure></s></p><p type="caption">

<s>Figura 87.<lb></lb>di sotto sostentare, perchè nel tirarlo in su si sentirà su­<lb></lb>bito tutto il peso e dell&#039;acqua che è nel vaso, e di quella <lb></lb>ancora che perpendicolarmente gli sovrasta. </s>

<s>L&#039;esperienza <lb></lb>può farsi facilmente così: Sia il fondo OC (fig. </s>

<s>87) del <lb></lb>continente prolungato, verso la parte M, in un tubo ci­<lb></lb>lindrico, e la superficie inferiore del vaso S rotondo sia <lb></lb>tutta profondata dentro di esso, sicchè l&#039;acqua stagnante <lb></lb>AC non iscorra sotto S. </s>

<s>E per levare ogni sospetto di <lb></lb>paura di vuoto, come anco per altro, vi siano, di lato alla detta superficie <lb></lb>inferiore, gli spiragli K, L, con le loro animelle, per potervi entrare libera­<lb></lb>mente l&#039;aria esteriore. </s>

<s>Dico che, tirando in su il vaso S, si sentirà il peso <lb></lb>dell&#039;acqua che è nel vaso, e di tutta la mole sovrastante. </s>

<s>” </s></p><p type="main">

<s>“ Intese bene le ragioni degli effetti predetti, si potranno facilmente in-<pb xlink:href="020/01/3207.jpg" pagenum="168"></pb>tendere quelle ancora di qual si voglia altri effetti simili che, contro l&#039;at­<lb></lb>tuale aggravamento delle parti fluide si sogliono o si potrebbero addurre, <lb></lb>quali, non parendo necessario l&#039;esaminarli qui ad uno ad uno, ci siam con­<lb></lb>tentati di mostrarne la cagione universale, onde possa ciascuno ai dubbi par­<lb></lb>ticolari per sè medesimo sodisfare ” (MSS. Cim., T. XXXIV, fol. </s>

<s>119-20). </s></p><p type="main">

<s>Le repressioni per cui s&#039;alleggerisce il peso della secchia, nell&#039;espe­<lb></lb>rienza illustrata dalla figura 86, promette il Viviani, com&#039;abbiamo udito, di <lb></lb>dimostrarle appresso, d&#039;onde apparisce l&#039;intenzion dell&#039;Autore di proseguire, <lb></lb>intorno all&#039;argomento, il discorso. </s>

<s>E così fece davvero, come si trova poco <lb></lb>più avanti, svolgendo le pagine del manoscritto. </s>

<s>Ma così fecondo, e di così <lb></lb>grande importanza si presentò alla mente dello stesso Viviani il soggetto, che <lb></lb>dell&#039;equilibrio de&#039;liquidi in sè medesimi, e con altri liquidi comunicanti, volle <lb></lb>di proposito trattarne in vari scritti, ora lasciati per qualche tempo interrotti, <lb></lb>ora ripresi, i quali, essendo stati da noi qua e là per le disperse carte rac­<lb></lb>colti, si pubblicheranno in altre occasioni. </s>

<s>Intanto è da veder come concor­<lb></lb>resse il Borelli a ravviar l&#039;Idrostatica sulla medesima rettitudine de&#039;sentieri. </s></p><p type="main">

<s>Il capitolo terzo <emph type="italics"></emph>De motionibus naturalibus,<emph.end type="italics"></emph.end> come general soggetto, da <lb></lb>trattarsi in quelle XXIV proposizioni ch&#039;ei comprende, porta scritto questo <lb></lb>titolo in fronte: <emph type="italics"></emph>Quodlibet corpus fluidum eorum quae innituntur super­<lb></lb>ficiei Telluris grave est, exercetque vim suae gravitatis etiam dum in pro­<lb></lb>prio loco, et in ipsomet fluido universali sui generis consistit ac quiescit<emph.end type="italics"></emph.end><lb></lb>(pag. </s>

<s>33). Incomincia l&#039;Autore a far osservare che l&#039;annunziata verità si con­<lb></lb>clude dall&#039;ipotesi, e s&#039;argomenta certissimamente dai processi, tenuti da Ar­<lb></lb>chimede in dimostrare le sue proposizioni. </s>

<s>E nonostante, soggiunge, vollero <lb></lb>ciò negare, e tutt&#039;altrimenti sentirono i Peripatetici, “ qui censent non sem­<lb></lb>per verum esse quod partes superiores corporis gravis comprimant, et vim <lb></lb>inferant inferioribus et contiguis, nisi infimae partes leves sint absolute vel <lb></lb>respective. </s>

<s>Unde concedunt terram ex. </s>

<s>gr. </s>

<s>super aquam aut super aerem po­<lb></lb>sitam vim et operationem gravitatis et compressionis exercere, non itidem <lb></lb>aquam super ipsam terram collocatam, nec aerem aquae incumbentem. </s>

<s>Immo <lb></lb>nec aerem supra aerem constitutum nec aquam supra aquam positam ” (ibid., <lb></lb>pag. </s>

<s>33, 34). </s></p><p type="main">

<s>I primi e principali argomenti, usati dal Borelli per confutare i Peripa­<lb></lb>tetici, eccettuata l&#039;esperienza della bolla di vetro, descritta già nell&#039;epistola <lb></lb>del Cornelio, e ripetuta qui nella XV proposizione; consistono nel dimostrar <lb></lb>la verità dell&#039;ipotesi d&#039;Archimede, e di tutte le conseguenze di lei. </s>

<s>Rivol­<lb></lb>giamo indietro lo sguardo sopra la nostra figura 78, che può servire a illu­<lb></lb>strar la V proposizione <emph type="italics"></emph>De insidentibus humido.<emph.end type="italics"></emph.end> Se l&#039;umido ALO, dice l&#039;Au­<lb></lb>tore, è in equilibrio con l&#039;umido OLB, sopraggiuntovi l&#039;umido EO da una <lb></lb>parte, e l&#039;umido OF dall&#039;altra; le due superficie AO, OB saranno ugual­<lb></lb>mente premute. </s>

<s>Ond&#039;è manifesto che Archimede, al contrario dei Peripate­<lb></lb>tici, suppone che l&#039;umido nell&#039;umido pesi. </s>

<s>Per confermare la verità della quale <lb></lb>supposizione, giacchè le due predette superficie AO, OB si riguardano come il <lb></lb>fondo solido di un vaso, il Borelli dimostra, nelle proposizioni XIII e XIV, che <pb xlink:href="020/01/3208.jpg" pagenum="169"></pb>un tal fondo è veramente premuto, come, lasciati tutti gli altri discorsi, lo atte­<lb></lb>stano i fatti, vedendosi l&#039;acqua “ ad ingentem altitudinem elevata, nedum so­<lb></lb>lum ac fundum vasis inflectit, sed ipsum multoties diffringit ” (ibid., pag. </s>

<s>41). </s></p><p type="main">

<s>Così disposte le cose, passa Archimede a dimostrare che il solido più <lb></lb>leggero, immerso per la sua parte C, è in equilibrio, perchè la mole H del­<lb></lb>l&#039;umido, uguale alla mole solida immersa, pesa quanto il solido intero. </s>

<s>Se <lb></lb>dunque tutti i Fisici e i Matematici del mondo hanno ripetuto e ripetono <lb></lb>queste dimostrazioni, essendo H nell&#039;umido, tutti i Fisici e i Matematici del <lb></lb>mondo con Archimede convengono che l&#039;umido dentro l&#039;umido pesi, perchè <lb></lb>altrimenti, dice il Borelli, s&#039;incorrerebbe nell&#039;assurdo che il nulla facesse <lb></lb>equilibrio a una gravezza assoluta. </s>

<s>Di più si riducevano i Peripatetici, col <lb></lb>loro assunto, nell&#039;impossibilità di spiegare come un solido pesi meno nel­<lb></lb>l&#039;acqua che nell&#039;aria. </s>

<s>Con la dottrina di Archimede si spiega il fatto, dicendo <lb></lb>che l&#039;acqua collaterale spinge in su l&#039;acqua a esso solido sottoposta: ra­<lb></lb>gione che non varrebbe, quando fosse vero che l&#039;acqua nell&#039;acqua non eser­<lb></lb>cita il momento della sua gravità naturale. (ivi, pag. </s>

<s>44, conferito con quel <lb></lb>che leggesi a pag. </s>

<s>168). </s></p><p type="main">

<s>Bastino questi accenni, a potere estimar giustamente l&#039;efficacia degli ar­<lb></lb>gomenti del Borelli: efficacia, che principalmente consiste nel dimostrar come <lb></lb>l&#039;ipotesi peripatetica rovescia tutta l&#039;Idrostatica da&#039;suoi fondamenti. </s>

<s>E per­<lb></lb>chè quella ipotesi fu ricevuta pure da Galileo, si direbbe che il capitolo III <lb></lb><emph type="italics"></emph>De motionibus naturalibus<emph.end type="italics"></emph.end> fu scritto dal Discepolo apposta, per confutare <lb></lb>una delle più perniciose dottrine del suo maestro. </s>

<s>Così è di fatto. </s>

<s>Risovven­<lb></lb>gaci di aver letto, nel Discorso famoso intorno alle galleggianti, esser falsis­<lb></lb>simo che l&#039;acqua possa accrescere peso alle cose in essa collocate, <emph type="italics"></emph>perchè <lb></lb>l&#039;acqua nell&#039;acqua non ha gravità veruna, poichè ella non vi discende.<emph.end type="italics"></emph.end><lb></lb>Contro questa ragione di Galileo è manifestamente scritta dal Borelli la pro­<lb></lb>posizione XXII: <emph type="italics"></emph>Corpora, in bilance aequilibrata, ideo quiescunt et torpent, <lb></lb>quia gravitatem exercent, comprimunturque aequalibus viribus ab ambien­<lb></lb>tibus corporibus pariter aequilibratis<emph.end type="italics"></emph.end> (ibid. </s>

<s>pag. </s>

<s>55). Dimostrata la quale, <lb></lb>immediatamente si soggiunge: ” Eodem fere modo in aqua idem aequili­<lb></lb>brium effici manifestum est, proindeque partes ipsius aquae partim superne <lb></lb>comprimi a superstantibus aquae partibus, partim vero inferne sursum expelli, <lb></lb>non propria vi, sed pondere collateralis aquae, quae cum illa libram imagi­<lb></lb>nariam, vel siphonem constituit ” (ibid., pag. </s>

<s>57). </s></p><p type="main">

<s>Benchè dunque la vera intenzion del Borelli sia facile penetrarla, non <lb></lb>è però ch&#039;ei ne faccia il minimo segno. </s>

<s>Anzi colà, dove nella proposizione CC <lb></lb>gli sarebbe occorso di correggere l&#039;errore di Galileo, il quale co&#039;Peripatetici <lb></lb>teneva non pesar l&#039;aria costituita sopra l&#039;acqua; par che lo voglia scusare, <lb></lb>dicendo che il peso dell&#039;aria stessa, scesa nella fossetta scavatasi dall&#039;assi­<lb></lb>cella d&#039;ebano galleggiante, è di così lieve momento, da potersi anche trascu­<lb></lb>rare. </s>

<s>“ Ex hydrostaticis, moles aquae aequalis spatio AOSB (fig. </s>

<s>69 del ca­<lb></lb>pitolo prec.) aeque ponderat ac lamina IS, una cum aere BI, qui, ob insen­<lb></lb>sibilem eius gravitatem, negligi potest ” (ibid., pag. </s>

<s>414). </s></p><pb xlink:href="020/01/3209.jpg" pagenum="170"></pb><p type="main">

<s>Si diceva che pare voglia il Borelli scusare il suo Maestro, benchè in <lb></lb>effetto non sia così, perchè Galileo non trascurò il peso dell&#039;aria nella fos­<lb></lb>setta come insensibile, ma come nullo affatto. </s>

<s>Sopra le denudate spalle del­<lb></lb>l&#039;esoso Cartesio sfoga piuttosto il Borelli l&#039;ira della sua sferza (propos. </s>

<s>XXXVI, <lb></lb>pag. </s>

<s>73), giacchè è un destino che i due orgogliosi competitori del nuovo <lb></lb>principato della scienza, mentre facevano aspro duello insieme, per l&#039;acqui­<lb></lb>sto di una verità, o per il merito di una scoperta, cadessero poi bene spesso, <lb></lb>pacificamente umiliati, nella medesima fossa. </s>

<s>Il Cartesio, inspiratosi forse a <lb></lb>quel che il microscopio gli rivelava nel formaggio e nell&#039;aceto, immaginò che <lb></lb>le molecole componenti l&#039;acqua rappresentassero la figura e la lubricità delle <lb></lb>anguille, per cui non fossero nè gravi nè leggere in sè stesse, come quelle <lb></lb>che continuamente si movono per tutti i versi: conclusione, alla quale Ga­<lb></lb>lileo era invece venuto dal considerare quelle stesse molecole costituite in una <lb></lb>assoluta impossibilità di scendere e di salire. </s></p><p type="main">

<s>Che se tali riguardi di non offendere la reputazione del proprio mae­<lb></lb>stro ebbe il Borelli, si può credere che non gli dovesse rimanere inferiore <lb></lb>il Viviani, il quale tanto riconoscendo importante dimostrare che il fluido nel <lb></lb>proprio fluido attualmente gravita, perchè da una tale verità dipende gran <lb></lb>parte della Filosofia naturale; veniva a confessare che Galileo aveva sopra <lb></lb>falsi fondamenti, in gran parte, fondate le sue istituzioni. </s>

<s>Eppure non tra­<lb></lb>sparisce un motto, nelle sue varie scritture d&#039;Idrostatica, ch&#039;ei l&#039;abbia di­<lb></lb>stese con l&#039;intenzione di raddirizzare alla scienza i sentieri, e di liberarla da <lb></lb>quelle angustie, nelle quali l&#039;aveva costretta il suo venerato Autore del Di­<lb></lb>scorso intorno alle cose che si muovono, o che stanno nell&#039;acqua. </s></p><p type="main">

<s>Alcuni loderanno forse questi atti del Viviani e del Borelli, molto simili <lb></lb>a quelli di un figlio, che ricopre di un velo pietosamente le vergogne del <lb></lb>padre. </s>

<s>Ma altri, ripensando che sotto quel velo si nascondeva un agguato, a <lb></lb>cui potevano rimaner facilmente presi i giovani studiosi; giudicarono meglio <lb></lb>di avvertirne, con più ragionevole pietà, gl&#039;incauti, di che il primo libero <lb></lb>esempio venne dato dalla cattedra stessa, dalla quale, pià di un mezzo se­<lb></lb>colo avanti, erasi lavorato l&#039;insidioso artificio di quegli agguati. </s>

<s>Stefano Degli <lb></lb>Angeli, leggendo nello studio di Padova il celebre discorso idrostatico di Ga­<lb></lb>lileo, aveva fatto notare ai suoi uditori che certi principii ivi professati non <lb></lb>erano veri, e giunto a quella general proposizione, nella quale l&#039;Autore con­<lb></lb>clude: <emph type="italics"></emph>Adunque la gravità del solido IS<emph.end type="italics"></emph.end> (nella nostra figura 69, interca­<lb></lb>lata nel capitolo avanti, e che corrisponde allo schema di Galileo) <emph type="italics"></emph>è uguale <lb></lb>alla gravità di una mole d&#039;acqua, eguale alla mole AS; ma la gravità <lb></lb>del solido IS è la medesima che la gravità del solido AS, composto del <lb></lb>solido IS e dell&#039;aria ABCI; adunque tanto pesa tutto il solido composto <lb></lb>AOSB, quanto pesa l&#039;acqua, che si conterrebbe nel luogo di esso compo­<lb></lb>sto AOSB<emph.end type="italics"></emph.end> (Alb. </s>

<s>XII, 63); diceva liberamente l&#039;Angeli che in questo ragio­<lb></lb>namento si contiene una aperta fallacia, perchè anche l&#039;aria ABCI è pesa, <lb></lb>nè il peso di lei può trascurarsi in un teorema, che si dimostra dall&#039;Autore <lb></lb>con metodo matematico, e che si vuol da lui esaltare alla dignità della Geo-<pb xlink:href="020/01/3210.jpg" pagenum="171"></pb>metria. </s>

<s>Essendo poi questa, come s&#039;è detto, proposizion generale, tutte le <lb></lb>altre che ne dipendono son dal medesimo vizio contaminate. </s></p><p type="main">

<s>L&#039;insegnamento orale, riconosciuta l&#039;importanza dell&#039;argomento, volle <lb></lb>poi l&#039;Angeli ridurre in scritto, in que&#039;dialoghi, che pubblicò <emph type="italics"></emph>Della gravità <lb></lb>dell&#039;aria e fluidi esercitata principalmente nelli loro omogenei,<emph.end type="italics"></emph.end> dove si sot­<lb></lb>topongono al giudizio imparziale dei dotti le fallacie peripatetiche del Di­<lb></lb>scorso intorno alle galleggianti. </s>

<s>Ond&#039;essendo questo un coraggioso esempio <lb></lb>di filosofica libertà, per non essere men pericoloso allora, come ora, scrivere <lb></lb>contro Galileo, di quel che fosse pericoloso a Galileo stesso scrivere contro <lb></lb>Aristotile; recheremo nella sua integrità dal Dialogo I l&#039;interlocuzione che <lb></lb>esso Angeli, sotto il nome di Matematico di Padova, finge di aver avuto, in <lb></lb>tal proposito, con un certo Ofredi. </s></p><p type="main">

<s>“ OFREDI. — Il Galileo è d&#039;opinione, in quel suo ammirabile trattato <lb></lb>delli galleggianti, che l&#039;aria nell&#039;acqua non graviti in conto alcuno. </s>

<s>Onde, <lb></lb>se V. S. dice di sì, contraria certo alla sua dottrina. </s>

<s>” </s></p><p type="main">

<s>“ MATEMATICO. — Io stimo che l&#039;aria pesi nell&#039;acqua, perchè io la tengo <lb></lb>per corpo grave, come pure è reputata dal Galileo medesimo; ond&#039;essendo <lb></lb>tale, deve gravitar da per tutto. </s>

<s>Ma il Galileo porta ragione o esperienza al­<lb></lb>cuna che l&#039;aria nell&#039;acqua non graviti? </s>

<s>” </s></p><p type="main">

<s>“ OFREDI. — No signore. </s>

<s>Solo lo suppone, come cosa nota e trivialis­<lb></lb>sima, a carte 42, ove ricerca che grossezza può avere una laminetta, di qual <lb></lb>si sia materia, più grave in specie dell&#039;acqua, acciocchè, collocata legger­<lb></lb>mente sopr&#039;essa, non s&#039;immerga. </s>

<s>Dice che la laminetta IS, nel suo schema, <lb></lb>entra nell&#039;acqua, che se gli alza sopra, facendo li arginetti BC, AI, li quali <lb></lb>contengono una fossarella piena di aria, della quale e della laminetta si fa <lb></lb>un prisma AS. </s>

<s>Ora dice che quest&#039;aggregato, il quale ha tanto momento, <lb></lb>quant&#039;è quello d&#039;una mole d&#039;acqua ad esso uguale; ha tanta gravità, quanta <lb></lb>è quella della sola laminetta IS, <emph type="italics"></emph>avvenga che,<emph.end type="italics"></emph.end> dice egli, <emph type="italics"></emph>la mole dell&#039;aria <lb></lb>AC non cresca o diminuisca la gravità della mole IS.<emph.end type="italics"></emph.end> Il medesimo da esso <lb></lb>viene assunto come cosa nota, nella proposizione generale, che segue a <lb></lb>carte 43. Onde, se questi supposti non sono veri, anco le dette proposizioni <lb></lb>saranno manchevoli. </s>

<s>” </s></p><p type="main">

<s>“ MATEMATICO. — Certo che essendo così, come realmente è, e questa <lb></lb>ed altre sue proposizioni, nelle quali suppone questa cosa, saranno difettose <lb></lb>in rigor geometrico, poichè in realtà AS è un aggregato di due corpi gravi, <lb></lb>e così l&#039;acqua, eguale al prisma AS, deve pesare quanto pesano tutte due <lb></lb>assieme. </s>

<s>Nè il modo di ritrovare l&#039;altezza delli arginetti BC, AI, sarà total­<lb></lb>mente quello, che insegna il Galileo. </s>

<s>” </s></p><p type="main">

<s>“ OFREDI. — <emph type="italics"></emph>Quod parum distat nihil distare videtur, e, parum pro <lb></lb>nihilo reputatur.<emph.end type="italics"></emph.end> Onde, anco quando vi sia qualche varietà, questa sarà <lb></lb>tanto poca, che nulla più. </s>

<s>Poichè, quanto può pesare un pochino d&#039;aria, <lb></lb>quant&#039;è il prisma AC? ” </s></p><p type="main">

<s>“ MATEMATICO. — Pochissimo certo. </s>

<s>Nulladimeno, signor Ofredi, potrà <lb></lb>essere che in pratica s&#039;esperimentasse che la Natura non sprezzasse questo <pb xlink:href="020/01/3211.jpg" pagenum="172"></pb>poco peso, e che l&#039;aria AC in fatti gravitasse, e il modo è questo. </s>

<s>Si prenda <lb></lb>la laminetta SI di materia, la quale nou si possa inzuppare, come sarebbe <lb></lb>argento, oro, ecc., e sia la massima, sicchè, niente più grossa, si profondasse, <lb></lb>e si collochi nell&#039;acqua. </s>

<s>È manifesto che, se l&#039;aria non aggiunge peso, come <lb></lb>dice il Galileo, anco quando s&#039;alterasse, facendosi più densa o più rara, non <lb></lb>per questo la laminetta farebbe mutazione alcuna, quanto al discendere. </s>

<s>Ma <lb></lb>se l&#039;aria AC in fatti gravita, ogni volta che, con qualche artificio, si farà più <lb></lb>densa, ed in conseguenza più grave; la laminetta SI subito discenderà, per­<lb></lb>chè allora AS sarà più grave in specie di altrettant&#039;acqua. </s>

<s>Ma checchè suc­<lb></lb>ceda di questa esperienza, io giudico che assolutamente non solo l&#039;acqua, <lb></lb>ma anco l&#039;aria graviti nella medesima acqua. </s>

<s>” (Padova, 1671, pag. </s>

<s>20, 21). </s></p><p type="main">

<s>Avrebbe fatto meglio l&#039;Angeli a descrivere con accuratezza l&#039;esperienza, <lb></lb>e dimostrare che così il fatto succede, com&#039;egli affermava, tanto più che fa­<lb></lb>cile glie ne porgevano allora il modo il Tubo torricelliano, e la Macchina <lb></lb>pneumatica. </s>

<s>Ma che avrebbe detto egli, che ne avrebbero detto i Lettori, se <lb></lb>il Bonaventuri fosse venuto 47 anni prima a mettere a loro sott&#039;occhio la <lb></lb>lettera a Tolomeo Nozzolini, nella quale Galileo descrive e mostra di aver <lb></lb>fatto, rarefacendo l&#039;aria al calore, la delicatissima esperienza, per dimostrar <lb></lb>con visibile effetto come l&#039;aria stessa contenuta nella fossetta ha tal sensi­<lb></lb>bile gravità, che, col crescerne o col diminuirne il momento, conferisce effi­<lb></lb>cacemente al sommergersi di più o al respirare dell&#039;assicella? </s>

<s>Avrebbero <lb></lb>detto tutti costoro che Galileo aveva riconosciuto il suo errore, e che voleva <lb></lb>emendarlo, indotti in questa opinione dal vedere essersi egli già ritrattato <lb></lb>rispetto a quel che aveva pronunziato della virtù calamitica dell&#039;aria in ri­<lb></lb>tirare in su, dentro il bicchiere inverso, la pallina galleggiante di cera. </s>

<s>Or <lb></lb>chi potrebbe avere il minimo dubbio intorno alla verità di un tal giudizio, <lb></lb>essendo le cose descritte nella lettera al Nozzolini di tanto chiara espres­<lb></lb>sione? </s></p><p type="main">

<s>Così, come tutti giudicherebbero, fu giudicato a principio anche da noi, <lb></lb>che credemmo fosse avvenuta la conversione dall&#039;essersi, mentr&#039;era sotto i <lb></lb>torchi la prima edizione del Discorso intorno alle galleggianti, diffusa la no­<lb></lb>tizia dell&#039;Idrostatica steviniana, l&#039;esperienza descritta nella quale, che cioè <lb></lb>tanto pesa un vaso pien d&#039;acqua, quanto essendo quasi vuoto, per averne <lb></lb>occupato il luogo un solido fisso a un muro; aveva fatto a Galileo, in ri­<lb></lb>spondere a&#039;suoi contradittori, un si bel gioco. </s></p><p type="main">

<s>Rimaneva nonostante il fatto di tanta curiosità, che per sodisfarla si sa­<lb></lb>rebbe desiderata una dichiarazione espressa di questa repentina mutazione <lb></lb>d&#039;idee. </s>

<s>Ma perchè dalla lettera al Nozzolini non s&#039;aveva speranza di rica­<lb></lb>varla, si pensò di ricorrere ad altri documenti, e fra questi a quelli parti­<lb></lb>colarmente riguardanti l&#039;Accademico incognito, di rispondere al quale, piut­<lb></lb>tosto che allo stesso Nozzolini, tanto si vede premere a Galileo. </s>

<s>Di qui si <lb></lb>venne naturalmente per noi a ricercar quel libretto, stampato in Pisa nel 1612, <lb></lb>col titolo di <emph type="italics"></emph>Considerazioni sopra il discorso del signor Galileo Galilei in­<lb></lb>torno alle cose che stanno in su l&#039;acqua, o che in quella si muovono,<emph.end type="italics"></emph.end><pb xlink:href="020/01/3212.jpg" pagenum="173"></pb><emph type="italics"></emph>fatte, a difesa e dichiarazione dell&#039;opinione d&#039;Aristotile, da Accademico <lb></lb>incognito,<emph.end type="italics"></emph.end> e ci fu gran ventura il ritrovarlo in quell&#039;esemplare, che Galileo <lb></lb>stesso postillò di sua propria mano. </s>

<s>Dall&#039;esame delle quali postille, e del <lb></lb>testo, ce ne resultò la piena intelligenza della lettera al Nozzolini, e una <lb></lb>conclusione inaspettata, ma la più certa che si potesse desiderare, ed è che, <lb></lb>nonostante l&#039;esperienza dimostrativa di tutto il contrario, Galileo persistè nel <lb></lb>credere co&#039;Peripatetici che l&#039;aria sopra l&#039;acqua non pesi. </s>

<s>La cosa ha tanto <lb></lb>dello strano, che non sarebbe facile il crederla, se non ne adducessimo i do­<lb></lb>cumenti. </s></p><p type="main">

<s>A pag. </s>

<s>14 l&#039;Accademico incognito dice: “ ..... pongo leggermente con <lb></lb>l&#039;altra mano la piastra di piombo dentro gli arginetti dell&#039;acqua sopra la <lb></lb>tavoletta d&#039;ebano, senza però toccare nè questa nè quelli, e tosto sospinta <lb></lb>l&#039;aria quivi rinchiusa, questa fuggendo se ne ritira nel suo elemento, et ab­<lb></lb>bandona la tavoletta, la quale nondimeno, restando salva sopra l&#039;acqua, già <lb></lb>la figura tutta galleggiando, grida vittoria vittoria. </s>

<s>” E Galileo in margine <lb></lb>scrive tale postilla: “ Opera l&#039;istesso quella pochissima aria, che se fosse <lb></lb>tutto pieno e non vi fusse la falda. </s>

<s>E mirabile esempio et esperienza sarà <lb></lb>il pigliare una bigoncia, ed accomodarvi dentro un maschio affisso poi fora <lb></lb>in qualche luogo stabile, sicchè tal maschio resti 4 dita lontano dal fondo, <lb></lb>e mezzo dito dalla sponda della bigoncia. </s>

<s>Perchè, infusovi poi quattro o sei <lb></lb>fiaschi d&#039;acqua, non si potrà alzare quelle quattro dita, e peserà come se <lb></lb>tutto fosse pieno d&#039;acqua. </s>

<s>Vedi più distintamente nel principio al segno.... ” </s></p><p type="main">

<s>Il segno richiama a un discorso, esplicativo di ciò che qui semplice­<lb></lb>mente s&#039;accenna, scritto nelle prime due carte bianche, che sono al libro di <lb></lb>guardia, perchè l&#039;angusto margine a tanto non bastava. </s>

<s>E perchè altrimenti <lb></lb>non sarebbe facile comprendere la virtù del nostro argomento, crediamo di <lb></lb><figure id="id.020.01.3212.1.jpg" xlink:href="020/01/3212/1.jpg"></figure></s></p><p type="caption">

<s>Figura 88.<lb></lb>dover dall&#039;autografo trascrivere fedelmente, così com&#039;ora fa­<lb></lb>remo, il detto discorso di Galileo: “ Sia un solido di piombo, <lb></lb>o altra materia gravissima AB (fig. </s>

<s>88), fermato in A, in guisa <lb></lb>che non discenda, ed intendasi un vaso CDE, capace della <lb></lb>mole di esso solido, e di un poco più, il qual vaso, collocato <lb></lb>prima più basso della base B del solido, empiasi d&#039;acqua, e <lb></lb>poi lentamente si elevi contro al solido, sicchè quello entran­<lb></lb>dovi faccia traboccar l&#039;acqua, ed uscire dal vaso. </s>

<s>Dico che <lb></lb>chi sosterrà il vaso, benchè per l&#039;ingresso del solido sia par­<lb></lb>tita quasi tutta l&#039;acqua, e benchè il solido sia fisso e sostenuto in A, sentirà <lb></lb>gravarsi dall&#039;istesso peso appunto, che quando sosteneva il vaso pieno d&#039;acqua. </s>

<s><lb></lb>Il che si farà manifesto se considereremo come la virtù sostenente il solido <lb></lb>posta in A, mentre tal solido era fuori di acqua, sentiva maggior peso, che <lb></lb>dopo che il solido è venuto immerso nell&#039;acqua. </s>

<s>Il qual peso, non potendo <lb></lb>essere andato in niente, è forza che si appoggi sopra quella virtù, che ha <lb></lb>sollevato il vaso. </s>

<s>Considerando poi quanto si sia scemata di fatica alla virtù, <lb></lb>che prima sosteneva il solido in aria, avanti che fosse locato in acqua, facil­<lb></lb>mente intenderemo tanto essere scemata la fatica della virtù in A, quanto <pb xlink:href="020/01/3213.jpg" pagenum="174"></pb>l&#039;acqua ha scemato la gravità del solido AB. </s>

<s>Ma già sappiamo che un solido <lb></lb>più grave dell&#039;acqua pesa in quella tanto meno, che nell&#039;aria, quant&#039;e il <lb></lb>peso in aria d&#039;una mole d&#039;acqua, uguale alla mole del solido sommersa; <lb></lb>adunque il solido AB grava sopra la virtù sostenente il vaso CDE tanto, <lb></lb>quant&#039;è il peso di tant&#039;acqua, quant&#039;è la mole del solido demersa. </s>

<s>Ma alla <lb></lb>mole del solido demersa è di mano in mano uguale l&#039;acqua, che si spande <lb></lb>fuor del vaso; adunque, per tale effusione di acqua, non si scema punto il <lb></lb>peso, che grava sopra la virtù, che sostiene il vaso. </s>

<s>Et è manifesto che il <lb></lb>solido AB, sebbene scaccia l&#039;acqua del vaso, nientedimeno, con l&#039;occuparvi <lb></lb>il luogo dell&#039;acqua scacciata, vi conserva tanto di gravità, quanta appunto è <lb></lb>quella dell&#039;acqua scacciata. </s>

<s>Però, signor Accademico, il solido di piombo, che <lb></lb>voi collocate nella cavità degli arginetti, scaccia ben l&#039;aria che vi trova, ma <lb></lb>egli stesso conferisce a quel vaso tanto appunto dei proprii momenti, quant&#039;era <lb></lb>il momento dell&#039;aria discacciata. </s>

<s>Bisogna, se voi volete vedere ciò che operi <lb></lb>e non operi l&#039;aria accoppiata con un solido, porvela prima, e poi rimoverla, <lb></lb>ma senza suggerire in suo luogo altro corpo, che possa fare l&#039;effetto stesso, <lb></lb>che ella faceva prima, ed un modo assai spedito e sensato sarà questo: </s></p><p type="main">

<s>“ Facciasi un vaso di vetro, simile all&#039;ABE (fig. </s>

<s>89), di qualsivoglia <lb></lb>grandezza, il quale abbia in A un foro assai angusto, nel fondo del quale, <lb></lb>o dentro o fuori, pongasi piombo, tanto che, messo tal vaso nell&#039;acqua, sendo <lb></lb><figure id="id.020.01.3213.1.jpg" xlink:href="020/01/3213/1.jpg"></figure></s></p><p type="caption">

<s>Figura 89.<lb></lb>il resto pieno di aria, si riduca all&#039;equilibrio, ovvero che <lb></lb>appena discenda al fondo. </s>

<s>Pongasi poi sopra il foco, sicchè <lb></lb>l&#039;aria contenuta in esso sia scacciata o in tutto o in gran <lb></lb>parte dalle sottilissime parti ignee che, passando per la <lb></lb>sostanza del vetro, vi entreranno dentro. </s>

<s>Et avanti che il <lb></lb>vaso si remova dal foco, serrisi esquisitamente il foro A, <lb></lb>sicchè l&#039;aria non vi possi rientrare. </s>

<s>Levisi poi dal foco e <lb></lb>lascisi stare, sinchè si freddi, e tornisi poi a metter nell&#039;acqua, e vedrassi <lb></lb>galleggiare, per essergli stata remossa o tutta o gran parte dell&#039;aria, che <lb></lb>prima lo riempiva, senza che in luogo di quella sia succeduto altro corpo, <lb></lb>siccome per esperienza si vedrà aprendo il foro A, per il quale con grand&#039;im­<lb></lb>peto si sentirà entrar l&#039;aria a riempire il vaso, che di nuovo posto nell&#039;acqua <lb></lb>come prima andrà al fondo. </s>

<s>Ma se il vaso ABE fosse tutto aperto di sopra, et <lb></lb>aggiustato col piombo, sicchè galleggiasse bene, ma fosse ridotto vicinissimo <lb></lb>al sommergersi; se alcuno scaccerà l&#039;aria, col porvi dentro un solido poco <lb></lb>minor del suo vano, sostenendo però tal solido con la mano, non aspetti di <lb></lb>veder respirare il vaso, nè punto sollevarsi sopra il livello dell&#039;acqua, come <lb></lb>nell&#039;altra esperienza accadeva, perchè il solido postovi scaccia ben, ma vi <lb></lb>rimette altrettanto del suo momento ” (MSS. Gal., P. II, T. XV, a tergo del <lb></lb>fol. </s>

<s>3 e fol. </s>

<s>4). </s></p><p type="main">

<s>Queste considerazioni poi s&#039;inserirono nella lettera al Nozzolini, ripulite <lb></lb>nella forma, e quasi ringentilitavi l&#039;esperienza, col trasformare il vaso ABE <lb></lb>in una caraffella di assai lungo collo, a somiglianza di quelle, che s&#039;usavano <lb></lb>per il Termometro, e così, dando luogo all&#039;invenzione di un nuovo strumento, <pb xlink:href="020/01/3214.jpg" pagenum="175"></pb>da misurare il peso dell&#039;aria in mezzo all&#039;acqua. </s>

<s>Che siano poi le cose de­<lb></lb>scritte non un esercizio rettorico, ma la relazione esatta di un fatto speri­<lb></lb>mentato, s&#039;argomenta da alcuni particolari, come dal voler che si tenga conto <lb></lb>del peso della cera, servita per turare la bocca alla caraffa, affinchè, scac­<lb></lb>ciata una volta dal foco, non abbia di fuori a sottentrarvi altr&#039;aria. </s></p><p type="main">

<s>Inoltre, che sia la fatta esperienza, come si diceva, delicatissima, potrà <lb></lb>giudicarsi da chiunque vada ripensando agli applausi, con i quali fu accolta <lb></lb>una simile esperienza, descritta nel suo libro <emph type="italics"></emph>De compositione et resolutione <lb></lb>mathematica<emph.end type="italics"></emph.end> dal Rinaldini (Bononiae 1655, pag. </s>

<s>179), il quale, trasformando <lb></lb>la caraffella galileiana nel tubo torricelliano, veniva con più facile modo e <lb></lb>squisito a espellere quell&#039;aria che, non gravando più come dianzi nello stru­<lb></lb>mento, era causa dell&#039;alleggerirsi di lui, e del sollevare il collo più sopra <lb></lb>l&#039;acqua. </s>

<s>Ond&#039;ei parrebbe che, come del Rinaldini, così di Galileo fosse l&#039;in­<lb></lb>tenzione quella di dimostrar che l&#039;aria, anche nell&#039;acqua, è pesa, e perciò <lb></lb>concluderne qui, diversamente da quel che aveva fatto nel Discorso intorno <lb></lb>alle galleggianti, dover l&#039;acqua, che riempirebbe lo spazio ABSO nel solito <lb></lb>schema, pesar quanto l&#039;assicella, non però sola, ma con tutta l&#039;aria conte­<lb></lb>nuta nella fossetta. </s></p><p type="main">

<s>Il vaso poi, disegnato nella figura 89, inteso tutto aperto di sopra, e <lb></lb>avente per fondo l&#039;assicella di piombo FG, a cui aderisse con l&#039;orlo infe­<lb></lb>riore; pareva fosse immaginato apposta per rendere più comoda, e d&#039;uso <lb></lb>più generale, l&#039;esperienza, sostituendo la stabilità delle solide pareti BC, DE <lb></lb>ai fragili arginetti, non sostenuti che dal visco dell&#039;acqua. </s>

<s>E dall&#039;altra parte, <lb></lb>dicendosi così chiaramente che il solido di piombo, collocato nella cavità degli <lb></lb>arginetti, come il maschio nella bigoncia, <emph type="italics"></emph>scaccia ben l&#039;aria che vi trova, <lb></lb>ma egli stesso conferisce a quel vaso tanto appunto dei propri momenti, <lb></lb>quant&#039;era il momento dell&#039;aria discacciata;<emph.end type="italics"></emph.end> non parrebbe da mettere in <lb></lb>dubbio se l&#039;aria, in mezzo agli arginetti, abbia momento di gravità, e perciò <lb></lb>se ella aggravi col suo peso la sottoposta assicella. </s>

<s>Eppure Galileo, colla <lb></lb>stessa ferma mano, con la quale aveva scritte queste parole, passava imme­<lb></lb>diatamente a scriver quest&#039;altre in una postilla, dove l&#039;Accademico, a pag. </s>

<s>11, <lb></lb>dice che, se l&#039;assicella diventa uno stesso corpo coll&#039;aria, si potrà rendere <lb></lb>così leggera, da formarsi all&#039;intorno non argini, ma montagne di acqua: <lb></lb>“ Diventa un istesso corpo con la tavoletta tutta l&#039;aria; e quando di tal corpo <lb></lb>se n&#039;è sommerso tanto, che tant&#039;acqua pesi quanto tutto, non va più giù. </s>

<s><lb></lb>e così accade, ma nota che tutta l&#039;aria in sè stessa, e sopra l&#039;acqua, non <lb></lb>pesa nulla. </s>

<s>Ma ben quella poca che è sommersa viene estrusa in su, et in <lb></lb>certo modo leggera nell&#039;acqua. </s>

<s>Nè si maravigli alcuno che tutta l&#039;aria non <lb></lb>pesi niente, perchè il simile è dell&#039;acqua. </s>

<s>” </s></p><pb xlink:href="020/01/3215.jpg" pagenum="176"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Peripatetico dunque rimastosi nell&#039;Idrostatica Galileo, e de&#039;vizii peripa­<lb></lb>tetici contaminatone l&#039;autorevole suo insegnamento, si narrò come i Disce­<lb></lb>poli aprissero finalmente gli occhi a riconoscere il vero. </s>

<s>Par dalla Storia che <lb></lb>si svegliassero troppo tardi, se si bada solamente agli atti esteriori, ma pe­<lb></lb>netrando nel segreto di quella Scuola, vi troviamo seder nuovo maestro il <lb></lb>Torricelli a restaurare la scienza, non dalla cattedra, o spiegatamente co&#039;li­<lb></lb>bri, ma ne&#039;privati colloqui con gli amici. </s>

<s>L&#039;eletta schiera solitaria si com­<lb></lb>pone del Magiotti, del Ricci, del Cornelio e del Nardi, il quale ultimo sa­<lb></lb>rebbe forse il più benemerito di tutti, se ne fossero diffusi quegli scritti, nei <lb></lb>quali ei censurava le dottrine di Galileo con libertà di giudizio, ne correg­<lb></lb>geva le fallacie con senno, e diceva imparzialmente il pro e il contro nella <lb></lb>gran questione, che, intorno al galleggiare le falde dei corpi più gravi in <lb></lb>specie dell&#039;acqua, ebbe con gli Aristotelici il suo proprio Maestro. </s>

<s>Crediamo <lb></lb>perciò non sia per dispiacere ai Lettori il vedersi messe sott&#039;occhio queste <lb></lb>poche pagine, che trascriviamo dalle <emph type="italics"></emph>Scene Accademiche.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Pare che l&#039;acqua e l&#039;aria appena forza abbiano di tenere insieme av­<lb></lb>vinte le loro particelle, onde, non che premere gli altri corpi, non possano <lb></lb>nemmeno resistere a qualsivoglia grave, che divider le voglia. </s>

<s>Così crede il <lb></lb>Galilei, ma il contrario credesi nel Liceo, dove, d&#039;una lamina di piombo che <lb></lb>nell&#039;acqua galleggi, altra ragione non rendesi, che la difficoltà quale essa <lb></lb>lamina, mercè della figura, trova nel divider l&#039;acqua. </s>

<s>Primieramente, quando <lb></lb>che tale sia dell&#039;acqua la natura, quale dell&#039;umido separato da ogni natural <lb></lb>liquore essere determina Archimede, è necessario che, se poniamo occuparsi <lb></lb>dall&#039;aere, fra gli argini rinchiuso dell&#039;acqua, lo spazio, che la distesa lamina <lb></lb>e quasi sepolta nell&#039;acqua cagiona; è necessario dico che, quando altrettanto <lb></lb>spazio insieme con l&#039;occupato dalla lamina occupato venga dall&#039;acqua, tanto <lb></lb>ancor pesi questa, quanto la lamina e l&#039;aria insieme. </s>

<s>” </s></p><p type="main">

<s>“ Ciò nondimeno, diranno i Peripatetici, non è render la ragione, onde <lb></lb>avvenga che la lamina non si sommerga affatto, essendo per natura il piombo <lb></lb>più grave dell&#039;acqua. </s>

<s>Di nuovo, pertanto, cercheranno perchè, in tale stato <lb></lb>sè medesima rattenendo, formi quell&#039;argine, e lo formi ancora, mentre che, <lb></lb>posta nell&#039;acqua la lamina, muovesi allo in giù. </s>

<s>Ancora cercheranno perchè, <lb></lb>se umida sia della lama la superficie, vi scorra sopra l&#039;acqua così, che nullo <lb></lb>argine fabbricar si possa. </s>

<s>Lo stesso scorgesi quasi, se pulita squisitamente <lb></lb>sia la superficie del metallo. </s>

<s>Pare ancora che, se l&#039;acqua, mediante il freddo, <lb></lb>rarefatta rigonfi, molto maggiormente e più facilmente faccia la stessa fossa. </s>

<s><lb></lb>E finalmente, se l&#039;acqua nel pavimento versiamo, osservasi la stessa fossetta <lb></lb>ivi fare, poichè l&#039;umore nella polvere sdrucciolare non pote. </s>

<s>Quindi conchiu-<pb xlink:href="020/01/3216.jpg" pagenum="177"></pb>deranno gli avversari che, non al solo peso, nè alla sola astrazione ricorrer <lb></lb>basti, mentre che molte altre cose possono avere in natura luogo. </s>

<s>” </s></p><p type="main">

<s>“ Veramente dubbio alcuno non pare che l&#039;acqua alla materia del piombo <lb></lb>si attacchi, e quindi, quasi in base fermandosi, acquisti vigore di sè stessa <lb></lb>rattenere e di contrastare all&#039;altra che, premuta dalla lamina viene incal­<lb></lb>zandola, sicchè, aggiungendosi la natural delle sue parti tenacità, non tra­<lb></lb>scorre verso il centro, a cui, senza tal patrocinio, obbedir convenivale. </s>

<s>Resta <lb></lb>dunque sospesa la lamina, perchè la forza che preme l&#039;acqua riflettesi in sè <lb></lb>medesima. </s>

<s>Ma perchè, in sì piccole cose, facilmente celansi le misure a ca­<lb></lb>pello, nè puote il senso nostro arrivarle precisamente, quindi è che, della la­<lb></lb>mina e dell&#039;umore parerà, per detto degli avversari, che tanta mole si formi, <lb></lb>quanto, per adattarla alle conseguenze da Archimede cavate, basti, il quale, <lb></lb>di più, parlare delle cose sommerse affatto nell&#039;umido, e non delle poste <lb></lb>sopra di esso diranno, e così tal caso essersi tralasciato. </s>

<s>” </s></p><p type="main">

<s>“ Pongasi frattanto che, se un solido preme l&#039;acqua, la prema secondo <lb></lb>la linea della profondità. </s>

<s>Onde, se lo stesso solido in figura distesa riducasi, <lb></lb>molto meno premer potrebbe, quando prima tocchi l&#039;acqua giacente che driz­<lb></lb>zato, poichè nel primo caso maggior quantità resistente d&#039;acqua circonda la <lb></lb>base e superficie del solido postavi, che nel secondo. </s>

<s>Èd essendo noto che la <lb></lb>superficie del solido giacente abbia all&#039;umida che lo bagna la stessa ragione, <lb></lb>che a quella ha la superficie uguale di un solido drizzatovi; ne segue che, <lb></lb>se il drizzatovi si sommerga affatto nell&#039;acqua (che si sommerga finalmente <lb></lb>è necessario, quando più grave sia dell&#039;umido, e s&#039;allunghi sempre assot­<lb></lb>tigliandosi) confessar fia bisogno che in tal posizione, più che nell&#039;altra, abbia <lb></lb>l&#039;acqua forzato. </s>

<s>Poichè dunque per lo lungo la lamina più premeva l&#039;acqua, <lb></lb>che non comportava dell&#039;umide particelle il visco, quindi si sommerse. </s>

<s>” </s></p><p type="main">

<s>“ Veramente dell&#039;acqua la resistenza alla divisione svanisce nei momenti <lb></lb>grandi, benchè per più vie rintracciarsi diranno i Peripatetici. </s>

<s>E così per <lb></lb>esempio i tondi e minimi sassolini a fatica e tortamente per l&#039;acqua scen­<lb></lb>dono, benchè i grandi e dì molt&#039;ampia figura presto e a dirittura scendanvi. </s>

<s><lb></lb>E sebbene con maggior ragione scemano i solidi, che le superficie loro, cre­<lb></lb>derassi nondimeno poter chiuder la strada a chiunque in tal proposito rico­<lb></lb>vrar si volesse, col prender qualche lamina di materia men grave assai dei <lb></lb>sassi: eppure scenderà, quando dell&#039;acqua più grave sia, veloce, in compa­<lb></lb>razione dei rotondi atomi, ancorchè di metallo questi siano. </s>

<s>La stess&#039;acqua <lb></lb>versata in un bicchier di vino, benchè più grave ella sia, non può colle sue <lb></lb>particelle il più basso luogo occupare, se non fosse con lunghissimo tempo. </s>

<s><lb></lb>Dunque non la sola figura delle cose similmente gravi cagione sarà del più <lb></lb>o men presto scendere nello stesso mezzo, ma ancora la grandezza concorrer <lb></lb>deveci, perchè con la mole cresce sovente o scema il momento in maggior <lb></lb>ragione, che nell&#039;acqua la resistenza al dividersi. </s>

<s>” </s></p><p type="main">

<s>“ Di nuovo la stessa facoltà, diranno i Peripatetici, è quella, che vieta <lb></lb>la semplice divisione, e che più facile o difficile la rende. </s>

<s>Ma noi, riguar­<lb></lb>dando agli effetti, stimiamo falsamente che allora nell&#039;acqua stata non sia <pb xlink:href="020/01/3217.jpg" pagenum="178"></pb>resistenza, quando divisa miriamola. </s>

<s>E se poi il ferro più che il piombo si <lb></lb>attacchi all&#039;acqua, non andranno col medesimo passo le ragioni del peso e <lb></lb>della sommersione di questi due metalli. </s>

<s>Lo stesso proporzionalmente nelle <lb></lb>figure occorre, nella pulitezza o asprezza, nella qualità dell&#039;acqua, e nella <lb></lb>disposizione secondo diversi tempi e luoghi. </s>

<s>” </s></p><p type="main">

<s>“ Archimede separa dagli umidi naturali ogni tenacità in quella ma­<lb></lb>niera che dalle lance tolse le braccia naturali, e le linee sostituì. </s>

<s>Seppe an­<lb></lb>cora da un corpo una superficie distinguere, di cui trovar volle il luogo dove <lb></lb>i suoi momenti concorrono. </s>

<s>Ma non è tanto al Filosofo naturale concesso, il <lb></lb>quale, comecchè verissime essere ad Archimede conceda le sue conclusioni <lb></lb>(poichè chi solamente astrae non suppone il falso) va ancora in conseguenza <lb></lb>che egli dalla materia cavolle, che altre nondimeno rimescolatamente lasciò <lb></lb>nella stessa materia, da considerare e distinguersi dal Fisico. </s>

<s>” </s></p><p type="main">

<s>“ Si maravigliano parimente i Peripatetici del Galileì che, avendo ogni <lb></lb>viscosità tolta all&#039;acqua, conceda poi all&#039;aere forza di reggere e sollevare per <lb></lb>l&#039;acqua di grandissimi corpi, il che fare senza molta tenacità di parti egli <lb></lb>non potrebbe. </s>

<s>Ma chi non sa che molto meno tenace è l&#039;aere che l&#039;acqua <lb></lb>o altri umori? </s>

<s>Chi non sa ancora che negli umori non vanno del pari la <lb></lb>gravità e la tenacità loro? </s>

<s>Domanderanno di più che cosa ritenga l&#039;acqua <lb></lb>dallo scorrere sopra la lamina. </s>

<s>Che ella stessa regga non è possibile, secondo <lb></lb>i principii del Galilei, perchè tenacità averebbe. </s>

<s>E se tenacità, ne segue che <lb></lb>sorreggerassi, sia pur qualsivoglia, ancorchè gravissima materia, posta sul­<lb></lb>l&#039;acqua, poichè, se la sua mole e figura in inflnito s&#039;estenda e s&#039;assottigli, <lb></lb>bisognerà alla fine che all&#039;uguagliarsi riducasi il momento suo e la tenacità <lb></lb>dell&#039;acqua, e ciò l&#039;esperienza approvar dirassi. </s>

<s>Che se poi dica il Galilei <lb></lb>l&#039;aria impedir l&#039;acqua, che non riempia la fossetta, altri anco dirà che le <lb></lb>stille dell&#039;acqua, quali nelle fronde sospese vedonsi, non da sè stesse so­<lb></lb>spese, ma dall&#039;aria si tengono, il che poi non so come approvare si possa, <lb></lb>nè lo stesso Galilei approvalo, anzi che negli ultimi Dialoghi resta perciò <lb></lb>anch&#039;ei sospeso. </s>

<s>Parimente, se le posizioni, che dell&#039;umido prende Archi­<lb></lb>mede, si debbano nella comunal acqua universalmente ricevere, per qual ca­<lb></lb>gione avviene poi che in un bicchiere ella si rigonfi intorno agli orli? </s>

<s>Ciò <lb></lb>far non doverebbe, anzi, non essendo egualmente le sue particelle premute, <lb></lb>trascorrer dovrebbe. </s>

<s>” </s></p><p type="main">

<s>“ Per ultimo, diranno contro il Galilei i seguaci d&#039;altro parere, essere <lb></lb>una mal fondata o almeno difficile a capirsi distinzione quella di che egli <lb></lb>servesi fra il resistere alla semplice, e il resistere alla facile o difficile divi­<lb></lb>sione. </s>

<s>Perchè l&#039;acqua, così, le condizioni del vano otterrebbe, mentre al sem­<lb></lb>plice dividersi nullæ resistenza avesse, ed inoltre premuta e penetrata sa­<lb></lb>rebbe dall&#039;aere, che grave stimasi dal Galilei, e grave anch&#039;io credolo. </s>

<s>Ma <lb></lb>forse che insensibilmente da quello penetrata viene, onde di continuo in mi­<lb></lb>nime parti risolvesi. </s>

<s>” </s></p><p type="main">

<s>“ Brevemente e benignamente dicasi per il Galilei, e per i capi prin­<lb></lb>cipali della dottrina, ch&#039;ei professa, come falsa è la cagione addotta del non <pb xlink:href="020/01/3218.jpg" pagenum="179"></pb>discender per l&#039;acqua corpi di essa più gravi a cagione della sola figura, <lb></lb>poichè l&#039;istessa figura nulla impedisce ai corpi più lievi dell&#039;acqua il salire <lb></lb>per essa, ed a tale esperienza cosa contraria addursi non può di rilievo. </s>

<s>È <lb></lb>ben vero che per ragion remota e parziale, il che s&#039;insinua nel sesto, rice­<lb></lb>ver si può l&#039;apportata da Aristotile. </s>

<s>Nè il Galilei toglie all&#039;acqua ogni te­<lb></lb>nacità delle parti sue, ma bene avverrà che tal tenacità sia superata da ogni <lb></lb>solido almeno sensibile, il quale, posto nell&#039;acqua, sia di essa più grave. </s>

<s><lb></lb>L&#039;acqua poi si propone come pura o non alterata. </s>

<s>E di più si considera se­<lb></lb>parata dalle sue particolari convenienze o disconvenienze con altri partico­<lb></lb>lari corpi, il che è un considerarla come umida solamente, e non come na­<lb></lb>turale e concreta. </s>

<s>Nello stesso modo una natural bilancia devesi solamente <lb></lb>come bilancia considerare dal Meccanico razionale. </s>

<s>Altrimenti avverrà che se <lb></lb>di ferro ella fosse, ma il sostegno e le circostanze fossero magnetiche, si re­<lb></lb>puterà falso quello, che gli Scientifici di quella dimostrano. </s>

<s>” </s></p><p type="main">

<s>“ Concludendo dunque diciamo che possono i naturali avvenimenti sco­<lb></lb>starsi alquanto dall&#039;indivisibile delle astratte verità, per ragione delle circo­<lb></lb>stanze. </s>

<s>Ma tolte queste, rimangono quellì nell&#039;assoluta necessità loro. </s>

<s>” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. XX, pag. </s>

<s>873-80). </s></p><p type="main">

<s>Così, tutte le questioni riguardanti il trattato idrostatico di Galileo ve­<lb></lb>nivano risolute in quel suo stile laconico dal Nardi, ora benigno paciere, ora <lb></lb>arguto censore. </s>

<s>E, prendendo più volentieri a fare quell&#039;ufficio che questo, <lb></lb>procede nelle censure indirettamente per via dei contrapposti: facendole cioè <lb></lb>risultare da una sentenza che, riscontrandola, si troverebbe tutt&#039;affatto con­<lb></lb>traria alla pronunziata da Galileo, com&#039;è questa: <emph type="italics"></emph>dico che, quando altret­<lb></lb>tanto spazio, insieme con l&#039;occupato dalla lamina, occupato venga dal­<lb></lb>l&#039;acqua; tanto ancora pesa questa, quanto la lamina e l&#039;aria insieme.<emph.end type="italics"></emph.end><lb></lb>Galileo attribuiva la causa del galleggiare la lamina e la pallina di cera nel <lb></lb>bicchiere inverso all&#039;attrazione dell&#039;aria, e il Nardi corregge destramente <lb></lb>una tale fallacia, insinuando il vero in quell&#039;altra sentenza: <emph type="italics"></emph>Resta dunque <lb></lb>sospesa la lamina, perchè la forza che preme l&#039;acqua riflettesi in sè me­<lb></lb><figure id="id.020.01.3218.1.jpg" xlink:href="020/01/3218/1.jpg"></figure></s></p><p type="caption">

<s>Figura 90.<lb></lb>desima.<emph.end type="italics"></emph.end> Ma contro il principio delle velocità virtuali, a <lb></lb>che tutta s&#039;informa l&#039;Idrostatica galileiana, insorgeva il <lb></lb>Nardi stesso più a viso aperto. </s></p><p type="main">

<s>“ Male, egli dice, si persuadono i Meccanici comu­<lb></lb>nemente compensarsi in una bilancia di disuguali braccia <lb></lb>la velocità del moto con la grandezza del momento, onde <lb></lb>cercano di render ragione perchè questi pesi disuguali, da <lb></lb>distanze reciprocamente disuguali, pesino ugualmente. </s>

<s>Ma <lb></lb>ciò non è in vero cagione dell&#039;equilibrio, perchè, così di­<lb></lb>scorrendo, s&#039;adduce di un effetto in atto una cagione in <lb></lb>potenza. </s>

<s>Il Galilei, nel libro delle Galleggianti, dice così: <lb></lb><emph type="italics"></emph>Sia continuata al vaso larghissimo EDF<emph.end type="italics"></emph.end> (fig. </s>

<s>90) <emph type="italics"></emph>l&#039;angu­<lb></lb>stissima canna CAB, ed intendasi in essi infusa l&#039;acqua sino al livello LGH, <lb></lb>la quale in questo stato si quieterà, non senza maraviglia di alcuno, che<emph.end type="italics"></emph.end><pb xlink:href="020/01/3219.jpg" pagenum="180"></pb><emph type="italics"></emph>non capirà così subito come esser possa che il grave carico della gran mole <lb></lb>dell&#039;acqua GD, premendo abbasso, non sollevi e scacci la piccola quan­<lb></lb>tità dell&#039;altra contenuta dentro alla canna CL, dalla quale gli vien con­<lb></lb>tesa e impedita la scesa. </s>

<s>Ma tal maraviglia cesserà se noi cominceremo <lb></lb>a fingere l&#039;acqua GD essersi abbassata solamente sino a Q, e considere­<lb></lb>remo poi ciò che averà fatto l&#039;acqua CL, la quale, per dare luogo all&#039;al­<lb></lb>tra, che si è scemata dal livello GH sino al livello Q, doverà per neces­<lb></lb>sità essersi nell&#039;istesso tempo alzata dal livello L, sino in AB, e esser la <lb></lb>salita LB tanto maggiore della scesa GD, quant&#039;è l&#039;ampiezza del vaso <lb></lb>GD maggiore della larghezza della canna LC, che insomma è quanto <lb></lb>l&#039;acqua GD è più della LC. </s>

<s>Ma essendo che il momento della velocità del <lb></lb>moto in un mobile compensa quello della gravità in un altro, qual ma­<lb></lb>raviglia sarà se la velocissima salita della poca acqua CL resisterà alla <lb></lb>tardissima scesa della molta GD?<emph.end type="italics"></emph.end> Sino a qui il mio Maestro. </s>

<s>” </s></p><p type="main">

<s>“ Ma la vera cagione onde l&#039;acqua, contenuta nel maggior vaso, non <lb></lb>preme la contenuta nella canna LC, dirà alcuno essere perchè non tutta la <lb></lb>quantità d&#039;acqua GD preme la detta LC, ma solo tanta parte, quanta v&#039;en­<lb></lb>tra per la cannella per cui insieme comunicano, restando tutta l&#039;altra late­<lb></lb>rale oziosa. </s>

<s>E così con tal principio immaginar ci dobbiamo nel maggior vaso <lb></lb>una simile ed uguale cannella IC, quale corrispondendogli preme l&#039;altra. </s>

<s>E <lb></lb>perchè uguali sono niuna supera l&#039;altra. </s>

<s>Quindi, se noi fingeremo la canna <lb></lb>continuata col vaso non più in L salire, ma in V, allora dal livello GH scen­<lb></lb>dere vedremo la quantità d&#039;acqua, fino che pareggi la bassezza di V, seb­<lb></lb>bene occorrerà che, secondo la stessa proporzione, l&#039;una scenda e l&#039;altra <lb></lb>salga: qual proporzione, nell&#039;altro caso, impedendo appresso il Galileo il <lb></lb>moto, dovrebbe anche in queste impedirlo. </s>

<s>E vedesi, in conferma, che, men­<lb></lb>tre l&#039;acqua GD s&#039;abbassa, apparirà nella superficie sua certa fossetta, cor­<lb></lb>rispondente in tutto al sito e larghezza della canna, nella qual fossa conti­<lb></lb>nuamente d&#039;ogni intorno l&#039;umor circostante sdrucciola. </s>

<s>Onde non tutta <lb></lb>l&#039;acqua, ma una parte sola premere, almeno principalmente, argomenterassi, <lb></lb>contenuta dentro alla canna, e in conseguenza non l&#039;ampiezza del vaso, ma <lb></lb>ben l&#039;altezza esser cagione che fosse o non fosse cacciata l&#039;una dall&#039;altra <lb></lb>acqua, e con più o meno impeto. </s>

<s>E se ancora, restando l&#039;acqua nel livello <lb></lb>di prima LGH, infondiamo per il foro A nuovo umore nella canna, vedremo <lb></lb>l&#039;infusa premer l&#039;acqua del maggior vaso, o per meglio dire, una parte di <lb></lb>esso, sino a che facciasi l&#039;equilibrio ” (ivi, pag. </s>

<s>862-64). </s></p><p type="main">

<s>L&#039;obiezione del Nardi, contro il processo dimostrativo di Galileo, fu ri­<lb></lb>petuta pubblicamente da alcuni, ai quali anche piacque meglio di dar del <lb></lb>paradosso idrostatico la spiegazione, che abbiamo ora tratta dal manoscritto. </s>

<s><lb></lb>Altri però non ebbero scrupolo di tenere i medesimi modi, usati nel trat­<lb></lb>tato delle Galleggianti, riducendo la dimostrazione all&#039;assurdo. </s>

<s>Di costoro <lb></lb>possiamo citare fra&#039;nostri il De Angeli, il quale, nel secondo Dialogo sopra <lb></lb>commemorato, all&#039;obiezione che soleva comunemente farsi contro il principio <lb></lb>delle velocità virtuali, che cioè di un effetto positivo, qual&#039;è la quiete, s&#039;ad-<pb xlink:href="020/01/3220.jpg" pagenum="181"></pb>duce per causa il moto, rispondeva “ non parer nuovo nelle cose che si di­<lb></lb>mostrano il procedere <emph type="italics"></emph>per deductionem ad impossibile,<emph.end type="italics"></emph.end> dimostrando che, <lb></lb>quando fosse vero il contrario, ne seguirebbe un assurdo in natura, o cosa <lb></lb>irragionevole ” <emph type="italics"></emph>(Della gravità dell&#039;aria ecc.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>58). Fra gli stranieri <lb></lb>poi basti citare il Mariotte, il quale, avendo proposto per principio univer­<lb></lb>sale della Meccanica quello delle velocità virtuali, che, andando reciproca­<lb></lb>mente ai pesi, mantengono in quiete la leva; rendeva la ragione dell&#039;equi­<lb></lb>librio fra due superficie, prese per base di due cilindri acquei di pari altezza, <lb></lb>nel vaso grande GD, e nella piccola canna CL; dicendo che se si moves­<lb></lb>sero, “ donc leurs vitesses avroient été reciproques a leurs poids, et ils <lb></lb>avroient eu une egale quantité de mouvement, ce qui est impossible. </s>

<s>Car, <lb></lb>par le Principe universel, ces cylindres d&#039;eau doivent faire equilibre, et l&#039;un <lb></lb>ne peut pas faire mouvoir l&#039;autre, puisqu&#039;ils sont disposes a prendre une <lb></lb>egale quantité de meuvement selon la meme direction ” <emph type="italics"></emph>(Oeuvres,<emph.end type="italics"></emph.end> T. II, a <lb></lb>l&#039;Haye 1740, pag. </s>

<s>367). </s></p><p type="main">

<s>Nonostante l&#039;obiezione del Nardi era, specialmente a que&#039;tempi, ripu­<lb></lb>tata di così grave momento, da indurre, come si sa, il Torricelli a ricono­<lb></lb>scere la causa dell&#039;equilibrio fra due corpi congiunti in un principio alquanto <lb></lb>diverso, qual&#039;è quello del non potere scendere il loro comun centro di gra­<lb></lb>vità. </s>

<s>Anche questo nuovo principio, come l&#039;altro delle velocità virtuali, era <lb></lb>indiretto, riducendosi nel medesimo modo all&#039;assurdo. </s>

<s>Il Terricelli infatti <lb></lb><figure id="id.020.01.3220.1.jpg" xlink:href="020/01/3220/1.jpg"></figure></s></p><p type="caption">

<s>Figura 91.<lb></lb>concludeva doversi, nella data ipotesi dell&#039;im­<lb></lb>mobilità del comun centro gravitativo, rimanere <lb></lb>i due corpi congiunti in quiete, <emph type="italics"></emph>alias enim fru­<lb></lb>stra moverentur.<emph.end type="italics"></emph.end> Siano i due corpi A, B (fig. </s>

<s>91) <lb></lb>disposti in distanze reciprocamente proporzio­<lb></lb>nali ai loro proprii pesi dal comun centro C. </s>

<s><lb></lb>Rimarranno quivi in quiete, perchè, se si mo­<lb></lb>vessero, come per esempio in A′, B′, le relazioni fra le loro distanze CD, CE <lb></lb>non sarebbero punto cambiate, per cui, sempre rimanendo C il loro centro <lb></lb>comune, quel moto sarebbe stato inutile, e perciò contrario alla Natura, che <lb></lb>nulla opera mai inutilmente. </s></p><p type="main">

<s>Il Torricelli però conduce la sua dimostrazione con tale artificio, da fare <lb></lb>sparire queste trite riduzioni all&#039;assurdo, e da chiudere nello stesso tempo <lb></lb>la bocca agli oppositori, non sostituendone propriamente un altro diverso, <lb></lb><figure id="id.020.01.3220.2.jpg" xlink:href="020/01/3220/2.jpg"></figure></s></p><p type="caption">

<s>Figura 92.<lb></lb>ma travestendo così il principio delle velocità <lb></lb>virtuali, da non riconoscerlo per quel desso. </s>

<s>In­<lb></lb>vece di considerare i gravi pendenti dall&#039;estre­<lb></lb>mità di una leva gl&#039;immagina congiunti con un <lb></lb>filo, e posati sopra due piani inclinati così, che <lb></lb>le loro lunghezze siano direttamente propor­<lb></lb>zionali ai pesi soprapposti. </s>

<s>L&#039;equilibrio, che anco in questo caso si osserva, <lb></lb>dipende dall&#039;avere i due corpi, benchè di diversa grandezza, egual disposi­<lb></lb>zione al moto o momento virtuale. </s>

<s>Imperocchè posto che A (fig. </s>

<s>92) stia a B, <pb xlink:href="020/01/3221.jpg" pagenum="182"></pb>come la lunghezza CD alla CE, e moversi i due corpi per tratti uguali DA, <lb></lb>BE lungo i due piani; gli spazi perpendicolarmente passati sarebbero AG, BH, <lb></lb>in reciproca ragione delle lunghezze de&#039;piani DC, CE, ossia de&#039;pesi B, A, <lb></lb>come nella leva. </s>

<s>Il Torricelli però suppone che, non virtualmente ma attual­<lb></lb>mente si movano i due corpi, l&#039;uno ascendendo, e discendendo l&#039;altro, come <lb></lb>porta l&#039;essere insieme congiunti, e dimostra, com&#039;è noto, che la via del cen­<lb></lb>tro di gravità del sistema percorre la medesima linea orizzontale, e perciò lì, <lb></lb>dove sono stati quegli stessi corpi rimossi, anche si rimangono nella mede­<lb></lb>sima quiete. </s></p><p type="main">

<s>Qual uso si facesse, specialmente nella Scuola galileiana, di questo prin­<lb></lb>cipio torricelliano, per trattare alcuni de&#039;più difficili problemi statici, oramai <lb></lb>si sa dalla storia della Meccanica. </s>

<s>Ma primo ad applicarlo all&#039;Idrostatica fu <lb></lb>il Pascal, non forse per sostituirlo a quell&#039;altro di Galileo, quasi lo repu­<lb></lb>tasse anch&#039;egli difettoso, ma per dare altro modo alla dimostrazione. </s>

<s>Se A <lb></lb>e B (fig. </s>

<s>93) son due cilindri di materia omogenea, con pari altezze, ma con <lb></lb>basi così diverse, da far sì che questo pesi, poniamo, cento volte più di <lb></lb><figure id="id.020.01.3221.1.jpg" xlink:href="020/01/3221/1.jpg"></figure></s></p><p type="caption">

<s>Figura 93.<lb></lb>quello; sospesi da una bilancia di braccia uguali <lb></lb>è certo che il maggiore prepondererà con cen­<lb></lb>tuplo momento. </s>

<s>E nonostante immersi ne&#039;due <lb></lb>tubi CD, EF, comunicantisi e pieni d&#039;acqua, <lb></lb>come due stantuffi in due corpi di tromba, si <lb></lb>vede la Bilancia ridursi in perfetto equilibrio. </s>

<s><lb></lb>Qual&#039;è, domanda a sè il Pascal, la ragione di <lb></lb>questo apparente paradosso? </s>

<s>E risponde osser­<lb></lb>vando che la forza, con la quale è premuto il <lb></lb>velo acqueo sottoposto allo stantuffo A, si comu­<lb></lb>nica al velo d&#039;acqua sottoposto allo stantuffo B, <lb></lb>il qual velo essendo centuplo riceverà il centu­<lb></lb>plo della forza, ugualmente distribuita per ogni sua parte, ond&#039;ei si verifica <lb></lb>qui quel che in ogni caso della comunicazione dei moti, che cioè le velocità <lb></lb>son reciprocamente proporzionali alle grandezze dei copi mossi. </s>

<s>“ D&#039;ou il <lb></lb>paroist qu&#039;un vaisseau plein d&#039;eau est un nouveau principe de Mechanique, <lb></lb>et une machine nouvelle pour multiplier les forces a tel degre qu&#039;on vou­<lb></lb>dra.... Et l&#039;on doit admirer qu&#039;il se rencontre en cette machine nouvelle <lb></lb>cet ordre constant, qui se trouve en toutes les anciennes, sçavoir le levier, <lb></lb>le tour, la vis sans fin etc. </s>

<s>qui est que le chemin est augmenté en mesme <lb></lb>proportion que la force.... de sorte que le chemin est au chemin comme la <lb></lb>force a la force. </s>

<s>Ce que l&#039;on peut prendre mesme pour la vraye cause de <lb></lb>cet effet, estant clair que c&#039;est la mesme chose de faire faire un poulce de <lb></lb>chemin a cent livres d&#039;eau, que de faire faire cent poulces de chemin a une <lb></lb>livre d&#039;eau. </s>

<s>Et qu&#039;ainsi lors qu&#039;une livre d&#039;eau est tellement ajustée avec cent <lb></lb>livres d&#039;eau, que les cent livres ne puissent se remuer un poulce, qu&#039;elles <lb></lb>ne faissent remuer la livre de cent poulces; il faut qu&#039;elles demuerent en <lb></lb>equilibre, une livre ayant autant de force pour faire faire un poulce de che-<pb xlink:href="020/01/3222.jpg" pagenum="183"></pb>min a cent livres, que cent livres pour faire faire cent poulces a une livre ” <lb></lb><emph type="italics"></emph>(De l&#039;equilibre des <expan abbr="liq.">lique</expan><emph.end type="italics"></emph.end> cit., pag. </s>

<s>6-8). </s></p><p type="main">

<s>Concludesi da questo discorso del Pascal, come da quello simile di Ga­<lb></lb>lileo, che l&#039;acqua tanto più velocemente si muove ne&#039;due corpi di tromba, <lb></lb>quanto son più piccole le loro sezioni, o i veli d&#039;acqua in esse compresi, i <lb></lb>quali veli, supposti conglobati in A, B, e pendenti all&#039;estremità di una leva <lb></lb>immaginaria, come nella 91a figura; staranno ivi dunque in quiete per le <lb></lb>medesime ragioni. </s>

<s>Di qui è che al Pascal sovviene di dimostrare altrimenti <lb></lb>questo idrostatico equilibrio, applicandovi il principio del Torricelli. </s>

<s>“ Voicy <lb></lb>encore une preuve qui ne pourra estre entendué, que par les seuls Geome­<lb></lb>tres, et peut estre passée par les autres. </s>

<s>Je prends pour principe que ja­<lb></lb>mais un corps ne se meut par son poids, sans que son centre de gravité <lb></lb>descende. </s>

<s>D&#039;ou je prouve que les deux pistons figurez en la figure 93 sont <lb></lb>en equilibre en cette sorte: Car leur centre de gravité commun est au point <lb></lb>qui divise la ligne qui joint leurs centres de gravité particuliers en la pro­<lb></lb>portion de leurs poids, qu&#039;ils se meuvent maintenant s&#039;il est possible. </s>

<s>Donc <lb></lb>leurs chemins seront entre eux comme leurs poids reciproqnement, comme <lb></lb>nous avons fait voir. </s>

<s>Or si on prend leur centre de gravité commun en cette <lb></lb>seconde situation, on le trouvera precisement au mesme endroit que la pre­<lb></lb>miere fois, car il se trouvera toujours au point qui divise la ligne, qui joint <lb></lb>leurs centres de gravité particuliers, en la proportion de leurs poids. </s>

<s>Donc, <lb></lb>à cause du parallelisme des lignes de leurs chemins, il se trouvera en l&#039;in­<lb></lb>tersection des deux lignes, qui joignent les centres de gravité dans les deux <lb></lb>situations. </s>

<s>Donc le centre de gravité commun sera au mesme point qu&#039;au­<lb></lb>paravant. </s>

<s>Donc le deux pistons considerez comme un seul corps, se sont <lb></lb>meus sans que le centre de gravité commun soit descendu, ce qui est con­<lb></lb>tre le principe. </s>

<s>Donc ils ne peuvent se mouvoir. </s>

<s>Donc ils seront en repos, <lb></lb>c&#039;est à dire en equilibre, ce qu&#039;il falloit demontrer ” (ivi, pag. </s>

<s>10-11). </s></p><p type="main">

<s>Valendo la medesima dimostrazione, siano i veli d&#039;acqua L, GH, nella <lb></lb>figura 90, allo stesso livello, o l&#039;uno rimanga sotto e l&#039;altro sopra, come a <lb></lb>torcere la canna ABC, e ridurla in dirittura con la CI; l&#039;un velo stia di <lb></lb>faccia all&#039;altro o in posizione diversa; l&#039;un dall&#039;altro vicino o lontano, <emph type="italics"></emph>car <lb></lb>la continuité et la fluidité de l&#039;eau rend toutes ces choses là égale et in­<lb></lb>differentes<emph.end type="italics"></emph.end> (pag. </s>

<s>9); resta così da esso Pascal dimostrato il paradosso idro­<lb></lb>statico sotto tutte le varietà de&#039;suoi aspetti, facilmente riducibili ai vasi della <lb></lb>forma rappresentata nelle figure 94 e 95, i fondi dei quali vasi, o i veli <lb></lb>acquei, o gli stantuffi CD, PQ, son premuti nel primo caso da una colonna <lb></lb>d&#039;acqua, avente per base CD e per altezza CM, perchè, supposto esso fondo <lb></lb>CD scendere, vinto dal peso soprastante, lo farebbe con velocità uguale a <lb></lb>quella, con cui scenderebbe il velo MN, tanto men velocemente del velo FG, <lb></lb>quanto la sezione FG è minore della CD. Nell&#039;altro caso essere il fondo PQ <lb></lb>della figura 95 premuto da una colonna liquida, avente per base PQ e per <lb></lb>altezza PS, si concluderà facilmente dai principii del Pascal con simile di­<lb></lb>scorso. </s></p><pb xlink:href="020/01/3223.jpg" pagenum="184"></pb><p type="main">

<s>Ma il Wolf, misurando le pressioni sulla regola delle forze morte, e pre­<lb></lb>supposto il principio delle velocità in ragion reciproca delle sezìoni, dimo­<lb></lb>strava più chiaramente la cosa con questa sua proposizione: “ Si bases va­<lb></lb><figure id="id.020.01.3223.1.jpg" xlink:href="020/01/3223/1.jpg"></figure></s></p><p type="caption">

<s>Figura 94.<lb></lb>sis FD (nella figura 94) inaequales fuerint, fundus eodem <lb></lb>modo premitur, ac si superior inferiori aequalis existeret ” <lb></lb><emph type="italics"></emph>(Elem. </s>

<s>Mathes. </s>

<s>universae,<emph.end type="italics"></emph.end> T. II, Genevae 1746, pag. </s>

<s>260). </s></p><p type="main">

<s>La dimostrazione si può condurre così speditamente: <lb></lb>La pressione totale P, fatta sopra il fondo CD, resulta <lb></lb>dalle pressioni parziali dell&#039;acqua AD e dell&#039;acqua EG. </s>

<s><lb></lb>E perchè le forze di queste pressioni, essendo morte, si <lb></lb>misurano dai prodotti delle masse per le velocità, che si <lb></lb>chiameranno V, V′; avremo P=CD.AC.V+FG.EF.V′. </s>

<s><lb></lb>Ma, stando le velocità in ragion reciproca delle sezioni, è CD.V=FG.V′; <lb></lb>dunque P=CD.V(AC+EF)=CD.CM.V: che vuol dire essere premuto <lb></lb>il fondo CD del vaso FD come se non si restringesse, ma fosse in fino a MN <lb></lb><figure id="id.020.01.3223.2.jpg" xlink:href="020/01/3223/2.jpg"></figure></s></p><p type="caption">

<s>Figura 95.<lb></lb>tutto andante. </s>

<s>Con simile ragionamento si concluderà che le <lb></lb>pressioni fatte sul fondo, o, come il Pascal lo chiama, sulla <emph type="italics"></emph>ou­<lb></lb>verture<emph.end type="italics"></emph.end> PQ del vaso, rappresentato nella fig. </s>

<s>95, è Pq.PS.V′: <lb></lb>e in generale “ que la mesure de cette force est toujours le <lb></lb>poids de toute l&#039;eau, qui seroit contenue dans une colonne de <lb></lb>la hauteur de l&#039;eau, et de la grosseur de l&#039;ouverture ” <emph type="italics"></emph>(De <lb></lb>l&#039;equilibre etc.,<emph.end type="italics"></emph.end> pag. </s>

<s>5). </s></p><p type="main">

<s>La dimostrazione data dal Wolf era implicita nel di­<lb></lb>scorso del Pascal. </s>

<s>Ma, o che il Varignon non ve la ricono­<lb></lb>scesse, o che, invaghito del suo principio generale di Meccanica, credesse <lb></lb>non si poter dare altra legittima dimostrazione de&#039;teoremi di lei, che per <lb></lb>via della composizion delle forze; è un fatto che, dop&#039;avere attribuito al <lb></lb>Pascal l&#039;esperienza del paradosso idrostatico, <emph type="italics"></emph>mais,<emph.end type="italics"></emph.end> soggiunge, <emph type="italics"></emph>sans que lui <lb></lb>ni aucun autre, que je sçhache, en ait donné la raison.<emph.end type="italics"></emph.end> Si vede che il <lb></lb>Varignon non sapeva nè del Benedetti, nè dello Stevino, nè di Galileo, nè <lb></lb>dello stesso Pascal, il quale, benchè in fretta e per <emph type="italics"></emph>les seuls Geometres,<emph.end type="italics"></emph.end> aveva <lb></lb>pure esteso il principio delle velocità virtuali a dimostrar l&#039;equilibrio de&#039;li­<lb></lb>quidi comunicanti, e le loro pressioni sopra <emph type="italics"></emph>les ouvertures<emph.end type="italics"></emph.end> dei vasi. </s></p><p type="main">

<s>Persuaso dunque il celebre Accademico parigino che a nessuno prima <lb></lb>di lui fosse ancora riuscito di trovar la desiderata ragione, ei soccorre sol­<lb></lb>lecito di sodisfare a questi desiderii della Scienza, nella sua <emph type="italics"></emph>Nouvelle mec­<lb></lb>canique,<emph.end type="italics"></emph.end> trattandovi, nella X sezione, <emph type="italics"></emph>De l&#039;equilibre des liqueurs.<emph.end type="italics"></emph.end> I teoremi <lb></lb>in proposito sono il XLII, il XLIII e XLIV. </s>

<s>Ma perchè i due secondi dipen­<lb></lb>dono dal primo, in cui si piglia a esempio un vaso cilindrico obliquo; di questo <lb></lb>solo teorema perciò basterà riferire il modo della dimostrazione, da che sarà <lb></lb>facile intendere il modo tenuto in dimostrar gli altri due, ne&#039;quali i vasi <lb></lb>hanno figura di un cono tronco, ora con la maggior base in alto, ora in basso. </s></p><p type="main">

<s>Premette un lemma l&#039;Autore, che a noi piace formulare cosi, come poi <lb></lb>fece l&#039;Herman: “ Pressiones, quas corpora quaecumque solida vel fluida in <pb xlink:href="020/01/3224.jpg" pagenum="185"></pb>se invicem exercent, fiunt iusta directiones communi plano contingenti cor­<lb></lb>pora perpendiculares, atque transeunt per contingentiae punctum eorumdem <lb></lb>corporum ” <emph type="italics"></emph>(Phoron.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>128). Se il globo A (fig. </s>

<s>96), spinto nella di­<lb></lb>rezione AF, preme il globo B, nel punto del contatto C, con una certa forza <lb></lb><figure id="id.020.01.3224.1.jpg" xlink:href="020/01/3224/1.jpg"></figure></s></p><p type="caption">

<s>Figura 96.<lb></lb>AF, decomposta questa in due, la prima AC perpen­<lb></lb>dicolare al piano DE del contatto, e la seconda AH a <lb></lb>esso piano parallela; è manifesto che dalla AC sola è <lb></lb>rappresentata la forza della pressione, essendo l&#039;altra AH <lb></lb>in premere inattiva. </s>

<s>E tale è la dimostrazione, che dà <lb></lb>l&#039;Herman del lemma premesso dal Varignon, il quale, <lb></lb>propostosi il vaso AKDX (fig. </s>

<s>97), infusovi il liquido <lb></lb>insino al livello GH, inalzata dal punto K la perpendi­<lb></lb>colare KY, e dal punto H abbassata la perpendico­<lb></lb>lare HL, dimostra che il liquido GKY riposa tutto sulla parete GK, e il li­<lb></lb>quido LHD preme sopra LD col peso della colonna LZ, d&#039;ond&#039;ei ne conclude <lb></lb>che tutto il fondo KD resiste alla pressione della colonna KZ. </s></p><p type="main">

<s>“ Il est manifeste, dice il Varignon, que les resistances, que les còtez <lb></lb>opposez AK, XD du tuyau incliné AKDX font en M, T, a la descente ver­<lb></lb>ticale de OM filet de liqueur, et a l&#039;ascension verticale de l&#039;autre filet RT, <lb></lb><figure id="id.020.01.3224.2.jpg" xlink:href="020/01/3224/2.jpg"></figure></s></p><p type="caption">

<s>Figura 97.<lb></lb>que les plus longs que lui tendant a <lb></lb>faire montere en S jusqu&#039;aleur niveau <lb></lb>GH prolongé vers Z; que ces resistan­<lb></lb>ces, que ces còtez opposez AK, XD font <lb></lb>aux filets OM, RT, sont suivant MN, <lb></lb>TV egales à des forces, qui les supplee­<lb></lb>roient en repoussant seulement comme <lb></lb>eux suivant ces directions les points M, <lb></lb>T de ces filets OM, RT de liqueur: <lb></lb>et qu&#039;ainsi chacune de ces resistances <lb></lb>se decompose comme en deux forces purement passives suivant MF, ME, et <lb></lb>TP, TQ, dont chacune des horizontales suivant MF, TP soutient, par son <lb></lb>invincibilité, ce que le liqueur peut avoir d&#039;action directement contraire a <lb></lb>cette resistance horizontale ” (A Paris 1725, pag. </s>

<s>253). </s></p><p type="main">

<s>Quanto alle altre forze, dirette secondo le verticali ME, TQ, egli è ma­<lb></lb>nifesto, prosegue il Varignon a dire, “ que la premiere suivant ME directe­<lb></lb>ment opposée au poids du filet OM, le soutient en M dans le repos, que lui <lb></lb>exige le supposé de ce qu&#039;il y a de liqueur dans le tuyau incliné AKDX, <lb></lb>sans lui laisser aucune action sur le fond KD de ce tuyau, le quel conse­<lb></lb>quemment n&#039;en est aucunement charge ” (ivi). Il medesimo si dimostra degli <lb></lb>altri infiniti filetti, per cuì si conclude che la mole fluida, compresa nello <lb></lb>spazio GKY, preme tutta sulla parete inclinata GK, e non punto sul fondo <lb></lb>del vaso. </s></p><p type="main">

<s>“ Mais en recompense, soggiunge tosto l&#039;Autore, ce qu&#039;il y a de cette <lb></lb>liqueur dans l&#039;espace HLD comprés entre le plan HL perpendiculaire a la <pb xlink:href="020/01/3225.jpg" pagenum="186"></pb>droite KD, et ce que ce plan retranche du coté de HD de la surface su­<lb></lb>perieure de ce tuyau incliné AKDX, presse ce fond horizontal KD d&#039;une <lb></lb>force egale a celle, dont il seroit pressé par la portion cylindrique HLDZ, <lb></lb>que ce meme plan HL retranche du cylindre droit KYZD de la meme li­<lb></lb>queur. </s>

<s>Car la force suivant TQ, resultante de la resistance, que le coté su­<lb></lb>pericur XD du tuyau incliné AKDX fait, suivant la perpendiculaire TV, a <lb></lb>l&#039;ascension du filet vertical RT de liqueur; se trouvant directement opposée <lb></lb>a l&#039;effort, dont le poids du surplus de longueur des plus longs tond a le <lb></lb>faire monter jusqu&#039;au point S de leur niveau GH, et empechant cet effet, <lb></lb>est egale a cet effort suivant RT, au quel, par la meme raison, le poids <lb></lb>d&#039;une portion ST de la meme liqueur seroit aussi egal. </s>

<s>Donc le force de <lb></lb>resistance, avec la quelle le cote oblique XD du tuyau incliné AKDX repouse <lb></lb>le filet vertical TR, suivant sa direction; est egale au poids d&#039;une portion <lb></lb>ST de cette liqueur. </s>

<s>Par consequent le poids de ce filet TR ainsi, repoussé <lb></lb>suivant TQ, fait le meme effort en ce sens, sur le fond vertical KD, du tuyau <lb></lb>incliné AKDX, qu&#039;y feroit ce meme poids du filet TR augmenté du poids <lb></lb>de ST, c&#039;est-a-dire, le meme effort, qu&#039;y feroit le poids d&#039;un filet vertical <lb></lb>entier SR de la meme liqueur ” (ivi, pag. </s>

<s>254). Le medesime cose dimo­<lb></lb>strandosi degli altri filetti, se ne conclude che il liquido HLD preme il fondo <lb></lb>LD con la forza del cilindro HD, e tutto il fondo del vaso obliquo vien per­<lb></lb>ciò gravato dal peso della colonna retta YD. </s></p><p type="main">

<s>Il discorso insomma del Varignon si riduce a dimostrare che l&#039;acqua <lb></lb>GKY non preme menomamente il fondo, e che in ricompensa l&#039;acqua KLD <lb></lb>lo preme col doppio del suo proprio peso. </s>

<s>È fresca nei nostri Lettori la me­<lb></lb>moria di questa dimostrazione, data già dallo Stevino: che se il novello Acca­<lb></lb>demico di Parigi si fosse contentato di vantare il suo modo come più facile, <lb></lb>e più breve di quel del Matematico del principe di Nassau, gli si potrebbe <lb></lb>anche concedere, facendogli però osservare che deriva un tal vantaggio, piut­<lb></lb>tosto che dal principio dei moti composti, da quello degl&#039;indivisibili, appli­<lb></lb>catovi il quale la dimostrazione, che si ricava dagli <emph type="italics"></emph>Elemens hydrostatiques,<emph.end type="italics"></emph.end><lb></lb>è assai più diretta e spedita, di quella che ne suggerì l&#039;Autore della <emph type="italics"></emph>Mecha­<lb></lb>nique nouvelle.<emph.end type="italics"></emph.end> Ridotta la parete a un punto, sopra cui perpendicolarmente <lb></lb>insista un filetto liquido, la prima parte del Teorema varignoniano è dagli <lb></lb>insegnamenti dello Stevino per sè manifesta. </s>

<s>Quanto all&#039;altra parte poi il <lb></lb>Varignon suppone quel che lo Stevino aveva ben dimostrato, che cioè nel <lb></lb>punto T la parete è premuta dal peso di un filetto liquido, alto quanto ST. </s>

<s><lb></lb>E perchè lo sforzo, riflesso da essa parete sul filetto TR, uguaglia lo sforzo <lb></lb>diretto ST, resta così, senz&#039;altro, concluso che il punto R del fondo è pre­<lb></lb>muto da tutto il peso del filetto RS. </s>

<s>Onde il paradosso idrostatico può spie­<lb></lb>garsi a quel modo che fa il Varignon, per rendere uniforme il metodo d <lb></lb>trattar, col principio della composizion delle forze, così fatte questioni: non <lb></lb>già che, senza un tal principio, non sia possibile, com&#039;ei pretende, riuscir <lb></lb>nell&#039;intento, o che sia vero non esservi prima di lui, e senza quel suo nuovo <lb></lb>aiuto, nessuno ancora riuscito. </s></p><pb xlink:href="020/01/3226.jpg" pagenum="187"></pb><p type="main">

<s>Il vantaggio, che viene alla dimostrazione, dal condurla sulla regola idro­<lb></lb>statica dello Stevino, piuttosto che su quella meccanica del Varignon, si com­<lb></lb>prenderà anche meglio, proponendosi il caso che i recipienti non siano ci­<lb></lb>lindrici o prismatici, ma irregolari. </s>

<s>Intorno a che un&#039;altra difficoltà fu <lb></lb>promossa contro il metodo usato da Galileo. </s>

<s>Siano i vasi comunicanti AC, <lb></lb>GD della figura 90, di qual si voglia forma più capricciosa: riman pure un <lb></lb>fatto che il liquido si dispone qua e là nel medesimo livello, ma come si <lb></lb>potrebbe applicare a spiegarlo il discorso dell&#039;Autore delle Galleggianti? </s>

<s><lb></lb>L&#039;obiezione risuonò alle orecchie di Tommaso Bonaventuri, editore nel 1718 <lb></lb>in Firenze delle opere galileiane, il quale riferì in una nota, d&#039;altre simili <lb></lb>cose erudita, la risposta avutane in proposito dal p. </s>

<s>ab. </s>

<s>Guido Grandi. </s>

<s>Sup­<lb></lb>posto che i vasi comunicanti siano ED, AZ (fig. </s>

<s>98), e che, abbassandosi nel­<lb></lb><figure id="id.020.01.3226.1.jpg" xlink:href="020/01/3226/1.jpg"></figure></s></p><p type="caption">

<s>Figura 98.<lb></lb>l&#039;uno il liquido da GR in QO, risalga <lb></lb>nell&#039;altro da LX in AB, conduce il <lb></lb>Grandi la sezione MN, media aritme­<lb></lb>tica fra GR e QO, e la sezione KT me­<lb></lb>dia aritmetica fra LX e AB, sopra le <lb></lb>quali due medie sezioni costruisce due <lb></lb>cilindri con le altezze GQ, AL, osser­<lb></lb>vando che, per essere nel moto iniziale <lb></lb>queste altezze piccolissime, le irregola­<lb></lb>rità de&#039;tubi tornano all&#039;esattezza de&#039;cilindri circoscritti, per cui la questione <lb></lb>si riduce al caso contemplato da Galileo, verificandosi anche qui “ che le su­<lb></lb>perficie GH, LX sono reciproche alle altezze o velocità AL, GQ, con le quali <lb></lb>dette superficie sono disposte a muoversi, nel bel principio del moto, e però <lb></lb>ne segue ottimamente che facciano equilibrio ” (Alb. </s>

<s>XII, 603). </s></p><p type="main">

<s>Così essendo, poteva il Bonaventuri citar piuttosto il Pascal, che tanti <lb></lb>anni prima, e più autorevolmente del Grandi, aveva risoluta ogni difficoltà <lb></lb>così, nel medesimo modo, geometricamente ragionando: “ Ces liqueurs se­<lb></lb>roient aussi bien en equilibre dans ces tuyaux irreguliers, que dans les uni­<lb></lb>formes, parce que les liqueurs ne pesent que suivant leur hauteur, et non <lb></lb>pas suivant leur largeur. </s>

<s>Et la demonstration en seroit facile en inscrivant <lb></lb>en l&#039;un et en l&#039;autre plusieurs petits tuyaux reguliers. </s>

<s>Car on seroit voir, <lb></lb>par ce que nous avons demontré, que deux de ces tuyaux inscripts, qui se <lb></lb>correspondent dans les deux vaisseaux, sont en equilibre. </s>

<s>Donc tous ceux <lb></lb>d&#039;un vaisseau seroient en equilibre avec tous ceux de l&#039;autre. </s>

<s>Ceux qui sont <lb></lb>accoutumez aux inscriptions, et aux circonscriptions de la Geometrie, n&#039;au­<lb></lb>ront nulle peine a entendre cela, et il seroit bien difficile de le demontrer <lb></lb>aux autres au moins geometriquement ” <emph type="italics"></emph>(De l&#039;equilibre des liqueurs<emph.end type="italics"></emph.end> cit., <lb></lb>pag. </s>

<s>17, 18). </s></p><p type="main">

<s>Alla Geometria degl&#039;inscritti successe più felicemente l&#039;altra degl&#039;indi­<lb></lb>visibili, per la quale vennero finalmente a sparire tutte le difficoltà contro <lb></lb>il principio delle velocità virtuali, professato, come accennammo, dal D&#039;Alem­<lb></lb>bert oramai senza scrupoli e senza timori. </s>

<s>Nonostante anche il vecchio me-<pb xlink:href="020/01/3227.jpg" pagenum="188"></pb>todo, usato dal Pascal e dal Grandi, si porgeva atto a dimostrare il para­<lb></lb>dosso idrostatico, nel caso altresi che uno o ambedue i tubi fossero inclinati. </s>

<s><lb></lb>Il Sinclaro, fatta la distinzione di gravità <emph type="italics"></emph>sensibile<emph.end type="italics"></emph.end> e <emph type="italics"></emph>insensibile,<emph.end type="italics"></emph.end> dimostrò <lb></lb>facilmente che il mercurio, “ aut quodvis aliud fluidum, in siphonis crure <lb></lb>contentum, gravitatem insensibilem deperdere, et lucrari iuxta eandem pro­<lb></lb>portionem, iuxta quam describuntur sinus, sive inaequales divisiones semi­<lb></lb>diametri ” <emph type="italics"></emph>(Ars magna<emph.end type="italics"></emph.end> cit., pag. </s>

<s>491): teorema che, ritenute le più comuni <lb></lb>denominazioni di gravità <emph type="italics"></emph>assoluta<emph.end type="italics"></emph.end> e di <emph type="italics"></emph>respettiva,<emph.end type="italics"></emph.end> i moderni, come Leonardo <lb></lb>Ximenes, in proposito di ridurre alle ragioni del moto il suo <emph type="italics"></emph>Timpano idrau­<lb></lb>lico,<emph.end type="italics"></emph.end> formulava dicendo che “ in qualunque fluido, racchiuso in un tubo ret­<lb></lb>tilineo inclinato all&#039;orizonte, sta la gravità assoluta alla respettiva, come il <lb></lb>seno totale al seno dell&#039;angolo di elevazione sopra l&#039;orizonte ” <emph type="italics"></emph>(Raccolta di <lb></lb>Autori che trattano del moto delle acqae,<emph.end type="italics"></emph.end> 2a ediz. </s>

<s>cit., T. IX, pag. </s>

<s>313). </s></p><p type="main">

<s>Per la dimostrazione si può ricorrere alla Meccanica, considerando il <lb></lb>fluido quale un corpo grave, che ora scenda nel perpendicolo, ora lungo <lb></lb><figure id="id.020.01.3227.1.jpg" xlink:href="020/01/3227/1.jpg"></figure></s></p><p type="caption">

<s>Figura 99.<lb></lb>l&#039;obliquità di qualche piano. </s>

<s>E come allora che, di un grave, <lb></lb>il peso assoluto sta al respettivo, come il seno totale sta al <lb></lb>seno dell&#039;angolo dell&#039;inclinazione, ossia come la lunghezza <lb></lb>del piano inclinato sta alla sua altezza perpendicolare, la <lb></lb>Meccanica dimostra che, congiunti insieme i due pesi, stanno <lb></lb>in equilibrio; così, con le medesime ragioni, può aversi <lb></lb>dall&#039;Idrostatica per dimostrato l&#039;equilibrio ne&#039;due tubi AB, <lb></lb>BC (fig. </s>

<s>99), dentro i quali sono i liquidi così congiunti, <lb></lb>che non può l&#039;uno scendere, se l&#039;altro non sale. </s></p><p type="main">

<s>Passa inoltre il Ximenes, in una terza proposizione, a dimostrare che <lb></lb>il fluido si dispone alla medesima altezza ne&#039;due rami del sifone, anco quando <lb></lb>fossero incurvati in qualunque maniera. </s>

<s>La dimostrazione può pure ricavarsi <lb></lb>utilmente dalla Meccanica, applicandovi il teorema VIII, dimostrato dall&#039;Huy­<lb></lb>ghens nella II parte del suo Orologio oscillatorio. </s></p><p type="main">

<s>Nel primo corollario della sopra annunziata terza proposizione dell&#039;ar­<lb></lb>ticolo V il Ximenes così dice: “ Se i due rami del sifone composto fossero <lb></lb>di differente diametro, non perciò muta punto il Teorema, purchè il tubo <lb></lb>non sia capillare. </s>

<s>Poichè quella parte di fluido, che nel tubo di maggiore <lb></lb>diametro eccede il diametro del tubo più angusto, non gravita sopra il fluido <lb></lb>del medesimo, ma esercita la sua pressione soltanto contro il risalto, che na­<lb></lb>sce interiormente, quando si fa passaggio dal diametro maggiore al minore ” <lb></lb><emph type="italics"></emph>(Raccolta<emph.end type="italics"></emph.end> e T. cit., pag. </s>

<s>316). </s></p><p type="main">

<s>La ragione è puramente fisica, e si direbbe perciò impropria, in mezzo <lb></lb>al rigore geometrico, con cui si conduce il rimanente di questa scrittura. </s>

<s>Più <lb></lb>appropriate erano senza dubbio le circoscrizioni, a cui ricorsero il Pascal e <lb></lb>il Grandi, ma, oltre che risentivano troppo dell&#039;imperfezione de&#039;metodi an­<lb></lb>tichi, parevano piuttosto cose quasi posticce, che connaturate con l&#039;Idrosta­<lb></lb>tica. </s>

<s>Ora chi crederebbe mai che la vera, propria e diretta ragione del li­<lb></lb>vellarsi i fluidi ne&#039;sifoni, siano questi perpendicolari o obliqui, retti o curvi, <pb xlink:href="020/01/3228.jpg" pagenum="189"></pb>andanti o spezzati, uniformi o irregolari fosse ritrovata da un Discopolo di <lb></lb>Galileo, pochi anni dopo essersi dato a rimeditare il libro delle Galleggianti <lb></lb>del suo Maestro? </s>

<s>È costui quel Niccolò Aggiunti, noto oramai in questa Sto­<lb></lb>ria quale insigne promotore dell&#039;Acustica e della Meccanica galileiana, che <lb></lb>non vuol mancare a sè medesimo in confermare nell&#039;assoluta verità delle sue <lb></lb>ragioni uno de&#039;principali teoremi dell&#039;Idrostatica. </s></p><p type="main">

<s>“ Quel che dimostra Herone del sifone torto, egli dice, non mi sodisfa in­<lb></lb>teramente. </s>

<s>Però mi messi per veder s&#039;io potevo investigarne miglior dimostra­<lb></lb>zione, quale penserei che fosse questa: Sia il vaso MN (fig. </s>

<s>100), ed in esso il <lb></lb>sifone torto PDCBA, la cui bocca A sia al pari del livello RS dell&#039;acqua infusa. </s>

<s><lb></lb>Dico che, intendendosi pieno d&#039;acqua il sifone, benchè la parte di esso D, C, B, A <lb></lb><figure id="id.020.01.3228.1.jpg" xlink:href="020/01/3228/1.jpg"></figure></s></p><p type="caption">

<s>Figura 100.<lb></lb>fosse difforme, e dove di grandissima, dove di po­<lb></lb>chissima tenuta; non potrà, cadendo l&#039;acqua dalla <lb></lb>bocca A, alzar l&#039;acqua del vaso dall&#039;altra parte P. ” </s></p><p type="main">

<s>“ Imperocchè, dovendosi far questo alzamento, <lb></lb>è necessario che l&#039;acqua nelle parti D, C, B, A di­<lb></lb>scenda, e così, con l&#039;impeto che avrà discendendo, <lb></lb>faccia montar l&#039;acqua del vaso. </s>

<s>Notisi dunque che <lb></lb>l&#039;acqua discendendo ha il suo momento composto <lb></lb>e della gravità di essa e della velocità, con la <lb></lb>quale ella si move. </s>

<s>Inoltre avvertasi che, passando <lb></lb>l&#039;istessa quantità d&#039;acqua per le parti A in tanto <lb></lb>tempo, in quanto era passata per le parti B, ovvero <lb></lb>C, ovvero D; è necessario che, nelle parti più anguste del sifone, ella corra <lb></lb>tanto più velocemente, e nelle più larghe tanto più tardamente, quanto ap­<lb></lb>punto esse parti son più o meno capaci. </s>

<s>Sicchè le velocità di qualsivoglia <lb></lb>parti saranno reciprocamente proporzionali alle capacità delle altre, con le <lb></lb>quali si conferiranno. </s>

<s>Ma come stanno le capacità delle parti del sifone, così <lb></lb>sono le moli d&#039;acqua in esse contenute, e come le moli dell&#039;acqua, così sono <lb></lb>fra loro le gravità di esse moli di acqua; adunque per tutto le velocità ri­<lb></lb>spondono contrariamente alle grandezze, e però l&#039;impeto delle acque cadenti <lb></lb>nelle parti A, B, C, D del sifone è per tutto lo stesso, e il suo momento per <lb></lb>tutte quelle parti eguale, e come se appunto fosse per tutto ugualmente <lb></lb>grosso come in A, come in C, ovvero in qualunque altra parte. </s>

<s>Ma quando <lb></lb>il sifone fosse per tutte le sue parti D, C, B, A uniformemente grosso, e la <lb></lb><figure id="id.020.01.3228.2.jpg" xlink:href="020/01/3228/2.jpg"></figure></s></p><p type="caption">

<s>Figura 101.<lb></lb>sua esteriore bocca pareggiasse solamente il livello <lb></lb>dell&#039;acqua, noi mostreremo che sempre è necessario <lb></lb>che l&#039;acqua RS non s&#039;alzi, benchè fosse pieno il si­<lb></lb>fone come sopra; adunque è impotente l&#039;acqua, in <lb></lb>D, C, B, A scorrendo, a sollevar l&#039;acqua del vaso <lb></lb>sopra il livello RS. ” </s></p><p type="main">

<s>“ Sia prima, per più chiara intelligenza, il si­<lb></lb>fone ABTR (fig. </s>

<s>101), dal quale se intenderemo uscir <lb></lb>l&#039;acqua SR è necessario, acciò non resti spazio va-<pb xlink:href="020/01/3229.jpg" pagenum="190"></pb>cuo, che dall&#039;altra bocca del sifone sormonti l&#039;acqua NM eguale alla SR. </s>

<s><lb></lb>Perchè dunque sono due prismi uguali, le basi corrisponderanno contraria­<lb></lb>mente alle altezze, cioè così starà NL ad SQ, come QR ad LM. </s>

<s>Ma come <lb></lb>sta NL ad SQ, così la velocità. </s>

<s>con la quale s&#039;alza l&#039;acqua NM, alla velo­<lb></lb>cità, con la quale s&#039;abbassa SR, e come sta QR ad LM, così sta il prisma <lb></lb>VR al prisma BM, cioè la gravezza dell&#039;acqua contenuta nell&#039;uno, alla gra­<lb></lb>vezza dell&#039;acqua contenuta nell&#039;altro; adunque le velocità rispondono con­<lb></lb>trariamente alle gravezze, e perciò, essendo in questo caso i momenti uguali, <lb></lb>si farà l&#039;equilibrio. </s>

<s>Ma se la bocca fosse in ST, più alta del livello dell&#039;acqua <lb></lb>OP, allora la proporzione delle velocità, con le quali si moverebbe l&#039;acqua, <lb></lb>sarebbe la stessa, ma quella della gravezza sarebbe alterata, ed averebbe la <lb></lb>gravezza dell&#039;acqua in VT, alla gravezza dell&#039;acqua in BM, minor propor­<lb></lb>zione che prima. </s>

<s>E però, essendo minor di quella che bisogneria, per ri­<lb></lb>spondere permutatamente a quella delle velocità, non saranno più i loro mo­<lb></lb>menti uguali, ma la BM prepondererà alla VT. </s>

<s>E per l&#039;opposito, se la bocca <lb></lb>fosse in CD, più bassa della superficie dell&#039;acqua OP, l&#039;acqua VD prepon­<lb></lb>dererebbe ” (MSS. Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>102). </s></p><p type="main">

<s>E per dar la questione, così sottile e perciò così controversa, per ogni <lb></lb>sua parte risoluta, passa l&#039;Aggiunti a considerare il caso che, essendo pure <lb></lb>il tubo di uniforme diametro, non sia andante, ma spezzato e flessuoso. </s>

<s>Pre­<lb></lb>mette un lemma, formulato però nella sola sua conclusione, tacendone o ac­<lb></lb><figure id="id.020.01.3229.1.jpg" xlink:href="020/01/3229/1.jpg"></figure></s></p><p type="caption">

<s>Figura 102.<lb></lb>cennandone oscuramente i principii, meritevoli in <lb></lb>qualunque modo d&#039;esser notati, o si derivino dalla <lb></lb>statica dello Stevino, o dalla dinamica di Galileo. </s>

<s><lb></lb>Quel lemma è tale: se sopra l&#039;orizonte LC (fig. </s>

<s>102) <lb></lb>si sollevino due linee congiunte in B, e lungo le <lb></lb>quali s&#039;intendano accomodati due solidi per tutto <lb></lb>ugualmente grossi, e nen tenacemente seco stessi <lb></lb>coerenti; la parte L non solleverà l&#039;altra C, ma staranno insieme in equi­<lb></lb>librio, e premeranno in L e in C quanto farebbe in M perpendicolarmente <lb></lb>il solido BM. </s></p><p type="main">

<s>È manifesto che la prima parte della proposizione piglia verità dal teo­<lb></lb>rema dello Stevino, supponendo essere i solidi BL, BC ridotti in sezioni tutte <lb></lb>uguali, rappresentanti gli anelli della catena: e, come questi, così stanno <lb></lb>quelle in equilibrio, essendo in numero proporzionali alle lunghezze de&#039;piani <lb></lb>LB, BC, su cui suppone l&#039;Aggiunti che siano accomodate. </s>

<s>La seconda parte <lb></lb>dipende dal principio dinamico di Galileo, che dice essere uguali gl&#039;impeti <lb></lb>o le velocità, dopo scese perpendicolari uguali. </s>

<s>Che siano poi queste appli­<lb></lb>cazioni della meccanica de&#039;solidi ai liquidi notabili, massime in un uomo, <lb></lb>morto due anni prima la pubblicazione de&#039;Dialoghi delle nuove Scienze; ne <lb></lb>converrà chiunque ripensi come la ragione del livellarsi il liquido, nei tubi <lb></lb>rappresentati dalla figura 99, si veniva a far per lui conseguire immediata­<lb></lb>mente dal dover esso liquido, sceso in B, avere acquistato tale impeto, da <lb></lb>risalire in A alla medesima altezza da cui fu sceso: e non dipendendo gli <pb xlink:href="020/01/3230.jpg" pagenum="191"></pb>impeti o le velocità dalla quantità di materia, ma da sola la quantità della <lb></lb>caduta; s&#039;intenderà senz&#039;altro come si dovesse verificare il teorema, qualun­<lb></lb>que fosse de&#039;tubi l&#039;inclinazione, la capacità e la forma. </s>

<s>Ma dovendo altrove <lb></lb>ritornare sull&#039;importante argomento, seguitiamo a leggere l&#039;interrotto ma­<lb></lb>noscritto. </s></p><p type="main">

<s>“ Se poi fosse un sifone con varie rivolte e flessuosità, come ABCDE, <lb></lb>nella medesima figura 102, purchè la bocca esteriore E sia nel medesimo <lb></lb>piano che il livello dell&#039;acqua FG, l&#039;acqua non si moverà, e si farà pari­<lb></lb>mente l&#039;equilibrio. </s>

<s>Il che, acciò sia manifesto, intendasi la linea AE orizon­<lb></lb>tale, sopra la quale sia la linea ABCDE in qualsivoglia modo variamente <lb></lb>inflessa. </s>

<s>Se noi lungo questa linea intenderemo accomodato un solido grave, <lb></lb>per tutto ugualmente grosso, e con le sue parti non tenacemente coerenti, <lb></lb>ma ad ogni minima forza flessibili; dico che, rimosso ogni altro impedimento <lb></lb>dalle estremità A, E, detto solido nondimeno non si moverà da niuna parte, <lb></lb>nè una estremità potrà sollevare l&#039;altra. </s>

<s>Perchè, tirisi dal punto C la linea <lb></lb>parallela all&#039;orizonte AE, qual sia LMCFH. Dipoi, dai punti L, B, D, H, ti­<lb></lb>rinsi le perpendicolari all&#039;orizonte LK, BM, DF, HG; la parte del grave, po­<lb></lb>sata in BC, equipondera a quella che posa in BL, perchè sì l&#039;uno che l&#039;altro <lb></lb>sosterrebbe in equilibrio un solido grave della medesima grossezza e mate­<lb></lb>ria che son loro, il quale pendesse secondo la linea BM, e fosse alto quanto <lb></lb>la linea BM. </s>

<s>E per la stessa cagione quella parte che posa in DH equipon­<lb></lb>dera a quella, che è nel declive DC, e quella parte, che è posta rasente HE, <lb></lb>equilibrerebbe un solido della medesima materia e grossezza, lungo solo <lb></lb>quanto HG, ovvero LK, se però egli fosse sospeso perpendicolarmente, e tanto <lb></lb>farebbe il grave locato in LA. </s>

<s>Adunque il grave in DHE equipondera il grave <lb></lb>posto in BLA. </s>

<s>Perchè dunque tutte le parti del grave, che lo tirano verso <lb></lb>l&#039;estremità E, sono d&#039;ugual momento con quelle, che lo tirano verso l&#039;altra <lb></lb>estremità A; perciò non si farà movimento alcuno, ma sì bene subito che <lb></lb>l&#039;una delle estremità si allungherà o scorcerà. </s>

<s>” </s></p><p type="main">

<s>“ Lo stesso possiamo tener per certo che avvenga ne&#039;sifoni ritorti, anco <lb></lb>con superficie curve, imperocchè la curvità della superficie non è altro che <lb></lb>infinita inclinazione di piani. </s>

<s>E non importa poi che in questa sorta di sifoni, <lb></lb>per i quali s&#039;ha da mover l&#039;acqua, la canna sia inegualmente grossa per tutto, <lb></lb>avendo noi già dimostrato esser lo stesso, atteso che nelle parti più larghe <lb></lb>l&#039;acqua si move men velocemente, e nelle strette più velocemente, sicchè i <lb></lb>suoi momenti vengono per tutto in questo modo ragguagliati ” (ivi, fol. </s>

<s>103). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Come la teoria del sifone ritorto, data così dall&#039;Aggiunti, sia applicabile <lb></lb>all&#039;equilibrio de&#039;liquidi nei vasi comunicanti, è cosa per sè manifesta, non <lb></lb>occorrendo a far altro, per ridurre alla medesima argione i due casi, che <pb xlink:href="020/01/3231.jpg" pagenum="192"></pb>riguardare il sifone stesso con le sue braccia rivolte in alto. </s>

<s>Nè meno evi­<lb></lb>dente è che si venivano, ragionando a quel modo, a togliere tutte le diffi­<lb></lb>coltà, che s&#039;incontravano nella dimostrazione di Galileo, sia rispetto al prin­<lb></lb>cipio da cui moveva, sia rispetto alle varietà, alle quali poteva andare sog­<lb></lb>getta la più semplice ipotesi ammessa da lui, delle forme cioè sempre <lb></lb>regolari dei vasì. </s>

<s>I successori usarono la medesima arte dell&#039;Aggiunti, per <lb></lb>salvar dalle contradizioni il metodo galileiano, che perciò rimane tuttavia in <lb></lb>onore, e anzi è bene spesso preferito agli altri dalla Scienza, quando, in qual­<lb></lb>che più difficile incontro, vuol più agile movere i passi. </s></p><p type="main">

<s>Sorte molto diversa ebbe però a subire quel metodo, quando Galileo <lb></lb>pensò di applicarlo a dimostrare i teoremi fondamentali dell&#039;Idrostatica. </s>

<s>Ri­<lb></lb>ducendosi in generale a conferire i momenti della resistenza dell&#039;acqua a <lb></lb>essere alzata, co&#039;momenti della gravità premente il solido, si fondava in una <lb></lb>tal supposizione, la quale, non verificandosi il discorso non riesce concludente, <lb></lb>essendo che il momento della resistenza dell&#039;acqua è manifestamente nullo, <lb></lb>quando il vaso è pieno, e l&#039;acqua stessa perciò, immergendovi il solido, non <lb></lb>s&#039;alza intorno a lui, ma si versa. </s>

<s>Inoltre, perchè la mole dell&#039;acqua alzata <lb></lb>è sempre minore del solido, potendosi dare il caso che l&#039;alzamento di quella <lb></lb>e l&#039;abbassamento di questo siano uguali, s&#039;avrebbero uguali velocità in due <lb></lb>grandezze diverse, per cui non sarebbe lecito, in tal contingenza, inferirne la <lb></lb>ragione dell&#039;equilibrio. </s></p><p type="main">

<s>Il difetto poi del metodo generale si fa risentire anche di più nei casi <lb></lb>particolari, come quando Galileo, per esempio, vuol dimostrare che un solido <lb></lb>è giustamente sostenuto dal momento dell&#039;acqua, che fa alzarglisi intorno, <lb></lb>sia il recipiente angustissimo o immenso, sembrando per lo meno cosa assai <lb></lb>strana l&#039;andar ricercando, nell&#039;alzamento che fa lungo i suoi lidi l&#039;acqua <lb></lb>dell&#039;oceano, il momento della forza, che vi sostien galleggiante una festuca. </s></p><p type="main">

<s>A strette di dubbi ben assai più forti metteva la proposizione prece­<lb></lb>dente a questa, che è la terza ordinata da noi dal trattato delle Galleggianti, <lb></lb>e nella quale Galileo, propostosi il prisma AF rappresentato dentro il vaso <lb></lb>DB della figura 66, e supposto men grave in specie dell&#039;acqua, vuol dimo­<lb></lb>strare che sarà sollevato dall&#039;acqua CE circonfusa, con queste precise parole <lb></lb>concludendo la sua dimostrazione: “ Adunque il peso assoluto dell&#039;acqua CE, <lb></lb>al peso assoluto del prisma AF, ha maggior proporzione che l&#039;alzamento del <lb></lb>prisma AF, all&#039;abbassamento di essa acqua CE. </s>

<s>Il momento dunque compo­<lb></lb>sto della gravità assoluta dell&#039;acqua CE, e della velocità del suo abbassa­<lb></lb>mento, mentre ella fa forza premendo di scacciare e di sollevare il solido AF, <lb></lb>è maggior del momento composto del peso assoluto del prisma AF, e della <lb></lb>tardità del suo alzamento, col qual momento egli contrasta allo scacciamento <lb></lb>e forza fattagli dal momento dell&#039;acqua: sarà dunque sollevato il prisma ” <lb></lb>(Alb. </s>

<s>XII, 21). </s></p><p type="main">

<s>A questo punto non potevano gli studiosi non lasciare in sospeso la let­<lb></lb>tura, per domandare a sè medesimi in che modo può l&#039;acqua CE esercitare <lb></lb>contro il solido la sua forza. </s>

<s>Si dice che essa acqua è circonfusa al prisma, <pb xlink:href="020/01/3232.jpg" pagenum="193"></pb>ma veramente ella non ne bagna che una faccia sola, rimanendo, per sup­<lb></lb>posizione, le altre tre laterali, e il fondo, aderenti alle pareti del vaso. </s>

<s>I li­<lb></lb>beri ingegni e imbevuti alle più sane dottrine dello Stevino, non avrebbero <lb></lb>penato a dire che il solido, nella fatta ipotesi, rimarrebbesi eternamente in <lb></lb>fondo al vaso, dove fu posto, e fosse men grave in specie dell&#039;acqua quanto <lb></lb>si voglia, e gli fosse questa circonfusa, e sollevatagli a qualunque più smi­<lb></lb>surata altezza. </s>

<s>Ma l&#039;esclusivo magistero di Galileo non permettendo una tale <lb></lb>libertà di giudizio, si tormentavano stranamente gl&#039;ingegni, per intendere in <lb></lb>che modo potesse l&#039;acqua scacciar dal fondo il solido, e levarselo in capo. </s>

<s><lb></lb>Diceva il Maestro che ella <emph type="italics"></emph>fa forza premendo,<emph.end type="italics"></emph.end> e premere non può, se non <lb></lb>la parete sola che ella bagna. </s>

<s>Come però da quest&#039;unica pressione potesse <lb></lb>resultarne il sollevamento era duro a intendere. </s>

<s>Fosse almeno bagnato il <lb></lb>prisma da due facce opposte si potrebbe rassomigliar l&#039;effetto a quel che si <lb></lb>osserva, quando due spingono l&#039;un contro l&#039;altro un peso, che nello stesso <lb></lb>tempo lo sollevano, ma uno solo, quanto si voglia gagliardo, facendo forza <lb></lb>nel medesimo modo, non riuscirebbe a sollevarlo mai di un capello. </s>

<s>Poi chi <lb></lb>così ragionava avrebbe voluto riaversi dalle pene del dubbio, ripensando che <lb></lb>forse la parete opposta a quella bagnata potrebbe contrastare con la sua <lb></lb>immobilità, facendo sforzo uguale a quello, che si sarebbe fatto dall&#039;acqua. </s></p><p type="main">

<s>Fra i seguaci di Galileo, che s&#039;aggiravano in tal guisa fra le angustie <lb></lb>del loro pensiero, troviamo l&#039;Aggiunti, mentre era intorno a risolvere un <lb></lb>problema idrostatico, applicandovi i nuovi principii insegnati dal suo Mae­<lb></lb>stro. </s>

<s>“ Sia, egli dice, GH (fig. </s>

<s>103) un vaso parallelepipedo, con la base ori­<lb></lb>zontale, ed in esso sia il solido CB, men grave in specie dell&#039;acqua, il quale, <lb></lb><figure id="id.020.01.3232.1.jpg" xlink:href="020/01/3232/1.jpg"></figure></s></p><p type="caption">

<s>Figura 103.<lb></lb>con la sua superficie AB e con l&#039;opposta, <lb></lb>combaci esquisitamente le superficie late­<lb></lb>rali del vaso, a quel modo che suppone <lb></lb>il Galileo nel suo <emph type="italics"></emph>Delle galleggianti.<emph.end type="italics"></emph.end> Dipoi <lb></lb>infondasi acqua dall&#039;una parte del vaso, <lb></lb>sicchè ella sia al livello ZU, nel quale stato <lb></lb>si faccia, tra il solido e l&#039;acqua, l&#039;equi­<lb></lb>librio. </s>

<s>Sia poi qualunque minima forza Y, <lb></lb>che tiri orizontalmente detto solido CB. </s>

<s>Di­<lb></lb>mostreremo tal solido, da qualunque mi­<lb></lb>nima forza, potere esser mosso e quanto, <lb></lb>purchè dall&#039;altra parte GK del vaso s&#039;in­<lb></lb>tenda di mano in mano tant&#039;acqua, che <lb></lb>pareggi il livello QZ. </s>

<s>E prima, considerisi <lb></lb>chè, se detto solido si avesse a movere nell&#039;orizonte GD, essendo il vaso <lb></lb>vuoto, allora sarebbe mosso da qualunque minima forza. </s>

<s>Ma perchè adesso, <lb></lb>movendosi verso la parte D, è necessario che la medesima acqua circonfusa DM, <lb></lb>da tal movimento spinta in vaso di minor base s&#039;inalzi, e a tale alzamento <lb></lb>ella contrasta anche lateralmente; adunque bisogna che noi dimostriamo, dalla <lb></lb>forza Y, all&#039;impulso laterale di quant&#039;acqua si possa far resistenza. </s>

<s>” </s></p><pb xlink:href="020/01/3233.jpg" pagenum="194"></pb><p type="main">

<s>“ Il peso di tutto il solido CB è uguale al peso di una mole di acqua, <lb></lb>eguale al solido RB. </s>

<s>Intendasi dunque il solido RB essere ugualmente grave <lb></lb>in specie all&#039;acqua, e la parte rimanente KC non aver peso alcuno, sicchè <lb></lb>il solido tutto CB rimarrà del medesimo momento che prima. </s>

<s>Sia inoltre la <lb></lb>forza Y uguale al peso della mole d&#039;acqua I, e sopra la base RS trovisi il <lb></lb>solido SP, uguale in mole ed in peso al solido I, e l&#039;altezza di detto solido <lb></lb>SP sia la linea VU. </s>

<s>Dalla linea poi VA piglisi la linea VN, eguale alla VU: <lb></lb>dico che il solido CB, dalla forza Y, sarà mosso tanto per l&#039;orizonte GD, <lb></lb>verso la parte D, sicche l&#039;acqua arrivi colla superficie di sopra al punto N. ” </s></p><p type="main">

<s>“ Perchè, intendasi mosso il solido CB talmente, che l&#039;acqua si sia al­<lb></lb>zata al detto punto N, e dopo tal movimento il solido CB sia venuto nel <lb></lb>sito XO, dimodochè il solido Q′M sia l&#039;istesso che il solido SP, e la linea <lb></lb>TL sia l&#039;istessa che VU, e TN sia la UN. </s>

<s>Perchè l&#039;acqua FZ è quella, che <lb></lb>era nel luogo, dove è subentrato il solido RQ′, adunque il solido RQ′ è uguale <lb></lb>al solido FZ, e però, come sta il solido MQ′ al solido RQ′, così starà al so­<lb></lb>lido FZ. </s>

<s>Ma al solido RQ′ egli sta come la linea LT, alla linea VT; dunque <lb></lb>l&#039;istesso solido MQ′, anco al solido FZ, sta come la linea LT, o vogliam dire <lb></lb>VU, cioè la VN, cioè la TN, poichè tutte queste sono uguali, alla TV. </s>

<s>Di­<lb></lb>remo dunque il solido Q′M, cioè il solido SP, cioè il solido I, cioè la forza, <lb></lb>ovver peso Y, sta all&#039;acqua FZ, come TN alla TV. </s>

<s>Ma perchè, nel mede­<lb></lb>simo tempo che il solido CB, cioè la forza Y (poichè il solido e la forza che <lb></lb>lo tira si muovono con ugual velocità) si è mosso per la distanza VT, l&#039;acqua <lb></lb>si è alzata per la distanza TN; adunque la velocità, con la quale si muove <lb></lb>il solido CB, cioè la forza ovvero peso Y, alla velocità, con la quale si move <lb></lb>l&#039;acqua, ovvero peso FZ: sta come la linea VT alla TN. </s>

<s>Ma il peso Y al <lb></lb>peso FZ stava come la TN alla TV; adunque la proporzione delle velocità, <lb></lb>con le quali detti pesi si movono, è contraria alla proporzione dei pesi. </s>

<s>Ma <lb></lb>quando sono due gravi, che faccian forza di movere l&#039;un l&#039;altro, ogni volta <lb></lb>che la gravità dell&#039;uno, alla gravità dell&#039;altro, sta come la velocità, con che <lb></lb>si moverebbe l&#039;altro, a quella con cui si moverebbe l&#039;uno, allora fra que&#039;due <lb></lb>gravi si fa l&#039;equilibrio, nè l&#039;uno vince l&#039;altro; adunque, essendo in tal modo <lb></lb>costituiti la forza Y e l&#039;acqua FZ, l&#039;acqua FZ non moverà la forza Y, nè in <lb></lb>conseguenza il solibo CB. ” </s></p><p type="main">

<s>“ Tutto questo passa bene, secondo la dottrina del signor Galileo, se <lb></lb>noi porremo che l&#039;acqua sia solamente dalla banda D. </s>

<s>Ma qui mi nascono <lb></lb>molte difficoltà, che fanno contro al Galileo ancora, perchè non pare che <lb></lb>basti, acciò un solido men grave in specie dell&#039;acqua sia alzato, che l&#039;acqua <lb></lb>lo bagni da una parte sola, e secondo quell&#039;altezza che vuole il Galileo, ma <lb></lb>tal sollevamento bisogna che sia a mio giudizio d&#039;ogni intorno, o almeno <lb></lb>almeno da ambe le superficie opposte. </s>

<s>Altrimenti, siccome due, spingendo <lb></lb>l&#039;un contro l&#039;altro un solido, e nel medesimo tempo alzando lo sollevano, <lb></lb>ma se fosse uno solo, quanto si voglia gagliardo, facendo forza nello stesso <lb></lb>modo, mai l&#039;alzerebbe; così l&#039;acqua da una parte sola, sia quanto si voglia <lb></lb>alta, non par che possa alzare un solido che tocchi il fondo. <emph type="italics"></emph>Sed haec pen-<emph.end type="italics"></emph.end><pb xlink:href="020/01/3234.jpg" pagenum="195"></pb><emph type="italics"></emph>siculatius<emph.end type="italics"></emph.end> (?).... Ma se il solido, dalla parte opposta alla bagnata, sarà ade­<lb></lb>rente alla sponda immobile del vaso, pare che si possa far l&#039;alzamento.... <lb></lb>Ma pure considera bene. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>106, 7). </s></p><p type="main">

<s>La tenzone dei dubbi così viva e vera, come la descrive l&#039;Aggiunti, era <lb></lb>poi quella, che si faceva nel pensiero di tutti gli altri, e che durò per più <lb></lb>di un mezzo secolo in quelli stessi, i quali più facevano onore alla Scuola <lb></lb>galileiana. </s>

<s>Gli stranieri più liberi, e con la mente aperta a ricevere il ristoro <lb></lb>di altre tradizioni, se imitarono l&#039;esempio di Galileo in applicare il principio <lb></lb>delle velocità virtuali a dimostrar l&#039;equilibrio ne&#039;vasi comunicanti, rifuggi­<lb></lb>rono saviamente dall&#039;usare il metodo di lui, riconosciuto vizioso e insuffi­<lb></lb>ciente, e dar la ragione de&#039;principali fatti idrostatici, per cui ritornarono <lb></lb>agli antichi modi archimedei, senza altra cura che di renderli più brevi, più <lb></lb>facili ed eleganti. </s></p><p type="main">

<s>Il Pascal, inoculando nel suo trattato il principio delle pressioni, riuscì <lb></lb>mirabilmente a condensare in una mezza paginetta il primo libro <emph type="italics"></emph>De insi­<lb></lb>dentibus humido.<emph.end type="italics"></emph.end> Supposto un solido immerso nell&#039;acqua in forma di cubo, <lb></lb>è premuto, egli dice, contro le facce laterali opposte ugualmente, ma più di <lb></lb>sotto che di sopra, con forza uguale al peso di una mole di acqua, pari alla <lb></lb>mole del solido stesso. </s>

<s>“ De sorte qu&#039;un corps, qui est dans l&#039;eau, y est porté <lb></lb>de la mesme sorte, que s&#039;il estoit dans un bassin de balance, dont l&#039;autre <lb></lb>fùt chargé d&#039;un volume d&#039;eau égal au sieu. </s>

<s>D&#039;où il paroist que, s&#039;il est de <lb></lb>cuivre ou d&#039;une autre matiere qui pese plus que l&#039;eau en pareil volume, il <lb></lb>tombe, car son poids l&#039;emporte sur celuy qui le contrebalance. </s>

<s>S&#039;il est de <lb></lb>bois, ou d&#039;une autre matiere plus legere que l&#039;eau en pareil volume, il monte <lb></lb>avec toute la force, dont le poids de l&#039;eau le surpasse. </s>

<s>Et s&#039;il pese egale­<lb></lb>ment, il ne descend ny ne monte comme la cire, qui se tient a peu pres <lb></lb>dans l&#039;eau au lieu ou on l&#039;a met ” <emph type="italics"></emph>(De l&#039;equil. </s>

<s>des liquers<emph.end type="italics"></emph.end> cit., pag. </s>

<s>26). </s></p><p type="main">

<s>Il Mariotte, in fine al discorso primo della parte seconda del suo trat­<lb></lb>tato <emph type="italics"></emph>Du mouvement des eaux,<emph.end type="italics"></emph.end> stabilisce quattro regole, la prima delle quali <lb></lb>corrisponde alla IV proposizione archimedea, la seconda alla V, e la terza e <lb></lb>la quarta alla VII. </s>

<s>Egli pure, lasciata addietro la teoria statica del vette, e <lb></lb>il metodo di conferire i momenti del liquido che s&#039;alza, e del solido che <lb></lb>si abbassa, posato sopra l&#039;umida superficie, fa ricorso alla solita bilancia im­<lb></lb>maginaria, concludendone con evidente facilità le ragioni dello stare, dello <lb></lb>scendere e del salire, nei vari casi, le varie grandezze immerse. <emph type="italics"></emph>(Oeuvres,<emph.end type="italics"></emph.end><lb></lb>T. II cit., pag. </s>

<s>372-80). </s></p><p type="main">

<s>L&#039;Huyghens proponeva, col principio della conservazion delle forze, in­<lb></lb>cluso nella prima ipotesi premessa alla parte IV dell&#039;Orologio oscillatorio, <lb></lb>che dice <emph type="italics"></emph>si pondera quodlibet vi gravitatis suae moveri incipiant, non posse <lb></lb>centrum gravitatis ex ipsis compositae altius quam, ubi incipiente motu <lb></lb>reperiebatur, ascendere;<emph.end type="italics"></emph.end> proponeva dicevasi di dimostrar tutto ciò, che aveva <lb></lb>dimostrato Archimede intorno alle proprietà dei corpi notanti. </s>

<s>“ Haec autem <lb></lb>hypothesis nostra ad liquida etiam corpora valet, ac per eam, non solum <lb></lb>omnia illa, quae de innatantibus habet Archimedes, demonstrari possunt, sed <pb xlink:href="020/01/3235.jpg" pagenum="196"></pb>et alia pleraque mechanica theoremata ” <emph type="italics"></emph>(Opera varia,<emph.end type="italics"></emph.end> Vol. </s>

<s>I, Lugduni <lb></lb>Batav. </s>

<s>1724, pag. </s>

<s>121 e 123). </s></p><p type="main">

<s>Unico forse tra&#039;matematici stranieri il Dechales intese di ritornare ai <lb></lb>metodi di Galileo. </s>

<s>Il principio, ch&#039;egli pone per fondamento alla sua Idro­<lb></lb>statica, è quello delle velocità, che stando contrariamente ai pesi danno la <lb></lb>ragione dell&#039;equilibrio nella stadera. </s>

<s>“ Ad hoc igitur principium revocabi­<lb></lb>mus quaecumque de natantibus in humido demonstrabuntur: ita enim exacte <lb></lb>hoc principium observatur in hac materia, ut nulla sit statera exactior ” <lb></lb><emph type="italics"></emph>(Cursus mathematicus editio secunda,<emph.end type="italics"></emph.end> T. III, Lugduni 1690, pag. </s>

<s>93). Se <lb></lb>dunque da una parte di questa esattissima stadera s&#039;intenda posto il corpo <lb></lb>immerso, e dall&#039;altra una mole di acqua, tutto il negozio si riduce a con­<lb></lb>ferire insieme i loro momenti. </s>

<s>“ Quare restat examinandum utriusque, tam <lb></lb>corporis demersi quam aquae ascendentis, momentum, ut de toto negotio <lb></lb>ferri possit iudicium ” (ibid., pag. </s>

<s>94). </s></p><p type="main">

<s>Incomincia l&#039;esame dal dimostrare che, se la superficie CB (fig. </s>

<s>104) <lb></lb>dell&#039;acqua circonfusa è uguale alla base AC del prisma, che vi s&#039;immerge, <lb></lb>ascenderà del liquido una mole, pari alla metà della parte del solido demersa. </s>

<s><lb></lb>La verità si rende facilmente manifesta, ripensando che, abbassatosi il pri­<lb></lb><figure id="id.020.01.3235.1.jpg" xlink:href="020/01/3235/1.jpg"></figure></s></p><p type="caption">

<s>Figura 104.<lb></lb>sma DC per esempio in D′C′, l&#039;acqua HB salita è <lb></lb>quella, che era dianzi in luogo di AC′, e HB, NC sono <lb></lb>uguali per supposizione, onde NC′, parte del solido <lb></lb>immersa, è doppia dell&#039;acqua HB, che il solido stesso <lb></lb>ha scacciata. </s></p><p type="main">

<s>Suppongasi ora, soggiunge il Dechales, che la <lb></lb>mole NC′ dell&#039;acqua, o la sua uguale HL, pesi quanto <lb></lb>il prisma D′C′: dico che i due pesi rimarranno in <lb></lb>equilibrio. </s>

<s>Chi però comincia a leggere la dimostra­<lb></lb>zione resta maravigliato a trovarci abbandonata la <lb></lb>statica dei momenti, in che si diceva consistere tutto questo negozio, per <lb></lb>tornare indietro ai modi fisici di Archimede. </s>

<s>Dice infatti l&#039;Autore che, se <lb></lb>suppongasi venire il prisma trasformato nell&#039;acqua NC′, pesando questa quanto <lb></lb>l&#039;acqua HL, le braccia uguali A′C′, C′L della bilancia immaginaria A′L non <lb></lb>possono non andare equilibrate. </s></p><p type="main">

<s>Chi prosegue anche a leggere scopre la ragione, per cui il Dechales, <lb></lb>che mostravasi sulle mosse così fedele, diserti a un tratto dalla scuola di <lb></lb>Galileo. </s>

<s>Quella ragione insomma è che, applicando i metodi di lui, si veniva <lb></lb>a concludere il contrario della verità dimostrata, non essendo, nella fatta sup­<lb></lb>posizione, il momento del prisma uguale, ma duplo al momento dell&#039;acqua. </s>

<s><lb></lb>Il momento infatti della discesa del prisma è misurato dal prodotto della ve­<lb></lb>locità CC′ per il peso D′C′, e il momento dell&#039;acqua dal prodotto della ve­<lb></lb>locità HC per il peso della mole fluida HB. Ma, perchè le due velocità sono <lb></lb>uguali, i momenti stanno dunque come i semplici pesi, ossia l&#039;uno è vera­<lb></lb>mente doppio dell&#039;altro, e perciò è impossibile che, tra il prisma immerso <lb></lb>e l&#039;acqua sollevata, si faccia l&#039;equilibrio. </s>

<s>“ Nascitur tamen difficultas ex su-<pb xlink:href="020/01/3236.jpg" pagenum="197"></pb>perioribus propositionibus. </s>

<s>Pars prismatis demersa est dupla aquae ascenden­<lb></lb>tis, et ascensus unius aequalis est descensus alterius: igitur non potest esse <lb></lb>aequilibrium ” (ibid., pag. </s>

<s>95). </s></p><p type="main">

<s>Rispondesi qui alle difficoltà, non direttamente difendendo il principio <lb></lb>assunto, ma indirettamente ricorrendo a uno nuovo, col dire che, seb bene il <lb></lb>prisma scaccia la sola acqua BH, contrasta nulladimeno e con l&#039;acqua BH, <lb></lb>e con l&#039;altra CL, <emph type="italics"></emph>prorsus modo ut si essent duo pondera in lance utra­<lb></lb>que staterae,<emph.end type="italics"></emph.end> la qual bilancia è necessariamente in equilibrio, perchè tanto <lb></lb>pesa il prisma sull&#039;un braccio immaginario A′C′, quanto l&#039;acqua HL sul­<lb></lb>l&#039;altro. </s>

<s>Ma questo era un confessare l&#039;impotenza del nuovo metodo galileiano <lb></lb>a dimostrare la verità del Teorema idrostatico, per cui fu costretto il Dechales, <lb></lb>suo malgrado, a abbandonarlo, e a ricorrere all&#039;antico: confessione ch&#039;egli <lb></lb>stesso esprime con queste parole: “ Ostendo item alio modo esse aequilibrium. </s>

<s><lb></lb>Cum ex suppositione aqua aequalis in mole parti prismatis NC′ sit duarum li­<lb></lb>brarum, in proposito exemplo, aqua HL erit etiam duarum librarum. </s>

<s>Aquae <lb></lb>igitur A′M, ML sunt in aequilibrio. </s>

<s>Sed aqua HL duarum librarum est in <lb></lb>aequilibrio cum prismate, quod supponitur etiam esse duarum librarum; ergo <lb></lb>aggregatum ex prismate et aqua A′M est in aequilibrio cum aggregato ex <lb></lb>aqua ML et LH. </s>

<s>Ergo omnia permanent in aequilibrio ” (ibid., pag. </s>

<s>96). </s></p><p type="main">

<s>Così dunque essendosi dimostrato che, se la parte del corpo immersa <lb></lb>sia uguale in mole all&#039;acqua che equipondera tutto il corpo, si farà l&#039;equi­<lb></lb>librio; passa l&#039;Autore a dimostrare, nelle seguenti proposizioni VII, VIII e IX, <lb></lb>la ragion del notare, dell&#039;immergersi tutto e dell&#039;affondare un solido, ritor­<lb></lb>nando alla bilancia archimedea, quasi non avesse nelle presenti novità sa­<lb></lb>puto ritrovar nulla di meglio al suo bisogno. </s></p><p type="main">

<s>Bastino questi esempi per quel che riguarda gli stranieri. </s>

<s>Ora è da ve­<lb></lb>dere come si portassero i Nostri, riappiccando il filo della Storia a quel punto, <lb></lb>in cui lasciammo l&#039;Aggiunti a combattere co&#039;suoi propri pensieri. </s>

<s>Par che <lb></lb>le cose volgessero in peggio nei successori, se il Michelini giunse a negare <lb></lb>anche quelle pressioni laterali, unico rifugio, che esso Aggiunti trovava, per <lb></lb>darsi a intendere in qualche modo come si potesse sollevare il prisma dal <lb></lb>fondo, a circonfondergli l&#039;acqua da una parte sola del vaso. </s>

<s>L&#039;errore, suc­<lb></lb>chiato dagl&#039;insegnamenti di Galileo, si trasfuse, per la concordia autorevole <lb></lb>dei due maestri nel Borelli e nel Viviani, i quali s&#039;ostinarono con incredi­<lb></lb>bile temerità a ripetere che i liquidi non premono, se non ciò che soggiace <lb></lb>a loro in direzione perpendicolare. </s>

<s>I depositari fedeli delle private dottrine <lb></lb>del Torricelli insorsero, per l&#039;amore e per la dignità della scienza, contro <lb></lb>così fatti deliri, e a costoro il Borelli particolarmente rispondeva com&#039;ebro <lb></lb>irritato ne&#039;suoi sopori. </s>

<s>Quelle risposte, nella loro integrità, si leggeranno <lb></lb>in altra occasione: basti per ora citarne una, tanto per persuadere chi non <lb></lb>crederebbe un tant&#039;uomo capace di commettere i paralogismi, che si con­<lb></lb>tengono in questo discorso: </s></p><p type="main">

<s>“ Passo ora alla ragione addotta dai medesimi signori oppositori, quando <lb></lb>dicono esser segno evidente che l&#039;acqua faccia forza da&#039;fianchi, perchè si <pb xlink:href="020/01/3237.jpg" pagenum="198"></pb>vede che, fatto un forame in una delle sponde del vivaio, o canale, l&#039;acqua <lb></lb>esce da esso. </s>

<s>Come per esempio, se nel vivaio ABCL (fig. </s>

<s>105) si aprirà un <lb></lb>forame in C, si vede che l&#039;acqua esce per CD; adunque è segno evidente <lb></lb>che l&#039;acqua non solamente preme perpendicolarmente verso B, ma ancora <lb></lb>fa forza al liquido per la linea inclinata AHC. </s>

<s>E qui io dico che, se il ve­<lb></lb><figure id="id.020.01.3237.1.jpg" xlink:href="020/01/3237/1.jpg"></figure></s></p><p type="caption">

<s>Figura 105.<lb></lb>dersi cader l&#039;acqua CD è effetto che necessariamente <lb></lb>segue dalle pressioni dell&#039;acqua, fatte obliquamente <lb></lb>per AHC; dunque se tal acqua, in cambio di scen­<lb></lb>dere all&#039;in giù per CD, si vederà salire all&#039;in su, <lb></lb>dovrebbe esser necessario argomento che l&#039;acqua sta­<lb></lb>gnante facesse forza premendo anco all&#039;in su. </s>

<s>Ma se <lb></lb>io farò nel fianco E un forame e vi salderò un can­<lb></lb>nello torto all&#039;in su, qual&#039;è EI, io vedrò scappare <lb></lb>l&#039;acqua da B, e salire all&#039;in su verso I, e tale spinta <lb></lb>vien fatta dalla forza dell&#039;acqua stagnante; adunque ella, oltre al premere <lb></lb>perpendicolarmente il fondo ed i fianchi, fa ancora forza all&#039;in su. </s>

<s>Ma que­<lb></lb>sto repugna alla natura de&#039;gravi; adunque ella non fa forza obliquamente <lb></lb>verso i lati del vivaio ” (MSS. Gal. </s>

<s>disc., T. XVII, fol. </s>

<s>5). </s></p><p type="main">

<s>Negate le pressioni fatte dal liquido lateralmente, e di sotto in su, è fa­<lb></lb>cile giudicare in quale stato si dovesse ritrovare a quel tempo la scienza <lb></lb>idrostatica nella mente del Borelli. </s>

<s>E supponendo che, nello studiare il Ga­<lb></lb>lileo, gli occorressero i medesimi dubbi dell&#039;Aggiunti, convien dire che non <lb></lb>avesse alcun modo a risolverli, se l&#039;acqua non preme il solido nè in su, <lb></lb>nè da lato, e se, per non repugnare alla natura dei gravi, non può ella far <lb></lb>altro che conficcare più fortemente il solido bagnato contro il fondo su cui <lb></lb>riposava. </s></p><p type="main">

<s>Al Viviani, giovane studente nella casa di Arcetri con l&#039;assistenza viva <lb></lb>di Galileo, parve tutto aureo e maraviglioso quel che leggeva nel Discorso <lb></lb>intorno alle cose che stanno, e che si movon nell&#039;acqua. </s>

<s>Anzi quelle descri­<lb></lb>zioni, che ei trovava, della immersione e della demersione de&#039;prismi retti di <lb></lb>base rettangolare dentro vasi parallelepipedi, a fin di paragonare le moli <lb></lb>acquee con le solide; tutt&#039;altro che dargli occasione di dubitare gli sugge­<lb></lb>rirono un&#039;invenzione, di cui poi vecchio, e per bene altri meriti gloriosis­<lb></lb>simo, si compiacque, e intorno alla quale vogliamo intrattenere alquanto il <lb></lb>discorso, per la curiosità del soggetto, e anche un poco per l&#039;importanza. </s></p><p type="main">

<s>Il Tartaglia, come si rammenteranno i nostri Lettori, concludeva la pro­<lb></lb>posizione prima del suo secondo Ragionamento, osservando che si poteva per <lb></lb>essa <emph type="italics"></emph>conoscere l&#039;area corporale de ogni strania forma di corpo.<emph.end type="italics"></emph.end> La solu­<lb></lb>zione era data per via di Matematica, ma quel richiamar che il Tartaglia <lb></lb>stesso faceva l&#039;attenzione dei Matematici sull&#039;esperienza, che si diceva aver <lb></lb>fatto Archimede, per scoprire il furto dell&#039;oro nella corona, sostituendo a mi­<lb></lb>gliore effetto l&#039;uso della sua Bilancetta; aveva fatto sovvenire ad alcuni un <lb></lb>modo assai più spedito e di facile esecuzione meccanica, per quadrare ogni <lb></lb>forma di corpo più irregolare. </s></p><pb xlink:href="020/01/3238.jpg" pagenum="199"></pb><p type="main">

<s>Il Clavio, nel quinto libro della sua <emph type="italics"></emph>Geometria pratica,<emph.end type="italics"></emph.end> diffuse la no­<lb></lb>tizia dell&#039;invenzione, che egli dice di aver letta in alcuni scrittori, e che poi <lb></lb>così descrive: “ Paretur arca lignea, ex asseribus levigatis, instar parallele­<lb></lb>pipedi cuiusdam, quae pice ita oblinatur, ut aquam continere possit. </s>

<s>Arca <lb></lb>haec tantae debet esse longitudinis, latitudinis atque altitudinis, ut corpus <lb></lb>metiendum, intra ipsam positum, aqua totum possit operiri. </s>

<s>Posita autem <lb></lb>hac arca horizonti aequidistante, beneficio libellae aut perpendiculi, infunda­<lb></lb>tur in eam tantum aquae, quantum satis est ut corpus impositum omnino <lb></lb>tegat, notenturque diligenter suprema latera aquae in asseribus arcae, ut <lb></lb>habeatur altitudo aquae usque ad arcae fundum. </s>

<s>Extracto deinde corpore, ita <lb></lb>tamen ut nihil aquae extra arcam cadat, notentur rursum latera aquae post­<lb></lb>quam quievit. </s>

<s>Quod si metiamur duo parallepipeda, quorum basis commu­<lb></lb>nis est arcae fundus, sive basis, altitudines vero rectae a lateribus aquae <lb></lb>notatis usque ad basem, et minus a maiore subtrahamus; relinquetur pa­<lb></lb>rallelepipedum soliditati corporis propositi omnino aequale ” (Romae 1604, <lb></lb>pag. </s>

<s>260, 61). In simile modo, soggiunge, s&#039;avrebbe meccanicamente la mi­<lb></lb>sura della capacità di un vaso di qualunque forma, sommergendolo prima <lb></lb>pieno di arena, ben chiuso dal suo testo che non ci avesse a entrar dentro <lb></lb>l&#039;acqua, e poi nuovamente sommergendovelo vuoto. </s></p><p type="main">

<s>Galileo, come apparisce dalla fine del suo Dialogo intorno alla Bilan­<lb></lb>cetta idrostatica da noi pubblicato, fu forse il primo, che applicò le im­<lb></lb>mersioni dentro l&#039;acqua, ricevuta in un vaso parallelepipedo, a quadrare le <lb></lb>figure piane e i solidi geometrici circoscritti da curve, ed essendo stato quel <lb></lb>Dialogo dettato allo stesso Viviani, il quale pure confessa di aver veduto an­<lb></lb>che il Clavio, si dovrebbe dire che poco rimanesse del merito nell&#039;inven­<lb></lb>zione allo studente nell&#039;ospizio di Arcetri, se non si ripensasse che egli non <lb></lb>aveva allora più che ventidue anni. </s>

<s>In ogni modo leggiamo quel ch&#039;egli dava <lb></lb>per frutto primaticcio de&#039;suoi studi: </s></p><p type="main">

<s>“ Dimostrazioni trovate da me Vincenzio Viviani, nel mese di aprile 1640. <lb></lb><emph type="italics"></emph>Teorema lemmatico.<emph.end type="italics"></emph.end> Se un cilindro sarà uguale, ed egualmente alto che un <lb></lb>parallelepipedo di base quadrata; dico che il cerchio base del cilindro sarà <lb></lb>uguale al quadrato base del parallipipedo ” (MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>30). <lb></lb>La dimostrazione è lunga e tediosa: un esercizio giovanile addiritura. </s>

<s>Dal­<lb></lb>l&#039;altra parte che due solidi prismatici uguali, aventi altezze uguali, debbano <lb></lb>avere uguali anche le basi, consegue immediatamente dalla loro stereometria. </s>

<s><lb></lb>Chiamati infatti P, P′ i detti prismi, A e A′, B e B′ le loro altezze e le loro <lb></lb>basi, se, nelle due equazioni P=A.B, P′=A′.B′, P è uguale a P′, e <lb></lb>A uguale ad A′, necessariamente anche B è uguale a B′. </s>

<s>Lasciamo perciò di <lb></lb>trascrivere la dimostrazione, che ne dà il Viviani di questo Lemma, e pas­<lb></lb>siamo al <emph type="italics"></emph>“ Problema meccanicamente risoluto:<emph.end type="italics"></emph.end> Dato un cerchio trovare un <lb></lb>quadrato eguale ad esso. </s>

<s>” </s></p><p type="main">

<s>“ Sia il dato circolo, il cui diametro A: si deve assegnare un rettan­<lb></lb>golo a esso uguale. </s>

<s>Preparisi un vaso di vetro, di figura di un prisma retto, <lb></lb>la cui base sia un rettangolo, la larghezza del quale non sia minore del dia <pb xlink:href="020/01/3239.jpg" pagenum="200"></pb>metro del dato cerchio, e questo vaso sia CD (fig. </s>

<s>106), la base il rettan­<lb></lb>golo MD, contenuto dai lati MN, ND, il minor de&#039;quali, se saranno dise­<lb></lb>guali, DN, quale si chiami <emph type="italics"></emph>larghezza del vaso,<emph.end type="italics"></emph.end> non sia minore del diametro <lb></lb>del cerchio dato A. </s>

<s>Infondasi nel detto vaso l&#039;acqua o altro liquido all&#039;al­<lb></lb>tezza dell&#039;altro lato MN del medesimo rettangolo MD, e sia questa DV, sic­<lb></lb><figure id="id.020.01.3239.1.jpg" xlink:href="020/01/3239/1.jpg"></figure></s></p><p type="caption">

<s>Figura 106.<lb></lb>chè FV sia il livello dell&#039;acqua infusa. </s>

<s>Sia poi <lb></lb>il cilindro retto AB, la cui base il cerchio dato A, <lb></lb>e l&#039;altezza BA la medesima DV del prisma <lb></lb>d&#039;acqua, sicchè, immergendo questo cilindro <lb></lb>nel prisma d&#039;acqua, la sua base A superiore <lb></lb>sarà nel medesimo piano del livello FV, e l&#039;in­<lb></lb>feriore nel piano del rettangolo MD, cioè, quando <lb></lb>il cilindro toccherà il fondo del vaso, si sarà <lb></lb>appunto finito di immergere tutto sotto il primo <lb></lb>livello dell&#039;acqua, ed averà scacciato sopra di <lb></lb>sè una mole d&#039;acqua uguale a sè stesso, la <lb></lb>quale terrà la figura del vaso, cioè di un pri­<lb></lb>sma, e sia questo CV. ” </s></p><p type="main">

<s>“ Averemo dunque il prisma d&#039;acqua CV, <lb></lb>uguale al cilindro AB, ed egualmente alto quanto <lb></lb>detto cilindro, pigliando per altezza di questo <lb></lb>prisma, non l&#039;alzamento dell&#039;acqua VE, ma la linea CT, la quale, essendo <lb></lb>uguale alla MN, sarà ancora eguale all&#039;altezza del cilindro, la quale si fece <lb></lb>eguale alla MN. Adunque, per il precedente teorema lemmatico, la base del <lb></lb>medesimo prisma CV, uguale ed ugualmente alto che il cilindro, sarà uguale <lb></lb>alla base del medesimo. </s>

<s>Ma la base del prisma è il rettangolo EG e del ci­<lb></lb>lindro è il cerchio dato A; adunque questo è uguale al detto rettangolo, <lb></lb>fatto dalla GV, larghezza del vaso, e dalla VE, alzamento dell&#039;acqua, il quale <lb></lb>si sarà potuto notare e segnare nell&#039;esterna superficie del vaso, siccome an­<lb></lb>cora il primo livello FV, per essersi fatto il vaso trasparente. </s>

<s>In questo modo <lb></lb>dunque potremo quadrare qualunque circolo, poichè, pigliando la media pro­<lb></lb>porzionale tra la larghezza VG e l&#039;alzamento VE, il suo quadrato sarà uguale <lb></lb>al circolo proposto, essendo il rettangolo delle estreme eguale al quadrato di <lb></lb>quelle di mezzo, quando tre linee sono continuamente proporzionali. </s>

<s>” </s></p><p type="main">

<s>“ E se la larghezza VG del vaso si farà uguale al diametro del cer­<lb></lb>chio proposto A, sicchè il cilindro AB entri per l&#039;appunto nel vaso, cioè <lb></lb>tocchi le sponde erette CN, SD, radendole nell&#039;immergersi; ne seguirà che <lb></lb>la medesima proporzione averà la larghezza VG, all&#039;alzamento dell&#039;acqua <lb></lb>VE, che il quadrato, circoscritto al cerchio A, al medesimo cerchio, il che <lb></lb>così fo manifesto ” (ivi, fol. </s>

<s>31). E seguita il Viviani a scrivere la dimostra­<lb></lb>zione, ciò che fatto, così osserva: “ Potevo più facilmente e più brevemente <lb></lb>dimostrar questo di sopra: poichè, pigliando la medesima proporzione tra la <lb></lb>larghezza e l&#039;alzamento, il quadrato di essa è uguale al dato cerchio, come <lb></lb>di sopra si è fatto manifesto. </s>

<s>Adunque qual proporzione averà la larghezza <pb xlink:href="020/01/3240.jpg" pagenum="201"></pb>all&#039;alzamento, tale l&#039;avrà il quadrato della medesima larghezza al quadrato <lb></lb>della media, cioè al cerchio dato. </s>

<s>Ma il quadrato della larghezza è il mede­<lb></lb>simo che il circoscritto al cerchio, essendo la larghezza uguale al diametro <lb></lb>del dato cerchio; adunque la medesima proporzione ha la larghezza del vaso <lb></lb>all&#039;alzamento del livello, che ha il quadrato, circoscritto al cerchio, al me­<lb></lb>desimo cerchio, quando il cilindro sarà grosso quanto la larghezza del vaso ” <lb></lb>(ivi, fol. </s>

<s>31 a tergo). </s></p><p type="main">

<s>Il discorso può compendiarsi in due parole. </s>

<s>Dall&#039;identica VG:VE= <lb></lb>VG:VE si ha VG:VE=VG2:VE.VG, che senz&#039;altro
conclude l&#039;intento, <lb></lb>essendo VG la larghezza del vaso, e VE l&#039;alzamento dell&#039;acqua. VG 2 poi è, <lb></lb>nella fatta supposizione, il quadrato circoscritto al cerchio, e VE. VG il ret­<lb></lb>tangolo che, per le cose dimostrate, s&#039;uguaglia a esso cerchio. </s></p><p type="main">

<s>Si comprende bene che il metodo può estendersi a qualunque figura si <lb></lb>voglia dare alla base A, come per esempio di ellisse, d&#039;iperbola, di para­<lb></lb>bola, di cicloide, delle quali sempre si ricaverebbe dal rettangolo EG la <lb></lb>quadratura. </s>

<s>Se avesse pensato a valersi di questa invenzione Galileo, si sa­<lb></lb>rebbe forse assicurato, più facilmente che col pesar le incise figure, dover <lb></lb>esser lo spazio cicloidale esattamente triplo di quello del circolo genitore: e <lb></lb>chi sa che il Nardi, fra le altre meccaniche esperienze, che gli rivelarono il <lb></lb>vero, non ricorresse anche a questa. </s></p><p type="main">

<s>Ma comunque sia di ciò, il Viviani ha un secondo <emph type="italics"></emph>“ Problema, non men <lb></lb>curioso dello antecedente, pur meccanicamente risoluto, e con facilità:<emph.end type="italics"></emph.end> Data <lb></lb>qualsivoglia figura solida, o regolare o irregolare, benchè rozzamente e strava­<lb></lb>gantissimamente configurata, questa si deve ridurre in un prisma o cilindro, <lb></lb>ovvero in frusto di cono o di piramide, o di altra figura, che da una parte <lb></lb>venga mancando, il che così conseguiremo, mettendo il problema in un parti­<lb></lb>colar caso, cioè: data una sfera, ridurla in un parallelepipedo ” (ivi, fol. </s>

<s>32). </s></p><p type="main">

<s>Reputiamo superfluo il trascrivere la soluzione, che deriva per facile co­<lb></lb>rollario dalla precedente, supposto che il cilindro AB sia una sfera, o altro <lb></lb>solido o frusto di solido, che faccia sopra il primo livello del vaso sollevare <lb></lb>un parallelepipedo d&#039;acqua, ugualissimo alla sua propria mole. </s>

<s>Dall&#039;altra <lb></lb>parte i lettori del Clavio, che avessero scelte figure geometriche rotonde, per <lb></lb>immergerle nella cassetta di legno spalmata di bitume, conseguivano il me­<lb></lb>desimo effetto che a immergerle in questa più elegante e tersa vasca di cri­<lb></lb>stallo. </s>

<s>Nonostante il Viviani si compiacque, come dicemmo, di questa sua <lb></lb>giovanile invenzione, benchè la riconoscesse per un giochetto, di cui scri­<lb></lb>veva così, nell&#039;atto di rivendicarsene la proprietà da un tale, che se l&#039;era <lb></lb>usurpato: <emph type="italics"></emph>E per dirla giusta questo giochetto mi sovvenne nello studiare <lb></lb>quell&#039;opuscolo d&#039;oro delle Galleggianti del mio sovrano Maestro, là dove <lb></lb>egli fa l&#039;immersione e la demersione de&#039;prismi retti di base rettangola o <lb></lb>de&#039;cilindri in que&#039;vasi parallelepipedi, con paragonar le moli acquee con <lb></lb>le solide a varii altri fini.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Un poco più tardi però, tornando il Viviani a studiar sopra l&#039;opuscolo <lb></lb>ammirato, ebbe a notar qualche macchia su quel che gli era prima apparito <pb xlink:href="020/01/3241.jpg" pagenum="202"></pb>oro schietto, e il quarto e il quinto teorema, per esempio, gli parve che si <lb></lb>sarebbero potuti dimostrare più facilmente di quel che non aveva fatto il suo <lb></lb>sovrano Maestro, e senza alcun bisogno di lemma antecedente. (MSS. Gal. </s>

<s><lb></lb>Disc., T. CX, a tergo del fol. </s>

<s>32). Ma dalla forma passando a cosa ben assai <lb></lb>più importante, alla sostanza, fu il Viviani stesso uno de&#039;primi ad avvertir <lb></lb>che il principio, a cui s&#039;informava il discorso di Galileo, rispetto al confe­<lb></lb>rire il momento della gravità dell&#039;acqua che sale, col momento della gravità <lb></lb>del solido che scende, per concluderne indi i vari stati di questo dopo l&#039;im­<lb></lb>mersione; non era applicabile universalmente. </s>

<s>“ Quando il vaso, nel quale <lb></lb>si fa l&#039;immersione del solido (scrive in una nota, da mettersi per postilla <lb></lb>alle Galleggianti della seconda edizione) sarà pieno d&#039;acqua, non pare che <lb></lb>cammini questo discorso, che fa qui il signor Galileo, perchè il momento <lb></lb>della gravità dell&#039;acqua all&#039;essere alzata o è nullo perchè immediatamente <lb></lb>segue il trabocco, o se è qualche cosa, è sempre l&#039;istessa. </s>

<s>Sicchè questo <lb></lb>pareggiamento di momenti tra l&#039;acqua e il solido o non ci dovrà esser mai, <lb></lb>o sempre, in qual si sia stato d&#039;immersione del detto solido ” (ivi, fol. </s>

<s>54). </s></p><p type="main">

<s>Del difetto capitale però di queste idrostatiche istituzioni galileiane non <lb></lb>s&#039;era, come il Borelli, accorto ancora nemmeno il Viviani, che, col mede­<lb></lb>simo zelo del suo collega, troviamo a quel tempo concorrere alla difesa del <lb></lb>Michelini. </s>

<s>Vedremo in quest&#039;altro Tomo le ragioni che egli speculava, e <lb></lb>l&#039;esperienza che immaginava, per provare che l&#039;acqua non preme obliqua­<lb></lb>mente, ma secondo la sola direzion perpendicolare, le sponde dei vivai. </s>

<s>Ora <lb></lb>convien dire come si venissero egli stesso e il Borelli a ravvedere di un tanto <lb></lb>errore, pigliandone occasione da quella leggerezza positiva, la confutazion <lb></lb>della quale gli aveva pure condotti a ritrattarsi intorno al credere che l&#039;acqua <lb></lb>in mezzo all&#039;acqua non pesa. </s></p><p type="main">

<s>Un solenne Peripatetico stringeva i suoi contradittori con un argomento, <lb></lb>ricavato dalle dottrine del loro proprio Maestro. </s>

<s>Il prisma, diceva, aderente <lb></lb>con la base al fondo, e con tre delle facce sue laterali a contatto intimo con <lb></lb>le pareti del vaso, benchè da una parte sola lo bagni l&#039;acqua, di cui si sup­<lb></lb>pone men grave in specie, nonostante vien da lei sollevato, come dimostra <lb></lb>in una delle sue proposizioni il vostro Galileo. </s>

<s>Irragionevolmente però egli <lb></lb>attribuisce quel sollevamento all&#039;acqua circonfusa, la quale, non facendo <lb></lb>forza nè di sotto in su, nè da lato, non opera dunque nulla&#039;in produr quel­<lb></lb>l&#039;effetto, che non si potrebbe perciò attribuire ad altro, che a una leggerezza <lb></lb>propria del solido, connaturata con lui e positiva. </s></p><p type="main">

<s>Il Borelli e il Viviani, che riconobbero conseguir l&#039;argomento, per lo­<lb></lb>gica necessità, dai loro propri principii, non avendo ragioni da rispondere, <lb></lb>ricorsero alle esperienze, che istituirono insieme nella loro Accademia, e dalle <lb></lb>quali risultò di fatto che il prisma adattato come sopra nel vaso, anche a <lb></lb>circonfondergli un liquido quanto più si voglia grave in specie, si rimane, <lb></lb>contro il supposto di Galileo e del Peripatetico, immobile sul fondo, anzi <lb></lb>affissovi più che mai. </s>

<s>L&#039;esperienze furono varie, ma la più bellamente di­<lb></lb>mostrativa fu quella, in secondo luogo descritta nel libro dei <emph type="italics"></emph>Saggi<emph.end type="italics"></emph.end> (Fi-<pb xlink:href="020/01/3242.jpg" pagenum="203"></pb>renze 1841, pag. </s>

<s>133, 34), consistente in un vaso di legno, incavatovi sul <lb></lb>fondo un emisfero perfettamente uguale a quello di una palla d&#039;avorio, la <lb></lb>quale non fu veduta crollarsi dal suo incastro, benchè si riempisse il vaso <lb></lb>del pesantissimo argento vivo. </s>

<s>“ Porro hoc experti sumus in Academia expe­<lb></lb>rimentali medicea ” disse poi il Borelli nella proposizione LXXXII <emph type="italics"></emph>De motion. </s>

<s><lb></lb>natur.<emph.end type="italics"></emph.end> (pag. </s>

<s>170). Ma quanto alle ragioni dell&#039;esperienza non sapeva egli <lb></lb>allora, nè i suoi Colleghi, far altro che ridurle a un nome vago, divenuto <lb></lb>per le platoniche tradizioni solenne, a quello di <emph type="italics"></emph>circumpulsione.<emph.end type="italics"></emph.end> Lo Stevino, <lb></lb>tanto tempo prima, aveva descritte simili esperienze, per confermarne la teo­<lb></lb>ria: i Nostri invece s&#039;erano incontrati nell&#039;esperienza, per non saperne la <lb></lb>teoria, la quale era inutile chiedere agl&#039;insegnamenti galileiani, dissipatori <lb></lb>di ogni idea, che si fosse avvicinata alle pressioni idrostatiche, e specialmente <lb></lb>a quelle che si producono in mezzo ai liquidi di basso in alto. </s></p><p type="main">

<s>Cercando dunque di ridursi sul diritto filo dai primi deliri, il Borelli <lb></lb>ebbe a riconoscere quanto irragionevolmente avesse creduto e scritto che non <lb></lb>può l&#039;acqua ripremere in su, perchè ciò repugna alla natura dei gravi. </s>

<s>An­<lb></lb>che nella stadera, pensava, se non è in equilibrio, va in su il peso che ha <lb></lb><figure id="id.020.01.3242.1.jpg" xlink:href="020/01/3242/1.jpg"></figure></s></p><p type="caption">

<s>Figura 107.<lb></lb>minore il momento, eppure, tutt&#039;altro che repugnare <lb></lb>alla gravità, è anzi questo un effetto naturale di lei. </s>

<s>Ora, <lb></lb>anche le parti componenti una mole fluida son congiunte <lb></lb>insieme, e mobili intorno a un centro immaginario, come <lb></lb>nella stadera, ond&#039;ei non è maraviglia se, prevalendo il <lb></lb>momento d&#039;una parte a quello dell&#039;altra, mentre l&#039;una <lb></lb>scende naturalmente, l&#039;altra, pure naturalmente, sia costretta a salire. </s>

<s>Scorto <lb></lb>da questi pensieri il Borelli confermò che essendo EG (fig. </s>

<s>107) il prisma, <lb></lb>come lo suppone Galileo, l&#039;acqua circonfusagli dalla parte FC non vale a <lb></lb>sollevarlo, perchè BC è sì veramente una libbra, “ non quidem convertibilem <lb></lb><figure id="id.020.01.3242.2.jpg" xlink:href="020/01/3242/2.jpg"></figure></s></p><p type="caption">

<s>Figura 108.<lb></lb>circa centrum G, sed stabilem et firmam cum in ea mi­<lb></lb>nime contrarii motus descensus partis GC, et ascensus <lb></lb>alterius radii GB fieri possint simul et semel. </s>

<s>Unde <lb></lb>mirum non est lignum GE e fundo vasis non ascen­<lb></lb>dere ” (ibid., pag. </s>

<s>167). Affinchè ciò avvenga, sog­<lb></lb>giunge il Borelli, si richiede una condizione, ed è che <lb></lb>l&#039;acqua FC (fig. </s>

<s>108) possa scendere, e scendendo sol­<lb></lb>levare l&#039;acqua con lei congiunta BL, quasi altro ba­<lb></lb>cino della bilancia. </s>

<s>“ Et haec est legitima et adae­<lb></lb>quata causa quare lignum a maiori impulsu aquae <lb></lb>collateralis prementis sursum impellitur ab aqua, quae infra eius basim in­<lb></lb>sinuatur ” (ibid., pag. </s>

<s>168). </s></p><p type="main">

<s>Di qui si vede che il Borelli giunse felicemente a sciogliere il problema, <lb></lb>innanzi a cui s&#039;era l&#039;Aggiunti mostrato così irresoluto, per vie tutte sue pro­<lb></lb>prie, men convenienti con quelle nuove segnate da Galileo, che con le an­<lb></lb>tiche di Archimede, alle quali (fatta esperienza dei difetti delle dottrine del <lb></lb>suo maestro) fece ritorno in dimostrare i principali teoremi dell&#039;Idrostatica. <pb xlink:href="020/01/3243.jpg" pagenum="204"></pb>Basti citar la proposizione LI, iu cui si dimostra così la VII del primo <emph type="italics"></emph>De <lb></lb>insidentibus humido:<emph.end type="italics"></emph.end> “ Intelligatur vas ELC (rappresentato dalla medesima <lb></lb>figura 108) aqua plenum, in eoque immergatur corpus aliquod grave durum <lb></lb>ac consistens DE, quod gravius sit aqua collaterali FC. </s>

<s>Patet ex Archimede <lb></lb>duo pondera DE et FC collocari in libra quadam imaginaria ac perpetua BC, <lb></lb>in qua excessus ponderis solidi DE supra gravitatem aquae FC, quae sit ae­<lb></lb>qualis mole ipsi DE, semper idem est, in quacumque aquae profunditate <lb></lb>solidum collocetur. </s>

<s>Sitque pondus E excessus, quo pondus DE superat gra­<lb></lb>vitatem aquae FC; igitur conatus, vis et impetus, quo solidum DE descen­<lb></lb>dit infra aquam, mensuratur a vi ponderis E ” (ibid., pag. </s>

<s>110, 11). </s></p><p type="main">

<s>Ma se il Borelli trovava in Archimede il filo, da ridursi in sulla diretta <lb></lb>via di dimostrare gli equilibri idrostatici, e di risolvere un problema, a cui <lb></lb>le dottrine di Galileo non somministravano i necessari argomenti, il Viviani <lb></lb>invece accusava il Siracusano di questo stesso difetto, dipendente dal non <lb></lb>aver egli trattata la scienza in modo universale. </s>

<s>Diceva che le dimostrazioni <lb></lb>di lui non valgono se no nel caso, clie le parti infime siano premute dalla <lb></lb>mole, che le sovrasta perpendicolarmente, ciò che poteva esser bene creduto <lb></lb>dall&#039;ossequioso Discepolo, avendoglielo insinuato il suo sovrano Maestro, ma <lb></lb>quanto fosse falsa una tale opinione è manifesto dalla Storia, dalla quale re­<lb></lb>sulta che Archimede, oltre al primo postulato, che l&#039;umido prema perpen­<lb></lb>dicolarmente, n&#039;aggiunge l&#039;altro che prema di sotto in su: condizione, alla <lb></lb>quale se avessero atteso gli studiosi, e fosse stata avvertita dal nostro Vi­<lb></lb>viani, non gli bisognava ricercar nulla di più a conseguire l&#039;intento suo prin­<lb></lb>cipale, qual&#039;era di dimostrare che, <emph type="italics"></emph>se alla superficie inferiore del grave non <lb></lb>sarà sottoposta mole alcuna di fluido, in cui è sommerso; quantunque più <lb></lb>grave in specie sia il fluido detto, ed ancorchè grande sia l&#039;altezza di <lb></lb>esso, il grave non verrà su.<emph.end type="italics"></emph.end> Avrebbe dovuto dunque più ragionevolmente <lb></lb>esso Viviani, invece che Archimede, accusare il suo proprio Maestro, e tutti <lb></lb>coloro che non avevano saputo comprendere in unità di scienza i due libri <lb></lb><emph type="italics"></emph>De insidentibus humido.<emph.end type="italics"></emph.end> Ma fisso in questa opinione, si volle applicare egli <lb></lb>stesso a dare all&#039;Idrostatica quella universalità, che diceva mancarle. </s></p><p type="main">

<s>Gli giovò molto in tale studio la nuova Idrodinamica del Torricelli, e <lb></lb>tutto gli parve si riducesse a dimostrare come mai una particella, premuta <lb></lb>da tutte le particelle liquide soprastanti infino alla più superficiale, acquisti <lb></lb>tale impeto, da risalire alla medesima altezza. </s>

<s>Cosicchè considerando tutta <lb></lb><figure id="id.020.01.3243.1.jpg" xlink:href="020/01/3243/1.jpg"></figure></s></p><p type="caption">

<s>Figura 109.<lb></lb>intera la mole come composta d&#039;infinito numero di <lb></lb>zampilli, o di filetti, o di <emph type="italics"></emph>raggi fluidi,<emph.end type="italics"></emph.end> come ei pro­<lb></lb>priamente gli chiama, riduceva tutto il negozio a con­<lb></lb>ferire i momenti nella perpendicolare con quelli fatti <lb></lb>secondo qualsiasi inclinazione. </s>

<s>Così concludeva che, es­<lb></lb>sendo il punto A per esempio (fig. </s>

<s>109) compreso fra <lb></lb>le due superficie orizontali CD, EF tanto è premuto perpendicolarmente dal <lb></lb>raggio BA quanto obliquamente dal raggio AG, e da tutti gli altri infiniti, <lb></lb>che indi si conducessero a CD, superficie del liquido stagnante. </s>

<s>AB poi e AG, <pb xlink:href="020/01/3244.jpg" pagenum="205"></pb>in mezzo alla mole liquida, di cui sono una parte componente infinitesima, <lb></lb>si possono così bene riguardar quai liberi zampilli o sifoni comunicanti, per <lb></lb>cui, dal farsi insìeme equilibrio i momenti di AB e di AG o dal prevaler l&#039;un <lb></lb>sopra l&#039;altro, dipenda del punto A soggiacente o la quiete o il moto. </s></p><p type="main">

<s>È dunque presentata dal Viviani sotto altra forma, ma in sostanza è la <lb></lb>medesima bilancia di Archimede, e vedremo che, trattata con simili ragioni, <lb></lb>anche serve ai medesimi usi. </s>

<s>Il vantaggio si consegue principalmente dal­<lb></lb>l&#039;applicatovi metodo degl&#039;indivisibili e il ridur la massa liquida a filetti, di <lb></lb>cui si possano, per i teoremi della Meccanica, calco ar le proporzioni dei mo­<lb></lb>menti gravitativi, porge al Viviani il mezzo, per giungere alla prima mate­<lb></lb>matica dimostrazione dell&#039;uguaglianza delle pressioni per tutti i versi. </s>

<s>Vera­<lb></lb>mente questo general trattato de&#039;raggi fluidi dovrebbe precedere il trattatello <lb></lb><emph type="italics"></emph>Degli abbassamenti, e sollevamenti de&#039;corpi ne&#039;fluidi diversamente gravi, <lb></lb>attesa la loro gravezza,<emph.end type="italics"></emph.end> che ora siam per produrre alla notizia de&#039;nostri <lb></lb>Lettori, non essendo questo stesso che una derivazione di quello. </s>

<s>Ma si è <lb></lb>creduto più opportuno tenere un ordine diverso, bastando aver accennato ai <lb></lb>principii, da&#039;quali presupposti noti, fa refluire il Viviani la universalità nella <lb></lb>scienza dei galleggianti. </s></p><p type="main">

<s>“ Archimede, nel libro intitolato <emph type="italics"></emph>Delle cose che stanno sull&#039;umido,<emph.end type="italics"></emph.end> prese <lb></lb>a dimostrativamente trattare la materia sopraddetta, il che fece egli ingegno­<lb></lb>samente come suole, ma con principii poco universali, ed insufficienti a di­<lb></lb>mostrare molti effetti, che in diversi casi sogliono intorno a tal materia occor­<lb></lb>rere, e da essa dipendere. </s>

<s>Poichè tutto il progresso delle sue dimostrazioni <lb></lb>non vale primieramente, se non in caso che le parti infime del fluido si tro­<lb></lb>vino ugualmente poste, e continuate fra loro, al che è necessario che si tro­<lb></lb>vino o sopra una medesima superficie orizontale collocate, o, com&#039;egli uni­<lb></lb>camente assume, nel comune centro concorrenti. </s>

<s>” </s></p><p type="main">

<s>“ Secondariamente, non vale se non in caso che le medesime parti <lb></lb>infime siano premute dalla mole, che le sovrasta perpendicolarmente. </s>

<s>Ma bi­<lb></lb>sogna che le dimostrazioni in tal materia valgano universalmente, in qua­<lb></lb>lunque irregolarità di superficie sottoposte, ed in qualunque caso che dalla <lb></lb>mole superiore, o perpendicolarmente o secondo qualunque inclinazione, obli­<lb></lb><figure id="id.020.01.3244.1.jpg" xlink:href="020/01/3244/1.jpg"></figure></s></p><p type="caption">

<s>Figura 110.<lb></lb>quamente vengano premute. </s>

<s>Il che fare sarà <lb></lb>a noi, per le cose dimostrate intorno ai mo­<lb></lb>menti de&#039;raggi fluidi, facilissimo, come dalle <lb></lb>proposizioni seguenti potrà ciascuno vedere. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE I. — <emph type="italics"></emph>Di qualunque gra­<lb></lb>vezza o l&#039;uno o l&#039;altro si sia, ogni corpo so­<lb></lb>pra ogni fluido comincia necessariamente a <lb></lb>scendere.<emph.end type="italics"></emph.end> ” </s></p><p type="main">

<s>“ Sopra qual si sia fluido AB (fig. </s>

<s>110), la cui superficie superiore AC, <lb></lb>intendasi posato qual si voglia corpo grave E, che, con tutta o parte della su­<lb></lb>perficie inferiore DF, tocchi qual si voglia porzione DF di esso. </s>

<s>Dico che E <lb></lb>scenderà necessariamente sotto AC. </s>

<s>Imperocchè premerà DF una mole sot-<pb xlink:href="020/01/3245.jpg" pagenum="206"></pb>toposta DK, il cui estremo inferiore LK, al di cui abbassamento resisterà una <lb></lb>mole simile, dalla sommità AC del fluido circostante seco inferiormente con­<lb></lb>corrente in LK, per esempio KM. </s>

<s>Poichè dunque a DK, oltre il proprio mo­<lb></lb>mento, è aggiunto il momento di E, sarà in LK il momento DK maggiore <lb></lb>del momento MK, e perciò preponderando si rifletterà verso KM, e si abbas­<lb></lb>serà dalla sommità AC, onde il corpo E verrà necessariamente a scendere. </s>

<s><lb></lb>Il che ecc. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE II. — <emph type="italics"></emph>Tanto qualsivoglia grave seguiterà a scendere <lb></lb>sotto il fluido, finchè il momento di tutto sia uguale al momento del fluido, <lb></lb>il cui luogo occupa la parte sommersa. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3245.1.jpg" xlink:href="020/01/3245/1.jpg"></figure></s></p><p type="caption">

<s>Figura 111.</s></p><p type="main">

<s>“ Intendasi nella figura 111 sommersa del grave, <lb></lb>sotto l&#039;AC, la porzione DFSR, che occupi nel fluido <lb></lb>AB il luogo DFSR. </s>

<s>Dico che se il momento del <lb></lb>fluido, in DFSR, sarà uguale al momento di tutto E, <lb></lb>resterà questo di scendere. </s>

<s>Imperocchè, essendo il <lb></lb>momento di DK, insieme col momento del fluido <lb></lb>DFSR, uguale in LK al momento MK; sarà ancora <lb></lb>il momento di DK, insieme col momento di E, uguale al momento di MK in <lb></lb>LK; onde non potrà DK più abbassarsi, ed il grave E scendere. </s>

<s>Il che ecc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario I.<emph.end type="italics"></emph.end> — Se il fluido sarà ugualmente grave in specie, il corpo <lb></lb>sommerso tanto seguiterà a scendere, fino che sia precisamente immerso tutto. </s>

<s><lb></lb>Imperocchè allora il momento della mole tutta sarà uguale al momento del <lb></lb>fluido, il cui luogo occupa la sommersa. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario II.<emph.end type="italics"></emph.end> — Se il fluido sarà più grave in specie, il corpo so­<lb></lb>prapposto resterà di scendere prima d&#039;esser sommerso tutto. </s>

<s>Imperocchè, es­<lb></lb>sendo il fluido più grave, tanto seguiterà a scendere, fin che occuperà il <lb></lb>luogo d&#039;una tal mole fluida, minor di tutto, che averà con esso momento <lb></lb>uguale. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario III.<emph.end type="italics"></emph.end> — Se il fluido sarà men grave in specie, il corpo <lb></lb>sommerso non resterà mai di scendere. </s>

<s>Imperocchè, ancora tutto sommerso, <lb></lb>ha momento necessariamente maggiore, che la mole del fluido, il cui luogo <lb></lb>occupa in esso. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE III. — <emph type="italics"></emph>Il momento del grave, allo scendere per un <lb></lb>fluido men grave in specie, è uguale all&#039;eccesso sopra il momento della <lb></lb>mole, il cui luogo egli occupa in esso. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3245.2.jpg" xlink:href="020/01/3245/2.jpg"></figure></s></p><p type="caption">

<s>Figura 112.</s></p><p type="main">

<s>“ Intendasi, nella figura 112, il grave E som­<lb></lb>merso tutto sotto AC, sicchè gli sovrasti una mole <lb></lb>fluida PR, e sia E più grave in specie che AB. </s>

<s><lb></lb>Dico il momento di E, allo scendere per AB, es­<lb></lb>sere quanto l&#039;eccesso del momento di E sopra <lb></lb>il momento della mole, il cui luogo DFRS oc­<lb></lb>cupa in AB. ” </s></p><p type="main">

<s>“ Il grave, col momento del proprio peso e del peso della mole sovra­<lb></lb>tante PR, cioè col momento di tutta la mole PF, preme la mole sottoposta, <pb xlink:href="020/01/3246.jpg" pagenum="207"></pb>al cui abbassamento resiste il momento della mole simile KM. </s>

<s>Allo scendere <lb></lb>dunque di E s&#039;oppone la mole KM, che da esso potrà essere respinta, e per­<lb></lb>ciò con tanto momento verrà a scendere verso LK, con quanto il momento <lb></lb>della di lui pressione in LK, cioè della mole PK, prepondererà sopra il mo­<lb></lb>mento della resistenza di MK in LK, che è tanto, quanto l&#039;eccesso di E sopra <lb></lb>il fluido, che era in DFRS. Poichè, quello essendo in DFRS, il momento della <lb></lb>mole PK in LK, al momento della mole MK, sarebbe uguale. </s>

<s>Il che ecc. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE IV. — <emph type="italics"></emph>Qualsivoglia grave, posto liberamente dentro <lb></lb>un fluido di lui più grave in specie, sarà dal fluido circostante respinto <lb></lb>per di sotto allo in su. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Intendasi, nella figura precedente, il fluido AB più grave in specie <lb></lb>del grave E posto dentro di esso. </s>

<s>Dico che il grave E sarà dalla mole MK <lb></lb>verso lo spazio PR respinto. </s>

<s>Imperocchè alla riflessione della mole MK verso <lb></lb>PR non resiste che il momento del grave E, insieme col momento della mole <lb></lb>sovrastante PR, cioè il momento di tutta la mole composta PF. </s>

<s>Perchè dun­<lb></lb>que il fluido, che era in DFRS, è più grave in specie del grave E, sarà il <lb></lb>momento di E minore del momento del fluido in DFRS, e perciò il momento <lb></lb>della mole PF in LK sarà tanto minore del momento della mole MK in LK, <lb></lb>quanto il momento di E è minore del momento del fluido, che era in DFRS, <lb></lb>onde preponderando MK in LK, si moverà col momento dell&#039;eccesso detto <lb></lb>verso lo spazio PR, e respingerà verso esso il grave E. </s>

<s>Il che ecc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario I.<emph.end type="italics"></emph.end> — Sicchè il momento, con che il fluido circostante più <lb></lb>grave in specie scaccia di sotto in su il grave che sta dentro, è uguale al­<lb></lb>l&#039;eccesso del momento del fluido, il cui luogo occupa il grave, sopra il mo­<lb></lb>mento di esso. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario II.<emph.end type="italics"></emph.end> — Onde universalmente il momento, con che un grave <lb></lb>dentro il fluido o va in giù o è scacciato in su, è uguale alla differenza del <lb></lb>momento del grave detto dal momento del fluido, il cui luogo egli occupa. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario III.<emph.end type="italics"></emph.end> — Dal che è manifesto, nel fluido egualmente grave <lb></lb>in specie, non potere il grave andare nè in su nè in giù con momento al­<lb></lb>cuno, non v&#039;essendo differenza alcuna di momento tra esso, e il fluido, il <lb></lb>cui luogo egli occupa. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE V. — <emph type="italics"></emph>Se alla superficie inferiore del grave non sarà <lb></lb>sottoposta mole alcuna di fluido, in cui è sommerso, quantunque più grave <lb></lb><figure id="id.020.01.3246.1.jpg" xlink:href="020/01/3246/1.jpg"></figure></s></p><p type="caption">

<s>Figura 113.<lb></lb>in specie sia il fluido detto, ed ancor che grande sia <lb></lb>l&#039;altezza di esso; il grave non verrà su. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Intendasi nel fluido AB (fig. </s>

<s>113) il grave E, alla <lb></lb>cui superficie inferiore LK non sia sottoposta parte alcuna <lb></lb>di AB, ma le sia immediatamente contigua la parte del <lb></lb>fondo LK. </s>

<s>Dico che, quantunque più grave in specie sia <lb></lb>AB, e quantunque grande la di lui altezza si sia, il grave E <lb></lb>non verrà su. </s>

<s>Imperocchè non potrà dal fluido circostante essere per di sotto <lb></lb>in su respinto. </s>

<s>Il medesimo seguirà se alla superficie LK sarà contigua per LK <lb></lb>l&#039;aria, onde cessa ogni sospetto che si potrebbe in ciò avere del vacuo. </s>

<s>” </s></p><pb xlink:href="020/01/3247.jpg" pagenum="208"></pb><p type="main">

<s>“ PROPOSIZIONE VI. — <emph type="italics"></emph>Se il fluido, sottoposto alla superficie inferiore <lb></lb>del grave sommerso, non averà comunicazione con alcun fluido superiore, <lb></lb>quantunque più grave in specie sia il fluido detto, e quantunque grande <lb></lb>la di lui altezza si sia; il grave non verrù su. </s>

<s>”<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3247.1.jpg" xlink:href="020/01/3247/1.jpg"></figure></s></p><p type="caption">

<s>Figura 114.</s></p><p type="main">

<s>“ Intendasi nel fluido AB (fig. </s>

<s>114) il grave E, alla <lb></lb>cui superficie inferiore DF sia sottoposta qualsivoglia mole <lb></lb>di esso DB, la quale, per essere DF alla superficie circo­<lb></lb>stante del vaso immediatamente contigua, non possa avere <lb></lb>comunicazione alcuna col fluido soprastante AF. </s>

<s>Dico che, <lb></lb>quantunque più grave in specie sia il fluido AB, e quan­<lb></lb>tunque grande sia la di lui altezza, il grave E non verrà <lb></lb>su. </s>

<s>Imperocchè, non avendo il fluido superiore AF comunicazione alcuna <lb></lb>coll&#039;inferiore DB, non potrà similmente il grave E essere da quello per di <lb></lb>sotto in su respinto. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSIZIONE VII. — <emph type="italics"></emph>Se il fluido, sottoposto al grave sommerso, non <lb></lb>avendo comunicazione col fluido soprastante, l&#039;averà con un altro supe­<lb></lb>riore, quantunque più grave in specie egli sia; può il grave, secondo va­<lb></lb>rie altezze di esso, venire o non venire in su. </s>

<s>”<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. XXXIV, <lb></lb>fol. </s>

<s>195-98). <lb></lb><figure id="id.020.01.3247.2.jpg" xlink:href="020/01/3247/2.jpg"></figure></s></p><p type="caption">

<s>Figura 115.</s></p><p type="main">

<s>La dimostrazione sembra a noi intorbidata <lb></lb>dalle troppe parole. </s>

<s>Se il grave E (fig. </s>

<s>115) dentro <lb></lb>il vaso AF ha di sopra il liquido AR, il quale però <lb></lb>di sotto non comunichi col fluido DKM, è mani­<lb></lb>festo che il momento esercitato dalla mole com­<lb></lb>posta AK sopra LK, qualunque egli sia, può sem­<lb></lb>pre essere vinto dal momento, con cui la mole <lb></lb>liquida MK preme la medesima LK, purchè il <lb></lb>livello MH giunga all&#039;altezza necessaria. </s>

<s>Ond&#039;ei <lb></lb>s&#039;intende come, secondo queste varie altezze, possa <lb></lb>il solido E rimanere o esser mosso, e anche s&#039;ha da questa proposizione che, <lb></lb>per via della sola altezza, vien l&#039;acqua ad acquistare tal forza, da vincero <lb></lb>qualunque resistenza a lei si opponga. </s></p><p type="main">

<s>Quest&#039;ultima principalmente è una di quelle verità, che il Viviani cre­<lb></lb>deva non si poter concludere dai teoremi di Archimede, di cui perciò la <lb></lb>scienza idrostatica s&#039;intendeva, per queste VII proposizioni con altro metodo <lb></lb>condotte, di rendere universale. </s>

<s>Non molti anni dopo, rimastisi questi gene­<lb></lb>rosi propositi del Nostro nelle sue private carte abbandonati, si ripresero con <lb></lb>ardore dall&#039;Herman, il quale, non solo si mostrò mal contento di Archimede, <lb></lb>ma del Pascal stesso, e di quanti altri lo avevano preceduto, dicendo che, <lb></lb>sebbene avessero tutti costoro dimostrato con facilità le ragioni degli equi­<lb></lb>libri fra i liquidi, e i solidi in essi notanti; non erano nulladimeno i loro <lb></lb>metodi universali. </s>

<s>“ Etsi me non lateat (dice nel cap. </s>

<s>III della seconda parte <lb></lb>della Foronomia) aequilibria fluidorum, cum inter se, tum etiam solidorum <lb></lb>corporum cum fluidis homogeneis ex aliis principiis nonnihil brevius posse <pb xlink:href="020/01/3248.jpg" pagenum="209"></pb>deduci, scilicet ex fundamento maximi descensus centri gravitatis, quem omnia <lb></lb>corpora inter se commissa affectant, seu, quod ferme eodem redit, ab aequa­<lb></lb>litate momentorum corporum inter se agitandorum, cuiusmodi principiis Pa­<lb></lb>scalius aliique usi sunt; verum, praeter quam quod talia principia indirecta <lb></lb>sunt, ea vix ac ne vix quidem absque longis ambagibus fluidis heterogeneis <lb></lb>applicari posse videntur, in ea universalitate, in qua praecedentes proposi­<lb></lb>tiones ex principiis suis proximis directe deduximus ” (Amsteledami 1716, <lb></lb>pag. </s>

<s>157). </s></p><p type="main">

<s>Ma noi osservammo che questi principii prossimi, da cui dice l&#039;Herman <lb></lb>id aver direttamente dedotte le sue proposizioni, erano quelli stessi supposti <lb></lb>già da Archimede, e da&#039;quali aveva egli stesso dedotte le sue ammirabili <lb></lb>proposizioni, scritte nel secondo libro <emph type="italics"></emph>De insidentibus humido.<emph.end type="italics"></emph.end> Non importa <lb></lb>ripeter qui quel che dicemmo nella seconda parte del capitolo primo di que­<lb></lb>sto Tomo, persuasi come siamo che i nostri Lettori non abbiano oramai più <lb></lb>nessun dubbio intorno alle pressioni idrostatiche di basso in alto, le quali, <lb></lb>ora essendo pari, ora inferiori, ora superiori alle pressioni d&#039;alto in basso, <lb></lb>prodotte dalle gravità naturali; fanno sì che i settori sferici, e i conoidei <lb></lb>parabolici propostisi dal Siracusano, ora galleggino stabilmente sull&#039;umido, <lb></lb>ora tornino in su violentemente sommersi, ora scendano senza poter aiutarsi, <lb></lb>e si rimangano al fondo. </s>

<s>È un fatto dunque che l&#039;universalità, che si vo­<lb></lb>leva dare alla Scienza, l&#039;aveva ella avuta già dallo stesso Archimede, di cui <lb></lb>sventuratamente nessuno seppe indagare il segreto. </s>

<s>Che sia così, dalla Sto­<lb></lb>ria vien dimostrato abbastanza, ma noi vogliamo che sia suggellato il di­<lb></lb>scorso per un esempio, offertoci dall&#039;interpetre più acuto e più dotto, che <lb></lb>abbia avuto Archimede fra&#039;nostri. </s></p><p type="main">

<s>Antonio Nardi, in quella parte del suo manoscritto, in cui <emph type="italics"></emph>ricerca<emph.end type="italics"></emph.end> le <lb></lb>opere del suo antico Maestro, giudicava così i due libri <emph type="italics"></emph>Delle cose che stanno <lb></lb>nell&#039;umido:<emph.end type="italics"></emph.end> “ Quest&#039;opera, che non si trova in greco, è parte fisica, e parte <lb></lb>meccanica. </s>

<s>È divisa in due libri, de&#039;quali il primo al secondo ha quasi la <lb></lb>stessa ragione, che ha il primo al secondo <emph type="italics"></emph>De&#039;superficiali equilibri.<emph.end type="italics"></emph.end> Investi­<lb></lb>gansi in essa gli equilibri dell&#039;umido, in quella maniera quasi, che nell&#039;aria <lb></lb>s&#039;investigano gli equilibri, in altra opera poco sopra rammentata. </s>

<s>Il soggetto <lb></lb>dunque è di delicata e sottil materia, sopra la quale moltissime considera­<lb></lb>zioni far si potrebbero. </s>

<s>” </s></p><p type="main">

<s>Come, a dire dunque del Nardi, nel primo libro <emph type="italics"></emph>De aequiponderanti­<lb></lb>bus<emph.end type="italics"></emph.end> si tratta dell&#039;invenzione del centro di gravità nelle figure piane circo­<lb></lb>scritte da linee rette, e nel secondo, del centro di gravità nelle superficie <lb></lb>paraboliche; così nel primo <emph type="italics"></emph>De insidentibus humido<emph.end type="italics"></emph.end> si tratta del notar dei <lb></lb>prismi, e nel secondo de&#039;conoidei parabolici. </s>

<s>Il confronto è per verità troppo <lb></lb>superficiale, e indegno di un tanto uomo, il quale pare impossibile non si <lb></lb>fosse accorto che il primo libro idrostatico d&#039;Archimede differisce dal secondo, <lb></lb>non già per la varietà delle figure galleggianti scelte ad esempio, ma per i <lb></lb>principii inclusi nelle due supposizioni, la prima delle quali presiede, per così <lb></lb>dire, al governo delle pressioni perpendicolari, per cui stanno e si muovono <pb xlink:href="020/01/3249.jpg" pagenum="210"></pb>o in su o in giù le solide grandezze, e la seconda presiede al governo delle <lb></lb>forze contrarie, restitutrici nella primiera stabilità di equilibrio i conoidali <lb></lb>inclinati. </s>

<s>Se si volesse instituire un paragone più giusto, si direbbe piutto­<lb></lb>sto che il primo libro <emph type="italics"></emph>De insidentibus humido<emph.end type="italics"></emph.end> sta al secondo, come gli Ele­<lb></lb>menti idrostatici stanno all&#039;Acrobatica dello Stevino: giudizio, a cui molto <lb></lb>s&#039;avvicinò il Lagrange, quando, del sopra memorato secondo libro archime­<lb></lb>deo, così scrisse: “ Ce livre est un des plus beaux monumens du genie <lb></lb>d&#039;Archimede, et renforme une theorie de la stabilité des corps flottans, a la <lb></lb>quelle les modernes ont peu ajòute ” <emph type="italics"></emph>(Mechan. </s>

<s>analyt.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>124). Nes­<lb></lb>sun altro forse aveva dato un giudizio cosi vero come questo, da cui perciò <lb></lb>vogliam cogliere l&#039;occasione di concludere il proposito fatto sui principii del <lb></lb>nostro discorso, qual&#039;era di mostrar come l&#039;Idrostatica, profuga per tanti se­<lb></lb>coli, finalmente tornasse ad Archimede, quasi a rivivere con lui delle so­<lb></lb>stanze paterne. </s></p><pb xlink:href="020/01/3250.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle pressioni idrostatiche<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del principio dell&#039;uguaglianza delle pressioni, proposto dal Torricelli, confermato dal Nardi e dal <lb></lb>Ri<gap></gap>ci, e sperimentalmente dimostrato dal Magiotti. </s>

<s>— II. </s>

<s>Del trattato dell&#039;equilibrio de&#039;liquidi <lb></lb>del Pascal, e de&#039;Paradossi idrostatici del Boyle. </s>

<s>— III. </s>

<s>Della riforma idrostatica avvenuta, per <lb></lb>l&#039;impulso delle tradizioni torricelliane, in Italia. </s>

<s>— IV. De&#039;raggi fluidi e delle ragioni dei loro <lb></lb>momenti: trattato di Vincenzo Viviani. </s>

<s>— V. </s>

<s>Della soluzion del problema: perchè gli animali <lb></lb>sott&#039;acqua non ne sentano il peso. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Quel rifuggir che fece la Scienza italiana dai savi metodi antichi, così <lb></lb>felicemente dallo Stevino proseguiti ne&#039;tempi nuovi, ci hanno le cose fin qui <lb></lb>narrate dimostrato di fatto che deve imputarsi a Galileo, il quale, tutto ridu­<lb></lb>cendo a conferire insieme le ragioni dei momenti virtuali, bandì dall&#039;Idro­<lb></lb>statica ogni idea di quelle pressioni, ch&#039;esercitano i liquidi fra loro, e sui <lb></lb>solidi immersi. </s>

<s>Or perchè gli Elementi idrostatici del Matematico di Bruges <lb></lb>furono per lo Snellio pubblicati quattro anni prima del Discorso intorno alle <lb></lb>galleggianti, importa molto sapere se fossero al Nostro, mentre scriveva, note <lb></lb>le proposizioni dimostrate dallo straniero. </s></p><p type="main">

<s>Ripensando alla distanza de&#039;paesi, e alla difficoltà de&#039;commerci letterari <lb></lb>a que&#039;tempi, è facile congetturare che non fossero bastanti quattr&#039;anni a fare <lb></lb>approdare in Italia un libro scientifico, scritto e stampato in Olanda. </s>

<s>Dal­<lb></lb>l&#039;altra parte Galileo, così geloso d&#039;ottenere il primato in tutto, e così tre­<lb></lb>pidante che non gli fosse tolto, non poteva pensare, nè si curava perciò nem­<lb></lb>men di cercare se altri l&#039;aveva prevenuto. </s></p><p type="main">

<s>Ma avvenne che si trovasse allora colà un suo carissimo amico, Daniele <lb></lb>Antonini, il quale, conversando con que&#039;dotti olandesi, udì da loro le nuove <lb></lb>maraviglie scoperte nelle proprietà dell&#039;acqua, e come avessero veduto una <pb xlink:href="020/01/3251.jpg" pagenum="212"></pb>bilancia di braccia uguali, sopra la quale un&#039;oncia d&#039;acqua da una parte <lb></lb>contrappesava cento libbre dall&#039;altra. </s>

<s>Comunicò l&#039;Antonini questa curiosità <lb></lb>a Galileo, che rispose non essergli la cosa riuscita punto nuova, perchè, avendo <lb></lb>egli già dimostrato come sia possibile <emph type="italics"></emph>che una nave così bene galleggi in <lb></lb>dieci botti d&#039;acqua come nell&#039;oceano<emph.end type="italics"></emph.end> (Alb. </s>

<s>XII, 26), aveva come lo Stevino, <lb></lb>e prima di lui, dietro questo principio, immaginato una bilancia, nella quale <lb></lb>un galeone poteva esser sostenuto da un&#039;inguistara d&#039;acqua. </s>

<s>Nonostante pre­<lb></lb>gava l&#039;amico gli descrivesse particolarmente l&#039;esperienza olandese, per vedere <lb></lb>se s&#039;accordava colla sua. </s></p><p type="main">

<s>Avuta la desiderata descrizione, Galileo riconobbe che si trattava d&#039;altro <lb></lb>da quel che s&#039;aspettava, e sentì che la cosa davvero era nuova: tanto anzi <lb></lb>nuova, che non ritrovava nella sua propria scienza ragioni da spiegarla. </s>

<s>Sem­<lb></lb>bra che gli si rintuzzasse da ciò la prima concepita baldanza così, da non <lb></lb>saper che si dire all&#039;Antonini, il quale, maravigliato del veder corrispondere <lb></lb>le sue premure con quella trascuratezza, veniva a tentar l&#039;amico lontano con <lb></lb>sì fatte parole scritte in una lettera il di 11 Gennaio 1611 da Linghen: <lb></lb>“ Nell&#039;altra mia V. S. avrà avuta quella Bilancia idrostatica di braccia uguali, <lb></lb>nella quale un&#039;oncia d&#039;acqua da una parte può sollevare facilmente cento <lb></lb>libbre di peso, dall&#039;altra parte posto, con il mezzo di quella forza, per la <lb></lb>quale potrebbe il galeone notare in una inguistara d&#039;acqua. </s>

<s>Non so se si <lb></lb>accorderà colla sua ” (MSS. Gal., P. VI, T. VIII, fol. </s>

<s>8). </s></p><p type="main">

<s>Di quest&#039;ultime parole dovette Galileo sentir la puntura acuta, costretto <lb></lb>a confessare che l&#039;invenzione dello Stevino non si poteva far nemmeno di­<lb></lb>pendere dai principii da sè professati, non che affermare che s&#039;accordava <lb></lb>colla sua. </s>

<s>Il Discorso delle galleggianti già scritto si dovette perciò man­<lb></lb>dare in pubblico senza l&#039;ornamento di quella magica Bilancia, la quale <lb></lb>ebbe a contentarsi di far poi nella privata lettera al Nozzolini più modesta <lb></lb>comparsa. </s></p><p type="main">

<s>Intanto Giovanni Bardi, in Roma, declamava ai Lincei quella disserta­<lb></lb>zione idrostatica, nella quale Galileo suo Maestro veniva assunto alla mede­<lb></lb>sima gloria con Archimede, e finiva per descrivere l&#039;esperienza steviniana <lb></lb>ai colleghi maravigliati. </s>

<s>Non è però il Bardi semplice relatore di una curio­<lb></lb>sità, come sembra che fosse l&#039;Antonini, ma parla in nome della scienza, sog­<lb></lb>giungendo le ragioni evidenti a dimostrar ciò che poteva apparire un para­<lb></lb>dosso anche agl&#039;ingegni meno volgari. </s>

<s>“ Nihil enim referre videtur gravis <lb></lb>sit vel levis cylinder, dummodo ab alio sustentetur, et aquae ut res postulat <lb></lb>immergatur, atque adeo munus obeat, vel aquae novem librarum quarum <lb></lb>locum occupat, vel cuiuscumque alterius corporis cum aqua gravitatis, hoc <lb></lb>enim si eumdem locum occupare cogitatur, non aliter quam ipsa aqua gra­<lb></lb>varet lancem, et una cum reliqua libra aquae decem plumbi vel marmoris <lb></lb>libris aeque ponderaret. </s>

<s>Ergo et cylinder, qui potentia gravitati illius corpo­<lb></lb>ris aequali intra aquam detinetur, eumdem quem idem corpus vel aqua <lb></lb>effectum praestabit ” (Targioni, <emph type="italics"></emph>Notizie degli aggrandim. </s>

<s>ecc.,<emph.end type="italics"></emph.end> Firenze 1786, <lb></lb>T. II, pag. </s>

<s>10). </s></p><pb xlink:href="020/01/3252.jpg" pagenum="213"></pb><p type="main">

<s>La spiegazione del paradosso steviniano, data qui, è quella medesima <lb></lb>che si legge nella lettera al Nozzolini: anzi la conclusione del Bardi, al ri­<lb></lb>scontro, è la fedel traduzione latina delle parole originali di Galileo: “ E così <lb></lb>verrebbe in certezza che il <emph type="italics"></emph>cilindro,<emph.end type="italics"></emph.end> sebbene scaccia l&#039;acqua del vaso, nien­<lb></lb>tedimeno, col solo occuparvi il luogo dell&#039;acqua scacciata, vi conserva tanto <lb></lb>di gravità, quanto appunto è quella dell&#039;acqua scacciata ” (Alb. </s>

<s>XII, 114). <lb></lb>Da ciò siamo certificati che la dissertazione accademica del Discepolo fu scritta <lb></lb>sotto la direzion del Maestro, che dovette lasciar correre la solenne comme­<lb></lb>morazione fattavi di Simone Stevino, dal <emph type="italics"></emph>vastissimo experimentorum oceano<emph.end type="italics"></emph.end><lb></lb>del quale diceva il Bardi d&#039;avere attinta la descrizione del maraviglioso stru­<lb></lb>mento. </s>

<s>Galileo invece ne parla come di cosa di sua propria invenzione, sug­<lb></lb>geritagli dalle critiche dell&#039;Accademico incognito, a cui solo perciò e non allo <lb></lb>Stevino professa di restare obbligato. </s>

<s>Ma se la prepotente autorità del Mae­<lb></lb>stro non valse a indurre il dissertante linceo ad attribuirgli la Bilancia idro­<lb></lb>statica, usò nulladimeno in quel suo dissertare ogni arte, per fare apparire <lb></lb>che alcune non men belle esperienze, proposte negli Elementi idrostatici, non <lb></lb>mancavano pure nel Discorso delle Galleggianti. </s></p><p type="main">

<s>La lamina di piombo che, sebben libera, non si stacca dall&#039;orlo infe­<lb></lb>riore del tubo di vetro, convenientemente profondatasi insieme con lui nel­<lb></lb>l&#039;acqua, e che lo Stevino descriveva nel suo libro, per dimostrare la pres­<lb></lb>sione fatta di sotto in su dal liquido; il Bardi la rassomiglia alla tavoletta <lb></lb>di ebano galleggiante secondo le posizioni di Galileo. </s>

<s>“ Videtis ut tabella haec <lb></lb>plumbea, haud parvi ponderis, cylindro vitreo adhaerescere mediis in undis <lb></lb>malit, quam in fundo loco suo proprio suaviter conquiescere? </s>

<s>Jucundissimum <lb></lb>profecto spectaculum, et philosopho mathematico dignissimum, in quo, nisi <lb></lb>plane caecutio, videre mihi videor miraculum Naturae iterum, quod paulo <lb></lb>ante in tabella natante una conspeximus. </s>

<s>Utrobique puteus aereus est, utro­<lb></lb>bique fundus e materia aqua graviore: parietes dumtaxat, qui illic sunt aquei <lb></lb>et fluidi, hic existunt vitrei ac solidi, eum in finem ut putei aerei altitudo <lb></lb>quae alioquin ad laminarum crassitiem definitam habet a natura proportio­<lb></lb>nem, augeri ad arbitrium queat. </s>

<s>Qua aucta, necesse est ut aquae moles quae <lb></lb>antea, cum libere natabat tabella, parti demersae aequalis erat et aeque gra­<lb></lb>vis, iam secundum molem aucta gravior evadat atque idcirco tabella plumbea <lb></lb>una cum vitro teneri quidem praeter Naturae leges intra aquam profundius <lb></lb>possit, mergi vero, quamvis libera sit, non possit ” (Targioni, <emph type="italics"></emph>Notizie<emph.end type="italics"></emph.end> e <lb></lb>Tomo cit., pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Questa eloquenza accademica del Bardi mandava soavi profumi d&#039;in­<lb></lb>censo alle segrete ambizioni del suo Maestro. </s>

<s>Il merito vero però non con­<lb></lb>sisteva nell&#039;inventare e nel descrivere spettacoli giocondissimi, ma nell&#039;illu­<lb></lb>strarli co&#039;principii della Scienza, ciò che, per reputarli veramente degni di <lb></lb>loro, avrebbero piuttosto desiderato i Filosofi matematici. </s>

<s>Ora è un fatto che <lb></lb>dal Bardi si declamano ossequiosamente gli errori imbevuti nell&#039;insegnamento <lb></lb>di Galileo, in cui non par che la Scienza steviniana abbia nulla giovato a <lb></lb>riformare i giudizi. </s>

<s>Non importa ripetere che, nelle postille all&#039;Incognito e <pb xlink:href="020/01/3253.jpg" pagenum="214"></pb>nella lettera al Nozzolini, si conferma essere il peso dell&#039;acqua, che riem­<lb></lb>pirebbe la fossetta scavatasi dall&#039;assicella di ebano, uguale al solo peso di <lb></lb>essa assicella; come pure il Bardi, sulla parola del suo maestro, confidente­<lb></lb>mente asserisce essere al solido, senza l&#039;aria che gli sovrasta, la detta mole <lb></lb>acquea <emph type="italics"></emph>aeque gravis:<emph.end type="italics"></emph.end> a provare che Galileo non ricevè alcun benefizio dalle <lb></lb>tradizioni precedenti, basta ripensare a quella attrazione calamitica dell&#039;aria, <lb></lb>alla quale principalmente egli attribuiva nel suo Discorso il galleggiare sul­<lb></lb>l&#039;acqua le palline di cera. </s>

<s>Lo Stevino aveva insegnata la vera e adeguata <lb></lb>causa di un tal galleggiamento nelle pressioni, che dì sotto in su si susci­<lb></lb>tano dentro la massa del liquido, onde, essendo per Galileo venuti l&#039;occa­<lb></lb>sione e il tempo di saper la verità a tutti oramai pubblicamente nota, si <lb></lb>crederebbe che da vero Filosofo si movesse egli il primo ad abbracciarla, per <lb></lb>valersene opportunamente nel rispondere al Nozzolini. </s></p><p type="main">

<s>A questi, allora professore nello studio di Pisa, pareva cosa dura affer­<lb></lb>mare che gli arginetti si reggano intorno alla cera e all&#039;ebano dalla virtù <lb></lb>attrattiva dell&#039;aria, ond&#039;egli avrebbe voluto dire piuttosto, a proposito del <lb></lb>bicchiere vuoto rivolto colla bocca in giù, e tuffato a forza nell&#039;acqua, in <lb></lb>fondo alla quale stia una pallina di cera; che, nel tirarlo in su, “ quella <lb></lb>cera seguita l&#039;aria di quel bicchiere <emph type="italics"></emph>ratione vacui,<emph.end type="italics"></emph.end> perchè tirandolo in su <lb></lb>con qualche velocità, bisogna che quel che v&#039;è dentro lo seguiti, siccome, <lb></lb>alzata con velocità la coperta di un libro, si tira dietro due o tre carte ” <lb></lb>(Alb. </s>

<s>XII, 99). </s></p><p type="main">

<s>Galileo pensò che sarebbe, per far più breve la risposta e renderla più <lb></lb>efficace, bastato il dichiararsi meglio intorno al modo, con cui la palla di <lb></lb>cera si solleva dal fondo, in virtù dell&#039;aria che se le manda col bicchiere <lb></lb>rovesciato, “ il qual modo, egli dice, non è altrimenti per attrazione di vacuo, <lb></lb>mentre che il bicchiere con velocità s&#039;alzasse, anzi è necessario sollevare il <lb></lb>bicchiere lentissimamente, dando tempo che l&#039;acqua possa subentrare a suo <lb></lb>bell&#039;agio a proibire il vacuo: ma la causa del sormontar la palla è l&#039;aria, <lb></lb>che le resta contigua ” (ivi, pag. </s>

<s>116). In questa sola contiguità poi fa Ga­<lb></lb>lileo consistere tutto l&#039;effetto, cosicchè rifioriscono qui le macchie sparse nel <lb></lb>Discorso idrostatico, e se qualche differenza ci è, si riduce al modo di spie­<lb></lb>gar come l&#039;aria così tenacemente si rimanga col galleggiante contigua, da <lb></lb>acompagnarlo per tutto il suo affondarsi nell&#039;acqua. </s>

<s>Aveva prima attribuito <lb></lb>il fatto a un&#039;attrazione calamitica, con scandalo universale, di cui però dà <lb></lb>la colpa al non essersi spiegato così bene allora, come ora che dice di voler <lb></lb>riferire, e di avere inteso sempre di riferire l&#039;aderenza dell&#039;aria con la falda <lb></lb>a quel <emph type="italics"></emph>solo contatto esquisito<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>105), che poi, nelle due Nuove Scienze, <lb></lb>attribuirà alla forza del vacuo. </s>

<s>Si ritorna dunque alle ripudiate ragioni del <lb></lb>Nozzolini, nè ciò nulla importa, purchè si stia lontani dal professare le pres­<lb></lb>sioni idrostatiche dello Stevino. </s></p><p type="main">

<s>Ma, per confermare anche meglio le prove dell&#039;argomento geloso, tor­<lb></lb>niamo alla Bilancia idrostatica di braccia uguali. </s>

<s>Si disse che tutt&#039;altro che <lb></lb>riconoscere, fra quella dello Stevino, e l&#039;altra, che gli era allora balenata <pb xlink:href="020/01/3254.jpg" pagenum="215"></pb>nella fantasia, un accordo; Galileo non ritrovava ne&#039;suoi principii nessuna <lb></lb>ragione valevole a spiegare il paradosso, cosicchè i momenti del solido e del <lb></lb>liquido, e le loro collazioni, a cui fu costretto ridursi, in conformità di que­<lb></lb>gli stessi principii; non riescono che a parole risonanti senza significato. </s>

<s>Che <lb></lb>cosa infatti significa conferire il maschio, all&#039;acqua rimasta nella bigoncia, <lb></lb>o all&#039;aria rimasta nel vaso, <emph type="italics"></emph>tanto de&#039;propri momenti, quant&#039;era il mo­<lb></lb>mento dell&#039;acqua o dell&#039;aria scacciata?<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>114). O intendendosi che <lb></lb>il solido supplisca al peso del liquido, di cui tiene il luogo, non era egli <lb></lb>questo il soggetto della dimostrazione, quale se l&#039;era proposto lo Stevino, <lb></lb>l&#039;intenzione del quale fu poi di confermar con l&#039;esperienza le verità concluse <lb></lb>dalla sola teoria? </s></p><p type="main">

<s>Ma che quelle professate da Galileo fossero propriamente parole, e non <lb></lb>teorie, s&#039;argomenta dalle strane conseguenze ch&#039;egli ne trasse, come s&#039;ar­<lb></lb>gomenta aver camminato al buio chi si trova caduto nella fossa. </s>

<s>— Se il <lb></lb>maschio è che conferisce il peso all&#039;acqua rimasta nella bigoncia, quest&#039;acqua <lb></lb>dunque non ha momento proprio, ma partecipato. </s>

<s>E potendosi fare il detto <lb></lb>maschio di gravità in specie pari a quella dell&#039;acqua, dunque, anche quando <lb></lb>il vaso sarà tutto pieno di questa, ella avrà sempre il momento partecipato, <lb></lb>e non premerà perciò, quanto a sè, altro che pochissimo sopra il fondo e <lb></lb>contro le pareti del vaso. </s>

<s>Potendosi anzi ridurre il liquido, rimasto preso fra <lb></lb>il maschio e la bigoncia, a un così sottilissimo velo, da considerarsi come <lb></lb>di nessun peso, nulla dunque può dirsi che sia la sua pressione. </s>

<s>— Così ap­<lb></lb>punto ragionava Galileo col Viviani, il quale, insieme con altri simili docu­<lb></lb>menti raccolti dalla viva voce del suo maestro in Arcetri, ci volle conservar <lb></lb>la memoria anche di questo, nelle due note seguenti: </s></p><p type="main">

<s>“ I. </s>

<s>Sit libra AB (fig. </s>

<s>115), cuius fulchrum E, in extremo A pondus X <lb></lb>decem librarum, in altero vero B tenuissimum vitreum vas CBD, in quo sit <lb></lb><figure id="id.020.01.3254.1.jpg" xlink:href="020/01/3254/1.jpg"></figure></s></p><p type="caption">

<s>Figura 115.<lb></lb>ligneum solidum F ita coaptatum, <lb></lb>ut ipsum vas nulla ex parte tangat, <lb></lb>sed suspensum maneat super sub­<lb></lb>stentaculum GH parieti infixum. </s>

<s><lb></lb>Dico iam si in spacio, quod inter <lb></lb>vas et masculum interest, superin­<lb></lb>fundatur aqua, ipsam, quamvis parvissimae molis, ope tamen solidi F aequi­<lb></lb>ponderare sum solido X, licet solidum F non a vase sed a brachio GH sustinea­<lb></lb>tur. </s>

<s>Parva igitur aquae moles, in interstitio CBD infusa, valet ad sustinendum <lb></lb>quodcumque vel gravissimum pondus X, dummodo id gravitatem vasis CBD, <lb></lb>una cum aqua eum replente, non excedat. </s>

<s>” </s></p><p type="main">

<s>“ Videtur hinc super aquas CBD tantum gravitare pauca illa aquae mo­<lb></lb>les inter vas et masculum intercepta, ac si idem vas aqua in totum reple­<lb></lb>tum fuerit, et interstitium CBD sit quantumlibet angustissimum. </s>

<s>At si vero <lb></lb>hoc, cur dici non poterit vas CBD, cum est aqua plenum, nihil ab ipsa <lb></lb>gravari? </s>

<s>” </s></p><p type="main">

<s>“ II. </s>

<s>Esto vas ex subtilissimo vitro confectum ABCD (fig. </s>

<s>116), cui adhae-<pb xlink:href="020/01/3255.jpg" pagenum="216"></pb>reat solidum X in parte tantum R. </s>

<s>In reliquis vero partibus sit undique di­<lb></lb>siunctum a continente ABCD. </s>

<s>Distet autem a vitri interiore superficie per <lb></lb><figure id="id.020.01.3255.1.jpg" xlink:href="020/01/3255/1.jpg"></figure></s></p><p type="caption">

<s>Figura 116.<lb></lb>angustissimum interstitium, eiusque gravitas in specie sit <lb></lb>eadem cum aqua. </s>

<s>Clarum est, cum solidum X non tangat <lb></lb>vas ABCD nisi in parte R, nullam aliam vitri partem premi <lb></lb>a solido X, cum a solido non tangatur. </s>

<s>Superinfundatur <lb></lb>ergo aqua inter vitrum et solidum, quae, cum sit paucis­<lb></lb>simae molis, parum etiam premet super vitrum, minusque <lb></lb>adhuc premeret, si spacium vacuum fuisset angustius. </s>

<s>Attamen aqua gravi­<lb></lb>tatem ponderis X substinebit, neque magis premet in puncto R, neque basem <lb></lb>vasis ABCD pressionem ullam patietur. </s>

<s>Si vero, pro solido X, intelligatur <lb></lb>aqua, idem veniet, ideoque vas aqua plenum in nulla sua parte premi ne­<lb></lb>cesse est. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. CXXXV, a tergo del fol. </s>

<s>13). </s></p><p type="main">

<s>Educato nella palestra di così fatti paralogismi, non è punto maraviglia <lb></lb>che poi si facesse il Viviani difensore così liberale del Michelini. </s>

<s>Ma ripen­<lb></lb>sando alle cure diligentissime, poste dallo Stevino per dimostrar la quantità <lb></lb>delle pressioni idrostatiche, non solo contro il fondo, ma e contro le pareti <lb></lb>dei vasi, secondo le loro ampiezze, figure e inclinazioni; si direbbe che s&#039;at­<lb></lb>tendeva in Italia, piuttosto che a promovere con amore la scienza, a farne <lb></lb>indegnamente la parodia. </s>

<s>S&#039;accennava però che alla Scuola galileiana ne <lb></lb>succedeva un&#039;altra, la quale avrebbe ridonati così alla primiera dignità gli <lb></lb>ingegni speculativi, da rimetterli nella via di progredire, e di avvantaggiar <lb></lb>gli stranieri. </s>

<s>Quella benefica scuola s&#039;istituiva dal Torricelli, e gli uffici, che <lb></lb>fu ordinata a fare nella vita dell&#039;Idrostatica, son quelli stessi della radice e <lb></lb>del cuore nella vita della pianta, e dell&#039;animale. </s></p><p type="main">

<s>Il mondo ha esaltato alla massima gloria un tal uomo, per essere stato <lb></lb>autore dell&#039;esperienza del vuoto, e inventor del Barometro. </s>

<s>Eppure noi l&#039;ab­<lb></lb>biamo udito confessar da sè stesso che l&#039;invenzione <emph type="italics"></emph>non gli fu potuta riu­<lb></lb>scire,<emph.end type="italics"></emph.end> e sappiamo d&#039;altronde che, essendo stata l&#039;esperienza del vacuo già <lb></lb>fatta, tutto il merito si riduceva a sostituire il mercurio all&#039;acqua, cosicchè <lb></lb>in un maneggevole tubo di vetro si potesse comodamente vedere quel che <lb></lb>in una canna si lunga, da giunger di terra a toccare il tetto di un palazzo <lb></lb>di Roma. </s>

<s>S&#039;osservi poi che l&#039;esperienza stessa, così accomodata, s&#039;appella <lb></lb>dall&#039;Autore col nome di <emph type="italics"></emph>filosofica,<emph.end type="italics"></emph.end> e, discorrendo con M. A. </s>

<s>Ricci di altri <lb></lb>simili fatti, gli dice che può averli per certi, <emph type="italics"></emph>come se ne avesse fatta espe­<lb></lb>rienza.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>È manifesto dunque che l&#039;opera del Torricelli è intorno a una specu­<lb></lb>lazione, e non intorno a una osservazione sensata, e consiste in quella spe­<lb></lb>culazione tutto il merito di lui, che la traviata Idrostatica di Galileo, con <lb></lb>generosa libertà, riduceva sopra i retti sentieri. </s>

<s>Com&#039;era possibile che co­<lb></lb>loro, a&#039;quali s&#039;insegnava che l&#039;acqua non preme in su, perchè ciò sarebbe <lb></lb>contrario alla sua gravità naturale; che un solido immerso non contrasta con <lb></lb>tutta l&#039;acqua, ma con quella parte sola di lei che si moverebbe, movendosi <lb></lb>esso solido; com&#039;era possibile cadesse in mente a costoro che sia la pres-<pb xlink:href="020/01/3256.jpg" pagenum="217"></pb>sione di tutta l&#039;altissima sfera dell&#039;aria la vera adeguata causa del sosten­<lb></lb>tarsi l&#039;argento vivo nel tubo? </s>

<s>Anzi avrebbero reluttato all&#039;idea, se fosse ve­<lb></lb>nuto qualcuno innanzi a loro a proporla, come il Torricelli già s&#039;aspettava, <lb></lb>e come di fatto gli avvenne col Ricci, il quale, appena avuta la descrizion <lb></lb>dall&#039;Autore, così il dì 2 Luglio 1644 gli rispondeva da Roma: </s></p><p type="main">

<s>“ Il modo, con che V. S. salva l&#039;esperienza fatta in riprova del vacuo, <lb></lb>cioè del salire le cose gravi contro la sua naturale inclinazione, io lo giudico <lb></lb>tanto più buono dell&#039;altro, quanto che con questo ci conformiamo alla sem­<lb></lb>plicità della Natura nelle opere sue, la quale, potendo salvare l&#039;unione dei <lb></lb>corpi col solo moto all&#039;in giù, invano averebbe inserito loro una nuova na­<lb></lb>turale inclinazione d&#039;obbedire alla Causa universale, moderatrice del mondo, <lb></lb>com&#039;essi dicono. </s>

<s>Ed ammiro il nobile ardimento di V. S. nell&#039;avere in con­<lb></lb>siderazione cosa non tocca da nessuno finora, la quale ha parimente tanto <lb></lb>di probabilità che, toltone due o tre obiezioni che sono per dire, e le quali <lb></lb>prego V. S. a volermele risolvere, siccome so che ella potrà fare agevol­<lb></lb>mente; stimo essere il più vero, ed il più ragionevole che possa dirsi in si­<lb></lb>mile questione ” (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>23, 24). </s></p><p type="main">

<s>Della prima obiezione ci passeremo, perchè non importante al presente <lb></lb>nostro proposito, e perchè se ne disse quanto basta a pag. </s>

<s>460 e 461 del <lb></lb>primo Tomo, trattenendoci piuttosto a esaminare la seconda e la terza, dal <lb></lb>Ricci stesso proposte in questa forma: “ Secondariamente, preso uno schiz­<lb></lb>zatoio, che suole essere usato assai in questo soggetto, e che abbia la sua <lb></lb>animella <emph type="italics"></emph>(stantuffo)<emph.end type="italics"></emph.end> dentro onninamente, acciò escluda con la sua corpulenza <lb></lb>ogni altro corpo; turando in cima il foro, e ritirando per forza l&#039;animella <lb></lb>indietro, sentiamo grandissima resistenza, e ciò non segue solamente, tenendo <lb></lb>in giù lo schizzatoio e voltando in su l&#039;animella, sopra il cui manico grava <lb></lb>l&#039;aria, ma segue per ogni verso che si faccia. </s>

<s>Eppure, non pare che si possa <lb></lb>in questi casi facilmente intendere come il peso dell&#039;aria v&#039;abbia che fare. </s>

<s><lb></lb>Finalmente un corpo immerso nell&#039;acqua non contrasta con tutta l&#039;acqua <lb></lb>che vi sta sopra, ma con quella sola, che al moto del corpo immerso si <lb></lb>muove, la quale non è maggiore di esso corpo. </s>

<s>E perchè stimerei che la <lb></lb>stessa dottrina fosse da applicarsi alla librazione dell&#039;argento vivo, dovrebbe <lb></lb>esso contrastare con tanto d&#039;aria, quanto è la sua mole. </s>

<s>Or come potrebbe <lb></lb>l&#039;aria preponderar mai? </s>

<s>” (ivi, fol. </s>

<s>24). </s></p><p type="main">

<s>A quel che il Ricci obiettava in secondo luogo rispondeva il Torricelli <lb></lb>a quel modo, che è più proprio a persuadere i semplici, per via dell&#039;apo­<lb></lb>logo socratico, con gentile arguzia avvertendo gli studiosi delle Galleggianti <lb></lb>galileiane (tutti insieme da lui compresi nella persona del suo giovane amico) <lb></lb>che per troppa semplicità erano rimasti ingannati. </s>

<s>“ Fu una volta un Filo­<lb></lb>sofo che, vedendo la cannella messa alla botte da un servitore, lo bravò con <lb></lb>dire che il vino non sarebbe mai venuto, perche natura de&#039;gravi è di pre­<lb></lb>mere in giù e non orizontalmente e dalle bande. </s>

<s>Ma il servitore fece toc­<lb></lb>cargli con mano che, sebbene i liquidi gravano per natura in giù, in ogni <lb></lb>modo spingono e schizzano per tutti i versi, anco allo in su, purchè trovino <pb xlink:href="020/01/3257.jpg" pagenum="218"></pb>luoghi dove andare, cioè luoghi tali, che resistano con forza minore della <lb></lb>forza di essi liquidi. </s>

<s>Infonda V. S. un boccale tutto nell&#039;acqua, colla bocca <lb></lb>all&#039;in giù, poi gli buchi il fondo, sicchè l&#039;aria possa uscire: vedrà con che <lb></lb>impeto l&#039;acqua si muove di sotto all&#039;in su per riempirlo ” <emph type="italics"></emph>(Dati, nella Let­<lb></lb>tera a&#039;Filaleti,<emph.end type="italics"></emph.end> Firenze 1663, pag. </s>

<s>23). </s></p><p type="main">

<s>L&#039;ultima obiezione si concludeva dal Ricci per un&#039;applicazion più di­<lb></lb>retta degli insegnamenti idrostatici di Galileo, il quale, dopo aver detto che <lb></lb>un solido più grave in specie dell&#039;acqua resiste all&#039;esser sollevato da lei su <lb></lb>dal fondo del vaso, con l&#039;eccesso del suo peso assoluto, sopra il peso asso­<lb></lb>luto di una mole acquea a sè uguale; soggiunge: “ E benchè si aggiungesse <lb></lb>poi grandissima quantità d&#039;acqua sopra il livello di quella, che pareggia l&#039;al­<lb></lb>tezza del solido, non però s&#039;accresce la pressione o aggravamento delle parti <lb></lb>circonfuse al detto solido, per la quale maggior pressione egli avesse ad esser <lb></lb>cacciato. </s>

<s>Perchè il contrasto non gli vien fatto se non da quelle parti del­<lb></lb>l&#039;acqua, le quali, al moto di esso solido, esse ancora si muovono, e queste <lb></lb>son quelle solamente, che son comprese tra le due superficie equidistanti <lb></lb>all&#039;orizonte, e fra di loro parallele, le quali comprendon l&#039;altezza del solido <lb></lb>immerso nell&#039;acqua ” (Alb. </s>

<s>XII, 26, 27). </s></p><p type="main">

<s>La proposizione, così assolutamente annunziata, è falsa non essendo vero, <lb></lb>come altrove osservammo, che per nuova aggiunta di liquido non s&#039;accre­<lb></lb>sca, intorno e sopra il solido, l&#039;aggravamento. </s>

<s>La ragion poi addotta da Ga­<lb></lb>lileo, e ripetuta dal Ricci, che cioè non si faccia il contrasto se non con sole <lb></lb>quelle parti dell&#039;aequa, le quali si moverebbero movendosi il solido, a cui <lb></lb>possono dette parti essere tutto al più uguali in mole, ma non mai mag­<lb></lb>giori; non vale se non nel caso che il corpo immerso abbia l&#039;acqua da&#039;lati <lb></lb>e di sopra. </s>

<s>Così, per esempio, nella figura 108 illustrativa delle dottrine del <lb></lb>Borelli, che si riferiscono alla presente questione, è vero che il solido EG <lb></lb>contrasta solamente con l&#039;acqua FC, se tutto il vaso AC sarà pieno. </s>

<s>Ma se, <lb></lb>facendo HF argine all&#039;acqua HI, lo spazio AF rimanga assolutamente vuoto, <lb></lb>o pieno di aria; e allora il grave solido EG contrasta con tutta l&#039;acqua HC, <lb></lb>e si farebbe sempre maggiore il contrasto, col crescer l&#039;altezza perpendico­<lb></lb>lare del liquido sopra il primo livello. <lb></lb><figure id="id.020.01.3257.1.jpg" xlink:href="020/01/3257/1.jpg"></figure></s></p><p type="caption">

<s>Figura 117.</s></p><p type="main">

<s>Ora il Torricelli, mentre illustrava e correggeva <lb></lb>la proposizione idrostatica di Galileo, mostrava al Ricci <lb></lb>che, avendo il mercurio dentro il tubo di sopra il vuoto, <lb></lb>falsamente ei ne concludeva dover esso mercurio con­<lb></lb>trastare con una parte minore, o tutt&#039;al più eguale a <lb></lb>sè in mole: ma confermava che un tal contrasto era <lb></lb>veramente con tutta l&#039;altezza dell&#039;ammosfera. </s>

<s>E, per <lb></lb>dargli a intender la cosa con più sensata dimostrazione, <lb></lb>ricorreva a un esempio, in cui l&#039;aria era invece del <lb></lb>vuoto, e invece dell aria l&#039;acqua. </s>

<s>Se nel sifone ABCD <lb></lb>(fig. </s>

<s>117), aperto in D, s&#039;infonda argento vivo, è certo <lb></lb>che si livellerà ugualmente in A, E nell&#039;un braccio e <pb xlink:href="020/01/3258.jpg" pagenum="219"></pb>nell&#039;altro. </s>

<s>Ma si cali lo strumento in fondo a un vaso, dentro cui si versi <lb></lb>acqua in sino a un certo livello. </s>

<s>Sopraggiungendone altra via via, si vedrà <lb></lb>che anche il mercurio s&#039;alza via via dentro la canna, con tal regola però <lb></lb>che sempre l&#039;altezza, a cui giunge dopo ogni infusione, sia la quattordicesima <lb></lb>parte di quella dell&#039;acqua. </s>

<s>Falso è dunque che, coll&#039;aggiungere nuova <lb></lb>quantità d&#039;acqua sopra il primo livello, non si venga a crescere la pressione, <lb></lb>e falso anco è perciò che il contrasto si faccia con una parte sola, e non <lb></lb>con tutta l&#039;acqua soprastante secondo la sua altezza perpendicolare. </s>

<s>Così <lb></lb>rispondeva in sostanza il Torricelli, e tali erano propriamente le sue parole: </s></p><p type="main">

<s>“ La terza obiezione non mi par troppo a proposito: certo è che è meno <lb></lb>valida dell&#039;altre, ancorchè, essendo presa dalla Geometria, paia più gagliarda <lb></lb>di tutte. </s>

<s>Che un corpo posto nell&#039;acqua contrasti solo con tanta mole d&#039;acqua, <lb></lb>quanta è la mole sua, è vero, ma il metallo sostenuto in quel collo di vaso <lb></lb>non mi pare che si possa dire nè immerso in acqua, nè in aria, nè in vetro, <lb></lb>nè in vacuo. </s>

<s>Solamente si può dire ch&#039;egli è un corpo fluido e libratile, <lb></lb>una superficie del quale confina col vacuo, o quasi vacuo, che non gravita <lb></lb>punto. </s>

<s>L&#039;altra superficie confina con aria premuta da tante miglia d&#039;aria <lb></lb>ammassata, e perciò quella superficie non premuta punto ascende scacciata <lb></lb>da quell&#039;altra, e ascende tanto, sin che il peso del metallo sollevato arrivi ad <lb></lb>agguagliare il peso dell&#039;aria premente dall&#039;altra parte. </s>

<s>” </s></p><p type="main">

<s>“ V. S. s&#039;immagini il vaso A col tubo BCD congiunto e aperto in D, <lb></lb>come sta dipinto, e sia il vaso A pieno d&#039;argento vivo: certo è che il me­<lb></lb>tallo salirà nel tubo fino al suo livello E. </s>

<s>Ma se immergerò detto strumento <lb></lb>nell&#039;acqua, sino al segno F, l&#039;argento vivo non salirà fino ad F, ma solo <lb></lb>tanto, fino che l&#039;altezza del livello nel tubo avanzi il livello del vaso A della <lb></lb>quattordicesima parte in circa dell&#039;altezza, che averà l&#039;acqua F sopra il li­<lb></lb>vello del vaso A, e questo V. S. l&#039;abbia per certo, come se avesse fatto <lb></lb>l&#039;esperienza. </s>

<s>Ora qui si vede che si può dar caso che l&#039;acqua F sia alta <lb></lb>quattordici braccia, ed il metallo nel tubo ED sia alto un braccio solo. </s>

<s>Dun­<lb></lb>que quel braccio solo di metallo non contrasta con altrettanta acqua, ma con <lb></lb>tutta l&#039;altezza d&#039;acqua, che è tra A ed F, ed in questi casi ella sa che non <lb></lb>si guarda alle larghezze e grossezze de&#039;solidi, ma solo alle perpendicolari, <lb></lb>ed alle gravità in specie, e non ai pesi assoluti. </s>

<s>” <emph type="italics"></emph>(Lettera ai Filateti<emph.end type="italics"></emph.end> cit., <lb></lb>pag. </s>

<s>23). </s></p><p type="main">

<s>Quattordici anni prima, l&#039;idea, che fosse la pressione ammosferica la <lb></lb>vera causa adequata del sostenersi l&#039;acqua a una determinata altezza, den­<lb></lb>tro un sifone costruito, e accomodato con la speranza di poter travasare un <lb></lb>lago da una valle in un&#039;altra, attraverso al monte di separazione; era bale­<lb></lb>nata alla mente del Baliani, che pure non avrebbe nemmen egli, come si <lb></lb>disse del Torricelli, ricevuto il benefico raggio di quella luce, se gli errori <lb></lb>idrostatici, predominanti allora nella scuola a cui s&#039;era educato il Ricci, glie <lb></lb>ne avessero adombrate le pupille. </s>

<s>Dal passo, da noi trascritto a pag. </s>

<s>439 del <lb></lb>primo Tomo, apparisce chiaro che il Baliani professa premer l&#039;acqua, l&#039;aria <lb></lb>e ogni altro fluido, non solo secondo la natural direzione dei gravi, ma an-<pb xlink:href="020/01/3259.jpg" pagenum="220"></pb>che di sotto in su e per tutti i versi: ogni fluido inoltre pesare nel suo pro­<lb></lb>prio elemento a proporzion dell&#039;altezza: e così sicuramente affermando che, <lb></lb>se fosse il nostro corpo costituito nel vuoto, si sentirebbe oppresso da tutto <lb></lb>il soprastante peso dell&#039;ammosfera, mostrava di aver saputo bene scansare <lb></lb>la terza difficoltà del Ricci, e di esser così per sè medesimo persuaso della <lb></lb>verità, da non aver bisogno che venisse a insegnargliela il Torricelli. </s></p><p type="main">

<s>Le splendide rivelazioni del Filosofo genovese, in attribuire alla pres­<lb></lb>sione dell&#039;aria esterna il non potersi l&#039;acqua aspirata dalle trombe solle­<lb></lb>varsi più su che a un&#039;altezza determinata; rimasero oscurate da&#039;pregiudizi <lb></lb>di Galileo, per cui l&#039;opera stessa restauratrice del fondamento idrostatico ri­<lb></lb>mase pel Baliani di nessuna efficacia. </s>

<s>Piu fortunato il Torricelli, che seppe <lb></lb>resistere alla tentatrice autorità del Maestro, e sugli amici che gli stavano <lb></lb>intorno pigliare egli stesso più legittima autorità, da instituire in mezzo a <lb></lb>quei valorosi una scuola nuova, la quale, benchè fosse ristretta in così piccol <lb></lb>numero di persone, e s&#039;esercitasse in private scritture, e in familiari collo­<lb></lb>qui, non mancò di produrre i suoi benefici effetti. </s></p><p type="main">

<s>Il Magiotti, com&#039;aveva dato mano a confermare con l&#039;esperienza il fon­<lb></lb>damento idrodinamico proposto dal Torricelli; così concorse poi con altre <lb></lb>esperienze maravigliose a dimostrare la verità de&#039;principii idrostatici rifor­<lb></lb>mati. </s>

<s>Vedremo più qua l&#039;efficacia, che in affrettare i progressi della scienza <lb></lb>ebbero le geniali invenzioni di lui, ma, del Nardi, i documenti già riferiti <lb></lb>bastano a farlo riconoscere e annoverare tra&#039;primi e più benemeriti rifor­<lb></lb>matori dell&#039;Idrostatica galileiana. </s>

<s>Nella questione delle lamine galleggianti, <lb></lb>v&#039;aveva egli già sgombrati gli errori, e ridotta la cosa alla verità delle sue <lb></lb>ragioni, dicendo che l&#039;acqua, sostentatrice del solido, pesa quant&#039;esso solido <lb></lb>e l&#039;aria insieme, nè tal forza di sostentamento riconosce in altro, che in <lb></lb>quelle pressioni di sotto in su, fatte prima avvertire, e sperimentalmente di­<lb></lb>mostrate dal Torricelli. </s>

<s>La verità della qual dimostrazione parve poi inten­<lb></lb>desse il Nardi di salvare dalle obiezioni, osservando che quel premer del <lb></lb>liquido in direzion contraria a quella, che hanno tutti i corpi gravi, era per <lb></lb>una riflessione del moto, direttamente causato dalla stessa gravità naturale. <lb></lb><emph type="italics"></emph>Resta dunque sospesa la lamina perchè la forza, che preme l&#039;acqua, ri­<lb></lb>flettesi in sè medesima.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In mezzo a questo fervoroso rinnovamento d&#039;idee non è da credere si <lb></lb>rimanesse inoperoso quel Ricci, a cui erano venuti i primi consigli. </s>

<s>Il Tor­<lb></lb>ricelli sapeva bene qual&#039;ingegno avesse, benchè giovane, colui col quale ei <lb></lb>trattava, intanto che lo spendervi molte parole, per rispondere alle proposte <lb></lb>difficoltà, lo reputava tedio comune, persuaso com&#039;era che una semplice rifles­<lb></lb>sione sarebbe all&#039;amico bastata, perchè potesse per sè medesimo deliberarsi <lb></lb>la mente da tutti i dubbi. </s>

<s>Così infatti avvenne, e si fece agli altri maestro <lb></lb>di quelle verità, alle quali gli aveva fatto ripensare il Torricelli. </s></p><p type="main">

<s>Il Cornelio, nel dedicare allo stesso Ricci il suo VII proginnasma <emph type="italics"></emph>De <lb></lb>vita,<emph.end type="italics"></emph.end> gli diceva: “ Nam, quum ego Romam venissem vulgari quadam im­<lb></lb><gap></gap>utus literatura, tu me ad Geometriae ac Physiologiae studia acrius incita-<pb xlink:href="020/01/3260.jpg" pagenum="221"></pb>sti, facemque mihi ad optimarum artium notitiam praetulisti ” (Neapoli 1688, <lb></lb>pag. </s>

<s>263, 64). Fra queste ottime arti una delle principali fu l&#039;Idrostatica, la <lb></lb>quale, com&#039;ebbe il Cornelio imbevuta in Roma dal Ricci, così ei la riversò <lb></lb>nell&#039;epistola <emph type="italics"></emph>De circumpulsione<emph.end type="italics"></emph.end> stampata infin dal 1648 sotto il finto nome <lb></lb>di Timeo Locrese, e d&#039;onde veniva a rendersi di pubblica utilità un gran <lb></lb>tesoro nascosto. </s>

<s>I seguaci di Galileo avrebbero potuto di lì, per la prima volta, <lb></lb>imparare che tutte le particelle stanno dentro la massa liquida in equilibrio, <lb></lb>perchè “ vis illa, qua singulae feruntur deorsum, aequalis est virtuti, qua <lb></lb>aeedem resistunt ac sursum impelluntur ” <emph type="italics"></emph>(Progymnasmata cit. </s>

<s>Appendix,<emph.end type="italics"></emph.end><lb></lb>pag. </s>

<s>341). Contro gl&#039;incredibili paralogismi, co&#039;quali si studiava il loro Mae­<lb></lb>stro di dimostrar che il liquido, non solamente non preme le pareti, ma nem­<lb></lb>meno il fondo dei vasi; udivano que&#039;Discepoli annunziarsi la salutare verità <lb></lb>di quest&#039;altri insegnamenti: “ Quemadmodum vero pila plumbea per pla­<lb></lb>num inclinatum, vel per tubum in helicis formam revolutum, a summo ad <lb></lb>imum repens tantam denique acquirit velocitatem, quantam propemodum in­<lb></lb>depta fuisset, si per rectam perpendicularem expositae altitudini aequalem <lb></lb>descendisset; ita ferme aqua in vase contenta, non modo subiectum fundum <lb></lb>sed et latera quoque urgens, aperto foramine erumpit tanto impetu, quan­<lb></lb>tum postulare videtur eiusdem altitudo ” (ibid., pag. </s>

<s>342). D&#039;onde prende <lb></lb>il Cornelio occasione di divulgare il principio delle pressioni, che ugualmente <lb></lb>si trasmettono per tutti i versi, come conseguenza del fatto semplicissimo <lb></lb>dell&#039;acqua, che per ogni verso zampilla, secondo che nella sua lettera al <lb></lb>Ricci aveva fatto osservare il Torricelli: “ Ubi similiter observandum aquam <lb></lb>e foramine rumpentem, non iuxta unam tantum situs determinationem ferri, <lb></lb>sed susque deque, dextrorsum ac sinistrorsum, et quocumque tandem fora­<lb></lb>men vergat proruere ” (ibid., pag. </s>

<s>343). </s></p><p type="main">

<s>Uno de&#039;più dannosi insegnamenti di Galileo consisteva nel dire che, per <lb></lb>aggiungere acqua sopr&#039;acqua, non s&#039;accresce perciò l&#039;aggravamento sugli <lb></lb>strati inferiori, perchè nessun fluido è grave nel suo proprio elemento. </s>

<s>L&#039;espe­<lb></lb>rienza torricelliana descritta al Ricci, e illustrata dalla figura 117, era oppor­<lb></lb>tunissima a dimostrare quanto fosse falso l&#039;assunto peripatetico, vedendosi <lb></lb>di fatto che l&#039;acqua nel vaso tanto ha più forza di sostener col suo peso il <lb></lb>mercurio dentro il cannello EF, quanto è maggiore il numero degli strati, <lb></lb>che si sopraggiungono al primo. </s>

<s>Alla quale esperienza sostituiva il Corne­<lb></lb>lio, nella sua epistola, l&#039;altra della caraffella di vetro, colla bocca all&#039;in giù, <lb></lb>piena d&#039;aria, la quale esperienza nuova, mentre da una parte si porgeva più <lb></lb>facile di quella del Torricelli, e si mostrava più spettacolosa; essendo dal­<lb></lb>l&#039;altra ugualmente dimostrativa del premere sempre maggiormente l&#039;acqua <lb></lb>dentro l&#039;acqua <emph type="italics"></emph>quo illa fuerit altior,<emph.end type="italics"></emph.end> avrebbe potuto conferire, non meno effi­<lb></lb>cacemente della torricelliana, a dissipare gli errori dall&#039;Idrostatica, alquanti <lb></lb>anni prima degli Accademici del Cimento. </s></p><p type="main">

<s>Da ciò che s&#039;è detto si potrà facilmente argomentare all&#039;importanza del­<lb></lb>l&#039;epistola del Cornelio, per la quale si divulgava in Italia, intorno alle pres­<lb></lb>sioni idrostatiche, una scienza affatto nuova. </s>

<s>Nè senza ragione s&#039;appella que-<pb xlink:href="020/01/3261.jpg" pagenum="222"></pb>sta da noi col nome di scienza, essendo che dallo Stevino si supponesse, <lb></lb>piuttosto che dimostrare, come il liquido preme per tutti i versi: e se qual­<lb></lb>che dimostrazione ei ne dà, non è che indiretta o sperimentale. </s>

<s>Il Nostro <lb></lb>invece la concludeva dai principii della Meccanica, e, riguardata la massa <lb></lb>fluida come compilata di filetti infiniti, comunque andanti o a diritto o fles­<lb></lb>suosi o perpendicolari o obliqui, riduceva la ragion del premere contro sè <lb></lb>stessi, e contro le pareti e il fondo de&#039;vasi, a quella de&#039;momenti de&#039;gravi <lb></lb>cadenti sopra varie inclinazioni di piani. </s>

<s>Vedremo come si svolgessero que­<lb></lb>sti concetti ordinati in un trattatello che, se fosse stato pubblicamente noto, <lb></lb>dava alla Scienza italiana la prima matematica dimostrazione delle pressioni <lb></lb>idrostatiche. </s>

<s>Ma mentre si rimaneva tuttavia nel campo della Fisica, veniva <lb></lb>a frugare gl&#039;ingegni una gran curiosità di sapere per quale intima causa, <lb></lb>in diffondersi per tutta intera la massa i moti, incominciati in qualunque <lb></lb>punto di lei, si differenzino così notabilmente i liquidi dai solidi. </s>

<s>La questione <lb></lb>si proponeva fra gli amici del Torricelli, e ora si vogliono da noi narrar le <lb></lb>occasioni, e dire i modi come fu risoluta. </s></p><p type="main">

<s>Ne&#039;primi tempi dell&#039;Accademia medicea il Torricelli stesso, dietro il <lb></lb>principio della rarefazione e della condensazione de&#039;corpi, secondo il crescere <lb></lb>e il diminuire della temperatura; aveva, per dar gusto al Granduca, inven­<lb></lb>tato il giochetto di una bolla di vetro, con un piccolo foro così, che immersa <lb></lb>standosi appena in fondo al vaso, bastasse aggiungervi un po&#039;d&#039;acqua tie­<lb></lb>pida, per veder quella stessa bolla salire a galla, e poi di nuovo scendere, <lb></lb>essendosi il liquido raffreddato. </s>

<s>Per render poi lo spettacolo anche più gio­<lb></lb>condo, aveva insieme con quella detta immersa un&#039;altra simile bolla, tutta <lb></lb>chiusa però e aggiustata in modo che galleggiasse, ma che riscaldandosi <lb></lb>l&#039;acqua scendesse, mentre risaliva l&#039;altra, che riposava in fondo, e raffred­<lb></lb>dandosi facessero i due mobili effetto contrario. </s>

<s>L&#039;invenzione deve esser occorsa <lb></lb>ne&#039;primi mesi del 1646, giacchè il di 7 novembre di quell&#039;anno, trovandosi <lb></lb>il Moncony in Firenze, ed essendo andato a far visita al Torricelli, narra <lb></lb>avergli sentito dire “ que le Gran Duc avoit divers Thermometres pour con­<lb></lb>noìtre le chaud et le froid, tout avec l&#039;eau de vie, et des boules de verre <lb></lb>pleines d&#039;air, mais une ou sont deux boules, l&#039;une en haut, l&#039;autre en bas. </s>

<s><lb></lb>Quand&#039;il fait chaud celle d&#039;en bas monte, et quand il fait froid celle d&#039;en <lb></lb>haut decend ” <emph type="italics"></emph>(Voyages,<emph.end type="italics"></emph.end> P. I, a Paris 1695, pag. </s>

<s>261). </s></p><p type="main">

<s>Gli strumenti, fatti costruire con eleganza, gli riteneva appresso di sè <lb></lb>il Granduca, e se ne serviva per divertire i curiosi che capitavano in palazzo, <lb></lb>e per tentare i dotti, ai quali proponeva di scoprire l&#039;occulta causa di que­<lb></lb>gli effetti. </s>

<s>Nè fra que&#039;dotti erano solamente i cortigiani fiorentini, ma quanti <lb></lb>si trovassero allora da per tutto cultori di questi studi più noti. </s>

<s>Narra il <lb></lb>gesuita Gaspero Scott che il problema fu mandato dal Granduca a Roma <lb></lb>“ ad celeberrimum sibique notissimum virum p. </s>

<s>Athanasium Kircherium, si­<lb></lb>mulque ad excellentissimum mathematicum Raphaelem Magiottum, ut utrius­<lb></lb>que de eo iudicium exquireret. </s>

<s>Nodum solvit uterque felicissime ” <emph type="italics"></emph>(Mecha­<lb></lb>nica hydraulica-pneumatica,<emph.end type="italics"></emph.end> Herbipoli 1657, pag. </s>

<s>292). </s></p><pb xlink:href="020/01/3262.jpg" pagenum="223"></pb><p type="main">

<s>Ma l&#039;aveva risoluto un anno prima, e non meno felicemente, il Cornelio, <lb></lb>il quale, nella citata epistola <emph type="italics"></emph>De circumpulsione,<emph.end type="italics"></emph.end> che ha la data del primo <lb></lb>di Giugno 1648, così scriveva: “ Jam volvitur alter annus ex quo Ludovi­<lb></lb>cus Casalius vir, ut nosti, non minus genere clarus, quam disciplinarum or­<lb></lb>namentis conspicuus, nunciavit mihi inventum fuisse Florentiae experimen­<lb></lb>tum huiusmodi. </s>

<s>Duo globuli vitrei, in cyatum aquae plenum immissi, sic <lb></lb>alternatim movebantur, ut, quum aqua frigidior esset, alter fundum peteret, <lb></lb>reliquo supernatante, et mox, adiecta aqua calida, ille e fundo adsurgeret, <lb></lb>atque hic e summa aquae superficie pessum iret ” <emph type="italics"></emph>(Progymnasm. </s>

<s>Appen­<lb></lb>dix<emph.end type="italics"></emph.end> cit., pag. </s>

<s>359). E soggiunge che, sebben rimanesse a sentir questa nuova <lb></lb>perplesso, e l&#039;inventore ne tacesse la struttura dell&#039;artificio, nonostante, ri­<lb></lb>ducendosi alla ragion fisica de&#039;condensamenti e delle rarefazioni, prodotte <lb></lb>dalle varie temperature ne&#039;corpi, gli venne fatto finalmente di scoprire <lb></lb>l&#039;arcano. </s></p><p type="main">

<s>“ Sed quum (così il Cornelio stesso prosegue il suo racconto) in eius­<lb></lb>modi ludicris inventis occuparemur, rumor ad aures nostras perfertur ver­<lb></lb>sari in manibus viri cuiusdam ingeniosi admirabile artificium, nempe vitreum <lb></lb>tubum aquae plenum, in quo plures orbiculi vitrei sursum deorsumque fere­<lb></lb>bantur ad nutum eius, qui tubi ostium digito obturabat ” (ibid., pag. </s>

<s>360, 61). <lb></lb>Quell&#039;uomo ingegnoso era Raffaello Magiotti, e noi dobbiamo ora dire in che <lb></lb>consistesse il maraviglioso artifizio, ch&#039;egli aveva per le mani. </s></p><p type="main">

<s>Era stato da lui felicemente, come diceva lo Scott, risoluto il problema <lb></lb>inviatogli da Firenze, ma, nel capovolgere il bocciolo, per osservare il con­<lb></lb>trario moto delle palline di vetro, o delle lumachelle, com&#039;ei le chiama, tu­<lb></lb>rando con la polpa del pollice, perchè non si versasse l&#039;acqua, la bocca al <lb></lb>vaso; ebbe con sua grande maraviglia a notare che i due corpiccioli im­<lb></lb>mersi, indipendentemente da ogni variazione di temperatura, si movevano <lb></lb>più o meno veloci secondo la maggiore o minor forza, con cui si veniva a <lb></lb>stringere il dito otturatore. </s>

<s>Certo com&#039;egli era che il liquido premuto ripreme <lb></lb>per tutti i versi, non ebbe difficolità a intender che l&#039;aria dentro la luma­<lb></lb>chella poteva esservi più o men costipata dalla maggiore o minor pressione <lb></lb>partecipatagli dal dito, e così produrre i medesimi effetti del calore e del <lb></lb>freddo. </s>

<s>Ma ciò che lo sorprese fu la trasmissione istantanea di que&#039;moti. </s>

<s><lb></lb>Ne&#039;fluidi aerosi, pensava, e anche ne&#039;corpi duri, non è così, perchè la per­<lb></lb>cossa per esempio del martello si comunica a tutto il cuneo con tempo, ciò <lb></lb>che dipendendo dal subire il legno o il ferro nel colpo qualche compressione <lb></lb>o rientramento in sè stesso, ne concludeva che dunque l&#039;acqua si mostrava <lb></lb>renitente a essere in qualunque modo compressa. </s>

<s>E in questa dimostrata <lb></lb>incompressibilità, per cui s&#039;intendeva come, premuto il liquido in una sua <lb></lb>parte qualunque, si trasmettesse ugualmente la forza per ogni verso, faceva <lb></lb>il Magiotti consistere il merito della sua invenzione. </s></p><p type="main">

<s>Si risolveva dunque un&#039;altissima questione della Scienza, mentre pa­<lb></lb>reva non s&#039;attendesse ad altro, che a scoprire l&#039;artifizio di un gioco, il quale, <lb></lb>essendo gustato dai più, fu portato attorno sull&#039;ali della fama, mentre il <pb xlink:href="020/01/3263.jpg" pagenum="224"></pb>Magiotti stesso pensava di scriverne ordinatamente, e di pubblicarne la no­<lb></lb>tizia. </s>

<s>Fu in questo tempo che pervenne la cosa all&#039;orecchio del Cornelio, il <lb></lb>quale ebbe a ritrovare facilmente da sè la fisica ragione del fatto. </s>

<s>Gli venne <lb></lb>anzi allora in mente che, essendo l&#039;acqua più o men premuta, secondo la <lb></lb>maggiore o minore altezza dell&#039;altr&#039;acqua che a lei sta sopra, si potevano <lb></lb>produrre i medesimi giocosi moti, a solo inclinare più o meno il bocciolo, <lb></lb>ridotto alla strettezza di un lungo tubo ritorto, “ nam ex inclinatione ipsius <lb></lb>tubi aquae altitudo decrescit, ac proinde eiusdem conatus fit minor ” (ibid., <lb></lb>pag. </s>

<s>363). </s></p><p type="main">

<s>Benchè il Cornelio non nomini espressamente l&#039;Autore, pure ei ricono­<lb></lb>sce il fatto come invenzione altrui. </s>

<s>Ma non mancarono alcuni, che se l&#039;at­<lb></lb>tribuirono, e ciò fece risolvere il Magiotti a stampare in fretta quel suo <lb></lb>primo discorso, rozzo, com&#039;ei lo chiama, e imperfetto, col quale aveva poche <lb></lb>settimane prima accompagnato al Granduca lo strumento. </s>

<s>Quel discorso por­<lb></lb>tava il titolo di <emph type="italics"></emph>Renitenza certissima dell&#039;acqua alla compressione,<emph.end type="italics"></emph.end> sotto­<lb></lb>scritto, con la data da Roma, il di 26 Luglio 1648, e dedicato al principe <lb></lb>don Lorenzo de&#039;Medici. </s>

<s>Essendo poi divenuto l&#039;opuscolo rarissimo, il Tar­<lb></lb>gioni lo inserì da pag. </s>

<s>182-91 nel secondo tomo delle sue <emph type="italics"></emph>Notizie.<emph.end type="italics"></emph.end> Si può <lb></lb>di qui raccogliere ciò che più importa al nostro argomento. </s>

<s>Incomincia a <lb></lb>dire il Magiotti che gli fu il problema inviato da Firenze nel 1648, verso la <lb></lb>fine di Giugno, e seguita a narrare in che modo gli venisse risoluto. </s>

<s>Poi sog­<lb></lb>giunge: “ L&#039;invenzione mia non consiste nel caldo e nel freddo, ma nella <lb></lb>renitenza alla compressione. </s>

<s>” </s></p><p type="main">

<s>“ Sia un cannello o cilindro AB (fig. </s>

<s>118), aperto da una delle basi, <lb></lb>come in A, e pieno o quasi pieno d&#039;acqua comune, o d&#039;ogni altro liquore, <lb></lb><figure id="id.020.01.3263.1.jpg" xlink:href="020/01/3263/1.jpg"></figure></s></p><p type="caption">

<s>Figura 118.<lb></lb>dove una caraffina C aperta in D, con difficoltà (ben s&#039;aggiusta con <lb></lb>filo di ottone o piombo) vi galleggi. </s>

<s>Questa, chiudendosi il cilindro <lb></lb>AB con il dito grosso o polpa della mano, scenderà più o meno <lb></lb>veloce, secondo la maggiore o minor compressione, che fa la mano <lb></lb>in chiudere il cilindro, e quanto più s&#039;allenterà la compressione, <lb></lb>o s&#039;aprirà il cilindro, tanto più presto tornerà a galleggiare. </s>

<s>Ciò <lb></lb>avviene, dato che il cilindro sia pieno, perchè l&#039;acqua, che non <lb></lb>ammette compressione, farà forza all&#039;aria della caraffina, salendo <lb></lb>per il collo di lei, come ben si vede, quando le caraffine son tra­<lb></lb>sparenti. </s>

<s>Dunque la caraffina sarà più grave in specie, per l&#039;acqua <lb></lb>che v&#039;è salita, e per l&#039;aria che s&#039;è condensata, e così discenderà. </s>

<s>Ma, nel <lb></lb>caso che sopra l&#039;acqua sia l&#039;aria, questa compressa dalla mano farà qualche <lb></lb>forza all&#039;acqua, e l&#039;acqua all&#039;aria della caraffina. </s>

<s>E finalmente, allentandosi <lb></lb>sempre più la compressione, sempre più scema quella forza, che si faceva <lb></lb>all&#039;aria della caraffina, ed ella sempre più respirando, e sputando l&#039;acqua, <lb></lb>si riduce in una costituzione da poter galleggiare ” (pag. </s>

<s>187). </s></p><p type="main">

<s>Il trasmettersi le pressioni per tutti i versi ugualmente, e in ogni punto <lb></lb>della massa liquida, come si mostra dal fatto delle caraffine, che scendono <lb></lb>e salgono in qualunque luogo sian poste; era dunque per il Magiotti un <pb xlink:href="020/01/3264.jpg" pagenum="225"></pb>effetto dimostrativo della renitenza alla compressione, nella quale riconoscendo <lb></lb>una delle più essenziali proprietà che differenziano i liquidi dai solidi, si di­<lb></lb>chiarava così intorno a ciò, che era la parte seria della sua invenzione: “ Noto <lb></lb>che, siccome un ferro o legno mosso da noi, si muove tutto, benchè lun­<lb></lb>ghissimo, nel medesimo istante; così dal dito o polpa della mano s&#039;imprime <lb></lb>nel medesimo istante la virtù in tutta l&#039;acqua del cilindro, sia pur lungo e <lb></lb>largo quanto un pozzo, e siano pur alte o basse le figurine come si vuole. </s>

<s>” </s></p><p type="main">

<s>“ La similitudine del ferro e dell&#039;acqua, circa l&#039;operazione istantanea, <lb></lb>corre benissimo, sebbene per movere il ferro ci vuol tanta forza, che superi <lb></lb>il peso di lui, ma nell&#039;acqua, fuor che quella particolar diligenza e forza nel <lb></lb>serrare il cilindro, non ci vuol altro che un minimo tratto e momento ba­<lb></lb>stante a sollevar quella pochissima acqua, che sale per le caraffine. </s>

<s>Adun­<lb></lb>que una forza minima imprime la virtù in tutta l&#039;acqua del cilindro, o d&#039;un <lb></lb>pozzo, sebben fosse lungo fino al centro della Terra. </s>

<s>E questa è una diffe­<lb></lb>renza tra i liquidi e i solidi molto notabile. </s>

<s>Or ecco un&#039;altra differenza si­<lb></lb>mile. </s>

<s>Se con un martello io percotessi quel ferro, o altro solido, la virtù <lb></lb>della percossa, sebbene infinita, con tempo si comunicherebbe a tutto il ferro, <lb></lb>mentre la vibrazione e frequenza ricerca e muove tutte le parti di lui: dove <lb></lb>quella minima forza del dito imprime nel medesimo istante la virtù a tutta <lb></lb>l&#039;acqua del cilindro, sebben fosse grande quanto sopra ” (pag. </s>

<s>189). </s></p><p type="main">

<s>A tal punto era, per i validi impulsi del Torricelli, stata promossa in <lb></lb>Italia, infin dal 1648, la Scienza idrostatica delle pressioni, ond&#039;ei non par­<lb></lb>rebbe credibile che nel 1663, quando il Michelini era in sul rivedere il ma­<lb></lb>noscritto del suo trattato Della direzione de&#039;fiumi, lasciasse correre la pro­<lb></lb>posizione, in cui pretendeva di dimostrare che l&#039;acqua o non preme affatto <lb></lb>o assai poco le sponde dei vasi, e che potesse aver del suo errore difensori <lb></lb>il Borelli e il Viviani. </s>

<s>Ma si spiega il fatto, osservando che rimase il filo <lb></lb>delle tradizioni torricelliane sventuratamente reciso nelle mani de&#039;cultori di <lb></lb>questa scienza, eccettuati que&#039;pochissimi che di Roma si fecero del Miche­<lb></lb>lini stesso liberi censori. </s>

<s>Le parole del Cornelio, nella sua epistola <emph type="italics"></emph>De cir­<lb></lb>cumpulsione,<emph.end type="italics"></emph.end> parvero scritte sopra foglie trasportate dal vento, per le ragioni <lb></lb>altrove narrate, ma principalmente perchè i documenti originali, che pote­<lb></lb>vano dare autorità a quelle nuove dottrine, cioè le lettere del Torricelli, ri­<lb></lb>masero nelle mani del Ricci infino al 1658, e non si fecero pubblicamente <lb></lb>note che nel 1663, nella Lettera ai Filaleti. </s></p><p type="main">

<s>Il Discorso poi del Magiotti si può dir che morisse appena nato. </s>

<s>La me­<lb></lb>moria di lui non era solamente spenta ai tempi del Targioni, ma molti anni <lb></lb>prima. </s>

<s>Nella stessa Accademia del Cimento, in un congresso, tenutovi cer­<lb></lb>tamente dopo il 1660, i problemi inviati dal Granduca Ferdinando II al Ma­<lb></lb>giotti, e al Kircher, dodici anni prima, si proponevano a risolvere come cosa <lb></lb>nuova. </s>

<s>“ Dopo scritto, così leggesi in un foglio del Viviani, mi è sovvenuto <lb></lb>un modo di risolvere un altro problema, che nel medesimo congresso d&#039;ieri <lb></lb>fu messo in campo, ed è come si possa far due corpi, come due pescetti di <lb></lb>vetro, che stando nell&#039;istesso tempo uno di loro a galla in un&#039;acqua, e l&#039;al-<pb xlink:href="020/01/3265.jpg" pagenum="226"></pb>tro in fondo nella medesima, ad un&#039;istessa mutazione che faccia nell&#039;acqua <lb></lb>di più calore, quello che è galleggiante se ne vada in fondo, e nello stesso <lb></lb>momento quello che è in fondo ne venga a galla. </s>

<s>E tornando a raffreddar <lb></lb>l&#039;acqua, quello di fondo torni a galla e l&#039;altro ne vada in fondo, onde la <lb></lb>medesima causa, nel medesimo tempo, partorisca contrari modi ” (MSS. <lb></lb>Cim., T. X, fol. </s>

<s>102). </s></p><p type="main">

<s>Così dunque certi essendo che del principio dell&#039;uguaglianza delle pres­<lb></lb>sioni, professato dal Torricelli e sperimentalmente dimostrato dal Magiotti, <lb></lb>ne fu perduta fra noi per qualche tempo ogni scienza, convien narrare in <lb></lb>che modo si venisse a recuperarla. </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Nell&#039;anno 1663, in cui si pubblicarono in Firenze le Lettere torricel­<lb></lb>liane al Ricci, usciva alla luce in Parigi il trattato del Pascal <emph type="italics"></emph>De l&#039;equilibre <lb></lb>des liqueurs,<emph.end type="italics"></emph.end> che dalle carte postume dell&#039;Autore diligentemente raccolsero <lb></lb>gli amici e gli ammiratori. </s>

<s>A ripensar che, sebben fosse pari de&#039;due uomini <lb></lb>la celebrità del nome, l&#039;uno nulladimeno gettava incidentalmente il seme <lb></lb>de&#039;suoi pensieri, che l&#039;altro svolgeva di proposito ordinatemente in un libro; <lb></lb>non fa maraviglia che una fama oramai universale abbia attribuito la scienza <lb></lb>del principio fondamentale idrostatico al Francese, piuttosto che al Nostro. </s>

<s><lb></lb>Fa però maraviglia che quella fama non sia stata, in più di due secoli e <lb></lb>mezzo, contradetta da chi, più attentamente leggendo, si sarebbe dovuto ac­<lb></lb>corgere che il Pascal non istituiva propriamente quella scienza idrostatica, <lb></lb>ma la supponeva, senza presumer forse di averci dato altr&#039;opera, o attri­<lb></lb>buirsi altro merito, che di averla esplicata, e confermata con qualche espe­<lb></lb>rienza. </s>

<s>La proposta deve ai nostri lettori apparir nuova, e perciò passeremo <lb></lb>senza indugio all&#039;esame di que&#039;fatti, che ce la mostrino vera. </s></p><p type="main">

<s>Descritti nel capitolo primo vari esempi di paradossi idrostatici, viene <lb></lb>il Pascal nel secondo a dire in qual modo potrebbero spiegarsi, assumendo <lb></lb>per principio della dimostrazione quel singolare fatto meccanico, che poi dette <lb></lb>così facilmente in mano al Bramah quel suo torchio nuovo. </s>

<s>È passato per <lb></lb>la mente a qualcuno che l&#039;idea di far equilibrare due stantuffi, in due corpi <lb></lb>di tromba comunicanti, benchè di diametro molto diverso, potesse esser sug­<lb></lb>gerita al Pascal da quella epistola al Capra, nella quale il Benedetti faceva <lb></lb>i primi generosi sforzi, per dimostrar come la molta acqua del mortaio possa <lb></lb>essere così facilmente sostenuta dalla poca della fistola annessa. </s>

<s>Le precise <lb></lb>parole che usa l&#039;Autore, dop&#039;aver divertito il discorso in provare, a quel <lb></lb>modo insufficiente che si riferì, come sia premuto il fondo del vaso, non in <lb></lb>ragione della quantità del liquido, ma dell&#039;altezza di lui perpendicolare; le <lb></lb>precise parole, scritte nella citata epistola, son queste: </s></p><pb xlink:href="020/01/3266.jpg" pagenum="227"></pb><p type="main">

<s>“ Sed redeundo ad vasa AU et F (fig. </s>

<s>119) dico quod, sicut aqua F <lb></lb>sufficit ad resistendum aquae AU; ita quodlibet aliud pondus aequale F, <lb></lb><figure id="id.020.01.3266.1.jpg" xlink:href="020/01/3266/1.jpg"></figure></s></p><p type="caption">

<s>Figura 119.<lb></lb>cuiusvis materiae, in fistula F positum, sufficiens erit, dum­<lb></lb>modo illud corpus ita sit adaequatum concavitati fistulae F, <lb></lb>quod non permittat transitum aliquem aquae vel aeris inter <lb></lb>convexum ipsius corporis et, devexum fistulae F, et hoc ex <lb></lb>se satis patet. </s>

<s>Sed in vasa AU, cum ex hypothesi latius sit <lb></lb>ipso F, nullum aliud corpus sufficiens erit ad resistendum <lb></lb>aquae ipsius F, quin tam grave sit quam tota aqua AU, exi­<lb></lb>stente AU tam alto quam F. Unde, si aqua ipsius F nil plus esset quam una <lb></lb>tantummodo libra, et vas AU existeret latius ipso F in decupla proportione; <lb></lb>tunc in ipso AU oporteret corpus adaequatum ipsi concavitati ponere, cuius <lb></lb>pondus esset decem librarum, ut sufficeret ad sustinendum aquam ipsius F: <lb></lb>et ad impellendum ipsam aquam F deberet esse plus quam decem librarum. </s>

<s><lb></lb>Ponamus nunc illud corpus ita densius esse aqua, ut maius intervallum non <lb></lb>occupet quam OE: corpus igitur OE sufficiens erit ad impellendum aquam <lb></lb>F, et non eo minus ” <emph type="italics"></emph>(Speculationum liber,<emph.end type="italics"></emph.end> Venetiis 1599, pag. </s>

<s>288). </s></p><p type="main">

<s>Secondo questa descrizione si potrebbe vedere in qualche modo rappre­<lb></lb>sentato, nello zaffo OE, uno degli stantuffi della macchina del Pascal, ma <lb></lb>non v&#039;è ben definito il peso dell&#039;altro stantuffo nella fistola F, e, quel che <lb></lb>più importa, non vi si tien conto dell&#039;acqua di comunicazion fra&#039;due solidi, <lb></lb>per cui, se questo scende, quello necessariamente è costretto a salire. </s>

<s>Il Be­<lb></lb>nedetti propone piuttosto un solido che, posto dentro il mortaio, sostiene <lb></lb>colla sua gravità propria la gravità dell&#039;acqua nella fistola aggiunta, purchè <lb></lb>sia esso solido tale, da adeguare la concavità che lo riceve, e da ciò ne con­<lb></lb>clude che dieci libbre da una parte possono pareggiare una libbra sola dal­<lb></lb>l&#039;altra. </s>

<s>Ma se la conclusione scenda dai legittimi principii professati dal Pascal, <lb></lb>e se possa essere sostanzialmente qualche somiglianza, o qualche punto di <lb></lb>riscontro, fra le due speculazioni; sel vedranno da sè i nostri giudiziosi <lb></lb>Lettori. </s></p><p type="main">

<s>Comunque sia, la scintilla, che doveva accender la face, la trasse il <lb></lb>Pascal da selce, per dir così, più domestica, e a quel nobile uso assai me­<lb></lb>glio disposta. </s>

<s>Il Magiotti, dop&#039;aver detto, ne&#039;principii del suo Discorso, che <lb></lb>aveva mostrata l&#039;operazione del suo strumento a molti virtuosi di Roma, e <lb></lb><figure id="id.020.01.3266.2.jpg" xlink:href="020/01/3266/2.jpg"></figure></s></p><p type="caption">

<s>Figura 120.<lb></lb>fra questi principalmente a que&#039;due pellegrini ingegni <lb></lb>di Michelangiolo Ricci e di Antonio Nardi; “ di più, <lb></lb>soggiunge, lo inviai in Francia, ed altre parti, a diversi <lb></lb>amici virtuosi come s&#039;usa. </s>

<s>Oggi mi viene accennato <lb></lb>che altri, con aggiungere o variare qualche cosa, vor­<lb></lb>rebbe farsene bello ” (Appresso il Targioni cit., pag. </s>

<s>183) <lb></lb>Quell&#039;aggiunta consisteva in uno stantuffo, fatto pas­<lb></lb>sare per la bocca A del vaso (fig. </s>

<s>120), ed essendo <lb></lb>esso stantuffo munito di un&#039;asticciola, con un botton­<lb></lb>cino in capo, si premeva più comodamente con questo il liquido sottoposto, <pb xlink:href="020/01/3267.jpg" pagenum="228"></pb>che con la polpa del dito, o con la palma della mano. </s>

<s>La variazione poi, che <lb></lb>si fece in Francia all&#039;invenzione del Magiotti, si riduceva a trasformare il <lb></lb>corpo della caraffina nella figura di un diavoletto, e il sottil collo di lei nella <lb></lb>lunga coda, con che il piccolo Minosse s&#039;avvinghia. </s>

<s>Non giovarono nulladi­<lb></lb>meno le parole del Nostro, per rivendicarsi e assicurarsi la proprietà dell&#039;in­<lb></lb>venzione, della quale oramai si era fatto bello il Cartesio. </s></p><p type="main">

<s>Così diffusasi tra i Francesi la notizia dello strumento, il Mersenno, nel <lb></lb>ritornare fra&#039;suoi, dop&#039;esser venuto a fiutar per tutto in Firenze e in Roma, <lb></lb>e a perquisire il Ricci, depositario della scienza del Torricelli e del Magiotti; <lb></lb>ne riferiva forse più particolarmente le ragioni idrostatiche, che in Italia si <lb></lb>davano di que&#039;giochi. </s>

<s>Fatto sta che, quando il Pascal rivolse il suo studio <lb></lb>all&#039;equilibrio de&#039;liquidi, era in Francia notissimo a tutti che la pressione, <lb></lb>fatta dallo stantuffo A (nella medesima figura 120) sopra l&#039;acqua che tocca, <lb></lb>si trasmette istantaneamente in tutta la massa, e si diffonde per ogni verso, <lb></lb>qualunque siasi l&#039;ampiezza e la figura del vaso. </s>

<s>Cosicchè, proseguiva il Pascal <lb></lb>a ragionare, se al cilindro AB ne fosse congiunto un altro CD, quanto si <lb></lb>voglia più ampio, si dovrebbe la pressione, esercitata dallo stantuffo A sopra <lb></lb>la superficie liquida EF, far risentire alla superficie GH, con tal impeto di <lb></lb>leva all&#039;in su, la misura del quale, forse dal Benedetti, ma più ragionevol­<lb></lb>mente dall&#039;esperienza, gli fu mostrata nel peso di un altro stantuffo C, della <lb></lb>medesima materia, di pari altezza, e <emph type="italics"></emph>adeguato alla concavità della fistola.<emph.end type="italics"></emph.end><lb></lb>Così, mentre sperava d&#039;aver trovata la via di spiegare un paradosso, si vide <lb></lb>il Pascal comparire innanzi la faccia mostruosa di un altro paradosso, qual&#039;era <lb></lb>che lo stantuffo C, del peso di cento libbre, non faceva all&#039;in giù maggiore <lb></lb>sforzo dello stantuffo A, di una libbra sola. </s>

<s>Ma poi, ripensando esser que­<lb></lb>sto il paradosso volgare offertoci dalla stadera, sospettò che avvenisse qui <lb></lb>quello, che in tutte le altre macchine, di che non penò molto a confermarsi <lb></lb>nel vero, osservando che, se lo stantuffo C è cento volte più peso, anche si <lb></lb>moverebbe cento volte più tardo. </s>

<s>Della semplice dimostrazion di ciò, con­<lb></lb>dotta dal principio delle velocità virtuali, se ne sarebbe potuto passare, aven­<lb></lb>dola già data magistralmente il nostro Galileo, ma s&#039;introduceva nella que­<lb></lb>stione un elemento nuovo, quello cioè della trasfusion delle forze, regolate <lb></lb>dalla legge che le velocità sempre son reciproche delle grandezze mosse. </s>

<s><lb></lb>Ond&#039;è che il moto impresso dallo stantuffo nella superficie E, trasfondendosi <lb></lb>nella superficie GH cento volte più grande, vi si riduce a velocità cento volte <lb></lb>minore. </s></p><p type="main">

<s>Da ciò ne concludeva il Pascal la ragione dell&#039;equilibrio idrostatico nei <lb></lb>due vasi, perchè l&#039;acqua è premuta ugualmente sotto i due stantuffi. </s>

<s>“ On <lb></lb>peut encore ajouter, pour plus grand eclaireissement, que l&#039;eau est egalement <lb></lb>pressée sous ces deux pistons. </s>

<s>Car, si l&#039;un a cent fois plus de poids que <lb></lb>l&#039;autre, aussi en revanche il touche cent fois plus de parties: et ainsi cha­<lb></lb>cune l&#039;est egalement. </s>

<s>Donc toutes doivent estre en repos, parce qu&#039;il n&#039;y à <lb></lb>pas plus de raison pourquoy l&#039;une cede que l&#039;autre ” <emph type="italics"></emph>(Traité<emph.end type="italics"></emph.end> cit., pag. </s>

<s>8). </s></p><p type="main">

<s>Qui pare che s&#039;ammetta l&#039;uguaglianza della pressione sotto le due varie <pb xlink:href="020/01/3268.jpg" pagenum="229"></pb>ampiezze di superficie, ma seguitando a leggere si trova stabilito per regola <lb></lb>certa che la parete di un vaso pieno di liquido soffre più o meno, a pro­<lb></lb>porzione della sua grandezza. </s>

<s>“ Si un vaisseau plein d&#039;eau n&#039;a qu&#039;une seule <lb></lb>ouverture large d&#039;un poulce, par exemple, ou l&#039;on mette un piston chargé <lb></lb>d&#039;un poids d&#039;une livre, ce poids fait effort contre toutes les parties du vais­<lb></lb>seau generalement, a cause de la continuité et de la fluidité de l&#039;eau. </s>

<s>Mais <lb></lb>pour determiner combien chaque partie souffre, en voicy la regle: Chaque <lb></lb>partie large d&#039;un poulce, comme l&#039;ouverture, souffre autant que si elle estoit <lb></lb>poussée par le poids d&#039;une livre (sans compter le poids de l&#039;eau, dont je ne <lb></lb>parle pas icy, car je ne parle que du poids du piston) parce que le poids <lb></lb>d&#039;une livre presse le piston qui est a l&#039;ouverture, et chaque portion du vais­<lb></lb>seau, plus ou moins grande, souffre precisement plus ou moins a proportion <lb></lb>de la grandeur ” (ivi, pag. </s>

<s>8, 9). </s></p><p type="main">

<s>La contradizione forse dipende dal confondersi, nel medesimo nome di <lb></lb>pressione, la <emph type="italics"></emph>potenza<emph.end type="italics"></emph.end> e la <emph type="italics"></emph>resistenza<emph.end type="italics"></emph.end> della macchina. </s>

<s>Se il peso A è la po­<lb></lb>tenza, il contrapposto a lei peso C sarà la resistenza, la quale è propria­<lb></lb>mente proporzionale alla superficie, ma i due momenti di qua e di là, in <lb></lb>ogni modo, rimangono uguali, per cui riesce una lusinghiera promessa quella <lb></lb>del Pascal, che cioè un vaso pien d&#039;acqua sia <emph type="italics"></emph>une machine nouvelle, pour <lb></lb>multiplier les forces a tel degré qu&#039;on vaudra<emph.end type="italics"></emph.end> (pag. </s>

<s>6, 7). Galileo aveva <lb></lb>saviamente avvertiti di questa vana presunzione i meccanici de&#039;suoi tempi, <lb></lb>e forse l&#039;acuto Francese si lasciava andar a un&#039;espression popolare, ma non <lb></lb>par che con la poca precision del linguaggio si possa scusar d&#039;errore il dire <lb></lb>che in tutte le macchine <emph type="italics"></emph>le chemin est augmenté en mesme proportion que <lb></lb>la force<emph.end type="italics"></emph.end> (pag. </s>

<s>7) e il formular poco appresso la legge <emph type="italics"></emph>que le chemin est <lb></lb>au chemin comme la force a la force.<emph.end type="italics"></emph.end> Che se poi dice esser la medesima <lb></lb>cosa tanto a far fare un pollice di cammino a cento libbre d&#039;acqua, quanto <lb></lb>a far fare cento pollici a una libbra, e ciò che fa fare è la forza; dunque <lb></lb>la forza non sta alla forza nella ragion semplice degli spazi, ma nella com­<lb></lb>posta di loro, e de&#039;pesi. </s></p><p type="main">

<s>Comunque sia, la novella macchina non era destinata dal Pascal ad <lb></lb>alzar pesi, ma a spiegare i paradossi idrostatici, i vari esempi offerti dai <lb></lb><figure id="id.020.01.3268.1.jpg" xlink:href="020/01/3268/1.jpg"></figure></s></p><p type="caption">

<s>Figura 121.<lb></lb>quali vi riducono alle pressioni, fatte nei vasi delle <lb></lb>figure 121 e 122. Supponiamo che il velo d&#039;acqua <lb></lb>AB (l&#039;<emph type="italics"></emph>ouverture<emph.end type="italics"></emph.end> insomma del <lb></lb>Pascal) riceva tale impeto da <lb></lb>moversi per lo spazio AC, in <lb></lb>un dato tempo: questo stesso <lb></lb>impeto, comunicato al velo in­<lb></lb>fimo EF, lo farebbe movere, <lb></lb>in quel medesimo tempo, per <lb></lb><figure id="id.020.01.3268.2.jpg" xlink:href="020/01/3268/2.jpg"></figure></s></p><p type="caption">

<s>Figura 122.<lb></lb>tale spazio EG, che ad AC avesse la ragion reciproca <lb></lb>della grandezza AB alla EF, in modo cioè che, prese <lb></lb>LM, LN uguali alle EF, EG, dovessero aversi l&#039;equa-<pb xlink:href="020/01/3269.jpg" pagenum="230"></pb>zioni AB.AC=EF.EG=LM.LN. </s>

<s>Dunque se il velo AB e il velo LM, <lb></lb>movendosi questo per lo spazio LN, mentre quello si muove per lo spazio AC, <lb></lb>fanno la medesima forza; il fondo EF del vaso tanto soffre dall&#039;acqua sopra­<lb></lb>stante AF, quanto da tutta l&#039;acqua FL. </s></p><p type="main">

<s>Con simile ragionamento si prova che il fondo CD, della figura 122, <lb></lb>sopporta la sola acqua ED, perchè il velo AB, mosso per lo spazio AG, co­<lb></lb>municando la sua forza al velo CD, lo farebbe movere per lo spazio misu­<lb></lb>rato dalla CH, quarta proporzionale dopo CD, AB, AG. Ond&#039;è manifesto che <lb></lb>presa EK=CH, tanta è la forza comprimente, fatta dal velo AB nel pas­<lb></lb>sare lo spazio AG, quant&#039;è la forza comprimente del velo EF, nel passare <lb></lb>lo spazio EK, e perciò il fondo CD soffre da tutta l&#039;acqua AD quel che dalla <lb></lb>sola ED. </s></p><p type="main">

<s>Così in sostanza si dimostra dal Pascal, nel suo capitolo secondo, <emph type="italics"></emph>pour­<lb></lb>quoy les liqueurs pesent suivant leur hauteur.<emph.end type="italics"></emph.end> Che poi la dimostrazione di <lb></lb>questi paradossi veramente dipenda dal principio, che governa la prima mac­<lb></lb>china descritta, e illustrata per la figura 120; è facile vederlo, perchè, anche <lb></lb>ne&#039;due contemplati esempi, la potenza, che facciasi risiedere nel moto del <lb></lb>velo acqueo AB (nella figura 121), alta resistenza del fondo EF, ha la pro­<lb></lb>porzion reciproca della velocità EG alla velocità AC, come in tutte le altre <lb></lb>macchine ordinarie, rappresentate nella leva, ad imitazion di ciò, che può <lb></lb>dirsi intorno alla quale, s&#039;è ridotto alla ragion dell&#039;uguaglianza de&#039;pesi LM, <lb></lb>EF, e delle velocità LN, EG, la ragion dell&#039;eguaglianza de&#039;momenti. </s>

<s>La virtù <lb></lb>dunque di concludere efficacemente si deriva tutta, nel discorso del Pascal, <lb></lb>dal fatto che le pressioni si trasmettono dalla porzione EF alla SH, così nei <lb></lb>vasi comunicanti rappresentati dalla figura 120, come dalla porzione AB si <lb></lb>trasmette alla EF nel vaso rappresentato dalla figura 121, e in tutti gli <lb></lb>altri, di qualunque forma siano, più capaci in basso che in alto: secondo <lb></lb>l&#039;espression propria dell&#039;Autore il fatto insomma è il medesimo “ soit que <lb></lb>cette portion soit vis a vis de l&#039;ouverture ou a costé, loin ou prest; car la <lb></lb>continuité et la fluidité de l&#039;eau rend toutes ces choses la egales et indiffe­<lb></lb>rentes ” <emph type="italics"></emph>(De l&#039;equil. </s>

<s>des liqueurs<emph.end type="italics"></emph.end> cit., pag. </s>

<s>9). </s></p><p type="main">

<s>Riducendosi ora qui tutta l&#039;importanza, può sembrare inconveniente che <lb></lb>il Pascal asserisca senza prove. </s>

<s>Ma a che provar ciò che a tutti era noto? </s>

<s><lb></lb>Bastava l&#039;esperienza del diavolino del Cartesio a persuadere chiunque che la <lb></lb>pressione fatta dallo stantuffo si comunica indifferentemente a ogni porzion <lb></lb>dell&#039;acqua, comunque ella sia disposta, perchè, dentro il foro del cannellino, <lb></lb>si vedeva essere spinto il liquido, o sia la figura in alto, in basso e nel <lb></lb>mezzo, o rimanga esso foro di sotto o di sopra, dal sinistro lato o dal de­<lb></lb>stro. </s>

<s>Tutt&#039;altro dunque ch&#039;essere stato primo, come si dice, il Pascal a di­<lb></lb>mostrare che la pressione, fatta sopra un punto qualunque del liquido, si <lb></lb>trasmette per tutto e per ogni verso in mezzo alla mole intera, ei la sup­<lb></lb>pone come cosa nota, non ai soli spettatori curiosi de&#039;giocattoli del Carte­<lb></lb>sia, ma a que&#039;dotti principalmente, i quali avevano applaudito all&#039;esperienza <lb></lb>dell&#039;argento vivo, come dimostrativa del peso dell&#039;ammostera, per cui si può <pb xlink:href="020/01/3270.jpg" pagenum="231"></pb>credere facilmente che, del principio dell&#039;uguaglianza delle pressioni, con­<lb></lb>fermato dalle spettacolose esperienze del Magiotti, riconoscesse il Pascal stesso <lb></lb>autore il Torricelli. </s></p><p type="main">

<s>In una cosa però differiva la dottrina del Francese: in attribuire cioè <lb></lb>alla continuità, e alla fluidità dell&#039;acqua, quel che i Nostri attribuivano alla <lb></lb>renitenza certissima di lei all&#039;esser compressa. </s>

<s>Nel vaso rappresentato dalla <lb></lb>figura 121, capace per esempio di una sola oncia d&#039;acqua, il fondo EF è <lb></lb>premuto dal peso di tutta l&#039;acqua LF, che può esser di cento libbre. </s>

<s>Di una <lb></lb>tale strana moltiplicazione di forza è causa la pressione che, esercitata sul <lb></lb>velo AB o dal proprio peso del velo AB, si trasmette istantaneamente al <lb></lb>velo EF, per la renitenza dell&#039;acqua alla compressione, diceva il Magiotti, <lb></lb>ma per la continuità e fluidità di lei diceva invece il Pascal, che dimostrava <lb></lb>il suo asserto con questa bella esperienza: S&#039;immagini essere il fondo EF <lb></lb>mobile come uno stantuffo dentro un corpo di tromba, e sia sostenuto per <lb></lb>mezzo di un filo, raccomandato a un braccio della bilancia: per mantener <lb></lb>l&#039;equilibrio converrà, nella fatta supposizione, appendere dall&#039;altro braccio <lb></lb>un peso di cento libbre, benchè propriamente l&#039;acqua contenuta nel vaso non <lb></lb>pesi che un oncia sola. </s>

<s>Nonostante che sia così come si dice, e come av­<lb></lb>viene di fatto, “ si cette eau vient à se glacer, et que la glace ne prenne <lb></lb>pas au vaisseau, comme en effet elle ne s&#039;y attache pas d&#039;ordinaire; il ne <lb></lb>faudra a l&#039;autre bras de la balances qu&#039;une once pour tenir le poids de la <lb></lb>glace en equilibre. </s>

<s>Mais si on approche du feu contre le vaisseau, qui faisse <lb></lb>fondre la glace, il faudra un poids de cent livres pour contrebalancer la pe­<lb></lb>santeur de cette glace fonduė en eau, quoy que nous ne la supposions que <lb></lb>d&#039;une once ” (ivi, pag. </s>

<s>3). </s></p><p type="main">

<s>Questi altri fatti, soggiunge altrove il Pascal, per conferma della sua <lb></lb>opinione: “ Si l&#039;eau qui est dans le petit tuyau se glacoit, et que celle qui <lb></lb>est dans le vaisseau large du fond demeurast liquide, il faudroit cent livres <lb></lb>pour soutenir le poids de cette glace. </s>

<s>Mais si l&#039;eau qui est dans le fond se <lb></lb>glace, soit que l&#039;autre se gele ou demeure liquide, il ne faut qu&#039;une once <lb></lb>pour la contrepeser ” (ivi, pagina 14). Dalle quali osservazioni l&#039;Autore <lb></lb>conclude “ que c&#039;est la liquidité du corps, qui communique d&#039;une des <lb></lb>ouvertures à l&#039;autre, qui cause cette multiplication de forces ” (ivi, <lb></lb>pagina 15). </s></p><p type="main">

<s>Comunque sia i Fisici composero insieme le ipotesi del Magiotti e del <lb></lb>Pascal, dicendo che, per la trasmissione istantanea delle pressioni per tutti <lb></lb>i versi, richiedevasi una perfetta liquidità, e una incompressibilità perfetta. </s>

<s><lb></lb>Poi dopo, quando si volle aver ricorso alle attrazioni e alle repulsioni mo­<lb></lb>lecolari, per spiegare il trasmettersi delle pressioni, secondo qualche loro so­<lb></lb>miglianza colla vibrazione e frequenza dell&#039;onde, si richiese non più la re­<lb></lb>nitenza, ma un certo assecondamento delle particelle dell&#039;acqua all&#039;esser <lb></lb>compresse e al dilatarsi, riducendo così, in qualche modo, anche i liquidi a <lb></lb>partecipare della costituzione e della natura dei corpi elastici. </s>

<s>Ma essendo <lb></lb>così fatte speculazioni il frutto di studi più maturi, le lasceremo, per non <pb xlink:href="020/01/3271.jpg" pagenum="232"></pb>dilungarci di troppo dai tempi, in cui la scienza delle pressioni idrostatiche <lb></lb>era ne&#039;suoi principii. </s></p><p type="main">

<s>Vedemmo quale di così fatti principii fosse l&#039;avvenimento in Italia, e <lb></lb>s&#039;accennava che di ciò erano ben persuasi col Pascal tutti que&#039;dotti, i quali <lb></lb>riconobbero nell&#039;esperienza famosa del Torricelli una dimostrazione non dub­<lb></lb>bia del peso dell&#039;ammosfera. </s>

<s>In Francia, sotto il dominio della Scuola car­<lb></lb>tesiana, si trovavano gli studiosi nelle medesime condizioni che fra noi. </s>

<s>Il <lb></lb>Cartesio e Galileo professavano in idrostatica i medesimi falsi principii, e non <lb></lb>fa perciò maraviglia che giungessero alla medesima falsità delle conclusioni. </s>

<s><lb></lb>Come poteva il Baliani, quando proponeva che la misura del vacuo fosse la <lb></lb>pressione ammosferica, alla quale si dovesse il non si poter sostener l&#039;acqua <lb></lb>nelle trombe, se non che sino a una determinata altezza; come poteva tro­<lb></lb>var favore in coloro, i quali credevano e insegnavano che i fluidi non pesano <lb></lb>nel loro proprio elemento, e nè perciò pesa l&#039;aria dentro il pozzo, per so­<lb></lb>stener l&#039;acqua nel tubo della tromba, come non pesa l&#039;aria nella fossetta <lb></lb>scavatasi dall&#039;assicella d&#039;ebano che galleggia? </s>

<s>Galileo perciò si ridusse a dire <lb></lb>che il limite di questa altezza nel tubo non era posto dal peso estraneo del­<lb></lb>l&#039;aria, ma dal peso proprio del cilindro liquido, rassomigliato a una corda, <lb></lb>che resiste in sino a un certo punto, oltrepassato il quale, necessariamente <lb></lb>si strappa. </s>

<s>Lo stesso diceva il Cartesio, nel rendere al Mersenno la ragione <lb></lb>del perchè sia meglio, per sollevar l&#039;acqua a qualche grande altezza, ser­<lb></lb>virsi del moto interrotto di più trombe, piuttosto che del continuato di una <lb></lb>tromba sola. </s>

<s>“ Ratio autem quamobrem praestaret interruptus motus, est <lb></lb>quod corium subtensum substinere debet totam aquae columnam viginti <lb></lb>sexpedas altam, quod quidem pondus est tantum, ut illud diu ferre nequeat <lb></lb>quin frangatur ” <emph type="italics"></emph>(Epistol.,<emph.end type="italics"></emph.end> P. II, Amstelodami 1682, pag. </s>

<s>128). </s></p><p type="main">

<s>Le ragioni, da cui fu mosso Galileo a ripudiare la proposta del Baliani, <lb></lb>erano quelle medesime, che davano ai galileiani occasione di dubitare della <lb></lb>proposta del Torricelli, il quale ebbe perciò a riformar l&#039;Idrostatica, dimo­<lb></lb>strando che anche l&#039;aria pesa nell&#039;aria, e che come fluido esercita le sue <lb></lb>pressioni per tutti i versi. </s>

<s>Quel che fece il Nostro nelle lettere private al <lb></lb>Ricci, e ne&#039;familiari colloqui con gli amici, volle poi fare il Pascal ordina­<lb></lb>tamente ne&#039;suoi due celebri trattati, per rispondere ai dubbi dei cartesiani. <lb></lb></s>

<s>“ C&#039;est pourquoy j&#039;ay monstré dans <emph type="italics"></emph>L&#039;equilibre des liqueurs,<emph.end type="italics"></emph.end> que l&#039;eau pese <lb></lb>dans elle mesme autant qu&#039;au dehors, et j&#039;y ay expliqué pourquoy nonobstant <lb></lb>ce poids un seau n&#039;y est pas difficile a hausser et pourquoy on n&#039;en sent <lb></lb>pas le poids. </s>

<s>Et dans le traité <emph type="italics"></emph>De la pesanteur de la masse de l&#039;air<emph.end type="italics"></emph.end> j&#039;ay <lb></lb>monstré la mesme chose de l&#039;air, afin d&#039;éclaireir tous les doutes ” <emph type="italics"></emph>(Conclu­<lb></lb>sion des deux traitez<emph.end type="italics"></emph.end> cit., pag. </s>

<s>132). </s></p><p type="main">

<s>Ma nella lettera del di 15 Novembre 1647 dichiarava il Pascal al Perier <lb></lb>anche più espressamente le ragioni, ch&#039;egli ebbe di congiungere insieme i <lb></lb>due trattati, e di premettere, a quello <emph type="italics"></emph>De la pesanteur de la masse de l&#039;air,<emph.end type="italics"></emph.end><lb></lb>l&#039;altro <emph type="italics"></emph>De l&#039;equilibre des liqueurs.<emph.end type="italics"></emph.end> “ J&#039;ay peine a croire que la Nature, qui <lb></lb>n&#039;est point animée ny sensible, soit susceptible d&#039;horreur, puisque les pas-<pb xlink:href="020/01/3272.jpg" pagenum="233"></pb>sions presupposent une ame capable de les ressentir, et j&#039;incline bien plus <lb></lb>a imputer tous ces effets a la pesanteur et pression de l&#039;air, parce que je <lb></lb>ne les considere que comme des cas particuliers d&#039;une proposition univer­<lb></lb>selle de l&#039;equilibre des liqueurs, qui doit faire la plus grande partie du Traité <lb></lb>que j&#039;ay promis. </s>

<s>” <emph type="italics"></emph>(Recit de la grande experience etc.<emph.end type="italics"></emph.end> in appendice ai due <lb></lb>trattati cit., pag. </s>

<s>168, 69). Ed essendo la promessa fatta nel detto anno 1647 <lb></lb>non fu mantenuta, se non che dopo il 1651, quando l&#039;esperienze eseguite <lb></lb>sul Puy de Domme, a Clermont, a Parigi e a Stokol<gap></gap>, confermarono essere <lb></lb>la maggiore o minore altezza, e perciò il maggiore o minor peso dell&#039;aria <lb></lb>verissima causa dell&#039;alzarsi e dell&#039;abbassarsi l&#039;argento vivo nel tubo torri­<lb></lb>celliano. </s></p><p type="main">

<s>Tale è la breve storia del libro, e dell&#039;argomento da lui trattato, a pro­<lb></lb>posito del quale nessuno dubiterà essere stato il Pascal, nel restaurar l&#039;Idro­<lb></lb>statica, preceduto dal Torricelli. </s>

<s>Ma forse alcuni potrebbero mettere in dub­<lb></lb>bio quel che s&#039;e dato da noi per certo, che cioè il Francese riconoscesse da <lb></lb>sè stesso così la preminenza del Nostro, da far quasi come il discepolo, che <lb></lb>commenta la lezione del suo maestro. </s>

<s>Ai dubitanti risponderemo, e confer­<lb></lb>meremo noi stessi e gli altri nella propria opinione, adducendo un esempio, <lb></lb>che dimostri come in un soggetto, da questo non molto diverso, il Pascal <lb></lb>adempia di fatto verso il Torricelli l&#039;ufficio che abbiamo detto. </s></p><p type="main">

<s>Come l&#039;equilibrio di un liquido in due vasi comunicanti, prima dimo­<lb></lb>strato col principio delle velocità virtuali, pensasse poi esso Pascal d&#039;assicu­<lb></lb>rarlo dalle contradizioni, invocando l&#039;assioma torricelliano de&#039;due corpi con­<lb></lb>giunti, che si rimangono in quiete, quando il loro comun centro di gravità <lb></lb>non può scendere; fu precedentemente da noi fatto notare. </s>

<s>Ora però sog­<lb></lb>giungiamo che il Torricelli, nel premettere al suo trattato quell&#039;assioma, <lb></lb>diceva che i due corpi congiunti, avverandosi la fatta supposizione dell&#039;im­<lb></lb>possibile scesa del loro comun centro gravitativo, si rimarrebbero in quiete <lb></lb>“ sive id libra fiat, sive troclea, sive qualibet alia mechanica ratione, grave <lb></lb>autem huiusmodi non movebitur unquam, nisi centrum gravitatis ipsius de­<lb></lb>scendat ” <emph type="italics"></emph>(Opera geom.,<emph.end type="italics"></emph.end> P. I, Florentiae 1644, pag. </s>

<s>99). </s></p><p type="main">

<s>La dimostrazione taciuta dal Torricelli fu distesa dal Pascal in un trat­<lb></lb>tatello delle Macchine, ch&#039;egli commemora con queste parole, quasi compia­<lb></lb>cente d&#039;aver salvata, col nuovo metodo torricelliano, la Meccanica, rimasta <lb></lb>da Aristotile a Galileo senza difesa, da&#039;contradittori delle velocità virtuali: <lb></lb>“ J&#039;ay démontré, par cette methode, dans un petit traité de Mechanique, la <lb></lb>raison de toutes les multiplications de forces, qui se trouvent en tous les <lb></lb>autres instrumens de Mechanique, qu&#039;on a jusques a present inventez. </s>

<s>Car <lb></lb>je fais voir en tous que les poids inegaux, qui se trouvent en equilibre, par <lb></lb>l&#039;avantage des machines sont tellement disposez, par la construction des ma­<lb></lb>chines, que leur centre de gravité commun ne sçavroit jamais descendre, <lb></lb>quelque situation qu&#039;ils prissent. </s>

<s>D&#039;ou il s&#039;ensuit qu&#039;ils doivent demeurer en <lb></lb>repos, c&#039;est a dire en equilibre ” <emph type="italics"></emph>(Traitez<emph.end type="italics"></emph.end> cit., pag. </s>

<s>11). </s></p><p type="main">

<s>Giovi aver resuscitata questa memoria, perchè si riconosca l&#039;importanza <pb xlink:href="020/01/3273.jpg" pagenum="234"></pb>di un tale trattato nella storia della Statica. </s>

<s>Ma quel che per ora a noi preme <lb></lb>è di concludere che il principio dell&#039;uguaglianza delle pressioni il Pascal non <lb></lb>lo dà come nuovo, ma, supponendolo già noto, lo conferma con esperienze <lb></lb>nuove, lo spiega con nuove ragioni, e l&#039;applica a dimostrar l&#039;equilibrio dei <lb></lb>liquidi con sè stessi, ch&#039;è l&#039;argomento della prima parte del suo libro. </s>

<s>Nella <lb></lb>seconda si propone di trattare <emph type="italics"></emph>De l&#039;equilibre d&#039;une liqueur avec un corps <lb></lb>solide,<emph.end type="italics"></emph.end> e supponendo questo solido aver forma di cubo, ed essere sotto l&#039;acqua <lb></lb>tutto sommerso, così comincia il suo ragionamento: “ Nous voyons par là <lb></lb>que l&#039;eau pousse en haut les corps qu&#039;elle touche par dessous; qu&#039;elle pousse <lb></lb>en bas ceux qu&#039;elle touche par dessus, et qu&#039;elle pousse de costé ceux qu&#039;elle <lb></lb>touche par le costé opposé. </s>

<s>D&#039;où il est aisé de conclure que quand un corps <lb></lb>est tout dans l&#039;eau, comme l&#039;eau le touche par dessus, par dessous, et par <lb></lb>tous les costez, elle fait effort pour le pousser en haut, en bas, et vers tous <lb></lb>les costés. </s>

<s>Mais comme sa hauteur est la mesure de la force, qu&#039;elle a dans <lb></lb>toutes ces impressions, on verra bien aisément le quel de tous ces efforts <lb></lb>doit prevaloir ” (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Quel che, nel principio di questo discorso, dice di aver fatto vedere il <lb></lb>Pascal, consiste nelle esperienze descritte nel capitolo precedente, una delle <lb></lb><figure id="id.020.01.3273.1.jpg" xlink:href="020/01/3273/1.jpg"></figure></s></p><p type="caption">

<s>Fig. </s>

<s>123.<lb></lb>quali è quella della canna AB (fig. </s>

<s>123), turata in fondo con lo <lb></lb>stoppaccio B a sfregamento dolce, che messa in acqua, in modo <lb></lb>però che la sua bocca A rimanga sempre aperta nell&#039;aria, mostra <lb></lb>come lo stoppaccio stesso è sempre spinto più in su, quanto più la <lb></lb>canna s&#039;abbassa. </s>

<s>L&#039;altra esperienza è della canna ritorta (fig. </s>

<s>124), <lb></lb>in cui lo stoppaccio al contrario è cacciato sempre più giù, e in <lb></lb>ultimo vien descritta la canna a gruccia (fig. </s>

<s>125), in cui si vede <lb></lb>esso stoppaccio premuto sempre più indentro e di traverso, secondo <lb></lb>che l&#039;immersione via via si fa più profonda. <lb></lb><figure id="id.020.01.3273.2.jpg" xlink:href="020/01/3273/2.jpg"></figure></s></p><p type="caption">

<s>Fig. </s>

<s>124.</s></p><p type="main">

<s>Da questi fatti il Pascal. </s>

<s>conclude che, essendo il solido cubo <lb></lb>premuto ugualmente sulla faccia davanti e su quella di dietro, <lb></lb>sulla faccia destra e sulla sinistra; se sarà altresì con pari forza <lb></lb>premuto anche sulla faccia di sotto e su quella di sopra, si rimarrà <lb></lb>in equilibrio. </s>

<s>Ma prevalendo le due spinte in giù e in su l&#039;una <lb></lb>all&#039;altra, il solido stesso o calerà in fondo o risalirà su a galla. <lb></lb></s>

<s>“ Car il paroist d&#039;abord que comme elle (l&#039;eau) a una pareille hau­<lb></lb>teur sur toutes les faces des costés, elle les poussera également, et <lb></lb><figure id="id.020.01.3273.3.jpg" xlink:href="020/01/3273/3.jpg"></figure></s></p><p type="caption">

<s>Figura 125.<lb></lb>partant ce corps ne recevra aucune impression vers aucun <lb></lb>costé, non plus qu&#039;une girovette entre deux vents égaux ” <lb></lb>(ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>Ora è notabile questo sentenziar così assoluto in cosa <lb></lb>di tanta importanza. </s>

<s>Non sembrava che dovesse essere prin­<lb></lb>cipale ufficio dello scrittore quello di provare che, essendo <lb></lb>l&#039;acqua di pari altezza, le facce laterali del cubo son pre­<lb></lb>mute tutte ugualmente? </s>

<s>Ma ei reputava inutile spendere in­<lb></lb>torno a ciò tante parole, avendosene dallo Stevino così chiara, <pb xlink:href="020/01/3274.jpg" pagenum="235"></pb>matematica dimostrazione. </s>

<s>Se la forza, che preme le opposte facce laterali <lb></lb>del cubo, uguaglia il peso della mezza colonna d&#039;acqua, avente per base <lb></lb>esse facce, e per altezza la perpendicolare, condotta in fin su al supremo <lb></lb>livello del liquido dal centro della figura; non era egli evidente che, essendo <lb></lb>le basi e le altezze uguali, debbono anche i pesi delle colonne prementi es­<lb></lb>sere uguali? </s></p><p type="main">

<s>Dunque il Pascal presupponeva la notizia degli Elementi idrostatici dello <lb></lb>Stevino, di cui intendeva render più facili e più naturali l&#039;esperienze di­<lb></lb>mostrative della spinta in su del liquido, e per tutti i versi. </s>

<s>Anzi è da os­<lb></lb>servare com&#039;anco, rispetto all&#039;equilibrio de&#039;liquidi con sè stessi, esso Pascal <lb></lb>presuppone i teoremi steviniani, la ragion de&#039;quali niente altro fa che con­<lb></lb>fermare col principio delle velocità virtuali, e della stabilità orizontale del <lb></lb>centro gratitativo, secondo il metodo di Galileo e l&#039;assioma meccanico del <lb></lb>Torricelli. </s>

<s>Non tutti i torti aveva dunque il Boyle, quando, dell&#039;aver ridotto <lb></lb>alle genuine leggi idrostatiche il premersi i liquidi in sè stessi, non dava <lb></lb>nessun merito al Pascal, ma l&#039;attribuiva tutto a sè stesso e allo Stevino. <lb></lb></s>

<s>“ Stevinus et ego, diversimode licet, particulatim probavimus, iuxta genui­<lb></lb>nae hydrostaticae leges, duorum liquorum prementium se invicem praeva­<lb></lb>lentiam determinandam non esse ex eorumdem quantitatem, sed tribuendam <lb></lb>ei qui excedit alterum in perpendiculari altitudine ” <emph type="italics"></emph>(De salsedine maris. </s>

<s><lb></lb>Op. </s>

<s>omnia,<emph.end type="italics"></emph.end> T. II, Venetiis 1697, pag. </s>

<s>342). </s></p><p type="main">

<s>Dalle cose dette fin qui l&#039;opera, data dal Pascal intorno all&#039;Idrostatica, <lb></lb>viene a mettersi nel suo proprio aspetto, così che non è difficile formarsene <lb></lb>il più giusto giudizio. </s>

<s>Il non avere insegnato in sostanza nulla di nuovo non <lb></lb>diminuisce perciò punto il suo merito, mancando agl&#039;insegnamenti dello Ste­<lb></lb>vino e del Torricelli le qualità necessarie al loro diffondersi con facilità, e <lb></lb>persuadere con efficacia. </s>

<s>Gli Elementi idrostatici dell&#039;Olandese avevano troppo <lb></lb>del matematico, non solo nell&#039;esposizion de&#039;principii generali, ma nelle loro <lb></lb>stesse applicazioni, e le teorie del Nostro, non essendo ancora pubblicamente <lb></lb>note le lettere al Ricci, si dovevano far conseguire dall&#039;esperienza dell&#039;ar­<lb></lb>gento vivo. </s>

<s>Il Pascal, premettendo il trattato <emph type="italics"></emph>Dell&#039;equilibrio de&#039;liquidi<emph.end type="italics"></emph.end> a <lb></lb>quello <emph type="italics"></emph>Del peso della massa dell&#039;aria,<emph.end type="italics"></emph.end> dimostrò l&#039;ordine logico di quelle <lb></lb>conseguenze, e ridusse a fatti fisici le matematiche astrazioni. </s>

<s>L&#039;ordine, la <lb></lb>precisione e la chiarezza, che dispensavano l&#039;Autore dalle molte parole, co­<lb></lb>sicchè il libro di lui si conclude in 44 pagine di un volumetto in 12°; ba­<lb></lb>stano a spiegar l&#039;efficacia, ch&#039;egli ebbe in diffondere e in persuadere la <lb></lb>scienza, la quale, apparendo nuova, non fa maraviglia se, contro l&#039;intenzion <lb></lb>dell&#039;Autore, tale anche fosse creduta. </s></p><p type="main">

<s>Istituitasi in ogni modo nel libro del Pascal l&#039;Idrostatica, non potevano <lb></lb>lungamente mancarne i promotori. </s>

<s>Roberto Boyle, esaminando il trattato <emph type="italics"></emph>De <lb></lb>l&#039;equilibre des liqueurs,<emph.end type="italics"></emph.end> lo trovò constare di conclusioni e di sperimenti: e <lb></lb>benchè di quelle, almeno in generale, non dubitasse, aveva questi però per <lb></lb>non bene dimostrativi, per diverse ragioni, la prima delle quali è “ quia <lb></lb>licet experimenta ab ipso commemorata eo modo tradantur, qui in consi-<pb xlink:href="020/01/3275.jpg" pagenum="236"></pb>gnandis rebus facti est solemnis, non tamen memini diserte eum affirmare <lb></lb>semet actu illa sumpsisse, atque ideo forte ea tradidit ceu talia, quae, ex eo <lb></lb>quod confidat se in ratiociniis suis non errasse, oporteat evenire ” <emph type="italics"></emph>(Para­<lb></lb>doxa hydros.,<emph.end type="italics"></emph.end> Roterodami 1670, pag. </s>

<s>4). E promette il Boyle di confermare <lb></lb>questo suo giudizio con qualche esempio, un de&#039;quali gli fu porto dall&#039;espe­<lb></lb>rienza, che il Pascal descrive così: “ Un tuyau ouvert par en haut et par <lb></lb>en bas, estant plein de vif argent, et enfoncé dans une riviere, pourveu que <lb></lb>le bout d&#039;en haut sorte hors de l&#039;eau, si le bont d&#039;en bas est a quatorze <lb></lb>pieds avant dans l&#039;eau, le vif argent tombera jusques à ce qu&#039;il n&#039;en reste <lb></lb>plus que la hauteur d&#039;un pied, et là il demereura suspendu par le poids de <lb></lb>l&#039;eau ” <emph type="italics"></emph>(De l&#039;equilibre etc.,<emph.end type="italics"></emph.end> pag. </s>

<s>20). </s></p><p type="main">

<s>A quanti però, benchè abilissimi sperimentatori, ci s&#039;erano provati, non <lb></lb>era riuscito mai di vedere questa curiosità del mercurio sospeso in mezzo <lb></lb>all&#039;acqua, e il Boyle confermava che, specialmente con quelle grossezze di <lb></lb>tubi soliti a usarsi, non era in nessun modo possibile che riuscisse, perchè <lb></lb>il liquido metallo, caduto da una tale altezza, acquista tant&#039;impeto, da scap­<lb></lb>par tutto fuori, vincendo ogni resistenza dell&#039;acqua. </s>

<s>Ond&#039;essendo anche al <lb></lb>Pascal la cosa d&#039;impossibile riuscita, s&#039;argomenta ragionevolmente non dover <lb></lb>aver egli messa in atto l&#039;esperienza, che solamente propone come consona <lb></lb>con le verità da lui professate. </s>

<s>“ Et sane, ni esset impetus, quem acquirit <lb></lb>mercurius ex tanta labens altitudine, haud indigna ipso foret ratiocinatio. </s>

<s><lb></lb>Sed experimenta nonnisi theorice vera proponi debebant ut talia, possuntque <lb></lb>ea saepius in praxi fallere ” <emph type="italics"></emph>(Paradoxa<emph.end type="italics"></emph.end> cit., pag. </s>

<s>63). </s></p><p type="main">

<s>Non diverso giudizio da questo fa il Boyle dello Stevino, a proposito <lb></lb>della terza esperienza, descritta nel V libro della Statica, <emph type="italics"></emph>commençant la <lb></lb>practique de l&#039;Hydrostatique:<emph.end type="italics"></emph.end> esperienza che, non essendo riuscita al Wal­<lb></lb>lis, doveva presentar tali difficoltà, da credere facilmente che nemmen lo <lb></lb>Stevino l&#039;avesse ridotta a rigoroso esame. </s>

<s>“ Et sane, propter difficultatem <lb></lb>ad examen ea reducendi, addubitavi ego nunquam hic Author experimenta <lb></lb>ista ipse sumpserit, an potius consignaverit eventa, quae ea omnino sortitura <lb></lb>supposuit, coniecturas suas ex veritate demonstrativa rite deductas persua­<lb></lb>sus ” (ibid., pag. </s>

<s>133). </s></p><p type="main">

<s>Son dietro a ciò facili a prevedersi le intenzioni del Boyle, le quali non <lb></lb>erano d&#039;istituire dell&#039;Idrostatica elementi o sistemi, ma di confermarla con <lb></lb>l&#039;esperienze, perfezionando le antiche, e proponendone delle nuove. </s>

<s>Così venne <lb></lb>a mettere in ordine quegli XI paradossi, pubblicati nel 1664 in Oxford in <lb></lb>lingua inglese, e de&#039;quali poi si vide in Rotterdam, nel 1670, la traduzione <lb></lb>latina, che si cita da noi. </s></p><p type="main">

<s>Così fatti Paradossi dunque, che lo Stevino e il Pascal proposero, e in­<lb></lb>gegnosamente ridussero alle vere loro ragioni, il Boyle vuol dimostrare con <lb></lb>l&#039;esperienze in un altro modo, giacchè quello tenuto da&#039;due suoi illustri pre­<lb></lb>decessori non lo sodisfa pienamente. </s>

<s>È perciò che, nel Paradosso VI, dopo <lb></lb>aver trascritta la X proposizione del libro dello Stevino, passa a esaminare <lb></lb>il terzo sperimento, quivi immaginato per confermarla, il quale sperimento, <pb xlink:href="020/01/3276.jpg" pagenum="237"></pb>sebbene sia di difficile esecuzione a quel modo, che l&#039;insegna a far l&#039;inven­<lb></lb>tore, mostra nulladimeno il Boyle con quale e con quanta diligenza debba <lb></lb>condursi, perchè si possa veder la pratica esattamente corrispondere con la <lb></lb>teoria. </s></p><p type="main">

<s>Similmente, ai curiosi di veder lo spettacolo del mercurio, sospeso non <lb></lb>solamente in mezzo all&#039;acqua, ma in mezzo a un liquido molto men grave <lb></lb>in specie di lei, qual&#039;è l&#039;olio di terebinto; sodisfaceva l&#039;Autore dei Para­<lb></lb>dossi, insegnando a prendere una canna di vetro, un po&#039;più stretta e più <lb></lb>corta di quella usata dal Pascal, e, immersa nel mercurio tanto che la bocca <lb></lb>inferiore n&#039;attinga un poco, turar la superiore col dito, come si fa del sag­<lb></lb>giatore del vino. </s>

<s>Estratta poi la canna, col liquido metallo rimastovi in fondo, <lb></lb>voleva s&#039;immergesse nell&#039;olio, dove, ora abbassandola ora alzandola, dopo <lb></lb>averle levato di sopra il dito, si vedrà, diceva, “ non iniucundo spectaculo <lb></lb>ponderosum mercurii corpus ut nunc surgat nunc cadat, ita tamen ut sem­<lb></lb>per super liquoris, ipso communi spiritus vini levioris, superficie fluitet ” <lb></lb>(pag. </s>

<s>100). </s></p><p type="main">

<s>Se tutto, nel Pascal e nello Stevino, fosse di questo genere, l&#039;assunto <lb></lb>del Boyle riusciva utilissimo all&#039;arte sperimentale. </s>

<s>Generalmente però l&#039;espe­<lb></lb>rienze idrostatiche prime non differiscono da queste nuove, che nella sem­<lb></lb>plicità degli strumenti, e nel modo più facile di usarli. </s>

<s>Per esempio: pre­<lb></lb>parare uno stoppaccio, uno zaffo, per turare in B la bocca della canna a <lb></lb>gruccia, disegnata nella figura 125; era molto più facile che procurarsi olio <lb></lb>della qualità richiesta, e canna adatta a ritenerlo dentro; e in sostanza la <lb></lb>pression laterale dell&#039;acqua veniva allo stesso modo ben dimostrata. </s>

<s>Simile <lb></lb>dicasi delle pressioni esercitate dal liquido di sotto in su, la maniera sem­<lb></lb>plicissima dì sperimentar le quali, come la suggerì il Torricelli al Ricci e il <lb></lb>Pascal ai suoi lettori, differisce in ciò solamente dalla maniera del Boyle, che <lb></lb>quella può facilmente praticare ognuno con gli oggetti comuni, e questa non <lb></lb>può che il Filosofo, e chiunque abbia un artefice costruttore degl&#039;immagi­<lb></lb>nati strumenti. </s>

<s>Il nobilissimo Barone inglese ridusse anche gli oggetti del <lb></lb>gabinetto fisico alla magnificenza e al lusso degli altri mobili di casa, i più <lb></lb>poveri de&#039;quali credeva non poter servire al medesimo uso, quasi che una <lb></lb>scranna di rozzo faggio non fosse buona a sedervi sopra, come una sedia <lb></lb>d&#039;ebano dorato. </s></p><p type="main">

<s>Si legga per esempio il Paradosso XI. </s>

<s>A questo, appena annunziato ai <lb></lb>colleghi della R. </s>

<s>Società di Londra, premette l&#039;Autore una tale osservazione: <lb></lb>“ Paradoxum hoc, cum nunquam fuerit, me quidem conscio, a quoquam <lb></lb>hactenus propositum, adeo parum verisimile iis fuit visum, quibus id obtuli, <lb></lb>mathematicis ipsis non exceptis, ut sperare vix possim illustrissimam hanc <lb></lb>Societatem ei prompte et universim assensuram, nisi inductam experientia ” <lb></lb>(pag. </s>

<s>175). Eppure la maraviglia, che si dava agli accademici di Londra per <lb></lb>nuova, era quella medesima annunziata cinquant&#039;anni prima da Giovanni <lb></lb>Bardi agli accademici di Roma, come cosa notissima a tutti, e descritta dallo <lb></lb>Stevino, la ragion del quale, rispetto al sostenersi in mezzo all&#039;acqua una <pb xlink:href="020/01/3277.jpg" pagenum="238"></pb>tavoletta di piombo, valeva altresì per un corpo molto più ponderoso, come <lb></lb>il cubo di bronzo, che ivi il Boyle propone. </s>

<s>La differenza poi tra il vecchio <lb></lb>paradosso e il nuovo non consiste se non in ciò, che a quello serve un sem­<lb></lb>plice tubo, applicato con esquisito contatto a una faccia del solido, il quale, <lb></lb>se in aria vuol essere sostenuto colla mano, tuffato in acqua a una profon­<lb></lb>dità conveniente non ha bisogno d&#039;altro sostegno, bastando a lui la spinta <lb></lb>idrostatica. </s>

<s>In questo poi, nel paradosso del Boyle, quanto sia più compli­<lb></lb>cato, e, diciamo così, lussureggiante l&#039;apparato dell&#039;esperienza, può facil­<lb></lb>mente riconoscersi da chiunque rivolga gli occhi alla figura XX, impressa <lb></lb>in fine al libro sulla tavola terza. </s></p><p type="main">

<s>Non poco si compiace il Boyle stesso di quella esperienza, ch&#039;egli crede <lb></lb>essere un&#039;invenzione sua nuova, per confermare il peso dell&#039;aria contro chi <lb></lb>lo metteva in dubbio perchè, usandovi il metodo aristotelico di gonfiarla e <lb></lb>di condensarla in una vescica, dicevano non doversi quell&#039;accrescimento di <lb></lb>gravità, mostrato dalla stadera, attribuire all&#039;aria stessa moltiplicata, ma agli <lb></lb>effluvii crassi espirati dal petto, e passati per la bocca dell&#039;uomo. </s>

<s>La van­<lb></lb>tata esperienza boileiana consisteva nell&#039;avere una bolla di vetro, in forma <lb></lb>di una pera col suo picciolo, dentro alla quale si rarefaceva l&#039;aria al calore, <lb></lb>e, sigillatone il picciolo alla fiamma, si lasciava freddare e s&#039;imponeva sul <lb></lb>bacino di una esattissima bilancia accuratamente equilibrata. </s>

<s>Rotto poi il <lb></lb>picciolo, e irrompendo violentemente dentro la bolla vuota l&#039;aria esterna, si <lb></lb>notò che subito lo strumento s&#039;inclinava da questa parte con insigne prepon­<lb></lb>deranza. </s>

<s>In questo modo avrebbe certamente dovuto istituir Galileo la sua <lb></lb>esperienza, per decider se vero o falso era quel che diceva un Peripatetico <lb></lb>suo avversario, aver cioè sensibile peso anche l&#039;aria in mezzo all&#039;altr&#039;aria. </s>

<s><lb></lb>E invece suggeriva di pesare “ una gran boccia di vetro, serrandovi dentro <lb></lb>l&#039;aria naturale, senza comprimerne altra, perchè, se poi si romperà la boc­<lb></lb>cia, e si peseranno i pezzi del vetro, si troverà l&#039;istesso peso a capello ” <lb></lb><emph type="italics"></emph>(Risposta a V. di Grazia,<emph.end type="italics"></emph.end> Alb. </s>

<s>XIII, 530). Ma in ogni modo la vera espe­<lb></lb>rienza decisiva sarebbe stata quella, descritta nella Lettera al Nozzolini, la <lb></lb>quale esperienza, mentre pareggiava la sopra riferita del Boyle nella preci­<lb></lb>sione, la superava forse per la semplicità e per la eleganza. </s></p><p type="main">

<s>È molto probabile che il Fisico inglese ignorasse quella scrittura gali­<lb></lb>leiana, non nota se non a pochi fra gli stessi Italiani, ma non si può in ogni <lb></lb>modo passar senza considerazione quel che dice nel Paradosso terzo, a pro­<lb></lb>posito del celebre teorema idrostatico, in cui dimostra Archimede che il so­<lb></lb>lido immerso tanto perde del suo proprio peso, quant&#039;è il peso di un&#039;egual <lb></lb>mole di liquido. </s>

<s>Il qual teorema, dice il Boyle, “ non memini me in ullo <lb></lb>vidisse libro excuso, et solide et clare demonstratum, doctissimo Stevino ipso, <lb></lb>ad quem recentiores nos remittere authores solent, nonnisi obscuram eius, <lb></lb>nec physicam demonstrationem tradente ” (pag. </s>

<s>71). Crede perciò che nes­<lb></lb>suno abbia ancora solidamente e chiaramente dimostrato il teorema prima <lb></lb>di lui, col proporre che fa e descrivere il seguente esperimento; “ Si enim <lb></lb>capias v. </s>

<s>g. </s>

<s>frustum plumbi, idque ex crine equino, qui supponitur aquae <pb xlink:href="020/01/3278.jpg" pagenum="239"></pb>proxime aequiponderare, ad unam lancium exactae trutinae appendas, sique <lb></lb>iusto sacomate alteri lanci imposito patiaris plumbum vasi aquam continen­<lb></lb>tem immergi, donec ea plane contegatur, sed libere in ipsa pendeat; sacoma <lb></lb>permultum praeponderabit. </s>

<s>Atque parte sacomatis exempta, donec rursus ad <lb></lb>aequilibrium reducatur bilanx, facile poteris, subducendo quod exemisti, idque <lb></lb>comparando cum toto pondere plumhi in aere, invenire quantam sui ponde­<lb></lb>ris partem amittat in aqua ” (ibid., pag. </s>

<s>72). </s></p><p type="main">

<s>Può ragionevolmente supporsi che il Boyle non sapesse quel che s&#039;era <lb></lb>speculato in Italia, intorno alla Bilancetta idrostatica, da Galileo, dal Castelli, <lb></lb>dal Viviani e da altri, che non pensarono a divulgare le loro invenzioni. </s>

<s>Ma <lb></lb>bastava aver letto il Ghetaldo, ch&#039;esso Boyle annovera, insieme col mede­<lb></lb>simo Galileo e con lo Stevino, fra i principali promotori dell&#039;Idrostatica: ba­<lb></lb>stava aver veduto il Tartaglia, per persuadersi che lo sperimento descritto <lb></lb>ne&#039;Paradossi inglesi era tutt&#039;altro che nuovo. </s>

<s>Nè l&#039;Autor di questi paradossi <lb></lb>inglesi credeva fosse rimasto indimostrato solo il teorema principale, ma e <lb></lb>i corollari di lui, concernenti le ragioni dell&#039;affondarsi i corpi più gravi del­<lb></lb>l&#039;acqua, e dell&#039;emergere i più leggeri. </s>

<s>Le nuove desiderate ragioni, solide <lb></lb>e chiare, poteva dirsi che mancavano in Galileo, ma no nello Stevino, in cui <lb></lb>anzi il Pascal le riconobbe di così facile deduzione, da stimare inutile il sug­<lb></lb>gerirle ai lettori. </s></p><p type="main">

<s>Ritorniamo sul capitolo V <emph type="italics"></emph>De l&#039;equilibre des liqueurs,<emph.end type="italics"></emph.end> in principio del <lb></lb>quale, supponendo l&#039;Autore i teoremi steviniani da sè stesso precedentemente <lb></lb>confermati con l&#039;esperienza, si propone un solido tutto sott&#039;acqua. </s>

<s>E dopo <lb></lb>aver quivi detto ch&#039;egli è premuto per ogni sua parte, e anche di basso in <lb></lb><figure id="id.020.01.3278.1.jpg" xlink:href="020/01/3278/1.jpg"></figure></s></p><p type="caption">

<s>Figura 126.<lb></lb>alto e d&#039;alto in basso, conclude: <emph type="italics"></emph>on verra bien le quel <lb></lb>de tous ces efforts doit prevaloir.<emph.end type="italics"></emph.end> Essendo infatti le <lb></lb>contrarie pressioni d&#039;avanti e indietro, da destra e si­<lb></lb>nistra, sempre necessariamente uguali, non può la que­<lb></lb>stion cadere se non che circa le pressioni di sopra in <lb></lb>giù, e di sotto in su, l&#039;uguaglianza o la prevalenza delle <lb></lb>quali si vedrà bene, vuol dire insomma il Pascal, per <lb></lb>gl&#039;insegnamenti dello Stevino, secondo cui la base AB <lb></lb>del solido CB (fig. </s>

<s>126) è spinta in su da una forza <lb></lb>uguale al peso della colonna d&#039;acqua, avente quella me­<lb></lb>desima base, e AE per altezza; in giù poi è calcata dal peso proprio del <lb></lb>solido, e da quello che gli soprasta: dalla colonna cioè, che ha per base la <lb></lb>base superiore del solido stesso, e per altezza CE, supposto che sia FG il <lb></lb>livello del liquido nel vaso. </s>

<s>Di qui si vedrà anche meglio <emph type="italics"></emph>le quel de ces <lb></lb>efforts doit prevaloir,<emph.end type="italics"></emph.end> perchè, se il solido è più grave in specie dell&#039;acqua, <lb></lb>il luogo della quale egli occupa nella colonna EB, prevarrà la spinta di <lb></lb>sopra, che lo tirerà in fondo; se è più leggero, prevarrà la spinta di sotto, <lb></lb>che lo menerà a galla. </s></p><p type="main">

<s>Ora questa pronta facilità, e sicurezza di ragioni, fa un singolare con­<lb></lb>trasto con l&#039;incerto procedere del Boyle, simile a quel di colui, che fosse <pb xlink:href="020/01/3279.jpg" pagenum="240"></pb>entrato per una via, da nessun orma segnata. </s>

<s>“ Ratio igitur emersionis le­<lb></lb>viorum corporum in gravioribus fluidis esse haec videtur: quod aquae, cor­<lb></lb>poris parti inferiori contiguae, conatus sursum fortius est eiusdem corporis <lb></lb>et aquae ei incumbenti, conatu deorsum ” <emph type="italics"></emph>(Parad.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>75). Ma questa <lb></lb>è ragion fisica. </s>

<s>Avrebbe dovuto sapere il Boyle altresì che lo Stevino sog­<lb></lb>giungeva un&#039;altra ragion matematica, per cui, non solamente veniva a pre­<lb></lb>cedere l&#039;idrostatica dei Paradossi, ma quella stessa, che si sarebbe insegnata <lb></lb>un secolo di poi. </s>

<s>Se O sia il centro di gravità del corpo CB, sarà, secondo <lb></lb>l&#039;autore dell&#039;Acrobatica, in quello stesso punto il centro della pressione, co­<lb></lb>sicchè concorreranno in O tre forze, una di basso in alto, uguale al peso C <lb></lb>della colonna d&#039;acqua già detta, e due d&#039;alto in basso: quella uguale al <lb></lb>peso P del solido, e questa uguale al peso C′ della colonna liquida, a lui <lb></lb>soprastante. </s>

<s>Onde, essendo C=P+C′, si farà l&#039;equilibrio: e se, rima­<lb></lb>nendo C′ invariabile, P cresce o scema, è manifesto quale sia, nelle due con­<lb></lb>trapposte direzioni, la forza che prevale. </s></p><p type="main">

<s>Si è supposto C′ invariabile, ed essendo CB men grave in specie del­<lb></lb>l&#039;acqua, s&#039;è, per queste chiarissime dottrine steviniane, concluso che verrà <lb></lb>spinto in alto. </s>

<s>Or s&#039;immagini il solido rimaner sulla medesima base AB, <lb></lb>ma raddoppiare in AD la sua altezza. </s>

<s>È manifesto che la spinta in su sarà <lb></lb>la medesima, ma diminuirà la spinta in giù, perchè l&#039;accrescimento del so­<lb></lb>lido è entrato in luogo dell&#039;acqua, la quale è per ipotesi più grave. </s>

<s>Ond&#039;è <lb></lb>che se CB, DB son due cubi, o due cilindri di legno, il più lungo verrà so­<lb></lb>spinto in su, con più veloce moto dell&#039;altro. </s></p><p type="main">

<s>Non è dunque vero che agli scrittori idrostatici mancassero le ragioni <lb></lb>da risolvere il problema, come si lusingava il Boyle, il quale, dop&#039;aver posto <lb></lb>il fondamento alle cose che stanno in sull&#039;acqua, o che in quella si muo­<lb></lb>vono, soggiungeva queste parole: “ Atque ex iisdem fundamentis afferre pos­<lb></lb>sumus (quam apud alios nondum invenimus) veram problematis istius a <lb></lb>scriptoribus hydraulicis propositi, solutionem, quare, scilicet, si baculus ali­<lb></lb>quis cylindricus secetur in duas partes, quarum una duplam habeat longi­<lb></lb>tudinem alterius, et ambae sub aqua aequali profunditate detentae dimittan­<lb></lb>tur, eodem tempore et emergere sinantur, maior celerius adscendet minori ” <lb></lb>(ibid., pag. </s>

<s>77). </s></p><p type="main">

<s>Constando dunque l&#039;Idrostatica, ne&#039;trattati dei precedenti Autori, vera­<lb></lb>mente di conclusioni e di sperimenti, si può dire che il Boyle non dette a <lb></lb>quelle nessuna promozione, cosicchè l&#039;opera sua si ridusse tutta a confer­<lb></lb>mare verità già dimostrate. </s>

<s>Quanto agli sperimenti non è che la Scienza, <lb></lb>prima di lui, ne patisse difetto, ma non erano tutti praticabili a quel modo, <lb></lb>che si proponevano dagli speculativi, e il Boyle mostrò come si dovevano <lb></lb>disporre ed esercitare gli strumenti, perchè rispondessero esattamente alle <lb></lb>intenzioni. </s>

<s>Spesso la prescrizione di certi organi è superflua: alcune osser­<lb></lb>vanze son così minuziose, da somigliare molto a pedanterie, ma è nono­<lb></lb>stante il Boyle, come sempre, anche qui grande maestro dell&#039;arte speri­<lb></lb>mentale. </s></p><pb xlink:href="020/01/3280.jpg" pagenum="241"></pb><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Tali furono i progressi, fatti dall&#039;Idrostatica appresso gli stranieri, mentre <lb></lb>in Italia si rimaneva tuttavia rattratta nel Discorso galileiano delle galleg­<lb></lb>gianti. </s>

<s>Eppure gl&#039;impulsi al progredire erano agli altri venuti da noi, comu­<lb></lb>nicandosi al Boyle dal Pascal, e al Pascal dal Torricelli e dal Magiotti. </s>

<s>Ma <lb></lb>come sia avvenuto che la scintilla delle tradizioni corresse prima ad accen­<lb></lb>dere il fuoco in Francia, si comprenderà dai fatti narrati, rammemorandoci <lb></lb>che le lettere torricelliane al Ricci non si resero pubblicamente note, che <lb></lb>nel 1663, insieme col trattato del Pascal, e un anno prima de&#039;Paradossi del <lb></lb>Boyle. </s>

<s>Quell&#039;anno 1663 segna l&#039;epoca del risorgimento dell&#039;Idrostatica in <lb></lb>Italia: risorgimento, che gli Accademici fiorentini par che volessero far pro­<lb></lb>clamare al Magliabechi solennemente, in questo, fra i suoi celebri <emph type="italics"></emph>Avvisi <lb></lb>letterari,<emph.end type="italics"></emph.end> che trascriviamo dall&#039;autografo: “ Il Boyle ha stampato in Oxford <lb></lb><emph type="italics"></emph>Paradoxa hydrostatica,<emph.end type="italics"></emph.end> dove con varie esperienze cerca di stabilire l&#039;equi­<lb></lb>librio de&#039;liquori secondo il libretto di monsù Pascal, o piuttosto secondo <lb></lb>l&#039;invenzione del Torricelli, che veramente fu il primo ” (MSS. Cim., T. XXI, <lb></lb>fol. </s>

<s>42). </s></p><p type="main">

<s>Si disse come l&#039;invenzione fosse spiegata, e pubblicamente da Tommaso <lb></lb>Cornelio diffusane la notizia. </s>

<s>E benchè l&#039;Epistola di lui si rimanesse per <lb></lb>quindici anni non curata, per le ragioni accennate, e per altre che non im­<lb></lb>porta mettersi a investigare; ora era naturale si rivolgessero gli studiosi con <lb></lb>vivo desiderio a lei, ch&#039;ebbe perciò la massima efficacia nel detto risorgi­<lb></lb>mento della Scienza. </s>

<s>Giovanni Finchio, mandato dal principe Leopoldo de&#039;Me­<lb></lb>dici per l&#039;Italia, a raccogliere oggetti di Storia naturale, notizie d&#039;autori e <lb></lb>di libri; non mancò d&#039;informarsi del Cornelio, che il Borelli, negli accade­<lb></lb>mici consessi intorno al confutar la leggerezza positiva, riconosceva beneme­<lb></lb>rito banditore dell&#039;Idrostatica torricelliana, attinta dalla bocca del Ricci. </s>

<s>“ A <lb></lb>Napoli (così il Finchio riferiva al Principe, in una lettera del 24 Novem­<lb></lb>bre 1663) abbiamo avuto particolarissima notizia del signor Tommaso Cor­<lb></lb>nelio, matematico e medico di grande grido, e amico del signor Michelan­<lb></lb>giolo Ricci. </s>

<s>Lui ha scritto un libro intitolato <emph type="italics"></emph>Progymnasmata:<emph.end type="italics"></emph.end> pretende che <lb></lb>lui sia stato inventore della ipotesi della compressione dell&#039;aria, e forza ela­<lb></lb>stica di lei, innanzi Pecqueto ” (ivi, T. XVII, fol. </s>

<s>224). </s></p><p type="main">

<s>Ma il Viviani, non contento a leggere l&#039;Epistola corneliana nell&#039;origi­<lb></lb>nale latino, si dette diligentemente a tradurla, o intendesse così d&#039;imprimer <lb></lb>meglio nella sua propria mente quelle dottrine, o di divulgarle negli altri, <lb></lb>così, più facilmente. </s>

<s>È notabile in ogni modo che rimanesse questa fatica <lb></lb>interrotta proprio colà, dove s&#039;entrava nell&#039;argomento dell&#039;Idrostatica, di­<lb></lb>stratto senza dubbio il Viviani dal concepire, e poi dal distendere il trattato <lb></lb>che diremo, e che gli fu suggerito dal rimeditar le cose, che stava per tra-<pb xlink:href="020/01/3281.jpg" pagenum="242"></pb>durre in su quel punto. </s>

<s>Ciò che n&#039;è rimasto è dal fol. </s>

<s>48-66 del T. CXXXVI <lb></lb>de&#039;Discepoli di Galileo, dove in principio, dopo l&#039;avvertenza <emph type="italics"></emph>Mia traduzione,<emph.end type="italics"></emph.end><lb></lb>si legge: “ Lettera all&#039;illustrissimo signor marchese Marcello Crescenti, di <lb></lb>Tommaso Cornelio da Cosenza, nella quale si esplicano, per mezzo della cir­<lb></lb>cumpulsione, secondo l&#039;opinione platonica, le vere cagioni di que&#039;moti, che <lb></lb>volgarmente dicono farsi per ragione di fuggire il vacuo. </s>

<s>Si sciolgono ancora <lb></lb>alcune questioni naturali, che cadono in proposito del discorso, e si appor­<lb></lb>tano in campo alcuni nuovi problemi. </s>

<s>Stampata in Roma nel 1648. ” </s></p><p type="main">

<s>Il passo originale in questa lettera, a cui rimase nel tradurre il Viviani, <lb></lb>per mettersi a svolgere ordinatamente i pensieri di lì concepiti, è il seguente, <lb></lb>che si trascrive dalla citata appendice ai <emph type="italics"></emph>Proginnasmi.<emph.end type="italics"></emph.end> “ Aqua premit in­<lb></lb>teriorem vasis superficiem, non modo iuxta perpendiculares, sed iuxta incli­<lb></lb>natas quoque lineas: immo, non solum iuxta rectas, sed etiam iuxta flexuo­<lb></lb>sas, quae rectis aequiparantur. </s>

<s>In omni tamen casu tantus fit impulsus, <lb></lb>quantus omnino fieret a perpendiculo aquae altitudinem definiente. </s>

<s>Eadem <lb></lb>enim pressioni aquarum contingunt, quae in motu gravium naturaliter de­<lb></lb>scendentium observantur, quum pressus hic oriatur ex propensione, quam <lb></lb>habet aqua ad motum deorsum. </s>

<s>Quemadmodum vero pila plumbea per pla­<lb></lb>num inclinatum, vel per tubum in helicis formam revolutum, a summo ad <lb></lb>imum repens, tantam denique acquirit velocitatem, quantam propemodum <lb></lb>indepta fuisset, si per rectam perpendicularem expositae altitudini aequalem <lb></lb>descendisset; ita ferme aqua in vase contenta non modo subiectum fundum, <lb></lb>sed et latera quoque urgens aperto foramine erumpit tanto impetu, quantum <lb></lb>postulare videtur eius altitudo ” (pag. </s>

<s>342). </s></p><p type="main">

<s>Come venisse di qui suggerito al Viviani quel suo metodo di risolvere <lb></lb>il liquido in una matassa di filetti infiniti, lungo i quali gravitassero le loro <lb></lb>moli, supposte concentrate in un punto, co&#039;momenti convenevoli alle scese <lb></lb>lungo piani inclinati, che di essi filetti avessero le medesime lunghezze e <lb></lb>direzioni; è assai facile a comprendere: nè men facile è a indovinare che <lb></lb>venisse di qui al Viviani stesso inspirata quella riforma, intesa a rendere i <lb></lb>processi idrostatici di Archimede universali. </s>

<s>Essendo già da noi pubblicato <lb></lb>addietro il trattatello, in cui restituiva l&#039;Autore alla desiderata universalità i <lb></lb>teoremi <emph type="italics"></emph>De insidentibus humido,<emph.end type="italics"></emph.end> sembrerebbe esser ora venuta l&#039;occasione <lb></lb>di mantenere le accennate promesse, riducendo dai manoscritti le generali <lb></lb>proposizioni, dimostrative delle ragioni, secondo le quali i raggi fluidi eser­<lb></lb>citano i loro momenti: ragioni, da cui i teoremi, scritti nel trattatello già <lb></lb>noto, dipendono come legittimi corollari immediati. </s>

<s>Indugeremo nonostante <lb></lb>ancora un poco a sodisfare alla dotta curiosità dei nostri Lettori, per tratte­<lb></lb>nerci a considerar brevemente quali altri benefici influssi piovessero dall&#039;epi­<lb></lb>stola del Cornelio a rinfrescare l&#039;aridità degli studii idrostatici del Borelli. </s></p><p type="main">

<s>Il fautore del Michelini, il corto interpetre di Archimede, che credeva <lb></lb>repugnare alla natura dell&#039;acqua, corpo anch&#039;essa grave, lo spingere in su, <lb></lb>e non potere perciò premere su sè stessa e contro i solidi sottoposti, se non <lb></lb>che in direzion perpendicolare; ecco, dopo aver meditata l&#039;Epistola del Cor-<pb xlink:href="020/01/3282.jpg" pagenum="243"></pb>nelio, come la pensi molto diversamente. </s>

<s>Nella proposizione CXC <emph type="italics"></emph>De motio­<lb></lb>nibus naturalibus,<emph.end type="italics"></emph.end> appena detto che Archimede suppone premere solamente <lb></lb>il fluido per linea perpendicolare all&#039;orizonte, così soggiunge: “ Hoc pro­<lb></lb><figure id="id.020.01.3282.1.jpg" xlink:href="020/01/3282/1.jpg"></figure></s></p><p type="caption">

<s>Figura 127.<lb></lb>fecto verissimum est, quotiescumque innatet intra aquam <lb></lb>prisma aliquod consistens et durum. </s>

<s>At si in vase BCEI <lb></lb>(fig. </s>

<s>127), aqua pleno, intra spatium AIFG collocetur <lb></lb>non prisma ligneum, sed aliud corpus molle vel fluidum <lb></lb>cedens, minus grave specie quam sit aqua collateralis; <lb></lb>tunc nedum fluidi IG sursum perpendiculariter superfi­<lb></lb>cies FG versus IA, sed praeterea latus eius AG propel­<lb></lb>letur constringeturque versus IF, ita ut eodem tempore <lb></lb>fluidum minus grave IG simul ascendat perpendiculariter <lb></lb>versus IA, et lateraliter quoque ab AG versus IF transportetur. </s>

<s>Hinc colligitur <lb></lb>quod aqua, seu quodlibet fluidum BG, gravius specie quam corpus IG, nedum <lb></lb>vim facit premendo perpendiculariter, sed etiam vim exercet lateraliter, non <lb></lb>quidem per horizontales lineas BA et HG, sed per lineas inclinatas BK et <lb></lb>LG. </s>

<s>Et hoc suppleri archimedeo assumpto debere censeo, cum instinctu na­<lb></lb>turae corpora omnia gravia descendere conentur versus terrae centrum, qui­<lb></lb>buscumque modis hoc ab eis consequi possit, nedum itinere perpendiculari <lb></lb>ad horizontem sed etiam inclinato ” )pag. </s>

<s>393). </s></p><p type="main">

<s>Questa teoria, che abbiamo con parole simili dianzi letta nel Cornelio, <lb></lb>il Borelli passa a confermare con l&#039;esperienza della borsa di pelle, tesa in <lb></lb>forma di parallelepipedo da verghe rigide, interiormente appuntate e rego­<lb></lb>larmente disposte, la qual borsa, dice il Borelli, se tu immergerai nell&#039;acqua, <lb></lb>in modo che la bocca di lei, come quella di un pozzo, rimanga fuori sco­<lb></lb>perta: “ videbis quod, nedum basis et fundum, sed etiam quatuor faces col­<lb></lb>laterales bursae incurventur convexe versus intermedium axim eiusdem pu­<lb></lb>tei. </s>

<s>Et si simul digiti aut virgulae educantur, nec amplius vim exerceant, <lb></lb>nedum basis et fundum putei ascendet sursum, sed etiam eius parietes <lb></lb>collaterales se se constringent, et ad se se invicem accedent, quod est evi­<lb></lb>dentissimum signum aquam, nedum vim facere sursum perpendiculariter <lb></lb>aerem expellendo, sed etiam lateraliter conari excurrere per lineas obliquas, <lb></lb>constringendo laterales parietes praedicti putei coriacei ” (ibid., pag. </s>

<s>394, 95). </s></p><p type="main">

<s>Il Borelli dunque, come il Pascal e il Boyle, non esce fuori de&#039;termini <lb></lb>delle esperienze, e la proposizione di lui è puramente fisica, come son tutte <lb></lb>quelle de&#039;suoi due illustri predecessori. </s>

<s>L&#039;Idrostatica matematica, perciò, in <lb></lb>questa che fu pure epoca gloriosa di risorgimento, parve rimanersi ne&#039;teo­<lb></lb>remi dello Stevino come assiderata. </s>

<s>Il Torricelli era opportunamente soccorso <lb></lb>a stiepidirne le membra, facendovi sopra riflettere i calori della idrodinamica <lb></lb>nuova, e il Cornelio, nella sua Epistola, aveva raccolti e indirizzati allo scopo <lb></lb>quei benefici raggi, come in uno specchio ustorio, nel foco del quale collo­<lb></lb>cando il Viviani la conveniente materia, venne ad accendere la nuova lam­<lb></lb>pada nel tempio della Scienza. </s></p><p type="main">

<s>Che il liquido si dovesse disporre in una superficie orizontale, concen-<pb xlink:href="020/01/3283.jpg" pagenum="244"></pb>trica con la terra, fu per Archimede e per lo Stevino piuttosto un&#039;ipotesi <lb></lb>che una dimostrazione. </s>

<s>E se pure qualche dimostrazione si provarono a darne <lb></lb>gl&#039;Idrostatici di poi, la desunsero dalle particolarità de&#039;fatti, e non dalla uni­<lb></lb>versaità dei principii. </s>

<s>Vedremo come, dall&#039;aver matematicamente dimostrato <lb></lb>dover nell&#039;umido stagnante ogni assegnato raggio finalmente posarsi in equi­<lb></lb>librio, fosse il primo il Viviani a concluderne, per matematica dimostrazione, <lb></lb>che di ogni umido stagnante la superficie è necessariamente sferica, e con­<lb></lb>centrica con la Terra. </s></p><p type="main">

<s>Le spinte idrostatiche di sotto in su il Torricelli s&#039;era contentato di <lb></lb>persuaderle frettolosamente al Ricci, per via di ovvie esperienze. </s>

<s>Il Nardi poi <lb></lb>accennava a una riflessione del moto, e se di questo moto riflesso aveva lo <lb></lb>Stevino detto le misure, non concludeva però da principii universali il suo <lb></lb>discorso. </s>

<s>Il Viviani fu il primo, dietro matematiche prenozioni, a dimostrar <lb></lb>che, se un raggio qualunque assegnato nell&#039;umido non trova sufficiente mo­<lb></lb>mento di resistenza in un altro adiacente raggio, a sè simile e dal comun <lb></lb>termine sporgente infino alla suprema superficie; verrà in su respinto neces­<lb></lb>sariamente. </s>

<s>Il teorema poi confermava con una esperienza, che, non paren­<lb></lb>doci bene il tacerla, mettiamo qui, per non riferirsi al trattato dei Raggi <lb></lb>fluidi, se non che come una nota, a piè di pagina, scritta, per avvertire i <lb></lb>lettori che le ragioni idrostatiche dei momenti si confermano dai pesi stessi <lb></lb>posti sulla stadera. </s>

<s>“ Nell&#039;abbassare con la mano un solido galleggiante nel <lb></lb>fluido di un vaso, posto sulla stadera, e sommergerlo più del suo stato na­<lb></lb>turale, purchè non si faccia toccare il fondo; non si altererà l&#039;equilibrio, <lb></lb>perchè tanta è la forza premente all&#039;in giù della mano, che quella del so­<lb></lb>lido nel volere ascendere e tornare al suo stato. </s>

<s>Lo stesso segue se, invece <lb></lb>di mano, si metterà sopra una molla, che sia ferma fuori del vaso, e posi <lb></lb>con tensione sopra il solido, perchè la molla servirà in luogo di mano ” <lb></lb>(MSS. Cim., T. X, fol. </s>

<s>46). </s></p><p type="main">

<s>Delle pressioni di sotto in su quelle fatte dal liquido lateralmente erano <lb></lb>una conseguenza necessaria, e abbiamo poco fa veduto come il Borelli le <lb></lb>dimostrasse sperimentalmente, e come, con operazioni alquanto diverse nei <lb></lb>modi, ma pur della medesima natura, le avessero dimostrate il Pascal e il <lb></lb>Boyle. </s>

<s>Il Magiotti, prima di tutti loro, aveva delle pressioni idrostatiche per <lb></lb>tutti i versi data la dimostrazione più bella e più efficace, ma nemmeno que­<lb></lb>sta usciva fuori de&#039;termini dell&#039;esperienza. </s></p><p type="main">

<s>La prima dimostrazion matematica, che in pubblico si sapesse, fu quella <lb></lb>tentata dal Guglielmini, per via del principio della composizion delle forze, <lb></lb>supponendo che le infinite molecole componenti il fluido siano per sè stesse <lb></lb>tutte uguali di peso, e in figura di tante esatte piccolissime sfere. </s>

<s>Glie ne <lb></lb>aveva dato l&#039;esempio il maestro suo Geminiano Montanari, il quale, per ri­<lb></lb>solvere alcuni problemi idrostatici, propostigli nella bolognese Accademia del­<lb></lb>l&#039;abate Sampieri, non volendo semplicemente supporre i principii, da cui si <lb></lb>deriverebbero le sue conclusioni, pensò di dimostrarli in altri modi, da quelli <lb></lb>dello Stevino e di Galileo. </s>

<s>“ Ma perchè, egli dice, di tai corpiccioli liquidi <pb xlink:href="020/01/3284.jpg" pagenum="245"></pb>ed insensibili, di che il liquido si compone, non può così bene l&#039;intelletto <lb></lb>discorrere, se prima non se gli propone come sensibili, e di una determinata <lb></lb>figura; non sarà perciò fuori di proposito, ad effetto d&#039;investigare la natura <lb></lb>de&#039;corpi liquidi, figurarci prima diversi vasi ripieni di palline di sensibile <lb></lb>grandezza, sferiche e perfettamente terse, e, conosciuta la natura ed opera­<lb></lb>zione loro, dedurne quelle conclusioni, che similmente a&#039;liquidi vederemo <lb></lb>potersi adattare. </s>

<s>Il che supponendo, vengo prima a provare come, dato un <lb></lb>vaso, il di cui fondo, per chiarezza di discorso, supporremo prima sia per­<lb></lb>fettamente posto orizontale, e le sponde erette al medesimo, e sia ripieno di <lb></lb>palline perfettamente terse, di egual peso e grandezza; intesa qualsivoglia <lb></lb>di dette palline sentirà essa porzione del peso di tutte quelle, che a lei in <lb></lb>livello sono superiori non solo a perpendicolo, ma lateralmente in qualsivo­<lb></lb>glia posto del vaso ” (Discorso idrostatico pubblicato dal Targioni, Aggran­<lb></lb>dimenti ecc. </s>

<s>cit., T. II, pag. </s>

<s>725). </s></p><p type="main">

<s>E dietro questa si fa via il Montanari a dimostrare altre tre proposi­<lb></lb>zioni idrostatiche, concludendo che la pressione patita da una delle palline <lb></lb>è quella stessa, che patiscono tutte le altre simili, disposte nel medesimo <lb></lb>strato orizontale, e che la forza di essa pressione da null&#039;altro dipende, se <lb></lb>non che dal numero degli strati soprapposti: cosicchè insomma la pressione <lb></lb>esercitata dal liquido contro il fondo è quella di una colonna, avente per <lb></lb>base esso fondo, e per altezza la perpendicolare, compresa fra lui e il su­<lb></lb>premo livello, qualunque sia la forma e la disposizione del vaso. </s></p><p type="main">

<s>Il Guglielmini introdusse la matematica nel discorso fisico del suo pro­<lb></lb>prio Maestro, e, nel capitolo primo del trattato <emph type="italics"></emph>Della natura dei fiumi,<emph.end type="italics"></emph.end> si <lb></lb>propose in primo luogo di dimostrare che “ se sarà uno strato retto di sfere, <lb></lb><figure id="id.020.01.3284.1.jpg" xlink:href="020/01/3284/1.jpg"></figure></s></p><p type="caption">

<s>Figura 1<gap></gap>8.<lb></lb>e sopra uno de&#039;di lui interstizi sarà situata un&#039;altra sfera; <lb></lb>premerà questa le quattro sottoposte egualmente, sì per la linea <lb></lb>perpendicolare, che per l&#039;orizzontale ” (Milano 1821, Vol. </s>

<s>I, <lb></lb>pag. </s>

<s>46). Supponendo esser Y (fig. </s>

<s>128) la sfera soprapposta, <lb></lb>e N una delle quattro soggiacenti, se per YN si rappresenta <lb></lb>la forza, con la quale l&#039;una delle dette sfere preme l&#039;altra, e <lb></lb>se una tal forza si decompone nella verticale YR, ossia PN, e <lb></lb>nella orizontale YP, ossia RN, è manifesto il proposito, perch&#039;essendo PR un <lb></lb>quadrato le linee PN, RN sono uguali, e perciò son altresì uguali le forze con <lb></lb>esse linee rappresentate, come in simil modo si dimostrerebbe di tutt&#039;e tre <lb></lb>le altre sfere premute dalla medesima Y. </s></p><p type="main">

<s>Di qui procede il Guglielmini alla dimostrazione delle proposizioni se­<lb></lb>guenti, fra le quali notabile è la IV, d&#039;onde si trae dall&#039;Autore questo prin­<lb></lb>cipale importantissimo corollario, che cioè “ un mucchio di sfere affetterà <lb></lb>sempre di avere la superficie disposta in uno strato, ossia piano orizontale: <lb></lb>o più propriamente in una superficie sferica, il cui centro sia quello dei <lb></lb>gravi ” (ivi, pag. </s>

<s>57). Nel qual discorso del Guglielmini il pubblico ebbe la <lb></lb>prima dimostrazion matematica del teorema secondo di Archimede. </s></p><p type="main">

<s>La novità conferi molto a dar sodisfazione agli speculativi, i quali però, <pb xlink:href="020/01/3285.jpg" pagenum="246"></pb>ripensando che la citata IV, insieme con le proposizioni precedentemente <lb></lb>scritte in principio del trattato della Natura dei fiumi, dipendevano dalla <lb></lb>prima, trovarono che questa per più ragioni era difettosa. </s>

<s>Iacopo Riccati, <lb></lb>come nelle sue <emph type="italics"></emph>Annotazioni<emph.end type="italics"></emph.end> riferisce il Manfredi (ivi, pag. </s>

<s>74), osservò che, <lb></lb>supponendo l&#039;acqua essere un aggregato di piccole sfere, non sarebbe pos­<lb></lb>sibile spiegare come si trovi in natura un corpo, che ecceda del doppio la <lb></lb>gravità specifica di lei. </s>

<s>Il D&#039;Alembert poi nel Dizionario enciclopedico delle <lb></lb>Matematiche, all&#039;articolo <emph type="italics"></emph>fluido,<emph.end type="italics"></emph.end> ridusse a tre le ragioni di quei difetti: pri­<lb></lb>mieramente, perchè l&#039;ipotesi che le particelle minime componenti il liquido <lb></lb>sian perfettamente sferiche è affatto arbitraria: in secondo luogo, perchè la <lb></lb>proposizione del Guglielmini è troppo limitata, supponendovisi i centri di <lb></lb>gravità delle sfere disposti in un piano orizontale, e finalmente perchè la <lb></lb>dimostrazione di lui non vale se non nel caso che la NY, secondo la quale <lb></lb>è diretta la forza della pressione, faccia con la verticale un angolo di 45 gradi. </s></p><p type="main">

<s>Il D&#039;Alembert giudicava così severamente, quando l&#039;uso oramai intro­<lb></lb>dotto del calcolo infinitesimale agevolava il modo di risolvere così fatti pro­<lb></lb>blemi, col ridurre il liquido a particelle infinitesime, delle quali perciò non <lb></lb>è propria nessuna figura, o determinata posizione di parte. </s>

<s>I vantaggi di que­<lb></lb>sto calcolo erano stati saggiati già da chi aveva imparato a far uso degli <lb></lb>indivisibili, come dal Castelli, per esempio, che considerava le correnti per <lb></lb>gli alvei e dentro i tubi esser divise in tante minime sezioni, e dall&#039;Aggiunti <lb></lb>e dal Cornelio, che riguardavano la massa fluida come composta di tanti <lb></lb>infiniti filetti, de&#039;quali si comparavano insieme i momenti, con la regola dei <lb></lb>gravi ora cadenti nel perpendicolo, ora lungo piani variamente inclinati. </s>

<s>Ma <lb></lb>chi dette esplicazione e ordine a questo primo pensiero fu il Viviani, la di­<lb></lb>mostrazion meccanica dell&#039;uguaglianza delle pressioni, e d&#039;altre idrostatiche <lb></lb>conseguenze, data dal quale, se va per vie più oblique di quelle del D&#039;Alem­<lb></lb>bert e del Bernoulli, non è perciò da dire nè men ferma, nè meno esatta. </s>

<s><lb></lb>Il Guglielmini perciò era stato, in queste matematiche applicazioni, prece­<lb></lb>duto dal Viviani, ciò che fu scritto dal quale, non saputo fin qui, è tempo <lb></lb>finalmente di dare alla luce. </s></p><p type="main">

<s>S&#039;intitola quella scrittura <emph type="italics"></emph>De radiis fluidis,<emph.end type="italics"></emph.end> per i quali che cosa debba <lb></lb>intendersi precisamente definisce in principio l&#039;Autore, dopo le prenozioni di <lb></lb>Statica, alle quali s&#039;informa, e dalle quali si svolge tutto intero il trattato. </s>

<s><lb></lb>Si vedrà questo resultar di XXV proposizioni, le quali, essendosi trovate di­<lb></lb>sperse per il volume manoscritto, si sono da noi ordinate, e ridotte a po­<lb></lb>tersi leggere dalle postille, e dalle confusissime cassature, ciò che s&#039;è creduto <lb></lb>sufficiente alla loro più chiara intelligenza, senza bisogno d&#039;altro commento. </s>

<s><lb></lb>I lettori troveranno forse le dimostrazioni prolisse, e giudicheranno che la <lb></lb>sostanza poteva raccogliersi in assai meno parole. </s>

<s>Ma se penseranno a quei <lb></lb>tempi, ne&#039;quali l&#039;Idrostatica aveva bisogno, specialmente fra noi, di una ri­<lb></lb>forma così radicale, da apparire quasi una Scienza nuova; vedranno quanto <lb></lb>saviamente il Viviani si consigliasse di condiscendere alle minuziose facilità <lb></lb>di un libro elementare. </s></p><pb xlink:href="020/01/3286.jpg" pagenum="247"></pb><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>DE RADIIS FLUIDIS<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>PRAENOTIONES<emph.end type="center"></emph.end></s></p><p type="main">

<s>Acturi itaque de humidorum gravitatibus, atque momentis, aliqua nobis <lb></lb>praemittenda necessario sunt de momentis gravium in genere. </s>

<s>Ex demonstra­<lb></lb>tis autem a&#039;Galileo, eiusque doctrinae promotore Torricellio, in libris <emph type="italics"></emph>De motu <lb></lb>gravium naturaliter descendentium,<emph.end type="italics"></emph.end> habemus: </s></p><p type="main">

<s>I. </s>

<s>Quod si in planis inaequaliter inclinatis, eamdem tamen elevatio­<lb></lb>nem habentibus, duo gravia constituantur, quae inter se eamdem homologe <lb></lb>rationem habeant quam habent longitudines planorum; gravia aequale mo­<lb></lb>mentum habebunt. </s></p><p type="main">

<s>II. </s>

<s>Quod momenta gravium aequalium, super planis inaequaliter in­<lb></lb>clinatis, eamdem tamen elevationem habentibus, sunt in reciproca ratione <lb></lb>cum longitudinibus planorum. </s></p><p type="main">

<s>III. </s>

<s>Quod momentum totale gravis, ad momentum quod habet in plano <lb></lb>inclinato, est ut longitudo ipsius plani inclinati ad perpendiculum. </s></p><p type="main">

<s>IV. </s>

<s>Quod momenta gravium aequalium, super planis inaequaliter in­<lb></lb>clinatis, sunt in homologa ratione cum perpendiculis partium aequalium. </s></p><p type="main">

<s><emph type="center"></emph>DEFINITIONES<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="italics"></emph>Radium<emph.end type="italics"></emph.end> seu lineam physicam dicemus uniformem cuiuscumque datae <lb></lb>molis tractum, seu longitudinem, nulla fere, quatenus imaginari nobis licet, <lb></lb>crassitudine praeditam. </s></p><p type="main">

<s><emph type="italics"></emph>Punctum<emph.end type="italics"></emph.end> vero <emph type="italics"></emph>physicum<emph.end type="italics"></emph.end> dicemus radii dicti principium sive extremum, <lb></lb>particulam scilicet nulla fere, quatenus nobis imaginari licet, aut crassitu­<lb></lb>dine aut longitudine praeditam. </s></p><p type="main">

<s><emph type="italics"></emph>Radios similes<emph.end type="italics"></emph.end> dicimus eos, qui eadem uniformi crassitudine sunt praediti. </s></p><p type="main">

<s><emph type="center"></emph>POSTULATUM<emph.end type="center"></emph.end></s></p><p type="main">

<s>Radiorum similium moles sunt invicem ut eorum inter se longitudines </s></p><p type="main">

<s>PROPOSITIO I. — <emph type="italics"></emph>Radii fluidi similes, ac specie aeque graves, ab eadem <lb></lb>horizontali ad eamdem aliam inferiorem, secundum perpendicularem li­<lb></lb>neam protensi, et secundum easdem gravitantes; momentum habent ae­<lb></lb>quale.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/3287.jpg" pagenum="248"></pb><p type="main">

<s>Sit ABC (fig. </s>

<s>129) superficies horizontalis superior, DEF inferior, BE <lb></lb>et CF radii similes, ac specie aeque graves, ab ABC ad EDF, secundum per­<lb></lb><figure id="id.020.01.3287.1.jpg" xlink:href="020/01/3287/1.jpg"></figure></s></p><p type="caption">

<s>Figura 129.<lb></lb>pendiculares lineas BE, et CF protensi, et secundum <lb></lb>easdem gravitantes: dico eorum momenta aequalia <lb></lb>esse. </s>

<s>Nam, ob concentritatem orizontalium ABC, DEF, <lb></lb>aequàles ostendent inter se perpendiculares longitu­<lb></lb>dines interceptae BE et CF. </s>

<s>Ut autem longitudines <lb></lb>invicem radiorum BE et CF, ita et totalia eorumdem <lb></lb>momenta. </s>

<s>Momenta autem radiorum BE et CF, secundum lineas BE, CF, <lb></lb>totalia sunt, cum eaee ponantur perpendiculares; erunt ergo ut longitudines, <lb></lb>adeoque aequalia. </s></p><p type="main">

<s>PROPOSITIO II. — <emph type="italics"></emph>Radii fluidi, ab una horizontali ad aliam inferio­<lb></lb>rem, secundum quamcumque lineam inclinatam, recta protensi, et secun­<lb></lb>dum eamdem gravitantes; momentum aequale est momento radii perpen­<lb></lb>dicularis inter easdem horizontales perpendiculariter gravitantis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sit HG (fig. </s>

<s>130) radius fluidus, secundum li­<lb></lb><figure id="id.020.01.3287.2.jpg" xlink:href="020/01/3287/2.jpg"></figure></s></p><p type="caption">

<s>Figura 130.<lb></lb>neam utcumque inclinatam GH, ab horizontali su­<lb></lb>periori ABC ad inferiorem DEF recta pertingens, et <lb></lb>secundum eamdem gravitans. </s>

<s>BE vero radius fluidus <lb></lb>similis, ac specie aeque gravis, perpendiculariter ab <lb></lb>eadem ABC ad eamdem DEF pertingens, ac perpen­<lb></lb>diculariter gravitans: dico momentum radii HG momento radii BE aequale esse. </s></p><p type="main">

<s>Sit enim radii inclinati HG perpendiculum HI. </s>

<s>Erit igitur momentum <lb></lb>actuale radii HG, secundum lineam HG gravitantis, ad momentum totale <lb></lb>eiusdem, ut longitudo perpendicularis HI, idest BE, ad longitudinem lineae <lb></lb>inclinatae HG. </s>

<s>Ut autem longitudo BE, ad longitudinem HG, ita etiam est <lb></lb>momentum totale radii BE, idest momentum actuale ipsius secundum per­<lb></lb>pendicularem BE, ad momentum totale radii HG. </s>

<s>Momentum igitur radii BE <lb></lb>secundum BE, ad momentum radii HG secundum HG, eamdem proportio­<lb></lb>nem habent ad momentum totale radii HG, eam videlicet quam longitudo <lb></lb>BE ad longitudinem HG. </s>

<s>Erunt igitur inter se necessario aequalia, quod etc. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> — Hinc radiorum omnium similium, ac specie aeque gra­<lb></lb>vium, ab eadem horizontali ad eamdem aliam inferiorem, secundum lineas <lb></lb>utcumque inclinatas, recta pertingentium, et secundum easdem gravitantium; <lb></lb>momenta erunt invicem aequalia. </s>

<s>Ostenditur enim singula eidem tertio ae­<lb></lb>qualia: momento scilicet radii similis, ac specie aeque gravis, ab eadem <lb></lb>horizontali ad eamdem perpendicularem protensi, ac perpendiculariter gra­<lb></lb>vitantis, ut patet ex praecedenti. <lb></lb><figure id="id.020.01.3287.3.jpg" xlink:href="020/01/3287/3.jpg"></figure></s></p><p type="caption">

<s>Figura 131.</s></p><p type="main">

<s>PROPOSITO III. — <emph type="italics"></emph>Sit OL<emph.end type="italics"></emph.end> (fig. </s>

<s>131) <emph type="italics"></emph>radius flui­<lb></lb>dus, ab horizontali ABC ad inferiorem DEF, se­<lb></lb>cundum lineam utcumque tortuosam OMNL per­<lb></lb>tingens, et secundum eamdem gravitans, BE vero <lb></lb>radius similis ac specie aeque gravis, ab eadem <lb></lb>ABC, ad eamdem DEF perpendiculariter proten-<emph.end type="italics"></emph.end><pb xlink:href="020/01/3288.jpg" pagenum="249"></pb><emph type="italics"></emph>sus: dico momentum radii OL, secundum lineam OMNL, aequale esse <lb></lb>momento radii BE, secundum perpendicularem BE.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Cum enim radii OL partes in directum, ob tortuositatem, non sint, erit <lb></lb>ab extremo O aliqua eius portio, quae primum cum alia sibi continuo suc­<lb></lb>cedenti in directum non est posita. </s>

<s>Sit huiusmodi portio OM. </s>

<s>Quidquid igi­<lb></lb>tur interiacet extremis OM tortuositate utique caret. </s>

<s>Per extremum itaque <lb></lb>ipsius M intelligatur transire horizontalis MS, quae concentrica cum sit ABC, <lb></lb>et punctum ipsius M cadat infra AB, tota necessario infra ABC cadet, se­<lb></lb>cabitque necessario radium BE, puta in S. </s>

<s>Erit igitur momentum portionis <lb></lb>OM aequale momento portionis BS. </s>

<s>Rursus ab extremo M erit alia portio <lb></lb>subsequens, puta MN, quae primum similiter cum reliqua sibi continuo suc­<lb></lb>cedenti in directum non est posita. </s>

<s>Si igitur extremum N infra horizontalem <lb></lb>MS cadit, transiens horizontaliter per N, secabit rursus BE, puta in Q, erit­<lb></lb>que similiter momentum portionis MN aequale momento portionis <expan abbr="Sq.">Sque</expan> Ea­<lb></lb>demque ratione reliqua, puta ultima radii OL portio, continuo succedens NL, <lb></lb>cum reliqua et ultima radii BE, continuo succedens, aequale momentum habe­<lb></lb>bit, ut ostendi potest, Adeoque totius radii OL momentum totius radii BE <lb></lb>momento aequale esse manifestum erit. </s></p><p type="main">

<s>Si vero portionis subsequentis MN extremum N supra horizontalem MS <lb></lb>cadat, ut in 132 schemate ostenditur, transiens scilicet per N horizontalis <lb></lb><figure id="id.020.01.3288.1.jpg" xlink:href="020/01/3288/1.jpg"></figure></s></p><p type="caption">

<s>Figura 132.<lb></lb>PNQ, secabit OM, puta in P, et BE, puta in <expan abbr="q.">que</expan> <lb></lb>Momentum autem radii OMN, ad N, aequale est mo­<lb></lb>mento portionis OP, supra horizontalem PNQ extan­<lb></lb>tis, adeoque momento portionis BQ, iisdem horizon­<lb></lb>talibus ABC et PNQ interceptae. </s>

<s>Eademque ratione <lb></lb>erit momentum reliquae et ultimae portionis continuo <lb></lb>subsequentis NL aequale momento reliquae, et ul­<lb></lb>timae continuo subsequentis QE. </s>

<s>Unde totius simul radii OL momentum <lb></lb>momento totius radii BE aequale erit. </s></p><p type="main">

<s>Si denique eiusdem portionis subsequentis MN extremum N in ipsa <lb></lb><figure id="id.020.01.3288.2.jpg" xlink:href="020/01/3288/2.jpg"></figure></s></p><p type="caption">

<s>Figura 133.<lb></lb>horizontali MS reperiatur, ut in 133 schemate, erit <lb></lb>momentum OMN, ad N, aequale momento BS, et <lb></lb>momentum reliquae atque ultimae NL momento re­<lb></lb>liquae et ultimae SE. </s>

<s>Unde momentum totius OL <lb></lb>momento totius BE semper aequale ostendetur. </s></p><p type="main">

<s>PROPOSITIO IV. — <emph type="italics"></emph>Si super punctis eiusdem <lb></lb>sphaericae superficiei, Orbi concentricae, intelligan­<lb></lb>tur gravitare duo radii similes, ac specie aeque graves, qui ad idem <lb></lb><figure id="id.020.01.3288.3.jpg" xlink:href="020/01/3288/3.jpg"></figure></s></p><p type="caption">

<s>Figura 134.<lb></lb>punctum alterius superficiei superioris sphae­<lb></lb>ricae pariter atque Orbi concentricae oblique <lb></lb>utcumque sint erecti; erunt momenta ipsorum <lb></lb>necessario aequalia.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Super punctis B, H (fig. </s>

<s>134) superficiei <lb></lb>ABHC, cuius centrum idem est ac centrum Or-<pb xlink:href="020/01/3289.jpg" pagenum="250"></pb>bis, intelligantur gravitare duo radii similes, ac specie aeque graves EH, <lb></lb>et EB, qui ad idem punctum E alterius sphaericae superficiei superioris DEG, <lb></lb>cuius idem est centrum, oblique utcumque sint erecti; dico radiorum EH et <lb></lb>EB momenta fore necessario inter se aequalia. </s></p><p type="main">

<s>Ducto enim, per pucta B et H, plano horizontali BH, intelligatur radio <lb></lb>EB subiectum planum immediate adiacens EB, radio vero EH planum im­<lb></lb>mediate adiacens EH. </s>

<s>Erunt utique plana EH et EB super eodem horizon­<lb></lb>tali plano BH inaequaliter inclinata, eamdem tamen supra ipsum perpendi­<lb></lb>cularem elevationem habentia, eruntque longitudines planorum dictorum aee­<lb></lb>dem ac longitudines radiorum sibi immediate adiacentium. </s>

<s>Ut autem radiorum <lb></lb>EH et EB longitudines inter se, ita, ob suppositam similitudinem, sunt <lb></lb>ipsorum inter se magnitudines seu moles. </s>

<s>Ut autem moles inter se, ita, ob <lb></lb>eamdem suppositam in specie gravitatem, sunt necessario inter se eorumdem <lb></lb>pondera. </s>

<s>Erunt igitur radiorum EH et EB inter se pondera ut eorumdem <lb></lb>inter se longitudines, scilicet pondus radii EH, ad pondus radii EB, ut lon­<lb></lb>gitudo radii EH ad longitudinem radii EB, adeoque ut longitudo plani EH, <lb></lb>ad longitudinem plani EB. </s>

<s>Igitur erunt graviorum datorum EH et EB pon­<lb></lb>dera in homologa ratione cum longitudinibus planorum, super quibus consti­<lb></lb>tuta intelliguntur. </s>

<s>Igitur aequalia necessario erunt ipsorum momenta. </s></p><p type="main">

<s>Si autem, demptis planis adiacentibus in eadem constructione erecti, <lb></lb>maneant iidem radii EH et EB, manifestum est quod eadem manebit ratio <lb></lb>momenti. </s>

<s>Unde universaliter huiusmodi radii sic dispositi aequalia erunt ne­<lb></lb>cessario momenta, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO V. — <emph type="italics"></emph>Si vero radiorum dictorum alter quidem oblique, <lb></lb>alter vero ad perpendiculum erectum ponatur, erunt ipsorum momenta <lb></lb>etiam aequalia.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sit radiorum EH et EB, in secunda constructione eiusdem schematis, <lb></lb>alter quidem nempe EH ad perpendiculum, alter vero, nempe EB, oblique <lb></lb>erectus: dico ipsorum momenta esse necessario inter se aequalia. </s>

<s>Erit enim <lb></lb>momentum totale radii EB, ad momentum quod modo habet super plano <lb></lb>inclinato EB, ut longitudo EB ad ipsius perpendiculum, nempe ad EH. </s>

<s>Et <lb></lb>convertendo erit momentum, quod modo habet EB radius super plano in­<lb></lb>clinato EB, ad momentum totale ipsius, ut longitudo perpendiculi EH, nempe <lb></lb>radii EH, ad longitudinem plani inclinati EB. </s>

<s>Ut autem longitudo radii EH, <lb></lb>ad longitudinem radii EB, ita etiam est, ob similitudinem, moles ad molem, <lb></lb>et, ob eamdem gravitatis speciem, pondus ad pondus. </s>

<s>Adeoque ut longitudo <lb></lb>ad longitudinem, ita momentum totale radii EH, ad momentum totale radii <lb></lb>EB. </s>

<s>Momentum autem, quod actu habet radius EH, totale est, cum ponatur <lb></lb>ad perpendiculum erectum; unde momentum, quod actu habet radius per­<lb></lb>pendicularis EH, ad momentum totale radii oblique erecti EB, est ut longi­<lb></lb>tudo ipsius radii perpendicularis EH, ad longitudinem radii oblique erecti <lb></lb>EB. </s>

<s>Dictum est autem quod momentum, quod actu habet EB, ad momen­<lb></lb>tum totale ipsius EB, est etiam ut longitudo perpendicularis EH, ad longi­<lb></lb>tudinem EB; momentum igitur actuale radii EB, et momentum actuale radii <pb xlink:href="020/01/3290.jpg" pagenum="251"></pb>EH, eamdem rationem habent ad idem tertium, nempe ad momentum to­<lb></lb>tale radii EB. </s>

<s>Erunt igitur momenta actualia radiorum EH et EB necessario <lb></lb>aequalia, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO VI. — <emph type="italics"></emph>Si super punctis eiusdem sphaericae superficiei, <lb></lb>Orbi concentricae, intelligantur gravitare duo radii similes, ac specie aeque <lb></lb>graves, qui extra superficiem cadentes alterius superficiei superioris, Orbi <lb></lb>pariter concentricae, oblique utcumque sint erecti; erunt ipsorum momenta <lb></lb>necessario aequalia.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Super punctis B et C (fig. </s>

<s>135) sphaericae superficiei HBC, cuius cen­<lb></lb>trum sit centrum Orbis, intelligantur gravitare duo radii similes, ac specie <lb></lb><figure id="id.020.01.3290.1.jpg" xlink:href="020/01/3290/1.jpg"></figure></s></p><p type="caption">

<s>Figura 135.<lb></lb>aeque graves AB et FC, qui extra superficiem HBC <lb></lb>cadentes ad puncta A et F alterius sphaericae superfi­<lb></lb>ciei superiori, atque Orbi pariter concentricae, oblique <lb></lb>utcumque sint erecti: dico radiorum AB et FC mo­<lb></lb>menta fore invicem necessario aequalia. </s>

<s>Intelligantur <lb></lb>enim ad eadem puncta A et F erecti, super eadem subiecta superficie HBC, <lb></lb>perpendiculares radii AH et FG, similes ac specie aeque graves cum radiis <lb></lb>AB et FC, eritque longitudo radii AH aequalis longitudini radii FG. </s>

<s>Igitur <lb></lb>moles moli, ob similitudinem, et pondus ponderi, ob eamdem gravitatis spe­<lb></lb>ciem, erit aequale. </s>

<s>Unde momentum totale unius momento totali alterius <lb></lb>erit aequale. </s>

<s>Momentum autem actuale radii AH, cum ponatur ad perpen­<lb></lb>diculum erectus, idem est ac momentum ipsius totale, eademque ratione <lb></lb>idem erit momentum actuale radii FG, ac momentum totale eiusdem. </s>

<s>Mo­<lb></lb>mentum igitur actuale radii AH aequale est momento actuale radii FG. </s>

<s><lb></lb>Atqui ex praecedenti momentum radii AH aequale est momento radii AB, <lb></lb>momentum vero radii FG aequale momento radii FC; momentum igitur <lb></lb>radii AB momento radii FC aequale erit, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s>PROPOSITIO VII. — <emph type="italics"></emph>Si super eodem puncto sphaericae superficiei, Orbi <lb></lb>concentricae, intelligantur gravitare duo radii similes, ac specie aeque gra­<lb></lb>ves. </s>

<s>qui extra superficiem datam cadentes ad puncta alterius superficiei su­<lb></lb>perioris, atque Orbi pariter concentricae, utcumque sint erecti; momenta ip­<lb></lb>sorum super dato puncto necessario erunt aequalia.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Super eodem puncto B (fig. </s>

<s>136) sphaericae super­<lb></lb><figure id="id.020.01.3290.2.jpg" xlink:href="020/01/3290/2.jpg"></figure></s></p><p type="caption">

<s>Figura 136.<lb></lb>ficiei HBF, cuius centrum idem est ac centrum Orbis, <lb></lb>intelligantur gravitare duo radii similes, ac specie aeque <lb></lb>graves BD, BE, qui extra superficiem dictam HBF <lb></lb>cadentes ad puncta D et E alterius sphaericae super­<lb></lb>ficiei superioris GDE, cuius pariter est centrum Orbis, utcumque sint erecti; <lb></lb>dico radiorum DB, EB momenta fore necessario inter se aequalia. </s>

<s>Erectis <lb></lb>enim super eadem superficie HBF, ad puncta D et E, perpendicularibus radiis <lb></lb>similibus, ac specie aeque gravibus DH, EF, erit ex demonstratis momentum <lb></lb>radii DH aequale momento radii DB, et momentum radii EF aequale momento <lb></lb>radii EB. Unde, cum momenta DH et EF ostensa sint in praecedentibus invicem <lb></lb>aequalia, erunt etiam momenta radiorum DB et EB invicem aequalia, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><pb xlink:href="020/01/3291.jpg" pagenum="252"></pb><p type="main">

<s>PROPOSITIO VIII. — <emph type="italics"></emph>Si radii similes, ac specie aeque graves, super <lb></lb>eadem sphaerica superficie Orbi concentrica erecti, aequale momentum <lb></lb>habuerint; eorum altitudinum termini in eadem sphaerica superficie, Orbi <lb></lb>pariter concentrica, necessario erunt.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sint super eadem sphaerica superficie ABC (fig. </s>

<s>137), cuius centrum est <lb></lb>centrum Orbis, erecti radii similes ac specie aeque graves EB, DB, quorum <lb></lb><figure id="id.020.01.3291.1.jpg" xlink:href="020/01/3291/1.jpg"></figure></s></p><p type="caption">

<s>Figura 137.<lb></lb>momenta sint aequalia: dico eorum altitudinum ter­<lb></lb>minos E et D in eadem sphaerica superficie, Orbi pa­<lb></lb>riter concentrica, reperiri. </s></p><p type="main">

<s>Non sint, si possibile est, termini E, D in eadem <lb></lb>superficie sphaerica Orbi concentrica. </s>

<s>Igitur non aequi­<lb></lb>distabunt a centro, sed alter eorum, ex gr. </s>

<s>E, erit centro <lb></lb>proprinquior quam D. </s>

<s>Itaque sphaerica ducatur superficie <lb></lb>EGH: cadet igitur terminus D extra superficiem dictam, cum sit a centro <lb></lb>remotior, et radius BD secabitur a superficie EGH in H. </s>

<s>Sunt igitur duo <lb></lb>radii similes, ac specie aeque graves, EB et BH, qui, super eadem sphae­<lb></lb>rica superficie Orbi concentrica ABC, erecti, ad eamdem superficiem sphae­<lb></lb>ricam superiorem, Orbi pariter concentricam, EGH pertingunt. </s>

<s>Igitur erunt <lb></lb>eorum momenta aequalia. </s>

<s>Maius autem est momentum radii DB, quam radii <lb></lb>BH, cum DB addat super BH momentum portionis HD; igitur maius erit <lb></lb>momentum radii BD, quam radii EB, quod est contra suppositionem. </s>

<s>Non <lb></lb>igitur cadit terminus D extra superficiem FGH, sed in eadem est necessario <lb></lb>cum termino E, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO IX. — <emph type="italics"></emph>Si cuiusvis molis gravis radius, a dato termino <lb></lb>sphaericae superficiei Orbi concentricae productus, non transiens per cen­<lb></lb>trum, superficiem dictam secet; tantum erit versus datum terminum dati <lb></lb>radii momentum gravitatis, quantum solius portionis ultra intersectionis <lb></lb>terminum utcumque productae.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>A dato termino B superficiei sphaericae, atque Orbi concentricae BAC <lb></lb>(fig. </s>

<s>138), intelligatur productus radius cuiuscumque molis gravis BCF, qui, <lb></lb><figure id="id.020.01.3291.2.jpg" xlink:href="020/01/3291/2.jpg"></figure></s></p><p type="caption">

<s>Figura 138.<lb></lb>per centrum Orbis K non transiens, superficiem di­<lb></lb>ctam secet ut in C: dico radii BCF momentum versus <lb></lb>terminum B tantum esse, quantum solius portionis <lb></lb>CF ultra terminum intersectionis C utcumque pro­<lb></lb>ductae. </s></p><p type="main">

<s>Ducatur a centro K recta KE secans BC bifa­<lb></lb>riam, puta in E, secabitque eam ad angulos rectos. </s>

<s><lb></lb>Si igitur semidiametro KE intelligatur ducta per <lb></lb>punctum E sphaerica superficies DEG, erit BC tangens DEG in E. </s>

<s>Sunt ita­<lb></lb>que super eodem termino E, superficiei Orbi concentricae DEG, erecti duo <lb></lb>radii similes, ac specie aeque graves BE et FE, unus a termino elevationis F <lb></lb>versus lineam FE, alter vero, scilicet BE, a termino elevationis B versus li­<lb></lb>neam BE, et proinde erit momentum radii BE momento radii FE directe <lb></lb>oppositum. </s>

<s>Momentum autem radii BE aequale est momento portionis oppo-<pb xlink:href="020/01/3292.jpg" pagenum="253"></pb>sitae CE, cum sint radii similes, specie aeque graves, et ab eodem termino <lb></lb>superficiei Orbi concentricae DEG, ad superficiem aliam Orbi pariter con­<lb></lb>centricam BAC exporrecti. </s>

<s>Non gravitat igitur radius FE versus terminum B, <lb></lb>nempe contra momentum oppositum radii BE, nisi secundum momentorum <lb></lb>excessus CF. </s>

<s>Tantum igitur est momentum totale radii BF versus termi­<lb></lb>num B, quantum solius portionis CF, <expan abbr="q.">que</expan> e. </s>

<s>propositum. </s></p><p type="main">

<s>PROPOSITIO X. — <emph type="italics"></emph>Si ab eodem termino sphaericae superficiei Orbi <lb></lb>concentricae duo radii similes, ac specie aeque graves protensi intelligan­<lb></lb>tur, quorum alter superficiem datam, sed non per centrum secet, alter vero <lb></lb>extra eamdem cadat, ambo tamen ad eamdem sphaericam superficiem <lb></lb>superiorem Orbi pariter concentricam pertingant; erunt momenta ipso­<lb></lb>rum versus communem terminum dictum necessario aequalia.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ab eodem termino B (fig. </s>

<s>139), sphaericae superficiei Orbi concentri­<lb></lb>cae ABC, intelligantur porrecti duo radii similes, ac specie aeque graves BF <lb></lb><figure id="id.020.01.3292.1.jpg" xlink:href="020/01/3292/1.jpg"></figure></s></p><p type="caption">

<s>Figura 139.<lb></lb>et BH, quorum alter, nempe BF, superficiem <lb></lb>ABC, sed non per centrum secet, puta in C, <lb></lb>alter vero, scilicet BH, extra eamdem cadat, <lb></lb>ita tamen ut ambo ad eamdem sphaericam <lb></lb>superficiem superiorem, Orbi pariter concen­<lb></lb>tricam, DHF pertingant: dico radiorum HB, et FB momenta, versus eum­<lb></lb>dem communem terminum B, esse necessario inter se aequalia. </s>

<s>Momentum <lb></lb>enim radii FB versus terminum B, ex antecedenti, tantum est, quantum to­<lb></lb>tius portionis CE. </s>

<s>Momentum autem radii CF aequale est momento radii sibi <lb></lb>similis, ac specie aeque gravis BH, super eadem superficie sphaerica Orbi <lb></lb>concentrica ABC, ad eamdem sphaericam superficiem, Orbi pariter concen­<lb></lb>tricam DHF, utcumque porrecti. </s>

<s>Radiorum igitur FB et HB, versus eumdem <lb></lb>terminum B, aequalia sunt momenta, quod erat propositum. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> — Unde universaliter si, ab eodem quolibet puncto com­<lb></lb>muni, duo radii similes ac specie aeque graves ad eamdem sphaericam su­<lb></lb>perficiem Orbi concentricam, utcumque erecti, pertingant; erunt ipsorum <lb></lb>momenta super communi puncto necessario aequalia. </s>

<s>Quodvis enim punctum <lb></lb>est in aliqua superficie sphaerica Orbi concentrica. </s>

<s>Ostensum est autem quod <lb></lb>radii similes ac specie aeque graves, sive extra ipsam cadant, sive ipsam <lb></lb>secent, dummodo ad eamdem aliam Orbi concentricam pertingant, aequalia <lb></lb>habebunt momenta. </s>

<s>Unde etc. </s></p><p type="main">

<s>PROPOSITIO XI. — <emph type="italics"></emph>Si dati cuiuscumque radii extremum versus quem­<lb></lb><figure id="id.020.01.3292.2.jpg" xlink:href="020/01/3292/2.jpg"></figure></s></p><p type="caption">

<s>Figura 140.<lb></lb>cumque terminum infra humidum stagnans moveri in­<lb></lb>telligatur, necesse est radium similem ei, cuius est extre­<lb></lb>mum, versus eam partem sibi directe oppositam im­<lb></lb>pellat.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Intelligatur radii cuiuscumque AB (fig. </s>

<s>140) extremum <lb></lb>punctum B, intra humidum KL existens, versus quemcum­<lb></lb>que terminum D moveri: dico quod a puncto B impelletur <lb></lb>necessario radius BD, similis radio AB. </s>

<s>Moveatur enim <pb xlink:href="020/01/3293.jpg" pagenum="254"></pb>punctum B versus D: impellet igitur versus D punctum sibi aequale, ac simile <lb></lb>sibi immediate succedens, cum in ipsius locum necesse est ipsum transire. </s>

<s><lb></lb>Eademque ratione, simul ac punctum primum versus D impellitur, necesse est <lb></lb>ut punctum secundum, aequale ac simile primo sibi immediate succedens, ver­<lb></lb>sus D impellat. </s>

<s>Eademque ratione quotquot fuerint inter B et D puncta aequa­<lb></lb>lia, ac similia, sibi immediate succedentia, ostendentur omnia ac singula <lb></lb>simul versus eamdem partem mota. </s>

<s>Series autem punctorum aequalium in­<lb></lb>vicem ac similium, inter extrema B et D immediate sibi succedentia, lineam <lb></lb>physicam uniformis subtilitatis, quem radium dicimus, constituit. </s>

<s>Qui, cum <lb></lb>singula eius puncta aequalia ac similia sint eidem puncto B radii AB, erit <lb></lb>eiusdem necessario subtilitatis ac radium AB. </s>

<s>Impellet igitur punctum B <lb></lb>radium BD similem radio AB, cuius est extremum, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO XII. — <emph type="italics"></emph>Si quaelibet humidae molis, sive perpendiculariter <lb></lb>sive oblique, super subiecto termino incumbentis, altitudo a directo de­<lb></lb>scensu, quacumque de causa, arceatur; ex ea parte, qua sufficiens non <lb></lb>invenerit resistentiae momentum, sursum transversimve reflectetur. </s>

<s>Et <lb></lb>quidquid in cedenti spatio alterius cuiuscumque molis praestiterit, versus <lb></lb>eamdem partem expellet.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Manifestum est hoc experientia siphonis ABC (fig. </s>

<s>141). <lb></lb><figure id="id.020.01.3293.1.jpg" xlink:href="020/01/3293/1.jpg"></figure></s></p><p type="caption">

<s>Figura 141.</s></p><p type="main">

<s>PROPOSITIO XIII. — <emph type="italics"></emph>Radius quilibet in humido, <lb></lb>super subiecta superficie stagnante, assignatus, nisi <lb></lb>sufficiens habuerit resistentiae momentum ab uno et <lb></lb>solo adiacientium radiorum sibi simili, et a communi <lb></lb>termino ad supremam humidi superficiem utcumque <lb></lb>porrecto; sursum impelletur.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sit in humido stagnante KL (fig. </s>

<s>142), cuius subiecta superficies sit OL, <lb></lb><figure id="id.020.01.3293.2.jpg" xlink:href="020/01/3293/2.jpg"></figure></s></p><p type="caption">

<s>Figura 142.<lb></lb>assignatus radius quilibet BC, et a puncto quolibet A su­<lb></lb>premae superficiei KAC intelligatur, ad communem ter­<lb></lb>minum B, porrectus radius AB: dico quod, nisi radius <lb></lb>BC sufficienter valebit resistere, a momento radii AB sur­<lb></lb>sum necessario impelletur. </s></p><p type="main">

<s>Non habeat itaque CB sufficiens resistentie momentum. </s>

<s>Data igitur est <lb></lb>altitudo quaedam humidae molis AB, quae recta deorsum versus B, ex sup­<lb></lb>positione, procedere non potest. </s>

<s>Ponitur autem radius BC sufficiens resisten­<lb></lb>tiae momentum non habere. </s>

<s>Igitur spatium BC sufficientis resistentiae mo­<lb></lb>mento ponitur expers. </s>

<s>Flectetur igitur a termino B moles AB, et in spatium <lb></lb>cedens BC pro viribus necessario erumpet versus C: nempe sursum impelletur <lb></lb>versus C radium in dato spatio praeesistente BC, quod erat primo propositum. </s></p><p type="main">

<s>Dico rursus radium BC a momento alterius radii ex adiacentibus, quot­<lb></lb>cumque tamdem illi sint, praeter AB impelli simul non posse. </s>

<s>In spatium <lb></lb>enim BC impossibile est flecti nisi unicum radium, similem radio BC, cuius <lb></lb>est adaequatum spatium. </s>

<s>Non expellet igitur radium BC a spatio BC, nisi <lb></lb>momentum unius dumtaxat radii sibi similis, quicumque tandem ille ex adia­<lb></lb>centibus ponatur esse, quod erat secundo loco propositum. </s></p><pb xlink:href="020/01/3294.jpg" pagenum="255"></pb><p type="main">

<s><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> — Ex quo patet radium quemlibet, in humido stagnante <lb></lb>assignatum, inter duo reperiri momenta opposita: alterum scilicet proprium <lb></lb>gravitatis quo deorsum premitur, alterum vero radii cuiusdam adiacentis si­<lb></lb>milis, a communi termino ad superficiem supremam porrecti, quo sursum, nisi <lb></lb>par habeat momentum, necessario repelletur. </s></p><p type="main">

<s>PROPOSITIO XIV. — <emph type="italics"></emph>Motu omni extrinsecus ablato, necesse est in hu­<lb></lb>mido stagnante radium quemlibet assignatum quiescere tandem ac librari.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In humido stagnante EM (fig. </s>

<s>143) sit radius quilibet assignatus AB. </s>

<s><lb></lb>Opponetur igitur eius descensui momentum solius radii ex adiacentibus si­<lb></lb><figure id="id.020.01.3294.1.jpg" xlink:href="020/01/3294/1.jpg"></figure></s></p><p type="caption">

<s>Figura 143.<lb></lb>milis, puta BH, qui a communi termino B ad <lb></lb>supremam humidi superficiem EAH porrectus <lb></lb>existit. </s>

<s>Dico radium AB, motu omni extrinsecus <lb></lb>ablato, quiescere tandem, et necessario libratum <lb></lb>manere cum radio BH. </s></p><p type="main">

<s>Cum enim ab eodem termino B erigantur <lb></lb>radii AB et BH, erunt utique super eadem <lb></lb>sphaerica superficie Orbi concentrica, quae in­<lb></lb>telligitur transire per B. </s>

<s>Si igitur eorum ter­<lb></lb>mini A et H in eadem fuerint sphaerica superficie Orbi concentrica, cum <lb></lb>similes positi sint ac specie aeque graves, manifestum est quod aequalia erunt <lb></lb>radiorum AB et BH super communi termino B momenta. </s>

<s>Premitur autem <lb></lb>deorsum radius AB momento ipsius AB, reprimitur vero sursum momento <lb></lb>radii adiacentis BH; aequalia igitur erunt contra radium AB sursum deor­<lb></lb>sumque momenta. </s>

<s>Neutram igitur in partem movebitur, sed quiescet neces­<lb></lb>sario ac libratus manebit. </s></p><p type="main">

<s>Si vero altitudinum termini A et C in eadem non fuerint sphaerica su­<lb></lb>perficie Orbi concentrica, non aequidistabunt a centro Orbis, sed alter eo­<lb></lb>rum, puta A, depressior erit, eidemque centro proprinquior quam C, sphae­<lb></lb>rica itaque ducatur superficies EAH: cadet igitur extra eam terminus C, <lb></lb>secabitque superficies EAH radium BC puta in H. </s>

<s>Momentum igitur radii AB <lb></lb>aequale erit momento radii BH, unde minus erit momentum radii AB quam <lb></lb>radii BC. </s>

<s>Cum igitur radius AB non habeat par momentum resistentiae, <lb></lb>expelletur sursum a momento opposito radii CB, qui in spatium cedens BA <lb></lb>necessario flectetur a puncto B, et descendet ab altitudine C. </s>

<s>Dividatur ita­<lb></lb>que excessus HC in partes HF, et FC, ita scilicet ut longitudo HF sit ad <lb></lb>longitudinem FC ut longitudo totius radii HB ad longitudinem totius radii BA. </s>

<s><lb></lb>Dico quod, si radio praeponderantis BC descenderit pars aequalis FC, aequale <lb></lb>fiet utriusque radii oppositi momentum super termino B. </s>

<s>Reflectetur itaque <lb></lb>CB in spatium cedens BA, et descendet infra terminum C pars ipsius aequa­<lb></lb>lis CF. </s>

<s>Manifestum est etiam quod radii BA elevabitur sursum, supra ter­<lb></lb>minum A, pars aequalis eidem CF, nempe NA. </s>

<s>Dempta igitur a radio BC <lb></lb>longitudine FC, remanet radio BH superaddita longitudo radii similis HF, <lb></lb>radio vero BA addita est longitudo radii similis NA. </s>

<s>Est autem longitudo <lb></lb>portionis additae NA, ad longitudinem portionis additae FH, ut longitudo <pb xlink:href="020/01/3295.jpg" pagenum="256"></pb>totius radii AB, ad longitudinem totius radii BH ex constructione; eamdem <lb></lb>itaque homologe rationem habebunt longitudines additae, ac ipsae radiorum, <lb></lb>quibus adduntur longitudines. </s>

<s>Unde, cum radiorum AB et BH momenta po­<lb></lb>sita sint aequalia, erunt etiam radiorum BN et BF momenta necessario ae­<lb></lb>qualia. </s>

<s>Librabitur itaque necessario radius BA, quod erat demonstrandum. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium I.<emph.end type="italics"></emph.end> — Unde patet radiorum BN et BF terminos N et F in <lb></lb>eadem esse superficie Orbi concentrica. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium II.<emph.end type="italics"></emph.end> — Cum igitur omnes et singuli radii cuiuscumque da­<lb></lb>tae molis humidae, motu omni extrinsecus ablato, necessario tandem libren­<lb></lb>tur, ac immoti quiescant; manifestum est quod universa ipsa moles cuius­<lb></lb>cuiusque dati humidi stagnantis necessario tandem, motu omni extrinsecus <lb></lb>cessante, manebit, ac immota quiescet. </s></p><p type="main">

<s>PROPOSITIO XV. — <emph type="italics"></emph>Omnis humidi manentis superficies sphaerica ne­<lb></lb>cessario est, atque Orbi concentrica.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sit humidum quodlibet manens EM (fig. </s>

<s>144). Dico superficiem eius <lb></lb>supremam ED sphaericam necessario esse, cuius centrum idem est ac cen­<lb></lb><figure id="id.020.01.3295.1.jpg" xlink:href="020/01/3295/1.jpg"></figure></s></p><p type="caption">

<s>Figura 144.<lb></lb>trum Orbis. </s>

<s>Si enim superficies ED sphaerica non sit, <lb></lb>atque Orbi concentrica, non aeque distabit quodlibet <lb></lb>ipsius punctum a centro Orbis, sed alterum altero re­<lb></lb>motius necessario erit. </s>

<s>Sit igitur punctum C remotius <lb></lb>puncto A, et a puncto A assignetur radius quilibet AB, <lb></lb>et a communi deinde termino B assignetur radius si­<lb></lb>milis, ad punctum C exporrectus. </s>

<s>Ducta igitur a puncto A sphaerica superficies <lb></lb>AGH, infra punctum C cadet, secabitque necessario radium BC, puta in H, <lb></lb>eritque momentum radii AB aequale momento radii BH. </s>

<s>Momentum igitur <lb></lb>radii BC maius erit momento radii BA, unde flectetur necessario a termino <lb></lb>B, et in spatium cedens BA expellet sursum radium BA. </s>

<s>Non manebit igitur <lb></lb>humidum FM, sed movebitur necessario, contra suppositionem. </s>

<s>Nullum igitur <lb></lb>superficiei ED manentis punctum remotius est altero a centro Orbis, sed <lb></lb>omnia et singula a centro dicto necessario aequidistant. </s>

<s>Adeoque in eadem <lb></lb>necessario sunt sphaerica superficie Orbi concentrica, quod erat propositum. </s></p><p type="main">

<s>PROPOSITIO XVI. — <emph type="italics"></emph>In humido manente quilibet ipsius radius inter <lb></lb>momenta opposita sursum deorsumque aequalia reperitur.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sit supra datam superficiem subiectam, puta ipsius Terrae DEF (fig. </s>

<s>145), <lb></lb>humidum quodlibet manens, cuius superficies ABCH, et sit quilibet eius ra­<lb></lb><figure id="id.020.01.3295.2.jpg" xlink:href="020/01/3295/2.jpg"></figure></s></p><p type="caption">

<s>Figura 145.<lb></lb>dius assignatus BE: dico radium BE inter momenta <lb></lb>opposita sursum deorsumque reperiri. </s>

<s>Cum enim hu­<lb></lb>midum manens ponatur, erit eius superficies ABCH <lb></lb>sphaerica necessario, atque Orbi concentrica. </s>

<s>Unde <lb></lb>momentum uniuscumque radii similis, ac specie <lb></lb>aeque gravis, a communi termino E ad eamdem su­<lb></lb>perficiem ABCH porrecti, aequale est momento radii <lb></lb>BE. </s>

<s>Radius autem BE non pellitur sursum, nisi momento solius radii similis <lb></lb>a communi termino E ad supremam superficiem ABH porrecti, puta EC. <pb xlink:href="020/01/3296.jpg" pagenum="257"></pb>Unde momentum EC, quo sursum pellitur BE, aequale necessario est mo­<lb></lb>mento ipsius BE. </s>

<s>Inter aequalia igitur momenta sursum deorsum reperire <lb></lb>necesse est, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s>PROPOSITIO XVII. — <emph type="italics"></emph>In quolibet humidi quiescentis puncto concur­<lb></lb>runt, secundum quamlibet lineam per ipsum ductam, duo momenta ae­<lb></lb>qualia ad oppositos terminos ipsum iungentia.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sit super qualibet continente superficie GBM (fig. </s>

<s>146) quiescens humi­<lb></lb>dum GAM, cuius superficies FAD, centrum habens centrum Terrae, et sit <lb></lb><figure id="id.020.01.3296.1.jpg" xlink:href="020/01/3296/1.jpg"></figure></s></p><p type="caption">

<s>Figura 146.<lb></lb>punctum quodlibet humidi C. </s>

<s>Manifestum est cuius­<lb></lb>libet lineae pereductae vel alterum extremum in­<lb></lb>cidet in superficie FAD, alterum in superficiem con­<lb></lb>tinentem GBM, vel utrumque incidet in superficiem <lb></lb>FAD, vel utrumque in superficiem continentem GBM. </s></p><p type="main">

<s>Transeat primo per punctum C quaelibet linea, <lb></lb>cuius utrumque extremum sit in superficie FAD, <lb></lb>puta ECH: dico quod in puncto C concurrunt <lb></lb>duo momenta aequalia, quorum unum ipsum impellit versus terminum E, <lb></lb>alterum vero versus terminum oppositum H. </s>

<s>Sit enim positus secundum li­<lb></lb>neam ECH quilibet radius ECH. </s>

<s>Versus lineam igitur HC, idest HE, gravi­<lb></lb>tat super C radius HC. </s>

<s>Versus lineam vero EC, idest EH, gravitat super C <lb></lb>radius similis EC. </s>

<s>Alter igitur versus terminum E, alter vero versus termi­<lb></lb>num H oppositum impellit idem punctum C. </s>

<s>Momenta autem radiorum si­<lb></lb>milium, ac specie aeque gravium EC et HC, super C aequalia sunt, cum sint <lb></lb>ab eodem puncto ad eamdem sphaericam superficiem Orbi concentricam por­<lb></lb>recti; unde etc. </s></p><p type="main">

<s>Transeat, secundo, per C (fig. </s>

<s>147) quaelibet linea, cuius alterum extre­<lb></lb>mum incidat in superficiem FAD, alterum vero in superficiem GBM, puta <lb></lb><figure id="id.020.01.3296.2.jpg" xlink:href="020/01/3296/2.jpg"></figure></s></p><p type="caption">

<s>Figura 147.<lb></lb>ACB. </s>

<s>Dico quod in puncto C concurrunt pariter <lb></lb>duo momenta aequalia, ad oppositos terminos A <lb></lb>et B, ipsum impellentia. </s>

<s>Sit enim secundum li­<lb></lb>neam AB quilibet radius AB, a cuius termino B <lb></lb>ad superficiem FAD porrigatur utcumque radius <lb></lb>alius similis BD, et semidiametro KC sit sphae­<lb></lb>rica superficies Orbi concentrica CL, secans BD <lb></lb>in L. </s>

<s>A radio igitur BD impelletur, nisi resisteret, versus linem C A, radium <lb></lb>ipsi conterminum BC, adeoque ipsum punctum C. </s>

<s>Momentum autem CB op­<lb></lb>ponitur momento aequali BL. </s>

<s>Radius igitur BC, ipsumque proinde punctum <lb></lb><figure id="id.020.01.3296.3.jpg" xlink:href="020/01/3296/3.jpg"></figure></s></p><p type="caption">

<s>Figura 148.<lb></lb>C, impelletur versus A momento solius radii LD. </s>

<s><lb></lb>Idem autem punctum C impellitur versus lineam <lb></lb>CB, idest terminum oppositum B, momento radii <lb></lb>AC, momenta enim AC et BL aequalia sunt; <lb></lb>concurrunt igitur in C momenta aequalia versus <lb></lb>terminos oppositos A et B, ipsum impellentia, <expan abbr="q.">que</expan> e. </s>

<s>d. </s></p><p type="main">

<s>Transeat, tertio, per punctum C (fig. </s>

<s>148) <pb xlink:href="020/01/3297.jpg" pagenum="258"></pb>quaelibet linea cuius utrumque extremum incidat in superficiem continentem <lb></lb>SBM, puta linea GCN. </s>

<s>Dico quod in C conveniunt etc. </s>

<s>ut supra. </s>

<s>Sit enim <lb></lb>radius GCN, cuius extremi G et N, secundum quamcumque lineam, pertin­<lb></lb>gant ad superficiem FPO, per radios similes PG et NO. </s>

<s>Nisi igitur resisten­<lb></lb>tiam invenerit, flectetur ON versus lineam NC, idest NG, impelletque pun­<lb></lb>ctum C. </s>

<s>Eademque ratione radius PGC impellet idem punctum C versus <lb></lb>oppositum terminum N. </s>

<s>Momenta autem radiorum tortuosorum PGC, et <lb></lb>ONC aequalia sunt, utpote qui ab eodem puncto C ad eamdem superficiem <lb></lb>Orbi concentricam FPO sint producti; unde etc. </s></p><p type="main">

<s>PROPOSITIO XVIII. — <emph type="italics"></emph>Puncto cuilibet intra manens humidum dato <lb></lb>momenta, secundum quamcumque lineam, aequalia opponuntur.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sit supra datam quamcumque superficiem continentem FGL (fig. </s>

<s>149) <lb></lb>humidum quiescens, cuius superficies ABD, et sit intra ipsum datum pun­<lb></lb><figure id="id.020.01.3297.1.jpg" xlink:href="020/01/3297/1.jpg"></figure></s></p><p type="caption">

<s>Figura 149.<lb></lb>ctum quodlibet C. </s>

<s>Dico quod secundum quam­<lb></lb>cumque lineam punctum C moveri intelli­<lb></lb>gatur, sive sursum, sive deorsum, sive tran­<lb></lb>sversim, momenta undique ei opponuntur <lb></lb>aequalia. </s></p><p type="main">

<s>Intelligatur primo moveri sursum secun­<lb></lb>dum lineam perpendicularem CB: repellet <lb></lb>igitur radium BC a termino C. </s>

<s>Gravitat autem <lb></lb>BC versus terminum C, unde momento quod <lb></lb>habet versus C, resistet motui puncti C. </s></p><p type="main">

<s>Deinde intelligatur moveri secundum lineam quamcumque obliquam CE, <lb></lb>aut CD, quae incidat directe in superficiem ABD. </s>

<s>Repellet igitur a termino C <lb></lb>radium CE aut CD similem radio BC. </s>

<s>Ponitur autem humidum datum quie­<lb></lb>scere. </s>

<s>Igitur eius superficies ABD sphaerica necessario est, cuius centrum <lb></lb>idem est ac centrum orbis K. </s>

<s>Radii igitur CB, CE, et CD, a communi ter­<lb></lb>mino C, ad eamdem sphaericam superficiem Orbi concentricam ABD sunt <lb></lb>porrecti. </s>

<s>Unde, cum similes ac specie acque graves sint, erunt momenta ipso­<lb></lb>rum versus terminum C invicem aequalia. </s>

<s>Sive igitur punctum C repellat a <lb></lb>termino C radium CB, sive radium CE, sive radium CD, semper opponetur <lb></lb>ci momentum aequale versus terminum C. </s>

<s>Idemque eadem ratione valebit <lb></lb>de quocumque alio radio a termino C ad superficiem ABD directe producto. </s>

<s><lb></lb>Unde secundum quamcumque lineam, ad superficiem ABD directe pertin­<lb></lb>gentem, moveri intelligatur punctum C, semper ei momentum opponetur <lb></lb>aequale. </s></p><p type="main">

<s>Denique intelligatur moveri idem punctum C secundum lineam quam­<lb></lb>libet, quae in superficiem continentem FGL impingat, sive perpendiculariter <lb></lb>ut CG, sive oblique ut CF. </s>

<s>Si itaque versus CG moveri intelligatur, impel­<lb></lb>let radium CG similem radio CB. </s>

<s>Radius autem CG, cum recta procedere <lb></lb>non possit versus G, flecti necesse est versus quamcumque lineam GH, im­<lb></lb>pelletque radium GH. </s>

<s>Motui igitur puncti C resistit momentum radii GH. </s>

<s><lb></lb>Semidiametro itaque KC sphaerica intelligatur ducta superficies NCM, quae <pb xlink:href="020/01/3298.jpg" pagenum="259"></pb>secabit radium GH, puta in O. </s>

<s>Erit igitur momento portionis OG oppositum <lb></lb>aequale momentum radii similis CG. </s>

<s>Remanet igitur, contra momentum <lb></lb>puncti C, momentum radii OH. </s>

<s>Momentum autem radii OH aequale est mo­<lb></lb>mento radii CB, aut CE, super eadem superficie sphaerica concentrica NCM <lb></lb>ad eamdem pariter ABD erecti. </s></p><p type="main">

<s>Si vero secundum lineam obliquam CI noveri intelligatur, eadem ra­<lb></lb>tione ac modo ostendetur motui puncti C resistere momentum solius por­<lb></lb>tionis AS, cuius momentum momento tum radii OH, tum radii CB ostende­<lb></lb>tur, ex dictis, aequale, et sic de quacumque alia linea reflexa. </s>

<s>Unde secundum <lb></lb>quamcumque lineam, sive directam, sive a continente superficie reflexam, <lb></lb>idem punctum C moveri intelligatur, semper ipsius motui invenietur oppo­<lb></lb>situm momentum aequale, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium I.<emph.end type="italics"></emph.end> — Humido igitur manente, quodlibet ipsius punctum, <lb></lb>ubicumque extiterit, ibi necessario manebit. </s>

<s>Cum enim aequalibus momentis <lb></lb>undique interceptum et circumpulsum existat, nulla ex parte cedere potest, <lb></lb>sed libratum necessario consistet. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium II.<emph.end type="italics"></emph.end> — Idemque patet de qualibet sensibili eiusdem humidi <lb></lb>mole. </s>

<s>Ostendetur enim de quolibet eius puncto quod libratum undique ne­<lb></lb>cessario maneat, nec moveri ratione gravitatis versus nullam lineam possit. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium III.<emph.end type="italics"></emph.end> — Idem denique patet de qualibet alia mole homoge­<lb></lb>nea, dummodo sit eiusdem gravitatis in specie cum humido, in quo existit. </s>

<s><lb></lb>Idem enim habebit momentum ac portio illa humidi, cuius loco substituitur, <lb></lb>unde idem perseverabit in humido aequilibrium. </s></p><p type="main">

<s>PROPOSITIO XIX. — <emph type="italics"></emph>Si radiorum similium, super eadem sphaerica su­<lb></lb>perficie Orbi concentrica utcumque erectorum, momenta fuerint aequalia, <lb></lb>perpendiculares eorum altitudines gravitatibus eorumdem in specie con­<lb></lb>trarie respondebunt.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sint super eadem superficie sphaerica, Orbi concentrica, DBF (fig. </s>

<s>150) <lb></lb>duo radii similes, cuiuscumque gravitatis in specie, AB et EF, qui aequale <lb></lb><figure id="id.020.01.3298.1.jpg" xlink:href="020/01/3298/1.jpg"></figure></s></p><p type="caption">

<s>Figura 150.<lb></lb>momentum habeant. </s>

<s>Dico quod altitudines perpendi­<lb></lb>culares radiorum AB, et EF gravitatibus eorumdem <lb></lb>in specie contrarie respondebunt. </s></p><p type="main">

<s>Sit autem radii EF altitudo perpendicularis EC, <lb></lb>et radii AB altitudo perpendicularis sit AD, sintque <lb></lb>perpendiculares radii AD, et EC, quorum AD similis <lb></lb>ac specie aeque gravis sit cum AB, EC autem similis, ac specie aeque <lb></lb>gravis cum EF. </s>

<s>Erit igitur momentum radii AD aequale momento radii <lb></lb>AB, momentum vero radii EC aequale momento radii EF. </s>

<s>Unde momentum <lb></lb>radii perpendicularis AD aequale erit momento radii perpendicularis EC. </s>

<s>Sunt <lb></lb>autem ambo perpendiculares, unde gravitas absoluta radii AD aequalis erit <lb></lb>gravitati absolutae radii EC. </s>

<s>Atqui demonstratum habemus a Galileo, in suo <lb></lb><emph type="italics"></emph>Discursu hydrostatico,<emph.end type="italics"></emph.end> quod, si gravitates absolutae aequales fuerint, moles <lb></lb>gravitatibus in specie contrarie respondebunt; ut igitur moles radii AD, ad <lb></lb>molem radii EC, ita reciproce erit gravitas in specie radii EC, ad gravita-<pb xlink:href="020/01/3299.jpg" pagenum="260"></pb>tem in specie radii AD. </s>

<s>Sunt autem radii similes, erunt igitur moles ut eo­<lb></lb>rumdem altitudines. </s>

<s>Ut igitur altitudo radii AD, ad altitudinem radii EC, ita <lb></lb>gravitas in specie radii EC, ad gravitatem in specie radii AD, idest gravitas <lb></lb>in specie radii EF ad gravitatem in specie radii AB. </s>

<s>Est autem EC altitudo <lb></lb>perpendicolaris radii EF, AD altitudo perpendicolaris radii AB; ut igitur al­<lb></lb>titudo perpendicularis radii AB, ad altitudinem perpendicolarem radii EF, ita <lb></lb>gravitas in specie radii EF ad gravitatem in specie radii AB, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s>PROPOSITIO XX. — <emph type="italics"></emph>Si supra quiescentis humidi superficiem humidum <lb></lb>aliud specie minus grave quieverit, nullus subiectae humidae superflciei <lb></lb>radius a superficie deprimetur aut assurget, sed sphaerica ac Orbi con­<lb></lb>centrica manebit eius superficies ut antea.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sit humidum quiescens FN (fig. </s>

<s>151), cuius superficies FG. </s>

<s>Supra ipsum <lb></lb>quiescens humidum sit aliud specie minus grave EG, cuius superficies ED: <lb></lb><figure id="id.020.01.3299.1.jpg" xlink:href="020/01/3299/1.jpg"></figure></s></p><p type="caption">

<s>Figura 151.<lb></lb>dico nullum humidi subiecti quiescentis FN radium a <lb></lb>superficie FG deprimi aut elevari. </s></p><p type="main">

<s>Si enim possibile est, sit quilibet radius BO, as­<lb></lb>surgens supra superficiem FG ad quamcumque altitu­<lb></lb>dinem HO, et producatur radius BHO usque ad super­<lb></lb>ficiem humidi quiescentis specie minus grave EG, ut <lb></lb>sit radius BA, et a termino B pertingat ad ED quilibet alius radius BMC, <lb></lb>secans FG in M. </s>

<s>Quia igitur HO pars est humidi subiecti specie magis <lb></lb>gravis, maius erit momentum radii AH, quam radii CM. </s>

<s>Posito igitur aequali <lb></lb>utrobique momento BH et BM, erit momentum radii AB maius momento <lb></lb>radii BC. </s>

<s>Flectetur igitur necessario versus lineam BC ac descendet radius <lb></lb>AB, quod est contra suppositum, ponitur enim humidum utrumque quie­<lb></lb>scere. </s>

<s>Unde etc. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium I.<emph.end type="italics"></emph.end> — Unde patet radium quemlibet, ab eodem puncto su­<lb></lb>biecti humidi, specie gravioris, ad supremam superficiem humidorum, specie <lb></lb>minus gravium ipsi incumbentium, utcumque pertingentem; aequale momen­<lb></lb>tum habere. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium II.<emph.end type="italics"></emph.end> — Unde facili negotio demonstrabitur in humido, ex <lb></lb>pluribus gravitate in specie differentibus, atque invicem incumbentibus com­<lb></lb>posito; punctum quodlibet a momentis aequalibus ad oppositos terminos se­<lb></lb>cundum quamcumque lineam per ipsum ductam urgeri, nec non aequalia <lb></lb>ipsi gravitatum momenta secundum quamcumque lineam opponi. </s></p><p type="main">

<s>PROPOSITIO XXI. — <emph type="italics"></emph>Humido quiescenti FG<emph.end type="italics"></emph.end> (fig. </s>

<s>152), <lb></lb><figure id="id.020.01.3299.2.jpg" xlink:href="020/01/3299/2.jpg"></figure></s></p><p type="caption">

<s>Figura 152.<lb></lb><emph type="italics"></emph>cuius superficies FI, tubi utcumque erecti LM inferius <lb></lb>orificium M demergatur, superius vero L ad quamcumque <lb></lb>altitudinem supra libellam NO promineat, et supra su­<lb></lb>biectam superficiem FI quiescat humidum aliud HI, <lb></lb>specie minus grave, cuius superficies HV, ita scilicet ut <lb></lb>summa ipsius altitudo ad orificium L non pertingat: <lb></lb>dico quod subiectum humidum, pondere superincum­<lb></lb>bentis humidi pressum, supra libellam NO assurget.<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/3300.jpg" pagenum="261"></pb><p type="main">

<s>Subiaceat enim libellae NO e directo sectio quaelibet NQ: ostendetur <lb></lb>quemlibet radium assignabilem in sectione NQ, vi prementis humidi HV, <lb></lb>supra libellam NO necessario extrudi. </s>

<s>Sit enim radius quilibet AB, et a ter­<lb></lb>mino B pertingat, secundum quamcumque lineam, ad superficiem HV radius <lb></lb>similis BDE, secans FI in D. </s>

<s>Gravitat igitur super puncto D, versus lineam <lb></lb>DB, totus et solus radius superincumbentis humidi ED, unde universus ra­<lb></lb>dius EDB gravitat super B. </s>

<s>Secundum lineam autem AB gravitat, super eo­<lb></lb>dem puncto B, solus radius AB, cui nullus superincumbit, ex suppositione, <lb></lb>radius humidi HI. </s>

<s>Posito igitur aequali utrobique momento AB et DB, maius <lb></lb>erit momentum radii EDB quam AB. </s>

<s>Flectetur igitur EDB secundum lineam <lb></lb>BA, impelletque ultra libellam NO radium BA, <expan abbr="q.">que</expan> e. </s>

<s>p. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium I.<emph.end type="italics"></emph.end> — Unde patet quilibet radio humidi, secundum quam­<lb></lb>cumque lineam assurgentis, non opponi nisi radium similem humidi sibi in­<lb></lb>cumbentis. </s>

<s>Patet enim radio AB non opponi nisi radium DB. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium II.<emph.end type="italics"></emph.end> — Quilibet subiecti humidi radius, vi superincumben­<lb></lb>tis humidi, supra libellam, pressura expertem, eatenus assurget, quatenus <lb></lb>portio assurgentis radii, supra libellam existens, momentum habet aequale <lb></lb>momento cuiuslibet radii humidi superincumbentis, ab eadem libella ad su­<lb></lb>premam eius superficiem producti. </s></p><p type="main">

<s>PROPOSITIO XXII. — <emph type="italics"></emph>Si, ut in figura praecedenti, extrudatur radius <lb></lb>BA supra libellam NO usque ad Y, ita scilicet ut portio AY, supra libel­<lb></lb>lam NO existens, momentum habeat aequale momento cuiuslibet radii <lb></lb>similis, ab eadem libella FI ad supremam humidi super incumbentis su­<lb></lb>perficiem HV producti, puta OS; radius BA ultra Y non impelletur.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Est enim momentum radii OS aequale momento radii DE, unde mo­<lb></lb>mentum AY aequale etiam erit momento radii DE. </s>

<s>Posito igitur aequali utro­<lb></lb>bique momento AY, et DE, erit momentum totius EDB aequale momento <lb></lb>totius YAB. </s>

<s>Non flectetur igitur EDB versus lineam BAY amplius, nec pro­<lb></lb>inde radius BAY ulterius, secundum lineam dictam impelletur. </s>

<s>Sed nec a <lb></lb>nullo alio radio sibi contermino impelletur, unde etc. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> — Ex hac igitur, et ex propositione XIX, colligetur: qui­<lb></lb>libet subiecti humidi radius, vi superincumbentis humidi extrusus, eatenus <lb></lb>supra libellam assurget, quatenus pressionis supra libellam existentis perpen­<lb></lb>dicularis altitudo, perpendiculari altitudini unius cuiuslibet radii ab eadem <lb></lb><figure id="id.020.01.3300.1.jpg" xlink:href="020/01/3300/1.jpg"></figure></s></p><p type="caption">

<s>Figura 153.<lb></lb>superficie ad supremam humidi incumbentis su­<lb></lb>perficiem producti, contrariam proportionem ha­<lb></lb>beat quam gravitas in specie, ad gravitatem. </s></p><p type="main">

<s>PROPOSITIO XXIII. — <emph type="italics"></emph>Humidi, intra humi­<lb></lb>dum homogeneum existentis, pondus quantum­<lb></lb>cumque sit, ab extrinsecus trahente aut retinente <lb></lb>impossibile est sentiri.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Sit, supra continentem superficiem EB (fig. </s>

<s><lb></lb>153), quiescens humidum, cuius superficies GAD, <lb></lb>et intra humidum dictum sit data quaelibet eius <pb xlink:href="020/01/3301.jpg" pagenum="262"></pb>portio P, intra ipsum ubicumque existens, per cuius extrema cadant a suprema <lb></lb>humidi superficie perpendiculares, eam undique intercipientes AE, CB, erit­<lb></lb>que comprehensa sectio humida AEBC. </s>

<s>Manifestum autem est quod quilibet <lb></lb>sectionis AB radius aequilibratur cum momento radii sibi similis, a communi <lb></lb>termino ad eamdem superficiem producti. </s>

<s>Omnes igitur simul radii sectio­<lb></lb>nis AB, sive aequalis, a communibus terminis ad supremam superflciem por­<lb></lb>rectis, aequilibrantur radiis comprehensis inter EH et BF. </s>

<s>Transeat itaque <lb></lb>immediate sub portione P superficies sphaerica Orbi concentrica NOM, se­<lb></lb>cabitque AB in RS, EH vero et BF, puta, in LN, et OM. </s>

<s>Sicut igitur sin­<lb></lb>gulis radiis contentis in AB respondebant singuli radii similes contenti in <lb></lb>EH, et BF; ita singulis portionis eorumdem radiorum, contentis in BR, re­<lb></lb>spondent singulae portiones similes contentae in ELN, et BOM, a communi­<lb></lb>bus terminis ad eamdem superficiem sphaericam, Orbi concentricam, NLOM <lb></lb>pertingentes. </s>

<s>Singularum igitur portionum contentarum in BR momentum, <lb></lb>momento singularum sibi respondentium, ac oppositarum in EL et BO ae­<lb></lb>quale est. </s>

<s>Ac proinde momentum totius molis BR momento totius molis EL, <lb></lb>et BO est aequale. </s>

<s>Unde reliquae molis AS momentum momento reliquae <lb></lb>GL et FM remanet aequale. </s></p><p type="main">

<s>His ita dispositis, dico pondus portionis P non posse ab ullo extrinse­<lb></lb>cus trahente aut retinente experiri, sed proinde se habere ac si non esset. </s>

<s><lb></lb>Extra humidi superficiem GAD sit enim libra, cuius centrum I, et aequales <lb></lb>a centro distantiae IK, IQ, et, manente centro I, intelligatur funiculus KP <lb></lb>retinens pondus molis P. </s>

<s>Dico quod, quantumcumque sit pondus molis P <lb></lb>pendentis ab extremo K, excepto pondere funiculi KP, non movebit deorsum <lb></lb>dictum extremum librae K, sed perinde manebit libra in aequipondio, ac si <lb></lb>nullum eius extremo pondus appensum fuisset. </s>

<s>Nam pondere molis BF et <lb></lb>EH impellitur sursum moles BR. </s>

<s>Resistit autem BR aequali momento, ex <lb></lb>dictis, momento molis EL et BO. </s>

<s>Momento igitur molis OD et NH impelli­<lb></lb>tur sursum moles BERS. </s>

<s>Impelli autem non potest sursum moles BERS, <lb></lb>nisi impellat sursum molem sibi immediate sursum obiectam P; eodem igi­<lb></lb>tur momento molis NH et OD impelletur sursum moles P. Unde, nisi mo­<lb></lb>les P maiori momento deorsum prematur, quam sit molis NH et OD, ipsam <lb></lb>sursum impellentis; non poterit moles P deorsum moveri. </s>

<s>Premitur autem P <lb></lb>deorsum tum proprio pondere, tum pondere molis APC, sibi ad perpendicu­<lb></lb>lum incumbentis; unde premitur P deorsum momento totius molis AS. </s>

<s>Mo­<lb></lb>mentum autem AS aequale ostensum est momento molis NH et OD, ideo­<lb></lb>que maius illo non est. </s>

<s>Igitur moles P moveri sursum nullatenus poterit, <lb></lb>nec igitur extremum K, cui appensam ponitur, deorsum trahet. </s>

<s>Quantum­<lb></lb>cumque igitur prematur pondus molis P, intra humidum homogeneum exi­<lb></lb>stentis, manebit necessario extremum K perinde ac si nullum ei pondus <lb></lb>appensum fuisset, quod erat ostendendum. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> — Unde patet qualiter, dato pondere in mole humida intra <lb></lb>humidum homogeneum posita, percipi id extrinsecus a retinente ex eo im­<lb></lb>possibile sit, quod pondus datum aequali semper momento a subiecta mole <pb xlink:href="020/01/3302.jpg" pagenum="263"></pb>repulsum sustentetur, atque a descensu prohibeatur. </s>

<s>Quod idem in omni <lb></lb>pondere continget, si ipsum, librae extremo appensum, subiecta manu, aut <lb></lb>quovis alio retinaculo, sustentetur, atque arceatur a descensu. </s></p><p type="main">

<s>PROPOSITIO XXIV. — <emph type="italics"></emph>Moles intra humidum specie minus grave exi­<lb></lb>stens, ubicumque fuerit, descendet, et momentum descensus eiusdem tan­<lb></lb>tum erit, quantus est excessus supra momentum molis humidae aequalis, <lb></lb>cuius locum occupat.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Iisdem positis, in locum molis homogeneae P, substituatur quaelibet alia <lb></lb>aequalis moles Z, sed eadem utcumque gravior in specie. </s>

<s>Dico quod moles Z <lb></lb>non manebit, sed descendet necessario, eritque momentum ipsius in descen­<lb></lb>dendo idem ac excessus supra momentum aequalis molis P, in cuius locum <lb></lb>substituitur. </s></p><p type="main">

<s>Cum enim moles Z mole P gravior in specie, eidemque aequalis pona­<lb></lb>tur; erit pondus molis Z maius pondere molis P. </s>

<s>Pondus autem molis P, <lb></lb>cum pondere reliquae molis APC, aequale momentum habere ostensum est <lb></lb>cum NH et OD. </s>

<s>Pondus igitur molis Z, cum pondere eiusdem molis APC, <lb></lb>maius momentum habebit quam NH et OD, tanto scilicet maius, quanto mo­<lb></lb>mentum gravioris molis Z maius est momento molis P sibi aequalis. </s>

<s>Premi­<lb></lb>tur itaque deorsum subiecta moles ES tum proprio pondere, tum pondere <lb></lb>molis APC et Z, ad perpendiculum sibi incumbentium, eius autem de­<lb></lb>scensui opponitur momentum molis EH et BF. </s>

<s>Cum igitur momentum ES <lb></lb>aequale sit, ex dictis, momento FL et BO; erit momentum totius AB maius <lb></lb>momento totius EH, et BF. </s>

<s>Cedet igitur EH et BF momento deorsum molis <lb></lb>ES, et descendet, ac proinde moles Z, cum mole APC ipsam premente, quod <lb></lb>erat primo ostendendum. </s></p><p type="main">

<s>Ostendam id, quod secundo venit, breviter sic: Si moles Z aequale mo­<lb></lb>mentum haberet cum mole sibi aequali P, momentum ei in descendendum <lb></lb>nullum esset. </s>

<s>Maneret enim necessario in aequilibrio, ut patet ex dictis. </s>

<s>Tan­<lb></lb>tum igitur momentum habebit in descendendo moles Z, quantum ei superest <lb></lb>praeter momentum aequale momento molis sibi aequalis P, cuius locum occu­<lb></lb>pat. </s>

<s>Unde manifestum est quod humidum quodlibet, ex momento deorsum <lb></lb>cuiuscumque molis intra ipsum existentis, momentum auferat aequale mo­<lb></lb>mento eius molis humidae, cuius locum occupat, idest molis humidae sibi <lb></lb>aequalis. </s></p><p type="main">

<s>PROPOSITIO XXV. — <emph type="italics"></emph>Si intra humidum, specie magis grave, moles <lb></lb>quaelibet extiterit, inter cuius inferiorem superficiem, superficiemque per­<lb></lb>pendicularem subiectam continentem, humidum intercesserit; data moles <lb></lb>non manebit, sed a subiecto sibi humido sursum necessario impelletur.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Iisdem positis, substituatur in locum molis P moles sibi aequalis X, sed <lb></lb>specie minus gravis, inter quam et continentem superficiem EB intercedat <lb></lb>humidum ES. </s>

<s>Dico quod moles X, a subiecto sibi humido ES, sursum ne­<lb></lb>cessario impelletur. </s>

<s>Erit enim moles X minus pondere molis sibi aequalis P. </s>

<s><lb></lb>Momentum autem molis ASP aequale ostensum est momento NH et DO. </s>

<s>Mo­<lb></lb>mentum igitur molis OD et NH maius erit momento ASX, tantoque maius, <pb xlink:href="020/01/3303.jpg" pagenum="264"></pb>quanto maius est momentum molis P momento sibi aequalis X. </s>

<s>Ostensum <lb></lb>autem est quod subiecta moles ES impellitur sursum momento molis NH <lb></lb>et OD. </s>

<s>Eius autem ascensui resistit momentum molis ASX, quod minus po­<lb></lb>situm est momento NH et OD, quo ES sursum impellitur; impellet igitur <lb></lb>sursum moles ES molem sibi immediate incumbentem X, quod erat osten­<lb></lb>dendum. </s></p><p type="main">

<s>Impellet autem ES molem X sursum ea momenti quantitate, qua mo­<lb></lb>mentum NH, OD, quo sursum impellitur, superat aequilibrium momenti, <lb></lb>quo X premitur deorsum, momenti scilicet ASX. </s>

<s>Ea autem quantitate osten­<lb></lb>sum est momentum NH et OD excedere momentum ASX, qua momentum <lb></lb>molis P excedit momentum molis sibi aequalis X. </s>

<s>Momentum igitur, quo X <lb></lb>sursum impellitur, aequale est ei axcessui, quo momentum ipsius X supe­<lb></lb>ratur a momento molis humidae sibi aequalis P, cuius locum occupat. </s>

<s>Unde <lb></lb>cuiuscumque molis, intra humidum specie magis grave existentis, momen­<lb></lb>tum sursum tantum erit, quantus est excessus momenti alterius molis, sibi <lb></lb>aequalis et dato humido, supra momentum ipsius. </s></p><p type="main">

<s><emph type="italics"></emph>Corollarium.<emph.end type="italics"></emph.end> — Hinc manifestum est quod, si intra humidum specie <lb></lb>magis grave moles quaelibet ita posita fuerit, ut, inter ipsam superficiemque <lb></lb>continentem perpendiculariter ei subiectam, humidum non intercesserit; nul­<lb></lb>lum habebit sursum momentum, sed a momento universae molis humidae, <lb></lb>ad perpendiculum sibi iucumbentis, deorsum pressa, necessario manebit, nec, <lb></lb>quantumcumque humidum gravius fuerit, per ipsum ascendet. </s></p><p type="main">

<s><emph type="italics"></emph>Experimentum.<emph.end type="italics"></emph.end> — Prisma, seu vas quodcumque aliud AB (fig. </s>

<s>154), <lb></lb>cuius fundum, puta ligneum, CD crassius existat, et ab ipsius superficie su­<lb></lb><figure id="id.020.01.3303.1.jpg" xlink:href="020/01/3303/1.jpg"></figure></s></p><p type="caption">

<s>Figura 154.<lb></lb>periori CB cavitas excidatur deorsum hemi­<lb></lb>sphaerica ELH, eique applicetur lignea sphaera, <lb></lb>cuius hemisphaerium alterum concavitati dic­<lb></lb>tae ELH congruat, alterum vero, puta EMH, <lb></lb>extra ipsam promineat. </s>

<s>Ea tamen industria <lb></lb>cavitati dictae sphaera inseratur, ut orificium <lb></lb>quidem EH perfecte obstruat, nec permittat <lb></lb>humidum per commissuras dilabi: interim <lb></lb>autem eidem orificio pertinaciter non adhereat, <lb></lb>sed levi motu trahente sequatur. </s>

<s>Hisce con­<lb></lb>stitutis, impleatur vas AB humido in specie <lb></lb>gravissimo, puta hydrargirio, et experimento <lb></lb>manifestum fiet quoniam lignea sphaera ELHM <lb></lb>per gravissimum hydrargirium non ascendet, sed manebit, ut supra a nobis <lb></lb>conclusum est. </s>

<s>Si quis autem vacui metum suspicetur, foramen aperiat ca­<lb></lb>vitati EGH, puta in G, ut aer ad subeundum in promptu sit, quoties sphae­<lb></lb>ram sursum elevari contigerit, nec propterea sphaera sursum movebitur, <lb></lb>sed manebit ut antea. (MSS. Cim., T. XXXIV, fol. </s>

<s>204-77). </s></p><pb xlink:href="020/01/3304.jpg" pagenum="265"></pb><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>In questo trattato del Viviani si può dire che sia compendiata la storia <lb></lb>delle pressioni idrostatiche, una delle principali questioni agitate intorno alle <lb></lb>quali, nell&#039;Accademia fiorentina, e anzi in tutta la Scuola galileiana, abbiamo <lb></lb>veduto esser quella de&#039;corpi più leggeri, che rimangono sul fondo del vaso, <lb></lb>quando l&#039;acqua non possa esercitarvi la sua circumpulsione. </s>

<s>Dunque, occor­<lb></lb>reva a domandar qui, in proposito della palla di legno esattamente incastrata <lb></lb>sul fondo del vaso pieno; l&#039;acqua di sopra, invece di conferire a sollevarla, <lb></lb>la conficca più fortemente che mai dentro il suo incavo? </s>

<s>Ed essendo così, <lb></lb>perchè i palombari non rimangono oppressi, e nel cupo de&#039;vivai si veggono <lb></lb>i pesci notare con sì agili moti? </s>

<s>Il problema sembrava non trovare, ne&#039;prin­<lb></lb>cipii idrostatici generali, la sua soluzione, e perciò il dire come vi si ridu­<lb></lb>cesse è di tale curiosità, e di tanta importanza, che senza ciò la storia delle <lb></lb>pressioni idrostatiche si rimarrebbe incompiuta. </s></p><p type="main">

<s>Già sappiamo quel che ne pensasse Herone Alessandrino, le ragioni del <lb></lb>quale si ripeterono da Galileo, e da tutti gl&#039;Idrostatici più savi, che, per una <lb></lb>parte, rifuggivano dalle sciocchezze di chi rassomigliava i pesci nell&#039;acqua <lb></lb>ai topi ne&#039;buchi del muro, e non volevano, per l&#039;altra, mettersi a tenzonare <lb></lb>co&#039;dubbi di Leonardo da Vinci. </s>

<s>A Leonardo, come a tutti gli altri, compresi <lb></lb>nel lungo spazio di tempo, che intercede fra Herone e Galileo; troppo an­<lb></lb>cora faceva difetto la Scienza che, instituitasi nuovamente dallo Stevino, a <lb></lb>lui solo dava in mano gli argomenti, da risolvere il problema curioso. </s>

<s>In <lb></lb>che modo ei veramente lo risolvesse lo vedemmo colà, dove si faceva la sto­<lb></lb>ria delle sue dottrine, le quali, come si neglessero per le altre parti, così <lb></lb>non si curarono nemmen per questa dalle due grandi scuole, allora domi­<lb></lb>natrici in Francia e in Italia. </s></p><p type="main">

<s>Viene un giorno il Mersenno a rammemorare al Cartesio le ragioni dette <lb></lb>dallo Stevino, perchè quelli che ci son sotto non sentano il peso dell&#039;acqua, <lb></lb>e il Cartesio orgogliosamente risponde: Quel che il vostro Stevino abbia <lb></lb>detto non mi ricordo, e non so, ma la ragion vera del fatto non può esser <lb></lb>che questa, “ quod non plus aquae gravitat in corpus, quod in aqua est vel <lb></lb>sub aqua, quam quantum aquae descenderet, si corpus illud loco suo cede­<lb></lb><figure id="id.020.01.3304.1.jpg" xlink:href="020/01/3304/1.jpg"></figure></s></p><p type="caption">

<s>Figura 155.<lb></lb>ret. </s>

<s>Sic ex. </s>

<s>gr. </s>

<s>si supponamus homo in vase B (fig. </s>

<s>155), qui <lb></lb>corpore suo ita incumbat foramini A, ut exitum aquae impediat, <lb></lb>sentiet sibi impendere totum pondus cylindri aquae ABC, cuius <lb></lb>basim suppono esse eiusdem magnitudinis cum foramine A, quia, <lb></lb>si ipse per illud foramen descenderet, totus etiam iste cylindrus <lb></lb>aquae descenderet. </s>

<s>Sed si paulo altius supponatur, ut ad B, ita <lb></lb>ut non prohibeat amplius egressum aquae per foramen A; tum <lb></lb>nullam gravitatem sentiet ex aqua, quae inter B et C ipsi super incumbit, <pb xlink:href="020/01/3305.jpg" pagenum="266"></pb>quia, si ipsa descenderet versus A, nequaquam descenderet aqua ista cum <lb></lb>illo, sed contra pars aquae, quae illi versus A subiacet, paris cum eius cor­<lb></lb>pore magnitudinis, in eius locum ascenderet. </s>

<s>Unde fit ut aqua illum sursum <lb></lb>evehat, potius quam deprimat, prout experientia comprobatur ” <emph type="italics"></emph>(Epistol.,<emph.end type="italics"></emph.end><lb></lb>P. II, Amstelodami 1682, pag. </s>

<s>123). </s></p><p type="main">

<s>Sembra che al Mersenno sodisfacesse meglio la ragione dello Stevino <lb></lb>che questa, e perciò, giacchè il Cartesio diceva di non saperla, o d&#039;averla <lb></lb>dimenticata, glie ne veniva ripetendo ne&#039;precisi termini il sillogismo, a cui <lb></lb>esso Cartesio però negava la virtù di concludere, scoprendosi falsa la minore. <lb></lb></s>

<s>“ Ad probandum quod homo in aqua demersus aquae gravitatem non sen­<lb></lb>tiat, pessimum est hoc argumentum: <emph type="italics"></emph>Omnis pressio, quae laedit corpus, <lb></lb>partem istius corporis aliquam loco suo naturali depellit. </s>

<s>Sed aqua, ae­<lb></lb>qualiter premens undique corpus in aqua demersum, nullam eius partem <lb></lb>loco suo naturali depellit; ergo etc.<emph.end type="italics"></emph.end> Nam neganda est minor, et falsissimum <lb></lb>est quod, si omnes hominis in aqua demersi partes satis valide ab illa com­<lb></lb>primantur, non possent loco suo naturali depelli, quamquam partes cutis <lb></lb>omnes aequaliter premerentur, satis enim depellerentur loco suo naturali, si <lb></lb>omnes tam aequaliter compellerentur introrsum, ut iste homo minus solito <lb></lb>spatii occuparet ” (ibid., pag. </s>

<s>132). E rimanendosi ostinato nella sua pro­<lb></lb>pria opinione, o per dirla addirittura nel suo errore intorno alla ragion vera <lb></lb>delle pressioni idrostatiche, soggiungeva: “ Sed praeterea falsum est quod <lb></lb>tota aqua, quae hominis corpori superincumbit, illum premat, immo po­<lb></lb>tius illum sublevat, cuius rei veram, ut opinor, rationem ad te antehac <lb></lb>scripsi ” (ibid.). </s></p><p type="main">

<s>Il Baliani in Italia, o fosse inspirato alle altrui dottrine, o concludesse <lb></lb>il discorso da ciò, che senza alcun progiudizio di scuola gli venivano sugge­<lb></lb>rendo la sua propria ragione e le naturali esperienze; fu il primo a far ri­<lb></lb>flettere, sull&#039;abbacinato pensiero dello Stevino, nuovi raggi vivi di luce. </s>

<s>“ Io <lb></lb>mi figuro, diceva, di esser nel fondo del mare, ove sta l&#039;acqua profonda die­<lb></lb>cimila piedi, e, se non fosse il bisogno di rifiatare, io credo che vi starei, <lb></lb>sebbene mi sentirei più compresso e premuto da ogni parte, di quel che io <lb></lb>mi sia di presente. </s>

<s>Ma dalla detta compressione in fuori io non sentirei altro <lb></lb>travaglio, nè sentirei maggiormente il peso dell&#039;acqua di quel ch&#039;io mi fac­<lb></lb>cia, quando, entrando sott&#039;acqua la state bagnandomi nel mare, io ho dieci <lb></lb>piedi d&#039;acqua sul capo, senza che io ne senta il peso. </s>

<s>Ma se io non fussi <lb></lb>entro l&#039;acqua, che mi preme da ogni parte, e fussi, non dico in vacuo, ma <lb></lb>nell&#039;aria, e che dalla mia testa in su vi fosse l&#039;acqua; allora io sentirei un <lb></lb>peso, che io non potrei sostenere, che quando avessi forza a lui proporzio­<lb></lb>nata.... Lo stesso mi è avviso che ci avvenga nell&#039;aria, che siamo nel fondo <lb></lb>della sua immensità, nè sentiamo nè il suo peso nè la compressione, che ci <lb></lb>fa d&#039;ogni parte, perchè il nostro corpo è stato fatto da Dio di tal qualità, <lb></lb>che possa resistere benissimo a questa compressione, senza sentirne offesa. </s>

<s><lb></lb>Anzi ci è per avvéntura necessaria, nè senza di lei si potrebbe stare, ond&#039;io <lb></lb>credo che, ancorchè non avessimo a respirare, non potremmo stare nel vacuo, <pb xlink:href="020/01/3306.jpg" pagenum="267"></pb>ma, se fossimo nel vacuo, allora si sentirebbe il peso dell&#039;aria, che avessimo <lb></lb>sopra il capo, il quale io credo grandissimo ” (Alb. </s>

<s>IX, 212, 13). </s></p><p type="main">

<s>Questi pensieri gli esponeva nel 1630 il Baliani in una lettera a Gali­<lb></lb>leo, il quale non gli poteva approvare in nesssun modo, perchè, sebbene a <lb></lb>quel tempo fossero in Italia oramai noti gli Elementi idrostatici steviniani, <lb></lb>ei non s&#039;era potuto ancora persuadere dell&#039;uguaglianza delle pressioni, che <lb></lb>si diceva fare i fluidi per tutti i versi: e persistendo nel credere che nè <lb></lb>l&#039;acqua nè l&#039;aria pesino su sè stesse, o sui corpi solidi a loro sottoposti, si <lb></lb>intende come, del non essere oppressi i palombari e i pesci, rifiutasse le ra­<lb></lb>gioni date nuovamente dal Baliani, per non rimoversi da quelle antiche di <lb></lb>Herone, fatte già sue da quarant&#039;anni. </s>

<s>Nè si ricredè Galileo nemmeno negli <lb></lb>ultimi tempi della sua vita, ne&#039;quali dettava al Viviani, come vedemmo, di­<lb></lb>mostrazioni del non premere i liquidi i fondi dei vasi, e nè perciò i corpi <lb></lb>sopr&#039;essi posati, o gli animali lungh&#039;essi repenti. </s>

<s>Cosicchè, volendo il gio­<lb></lb>vane alunno rendersi particolarmente le ragioni di questo problema curioso, <lb></lb>le riduceva così dai manoscritti <emph type="italics"></emph>Sermones de motu gravium,<emph.end type="italics"></emph.end> mutando qual­<lb></lb>che parola nella scrittura del suo Maestro: </s></p><p type="main">

<s>“ Dubitatur quomodo pisces in aqua et homines, tam in aqua, quam <lb></lb>in aere existentes, vastissimam aquae et aeris gravitatem sustinere possint. </s>

<s><lb></lb>Forsan quia tunc dicimur gravari, quando super nos incumbit aliquod pon­<lb></lb>dus, quod sua gravitate deorsum tendit, nobis autem opus est nostra vi re­<lb></lb>sistere ne amplius descendat; illud autem resistere est quod gravari appel­<lb></lb>lamus. </s>

<s>At quia Archimedes demonstravit corpora quae sunt aqua graviora <lb></lb>in aquam demissa descendere, et esse in humido gravia quidem, attamen <lb></lb>minus gravia quam in aere, quanta est gravitas molis aquae aequalis molis <lb></lb>illius corporis; leviora autem aqua, vi sub aqua impulsa, sursum attolli tanta <lb></lb>vi, quanta moles aquae aequalis moli illius corporis gravior est illo corpore; <lb></lb>quae autem sunt aeque gravia ac aqua, in aqua submersa, neque sursum <lb></lb>neque deorsum ferri, sed ibi manere ubi collocantur, si tamen tota fuerint <lb></lb>sub aqua; ex hoc patet quod, si fuerimus sub aqua, et super nos incumbat <lb></lb>aliquod corpus aqua gravius ut lapis, gravabimur quidem, sed minus quam <lb></lb>si essemus in aere, quia lapis in aqua est minus gravis quam in aere. </s>

<s>” </s></p><p type="main">

<s>“ Si autem, in aqua existentibus nobis, aliquod corpus aqua levius alli­<lb></lb>gatum fuerit, nedum gravabimur, verum etiam attolleremur ab illo, ut patet <lb></lb>in natantibus cum cucurbita, cum alioquin, in aere existentes, a cucurbita <lb></lb>gravaremur. </s>

<s>Et ratio est quia cucurbita, sub aqua impulsa, fertur sursum <lb></lb>et allevat, in aere autem fertur deorsum et gravat. </s>

<s>Si autem in aqua exi­<lb></lb>stentes aliquod corpus aeque grave ac aqua nobis immineat, neque ab illo <lb></lb>gravabimur neque attollemur, quia neque sursum neque deorsum ferretur. </s>

<s><lb></lb>At non invenitur corpus quod magis aequet gravitatem vel levitatem aquae, <lb></lb>quam ipsa aqua; non ergo est mirum, si aqua in aqua non descendat et <lb></lb>gravet, neque ascendat et attollat: diximus autem gravari esse resistere, no­<lb></lb>stra vi, corpori deorsum petenti. </s>

<s>Et eadem ratio de aere habeatur ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXXXV, fol. </s>

<s>23, e Alb. </s>

<s>XI, 31, 32). </s></p><pb xlink:href="020/01/3307.jpg" pagenum="268"></pb><p type="main">

<s>Galileo e il Cartesio, avendo nell&#039;Idrostatica comune la falsità dei prin­<lb></lb>cipii, non discordavano dunque nemmen nelle conclusioni, che però non po­<lb></lb>tevano non essere sospette ad alcuni de&#039;loro discepoli più sagaci. </s>

<s>Anche il <lb></lb>Viviani mette in dubbio la spiegazione, che il suo Maestro faceva pronun­<lb></lb>ziare al protagonista del Dialogo, in forma così assoluta. <emph type="italics"></emph>Forsan quia....<emph.end type="italics"></emph.end><lb></lb>Nè cessarono i dubbi che per opera del Pascal, l&#039;arte usata dal quale appa­<lb></lb>risce da questo lato più che mai maravigliosa. </s>

<s>S&#039;avvide il prudente uomo <lb></lb>che i Fisici de&#039;suoi tempi, sedotti dall&#039;autorità de&#039;due loro grandi maestri, <lb></lb>rifuggivano inconsideratamente dalle verità steviniane, e fece come certe nu­<lb></lb>trici che, rifiutato un siroppo ristorativo dal bambino per disgustoso, glie <lb></lb>l&#039;hanno fatto poi parer dolce, e avidamente sorbire, a solo mutar figura e <lb></lb>materia all&#039;ampolla. </s>

<s>Quell&#039;arte, che in tutto intero il trattato <emph type="italics"></emph>De l&#039;equilibre <lb></lb>des ligueurs<emph.end type="italics"></emph.end> è davvero, come si diceva, maravigliosa, spicca anche di più nel <lb></lb>capitolo ultimo, in cui l&#039;Autore non fa che rompere le giunture al sillogi­<lb></lb>smo dello Stevino, la maggior del quale, tolta di sotto alla pressa dialettica, <lb></lb>si sciorina così più amabilmente alla vista: </s></p><p type="main">

<s>“ La douleur que nous sentons, quand quelque chose nous presse, est <lb></lb>grande, si la compression est grande, parce que la partie pressée est épuis­<lb></lb>sée de sang, et que les chairs, les nerfs, et les autre partie qui la compo­<lb></lb>sent, sont poussées hors de leur place naturelle, et cette violence ne peut <lb></lb>arriver sans douleur. </s>

<s>Mais si la compression est petite, comme quand on <lb></lb>effleure si doucement la peau avec le doigt, qu&#039;on ne prive pas la partie <lb></lb>qu&#039;on touche de sang, qu&#039;on n&#039;en detourne ny la chair ny les nerfs, et qu&#039;on <lb></lb>n&#039;y apporte aucun changement; il n&#039;y doit aussi avoir aucune douleur sen­<lb></lb>sible ” (pag. </s>

<s>38). E insomma non può la sensibilità eccitarsi sull&#039;animale, <lb></lb>se non a queste due condizioni: o che il corpo estraneo tocchi le parti sen­<lb></lb>sibili in un punto solo, o che le tocchi tutte ugualmente, fuor che in un <lb></lb>punto. </s>

<s>Per conferma di che proponeva il Pascal l&#039;esperienza di un uomo, <lb></lb>seduto sul cupo fondo di un vivaio. </s>

<s>Ei veramente non soffre alcuna passione <lb></lb>dal peso dell&#039;acqua, quand&#039;ella lo circonda tutto, ma se s&#039;applica la bocca <lb></lb>di un lungo tubo a una coscia, in modo che l&#039;altra bocca di sopra resti <lb></lb>aperta nell&#039;aria, “ sa chair s&#039;enflera, a la partie qu&#039;est a l&#039;ouverture du <lb></lb>tuyau, et il s&#039;y formera une grosse tumeur avec douleur, comme si sa chair <lb></lb>y estoit succée et attirée par une vantouze ” (pag. </s>

<s>32). </s></p><p type="main">

<s>La minore del sillogismo dello Stevino udimmo come il Cartesio la con­<lb></lb>dannasse per falsa, e il Pascal risolutamente invece l&#039;assolveva, condensando <lb></lb>le virtù delle verità precedentemente dimostrate in questa sentenza: “ La <lb></lb>vraye cause, qui fait que les animaux dans l&#039;eau n&#039;en sentent pas le poids, <lb></lb>est qu&#039;ils sont pressez egalement de toutes partes ” (pag. </s>

<s>40). E perchè il <lb></lb>Cartesio audacemente negava anche queste pressioni per tutto le parti, di­<lb></lb>cendo che l&#039;animale, non ch&#039;essere oppresso dal peso dell&#039;acqua, n&#039;è sol­<lb></lb>levato; il Pascal, a confermare la verità del fatto, proponeva una tale espe­<lb></lb>rienza: Prendasi un bocciolo di vetro, e ripieno d&#039;acqua vi s&#039;infondano tre <lb></lb>cose: una vescica ben gonfiata e distesa, un&#039;altra flaccida, e una mosca (car <pb xlink:href="020/01/3308.jpg" pagenum="269"></pb>elle vit dans l&#039;eau tiede aussi bien que dans l&#039;air) e comprimendo l&#039;acqua <lb></lb>fortemente con uno stantuffo si vedrà la seconda vescica costringersi di più <lb></lb>alla pressione, ma la prima rimanersi immutata, e la mosca “ se promener <lb></lb>avec liberté et vivacité le long du verre, et mesme s&#039;envoler des qu&#039;elle sera <lb></lb>hors de cette prison ” (pag. </s>

<s>41), eppure ella non doveva esser premuta meno <lb></lb>della seconda vescica, che, così visibilmente cedendo allo sforzo, rientrava in <lb></lb>sè stessa. </s></p><p type="main">

<s>Che il Pascal, rendendo così alla libertà della vita lo Stevino, intendesse <lb></lb>di rivendicarne l&#039;onta fattagli da&#039;seguaci di Galileo e del Cartesio, si par <lb></lb>dal tuono insolito che piglia, verso la fine il suo discorso, simile a quello, <lb></lb>con cui concluderebbe una lunga riprensione qualche padre adirato o qual­<lb></lb>che maestro. </s>

<s>“ Qu&#039;on ne dise donc plus que c&#039;est parce que l&#039;eau ne pese <lb></lb>pas sur elle mesme; car elle pese par tout également: ou qu&#039;elle pese d&#039;une <lb></lb>autre maniere que les corps solides, car tous les poids sont de mesme na­<lb></lb>ture, et voicy un poids solide qu&#039;une mouche supporte sans le sentir ” (pag. </s>

<s>43). <lb></lb>Provate infatti ad aggiungere nel bocciolo alla prima altr&#039;acqua, che equi­<lb></lb>valga in peso alla forza fatta dallo stantuffo, e osserverete le medesime cose. </s>

<s><lb></lb>Che se al pesce non rimanga in fondo alla vasca se non l&#039;acqua che lo cir­<lb></lb>conda, essendosi il resto indurato nel ghiaccio, serberà l&#039;agilità che aveva <lb></lb>prima, e che serberebbe anche dopo essersi tutta l&#039;acqua liquefatta. </s>

<s>Dun­<lb></lb>que, così finalmente concludeva il Pascal, a favore dello Stevino, e contro i <lb></lb>paralogismi del Cartesio; “ les animaux dans l&#039;eau n&#039;en sentent pas le poids, <lb></lb>non pas parce que ce n&#039;est que de l&#039;eau qui pese dessus, mais parce que <lb></lb>c&#039;est de l&#039;eau qui les environne ” (pag. </s>

<s>44). </s></p><p type="main">

<s>La questione parve al Boyle di tanta curiosità e di tanta importanza, <lb></lb>che volle riserbare l&#039;appendice II de&#039;suoi Paradossi a esaminarla. </s>

<s>Gli cade <lb></lb>per prima cosa sotto la considerazione il detto di uno scrittore d&#039;Idrostatica, <lb></lb>ch&#039;egli chiama celebre, non sappiamo per qual titolo, ma che certamente era <lb></lb>gonfio di filosofico orgoglio cartesiano, affermando che, del non sentire il peso <lb></lb>dell&#039;acqua gli animali che ci son sotto, non poteva esser altra la causa, da <lb></lb>quella in fuori, ch&#039;egli stesso assegnava con questo discorso: Le parti supe­<lb></lb>riori dell&#039;acqua non premono le inferiori, se non sia in mezzo a queste col­<lb></lb>locato un corpo più leggero dell&#039;acqua stessa. </s>

<s>Ma il corpo dell&#039;uomo è anzi <lb></lb>più grave, dunque ecc. </s>

<s>concludendo che chiunque dice altrimenti s&#039;inganna. </s>

<s><lb></lb>A cui il Boyle rispondeva che, nonostante una si gran fiducia, era certo do­<lb></lb>verci essere, e che fosse perciò da ricercarsi del fatto una causa diversa. <lb></lb></s>

<s>“ Abunde enim probavi quod (contra assertionem cui innititur eius explica­<lb></lb>tio) partes aquae superiores premunt inferiores, sive corpus aqua in specie <lb></lb>gravius, sive levius sit infra inferiores ” <emph type="italics"></emph>(Paradoxa<emph.end type="italics"></emph.end> cit., pag. </s>

<s>216) </s></p><p type="main">

<s>L&#039;altra soluzion del problema, che l&#039;autore di questi Paradossi passa <lb></lb>a esaminare nella detta Appendice, è quella che il Cartesio dava al Mer­<lb></lb>senno, nella forma per noi dianzi ritratta dall&#039;epistola XXXII della parte <lb></lb>seconda. </s>

<s>Ciò che avendo fatto anche il Boyle, appena finito di trascrivere, <lb></lb>così dice: Hactenus subtilis hic Philosophus, cuius ratiocinationes, licet magni <pb xlink:href="020/01/3309.jpg" pagenum="270"></pb>facere sim solitus, libere tamen fatendum hance mihi non satisfacere. </s>

<s>Ete­<lb></lb>nim, cum iam satis superque probaverim superiores partes aquae premere <lb></lb>inferiores, corporaque iis subiacentia, sive corpora illa sint aqua in specie <lb></lb>leviora, sive graviora; fundamentum evertimus, cui domini Cartesii ingeniosa <lb></lb>at minus solida superstruitur explicatio ” (ibid., pag. </s>

<s>223, 24). </s></p><p type="main">

<s>Soggiungerò anche di più, dice il Boyle, che il Cartesio s&#039;inganna, at­<lb></lb>tribuendo la causa del sentirne o no l&#039;uomo il peso allo scendere o no che <lb></lb>fa l&#039;acqua insieme con lui. </s>

<s>Perchè poniamo che quell&#039;uomo, il quale gia­<lb></lb>cendosi sul foro A (nella figura 155) lo turava, sia collocato in B, d&#039;onde <lb></lb>egli poi scenda, insieme con l&#039;acqua C, verso il foro A rimasto aperto: se <lb></lb>vero fosse quel che dice il Cartesio, dovrebbe il marangone sentire il peso <lb></lb>dell&#039;acqua C. Eppure, verificandosi la chiesta posizione, è certo che non sen­<lb></lb>tirebbe niente. </s>

<s>Dunque il conferire i momenti delle scese de&#039;liquidi con quelle <lb></lb>dei solidi, come fa il Cartesio, calcando, senza voler parere, le orme di Ga­<lb></lb>lileo; è mezzo ingannevole e insufficiente a risolvere una questione idrosta­<lb></lb>tica così sottile, la quale da null&#039;altra vera causa dipende se non dall&#039;avere <lb></lb>in B il marangone acqua di sotto e di sopra, e in A acqua solamente di <lb></lb>sopra, e di sotto aria. </s>

<s>“ Dico itaque causam cur solidum quod, dum est ad A, <lb></lb>magnam sustinebat pressionem ab aqua incumbente non sentiat pondus eius, <lb></lb>quando locatur ad B, non esse quam assignat dom. </s>

<s>Des-Cartes, sed hanc <lb></lb>quod solido aqua circumdato aqua subiacens, ut frequens nobis fuit occasio <lb></lb>ostendendi, illud sursum premit aeque omnino vehementer, et aliquando am­<lb></lb>plius, ac pondus aquae incumbentis id premit deorsum. </s>

<s>Cum e contra, quando <lb></lb>solidum erat id solum quod tegebat obturabatque foramen, causa esset ma­<lb></lb>nifesta cur id cum violentia deorsum truderetur a pondere incumbentis aquae <lb></lb>ABC. </s>

<s>In isto quippe casu nulla ei subiacebat aqua ad A, quae solidum su­<lb></lb>stentaret ac sua sursum pressione ipsum vi instrueret tanto ponderi resi­<lb></lb>stendi ” (ibid., pag. </s>

<s>225, 26). </s></p><p type="main">

<s>Rimane, prosegue il Boyle, a esaminar la soluzione, che di questo pro­<lb></lb>blema avea dato lo Stevino, assai prima del Cartesio, e, riferita l&#039;argomen­<lb></lb>tazione tradotta in latino dal libro degli Elementi idrostatici, soggiunge: “ Hanc <lb></lb>solutionem Stevini longe existimem esse praeferendam iis, quae de difficili <lb></lb>hoc problemate afferri solent ” (ibid., pag. </s>

<s>230). </s></p><p type="main">

<s>Nonostante esso Boyle, che aveva accusato l&#039;autore degli Elementi idro­<lb></lb>statici d&#039;aver proposte esperienze, piuttosto razionali che di fatto, a confer­<lb></lb>mare la verità degli altri suoi teoremi; non può passare ora in questo l&#039;esem­<lb></lb>pio dell&#039;uomo in fondo al tino ripieno d&#039;acqua, che, dovendovi necessariamente <lb></lb>rimanere affogato, non potrebbe far testimonianza nè della insensibilità pro­<lb></lb>vata, nè della passione. </s>

<s>Vero è bene che, dalla somiglianza di quel che segue <lb></lb>alle cose insensibili, come alle tavolette di legno o di metallo poste nelle <lb></lb>medesime condizioni; si può ragionevolmente argomentare a ciò, che pati­<lb></lb>rebbe un uomo, supposto ch&#039;egli durasse a vivere anche nell&#039;acqua. </s>

<s>Nulla­<lb></lb>dimeno, dice il Boyle, si può l&#039;esperienza praticar facilmente e con esattis­<lb></lb>sima somiglianza dei fatti, per via della mia Macchina pneumatica. </s>

<s>“ Etenim, <pb xlink:href="020/01/3310.jpg" pagenum="271"></pb>licet aer sit fluidum grave, licetque, dum uniformiter premit totam corporis <lb></lb>superficiem, pressionem eius non sentiamus; et quamvis hanc ob causam <lb></lb>palmam manus imponere possis, aperto orificio parvi cylindri aenei, appli­<lb></lb>cati machinae loco <emph type="italics"></emph>Recipientis,<emph.end type="italics"></emph.end> citra ullam noxam; quando tamen, antliam <lb></lb>exercendo, aer qui prius suberat palmae manus est subductus, proindeque <lb></lb>conferre nil amplius potest ad manum, adversus aeris externi et incumben­<lb></lb>tis, pressionem sustentandam; utique aer externus tam graviter incumbet <lb></lb>manus metacarpio, ac si pondus quoddam grave ipsi esset impositum. </s>

<s>Ac <lb></lb>memini, tali facto experimento, non tantum manum meam gravi dolore fuisse <lb></lb>affectam, sed et convexitatem eius ultro deorsum pressam, ac si fracturae <lb></lb>esset periculum ” (ibid., pag. </s>

<s>233). </s></p><p type="main">

<s>Benchè questa esperienza, fatta con la Macchina pneumetica, possa qual­<lb></lb>che poco diminuir la difficoltà, riman nonostante, dice il Boyle, sempre a <lb></lb>stupire come, sotto il peso, che, secondo i calcoli dello stesso Stevino, è in­<lb></lb>gente, costringendosi le costole verso la cavità del petto, e i muscoli contro <lb></lb>l&#039;ossa; il marangone non senta alcun dolore. </s>

<s>L&#039;esperienza della mosca de­<lb></lb>scritta dal Pascal era lusinghiera, ma in sul primo leggerla sospettò il Boyle <lb></lb>che, insieme co&#039;naturalisti di que&#039;tempi, anche l&#039;Autore credesse non avere <lb></lb>gli insetti bisogno alcuno di respirare, e che perciò quella, come e altre che <lb></lb>si trovano in mezzo al libro di lui, non foss&#039;altro che una semplice specu­<lb></lb>lazione. </s>

<s>Provato infatti più volte a sommergere nell&#039;acqua anche tiepida mo­<lb></lb>sche assai gagliarde, ebbe a trovar che sempre vi rimanevano immobili, come <lb></lb>cose morte. </s>

<s>Allora pensò di far l&#039;esperienza con qualche animale acquatico, <lb></lb>fra cui scelse i <emph type="italics"></emph>girini,<emph.end type="italics"></emph.end> per la loro piccolezza e mollezza di membra, più facil­<lb></lb>mente sensibili alla pressione. </s>

<s>Messo dunque l&#039;animaletto nello strumento del <lb></lb>Pascal, e premuto lo stantuffo così, che il Boyle stesso calcolò uguagliar la <lb></lb>pressione al peso di un cilindro d&#039;acqua, di quasi trecento piedi di altezza; <lb></lb>“ nihilominus, licet gyrinus in paulo minorem quam prius molem videre­<lb></lb>tur compressus, libere tamen ipse hac illac in aqua natabat, subinde etiam <lb></lb>in summitatem ipsam pervadens. </s>

<s>Nec manifestum erat nobis laesum fuisse <lb></lb>ab hac compressione animalculum: manifestissimum vero erat id contusum <lb></lb>non fuisse ad necem, sensibilemve ei noxam illatam ” (ibid., pag. </s>

<s>238). </s></p><p type="main">

<s>Il curioso e difficile problema, qual&#039;era stato risoluto dallo Stevino, ve­<lb></lb>niva dunque a confermarsi così per ogni sua parte, che agli scrittori d&#039;Idro­<lb></lb>statica non rimase poi a fare altro ufficio, che diffondere la notizia. </s>

<s>A tale <lb></lb>infatti si riduce insomma il merito del Sinclaro, che, nel terzo libro della <lb></lb>sua <emph type="italics"></emph>Ars magna,<emph.end type="italics"></emph.end> riserbò il secondo dialogo, per applicare all&#039;argomento le <lb></lb>verità idrostatiche, rimaste vincitrici. </s>

<s>Il principio alla battaglia vedemmo come <lb></lb>fosse dato in Italia, la quale parve nonostante esser venuta una delle ultime <lb></lb>a raccogliere i frutti della vittoria. </s></p><p type="main">

<s>Non prima del 1670 apparve in Reggio dell&#039;Emilia il libro <emph type="italics"></emph>De motio­<lb></lb>nibus naturalibus,<emph.end type="italics"></emph.end> in cui il Borelli, ravvedutosi già degli errori imbevuti <lb></lb>alle fonti galileiane, risolveva il problema <emph type="italics"></emph>quare animal nullam noxam ex <lb></lb>compressione aquae incumbentis pati debeat,<emph.end type="italics"></emph.end> applicandovi il principio del-<pb xlink:href="020/01/3311.jpg" pagenum="272"></pb>l&#039;uguaglianza delle pressioni per tutti i versi. </s>

<s>Abbiasi, diceva, una vessica <lb></lb>tutta piena d&#039;acqua, o di mercurio, o d&#039;arena, o d&#039;altri minutissimi corpi <lb></lb>cristallini, che perciò saranno incompressibili, e s&#039;immerga nel liquido di un <lb></lb>vaso. </s>

<s>Essendo quivi ugualmente premuta tutta intorno, come da tanti cunei <lb></lb>confitti in ogni punto di una vòlta sferica, è facile dimostrare come nessun <lb></lb>granello di arena, e nessuna particella d&#039;acqua o di mercurio potrà cedere <lb></lb>a un&#039;altra il suo proprio posto. </s>

<s>Or suppongasi che la detta vessica sia la <lb></lb>pelle involgente l&#039;ossa, i muscoli e gli umori dell&#039;animale: non potendosi <lb></lb>sentir passione per altra causa, che per la division del continuo, la quale, <lb></lb>per le cose dette, è impossibile ad avvenir nelle parti involte e ugualmente <lb></lb>premute; ne segue che l&#039;acqua non fa sul corpo animale sentir lo sforzo, <lb></lb>benchè grandissimo, del suo peso. </s>

<s>“ Quapropter, cum urinatores in profundo <lb></lb>mari demersi ab aqua aequali vi undique comprimantur, superne scilicet, <lb></lb>inferne et lateraliter, circumcirca a pondere ipsius aquae; sequitur ex de­<lb></lb>monstratis nullam scissionem, luxationem aut contusionem in eis creari: sci­<lb></lb>licet nullam continui divisionem a pondere aquae incumbentis produci. </s>

<s>Igi­<lb></lb>tur nullam noxam, nec sensum dolorificum patientur ” (pag. </s>

<s>69, 70). </s></p><p type="main">

<s>Non si può nonostante negare, soggiunge il Borelli, che non siano nel­<lb></lb>l&#039;animale alcune parti aerose, le qualr, compresse, venendo a cedere, parrebbe <lb></lb>che inevitabilmente dovessero produr qualche senso di dolore, se non si ri­<lb></lb>pensasse che anco questa compressione non si fa in un luogo solo, ma è <lb></lb>universale. </s>

<s>Quanto differentemente non siam noi, che viviamo in fondo al­<lb></lb>l&#039;oceano dell&#039;aria, gravati dal peso di lei, o quando stiamo in riva al mare, <lb></lb>o quando sulla vetta di un altissimo monte? </s>

<s>Eppure, per la differenza di <lb></lb>questi due stati, non sentiamo dolerci in nessuna parte (Proposiz. </s>

<s>XXV, <lb></lb>pag. </s>

<s>71, 72). </s></p><p type="main">

<s>Vedemmo il Viviani, a cui mancavano ancora i principii necessari, come, <lb></lb>nel presente proposito, s&#039;accostasse, benchè dubitoso, col suo Galileo. </s>

<s>Ma <lb></lb>sovvenutigli quei principii, ritrovò e scrisse la vera spiegazione del fatto, la <lb></lb>quale non dee far maraviglia che in molte parti riscontri con quella del suo <lb></lb>Collega, e degli stranieri suoi precursori, perch&#039;essendo il termine fisso, e <lb></lb>fisso il punto della partenza, la via di ricongiunzione non poteva variare che <lb></lb>nell&#039;essere più o meno piana, più o men tortuosa. </s></p><p type="main">

<s>“ I marangoni stando sott&#039;acqua (scrive ora il Viviani nella sua propria <lb></lb>casa molto diversamente, da quel che aveva fatto nell&#039;ospizio di Arcetri) <lb></lb>non sentono il peso dell&#039;acqua, che all&#039;altezza talvolta di venti o più brac­<lb></lb>cia gli sovrasta, dal che pare a taluno evidente che il peso dell&#039;acqua non <lb></lb>aggravi i corpi, che in essa sono, e per conseguenza che ella nel proprio <lb></lb>luogo attualmente non pesi. </s>

<s>Ma, per la prima, la conseguenza è falsa, ne è <lb></lb>necessario che, gravitando attualmente un peso sopra un corpo sensitivo, an­<lb></lb>corchè tenero e cedente, ei lo senta. </s>

<s>Imperocchè si può dare il caso che, da <lb></lb>forza grandissima di peso o d&#039;altro, premuto, ad ogni modo gli sia impos­<lb></lb>sibile il poterlo sentire, il che avverrà necessariamente, quando, essendo egli <lb></lb>incapace di restringimento, sarà la di lui superficie ugualmente, secondo qual <pb xlink:href="020/01/3312.jpg" pagenum="273"></pb>si voglia linea assegnabile, nel medesimo tempo premuta o respinta, come <lb></lb>per chiarezza nella seguente figura 156 dimostreremo. </s>

<s>” </s></p><p type="main">

<s>“ Sia ABC superficie di qualsivoglia dato corpo sensitivo D, quantunque <lb></lb>tenero e cedente, purchè incapace di ristringimento, la quale s&#039;intenda se­<lb></lb><figure id="id.020.01.3312.1.jpg" xlink:href="020/01/3312/1.jpg"></figure></s></p><p type="caption">

<s>Figura 156.<lb></lb>condo qualsivoglia linea assegnabile con egual forza pre­<lb></lb>muta o respinta. </s>

<s>Dico essere impossibile che tal forza sia <lb></lb>in modo alcuno dal detto corpo sentita. </s>

<s>Imperocchè in­<lb></lb>tanto il corpo sensitivo D può sentire la forza premente, <lb></lb>in quanto fa nella di lui superficie qualche impressione. </s>

<s><lb></lb>Se dunque, per qualsisia cagione ciò avvenga, si darà il <lb></lb>caso che dalla forza detta non venga la superficie a patire <lb></lb>impressione alcuna o alterazion di figura; resterà ancora <lb></lb>dimostrato che non puossi la detta forza, quantunque grandissima, dal corpo D <lb></lb>sentire, il che così mostreremo. </s>

<s>” </s></p><p type="main">

<s>“ Si pigli in ABC qualsivoglia punto B, il quale, secondo qualsivoglia <lb></lb>linea EB premuto, ceda se è possibile, e si rimova dal suo luogo verso qua­<lb></lb>lunque linea, o per di fuori del corpo D, come per BF, o per di dentro, come <lb></lb>per BH. Ma, per la supposizione, tanto secondo la BF, quanto secondo la BH, <lb></lb>vi s&#039;oppone forza di pressione e di resistenza uguale alla forza premente <lb></lb>secondo EB; dunque il punto B, secondo EB premuto, non potrà verso parte <lb></lb>alcuna cedere o mutarsi di luogo. </s>

<s>E così di qualsivoglia altro punto assegna­<lb></lb>bile in ABC. Ond&#039;è manifesto che, non potendo ABC, secondo alcuno suo <lb></lb>punto assegnabile, alla forza della pressione, quantunque grandissima, ce­<lb></lb>dere; non potrà patire da essa impressione alcuna o alterazione della propria <lb></lb>figura. </s>

<s>” </s></p><p type="main">

<s>“ Ora, per venire al particolare dei marangoni, come mai il peso del­<lb></lb>l&#039;acqua, che aggrava e preme manifestamente i mantici e le palle di vetro, <lb></lb>può non aggravare e premere similmente gli uomini? </s>

<s>” </s></p><p type="main">

<s>“ Che dal non sentire il gran peso della mole che gli sovrasta sia falso <lb></lb>l&#039;argomento che attualmente non gli aggravi e prema, si dimostrerà chia­<lb></lb>ramente con un caso nel quale, benchè per ognuno sia certo che l&#039;uomo sia <lb></lb>dal di lei peso attualmente aggravato e premuto, nonostante egli similmente <lb></lb>non lo senta. </s>

<s>Intendasi sopra il fondo di un vaso posta dell&#039;arena o altra <lb></lb>materia incapace di restringersi, che serva per letto, sul quale si distenda <lb></lb>un uomo, sicchè, sovrappostoli qualche mole di acqua, egli verrà ad essere <lb></lb>il fondo, sul quale immediatamente l&#039;acqua sovrastante si posa, e non si può <lb></lb>revocare in dubbio che tutto il peso dell&#039;acqua sovrastante farà forza per­<lb></lb>pendicolare ad aggravare la superficie dell&#039;uomo sottoposto per fondo. </s>

<s>Ep­<lb></lb>pure è vero che egli il di lei peso nella medesima maniera non sentirà che <lb></lb>se fosse in qualunque altro luogo di essa collocato. </s>

<s>” </s></p><p type="main">

<s>“ Ma che un poco ad ogni modo lo senta, può ancora, a chi diligen­<lb></lb>temente vorrà abbadarvi, per esperienza essere manifesto. </s>

<s>Imperocchè, men­<lb></lb>tre pian piano anderà sott&#039;acqua tuffandosi, sentirà principalmente intorno <lb></lb>al petto e alla gola una tale oppressione o soffocazione, che gli arrecherà il <pb xlink:href="020/01/3313.jpg" pagenum="274"></pb>peso circostante, e questa ne&#039;marangoni, che sotto altezze d&#039;acqua assai con­<lb></lb>siderabili restano sepolti, viene ad essere ancora più notabile. </s>

<s>Ma eglino però <lb></lb>che molto maggiore dal peso dell&#039;acqua soprastante se l&#039;aspettano, all im­<lb></lb>pedimento della respirazione piuttosto cotale oppressione o soffocamento at­<lb></lb>tribuiscono. </s>

<s>Ma, se faranno l&#039;esperienza, accorgerannosi che, ritenendo il <lb></lb>fiato fuor dell&#039;acqua per lo spazio medesimo di tempo, non sentiranno il <lb></lb>medesimo, ma molto minore affanno. </s>

<s>” </s></p><p type="main">

<s>“ Resta ora che dichiamo la cagione, per la quale non tutto ma parte <lb></lb>solamente del detto peso sentir ne debbano. </s>

<s>Bisogna dunque sapere qual­<lb></lb>mente alla superficie d&#039;un corpo, di consistenza simile all&#039;umano, posta <lb></lb>dentro l&#039;acqua, o a qualsivoglia altro fluido, stanno d&#039;intorno, secondo ogni <lb></lb>linea assegnabile, momenti di pressione e di resistenza uguali, e da questo <lb></lb>canto, se fosse incapace di restringimento, non averebbe egli, per quel che <lb></lb>s&#039;è di sopra dimostrato, a sentirne punto del di lui peso. </s>

<s>Ma perchè nel <lb></lb>corpo umano vi sono molte cavità, che danno all&#039;aria ricetto, e per conto di <lb></lb>esse di qualche compressione e restringimento capace lo rendono; quindi è <lb></lb>che al peso del sovrastante fluido in qualche parte gli è forza cedere, cioè <lb></lb>infino a tanto che l&#039;aria contenuta puo dal detto peso essere ristretta. </s>

<s>Al <lb></lb>qual segno pervenuta, il cedere della di lui superficie, e conseguentemente <lb></lb>il senso dell&#039;aggravamento, naturalmente cessa. </s>

<s>” </s></p><p type="main">

<s>“ E perchè chiaramente apparisce come il peso dell&#039;acqua, sovrastante <lb></lb>il corpo in essa collocato, attualmente aggravi e prema, ma, stando intorno <lb></lb>la di lui superficie momenti di pressione e di resistenza uguali, e non po­<lb></lb>tendo perciò quella secondo alcun suo punto cedere, non possa egli la forza <lb></lb>di cotal peso sentire; tolgasi per qualche via o la pressione o la resistenza <lb></lb>secondo qualche linea, sicchè possa verso quella alla circostante pressione <lb></lb>cedere, e la forza del peso si verrà subitamente in tal parte a sentire. </s>

<s>Del <lb></lb>quale effetto in cotal guisa potrà farsene l&#039;esperienza. </s>

<s>” </s></p><p type="main">

<s>“ S&#039;applichi un marangone, a qualche parte polposa del corpo, la bocca <lb></lb>d&#039;una lunga canna di vetro, in maniera che non possa l&#039;acqua tra il vetro <lb></lb>e la carne trovar adito, e tuffandosi notabilmente sott&#039;acqua, purchè intanto <lb></lb>l&#039;altra bocca della canna resti sempre di fuora; ei sentirà in quella parte <lb></lb>la forza della oppressione. </s>

<s>Imperocchè il peso dell&#039;acqua intorno premente, <lb></lb>non trovando resistenza verso lo spiracolo cedente della canna, scaccerà verso <lb></lb>quello la carne, non senza qualche senso di dolore. </s>

<s>” (MSS. Cim., T. XXXIV, <lb></lb>fol. </s>

<s>122-27). </s></p><p type="main">

<s>Questa esperienza fa tornare a mente il Pascal, benchè il Francese ci <lb></lb>rappresenti l&#039;uomo in fondo al pelago come una naiade favolosa, e il Nostro <lb></lb>riduca il caso alla realtà dei marangoni, che respirano di fatto, e vivono <lb></lb>e sentono dentro alla loro campana. </s>

<s>In ogni modo deve la detta esperienza <lb></lb>essere stata suggerita al Viviani dalla lettura del capitolo VI <emph type="italics"></emph>De l&#039;equilibre <lb></lb>des liqueurs,<emph.end type="italics"></emph.end> trattato, che non poteva in Italia non trovare lieta accoglienza. </s>

<s><lb></lb>L&#039;intenzione infatti, ch&#039;ebbe principalmente l&#039;Autore, fu quella di esplicare <lb></lb>e di confermare la grande Esperienza torricelliana, la quale sanno bene i <pb xlink:href="020/01/3314.jpg" pagenum="275"></pb>nostri Lettori che non riuscì all&#039;invenzione dello strumento desiderato, ma <lb></lb>alla fisica dimostrazione del premere, che fanno i fluidi in sè stessi e sui <lb></lb>corpi sottoposti, no nella sola direzion verticale, ma per tutti i versi, cosic­<lb></lb>chè, dalle vette del Puy de Domme, si può dire che movessero l&#039;aure a in­<lb></lb>sufflar l&#039;anima nella scienza plasmata dallo Stevino. </s></p><p type="main">

<s>Nonostante è notabile che al Pascal si facesse forse maggiore accoglienza <lb></lb>in Italia, che in Francia, dove l&#039;Idrostatica cartesiana aveva messe più lar­<lb></lb>ghe e più profonde le radici, che la galileiana fra noi, e là come qua non <lb></lb>erano stati con pari soavità di potenza scommossi gli errori dal grande av­<lb></lb>venimento patrio del Torricelli. </s>

<s>Così, se a riavviarsi nella rettitudine de&#039;sen­<lb></lb>tieri bastarono agli Accadem̀ici fiorentini quasi sole le lettere a M. A. Ricci, <lb></lb>bisognò a&#039;Francesi aspettare quella universale potenza, che doveva tutta la <lb></lb>natural Filosofia cartesiana rovesciare dai fondamenti. </s>

<s>Del turbinare tempe­<lb></lb>stoso e polveroso de&#039;vortici fu sgombrato il cielo della Scienza dal benefico <lb></lb>apparire dell&#039;astro di una Filosofia nuova, che si stabiliva, non sopra le chi­<lb></lb>mere, ma sui principii della Matematica. </s></p><p type="main">

<s>Il Newton insomma, com&#039;era venuto a restaurare matematicamente ogni <lb></lb>altra parte della Fisica, cosi, nella sezione V del suo tomo secondo, non la­<lb></lb>sciava di provvedere all&#039;Idrostatica. </s>

<s>Incomincia dal dimostrare l&#039;uguaglianza <lb></lb>delle pressioni, proponendosi un vaso sferico tutto pieno di un fluido omo­<lb></lb>geneo, e d&#039;ogni parte ugualmente compresso, come la vessica del Borelli, a <lb></lb>cui molto somiglia il Newton anche nel modo di ragionare. </s>

<s>Ma non era spe­<lb></lb>ranza di persuadere che il liquido preme ugualmente i corpi ch&#039;egli cir­<lb></lb>conda, in modo da mantenere inalterata la loro figura, se non sradicavasi <lb></lb>prima dalle menti quel dannosissimo pregiudizio, che nessuna porzion di <lb></lb>liquido pesa in mezzo a tutta l&#039;altra mole. </s>

<s>È cosa veramente da stupire come <lb></lb>Galileo non ripensasse che, se nessuno strato fluido pesa in sè non potrebbe <lb></lb>nemmeno pesar nel tutto, sulla mano che sostiene, e sulla bilancia che equi­<lb></lb>libra il vaso pieno, le pareti del quale, se sian troppo deboli, si vedon ce­<lb></lb>dere allo sforzo. </s>

<s>E anco è più da stupire che, contro una tale evidenza di <lb></lb>fatto, Galileo stesso dettasse al Viviani quelle due proposizioni, da noi rife­<lb></lb>rite di sopra, nelle quali contenevasi un paralogismo molto simile all&#039;altro <lb></lb>di quell&#039;antico Filosofo, che voleva, passeggiando, provare non darsi in na­<lb></lb>tura il moto. </s></p><p type="main">

<s>L&#039;Idrostatica del Cartesio s&#039;avvolgeva ne&#039;medesimi paralogismi, a cor­<lb></lb>reggere i quali i discorsi lunghi del Boyle, confortati d&#039;esperienze così la­<lb></lb>boriose, non valsero quanto le matematiche proposizioni del Newton, pene­<lb></lb>tranti come punte di freccie, che si sentono ferire, prima di saper come, e <lb></lb>d&#039;onde siano venute. </s>

<s>Egli pone il fondamento al discorso in quella stessa <lb></lb>evidenza che, sebbene rimanesse annuvolata alle menti dei due grandi <lb></lb>Maestri, suoi precursori, rifulgeva pure così limpida al senso comune, <lb></lb>dimostrando che, diviso il liquido in tante sezioni, porzion ciascuna di <lb></lb>un orbe concentrico con la terra, la seconda, la terza, la quarta, ecc., <lb></lb>oltre al proprio peso, hanno quello delle sezioni, che a loro stanno di sopra, <pb xlink:href="020/01/3315.jpg" pagenum="276"></pb>cosicchè l&#039;infima grava il fondo del vaso con la forza dovuta alla gravità sua <lb></lb>propria, moltiplicata per il numero delle sezioni, o degli orbi concentrici infino <lb></lb>alla superficie. </s>

<s>“ Pressio igitur, qua superficies unaquaeque urgetur, non est <lb></lb>ut quantitas solida fluidi incumbentis, sed ut numerus orbium ad usque sum­<lb></lb>mitatem fluidi, et aequatur gravitati orbis infimi multiplicati per numerum <lb></lb>orbium ” (Genevae 1711, pag. </s>

<s>169). Derivava di qui, per corollario imme­<lb></lb>diato, che la pressione sul fondo del vaso è la medesima, “ sive fluidum a <lb></lb>superficie pressa sursum continuatum surgat perpendiculariter, secundum <lb></lb>lineam rectam, sive serpit oblique per tortas cavitates et canales, easque re­<lb></lb>regulares, vel maxime irregulares, amplas vel angustissimas ” (ibid., pag. </s>

<s>171). </s></p><p type="main">

<s>Per quinto corollario della medesima proposizione si derivano i teoremi <lb></lb>idrostatici di Archimede, osservando, a quel modo che avevano fatto il Pa­<lb></lb>scal e il Borelli, costituirsi in mezzo al fluido una specie di bilancia, sulla <lb></lb>quale i corpi da una parte discendono o ascendono, in ragion degli eccessi <lb></lb>e de&#039;difetti de&#039;pesi relativi a un egual volume di acqua, che s&#039;immagini <lb></lb>contrappesare dall&#039;altra. </s>

<s>Ma il sesto corollario è quello, in cui si propone il <lb></lb>Newton di scoprire per quale volgarità di fallacie si lasciassero aggirare co­<lb></lb>loro, i quali ripetevano col Galileo e col Cartesio che il fluido in mezzo al <lb></lb>fluido non è nè grave nè leggero, perchè non tende a moversi nè in basso <lb></lb>nè in alto. </s>

<s>“ Corporum igitur in fluidis constitutorum duplex est gravitas: <lb></lb>altera vera et absoluta, altera apparens, vulgaris et comparativa. </s>

<s>Gravitas <lb></lb>absoluta est vis tota, qua corpus deorsum tendit; relativa et vulgaris est <lb></lb>excessus gravitatis, quo corpus magis tendit deorsum quam fluidum am­<lb></lb>biens. </s>

<s>Prioris generis gravitate partes fluidorum et corporum omnium gra­<lb></lb>vitant in locis suis, ideoque coniunctis ponderibus componunt pondus totius. </s>

<s><lb></lb>Nam totum omne grave est, ut in vasis liquorum plenis experiri licet, et <lb></lb>pondus totius aequale est ponderibus omnium partium, ideoque ex iisdem <lb></lb>componitur. </s>

<s>Alterius generis gravitate corpora non gravitant in locis suis, <lb></lb>idest inter se collata non praegravant, sed mutuos ad descendendum cona­<lb></lb>tus impedientia permanent in locis suis, perinde ac si gravia non essent.... <lb></lb>Quae vero, nec praegravando descendunt, nec praegravanti cedendo ascen­<lb></lb>dunt, etiamsi veris suis ponderibus adaugeant pondus totius, comparative ta­<lb></lb>men et in sensu vulgi non gravitant in aqua ” (ibid., pag. </s>

<s>172, 73). Or chi, <lb></lb>non dietro l&#039;autorità dell&#039;Uomo, ma, per la forza del suo argomento, non <lb></lb>si sarebbe finalmente persuaso che la ragione addotta del non gravare il <lb></lb>liquido nel liquido, perchè non vi ascende nè vi discende, era veramente non <lb></lb>filosofica ma volgare? </s></p><p type="main">

<s>E perchè fra i problemi idrostatici quello, risoluto in ultimo luogo nel <lb></lb>libro dello Stevino, era, specialmente per l&#039;opera datavi dal Pascal. </s>

<s>dal Boyle <lb></lb>e dal Borelli, uno de&#039;più famosi; il Newton così, nell&#039;ultimo corollario, com­<lb></lb>pendiosamente ne confermava, contro Galileo e il Cartesio, la verità delle <lb></lb>ragioni: “ Cum autem fluida, premendo corpora inclusa, non mutent eorum <lb></lb>figuras externas, patet insuper, per corollarium propos XIX, quod non mu­<lb></lb>tabunt situm partium internarum inter se; proindeque, si animalia immergan-<pb xlink:href="020/01/3316.jpg" pagenum="277"></pb>tur et sensatio omnis a motu partium oriatur, nec laedent corpora immersa, <lb></lb>nec sensationem ullam excitabunt nisi quatenus haec corpora a compres­<lb></lb>sione condensari possunt ” (ibid., pag. </s>

<s>173). </s></p><p type="main">

<s>Così il Newton potentemente riassumeva gli svolgimenti, ch&#039;ebbe il <lb></lb>primo libro idrostatico di Archimede dallo Stevino e dal Torricelli, dal Pa­<lb></lb>scal e dal Boyle, dal Borelli e dal Viviani. </s>

<s>Poi l&#039;Herman additava la scienza, <lb></lb>che ascondevasi sotto il velo de&#039;conoidi galleggianti, descritti dal Siracusano <lb></lb>nel suo libro secondo, per cui, tra il finir del secolo XVII, e il cominciar <lb></lb>del seguente, prese l&#039;Idrostatica il suo libero e sicuro cammino, per andar <lb></lb>presto a scendere in quel mare dell&#039;infinito, apertole dal Bernoulli, dal <lb></lb>D&#039;Alembert e dal Lagrange, per le placide e profonde acque del quale si <lb></lb>può ora navigare da noi. </s></p><pb xlink:href="020/01/3317.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO V.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della viscosità dei liquidi e delle azioni capillari<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle questioni, insorte fra i Peripatetici e Galileo, intorno alla viscosità dell&#039;acqua, e all&#039;efficacia <lb></lb>di lei in sostenere le tavolette d&#039;ebano gallegginnti: e come le osservazioni, l&#039;esperienze, le ipo­<lb></lb>tesi, e finalmente le teorie neutoniane aggiudicassero il torto a Galileo. </s>

<s>— II. </s>

<s>Delle osservazioni <lb></lb>e delle esperienze, fatte in Italia e in Francia, e poi in Inghilterra intorno alle azioni capillari. <lb></lb></s>

<s>— III. </s>

<s>Delle varie ipotesi immaginate a spiegar gli effetti delle azioni capillari. </s>

<s>— IV. </s>

<s>Delle <lb></lb>forze attrattive, che l&#039;esperienze rivelarono esser causa degli effetti capillari. </s>

<s>— V. </s>

<s>Delle me­<lb></lb>desime forze attrattive assoggettate all&#039;anahsi matematica. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>I deliri dell&#039;Idrostatica, fin qui particolarmente narrati, è dunque ma­<lb></lb>nifesto non avere avuto d&#039;altronde l&#039;origine che dal non essersi riconosciuti, <lb></lb>della rettitudine, i vestigi rimasti ne&#039;libri di Archimede leggermente segnati. </s>

<s><lb></lb>Cotesta leggerezza si rassomiglia molto a quella di chi corre velocissima­<lb></lb>mente, nel quale atto il corpo, vinta la natural tendenza dei gravi, non la­<lb></lb>scia sul suolo visibile orma del piede. </s>

<s>Così par che avvenga delle cose fisiche <lb></lb>trattate da Archimede, il quale, come tolse, per citar uno solo de&#039;tanti esempi, <lb></lb>le braccia materiali alle bilance, per sostituirvi le linee geometriche; così <lb></lb>tolse ogni tenacità fra le liquide particelle. </s>

<s>A che non ripensando il Tarta­<lb></lb>glia e il Commandino male tradussero nella parola <emph type="italics"></emph>acqua<emph.end type="italics"></emph.end> quella di umido, <lb></lb>per cui si voleva intendere un corpo, che avesse l&#039;essenza pura, senza le <lb></lb>passioni e le proprietà dei liquidi naturali. </s>

<s>E di qui avvenne che negassero <lb></lb>alcuni all&#039;acqua quella tenacità, dalla quale s&#039;astraeva nell&#039;umido contem­<lb></lb>plato dal Siracusano. </s></p><p type="main">

<s>Notabili fra costoro, che non entrarono addentro ai sensi archimedei, <lb></lb>sono il Cartesio e Galileo. </s>

<s>Ma se il primo salvò i fatti, attribuendo al moto <lb></lb>intestino, e all&#039;implicarsi le molecole anguilliformi dell&#039;acqua quella, che vol-<pb xlink:href="020/01/3318.jpg" pagenum="279"></pb>garmente si chiama viscosità di lei; il secondo la negò assolutamente, osser­<lb></lb>vando che l&#039;acqua stessa, così nella superficie come nel mezzo, non fa mi­<lb></lb>nima resistenza alla divisione. </s>

<s>Il pensiero ebbe occasion d&#039;esplicarsi ne&#039;suoi <lb></lb>più minuti particolari, a proposito d&#039;una disputa, che Galileo ebbe co&#039;Peri­<lb></lb>patetici, intorno alla ragione del galleggiar sull&#039;acqua lamine sottilissime di <lb></lb>metallo o d&#039;altra materia più grave in specie di lei. </s></p><p type="main">

<s>La questione era stata proposta da Aristotile, nell&#039;ultimo capitolo del <lb></lb>quarto libro <emph type="italics"></emph>De coelo,<emph.end type="italics"></emph.end> sotto questa forma: “ Dubitatur nunc cur lata ferra­<lb></lb>menta et plumbum innatant super aquam, alia autem minora et minus gra­<lb></lb>via, si rotunda sint aut longa ut acus, deorsum feruntur ” <emph type="italics"></emph>(Operum,<emph.end type="italics"></emph.end> T. V, <lb></lb>Venetiis 1560, a t. </s>

<s>del fol. </s>

<s>272). E si risolve dal Filosofo, attribuendo il fatto <lb></lb>alla maggiore ampiezza delle figure, che perciò trovano resistenza tanto mag­<lb></lb>giore, quanto son più le particelle dell&#039;acqua, che si debbon distrarre. </s>

<s>“ Quae <lb></lb>igitur habent latitudinem, quia multum comprehendunt, supra manent, pro­<lb></lb>pterea quod non facile distrahitur quod maius est. </s>

<s>Quae vero contrario modo <lb></lb>se se habent figuris, quia pauca comprehendunt, feruntur deorsum ” (ibid., <lb></lb>fol. </s>

<s>274). </s></p><p type="main">

<s>La spiegazione di Aristotile era quella medesima, che si dava dai Peri­<lb></lb>patetici contemporanei di Galileo, il quale invece, affermando non aver la <lb></lb>resistenza dell&#039;acqua nessuna parte nel fatto, riduceva tutto esattamente alle <lb></lb>ragioni dell&#039;equilibrio idrostatico. </s>

<s>La propria opinione, così contraria alla pe­<lb></lb>ripatetica, la confortava l&#039;autore del Discorso intorno i galleggianti non so­<lb></lb>lamente per via dell&#039;esperienza, ma anche a priori, ritirandosi a più interna <lb></lb>contemplazione della natura dei fluidi. </s>

<s>Così facendo, egli dice, “ forse scor­<lb></lb>geremmo la costituzione delle parti loro esser tale che, non solamente non <lb></lb>contrasti alla divisione, ma che niente vi sia che a divider s&#039;abbia, sicchè <lb></lb>la resistenza che si sente nel moversi per l&#039;acqua sia simile a quella, che <lb></lb>proviamo nel camminare avanti per una gran calca di persone, dove sen­<lb></lb>tiamo impedimento, e non per difficoltà che si abbia nel dividere, non si di­<lb></lb>videndo alcuni di quelli, onde la calca è composta; ma solamente nel mover <lb></lb>lateralmente le persone già divise, e non congiunte. </s>

<s>E così proviamo resi­<lb></lb>stenza nel cacciare un legno in un monte di rena, non perchè parte alcuna <lb></lb>della rena si abbia a segare, ma solamente a muovere e sollevare. </s>

<s>Due ma­<lb></lb>niere pertanto di penetrare ci si rappresentano, una nel corpo, le cui parti <lb></lb>fossero continue, e qui par necessaria la divisione: l&#039;altra, negli aggregati <lb></lb>di parti, non continue ma contigue solamente, e qui non fa bisogno di divi­<lb></lb>dere, ma di movere solamente. </s>

<s>Ora io non son ben risoluto se l&#039;acqua e <lb></lb>gli altri fluidi si debbano stimar di parti continue o contigue solamente: <lb></lb>sento ben inclinarmi al crederle più presto contigue ” (Alb. </s>

<s>XII, 57). </s></p><p type="main">

<s>Comunque sia, non aver le particelle dell&#039;acqua coerenza tale, da im­<lb></lb>pedire a un solido più grave in specie, benchè di minimo peso assoluto, il <lb></lb>dividerle, per fare in mezzo ad esse la sua naturale discesa; ci vien dimo­<lb></lb>strato da varie esperienze. </s>

<s>“ E qual maggiore esperienza di ciò, dice Galileo, <lb></lb>ricercheremo noi di quella, che tutto il giorno veggiamo nell&#039;acque torbide, <pb xlink:href="020/01/3319.jpg" pagenum="280"></pb>le quali, riposte in vasi ad uso di bere, ed essendo dopo la deposizione di <lb></lb>alcune ore ancora, come diciamo noi, albicce, finalmente, dopo il quarto o <lb></lb>il sesto giorno, depongono il tutto restando pure e limpide? </s>

<s>Nè può la loro <lb></lb>resistenza alla penetrazione fermare quegli impalpabili e insensibili atomi di <lb></lb>rena, che per la loro minimissima forza consumano sei giorni a discendere <lb></lb>lo spazio di un mezzo braccio ” (ivi, pag. </s>

<s>54). E dopo questa esperienza Ga­<lb></lb>lileo ne soggiunge altre due, dimostrative del medesimo assunto: quella cioè <lb></lb>di una larga falda di cera che, costretta a rimanersi in fondo al vaso per <lb></lb>l&#039;aggiunta di tanto piombo, quant&#039;è la quarta parte di un grano di miglio; <lb></lb>tolto questo, risale, benchè lentamente su a galla: e l&#039;altra di qualunque <lb></lb>grandissima mole collocata in acqua ferma e stagnante, che si può, senza <lb></lb>contrasto alcuno, condurre di luogo in luogo, tirandola con un solo capello <lb></lb>di donna (ivi, pag. </s>

<s>55, 56). </s></p><p type="main">

<s>A difendere le dottrine peripatetiche contro Galileo sorsero alcuni, fra <lb></lb>i quali Lodovico delle Colombe, che in un suo Discorso adduceva molte sen­<lb></lb>sate ragioni, da persuader che nell&#039;acqua doveva essere una certa viscosità, <lb></lb>come conseguenza dell&#039;esser ella costituita di particelle continue, tutte in­<lb></lb>sieme comprese sotto un&#039;unica superficie. </s>

<s>“ Quelle gocciole d&#039;acqua, diceva, <lb></lb>che pendono dalle gronde dei tetti, se non fossero viscose, non caderebbono <lb></lb>a poco a poco allungando, e non si staccano fin che il soverchio peso non <lb></lb>vinca la tenacità loro, che però il verno si veggono alle gronde alcuni ghiac­<lb></lb>cioli così lunghi, che paiono di cera. </s>

<s>Aggiungo un esempio vostro, per pro­<lb></lb>var più chiaramente al senso la crassizie dell&#039;acqua, e insieme la continuità. </s>

<s><lb></lb>Ricordatevi a c. </s>

<s>75, che voi fate abbassar la testa all&#039;amico, e gli mostrate <lb></lb>che, nel cavar l&#039;assicella fuor dell&#039;acqua, seguita sopra il suo livello, per la <lb></lb>grossezza d&#039;una piastra, di stare attaccata alla superficie di sotto di detta <lb></lb>assicella, e l&#039;abbandona mal volentieri, come anche dite a c. </s>

<s>53, concedendo <lb></lb>la violenza alla divisione per la resistenza del divisibile: segno che, non solo <lb></lb>è continua, ma viscosa ancora, il che non può fare nè la rena nè la farina ” <lb></lb><emph type="italics"></emph>(Discorso apologetico di L. delle Colombe,<emph.end type="italics"></emph.end> Alb. </s>

<s>XII, 145). E più sotto ar­<lb></lb>gomenta il Colombo alla viscosità dell&#039;acqua dal vederla, distendendosi, ora <lb></lb>pannicolarsi, come fra le maglie di una rete, e ora avvolgersi, come nella <lb></lb>pelle di una vescica, quando agitata forma bolle e sonagli. </s>

<s>“ Quelle bolle, <lb></lb>che i fanciulli chiamano sonagli, che vedete fare alle volte nei rigagnoli, per <lb></lb>qualche grossa pioggia, come si farebbero, se l&#039;acqua non fosse continova <lb></lb>e tenace? </s>

<s>” (ivi, pag. </s>

<s>136). </s></p><p type="main">

<s>Queste prove erano così semplici e concludenti, che, non osando Gali­<lb></lb>leo contradirle ne&#039;fatti, s&#039;argomentò d&#039;infirmarle nelle ragioni, fatte consi­<lb></lb>stere in quella tenacità, che tutti i Peripatetici ammettevan nell&#039;acqua. </s>

<s>E <lb></lb>perchè, per una delle principali tra così fatte ragioni, s&#039;adduceva dal Co­<lb></lb>lombo quella del vedersi due liquidi con tanta facilità rimescolarsi insieme; <lb></lb>Galileo insisteva nel contradirgli, così ragionando: “ E più vi dirò che chi <lb></lb>ben considera questo mescolamento che da esso trarrà più presto conghiet­<lb></lb>tura di discontinuazione delle parti de&#039;corpi, che si mescolano, che per l&#039;op-<pb xlink:href="020/01/3320.jpg" pagenum="281"></pb>posito. </s>

<s>Perchè, se io metterò due corpi solidi insieme, ancorchè alcuno molto <lb></lb>gli commovesse e agitasse, mai non si mescolerebbono, ma, se i medesimi <lb></lb>si dividessero in molte parti, queste più agevolmente si confonderebbono, e <lb></lb>ci apparirebbono mescolarsi, e finalmente molto più farebbono ciò, se in sot­<lb></lb>tilissima polvere si risolvessero, che è quanto a dire che sommamente si di­<lb></lb>scontinuassero. </s>

<s>Ora, perchè le parti de&#039;fluidi agitate e commosse assai pronta­<lb></lb>mente si confondono e mescolano, quindi è che molto ragionevolmente discon­<lb></lb>tinuatissime si devono stimare ” <emph type="italics"></emph>(Risposta a L. delle Colombe,<emph.end type="italics"></emph.end> ivi, pag. </s>

<s>333). </s></p><p type="main">

<s>In ogni modo, soggiunge Galileo, anche quando si dovesse ammettere <lb></lb>una continuità di parti nella costituzione dell&#039;acqua, non perciò ne segui­<lb></lb>rebbe la pretesa viscosità di lei: anzi bisognerebbe argomentare tutto al ro­<lb></lb>vescio di quel che fa il signor Colombo, “ perchè il corpo, che fusse vera­<lb></lb>mente continuo, non ha bisogno di visco o colla, che tenga unite le sue <lb></lb>parti, ma bene con ragione si può domandare qual sia il visco, che tiene <lb></lb>attaccate le parti di un aggregato discreto. </s>

<s>E così ragionevolmente doman­<lb></lb>derà alcuno qual sia il glutine, che tiene attaccate le parti di una tavola <lb></lb>commessa di mille pezzetti di marmi, ma il ricercare tal viscosità in un sol <lb></lb>pezzo di marmo, che forse, secondo il sig. </s>

<s>Colombo, è un corpo solo conti­<lb></lb>nuato; sarebbe bene gran semplicità. </s>

<s>E però, se l&#039;acqua è un continuo, non <lb></lb>si ricerca in lei viscosità alcuna ” (ivi, pag. </s>

<s>335, 36). </s></p><p type="main">

<s>Contro poi Vincenzio di Grazia, altro peripatetico insorto alla difesa di <lb></lb>Aristotile, Galileo argomentava che, se l&#039;acqua fosse un corpo continuo, e <lb></lb>che le particelle di lei resistessero alla divisione; non solamente le tavolette <lb></lb>di ebano, ma nemmeno qualsivoglia altro corpo gravissimo sarebbe potente <lb></lb>a dividerle, “ perchè, essendo le parti del continuo innumerabili, per pic­<lb></lb>cola che fosse la resistenza di ciascheduna nel separarsi dall&#039;altra, ad im­<lb></lb>mensa forza potrebbono resistere, al che contraria l&#039;esperienza. </s>

<s>Onde mi <lb></lb>pare di mettervi in necessità di confessare la resistenza delle parti dell&#039;acqua <lb></lb>alla divisione esser nulla ” <emph type="italics"></emph>(Risposta al V. di Grazia,<emph.end type="italics"></emph.end> ivi, pag. </s>

<s>539). </s></p><p type="main">

<s>In mezzo a queste dispute, che nè per l&#039;una parte nè per l&#039;altra an­<lb></lb>darono esenti, com&#039;è naturale, da motti mordaci, sorprendono queste parole <lb></lb>di Lodovico delle Colombe, che con la vittoria sopra le labbra, e col pre­<lb></lb>sentimento della sconfitta nel cuore, par che voglia consolarsene e vendicar­<lb></lb>sene con la speranza che il vincitore superbo si sarebbe inchinato a terra, <lb></lb>a raccogliere l&#039;armi stesse del vinto: “ Signori lettori, l&#039;avversario mio co­<lb></lb>mincia dolcemente a calar le vele, e rendersi vinto, perchè, nella aggiunta <lb></lb>che seguita la soprannominata, non istà più tanto risoluto nel parer suo, che <lb></lb>nell&#039;acqua non sia resistenza alla divisione, dicendo egli: <emph type="italics"></emph>Ora io non son ben <lb></lb>risoluto, se l&#039;acqua e gli altri fluidi si devon chiamare di parti continue o <lb></lb>contigue solamente.<emph.end type="italics"></emph.end> Non vi paia gran fatto che egli dica di inclinare a cre­<lb></lb>dere che siano contigue, perchè la cagione che lo muove, sebbene è senza <lb></lb>fondamento, non è stata conosciuta da lui come tale, come conoscerà per <lb></lb>questi miei scritti, dove s&#039;è provato efficacissimamente l&#039;acqua esser conti­<lb></lb>nua ” <emph type="italics"></emph>(Discorso apolog. </s>

<s>citato,<emph.end type="italics"></emph.end> pag. </s>

<s>140). </s></p><pb xlink:href="020/01/3321.jpg" pagenum="282"></pb><p type="main">

<s>Avrebbe Galileo rinnegata la sua propria coscienza, se si fosse ardita <lb></lb>di testimoniar l&#039;efficacia degli scritti altrui, in riformare i suoi propri pen­<lb></lb>sieri, a quel modo che si chiuse gli orecchi, per non ascoltare la esecrata <lb></lb>sentenza profferitagli da Lodovico poche righe più sotto, <emph type="italics"></emph>mille volte al di <lb></lb>vuole e disvuole.<emph.end type="italics"></emph.end> Ma come è un fatto che Galileo si ridisse più volte, anche <lb></lb>nel medesimo Discorso intorno i galleggianti; così è un fatto che, rimasto <lb></lb>a principio ambiguo, e poi inchinando ad ammettere la contiguità nelle parti <lb></lb>dell&#039;acqua, finì davvero per convertirsi alle ragioni dell&#039;avversario, profes­<lb></lb>sando con lui la continuità peripatetica. </s></p><p type="main">

<s>La conversione dev&#039;essere incominciata pochi mesi dopo, e precisamente <lb></lb>in quel tempo, che Galileo attendeva a postillar sottilmente le Considerazioni <lb></lb>d&#039;Accademico incognito, perchè, in fronte a una delle carte, che fan da guar­<lb></lb>dia al volume postillato, fuor di proposito dalla rimanente scrittura, e perciò <lb></lb>separata da lei per una linea, si legge scritta questa nota: “ Un metallo <lb></lb>resta nell&#039;acqua forte senza discendere, perchè la mistione è fatta per gli <lb></lb>ultimi indivisibili ” (MSS. Gal., P. II, T. XV, fol. </s>

<s>4). </s></p><p type="main">

<s>Il motivo di riformare i primi giudizi intorno alla costituzione de&#039;liquidi, <lb></lb>deve a Galileo esser venuto dal sentirsi opporre che, sebbene sia vero andar <lb></lb>finalmente al fondo le minime particelle terrose, che intorbidan l&#039;acqua dei <lb></lb>fiumi; rimangono nonostante immobili, sciolti nell&#039;acqua forte, i metalli. </s>

<s>Nè <lb></lb>si vedeva come poter meglio rispondere che col dire essere i metalli stessi <lb></lb>ridotti a tal divisione di parti, da somigliare a quelle dei liquidi, per cui me­<lb></lb>scolate insieme non si discernono, come non si discerne l&#039;acqua mescolata <lb></lb>col vino. </s>

<s>E di qui venne Galileo a concludere che i liquidi son corpi, ridotti <lb></lb>ultimamente così ne&#039;loro atomi, da tornar veramente in quel continuo, che <lb></lb>contro il Colombo e il Grazia aveva prima negato. </s>

<s>I riformati pensieri fu­<lb></lb>rono poi solennemente espressi nella prima Giornata delle due Nuove Scienze, <lb></lb>dove, che i fluidi sian tali, perchè son risoluti ne&#039;loro primi indivisibili com­<lb></lb>ponenti, lo prova così ragionando il Salviati: </s></p><p type="main">

<s>“ Mentre io piglio un corpo duro, o sia pietra o metallo, e che con un <lb></lb>martello o sottilissima lima lo vo al possibile dividendo in minutissima e <lb></lb>impalpabile polvere, chiara cosa è che i suoi minimi, ancorchè per la lor <lb></lb>piccolezza siano impercettibili a uno a uno dalla nostra vista e dal tatto; <lb></lb>tuttavia sono eglino ancor quanti, figurati e numerabili, e di essi accade che <lb></lb>accumulati insieme si sostengono ammucchiati, e scavati sino a certo segno <lb></lb>resta la cavità, senza che le parti d&#039;intorno scorrano a riempirla: agitati e <lb></lb>commossi, subito si fermano, tantosto che il motore esterno li abbandona. </s>

<s><lb></lb>E questi medesimi effetti fanno ancora tutti gli aggregati di corpuscoli mag­<lb></lb>giori e maggiori, e di ogni figura, ancor che sferica, come vediamo nei monti <lb></lb>di miglio, di grano, di migliarole di piombo e di ogni altra materia. </s>

<s>Ma se <lb></lb>noi tenteremo di vedere tali accidenti nell&#039;acqua, nessuno ve ne troveremo, <lb></lb>ma sollevata immediatamente si spiana. </s>

<s>Se da vaso o altro esterno ritegno <lb></lb>non sia sostenuta, incavata, subito scorre a riempire la cavità, ed agitata per <lb></lb>lunghissimo tempo va fluttuando, e per ispazi grandissimi distendendo le sue <pb xlink:href="020/01/3322.jpg" pagenum="283"></pb>onde. </s>

<s>Da questo mi par di potere molto ragionevolmente arguire i minimi <lb></lb>dell&#039;acqua, nei quali ella pur sembra esser risoluta,.... esser differentissimi <lb></lb>dai minimi quanti e divisibili, nè saprei ritrovarvi altra differenza, che l&#039;es­<lb></lb>sere indivisibili ” (Alb. </s>

<s>XIII, 43, 44). </s></p><p type="main">

<s>Quanto però al concluderne, da così fatta costituzione de&#039;fluidi, la tena­<lb></lb>cità, Galileo si mantenne contrario ai Peripatetici. </s>

<s>Più avanti infatti, in que­<lb></lb>sto stesso Dialogo primo, dop&#039;aver descritta l&#039;esperienza della palla di cera, <lb></lb>ch&#039;essendo scesa in un&#039;acqua bastava aggiungervi pochi grani di sale per <lb></lb>farvela risalire, il Salviati soggiunge: “ Or vedete quanto s&#039;ingannino quei <lb></lb>Filosofi, che voglion metter nell&#039;acqua viscosità o altra coagulazione di parti, <lb></lb>che la facciano resistente alla divisione o penetrazione ” (ivi, pag. </s>

<s>73). </s></p><p type="main">

<s>Apparisce manifesto di qui non aver Galileo riformate le proprie opi­<lb></lb>nioni, espresse nel Discorso intorno ai Galleggianti, se non che rispetto alla <lb></lb>costituzione dei liquidi, ma che del resto perseverò infino all&#039;ultimo nell&#039;as­<lb></lb>serire che il galleggiar dell&#039;assicelle di ebano dipendeva solamente dall&#039;equi­<lb></lb>librio idrostatico. </s>

<s>L&#039;Accademico incognito terminava le sue <emph type="italics"></emph>Considerazioni<emph.end type="italics"></emph.end><lb></lb>con una proposta di pace, che consisteva nel dover Galileo ammettere la re­<lb></lb>sistenza del liquido, e i Peripatetici l&#039;effetto della leggerezza dell&#039;aria, nel <lb></lb>qual mezzo avrebbe voluto volentieri far convenire le parti, se avesse avuto <lb></lb>speranza che si fosse contentata ciascuna della metà della vittoria. </s>

<s>Galileo <lb></lb>di fatti non se ne contentò, e volle avere la vittoria intera, come resulta dal <lb></lb>sopra riferito documento, ma se ne sarebbero contentati i Peripatetici più <lb></lb>modesti, e specialmente Lodovico delle Colombe, il quale anzi era andato <lb></lb>spontaneo a costituirsi in quel mezzo, in cui si voleva far riposare la pace <lb></lb>fra i dissidenti, non negando che, fra le cause del galleggiar le assicelle, si <lb></lb>dovessero mettere quelle volute da Galileo, ma nel medesimo tempo affer­<lb></lb>mando non si potere escludere dagli efficienti la larghezza della figura, che <lb></lb>perciò trova nell&#039;acqua una resistenza maggiore all&#039;esser divisa. </s>

<s>“ Perchè la <lb></lb>gravità dell&#039;acqua, egli dice, non è sufficiente a resistere a un corpo più <lb></lb>grave di lei, che non la penetri e divida; di qui è che altre cagioni bisogna <lb></lb>che concorrano a far la totale resistenza, tra le quali è principale la figura, <lb></lb>delle cagioni estrinseche parlando, come intese Aristotile, che perciò attribui <lb></lb>a lei cotali accidenti, non escludendo l&#039;altre cagioni ” <emph type="italics"></emph>(Discorso apolog. </s>

<s>cit.,<emph.end type="italics"></emph.end><lb></lb>pag. </s>

<s>133). In ogni modo ebbe il Colombo a cedere alla prepotenza dell&#039;av­<lb></lb>versario, ma ora verrà la Storia a rivendicare i diritti dell&#039;oppresso. </s></p><p type="main">

<s>Incominceremo dalla viscosità dell&#039;acqua, a rivendicar la verità della <lb></lb>quale concorsero tutti i Fisici, e particolarmente i Discepoli stessi di Gali­<lb></lb>leo. </s>

<s>Non importa ripeter le censure alle dottrine galileiane fatte in questo <lb></lb>proposito dal Nardi, e nemmeno osservar che l&#039;Aggiunti non intese propria­<lb></lb>mente negare l&#039;esistenza di un glutine nell&#039;acqua, ma volle solamente dire <lb></lb>che da questo glutine non poteva dipendere il formarsi, e lo stare attaccate <lb></lb>ai fili dell&#039;erba le gocciole della rugiada. </s>

<s>Del Viviani idraulico, e che tanto <lb></lb>ben conobbe le resistenze incontrate nelle acque correnti, per la loro ade­<lb></lb>sione alle asperità degli alvei, e delle ripe dei fiumi; non parrebbe da du-<pb xlink:href="020/01/3323.jpg" pagenum="284"></pb>bitare, nonostante qualche nota, scritta da lui, ma dettatagli da Galileo, come <lb></lb>postilla al Discorso dei galleggianti, o al primo dialogo delle due nuove <lb></lb>Scienze, per dichiarar meglio e confermare le sue proprie opinioni. </s>

<s>Tale, fra <lb></lb>le dette note, sarebbe questa, l&#039;esperienza descritta nella quale fu poi pro­<lb></lb>posta agli Accademici del Cimento: “ Fare una piastra tonda di cera, che <lb></lb>salga lentamente per taglio: posta poi per piano, si vede che la figura non <lb></lb>è impotente a fender l&#039;acqua, e che in essa non ci è minima coesione o vi­<lb></lb>scosità ” (MSS. Cim., T. X, fol. </s>

<s>27). E per meglio dichiarar le ragioni della <lb></lb>continuità dei liquidi, col paragonare gli effetti, che si osservano in loro e <lb></lb>ne&#039;corpi così detti discreti, secondo quel che aveva fatto dire al Salviati, nel <lb></lb>primo dialogo delle due nuove Scienze, a pag. </s>

<s>44 della citata edizione del­<lb></lb>l&#039;Albèri; Galileo dettava una tale postilla allo stesso Viviani. </s>

<s>“ Che i mi­<lb></lb>nimi dell&#039;acqua non siano quanti ce ne dà assai gagliardo argomento il <lb></lb>vedere che i minimi di qualsivoglia minutissima polvere, di materie anco gra­<lb></lb>vissime, e le migliarole di piombo, benchè minutissime, agitate non riten­<lb></lb>gono il moto, ma subito si fermano. </s>

<s>Ma l&#039;acqua agitata conserva per lungo <lb></lb>tempo la fluttuazione; par dunque l&#039;acqua esser costituita d&#039;infiniti indivi­<lb></lb>sibili, e perciò essere come un continuo ” (MSS, Gal. </s>

<s>Disc., T. CXXXV, <lb></lb>fol. </s>

<s>22). </s></p><p type="main">

<s>Che il Viviani fosse persuaso allora di ciò, che con tanta autorità gli <lb></lb>s&#039;insinuava, non fa maraviglia, nè fa pur maraviglia che rimanessero salde <lb></lb>in lui le medesime opinioni, anche qualche tempo dopo la morte del suo <lb></lb>Maestro, com&#039;apparisce da ciò, che soggiunge in quest&#039;altra nota, dop&#039;aver <lb></lb>argomentato alla resistenza, che oppone al moto di un proiettile il mezzo, <lb></lb>da quel che si osserva in esso proiettile, quando trapassa dall&#039;aria imme­<lb></lb>diatamente nell&#039;acqua. </s>

<s>“ Eppure l&#039;acqua, egli dice, come priva in tutto di <lb></lb>tenacità, non resiste con altro, che col doversi movere lateralmente, come a <lb></lb>lungo dimostrò il Galileo nel suo trattato delle Galleggianti ” (ivi, fol. </s>

<s>15). </s></p><p type="main">

<s>La saldezza di queste opinioni, intorno al non aver l&#039;acqua nessuna te­<lb></lb>nacità di parti, incominciò a crollar nel Viviani alle osservazioni e all&#039;espe­<lb></lb>rienze, che gli contrapponeva il Borelli nell&#039;Accademia: poi gli studiati moti <lb></lb>delle acque per gli alvei dei fiumi, e per gli stessi canali artificiali, finirono <lb></lb>di persuadergli che a così fatta tenacità si dovevano principalmente attribuire <lb></lb>le cause ritardatrici di que&#039;moti. </s>

<s>Ma nella Scuola galileiana il primo, che <lb></lb>sorgesse a contradire apertamente e in pubblico le dottrine del Maestro, fu <lb></lb>Geminiano Montanari, che ne prese motivo da certe esperienze instituitesi <lb></lb>nella bolognese Accademia dell&#039;abate Sampieri, e dalla quale resultava che <lb></lb>i corpi gravi discendono più velocemente che per l&#039;acquavite e per l&#039;olio, <lb></lb>per l&#039;acqua comune. </s></p><p type="main">

<s>Ripensando il Montanari a ciò, che potesse esser causa di questa varietà <lb></lb>di moti, si sentì fortemente tentato d&#039;attribuirla alla varia viscosità de&#039;li­<lb></lb>quidi, come, con queste parole, significava in una lettera al principe Leo­<lb></lb>poldo de&#039;Medici: “ Essendosi nelle nostre radunanze appresso il sig. </s>

<s>ab. </s>

<s>Sam­<lb></lb>pieri, osservato per esperienza che li corpi discendono più velocemente per <pb xlink:href="020/01/3324.jpg" pagenum="285"></pb>l&#039;acqua comune, che per l&#039;acquavite e per l&#039;olio comune ed altri; si è con­<lb></lb>derato cio poter provenire dalla viscosità maggiore, nelle parti dell&#039;acquavite <lb></lb>e dell&#039;olio, che di quelle dell&#039;acqua. </s>

<s>E perciò si è supposto che, oltre la di­<lb></lb>versità della levigatezza de&#039;mobili, della mole de&#039;medesimi, della gravità in <lb></lb>spezie di essi, e de&#039;liquidi per li quali si muovono; essere in primo luogo <lb></lb>causa potentissima a ritardare la velocità loro questa diversità della visco­<lb></lb>sità, o se pure altra cosa ne fosse cagione dell&#039;effetto suddetto.... Si ricerca <lb></lb>dunque il modo di potere, osservando le velocità delle scese de&#039;solidi in di­<lb></lb>versi liquidi, separarne così le prime tre cause accennate, che ci rimanga <lb></lb>nuda la proporzione, che ha la viscosità, o se con altro nome si dee chia­<lb></lb>mar la supposta causa suddetta, in un liquido e in un&#039;altro ” (MSS. Cim., <lb></lb>T. XIX, fol. </s>

<s>69). </s></p><p type="main">

<s>La titubanza, che apparisce da queste parole, nasceva dal dover mani­<lb></lb>festamente contradire all&#039;opinione di Galileo. </s>

<s>Ma pure i nuovi fatti osser­<lb></lb>vati decidevano contro di lui, perchè, se veramente i liquidi non resistessero <lb></lb>che col doversi movere lateralmente, è chiaro che l&#039;acqua e l&#039;olio avrebbero <lb></lb>meno impedito il solido, il quale vi si sarebbe perciò dovuto scendere più <lb></lb>veloce, che in mezzo all&#039;acqua, contro l&#039;esperienza. </s>

<s>In ogni modo non avrebbe <lb></lb>forse osato il Montanari di mettere in campo la viscosità, se non gli veniva <lb></lb>l&#039;animo di farlo da due potentissimi esempi. </s>

<s>Il primo fu quello del Grimaldi, <lb></lb>il quale, tutto in pensiero di cercar la causa dell&#039;ascendere i liquidi ne&#039;tu­<lb></lb>betti capillari, non vide come ritrovarla migliore, che in quella viscosità, la <lb></lb>quale, sebben sapesse esser negata da alcuni, resultava in ogni modo dalle <lb></lb>quotidiane osservazioni volgari. </s>

<s>“ Consideravi aquam esse corpus aliqua tan­<lb></lb>dem viscositate praeditum ” <emph type="italics"></emph>(De lumine,<emph.end type="italics"></emph.end> Bononiae 1665, pag. </s>

<s>106). </s></p><p type="main">

<s>Ma l&#039;impulso più efficace venne al Montanari da ciò che i fratelli Del <lb></lb>Buono, amici suoi e Accademici del Cimento, gli avevano riferito del Bo­<lb></lb>relli, dicendogli come questi, non perdonando al suo proprio Maestro, dimo­<lb></lb>strasse nella stessa Accademia, con ragioni comuni e con filosofiche espe­<lb></lb>rienze, dover essere tutti i fluidi nelle loro parti viscosi. </s>

<s>E, rimanendosi la <lb></lb>questione tuttavia ne&#039;privati atti accademici, prese animo il Montanari di <lb></lb>darla pubblicamente risoluta nei suoi <emph type="italics"></emph>Pensieri fisico-matematici.<emph.end type="italics"></emph.end> “ E pri­<lb></lb>mieramente non è dubbio alcuno, egli dice, darsi nell&#039;acqua ed altri liquidi <lb></lb>quella coerenza o adesione di parti, che viscosità sogliamo chiamare, osser­<lb></lb>vata dal p. </s>

<s>Grimaldi, e conosciuta da tutti, per quotidiane esperienze che se <lb></lb>ne vedono, e della quale abbiamo fatti, come sapete, in altre nostre espe­<lb></lb>rienze lunghi esami, per conoscere in qual proporzione rispondessero fra di <lb></lb>loro le viscosità di diversi liquidi, ed altre particolarità. </s>

<s>E da questa ade­<lb></lb>sione delle parti fra loro nasce che non può facilmente moversi l&#039;una di <lb></lb>esse, che seco non ne tragga molt&#039;altre, che per tal cagione a lei s&#039;attac­<lb></lb>cano ” (Bologna 1667, pag. </s>

<s>30). </s></p><p type="main">

<s>Tre anni dipoi, pubblicando il Borelli il suo libro <emph type="italics"></emph>De motionibus natu­<lb></lb>ralibus,<emph.end type="italics"></emph.end> v&#039;inseriva quelle ragioni e quelle esperienze, con le quali aveva dianzi <lb></lb>persuasi gli Accademici fiorentini esser necessariamente ne&#039;fluidi un glutine, <pb xlink:href="020/01/3325.jpg" pagenum="286"></pb>che ne tenga insieme le minime parti. </s>

<s>Notabile è che così fatte ragioni, quali <lb></lb>si leggono esposte nella proposizione CLVI, sian quelle medesime di Lodo­<lb></lb>vico delle Colombe, di cui si ripetono gli argomenti, ricavati dal vedersi cre­<lb></lb>scere all&#039;acqua la viscosità, mescendovi albume d&#039;uovo o farina: nè si tace <lb></lb>pure l&#039;esempio delle bolle di sapone che, soffiando con le guancie, sogliono <lb></lb>formar per gioco i fanciulli (ediz. </s>

<s>cit., pag. </s>

<s>327). </s></p><p type="main">

<s>Sopra il Peripatetico però si solleva il Borelli, quando ripensa alla grande <lb></lb>importanza di questa fisica proprietà nel modificare le leggi delle acque cor­<lb></lb>renti, per esempio dentro fistole strette, e tenute verticalmente erette, in cui <lb></lb>il liquido và più veloce nel mezzo, intorno all&#039;asse, che non da&#039;lati a con­<lb></lb>tatto con le pareti, come s&#039;argomenta dal veder la liquida superficie incur­<lb></lb>varsi di sopra in forma di scodella, e protuberare di sotto in una gocciola <lb></lb>conoidea. </s>

<s>Ora, come si potrebbe spiegar ciò, se non fosse un glutine nel­<lb></lb>l&#039;acqua, “ quae superficiei asperae internae fistulae adhaerendo, magis re­<lb></lb>tardat descensum et fluxum aquae, quam in intermedia parte cavitatis fistu­<lb></lb>lae, ubi insensibili tenacitate aquae particulae vicissim impediuntur? </s>

<s>” (ibid., <lb></lb>pag. </s>

<s>454). E nella proposizione appresso, che è la CCXVI, osserva il Borelli <lb></lb>che, cadendo liberamente l&#039;acqua uscita da un tubo, non potrebbe nemmen <lb></lb>presso alla bocca mantenersi unita, per la progressiva e rapida accelerazione <lb></lb>delle parti anteriori. </s>

<s>E perciò, considerate due sezioni o lamine nel primo <lb></lb>tempo contigue, “ igitur in secundo tempore divelli ac separari ab invicem <lb></lb>deberent, quod, cum non contingat, procul dubio aderit aliqua causa, a qua <lb></lb>colligatae retinerentur, et haec profecto erit gluten et viscositas illa exigua <lb></lb>superius declarata ” (ibid., pag. </s>

<s>456). </s></p><p type="main">

<s>Così veniva il Borelli a salvare le ragioni di Lodovico delle Colombe <lb></lb>contro gli assalti di Galileo, il quale insomma riduceva ogni ragione speri­<lb></lb>mentale del non resister l&#039;acqua alla menoma forza di divisione, e del non <lb></lb>essere perciò viscosa, al fatto delle torbide ne&#039;fiumi, che col tempo si chia­<lb></lb>rificano pur finalmente, di modo che a tali minime particelle terrose è in­<lb></lb>dugiato sì il moto della discesa, ma è impossibile che vi sian ridotte alla <lb></lb>quiete assoluta, “ ut fatentur Ghetaldus, Stevinus et alii “ (pag. </s>

<s>332). Fra <lb></lb>cotesti <emph type="italics"></emph>alii<emph.end type="italics"></emph.end> intendeva certamente il Borelli comprendere Galileo, che non no­<lb></lb>mina apertamente, perchè la proposizione, insieme con tutte l&#039;altre in que­<lb></lb>sto subietto, è scritta per convincerne di falsità le dottrine, della qual falsità <lb></lb>l&#039;esser fatto complice col Ghetaldo dovrebbe dar gran materia di pensare <lb></lb>agli ammiratori della originalità de&#039;principii professati nel Discorso intorno <lb></lb>alle galleggianti. </s></p><p type="main">

<s>Stavasene dunque Galileo col suo Ghetaldo sicuro, quando inaspettata­<lb></lb>mente venne un gran colpo a turbargli quel riposo: i sali, che si rimangono <lb></lb>in assoluta quiete sciolti nell&#039;acqua dei mari; i metalli attaccati dall&#039;acqua­<lb></lb>forte. </s>

<s>S&#039;accennò come fosse questa obiezione, che lo fece andare ad ammet­<lb></lb>tere la continuità de&#039;fluidi, e la riduzione delle loro particelle agli ultimi <lb></lb>indivisibili. </s>

<s>Ma questi indivisibili, intesi al modo cavalieriano, non essendo <lb></lb>altro insomma che gl&#039;infinitamente piccoli dei matematici, non potevano es-<pb xlink:href="020/01/3326.jpg" pagenum="287"></pb>sere accetti a coloro, i quali erano persuasi non darsi l&#039;infinito fisico, o in <lb></lb>atto. </s>

<s>Le dottrine perciò, esposte nel primo dialogo delle due Scienze nuove, <lb></lb>venivano prima ripudiate dalla Filosofia speculativa, e poi dalla Naturale, la <lb></lb>quale ebbe a rivolgersi a cercare altre ragioni, onde spiegare come potes­<lb></lb>sero rimanersi imperturbatamente sospese, in mezzo a liquidi tanto men gravi <lb></lb>in specie, le solide particelle dei sali e dei metalli. </s></p><p type="main">

<s>Luc&#039;Antonio Porzio, sotto gl&#039;influssi della Filosofia cartesiana, era ri­<lb></lb>corso a un agitamento intestino, di che credeva esser naturalmente compresi <lb></lb>i fluidi, i quali non si compongono perciò in quiete assoluta, ma solo appa­<lb></lb>rente ai deboli occhi nostri. </s>

<s>“ Ed io stimo, diceva, che conforme senza ar­<lb></lb>tificio non possiamo noi osservare il velocissimo corso d&#039;alcuni fiumi, nè il <lb></lb>moto rapido di molte altre sostanze; così nemmeno possa il nostro senso, <lb></lb>ne&#039;licori che ci appariscono stagnanti, conoscere il moto e l&#039;agitazione con­<lb></lb>tinua delle loro parti. </s>

<s>Avvegnachè le parti de&#039;liquidi, o siano similissime <lb></lb>tra loro, o se pure abbiano qualche dissomiglianza sia ella impercettibile <lb></lb>dagli occhi nostri, i quali non han virtù di conoscere ciò che v&#039;è nelle cose, <lb></lb>nè di osservare tutte le similitudini e dissimilitudini delle loro parti. </s>

<s>Laonde, <lb></lb>movendosi i licori, e agitandosi le loro parti, perchè sempre ad una che muti <lb></lb>luogo succede un&#039;altra simile; pare all&#039;occhio nostro di veder l&#039;istessa che <lb></lb>prima vedeva, e crede che ella non abbia mutato luogo. </s>

<s>E che ciò sia vero <lb></lb>chiaramente a mio parere lo dimostrano tutte l&#039;estrazioni chimiche, e i di­<lb></lb>scioglimenti delle varie sostanze ne&#039;licori, e l&#039;amalgamazione de&#039;metalli col <lb></lb>mercurio, ed il mescolamento insieme di varii corpi liquidi ” <emph type="italics"></emph>(Del sorgi­<lb></lb>mento de&#039;licori nelle fistole,<emph.end type="italics"></emph.end> Venezia 1667, pag. </s>

<s>48). </s></p><p type="main">

<s>Il Guglielmini, qualche tempo dopo, ripeteva col Porzio che le particelle <lb></lb>de&#039;sali, dissoluti dall&#039;acqua, son ridotte a tal minima piccolezza, da non re­<lb></lb>sistere al moto intestino, che si progaga per tutta intera la liquida sostanza, <lb></lb>ma soggiungeva di più le ragioni di quel moto intestino, e ne assegnava le <lb></lb>varie forze motrici, notabili, perchè parvero poi confermate dall&#039;esperienza <lb></lb>del <emph type="italics"></emph>Radiometro.<emph.end type="italics"></emph.end> “ Cumque tales potentiae motrices plures adsint, aether <lb></lb>praeterfluens, lucis pressio, et praecipue calor, cuius, in media licet hyeme, <lb></lb>semper aliquis gradus in aere existit; vix possumus nos cohibere quin cre­<lb></lb>damus, non modo promptissima mobilitate pollere globulos aquae, sed con­<lb></lb>tinuo motu agitari ” <emph type="italics"></emph>(De salibus,<emph.end type="italics"></emph.end> Venetiis 1705, pag. </s>

<s>99). </s></p><p type="main">

<s>Se questi pensieri del Guglielmini non erano ancora noti al Borelli, sa­<lb></lb>peva egli però molto bene quegli del Porzio, amico suo e connazionale, con­<lb></lb>tro cui par che sia scritta la proposizione CLV, dove l&#039;Autore <emph type="italics"></emph>De motionibus <lb></lb>naturalibus,<emph.end type="italics"></emph.end> parlando de&#039;metalli sciolti nell&#039;acqua forte, attribuiva alla so­<lb></lb>stanza ignea, spremuta dal metallo nell&#039;atto della sua dissoluzione, l&#039;esser <lb></lb>le minime particelle gittate e sparse per tutta la massa liquida. </s>

<s>Che se quivi <lb></lb>si vedono rimanere in perpetua quiete, da null&#039;altro dipende che dalla vi­<lb></lb>scosità del menstruo, sopraggiunta a impedirne la scesa, appena cessato quel <lb></lb>primo fervor del fuoco, da cui, come più manifestamente osservasi nella <lb></lb>calce, nasceva quell&#039;intestino moto fermentativo. </s>

<s>“ Unde elicere possumus <pb xlink:href="020/01/3327.jpg" pagenum="288"></pb>quod, ex praedicto motu fermentationis, deduci non potest quod in fluido <lb></lb>partes eius perpetuo intestino motu agitentur, a qua commotione fluiditas <lb></lb>efficiatur, et ab hac causa dissolutiones salium, metallorum etc. </s>

<s>non depen­<lb></lb>deant ” (pag. </s>

<s>324). </s></p><p type="main">

<s>Ciò che il Porzio attribuiva al moto intestino, da cui naturalmente è <lb></lb>invasa la massa fluida, doversi invece attribuire alla viscosità, l&#039;aveva dimo­<lb></lb>strato il Borelli nella proposizione CLII, la quale vogliamo riferir con le pa­<lb></lb>role del Montanari, perchè si confermi com&#039;egli veramente derivasse i suoi <lb></lb>pensieri da chi gli era stato maestro con la voce viva, prima che co&#039;libri <lb></lb>stampati. </s>

<s>“ Io considero dunque, egli dice, che dovendo i corpi, che per un <lb></lb>fluido si muovono, superare con l&#039;impeto o momento loro la resistenza, che <lb></lb>dal fluido gli vien fatta, mediante non solo la necessità che ha questo di <lb></lb>muoversi cedendole il luogo (il che non può farsi che in tempo, come ben <lb></lb>considera il Galileo) ma anche mediante la viscosità delle sue parti; che non <lb></lb>senza alcuna difficoltà si separano. </s>

<s>Ed essendo perciò questa resistenza dei <lb></lb>fluidi proporzionata alle basi...., ed essendo vero eziandio che de&#039;corpi si­<lb></lb>mili di figura, ma differenti in grandezza, la proporzione della superficie del <lb></lb>grande a quella del piccolo è sempre suddupla della proporzion della mole <lb></lb>del grande a quella del piccolo ....; seguitando tali suddivisioni, finalmente <lb></lb>si giungerebbe ad avere così diminuita la forza di quel mobile, che in pro­<lb></lb>porzione della resistenza ella resterebbe minore, e perciò impotente a fen­<lb></lb>dere quel fluido, nel quale ella fosse immersa, essendochè tale resistenza, <lb></lb>come ho detto, non solo dalla necessità di moversi, come asseriva il famoso <lb></lb>Galileo, e nel qual caso, almeno in lungo tempo sarebbe superata; ma da <lb></lb>questa e dalla viscosità, che tiene unite quelle parti, procede. </s>

<s>Nel qual caso, <lb></lb>avendo la viscosità predetta una forza determinata, che dal solo tempo non <lb></lb>può essere superata, fa di mestieri che il momento del corpo, che deve su­<lb></lb>perarla, sia di lei maggiore, altrimenti per alcuna lunghezza di tempo non <lb></lb>potrebbe disciorla. </s>

<s>E infatti noi vediamo, fra le altre esperienze, che il sale, <lb></lb>quantunque più grave dell&#039;acqua, quando in essa è liquefatto, non scende <lb></lb>più abbasso, ma egualmente per esso disperso si mantiene, anzi ascende dal <lb></lb>fondo ” <emph type="italics"></emph>(Pensieri fisico-matem. </s>

<s>cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>71). </s></p><p type="main">

<s>L&#039;Hauksbee però ebbe a considerare che se fosse questa creduta dal <lb></lb>Montanari, e confermata poi più autorevolmente dal Borelli, la vera causa <lb></lb>del rimaner galleggianti le particelle saline, e le altre minuzie de&#039;corpi spe­<lb></lb>cificamente più gravi de&#039;loro menstrui; dovrebbe riscontrarsi qualche nota­<lb></lb>bile differenza a pesar nell&#039;acqua un corpo intero o minutamente diviso. </s>

<s>Die­<lb></lb>tro ciò, prese una lamina di ottone, un dito quadra, del giusto peso di <lb></lb>482 grani, e il medesimo peso avendo fatto con 255 simili quadrati di or­<lb></lb>pello, s&#039;aspettava che, avendosi così gran differenza tra le superficie, non <lb></lb>piccola dovess&#039;esser ne&#039;pesi. </s>

<s>Ma con sua gran maraviglia trovò che quella <lb></lb>differenza non andava punto più là di due grani. </s>

<s>Da che fu indotto a con­<lb></lb>cludere che, non potendo esser quella generalmente ammessa la causa vera <lb></lb>del fatto, ce ne doveva essere un&#039;altra. </s>

<s>“ Insomma, egli dice, la sospensione <pb xlink:href="020/01/3328.jpg" pagenum="289"></pb>delle più gravi particelle delle materie ne&#039;liquidi io l&#039;attribuisco alla mede­<lb></lb>sima cagione, che tiene i liquori sospesi ne&#039;piccoli tubi, voglio dire all&#039;attra­<lb></lb>zione. </s>

<s>Le minute parti dei corpi, che costano di superficie piane, essendo <lb></lb>gagliardamente attratte dalle parti di un fluido, in cui elle siano poste, e <lb></lb>perciò reciprocamente attraendo di nuovo le parti di quel fluido; possono <lb></lb>dall&#039;azione di queste forze essere colà dentro tenute sospese. </s>

<s>E quei piccoli <lb></lb>corpi, che non sono o che non vogliono essere sospesi in un liquido ...., <lb></lb>credo che sieno di tal natura, per una di queste due cause: o che le parti <lb></lb>del liquido più gagliardamente attraggansi l&#039;una l&#039;altra, che elle si attrag­<lb></lb>gano quei piccoli corpi sparsi, ovvero che, per mezzo della propria loro at­<lb></lb>trazione, si compongano in piccoli mucchietti, la cui mole e superior mo­<lb></lb>mento gli aiuta a precipitare all&#039;ingiù ” <emph type="italics"></emph>(Esperienze fisico-meccaniche,<emph.end type="italics"></emph.end> trad. </s>

<s><lb></lb>dall&#039;inglese, Firenze 1716, pag. </s>

<s>150). </s></p><p type="main">

<s>Nonostante, ne&#039;primi anni di questo secolo, il Rumfort tornò a profes­<lb></lb>sare l&#039;ipotesi del Borelli, e com&#039;esso persuaso che la tenacità del liquido <lb></lb>resiste alla gravità naturale de&#039;minutissimi gravi dentrovi sospesi; pensò che <lb></lb>si potesse ritrovar la misura della detta tenacità dai gradi di quella stessa <lb></lb>resistenza. </s>

<s>Per far ciò pesava prima nell&#039;acqua una matassa attorta di seta, <lb></lb>e poi nuovamente sparsa nelle sue fila, e trovò che i due pesi differivano <lb></lb>tra loro, secondo quella giusta ragione, che la così tanto moltiplicata super­<lb></lb>ficie gli prometteva. <emph type="italics"></emph>(Bibloteque britanniques,<emph.end type="italics"></emph.end> T. XXXIV). </s></p><p type="main">

<s>I commemorati autori di queste esperienze non ebbero nessuno l&#039;inten­<lb></lb>zione, almeno diretta ed espressa, di servirsene a risolvere la questione an­<lb></lb>tica insorta fra Galileo e i Peripatetici de&#039;suoi tempi, ma dopo che il Bo­<lb></lb>naventuri e i suoi colleghi vennero a dare alla critica delle Opere galileiane <lb></lb>gl&#039;inizi, Giovan Batista Venturi si propose a risolvere questo primo quesito: <lb></lb>“ È egli vero, come sostenne il Galileo, che l&#039;acqua nel suo interno possa <lb></lb>bene colla sua inerzia ritardare il movimento de&#039;corpi nella medesima im­<lb></lb>mersi, ma non possa mai impedirlo affatto, ove siavi un qualunque menomo <lb></lb>disquilibrio di gravità tra il corpo immerso e l&#039;acqua stessa? </s>

<s>” <emph type="italics"></emph>(Memorie <lb></lb>e Lettere inedite di Galileo,<emph.end type="italics"></emph.end> Modena 1818, P. I, pag. </s>

<s>197). </s></p><p type="main">

<s>La risposta si fa dipendere dalla descrizione di due esperimenti, nel <lb></lb>primo dei quali s&#039;abbiano due vasi cilindrici, co&#039;fondi comunicantisi per <lb></lb>uno assai lungo e strettissimo tubo, e pieni d&#039;acqua in fino a mezzo. </s>

<s>So­<lb></lb>prainfusavene poi un&#039;altra piccola quantità, con un cucchiaino, trovò il Ven­<lb></lb>turi che un centoventesimo di linea d&#039;altezza produceva una pressione suf­<lb></lb>ficiente a far movere il liquido nel suo interno, per ridursi dalle due parti <lb></lb>in perfetto equilibrio. </s>

<s>L&#039;altro esperimento consisteva nell&#039;osservare che il <lb></lb>moto dell&#039;acqua, dentro un tubo di vetro da livella, avveniva anche quando <lb></lb>il seno dell&#039;inclinazione non era che la settantamillesima parte del seno to­<lb></lb>tale, o della lunghezza dello stesso tubo, d&#039;onde ne concludeva il Venturi <lb></lb>che, a far movere l&#039;acqua nel suo interno basta una forza uguale alla set­<lb></lb>tantamillesima parte della sua gravità assoluta (ivi, pag. </s>

<s>197, 98). </s></p><p type="main">

<s>Veramente non sarebbe stato necessario, per giungere a queste conclu-<pb xlink:href="020/01/3329.jpg" pagenum="290"></pb>sioni, valersi di strumenti così raffinati, come con tanta diligenza se li volle <lb></lb>procacciare il Venturi. </s>

<s>Dal diavolino del Cartesio già sapevano tutti che la <lb></lb>più leggera pressione alla superficie del liquido bastava per mettere in su­<lb></lb>bitaneo moto le parti nell&#039;interno, e sapevasi pure che non solo con una <lb></lb>inclinazione minima, ma nulla affatto, si sarebbe mosso il liquido dentro il <lb></lb>tubo di vetro, quando gli si fosse aperto un piccolo foro a uno estremo, a <lb></lb>quel modo che i Meccanici insegnano non volerci nessuna forza a movere <lb></lb>un perfetto globo sopra un perfettissimo piano orizontale. </s>

<s>Da che si può con­<lb></lb>cludere che gli sperimenti del Venturi, oltre ad avere una squisitezza super­<lb></lb>flua, non valevano a risolvere la questione, perchè non si disputava delle <lb></lb>difficoltà del moversi l&#039;una particella d&#039;acqua intorno a un&#039;altra, con sola­<lb></lb>mente variare il punto del contatto, ma della difficoltà della separazione di <lb></lb>due o più particelle per una qualche sensibile distanza, qual sarebbe il diame­<lb></lb>tro per esempio di quei granellini terrosi che intorbidano i fiumi. </s></p><p type="main">

<s>Non risolvendosi dunque il quesito da&#039;suoi veri principii, non par si <lb></lb>possa logicamente concludere che, supposto non intercedere alcuna affinità <lb></lb>tra il liquido e il solido, avesse Galileo ragione di dire che le minuzie gal­<lb></lb>leggianti dei corpi son dal mezzo ritardate nello scendere, ma non affatto <lb></lb>impedite, perchè riman sempre fra le particelle liquide un&#039;aderenza mutua <lb></lb>o tenacità, che resiste alla loro divisione. </s>

<s>A che ripensando non s&#039;intende <lb></lb>come, secondo l&#039;Hauksbee, vi possano essere certi piccoli corpi naturalmente <lb></lb>scendenti in mezzo a un liquido, quando le molecole di lui s&#039;attraggono più <lb></lb>gagliardamente, ossia, quando più fortemente resistono ad aprire in mezzo <lb></lb>a loro il passaggio a corpi stranieri. </s>

<s>Che del resto i resultati sperimentali <lb></lb>del Fisico inglese, rispetto al pesar nell&#039;acqua ora un solido intero, ora mi­<lb></lb>nutamente diviso; si vedrà che non contradicono ai resultati sperimentali del <lb></lb>Rumfort, considerando che altrimenti si comportano verso l&#039;acqua l&#039;ottone <lb></lb>e la seta. </s></p><p type="main">

<s>Il Borelli non faceva a&#039;suoi tempi questa distinzione, ma, supponendo <lb></lb>che i sali e i metalli dissoluti non rimanessero ad altra forza soggetti, che <lb></lb>a quella della loro gravità naturale, rettamente concludeva che, ridotti a una <lb></lb>certa piccolezza, era la solita tenacità del menstruo che ve li tratteneva. </s>

<s>È <lb></lb>senza dubbio una finzione alla cartesiana quella lanugine, di che egli volle <lb></lb>tutto intorno rivestir le molecole dell&#039;acqua, per darsi a intendere com&#039;elle <lb></lb>si tengano insieme: ciò che ora s&#039;attribuisce all&#039;attrazione molecolare, e quel <lb></lb>glutine immaginario prende il nome di coesione. </s>

<s>Ma la Fisica moderna ha <lb></lb>confermato esser di fatto nell&#039;acqua, a volerne staccare una parte dall&#039;altra, <lb></lb>resistenza molto maggiore di quella, che non avessero pensato il Borelli, e <lb></lb>Lodovico delle Colombe. </s></p><p type="main">

<s>Quel Gay-Lussac, che il Laplace diceva aver introdotto in questo genere <lb></lb>d&#039;esperienze <emph type="italics"></emph>l&#039;exactitudo des observations astronomiques<emph.end type="italics"></emph.end> (Mecanique cele­<lb></lb>ste, T. IV, Supplement II, pag. </s>

<s>76) misurava la detta resistenza alla separa­<lb></lb>zion delle parti dal peso, che si doveva aggiungere a uno de&#039;bracci della <lb></lb>bilancia, per far sollevar l&#039;altro, da cui pendeva una lamina di vetro, appli-<pb xlink:href="020/01/3330.jpg" pagenum="291"></pb>cata alla superficie dell&#039;acqua. </s>

<s>Altri fisici osservarono che questo modo di <lb></lb>sperimentare non era esatto, e insomma Tommaso Young ridusse quelle mi­<lb></lb>sure tali, che parvero esagerate, ma che pure confermavano la legittimità <lb></lb>della difesa del Borelli a favore di Lodovico delle Colombe, e contro Gali­<lb></lb>leo. </s>

<s>Nè si volle questa difesa limitare alla detta proprietà dell&#039;acqua, ma si <lb></lb>estese all&#039;efficacia, che ha la viscosità stessa nel sostener le tavolette d&#039;ebano, <lb></lb>o d&#039;altre più gravi materie, incominciandosi a dimostrar così, nel citato libro <lb></lb><emph type="italics"></emph>De motion. </s>

<s>natural.,<emph.end type="italics"></emph.end> la CLVIII proposizione: “ Dici potest quod revera adsit <lb></lb>pusilla aliqua resistentia, cum dura lamina fluidum penetrat, et confricat la­<lb></lb>terales partes eius ” (pagi 331), ch&#039;era ciò insomma, che contro Galileo si <lb></lb>voleva sostener dal Colombo, la completa rivendicazion del quale, dalle pa­<lb></lb>tite oppressioni, non si fece però, com&#039;ora siam per narrare, che un secolo <lb></lb>e mezzo più tardi. </s></p><p type="main">

<s>La filosofica libertà del Borelli, la quale aveva dato animo al Montanari, <lb></lb>infin da quando si manifestò dai privati consessi accademici, parve aver rotto <lb></lb>ogni vincolo, dopo la pubblicazione del libro <emph type="italics"></emph>De motionibus naturalibus.<emph.end type="italics"></emph.end><lb></lb>S&#039;era aggiunto allora un altro validissimo motivo di disertare dalle opinioni <lb></lb>di Galileo, il quale, a spiegar certi fatti, che s&#039;attribuivano comunemente alla <lb></lb>viscosità, come per esempio il rotondarsi le gocciole della pioggia e della ru­<lb></lb>giada; invocava <emph type="italics"></emph>una dissensione tra l&#039;aria e l&#039;acqua<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 73) essen­<lb></lb>dosi fatto oramai pubblicamente noto, per l&#039;esperienze dell&#039;Accademia del <lb></lb>Cimento, che le dette gocciole serbano la medesima forma rotonda, anche <lb></lb>nel vuoto torricelliano. </s>

<s>Di qui è che, del sostenersi i globi d&#039;acqua assai <lb></lb>rilevati e grandi, nessuno pensò più che la causa risedesse di fuori, come <lb></lb>nel primo dialogo delle due nuove Scienze insinuava il Salviati, ma, tutti <lb></lb>essendo ben persuasi che dovesse essere interna, si volsero con gran pre­<lb></lb>mura a cercarla. </s></p><p type="main">

<s>È fra costoro da annoverare principalmente Giuseppe Del Papa, il quale, <lb></lb>ripensando come si potesse conciliare la fluidità con certi fatti, che mostra­<lb></lb>vano essere le liquide particelle fra loro insieme tenaci; immaginò di esse <lb></lb>particelle una costituzione molto diversa da quella, ch&#039;era stata descritta dal <lb></lb>Borelli, dicendole composte di un nucleo duro, involto da una membrana <lb></lb>tessuta di fila resistenti, contrattili e appiccaticce. </s>

<s>“ Anzi, egli aggiunge, le <lb></lb>medesime membrane, nei sopradetti corpulenti ed opachi liquori, appariscono <lb></lb>con assai di chiarezza, essendo che alcune di esse possano ancora distaccarsi <lb></lb>dalle fluide particelle, mercè della quale separazione quegli stessi liquori vie <lb></lb>più liquidi e più purgati divengono. </s>

<s>Ed è ciò manifesto ad ognuno, il quale <lb></lb>abbia alcuna volta, per mera curiosità, maneggiato l&#039;argentovivo o i metalli <lb></lb>liquefatti, perocchè, comprimendo, con un ferro o con altro solido corpo, una <lb></lb>qualche loro porzione, si vedono da essa immantinente fuggire alcune parti <lb></lb>fluide, restando al predetto ferro attaccate ed immobili alcune altre parti, <lb></lb>inabili per loro medesime a fluire ed a scorrere, la di cui materia vedesi <lb></lb>essere a guisa di una pelle molto flessibile, e idonea ad attaccarsi seco me­<lb></lb>desima e con molti altri corpi, da cui sia toccata, la qual materia molto pro-<pb xlink:href="020/01/3331.jpg" pagenum="292"></pb>babile cosa è che ella, quand&#039;era nella composizion del metallo, facesse l&#039;of­<lb></lb>ficio d&#039;involucro o di vesta ai volubili corpicelli di esso ” <emph type="italics"></emph>(Della natura <lb></lb>dell&#039;umido e del secco,<emph.end type="italics"></emph.end> Firenze 1681, pag. </s>

<s>117). </s></p><p type="main">

<s>È manifesto di qui esser sovvenuta l&#039;immagine di così fatte pellicole <lb></lb>superficiali da ciò, che è un effetto estraneo alla natura del liquido metallo, <lb></lb>com&#039;è estraneo anche all&#039;acqua, la pellicola involgente la quale, visibile con <lb></lb>assai chiarezza, è dovuta talvolta al carbonato di calce, che si forma al con­<lb></lb>tatto con l&#039;aria. </s>

<s>Ma, indipendentemente da ogni azione chimica, non pote­<lb></lb>vano essere sfuggite all&#039;osservazione le colmature de&#039;bicchieri, ne&#039;quali par <lb></lb>che naturalmente vi sia ritenuta l&#039;acqua dalla resistenza di un panno, cuci­<lb></lb>tovi intorno agli orli, e che a squarciarlo fa per la rottura versare il liquido <lb></lb>contenuto. </s>

<s>Nè poteva non esser palese al senso quella borsa di pelle, che <lb></lb>circonda le gocciole della pioggia: borsa che, nel cader su un piano duro e <lb></lb>asciutto, per la diminuita capacità nello schiacciarsi, si squarcia e getta il <lb></lb>liquido che aveva dentro in que&#039;filamenti, de&#039;quali ella stessa tutto intorno <lb></lb>s&#039;irraggia. </s>

<s>A che s&#039;aggiunga, come più evidente di tutte le altre, la quoti­<lb></lb>diana osservazione dell&#039;acqua pannicolata intorno agli orli degli anelli, o alle <lb></lb>maglie delle reti da pescare, nell&#039;estrarle dai fiumi. </s></p><p type="main">

<s>Che non fossero poi questi pannicoli illusioni l&#039;avrà persuaso al volgo <lb></lb>le mille volte il vederli sostenere, senza sfondarsi, i granelli dell&#039;arena, a caso <lb></lb>rimastivi sopra. </s>

<s>Conferiva ciò molto a confermare che non fossero illusioni <lb></lb>nemmeno le pellicole involgenti i colmi dei piccoli vasi, d&#039;onde prendevasi <lb></lb>ragionevole occasione di credere che simile avvenisse anche ne&#039;vasi più lar­<lb></lb>ghi, l&#039;acqua de&#039;quali avesse la superficie coperta come da un sottilisssimo <lb></lb>lenzuolo, distesovi sopra. </s>

<s>Da questo sostenuti gl&#039;insetti, conosciuti sotto il <lb></lb>nome di <emph type="italics"></emph>idrometri,<emph.end type="italics"></emph.end> passeggiano sopra gli stagni a piedi asciutti, e le mo­<lb></lb>sche pure son sostenute da quel medesimo velo, che cede alquanto senza <lb></lb>rompersi sotto i loro piedi, com&#039;ebbe a osservare il Newton, bench&#039;egli at­<lb></lb>tribuisca il fatto a una causa più sottile, cioè alla repulsione molecolare. <lb></lb></s>

<s>“ Porro eidem vi repellenti tribuendum videtur quod muscae in aqua inam­<lb></lb>bulent, nec tamen pedes suos madefaciant ” <emph type="italics"></emph>(Op. </s>

<s>optica omnia,<emph.end type="italics"></emph.end> Patavii 1773, <lb></lb>pag. </s>

<s>162). E alla medesima resistenza della pellicola superficiale si deve at­<lb></lb>tribuire il sostenersi a galla quelle minute polveri terrose, che sulla super­<lb></lb>ficie di un&#039;acqua ferma vi lasciano talvolta cadere i venti. </s></p><p type="main">

<s>Tutte queste osservazioni, applicate al galleggiare delle assicelle d&#039;ebano, <lb></lb>sarebbero state altrettanti validissimi argomenti, da decidere la questione agi­<lb></lb>tatasi nel famoso Discorso intorno a quelle cose che stanno o che si muo­<lb></lb>vono per l&#039;acqua, ma la sentenza non avrebbe forse avuto ancora l&#039;autorità <lb></lb>necessaria, per far cancellare dal libro dell&#039;Idrostatica un insegnamento di <lb></lb>Galileo. </s>

<s>Quell&#039;autorità dunque, che le mancava, venne presto ad acquistarla, <lb></lb>quando salirono in potenza gl&#039;insegnamenti neutoniani, per i quali si ven­<lb></lb>nero a ridurre alla loro vera e propria natura que&#039;vischi e quelle mem­<lb></lb>brane, intorno a che il Borelli e il Del Papa avevano lavorato più di fanta­<lb></lb>sia, che di scienza. </s></p><pb xlink:href="020/01/3332.jpg" pagenum="293"></pb><p type="main">

<s>Essere la viscosità de&#039;liquidi un effetto dell&#039;attrazion molecolare, che si <lb></lb>distinse col nome di <emph type="italics"></emph>coesione,<emph.end type="italics"></emph.end> conseguiva immediatamente dalle nuove dot­<lb></lb>trine, ma intorno a quelle pellicole superficiali i neutoniani stessi rimasero <lb></lb>incerti. </s>

<s>Il Monge, il Rumfort, l&#039;Young, che ci dispensano dal nominarne <lb></lb>altri, seguitarono ad usare il medesimo linguaggio metaforico del nostro Del <lb></lb>Papa, infino al Laplace, da cui i Fisici derivarono il vero, riducendone a più <lb></lb>legittima conclusione il ragionamento di lui, ch&#039;è tale: Se in mezzo a una <lb></lb>massa indefinita d&#039;acqua stagnante s&#039;immagina un canale infinitamente <lb></lb>stretto, e di pareti infinitamente sottili, con le sue due estremità a fior <lb></lb>d&#039;acqua, tutti gli strati liquidi, situati in esso canale a sensibili distanze dal <lb></lb>supremo livello, saranno ugualmente premuti da una parte e dall&#039;altra. <lb></lb></s>

<s>“ Chaque couche du liquide interieur est donc comprimée par ces deux for­<lb></lb>ces opposées. </s>

<s>A la surface du liquide, cette compression est evidemment <lb></lb>nulle ” <emph type="italics"></emph>(Supplement II cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>74). </s></p><p type="main">

<s>I Fisici però non convennero in questa sentenza, la quale parve a loro <lb></lb>essere stata pronunziata dal riguardare la massa liquida come continua, e <lb></lb>non come discreta ne&#039;suoi atomi componenti, sollecitati ciascuno da una forza <lb></lb>attrattiva verso tutti gli altri, che lo circondano, e che riattraggono scambie­<lb></lb>volmente con forze uguali da tutte le parti, cosicchè ognuno si rimane al <lb></lb>suo posto in equilibrio. </s>

<s>Ma se così è dentro il liquido, diversamente avviene <lb></lb>alla superficie, gli atomi componenti la quale non son così attratti dai so­<lb></lb>prastanti, che non esistono, come dai sottostanti, verso i quali debbon dun­<lb></lb>que, al contrario di quel che aveva sentenziato il Laplace, patire una pres­<lb></lb>sione, da cui solamente, e non da altro, dipende quella maggior coerenza, <lb></lb>che la stessa superficie liquida fece rassomigliare a una membrana. </s></p><p type="main">

<s>A questo punto si credè la Scienza di esser giunta a tale autorità, da <lb></lb>dar sentenza definitiva nella disputa, che Galileo ebbe co&#039;peripatetici intorno <lb></lb>al galleggiare dei corpi, e per pronunziarla si servì del ministero di Giovan <lb></lb>Batista Venturi. </s>

<s>Egli, descrivendo gli sperimenti fatti in questo proposito, dice <lb></lb>di aver preso dischi di latta unti con burro, e posatili lievemente sull&#039;acqua <lb></lb>aver trovato che si scavavano una fossetta, non però tanto fonda, quanto si <lb></lb>sarebbe richiesta, perchè si potesse attribuire il galleggiamento al solo equili­<lb></lb>brio idrostatico, e così ne concluse: “ A sostenere i dischi, oltre l&#039;equilibrio <lb></lb>della gravità, concorre l&#039;altra cagione della consistenza della pellicola dell&#039;acqua, <lb></lb>la quale non può cedere all&#039;interno senza spinger fuori, sia all&#039;alto, sia ai lati <lb></lb>del colmo, le parti vicine, sicchè queste resistono per la loro coesione super­<lb></lb>ficiale. </s>

<s>Quindi i piccoli dischi profondan la pozza notabilmente meno di ciò, <lb></lb>che importerebbe l&#039;equilibrio della gravità ” <emph type="italics"></emph>(Memorie cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>201). </s></p><p type="main">

<s>Aveva dunque ragione Lodovico delle Colombe a dire che, non dubi­<lb></lb>tando pure della verità de&#039;teoremi archimedei, non piccola parte, in soste­<lb></lb>ner le tavolette d&#039;ebano a galla, aveva l&#039;ampiezza della figura, la quale trova <lb></lb>maggior difficoltà a rompere il velo superficiale dell&#039;acqua, e a vincere quella <lb></lb>coesione delle particelle di lei, che, rappresentatasi sotto il nome di viscosità, <lb></lb>Galileo così a torto negava. </s></p><pb xlink:href="020/01/3333.jpg" pagenum="294"></pb><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La coesione tra le molecole superficiali di una massa liquida, e il for­<lb></lb>marsi che indi nasce que&#039;rotondi arginetti, intorno alle solide lamine gal­<lb></lb>leggianti, si riferiscono a quel genere di fatti fisici, che si designarono col <lb></lb>nome di capillari, perchè si rivelano principalmente, per la somiglianza delle <lb></lb>cause, nell&#039;ascese de&#039;liquidi dentro cannellini di così piccolo diametro, da <lb></lb>passarvi appena un capello. </s>

<s>L&#039;incertezza e l&#039;insufficienza a penetrar le ra­<lb></lb>gioni di questi fatti, ingenuamente confessate da Galileo, son documento certo <lb></lb>dello stato, in cui si trovava questa nobilissima parte della Scienza idrosta­<lb></lb>tica a que&#039;tempi, quando anzi i fatti stessi, più notabili in tale soggetto, si <lb></lb>passavano inosservati. </s>

<s>Nella prefazione ai due trattati postumi del Pascal si <lb></lb>avverte che l&#039;Autore, nel dimostrar l&#039;uguaglianza di livello d&#039;un medesimo <lb></lb>liquido in due vasi comunicanti, non ha eccettuato il caso, che uno dei detti <lb></lb>vasi sia un cannello strettissimo, perchè, quand&#039;egli scriveva, “ on n&#039;avoit <lb></lb>pas encore trouvé ces nouvelles experiences des petits tuyaux, dont l&#039;invention <lb></lb>est deué a monsieur Rho, qui a une adresse meveilleuse peur trouver de <lb></lb>experiences, et pour les expliquez ” <emph type="italics"></emph>(Traitez cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>XXII). Dunque in <lb></lb>Francia nel 1651 non era stato ancora osservato lo spontaneo ascendere dei <lb></lb>liquidi ne&#039;sottilissimi tubi, per conferma di che, nel 1645, com&#039;osservammo <lb></lb>a suo luogo, il Pecquet non seppe assegnare altra causa all&#039;impulsion del <lb></lb>chilo nel mesenterio degli animali, che la contrazion vermicolare dei vasi, <lb></lb>e la compressione toracica prodotta dai moti respiratorii. </s></p><p type="main">

<s>In Inghilterra il Boyle, che nel 1659 pubblicava i suoi Nuovi esperi­<lb></lb>menti fisico-meccanici, confessava, nel descriver l&#039;esperimento XXXV, d&#039;aver <lb></lb>avuto poco fa da un insigne matematico amico suo la notizia delle nuove <lb></lb>osservazioni, fatte da alcuni francesi, de&#039;quali dice di non sapere il nome, <lb></lb>ma che dovevano senza dubbio essere il Rho e il Therenot, e soggiunge <lb></lb>che gli tornò allora a mente d&#039;avere osservato questa spontanea ascesa dei <lb></lb>liquidi in que&#039;sottili cannellini di vetro, fatti da sè fabbricare apposta per <lb></lb>uso di termometri “ quamvis, casu illud evenisse suspicatus, pene animad­<lb></lb>versum praeterierim ” <emph type="italics"></emph>(Opera omnia,<emph.end type="italics"></emph.end> T. I, Venetiis 1697, pag. </s>

<s>79). </s></p><p type="main">

<s>In Italia però, anche noi ripeteremo col Borelli, <emph type="italics"></emph>erano queste materie <lb></lb>un pezzo fa considerate,<emph.end type="italics"></emph.end> e per non ritornare su quel che altrove dicemmo <lb></lb>del Cesalpino, che all&#039;azion capillare dei vasi attribuiva l&#039;ascender così fa­<lb></lb>cilmente la linfa su dalle radici degli alberi ai rami; citeremo, l&#039;Aggiunti, <lb></lb>le note del quale, scritte poco dopo il 1630, e in parte pubblicate dal Nelli, <lb></lb>riduciamo qui con fedele integrità dai manoscritti: </s></p><p type="main">

<s>“ Lo scoprimento del moto occulto dell&#039;acqua risolverà moltisssimi pro­<lb></lb>blemi: I. </s>

<s>Perchè una quisquilia, festuca o paglia s&#039;inclini all&#039;acqua, e con <lb></lb>questo insegneremo il modo di fare un uccello, che di per sè, accostato al-<pb xlink:href="020/01/3334.jpg" pagenum="295"></pb>l&#039;acqua, abbassi il capo e beva. </s>

<s>— II. </s>

<s>Come possino (bevere) le zanzare, <lb></lb>mosche, ecc., alle quali abbiamo osservato la Natura aver fatto la proboscide <lb></lb>piena d&#039;umido, per cui per essa più facilmente ascende l&#039;alimento umido, <lb></lb>e l&#039;estate mi sono abbattuto più di una volta a vedergli in cima di essa una <lb></lb>sperettina di umido limpido, che da loro veniva risorbito e rigettato scam­<lb></lb>bievolmente. (Così fanno) forse le api e farfalline bianche con occhi neri, <lb></lb>nate di que&#039;bruchi, de&#039;quali a questi anni ne fu tanti. </s>

<s>Queste farfalline, <lb></lb>come anco tutte quelle, che hanno sotto il muso un sottil filo o viticchio <lb></lb>avvolto in spira, si nutriscono, ne attraggono il nutrimento dai fiori o altro, <lb></lb>con quel filo o cannellino avvolto, che allora svolgono e distendono. </s>

<s>Le mo­<lb></lb>sche hanno comodità di mangiare il zucchero, perchè l&#039;inumidiscono con <lb></lb>l&#039;umido della loro proboscide, e così facilmente lo fanno ascendere in alto. </s>

<s>” </s></p><p type="main">

<s>“ III. (S&#039;intenderà inoltre) come possino i moscioni succhiar dalle botti <lb></lb>il vino, le pulci, cimici, che hanno manifestamente un cannellino diritto in <lb></lb>cima al capo, ed infiniti altri animalucci: come possino, dico, nutrirsi e ci­<lb></lb>barsi. </s>

<s>Che se non fusse questo natural movimento dell&#039;umido nell&#039;angustie, <lb></lb>gli sarebbe stato difficile l&#039;attrarlo nel succhiare, attesochè, a far salire e <lb></lb>movere l&#039;umido in cannelli stretti, col tirare a sè il fiato, ci è fatica gran­<lb></lb>dissima, per il molto contatto, siccome si prova in fatto. </s>

<s>” </s></p><p type="main">

<s>“ IV. (Da ciò nasce) il velo d&#039;acqua, che si fa alle fonti, col far che <lb></lb>l&#039;acqua esca per sottilissima angustia; — V. per che causa, con un can­<lb></lb>nello, si cavi l&#039;acqua d&#039;un vaso: il cannello diventa un sifone, del quale <lb></lb>l&#039;estremo più alto viene ad esser l&#039;acqua intorno ad esso; — VI. perchè <lb></lb>si sostenghino le gocce d&#039;acqua a un dito o altro; — VII. come si possino <lb></lb>nutrire le piante ed i vegetabili: il basilico minuto nell&#039;acqua perchè cre­<lb></lb>sca e si nutrisca: perchè si conservino i fiori in molle: perchè le spugne, <lb></lb>pannilini e altro attragghino l&#039;umido: riprovar la sciocchezza de&#039;Peripate­<lb></lb>tici in questo proposito. </s>

<s>” </s></p><p type="main">

<s>“ (Da ciò pure s&#039;intende), VIII, perchè l&#039;acqua non si livelli in un vaso <lb></lb>così fatto (come si rappresenta dalla figura 157) ma sia più alta nella can­<lb></lb><figure id="id.020.01.3334.1.jpg" xlink:href="020/01/3334/1.jpg"></figure></s></p><p type="caption">

<s>Figura 157.<lb></lb>nella angusta; IX. perchè si dilatino le macchie di olio, <lb></lb>su qualunque cosa, in una piccola parte tocca dall&#039;umido: <lb></lb>perchè si vegga in più largo spazio bagnato un panno; <lb></lb>X. perchè un grano di frumento si corrompa per germo­<lb></lb>gliare, e divenga umido, e perchè il nostro nutrimento, e <lb></lb>di qualsivoglia animale, divenga chilo tenuissimo, acciò più <lb></lb>facilmente sormonti alla nutrizion delle parti. </s>

<s>Errore dei <lb></lb>medici nel dire che la parte da nutrirsi attragga a sè il nutrimento, essendo <lb></lb>l&#039;opposto che il nutrimento sale lui a nutrire, o almeno cospira e inclina a <lb></lb>salire e infondersi, perchè tanto ascende in un angusto meato di carne, quanto <lb></lb>di vetro. </s>

<s>” </s></p><p type="main">

<s>“ XI. (È di qui anco facile intendere) perchè bisogni applicare nei ne­<lb></lb>sti e surcoli e gemme, che corrispondano co&#039;lor meati a quelli del ramo <lb></lb>innestato, e l&#039;umore subentri in essi, e non è maraviglia se, colla medesima <pb xlink:href="020/01/3335.jpg" pagenum="296"></pb>diligenza fatti alcuni nesti, si attaccano ed altri no, perchè, secondo che po­<lb></lb>chi o molti meati, per i quali ha da passare il nutrimento, corrisponderanno <lb></lb>con quelli della parte innestata, dalla quale vien somministrato il succo nu­<lb></lb>tritivo; succederà il fatto: e perchè, a far questa corrispondenza, ci ha parte <lb></lb>più la fortuna che l&#039;arte, non arrivando il nostro senso a conoscere questa <lb></lb>differenza. </s>

<s>XII. (S&#039;intenderà finalmente per questo moto occulto dell&#039;acqua) <lb></lb>perchè, sendo l&#039;istessa materia il foglio e la corda, l&#039;uno bagnato allunghi, <lb></lb>e l&#039;altra si serri e indurisca: provar quel che fa un panno lino tirato su <lb></lb>un telaio, quale non credo che bagnato venga tirato più che asciutto ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. XVIII, fol. </s>

<s>59, 60). </s></p><p type="main">

<s>Possono di qui giudicare i Lettori quale finezza di osservazioni avesse <lb></lb>portato, nell&#039;esame de&#039;fatti capillari, l&#039;Aggiunti, e come avesse felicemente <lb></lb>applicato quegli stessi fatti osservati alla soluzione de&#039;più varii e più incerti <lb></lb>problemi della Fisica, e della Storia naturale. </s>

<s>Nonostante, a giudicare anche <lb></lb>meglio i meriti di lui, giova osservare com&#039;ei riducesse sotto un&#039;unica causa <lb></lb>effetti così molteplici, e in apparenza così dissomiglianti, com&#039;è l&#039;ascendere <lb></lb>il liquido per i sottilissimi tubi, sia continuati che interrotti, e il rotondarsi <lb></lb>le gocciole pendenti dall&#039;estremità di un fuscello, o il circondarsi di que&#039;cer­<lb></lb>chi lucidi e rilevati le superficie dell&#039;acqua, rasente le pareti di un bicchiere <lb></lb>o di un pozzo. </s>

<s>Eppure anche questi fatti, o trascurati fin allora o male in­<lb></lb>tesi, non dubitò l&#039;Aggiunti di attribuire al moto occulto dell&#039;acqua, riducen­<lb></lb>doli insomma, come poi fecero i Fisici, al medesimo genere de&#039;fenomeni <lb></lb>capillari. </s></p><p type="main">

<s>“ In puteorum aquis quid sit lucidus ille circulus, qui in summae aquae <lb></lb>extremo habitu circumquaque visitur, aquae clandestina motio docebit. </s>

<s>Aquae <lb></lb>gutta digito, aut bacillo, pendula, adhaerescit nec decidit, non quia glutine <lb></lb>aliquo eius partes iungantur, nam, si hoc esset cum guttulam illam penden­<lb></lb>tem alteri corpori paullatim admovimus, et vix minima eius particula corpus <lb></lb>aliquod tangimus, cur statim distrahitur et alteri corpori, cui admovetur, se <lb></lb>iungit, nec eo glutine impeditur? </s>

<s>Profecto tunc multo magis digito tota hae­<lb></lb>rere deberet, cum non adeo suo pondere degravetur, sed subiecto plano su­<lb></lb>stineatur. </s>

<s>Non tamen sustinet; ergo neque hoc argumento aquae gluten ali­<lb></lb>quod esse probatur, neque aquae suspensionis causa redditur, quae non <lb></lb>aliunde petenda est, nisi ab illo quem diximus motum occultum aquae ad <lb></lb>omnes partes ” (ibid., fol. </s>

<s>61). </s></p><p type="main">

<s>Quale efficacia avessero queste tradizioni, a far progredire in Italia la <lb></lb>fisica dei capillari, non è difficile indovinarlo, ripensando che l&#039;Aggiunti do­<lb></lb>vette aver diffusa dalla Cattedra pisana la notizia de&#039;fatti osservati, e la sco­<lb></lb>perta dell&#039;occulta causa, dalla quale, secondo lui, eran prodotti. </s>

<s>I cenni, <lb></lb>che ne fa ne&#039;suoi <emph type="italics"></emph>Circoli<emph.end type="italics"></emph.end> il Beriguardi, starebbero a confermare una tale <lb></lb>opinione. </s></p><p type="main">

<s>Comunque sia, i rivoli sotterranei delle dette tradizioni, benchè trape­<lb></lb>lino più su da molte parti, non si vedono scaturire all&#039;aperto, che nelle <lb></lb>prime sessioni dell&#039;Accademia del Cimento. </s>

<s>Fedel guida di questi, non altro <pb xlink:href="020/01/3336.jpg" pagenum="297"></pb>per verità che sprazzi o zampilli, ci sono i Diarii, in uno de&#039;quali si legge: <lb></lb>“ A&#039;di 22 Giugno 1657, si provò quanto salisse l&#039;acqua in proporzione del <lb></lb>suo scendere, e si trovò che in un sifone, che abbia l&#039;istesso diametro, tanto <lb></lb>nella scesa quanto nella ritorta, sale a capello quanto scende. </s>

<s>Ma se il sifone <lb></lb>sarà, dalla parte dove sale, stretto assaissimo, come nella figura 157; allora, <lb></lb>essendo più grosso di dove scende, sale notabilmente più su che non cala ” <lb></lb>(Targioni, <emph type="italics"></emph>Notizie degli aggrandimenti ecc.,<emph.end type="italics"></emph.end> T. II, Firenze 1780, pag. </s>

<s>652). </s></p><p type="main">

<s>Par che si volesse dare a questi studii principio col confermar l&#039;espe­<lb></lb>rienza dell&#039;Aggiunti, ma si fecero presto notabili progressi, e il di 29 Lu­<lb></lb>glio appresso si osservarono, di differenti fluidi, <emph type="italics"></emph>le differenze dell&#039;ascenso <lb></lb>per un sifoncino di cristallo, assai ben lavorato, e d&#039;apertura quanto vi <lb></lb>potesse entrare uno spillo di mediocre grandezza<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>657). Nel dì 11 <lb></lb>poi del seguente Agosto, fu riconosciuto un fatto importantissimo e nuovo, <lb></lb>che cioe, “ dove gli altri liquidi s&#039;alzano in velo sottilissimo, come argini <lb></lb>intorno ad un solido, o sia stilo o cilindro immerso in essi; l&#039;argento vivo <lb></lb>per contrario attorno attorno si profonda, arginandosegli incontro all&#039;ingiù ” <lb></lb>(ivi, pag. </s>

<s>637, 38). </s></p><p type="main">

<s>Pochi giorni prima però aveva il Segretario dell&#039;Accademia registrato <lb></lb>nel Diario l&#039;osservazione di certi fatti, intorno a cui ci dobbiamo intratte­<lb></lb>nere alquanto, non perdonando a interrompere e accavallare il filo della sto­<lb></lb>ria. </s>

<s>Quel che ivi s&#039;ha in proposito è questo: “ A&#039;dì 7 Agosto 1657. Di vari <lb></lb>galleggianti alcuni si profondano sotto il livello dell&#039;acqua, facendosi attorno <lb></lb>arginetti, altri s&#039;inalzano, come un velo sottilissimo, a foggia di padiglione. </s>

<s><lb></lb>Ora questi accostandosi a quei primi, come attratti da virtù magnetica, sol­<lb></lb>levandoli dal loro abbassamento gli attraggono, facendoli salire sul velo al­<lb></lb>zato attorno di loro medesimi ” (ivi, pag. </s>

<s>654). </s></p><p type="main">

<s>Chi prima s&#039;è imbattuto a legger ciò, sentesi curioso di domandare: è <lb></lb>ella questa un&#039;osservazione a que&#039;tempi nuova, o gli Accademici almeno <lb></lb>la credevano tale? </s>

<s>Per rispondere convien travalicare dieci anni, a leggere, <lb></lb>nei <emph type="italics"></emph>Pensieri fisici matematici<emph.end type="italics"></emph.end> del Montanari, l&#039;elenco di quelle XXXVI espe­<lb></lb>rienze intorno a vari fenomeni capillari, che l&#039;Autore dice essersi istituite <lb></lb>nella bolognese Accademia dell&#039;abate Sampieri. </s>

<s>Le XXXIII, XXXIV e XXXV <lb></lb>delle dette esperienze vi sono così descritte: “ Posti in acqua piana più cor­<lb></lb>piccioli galleggianti, in certa distanza fra loro, corrono un contro l&#039;altro ad <lb></lb>accostarsi, com&#039;avessero virtù magnetica. </s>

<s>— Accostando un fuscello alle sud­<lb></lb>dette cose, atto a bagnarsi, esse vi corrono, e lo seguono ovunque si muove. <lb></lb></s>

<s>— Se detti corpiccioli non saranno facili a inumidirsi esteriormente, invece <lb></lb>di accostarsi, si scostano d&#039;insieme, e fuggono il contatto d&#039;un fuscello che <lb></lb>gli s&#039;accosti ” (Bologna 1667, pag. </s>

<s>13). </s></p><p type="main">

<s>Il libretto dov&#039;erano, fra le altre, narrate queste esperienze, e che si <lb></lb>componeva di varie epistole raccolte insieme col titolo sopra detto di <emph type="italics"></emph>Pen­<lb></lb>sieri fisici matematici,<emph.end type="italics"></emph.end> capitò alle mani del Borelli che, ritiratosi dalla To­<lb></lb>scana, se ne stava allora tutto incocciato a Messina, di dove il dì primo Di­<lb></lb>cembre 1667, dopo varie altre cose, scriveva così a Firenze al principe <pb xlink:href="020/01/3337.jpg" pagenum="298"></pb>Leopoldo: “ Ho anche avute certe epistole, ultimamente stampate dal Mon­<lb></lb>tanari, nelle quali scrive come cosa propria quello, che egli sa essere stato <lb></lb>molti e molti anni prima esperimentato pubblicamente nell&#039;Accademia di <lb></lb>V. A., e particolarmente pone quell&#039;accostarsi e scostarsi fra di loro i fu­<lb></lb>scellini galleggianti, la qual cosa ricordo a V. A. che io la prima volta la <lb></lb>mostrai, dodici anni sono, al serenissimo Granduca, e a V. A., e al serenis­<lb></lb>simo signor Principe, e vi erano anco presenti, credo, il signor marchese <lb></lb>Corsini, ed altri signori di corte, una sera, in camera di S. A. </s>

<s>E di più mi <lb></lb>ricordo che il signor Volunnio Bandinelli, poi cardinale, domandato dal Gran­<lb></lb>duca della cagione, rispose esser la simpatia. </s>

<s>E poi, negli anni seguenti, <lb></lb>V. A. sa benissimo che, nella sua Accademia, feci più volte tale esperienza, <lb></lb>ed al p. </s>

<s>Kircher la diedimo a bere per cosa simpatica. </s>

<s>E perchè nel mede­<lb></lb>simo tempo dimorava a Firenze il detto Montanari, e praticando con i si­<lb></lb>gnori Buoni <emph type="italics"></emph>(Del Buono)<emph.end type="italics"></emph.end> da loro s&#039;informava di tutte le cose; non può alle­<lb></lb>gare ignoranza di queste cose: parlo delle esperienze, non delle ragioni quali <lb></lb>adduce, che tutte gli si possono donare, per non essere il filosofare mestiero <lb></lb>da procuratore. </s>

<s>Ho ricordato questo a V. A., vedendo la troppa avidità di <lb></lb>gloria, che ha questo giovane, e la poca gratitudine che ha con i suoi mae­<lb></lb>stri ” (MSS. Cim., T. XIX, fol. </s>

<s>96). </s></p><p type="main">

<s>Ma chi aveva detto al Borelli che il Montanari si voleva appropriar <lb></lb>quelle cose? </s>

<s>Da nessuna parte degli scritti di lui apparisce per verità che <lb></lb>tale fosse la sua intenzione, la quale anzi è solamente quella di raccogliere <lb></lb>il più gran numero di fatti, alcuni, sì, nuovamente osservati, ma la mag­<lb></lb>gior parte richiamati al cimento, per confermare la verità di ciò, che ave­<lb></lb>vano detto i loro primi osservatori. </s>

<s>Così, il Borelli, se avesse avuto l&#039;animo <lb></lb>sereno, poteva aver riscontrato che, nell&#039;elenco del Montanari, venivano quasi <lb></lb>tutte comprese l&#039;esperienze varie, che il Thevenot aveva mandato per sag­<lb></lb>gio al principe Leopoldo dei Medici, nè perciò avrebbe potuto dire che gli <lb></lb>Accademici di Bologna s&#039;erano appropriate le scoperte degli Accademici pa­<lb></lb>rigini. </s></p><p type="main">

<s>Ma è bene rammemorare alcuni esempi, ne&#039;quali altri avrebbero potuto <lb></lb>reclamare con uguali, anzi con maggiori diritti, e nonostante tacquero, per <lb></lb>non parere ingiusti, o ridicolmente gelosi. </s>

<s>L&#039;esperienze, che il Borelli stesso <lb></lb>aveva mostrate a spettacolo de&#039;curiosi nella corte del Granduca, e poi ai <lb></lb>colleghi nell&#039;Accademia, destarono, così com&#039;era avvenuto d&#039;altri soggetti, <lb></lb>l&#039;emulazion del Viviani, il quale, avendo prese per galleggianti palline di <lb></lb>cera, e quelle monete, coniate in sottilissima foglia di argento, del valore di <lb></lb>sette centesimi della lira presente, allora e molto tempo di poi in corso per <lb></lb>la Toscana, sotto il nome di <emph type="italics"></emph>crazie;<emph.end type="italics"></emph.end> osservò certi fatti, non meno spetta­<lb></lb>colosi di quelli, de&#039;quali s&#039;andava tanto compiacendo il suo geloso rivale. </s>

<s><lb></lb>Di queste osservazioni n&#039;è rimasto memoria in una nota, che il Viviani <lb></lb>stesso ci lasciava così manoscritta: </s></p><p type="main">

<s>“ Ne&#039;corpi galleggianti (due palle di cera) argine con argine si unisce, <lb></lb>cioè alto con alto. </s>

<s>Due crazie, fossa con fossa, s&#039;uniscono, cioè basso con <pb xlink:href="020/01/3338.jpg" pagenum="299"></pb>basso. </s>

<s>Una palla e una crazia, argine con fossa, si sfuggono, cioè alto con <lb></lb>basso. </s>

<s>” </s></p><p type="main">

<s>“ Su l&#039;acqua di un bicchier colmo posata una crazia, che si fa argine <lb></lb>intorno, ed un fiocchetto di bambagia asciutta, posto leggermente in mezzo, <lb></lb>corre alle sponde, perchè scende per un piano inclinato, e perchè basso con <lb></lb>basso s&#039;uniscono. </s>

<s>Legnuzzi galleggianti su dettà acqua colma, che s&#039;inzup­<lb></lb>pino e s&#039;immergano sotto il livello, alzandosi argini attorno, posti alle sponde <lb></lb>tornano verso il mezzo, perchè.... o perchè alto con basso si fuggono ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>11). </s></p><p type="main">

<s>Ora, la seconda parte di questa descrizione corrisponde perfettamente <lb></lb>con l&#039;esperienze scritte sotto i numeri XXX e XXXI del Montanari: “ Se <lb></lb>si pongono corpiccioli galleggianti sulla superficie dell&#039;acqua d&#039;un vaso colmo, <lb></lb>ancorchè s&#039;applicassero alle parti basse del liquido vicino all&#039;orlo, montano <lb></lb>in alto, nè di li scendono. </s>

<s>— Se si pone in detti vasi bambagia, lana o altro <lb></lb>corpo, che non così facilmente s&#039;inumidisca, fanno contrario effetto, scen­<lb></lb>dendo in mezzo ne&#039;vasi non pieni, e cadendo dal colmo verso l&#039;orlo, ne&#039;vasi <lb></lb>colmeggianti e untuosi ” <emph type="italics"></emph>(Pensieri fisici matem. </s>

<s>cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>12, 13). </s></p><p type="main">

<s>Si dirà che il Montanari seppe anche ciò dai signori Buoni? </s>

<s>Ma questa <lb></lb>volta si sarebbe potuto risparmiar l&#039;industria di spiare il segreto, essendo <lb></lb>in pubblico rivelato da Isacco Vossio, nel suo libro pubblicato nel 1663 al­<lb></lb>l&#039;Aia col titolo <emph type="italics"></emph>De motu marium et ventorum.<emph.end type="italics"></emph.end> Quivi, contratto il mare in <lb></lb>un bicchier d&#039;acqua, e un gran naviglio in un guscio di castagna, vede <lb></lb>fra&#039;due galleggianti l&#039;Autore una stupenda analogia, perchè, come il navi­<lb></lb>glio in superar l&#039;equatore ascende facilmente il clivo dell&#039;acqua, ma ascesovi <lb></lb>difficilmente ne discende; così fa il guscio che, messo nel bicchiere scemo, <lb></lb>si vede “ ad marginem confluere et altiora petere, idque tanto velocius, <lb></lb>quanto propius a margine abfuerit. </s>

<s>Affundatur dein leniter alia aqua, et im­<lb></lb>pleatur vitrum, ita ut aqua protuberet et excedat crepidinem, illicoque vi­<lb></lb>debis corpuscula istaec, relicta ora, ascendere versus medium et ibi consi­<lb></lb>stere ” (pag. </s>

<s>43). </s></p><p type="main">

<s>Il Vossio stava troppo lontano, per sapere quel che si stampava a Bo­<lb></lb>logna, ma è certo che il libro dei <emph type="italics"></emph>Pensieri fisici matematici<emph.end type="italics"></emph.end> recapitò al <lb></lb>Viviani, che vi lesse le sue proprie osservazioni, e non se ne offese, nè re­<lb></lb>clamò. </s>

<s>Giova anzi credere sentisse gratitudine verso il Montanari, che pub­<lb></lb>blicamente confermava l&#039;esattezza delle osservazioni, e dall&#039;altra parte pen­<lb></lb>sava che di nessuna disse il nome proprio degli osservatori, perchè, ad asserir <lb></lb>con coscienza una tal proprietà di tutte, gli mancavano i documenti. </s></p><p type="main">

<s>Mancavano questi documenti particolarmente rispetto al Borelli, l&#039;espe­<lb></lb>rienze del quale non appartenevano per diritto a lui solo, ma a tutta l&#039;Ac­<lb></lb>cademia. </s>

<s>Tanto è vero che Donato Rossetti, alle orecchie del quale non erano <lb></lb>ancora giunti da Messina i rumori, accennando, in principio al Dialogo se­<lb></lb>condo della sua <emph type="italics"></emph>Antignome,<emph.end type="italics"></emph.end> all&#039;esperienze fatte in Bologna, ingenuamente <lb></lb>soggiungeva: “ oppure, come confessa il signor Montanari, osservate nella <lb></lb>corte di Toscana, prima che in niuno altro luogo ” (Livorno 1667, pag. </s>

<s>51). <pb xlink:href="020/01/3339.jpg" pagenum="300"></pb>Ma il Borelli, che attendeva allora a scrivere il suo libro <emph type="italics"></emph>De motionibus <lb></lb>naturalibus,<emph.end type="italics"></emph.end> in cui le attrazioni e le repulsioni dei piccoli galleggianti do­<lb></lb>vevano fare la loro prima e solenne comparsa; si sdegnava più fieramente <lb></lb>che mai che un giovane suo discepolo, vinta la gratitudine dall&#039;ambizione, <lb></lb>l&#039;avesse così prevenuto. </s>

<s>Nel turbine della quale ira temendo di trovarsi an­<lb></lb>che involto il Rossetti, penso di ripararsene alla prima occasione, che gli si <lb></lb>porse nel 1668, quando pubblicò l&#039;opuscolo delle <emph type="italics"></emph>Sette proposizioni,<emph.end type="italics"></emph.end> nella <lb></lb>sesta pagina innumerata del quale, tra le altre cose, che prega voler tener <lb></lb>bene a mente i lettori, mette anche questa: “ Che fu più che inavvertenza, <lb></lb>quando al suo luogo non confessai che l&#039;eccellentissimo signor dottor Bo­<lb></lb>relli fosse il primo osservatore, ed il primo che agli altri lo mostrasse, di <lb></lb>quell&#039;incontrarsi e fuggirsi che fanno i fuscelli o altro che galleggi. </s>

<s>” </s></p><p type="main">

<s>Ma con qual pudore si potesse pretendere un tal primato, e con qual <lb></lb>coscienza si potesse essere di una tal pretensione così facili fautori, non si <lb></lb>comprende. </s>

<s>L&#039;incontrarsi e il fuggirsi, che fanno i fuscelli bagnati, era stato <lb></lb>osservato e descritto in un libro de&#039;più celebri, e da cui come dalla più <lb></lb><figure id="id.020.01.3339.1.jpg" xlink:href="020/01/3339/1.jpg"></figure></s></p><p type="caption">

<s>Figura 158.<lb></lb>larga fonte, infin dal primo anno del secolo XVII, era <lb></lb>scaturita, e seguitava a diffondersi per tutto una delle <lb></lb>più nobili parti della Filosofia sperimentale. </s>

<s>Guglielmo <lb></lb>Gilbert, nel capitolo secondo del secondo libro <emph type="italics"></emph>De ma­<lb></lb>gnete,<emph.end type="italics"></emph.end> scriveva queste parole: “ Perinde uniri corpora <lb></lb>contendunt, et moventur in superficie aquarum veluti <lb></lb>bacillum quod immittitur paululum in aquas. </s>

<s>Manife­<lb></lb>stum est quod EF (fig. </s>

<s>158) bacillum, quod propter <lb></lb>corticem H natat in aqua, et finem habet tantum F <lb></lb>udum supra superficiem aquarum, attrahitur a ba­<lb></lb>cillo C, si bacillum C udum fuerit paululum sopra aquae superficiem..... <lb></lb>Sin vero bacillum totum supra aquam siccum fuerit, non amplius attrahit sed <lb></lb>fugat virgulam EF. </s>

<s>In bullis etiam illis idem conspicitur, quae in aqua fue­<lb></lb>rint: videmus enim unam ad aliam appellere, et eo velocius quo proximiora <lb></lb>fuerint ” (Londini 1600, pag. </s>

<s>57, 58). </s></p><p type="main">

<s>Più gran maraviglia fa la temerità del Borelli, in quanto che egli stesso <lb></lb>narra di essersi incontrato a osservar l&#039;amplesso e la fuga de&#039;piccoli na­<lb></lb>tanti, all&#039;occasione di voler verificare se i filamenti di ferro, posti su un su­<lb></lb>ghero nell&#039;acqua, prendano spontaneamente la direzione medesima, che ave­<lb></lb>vano nel batterli sull&#039;incudine, <emph type="italics"></emph>ut Gulielmus Gilbertus ait.<emph.end type="italics"></emph.end> Potrebb&#039;essere <lb></lb>che la mente del Borelli si concentrasse così nel concetto, da creder sua <lb></lb>l&#039;esplicazion del Gilberto, ma non si può tanto concedere alle illusioni pa­<lb></lb>terne, che, nello stesso atto di carezzare il parto, non si dovesse accorgere <lb></lb>che non era legittimo. </s>

<s>In più di trent&#039;anni, che durò questa illusione, biso­<lb></lb>gna dir che il Borelli non tornasse mai più a svolgere il libro <emph type="italics"></emph>De magnete,<emph.end type="italics"></emph.end><lb></lb>o che tornandovi non posasse mai gli occhi sopra quelle figure de&#039;fuscelli <lb></lb>bagnati, con largo margine intercalate a illustrare la descrizione del testo. </s></p><p type="main">

<s>In qualunque modo, non essendo a noi possibile penetrare così fatti se-<pb xlink:href="020/01/3340.jpg" pagenum="301"></pb>greti, seguitiamo il Borelli nelle sue proprie illusioni. </s>

<s>Incomincia il capi­<lb></lb>tolo IX <emph type="italics"></emph>De motionibus naturalibus<emph.end type="italics"></emph.end> col dire che erano passati <emph type="italics"></emph>fere triginta <lb></lb>duo anni,<emph.end type="italics"></emph.end> da che all&#039;occasione di verificare il detto del Gilberto, “ mirabile <lb></lb>spectaculum se se obtulit, hactenus non animadversum, quod nimirum ali­<lb></lb>quae extremitates natantium corporum avido cursu se uniebant amplecte­<lb></lb>banturque, aliae vero segregabantur, non secus ac in magnete et ferro con­<lb></lb>tingit ” (pag. </s>

<s>386). </s></p><p type="main">

<s>Essendo queste parole pronunziate nel 1670, dunque il maraviglioso <lb></lb>spettacolo dell&#039;amore e dell&#039;odio de&#039;piccoli galleggianti s&#039;offerse, infin dal <lb></lb>1638, agli occhi del Borelli, il quale, scrivendo poi nel 1667 esser dodici <lb></lb>anni, che per la prima volta l&#039;aveva mostrato al Granduca, e a&#039;suoi corti­<lb></lb>giani; ne fa argomentare che, non prima del 1655, si diffondesse la notizia <lb></lb>dell&#039;esperienza nella corte di Toscana. </s>

<s>E di qui, dopo tanto divagare, viene <lb></lb>la risposta alla domanda, che speriamo i nostri Lettori non abbiano dimen­<lb></lb>ticata: l&#039;osservazione fatta il dì 7 Agosto 1657 non riusciva agli Accademici <lb></lb>cosa nuova, ma il Borelli, che l&#039;aveva prima proposta ai cortigiani curiosi, <lb></lb>tornava ora a ripeterla, in quel medesimo palazzo granducale, ai suoi dotti <lb></lb>Colleghi, de&#039;quali, ripigliando il filo della storia, vorremmo seguitare a nar­<lb></lb>rar gli esercizi intorno ai capillari, se una notizia non fosse in questo tempo <lb></lb>venuta a infiacchire la giovanile alacrità di quei primi passi. </s></p><p type="main">

<s>La notizia si partecipava così dallo stesso Borelli, in una lettera, scritta <lb></lb>il dì 11 Novembre 1658 di Pisa al principe Leopoldo de&#039;Medici: “ Il signor <lb></lb>Thevenot i giorni addietro mi scrisse dell&#039;Accademia nuova di Parigi, la <lb></lb>quale concorse ne&#039;medesimi pensieri di cotesta, che si fa sotto gli auspici <lb></lb>dei serenissimi Principi di Toscana. </s>

<s>Dice che hanno esaminato quel solle­<lb></lb>varsi dell&#039;acqua sopra il suo ordinario livello, quando s&#039;immerge un sotti­<lb></lb>lissimo cannello di vetro, e quando l&#039;acqua è in una caraffa di collo sottile, <lb></lb>e si alza tanto più, quanto più è sottile il cannello e il collo.... Queste in <lb></lb>Italia, come sa V. A., sono materie un pezzo fa considerate. </s>

<s>Se poi quei <lb></lb>signori Francesi hanno trovato la vera ragione di tutto questo, allora dirò <lb></lb>che abbiano preoccupato in ciò il posto e la gloria agl&#039;ingegni italiani ” <lb></lb>(Fabbroni, <emph type="italics"></emph>Lettere inedite,<emph.end type="italics"></emph.end> T. I, Firenze 1773, pag. </s>

<s>115, 16). </s></p><p type="main">

<s>Nonostante la baldanza di queste espressioni, è un fatto che il saper <lb></lb>d&#039;aver emuli e concorrenti conferì molto a raffreddare il primo fervore negli <lb></lb>Accademici fiorentini, i quali, ne&#039;dì 1, 5 e 8 Giugno 1660, si perderono inu­<lb></lb>tilmente intorno al misurar le altezze di varie qualità di liquidi, in un me­<lb></lb>desimo cannello, per veder se corrispondessero con le loro gravità in specie ” <lb></lb>(Targioni, T. cit., pag. </s>

<s>659, 60). </s></p><p type="main">

<s>Intanto, entrato il Thevenot in diretta corrispondenza col principe Leo­<lb></lb>poldo, a lui presentava di Parigi, il dì 7 Aprile 1661, la nota di XXXVII os­<lb></lb>servazioni, fatte nella nuova Accademia intorno ai fenomeni capillari, aggiun­<lb></lb>tevi altre sei osservazioni relative al medesimo soggetto. </s>

<s>Bene esaminati in <lb></lb>Firenze gli articoli di questa Nota, si dovè confessare che s&#039;erano osservate <lb></lb>molte cose di più del semplice sollevarsi l&#039;acqua, sull&#039;ordinario livello, nei <pb xlink:href="020/01/3341.jpg" pagenum="302"></pb>sottilissimi cannelli, e ciò tanto più, quanto sono più stretti. </s>

<s>Potevano com­<lb></lb>piacersi i Nostri d&#039;essere stati primi a osservar che l&#039;argento vivo non fa, <lb></lb>intorno ai solidi che tocca, un&#039;argine ma una fossa. </s>

<s>Leggendo però il foglio <lb></lb>del Thevenot ebbero a riconoscere che la loro osservazione non era com­<lb></lb>piuta, perchè il liquido metallo non si comporta così con tutti i solidi, come <lb></lb>avevano creduto, ma solo con la maggior parte di essi, eccettuati l&#039;oro, <lb></lb>l&#039;argento, lo stagno e il piombo, ne&#039;vasi formati da&#039;quali, purchè siano ben <lb></lb>puliti, il mercurio si solleva arginandosi intorno alle pareti. </s>

<s>Il fatto è più <lb></lb>compiutamente descritto dal Thevenot, nelle due forme seguenti: “ Se s&#039;im­<lb></lb>mergerà in qualche parte nell&#039;argento vivo un pezzuol di vetro, di legno, <lb></lb>di ferro, d&#039;ottone, ecc., l&#039;argento si profonderà, facendogli arginetti all&#039;in­<lb></lb>torno. </s>

<s>— Al contrario, tuffandoci una verghetta ben pulita d&#039;oro, d&#039;argento, <lb></lb>di stagno o di piombo, si vedrà il medesimo argento sollevarsegli intorno ” <lb></lb>(ivi, pag. </s>

<s>718). </s></p><p type="main">

<s>È molto probabile che, nell&#039;Accademia di Firenze, si verificassero que­<lb></lb>sti con tutti gli altri fatti sperimentali, dal Thevenot particolarmente descritti, <lb></lb>benchè gli Accademici non si curassero di tenerne conto nei loro Diari. </s>

<s>Ma <lb></lb>si notò bene qualche punto, in cui le osservazioni erano discordi, come in <lb></lb>questa per esempio, che riguarda le differenti altezze de&#039;liquidi nei cannel­<lb></lb>lini, secondo le varie temperature. </s>

<s>Parve ai Francesi di poter asserir da <lb></lb>molte osservazioni <emph type="italics"></emph>che l&#039;acqua fredda si sollevi assai più della calda<emph.end type="italics"></emph.end> (Tar­<lb></lb>gioni, T. cit., pag. </s>

<s>719) mentre i Nostri fecero per contrapposto scrivere nel <lb></lb>loro diario, sotto il dì 28 Novembre 1661, la conclusione seguente: “ Messo <lb></lb>un cannellino nell&#039;acqua fredda, e notato l&#039;altezza, alla quale per esso si <lb></lb>inalza l&#039;acqua, votata per attrazione l&#039;acqua fredda del vaso, e messavene <lb></lb>ugual mole della calda; l&#039;altezza di quella che si solleva si mantiene l&#039;istessa ” <lb></lb>(ivi, pag. </s>

<s>660). </s></p><p type="main">

<s>Molte, nella Nota dataci dai Fisici francesi, son minuzie da non doverne <lb></lb>menar tanta gloria, ma ci sono osservazioni nuove, l&#039;importanza delle quali <lb></lb>si può ora stimar da noi, dopo le teorie del Clairaut e del Laplace, molto <lb></lb>più giustamente degli Accademici di Firenze, e di quelli stessi di Parigi. </s>

<s><lb></lb>Tali sarebbero le seguenti: “ La superficie dell&#039;acqua, sollevata nel cannello <lb></lb>inclinato e contiguo all&#039;aria, apparisce concava. </s>

<s>— Se la figura del cannello <lb></lb>andasse restringendosi dall&#039;una all&#039;altra estremità, quale sarebbe la figura <lb></lb>di un cono, l&#039;acqua sollevata dal vertice potrà ben discendere verso la base, <lb></lb>purchè, voltato sossopra il cannello, si tenesse perpendicolare all&#039;orizzonte. </s>

<s><lb></lb>Ma ancorchè l&#039;acqua si fosse presso che condotta all&#039;inferiore estremità del <lb></lb>cannello, dandosi a questo una benchè minima inclinazione, quella tornerà <lb></lb>a sollevarsi colassù, d&#039;onde era discesa ” (ivi, pag. </s>

<s>718, 19). </s></p><p type="main">

<s>Riconosciutasi da&#039;Nostri la superiorità dei Francesi, rispetto all&#039;abbon­<lb></lb>dante varietà e alla squisitezza delle osservazioni, non rimaneva, secondo il <lb></lb>proposito del Borelli, a far altro, per non lasciarsi preoccupar nella gloria, <lb></lb>che a ritrovare la causa vera di quegli effetti. </s>

<s>E il Borelli si lusingava di <lb></lb>averla ritrovata davvero, in que&#039;fantastici macchinamenti, che poi descrisse <pb xlink:href="020/01/3342.jpg" pagenum="303"></pb>nel suo libro dei Moti naturali. </s>

<s>A quelle fantasie s&#039;era, per dirla giusta, <lb></lb>studiato di dar qualche fondamento in certi fatti esaminati da lui stesso nel­<lb></lb>l&#039;Accademia, e che, essendo passati di vista ai Francesi, costituivano forse <lb></lb>l&#039;unico punto della superiorità, che, dopo il 1661, ebbero verso que&#039;loro <lb></lb><figure id="id.020.01.3342.1.jpg" xlink:href="020/01/3342/1.jpg"></figure></s></p><p type="caption">

<s>Figura 159.<lb></lb>emuli gli Accademici nostri. </s>

<s>“ Sit fistula stricta vitrea (così pub­<lb></lb>blicava il Borelli le sue proprie accademiche osservazioni) haec <lb></lb>quidem arida, perpendiculariter aquam contingens, eam elevet <lb></lb>per spatium BF (fig. </s>

<s>159). Si vero interne fistula prius humectata <lb></lb>fuerit, et deinde exinanita, in contactu aquae subiectae altius ele­<lb></lb>vatur per spatium BE. </s>

<s>Si postea eadem fistula profundius demer­<lb></lb>gatur infra aquam, vel inclinetur, aqua exucta maius spatium BC <lb></lb>occupabit. </s>

<s>” </s></p><p type="main">

<s>“ His positis, transportetur integra fistula, una cum aqua <lb></lb>contenta, ab aqua ad aerem, perpendiculariter tamen erecta ad <lb></lb>planum horizontis: tunc effluere cunctanter conspicitur ab infimo <lb></lb>orificio B guttula quaedam, quae sensim colligitur tumescitque, <lb></lb>et hoc contingit quando valde excedens est altitudo aquae BC. </s>

<s><lb></lb>At si non nimia fuerit quiescet in situ perpendiculari, absque <lb></lb>eo quod ex orificio B defluat nova aquae gutta. </s>

<s>Modo, dum aqua <lb></lb>supra terminum E, versus C, perseverat, orificium fistulae B contingat <lb></lb>aquam vasis, vel guttulam D suspensam a palma manus, vel adhaerentem <lb></lb>externae et extremae parti ipsius fistulae B: videbis aquam BC deprimi deor­<lb></lb>sum usque ad E, ubi nimirum consistebat aqua exucta e vase, quando in­<lb></lb>terna cavitas humectata fuerat. </s>

<s>E contra, si altitudo aquae internae valde <lb></lb>diminuta fuerit, ut BG, tunc quidem, in contactu guttulae inferioris, augetur <lb></lb>eius altitudo, exugendo nimirum aquam ipsius guttulae D ” <emph type="italics"></emph>(De motion. </s>

<s><lb></lb>natur. </s>

<s>cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>378, 79). </s></p><p type="main">

<s>I colleghi del Borelli avranno con applauso accolte queste dimostrazioni, <lb></lb>e specialmente l&#039;osservazione, che dev&#039;essere a loro apparita nuova, del ri­<lb></lb>salire più su il liquido ne&#039;cannellini bagnati che negli asciutti. </s>

<s>S&#039;è detto che <lb></lb>dev&#039;essere apparita nuova, perchè, sebbene anche il Boyle avesse già osser­<lb></lb>vato “ quod, quoties interna tubi superficies prius erat humore aliquo made­<lb></lb>facta, toties quam et arida, multo melius aqua insurgeret ” <emph type="italics"></emph>(Opera omnia cit.,<emph.end type="italics"></emph.end><lb></lb>T. I, pag. </s>

<s>81); non era facile che ne fossè giunta a Firenze la notizia. </s>

<s>Ma <lb></lb>le ragioni che s&#039;adducevano dal Borelli stesso a spiegare i fatti osservati <lb></lb>ebbero sorte molto diversa. </s>

<s>Quelle addentellature delle pareti, nelle quali si <lb></lb>facevano incastrar le sporgenze delle molecole liquide per salire; anzi che <lb></lb>ingegnose, come le teneva l&#039;inventore, parvero cose di una meccanica troppo <lb></lb>volgare. </s>

<s>Più ragionevole, o a dir meglio più lusinghiera ai memori, e com­<lb></lb>partecipi de&#039;trionfi del Tubo torricelliano, riusciva la ragion di coloro, i quali <lb></lb>dicevano che, per le angustie de&#039;cannellini rallentandosi all&#039;aria la molla, <lb></lb>non è maraviglia se, premendovi meno, fa risalire il liquido sopra l&#039;altezza <lb></lb>sua ordinaria. </s></p><p type="main">

<s>Ma svani presto anche questa lusinga. </s>

<s>In tutte l&#039;esperienze, che dal <pb xlink:href="020/01/3343.jpg" pagenum="304"></pb>22 Novembre 1661, al 9 Settembre 1662, s&#039;instituirono nell&#039;Accademia del <lb></lb>Cimento, intorno ai fenomeni capillari (Targioni, T. cit., pag. </s>

<s>217, 434, <lb></lb>660, 661) non s&#039;attese ad altro, se non a vedere “ se i cannellini, che at­<lb></lb>traggono l&#039;acqua per la immersione, l&#039;attraessero in un vaso pien d&#039;aria <lb></lb>rarissima a quell&#039;altezza medesima, che sogliono nell&#039;aria libera ” (MSS. <lb></lb>Cim., T, II, P. I, fol. </s>

<s>217). E furono i resultati pubblicamente esposti nel <lb></lb>libro de&#039;<emph type="italics"></emph>Saggi,<emph.end type="italics"></emph.end> dove, descrivendosi le varie delicatissime esperienze intorno <lb></lb>al sollevamento de&#039;fluidi, nel vano de&#039;cannellini sottilissimi, dentro al voto; <lb></lb>il Segretario termina con queste parole: “ Onde, da tutte queste esperienze, <lb></lb>e da qualche altra di simil sorta, che ora non è tempo di raccontare, parve <lb></lb>ad alcuno di poter fermare che quest&#039;opinione del premer più languido, che <lb></lb>fa l&#039;aria per gli angustissimi seni, presa così assolutamente, non sia per sè <lb></lb>sola bastante a spiegar questi ed altri simili effetti, ma credono che per lo <lb></lb>meno alcun altra cagione debba unitamente concorrervi ” (Firenze 1691, <lb></lb>pag. </s>

<s>CVIII). </s></p><p type="main">

<s>Si sente da queste espressioni quanto mal volentieri, quegli esecutori <lb></lb>fedeli e promotori indefessi dell&#039;esperienza dell&#039;argento vivo, abbandonassero <lb></lb>la speranza d&#039;ingerire le pressioni dell&#039;aria nella spiegazione di quegli ef­<lb></lb>fetti. </s>

<s>Tanto era poi seducente per tutti i Fisici, specialmente italiani, quella <lb></lb>facile via di aprire il mistero, che molti, o ignari delle esperienze degli Ac­<lb></lb>cademici del Cimento non ancora pubblicate, o colla speranza di deluderne <lb></lb>o d&#039;attenuarne almeno il rigore della sentenza, seguitarono ad affidare il ge­<lb></lb>loso ufficio di sostenere i liquidi nei cannellini alle differenti pressioni del­<lb></lb>l&#039;aria. </s>

<s>Fra costoro è da annoverare principalmente il Montanari, con tutta <lb></lb>l&#039;Accademia di Bologna, alla quale nonostante è dovuto il merito d&#039;aver ge­<lb></lb>nerosamente proseguita l&#039;opera, lasciata a mezzo dall&#039;Accademia di Firenze, <lb></lb>per le gelosie, che si prese il Borelli del Thevenot e de&#039;suoi partigiani. </s>

<s>I <lb></lb>Bolognesi invece, con animo più tranquillo, riconobbero che alcune tra le <lb></lb>osservazioni di costoro, e delle più importanti, non eran perfette, e che non <lb></lb>avevano posti così i segni agli osservatori futuri, da non rimanere a loro <lb></lb>nulla da scoprirvi di nuovo. </s></p><p type="main">

<s>In Parigi, per esempio, s&#039;era solamente osservato che la superficie del­<lb></lb>l&#039;acqua nei cannellini <emph type="italics"></emph>apparisce concava,<emph.end type="italics"></emph.end> ma in Bologna si defini che così <lb></lb>era veramente, quando essi cannellini sono scemi, com&#039;è di fatto convessa <lb></lb>quella medesima superficie, quando invece son colmi. </s>

<s>Vero è bene che il <lb></lb>Boyle, non solo aveva detto <emph type="italics"></emph>guod aquac superficies soleat essc concava,<emph.end type="italics"></emph.end> e <lb></lb>che aveva soggiunto di più <emph type="italics"></emph>quod in hydrargirio sit convexa et depressior<emph.end type="italics"></emph.end><lb></lb><emph type="italics"></emph>(Op. </s>

<s>omnia,<emph.end type="italics"></emph.end> T. </s>

<s>I cit., pag. </s>

<s>81); ma i Nostri vi fecero intorno esame più di­<lb></lb>ligente. </s>

<s>Nè s&#039;affidarono in ciò all&#039;occhio solo, ma all&#039;acume di lui scorto <lb></lb>dalla ragione, considerando quel che dovrebbe avvenire in un vaso rotondo, <lb></lb>qual sarebbe un bicchiere, supposto che il diametro di lui si venisse a re­<lb></lb>stringere via via, infino a ridursi a quello di un tubo capillare. </s>

<s>L&#039;alzamento <lb></lb>dell&#039;acqua alle sponde si mantiene, anche in questa supposizione, costante, <lb></lb>e fu trovato <emph type="italics"></emph>esser circa un quarto d&#039;un dito sopra il livello di mezzo<emph.end type="italics"></emph.end> (Pen-<pb xlink:href="020/01/3344.jpg" pagenum="305"></pb>sieri fisici matem. </s>

<s>cit., pag. </s>

<s>12). Di qui è che, diminuendosi sempre più il <lb></lb>raggio del detto vaso rotondo, si deve giungere a un punto, in cui il livello <lb></lb>di mezzo sparisce, e non rimangon che gli argini, i quali raggiungendosi <lb></lb>co&#039;loro lembi inferiori, chiudono la superficie intera nella concavità di un <lb></lb>menisco. </s>

<s>Gli Accademici di Bologna assegnarono per limiti alla diminuzion <lb></lb>del raggio, affinchè la liquida superficie si disponga in quella figura, una <lb></lb>mezz&#039;oncia circa del loro piede. </s>

<s>“ Il tondeggiamento colmo o concavo del­<lb></lb>l&#039;acqua presso alle sponde, ne&#039;vasi che non passino un&#039;oncia circa di piede <lb></lb>bolognese di diametro, giunge fino al mezzo della superficie, non lasciandone <lb></lb>parte alcuna piana. </s>

<s>Ma in vasi di maggior larghezza ne lascia porzione <lb></lb>piana ” (ivi). </s></p><p type="main">

<s>Nel foglio del Thevenot niente altro più si leggeva, se non che l&#039;acqua, <lb></lb>ne&#039;sifoncini ritorti e ne&#039;cannellini diritti, <emph type="italics"></emph>s&#039;alza tanto maggiormente, quanto <lb></lb>l&#039;orifizio è più angusto,<emph.end type="italics"></emph.end> ma i Bolognesi determinarono l&#039;esatta proporzione, <lb></lb>formulando essi i primi la legge sperimentale delle altezze reciprocamente <lb></lb>proporzionali ai raggi dei tubi capillari. </s>

<s>“ Si è preso un cannellino sottile, <lb></lb>e trovato un filo d&#039;ottone di trafila, che precisamente empiva l&#039;interno cavo <lb></lb>di esso, poi s&#039;è trovato un cannellino più grosso, nel foro del quale entra­<lb></lb>vano precisamente due dei suddetti fili del pari, onde il diametro di questi <lb></lb>si giudicò doppio del primo. </s>

<s>E provati ambedue con diligenza, l&#039;acqua sa­<lb></lb>liva nel più sottile precisamente il doppio in altezza, di quello che facesse <lb></lb>nell&#039;altro più grosso ” (ivi, pag. </s>

<s>9, 10). </s></p><p type="main">

<s>Che poi, oltre a render compiute le osservazioni de&#039;Francesi, i Nostri <lb></lb>ne trovassero da far delle nuove, se ne potrebbe persuader facilmente chiun­<lb></lb>que percorresse quelle loro XXXVI descrizioni, fra le quali basti a noi citar <lb></lb>questa, che ci comparisce nella storia sotto un suo particolare aspetto di no­<lb></lb>vità e d&#039;importanza. </s>

<s>“ Prese due lastre di vetro piane, legate insieme con <lb></lb>un foglio di carta framezzo, ed adattato in modo che, levandone il foglio <lb></lb>destramente, restino senza accostarsi di più; applicato poi il fesso perpendi­<lb></lb>colarmente all&#039;acqua, essa vi s&#039;inalza come ne&#039;cannellini, ed il simile fa <lb></lb>qualsivoglia fessura di corpi solidi, purchè piccola ella sia ” (ivi, pag. </s>

<s>10). </s></p><p type="main">

<s>Dietro questi cenni, i Lettori si faranno del Montanari, e dell&#039;Accade­<lb></lb>mia, ch&#039;egli col suo proprio senno presiedeva, un giudizio molto diverso da <lb></lb>quello, che gli avrebbero voluto insinuare le malevole parole del Borelli e <lb></lb>del Rossetti. </s>

<s>Meno usurpatori dell&#039;altrui, che prodighi del proprio, que&#039;be­<lb></lb>nemeriti Bolognesi raccolsero tutto insieme ciò che s&#039;era esaminato dalla Re­<lb></lb>pubblica degli scienziati, intorno ai fenomeni capillari, e lo tramandarono <lb></lb>qual prezioso documento alla Storia. </s>

<s>Delle notizie poi di tali esami la rac­<lb></lb>colta si fece più dai portati della fama, che dalla lettura dei libri, i quali <lb></lb>non si riducevano insomma che ai soli due del Gilberto e del Grimaldi. </s>

<s>Il <lb></lb>celebre istitutore della Scienza del Magnete, e il non men celebre promo­<lb></lb>tore dell&#039;Ottica, non potevano non avere una grande efficacia in diffondere <lb></lb>lo studio dei fenomeni capillari sotto le loro due più svariate forme dell&#039;at­<lb></lb>trazion de&#039;corpuscoli galleggianti, e della salita per i sottilissimi cannelli. </s>

<s>Or <pb xlink:href="020/01/3345.jpg" pagenum="306"></pb>chi sa quanti altri avranno avuto l&#039;inspirazione dal Gilbert a invenzioni an­<lb></lb>teriori di tempo, e più spettacolose nell&#039;apparenza, di quelle stesse descritteci <lb></lb>dall&#039;autor del libro dei Moti naturali? </s>

<s>Rammentiamoci dell&#039;uccellino auto­<lb></lb>matico dell&#039;Aggiunti. </s>

<s>Tutti coloro dunque volevano essere saputi e comme­<lb></lb>morati dal Montanari? </s>

<s>Ma sarebbe bastato a lui, per far giustizia di tutti, <lb></lb>citare il solo Gilberto, di cui anzi poteva dire che s&#039;era appropriata l&#039;inven­<lb></lb>zione il Borelli. </s></p><p type="main">

<s>Il Grimaldi coglieva l&#039;occasione, a trattar degli effetti capillari, dalla so­<lb></lb>luzione di questo assai volgare problema: perchè, nel far la zuppa, la mi­<lb></lb>dolla del pane attragga così avidamente il vino da ogni sua parte? </s>

<s>E rispon­<lb></lb>deva che le sostanze porose, o intessute di filamenti, formano, in continuità <lb></lb>fra loro, tanti sottilissimi tubi. </s>

<s>Sembra ora a noi ovvia la risposta, ma venne <lb></lb>di qui non lieve impulso alla Fisica capillare, e furono suggerite di qui al­<lb></lb>cune osservazioni agli Accademici bolognesi, come quella per esempio che il <lb></lb>liquido sale sul convesso di più cannellini legati insieme, o in que&#039;pennelli <lb></lb>di vetro, che si fabbricavano in Venezia per ornamento delle donne: ma anche <lb></lb>meglio sentesi l&#039;ispirazione in quest&#039;altra esperienza, così descritta: “ Si <lb></lb>sono provati molti legni, de&#039;quali ponendone un pezzo tagliato, come si dice, <lb></lb>per testa, su un piano bagnato d&#039;acqua, si veggono comparire d&#039;improvviso <lb></lb>nella parte superiore gocciole d&#039;acqua in diversi luoghi, salite per li pori del <lb></lb>legno, come fa ne&#039;cannellini, ed in breve si inumidisce tutto il legno den­<lb></lb>tro e fuori ” (Montanari, <emph type="italics"></emph>Pensieri cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>11). </s></p><p type="main">

<s>Ma il Montanari, così riferendo le cose a nome dell&#039;Accademia, con­<lb></lb>fessa l&#039;efficacia ch&#039;ebbe il Grimaldi in promovere questi loro studi, ciò che <lb></lb>non si poteva dir del Borelli, il libro del quale avrebbe indugiato ancora a <lb></lb>venire alla luce cinque anni. </s>

<s>Il sospetto delle relazioni, ch&#039;esso Montanari <lb></lb>ebbe co&#039;fratelli Del Buono, non ha nessun fondamento, e quand&#039;anche avesse <lb></lb>per questo mezzo risaputo quel che s&#039;era sperimentato nell&#039;Accademia del <lb></lb>Cimento, non sarebbe stato prudenza preoccupare gli uffici del Segretario. </s>

<s><lb></lb>Prudenza fu invece il tacere, e nel silenzio lasciare a ciascuno osservatore <lb></lb>la parte del merito non distribuita, incerto così com&#039;era, per mancanza di <lb></lb>documenti, di fare la distribuzion con giustizia. </s>

<s>Queste considerazioni poi <lb></lb>vogliamo applicare a noi stessi, che francamente assegniamo il primato a <lb></lb>quello e a quell&#039;altro, dietro i soli documenti scarsi, che si son potuti esa­<lb></lb>minare. </s>

<s>Ma chi sa quanti ce ne sono, non saputi da noi, i quali essendo <lb></lb>prodotti scoprirebbero le imperfezioni della nostra Storia, e ci meriterebbero <lb></lb>un&#039;accusa, dal timor della quale fece bene a liberarsene il Montanari. </s></p><p type="main">

<s>Fin qui non abbiamo trovato concorrere nello studio di questi fatti, che <lb></lb>l&#039;Italia e la Francia. </s>

<s>L&#039;Inghilterra, non essendo troppo facile riconoscere le <lb></lb>relazioni, che passano fra le attrazioni elettriche de&#039;fuscelli galleggianti de­<lb></lb>scritti dal Gilberto, e le salite de&#039;liquidi nei tubi capillari; dicemmo come <lb></lb>tardi si risvegliasse nel Boyle. </s>

<s>E anche, mentre altrove era un gran fervore, <lb></lb>ella parve dormirsene nell&#039;inerzia, ma era invece quel benefico sonno, ristora­<lb></lb>tor delle forze, che poi si risvegliarono nell&#039;Hauksbee, e nel Newton. </s>

<s>Le loro <pb xlink:href="020/01/3346.jpg" pagenum="307"></pb>esperienze istituite, con non lungo intervallo di tempo, innanzi alla R. </s>

<s>Società <lb></lb>di Londra, si consociano veramente, e quasi si direbbe si contessono, come <lb></lb>i rami e le fronde di due alberi vicini, de&#039;quali ora vien che descriviamo <lb></lb>la fraganza de&#039;fiori, e la squisitezza dei frutti. </s></p><p type="main">

<s>Il libro delle <emph type="italics"></emph>Esperienze fisico-meccaniche sopra vari soggetti<emph.end type="italics"></emph.end> comparve <lb></lb>provvidamente in mezzo a noi, in veste italiana, e possiamo perciò conver­<lb></lb>sare alla dimestica con l&#039;Autore, per sapere da lui quello che più c&#039;importa. </s></p><p type="main">

<s>Le narrazioni, con le quali incomincia l&#039;Hauksbee la V sezione, non son <lb></lb>altro che un autorevole conferma di cose già note, premendosi principal­<lb></lb>mente nel dimostrare che non può esser l&#039;aria la causa del risalire i liquidi <lb></lb>nei piccoli tubi (Firenze 1716, pag. </s>

<s>63-66). Divagatosi lungamente l&#039;Autore <lb></lb>ne&#039;racconti d&#039;esperienze di vario genere, ritorna finalmente ai fenomeni ca­<lb></lb>pillari, ora osservati in varie accidentalità di tubi, ora nelle superficie quasi <lb></lb>contigue dei corpi. </s>

<s>All&#039;ordine di queste prime osservazioni appartien la se­<lb></lb>guente: “ Avendo procurato due tubi, i diametri delle cui cavità erano vi­<lb></lb>cini ad essere uguali, quanto era stato possibile il fargli, ma uno di vetro <lb></lb>grosso, almeno dieci volte più dell&#039;altro; gli messi nel preaccennato liquore <lb></lb>tinto. </s>

<s>L&#039;effetto si fu che non si potè distinguere differenza alcuna tra l&#039;al­<lb></lb>tezze, che il liquore in ambi i tubi aveva salite ” (ivi, pag. </s>

<s>123). </s></p><p type="main">

<s>Quest&#039;osservazione dell&#039;Accademico di Londra non vuol esser disgiunta <lb></lb>da quell&#039;altre, ch&#039;erano state fatte dagli Accademici di Bologna, quasi parti <lb></lb>di una medesima armatura, della quale vedremo come, a combattere gli er­<lb></lb>rori, si servisse la teoria; perchè se, per l&#039;Inglese, veniva a escludersi dalle <lb></lb>cause dell&#039;ascesa del liquido la grossezza del tubo, per i Nostri era venuta <lb></lb>a escludersene altresì la lunghezza. </s>

<s>“ Dop&#039;avere adoperato un cannellino <lb></lb>assai lungo (si legge ne&#039;<emph type="italics"></emph>Pensieri<emph.end type="italics"></emph.end> del Montanari) e notate l&#039;altezze, ove si ri­<lb></lb>duce l&#039;acqua per la nona esperienza, rompendo parte del cannellino mede­<lb></lb>simo, sino al ridurlo poco più lungo di quanto s&#039;alzava l&#039;acqua la prima <lb></lb>volta; ella sempre vi saglie alla medesima altezza. </s>

<s>— Se la canna maggiore <lb></lb>sarà lunga due, o tre braccia o quanto si vuole, ponendoci in fondo un poco <lb></lb>d&#039;acqua, v. </s>

<s>g. </s>

<s>all&#039;altezza di un dito o due, sicchè il rimanente resti vuoto; <lb></lb>si solleva nel cannellino sottile con altrettanta differenza, quanta ne fa poi <lb></lb>togliendo via tutta la canna lunga ” (pag. </s>

<s>8, 9). </s></p><p type="main">

<s>A questo medesimo genere di osservazioni appartien quell&#039;altra, descritta <lb></lb>dall&#039;Hauksbee, intorno alla salita dell&#039;acqua dentro un tubo pieno di cenere, <lb></lb>calcatavi ben bene con una bacchetta, e che può avere l&#039;esempio naturale <lb></lb>nella straordinaria altezza, a cui giunge talvolta l&#039;umidità del suolo, su per <lb></lb>l&#039;intonaco di una vecchia muraglia. </s>

<s>Il moto dell&#039;ascesa, qua e là si fa lento e <lb></lb>sempre più ritardato, ciò che l&#039;Hauksbee stesso attribuisce alla sempre più cre­<lb></lb>scente resistenza dell&#039;aria, in luogo della quale vuole a forza sottentrar l&#039;acqua. </s></p><p type="main">

<s>Quanto poi all&#039;ascendimento de&#039;liquidi, tra le superficie quasi contigue, <lb></lb>l&#039;Hauksbee, dalle lastre di vetro, sole usate dagli Accademici di Bologna, <lb></lb>estese le osservazioni ai piani di marmo e di ottone, variandone la figura, <lb></lb>da rettangolare o quadrata, in circolare, dalla quale, fatta toccare in qualche <pb xlink:href="020/01/3347.jpg" pagenum="308"></pb>punto allo spirito di vino o all&#039;olio di trementina, vedeva il liquido risalire, <lb></lb>in sottili filamenti divisi, con gran velocità su agli orli, come corde, dal me­<lb></lb>desimo punto inferiore di un diametro perpendicolare, tirate alla circonfe­<lb></lb>renza. </s>

<s>E supponendo che giungessero que&#039;raggi fluidi lutti a essa circonfe­<lb></lb>renza in un tempo, come vide fare l&#039;Hauksbee, senz&#039;alcuna differenza no­<lb></lb>tabile al senso, “ abbiamo qui dunque, egli dice, in un certo modo, per la <lb></lb>contraria, la riprova della famosa proposizione del Galileo, sopra l&#039;equitem­<lb></lb>poranee discese de&#039;corpi pesanti nelle corde d&#039;un cerchio. </s>

<s>Poichè in questo <lb></lb>caso l&#039;ascendente liquido le descrive tutte in tempi eguali, come in quel caso <lb></lb>fa il discendente solido. </s>

<s>E se l&#039;uno sale e l&#039;altro scende, per virtù d&#039;una <lb></lb>medesima causa, come io non posso far di meno di non credere che segua; <lb></lb>egli non è maraviglia dunque che vi sia una concordia tale fra loro, e che <lb></lb>la medesima causa produca un somigliante effetto, così ne&#039;solidi come ne&#039;li­<lb></lb>quidi, quando vengono supposte somiglianti circostanze per ambe le parti. </s>

<s><lb></lb>E il tutto per null&#039;altro ascende, se non per l&#039;attrazione all&#039;in su in un <lb></lb>caso, e all&#039;ingiù nell&#039;altro, e ciò nella medesima sorta di figura, nominata­<lb></lb>mente in un cerchio ” <emph type="italics"></emph>(Esperienze fisico-meccaniche cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>125, 26). </s></p><p type="main">

<s>Vedremo più qua l&#039;importanza di queste analogie tra la meccanica dei <lb></lb>liquidi e de&#039;solidi, ma, per non interrompere il filo della storia, si noti qui <lb></lb>un&#039;altra analogia, che intravide l&#039;Hauksbee tra i cannelli cilindrici, e le su­<lb></lb>perficie quasi contigue dei corpi, dicendo che queste <emph type="italics"></emph>compongono un tubo <lb></lb>della forma di un parallelepipedo, la cui grossezza è eccedentemente pic­<lb></lb>cola<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>127). Soggiungendo poi l&#039;Autore esser medesima la causa, che <lb></lb>fa ascendere il liquido per i due sottilissimi spazi, ne fa ragionevolmente <lb></lb>argomentare che procedessero altresì con analoghi effetti, cosicchè se per <lb></lb>esempio il diametro di un cannellino è un millimetro, e un millimetro pure <lb></lb>è la distanza fra le due lastre, il liquido giunga a pari altezza, nel cilin­<lb></lb>dretto, e nel prisma di un millimetro di base quadrata. </s>

<s>L&#039;argomentazione <lb></lb>dall&#039;altra parte era così seducente, che vi rimasero presi in fallacia tutti i <lb></lb>Fisici, infino al Newton, a cui resultò, per esperienze fatte innanzi alla R. </s>

<s>So­<lb></lb>cietà di Londra, che l&#039;altezza del liquido è la medesima, non già quando la <lb></lb>distanza fra le due lastre vicine uguaglia il diametro, ma si bene il rag­<lb></lb>gio del tubo capillare. </s>

<s>“ Quod si tubuli vitrei tenues in aquam stagnantem <lb></lb>ab inferiore sui parte intingantur, aqua intra tubulum ascendet, idque ea <lb></lb>ratione, ut eius altitudo reciproce proportionalis sit tubi cavitatis diametro, <lb></lb>et par altitudini aquae inter binas laminas vitreas ascendentis, siquidem tubi <lb></lb>cavitas semidiametro par sit, aut fere par laminarum istarum intervallo. </s>

<s>At­<lb></lb>que horum quidem omnium experimentorum, coram Societate regia capto­<lb></lb>rum, sive in vacuo, sive in aperto aere, unus fuit exitus ” <emph type="italics"></emph>(Optices,<emph.end type="italics"></emph.end> Lib. </s>

<s>III, <lb></lb>quaestio XXXI, Patavii 1773, pag. </s>

<s>160). </s></p><p type="main">

<s>Ma comunque fossero le ragioni, da istituirsi fra i diametri o i raggi, <lb></lb>rimaneva sempre vero che, anche tra le due lastre, le altezze son reciproche <lb></lb>alle distanze, ciò che volle sperimentare l&#039;Hauksbee in due modi, ora sco­<lb></lb>stando parallelamente, ora facendo inclinar l&#039;una lastra sull&#039;altra. </s>

<s>E perciò <pb xlink:href="020/01/3348.jpg" pagenum="309"></pb>sembra si debba a lui il primo la bella esperienza, che rappresenta la su­<lb></lb>perficie del liquido fra le due lastre scendere dallo spigolo verticale, via via <lb></lb>disponendosi in quella curva elegante, che poi non difficilmente si dimostrò <lb></lb>essere una <emph type="italics"></emph>iperbola equilatera.<emph.end type="italics"></emph.end> “ L&#039;altezza della salita del liquido tinto <lb></lb>(affinchè si sappia ciò che propriamente osservò l&#039;Hauksbee in questo pro­<lb></lb>posito) variava secondo la distanza de&#039;piani. </s>

<s>Poichè, se invece d&#039;un pezzo <lb></lb>di foglio per la sua grossezza, ve n&#039;erano posti due, il liquore non giungeva <lb></lb>a salire tant&#039;alto in questo caso, come nell&#039;altro, quando i piani erano so­<lb></lb>lamente separati da un semplice pezzo di foglio. </s>

<s>E allora, se i piani pende­<lb></lb>vano da qualche parte, il liquore sempre si spandeva più e più oltre, pro­<lb></lb>porzionatamente al grado della declinazione. </s>

<s>E a diverse prove tutto questo <lb></lb>successe nel medesimo modo ” <emph type="italics"></emph>(Esperienze fisico-meccan. </s>

<s>cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>115). </s></p><p type="main">

<s>Lo spigolo, formato dalla detta pendenza, s&#039;intende bene come rima­<lb></lb>nesse eretto perpendicolarmente, ma l&#039;Hauksbee variò il caso, tenendo la <lb></lb>soggetta lamina orizontale, cosicchè pure orizontale rimanesse lo spigolo, for­<lb></lb>mato dalla congiunzione di questa con la lamina superiore. </s>

<s>Se possa aver <lb></lb>avuto qualche efficacia, a così fatte promozioni, quel che ne&#039;tubi conici era <lb></lb>stato osservato dagli Accademici parigini, non è facile a decidersi. </s>

<s>Ma è un <lb></lb>fatto che, da&#039;piani con i quali sperimentava il Fisico inglese, vedremo poi <lb></lb>ritornare ai tubi conici un Francese insigne, per quel perpetuo circolo della <lb></lb>vita, che si scopre fra le idee de&#039;vari Autori, quasi corrente elettrica, che <lb></lb>per tacita influenza trapassa da un globo metallico a un altro, benchè vario <lb></lb>di materia e succedentegli a distanza. </s>

<s>Prima però di passare a riferir ciò, <lb></lb>che osservasse l&#039;Hauksbee, nel liquido interposto fra la lastra inferiore ori­<lb></lb>zontale, e la superiore inclinata, osserviamo che la descrizione non si trova <lb></lb>raccolta fra le altre Esperienze fisico-meccaniche, ma in una loro Appendice, <lb></lb>dalla quale il Laplace la tradusse in francese <emph type="italics"></emph>(Supplement au X livre du <lb></lb>Mechan. </s>

<s>celeste)<emph.end type="italics"></emph.end> e molto prima il Newton l&#039;aveva così ridotta nel libro delle <lb></lb>Questioni: “ Si duo planae et politae vitri laminae, uncias ternas aut qua­<lb></lb>ternas latae, et vicenas aut vicenas quinas longae, ita disponantur, ut earum <lb></lb>altera horizonti parallela iaceat altera autem ei ita interponatur, ut earum <lb></lb>extremitates alterae se inter se contingant, angulumque circiter 10 aut 15 mi­<lb></lb>nutorum contineant; harum autem laminarum facies interiores linteo mundo, <lb></lb>in mali aurei oleum vel sqiritum terebinthinum intincto prius madefiant, et <lb></lb>deinde olei istius, sive spiritus, gutta una vel altera in vitri inferioris extre­<lb></lb>mum, id quod a dicto angulo maxime distat, demittatur, utique simul pri­<lb></lb>mum ac vitri lamina superior inferiori ita superposita sit, ut eam, quomodo <lb></lb>supra dictum est, altera sui extremitate contingat, altera autem guttam, con­<lb></lb>tinens nimirum cum inferiori vitro angulum circiter 10 aut 15 minutorum; <lb></lb>gutta continuo eam se in partem, qua parte binae laminae se contingunt <lb></lb>inter se, movere incipiet, motuque ferri perget perpetim accelerato, usque <lb></lb>dum ad ipsum vitrorum concursum perveniat. </s>

<s>Etenim bina vitra guttam at­<lb></lb>trahunt, efficiuntque ut illa illo moveatur, quo attractiones vergunt ” <emph type="italics"></emph>(Opti­<lb></lb>ces,<emph.end type="italics"></emph.end> lib. </s>

<s>cit., pag. </s>

<s>160). </s></p><pb xlink:href="020/01/3349.jpg" pagenum="310"></pb><p type="main">

<s>Questa esperienza fu ridotta alla sua massima semplicità, e alla sua più <lb></lb>conveniente significazione, per la teoria del Laplace, il quale, tornando a ri­<lb></lb>prendere in mano uno strumento de&#039;suoi antenati, forse da lui stesso dimen­<lb></lb>ticato, osservò che “ une petite colonne d&#039;eau, dans un tube conique ouvert <lb></lb>par ses deux extremités, et maintenu horizontalement, se porte vers le som­<lb></lb>met du tube, et la surface de la colonne fluide est concave a ses deux extre­<lb></lb>mités.... Si la colonne fluide est de mercure, alors sa surface est convexe <lb></lb>et la colonne doit se porter vers la base du tube ” (<emph type="italics"></emph>Supplement I cit.,<emph.end type="italics"></emph.end><lb></lb>pag. </s>

<s>6, 7). Ma perchè così fatte esperienze si riferiscono troppo strettamente <lb></lb>alle teorie, delle quali non è ancora il tempo a parlare, giova porre il ter­<lb></lb>mine alla presente storia col rammemorare un fatto singolarissimo, che, ap­<lb></lb>parito ai Fisici senza legge, il Newton ridusse al genere de&#039;fenomeni ca­<lb></lb>pillari. </s></p><p type="main">

<s>Negli Esperimenti fisico-meccanici del Boyle, pubblicati nel 1661 in in­<lb></lb>glese, e nell&#039;anno appresso tradotti in latino, si leggeva la descrizione di <lb></lb>quel tubo di vetro da termometri, che pieno d&#039;acqua, e secondo il modo tor­<lb></lb>ricelliano capovolto in una vaschetta, restava pieno, così stando all&#039;aperto, <lb></lb>ma sotto la campana della macchina pneumatica si votava, tanto rimanen­<lb></lb>dovene solo, quanto a dire del Boyle si potesse credere esservi sostenuto dal <lb></lb>debole sforzo dell&#039;aria rarefatta. </s>

<s>L&#039;Huyghens fu curioso di veder co&#039;suoi <lb></lb>propri occhi la cosa, e trovò che veramente avveniva com&#039;aveva detto il <lb></lb>Boyle, se però l&#039;acqua era mescolata con l&#039;aria. </s>

<s>Ma se di questa si fosse <lb></lb>quella in qualche modo espurgata, il tubo rimaneva pieno, anche nel vuoto <lb></lb>della campana. </s>

<s>Parve a principio l&#039;annunzio tanto strano, che non si volle <lb></lb>credere, ma venutisi alle prove, che si fecero nel 1663 innanzi alla R. </s>

<s>So­<lb></lb>cietà di Londra, e ripetutesi per maggior conferma col mercurio nello stru­<lb></lb>mento torricelliano dallo stesso Boyle, ebbe questi a convincersi con sua gran <lb></lb>maraviglia che, dai 27 o 28 pollici consueti, il liquido si poteva ridurre infino <lb></lb>a 75 alto dentro la canna. </s></p><p type="main">

<s>Riposati gli animi dallo stupore, s&#039;incominciò a ripensare qual potesse <lb></lb>esser la causa di un fatto così nuovo. </s>

<s>L&#039;Huyghens, che stava allora fanta­<lb></lb>sticando intorno a quel suo etere cosmico, da sostituirsi alla materia sottile <lb></lb>del Cartesio, onde spiegare la gravità naturale de&#039;corpi, e le proprietà della <lb></lb>luce; non dubitò d&#039;ingerire il vagheggiato idolo suo taumaturgo a spiegare <lb></lb>i misteri dello sperimento boileiano. </s>

<s>Disse che, estratta l&#039;aria, vi sottentra <lb></lb>l&#039;etere, penetrativo come di tutti i corpi così e del vetro della campana, a <lb></lb>sostener l&#039;acqua e il mercurio a una tale incredibile altezza. </s>

<s>Ma ascoltiamo <lb></lb>com&#039;egli stesso più efficacemente si esprima, in uno di que&#039;suoi, che i di­<lb></lb>ligenti raccoglitori intitolarono <emph type="italics"></emph>Experimenta phisica.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Praeter pressionem aeris, quae sustinet mercurium ad altitudinem <lb></lb>27 pollicum in experimento torricelliano, et quam dari ex infinitis aliis effe­<lb></lb>ctibus quos videmus constat; concipio et aliam pressionem illa fortiorem, <lb></lb>materiae aere subtilioris, quae haud difficulter penetrat vitrum, aquam, mer­<lb></lb>curium, et omnia alia corpora, quae aeri impenetrabilia observamus. </s>

<s>Haec <pb xlink:href="020/01/3350.jpg" pagenum="311"></pb>pressio, addita ad aeris pressionem, potest sustinere 75 pollices mercurii, et <lb></lb>forte adhuc plures, quam diu tantum agit in superficiem inferiorem, vel in <lb></lb>superficiem mercurii, in quem aperta tubi extremitas immergitur. </s>

<s>Sed quam <lb></lb>primum materia haec potest agere etiam ad alteram partem, quod evenit si <lb></lb>tubum concutiendo, vel immittendo parvam aeris bullam occasio detur huic <lb></lb>materiae effectum suum inchoandi; pressio illius aequalis erit ab utraque <lb></lb>parte, ita ut sola supersit aeris pressio, quae sustinet mercurium ad ordina­<lb></lb>riam altitudinem 27 pollicum. </s>

<s>” </s></p><p type="main">

<s>“ Eadem de causa, in experimento aquae aere purgatae, post remotam <lb></lb>pressionem aeris, evacuando recipiens B (fig. </s>

<s>160), altera illa pressio eius­<lb></lb>dem materiae agit etiam ut antea in superficiem aquae in vitro D, et cohi­<lb></lb>bet ne aqua in phiala C descendat. </s>

<s>Sed ubi minima bulla aeris intrat phia­<lb></lb><figure id="id.020.01.3350.1.jpg" xlink:href="020/01/3350/1.jpg"></figure></s></p><p type="caption">

<s>Figura 160.<lb></lb>lam, materia, quam dixi transire per vitrum et aquam, <lb></lb>subito inflat bullam, editque pressionem aequalem illi, <lb></lb>quae agit in superficie aquae in vitro D. </s>

<s>Quare omnis <lb></lb>aqua phialae defluit, et ad libellam cum illa, quae est <lb></lb>in vitro, se constituit ” (<emph type="italics"></emph>Opera varia,<emph.end type="italics"></emph.end> T. II, Lugd. </s>

<s><lb></lb>Batav. </s>

<s>1724, pag. </s>

<s>773, 74). </s></p><p type="main">

<s>Nel quinto esperimento poi conferma l&#039;Huyghens <lb></lb>l&#039;esperienza dell&#039;etere, attribuendo alla pressione di lui <lb></lb>il rimanere aderenti due lastre contigue da specchi, <lb></lb>anche nel vuoto. </s>

<s>Ma venuto poi il Newton disse che, <lb></lb>così questo fatto, come l&#039;altro del sostenersi l&#039;acqua <lb></lb>e il mercurio, purificati dall&#039;aria, nel tubo torricelliano, <lb></lb>a maggiore altezza di quella dovuta alla pressione ammosferica; non era da <lb></lb>attribuirsi ad altro, che all&#039;attrazione molecolare del liquido in sè, e alla ma­<lb></lb>teria del vetro: attrazion ch&#039;è rotta, sia per l&#039;interposizione dell&#039;aria, sia per <lb></lb>la violenta succussione del tubo. </s>

<s>“ Porro rem eamdem inde quoque infero <lb></lb>quod bina marmora perpolita cohaereant, etiam in vacuo, et quod argentum <lb></lb>vivum in Barometro subsistat ad altitudinem 50, 60 vel 70 unciarum, vel <lb></lb>etiam amplius eo: ita scilicet si prius ab aere omni probe depurgatum fue­<lb></lb>rit, et in tubum cauta manu infusum, ut adeo partes eius sint usquequaque <lb></lb>contiguae, et sibi invicem et vitro. </s>

<s>Atmosphaera pondere suo argentum vi­<lb></lb>vum sursum in tubum premit ad usque altitudinem 29 aut 30 unciarum. </s>

<s><lb></lb>Alia autem aliqua causa efficiens id deinceps amplius sustollit, non id in tu­<lb></lb>bum sursum premendo, sed efficiendo ut partes eius et vitro et sibi invicem <lb></lb>adhaerescant. </s>

<s>Etenim, si quò pacto partes eius, vel interiectis bullulis, vel <lb></lb>succutiendo vitrum, disiungantur, corruit continuo argentum vivum omne, <lb></lb>usque eo donec haud amplius 29 aut 30 uncias in altitudinem habeat ” <lb></lb>(<emph type="italics"></emph>Opticae,<emph.end type="italics"></emph.end> lib. </s>

<s>III cit., pag. </s>

<s>158). </s></p><p type="main">

<s>Così dunque il Newton veniva ad arricchire la Fisica capillare di un <lb></lb>fatto nuovo, in cui gloriosamente si compie la storia di queste osservazioni, <lb></lb>le quali anche noi col Laplace, chiameremo antiche. </s>

<s>Delle nuove, che servi­<lb></lb>rono o per più sicura scorta o per più piena conferma delle teorie, diremo <pb xlink:href="020/01/3351.jpg" pagenum="312"></pb>più qua, quando, passata dalle ipotesi vaghe, vedremo la Scienza studiosa di <lb></lb>fermare il piè ne&#039;teoremi. </s></p><p type="main">

<s>Per queste ipotesi non s&#039;intende però, secondo la comune accettazione <lb></lb>della parola, un principio che sembra ragionevolmente vero, e che aspetti <lb></lb>d&#039;essere dimostrato, ma una cogitazione qualunque che, venuta a mancare <lb></lb>la notizia del vero, siasi presa a rappresentarlo e a supplirlo. </s>

<s>Le scambie­<lb></lb>voli attrazioni delle particelle della materia, da che dipendono i fenomeni ca­<lb></lb>pillari, costituiscon quel vero, che poi venne per qualche tempo a mancare, <lb></lb>e che intanto, prima di riaversi negli spiriti e nella libertà della vita, fu sup­<lb></lb>plito dalle ipotesì che si diceva, a quel modo che si supplisce talvolta all&#039;in­<lb></lb>terruzione di una linea curva, tirata con lo strumento in perfetta regola, <lb></lb>ricongiungendone i tratti con la mano incerta. </s>

<s>La somiglianza tra l&#039;imma­<lb></lb>gine e la realtà viene ora a dimostrarsi per la seguente storia. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Una delle forme più ovvie, sotto cui si rappresentano le azioni della ca­<lb></lb>pillarità, s&#039;offerse nelle gocciole dell&#039;acqua, che attirarono a sè da lungo <lb></lb>tempo l&#039;attenzione e lo studio dei Fisici, com&#039;è manifesto dagli scritti di Leo­<lb></lb>nardo da Vinci. </s>

<s>Il fatto che due delle dette gocciole, poste a breve distanza <lb></lb>fra loro, s&#039;attraggono a vicenda come la calamita e il ferro, era allora co­<lb></lb>munemente noto, e perciò Leonardo avvertiva, in principio al suo libro <emph type="italics"></emph>Del <lb></lb>moto e della misura dell&#039;acque,<emph.end type="italics"></emph.end> non essere sua intenzione di trattarvi di <lb></lb>una tale occulta proprietà de&#039;liquidi minutamente divisi, ma di quelle, che <lb></lb>più manifestamente si osservano in essi, essendo raccolti insieme in più grandi <lb></lb>moli. </s>

<s>“ Non parlo, egli dice nel capitolo IV del libro citato, delle gocciole o <lb></lb>altre piccole quantità, che si tirano l&#039;una all&#039;altra, come l&#039;acciaio la sua li­<lb></lb>matura, ma delle gran quantità ” (Bologna 1828, pag. </s>

<s>275). </s></p><p type="main">

<s>Non contenti que&#039;Fisici d&#039;osservare il fatto, si dettero a specularne an­<lb></lb>che le ragioni, e Leonardo dice le sue, risolvendo con esse alcuni problemi, <lb></lb>relativi a questo soggetto, dei più curiosi, come sarebbe questo, in cui si <lb></lb>domanda: <emph type="italics"></emph>perchè quella gocciola fia di più perfetta sfericità, la quale sia <lb></lb>di minor quantità;<emph.end type="italics"></emph.end> o quell&#039;altro assai simile: <emph type="italics"></emph>perchè, se due liquidi sfe­<lb></lb>rici di quantità ineguali verranno al principio del contatto infra loro, il <lb></lb>maggiore tira a sè il minore, e immediatamente se lo incorpora, senza <lb></lb>distruggere la perfezione della sua sfericità.<emph.end type="italics"></emph.end> E benchè confessi di sentire <lb></lb>tutta la difficoltà della proposizione, “ non per questo, soggiunge Leonardo, <lb></lb>resterò di dire il mio parere. </s>

<s>L&#039;acqua, vestita dell&#039;aria, naturalmente desi­<lb></lb>dera stare unita nella sua sfera, perchè in tal sito essa si priva di sua gra­<lb></lb>vità, la qual gravità è dupla: cioè che il suo tutto ha gravità, atteso al cen­<lb></lb>tro degli elementi; la seconda gravità, atteso al centro della sfericità del­<lb></lb>l&#039;acqua. </s>

<s>Il che, se così non fosse, essa farebbe di sè solamente una mezza <pb xlink:href="020/01/3352.jpg" pagenum="313"></pb>sfera, la quale è quella, che sta dal centro in su. </s>

<s>Ma di questo non vedo <lb></lb>nell&#039;umano ingegno modo di darne scienzia, ma direi come si dice della ca­<lb></lb>lamita, che tira il ferro, cioè che tale virtù è occulta proprietà, delle quali <lb></lb>ve ne sono infinite in natura ” (ivi, pag. </s>

<s>291). </s></p><p type="main">

<s>È manifesto dunque che, nel concetto di Leonardo, si trova involuto <lb></lb>quello di una attrazione della massa fluida al centro della Terra: attrazione <lb></lb>distinta da quell&#039;altra simile, che le particelle componenti esercitano fra sè <lb></lb>medesime, come tra il ferro e la calamita. </s>

<s>La relazione che passa fra que­<lb></lb>ste, e le idee del Newton, è manifesta, ma che fossero veramente in Leo­<lb></lb>nardo involute, e impedite di schiudersi liberamente, serrate e strette, diciam <lb></lb>così, da una certa dura corteccia peripatetica; si par dal modo com&#039;ei ri­<lb></lb>sponde al nuovo propostosi quesito: <emph type="italics"></emph>perchè è più perfezione nella minore <lb></lb>sfera del liquido, che nella grande.<emph.end type="italics"></emph.end> Sembrava che si dovesse direttamente <lb></lb>concludere, dai professati principii, così la risposta: perchè, nella grande, <lb></lb>maggiormente prevale l&#039;attrazione al centro degli elementi, sopra quella al <lb></lb>centro della sfericità dell&#039;acqua, ma sfuggì a Leonardo la considerazione di <lb></lb>queste forze interne, per ridursi a non attribuir l&#039;effetto che all&#039;azione esterna <lb></lb>dell&#039;ambiente. </s>

<s>“ Qui si risponde che la minima goccia ha levità più simile <lb></lb>all&#039;aria, che la circonda, che la gocciola grande, e per la poca differenza è <lb></lb>sostenuta più dal mezzo in giù da essa aria, che la grande. </s>

<s>E per prova di <lb></lb>questo si allegherà le minime gocciole, che sono di tanto minima figura, che <lb></lb>elle sono quasi invisibili per sè. </s>

<s>Ma molte ed in quantità sono visibili, e que­<lb></lb>ste sono le particole componenti le nuvole, la nebbia, la pioggia etc. </s>

<s>” (ivi). </s></p><p type="main">

<s>Le attrazioni calamitiche fra le minime particelle dell&#039;acqua, che il Gil­<lb></lb>berto trovò così bene studiate dai Fisici anteriori, gli resero un bel servigio, <lb></lb>per confermare il principio, da sè posto per uno de&#039;principali fondamenti <lb></lb>alla sua Filosofia magneto-elettrica, dell&#039;umido cioè <emph type="italics"></emph>rerum omnium unito­<lb></lb>ris.<emph.end type="italics"></emph.end> La descrizione de&#039;fuscelli galleggianti ricorre a questo proposito, e dice <lb></lb>che s&#039;attraggono “ veluti gutta adiuncta guttae attrahitur, et subito uniun­<lb></lb>tur. </s>

<s>Sic humidum in aquae superficie unitatem petit humidi, cum aquae su­<lb></lb>perficies in utrisque attollitur, quae illico, sicut guttae aut bullae, conflu­<lb></lb>unt, sunt in maiore multo proprinquitate, quam electrica et vapidis naturis <lb></lb>uniuntur ” (<emph type="italics"></emph>De magnete cit.,<emph.end type="italics"></emph.end> pag. </s>

<s>57). </s></p><p type="main">

<s>Pochi convennero per verità che i moti descritti dal Gilberto dipendes­<lb></lb>sero dall&#039;attrazione elettrica delle cose umide, e il Cabeo, fra gli altri uno <lb></lb>de&#039;più animosi, insorgeva a contradirlo così ragionando: “ Nunc ostendo illos <lb></lb>motus a Gilberto enumeratos esse motus elementares gravium, quae tendunt <lb></lb>ad centrum, non electricas humidorum attractiones. </s>

<s>Imo ad hominem contra <lb></lb>Gilbertum prius dico: sicut bacillum siccum non attrahit humidum, vel con­<lb></lb>tra nec fluit ad siccam ripam humidum: igitur solum humida in se mutuo <lb></lb>trahunt. </s>

<s>Ergo etiam electrica, quae trahuntur ex humiditate, non trahent <lb></lb>nisi humida, sicca fugabunt. </s>

<s>Sed trahunt omnia sicca, immo fortasse luben­<lb></lb>tius; ergo non trahunt ex humiditate ” (<emph type="italics"></emph>Philosophia magnetica,<emph.end type="italics"></emph.end> Colo­<lb></lb>niae 1629, pag. </s>

<s>187). </s></p><pb xlink:href="020/01/3353.jpg" pagenum="314"></pb><p type="main">

<s>Nonostante che pochi, per queste dette dal Cabeo, e per simili altre ra­<lb></lb>gioni, accettassero le nuove teorie elettriche, giovarono le osservazioni e le spet­<lb></lb>tacolose esperienze del Gilberto a confermare l&#039;essere e la natura di una occulta <lb></lb>virtù calamitica, fra le particelle componenti l&#039;acqua. </s>

<s>Galileo, nel suo Discorso <lb></lb>idrostatico, la professava apertamente, e vedeva in essa quella copula che tiene <lb></lb>unite le particelle non dell&#039;acqua sola, ma e di tutti i corpi. </s>

<s>Questa calami­<lb></lb>tica virtù poi non differisce che nel nome dall&#039;attrazione molecolare del New­<lb></lb>ton, e da quel moto occulto dell&#039;acqua <emph type="italics"></emph>ad omnes partes,<emph.end type="italics"></emph.end> da cui sapientemente <lb></lb>l&#039;Aggiunti derivava la causa universale dei multiformi fenomeni capillari. </s></p><p type="main">

<s>Ora è notabile che, non giunto ancora il secolo XVII a compiere i suoi <lb></lb>primi quarant&#039;anni, erano già state spente queste luminose apparizioni della <lb></lb>Fisica molecolare. </s>

<s>Ne fu causa il vento sollevatosi, dalle due parti opposte <lb></lb>dell&#039;orizonte scientifico, a dissipare quelle occulte proprietà della materia, <lb></lb>nelle quali troppo spesso andavasi a rifugiare la Fisica peripatetica. </s>

<s>Galileo <lb></lb>ha in tal proposito certe espressioni, significantissime di questo incorrere le <lb></lb>idee nuove contro le vecchie, là dove, al nome di <emph type="italics"></emph>simpatia,<emph.end type="italics"></emph.end> sotto il quale <lb></lb>si velavano ai peripatetici le repulsioni o le indebolite forze attrattive del­<lb></lb>l&#039;aria verso l&#039;acqua, si studia di sostituire i nomi di <emph type="italics"></emph>dissensione<emph.end type="italics"></emph.end> o di <emph type="italics"></emph>discon­<lb></lb>venienza.<emph.end type="italics"></emph.end> Di che accortosi Simplicio, così argutamente dice al suo interlo­<lb></lb>cutore: “ Mi vien quasi da ridere nel veder la grande antipatia, che ha il <lb></lb>signor Salviati con l&#039;antipatia, che neppur vuol nominarla, eppure è tanto <lb></lb>accomodata a scior la difficoltà ” (Alb. </s>

<s>XIII, 74). </s></p><p type="main">

<s>Ma l&#039;usare un nome piuttosto che un altro non era certo un far pro­<lb></lb>gredire la Scienza, la quale anzi ebbe a indietreggiare per Galileo, quando <lb></lb>all&#039;attrazion calamitica, copulatrice delle particelle discrete dei corpi, secondo <lb></lb>le idee, che prevalevano nel tempo, in cui fu scritto il Discorso delle gal­<lb></lb>leggianti; sostituì, ne&#039;Dialoghi delle due nuove Scienze, per antipatia alle <lb></lb>qualità occulte, le pressioni prodotte dal peso dell&#039;aria. </s>

<s>E così egli si lusingò <lb></lb>d&#039;aver progredito, mostrando palese al di fuori quel che invisibile si credeva <lb></lb>esser dentro. </s>

<s>Ebbe da ciò motivo la riforma delle dottrine, che Galileo stesso <lb></lb>applicava a rendere la ragione del sostenersi i globuli d&#039;acqua sollevati e <lb></lb>grandi. </s>

<s>E benchè confessi di non saper come propriamente vada il negozio, <lb></lb>egli è però certo che di un tale effetto non sia la causa interna, ma che ne­<lb></lb>cessariamente risegga fuori. </s>

<s>“ Che ella non sia interna, oltre all&#039;esperienze <lb></lb>mostrate, ve lo posso confermare con un&#039;altra efficacissima. </s>

<s>Se le parti di <lb></lb>quell&#039;acqua, che rilevata si sostiene, mentre è circondata dall&#039;aria, avessero <lb></lb>cagione interna per ciò fare, molto più si sosterrebbono circondate che fos­<lb></lb>sero da un mezzo, nel quale avessero minor propensione di discendere, che <lb></lb>nell&#039;aria ambiente non hanno. </s>

<s>Ma un mezzo tale sarebbe ogni fluido più <lb></lb>grave dell&#039;aria, v. </s>

<s>g. </s>

<s>il vino, e però, infondendo intorno a quel globo d&#039;acqua <lb></lb>del vino, se gli potrebbe alzare intorno intorno, senza che le parti dell&#039;acqua, <lb></lb>conglutinate dall&#039;interna viscosità, si dividessero. </s>

<s>Ma ciò non accade egli, <lb></lb>anzi non prima se gli accosterà il liquido sparsogli intorno, che, senza aspet­<lb></lb>tar che molto se gli elevi intorno, si dissolverà e spianerà, restandogli di <pb xlink:href="020/01/3354.jpg" pagenum="315"></pb>sotto, se sarà vino rosso. </s>

<s>È dunque esterna, e forse dell&#039;aria ambiente, la <lb></lb>cagione di tale effetto ” (ivi, pag. </s>

<s>73). </s></p><p type="main">

<s>Le cose, che Galileo soggiunge intorno alla gran dissensione tra l&#039;aria <lb></lb>e l&#039;acqua, dimostrata per l&#039;esperienza della palla di cristallo, dall&#039;angustis­<lb></lb>simo foro della quale l&#039;acqua stessa contenutavi è proibita d&#039;uscir fuori dal­<lb></lb>l&#039;aria ambiente, e no dal vino; par che non si riferiscano direttamente ai <lb></lb>fenomeni capillari. </s>

<s>Ma vedremo come s&#039;invocassero opportunamente nella <lb></lb>Scuola galieiana, a spiegar il salir l&#039;acqua, e l&#039;abbassarsi il mercurio in­<lb></lb>torno ai corpi solidi, e nell&#039;interno dei sottilissimi tubi. </s></p><p type="main">

<s>L&#039;altro vento, che si diceva essersi sollevato a spazzare il chicco del <lb></lb>grano, rimasto fra le pule della Fisica peripatetica, veniva non meno ga­<lb></lb>gliardamente soffiato dalle guance del Cartesio, il quale, a legger che Gali­<lb></lb>leo confessava di non sapere il negozio delle gocciole d&#039;acqua, che così ro­<lb></lb>tonde stanno sulle foglie de&#039;cavoli; se ne fece gran maraviglia, tanto più <lb></lb>ch&#039;egli presumeva di aver nelle sue <emph type="italics"></emph>Meteore<emph.end type="italics"></emph.end> già spiegato il fatto abbastanza. <lb></lb></s>

<s>“ Dicit Galileus se ignorare causam, quae guttas aquae super brassicis su­<lb></lb>stentet, quam quidem in Meteoris meis satis explicui ” (<emph type="italics"></emph>Epistolar.,<emph.end type="italics"></emph.end> P. II, <lb></lb>Amstelodami 1682, pag. </s>

<s>279). </s></p><p type="main">

<s>Andiamo a cercare i discorsi <emph type="italics"></emph>Delle meteore,<emph.end type="italics"></emph.end> e leggiamo per curiosità <lb></lb>quel che dice il Cartesio essere ragion certissima del formarsi le gocciole <lb></lb>dell&#039;acqua esattamente rotonde. </s>

<s>“ La matiere subtile coulant par les pores <lb></lb>des autres cors, en mesme façon qu&#039;une rivìere par les intervalles des her­<lb></lb>bas, qui croissent en son lit, et passant plus librement d&#039;un endroit de l&#039;air <lb></lb>en l&#039;autre, et d&#039;un endroit de l&#039;eau aussy en l&#039;autre, que de l&#039;air en l&#039;eau <lb></lb>au reciproquement de l&#039;eau en l&#039;air, comme il a esté ailleurs remarqué; elle <lb></lb>doit tournoyer au dedans de ce goutte, et aussi au dehors en l&#039;air qui l&#039;en­<lb></lb>vironne, mais d&#039;autre mesure qu&#039;au dedans, et par ce moyen disposer en <lb></lb>rond toutes les parties de sa superficie. </s>

<s>Car elles ne peuvent manquer d&#039;obeir <lb></lb>a ses mouvemens, d&#039;autant que l&#039;eau est un cors liquide. </s>

<s>Et sans doute cecy <lb></lb>est suffisant pour faire entendre que les gouttes d&#039;eau doivent estre exacte­<lb></lb>ment rondes ” (<emph type="italics"></emph>Discours de la methode,<emph.end type="italics"></emph.end> a Leyde 1637, pag. </s>

<s>205). </s></p><p type="main">

<s>Non resulta dai documenti osservati da noi se il Cartesio estendesse lo <lb></lb>studio dell&#039;azion capillare anche alle altre forme, sotto cui suole manifestarsi, <lb></lb>e principalmente alla salita de&#039;liquidi nei sottilissimi cannellini, ma i seguaci <lb></lb>di lui trovaron facile modo a spiegare il fatto, ricorrendo a quelle flessuosità <lb></lb>anguilliformi, che a tutte le particelle componenti i liquidi aveva per loro <lb></lb>proprietà naturale assegnate il Maestro. </s>

<s>Così, per via di questi moti intestini, <lb></lb>e della pressione dell&#039;aria, ora accomunandosi dalle due scuole del Cartesio <lb></lb>e di Galileo gli argomenti, ora adoprandoli ciascuna per sè divisi, s&#039;inco­<lb></lb>minciò, e si prosegul per varie vicende a dare scienza de&#039;fenomeni capillari, <lb></lb>ripudiata ogni idea di attrazion calamitica fra le particelle della materia. </s></p><p type="main">

<s>Ai nostri Accademici fiorentini, così aborrenti dalle girandole cartesiane, <lb></lb>fu sufficiente invocare l&#039;azion dell&#039;aria, suggerita già dal loro Galileo, e con­<lb></lb>fermata dall&#039;esperienza del Torricelli. </s>

<s>Com&#039;era possibile infatti, colla mente <pb xlink:href="020/01/3355.jpg" pagenum="316"></pb>com&#039;avevano piena del grande avvenimento, che vedendo una così grande <lb></lb>analogia tra il sostenersi l&#039;acqua nel cannellino, e il mercurio nel tubo, non <lb></lb>pensassero che si dovessero attribuire i due effetti a somiglianti cagioni? </s>

<s>Nè <lb></lb>la somiglianza era difficile a ravvisarsi, perchè, se sopra il tubo chiuso ri­<lb></lb>mane il vuoto, sopra il cannellino aperto riman l&#039;aria, debilitata, per le an­<lb></lb>gustie in cui si trova, d&#039;esercitare il libero momento della sua spira, e perciò <lb></lb>qua e là, prevalendo similmente il peso dell&#039;aria esterna, la diversità delle <lb></lb>pressioni sembrava dover esser giusta causa proporzionata delle differenti al­<lb></lb>tezze, a cui giungono il mercurio e l&#039;acqua ne&#039;due diversi strumenti. </s>

<s>Vero <lb></lb>è bene che quella prima compiacenza venne presto amareggiata dai dubbi, <lb></lb>non potendosi star sicuri nella verità della supposta ragione, senza prima <lb></lb>esaminar diligentemente come la cosa procedesse nel vuoto. </s>

<s>Ma il vuoto, come <lb></lb>sempre s&#039;usò di fare a Firenze, per via cioè del tubo torricelliano, senza <lb></lb>l&#039;uso diretto della Macchina pneumatica, prolungò a que&#039;dubbi l&#039;agonia, non <lb></lb>finita se non in quella sentenza, che i Nostri accademici furono costretti di <lb></lb>sottoscrivere, della loro propria condanna. </s></p><p type="main">

<s>Ma mentre fiorivano ancora le prime speranze, corse voce di questa in­<lb></lb>gerenza dell&#039;aria in sostenere i liquidi ne&#039;sottilissimi tubi, e giuntane la no­<lb></lb>tizia alle orecchie del Boyle, fu giudicata da lui una congettura ingegnosa. </s>

<s><lb></lb>L&#039;uso che egli, come inventore, faceva assiduo della Macchina pneumatica, <lb></lb>sembrava che dovesse affrettare la decisione della sentenza, ma qui occorre <lb></lb>un fatto singolare. </s>

<s>Il Boyle è così lusingato anch&#039;egli da quella congettura, <lb></lb>e n&#039;è si geloso, che quasi non vorrebbe venissero gli occhi a disingannarlo, <lb></lb>infirmandone il valore della testimonianza col dire che, sebbene avesse usato, <lb></lb>invece dell&#039;acqua vin rosso, quel sottilissimo filettino nulladimeno <emph type="italics"></emph>aegre per­<lb></lb>ceptibilis erat<emph.end type="italics"></emph.end> attraverso alla crassizie del vetro. </s>

<s>Come poi questo detto si <lb></lb>concilii con ciò che immediatamente soggiunge “ quantum autem nos digno­<lb></lb>scere potuimus nulla magna inde (cioè dall&#039;essere il tubo sotto la campana <lb></lb>della Macchina pneumatica) liquori contigit alteratio ” da quando cioè era al­<lb></lb>l&#039;aperto; non si comprende, senz&#039;ammetter che il Boyle fosse allora preoc­<lb></lb>cupato dal timore che la realtà de&#039;fatti si mostrasse ritrosa d&#039;accomodarsi <lb></lb>a secondare le lusinghe della ragione. </s></p><p type="main">

<s>In qualunque modo, par ch&#039;egli dica, se non si vogliono far gli occhi <lb></lb>complici di queste lusinghe, confessiamo liberamente che l&#039;altezza del liquido <lb></lb>non si muti, per passar che si faccia il cannello dall&#039;aria aperta sotto la <lb></lb>campana della Macchina pneumatica: non è per questo che si debba renun­<lb></lb>ziare alla congettura, perchè l&#039;aria non è tolta affatto dal recipiente, ma vi <lb></lb>riman rarefatta, onde essendo così debilitata la forza della sua spira propor­<lb></lb>zionatamente sopra la superficie del liquido nel vaso dell&#039;immersione, e nel <lb></lb>cannellino; non è maraviglia se il fatto ne&#039;due casi si mostra inalterato. <lb></lb></s>

<s>“ Quod ideo minus admirandum videbatur quod illius aeris spira, quae aquam <lb></lb>in tubo deprimere posset, aeque fuit debilitata cum ea, quae superficiei aquae, <lb></lb>in parvo vitro contentae, innixa permansit ” (<emph type="italics"></emph>Nova experimenta physico­<lb></lb>mechanica, Op. </s>

<s>omnia,<emph.end type="italics"></emph.end> T. </s>

<s>I cit., pag. </s>

<s>82). </s></p><pb xlink:href="020/01/3356.jpg" pagenum="317"></pb><p type="main">

<s>Per conferma di che il Boyle aggiunge l&#039;esperienza del riseder l&#039;acqua <lb></lb>a un tratto, aspirando l&#039;aria con la bocca applicata alla sommità del can­<lb></lb>nello, e conclude il suo discorso così, inserendo fra parentesi, a questi argo­<lb></lb>menti derivati dalla scuola di Galileo, quegli altri, che venivano suggeriti <lb></lb>dalla scuola del Cartesio: “ Quocirca in ingeniosae illius coniecturae patro­<lb></lb>cinium, qui isthoc de quo hic agitur phaenomenon vertendum duxerit po­<lb></lb>tentiori in aquam pressioni aeris, qui extra tubum erat, quam qui intra eum­<lb></lb>dem, ubi tantum aquae (quae ex corpusculis forsitan flexilioribus, et facilius <lb></lb>internis vitri superficiebus cedentibus corpusculis constare possit) lateribus <lb></lb>erat contiguum; ostensum est quod, si parvulum illud vas vitreum, quod <lb></lb>aquam cuius pars in exilem illud siphonem ascenderat continebat, ita occlu­<lb></lb>deretur, ut quis ore suo inde posset aerem exugere, aqua in exilem tubum <lb></lb>elata derepente subsideret. </s>

<s>Quod quidem arguere videretur priorem illius <lb></lb>ascensum a pressione sola aeris incumbentis fuisse ortum, nisi (quam iuste <lb></lb>non statuo) obiici posset hoc fortasse non eventurum, si superius tubi extre­<lb></lb>mum in vacuo sisteretur ” (ibid.). </s></p><p type="main">

<s>Si sente bene che il Boyle, benchè se ne sia con ogni arte schermito, <lb></lb>si trova tuttavia assalito dal dubbio, nè trovando modo a liberarsene, abban­<lb></lb>dona l&#039;argomento, rimettendo il discuterne ulteriormente a cui <emph type="italics"></emph>non desit <lb></lb>otium.<emph.end type="italics"></emph.end> “ Utcumque, hoc unum te velim commonifacere quod, si speculatio­<lb></lb>nem hane tibi adlubescat ulterius prosequi, ad rem etiam erit excrutari quo <lb></lb>pacto fiat quod aquae superficies, ut in tubis est manifestum, soleat esse con­<lb></lb>cava, in medio scilicet depressior, in lateribus altior. </s>

<s>Et e contra qui fiat <lb></lb>quod in hydrargyrio, non solum convexa sit in medio atque illic intumescat <lb></lb>superficies, verum, si exilioris tubi extremum ei immergas, superficies liquo­<lb></lb>ris intra tubum, quam axtra eumdem, erit depressior ” (ibid.). Così venivano <lb></lb>a proporsi due capitalissimi problemi, de&#039;quali è notabile che il proponente <lb></lb>solo riconoscesse l&#039;importanza, sfuggita forse all&#039;attenzione di tutti, per la <lb></lb>difficoltà che appariva in voler risolverli nelle loro ragioni, le quali non si <lb></lb>sarebbero potute dedurre, come il Boyle sperava, nè dalla figura de&#039;corpu­<lb></lb>scoli mercuriali, nè dalla fabbrica delle particelle elastiche dell&#039;aria. </s>

<s>Questi <lb></lb>argomenti, temperati alla fucina del Cartesio, troppo erano deboli e spropor­<lb></lb>zionati all&#039;effetto, ond&#039;esso Boyle avrebbe dovuto ancora aspettare un mezzo <lb></lb>secolo, prima di vedere adempito il suo voto. </s></p><p type="main">

<s>Il modo, come dal celebre uomo trattavasi l&#039;argomento, pareva studiato <lb></lb>apposta, per disanimare chiunque avesse osato d&#039;entrar con lui nell&#039;arringo, <lb></lb>come di fatto avvenne per qualche tempo, infin tanto che Roberto Hook, <lb></lb>amico al Boyle, connazionale e collega, presa occasione dal XXXV esperi­<lb></lb>mento fisico-meccanico, non tolse via gli scrupoli, confortandolo di nuove ra­<lb></lb>gioni, e studiandosi di persuadere che precipua causa del salire i liquidi su <lb></lb>per i sottilissimi tubi non era altra veramente, che la pressione dell&#039;aria. </s></p><p type="main">

<s>Intanto che si sgombravano così i sentieri ai progressi boileiani, il Gri­<lb></lb>maldi, che non addetto a nessuna delle due Scuole dominanti faceva parte <lb></lb>da sè, e con più libertà forse, ma certo con più acume degli altri contem-<pb xlink:href="020/01/3357.jpg" pagenum="318"></pb>plava gli spettacoli della Natura; dava del fenomeno capillare una spiega­<lb></lb>zione molto semplice, benchè non fosse la vera. </s>

<s>Persuaso, in mezzo alle con­<lb></lb>troversie che s&#039;agitavano allora, tenersi insieme le particelle dell&#039;acqua per <lb></lb>una certa loro viscosità naturale, considerava che il sottilissimo filetto liquido, <lb></lb>per questa stessa viscosità e per la piccolezza delle sue parti, non poteva <lb></lb>conglobarsi a premere con tutta la libertà del suo peso, sostenuto com&#039;è fra <lb></lb>le angustie della concava parete: ond&#039;è che l&#039;acqua, nel vaso ampio e nella <lb></lb>fistola, non possa consistere in equilibrio, se non a patto che la maggiore <lb></lb>altezza compensi la subita diminuzione del momento gravitativo. </s>

<s>“ Cogitan­<lb></lb>dum est non aeque ponderare aquam utramque, illam scilicet quae in fistula <lb></lb>includitur, et illam quae in vase extra fistulam. </s>

<s>Quamvis enim per se et na­<lb></lb>tura sua utraque aequaliter gravitet, per accidens tamen quae in fistula con­<lb></lb>tinetur minus gravitat, co quod sustinetur ab interna cavitate fistulae, et a <lb></lb>difficultate defluxus iam explicata. </s>

<s>Igitur non debet utraque aqua consistere <lb></lb>in aequilibrio, sed potius, compensatis momentis gravitationis, ea quae in vase <lb></lb>continetur utpote gravior, debet se totam ita dimittere, ut subingrediendo <lb></lb>per imum fistulae immersae pellat sursum eam, quae in fistula continetur, <lb></lb>et haec suapte, ut tamquam levior, debet altius evehi ” (<emph type="italics"></emph>De lumine<emph.end type="italics"></emph.end> cit., <lb></lb>pag. </s>

<s>106, 7). </s></p><p type="main">

<s>Ricordiamoci però che il Grimaldi non intendeva di trattar di proposito <lb></lb>de&#039;fenomeni capillari, contento a risolvere il problema dell&#039;attrarsi nella zuppa <lb></lb>il vino alla midolla del pane, in mezzo a cui diceva formarsi, dalla conti­<lb></lb>nuità de&#039;pori, l&#039;intricato laberinto di tanti sottilissimi tubi. </s>

<s>Lasciava perciò <lb></lb>l&#039;Autore a desiderar la ragione del vedersi fare al mercurio contrari effetti <lb></lb>a quelli dell&#039;acqua e del vino, come pure lasciava in desiderio di sapere il <lb></lb>perchè di tanti altri fatti curiosi, che in questo stesso genere s&#039;erano speri­<lb></lb>mentati. </s>

<s>D&#039;onde avvenne che pensasse di soddisfare a un tal desiderio Isacco­<lb></lb>Vossio, il quale attribui alla viscosità dell&#039;acqua e all&#039;aderenza di lei al vetro <lb></lb>(per cui ella viene a privarsi del proprio peso) il risalir ch&#039;ella fa sul li­<lb></lb>vello ordinario. </s>

<s>“ Quia vero caret pondere attollitur et expellitur supra libra­<lb></lb>mentum ambientis aquae ” (<emph type="italics"></emph>De Nili origine,<emph.end type="italics"></emph.end> Hagae Comitis 1666, pag. </s>

<s>6). <lb></lb>Al mercurio poi, mancando questa viscosità e aderenza, non fa maraviglia <lb></lb>se invece di alzarsi, per le angustie del tubo che ne retundono il moto, si <lb></lb>abbassa. </s>

<s>“ Cum vero hydrargyrius careat illa viscositate, minimeque adhae­<lb></lb>reat, et insuper conatus ille qui aequilibrium adfectat retardetur, et retun­<lb></lb>datur ab angustia fistulae exilioris; nequaquam mirum videri debet si mi­<lb></lb>nus alte in fistulis quam in spatiis latis et minus in minutis quam in laxis <lb></lb>ascendat canalibus ” (ibid.). </s></p><p type="main">

<s>Il Vossio aveva avvertita questa legge, che cioè le depressioni del mer­<lb></lb>curio e le altezze dell&#039;acqua nei cannelli stanno in ragion reciproca delle se­<lb></lb>zioni, e come i nostri Accademici di Bologna la dimostrarono sperimental­<lb></lb>mente, così egli, il Vossio, fu il primo a riconoscerne la causa, geometrica­<lb></lb>mente concludendola dal principio che i corpi piccoli hanno, a proporzione <lb></lb>delle moli, superficie maggiore dei grandi. </s>

<s>“ Quod autem quanto fiant mi-<pb xlink:href="020/01/3358.jpg" pagenum="319"></pb>nutiores fistulae, tanto altius ascendat aqua, huius rei ratio est manifesta. </s>

<s><lb></lb>Quemadmodum enim minora corpora maiorem habent superficiem respectu <lb></lb>suae molis, quam magna; similiter etiam minores canales plura habent puncta <lb></lb>contactus, ratione sui spatii, quam maiores. </s>

<s>Quanto autem plus superficiei, <lb></lb>pluraque contactus sunt puncta, tanto facilius aqua adhaeret ” (ibid.). </s></p><p type="main">

<s>A ripensare che questa è la ragion medesima del Borelli e del Newton, <lb></lb>e che nessun altro a que&#039;tempi aveva nè più facilmente, nè più compiuta­<lb></lb>mente del Vossio spiegati i fenomeni capillari; ognuno s&#039;aspetterebbe di sen­<lb></lb>tir dire che con applauso fossero accolti gl&#039;insegnamenti di lui. </s>

<s>Noi invece <lb></lb>siam qui per annunziare che quella accoglienza se l&#039;ebbe tutta il Boyle. </s>

<s>La <lb></lb>preferenza, che non si saprebbe a primo aspetto spiegare, si comprende poi <lb></lb>facilmente, ripensando all&#039;efficacia, che dovette avere sul giudizio di tutti i <lb></lb>fisici la somiglianza tra il barometro, e questi tubi capillari: efficacia, che <lb></lb>l&#039;Hook contribuì a rendere più potente, sia riducendo il fatto a rappresen­<lb></lb>tarsi inalterato o in mezzo all&#039;aria naturale o in mezzo alla rarefatta dentro <lb></lb>la campana della Macchina pneumatica, sia dicendo il perchè l&#039;aria stessa <lb></lb>o naturale o rarefatta preme assai meno sulla superficie della fistola stretta, <lb></lb>che dell&#039;ampia del vaso. </s>

<s>Il Boyle aveva appena accennato che questa minor <lb></lb>pressione dipendeva dall&#039;essere l&#039;elaterio dell&#039;aria impedito dalla troppa an­<lb></lb>gustia dello spazio, ma l&#039;Hook sostituì a questa meccanica l&#039;altra causa fisica <lb></lb>dell&#039;affinità al vetro, che l&#039;aria mostra di aver sempre minore dell&#039;acqua. </s>

<s>I <lb></lb>principii insomma dell&#039;Hook si riducevano a questi due: “ I.o Quod inae­<lb></lb>qualis aeris incumbentis pressura efficiat inaequalem altitudinem in superfi­<lb></lb>ciebus aquarum, id quod experimento probatur, ope inversi siphonis vitrei, <lb></lb>cui, si indatur aliqua quantitas aquae, et applicato ore ad alteram eius extre­<lb></lb>mitatem leniter infletur; statim elevatur in opposito erure aquae superficies, <lb></lb>et si leniter sugatur statim deprimitur. </s>

<s>II.o Quod in his phaenomenis occur­<lb></lb>rat eiusmodi inaequalis aeris pressura, et illa quidem oriunda ex maiore non <lb></lb>conformitate, seu incongruitate aeris ad vitrum, quam aquae ad idem vitrum. </s>

<s>” </s></p><p type="main">

<s>Questi due principii dell&#039;Hook, così come gli abbiamo trascritti, si leg­<lb></lb>gono formulati a pag. </s>

<s>82 del <emph type="italics"></emph>Collegium experimentale<emph.end type="italics"></emph.end> di Cristoforo Sturm, <lb></lb>a cui siam debitori delle seguenti notizie storiche: “ Post Boylium quidam <lb></lb>eius cultor R. H. (non sappiamo perchè siasi attorzato in questo monogramma <lb></lb>il fulgor del nome di Roberto Hook) occasione arrepta ex ipso illo experi­<lb></lb>mento XXXV, quod sub initium citavimus anglico scrmone, observationis no­<lb></lb>vellae causam hypothesi peculiari declarare conatus est, quam in latinum <lb></lb>sermonem conversam anno 1662 edidit quidam M. Bohem, sub inscriptione <lb></lb><emph type="italics"></emph>Conatus ad explicanda phaenomena notabilia, in Experimento publicato <lb></lb>ab honorabili viro Roberto Boyle ”<emph.end type="italics"></emph.end> (<emph type="italics"></emph>Colleg. </s>

<s>experim.,<emph.end type="italics"></emph.end> Norimbergae 1676, <lb></lb>pag. </s>

<s>78). </s></p><p type="main">

<s>La spiegazion del fenomeno, qual si leggeva nell&#039;opuscolo del Bohem, <lb></lb>lo Sturm la dice <emph type="italics"></emph>nostrae quidem cognatam,<emph.end type="italics"></emph.end> ma prima che in Germania <lb></lb>s&#039;era diffusa in Francia, e in Italia, quando ancora i progressi, diretti dal­<lb></lb>l&#039;Hook, non erano venuti ad arrestarsi innanzi all&#039;esperienze degli Accade-<pb xlink:href="020/01/3359.jpg" pagenum="320"></pb>mici fiorentini. </s>

<s>Per quel che riguarda i Francesi il Monconys ci lasciò larga <lb></lb>copia di documenti. </s>

<s>Descrivendo il suo viaggio erudito in Inghilterra, narra <lb></lb>come una mattina del Giugno 1663 partì di Londra, in carrozza, insieme col <lb></lb>suo proprio figlio e coll&#039;Oldemburg, per andare a far visita al Boyle, che vil­<lb></lb>leggiava a tre miglia di distanza. </s>

<s>Entrato in discorso de&#039;mirabili effetti, che <lb></lb>s&#039;osservano nei tubi capillari, il Boyle, riferita l&#039;opinion di coloro che gli at­<lb></lb>tribuivano all&#039;aria, concludeva <emph type="italics"></emph>que estoit la veritable.<emph.end type="italics"></emph.end> (<emph type="italics"></emph>Journal des voyages,<emph.end type="italics"></emph.end><lb></lb>seconde partie, a Lion 1666, Voyage d&#039;Angleterre, pag. </s>

<s>44). Poi riferì agli <lb></lb>ospiti quel che un amico suo ne pensava della convenienza che l&#039;acqua ha <lb></lb>col vetro, maggiore dell&#039;aria, affermando <emph type="italics"></emph>que la pensee luy plaisoit fort<emph.end type="italics"></emph.end> (ivi). </s></p><p type="main">

<s>Inspirato da queste dottrine, attinte in Inghilterra, il Monconys scrisse <lb></lb>un suo trattatello <emph type="italics"></emph>De humidorum aequilibrio in syphonibus,<emph.end type="italics"></emph.end> dove, propo­<lb></lb>nendosi un sifone, sull&#039;andare di quello rappresentato da noi nella figura 157, <lb></lb>dimostrava che, dato premer l&#039;aria alquanto meno nel cannello stretto che <lb></lb>nel più largo, il liquido deve in quello risalire a maggiore altezza che in <lb></lb>questo. </s>

<s>“ Aer autem potest minus gravitare in angustioribus, quam in latio­<lb></lb>ribus tubis, ex multiplici capite. </s>

<s>Primum, si moleculae, quibus texitur aer, <lb></lb>et quae perpetuo motu cientur, ut in sole videre est, non possint in exilio­<lb></lb>ribus tubis perinde agitari et moveri, propter angustias loci, uti moventur <lb></lb>in latioribus, sicuti librae vel staterae pondera, dum quiescunt, minus gra­<lb></lb>vitare: ubi autem moventur, magis ponderare quotidie cernimus. </s>

<s>” </s></p><p type="main">

<s>“ Deinde cum superficies tuborum, sicut omnium corporum, sint aspe­<lb></lb>rae et salebrosae, ita ut quaedam partes caeteris promineant, fieri potest ut <lb></lb>illae partes prominentes sistant, et morentur gravitatem superioris aeris, ideo­<lb></lb>que procul dubio iuxta eas superficies aer suam gravitatem minus exercere <lb></lb>videbitur. </s>

<s>Unde, quo tubi plus superficiei habebunt, plus etiam in iis de­<lb></lb>trahitur ex gravitate aeris, quem continent. </s>

<s>Et quia, quo tubi eiusdem alti­<lb></lb>tudinis angustiores evadunt, plus habent superficiei, respectu aliorum (nam <lb></lb>capacitates eorum decrescunt in ratione duplicata diametrorum, superficies <lb></lb>autem solum ut diametri, et sic duplo magis decrescunt soliditates quam su­<lb></lb>perficies corum) ergo in tubis exilioribus, hoc est minoris diametri, plus de­<lb></lb>trahetur ex gravitate aeris, propter obicem factum a superficiei salebris, quam <lb></lb>in tubis latioribus. </s>

<s>Ideoque minus gravitabit aer in exiliori tubo quam in <lb></lb>patentiori ” (<emph type="italics"></emph>Journal des voyages,<emph.end type="italics"></emph.end> III partie, a Lion 1666, pag. </s>

<s>31, 32). </s></p><p type="main">

<s>A questo trattatello latino succede un discorso accademico <emph type="italics"></emph>Sur l&#039;ascen­<lb></lb>sion de l&#039;eau sur un niveau en un tuyau estroit,<emph.end type="italics"></emph.end> dove, confermata la sua <lb></lb>propria opinione, il Monconys riferisce quella di parecchi altri suoi colleghi, <lb></lb>fra&#039;quali il Tornier <emph type="italics"></emph>docte personnage et sçavant philosophe<emph.end type="italics"></emph.end> è notabile per <lb></lb>la novità del pensiero. </s>

<s>“ Il disoit que l&#039;air, de sa nature estant plus chaud <lb></lb>que l&#039;eau, si tost qu&#039;on appliquoit le tuyau sur l&#039;eau elle communiquoit la <lb></lb>froideur et au verre du tuyau, et a l&#039;air qui y estoit contenu, le quel par <lb></lb>cette froideur se condensoit: que la condensation, se faisant de la circum­<lb></lb>ference au centre, tout l&#039;air se reduisoit en un petit cylindre, au milieu de <lb></lb>canal du tuyau, et laissoit tout autour de luy un vuide, ou l&#039;eau se pouvoit <pb xlink:href="020/01/3360.jpg" pagenum="321"></pb>introduire iusques au haut du tuyau. </s>

<s>Mas parce qu&#039;en montant ainsi entre <lb></lb>le cylindre d&#039;eau, et le canal du tuyau, l&#039;air qu&#039;elle eust enveloppé estoit <lb></lb>d&#039;une nature plus legere qu&#039;elle, il estoit obligé de remonter iusques en haut, <lb></lb>et l&#039;eau occupoit apres ou en mesme temps toute la place qu&#039;il quittoit, et <lb></lb>montoit ainsi tres-promptement apres luy en le chassant, a mesure qu&#039;il le <lb></lb>condensoit ” (ivi, pag. </s>

<s>15, 16). </s></p><p type="main">

<s>Questa sottile ragione, soggiunge il Monconys, <emph type="italics"></emph>n&#039;est plus considerable, <lb></lb>apres avoir l&#039;experience de l&#039;ascension de l&#039;eau chaude,<emph.end type="italics"></emph.end> e termina con un <lb></lb>elenco delle varie ragioni pensate in così difficile soggetto dal Roberval, dal <lb></lb>Rò, dall&#039;Ausoul, dal Pecquet, dal De Mommor. </s>

<s>Il Roberval la pensava presso <lb></lb>a poco come il nostro Grimaldi, attribuendo il fatto alla viscosità del liquido, <lb></lb>che lo fa aderire alle pareti del tubo, ma il Rò cartesiano rifletteva che, non <lb></lb>potendosi il liquido intestinamente agitato spandersi orizontalmente per lo <lb></lb>largo, essendo impedito, si sfoga dirigendosi tutto su in alto. </s>

<s>L&#039;Ausoul si ri­<lb></lb>scontrò co&#039;pensieri del nostro Rossetti, ammettendo ora una convenienza, ora <lb></lb>una disconvenienza del liquido con la materia del tubo, mentre il Pecquet, <lb></lb>non sapendo rinunziare all&#039;azione dell&#039;aria, diceva che nel tubo stretto ri­<lb></lb>man sospesa, come lo stoppaccio dentro la canna di uno schizzatoio, e perciò <lb></lb>fa sopra il liquido sottoposto minore la sua presssione. </s>

<s>Il De Mommor final­<lb></lb>mente “ dit presque la mesme chose de la diversité de la nature de l&#039;air, <lb></lb>dont les parties grossieres ne peuvent entrer dans un petit canal, les quel­<lb></lb>les entrent bien dans un gros et de plus que les parties du premier element <lb></lb>cartesien, poussant esgalement de tous les costes toutes les parties du troi­<lb></lb>sieme element; les plus grosses de ce troisieme sont plus agitees, et les pe­<lb></lb>tites moins. </s>

<s>Ainsi l&#039;air du petit tuyau, resistant moins au mouvement, qui <lb></lb>luy vient d&#039;en bas, est contraint de ceder, et de faire place a l&#039;eau, qui est <lb></lb>poussée par le grand air ambient ” (ivi, pag. </s>

<s>37, 38). </s></p><p type="main">

<s>Manca nell&#039;elenco del Monconys Onorato Fabry, il quale, come a tutte <lb></lb>le altre idee, così dava anche a questa la stampa mostruosa del suo cer­<lb></lb>vello. </s>

<s>I raggi aerei prementi, immaginati da lui a spiegare il flusso marino, <lb></lb>son quelli stessi che invoca per i fenomeni capillari, prendendo per princi­<lb></lb>pio che, tanto più premono i detti raggi, quanto concorrono con angolo meno <lb></lb>acuto. </s>

<s>Di qui conclude “ aquam attolli altius in longiore canaliculo: nempe <lb></lb>in longiore angulus pressionis acutior et minor est, quam in breviore ” (<emph type="italics"></emph>De <lb></lb>motu Terrae,<emph.end type="italics"></emph.end> Lugduni 1665, pag. </s>

<s>162). <lb></lb><figure id="id.020.01.3360.1.jpg" xlink:href="020/01/3360/1.jpg"></figure></s></p><p type="caption">

<s>Figura 161.</s></p><p type="main">

<s>Con questi medesimi principii non dubita di risolvere il <lb></lb>problema proposto dal Boyle perchè la superficie dell&#039;acqua <lb></lb>nel cannellino sia concava. </s>

<s>Risponde che, supposto essere il <lb></lb>cannellino AC (fig. </s>

<s>161) l&#039;acqua in D, essendo più premuta <lb></lb>che in H e in K, perchè l&#039;angolo ADB è maggiore di AHB, <lb></lb>e anche di AKB, <emph type="italics"></emph>ut patet ex geometria<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>163); non <lb></lb>fa maraviglia che in D la superficie dell&#039;acqua sia più de­<lb></lb>pressa. </s>

<s>Eppure ei si compiace di aver prescrutata così la causa <lb></lb>di un effetto sì pellegrino, <emph type="italics"></emph>nec erediderim ab ullo uspiam proditum fuisse.<emph.end type="italics"></emph.end><pb xlink:href="020/01/3361.jpg" pagenum="322"></pb>Anzi ne poteva esser certo, come era certo d&#039;esser superiore agli altri nella <lb></lb>ricchezza delle invenzioni, di così facile acquisto per lui, che ai fogli raccat­<lb></lb>tati nella spazzatura dava il valore dei biglietti di banca. </s></p><p type="main">

<s>Si potrebbero aggiungere a queste le ragioni, che dava il Fabry, del <lb></lb>deprimersi il mercurio intorno alle pareti del tubo, per non avere, diceva, <lb></lb>ad esso aderenza, la quale, dipendendo secondo lui dall&#039;entrar che fa il li­<lb></lb>quido nella cavità delle strie, e per le boccuzze de&#039;pori del vetro “ certe <lb></lb>mercurius, prae crassitudine, in eas angustias sese minime ingerit ” (ibid., <lb></lb>pag. </s>

<s>169). Ma basti questo a dimostrar lo stato della cultura, che ebbe a <lb></lb>que&#039;tempi la Fisica de&#039;capillari appresso i Francesi. </s></p><p type="main">

<s>Fra&#039;nostri abbiamo in primo luogo a citare il Montanari. </s>

<s>Qualunque <lb></lb>siano le pretese relazioni, ch&#039;egli ebbe co&#039;fratelli Del Buono, è certo che <lb></lb>l&#039;indirizzo a questi studii l&#039;ebbe, come tutti gli altri, dagli Sperimenti boi­<lb></lb>leiani, i quali egli non ha appena citati, nel principio del suo discorso, che <lb></lb>immediatamente soggiunge. </s>

<s>“ E veramente il Boyle, come ingegno che non <lb></lb>così di tutto s&#039;appaga sinceramente, ha confessato la difficoltà della questione, <lb></lb>ed accennando solo alcuna cosa circa la pressione maggiore dell&#039;aria esterna, <lb></lb>che dell&#039;interna al cannellino sopra l&#039;acqua sottoposta, vi frammette in pa­<lb></lb>rentesi non so che della flessibilità delle particole acquee, che meglio s&#039;adat­<lb></lb>tano al vetro, e senza dilatarsi a spiegare più oltre i suoi pensieri, lascia inde­<lb></lb>ciso il problema. </s>

<s>Onde piuttosto gli si deve la lode d&#039;aver tentando ricono­<lb></lb>sciuta, sebbene in dubbio, la via di scioglierlo, che di averlo perfettamente <lb></lb>disciolto ” (<emph type="italics"></emph>Pensieri fisico-matem.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>15). </s></p><p type="main">

<s>Il Montanari non crede dunque gli sia rimasto altro ufficio, che di dar <lb></lb>perfezione all&#039;opera altrui. </s>

<s>I due suoi nemici più fieri, Borelli e Rossetti, lo <lb></lb>censurarono aspramente, o per dir più giusto lo calunniarono, ma pure, in <lb></lb>mezzo agli errori, gli rimane un merito singolare, quello di essere stato il <lb></lb>primo e l&#039;unico, infino al Clairaut e al Laplace, a dare importanza al me­<lb></lb>nisco concavo, facendo principalmente da lui dipendere la salita dell&#039;acqua <lb></lb>ne&#039;sottilissimi tubi di vetro. </s>

<s>“ Perchè dunque vediamo l&#039;acqua, e altri li­<lb></lb>quidi che per i cannellini ascendono, tali essere che, o per la figura parti­<lb></lb>colare de&#039;loro minimi, o per la flessibilità dei medesimi, meglio s&#039;adattano <lb></lb>alla superficie di esso vetro, che non fa l&#039;aria; non sarà difficile da capire, <lb></lb>come, intorno alle sponde d&#039;un vaso, per necessità debbano sollevarsi più <lb></lb>dal livello che in mezzo, essendo che, per esser premuti nel mezzo dall&#039;aria <lb></lb>soprastante, sono forzati subentrare in tutti que&#039;luoghi, ove comodo loro rie­<lb></lb>sce d&#039;entrare, e dove meno resistenza essi trovano, di quello sia la pressione <lb></lb>che gli sospinge ” (ivi, pag. </s>

<s>34). </s></p><p type="main">

<s>E perchè si poteva dubitare che, sollevandosi le sole particelle contigue <lb></lb>al tubo, lascerebbero una cavità cilindrica, piuttosto che un menisco; il Mon­<lb></lb>tanari soggiunge che le dette particelle, a cagione della loro viscosità, non <lb></lb>solo conducono in alto le particelle sottoposte a perpendicolo “ ma molte <lb></lb>laterali ancora verso il mezzo del vaso, le quali nel sollevarsi incontrano la <lb></lb>gravità dell&#039;aria che li sovrasta, onde, tanto solamente si sollevano contro il <pb xlink:href="020/01/3362.jpg" pagenum="323"></pb>peso dell&#039;aria, quanto la forza di quell&#039;ultime, che sono immediate alla <lb></lb>sponda del vaso, può sollevarle ” (ivi, pag. </s>

<s>35, 36). </s></p><p type="main">

<s>Quanto ai contrari effetti, che si osservano nel mercurio, benchè il Mon­<lb></lb>tanari censuri l&#039;opinione del Fabry, dicendo che, se il liquido crasso trova <lb></lb>difficoltà a entrar ne&#039;pori e nelle strie del vetro, dovrebbe anche trovarla <lb></lb>simile nell&#039;uscire; non sa sostituirvi molto di meglio. </s>

<s>“ Non è punto inve­<lb></lb>risimle, egli dice, che siccome sono alcuni fluidi, che meglio s&#039;accomodano <lb></lb>alla superficie d&#039;alcuni corpi, che non fa l&#039;aria; così alcun altro si trovi che <lb></lb>peggio di lui vi s&#039;adatti, come sarebbe il mercurio. </s>

<s>Onde, siccome l&#039;acqua <lb></lb>s&#039;inalza alle sponde de&#039;vasi, per riempire li spazietti fra l&#039;aria e le sponde; <lb></lb>così, per le medesime ragioni, dovrà l&#039;aria appresso le medesime sponde <lb></lb>profondarsi, a riempir quelli che fra il mercurio e le sponde rimangono ” <lb></lb>(ivi, pag. </s>

<s>40, 41). </s></p><p type="main">

<s>La corrente delle idee, pel giro della quale abbiamo fin qui menati i <lb></lb>Lettori, ebbe, come si disse, gl&#039;impulsi dall&#039;Accademia del Cimento, rima­<lb></lb>sta tuttavia chiusa dalle porte del palazzo mediceo, che noi dobbiam pene­<lb></lb>trare. </s>

<s>Che la salita de&#039;liquidi nei cannellini fosse da attribuire alle pressioni <lb></lb>dell&#039;aria, fu opinione degli Accademici, infino dal 1658, quando, almeno per <lb></lb>avere investigate le ragioni del fatto, si compiacquero di restar superiori ai <lb></lb>Francesi. </s>

<s>Non poteva però la compiacenza essere assoluta, se quella loro opi­<lb></lb>nione non si vedeva confermata dalla esperienza, osservando quel che av­<lb></lb>viene, costituito lo strumento capillare nel vuoto. </s>

<s>E perchè i Nostri usarono <lb></lb>sempre di farlo col tubo torricelliano, dovettero incontrare quelle difficoltà, <lb></lb>delle quali fanno testimonianza gli stessi loro diari, relativi ai giorni 14, 15 <lb></lb>e 16 Giugno 1660, ne&#039;quali il frutto, che se ne raccolse, è confessato da <lb></lb>queste parole: “ Nulla però si potè ritrarre da tal maniera di praticare que­<lb></lb>ste esperienze ” (Targioni, <emph type="italics"></emph>Notizie<emph.end type="italics"></emph.end> cit., T. II, pag. </s>

<s>435). </s></p><p type="main">

<s>Letta la nota del Thevenot, e per essa facilmente persuasi che, rimasti <lb></lb>indietro ai Francesi per la copia delle osservazioni dei fatti, non s&#039;aveva <lb></lb>altra speranza di superiorità, che nella scoperta delle loro vere cagioni; gli <lb></lb>Accademici fiorentini, negli ultimi giorni del mese d&#039;Agosto 1662, ripresero <lb></lb>in mano l&#039;esperienze, che poi ridussero a tal perfezione, quale apparisce dalle <lb></lb>descrizioni del loro libro dei <emph type="italics"></emph>Saggi.<emph.end type="italics"></emph.end> I resultati, che così ottennero, erano de­<lb></lb>cisivi, non lasciando oramai più appiglio a introdur nella questione l&#039;aria <lb></lb>rarefatta, che, se può rimaner sotto la campana del Boyle, viene affatto <lb></lb>esclusa dal tubo del Torricelli. </s>

<s>E fu la decisione, come sappiamo, che il pre­<lb></lb>mer più languido, che fa l&#039;aria per gli angustissimi seni dei cannellini, non <lb></lb>sia per sè sola causa bastante a spiegare i loro effetti. </s></p><p type="main">

<s>Reciso così dalle radici il rigoglio dell&#039;ipotesi boileiana, la scienza dei <lb></lb>fenomeni capillari cadde d&#039;un colpo, e a rilevarla concorsero primi coloro <lb></lb>che, costretti da una certa fatale necessità, avevano menato la scure. </s>

<s>Il Ri­<lb></lb>naldini, uscito fuori dall&#039;Accademia, dette il primo pubblico documento della <lb></lb>restaurazione, la quale si faceva consistere nell&#039;ammetter che il liquido sale <lb></lb>su per il cannellino, perchè fra le angustie di lui molto perde del suo pro-<pb xlink:href="020/01/3363.jpg" pagenum="324"></pb>prio momento. </s>

<s>S&#039;era, egli dice, creduto da principio che la cosa dipendesse <lb></lb>dalla pressione dell&#039;aria, “ non autem sic se habet, nam idem contingit in <lb></lb>loco, ubi nullus aer, vel saltem adeo exiguae quantitatis, ne vix credas ei <lb></lb>quidquam deferendum, quod nos Florentiae sumus experti. </s>

<s>Sed potius aliunde <lb></lb>id provenit, quia scilicet dum exilis ille tubulus immergitur nonnihil in flui­<lb></lb>dum, huius pars inclusa in angustia ipsius tubuli multum amittit momenti, <lb></lb>unde nequit aeque ponderare partibus circumiacentibus, sed his urgentibus <lb></lb>prementibusque cylindrus ex humido intra tubuli angustiam cedit, eousque <lb></lb>ascendens, ut eius altitudo possit in aequilibrio esse cum cylindris ex humido <lb></lb>circumiacente. </s>

<s>Nihil enim refert, sive desuper premat, vel non premat aer ” <lb></lb>(<emph type="italics"></emph>De resolutione et compositione<emph.end type="italics"></emph.end> cit., pag. </s>

<s>160). </s></p><p type="main">

<s>D&#039;onde avvenga però che il liquido perde fra le angustie del cannellino <lb></lb>parte del suo momento, il Rinaldini non dice, ma supplisce al difetto il Bo­<lb></lb>relli, il quale narra che l&#039;opinioni proposte, esclusa quella di coloro che in­<lb></lb>vocavano la pressione dell&#039;aria, si riducevano a due: l&#039;una delle quali era <lb></lb>che l&#039;acqua non scendesse, rimanendo sospessa ne&#039;cannellini, per l&#039;asprezza <lb></lb>delle loro superficie; l&#039;altra che l&#039;acqua stessa salisse per impulso suo pro­<lb></lb>prio e naturale. </s>

<s>Questa opinione era merce straniera, insinuatasi nell&#039;Acca­<lb></lb>demia da&#039;cartesiani, al numero de&#039;quali apparteneva Luc&#039;Antonio Porzio, <lb></lb>che così scrisse: “ Sorge l&#039;acqua, nelle fistole molto anguste aperte da am­<lb></lb>bedue gli estremi, essendo elle umide alquanto, cioè contenendo ne&#039;loro pori, <lb></lb>appunto come se fossero piccole conchette, o acqua o altro licore analogo <lb></lb>all&#039;acqua, e vi sorge ella da sè stessa, in virtù del suo proprio momento, col <lb></lb>quale si unisce e mischia coll&#039;acqua contenuta ne&#039;pori delle fistole. </s>

<s>Laonde, <lb></lb>essendo elle molto anguste, di modo che l&#039;acqua da un lato di avvantaggio <lb></lb>possa toccar l&#039;acqua del lato opposto; se ne vedranno ripiene fin a cinque <lb></lb>o sei dita della loro longitudine e talora assai più ” (<emph type="italics"></emph>Del sorgimento de&#039;li­<lb></lb>cori<emph.end type="italics"></emph.end> cit., pag. </s>

<s>84). </s></p><p type="main">

<s>Il Borelli facilmente confutò queste due opinioni, proponendone una sua <lb></lb>propria, dietro il supposto che le molecole liquide siano rivestite di una certa <lb></lb>lanugine, i peli della quale entrando nella porosità delle pareti, e nelle emi­<lb></lb>nenze di esse ritrovando il convenevole appoggio, facessero le funzioni di <lb></lb>vette, e così venissero a sollevarsi via via le particelle stesse aderenti alle <lb></lb>dette pareti, in virtù di un tale macchinamento. </s>

<s>“ Quia aquae particulae, <lb></lb>adhaerentes parieti vasis, insinuant ramos suarum machinularum intra po­<lb></lb>rositates et foveolas parietis, a cuius eminentiis et asperitatibus fulciuntur <lb></lb>extremitates particularum aquae, quarum oppositi termini sustinentur, a su­<lb></lb>biecta collaterali aqua; propterea efficiuntur veluti totidem vectes, converti­<lb></lb>biles circa eorum fulcimenta, parieti annexa. </s>

<s>Hinc fit ut praedictae aquae <lb></lb>particulae exiguam vim compressivam exerceant, et minori momento su­<lb></lb>biectam aquam comprimant, cum partes aquae collaterales, libere premendo <lb></lb>supra aquam subiectam, integram suam vim et momentum exerceant. </s>

<s>Igi­<lb></lb>tur partes minus pressae sursum impelli debent a partibus magis compres­<lb></lb>sis ” (<emph type="italics"></emph>De motion. </s>

<s>natur.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>371). </s></p><pb xlink:href="020/01/3364.jpg" pagenum="325"></pb><p type="main">

<s>Prosegue il Borelli ad applicare la meccanica di questi moti alla spie­<lb></lb>gazione dei vari fenomeni, osservati nelle fistole capillari, e finalmente riserba <lb></lb>il capitolo IX dell&#039;opera a trattar dell&#039;amplesso e della fuga de&#039;corpuscoli <lb></lb>galleggianti. </s>

<s>Descritte particolarmente l&#039;esperienze, che si riducon per lui a <lb></lb>far galleggiare sull&#039;acqua ora due laminette di rame insieme, ora due assi­<lb></lb>celle di legno, e ora una laminetta e un&#039;assicella; fa consistere il merito <lb></lb>della sua scoperta nell&#039;avere osservato che tutto il negozio da null&#039;altro di­<lb></lb>pende, che dal formarsi o una fossa o un&#039;argine intorno ai detti corpuscoli, <lb></lb>e conclude all&#039;ultimo così il suo discorso: “ Et haec est vera et accurata <lb></lb>historia huius admirandi effectus. </s>

<s>Non igitur miror veram causam huius <lb></lb>effectus adductam non fuisse, cum non constabat, neque perfecte inno­<lb></lb>tuerat, historia huius operationis, quae tantummodo clare et evidenter ob­<lb></lb>servari potest, mediantibus supradictis laminulis a me excogitatis ” (ibid., <lb></lb>pag. </s>

<s>389). </s></p><p type="main">

<s>Il Viviani, come i nostri Lettori già sanno, aveva creduto di poter ren­<lb></lb>dere l&#039;ammirabile effetto ugualmente chiaro e manifesto, anche senza queste <lb></lb>lamine così elaborate, servendosi con molta semplicità delle pallottole di cera, <lb></lb>e delle crazie, e nello stesso tempo formulava queste leggi col dire che ar­<lb></lb>gine con argine, e fossa con fossa si uniscono, e argine con fossa si sfug­<lb></lb>gono. </s>

<s>Ma soggiungeva oltre a ciò, in questo genere, uno spettacolo nuovo, <lb></lb>di cui non fa menzione il Borelli, quello cioè del vedere alcuni corpuscoli dal <lb></lb>mezzo di un bicchiere colmo scendere ai labbri, mentre altri dai labbri ri­<lb></lb>salivano a posarsi nel mezzo. </s>

<s>Il Vossio, che come si disse fu primo a descri­<lb></lb>vere e a divulgar questo gioco, pensò che l&#039;osservata contrarietà degli effetti <lb></lb>dipendesse dal peso assoluto dei galleggianti, ingannato senza dubbio dalla <lb></lb>qualità delle materie scelte a quest&#039;uso, ch&#039;erano limature di vari metalli, <lb></lb>e gusci di noci. </s>

<s>“ Immittatur in aquam putamen nucis, aut sphaera vitrea <lb></lb>intus cava, aut quaecumque alia res aqua levior: illico videbis corpuscula <lb></lb>istaec, relicta ora, adscendere versus medium, et ibi consistere.... Quod si <lb></lb>etiam alia immiseris corpuscula innatantia, quae sint aqua graviora, scobem <lb></lb>nempe ferri, aeris, aut alius metalli, contrarium videbis: illa quippe ad de­<lb></lb>pressiorem oram descendent ” (<emph type="italics"></emph>De motu marium et ventor<emph.end type="italics"></emph.end> cit., pag. </s>

<s>43). </s></p><p type="main">

<s>Il Mariotte poi (<emph type="italics"></emph>Du mouvement des eaux,<emph.end type="italics"></emph.end> Oeuvres, a Leyde 1727, <lb></lb>pag. </s>

<s>374) corresse l&#039;errore, osservando che non dalla leggerezza o dalla gra­<lb></lb>vità de&#039;corpuscoli, ma dall&#039;essere o no bagnati dall&#039;acqua dipendono le con­<lb></lb>trarietà de&#039;loro moti, a quel modo che, nella nota autografa pubblicata da <lb></lb>noi di sopra, aveva prima scritto il Viviani. </s></p><p type="main">

<s>Il Viviani nulladimeno non sembra che fosse, come il Borelli, geloso <lb></lb>della scoperta, ripensando che ella principalmente consisteva, no nella chiara <lb></lb>ed evidente dimostrazione degli argini e delle fosse, ma nella vera ragione <lb></lb>del loro formarsi così intorno alle pareti dei galleggianti. </s>

<s>Quel che del resto <lb></lb>aveva, a questo effetto, immaginato esso Borelli si disse che non trovò quella <lb></lb>piena e perfetta approvazione, che egli sperava ne&#039;suoi colleghi. </s>

<s>Venuta a <lb></lb>mancar la pressione dell&#039;aria, questi vollero confessar piuttosto, con filosofica <pb xlink:href="020/01/3365.jpg" pagenum="326"></pb>ingenuità, di non sapere a che altro dare ingerenza di sostenere i liquidi nei <lb></lb>sottilissimi tubi. </s></p><p type="main">

<s>In mezzo a questi accorati silenzi, uscì fuori la voce di Donato Rossetti <lb></lb>che, vedute le male prove delle ipotesi nuove, prese animo di restaurare le <lb></lb>antiche. </s>

<s>Se dell&#039;effetto in questione, cominciò a dire, la causa non è esterna <lb></lb>nel peso dell&#039;aria, è forza ricorrere a un&#039;interna virtù calamitica, che faccia <lb></lb>l&#039;acqua correre al vetro per esservi attratta. </s>

<s>“ E perchè, soggiunge, la na­<lb></lb>tura elegge la via più facile, è cosa sicura che l&#039;acqua sempre orizontal­<lb></lb>mente corre al vetro. </s>

<s>Ma, per essere in maggior numero i minimi, che vi <lb></lb>accorrono, di quelli che possono fare una circonferenza fisica, e coronare la <lb></lb>sponda interiore del vaso; di qui è che i contendenti e sottendenti elevino <lb></lb>già li aderenti, col sottentrare e subsottentrare, dal che ne segue la massa <lb></lb>elevata ” (<emph type="italics"></emph>Antignome fisico-matem.,<emph.end type="italics"></emph.end> Livorno 1667, pag. </s>

<s>72). </s></p><p type="main">

<s>Che se, essendo unto il vetro, o in luogo dell&#039;acqua il mercurio, s&#039;os­<lb></lb>serva la massa non s&#039;elevar, ma abbassarsi, è da dire che tra il liquido e il <lb></lb>solido è un respingimento, piuttosto che un&#039;attrazione; un aborrimento in­<lb></lb>vece di un&#039;appetenza. </s>

<s>“ E così l&#039;aria nell&#039;acqua si restringe in palla, per <lb></lb>esser contigua a minor superficie d&#039;acqua, che sia possibile, e così fa l&#039;acqua <lb></lb>nell&#039;aria, che nel piano sottoposto vi si stende più o meno o punto, secondo <lb></lb>l&#039;appetenza che vi ha, ma dalla parte dell&#039;aria si stringe al possibile, e si <lb></lb>ammassa o in sfera o in porzion di quella, per esser circondata da meno <lb></lb>aria, che gli sia riuscibile. </s>

<s>E questa è la cagione perchè l&#039;acqua si faccia <lb></lb>colma in vasi untuosi, ed il mercurio nei vasi di vetro. </s>

<s>E per questa ragione, <lb></lb>e per il resistere alla cessione repugnante e violenta, se ne causa il colmeg­<lb></lb>giare de&#039;liquidi ne&#039;vasi pieni. </s>

<s>Adunque, perchè il mercurio quasi sopra tutti <lb></lb>i piani s&#039;agglobi, n&#039;è cagion l&#039;appetenza, che le sue particelle hanno tra <lb></lb>sè, e l&#039;aborrimento, che ha all&#039;aria ed al piano, sopra il quale scorre, per <lb></lb>non vi avere confacenza ed appetenza alcuna ” (ivi, pag. </s>

<s>83). </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Essendo l&#039;<emph type="italics"></emph>Antignome<emph.end type="italics"></emph.end> distesa in dialogo, fa dire il Rossetti a uno dei <lb></lb>suoi interlocutori che questi pensieri gli giungevano nuovi. </s>

<s>Nè desta punto <lb></lb>la maraviglia l&#039;apparizione di una tal novità, specialmente agli amici del­<lb></lb>l&#039;Autore, perchè quei pensieri, che spuntavano dal Discorso galileiano in­<lb></lb>torno alle galleggianti, erano rimasti soffocati dai discorsi nuovi del Salviati, <lb></lb>quasi costrutto già scritto, sopra il quale, invece che a cancellarlo, sia pas­<lb></lb>sata la punta della penna a sostituirvene un altro, con carattere più scolpito. </s></p><p type="main">

<s>Avvenne perciò ai pensieri del Rossetti quel ch&#039;è solito avvenire a tutte <lb></lb>le cose nuove, ma veramente mancavano a loro, per trovar nel pubblico la <lb></lb>meritata accoglienza, certe qualità, che s&#039;intenderanno meglio per questa di­<lb></lb>versione del nostro discorso. </s></p><pb xlink:href="020/01/3366.jpg" pagenum="327"></pb><p type="main">

<s>Sulla superficie AB (fig. </s>

<s>162) di un&#039;acqua galleggi l&#039;assicella CD, che <lb></lb>sostiene la gocciola concentrata in K. Un&#039;altra simile gocciola pendente, col <lb></lb>centro in I, dalla lamina EF, si accosti alla prima, per via del filo HG, te­<lb></lb><figure id="id.020.01.3366.1.jpg" xlink:href="020/01/3366/1.jpg"></figure></s></p><p type="caption">

<s>Figura 162.<lb></lb>nuto, per il suo capo G, in mano. </s>

<s>Si osserva che le due <lb></lb>dette gocciole non s&#039;acquietano nel contatto, ma segui­<lb></lb>tano a moversi, stringendosi l&#039;una sempre più contro <lb></lb>l&#039;altra, infin tanto che i loro vertici non cadano sopra <lb></lb>la medesima linea perpendicolare all&#039;orizonte. </s>

<s>Il Borelli, <lb></lb>che osservò e descrisse il fatto curioso, disse, volendolo <lb></lb>spiegare, che avvien delle due gocciole quel che di due <lb></lb>lastre di vetro ben piane a contatto, le quali, benchè siano così renitenti a <lb></lb>separarsi, mettendosi a tirarle, in direzione perpendicolare alla loro superfi­<lb></lb>cie, scivolano poi facilmente, ponendole inclinate, “ impulsa ab istinctu na­<lb></lb>turali, quo gravia conantur semper magis ad centrum gravium accedere, <lb></lb>eo modo quo possunt; scilicet via inclinata, cum directa et perpendicularis <lb></lb>fuerit impedita ” (<emph type="italics"></emph>De motion. </s>

<s>natur.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>390). </s></p><p type="main">

<s>Avendo il Montanari osservato che l&#039;aderenza fra le due lastre di vetro <lb></lb>si ottiene anche più facilmente, quando interceda fra loro un sottilissimo velo <lb></lb>di acqua; volle a modo suo anche spiegare perchè, strisciando l&#039;una sopra <lb></lb>l&#039;altra, benchè tenute orizontalmente, cedano alla più piccola forza. </s>

<s>La spie­<lb></lb>gazione però fu giudicata dal Rossetti insufficiente, anzi falsa, sostituendovi, <lb></lb>dietro il principio dell&#039;attrazione molecolare, quest&#039;altra, che secondo lui era <lb></lb>la vera: “ Ma volete vedere colla mia dottrina quanto mirabilmente si spie­<lb></lb>ghino questi effetti? </s>

<s>Da voi medesimo consideratelo, che concluderete che, <lb></lb>avendo l&#039;acqua <emph type="italics"></emph>appetenza<emph.end type="italics"></emph.end> al vetro, con quello sta <emph type="italics"></emph>aderente<emph.end type="italics"></emph.end> a segno, che non <lb></lb>si distaccherà, senza qualche violenza. </s>

<s>Ma perchè, a volerle staccare per le <lb></lb>perpendicolari, devesi far violenza nel medesimo tempo a tutti i minimi <lb></lb>d&#039;acqua, che sono fra le due lastre, e che ad ambedue stanno aderenti, ov­<lb></lb>vero fra loro e con la lastra, e per staccarli lateralmente non si fa violenza, <lb></lb>se non che a tanti minimi, quanti bastano a fare una linea fisica lunga, <lb></lb>quant&#039;è larga la lastra per quel verso, dal quale si tira, perchè questi soli <lb></lb>devono lasciare in tanto tempo una lastra; quindi ne è che, con pochissima <lb></lb>forza e facilissimamente, si staccano tali lastre, a guidarle orizontalmente. </s>

<s><lb></lb>Ma a perpendicolo fa di mestieri ciò segua per una gran forza, e per una <lb></lb>forza tale, che abbia a quella prima forza la proporzione, che hanno tutti i <lb></lb>minimi, che <emph type="italics"></emph>aderiscono<emph.end type="italics"></emph.end> alle lastre, a quelli che compongono l&#039;accennata linea <lb></lb>fisica ” (<emph type="italics"></emph>Insegnamenti fisico-matem.,<emph.end type="italics"></emph.end> Livorno 1669, pag. </s>

<s>169). </s></p><p type="main">

<s>Applicando queste dottrine del Rossetti al fatto delle gocciole, descritto <lb></lb>dal Borelli, si direbbe che l&#039;aderenza è un effetto della loro scambievole <lb></lb>attrazione, la forza della quale essendo rappresentata per IK (nella medesima <lb></lb>ultima figura) se questa si decomponga nella orizontale IL, e nella verticale <lb></lb>IM, avremo la ragion manifesta dello spettacoloso moto descritto e della <lb></lb>quiete. </s>

<s>Imperocchè, essendo la IM equilibrata dal filo HG, riman la sola IL <lb></lb>attiva in far avvicinar sempre più le gocciole insieme. </s>

<s>E perchè questa atti-<pb xlink:href="020/01/3367.jpg" pagenum="328"></pb>vità diminuisce via via, col diminuir dell&#039;angolo KIM, e con esso finalmente <lb></lb>svanisce; “ hae duae guttulae non quiescent, sed lateraliter excurrent, quo­<lb></lb>usque vertices earum in eadem recta perpendiculari ad horizontem excide­<lb></lb>rint ” come dice, nell&#039;annunziare la sua CLXXXIX proposizione, il Borelli <lb></lb>(Op. </s>

<s>cit., 390). </s></p><p type="main">

<s>Ora, il libero e sincero uso del parallelogrammo delle, forze era una di <lb></lb>quelle qualità che, siccome a quelle del Borelli, venivano a mancare alle <lb></lb>nuove dottrine del Rossetti. </s>

<s>Ma è da soggiungere che qualità più intrinseche <lb></lb>mancavano a quelle stesse dottrine, affinchè tutti le potessero accoglier con <lb></lb>fede. </s>

<s>Il principio dell&#039;attrazione molecolare fra i corpi si può dire una gemma <lb></lb>sepolta, che l&#039;aratro abbia messa a fior di terra. </s>

<s>Il luccicare però al sole, <lb></lb>in mezzo alle zolle, non bastava ai riguardanti, per riconoscerne il pregio, <lb></lb>che nessuno poi metterebbe più in dubbio, quando se ne vedesse il cristallo <lb></lb>legato in un anello d&#039;oro, e che di più quell&#039;anello splendesse a un gran <lb></lb>signore nel dito. </s>

<s>L&#039;orefice fu la Matematica di Filosofia naturale, che legò <lb></lb>la sciolta dottrina del Rossetti nell&#039;universal sistema dell&#039;attrazione, e quel <lb></lb>gran signore che si diceva è Isacco Newton. </s>

<s>Il primo Tomo della grande <lb></lb>Opera di lui si conclude in alcuni teoremi, dimostrativi dell&#039;intensità, e della <lb></lb>direzione delle forze sollecitanti un corpuscolo, che sia attratto, e che passi <lb></lb>attraverso a un mezzo similare. </s>

<s>Applicando poi questi teoremi alla luce, che <lb></lb>il Newton non dubita di riguardar come composta di minutissimi corpuscoli <lb></lb>duri, attratti al cristallo, per mezzo al quale trapassano, osservando le leggi <lb></lb>precedentemente dimostrate; ne desume le principali proprietà delle ottiche <lb></lb>rifrazioni. </s></p><p type="main">

<s>Come, seguitandosi ad agitar tuttavia la questione dei capillari, fosse <lb></lb>di qui suggerita all&#039;Hauksbee l&#039;idea dell&#039;attrazione dei corpuscoli, compo­<lb></lb>nenti l&#039;acqua, al vetro del tubo, con cui sono a contatto; si comprenderà <lb></lb>assai facilmente. </s>

<s>Quell&#039;insigne uomo del cav. </s>

<s>Isacco Newton, che esso Hauk­<lb></lb>sbee commemora qual gloria della sua Nazione, e della Società regia, gli <lb></lb>avrebbe altresi suggerito il modo di decomporre nel parallelogrammo quelle <lb></lb>forze attrattive. </s>

<s>E bench&#039;egli mostri di non sapersene prevalere con tutta la <lb></lb><figure id="id.020.01.3367.1.jpg" xlink:href="020/01/3367/1.jpg"></figure></s></p><p type="caption">

<s>Figura 163.<lb></lb>perfezione, non lascia però la speranza che, della ra­<lb></lb>gion del salire i liquidi nei piccoli tubi, non sia la se­<lb></lb>guente sua una <emph type="italics"></emph>narrativa appagante.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia ABCD (fig. </s>

<s>163) un piccolo tubo, perpendico­<lb></lb>larmente immerso in un liquido, la superficie orizontale <lb></lb>di cui sia EF. </s>

<s>Le parti del fluido X, Y, congiungendosi <lb></lb>alla concava superficie del tubo, ne sono gagliardamente <lb></lb>attratte, e ciò in una direzione perpendicolare ai lati del <lb></lb>vetro cilindrico. </s>

<s>Ora le particelle X, Y; gravitando in <lb></lb>direzioni perpendicolari ad EF, hanno tutte un molto <lb></lb>minor momento o forza gravante di quello, che elle per altro avrebbero, <lb></lb>se fosse tolta via l&#039;attrazione. </s>

<s>Perciò le parti del fluido, che sono a loro <lb></lb>immediatamente sotto, ricevono minor pressione di quella, che altrimenti <pb xlink:href="020/01/3368.jpg" pagenum="329"></pb>avrebbero. . . . Ma le parti del fluido, che stanno nel mezzo tra la superficie <lb></lb>EF e il fondo del tubo, in più rimota distanza dai lati del tubo, di quella <lb></lb>del proprio loro semidiametro; queste particelle, dico, essendo fuori del tiro <lb></lb>di tali attrazioni, gravitano con tutta quanta la loro forza o momento sopra <lb></lb>le parti, che stanno loro sotto. </s>

<s>Onde appare che, per l&#039;immersione del pic­<lb></lb>colo tubo dentro il liquido, si distrugga l&#039;equilibrio tra quelle parti del li­<lb></lb>quido giacenti dentro la circonferenza della base inferiore, e quelle che sono <lb></lb>al di fuori. </s>

<s>Laonde, secondo le leggi idrostatiche, bisogna che il liquido salga <lb></lb>dentro la superficie del tubo ” (<emph type="italics"></emph>Esperienze fisico-meccan.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>130, 31). </s></p><p type="main">

<s>Essendosi dimostrate le ragioni, prosegue a dire l&#039;Hauksbee, del risa­<lb></lb>lire i liquidi ne&#039;piccoli tubi, resta a dire perchè maggiori siano queste ri­<lb></lb>salite nei più stretti. </s>

<s>E per venire alla conclusione, osserva che, essendo le <lb></lb>forze attrattive proporzionali alle superficie concave dei tubi, e i pesi alle <lb></lb>colonne liquide, che gli riempiono; quelle stanno a questi come le circon­<lb></lb>ferenze alle superficie dei circoli. </s>

<s>Ora, perchè sempre è maggior proporzione <lb></lb>tra la circonferenza e la superficie nei cerchi piccoli, che ne&#039;grandi; perciò <lb></lb>il piccolo tubo è maggiormente proporzionato del grande a sollevare il peso, <lb></lb>“ e per questa ragione il liquido dovrà salire più alto nel primo, che nel <lb></lb>secondo ” (ivi, pag. </s>

<s>134). </s></p><p type="main">

<s>A questo proposito non si vuol lasciare inosservato che il Borelli aveva, <lb></lb>dopo il Vossio, assegnato del fatto le medesime ragioni. </s>

<s>Se non che il Nostro, <lb></lb>misurando l&#039;effetto non solo estensivamente, ma anche intensivamente, ne ren­<lb></lb>deva più compiuta la dimostrazione, e tale che, se l&#039;aderenza dell&#039;acqua al <lb></lb>vetro di cui parla, si volesse attribuire all&#039;attrazione molecolare, s&#039;accenne­<lb></lb>rebbe dal Borelli a un&#039;altra causa del sostenersi maggiormente i liquidi nei <lb></lb>tubi più stretti, sfuggita forse alla sottilissima analisi dei moderni: “ Et <lb></lb>quoad extensionem pertinet, quia vis adhaesionis mensuratur a contactibus, <lb></lb>et ideo a superficie interna canaliculorum, e contra resistentia mensuratur <lb></lb>a pondere cylindri aquei, contenti in iisdem canaliculis, estque proportio cy­<lb></lb>lindrorum aqueorum eiusdem altitudinis duplicata eius rationis, quam habent <lb></lb>eorum perimetri interni; igitur quanto magis crescit interna canalis ampli­<lb></lb>tudo, tanto magis minuitur adhaesio, et augetur resistentia ponderis ipsius <lb></lb>aquae contentae. </s>

<s>Imminuitur postea gradus intensivus internae adhaesionis, <lb></lb>propterea quod, ut dictum est supra, non est aeque valida facultas et ener­<lb></lb>gia adhaesionis aquae, et connexionis cum parietibus internis in universo illo <lb></lb>argine montuoso, sed est minus efficax, quanto magis ab internis parietibus <lb></lb>removetur. </s>

<s>Modo in fistulis amplioribus aqua contenta versus axim cavitatis <lb></lb>eius magis recedit a superficie interna fistulae dilatatae, quam in fistula stri­<lb></lb>ctiori, et ideo in illa debilius aqua sustinebitur suspendeturque. </s>

<s>Et quanto mi­<lb></lb>nor est vis sustinens et elevans, respectu ponderis fluidi contenti, tanto debet <lb></lb>imminui sublimitas eius elevationis ” (<emph type="italics"></emph>De motion. </s>

<s>natur.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>384, 85). </s></p><p type="main">

<s>Ora, per tornare all&#039;Hauksbee, avendo egli già detto perchè il liquido <lb></lb>salga a maggiore altezza ne&#039;cannellini più stretti, vorrebbe assegnarne inol­<lb></lb>tre le proporzioni; vorrebbe dimostrare cioè che le altezze stanno reciproca-<pb xlink:href="020/01/3369.jpg" pagenum="330"></pb>mente come i raggi delle sezioni. </s>

<s>Non sembra però a noi che ci riesca, al­<lb></lb>meno con quella precisione, che si richiederebbe a un teorema di Geometria, <lb></lb>e chi così legge potrebbe per sè medesimo darne più giusto giudizio: “ Come <lb></lb>la diminuita gravità del liquido nei tubi sta all&#039;assoluta gravità del cilindro <lb></lb>collaterale del liquido esterno; così starà la profondità dell&#039;immersione al­<lb></lb>l&#039;altezza del liquido nel piccolo tubo. </s>

<s>Poichè suppongo che il cilindro di <lb></lb>fluido nel tubo sia equilibrato da un altro al di fuori, che abbia la medesima <lb></lb>base, e la cui altezza sia uguale all&#039;immersione. </s>

<s>Conciossiachè, le basi es­<lb></lb>sendo le medesime, l&#039;altezze stanno come i contenuti, ovvero le quantità <lb></lb>della materia. </s>

<s>E per fare un equilibrio o eguaglianza di momenti, le forze <lb></lb>debbon essere reciprocamente conforme le moli o quantità, cioè, in questo <lb></lb>caso, reciprocamente quanto le altezze ” (<emph type="italics"></emph>Esperienze fisico-meccaniche<emph.end type="italics"></emph.end> cit., <lb></lb>pag. </s>

<s>134). </s></p><p type="main">

<s>È nonostante l&#039;Hauksbee benemerito di questi studii, per aver dimo­<lb></lb>strato quanto ragionevolmente si spieghino i fatti in questione, per via del­<lb></lb>l&#039;attrazion molecolare. </s>

<s>In questo tempo il Newton veniva, nel terzo libro <lb></lb>dell&#039;Ottica, a dare autorità a così fatti principii, estendendogli a ogni qua­<lb></lb>lità di materia, ch&#039;egli riguardava come composta d&#039;innumerevoli particelle <lb></lb>dure, le quali diceva non s&#039;intenderebbe come potessero nella composizione <lb></lb>dei corpi così tenacemente aderire insieme, “ nisi causa sit aliqua, quae ef­<lb></lb>ciat ut aee ad se invicem attrahantur ” (<emph type="italics"></emph>Opera aptica omnia<emph.end type="italics"></emph.end> cit., pag. </s>

<s>159). <lb></lb>Soggiunge poi le leggi, che governano questa attrazione, l&#039;intensità della <lb></lb>quale diminuisce così rapidamente, che a una distanza sensibile non sola­<lb></lb>mente riesce nulla, ma si converte in una repulsione. </s>

<s>“ Jam quidem fieri <lb></lb>potest ut materiae particulae exiguissimae attractionibus fortissimis inter se <lb></lb>cohaereant, constituantque particulas maiusculas, quarum vis illa attrahens <lb></lb>debilior sit, harumque particularum maiuscularum permultae, inter se iti­<lb></lb>dem cohaerentes, particulas maiores constituant, quarum vis attrahens adhuc <lb></lb>sit debilior. </s>

<s>Et sic deinceps continuata serie, donec ad maximas tandem de­<lb></lb>ventum sit particularum illarum, a quibus operationes chymicae et colores <lb></lb>corporum naturalium pendent, quaeque, inter se cohaerentes, corpora demum <lb></lb>constituant, magnitudine sub sensum cadente. . . . Et sicuti in algebra, ubi <lb></lb>quantitates affirmativae evanescunt et desinunt, ibi negativae incipiunt; ita <lb></lb>in mechanicis, ubi attractio desinit, ibi vis repellens succedere debet ” (ibid., <lb></lb>pag. </s>

<s>161). </s></p><p type="main">

<s>Per rendere poi accettevole l&#039;applicazione di queste dottrine ai fenomeni <lb></lb>capillari, il Newton, come non mancò di verificare i fatti osservati dall&#039;Hauk­<lb></lb>sbee, così non lasciò di confutare la falsità delle correnti opinioni. </s>

<s>L&#039;Hook, <lb></lb>nell&#039;osservazione VI della Micrografia, e più diffusamente nell&#039;opuscolo del <lb></lb>Bohem; il Sinclaro, lo Sturm, il Fabry nelle opere da noi citate; e più pros­<lb></lb>simamente il Leeuwenhock nell&#039;epistola CXXXI, in continuazione degli <emph type="italics"></emph>Ar­<lb></lb>cani della Natura;<emph.end type="italics"></emph.end> il Rohault, nel suo trattato di Fisica, il Mairan, nella <lb></lb>sua Storia dell&#039;Accademia di Parigi; avevano dato, e seguitavano tuttavia a <lb></lb>dare autorità all&#039;opinione che, del salire i liquidi nei tubi capillari, fossero <pb xlink:href="020/01/3370.jpg" pagenum="331"></pb>unica causa il peso e l&#039;elasticità dell&#039;aria. </s>

<s>S&#039;aggiungeva a questi autori <lb></lb>Giacomo Bernoulli, che, pubblicando nel 1683 quella sua così celebrata dis­<lb></lb>sertazione <emph type="italics"></emph>De gravitate aetheris,<emph.end type="italics"></emph.end> citava, a proposito dell&#039;argomento che ora <lb></lb>trattiamo, l&#039;ipotesi di alcuni Fisici, per confermarla con le ragioni e coi <lb></lb>fatti. </s>

<s>“ Secundum itaque Physiologos modernos in aere, praeter gravitatem, <lb></lb>considerare debemus vim quamdam, quam vocant elasticam, ita comparatam, <lb></lb>ut minima portio aeris alicubi incarcerati vel inclusi, in sustentandis aut <lb></lb>pellendis liquoribus, tantum possit, quantum totius atmosphaerae pondus ” <lb></lb>(<emph type="italics"></emph>Opera,<emph.end type="italics"></emph.end> Genevae 1744, pag. </s>

<s>82). </s></p><p type="main">

<s>Il Newton aveva, insieme con l&#039;Hauksbee, concluso il suo discorso dei <lb></lb>fenomeni capillari, come udimmo, in una sentenza tutt&#039;affatto contraria: <lb></lb><emph type="italics"></emph>Quare ex atmosphaerae pondere aut pressu nullo modo pendent.<emph.end type="italics"></emph.end> Il Ber­<lb></lb>noulli nonostante e l&#039;Huyghens avevano aperto un refugio, over ripararsi dai <lb></lb>colpi della detta sentenza (pronunziata già dagli Accademici del Cimento, e <lb></lb>confermata dal Rossetti assai prima) dicendo che, a sostentare i liquidi nei <lb></lb>sottilissimi tubi, sottentra la gravità dell&#039;etere a quella dell&#039;aria evacuata. </s>

<s><lb></lb>E perciò il Newton volle cacciar l&#039;errore anco da questo suo nascondiglio, <lb></lb>dimostrando, come si disse, che l&#039;adesione delle due lamine levigate, e la <lb></lb>sospension dell&#039;acqua o del mercurio dentro il tubo torricelliano, anche nel <lb></lb>vuoto; eran fatti, da non si dovere attribuire alla gravità dell&#039;etere, ma al­<lb></lb>l&#039;attrazione molecolare. </s></p><p type="main">

<s>Comunque sia però bisogna confessare che, sebbene l&#039;Hauksbee dichia­<lb></lb>rasse più particolarmente, e il Newton confermasse con la sua autorità il <lb></lb>principio dell&#039;attrazione fra i solidi e i liquidi, applicandolo alla spiegazion <lb></lb>dei fenomeni capillari; i due insigni uomini non promossero da pari loro la <lb></lb>scienza, lasciandola al punto, dove l&#039;aveva condotta il Rossetti. </s>

<s>Egli usò la <lb></lb>parola <emph type="italics"></emph>appetenza,<emph.end type="italics"></emph.end> alla quale i due Inglesi ne sostituirono un&#039;altra meno me­<lb></lb>taforica, e quel bisticcio del <emph type="italics"></emph>sottoentrare e subsottoentrare delle molecole <lb></lb>contendenti e sottendenti<emph.end type="italics"></emph.end> usato dal Nostro, dettero, con più proprio e con­<lb></lb>veniente linguaggio, risoluto nella ragion meccanica dei momenti fra le forze <lb></lb>attrattive. </s></p><p type="main">

<s>La promozione, che mancò di dare il Newton ai fatti particolari della <lb></lb>Fisica, per essere il suo scopo quello di prestabilirle i principii matematici <lb></lb>universali; venne presto ad aversi per Guglielmo Giacomo&#039;s Gravesande, <lb></lb>che i suoi Elementi dichiarava col titolo <emph type="italics"></emph>Introductio ad Philosophiam newto­<lb></lb>nianam.<emph.end type="italics"></emph.end> Nel capitolo V del I libro, trattando <emph type="italics"></emph>De cohaesione partium,<emph.end type="italics"></emph.end> mo­<lb></lb>stra come un effetto insigne di questa coesione si riveli ne&#039;fenomeni capil­<lb></lb>lari, secondo le esperienze hausbeiane, ch&#039;egli cita dalle Filosofiche transa­<lb></lb>zioni, perchè forse, quando scriveva, non era stata fatta quella raccolta, nella <lb></lb>quale lo stesso Hauksbee, non contento di descrivere i fatti, ne concludeva <lb></lb>dai principii del Newton altresì le ragioni. </s>

<s>Di qui è che&#039;s Gravesande parla <lb></lb>come se fosse venuto il primo a bandire il vero, raccomandando di non dar <lb></lb>retta a quel che tutti gli altri ne avessero predicato. </s>

<s>“ Plures de causis ho­<lb></lb>rum phaenomenorum scripserunt, sed nos ex aliis principiis haec in scholiis <pb xlink:href="020/01/3371.jpg" pagenum="332"></pb>illustrare conamur. </s>

<s>Quare iis, quae alii dederunt, inhaerendum non est ” <lb></lb>(<emph type="italics"></emph>Physicae elementa mathem. </s>

<s>editio IV,<emph.end type="italics"></emph.end> Leidae 1748, Praefatio pag. </s>

<s>XIX). </s></p><p type="main">

<s>Definita la forza dell&#039;attrazione molecolare, secondo i principii della Fi­<lb></lb>losofia newtoniana, e soggiunto ch&#039;ella non agisce a sensibile distanza, dove <lb></lb>anzi convertesi in repulsione; descrive esso&#039;s Gravesande alcune esperienze <lb></lb>scelte da vari Autori, sopra le quali poi passa a ragionar matematicamente <lb></lb>in quattro Scolii. </s>

<s>De&#039;primi due son queste che trascriviamo le conclusioni: <lb></lb>“ Vis ergo, quae sustinet aquam, proportionem sequitur latitudinis superfi­<lb></lb>ciei, iuxta quam aqua ascendit, mensuratae ad altitudinem, ad quam aqua <lb></lb>pertingit in linea, ad superficiem ipsius aquae parallela. </s>

<s>Quam eamdem ra­<lb></lb>tionem sequitur pondus aquae elevatae. </s>

<s>” </s></p><p type="main">

<s>“ Aquam in tubos vitreos minores sponte adscendere vidimus, quod <lb></lb>quomodo fiat nunc evidenter patet. </s>

<s>Quantitas autem aquae quae sustinetur <lb></lb>sequitur rationem circumferentiae superficiei aquae elevatae, et circumfe­<lb></lb>rentia haec, si agatur de tubis cylindricis perpendiculariter immersis, ad <lb></lb>instar diametri ipsius tubi crescit aut minuitur. </s>

<s>” </s></p><p type="main">

<s>“ Sint duo tubi, quorum diametri dicantur D, <emph type="italics"></emph>d;<emph.end type="italics"></emph.end> altitudines aquae in <lb></lb>tubis A, <emph type="italics"></emph>a<emph.end type="italics"></emph.end>: quantitates aquae elevatae erunt inter se ut D2.A ad <emph type="italics"></emph>d<emph.end type="italics"></emph.end>2.<emph type="italics"></emph>a.<emph.end type="italics"></emph.end><lb></lb>Ideo D2.A:<emph type="italics"></emph>d2.a<emph.end type="italics"></emph.end>=D:<emph type="italics"></emph>d.<emph.end type="italics"></emph.end> Dividendo antecedentia per D2, et consequentia <lb></lb>per <emph type="italics"></emph>d2,<emph.end type="italics"></emph.end> habebimus A:<emph type="italics"></emph>a=d<emph.end type="italics"></emph.end>:D, idest altitudines sunt inverse ut diame­<lb></lb>tri ” (ibid., T. I, pag. </s>

<s>26): ciò che però non è conseguenza del calcolo, ma del­<lb></lb>l&#039;esperienza, sopra la quale è fondata la conclusione scritta nel primo Scolio. </s></p><p type="main">

<s>Il Musschenbroek fu più preciso e ordinato. </s>

<s>Nel secondo capitolo della <lb></lb>sua dissertazione <emph type="italics"></emph>De tubis capillaribus vitreis,<emph.end type="italics"></emph.end> dop&#039;aver concluso, dietro le <lb></lb>più diligenti esperienze, che “ sunt altitudines aquae in his tubis accurate <lb></lb>in ratione inversa diametrorum tuborum ” (Lugduni Batav. </s>

<s>1729, pag. </s>

<s>296); <lb></lb>ne trae, dall&#039;osservazione del fatto, i seguenti corollari: </s></p><p type="main">

<s>Chiamate A, A′ le altezze, a cui sale il liquido in due tubi capillari, i <lb></lb>raggi interni de&#039;quali siano R, R′, ricorrono le proporzioni A:A′=R′:R= <lb></lb>2<foreign lang="grc">π</foreign>R′:2<foreign lang="grc">π</foreign>R; dunque “ erunt adscensus aquae in hos tubos in ratione in­<lb></lb>versa peripheriarum basium ” (ibid.). Se L è la lunghezza uguale di due <lb></lb>tubi, A:A′=2<foreign lang="grc">π</foreign>R′.L:2<foreign lang="grc">π</foreign>R.L, ossia, “ sunt adscensus aquae, in tubos <lb></lb>aeque altos, in ratione inversa superficierum, quas tubi habent interne ” (ibid) <lb></lb>e si può soggiungere che, dalla proporzione A:A′=2<foreign lang="grc">π</foreign>R′:2<foreign lang="grc">π</foreign>R resultando <lb></lb>2<foreign lang="grc">π</foreign>R.A=2<foreign lang="grc">π</foreign>R′.A′, le interne superficie bagnate, ne&#039;due tubi, sono uguali. </s>

<s><lb></lb>Se poi si moltiplichino ambedue i membri di questa equazione per R.R′, <lb></lb>avremo 2<foreign lang="grc">π</foreign>R2.R′.A=2<foreign lang="grc">π</foreign>R′2.R.A′, ossia <foreign lang="grc">π</foreign>R2.A:<foreign lang="grc">π</foreign>R′2.A′=R:R′. <lb></lb>“ Erunt itaque quantitates aquae elevatae, in omnibus his tubis tam amplis <lb></lb>quam angustis, uti sunt semidiametri basium inter se. . . . Quamobrem tubi <lb></lb>ampliores maiorem quantitatem aquae elevant quam angustiores, licet ad <lb></lb>maiorem altitudinem elevent suam aquam, nam semper sunt quantitates ele­<lb></lb>vatae uti semidiametri basium ” (ibid., pag. </s>

<s>297). </s></p><p type="main">

<s>Nel III Scolio&#039;s Gravesande dimostra che la curva, in cui si dispone <lb></lb>il lembo superiore del velo d&#039;acqua sollevatasi fra due lamine di vetro, la <pb xlink:href="020/01/3372.jpg" pagenum="333"></pb>piccolissima inclinazion delle quali le faccia concorrere in una linea perpen­<lb></lb>dicolare all&#039;orizonte; è un&#039;iperbola. </s>

<s>I Matematici di que&#039;tempi, fra&#039;quali il <lb></lb>Musschenbroek, nella dissertazione <emph type="italics"></emph>De attractione speculorum planorum vi­<lb></lb>treorum,<emph.end type="italics"></emph.end> soggiunta all&#039;altra dei tubi capillari; fecero alla detta dimostrazione <lb></lb>accoglienza, per la facilità dei principii geometrici, sopra i quali, a questo <lb></lb>modo che riferiamo, presso a poco è condotta. </s>

<s>Sia ACB (fig. </s>

<s>164) il semian­<lb></lb>golo formato dalle due lamine o specchi di vetro, e presa AT, che rappre­<lb></lb><figure id="id.020.01.3372.1.jpg" xlink:href="020/01/3372/1.jpg"></figure></s></p><p type="caption">

<s>Figura 164.<lb></lb>senti la superficie dell&#039;acqua nel vaso dell&#039;immer­<lb></lb>sione, uguale a BC, e sopra alzatavi perpendicolar­<lb></lb>mente la TS, che rappresenti lo spigolo fatto dalle <lb></lb>due lamine: suppongasi che il velo d&#039;acqua, sol­<lb></lb>levatosi in mezzo ad esse, incurvi il suo lembo su­<lb></lb>periore, disponendosi secondo la NPV, della qual <lb></lb>curva si vuol cercar l&#039;equazione riferita agli assi <lb></lb>AT, TS. </s>

<s>Siano le due ordinate NM, PO le altezze <lb></lb>corrispondenti alle colonne liquide, aventi per basi <lb></lb>DG, HL. </s>

<s>Se i due specchi fossero paralleli, queste <lb></lb>colonne sarebbero uguali, e tali pure potendosi ri­<lb></lb>tenere nel nostro caso, in cui la convergenza verso <lb></lb>l&#039;angolo C si suppon piccolissima, avremo DG.MN=HL.OP, ossia DG:HL= <lb></lb>OP:MN. </s>

<s>E perchè, per le medesime ragioni, DG, HL si possono considerar <lb></lb>come rettangoli, i quali, avendo le basi EG, IL per costruzione uguali, stanno <lb></lb>come le altezze DE, HI, ossia come le EC, CI, o come le TM, TO; sarà <lb></lb>dunque TM:TO=OP:MN, e perciò la curva un&#039;iperbola, descritta fra <lb></lb>gli asintoti AT, TS. </s></p><p type="main">

<s>Gli Elementi di&#039;s Gravesande, che introdussero le esperienze dell&#039;Hauk­<lb></lb>sbee nelle scuole, ebbero grandissima efficacia in diffondere i principii neu­<lb></lb>toniani dell&#039;attrazione molecolare, specialmente applicata ai fenomeni capil­<lb></lb>lari. </s>

<s>Ma non mancarono le contradizioni di chi sempre si mostra ritroso alle <lb></lb>novità, intorno a qualunque soggetto esse versino, e da qualunque autorità <lb></lb>sian promosse. </s>

<s>Il Jurin non rimaneva sodisfatto della teoria hausbeiana, se­<lb></lb>condo la quale sarebbero le forze attrattive diffuse per tutta l&#039;interiore su­<lb></lb>perficie del tubo. </s>

<s>Dal fatto che sempre le altezze de&#039;liquidi sollevati sono in <lb></lb>ragion reciproca de&#039;diametri dei cannellini, se ne conclude, ei ragionava, che <lb></lb>le superficie bagnate, e perciò le forze attrattive ad esse superficie propor­<lb></lb>zionali, sono in ogni caso sempre le medesime, mentre il tubo più largo <lb></lb>solleva maggior copia di liquido del più stretto. </s>

<s>Ma non possono forze uguali <lb></lb>sostener pesi differenti; dunque, ne concludeva il Jurin, dev&#039;essere una fal­<lb></lb>lacia nell&#039;assunto dell&#039;Hauksbee, e per ritrovare il vero si rivolse alle espe­<lb></lb>rienze. </s>

<s>Fra quèste, ad aprirgli la mente, glie ne sovvenne una, che fra le <lb></lb>narrate da noi comparisce nuova, ed è che, variando il tubo di raggio, come <lb></lb>se fossero due tronchi saldati insieme, e l&#039;uno perpendicolarmente soprap­<lb></lb>posto all&#039;altro; la regola della salita è data sempre da quello di sopra. </s></p><p type="main">

<s>Così, per esempio, se il tubo avesse da A infino in B diametro più pic-<pb xlink:href="020/01/3373.jpg" pagenum="334"></pb>colo, che da B fino in C, come nella fig. </s>

<s>165; o se da D fino in E l&#039;avesse <lb></lb>più grande, che da E fino in F come nella figura 166; immerse le bocche <lb></lb>inferiori CH, FN nel liquido, questo non salirà verso le bocche superiori AG, <lb></lb><figure id="id.020.01.3373.1.jpg" xlink:href="020/01/3373/1.jpg"></figure></s></p><p type="caption">

<s>Figura 165.<lb></lb><figure id="id.020.01.3373.2.jpg" xlink:href="020/01/3373/2.jpg"></figure></s></p><p type="caption">

<s>Figura 166.<lb></lb>DO, secondo la regola de&#039;diametri CH, FN, ma <lb></lb>degli altri AG, DO, d&#039;onde il Jurin argomentava es­<lb></lb>sere le forze attrattive solamente limitate agli anelli <lb></lb>del vetro, che han per diametri AG, DO, e non <lb></lb>estese a tutta la superficie. </s>

<s>E così, soggiungeva, è <lb></lb>ragionevole che sia, avendosi allora propriamente le <lb></lb>cause proporzionali agli effetti. </s>

<s>Se infatti il liquido nel <lb></lb>cannello maggiore AF, rappresentato dalla fig. </s>

<s>167, <lb></lb>risale infino a BC, e nel minore infino a LM (fig. </s>

<s>168); <lb></lb>la forza in BC, alla forza in LM, sta come BC a LM. </s>

<s>Ma come GF ad HE, <lb></lb>ossia, come BC ad LM, stanno anche le colonne liquide; dunque le forze <lb></lb>sollevatrici son proporzionali ai pesi sollevati. <lb></lb><figure id="id.020.01.3373.3.jpg" xlink:href="020/01/3373/3.jpg"></figure></s></p><p type="caption">

<s>Figura 167.</s></p><p type="main">

<s>Altri Fisici non attaccarono la teoria hausbeiana nella forma, <lb></lb>ma la negarono nella sostanza. </s>

<s>Contro costoro il Musschenbroek, <lb></lb>annunziando ai Lettori i soggetti delle sue varie Dissertazioni, e <lb></lb>particolarmente di quella, in cui si proponeva di dimostrare che la <lb></lb>causa della ascesa dei liquidi nei tubi capillari è dovuta all&#039;attra­<lb></lb>zione; si rivolgeva con queste parole: “ Non dubito fore plerosque, <lb></lb>qui <emph type="italics"></emph>attractionis<emph.end type="italics"></emph.end> voce offendantur, eamque contemnant, derideant, <lb></lb>explodant. </s>

<s>His autem, si tanta sit animi aequitas, ut suspenso <lb></lb>praeiudicio Experimenta prius legant, et inter se comparent; tum, <lb></lb><figure id="id.020.01.3373.4.jpg" xlink:href="020/01/3373/4.jpg"></figure></s></p><p type="caption">

<s>Figura 168.<lb></lb>causam eorum eruere conantibus, facile apparebit propter quasnam <lb></lb>rationes hac voce usi fuimus ” (<emph type="italics"></emph>Dissertationes physicae experi­<lb></lb>mentales,<emph.end type="italics"></emph.end> Lugduni Batav. </s>

<s>1729, pag. </s>

<s>IV). </s></p><p type="main">

<s>Anche il Musschenbroek però ebbe a partecipare degli errori <lb></lb>del Jurin, studiandosi di ricavare dall&#039;esperienza le leggi dell&#039;at­<lb></lb>trazione. </s>

<s>“ Haec vis (egli dice dop&#039;avere sfrattate con lungo di­<lb></lb>scorso le virtù del suo argomento) terminatur in crustam aeream <lb></lb>tuborum antiquorum, in qua attrahendo se totam consumit, vel <lb></lb>impendit maximam saltem sui partem, hinc inepta est elevando <lb></lb>liquori aut debilitata admodum. </s>

<s>Et quia haec vis eo est fortior quo cor­<lb></lb>poreo sui puncto, e quo egreditur, est propior; erit fortissima, cum super­<lb></lb>ficies cava proxima sibi puncta habebit, sive cum crit arctissima. </s>

<s>Idcirco <lb></lb>altissime elevabitur liquor a tubis gracillimis, humilius ab amplioribus: imo <lb></lb>in graciles maiori velocitate adscendet, utpote actus maioribus viribus quam <lb></lb>in amplos. </s>

<s>Haec vis, ex quolibet puncto sui corporis emissa ad distantiam <lb></lb>aliquam, non modo elevat particulas liquoris superficiei tubi proximas, sed <lb></lb>quoque alias contiguas prioribus, aliasque hisce iterum contiguas, licet mi­<lb></lb>nori robore, quae tamen, cum eamdem gravitatem inter se habent, minus ele­<lb></lb>vari possunt: idcirco superficiem concavam componentes ” (ibid., pag. </s>

<s>331). </s></p><p type="main">

<s>Quella <emph type="italics"></emph>crusta aerea,<emph.end type="italics"></emph.end> della quale si tratta nel principio della citazione, <pb xlink:href="020/01/3374.jpg" pagenum="335"></pb>dette al Musschenbroek motivo a scoprir l&#039;origine delle fallacie del Boyle, <lb></lb>e di altri esperimentatori insieme con lui, i quali, se trovarono che il li­<lb></lb>quido sale più su nei tubi prima bagnati, che negli asciutti, fu perchè si <lb></lb>servirono di vetri usati, piuttosto che nuovi (ivi, pag. </s>

<s>281). Ma più devono <lb></lb>gli orecchi dei Lettori essere rimasti offesi da quel che soggiunge l&#039;Autore <lb></lb>delle forze attrattive del solido, che si fanno sentire al liquido a distanza, <lb></lb>anzi a grande distanza: “ Agit igitur vis elevans tubi in distantiam, et qui­<lb></lb>dem in magnam ” (ibid. </s>

<s>pag. </s>

<s>287), ciò che egli conclude dietro l&#039;esperienza <lb></lb>descritta nel capitolo I della sua Dissertazione. </s></p><p type="main">

<s>Si narrò come nell&#039;Accademia di Bologna si sperimentasse essere le al­<lb></lb>tezze dei liquidi indipendenti dalle lunghezze dei tubi, e come il Montanari <lb></lb>avesse disingannato il Fabry, a cui parvero quelle altezze maggiori nei can­<lb></lb>nellini più lunghi. </s>

<s>Ora il Musschenbroek, rimproverando il Carré, caduto poi <lb></lb>nel medesimo errore del Montanari “ miror, egli dice, cl. </s>

<s>Carreum non con­<lb></lb>suluisse observationes Honorati Fabry, in <emph type="italics"></emph>Phys.,<emph.end type="italics"></emph.end> lib. </s>

<s>II, atque Sturmium, in <lb></lb><emph type="italics"></emph>Colleg. </s>

<s>curios.,<emph.end type="italics"></emph.end> qui observaverunt quo altius emineret tubulus, super aquae <lb></lb>superficiem, eo altius in ipsum adscendere aquam ” (ibid., pag. </s>

<s>285). </s></p><p type="main">

<s>Che la lunghezza immobile del cannello faccia qualche differenza dalla <lb></lb>lunghezza, che se gli aggiunge via via, sollevandolo sempre più sul livello <lb></lb>dell&#039;acqua, dove aveva la bocca immersa; non fa maraviglia, e con ciò ven­<lb></lb>gono a conciliarsi le apparenti contrarietà delle esperienze. </s>

<s>Ma ben fa più <lb></lb>maraviglia che, sopra una tal differenza accidentale, fondasse il Musschen­<lb></lb>broek una conclusione tanto importante, qual&#039;è che le forze attrattive si <lb></lb>estendano per tutta la lunghezza del tubo, anche molto di sopra al punto, <lb></lb>dove è salito il liquido che lo bagna. </s>

<s>“ Concludimus ex his experimentis vim <lb></lb>aut causam elevantem aquam per totam tubi longitudinem esse diffusam. </s>

<s><lb></lb>Quo igitur longior tubus existit, eo maior quantitas virium elevantium aquam <lb></lb>datur ” (ibid., pag. </s>

<s>287), ciò che ben si comprende essere l&#039;errore stesso <lb></lb>del Jurin, molto più esagerato. </s>

<s>L&#039;Hauksbee invece aveva concluso che son <lb></lb>solamente attratte le particelle dell&#039;acqua contigue al vetro, e che gli strati <lb></lb>cilindrici esterni, e concentrici alla superficie di contatto, per essere a sen­<lb></lb>sibile distanza, non hanno efficacia in attrarre, e in far sollevare il liquido <lb></lb>nell&#039;interno. </s>

<s>Lo&#039;s Gravesande pure, in piena conformità con le dottrine del <lb></lb>Newton, aveva scritto: “ Haec autem attractio minimarum particularum hisce <lb></lb>legibus subiicitur, ut in ipso particularum contactu sit per quam magna, et <lb></lb>subito decrescat, ita ut, ad distantiam quam minimam, quae sub sensus ca­<lb></lb>dit, non agat ” (<emph type="italics"></emph>Physicae elem.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>18). </s></p><p type="main">

<s>Questi Elementi di fisica matematica, de&#039;quali, dal 1719 al 1748, si fe­<lb></lb>cero quattro edizioni, e le <emph type="italics"></emph>Esperienze fisico-meccaniche<emph.end type="italics"></emph.end> dell&#039;Hauksbee, dal­<lb></lb>l&#039;originale inglese tradotte in varie lingue; cooperarono così in stabilir la <lb></lb>Fisica molecolare, che, verso la metà del secolo XVIII, nessuno oramai più <lb></lb>dubitava che la salita de&#039;liquidi nei cannellini non fosse per effetto del ve­<lb></lb>tro, che potentemente gli attrae a non sensibile distanza. </s>

<s>In tali condizioni <lb></lb>trovava appunto la scienza M. Clairaut, il quale, de&#039;tanti che l&#039;avevano trat-<pb xlink:href="020/01/3375.jpg" pagenum="336"></pb>tata, giudicò il Jurin il più eccellente, e perciò raccomandava la dissertazione <lb></lb>di lui, inserita nelle <emph type="italics"></emph>Filosofiche transazioni,<emph.end type="italics"></emph.end> a chiunque si volesse erudire <lb></lb>intorno alla Storia sperimentale dei fenomeni capillari. </s>

<s>“ Mais, seggiunge, <lb></lb>quoiqu&#039;il y ait beaucoup à profiter dans la lecture de cette piece, j&#039;avoue que <lb></lb>je n&#039;ai pas pù ètre satisfait de la theorie, que M. </s>

<s>Jurin y donné, et que j&#039;ai <lb></lb>crû que l&#039;examen de cette question demandoit plus de principes, que cet <lb></lb>Auteur n&#039;en a employés ” (<emph type="italics"></emph>Theorie de la figure de la Terre,<emph.end type="italics"></emph.end> a Paris 1743, <lb></lb>pag. </s>

<s>106). </s></p><p type="main">

<s>Il principio impiegato dal Jurin si riduce a quello dell&#039;attrazione, non <lb></lb>determinata però nei particolari modi di agire, se non per un argomento <lb></lb>logico, e per varii altri tutti sperimentali. </s>

<s>Quanto a quello osservava il Clai­<lb></lb>raut che gli effetti son proporzionali alle cause solamente, quando si risale <lb></lb>a una causa prima e unica, ma non quando s&#039;esamina un effetto, risultante <lb></lb>dal concorso di più cause particolari (ivi, pag. </s>

<s>108). Quanto agli argomenti <lb></lb>sperimentali, e a quello principalmente che suggeri al Jurin l&#039;idea di limi­<lb></lb>tare le forze attrattive del vetro a quel solo anello di lui, che sovrasta im­<lb></lb>mediatamente alla superficie dell&#039;acqua; il Clairaut, considerando i filetti <lb></lb>liquidi IK, LM, lungo l&#039;asse dei tubi rappresentati dalle figure 165 e 166, <lb></lb>concludeva dalla sua analisi matematica che i due tronchi inferiori, attraendo <lb></lb>in alto e in basso con forze eguali le porzioni de&#039;filetti da essi circoscritti, <lb></lb>è come se non esistessero, o come se i due tubi procedessero in basso, per <lb></lb>tutte le loro altezze IK, LM, colle medesime aperture dei raggi AI, DL, che <lb></lb>hanno alle cime (ivi, pag. </s>

<s>125-27). </s></p><p type="main">

<s>I modi poi dell&#039;attrazione, proseguiva a ragionare il Clairaut, non si <lb></lb>possono determinare, se non col sottoporre a un calcolo esatto tutte le forze <lb></lb>attrattive, ciò che se avesse fatto il Jurin si sarebbe facilmente accorto che, <lb></lb>pur supponendo esser le forze dell&#039;anello di vetro in ragion costante col suo <lb></lb>diametro, “ on n&#039;en pourrait pas conclure qu&#039;une colonne de fluide d&#039;un <lb></lb>poids proportionnel a cette force seroit suspendue par son moyen ” (ivi, <lb></lb>pag. </s>

<s>109). Nè alcun altro ancora s&#039;era applicato a questo calcolo esatto. </s>

<s>Che <lb></lb>se&#039;s Gravesande aveva ritrovata l&#039;equazione alla curva, in cui termina il <lb></lb>velo d&#039;acqua, risalito fra i due specchi inclinati; non poteva non sentire che, <lb></lb>a condur la sottile dimostrazione, troppo ottuso strumento erano gli Ele­<lb></lb>menti di Euclide e i Conici di Apollonio. </s>

<s>Ma in ogni modo gli fu forza ar­<lb></lb>retrarsi, quando nel IV dei citati Scolii si popose di trattare <emph type="italics"></emph>De motu gut­<lb></lb><figure id="id.020.01.3375.1.jpg" xlink:href="020/01/3375/1.jpg"></figure></s></p><p type="caption">

<s>Figura 169.<lb></lb>tae,<emph.end type="italics"></emph.end> della gocciola cioè dell&#039;olio, che, compresa fra <lb></lb>due specchi inclinati, spontaneamente si muove, <lb></lb>spandendosi verso l&#039;angolo dell&#039;inclinazione. </s></p><p type="main">

<s>Il Musschenbroek, in tanta necessità, pensò <lb></lb>d&#039;invocare il valido aiuto del parallelogrammo <lb></lb>delle forze. </s>

<s>Siano i due specchi AC, AE (fig. </s>

<s>169), <lb></lb>e il centro O della gocciola d&#039;olio sia attratto <lb></lb>dalle forze OP, OS. </s>

<s>La resultante OB dimostra <lb></lb>senza dubbio che il moto della gocciola è diretto <pb xlink:href="020/01/3376.jpg" pagenum="337"></pb>verso l&#039;angolo A, come, trasformandosi le supposte forze attrattive nelle re­<lb></lb>pulsive OD, OH, la resultante OF mostrerebbe che il moto è rivolto in verso <lb></lb>contrario, ciò che di fatto s&#039;osserverebbe accadere, se la gocciola O fosse mer­<lb></lb>curio. </s>

<s>Ma tutto questo non è preparazion sufficiente alle conclusioni, che il <lb></lb>Musschenbroek stesso soggiunge: “ Insuper, quo centrum gravitatis O pro­<lb></lb>pius accesserit ad speculorum superficies, eo fortius attrahetur, sed propius <lb></lb>accedit, quo gutta magis applanatur, hoc est magis ad A approprinquarit. </s>

<s><lb></lb>Adeoque fortius attracta gutta a superficiebus, et obliqua directione, neces­<lb></lb>sario velocius feretur, quae est altera causa accelerati motus in gutta obser­<lb></lb>vati. </s>

<s>Fortissima quoque speculorum attractio, cum sit in contactu A, necesse <lb></lb>est ut gutta secundum hunc contactum expandatur per omnem speculorum <lb></lb>latitudinem ” (<emph type="italics"></emph>Dissertationes<emph.end type="italics"></emph.end> cit., pag. </s>

<s>347, 48). </s></p><p type="main">

<s>Che la conclusione non sia veramente, come si diceva, compresa nei <lb></lb>principii, è facile riconoscerlo, a pensar solamente che, se le forze OP, OS <lb></lb>crescono, con l&#039;avvicinarsi che fa la gocciola ad A, la resultante OB invece <lb></lb>diminuisce. </s>

<s>Ond&#039;è che, anco a spiegar l&#039;accelerazione del moto, le sopra <lb></lb>dette dall&#039;Autore non son ragioni assolute, e nè perciò sufficienti. </s>

<s>L&#039;insuf­<lb></lb>ficienza poi si rende anche più manifesta, osservando che, nella spiegazione <lb></lb>di questi fatti, si tien solamente conto dell&#039;attrazione del solido, trascurata <lb></lb>quella del liquido in sè medesimo. </s>

<s>Di che accortosi il sagace Clairaut, con­<lb></lb>cluse che non si sarebbe potuta esaminar bene la questione dei tubi capil­<lb></lb>lari, se non applicandovi la legge generale dell&#039;equilibrio dei fluidi. </s>

<s>“ Je <lb></lb>vais donc examiner la question des tuyaux capillaires, par les loix generales <lb></lb>de l&#039;equilibre des fluides ” (<emph type="italics"></emph>Theorie<emph.end type="italics"></emph.end> cit., pag. </s>

<s>109, 10). </s></p><p type="main">

<s>In che questo esame consista, e come cominciassero di qui le gocciole <lb></lb>della rugiada, sopra le foglie dei cavoli, a riconoscer loro cognate le stelle <lb></lb>erranti per gli eterei spazii celesti, è ciò che ne rimane a dire in quest&#039;ul­<lb></lb>tima parte del nostro discorso. </s></p><p type="main">

<s><emph type="center"></emph>V.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Il Clairaut era giunto a questa conclusione: che se le parti di una gran <lb></lb>mole fluida, rivolgentesi intorno a un asse, come sarebbe il nostro globo ter­<lb></lb>racqueo, o un pianeta, sarauno attratte al centro nella semplice ragion di­<lb></lb>retta delle distanze; il pianeta stesso deve configurarsi in una sferoide ellit­<lb></lb>tica (ivi, pag. </s>

<s>61): cosicchè tutte le sezioni, condotte perpendicolarmente sul­<lb></lb>l&#039;asse di rotazione, son circoli, e la superficie del corpo, che in sè stessa è <lb></lb>rotonda, per un breve spazio apparisce piana. </s>

<s>Nonostante, intorno agli orli <lb></lb>dei piccoli vasi, o a contatto di certi corpi, quella stessa superficie si vede <lb></lb>incurvarsi, nè ciò può avvenire, se non perchè alla gravità naturale s&#039;aggiun­<lb></lb>gono altre forze, dal concorso delle quali viene a resultarne una direzione <lb></lb>diversa. </s></p><pb xlink:href="020/01/3377.jpg" pagenum="338"></pb><p type="main">

<s>In questo ragionamento del Clairaut, molto più espressamente che in <lb></lb>quello degli sperimentatori precedenti, viene la Filosofia neutoniana a com­<lb></lb>prendere nel suo magistero le gocciole dell&#039;acqua, e le moli de&#039;pianeti. </s>

<s>Per­<lb></lb>chè, se l&#039;attrazione al centro dello sferoide è quella, che ne rende regolare <lb></lb>la superficie, l&#039;attrazione, agli orli del vaso o al solido immerso deve essere <lb></lb>che la perturba. </s>

<s>Sottoporre a un calcolo rigoroso queste forze perturbatrici, ciò <lb></lb>che nessuno aveva ancora tentato, è l&#039;intenzione dell&#039;Accademico di Parigi. </s></p><p type="main">

<s>L&#039;Hauksbee non aveva saputo dir altro, se non che la gravità naturale <lb></lb>di una particella d&#039;acqua, sopravvenendo l&#039;attrazione al vetro, perde alquanto <lb></lb>del suo proprio momento. </s>

<s>Con qual ragione si faccia questa perdita, che pure <lb></lb>per un altro liquido, come per esempio il mercurio, o in altre condizioni del <lb></lb><figure id="id.020.01.3377.1.jpg" xlink:href="020/01/3377/1.jpg"></figure></s></p><p type="caption">

<s>Figura 170.<lb></lb>vetro potrebb&#039;essere invece un acquisto; il Clairaut <lb></lb>lo dimostrava in questo modo: Sia AD (fig. </s>

<s>170) <lb></lb>la sezione di un tubo, o di un solido immerso in­<lb></lb>fino al livello MN in qual si voglia liquido, di cui N <lb></lb>è una particella a contatto. </s>

<s>Questa verrà sollecitata <lb></lb>da tre forze: dalla gravità naturale, rappresentata <lb></lb>per NO; dall&#039;attrazione al solido, rappresentata per <lb></lb>NL, e dall&#039;attrazione verso l&#039;interno della massa <lb></lb>liquida, per trovar la misura e la direzion della <lb></lb>quale si oostruisca il quadrato MO. Nell&#039;incontro K <lb></lb>delle due diagonali una molecola ivi costituita, es­<lb></lb>sendo in equilibrio, perchè è ugualmente attratta, <lb></lb>e attrae le molecole D, N; può dunque KN pren­<lb></lb>dersi per la direzione, e per la misura della forza, con cui la stessa mole­<lb></lb>cola N è attratta verso l&#039;interno di tutta la mole. </s>

<s>Di qui è manifesto come <lb></lb>la disposizion naturale, che prenderebbe N nella liquida superficie, quando <lb></lb>non avesse altra sollecitazione che dalla NO; vien perturbata dal concorso <lb></lb>delle forze KN, NL, la resultante delle quali è NR. </s>

<s>E perchè la detta dispo­<lb></lb>sizion naturale era perpendicolare a NO, e la perturbazione subita la co­<lb></lb>stringe invece a disporsi perpendicolarmente a NR; è altresì manifesto come <lb></lb>il liquido stagnante, di piano che sarebbe stato per sua natura, debba incur­<lb></lb>varsi verso il solido AD che l&#039;attrae, in una concava superficie. </s></p><p type="main">

<s>Qui il Clairaut ci richiama a considerar meglio la resultante delle forze <lb></lb>perturbatrici, dalla sola direzion della quale nascono i varii effetti. </s>

<s>Perchè <lb></lb>se, essendo tal direzione secondo NR, la superficie liquida è concava, e se <lb></lb>secondo NO è piana; quando invece fosse secondo NH riuscirebbe convessa. </s>

<s><lb></lb>Ora la varietà di queste direzioni si vede bene che dipende dal variar del <lb></lb>lato NL, o del suo uguale KR, che è uno dei lati, sopra il quale si costrui­<lb></lb>sce il parallelogrammo delle forze; e la variazione si fa intorno al punto C, <lb></lb>per accesso o per recesso dal punto K. </s>

<s>In C poi è il giusto mezzo della NO, <lb></lb>e KC, NC, OC son linee tutte uguali, come raggi del semicircolo circoscritto <lb></lb>a KNO, angolo retto. </s>

<s>Dunque, quando NF=KC=NC=NO/2, ossia, quando <pb xlink:href="020/01/3378.jpg" pagenum="339"></pb>l&#039;attrazione del solido sopra la molecola liquida uguaglia la metà dell&#039;attra­<lb></lb>zione della molecola stessa al centro dello sferoide terrestre; la superficie è <lb></lb>piana. </s>

<s>E perchè le resultanti divengono ora NR, ora NH, cioè quella positiva <lb></lb>e questa negativa rispetto alla direzion normale NO, secondo che NL&gt;NO/2, <lb></lb>o NE&lt;NO/2; dunque la superficie è concava o convessa, secondo che l&#039;at­<lb></lb>trazion del solido è maggiore o minore della metà dell&#039;attrazione della mo­<lb></lb>lecola liquida al centro dello sferoide terrestre; ossia, secondo che la resul­<lb></lb>tante delle forze perturbatrici è positiva o negativa, rispetto alla verticale. <lb></lb><figure id="id.020.01.3378.1.jpg" xlink:href="020/01/3378/1.jpg"></figure></s></p><p type="caption">

<s>Figura 171.</s></p><p type="main">

<s>Da ciò venne il Clairaut ad aprirsi la <lb></lb>via di risolvere analiticamente il problema <lb></lb>de&#039;fenomeni capillari, assoggettando al cal­<lb></lb>colo tutte le forze che, sollecitando in basso <lb></lb>il filetto liquido IK (fig. </s>

<s>171) lungo l&#039;asse <lb></lb>del tubo di vetro, di cui la sezion verticale <lb></lb>sia AH, e il raggio interno sia <emph type="italics"></emph>b;<emph.end type="italics"></emph.end> lo man­<lb></lb>tengono in equilibrio col filetto ML, preso <lb></lb>in mezzo al liquido, nel quale il detto tubo, <lb></lb>infino al livello MP, si supponga essere <lb></lb>immerso. </s>

<s>Chiamata <emph type="italics"></emph>h<emph.end type="italics"></emph.end> l&#039;intensità dell&#039;at­<lb></lb>trazione del vetro, <emph type="italics"></emph>k<emph.end type="italics"></emph.end> quella dell&#039;acqua, una <lb></lb>delle principali forze, che sollecitano le mo­<lb></lb>lecole componenti il filetto ML, è quella <lb></lb>del loro peso <emph type="italics"></emph>p:<emph.end type="italics"></emph.end> forza, che perciò sarà <lb></lb>espressa da <emph type="italics"></emph>p<emph.end type="italics"></emph.end>.ML. S&#039;aggiunga a questa <lb></lb>l&#039;attrazion delle molecole sopra sè mede­<lb></lb>sime, la quale essendo in funzione della distanza <emph type="italics"></emph>x<emph.end type="italics"></emph.end> dal centro attrattivo, e <lb></lb>dovendo avere per coefficiente <emph type="italics"></emph>k,<emph.end type="italics"></emph.end> sarà, per una sola particella, misurata da <lb></lb><emph type="italics"></emph>kdx<foreign lang="grc">φ</foreign>(x),<emph.end type="italics"></emph.end> e per tutte sommate insieme da <emph type="italics"></emph>Ŗkdx<foreign lang="grc">φ</foreign>(x).<emph.end type="italics"></emph.end> Ond&#039;è che, signifi­<lb></lb>candosi con P la pression totale, che il soprastante filetto liquido fa in L; <lb></lb>avremo <emph type="italics"></emph>P=p.ML+Ŗkdx<foreign lang="grc">φ</foreign>(x).<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Fra le forze sollecitanti il filetto IK si distingueranno quelle, applicate <lb></lb>alla parte superiore I, dall&#039;altre applicate verso O, alla parte inferiore. </s>

<s>Si <lb></lb>consideri la molecola <emph type="italics"></emph>m,<emph.end type="italics"></emph.end> alla quale si vedrà essere applicate tre forze: la <lb></lb>prima dovuta all&#039;attrazione dell&#039;acqua soggiacente al piano ST, e che, per <lb></lb>le cose dette, e ritenute le medesime denominazioni, la tira in basso con una <lb></lb>intensità uguale a <emph type="italics"></emph>kŖdx<foreign lang="grc">φ</foreign>(x);<emph.end type="italics"></emph.end> le altre due, che la detta molecola tirano in <lb></lb>verso contrario; son dovute all&#039;attrazione delle pareti solide AV, ET, e del <lb></lb>menisco liquido YX. </s>

<s>Ed essendo quella in funzione del raggio del tubo, e <lb></lb>della distanza dal centro di attrazione, e perciò espressa da <emph type="italics"></emph><foreign lang="grc">φ</foreign>(b, x),<emph.end type="italics"></emph.end> che fa­<lb></lb>remo uguale a <foreign lang="grc">Φ</foreign>, e questa in funzione del raggio, della detta distanza cen­<lb></lb>trale, e inoltre delle attrazioni del vetro e dell&#039;acqua, e perciò espressa da <lb></lb><emph type="italics"></emph><foreign lang="grc">φ</foreign> (b, x, h, k)<emph.end type="italics"></emph.end> che faremo uguale a <foreign lang="grc">Φ</foreign>′; saranno nella somma di tutti i loro <pb xlink:href="020/01/3379.jpg" pagenum="340"></pb>elementi quelle stesse forze rappresentate da <emph type="italics"></emph>kŖdx<foreign lang="grc">Φ</foreign>,Ŗdx<foreign lang="grc">Φ</foreign>′.<emph.end type="italics"></emph.end> “ Donc le <lb></lb>poids total de toutes les parties voisines de I sera <emph type="italics"></emph>kŖdx<foreign lang="grc">φ</foreign>(x)—kŖdx<foreign lang="grc">Φ</foreign>— <lb></lb>Ŗdx<foreign lang="grc">Φ</foreign>′ ”<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>117). </s></p><p type="main">

<s>Resta a calcolar le forze, che sollecitano le particelle del filetto liquido <lb></lb>verso la bocca inferiore del tubo, terminata dal piano DG, a ugual distanza <emph type="italics"></emph>x<emph.end type="italics"></emph.end><lb></lb>dal quale considerati due elementi Q, R, si vedrà che son con pari forze <lb></lb>attratti in giù dall&#039;acqua soggiacente al piano DG, e in su dal vetro: di modo <lb></lb>che, il coefficiente della loro funzione essendo <emph type="italics"></emph>h—k,<emph.end type="italics"></emph.end> s&#039;avranno le dette <lb></lb>forze espresse da <emph type="italics"></emph>(k—h)dx<foreign lang="grc">Φ</foreign>,<emph.end type="italics"></emph.end> e perciò le forze di tutti gli elementi in­<lb></lb>sieme s&#039;otterranno dal prendere due volte la somma di <emph type="italics"></emph>(k—h)dx<foreign lang="grc">Φ</foreign>,<emph.end type="italics"></emph.end> ossia <lb></lb>da — <emph type="italics"></emph>2(h—k)dx<foreign lang="grc">Φ</foreign>.<emph.end type="italics"></emph.end> Dunque, raccogliendo insieme le forze, all&#039;impulso <lb></lb>delle quali va soggetto il filetto liquido IK, e aggiuntavi quella della sua gra­<lb></lb>vità naturale <emph type="italics"></emph>p<emph.end type="italics"></emph.end>.IK; avremo la pressione Q, ch&#039;egli esercita in K, espressa da <lb></lb><emph type="italics"></emph>Q=p.IK+kŖdx<foreign lang="grc">φ</foreign>(x)—kŖdx<foreign lang="grc">Φ</foreign>—Ŗdx<foreign lang="grc">Φ</foreign>′—2(h—k)dx<foreign lang="grc">Φ</foreign>.<emph.end type="italics"></emph.end><lb></lb>Uguagliando insieme i valori di P e di Q, sottraendo l&#039;uno dall&#039;altro, e fa­<lb></lb>cendo le assai facili riduzioni, s&#039;ottiene finalmente la formula <lb></lb>IK—ML=IU=<emph type="italics"></emph>((2h—k)dx<foreign lang="grc">Φ</foreign>+Ŗdx<foreign lang="grc">Φ</foreign>′)/p.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ On tire de l&#039;expression precedente de IU, dice il Clairaut, une propo­<lb></lb>sition assez singuliere ” (ivi, pag. </s>

<s>121): singolarità che si rende anche più <lb></lb>manifesta esplicando il concetto dell&#039;Autore, col mettere da ogni parte a ri­<lb></lb>scontro questa soluzione analitica con la geometrica, illustrata dalla nostra <lb></lb>CLXX figura. </s>

<s>Da <emph type="italics"></emph>k<emph.end type="italics"></emph.end> è sempre rappresentata NO, ma da <emph type="italics"></emph>h<emph.end type="italics"></emph.end> le lunghezze va­<lb></lb>riabili NL, NF, NE, di una delle componenti: come da <foreign lang="grc">Φ</foreign>′ si rappresentano <lb></lb>le variabili direzioni NR, NC, NH delle resultanti. </s>

<s>Se <emph type="italics"></emph>k=2h,<emph.end type="italics"></emph.end> il primo ter­<lb></lb>mine dell&#039;espressione di IU è zero. </s>

<s>Ma è assai facile vedere che zero è anche <lb></lb>il secondo, a cagion di <foreign lang="grc">Φ</foreign>′, da cui viene allora a rappresentarsi la direzione <lb></lb>verticale NC della resultante. </s>

<s>Dunque IU è zero, ossia il liquido, ne&#039;due rami <lb></lb>del sifone MLKU, è a perfetto livello, ciò che sempre avviene, quando la su­<lb></lb>perficie del liquido non è perturbata dalla sua natural direzione al centro <lb></lb>dello sferoide terrestre, e perciò la formola del Clairaut esprime analitica­<lb></lb>mente in questo caso l&#039;uguaglianza di livello e d&#039;equilibrio de&#039;liquidi nei <lb></lb>vasi comunicanti. </s></p><p type="main">

<s>Se <emph type="italics"></emph>k<emph.end type="italics"></emph.end> è minore di 2<emph type="italics"></emph>h,<emph.end type="italics"></emph.end> e perciò <foreign lang="grc">Φ</foreign>′ rappresenta la direzion della resul­<lb></lb>tante NR, alla destra di NC; ambedue i termini di IU, e perciò IU stessa <lb></lb>è positiva, ossia il liquido risalirà sopra il livello MP, che è il caso dell&#039;acqua <lb></lb>in un tubo capillare di vetro. </s>

<s>Se finalmente <emph type="italics"></emph>k<emph.end type="italics"></emph.end> è maggiore di 2<emph type="italics"></emph>h,<emph.end type="italics"></emph.end> e <foreign lang="grc">Φ</foreign>′ rap­<lb></lb>presenta la direzione della resultante a sinistra, IU sarà negativa, ossia il <lb></lb>liquido s&#039;abbasserà al di sotto del livello MP, che è il caso del mercurio. </s></p><p type="main">

<s>Il Clairaut dice di non volere spingere oltre il suo calcolo “ pour sça­<lb></lb>voir ce que seroient les quantités <foreign lang="grc">Φ</foreign> et <foreign lang="grc">Φ</foreign>′, suivant les differentes fonctions <lb></lb>de la distance qu&#039;on pourroit prendre pour exprimer la loi de l&#039;attraction ” <pb xlink:href="020/01/3380.jpg" pagenum="341"></pb>(ivi, pag. </s>

<s>121). Ciò ei lasciava allo studio dei Matematici suoi successori, i <lb></lb>quali, riconoscendo la difficoltà dell&#039;impresa, pensarono di volgersi ad altro <lb></lb>partito. </s>

<s>L&#039;equazione della catenaria, o della lamina elastica, o della velaria, <lb></lb>felicemente ritrovata per via del nuovo calcolo infinitesimale, ingerì nel Se­<lb></lb>gner e in Tommaso Young la speranza di risolvere il problema dei capil­<lb></lb>lari, assomigliando a quelle curve i menischi che, per la tensione e per la <lb></lb>elasticità superficiale dei liquidi, si formano dentro i tubi capillari. </s>

<s>Il La­<lb></lb>place invece credè non c&#039;essere altra via diretta, da condursi alla desiderata <lb></lb>soluzione, che quella di determinare le funzioni della formula del Clairaut, <lb></lb>nella legge di un&#039;attrazione insensibile a sensibili distanze, come nella luce. </s>

<s><lb></lb>Di che avendo già trattato nel X libro della Meccanica celeste, a proposito <lb></lb>delle rifrazioni astronomiche, pensò di aggiungere al detto libro un Supple­<lb></lb>mento, in cui le medesime leggi ottiche si applicherebbero ai fenomeni ca­<lb></lb>pillari. </s></p><p type="main">

<s>Le benefiche inspirazioni, ricevute dal Clairaut, come il Laplace le sentì <lb></lb>nell&#039;animo, così l&#039;espresse con le parole: “ Clairaut est le premier et jusqu&#039;à <lb></lb>présent le seul, qui ait soumis a un calcul rigoureux les phénoménes des <lb></lb>tubes capillaires, dans son traité sur la Figure de la Terre ” (<emph type="italics"></emph>Supplement <lb></lb>au X livre du traité De mecanique celeste,<emph.end type="italics"></emph.end> T. IV, a Paris 1805, pag. </s>

<s>2). <lb></lb>Nonostante fa alcune censure, che a noi per verità non sembrano giuste, <lb></lb>come per avere il Clairaut supposto che l&#039;attrazion del vetro si faccia sen­<lb></lb>tire a distanza sul filetto liquido, che riempie l&#039;asse del tubo, contro le no­<lb></lb>tissime esperienze dell&#039;Hauksbee. </s>

<s>Vero è che questi, sperimentando con due <lb></lb>tubi ugualmente cavi, ma differentemente massicci, “ non potè distinguere <lb></lb>differenza alcuna tra le altezze, che il liquore in ambi i tubi aveva salite ” <lb></lb>(<emph type="italics"></emph>Esperienze fisico-meccan.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>123), e poche pagine appresso, da quelle <lb></lb>stesse esperienze e dalle analogie con la calamita, conclude “ che l&#039;attrat­<lb></lb>tiva potenza delle piccole particelle della materia opera solamente sopra quei <lb></lb>tali corpiccioli, che le toccano, ovvero che siano da loro a una infinitamente <lb></lb>piccola distanza rimosse ” (ivi, pag. </s>

<s>130). Ma prima di sentenziare che il <lb></lb>Clairaut non seppe, o non volle tener conto di queste verità dimostrate, con­<lb></lb>veniva pensar che la formula scritta da lui sussiste anche nel caso che <emph type="italics"></emph>b,<emph.end type="italics"></emph.end><lb></lb>raggio del tubo, sia d&#039;insensibile lunghezza. </s>

<s>Il Laplace, e tutti coloro che <lb></lb>ripeterono le censure di lui, forse rimasero ingannati dalle dimensioni esa­<lb></lb>gerate, che l&#039;Autore fu costretto di dare alla sua figura. </s>

<s>Nè meno ingiusta <lb></lb>sembra a noi l&#039;altra accusa, dallo stesso Laplace data al Clairaut, che cioè <lb></lb>il gran Geometra “ n&#039;à pas expliqué le principal phenomène capillaire, celui <lb></lb>de l&#039;ascension et de la depression des liquides dans des tubes tres-étroits, <lb></lb>en raison inverse du diametre de ces tubes ” (<emph type="italics"></emph>Supplement au supplement<emph.end type="italics"></emph.end><lb></lb>cit., pag. </s>

<s>76), considerando che il valore di IU è dato in ragione inversa di <lb></lb><emph type="italics"></emph>p,<emph.end type="italics"></emph.end> ossia de&#039;pesi delle colonne liquide, le quali si sa essere proporzionali ai <lb></lb>raggi delle basi. </s></p><p type="main">

<s>L&#039;ispirazione più principalmente benefica, che dal Clairaut ricevesse il <lb></lb>Laplace, fu quella di attendere e di dare importanza ai menischi. </s>

<s>“ Les phy-<pb xlink:href="020/01/3381.jpg" pagenum="342"></pb>siciens n&#039;ayant considere jusqu&#039;ici la concavité et la convexité des surfaces <lb></lb>des fluides, dans les espaces capillaires, que comme un effet secondaire de <lb></lb>la capillarité ” (<emph type="italics"></emph>Supplement<emph.end type="italics"></emph.end> cit., pag. </s>

<s>8). L&#039;Hauksbee anzi e il Jurin riguar­<lb></lb>darono quelle superficie come piane, e le loro curvità, per le loro dimostra­<lb></lb>zioni, come indifferenti. </s>

<s>Il Laplace invece sentì che risiedeva quivi <emph type="italics"></emph>la prin­<lb></lb>cipale cause de ce genre de phenomènes,<emph.end type="italics"></emph.end> cosicchè la stessa attrazione dei <lb></lb>tubi capillari, in che facevano i detti fisici consistere quella causa principale, <lb></lb>“ n&#039;a d&#039;influence sur l&#039;elevation, ou sur l&#039;abaissement des fluides, qu&#039;ils ren­<lb></lb>ferment, qu&#039;en determinant l&#039;inclinaison des premiers plans de la surface du <lb></lb>fluide interieur, extremement voisins des parois du tube: inclinaison, dont <lb></lb>dépend la concavité ou la convexité de cette surface, et la grandeur de son <lb></lb>rayon ” (ivi, pag. </s>

<s>5). </s></p><p type="main">

<s>Fu per questa riconosciuta influenza che il Laplace attese a istituir di <lb></lb>proposito, e con la massima diligenza, l&#039;esperienze che gli dovevano prima <lb></lb>servir di regola, e poi di conferma alla teoria. </s>

<s>Sia ABC (fig. </s>

<s>172) un sifone <lb></lb><figure id="id.020.01.3381.1.jpg" xlink:href="020/01/3381/1.jpg"></figure></s></p><p type="caption">

<s>Figura 172.<lb></lb>capillare di vetro, e si tuffi nell&#039;acqua in modo, che il suo <lb></lb>ramo più corto AB rimanga tutto sommerso. </s>

<s>Siasi elevato <lb></lb>il liquido infino in G, nel ramo più lungo: estratto lo stru­<lb></lb>mento si formerà in A una gocciola, e il liquido si vedrà <lb></lb>risalire più su di G. </s>

<s>Levisi col dito la gocciola, e il liquido <lb></lb>si abbasserà sotto G. </s>

<s>Si ritorni con una pipetta legger­<lb></lb>mente a rimetter la gocciola, e il liquido raggiungerà di <lb></lb>nuovo il primiero livello. </s></p><p type="main">

<s>Per dimostrare anche più efficacemente gli effetti dei <lb></lb>menischi sia, soggiunge il Laplace, ABC (fig. </s>

<s>173) un si­<lb></lb>fone capillare, dentro cui, tenuto colle braccia verticali, <lb></lb>s&#039;equilibri il mercurio. </s>

<s>Inclinando lo strumento dalla parte <lb></lb><figure id="id.020.01.3381.2.jpg" xlink:href="020/01/3381/2.jpg"></figure></s></p><p type="caption">

<s>Figura 173.<lb></lb>di A, il liquido risale in A′, e scende in C′, dalla parte op­<lb></lb>posta. </s>

<s>Riducendolo alla primiera stazione, si osserva che non <lb></lb>perciò il liquido torna al primiero livello orizontale, ma ri­<lb></lb>mane alquanto più elevato dalla parte di A, dove il meni­<lb></lb>sco s&#039;è fatto anche meno convesso che dall&#039;altra. </s>

<s>“ Cette <lb></lb>differance, dans la convexité des deux surfaces, tient au frot­<lb></lb>tement du mercure contre les parois du tube: les parties <lb></lb>de la surface, dans la branche AB, qui se retirent vers A, <lb></lb>et qui touchent le tube, sont un peu arretrées par ce frot­<lb></lb>tement, tandis que les parties du milieu de cette surface n&#039;éprouvent point <lb></lb>le mème obstacle; et de là doit resulter une surface moins convexe; au <lb></lb>lieu que le même frottement doit produire un effet contraire sur la sur­<lb></lb>face du mercure de la branche BC. </s>

<s>Or de ce que la premiere de ces surfa­<lb></lb>ces est moins convexe que la seconde, il en resulte que le mercure éprouve, <lb></lb>par son action sur lui-meme, une moindre pression dans la branche BA, que <lb></lb>dans la branche BC, et qui ainsi sa hauteur, dans la premiere de ces deux <lb></lb>branches, doit surpasser un peu sa hauteur dans la seconde ” (ivi, pag. </s>

<s>61, 62). </s></p><pb xlink:href="020/01/3382.jpg" pagenum="343"></pb><p type="main">

<s>Tale essendo l&#039;efficacia del menisco concavo YIZ, nella figura CLXXI, <lb></lb>si ricerca il modo dell&#039;operare di lui, il quale non può consistere in altro, <lb></lb>che in attrarre il filetto liquido IK, cosicchè questo, divenuto quasi più leg­<lb></lb>gero, debba sollevarsi, per equilibrar la pressione del filetto LM. “ La loi de <lb></lb>cette ascension, dans les tubes de differens diametres, depend de l&#039;attraction <lb></lb>du ménisque, et ici, comme dans la theorie de la figure des planétes, il y <lb></lb>a una dependance reciproque de la figure, et de l&#039;attraction du corps, qui <lb></lb>rend leur determination difficile. </s>

<s>Pour y parvenir nous allons considerer <lb></lb>l&#039;action d&#039;un corps, de figure quelconque, sur une colonne fluide renformée <lb></lb>dans un canal infiniment etroit perpendiculaire à se surface, et dont nous <lb></lb>prendrons la base pour unité ” (ivi, pag. </s>

<s>10). </s></p><p type="main">

<s>Si prepara il Laplace la via alla general considerazione di un corpo qua­<lb></lb>lunque, supponendo primieramente che quel corpo sia una sfera di raggio <emph type="italics"></emph>b,<emph.end type="italics"></emph.end><lb></lb>compaginata di strati indivisibili concentrici, l&#039;azione d&#039;un de&#039;quali, avente <lb></lb>per raggio <emph type="italics"></emph>u,<emph.end type="italics"></emph.end> sul filetto, trova essere espressa da <emph type="italics"></emph>2<foreign lang="grc">π</foreign>udu/b.<foreign lang="grc">Ψ</foreign>(b—u)<emph.end type="italics"></emph.end> dove <lb></lb><foreign lang="grc">Ψ</foreign> è il resultato di quantità dipendenti da <emph type="italics"></emph>Ŗdf<foreign lang="grc">φ</foreign>(f),<emph.end type="italics"></emph.end> intendendosi per <emph type="italics"></emph><foreign lang="grc">φ</foreign>(f)<emph.end type="italics"></emph.end><lb></lb>la legge dell&#039;attrazione molecolare, alla distanza <emph type="italics"></emph>f.<emph.end type="italics"></emph.end> Se invece dell&#039;attrazione <lb></lb>dello strato sferico si considera la pressione, esercitata sul filetto liquido in <lb></lb>virtù della detta attrazione, è manifesto che <emph type="italics"></emph>2<foreign lang="grc">π</foreign>udu/b.<foreign lang="grc">Ψ</foreign>(b—u)<emph.end type="italics"></emph.end> deve con­<lb></lb>vertirsi in — <emph type="italics"></emph>2<foreign lang="grc">π</foreign>udu/b.<foreign lang="grc">Ψ</foreign> (b—u)<emph.end type="italics"></emph.end> e perciò, fatto <emph type="italics"></emph>b—u=z,<emph.end type="italics"></emph.end> s&#039;avrà l&#039;azione S <lb></lb>della sfera intera espressa da <emph type="italics"></emph>2<foreign lang="grc">π</foreign>Ŗ(b—z)/b.dz<foreign lang="grc">Ψ</foreign>z,<emph.end type="italics"></emph.end> ossia da <emph type="italics"></emph>S′=2<foreign lang="grc">π</foreign>Ŗdz<foreign lang="grc">Ψ</foreign>z= <lb></lb>2<foreign lang="grc">π</foreign>Ŗzdz/b.<foreign lang="grc">Ψ</foreign>z,<emph.end type="italics"></emph.end> esteso l&#039;integrale da <emph type="italics"></emph>z=o,<emph.end type="italics"></emph.end> infino a <emph type="italics"></emph>z=b.<emph.end type="italics"></emph.end> Facendosi poi <lb></lb><emph type="italics"></emph>2<foreign lang="grc">π</foreign>Ŗdz<foreign lang="grc">Ψ</foreign>z=H,<emph.end type="italics"></emph.end> e <emph type="italics"></emph>2<foreign lang="grc">π</foreign>Ŗzdz<foreign lang="grc">Ψ</foreign>z=K,<emph.end type="italics"></emph.end> si ridurrà la formula alla semplicis­<lb></lb>sima significazione di S=H—K/<emph type="italics"></emph>b.<emph.end type="italics"></emph.end> Se <emph type="italics"></emph>b<emph.end type="italics"></emph.end> è negativo, ossia se la sfera com­<lb></lb>prende il filetto liquido, e la superficie YIZ concava si trasforma nella con­<lb></lb>vessa Y′IZ′, sarà invece S=K+H/<emph type="italics"></emph>b.<emph.end type="italics"></emph.end> Dunque, “ l&#039;action d&#039;un corps, terminé <lb></lb>per una portion sensible de surface spherique, sera K±H/<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> le signe+ayant <lb></lb>lieu, si la surface est convexe, et le signe — si elle est concave ” (ivi, pag. </s>

<s>15). </s></p><p type="main">

<s>L&#039;espressione dell&#039;azion della sfera intera s&#039;è applicato ai menischi YIZ, <lb></lb>Y′IZ′, ossia ai segmenti sferici sensibili, fatti per un piano, a cui il filetto o <lb></lb>la colonna liquida IK sia perpendicolare: applicazione, che può nel presente <lb></lb>caso farsi a buon diritto, “ car la partie de la sfhère, située au-delà de ce <lb></lb>plan, etant à une distance sensible de la colonne, sen action sur cette co­<lb></lb>lonne est insensible ” (ivi, pag. </s>

<s>14). </s></p><p type="main">

<s>La ritrovata formula K±H/<emph type="italics"></emph>b<emph.end type="italics"></emph.end> è perciò applicabile ai menischi, che si <pb xlink:href="020/01/3383.jpg" pagenum="344"></pb>formano dai vari liquidi, dentro i tubi capillari, ma prima di venire a farne <lb></lb>l&#039;applicazione giova, col Laplace, premettere alcune osservazioni. </s>

<s>Resultando <lb></lb>K=H.<emph type="italics"></emph>z/b,<emph.end type="italics"></emph.end> e <emph type="italics"></emph>z/b<emph.end type="italics"></emph.end> essendo un rotto proprio, è manifesto che il valore di S <lb></lb>è sempre notabilmente più piccolo del primo. </s>

<s>Si noti inoltre il diverso uffi­<lb></lb>cio rappresentativo, che hanno i due termini componenti il detto valore di S. <lb></lb>“ K represente l&#039;action d&#039;un corps, terminé par une surface plane, car alors <emph type="italics"></emph>b<emph.end type="italics"></emph.end><lb></lb>etant infini, le terme H/<emph type="italics"></emph>b<emph.end type="italics"></emph.end> disparait ” (ivi), ond&#039;è che resta particolarmente al <lb></lb>termine H/<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> essendo <emph type="italics"></emph>b<emph.end type="italics"></emph.end> finito, l&#039;ufficio di rappresentare l&#039;azion del menisco. </s>

<s><lb></lb>Ed essendo una tale azione in ragion reciproca del raggio della curvatura, <lb></lb>ne consegue manifestamente che, nel caso di K—H/<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> ossia quando il me­<lb></lb>nisco è concavo, che la pressione cresce insieme col crescer del raggio, men­<lb></lb>tre, nel caso di K+H/<emph type="italics"></emph>b<emph.end type="italics"></emph.end> ossia, quando il menisco è convesso, crescendo il <lb></lb>raggio, la pressione invece diminuisce. </s></p><p type="main">

<s>Si può graficamente così rappresentare l&#039;espressione propria a ciascuno <lb></lb>dei due detti termini. </s>

<s>Sia il tubo ABCD (fig. </s>

<s>174) e nel filetto EF, lungo <lb></lb><figure id="id.020.01.3383.1.jpg" xlink:href="020/01/3383/1.jpg"></figure></s></p><p type="caption">

<s>Figura 174.<lb></lb>l&#039;asse, si consideri la molecola S fra gli archi simmetrici <lb></lb>GEH, IRK, che ne limitano la sfera dell&#039;attrazione. </s>

<s>Si <lb></lb>conduca al piano LM parallelo il piano NO, e all&#039;arco AEB <lb></lb>simmetrico l&#039;arco <expan abbr="PRq.">PRque</expan> È manifesto che, sopra la mole­<lb></lb>cola S, non agisce per attrazione se non che il liquido <lb></lb>sottoposto, venga egli limitato dal piano NO, o dal meni­<lb></lb>sco PRQ, simmetrico al concavo AEB, o dal menisco IRK, <lb></lb>simmetrico al convesso GEH. </s>

<s>Nel primo caso, essendo NO <lb></lb>piano e perciò il raggio <emph type="italics"></emph>b<emph.end type="italics"></emph.end> della formula infinito; non ri­<lb></lb>mane che il termine K, da cui vien perciò rappresentata <lb></lb>l&#039;azione del liquido NODC. </s>

<s>Nel secondo caso, tutta la forza <lb></lb>attrattiva risiede nel liquido PRQDC, uguale a ND, dimi­<lb></lb>nuito di PRQON, a cui perciò nella formula corrisponde <lb></lb>il termine —K/<emph type="italics"></emph>b.<emph.end type="italics"></emph.end> Nel terzo caso finalmente l&#039;azione s&#039;estende al liquido <lb></lb>IRKDC, ossia al liquido ND, insieme col liquido INROK, a cui nella formula <lb></lb>corrisponde il termine +K/<emph type="italics"></emph>b.<emph.end type="italics"></emph.end> Come poi, trasformandosi col diminuire del <lb></lb>raggio l&#039;arco PRQ in P′RQ′, e l&#039;arco IRK in I′RK′, l&#039;azione diminuisca <lb></lb>nel primo caso e cresca nel secondo; e come il liquido NOQRP sia picco­<lb></lb>lissimo, rispetto al liquido ND, a quel modo si dimostrò H/<emph type="italics"></emph>b<emph.end type="italics"></emph.end> esser piccolissimo <lb></lb>rispetto a K; son cose tanto parventi alla vista, da non aver bisogno di prove. </s></p><p type="main">

<s>Ma si ascolti il Laplace stesso, che nella prefazione al citato <emph type="italics"></emph>Supple-<emph.end type="italics"></emph.end><pb xlink:href="020/01/3384.jpg" pagenum="345"></pb><emph type="italics"></emph>mento<emph.end type="italics"></emph.end> così discorre intorno al carattere proprio a ciascuno dei due termini, <lb></lb>di che si comporrebbe la sua formula: “ Son expression analityque est com­<lb></lb>posée de deux termes: le premier, beaucoup plus grand que le second, <lb></lb>exprime l&#039;action de la masse, terminée par une surface plane; et je pense <lb></lb>que de ce terme dépendent la suspension du mercure, dans un tube de ba­<lb></lb>rometre, a une hauteur deux ou trois fois plus grande que celle, qui est <lb></lb>due à la pression de l&#039;atmosphère, le pouvoir refringent de corps diaphanes <lb></lb>la cohesion, et generalement les affinités chimiques. </s>

<s>Le second terme exprime <lb></lb>la partie de l&#039;action due à la sphericité de la surface, c&#039;est-a-dire l&#039;action du <lb></lb>menisque, compris entre cette surface, et le plan qui la touche. </s>

<s>Cette action <lb></lb>s&#039;ajoute a la precedente, ou s&#039;en tranche, suivant que la surface est convexe <lb></lb>ou concave. </s>

<s>Elle est reciproque au rayon de la surface spherique: il est vi­<lb></lb>sible en effet que, plus ce rayon est petit, plus le menisque est considera­<lb></lb>ble, pres du point de contingence. </s>

<s>C&#039;est a ce second terme, <lb></lb>qu&#039;est due l&#039;action capillaire, qui diffère ainsi des affinité <lb></lb>chimiques representées par le premier terme ” (pag. </s>

<s>3, 4). </s></p><p type="main">

<s>Le varie forme, sotto cui si presentano queste azioni <lb></lb><figure id="id.020.01.3384.1.jpg" xlink:href="020/01/3384/1.jpg"></figure></s></p><p type="caption">

<s>Figura 175.<lb></lb>capillari, si possono ridurre a quelle, che si osservano ne&#039;due <lb></lb>vasi di vetro comunicanti ABC (fig. </s>

<s>175) e DEF (fig. </s>

<s>176) <lb></lb>nel primo de&#039;quali sia l&#039;acqua, e nel secondo il mercurio. </s>

<s><lb></lb>Resulta costantemente da così fatte osservazioni che, nel <lb></lb>ramo del tubo più largo, della figura 175, il livello del li­<lb></lb>quido è più basso che nel cannello più stretto, mentre, nel <lb></lb><figure id="id.020.01.3384.2.jpg" xlink:href="020/01/3384/2.jpg"></figure></s></p><p type="caption">

<s>Figura 176.<lb></lb>sifone rappresentato dalla figura 176, le dette altezze di li­<lb></lb>vello si rispondono al contrario. </s>

<s>La ragion del fatto sarebbe <lb></lb>manifesta, quando il concavo GH premesse in giù il liquido <lb></lb>sottoposto, con più forza del concavo IK, e il convesso <lb></lb>LM premesse invece, nella medesima direzione, con minor <lb></lb>forza del convesso NO. </s>

<s>Ma tale è giusto il responso che <lb></lb>ne dà la formula del Laplace interpetrata. </s>

<s>Le colonne li­<lb></lb>quide infatti, e infinitamente strette, PQ, RS, possono, con <lb></lb>le loro estremità superiori, terminare o in una superficie <lb></lb>piana, o nel respettivo menisco, secondo che maggiore o <lb></lb>minore è il diametro del tubo. </s>

<s>Se la superficie è piana, la <lb></lb>pressione S in P è S=K, e nel mezzo di IK è S′=K—H/<emph type="italics"></emph>b′.<emph.end type="italics"></emph.end> Se la su­<lb></lb>perficie è concava, la pressione in P è S=K—H/<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> e nel mezzo di IK è <lb></lb>S′=K—H/<emph type="italics"></emph>b′.<emph.end type="italics"></emph.end> Ma perchè <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> raggio dell&#039;arco GH, è maggiore di <emph type="italics"></emph>b′,<emph.end type="italics"></emph.end> raggio <lb></lb>dell&#039;arco IK; è dunque il portato della formula che sempre GH preme in giù <lb></lb>maggiormente che IK, d&#039;onde avviene quella differente altezza di livello, che <lb></lb>s&#039;è detto osservarsi per esperienza. </s></p><p type="main">

<s>Se la colonnetta liquida RS, nella figura 176, termina in R, a una su-<pb xlink:href="020/01/3385.jpg" pagenum="346"></pb>perficie piana, abbiamo S=K, S′=K+H/<emph type="italics"></emph>b′:<emph.end type="italics"></emph.end> se poi termina alla conves­<lb></lb>sità del menisco, sono invece l&#039;equazioni S=K+H/<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> S′=K+H/<emph type="italics"></emph>b′.<emph.end type="italics"></emph.end><lb></lb>E perche <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> raggio della curvatura LRM, è maggiore dì <emph type="italics"></emph>b′,<emph.end type="italics"></emph.end> raggio della cur­<lb></lb>vatura NO, è dunque manifesto che in R è sempre minor la pressione, che <lb></lb>nel mezzo del medesimo arco NO, e per conseguenza quella delle due co­<lb></lb>lonne liquide sottoposte deve rimanere, come di fatto s&#039;osserva che rimane, <lb></lb>più sollevata di questa. </s></p><p type="main">

<s>La resultante della forza maggiore sulla minore, ne&#039;due descritti sifoni, <lb></lb>non è visibile in atto perchè, per l&#039;uguaglianza de&#039;momenti idrostatici, nei <lb></lb>due rami si fa l&#039;equilibrio, a quel modo che da un peso di due libbre non <lb></lb>si vede sollevare il peso di una libbra sola, posto a una distanza doppia dal <lb></lb>centro della bilancia. </s>

<s>Ma se, come nella bilancia dì braccia uguali, si potes­<lb></lb>sero disporre i liquidi nei recipienti, si vedrebbero attualmente i menischi <lb></lb>GH, NO di maggiori potenze spingere le colonne alla parte opposta, dove le <lb></lb>resistenze si sono dimostrate minori. </s>

<s>La desiderata disposizione la trovò bene <lb></lb>il Laplace in una esperienza antica, e della quale il Musschenbroek, benchè <lb></lb>s&#039;aiutasse col parallelogrammo delle forze, non riuscì, come vedemmo, a <lb></lb>dare una dimostrazione assoluta. </s></p><p type="main">

<s>“ Considerons maintenant une petite colonne de fluide, renformée dans <lb></lb>un tube conique capillaire, ouvert par ses deux extremité. </s>

<s>Soit ABCD (fig. </s>

<s>177) <lb></lb>ce tube, et M M′N′N le colonne fluide. </s>

<s>Supposons d&#039;abord l&#039;axe OE du tube <lb></lb><figure id="id.020.01.3385.1.jpg" xlink:href="020/01/3385/1.jpg"></figure></s></p><p type="caption">

<s>Figura 177.<lb></lb>horizontal, O étant le sommet du còne pro­<lb></lb>longé par la pensée. </s>

<s>Supposons de plus <lb></lb>la surface du fluide concave. </s>

<s>Il viessible <lb></lb>que le tube, etant plus etroit en <emph type="italics"></emph>p<emph.end type="italics"></emph.end> qu&#039;en <emph type="italics"></emph>p′,<emph.end type="italics"></emph.end><lb></lb>le rayon de courbure de sa surface est plus <lb></lb>petit, dans le premier point, que dans le <lb></lb>second. </s>

<s>En nominant donc <emph type="italics"></emph>b<emph.end type="italics"></emph.end> et <emph type="italics"></emph>b′<emph.end type="italics"></emph.end> ces ra­<lb></lb>yons l&#039;action du fluide en <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> sur un canal infiniment etroit <emph type="italics"></emph>pp′,<emph.end type="italics"></emph.end> sera K—H/<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> et <lb></lb>en <emph type="italics"></emph>p′<emph.end type="italics"></emph.end> cette action sera K—H/<emph type="italics"></emph>b:<emph.end type="italics"></emph.end> ainsi <emph type="italics"></emph>b′<emph.end type="italics"></emph.end> étant plus grand que <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> cette action <lb></lb>sera plus grande en <emph type="italics"></emph>p′<emph.end type="italics"></emph.end> qu&#039;en <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> et par conséquent le fluide renformé dans <lb></lb>le canal tendra a se mouvroir vers le sommet O du còne. </s>

<s>Ce serait le con­<lb></lb>traire, si la surface du fluide était convexe, car alors ces actions seraient <lb></lb>respectivement K+H<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> et K—H/<emph type="italics"></emph>b′.<emph.end type="italics"></emph.end> L&#039;action du fluide sur le canal est donc <lb></lb>alors plus grande en <emph type="italics"></emph>p<emph.end type="italics"></emph.end> qu&#039;en <emph type="italics"></emph>p′,<emph.end type="italics"></emph.end> et par consequent le fluide tend a se mou­<lb></lb>voir de <emph type="italics"></emph>p<emph.end type="italics"></emph.end> vers <emph type="italics"></emph>p′<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>32, 33), ce que (ripeteremo il detto dal Laplace <lb></lb>in altri simili propositi) l&#039;experience indique encore ” (ivi, pag. </s>

<s>25). </s></p><p type="main">

<s>A così fatte matematiche ragioni l&#039;autore del Supplemento al X libro <lb></lb>della Meccanica celeste riduceva il moto dell&#039;ascesa e della discesa de&#039;li-<pb xlink:href="020/01/3386.jpg" pagenum="347"></pb>quidi nei tubi capillari, non rimanendogli a far altro che dimostrare come <lb></lb>conseguissero dalla teoria i particolari accidenti, che si osservano in simili <lb></lb>esperienze, e particolarmente quello del vedere le dette ascese e discese farsi <lb></lb>con lunghezze, che sempre stanno in reciproca ragione dei raggi. </s>

<s>Attribuito <lb></lb>ad H il solito valore, e intendendosi per <foreign lang="grc">θ</foreign>, nella figura 171, l&#039;angolo IYV, <lb></lb>che il liquido, la gravità del quale sia <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> fa con la parete del tubo di rag­<lb></lb>gio <emph type="italics"></emph>l;<emph.end type="italics"></emph.end> il Laplace, nel caso che esso liquido salga, ne ritrova l&#039;altezza <emph type="italics"></emph>q<emph.end type="italics"></emph.end><lb></lb>espressa dall&#039;equazione <emph type="italics"></emph>q=H/g.cos<foreign lang="grc">θ</foreign>/l.<emph.end type="italics"></emph.end> Tale espressione analitica completa­<lb></lb>mente risponde ai fatti, la verità dei quali sappiamo oramai che dipende <lb></lb>dalla figura della superficie di livello, ossia dall&#039;angolo <foreign lang="grc">θ</foreign>, che, potend&#039;essere <lb></lb>o minore o uguale o maggiore di novanta gradi, fa sì che la detta superfi­<lb></lb>cie ora sia concava, ora piana, ora convessa. </s>

<s>Nel primo caso <emph type="italics"></emph>cos<foreign lang="grc">θ</foreign><emph.end type="italics"></emph.end> è positivo, <lb></lb>e positivo con esso anche <emph type="italics"></emph>q,<emph.end type="italics"></emph.end> e ciò vuol dire che il liquido s&#039;alza al di sopra <lb></lb>dell&#039;ordinario livello idrostatico. </s>

<s>Nel secondo caso <emph type="italics"></emph>cos<foreign lang="grc">θ</foreign><emph.end type="italics"></emph.end> e <emph type="italics"></emph>q<emph.end type="italics"></emph.end> sono zero, o sia <lb></lb>il liquido non s&#039;alza nè s&#039;abbassa: nel terzo caso finalmente <emph type="italics"></emph>cos<foreign lang="grc">θ</foreign>,<emph.end type="italics"></emph.end> e perciò <emph type="italics"></emph>q,<emph.end type="italics"></emph.end><lb></lb>son negativi, e ciò significa che .il liquido si abbassa. </s></p><p type="main">

<s>Per concluderne poi di qui che, o avvenga un&#039;elevazione o un abbas­<lb></lb>samento, sempre le distanze dal livello ordinario son reciprocamente propor­<lb></lb>zionali alle grandezze dei raggi, preso un tubo di raggio <emph type="italics"></emph>l′<emph.end type="italics"></emph.end> diverso da <emph type="italics"></emph>l,<emph.end type="italics"></emph.end> e <lb></lb>in cui l&#039;altezza della salita sia <emph type="italics"></emph>q′,<emph.end type="italics"></emph.end> avremo <emph type="italics"></emph>q:q′=H/g.cos<foreign lang="grc">θ</foreign>/l:H/g.cos<foreign lang="grc">θ</foreign>′/l′,<emph.end type="italics"></emph.end><lb></lb>ossia, nel caso che medesimo sia il liquido, e medesima la materia del tubo, <lb></lb><emph type="italics"></emph>q:q′=l′cos<foreign lang="grc">θ</foreign>:lcos<foreign lang="grc">θ</foreign>′.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Si osservi ora che <foreign lang="grc">θ</foreign> e <foreign lang="grc">θ</foreign>′ son, nella figura 170, l&#039;angolo formato dalla NR <lb></lb>(condotta perpendicolare alla tangente la curvità dell&#039;arginetto nel punto N) <lb></lb>con essa tangente: la quale NR essendo la resultante delle NL, NK, non <lb></lb>varia direzione, mentre che invariabili rimangano le materie del solido e del <lb></lb>liquido, nè dipende affatto dallo spazio, in cui s&#039;è descritto il quadrato MO, <lb></lb>o dalla distanza della parete AO all&#039;altra opposta del vaso: e insomma, trat­<lb></lb>tandosi di vasi cilindrici, quali sono i tubi che contempliamo, è affatto indi­<lb></lb>pendente dalla grandezza dei loro diametri. </s>

<s>Il Laplace faceva le medesime <lb></lb>osservazioni con quest&#039;altro, forse men facile, e meno chiaro discorso: “ La <lb></lb>surface du tube peut donc <gap></gap>tre considerée comme etant plane a tres-peu­<lb></lb>pres, dans un rayon egal a celui de sa sphère d&#039;activité sensible. </s>

<s>Le fluide <lb></lb>dans cette intervalle s&#039;abaissera donc ou s&#039;elevera depuis cette surface, a <lb></lb>tres-peu-pres comme si elle etait plane. </s>

<s>Au-de-la ce fluide, n&#039;etant plus sou­<lb></lb>mis sensiblement qu&#039;à la pesanteur et a son action sur lui-meme, sa surface <lb></lb>sera à-peu-pres celle d&#039;un segment sphèrique, dont les plans extrèmes etant <lb></lb>ceux de la surface fluide, aux limites de la sphère d&#039;activité sensible du tube, <lb></lb>seront à tres-peu-pres dans le divers tubes egalement inclinés à leurs pa­<lb></lb>rois, d&#039;ou il suit que tous ces segmens seroint semblables ” (pag. </s>

<s>4, 5). </s></p><p type="main">

<s>Se dunque <foreign lang="grc">θ</foreign> e <foreign lang="grc">θ</foreign>′ sono uguali, <emph type="italics"></emph>q:q′=l′:l,<emph.end type="italics"></emph.end> secondo che, per corri­<lb></lb>spondere con l&#039;esperienza, doveva resultarne dalla teoria. </s>

<s>Come poi ciò re-<pb xlink:href="020/01/3387.jpg" pagenum="348"></pb>sultasse anche dalla formula del Clairaut, fu da noi già fatto notare, contro <lb></lb>il giudizio che ne dette lo stesso Laplace, il quale ebbe nonostante ragione, <lb></lb>quando disse che quel grande Geometra non aveva nella sua formula inse­<lb></lb>riti i principii, dai quali far conseguire un&#039;altra legge, che s&#039;osserva costan­<lb></lb>temente nella quantità dell&#039;ascesa de&#039;liquidi su per spazii strettissimi, in co­<lb></lb>lonne parallelepipede, come fra due lamine parallele di vetro, pochissimo fra <lb></lb>sè distanti. </s>

<s>L&#039;impotenza di dimostrar la qual legge fece il Laplace derivare <lb></lb>dal non aver saputo il Clairaut spiegare co&#039;suoi principii le proporzioni delle <lb></lb>salite de&#039;liquidi, nei tubi cilindrici, in virtù di alcune proprie e ben definite <lb></lb>leggi dell&#039;attrazione. </s>

<s>“ La connaissance de ces lois est cependant le point <lb></lb>le plus delicat, et le plus important de cette theorie: elle est indispensable <lb></lb>pour lier entre eux les divers phénomènes capillaires, et Clairaut en eùt <lb></lb>lui-meme reconnu la necessité, s&#039;il eût voulu, par exemple, passer des tubes <lb></lb>aux espaces capillaires renformés entre des plans paralleles, et deduire de <lb></lb>l&#039;analyse le rapport d&#039;egalité, que l&#039;experience indique entre l&#039;ascension du <lb></lb>fluide dans un tube cylindrique, et son ascension entre deux plans paralle­<lb></lb>les, dont la distance mutuelle est égale au demì-diametre du tube, ce que <lb></lb>personne encore n&#039;a tenté d&#039;expliquer ” (ivi, pag. </s>

<s>2). </s></p><p type="main">

<s>Di giungere alla quale spiegazione il Laplace si preparava le vie, appli­<lb></lb>cando l&#039;analisi precedente a determinar l&#039;altezza, a cui può giungere un li­<lb></lb>quido, dentro l&#039;angusto spazio interposto fra la superficie convessa di un ci­<lb></lb>lindro solido, e la concava di un tubo a lui concentrico, e ambedue composte <lb></lb>della stessa materia. </s>

<s>Se <emph type="italics"></emph>l<emph.end type="italics"></emph.end> sia il raggio della sezione del tubo, e <emph type="italics"></emph>l′<emph.end type="italics"></emph.end> quello <lb></lb>della sezion del cilindro, rappresentando H, <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> <foreign lang="grc">θ</foreign> i medesimi valori della for­<lb></lb>mula precedente, il Laplace giunge à determinare la quantità <emph type="italics"></emph>q′<emph.end type="italics"></emph.end> della richie­<lb></lb>sta altezza, per via dell&#039;equazione <emph type="italics"></emph>q′=H/g.cos<foreign lang="grc">θ</foreign>/(l—l′),<emph.end type="italics"></emph.end> la quale, paragonata con <lb></lb>quell&#039;altra di <emph type="italics"></emph>q,<emph.end type="italics"></emph.end> che dianzi l&#039;Autore stesso ritrovava; gli fa legittimamente <lb></lb>argomentare essere l&#039;altezza del liquido dentro l&#039;anello la medesima, che <lb></lb>dentro un tubo cilindrico, avente raggio uguale a <emph type="italics"></emph>l—l&#039;.<emph.end type="italics"></emph.end> Giunto alla qual <lb></lb>conclusione, è notabile che il Laplace confidi al corollario seguente il me­<lb></lb>rito e i vanti della sua scoperta: “ En supposant infinis les rayon du tube <lb></lb>et du cylindre, on avra le cas de deux plans verticaus et paralleles tres­<lb></lb>precues l&#039;un de l&#039;autre: le theorema precedent a donc encore lieu dans ce cas, <lb></lb>que nous allons traiter par une analyse particuliere ” (ivi, pag. </s>

<s>28). </s></p><p type="main">

<s>Da questa storia argomenteranno forse i Lettori che le speculazioni ana­<lb></lb>litiche del Laplace, quanto sono ingegnose, altrettanto sian semplici. </s>

<s>Vero è <lb></lb>bene che, de&#039;calcoli di lui, abbiamo riferite le sole conclusioni, ma chi vo­<lb></lb>lesse ritesserne i processi non ci troverebbe difficoltà, pur che egli avesse <lb></lb>notizia delle regole elementari del calcolo infinitesimale. </s>

<s>Nonostante, chiun­<lb></lb>que si metta a svolgere le pagine del citato <emph type="italics"></emph>Supplemento,<emph.end type="italics"></emph.end> in ritrovarle così <lb></lb>per tutto cincischiate di simboli algebriei e d&#039;equazioni, involte in grappe <lb></lb>corpulente, e in parentesi, riformerebbe il giudizio intorno alla semplicità delle <lb></lb>supposte regole elementari. </s></p><pb xlink:href="020/01/3388.jpg" pagenum="349"></pb><p type="main">

<s>Di qui coglieranno i curiosi occasione di domandare: se quel suntuoso <lb></lb>macchinamento di calcoli fu scelto dall&#039;Autore, per fare sfoggio della sua <lb></lb>arte analitica, o perchè veramente fosse di necessità richiesto dall&#039;indole del <lb></lb>soggetto. </s>

<s>Per rispondere a ciò, giova rammemorare quel che altrove osser­<lb></lb>vammo dell&#039;onnipotenza, che s&#039;incominciò ad attribuire all&#039;analisi matema­<lb></lb>tica, dopo l&#039;Eulero. </s>

<s>Per quel che poi particolarmente riguarda il Laplace, <lb></lb>non si vuol dimenticare l&#039;esempio, che ne dette nella dimostrazione del pa­<lb></lb>rallelogrammo delle forze: e come questa, condotta per via del calcolo dif­<lb></lb>ferenziale, riuscì inutile, anzi dannosa; così potrebb&#039;essere che inutili e dan­<lb></lb>nosi riuscissero certi processi, nel trattato delle azioni capillari. </s>

<s>Si vorrà <lb></lb>dunque dire che fu questa un&#039;arte dell&#039;Autore, per soggiogare gl&#039;ingegni? </s>

<s><lb></lb>Veramente una tal&#039;arte è molto in voga presso certi filosofi, e certi poeti, <lb></lb>che si fanno ammirare, per non essere intesi, e per saper, con un gioco di <lb></lb>prospettiva, far apparire gli oggetti così lontani, da non si credere accessi­<lb></lb>bili alle braccia di tutti, i quali perciò si rassegnano a riconoscersi pigmei, <lb></lb>umiliandosi a quelli, che, rispetto a loro, debbon dunque esser giganti. </s></p><p type="main">

<s>Comunque sia, il Laplace trovò molti che rimasero così soggiogati, fra <lb></lb>i quali il Rumfort basti per tutti. </s>

<s>Gettandosi in faccia al valoroso Fisico che <lb></lb>la pellicola superficiale de&#039;liquidi veniva a dissiparsi, come un fantasma, in­<lb></lb>nanzi alle verità dimostrate dal Laplace; rispondeva che la <emph type="italics"></emph>coesione<emph.end type="italics"></emph.end> fra le <lb></lb>minime particelle, necessaria al formarsi le dette pellicole, non differiva in <lb></lb>sostanza dall&#039;attrazione molecolare. </s>

<s>Che se non ne aveva dimostrate le leggi, <lb></lb>ingenuamente confessava esserne causa la così poco profonda conoscenza, che <lb></lb>trovava in sè dell&#039;alta analisi matematica. </s>

<s>“ Je dois pourtant avouer que je <lb></lb>ne suis pas assez versé dans la haute Geometrie, pour pouvoir bien com­<lb></lb>prendre les calculs de M. </s>

<s>De la Place sur ce sujet, et je me garderai bien <lb></lb>de les juger. </s>

<s>Il faudroit sans doute avoir une connoissance tres-profonde des <lb></lb>methodes analityques, pour sentir la force de ses demonstrations ” (<emph type="italics"></emph>Bibl. </s>

<s><lb></lb>Brit., mois de Mai 1807, Sciences et Arts,<emph.end type="italics"></emph.end> pag. </s>

<s>3). </s></p><p type="main">

<s>Quel che però a noi più importa è di narrare le sorti, che le teorie del <lb></lb>Laplace incontrarono in Italia: sorti ch&#039;essendo state varie ci contenteremo <lb></lb>di veder rappresentate negli scritti de&#039;due valenti fisici e matematici, Gio­<lb></lb>vacchino Pessuti, e Fabrizio Mossotti. </s></p><p type="main">

<s>Il dì 22 Maggio 1808 la Società italiana delle Scienze riceveva la Me­<lb></lb>moria del Pessuti intorno alla <emph type="italics"></emph>Teoria dell&#039;azion capillare del signor De-la­<lb></lb>Place, ridotta alla più semplice ed elementare Geometria.<emph.end type="italics"></emph.end> Diceva nel proe­<lb></lb>mio l&#039;Autore di essersi messo all&#039;opera, in grazia di coloro che, non avendo <lb></lb>le sottigliezze dell&#039;analisi sublime così familiari, erano perciò impediti di gu­<lb></lb>star le bellezze delle verità dimostrate dall&#039;Autore della Meccanica celeste. </s>

<s><lb></lb>Ma accadde per verità al Pessuti come a chi troppo largamente promette. </s>

<s><lb></lb>La semplice Geometria elementare, essendo strumento troppo ottuso a pene­<lb></lb>trar la durezza del soggetto; non potè nemmeno il Nostro fare a meno di <lb></lb>introdurre qualche equazione differenziale, con i suoi integrali, chi sa la re­<lb></lb>gola delle quali operazioni non trova difficoltà nel tener dietro ai passi del <pb xlink:href="020/01/3389.jpg" pagenum="350"></pb>Matematico francese, benchè siano più lunghi, e più intricati. </s>

<s>Nè dall&#039;altra <lb></lb>parte ci deliberano da questa pena parecchie analisi geometriche della detta <lb></lb>Memoria, il merito della quale consiste nell&#039;aver dato miglior ordine al me­<lb></lb>todo, d&#039;onde vengono a scoprirsi certe fallacie, e a scansarsi alcuni errori, <lb></lb>ne&#039;quali nessuno forse, prima del Pessuti, avrebbe sospettato mai fosse ca­<lb></lb>duto un matematico come il Laplace. </s></p><p type="main">

<s>Nel citato <emph type="italics"></emph>Supplemento<emph.end type="italics"></emph.end> fa l&#039;Autore conseguir dalla sua analisi generale <lb></lb>la soluzion del problema, fisicamente risoluto già dal Borelli, il quale però <lb></lb>non aveva ancora osservato che quell&#039;attrarsi scambievole de&#039;leggieri corpu­<lb></lb><figure id="id.020.01.3389.1.jpg" xlink:href="020/01/3389/1.jpg"></figure></s></p><p type="caption">

<s>Figura 178.<lb></lb>scoli sull&#039;acqua, era proprio anche a due la­<lb></lb>stre di vetro, poste nelle medesime condizioni. </s></p><p type="main">

<s>Siano NR, MB (fig. </s>

<s>178) i profili delle <lb></lb>due dette lastre, fra le quali, standosi elle <lb></lb>prossime, salga sopra il naturale livello VPV′ <lb></lb>il liquido infino in NOM, formando all&#039;esterno <lb></lb>gli arginetti VZ, V′Z′. </s>

<s>Il Laplace dimostra <lb></lb>che la pressione del liquido sopra la NR, per <lb></lb>farla aderire alla MB, uguaglia il peso di <lb></lb>una mezza colonna parallelepipeda di liquido, <lb></lb>avente per base il rettangolo di NZ nella lar­<lb></lb>ghezza della lastra, e per altezza NG+GZ. </s>

<s><lb></lb>Dopo che immediatamente così soggiunge: <lb></lb>“ Un resultat semblable a lieu pour le plan MB, on a donc ainsi la force, <lb></lb>avec la quelle les deux plans tendent a se rapprocher, et l&#039;on voit que cette <lb></lb>force eroit en raison inverse de leur distance mutuelle ” (pag. </s>

<s>44). </s></p><p type="main">

<s>Ma si contiene in queste parole un&#039;errore manifesto. </s>

<s>Chiamata infatti L <lb></lb>la larghezza della lamina, la forza F della pressione è dunque, secondo il <lb></lb>Laplace, uguale a (L.NZ(NG+GZ))/2=(L.NZ(NZ+2GZ))./2 Accostandosi di <lb></lb>più o scostandosi NR da MB, e perciò il livello da N alzandosi o abbassan­<lb></lb>dosi in N′, la nuova forza che ne resulta sarà uguale a L.N′Z(N′Z+2GZ)/2, <lb></lb>e perciò avremo F:F′=NZ(NZ+2GZ):N′Z(N′Z+2GZ). E perchè <lb></lb>GZ, che è quantità piccolissima rispetto a NZ e a N′Z, può trascurarsi; <lb></lb>F:F′=NZ2:N′Z2. </s>

<s>Considerando poi che, essendo uguali gli arginetti dalla <lb></lb>parte di dentro e da quella di fuori, NL=ZG, e perciò NZ=OP, N′Z= <lb></lb>O′P: e che inoltre OP, OP′, altezze delle colonne liquide fra le due lastre, <lb></lb>stanno reciprocamente come le D′, D, loro mutue distanze; s&#039;otterrà final­<lb></lb>mente F:F′=D′2:D2. </s>

<s>E di qui appar manifesto che le forze impellenti <lb></lb>le lastre al contatto sono in ragion dei quadrati, e non in semplice <emph type="italics"></emph>raison <lb></lb>inverse de leur distance mutuelle.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il Pessuti si conferma nella verità di questa legge, per analogia di ciò <lb></lb>che si osserva in tutte le attrazioni a sensibile distanza, e attribuisce l&#039;as­<lb></lb>serzione del signor De la Place, che lo fa stupire, <emph type="italics"></emph>o a una svista o a un<emph.end type="italics"></emph.end><pb xlink:href="020/01/3390.jpg" pagenum="351"></pb><emph type="italics"></emph>crrore di stampa. (Memorie<emph.end type="italics"></emph.end> cit., T. XIV, P. I, Verona 1809, pag. </s>

<s>142 in <lb></lb>nota). Comunque sia, non sembra a noi che valgano queste scuse là, dove <lb></lb>il Laplace stesso deduce, dal valore di <emph type="italics"></emph>q′=H/g.cos<foreign lang="grc">θ</foreign>′/(l—l′),<emph.end type="italics"></emph.end> la quantità del­<lb></lb>l&#039;altezza, a cui giunge il liquido fra due lastre parallele, supponendo che <lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end> e <emph type="italics"></emph>l′,<emph.end type="italics"></emph.end> raggi, siano di lunghezza infinita. </s>

<s>Perch&#039;essendo gl&#039;infiniti uguali, la <lb></lb>loro differenza <emph type="italics"></emph>l—l′<emph.end type="italics"></emph.end> è zero, e il non si concluder nulla dall&#039;equazione dà <lb></lb>segno manifesto che il metodo è sbagliato. </s></p><p type="main">

<s>L&#039;origine dello sbaglio è dall&#039;avere il Laplace giudicata la formula del <lb></lb>Clairaut difettosa, in dimostrare le proporzioni dell&#039;ascesa de&#039;liquidi in due <lb></lb>tubi di vario diametro, e in mezzo a due lastre, poste a più o men prossima <lb></lb>distanza fra loro. </s>

<s>Ma principalmente è a riconoscersi quella origine dall&#039;aver <lb></lb>voluto far dipendere la dimostrazione dei due fatti distinti da una medesima <lb></lb>analisi generale. </s>

<s>Il bisogno di questa analisi non si faceva però giustamente <lb></lb>sentire, se non colà, dove, dai semmenti di sfera o dai menischi, si faceva <lb></lb>trapasso ad altra qualità di figure, come sarebbe quella, che prende la li­<lb></lb>quida superficie fra due lastre di vetro, molto prossime e parallele. </s></p><p type="main">

<s>Che del resto la particolar formula del Clairaut, non solo era sufficiente, <lb></lb>ma porgeva il mezzo più semplice e più diretto di dimostrare che, nei tubi <lb></lb>assai stretti, le altezze son reciprocamento proporzionali ai raggi delle se­<lb></lb>zioni, come conseguenza immediata delle forze attrattive dei menischi. </s>

<s>Il La­<lb></lb>place invece volle ciò dedurre dalla formula generale, che concludeva il va­<lb></lb>lore di quelle stesse forze attrattive per qualunque genere di superficie, e <lb></lb>giunse, come si sa, a dar l&#039;altezza della colonna liquida nell&#039;interno del <lb></lb>tubo, espressa dal prodotto della costante H, nel coseno di <foreign lang="grc">θ</foreign>, diviso per il <lb></lb>raggio. </s>

<s>Per fare apparir poi la relazione, che questa legge della salita nei <lb></lb>tubi cilindrici ha con la legge della salita nell&#039;interstizio di due lastre pa­<lb></lb>rallele, collega i due fatti con quello della salita su per lo spazio annulare, <lb></lb>lasciato fra un cilindro e il tubo che lo circonda, perche questi, mentre <lb></lb>partecipano delle proprietà de&#039;cannelli, essendo piccoli i raggi, si rendono <lb></lb>poi facilmente alle condizioni delle lastre parallele, supponendo quegli stessi <lb></lb>raggi grandissimi o infiniti. </s>

<s>Ma come in questo caso divenga muta di ogni <lb></lb>espressione la formula del Laplace, già fu detto, e di ciò accortosi il Pes­<lb></lb>suti, pur serbandosi fedele alle dottrine del grande Matematico francese, <lb></lb>dette altr&#039;ordine al metodo di lui, e, se non sempre più semplice, lo ridusse <lb></lb>certamente a più logica ragione. </s></p><p type="main">

<s>Come, dal caso particolare che la superficie attraente sia in figura di <lb></lb>semmento sferico, si deduca la quantità dell&#039;altezza del liquido, in un can­<lb></lb>nello cilindrico, molto più facilmente che deducendola dalla general formula <lb></lb>del Laplace; il Pessuti lo dimostra con un esempio, che si può, col seguente <lb></lb>discorso, rendere anche più semplice e più spedito. </s>

<s>Sia nel tubo AF (fig. </s>

<s>179) <lb></lb>il solito filetto DQ, comunicante, per mezzo del canaliculo QR, con RI, ter­<lb></lb>minato in I a un punto della GH, superficie del liquido, in cui si suppone <lb></lb>il detto tubo essere immerso. </s>

<s>Tenendosi per ragione idrostatica IR con LQ <pb xlink:href="020/01/3391.jpg" pagenum="352"></pb>in equilibrio, dunque DL non preme niente sopra la sua base L, ciò che <lb></lb>dev&#039;essere, perchè alla forza del peso di lui è uguale e contraria l&#039;azion del <lb></lb>menisco. </s>

<s>Ma questa è K/<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> e quello, cioe il peso della porzione DL, chia­<lb></lb>mata <emph type="italics"></emph>g<emph.end type="italics"></emph.end> la gravità specifica del liquido, è manifestamente <emph type="italics"></emph>g<emph.end type="italics"></emph.end>.DL; dunque <lb></lb><emph type="italics"></emph>K/b=g.DL,<emph.end type="italics"></emph.end> ossia DL=K/<emph type="italics"></emph>g.b.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Come poi questa espressione semplicissima risponda alle varie condi­<lb></lb><figure id="id.020.01.3391.1.jpg" xlink:href="020/01/3391/1.jpg"></figure></s></p><p type="caption">

<s>Figura 179.<lb></lb>zioni del problema, non meno di <lb></lb>quell&#039;altra, che il Laplace ricavò <lb></lb>con calcolo sì laborioso dalla sua <lb></lb>formula generale; si vedrà facil­<lb></lb>mente per ognuno, che voglia met­<lb></lb>tersi a farne la prova. </s>

<s>Se <emph type="italics"></emph>b<emph.end type="italics"></emph.end> infatti <lb></lb>che risponde al raggio DC, dise­<lb></lb>gnato nella figura, è infinito (ciò <lb></lb>che significa essere la superficie <lb></lb>piana) DL è zero. </s>

<s>E se <emph type="italics"></emph>b<emph.end type="italics"></emph.end> è nega­<lb></lb>tivo, che vuol dire trasformarsi la <lb></lb>superficie di concava in convessa, <lb></lb>anche DL ha valor negativo, ossia, <lb></lb>come nel mercurio si osserverebbe, <lb></lb>avremmo una depressione della co­<lb></lb>lonnetta liquida sotto il livello di <lb></lb>GH, in luogo di un alzamento. </s></p><p type="main">

<s>Con la medesima semplicità vien portato, da questo indirizzo, il Pessuti <lb></lb>a concludere le ragioni delle altezze, in due tubi, reciproche alle lunghezze <lb></lb>dei raggi. </s>

<s>Perchè, preso insieme con l′AF, un altro tubo NM, in cui l&#039;al­<lb></lb>tezza del liquido viene espressa per XM=K/<emph type="italics"></emph>g.b′,<emph.end type="italics"></emph.end> essendo <emph type="italics"></emph>b′<emph.end type="italics"></emph.end>=PX, raggio <lb></lb>della curvatura del menisco NXO; si giunge alla proporzione DL:XM= <lb></lb>PX:CD. </s>

<s>E perchè i raggi PX, CD, per la similitudine degli archi NXO, <lb></lb>ADB, stanno come le respettive corde, che sono i diametri dei tubi; dun­<lb></lb>que DL:XM=NO:AB. </s></p><p type="main">

<s>Il teorema della salita del liquido, fra due lamine parallele, è di un or­<lb></lb>dine superiore a questo, e perciò saggiamente il Pessuti ne distinse la dimo­<lb></lb>strazione, facendola dipendere da principii più complicati, secondo il com­<lb></lb>plicarsi della figura, che là era un semmento di sfera o un menisco, e qua <lb></lb>un semmento di cilindro o una doccia. </s>

<s>Nella sfera basta la sezione di un <lb></lb>piano, essendo la curvatura simmetrica intorno a un asse solo. </s>

<s>Ma, dove <lb></lb>manca una tale semplicità di simmetria, ci vogliono due sezioni perpendi­<lb></lb>colari, e perciò due saranno i raggi delle curvature, o delle osculazioni, che <lb></lb>debbono considerarsi. </s>

<s>Di qui è che il Laplace formulava così quel suo prin­<lb></lb>cipio generale, per altre più semplici vie dimostrato poi dal nostro Pessuti: <pb xlink:href="020/01/3392.jpg" pagenum="353"></pb>“ Dans toutes les lois, qui rendent l&#039;attraction insensible à des distances sen­<lb></lb>sibles, l&#039;action d&#039;un corps terminé par une surface courbe, sur un canal in­<lb></lb>terieur infiniment etroit, perpendiculaire a cette surface, dans un point quel­<lb></lb>conque; est egale à la demi-somme des actions sur le meme canal de deux <lb></lb>sphères, qui auraient pour rayons le plus grand, et le plus petit des rayons <lb></lb>osculateurs de la surface a ce point ” (<emph type="italics"></emph>Supplement<emph.end type="italics"></emph.end> cit., pag. </s>

<s>4). E perciò <lb></lb>sarà per simboli questo principio espresso da <emph type="italics"></emph>H/z(1/b+1/b′)<emph.end type="italics"></emph.end> dove H è la <lb></lb>solita costante, e <emph type="italics"></emph>b, b′<emph.end type="italics"></emph.end> i due detti raggi osculatori. </s></p><p type="main">

<s>Rappresenti ora ABCD (fig. </s>

<s>180) un piccolo tratto della doccia, secondo <lb></lb>la quale si dispone il livello del liquido, fra le due lastre, e si consideri <lb></lb>l&#039;azione attrattiva di lei nel punto I, uno de&#039;raggi osculatori al quale, cioè <lb></lb><emph type="italics"></emph>b<emph.end type="italics"></emph.end> sarà quello del circolo, a cui appartiene l&#039;arco BIC. </s>

<s>Ma l&#039;altro raggio, rap­<lb></lb>presentato da <emph type="italics"></emph>b′<emph.end type="italics"></emph.end> e diretto secondo la IK, tornerà infinito, essendo EF una <lb></lb>linea retta. </s>

<s>Dunque in questo caso 1/<emph type="italics"></emph>b′<emph.end type="italics"></emph.end> sparisce dalla formula, la quale perciò <lb></lb>si riduce ad H/2<emph type="italics"></emph>b.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ciò stante, si applichi l&#039;azione della superficie ABCD in attrarre il filetto <lb></lb>IG in mezzo alla colonna parallelepipeda AM, e si consideri insieme il me­<lb></lb><figure id="id.020.01.3392.1.jpg" xlink:href="020/01/3392/1.jpg"></figure></s></p><p type="caption">

<s>Figura 180.<lb></lb>nisco NOP, il raggio di curva­<lb></lb>tura del quale uguagli quello di <lb></lb>BC, applicato ad attrarre nel <lb></lb>punto O il filetto OQ, dentro <lb></lb>il cilindro NR. </s>

<s>Essendo la su­<lb></lb>perficie, nel vaso dell&#039;immer­<lb></lb>sione, TV, e SG in equilibrio <lb></lb>idrostatico con LH, il peso della <lb></lb>porzione IS, che, ritenute le de­<lb></lb>nominazioni di sopra, è <emph type="italics"></emph>g<emph.end type="italics"></emph.end>.IK, <lb></lb>vien sostenuto dall&#039;azion contra­<lb></lb>ria della superficie a doccia, nel <lb></lb>punto I. </s>

<s>E perchè l&#039;intensità di quest&#039;azione ha, come s&#039;è detto, per misura H/2<emph type="italics"></emph>b;<emph.end type="italics"></emph.end><lb></lb>dunque <emph type="italics"></emph>g.IS=H/2b.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Similmente, essendo XQ equilibrato da YQ, e il peso della porzione OX, <lb></lb>che è uguale a <emph type="italics"></emph>g<emph.end type="italics"></emph.end>.OX, sostenuto dall&#039;azione attrattiva del menisco nel punto O, <lb></lb>con intensità espressa da H/<emph type="italics"></emph>b;<emph.end type="italics"></emph.end> s&#039;avrà <emph type="italics"></emph>g.OX=H/b,<emph.end type="italics"></emph.end> e perciò IS:OX=1:2. <lb></lb>Abbiasi poi un altro tubo cilindrico, di diametro uguale alla metà di NP, e <lb></lb>in cui salga il medesimo liquido all&#039;altezza A: sarà per la nota legge spe­<lb></lb>rimentale OX:A=2:1, la qual proporzione, moltiplicata per la prece­<lb></lb>dente, dà IS.OX=A.OX, ossia IS=A. </s>

<s>Ciò vuol dire tale essere l&#039;al-<pb xlink:href="020/01/3393.jpg" pagenum="354"></pb>tezza della colonna parallelepipeda AM, e di tutte le altre simili, in che può <lb></lb>distinguersi il liquido, salito fra due lamine parallele, quale in un tubo cilin­<lb></lb>drico, avente un raggio pari alla distanza fra le lamine stesse, conforme a ciò <lb></lb>che fu primo a dimostrare il Laplace, e che fu l&#039;oggetto delle sue compiacenze. </s></p><p type="main">

<s>L&#039;altro simile teorema delle salite de&#039;liquidi su per gl&#039;interstizi annu­<lb></lb>lari; dallo stesso Laplace introdotto, per collegare insieme gli effetti, che si <lb></lb>osservano nei tubi cilindrici, con quelli, che si osservano nelle lamine paral­<lb></lb>lele, diviene per il Pessuti indipendente, e può riguardarsi come nn corol­<lb></lb>lario delle azioni attrattive della liquida superficie fra le lamine stesse. </s>

<s>È ma­<lb></lb>nifesto infatti valere la medesima dimostrazione, sia quando la base della <lb></lb>superficie a doccia è un rettangolo, sia quando ella invece è un trapezio, per <lb></lb>essere il lato del poligono inscritto al tubo sempre maggiore del corrispon­<lb></lb>dente lato del poligono circoscritto al cilindro concentrico, fra cui e lo stesso <lb></lb>tubo si forma l&#039;anello. </s></p><p type="main">

<s>Non è che, sebben rese così più dimestiche, le teorie del Laplace sodi­<lb></lb>sfacessero in tutto ai nostri Fisici e Matematici. </s>

<s>Ma la fama dell&#039;Autore, il <lb></lb>periglioso gorgo, toccato in ogni più riposto seno del suo fondo, e lo stesso <lb></lb>magnifico apparato dell&#039;analisi infinitesimale, concorsero tutt&#039;insieme a dif­<lb></lb>fondere anche fra noi le dottrine del Matematico francese, più efficacemente <lb></lb>dei commentarii fattivi dal Pessuti. </s>

<s>Esaminatasi poi, con mente più riposata, <lb></lb>la sottile questione, la facile onda dei plausi s&#039;arretrò al soffiare avverso <lb></lb>delle censure, intanto che il Mossotti (<emph type="italics"></emph>Lezioni di Fisica matemat.,<emph.end type="italics"></emph.end> T. I, Fi­<lb></lb>renze 1843, pag. </s>

<s>130) giudicò non aver fatto altro il Laplace che <emph type="italics"></emph>adombrare, <lb></lb>con poca esattezza,<emph.end type="italics"></emph.end> la teoria del Joung, ripresa dal Poisson, e condotta alla <lb></lb>sua perfezione. </s></p><p type="main">

<s>Il quinto libro del <emph type="italics"></emph>Traité de Macanique<emph.end type="italics"></emph.end> è dal Poisson riserbato all&#039;Idro­<lb></lb>statica, e nel secondo capitolo si propone di trovar l&#039;equazion generale del­<lb></lb>l&#039;equilibrio dei fluidi, le particelle de&#039;quali, prese d&#039;insensibile grandezza, <lb></lb><figure id="id.020.01.3393.1.jpg" xlink:href="020/01/3393/1.jpg"></figure></s></p><p type="caption">

<s>Figura 181.<lb></lb>si possono riguardare, egli dice, <emph type="italics"></emph>comme <lb></lb>une masse continue, dont la densité est <lb></lb>constante,<emph.end type="italics"></emph.end> benchè anch&#039;essi fluidi, come <lb></lb>tutte le altre sostanze, e i corpi solidi, <lb></lb>nel complesso della loro mole, siano com­<lb></lb>posti <emph type="italics"></emph>des molecoles disjointes et separées <lb></lb>par des espaces vides<emph.end type="italics"></emph.end> (Bruxelles 1838, <lb></lb>pag. </s>

<s>366). Dentro la massa fluida ABCD <lb></lb>(fig. </s>

<s>181) si consideri un punto M, rife­<lb></lb>rito ai tre assi ortogonali O<emph type="italics"></emph>x,<emph.end type="italics"></emph.end> O<emph type="italics"></emph>y,<emph.end type="italics"></emph.end> O<emph type="italics"></emph>z<emph.end type="italics"></emph.end> dalle <lb></lb>ordinate <emph type="italics"></emph>x, y, z,<emph.end type="italics"></emph.end> e siano X, Y, Z le forze <lb></lb>date, che lo sollecitano secondo quelle tre <lb></lb>direzioni: chiamata <foreign lang="grc">ρ</foreign> la densità del fluido, la pressione <emph type="italics"></emph>p<emph.end type="italics"></emph.end> sofferta dal detto <lb></lb>punto M è per il Poisson espressa dall&#039;equazione <emph type="italics"></emph>dp=<foreign lang="grc">ρ</foreign>(Xdx+Ydy+Zdz).<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Lorsque le point M (osserva poi l&#039;Autore) est situe a la surface du <lb></lb>fluide, ou qu&#039;il n&#039;en est eloigné que d&#039;une distance moindre que le rayon <pb xlink:href="020/01/3394.jpg" pagenum="355"></pb>d&#039;activité des forces moleculaires, on doit avoir égard a ces forces, et à la <lb></lb>variation rapide de la densité superficielle, dans le calcul des composantes <lb></lb>X, Y, Z, et par suite de la valeur de <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> déduite de la formule. </s>

<s>Il en resulte <lb></lb>une influence des forces moleculaires sur la figure du liquide en equilibre, <lb></lb>qui n&#039;est pas sensible en general, et qui ne le devient que dans les espaces <lb></lb>capillaires. </s>

<s>On ny aura point égard dans ce Traité, et, pour tout ce qui con­<lb></lb>cerne les phenomènes de la capillarité, je renverrai à la <emph type="italics"></emph>Nouvelle theorie <lb></lb>de l&#039;action capillaire,<emph.end type="italics"></emph.end> que j&#039;ai publiée il y a deux ans ” (ivi, pag. </s>

<s>375). </s></p><p type="main">

<s>Abbiamo voluto trascrivere nella sua integrità questo passo, perchè con­<lb></lb>tiene in germe la teoria, che il Poisson dava delle azioni capillari, per ve­<lb></lb>dere lo svolgimento della quale converrebbe consultare il trattato, che vi sì <lb></lb>cita, e donde apparirebbero i criteri, a cui s&#039;informò il giudizio del Mos­<lb></lb>sotti. </s>

<s>Ma di questa consultazione dobbiam lasciare agli studiosi ogni cura, <lb></lb>per non dilungarci di troppo dai termini, che sono stati imposti alla nostra <lb></lb>Storia. </s></p><pb xlink:href="020/01/3395.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VI.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Delle prime speculazioni ed esperienze <lb></lb>d&#039;Idrodinamica<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Delle leggi idrodinamiche incluse nei teoremi idrostatici di Galileo, e spiegate dal Castelli nel primo <lb></lb>libro Della misura delle acque correnti. </s>

<s>— II. </s>

<s>Delle relazioni tra il Discorso galileiano intorno <lb></lb>i galleggianti, e il primo libro Della misura delle acque correnti: della pubblicazione di questo <lb></lb>libro, di cui si volle dire che la scienza non era nuova. </s>

<s>— III. </s>

<s>Della legge delle velocitá pro­<lb></lb>porzionali alle altezze, assegnata dal Castelli nel secondo libro Della misura delle acque cor­<lb></lb>renti, di cui si difende la proprietà contro le accuse di plagio. </s>

<s>— IV. </s>

<s>Delle prime rivelazioni, <lb></lb>e delle prime proposte relative alla legge delle velocità proporzionali alle radici delle altezze, </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>L&#039;ascesa dei liquidi nei tubi capillari, e la loro discesa rispetto al li­<lb></lb>vello del più largo vaso, dentro cui si siano immersi, o la differente altezza, <lb></lb>a cui essi liquidi giungono, essendo il cannello e il vaso continuati, si no­<lb></lb>tarono da lungo tempo come fatti eccezionali alla legge idrostatica, che co­<lb></lb>stantemente s&#039;osserva in tutti i fluidi comunicanti. </s>

<s>Altri fatti però occorsero <lb></lb>ad osservarsi, che fanno alla detta legge un&#039;eccezione anche più singolare, <lb></lb>per cui richiamarono a sè l&#039;attenzione dei Fisici moderni. </s></p><p type="main">

<s>Vincenzo Brunacci incomincia così un suo opuscolo che, insieme con <lb></lb>altri scritti in diverse occasioni, fu pubblicato dal Silvestri di Milano, dopo <lb></lb>la <emph type="italics"></emph>Memoria sulla dispensa delle acque<emph.end type="italics"></emph.end> del medesimo Autore: “ Dal sapersi <lb></lb>dimostrato nella Idraulica che in due vasi comunicanti il fluido si pone al <lb></lb>livello; dal vedersi sempre verificata questa legge negli sperimenti instituiti <lb></lb>a bella posta, e riferiti in tutte le Scuole; è dessa passata, per così dire, in <lb></lb>proverbio, in guisa che, anche gl&#039;ignari delle più semplici dottrine delle acque <lb></lb>correnti, ogni momento te la ripetono. </s>

<s>Ma è ella poi vera, anco quando la <pb xlink:href="020/01/3396.jpg" pagenum="357"></pb>comunicazione da un vaso all&#039;altro è oltremodo difficile ed impedita? </s>

<s>” (<emph type="italics"></emph>Bi­<lb></lb>blioteca scelta,<emph.end type="italics"></emph.end> T. CCVIII, Milano 1827, pag. </s>

<s>151). </s></p><p type="main">

<s>Che il fatto comunemente asserito non si verifichi, nel caso che alla <lb></lb>libera comunicazione si frapponga qualche impedimento, il Brunacci lo dimo­<lb></lb>stra con tre varie esperienze, nelle quali l&#039;acqua non può comunicare da un <lb></lb>vaso all&#039;altro, se non che attraversando strati ora di terra, ora di sabbia, <lb></lb>ora di ghiaia. </s>

<s>Nè a diverse cause da questa, cioè dalla comunicazione impe­<lb></lb>dita, attribuisce il fatto delle pozzanghere, che si osservano a piè degli ar­<lb></lb>gini, e sul fondo delle navi, dove l&#039;acqua, che dee filtrare attraverso ai <lb></lb>pori della terra e alle commessure del legno, rimane di tanto inferiore al <lb></lb>livello del fiume. </s></p><p type="main">

<s>Altre simili esperienze, descritte dall&#039;Hauksbee e confermate dal Newton, <lb></lb>avevano condotto a resultati tutt&#039;affatto contrari, ma è da osservare che, <lb></lb>sebbene l&#039;acqua, su per il tubo pieno di cenere, incontra non lieve la resi­<lb></lb>stenza, com&#039;apparisce dal vedere la velocità della sua ascesa sempre più ri­<lb></lb>tardata; viene a superarsi nulladimeno una tal resistenza dall&#039;attrazione mo­<lb></lb>lecolare, che tanto si fa maggiore, quanto la cenere stessa dentro il tubo è <lb></lb>più fortemente compressa. </s></p><p type="main">

<s>In qualunque modo, anche il dislivello, che si osserva ne&#039;tubi capillari, <lb></lb>si può ridurre al principio della comunicazione impedita. </s>

<s>Ne&#039;vasi infatti, rap­<lb></lb>presentati dalle figure 175 e 176 intercalate qui addietro, il livello GH del­<lb></lb>l&#039;acqua non risale infino al livello IK, perchè il menisco maggiore, anche <lb></lb>maggiormente ne impedisce il moto. </s>

<s>In simil guisa il mercurio NO non rag­<lb></lb>giunge il livello del mercurio LM, perchè nella canna più stretta trova mag­<lb></lb>giore la resistenza. </s>

<s>Sempre dunque il dislivello idrostatico è un effetto delle <lb></lb>resistenze, siano queste dovute alle azioni capillari o ad altre cause mecca­<lb></lb>niche. </s>

<s>Quindi è che, negli esperimenti instituiti a bella posta e riferiti in <lb></lb>tutte le Scuole, i liquidi si costituiscono ad ugual livello, perch&#039;essendo i vasi <lb></lb>piccoli, e perciò i moti brevi, gl&#039;impedimenti sono insensibili. </s>

<s>Ma nei grandi <lb></lb>condotti, come sarebbero per esempio quelli costruiti per menar l&#039;acqua da <lb></lb>un colle vicino sulla piazza di una città, non è possibile far sì che l&#039;acqua <lb></lb>stessa, nei getti e nelle conserve, giunga alla precisa altezza da cui fu scesa. </s></p><p type="main">

<s>A mezzo il secolo XVI sembra che gl&#039;ingneri d&#039;acque, anch&#039;essi illusi <lb></lb><figure id="id.020.01.3396.1.jpg" xlink:href="020/01/3396/1.jpg"></figure></s></p><p type="caption">

<s>Figura 182.<lb></lb>dall&#039;esperienze delle Scuole, non avessero fatto una <lb></lb>tale avvertenza, per cui spesso rimasero senza effetto <lb></lb>le loro imprese, con grave danno del pubblico e dei <lb></lb>privati. </s>

<s>Sorse allora il Cardano, con grande zelo, a <lb></lb>fargli ravvedere dei loro errori, osservando che altri­<lb></lb>menti avviene nei lunghi condotti, ne&#039;quali l&#039;acqua <lb></lb>prima scende e poi sale, da quel che avvien nei sifoni <lb></lb>da travasare, ne&#039;quali il liquido prima sale e poi scende. <lb></lb></s>

<s>“ Si autem aqua descendat primo, deinde ascendat ut <lb></lb>in figura sequenti 182 ex A in B, inde in E, et postmo­<lb></lb>dum in C et in D: tune pervenire poterit si D minus <pb xlink:href="020/01/3397.jpg" pagenum="358"></pb>distet a linea BC, quam A locus ex quo descendit. </s>

<s>Sed oportet in singulis <lb></lb>spatiis certam esse differentiam altitudinis A et D. </s>

<s>Quanto enim longior via <lb></lb>fuerit eo maior differentia A et D, iuxta altitudinis mensuram, esse debet. </s>

<s><lb></lb>Hinc errores quorumdam, qui, ad libramentum eum conati essent aquas de­<lb></lb>ducere, maximas iacturas impensarum susceperunt. </s>

<s>In singulis igitur milli­<lb></lb>bus passuum A altius palmo esse debet quam D, ut in decem millibus pas­<lb></lb>suum decem palmis ” (<emph type="italics"></emph>De subtilitate,<emph.end type="italics"></emph.end> Lugduni 1580, pag. </s>

<s>25). </s></p><p type="main">

<s>Notabile è però la causa, che il Cardano assegna a questo rimaner l&#039;acqua <lb></lb>che sale, al di sotto di quella che scende, un palmo per miglio. </s>

<s>E benchè, <lb></lb>accennando al bisogno di ristorar l&#039;impeto perduto, sembri voler dar qual­<lb></lb>che parte alle resistenze, la ragion principale nulladimeno ei la riconosce <lb></lb>dall&#039;evidente rotondità dell&#039;acqua, la quale dalla superficie degli orci pieni <lb></lb>è manifesta. </s>

<s>“ Causa huius est aquae rotunditas evidens, quae etiam in ur­<lb></lb>ceorum superficie apparet. </s>

<s>Unde ad libramentum, licet A sit altius quam D <lb></lb>(non tamen erit altius, quandoque loco medio inter A et D) indiget etiam <lb></lb>impetu quodam. </s>

<s>Sed haec nunc praeter intentum quasi sunt: volui tamen, <lb></lb>ob magnitudinem periculi et erroris frequentiam, haec subiecisse ” (ibid.). </s></p><p type="main">

<s>Se O, nella medesima figura 182, è il centro della sfera dell&#039;acqua, e <lb></lb>AO, DO sono i raggi, che ne misurano le distanze, apparisce chiaro perchè, <lb></lb>secondo il Cardano, il punto D sia costituito in più umile luogo di A. L&#039;er­<lb></lb>rore dunque dipende dalle illusioni, che la rotondità del mare suol fare agli <lb></lb>occhi dei naviganti, ond&#039;è che il Porta non ebbe tutti i torti a riconoscere <lb></lb>per una pazzia questa vantata sottilità di pensieri. </s>

<s>“ Cardano dice che la <lb></lb>superficie del mare sia rotonda, e si riconosce per gli orcioli pieni. </s>

<s>Ma io <lb></lb>non so com&#039;egli possa lasciarsi uscir di bocca tante pazzie ” (Spiritali, Na­<lb></lb>poli 1606, pag. </s>

<s>23). </s></p><p type="main">

<s>In ogni modo, non curandoci per ora delle teorie, dietro i fatti, da così <lb></lb>lungo tempo osservati negli equilibri idrostatici, si può dunque concludere <lb></lb>che i liquidi soggiacciono alle medesime leggi dei solidi, i quali risalirebbero <lb></lb>alla medesima altezza da cui scesero, sempre che se ne rimovessero tutti <lb></lb>gl&#039;impedimenti. </s>

<s>E perchè questo è uno dei principii fondamentali della Di­<lb></lb>namica nuova sembrerebbe che a Galileo si dovesse presentare spontenea <lb></lb>l&#039;applicazione di quello stesso principio, a rinnovellare l&#039;Idrodinamica. </s>

<s>Tanto <lb></lb>più che, a ingerire una tale opinione, predisponeva le menti qualche passo, <lb></lb>da noi citato a suo luogo dai dialoghi dei due Massimi Sistemi, in cui l&#039;Au­<lb></lb>tore, per confermare il supposto che, nella scesa, il solido acquista tant&#039;im­<lb></lb>peto, da risalire alla medesima altezza perpendicolare; adduceva per argo­<lb></lb>mento il ridursi l&#039;acqua, ne&#039;due rami del sifone, allo stesso livello. </s>

<s>E vera­<lb></lb>mente da questa esperienza fatta in vasi piccoli, e conferita con ciò che <lb></lb>altrimenti s&#039;osserva nei lunghi condotti, s&#039;ebbero, come vedremo, le prime <lb></lb>rivelazioni d&#039;Idrodinamica nuova. </s>

<s>Apparirono però più tardi di quel che non <lb></lb>pareva prometterci Galileo, il quale ebbe a trovare non poche difficoltà, a <lb></lb>riconoscer che il liquido, nella sua mole continuata, giunto in fondo al si­<lb></lb>fone, acquista quell&#039;impeto, che si concepirebbe da una sfera solida in sè <pb xlink:href="020/01/3398.jpg" pagenum="359"></pb>raccolta e distinta. </s>

<s>Di qui è che, rimanendogli circoscritti i pensieri dentro <lb></lb>gl&#039;insegnamenti della Statica antica, secondo cui le pressioni fatte sul fondo <lb></lb>del vaso son misurate dal numero degli strati sopraincumbenti, o dalle sem­<lb></lb>plici altezze; l&#039;Idrodinamica non venne perciò promossa da lui, nè dallo stesso <lb></lb>Castelli se non che assai debolmente. </s>

<s>La conclusione che si pronunzia ora <lb></lb>da noi così sentenziosa, ci verrà dimostrata dalla Storia, al più ordinato svol­<lb></lb>gimento della quale convien premettere alcune considerazioni intorno allo <lb></lb>stato della Scienza antica, per vedere com&#039;ella preparasse i progressi alla <lb></lb>nuova. </s></p><p type="main">

<s>La Dinamica riconosce le sue prime e più antiche origini dal modo usato <lb></lb>di misurare i momenti, e quelle che poi si dissero quantità di moto, dal <lb></lb>prodotto della massa per la velocità impressa. </s>

<s>In Aristotile si trova questo <lb></lb>principio sotto la forma di quell&#039;altro, più noto oggidì col nome di principio <lb></lb>delle velocità virtuali, applicato a dimostrar l&#039;equilibrio nelle Macchine, ma <lb></lb>il Nemorario fu che l&#039;estese ai gravi naturalmente cadenti. </s>

<s>E perchè dal nu­<lb></lb>mero dei corpi gravi non si escludono i liquidi, s&#039;intende come la Dinamica <lb></lb>e l&#039;Idrodinamica, infin da quei tempi, nascessero gemelle. </s>

<s>Dalla detta mi­<lb></lb>sura universale dei momenti, applicata al moto dell&#039;acque, conseguiva legit­<lb></lb>timamente, e quale verità immediata, doversi la quantità de&#039;flussi e delle <lb></lb>correnti misurare dal prodotto delle velocità per le sezioni, d&#039;onde, suppo­<lb></lb>ste le quantità uguali, resultava dimostrata la legge fondamentale idrodina­<lb></lb>mica del rispondersi le velocità e le sezioni in ragione contraria. </s>

<s>Similmente, <lb></lb>dall&#039;essere, in eguale quantità di discesa perpendicolare, uguali i momenti <lb></lb>di due moli uguali, si concludeva legittimamente che da due bocche uguali <lb></lb>uscivano nel medesimo tempo quantità uguali d&#039;acqua, comunque fossero i <lb></lb>canali inclinati. </s>

<s>Quale esplicazione avessero questi principii, e quali appli­<lb></lb>cazioni ne facessero gl&#039;Idraulici del secolo XVI, alla dispensa delle acque e <lb></lb>al regolamento dei fiumi, di disse nel capitolo primo di questo Tomo e basta <lb></lb>il già detto quivi a rappresentare lo stato, in cui si trovava la Scienza poco <lb></lb>tempo prima di quella sua, ch&#039;ebbe il nome di restaurazione. </s>

<s>Ci esprimiamo <lb></lb>così, perchè in verità fu piuttosto una demolizione, come or ora vedremo, <lb></lb>dop&#039;avere accennato ai progressi, che naturalmente s&#039;aspettava da un tale <lb></lb>stato di cose. </s></p><p type="main">

<s>È assai facile intendere che quei progressi consisterebbero nel sostituire <lb></lb>la vera legge delle velocità, acceleratrici il moto delle acque, a quella, che <lb></lb>i Matematici del secolo XVI assegnavano alle cadute di tutti i corpi gravi. </s>

<s><lb></lb>Si sa dalla Storia della Meccanica che costoro ammettevano le dette velocità <lb></lb>proporzionali agli spazi, e non eccettuando, com&#039;era giusto, da questa gene­<lb></lb>ralità i liquidi, ne conclusero legittimamente essere proporzionali alle sem­<lb></lb>plici altezze le velocità delle acque correnti. </s>

<s>Galileo, dimostrando che gli <lb></lb>spazi passati non serbano altrimenti la proporzione delle velocità semplici, <lb></lb>ma dei loro quadrati, aveva rinnovellata la Dinamica, e, se procedeva con <lb></lb>la logica degli antichi, avrebbe nello stesso tempo rinnovellata altresì l&#039;Idro­<lb></lb>dinamica, argomentando che, per essere i liquidi corpi come tutti gli altri <pb xlink:href="020/01/3399.jpg" pagenum="360"></pb>gravi, le velocità delle loro cadute perpendicolari, non avrebbero dovuto cor­<lb></lb>rispondere con le semplici altezze, ma con le loro radici. </s>

<s>Questi erano i pro­<lb></lb>gressi che la Scienza del moto delle acque s&#039;aspettava da Galileo, e ora è <lb></lb>da narrare come ne rimanesse defraudata. </s></p><p type="main">

<s>S&#039;accennava di sopra a una demolizione, alla quale soggiacque la Di­<lb></lb>namica, miseramente avvolta fra le rovine dell&#039;edifizio peripatetico. </s>

<s>Dal Be­<lb></lb>nedetti Galileo, e da Galileo il Cartesio prese l&#039;esempio, ma ambedue gli <lb></lb>arditi rinnovatori trapassarono le intenzioni del Matematico veneziano, che <lb></lb>da quella distruzione avrebbe prudentemente voluto salvare il buono, e non <lb></lb>disperdere i materiali utili, ma servirsene alla costruzione del nuovo edifi­<lb></lb>zio. </s>

<s>Che del buono e dell&#039;utile, particolarmente rispetto all&#039;Idrodinamica, <lb></lb>veramente ci fosse, lo sanno oramai bene i nostri Lettori, ai quali additammo <lb></lb>gli esempi, datine dai discepoli del Nemorario, rimasti segnatamente impressi <lb></lb>nelle opere del Cardano. </s>

<s>Ma Galileo non vuol nulla saper di costoro, i quali <lb></lb>non scrissero, intorno alla Scienza, a parer suo, fuor che favole e romanzi, <lb></lb>cosicchè sopra un&#039;area più libera vuol esserne ricostruito l&#039;edifizio da&#039;suoi <lb></lb>fondamenti, in disparte, e lontano dall&#039;edifizio peripatetico, che non avesse a <lb></lb>nuocere colle rovine e coll&#039;ombra. </s></p><p type="main">

<s>La prima mano alla costruzione fu data col Discorso intorno alle cose <lb></lb>che stanno in su l&#039;acqua, o che in quella si muovono. </s>

<s>Ci avverte in prin­<lb></lb>cipio l&#039;Autore che di ciò fu trattato già da Archimede, ma ch&#039;egli viene a <lb></lb>confermarne la verità delle dimostrazioni <emph type="italics"></emph>con metodo differente, e con altri <lb></lb>mezzi<emph.end type="italics"></emph.end> (Alb. </s>

<s>XII, 13). Quel metodo però, che consiste nel fare i ragguaglia­<lb></lb>menti tra la gravità e la velocità, confessa che non è nuovo, ma che <emph type="italics"></emph>fu con­<lb></lb>siderato da Aristotile come principio, nelle sue Questioni meccaniche<emph.end type="italics"></emph.end> (ivi, <lb></lb>pag. </s>

<s>16) ed è precisamente il principio delle velocità virtuali, che Galileo <lb></lb>vuole applicare all&#039;equilibrio tra i liquidi e i solidi immersi, e perciò tutta <lb></lb>la novità si farebbe consistere in così fatte applicazioni. </s></p><p type="main">

<s>Ma era ella questa propriamente una novità? </s>

<s>Potrebbe forse ritenersi <lb></lb>per tale, rispetto al particolar modo di dimostrare i teoremi di Archimede, <lb></lb>ma nella sua universalità quel metodo l&#039;avevano usato i Matematici del se­<lb></lb>colo precedente, con applicar la misura dei momenti a ogni genere di que­<lb></lb>stioni idrostatiche. </s>

<s>I teoremi di Galileo si può dire insomma che fossero un <lb></lb>corollario di proposizioni precedentemente già dimostrate, e dal non aver ri­<lb></lb>conosciuto l&#039;ordine assiomatico di questo processo logico si può dir che di­<lb></lb>penda tutta l&#039;imperfezione dell&#039;opera data all&#039;Idrodinamica da lui stesso. </s>

<s>Ma <lb></lb>a voler che avesse riconosciuto ciò bisognava non avesse disprezzate, così <lb></lb>come fece, le tradizioni precedenti, o che non le avesse accolte solo in parte <lb></lb>ma intere: non si doveva trattener nelle Questioni di Aristotile, ma consi­<lb></lb>derare gli svolgimenti, che avevano avuto dai Discepoli del Nemorario, quali <lb></lb>furono per esempio il Tartaglia, il Cardano e il Buteone. </s>

<s>Le voci di costoro <lb></lb>risonavano allora alte per tutto il mondo scientifico, e per quanto Galileo si <lb></lb>turasse le orecchie, o ne rifuggisse lontano, non era possibile che non gli <lb></lb>rimanessero impresse l&#039;arie, se non le parole, del canto. </s>

<s>Come poteva, nel <pb xlink:href="020/01/3400.jpg" pagenum="361"></pb>trattar de&#039;proietti, usare il linguaggio stesso introdotto nell&#039;arte dal Tarta­<lb></lb>glia, senza risentirne l&#039;eco delle dottrine? </s>

<s>E nella legge delle cadute dei <lb></lb>gravi lungo i piani inclinati, o nell&#039;uso della Bilancetta idrostatica, com&#039;è <lb></lb>credibile che, inconsapevole affatto, si riscontrasse nei teoremi e nelle inven­<lb></lb>zioni del rude Matematico di Brescia? </s></p><p type="main">

<s>Ma non si può tacere in questo proposito un esempio offertoci dal Bu­<lb></lb>teone. </s>

<s>Fra le Opere geometriche di lui, applicate a questioni giuridiche, si <lb></lb>legge un capitoletto intitolato <emph type="italics"></emph>Geometriae cognitionem Jureconsulto neces­<lb></lb>sariam,<emph.end type="italics"></emph.end> a dimostrare la qual necessità propone questo caso curioso: Tizio, <lb></lb>essendo in viaggio, lascia a Lucio un sacco, formato d&#039;un&#039;assicella rotonda <lb></lb>per fondo, intorno alla quale essendo cucita una tela, tenuto ritto, figurava <lb></lb>un cilindro; perchè glie lo empisse di grano, dandogli libertà, se gli fosse <lb></lb>tornato comodo, di metter la medesima misura in altri sacchi. </s>

<s>Ora, Lucio, <lb></lb>misurato il fondo di quello portatogli da Tizio, e trovatolo sedici piedi di <lb></lb>circonferenza, e sei di altezza della tela, empì quattro sacchi della medesima <lb></lb>forma, ma di quattro piedi di circonferenza ciascuno e ugualmente alti, e <lb></lb>tornato il compratore gli disse, nell&#039;atto di volerglieli consegnare, che i quat­<lb></lb>tro piccoli facevano insieme la misura stessa del grande, secondo la richie­<lb></lb>sta. </s>

<s>Tizio, per qualche esperienza che ne aveva, sospettò che vi fosse in­<lb></lb>ganno, ma quell&#039;altro badava a dire che la cosa era certa, come si può essere <lb></lb>certi d&#039;aver sedici da quattro via quattro. </s>

<s>“ Sed quid faciat, soggiunge il <lb></lb>Buteone, aut quo se vertat Titius, volens contra Lucium agere depositi? </s>

<s>Nus­<lb></lb>quam enim patronum sibi, nisi sit idem Geometriae peritus inveniet, qui <lb></lb>causam tam apparenter malam defendere velit, aut certe possit. </s>

<s>Sed pona­<lb></lb>mus invenisse: is igitur apud Praetorem causam sui clientis sustinebit in <lb></lb>hunc modum. </s>

<s>Dolo malo fecit Lucius, illustrissime Praeses, qui solum qua­<lb></lb>drantem depositi pro toto reddere falsis argumentis praetendit: hoc est qua­<lb></lb>tuor saccos frumenti pro sexdecim quot habuit depositum. </s>

<s>Hoc autem ita de­<lb></lb>monstro ” (<emph type="italics"></emph>Opera geometrica,<emph.end type="italics"></emph.end> Lugduni 1554, pag. </s>

<s>136). </s></p><p type="main">

<s>La dimostrazione, che fa l&#039;avvocato di Tizio innanzi al Pretore, è con­<lb></lb>dotta facilmente così, dietro le regole più elementari della Stereometria. </s>

<s>Si <lb></lb>chiami S il sacco grande, col fondo circolare di raggio R, <emph type="italics"></emph>ss<emph.end type="italics"></emph.end> si chiamino i <lb></lb>quattro sacchi più piccoli, col fondo di raggio <emph type="italics"></emph>r<emph.end type="italics"></emph.end> ciascuno, e sia A l&#039;altezza <lb></lb>uguale per tutti. </s>

<s>Dalle due equazioni S=8.R.A, <emph type="italics"></emph>ss=4.2r.A,<emph.end type="italics"></emph.end> verrà <lb></lb>istituita la proporzione <emph type="italics"></emph>S:ss=R:r.<emph.end type="italics"></emph.end> E perchè i raggi stanno come le cir­<lb></lb>conferenze, ossia nel caso proposto come 16 a 4; dunque S:<emph type="italics"></emph>ss<emph.end type="italics"></emph.end>=16:4= <lb></lb>4:1, d&#039;onde viene a decidersi aver avuto Tizio ragione di reclamar contro <lb></lb>Lucio, non contenendo i quattro sacchi piccoli, se non che la quarta parte <lb></lb>del grano, che si sarebbe contenuta nel grande. </s></p><p type="main">

<s>Ora si sovverranno i Lettori che, nella prima giornata delle due Scienze <lb></lb>nuove, Galileo risolveva un problema assai simile a questo, d&#039;onde viene a <lb></lb>rendere “ la ragione di un accidente, che non senza maraviglia vien sentito <lb></lb>dal popolo, ed è come possa essere che il medesimo pezzo di tela, più lungo <lb></lb>per un verso che per l&#039;altro, se se ne facesse un sacco da tenervi dentro <pb xlink:href="020/01/3401.jpg" pagenum="362"></pb>del grano, come costumano di fare con un fondo di tavola, terrà più, ser­<lb></lb>vendoci per l&#039;altezza del sacco della minor misura della tela, e con l&#039;altra <lb></lb>circondando la tavola del fondo, che facendo per l&#039;opposito ” (Alb. </s>

<s>XIII, 59). </s></p><p type="main">

<s>Non diremo che Galileo perdesse i suoi sonni a meditar sulle opere geo­<lb></lb>metriche del Buteone, ma sì che egli, riprendendo la solita immagine, sentì <lb></lb>nelle orecchie spirarsi l&#039;aria o le intonazioni, se non le precise parole del <lb></lb>canto, che penetravano allora per tutto, anche attraverso alle più salde pa­<lb></lb>reti. </s>

<s>Dall&#039;altra parte era in quell&#039;aria certa armonia, la quale si sarebbe <lb></lb>tanto meglio notata, in mezzo alle stonature: e il carattere scientifico del Di­<lb></lb>scorso intorno i galleggianti non si potrebbe forse ritrar meglio, che col dire <lb></lb>aver Galileo a quell&#039;aria languida e incerta adattate le proprie parole, che, <lb></lb>non rendendo intero il costrutto, non fa maraviglia s&#039;egli stesso talvolta non <lb></lb>ne riconosce l&#039;ampiezza del significato. </s></p><p type="main">

<s>Nella V proposizione idrostatica del citato Discorso galileiano, secondo <lb></lb>l&#039;esposizione, che analiticamente se ne fece da noi nella seconda parte del <lb></lb>capitolo secondo di questo Tomo, chiamando <emph type="italics"></emph>v<emph.end type="italics"></emph.end> la velocità dell&#039;abbassamento <lb></lb>della piccolissima mole o della sezione <emph type="italics"></emph>s<emph.end type="italics"></emph.end> dell&#039;acqua contenuta nel vaso, in <lb></lb>cui si suppone essere immerso il solido, V la velocità dell&#039;abbassamento della <lb></lb>grandissima mole, o della sua sezione S; vedemmo che il ragionamento del­<lb></lb>l&#039;Autore portava a concludere <emph type="italics"></emph>v:V=S:s,<emph.end type="italics"></emph.end> ossia che, avendosi quantità <lb></lb>d&#039;acqua uguali, le velocità stanno reciprocamente alle sezioni. </s></p><p type="main">

<s>Questa medesima legge anche più immediatamente si concludeva dalla <lb></lb>dimostrazione, che in questo stesso Discorso si dà dell&#039;equilibrio nel sifone <lb></lb>tra l&#039;acqua contenuta nel vaso più largo, e nella canna con lui continuata, <lb></lb>perchè quel che quivi si dice “ essere la salita IH (fig. </s>

<s>183) tanto maggiore <lb></lb>della scesa LD, quant&#039;è l&#039;ampiezza ML del vaso maggiore della larghezza IG <lb></lb><figure id="id.020.01.3401.1.jpg" xlink:href="020/01/3401/1.jpg"></figure></s></p><p type="caption">

<s>Figura 183.<lb></lb>della canna ” (Alb. </s>

<s>XII, 25, 26); si traduce, per <lb></lb>essere gli spazi proporzionali alle velocità, nella for­<lb></lb>mula che esse velocità son reciproche delle sezioni. </s>

<s><lb></lb>Ora, che Galileo, tutto intento a dimostrare le pro­<lb></lb>posizioni idrostatiche di Archimede, con metodo di­<lb></lb>verso, non si accorgesse che da questo stesso me­<lb></lb>todo veniva condotto a dimostrare altresì una legge <lb></lb>idrodinamica fondamentale; è quel che da noi s&#039;as­<lb></lb>seriva, e che si rappresenterà come cosa di fatto, <lb></lb>dop avere investigate le cause di una tale inco­<lb></lb>scienza. </s></p><p type="main">

<s>Queste cause si riducono da noi, come s&#039;ac­<lb></lb>cennava di sopra, e come fu notato in altro pro­<lb></lb>posito, al non aver saputo Galileo formulare nella sua universalità quella <lb></lb>massima legge dinamica, dalla quale conseguivano e la teoria statica dei <lb></lb>momenti, e le ragioni della comunicazione dei moti. </s>

<s>Di qui avvenne che il <lb></lb>Nostro rimanesse tanto inferiore a Giovan Marco, nel confutare l&#039;errore ari­<lb></lb>stotelico delle velocità proporzionali alle masse, e che tanto imperfettamente <pb xlink:href="020/01/3402.jpg" pagenum="363"></pb>discorresse della forza della percossa. </s>

<s>La statica stessa dei momenti, che Ga­<lb></lb>lileo non sdegnò di ricevere da Aristotile, e della quale unica fece l&#039;appli­<lb></lb>cazione alle sue questioni idrostatiche, era nella rinnovellata scienza così <lb></lb>dubbiosa, che il Nardi e poi tutti i suoi condiscepoli finirono per rifiutarla. </s>

<s><lb></lb>Dicevano come si sa che, nel trattare di così fatte questioni idrostatiche, di <lb></lb>un effetto in atto s&#039;adduceva una cagione in potenza, e che non era logico <lb></lb>dal moto argomentare alla quiete. </s>

<s>Il Maestro non aveva che rispondere a <lb></lb>queste difficoltà, e perciò non a torto il Viviani, ne&#039;Dialoghi delle due <lb></lb>Scienze nuove, e il Nardi, nel Discorso intorno i galleggianti, volevano far­<lb></lb>gli sostituire a quello delle velocità virtuali altro più ragionevole principio, <lb></lb>e non aveva Galileo che si rispondere perch&#039;era persuaso che il moto e la <lb></lb>quiete fossero due posizioni contrarie. </s>

<s>I precedenti Maestri però, ch&#039;ei di­<lb></lb>sprezzava, avevano invece insegnato non esser altro la quiete che il termine <lb></lb>del moto, per cui successive e non contrarie son le due posizioni, e l&#039;argo­<lb></lb>mentar l&#039;una dall&#039;altra è anzi logica necessità, dalla quale il volgo stesso è <lb></lb>menato, nel pesare specialmente gli oggetti preziosi. </s>

<s>I venditori infatti non <lb></lb>s&#039;assicurano dell&#039;equilibrio, se non col fare ondeggiare le braccia della bi­<lb></lb>lancia o far sollevare l&#039;ago della stadera, onde anch&#039;essi non argomentano <lb></lb>alla quiete, se non che dagli inizi o dai termini del moto. </s>

<s>Di qui si può <lb></lb>comprendere quanto sani e saldi fondamenti avesse ne&#039;matematici antichi <lb></lb>il principio delle velocità virtuali, e come di una simile certezza fisica e ma­<lb></lb>tematica partecipasse per loro la legge della comunicazione dei moti: fon­<lb></lb>damentale certezza che, come mancò a Galileo, così venne a mancare nella <lb></lb>massima parte de&#039;suoi seguaci. </s></p><p type="main">

<s>Il più insigne esempio di ciò l&#039;abbiamo nel Castelli. </s>

<s>Egli dava nel 1628 <lb></lb>alla luce in Roma il suo primo libro <emph type="italics"></emph>Della misura delle acque correnti,<emph.end type="italics"></emph.end><lb></lb>annunziando che il mondo era stato fin allora in errore, intorno al deter­<lb></lb>minar giustamente la quantità del moto nei fluidi. </s>

<s>Per ridurre però alla ve­<lb></lb>rità gli erranti, non risale alla Scienza meccanica, che avrebbe potuto dare <lb></lb>alle sue invenzioni una certezza matematica, ma si contenta di quella sola <lb></lb>certezza fisica, che gli poteva derivare dall&#039;esperienza. </s>

<s>Dop&#039;avere infatti ac­<lb></lb>cennato, in sul principio del libro, ai dubbi che gli nacquero dal ripensare <lb></lb>al modo comunemente usato dai periti e dagli ingegneri per misurar la me­<lb></lb>desima acqua corrente ora nei fossì, ora nelle cascate; ringrazia il Ciampoli <lb></lb>d&#039;avergli dato generosamente “ occasione, alli anni passati, di tentare, con <lb></lb>esatta esperienza, quanto passava intorno a questo particolare ” (Edizione del <lb></lb>Manolessi, Bologna 1660, pag. </s>

<s>4). E dietro questa esperienza, senza proporre <lb></lb>altro principio fondamentale, ne concludeva doversi misurare l&#039;acqua, che <lb></lb>esce dalla bocca di un canale o che passa per la sezione di un fiume, non <lb></lb>già dalla sezione sola, com&#039;allora si faceva da tutti, ma dal prodotto di lei <lb></lb>per la velocità impressa, onde “ essendo verissimo che in diverse parti del <lb></lb>medesimo fiume o alveo di acqua corrente sempre passano eguali quantità <lb></lb>d&#039;acqua in tempi uguali, ed essendo ancora vero che in diverse parti il me­<lb></lb>desimo fiume può avere varie o diverse velocità; ne seguirà per necessaria <pb xlink:href="020/01/3403.jpg" pagenum="364"></pb>conseguenza che, dove averà il fiume minore velocità, sarà di maggior misura, <lb></lb>ed in quelle parti, nelle quali averà maggior velocità, sarà di minor misura, <lb></lb>ed insomma le velocità di diverse parti dell&#039;istesso fiume averanno eterna­<lb></lb>mente reciproca e scambievole proporzione con le loro misure ” (ivi, pag. </s>

<s>7). </s></p><p type="main">

<s>Nello stesso Trattato geometrico, aggiunto nella fine del libro, la pro­<lb></lb>posizione II, dalla quale facilmente si svolgono tutte le altre, ha il suo fon­<lb></lb>damento nei cinque pronunziati premessi, i quali sono altrettanti fatti par­<lb></lb>ticolarmente osservati, e insigniti perciò di quella sola certezza fisica, che può <lb></lb>essere a loro partecipata dall&#039;esperienza. </s>

<s>Sperimentale dunque, benchè sotto <lb></lb>le apparenze geometriche, è quella stessa seconda proposizione, che dal Ca­<lb></lb>stelli si mette in questa forma: “ Se saranno due sezioni di fiumi, la quan­<lb></lb>tità dell&#039;acqua che passa per la prima, a quella che passa per la seconda, <lb></lb>ha la proporzione composta delle proporzioni della prima sezione alla seconda, <lb></lb>e della velocità per la prima, alla velocità per la seconda ” (ivi, pag. </s>

<s>65). </s></p><p type="main">

<s>Del medesimo carattere sperimentale rimangono perciò impresse tutte <lb></lb>le proposizioni, che conseguon da questa, la dimostrazion delle quali, che <lb></lb>secondo il metodo usato dall&#039;Autore riesce prolissa, intralciata così com&#039;è di <lb></lb>mezzi termini geometrici, si può rendere, con l&#039;analisi, facilissima e spedita. </s>

<s><lb></lb>Chiamate infatti Q, S, V; <emph type="italics"></emph>q, s, v<emph.end type="italics"></emph.end> le due diverse quantità, sezioni, e velocità <lb></lb>respettive, l&#039;annunziata proposizione seconda è conclusa nella formula (1) <lb></lb><emph type="italics"></emph>Q:q=S.V:s.v.<emph.end type="italics"></emph.end> Che se Q=<emph type="italics"></emph>q,<emph.end type="italics"></emph.end> dalla proporzionalità, che ne consegue, <lb></lb><emph type="italics"></emph>S:s=v:V,<emph.end type="italics"></emph.end> viene immediatamente a dimostrarsi la terza proposizion del <lb></lb>Castelli, ch&#039;è tale: “ Se saranno due sezioni ineguali, per le quali passino <lb></lb>quantità d&#039;acqua eguali, in tempi eguali; le sezioni hanno fra di loro reci­<lb></lb>proca proporzione delle loro velocità ” (ivi, pag. </s>

<s>67). </s></p><p type="main">

<s>Seguitando pure a supporre Q=<emph type="italics"></emph>q,<emph.end type="italics"></emph.end> se, intendendosi per A, <emph type="italics"></emph>a<emph.end type="italics"></emph.end> le altezze, <lb></lb>e per L, <emph type="italics"></emph>l<emph.end type="italics"></emph.end> le larghezze respettive delle due sezioni, si faccia S=A,L, <lb></lb><emph type="italics"></emph>s=a.l;<emph.end type="italics"></emph.end> dalla citata proporzione (1) si deriva l&#039;equazione A.L.V= <lb></lb><emph type="italics"></emph>a.l.v,<emph.end type="italics"></emph.end> e da questa la nuova proporzione <emph type="italics"></emph>a:A=L.V:l.v,<emph.end type="italics"></emph.end> la quale è <lb></lb>dimostrativa della quarta proposizione, dal Castelli formulata in tal guisa: <lb></lb>“ Se un fiume entrerà in un altro fiume, l&#039;altezza del primo nel proprio <lb></lb>alveo, all&#039;altezza che farà nel secondo alveo, ha la proporzione composta delle <lb></lb>proporzioni della larghezza dell&#039;alveo del secondo, alla larghezza, dell&#039;alveo <lb></lb>del primo, e della velocità, acquistata nell&#039;alveo del secondo, e quella, che <lb></lb>aveva nel proprio e primo alveo ” (ivi, pag. </s>

<s>79). </s></p><p type="main">

<s>La proporzione (2) <emph type="italics"></emph>Q:q=A.L.V:a.l.v,<emph.end type="italics"></emph.end> che si ottiene sostituendo <lb></lb>i valori di S, <emph type="italics"></emph>s<emph.end type="italics"></emph.end> nella (1), trattandosi del medesimo fiume, ed essendo perciò <lb></lb>L=<emph type="italics"></emph>l;<emph.end type="italics"></emph.end> si riduce nell&#039;altra <emph type="italics"></emph>Q:q=A.V:a.v,<emph.end type="italics"></emph.end> dalla quale è significata <lb></lb>la Va proposizione, che dal Castelli è così espressa: “ Se un fiume seari­<lb></lb>cherà una quantità d&#039;acqua in un tempo, e poi gli sopravverrà una piena, <lb></lb>la quantità dell&#039;acqua, che si scarica in altrettanto tempo nella piena, a quella <lb></lb>che si scaricava prima, mentre il fiume era basso; ha la proporzione com­<lb></lb>posta delle proporzioni della velocità della piena alla velocità della prima <lb></lb>acqua, e dell&#039;altezza della piena all&#039;altezza della prima acqua ” (ivi, pag. </s>

<s>72). </s></p><pb xlink:href="020/01/3404.jpg" pagenum="365"></pb><p type="main">

<s>Nella sopra scritta proporzione (2) suppongasi Q=<emph type="italics"></emph>q,<emph.end type="italics"></emph.end> ed L=<emph type="italics"></emph>l,<emph.end type="italics"></emph.end> trat­<lb></lb>tandosi al solito del medesimo torrente: essa verrà a ridursi all&#039;equazione <lb></lb>A.V=<emph type="italics"></emph>a.v,<emph.end type="italics"></emph.end> la quale, sotto la forma proporzionale A:<emph type="italics"></emph>a<emph.end type="italics"></emph.end>=<emph type="italics"></emph>v:<emph.end type="italics"></emph.end>V, dimo­<lb></lb>strerà la VI proposizione del Castelli, che dice: “ Se due piene uguali del <lb></lb>medesimo torrente entreranno in un fiume, in diversi tempi, l&#039;altezze fatte <lb></lb>dal torrente nel fiume averanno fra di loro la proporzione reciproca delle <lb></lb>velocità acquistate nel fiume ” (ivi, pag. </s>

<s>74). </s></p><p type="main">

<s>Questo trattatello geometrico della Misura delle acque correnti, che fu <lb></lb>come si disse pubblicato nel 1628, era stato già composto nel Novembre del <lb></lb>1625, ne&#039;primi giorni del qual mese il Castelli conferiva i frutti delle sue <lb></lb>proprie esperienze con Galileo, a cui diceva che, dovendosi misurar l&#039;acqua <lb></lb>che passa per un canale compostamente dalla velocità e dalla sezione, essendo <lb></lb>le quantità uguali, velocità e sezioni si debbono necessariamente corrispon­<lb></lb>dere in ragione contraria. </s>

<s>Il dì 12 di quel medesimo mese, tornato il Ca­<lb></lb>stelli a Pisa, col pensiero tutto rivolto alla Geometria delle acque, della quale, <lb></lb>nei passati familiari colloqui in Firenze, aveva manifestato il principio; sog­<lb></lb>giungeva, per lettera al suo proprio Maestro, un tale avviso: “ In questi <lb></lb>giorni ho dimostrato geometricamente la seguente proposizione, con assai <lb></lb>facilità: <emph type="italics"></emph>Che la quantità di acqua, che scorre per un fiume, mentre è con <lb></lb>una altezza d&#039;acqua, alla quantità dell&#039;acqua che scorre nel medesimo <lb></lb>fiume, mentre si ritroverà in un&#039;altra altezza d&#039;acqua; ha la propor­<lb></lb>zione composta della velocità alla velocità, e dell&#039;altezza all&#039;altezza ”<emph.end type="italics"></emph.end><lb></lb>(MSS. Gal., P. VI, T. X, fol. </s>

<s>216). </s></p><p type="main">

<s>La proposizione così annunziata si riconosce bene per quella che, nel <lb></lb>trattatello a stampa, ricorre in ordine la Va, e preso così l&#039;indirizzo era fa­<lb></lb>cile progredire alla dimostrazione delle altre proposizioni, delle quali, pochi <lb></lb>giorni dopo, il Castelli mandava a Galileo il solo pronunziato. </s>

<s>Queste propo­<lb></lb>sizioni, in cui consisteva quel progresso idraulico, di che il Castelli stesso <lb></lb>si compiaceva nel darne avviso al Maestro, erano tre: cioè la IV e la VI del <lb></lb>trattatello geometrico, alle quali se n&#039;aggiungeva un&#039;altra, che poi, nella <lb></lb>ristampa del libro, fu dall&#039;Autore inserita nella XII appendice, sotto la forma: <lb></lb>“ Se sarà un vaso d&#039;acqua di qualsivoglia grandezza, e che abbia un emis­<lb></lb><figure id="id.020.01.3404.1.jpg" xlink:href="020/01/3404/1.jpg"></figure></s></p><p type="caption">

<s>Figura 184.<lb></lb>sario, per il quale si scarichi la sua acqua; qual propor­<lb></lb>zione ha la superficie del vaso alla misura della sezione <lb></lb>dell&#039;emissario, tale averà la velocità delle acque per <lb></lb>l&#039;emissario all&#039;abbassamento del lago ” (<emph type="italics"></emph>Della misura <lb></lb>delle acque correnti<emph.end type="italics"></emph.end> cit., pag. </s>

<s>44.) </s></p><p type="main">

<s>La dimostrazione, usandovi il metodo analitico, non <lb></lb>presentava difficoltà punto maggiori delle altre. </s>

<s>Sia in­<lb></lb>fatti un vaso AG (fig. </s>

<s>184) dal quale si scarichi l&#039;acqua <lb></lb>per il tubo addizionale IH. </s>

<s>Chiamisi S la sezione CD <lb></lb>del vaso, <emph type="italics"></emph>s<emph.end type="italics"></emph.end> la sezione IG del tubo. </s>

<s>Se in un dato tempo, <lb></lb>per l&#039;esito da questo, l&#039;acqua si sia abbassata da D in F dentro il vaso, la <lb></lb>quantità Q=S.DF è quella medesima dell&#039;acqua uscita nel medesimo <pb xlink:href="020/01/3405.jpg" pagenum="366"></pb>tempo dal tubo, la quale è misurata da Q=<emph type="italics"></emph>s<emph.end type="italics"></emph.end>.V. chiamandosi con V la ve­<lb></lb>locità propria dell&#039;efflusso. </s>

<s>E perchè queste due quantità debbono essere evi­<lb></lb>dentemente uguali, sarà dunque S.DF=<emph type="italics"></emph>s.<emph.end type="italics"></emph.end> V, ossia S:<emph type="italics"></emph>s<emph.end type="italics"></emph.end>=V:DF, secondo <lb></lb>che si proponeva di dimostrare il Castelli. </s></p><p type="main">

<s>Nonostante parve a Galileo la dimostrazione di questa, e delle due pre­<lb></lb>cedenti, men facile a ritrovarsi di quella prima annunziatagli da Pisa, nella <lb></lb>lettera del dì 12 Novembre, e il dì 21 appresso se ne esprimeva così con lo <lb></lb>stesso Castelli: “ Mi rallegro assai del progresso idraulico, e aspetterò con <lb></lb>desiderio le tre ultime proposizioni con le loro dimostrazioni: dico di queste <lb></lb>tre, perchè la prima è assai chiara, atteso che, stante la medesima altezza, <lb></lb>l&#039;acqua che passa è come la velocità, e, stante la medesima velocità, l&#039;acque <lb></lb>che passano son come l&#039;altezze, e però, mutate altezze e velocità, l&#039;acque che <lb></lb>passano hanno la proporzione composta delle due dette ” (Alb. </s>

<s>VI, 305, 6). </s></p><p type="main">

<s>Il desiderio, manifestatosi nel principio di queste parole, non tardò molto <lb></lb>a essere sodisfatto. </s>

<s>A mezzo Dicembre il Discorso della misura delle acque <lb></lb>correnti, con alcuni corollari, aggiuntevi le dimostrazioni geometriche, era <lb></lb>fatto recapitar manoscritto a Firenze nelle mani di Mario Guiducci, affinchè <lb></lb>lo presentasse a Galileo, il quale in una lettera del dì 27 da Bellosguardo <lb></lb>così scriveva all&#039;Autore: “ Non ho ancor veduto l&#039;ultime sue scritture: ma <lb></lb>intendo che sono in mano del signor Mario, e le vedrò presto. </s>

<s>Io ancora <lb></lb>vò ghiribizzando, e tra gli altri problemi sono attorno all&#039;investigare come <lb></lb>cammini il negozio dell&#039;accelerarsi l&#039;acqua, nel dover passare per un canale <lb></lb>più stretto, ancorchè il letto abbia l&#039;istessa declività nel largo e nell&#039;angu­<lb></lb>sto ” (ivi, pag. </s>

<s>308). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Si rileva dai riferiti documenti che a Galileo giunsero nuove queste spe­<lb></lb>culazioni idrauliche, e che il Castelli gli dette occasione di rivolgervi allora <lb></lb>intorno la mente. </s>

<s>Quelle applicazioni della Geometria al moto delle acque <lb></lb>gli fecero nascere il pensiero di altre simili applicazioni, che si potrebbero <lb></lb>fare delle leggi geometriche, già da sè dimostrate intorno ai moti locali, e <lb></lb>in cui vedeva, secondo che egli stesso si esprime, la chiave per aprire in­<lb></lb>gressi ad accidenti maggiori. </s>

<s>Gli sovvenne di qui quella prima idea di ri­<lb></lb>guardar le acque dei fiumi, correnti per il pendio de&#039;loro alvei, come corpi <lb></lb>gravi, che scendono lungo piani inclinati: idea, che più tardi gli si svolse <lb></lb>nella lettera allo Staccoli, ma che intanto, manifestata al Castelli, questi così <lb></lb>rispondeva agl&#039;impulsi, che di proseguire per l&#039;intrapresa via gli venivano dal <lb></lb>Maestro: “ Rendo molte grazie a V.S., che si sia degnata di mandarmi le sue <lb></lb>considerazioni intorno al moto de&#039;fiumi, e maggiore sarà il mio obbligo, se <lb></lb>lei applicherà la mente a quelle chiavi per aprire ingressi ad accidenti mag­<lb></lb>giori, come mi accenna nella sua ” (Campori, Carteggio cit., pag. </s>

<s>231). </s></p><pb xlink:href="020/01/3406.jpg" pagenum="367"></pb><p type="main">

<s>Il problema, intorno al quale diceva dianzi Galilco di andare ghiribiz­<lb></lb>zando, si collegava con la memoria di speculazioni anteriori, e che gli avevan <lb></lb>preoccupata la mente, in fin da quando volle rendersi, del flusso e riflusso <lb></lb>del mare, una ragione, alla quale si riferisce, fra le altre considerazioni che <lb></lb>si leggono nell&#039;ultimo dialogo dei due Massimi sistemi, anche la seguente: <lb></lb>“ Inoltre, considerando come la medesima quantità d&#039;acqua mossa, benchè <lb></lb>lentamente, per un alveo spazioso, nel dover poi passare per luogo ristretto, <lb></lb>per necessità scorre con impeto grande; non avremo difficoltà d&#039;intendere <lb></lb>la causa delle gran correnti, che si fanno nello stretto canale, che separa la <lb></lb>Calabria dalla Sicilia, poichè tutta l&#039;acqua, che dall&#039;ampiezza dell&#039;isola e dal <lb></lb>Golfo ionico vien sostenuta nella parte del mare orientale, benchè in quello, <lb></lb>per la sua ampiezza, lentamente discenda verso occidente, tuttavia nel re­<lb></lb>stringersi nel Bosforo, fra Scilla e Cariddi, rapidamente cala, e fa grandis­<lb></lb>sima agitazione. </s>

<s>Simile alla quale, e molto maggiore, s&#039;intende esser tra <lb></lb>l&#039;Affrica e la grande isola di S. </s>

<s>Lorenzo ” (Alb. </s>

<s>I, 470). </s></p><p type="main">

<s>Ai fatti così semplicemente descritti si riferiva la proposizione III del <lb></lb>trattatello geometrico del Castelli, e in sentirsela così formulare Galileo tornò <lb></lb>a ghiribizzare intorno alle ragioni di quegli stessi fatti, osservati negli stretti <lb></lb>di mare, e negli alvei dei fiumi, con quali effetti vedremo tra poco. </s>

<s>Ma prin­<lb></lb>cipalmente efficaci sulla mente del Maestro furono que&#039;privati colloqui che, <lb></lb>nei primi giorni del Novembre 1625, ebbe con esso lui lo stesso Castelli, <lb></lb>quando gli scopriva le ragioni dell&#039;essersi fin allora trascurate le velocità <lb></lb>nella misura delle acque correnti: ragioni, che poi gli venne a ripetere in <lb></lb>pubblico confermandole con queste parole: “ Forse tale mancamento è stato <lb></lb>commesso per essere riputata la lunghezza dell&#039;acqua corrente in un certo <lb></lb>modo infinita, mentre non finisce mai di passare, e come infinita è stata <lb></lb>giudicata incomprensibile, e tale che non se ne possa avere determinata no­<lb></lb>tizia, e per tanto non è stato di essa tenuto conto alcuno ” (<emph type="italics"></emph>Copia di let­<lb></lb>tera al sig. </s>

<s>G. </s>

<s>Galilei aggiunta al libro della Misura delle acque cor­<lb></lb>renti,<emph.end type="italics"></emph.end> Bologna 1660, pag. </s>

<s>58). </s></p><p type="main">

<s>Fra il numero degli illusì, rispetto al reputare impossibile di misurar <lb></lb>l&#039;acqua fluente, per essere d&#039;indefinita lunghezza, ebbe Galileo a riconoscere <lb></lb>anche sè stesso, ripensando che aveva disperato d&#039;ottener la quantità del­<lb></lb>l&#039;acqua cadente fra l&#039;una e l&#039;altra delle due secchie, descritte, in sul comin­<lb></lb>ciar del suo Dialogo, per la misura della forza della percossa. </s>

<s>I teoremi del <lb></lb>Castelli invece mostravano che il misurare la data quantità dell&#039;acqua nella <lb></lb>troscia si riduceva a una assai semplice questione di Geometria. </s>

<s>Ma in ri­<lb></lb>pensare a ciò Galileo s&#039;accorse che i medesimi teoremi erano inclusi in quegli <lb></lb>altri, da tanto tempo scritti nel Discorso intorno i galleggianti, d&#039;ond&#039;egli <lb></lb>prese animo di risolvere il problema, innanzi al quale erasi arretrato il Sal­<lb></lb>viati, derivandolo non dalle altrui, ma dalle sue proprie dottrine. </s>

<s>Documento <lb></lb>importantissimo di ciò son le cose seguenti, che Galileo stesso, aspettando il <lb></lb>tempo di distenderle in dialogo, scriveva cosi, come si direbbe, in punta <lb></lb>di penna: </s></p><pb xlink:href="020/01/3407.jpg" pagenum="368"></pb><p type="main">

<s><emph type="italics"></emph>“ Per poter misurare e pesare la quantità dell&#039;acqua, compresa in <lb></lb>aria tra le due secchie. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Quando tu sollevi il solido M (fig. </s>

<s>185) dal vaso, l&#039;acqua gli entra di <lb></lb>sotto a riempire il vacuo lasciato, e così avviene a lei come se, da un can­<lb></lb>none largo quanto il vaso, entrasse per uno stretto quanto il solido. </s>

<s>Ma io <lb></lb><figure id="id.020.01.3407.1.jpg" xlink:href="020/01/3407/1.jpg"></figure></s></p><p type="caption">

<s>Figura 185.<lb></lb>t&#039;ho dimostrato, nel mio Discorso delle cose che <lb></lb>galleggiano, che l&#039;abbassamento della superficie <lb></lb>AC è superato dall&#039;alzamento della superficie EF, <lb></lb>quanto questa in larghezza è superata da quella; <lb></lb>dunque potrai tenere per cosa certa e dimostrata <lb></lb>che, quando l&#039;acqua da un cannone largo entra <lb></lb>in un più stretto, vi si muove dentro tanto più veloce a quella proporzione, <lb></lb>che lo stretto entra nel largo. </s>

<s>” </s></p><p type="main">

<s>“ Vedrai farsi la cosa più manifesta nel moto dell&#039;acqua dentro il vaso <lb></lb>MLB (fig. </s>

<s>183 qui addietro), che tu puoi immaginare larghissimo, e nella <lb></lb>angustissima canna AHC, che gli è congiunta. </s>

<s>Metti uno zaffo e pigialo in <lb></lb>giù, come tu faresti in uno schizzatoio, sicchè l&#039;acqua nel vaso così sforzata <lb></lb>s&#039;abbassi da L in D, risalendo da I in H alla parte opposta. </s>

<s>Non si può du­<lb></lb>bitare che i due cilindri MD, HG non siano uguali. </s>

<s>Mà in cilindri uguali le <lb></lb>basi corrispondono contrariamente alle altezze, le quali son la misura delle <lb></lb>velocità, come le basi son la misura delle larghezze o delle sezioni; dunque <lb></lb>le velocità, con cui si muovono l&#039;acque, nel largo e nello stretto, son reci­<lb></lb>proche delle sezioni. </s>

<s>” </s></p><p type="main">

<s>“ Di qui caverai la risposta a un bel quesito: Immagina che, dopo di <lb></lb>aver pigiato lo zaffo, tu non avessi avvertito o non ti ricordassi più a qual <lb></lb>punto giungeva l&#039;acqua, quietandosi nei due vasi, e che tu volessi ora ritro­<lb></lb>varlo per regola geometrica ......... ” </s></p><p type="main">

<s>“ Questo che io t&#039;ho concluso dal mio nuovo modo di dimostrare le <lb></lb><figure id="id.020.01.3407.2.jpg" xlink:href="020/01/3407/2.jpg"></figure></s></p><p type="caption">

<s>Figura 186.<lb></lb>proposizioni di Archimede, con conferire insieme i mo­<lb></lb>menti dell&#039;acqua che sale, con quella che scende, ho io <lb></lb>tante volte osservato in natura nell&#039;acqua dei ruscelli o <lb></lb>delle fosse aperte per i campi, le quali acque essendo <lb></lb>sparse vanno pigramente, ma, come elle sono entrate nello <lb></lb>stretto della fossa si mettono a correre con furia improv­<lb></lb>visa, e, se alla fossa s&#039;attraversasse un sasso o altro osta­<lb></lb>colo, sfogano mormorando l&#039;ira e, raddoppiando la fretta, <lb></lb>fuggono via. </s>

<s>Simile assottigliamento di parti s&#039;osserva <lb></lb>nelle trosce cadenti per l&#039;aria libera. </s>

<s>E a quel modo che <lb></lb>restringendosi lo spazio ne consegue augumento di velo­<lb></lb>cità, cosi dal farsi augumento di velocità s&#039;argomenta do­<lb></lb>versi restringere lo spazio. </s>

<s>” </s></p><p type="main">

<s>“ Sia ora la secchia CBD (fig. </s>

<s>186) col foro aperto <lb></lb>in B, da cui cada la troscia BH. </s>

<s>Sia l&#039;altezza del cilindro, <lb></lb>nel primo tempo dell&#039;effusione, BE: nel secondo tempo <pb xlink:href="020/01/3408.jpg" pagenum="369"></pb>sarà EF, tripla di BE, nel terzo sarà FG, quintupla della stessa BE, e così <lb></lb>seguitando col progresso de&#039;numeri impari ab unitate, come io ho dimostrato <lb></lb>essere l&#039;affrettamento di tutti i gravi cadenti. </s>

<s>Intorno a FE, a FG ecc. </s>

<s>do­<lb></lb>vendo essere la medesima acqua, che intorno a BE, si vedrà che i cilindri <lb></lb>tanto debbono diminuire le basi, quanto sono cresciute le altezze, e così la <lb></lb>base del cilindro EF dovrà essere tre volte più piccola della B, e la base del <lb></lb>cilindro FG cinque volte più piccola, e così sempre con simile progresso. </s>

<s>” </s></p><p type="main">

<s>“ La quantità dunque dell&#039;acqua che è nella troscia BG s&#039;averà dalla <lb></lb>somma dei detti cilindri, e universalmente la mole d&#039;acqua, contenuta in <lb></lb>qualsivoglia effusione come in BH, se tu la vorrai conferire col cilindro sopra <lb></lb>il foro B, e avente la medesima altezza BH; potrai facilmente conseguire la <lb></lb>desiderata proporzione facendo la detta mole al cilindro come l&#039;AB a quella, <lb></lb>che è media proporzionale tra la stessa AB, o tra la BE che suppongo es­<lb></lb>sere ad AB uguale, e la BH. ” </s></p><p type="main">

<s>Queste note, prese così in fretta, le abbiamo trascritte dal volume, altre <lb></lb>volte citato, <emph type="italics"></emph>Roba del gran Galileo, in parte copiata dagli originali, e in <lb></lb>parte dettata da lui cieco a me Vincenzio Viviani, mentre dimoravo nella <lb></lb>sua casa di Arcetri.<emph.end type="italics"></emph.end> Poche pagine appresso si trova messa in dialogo la <lb></lb>sostanza di queste note, e in principio vi si legge <emph type="italics"></emph>ad mentem Galilei,<emph.end type="italics"></emph.end> come <lb></lb>in capo a esse note leggevasi <emph type="italics"></emph>di questo ho l&#039;originale.<emph.end type="italics"></emph.end> Ma fra la prima copia <lb></lb>di tale scrittura originale, e la stesura del Dialogo dovette intercedere un <lb></lb>certo spazio di tempo, della succession del quale ci rimangono le vestigia <lb></lb>nei fatti seguenti. </s></p><p type="main">

<s>Essendo il dialogo della forza della percossa, che Galileo aveva comin­<lb></lb>ciato a scrivere, rimasto ignoto a tutti, come sì sa dalla Storia, nel cap. </s>

<s>III <lb></lb>del Tomo precedente da noi narrata; il Viviani non era ancora entrato adden­<lb></lb>tro nel significato di quelle parole: <emph type="italics"></emph>Per poter misurare e pesare la quan­<lb></lb>tità dell&#039;acqua, compresa in aria fra le due secchie.<emph.end type="italics"></emph.end> Ond&#039;è che, creden­<lb></lb>dolo un problema astratto proposto a sè medesimo da Galileo, per sodisfare <lb></lb>a una delle sue solite filosofiche curiosità, non si dette a principio altra cura <lb></lb>che di compiere, e d&#039;illustrare la scrittura del suo proprio Maestro. </s>

<s>Il que­<lb></lb>sito di ritrovare il punto, infino a cui nella cannella scenderebbe l&#039;acqua, <lb></lb>tenutavi sollevata violentemente dalla pression dello zaffo, sopra l&#039;acqua del <lb></lb>vaso più grande; mancava della sua risposta, e il Viviani vi supplì in que­<lb></lb>sta maniera: “ Se nel sifone ABC (fig. </s>

<s>183 qui poco addietro) fosse un tal <lb></lb>fluido, il quale in una parte di esso sifone stesse all&#039;altezza AD, e nell&#039;al­<lb></lb>tra si reggesse, con usar qualche artifizio che molti ce ne sono, all&#039;altezza C <lb></lb>superiore al livello AD; cercasi, posto tal fluido in libertà, nel librarsi nel­<lb></lb>l&#039;uno e nell&#039;altro cannello, a qual segno sia per arrivare. </s>

<s>” </s></p><p type="main">

<s>“ Prolunghisi il livello AD in EF, e facciasi come la grossezza del can­<lb></lb>nello AD, alla grossezza del cannello HC, cioè come il cerchio AD al cer­<lb></lb>chio HC, ovvero EF (supposti i cannelli cilindrici e di note grossezze) così <lb></lb>l&#039;altezza CG alla GF; ovvero dividasi l&#039;altezza CF in G nella proporzione <lb></lb>dei detti cerchi: che il punto G sarà il punto cercato. </s>

<s>Poichè prodotto il li-<pb xlink:href="020/01/3409.jpg" pagenum="370"></pb>vello GILM, sta il cilindro AL al cilindro EG come la base AD alla EF, ov­<lb></lb>vero, per costruzione, come la GC alla GF, ovvero, come il cilindro CI al <lb></lb>cilindro EG. </s>

<s>Dunque i cilindri AL, CI, cioè le moli del fluido, sono uguali, <lb></lb>e però ecc. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. CX, fol. </s>

<s>53). </s></p><p type="main">

<s>Quanto al misurar l&#039;acqua, compresa nella troscia, Galileo non aveva <lb></lb>messo altro che la conclusione, e il Viviani si studiò di ritrovarne, così ra­<lb></lb>gionando, i principii: “ Esto infundibulum CBD (nell&#039;ultima figura 186) <lb></lb>aqua indeficienter plenum, ex cuius fundo B perforato effluat aqua, sitque <lb></lb>fluxus altitudo vel BE, vel BF, vel BG, vel BH: quaeritur aquae quantitas, <lb></lb>quae semper extra vas reperitur. </s>

<s>” </s></p><p type="main">

<s>“ Sit altitudo aquae in infundibulo secundum imaginarium cylindrum <lb></lb>BA, aequalis BE, eiusdem vero sit tripla EF, quintupla FG, septupla BH etc., <lb></lb>secundum proportionem accelerationis motus naturalis, a Galileo assignatum. </s>

<s><lb></lb>Quo tempore aliqua pars aquae permeat intervallum BE, eodem vel aequali <lb></lb>permeat alia spacia EE, FG, GH. </s>

<s>Ergo moles aquae, in singulis partibus effu­<lb></lb>sionis BE, EF, FG, GH sunt aequales. </s>

<s>Ipsae autem ad cylindrum aqueum, <lb></lb>cuius hasis sit foramen B, altitudo vero BH, eam habent rationem, quam <lb></lb>numerus BE, EF, FG, GH etc. </s>

<s>ad quadratum eiusdem numeri. </s>

<s>Ita ut tan­<lb></lb>dem universaliter quaecumque moles aquae, in qualibet effusione BH con­<lb></lb>tenta, ad cylindrum aqueum eiusdem altitudinis BH, super basi foraminis <lb></lb>erecti, eam habeat rationem quam altitudo AB, ad eam quae inter AB et BH <lb></lb>sit media proportionalis ” (ibid., T. CXXXV, fol. </s>

<s>15). </s></p><p type="main">

<s>Tale è la conclusione di Galileo, alla quale sta bene che si siano ritro­<lb></lb>vati i principii. </s>

<s>Ma quei principii non erano legittimi, ne la soluzion del pro­<lb></lb>blema idrodinamico, data dallo stesso Galileo, era la vera, com&#039;appariva ma­<lb></lb>nifesto a chiunque avesse conferito queste dottrine con quelle <emph type="italics"></emph>De motu aqua­<lb></lb>rum,<emph.end type="italics"></emph.end> allora già insegnate dal Torricelli, dalla VI proposizion del quale <lb></lb>resultava che la troscia non piglia forma di un cono, ma di un conoide, quale <lb></lb>si descriverebbe dal rivolgersi intorno all&#039;asse BH, come a suo asintoto prin­<lb></lb>cipale, un&#039;iperbola biquadratica. </s>

<s>Al qual difetto della soluzione galileiana <lb></lb>accennava il Viviani con queste parole, con le quali egli terminava la rife­<lb></lb>rita illustrazione: “ Num autem hoc verum sit, diligenter expende, et ideo <lb></lb>ad doctrinam Torricellii <emph type="italics"></emph>De motu aquarum<emph.end type="italics"></emph.end> te conferas ” (ibid.). </s></p><p type="main">

<s>Qualunque si fosse l&#039;intenzione, ch&#039;ebbe il Viviani di spiegare così i <lb></lb>pensieri del suo proprio Maestro, era tuttavia lontano dall&#039;indovinare che se <lb></lb>ne sarebbe un giorno servito per quel Dialogo della forza della percossa, di <lb></lb>cui anch&#039;egli a que&#039;tempi deplorava, col Torricelli e col principe Leopoldo <lb></lb>dei Medici, la irreparabile iattura. </s>

<s>Ma pervenutogli, per quelle avventure che <lb></lb>si narrarono a suo tempo, il detto Dialogo alle mani, ebbe a leggervi la <lb></lb>proposta, messa in bocca all&#039;Aproino, che quando fosse possibile misurare <lb></lb>e pesare la quantità dell&#039;acqua, compresa in aria fra&#039;due secchi appesi alla <lb></lb>bilancia, si potrebbe anche sicuramente affermare “ la tal percossa esser po­<lb></lb>tente ad operar gravitando quello che opera un peso uguale a dieci o dodici <lb></lb>libbre d&#039;acqua cadente ” (Alb. </s>

<s>XIII, 331). Ma perchè il Salviati reputava la <pb xlink:href="020/01/3410.jpg" pagenum="371"></pb>misura di quell&#039;acqua in aria impossibile, si volge a immaginar altre espe­<lb></lb>rienze, per agevolarsi la strada all&#039;intera cognizione desiderata. </s></p><p type="main">

<s>Or il Viviani, risovvenendosi, in legger ciò, di quel che aveva, parecchi <lb></lb>anni prima, letto nell&#039;originale, fatto poi copiare fra l&#039;altra <emph type="italics"></emph>Roba<emph.end type="italics"></emph.end> nel citato <lb></lb>volume; intese che Galileo aveva finalmente ritrovata ne&#039;suoi propri teoremi <lb></lb>idrostatici la chiave a quell&#039;entrata, ch&#039;egli aveva creduto prima impossi­<lb></lb>bile, e che perciò avrebbe riformato in quella parte il suo Dialogo, sosti­<lb></lb>tuendo alle confessate difficoltà la diretta risoluzion del problema. </s>

<s>Il propo­<lb></lb>sito però non fu mandato ad effetto (forse perchè Galileo pensò alla forza <lb></lb>della percossa molto meno di quel che volle fare apparire) e perciò attese <lb></lb>a supplirvi il Viviani, dialogizzando le note del suo Maestro, ed esplicandole <lb></lb>così, come le abbiamo lette, e con fedeltà ricopiate dal manoscritto. </s></p><p type="main">

<s>“ APROINO. — <emph type="italics"></emph>Il discorso di V. S. è puntualmente conforme a quello <lb></lb>che facemmo noi di subito sopra la veduta esperienza; ed a noi ancora <lb></lb>parve di poter concludere che l&#039;operazione della sola velocità, acquistata <lb></lb>per la caduta di quella quantità di acqua, dall&#039;altezza delle due braccia, <lb></lb>operasse nell&#039;aggravare senza il peso dell&#039;acqua quel medesimo appunto, <lb></lb>che il peso dell&#039;acqua senza l&#039;impeto della percossa. </s>

<s>Sicchè, quando si <lb></lb>potesse misurare e pesare la quantità dell&#039;acqua compresa in aria tra i <lb></lb>vasi, si potesse sicuramente affermare la tal percossa esser potente ad ope­<lb></lb>rare gravitando quello, che opera un peso uguale a dieci o dodici libbre <lb></lb>dell&#039;acqua cadente ”<emph.end type="italics"></emph.end> (Alb. </s>

<s>XIII, 311). </s></p><p type="main">

<s>“ SALVIATI. — Piacemi molto l&#039;arguta invenzione, e benchè da voi si­<lb></lb>gnor Aproino, si creda di dovervi incontrare grande difficoltà quanto al poter <lb></lb>misurare la mole dell&#039;acqua, compresa in aria tra i vasi, io ho nonostante <lb></lb>pensato al modo di ritrovare dimostrativamente, e con una certa precisione, <lb></lb>quella desiderata misura. </s>

<s>E per primo e principal fondamento di quella spe­<lb></lb>culazione io vi porrò innanzi a considerare il fatto, che la troscia si va sem­<lb></lb>pre più assottigliando, com&#039;ella si dilunga sempre più dal suo principio, co­<lb></lb>sicchè non mantiene la sua prima figura di cilindro, ma s&#039;assottiglia via via, <lb></lb>affusolandosi, per così dire, e riducendosi nell&#039;aspetto di un cono. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — Questo io penserei che avvenga per lo continuo accre­<lb></lb>scersi la velocità, nelle particelle dell&#039;acqua, secondo che più e più si dipar­<lb></lb>tono dal principio del moto, ma come da ciò direttamente consegua quel­<lb></lb>l&#039;assottigliamento, che sempre si osserva, cadendo l&#039;acqua da una doccia <lb></lb>per aria, io non so per me trovare così ragionevole discorso, che me lo <lb></lb>persuada. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Non mancherebbe questo ragionevole fondamento al vo­<lb></lb>stro discorso, quando voi ritornaste col pensiero sopra ciò, che il nostro <lb></lb>Accademico ha dimostrato nel suo libro delle cose che stanno, o che si muo­<lb></lb>von per l&#039;acqua, dov&#039;ei riduce, come nella libbra, quel loro stare o quel loro <lb></lb>muoversi alle ragioni dei momenti, composti come sepete, delle velocità e <lb></lb>delle moli. </s>

<s>Il metodo, affatto nuovo a chi non aveva saputo scostarsi dai <lb></lb>processi antichi di Archimede, portava a conseguenze ammirande e nuove, <pb xlink:href="020/01/3411.jpg" pagenum="372"></pb>intorno al misurare, per via dei momenti, le quantità di un&#039;acqua che corre. </s>

<s><lb></lb>Perchè se i detti momenti stanno compostamente come le velocità e le moli, <lb></lb>essendo essi momenti uguali, necessariamente le velocità debbono in ragione <lb></lb>contraria, corrispondere colle moli. </s>

<s>Ora io vi dico che questa applicazione della <lb></lb>Scienza meccanica all&#039;acque fu fatta dal nostro Accademico, nel suo Discorso <lb></lb>intorno ai galleggianti, dove con vari esempi conclude che, passando una me­<lb></lb>desima quantità d&#039;acqua da un cannone più largo in un più stretto, tanto ella <lb></lb>acquista velocità nel correre, quanto ella viene a diminuir nella mole. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — Voi mi fate stupir veramente, perchè, sebbene io abbia <lb></lb>letto e riletto il Discorso del nostro Amico, non ci ho trovato mai, nè perciò <lb></lb>m&#039;è rimasto memoria di queste cose. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — E a me pure succede lo stesso, nè so risovvenirmi d&#039;al­<lb></lb>tro, ora che ci ripenso, se non che lì si tratta di vasi e di solidi immersi. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — È vero che per lo più si rappresentano que&#039;vasi e que&#039;so­<lb></lb>lidi in figura di prismi, ma la dimostrazione correrebbe ugualmente bene, <lb></lb>quando fossero cilindri. </s>

<s>Supponete perciò che sia cilindrico il solido M (nella <lb></lb>figura 185) e cilindrico il vaso AD, nell&#039;acqua del quale s&#039;intenda essere <lb></lb>immerso. </s>

<s>Sollevandosi il detto solido, l&#039;acqua che sottentra in suo luogo è <lb></lb>come se, da un tubo largo quanto AC, entrasse in uno stretto quanto EF. </s>

<s><lb></lb>Ora il nostro Accademico dimostra che l&#039;alzamento della superficie EF, che <lb></lb>seguita l&#039;alzamento del solido, all&#039;abbassamento della superficie AC, ha la <lb></lb>medesima proporzione, che la superficie AC alla superficie EF. </s>

<s>Ma da que­<lb></lb>ste superficie son misurate le larghezze delle sezioni dei tubi, e da quegli <lb></lb>alzamenti e abbassamenti le velocità dell&#039;acque per essi tubi correnti; dun­<lb></lb>que le velocità stanno in reciproca ragione delle sezioni. </s>

<s>Voi avreste però <lb></lb>potuta ritrovare la dimostrazione anche più esplicita di questa legge in que&#039;due <lb></lb>vasi, uno dei quali larghissimo come MLB (nella passata figura 183) e l&#039;altro <lb></lb>con lui continuato e angusto come la cannella BHC, secondo che lo stesso <lb></lb>nostro Accademico descrive nel citato Discorso, concludendo esser la salita IH <lb></lb>tanto maggiore della discesa MA, quant&#039;è l&#039;ampiezza ML del vaso maggiore <lb></lb>della larghezza HC della canna, la qual conclùsione si riduce dunque a dire <lb></lb>quel che si diceva di sopra, che cioè le velocità stanno in ragion reciproca <lb></lb>delle sezioni. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Il signor Salviati ha fatto il miracolo di restituire la vista <lb></lb>ai ciechi, intanto che ora vedo, per vostro benefizio, come, essendo livellato <lb></lb>in ML e in IG il liquido nei due vasi, se io introducessi nella bocca di que­<lb></lb>sto o di quello uno zaffo, e se con esso premendo facessi violentemente abbas­<lb></lb>sare il liquido sottoposto nell&#039;uno; potrei con certa regola geometrica sapere <lb></lb><gap></gap>uanto fosse per sollevarsi nell&#039;altro. </s>

<s>Come per esempio, se nel vaso grande <lb></lb><gap></gap> facessi l&#039;abbassamento da M in A, potrei sapere l&#039;alzamento giusto IH, <lb></lb><gap></gap>e gli corrisponde nel vaso piccolo, perchè stando, per le cose dimostrate <lb></lb><gap></gap>nostro Accademico, IG a LM, come AM a IH, ed essendomi le prime tre <lb></lb><gap></gap>tità, com&#039;io presuppongo, note, mi sarà nota anche insieme la IH loro <lb></lb><gap></gap> proporzionale. </s>

<s>” </s></p><pb xlink:href="020/01/3412.jpg" pagenum="373"></pb><p type="main">

<s>“ SALVIATI. — Si potrebbe anzi, signor Sagredo, sciogliere, con questa <lb></lb>medesima scienza suggeritaci dal nostro Amico, il problema inverso, non <lb></lb>men bello ó meno curioso. </s>

<s>Supponete che, in forza dello zaffo da voi cac­<lb></lb>ciato nel maggior vaso infino ad AD, il liquido nel minore si sia violente­<lb></lb>mente sollevato in HC, e che, lasciato poi a un tratto in libertà, col rimo­<lb></lb>vere il detto zaffo, voi voleste, non avendoci fatto prima avvertenza, ritrovare <lb></lb>il segno, in cui scendendo esso liquido si fermerà, dop&#039;aver fatti i soliti on­<lb></lb>deggiamenti. </s>

<s>Prolungate il livello AD in EF, e l&#039;altezza FC dividete in G <lb></lb>per modo, che stia CG a GF come la sezione o il circolo AD alla sezione <lb></lb>o al circolo EF. Poi, dal punto G conducete la orizontale GILM, che ne&#039;punti <lb></lb>segnati da lei si costituiranno le cercate superficie nei due vasi. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Mi par che tutto si riduca a dimostrare che il cilindro <lb></lb>d&#039;acqua CI, di che si scema la canna, è uguale al cilindro d&#039;acqua DM, di <lb></lb>che s&#039;accresce il vaso, nè la dimostrazione mi si presenta molto difficile. </s>

<s>Per­<lb></lb>chè il cilindro AL, al cilindro EG di pari altezza, sta come la base AD alla <lb></lb>base EF, ossia, per la costruzione del signor Salviati, come la CG alla GF, <lb></lb>e anche come CG moltiplicata per la base IG, alla GF moltiplicata per la <lb></lb>medesima IC, o per la sua uguale EF. </s>

<s>Ma l&#039;altezza CG, moltiplicata per la <lb></lb>base IG, dà la misura del cilindro IC, e l&#039;altezza GF, moltiplicata per la base <lb></lb>EF, dà la misura del cilindro EG; dunque il cilindro AL sta al cilindro EG <lb></lb>come il cilindro CI sta al medesimo cilindro EG, e perciò, essendo i conse­<lb></lb>guenti uguali, saranno anche insieme uguali gli antecedenti, cioè il cilindro <lb></lb>AM uguale al cilindro CI, come si richiedeva per confermare la verità della <lb></lb>soluzione di questo problema, data dal nostro signor Salviati. </s></p><p type="main">

<s>“ APROINO. — Bellissime verità mi avete scoperte intorno ai mirabili <lb></lb>effetti, che produce nell&#039;acqua il moto più o meno veloce, ma di questi ef­<lb></lb>fetti non mi avete ancora, signor Salviati, dichiarato quello, che da me mag­<lb></lb>giormente si desiderava, come cioè si possa misurare e pesare la quantità <lb></lb>dell&#039;acqua cadente fra le due secchie. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Il problema proposto dal signor Sagredo, e quell&#039;altro <lb></lb>simile, che mi ha fatto sovvenire a quel proposito, hanno interrotto il filo <lb></lb>del nostro discorso, che mi avrebbe direttamente guidato a sodisfare il vo­<lb></lb>stro principal desiderio. </s>

<s>Vi ricorderete, signor Aproino, che voi diceste poter <lb></lb>essere la maggiore velocità, acquistata dalle particelle dell&#039;acqua nel cadere, <lb></lb>causa efficiente dell&#039;assottigliarsi la troscia: e come dalla scienza del nostro <lb></lb>Accademico s&#039;è ricavato che, restringendosi le sezioni crescono a quella pro­<lb></lb>porzione le velocità; così, per la conversa, argomenteremo che, crescendo le <lb></lb>velocità, a quella medesima ragione, diminuiscono le sezioni. </s>

<s>Per dichiararvi <lb></lb>anche meglio il mìo pensiero, sia CBD (nella figura 186 ultimamente im­<lb></lb>pressa) la secchia di sopra, col foro aperto in B, da cui cada l&#039;acqua intorno <lb></lb>all&#039;asse verticale BH. </s>

<s>Essendo BA l&#039;altezza del liquido nel vaso, consideriamo <lb></lb>il cilindro AB, che nel primo tempo dell&#039;effusione giunga in E, da un&#039;al­<lb></lb>tezza BE, uguale ad AB. </s>

<s>Nel secondo tempo passerà lo spazio EF triplo di <lb></lb>BE, nel terzo lo spazìo FG quintuplo di BE, e così seguitando, secondo la <pb xlink:href="020/01/3413.jpg" pagenum="374"></pb>legge dal nostro Accademico scoperta, e dimostrata in tutti i gravi cadenti. </s>

<s><lb></lb>Essendo ora intorno EF, intorno FG, e intorno a tutte le altre parti rima­<lb></lb>nenti la medesima quantità d&#039;acqua, che intorno a BE, dovrà in E la se­<lb></lb>zione o la base del cilindro successivo tanto restringersi, quanto l&#039;altezza EF <lb></lb>è cresciuta sopra la BE, e in F restringersi ancora più che in E, quanto <lb></lb>la FG sopra la EF è cresciuta di grandezza. </s>

<s>Così proseguendo il discorso, <lb></lb>averemo le ragioni dell&#039;assottigliarsi sempre più l&#039;acqua, com&#039;ella si va sem­<lb></lb>pre più dilungando dal fondo B della secchia. </s>

<s>” </s></p><p type="main">

<s>“ SAGREDO. — Di modo che, supponendo che il termine sia G, l&#039;acqua <lb></lb>compresa in aria fra G e B è tanta, quant&#039;è quella dei tre cilindri, intorno <lb></lb>gli assi BE, EF, FG; ossia quant&#039;è nel cilindro BE, preso tre volte, essendo <lb></lb>a lui, per supposizione, i cilindri intorno EF, FG ciascuno uguali di mole. </s>

<s><lb></lb>Se s&#039;avesse poi da conferire questa quantità d&#039;acqua, contenuta nella tro­<lb></lb>scia, con la quantità contenuta nel cilindro sopra la medesima base B, e con <lb></lb>l&#039;altezza BG; imperocchè tale altezza è nove volte più grande della BE, di­<lb></lb>remo dunque che quella, cioè la troscia, sta al cilindro a lei circoscritto, come <lb></lb>tre sta a nove. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Così è la verità, come voi, signor Sagredo, da buon ma­<lb></lb>tematico ragionando, l&#039;avete conclusa. </s>

<s>Se supponete inoltre che i cilindri o <lb></lb>le parti dello spazio, passato nella caduta in tempi uguali, sian quattro, il <lb></lb>vostro ragionamento v&#039;avrebbe portato a concludere che la troscia sta al ci­<lb></lb>lindro, come quattro sta a sedici, e universalmente, come il numero delle <lb></lb>parti sta al quadrato di questo stesso numero. </s>

<s>Che se voi voleste ridurvi <lb></lb>alla ragione geometrica, direte che, per qualunque effusione BH, la mole <lb></lb>d&#039;acqua al cilindro circoscritto sta come l&#039;altezza AB del livello nel vaso, a <lb></lb>quella che è media proporzionale tra la stessa AB e la BH. ” </s></p><p type="main">

<s>“ SAGREDO. — Questa vostra data ragione geometrica io la credo veris­<lb></lb>sima, ma perchè la non mi appare così manifesta, non vi dispiaccia, signor <lb></lb>Salviati, di condurmela dai suoi principii. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Vi farò a questo effetto dunque prima considerare che <lb></lb>il numero delle parti cilindriche, nelle quali s&#039;è divisa mentalmente la tro­<lb></lb>scia, è dato dalla radice del numero delle parti, tutte uguali ad AB, che en­<lb></lb>trano nella lunghezza di essa troscia. </s>

<s>Così voi vedete come nella lunghezza <lb></lb>BF, che è quattro volte AB, e nella lunghezza BG, che è nove volte la <lb></lb>stessa AB, entrano due e tre parti, che sono i numeri corrispondenti alle <lb></lb>radici di quattro e di nove. </s>

<s>E perciò, in universale argomentando, diremo <lb></lb>che, se la lunghezza sia qualunque BH, il numero delle parti sarà dato dalla <lb></lb>radice di BH, divisa per la radice di AB. Ora, poichè fu convenuto che la <lb></lb>troscia sta al cilindro come il numero delle parti sta al suo quadrato, o come <lb></lb>l&#039;unità sta al medesimo numero; anche diremo stare le due dette quantità <lb></lb>d&#039;acqua cadente come l&#039;unità alla radice di BH, divisa per la radice di AB, <lb></lb>o come la radice di AB alla radice di BH, o finalmente come l&#039;AB sta alla <lb></lb>radice di BH, moltiplicata per la radice di AB. </s>

<s>Ma alla radice di BH mol­<lb></lb>tiplicata per la radice di AB s&#039;uguaglia la linea, che media fra BH e AB; <pb xlink:href="020/01/3414.jpg" pagenum="375"></pb>dunque la troscia sta al cilindro a lei circoscritto come l&#039;AB sta a quella, <lb></lb>che è media proporzionale tra la stessa AB e la BH. ” </s></p><p type="main">

<s>“ APROINO. — Il signor Sagredo mostra di aver avuto sodisfazione con <lb></lb>gli atti, e io la confermo con le parole, quanto all&#039;approvare la verità della <lb></lb>vostra ultima conclusione geometrica, ma non per ciò mi si viene a rimo­<lb></lb>vere un dubbio, che mi nasce da un&#039;altra parte. </s>

<s>Voi, signor Salviati, sup­<lb></lb>ponete che l&#039;altezza AB del livello, per qualunque tempo dell&#039;effusione, si <lb></lb>mantenga costante, ossia ammettete che il vaso non iscemi, come farebbe <lb></lb>se ricevesse dentro sè tant&#039;acqua nuova, quant&#039;è quella che ha versato di <lb></lb>fuori. </s>

<s>Tal supposizione però non si verifica delle due secchie, quali io vi <lb></lb>dissi che il nostro Accademico aveva immaginate, per conseguire qualche <lb></lb>notizia della recondita forza della percossa. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Si potrebbe nonostante far la secchia tanto larga, ri­<lb></lb>spetto al foro, che per quell&#039;istante dell&#039;effusione, richiesto per l&#039;effetto <lb></lb>principale dell&#039;esperienza, il livello s&#039;abbassasse così poco, da riguardarlo <lb></lb>come invariato. </s>

<s>” </s></p><p type="main">

<s>“ APROINO. — Vi si potrebbe senza difficoltà concedere questo che voi <lb></lb>volete, ma altro anco di più richiede il vostro discorso, a danno del buon <lb></lb>esito della esperienza, ed è che l&#039;acqua nella secchia sia pochissimo fonda. </s>

<s><lb></lb>Perchè, a voler ridurre la continuità della troscia a que&#039;vostri cilindri, e <lb></lb>affinchè spariscano quegli addentellati nell&#039;uniformità della superficie conter­<lb></lb>mina all&#039;acqua cadente, convien che dei detti cilindri la lunghezza sia pic­<lb></lb>colissima, intanto che quella, che serve a loro per unità di misura, e che è <lb></lb>uguale all&#039;altezza del livello, fosse quasi insensibile, e insomma, per aggiu­<lb></lb>star le cose alla vostra dimostrazione, il liquido dovrebb&#039;essere così poco nel <lb></lb>vaso, da ricoprirne appena appena la superficie del fondo. </s>

<s>” </s></p><p type="main">

<s>“ SALVIATI. — Comunque sia, poichè sento che vi arreca ancora qual­<lb></lb>che ambiguità la difficultà del misurare la quantità dell&#039;acqua cadente; po­<lb></lb>tremo ” ecc., come nella edizion dell&#039;Albèri, alla pagina sopra citata. </s></p><p type="main">

<s>Se avesse avuto il Viviani occasione di pubblicare egli stesso il Dialogo <lb></lb>della forza della percossa, non è dubbio che vi avrebbe, insieme con altre <lb></lb>parti, forse meno importanti, ridotto anche questa. </s>

<s>Ma perchè l&#039;ufficio era <lb></lb>riserbato al Bonaventuri, se questi non integrò così come sarebbesi deside­<lb></lb>rato la sua edizione, è da credere non fosse per altro, se non perchè il Grandi, <lb></lb>che doveva aver letto questo dialogismo fra le carte ricevute dal Panzanini, <lb></lb>non lo esibì all&#039;amico editore, qualunque poi se ne fosse il motivo. </s></p><p type="main">

<s>Ma è da tornare al Castelli, che attendendo in questo tempo con grande <lb></lb>alacrità a dar perfezione al suo manoscritto Della misura delle acque cor­<lb></lb>renti, incominciava così, il dì primo del 1626, una sua lettera indirizzata da <lb></lb>Pisa a Galileo: “ Non scrissi a V. S., per l&#039;ordinario passato, perchè non <lb></lb>avevo ricevuta la sua de&#039;27, e non avendo cosa di nuovo, se non due Ap­<lb></lb>pendice al mio trattatello del moto de&#039;fiumi, che mandai al sig. </s>

<s>Mario, pre­<lb></lb>gandolo le comunicasse a V. S. </s>

<s>In una toccavo un particolare scritto da Giu­<lb></lb>lio Frontino, antico scrittore illustre <emph type="italics"></emph>De Aquaeductibus Romae,<emph.end type="italics"></emph.end> nel quale <pb xlink:href="020/01/3415.jpg" pagenum="376"></pb>mi pare che Frontino possa avere errato nella misura dell&#039;acqua, per non <lb></lb>aver considerata la velocità, e tocco volentieri questo punto, perchè insieme <lb></lb>vengo a significare che il mio pensiero non è stato messo in campo da nes­<lb></lb>suno ancora. </s>

<s>Nell&#039;altra Appendice noto il mancamento specificatamente degli <lb></lb>ingegneri del nostro tempo, e più di quei di Ferrara, i quali, nel concludere <lb></lb>l&#039;alzamento che può fare il Reno in Po, non tengono conto della variazione <lb></lb>della velocità ” (Campori, Carteggio cit., pag. </s>

<s>253). </s></p><p type="main">

<s>A queste prime Appendici ne aggiunse il Castelli altre, che gli sovven­<lb></lb>nero via via, intanto che si ridussero al numero di XI, quasi scolii al Di­<lb></lb>scorso della misura delle acque correnti. </s>

<s>Gli amici di Firenze avevano dimo­<lb></lb>strato gran desiderio di veder questo Discorso, che avevano letto manoscritto, <lb></lb>uscir fuori per le stampe, le quali poi ebbero effetto per le premure di quegli <lb></lb>altri amici di Roma, e specialmente de&#039;due monsignori Ciampoli e Corsini, <lb></lb>che fecero conoscere l&#039;utilità e l&#039;importanza di quelle nuove scritture idrau­<lb></lb>liche ai così detti Padroni, quali erano allora papa Urbano VIII, e i prin­<lb></lb>cipi Barberini. </s>

<s>Il dì 16 Settembre 1628 il Castelli dava da Roma in una let­<lb></lb>tera a Galileo questo annunzio: “ Oggi ho avuto ordine dai Padroni di far <lb></lb>stampare la mia scrittura dell&#039;Acqua, e fa la spesa la Camera ” (ivi, pag. </s>

<s>272). <lb></lb>Sul finir di quell&#039;anno infatti usciva in Roma, dalla Stamperia Camerale, alla <lb></lb>luce il Discorso della misura delle acque correnti, con XVI corollari e XI <lb></lb>appendici, dedicato a papa Urbano VIII, aggiuntevi le Dimostrazioni geome­<lb></lb>triche dedicate al principe don Taddeo Barberini. </s></p><p type="main">

<s>Nella lettera del dì 16 Settembre, ora citata, soggiungeva il Castelli a <lb></lb>Galileo, dop&#039;avergli annunziato l&#039;ordine di stampare la sua scrittura: “ Stam­<lb></lb>pata che sarà, glie ne manderò copia, e vedrà una moltitudine di strava­<lb></lb>ganti particolari, tutti dipendenti dal medesimo principio. </s>

<s>Son però stato ne­<lb></lb>cessitato ridurla a chiarezza tale, che possa essere intesa ancora da quelli, <lb></lb>che non hanno mai inteso niente di bello ” (ivi). Il dì 17 del seguente No­<lb></lb>vembre tornava a scrivere: “ Per l&#039;ordinario che viene, non avendo potuto <lb></lb>finire, per diversi rispetti, manderò il mio trattato Della misura delle acque <lb></lb>correnti, e ne manderò alcune copie a V. S., da distribuire a cotesti signori <lb></lb>miei Padroni ” (MSS. Gal., P. I, T. IX, fol. </s>

<s>133). Nell&#039;ultima settimana del <lb></lb>detto mese, poche copie ancora essendone tirate, ne mandò a Galileo tre: <lb></lb>una, perchè se la ritenesse per sè, e delle altre due facesse presente al Gran­<lb></lb>duca, e al principe don Lorenzo dei Medici. </s>

<s>Verso la fine di Dicembre, es­<lb></lb>sendo oramai le copie finite di tirar tutte, ne furono da Roma spedite a Ga­<lb></lb>lileo 50 copie, perchè a nome dell&#039;Autore, le dispensasse fra gli amici e <lb></lb>studiosi padroni suoi di Toscana. </s>

<s>“ Mando a V. S. cinquanta copie della mia <lb></lb>Scrittura, acciò le dispensi a quei Signori miei padroni che lei sa che sono <lb></lb>la mia corona ” (Alb. </s>

<s>IX, 141). </s></p><p type="main">

<s>Non è tempo ancora di riferire particolarmente i giudizi, che si fecero <lb></lb>dell&#039;Opera, così diffusa: basti il dire che fu ricevuta con ammirazione, e sa­<lb></lb>lutata in generale quale rivelazion benefica di una scienza utilissima e nuova. <lb></lb></s>

<s>“ La Scrittura, scriveva Galileo all&#039;Autore nel Gennaio 1629, è piaciuta a <pb xlink:href="020/01/3416.jpg" pagenum="377"></pb>tutti che l&#039;hanno letta, e quà si trattava di ristamparla, ma intendo che ella <lb></lb>non se ne contenta ” (Alb. </s>

<s>VI, 324). Nel 1634 però, mutato consiglio, il Ca­<lb></lb>stelli stesso iniziava le trattative di questa seconda edizione, da farsi in Fi­<lb></lb>renze, come apparisce da queste parole, che il dì primo Novembre di quel­<lb></lb>l&#039;anno scriveva di Roma in una sua lettera a Galileo: “ Gli ho dato ordine <lb></lb>(al padre Francesco, cioè a don Famiano Michelini) che tratti col signor An­<lb></lb>drea Arrighetti di fargli stampare il mio Discorso della misura delle acque <lb></lb>correnti, e perchè forse vi sarà qualche aggiunta e di postille e di scolii, <lb></lb>supplico V. S. farmi grazia ed onore di qualche particolare, che avesse os­<lb></lb>servato in questa materia ” (Campori, Carteggio cit., pag. </s>

<s>417). </s></p><p type="main">

<s>Queste trattative però non ebbero effetto, e la nuova edizione indugiò <lb></lb>ancora per qualche anno, infintantochè nel 1639 non si fece anch&#039;essa in <lb></lb>Roma dalla stamperia di Francesco Cavalli. </s>

<s>Le appendici vi son ridotto al <lb></lb>numero di XIII, e si fa ad esse succedere la “ Copia di lettera al signor Ga­<lb></lb>lileo Galilei, primo Filosofo del serenissimo Granduca di Toscana. </s>

<s>” Nei primi <lb></lb>di Agosto ricevè copia del nuovo libro Galileo stesso, che il dì 8, da Arce­<lb></lb>tri, così rispondeva all&#039;Autore: “ Mentre stavo aspettando lettere dalla P. V. <lb></lb>Reverendissima, m&#039;è pervenuto il trattato Delle acque correnti da lei ristam­<lb></lb>pato, con l&#039;aggiunta della sua curiosissima e ingegnosa Lettera, da lei a me <lb></lb>scritta in proposito del lago Trasimeno, e del Diluvio universale registrato <lb></lb>nelle Sacre carte. </s>

<s>Per lo che la ringrazio della memoria che tiene di me, <lb></lb>e del procurare che il mio nome non s&#039;estingua, ma si vada continuando <lb></lb>nella memoria delle future genti ” (Alb. </s>

<s>VII, 232). </s></p><p type="main">

<s>Detto ciò che riguarda la pubblicazione, è tempo di soggiungere i giu­<lb></lb>dizi, che particolarmente si dettero dell&#039;Opera nuova, incominciando da quelli <lb></lb>stessi richiesti dall&#039;Autore. </s>

<s>Dopo Galileo, uno de&#039;più stimati in questa Scienza, <lb></lb>che si ritrovassero allora in Italia, era Giovan Batista Baliani. </s>

<s>Con lui il Ca­<lb></lb>stelli, mentre attendeva a perfezionare il suo manoscritto, si volle consigliare <lb></lb>intorno alle leggi delle velocità, da applicarsi più propriamente al moto del­<lb></lb>l&#039;acqua, mandandogli nello stesso tempo quelle due prime Appendici, man­<lb></lb>date già a Galileo, intorno all&#039;errore in che era incorso Frontino, e in cui <lb></lb>incorrevano tuttavia gli ingegneri moderni, rispetto all&#039;alzamento, che fareb­<lb></lb>bero le piene, mettendosi in Po il Reno. </s>

<s>Il Baliani dunque, dop&#039;aver fatto <lb></lb>osservare che i liquidi, per aver le parti disgiunte, non vanno nello stesso <lb></lb>modo come i solidi, soggiungeva: “ La penna mi ha trasportato forse troppo <lb></lb>avanti, mentre che io voleva solo accennare il dubbio che io ho avuto in <lb></lb>quella seconda Appendice, come che del resto non mi paia che al suo di­<lb></lb>scorso, tanto circa le dimostrazioni, come a&#039;corollari e prime Appendice, vi <lb></lb>sia che aggiungere ” (Alb. </s>

<s>IX, 142, 43). </s></p><p type="main">

<s>Ma era naturale che, più di quegli del Baliani, premessero al Castelli <lb></lb>i giudizi di Galileo, il quale sebben fosse, per le sue proprie esperienze, per­<lb></lb>suaso pur troppo che ne&#039;tempi anteriori era a tutti rimasto incomprensibile <lb></lb>il modo di misurar l&#039;acque, per esssere il loro corso indeficiente; dubitava <lb></lb>nulladimeno se il riconoscer gli effetti della velocità, in quelle misure, fosse <pb xlink:href="020/01/3417.jpg" pagenum="378"></pb>pensiero del tutto nuovo. </s>

<s>Il dubbio prese forma definita, quando in quella <lb></lb>copia del libro, che dicemmo avergli mandata il Castelli stesso nell&#039;ultima <lb></lb>settimana del Novembre 1728, lesse attentamente la quarta Appendice, dalla <lb></lb>quale resultava che non tutti gl&#039;ingegneri e i periti dovevano aver trascu­<lb></lb>rato di considerare le velocità, se agli effetti di loro, mettendosi il Reno in <lb></lb>Po, attribuivano il non farsi alzamento nessuno d&#039;acqua. </s>

<s>Al qual dubbio il <lb></lb>Castelli, che aveva prima assolutamente asserito <emph type="italics"></emph>non essere il suo pensiero <lb></lb>stato messo in campo da nessuno ancora,<emph.end type="italics"></emph.end> rispondeva così, limitando il suo <lb></lb>asserto: “ Quanto allo scrupolo, che V. S. mi scrive, che nella quarta Ap­<lb></lb>pendice pare che io ammetta che altri abbiano avuto considerazione della ve­<lb></lb>locità, mentre noto che alcuni hanno avuto pensiero che, mettendosi il Reno <lb></lb>in Po non sarebbe cresciuto il Po; sappia che io non nego che non sia stata <lb></lb>avvertita la velocità nell&#039;acqua, ma dico bene che non è stata mai bene in­<lb></lb>tesa, e nel particolare di quell&#039;Appendice tocco di un Bolognese, il quale <lb></lb>semplicemente dice che il Reno non farebbe crescere il Po, mettendo certe <lb></lb>considerazioni ridicole, senza considerare la forza della velocità ” (Alb. </s>

<s>IX, 141). </s></p><p type="main">

<s>Questo discorso non mancò di produrre il suo effetto. </s>

<s>Tanto è vero che, <lb></lb>proponendosi una questione simile, quando si trattava degli alzamenti, che <lb></lb>farebbero nel Bisenzio le acque dell&#039;Ormannoro, Galileo la risolveva espres­<lb></lb>samente invocando gli avvertimenti, dati in questo proposito agl&#039;ingegneri <lb></lb>dal padre don Benedetto Castelli. </s>

<s>“ Quanto all&#039;ovviare (si legge in una nota <lb></lb>autografa) che sopraggiungendo le piene di Bisenzio proprio non trovino oc­<lb></lb>cupato parte dell&#039;alveo loro dall&#039;acque dell&#039;Ormannoro, che ciò possa esser <lb></lb>di qualche poco di profitto come si propone; concorro a dire che tal giova­<lb></lb>mento sarebbe poco, anzi pochissimo, e quasi insensibile. </s>

<s>E qui è da notarsi <lb></lb>quel gravissimo errore mai stato avvertito da alcuno degli ingegneri antichi <lb></lb>e moderni, ma scoperto dal M. R. padre don Benedetto Castelli, nel suo trat­<lb></lb>tato Del corso dei fiumi, il quale errore era che, entrando un fiume in un <lb></lb>altro, con acqua, che sia verbigrazia la terza parte di quella del principale; <lb></lb>debba accrescergli la terza parte di più della prima altezza: cosa che è fal­<lb></lb>sissima, imperocchè l&#039;acqua sopravveniente, con alzar la prima, gli dà tanto <lb></lb>maggior pendenza ed impeto, cioè velocità, che amendue si smaltiscono e <lb></lb>scaricano con poco più d&#039;alzamento. </s>

<s>Onde al nostro proposito quell&#039;acqua <lb></lb>dell&#039;Ormannoro, la quale averà alzato quella di Bisenzio, avanti l&#039;arrivo della <lb></lb>sua piena, per esempio, un braccio, non importerà talvolta, in far ricrescere <lb></lb>la sopravvegnente piena di Bisenzio, quattro dita, con tanta furia verrà quella <lb></lb>di Bisenzio, e porterà seco quella dell&#039;Ormannoro ” (MSS. Gal., P. V, T. III, <lb></lb>fol. </s>

<s>16). </s></p><p type="main">

<s>Dagli scrupoli però, così facilmente in Galileo rimossi, e dai dubbi, così <lb></lb>prestamente risoluti nel Baliani, si passò presto per altri a censure più gravi. </s>

<s><lb></lb>Iu quella lettera del dì primo Novembre 1634, dopo le cose riferite più sopra, <lb></lb>il Castelli così soggiungeva: “ Mi viene anco scritto di Firenze che il signor <lb></lb>Aggiunti ci ha notati alcuni errori gravi, presi da me, e che se ne dichiara <lb></lb>assai largamente. </s>

<s>Mi pare strano che con me non ne abbia mai trattato: mi <pb xlink:href="020/01/3418.jpg" pagenum="379"></pb>consolo però dall&#039;intendere che i miei pensieri sono conosciuti veri, e le sue <lb></lb>obiezioni per false, e tanto mi basta ” (Campori, Carteggio cit., pag. </s>

<s>417). </s></p><p type="main">

<s>Quali erano particolarmente gli errori notati dall&#039;Aggiunti? </s>

<s>Il Castelli <lb></lb>stesso mostra di averne avuto un&#039;assai vaga notizia, la quale, se non si ri­<lb></lb>duce ne&#039;termini precisi, non è possibile decidere se le apposte censure siano <lb></lb>state dettate da un retto giudizio, o da qualche malevolenza verso l&#039;Autore. </s>

<s><lb></lb>E perchè la questione è di non lieve importanza, giova rapidamente risalire <lb></lb>a trattarla dai suoi principii. </s></p><p type="main">

<s>La prima e più efficace occasione di pensare al moto delle acque l&#039;ebbe <lb></lb>senza dubbio anche l&#039;Aggiunti da quelle proposizioni geometriche, e da quel <lb></lb>progresso idraulico, che nella sua propria casa si senti leggere, in Firenze, <lb></lb>da Galileo, il quale giusto di lì rispondeva al Castelli: “ Scrivo in fretta in <lb></lb>casa del signor Niccolò Aggiunti ” (Alb. </s>

<s>VI, 306) insieme col quale finiva <lb></lb>per baciargli le mani. </s>

<s>Intorno all&#039;argomento, che nelle condizioni, in cui tro­<lb></lb>vavasi allora la rinnovata Scuola sperimentale, si presentava sotto l&#039;aspetto <lb></lb>di una novità curiosa e di sì grande importanza; era naturalissimo che si <lb></lb>rivolgessero a speculare Galileo e l&#039;Aggiunti, comunicandosi insieme i loro <lb></lb>propri pensieri. </s>

<s>De&#039;frutti di questa comunione di studii, benchè non molti <lb></lb>se n&#039;abbiano i documenti, si potrebbero pure addurre alcuni prestantissimi <lb></lb>esempi, fra quali il primo sia quello delle leggi de&#039;momenti de&#039;gravi sopra <lb></lb>i piani inclinati, applicate dall&#039;uno de&#039;due ora commemorati all&#039;equilibrio <lb></lb>dei liquidi ne&#039;sifoni ritorti, e dall&#039;altro al corso dell&#039;acqua per l&#039;alveo dei <lb></lb>fiumi. </s></p><p type="main">

<s>Si sovverrano forse i nostri Lettori che, rappresentandosi con BA, BE <lb></lb>(fig. </s>

<s>187) i due rami del sifone, dimostrava l&#039;Aggiunti equilibrarvisi dentro <lb></lb>il liquido, perchè sui punti A ed E della medesima linea orizontale preme <lb></lb><figure id="id.020.01.3418.1.jpg" xlink:href="020/01/3418/1.jpg"></figure></s></p><p type="caption">

<s>Figura 187.<lb></lb>ugualmente: e per dimostrar ciò considerava i due <lb></lb>corpi d&#039;acqua BA, BE come due solidi d&#039;ugual <lb></lb>materia, e di pari grossezza, attestati in B, i quali <lb></lb>solidi diceva che, avendo in premere ugual mo­<lb></lb>mento, necessariamente perciò rimangono in equi­<lb></lb>librio. </s>

<s>Ora, dietro le poste condizioni, è manifesto <lb></lb>che il principio, da cui fa l&#039;Aggiunti dipendere la sua conclusione, è il teo­<lb></lb>rema meccanico dell&#039;uguaglianza dei momenti di due solidi, quando le loro <lb></lb>gravità assolute son proporzionali alle lunghezze dei piani inclinati. </s>

<s>Immagi­<lb></lb>nando infatti il liquido esser ridotto in tante minime sfere, di raggio tutte <lb></lb>uguali, è chiaro che queste tanto son più di numero, e perciò di peso, quanto <lb></lb>maggiori son le lunghezze dei tubi. </s>

<s>Il teorema famoso dello Stevino avrebbe <lb></lb>ritrovato in queste sferette d&#039;acqua più propria, e più elegante conferma <lb></lb>sperimentale, che negli anelli della catena. </s></p><p type="main">

<s>Simile al discorso dell&#039;Aggiunti era quell&#039;altro, che faceva Galileo, per <lb></lb>provare che, essendo BA, BE due alvei, come il tortuoso e il diritto, in cui <lb></lb>si voleva ridurre il Bisenzio, “ tanto scarica il più lungo e meno declive, <lb></lb>quanto il più corto e il più pendente: cioè tanto il tortuoso quanto il diritto ” <pb xlink:href="020/01/3419.jpg" pagenum="380"></pb>(Alb. </s>

<s>VI, 357). Avendo le quantità la ragion composta degl&#039;impeti e delle <lb></lb>sezioni, che son manifestamente uguali, dovendo avere il Bisenzio corretto <lb></lb>il medesimo sbocco, tutto riducevasi a dimostrare che in A e in E, cioè agli <lb></lb>sbocchi dell&#039;alveo diritto e del tortuoso, giunge sempre la piena con impeti <lb></lb>uguali: e per dimostrar ciò, Galileo ricorre e applica, come l&#039;Aggiunti, al­<lb></lb>l&#039;acque le leggi de&#039;momenti dei solidi sopra piani ugualmente cadenti, ben­<lb></lb>chè variamente inclinati. </s>

<s>E perchè pareva agli avversari duro il concedere <lb></lb>che, essendo tanto più l&#039;acqua nel canale BE che nel BA, ne dovesse nono­<lb></lb>stante giungere una medesima quantità allo sbocco: o ammettendosi pure <lb></lb>le dottrine del Castelli, professate anche qui, perchè non pareva possibile che, <lb></lb>essendo in A l&#039;acqua tanto più precipitosa che in E, dovessero nulladimeno <lb></lb>avere in ambedue i casi l&#039;impeto stesso; Galileo risolveva il liquido in tante <lb></lb>sfere, e supposto che in BA ne fossero quattro, e in BE otto, diceva non <lb></lb>dovere far maraviglia se l&#039;ultima sfera in A ha impeto quanto l&#039;ultima sfera <lb></lb>in E, perchè, sebben quella abbia la metà del pendio, questa è incalzata e <lb></lb>premuta da un doppio numero di sfere, ond&#039;è manifesto come, compensan­<lb></lb>dosi le parti, si vengano qua e là nella composizione a ragguagliare i mo­<lb></lb>menti. </s></p><p type="main">

<s>Un altro esempio del comunicarsi insieme Galileo e l&#039;Aggiunti, intorno <lb></lb>al moto delle acque, i loro pensieri, l&#039;abbiamo nella proposta, e nella solu­<lb></lb>zione di un problema, che nell&#039;Idraulica vedremo essere dei principali, “ come <lb></lb>cioè cammini il negozio dell&#039;accelerarsi l&#039;acqua nel dover passare in un ca­<lb></lb>nale più stretto ” (Alb. </s>

<s>VI, 303). Intorno a ciò sappiamo che ghiribizzava <lb></lb>Galileo, infin da quando il primo libro del Castelli correva per Firenze ma­<lb></lb>noscritto, e lo leggeva l&#039;Aggiunti insieme con Galileo stesso, che a quella <lb></lb>occasione e in quel tempo, essendogli sovvenuto il sopraddetto problema idrau­<lb></lb>lico, intanto che ci ripensava egli fra sè, ne proponeva la soluzione al disce­<lb></lb>polo e all&#039;amico. </s>

<s>L&#039;investigare quali fossero i pensieri d&#039;ambedue è la pre­<lb></lb>sente nostra intenzione, e fra&#039;documenti, dietro i quali ella s&#039;indirizza, per <lb></lb>quel che principalmente riguarda Galileo, uno ci se ne presenta, da cui si <lb></lb>vede ch&#039;egli, in mezzo a tante incertezze, ricercava ne&#039;fatti qualche scorta <lb></lb>più fida. </s>

<s>L&#039;osservazione di questi fatti, non fidandosi forse degli occhi pro­<lb></lb>pri, la raccomandava alla sperimentata diligenza del Castelli, che in tal pro­<lb></lb>posito così rispondeva: “ Del resto, quanto al problema, che V. S. m&#039;ac­<lb></lb>cenna, potrei dirli quello che ho considerato qui in Pisa nelle piene d&#039;Arno, <lb></lb>mentre l&#039;acqua passa sotto gli archi dei ponti, minore sezione di quelle che <lb></lb>sono avanti il ponte, e dopo passato il ponte. </s>

<s>Ma perchè ci vorrebbe piutto­<lb></lb>sto comodità di voce, che di penna, mi riserbo a dirle questo con alcune <lb></lb>altre cosette a bocca ” (Campori, Carteggio cit., pag. </s>

<s>253, 54). Ma perchè <lb></lb>quel che disse a bocca il Castelli a Galileo non ci è noto, il primo docu­<lb></lb>mento de&#039;pensieri, ch&#039;ebbe esso Galileo intorno all&#039;accelerarsi l&#039;acqua, pas­<lb></lb>sando per uno stretto, si ricava da una lettera, nella quale s&#039;espone il dubbio, <lb></lb>natogli in leggere, nel corollario XI della misura delle acque correnti, l&#039;ar­<lb></lb>ticolo VI. </s>

<s>Quivi s&#039;accusa dall&#039;Autore di debolezza l&#039;ingegnere Giovanni Fon-<pb xlink:href="020/01/3420.jpg" pagenum="381"></pb>tana, per aver detto che passasse sotto il ponte Quattrocapi cento cinquant&#039;una <lb></lb>canna d&#039;acqua premuta, quasi fosse bambagia o lana (Ediz. </s>

<s>cit., pag. </s>

<s>19). <lb></lb>Ora a Galileo, che aveva anch&#039;egli pensato doversi attribuire l&#039;acceleramento <lb></lb>dell&#039;acqua sotto il ponte a qualche pressione, parve l&#039;accusa del Castelli incon­<lb></lb>siderata, potendo esser premute anche le materie, che non cedono, come cede <lb></lb>la bambagia o la lana: anzi il non cedere è talvolta condizione richiesta al <lb></lb>moto progressivo, com&#039;avviene del nocciolo di ciriegia premuto dalle dita. </s></p><p type="main">

<s>A questo esempio, che tante volte ricorre in Aristotile e nei seguaci di <lb></lb>lui, pare si riducesse per Galileo a principio la desiderata soluzione, alla <lb></lb>quale però sentiva di non potere acquietarsi, per aver troppo del peripate­<lb></lb>tico e del volgare. </s>

<s>Rivolgendosi perciò a cercare qualche altra cosa di me­<lb></lb>glio, pensò a quelle pressioni, che si fanno perpendicolarmente dall&#039;acqua, <lb></lb>sopra l&#039;acqua che le soggiace, o che si producono dall&#039;embolo dello stan­<lb></lb>tuffo dentro una canna, secondo qualunque direzione: pensiero, natogli senza <lb></lb>dubbio dalla languida risonanza di quelle tradizioni, alle quali l&#039;Innovator <lb></lb>baldanzoso protestava di voler chiuder le orecchie. </s>

<s>Le relazioni che, per lo­<lb></lb>gica e naturale necessità, passano fra il nuovo e l&#039;antico, appariranno in <lb></lb>seguito più manifeste, ma intanto è bene riferire quel documento di lettera. </s>

<s><lb></lb>che il dì 8 Gennaio 1629 Galileo scriveva al Castelli: “ Per diligenza usata, <lb></lb>così egli comincia, non ho potuto ritrovare le cinquanta copie, che scrive <lb></lb>mandarmi della sua Scrittura, ed essa non mi dice niente dove io debba far <lb></lb>capo per ritrovarle: però supplisca con altra sua. </s>

<s>Feci presentare le due al <lb></lb>serenissimo Granduca, e principe don Lorenzo, da Vincenzio mio figlio, es­<lb></lb>sendo che li tempi contrarissimi alla mia sanità m&#039;hanno tenuto finora per <lb></lb>tre settimane con doglie acerbissime. </s>

<s>La Scrittura è piaciuta assai a tutti che <lb></lb>l&#039;hanno letta, e qua si trattava di ristamparla, ma intendo ch&#039;ella non se <lb></lb>ne contenta. </s>

<s>Io la rileggerò più volte, e se mi parrȧ alcuna cosa da notarsi <lb></lb>l&#039;avviserò, in occasione che bisognasse ristamparla, e per ora mi sovviene di <lb></lb>quell&#039;acqua premuta, che ella interpetra come condensata, dalla quale oppo­<lb></lb>sizione potrebbe l&#039;Autore difendersi che non è necessario che l&#039;acqua pre­<lb></lb>muta si condensi, per scappar con maggior impeto, siccome il nocciolo di <lb></lb>ciriegia, premuto dalle dita, scappa con velocità senza condensarsi, e l&#039;acqua <lb></lb>stessa premuta nello schizzatoio salta anche in su, e compressa dal proprio <lb></lb>peso esce dalla botte velocemente ” (Alb. </s>

<s>VI, 323, 24). </s></p><p type="main">

<s>Dopo due settimane il Castelli rispondeva a questa di Roma così, dimo­<lb></lb>strando di non esser ben penetrato addentro al pensiero di Galileo: “ Quanto <lb></lb>a quella difficoltà, che fa dell&#039;acqua premuta, non credo che il Fontana possa <lb></lb>pretendere quella fuga, che V. S. pensa: prima, perchè non l&#039;ha detto, e <lb></lb>di più, se lo voleva dire, e se intendeva questo punto della velocità, fu in <lb></lb>tutto vanissima l&#039;opera sua di quelle misure. </s>

<s>Ma rispondendo più vivamente <lb></lb>dico che in tal senso non è vero che l&#039;acqua occupi minor loco, per essere <lb></lb>premuta, come dice il Fontana, ma per essere veloce, come dico io ” (ivi. </s>

<s><lb></lb>IX, 147). Ripetiamo che il Castelli, cosi rispondendo, non aveva penetrato il <lb></lb>pensiero di Galileo, qual&#039;era, non d&#039;investigar la ragione perchè l&#039;acqua <pb xlink:href="020/01/3421.jpg" pagenum="382"></pb>occupi minor luogo, ciò che egli non dubitava d&#039;attribuire alla sopravvenuta <lb></lb>velocità, ma di ricercar la causa, che produce una tale velocità, e per cui <lb></lb>di fatto passa tutta la piena sotto l&#039;arco del ponte. </s>

<s>Dichiaratosi perciò me­<lb></lb>glio col Castelli, e significatogli espressamente non potere la ricercata causa <lb></lb>dipender da altro, che da qualche pressione, comunque ella avvenga, e in <lb></lb>qualunque modo si faccia; avendo esso Castelli allora ben inteso lo stato <lb></lb>della questione, vi rivolse sopra il pensiero, e per lettera del 24 Febbraio 1629 <lb></lb>annunziava così di averla risoluta: “ Io credo di avere incontrate alcune cose <lb></lb>belle in risposta di quell&#039;acqua premuta, le quali non ho ancora ben disteso <lb></lb>in netto, ed avrei estremo bisogno d&#039;esserle per quattro o sei giorni appresso, <lb></lb>ma in ogni modo spero, per l&#039;ordinario che viene, mandarle l&#039;ossatura del <lb></lb>mio pensiero, che credo che le sarà di gusto ” (Campori, Casteggio cit., <lb></lb>pag. </s>

<s>279). </s></p><p type="main">

<s>Ignoriamo se queste speranze avessero effetto, e non si potendo perciò dire <lb></lb>ai Lettori qual si fosse propriamente il pensiero del Castelli, passeremo a ri­<lb></lb>ferire quello di Galileo, che si è intanto risoluto di mezzo ai dubbi, e di que­<lb></lb>sta risoluzione ci è rimasto spiegatissimo documento. </s>

<s>Ripudiata l&#039;ipotesi che <lb></lb>l&#039;acqua possa scivolare, premuta dalle pile del ponte, come, fra le dita che lo <lb></lb>premono, schizza il nocciolo di ciriegia; non rimaneva a Galileo di scegliere, <lb></lb>in quelle sue prime speculazioni, se non che fra l&#039;ipotesi degli Idraulici con­<lb></lb>temporanei di Leonardo da Vinci, che cioè le pressioni nascessero dal peso <lb></lb>dell&#039;acqua sollevatosi prima d&#039;entrar nello stretto, o fra quell&#039;altra ipotesi <lb></lb>del Cardano, che cioè le moli stesse sollevatesi precedentemente, incalzino <lb></lb>via via e sospingano al moto le susseguenti. </s>

<s>Ma poi ripudiò anche queste <lb></lb>ragioni, per attenersi a una sua propria nuovamente pensata, e che è gran <lb></lb>parte dell&#039;Idraulica galileiana; quella vogliam dire che gli accrescimenti delle <lb></lb>velocità, piuttosto che alla pendenza dell&#039;alveo, si debbano attribuire alla <lb></lb>pendenza della superficie. </s>

<s>Nella maggior pendenza dunque, che prende l&#039;acqua <lb></lb>in passar sotto gli archi dei ponti, Galileo riconosceva la causa di quella mag­<lb></lb>gior velocità, che fa smaltire la piena come se corresse libera fra le aperte <lb></lb>sponde del fiume. </s>

<s>“ Forse potrebbe accadere (così leggesi nel trattato allo <lb></lb>Staccoli intorno al regolare il Bisenzio) che l&#039;acqua rigurgitando, rigonfiasse <lb></lb>alquanto sulle svolte: ma questo non diminuirà punto la sua velocità, perchè <lb></lb>tale alzamento le servirà per far divenire la sua pendenza maggiore nella <lb></lb>parte del canale seguente, dove col crescer velocità verrà a compensare il <lb></lb>ritardamento patito sul principio della svolta, operando un effetto simile a <lb></lb>quello, che noi giornalmente vediamo accader nei fiumi assai colmi, mentre <lb></lb>nel passare sotto gli archi dei ponti, urtando nelle pile o imposte di detti <lb></lb>archi, gli conviene ristringere l&#039;acque, le quali rialzandosi nelle parti di sopra <lb></lb>si fanno pendenza tale sotto gli archi, che correndovi velocissimamente senza <lb></lb>scapito alcuno, continovando il corso loro non consumano un sol momento <lb></lb>di tempo di più nel loro intero viaggio, che se avessero avuto il canale li­<lb></lb>bero ” (Alb. </s>

<s>VI, 366, 67). </s></p><p type="main">

<s>Così veniva finalmente risoluto da Galileo il problema del crescersi le <pb xlink:href="020/01/3422.jpg" pagenum="383"></pb>velocità, diminuendosi le sezioni, intorno al quale era stato per lungo tempo <lb></lb>in così gran travaglio. </s>

<s>E come l&#039;ebbe risoluto, lo conferì negli amichevoli <lb></lb>colloqui con l&#039;Aggiunti, che ebbe presto, ripensandoci meglio, a scoprire in <lb></lb>quella soluzione qualche difetto, sembrandogli derivata piuttosto da partico­<lb></lb>lari osservazioni, che da leggi universali. </s>

<s>L&#039;acqua diceva non s&#039;affretta so­<lb></lb>lamente sotto gli archi dei ponti in tempo di piena, ma e nello stretto di <lb></lb>piccoli canali, dove l&#039;alzamento della superficie che precede l&#039;entrata, e il <lb></lb>pendio di quella che succede son di tanto poco momento, da non si potere <lb></lb>attribuire a loro la causa di così repentina sollecitazione di moto. </s></p><p type="main">

<s>Non potendosi dunque, proseguiva l&#039;Aggiunti a ragionare, fare in tali <lb></lb>accidentalità di superficie consistere un effetto tanto essenziale, convien ri­<lb></lb>dursi a più alti principii. </s>

<s>Si sa dalle Storie passate che egli fu il primo e <lb></lb>l&#039;unico, nella Scuola galileiana, a formulare le leggi della comunicazione dei <lb></lb>moti, derivandole dal modo di misurar le forze compostamente per la velo­<lb></lb>cità, e per la quantità di materia. </s>

<s>Di qui veniva a formularsi la proposizione, <lb></lb>in particolar modo da lui stesso poi dimostrata: <emph type="italics"></emph>La medesima velocità, nelle <lb></lb>maggiori e minori quantità di materia, opera più o meno potentemente, <lb></lb>secondo la proporzione di essa materia.<emph.end type="italics"></emph.end> Che se le potenze o le forze sol­<lb></lb>lecitanti al moto sono uguali, velocità dunque e quantitȧ di materia si rispon­<lb></lb>deranno costantemente in ragione contraria. </s>

<s>Ecco a quali principii essenziali <lb></lb>s&#039;informava, e da quale appropriata universalità di ragioni faceva l&#039;Aggiunti <lb></lb>dipendere la soluzion del problema: La potenza che incalza la piena è la me­<lb></lb>desima nel largo dell&#039;alveo e sotto l&#039;arco del ponte: ma perchè qui la quan­<lb></lb>tità di materia è diminuita, necessariamente consegue che a quella propor­<lb></lb>zione la velocità invece s&#039;accresca. </s></p><p type="main">

<s>La principal proposizione, dalla quale svolgevasi il progresso idraulico <lb></lb>del Castelli, veniva così dimostrata dai suoi veri principii, e a ciò intende­<lb></lb>vano le critiche dell&#039;Aggiunti. </s>

<s>Non è vero ch&#039;egli avesse, come fu riferito <lb></lb>da malevoli o da male informati all&#039;Autore della Misura delle acque correnti, <lb></lb>notati errori nel libro di lui: non si dubitava per niente della verità delle <lb></lb>conclusioni, ma si diceva solo che mancavano di fondamento, perchè i sem­<lb></lb>plici fatti osservati e l&#039;esperienze non possono partecipare alle proposizioni <lb></lb>quella certezza geometrica, della quale presumeva di averle insignite lo stesso <lb></lb>Castelli. </s>

<s>Noi, mentre da una parte confermiamo che l&#039;Aggiunti, in tal pro­<lb></lb>posito, aveva ragione, non possiamo non deplorare dall&#039;altra i danni dalla <lb></lb>morte recati ai progressi della Scienza italiana, la quale sarebbe venuta per <lb></lb>lui a dare così per tempo le leggi della percossa e del corso dei fiumi, non <lb></lb>dimostrate dietro alcune fisiche proprietà dei solidi e dei liquidi, com&#039;ave­<lb></lb>vano fatto Galileo e il Castelli, ma concluse da quella universalità di prin­<lb></lb>cipii, da cui dipendono le ragioni del moto in ogni sorta di corpi gravi. </s></p><p type="main">

<s>Le censure dell&#039;Aggiunti, come si vede, erano cose di bene altra im­<lb></lb>portanza, da que&#039;primi dubbi mossi da Galileo intorno a certe storiche im­<lb></lb>proprietà, che alcuno avrebbe potuto notar facilmente nel libro del Castelli. </s>

<s><lb></lb>Bench&#039;esso Galileo sembrasse rimaner sodisfatto delle risposte, forse non si <pb xlink:href="020/01/3423.jpg" pagenum="384"></pb>rimosse mai dalla mente di lui la persuasione che a nessuno fosse prima <lb></lb>sovvenuto il pensiero d&#039;applicare le velocità alla misura delle acque correnti. </s>

<s><lb></lb>Dai documenti poco addietro citati apparisce che il Castelli stesso ebbe a <lb></lb>temperare quella sua prima sentenza, così assolutamente pronunziata, intorno <lb></lb>alla novità della sua Scienza idraulica, e quasi presentisse nell&#039;animo che <lb></lb>le osservazioni amorevoli del Maestro si sarebbero nel più libero giudizio <lb></lb>dei posteri convertite in accuse acerbe di plagio; è sollecito di dichiararsi <lb></lb>ch&#039;ei non nega essere le velocità state prima avvertite, ma vuol dir sola­<lb></lb>mente che non furono bene intese e spiegate. </s>

<s>Aveva infatti appena finito di <lb></lb>rispondere in fretta a Galileo, giustificandosi dell&#039;accusa data all&#039;ingegnere <lb></lb>Fontana, che così caldamente soggiunge: “ La voglio solo pregare che os­<lb></lb>servi la cautela, con la quale io cammino nella mia scrittura, di dire sem­<lb></lb>pre che non è stata bene intesa, pìenamente spiegata, al vivo penetrata, e <lb></lb>simili cose, la velocità dell&#039;acqua e la sua forza in fare scemare la misura ” <lb></lb>(Alb. </s>

<s>IX, 146, 47). </s></p><p type="main">

<s>Nonostante queste cautele, rimase la scrittura del Castelli improntata di <lb></lb>tale presunzione, che, non potendola alcuni patire, non risparmiarono perciò <lb></lb>all&#039;Autore quella presentita acerbità delle censure. </s>

<s>Raffaello Fabbretti, nel <lb></lb>suo trattato <emph type="italics"></emph>De aquis et aquaeductibus veteris Romae,<emph.end type="italics"></emph.end> non poteva natural­<lb></lb><gap></gap>ente dispensarsi dal commemorare Giulio Sesto Frontino, dai citati passi <lb></lb>del quale argomentando alla principale importanza, che dall&#039;antico Prefetto <lb></lb>romano si dava alle velocità nel dispensar l&#039;acque, secondo la loro più giu­<lb></lb>sta misura; conclude con l&#039;ironia di queste parole: “ Unde explodendum <lb></lb>esse dicimus p. </s>

<s>Castelli, quasi Frontinus magnum illud suum theorema, ex <lb></lb>velocitate aquae modum ipsius variare ignoraverit ” (<emph type="italics"></emph>De aquis<emph.end type="italics"></emph.end> cit., Ro­<lb></lb>mae 1680, pag. </s>

<s>128). Segue poi il Fabbretti a citar da Frontino l&#039;articolo, <lb></lb>in cui, dop&#039;aver narrato com&#039;avesse raccolte varie misure d&#039;acqua, in vari <lb></lb>stati e condizioni di un medesimo acquedotto; soggiunge: “ cuius rei ratio <lb></lb>est quod vis aquae rapacior, ut ex largo et celeri flumine excepta, <emph type="italics"></emph>veloci­<lb></lb>tate ipsa ampliat modum ”<emph.end type="italics"></emph.end> (ibid.). E perchè insomma, a giudizio dello <lb></lb>stesso Fabbretti, non ha fatto altro il Castelli che stemperare in lunghe e <lb></lb>noiose parole il laconico linguaggio dello Scrittore antico, per dare di ciò una <lb></lb>prova ai Lettori, vuol che confrontino quel che si legge, nel proemio del <lb></lb>Moderno, dell&#039;acqua che, uscendo da due cannelle soprapposte, la più alta <lb></lb>getta men della più bassa a proporzion dell&#039;altezza; con questo che Fron­<lb></lb>tino, fatta la medesima supposizione, potentemente condensa in tali parole: <lb></lb><emph type="italics"></emph>“ Inferior plus trahit, superius minus ducit quia cursus aquae ab infe­<lb></lb>riori rapitur ”<emph.end type="italics"></emph.end> (ibid.). </s></p><p type="main">

<s>Dopo il Fabbretti venne il Poleni, che divulgando, come altrove dicemmo, <lb></lb>la scrittura geometrica del Buteone, <emph type="italics"></emph>De fluentis aquae mensura,<emph.end type="italics"></emph.end> ebbe inten­<lb></lb>zione di rammentare a chi l&#039;aveva oramai dimenticato come, infino dal 1554, <lb></lb>che vuol dire 74 anni prima del Castelli, era in Francia divulgato un libro, <lb></lb>in cui s&#039;insegnava il più giusto modo di dispensar l&#039;acqua, misurandone la <lb></lb>velocità del corso con l&#039;orologio alla mano, non importa s&#039;egli era una cles-<pb xlink:href="020/01/3424.jpg" pagenum="385"></pb>sidra antica, invece di un pendolo nuovo. </s>

<s>All&#039;ultimo il Venturi, mandando <lb></lb>il fiato dalla sua propria trachea nella muta laringe dell&#039;Arconati, annun­<lb></lb>ziava al mondo scientifico, stupito, che la Scienza idraulica del Castelli, tutt&#039;al­<lb></lb>tro ch&#039;essere a quel tempo nuova, si trovava più ampiamente e più sottil­<lb></lb>mente trattata nei manoscritti di Leonardo da Vinci. </s>

<s>La piccola scintilla, <lb></lb>in Parigi, secondò quella gran fiamma, che trovò pascolo così gradito nella <lb></lb>penna di tanti scrittori, alcuni de&#039;quali, per vendetta dell&#039;usurpazione e per <lb></lb>amor di giustizia, proposero che l&#039;essere le velocità in reciproca ragione delle <lb></lb>sezioni si dovesse dire dall&#039;ora in poi legge di Leonardo da Vinci, e non più <lb></lb>del Castelli. </s></p><p type="main">

<s>Vorremmo volentieri sussurrar nelle orecchie di cotesti zelanti che più <lb></lb>giusto sarebbe stato appellare la detta legge idraulica dal nome del Cardano, <lb></lb>il quale non la scrisse in private carte disperse, ma in bei volumoni in folio <lb></lb>stampati, se non ci premesse maggiore curiosità di domandare, perchè mai, <lb></lb>volendosi in ogni modo far la rivendicazione a favore di un nome famoso, <lb></lb>non preferissero costoro a Leonardo lontano, e dal partecipare con gli studii <lb></lb>del Castelli sì alieno, il più prossimo e immediato magistero di Galileo. </s>

<s>Dai <lb></lb>teoremi idrostatici di lui infatti vedemmo come scendesse per facile corolla­<lb></lb>rio la legge delle velocità reciproche delle sezioni. </s>

<s>Anzi è notabile che Ga­<lb></lb>lileo stesso, nelle sì frequenti conferenze ch&#039;egli ebbe col Castelli intorno al <lb></lb>moto dell&#039;acqua, non ne facesse mai motto, e lasciasse intera al Discepolo <lb></lb>la compiacenza di quel ch&#039;egli diceva pensiero suo nuovo. </s>

<s>Nemmeno il Vi­<lb></lb>viani, anche dopo aver vedute le note, nelle quali Galileo si proponeva di <lb></lb>risolvere il problema della quantità d&#039;acqua compresa nella troscia, accennò <lb></lb>mai, che da noi si sappia, alle relazioni che passano fra le dottrine del Di­<lb></lb>scorso intorno i galleggianti, e il libro della Misura delle acque correnti. </s></p><p type="main">

<s>Unico forse il Montanari, in mezzo alla numerosa Scuola galileiana, in­<lb></lb>dicò le dette relazioni nel suo dialogo intitolato <emph type="italics"></emph>Le forze di Eolo,<emph.end type="italics"></emph.end> là dove, <lb></lb>dai momenti nella stadera passando ai momenti nel sifone idrostatico, af­<lb></lb>ferma che le loro leggi, dimostrate da Galileo nel suo strumento, son quelle <lb></lb>stesse applicate poi dal Castelli al corso dei fiumi. </s>

<s>“ Leggete, dice nel Dia­<lb></lb>logo citato il Montanari stesso all&#039;interlocutor suo Gozzadini, a carte 15 delle <lb></lb>Galleggianti, ove il Galileo mostra come la forza, ossia il momento dell&#039;acqua <lb></lb>stagnante in un vaso grande, che comunica con altro vaso angusto, e seco <lb></lb>s&#039;equilibra in orizonte, non per altro s&#039;eguaglia al momento di quella del <lb></lb>vaso più angusto, se non perchè l&#039;acqua, nel vaso più angusto, quando do­<lb></lb>vesse moversi, e cedere alla pressione del maggiore, si moverebbe ad alto <lb></lb>con velocità, appunto tanto più grande dell&#039;abbassamento che ella farebbe <lb></lb>nel vaso maggiore, quanto è più grande la superficie del maggiore di quella <lb></lb>del minore. </s>

<s>Onde, a causa di questa reciproca proporzione della poca ve­<lb></lb>locità nel primo, alla molta nel secondo, e dell&#039;angusta sezione del secondo <lb></lb>vaso alla più ampia e capace del primo; si mantengono in equilibrio. </s>

<s>Ed <lb></lb>a maggior chiarezza notate ancora ciò che dimostra l&#039;abate Castelli, nelle <lb></lb>sue <emph type="italics"></emph>Acque correnti,<emph.end type="italics"></emph.end> ove fa vedere che un fiume, correndo per un canale <pb xlink:href="020/01/3425.jpg" pagenum="386"></pb>or più largo or più stretto, ad ogni modo passa in tempi uguali ugual quan­<lb></lb>tità d&#039;acqua per le sezioni medesime, ancorchè tanto disuguali, mercecchè <lb></lb>nella sezione più angusta egli per appunto altrettanto più veloce si muove <lb></lb>che nell&#039;ampla, quanto questa è più grande di quella. </s>

<s>Onde potiamo dire <lb></lb>che tutta la forza e momento di quel fiume, che era diffusa nell&#039;alveo più <lb></lb>amplo, al passar per un altro più angusto si converte in tanta maggior ve­<lb></lb>locità, quanta è la diminuzione che gli accade nell&#039;ampiezza ” (Parma 1694, <lb></lb>pag. </s>

<s>146, 47). </s></p><p type="main">

<s>L&#039;osservazione giustissima del Montanari sfuggi ai magnificatori di Ga­<lb></lb>lileo, che perciò a lei sostituirono giudizi senza criterio. </s>

<s>Il Nelli per esem­<lb></lb>pio asserì e confermò che “ il Trattato sopra la misura delle acque correnti, <lb></lb>pubblicato dal Castelli, è parto dell&#039;ingegno di Galileo, e che questo Filosofo <lb></lb>permesse a quel Monaco di pubblicarlo col suo nome, come fece della scrit­<lb></lb>tura contro Lodovico delle Colombe ” (<emph type="italics"></emph>Vita di Galileo,<emph.end type="italics"></emph.end> Losanna 1793, <lb></lb>pag. </s>

<s>490). L&#039;Albèri, in nota a pag. </s>

<s>324 del T. VI della sua Edizione com­<lb></lb>pleta, ridusse a miglior senno l&#039;asserzione inconsiderata, ma ambedue troppo <lb></lb>alla lettera interpetrarono l&#039;espressione: <emph type="italics"></emph>se le cose che sono scritte nell&#039;ope­<lb></lb>retta son vere, come io credo, ella sa che l&#039;opera è sua<emph.end type="italics"></emph.end> (Alb. </s>

<s>IX, 146): <lb></lb>espressione, che poteva ridursi al suo vero significato, collazionandola con <lb></lb>quest&#039;altra, dallo stesso Castelli precedentemente usata nello scrivere al me­<lb></lb>desimo Galileo: <emph type="italics"></emph>ho cercato di seguitare i vestigi di V. S., alla quale, se <lb></lb>nella mia Scrittura ci è cosa di buono, tutto riferisco<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>141). </s></p><p type="main">

<s>Del resto la questione del mio e del tuo, relativamente alla risposta <lb></lb>contro Lodovico delle Colombe, è decisa dalle seguenti parole, scritte a Ga­<lb></lb>lileo il dì 21 Gennaio 1615 dal Castelli, a proposito della pubblicazione della <lb></lb>citata Scrittura apologetica: “ Mi vien fatta istanza grandissima del mio <lb></lb>libro, se però si può chiamar mio, dove V. S. ha posto tanto del suo ” (MSS. <lb></lb>Gal., P. III, T. VII, fol. </s>

<s>40): come l&#039;altra questione, relativa al trattato delle <lb></lb>acque correnti, resta con non minor certezza decisa dai fatti sopra narrati, <lb></lb>dai quali apparisce che Galileo si mostrò nuovo alle proposte del Castelli, e <lb></lb>ricevè da esse, a speculare intorno al moto delle acque, l&#039;occasione e l&#039;im­<lb></lb>pulso. </s>

<s>Le quali cose, quando fossero state considerate dal Zendrini, non si <lb></lb>sarebbe fatto maraviglia, nella sua prefazione al Trattato delle acque cor­<lb></lb>renti, che la repubblica di Venezia, allora in gran sollecitudine e dispendio <lb></lb>di dare un nuovo alveo al Po e alla Brenta, non avesse consultato mai in­<lb></lb>torno a ciò Galileo, suo celebre matematico nello studio di Padova (<emph type="italics"></emph>Autori <lb></lb>che trattano del moto delle acque,<emph.end type="italics"></emph.end> T. VIII, Firenze 1770, pag. </s>

<s>XIII). </s></p><p type="main">

<s>La scienza era da&#039;suoi principii matematici dimostrata nelle Scuole, ai <lb></lb>tempi di Leonardo da Vinci, e le dimostrazioni scientifiche venivano divul­<lb></lb>gate dai libri del Cardano e del Buteone, ma intanto, non solamente in Ve­<lb></lb>nezia e nel rimanente d&#039;Italia, ma anche appresso le altre nazioni erano le <lb></lb>opere idrauliche affidate alla pratica dei così detti Periti ingegneri, e nella <lb></lb>dispensa delle acque si duravano a commettere i medesimi errori, così nel <lb></lb>Delfinato, patria del Buteone, come nella Lombardia, patria del nostro Ca-<pb xlink:href="020/01/3426.jpg" pagenum="387"></pb>stelli. </s>

<s>Qualunque siano perciò le censure, date al Matematico di Papa Ur­<lb></lb>bano VIII, nessuno potrà negare che da lui primo e solo cominciò la scienza <lb></lb>a dar regola all&#039;arte: da lui primo e solo s&#039;imparò a far con giustizia la <lb></lb>dispensa delle acque. </s></p><p type="main">

<s>Ma, esaminando più diligentemente, quelle censure si trovano concluse <lb></lb>nel dire che la scienza del Castelli non era nuova. </s>

<s>Il detto verissimo, e con­<lb></lb>fermato già dalla Storia, non dissente dal concedere che il Castelli abbia <lb></lb>fatto rivivere una cosa morta, ciò che alcuni riducono a qualche clandestino <lb></lb>connubio con le vecchie tradizioni, repudiate allora da tutti, e perciò da tutti <lb></lb>dimenticate. </s>

<s>La falsità però di questa opinione si scopre, ripensando alle ori­<lb></lb>gini tanto diverse per la scienza degli Autori antichi, e per quella del mo­<lb></lb>derno Scrittore, cosicchè questi potè con coscienza pura asserire che il suo <lb></lb>pensiero, se non così nudo come lo presentava anche Frontino, almeno qual <lb></lb>si dava ordinato a sistema, era nuovo. </s>

<s>Mentre infatti l&#039;Idraulica di Leonardo <lb></lb>e del Cardano s&#039;informava ai principii matematici del Nemorario, quella del <lb></lb>Castelli non ebbe altro fondamento che nella osservazione di alcuni fatti pre­<lb></lb>senti, e dai quali con rammarico si conosceva doverne non legger danno se­<lb></lb>guitare al pubblico e ai privati. </s>

<s>Da questa medesima diversa origine di prin­<lb></lb>cipii s&#039;argomenta altresì all&#039;indipendenza del Castelli dal magistero di Galileo, <lb></lb>il quale, non dai fatti, ma dalle leggi dei momenti dimostrando le ragioni <lb></lb>degli equilibrii idrostatici, dava altro modo a dedur che le velocità hanno <lb></lb>reciproca ragione delle sezioni. </s></p><p type="main">

<s>Tale essendosi dunque la conclusione, alla quale siamo stati condotti dal <lb></lb>confrontare la scienza antica con la nuova, per quel che semplicemente ri­<lb></lb>guarda la considerazione delle velocità nella misura delle acque correnti; cì <lb></lb>rimane, come soggetto anche di maggiore importanza, a proseguire il con­<lb></lb>fronto, tra le leggi assegnate a quelle medesime velocità nell&#039;Idraulica trattata <lb></lb>da Leonardo e dal Cardano, e in quella nuovamente restaurata dal Castelli. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Come le leggi delle velocità nei solidi ebbero una trattazione diversa, <lb></lb>ora considerandoli nelle loro libere cadute, ora nelle loro scese lungo i piani <lb></lb>inclinati; così per analogia dev&#039;essere stato delle acque. </s>

<s>Diremo perciò di­<lb></lb>stintamente delle proporzioni delle velocità assegnate dai varii autori al moto <lb></lb>di esse acque, sia quando scendono o salgono nel fluire dai vasi, in trosce <lb></lb>e in zampilli, sia quando scorrono per le pendenze dei canali o per gli alvei <lb></lb>dei fiumi. </s></p><p type="main">

<s>Per quel che riguarda le trosce, anche gli antichi, come s&#039;ha da alcune <lb></lb>note di Leonardo da Vinci, attribuivano il loro assottigliarsi agl&#039;incrementi <lb></lb>successivi delle velocità, le quali non dubitarono di far proporzionali agli <lb></lb>spazi, a quel modo che facevano per tutti gli altri corpi gravi cadenti. </s>

<s>Sco-<pb xlink:href="020/01/3427.jpg" pagenum="388"></pb>pertosi poi che esse velocità stanno invece come le radici degli spazi, pareva <lb></lb>certissima l&#039;applicazione della nuova legge anche ai liquidi. </s>

<s>Galileo infatti <lb></lb>ne porgeva l&#039;esempio nel risolvere il problema, per noi fatto noto, della quan­<lb></lb>tità d&#039;acqua compresa nella troscia cadente dalla secchia, per la misura della <lb></lb>forza della percossa, e nel segnar la scala degli spazi sempre più brevi, pas­<lb></lb>sati dalle gocciole separate, quanto più zampillando salgono in alto, dove il <lb></lb>moto è più lento (V. nel nostro V Tomo a pag. </s>

<s>217). </s></p><p type="main">

<s>Il Castelli però lascia i Lettori in una incertezza penosa. </s>

<s>Nel XV corol­<lb></lb>lario del suo primo libro, applicando la proposizione, da sè generalmente di­<lb></lb>mostrata, a spiegar quell&#039;assottigliarsi, che si osserva nelle acque cadenti; <lb></lb>dice un tal fatto da null&#039;altro dipendere, che dall&#039;acquisto di maggior ve­<lb></lb>locità dell&#039;acqua nel seguitare a cadere, “ essendo notissima conclusione ap­<lb></lb>presso i Filosofi che i corpi gravi cadenti, quanto più si scostano dal princi­<lb></lb>pio del loro movimento, tanto più acquistano di velocità, e perciò l&#039;acqua, <lb></lb>come corpo grave cadendo, si va velocitando, e però scema di misura e si <lb></lb>rassottiglia (<emph type="italics"></emph>Della misura delle acque<emph.end type="italics"></emph.end> cit., pag. </s>

<s>28). Qui la legge della ve­<lb></lb>locità, rispetto al tempo e allo spazio, non è determinata, e non si dubite­<lb></lb>rebbe doversi intendere per que&#039;Filosofi i peripatetici (che pure ammette­<lb></lb>vano tanto più velocitarsi i cadenti, quanto più si dilungano dal principio del <lb></lb>moto) piuttosto che Galileo, quando a intender così non consigliasse il pensiero <lb></lb>che doveva esser già partecipata al Castelli, dal suo proprio Maestro, la sco­<lb></lb>perta legge dei moti accelerati. </s>

<s>Nè da altro che dal pensar così dee essere <lb></lb>il Barattieri stato indotto a scriver queste parole: “ Può nascere ancora <lb></lb>qualche difficoltà nel considerare quell&#039;effetto, che si concede a&#039;pesi gravi <lb></lb>cadenti, che si fanno più veloci quanto più si discostano dal suo principio, <lb></lb>pensando forse che si abbi da considerare che segua tal effetto, anche nel <lb></lb>corso delle acque correnti dei fiumi, come appunto pare che ne sia il pen­<lb></lb>siero dell&#039;abbate Castelli, al XV de&#039;suoi corollari, e del sig. </s>

<s>Bagliani, quando <lb></lb>nel proemio de&#039;suoi Liquidi mostra che tale aumento non solo si faccia, ma <lb></lb>che segua, crescendo la sua velocità con la regola delle progressioni aritme­<lb></lb>tiche. </s>

<s>” Così il Barattieri (<emph type="italics"></emph>Architettura delle acque,<emph.end type="italics"></emph.end> P. I, Piacenza 1697, <lb></lb>pag. </s>

<s>169, 70) senza dichiararsi che il Baliani certamente intendeva, che <lb></lb>quelle progressioni aritmetiche erano de&#039;numeri impari ab unitate. </s></p><p type="main">

<s>In ogni modo, come nel corollario XV <emph type="italics"></emph>pare<emph.end type="italics"></emph.end> che il Castelli ammetta ve­<lb></lb>locitarsi l&#039;acqua, che liberamente cade, a proporzione delle radici delle al­<lb></lb>tezze; così <emph type="italics"></emph>pare<emph.end type="italics"></emph.end> che nel Proemio ammetta essere le velocità degli efflussi dai <lb></lb>vasi proporzionali alle semplici altezze dei livelli. </s>

<s>“ Esca, egli dice, l&#039;acqua <lb></lb>per due cannelle uguali d&#039;ampiezza, una posta nella parte inferiore del vaso, <lb></lb>e l&#039;altra nella parte superiore: è manifesto che, nel tempo, nel quale dalla <lb></lb>parte superiore uscirà una determinata misura d&#039;acqua, dalla parte inferiore <lb></lb>usciranno quattro, cinque e assai più delle medesime misure, secondo che <lb></lb>sarà maggior la differenza dell&#039;altezza delle cannelle, e la lontananza della <lb></lb>superiore cannella dalla superficie o livello dell&#039;acqua del vaso ” (<emph type="italics"></emph>Della mi­<lb></lb>sura ecc.,<emph.end type="italics"></emph.end> pag. </s>

<s>5). </s></p><pb xlink:href="020/01/3428.jpg" pagenum="389"></pb><p type="main">

<s>Elia Lombardini argutamente notò che in questa proposizione si con­<lb></lb>tiene un errore manifesto, “ non già di stampa, ma di concetto, dovendo <lb></lb>essere maggiore l&#039;efflusso della cannella inferiore, al confronto della supe­<lb></lb>riore, quanto <emph type="italics"></emph>minore<emph.end type="italics"></emph.end> e non <emph type="italics"></emph>maggiore<emph.end type="italics"></emph.end> è la distanza di questa dalla super­<lb></lb>ficie della conserva ” (<emph type="italics"></emph>Dell&#039;origine e del progresso dell&#039;Idraulica in Italia,<emph.end type="italics"></emph.end><lb></lb>Milano 1872, pag. </s>

<s>48). Noi saremmo inclinati ad attribuir l&#039;errore, se non <lb></lb>alla stampa, a una certa sbadataggine nell&#039;Autore, occasionata senza dubbio <lb></lb>dall&#039;esser certo da una parte <emph type="italics"></emph>che l&#039;acqua per la cannella inferiore corre <lb></lb>e passa con assai maggiore velocità, di quello che fa per la superiore,<emph.end type="italics"></emph.end> e <lb></lb>dal non potere intendere dall&#039;altra <emph type="italics"></emph>qual si sia la cagione di questo negozio.<emph.end type="italics"></emph.end><lb></lb>Ma che una tale ignoranza, così dallo Scrittore stesso confessata, consista nel <lb></lb>non aver egli saputo intendere che la botte, quanto è più piena, per aver <lb></lb>maggior carico di sopra, tanto getta con più ìmpeto dalla cannella; non si <lb></lb>consentirà al Lombardini da nessuno, che non voglia fare il Castelli piu stu­<lb></lb>pido dei villici e dei canovai. </s></p><p type="main">

<s>Il mistero dunque non riguardava propriamente le pressioni, fatte se­<lb></lb>condo le altezze perpendicolari. </s>

<s>Quel che non sapeva intendere il Castelli <lb></lb>era come quelle pressioni, che dietro la prima supposizione archimedea aveva <lb></lb>creduto non poter essere che perpendicolari, si rivolgessero poi orizontal­<lb></lb>mente, anzi per tutti i versi. </s>

<s>Così viene a scoprirsi la radice del male, che <lb></lb>non in altro s&#039;asconde, se non in que&#039;difetti, ne&#039;quali si rimaneva la domi­<lb></lb>nante Idrostatica galileiana, e della quale, come fu imbevuto il Castelli, così <lb></lb>ritroveremo il Cavalieri, insieme con gli altri della medesima Scuola infino <lb></lb>al Torricelli, che felicemente applicò all&#039;Idrodinamica la dottrina steviniana <lb></lb>dell&#039;uguaglianza delle pressioni. </s></p><p type="main">

<s>Il concetto nonostante di una tale uguaglianza essendo balenato per la <lb></lb>mente degli Idraulici del secolo precedente, fu potissima causa dell&#039;essere, <lb></lb>intorno al modo di risolvere così fatte questioni, rimasti superiori al Disce­<lb></lb>polo di Galileo i seguaci del Nemorario. </s>

<s>Questi trovarono assai facile spie­<lb></lb>gare, come fra gli altri fece il Cardano, “ cur aquae, a lateribus etiam stan­<lb></lb>tium paludum, per rimas tabularum impetum secum afferant, cum aqua, <lb></lb>quae sursum est, et a lateribus premat, ideoque etiam, absque alio cursu <lb></lb>impetum faciat et impellat. </s>

<s>Velociter igitur aqua fertur per angusta foramina <lb></lb>iuxta proportionem prementis aquae, ad eam quae protruditur ” (<emph type="italics"></emph>De rerum <lb></lb>var.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>69). La pressione dunque dell&#039;acqua <emph type="italics"></emph>quae sursum est,<emph.end type="italics"></emph.end> si ri­<lb></lb>flette con egual forza anche <emph type="italics"></emph>a lateribus,<emph.end type="italics"></emph.end> ed ecco come riuscisse facile al Car­<lb></lb>dano spiegare il fatto, rimasto inesplicabile al Castelli, del correr maggior­<lb></lb>mente veloce l&#039;acqua nella cannella inferiore che nella superiore; e nel <lb></lb>medesimo tempo ecco aperta la via di dimostrare come, essendo le due can­<lb></lb>nelle uguali, le quantità dell&#039;acqua, versate da quella di sotto e da quella <lb></lb>di sopra, sian proporzionali alle loro respettive distanze dal supremo livello. </s></p><p type="main">

<s>Leonardo, nella potente sobrietà del suo proprio linguaggio, va, anche <lb></lb>più direttamente, a coglier nel segno. </s>

<s>Dop&#039;avere stabilito che le pressioni <lb></lb>perpendicolari crescono come le altezze del liquido soprapposto, rispetto alle <pb xlink:href="020/01/3429.jpg" pagenum="390"></pb>orizzontali conclude che, in ogni grado d&#039;altezza del liquido, la cannella <lb></lb><emph type="italics"></emph>acquista gradi di distantia nel gettar da lontano:<emph.end type="italics"></emph.end> che vuol dire essere <lb></lb>le velocità del corso, dentro la cannella orizzontale, proporzionali alle altezze. </s>

<s><lb></lb>Di qui riuscì a concludere, con tutta quella precision di linguaggio scientifico <lb></lb>che tanto si fa desiderar nel Castelli, la proposizione altrove da noi citata: <lb></lb><emph type="italics"></emph>Dell&#039;acqua, che non manca di una ordinata altezza nella sua superficie, <lb></lb>tale sarà la quantità dell&#039;acqua, che versa per un dato spiracolo in un <lb></lb>dato tempo, quale quella della data altezza di esso spiracolo.<emph.end type="italics"></emph.end> Cosicchè, se <lb></lb>l&#039;altezza sopra lo spiracolo B è la metà di quella sopra lo spiracolo G, <emph type="italics"></emph>dico,<emph.end type="italics"></emph.end><lb></lb>soggiunge quivi Leonardo, <emph type="italics"></emph>che G verserà due tanti più di B, nel medesimo <lb></lb>tempo, perchè ha due tanti più di peso d&#039;acqua sopra di sè.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Passiamo ora a narrare le varie opinioni intorno alle leggi del veloci­<lb></lb>tarsi l&#039;acqua, nei canali inclinati, e dentro l&#039;alveo dei fiumi. </s>

<s>Il Cardano, <lb></lb>in conformità co&#039;principii già professati, pronunziò dell&#039;acqua corrente per <lb></lb>un canale inclinato che <emph type="italics"></emph>quanto magis a principio ortus distiterit<emph.end type="italics"></emph.end> (prese le <lb></lb>distanze secondo le cadenti perpendicolari) <emph type="italics"></emph>eo velocius movebit.<emph.end type="italics"></emph.end> E così ve­<lb></lb>demmo anche Leonardo applicare al corso dei fiumi la legge delle velocità <lb></lb>proporzionali alle altezze perpendicolari, secondo gl&#039;insegnamenti dati a lui, <lb></lb>e a tutti gli altri di que&#039;tempi, dal gran Maestro <emph type="italics"></emph>De ponderibus.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Venuto l&#039;altro grande Maestro ad assegnare ai cadenti altre leggi, il Ca­<lb></lb>stelli, anche in questo caso, incominciò a dubitare se fosse la nuova legge <lb></lb>scoperta applicabile al moto dell&#039;acque. </s>

<s>Volle perciò, in tali dubbi, aver con­<lb></lb>siglio con Giovan Batista Baliani, il quale rispose che, da qualche accenno <lb></lb>avutone da Galileo, venne a incontrarsi, senza cercarla, nella proposizione <lb></lb>che i corpi di moto naturale vanno aumentando le loro velocità, con la pro­<lb></lb>gressione dei numeri impari, e soggiungeva non creder questa legge appli­<lb></lb>cabile all&#039;acque, se non fosse per qualche loro breve corso e assai poco in­<lb></lb>clinato, come il fosso di un mulino. </s>

<s>Ma trattandosi di un canale lungo o di <lb></lb>un fiume, che declini circa sei o otto per cento, “ non mi pare, egli dice, <lb></lb>che l&#039;acqua si vada aumentando di velocità con quella proporzione, che cor­<lb></lb>rerebbe una palla sferica in un piano perfettamente declinante. </s>

<s>So che il <lb></lb>fiume terminando al mare non casca, ma ritrova intoppo dell&#039;acqua, che lo <lb></lb>va trattenendo, onde l&#039;acqua del fiume, per questo trattenimento, fa anche <lb></lb>resistenza a quella di dietro: però non mi pare che questa sia bastante ra­<lb></lb>gione per un tal effetto ” (Alb. </s>

<s>IX, 142). </s></p><p type="main">

<s>Parve anche al Castelli ragionevole l&#039;opinione del suo dotto amico, ma <lb></lb>così incerto come rimaneva in assegnare ai liquidi una legge delle velocità, <lb></lb>che fosse a loro tutta propria, scansò di entrare nei fatti particolari. </s>

<s>Anche <lb></lb>Galileo sentì questa difficoltà, ripensando alle differenze del moto, che son <lb></lb>tra i solidi e i liquidi, a&#039;quali ultimi applicò diversa legge, secondo il diverso <lb></lb>riguardo che aveva, ora alla sola corpulenza delle loro escrescenze, ora al <lb></lb>solo impeto delle loro cadute. </s></p><p type="main">

<s>Dop&#039;aver dimostrato all&#039;ingegner Bartolotti che una sfera solida ha uguale <lb></lb>velocità sopra due piani, benchè variamente inclinati, purchè sia scesa per <pb xlink:href="020/01/3430.jpg" pagenum="391"></pb>un uguale spazio perpendicolare; soggiunge che “ sebbene tali conseguenze <lb></lb>ben seguano nei mobili solidi, nei fluidi credo che procedano assai differen­<lb></lb>temente ” (Alb. </s>

<s>VI, 361). Imperocchè, posta la detta sfera sopra un piano <lb></lb>perfettamente orizontale, non si muove nè dall&#039;una parte nè dall&#039;altra, ma <lb></lb>resta in quiete, mentre, immaginando una mole sferica d&#039;acqua, questa si <lb></lb>dissolverà spianandosi per tutti i versi. </s>

<s>“ E se le bocche del canale, sog­<lb></lb>giunge, saranno aperte, scolerà fuora tutta, salvo che quella minima parti­<lb></lb>cella, che rimane solamente bagnando il fondo del canale .... essendo che <lb></lb>l&#039;acqua nello spianarsi acquista pendio ” (ivi). </s></p><p type="main">

<s>Questa pendenza della superficie nulladimeno non parve a Galileo in <lb></lb>tutti i casi sufficiente ragione del moto, vedendosi, per esempio nelle piene <lb></lb>dell&#039;Arno, non aver proporzione il declivio superficiale dell&#039;acqua, verso la <lb></lb>gran velocità, che le si vede acquistare nel corso. </s>

<s>“ Bisogna dunque, con­<lb></lb>clude, ricorrere ad altro, per causa del grande augumento nella velocità, che <lb></lb>all&#039;accrescimento della pendenza, e dire che pur una delle potenti ragioni è <lb></lb>che, nell&#039;accrescere in tal modo la pendenza, s&#039;accresce sommamente la mole <lb></lb>e il cumulo dell&#039;acqua, la quale, gravitando e premendo sopra le parti pre­<lb></lb>cedenti, col peso delle susseguenti, le spinge impetuosamente ” (ivi, pag. </s>

<s>364). <lb></lb>Or perchè le prementi gravità crescono come le altezze, si può concludere <lb></lb>da queste galileiane dottrine che le crescenti acque del fiume ne fanno cre­<lb></lb>scere la velocità, a proporzion delle semplici altezze. </s></p><p type="main">

<s>Trattandosi però delle accelerazioni, che in esse acque sopraggiungono <lb></lb>per effetto delle sole cadute, è un fatto che Galileo assegna a loro la ragion <lb></lb>delle radici delle altezze, applicandovi i teoremi dimostrati in quel, ch&#039;egli <lb></lb>stesso cita, suo <emph type="italics"></emph>Libro del moto.<emph.end type="italics"></emph.end> Proposto infatti il caso che l&#039;alveo d&#039;incli­<lb></lb>nato si faccia orizontale, “ non temerei, egli dice, che l&#039;acqua fosse per allen­<lb></lb>tare il suo corso, essendo sicuro che nel piano orizontale (quando non vi <lb></lb>sieno impedimenti esterni ed accidentari) la velocità, concepita dal mobile nel <lb></lb>moto precedente sopra un piano declive, si conserva uniforme e tale, che nel <lb></lb>piano passerà spazio doppio del passato nell&#039;inclinato, in tempo uguale al tempo <lb></lb>del passaggio per l&#039;inclinato, mentre il suo principio fu dallo stato di quiete, <lb></lb>come io dimostro nel mio soprannominato libro del moto (ivi, pag. </s>

<s>371). Dal <lb></lb>qual libro aveva poco prima citato il teorema del brachistocronismo per gli <lb></lb>archi, rispetto alle corde suttese, applicandolo agli alvei e alle svolte dei fiumi. </s></p><p type="main">

<s>In queste applicazioni della dinamica dei solidi, a quella dei fluidi, sta <lb></lb>come accennammo la chiave, che Galileo diceva d&#039;aver trovata, <emph type="italics"></emph>per aprire <lb></lb>ingressi ad accidenti maggiori<emph.end type="italics"></emph.end> di quegli stessi scoperti dal Castelli, ma non <lb></lb>si vedrà volgersi dentro la chiusura libera e spedita, se non che nelle mani <lb></lb>del Baliani e del Borelli, dopo che il Torricelli sarà venuto a inciderne sottil­<lb></lb>mente gl&#039;ingegni. </s>

<s>Forse Galileo scansò le incertezze e si dispensò dalle cure <lb></lb>di dare espressione più propria al teorema delle velocità delle acque cadenti, <lb></lb>proporzionali alle radici delle altezze, perchè ciò non pareva richiedersi dal­<lb></lb>l&#039;intenzion sua principale, qual&#039;era di dimostrar che il Bisenzio, così per <lb></lb>l&#039;alveo tortuoso, come per il raddirizzato, giunge ugualmente veloce al me-<pb xlink:href="020/01/3431.jpg" pagenum="392"></pb>desimo sbocco. </s>

<s>Vedemmo come la conclusione fosse già scesa dalla Dina­<lb></lb>mica vecchia, la quale pronunziò per bocca di Leonardo che <emph type="italics"></emph>la obliquità <lb></lb>del corso dell&#039;acqua adopera come fussi perpendicolare,<emph.end type="italics"></emph.end> qualunque poi si <lb></lb>fosse il modo del così adoperare. </s>

<s>Mentre però Leonardo non pronunziava che <lb></lb>una proposizione astratta, Galileo la intendeva in concreto, non rimovendosi <lb></lb>dall&#039;opinione “ che l&#039;acqua si serva per canale ugualissimo della stessa sua <lb></lb>acqua ambiente, sicchè scorre per un letto o condotto sommamente terso e <lb></lb>polito ” (MSS. Gal., P. V, T. III, fol. </s>

<s>14). Da che è facile argomentare che <lb></lb>essa acqua corrente per l&#039;alveo di un fiume osserva le leggi dell&#039;accelera­<lb></lb>zione del moto, più puntualmente di quella palla di bronzo, che nel III dia­<lb></lb>logo delle due Nuove Scienze ci vien descritta discendere sopra un piano <lb></lb>inclinato, ricoperto di carta pecora zannata (Alb. </s>

<s>XIII, 172). Come poi que­<lb></lb>ste cose si concilino con quell&#039;altre, scritte nella lettera allo Staccoli, è dif­<lb></lb>ficile indovinare, e noi non vi ci intratterremo qui, dovendoci tornar sopra <lb></lb>nel Tomo seguente. </s>

<s>Ma pure non vogliamo lasciar l&#039;occasione di riferire un <lb></lb>documento, da cui apparisce che il Castelli, dop&#039;aver letto il Discorso in­<lb></lb>torno al fiume Bisenzio, non rimase persuaso delle ragioni di Galileo, ma <lb></lb>che anzi più stabilmente si confermò in quel che, essendo vero, aveva come <lb></lb>verissimo creduto e scritto nella VII appendice: “ Pare che si possa osser­<lb></lb>vare che, mentre l&#039;acqua scorre per un alveo, canale o condotto, venga ri­<lb></lb>tardata, trattenuta e impedita la sua velocità dal toccamento, che fa con la <lb></lb>ripa o sponda del canale o alveo, la quale come immobile, non secondando <lb></lb>il moto dell&#039;acqua, interrompe la sua velocità ” (<emph type="italics"></emph>Della misura delle acque <lb></lb>correnti,<emph.end type="italics"></emph.end> lib. </s>

<s>I cit., pag. </s>

<s>32). Quel documento poi che si diceva lo raccolsero <lb></lb>i discepoli dello stesso Castelli dalla viva voce del Maestro, e nella forma, che <lb></lb>qui appresso riproduciamo, ne lasciarono diligente memoria: </s></p><p type="main">

<s>“ Dicono che il padre don Benedetto faciliti assai i mulini, con osser­<lb></lb>vare che le ruote avessero le pale, che stessero forte, acciò non si perdesse <lb></lb>il colpo dell&#039;acqua: l&#039;acqua cascasse in luogo più lontano che si può dal <lb></lb>centro di detta ruota. </s>

<s>Per di più, ai ritrecini, che la doccia che porta l&#039;acqua <lb></lb>non fosse inclinata come la BI (fig. </s>

<s>188), ma fosse detto ritrecine AIS sfon­<lb></lb><figure id="id.020.01.3431.1.jpg" xlink:href="020/01/3431/1.jpg"></figure></s></p><p type="caption">

<s>Figura 188.<lb></lb>dato o voto fino al fondo AS, e l&#039;acqua uscisse <lb></lb>per la bocca A, e percotesse nella ruota. </s>

<s>E <lb></lb>sebbene in teoria è vero che l&#039;impeto, che <lb></lb>acquista detta acqua perpendicolare IO, è <lb></lb>uguale a quello, che acquista per la inclinata <lb></lb>IB; la sperienza nonostante mostra di no, <lb></lb>mediante gl&#039;impedimenti che, nello scorrere <lb></lb>per la doccia inclinata, continuamente riceve <lb></lb>l&#039;acqua, ancora che piccoli. </s>

<s>Ma ricevendoli in <lb></lb>tutti i luoghi di detta acqua, che tocca la <lb></lb>doccia, e in tutti i tempi, e la perpendicolare non ne ricevendo veruno; ven­<lb></lb>gono a operare in maniera, che la sperienza ne mostra variazioni assai <lb></lb>grandi ” (<emph type="italics"></emph>Appendice ai MSS. Gal. </s>

<s>della Bibliot. </s>

<s>naz. </s>

<s>di Firenze<emph.end type="italics"></emph.end>). </s></p><pb xlink:href="020/01/3432.jpg" pagenum="393"></pb><p type="main">

<s>Nella VII appendice, sopra citata, lo stesso p. </s>

<s>don Benedetto prosegue <lb></lb>a dare utili avvertimenti intorno al variarsi le misure dell&#039;acqua, mentre <lb></lb>vengono rallentate nel loro impeto dagli attriti contro l&#039;ambito delle fistole, <lb></lb>formulando in tal proposito questo teorema: “ L&#039;acqua che passa per la <lb></lb>maggior fistola, a quella che passa per la minore, ha sempre maggior pro­<lb></lb>porzione che la fistola maggiore alla fistola minore ” (<emph type="italics"></emph>Della misura ecc.,<emph.end type="italics"></emph.end><lb></lb>lib. </s>

<s>I cit., pag. </s>

<s>34): ciò che supposte le fistole cilindriche, e le loro bocche <lb></lb>circolari, ha la sua facile dimostrazione nelle proprietà geometriche delle cir­<lb></lb>conferenze, che crescono come i raggi, e de&#039;circoli, che crescono invece come <lb></lb>i quadrati dei raggi. </s></p><p type="main">

<s>Come il teorema si trovasse dimostrato così, nei manoscritti di Leonardo <lb></lb>da Vinci, è ben noto ai nostri Lettori. </s>

<s>Ma ora è il tempo di soggiungere che <lb></lb>il discepolo del Nemorario riman superiore al discepolo di Galileo, non per <lb></lb>la sola precedenza del tempo, ma, ciò che importa anche più, per la mag­<lb></lb>giore perfezione dell&#039;opera. </s>

<s>Suppongasi che la bocca della fistola sia in figura <lb></lb>di un triangolo equilatero, ora con l&#039;apice in basso, ora con la base. </s>

<s>Per il <lb></lb>teorema del Castelli dovrebbe la fistola rendere la medesima quantità in am­<lb></lb>bedue le posizioni, mentre per Leonardo vedemmo esser concluso che, stando <lb></lb>il vertice del triangolo in alto, la fistola rende più che stando in alto la base, <lb></lb>e fu la ragion della conclusione che, essendo gli strati inferiori più premuti, <lb></lb>e perciò più velocemente sospinti dei superiori, maggior quantità d&#039;acqua <lb></lb>premuta e velocitata si trova dal mezzo in giù nel triangolo risedente, che <lb></lb>nel supino. </s></p><p type="main">

<s>Se non s&#039;intendono dunque i vari strati ridotti alle loro velocità medie, <lb></lb>il teorema del Castelli, che fisicamente è imperfetto, geometricamente è ad­<lb></lb>dirittura falso. </s>

<s>E perchè si tratta di cosa di non lieve importanza, si vuol <lb></lb>più diligentemente ricercare questo punto di Storia, a far che, il seguente <lb></lb>passo di lettera, scritta dallo stesso Castelli a Galileo il dì 10 Dicembre 1625; <lb></lb>ci viene a preparare la via: “ Mi occorre signifìcargli un garbuglio, che mi <lb></lb>passa per il capo, il quale è stato in gran parte e forse totale causa che io <lb></lb>non dimostrassi i due ultimi Pronunziati, e che, nel dimostrare la III pro­<lb></lb>posizione, io tenessi il metodo, che ho tenuto. </s>

<s>Il garbuglio è questo, che non <lb></lb>ho mai potuto saldar la partita, nè trovo modo di saldarla: se l&#039;acqua corra <lb></lb>con la medesima velocità nelle parti superiori come nelle inferiori, e per­<lb></lb>tanto, per isfuggire questo punto, o per dir meglio, per non averne bisogno, <lb></lb>ho tralasciato il concetto di quei prismi d&#039;acqua, che passano per le se­<lb></lb>zioni ecc. </s>

<s>Perchè se queste correnti non sono le medesime nelle parti su­<lb></lb>periori che nelle inferiori, non ritrovo quei prismi, e so che nasce dalla mia <lb></lb>debolezza. </s>

<s>Però V. S. mi scusi, e apra la mente, perchè dovento matto in­<lb></lb>torno a questa materia ” (Campori, Carteggio cit., pag. </s>

<s>231). </s></p><p type="main">

<s>Benchè non ci sia nota la risposta di Galileo, pur crediamo di assicu­<lb></lb>rare i Lettori che non furono per lui saldate le partite, nè aperta per lui <lb></lb>la mente del Castelli, a levargli di dentro il male di quella mattia. </s>

<s>Non era <lb></lb>a ciò infatti altro rimedio, che nel principio dell&#039;uguaglianza delle pressioni, <pb xlink:href="020/01/3433.jpg" pagenum="394"></pb>rimasto ignoto parimente al Discepolo e al Maestro. </s>

<s>Alla penosa incertezza <lb></lb>però d&#039;ambedue fa notabile riscontro la franchezza di Leonardo da Vinci, il <lb></lb><figure id="id.020.01.3433.1.jpg" xlink:href="020/01/3433/1.jpg"></figure></s></p><p type="caption">

<s>Figura 189.<lb></lb>quale passava, così ragionando, a trovar la legge del corso <lb></lb>dalla stagnante acqua del vaso. </s>

<s>Segnati i gradi delle al­<lb></lb>tezze BE, EF, FG, ecc. (fig. </s>

<s>189) nel vaso pieno AD, s&#039;im­<lb></lb>magini rimossa la parete AB: l&#039;acqua ferma piglierà corso, <lb></lb>servando i vari strati di lei le medesime velocità orizon­<lb></lb>tali, eccitate dalle pressioni perpendicolari, cosicchè il moto <lb></lb>non è per tutto uniforme, ma nelle parti inferiori più ve­<lb></lb>loce che nelle superiori, a proporzion delle altezze. </s>

<s>Gli at­<lb></lb>triti contro le ineguaglianze dell&#039;alveo e delle ripe per­<lb></lb>turbano questa legge, ma non le tolgono il predominio, come Leonardo stesso <lb></lb>sperimentò con l&#039;Idrometro baculare, descrittoci nelle sue note. </s></p><p type="main">

<s>Colà, dove noi ne riferimmo la descrizione, si narrò le contradizioni del <lb></lb>Cardano, il quale non negava gli effetti delle pressioni perpendicolari, che <lb></lb>con uguale impulso si volgono per l&#039;orizonte e per altri versi, ma diceva <lb></lb>che le minori velocità degli strati superiori son così compensate dalle mag­<lb></lb>giori velocità degli strati inferiori, che ne risulta nel tutto una velocità media. </s>

<s><lb></lb>Di qui è che, tenendo per illusorie le osservazioni fatte con l&#039;Idrometro ba­<lb></lb>culare, credè che impunemente si potesse sostituire a lui nel medesimo uffi­<lb></lb>cio qualunque semplice galleggiante. </s></p><p type="main">

<s>Il Castelli non trovò riposo alla mente, in pericolo di ammattire, che <lb></lb>riducendosi a professare queste medesime cardaniche dottrine. </s>

<s>Nell&#039;XI Ap­<lb></lb>pendice, per esaminare e confrontare la velocità dell&#039;acqua, che passa per un <lb></lb>fosso, a quella che passa per un altro, insegna “ a tener conto per quanto <lb></lb>spazio sia trasportata una palla di legno, o di altro corpo che galleggi, in <lb></lb>un determinato tempo, come sarebbe v. </s>

<s>g. </s>

<s>in cinquanta battute di polso ” <lb></lb>(<emph type="italics"></emph>Della misura<emph.end type="italics"></emph.end> ecc., lib. </s>

<s>I cit., pag. </s>

<s>41) evidentemente supponendo che il <lb></lb>fosso, per tutta la profondità, serbi il medesimo corso che nella superficie. </s>

<s><lb></lb>Sembrerebbe di qui che anch&#039;egli, il Castelli, volesse fare, come il Cardano, <lb></lb>la riduzione alle velocità medie, in che forse veniva a ritrovare que&#039;prismi, <lb></lb>che aveva creduti vacillanti, e che, nel dubbio non corresse l&#039;acqua per <lb></lb>tutto con la medesima velocità, vedeva andare smarriti. </s>

<s>Per conferma della <lb></lb>quale opinione soccorrerebbero la seconda definizione, e la proposizione se­<lb></lb>conda del secondo libro delle Acque correnti, ma più espressamente la te­<lb></lb>stimonianza di uno dei più affezionati discepoli del Castelli, Giovan Batista <lb></lb>Hodierna. </s>

<s>Nell&#039;opuscolo, che questi intitolò <emph type="italics"></emph>Stadera del momento,<emph.end type="italics"></emph.end> trattando <lb></lb>dello scompartir l&#039;acque più giustamente che sia possibile, accenna al ritar­<lb></lb>damento, ch&#039;elle subiscono, per attaccarsi le loro parti contigue all&#039;ambito <lb></lb>del canaletto, per l&#039;aperta del quale escon fuori. </s>

<s>“ Ma tolto questo impedi­<lb></lb>mento, soggiunge, e supposto che da ciaschedun canaletto scorra liberamente <lb></lb>l&#039;acqua, secondo la misura che contiene; ve n&#039;è un altro, qual&#039;è che, situati <lb></lb>diversi canaletti di diverse misure sotto l&#039;istessa altezza dell&#039;acqua, sicchè <lb></lb>v. </s>

<s>g. </s>

<s>l&#039;orizzonte dell&#039;acqua s&#039;elevasse mezzo palmo, sopra il centro delli fo-<pb xlink:href="020/01/3434.jpg" pagenum="395"></pb>rami; dico che in questo caso delli forami maggiori non scorre quella quan­<lb></lb>tità d&#039;acqua per tutte le bande, perchè, dal centro in giù, l&#039;acque scorrono <lb></lb>con più velocità che dal centro in su, per essere le parti inferiori dell&#039;acqua <lb></lb>più compresse delle superiori. </s>

<s>Ma in questo caso non si perderebbe, perchè <lb></lb>già la maggior celerità delle parti inferiori ricompensa precisamente la tar­<lb></lb>dità delle superiori ” (Palermo 1641, pag. </s>

<s>67, 68). </s></p><p type="main">

<s>Noi crediamo che questi dell&#039;Hodierna fossero i pensieri medesimi del <lb></lb>Castelli, il quale industriosamente seguitava a sfuggire il punto della que­<lb></lb>stione: <emph type="italics"></emph>se l&#039;acqua corra con la medesima velocità nelle parti superiori, <lb></lb>come nelle inferiori,<emph.end type="italics"></emph.end> scusandosi di aver tralasciato un tal concetto, <emph type="italics"></emph>per non <lb></lb>averne bisogno.<emph.end type="italics"></emph.end> Ma perchè giusto in questo concetto consisteva la perfezione <lb></lb>della Scienza che professava, non penò molto il bisogno a farglisi sentire, e <lb></lb>ora vien per noi che si narri a quale occasione, e com&#039;ei lo sodisfacesse. </s></p><p type="main">

<s>L&#039;occasione venne nell&#039;estate del 1641, a proposito della laguna di Ve­<lb></lb>nezia, disputandosi allora vivamente intorno agli effetti, che vi produrreb­<lb></lb>bero le diversioni o le influenze dell&#039;acque della Brenta e degli altri fiumi. </s>

<s><lb></lb>I periti si regolavano in questo negozio, supponendo che gli alzamenti del <lb></lb>livello si facessero a proporzione delle quantità d&#039;acqua versate, e così tra­<lb></lb>scorrevano, sccondo il Castelli, in que&#039;medesimi errori degli Ingegneri bolo­<lb></lb>gnesi e ferraresi, quando giudicarono che, mettendosi il Reno in Po, ne <lb></lb>avrebbe fatto alzar tanto l&#039;acqua, da temerne straordinarie inondazioni. </s>

<s>“ Ma <lb></lb>ora, soggiunge nella III appendice, dalle cose dimostrate è manifesto che la <lb></lb>misura del Reno in Reno sarebbe diversa dalla misura del Reno in Po, ogni <lb></lb>volta che sarà diversa la velocità del Reno in Po, dalla velocità del Reno <lb></lb>in Reno, come più esattamente si determina nella quarta proposizione ” <lb></lb>(<emph type="italics"></emph>Della misura delle acque ecc.,<emph.end type="italics"></emph.end> lib. </s>

<s>I cit., pag. </s>

<s>31). </s></p><p type="main">

<s>Da quella quarta proposizione infatti si conclude che nel medesimo fiume, <lb></lb>rimanendo la medesima quantità d&#039;acqua, le altezze son reciproche delle ve­<lb></lb>locità, cosicchè se il Reno non facesse altro che velocitare il Po, vi produr­<lb></lb>rebbe uno sbassamento, tutt&#039;altro che una piena. </s>

<s>Ma perchè la quantità del­<lb></lb>l&#039;acqua, versata dal minor fiume nel maggiore, non è trascurabile, e vi pro­<lb></lb>duce perciò un certo alzamento necessariamente, si trattava di cercar la <lb></lb>proporzione di questo a quella; si proponeva cioè a risolvere un tale pro­<lb></lb>blema: Se, raddoppiandosi la quantità d&#039;acqua, l&#039;alzamento, come s&#039;apprende <lb></lb>dalla detta quarta proposizione, è men che doppio, contro l&#039;opinion di co­<lb></lb>loro, che furono ammoniti nella III appendice, ed è più che nulla, contro <lb></lb>l&#039;opinion di quegli altri ammoniti nell&#039;appendice IV: si domanda qual&#039;è, <lb></lb>fra questi due termini estremi, la ragion di mezzo precisa? </s>

<s>Nè ritrovando <lb></lb>il Castelli, nelle sue proprie teorie, la soluzione desiderata, si volse con gran <lb></lb>deligenza agli esperimenti. </s>

<s>Pensò dunque a quella macchina semplicissima, <lb></lb>detta il <emph type="italics"></emph>Regolatore,<emph.end type="italics"></emph.end> per la più precisa misura delle sezioni: e per la misura delle <lb></lb>velocità o dei tempi, lasciate quelle battute di polso, proposte già per eseguire <lb></lb>le operazioni descritte nella XI appendice; si servì in vece di strumento assai <lb></lb>più esatto, qual era il pendolo a secondi, che mandava lungo tre piedi romani. </s></p><pb xlink:href="020/01/3435.jpg" pagenum="396"></pb><p type="main">

<s>Così sperimentando, gli parve aver trovato che, se una quantità d&#039;acqua <lb></lb>fa un alzamento, per avere un alzamento doppio, triplo, quadruplo, ecc., ci <lb></lb>volevano quattro, nove, sedici quantità d&#039;acqua, e così sempre, secondo la <lb></lb>serie progressiva dei numeri quadrati. </s>

<s>Non credendo a sè medesimo di avere <lb></lb>scoperto un tal miracolo della Natura, andò più volte, e in vario modo, ri­<lb></lb>petendone l&#039;esperienza, e finalmente concluse per certissima legge, da dimo­<lb></lb>strare infino a qual punto eran giunti gli errori di coloro, che avevano con­<lb></lb>sigliato di divertire la Brenta dalla laguna; che le quantità influenti son pro­<lb></lb>porzionali ai quadrati, e non alle semplici altezze che farebbero nel recipiente. </s></p><p type="main">

<s>A persuadere anche meglio la verità di questi naturali effetti, e per aver <lb></lb>comodità di darne dimostrazione, ogni volta che lo richiedessero i curiosi o <lb></lb>i diffidenti, fece costruire quello strumento, che poi ci dette descritto così nel <lb></lb>suo libro: “ Io ho preparato cento sifoni, o vogliam dir canne ritorte, tutte <lb></lb>uguali, e postele al labbro d&#039;un vaso, nel quale si mantiene l&#039;acqua con uno <lb></lb>stesso livello, o lavorino tutte le canne, o qualsivoglia numero di loro, col­<lb></lb>locate le bocche, dalle quali esce l&#039;acqua, tutte al medesimo livello parallelo <lb></lb>all&#039;orizonte, ma più basse di livello dell&#039;acqua del vaso. </s>

<s>E raccolta tutta <lb></lb>l&#039;acqua cadente dai sifoni in un altro vaso più basso, l&#039;ho fatta scorrere per <lb></lb>un canale, inclinandolo in modo che; mancando l&#039;acque dai sifoni, il canale <lb></lb>rimane affatto senz&#039;acqua asciutto. </s>

<s>” </s></p><p type="main">

<s>“ E fatto questo misurai l&#039;altezza viva del canale diligentemente, e poi <lb></lb>la divisi in dieci parti uguali precisamente. </s>

<s>E facendo levare via 19 di que­<lb></lb>sti sifoni, in modo che nel canale non scorreva l&#039;acqua se non di 81 di <lb></lb>questi sifoni, di nuovo, osservando l&#039;altezza viva dell&#039;acqua nel medesimo <lb></lb>sito osservato di prima, trovai che l&#039;altezza sua era scemata la decima parte <lb></lb>precisamente di tutta la sua prima altezza. </s>

<s>E così, seguitando a levare altri <lb></lb>17 sifoni, l&#039;altezza era pure scemata un decimo di tutta la prima sua al­<lb></lb>tezza viva. </s>

<s>E provando a levare 15 sifoni, poi 13, poi 11, e poi 9, e poi 7, <lb></lb>poi 5 e poi 3, sempre in queste diversioni, fatte ordinatamente come s&#039;è <lb></lb>detto, ne seguiva ogni sbassamento di un decimo di tutta l&#039;altezza ” (<emph type="italics"></emph>Della <lb></lb>misura delle acque,<emph.end type="italics"></emph.end> lib. </s>

<s>II, Bologna 1660, pag. </s>

<s>92, 93). Soggiunge poi come <lb></lb>aprendosi le cannelle stesse in ordine contrario, trovò che se una sola fa un <lb></lb>decimo di altezza, non più di un decimo se ne fa aggiungendovene 3, 5, 7, <lb></lb>e così di seguito crescendo il numero dei confluenti. </s></p><p type="main">

<s>Tanto rimase commosso il Castelli, e tanto paterno amore sentì per que­<lb></lb>sta sua scoperta, che fatto dello strumento un modello in piccolo, con quat­<lb></lb>tro o cinque scompartimenti, il primo di una cannella, il secondo di quattro, <lb></lb>il terzo di nove, il quarto di sedici, lo collocò nelle stanze terrene della sua <lb></lb>abbazia, per ricrearne i forestieri che capitavano e gli amici. </s>

<s>E certo era <lb></lb>spettacolo non ingiocondo il vedere le sedici cannelle vomitar acqua dalle <lb></lb>bocche aperte in gareggiante concordia, e nè perciò fare ingrossare il fiumi­<lb></lb>cello un pelo di più di quel che facessero da sè sole nove, anzi quattro, anzi <lb></lb>una cannella sola! </s></p><p type="main">

<s>Di qui ebbe origine il secondo libro Della misura delle acque correnti: <pb xlink:href="020/01/3436.jpg" pagenum="397"></pb>origine dunque puramente sperimentale, come l&#039;aveva avuta il primo. </s>

<s>Se non <lb></lb>che tanto più difficile di questo trovò quello il Castelli a ridursi alle ragioni <lb></lb>geometriche, che si rivolse a invocare il valido aiuto del Cavalieri. </s>

<s>Questi <lb></lb>rispose che dalla V proposizione delle <emph type="italics"></emph>Dimostrazioni geometriche<emph.end type="italics"></emph.end> s&#039;avrebbe <lb></lb>facilmente concluso l&#039;intento, qual&#039;era di provare che le quantità son pro­<lb></lb>porzionali ai quadrati delle altezze, quando fosse vero che le velocità stanno <lb></lb>come le semplici altezze. </s>

<s>Essendo infatti quella V proposizione espressa dai <lb></lb>noti simboli Q:<emph type="italics"></emph>q<emph.end type="italics"></emph.end>=A.V:<emph type="italics"></emph>a.v,<emph.end type="italics"></emph.end> se V:<emph type="italics"></emph>v<emph.end type="italics"></emph.end>=A:<emph type="italics"></emph>a,<emph.end type="italics"></emph.end> è manifestamente Q:<emph type="italics"></emph>q<emph.end type="italics"></emph.end>= <lb></lb>A2:<emph type="italics"></emph>a<emph.end type="italics"></emph.end>2. </s>

<s>Ma per ammettere che le velocità son proporzionali alle altezze, “ non <lb></lb>ho, confessava ingenuamente il Cavalieri, avuto fortuna d&#039;incontrarmi in ra­<lb></lb>gione, che appieno mi sodisfaccia ” (<emph type="italics"></emph>Autori che trattano del moto delle <lb></lb>acque,<emph.end type="italics"></emph.end> T. I, Firenze 1765, pag. </s>

<s>175). </s></p><p type="main">

<s>Consistendo un tal fortunato incontro nel principio dell&#039;uguaglianza delle <lb></lb>pressioni, che così buon servigio aveva prestato a Leonardo da Vinci, ma che <lb></lb>poi fu travolto nella ruina di tutte l&#039;altre tradizioni; non sarebbe rimasto <lb></lb>al Cavalieri altro esempio, che quello dato da Galileo, il quale, come accen­<lb></lb>nammo, dal suppor che le moli d&#039;acqua precedenti, gravitando sopra le sus­<lb></lb>seguenti, le sospingano al moto, lasciava a concluderne immediatamente che <lb></lb>i momenti delle velocità crescono come 1e moli, o come le altezze vive delle <lb></lb>sezioni. </s>

<s>Nonostante, il metodo degli indivisibili trasportava il Cavalieri per <lb></lb>altre vie, e riguardando la corrente divisa in strati paralleli dal fondo alla <lb></lb>superficie, e considerando che gli strati superiori, oltre al proprio moto di­<lb></lb>pendente dall&#039;inclinazione dell&#039;alveo, partecipano di quello degl&#039;inferiori, <lb></lb>sopra cui come da veicolo son trasportati; ne concludeva che dunque le ve­<lb></lb>locità debbon crescere come il numero degli strati superiori, ossia come le <lb></lb>altezze medesime della corrente. </s>

<s>Ma giova ascoltare il Cavalieri stesso, che, <lb></lb>in una sua lettera dell&#039;11 Gennaio 1642, diceva al Castelli il proprio e par­<lb></lb>ticolar modo del suo discorso: </s></p><p type="main">

<s>“ Io discorro così: Sia, nella fig. </s>

<s>190, ABCD l&#039;alveo, nel quale cam­<lb></lb>mini l&#039;acqua per la sezione EC, alta come BE, con una tale velocità. </s>

<s>Inten­<lb></lb><figure id="id.020.01.3436.1.jpg" xlink:href="020/01/3436/1.jpg"></figure></s></p><p type="caption">

<s>Figura 190.<lb></lb>dasi poi messa tant&#039;acqua nello stesso fiume, che cresca <lb></lb>sino in GH, correndo nel fiume con l&#039;altezza BG, dop­<lb></lb>pia di EB. </s>

<s>Dico che l&#039;acqua vi camminerà con doppia <lb></lb>velocità, e per concludere questo, intendo tutta l&#039;acqua <lb></lb>che scorre per GC divisa in due pezzi GF, EC, me­<lb></lb>diante la superficie superiore dell&#039;acqua EC, che passa <lb></lb>per EF, e considero che l&#039;acqua GF, come portata dal­<lb></lb>l&#039;acqua EC, dee fare nello stesso tempo lo spazio, che <lb></lb>farà la EC, e di più, intendendosi scorrere l&#039;acqua GF <lb></lb>sopra la superficie che passa per EF, come sopra suo letto, nella guisa che <lb></lb>EC scorre sopra il fondo; dee l&#039;acqua GF avere forza di trapassare altret­<lb></lb>tanto spazio, quanto ne passa la EC. </s>

<s>Adunque l&#039;acqua GF averà la forza di <lb></lb>trapassare doppio spazio di quello, che passa la EC nell&#039;istesso tempo, onde <lb></lb>sarà doppiamente veloce ” (ivi, pag. </s>

<s>175, 76). </s></p><pb xlink:href="020/01/3437.jpg" pagenum="398"></pb><p type="main">

<s>Aveva il Cavalieri finito appena di scrivere questa dimostrazione, che <lb></lb>la sentì forte combattuta da due dubbi: il primo, per il supposto che gli <lb></lb>strati acquei siano tutti paralleli fra loro, e il secondo, per il corollario che <lb></lb>la scala delle velocità sia in un triangolo col suo vertice in basso. </s>

<s>Cose, che <lb></lb>non sapeva come s&#039;accordassero con l&#039;esperienza, dalla quale si par che in <lb></lb>tempo di piena la superficie del fiume non sia parallela al fondo, ma con­<lb></lb>verga con lui verso lo sbocco, e che le velocità debban piuttosto crescere <lb></lb>dalla superficie al fondo che dal fondo alla superficie. </s></p><p type="main">

<s>Lette e meditate queste cose, il Castelli sentì allora imperiosamente <lb></lb>l&#039;invito a dichiararsi finalmente intorno a quel concetto, che aveva potuto <lb></lb>fin qui scansar destramente, se cioè gli strati, che corrono per una sezione, <lb></lb>vadano, come diceva Leonardo, a un medesimo o a differente aspetto. </s>

<s>E pa­<lb></lb>rendogli veramente non consentito dall&#039;esperienza il corollario del Cavalieri, <lb></lb>lo accomodò nella dimostrazione di lui, il processo della quale del resto ac­<lb></lb>cettava, pensando che, sebbene gli strati superiori sian trasportati dagl&#039;in­<lb></lb>feriori, ne resulta d&#039;ambedue nonostante un moto misto ossia medio: co­<lb></lb>sicchè la scala, che riferisce le velocità degli strati AB, CD, EF (fig. </s>

<s>191) <lb></lb><figure id="id.020.01.3437.1.jpg" xlink:href="020/01/3437/1.jpg"></figure></s></p><p type="caption">

<s>Figura 191.<lb></lb>non sia nel triangolo AEG, ma nel rettan­<lb></lb>golo LE che lo uguaglia, per essere l&#039;AG nel <lb></lb>punto I divisa nel mezzo. </s>

<s>Quanto al dubbio <lb></lb>poi se gli strati della corrente siano tutti <lb></lb>paralleli fra loro, il Castelli non ne fece <lb></lb>alcun conto, mantenendo ferma la suppo­<lb></lb>sizione del Cavalieri. </s>

<s>Così gli venne fatta la <lb></lb>dimostrazione di quella, che fu in secondo luogo scritta fra le proposizioni del <lb></lb>secondo libro delle Acque correnti, e che noi non possiamo non compian­<lb></lb>gere, per essere stata così disgraziata infin dal suo primo apparire alla luce <lb></lb>in Bologna, per le stampe del Dozza. </s></p><p type="main">

<s>Desiderosi di ridurla pietosamente alla sua vera lezione, non s&#039;è potuto <lb></lb>in tutto conseguire l&#039;intento, per esserci venuto a mancare l&#039;autografo, o la <lb></lb>copia autentica di lui, quale, sapendosi essere stata depositata dall&#039;Autore <lb></lb>stesso nelle mani del principe Leopoldo de&#039;Medici, si sperava di ritrovare <lb></lb>nella Raccolta palatina fra i Manoscritti galileiani. </s>

<s>Ma nel primo volume della <lb></lb>sezione <emph type="italics"></emph>Discepoli,<emph.end type="italics"></emph.end> in cui sono alligati i manoscritti del Castelli, e gli altri <lb></lb>relativi alle Opere di lui, non abbiamo trovato, di quel che si cercava, se non <lb></lb>una copia di mano del Viviani, che và fino alla Considerazione seconda, dopo <lb></lb>la quinta proposizione. </s>

<s>Quivi dunque consultando, al foglio 85, la detta pro­<lb></lb>posizione II, la riscontrammo fedelmente copiata dalla stampa bolognese, non <lb></lb>correttovi nemmeno il così evidentemente sbagliato richiamo alla <emph type="italics"></emph>terza sup­<lb></lb>posizione,<emph.end type="italics"></emph.end> invece che alla seconda. </s></p><p type="main">

<s>Non sapendo perciò farci altro di meglio, collazionammo questa del Ma­<lb></lb>nolessi con l&#039;edizione del Barattieri (<emph type="italics"></emph>Architettura d&#039;acque,<emph.end type="italics"></emph.end> P. II, ediz. 2a, <lb></lb>Piacenza 1699, pag. </s>

<s>57) e ci parve ricavarne una lezione, se non certamente <lb></lb>conforme con l&#039;autografo, corretta però in modo, da riferire almeno il si-<pb xlink:href="020/01/3438.jpg" pagenum="399"></pb>gnificato dell&#039;Autore, se non il preciso costrutto grammaticale. </s>

<s>Propostasi la <lb></lb>figura medesima 190 del Cavalieri, anche il Castelli afferma che, essendo <lb></lb>l&#039;altezza EB raddoppiata in BG, vien perciò l&#039;acqua GC ad acquistare una <lb></lb>velocità doppia dell&#039;acqua EC, per queste ragioni, che, secondo ci è resul­<lb></lb>tato dalla detta collazione, debbon essere state espresse nella forma seguente: <lb></lb><emph type="italics"></emph>Imperocchè, havendo l&#039;acqua GF per suo letto il fondo EF, ugualmente <lb></lb>inclinato come il letto BC, ed essendo la sua altezza viva GE uguale àl­<lb></lb>l&#039;altezza viva EB, ed havendo la medesima larghezza BC: haverà per sè <lb></lb>stessa una velocità uguale alla velocità della prima acqua EC. </s>

<s>Ma perchè, <lb></lb>oltre al proprio moto, vien portata dal moto dell&#039;acqua EC, haverà an­<lb></lb>cora, oltre al proprio moto, il moto dell&#039;EC. </s>

<s>E perchè le due acque GF <lb></lb>ed EC sono simili di velocità, per la seconda supposizione, però tutta <lb></lb>l&#039;acqua GC sarà doppia di velocità di quella, che haverà l&#039;acqua EC, <lb></lb>che era quello che si doveva dimostrare.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ma, a dover dire un parto disgraziato, basta il non essersi meritate le <lb></lb>affezioni paterne: il Castelli infatti si dichiarò, come vedremo, di non esser <lb></lb>rimasto contento di questa dimostrazione. </s>

<s>I dubbi del Cavalieri non gli par­<lb></lb>vero affatto risoluti, specialmente per ciò che riguardava la scala delle ve­<lb></lb>locità: e da quelle loro similitudini, benchè così studiosamente introdotte, si <lb></lb>sentiva penosamente aggirato in qualche paralogismo. </s>

<s>E in vero la somi­<lb></lb>glianza, tra le velocità di due fiumi di larghezze uguali, non può riferirsi <lb></lb>ad altro, che alle altezze, per cui, tanto essendo il supporre essere le velo­<lb></lb>cità simili nelle altezze, quanto il dimostrare che le velocità son proporzio­<lb></lb>nali alle altezze; il paralogismo che si diceva consiste nell&#039;aver dimostrata <lb></lb>una proposizione, che già supponevasi vera. </s></p><p type="main">

<s>Nonostante, la maggiore di tutte le disgrazie, alle quali andò soggetta <lb></lb>questa stessa proposizione, fu quella di avere attirato addosso all&#039;Autore l&#039;ob­<lb></lb>brobriosa accusa di plagio. </s>

<s>Il Lombardini, nello scritto sopra citato, annun­<lb></lb>ziava proemiando, dimostrava discorrendo, e finalmente riepilogava la sen­<lb></lb>tenza essersi il Castelli <emph type="italics"></emph>valso degli autografi di Leonardo da Vinci, della <lb></lb>Scienza idraulica del quale s&#039;attribuiva il merito<emph.end type="italics"></emph.end> (pag. </s>

<s>72). Il valente critico, <lb></lb>per provare il suo assunto, confronta la proposizione, da noi trascritta a pag. </s>

<s>69 <lb></lb>qui addietro, con la seconda del secondo libro delle Acque correnti, e perchè <lb></lb>ebbe a mano una di quelle edizioni del Manolessi, nella quale la dimostrazione <lb></lb>mancava, l&#039;andò a cercare nel Barattieri, al luogo sopra citato, notandovi prin­<lb></lb>cipalmente questo argomento: <emph type="italics"></emph>E perchè l&#039;acqua EB vien caricata di proprio <lb></lb>peso, per avere il peso di sè stessa, e quello di EG, per la quale riceve anche <lb></lb>doppio impulso, e forma perciò doppia la sua potenza nella velocità.....<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Poteva un tal censore avvedersi dello sbaglio <emph type="italics"></emph>caricata di proprio peso,<emph.end type="italics"></emph.end><lb></lb>e liberamente correggere <emph type="italics"></emph>caricata di doppio peso,<emph.end type="italics"></emph.end> ma quel che non seppe <lb></lb>è che un tale argomento, com&#039;apparisce dalla vera lezione, manca nell&#039;ori­<lb></lb>ginale del Castelli, dentro cui d&#039;altra mano fu intruso, onde al discorso del <lb></lb>Lombardini viene a mancare ogni virtù di concluder l&#039;intento, venendogli a <lb></lb>mancare uno dei termini del confronto. </s></p><pb xlink:href="020/01/3439.jpg" pagenum="400"></pb><p type="main">

<s>Ma chi mai, dop&#039;avere ascoltata ne&#039;suoi particolari la storia del prin­<lb></lb>cipio e de&#039;progressi della scoperta, a cui diceva il Castelli <emph type="italics"></emph>non poter far di <lb></lb>meno di non pensarci giorno e notte;<emph.end type="italics"></emph.end> vorrà credere alle asserzioni di que­<lb></lb>sti critici novelli? </s>

<s>Se i teoremi delle velocità proporzionali alle altezze, e <lb></lb>delle quantità proporzionali ai quadrati delle altezze, furono ricopiati dagli <lb></lb>autografi di Leonardo da Vinci, a che ricorrere il Castelli, per la sua dimo­<lb></lb>strazione, agli aiuti del Cavalieri? </s>

<s>Il qual Cavalieri dunque dovrebbe esser <lb></lb>complice del plagio, suo essendo quel modo di dimostrare: modo lubrico e fal­<lb></lb>lace, per questo solo motivo seguitato da lui, come vedemmo, perchè non gli era <lb></lb>approdato l&#039;altro più legittimo, di che aveva potuto far uso lo stesso Leonardo. </s></p><p type="main">

<s>In ogni modo, l&#039;assunto del Lombardini è falso nella sua radice, e con­<lb></lb>trario alla legge storica: falso cioè che fosse esso Leonardo il creatore del­<lb></lb>l&#039;Idraulica, e che dagli autografi di lui si divulgassero i teoremi, riappariti <lb></lb>per tutt&#039;altre vie, più di un secolo dopo, nelle opere del Castelli. </s>

<s>Cotesti <lb></lb>teoremì erano già germogliati nella scuola del Nemorario, e da essa deriva­<lb></lb>rono negl&#039;Idraulici del secolo XV, e del XVI per tradizione, che ai tempi <lb></lb>del così detto <emph type="italics"></emph>Instauramento del metodo sperimentale<emph.end type="italics"></emph.end> rimase infelicemente <lb></lb>interrotta. </s>

<s>Largo campo s&#039;aprirebbe di qui al nostro discorso, a cui ora solo <lb></lb>ci contentiamo di aggiungere quel tanto, che valga a confermare il già detto. </s></p><p type="main">

<s>Fra gl&#039;idraulici del secolo XVI il più noto e più celebre di tutti è il <lb></lb>Cardano, ne&#039;libri del quale vedemmo, non solamente proposti, ma dimo­<lb></lb>strati dai loro principii matematici quei due massimi teoremi, quali sono che <lb></lb>le quantità dell&#039;acqua stanno in ragion composta delle velocità e delle se­<lb></lb>zioni, e che le velocità stesse son proporzionali alle altezze. </s>

<s>Di qui veniva a <lb></lb>concludersi legittimamente la proposizione, principale soggetto del presente <lb></lb>discorso, che le quantità stanno come i quadrati delle altezze. </s>

<s>Le premesse <lb></lb>poi a una tal conclusione erano tanto ben confermate nella scienza del Car­<lb></lb>dano, ch&#039;egli non vuol però accettarle così assolutamente, com&#039;avevano fatto <lb></lb>i suoi precedessori, senza eccettuare il caso dei grandi fiumi, ne&#039;quali par <lb></lb>che l&#039;acqua, per esser più alta, anche più lentamente si muova. </s>

<s>“ Tertium <lb></lb>scitu dignum, et quod omnibus difficilius, est an altior aqua tardius mo­<lb></lb>veatur. </s>

<s>Nam sic esse videtur, quod omnia flumina magna lentius fluere vi­<lb></lb>deamur ” (<emph type="italics"></emph>De rerum var.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>69). La soluzion del problema la fa il <lb></lb>Cardano dipendere daì principio delle velocità medie, e dal supposto che, <lb></lb><figure id="id.020.01.3439.1.jpg" xlink:href="020/01/3439/1.jpg"></figure></s></p><p type="caption">

<s>Figura 192.<lb></lb>quanto più cresce l&#039;acqua d&#039;un gran <lb></lb>fiume, tanto più la superficie di lui si <lb></lb>riduca all&#039;equilibrio, cioè s&#039;avvicini ad <lb></lb>essere orizontale. </s></p><p type="main">

<s>Così, per esempio, se la linea CD <lb></lb>(fig. </s>

<s>192) rappresenta la pendenza del­<lb></lb>l&#039;alveo, e per un&#039;altezza CE la super­<lb></lb>ficie declina secondo EF assai meno di <lb></lb>CD, crescendo il fiume fino in CK, la superficie AK si dispone quasi in un <lb></lb>piano orizontale, e perciò la velocità media degli strati, compresi fra AK, <pb xlink:href="020/01/3440.jpg" pagenum="401"></pb>e DC, deve resultare minore della velocità media degli strati compresi fra <lb></lb>FE, e DC. “ Unde etiam tertii quaesiti explicatio apparet: aqua enim velut <lb></lb>iuxta inclinationem eamdem lentius movetur sub longiore distantia; ita etiam <lb></lb>sub pari inclinatione, maioreque altitudine, quoniam enim, ut dictum est, in <lb></lb>imo inclinationem habet, in summo dum fluit nullam, tota vero aequaliter. </s>

<s><lb></lb>Igitur iuxta mediae inclinationis impetum tota aqua movebitur, atque ita <lb></lb>omnia flumina quo altiora eo lenius feruntur ” (ibid., pag. </s>

<s>71). Ora in que­<lb></lb>ste discussioni il Cardano rivolge il discorso in generale agli Idraulici, che <lb></lb>l&#039;avevano preceduto e non personalmente a Leonardo da Vinci, che nessuno <lb></lb>riconosceva di questa Scienza maestro, ma condiscepolo con tutti gli altri di <lb></lb>un Maestro più antico, del qual condiscepolo, se l&#039;Autor <emph type="italics"></emph>De rerum varie­<lb></lb>tate<emph.end type="italics"></emph.end> aveva notizia per la fama, non aveva certamente studiato i manoscritti <lb></lb>di lui, e, straniero all&#039;arte del disegno, non avrà forse desiderato di vederli, <lb></lb>come tanti, di null&#039;altro propriamente curiosi, che d&#039;ammirare nelle carte <lb></lb>preziose i prodigi della penna e della matita. </s></p><p type="main">

<s>Che poi le tradizioni della scuola del Nemorario avessero libero corso, <lb></lb>non arrestato per la reclusione dei manoscritti vinciani nella villa di Vaprio, <lb></lb>si potrebbe provare con varii esempi, e specialmente con quello offertoci da <lb></lb>Alessandro Betinzoli di Crema, nelle carte postume del quale il Barattieri atte­<lb></lb>sta di aver letto il teorema delle quantità proporzionali ai quadrati delle altezze, <lb></lb>proposto e dimostrato in questa maniera: “ Volendosi sapere quanto cresce <lb></lb>un&#039;acqua, alzandosi a oncia per oncia, si dee sapere che un&#039;oncia d&#039;altezza <lb></lb>fa un&#039;oncia: che due oncie alte faranno quattro volte tant&#039;acqua, perchè <lb></lb>due volte sarà per la quantità del corpo, e due volte per la quantità della <lb></lb>gravezza, che cresce per l&#039;altezza: e alzandosi a once tre farà nove volte tanto, <lb></lb>e quattro d&#039;altezza faranno sedici volte tanto ” (<emph type="italics"></emph>Architettura d&#039;acque<emph.end type="italics"></emph.end> cit., <lb></lb>P. I, pag. </s>

<s>182). </s></p><p type="main">

<s>Al qual Betinzoli soggiunge il Barattieri doversi molta lode, per aver <lb></lb>preceduto di parecchi anni il Castelli: lode, che ora il Lombardini gli vor­<lb></lb>rebbe detrarre, facendo anche di lui un plagiario o un frugatore delle al­<lb></lb>trui carte, giudizioso e fortunato. </s>

<s>Dalla quale opinione viene ora a rimoverci <lb></lb>una critica più sana, dimostrandoci com&#039;esso Betinzoli e tutti gli altri, dei <lb></lb>quali a nessuno caddero sotto gli occhi i manoscritti vinciani, attingessero la <lb></lb>loro scienza, non a un privato bottino chiuso a chiave, ma alla bocca aperta <lb></lb>di una pubblica fonte. </s></p><p type="main">

<s>Come poi il libero corso di queste tradizioni non andasse a cader tutto <lb></lb>nel morto e profondo pozzo di Vaprio, ma proseguisse all&#039;aperto, infin presso <lb></lb>alla soglia del secolo XVII, e di li fosse risospinto indietro, come una pu­<lb></lb>trida gora, che venisse a intorbidare le nuove scaturigini rigogliose; appa­<lb></lb>risce da un documento, che vuol essere ora meglio esaminato, e che consi­<lb></lb>ste in quella scrittura idraulica di Galileo, alla quale i primi editori posero <lb></lb>il titolo di <emph type="italics"></emph>Risposta al Bertizzolo.<emph.end type="italics"></emph.end> Forse era scritto <emph type="italics"></emph>Bertazzolo,<emph.end type="italics"></emph.end> e dee esser <lb></lb>costui quel Gabriele, che pubblicò nel 1609 in Mantova il <emph type="italics"></emph>Discorso sopra <lb></lb>il nuovo sostegno alla chiusa di Governolo:<emph.end type="italics"></emph.end> ingegnere idraulico allora di <pb xlink:href="020/01/3441.jpg" pagenum="402"></pb>sì gran nome in Italia, che fu chiamato a Firenze a prepararvi certi giochi <lb></lb>argonautici, per una festa nuziale di corte. </s></p><p type="main">

<s>Questo Bertizzolo dunque professava, in un suo Discorso in materia di <lb></lb>acque, che, secondo crescono esse acque in altezza, debbono ancora crescere <lb></lb>in velocità, e di qui concludeva che le quantità versate in un dato tempo <lb></lb>dovevano aver la proporzione medesima de&#039;quadrati delle altezze: professava <lb></lb>perciò e riusciva alle conclusioni medesime di Leonardo, del Cardano e del <lb></lb>Betinzoli, e così, quella che il Castelli dava per la scoperta nuova di un mira­<lb></lb>colo della Natura, s&#039;annunziava quarant&#039;anni prima al maestro di lui, a Ga­<lb></lb>lileo, a cui la novità parve, invece di un miracolo, un mostro, e come tale <lb></lb>studiavasi, ragionando in tal guisa, di cacciarlo da sè con la forca di una <lb></lb>scienza nuova: “ Molto vivamente e con gran sottigliezza risponde il sig. </s>

<s>Ber­<lb></lb>tizzolo alle mie difficoltà, per mantenere in piede la sua conclusione, che se­<lb></lb>condo che cresce l&#039;altezza dell&#039;acqua sopra il medesimo declive, e per con­<lb></lb>seguenza la gravità, debba ancora crescere la celerità del suo moto, il che <lb></lb>era stato da me messo in dubbio, pigliando occasione di dubitare da quello, <lb></lb>che vedo per esperienza farsi nelli altri movimenti naturali, ne&#039;quali i mo­<lb></lb>bili omogenei, ancorchè disugualissimi in moto, e per conseguenza in peso, <lb></lb>si muovono tuttavia con pari velocità, come ciascheduno può ad ogni ora ve­<lb></lb>dere in due palle di ferro, o d&#039;altra materia grave, delle quali una sia gran­<lb></lb>dissima e l&#039;altra piccolissima, che cadendo a perpendicolo, ovvero sopra il me­<lb></lb>desimo piano inclinato, si muovono con la medesima velocità ” (Alb. </s>

<s>VII, 222). <lb></lb>E dopo aver confermato, co&#039;soliti argomenti sperimentali, che le velocità di <lb></lb>ogni cadente son le medesime, comunque se gli aggiunga gravità con accre­<lb></lb>scergli la mole; francamente Galileo ne conclude “ che sopra il medesimo <lb></lb>declive con tanta velocità anderà un&#039;acqua alta cento braccia, con quanta <lb></lb>una che sia alta un solo ” (ivi, pag. </s>

<s>224). </s></p><p type="main">

<s>Confutato il teorema delle velocità proporzionali alle altezze, per passare <lb></lb>a confutar l&#039;altro delle quantità proporzionali ai quadrati delle altezze, che <lb></lb>il Bertizzolo ne faceva per logica necessità conseguire, Galileo ebbe ricorso <lb></lb>alle esperienze. </s>

<s>Siano, egli dice, due canali parallelepipedi serrati AB, CD <lb></lb>(fig. </s>

<s>193) colle lunghezze EF, GH delle bocche rettangolari uguali, ma con <lb></lb>le altezze AE, CG differenti, ed abbiano essi canali la medesima inclinazione, <lb></lb><figure id="id.020.01.3441.1.jpg" xlink:href="020/01/3441/1.jpg"></figure></s></p><p type="caption">

<s>Figura 193.<lb></lb>e da vene inessiccabili passin l&#039;acque dalle <lb></lb>parti B, D verso AF, CH. </s>

<s>Avendo le quantità, <lb></lb>secondo il Bertizzolo la ragion composta delle <lb></lb>velocità e delle sezioni, e tanto queste, per es­<lb></lb>sere ugualmente larghe, quanto quelle, per le <lb></lb>posizioni dell&#039;avversario, stando come le al­<lb></lb>tezze; manifestamente dovrebbe l&#039;acqua ver­<lb></lb>sata dalla bocca CH esser tanto maggiore di <lb></lb>quella versata dalla bocca AF, quanto il qua­<lb></lb>drato di CG è maggiore del quadrato di AE. Cosicchè, se CG ad AE fosse <lb></lb>doppio, dovrebbe la bocca CH gittare il quadruplo della AF. “ La qual cosa, <pb xlink:href="020/01/3442.jpg" pagenum="403"></pb>conclude Galileo, indubitatamente non si troverà esser così, nè si vedrà but­<lb></lb>tare il canale DC una goccia più che il doppio di BA, segno necessarissimo <lb></lb>che l&#039;acque, nell&#039;uno e nell&#039;altro, vanno con pari corso ” (ivi, pag. </s>

<s>226). </s></p><p type="main">

<s>L&#039;esperienza non si poteva asserire con tanta sicurtà, se non fosse stata <lb></lb>trovata vera. </s>

<s>Ed essendo verissima, c&#039;incontriamo con nostra maraviglia nella <lb></lb>soluzione di un magno problema, per cui dunque non dovevano allora man­<lb></lb>care gli argomenti. </s>

<s>Come poteva Galileo essersi certificato che la bocca CH <lb></lb>non getta una gocciola più del doppio della bocca AF, se non raccoglien­<lb></lb>done l&#039;acqua, uscita qua e là nel medesimo tempo, in un vaso cilindrico o <lb></lb>prismatico e, misuratene le altezze, veder l&#039;una tornare al doppio dell&#039;altra? </s>

<s><lb></lb>E qual era lo strumento usato per la misura del tempo? </s>

<s>Alle quali domande <lb></lb>non si può aspettar la risposta da Galileo ma dal Bertizzolo, con l&#039;esperienza <lb></lb>del quale si conformava Galileo stesso, per ridurre <emph type="italics"></emph>ad hominem<emph.end type="italics"></emph.end> la sua con­<lb></lb>futazione, e perciò renderla più efficace. </s></p><p type="main">

<s>Forse il Buteone aveva trovato qualcuno de&#039;più sagaci, che raccolse il <lb></lb>seme delle sue parole, e il Bertizzolo, facendo uso della clessidra ad acqua, <lb></lb>e de&#039;metodi di lui, erasi assicurato che l&#039;esperienza confermava così la teo­<lb></lb>ria, da non rimoverne il pensiero per le contradizioni del suo potente av­<lb></lb>versario. </s>

<s>Non ci son note le ragioni di questa filosofica fermezza, ma le deve <lb></lb>aver ricavate dalle dottrine de&#039;suoi maestri, dietro le quali non gli fu diffi­<lb></lb>cile il darsi una spiegazione dell&#039;anomalia, che l&#039;esperienza di Galileo faceva <lb></lb>alla legge universale. </s>

<s>Nel Cardano si leggevano queste cose, da noi riferite <lb></lb>anche altrove: <emph type="italics"></emph>Itaque haud dubium est aquas, quae per fistulas et sipho­<lb></lb>nes deducuntur, et impetu, et continuitute agi: quae vero per canales, <lb></lb>rivos et locos patentes, solo impetu. </s>

<s>Quamobrem velocius semper fertur <lb></lb>aqua per siphones quam per rivos, pari ratione, paribusque auxiliis et <lb></lb>impedimentis constitutis.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Ora essendo i due canali AB, CD di Galileo due sifoni, è manifesto per­<lb></lb>chè non si osservino in essi le medesime leggi, che ne&#039;canali aperti o neì <lb></lb>rivi patenti: perchè, cioè, l&#039;acqua v&#039;è dedotta in quelli, non per solo im­<lb></lb>peto come in questi, ma per impeto e continuità, non potendo l&#039;una sezione, <lb></lb>per esser maggiormente velocitata, dilungarsi dall&#039;altra, senza lasciarvi fra <lb></lb>mezzo uno spazio vuoto, d&#039;onde il moto ne&#039;sifoni è più veloce, come quello <lb></lb>che, secondo il Cardano stesso, <emph type="italics"></emph>ab aere iuvatur.<emph.end type="italics"></emph.end> Consegue, per la detta ra­<lb></lb>gion della continuità, che gl&#039;impeti del gettare sono que&#039;medesimi, con cui <lb></lb>si muovono le sezioni per tutta la lunghezza dei canali. </s>

<s>E perchè cotali im­<lb></lb>peti dipendono dalle sole cadute, che sono uguali, supponendosi uguali le <lb></lb>inclinazioni; dunque anche essi impeti sono uguali. </s>

<s>Ora stando in questo <lb></lb>caso le quantità come le semplici altezze non fa maraviglia che la bocca GH, <lb></lb>rispetto alla AF, non si trovi gittar nel medesimo tempo altro che il doppio. </s>

<s><lb></lb>Nei canali aperti invece e nei fiumi, intorno a che propriamente cadeva la <lb></lb>controversia, il moto non è uniforme per tutta la lunghezza dell&#039;alveo, ma <lb></lb>sempre più accelerato. </s>

<s>Ond&#039;essendo le velocità varie, le quantità non stanno <lb></lb>nella ragion semplice delle altezze, ma nella composta di loro e delle sezioni, <pb xlink:href="020/01/3443.jpg" pagenum="404"></pb>e perciò per una sezione di doppia altezza deve necessariamente passare una <lb></lb>mole d&#039;acqua quadruplicata. </s></p><p type="main">

<s>Nè possiamo qui trattenerci dal ripensare alle dovizie della Scienza, così <lb></lb>improvvidamente rifiutate da Galileo. </s>

<s>Si potrebbe disputar se le perdite va­<lb></lb>lessero i nuovi acquisti, ma non si può da nessuno non prevedere la tanto <lb></lb>maggiore ubertà, a cui sarebbe potuto giungere l&#039;albero della Scienza, quando <lb></lb>il surculo nuovo fosse stato inserito nella vecchia radice. </s>

<s>La faticosa eredità <lb></lb>di tanti secoli, non inerti certamente, al giudizio dei savi, l&#039;avrebbero po­<lb></lb>tuta Galileo e il Cartesio tramandare intera, e invece la dilapidarono per una <lb></lb>insana ambizione d&#039;esser essi i primi e i soli, costringendo i discepoli a <lb></lb>riconquistar a frusto a frusto, con la propria fatica, le disperse sostanze degli <lb></lb>avi. </s>

<s>L&#039;esempio di ciò vivo e presente l&#039;abbiamo nel Castelli, che dovette da <lb></lb>sè ricostruire pietra per pietra il demolito edifizio idraulico, di che a lui <lb></lb>solo, e non già a Frontino o a Leonardo da Vinci, noi posteri dobbiam tutto <lb></lb>il merito: merito, che non gli potrebbe esser mai tolto nè menomato dal­<lb></lb>l&#039;eloquenza dei Fabbretti e dei Lombardini. </s></p><p type="main">

<s>Consideriamo le condizioni, a cui si ridusse lo stesso Galileo, che, avendo <lb></lb>rifiutato di sedersi al lauto convito de&#039;suoi precursori, si chinò poi a raccat­<lb></lb>tare le miche dalla mensa, che il suo Discepolo aveva scarsamente riappa­<lb></lb>recchiata. </s>

<s>Le controversie col Bertizzolo risalgono ai principii del secolo XVII, <lb></lb>e a questo tempo è da riferire il Discorso galileiano in risposta a lui: scrit­<lb></lb>tura, che non ha forma epistolare, e tanto meno ha la data del 1638, asse­<lb></lb>gnatale dall&#039;Albèri (VII, 222 in nota). Nel 1625 le risecchite dottrine del <lb></lb>Bertizzolo rinverdirono nel <emph type="italics"></emph>Progresso idraulico<emph.end type="italics"></emph.end> del Castelli, e Galileo accet­<lb></lb>tava dalle amiche mani del Discepolo ciò che prima aveva così risolutamente <lb></lb>rifiutato da quelle dell&#039;avversario. </s>

<s>Allora aveva affermato e dimostrato che <lb></lb>una palla di ferro e una mole di acqua non variano velocità, se con accre­<lb></lb>scimento di gravitante materia si facciano scendere nel perpendicolo o lungo <lb></lb>un piano inclinato, e ora, nella lettera sul fiume Bisenzio, dice che, sebbene <lb></lb>ciò propriamente segua nei mobili solidi, <emph type="italics"></emph>ne&#039;fluidi però credo che la cosa <lb></lb>proceda assai differentemente.<emph.end type="italics"></emph.end> Allora aveva attribuito tutto il velocitarsi dei <lb></lb>fiumi alla pendenza della superficie, e ora avverte che questa non può es­<lb></lb>sere causa sufficiente, se non si ricorre al premere, che le sezioni precedenti <lb></lb>fanno gravitando sopra le susseguenti, d&#039;onde si viene a concludere quel <lb></lb>teorema delle velocità proporzionali alle altezze, che prima aveva confutato <lb></lb>al Bertizzolo, con tante prove di ragioni e di fatti. </s></p><p type="main">

<s>Nonostante questa lettera galileiana, scritta a Raffaello Staccoli il di <lb></lb>16 Gennaio 1631, è documento importante alla storia dell&#039;Idrodinamica, per <lb></lb>le prime applicazioni, che vi si fanno all&#039;acque, delle leggi nuovamente sco­<lb></lb>perte intorno al moto dei gravi. </s>

<s>La Scienza v&#039;è senza dubbio sostanzialmente <lb></lb>promossa, ma rimane così in difetto, in ordine all&#039;unità dei principii, che <lb></lb>la nuova istituzione rimane da questa parte alquanto inferiore all&#039;antica. </s>

<s><lb></lb>Abbiamo veduto infatti come Leonardo, il Cardano e tutti gl&#039;Idraulici di <lb></lb>que&#039;tempi, applicassero universalmente ai fluidi quella legge delle velocità <pb xlink:href="020/01/3444.jpg" pagenum="405"></pb>proporzionali alle altezze, che avevano creduto esser propria a tutti i gravi <lb></lb>cadenti, mentre Galileo e il Castelli professarono questa stessa legge in certi <lb></lb>casi, eccettuándone altri, ai quali soli applicarono la nuova legge delle ve­<lb></lb>locità proporzionali alle radici delle altezze. </s></p><p type="main">

<s>Per questa mancanza d&#039;unità nel principio informativo, l&#039;Idrodinamica, <lb></lb>nonostante i felici ardimenti di Galileo, non si poteva dire istituita, e perchè <lb></lb>ciò avvenisse, era necessario che se la legge degli spazii proporzionali ai <lb></lb>quadrati dei tempi era vera, dovesse anch&#039;essere universale, e perciò indi­<lb></lb>pendente da ogni accidental differenza, che potesse passare fra solidi e liquidi, <lb></lb>e dal diverso modo del fluire di questi dai vasi artificiali, o dal loro correre <lb></lb>naturalmente nei fiumi. </s>

<s>L&#039;universalità poi di questa legge, per la quale venne <lb></lb>a istituirsi l&#039;Idrodinamica nuova, fu con metodi matematici dimostrata dal <lb></lb>Torricelli, e rimane ora a noi a narrare della felice istituzione i principii <lb></lb>avventurosi e i progressi. </s></p><p type="main">

<s><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Per risalire a cotesti principii convien penetrare in quelle stanze delle <lb></lb>ville di Bellosguardo e di Arcetri, nelle quali Galileo raccoglieva intorno a sè <lb></lb>gli amici, che per il soggetto della conversazione si rendevano altrettanti sco­<lb></lb>lari. </s>

<s>Erano per lo più gentiluomini fiorentini, fra&#039;quali Mario Guiducci, Lo­<lb></lb>dovico Incontri, Tommaso Renuccini, Niccolò e Andrea Arrighetti, che sta­<lb></lb>vano volentieri ad ascoltare il Maestro, perchè aveva sempre qualche cosa di <lb></lb>nuovo tra curioso e utile a sapersi, e per cui pareva che diventassero a così <lb></lb>dire umane, le astratte speculazioni della Scienza. </s>

<s>Ora aveva ricette da gua­<lb></lb>rire alcune fra le infermità o incomodi più comuni, ora suggeriva espedienti <lb></lb>contro gl&#039;insetti nocivi, ora insegnava certi segreti, da far nelle più umili <lb></lb>domestiche faccende apparir l&#039;eccellenza del filosofo sopra la gente volgare. </s>

<s><lb></lb>Ma più spesso erano così fatti segreti intorno agli esercizi dell&#039;agricoltura, <lb></lb>e que&#039;gentiluomini, tutti possessori di ville nelle campagne toscane, erano <lb></lb>curiosi di ascoltarli sopra gli altri, perchè, praticandoli, si dilettavano di farne <lb></lb>stupire i loro villici e i castaldi. </s></p><p type="main">

<s>Di tutto ciò, come di cose indegne della fama e della sapienza di Ga­<lb></lb>lileo, non ci sarebbe rimasto memoria, se il Viviani non ce l&#039;avesse conser­<lb></lb>vata in uno de&#039;suoi tanti volumi manoscritti, in cui l&#039;esperienze e i pen­<lb></lb>sieri raccoltivi dentro, con mano giovanile, ci siam dovuti persuadere oramai <lb></lb>che son per la massima parte non suoi, ma del Maestro. </s>

<s>Fra cotesti varii <lb></lb>pensieri intorno a materie meccaniche, fisiche, astronomiche, filosofiche e <lb></lb>altro, che il Viviani stesso dice di avere scritti senz&#039;ordine, ci troviamo rac­<lb></lb>colti anche questi: “ I calli de&#039;piedi, racconta chi l&#039;ha sperimentato in sè <lb></lb>e in altri, che si guariscono per sempre col tenere i piedi nell&#039;acqua del <lb></lb>bagno detto della Doccia, lontan da Pisa due miglia, per tempo di un&#039;ora e <pb xlink:href="020/01/3445.jpg" pagenum="406"></pb>mezzo il giorno, per tre o quattro giorni ” (MSS. Gal. </s>

<s>Disc., T. CXXXV, <lb></lb>fol. </s>

<s>4). “ Per far morire i moscerini del grano, nella medesima stanza, farai <lb></lb>prendere il tabacco in fumo, e ben piena di detto fumo chiudi la stanza, <lb></lb>che quel fumo gli ammazzerà. </s>

<s>Non per anco provato. </s>

<s>— Per levar via la <lb></lb>febbre, acqua stillata di gusci verdi di noci fresche: prendine quanto un bic­<lb></lb>chiere nel principio della febbre, che ti libererà. </s>

<s>— Per il dolore dei denti, <lb></lb>cera gialla, seme di porri, seme iusquiamo o veramente di dente cavallino: <lb></lb>fattone palla, quale posta sopra un ferro infocato e per mezzo di un imbuto, <lb></lb>che con la campana di esso riceva il fumo, e col fusto faccia penetrare il <lb></lb>dente guasto; che leverà il dolore. </s>

<s>— Per lavare indiane, pezzuole di seta, <lb></lb>di filaticcio o di stame, prendi il fiele di bue o di vitello: dimenalo ben bene <lb></lb>in una catinella, tanto che faccia molta schiuma, e poi lava in detto fiele <lb></lb>quello che vuoi di seta, bambagia o stame, che sia colorito, e poi risciac­<lb></lb>qualo in acqua fresca; che lo vederai pulito, senza perder punto di colore. </s>

<s><lb></lb>Provato e riuscito ” (ivi, fol. </s>

<s>10 a tergo). </s></p><p type="main">

<s>Ma ad avviarci più direttamente per i nostri sentieri, fa a proposito la <lb></lb>nota seguente: “ Per cavar da un medesimo tino il vino dolce e maturo, <lb></lb>e far che vi resti l&#039;agro, si faccia empire il tino di uve senza ammostare in <lb></lb>grappoli interi, e si lasci così stare per qualche poco di tempo, che, stu­<lb></lb>rando la cannella, uscirà vino maturo, che sarà quello dei grani dell&#039;uva più <lb></lb>maturi, spremuti dal peso e carico proprio de&#039;grappoli, che sono i primi a <lb></lb>scoppiare. </s>

<s>E dopo che sarà uscito tal vino dolce, pigiando e ammostando <lb></lb>l&#039;uve, ne uscirà il vino assai meno maturo, anzi assai aspro, secondo però <lb></lb>che l&#039;uve per loro stesse saranno più o meno mature generalmente. </s>

<s>Inven­<lb></lb>zione del Galileo provata e riuscita, e insegnata dal sig. </s>

<s>Andrea Arrighetti ” <lb></lb>(ivi, fol. </s>

<s>7). </s></p><p type="main">

<s>Un&#039;altra volta, essendo il discorso caduto in un argomento di simil <lb></lb>genere, fu proposta la soluzioue di un tal problema: — in che maniera <lb></lb>il primo vino, che esce da una botte quando si manomette, è più debole di <lb></lb>quello ch&#039;esce di poi, e perchè, per un po&#039;di tempo, si trova che va mi­<lb></lb>gliorando? </s>

<s>— Furono date varie risposte, e la migliore, che sembra avere <lb></lb>approvata anche Galileo, si riduceva a dire che, insieme col primo vino, <lb></lb>escono le fecce, deposte e appastate intorno allo zipolo o alla cannella, di <lb></lb>che, venendosi via via a rilavare il foro, è perciò che il vino stesso si sente <lb></lb>venir via via sempre più migliorando. </s>

<s>Andrea Arrighetti però non rimaneva <lb></lb>sodisfatto di queste ragioni, e ripensando a ciò, che aveva tante volte osser­<lb></lb>vato negli orologi a polvere, stimò che similmente avvenisse del vino della <lb></lb>botte, cosicchè, scendendo al foro per il primo quello, che è alla superficie, <lb></lb>per questo solo si mostri più debole dell&#039;altro, perchè, rimasto nello scemare <lb></lb>al contatto con l&#039;aria filtratavi di fuori, non può non aver preso, e non rite­<lb></lb>nere in sè alquanto dello scipito. </s></p><p type="main">

<s>Il pensiero, nato nella mente dell&#039;Arrighetti da così umile luogo, trovò <lb></lb>presto da nobilitarsi nella risoluzione di alcuni problemi, che a chiunque <lb></lb>avesse professate le dottrine idrostatiche di Galileo rimanevano irresolubili. <pb xlink:href="020/01/3446.jpg" pagenum="407"></pb>Insegnandosi infatti, nel Discorso intorno i galleggianti, che l&#039;acqua nel­<lb></lb>l&#039;acqua non pesa, si veniva a escludere, dai vari mezzi di dimostrare le ve­<lb></lb>rità fondamentali della Scienza, quel principio delle pressioni proporzionali <lb></lb>al numero degli strati soprapposti, di che avevano fatto uso il Cardano e <lb></lb>Leonardo da Vinci, e a cui perciò il Cavalieri e il Castelli sostituirono il <lb></lb>moto di que&#039;medesimi strati, dipendente dall&#039;inclinazione dei letti. </s>

<s>Ma es­<lb></lb>sendo l&#039;acqua stagnante, cioè senza peso e senza moto, rimaneva inesplica­<lb></lb>bile come mai, attraverso al medesimo foro, partendosi in ogni modo il li­<lb></lb>quido dalla quiete, si vedesse nulladimeno uscire più veloce dal vaso pieno, <lb></lb>che dallo scemo. </s>

<s>Ora l&#039;Arrighetti, in quel suo nuovo pensiero, trovava fa­<lb></lb>cile la soluzione di questo dubbio, dicendo che le velocità non dipendono dai <lb></lb>pesi ma dalle cadute, le quali, quanto il vaso è più pieno, tanto natural­<lb></lb>mente si fanno da maggiori altezze. </s>

<s>Incominciatosi poi a diffidare del prin­<lb></lb>cipio delle velocità virtuali, anco il paradosso idrostatico rimaneva negli in­<lb></lb>segnamenti galileiani senza spiegazione, che l&#039;Arrighetti dall&#039;altra parte <lb></lb>ricavava assai facilmente dal suo proprio supposto, perchè se l&#039;equilibrio, fra <lb></lb>l&#039;acqua del vaso grande e della piccola canna con lui congiunta, non dipende <lb></lb>dalla quantità di materia, ma da sola la velocità, s&#039;intende come, per con­<lb></lb>dizion necessaria di esso equilibrio, non si richieda se non che siano uguali <lb></lb>le velocità naturalmente acquistate per la discesa, ossia che siano uguali le <lb></lb>altezze de&#039;supremi livelli. </s></p><p type="main">

<s>Di queste speculazioni, rimaste per qualche tempo un commento a&#039;suoi <lb></lb>privati studi d&#039;Idrostatica, trovò l&#039;Arrighetti da farne l&#039;applicazione, quando <lb></lb>fu chiamato a consulto dal Granduca intorno al riparare i guasti, e a prov­<lb></lb>vedere che avesse buon effetto il condotto delle acque dalla collina di Mon­<lb></lb>tereggi nel giardino di Boboli. </s>

<s>S&#039;incorreva dagl&#039;ingegneri in quell&#039;errore, <lb></lb>ammonito già dal Cardano, che dovesse l&#039;acqua risalire in ogni modo alla <lb></lb>medesima altezza da cui fu scesa, come nei piccoli vasi comunicanti, e le re­<lb></lb>sistenze, che dovevano far le canne del condotto, si calcolavano dal solo peso <lb></lb>morto dell&#039;acqua. </s>

<s>Ora l&#039;Arrighetti aveva intorno a questo proposito altri pen­<lb></lb>sieri, e prima di comunicargli volle sentire il parere del Castelli, a cui scrisse <lb></lb>sopra questo soggetto varie lettere, in una delle quali diceva ch&#039;egli consi­<lb></lb>glierebbe di fare le dette canne, non di più resistente materia, ma più lar­<lb></lb>ghe, acciocchè meglio potessero resistere alla forza, “ che gli farà il peso, o <lb></lb>per dir meglio la velocità, che andrà acquistando l&#039;acqua nel venire a basso. </s>

<s><lb></lb>Dico nel venire a basso, perchè, come comincierà a trovare qualche salita <lb></lb>o altro impedimento, quanto si andrà ritardando la sua velocità in qualsi­<lb></lb>voglia luogo, tanto andrà scemando la forza, che ricevono le canne nel me­<lb></lb>desimo luogo, essendo io di parere che dipenda interamente dalle velocità, <lb></lb>e non dal peso dell&#039;acqua, nè credo che in questo negozio il peso operi cosa <lb></lb>alcuna, mentre non sia congiunto con velocità ” (<emph type="italics"></emph>Autori che trattano del <lb></lb>moto dell&#039;acque,<emph.end type="italics"></emph.end> ediz. </s>

<s>cit., T. IV, pag. </s>

<s>204). </s></p><p type="main">

<s>La proposizione riscontra con quell&#039;altra, che così leggemmo altrove <lb></lb>dall&#039;Aggiunti formulata: <emph type="italics"></emph>Anco la sola velocità, senza il peso, opera ed ha<emph.end type="italics"></emph.end><pb xlink:href="020/01/3447.jpg" pagenum="408"></pb><emph type="italics"></emph>momento.<emph.end type="italics"></emph.end> E come a provarla esso Aggiunti ricorreva all&#039;esempio dei venti, <lb></lb><emph type="italics"></emph>i quali, non essendo altro che aria mossa nell&#039;aria, non hanno forza altro <lb></lb>che dalla velocità, perchè un grave, in un mezzo ugualmente grave in <lb></lb>specie, come dimostra Archimede, non ha peso alcuno in detto mezzo;<emph.end type="italics"></emph.end><lb></lb>così l&#039;Arrighetti diceva persuadergli la verità della medesima proposizione <lb></lb>“ il vedere che l&#039;acqua nell&#039;acqua non pesa, e che in un sifone piramidale <lb></lb>tanto si livella nel vaso l&#039;una, quanto l&#039;altra estremità ” (ivi). </s></p><p type="main">

<s>Così, avendo fatto apparire il pensiero per spiraglio, non potè l&#039;Arri­<lb></lb>ghetti ritenersi dall&#039;aprir tutto, e dal rendere scoperto alla vista del Castelli <lb></lb>quello, cli&#039;egli chiamava una girandola, una fantasia, un sogno, una cosa <lb></lb>insomma, da non si registrar fra le chiare e certe. </s>

<s>“ Io osservo, egli dice, <lb></lb>negli orologi a polvere, nelle tramogge e in altri simili vasi, che come sieno <lb></lb>avvivati fanno di sopra un certo foro, per il quale va calando la polvere o <lb></lb>altro, riducendosi verso il pertugio, che è nel fondo di detto vaso, e pare che <lb></lb>le particelle superiori, nel calare abbasso per quel declive, impediscano in <lb></lb>un certo modo, con la velocità del loro moto quasi perpendicolare, il moto <lb></lb>transversale, che le particelle inferiori dovrebbero fare, per accostarsi al detto <lb></lb>foro. </s>

<s>Il medesimo effetto, e molto più, pare che si osservi in un pilo o altro <lb></lb>vaso, che nel versare l&#039;acqua o altro fa di sopra ancor lui il medesimo, sic­<lb></lb>chè, avviato che sia, per le medesime ragioni, pare che le particelle dell&#039;acqua <lb></lb>superiori debbano impedire, con il loro moto perpendicolare, il moto trasver­<lb></lb>sale delle parti inferiori ed esser le prime a calare a basso, accrescendo la <lb></lb>velocità continuamente, finchè arrivate al buco, che è nel fondo del vaso, si <lb></lb>partano dal detto luogo con quella velocità, che hanno acquistata fin lì. </s>

<s>E <lb></lb>questa mi viene in fantasia che possa essere la cagione, mediante la quale <lb></lb>un tino o botte getta, per la medesima canna, più quando è pieno, che <lb></lb>quando è scemo, poichè quel lquido arriva alla canna con maggior velocità <lb></lb>una volta che l&#039;altra, secondo che la caduta è maggiore o minore, non es­<lb></lb>sendo io capace che se, quando comincia a uscire per la cannella, si parte <lb></lb>dalla quiete tanto quando è pieno, che quando è scemo, non abbia da uscire <lb></lb>sempre con la medesima velocità. </s>

<s>E questa per avventura potria essere la <lb></lb>soluzione di un problema assai ridicolo di questi canovai, che dicono che il <lb></lb>primo vino, che esce da una botte, quando si manomette, è più debole di <lb></lb>quello, ch&#039;esce dipoi, e che per un po&#039;di tempo va migliorando, che po­<lb></lb>trebb&#039;essere, come dicono loro, che uscisse prima quel di sopra, molto più <lb></lb>debole per essere stato scemo. </s>

<s>Il che, come mi son dichiarato, sia detto per <lb></lb>un sogno, e solo per significarle le difficoltà, che mi s&#039;aggirano per la fan­<lb></lb>tasia circa quello, che possa operare il peso in questo particolare, che non <lb></lb>credo ci operi cosa alcuna, ma sibbene la maggiore o minor calata ” (ivi, <lb></lb>pag. </s>

<s>204, 5). </s></p><p type="main">

<s>Se dunque le velocità son tali, quali si convengono alle calate dal su­<lb></lb>premo livello del liquido, il discorso dell&#039;Arrighetti portava manifestamente <lb></lb>a concludere, per le leggi galileiane nuovamente pubblicate, che esse velo­<lb></lb>cità son proporzionali alle radici delle altezze, da cui si suppongon calare: <pb xlink:href="020/01/3448.jpg" pagenum="409"></pb>conclusione, che se il Castelli non reputò una girandola, un sogno, una fan­<lb></lb>tasia, è un fatto però che non seppe riconoscerne allora l&#039;importanza, e per­<lb></lb>suaso esser differente il modo del correr l&#039;acqua dentro i sifoni e per gli <lb></lb>alvei, non dubitò punto, ammaestrato dall&#039;esperienze, della verità della pro­<lb></lb>posizione, che poi dimostrerebbe, dicendo che, se diventa un fiume alto il <lb></lb>doppio, si deve anche movere doppiamente veloce. </s>

<s>Dalla qual proposizione, <lb></lb>ricalcando l&#039;orme del Cavalieri, passava immediatamente anche il Castelli a <lb></lb>dimostrar l&#039;altra, che dice aver le quantità dell&#039;acqua la proporzion com­<lb></lb>posta dell&#039;altezza viva all&#039;altezza viva, e della velocità alla velocità. </s>

<s>E perchè <lb></lb>questa della velocità alla velocità aveva prima dimostrato esser la propor­<lb></lb>zion medesima, che ha l&#039;altezza all&#039;altezza; ne faceva finalmente conseguire <lb></lb>di qui la verità desiderata, che cioè “ la quantità dell&#039;acqua che scorre, <lb></lb>quando il fiume è alto, a quella che scorre, mentre è basso, ha duplicata <lb></lb>proporzione dell&#039;altezza all&#039;altezza, cioè la proporzione, che hanno i quadrati <lb></lb>delle altezze ” (<emph type="italics"></emph>Della misura delle acque,<emph.end type="italics"></emph.end> lib. </s>

<s>II, Bologna 1660, pag. </s>

<s>83). </s></p><p type="main">

<s>Di queste proposizioni, ordinatamente disposte, illustrate con considera­<lb></lb>zioni, e svolte in corollari, aggiuntivi alcuni discorsi, ne&#039;quali s&#039;applicavano <lb></lb>le dimostrate dottrine alle questioni della laguna veneta; il Castelli aveva <lb></lb>compilata una scrittura, che quasi secondo libro poteva aggiungersi a quello <lb></lb>già pubblicato della Misura delle acque correnti. </s>

<s>Il manoscritto fu spedito di <lb></lb>Roma il dì 20 Settembre 1642 al principe Leopoldo de&#039;Medici, per dedicar <lb></lb>l&#039;opera <emph type="italics"></emph>subito nata<emph.end type="italics"></emph.end> ai felicissimi natali di colui, che fu poi Cosimo III di <lb></lb>Toscana, e il Castelli così diceva a esso principe Leopoldo nella lettera, con <lb></lb>la quale gli accompagnava l&#039;offerta: “ Quando non sia per servizio del se­<lb></lb>renissimo Granduca, mi sarebbe caro che non si pubblicasse ad alcuno que­<lb></lb>sto mio ritrovamento, eccettuati il p. </s>

<s>Francesco delle Scuole pie (Famiano <lb></lb>Michelini) ed i signori Andrea Arrighetti, Mario Guiducci, Tommaso Rinuc­<lb></lb>cini ed Evangelista Torricelli, i quali desidero che vedano la scrittura per <lb></lb>emendare i miei falli ” (Fabbroni, <emph type="italics"></emph>Lettere inedite,<emph.end type="italics"></emph.end> T. I, Firenze 1773, pag. </s>

<s>78). </s></p><p type="main">

<s>Fra gli esaminatori della scrittura, che il Castelli stesso così a nome <lb></lb>additava, il principe Leopoldo scelse particolarmente il Torricelli e l&#039;Arri­<lb></lb>ghetti: il primo per la celebrità del nome, acquistatasi in ogni genere di <lb></lb>scienze fisiche e matematiche, il secondo per i saggi, che aveva dato de&#039;suoi <lb></lb>studi in materia di acque. </s>

<s>L&#039;Arrighetti fermò principalmente la sua atten­<lb></lb>zione sopra quella, che trovò messa nel manoscritto per la proposizione se­<lb></lb>conda, e conferendo i dubbi, che si sentiva nascere di li, col Torricelli, gli <lb></lb>esplicava il suo proprio pensiero, concludendogli che, se non era una giran­<lb></lb>dola o un sogno, le velocità dell&#039;acqua, corrente attraverso il regolatore di <lb></lb>un fiume, dovevano crescere come le radici, e non come le semplici altezze. </s></p><p type="main">

<s>Questa volta il fecondo seme dell&#039;Idrodinamica cadde sul terreno meglio <lb></lb>disposto a riceverlo, e a farlo germogliare. </s>

<s>Il Torricelli infatti supporrà tra <lb></lb>poco, per fondamento al suo nuovo edifizio, il pensiero stesso dell&#039;Arrighetti: <lb></lb>“ Supponimus aquas violenter erumpentes, in ipso eruptionis puncto, eum­<lb></lb>dem impetum habere, quem haberet grave aliquod, sive ipsius aquae gutta <pb xlink:href="020/01/3449.jpg" pagenum="410"></pb>una, si ex suprema eiusdem aquae superficie, usque ad orificium eruptionis, <lb></lb>naturaliter cecidisset ” (<emph type="italics"></emph>Opera geom.,<emph.end type="italics"></emph.end> P. I, Florentiae 1644, pag. </s>

<s>191). </s></p><p type="main">

<s>Se non che, mentre l&#039;Arrighetti non aveva a confortare la verità del <lb></lb>suo supposto che l&#039;osservazione della <emph type="italics"></emph>cateratta,<emph.end type="italics"></emph.end> formatasi dentro la polvere <lb></lb>degli orologi, o dentro l&#039;acqua de&#039;pili; il Torricelli pensò ad altre osserva­<lb></lb>zioni o sperienze che, illustrate dalla nuova scienza del moto, sarebbero per <lb></lb>riuscire anche più concludenti. </s>

<s>Il primo pensiero fu quello dell&#039;acqua che, <lb></lb>scesa in fondo a uno de&#039;rami del sifone ritorto, acquista impeto di risalire <lb></lb>alla medesima altezza nell&#039;altro, a quel modo che Galileo aveva supposto ve­<lb></lb>rificarsi ne&#039;rimbalzi di una palla perfettamente elastica, e dalla quale s&#039;in­<lb></lb>tendesse rimossa ogni sorta d&#039;impedimenti. </s>

<s>Che se ciò avviene nel risalir <lb></lb>che fa l&#039;acqua, ritenutà dalle pareti del tubo, par verosimile, proseguiva a <lb></lb>ragionare il Torricelli, che non altrimenti da ciò avvenga, quando erompe <lb></lb>nell&#039;aria aperta, come si ricordava di avere osservato più volte negli zampilli. </s></p><p type="main">

<s>Considerava inoltre che, per questa eruzione violenta, ogni gocciola <lb></lb>d&#039;acqua è un proietto, in cui, dovendosi verificare le proprietà del moto pa­<lb></lb>rabolico, soccorrerebbero dunque opportune le esperienze a decidere della <lb></lb>verità del supposto. </s>

<s>Dato infatti un foro aperto nella parete verticale di un <lb></lb>vaso, la distanza di lui, dal livello del liquido che gli sta sopra, sarebbe la <lb></lb>sublimità della parabola, della quale calcolandosi per i teoremi galileiani <lb></lb>l&#039;ampiezza, per l&#039;estremità di lei, eretta perpendicolarmente alla parete, si <lb></lb>dovrebbe veder passare la curva del getto. </s>

<s>A queste esperienze meccaniche <lb></lb>pensava il Torricelli stesso che se ne sarebbe potuta aggiungere un&#039;altra <lb></lb>idrometrica, prendendo vari vasi cilindrici o prismatici, tutti di fondo uguale, <lb></lb>ma con altezze, che crescessero via via da uno, a quattro, a nove, a sedici, <lb></lb>secondo la serie dei numeri quadrati. </s>

<s>Fatti in fondo a ciascun vaso fori <lb></lb>uguali, e mantenutavi l&#039;acqua indeficiente in tutti, raccogliendo con diligenza <lb></lb>le quantità fluite nel medesimo tempo, si dovrebbe trovar che stanno come <lb></lb>uno, due, tre, quattro, secondo la serie dei numeri naturali, se fosse vero <lb></lb>che gl&#039;impeti nell&#039;uscire dai fori son qualmente si convengono alle cadute, <lb></lb>e perciò proporzionali alle radici delle linee, che misurano nel perpendicolo <lb></lb>quelle stesse cadute. </s></p><p type="main">

<s><emph type="italics"></emph>Haec speculatio convenit exactissime cum experimento, a nobis cum <lb></lb>summa diligentia facto,<emph.end type="italics"></emph.end> scrisse poi il Torricelli (<emph type="italics"></emph>Op. </s>

<s>geom.<emph.end type="italics"></emph.end> cit., pag. </s>

<s>200), <lb></lb>benchè poco prima avesse confessato che lo sperimento l&#039;aveva eseguito in <lb></lb>Roma l&#039;amico suo Raffaello Magiotti, <emph type="italics"></emph>eruditissimus vir, aeque literis scien­<lb></lb>tiisque omnibus ornatus<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>196). Nè solamente l&#039;esperienza idro­<lb></lb>metrica crediamo essere stata fatta dal Magiotti, ma le due meccaniche sopra <lb></lb>dette altresi, almeno con quella diligenza, con la quale il Torricelli stesso <lb></lb>poi le descrisse nel suo libro, per rimovere dai lettori ogni occasione di <lb></lb>dubbio. </s></p><p type="main">

<s>Il Magiotti dunque, dietro le proposte venutegli di Firenze per lettera <lb></lb>dell&#039;amico, fece costruire una cassetta parallelepipeda di rame, <emph type="italics"></emph>cuius alti­<lb></lb>tudo passum geometricum excedebat, cuius basis uno palmo quadrato non<emph.end type="italics"></emph.end><pb xlink:href="020/01/3450.jpg" pagenum="411"></pb><emph type="italics"></emph>erat minor<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>164). In fondo alla cassetta era applicato un tubo, <lb></lb>pure parallelepipedo, colla bocca esteriore chiuso, e sul fondo superiore di­<lb></lb>sposto in perfetto piano orizontale, praticatovi un foro <emph type="italics"></emph>circulo humanae pu­<lb></lb>pillae maior, non perperam factum, sed solertissime excavatum in lamella <lb></lb>cuprea<emph.end type="italics"></emph.end> (ibid.). Turato poi il foro, mantenuto indeficientemente pien d&#039;acqua <lb></lb>il vaso in fino all&#039;orlo, sopra il quale posata sporgeva una riga per segnare <lb></lb>il livello, dato l&#039;esito, vedeva il Magiotti risalir lo zampillo così fin presso <lb></lb>al segno, da poter dire che fosse giunto all&#039;altezza medesima, da cui sup­<lb></lb>ponevasi sceso, avuto riguardo alla resistenza dell&#039;aria e all&#039;impedimento, <lb></lb>che le prime gocciole, nel dar la volta in giù, fanno sopra le antecedenti, <lb></lb>che non hanno ancora finito di salire. </s>

<s>Che poi a così fatte cause fosse da <lb></lb>attribuire il non rispondere sempre puntualmente l&#039;esperienze alle teorie, se <lb></lb>ne persuadeva il Magiotti con l&#039;osservare che, aprendosi il foro a un tratto, <lb></lb>le prime gocciole, che non avevano chi le antecedesse, giungevano più ad <lb></lb>alto, e col sostituire all&#039;acqua il mercurio, che pure si vide toccar più presso <lb></lb>al segno, perchè la maggior gravità naturale è meglio atta a vincere la re­<lb></lb>ristenza del mezzo. </s></p><p type="main">

<s>Quanto ai getti fu pure sperimentato dallo stesso Magiotti che, se usci­<lb></lb>vano con direzione orizontale, descrivevano una mezza parabola, e se con <lb></lb>direzione inclinata una parabola intera, esattamente corrispondente con ciò, <lb></lb>che Galileo aveva dimostrato dei moti proiettizi. </s>

<s>Perchè poi non dovessero <lb></lb>opporre alcuni alla teoria, non trovando la predetta corrispondenza coi fatti, <lb></lb>notava alcune diligenze, che lo sperimentatore non avrebbe dovuto trascu­<lb></lb>rare, e prima di tutto che il foro è da farsi in una lamina sottilissima e <lb></lb>piana, applicata alla bocca del tubo esterno, e talmente disposta, da tornar <lb></lb>perpendicolare alla tangente la curva, descritta dal getto nel punto in cui <lb></lb>comincia. </s>

<s>“ Reliquum vero exterioris tubi, usque ad initium aequaeductus, <lb></lb>debet esse capacissimum, quo enim laxius erit, eo exactius experimentum <lb></lb>evadet. </s>

<s>Quotiescumque autem aqua, per tubum latentem decurrens, per an­<lb></lb>gustias transire debuerit, falsa omnia reperientur. </s>

<s>Quemadmodum accidet <lb></lb>etiam si, prae nimio impetu, aqua, statim atque emissa est, in tenuissum <lb></lb>rorem dispergatur ” (ibid., pag. </s>

<s>198). </s></p><p type="main">

<s>Vedendo il Torricelli così ben confermato, per queste esperienze, che il <lb></lb>liquido esce dal foro aperto nelle pareti del vaso con tal impeto, quale si con­<lb></lb>verrebbe, se fosse sceso dal supremo livello; pensava fra sè medesimo come <lb></lb><figure id="id.020.01.3450.1.jpg" xlink:href="020/01/3450/1.jpg"></figure></s></p><p type="caption">

<s>Figura 194.<lb></lb>si potesse il fatto, sperimentato nei vasi, applicare <lb></lb>alle acque correnti, persuaso che non si dovevano <lb></lb>nemmen queste sottrarre alla legge universale <lb></lb>dei gravi. </s>

<s>E il pensiero lo condusse a riguardare <lb></lb>nell&#039;acqua stagnante un conato al moto, che <lb></lb>si attua rompendo la parete, o sollevando a un <lb></lb>tratto la cateratta dallo sbocco di un canale. </s></p><p type="main">

<s>Sia di questo canale rappresentata in CB (fig. </s>

<s>194) la sezione, e in CD <lb></lb>la cateratta, sopra gl&#039;infiniti punti della quale, come in D e in A, l&#039;acqua <pb xlink:href="020/01/3451.jpg" pagenum="412"></pb>esercitando il suo conato, uscirebbe in moto attuale per essi, supposti forati, <lb></lb>con gl&#039;impeti convenienti alle cadute naturali dalle altezze CD, CA, cosic­<lb></lb>chè, se sopra CL, intesa verticalmente eretta, s&#039;alzino le ordinate perpen­<lb></lb>dicolari DE, AF, a rappresentare le velocità respettive; queste staranno come <lb></lb>le radici delle altezze corrispondenti CD, CA. </s>

<s>Facendosi poi le medesime cò­<lb></lb>struzioni per tutti gli altri infiniti punti compresi fra CA, AD, verrà così <lb></lb>descritta la scala delle velocità, la quale dunque, concludeva il Torricelli il <lb></lb>suo ragionamento, non è in un triangolo supino, dove la poneva il Cava­<lb></lb>lieri, e tanto meno in un rettangolo, in che s&#039;argomentava di ridurla il Ca­<lb></lb>stelli, ma in una semiparabola. </s></p><p type="main">

<s>Venendo ora a istituire il confronto, fra ciò che si concludeva da così <lb></lb>fatti principii, e ciò che si annunziava nella seconda proposizione della scrit­<lb></lb>tura, sopra la quale si doveva dare il giudizio, il Torricelli v&#039;ebbe a notare <lb></lb>una sostanzial differenza. </s>

<s>Da A, nella medesima figura, risalga l&#039;acqua in C <lb></lb>a un&#039;altezza doppia: dimostra il Castelli, nella detta proposizione, che la ve­<lb></lb>locità del fiume in questo stato, alla velocità che aveva in quello, sta come <lb></lb>due a uno, o come quattro a due, mentre, per la legge dei cadenti appli­<lb></lb>cata all&#039;acqua, dovrebbe stare come quattro alla radice di due. </s></p><p type="main">

<s>Si rappresentino infatti, per rendere analiticamente più spedito il di­<lb></lb>scorso del Torricelli, le due velocità con le due semiparabole CED, CFA, <lb></lb>rappresentate per la medesima figura 194, e che chiameremo P, <emph type="italics"></emph>p.<emph.end type="italics"></emph.end> Essendo, <lb></lb>per le cose dimostrate nel libro <emph type="italics"></emph>De dimensione parabolae,<emph.end type="italics"></emph.end> P=2/3 ED.DC, <lb></lb><emph type="italics"></emph>p<emph.end type="italics"></emph.end>=2/3 AF.AC, avremo P:<emph type="italics"></emph>p<emph.end type="italics"></emph.end>=ED.DC:AF.AC. </s>

<s>E perchè DC=2AC <lb></lb>per supposizione, e per la nuova professata teoria, ED:AF=√DC:√AC; <lb></lb>dunque P:<emph type="italics"></emph>p<emph.end type="italics"></emph.end>=2√DC:√AC. </s>

<s>Che se facciasi AC uguale a due, e DC uguale <lb></lb>a quattro, se ne concluderà, estraendo dal quarto termine la radice, P:<emph type="italics"></emph>p<emph.end type="italics"></emph.end>= <lb></lb>2.2:√2, ossia che le velocità della corrente stanno, conforme a ciò che fu <lb></lb>pronunziato, come quattro alla radice di due. </s></p><p type="main">

<s>Un tal giudizio, fondato sulla differenza di così fatte conclusioni, fu dal <lb></lb>Torricelli riferito al principe Leopoldo, il quale temeva che potesse dispia­<lb></lb>cere al Castelli, e fu forse per questo motivo che consigliò il Torricelli stesso <lb></lb>a rivolgersi piuttosto al Cavalieri, tanto più che oramai sapevasi molto bene <lb></lb>essere invenzione di lui quel proprio modo di condurre la dimostrazione, in­<lb></lb>torno a cui cadevano i dubbi. </s>

<s>Infatti, sul finir di Ottobre del 1642, giungeva <lb></lb>a fra Bonaventura una lettera, scritta il dì 25 di quello stesso mese da Fi­<lb></lb>renze, nella quale il Torricelli, dop&#039;avere accennato a que&#039;vetri per i Tele­<lb></lb>scopi, de&#039;quali allora aveva piena la testa, così soggiungeva: “ Intesi poi <lb></lb>anche che ella s&#039;ingegnava di provare una conclusione intorno all&#039;acque, <lb></lb>nella quale ho qualche scrupolo, tanto nella conclusione, quanto nella dimo­<lb></lb>strazione. </s>

<s>Che la conclusione sia vera io lo credo, ma la difficoltà, quanto a <lb></lb>me, io non la so sciorre. </s>

<s>La proporrò pertanto a V. P., supplicandola a si­<lb></lb>gnificarmi brevemente se è una vanità. </s>

<s>” </s></p><p type="main">

<s>“ Suppongo che, se un tubo o altro vaso, sempre pieno d&#039;acqua AB <lb></lb>(fig. </s>

<s>195), sarà forato in diversi luoghi C, D, ecc.; suppongo che l&#039;acqua, <pb xlink:href="020/01/3452.jpg" pagenum="413"></pb>che esce dal foro C, abbia tant&#039;impeto, quanto avrebbe una goccia d&#039;acqua, <lb></lb>caduta dal livello A fino in C: cioè che gl&#039;impeti delle acque scaturienti <lb></lb><figure id="id.020.01.3452.1.jpg" xlink:href="020/01/3452/1.jpg"></figure></s></p><p type="caption">

<s>Figura 195.<lb></lb>da C, D ecc. </s>

<s>siano gli stessi, che di una gocciola caduta per gli <lb></lb>spazi AC, AD. </s>

<s>Questo si prova con alcune ragioni, e con più <lb></lb>di una esperienza. </s>

<s>Ne dirò una fatta in Roma esattamente, ed è <lb></lb>che, posti uguali li fori C, D, l&#039;acqua, che nel medesimo tempo <lb></lb>esce per C, a quella che esce per D, sta in sudduplicata pro­<lb></lb>porzione delle altezze AC, AD, e questo basta per la mia sup­<lb></lb>posizione. </s>

<s>” </s></p><p type="main">

<s>“ Ora, sia un&#039;acqua AB (nella precedente fig. </s>

<s>194) la quale <lb></lb>poi venga accresciuta tanto, che la sezione CB sia doppia d&#039;altezza della prima <lb></lb>AB. </s>

<s>Si crede che anco la velocità sarà cresciuta al doppio. </s>

<s>Ora discorro così: <lb></lb>Facciasi intorno al diametro CD una semiparabola. </s>

<s>L&#039;impeto adunque del velo <lb></lb>d&#039;acqua, che passa per A, è misurato dalla linea AF, <emph type="italics"></emph>et sic de reliquis.<emph.end type="italics"></emph.end> Però <lb></lb>tutti gl&#039;impeti della sezione CB, a tutti gl&#039;impeti della sezione AB, saranno <lb></lb>come la semiparabola ECD, alla semiparabola FCA, cioè come quattro alla <lb></lb>radice di due, e non a due come si crede. </s>

<s>” </s></p><p type="main">

<s>“ So che questo mio è qualche paralogismo, in materia tanto difficile, <lb></lb>però non ne fo capitale alcuno. </s>

<s>So bene certo che sarà subito scoperto dal <lb></lb>perspicacissimo ingegno di V. P. </s>

<s>Non mi sono neanco spiegato bene intera­<lb></lb>mente, perchè troppa sarebbe stata la prolissità. </s>

<s>Riverisco ecc. </s>

<s>” (MSS Gal. </s>

<s><lb></lb>Disc., T. XL, fol. </s>

<s>119, 29). </s></p><p type="main">

<s>Notabile cosa è che sebbene, nella loro concisione, le parole del Torri­<lb></lb>celli riescano a tutti noi così chiare, al Cavalieri nulladimeno facessero dav­<lb></lb>vero l&#039;effetto di chi non s&#039;è neanco spiegato bene interamente, come appa­<lb></lb>risce dalla seguente risposta, fatta pochi giorni dopo, per lettera del dì 29 Ot­<lb></lb>tobre da Bologna: “ Circa l&#039;acqua non sono ne anch&#039;io lontano dal suo pen­<lb></lb>siero di credere che non sia così certa la conclusione, nè la supposta dimo­<lb></lb>strazione, da me mandata al padre don Benedetto, siccome egli potè vedere <lb></lb>i dubbi, che io avevo nella medesima lettera, che gli scrissi sopra questo <lb></lb>fatto. </s>

<s>Vero è che la sua supposizione non mi leva affatto l&#039;assenso, poichè, <lb></lb>stante il suo esempio del vaso pieno d&#039;acqua forato in diverse altezze, parmi <lb></lb>che ella consideri nell&#039;acqua solo l&#039;impeto, cagionato dal premer dell&#039;acqua <lb></lb>superiore mediante la di lei gravezza. </s>

<s>Ma nell&#039;acqua de&#039;fiumi parmi che, <lb></lb>oltre quella, vi sia ancora da considerare l&#039;impeto o velocità, che conferisce <lb></lb>l&#039;acqua inferiore alla superiore, onde un tal velo d&#039;acqua parmi che, non <lb></lb>solo alteri il detto impeto, cagionato dalla gravezza dell&#039;acqua superiore, ma <lb></lb>anco quello, che gli conferisce l&#039;acqua inferiore, che si muove per la pen­<lb></lb>denza del letto, ciò che non mi pare accada nel vaso. </s>

<s>E perciò resto ancora <lb></lb>irresoluto in questo negozio, non avendo avuto tempo d&#039;applicarvi, ma credo <lb></lb>che lei, con la sua sottigliezza, chiarirà il tutto ” (ivi, T. LXI, fol. </s>

<s>132, 33). </s></p><p type="main">

<s>Apparisce di qui manifesto che il Cavalieri non era entrato addentro al <lb></lb>pensiero del Torricelli, il quale non consisteva nel considerare i conati, pro­<lb></lb>dotti dalla gravità dell&#039;acqua contro le pareti del vaso, o quelle che, con vo-<pb xlink:href="020/01/3453.jpg" pagenum="414"></pb>cabolo non usato allora, si dicono <emph type="italics"></emph>forze morte,<emph.end type="italics"></emph.end> ma nel considerare il moto <lb></lb>attuale, o le forze che, per effetto di questa attuazione, diventano <emph type="italics"></emph>vive.<emph.end type="italics"></emph.end> La <lb></lb>proposta inaspettata, e la fretta dell&#039;esaminarla, dovettero esser le cause, <lb></lb>per cui il valent&#039;uomo non senti la fecondità del pensiero torricelliano, com­<lb></lb>prendente in sè il vero modo di misurare le forze vive dai quadrati delle <lb></lb>velocità, e l&#039;applicazione del principio dell&#039;uguaglianza delle pressioni. </s>

<s>Ma <lb></lb>rimane tuttavia a far le maraviglie come mai non s&#039;avvedesse che la sua <lb></lb>risposta, non solamente non faceva al proposito, ma che di più contradiceva <lb></lb>alle sue proprie intenzioni. </s>

<s>Se il pensiero infatti del Torricelli fosse stato <lb></lb>quello di considerar solamente l&#039;impeto, cagionato dal premer che fa l&#039;acqua <lb></lb>superiore contro l&#039;inferiore, mediante la di lei gravezza; essendo questa gra­<lb></lb>vezza proporzionale al numero degli strati, non avrebbe potuto altro conclu­<lb></lb>dere da ciò, se non che le velocità stanno come le altezze, e invece ne con­<lb></lb>cludeva che stanno come le radici delle altezze. </s>

<s>Se poi si dice che questa <lb></lb>conclusione è solamente applicabile alle acque stagnanti, e no alle correnti, <lb></lb>nelle quali all&#039;impeto cagionato dalla gravezza delle acque superiori s&#039;ag­<lb></lb>giunge quello, che conferisce a loro il moto delle acque inferiori; si viene <lb></lb>a concedere che in esse acque correnti le velocità non siano proporzionali <lb></lb>alle altezze, come nelle stagnanti, che contradice all&#039;intenzione del rispon­<lb></lb>dente, qual era di mantener la verità della prima proposta contro la nuova. </s></p><p type="main">

<s>Dei dubbi venuti da Firenze dando parte il Cavalieri al Castelli, gli fa­<lb></lb>ceva insieme premura di pensare a una soluzione migliore della sua, di che <lb></lb>però il Lombardini non ha speranza, perchè, se noi dicemmo che il Cava­<lb></lb>lieri non riuscì a trovarla per la fretta, egli crede che il Castelli non ci <lb></lb>avrebbe potuto nemmen pensare, per trovarsi, a cagione della vecchiaia, la <lb></lb>mente <emph type="italics"></emph>alquanto indebolita. (Dell&#039;origine ecc.,<emph.end type="italics"></emph.end> Discorso cit., pag. </s>

<s>40). Per <lb></lb>conferma di che il Lombardini dice che, sebbene fosse all&#039;Autore del secondo <lb></lb>libro della Misura delle acque correnti nota la vera legge torricelliana, egli <lb></lb>attese nonostante, nella seconda proposizione, a dimostrare che le velocità <lb></lb>stanno, non come le radici, ma come le semplici altezze. </s>

<s>Che poi il Castelli <lb></lb>conoscesse allora la vera legge torricelliana l&#039;argomenta il Lombardini da <lb></lb>quelle parole, ch&#039;egli, a pag. </s>

<s>4 del citato Discorso storico, trascrive dalla <lb></lb>Considerazione seconda dopo la V proposizione, dove così soggiunge il Ca­<lb></lb>stelli, avendo prima notati i disordini, che si commettono nelle operazioni <lb></lb>idrauliche tutti i giorni, “ i quali disordini saranno fuggiti dall&#039;ingegnere, <lb></lb>instruito delle cose sopradette, particolarmente ove a queste notizie aggiun­<lb></lb>gesse la cognizione della Filosofia e Matematica, conforme a quello, che al­<lb></lb>tamente ha penetrato il signor Galileo, e dopo lui, passando più oltre, il <lb></lb>signor Evangelista Torricelli, matematico del serenissimo Granduca di To­<lb></lb>scana, <emph type="italics"></emph>il quale sottilmente e maravigliosamente tutta questa materia del <lb></lb>moto ha trattata. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Richiama il Lombardini particolarmente l&#039;attenzion dei lettori sopra <lb></lb>queste ultime parole, quasi volessero significare che il Torricelli, insieme con <lb></lb>tutte le altre materie del moto, avesse in fin d&#039;allora sottilmente e maravi-<pb xlink:href="020/01/3454.jpg" pagenum="415"></pb>gliosamente trattato anche dell&#039;acqua. </s>

<s>L&#039;inganno dell&#039;interpetrazione è sco­<lb></lb>perto già dalla storia, per illustrar meglio la quale giova rammemorare che, <lb></lb>essendo stato il Torricelli in Roma discepolo del Castelli, e attendendovi poi <lb></lb>per suo proprio esercizio a illustrare e a promovere la Scienza meccanica, <lb></lb>studiata ne&#039;Dialoghi delle due Scienze nuove; gli vennero composti due libri, <lb></lb>uno <emph type="italics"></emph>De motu gravium naturaliter descendentium,<emph.end type="italics"></emph.end> e l&#039;altro <emph type="italics"></emph>De motu pro­<lb></lb>iectorum,<emph.end type="italics"></emph.end> che veduti dal Maestro gli stimò degni d&#039;essere presentati allo <lb></lb>stesso Galileo, a cui scriveva da Roma il dì 2 Marzo 1641: “ Spero (nel <lb></lb>venire a Firenze a riverire V. S.) di portargli un libro, e forse ancora il se­<lb></lb>condo, fatto da un mio discepolo, il quale, avendo avuti i primi principii di <lb></lb>Geometria dieci anni sono alla mia Scuola, ha poi fatto tal progresso, che <lb></lb>ha dimostrate molte proposizioni di quelle <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> dimostrate già da V. S., <lb></lb>ma diversamente ” (Alb. </s>

<s>X, 407, 8). Il dì 15 del detto mese di Marzo par­<lb></lb>tiva infatti il Castelli da Roma, portandosi nel baule i due libri manoscritti, <lb></lb>de&#039;quali fece pochi giorni appresso la presentazione, insieme con una lettera <lb></lb>del Torricelli, nella quale si scusava delle imperfezioni, specialmente rima­<lb></lb>ste nella seconda parte dell&#039;opera, trattante <emph type="italics"></emph>De motu proiectorum,<emph.end type="italics"></emph.end> non rico­<lb></lb>piata “ ma scritta per la prima volta con molta fretta ” (ivi, pag. </s>

<s>413). </s></p><p type="main">

<s>Ecco quali sono i libri in materia di moto, da applicarsi utilmente al­<lb></lb>l&#039;acqua, de&#039;quali intendeva parlare il Castelli, nel luogo sopra trascritto dal <lb></lb>Lombardini. </s>

<s>Ma l&#039;applicazione, benchè presentita, e della quale, nella lettera <lb></lb>allo Staccoli sopra il fiume Bisenzio, s&#039;avevano alcuni esempi; non era stata <lb></lb>fatta ancora nel 1641: non era cioè stata fatta ancora, alla seconda parte del <lb></lb>trattato torricelliano <emph type="italics"></emph>De motum geavium<emph.end type="italics"></emph.end> presentato manoscritto a Galileo, <lb></lb>l&#039;aggiunta <emph type="italics"></emph>De motu aquarum,<emph.end type="italics"></emph.end> alla quale occorsero, tra il Settembre e l&#039;Ot­<lb></lb>tobre del 1642, come vedemmo, il principio e l&#039;occasione, e non prima del 1644 <lb></lb>fu data dall&#039;Autore in Firenze alla luce. </s></p><p type="main">

<s>Essendo dunque un fatto che, quando il Castelli presentò il suo mano­<lb></lb>scritto al principe Leopoldo di Firenze, la legge degli efflussi non era stata <lb></lb>dimostrata ancora dal Torricelli, il quale anzi dall&#039;esame del detto ma­<lb></lb>noscritto prese motivo di far la scoperta; riman privo del suo principale ar­<lb></lb>gomento il giudizio del Lombardini, a cui ne prevale un altro tutt&#039;affatto <lb></lb>contrario, che cioè il Castelli serbava allora tutta la vigoria della mente, <lb></lb>benchè temperata dal senno e dalla prudenza senile, come apparirà dalla <lb></lb>storia, quale sia ora a noi lecito ordire sopra la trama offertaci dai do­<lb></lb>cumenti. </s></p><p type="main">

<s>Informato dal Cavalieri di tutto ciò, ch&#039;era passato fra lui e il Torri­<lb></lb>celli, relativamente alle proporzioni da assegnarsi tra le velocità e le altezze <lb></lb>nel moto delle acque, il Castelli, a cui troppo premeva la questione, si dette <lb></lb>a esaminarla con tutta la diligenza. </s>

<s>Era naturale che in questo esame occor­<lb></lb>resse anche a lui a fare la distinzione, fra l&#039;acqua fluente dai vasi, e la cor­<lb></lb>rente per le sezioni dei fiumi. </s>

<s>In proposito del primo caso deve essersi sov­<lb></lb>venuto del pensiero, che otto anni fa l&#039;Arrighetti gli aveva confidato come <lb></lb>una sua fantasia, da non farne conto, ma che ora vedeva esaltata alla di-<pb xlink:href="020/01/3455.jpg" pagenum="416"></pb>gnità di teorema; e dall&#039;altra parte aveva in Roma presente quello stesso <lb></lb>Magiotti, da cui s&#039;era con le sue esperienze così efficacemente cooperato a <lb></lb>confermare la verità della nuova proposta. </s>

<s>Spettatore di così fatte esperienze, <lb></lb>non poteva il Castelli dubitare che le copie dell&#039;acqua, raccolta dai fori aperti <lb></lb>nelle cassette parallelepipede di rame preparate dal Magiotti, non facessero <lb></lb>necessariamente argomentare esser le velocità degli efflussi proporzionali alle <lb></lb>radici delle altezze dei livelli. </s>

<s>Dall&#039;altro canto il Magiotti spettatore delle <lb></lb>esperienze, fatte nelle stanze terrene dell&#039;abbazia di S. Callisto, non poteva <lb></lb>negare che, dal vedersi far la medesima altezza nel fiumicello, sia da una, <lb></lb>sia da quattro, sia da nove cannelle aperte, o dal veder che se una cannella <lb></lb>sola faceva un&#039;altezza, aggiungendovene tre, cinque, sette, l&#039;altezza si faceva <lb></lb>solamente doppia, tripla, quadrupla; non si dovesse necessariamente argo­<lb></lb>mentarne che le velocità della corrente stanno come le semplici altezze delle <lb></lb>sezioni. </s></p><p type="main">

<s>Strigar questo nodo non era davvero da menti indebolite, e il Castelli <lb></lb>lo strigava col vigore assennato della sua mente, ripensando che, poichè da <lb></lb>due fatti certissimi s&#039;avevano due conclusioni diverse; diverso dovess&#039;essere <lb></lb>il modo del fluire l&#039;acqua dai vasi o del correre per i canali. </s>

<s>Ma poi, riflet­<lb></lb>tendo che costante dev&#039;esser il modo dell&#039;operar la Natura in ogni genere <lb></lb>di gravi, ne ebbe a concludere che universalmente si verifica la legge delle <lb></lb>velocità proporzionali alle radici delle altezze, ma che nelle acque correnti <lb></lb>questa medesima legge viene alterata, sia per non esser l&#039;acqua un corpo <lb></lb>unito, come gli aveva detto il Baliani, sia per conferire gli strati inferiori <lb></lb>al moto de&#039;superiori, come ora gli veniva dicendo il Cavalieri, sia per altre <lb></lb>ragioni inescogitabili a lui. </s></p><p type="main">

<s>Dietro ciò si proponeva di rimetter mano al secondo libro delle Acque <lb></lb>correnti, in cui si darebbe per legge universale delle velocità quella, che re­<lb></lb>sultava dalle nuove speculazioni e dalle esperienze del Torricelli. </s>

<s>Quanto poi <lb></lb>alla proposizione seconda, avrebbe avvertito che, secondo la teoria, la scala <lb></lb>delle velocità nelle varie parti della corrente dovrebb&#039;essere una parabola, <lb></lb>ma in effetto, qualunque siasi la ragione, è un triangolo, non supino, ma <lb></lb>con la base in basso. </s>

<s>O altrimenti: se un fiume, movendosi con una tal ve­<lb></lb>locità per un suo regolatore, avrà una data altezza viva, e poi per nuova <lb></lb>acqua crescerà il doppio; per la teoria la velocità nel primo stato, alla ve­<lb></lb>locità nel secondo, dovrebbe avere la proporzione della radice di due a quat­<lb></lb>tro, ma in effetto quella proporzione si troverà essere invece di due e quat­<lb></lb>tro, ossia del semplice doppio. </s>

<s>Avrebbe voluto trattar di ciò a voce col Torricelli, <lb></lb>e non potendo far altro, significava intanto così, per lettera, pubblicata in parte <lb></lb>dal Bonaventuri, i suoi desiderii: “ Io avrei bisogno estremo di essere con <lb></lb>V. S., per dare l&#039;ultima mano al secondo libro Della misura delle acque cor­<lb></lb>renti, non già per istamparlo adesso, ma per finirlo in termine di poterlo <lb></lb>stampare, occorrendo come spero ch&#039;io sia chiamato a Venezia. </s>

<s>Basta, se il <lb></lb>caso succederà, passerò per Firenze e ci vedremo. </s>

<s>Mi pare d&#039;avere scoperto <lb></lb>una mano di cose totalmente incognite, e di grandissimo momento, e di più <pb xlink:href="020/01/3456.jpg" pagenum="417"></pb>vedo il campo aperto per scoprimenti maggiori, ma conosco che la materia <lb></lb>supera la mia debolezza. </s>

<s>V. S. tenga conto delle cose, che ella va ritrovando <lb></lb>in questa materia d&#039;acque, perch&#039;io penso d&#039;ornare il mio libro col nome, <lb></lb>e con l&#039;opere di V. S., come, piacendo a Dio, dirò a bocca ” (<emph type="italics"></emph>Prefaz. </s>

<s>alle <lb></lb>Lezioni accad. </s>

<s>del Torricelli,<emph.end type="italics"></emph.end> Milano 1823, pag. </s>

<s>59). </s></p><p type="main">

<s>Di quel che deve aver detto a bocca il Castelli a colui, ch&#039;essendogli <lb></lb>stato discepolo ora si faceva collega de&#039;suoi studi, e prometteva di divenirne <lb></lb>maestro; siamo oramai prevenuti: deve avergli confessato che il modo di <lb></lb>dimostrare la sua seconda proposizione conteneva un paralogismo, ma che <lb></lb>non poteva cader dubbio sopra la verità di lei, essendo il resultato d&#039;espe­<lb></lb>rienze ripetute cento volte alla presenza di tanti, fra&#039;quali, a farne testimo­<lb></lb>nianza, il Magiotti solo sarebbe bastato per tutti. </s>

<s>Il Torricelli, che per sola <lb></lb>teoria aveva intorno a quella seconda proposizione concluso i suoi dubbi, se <lb></lb>n&#039;ebbe a persuader facilmente, e tanto è ciò vero che, mettendosi poi a <lb></lb>esplicare nell&#039;appendice <emph type="italics"></emph>De motu aquarum<emph.end type="italics"></emph.end> quel suo concetto, significato <lb></lb>nella lettera al Cavalieri, applica la nuova legge idrodinamica a&#039;soli efflussi <lb></lb>dai vasi, o agli zampilli dai piccoli fori, lasciando intatta la questione dei <lb></lb>fiumi, per la quale si rimetterebbe a ciò che, pubblicando il suo manoscritto <lb></lb>corretto, ne deciderebbe il Castelli. </s>

<s>E così, come prudentemente s&#039;era intorno <lb></lb>a ciò governato il Maestro, fecero, secondo si narrerà nel capitolo appresso, <lb></lb>i discepoli, i quali, mentre da una parte attendevano a esplicare i teoremi di <lb></lb>lui concernenti le cadute accelerate delle gocciole dal supremo livello verso <lb></lb>il foro, e il moto parabolico, che da una tale accelerazione consegue; accet­<lb></lb>tarono dall&#039;altra le verità sperimentali, descritte nel secondo libro delle Acque <lb></lb>correnti: verità, che si mantennero salve nella scienza, infino al Guglielmini <lb></lb>e all&#039;Herman, primi a rimettere in onore la scala parabolica, e perciò a re­<lb></lb>stituire alla prima universalità, proposta nella detta lettera al Cavalieri, la <lb></lb>Scienza idrodinamica, rimastasi instituita solo a mezzo in quell&#039;appendice <lb></lb>del Torricelli, dalla quale si vuole incominciare il seguente nostro discorso. </s></p><pb xlink:href="020/01/3457.jpg"></pb><p type="main">

<s><emph type="center"></emph>CAPITOLO VII.<emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph><emph type="bold"></emph>Della nuova istituzione idrodinamica del Torricelli <lb></lb>e delle prime promozioni di lei<emph.end type="bold"></emph.end><emph.end type="center"></emph.end></s></p><p type="main">

<s><emph type="center"></emph>SOMMARIO<emph.end type="center"></emph.end></s></p><p type="main">

<s>I. </s>

<s>Del trattato torricelliano <emph type="italics"></emph>De motu aquarum,<emph.end type="italics"></emph.end> illustrato e ampliato dal Viviani. </s>

<s>— II. Dell&#039;Idrodi­<lb></lb>namica torricelliana, nelle Cogitazioni fisico-matematiche del Mersenno, nelle Epistole del Car­<lb></lb>tesio, e nel trattato <emph type="italics"></emph>De motu liquidorum<emph.end type="italics"></emph.end> di G. B. Baliani. </s>

<s>— III. Dell&#039;Idrodinamica torricel­<lb></lb>liana, esclusa dalle applicazioni al corso del fiumi, come principalmente resulta dalla storia <lb></lb>delle correzioni, che si pensò di fare all&#039;Idrometria del Castelli. </s></p><p type="main">

<s><emph type="center"></emph>I.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Benchè quella, che l&#039;Arrighetti chiamava e forse anche credeva una <lb></lb>fantasia, sembrasse prendere aspetto di realtà, per le varie esperienze del <lb></lb>Magiotti, nonostante il Torricelli andava con passo incerto, in proporre al <lb></lb>pubblico una cosa tanto nuova. </s>

<s>Il dubbio, che gli tenzonava nella mente, <lb></lb>l&#039;esprimeva così con queste parole: “ Caeterum si quis, praedictis rationi­<lb></lb>bus non acquiescat, videat an inter sequentes propositiones ullam probet: <lb></lb>quod, si ita erit, facile per resolutionem, ex approbata propositione, primam <lb></lb>suppositionem demonstrabimus. </s>

<s>Sin minus, totam hanc Appendicem de motu <lb></lb>aquarum, vel saltu praetermittat, vel funditus e libello evellat, quod equidem <lb></lb>libentissime concedo ” (Op. </s>

<s>geom. </s>

<s>cit., P. I, pag. </s>

<s>193). La sincerità delle <lb></lb>quali parole sembra a noi confermata dal fatto che, nel dimostrare le XIV pro­<lb></lb>posizioni, delle quali si compone la detta Appendice; procede l&#039;Autore con <lb></lb>quella fretta, che sogliono usare le persone discrete, nel proporre un partito, <lb></lb>a cui s&#039;aspettano che pochi faranno accoglienza. </s></p><p type="main">

<s>Invece avvenne tutto il contrario: son già passati più di due secoli e <lb></lb>mezzo, e in fronte a tutti i trattati d&#039;Idrodinamica, in qualunque lingua <pb xlink:href="020/01/3458.jpg" pagenum="419"></pb>dettati, e di qualunque nazione siano gli autori, è scritto solennemente il <lb></lb>nome del Torricelli. </s>

<s>L&#039;appendice di lui, tutt&#039;altro ch&#039;essere svelta <emph type="italics"></emph>funditus<emph.end type="italics"></emph.end><lb></lb>dal trattato <emph type="italics"></emph>De motu proiectorum,<emph.end type="italics"></emph.end> fu subito coltivata con tanta industria, che <lb></lb>l&#039;umile rampollo giunse presto a emulare la stessa pianta madre, a lato alla <lb></lb>quale ora grandeggia nel campo della scienza. </s></p><p type="main">

<s>Fra que&#039;primi cultori sarebbero da annoverare i Francesi, se dovesse <lb></lb>la Storia starsene solamente a ciò, che è noto per i pubblici documenti. </s>

<s>Ma <lb></lb>le private e, per dir così, domestiche notizie, che ci sono rimaste, confer­<lb></lb>mano, com&#039;è da aspettarsi, quel legittimo primato de&#039;Nostri, che furono <lb></lb>amici e discepoli del Torricelli, il più operoso fra i quali, come in ogni altro <lb></lb>proposito, così e in questo, ci si presenta il Viviani. </s>

<s>Fra i manoscritti di lui <lb></lb>gli argomenti idrodinamici, e le questioni d&#039;Idrometria, son quelle, che vi si <lb></lb>trattano più diffusamente. </s>

<s>Sembra anzi a noi di scoprire, per questi studi <lb></lb>intorno al moto dell&#039;acque, una certa predilezione, natagli forse dal trovarsi <lb></lb>aperto innanzi un così largo campo, da poter nel percorrerlo misurarvi den­<lb></lb>tro la validità delle sue proprie forze. </s>

<s>Basti dire che le principali proposi­<lb></lb>zioni d&#039;Idrodinamica, di che tanto onore si fecero il Guglielmini e il Grandi, <lb></lb>si trovano tutte premostrate in quei manoscritti. </s>

<s>Chi proseguirà, senza stan­<lb></lb>carsi, la lettura di questa storia, troverà di quel che s&#039;è annunziato la più <lb></lb>piena conferma, ma qualunque sia l&#039;importanza, e qualunque il merito del­<lb></lb>l&#039;opera data dal Viviani all&#039;Idrometria, egli non riconosce altro maestro che <lb></lb>il Torricelli, dallo studio di cui confessa essergli venute le inspirazioni, le <lb></lb>prime delle quali cominciano da quel mettersi, ch&#039;egli fece intorno ad am­<lb></lb>pliare l&#039;appendice <emph type="italics"></emph>De motu aquarum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Interrotto l&#039;esercizio, e tante volte ripreso, scriveva sul primo foglio, che <lb></lb>gli veniva a mano, ora frettolosamente, ora a stento, le proposizioni da ag­<lb></lb>giungersi, e i commenti da farsi, e così il materiale, benchè disperso, non <lb></lb>solamente fra le varie pagine, ma fra i varii volumi manoscritti, in qualche <lb></lb>modo s&#039;è potuto ritrovare, almeno nella sua parte migliore. </s>

<s>Ma è difficile <lb></lb>indovinare la forma, che il Viviani stesso aveva intenzion di dare al nuovo <lb></lb>trattato. </s>

<s>Alcune proposizioni sono scritte in latino, altre in volgare, ma sem­<lb></lb>bra che dovess&#039;esser tutto dettato in questa lingua, nella quale si trova es­<lb></lb>sere stata già distesa una specie di prefazione. </s>

<s>Comunque sia, l&#039;ufficio no­<lb></lb>stro di storici, e non di editori, concedendoci libertà di riferire i documenti <lb></lb>con qual ordine meglio ci piace, ne abbiamo scelto uno, che consiste nel­<lb></lb>l&#039;inserire fra le proposizioni torricelliane le relative soggiunte dal Viviani, <lb></lb>segnate con numeri progressivi, senza tralasciar la scrittura, che, quale ora <lb></lb>da noi si produce, doveva servir di proemio all&#039;opera riformata. </s></p><p type="main">

<s>“ L&#039;acutissimo dei geometri, Evangelista Torricelli necessitato dalla forza <lb></lb>del vero a seguitar la dottrina del mio Galileo, primo e vero scrutatore della <lb></lb>Natura, e delle proprietà dei moti equabile, naturale e violento; suppose che <lb></lb>l&#039;acqua, forzata dal carico della propria altezza, nell&#039;istante del suo scap­<lb></lb>pare da qualche foro di un vase, in cui ella si trovi, abbia in sè quell&#039;im­<lb></lb>peto stesso o velocità, che avrebbe un grave libero o una gocciola di detta <pb xlink:href="020/01/3459.jpg" pagenum="420"></pb>acqua, se ella, col progresso dell&#039;accelerazione già assegnata dal medesimo <lb></lb>Galileo, cadesse naturalmente dal suo supremo livello, fino all&#039;orifizio del <lb></lb>foro d&#039;onde ella scappa. </s>

<s>” </s></p><p type="main">

<s>“ Questo tal supposto s&#039;ingegnò il Torricelli di comprovarlo coll&#039;espe­<lb></lb>rienza, mostrando che, quando nella sponda di un vaso, tenuto sempre pieno <lb></lb>d&#039;acqua, sta inserita orizontalmente una cannella prossima al fondo, la qual <lb></lb>serrata all&#039;estremità abbia un solo angustissimo foro ben tondo sul colmo <lb></lb>del suo dorso, e che questo, tenuto chiuso col polpastrello di un dito, a ora <lb></lb>a ora si va serrando e subito sturando; quella prima minutissima gocciola, <lb></lb>che ne schizza in aria, s&#039;alza poco men che al piano del sopraddetto livello, <lb></lb>massime, quando l&#039;ampiezza del vaso sia molta, rispetto a quella del foro, <lb></lb>e poca sia l&#039;altezza dell&#039;acqua, ponendo egli in considerazione che, del non <lb></lb>arrivarvi precisamente, nei casi di maggiori altezze, ne sia cagione la mag­<lb></lb>gior resistenza, che trova l&#039;acqua nel passare per la corpulenza dell&#039;aria. </s>

<s>Con <lb></lb>che, se invece di acqua si pigliasse, per far questa prova, dell&#039;argento vivo, <lb></lb>quella sua prima gocciola che sale in su, come in sè stessa tante volte più <lb></lb>grave dell&#039;acqua, e perciò più atta a ritenere per più tempo l&#039;impeto con­<lb></lb>ceputo, e a superar la resistenza dell&#039;aria; si osserverebbe esattamente ar­<lb></lb>rivare al livello interno del vaso. </s>

<s>Lo che ha molto del verisimile, imperoc­<lb></lb>chè tale impedimento manca bensì all&#039;acqua premente dentro il vaso, ma <lb></lb>non già alla spremuta fuori e fendente la corpulenza dell&#039;aria. </s>

<s>Tanto più <lb></lb>che e&#039;si vede che nell&#039;altro caso, quando cioè quell&#039;orifizio va su su accom­<lb></lb>pagnato con un cannello fin sopra il piano dell&#039;acqua del vaso congiuntogli, <lb></lb>questa allora non ha difficoltà a sormontare appunto fino a quel piano, sia <lb></lb>pure il vaso e il cannello alto e lungo quanto si voglia. </s>

<s>” </s></p><p type="main">

<s>“ Se dunque la prima gocciola sola vi arriva, e se, per la Scienza ga­<lb></lb>lileiana del moto naturale dei gravi, qualunque di questi, rimossi gl&#039;impe­<lb></lb>dimenti, quando si solleva da basso in alto si parte con un impeto eguale <lb></lb>a quello, che egli acquisterebbe per altrettanta caduta dalla quiete; ciò è <lb></lb>segno che quella gocciola saliente, nell&#039;atto dell&#039;uscir da quel foro angusto, <lb></lb>si trovò imbevuta dell&#039;impeto stesso, che nel cader dalla medesima altezza <lb></lb>ella vi averebbe naturalmente acquistato. </s>

<s>” </s></p><p type="main">

<s>“ Con tal supposto dunque, assai chiaro, diedi ancor io principio a questo <lb></lb>trattato più ampio, in supplemento del promosso dal Torricelli ” (MSS. Gal. <lb></lb><figure id="id.020.01.3459.1.jpg" xlink:href="020/01/3459/1.jpg"></figure></s></p><p type="caption">

<s>Figura 196.<lb></lb>Disc., T. CXVIII, fol. </s>

<s>16). E comincia dal dimo­<lb></lb>strare alcune proposizioni illustrative di quelle, <lb></lb>che ricorrono in ordine le ultime dello stesso <lb></lb>trattato, che s&#039;intendeva di ampliare. </s>

<s>Secondo il <lb></lb>nostro sopra espresso proposito, invece, comince­<lb></lb>remo dal riferire le prime proposizioni torricel­<lb></lb>liane, dipendenti, secondo la fatta supposizione, <lb></lb>dal moto parabolico, così ordinatamente pronun­<lb></lb>ziate colle parole medesime dell&#039;Autore. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO I. — <emph type="italics"></emph>Dato tubo AB<emph.end type="italics"></emph.end> (fig. </s>

<s>196), <pb xlink:href="020/01/3460.jpg" pagenum="421"></pb><emph type="italics"></emph>semper pleno et apte perforato foraminibus C, D, E, hoc est quae sint <lb></lb>figurae circularis, sitque illorum ductus horizontalis, hoc est in tenui la-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3460.1.jpg" xlink:href="020/01/3460/1.jpg"></figure></s></p><p type="caption">

<s>Figura 197.<lb></lb><emph type="italics"></emph>mella planá perpendiculari, datoque horizonte quolibet <lb></lb>BG; invenire amplitudinem uniuscuiusque parabolae ”<emph.end type="italics"></emph.end><lb></lb>(Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>194). </s></p><p type="main">

<s>“ PROPOSITIO II. — <emph type="italics"></emph>Dato dolio, sive tubo AB<emph.end type="italics"></emph.end> (fig. </s>

<s>197), <lb></lb><emph type="italics"></emph>quod apte perforatum sit in C, et emissionem faciat CD, <lb></lb>invenienda sit aqua in tubo latentis libella horizontalis, <lb></lb>sive superficies suprema ”<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>195). </s></p><p type="main">

<s>“ PROPOSITIO III. — <emph type="italics"></emph>Si tubus AB<emph.end type="italics"></emph.end> (in eadem figura) <lb></lb><emph type="italics"></emph>apte perforetur ubicumque in C, emissio fluentis aquae <lb></lb>coni rectanguli superficiem continget, cuius axis sit ipse tubus, vertex vero <lb></lb>sit in aquae libella ”<emph.end type="italics"></emph.end> (ibid.). </s></p><p type="main">

<s>“ PROPOSITIO IV. — <emph type="italics"></emph>Aquarum, ex tubo AB<emph.end type="italics"></emph.end> (fig. </s>

<s>198), <emph type="italics"></emph>perforato, erum­<lb></lb>pentium, velocitates sunt ut lineae in parabola applicatae ad suam unius­<lb></lb>cuiusque sublimitatem ”<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>196). <lb></lb><figure id="id.020.01.3460.2.jpg" xlink:href="020/01/3460/2.jpg"></figure></s></p><p type="caption">

<s>Figura 198.</s></p><p type="main">

<s>Tutte queste quattro, così proposte, vengono con <lb></lb>gran facilità e speditezza dimostrate e risolute die­<lb></lb>tro le note proprietà dei moti parabolici. </s>

<s>Basta infatti <lb></lb>risovvenirsi che la metà dell&#039;ampiezza è media pro­<lb></lb>porzionale fra l&#039;altezza e la sublimità, per veder che <lb></lb>il seno EI, nella figura 196, medio proporzionale fra <lb></lb>il segmento AE, sublimità, e il segmento EB, al­<lb></lb>tezza della parabola EG; è quello, che risolve il <lb></lb>primo problema. </s>

<s>Il secondo altresì è risoluto dal <lb></lb>medesimo principio, perchè, chiamate A, M, S l&#039;altezza, la metà dell&#039;am­<lb></lb>piezza, e la sublimità, dall&#039;equazione A:M=M:S, nella quale A e M <lb></lb>son note, s&#039;ha direttamente S sublimità cercata. </s>

<s>La verità della III pro­<lb></lb>posizione dipende dalle note proprietà della tangente alla parabola, la qual <lb></lb>tangente, che sia per esempio AD nella figura 197, rivolgendosi intorno <lb></lb>all&#039;asse AB, descrive la superficie di un cono. </s>

<s>La IV infine è una conse­<lb></lb>guenza immediata del supposto principio sperimentale, perchè, se le velocità <lb></lb>in C e in D, rappresentate dalla figura 198, son proporzionali alle radici <lb></lb>delle altezze AC, AD; sono anche proporzionali alle linee CE, DF, ordina­<lb></lb>tamente applicate a qualunque parabola che, col vertice in A, intorno al­<lb></lb>l&#039;asse AD sia descritta. </s></p><p type="main">

<s>Di qui è che, stando le quantità in ragion composta delle velocità e <lb></lb>delle sezioni, essendo i fori C, D uguali, staranno in ragion semplice delle <lb></lb>radici delle altezze, e in reciproca ragione di queste saranno le sezioni, se le <lb></lb>quantità si suppongano uguali: corollari espressamente notati dal Torricelli, <lb></lb>perchè continuamente si richiamano come principii, da cui son per dipendere le <lb></lb>future conclusioni, la prima fra le quali, che in ordine succede, è la seguente: </s></p><p type="main">

<s>“ PROPOSITIO V. — <emph type="italics"></emph>Si tubus AB<emph.end type="italics"></emph.end> (fig. </s>

<s>199) <emph type="italics"></emph>cylindricus, sive prismati­<lb></lb>cus, perforatus in fundo B fluat, neque alius humor superinfundatur,<emph.end type="italics"></emph.end><pb xlink:href="020/01/3461.jpg" pagenum="422"></pb><emph type="italics"></emph>velocitates supremae superficiei humoris latentis decrescent cum eadem <lb></lb><figure id="id.020.01.3461.1.jpg" xlink:href="020/01/3461/1.jpg"></figure></s></p><p type="caption">

<s>Figura 199.<lb></lb>ratione, qua decrescunt etiam lineae ordinatim ap­<lb></lb>plicatae in parabola BD, quae axem habeat BA, <lb></lb>verticem vero B ”<emph.end type="italics"></emph.end> (ibid., pag. </s>

<s>197). </s></p><p type="main">

<s>Per la dimostrazione, se ne spedisce il Torri­<lb></lb>celli dicendo <emph type="italics"></emph>hoc manifestum est,<emph.end type="italics"></emph.end> ciò che però a <lb></lb>molti non parve, onde il Viviani, quasi postilla al <lb></lb>testo, così scriveva: “ Questa dimostrazione, deside­<lb></lb>randosi da qualcuno di averla un po&#039;più spiegata, <lb></lb>me ne ingegnai come appresso: ” </s></p><p type="main">

<s>“ Sit tubus cylindricus, vel prismaticus, AB (nella medesima figura 199) <lb></lb>perforatus in fundo B: fluat, neque alius humor superinfundatur. </s>

<s>Erunt ve­<lb></lb>locitates aquae, exeuntes per B, positis libellis C et E, ut sunt lineae appli­<lb></lb>catae ex punctis libellarum CD, EF in parabola CFD, cuius axis sit BC, ver­<lb></lb>tex foramen B. ” </s></p><p type="main">

<s>“ Ponatur CG aequalis BE, et circa eumdem axem CB, vertice C, de­<lb></lb>scribatur parabola CHI, penitus ipsi BFD aequalis. </s>

<s>Essent BI, GH ordinatim <lb></lb>applicatae aequales CD, EF. </s>

<s>Cum enim velocitas per foramen B, post CB, <lb></lb>ad velocitatem per aequale foramen G, post CG, sit, per praecedentem, ut BI <lb></lb>ad GH, vel ut CD ad EF, et velocitas in G, post CG, eadem sit ac veloci­<lb></lb>tas in B, post EB, cum CG, EB, per constructionem, sint aequales; ergo ve­<lb></lb>locitas in B, post CB, ad velocitatem B, post EB, erit ut CD ad EF, quod <lb></lb>fuit propositum ” (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>44, 45). </s></p><p type="main">

<s>La proposizione, che immediatamente succede nell&#039;appendice del Tor­<lb></lb><figure id="id.020.01.3461.2.jpg" xlink:href="020/01/3461/2.jpg"></figure></s></p><p type="caption">

<s>Figura 200.<lb></lb>ricelli, dopo questa che il Viviani ha così <lb></lb>spiegata, è quella del <emph type="italics"></emph>Solido dell&#039;acqua,<emph.end type="italics"></emph.end><lb></lb>messa dall&#039;Autore stesso in tal forma: </s></p><p type="main">

<s>“ PROPOSITIO VI. — <emph type="italics"></emph>Sit vas aqua sem­<lb></lb>per plenum CE<emph.end type="italics"></emph.end> (fig. </s>

<s>200) <emph type="italics"></emph>amplissimum, <lb></lb>cuius foramen in fundo circulare sit AB, <lb></lb>solidum autem aquae ex eo fluentis sit <lb></lb>ASNB, et solidi axis sit IH: Dico lineam <lb></lb>BN, solidi huius genitricem, talem esse ut <lb></lb>numerus biquadratus diametri AB, ad bi­<lb></lb>quadratum diametri SN, sit reciproce ut <lb></lb>altitudo IH ad altitudinem IG ”<emph.end type="italics"></emph.end> (Op. </s>

<s>geom. </s>

<s><lb></lb>cit., pag. </s>

<s>197). </s></p><p type="main">

<s>La dimostrazione si conduce con un <lb></lb>solo e brevissimo passo dalla IVa, e dai co­<lb></lb>rollari di lei. </s>

<s>Imperocchè, dovendo, per il <lb></lb>circolo AB e per l&#039;SN, passare nel medesimo tempo uguale quantità d&#039;acqua, <lb></lb>le sezioni dunque staranno reciprocamente come le radici delle altezze, onde <lb></lb>non altro occorre a fare che a quadrar l&#039;equazione AB2:SN2=√IH:√IG, <lb></lb>per conseguire il proposito. </s></p><pb xlink:href="020/01/3462.jpg" pagenum="423"></pb><p type="main">

<s>Di qui il Guglielmini, nella proposizione IX del V libro <emph type="italics"></emph>Mensura aqua­<lb></lb>rum fluentium,<emph.end type="italics"></emph.end> e il Grandi, nella proposizione IX del suo trattato <emph type="italics"></emph>Del mo­<lb></lb>vimento delle acque,<emph.end type="italics"></emph.end> facilmente conclusero che il solido dell&#039;acqua, così <lb></lb>astrattamente considerato come lo considera il Torricelli, è un&#039;iperboloide, <lb></lb>quale si descriverebbe dal rivolgersi, intorno all&#039;asse GH, la linea BN, la <lb></lb>quale nient&#039;altro è che un&#039;iperbola del quarto grado. </s>

<s>Il Jurin e gli annotatori <lb></lb>del Newton poi, riducendo la teoria a più prossima corrispondenza coi fatti, <lb></lb>dimostrarono che tale è pur la figura del vano o della <emph type="italics"></emph>cateratta,<emph.end type="italics"></emph.end> che si forme­<lb></lb>rebbe intorno all&#039;asse IG, in mezzo all&#039;acqua del pilo. </s>

<s>Ma prima di tutti <lb></lb>costoro il Viviani aveva risoluto, intorno al solido torricelliano dell&#039;acqua, <lb></lb>varii problemi, che, fatti ora noti, si giudicheranno uno dei più belli orna­<lb></lb>menti all&#039;appendice <emph type="italics"></emph>De motu aquarum.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ PROPOSITIO VII. — <emph type="italics"></emph>Data la grossezza o&#039;il diametro AB<emph.end type="italics"></emph.end> (nella me­<lb></lb>desima figura 200) <emph type="italics"></emph>di un foro circolare, fatto nel fondo DE, il quale stia <lb></lb>sempre pieno d&#039;acqua fino all&#039;altezza GI perpendicolare ad esso fondo <lb></lb>sul centro G di esso foro, pel quale esce l&#039;acqua cadente; si cerchi, del <lb></lb>corpo acqueo, che si formerà sotto esso fondo, quale sia per essere il dia­<lb></lb>metro della grossezza di esso corpo cadente, in tanta distanza dal mede­<lb></lb>simo fondo DE, quanta è GH ”<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>13). </s></p><p type="main">

<s>Per la risoluzione della proposta s&#039;invoca l&#039;aiuto di un Lemma mate­<lb></lb>matico, che vedremo servire al Viviani per altri simili bisogni, dimostran­<lb></lb>dolo però volta per volta, secondo i vari casi particolari. </s>

<s>A ciò fare lo co­<lb></lb>stringeva il metodo, a cui sempre vollesi mantenere fedele, contro le novità <lb></lb>dell&#039;analisi cartesiana, per via della quale nonostante si sarebbe potuto pro­<lb></lb>porre una volta sola quello stesso Lemma, così generalmente pronunziandolo, <lb></lb>in questa forma: <emph type="italics"></emph>Se sia un numero<emph.end type="italics"></emph.end> n <emph type="italics"></emph>qualunque di quantità continua­<lb></lb>mente proporzionali, la prima starà all&#039;ultima come la potenza<emph.end type="italics"></emph.end> n-1 <emph type="italics"></emph>della <lb></lb>prima sta alla potenza<emph.end type="italics"></emph.end> n-1 <emph type="italics"></emph>della seconda.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Esser ciò vero poteva resultare per induzione anche dalle regole tenute <lb></lb>dal Viviani, le quali in ogni modo si rendono così, con metodo analitico, più <lb></lb>spedite. </s></p><p type="main">

<s>Siano tre i termini continuamente proporzionali <emph type="italics"></emph>a:b=b:c.<emph.end type="italics"></emph.end> Sarà <emph type="italics"></emph>b2= <lb></lb>ac,<emph.end type="italics"></emph.end> e anche <emph type="italics"></emph>ab2=a2c,<emph.end type="italics"></emph.end> e perciò <emph type="italics"></emph>a:c=a2:b2.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Siano i detti termini quattro, <emph type="italics"></emph>a:b=b:c=c:d.<emph.end type="italics"></emph.end> Sostituendo, nel­<lb></lb>l&#039;equazione <emph type="italics"></emph>b2=ac,<emph.end type="italics"></emph.end> il valore di <emph type="italics"></emph>c,<emph.end type="italics"></emph.end> verrà <emph type="italics"></emph>b2=a√bd.<emph.end type="italics"></emph.end> Quadrando, <emph type="italics"></emph>b1=a2bd,<emph.end type="italics"></emph.end><lb></lb>ossia <emph type="italics"></emph>b3=a2d.<emph.end type="italics"></emph.end> Moltiplicando per <emph type="italics"></emph>a, ab3=a3d,<emph.end type="italics"></emph.end> e perciò <emph type="italics"></emph>a:d=a3:b3.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Se poi i termini saranno cinque <emph type="italics"></emph>a:b=b:c=c:d=d:e,<emph.end type="italics"></emph.end> sostituendo
<lb></lb>nella <emph type="italics"></emph>b3=a3d,<emph.end type="italics"></emph.end> trovata di sopra, il valore di <emph type="italics"></emph>d=ae/b,<emph.end type="italics"></emph.end> avremo <emph type="italics"></emph>b3=a3e/b,<emph.end type="italics"></emph.end><lb></lb>ossia <emph type="italics"></emph>b4=a3e.<emph.end type="italics"></emph.end> Moltiplicando per <emph type="italics"></emph>a, ab4=a4e,<emph.end type="italics"></emph.end> e perciò <emph type="italics"></emph>a:e=a4:b4....<emph.end type="italics"></emph.end><lb></lb>Proseguendo si troverà questa regola costante, che cioè il grado della potenza <lb></lb>è sempre meno uno de&#039;termini in proporzione continua, e perciò, se i ter­<lb></lb>mini sono <emph type="italics"></emph>n,<emph.end type="italics"></emph.end> e l&#039;ultimo si chiami <emph type="italics"></emph>z<emph.end type="italics"></emph.end>, se ne potrà concludere <emph type="italics"></emph>a:z= <lb></lb>a n-1:b n-1,<emph.end type="italics"></emph.end> equazione, che riduce gli sparsi lemmi del Viviani in una formula <pb xlink:href="020/01/3463.jpg" pagenum="424"></pb>generale. </s>

<s>Da questa scendono alcuni corollari importanti, de&#039;quali però no­<lb></lb>teremo due soli, perchè si vedranno in seguito invocati dal Viviani stesso per <lb></lb>lemmi alla dimostrazione di altre sue proposizioni d&#039;Idrometria. </s></p><p type="main">

<s><emph type="italics"></emph>Corollario I.<emph.end type="italics"></emph.end> — Nel caso, che le quantità continue siano tre, s&#039;è dimo­<lb></lb>strato <emph type="italics"></emph>a:c=a2:b2,<emph.end type="italics"></emph.end> ossia <emph type="italics"></emph>ab2=ca2.<emph.end type="italics"></emph.end> Moltiplichiamo questa per <emph type="italics"></emph>b2<emph.end type="italics"></emph.end>, e avremo <lb></lb><emph type="italics"></emph>ab4=ca2b2.<emph.end type="italics"></emph.end> Poniamo in questo secondo membro <emph type="italics"></emph>b2=ac,<emph.end type="italics"></emph.end> e avremo <emph type="italics"></emph>ab4= <lb></lb>ca2.ac=a3c2,<emph.end type="italics"></emph.end> che dimostra il teorema così proposto dal Viviani: <emph type="italics"></emph>Se tre <lb></lb>linee sono in continua proporzione geometrica, il fatto dalla prima nel <lb></lb>quadrato della seconda, è uguale al fatto dal cubo della prima nel qua­<lb></lb>drato della terza.<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. CXVI, fol. </s>

<s>113). </s></p><p type="main">

<s><emph type="italics"></emph>Corollario II.<emph.end type="italics"></emph.end> — Nel caso, che le continue sian quattro, da <emph type="italics"></emph>b2=ac<emph.end type="italics"></emph.end><lb></lb>abbiamo <emph type="italics"></emph>c3=b6/a3,<emph.end type="italics"></emph.end> e da <emph type="italics"></emph>b4=a2bd<emph.end type="italics"></emph.end> abbiamo <emph type="italics"></emph>a3=ab3,/d<emph.end type="italics"></emph.end> e perciò <emph type="italics"></emph>a3:c3= <lb></lb>ab3/d:b6/a3=a4.b3:db6=a4:db3.<emph.end type="italics"></emph.end> E perchè <emph type="italics"></emph>b3=a2d,<emph.end type="italics"></emph.end> dunque <emph type="italics"></emph>a3:c3= <lb></lb>a4:d2a2=a2:d2,<emph.end type="italics"></emph.end> che dimostra l&#039;altro pronunziato del Viviani: <emph type="italics"></emph>Se quat­<lb></lb>tro linee sono in continua proporzione geometrica, il cubo della prima, al <lb></lb>cubo della terza, sta come il quadrato della prima al quadrato della <lb></lb>quarta<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>120). </s></p><p type="main">

<s>Premesse le quali cose, in servigio delle proposizioni d&#039;Idrometria, che il <lb></lb>Viviani dimostrerà qui, e nel capitolo seguente, ecco intanto l&#039;uso, ch&#039;egli stesso <lb></lb>fa del detto Lemma generale, nella dimostrazione della VII ora annunziata. </s></p><p type="main">

<s>“ Si prenda IL (nella stessa figura 200) media proporzionale fra le <lb></lb>HI, IG, ed anche la IM, media proporzionale fra le HI, IL, e di poi, come <lb></lb>la nota IH, alla trovata IM, così si faccia il semidiametro BG noto, all&#039;HN, <lb></lb>quale da H s&#039;applichi parallelo alla GR: dico che l&#039;HN è il semidiametro <lb></lb>della grossezza cercata. </s>

<s>” </s></p><p type="main">

<s>“ Prendasi IO media proporzionale fra le LI, IG. </s>

<s>Or perchè IH all&#039;IL <lb></lb>sta come IL all&#039;IG, ed è l&#039;IM media fra HI, IL, siccome la IO è media fra <lb></lb>le LI, IG; saranno le cinque IH, IM, IL, IO, IG in una medesima continua <lb></lb>proporzione, e perciò, in virtù del premesso Lemma, la prima HI, alla quinta <lb></lb>IG, sta come il quadrato-quadrato della prima HI, al quadrato-quadrato della <lb></lb>seconda IM. </s>

<s>Ma come HI all&#039;IM, così sta ancora la GB alla HN; che però <lb></lb>anche il quadrato-quadrato HI, al quadrato-quadrato IM, sta come il quadrato­<lb></lb>quadrato GB, al quadrato-quadrato HN. </s>

<s>Adunque ancora la HI alla IG sta come <lb></lb>il quadrato-quadrato GB, al quadrato-quadrato HN ” (ivi, T. CXVII, fol. </s>

<s>13). </s></p><p type="main">

<s>Per dichiarar meglio le premesse di questa conclusione, si ordinino le <lb></lb>quattro istituite proporzioni: 1.a HI:IL=IL:IG, 2.a HI:IM=IM:IL, <lb></lb>3.a HI:IM=GB:HN, 4.a IL:IO=IO:IG. </s>

<s>Preso ora il valore di IL <lb></lb>dalla seconda, e sostituito nella prima, in luogo del secondo termine della <lb></lb>prima ragione; preso inoltre il valore di IG dalla quarta, e sostituito in luogo <lb></lb>del secondo termine nella seconda ragione della detta prima; avremo </s></p><p type="main">

<s><emph type="center"></emph>HI:IM2/HI=IL=IO2/IL,<emph.end type="center"></emph.end><pb xlink:href="020/01/3464.jpg" pagenum="425"></pb>ossia, riducendo e estraendo la radice, HI:IM=IL:IO, dalla quale, inse­<lb></lb>rita in continuità fra la seconda e la terza, avremo HI:IM=IM:IL= <lb></lb>IL:IO=IO:IG. </s>

<s>Così essendo cinque quantità continuamente proporzionali <lb></lb>s&#039;avrà, in virtù dello stesso predetto lemma, HI:IG=HI4:IM4, e anche <lb></lb>insieme, biquadrando la terza, (*) HI:IG=GB4:HN4, secondo era stato <lb></lb>trovato dal Viviani, il quale così conclude l&#039;interrotto discorso: “ Se dun­<lb></lb>que le altezze HI, IG hanno proporzion reciproca del quadrato-quadrato GB, <lb></lb>al quadrato-quadrato HN, questo, per la proposizione VI del Torricelli, sarà <lb></lb>il semidiametro della grossezza che averà il corpo fluido nel dato punto H. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Aggiunta I.<emph.end type="italics"></emph.end> — Di qui si ha il modo pratico di segnare per punti <lb></lb>continuati questa curva BN, la quale non è altro che l&#039;iperbola quadrato­<lb></lb>quadratica, cioè la quarta delle infinite iperbole, il di cui centro è il punto I, <lb></lb>e li asintoti sono IF, IH, e ciò si farà col prendere IL media proporzionale <lb></lb>fra le IH, IG, date altezze, e poi la IM, media fra le IH, IL, e tagliare HV <lb></lb>eguale a GB, congiungere I, V, per M tirare MR parallela ad HV, ed infine <lb></lb>pigliare HN eguale ad MR, che il punto N col B si trova nella detta iper­<lb></lb>bola biquadratica, perchè sta HV, ovvero GB, ad MR, cioè ad HN, come HI <lb></lb>ad IM. </s>

<s>E nello stesso modo si troveranno altri punti di tale iperbola ” (ivi). </s></p><p type="main">

<s>L&#039;equazione infatti GB:HN=HI:IM si riduce alla forma ordinaria <lb></lb>dell&#039;iperbola del quarto grado, biquadrandola, e sostituendo, alla ragione di <lb></lb>HI4 a IM4, quella di HI a IG, data dalla contrassegnata di sopra con (*). Per <lb></lb>la qual semplicissima operazione s&#039;ottiene HI:IG=GB4:HN4. </s></p><p type="main">

<s><emph type="italics"></emph>“ Aggiunta II.<emph.end type="italics"></emph.end> — Essendosi fatto, nella costruzione del passato pro­<lb></lb>blema, che il semidiametro GB all&#039;HM sta come l&#039;altezza HI alla IM, se­<lb></lb>conda delle cinque continue proporzionali, starà anche il quadrato GB, al <lb></lb>quadrato HN, come il quadrato HI al quadrato IM; cioè come la linea HI <lb></lb>alla IL, terza proporzionale dopo HI, IM. </s>

<s>Ma la linea HI alla IL, che è media <lb></lb>proporzionale tra le HI, IG, ha suddupla proporzione della HI alla IG; adun­<lb></lb>que anche il quadrato GB, al quadrato HN, cioè il foro circolare AB, alla <lb></lb>sezione circolare SN, ha suddupla proporzione di quella, che è fra le HI, IG, <lb></lb>altezze reciproche delle sezioni del supremo livello del fluido contenuto nel <lb></lb>vaso DF ” (ivi, fol. </s>

<s>14). </s></p><p type="main">

<s>Con più chiarezza potremo giungere così alla medesima conclusione. </s>

<s><lb></lb>Quadrando la terza fra le ordinate di sopra, viene HI2:IM2=GB2:HN2, e <lb></lb>sostituendovi il valore di IM2, preso dalla seconda delle medesime, </s></p><p type="main">

<s><emph type="center"></emph>HI2:HI.IL=GB2:HN2=HI:IL.<emph.end type="center"></emph.end></s></p><p type="main">

<s>Essendo poi, per la prima, IL=√HI.IG, dunque HI:√HI.IG=GB2:HN2, <lb></lb>ossia √HI:√IG=<foreign lang="grc">π</foreign> GB2:<foreign lang="grc">π</foreign> HN2, secondo che conclude il Viviani, e anche <lb></lb><foreign lang="grc">π</foreign> GB2:<foreign lang="grc">π</foreign> HN2=HI:IL, secondo che il Viviani stesso soggiunge nel se­<lb></lb>guente </s></p><p type="main">

<s><emph type="italics"></emph>Corollario.<emph.end type="italics"></emph.end> — “ Di qui è che nel solido fluido, che si forma sotto il <lb></lb>vaso, la sezione AB maggiore del fondo, a qualunque altra minore SN, sta <lb></lb>come la maggiore altezza HI, alla IL, presa media fra la maggiore HI, e la <pb xlink:href="020/01/3465.jpg" pagenum="426"></pb>minore IG, altezza del fluido nel vaso. </s>

<s>Poichè HI ad IL ha pure suddupla <lb></lb>proporzione della HI alla IG ” (ivi). </s></p><p type="main">

<s>“ PPOPOSITIO VIII. — <emph type="italics"></emph>Dato il diametro AB<emph.end type="italics"></emph.end> (nella medesima figura 200) <lb></lb><emph type="italics"></emph>del foro nel fondo della conserva, ed il diametro SN del fluido cadente <lb></lb>nella nota distanza GH; assegnar quanta sia l&#039;altezza ignota del fluido, <lb></lb>dentro la medesima conserva. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Prendansi dopo AB, SN, le tre T, V, X continue proporzionali, ed <lb></lb>alla prima AB si tolga AY, eguale all&#039;ultima X, e come BY a YA così si <lb></lb>faccia HG a GI, che questa è la cercata altezza del fluido dentro la con­<lb></lb>serva. </s>

<s>” </s></p><p type="main">

<s>“ Imperocchè, stando BY a YA come HG a GI, componendo, starà AB <lb></lb>ad AY, ossia ad X, come HI ad IG. </s>

<s>Ma AB, prima, ad X, quinta della pro­<lb></lb>porzione, sta, per il solito Lemma, come il quadrato-quadrato della prima <lb></lb>AB, al quadrato-quadrato della seconda SN; adunque anche HI ad IG sta <lb></lb>come il quadrato-quadrato AB, al quadrato-quadrato SN, e però IG è l&#039;al­<lb></lb>tezza cercata ” (ivi). </s></p><p type="main">

<s>“ PROPOSITIO IX. — <emph type="italics"></emph>L&#039;altezze vive invariabili, che si fanno dall&#039;acqua <lb></lb>medesima di un fonte, ch&#039;entri in un vaso, nell&#039;uscirne dal fondo di esso, <lb></lb>per diversi fori tondi di figure simili orizontali; sono tra loro in ragion <lb></lb>reciproca de&#039;quadrato-quadrati de&#039;lati omologhi de&#039;medesimi fori. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Siano i fori B, C (fig. </s>

<s>201) orizontali, di forma per es. </s>

<s>circolare, fatti <lb></lb><figure id="id.020.01.3465.1.jpg" xlink:href="020/01/3465/1.jpg"></figure></s></p><p type="caption">

<s>Figura 201.<lb></lb>nel fondo orizontale GH del vaso AH, e sia l&#039;altezza <lb></lb>viva invariabile del fluido, che esce per B, la FG, e <lb></lb>quella viva invariabile del medesimo fluido, che esce <lb></lb>per C, altro foro circolare, sia la AG. </s>

<s>Dico che l&#039;al­<lb></lb>tezza viva FG sul foro B, alla viva AG sul foro C, sta <lb></lb>come il quadrato-quadrato del diametro del foro C, al <lb></lb>quadrato-quadrato del diametro del foro B. ” </s></p><p type="main">

<s>“ Imperocchè, per l&#039;Aggiunta seconda alla precedente, l&#039;altezza AG, <lb></lb>alla FG, ha doppia ragione del cerchio B al cerchio C, ed il cerchio B al C <lb></lb>ha doppia ragione del diametro al diametro. </s>

<s>Ma anche il quadrato-quadrato <lb></lb>del diametro di B, al quadrato-quadrato del diametro di C, ha doppia ra­<lb></lb>gione di quella de&#039;medesimi cerchi; adunque l&#039;altezza viva AG sul foro C, <lb></lb>alla viva FG sul foro B, sta come il quadrato-quadrato del diametro del foro <lb></lb>B, al quadrato-quadrato del diametro del foro C, il che ecc. </s>

<s>” (ivi, fol. </s>

<s>5). <lb></lb><figure id="id.020.01.3465.2.jpg" xlink:href="020/01/3465/2.jpg"></figure></s></p><p type="caption">

<s>Figura 202.</s></p><p type="main">

<s>Con queste tre proposiz̀ioni venendo ampliata dal <lb></lb>Viviani la VI del Torricelli, quella, che era la VII nel <lb></lb>l&#039;Appendice di lui, diventa in ordine la X, così for­<lb></lb>mulata: </s></p><p type="main">

<s>“ PROPOSITIO X. — <emph type="italics"></emph>Data BD<emph.end type="italics"></emph.end> (figura 202) <emph type="italics"></emph>di­<lb></lb>rectione fistulae AB, et puncto C, in quod incidat <lb></lb>aqua fluens, invenire summam latentis aquae libel­<lb></lb>lam, sive superficiem. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Dal punto C condotta a BD una parallela, che <pb xlink:href="020/01/3466.jpg" pagenum="427"></pb>incontri in F il perpendicolo BF, è manifesto che, data l&#039;ampiezza FC, e BF <lb></lb>altezza della parabola, ciò che si cerca è la sublimità. </s>

<s>Onde il presente pro­<lb></lb>blema, non essendo altro in sostanza che il IIo proposto sotto altra forma, <lb></lb>si può risolvere perciò allo stesso modo. </s></p><p type="main">

<s>Succede a questo, nell&#039;Appendice torricelliana, un problema, e l&#039;oc­<lb></lb>casione, ch&#039;ebbe l&#039;Autore di metterlo qui, è meritevole di storia, per le <lb></lb>strette relazioni, ch&#039;egli ha con la scienza de&#039;proietti. </s>

<s>Le tavole ballisti­<lb></lb>che di Galileo, come e quelle medesime costruite dal Torricelli, non da­<lb></lb>vano altro che l&#039;ampiezze paraboliche sopra un piano orizontale. </s>

<s>Ma spesso <lb></lb>occorrendo di adoprare le artiglierie, per tirar sopra una spiaggia o sopra <lb></lb>un colle acclive o declive, e non potendosi dalle Tavole, in questo caso, ri­<lb></lb>cavare l&#039;ampiezza del tiro, era necessario istituire un calcolo particolare, <lb></lb>che dette al Torricelli stesso occasione di risolvere in Ballistica un pro­<lb></lb>blema nuovo. </s></p><p type="main">

<s>Sopra la spiaggia AB (fig. </s>

<s>203), inclinata con l&#039;orizzonte AC di un an­<lb></lb>golo noto, perchè si suppone essere stato esattamente misurato con lo stru­<lb></lb><figure id="id.020.01.3466.1.jpg" xlink:href="020/01/3466/1.jpg"></figure></s></p><p type="caption">

<s>Figura 203.<lb></lb>mento, si faccia da A, secondo la direzione AE, il tiro <lb></lb>ADB, di cui si cerca l&#039;ampiezza AB. </s>

<s>Le Tavole ballistiche, <lb></lb>com&#039;erano costruite, non davano altro che il tratto orizon­<lb></lb>tale AD, misurato in passi. </s>

<s>Il rimanente si lasciava alle <lb></lb>inquisizioni della Geometria, la quale suggerì, per primo <lb></lb>espediente, al Torricelli di condurre, per D e per B, le <lb></lb>due verticali, e perciò parallele fra loro, FH, EB, d&#039;onde, <lb></lb>per via dei triangoli ADH, ACB, nati dalla fatta costru­<lb></lb>zione, veniva ad aversi AB, quarta proporzionale dopo <lb></lb>AD, AH e AC. Ora, essendo AD nota, e nota pure AH, <lb></lb>secante dell&#039;angolo dell&#039;inclinazione della spiaggia, rima­<lb></lb>neva solo a notificarsi DC, che, dovendo perciò far parte di un triangolo, sug­<lb></lb>gerì al Geometra di condurre la linea CH, la quale fece mirabilmente il gioco <lb></lb>che si voleva. </s>

<s>Perchè, avendosi dimostrato da Archimede, nel libro degli Sfe­<lb></lb>roidei e Conoidei, che HB ad AH sta come HD e DF, ossia come BC a CE; <lb></lb>ne resultava che HC è parallela ad AE, e che perciò, tornando simili i trian­<lb></lb>goli ADF, HDC, la DC richiesta era quarta proporzionale dopo FD, tangente <lb></lb>dell&#039;angolo dell&#039;elevazione del tiro, DH, tangente dell&#039;angolo dell&#039;inclinazione <lb></lb>della spiaggia, ambedue note, e AD, pure essa nota. </s></p><p type="main">

<s>Nel tempo che il Torricelli attendeva a così fatti esercizi ballistici, fer­<lb></lb>veva tuttavia fra i Geometri una gara di proporre modi nuovi, per descri­<lb></lb>vere le parabole e anche a lui n&#039;era sovvenuto uno, che lo fece compiacere <lb></lb>d&#039;essere entrato nel numero degli applauditi inventori. </s>

<s>La compiacenza però <lb></lb>s&#039;ebbe a convertire in dispetto, quando la bella invenzione, che credeva tutta <lb></lb>sua, lesse nello Specchio ustorio del Cavalieri essere, molto prima, stata fatta <lb></lb>e divulgata da Bartolommeo Sovero. </s>

<s>Ripensando poi meglio al problema bal­<lb></lb>listico, che aveva dianzi risoluto, come s&#039;è detto, ricoverò la speranza certa <lb></lb>di rivendicarsi il merito perduto, venendogli di lì suggerito un modo facile <pb xlink:href="020/01/3467.jpg" pagenum="428"></pb>di descrivere la parabola per punti, che questa volta credeva essere esclusivo <lb></lb>parto del suo cervello, se il diavolo non gli faceva qualche altro scherzo. </s>

<s>Mo­<lb></lb>vendosi infatti la linea AC intorno al centro A, dentro l&#039;angolo BAE, con <lb></lb>qualunque inclinazione, se dal punto, dov&#039;ella tocca con la sua estremità la <lb></lb>verticale BE, si conduca la CH parallela alla direzione AE, e da H si alzi <lb></lb>la HF verticale; il punto dell&#039;intersezione di questa con la linea AC, comun­<lb></lb>que ella venga da A tirata, sarà, per quel ch&#039;è stato detto, sempre nella <lb></lb>parabola, che dentro il triangolo AEB può esser descritta. </s></p><p type="main">

<s>Significava il Torricelli stesso queste passioni della vita sua matematica, <lb></lb>per lettera scritta da Fabriano il dì 8 gennaio 1640, al Magiotti, e nò al <lb></lb>Renieri, come parve a qualcuno, che troppo superficialmente svolse il ma­<lb></lb>noscritto, nel quale autografa è rimasta la sopraccarta: <emph type="italics"></emph>Al molto illustre e <lb></lb>Rev.do sig. </s>

<s>Pron Colmo il sig. </s>

<s>d. </s>

<s>Raffaello Magiotti, in S. </s>

<s>Lucia della Chia­<lb></lb>vica, a Roma<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s>Disc., T. XL, fol. </s>

<s>21). Quel che poi, nel presente <lb></lb>proposito, quivi autografo si legge è come segue: </s></p><p type="main">

<s>“ Mi venne voglia di stracciare ogni cosa, quando un giorno, sul li­<lb></lb>bretto dello Specchio ustorio di fra Bonaventura, lessi quel modo di descri­<lb></lb>vere la parabola (fra Bonaventura l&#039;attribuisce al Sovero) che era in questo <lb></lb>libro mio <emph type="italics"></emph>De motu proiectorum,<emph.end type="italics"></emph.end> dop&#039;averlo stimato per mia invenzione, già <lb></lb>sono più di due anni. </s>

<s>È vero che bisogna che io l&#039;avessi visto già sette o <lb></lb>ott&#039;anni sono, ma il galantuomo m&#039;era uscito di memoria, e poi ci era ri­<lb></lb>tornato come mio. </s>

<s>Ora, basta, questo errore di memoria è stato causa che <lb></lb>io abbi trattato del descriver la parabola, perchè, se non stimavo per mia <lb></lb>questa invenzione, non ne avrei parlato, perchè questa mi piace più di tutte <lb></lb>quelle, che abbi mai visto appresso tanti Autori, che tutti vogliono dar del <lb></lb>naso a descrivere la parabola. </s>

<s>” </s></p><p type="main">

<s>“ In questi altri fogli ne averò uno, il quale, se il demonio non fa un <lb></lb>altro miracolo, lo stimo per mio, ed è tale, a proposito de&#039;proietti: Dato il <lb></lb>cannone AB (fig. </s>

<s>204) d&#039;una fontana appresso un muro, ovvero che sia un <lb></lb><figure id="id.020.01.3467.1.jpg" xlink:href="020/01/3467/1.jpg"></figure></s></p><p type="caption">

<s>Figura 204.<lb></lb>pezzo d&#039;artiglieria, e dato un solo punto C, per dove <lb></lb>passi o l&#039;acqua o la palla; io fo tutta la parabola in <lb></lb>queste modo: ” </s></p><p type="main">

<s>“ Prolungo la AB fino in D, e alzo CD perpen­<lb></lb>dicolare all&#039;orizzonte, e congiungo BC. </s>

<s>Fatto il trian­<lb></lb>golo BCD, tiro a caso la BE dal punto B, e faccio EF <lb></lb>parallela a BD, ed FH parallela a CD, e per H passa <lb></lb>la parabola. </s>

<s>E nello stesso modo trovo più e più punti, <lb></lb>finchè bastano per tirar la linea curva ” (ivi, fol. </s>

<s>17). </s></p><p type="main">

<s>La gentile invenzione, affinchè non andasse smarrita, volle il Torricelli <lb></lb>stesso raccoglierla nel suo trattatello <emph type="italics"></emph>De motu aquarum,<emph.end type="italics"></emph.end> proponendola in <lb></lb>questa forma: </s></p><p type="main">

<s>“ PROPOSITIO XI. — <emph type="italics"></emph>Data directione AD tubi, sive fistulae BA, et <lb></lb>puncto C, in quod incidat aquae emissio; totam parabolam aquae fluen­<lb></lb>tis describere<emph.end type="italics"></emph.end> “ (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>198). </s></p><pb xlink:href="020/01/3468.jpg" pagenum="429"></pb><p type="main">

<s>Parve al Viviani così bello, nella sua facilità, questo argomento dei getti <lb></lb>parabolici, che volle ampliarlo con quest&#039;altra sua proposizione. </s></p><p type="main">

<s>“ PROPOSITIO XII. — <emph type="italics"></emph>Date, nel medesimo perpendicolo AB<emph.end type="italics"></emph.end> (fig. </s>

<s>205), <lb></lb><emph type="italics"></emph>le distanze CE di due zampilli CLD, ELF, con proiezione orizontale dai <lb></lb><figure id="id.020.01.3468.1.jpg" xlink:href="020/01/3468/1.jpg"></figure></s></p><p type="caption">

<s>Figura 205.<lb></lb>fori C, E, per un medesimo piano verticale, e <lb></lb>con diversi carichi o sublimità note, cioè il più <lb></lb>alto C con la sublimità AC, ed il più basso E <lb></lb>con la sublimità GE; cercasi dove questi s&#039;in­<lb></lb>contreranno. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Io prendo GH eguale ad AC, e come EH <lb></lb>ad HG, così si faccia CE ad EI, e per I si tiri <lb></lb>l&#039;orizontale IL, segante uno degli zampilli, come <lb></lb>l&#039;ELF, in L: dico che l&#039;altro ancora passa per L ” <lb></lb>(MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>7). </s></p><p type="main">

<s>La verità dell&#039;asserto rimarrebbe confermata <lb></lb>dal dimostrare che IL è l&#039;ampiezza comune alle <lb></lb>due parabole. </s>

<s>Chiamato P, infatti, il parametro <lb></lb>della CLP, P&#039;il parametro della ELF, per le note proprietà <emph type="italics"></emph>De motu proiecto­<lb></lb>rum,<emph.end type="italics"></emph.end> abbiamo IL2=P.CI, IL2=P′.EI. </s>

<s>E perchè P=4AC, P′=4GE, <lb></lb>dunque tutto si riduce a provare che IL2=AC.CI=GE.EI, come fa il <lb></lb>Viviani, così proseguendo il discorso: “ Imperocchè stando, per costruzione, EH <lb></lb>ad HG come CE ad EI, componendo, EG a GH, ovvero a CA, starà come CI <lb></lb>a IE, onde il rettangolo di EG in IE è uguale al rettangolo di CA in CI ” (ivi). </s></p><p type="main">

<s>Ritornando al Torricelli, la proposizion che succede a quella, nella quale, <lb></lb>dato un punto dove cade una gocciola d&#039;acqua e la direzione del tubo, si <lb></lb>insegna a rintracciar la via parabolica, per la quale dietro a lei passò tutto <lb></lb>lo zampillo; è come segue: </s></p><p type="main">

<s>“ PROPOSITIO XIII. — <emph type="italics"></emph>Posito vase AB<emph.end type="italics"></emph.end> (fig. </s>

<s>206), <emph type="italics"></emph>sive cylindrico sive <lb></lb>prismatico, quod in fundo perforatum sit foramine B; velocitas aquae <lb></lb><figure id="id.020.01.3468.2.jpg" xlink:href="020/01/3468/2.jpg"></figure></s></p><p type="caption">

<s>Figura 206.<lb></lb>exeuntis ex B, velocitati libellae, sive supremae su­<lb></lb>perficiei descendentis in vase, semper eadem ratione <lb></lb>respondebit ”<emph.end type="italics"></emph.end> (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>199). </s></p><p type="main">

<s>Costruite intorno alla parete AM, come intorno <lb></lb>a loro proprio asse, le due parabole MLC, MIE, co­<lb></lb>sicchè quella sia maggiore di questa, risulta dalle pre­<lb></lb>cedenti istituzioni che la velocità dell&#039;acqua versata <lb></lb>dal foro B, alla velocità della scesa dal livello, in <lb></lb>qualunque punto si trovi dell&#039;altezza del vaso, sta <lb></lb>sempre come la linea applicata nella parabola maggiore, all&#039;applicata dal <lb></lb>medesimo punto nella minore: <emph type="italics"></emph>hoc est in eadem semper ratione.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Quella che soggiunge il Torricelli in X luogo della sua Appendice, es­<lb></lb>sendosi avuta già per corollario dalla IVa, si tralascia, tanto più che la ve­<lb></lb>dremo scendere pure per corollario da un&#039;altra, e si passa a un problema, <lb></lb>che il Torricelli stesso nel suo libro propone in tal maniera. </s></p><pb xlink:href="020/01/3469.jpg" pagenum="430"></pb><p type="main">

<s>“ PROPOSITIO XIV. — <emph type="italics"></emph>Quoddam vas, cuius summitas A<emph.end type="italics"></emph.end> (fig. </s>

<s>207), <lb></lb><emph type="italics"></emph>perforatum est foramine B ita ut, superinfluente quodam aquae ductu<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3469.1.jpg" xlink:href="020/01/3469/1.jpg"></figure></s></p><p type="caption">

<s>Figura 207.<lb></lb><emph type="italics"></emph>in A, semper plenum permaneat. </s>

<s>Quaeritur quo fora­<lb></lb>mine perforari debeat in C, ut, eadem superinfluente <lb></lb>aqua, plenum praecise sicut antea permaneat ”<emph.end type="italics"></emph.end> (ibid., <lb></lb>pag. </s>

<s>200). </s></p><p type="main">

<s>Dovendo essere le quantità versate uguali, l&#039;apertura <lb></lb>e la sezione data B, alla cercata X, dovrà reciprocamente <lb></lb>stare come la velocità alla velocità. </s>

<s>Ond&#039;è che, descritta <lb></lb>la parabola ADE, e condottevi da B e da C le ordinate <lb></lb>BD, CE, sarà CE:BD=B:X, l&#039;equazione che risolve il problema. </s></p><p type="main">

<s>Il Viviani promosse questo del Torricelli in un altro problema idrome­<lb></lb>trico più complicato, così proponendolo: </s></p><p type="main">

<s>“ PROPOSITIO XV. — <emph type="italics"></emph>Data una botte, o una conserva d&#039;acqua ABCD<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>208), <emph type="italics"></emph>mantenuta da una indeficiente o soprabbondante fontana sem-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3469.2.jpg" xlink:href="020/01/3469/2.jpg"></figure></s></p><p type="caption">

<s>Figura 208.<lb></lb><emph type="italics"></emph>pre piena fino al livello AD, cd in uno dei <lb></lb>lati di essa cisterna, come in AB, sia un foro <lb></lb>B, per il quale, senza variarsi il livello AD, <lb></lb>in un dato tempo, esca per B una nota quan­<lb></lb>tità d&#039;acqua, la quale sia rappresentata per <lb></lb>esempio dalla retta BG, presa perpendicolar­<lb></lb>mente ad AB; sia proposto di fare, nel mede­<lb></lb>simo corpo della conserva, un nuovo foro, in <lb></lb>un altro dato luogo E, pel quale ancora esca <lb></lb>nel medesimo tempo un&#039;altra data quantità d&#039;acqua che, rispetto alla <lb></lb>prima CB, sia GH. </s>

<s>Cercasi quanto dovrà esser largo il foro in E. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Intorno all&#039;asse AB, per la cima A e sulla mezza ordinata BG, si <lb></lb>descriva la mezza parabola AFG, dentro la quale, da E, s&#039;applichi ordina­<lb></lb>tamente la EF. </s>

<s>Di poi, come EF a GH, così si faccia il foro B ad un altro <lb></lb>nuovo, che questo sarà quello, che fatto in E getterà in detto tempo la quan­<lb></lb>tità GH. ” </s></p><p type="main">

<s>“ S&#039;immagini in E un foro, uguale al B: la quantità dunque dell&#039;acqua, <lb></lb>che esce per B, a quella, che esce per l&#039;egual foro E, starà, per la IVa del <lb></lb>Torricelli, come BG a EF, e la quantità dell&#039;acqua, che esce pel foro E, <lb></lb>uguale al B, alla quantità, che esce pel nuovo foro fatto in E, sta come il <lb></lb>foro in E, uguale al B, al foro in E fatto di nuovo (stante che l&#039;una e l&#039;al­<lb></lb>tra esca dal luogo E con la stessa velocità, mediante che l&#039;altezza premente <lb></lb>sia sempre la stessa AE) cioè come FE a GH. Adunque, per l&#039;egualità, la <lb></lb>quantità dell&#039;acqua per B, alla quantità pel nuovo foro in E, sta come la <lb></lb>BG alla GH. </s>

<s>Ma la quantità, che esce per B, è rappresentata dalla BG; dun­<lb></lb>que la quantità, che esce pel detto nuovo foro in E, verrà rappresentata <lb></lb>dalla GH, che è la quantità data, che si voleva uscisse dal nuovo foro in E. </s>

<s><lb></lb>Il che ecc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario.<emph.end type="italics"></emph.end> — Dalla costruzione del problema si cava che, se la quan-<pb xlink:href="020/01/3470.jpg" pagenum="431"></pb>tità richiesta GH per il nuovo foro da farsi in E, sarà uguale a quella che <lb></lb>esce pel foro B; sarà la GH uguale alla BG. </s>

<s>Ed essendosi fatto, come EF <lb></lb><figure id="id.020.01.3470.1.jpg" xlink:href="020/01/3470/1.jpg"></figure></s></p><p type="caption">

<s>Figura 209.<lb></lb>GH, così il foro dato B, al nuovo in E; tali fori B, E, per <lb></lb>i quali escono quantità d&#039;acqua uguali, sono in proporzione <lb></lb>reciproca delle ordinate per essi nella parabola AFG ” (MSS. <lb></lb>Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>13). </s></p><p type="main">

<s>La proposizione del Torricelli, che vien dopo questa, dal <lb></lb>Viviani così promossa, nelle prime bozze del manoscritto era <lb></lb>stata messa in tal forma: </s></p><p type="main">

<s>“ PROPOSITIO XVI. — <emph type="italics"></emph>Vas aliquod ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>209), <emph type="italics"></emph>cu­<lb></lb>iuscumque figurae, sit perforatum in fundo foramine B. </s>

<s><lb></lb>Influat in vas aqua tubi F, faciatque intra eum altitudi­<lb></lb>nem BE. </s>

<s>Quaeritur quantitas aquae, quae influens fa­<lb></lb>ciat intra vas altitudinem BL ”<emph.end type="italics"></emph.end> (Fra i MSS. di Gal., P. V, T. V). </s></p><p type="main">

<s>La soluzion del problema è ridotta all&#039;assurdo, col dimostrare l&#039;impos­<lb></lb>sibilità del rimanersi il livello dell&#039;acqua dentro il vaso, o superiore o infe­<lb></lb><figure id="id.020.01.3470.2.jpg" xlink:href="020/01/3470/2.jpg"></figure></s></p><p type="caption">

<s>Figura 210.<lb></lb>riore a quello, che vien designato da questa imperata costru­<lb></lb>zione: “ Sumatur media proportionalis inter BE, BL, quae sit <lb></lb>BI, fiatque, ut BE ad BI, ita aqua F ad aliam O. </s>

<s>Dico aquam <lb></lb>O solam facere altitudinem BL ” (ibid.). </s></p><p type="main">

<s>Poi nel dare il trattato alle stampe preferì il Torricelli la <lb></lb>via diretta, nel dimostrar la medesima proposizione, messa però <lb></lb>così sotto altra forma: “ Quoddam vas AB (fig. </s>

<s>210), cum per­<lb></lb>foratum sit in fundo foramine B, superinfluente quodam dato <lb></lb>aquae ductu D plenum permanet usque ad signum C. </s>

<s>Quaeri­<lb></lb>tur quantitas aquae in idem vas ingerendae ad hoc, ut repleatur <lb></lb>usque ad signum A ” (Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>200, 1). </s></p><p type="main">

<s>La via diretta del dimostrare, quivi tenuta, consiste nell&#039;osservare che, <lb></lb>per essere le sezioni uguali, la quantità data D, e la cercata X, stanno come <lb></lb>le radici delle altezze: cioè √CB:√AB=CB:√CB.AB=D:X. </s>

<s>E perciò, <lb></lb>essendo CB e D note, il problema vien risoluto col ritrovar la media pro­<lb></lb>porzionale fra le CB, AB, altezze date. <lb></lb><figure id="id.020.01.3470.3.jpg" xlink:href="020/01/3470/3.jpg"></figure></s></p><p type="caption">

<s>Figura 211.</s></p><p type="main">

<s>Risoluto in un modo, che presso a poco si riduce a que­<lb></lb>sto, il problema, si soggiungono dall&#039;Autore alcune parole, <lb></lb>alle quali il Viviani riferisce la seguente sua avvertenza: <lb></lb>“ Il Torricelli, verso il fine, del suo trattatello dell&#039;Acque, <lb></lb>un dopo l&#039;altro, scioglie tre curiosi problemi, e nell&#039;estremo <lb></lb>soggiunge: <emph type="italics"></emph>quod, cum multis aliis huius generis, facile de­<lb></lb>monstratur ex praecedentibus.<emph.end type="italics"></emph.end> Ora tra questi molti altri io <lb></lb>me ne proposi alcuni, facili veramente, ma perchè la faci­<lb></lb>lità non toglie loro l&#039;esser veri, per questa ragione dell&#039;esser <lb></lb>veri, che è pure assai, e per l&#039;altra ancora dell&#039;esser fa­<lb></lb>cili, mi piace addurgli e sono i seguenti: ” </s></p><p type="main">

<s>“ PROPOSITIO XVII. — <emph type="italics"></emph>Dato il vaso ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>211), <pb xlink:href="020/01/3471.jpg" pagenum="432"></pb><emph type="italics"></emph>forato nel fondo B e mantenuto pieno dalla fonte D fino al livello AC, <lb></lb>alto sopra il foro quanto CE, si cerca a qual altezza sia per mantenersi <lb></lb>l&#039;acqua, che esce per B, ricevuta nel sottoposto vaso FGH, forato col foro <lb></lb>G, di nota proporzione col foro B. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Si faccia, come il foro G al B, così l&#039;altezza nota CE, alla I, dopo <lb></lb>le quali si prenda terza proporzionale la HL, posta sopra il foro G, che que­<lb></lb>sta sarà l&#039;altezza cercata. </s>

<s>Imperocchè, essendo l&#039;acqua, che esce per B, uguale <lb></lb>a quella, che entra nel vaso di sotto, e che, alzatavi sino ad un livello per­<lb></lb>manente, esce pel foro G; sarà la velocità per B, alla velocità per G, come <lb></lb>il foro G al B, per la IVa di questo, cioè sarà come CE ad I. </s>

<s>Ma CE ad I <lb></lb>ha suddupla ragione di CE ad HL, dunque anche il foro G al B ha suddu­<lb></lb>pla ragione di CE ad HL. </s>

<s>Ma CE è l&#039;altezza invariabile del vaso ABC, dun­<lb></lb>que HL è l&#039;altezza invariabile cercata del vaso FGH ” (MSS. Gal. </s>

<s>Disc., <lb></lb>T. CXVII, fol. </s>

<s>3). </s></p><p type="main">

<s>“ PROPOSITIO XVIII. — <emph type="italics"></emph>Date le AB, DE<emph.end type="italics"></emph.end> (fig. </s>

<s>212), <emph type="italics"></emph>altezze invariabili <lb></lb>dell&#039;acqua, che da due fonti entra in due vasi ABC, DEF, e dati i fori<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3471.1.jpg" xlink:href="020/01/3471/1.jpg"></figure></s></p><p type="caption">

<s>Figura 212.<lb></lb><emph type="italics"></emph>G, H ne&#039;loro fondi, per i quali ella esce; asse­<lb></lb>gnare la proporzione delle quantità, che ne <lb></lb>scappano dentro un medesimo tempo, o che <lb></lb>gettano i fonti. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Si prenda la I, media proporzionale fra <lb></lb>le altezze AB, DE, e come il foro G, al foro H, <lb></lb>così sia I ad L: dico che la quantità per G, alla <lb></lb>quantità per H, sta come AB ad L. </s>

<s>Imperocchè <lb></lb>la quantità per G, alla quantità per H, ha ragion composta della velocità <lb></lb>per G, alla velocità per H, e del foro G al foro H. </s>

<s>Ma la velocità per G, <lb></lb>alla velocità per H, ha suddupla ragione dell&#039;altezza AB alla DE, cioè sta <lb></lb>come AB ad I, ed il foro G, all&#039;H, sta come I ad L, per costruzione, e AB <lb></lb>ad L ha ragion composta di AB ad I, e di I ad L; adunque la quantità per <lb></lb>G, a quella per H, sta come AB ad L. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Esempio.<emph.end type="italics"></emph.end> — Sia AB parti 26, e DE 5: il foro G once 4, e H once 1. <lb></lb>Si prenda la media proporzionale fra 20 e 5, che è 10, e si faccia, come <lb></lb>4 a 1, così 10 a 2 1/2, chè la quantità per G, alla quantità per H, starà <lb></lb><figure id="id.020.01.3471.2.jpg" xlink:href="020/01/3471/2.jpg"></figure></s></p><p type="caption">

<s>Figura 213.<lb></lb>come 20 a 2 1/2, cioè come 40 a 5. Onde, se in un tal <lb></lb>tempo, per G, usciranno 40 barili di acqua, nel mede­<lb></lb>simo tempo, per H, ne usciranno barili 5, ed altrettanto <lb></lb>ne renderanno le fonti, che s&#039;introducono in tali vasì ” <lb></lb>(ivi, fol. </s>

<s>4). </s></p><p type="main">

<s>“ PROPOSITIO XIX. — <emph type="italics"></emph>Data la proporzione di H <lb></lb>ad I, fra le quantità dell&#039;acqua, che escono da due <lb></lb>fonti invariabili A e B<emph.end type="italics"></emph.end> (fig. </s>

<s>213), <emph type="italics"></emph>e data l&#039;altezza CD, <lb></lb>che uno di essi A mantiene dentro il vaso CDE, nel­<lb></lb>l&#039;uscire per il noto foro F del fondo: assegnare l&#039;altezza, che vi manter­<lb></lb>ranno ambedue, nell&#039;uscire pel medesimo foro F. ”<emph.end type="italics"></emph.end></s></p><pb xlink:href="020/01/3472.jpg" pagenum="433"></pb><p type="main">

<s>“ Si faccia come H, ad H con I, così DC a DL, e dopo questa si prenda <lb></lb>la terza proporzionale, chè questa sarà l&#039;altezza cercata. </s>

<s>Imperocchè, essendo <lb></lb>H ad I come la quantità dell&#039;acqua, che rende la fonte A, alla quantità che, <lb></lb>nel medesimo tempo, rende la fonte B; starà H ad H con I, cioè, per co­<lb></lb>struzione, DC a DL, come la quantità A, alle quantità A e B insieme prese. </s>

<s><lb></lb>Ma DC a DL ha suddupla ragione dell&#039;altezza DC, alla terza proporzionale <lb></lb>DM, adunque anche la quantità di A, alle due insieme A, B, ha suddupla <lb></lb>ragione dell&#039;altezza DC, all&#039;altezza DM. </s>

<s>Ma la quantità di A si pose esser <lb></lb>quella, che introdotta nel vaso esce per F, e vi fa l&#039;altezza invariabile DC; <lb></lb>dunque le due quantità insieme A, B, nell&#039;uscire pel medesimo foro F, vi <lb></lb>faranno l&#039;altezza MD, onde questa è la cercata. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Esempio.<emph.end type="italics"></emph.end> — Renda la fonte A 60 barili l&#039;ora, e la B 37, e l&#039;altezza nota <lb></lb>CD sia parti 34. Facciasi, come 60 a 97, somma della rendita, così 34 al nu­<lb></lb>mero, che se ne ottiene; e come 34 al numero ottenuto, così lo stesso numero <lb></lb>ottenuto a un altro, chè tante parti sarà l&#039;altezza cercata DM ” (ivi, fol. </s>

<s>8). </s></p><p type="main">

<s>“ PROPOSITIO XX. — <emph type="italics"></emph>La medesima quantità d&#039;acqua, che, uscendo <lb></lb>dal fonte invariabile E<emph.end type="italics"></emph.end> (fig. </s>

<s>214), <emph type="italics"></emph>entra nel vaso ABCD, secondo la diver-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3472.1.jpg" xlink:href="020/01/3472/1.jpg"></figure></s></p><p type="caption">

<s>Figura 214.<lb></lb><emph type="italics"></emph>sità de&#039;fori B, C orizontali, di nota grandezza, vi <lb></lb>s&#039;alza a diverse altezze ignote invariabili FG, AG: <lb></lb>cercasi la proporzione di tali altezze. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Si faccia, come il foro B al C, così il C ad un <lb></lb>altro I. </s>

<s>Dico che l&#039;altezza AG, alla FG, sta come B ad I. </s>

<s><lb></lb>Giacchè per B esce la quantità dell&#039;acqua, che in qua­<lb></lb>lunque tempo rende la fonte E, col far nel vaso l&#039;al­<lb></lb>tezza invariabile FG, e per C, nel medesimo tempo, <lb></lb>esce la medesima quantità, con farvi l&#039;altezza invaria­<lb></lb>bile AG; il foro B al C starà reciprocamente come la velocità per C. alla <lb></lb>velocità per B. </s>

<s>Ma la velocità per C, alla velocità per D, ha suddupla ragione <lb></lb>di quella delle loro proprie altezze AG, FG; adunque anche il foro B, al <lb></lb>foro C, ha suddupla ragione di quella dell&#039;altezza AG alla FG. </s>

<s>Ma il foro <lb></lb>B al C ha parimente suddupla ragione del B all&#039;I, adunque l&#039;altezza AG, <lb></lb>alla FG, sta come il foro B all&#039;I, il che ecc. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Esempio.<emph.end type="italics"></emph.end> — Sia il foro B once 5, ed il C once 4, e si faccia, come <lb></lb>5 a 4, così 4 a 3 1/5, che l&#039;altezza AG, alla FG, starà come 5 a 3 1/5, o <lb></lb>come 25 a 16. Onde, se una di queste sarà nota in parti 25, si farà nota <lb></lb>anche l&#039;altra in parti 16. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollario.<emph.end type="italics"></emph.end> — Conclusi dianzi che l&#039;altezza AG, alla FG, sta come il <lb></lb>foro B al foro I. </s>

<s>Ma il foro B all&#039;I ha doppia ragione del B al C, adunque <lb></lb>anche l&#039;altezza AG, alla FG, ha doppia ragione del foro B al C. ” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scolio I.<emph.end type="italics"></emph.end> — Se i fori B, C, orizontali nel fondo del vaso, saranno di <lb></lb>figure simili come di cerchi, la proporzione cercata delle altezze invariabili <lb></lb>sopraddette sempre è la stessa della proporzione de&#039;lati omologhi dei fori, <lb></lb>cioè, qui, dei diametri. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scolio II.<emph.end type="italics"></emph.end> — Notisi che ho sempre inteso, ed intendo, che i fori dei <pb xlink:href="020/01/3473.jpg" pagenum="434"></pb>vasi sien fatti orizontali, e non verticali, come spesso gli considera il Torri­<lb></lb>celli, perchè le rendite di quegli son sempre proporzionali ai medesimi fori, <lb></lb>e non già di questi, mentre però le figure loro ne&#039;piani verticali non si <lb></lb><figure id="id.020.01.3473.1.jpg" xlink:href="020/01/3473/1.jpg"></figure></s></p><p type="caption">

<s>Figura 215.<lb></lb>dessero condizionate, lo che non è mai necessario in quegli <lb></lb>altri, potendo esser fra loro di qualunque diversa figura ” <lb></lb>(ivi, fol. </s>

<s>11). </s></p><p type="main">

<s>“ PROPOSITIO XXI. — <emph type="italics"></emph>Data A la quantità dell&#039;acqua, <lb></lb>che esce per il dato foro B nel fondo del vaso CDE<emph.end type="italics"></emph.end> (fig. </s>

<s>215), <lb></lb><emph type="italics"></emph>con la data invariabile altezza CD, e dato il foro F e l&#039;al-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3473.2.jpg" xlink:href="020/01/3473/2.jpg"></figure></s></p><p type="caption">

<s>Figura 216.<lb></lb><emph type="italics"></emph>tezza invariabile GH, nel medesimo o in altro vaso GHI<emph.end type="italics"></emph.end> (fig. </s>

<s>216): <lb></lb><emph type="italics"></emph>díre la quantità dell&#039;acqua che, a proporzione della data quan­<lb></lb>tità, ne uscirà per questo. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Si prenda HL media proporzionale fra le date altezze HG, <lb></lb>DC, e come DC ad HL, così sia A ad M, e come il foro B al foro <lb></lb>F, così sia M ad N: dico che la quantità nota per B, alla quantità <lb></lb>ignota per F, sta come A ad N. </s>

<s>Imperocchè la quantità per B, con l&#039;altezza <lb></lb>CD, alla quantità per F, con l&#039;altezza GH, ha ragion composta della velocità <lb></lb>per B, alla velocità per F, cioè della CD alla HL, cioè di A ad M, e del <lb></lb>foro B al foro F, ossia della M alla N. </s>

<s>Ma anche A ad N ha ragion com­<lb></lb>posta della medesima di A ad M, e di M ad N; adunque anche la quantità <lb></lb>per B, alla quantità per F, sta come A ad N. </s>

<s>Ma A esprime la quantità <lb></lb>per B coll&#039;altezza CD, adunque anche N esprime la quantità per F, coll&#039;al­<lb></lb>tezza GH, il che ecc. </s>

<s>” (ivi, fol. </s>

<s>9). </s></p><p type="main">

<s>In queste cinque proposizioni il Viviani mostrava di quanta fecondità <lb></lb>fosse l&#039;applicazione delle nuove dottrine insegnate dal Torricelli, il quale, in <lb></lb>sul finire del suo trattato, ne aveva egli stesso già dati alcuni esempi. </s>

<s>La <lb></lb>chiusa però di quel medesimo trattato sembra rassomigliarsi a una cateratta, <lb></lb>calata innanzi a una fiaccola, nell&#039;atto stesso che più prometteva di sfolgo­<lb></lb>rare, ond&#039;ei non è maraviglia che il Viviani si studiasse di sollevarla, per <lb></lb>diffondere la benefica luce più largamente sopra i campi della Scienza. </s>

<s>Il <lb></lb><figure id="id.020.01.3473.3.jpg" xlink:href="020/01/3473/3.jpg"></figure></s></p><p type="caption">

<s>Figura 217.<lb></lb>centro di cotesta diffusione è un teorema, che il <lb></lb>Torricelli stesso così, in ultimo luogo, proponeva: <lb></lb>“ Esto vas irregulare GHDEF (fig. </s>

<s>217) perforatum <lb></lb>in fundo foramine D, et considerentur duae ipsius <lb></lb>sectiones GH, HE. </s>

<s>Dico velocitatem summae su­<lb></lb>perficiei aquae descendentis, quando erit GF, ad <lb></lb>velocitatem superficiei, quando erit HE, rationem <lb></lb>habere compositam ex ratione subduplicata altitu­<lb></lb>dinum GD ad HD, et reciproca sectionum, nempe sectionis HE ad GF ” <lb></lb>(Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>203). </s></p><p type="main">

<s>Il primo pensiero del Viviani fu quello di esplanare una difficoltà, la <lb></lb>quale nasceva dal non sapersi ridurre a significato fisico la ragion geome­<lb></lb>trica delle linee, che si fanno entrare in composizione co&#039;veli acquei delle <lb></lb>sezioni, intorno a che dettava la seguente nota. </s></p><pb xlink:href="020/01/3474.jpg" pagenum="435"></pb><p type="main">

<s>“ Quando il Torricelli, nell&#039;ultima sua proposizione, dice che la velocità <lb></lb>del supremo livello GF (nella medesima figura 217) alla velocità del supremo <lb></lb>livello HE, ha proporzione composta della GD alla ID, media proporzionale <lb></lb>fra le altezze GD, HD, e della proporzione della sezione per HE, alla sezione <lb></lb>per GF: quella prima proporzione di HD a ID la considera come esprimente <lb></lb>la proporzione, che è fra la quantità del fluido, che passa in quell&#039;istante <lb></lb>per la sezione GF, quando il vaso dall&#039;altezza GD si vota pel foro D, e la <lb></lb>quantità del fluido, che in quell&#039;istante, premuto dall&#039;altezza HD, passa per <lb></lb>la sezione HE, nell&#039;uscire pel medesimo foro D. ” </s></p><p type="main">

<s>“ Esser questo verissimo così lo provo: Perchè, mantenuta l&#039;altezza GD, <lb></lb>per la Ia proposizion del Castelli, tanta è l&#039;acqua che esce in un tal tempo <lb></lb>pel foro D, che quella, che passa nel medesimo tempo per la sezione GF: <lb></lb>e tanta è l&#039;acqua, che in un tal tempo, esce pel foro D, mantenuta l&#039;al­<lb></lb>tezza HD, che quella, che nel medesimo tempo passa per la sezione HE. </s>

<s>Ma <lb></lb>la quantità dell&#039;acqua, che in un tal tempo esce per D dall&#039;altezza GD, alla <lb></lb>quantità, che nel medesimo tempo esce per D dall&#039;altezza HD, sta come la <lb></lb>GD alla ID, per la Xa del Torricelli; adunque anche la quantità dell&#039;acqua, <lb></lb>che passa per GF, nel votarsi il vaso per D dall&#039;altezza GD, alla quantità <lb></lb>dell&#039;acqua, che passa per HE, nel votarsi per C dall&#039;altezza HD; sta come <lb></lb>GD a ID, il che ecc. </s>

<s>” (MSS. Gal. </s>

<s>Disc., T. CXVI, fol. </s>

<s>118). </s></p><p type="main">

<s>Non bastò al Viviani d&#039;aver dichiarate queste parti, intorno alla Propo­<lb></lb>sizione torricelliana, la quale, per costituirsi qual fondamento alle nuove spe­<lb></lb>culazioni, che gli si paravano nella mente, riconobbe essere di tanta impor­<lb></lb>tanza, che volle renderla anche più perfetta. </s>

<s>Pensò, per questo, di applicare <lb></lb>all&#039;asse del vaso, per la scala della velocità, la parabola, e si dispensò dal <lb></lb>ridurre il vaso stesso, dato irregolare, a prismatico, com&#039;aveva fatto il Tor­<lb></lb>ricelli, il teorema stesso del quale proponeva così, sotto altra forma, e ne <lb></lb>conduceva così la dimostrazione per un&#039;altra via, se non più breve, senza <lb></lb>dubbio più retta: </s></p><p type="main">

<s>“ PROPOSITIO XXII. — <emph type="italics"></emph>Se qualunque vaso GDF<emph.end type="italics"></emph.end> (nella medesima figura <lb></lb>ultima) <emph type="italics"></emph>sarà pieno di fluido fino al livello GF, col foro in fondo D, pel <lb></lb>quale e&#039;vada votandosi, e la sua altezza sia GD, intorno alla quale come <lb></lb>asse, per la cima D, sia descritta qualunque parabola supina DNM, e no­<lb></lb>tato nel vaso qualsiasi altro livello HE, segante l&#039;asse in H, e per G, H, <lb></lb>dentro essa parabola, siano ordinatamente applicate all&#039;asse le GM, HN; <lb></lb>dico che, nel votarsi il vaso, la velocità del superiore livello GF, alla ve­<lb></lb>locità dell&#039;inferiore HE, quando egli è calato in HE, ha ragion compo­<lb></lb>sta dell&#039;ordinata GM alla HN, e della sezione del vaso, pel livello HE, <lb></lb>alla sezione pel livello GF, così reciprocamente prese. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Imperocchè la ragion della velocità del livello fluido, per la sezione GF, <lb></lb>nell&#039;uscire pel foro D dall&#039;altezza GD, alla velocità del livello fluido, per la <lb></lb>sezione HE, nell&#039;uscire per il medesimo foro D dall&#039;altezza HD, è compo­<lb></lb>sta di tre ragioni: cioè della ragione della velocità per GF dall&#039;altezza GD, <lb></lb>alla velocità per D dalla medesima altezza GD, cioè, per la dottrina di d. </s>

<s>Be-<pb xlink:href="020/01/3475.jpg" pagenum="436"></pb>nedetto Castelli, della ragione della sezione del foro D, alla sezione per GF, <lb></lb>così reciprocamente prese (stante che il fluido medesimo esce per l&#039;una e <lb></lb>per l&#039;altra sezione nel medesimo tempo) e della ragione della velocità per D, <lb></lb>dalla detta altezza GD, alla velocità per esso foro D, dall&#039;altezza minore HD, <lb></lb>cioè della ragione della ordinata GM alla HN, nella parabola DNM, e della <lb></lb>ragione della velocità pel medesimo foro D, dalla medesima altezza HD, alla <lb></lb>velocità per la sezione HE, dall&#039;istessa altezza HD; cioè, per la stessa dot­<lb></lb>trina del Castelli, della ragione della sezione HE alla sezione D, così alter­<lb></lb>nativamente prese. </s>

<s>Ma di queste tre ragioni, la terza, cioè quella della se­<lb></lb>zione HE alla D, e la prima, cioè quella della sezione D alla GF, compon­<lb></lb>gono la ragione della sezione HE alla GF; adunque la ragion della velocità <lb></lb>del livello, per la sezione GF, superiore al foro quanto è la GD, alla velo­<lb></lb>cità del livello per la sezione HE, superiore al foro quanto è l&#039;HD, è com­<lb></lb>posta di due sole ragioni, cioè di quella dell&#039;ordinata GM alla HN, e di <lb></lb>quest&#039;ultima ridotta: cioè della sezione HE alla sezione GF, così reciproca­<lb></lb>mente prese, osservando qui, come si fece per la dimostrazione del Torri­<lb></lb>celli, ciò che importi la ragione fra l&#039;ordinata GM alla HN, fra quelle due <lb></lb>proporzioni componenti la proporzione delle velocità del primo supremo li­<lb></lb>vello GF, alla velocità del secondo inferiore livello HE, essendosi veduto che <lb></lb>tal ragione altro non esprime, che quella, che è fra le quantità del fluido, <lb></lb>che passa per la sezione del livello GF, alla quantità, che nel medesimo <lb></lb>tempo passa per l&#039;altra sezione del livello HE ” (MSS. Gal. </s>

<s>Disc., T. CXVII, <lb></lb>fol. </s>

<s>18 e 20). </s></p><p type="main">

<s>Tanto poi parve premesse al Viviani questa osservazione, che volle con­<lb></lb>fermarla col soggiungere la seguente </s></p><p type="main">

<s>“ PROPOSITIO XXIII. — <emph type="italics"></emph>Se qualunque vaso, rotondo o non rotondo<emph.end type="italics"></emph.end><lb></lb>(fig. </s>

<s>218), <emph type="italics"></emph>forato nel fondo in O, sia mantenuto pieno d&#039;acqua or fino al<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3475.1.jpg" xlink:href="020/01/3475/1.jpg"></figure></s></p><p type="caption">

<s>Figura 218.<lb></lb><emph type="italics"></emph>livello AF, formante la superficie o la sezione G, <lb></lb>ed or fino al livello BE, formante la superficie <lb></lb>o sezione H; la quantità dell&#039;acqua, che esce per <lb></lb>O, quando il livello è G, alla quantità dell&#039;acqua, <lb></lb>che nel medesimo tempo esce per O, quando il <lb></lb>livello è H, sta sempre come l&#039;ordinata FM al­<lb></lb>l&#039;ordinata EL, nella parabola intorno all&#039;asse FK, <lb></lb>alto quanto è il superiore livello G sopra il foro O. ”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Imperocchè, allor che il vaso sta sempre pieno sino al livello G, tanta <lb></lb>è la mole dell&#039;acqua, che esce pel foro O, quanta quella, che passa nel me­<lb></lb>desimo tempo per la sezione G. </s>

<s>E parimente, allor che il vaso sta sempre <lb></lb>pieno sino al livello H, tanta è la mole del fluido, che esce pel medesimo <lb></lb>foro O, quanta è quella, che nel medesimo tempo passa per la sezione H. </s>

<s><lb></lb>Ma la mole, che passa per la sezione G, alla mole, che nel medesimo tempo <lb></lb>passa per la sezione H, ha ragion composta della velocità per G, alla velo­<lb></lb>cità per H, e della sezione G, alla sezione H, e la velocità per G, alla ve­<lb></lb>locità per H, sta, per la precedente, come il prodotto della ordinata FM nella <pb xlink:href="020/01/3476.jpg" pagenum="437"></pb>sezione H, al prodotto della ordinata EL nella sezione G; adunque la mole <lb></lb>per G, alla mole per H, ha ancora ragion composta del prodotto della FM <lb></lb>nella sezione H, al prodotto della EL nella sezione G, e della sezione G alla <lb></lb>sezione H: ciò che tutto viene a ridursi alla semplice ragione della ordinata <lb></lb>FM, alla EL. </s>

<s>Onde abbiam dimostrato quel che si proponeva, esser la mole <lb></lb>per G alla mole per H, cioè la mole per O, quando il vaso è pieno sino <lb></lb>al livello G, alla mole, che nel medesimo tempo esce per O, quando egli è <lb></lb>pieno sino al livello H, come la FM, alla NL ” (MSS. Gal. </s>

<s>Disc., T. XCIII, <lb></lb>fol. </s>

<s>86). </s></p><p type="main">

<s>Confermata così meglio, e dichiarata fra le linee ordinate nella parabola <lb></lb>e le liquide sezioni, quella ragione, che s&#039;annunziava e si concludeva di sopra <lb></lb>nella XXII proposizione; il Viviani volle applicar questa medesima a dimo­<lb></lb>strar generalmente ciò che il Torricelli aveva solo considerato in un caso <lb></lb>particolare: la proporzion cioè degli spazi passati in tempi uguali dai livelli <lb></lb>dell&#039;acqua, che si versa per foro in fondo a un vaso, non tirato a perfezion <lb></lb>di cilindro o di prisma, ma proposto della più irregolare figura, che a uno <lb></lb>piaccia. </s></p><p type="main">

<s>“ PROPOSITIO XXIV. — <emph type="italics"></emph>In qualunque vaso forato in fondo, la velo­<lb></lb>cità che ha il fluido, nell&#039;uscire dal principio del votar del vaso, sino al-<emph.end type="italics"></emph.end><lb></lb><figure id="id.020.01.3476.1.jpg" xlink:href="020/01/3476/1.jpg"></figure></s></p><p type="caption">

<s>Figura 219.<lb></lb><emph type="italics"></emph>l&#039;ultimo, considerata in quegli istanti, nei <lb></lb>quali si trovano i livelli discesi a diverse al­<lb></lb>tezze sopra il fondo; son proporzionali alle <lb></lb>velocità, che alle medesime altezze avrebbe un <lb></lb>proietto, che da qualche impellente fosse cac­<lb></lb>ciato dal fondo allo in su perpendicolar­<lb></lb>mente. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sia ABCD (fig. </s>

<s>219) qualunque vaso, <lb></lb>forato nel fondo in BC, col fluido, che a prin­<lb></lb>cipio arrivi al livello AD, alto quanto AE, e <lb></lb>fatta la parabola EFG, per la cima E, intorno <lb></lb>l&#039;asse EA, si consideri il vaso andarsi votando <lb></lb>per BC, e il livello AD pervenire in HI. </s>

<s>Dico che la velocità per BC, quando <lb></lb>il livello è in AD, alla velocità, quando è in HI, sta come l&#039;ordinata AG <lb></lb>alla OF. ” </s></p><p type="main">

<s>“ La velocità per la sezione BC dall&#039;altezza AE, alla velocità della se­<lb></lb>zione del livello AD, sta come la sezione del livello AD, alla sezione BC, per <lb></lb>il Castelli, o come il fatto dalla sezione AD nella OF, al fatto dalla sezione BC <lb></lb>nell&#039;OF. </s>

<s>E la velocità della sezione AD, alla velocità della sezione HI, sta, per <lb></lb>la XXII di questo, come il fatto dalla sezione HI nella AG, al fatto dalla <lb></lb>sezione AD nella OF. Adunque, per la ugualità perturbata, la velocità per <lb></lb>la sezione BC dall&#039;altezza AE, alla velocità per la sezione HI, sta come il <lb></lb>fatto dalla sezione HI nella AG, al fatto dalla sezione BC nella OF. </s>

<s>E la ve­<lb></lb>locità per la sezione HI, alla velocità per la BC dall&#039;altezza OE, sta, per il <lb></lb>Castelli, come la sezione BC alla sezione HI, o come il fatto dalla sezione <pb xlink:href="020/01/3477.jpg" pagenum="438"></pb>BC nella OF, al fatto dalla sezione HI nella medesima OF; adunque, per <lb></lb>l&#039;ugualità ordinata, la velocità per la sezione BC dall&#039;altezza AE, alla velo­<lb></lb>cità per la medesima BC dall&#039;altezza OE, sta come il fatto dalla sezione HI <lb></lb>nella AG, al fatto dalla medesima sezione HI nella OF: cioè sta come la AG <lb></lb>alla OF, nella parabola. </s>

<s>Ma le velocità, procedenti secondo le ordinate AG, OF <lb></lb>in essa parabola, son proporzionali a quelle di un grave ascendente con moto <lb></lb>di proiezione da E in A; adunque è manifesto quanto fu proposto di dimo­<lb></lb>strare ” (ivi, T. CXVIII, fol. </s>

<s>128). </s></p><p type="main">

<s>Se il vaso non è irregolare, come qui suppone il Viviani, ma cilindrico <lb></lb>o prismatico, cosicchè tutte le sezioni di lui, dal supremo livello infino al <lb></lb>fondo, si mantengano uguali, le velocità delle scese nel votarsi il vaso, <lb></lb>non solamente avranno ragione di proporzionalità, ma d&#039;uguaglianza, verso <lb></lb>le velocità, che raggiungerebbe ne&#039;punti omologhi un proietto, il quale fosse <lb></lb>da qualche impellente cacciato dal fondo in su alla medesima altezza per­<lb></lb>pendicolare. </s>

<s>Non è dunque che un corollario di questa la proposizione stessa <lb></lb>dal Torricelli così formulata: “ Vasa cylindrica, sive prismatica in fundo per­<lb></lb>forata, ea lege exhauriuntur, ut, diviso tempore in partes aequales, emissio <lb></lb>ultimi temporis sit ut unum, emissio autem penultimi temporis sit ut 3, an­<lb></lb>tepenultimi temporis ut 5, et sic deinceps ut numeri impares ab unitate ” <lb></lb>(Op. </s>

<s>geom. </s>

<s>cit., pag. </s>

<s>202). </s></p><p type="main">

<s>È manifesto infatti che, immaginata l&#039;altezza QB (nella medesima <lb></lb>figura 219) uguale e antipoda alla BP, se ambedue si dividano negli uguali <lb></lb>spazi VP, BS; VT, SR; TB, RQ, crescenti da uno a tre a cinque ecc., <lb></lb>l&#039;acqua, votandosi pel foro BC, e perciò scendendo via via dentro il vaso, <lb></lb>avrà in R, in S, in B raggiunta la velocità medesima, che si troverebbe <lb></lb>avere in T, V, P un proietto, il quale fosse, con l&#039;impeto acquistato dal­<lb></lb>l&#039;acqua stessa nel cadere da Q in B, cacciato in su perpendicolarmente in­<lb></lb>fino all&#039;altezza P. È anche manifesto che, essendo gli spazi BS, SR, RQ pas­<lb></lb>sati nel medesimo tempo, le quantità dell&#039;acqua, o le sue emissioni, suppo­<lb></lb>sto il vaso prismatico, crescono come essi spazi, cioè secondo la serie de&#039;nu­<lb></lb>meri impari, cosicchè, se una misura sola è quella versata nell&#039;ultimo tempo, <lb></lb>nel penultimo ne saranno state versate tre, nell&#039;antipenultimo cinque, e così <lb></lb>sempre di seguito. </s></p><p type="main">

<s>Notava il Viviani, dop&#039;aver dimostrata a quel modo che abbiamo letto, <lb></lb>la corrispondenza del moto fra l&#039;acqua che scende, e il proietto che sale, <lb></lb><emph type="italics"></emph>esser questo un teorema elementare e importantissimo alla cognizione di <lb></lb>altre curiose, e assai utili dottrine.<emph.end type="italics"></emph.end> Fra queste una delle più curiose e utili <lb></lb>che, come ora si vedrà, e meglio nel capitolo seguente, furono dal Viviani <lb></lb>stesso più promosse, è quella che riguarda il tempo del votarsi l&#039;acqua, ri­<lb></lb>cevuta dentro varie forme di vasi, fra le quali il Torricelli non accennava <lb></lb>che a solo il conoide parabolico. </s>

<s>E par che facesse questo, più per stuzzi­<lb></lb>care la curiosità dei lettori, che per darne scienza, contentandosi di avver­<lb></lb>tirli che si rimarrebbero ingannati a credere essere esso conoide quello che <lb></lb>si vuota equabilmente, facendosi anzi gli abbassamenti dell&#039;acqua dentro lui <pb xlink:href="020/01/3478.jpg" pagenum="439"></pb>con moto sempre più accelerato, di che volle il Viviani non lasciare i Let­<lb></lb>tori in desiderio d&#039;averne la dimostrazione espressa, soggiungendo la se­<lb></lb>guente. </s></p><p type="main">

<s>“ PROPOSITIO XXV. — <emph type="italics"></emph>Si vas conoidale parabolicum, aqua plenum, <lb></lb>perforetur in fundo, dico velocitatem supremae superficiei, ad velocitatem <lb></lb>inferioris eiusdem aquae descendentis, esse ut ordinatim applicatae, vel <lb></lb>diametri earumdem superficierum, vel sectionum, reciproce sumptarum ”<emph.end type="italics"></emph.end><lb></lb>(MSS. Gal., T. CXVII, fol. </s>

<s>44). </s></p><p type="main">

<s>Rappresentandoci infatti, nella figura 220, la parabola genitrice del vaso, <lb></lb>e intendendo per <emph type="italics"></emph>V<emph.end type="italics"></emph.end> significata la velocità, abbiamo, per la XXII di questo, <lb></lb><emph type="italics"></emph>V<emph.end type="italics"></emph.end>.AC:<emph type="italics"></emph>V<emph.end type="italics"></emph.end>.GF=<foreign lang="grc">π</foreign>GF2.AC:<foreign lang="grc">π</foreign>AC2.GF=GF:AC.E perchè AC è ma­<lb></lb><figure id="id.020.01.3478.1.jpg" xlink:href="020/01/3478/1.jpg"></figure></s></p><p type="caption">

<s>Figura 220.<lb></lb>giore di GF, dunque anche la velocità di GF sarà maggiore <lb></lb>della velocità di AC, e così sarà sempre di ciascuna sezione <lb></lb>inferiore, rispetto alla superiore. </s></p><p type="main">

<s>La curiosità, che si disse aver avuto intenzione il Tor­<lb></lb>ricelli di destar nei Lettori, si modulava in questa domanda: <lb></lb>se non è il conoide parabolico, che equabilmente si vuota, <lb></lb>quale dunque altra forma di vaso è quella, che fa l&#039;effetto? <lb></lb></s>

<s>È naturale che, nel numero di così fatti curiosi, fosse principalmente il Vi­<lb></lb>viani, il quale dette, come vedremo, al quesito la più ampia risposta, che <lb></lb>si potesse desiderare. </s>

<s>Ma intanto egli non vuol divagare la speculazione <lb></lb>dal propostogli esempio del conoide, a cui mette a riscontro il cono, e fin­<lb></lb>gendosi vasi di questa forma pieni di acqua, che si versa per foro in <lb></lb>fondo, gli viene felicemente in pensiero di rappresentarsi la successione e <lb></lb>la quantità degli abbassamenti, per via di una serie ordinata di linee termi­<lb></lb>nate a una curva, la quale s&#039;incominciò a chiamare per lui <emph type="italics"></emph>Scala delle ve­<lb></lb>locità.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>PROPOSITIO XXVI. — <emph type="italics"></emph>La scala delle velocità, per la quale scendono <lb></lb>i livelli dell&#039;acqua, nel votarsi che ella fa per foro in fondo a un vaso, <lb></lb>in figura di conoide parabolico, è nelle ordinatamente applicate a un&#039;iper­<lb></lb>bola del secondo grado. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il Grandi, nel corollario III alla XXII del suo trattato <emph type="italics"></emph>Del movimento delle <lb></lb>acque<emph.end type="italics"></emph.end> (Raccolta di Autori cit., T. III, pag. </s>

<s>90) fu primo a pubblicare per <lb></lb>sua la nuova proposta, da lui stesso senza dubbio veduta in questi mano­<lb></lb>scritti, che, per esaminarli e ricavarne il meglio, furono a lui consegnati dal <lb></lb>Panzanini. </s>

<s>La dimostrazione, com&#039;era da aspettarsi, comparve in pubblico <lb></lb>ordinata e più facile che nell&#039;originale, specialmente in quel primo, prepa­<lb></lb>rato per servire ad ampliare il Torricelli, e che di lungo tempo precedette <lb></lb>all&#039;altro, in cui si distendeva la medesima proposizione, per inserirla fra le <lb></lb>altre nel generale trattato delle Clessidre. </s>

<s>Vedremo quivi l&#039;Autore procedere <lb></lb>con mano più sicura, ma la prima rivelazione della nuova verità matema­<lb></lb>tica gli resultò da un calcolo, alquanto laborioso, che a volerlo riferire ana­<lb></lb>litieamente, sopra la rappresentazione della figura 221, e facendo uso de&#039;so­<lb></lb>liti simboli, procedeva in questa maniera. </s></p><pb xlink:href="020/01/3479.jpg" pagenum="440"></pb><p type="main">

<s>Se DA, EB segnano due livelli dell&#039;acqua, dentro il vaso conoideo descritto <lb></lb>dalla semiparabola DCA, abbiamo, per la XXII di questo, <emph type="italics"></emph>V<emph.end type="italics"></emph.end>.DA:<emph type="italics"></emph>V<emph.end type="italics"></emph.end>.EB= <lb></lb>EB2.√DC:DA2.√CE, e per la similitudine dei triangoli, e per le proprietà <lb></lb><figure id="id.020.01.3479.1.jpg" xlink:href="020/01/3479/1.jpg"></figure></s></p><p type="caption">

<s>Figura 221.<lb></lb>della parabola, EH:AD=CE:CD=EB2:AD2, <lb></lb>onde EH:1=EB2:AD, ossia EH:EB=EB: <lb></lb>EH. </s>

<s>La parabola stessa poi dà (*) EB2:DA2= <lb></lb>CE:CD=EH:EG; dunque <emph type="italics"></emph>V<emph.end type="italics"></emph.end>.DA:<emph type="italics"></emph>V<emph.end type="italics"></emph.end>.EB= <lb></lb>EH.EB:EG.EH=EB:EG.E perchè, essendo <lb></lb>DA uguale ad EG, abbiamo, per la segnata con <lb></lb>asterisco, EG2=(EB2.EG)/EH, d&#039;onde EB:EG= <lb></lb>FG:(EB.EG)/HE; presa EO, quarta proporzionale <lb></lb>dopo EH, EB, EG, s&#039;otterrà la nuova espressione <emph type="italics"></emph>V<emph.end type="italics"></emph.end>.DA:<emph type="italics"></emph>V<emph.end type="italics"></emph.end>.EB=EG:EO. <lb></lb>Ora, avendosi, per la medesima sopra segnata, CE:CD=EH:EG= <lb></lb>EG2:EG3/EH, e osservando che EG3/EH=EO2, ne conseguirà finalmente CE:CD= <lb></lb>EG2:EO2=DA2:EO2. </s>

<s>“ Quare (dal lungo giro di questo calcolo ne con­<lb></lb>cludeva il Viviani) scala ordinatarum ad DC, repraesentantium velocitates su­<lb></lb>premarum velocitatum, dum vas conoidale parabolicum exinanitur; est ad <lb></lb>curvam lineam PAO, fortasse infinitam: infinitam profecto, cum sit hyper­<lb></lb>bola secunda, nempe in qua quadrata applicatarum DA, EO, sunt reciproce <lb></lb>ut CE, CD ” (MSS. Gal. </s>

<s>Disc., T. CXVII, fol. </s>

<s>30). </s></p><p type="main">

<s>Si supponga che, rivolgendosi intorno all&#039;asse DC della parabola il ret­<lb></lb>tangolo IC, generi un vaso cilindrico. </s>

<s>In questo le velocità del supremo li­<lb></lb>vello si sa, per le precedenti dimostrazioni, che scemano come le applicate <lb></lb>alla parabola da D in C, mentre, nel conoide parabolico, crescono secondo <lb></lb>le medesime applicate, che però debbon prendersi in ordine inverso, cioè da <lb></lb>C in D. </s>

<s>La quale osservazione dà luogo al Viviani di soggiungere il seguente </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollarium I.<emph.end type="italics"></emph.end> — In vase cylindrico, vel prismatico IC, et in conoide <lb></lb>parabolico ICA, velocitates EF, ID; ID, EH augentur in continua eademque <lb></lb>ratione, cum inter se rationem habeant EH ad ID. </s>

<s>Hinc schala velocitatum, <lb></lb>etiam in vase cylindrico, est in lineis ordinatim ductis ad hyperbola quadra­<lb></lb>tica PAO, cuius asymptoti sint DC, CM ” (ibid., fol. </s>

<s>44). </s></p><p type="main">

<s>Si supponga inoltre essere il triangolo ICD, nella medesima figura 221, <lb></lb>il lato di un prisma vuoto, con la base orizontalmente collocata in alto, e <lb></lb>forato in qualche punto del suo spigolo inferiore, d&#039;onde versando l&#039;acqua <lb></lb>è certo che si abbasserà in modo (dice ancora il Grandi nel Corollario IV <lb></lb>dopo la citata proposizione del <emph type="italics"></emph>Movimento delle acque<emph.end type="italics"></emph.end>) analogo al conoide <lb></lb>parabolico. </s>

<s>Avendo infatti tutte le sezioni rettangolari del detto prisma la <lb></lb>medesima lunghezza, staranno come le basi ID, PR, ossia come le ascisse <lb></lb>DC, RC, o i quadrati delle ordinate DI, RQ, o finalmente come le sezioni <lb></lb>circolari del conoide. </s>

<s>Di qui ne concludeva il Viviani l&#039;altro corollario, che <lb></lb>cioè medesima è la scala delle velocità, per ambedue le forme dei vasi. </s></p><pb xlink:href="020/01/3480.jpg" pagenum="441"></pb><p type="main">

<s><emph type="italics"></emph>“ Corollarium II.<emph.end type="italics"></emph.end> — In prismate basis triangularis ICD ordinatae DA, <lb></lb>EO exhibent velocitates superficierum supremarum ID, PR, dum vas esina­<lb></lb>nitur ” (ibid., fol. </s>

<s>116). </s></p><p type="main">

<s>Lieto di così fatti progressi il Viviani sentì nascersi la curiosità di ritro­<lb></lb>vare la scala, per la quale scendono dentro il cono i livelli dell&#039;acqua, che <lb></lb>si versa per la troncata punta rivolta in basso. </s>

<s>Al Grandi, che aveva tro­<lb></lb>vato in questi manoscritti essere la detta scala nelle ordinatamente applicate <lb></lb>a una iperbola cubica del secondo grado, fu facile cosa confermarne la ve­<lb></lb>rità, concludendola immediatamente dai principii idrodinamici già dimostrati. </s>

<s><lb></lb>Se infatti è ABC, nella figura 222, il triangolo genitore del vaso, dentro il <lb></lb>quale siano le velocità dei livelli in AC, DE ordinatamente rappresentate <lb></lb>dalle linee AC, DL; abbiamo, per la XXII di questo, <lb></lb>AC:DL=DE2.√AB:AC2.√BD. </s>

<s><lb></lb>E perchè, per la similitudine de&#039;triangoli, DE2:AC2=BD2:AB2, sarà <lb></lb>AC:DL=BD2.√AB:AB2.√BD. </s>

<s>E quadrando, <lb></lb>AC2:DL2=BD4.AB:AB4.BD=BD3:AB3, <lb></lb>ond&#039;è veramente, come il Grandi stesso concludeva, nel corollario V della <lb></lb>citata proposizione XXII del suo trattato del Movimento delle acque, la scala <lb></lb><figure id="id.020.01.3480.1.jpg" xlink:href="020/01/3480/1.jpg"></figure></s></p><p type="caption">

<s>Figura 222.<lb></lb>delle velocità del liquido, fluente <lb></lb>per l&#039;apice di un vaso conico, una <lb></lb>iperbola cubica del secondo gra­<lb></lb>do. (Raccolta d&#039;Autori cit., T. III, <lb></lb>pag. </s>

<s>91). </s></p><p type="main">

<s>Il Viviani però, che non sa­<lb></lb>peva ancora sotto quale aspetto gli <lb></lb>si presenterebbe la verità, rimasta <lb></lb>agli occhi dei Matematici tuttavia <lb></lb>nascosta; non ha la mano così <lb></lb>franca e spedita, nello svilupparle <lb></lb>il geloso velo dalla faccia divina. </s>

<s><lb></lb>Ma riconosciuto appena il mistero, <lb></lb>quasi a modo di epigrafe solen­<lb></lb>nemente commemorativa del fatto, <lb></lb>scrive in linea, che seconda la concavità della disegnata curva PCL, <emph type="italics"></emph>Hyper­<lb></lb>bola, in qua quadrata ordinatarum sunt ut cubi abscissarum reciproce, <lb></lb>et punctum B est omnium centrum, asymptoti vero BA, BM<emph.end type="italics"></emph.end> (MSS. Gal. </s>

<s><lb></lb>Disc., T. CXVII, fol. </s>

<s>9). Il calcolo, che si concludeva in questa iscrizione, è <lb></lb>al solito avvolto come i passi di chi è incerto dove sarà per riuscire. </s>

<s>Tali <lb></lb>poi, quali noi le riferiamo in modo analitico, sono del detto calcolo le tracce, <lb></lb>rimasteci nel manoscritto, il quale comincia dal comandare che, dopo le DE, <lb></lb>DF, DG, sian prese le tre continue proporzionali DH, DI, DL. </s></p><p type="main">

<s>È per la XXII di questo, <emph type="italics"></emph>V<emph.end type="italics"></emph.end>,AC:<emph type="italics"></emph>V<emph.end type="italics"></emph.end>.DE=DG.DE2:DF.DG2, e <pb xlink:href="020/01/3481.jpg" pagenum="442"></pb>per costruzione DE:DF=DF:DG=DG:DH=DH:DI=DI:DL, fra <lb></lb>la serie delle quali equazioni si noti particolarmente la DE:DG=DG:DI, <lb></lb>d&#039;onde DG2/DE=DI. Ora, per l&#039;identica DE2:DG2=DE2/DE:DG2/DE, sarà <lb></lb>DE2:DG2=DE:DI, e perciò <emph type="italics"></emph>V<emph.end type="italics"></emph.end> AC:<emph type="italics"></emph>V<emph.end type="italics"></emph.end>.DE=DG.DE:DF.DI.E per­<lb></lb>chè, per la stessa imperata costruzione, DE:DI=DF:DL; dunque in ul­<lb></lb>timo <emph type="italics"></emph>V<emph.end type="italics"></emph.end>.AC:<emph type="italics"></emph>V<emph.end type="italics"></emph.end>.DE=DG.DF=DF.DL=DG:DL=AC:DL. </s>

<s>Al <lb></lb>qual punto ridottosi il calcolo, non rimane a far altro che a invocare il <lb></lb>Lemma matematico, premesso alla VII di questo, per concluder l&#039;intento <lb></lb>così, come lo conclude propriamente il Viviani con queste parole: “ Ma per­<lb></lb>chè le quattro DG, DH, DI, DL son continue proporzionali, il quadrato DG, <lb></lb>ovvero AC, al DL, starà come il cubo DG al cubo DI, per il mio Lemma, <lb></lb>o come il cubo DE al cubo DG, o come il cubo BD al BA. </s>

<s>Adunque i punti <lb></lb><figure id="id.020.01.3481.1.jpg" xlink:href="020/01/3481/1.jpg"></figure></s></p><p type="caption">

<s>Figura 223.<lb></lb>C, L sono all&#039;iperbola, nella quale i quadrati delle or­<lb></lb>dinate son fra loro in ragion reciproca de&#039;cubi delle <lb></lb>ascisse ” (ivi). </s></p><p type="main">

<s>Sembrava perciò che fosse per formularsi la pro­<lb></lb>posizione: <emph type="italics"></emph>Scala velocitatis in cono, dum esinanitur, <lb></lb>est hyperbola, in qua quadrata ordinatarum sunt ut <lb></lb>cubi abscissarum reciproce,<emph.end type="italics"></emph.end> ma pure piacque al Vi­<lb></lb>viani di metterla piuttosto sotto quest&#039;altra forma: </s></p><p type="main">

<s>“ PROPOSITIO XXVII. — <emph type="italics"></emph>In cono ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>223) <lb></lb><emph type="italics"></emph>velocitas superioris superficiei AB aquae descendentis, <lb></lb>et per forum C in fundo exeuntis, ad velocitatem <lb></lb>ciusdem superficiei in DE, est ut FC, media inter <lb></lb>altitudines HC, GC, ad tertiam proportionalem CI <lb></lb>continuam post CG, CH ”<emph.end type="italics"></emph.end> (ivi, fol. </s>

<s>44). </s></p><p type="main">

<s>Soggiungesi immediatamente a queste parole del manoscritto: <emph type="italics"></emph>Hine <lb></lb>scula velocitatum in cono.<emph.end type="italics"></emph.end> E che veramente resulti dalla nuova forma pro­<lb></lb>posta la scala delle velocità, dimostrata dianzi dallo stesso Autore per altra <lb></lb>via, è facile persuadersene così ragionando: Secondo la proposta, AB:DE= <lb></lb>FC:CI. </s>

<s>Ma FC=VHC.CG, e, dall&#039;esser per costruzione CG:CH= <lb></lb>HC:CI, ne viene CI=CH2/CG; dunque AB:DE=VHC.CG:CH2/CG= <lb></lb>√HC.CG3:CH2=√CG3:CH2/√CH=√CG3:√CH3, e perciò AB2:DE2= <lb></lb>CG3:CH3, che è l&#039;equazione alla seconda iperbola cubica, nelle ordinate alla <lb></lb>quale era stata imposta la scala delle velocità del cono, mentre, essendo <lb></lb>stato ripieno d&#039;acqua, a poco a poco si vuota. </s></p><p type="main">

<s>Il Viviani preferì questa seconda forma di proposizione alla prima, per­<lb></lb>ch<gap></gap> gli serviva meglio all&#039;intenzion di paragonare insieme le velocità de&#039;li­<lb></lb>velli supremi, nel votarsi il cono e il conoide parabolico della medesima base <lb></lb>e della medesima altezza, ricavandone un corollario notabile, qual&#039;è che il <lb></lb>cono, benchè vaso minore e contenuto, s&#039;evacua assai più presto del conoide, <pb xlink:href="020/01/3482.jpg" pagenum="443"></pb>vaso maggiore e contenente. </s>

<s>Nel conoide ADCEB infatti la velocità del li­<lb></lb>vello DE, a quella del livello AB, sta, per le cose dimostrate, come HC a <lb></lb>CF, e nel cono la velocità del livello medesimo AB, alla velocità del livello <lb></lb>D′E′, sta come CF a CI. Così, dal moltiplicare insieme queste due propor­<lb></lb>zioni, ne resulta, riducendole, che la velocità della sezione DE del conoide, <lb></lb>alla velocità della sezione D′E′ del cono, sta come CH a CI, ond&#039;è minore in <lb></lb>quello che in questo, come dice, nelle proprie parole dell&#039;Autore, il seguente </s></p><p type="main">

<s><emph type="italics"></emph>“ Corollarium.<emph.end type="italics"></emph.end> — Si circa ABC (nella medesima figura 223) describa­<lb></lb>tur conois parabolicus ADCEB, patet superficiem superiorem aquae, descen­<lb></lb>dentis in utroque vase, velocius descendere in cono, quam in conoide, cum, <lb></lb>per praecedentem, in conoide velocitas DE, ad velocitatem AB, sit ut HC <lb></lb>ad CF, et velocitas AB in cono, per praesentem, ad velocitatem D′E′ in cono, <lb></lb>est ut CF ad CI. </s>

<s>Ergo velocitas DE in conoide, ad velocitatem D′E′ in cono, est <lb></lb>ut CH ad CI. </s>

<s>Ergo maior in cono, quam in conoide. </s>

<s>Si igitur superficies su­<lb></lb>perior aquae velocius descendit in cono, quam in conoide eiusdem altitudi­<lb></lb>nis et basis, breviori etiam tempore vacuus remanebit conus, quam conois: <lb></lb>hoc est vas minus et contentum, quam maius ac continens ” (ivi, fol. </s>

<s>45). </s></p><p type="main">

<s>Così veniva il Viviani a svolgere, intorno al conoide parabolico che si <lb></lb>vuota, il concetto del Torricelli. </s>

<s>Ma ai Lettori, che avevano per le mani il <lb></lb>trattato <emph type="italics"></emph>De motu aquarum,<emph.end type="italics"></emph.end> anche quando fossero state notificate queste <lb></lb>belle illustrazioni, rimaneva intera la curiosità d&#039;aver quella propria forma <lb></lb>di vaso, in cui i livelli del liquido nel votarsi scendono per uguali parti del­<lb></lb>l&#039;asse, in tempi uguali. </s>

<s>Fra cotesti curiosi ha la storia principalmente da <lb></lb>commemorare il Mersenno, che, avendo assistito in Roma, ne&#039;familiari col­<lb></lb>loqui col Magiotti e col Ricci, al concepimento dell&#039;Idrodinamica torricel­<lb></lb>liana; n&#039;ebbe poi in Firenze, per le mani dell&#039;Autore stesso, pubblicamente <lb></lb>esposto il parto in quel libro, dove si trattava delle acque salienti. </s>

<s>Quivi leg­<lb></lb>gendo il Mersenno per viaggio, nel tornarsene a Roma, avrebbe voluto vo­<lb></lb>lentieri dare indietro, per sentire che cosa l&#039;Autore stesso gli risponderebbe, <lb></lb>a leggergli ciò che aveva scritto a pagine 202 e 203 del suo libro, e a do­<lb></lb>mandargli di quale altra figura si dovesse dunque costruire il vaso, che, per <lb></lb>la novità dell&#039;invenzione di misurare il tempo, si sarebbe tanto desiderato. </s>

<s><lb></lb>Ma costretto a proseguire, appena giunto al termine del suo viaggio, se ne <lb></lb>andò tutto premuroso in cerca del Ricci, il quale ingenuamente confessò rima­<lb></lb>nersi tuttavia il problema un desiderio anche per lui, promettendo nonostante <lb></lb>che avrebbe pregato il Torricelli a dare sodisfazione di ciò, almeno agli amici, <lb></lb>come infatti mantenne, così scrivendo, nella prima parte della lettera, che <lb></lb>ha la data del 31 Dicembre 1644. “ Il Mersenno mi ha pregato che volessi <lb></lb>scrivere a V. S. qual debba esser quel vaso, che, riempito d&#039;acqua e poi <lb></lb>votato per di sotto, in esso scenda la superficie dell&#039;acqua contenutavi per <lb></lb>parti uguali dell&#039;asse, in tempi uguali, supposto l&#039;asse perpendicolare al­<lb></lb>l&#039;orizonte. </s>

<s>E così è indotto a far la presente richiesta, per aver letto nel <lb></lb>libro di V. S. che il vaso parabolico mostra a prima vista di prestar questo, <lb></lb>ma in effetto poi così non succede ” (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>69). </s></p><pb xlink:href="020/01/3483.jpg" pagenum="444"></pb><p type="main">

<s>Fu risposto pochi giorni dopo dover essere il vaso desiderato quello, che <lb></lb>si descriverebbe da una semiparabola biquadratica, rivolgendosi intorno al­<lb></lb>l&#039;asse. </s>

<s>La dimostrazione di ciò correva tuttayia per le poste da Firenze a <lb></lb>Roma, quando il Mersenno, impaziente dell&#039;indugio di soli dieci giorni da <lb></lb>che aveva fatta la domanda, così direttamente scriveva allo stesso Torricelli, <lb></lb>sollecitandone la risposta: “ Credo dominum Ricci ad te scripsisse ut for­<lb></lb>mam vasis ad nos mittas, quod aquam suam, per idem foramen, in tempo­<lb></lb>ribus aequalibus redderet, cum conoidale parabolicum, pag. </s>

<s>202 minime tibi <lb></lb>satisfecerit. </s>

<s>Itaque vas ad id proprium expectamus, quod, ubi vino falerno <lb></lb>oppletum fuerit, tuae saluti, paribus intervallis et temporibus, evacuemus ” <lb></lb>(ivi, T. XLI, fol. </s>

<s>15). </s></p><p type="main">

<s>La lettera, nella quale si mandava scritta la forma del vaso, aveva avuto <lb></lb>recapito, e il Ricci l&#039;aveva già partecipata, ma rimaneva a sapersi il modo <lb></lb>di scavar la clessidra, che, prima d&#039;esser forata in fondo e ripiena d&#039;acqua, <lb></lb>doveva, secondo la promessa, servir da calice pieno di generoso falerno, per <lb></lb>farne un brindisi con gli amici alla salute del Torricelli. </s>

<s>E il Torricelli, ap­<lb></lb>pena richiestone, mandava descritto il modo di segnar per punti la parabola <lb></lb>biquadratica, la quale, usata per sagoma, avrebbe dato in mano all&#039;artefice <lb></lb>il tornio esatto del calice e della clessidra. </s>

<s>Ma del brindisi non se ne di­<lb></lb>scorse più: il fervore di quella prima curiosità s&#039;attutì a un tratto, come a <lb></lb>una pentola che bolla, sollevandone il testo. </s>

<s>Il Torricelli stesso n&#039;ebbe a re­<lb></lb>stare con maraviglia, anzi, a parer nostro, mortificato, cosicchè, vedendo la <lb></lb>sua invenzione, contro ciò che si sarebbe aspettato, così indegnamente di­<lb></lb>menticata, disse un giorno a sè stesso: — O vediamo un po&#039;se, dopo tanto <lb></lb>tempo, mi ricordo di quel che scrissi a quel giovanotto del Ricci — e parve <lb></lb>se ne ricordasse molto bene, perchè seguitò a scrivere in fretta, sopra un <lb></lb>prezioso foglio che c&#039;è rimasto, la dimostrazione della figura del vaso, che <lb></lb>equabilmente si vuota, insieme col modo di descrivere, per fabbricarla, la <lb></lb>parabola del quarto grado. </s></p><p type="main">

<s>Rimasto però quel foglio, insieme con la mano che l&#039;aveva scritto, lun­<lb></lb>gamente sepolto, nessuno seppe nulla della nuova proposizione, che, per so­<lb></lb>disfare la curiosità de&#039;Lettori, aveya preparato l&#039;Autore, da aggiungersi al <lb></lb>libro <emph type="italics"></emph>De motu aquarum,<emph.end type="italics"></emph.end> il qual libro, lasciato nella speculazione del conoide <lb></lb>parabolico così imperfetto, fece credere a molti che il Torricelli si fosse pro­<lb></lb>vato bene a investigar la figura della clessidra, ma che non fosse per la diffi­<lb></lb>coltà riuscito a sciogliere il problema. </s></p><p type="main">

<s>È fra costoro notabile il Mariotte, il quale, dop&#039;avere nel III discorso <lb></lb>della III parte del suo trattato <emph type="italics"></emph>Du mouvement des eaux,<emph.end type="italics"></emph.end> spiegata la XIII pro­<lb></lb>posizione, nella quale si dimostra dal Nostro che le emissioni dei vasi cilin­<lb></lb>drici stanno come la serie dei numeri impari ab unitate; soggiunge: “ Il est <lb></lb>bon de resoudre icy un probleme assez curieux, que Torricelly n&#039;a pas en­<lb></lb>trepris de resoudre, quoy qu&#039;il l&#039;ait proposé ” (A Paris 1686, pag. </s>

<s>292): no­<lb></lb>tabile si disse, perchè, fra le tante maniere di dimostrare che la figura del <lb></lb>vaso, dentro cui l&#039;acqua scende con moto eguale, è la rotonda, generata dal <pb xlink:href="020/01/3484.jpg" pagenum="445"></pb>rivolgimento di una semiparabola quadrato-quadratica; se ne sceglie per l&#039;ap­<lb></lb>punto una somigliantissima a quella, che ci è rimasta nel manoscritto tor­<lb></lb>ricelliano. </s></p><p type="main">

<s>Così venne a ingerirsi fra i matematici l&#039;opinione che fosse il Mariotte <lb></lb>primo ritrovatore di questa bella novità, la quale, pure ignorandosene ancora <lb></lb>la storia, ebbe nel mondo il nome di teorema celebre. </s>

<s>Basti per tutti citare <lb></lb>il Varignon, autore della <emph type="italics"></emph>Maniere geometrique et generale de faire des <lb></lb>clapsydres,<emph.end type="italics"></emph.end> che, a proposito della clessidra <emph type="italics"></emph>de descente uniforme,<emph.end type="italics"></emph.end> scriveva: <lb></lb>la quelle semble avoir été cherchée par Torricelli, et que M. </s>

<s>Mariotte a trou­<lb></lb>vée ” (Fra le Memorie dell&#039;Accademia di Parigi per l&#039;anno 1699, Paris 1627, <lb></lb>pag. </s>

<s>61). </s></p><p type="main">

<s>Nè si creda che così giudicassero solamente gli stranieri: era tale l&#039;opi­<lb></lb>nione anche dei Nostri, i quali dissero, per pudore, non che al Torricelli <lb></lb>non era riuscito, ma che aveva voluto far così, per provocare i lettori col <lb></lb>silenzio. </s>

<s>In tal modo, fra gli altri, la pensava il Viviani, uno de&#039;pochi i quali <lb></lb>accettaron la provoca, e che poi si compiacque d&#039;esserne rimasto vincitore, <lb></lb>proponendo per segno di ciò, come vedremo, la clessidra parabolica in forma <lb></lb>di cuna. </s>

<s>Ciò gli occorse verso il 1650, mentre studiava il libro <emph type="italics"></emph>De motu <lb></lb>aquarum,<emph.end type="italics"></emph.end> e mentre che, morto l&#039;Autore di questo, i manoscritti di lui si <lb></lb>conservavano gelosamente dal Serenai. </s>

<s>Quando poi questi stessi manoscritti <lb></lb>furono consegnati, perchè gli mettesse in ordine e gli pubblicasse, al Viviani, <lb></lb>egli ebbe a leggervi, maravigliato che non se ne fosse diffusa, almeno fra i <lb></lb>discepoli di tanto Autore, la desiderata notizia, anche il teorema della clas­<lb></lb>sidra, e lo ricopiò la prima volta per suo proprio memoriale, e tornò a ri­<lb></lb>copiarlo anche la seconda, per inserirlo fra le altre proposizioni, delle quali <lb></lb>intendeva di compilare il trattatello <emph type="italics"></emph>De motu ac momentis.<emph.end type="italics"></emph.end> Ma rimasto senza <lb></lb>effetto il proposito di pubblicar, così questa come e le altre opere postume <lb></lb>del Torricelli, il prezioso documento, brevemente resuscitato, ritornò a gia­<lb></lb>cersi dentro l&#039;arche dorate del palazzo Pitti, dov&#039;ebbe più nobilmente custo­<lb></lb>dito il sepolcro. </s>

<s>Venne quivi nonostante a visitarlo il Fabbroni, con queste <lb></lb>parole, scritte in quel suo classico latino, commemorandolo ai vivi: “ Quod <lb></lb>ad hydraulica Toricelli scripta pertinet, commemorandum videtur problema, <lb></lb>quod nemini tum notum, propositumque a Michaele Angelo Riccio, ipse fa­<lb></lb>cillime solvit. </s>

<s>Quaerebatur enim quaenam esse deberet figura vasis, quod <lb></lb>aequabili motu exhauriretur ” (<emph type="italics"></emph>Vitae Italorum,<emph.end type="italics"></emph.end> Vol. </s>

<s>I, Pisis 1778, pag. </s>

<s>369). </s></p><p type="main">

<s>Ma ora è tempo di coronar l&#039;opera ampliatrice del Viviani con quella <lb></lb>proposizione, che l&#039;Autore stesso <emph type="italics"></emph>De motu aquarum<emph.end type="italics"></emph.end> ci lasciò scritta di sua <lb></lb>propria mano, forse con la speranza che verrebbe un giorno qualcuno a ri­<lb></lb>vendicargli, dall&#039;invidia della morte e dalla ingratitudine degli uomini, l&#039;an­<lb></lb>tica proprietà, e il primato dell&#039;invenzione. </s></p><p type="main">

<s>“ Ingeniosissimus iuvenis M. A. </s>

<s>Riccius certiorem fecit me de deside­<lb></lb>derio suo, circa illud vas quod aequabili motu exhauritur. </s>

<s>Dicam igitur, si <lb></lb>per memoriam licebit. </s>

<s>” </s></p><p type="main">

<s>“ PROPOSITIO XXVIII. — <emph type="italics"></emph>Esto conoides parabolae quadratoquadra-<emph.end type="italics"></emph.end><pb xlink:href="020/01/3485.jpg" pagenum="446"></pb><emph type="italics"></emph>ticae ABC<emph.end type="italics"></emph.end> (fig. </s>

<s>224) <emph type="italics"></emph>perforatum in fundo B. </s>

<s>Dico illud ea lege exhauriri, <lb></lb>ut motus supremae superficiei humoris contenti AC aequabilis sit. </s>

<s>”<emph.end type="italics"></emph.end></s></p><p type="main">

<s>“ Sumatur enim quaelibet alia vasis sectio DI, et super basi AC con­<lb></lb>cipiatur cylindrus AE. </s>

<s>Esto BO media proportionalis inter GB, BH, et quo­<lb></lb><figure id="id.020.01.3485.1.jpg" xlink:href="020/01/3485/1.jpg"></figure></s></p><p type="caption">

<s>Figura 224.<lb></lb>niam est quadratoquadratum AG, ad quadratoquadratum <lb></lb>DH, ut GB ad BH erit quadratum AG, ad quadratum <lb></lb>DH, ut GB ad BO. </s>

<s>Jam velocitas superficiei descenden­<lb></lb>tis, quando est AG, ad velocitatem superficiei, quando <lb></lb>erit FH in cylindro, est, per demonstrata, ut CB ad BO, <lb></lb>sive ut quadratum AG, ad quadratum DH. </s>

<s>Velocitas vero <lb></lb>sectionis FH, ad HD, est ut quadratum HD ad HF, sive <lb></lb>ut quadratum HD, ad quadratum AG. </s>

<s>Ergo ex aequeo velocitas sectionis AG, <lb></lb>ad velocitatem sectionis DH, erit ut quadratum AG ad quadratum AG, nempe <lb></lb>aequalis. </s>

<s>” </s></p><p type="main">

<s><emph type="italics"></emph>“ Scholium.<emph.end type="italics"></emph.end> — Si quis desideret descriptionem eiusmodi lineae, nempe <lb></lb>parabolae quadratoquadraticae, talem excogitabamus: Ponatur parabola qua­<lb></lb><figure id="id.020.01.3485.2.jpg" xlink:href="020/01/3485/2.jpg"></figure></s></p><p type="caption">

<s>Figura 225.<lb></lb>dratica vulgaris ABC (fig. </s>

<s>225), cuius axis AD, <lb></lb>una applicata BD. </s>

<s>Secetur AE aequalis BD, et <lb></lb>item BF aequalis CE, eritque punctum F in <lb></lb>parabola quaesita, et sic de reliquis punctis. </s>

<s>” </s></p><p type="main">

<s>“ Quod verum sit hoc, sumatur AH latus <lb></lb>rectum parabolae quadraticae, et erunt aequa­<lb></lb>les GH, AH. </s>

<s>Tum quadratum GH ad quadra­<lb></lb>tum BD, sive quadratum AH ad AE, erit ut <lb></lb>recta HA ad AD. </s>

<s>Ergo continuae sunt AH, AE, <lb></lb>AD. Propterea, si quadratum GH ad CE, vel <lb></lb>FD, est ut recta HA ad AE, erit quadratoqua­<lb></lb>dratum GH, ad quadratoquadratum FD, ut AH ad AD. </s>

<s>Deinde ex aequo pro­<lb></lb>batur quadratoquadratum FD ad IM esse ut recta DA ad AM. ” (MSS. Gal. </s>

<s><lb></lb>Disc., T. XXVI a tergo del fol. </s>

<s>167). </s></p><p type="main">

<s><emph type="center"></emph>II.<emph.end type="center"></emph.end></s></p><p type="main">

<s>In quel medesimo anno 1644, in cui, dalla tipografia de&#039;Landi, usciva <lb></lb>in Firenze, insieme con l&#039;altre opere geometriche del Torricelli, il trattato <lb></lb><emph type="italics"></emph>De motu gravium,<emph.end type="italics"></emph.end> con l&#039;appendice <emph type="italics"></emph>De motu aquarum<emph.end type="italics"></emph.end> di sole XIV propo­<lb></lb>sizioni, fecondissime però di tante altre ad esempio delle aggiuntevi dal Vi­<lb></lb>viani; il Mersenno pubblicava in Parigi, a spese del Bertier, i suoi <emph type="italics"></emph>Cogitata <lb></lb>physico-matematica,<emph.end type="italics"></emph.end> fra&#039;quali principalmente si comprendeva l&#039;<emph type="italics"></emph>Hydraulica.<emph.end type="italics"></emph.end><lb></lb>Come il titolo era nuovo, così nuovo efa in quel paese il soggetto, che si <lb></lb>svolgeva in sostanza da quello stesso pensiero, scritto dal Torricelli, per let­<lb></lb>tera del 25 Ottobre 1642, al Cavalieri, e che s&#039;incardinava in quelle mede-<pb xlink:href="020/01/3486.jpg" pagenum="447"></pb>sime esperienze fatte in Roma, per confermare la supposta verità, da Raf­<lb></lb>faello Magiotti. </s></p><p type="main">

<s>L&#039;opera del Francese, standosene ai numeri, appariva contemporanea <lb></lb>con quella del Nostro, ma ne facevano argomentare la pretension di un di­<lb></lb>ritto di precedenza certe espressioni, come sarebbe quella, in cui, dop&#039;aver <lb></lb>commemorato Galileo insieme co&#039;più illustri Matematici francesi, taccio, si <lb></lb>soggiunge, la sottile Geometria nuova del Cavalieri, “ praeclarosque tracta­<lb></lb>tus, quos ab acutissimo Tauricello, Galilaei successore, brevi speramus ” <lb></lb>(Hydraulica cit., pag. </s>

<s>193). </s></p><p type="main">

<s>Così essendo, non fa maraviglia se alcuni dotti, specialmente stranieri, <lb></lb>leggendo in questo libro d&#039;Idraulica per la prima volta annunziato che le <lb></lb>altezze dell&#039;acqua fiuente dai tubi stanno in ragione duplicata dei tempi; <lb></lb>credettero che del nuovo teorema fosse autore il Mersenno. </s>

<s>Fra i seguaci di <lb></lb>così fatta opinione è principalissimo il Boyle, che in una sua operetta in­<lb></lb>torno all&#039;utilità della Filosofia sperimentale, annoverando le più insigni sco­<lb></lb>perte fatte dai varii cultori di essa, non lascia, come degnissimo di esser <lb></lb>notato, quel “ theorema hydrostaticum, cuius inventionem Mersenno debe­<lb></lb>mus, a scriptore quodam recentiori ita propositum: Velocitates motus aquae <lb></lb>descendentis, et effluentis per tubos aequalium foraminum sed inaequalium <lb></lb>altitudinum, habent subduplicatam rationem ” (Opera omnia, T. II, Vene­<lb></lb>tiis 1607, pag. </s>

<s>850). E più sotto, accennando ai getti parabolici dell&#039;acqua, <lb></lb>e come dalla proporzione che passa tra l&#039;altezza del liquido e il diametro <lb></lb>del foro sia possibile computar giustamente la velocità e la quantità stessa <lb></lb>del flusso; dice lo stesso Boyle essere a tutti venuta a mancare una si bella <lb></lb>notizia, “ donec Galileius et diligentissimus Mersennus (quibus observatio­<lb></lb>nes quasdam et nos iunximus) materiam hanc definire conati fluerint ” (ibid., <lb></lb>pag. </s>

<s>886). </s></p><p type="main">

<s>Essendo le esercitazioni boileiane, dalle quali abbiamo estratti questi do­<lb></lb>cumenti, scritte dopo il 1680, par che non fossero fino a quel tempo in In­<lb></lb>ghilterra penetrate le nuove dottrine idrodinamiche direttamente d&#039;Italia, ma <lb></lb>di Francia, per il magistero del Mersenno, il quale perciò verrebbe a riven­<lb></lb>dicarsi un merito e un&#039;importanza che, a giudicare dai fatti fin qui occor­<lb></lb>sici, gli fu sempre giustamente negata. </s>

<s>Fra cotesti giudizii il più antico e il <lb></lb>più a proposito è quello del Magiotti, il quale scriveva così a Galileo da <lb></lb>Roma, il dì 25 Aprile 1637, quando gli Elzeviri in Olanda erano proprio in <lb></lb>sul punto di pubblicare i dialoghi delle due Scienze nuove, in appendice ai <lb></lb>quali era stabilito di mettere le dimostrazioni <emph type="italics"></emph>De centro gravitatis;<emph.end type="italics"></emph.end> “ Non <lb></lb>credo che queste dimostrazioni siano arrivate in Francia con le altre opere, <lb></lb>perchè il p. </s>

<s>Mersenno minorita, che ha veduto il libro <emph type="italics"></emph>De motu,<emph.end type="italics"></emph.end> con le altre <lb></lb>osservazioni, di queste non fa menzione alcuna, eppure è vero che egli vuole <lb></lb>scompuzzare ogni cosa. </s>

<s>Questo frate stampa grandi e molti libracci, cercando <lb></lb>con lo sgradire altrui di acquistarsi reputazione, e forse gli riuscirà appresso <lb></lb>della marmaglia. </s>

<s>L&#039;opere, che mi sono state prestate di suo, la maggior <lb></lb>parte sono in francese, e mi sa male non esserne padrone, chè le manderei <pb xlink:href="020/01/3487.jpg" pagenum="448"></pb>acciò ella le vedesse, e a suo tempo e luogo l&#039;arrivasse con qualche fru­<lb></lb>stata ” (Alb. </s>

<s>X, 205). E in quello stesso giorno scriveva esso Magiotti nella <lb></lb>medesima sentenza al Michehni, soggiungendo che fra gli emuli, i sindaca­<lb></lb>tori, anzi i nemicissimi, che Galileo aveva in Fiandra e in Francia, poneva <lb></lb>tra i primi <emph type="italics"></emph>l&#039;abate Mersenno minorita<emph.end type="italics"></emph.end> (ivi, pag. </s>

<s>206). </s></p><p type="main">

<s>Questi erano però giudizi passionati. </s>

<s>L&#039;emulazione, veramente non pro­<lb></lb>pria d&#039;altri che del Cartesio, era facile attribuirla a tutti i Francesi capita­<lb></lb>nati da lui, e il Magiotti si veniva a confermare in questo sospetto da qualche <lb></lb>cosa, intraveduta ne&#039;primi libri mersenniani pubblicati in lingua francese, come <lb></lb>quella per esempio, che riguarda la linea percorsa da un grave cadente dalla <lb></lb>cima di una torre, rivolgendosi la Terra intorno al suo proprio asse, benchè <lb></lb>poi non facesse, rispetto a ciò, il Mersenno altro che ripetere quel che aveva <lb></lb>udito dire al Fermat, e il Fermat veramente non censurasse in odio all&#039;Au­<lb></lb>tore dei dialoghi de&#039;due Massimi sistemi, ma per solo amore del vero. </s></p><p type="main">

<s>Dell&#039;ingiusta accusa dev&#039;essersi poi ravveduto il Magiotti, quando in <lb></lb>Roma ebbe a conversare familiarmente col Mersenno, e quando, a svolgere <lb></lb>d&#039;Idraulica di lui, dop&#039;aver letto in fronte alla pag. </s>

<s>193 il titolo <emph type="italics"></emph>Magni Ga­<lb></lb>lilei, et nostrorum geometrarum elogium utile,<emph.end type="italics"></emph.end> trovò nelle due proposizioni <lb></lb>appresso compendiato, con lucido ordine e con studio a<gap></gap>oroso, il Discorso <lb></lb>galileiano delle Galleggianti. </s>

<s>Quanto però al giudicare il Frate uno scompuz­<lb></lb>zatore, i fatti, che si potevano così spesso notare leggendo, assicurarono il Ma­<lb></lb>giotti che non s&#039;era punto ingannato. </s>

<s>Ci par di vederlo sogghignar sopra il <lb></lb>libro, tenutosi innanzi aperto alla pag. </s>

<s>137, tutto intento a quel <emph type="italics"></emph>Monitum<emph.end type="italics"></emph.end><lb></lb>soggiunto alla XXVII proposizione, e le seguenti notizie gioveranno ai nostri <lb></lb>Lettori, perchè possano penetrare addentro alle ragioni di quei sogghigni. </s></p><p type="main">

<s>Dalla lettera, in altra occasione da noi citata, scritta dal Torricelli nei <lb></lb>primi giorni del 1640 al Magiotti, resulta che, fin da quel tempo, era stato <lb></lb>composto il trattato <emph type="italics"></emph>De motu proicctorum,<emph.end type="italics"></emph.end> al quale argomento si riferiva <lb></lb>l&#039;altro libretto sul principio della detta lettera commemorato, e in cui di­<lb></lb>ceva il Torricelli stesso non esister che baie, rispetto all&#039;altro che gli pa­<lb></lb>reva contenere in sè qualche cosa di suo gusto. </s>

<s>Così fatte espressioni fecero <lb></lb>nascere nel Magiotti la curiosità di vedere un saggio di quelle proposizioni <lb></lb>intorno ai proietti, nelle quali s&#039;aspettava che non qualche cosa, ma che tutto <lb></lb>anzi dovess&#039;esservi di squisitissimo gusto. </s>

<s>E il Torricelli volle compiacere <lb></lb>l&#039;amico, mandandogli da Fabriano a Roma, fra le altre proposizioni, dimo­<lb></lb>strata anche quella inserita poi a pag. </s>

<s>183 del libro stampato, e che dice <lb></lb><figure id="id.020.01.3487.1.jpg" xlink:href="020/01/3487/1.jpg"></figure></s></p><p type="caption">

<s>Figura 226.<lb></lb>come, essendo descritta intorno all&#039;asse verticale BA <lb></lb>(fig. </s>

<s>226) una parabola BDC, tutti i tiri, che col mede­<lb></lb>simo impeto e con qualunque inclinazione sian fatti da <lb></lb>A, punto focale, toccano in qualche parte la concavità <lb></lb>della parabola stessa. </s></p><p type="main">

<s>Al Magiotti parve la proposizione bellissima, e ap­<lb></lb>plicandola ai getti dell&#039;acqua, circoscritti intorno al <lb></lb>punto A, con varie inclinazioni, da riempir sufficien-<pb xlink:href="020/01/3488.jpg" pagenum="449"></pb>temente lo spazio angolare BAC; si vide apparire nella viva immaginazione <lb></lb>lo spettacolo graziosissimo di una fontana, le ripioventi fila della quale si <lb></lb>componevano insieme in una chioma configurata in conoide parabolico. </s>

<s>Pochi <lb></lb>giorni dopo correva la voce per Roma che, suggerita da un teorema del Tor­<lb></lb>ricelli, si sarebbe veduta la nuova Naiade, con sì gentile geometrico artifi­<lb></lb>zio chiomata, nei giardini del cardinale Sacchetti, alla corte del quale il Ma­<lb></lb>giotti apparteneva. </s></p><p type="main">

<s>Quella voce giunse alle orecchie del Mersenno, che si trovava allora colà, <lb></lb>e tutto affaccendato com&#039;era in rifondere i teoremi di Galileo, intorno al <lb></lb>moto de&#039;proietti, pensò di ornare la sua <emph type="italics"></emph>Ballistica<emph.end type="italics"></emph.end> della bella osservazione <lb></lb>torricelliana, come di fatti fece nella proposizione XXVIII, dop&#039;averne dato <lb></lb>un cenno in quel <emph type="italics"></emph>Monitum,<emph.end type="italics"></emph.end> sopra il quale abbiamo dianzi lasciato il Ma­<lb></lb>giotti a sogghignare così leggendo. </s>

<s>“ Plurima hic adderem de salientibus, si <lb></lb>figurae incisae non de<gap></gap>ssent, quibus lectores subleventur: v. </s>

<s>g. </s>

<s>mediam sa­<lb></lb>lientem longitudine duplam esse verticalis, altitudine vero subduplam. </s>

<s>Cum <lb></lb>verticalis est pars quarta parametri, omnes alias salientes, inter verticalem <lb></lb>et horizontalem interceptas, tangere concavam conoidis parabolici superficiem, <lb></lb>cuius focus est in medio salientium lumine, quod a clarissimo Toricello iam <lb></lb>observatum didici ” (Hydraulica cit.). </s></p><p type="main">

<s>Nella Ballistica, essendo state già le figure incise, tornò il Mersenno a <lb></lb>mostrare, con l&#039;aiuto di quelle, come nelle medie salienti, ossia ne&#039;getti in­<lb></lb>clinati ad angolo semiretto, la parabola sia nell&#039;ampiezza doppia, e nell&#039;al­<lb></lb>tezza la metà della verticale, ossia della sublimità, non lasciando d&#039;osservar <lb></lb>la tangenza di tutte le parabole interne, quali AEDC, AFC, nella medesima <lb></lb>figura 226, con la parabola esterna BDC, e concludendo così il suo discorso: <lb></lb>“ Reliqua istius figurae explicatio in Hydraulicorum praefatione videatur, <lb></lb>donec sublimiora egregii Tauricelli liber docuerit ” (Paris, 1644, pag. </s>

<s>96). </s></p><p type="main">

<s>Il Magiotti avrebbe voluto che di queste cose fosse lasciato libero il ma­<lb></lb>gistero a chi s&#039;apparteneva, senza quell&#039;altrui preventiva non richiesta in­<lb></lb>gerenza, che nel materno suo linguaggio toscano efficacemente esprimeva col <lb></lb>verbo <emph type="italics"></emph>scompuzzare.<emph.end type="italics"></emph.end> Che se, rispetto alla Ballistica, della quale il Torricelli <lb></lb>non era poi infine che un promotore di Galileo, quella inopportuna inge­<lb></lb>renza fratesca fini per eccitar sulle labbra del Magiotti un sogghigno; veniva <lb></lb>però a commovergli l&#039;animo negl&#039;insulti dell&#039;ira, quando si trattava di pre­<lb></lb>venir l&#039;opera del Torricelli e sua, in una istituzione di tanta novità e di <lb></lb>tanta importanza, qual&#039;era l&#039;ldrodinamica. </s>

<s>E perchè non si dubiti da nes­<lb></lb>suno della giusta ragione di questi primi risentimenti, ascoltiamo la storia <lb></lb>che cerca, esamina e giudica i fatti. </s></p><p type="main">

<s>In un libro, che il Mersenno aveva scritto in latino, e poi più ampia­<lb></lb>mente in francese, intorno ai suoni armonici, aveva proposto a risolvere ai <lb></lb>fisici de&#039;suoi tempi il problema: perchè mai, a voler portare una corda al <lb></lb>diapason, in cui va doppiamente veloce, non basta raddoppiare il peso che <lb></lb>la tende, ma bisogna quadruplicarlo? </s>

<s>Nessuno ancora aveva dato in Francia <lb></lb>sodisfacente risposta, quando il Mersenno stesso fece il suo primo viaggio in <pb xlink:href="020/01/3489.jpg" pagenum="450"></pb>Italia, e passato per Firenze si trattenne in Roma, dove tornò a proporre il <lb></lb>quesito armonico, in quel tempo che il Magiotti attendeva con ogni diligenza <lb></lb>a fare e a ripetere quelle esperienze idrodinamiche, raccomandategli, per <lb></lb>confermare la verità del suo supposto, pochi giorni prima dal Torricelli. </s>

<s>Si <lb></lb>discorreva da tutti i dotti della città di queste esperienze, dalle quali resul­<lb></lb>tava con certezza che, a voler attinger da un vaso doppia quantità d&#039;acqua <lb></lb>nel medesimo tempo, come a fare che il getto sopra la medesima orizontale <lb></lb>salti a doppia distanza, non basta raddoppiar nel vaso il liquido, ma biso­<lb></lb>gna quadruplicarlo. </s>

<s>Il Mersenno allora fu sorpreso da grande ammirazione, <lb></lb>ripensando all&#039;analogia che vedeva passare fra il salto della corda, e quello <lb></lb>dell&#039;acqua, rallegrandosi che un medesimo argomento sarebbe servito per <lb></lb>risolvere ambedue i curiosi problemi. </s>

<s>Rimasero però per un poco deluse le <lb></lb>sue speranze, quando seppe che la questione idraulica si riduceva alle leggi <lb></lb>dei gravi cadenti, le quali non vedeva allora per sè medesimo come si po­<lb></lb>tessero accomodare alle corde, che producono i suoni. </s>

<s>Bastò nulladimeno quel <lb></lb>che potè raccogliere in Roma dal Magiotti e dal Ricci, e in Firenze dallo <lb></lb>stesso Torricelli, perchè, tornato a Parigi, si trovasse in mano tanta mate­<lb></lb>ria, che, stemperata nelle sue proprie speculazioni, bastasse a compilare il <lb></lb>volume intitolato <emph type="italics"></emph>Hydraulica,<emph.end type="italics"></emph.end> tutta l&#039;importanza del quale si riduce alle <lb></lb>prime proposizioni, in cui si dimostrano le velocità proporzionali alle radici <lb></lb>delle altezze, e a que&#039;teoremi, che si propongono di mettere in relazione fra <lb></lb>loro gli elementi parabolici dei getti inclinati. </s></p><p type="main">

<s>Nella seconda proposizione idraulica non si fa altro che annunziare il <lb></lb>semplice fatto sperimentale, affermandosi che in egual tempo, e per luci <lb></lb>eguali, “ erit inter aquae fusae quantitates ratio subduplicata altitudinum, <lb></lb>quas tubi habuerint ” (pag. </s>

<s>47), e nella III si rende la ragion del fatto, di <lb></lb>cui, dice l&#039;Autore, tu che leggi potresti forse restar maravigliato: “ Verum <lb></lb>mirari desines, ubi noveris aquam eo solummodo premere, vel ea dumtaxat <lb></lb>velocitate tubum egredi qua moveretur, si ex eadem tubi altitudine cecidis­<lb></lb><figure id="id.020.01.3489.1.jpg" xlink:href="020/01/3489/1.jpg"></figure></s></p><p type="caption">

<s>Figura 227.<lb></lb>set, adeo ut sit eadem istius phaenomeni ratio, quae descensus <lb></lb>gravium ” (ibid., pag. </s>

<s>51). Nella quarta proposizione poi si dimo­<lb></lb>stra tanto esser maggiore la quantità dell&#039;acqua, quanto è mag­<lb></lb>giore la luce d&#039;ond&#039;esce, rimanendo però sempre il tubo pieno <lb></lb>alla medesima altezza (pag. </s>

<s>55). </s></p><p type="main">

<s>Si prosegue di qui a dimostrar cose, che sono un semplice <lb></lb>corollario di queste, infin tanto che si passa a confermare le leggi <lb></lb>proprie delle velocità, desumendole dalle relazioni che passano tra <lb></lb>le ampiezze, e le sublimità paraboliche delle <lb></lb>salienti. </s>

<s>Se quando l&#039;altezza è BH (fig. </s>

<s>227) <lb></lb>l&#039;acqua salta dalla bocca C del tubo in D, <lb></lb>per lo spazio orizontale GD, a volere che <lb></lb>salti in F, per doppio spazio, dimostravano <lb></lb>l&#039;esperienze fatte in Roma, e verificate poi <lb></lb>dal Mersenno, che non basta raddoppiare <pb xlink:href="020/01/3490.jpg" pagenum="451"></pb>l&#039;altezza in I, ma che è necessario in A quadruplicarla. </s>

<s>Ora, i lunghi di­<lb></lb>scorsi dell&#039;Autore, per confermare dai fatti, in questo modo nuovo osservati, <lb></lb>la legge delle velocità proporzionali alle radici delle altezze, come in tutti i <lb></lb>gravi cadenti; si compendiano facilmente riducendoci ai teoremi dimostrati <lb></lb>da Galileo e dal Torricelli intorno ai proietti, per i quali teoremi è noto <lb></lb>come, essendo le altezze uguali, le sublimità delle parabole BCD, BCF stanno <lb></lb>come i quadrati delle ampiezze GD, GF. </s>

<s>E perchè queste, essendo equabil­<lb></lb>mente passate nell&#039;orizzonte, son le misure delle velocità, si vedranno da <lb></lb>queste semplici osservazioni intorno al moto de&#039;proietti derivare tutte le <lb></lb>conseguenze, che il Mersenno fa soggetto delle sue proposizioni, relative alle <lb></lb>proprietà delle acque salienti. </s></p><p type="main">

<s>Quel che dunque era passato ne&#039;privati scientifici commerci fra sè e il <lb></lb>Torricelli, ora se lo vedeva il Magiotti palesato da uno straniero, con tale <lb></lb>indiscretezza, da giustificare in lui que&#039;primi risentimenti dell&#039;ira. </s>

<s>Forse una <lb></lb>cosa veniva a temperargliela, ed è che il Mersenno, benchè nella seconda <lb></lb>proposizione lasciasse credere come propria l&#039;esperienza, la ragion nulladi­<lb></lb>meno dell&#039;esperienza, che passa a dare nella proposizione terza, confessa in­<lb></lb>genuamente che non è sua. </s>

<s>Fra le XIV dichiarazioni infatti ch&#039;egli premette, <lb></lb>chiedendo scusa al lettore di non averlo fatto nel corpo dell&#039;opera, è scritta <lb></lb>anche questa: “ Decimumtertium addo Virum illustrem rogatum cur tubi <lb></lb>ex quibus salit aqua debeant esse in ratione duplicata, ut duplam aquam <lb></lb>tribuant, eamdem quam III propos. </s>

<s>Hydraulicorum assero, confestim inve­<lb></lb>nisse, idque hoc modo ” (Praefatio ad Lectorem, pag. </s>

<s>XXXIII), e il modo è <lb></lb>tale, da non restar dubbio a nessuno, ma specialmente al Magiotti, che quel­<lb></lb>l&#039;uomo illustre era lo stesso Torricelli. </s>

<s>Certo non il Magiotti solo, ma tutti <lb></lb>gli uomini onesti, direbbero che avrebbe fatto molto meglio il Mersenno a <lb></lb>pronunziare espresso quel nome, ma gli perdoneranno volentieri il fatto, in <lb></lb>grazia di quel suo XIII avvertimento, da cui principalmente ci si rivela che <lb></lb>esso Mersenno, per aver la ragione dei fatti uditi in Roma, si rivolse allo <lb></lb>stesso Torricelli, che lo fece stupire di quella sua così pronta risposta. </s>

<s>Que­<lb></lb>sta, a metterla in termini, si riduceva a una proposizione e ad uno scolio. </s>

<s><lb></lb>La proposizione rimaneva per sè medesima dimostrata, riguardando le goc­<lb></lb>ciole dell&#039;acqua affilate lungo l&#039;asse del tubo rappresentato dalla 227a figura, <lb></lb>come liberamente cadenti da A e da H in B, dove giunte hanno, per la <lb></lb>legge galileiana, acquistato tali gradi di velocità, che stanno come le radici <lb></lb>degli spazi passati. </s>

<s>Ma lo scolio, soggiunto dal Torricelli alla proposizione, <lb></lb>è tale, quale così il Mersenno lo riferisce: “ Nec obstat quod aquae prima <lb></lb>gutta incumbens lumini B (nella medesima figura) non descenderit revera <lb></lb>ex A, cum enim gutta in A, postquam descendit usque ad lumen B, sa­<lb></lb>liat eadem velocitate ex B, qua gutta prior, quae non descenderat ex A; se­<lb></lb>quitur quamcumque aliam guttam eadem velocitate ex B salire, quamdiu <lb></lb>tubus BA plenus est ” (ibid., pag. </s>

<s>XXXIV). </s></p><p type="main">

<s>Le altre cose, che ci si rivelano di qui, riguardano le ragioni del sup­<lb></lb>posto torricelliano. </s>

<s>Come mai, si saranno domandati i Lettori di questa sto-<pb xlink:href="020/01/3491.jpg" pagenum="452"></pb>ria, il Torricelli non fece nessun conto delle osservazioni della <emph type="italics"></emph>cateratta,<emph.end type="italics"></emph.end> da <lb></lb>cui mossero le speculazioni dell&#039;Arrighetti: e, potendo mostrare che la su­<lb></lb>prema superficie dell&#039;acqua scende al foro di fatto, si contentò di supporlo, <lb></lb>con tutt&#039;altri argomenti confortando la ragionevolezza del suo supposto? </s>

<s>Si <lb></lb>risponde che l&#039;osservazione fatta dall&#039;Arrighetti, nella polvere degli orioli e <lb></lb>nella farina delle tramogge, la stimò lusinghiera, e in ogni modo gli parve <lb></lb>non si verificare nell&#039;acqua de&#039;pili. </s>

<s>Il documento di ciò l&#039;abbiamo da un <lb></lb>Registro d&#039;esperienze, che si dicono essere state <emph type="italics"></emph>fatte dal serenissimo gran­<lb></lb>duca Ferdinando <gap></gap>, e da alcuni suoi cortigiani,<emph.end type="italics"></emph.end> ma che sappiamo oramai <lb></lb>doversi attribuire al Torricelli, per quella parte almeno che fra esse è di più <lb></lb>importante. </s>

<s>Quivi dunque, sotto il numero LXI, trovasi registrato: “ Messo <lb></lb>in un vaso acqua e sopra vino, di grossezza due dita, uscì prima l&#039;acqua che <lb></lb>stava sotto il vino ” (Targioni, <emph type="italics"></emph>Notizie degli aggrandimenti ecc.,<emph.end type="italics"></emph.end> T. <gap></gap> cit., <lb></lb>pag. </s>

<s>173). Ritrovato poi questo cenno dell&#039;esperienza, gli Accademici del Ci­<lb></lb>mento la vollero verificare il dì 16 Luglio 1657, lasciandocela così più par­<lb></lb>ticolarmente descritta: “ Per conoscere quali parti nei liquidi sono le prime <lb></lb>a scendere nell&#039;uscire da un vaso, si empi d&#039;acqua un cilindro di vetro, e <lb></lb>sopra di essa diligentemente si messero due dita di vin rosso, in modo che <lb></lb>galleggiasse. </s>

<s>E poi fatto un buco in fondo al vaso si vidde uscire tutta l&#039;acqua <lb></lb>ed il vino rimanere sempre l&#039;ultimo a calare, senza mai vedersi punto fili <lb></lb>di esso discendere per la profondità del vaso ” (ivi, pag. </s>

<s>661). </s></p><p type="main">

<s>Di qui, entrato in sospetto il Torricelli se le polveri e i liquidi calino <lb></lb>propriamente, come credeva l&#039;Arrighetti, per quella cavità o per quell&#039;im­<lb></lb>buto, che si osserva in essi, riducendosi verso il pertugio del vaso; non stimò <lb></lb>prudente fondare la nuova Idrodinamica sopra un&#039;osservazione, che non si <lb></lb>trovava corrispondere con l&#039;esperienza. </s>

<s>E giacchè, se il liquido non cala di <lb></lb>fatto, opera nonostante colla pressione come se vi fosse calato, pensò di ri­<lb></lb>durre il principio a un semplice supposto, come fece nel proemio al <emph type="italics"></emph>De motu <lb></lb>aquarum,<emph.end type="italics"></emph.end> che è una più larga esplicazion dello scolio, nella detta risposta <lb></lb>al Mersenno. </s></p><p type="main">

<s>Che il Boyle non penetrasse addentro a questi segreti facilmente si com­<lb></lb>prende, ma non si comprende com&#039;egli potesse credere autore del teorema <lb></lb>idrodinamico il Mersenno, se il Mersenno stesso pubblicamente confessa di <lb></lb>averlo avuto da un <emph type="italics"></emph>illustre uomo.<emph.end type="italics"></emph.end> Ben però era in grado di penetrare le cose <lb></lb>il Magiotti, nell&#039;animo del quale, se si attutì alquanto l&#039;ira, rimase oggetto <lb></lb>di pietà e di disprezzo uno scrittore, che cercava d&#039;acquistarsi reputazione, <lb></lb>talora forse con lo sgradire, ma più spesso col rivestirsi de&#039;panni altrui. </s>

<s>No­<lb></lb>nostante non fu mai meglio qualificato il Mersenno, che dal Dati: ricono­<lb></lb>sciutosi povero del suo, s&#039;aiutava, quanto poteva più, col negoziare la merce, <lb></lb>e con lo spendere il danaro dei ricchi. </s>

<s>L&#039;avrebbero potuto rimproverare di <lb></lb>ciò costoro, se avessero sempre saputo o voluto fare da sè, ma trattandosi <lb></lb>del nascosto tesoro di certi avari, o delle robe di certi inetti o ritrosi ai liberi <lb></lb>scambi, l&#039;operosità di quell&#039;ape industriosa riusciva profittevolissima, come <lb></lb>nell&#039;esempio che abbiamo ora fra mano, dal quale apparisce essere stata, <pb xlink:href="020/01/3492.jpg" pagenum="453"></pb>sull&#039;ali e sul dorso di quell&#039;istancabile volante, trasportata l&#039;Idraulica d&#039;Italia <lb></lb>al di là delle alpi. </s></p><p type="main">

<s>Che infino al 1644 non fosse ancora penetrata colà nessuna notizia di <lb></lb>quella Idrometria, alla quale il nostro Castelli aveva da sedici anni dato or­<lb></lb>dine di scienza, si rileva da ciò che, intorno a questo argomento, scrive in <lb></lb>varie sue epistole il Cartesio. </s>

<s>A lui deve, senza dubbio, il Mersenno aver <lb></lb>mandato il libro delle sue Cogitazioni fisico-matematiche appena stampato, <lb></lb>ma perchè il Filosofo era avvezzo a non spender più che un quarto d&#039;ora, <lb></lb>o alla più lunga un giorno intorno a un libro di scienza nuova, per com­<lb></lb>prenderlo e per giudicarlo, com&#039;aveva fatto della Geometria del Cavalieri <lb></lb>e de&#039;Dialoghi di Galileo; non sarebbe nella mente rimasto forse vestigio del­<lb></lb>l&#039;Idraulica mersenniana, se l&#039;Autore stesso non fosse venuto via via a ri­<lb></lb>chiamargliene l&#039;attenzione sopra le verità più fondamentali, o a viva voce <lb></lb>o per lettere familiari, alla prima delle quali così rispondeva: “ Non me­<lb></lb>mini te scripsisse antehac ad me quod altitudo aquae sit in ratione dupli­<lb></lb>cata temporis, quo per foramen effluit ” (R. Descartes, Epistolae, T. II, <lb></lb>Amstelodami 1682, pag. </s>

<s>116). E pochi giorni appresso: “ Experimentum <lb></lb>tuum verissimum puto, scilicet aquam, quae ex tubo novempedali effluit, de­<lb></lb>bere triplo fere celerius effluere quam aquam, quae ex tubo pedali effluit, <lb></lb>per foramen eiusdem magnitudinis ” (ibid., pag. </s>

<s>119). </s></p><p type="main">

<s>Ma perchè il Mersenno, annunziando i semplici fatti voleva dar motivo <lb></lb>a ritrovarne le ragioni, il Cartesio si sentì mancar nella mente il fondamento <lb></lb>idrometrico necessario. </s>

<s>Quel fondamento si riduceva al teorema del Castelli, <lb></lb>che cioè le quantità fluenti stanno in ragion composta delle velocità e delle <lb></lb>luci, nè occorreva far altro che sostituire alla ragion delle velocità quella <lb></lb>delle radici delle altezze, per confermare la verità degli sperimenti mersen­<lb></lb>niani. </s>

<s>Invece il Cartesio formulava il teorema idrometrico dietro un certo <lb></lb>giudizio, che si suole di queste cose formar la gente volgare, dicendo che le <lb></lb>quantità dell&#039;acqua dipendono dal tempo dell&#039;efflusso e dall&#039;altezza ch&#039;ella <lb></lb>ha nel tubo. </s>

<s>“ Mihi videtur posse probari quod altitudo aquae sit in ratione <lb></lb>duplicata temporis, eodem modo quo d. </s>

<s>De Beaune probavit tensionem chor­<lb></lb>darum esse suorum sonorum duplicatam. </s>

<s>Nam, quandoquidem quantitas quae <lb></lb>per foramen effluentis pendet ex tempore quo effluit, et ex altitudine tubi, <lb></lb>potest illa repraesentari per areas triangulorum ” (ibid., pag. </s>

<s>116). </s></p><p type="main">

<s>Si chiamino Q, T, A, <emph type="italics"></emph>q, t, a<emph.end type="italics"></emph.end> due diverse quantità d&#039;acqua, due diversi <lb></lb>tempi dei flussi, e due altezze diverse del liquido, nel medesimo o in due <lb></lb>tubi distinti. </s>

<s>Sarà secondo il Cartesio Q:<emph type="italics"></emph>q<emph.end type="italics"></emph.end>=A.T:<emph type="italics"></emph>a.t.<emph.end type="italics"></emph.end> E perchè da lui <lb></lb>si propone come da dimostrarsi per vera la proporzione A.<emph type="italics"></emph>a<emph.end type="italics"></emph.end>=T2:<emph type="italics"></emph>t2<emph.end type="italics"></emph.end>, dun­<lb></lb>que <expan abbr="q.">que</expan><emph type="italics"></emph>q<emph.end type="italics"></emph.end>=T′:<emph type="italics"></emph>t3<emph.end type="italics"></emph.end>, e ciò manifestamente contradice all&#039;esperienza che si <lb></lb>voleva confermar per verissima. </s></p><p type="main">

<s>Il medesimo paralogismo veniva altresì a scoprirsi da quell&#039;altro modo, <lb></lb>che così sovvenne al Cartesio, per dimostrare la verità della stessa espe­<lb></lb>rienza: “ Sit tulms AHB (nella figura 227) plenus aqua usque ad A: atten­<lb></lb>dendum est quod aqua, quae effluit per B, defluat ex alto A, et quod, si <pb xlink:href="020/01/3493.jpg" pagenum="454"></pb>totus ille tubus esset vacuus, atque una tantum aquae gutta decideret ex A <lb></lb>versus B, et alia ex H, etiam versus B, esset autem HB 1/8 AB, nec plures <lb></lb>essent in isto tubo quam duae illae guttae, una ad A, altera ad H, quae se­<lb></lb>paratim descendentes concurrerent et coniungerentur in puncto B; liquet <lb></lb>guttam aquae a puncto A demissam, ubi pervenerit ad punctum B, habitu­<lb></lb>ram noncuplum velocitatis eius quam habet gutta illa, quae ex puncto H de­<lb></lb>scendit. </s>

<s>Et proinde harum duarum guttarum simul iunctarum in puncto B, <lb></lb>velocitatem fore mediam proportionalem inter 1 et 9, hoc est triplam ” (ibid., <lb></lb>pag. </s>

<s>120). </s></p><p type="main">

<s>Se dunque le velocità son proporzionali alle radici delle altezze, si so­<lb></lb>stituisca nella proporzion sopra scritta alla ragione di T a <emph type="italics"></emph>t,<emph.end type="italics"></emph.end> quella di V a <emph type="italics"></emph>v,<emph.end type="italics"></emph.end><lb></lb>significanti le velocità, e si sostituisca ancora a quella di V a <emph type="italics"></emph>v<emph.end type="italics"></emph.end> la ragion <lb></lb>della radice di A alla radice di <emph type="italics"></emph>a<emph.end type="italics"></emph.end>:sarà Q:<emph type="italics"></emph>q<emph.end type="italics"></emph.end>=√A3:√<emph type="italics"></emph>a3<emph.end type="italics"></emph.end>, che sotto altra <lb></lb>forma contradice alla creduta verità dell&#039;esperienza. </s>

<s>Di che accortosi il Car­<lb></lb>tesio, disse fra sè — smettiamo, mi bisogna studiar queste cose un po&#039;me­<lb></lb>glio — e poi confermava il poposito fatto, così scrivendo al Mersenno: “ Sed <lb></lb>animus est ea omnia, quae ad hanc de motibus aquae materiam pertinent, <lb></lb>aliquando, curiosius examinare. </s>

<s>Et ne porro cogar quae iam scripsero re­<lb></lb>tractare, nihil superaddam ” (ibid., pag. </s>

<s>120). </s></p><p type="main">

<s>Quell&#039;<emph type="italics"></emph>aliquando<emph.end type="italics"></emph.end> però, a cui rimetteva il Cartesio lo studio dell&#039;Idrome­<lb></lb>tria, non venne così presto. </s>

<s>Alcune settimane dopo il Mersenno tornava ad <lb></lb>annunziargli un altro simile sperimento, dicendogli di aver raccolto quattro <lb></lb>volte meno acqua da una luce circolare di una mezza linea di diametro, che <lb></lb>da quella di una linea intera, supposto che rimanga il tubo pieno, in am­<lb></lb>bedue i casi, alla medesima altezza. </s>

<s>Il fatto conseguiva immediatamente certo <lb></lb>dal teorema del Castelli, che dava, essendo uguali le altezze, le quantità pro­<lb></lb>porzionali alle aree delle luci, le quali aree, stando come i quadrati de&#039;raggi, <lb></lb>ossia, nella fatta supposizione, come uno a quattro; doveva necessariamente <lb></lb>la portata della luce piccola essere un quarto solo della più grande. </s>

<s>Così pure <lb></lb>aveva dimostrato il Mersenno, nella sua IV proposizione, e così aveva con­<lb></lb>cluso, astrazion fatta da tutte le resistenze, secondo l&#039;avvertimento ch&#039;egli <lb></lb>cita dalla VII appendice del Castelli. </s>

<s>Il Cartesio però che non avendo preso <lb></lb>ancora abito di scienza in queste cose, giudicava a modo del volgo, disse pa­<lb></lb>rergli incredibile che per solo diminuire della metà il raggio alla luce, le <lb></lb>altre cose rimanendo pari, si dovesse ridurre a un quarto l&#039;erogazione. <lb></lb></s>

<s>“ Experimentum tuum, quo dimidiae lineae foramen quadruplo pauciorem <lb></lb>aquam effundit quam integrae, mihi videtur prorsus incredibile, caeteris pa­<lb></lb>ribus, hoc est curando ut tubus usque ad fastigium semper plenus maneat ” <lb></lb>(ibid., pag. </s>

<s>131). </s></p><p type="main">

<s>Nell&#039;epistola seguente par che tenga più credibile essere le portate pro­<lb></lb>porzionali ai diametri delle luci (ivi, pag. </s>

<s>136), ma finalmente incominciano <lb></lb>a rivelarglisi le cose nel loro più vero aspetto. </s>

<s>Se i due tubi AE, BG (fig. </s>

<s>228) <lb></lb>sian fra le medesime parallele AC, DG, e sian dal piano orizontale, che passa <lb></lb>per DG, tagliati in modo, che l&#039;area dell&#039;ellisse FG torni uguale all&#039;area <pb xlink:href="020/01/3494.jpg" pagenum="455"></pb>del circolo ED; credeva il Cartesio che, anch&#039;essendo BG più stretto di AE, <lb></lb>verserebbero ambedue i tubi dalle loro bocche uguali quantità d&#039;acqua, nei <lb></lb><figure id="id.020.01.3494.1.jpg" xlink:href="020/01/3494/1.jpg"></figure></s></p><p type="caption">

<s>Figura 228.<lb></lb>medesimi tempi. </s>

<s>“ Si tubi AE, BG inter parallelas <lb></lb>AC, DG positi sint, aut inter corum aperturas, seu <lb></lb>bases aequales et similes, etiamsi si longior sit <lb></lb>breviori angustior, credo illos parem aquae quan­<lb></lb>titatem emissuros ” (ibid., pag. </s>

<s>166). Nè del creder <lb></lb>così poteva d&#039;altronde essergli venuto il motivo, <lb></lb>che dall&#039;essersi finalmente persuaso non dipendere <lb></lb>le quantità dalle altezze e dal tempo, ma dalle <lb></lb>sezioni, e dalle velocità, che sono manifestamente uguali, essendo, così nel <lb></lb>tubo retto come nell&#039;inclinato, scese l&#039;acque per uguali spazi perpendicolari. </s></p><p type="main">

<s>In ogni modo la certezza di queste verità idrometriche non apparisce, <lb></lb>che dopo qualche tempo, in una, che è delle ultime epistole raccolte in que­<lb></lb>sta seconda parte. </s>

<s>Quivi, ammettendo il Cartesio che le gocciole scendano <lb></lb>realmente dalla sommità del tubo, rappresentato nella figura 227, e giunte <lb></lb>in B, con l&#039;accelerazione della discesa, si rivolgano orizontalmente per la <lb></lb>CL; dimostra che le CD, CF son curve paraboliche, “ quemadmodum optime <lb></lb>observavit Galileius ” (ivi, pag. </s>

<s>392). Ma il più bello argomento, da provare <lb></lb>che, dopo tanti penosi errori, la mente del Cartesio erasi finalmente riposata <lb></lb>nel vero, è una osservazione, nella quale poi s&#039;incontrò il Borelli. </s>

<s>Se in <lb></lb>fondo al vaso AB (fig. </s>

<s>229), mantenuto costantemente pieno fino al livello <lb></lb><figure id="id.020.01.3494.2.jpg" xlink:href="020/01/3494/2.jpg"></figure></s></p><p type="caption">

<s>Figura 229.<lb></lb>AC, siano applicati due tubi DF, FG, d&#039;ugual diametro, <lb></lb>ma di differente lunghezza, i due cilindri d&#039;acqua escono <lb></lb>dalle bocche E, G con velocità proporzionali alle radici <lb></lb>delle altezze EH, GI, cosicchè le quantità d&#039;acqua, rac­<lb></lb>colte qua e là nel medesimo tempo, corrispondono ai teo­<lb></lb>remi, che il Mersenno traduceva nella sua Idraulica dal <lb></lb>trattato del Castelli, e dalle speculazioni del Torricelli. <lb></lb></s>

<s>“ Deinde etiam adverto cylindros ex aqua, aut ex alia­<lb></lb>que vis materia, primo quo incipiunt descendere mo­<lb></lb>mento, co celerius moveri, quo longiores sunt, idque in ratione longitudinum <lb></lb>subduplicata ” (ibid., pag. </s>

<s>392). </s></p><p type="main">

<s>A questo punto non vogliamo proseguire la storia, senza fare un&#039;osser­<lb></lb>vazione. </s>

<s>Ci tornano alla memoria coloro, che intesero di togliere o di me­<lb></lb>nomare i meriti del Castelli, dicendolo un plagiario, un restauratore della <lb></lb>scienza di Frontino e del Buteone. </s>

<s>Ora è certo che, mentre la letteratura <lb></lb>romana era a Italiani e a Francesi comune, i Francesi avevano il Buteone <lb></lb>per loro connazionale, e nonostante s&#039;è, per l&#039;esempio del Mersenno e del <lb></lb>Cartesio, veduto come nel 1644, quando fra noi era da sedici anni divulgato <lb></lb>il libro della Misura delle acque correnti, là s&#039;ignorassero dell&#039;Idrometria i <lb></lb>primi principii. </s></p><p type="main">

<s>S&#039;osservi inoltre che quasi connazionale ai Francesi era lo Stevino, e <lb></lb>nonostante aspettarono, a riconoscere le pressioni idostatiche, che il Pascal <pb xlink:href="020/01/3495.jpg" pagenum="456"></pb>s&#039;inspirasse alle spiegazioni, che il Torricelli dava dell&#039;esperienza dell&#039;ar­<lb></lb>gento vivo. </s>

<s>Chi vuol conoscere in quali condizioni si trovasse fra loro l&#039;Idro­<lb></lb>statica, prima di questo tempo, ripensi alle parole, che premetteva alla sua <lb></lb>XLIII proposizione il Mersenno: “ Omnes fere eredunt corpus aqua gravius <lb></lb>ad usque fundum descendere, quod moles aquae illi corpori aequalis nequeat <lb></lb>ei resistere, vique maiore cogatur loco cedere: corpus vero aqua levius ali­<lb></lb>quam sui partem mergere, quod vim habeat eiiciendi, et elevandi aquae mo­<lb></lb>lem parti mersae aequalem ” (Hydraulica cit., pag. </s>

<s>195). E a ridurre al <lb></lb>senno le menti, così dannosamente traviate, di quasi tutti, non le richiama <lb></lb>il Mersenno alla verità delle proposizioni steviniane, ma al Discorso di Ga­<lb></lb>lileo intorno alle galleggianti, ch&#039;ei magnifica, e dentro cui crede pigliar sug­<lb></lb>gello di verità anche le proposizioni, che dalla verità son più aliene, qual&#039;è <lb></lb>quella per esempio che non si senta il marangone oppresso, certi essendo <lb></lb>“ aquam, in aqua gravitatis aequalis, nihil ponderare ” (ibid., pag. </s>

<s>205). </s></p><p type="main">

<s>Ma benchè sia la fiaccola fumosa, è pure un gran benefizio a chi ri­<lb></lb>trovasi al buio. </s>

<s>Del qual benefizio debbono i Francesi esser grati al Mer­<lb></lb>senno, che recò a loro, insieme con l&#039;Idrostatica di Galileo, l&#039;Idrometria del <lb></lb>Castelli, e l&#039;Idrodinamica torricelliana. </s>

<s>Grati pure, placate l&#039;ire al Magiotti, <lb></lb>glie ne dovrebbero essere gl&#039;Italiani, non solamente per avere diffusa la loro <lb></lb>scienza oltremonti, ma per essere stato cote ai loro ingegni. </s>

<s>Gli esempi, che <lb></lb>di ciò ne porge la storia in vari soggetti, non mancano in questo, che ab­<lb></lb>biamo per le mani. </s></p><p type="main">

<s>Il trattato <emph type="italics"></emph>De motu aquarum<emph.end type="italics"></emph.end> era già da un anno venuto in Firenze alla <lb></lb>luce. </s>

<s>Il Mersenno sente che ci manca qualche cosa, e vuol che il Torricelli <lb></lb>riduca l&#039;opera alla sua perfezione. </s>

<s>Tendono a questo fine le seguenti parole, <lb></lb>che scriveva, non all&#039;emulo, ma al maestro, da Roma, il di 15 Marzo 1645: <lb></lb>“ Hactenus expectavi Vir illustrissime, mei dubii harmonici solutionem, quam <lb></lb>Vestra Dommatio meditata est: cur nempe nervus ad aliquem sonum acu­<lb></lb>tiorem adducendo ac tendendo, pondera seu vires tendentes in ratione du­<lb></lb>plicata intervallorum harmonicorum appendenda sint. </s>

<s>Cum enim, ut iam <lb></lb>scripseram, diapason v. </s>

<s>g. </s>

<s>habeat suam rationem 1 ad 2, quare vis tendens <lb></lb>nervum ad sonum acutum ut 2 debet esse, ad vim facientem sonum ut <lb></lb>unum, ut 4 ad 1. Erat etiam ex re ut doceret V. D. cur aqua fluens ex fo­<lb></lb>ramine facto in imo tubi censeatur eadem exilire velocitate, ac si descendis­<lb></lb>set a tubi summitate. </s>

<s>Id enim supponit V. D., et tamen aqua in imo fluens <lb></lb>re vera non descendit ex summitate tubi ” (MSS. Gal. </s>

<s>Disc., T. XLI, fol. </s>

<s>16). </s></p><p type="main">

<s>Si vede che di ciò, che aveva scritto nella prefazione <emph type="italics"></emph>ad Lectorem,<emph.end type="italics"></emph.end> “ Nec <lb></lb>obstat quod aquae prima gutta non descenderit revera ” il Mersenno o se <lb></lb>n&#039;era dimenticato, o che gli era in questo tempo venuta a mancar la fede <lb></lb>a quell&#039;Uomo illustre che, domandato del perchè si richiedesse altezza qua­<lb></lb>drupla a voler ottenere quantità doppia, l&#039;aveva compiaciuto di così pronta <lb></lb>risposta. </s>

<s>Il Torricelli dall&#039;altra parte che, nel proemio alla sua appendice <lb></lb><emph type="italics"></emph>De motu aquarum,<emph.end type="italics"></emph.end> credeva d&#039;essersi intorno a ciò spiegato abbastanza, ri­<lb></lb>mase in silenzio, ma il Mersenno, anche tornato a Parigi, non gli dava pace. <pb xlink:href="020/01/3496.jpg" pagenum="457"></pb>Di là scrivendogli il dì 26 Agosto 1646, dop&#039;avergli fatto un monte di do­<lb></lb>mande, “ denique, voleva sapere, si rationem repereris meae, quum essem <lb></lb>Romae, quaestionis de Musica: nempe cur vis requiratur quadrupla ad ner­<lb></lb>vum elevandum vel acuendum usque ad diapason seu octavam, cum ratio <lb></lb>diapasonis sit tantum dupla. </s>

<s>Me novis amiciliae vinculis obstringes, si eam <lb></lb>mihi explicaveris, quemadmodum et cur tubus aqueus debeat esse in ratione <lb></lb>dupla quoad altitudinem, ut duplam aquam effundat, utriusque enim diffi­<lb></lb>cultatis vel eamdem vel germanam rationem esse vix dubito ” (ivi, fol. </s>

<s>64). </s></p><p type="main">

<s>Il pensiero gli era nato, come dicemmo, quattro anni prima in Roma, <lb></lb>ma non aveva ancora potuto trovar chi gli dicesse quella ragione, che alle <lb></lb>due difficoltà sentiva dover esser germana. </s>

<s>Solamente monsù De Beaune <lb></lb>aveva in questo tempo tentato di risolvere il quesito armonico, per via di <lb></lb>due triangoli, gli spazi de&#039;quali, presi a rappresentare le forze tendenti la <lb></lb>corda, dimostrava esser proporzionali ai quadrati de&#039;lati omologhi, rappre­<lb></lb>sentanti le celerità delle vibrazioni, da cui dipendono le acutezze dei suoni. </s>

<s><lb></lb>Il Cartesio vedemmo come, nell&#039;epistola XXIX, si studiasse di applicare il <lb></lb>metodo del Beaune a risolvere il quesito armonico, ma non par che il Mer­<lb></lb>senno ne rimanesse appagato. </s>

<s>In una infatti delle ultime proposizioni della <lb></lb><emph type="italics"></emph>Ballistica,<emph.end type="italics"></emph.end> mentre la difficoltà “ de necessaria chordae tensione in ratione <lb></lb>quadrupla, ut duplo moveatur celerius ” dice “ ab acutissimo viro domino De <lb></lb>Beaune explicata ” (Paris 1644, pag. </s>

<s>132), dell&#039;altra difficoltà, riguardante <lb></lb>l&#039;acqua, dà una spiegazione diversa, e tale da valer veramente per ambedue i <lb></lb>quesiti. </s>

<s>“ Quemadmodum enim, cum tubus aquae libra plenus salit uno gradu <lb></lb>velocitatis a lumine, debent addì 3 librae ut duplo, quinque praeterea librae <lb></lb>ut triplo, et postea 7 aquae librae ut quadruplo velocitatis gradu saliant; <lb></lb>ita funi seu fidibus addenda sunt pondera 1, 4, 9 et 16, ut praedictis gra­<lb></lb>dibus vadant et redeant ” (ibid., pag. </s>

<s>130). </s></p><p type="main">

<s>Risoluto, in questa medesima proposizione XXXVI della <emph type="italics"></emph>Ballistica,<emph.end type="italics"></emph.end> infino <lb></lb>dal 1644, il quesito delle corde tese, e insieme anche l&#039;altro delle acque sa­<lb></lb>lienti; nel 1646 il Mersenno stesso tornava a domandar di ciò la soluzione <lb></lb>al Torricelli, il quale aveva mostrato di non approvare la sopra riferita ana­<lb></lb>logia. </s>

<s>Ma ora sarebbe il tempo di dire quello che ne pensava, giacchè di <lb></lb>pensarci aveva promesso, e si sperava che avesse mantenuto. <emph type="italics"></emph>Hactenus <lb></lb>expectavi solutionem quam V. D. meditata est.<emph.end type="italics"></emph.end> A voler sapere con cer­<lb></lb>tezza il resultato di queste meditazioni bisognerebbe veder le lettere del Tor­<lb></lb>ricelli al Mersenno, ma perchè queste ci mancano, non si può che per via <lb></lb>di congetture, in qualche modo, supplire al difetto. </s></p><p type="main">

<s>S&#039;accennò altrove che la nuova regola di misurare le quantità dell&#039;acqua <lb></lb>era quella medesima, che un mezzo secolo dopo si proporrebbe generalmente, <lb></lb>per misurare qualunque sorta di forze vive. </s>

<s>Come Galileo paragonava la forza <lb></lb>della percossa ai pesi morti, così il Castelli prendeva le pressioni dell&#039;acqua <lb></lb>stagnante per la misura delle velocità dell&#039;acque correnti. </s>

<s>Quest&#039;errore degli <lb></lb>antichi, e di cui non s&#039;erano avveduti i due grandi Maestri, fu sagacemente <lb></lb>scoperto dal Torricelli, il quale pensò che, per passar dal conato al moto at-<pb xlink:href="020/01/3497.jpg" pagenum="458"></pb>tuale, era necessario che la virtù si moltiplicasse in sè stessa, cosicchè di <lb></lb>doppia diventasse quadrupla, di tripla nonupla e così di seguito, secondo la <lb></lb>progressione dei numeri quadrati, d&#039;onde la regola di misurare dai quadrati <lb></lb>delle velocità tutte le forze vive. </s></p><p type="main">

<s>Il ragionamento germano a questo, fatto dal Torricelli per risolvere l&#039;al­<lb></lb>tra difficoltà relativa alle corde armoniche, secondo che desiderava il Mer­<lb></lb>senno, è facile congetturare di qui che fosse tale: Un peso doppio può dop­<lb></lb>piamente tendere la corda. </s>

<s>Ma perchè la forza morta della tensione diventi <lb></lb>viva, nel moto doppio della v<gap></gap>brazione, bisogna che si moltiplichi in sè stessa, <lb></lb>cosicchè, se quella era due, questa si riduca a quattro, com&#039;è confermato <lb></lb>dall&#039;esperienza. </s></p><p type="main">

<s>Il Mersenno non poteva penetrare la profondità di questi pensieri, come <lb></lb>non la penetrarono i Matematici contemporanei e i posteriori, che dettero <lb></lb>tanta faccenda al Leibniz, quando volle formulare il teorema delle forze vive: <lb></lb>Di qui è che i primi promotori dell&#039;Idrodinamica torricelliana trovarono espe­<lb></lb>diente l&#039;ammettere che la velocità dell&#039;acqua, nell&#039;atto dell&#039;uscire dai fori <lb></lb>dei vasi, sia tale, non perchè essa acqua operi con la sua pressione come se <lb></lb>vi fosse scesa dal supremo livello, secondo che supponeva il Torricelli, ma <lb></lb>perchè ella vi discenda in realtà, non in tutta la sua mole, ma nelle goc­<lb></lb>ciole via via componenti il cilindro liquido, che ha l&#039;apertura del foro per <lb></lb>base. </s>

<s>“ Neque enim dubium est, osservava il Cartesio, quin primae quaelibet <lb></lb>guttae huius aquae eadem cum sequentibus celeritate effluant, modo suppo­<lb></lb>natur tubus manere interea semper aequaliter plenus, et si attendatur quod, <lb></lb>cum aqua ex hoc tubo effluit per foramen C (figura 227 qui addietro), non <lb></lb>opus est ut tota aqua in eo contenta moveatur, sed solum ut guttae omnes <lb></lb>quae componunt exiguum cylindrum, cuius basis est foramen C, et qui ad <lb></lb>fastigium usque extenditur, alia post aliam descendant; facile concipietur fore <lb></lb>ut gutta, quae est in puncto A, postquam pervenerit ad puntum C, acquisi­<lb></lb>verit, descendendo ab A usque ad C, duplum celeritatis eius, quam acqui­<lb></lb>sivisset si descendisset tantum ab H, et proinde, cum egreditur per C, duplo <lb></lb>celerius movetur, quando tubus ad quatuor pedum, quam cum ad unius tan­<lb></lb>tum altitudinem plenus est, atque idem est de reliquis guttis, quandoquidem <lb></lb>eadem vi moventur (Epistol., P. </s>

<s>H cit., pag. </s>

<s>391). </s></p><p type="main">

<s>A questa medesima conclusione conduceva il ragionamento del Nardi, <lb></lb>quando, alla ragion meccanica di Galileo, volle sostituirne una fisica, per <lb></lb>poter più facilmente spiegare l&#039;equilibrio de&#039;liquidi in vasi comunicanti di <lb></lb><gap></gap> grandezze, come sarebbe un tino e una gracile canna, dicendo che <lb></lb>l&#039;acqua in questa è solamente premuta da altrettant&#039;acqua, quanta se ne <lb></lb>conterrebbe in una simile canna, immaginata continuarsi in mezzo al liquido <lb></lb>del vaso grande: c<gap></gap>ò che si conferma, dice egli, <emph type="italics"></emph>dall&#039;apparire nella super­<lb></lb>ficie sua certa fossetta, corrispondente in tutto al sito e lunghezza della <lb></lb>canna, nella qual fossa continuamente d&#039;ogni intorno l&#039;umore circostante <lb></lb>sdrucciola.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>Il Borelli pur<gap></gap>olse questi pensieri del Nardi, nel suo hbro <emph type="italics"></emph>De mo-<emph.end type="italics"></emph.end><pb xlink:href="020/01/3498.jpg" pagenum="459"></pb><emph type="italics"></emph>tionibus naturalibus<emph.end type="italics"></emph.end> alla CCXVII proposizione, dove, per dichiarar come le <lb></lb>velocità e le moli attinte dipendono solamente dalla grandezza del foro, e <lb></lb>dall&#039;altezza del liquido, qualunque sia del resto l&#039;ampiezza del vaso, si serve <lb></lb>di questo esempio: “ Si fuerit fistula aliqua vitrea ad horizontem perpen­<lb></lb>dicularis, et puteus aeque altus, in cuius fundo aperiatur foramen, prorsus <lb></lb>aequale infimo fistulae foramini; tunc aqua ab orificio putei profluit eadem <lb></lb>fere velocitate, et aequali mole ac ex illa fistula vitrea aeque plena egredi­<lb></lb>tur, proterea quod in aqua putei concipi debet fistula perpendiculariter <lb></lb>horizonti erecta ab infimo foramine usque ad summitatem aquae, et solum­<lb></lb>modo praedicta aqua in fistula imaginaria contenta fluit, reliqua vero colla­<lb></lb>teralis innititur sustentaturque a fundo impenetrabili et firmo ipsius putei, <lb></lb>a quo aquae fluxus perpendicularis impeditur, et ideo perinde aqua excur­<lb></lb>rit perpendiculariter, ac si in fistula vitrea contineretur ” (pag. </s>

<s>457). </s></p><p type="main">

<s>Il Nardi e il Borelli toccarono il soggetto per incidenza, ma il Baliani <lb></lb>ne compose un trattato a parte, intitolato <emph type="italics"></emph>De motu gravium liquidorum,<emph.end type="italics"></emph.end><lb></lb>che distinse in tre libri. </s>

<s>Per dare un&#039;idea del particolar modo della tratta­<lb></lb>zione, vogliamo citare dal libro primo il teorema secondo, e i due problemi <lb></lb>che gli succedono. </s>

<s>Quel teorema è proposto così: “ In pluribus canalibus, <lb></lb>ductis ad idem planum orizontale, aquae quantitates sunt ut canales ” (Ge­<lb></lb>nuae 1646, pag. </s>

<s>117). E si dimostra dietro il postulato che le quantità d&#039;acqua <lb></lb>son proporzionali ai tempi degli efflussi, applicandovi il teorema di Mecca­<lb></lb>nica che dice i tempi stare come le lunghezze dei piani, ossia, nel caso pre­<lb></lb>sente, come le lunghezze degli stessi canali. </s></p><p type="main">

<s>Il primo poi dei detti problemi è tale: “ In canali declinante reperire <lb></lb>portionem continentem aquam aequalem eius, quae est in perpendiculari ” <lb></lb><figure id="id.020.01.3498.1.jpg" xlink:href="020/01/3498/1.jpg"></figure></s></p><p type="caption">

<s>Figura 230.<lb></lb>(ibid., pag. </s>

<s>118). E supposto essere sopra l&#039;orizontale CB <lb></lb>(fig. </s>

<s>230) il canale inclinato AC, e il perpendicolo AD, si <lb></lb>risolve il quesito conducendo da B, sopra l&#039;AC, la perpen­<lb></lb>dicolare DB, che precide in D tal porzione AD del canale, <lb></lb>qual&#039;è quella richiesta. </s></p><p type="main">

<s>L&#039;altro problema, che si diceva, è così esposto: “ In <lb></lb>quibusdam canalibus, quomodolibet inclinatis, reperire por­<lb></lb>tiones continentes aquam aequalem cuiusvis dicti canalis ” (ibid., pag. </s>

<s>119). <lb></lb><figure id="id.020.01.3498.2.jpg" xlink:href="020/01/3498/2.jpg"></figure></s></p><p type="caption">

<s>Figura 231.<lb></lb>Siano AB, AC, AD (fig. </s>

<s>231) i proposti canali: se in­<lb></lb>torno al perpendicolo AE si descriva un mezzo cer­<lb></lb>chio, le porzioni AB′, AC′, AD′, tagliate da lui, son <lb></lb>quelle cercate. </s></p><p type="main">

<s>Si vede bene come, così procedendo, tutte le pro­<lb></lb>posizioni del terzo dialogo delle due Nuove Scienze si <lb></lb>possano trasformare in un trattato d&#039;Idrodinamica, senza <lb></lb>far altro che cambiare i piani inclinati e le cadenti per­<lb></lb>pendicolari in canali pieni d&#039;acque correnti. </s>

<s>Nè diversa <lb></lb>indole da questo ha il libro secondo. </s>

<s>Nel terzo poi, pro­<lb></lb>ponendosi l&#039;Autore di trattare del flusso dai vasi, a <pb xlink:href="020/01/3499.jpg" pagenum="460"></pb>dimostrar la proposizione fondamentale formulata: “ Impetus foraminum <lb></lb>aequalium vasis sunt in subduplicata ratione distantiae a summo vasis ” <lb></lb>(pag. </s>

<s>162), gli basta richiamarsi all&#039;esperienza, che mostra l&#039;acqua ca­<lb></lb>dere al foro con l&#039;impeto suo naturale dal sommo dal vaso. </s>

<s>“ Aqua tran­<lb></lb>siens per vasis foramen decurrit a summo vasis ad foramen, tamquam per <lb></lb>canalem perpendicularem. </s>

<s>Quod experieris, si vas aqua plenum, in cuius imo <lb></lb>sit foramen, sit perspicuum: videbis etenim in eo formali canale per quod <lb></lb>aqua superior exeat ” (ibid., pag. </s>

<s>158). </s></p><p type="main">

<s>Ai magnificatori del Newton, autore della famosa cateratta, questi del <lb></lb>Cartesio, del Nardi, del Borelli e del Baliani sembreranno promozioni di <lb></lb>grande importanza. </s>

<s>L&#039;importanza però svanisce in tutto o in grandissima <lb></lb>parte, riflettendo che al Torricelli non era sfuggito il pensiero di tutti i suoi <lb></lb>promotori, dal Cartesio al Newton, ma ch&#039;egli fu costretto a rinunziarvi dalle <lb></lb>diligenti osservazioni dei fatti. </s>

<s>La promozione desiderata si sarebbe dovuta <lb></lb>far consistere piuttosto nell&#039;applicazione delle leggi delle velocità al corso <lb></lb>dei fiumi, ma nessun si rimosse, rispetto a ciò, dal proposito del Torricelli, <lb></lb>da noi esposto con le ultime parole del capitolo precedente. </s></p><p type="main">

<s>Il Mersenno, dop&#039;aver notate le differenze del moto dell&#039;acqua, dentro <lb></lb>i tubi o per i fiumi, mentre per quelli dimostra verificarsi, come vedemmo, <lb></lb>la legge torricelliana, per questi non crede prudente dilungarsi dai principii <lb></lb>e dalla proposizion del Castelli, benchè conosca dover questa venire alterata <lb></lb>da innumerevoli impedimenti. </s>

<s>“ Jam vero statuamus fluminis alicuius cur­<lb></lb>rentis altitudinem, ex alterius fluminis aequalis adventu, duplo maiorem. </s>

<s>Si <lb></lb>praeterea novi fluminis advenientis impetus seu velocitas prioris fluminis sit <lb></lb>duplo maior, fiat altitudo nova composita ex ratione altitudinum et ex ra­<lb></lb>tione velocitatum utriusque fluvii, adeo ut qui prius, ob solam aequalem <lb></lb>advenientis altitudinem duplo fuerat altior, ob duplam advenientis veloci­<lb></lb>tatem quadruplo fiat altior. </s>

<s>Sed cum mare refluens non parum videatur in­<lb></lb>terturbare fluviorum in illud ingredientium velocitates, et alia occurrant im­<lb></lb>pedimenta innumera, haec libenter omitto studiosoribus: videatur interea <lb></lb>tractatus Benidicti Castelli, qui nuper ad plures abiit ” (Hydraulica cit., <lb></lb>pag. </s>

<s>177, 78). </s></p><p type="main">

<s>Tale udimmo essere stato il motivo per cui, volendo il Baliani passar <lb></lb>da quello de&#039;solidi a trattar del moto de&#039;liquidi, lasciò l&#039;opera imperfetta <lb></lb>(Alb. </s>

<s>IX, 142). E il Cartesio, dop&#039;aver risposto secondo qual proporzione si <lb></lb>faccia il moto dell&#039;acqua dentro i tubi, soggiungeva: “ Sed hoc ad flumi­<lb></lb>num decursum aptari nequit, co quod ad ostium suum occursu maris valde <lb></lb>tardentur ” (Epist. </s>

<s>cit., pag. </s>

<s>137). Altrove, mettendo in campo la questione <lb></lb>se il fiume corra più lento in fondo o alla superficie, e risolvendola a modo <lb></lb>del Cardano, terminava il Cartesio stesso così, con questa notabile osserva­<lb></lb>zione, il suo discorso: “ Neque etiam credo posse illorum declivitatem ex <lb></lb>illorum celeritatis inaequalitate colligi, sed solum libella explorando ” (ibid., <lb></lb>pag. </s>

<s>167), come, a proposito delle Chiane, diceva il Torricelli, e aveva detto <lb></lb>già Galileo, a proposito del Bisenzio. </s></p><pb xlink:href="020/01/3500.jpg" pagenum="461"></pb><p type="main">

<s>Il Borelli, dop&#039;aver, nel capitolo XI <emph type="italics"></emph>De motionibus natur.,<emph.end type="italics"></emph.end> illustrata in <lb></lb>modi nuovi la legge delle velocità proporzionali alle radici delle altezze, men­<lb></lb>tre si consideri l&#039;acqua scorrere per i tubi; trattandosi poi dei fiumi ritè­<lb></lb>neva anch&#039;egli per verissima la proposizione seconda del secondo libro idro­<lb></lb>metrico del Castelli. </s>

<s>Il documento di ciò ce lo esibisce la storia delle correzioni <lb></lb>da farsi alla dimostrazion della detta proposizione. </s>

<s>E perchè in essa storia <lb></lb>si comprendono, insieme col Borelli, i più valenti Idraulici italiani di quei <lb></lb>tempi, non vogliamo lasciar di narrarla ne&#039;suoi particolari, sembrandoci che <lb></lb>in tanta varietà d&#039;ingegni non si possa meglio che di qui far apparire la <lb></lb>concorde unità delle opinioni. </s></p><p type="main">

<s><emph type="center"></emph>III.<emph.end type="center"></emph.end></s></p><p type="main">

<s>La radicale riforma, che veniva a subir l&#039;opera della Misura delle acque <lb></lb>correnti dopo la nuova istituzione idrodinamica, vedemmo come fosse sen­<lb></lb>tita e consentita dal Castelli stesso ne&#039;colloqui, e negli epistolari commerci <lb></lb>col Torricelli. </s>

<s>Si disse, in sull&#039;ultimo del precedente capitolo, altresì il modo <lb></lb>come si pensava particolarmente d&#039;introdur nel libro la detta riforma, asse­<lb></lb>gnando alle acque fluenti dai piccoli fori dei vasi altra legge, che a quelle <lb></lb>correnti per i canali e per gli alvei dei fiumi, secondo che, dietro esperienze <lb></lb>diligentemente istituite in ambedue i casi, pareva consigliar la Natura stessa <lb></lb>alla scienza dell&#039;uomo. </s>

<s>Ma gli stami, così bene orditi dal Castelli, furono <lb></lb>nell&#039;Aprile del 1643 recisi dalla morte, cosicchè il manoscritto originale del <lb></lb>secondo libro Delle acque correnti si rimase in Roma, nella cella del mona­<lb></lb>stero di S. Callisto, non variato di nulla dalla copia dedicata al neonato prin­<lb></lb>cipe di Toscana, e consegnata come si disse nelle mani del principe Leopoldo. </s></p><p type="main">

<s>Il Torricelli allora sentì nel pio animo il dovere di ricambiare il be­<lb></lb>nefizio. </s>

<s>E come il Castelli avevagli promesso di onorare col nome e con le <lb></lb>opere di lui il suo libro della Misura delle acque correnti, così ora egli pro­<lb></lb>poneva di ornare il suo trattato <emph type="italics"></emph>De motu aquarum<emph.end type="italics"></emph.end> col nome e con l&#039;opere <lb></lb>del Castelli. </s>

<s>L&#039;idrometria di questo, che nell&#039;aspetto presente discordava, si <lb></lb>doveva conciliar con l&#039;Idrodinamica nuova, e la bellezza e la perfezion del­<lb></lb>l&#039;opera, che ne sarebbe di qui resultata, si può facilmente immaginar da <lb></lb>ognuno, che ripensi all&#039;ingegno del Torricelli, e allo zelo di mantenere inte­<lb></lb>merata dagli attacchi degli emuli la reputazione del suo caro maestro. </s>

<s>Ma <lb></lb>tutto intento com&#039;era allora alle opere sue geometriche, aspettava, a metter <lb></lb>mano al nuovo libro del Moto delle acque, di aver dato quelle stesse opere <lb></lb>alle stampe. </s></p><p type="main">

<s>Intanto a Michelangiolo Ricci era aperta dai monaci la cella, dov&#039;era <lb></lb>morto colui, che l&#039;aveva amato e onorato tanto, e gli erano presentate le <lb></lb>opere postume perchè l&#039;esaminasse, e specialmente il secondo libro della <lb></lb>Misura delle acque. </s>

<s>Concorse allora col desiderio di quei padri il suo vivis-<pb xlink:href="020/01/3501.jpg" pagenum="462"></pb>simo di pubblicare il manoscritto, de&#039;pregi del quale era assai bastante ca­<lb></lb>parra il nome dell&#039;Autore. </s>

<s>E mentre era in trattare di ciò col tipografo, ne <lb></lb>dette avviso a Firenze al Torricelli, il quale volle avvertirlo di quel ch&#039;era <lb></lb>passato fra sè e il padre don Benedetto, a proposito di alcune correzioni da <lb></lb>farsi al libro di lui, e come, lasciandolo uscir fuori a quel modo, potrebbe <lb></lb>dare occasion di censure agli emuli, e di calunnie agli invidiosi, specialmente <lb></lb>stranieri: per cui, speditosi appena il suo, avrebbe dato mano a pubblicare <lb></lb>il libro del Castelli. </s>

<s>Inteso ciò, rispondeva il Ricci così da Roma, in una <lb></lb>lettera del dì 12 Settembre 1643: </s></p><p type="main">

<s>“ Fu mio pensiero il procurar la luce della stampa delle opere di don <lb></lb>Benedetto, avendomi ciò persuaso quella gratitudine, che io sempre ho detto <lb></lb>a V. S. aver nell&#039;animo mio altamente fisse le sue radici. </s>

<s>Sono troppo grandi <lb></lb>le obbligazioni, che io debbo alla memoria immortale di quel Padre, che con <lb></lb>affetti di non ordinaria umanità sempre mi ha ricevuto ed onorato e amato. </s>

<s><lb></lb>Ma poichè le cose passano nel modo che ella mi dice, ed il pubblicar le sue <lb></lb>scritture potrebbe fomentare in altrui qualche livido affetto di malignità, non <lb></lb>tirerò più avanti il negoziato, ma distornerò quel poco trattato, che ordito <lb></lb>avevo co&#039;monaci e con il libraio, e attenda pure frattanto V. S. a sollecitare <lb></lb>il suo libro, perchè possa poi affaticare a pubblica utilità, e ridurre in netto <lb></lb>quest&#039;opera di don Benedetto ” (MSS. Gal. </s>

<s>Disc., T. XLII, fol. </s>

<s>9). </s></p><p type="main">

<s>Il libro a cui qui s&#039;accenna, contenente le due parti delle Opere geo­<lb></lb>metriche, era da qualche mese venuto in Firenze alla luce, e in questo tempo <lb></lb>un tipografo s&#039;era profferto ai monaci di S. </s>

<s>Callisto di pubblicare le opere <lb></lb>postume del loro padre abate, a sue spese. </s>

<s>Onde il Ricci avendo, l&#039;ultimo <lb></lb>giorno dell&#039;anno 1644, occasione di scrivere al Torricelli, lo pregava così a <lb></lb>voler mantener le fatte promesse, prendendosi egli la cura dell&#039;edizione: <lb></lb>“ Un monaco di S. Callisto, che tien cura delle scritture postume del padre <lb></lb>abate Castelli, prega V. S. a volergli far grazia del proprio parere intorno <lb></lb>la seconda parte delle Acque correnti, perchè si trova un libraro che la <lb></lb>stamperebbe a sue spese, e li padri non vedono volentieri sepolte le gloriose <lb></lb>fatiche del buon vecchio. </s>

<s>Quando ancora V. S. si trovasse in istato di porvi <lb></lb>mano, e perfezionarle, credo che i padri se ne reputerebbero favoriti ” (ivi, <lb></lb>fol. </s>

<s>71). </s></p><p type="main">

<s>Il perfezionamento però, quale s&#039;intendeva dare allo scritto altrui dallo <lb></lb>squisito gusto del Torricelli, non era faccenda nè così lieve, nè così pronta. </s>

<s><lb></lb>La mano voleva esser rimessa, non sopra il secondo libro solamente, ma e <lb></lb>sopra il primo, in cui si poneva per legge fondamentale dei flussi laterali <lb></lb>dai vasi le velocità proporzionali alle semplici altezze. </s>

<s>In che modo si po­<lb></lb>tesse a questa sostituire la legge idrodinamica nuovamente scoperta, e dalle <lb></lb>esperienze approvata, senza che perciò venisse a offendersene il magistero <lb></lb>del Castelli, per varii anni oramai, e con tanta autorità pubblicamente eser­<lb></lb>citato; era quel che metteva in gran pensiero il Torricelli, e mentre pas­<lb></lb>sava, nel tacito meditar, da un proposito a un altro, lo venne inaspettata­<lb></lb>mente a coglier la morte. </s>

<s>Distratto il Ricci dagli onori della dignità cardi-<pb xlink:href="020/01/3502.jpg" pagenum="463"></pb>nalizia e dagli uffici, successi altri monaci a quelli, co&#039;quali era convissuto <lb></lb>il Castelli, nessuno poi pensò più agli scritti postumi di lui, de&#039;quali nono­<lb></lb>stante si lasciò prendere copia ad alcuni periti d&#039;acque, per servirsene ai <lb></lb>loro studii. </s></p><p type="main">

<s>Una di coteste copie giunse alle mani del Barattieri quando, pubblicata <lb></lb>nel 1656 la prima parte della sua <emph type="italics"></emph>Architettura d&#039;acque,<emph.end type="italics"></emph.end> attendeva a scri­<lb></lb>vere la seconda. </s>

<s>E perchè l&#039;esperienze, che avevano indotto il Castelli a sta­<lb></lb>bilire le velocità proporzionali alle altezze, trovò che riscontravano con le sue <lb></lb>proprie, fatte nell&#039;acquedotto della Codogna; volle che ne fosse nota a tutti <lb></lb>la dimostrazione, incominciando a inserir nella stampa delle cose sue le pro­<lb></lb>posizioni inedite dello stesso Castelli. </s>

<s>Varietà d&#039;accidenti avendo fermata <lb></lb>l&#039;impressione dell&#039;Opera alla fine del quarto libro, quando il Barattieri tornò <lb></lb>a ripigliarla in mano erano già in Bologna dal Manolessi mandati insieme <lb></lb>alla luce per le stampe del Dozza, i due libri della Misura delle acque cor­<lb></lb>renti, conforme all&#039;edizione del 1626 rispetto al primo, e conforme al ma­<lb></lb>noscritto, copiato nell&#039;abbazia di S. </s>

<s>Callisto di Roma, rispetto al secondo. </s>

<s><lb></lb>Alcuni forse dei nostri Lettori, syolgendo il volume, avranno a pag. </s>

<s>82 tro­<lb></lb>vata scritta la proposizione seconda con la sua dimostrazione; altri però, <lb></lb>benchè lusingati d&#039;aver copia identica a questa, come quella che in tutto <lb></lb>corrisponde all&#039;esterno, e che è del medesimo anno, e del medesimo edi­<lb></lb>tore; troveranno alla detta pagina, invece della dimostrazione, un avverti­<lb></lb>mento scritto in carattere corsivo. </s>

<s>Il fatto, non nuovo forse ai bibliofili, ma <lb></lb>però non comune, deve aver messo una certa curiosità in tutti coloro che <lb></lb>l&#039;hanno osservato, e noi ci proponiamo di sodisfarla, com&#039;assunto princi­<lb></lb>pale di questa storia. </s></p><p type="main">

<s>Si disse che, andato a monte il negoziato del Ricci, nessuno pensava <lb></lb>più alla pubblicazione degli scritti postumi del Castelli, e ne aveva forse de­<lb></lb>posta ogni speranza lo stesso principe Leopoldo dei Medici, nelle mani del <lb></lb>quale erano i venerati manoscritti, perchè, venuta la morte a rapirgli di pa­<lb></lb>lazzo il Torricelli, non vedeva chi tra i discepoli potesse degnamente sosti­<lb></lb>tuirlo nel glorioso ufficio di correggere l&#039;opera del Maestro. </s>

<s>Ma la notizia <lb></lb>ch&#039;egli ebbe della stampa in Bologua, nell&#039;atto stesso del venir pubblicata, <lb></lb>non lasciava oramai più a dubitare di quel che fosse da farsi: al marchese <lb></lb>Cospi, luogotenete del Granduca a Bologna, faceva scrivere in tali termini, <lb></lb>quali si ricavano dalla seguente minuta, che c&#039;è rimasta: </s></p><p type="main">

<s>“ Il Manolessi, stampatore di Bologna, ha già finito di stampare le opere <lb></lb>di don Benedetto Castelli sopra l&#039;Acque correnti, e di più v&#039;ha aggiunte <lb></lb>altre cosette, o rifiutate o falsamente attribuite al detto Padre. </s>

<s>Però si de­<lb></lb>sidera che il Manolessi sospenda la pubblicazione di tale opera, e ne mandi <lb></lb>qua una copia, per poterla far correggere dai discepoli del detto padre Ca­<lb></lb>stelli, ed anco s&#039;invieranno due altri libretti bellissimi, e desideratissimi, del <lb></lb>medesimo Autore, uno <emph type="italics"></emph>Del modo di farsi la vista,<emph.end type="italics"></emph.end> e l&#039;altro <emph type="italics"></emph>Del bianco e <lb></lb>del nero,<emph.end type="italics"></emph.end> non mai stampati, i quali rendano più caro e desiderato il libro <lb></lb>di quel grand&#039;Uomo, di quel che non sarà pubblicandolo manchevole ed adul-<pb xlink:href="020/01/3503.jpg" pagenum="464"></pb>terato, com&#039;egli è, nella forma che l&#039;ha stampato il Manolessi ” (MSS. Cim., <lb></lb>T. XXIII, fol. </s>

<s>22). </s></p><p type="main">

<s>Il qual Manolessi, ricevutone così il comando, sospese la pubblicazione, <lb></lb>e spedì la copia desiderata, avuta la quale in mano è naturale che il Prin­<lb></lb>cipe ricorresse con l&#039;occhio e col pensiero alla proposizione seconda del se­<lb></lb>condo libro, e al trovarla stampata conforme al manoscritto si deve essere <lb></lb>risovvenuto del Torricelli, e come gli avesse, 17 anni fa, fatto osservare che <lb></lb>se<gap></gap>la nuova acqua nel regolatore del fiume sta in altezza alla prima come <lb></lb>quattro a due; non però come quattro a due staranno le velocità respettive, <lb></lb>ma come quattro alla radice di due. </s>

<s>Dev&#039;essere inoltre esso Principe stato <lb></lb>informato come, risaputa l&#039;osservazione, il Castelli rispondesse, che sebben <lb></lb>non si trovasse sodisfatto della dimostrazione, nonostante la proposizione in <lb></lb>sè stessa, essendo il legittimo resultato dell&#039;esperienza, non poteva non esser <lb></lb>vera. </s>

<s>Ond&#039;essendo dovuto convenir di ciò il Torricelli, non rimaneva dubbio <lb></lb>intorno alla parte della detta proposizione, che aveva bisogno d&#039;esser cor­<lb></lb>retta, secondo le convenzioni stesse fatte fra que&#039;due grandi uomini. </s>

<s>La dif­<lb></lb>ficoltà però consisteva nel saper trovare la ragion di un fatto particolare, che <lb></lb>si sottrae alle leggi universali de&#039;corpi naturalmente cadenti, per cui, essendo <lb></lb>in quel punto presente in Firenze il-Borelli, volle il principe Leopoldo con­<lb></lb>ferir la cosa primieramente con lui, comandandogli di dirne il suo parere. </s>

<s><lb></lb>Il Borelli allora rispose che questo sarebbe di sopprimere la dimostrazione, <lb></lb>e in carattere corsivo stamparvi invece un avvertimento, che dicesse come <lb></lb>quella mancava, perchè l&#039;Autore fu sorpreso dalla morte, mentr&#039;era in cer­<lb></lb>carla, e che perciò aveva pensato di supplirvi uno scolare di lui, mettendola <lb></lb>in fondo al libro. </s>

<s>Non decidendo il Principe nulla ancora del resto, comandò <lb></lb><figure id="id.020.01.3503.1.jpg" xlink:href="020/01/3503/1.jpg"></figure></s></p><p type="caption">

<s>Figura 232.<lb></lb>al Borelli facesse egli stesso quella <lb></lb>dimostrazione, che pochi giorni <lb></lb>dopo recapitava in palazzo, scritta <lb></lb>in questa maniera: </s></p><p type="main">

<s>“ Sia il fiume SBC (fig. </s>

<s>232) <lb></lb>per il regolatore CEBF, annesso al <lb></lb>vaso QIDR, che sia prisma con le <lb></lb>sponde erette all&#039;orizonte. </s>

<s>E prima, <lb></lb>l&#039;origine del fiume M versi tanta <lb></lb>acqua, che arrivi al livello OP, e <lb></lb>scorrendo con la velocità S faccia <lb></lb>nel regolatore la sezione rettangolare EBH. </s>

<s>Poi l&#039;altro sifone o torrente N, <lb></lb>versi nuova acqua, ed arrivi al livello QR, e scorrendo con la velocità T <lb></lb>per il fiume riempia la sezione rettangolare EF. </s>

<s>Dico che la velocità T, alla <lb></lb>velocità S, ha l&#039;istessa proporzione che l&#039;altezza FB, all&#039;altezza HB. ” </s></p><p type="main">

<s>“ La quantità d&#039;acqua, che passa per la sezione EF, cioè il prisma <lb></lb>acqueo QIDR, alla quantità dell&#039;acqua, che passa per la sezione EH, cioè il <lb></lb>prisma acqueo OIDP, ha l&#039;istessa proporzione che l&#039;altezza QI all&#039;altezza <lb></lb>OI, per avere i detti prismi la base comune. </s>

<s>Di più, la velocità T, con la </s></p><pb xlink:href="020/01/3504.jpg" pagenum="465"></pb><p type="main">

<s>Finito di stampare in Bologna presso la <lb></lb>Libreria Editrice Forni nel
Giugno 1970 </s></p></chap></body><back></back>	</text></archimedes>